id	sid	tid	token	lemma	pos
ejpam-5901	1	1	european	european	PROPN
ejpam-5901	1	2	journal	journal	PROPN
ejpam-5901	1	3	of	of	ADP
ejpam-5901	1	4	pure	pure	ADJ
ejpam-5901	1	5	and	and	CCONJ
ejpam-5901	1	6	applied	applied	ADJ
ejpam-5901	1	7	mathematics	mathematic	NOUN
ejpam-5901	1	8	2025	2025	NUM
ejpam-5901	1	9	,	,	PUNCT
ejpam-5901	1	10	vol	vol	NOUN
ejpam-5901	1	11	.	.	PROPN
ejpam-5901	1	12	18	18	NUM
ejpam-5901	1	13	,	,	PUNCT
ejpam-5901	1	14	issue	issue	NOUN
ejpam-5901	1	15	2	2	NUM
ejpam-5901	1	16	,	,	PUNCT
ejpam-5901	1	17	article	article	NOUN
ejpam-5901	1	18	number	number	NOUN
ejpam-5901	1	19	5901	5901	NUM
ejpam-5901	1	20	issn	issn	PROPN
ejpam-5901	1	21	1307	1307	NUM
ejpam-5901	1	22	-	-	SYM
ejpam-5901	1	23	5543	5543	NUM
ejpam-5901	1	24	–	–	PUNCT
ejpam-5901	1	25	ejpam.com	ejpam.com	X
ejpam-5901	1	26	published	publish	VERB
ejpam-5901	1	27	by	by	ADP
ejpam-5901	1	28	new	new	PROPN
ejpam-5901	1	29	york	york	PROPN
ejpam-5901	1	30	business	business	PROPN
ejpam-5901	1	31	global	global	ADJ
ejpam-5901	1	32	impact	impact	NOUN
ejpam-5901	1	33	of	of	ADP
ejpam-5901	1	34	fractal	fractal	ADJ
ejpam-5901	1	35	-	-	PUNCT
ejpam-5901	1	36	fractional	fractional	ADJ
ejpam-5901	1	37	dynamics	dynamic	NOUN
ejpam-5901	1	38	on	on	ADP
ejpam-5901	1	39	pneumonia	pneumonia	NOUN
ejpam-5901	1	40	transmission	transmission	NOUN
ejpam-5901	1	41	modeling	modeling	NOUN
ejpam-5901	1	42	sayed	say	VERB
ejpam-5901	1	43	saber1,2	saber1,2	PROPN
ejpam-5901	1	44	,	,	PUNCT
ejpam-5901	1	45	abdullah	abdullah	PROPN
ejpam-5901	1	46	a.	a.	PROPN
ejpam-5901	1	47	alahmari3,∗	alahmari3,∗	PROPN
ejpam-5901	1	48	1	1	NUM
ejpam-5901	1	49	mathematics	mathematics	PROPN
ejpam-5901	1	50	department	department	NOUN
ejpam-5901	1	51	,	,	PUNCT
ejpam-5901	1	52	faculty	faculty	NOUN
ejpam-5901	1	53	of	of	ADP
ejpam-5901	1	54	science	science	NOUN
ejpam-5901	1	55	,	,	PUNCT
ejpam-5901	1	56	al	al	PROPN
ejpam-5901	1	57	-	-	PUNCT
ejpam-5901	1	58	baha	baha	PROPN
ejpam-5901	1	59	university	university	PROPN
ejpam-5901	1	60	,	,	PUNCT
ejpam-5901	1	61	saudi	saudi	PROPN
ejpam-5901	1	62	arabia	arabia	PROPN
ejpam-5901	1	63	2	2	NUM
ejpam-5901	1	64	department	department	NOUN
ejpam-5901	1	65	of	of	ADP
ejpam-5901	1	66	mathematics	mathematic	NOUN
ejpam-5901	1	67	and	and	CCONJ
ejpam-5901	1	68	computer	computer	NOUN
ejpam-5901	1	69	science	science	NOUN
ejpam-5901	1	70	,	,	PUNCT
ejpam-5901	1	71	faculty	faculty	NOUN
ejpam-5901	1	72	of	of	ADP
ejpam-5901	1	73	science	science	NOUN
ejpam-5901	1	74	,	,	PUNCT
ejpam-5901	1	75	beni	beni	ADJ
ejpam-5901	1	76	-	-	ADJ
ejpam-5901	1	77	suef	suef	ADJ
ejpam-5901	1	78	university	university	NOUN
ejpam-5901	1	79	,	,	PUNCT
ejpam-5901	1	80	egypt	egypt	PROPN
ejpam-5901	1	81	3	3	NUM
ejpam-5901	1	82	mathematics	mathematics	PROPN
ejpam-5901	1	83	department	department	NOUN
ejpam-5901	1	84	,	,	PUNCT
ejpam-5901	1	85	faculty	faculty	NOUN
ejpam-5901	1	86	of	of	ADP
ejpam-5901	1	87	science	science	NOUN
ejpam-5901	1	88	,	,	PUNCT
ejpam-5901	1	89	umm	umm	INTJ
ejpam-5901	1	90	al	al	PROPN
ejpam-5901	1	91	-	-	PUNCT
ejpam-5901	1	92	qura	qura	PROPN
ejpam-5901	1	93	university	university	NOUN
ejpam-5901	1	94	,	,	PUNCT
ejpam-5901	1	95	saudi	saudi	PROPN
ejpam-5901	1	96	arabia	arabia	PROPN
ejpam-5901	1	97	abstract	abstract	NOUN
ejpam-5901	1	98	.	.	PUNCT
ejpam-5901	2	1	in	in	ADP
ejpam-5901	2	2	this	this	DET
ejpam-5901	2	3	study	study	NOUN
ejpam-5901	2	4	,	,	PUNCT
ejpam-5901	2	5	we	we	PRON
ejpam-5901	2	6	develop	develop	VERB
ejpam-5901	2	7	a	a	DET
ejpam-5901	2	8	fractal	fractal	ADJ
ejpam-5901	2	9	-	-	PUNCT
ejpam-5901	2	10	fractional	fractional	ADJ
ejpam-5901	2	11	pneumonia	pneumonia	NOUN
ejpam-5901	2	12	transmission	transmission	NOUN
ejpam-5901	2	13	model	model	NOUN
ejpam-5901	2	14	using	use	VERB
ejpam-5901	2	15	the	the	DET
ejpam-5901	2	16	atangana	atangana	PROPN
ejpam-5901	2	17	-	-	PUNCT
ejpam-5901	2	18	baleanu	baleanu	PROPN
ejpam-5901	2	19	derivative	derivative	NOUN
ejpam-5901	2	20	to	to	PART
ejpam-5901	2	21	capture	capture	VERB
ejpam-5901	2	22	long	long	ADJ
ejpam-5901	2	23	-	-	PUNCT
ejpam-5901	2	24	memory	memory	NOUN
ejpam-5901	2	25	effects	effect	NOUN
ejpam-5901	2	26	.	.	PUNCT
ejpam-5901	3	1	we	we	PRON
ejpam-5901	3	2	analyze	analyze	VERB
ejpam-5901	3	3	the	the	DET
ejpam-5901	3	4	existence	existence	NOUN
ejpam-5901	3	5	and	and	CCONJ
ejpam-5901	3	6	uniqueness	uniqueness	NOUN
ejpam-5901	3	7	of	of	ADP
ejpam-5901	3	8	the	the	DET
ejpam-5901	3	9	model	model	NOUN
ejpam-5901	3	10	’s	’s	PART
ejpam-5901	3	11	solutions	solution	NOUN
ejpam-5901	3	12	and	and	CCONJ
ejpam-5901	3	13	examine	examine	VERB
ejpam-5901	3	14	its	its	PRON
ejpam-5901	3	15	stability	stability	NOUN
ejpam-5901	3	16	using	use	VERB
ejpam-5901	3	17	hyers	hyers	PROPN
ejpam-5901	3	18	-	-	PUNCT
ejpam-5901	3	19	ulam	ulam	PROPN
ejpam-5901	3	20	criteria	criterion	NOUN
ejpam-5901	3	21	.	.	PUNCT
ejpam-5901	4	1	numerical	numerical	ADJ
ejpam-5901	4	2	simulations	simulation	NOUN
ejpam-5901	4	3	are	be	AUX
ejpam-5901	4	4	conducted	conduct	VERB
ejpam-5901	4	5	to	to	PART
ejpam-5901	4	6	explore	explore	VERB
ejpam-5901	4	7	the	the	DET
ejpam-5901	4	8	influence	influence	NOUN
ejpam-5901	4	9	of	of	ADP
ejpam-5901	4	10	different	different	ADJ
ejpam-5901	4	11	fractional	fractional	ADJ
ejpam-5901	4	12	orders	order	NOUN
ejpam-5901	4	13	on	on	ADP
ejpam-5901	4	14	disease	disease	NOUN
ejpam-5901	4	15	dynamics	dynamic	NOUN
ejpam-5901	4	16	.	.	PUNCT
ejpam-5901	5	1	the	the	DET
ejpam-5901	5	2	results	result	NOUN
ejpam-5901	5	3	indicate	indicate	VERB
ejpam-5901	5	4	that	that	SCONJ
ejpam-5901	5	5	fractional	fractional	ADJ
ejpam-5901	5	6	-	-	PUNCT
ejpam-5901	5	7	order	order	NOUN
ejpam-5901	5	8	modeling	modeling	NOUN
ejpam-5901	5	9	provides	provide	VERB
ejpam-5901	5	10	a	a	DET
ejpam-5901	5	11	more	more	ADV
ejpam-5901	5	12	flexible	flexible	ADJ
ejpam-5901	5	13	and	and	CCONJ
ejpam-5901	5	14	accurate	accurate	ADJ
ejpam-5901	5	15	framework	framework	NOUN
ejpam-5901	5	16	than	than	ADP
ejpam-5901	5	17	classical	classical	ADJ
ejpam-5901	5	18	integer	integer	NOUN
ejpam-5901	5	19	-	-	PUNCT
ejpam-5901	5	20	order	order	NOUN
ejpam-5901	5	21	models	model	NOUN
ejpam-5901	5	22	,	,	PUNCT
ejpam-5901	5	23	particularly	particularly	ADV
ejpam-5901	5	24	in	in	ADP
ejpam-5901	5	25	representing	represent	VERB
ejpam-5901	5	26	population	population	NOUN
ejpam-5901	5	27	heterogeneities	heterogeneity	NOUN
ejpam-5901	5	28	and	and	CCONJ
ejpam-5901	5	29	intervention	intervention	NOUN
ejpam-5901	5	30	strategies	strategy	NOUN
ejpam-5901	5	31	such	such	ADJ
ejpam-5901	5	32	as	as	ADP
ejpam-5901	5	33	vaccination	vaccination	NOUN
ejpam-5901	5	34	and	and	CCONJ
ejpam-5901	5	35	treatment	treatment	NOUN
ejpam-5901	5	36	.	.	PUNCT
ejpam-5901	6	1	this	this	DET
ejpam-5901	6	2	approach	approach	NOUN
ejpam-5901	6	3	enhances	enhance	VERB
ejpam-5901	6	4	our	our	PRON
ejpam-5901	6	5	understanding	understanding	NOUN
ejpam-5901	6	6	of	of	ADP
ejpam-5901	6	7	pneumonia	pneumonia	NOUN
ejpam-5901	6	8	transmission	transmission	NOUN
ejpam-5901	6	9	and	and	CCONJ
ejpam-5901	6	10	offers	offer	VERB
ejpam-5901	6	11	valuable	valuable	ADJ
ejpam-5901	6	12	insights	insight	NOUN
ejpam-5901	6	13	for	for	ADP
ejpam-5901	6	14	public	public	ADJ
ejpam-5901	6	15	health	health	NOUN
ejpam-5901	6	16	decision	decision	NOUN
ejpam-5901	6	17	-	-	PUNCT
ejpam-5901	6	18	making	making	NOUN
ejpam-5901	6	19	.	.	PUNCT
ejpam-5901	7	1	2020	2020	NUM
ejpam-5901	7	2	mathematics	mathematic	NOUN
ejpam-5901	7	3	subject	subject	NOUN
ejpam-5901	7	4	classifications	classification	NOUN
ejpam-5901	7	5	:	:	PUNCT
ejpam-5901	7	6	34a08	34a08	NUM
ejpam-5901	7	7	,	,	PUNCT
ejpam-5901	7	8	92d30	92d30	NUM
ejpam-5901	7	9	key	key	ADJ
ejpam-5901	7	10	words	word	NOUN
ejpam-5901	7	11	and	and	CCONJ
ejpam-5901	7	12	phrases	phrase	NOUN
ejpam-5901	7	13	:	:	PUNCT
ejpam-5901	7	14	fractal	fractal	ADJ
ejpam-5901	7	15	-	-	PUNCT
ejpam-5901	7	16	fractional	fractional	ADJ
ejpam-5901	7	17	dynamics	dynamic	NOUN
ejpam-5901	7	18	,	,	PUNCT
ejpam-5901	7	19	pneumonia	pneumonia	NOUN
ejpam-5901	7	20	transmission	transmission	NOUN
ejpam-5901	7	21	,	,	PUNCT
ejpam-5901	7	22	atanganabaleanu	atanganabaleanu	NOUN
ejpam-5901	7	23	derivative	derivative	ADJ
ejpam-5901	7	24	,	,	PUNCT
ejpam-5901	7	25	long	long	ADJ
ejpam-5901	7	26	-	-	PUNCT
ejpam-5901	7	27	memory	memory	NOUN
ejpam-5901	7	28	effects	effect	NOUN
ejpam-5901	7	29	1	1	NUM
ejpam-5901	7	30	.	.	PUNCT
ejpam-5901	8	1	introduction	introduction	NOUN
ejpam-5901	8	2	pneumonia	pneumonia	NOUN
ejpam-5901	8	3	remains	remain	VERB
ejpam-5901	8	4	a	a	DET
ejpam-5901	8	5	major	major	ADJ
ejpam-5901	8	6	public	public	ADJ
ejpam-5901	8	7	health	health	NOUN
ejpam-5901	8	8	concern	concern	NOUN
ejpam-5901	8	9	,	,	PUNCT
ejpam-5901	8	10	affecting	affect	VERB
ejpam-5901	8	11	millions	million	NOUN
ejpam-5901	8	12	worldwide	worldwide	ADV
ejpam-5901	8	13	and	and	CCONJ
ejpam-5901	8	14	leading	lead	VERB
ejpam-5901	8	15	to	to	ADP
ejpam-5901	8	16	severe	severe	ADJ
ejpam-5901	8	17	complications	complication	NOUN
ejpam-5901	8	18	,	,	PUNCT
ejpam-5901	8	19	particularly	particularly	ADV
ejpam-5901	8	20	among	among	ADP
ejpam-5901	8	21	young	young	ADJ
ejpam-5901	8	22	children	child	NOUN
ejpam-5901	8	23	and	and	CCONJ
ejpam-5901	8	24	the	the	DET
ejpam-5901	8	25	elderly	elderly	ADJ
ejpam-5901	8	26	.	.	PUNCT
ejpam-5901	9	1	traditional	traditional	ADJ
ejpam-5901	9	2	epidemiological	epidemiological	ADJ
ejpam-5901	9	3	models	model	NOUN
ejpam-5901	9	4	,	,	PUNCT
ejpam-5901	9	5	often	often	ADV
ejpam-5901	9	6	based	base	VERB
ejpam-5901	9	7	on	on	ADP
ejpam-5901	9	8	integer	integer	NOUN
ejpam-5901	9	9	-	-	PUNCT
ejpam-5901	9	10	order	order	NOUN
ejpam-5901	9	11	differential	differential	ADJ
ejpam-5901	9	12	equations	equation	NOUN
ejpam-5901	9	13	,	,	PUNCT
ejpam-5901	9	14	provide	provide	VERB
ejpam-5901	9	15	valuable	valuable	ADJ
ejpam-5901	9	16	insights	insight	NOUN
ejpam-5901	9	17	into	into	ADP
ejpam-5901	9	18	disease	disease	NOUN
ejpam-5901	9	19	dynamics	dynamic	NOUN
ejpam-5901	9	20	but	but	CCONJ
ejpam-5901	9	21	fail	fail	VERB
ejpam-5901	9	22	to	to	PART
ejpam-5901	9	23	capture	capture	VERB
ejpam-5901	9	24	complex	complex	ADJ
ejpam-5901	9	25	real	real	ADJ
ejpam-5901	9	26	-	-	PUNCT
ejpam-5901	9	27	world	world	NOUN
ejpam-5901	9	28	characteristics	characteristic	NOUN
ejpam-5901	9	29	such	such	ADJ
ejpam-5901	9	30	as	as	ADP
ejpam-5901	9	31	memory	memory	NOUN
ejpam-5901	9	32	effects	effect	NOUN
ejpam-5901	9	33	,	,	PUNCT
ejpam-5901	9	34	heterogeneity	heterogeneity	NOUN
ejpam-5901	9	35	in	in	ADP
ejpam-5901	9	36	disease	disease	NOUN
ejpam-5901	9	37	progression	progression	NOUN
ejpam-5901	9	38	,	,	PUNCT
ejpam-5901	9	39	and	and	CCONJ
ejpam-5901	9	40	long	long	ADJ
ejpam-5901	9	41	-	-	PUNCT
ejpam-5901	9	42	term	term	NOUN
ejpam-5901	9	43	dependencies	dependency	NOUN
ejpam-5901	9	44	in	in	ADP
ejpam-5901	9	45	population	population	NOUN
ejpam-5901	9	46	interactions	interaction	NOUN
ejpam-5901	9	47	.	.	PUNCT
ejpam-5901	10	1	these	these	DET
ejpam-5901	10	2	limitations	limitation	NOUN
ejpam-5901	10	3	necessitate	necessitate	ADJ
ejpam-5901	10	4	the	the	DET
ejpam-5901	10	5	exploration	exploration	NOUN
ejpam-5901	10	6	of	of	ADP
ejpam-5901	10	7	more	more	ADV
ejpam-5901	10	8	advanced	advanced	ADJ
ejpam-5901	10	9	mathematical	mathematical	ADJ
ejpam-5901	10	10	frameworks	framework	NOUN
ejpam-5901	10	11	to	to	PART
ejpam-5901	10	12	enhance	enhance	VERB
ejpam-5901	10	13	predictive	predictive	ADJ
ejpam-5901	10	14	accuracy	accuracy	NOUN
ejpam-5901	10	15	and	and	CCONJ
ejpam-5901	10	16	model	model	NOUN
ejpam-5901	10	17	realism	realism	NOUN
ejpam-5901	10	18	.	.	PUNCT
ejpam-5901	11	1	pneumonia	pneumonia	NOUN
ejpam-5901	11	2	,	,	PUNCT
ejpam-5901	11	3	a	a	DET
ejpam-5901	11	4	lung	lung	NOUN
ejpam-5901	11	5	disease	disease	NOUN
ejpam-5901	11	6	,	,	PUNCT
ejpam-5901	11	7	affects	affect	VERB
ejpam-5901	11	8	everyone	everyone	PRON
ejpam-5901	11	9	of	of	ADP
ejpam-5901	11	10	varying	vary	VERB
ejpam-5901	11	11	severity	severity	NOUN
ejpam-5901	11	12	.	.	PUNCT
ejpam-5901	12	1	it	it	PRON
ejpam-5901	12	2	is	be	AUX
ejpam-5901	12	3	typically	typically	ADV
ejpam-5901	12	4	diagnosed	diagnose	VERB
ejpam-5901	12	5	through	through	ADP
ejpam-5901	12	6	physical	physical	ADJ
ejpam-5901	12	7	examinations	examination	NOUN
ejpam-5901	12	8	,	,	PUNCT
ejpam-5901	12	9	a	a	DET
ejpam-5901	12	10	patient	patient	NOUN
ejpam-5901	12	11	history	history	NOUN
ejpam-5901	12	12	,	,	PUNCT
ejpam-5901	12	13	and	and	CCONJ
ejpam-5901	12	14	diagnostic	diagnostic	ADJ
ejpam-5901	12	15	tests	test	NOUN
ejpam-5901	12	16	.	.	PUNCT
ejpam-5901	13	1	pneumonia	pneumonia	NOUN
ejpam-5901	13	2	is	be	AUX
ejpam-5901	13	3	characterized	characterize	VERB
ejpam-5901	13	4	by	by	ADP
ejpam-5901	13	5	lung	lung	NOUN
ejpam-5901	13	6	inflammation	inflammation	NOUN
ejpam-5901	13	7	,	,	PUNCT
ejpam-5901	13	8	often	often	ADV
ejpam-5901	13	9	caused	cause	VERB
ejpam-5901	13	10	by	by	ADP
ejpam-5901	13	11	microbial	microbial	ADJ
ejpam-5901	13	12	or	or	CCONJ
ejpam-5901	13	13	fungal	fungal	ADJ
ejpam-5901	13	14	infections	infection	NOUN
ejpam-5901	13	15	,	,	PUNCT
ejpam-5901	13	16	though	though	SCONJ
ejpam-5901	13	17	certain	certain	ADJ
ejpam-5901	13	18	cases	case	NOUN
ejpam-5901	13	19	arise	arise	VERB
ejpam-5901	13	20	from	from	ADP
ejpam-5901	13	21	inhaling	inhale	VERB
ejpam-5901	13	22	harmful	harmful	ADJ
ejpam-5901	13	23	substances	substance	NOUN
ejpam-5901	13	24	.	.	PUNCT
ejpam-5901	14	1	while	while	SCONJ
ejpam-5901	14	2	most	most	ADJ
ejpam-5901	14	3	pneumococcal	pneumococcal	ADJ
ejpam-5901	14	4	toxins	toxin	NOUN
ejpam-5901	14	5	are	be	AUX
ejpam-5901	14	6	∗corresponding	∗corresponde	VERB
ejpam-5901	14	7	author	author	NOUN
ejpam-5901	14	8	.	.	PUNCT
ejpam-5901	15	1	doi	doi	PROPN
ejpam-5901	15	2	:	:	PUNCT
ejpam-5901	15	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5901	https://doi.org/10.29020/nybg.ejpam.v18i2.5901	VERB
ejpam-5901	15	4	email	email	NOUN
ejpam-5901	15	5	addresses	address	NOUN
ejpam-5901	15	6	:	:	PUNCT
ejpam-5901	15	7	sayed011258@science.bsu.edu.eg	sayed011258@science.bsu.edu.eg	ADP
ejpam-5901	15	8	(	(	PUNCT
ejpam-5901	15	9	s.	s.	PROPN
ejpam-5901	15	10	saber	saber	PROPN
ejpam-5901	15	11	)	)	PUNCT
ejpam-5901	15	12	,	,	PUNCT
ejpam-5901	15	13	aaahmari@uqu.edu.sa	aaahmari@uqu.edu.sa	PROPN
ejpam-5901	15	14	(	(	PUNCT
ejpam-5901	15	15	a.	a.	NOUN
ejpam-5901	15	16	a.	a.	NOUN
ejpam-5901	15	17	alahmari	alahmari	PROPN
ejpam-5901	15	18	)	)	PUNCT
ejpam-5901	15	19	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5901	16	1	1	1	NUM
ejpam-5901	16	2	copyright	copyright	NOUN
ejpam-5901	16	3	:	:	PUNCT
ejpam-5901	16	4	©	©	PROPN
ejpam-5901	16	5	2025	2025	NUM
ejpam-5901	16	6	the	the	DET
ejpam-5901	16	7	author(s	author(s	NOUN
ejpam-5901	16	8	)	)	PUNCT
ejpam-5901	16	9	.	.	PUNCT
ejpam-5901	17	1	(	(	PUNCT
ejpam-5901	17	2	cc	cc	NOUN
ejpam-5901	17	3	by	by	ADP
ejpam-5901	17	4	-	-	PUNCT
ejpam-5901	17	5	nc	nc	PROPN
ejpam-5901	17	6	4.0	4.0	NUM
ejpam-5901	17	7	)	)	PUNCT
ejpam-5901	17	8	s.	s.	PROPN
ejpam-5901	17	9	saber	saber	PROPN
ejpam-5901	17	10	,	,	PUNCT
ejpam-5901	17	11	a.	a.	NOUN
ejpam-5901	17	12	a.	a.	NOUN
ejpam-5901	17	13	alahmari	alahmari	PROPN
ejpam-5901	17	14	/	/	SYM
ejpam-5901	17	15	eur	eur	PROPN
ejpam-5901	17	16	.	.	PUNCT
ejpam-5901	18	1	j.	j.	PROPN
ejpam-5901	18	2	pure	pure	PROPN
ejpam-5901	18	3	appl	appl	PROPN
ejpam-5901	18	4	.	.	PROPN
ejpam-5901	18	5	math	math	PROPN
ejpam-5901	18	6	,	,	PUNCT
ejpam-5901	18	7	18	18	NUM
ejpam-5901	18	8	(	(	PUNCT
ejpam-5901	18	9	2	2	NUM
ejpam-5901	18	10	)	)	PUNCT
ejpam-5901	18	11	(	(	PUNCT
ejpam-5901	18	12	2025	2025	NUM
ejpam-5901	18	13	)	)	PUNCT
ejpam-5901	18	14	,	,	PUNCT
ejpam-5901	18	15	5901	5901	NUM
ejpam-5901	18	16	2	2	NUM
ejpam-5901	18	17	of	of	ADP
ejpam-5901	18	18	23	23	NUM
ejpam-5901	18	19	harmless	harmless	ADJ
ejpam-5901	19	1	,	,	PUNCT
ejpam-5901	19	2	some	some	PRON
ejpam-5901	19	3	can	can	AUX
ejpam-5901	19	4	cause	cause	VERB
ejpam-5901	19	5	serious	serious	ADJ
ejpam-5901	19	6	health	health	NOUN
ejpam-5901	19	7	problems	problem	NOUN
ejpam-5901	19	8	,	,	PUNCT
ejpam-5901	19	9	such	such	ADJ
ejpam-5901	19	10	as	as	ADP
ejpam-5901	19	11	brain	brain	NOUN
ejpam-5901	19	12	damage	damage	NOUN
ejpam-5901	19	13	and	and	CCONJ
ejpam-5901	19	14	hearing	hear	VERB
ejpam-5901	19	15	loss	loss	NOUN
ejpam-5901	19	16	.	.	PUNCT
ejpam-5901	20	1	pneumococcal	pneumococcal	ADJ
ejpam-5901	20	2	meningitis	meningitis	NOUN
ejpam-5901	20	3	,	,	PUNCT
ejpam-5901	20	4	the	the	DET
ejpam-5901	20	5	most	most	ADV
ejpam-5901	20	6	severe	severe	ADJ
ejpam-5901	20	7	condition	condition	NOUN
ejpam-5901	20	8	,	,	PUNCT
ejpam-5901	20	9	primarily	primarily	ADV
ejpam-5901	20	10	affects	affect	VERB
ejpam-5901	20	11	children	child	NOUN
ejpam-5901	20	12	under	under	ADP
ejpam-5901	20	13	five	five	NUM
ejpam-5901	20	14	years	year	NOUN
ejpam-5901	20	15	old	old	ADJ
ejpam-5901	20	16	but	but	CCONJ
ejpam-5901	20	17	also	also	ADV
ejpam-5901	20	18	impacts	impact	VERB
ejpam-5901	20	19	adults	adult	NOUN
ejpam-5901	20	20	.	.	PUNCT
ejpam-5901	21	1	bacteria	bacteria	NOUN
ejpam-5901	21	2	causing	cause	VERB
ejpam-5901	21	3	pneumococcal	pneumococcal	ADJ
ejpam-5901	21	4	infections	infection	NOUN
ejpam-5901	21	5	can	can	AUX
ejpam-5901	21	6	spread	spread	VERB
ejpam-5901	21	7	through	through	ADP
ejpam-5901	21	8	the	the	DET
ejpam-5901	21	9	bloodstream	bloodstream	NOUN
ejpam-5901	21	10	,	,	PUNCT
ejpam-5901	21	11	and	and	CCONJ
ejpam-5901	21	12	approximately	approximately	ADV
ejpam-5901	21	13	1	1	NUM
ejpam-5901	21	14	%	%	NOUN
ejpam-5901	21	15	of	of	ADP
ejpam-5901	21	16	children	child	NOUN
ejpam-5901	21	17	under	under	ADP
ejpam-5901	21	18	five	five	NUM
ejpam-5901	21	19	infected	infect	VERB
ejpam-5901	21	20	with	with	ADP
ejpam-5901	21	21	this	this	DET
ejpam-5901	21	22	disease	disease	NOUN
ejpam-5901	21	23	succumb	succumb	VERB
ejpam-5901	21	24	to	to	ADP
ejpam-5901	21	25	it	it	PRON
ejpam-5901	21	26	.	.	PUNCT
ejpam-5901	22	1	additionally	additionally	ADV
ejpam-5901	22	2	,	,	PUNCT
ejpam-5901	22	3	pneumococcal	pneumococcal	ADJ
ejpam-5901	22	4	pneumonia	pneumonia	NOUN
ejpam-5901	22	5	is	be	AUX
ejpam-5901	22	6	a	a	DET
ejpam-5901	22	7	leading	lead	VERB
ejpam-5901	22	8	cause	cause	NOUN
ejpam-5901	22	9	of	of	ADP
ejpam-5901	22	10	death	death	NOUN
ejpam-5901	22	11	among	among	ADP
ejpam-5901	22	12	the	the	DET
ejpam-5901	22	13	elderly	elderly	ADJ
ejpam-5901	22	14	,	,	PUNCT
ejpam-5901	22	15	with	with	ADP
ejpam-5901	22	16	a	a	DET
ejpam-5901	22	17	mortality	mortality	NOUN
ejpam-5901	22	18	rate	rate	NOUN
ejpam-5901	22	19	of	of	ADP
ejpam-5901	22	20	approximately	approximately	ADV
ejpam-5901	22	21	5	5	NUM
ejpam-5901	22	22	%	%	NOUN
ejpam-5901	22	23	,	,	PUNCT
ejpam-5901	22	24	rising	rise	VERB
ejpam-5901	22	25	significantly	significantly	ADV
ejpam-5901	22	26	in	in	ADP
ejpam-5901	22	27	this	this	DET
ejpam-5901	22	28	population	population	NOUN
ejpam-5901	22	29	.	.	PUNCT
ejpam-5901	23	1	ong’ala	ong’ala	PROPN
ejpam-5901	23	2	et	et	PROPN
ejpam-5901	23	3	al	al	PROPN
ejpam-5901	23	4	.	.	PUNCT
ejpam-5901	24	1	[	[	X
ejpam-5901	24	2	1	1	X
ejpam-5901	24	3	]	]	PUNCT
ejpam-5901	24	4	developed	develop	VERB
ejpam-5901	24	5	a	a	DET
ejpam-5901	24	6	mathematical	mathematical	ADJ
ejpam-5901	24	7	model	model	NOUN
ejpam-5901	24	8	of	of	ADP
ejpam-5901	24	9	bacteremic	bacteremic	ADJ
ejpam-5901	24	10	pneumonia	pneumonia	NOUN
ejpam-5901	24	11	in	in	ADP
ejpam-5901	24	12	young	young	ADJ
ejpam-5901	24	13	children	child	NOUN
ejpam-5901	24	14	(	(	PUNCT
ejpam-5901	24	15	under	under	ADP
ejpam-5901	24	16	five	five	NUM
ejpam-5901	24	17	years	year	NOUN
ejpam-5901	24	18	old	old	ADJ
ejpam-5901	24	19	)	)	PUNCT
ejpam-5901	24	20	to	to	PART
ejpam-5901	24	21	describe	describe	VERB
ejpam-5901	24	22	the	the	DET
ejpam-5901	24	23	disease	disease	NOUN
ejpam-5901	24	24	’s	’s	PART
ejpam-5901	24	25	occurrence	occurrence	NOUN
ejpam-5901	24	26	.	.	PUNCT
ejpam-5901	25	1	they	they	PRON
ejpam-5901	25	2	analyzed	analyze	VERB
ejpam-5901	25	3	transmission	transmission	NOUN
ejpam-5901	25	4	rates	rate	NOUN
ejpam-5901	25	5	between	between	ADP
ejpam-5901	25	6	carriers	carrier	NOUN
ejpam-5901	25	7	and	and	CCONJ
ejpam-5901	25	8	infected	infect	VERB
ejpam-5901	25	9	individuals	individual	NOUN
ejpam-5901	25	10	using	use	VERB
ejpam-5901	25	11	bifurcation	bifurcation	NOUN
ejpam-5901	25	12	theory	theory	NOUN
ejpam-5901	25	13	and	and	CCONJ
ejpam-5901	25	14	equilibrium	equilibrium	NOUN
ejpam-5901	25	15	stability	stability	NOUN
ejpam-5901	25	16	analysis	analysis	NOUN
ejpam-5901	25	17	.	.	PUNCT
ejpam-5901	26	1	mochan	mochan	PROPN
ejpam-5901	26	2	et	et	PROPN
ejpam-5901	26	3	al	al	PROPN
ejpam-5901	26	4	.	.	PUNCT
ejpam-5901	27	1	[	[	X
ejpam-5901	27	2	2	2	X
ejpam-5901	27	3	]	]	PUNCT
ejpam-5901	27	4	proposed	propose	VERB
ejpam-5901	27	5	a	a	DET
ejpam-5901	27	6	dynamic	dynamic	ADJ
ejpam-5901	27	7	ordinary	ordinary	ADJ
ejpam-5901	27	8	differential	differential	ADJ
ejpam-5901	27	9	equation	equation	NOUN
ejpam-5901	27	10	(	(	PUNCT
ejpam-5901	27	11	ode	ode	PROPN
ejpam-5901	27	12	)	)	PUNCT
ejpam-5901	27	13	model	model	NOUN
ejpam-5901	27	14	to	to	PART
ejpam-5901	27	15	capture	capture	VERB
ejpam-5901	27	16	the	the	DET
ejpam-5901	27	17	immunological	immunological	ADJ
ejpam-5901	27	18	response	response	NOUN
ejpam-5901	27	19	to	to	ADP
ejpam-5901	27	20	bacterial	bacterial	ADJ
ejpam-5901	27	21	pneumonia	pneumonia	NOUN
ejpam-5901	27	22	in	in	ADP
ejpam-5901	27	23	murine	murine	ADJ
ejpam-5901	27	24	strains	strain	NOUN
ejpam-5901	27	25	.	.	PUNCT
ejpam-5901	28	1	drusano	drusano	PROPN
ejpam-5901	28	2	et	et	PROPN
ejpam-5901	28	3	al	al	PROPN
ejpam-5901	28	4	.	.	PUNCT
ejpam-5901	29	1	[	[	X
ejpam-5901	29	2	3	3	NUM
ejpam-5901	29	3	]	]	PUNCT
ejpam-5901	29	4	investigated	investigate	VERB
ejpam-5901	29	5	the	the	DET
ejpam-5901	29	6	role	role	NOUN
ejpam-5901	29	7	of	of	ADP
ejpam-5901	29	8	granulates	granulate	NOUN
ejpam-5901	29	9	in	in	ADP
ejpam-5901	29	10	preventing	prevent	VERB
ejpam-5901	29	11	bacterial	bacterial	ADJ
ejpam-5901	29	12	growth	growth	NOUN
ejpam-5901	29	13	and	and	CCONJ
ejpam-5901	29	14	concluded	conclude	VERB
ejpam-5901	29	15	that	that	SCONJ
ejpam-5901	29	16	antibiotics	antibiotic	NOUN
ejpam-5901	29	17	play	play	VERB
ejpam-5901	29	18	no	no	DET
ejpam-5901	29	19	role	role	NOUN
ejpam-5901	29	20	in	in	ADP
ejpam-5901	29	21	this	this	DET
ejpam-5901	29	22	specific	specific	ADJ
ejpam-5901	29	23	process	process	NOUN
ejpam-5901	29	24	.	.	PUNCT
ejpam-5901	30	1	ndelwa	ndelwa	PROPN
ejpam-5901	30	2	et	et	PROPN
ejpam-5901	30	3	al	al	PROPN
ejpam-5901	30	4	.	.	PUNCT
ejpam-5901	31	1	[	[	X
ejpam-5901	31	2	4	4	NUM
ejpam-5901	31	3	]	]	PUNCT
ejpam-5901	31	4	analyzed	analyze	VERB
ejpam-5901	31	5	pneumonia	pneumonia	NOUN
ejpam-5901	31	6	transmission	transmission	NOUN
ejpam-5901	31	7	dynamics	dynamic	NOUN
ejpam-5901	31	8	,	,	PUNCT
ejpam-5901	31	9	incorporating	incorporate	VERB
ejpam-5901	31	10	screening	screening	NOUN
ejpam-5901	31	11	and	and	CCONJ
ejpam-5901	31	12	medication	medication	NOUN
ejpam-5901	31	13	,	,	PUNCT
ejpam-5901	31	14	and	and	CCONJ
ejpam-5901	31	15	explored	explore	VERB
ejpam-5901	31	16	the	the	DET
ejpam-5901	31	17	associated	associated	ADJ
ejpam-5901	31	18	consequences	consequence	NOUN
ejpam-5901	31	19	.	.	PUNCT
ejpam-5901	32	1	kosasih	kosasih	PROPN
ejpam-5901	32	2	et	et	PROPN
ejpam-5901	32	3	al	al	PROPN
ejpam-5901	32	4	.	.	PUNCT
ejpam-5901	33	1	[	[	X
ejpam-5901	33	2	5	5	NUM
ejpam-5901	33	3	]	]	PUNCT
ejpam-5901	33	4	employed	employ	VERB
ejpam-5901	33	5	a	a	DET
ejpam-5901	33	6	wavelet	wavelet	NOUN
ejpam-5901	33	7	-	-	PUNCT
ejpam-5901	33	8	based	base	VERB
ejpam-5901	33	9	crackling	crackle	VERB
ejpam-5901	33	10	detection	detection	NOUN
ejpam-5901	33	11	technique	technique	NOUN
ejpam-5901	33	12	to	to	ADP
ejpam-5901	33	13	model	model	NOUN
ejpam-5901	33	14	cough	cough	NOUN
ejpam-5901	33	15	sounds	sound	NOUN
ejpam-5901	33	16	,	,	PUNCT
ejpam-5901	33	17	facilitating	facilitate	VERB
ejpam-5901	33	18	rapid	rapid	ADJ
ejpam-5901	33	19	identification	identification	NOUN
ejpam-5901	33	20	of	of	ADP
ejpam-5901	33	21	bacterial	bacterial	ADJ
ejpam-5901	33	22	pneumonia	pneumonia	NOUN
ejpam-5901	33	23	in	in	ADP
ejpam-5901	33	24	young	young	ADJ
ejpam-5901	33	25	patients	patient	NOUN
ejpam-5901	33	26	.	.	PUNCT
ejpam-5901	34	1	césar	césar	PROPN
ejpam-5901	34	2	et	et	PROPN
ejpam-5901	34	3	al	al	PROPN
ejpam-5901	34	4	.	.	PUNCT
ejpam-5901	35	1	[	[	X
ejpam-5901	35	2	6	6	NUM
ejpam-5901	35	3	]	]	PUNCT
ejpam-5901	35	4	presented	present	VERB
ejpam-5901	35	5	a	a	DET
ejpam-5901	35	6	mathematical	mathematical	ADJ
ejpam-5901	35	7	model	model	NOUN
ejpam-5901	35	8	for	for	ADP
ejpam-5901	35	9	pediatric	pediatric	ADJ
ejpam-5901	35	10	asthma	asthma	NOUN
ejpam-5901	35	11	and	and	CCONJ
ejpam-5901	35	12	pneumonia	pneumonia	NOUN
ejpam-5901	35	13	in	in	ADP
ejpam-5901	35	14	a	a	DET
ejpam-5901	35	15	large	large	ADJ
ejpam-5901	35	16	population	population	NOUN
ejpam-5901	35	17	.	.	PUNCT
ejpam-5901	36	1	marchello	marchello	PROPN
ejpam-5901	36	2	et	et	PROPN
ejpam-5901	36	3	al	al	PROPN
ejpam-5901	36	4	.	.	PUNCT
ejpam-5901	37	1	[	[	X
ejpam-5901	37	2	7	7	X
ejpam-5901	37	3	]	]	PUNCT
ejpam-5901	37	4	demonstrated	demonstrate	VERB
ejpam-5901	37	5	that	that	SCONJ
ejpam-5901	37	6	atypical	atypical	ADJ
ejpam-5901	37	7	bacterial	bacterial	ADJ
ejpam-5901	37	8	infections	infection	NOUN
ejpam-5901	37	9	predominantly	predominantly	ADV
ejpam-5901	37	10	drive	drive	VERB
ejpam-5901	37	11	the	the	DET
ejpam-5901	37	12	spread	spread	NOUN
ejpam-5901	37	13	of	of	ADP
ejpam-5901	37	14	respiratory	respiratory	ADJ
ejpam-5901	37	15	illnesses	illness	NOUN
ejpam-5901	37	16	such	such	ADJ
ejpam-5901	37	17	as	as	ADP
ejpam-5901	37	18	coughing	cough	VERB
ejpam-5901	37	19	,	,	PUNCT
ejpam-5901	37	20	bronchitis	bronchitis	NOUN
ejpam-5901	37	21	,	,	PUNCT
ejpam-5901	37	22	and	and	CCONJ
ejpam-5901	37	23	chronic	chronic	ADJ
ejpam-5901	37	24	obstructive	obstructive	ADJ
ejpam-5901	37	25	pulmonary	pulmonary	ADJ
ejpam-5901	37	26	disease	disease	NOUN
ejpam-5901	37	27	(	(	PUNCT
ejpam-5901	37	28	copd	copd	PROPN
ejpam-5901	37	29	)	)	PUNCT
ejpam-5901	37	30	.	.	PUNCT
ejpam-5901	38	1	cheng	cheng	PROPN
ejpam-5901	38	2	et	et	PROPN
ejpam-5901	38	3	al	al	PROPN
ejpam-5901	38	4	.	.	PUNCT
ejpam-5901	39	1	[	[	X
ejpam-5901	39	2	8	8	NUM
ejpam-5901	39	3	]	]	PUNCT
ejpam-5901	39	4	proposed	propose	VERB
ejpam-5901	39	5	a	a	DET
ejpam-5901	39	6	dynamical	dynamical	ADJ
ejpam-5901	39	7	mathematical	mathematical	ADJ
ejpam-5901	39	8	model	model	NOUN
ejpam-5901	39	9	of	of	ADP
ejpam-5901	39	10	influenza	influenza	NOUN
ejpam-5901	39	11	a	a	DET
ejpam-5901	39	12	virus	virus	NOUN
ejpam-5901	39	13	secondary	secondary	ADJ
ejpam-5901	39	14	pneumonia	pneumonia	NOUN
ejpam-5901	39	15	(	(	PUNCT
ejpam-5901	39	16	iavsp	iavsp	PROPN
ejpam-5901	39	17	)	)	PUNCT
ejpam-5901	39	18	,	,	PUNCT
ejpam-5901	39	19	providing	provide	VERB
ejpam-5901	39	20	a	a	DET
ejpam-5901	39	21	quantitative	quantitative	ADJ
ejpam-5901	39	22	risk	risk	NOUN
ejpam-5901	39	23	assessment	assessment	NOUN
ejpam-5901	39	24	framework	framework	NOUN
ejpam-5901	39	25	to	to	PART
ejpam-5901	39	26	improve	improve	VERB
ejpam-5901	39	27	copd	copd	NOUN
ejpam-5901	39	28	-	-	PUNCT
ejpam-5901	39	29	related	relate	VERB
ejpam-5901	39	30	respiratory	respiratory	ADJ
ejpam-5901	39	31	health	health	NOUN
ejpam-5901	39	32	.	.	PUNCT
ejpam-5901	40	1	kosasih	kosasih	PROPN
ejpam-5901	40	2	et	et	PROPN
ejpam-5901	40	3	al	al	PROPN
ejpam-5901	40	4	.	.	PUNCT
ejpam-5901	41	1	[	[	X
ejpam-5901	41	2	9	9	NUM
ejpam-5901	41	3	]	]	PUNCT
ejpam-5901	41	4	discussed	discuss	VERB
ejpam-5901	41	5	diagnostic	diagnostic	ADJ
ejpam-5901	41	6	measures	measure	NOUN
ejpam-5901	41	7	for	for	ADP
ejpam-5901	41	8	childhood	childhood	ADJ
ejpam-5901	41	9	pneumonia	pneumonia	NOUN
ejpam-5901	41	10	in	in	ADP
ejpam-5901	41	11	low	low	ADJ
ejpam-5901	41	12	-	-	PUNCT
ejpam-5901	41	13	income	income	NOUN
ejpam-5901	41	14	areas	area	NOUN
ejpam-5901	41	15	,	,	PUNCT
ejpam-5901	41	16	identifying	identify	VERB
ejpam-5901	41	17	key	key	ADJ
ejpam-5901	41	18	contributing	contributing	NOUN
ejpam-5901	41	19	factors	factor	NOUN
ejpam-5901	41	20	.	.	PUNCT
ejpam-5901	42	1	tilahun	tilahun	PROPN
ejpam-5901	42	2	et	et	PROPN
ejpam-5901	42	3	al	al	PROPN
ejpam-5901	42	4	.	.	PUNCT
ejpam-5901	43	1	[	[	X
ejpam-5901	43	2	10	10	NUM
ejpam-5901	43	3	,	,	PUNCT
ejpam-5901	43	4	11	11	NUM
ejpam-5901	43	5	]	]	PUNCT
ejpam-5901	43	6	introduced	introduce	VERB
ejpam-5901	43	7	a	a	DET
ejpam-5901	43	8	co	co	NOUN
ejpam-5901	43	9	-	-	ADJ
ejpam-5901	43	10	infection	infection	ADJ
ejpam-5901	43	11	model	model	NOUN
ejpam-5901	43	12	for	for	ADP
ejpam-5901	43	13	pneumonia	pneumonia	NOUN
ejpam-5901	43	14	and	and	CCONJ
ejpam-5901	43	15	typhoid	typhoid	NOUN
ejpam-5901	43	16	,	,	PUNCT
ejpam-5901	43	17	examining	examine	VERB
ejpam-5901	43	18	the	the	DET
ejpam-5901	43	19	interplay	interplay	NOUN
ejpam-5901	43	20	of	of	ADP
ejpam-5901	43	21	curative	curative	ADJ
ejpam-5901	43	22	and	and	CCONJ
ejpam-5901	43	23	therapeutic	therapeutic	ADJ
ejpam-5901	43	24	strategies	strategy	NOUN
ejpam-5901	43	25	.	.	PUNCT
ejpam-5901	44	1	raj	raj	PROPN
ejpam-5901	44	2	et	et	PROPN
ejpam-5901	44	3	al	al	PROPN
ejpam-5901	44	4	.	.	PUNCT
ejpam-5901	45	1	[	[	X
ejpam-5901	45	2	12	12	NUM
ejpam-5901	45	3	]	]	PUNCT
ejpam-5901	45	4	analyzed	analyze	VERB
ejpam-5901	45	5	asthma	asthma	NOUN
ejpam-5901	45	6	and	and	CCONJ
ejpam-5901	45	7	pneumonia	pneumonia	NOUN
ejpam-5901	45	8	classification	classification	NOUN
ejpam-5901	45	9	in	in	ADP
ejpam-5901	45	10	low	low	ADJ
ejpam-5901	45	11	-	-	PUNCT
ejpam-5901	45	12	resource	resource	NOUN
ejpam-5901	45	13	settings	setting	NOUN
ejpam-5901	45	14	using	use	VERB
ejpam-5901	45	15	mathematical	mathematical	ADJ
ejpam-5901	45	16	properties	property	NOUN
ejpam-5901	45	17	of	of	ADP
ejpam-5901	45	18	cough	cough	NOUN
ejpam-5901	45	19	sounds	sound	NOUN
ejpam-5901	45	20	.	.	PUNCT
ejpam-5901	46	1	kizito	kizito	NOUN
ejpam-5901	46	2	et	et	PROPN
ejpam-5901	46	3	al	al	PROPN
ejpam-5901	46	4	.	.	PUNCT
ejpam-5901	47	1	[	[	X
ejpam-5901	47	2	13	13	NUM
ejpam-5901	47	3	]	]	PUNCT
ejpam-5901	47	4	developed	develop	VERB
ejpam-5901	47	5	a	a	DET
ejpam-5901	47	6	mathematical	mathematical	ADJ
ejpam-5901	47	7	model	model	NOUN
ejpam-5901	47	8	to	to	PART
ejpam-5901	47	9	illustrate	illustrate	VERB
ejpam-5901	47	10	how	how	SCONJ
ejpam-5901	47	11	microorganisms	microorganism	NOUN
ejpam-5901	47	12	inhibit	inhibit	VERB
ejpam-5901	47	13	pneumonia	pneumonia	NOUN
ejpam-5901	47	14	spread	spread	NOUN
ejpam-5901	47	15	,	,	PUNCT
ejpam-5901	47	16	examining	examine	VERB
ejpam-5901	47	17	vaccine	vaccine	NOUN
ejpam-5901	47	18	formulation	formulation	NOUN
ejpam-5901	47	19	and	and	CCONJ
ejpam-5901	47	20	treatment	treatment	NOUN
ejpam-5901	47	21	dynamics	dynamic	NOUN
ejpam-5901	47	22	.	.	PUNCT
ejpam-5901	48	1	mbabazi	mbabazi	PROPN
ejpam-5901	48	2	et	et	PROPN
ejpam-5901	48	3	al	al	PROPN
ejpam-5901	48	4	.	.	PUNCT
ejpam-5901	49	1	[	[	X
ejpam-5901	49	2	14	14	NUM
ejpam-5901	49	3	]	]	PUNCT
ejpam-5901	49	4	presented	present	VERB
ejpam-5901	49	5	a	a	DET
ejpam-5901	49	6	nonlinear	nonlinear	ADJ
ejpam-5901	49	7	mathematical	mathematical	ADJ
ejpam-5901	49	8	model	model	NOUN
ejpam-5901	49	9	describing	describe	VERB
ejpam-5901	49	10	the	the	DET
ejpam-5901	49	11	interplay	interplay	NOUN
ejpam-5901	49	12	between	between	ADP
ejpam-5901	49	13	influenza	influenza	NOUN
ejpam-5901	49	14	a	a	DET
ejpam-5901	49	15	virus	virus	NOUN
ejpam-5901	49	16	and	and	CCONJ
ejpam-5901	49	17	pneumonia	pneumonia	NOUN
ejpam-5901	49	18	within	within	ADP
ejpam-5901	49	19	the	the	DET
ejpam-5901	49	20	host	host	NOUN
ejpam-5901	49	21	.	.	PUNCT
ejpam-5901	50	1	tilahun	tilahun	PROPN
ejpam-5901	50	2	et	et	PROPN
ejpam-5901	50	3	al	al	PROPN
ejpam-5901	50	4	.	.	PUNCT
ejpam-5901	51	1	[	[	X
ejpam-5901	51	2	15	15	NUM
ejpam-5901	51	3	,	,	PUNCT
ejpam-5901	51	4	16	16	NUM
ejpam-5901	51	5	]	]	PUNCT
ejpam-5901	51	6	formulated	formulate	VERB
ejpam-5901	51	7	a	a	DET
ejpam-5901	51	8	pneumonia	pneumonia	NOUN
ejpam-5901	51	9	-	-	PUNCT
ejpam-5901	51	10	meningitis	meningitis	ADJ
ejpam-5901	51	11	co	co	NOUN
ejpam-5901	51	12	-	-	NOUN
ejpam-5901	51	13	infection	infection	NOUN
ejpam-5901	51	14	model	model	NOUN
ejpam-5901	51	15	using	use	VERB
ejpam-5901	51	16	odes	ode	NOUN
ejpam-5901	51	17	and	and	CCONJ
ejpam-5901	51	18	highlighted	highlight	VERB
ejpam-5901	51	19	disease	disease	NOUN
ejpam-5901	51	20	eradication	eradication	NOUN
ejpam-5901	51	21	strategies	strategy	NOUN
ejpam-5901	51	22	.	.	PUNCT
ejpam-5901	52	1	diah	diah	PROPN
ejpam-5901	52	2	et	et	PROPN
ejpam-5901	52	3	al	al	PROPN
ejpam-5901	52	4	.	.	PUNCT
ejpam-5901	53	1	[	[	X
ejpam-5901	53	2	17	17	NUM
ejpam-5901	53	3	]	]	PUNCT
ejpam-5901	53	4	evaluated	evaluate	VERB
ejpam-5901	53	5	pneumonia	pneumonia	NOUN
ejpam-5901	53	6	risk	risk	NOUN
ejpam-5901	53	7	using	use	VERB
ejpam-5901	53	8	dynamic	dynamic	ADJ
ejpam-5901	53	9	mathematical	mathematical	ADJ
ejpam-5901	53	10	models	model	NOUN
ejpam-5901	53	11	.	.	PUNCT
ejpam-5901	54	1	mbabazi	mbabazi	NOUN
ejpam-5901	54	2	et	et	PROPN
ejpam-5901	54	3	al	al	PROPN
ejpam-5901	54	4	.	.	PUNCT
ejpam-5901	55	1	[	[	X
ejpam-5901	55	2	18	18	NUM
ejpam-5901	55	3	]	]	PUNCT
ejpam-5901	55	4	proposed	propose	VERB
ejpam-5901	55	5	a	a	DET
ejpam-5901	55	6	hopf	hopf	ADJ
ejpam-5901	55	7	-	-	PUNCT
ejpam-5901	55	8	bifurcation	bifurcation	NOUN
ejpam-5901	55	9	analysis	analysis	NOUN
ejpam-5901	55	10	to	to	PART
ejpam-5901	55	11	study	study	VERB
ejpam-5901	55	12	pneumococcal	pneumococcal	ADJ
ejpam-5901	55	13	pneumonia	pneumonia	NOUN
ejpam-5901	55	14	with	with	ADP
ejpam-5901	55	15	temporal	temporal	ADJ
ejpam-5901	55	16	delays	delay	NOUN
ejpam-5901	55	17	.	.	PUNCT
ejpam-5901	56	1	otoo	otoo	PROPN
ejpam-5901	56	2	et	et	PROPN
ejpam-5901	56	3	al	al	PROPN
ejpam-5901	56	4	.	.	PUNCT
ejpam-5901	57	1	[	[	X
ejpam-5901	57	2	19	19	NUM
ejpam-5901	57	3	]	]	PUNCT
ejpam-5901	57	4	examined	examine	VERB
ejpam-5901	57	5	the	the	DET
ejpam-5901	57	6	efficacy	efficacy	NOUN
ejpam-5901	57	7	of	of	ADP
ejpam-5901	57	8	bacterial	bacterial	ADJ
ejpam-5901	57	9	pneumonia	pneumonia	NOUN
ejpam-5901	57	10	transmission	transmission	NOUN
ejpam-5901	57	11	models	model	NOUN
ejpam-5901	57	12	,	,	PUNCT
ejpam-5901	57	13	emphasizing	emphasize	VERB
ejpam-5901	57	14	immunization	immunization	NOUN
ejpam-5901	57	15	’s	’s	PART
ejpam-5901	57	16	role	role	NOUN
ejpam-5901	57	17	in	in	ADP
ejpam-5901	57	18	disease	disease	NOUN
ejpam-5901	57	19	prevention	prevention	NOUN
ejpam-5901	57	20	.	.	PUNCT
ejpam-5901	58	1	zephaniah	zephaniah	PROPN
ejpam-5901	58	2	et	et	PROPN
ejpam-5901	58	3	al	al	PROPN
ejpam-5901	58	4	.	.	PUNCT
ejpam-5901	59	1	[	[	X
ejpam-5901	59	2	20	20	NUM
ejpam-5901	59	3	]	]	PUNCT
ejpam-5901	59	4	provided	provide	VERB
ejpam-5901	59	5	graphical	graphical	ADJ
ejpam-5901	59	6	representations	representation	NOUN
ejpam-5901	59	7	of	of	ADP
ejpam-5901	59	8	dynamic	dynamic	ADJ
ejpam-5901	59	9	pneumonia	pneumonia	NOUN
ejpam-5901	59	10	models	model	NOUN
ejpam-5901	59	11	.	.	PUNCT
ejpam-5901	60	1	ming	ming	PROPN
ejpam-5901	60	2	et	et	PROPN
ejpam-5901	60	3	al	al	PROPN
ejpam-5901	60	4	.	.	PUNCT
ejpam-5901	61	1	[	[	X
ejpam-5901	61	2	21	21	NUM
ejpam-5901	61	3	]	]	PUNCT
ejpam-5901	61	4	reported	report	VERB
ejpam-5901	61	5	the	the	DET
ejpam-5901	61	6	rise	rise	NOUN
ejpam-5901	61	7	of	of	ADP
ejpam-5901	61	8	coronavirus	coronavirus	NOUN
ejpam-5901	61	9	pneumonia	pneumonia	NOUN
ejpam-5901	61	10	in	in	ADP
ejpam-5901	61	11	wuhan	wuhan	PROPN
ejpam-5901	61	12	,	,	PUNCT
ejpam-5901	61	13	china	china	PROPN
ejpam-5901	61	14	,	,	PUNCT
ejpam-5901	61	15	confirmed	confirm	VERB
ejpam-5901	61	16	by	by	ADP
ejpam-5901	61	17	clinical	clinical	ADJ
ejpam-5901	61	18	testing	testing	NOUN
ejpam-5901	61	19	led	lead	VERB
ejpam-5901	61	20	by	by	ADP
ejpam-5901	61	21	jung	jung	PROPN
ejpam-5901	61	22	et	et	PROPN
ejpam-5901	61	23	al	al	PROPN
ejpam-5901	61	24	.	.	PUNCT
ejpam-5901	62	1	[	[	X
ejpam-5901	62	2	22	22	NUM
ejpam-5901	62	3	]	]	PUNCT
ejpam-5901	62	4	.	.	PUNCT
ejpam-5901	63	1	wafula	wafula	PROPN
ejpam-5901	63	2	et	et	PROPN
ejpam-5901	63	3	al	al	PROPN
ejpam-5901	63	4	.	.	PUNCT
ejpam-5901	64	1	[	[	X
ejpam-5901	64	2	23	23	NUM
ejpam-5901	64	3	]	]	PUNCT
ejpam-5901	64	4	developed	develop	VERB
ejpam-5901	64	5	a	a	DET
ejpam-5901	64	6	deterministic	deterministic	ADJ
ejpam-5901	64	7	model	model	NOUN
ejpam-5901	64	8	for	for	ADP
ejpam-5901	64	9	pneumonia	pneumonia	NOUN
ejpam-5901	64	10	-	-	PUNCT
ejpam-5901	64	11	hiv	hiv	PROPN
ejpam-5901	64	12	co	co	NOUN
ejpam-5901	64	13	-	-	NOUN
ejpam-5901	64	14	infection	infection	NOUN
ejpam-5901	64	15	,	,	PUNCT
ejpam-5901	64	16	incorporating	incorporate	VERB
ejpam-5901	64	17	anti	anti	NOUN
ejpam-5901	64	18	-	-	NOUN
ejpam-5901	64	19	pneumonia	pneumonia	NOUN
ejpam-5901	64	20	and	and	CCONJ
ejpam-5901	64	21	art	art	NOUN
ejpam-5901	64	22	therapies	therapy	NOUN
ejpam-5901	64	23	as	as	ADP
ejpam-5901	64	24	optimal	optimal	ADJ
ejpam-5901	64	25	controls	control	NOUN
ejpam-5901	64	26	.	.	PUNCT
ejpam-5901	65	1	oluwatobi	oluwatobi	PROPN
ejpam-5901	65	2	et	et	PROPN
ejpam-5901	65	3	al	al	PROPN
ejpam-5901	65	4	.	.	PUNCT
ejpam-5901	66	1	[	[	X
ejpam-5901	66	2	24	24	NUM
ejpam-5901	66	3	]	]	PUNCT
ejpam-5901	66	4	investigated	investigate	VERB
ejpam-5901	66	5	pneumonia	pneumonia	NOUN
ejpam-5901	66	6	transmission	transmission	NOUN
ejpam-5901	66	7	s.	s.	PROPN
ejpam-5901	66	8	saber	saber	PROPN
ejpam-5901	66	9	,	,	PUNCT
ejpam-5901	66	10	a.	a.	NOUN
ejpam-5901	66	11	a.	a.	NOUN
ejpam-5901	66	12	alahmari	alahmari	PROPN
ejpam-5901	66	13	/	/	SYM
ejpam-5901	66	14	eur	eur	PROPN
ejpam-5901	66	15	.	.	PUNCT
ejpam-5901	67	1	j.	j.	PROPN
ejpam-5901	67	2	pure	pure	PROPN
ejpam-5901	67	3	appl	appl	PROPN
ejpam-5901	67	4	.	.	PROPN
ejpam-5901	67	5	math	math	PROPN
ejpam-5901	67	6	,	,	PUNCT
ejpam-5901	67	7	18	18	NUM
ejpam-5901	67	8	(	(	PUNCT
ejpam-5901	67	9	2	2	NUM
ejpam-5901	67	10	)	)	PUNCT
ejpam-5901	67	11	(	(	PUNCT
ejpam-5901	67	12	2025	2025	NUM
ejpam-5901	67	13	)	)	PUNCT
ejpam-5901	67	14	,	,	PUNCT
ejpam-5901	67	15	5901	5901	NUM
ejpam-5901	67	16	3	3	NUM
ejpam-5901	67	17	of	of	ADP
ejpam-5901	67	18	23	23	NUM
ejpam-5901	67	19	dynamics	dynamic	NOUN
ejpam-5901	67	20	,	,	PUNCT
ejpam-5901	67	21	fundamental	fundamental	ADJ
ejpam-5901	67	22	reproduction	reproduction	NOUN
ejpam-5901	67	23	numbers	number	NOUN
ejpam-5901	67	24	,	,	PUNCT
ejpam-5901	67	25	and	and	CCONJ
ejpam-5901	67	26	equilibrium	equilibrium	NOUN
ejpam-5901	67	27	points	point	NOUN
ejpam-5901	67	28	.	.	PUNCT
ejpam-5901	68	1	sayed	sayed	PROPN
ejpam-5901	68	2	saber	saber	PROPN
ejpam-5901	68	3	et	et	PROPN
ejpam-5901	68	4	al	al	PROPN
ejpam-5901	68	5	.	.	PUNCT
ejpam-5901	69	1	[	[	X
ejpam-5901	69	2	25	25	NUM
ejpam-5901	69	3	,	,	PUNCT
ejpam-5901	69	4	26	26	NUM
ejpam-5901	69	5	]	]	PUNCT
ejpam-5901	69	6	proposed	propose	VERB
ejpam-5901	69	7	a	a	DET
ejpam-5901	69	8	fractional	fractional	ADJ
ejpam-5901	69	9	svcir	svcir	NOUN
ejpam-5901	69	10	model	model	NOUN
ejpam-5901	69	11	to	to	PART
ejpam-5901	69	12	analyze	analyze	VERB
ejpam-5901	69	13	pneumonia	pneumonia	NOUN
ejpam-5901	69	14	spread	spread	NOUN
ejpam-5901	69	15	.	.	PUNCT
ejpam-5901	70	1	muhammad	muhammad	PROPN
ejpam-5901	70	2	naveed	naveed	PROPN
ejpam-5901	70	3	et	et	PROPN
ejpam-5901	70	4	al	al	PROPN
ejpam-5901	70	5	.	.	PUNCT
ejpam-5901	71	1	[	[	X
ejpam-5901	71	2	27	27	NUM
ejpam-5901	71	3	]	]	PUNCT
ejpam-5901	71	4	examined	examine	VERB
ejpam-5901	71	5	a	a	DET
ejpam-5901	71	6	delayed	delay	VERB
ejpam-5901	71	7	variant	variant	NOUN
ejpam-5901	71	8	of	of	ADP
ejpam-5901	71	9	the	the	DET
ejpam-5901	71	10	scir	scir	PROPN
ejpam-5901	71	11	model	model	NOUN
ejpam-5901	71	12	and	and	CCONJ
ejpam-5901	71	13	conducted	conduct	VERB
ejpam-5901	71	14	its	its	PRON
ejpam-5901	71	15	mathematical	mathematical	ADJ
ejpam-5901	71	16	analysis	analysis	NOUN
ejpam-5901	71	17	.	.	PUNCT
ejpam-5901	72	1	many	many	ADJ
ejpam-5901	72	2	mathematical	mathematical	ADJ
ejpam-5901	72	3	models	model	NOUN
ejpam-5901	72	4	have	have	AUX
ejpam-5901	72	5	been	be	AUX
ejpam-5901	72	6	solved	solve	VERB
ejpam-5901	72	7	by	by	ADP
ejpam-5901	72	8	analytical	analytical	ADJ
ejpam-5901	72	9	and	and	CCONJ
ejpam-5901	72	10	numerical	numerical	ADJ
ejpam-5901	72	11	methods	method	NOUN
ejpam-5901	72	12	such	such	ADJ
ejpam-5901	72	13	as	as	ADP
ejpam-5901	72	14	vim	vim	PROPN
ejpam-5901	72	15	,	,	PUNCT
ejpam-5901	72	16	adm	adm	PROPN
ejpam-5901	72	17	,	,	PUNCT
ejpam-5901	72	18	etc	etc	X
ejpam-5901	72	19	,	,	PUNCT
ejpam-5901	72	20	[	[	X
ejpam-5901	72	21	28–31	28–31	NUM
ejpam-5901	72	22	]	]	PUNCT
ejpam-5901	72	23	.	.	PUNCT
ejpam-5901	73	1	fractional	fractional	ADJ
ejpam-5901	73	2	calculus	calculus	NOUN
ejpam-5901	73	3	has	have	AUX
ejpam-5901	73	4	gained	gain	VERB
ejpam-5901	73	5	significant	significant	ADJ
ejpam-5901	73	6	attention	attention	NOUN
ejpam-5901	73	7	for	for	ADP
ejpam-5901	73	8	its	its	PRON
ejpam-5901	73	9	applications	application	NOUN
ejpam-5901	73	10	in	in	ADP
ejpam-5901	73	11	engineering	engineer	VERB
ejpam-5901	73	12	[	[	X
ejpam-5901	73	13	32	32	NUM
ejpam-5901	73	14	]	]	PUNCT
ejpam-5901	73	15	,	,	PUNCT
ejpam-5901	73	16	plant	plant	NOUN
ejpam-5901	73	17	epidemiology	epidemiology	NOUN
ejpam-5901	73	18	[	[	X
ejpam-5901	73	19	33	33	NUM
ejpam-5901	73	20	]	]	PUNCT
ejpam-5901	73	21	,	,	PUNCT
ejpam-5901	73	22	mathematical	mathematical	ADJ
ejpam-5901	73	23	biology	biology	NOUN
ejpam-5901	73	24	[	[	X
ejpam-5901	73	25	34	34	NUM
ejpam-5901	73	26	]	]	PUNCT
ejpam-5901	73	27	,	,	PUNCT
ejpam-5901	73	28	medicine	medicine	NOUN
ejpam-5901	73	29	[	[	X
ejpam-5901	73	30	35	35	NUM
ejpam-5901	73	31	]	]	PUNCT
ejpam-5901	73	32	,	,	PUNCT
ejpam-5901	73	33	as	as	ADV
ejpam-5901	73	34	well	well	ADV
ejpam-5901	73	35	as	as	ADP
ejpam-5901	73	36	psychological	psychological	ADJ
ejpam-5901	73	37	and	and	CCONJ
ejpam-5901	73	38	life	life	NOUN
ejpam-5901	73	39	sciences	science	NOUN
ejpam-5901	73	40	[	[	X
ejpam-5901	73	41	36	36	NUM
ejpam-5901	73	42	]	]	PUNCT
ejpam-5901	73	43	.	.	PUNCT
ejpam-5901	74	1	several	several	ADJ
ejpam-5901	74	2	types	type	NOUN
ejpam-5901	74	3	of	of	ADP
ejpam-5901	74	4	fractional	fractional	ADJ
ejpam-5901	74	5	derivatives	derivative	NOUN
ejpam-5901	74	6	are	be	AUX
ejpam-5901	74	7	used	use	VERB
ejpam-5901	74	8	in	in	ADP
ejpam-5901	74	9	this	this	DET
ejpam-5901	74	10	field	field	NOUN
ejpam-5901	74	11	,	,	PUNCT
ejpam-5901	74	12	including	include	VERB
ejpam-5901	74	13	the	the	DET
ejpam-5901	74	14	riemann	riemann	PROPN
ejpam-5901	74	15	-	-	PUNCT
ejpam-5901	74	16	liouville	liouville	PROPN
ejpam-5901	74	17	,	,	PUNCT
ejpam-5901	74	18	caputo	caputo	PROPN
ejpam-5901	74	19	,	,	PUNCT
ejpam-5901	74	20	caputo	caputo	PROPN
ejpam-5901	74	21	-	-	PUNCT
ejpam-5901	74	22	fabrizio	fabrizio	PROPN
ejpam-5901	74	23	,	,	PUNCT
ejpam-5901	74	24	and	and	CCONJ
ejpam-5901	74	25	atangana	atangana	PROPN
ejpam-5901	74	26	-	-	PUNCT
ejpam-5901	74	27	baleanu	baleanu	PROPN
ejpam-5901	74	28	operators	operator	NOUN
ejpam-5901	74	29	.	.	PUNCT
ejpam-5901	75	1	these	these	PRON
ejpam-5901	75	2	have	have	VERB
ejpam-5901	75	3	applications	application	NOUN
ejpam-5901	75	4	in	in	ADP
ejpam-5901	75	5	physics	physics	NOUN
ejpam-5901	75	6	[	[	X
ejpam-5901	75	7	37–46	37–46	NUM
ejpam-5901	75	8	]	]	PUNCT
ejpam-5901	75	9	,	,	PUNCT
ejpam-5901	75	10	viscoelasticity	viscoelasticity	NOUN
ejpam-5901	76	1	[	[	X
ejpam-5901	76	2	47	47	NUM
ejpam-5901	76	3	]	]	PUNCT
ejpam-5901	76	4	,	,	PUNCT
ejpam-5901	76	5	electromagnetic	electromagnetic	ADJ
ejpam-5901	76	6	wave	wave	NOUN
ejpam-5901	76	7	propagation	propagation	NOUN
ejpam-5901	77	1	[	[	X
ejpam-5901	77	2	48	48	NUM
ejpam-5901	77	3	]	]	PUNCT
ejpam-5901	77	4	,	,	PUNCT
ejpam-5901	77	5	quantum	quantum	NOUN
ejpam-5901	77	6	dynamics	dynamic	NOUN
ejpam-5901	77	7	[	[	X
ejpam-5901	77	8	49	49	NUM
ejpam-5901	77	9	]	]	PUNCT
ejpam-5901	77	10	,	,	PUNCT
ejpam-5901	77	11	langevin	langevin	PROPN
ejpam-5901	77	12	systems	system	NOUN
ejpam-5901	77	13	[	[	X
ejpam-5901	77	14	50	50	NUM
ejpam-5901	77	15	]	]	PUNCT
ejpam-5901	77	16	,	,	PUNCT
ejpam-5901	77	17	diabetes	diabete	VERB
ejpam-5901	77	18	[	[	X
ejpam-5901	77	19	51	51	NUM
ejpam-5901	77	20	–	–	PUNCT
ejpam-5901	77	21	56	56	NUM
ejpam-5901	77	22	]	]	PUNCT
ejpam-5901	77	23	.	.	PUNCT
ejpam-5901	78	1	fractal	fractal	ADJ
ejpam-5901	78	2	-	-	PUNCT
ejpam-5901	78	3	fractional	fractional	ADJ
ejpam-5901	78	4	(	(	PUNCT
ejpam-5901	78	5	ff	ff	NOUN
ejpam-5901	78	6	)	)	PUNCT
ejpam-5901	78	7	models	model	NOUN
ejpam-5901	78	8	describe	describe	VERB
ejpam-5901	78	9	complex	complex	ADJ
ejpam-5901	78	10	,	,	PUNCT
ejpam-5901	78	11	real	real	ADJ
ejpam-5901	78	12	-	-	PUNCT
ejpam-5901	78	13	world	world	NOUN
ejpam-5901	78	14	phenomena	phenomenon	NOUN
ejpam-5901	78	15	effectively	effectively	ADV
ejpam-5901	78	16	.	.	PUNCT
ejpam-5901	79	1	they	they	PRON
ejpam-5901	79	2	have	have	AUX
ejpam-5901	79	3	been	be	AUX
ejpam-5901	79	4	extensively	extensively	ADV
ejpam-5901	79	5	studied	study	VERB
ejpam-5901	79	6	in	in	ADP
ejpam-5901	79	7	various	various	ADJ
ejpam-5901	79	8	systems	system	NOUN
ejpam-5901	79	9	,	,	PUNCT
ejpam-5901	79	10	including	include	VERB
ejpam-5901	79	11	excitation	excitation	NOUN
ejpam-5901	79	12	-	-	PUNCT
ejpam-5901	79	13	relaxation	relaxation	NOUN
ejpam-5901	79	14	and	and	CCONJ
ejpam-5901	79	15	natural	natural	ADJ
ejpam-5901	79	16	oscillatory	oscillatory	ADJ
ejpam-5901	79	17	systems	system	NOUN
ejpam-5901	79	18	[	[	X
ejpam-5901	79	19	57–61	57–61	NUM
ejpam-5901	79	20	]	]	PUNCT
ejpam-5901	79	21	.	.	PUNCT
ejpam-5901	80	1	ff	ff	NOUN
ejpam-5901	80	2	models	model	NOUN
ejpam-5901	80	3	provide	provide	VERB
ejpam-5901	80	4	superior	superior	ADJ
ejpam-5901	80	5	accuracy	accuracy	NOUN
ejpam-5901	80	6	to	to	ADP
ejpam-5901	80	7	traditional	traditional	ADJ
ejpam-5901	80	8	integer	integer	NOUN
ejpam-5901	80	9	-	-	PUNCT
ejpam-5901	80	10	order	order	NOUN
ejpam-5901	80	11	models	model	NOUN
ejpam-5901	80	12	by	by	ADP
ejpam-5901	80	13	capturing	capture	VERB
ejpam-5901	80	14	long	long	ADJ
ejpam-5901	80	15	-	-	PUNCT
ejpam-5901	80	16	memory	memory	NOUN
ejpam-5901	80	17	behaviors	behavior	NOUN
ejpam-5901	80	18	,	,	PUNCT
ejpam-5901	80	19	heavy	heavy	ADJ
ejpam-5901	80	20	-	-	PUNCT
ejpam-5901	80	21	tailed	tail	VERB
ejpam-5901	80	22	distributions	distribution	NOUN
ejpam-5901	80	23	,	,	PUNCT
ejpam-5901	80	24	and	and	CCONJ
ejpam-5901	80	25	short	short	ADJ
ejpam-5901	80	26	-	-	PUNCT
ejpam-5901	80	27	range	range	NOUN
ejpam-5901	80	28	autocorrelation	autocorrelation	NOUN
ejpam-5901	80	29	dependencies	dependency	NOUN
ejpam-5901	80	30	.	.	PUNCT
ejpam-5901	81	1	the	the	DET
ejpam-5901	81	2	atangana	atangana	PROPN
ejpam-5901	81	3	-	-	PUNCT
ejpam-5901	81	4	baleanu	baleanu	ADJ
ejpam-5901	81	5	fractal	fractal	ADJ
ejpam-5901	81	6	-	-	PUNCT
ejpam-5901	81	7	fractional	fractional	ADJ
ejpam-5901	81	8	operator	operator	NOUN
ejpam-5901	81	9	,	,	PUNCT
ejpam-5901	81	10	which	which	PRON
ejpam-5901	81	11	integrates	integrate	VERB
ejpam-5901	81	12	fractal	fractal	ADJ
ejpam-5901	81	13	geometry	geometry	NOUN
ejpam-5901	81	14	into	into	ADP
ejpam-5901	81	15	the	the	DET
ejpam-5901	81	16	fractional	fractional	ADJ
ejpam-5901	81	17	calculus	calculus	NOUN
ejpam-5901	81	18	framework	framework	NOUN
ejpam-5901	81	19	,	,	PUNCT
ejpam-5901	81	20	has	have	AUX
ejpam-5901	81	21	been	be	AUX
ejpam-5901	81	22	instrumental	instrumental	ADJ
ejpam-5901	81	23	in	in	ADP
ejpam-5901	81	24	analyzing	analyze	VERB
ejpam-5901	81	25	pneumonia	pneumonia	NOUN
ejpam-5901	81	26	dynamics	dynamic	NOUN
ejpam-5901	81	27	.	.	PUNCT
ejpam-5901	82	1	this	this	DET
ejpam-5901	82	2	operator	operator	NOUN
ejpam-5901	82	3	helps	helps	AUX
ejpam-5901	82	4	identify	identify	VERB
ejpam-5901	82	5	infection	infection	NOUN
ejpam-5901	82	6	mechanisms	mechanism	NOUN
ejpam-5901	82	7	,	,	PUNCT
ejpam-5901	82	8	improve	improve	VERB
ejpam-5901	82	9	treatment	treatment	NOUN
ejpam-5901	82	10	strategies	strategy	NOUN
ejpam-5901	82	11	,	,	PUNCT
ejpam-5901	82	12	and	and	CCONJ
ejpam-5901	82	13	gain	gain	VERB
ejpam-5901	82	14	insights	insight	NOUN
ejpam-5901	82	15	into	into	ADP
ejpam-5901	82	16	pneumonia	pneumonia	NOUN
ejpam-5901	82	17	pathogenesis	pathogenesis	NOUN
ejpam-5901	82	18	.	.	PUNCT
ejpam-5901	83	1	with	with	ADP
ejpam-5901	83	2	atangana	atangana	PROPN
ejpam-5901	83	3	-	-	PUNCT
ejpam-5901	83	4	baleanu	baleanu	ADJ
ejpam-5901	83	5	fractal	fractal	ADJ
ejpam-5901	83	6	-	-	PUNCT
ejpam-5901	83	7	fractional	fractional	ADJ
ejpam-5901	83	8	operators	operator	NOUN
ejpam-5901	83	9	,	,	PUNCT
ejpam-5901	83	10	infectious	infectious	ADJ
ejpam-5901	83	11	disease	disease	NOUN
ejpam-5901	83	12	spread	spread	VERB
ejpam-5901	83	13	,	,	PUNCT
ejpam-5901	83	14	vaccine	vaccine	NOUN
ejpam-5901	83	15	and	and	CCONJ
ejpam-5901	83	16	drug	drug	NOUN
ejpam-5901	83	17	efficacy	efficacy	NOUN
ejpam-5901	83	18	,	,	PUNCT
ejpam-5901	83	19	and	and	CCONJ
ejpam-5901	83	20	public	public	ADJ
ejpam-5901	83	21	health	health	NOUN
ejpam-5901	83	22	interventions	intervention	NOUN
ejpam-5901	83	23	can	can	AUX
ejpam-5901	83	24	be	be	AUX
ejpam-5901	83	25	studied	study	VERB
ejpam-5901	83	26	.	.	PUNCT
ejpam-5901	84	1	in	in	ADP
ejpam-5901	84	2	addition	addition	NOUN
ejpam-5901	84	3	,	,	PUNCT
ejpam-5901	84	4	masks	mask	NOUN
ejpam-5901	84	5	are	be	AUX
ejpam-5901	84	6	used	use	VERB
ejpam-5901	84	7	and	and	CCONJ
ejpam-5901	84	8	contact	contact	NOUN
ejpam-5901	84	9	tracing	trace	VERB
ejpam-5901	84	10	is	be	AUX
ejpam-5901	84	11	done	do	VERB
ejpam-5901	84	12	.	.	PUNCT
ejpam-5901	85	1	these	these	DET
ejpam-5901	85	2	operators	operator	NOUN
ejpam-5901	85	3	also	also	ADV
ejpam-5901	85	4	enable	enable	VERB
ejpam-5901	85	5	policymakers	policymaker	NOUN
ejpam-5901	85	6	to	to	PART
ejpam-5901	85	7	assess	assess	VERB
ejpam-5901	85	8	intervention	intervention	NOUN
ejpam-5901	85	9	impacts	impact	NOUN
ejpam-5901	85	10	and	and	CCONJ
ejpam-5901	85	11	develop	develop	VERB
ejpam-5901	85	12	long	long	ADJ
ejpam-5901	85	13	-	-	PUNCT
ejpam-5901	85	14	term	term	NOUN
ejpam-5901	85	15	mitigation	mitigation	NOUN
ejpam-5901	85	16	strategies	strategy	NOUN
ejpam-5901	85	17	.	.	PUNCT
ejpam-5901	86	1	the	the	DET
ejpam-5901	86	2	paper	paper	NOUN
ejpam-5901	86	3	analyzes	analyze	VERB
ejpam-5901	86	4	a	a	DET
ejpam-5901	86	5	mathematical	mathematical	ADJ
ejpam-5901	86	6	model	model	NOUN
ejpam-5901	86	7	for	for	ADP
ejpam-5901	86	8	pneumonia	pneumonia	NOUN
ejpam-5901	86	9	using	use	VERB
ejpam-5901	86	10	fractal	fractal	ADJ
ejpam-5901	86	11	-	-	PUNCT
ejpam-5901	86	12	fractional	fractional	ADJ
ejpam-5901	86	13	operators	operator	NOUN
ejpam-5901	86	14	.	.	PUNCT
ejpam-5901	87	1	the	the	DET
ejpam-5901	87	2	novelty	novelty	NOUN
ejpam-5901	87	3	of	of	ADP
ejpam-5901	87	4	this	this	DET
ejpam-5901	87	5	study	study	NOUN
ejpam-5901	87	6	lies	lie	VERB
ejpam-5901	87	7	in	in	ADP
ejpam-5901	87	8	extending	extend	VERB
ejpam-5901	87	9	previous	previous	ADJ
ejpam-5901	87	10	results	result	NOUN
ejpam-5901	87	11	to	to	ADP
ejpam-5901	87	12	fractal	fractal	ADJ
ejpam-5901	87	13	-	-	PUNCT
ejpam-5901	87	14	fractional	fractional	ADJ
ejpam-5901	87	15	models	model	NOUN
ejpam-5901	87	16	and	and	CCONJ
ejpam-5901	87	17	demonstrating	demonstrate	VERB
ejpam-5901	87	18	enhanced	enhanced	ADJ
ejpam-5901	87	19	accuracy	accuracy	NOUN
ejpam-5901	87	20	and	and	CCONJ
ejpam-5901	87	21	predictive	predictive	ADJ
ejpam-5901	87	22	capabilities	capability	NOUN
ejpam-5901	87	23	.	.	PUNCT
ejpam-5901	88	1	this	this	DET
ejpam-5901	88	2	study	study	NOUN
ejpam-5901	88	3	presents	present	VERB
ejpam-5901	88	4	a	a	DET
ejpam-5901	88	5	novel	novel	ADJ
ejpam-5901	88	6	fractal	fractal	ADJ
ejpam-5901	88	7	-	-	PUNCT
ejpam-5901	88	8	fractional	fractional	ADJ
ejpam-5901	88	9	pneumonia	pneumonia	NOUN
ejpam-5901	88	10	transmission	transmission	NOUN
ejpam-5901	88	11	model	model	NOUN
ejpam-5901	88	12	incorporating	incorporate	VERB
ejpam-5901	88	13	the	the	DET
ejpam-5901	88	14	atangana	atangana	PROPN
ejpam-5901	88	15	-	-	PUNCT
ejpam-5901	88	16	baleanu	baleanu	PROPN
ejpam-5901	88	17	derivative	derivative	NOUN
ejpam-5901	88	18	,	,	PUNCT
ejpam-5901	88	19	offering	offer	VERB
ejpam-5901	88	20	a	a	DET
ejpam-5901	88	21	more	more	ADV
ejpam-5901	88	22	accurate	accurate	ADJ
ejpam-5901	88	23	representation	representation	NOUN
ejpam-5901	88	24	of	of	ADP
ejpam-5901	88	25	disease	disease	NOUN
ejpam-5901	88	26	dynamics	dynamic	NOUN
ejpam-5901	88	27	compared	compare	VERB
ejpam-5901	88	28	to	to	ADP
ejpam-5901	88	29	traditional	traditional	ADJ
ejpam-5901	88	30	integer	integer	NOUN
ejpam-5901	88	31	-	-	PUNCT
ejpam-5901	88	32	order	order	NOUN
ejpam-5901	88	33	and	and	CCONJ
ejpam-5901	88	34	classical	classical	ADJ
ejpam-5901	88	35	fractional	fractional	ADJ
ejpam-5901	88	36	models	model	NOUN
ejpam-5901	88	37	.	.	PUNCT
ejpam-5901	89	1	the	the	DET
ejpam-5901	89	2	results	result	NOUN
ejpam-5901	89	3	demonstrate	demonstrate	VERB
ejpam-5901	89	4	that	that	SCONJ
ejpam-5901	89	5	our	our	PRON
ejpam-5901	89	6	approach	approach	NOUN
ejpam-5901	89	7	captures	capture	VERB
ejpam-5901	89	8	long	long	ADJ
ejpam-5901	89	9	-	-	PUNCT
ejpam-5901	89	10	memory	memory	NOUN
ejpam-5901	89	11	effects	effect	NOUN
ejpam-5901	89	12	and	and	CCONJ
ejpam-5901	89	13	population	population	NOUN
ejpam-5901	89	14	heterogeneity	heterogeneity	NOUN
ejpam-5901	89	15	more	more	ADV
ejpam-5901	89	16	effectively	effectively	ADV
ejpam-5901	89	17	,	,	PUNCT
ejpam-5901	89	18	leading	lead	VERB
ejpam-5901	89	19	to	to	ADP
ejpam-5901	89	20	improved	improve	VERB
ejpam-5901	89	21	predictions	prediction	NOUN
ejpam-5901	89	22	of	of	ADP
ejpam-5901	89	23	disease	disease	NOUN
ejpam-5901	89	24	progression	progression	NOUN
ejpam-5901	89	25	and	and	CCONJ
ejpam-5901	89	26	intervention	intervention	NOUN
ejpam-5901	89	27	outcomes	outcome	NOUN
ejpam-5901	89	28	.	.	PUNCT
ejpam-5901	90	1	the	the	DET
ejpam-5901	90	2	incorporation	incorporation	NOUN
ejpam-5901	90	3	of	of	ADP
ejpam-5901	90	4	hyers	hyer	NOUN
ejpam-5901	90	5	-	-	PUNCT
ejpam-5901	90	6	ulam	ulam	PROPN
ejpam-5901	90	7	stability	stability	PROPN
ejpam-5901	90	8	analysis	analysis	NOUN
ejpam-5901	90	9	further	far	ADV
ejpam-5901	90	10	strengthens	strengthen	VERB
ejpam-5901	90	11	the	the	DET
ejpam-5901	90	12	theoretical	theoretical	ADJ
ejpam-5901	90	13	foundation	foundation	NOUN
ejpam-5901	90	14	of	of	ADP
ejpam-5901	90	15	the	the	DET
ejpam-5901	90	16	model	model	NOUN
ejpam-5901	90	17	,	,	PUNCT
ejpam-5901	90	18	differentiating	differentiate	VERB
ejpam-5901	90	19	it	it	PRON
ejpam-5901	90	20	from	from	ADP
ejpam-5901	90	21	previous	previous	ADJ
ejpam-5901	90	22	research	research	NOUN
ejpam-5901	90	23	.	.	PUNCT
ejpam-5901	91	1	numerical	numerical	ADJ
ejpam-5901	91	2	simulations	simulation	NOUN
ejpam-5901	91	3	confirm	confirm	VERB
ejpam-5901	91	4	that	that	SCONJ
ejpam-5901	91	5	varying	vary	VERB
ejpam-5901	91	6	fractional	fractional	ADJ
ejpam-5901	91	7	orders	order	NOUN
ejpam-5901	91	8	significantly	significantly	ADV
ejpam-5901	91	9	influence	influence	VERB
ejpam-5901	91	10	disease	disease	NOUN
ejpam-5901	91	11	behavior	behavior	NOUN
ejpam-5901	91	12	,	,	PUNCT
ejpam-5901	91	13	highlighting	highlight	VERB
ejpam-5901	91	14	the	the	DET
ejpam-5901	91	15	flexibility	flexibility	NOUN
ejpam-5901	91	16	of	of	ADP
ejpam-5901	91	17	the	the	DET
ejpam-5901	91	18	proposed	propose	VERB
ejpam-5901	91	19	framework	framework	NOUN
ejpam-5901	91	20	.	.	PUNCT
ejpam-5901	92	1	future	future	ADJ
ejpam-5901	92	2	research	research	NOUN
ejpam-5901	92	3	could	could	AUX
ejpam-5901	92	4	explore	explore	VERB
ejpam-5901	92	5	the	the	DET
ejpam-5901	92	6	integration	integration	NOUN
ejpam-5901	92	7	of	of	ADP
ejpam-5901	92	8	environmental	environmental	ADJ
ejpam-5901	92	9	and	and	CCONJ
ejpam-5901	92	10	social	social	ADJ
ejpam-5901	92	11	factors	factor	NOUN
ejpam-5901	92	12	into	into	ADP
ejpam-5901	92	13	the	the	DET
ejpam-5901	92	14	model	model	NOUN
ejpam-5901	92	15	,	,	PUNCT
ejpam-5901	92	16	as	as	ADV
ejpam-5901	92	17	well	well	ADV
ejpam-5901	92	18	as	as	ADP
ejpam-5901	92	19	the	the	DET
ejpam-5901	92	20	application	application	NOUN
ejpam-5901	92	21	of	of	ADP
ejpam-5901	92	22	alternative	alternative	ADJ
ejpam-5901	92	23	numerical	numerical	ADJ
ejpam-5901	92	24	methods	method	NOUN
ejpam-5901	92	25	to	to	PART
ejpam-5901	92	26	enhance	enhance	VERB
ejpam-5901	92	27	computational	computational	ADJ
ejpam-5901	92	28	efficiency	efficiency	NOUN
ejpam-5901	92	29	.	.	PUNCT
ejpam-5901	93	1	additionally	additionally	ADV
ejpam-5901	93	2	,	,	PUNCT
ejpam-5901	93	3	extending	extend	VERB
ejpam-5901	93	4	the	the	DET
ejpam-5901	93	5	model	model	NOUN
ejpam-5901	93	6	to	to	ADP
ejpam-5901	93	7	other	other	ADJ
ejpam-5901	93	8	infectious	infectious	ADJ
ejpam-5901	93	9	diseases	disease	NOUN
ejpam-5901	93	10	could	could	AUX
ejpam-5901	93	11	provide	provide	VERB
ejpam-5901	93	12	further	further	ADJ
ejpam-5901	93	13	insights	insight	NOUN
ejpam-5901	93	14	into	into	ADP
ejpam-5901	93	15	the	the	DET
ejpam-5901	93	16	role	role	NOUN
ejpam-5901	93	17	of	of	ADP
ejpam-5901	93	18	fractional	fractional	ADJ
ejpam-5901	93	19	calculus	calculus	NOUN
ejpam-5901	93	20	in	in	ADP
ejpam-5901	93	21	epidemiological	epidemiological	ADJ
ejpam-5901	93	22	modeling	modeling	NOUN
ejpam-5901	93	23	.	.	PUNCT
ejpam-5901	94	1	the	the	DET
ejpam-5901	94	2	paper	paper	NOUN
ejpam-5901	94	3	analyzes	analyze	VERB
ejpam-5901	94	4	a	a	DET
ejpam-5901	94	5	mathematical	mathematical	ADJ
ejpam-5901	94	6	model	model	NOUN
ejpam-5901	94	7	for	for	ADP
ejpam-5901	94	8	pneumonia	pneumonia	NOUN
ejpam-5901	94	9	using	use	VERB
ejpam-5901	94	10	fractal	fractal	ADJ
ejpam-5901	94	11	-	-	PUNCT
ejpam-5901	94	12	fractional	fractional	ADJ
ejpam-5901	94	13	operators	operator	NOUN
ejpam-5901	94	14	.	.	PUNCT
ejpam-5901	95	1	the	the	DET
ejpam-5901	95	2	novelty	novelty	NOUN
ejpam-5901	95	3	of	of	ADP
ejpam-5901	95	4	this	this	DET
ejpam-5901	95	5	study	study	NOUN
ejpam-5901	95	6	lies	lie	VERB
ejpam-5901	95	7	in	in	ADP
ejpam-5901	95	8	extending	extend	VERB
ejpam-5901	95	9	previous	previous	ADJ
ejpam-5901	95	10	results	result	NOUN
ejpam-5901	95	11	to	to	ADP
ejpam-5901	95	12	fractal	fractal	ADJ
ejpam-5901	95	13	-	-	PUNCT
ejpam-5901	95	14	fractional	fractional	ADJ
ejpam-5901	95	15	models	model	NOUN
ejpam-5901	95	16	and	and	CCONJ
ejpam-5901	95	17	demonstrating	demonstrate	VERB
ejpam-5901	95	18	enhanced	enhanced	ADJ
ejpam-5901	95	19	accuracy	accuracy	NOUN
ejpam-5901	95	20	and	and	CCONJ
ejpam-5901	95	21	predictive	predictive	ADJ
ejpam-5901	95	22	capabilities	capability	NOUN
ejpam-5901	95	23	.	.	PUNCT
ejpam-5901	96	1	in	in	ADP
ejpam-5901	96	2	this	this	DET
ejpam-5901	96	3	study	study	NOUN
ejpam-5901	96	4	,	,	PUNCT
ejpam-5901	96	5	we	we	PRON
ejpam-5901	96	6	develop	develop	VERB
ejpam-5901	96	7	a	a	DET
ejpam-5901	96	8	fractal	fractal	ADJ
ejpam-5901	96	9	-	-	PUNCT
ejpam-5901	96	10	fractional	fractional	ADJ
ejpam-5901	96	11	mathematical	mathematical	ADJ
ejpam-5901	96	12	model	model	NOUN
ejpam-5901	96	13	to	to	PART
ejpam-5901	96	14	describe	describe	VERB
ejpam-5901	96	15	pneumonia	pneumonia	NOUN
ejpam-5901	96	16	transmission	transmission	NOUN
ejpam-5901	96	17	,	,	PUNCT
ejpam-5901	96	18	incorporating	incorporate	VERB
ejpam-5901	96	19	the	the	DET
ejpam-5901	96	20	atangana	atangana	PROPN
ejpam-5901	96	21	-	-	PUNCT
ejpam-5901	96	22	baleanu	baleanu	PROPN
ejpam-5901	96	23	s.	s.	PROPN
ejpam-5901	96	24	saber	saber	PROPN
ejpam-5901	96	25	,	,	PUNCT
ejpam-5901	96	26	a.	a.	NOUN
ejpam-5901	96	27	a.	a.	NOUN
ejpam-5901	96	28	alahmari	alahmari	PROPN
ejpam-5901	96	29	/	/	SYM
ejpam-5901	96	30	eur	eur	PROPN
ejpam-5901	96	31	.	.	PUNCT
ejpam-5901	97	1	j.	j.	PROPN
ejpam-5901	97	2	pure	pure	PROPN
ejpam-5901	97	3	appl	appl	PROPN
ejpam-5901	97	4	.	.	PROPN
ejpam-5901	97	5	math	math	PROPN
ejpam-5901	97	6	,	,	PUNCT
ejpam-5901	97	7	18	18	NUM
ejpam-5901	97	8	(	(	PUNCT
ejpam-5901	97	9	2	2	NUM
ejpam-5901	97	10	)	)	PUNCT
ejpam-5901	97	11	(	(	PUNCT
ejpam-5901	97	12	2025	2025	NUM
ejpam-5901	97	13	)	)	PUNCT
ejpam-5901	97	14	,	,	PUNCT
ejpam-5901	97	15	5901	5901	NUM
ejpam-5901	97	16	4	4	NUM
ejpam-5901	97	17	of	of	ADP
ejpam-5901	97	18	23	23	NUM
ejpam-5901	97	19	derivative	derivative	NOUN
ejpam-5901	97	20	to	to	PART
ejpam-5901	97	21	account	account	VERB
ejpam-5901	97	22	for	for	ADP
ejpam-5901	97	23	long	long	ADJ
ejpam-5901	97	24	-	-	PUNCT
ejpam-5901	97	25	memory	memory	NOUN
ejpam-5901	97	26	effects	effect	NOUN
ejpam-5901	97	27	.	.	PUNCT
ejpam-5901	98	1	we	we	PRON
ejpam-5901	98	2	analyze	analyze	VERB
ejpam-5901	98	3	the	the	DET
ejpam-5901	98	4	existence	existence	NOUN
ejpam-5901	98	5	and	and	CCONJ
ejpam-5901	98	6	uniqueness	uniqueness	NOUN
ejpam-5901	98	7	of	of	ADP
ejpam-5901	98	8	solutions	solution	NOUN
ejpam-5901	98	9	,	,	PUNCT
ejpam-5901	98	10	investigate	investigate	VERB
ejpam-5901	98	11	the	the	DET
ejpam-5901	98	12	stability	stability	NOUN
ejpam-5901	98	13	of	of	ADP
ejpam-5901	98	14	equilibrium	equilibrium	NOUN
ejpam-5901	98	15	points	point	NOUN
ejpam-5901	98	16	using	use	VERB
ejpam-5901	98	17	hyers	hyers	PROPN
ejpam-5901	98	18	-	-	PUNCT
ejpam-5901	98	19	ulam	ulam	PROPN
ejpam-5901	98	20	criteria	criterion	NOUN
ejpam-5901	98	21	,	,	PUNCT
ejpam-5901	98	22	and	and	CCONJ
ejpam-5901	98	23	conduct	conduct	VERB
ejpam-5901	98	24	numerical	numerical	ADJ
ejpam-5901	98	25	simulations	simulation	NOUN
ejpam-5901	98	26	to	to	PART
ejpam-5901	98	27	explore	explore	VERB
ejpam-5901	98	28	the	the	DET
ejpam-5901	98	29	impact	impact	NOUN
ejpam-5901	98	30	of	of	ADP
ejpam-5901	98	31	different	different	ADJ
ejpam-5901	98	32	fractional	fractional	ADJ
ejpam-5901	98	33	orders	order	NOUN
ejpam-5901	98	34	on	on	ADP
ejpam-5901	98	35	disease	disease	NOUN
ejpam-5901	98	36	progression	progression	NOUN
ejpam-5901	98	37	.	.	PUNCT
ejpam-5901	99	1	our	our	PRON
ejpam-5901	99	2	results	result	NOUN
ejpam-5901	99	3	demonstrate	demonstrate	VERB
ejpam-5901	99	4	that	that	SCONJ
ejpam-5901	99	5	fractal	fractal	ADJ
ejpam-5901	99	6	-	-	PUNCT
ejpam-5901	99	7	fractional	fractional	ADJ
ejpam-5901	99	8	models	model	NOUN
ejpam-5901	99	9	provide	provide	VERB
ejpam-5901	99	10	a	a	DET
ejpam-5901	99	11	more	more	ADV
ejpam-5901	99	12	flexible	flexible	ADJ
ejpam-5901	99	13	and	and	CCONJ
ejpam-5901	99	14	accurate	accurate	ADJ
ejpam-5901	99	15	framework	framework	NOUN
ejpam-5901	99	16	than	than	ADP
ejpam-5901	99	17	classical	classical	ADJ
ejpam-5901	99	18	integer	integer	NOUN
ejpam-5901	99	19	-	-	PUNCT
ejpam-5901	99	20	order	order	NOUN
ejpam-5901	99	21	models	model	NOUN
ejpam-5901	99	22	,	,	PUNCT
ejpam-5901	99	23	offering	offer	VERB
ejpam-5901	99	24	valuable	valuable	ADJ
ejpam-5901	99	25	insights	insight	NOUN
ejpam-5901	99	26	into	into	ADP
ejpam-5901	99	27	disease	disease	NOUN
ejpam-5901	99	28	control	control	NOUN
ejpam-5901	99	29	strategies	strategy	NOUN
ejpam-5901	99	30	,	,	PUNCT
ejpam-5901	99	31	including	include	VERB
ejpam-5901	99	32	vaccination	vaccination	NOUN
ejpam-5901	99	33	and	and	CCONJ
ejpam-5901	99	34	treatment	treatment	NOUN
ejpam-5901	99	35	interventions	intervention	NOUN
ejpam-5901	99	36	.	.	PUNCT
ejpam-5901	100	1	the	the	DET
ejpam-5901	100	2	atangana	atangana	PROPN
ejpam-5901	100	3	-	-	PUNCT
ejpam-5901	100	4	baleanu	baleanu	ADJ
ejpam-5901	100	5	fractional	fractional	ADJ
ejpam-5901	100	6	derivative	derivative	NOUN
ejpam-5901	100	7	was	be	AUX
ejpam-5901	100	8	chosen	choose	VERB
ejpam-5901	100	9	over	over	ADP
ejpam-5901	100	10	alternative	alternative	ADJ
ejpam-5901	100	11	approaches	approach	NOUN
ejpam-5901	100	12	due	due	ADJ
ejpam-5901	100	13	to	to	ADP
ejpam-5901	100	14	its	its	PRON
ejpam-5901	100	15	superior	superior	ADJ
ejpam-5901	100	16	ability	ability	NOUN
ejpam-5901	100	17	to	to	PART
ejpam-5901	100	18	model	model	VERB
ejpam-5901	100	19	memory	memory	NOUN
ejpam-5901	100	20	effects	effect	NOUN
ejpam-5901	100	21	and	and	CCONJ
ejpam-5901	100	22	non	non	ADJ
ejpam-5901	100	23	-	-	NOUN
ejpam-5901	100	24	locality	locality	NOUN
ejpam-5901	100	25	in	in	ADP
ejpam-5901	100	26	real	real	ADJ
ejpam-5901	100	27	-	-	PUNCT
ejpam-5901	100	28	world	world	NOUN
ejpam-5901	100	29	epidemiological	epidemiological	ADJ
ejpam-5901	100	30	systems	system	NOUN
ejpam-5901	100	31	.	.	PUNCT
ejpam-5901	101	1	unlike	unlike	ADP
ejpam-5901	101	2	the	the	DET
ejpam-5901	101	3	classical	classical	ADJ
ejpam-5901	101	4	caputo	caputo	PROPN
ejpam-5901	101	5	and	and	CCONJ
ejpam-5901	101	6	riemann	riemann	PROPN
ejpam-5901	101	7	-	-	PUNCT
ejpam-5901	101	8	liouville	liouville	VERB
ejpam-5901	101	9	derivatives	derivative	NOUN
ejpam-5901	101	10	,	,	PUNCT
ejpam-5901	101	11	which	which	PRON
ejpam-5901	101	12	rely	rely	VERB
ejpam-5901	101	13	on	on	ADP
ejpam-5901	101	14	singular	singular	ADJ
ejpam-5901	101	15	kernels	kernel	NOUN
ejpam-5901	101	16	,	,	PUNCT
ejpam-5901	101	17	the	the	DET
ejpam-5901	101	18	atangana	atangana	PROPN
ejpam-5901	101	19	-	-	PUNCT
ejpam-5901	101	20	baleanu	baleanu	ADJ
ejpam-5901	101	21	derivative	derivative	NOUN
ejpam-5901	101	22	employs	employ	VERB
ejpam-5901	101	23	a	a	DET
ejpam-5901	101	24	non	non	ADJ
ejpam-5901	101	25	-	-	ADJ
ejpam-5901	101	26	singular	singular	ADJ
ejpam-5901	101	27	and	and	CCONJ
ejpam-5901	101	28	non	non	ADJ
ejpam-5901	101	29	-	-	ADJ
ejpam-5901	101	30	local	local	ADJ
ejpam-5901	101	31	mittag	mittag	ADJ
ejpam-5901	101	32	-	-	PUNCT
ejpam-5901	101	33	leffler	leffler	NOUN
ejpam-5901	101	34	kernel	kernel	NOUN
ejpam-5901	101	35	.	.	PUNCT
ejpam-5901	102	1	this	this	PRON
ejpam-5901	102	2	allows	allow	VERB
ejpam-5901	102	3	for	for	ADP
ejpam-5901	102	4	more	more	ADV
ejpam-5901	102	5	accurate	accurate	ADJ
ejpam-5901	102	6	representation	representation	NOUN
ejpam-5901	102	7	of	of	ADP
ejpam-5901	102	8	long	long	ADJ
ejpam-5901	102	9	-	-	PUNCT
ejpam-5901	102	10	memory	memory	NOUN
ejpam-5901	102	11	effects	effect	NOUN
ejpam-5901	102	12	and	and	CCONJ
ejpam-5901	102	13	biological	biological	ADJ
ejpam-5901	102	14	processes	process	NOUN
ejpam-5901	102	15	such	such	ADJ
ejpam-5901	102	16	as	as	ADP
ejpam-5901	102	17	immune	immune	ADJ
ejpam-5901	102	18	response	response	NOUN
ejpam-5901	102	19	delays	delay	NOUN
ejpam-5901	102	20	and	and	CCONJ
ejpam-5901	102	21	heterogeneous	heterogeneous	ADJ
ejpam-5901	102	22	transmission	transmission	NOUN
ejpam-5901	102	23	patterns	pattern	NOUN
ejpam-5901	102	24	.	.	PUNCT
ejpam-5901	103	1	additionally	additionally	ADV
ejpam-5901	103	2	,	,	PUNCT
ejpam-5901	103	3	the	the	DET
ejpam-5901	103	4	atangana	atangana	PROPN
ejpam-5901	103	5	-	-	PUNCT
ejpam-5901	103	6	baleanu	baleanu	PROPN
ejpam-5901	103	7	approach	approach	NOUN
ejpam-5901	103	8	ensures	ensure	VERB
ejpam-5901	103	9	stability	stability	NOUN
ejpam-5901	103	10	and	and	CCONJ
ejpam-5901	103	11	better	well	ADJ
ejpam-5901	103	12	numerical	numerical	ADJ
ejpam-5901	103	13	convergence	convergence	NOUN
ejpam-5901	103	14	,	,	PUNCT
ejpam-5901	103	15	making	make	VERB
ejpam-5901	103	16	it	it	PRON
ejpam-5901	103	17	more	more	ADV
ejpam-5901	103	18	suitable	suitable	ADJ
ejpam-5901	103	19	for	for	ADP
ejpam-5901	103	20	capturing	capture	VERB
ejpam-5901	103	21	complex	complex	ADJ
ejpam-5901	103	22	disease	disease	NOUN
ejpam-5901	103	23	dynamics	dynamic	NOUN
ejpam-5901	103	24	,	,	PUNCT
ejpam-5901	103	25	such	such	ADJ
ejpam-5901	103	26	as	as	ADP
ejpam-5901	103	27	pneumonia	pneumonia	NOUN
ejpam-5901	103	28	spread	spread	NOUN
ejpam-5901	103	29	,	,	PUNCT
ejpam-5901	103	30	compared	compare	VERB
ejpam-5901	103	31	to	to	ADP
ejpam-5901	103	32	other	other	ADJ
ejpam-5901	103	33	fractional	fractional	ADJ
ejpam-5901	103	34	derivatives	derivative	NOUN
ejpam-5901	103	35	.	.	PUNCT
ejpam-5901	104	1	the	the	DET
ejpam-5901	104	2	improved	improve	VERB
ejpam-5901	104	3	flexibility	flexibility	NOUN
ejpam-5901	104	4	and	and	CCONJ
ejpam-5901	104	5	accuracy	accuracy	NOUN
ejpam-5901	104	6	provided	provide	VERB
ejpam-5901	104	7	by	by	ADP
ejpam-5901	104	8	this	this	DET
ejpam-5901	104	9	operator	operator	NOUN
ejpam-5901	104	10	justify	justify	VERB
ejpam-5901	104	11	its	its	PRON
ejpam-5901	104	12	selection	selection	NOUN
ejpam-5901	104	13	for	for	ADP
ejpam-5901	104	14	this	this	DET
ejpam-5901	104	15	study	study	NOUN
ejpam-5901	104	16	.	.	PUNCT
ejpam-5901	105	1	to	to	PART
ejpam-5901	105	2	validate	validate	VERB
ejpam-5901	105	3	the	the	DET
ejpam-5901	105	4	main	main	ADJ
ejpam-5901	105	5	theorems	theorem	NOUN
ejpam-5901	105	6	of	of	ADP
ejpam-5901	105	7	this	this	DET
ejpam-5901	105	8	study	study	NOUN
ejpam-5901	105	9	,	,	PUNCT
ejpam-5901	105	10	a	a	DET
ejpam-5901	105	11	comparison	comparison	NOUN
ejpam-5901	105	12	with	with	ADP
ejpam-5901	105	13	previous	previous	ADJ
ejpam-5901	105	14	research	research	NOUN
ejpam-5901	105	15	is	be	AUX
ejpam-5901	105	16	necessary	necessary	ADJ
ejpam-5901	105	17	.	.	PUNCT
ejpam-5901	106	1	traditional	traditional	ADJ
ejpam-5901	106	2	integer	integer	NOUN
ejpam-5901	106	3	-	-	PUNCT
ejpam-5901	106	4	order	order	NOUN
ejpam-5901	106	5	models	model	NOUN
ejpam-5901	106	6	often	often	ADV
ejpam-5901	106	7	fail	fail	VERB
ejpam-5901	106	8	to	to	PART
ejpam-5901	106	9	capture	capture	VERB
ejpam-5901	106	10	the	the	DET
ejpam-5901	106	11	long	long	ADJ
ejpam-5901	106	12	-	-	PUNCT
ejpam-5901	106	13	memory	memory	NOUN
ejpam-5901	106	14	effects	effect	NOUN
ejpam-5901	106	15	inherent	inherent	ADJ
ejpam-5901	106	16	in	in	ADP
ejpam-5901	106	17	infectious	infectious	ADJ
ejpam-5901	106	18	disease	disease	NOUN
ejpam-5901	106	19	dynamics	dynamic	NOUN
ejpam-5901	106	20	.	.	PUNCT
ejpam-5901	107	1	studies	study	NOUN
ejpam-5901	107	2	using	use	VERB
ejpam-5901	107	3	classical	classical	ADJ
ejpam-5901	107	4	fractional	fractional	ADJ
ejpam-5901	107	5	derivatives	derivative	NOUN
ejpam-5901	107	6	,	,	PUNCT
ejpam-5901	107	7	such	such	ADJ
ejpam-5901	107	8	as	as	ADP
ejpam-5901	107	9	the	the	DET
ejpam-5901	107	10	caputo	caputo	PROPN
ejpam-5901	107	11	and	and	CCONJ
ejpam-5901	107	12	riemann	riemann	PROPN
ejpam-5901	107	13	-	-	PUNCT
ejpam-5901	107	14	liouville	liouville	VERB
ejpam-5901	107	15	approaches	approach	NOUN
ejpam-5901	107	16	,	,	PUNCT
ejpam-5901	107	17	provide	provide	VERB
ejpam-5901	107	18	improvements	improvement	NOUN
ejpam-5901	107	19	but	but	CCONJ
ejpam-5901	107	20	still	still	ADV
ejpam-5901	107	21	rely	rely	VERB
ejpam-5901	107	22	on	on	ADP
ejpam-5901	107	23	singular	singular	ADJ
ejpam-5901	107	24	kernels	kernel	NOUN
ejpam-5901	107	25	,	,	PUNCT
ejpam-5901	107	26	which	which	PRON
ejpam-5901	107	27	limit	limit	VERB
ejpam-5901	107	28	their	their	PRON
ejpam-5901	107	29	applicability	applicability	NOUN
ejpam-5901	107	30	in	in	ADP
ejpam-5901	107	31	modeling	model	VERB
ejpam-5901	107	32	realistic	realistic	ADJ
ejpam-5901	107	33	transmission	transmission	NOUN
ejpam-5901	107	34	scenarios	scenario	NOUN
ejpam-5901	107	35	.	.	PUNCT
ejpam-5901	108	1	in	in	ADP
ejpam-5901	108	2	contrast	contrast	NOUN
ejpam-5901	108	3	,	,	PUNCT
ejpam-5901	108	4	our	our	PRON
ejpam-5901	108	5	model	model	NOUN
ejpam-5901	108	6	,	,	PUNCT
ejpam-5901	108	7	based	base	VERB
ejpam-5901	108	8	on	on	ADP
ejpam-5901	108	9	the	the	DET
ejpam-5901	108	10	atangana	atangana	PROPN
ejpam-5901	108	11	-	-	PUNCT
ejpam-5901	108	12	baleanu	baleanu	PROPN
ejpam-5901	108	13	derivative	derivative	NOUN
ejpam-5901	108	14	,	,	PUNCT
ejpam-5901	108	15	enhances	enhance	VERB
ejpam-5901	108	16	accuracy	accuracy	NOUN
ejpam-5901	108	17	by	by	ADP
ejpam-5901	108	18	incorporating	incorporate	VERB
ejpam-5901	108	19	a	a	DET
ejpam-5901	108	20	non	non	ADJ
ejpam-5901	108	21	-	-	ADJ
ejpam-5901	108	22	singular	singular	ADJ
ejpam-5901	108	23	,	,	PUNCT
ejpam-5901	108	24	non	non	ADJ
ejpam-5901	108	25	-	-	ADJ
ejpam-5901	108	26	local	local	ADJ
ejpam-5901	108	27	kernel	kernel	NOUN
ejpam-5901	108	28	,	,	PUNCT
ejpam-5901	108	29	allowing	allow	VERB
ejpam-5901	108	30	for	for	ADP
ejpam-5901	108	31	more	more	ADV
ejpam-5901	108	32	realistic	realistic	ADJ
ejpam-5901	108	33	disease	disease	NOUN
ejpam-5901	108	34	dynamics	dynamic	NOUN
ejpam-5901	108	35	.	.	PUNCT
ejpam-5901	109	1	the	the	DET
ejpam-5901	109	2	stability	stability	NOUN
ejpam-5901	109	3	analysis	analysis	NOUN
ejpam-5901	109	4	using	use	VERB
ejpam-5901	109	5	hyers	hyers	PROPN
ejpam-5901	109	6	-	-	PUNCT
ejpam-5901	109	7	ulam	ulam	PROPN
ejpam-5901	109	8	criteria	criterion	NOUN
ejpam-5901	109	9	further	far	ADV
ejpam-5901	109	10	differentiates	differentiate	VERB
ejpam-5901	109	11	our	our	PRON
ejpam-5901	109	12	work	work	NOUN
ejpam-5901	109	13	by	by	ADP
ejpam-5901	109	14	offering	offer	VERB
ejpam-5901	109	15	a	a	DET
ejpam-5901	109	16	more	more	ADV
ejpam-5901	109	17	rigorous	rigorous	ADJ
ejpam-5901	109	18	mathematical	mathematical	ADJ
ejpam-5901	109	19	foundation	foundation	NOUN
ejpam-5901	109	20	.	.	PUNCT
ejpam-5901	110	1	numerical	numerical	PROPN
ejpam-5901	110	2	comparisons	comparison	NOUN
ejpam-5901	110	3	indicate	indicate	VERB
ejpam-5901	110	4	that	that	SCONJ
ejpam-5901	110	5	our	our	PRON
ejpam-5901	110	6	model	model	NOUN
ejpam-5901	110	7	provides	provide	VERB
ejpam-5901	110	8	a	a	DET
ejpam-5901	110	9	more	more	ADV
ejpam-5901	110	10	flexible	flexible	ADJ
ejpam-5901	110	11	and	and	CCONJ
ejpam-5901	110	12	robust	robust	ADJ
ejpam-5901	110	13	framework	framework	NOUN
ejpam-5901	110	14	for	for	ADP
ejpam-5901	110	15	predicting	predict	VERB
ejpam-5901	110	16	disease	disease	NOUN
ejpam-5901	110	17	spread	spread	VERB
ejpam-5901	110	18	,	,	PUNCT
ejpam-5901	110	19	making	make	VERB
ejpam-5901	110	20	it	it	PRON
ejpam-5901	110	21	a	a	DET
ejpam-5901	110	22	valuable	valuable	ADJ
ejpam-5901	110	23	extension	extension	NOUN
ejpam-5901	110	24	of	of	ADP
ejpam-5901	110	25	previous	previous	ADJ
ejpam-5901	110	26	epidemiological	epidemiological	ADJ
ejpam-5901	110	27	models	model	NOUN
ejpam-5901	110	28	.	.	PUNCT
ejpam-5901	111	1	the	the	DET
ejpam-5901	111	2	remainder	remainder	NOUN
ejpam-5901	111	3	of	of	ADP
ejpam-5901	111	4	this	this	DET
ejpam-5901	111	5	paper	paper	NOUN
ejpam-5901	111	6	is	be	AUX
ejpam-5901	111	7	structured	structure	VERB
ejpam-5901	111	8	as	as	SCONJ
ejpam-5901	111	9	follows	follow	VERB
ejpam-5901	111	10	:	:	PUNCT
ejpam-5901	111	11	section	section	NOUN
ejpam-5901	111	12	shows	show	VERB
ejpam-5901	111	13	the	the	DET
ejpam-5901	111	14	preliminary	preliminary	ADJ
ejpam-5901	111	15	definitions	definition	NOUN
ejpam-5901	111	16	.	.	PUNCT
ejpam-5901	112	1	section	section	NOUN
ejpam-5901	112	2	3	3	NUM
ejpam-5901	112	3	presents	present	VERB
ejpam-5901	112	4	the	the	DET
ejpam-5901	112	5	formulation	formulation	NOUN
ejpam-5901	112	6	of	of	ADP
ejpam-5901	112	7	the	the	DET
ejpam-5901	112	8	fractal	fractal	ADJ
ejpam-5901	112	9	-	-	PUNCT
ejpam-5901	112	10	fractional	fractional	ADJ
ejpam-5901	112	11	pneumonia	pneumonia	NOUN
ejpam-5901	112	12	model	model	NOUN
ejpam-5901	112	13	.	.	PUNCT
ejpam-5901	113	1	section	section	NOUN
ejpam-5901	113	2	4	4	NUM
ejpam-5901	113	3	discusses	discuss	VERB
ejpam-5901	113	4	the	the	DET
ejpam-5901	113	5	theoretical	theoretical	ADJ
ejpam-5901	113	6	analysis	analysis	NOUN
ejpam-5901	113	7	of	of	ADP
ejpam-5901	113	8	solution	solution	NOUN
ejpam-5901	113	9	existence	existence	NOUN
ejpam-5901	113	10	.	.	PUNCT
ejpam-5901	114	1	section	section	NOUN
ejpam-5901	114	2	5	5	NUM
ejpam-5901	114	3	discusses	discuss	VERB
ejpam-5901	114	4	the	the	DET
ejpam-5901	114	5	theoretical	theoretical	ADJ
ejpam-5901	114	6	analysis	analysis	NOUN
ejpam-5901	114	7	of	of	ADP
ejpam-5901	114	8	solution	solution	NOUN
ejpam-5901	114	9	uniqueness	uniqueness	NOUN
ejpam-5901	114	10	.	.	PUNCT
ejpam-5901	115	1	section	section	NOUN
ejpam-5901	115	2	6	6	NUM
ejpam-5901	115	3	discusses	discuss	VERB
ejpam-5901	115	4	the	the	DET
ejpam-5901	115	5	stability	stability	NOUN
ejpam-5901	115	6	analysis	analysis	NOUN
ejpam-5901	115	7	of	of	ADP
ejpam-5901	115	8	the	the	DET
ejpam-5901	115	9	model	model	NOUN
ejpam-5901	115	10	.	.	PUNCT
ejpam-5901	116	1	section	section	NOUN
ejpam-5901	116	2	7	7	NUM
ejpam-5901	116	3	provides	provide	VERB
ejpam-5901	116	4	numerical	numerical	ADJ
ejpam-5901	116	5	simulations	simulation	NOUN
ejpam-5901	116	6	and	and	CCONJ
ejpam-5901	116	7	interpretations	interpretation	NOUN
ejpam-5901	116	8	.	.	PUNCT
ejpam-5901	117	1	section	section	NOUN
ejpam-5901	117	2	5	5	NUM
ejpam-5901	117	3	concludes	conclude	VERB
ejpam-5901	117	4	the	the	DET
ejpam-5901	117	5	conclusion	conclusion	NOUN
ejpam-5901	117	6	and	and	CCONJ
ejpam-5901	117	7	future	future	ADJ
ejpam-5901	117	8	research	research	NOUN
ejpam-5901	117	9	directions	direction	NOUN
ejpam-5901	117	10	.	.	PUNCT
ejpam-5901	118	1	2	2	X
ejpam-5901	118	2	.	.	X
ejpam-5901	118	3	preliminary	preliminary	ADJ
ejpam-5901	118	4	definitions	definition	NOUN
ejpam-5901	118	5	the	the	DET
ejpam-5901	118	6	fractal	fractal	ADJ
ejpam-5901	118	7	-	-	PUNCT
ejpam-5901	118	8	fractional	fractional	ADJ
ejpam-5901	118	9	framework	framework	NOUN
ejpam-5901	118	10	extends	extend	VERB
ejpam-5901	118	11	the	the	DET
ejpam-5901	118	12	scir	scir	PROPN
ejpam-5901	118	13	model	model	NOUN
ejpam-5901	118	14	using	use	VERB
ejpam-5901	118	15	the	the	DET
ejpam-5901	118	16	atangana	atangana	PROPN
ejpam-5901	118	17	-	-	PUNCT
ejpam-5901	118	18	baleanu	baleanu	PROPN
ejpam-5901	118	19	derivative	derivative	NOUN
ejpam-5901	118	20	.	.	PUNCT
ejpam-5901	119	1	the	the	DET
ejpam-5901	119	2	fractal	fractal	ADJ
ejpam-5901	119	3	-	-	PUNCT
ejpam-5901	119	4	fractional	fractional	ADJ
ejpam-5901	119	5	derivative	derivative	NOUN
ejpam-5901	119	6	on	on	ADP
ejpam-5901	119	7	(	(	PUNCT
ejpam-5901	119	8	a	a	DET
ejpam-5901	119	9	,	,	PUNCT
ejpam-5901	119	10	b	b	NOUN
ejpam-5901	119	11	)	)	PUNCT
ejpam-5901	119	12	of	of	ADP
ejpam-5901	119	13	order	order	NOUN
ejpam-5901	119	14	0	0	PUNCT
ejpam-5901	119	15	<	<	X
ejpam-5901	119	16	ϱ2	ϱ2	ADJ
ejpam-5901	119	17	≤	≤	NOUN
ejpam-5901	119	18	1	1	NUM
ejpam-5901	119	19	is	be	AUX
ejpam-5901	119	20	defined	define	VERB
ejpam-5901	119	21	as	as	ADP
ejpam-5901	119	22	:	:	PUNCT
ejpam-5901	119	23	definition	definition	NOUN
ejpam-5901	119	24	1	1	NUM
ejpam-5901	119	25	(	(	PUNCT
ejpam-5901	119	26	[	[	X
ejpam-5901	119	27	57	57	NUM
ejpam-5901	119	28	]	]	NUM
ejpam-5901	119	29	)	)	PUNCT
ejpam-5901	119	30	.	.	PUNCT
ejpam-5901	120	1	the	the	DET
ejpam-5901	120	2	atangana	atangana	PROPN
ejpam-5901	120	3	-	-	PUNCT
ejpam-5901	120	4	baleanu	baleanu	ADJ
ejpam-5901	120	5	fractal	fractal	ADJ
ejpam-5901	120	6	-	-	PUNCT
ejpam-5901	120	7	fractional	fractional	ADJ
ejpam-5901	120	8	derivative	derivative	NOUN
ejpam-5901	120	9	is	be	AUX
ejpam-5901	120	10	given	give	VERB
ejpam-5901	120	11	by	by	ADP
ejpam-5901	120	12	:	:	PUNCT
ejpam-5901	120	13	ff−abdϱ1,ϱ2	ff−abdϱ1,ϱ2	PROPN
ejpam-5901	120	14	t	t	PROPN
ejpam-5901	120	15	ϵ(t	ϵ(t	NOUN
ejpam-5901	120	16	)	)	PUNCT
ejpam-5901	120	17	=	=	PUNCT
ejpam-5901	121	1	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	121	2	)	)	PUNCT
ejpam-5901	121	3	1−	1−	NUM
ejpam-5901	121	4	ϱ1	ϱ1	NOUN
ejpam-5901	122	1	d	d	NOUN
ejpam-5901	122	2	dtϱ2	dtϱ2	PROPN
ejpam-5901	122	3	∫	∫	PROPN
ejpam-5901	122	4	t	t	PROPN
ejpam-5901	122	5	0	0	NUM
ejpam-5901	122	6	ϵ(s)eϱ1	ϵ(s)eϱ1	PUNCT
ejpam-5901	123	1	[	[	PUNCT
ejpam-5901	123	2	−	−	PROPN
ejpam-5901	123	3	ϱ1	ϱ1	PROPN
ejpam-5901	123	4	1−	1−	NUM
ejpam-5901	123	5	ϱ1	ϱ1	NOUN
ejpam-5901	123	6	(	(	PUNCT
ejpam-5901	123	7	t−	t−	PROPN
ejpam-5901	123	8	s)ϱ1	s)ϱ1	PROPN
ejpam-5901	123	9	]	]	PUNCT
ejpam-5901	123	10	ds	ds	PROPN
ejpam-5901	123	11	,	,	PUNCT
ejpam-5901	123	12	where	where	SCONJ
ejpam-5901	123	13	b∗(ϱ1	b∗(ϱ1	ADJ
ejpam-5901	123	14	)	)	PUNCT
ejpam-5901	123	15	=	=	SYM
ejpam-5901	123	16	1−	1−	NUM
ejpam-5901	123	17	ϱ1	ϱ1	NOUN
ejpam-5901	123	18	+	+	CCONJ
ejpam-5901	123	19	ϱ1	ϱ1	NOUN
ejpam-5901	123	20	γ(ϱ1	γ(ϱ1	NOUN
ejpam-5901	123	21	)	)	PUNCT
ejpam-5901	123	22	and	and	CCONJ
ejpam-5901	123	23	dϵ(s	dϵ(s	NUM
ejpam-5901	123	24	)	)	PUNCT
ejpam-5901	123	25	dsϱ2	dsϱ2	NOUN
ejpam-5901	123	26	=	=	PUNCT
ejpam-5901	123	27	limt→s	limt→	NOUN
ejpam-5901	123	28	ϵ(t)−ϵ(s	ϵ(t)−ϵ(	NOUN
ejpam-5901	123	29	)	)	PUNCT
ejpam-5901	123	30	tϱ2−sϱ2	tϱ2−sϱ2	NOUN
ejpam-5901	123	31	.	.	PUNCT
ejpam-5901	124	1	s.	s.	PROPN
ejpam-5901	124	2	saber	saber	PROPN
ejpam-5901	124	3	,	,	PUNCT
ejpam-5901	124	4	a.	a.	NOUN
ejpam-5901	124	5	a.	a.	NOUN
ejpam-5901	124	6	alahmari	alahmari	PROPN
ejpam-5901	124	7	/	/	SYM
ejpam-5901	124	8	eur	eur	PROPN
ejpam-5901	124	9	.	.	PUNCT
ejpam-5901	125	1	j.	j.	PROPN
ejpam-5901	125	2	pure	pure	PROPN
ejpam-5901	125	3	appl	appl	PROPN
ejpam-5901	125	4	.	.	PROPN
ejpam-5901	125	5	math	math	PROPN
ejpam-5901	125	6	,	,	PUNCT
ejpam-5901	125	7	18	18	NUM
ejpam-5901	125	8	(	(	PUNCT
ejpam-5901	125	9	2	2	NUM
ejpam-5901	125	10	)	)	PUNCT
ejpam-5901	125	11	(	(	PUNCT
ejpam-5901	125	12	2025	2025	NUM
ejpam-5901	125	13	)	)	PUNCT
ejpam-5901	125	14	,	,	PUNCT
ejpam-5901	125	15	5901	5901	NUM
ejpam-5901	125	16	5	5	NUM
ejpam-5901	125	17	of	of	ADP
ejpam-5901	125	18	23	23	NUM
ejpam-5901	125	19	the	the	DET
ejpam-5901	125	20	corresponding	corresponding	ADJ
ejpam-5901	125	21	fractal	fractal	ADJ
ejpam-5901	125	22	-	-	PUNCT
ejpam-5901	125	23	fractional	fractional	ADJ
ejpam-5901	125	24	integral	integral	ADJ
ejpam-5901	125	25	is	be	AUX
ejpam-5901	125	26	:	:	PUNCT
ejpam-5901	125	27	definition	definition	NOUN
ejpam-5901	125	28	2	2	NUM
ejpam-5901	125	29	.	.	PUNCT
ejpam-5901	126	1	the	the	DET
ejpam-5901	126	2	fractal	fractal	ADJ
ejpam-5901	126	3	-	-	PUNCT
ejpam-5901	126	4	fractional	fractional	ADJ
ejpam-5901	126	5	integral	integral	ADJ
ejpam-5901	126	6	in	in	ADP
ejpam-5901	126	7	the	the	DET
ejpam-5901	126	8	atangana	atangana	PROPN
ejpam-5901	126	9	-	-	PUNCT
ejpam-5901	126	10	baleanu	baleanu	ADJ
ejpam-5901	126	11	framework	framework	NOUN
ejpam-5901	126	12	is	be	AUX
ejpam-5901	126	13	:	:	PUNCT
ejpam-5901	126	14	ffmiϱ1,ϱ20,t	ffmiϱ1,ϱ20,t	PROPN
ejpam-5901	126	15	[	[	X
ejpam-5901	126	16	g(t	g(t	PROPN
ejpam-5901	126	17	)	)	PUNCT
ejpam-5901	126	18	]	]	PUNCT
ejpam-5901	127	1	=	=	PUNCT
ejpam-5901	127	2	ϱ1ϱ2	ϱ1ϱ2	PROPN
ejpam-5901	127	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	127	4	)	)	PUNCT
ejpam-5901	127	5	∫	∫	PROPN
ejpam-5901	127	6	t	t	PROPN
ejpam-5901	127	7	0	0	NUM
ejpam-5901	127	8	ϵϱ2−1g(ϵ)(t−	ϵϱ2−1g(ϵ)(t−	NOUN
ejpam-5901	127	9	ϵ)ϱ1−1dϵ	ϵ)ϱ1−1dϵ	NUM
ejpam-5901	127	10	+	+	CCONJ
ejpam-5901	127	11	ϱ2(1−	ϱ2(1−	ADJ
ejpam-5901	127	12	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	127	13	ϱ2−1g(t	ϱ2−1g(t	PROPN
ejpam-5901	127	14	)	)	PUNCT
ejpam-5901	127	15	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	127	16	)	)	PUNCT
ejpam-5901	127	17	.	.	PUNCT
ejpam-5901	128	1	3	3	X
ejpam-5901	128	2	.	.	X
ejpam-5901	128	3	fractal	fractal	ADJ
ejpam-5901	128	4	-	-	PUNCT
ejpam-5901	128	5	fractional	fractional	ADJ
ejpam-5901	128	6	pneumonia	pneumonia	NOUN
ejpam-5901	128	7	model	model	NOUN
ejpam-5901	128	8	extension	extension	NOUN
ejpam-5901	128	9	the	the	DET
ejpam-5901	128	10	scir	scir	PROPN
ejpam-5901	128	11	model	model	NOUN
ejpam-5901	128	12	,	,	PUNCT
ejpam-5901	128	13	proposed	propose	VERB
ejpam-5901	128	14	by	by	ADP
ejpam-5901	128	15	kamaledin	kamaledin	VERB
ejpam-5901	128	16	abodayeh	abodayeh	PROPN
ejpam-5901	128	17	et	et	PROPN
ejpam-5901	128	18	al	al	PROPN
ejpam-5901	128	19	.	.	PUNCT
ejpam-5901	129	1	in	in	ADP
ejpam-5901	129	2	[	[	X
ejpam-5901	129	3	62	62	NUM
ejpam-5901	129	4	]	]	PUNCT
ejpam-5901	129	5	,	,	PUNCT
ejpam-5901	129	6	is	be	AUX
ejpam-5901	129	7	formulated	formulate	VERB
ejpam-5901	129	8	as	as	SCONJ
ejpam-5901	129	9	follows	follow	VERB
ejpam-5901	129	10	:	:	PUNCT
ejpam-5901	129	11	ds(t	ds(t	ADJ
ejpam-5901	129	12	)	)	PUNCT
ejpam-5901	129	13	dt	dt	NOUN
ejpam-5901	130	1	=	=	PUNCT
ejpam-5901	130	2	π−	π−	PROPN
ejpam-5901	130	3	λ	λ	PROPN
ejpam-5901	130	4	s(t)−	s(t)−	PROPN
ejpam-5901	130	5	µ	µ	X
ejpam-5901	130	6	s(t	s(t	PROPN
ejpam-5901	130	7	)	)	PUNCT
ejpam-5901	130	8	+	+	NUM
ejpam-5901	130	9	ηr(t	ηr(t	NOUN
ejpam-5901	130	10	)	)	PUNCT
ejpam-5901	130	11	,	,	PUNCT
ejpam-5901	130	12	dc(t	dc(t	NOUN
ejpam-5901	130	13	)	)	PUNCT
ejpam-5901	130	14	dt	dt	NOUN
ejpam-5901	131	1	=	=	PUNCT
ejpam-5901	131	2	λϑ	λϑ	PROPN
ejpam-5901	131	3	s(t)−	s(t)−	PROPN
ejpam-5901	131	4	(	(	PUNCT
ejpam-5901	131	5	π	π	PROPN
ejpam-5901	131	6	+	+	NUM
ejpam-5901	131	7	β	β	X
ejpam-5901	131	8	+	+	SYM
ejpam-5901	131	9	µ	µ	X
ejpam-5901	131	10	)	)	PUNCT
ejpam-5901	131	11	c(t	c(t	PROPN
ejpam-5901	131	12	)	)	PUNCT
ejpam-5901	131	13	,	,	PUNCT
ejpam-5901	131	14	d	d	X
ejpam-5901	131	15	i(t	i(t	PROPN
ejpam-5901	131	16	)	)	PUNCT
ejpam-5901	131	17	dt	dt	NOUN
ejpam-5901	132	1	=	=	SYM
ejpam-5901	132	2	λ(1−	λ(1−	PROPN
ejpam-5901	132	3	ϑ	ϑ	NOUN
ejpam-5901	132	4	)	)	PUNCT
ejpam-5901	132	5	s(t	s(t	PROPN
ejpam-5901	132	6	)	)	PUNCT
ejpam-5901	133	1	+	+	CCONJ
ejpam-5901	133	2	πc(t)−	πc(t)−	PROPN
ejpam-5901	133	3	(	(	PUNCT
ejpam-5901	133	4	µ+	µ+	X
ejpam-5901	133	5	τ	τ	PROPN
ejpam-5901	133	6	+	+	PROPN
ejpam-5901	133	7	σ	σ	PROPN
ejpam-5901	133	8	)	)	PUNCT
ejpam-5901	133	9	i(t	i(t	PROPN
ejpam-5901	133	10	)	)	PUNCT
ejpam-5901	133	11	,	,	PUNCT
ejpam-5901	133	12	dr(t	dr(t	PUNCT
ejpam-5901	133	13	)	)	PUNCT
ejpam-5901	133	14	dt	dt	NOUN
ejpam-5901	134	1	=	=	PUNCT
ejpam-5901	134	2	β	β	X
ejpam-5901	134	3	c(t	c(t	PROPN
ejpam-5901	134	4	)	)	PUNCT
ejpam-5901	135	1	+	+	CCONJ
ejpam-5901	135	2	τ	τ	PROPN
ejpam-5901	135	3	i(t)−	i(t)−	PROPN
ejpam-5901	135	4	(	(	PUNCT
ejpam-5901	135	5	µ+	µ+	VERB
ejpam-5901	135	6	η)r(t	η)r(t	NOUN
ejpam-5901	135	7	)	)	PUNCT
ejpam-5901	135	8	,	,	PUNCT
ejpam-5901	135	9	(	(	PUNCT
ejpam-5901	135	10	1	1	X
ejpam-5901	135	11	)	)	PUNCT
ejpam-5901	135	12	where	where	SCONJ
ejpam-5901	135	13	λ	λ	PROPN
ejpam-5901	135	14	=	=	SYM
ejpam-5901	135	15	δ(i(t)+ϖc(t	δ(i(t)+ϖc(t	PROPN
ejpam-5901	135	16	)	)	PUNCT
ejpam-5901	135	17	)	)	PUNCT
ejpam-5901	136	1	n	n	CCONJ
ejpam-5901	136	2	.	.	PUNCT
ejpam-5901	137	1	the	the	DET
ejpam-5901	137	2	initial	initial	ADJ
ejpam-5901	137	3	conditions	condition	NOUN
ejpam-5901	137	4	are	be	AUX
ejpam-5901	137	5	:	:	PUNCT
ejpam-5901	137	6	s(0	s(0	ADJ
ejpam-5901	137	7	)	)	PUNCT
ejpam-5901	137	8	=	=	PROPN
ejpam-5901	137	9	s0	s0	PROPN
ejpam-5901	137	10	≥	≥	NUM
ejpam-5901	137	11	0	0	NUM
ejpam-5901	137	12	,	,	PUNCT
ejpam-5901	137	13	c(0	c(0	NOUN
ejpam-5901	137	14	)	)	PUNCT
ejpam-5901	138	1	=	=	SYM
ejpam-5901	138	2	c0	c0	X
ejpam-5901	138	3	≥	≥	NUM
ejpam-5901	138	4	0	0	NUM
ejpam-5901	138	5	,	,	PUNCT
ejpam-5901	138	6	i(0	i(0	PROPN
ejpam-5901	138	7	)	)	PUNCT
ejpam-5901	138	8	=	=	SYM
ejpam-5901	138	9	i0	i0	PROPN
ejpam-5901	138	10	≥	≥	NUM
ejpam-5901	138	11	0	0	NUM
ejpam-5901	138	12	,	,	PUNCT
ejpam-5901	138	13	r(0	r(0	PROPN
ejpam-5901	138	14	)	)	PUNCT
ejpam-5901	138	15	=	=	PUNCT
ejpam-5901	138	16	r0	r0	NOUN
ejpam-5901	138	17	≥	≥	NOUN
ejpam-5901	138	18	0	0	NUM
ejpam-5901	138	19	.	.	PUNCT
ejpam-5901	139	1	in	in	ADP
ejpam-5901	139	2	this	this	DET
ejpam-5901	139	3	model	model	NOUN
ejpam-5901	139	4	,	,	PUNCT
ejpam-5901	139	5	s(t	s(t	PROPN
ejpam-5901	139	6	)	)	PUNCT
ejpam-5901	139	7	represents	represent	VERB
ejpam-5901	139	8	the	the	DET
ejpam-5901	139	9	susceptible	susceptible	ADJ
ejpam-5901	139	10	population	population	NOUN
ejpam-5901	139	11	at	at	ADP
ejpam-5901	139	12	risk	risk	NOUN
ejpam-5901	139	13	of	of	ADP
ejpam-5901	139	14	acquiring	acquire	VERB
ejpam-5901	139	15	pneumonia	pneumonia	NOUN
ejpam-5901	139	16	,	,	PUNCT
ejpam-5901	139	17	c(t	c(t	PROPN
ejpam-5901	139	18	)	)	PUNCT
ejpam-5901	139	19	denotes	denote	NOUN
ejpam-5901	139	20	carriers	carrier	NOUN
ejpam-5901	139	21	who	who	PRON
ejpam-5901	139	22	may	may	AUX
ejpam-5901	139	23	transmit	transmit	VERB
ejpam-5901	139	24	the	the	DET
ejpam-5901	139	25	disease	disease	NOUN
ejpam-5901	139	26	,	,	PUNCT
ejpam-5901	139	27	i(t	i(t	PROPN
ejpam-5901	139	28	)	)	PUNCT
ejpam-5901	139	29	represents	represent	VERB
ejpam-5901	139	30	infected	infected	ADJ
ejpam-5901	139	31	individuals	individual	NOUN
ejpam-5901	139	32	,	,	PUNCT
ejpam-5901	139	33	and	and	CCONJ
ejpam-5901	139	34	r(t	r(t	NOUN
ejpam-5901	139	35	)	)	PUNCT
ejpam-5901	139	36	denotes	denote	NOUN
ejpam-5901	139	37	recovered	recover	VERB
ejpam-5901	139	38	individuals	individual	NOUN
ejpam-5901	139	39	.	.	PUNCT
ejpam-5901	140	1	key	key	ADJ
ejpam-5901	140	2	parameters	parameter	NOUN
ejpam-5901	140	3	are	be	AUX
ejpam-5901	140	4	defined	define	VERB
ejpam-5901	140	5	as	as	SCONJ
ejpam-5901	140	6	follows	follow	VERB
ejpam-5901	140	7	:	:	PUNCT
ejpam-5901	140	8	µ	µ	NUM
ejpam-5901	140	9	:	:	PUNCT
ejpam-5901	140	10	natural	natural	ADJ
ejpam-5901	140	11	mortality	mortality	NOUN
ejpam-5901	140	12	rate	rate	NOUN
ejpam-5901	140	13	,	,	PUNCT
ejpam-5901	140	14	π	π	NOUN
ejpam-5901	140	15	:	:	PUNCT
ejpam-5901	140	16	recruitment	recruitment	NOUN
ejpam-5901	140	17	rate	rate	NOUN
ejpam-5901	140	18	to	to	ADP
ejpam-5901	140	19	the	the	DET
ejpam-5901	140	20	susceptible	susceptible	ADJ
ejpam-5901	140	21	population	population	NOUN
ejpam-5901	140	22	,	,	PUNCT
ejpam-5901	140	23	π	π	PROPN
ejpam-5901	140	24	:	:	PUNCT
ejpam-5901	140	25	recruitment	recruitment	NOUN
ejpam-5901	140	26	rate	rate	NOUN
ejpam-5901	140	27	into	into	ADP
ejpam-5901	140	28	the	the	DET
ejpam-5901	140	29	carrier	carrier	NOUN
ejpam-5901	140	30	population	population	NOUN
ejpam-5901	140	31	,	,	PUNCT
ejpam-5901	140	32	ϑ	ϑ	NOUN
ejpam-5901	140	33	:	:	PUNCT
ejpam-5901	140	34	proportion	proportion	NOUN
ejpam-5901	140	35	of	of	ADP
ejpam-5901	140	36	susceptibles	susceptible	NOUN
ejpam-5901	140	37	joining	join	VERB
ejpam-5901	140	38	the	the	DET
ejpam-5901	140	39	carrier	carrier	NOUN
ejpam-5901	140	40	population	population	NOUN
ejpam-5901	140	41	,	,	PUNCT
ejpam-5901	140	42	σ	σ	PROPN
ejpam-5901	140	43	:	:	PUNCT
ejpam-5901	140	44	disease	disease	NOUN
ejpam-5901	140	45	-	-	PUNCT
ejpam-5901	140	46	induced	induce	VERB
ejpam-5901	140	47	mortality	mortality	NOUN
ejpam-5901	140	48	rate	rate	NOUN
ejpam-5901	140	49	,	,	PUNCT
ejpam-5901	140	50	β	β	NOUN
ejpam-5901	140	51	:	:	PUNCT
ejpam-5901	140	52	recovery	recovery	NOUN
ejpam-5901	140	53	rate	rate	NOUN
ejpam-5901	140	54	of	of	ADP
ejpam-5901	140	55	carriers	carrier	NOUN
ejpam-5901	140	56	,	,	PUNCT
ejpam-5901	140	57	τ	τ	PROPN
ejpam-5901	140	58	:	:	PUNCT
ejpam-5901	140	59	recovery	recovery	NOUN
ejpam-5901	140	60	rate	rate	NOUN
ejpam-5901	140	61	of	of	ADP
ejpam-5901	140	62	infected	infected	ADJ
ejpam-5901	140	63	individuals	individual	NOUN
ejpam-5901	140	64	,	,	PUNCT
ejpam-5901	140	65	η	η	NOUN
ejpam-5901	140	66	:	:	PUNCT
ejpam-5901	140	67	rate	rate	NOUN
ejpam-5901	140	68	of	of	ADP
ejpam-5901	140	69	treated	treat	VERB
ejpam-5901	140	70	individuals	individual	NOUN
ejpam-5901	140	71	becoming	become	VERB
ejpam-5901	140	72	susceptible	susceptible	ADJ
ejpam-5901	140	73	again	again	ADV
ejpam-5901	140	74	,	,	PUNCT
ejpam-5901	140	75	ϖ	ϖ	NOUN
ejpam-5901	140	76	:	:	PUNCT
ejpam-5901	140	77	rate	rate	NOUN
ejpam-5901	140	78	of	of	ADP
ejpam-5901	140	79	treated	treat	VERB
ejpam-5901	140	80	individuals	individual	NOUN
ejpam-5901	140	81	becoming	becoming	AUX
ejpam-5901	140	82	vaccinated	vaccinate	VERB
ejpam-5901	140	83	,	,	PUNCT
ejpam-5901	140	84	-the	-the	DET
ejpam-5901	140	85	transmission	transmission	NOUN
ejpam-5901	140	86	coefficient	coefficient	NOUN
ejpam-5901	140	87	λ	λ	NOUN
ejpam-5901	140	88	represents	represent	VERB
ejpam-5901	140	89	the	the	DET
ejpam-5901	140	90	infection	infection	NOUN
ejpam-5901	140	91	force	force	NOUN
ejpam-5901	140	92	,	,	PUNCT
ejpam-5901	140	93	and	and	CCONJ
ejpam-5901	140	94	p	p	NOUN
ejpam-5901	140	95	is	be	AUX
ejpam-5901	140	96	the	the	DET
ejpam-5901	140	97	probability	probability	NOUN
ejpam-5901	140	98	that	that	SCONJ
ejpam-5901	140	99	contact	contact	NOUN
ejpam-5901	140	100	results	result	VERB
ejpam-5901	140	101	in	in	ADP
ejpam-5901	140	102	infection	infection	NOUN
ejpam-5901	140	103	.	.	PUNCT
ejpam-5901	141	1	applying	apply	VERB
ejpam-5901	141	2	the	the	DET
ejpam-5901	141	3	atangana	atangana	PROPN
ejpam-5901	141	4	-	-	PUNCT
ejpam-5901	141	5	baleanu	baleanu	ADJ
ejpam-5901	141	6	operator	operator	NOUN
ejpam-5901	141	7	to	to	ADP
ejpam-5901	141	8	the	the	DET
ejpam-5901	141	9	scir	scir	PROPN
ejpam-5901	141	10	model	model	NOUN
ejpam-5901	141	11	yields	yield	NOUN
ejpam-5901	141	12	:	:	PUNCT
ejpam-5901	141	13	ff−abdϱ1,ϱ2	ff−abdϱ1,ϱ2	PROPN
ejpam-5901	141	14	t	t	PROPN
ejpam-5901	141	15	s(t	s(t	PROPN
ejpam-5901	141	16	)	)	PUNCT
ejpam-5901	142	1	=	=	PUNCT
ejpam-5901	142	2	π−	π−	PROPN
ejpam-5901	142	3	λ	λ	PROPN
ejpam-5901	142	4	s(t)−	s(t)−	PROPN
ejpam-5901	142	5	µs(t	µs(t	PUNCT
ejpam-5901	142	6	)	)	PUNCT
ejpam-5901	143	1	+	+	NUM
ejpam-5901	143	2	ηr(t	ηr(t	NOUN
ejpam-5901	143	3	)	)	PUNCT
ejpam-5901	143	4	,	,	PUNCT
ejpam-5901	143	5	ff−abdϱ1,ϱ2	ff−abdϱ1,ϱ2	PROPN
ejpam-5901	143	6	t	t	PROPN
ejpam-5901	143	7	c(t	c(t	PROPN
ejpam-5901	143	8	)	)	PUNCT
ejpam-5901	143	9	=	=	PRON
ejpam-5901	144	1	λϑ	λϑ	DET
ejpam-5901	144	2	s(t)−	s(t)−	PROPN
ejpam-5901	144	3	(	(	PUNCT
ejpam-5901	144	4	π	π	PROPN
ejpam-5901	144	5	+	+	NUM
ejpam-5901	144	6	β	β	X
ejpam-5901	144	7	+	+	SYM
ejpam-5901	144	8	µ	µ	X
ejpam-5901	144	9	)	)	PUNCT
ejpam-5901	144	10	c(t	c(t	PROPN
ejpam-5901	144	11	)	)	PUNCT
ejpam-5901	144	12	,	,	PUNCT
ejpam-5901	144	13	ff−abdϱ1,ϱ2	ff−abdϱ1,ϱ2	PROPN
ejpam-5901	144	14	t	t	PROPN
ejpam-5901	144	15	i(t	i(t	PROPN
ejpam-5901	144	16	)	)	PUNCT
ejpam-5901	145	1	=	=	PUNCT
ejpam-5901	145	2	λ(1−	λ(1−	PROPN
ejpam-5901	145	3	ϑ	ϑ	NOUN
ejpam-5901	145	4	)	)	PUNCT
ejpam-5901	145	5	s(t	s(t	PROPN
ejpam-5901	145	6	)	)	PUNCT
ejpam-5901	146	1	+	+	CCONJ
ejpam-5901	146	2	πc(t)−	πc(t)−	PROPN
ejpam-5901	146	3	(	(	PUNCT
ejpam-5901	146	4	µ+	µ+	X
ejpam-5901	146	5	τ	τ	PROPN
ejpam-5901	146	6	+	+	PROPN
ejpam-5901	146	7	σ	σ	PROPN
ejpam-5901	146	8	)	)	PUNCT
ejpam-5901	146	9	i(t	i(t	PROPN
ejpam-5901	146	10	)	)	PUNCT
ejpam-5901	146	11	,	,	PUNCT
ejpam-5901	146	12	ff−abdϱ1,ϱ2	ff−abdϱ1,ϱ2	PROPN
ejpam-5901	146	13	t	t	PROPN
ejpam-5901	146	14	r(t	r(t	NOUN
ejpam-5901	146	15	)	)	PUNCT
ejpam-5901	147	1	=	=	SYM
ejpam-5901	147	2	β	β	X
ejpam-5901	147	3	c(t	c(t	PROPN
ejpam-5901	147	4	)	)	PUNCT
ejpam-5901	148	1	+	+	CCONJ
ejpam-5901	148	2	τ	τ	PROPN
ejpam-5901	148	3	i(t)−	i(t)−	PROPN
ejpam-5901	148	4	(	(	PUNCT
ejpam-5901	148	5	µ+	µ+	NOUN
ejpam-5901	148	6	η)r(t	η)r(t	NOUN
ejpam-5901	148	7	)	)	PUNCT
ejpam-5901	148	8	.	.	PUNCT
ejpam-5901	149	1	(	(	PUNCT
ejpam-5901	149	2	2	2	X
ejpam-5901	149	3	)	)	PUNCT
ejpam-5901	149	4	s.	s.	PROPN
ejpam-5901	149	5	saber	saber	PROPN
ejpam-5901	149	6	,	,	PUNCT
ejpam-5901	149	7	a.	a.	NOUN
ejpam-5901	149	8	a.	a.	NOUN
ejpam-5901	149	9	alahmari	alahmari	PROPN
ejpam-5901	149	10	/	/	SYM
ejpam-5901	149	11	eur	eur	PROPN
ejpam-5901	149	12	.	.	PUNCT
ejpam-5901	150	1	j.	j.	PROPN
ejpam-5901	150	2	pure	pure	PROPN
ejpam-5901	150	3	appl	appl	PROPN
ejpam-5901	150	4	.	.	PROPN
ejpam-5901	150	5	math	math	PROPN
ejpam-5901	150	6	,	,	PUNCT
ejpam-5901	150	7	18	18	NUM
ejpam-5901	150	8	(	(	PUNCT
ejpam-5901	150	9	2	2	NUM
ejpam-5901	150	10	)	)	PUNCT
ejpam-5901	150	11	(	(	PUNCT
ejpam-5901	150	12	2025	2025	NUM
ejpam-5901	150	13	)	)	PUNCT
ejpam-5901	150	14	,	,	PUNCT
ejpam-5901	150	15	5901	5901	NUM
ejpam-5901	150	16	6	6	NUM
ejpam-5901	150	17	of	of	ADP
ejpam-5901	150	18	23	23	NUM
ejpam-5901	150	19	the	the	DET
ejpam-5901	150	20	system	system	NOUN
ejpam-5901	150	21	can	can	AUX
ejpam-5901	150	22	be	be	AUX
ejpam-5901	150	23	expressed	express	VERB
ejpam-5901	150	24	in	in	ADP
ejpam-5901	150	25	vector	vector	NOUN
ejpam-5901	150	26	form	form	NOUN
ejpam-5901	150	27	as	as	ADP
ejpam-5901	150	28	:	:	PUNCT
ejpam-5901	150	29	ff−abdϱ1,ϱ2	ff−abdϱ1,ϱ2	NUM
ejpam-5901	150	30	0,t	0,t	PROPN
ejpam-5901	150	31	ψ(t	ψ(t	PROPN
ejpam-5901	150	32	)	)	PUNCT
ejpam-5901	150	33	=	=	SYM
ejpam-5901	150	34	ϱ2	ϱ2	PROPN
ejpam-5901	150	35	t	t	PROPN
ejpam-5901	150	36	ϱ2−1w	ϱ2−1w	NOUN
ejpam-5901	150	37	(	(	PUNCT
ejpam-5901	150	38	t	t	PROPN
ejpam-5901	150	39	,	,	PUNCT
ejpam-5901	150	40	ψ(t	ψ(t	PROPN
ejpam-5901	150	41	)	)	PUNCT
ejpam-5901	150	42	)	)	PUNCT
ejpam-5901	151	1	=	=	SYM
ejpam-5901	151	2	ξ(t	ξ(t	NOUN
ejpam-5901	151	3	,	,	PUNCT
ejpam-5901	151	4	ψ(t	ψ(t	PROPN
ejpam-5901	151	5	)	)	PUNCT
ejpam-5901	151	6	)	)	PUNCT
ejpam-5901	151	7	,	,	PUNCT
ejpam-5901	151	8	where	where	SCONJ
ejpam-5901	151	9	ψ(t	ψ(t	VERB
ejpam-5901	151	10	)	)	PUNCT
ejpam-5901	151	11	=	=	SYM
ejpam-5901	151	12	(	(	PUNCT
ejpam-5901	151	13	s(t),c(t	s(t),c(t	NOUN
ejpam-5901	151	14	)	)	PUNCT
ejpam-5901	151	15	,	,	PUNCT
ejpam-5901	151	16	i(t),r(t	i(t),r(t	PROPN
ejpam-5901	151	17	)	)	PUNCT
ejpam-5901	151	18	)	)	PUNCT
ejpam-5901	151	19	,	,	PUNCT
ejpam-5901	151	20	and	and	CCONJ
ejpam-5901	151	21	ψ(0	ψ(0	PROPN
ejpam-5901	151	22	)	)	PUNCT
ejpam-5901	151	23	=	=	SYM
ejpam-5901	151	24	(	(	PUNCT
ejpam-5901	151	25	s(0),c(0	s(0),c(0	NOUN
ejpam-5901	151	26	)	)	PUNCT
ejpam-5901	151	27	,	,	PUNCT
ejpam-5901	151	28	i(0),r(0	i(0),r(0	PROPN
ejpam-5901	151	29	)	)	PUNCT
ejpam-5901	151	30	)	)	PUNCT
ejpam-5901	151	31	,	,	PUNCT
ejpam-5901	151	32	andw	andw	NOUN
ejpam-5901	151	33	(	(	PUNCT
ejpam-5901	151	34	t	t	PROPN
ejpam-5901	151	35	,	,	PUNCT
ejpam-5901	151	36	ψ(t	ψ(t	PROPN
ejpam-5901	151	37	)	)	PUNCT
ejpam-5901	151	38	)	)	PUNCT
ejpam-5901	151	39	=	=	SYM
ejpam-5901	151	40	(	(	PUNCT
ejpam-5901	151	41	w1(t	w1(t	PROPN
ejpam-5901	151	42	,	,	PUNCT
ejpam-5901	151	43	ψ(t)),w2(t	ψ(t)),w2(t	NOUN
ejpam-5901	151	44	,	,	PUNCT
ejpam-5901	151	45	ψ(t)),w3(t	ψ(t)),w3(t	PROPN
ejpam-5901	151	46	,	,	PUNCT
ejpam-5901	151	47	ψ(t)),w4(t	ψ(t)),w4(t	NOUN
ejpam-5901	151	48	,	,	PUNCT
ejpam-5901	151	49	ψ(t	ψ(t	PROPN
ejpam-5901	151	50	)	)	PUNCT
ejpam-5901	151	51	)	)	PUNCT
ejpam-5901	151	52	)	)	PUNCT
ejpam-5901	151	53	,	,	PUNCT
ejpam-5901	151	54	with	with	ADP
ejpam-5901	151	55	w1(t	w1(t	PROPN
ejpam-5901	151	56	,	,	PUNCT
ejpam-5901	151	57	s	s	PART
ejpam-5901	151	58	)	)	PUNCT
ejpam-5901	151	59	=	=	SYM
ejpam-5901	151	60	π−	π−	PROPN
ejpam-5901	151	61	λ	λ	PROPN
ejpam-5901	151	62	s−µ	s−µ	NOUN
ejpam-5901	151	63	s+ηr	s+ηr	PROPN
ejpam-5901	151	64	,	,	PUNCT
ejpam-5901	151	65	w2(t	w2(t	PROPN
ejpam-5901	151	66	,	,	PUNCT
ejpam-5901	151	67	c	c	NOUN
ejpam-5901	151	68	)	)	PUNCT
ejpam-5901	151	69	=	=	SYM
ejpam-5901	152	1	λϑ	λϑ	DET
ejpam-5901	152	2	s−(π	s−(π	PROPN
ejpam-5901	152	3	+	+	NUM
ejpam-5901	152	4	β	β	X
ejpam-5901	152	5	+	+	X
ejpam-5901	152	6	µ	µ	X
ejpam-5901	152	7	)	)	PUNCT
ejpam-5901	152	8	c	c	NOUN
ejpam-5901	152	9	,	,	PUNCT
ejpam-5901	152	10	w3(t	w3(t	PROPN
ejpam-5901	152	11	,	,	PUNCT
ejpam-5901	152	12	i	i	NOUN
ejpam-5901	152	13	)	)	PUNCT
ejpam-5901	153	1	=	=	PUNCT
ejpam-5901	153	2	λ(1−	λ(1−	PROPN
ejpam-5901	153	3	ϑ	ϑ	NOUN
ejpam-5901	153	4	)	)	PUNCT
ejpam-5901	153	5	s+πc−(µ+	s+πc−(µ+	PROPN
ejpam-5901	153	6	τ	τ	PROPN
ejpam-5901	153	7	+	+	PROPN
ejpam-5901	153	8	σ	σ	PROPN
ejpam-5901	153	9	)	)	PUNCT
ejpam-5901	153	10	i	i	PROPN
ejpam-5901	153	11	,	,	PUNCT
ejpam-5901	153	12	w4(t	w4(t	PROPN
ejpam-5901	153	13	,	,	PUNCT
ejpam-5901	153	14	r	r	NOUN
ejpam-5901	153	15	)	)	PUNCT
ejpam-5901	153	16	=	=	NOUN
ejpam-5901	153	17	β	β	NOUN
ejpam-5901	153	18	c+τ	c+τ	NUM
ejpam-5901	153	19	i−(µ+	i−(µ+	PROPN
ejpam-5901	153	20	η)r	η)r	NOUN
ejpam-5901	153	21	.	.	PUNCT
ejpam-5901	154	1	(	(	PUNCT
ejpam-5901	154	2	3	3	X
ejpam-5901	154	3	)	)	PUNCT
ejpam-5901	154	4	4	4	NUM
ejpam-5901	154	5	.	.	PUNCT
ejpam-5901	155	1	existence	existence	NOUN
ejpam-5901	155	2	of	of	ADP
ejpam-5901	155	3	the	the	DET
ejpam-5901	155	4	model	model	NOUN
ejpam-5901	155	5	solutions	solution	NOUN
ejpam-5901	155	6	by	by	ADP
ejpam-5901	155	7	r+	r+	NOUN
ejpam-5901	155	8	,	,	PUNCT
ejpam-5901	155	9	we	we	PRON
ejpam-5901	155	10	refer	refer	VERB
ejpam-5901	155	11	to	to	ADP
ejpam-5901	155	12	the	the	DET
ejpam-5901	155	13	set	set	NOUN
ejpam-5901	155	14	of	of	ADP
ejpam-5901	155	15	all	all	DET
ejpam-5901	155	16	positive	positive	ADJ
ejpam-5901	155	17	real	real	ADJ
ejpam-5901	155	18	numbers	number	NOUN
ejpam-5901	155	19	,	,	PUNCT
ejpam-5901	155	20	ω	ω	PROPN
ejpam-5901	155	21	=	=	SYM
ejpam-5901	155	22	{	{	PUNCT
ejpam-5901	155	23	(	(	PUNCT
ejpam-5901	155	24	s	s	X
ejpam-5901	155	25	,	,	PUNCT
ejpam-5901	155	26	c	c	X
ejpam-5901	155	27	,	,	PUNCT
ejpam-5901	155	28	i	i	PRON
ejpam-5901	155	29	,	,	PUNCT
ejpam-5901	155	30	r	r	NOUN
ejpam-5901	155	31	)	)	PUNCT
ejpam-5901	155	32	∈	∈	NOUN
ejpam-5901	155	33	r4	r4	NOUN
ejpam-5901	155	34	+	+	CCONJ
ejpam-5901	155	35	:	:	PUNCT
ejpam-5901	155	36	s	s	X
ejpam-5901	155	37	≥	≥	NOUN
ejpam-5901	155	38	0	0	NUM
ejpam-5901	155	39	,	,	PUNCT
ejpam-5901	155	40	c	c	X
ejpam-5901	155	41	≥	≥	NUM
ejpam-5901	155	42	0	0	NUM
ejpam-5901	155	43	,	,	PUNCT
ejpam-5901	155	44	i	i	PRON
ejpam-5901	155	45	≥	≥	VERB
ejpam-5901	155	46	0	0	NUM
ejpam-5901	155	47	,	,	PUNCT
ejpam-5901	155	48	r	r	NOUN
ejpam-5901	155	49	≥	≥	NOUN
ejpam-5901	155	50	0	0	NUM
ejpam-5901	155	51	,	,	PUNCT
ejpam-5901	155	52	max	max	PROPN
ejpam-5901	155	53	(	(	PUNCT
ejpam-5901	155	54	|	|	NOUN
ejpam-5901	155	55	s	s	VERB
ejpam-5901	155	56	|	|	NOUN
ejpam-5901	155	57	,	,	PUNCT
ejpam-5901	155	58	|c	|c	ADJ
ejpam-5901	155	59	|	|	NOUN
ejpam-5901	155	60	,	,	PUNCT
ejpam-5901	156	1	|	|	ADV
ejpam-5901	156	2	i	i	PRON
ejpam-5901	156	3	|	|	ADV
ejpam-5901	156	4	,	,	PUNCT
ejpam-5901	156	5	|r|	|r|	NOUN
ejpam-5901	156	6	)	)	PUNCT
ejpam-5901	156	7	≤	≤	NOUN
ejpam-5901	156	8	n	n	CCONJ
ejpam-5901	156	9	}	}	PUNCT
ejpam-5901	156	10	.	.	PUNCT
ejpam-5901	157	1	when	when	SCONJ
ejpam-5901	157	2	the	the	DET
ejpam-5901	157	3	fixed	fix	VERB
ejpam-5901	157	4	point	point	NOUN
ejpam-5901	157	5	theory	theory	NOUN
ejpam-5901	157	6	is	be	AUX
ejpam-5901	157	7	applied	apply	VERB
ejpam-5901	157	8	and	and	CCONJ
ejpam-5901	157	9	the	the	DET
ejpam-5901	157	10	fractal	fractal	ADJ
ejpam-5901	157	11	-	-	PUNCT
ejpam-5901	157	12	fractional	fractional	ADJ
ejpam-5901	157	13	integral	integral	ADJ
ejpam-5901	157	14	operator	operator	NOUN
ejpam-5901	157	15	is	be	AUX
ejpam-5901	157	16	utilized	utilize	VERB
ejpam-5901	157	17	,	,	PUNCT
ejpam-5901	157	18	the	the	DET
ejpam-5901	157	19	constructed	constructed	ADJ
ejpam-5901	157	20	model	model	NOUN
ejpam-5901	157	21	(	(	PUNCT
ejpam-5901	157	22	2	2	NUM
ejpam-5901	157	23	)	)	PUNCT
ejpam-5901	157	24	can	can	AUX
ejpam-5901	157	25	be	be	AUX
ejpam-5901	157	26	converted	convert	VERB
ejpam-5901	157	27	into	into	ADP
ejpam-5901	157	28	an	an	DET
ejpam-5901	157	29	integral	integral	ADJ
ejpam-5901	157	30	equation	equation	NOUN
ejpam-5901	157	31	.	.	PUNCT
ejpam-5901	158	1	s(t)−	s(t)−	PROPN
ejpam-5901	158	2	s(0	s(0	PROPN
ejpam-5901	158	3	)	)	PUNCT
ejpam-5901	158	4	=	=	PUNCT
ejpam-5901	158	5	ϱ2(1−	ϱ2(1−	PROPN
ejpam-5901	158	6	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	158	7	ϱ2−1	ϱ2−1	ADP
ejpam-5901	158	8	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	158	9	)	)	PUNCT
ejpam-5901	159	1	(	(	PUNCT
ejpam-5901	159	2	π−	π−	PROPN
ejpam-5901	159	3	λ	λ	X
ejpam-5901	159	4	s−µs+ηr	s−µs+ηr	NOUN
ejpam-5901	159	5	)	)	PUNCT
ejpam-5901	159	6	+	+	CCONJ
ejpam-5901	159	7	ϱ1ϱ2	ϱ1ϱ2	PROPN
ejpam-5901	159	8	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	159	9	)	)	PUNCT
ejpam-5901	159	10	∫	∫	PROPN
ejpam-5901	160	1	t	t	PROPN
ejpam-5901	160	2	0	0	NUM
ejpam-5901	161	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	161	2	ϵ)ϱ1−1(π−	ϵ)ϱ1−1(π−	NOUN
ejpam-5901	161	3	λ	λ	NOUN
ejpam-5901	161	4	s−µ	s−µ	NOUN
ejpam-5901	161	5	s+ηr)dϵ	s+ηr)dϵ	NOUN
ejpam-5901	161	6	,	,	PUNCT
ejpam-5901	161	7	c(t)−	c(t)−	PROPN
ejpam-5901	161	8	c(0	c(0	PROPN
ejpam-5901	161	9	)	)	PUNCT
ejpam-5901	161	10	=	=	PUNCT
ejpam-5901	162	1	ϱ2(1−	ϱ2(1−	PROPN
ejpam-5901	162	2	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	162	3	ϱ2−1	ϱ2−1	ADP
ejpam-5901	162	4	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	162	5	)	)	PUNCT
ejpam-5901	162	6	(	(	PUNCT
ejpam-5901	162	7	λϑ	λϑ	PRON
ejpam-5901	162	8	s−(π	s−(π	PROPN
ejpam-5901	162	9	+	+	NUM
ejpam-5901	162	10	β	β	X
ejpam-5901	162	11	+	+	X
ejpam-5901	162	12	µ	µ	X
ejpam-5901	162	13	)	)	PUNCT
ejpam-5901	162	14	c	c	NOUN
ejpam-5901	162	15	)	)	PUNCT
ejpam-5901	163	1	+	+	CCONJ
ejpam-5901	163	2	ϱ1ϱ2	ϱ1ϱ2	PROPN
ejpam-5901	163	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	163	4	)	)	PUNCT
ejpam-5901	163	5	∫	∫	PROPN
ejpam-5901	164	1	t	t	PROPN
ejpam-5901	164	2	0	0	NUM
ejpam-5901	165	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	165	2	ϵ)ϱ1−1(λϑs−(π	ϵ)ϱ1−1(λϑs−(π	PROPN
ejpam-5901	166	1	+	+	NUM
ejpam-5901	166	2	β	β	X
ejpam-5901	166	3	+	+	ADJ
ejpam-5901	166	4	µ	µ	X
ejpam-5901	166	5	)	)	PUNCT
ejpam-5901	166	6	c)dϵ	c)dϵ	PROPN
ejpam-5901	166	7	,	,	PUNCT
ejpam-5901	166	8	i(t)−	i(t)−	PROPN
ejpam-5901	166	9	i(0	i(0	PROPN
ejpam-5901	166	10	)	)	PUNCT
ejpam-5901	166	11	=	=	PUNCT
ejpam-5901	166	12	ϱ2(1−	ϱ2(1−	PROPN
ejpam-5901	166	13	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	166	14	ϱ2−1	ϱ2−1	ADP
ejpam-5901	166	15	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	166	16	)	)	PUNCT
ejpam-5901	166	17	(	(	PUNCT
ejpam-5901	166	18	λ(1−	λ(1−	PROPN
ejpam-5901	166	19	ϑ	ϑ	NOUN
ejpam-5901	166	20	)	)	PUNCT
ejpam-5901	166	21	s+πc−(µ+	s+πc−(µ+	NOUN
ejpam-5901	166	22	τ	τ	PROPN
ejpam-5901	166	23	+	+	PROPN
ejpam-5901	166	24	σ	σ	PROPN
ejpam-5901	166	25	)	)	PUNCT
ejpam-5901	166	26	i	i	PROPN
ejpam-5901	166	27	)	)	PUNCT
ejpam-5901	167	1	+	+	CCONJ
ejpam-5901	167	2	ϱ1ϱ2	ϱ1ϱ2	PROPN
ejpam-5901	167	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	167	4	)	)	PUNCT
ejpam-5901	167	5	∫	∫	PROPN
ejpam-5901	168	1	t	t	PROPN
ejpam-5901	168	2	0	0	NUM
ejpam-5901	169	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	169	2	ϵ)ϱ1−1(λ(1−	ϵ)ϱ1−1(λ(1−	PROPN
ejpam-5901	169	3	ϑ	ϑ	PROPN
ejpam-5901	169	4	)	)	PUNCT
ejpam-5901	169	5	s+πc−(µ+	s+πc−(µ+	PROPN
ejpam-5901	169	6	τ	τ	PROPN
ejpam-5901	169	7	+	+	PROPN
ejpam-5901	169	8	σ	σ	PROPN
ejpam-5901	169	9	)	)	PUNCT
ejpam-5901	169	10	i)dϵ	i)dϵ	PROPN
ejpam-5901	169	11	,	,	PUNCT
ejpam-5901	169	12	r(t)−	r(t)−	PROPN
ejpam-5901	169	13	r(0	r(0	PROPN
ejpam-5901	169	14	)	)	PUNCT
ejpam-5901	169	15	=	=	PUNCT
ejpam-5901	169	16	ϱ2(1−	ϱ2(1−	PROPN
ejpam-5901	169	17	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	169	18	ϱ2−1	ϱ2−1	ADP
ejpam-5901	169	19	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	169	20	)	)	PUNCT
ejpam-5901	169	21	(	(	PUNCT
ejpam-5901	169	22	β	β	X
ejpam-5901	169	23	c+τ	c+τ	PROPN
ejpam-5901	169	24	i−(µ+	i−(µ+	NOUN
ejpam-5901	169	25	η)r	η)r	NOUN
ejpam-5901	169	26	)	)	PUNCT
ejpam-5901	170	1	+	+	CCONJ
ejpam-5901	170	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	170	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	170	4	)	)	PUNCT
ejpam-5901	170	5	∫	∫	PROPN
ejpam-5901	170	6	t	t	PROPN
ejpam-5901	170	7	0	0	NUM
ejpam-5901	171	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	171	2	ϵ)ϱ1−1(β	ϵ)ϱ1−1(β	PROPN
ejpam-5901	171	3	c+τ	c+τ	PROPN
ejpam-5901	171	4	i−(µ+	i−(µ+	NOUN
ejpam-5901	171	5	η)r)dϵ.	η)r)dϵ.	NOUN
ejpam-5901	171	6	to	to	PART
ejpam-5901	171	7	be	be	AUX
ejpam-5901	171	8	able	able	ADJ
ejpam-5901	171	9	to	to	PART
ejpam-5901	171	10	derive	derive	VERB
ejpam-5901	171	11	our	our	PRON
ejpam-5901	171	12	results	result	NOUN
ejpam-5901	171	13	,	,	PUNCT
ejpam-5901	171	14	we	we	PRON
ejpam-5901	171	15	need	need	VERB
ejpam-5901	171	16	to	to	PART
ejpam-5901	171	17	take	take	VERB
ejpam-5901	171	18	into	into	ADP
ejpam-5901	171	19	consideration	consideration	NOUN
ejpam-5901	171	20	the	the	DET
ejpam-5901	171	21	following	follow	VERB
ejpam-5901	171	22	assumptions	assumption	NOUN
ejpam-5901	171	23	:	:	PUNCT
ejpam-5901	171	24	(	(	PUNCT
ejpam-5901	171	25	q∗	q∗	NOUN
ejpam-5901	171	26	):	):	PUNCT
ejpam-5901	171	27	let	let	AUX
ejpam-5901	171	28	assume	assume	VERB
ejpam-5901	171	29	that	that	SCONJ
ejpam-5901	171	30	s(t),c(t	s(t),c(t	PROPN
ejpam-5901	171	31	)	)	PUNCT
ejpam-5901	171	32	,	,	PUNCT
ejpam-5901	171	33	i(t	i(t	PROPN
ejpam-5901	171	34	)	)	PUNCT
ejpam-5901	171	35	and	and	CCONJ
ejpam-5901	171	36	r(t	r(t	NOUN
ejpam-5901	171	37	)	)	PUNCT
ejpam-5901	171	38	are	be	AUX
ejpam-5901	171	39	bounded	bound	VERB
ejpam-5901	171	40	satisfies	satisfie	NOUN
ejpam-5901	171	41	∥s(t)∥	∥s(t)∥	PROPN
ejpam-5901	171	42	≤	≤	PROPN
ejpam-5901	171	43	ξ1	ξ1	NOUN
ejpam-5901	171	44	,	,	PUNCT
ejpam-5901	171	45	∥c(t)∥	∥c(t)∥	PROPN
ejpam-5901	171	46	≤	≤	PROPN
ejpam-5901	171	47	ξ2	ξ2	NOUN
ejpam-5901	171	48	,	,	PUNCT
ejpam-5901	171	49	∥	∥	X
ejpam-5901	171	50	i(t)∥	i(t)∥	NOUN
ejpam-5901	171	51	≤	≤	NUM
ejpam-5901	171	52	ξ1	ξ1	NOUN
ejpam-5901	171	53	,	,	PUNCT
ejpam-5901	171	54	∥r(t)∥	∥r(t)∥	PROPN
ejpam-5901	171	55	≤	≤	PROPN
ejpam-5901	171	56	ξ2	ξ2	NOUN
ejpam-5901	171	57	.	.	PUNCT
ejpam-5901	172	1	lemma	lemma	PROPN
ejpam-5901	172	2	1	1	NUM
ejpam-5901	172	3	.	.	PUNCT
ejpam-5901	173	1	the	the	DET
ejpam-5901	173	2	kernels	kernel	NOUN
ejpam-5901	173	3	wi	wi	PROPN
ejpam-5901	173	4	fulfill	fulfill	NOUN
ejpam-5901	173	5	lipschitz	lipschitz	NOUN
ejpam-5901	173	6	condition	condition	NOUN
ejpam-5901	173	7	under	under	ADP
ejpam-5901	173	8	the	the	DET
ejpam-5901	173	9	assumption	assumption	NOUN
ejpam-5901	173	10	(	(	PUNCT
ejpam-5901	173	11	q∗	q∗	NOUN
ejpam-5901	173	12	)	)	PUNCT
ejpam-5901	173	13	and	and	CCONJ
ejpam-5901	173	14	φi	φi	ADP
ejpam-5901	173	15	<	<	X
ejpam-5901	173	16	1	1	NUM
ejpam-5901	173	17	,	,	PUNCT
ejpam-5901	173	18	for	for	ADP
ejpam-5901	173	19	i	i	PROPN
ejpam-5901	173	20	∈	∈	PROPN
ejpam-5901	173	21	n4	n4	PROPN
ejpam-5901	173	22	1	1	NUM
ejpam-5901	173	23	.	.	PUNCT
ejpam-5901	174	1	s.	s.	PROPN
ejpam-5901	174	2	saber	saber	PROPN
ejpam-5901	174	3	,	,	PUNCT
ejpam-5901	174	4	a.	a.	NOUN
ejpam-5901	174	5	a.	a.	NOUN
ejpam-5901	174	6	alahmari	alahmari	PROPN
ejpam-5901	174	7	/	/	SYM
ejpam-5901	174	8	eur	eur	PROPN
ejpam-5901	174	9	.	.	PUNCT
ejpam-5901	175	1	j.	j.	PROPN
ejpam-5901	175	2	pure	pure	PROPN
ejpam-5901	175	3	appl	appl	PROPN
ejpam-5901	175	4	.	.	PROPN
ejpam-5901	175	5	math	math	PROPN
ejpam-5901	175	6	,	,	PUNCT
ejpam-5901	175	7	18	18	NUM
ejpam-5901	175	8	(	(	PUNCT
ejpam-5901	175	9	2	2	NUM
ejpam-5901	175	10	)	)	PUNCT
ejpam-5901	175	11	(	(	PUNCT
ejpam-5901	175	12	2025	2025	NUM
ejpam-5901	175	13	)	)	PUNCT
ejpam-5901	175	14	,	,	PUNCT
ejpam-5901	175	15	5901	5901	NUM
ejpam-5901	175	16	7	7	NUM
ejpam-5901	175	17	of	of	ADP
ejpam-5901	175	18	23	23	NUM
ejpam-5901	175	19	proof	proof	NOUN
ejpam-5901	175	20	.	.	PUNCT
ejpam-5901	176	1	∥w1(t	∥w1(t	ADJ
ejpam-5901	176	2	,	,	PUNCT
ejpam-5901	176	3	s)−w1(t	s)−w1(t	VERB
ejpam-5901	176	4	,	,	PUNCT
ejpam-5901	176	5	s1)∥	s1)∥	PROPN
ejpam-5901	176	6	=	=	SYM
ejpam-5901	176	7	∥(π−	∥(π−	PROPN
ejpam-5901	176	8	λ	λ	NOUN
ejpam-5901	176	9	s−µ	s−µ	NOUN
ejpam-5901	176	10	s+ηr)−	s+ηr)−	NOUN
ejpam-5901	176	11	(	(	PUNCT
ejpam-5901	176	12	π−	π−	PROPN
ejpam-5901	176	13	λ	λ	PROPN
ejpam-5901	176	14	s∗∗−µs∗	s∗∗−µs∗	ADJ
ejpam-5901	176	15	+	+	CCONJ
ejpam-5901	176	16	ηr)∥	ηr)∥	NOUN
ejpam-5901	176	17	≤	≤	NOUN
ejpam-5901	176	18	(	(	PUNCT
ejpam-5901	176	19	|λ|+	|λ|+	ADJ
ejpam-5901	176	20	µ)∥(s	µ)∥(s	NOUN
ejpam-5901	176	21	−	−	PROPN
ejpam-5901	176	22	s1)∥	s1)∥	PROPN
ejpam-5901	176	23	≤	≤	PROPN
ejpam-5901	176	24	φ1∥s	φ1∥s	NOUN
ejpam-5901	176	25	−	−	NOUN
ejpam-5901	176	26	s1∥	s1∥	PROPN
ejpam-5901	176	27	,	,	PUNCT
ejpam-5901	176	28	where	where	SCONJ
ejpam-5901	176	29	φ1	φ1	NOUN
ejpam-5901	176	30	=	=	PUNCT
ejpam-5901	176	31	δ	δ	PROPN
ejpam-5901	176	32	+	+	PROPN
ejpam-5901	176	33	ϖ	ϖ	X
ejpam-5901	176	34	+	+	NUM
ejpam-5901	176	35	µ.	µ.	NOUN
ejpam-5901	176	36	.∥w2(t	.∥w2(t	PUNCT
ejpam-5901	176	37	,	,	PUNCT
ejpam-5901	176	38	c)−w2(t	c)−w2(t	ADJ
ejpam-5901	176	39	,	,	PUNCT
ejpam-5901	176	40	c1))∥	c1))∥	NOUN
ejpam-5901	176	41	=	=	SYM
ejpam-5901	176	42	∥(λϑ	∥(λϑ	NOUN
ejpam-5901	176	43	s−(π	s−(π	NOUN
ejpam-5901	176	44	+	+	CCONJ
ejpam-5901	176	45	β	β	X
ejpam-5901	176	46	+	+	SYM
ejpam-5901	176	47	µ	µ	X
ejpam-5901	176	48	)	)	PUNCT
ejpam-5901	176	49	c)−	c)−	PROPN
ejpam-5901	176	50	(	(	PUNCT
ejpam-5901	176	51	λϑ	λϑ	PRON
ejpam-5901	176	52	s−(π	s−(π	PROPN
ejpam-5901	176	53	+	+	NUM
ejpam-5901	176	54	β	β	X
ejpam-5901	176	55	+	+	X
ejpam-5901	176	56	µ	µ	X
ejpam-5901	176	57	)	)	PUNCT
ejpam-5901	176	58	c∗∗)∥	c∗∗)∥	ADJ
ejpam-5901	176	59	≤	≤	PUNCT
ejpam-5901	176	60	φ2∥c	φ2∥c	NOUN
ejpam-5901	176	61	−	−	PROPN
ejpam-5901	176	62	c1∥	c1∥	PROPN
ejpam-5901	176	63	,	,	PUNCT
ejpam-5901	176	64	where	where	SCONJ
ejpam-5901	176	65	φ2	φ2	PROPN
ejpam-5901	176	66	=	=	SYM
ejpam-5901	176	67	µ+	µ+	X
ejpam-5901	176	68	β	β	X
ejpam-5901	176	69	+	+	PROPN
ejpam-5901	176	70	π	π	PROPN
ejpam-5901	176	71	.	.	PUNCT
ejpam-5901	176	72	∥w3(t	∥w3(t	NOUN
ejpam-5901	176	73	,	,	PUNCT
ejpam-5901	176	74	i)−w3(t	i)−w3(t	VERB
ejpam-5901	176	75	,	,	PUNCT
ejpam-5901	176	76	i1)∥	i1)∥	PROPN
ejpam-5901	176	77	=	=	SYM
ejpam-5901	176	78	∥λ(1−	∥λ(1−	PROPN
ejpam-5901	176	79	ϑ	ϑ	X
ejpam-5901	176	80	)	)	PUNCT
ejpam-5901	176	81	s+πc−(µ+	s+πc−(µ+	NOUN
ejpam-5901	176	82	τ	τ	PROPN
ejpam-5901	176	83	+	+	PROPN
ejpam-5901	176	84	σ	σ	PROPN
ejpam-5901	176	85	)	)	PUNCT
ejpam-5901	176	86	i	i	PROPN
ejpam-5901	176	87	)	)	PUNCT
ejpam-5901	176	88	−	−	PROPN
ejpam-5901	177	1	(	(	PUNCT
ejpam-5901	177	2	λ(1−	λ(1−	PROPN
ejpam-5901	177	3	ϑ	ϑ	NOUN
ejpam-5901	177	4	)	)	PUNCT
ejpam-5901	177	5	s+πc−(µ+	s+πc−(µ+	NOUN
ejpam-5901	177	6	τ	τ	PROPN
ejpam-5901	177	7	+	+	PROPN
ejpam-5901	177	8	σ	σ	PROPN
ejpam-5901	177	9	)	)	PUNCT
ejpam-5901	177	10	i1)∥	i1)∥	PROPN
ejpam-5901	177	11	≤	≤	NUM
ejpam-5901	177	12	φ3∥	φ3∥	NOUN
ejpam-5901	177	13	i−i1∥	i−i1∥	NOUN
ejpam-5901	177	14	,	,	PUNCT
ejpam-5901	177	15	where	where	SCONJ
ejpam-5901	177	16	φ3	φ3	NOUN
ejpam-5901	177	17	=	=	SYM
ejpam-5901	177	18	τ	τ	PROPN
ejpam-5901	177	19	+	+	NUM
ejpam-5901	177	20	µ+	µ+	PROPN
ejpam-5901	177	21	σ	σ	PROPN
ejpam-5901	177	22	.	.	PUNCT
ejpam-5901	177	23	.∥w4(t	.∥w4(t	PUNCT
ejpam-5901	177	24	,	,	PUNCT
ejpam-5901	177	25	r)−w4(t	r)−w4(t	NOUN
ejpam-5901	177	26	,	,	PUNCT
ejpam-5901	177	27	r1))∥	r1))∥	NOUN
ejpam-5901	177	28	=	=	SYM
ejpam-5901	177	29	∥(β	∥(β	ADJ
ejpam-5901	177	30	c+τ	c+τ	VERB
ejpam-5901	177	31	i−(µ+	i−(µ+	PROPN
ejpam-5901	177	32	η)r)−	η)r)−	X
ejpam-5901	177	33	(	(	PUNCT
ejpam-5901	177	34	β	β	X
ejpam-5901	177	35	c+τ	c+τ	NUM
ejpam-5901	177	36	i−(µ+	i−(µ+	PROPN
ejpam-5901	177	37	η)r∗∗)∥	η)r∗∗)∥	ADJ
ejpam-5901	177	38	≤	≤	NOUN
ejpam-5901	177	39	φ4∥(r−r1)∥	φ4∥(r−r1)∥	PUNCT
ejpam-5901	177	40	,	,	PUNCT
ejpam-5901	177	41	where	where	SCONJ
ejpam-5901	177	42	φ4	φ4	NOUN
ejpam-5901	177	43	=	=	SYM
ejpam-5901	177	44	µ+	µ+	X
ejpam-5901	177	45	η	η	PROPN
ejpam-5901	177	46	.	.	PROPN
ejpam-5901	177	47	thus	thus	ADV
ejpam-5901	177	48	,	,	PUNCT
ejpam-5901	177	49	we	we	PRON
ejpam-5901	177	50	have	have	VERB
ejpam-5901	177	51	that	that	DET
ejpam-5901	177	52	wi	wi	PROPN
ejpam-5901	177	53	for	for	ADP
ejpam-5901	177	54	i	i	PROPN
ejpam-5901	177	55	=	=	NOUN
ejpam-5901	177	56	1	1	NUM
ejpam-5901	177	57	,	,	PUNCT
ejpam-5901	177	58	2	2	NUM
ejpam-5901	177	59	,	,	PUNCT
ejpam-5901	177	60	3	3	NUM
ejpam-5901	177	61	,	,	PUNCT
ejpam-5901	177	62	4	4	NUM
ejpam-5901	177	63	,	,	PUNCT
ejpam-5901	177	64	satisfy	satisfy	VERB
ejpam-5901	177	65	the	the	DET
ejpam-5901	177	66	lipschitz	lipschitz	NOUN
ejpam-5901	177	67	property	property	NOUN
ejpam-5901	177	68	and	and	CCONJ
ejpam-5901	177	69	the	the	DET
ejpam-5901	177	70	result	result	NOUN
ejpam-5901	177	71	is	be	AUX
ejpam-5901	177	72	accomplished	accomplish	VERB
ejpam-5901	177	73	.	.	PUNCT
ejpam-5901	178	1	considering	consider	VERB
ejpam-5901	178	2	w1	w1	NOUN
ejpam-5901	178	3	,	,	PUNCT
ejpam-5901	178	4	w2	w2	NOUN
ejpam-5901	178	5	,	,	PUNCT
ejpam-5901	178	6	w3	w3	PROPN
ejpam-5901	178	7	,	,	PUNCT
ejpam-5901	178	8	and	and	CCONJ
ejpam-5901	178	9	w4	w4	NOUN
ejpam-5901	178	10	in	in	ADP
ejpam-5901	178	11	(	(	PUNCT
ejpam-5901	178	12	3	3	NUM
ejpam-5901	178	13	)	)	PUNCT
ejpam-5901	178	14	with	with	ADP
ejpam-5901	178	15	initial	initial	ADJ
ejpam-5901	178	16	conditions	condition	NOUN
ejpam-5901	178	17	s(0	s(0	PROPN
ejpam-5901	178	18	)	)	PUNCT
ejpam-5901	178	19	=	=	SYM
ejpam-5901	178	20	s0	s0	PROPN
ejpam-5901	178	21	,	,	PUNCT
ejpam-5901	178	22	c(0	c(0	NOUN
ejpam-5901	178	23	)	)	PUNCT
ejpam-5901	178	24	=	=	SYM
ejpam-5901	178	25	c0	c0	NOUN
ejpam-5901	178	26	,	,	PUNCT
ejpam-5901	178	27	i(0	i(0	PROPN
ejpam-5901	178	28	)	)	PUNCT
ejpam-5901	178	29	=	=	SYM
ejpam-5901	178	30	i0	i0	PROPN
ejpam-5901	178	31	,	,	PUNCT
ejpam-5901	178	32	r(0	r(0	PROPN
ejpam-5901	178	33	)	)	PUNCT
ejpam-5901	178	34	=	=	SYM
ejpam-5901	178	35	r0	r0	NOUN
ejpam-5901	178	36	,	,	PUNCT
ejpam-5901	178	37	using	use	VERB
ejpam-5901	178	38	fractalfractional	fractalfractional	ADJ
ejpam-5901	178	39	,	,	PUNCT
ejpam-5901	178	40	s(t)−	s(t)−	PROPN
ejpam-5901	178	41	s(0	s(0	PROPN
ejpam-5901	178	42	)	)	PUNCT
ejpam-5901	178	43	=	=	PUNCT
ejpam-5901	178	44	ϱ2(1−	ϱ2(1−	PROPN
ejpam-5901	178	45	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	178	46	ϱ2−1	ϱ2−1	ADP
ejpam-5901	178	47	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	178	48	)	)	PUNCT
ejpam-5901	178	49	w1(t	w1(t	PROPN
ejpam-5901	178	50	,	,	PUNCT
ejpam-5901	178	51	s(t	s(t	PROPN
ejpam-5901	178	52	)	)	PUNCT
ejpam-5901	178	53	)	)	PUNCT
ejpam-5901	179	1	+	+	CCONJ
ejpam-5901	179	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	179	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	179	4	)	)	PUNCT
ejpam-5901	179	5	∫	∫	PROPN
ejpam-5901	179	6	t	t	PROPN
ejpam-5901	179	7	0	0	NUM
ejpam-5901	180	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	180	2	ϵ)ϱ1−1w1(ϵ	ϵ)ϱ1−1w1(ϵ	PROPN
ejpam-5901	180	3	,	,	PUNCT
ejpam-5901	180	4	s(ϵ))dϵ	s(ϵ))dϵ	PROPN
ejpam-5901	180	5	,	,	PUNCT
ejpam-5901	180	6	c(t)−	c(t)−	PROPN
ejpam-5901	180	7	c(0	c(0	PROPN
ejpam-5901	180	8	)	)	PUNCT
ejpam-5901	180	9	=	=	PUNCT
ejpam-5901	181	1	ϱ2(1−	ϱ2(1−	PROPN
ejpam-5901	181	2	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	181	3	ϱ2−1	ϱ2−1	ADP
ejpam-5901	181	4	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	181	5	)	)	PUNCT
ejpam-5901	181	6	w2(t	w2(t	PROPN
ejpam-5901	181	7	,	,	PUNCT
ejpam-5901	181	8	c(t	c(t	PROPN
ejpam-5901	181	9	)	)	PUNCT
ejpam-5901	181	10	)	)	PUNCT
ejpam-5901	182	1	+	+	CCONJ
ejpam-5901	182	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	182	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	182	4	)	)	PUNCT
ejpam-5901	182	5	∫	∫	PROPN
ejpam-5901	182	6	t	t	PROPN
ejpam-5901	182	7	0	0	NUM
ejpam-5901	183	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	183	2	ϵ)ϱ1−1w2(ϵ	ϵ)ϱ1−1w2(ϵ	NOUN
ejpam-5901	183	3	,	,	PUNCT
ejpam-5901	183	4	c(ϵ))dϵ	c(ϵ))dϵ	PROPN
ejpam-5901	183	5	,	,	PUNCT
ejpam-5901	183	6	i(t)−	i(t)−	PROPN
ejpam-5901	183	7	i(0	i(0	PROPN
ejpam-5901	183	8	)	)	PUNCT
ejpam-5901	183	9	=	=	PUNCT
ejpam-5901	184	1	ϱ2(1−	ϱ2(1−	PROPN
ejpam-5901	184	2	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	184	3	ϱ2−1	ϱ2−1	ADP
ejpam-5901	184	4	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	184	5	)	)	PUNCT
ejpam-5901	184	6	w3(t	w3(t	PROPN
ejpam-5901	184	7	,	,	PUNCT
ejpam-5901	184	8	i(t	i(t	PROPN
ejpam-5901	184	9	)	)	PUNCT
ejpam-5901	184	10	)	)	PUNCT
ejpam-5901	185	1	+	+	CCONJ
ejpam-5901	185	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	185	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	185	4	)	)	PUNCT
ejpam-5901	185	5	∫	∫	PROPN
ejpam-5901	185	6	t	t	PROPN
ejpam-5901	185	7	0	0	NUM
ejpam-5901	186	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	186	2	ϵ)ϱ1−1w3(ϵ	ϵ)ϱ1−1w3(ϵ	ADJ
ejpam-5901	186	3	,	,	PUNCT
ejpam-5901	186	4	i(ϵ))dϵ	i(ϵ))dϵ	PROPN
ejpam-5901	186	5	,	,	PUNCT
ejpam-5901	186	6	r(t)−	r(t)−	PROPN
ejpam-5901	186	7	r(0	r(0	PROPN
ejpam-5901	186	8	)	)	PUNCT
ejpam-5901	186	9	=	=	PUNCT
ejpam-5901	187	1	ϱ2(1−	ϱ2(1−	PROPN
ejpam-5901	187	2	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	187	3	ϱ2−1	ϱ2−1	ADP
ejpam-5901	187	4	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	187	5	)	)	PUNCT
ejpam-5901	187	6	w4(t	w4(t	PROPN
ejpam-5901	187	7	,	,	PUNCT
ejpam-5901	187	8	r(t	r(t	NOUN
ejpam-5901	187	9	)	)	PUNCT
ejpam-5901	187	10	)	)	PUNCT
ejpam-5901	188	1	+	+	CCONJ
ejpam-5901	188	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	188	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	188	4	)	)	PUNCT
ejpam-5901	188	5	∫	∫	PROPN
ejpam-5901	188	6	t	t	PROPN
ejpam-5901	188	7	0	0	NUM
ejpam-5901	189	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	189	2	ϵ)ϱ1−1w4(ϵ	ϵ)ϱ1−1w4(ϵ	NOUN
ejpam-5901	189	3	,	,	PUNCT
ejpam-5901	189	4	r(ϵ))dϵ.	r(ϵ))dϵ.	NOUN
ejpam-5901	189	5	s.	s.	PROPN
ejpam-5901	189	6	saber	saber	PROPN
ejpam-5901	189	7	,	,	PUNCT
ejpam-5901	189	8	a.	a.	NOUN
ejpam-5901	189	9	a.	a.	NOUN
ejpam-5901	189	10	alahmari	alahmari	PROPN
ejpam-5901	189	11	/	/	SYM
ejpam-5901	189	12	eur	eur	PROPN
ejpam-5901	189	13	.	.	PUNCT
ejpam-5901	190	1	j.	j.	PROPN
ejpam-5901	190	2	pure	pure	PROPN
ejpam-5901	190	3	appl	appl	PROPN
ejpam-5901	190	4	.	.	PROPN
ejpam-5901	190	5	math	math	PROPN
ejpam-5901	190	6	,	,	PUNCT
ejpam-5901	190	7	18	18	NUM
ejpam-5901	190	8	(	(	PUNCT
ejpam-5901	190	9	2	2	NUM
ejpam-5901	190	10	)	)	PUNCT
ejpam-5901	190	11	(	(	PUNCT
ejpam-5901	190	12	2025	2025	NUM
ejpam-5901	190	13	)	)	PUNCT
ejpam-5901	190	14	,	,	PUNCT
ejpam-5901	190	15	5901	5901	NUM
ejpam-5901	190	16	8	8	NUM
ejpam-5901	190	17	of	of	ADP
ejpam-5901	190	18	23	23	NUM
ejpam-5901	190	19	the	the	DET
ejpam-5901	190	20	iterative	iterative	NOUN
ejpam-5901	190	21	scheme	scheme	NOUN
ejpam-5901	190	22	of	of	ADP
ejpam-5901	190	23	model	model	NOUN
ejpam-5901	190	24	(	(	PUNCT
ejpam-5901	190	25	2	2	NUM
ejpam-5901	190	26	)	)	PUNCT
ejpam-5901	190	27	should	should	AUX
ejpam-5901	190	28	be	be	AUX
ejpam-5901	190	29	defined	define	VERB
ejpam-5901	190	30	as	as	SCONJ
ejpam-5901	190	31	follows	follow	VERB
ejpam-5901	190	32	:	:	PUNCT
ejpam-5901	190	33	sn(t)−	sn(t)−	PROPN
ejpam-5901	190	34	s(0	s(0	PROPN
ejpam-5901	190	35	)	)	PUNCT
ejpam-5901	190	36	=	=	PUNCT
ejpam-5901	190	37	ϱ2(1−	ϱ2(1−	PROPN
ejpam-5901	190	38	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	190	39	ϱ2−1	ϱ2−1	ADP
ejpam-5901	190	40	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	190	41	)	)	PUNCT
ejpam-5901	190	42	w1(t	w1(t	PROPN
ejpam-5901	190	43	,	,	PUNCT
ejpam-5901	190	44	sn−1(t	sn−1(t	PROPN
ejpam-5901	190	45	)	)	PUNCT
ejpam-5901	190	46	)	)	PUNCT
ejpam-5901	191	1	+	+	CCONJ
ejpam-5901	191	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	191	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	191	4	)	)	PUNCT
ejpam-5901	191	5	∫	∫	PROPN
ejpam-5901	191	6	t	t	PROPN
ejpam-5901	191	7	0	0	NUM
ejpam-5901	192	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	192	2	ϵ)ϱ1−1w1(ϵ	ϵ)ϱ1−1w1(ϵ	PROPN
ejpam-5901	192	3	,	,	PUNCT
ejpam-5901	192	4	sn−1(ϵ))dϵ	sn−1(ϵ))dϵ	PROPN
ejpam-5901	192	5	,	,	PUNCT
ejpam-5901	192	6	cn(t)−	cn(t)−	PROPN
ejpam-5901	192	7	c(0	c(0	PROPN
ejpam-5901	192	8	)	)	PUNCT
ejpam-5901	192	9	=	=	PUNCT
ejpam-5901	192	10	ϱ2(1−	ϱ2(1−	PROPN
ejpam-5901	192	11	ϱ1)t2ϱ2	ϱ1)t2ϱ2	PROPN
ejpam-5901	192	12	−	−	PROPN
ejpam-5901	192	13	1	1	NUM
ejpam-5901	192	14	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	192	15	)	)	PUNCT
ejpam-5901	192	16	w2(t	w2(t	PROPN
ejpam-5901	192	17	,	,	PUNCT
ejpam-5901	192	18	cn−1(t	cn−1(t	PROPN
ejpam-5901	192	19	)	)	PUNCT
ejpam-5901	192	20	)	)	PUNCT
ejpam-5901	193	1	+	+	CCONJ
ejpam-5901	193	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	193	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	193	4	)	)	PUNCT
ejpam-5901	193	5	∫	∫	PROPN
ejpam-5901	193	6	t	t	PROPN
ejpam-5901	193	7	0	0	NUM
ejpam-5901	194	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	194	2	ϵ)ϱ1−1w2(ϵ	ϵ)ϱ1−1w2(ϵ	NOUN
ejpam-5901	194	3	,	,	PUNCT
ejpam-5901	194	4	cn−1(ϵ))dϵ	cn−1(ϵ))dϵ	PROPN
ejpam-5901	194	5	,	,	PUNCT
ejpam-5901	194	6	in(t)−	in(t)−	PROPN
ejpam-5901	194	7	i(0	i(0	PROPN
ejpam-5901	194	8	)	)	PUNCT
ejpam-5901	194	9	=	=	PUNCT
ejpam-5901	194	10	ϱ2(1−	ϱ2(1−	PROPN
ejpam-5901	194	11	ϱ1)t2ϱ2	ϱ1)t2ϱ2	PROPN
ejpam-5901	194	12	−	−	PROPN
ejpam-5901	194	13	1	1	NUM
ejpam-5901	194	14	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	194	15	)	)	PUNCT
ejpam-5901	194	16	w3(t	w3(t	PROPN
ejpam-5901	194	17	,	,	PUNCT
ejpam-5901	194	18	in−1(t	in−1(t	ADJ
ejpam-5901	194	19	)	)	PUNCT
ejpam-5901	194	20	)	)	PUNCT
ejpam-5901	195	1	+	+	CCONJ
ejpam-5901	195	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	195	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	195	4	)	)	PUNCT
ejpam-5901	195	5	∫	∫	PROPN
ejpam-5901	195	6	t	t	PROPN
ejpam-5901	195	7	0	0	NUM
ejpam-5901	196	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	196	2	ϵ)ϱ1−1w3(ϵ	ϵ)ϱ1−1w3(ϵ	ADJ
ejpam-5901	196	3	,	,	PUNCT
ejpam-5901	196	4	in−1(ϵ))dϵ	in−1(ϵ))dϵ	PROPN
ejpam-5901	196	5	,	,	PUNCT
ejpam-5901	196	6	rn(t)−	rn(t)−	PROPN
ejpam-5901	196	7	r(0	r(0	PROPN
ejpam-5901	196	8	)	)	PUNCT
ejpam-5901	196	9	=	=	PUNCT
ejpam-5901	197	1	ϱ2(1−	ϱ2(1−	PROPN
ejpam-5901	197	2	ϱ1)t2ϱ2	ϱ1)t2ϱ2	PROPN
ejpam-5901	197	3	−	−	PROPN
ejpam-5901	197	4	1	1	NUM
ejpam-5901	197	5	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	197	6	)	)	PUNCT
ejpam-5901	197	7	w4(t	w4(t	PROPN
ejpam-5901	197	8	,	,	PUNCT
ejpam-5901	197	9	rn−1(t	rn−1(t	PROPN
ejpam-5901	197	10	)	)	PUNCT
ejpam-5901	197	11	)	)	PUNCT
ejpam-5901	198	1	+	+	CCONJ
ejpam-5901	198	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	198	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	198	4	)	)	PUNCT
ejpam-5901	198	5	∫	∫	PROPN
ejpam-5901	198	6	t	t	PROPN
ejpam-5901	198	7	0	0	NUM
ejpam-5901	199	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	199	2	ϵ)ϱ1−1w4(ϵ	ϵ)ϱ1−1w4(ϵ	NOUN
ejpam-5901	199	3	,	,	PUNCT
ejpam-5901	199	4	rn−1(ϵ))dϵ.	rn−1(ϵ))dϵ.	VERB
ejpam-5901	199	5	we	we	PRON
ejpam-5901	199	6	now	now	ADV
ejpam-5901	199	7	examine	examine	VERB
ejpam-5901	199	8	the	the	DET
ejpam-5901	199	9	differences	difference	NOUN
ejpam-5901	199	10	in	in	ADP
ejpam-5901	199	11	the	the	DET
ejpam-5901	199	12	following	following	ADJ
ejpam-5901	199	13	manner	manner	NOUN
ejpam-5901	199	14	:	:	PUNCT
ejpam-5901	199	15	∆sn+1(t	∆sn+1(t	ADJ
ejpam-5901	199	16	)	)	PUNCT
ejpam-5901	200	1	=	=	PROPN
ejpam-5901	200	2	sn+1(t)−	sn+1(t)−	PROPN
ejpam-5901	200	3	sn(t	sn(t	PRON
ejpam-5901	200	4	)	)	PUNCT
ejpam-5901	200	5	,	,	PUNCT
ejpam-5901	200	6	with	with	ADP
ejpam-5901	200	7	∆sn+1(t	∆sn+1(t	PROPN
ejpam-5901	200	8	)	)	PUNCT
ejpam-5901	200	9	=	=	PUNCT
ejpam-5901	201	1	ϱ2(1−	ϱ2(1−	INTJ
ejpam-5901	201	2	ϱ1)t2	ϱ1)t2	PROPN
ejpam-5901	201	3	−	−	PROPN
ejpam-5901	201	4	1	1	NUM
ejpam-5901	201	5	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	201	6	)	)	PUNCT
ejpam-5901	201	7	w1(t	w1(t	PROPN
ejpam-5901	201	8	,	,	PUNCT
ejpam-5901	201	9	sn(t	sn(t	NOUN
ejpam-5901	201	10	)	)	PUNCT
ejpam-5901	201	11	)	)	PUNCT
ejpam-5901	202	1	+	+	CCONJ
ejpam-5901	202	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	202	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	202	4	)	)	PUNCT
ejpam-5901	202	5	∫	∫	PROPN
ejpam-5901	202	6	t	t	PROPN
ejpam-5901	202	7	0	0	NUM
ejpam-5901	203	1	ϵϱ2−1(t−	ϵϱ2−1(t−	NOUN
ejpam-5901	203	2	ϵ)ϱ1−1w1(ϵ,sn(ϵ))dϵ	ϵ)ϱ1−1w1(ϵ,sn(ϵ))dϵ	X
ejpam-5901	204	1	−	−	PROPN
ejpam-5901	204	2	(	(	PUNCT
ejpam-5901	204	3	ϱ2(1−	ϱ2(1−	INTJ
ejpam-5901	204	4	ϱ1)t2	ϱ1)t2	PROPN
ejpam-5901	204	5	−	−	PROPN
ejpam-5901	204	6	1	1	NUM
ejpam-5901	204	7	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	204	8	)	)	PUNCT
ejpam-5901	204	9	w1(t	w1(t	PROPN
ejpam-5901	204	10	,	,	PUNCT
ejpam-5901	204	11	sn−1(t	sn−1(t	PROPN
ejpam-5901	204	12	)	)	PUNCT
ejpam-5901	204	13	)	)	PUNCT
ejpam-5901	205	1	+	+	CCONJ
ejpam-5901	205	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	205	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	205	4	)	)	PUNCT
ejpam-5901	205	5	∫	∫	PROPN
ejpam-5901	205	6	t	t	PROPN
ejpam-5901	205	7	0	0	NUM
ejpam-5901	206	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	206	2	ϵ)ϱ1−1w1(ϵ,sn−1(ϵ))dϵ	ϵ)ϱ1−1w1(ϵ,sn−1(ϵ))dϵ	PROPN
ejpam-5901	206	3	)	)	PUNCT
ejpam-5901	207	1	=	=	PUNCT
ejpam-5901	208	1	ϱ2(1−	ϱ2(1−	INTJ
ejpam-5901	208	2	ϱ1)t2	ϱ1)t2	PROPN
ejpam-5901	208	3	−	−	PROPN
ejpam-5901	208	4	1	1	NUM
ejpam-5901	208	5	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	208	6	)	)	PUNCT
ejpam-5901	208	7	(	(	PUNCT
ejpam-5901	208	8	w1(t	w1(t	PROPN
ejpam-5901	208	9	,	,	PUNCT
ejpam-5901	208	10	sn(t))−w1(t	sn(t))−w1(t	PROPN
ejpam-5901	208	11	,	,	PUNCT
ejpam-5901	208	12	sn−1(t	sn−1(t	PROPN
ejpam-5901	208	13	)	)	PUNCT
ejpam-5901	208	14	)	)	PUNCT
ejpam-5901	208	15	)	)	PUNCT
ejpam-5901	209	1	+	+	CCONJ
ejpam-5901	209	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	209	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	209	4	)	)	PUNCT
ejpam-5901	209	5	∫	∫	PROPN
ejpam-5901	209	6	t	t	PROPN
ejpam-5901	209	7	0	0	NUM
ejpam-5901	210	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	210	2	ϵ)ϱ1−1(w1(ϵ	ϵ)ϱ1−1(w1(ϵ	PROPN
ejpam-5901	210	3	,	,	PUNCT
ejpam-5901	210	4	sn(ϵ))−w1(ϵ,sn−1(ϵ)))dϵ	sn(ϵ))−w1(ϵ,sn−1(ϵ)))dϵ	PROPN
ejpam-5901	210	5	,	,	PUNCT
ejpam-5901	210	6	and	and	CCONJ
ejpam-5901	210	7	∆cn+1(t	∆cn+1(t	PROPN
ejpam-5901	210	8	)	)	PUNCT
ejpam-5901	211	1	=	=	PROPN
ejpam-5901	211	2	cn+1(t)−	cn+1(t)−	PROPN
ejpam-5901	211	3	cn(t	cn(t	PRON
ejpam-5901	211	4	)	)	PUNCT
ejpam-5901	211	5	,	,	PUNCT
ejpam-5901	211	6	s.	s.	PROPN
ejpam-5901	211	7	saber	saber	PROPN
ejpam-5901	211	8	,	,	PUNCT
ejpam-5901	211	9	a.	a.	NOUN
ejpam-5901	211	10	a.	a.	NOUN
ejpam-5901	211	11	alahmari	alahmari	PROPN
ejpam-5901	211	12	/	/	SYM
ejpam-5901	211	13	eur	eur	PROPN
ejpam-5901	211	14	.	.	PUNCT
ejpam-5901	212	1	j.	j.	PROPN
ejpam-5901	212	2	pure	pure	PROPN
ejpam-5901	212	3	appl	appl	PROPN
ejpam-5901	212	4	.	.	PROPN
ejpam-5901	212	5	math	math	PROPN
ejpam-5901	212	6	,	,	PUNCT
ejpam-5901	212	7	18	18	NUM
ejpam-5901	212	8	(	(	PUNCT
ejpam-5901	212	9	2	2	NUM
ejpam-5901	212	10	)	)	PUNCT
ejpam-5901	212	11	(	(	PUNCT
ejpam-5901	212	12	2025	2025	NUM
ejpam-5901	212	13	)	)	PUNCT
ejpam-5901	212	14	,	,	PUNCT
ejpam-5901	212	15	5901	5901	NUM
ejpam-5901	212	16	9	9	NUM
ejpam-5901	212	17	of	of	ADP
ejpam-5901	212	18	23	23	NUM
ejpam-5901	212	19	with	with	ADP
ejpam-5901	212	20	∆cn+1(t	∆cn+1(t	PROPN
ejpam-5901	212	21	)	)	PUNCT
ejpam-5901	212	22	=	=	PUNCT
ejpam-5901	212	23	ϱ2(1−	ϱ2(1−	PROPN
ejpam-5901	212	24	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	212	25	ϱ2−1	ϱ2−1	ADP
ejpam-5901	212	26	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	212	27	)	)	PUNCT
ejpam-5901	212	28	w2(t	w2(t	PROPN
ejpam-5901	212	29	,	,	PUNCT
ejpam-5901	212	30	cn(t	cn(t	NOUN
ejpam-5901	212	31	)	)	PUNCT
ejpam-5901	212	32	)	)	PUNCT
ejpam-5901	213	1	+	+	CCONJ
ejpam-5901	213	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	213	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	213	4	)	)	PUNCT
ejpam-5901	213	5	∫	∫	PROPN
ejpam-5901	213	6	t	t	PROPN
ejpam-5901	213	7	0	0	NUM
ejpam-5901	214	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	214	2	ϵ)ϱ1−1w2(ϵ	ϵ)ϱ1−1w2(ϵ	NOUN
ejpam-5901	214	3	,	,	PUNCT
ejpam-5901	214	4	cn(ϵ))dϵ	cn(ϵ))dϵ	PROPN
ejpam-5901	214	5	−	−	PROPN
ejpam-5901	214	6	(	(	PUNCT
ejpam-5901	214	7	ϱ2(1−	ϱ2(1−	INTJ
ejpam-5901	214	8	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	214	9	ϱ2−1	ϱ2−1	ADP
ejpam-5901	214	10	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	214	11	)	)	PUNCT
ejpam-5901	214	12	w2(t	w2(t	PROPN
ejpam-5901	214	13	,	,	PUNCT
ejpam-5901	214	14	cn−1(t	cn−1(t	PROPN
ejpam-5901	214	15	)	)	PUNCT
ejpam-5901	214	16	)	)	PUNCT
ejpam-5901	215	1	+	+	CCONJ
ejpam-5901	215	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	215	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	215	4	)	)	PUNCT
ejpam-5901	215	5	∫	∫	PROPN
ejpam-5901	215	6	t	t	PROPN
ejpam-5901	215	7	0	0	NUM
ejpam-5901	216	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	216	2	ϵ)ϱ1−1w2(ϵ	ϵ)ϱ1−1w2(ϵ	NOUN
ejpam-5901	216	3	,	,	PUNCT
ejpam-5901	216	4	cn−1(ϵ))dϵ	cn−1(ϵ))dϵ	PROPN
ejpam-5901	216	5	)	)	PUNCT
ejpam-5901	216	6	=	=	PUNCT
ejpam-5901	216	7	ϱ2(1−	ϱ2(1−	PROPN
ejpam-5901	216	8	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	216	9	ϱ2−1	ϱ2−1	ADP
ejpam-5901	216	10	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	216	11	)	)	PUNCT
ejpam-5901	216	12	(	(	PUNCT
ejpam-5901	216	13	w2(t	w2(t	PROPN
ejpam-5901	216	14	,	,	PUNCT
ejpam-5901	216	15	in(t))−w2(t	in(t))−w2(t	PROPN
ejpam-5901	216	16	,	,	PUNCT
ejpam-5901	216	17	in−1(t	in−1(t	ADJ
ejpam-5901	216	18	)	)	PUNCT
ejpam-5901	216	19	)	)	PUNCT
ejpam-5901	216	20	)	)	PUNCT
ejpam-5901	217	1	+	+	CCONJ
ejpam-5901	217	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	217	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	217	4	)	)	PUNCT
ejpam-5901	217	5	∫	∫	PROPN
ejpam-5901	217	6	t	t	PROPN
ejpam-5901	217	7	0	0	NUM
ejpam-5901	217	8	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	217	9	ϵ)ϱ1−1(w2(ϵ	ϵ)ϱ1−1(w2(ϵ	PROPN
ejpam-5901	217	10	,	,	PUNCT
ejpam-5901	217	11	cn(ϵ))−w2(ϵ	cn(ϵ))−w2(ϵ	NOUN
ejpam-5901	217	12	,	,	PUNCT
ejpam-5901	217	13	cn−1(ϵ)))dϵ	cn−1(ϵ)))dϵ	NOUN
ejpam-5901	217	14	,	,	PUNCT
ejpam-5901	217	15	and	and	CCONJ
ejpam-5901	217	16	∆in+1(t	∆in+1(t	PROPN
ejpam-5901	217	17	)	)	PUNCT
ejpam-5901	218	1	=	=	SYM
ejpam-5901	218	2	in+1(t)−	in+1(t)−	PROPN
ejpam-5901	218	3	in(t	in(t	NUM
ejpam-5901	218	4	)	)	PUNCT
ejpam-5901	218	5	,	,	PUNCT
ejpam-5901	218	6	with	with	ADP
ejpam-5901	218	7	∆in+1(t	∆in+1(t	PROPN
ejpam-5901	218	8	)	)	PUNCT
ejpam-5901	218	9	=	=	PUNCT
ejpam-5901	218	10	ϱ2(1−	ϱ2(1−	PROPN
ejpam-5901	218	11	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	218	12	ϱ2−1	ϱ2−1	ADP
ejpam-5901	218	13	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	218	14	)	)	PUNCT
ejpam-5901	218	15	w3(t	w3(t	PROPN
ejpam-5901	218	16	,	,	PUNCT
ejpam-5901	218	17	in(t	in(t	NOUN
ejpam-5901	218	18	)	)	PUNCT
ejpam-5901	218	19	)	)	PUNCT
ejpam-5901	219	1	+	+	CCONJ
ejpam-5901	219	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	219	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	219	4	)	)	PUNCT
ejpam-5901	219	5	∫	∫	PROPN
ejpam-5901	219	6	t	t	PROPN
ejpam-5901	219	7	0	0	NUM
ejpam-5901	220	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	220	2	ϵ)ϱ1−1w3(ϵ	ϵ)ϱ1−1w3(ϵ	NOUN
ejpam-5901	220	3	,	,	PUNCT
ejpam-5901	220	4	in(ϵ))dϵ	in(ϵ))dϵ	PROPN
ejpam-5901	220	5	−	−	PROPN
ejpam-5901	220	6	(	(	PUNCT
ejpam-5901	220	7	ϱ2(1−	ϱ2(1−	INTJ
ejpam-5901	220	8	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	220	9	ϱ2−1	ϱ2−1	ADP
ejpam-5901	220	10	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	220	11	)	)	PUNCT
ejpam-5901	220	12	w3(t	w3(t	PROPN
ejpam-5901	220	13	,	,	PUNCT
ejpam-5901	220	14	in−1(t	in−1(t	ADJ
ejpam-5901	220	15	)	)	PUNCT
ejpam-5901	220	16	)	)	PUNCT
ejpam-5901	221	1	+	+	CCONJ
ejpam-5901	221	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	221	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	221	4	)	)	PUNCT
ejpam-5901	221	5	∫	∫	PROPN
ejpam-5901	221	6	t	t	PROPN
ejpam-5901	221	7	0	0	NUM
ejpam-5901	222	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	222	2	ϵ)ϱ1−1w3(ϵ	ϵ)ϱ1−1w3(ϵ	ADJ
ejpam-5901	222	3	,	,	PUNCT
ejpam-5901	222	4	in−1(ϵ))dϵ	in−1(ϵ))dϵ	NOUN
ejpam-5901	222	5	)	)	PUNCT
ejpam-5901	222	6	=	=	PUNCT
ejpam-5901	222	7	ϱ2(1−	ϱ2(1−	PROPN
ejpam-5901	222	8	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	222	9	ϱ2−1	ϱ2−1	ADP
ejpam-5901	222	10	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	222	11	)	)	PUNCT
ejpam-5901	222	12	(	(	PUNCT
ejpam-5901	222	13	w3(t	w3(t	PROPN
ejpam-5901	222	14	,	,	PUNCT
ejpam-5901	222	15	in(t))−w3(t	in(t))−w3(t	NOUN
ejpam-5901	222	16	,	,	PUNCT
ejpam-5901	222	17	in−1(t	in−1(t	NOUN
ejpam-5901	222	18	)	)	PUNCT
ejpam-5901	222	19	)	)	PUNCT
ejpam-5901	222	20	)	)	PUNCT
ejpam-5901	223	1	+	+	CCONJ
ejpam-5901	223	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	223	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	223	4	)	)	PUNCT
ejpam-5901	223	5	∫	∫	PROPN
ejpam-5901	223	6	t	t	PROPN
ejpam-5901	223	7	0	0	NUM
ejpam-5901	224	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	224	2	ϵ)ϱ1−1(w3(ϵ	ϵ)ϱ1−1(w3(ϵ	NOUN
ejpam-5901	224	3	,	,	PUNCT
ejpam-5901	224	4	in(ϵ))−w3(ϵ	in(ϵ))−w3(ϵ	NOUN
ejpam-5901	224	5	,	,	PUNCT
ejpam-5901	224	6	in−1(ϵ)))dϵ	in−1(ϵ)))dϵ	NOUN
ejpam-5901	224	7	,	,	PUNCT
ejpam-5901	224	8	and	and	CCONJ
ejpam-5901	224	9	∆rn+1(t	∆rn+1(t	ADJ
ejpam-5901	224	10	)	)	PUNCT
ejpam-5901	224	11	=	=	SYM
ejpam-5901	224	12	rn+1(t)−rn(t	rn+1(t)−rn(t	PROPN
ejpam-5901	224	13	)	)	PUNCT
ejpam-5901	224	14	,	,	PUNCT
ejpam-5901	224	15	s.	s.	PROPN
ejpam-5901	224	16	saber	saber	PROPN
ejpam-5901	224	17	,	,	PUNCT
ejpam-5901	224	18	a.	a.	NOUN
ejpam-5901	224	19	a.	a.	NOUN
ejpam-5901	224	20	alahmari	alahmari	PROPN
ejpam-5901	224	21	/	/	SYM
ejpam-5901	224	22	eur	eur	PROPN
ejpam-5901	224	23	.	.	PUNCT
ejpam-5901	225	1	j.	j.	PROPN
ejpam-5901	225	2	pure	pure	PROPN
ejpam-5901	225	3	appl	appl	PROPN
ejpam-5901	225	4	.	.	PROPN
ejpam-5901	225	5	math	math	PROPN
ejpam-5901	225	6	,	,	PUNCT
ejpam-5901	225	7	18	18	NUM
ejpam-5901	225	8	(	(	PUNCT
ejpam-5901	225	9	2	2	NUM
ejpam-5901	225	10	)	)	PUNCT
ejpam-5901	225	11	(	(	PUNCT
ejpam-5901	225	12	2025	2025	NUM
ejpam-5901	225	13	)	)	PUNCT
ejpam-5901	225	14	,	,	PUNCT
ejpam-5901	225	15	5901	5901	NUM
ejpam-5901	225	16	10	10	NUM
ejpam-5901	225	17	of	of	ADP
ejpam-5901	225	18	23	23	NUM
ejpam-5901	225	19	with	with	ADP
ejpam-5901	225	20	∆rn+1(t	∆rn+1(t	PROPN
ejpam-5901	225	21	)	)	PUNCT
ejpam-5901	225	22	=	=	PUNCT
ejpam-5901	225	23	ϱ2(1−	ϱ2(1−	PROPN
ejpam-5901	225	24	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	225	25	ϱ2−1	ϱ2−1	ADP
ejpam-5901	225	26	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	225	27	)	)	PUNCT
ejpam-5901	225	28	w4(t	w4(t	PROPN
ejpam-5901	225	29	,	,	PUNCT
ejpam-5901	225	30	rn(t	rn(t	NUM
ejpam-5901	225	31	)	)	PUNCT
ejpam-5901	225	32	)	)	PUNCT
ejpam-5901	226	1	+	+	CCONJ
ejpam-5901	226	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	226	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	226	4	)	)	PUNCT
ejpam-5901	226	5	∫	∫	PROPN
ejpam-5901	226	6	t	t	PROPN
ejpam-5901	226	7	0	0	NUM
ejpam-5901	227	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	227	2	ϵ)ϱ1−1w4(ϵ	ϵ)ϱ1−1w4(ϵ	NOUN
ejpam-5901	227	3	,	,	PUNCT
ejpam-5901	227	4	rn(ϵ))dϵ	rn(ϵ))dϵ	PROPN
ejpam-5901	227	5	−	−	PROPN
ejpam-5901	227	6	(	(	PUNCT
ejpam-5901	227	7	ϱ2(1−	ϱ2(1−	X
ejpam-5901	227	8	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	227	9	ϱ2−1	ϱ2−1	ADP
ejpam-5901	227	10	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	227	11	)	)	PUNCT
ejpam-5901	227	12	w4(t	w4(t	PROPN
ejpam-5901	227	13	,	,	PUNCT
ejpam-5901	227	14	rn−1(t	rn−1(t	PROPN
ejpam-5901	227	15	)	)	PUNCT
ejpam-5901	227	16	)	)	PUNCT
ejpam-5901	228	1	+	+	CCONJ
ejpam-5901	228	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	228	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	228	4	)	)	PUNCT
ejpam-5901	228	5	∫	∫	PROPN
ejpam-5901	228	6	t	t	PROPN
ejpam-5901	228	7	0	0	NUM
ejpam-5901	229	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	229	2	ϵ)ϱ1−1w4(ϵ	ϵ)ϱ1−1w4(ϵ	NOUN
ejpam-5901	229	3	,	,	PUNCT
ejpam-5901	229	4	rn−1(ϵ))dϵ	rn−1(ϵ))dϵ	PROPN
ejpam-5901	229	5	)	)	PUNCT
ejpam-5901	229	6	=	=	PUNCT
ejpam-5901	229	7	ϱ2(1−	ϱ2(1−	PROPN
ejpam-5901	229	8	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	229	9	ϱ2−1	ϱ2−1	ADP
ejpam-5901	229	10	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	229	11	)	)	PUNCT
ejpam-5901	229	12	(	(	PUNCT
ejpam-5901	229	13	w4(t	w4(t	PROPN
ejpam-5901	229	14	,	,	PUNCT
ejpam-5901	229	15	rn(t))−w4(t	rn(t))−w4(t	ADJ
ejpam-5901	229	16	,	,	PUNCT
ejpam-5901	229	17	in−1(t	in−1(t	ADJ
ejpam-5901	229	18	)	)	PUNCT
ejpam-5901	229	19	)	)	PUNCT
ejpam-5901	229	20	)	)	PUNCT
ejpam-5901	230	1	+	+	CCONJ
ejpam-5901	230	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	230	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	230	4	)	)	PUNCT
ejpam-5901	230	5	∫	∫	PROPN
ejpam-5901	230	6	t	t	PROPN
ejpam-5901	230	7	0	0	NUM
ejpam-5901	230	8	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	230	9	ϵ)ϱ1−1(w4(ϵ	ϵ)ϱ1−1(w4(ϵ	NOUN
ejpam-5901	230	10	,	,	PUNCT
ejpam-5901	230	11	rn(ϵ))−w4(ϵ	rn(ϵ))−w4(ϵ	NOUN
ejpam-5901	230	12	,	,	PUNCT
ejpam-5901	230	13	rn−1(ϵ)))dϵ.	rn−1(ϵ)))dϵ.	NOUN
ejpam-5901	230	14	using	use	VERB
ejpam-5901	230	15	the	the	DET
ejpam-5901	230	16	norms	norm	NOUN
ejpam-5901	230	17	,	,	PUNCT
ejpam-5901	230	18	we	we	PRON
ejpam-5901	230	19	are	be	AUX
ejpam-5901	230	20	able	able	ADJ
ejpam-5901	230	21	to	to	PART
ejpam-5901	230	22	get	get	VERB
ejpam-5901	230	23	the	the	DET
ejpam-5901	230	24	following	follow	VERB
ejpam-5901	230	25	result	result	NOUN
ejpam-5901	230	26	:	:	PUNCT
ejpam-5901	230	27	∥∆sn+1(t)∥	∥∆sn+1(t)∥	PROPN
ejpam-5901	230	28	=	=	SYM
ejpam-5901	231	1	∥ϱ2(1−	∥ϱ2(1−	NUM
ejpam-5901	231	2	ϱ1)t	ϱ1)t	NOUN
ejpam-5901	231	3	ϱ2−1	ϱ2−1	ADP
ejpam-5901	231	4	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	231	5	)	)	PUNCT
ejpam-5901	231	6	(	(	PUNCT
ejpam-5901	231	7	w1(t	w1(t	PROPN
ejpam-5901	231	8	,	,	PUNCT
ejpam-5901	231	9	sn(t))−w1(t	sn(t))−w1(t	PROPN
ejpam-5901	231	10	,	,	PUNCT
ejpam-5901	231	11	sn−1(t	sn−1(t	PROPN
ejpam-5901	231	12	)	)	PUNCT
ejpam-5901	231	13	)	)	PUNCT
ejpam-5901	231	14	)	)	PUNCT
ejpam-5901	232	1	+	+	CCONJ
ejpam-5901	232	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	232	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	232	4	)	)	PUNCT
ejpam-5901	232	5	∫	∫	PROPN
ejpam-5901	232	6	t	t	PROPN
ejpam-5901	232	7	0	0	NUM
ejpam-5901	233	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	233	2	ϵ)ϱ1−1(w1(ϵ,sn(ϵ))−w1(ϵ,sn−1(ϵ)))dϵ∥	ϵ)ϱ1−1(w1(ϵ,sn(ϵ))−w1(ϵ,sn−1(ϵ)))dϵ∥	PROPN
ejpam-5901	233	3	,	,	PUNCT
ejpam-5901	233	4	∥∆cn+1(t)∥	∥∆cn+1(t)∥	X
ejpam-5901	233	5	=	=	SYM
ejpam-5901	233	6	∥ϱ2(1−	∥ϱ2(1−	NUM
ejpam-5901	233	7	ϱ1)t	ϱ1)t	NOUN
ejpam-5901	233	8	ϱ2−1	ϱ2−1	ADP
ejpam-5901	233	9	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	233	10	)	)	PUNCT
ejpam-5901	233	11	(	(	PUNCT
ejpam-5901	233	12	w2(t	w2(t	PROPN
ejpam-5901	233	13	,	,	PUNCT
ejpam-5901	233	14	cn(t))−w2(t	cn(t))−w2(t	NOUN
ejpam-5901	233	15	,	,	PUNCT
ejpam-5901	233	16	cn−1(t	cn−1(t	PROPN
ejpam-5901	233	17	)	)	PUNCT
ejpam-5901	233	18	)	)	PUNCT
ejpam-5901	233	19	)	)	PUNCT
ejpam-5901	234	1	+	+	CCONJ
ejpam-5901	234	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	234	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	234	4	)	)	PUNCT
ejpam-5901	234	5	∫	∫	PROPN
ejpam-5901	234	6	t	t	PROPN
ejpam-5901	234	7	0	0	NUM
ejpam-5901	234	8	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	234	9	ϵ)ϱ1−1(w2(ϵ	ϵ)ϱ1−1(w2(ϵ	NOUN
ejpam-5901	234	10	,	,	PUNCT
ejpam-5901	234	11	cn(ϵ))−w2(ϵ	cn(ϵ))−w2(ϵ	NOUN
ejpam-5901	234	12	,	,	PUNCT
ejpam-5901	234	13	cn−1(ϵ)))dϵ∥	cn−1(ϵ)))dϵ∥	NOUN
ejpam-5901	234	14	,	,	PUNCT
ejpam-5901	234	15	∥∆in+1(t)∥	∥∆in+1(t)∥	X
ejpam-5901	234	16	=	=	SYM
ejpam-5901	234	17	∥ϱ2(1−	∥ϱ2(1−	PUNCT
ejpam-5901	234	18	ϱ1)t	ϱ1)t	NOUN
ejpam-5901	234	19	2−1	2−1	NUM
ejpam-5901	234	20	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	234	21	)	)	PUNCT
ejpam-5901	234	22	(	(	PUNCT
ejpam-5901	234	23	w3(t	w3(t	PROPN
ejpam-5901	234	24	,	,	PUNCT
ejpam-5901	234	25	in(t))−w3(t	in(t))−w3(t	NOUN
ejpam-5901	234	26	,	,	PUNCT
ejpam-5901	234	27	in−1(t	in−1(t	NOUN
ejpam-5901	234	28	)	)	PUNCT
ejpam-5901	234	29	)	)	PUNCT
ejpam-5901	234	30	)	)	PUNCT
ejpam-5901	235	1	+	+	CCONJ
ejpam-5901	235	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	235	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	235	4	)	)	PUNCT
ejpam-5901	235	5	∫	∫	PROPN
ejpam-5901	235	6	t	t	PROPN
ejpam-5901	235	7	0	0	NUM
ejpam-5901	236	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	236	2	ϵ)ϱ1−1(w3(ϵ	ϵ)ϱ1−1(w3(ϵ	NOUN
ejpam-5901	236	3	,	,	PUNCT
ejpam-5901	236	4	in(ϵ))−w3(ϵ	in(ϵ))−w3(ϵ	NOUN
ejpam-5901	236	5	,	,	PUNCT
ejpam-5901	236	6	in−1(ϵ)))dϵ∥	in−1(ϵ)))dϵ∥	NUM
ejpam-5901	236	7	,	,	PUNCT
ejpam-5901	236	8	∥∆rn+1(t)∥	∥∆rn+1(t)∥	X
ejpam-5901	236	9	=	=	SYM
ejpam-5901	236	10	∥ϱ2(1−	∥ϱ2(1−	PROPN
ejpam-5901	236	11	ϱ1)t	ϱ1)t	NOUN
ejpam-5901	236	12	ϱ2−1	ϱ2−1	ADP
ejpam-5901	236	13	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	236	14	)	)	PUNCT
ejpam-5901	236	15	(	(	PUNCT
ejpam-5901	236	16	w4(t	w4(t	PROPN
ejpam-5901	236	17	,	,	PUNCT
ejpam-5901	236	18	rn(t))−w4(t	rn(t))−w4(t	ADJ
ejpam-5901	236	19	,	,	PUNCT
ejpam-5901	236	20	sn−1(t	sn−1(t	PROPN
ejpam-5901	236	21	)	)	PUNCT
ejpam-5901	236	22	)	)	PUNCT
ejpam-5901	236	23	)	)	PUNCT
ejpam-5901	237	1	+	+	CCONJ
ejpam-5901	237	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	237	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	237	4	)	)	PUNCT
ejpam-5901	237	5	∫	∫	PROPN
ejpam-5901	237	6	t	t	PROPN
ejpam-5901	237	7	0	0	NUM
ejpam-5901	237	8	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	237	9	ϵ)ϱ1−1(w4(ϵ	ϵ)ϱ1−1(w4(ϵ	NOUN
ejpam-5901	237	10	,	,	PUNCT
ejpam-5901	237	11	rn(ϵ))−w4(ϵ	rn(ϵ))−w4(ϵ	NOUN
ejpam-5901	237	12	,	,	PUNCT
ejpam-5901	237	13	rn−1(ϵ)))dϵ∥.	rn−1(ϵ)))dϵ∥.	ADJ
ejpam-5901	237	14	lemma	lemma	PROPN
ejpam-5901	237	15	2	2	NUM
ejpam-5901	237	16	.	.	PUNCT
ejpam-5901	237	17	based	base	VERB
ejpam-5901	237	18	on	on	ADP
ejpam-5901	237	19	the	the	DET
ejpam-5901	237	20	assumption	assumption	NOUN
ejpam-5901	237	21	(	(	PUNCT
ejpam-5901	237	22	q∗	q∗	NOUN
ejpam-5901	237	23	)	)	PUNCT
ejpam-5901	237	24	,	,	PUNCT
ejpam-5901	237	25	model	model	NOUN
ejpam-5901	237	26	(	(	PUNCT
ejpam-5901	237	27	2	2	X
ejpam-5901	237	28	)	)	PUNCT
ejpam-5901	237	29	admits	admit	VERB
ejpam-5901	237	30	a	a	DET
ejpam-5901	237	31	solution	solution	NOUN
ejpam-5901	237	32	whenever	whenever	SCONJ
ejpam-5901	237	33	κ	κ	NOUN
ejpam-5901	237	34	=	=	NOUN
ejpam-5901	237	35	max{φ1	max{φ1	NOUN
ejpam-5901	237	36	,	,	PUNCT
ejpam-5901	237	37	φ2	φ2	PROPN
ejpam-5901	237	38	,	,	PUNCT
ejpam-5901	237	39	φ3	φ3	NOUN
ejpam-5901	237	40	,	,	PUNCT
ejpam-5901	237	41	φ4	φ4	NOUN
ejpam-5901	237	42	}	}	PUNCT
ejpam-5901	237	43	<	<	X
ejpam-5901	237	44	1	1	NUM
ejpam-5901	237	45	,	,	PUNCT
ejpam-5901	237	46	for	for	ADP
ejpam-5901	237	47	φi	φi	ADV
ejpam-5901	237	48	as	as	ADV
ejpam-5901	237	49	defined	define	VERB
ejpam-5901	237	50	in	in	ADP
ejpam-5901	237	51	the	the	DET
ejpam-5901	237	52	proof	proof	NOUN
ejpam-5901	237	53	of	of	ADP
ejpam-5901	237	54	lemma	lemma	PROPN
ejpam-5901	237	55	1	1	NUM
ejpam-5901	237	56	,	,	PUNCT
ejpam-5901	237	57	for	for	ADP
ejpam-5901	237	58	i	i	PROPN
ejpam-5901	237	59	=	=	SYM
ejpam-5901	237	60	1	1	NUM
ejpam-5901	237	61	,	,	PUNCT
ejpam-5901	237	62	2	2	NUM
ejpam-5901	237	63	,	,	PUNCT
ejpam-5901	237	64	3	3	NUM
ejpam-5901	237	65	,	,	PUNCT
ejpam-5901	237	66	4	4	NUM
ejpam-5901	237	67	.	.	PUNCT
ejpam-5901	237	68	s.	s.	PROPN
ejpam-5901	237	69	saber	saber	PROPN
ejpam-5901	237	70	,	,	PUNCT
ejpam-5901	237	71	a.	a.	NOUN
ejpam-5901	237	72	a.	a.	NOUN
ejpam-5901	237	73	alahmari	alahmari	PROPN
ejpam-5901	237	74	/	/	SYM
ejpam-5901	237	75	eur	eur	PROPN
ejpam-5901	237	76	.	.	PUNCT
ejpam-5901	238	1	j.	j.	PROPN
ejpam-5901	238	2	pure	pure	PROPN
ejpam-5901	238	3	appl	appl	PROPN
ejpam-5901	238	4	.	.	PROPN
ejpam-5901	238	5	math	math	PROPN
ejpam-5901	238	6	,	,	PUNCT
ejpam-5901	238	7	18	18	NUM
ejpam-5901	238	8	(	(	PUNCT
ejpam-5901	238	9	2	2	NUM
ejpam-5901	238	10	)	)	PUNCT
ejpam-5901	238	11	(	(	PUNCT
ejpam-5901	238	12	2025	2025	NUM
ejpam-5901	238	13	)	)	PUNCT
ejpam-5901	238	14	,	,	PUNCT
ejpam-5901	238	15	5901	5901	NUM
ejpam-5901	238	16	11	11	NUM
ejpam-5901	238	17	of	of	ADP
ejpam-5901	238	18	23	23	NUM
ejpam-5901	238	19	proof	proof	NOUN
ejpam-5901	238	20	.	.	PUNCT
ejpam-5901	239	1	define	define	VERB
ejpam-5901	239	2	four	four	NUM
ejpam-5901	239	3	functions	function	NOUN
ejpam-5901	239	4	,	,	PUNCT
ejpam-5901	239	5	z1n(t	z1n(t	PROPN
ejpam-5901	239	6	)	)	PUNCT
ejpam-5901	239	7	,	,	PUNCT
ejpam-5901	239	8	z2n(t	z2n(t	PROPN
ejpam-5901	239	9	)	)	PUNCT
ejpam-5901	239	10	,	,	PUNCT
ejpam-5901	239	11	z3n(t	z3n(t	PROPN
ejpam-5901	239	12	)	)	PUNCT
ejpam-5901	239	13	and	and	CCONJ
ejpam-5901	239	14	z4n(t	z4n(t	PROPN
ejpam-5901	239	15	)	)	PUNCT
ejpam-5901	239	16	,	,	PUNCT
ejpam-5901	239	17	as	as	ADP
ejpam-5901	239	18	z1n(t	z1n(t	PROPN
ejpam-5901	239	19	)	)	PUNCT
ejpam-5901	239	20	=	=	PROPN
ejpam-5901	239	21	sn+1(t)−	sn+1(t)−	PROPN
ejpam-5901	239	22	s(t	s(t	PROPN
ejpam-5901	239	23	)	)	PUNCT
ejpam-5901	239	24	,	,	PUNCT
ejpam-5901	239	25	z2n(t	z2n(t	X
ejpam-5901	239	26	)	)	PUNCT
ejpam-5901	240	1	=	=	SYM
ejpam-5901	240	2	cn+1(t)−	cn+1(t)−	PROPN
ejpam-5901	240	3	c(t	c(t	PROPN
ejpam-5901	240	4	)	)	PUNCT
ejpam-5901	240	5	,	,	PUNCT
ejpam-5901	240	6	z3n(t	z3n(t	PROPN
ejpam-5901	240	7	)	)	PUNCT
ejpam-5901	241	1	=	=	SYM
ejpam-5901	241	2	in+1(t)−	in+1(t)−	PROPN
ejpam-5901	241	3	i(t	i(t	PROPN
ejpam-5901	241	4	)	)	PUNCT
ejpam-5901	241	5	,	,	PUNCT
ejpam-5901	241	6	z4n(t	z4n(t	PROPN
ejpam-5901	241	7	)	)	PUNCT
ejpam-5901	241	8	=	=	SYM
ejpam-5901	242	1	rn+1(t)−	rn+1(t)−	NOUN
ejpam-5901	242	2	r(t	r(t	NOUN
ejpam-5901	242	3	)	)	PUNCT
ejpam-5901	242	4	.	.	PUNCT
ejpam-5901	243	1	as	as	ADP
ejpam-5901	243	2	a	a	DET
ejpam-5901	243	3	result	result	NOUN
ejpam-5901	243	4	∥z1n(t)∥	∥z1n(t)∥	PROPN
ejpam-5901	243	5	=	=	SYM
ejpam-5901	243	6	∥ϱ2(1−	∥ϱ2(1−	NUM
ejpam-5901	243	7	ϱ1)t	ϱ1)t	NOUN
ejpam-5901	243	8	ϱ2−1	ϱ2−1	ADP
ejpam-5901	243	9	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	243	10	)	)	PUNCT
ejpam-5901	243	11	(	(	PUNCT
ejpam-5901	243	12	w1(t	w1(t	PROPN
ejpam-5901	243	13	,	,	PUNCT
ejpam-5901	243	14	sn(t))−w1(t	sn(t))−w1(t	PROPN
ejpam-5901	243	15	,	,	PUNCT
ejpam-5901	243	16	s(t	s(t	PROPN
ejpam-5901	243	17	)	)	PUNCT
ejpam-5901	243	18	)	)	PUNCT
ejpam-5901	243	19	)	)	PUNCT
ejpam-5901	244	1	+	+	CCONJ
ejpam-5901	244	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	244	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	244	4	)	)	PUNCT
ejpam-5901	244	5	∫	∫	PROPN
ejpam-5901	244	6	t	t	PROPN
ejpam-5901	244	7	0	0	NUM
ejpam-5901	245	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	245	2	ϵ)ϱ1−1(w1(ϵ,sn(ϵ))−w1(ϵ	ϵ)ϱ1−1(w1(ϵ,sn(ϵ))−w1(ϵ	PROPN
ejpam-5901	245	3	,	,	PUNCT
ejpam-5901	245	4	s(ϵ)))dϵ∥	s(ϵ)))dϵ∥	VERB
ejpam-5901	245	5	≤	≤	NOUN
ejpam-5901	245	6	ϱ2(1−	ϱ2(1−	NOUN
ejpam-5901	245	7	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	245	8	2	2	NUM
ejpam-5901	245	9	−	−	PROPN
ejpam-5901	245	10	1	1	NUM
ejpam-5901	245	11	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	245	12	)	)	PUNCT
ejpam-5901	245	13	∥w1(t	∥w1(t	ADJ
ejpam-5901	245	14	,	,	PUNCT
ejpam-5901	245	15	sn(t))−w1(t	sn(t))−w1(t	NOUN
ejpam-5901	245	16	,	,	PUNCT
ejpam-5901	245	17	s(t))∥	s(t))∥	PUNCT
ejpam-5901	245	18	+	+	X
ejpam-5901	245	19	ϱ1ϱ2	ϱ1ϱ2	PROPN
ejpam-5901	245	20	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	245	21	)	)	PUNCT
ejpam-5901	245	22	∫	∫	PROPN
ejpam-5901	246	1	t	t	PROPN
ejpam-5901	246	2	0	0	NUM
ejpam-5901	247	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	247	2	ϵ)ϱ1−1∥w1(ϵ,sn(ϵ))−w1(ϵ	ϵ)ϱ1−1∥w1(ϵ,sn(ϵ))−w1(ϵ	PROPN
ejpam-5901	247	3	,	,	PUNCT
ejpam-5901	247	4	s(ϵ))∥dϵ	s(ϵ))∥dϵ	ADJ
ejpam-5901	247	5	≤	≤	NUM
ejpam-5901	247	6	ϱ2(1−	ϱ2(1−	VERB
ejpam-5901	247	7	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	247	8	ϱ2−1	ϱ2−1	ADP
ejpam-5901	247	9	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	247	10	)	)	PUNCT
ejpam-5901	247	11	φ1∥	φ1∥	PROPN
ejpam-5901	247	12	sn−s	sn−s	VERB
ejpam-5901	247	13	∥	∥	NOUN
ejpam-5901	247	14	+	+	CCONJ
ejpam-5901	247	15	ϱ1	ϱ1	NOUN
ejpam-5901	247	16	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	247	17	)	)	PUNCT
ejpam-5901	248	1	∫	∫	PROPN
ejpam-5901	249	1	t	t	PROPN
ejpam-5901	249	2	0	0	NUM
ejpam-5901	250	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	250	2	ϵ)ϱ1−1φ1∥	ϵ)ϱ1−1φ1∥	NOUN
ejpam-5901	250	3	sn−s	sn−s	PROPN
ejpam-5901	250	4	∥dϵ	∥dϵ	ADV
ejpam-5901	250	5	≤	≤	NOUN
ejpam-5901	250	6	(	(	PUNCT
ejpam-5901	250	7	ϱ2(1−	ϱ2(1−	ADJ
ejpam-5901	250	8	ϱ1	ϱ1	NOUN
ejpam-5901	250	9	)	)	PUNCT
ejpam-5901	251	1	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	251	2	)	)	PUNCT
ejpam-5901	252	1	+	+	CCONJ
ejpam-5901	252	2	ϱ1ϱ2γ(ϱ2	ϱ1ϱ2γ(ϱ2	NOUN
ejpam-5901	252	3	)	)	PUNCT
ejpam-5901	252	4	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	PUNCT
ejpam-5901	253	1	+	+	NUM
ejpam-5901	253	2	ϱ2	ϱ2	NOUN
ejpam-5901	253	3	)	)	PUNCT
ejpam-5901	253	4	)	)	PUNCT
ejpam-5901	254	1	φ1∥	φ1∥	PROPN
ejpam-5901	254	2	sn−s	sn−s	ADJ
ejpam-5901	254	3	∥	∥	PUNCT
ejpam-5901	254	4	≤	≤	NOUN
ejpam-5901	254	5	(	(	PUNCT
ejpam-5901	254	6	ϱ2(1−	ϱ2(1−	ADJ
ejpam-5901	254	7	ϱ1	ϱ1	NOUN
ejpam-5901	254	8	)	)	PUNCT
ejpam-5901	254	9	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	254	10	)	)	PUNCT
ejpam-5901	255	1	+	+	CCONJ
ejpam-5901	255	2	ϱ1ϱ2γ(ϱ2	ϱ1ϱ2γ(ϱ2	NOUN
ejpam-5901	255	3	)	)	PUNCT
ejpam-5901	255	4	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	PUNCT
ejpam-5901	256	1	+	+	NUM
ejpam-5901	256	2	ϱ2	ϱ2	NOUN
ejpam-5901	256	3	)	)	PUNCT
ejpam-5901	256	4	)	)	PUNCT
ejpam-5901	257	1	nφn	nφn	NOUN
ejpam-5901	257	2	1∥	1∥	NUM
ejpam-5901	257	3	s1−s	s1−s	PROPN
ejpam-5901	257	4	∥	∥	PROPN
ejpam-5901	257	5	,	,	PUNCT
ejpam-5901	257	6	in	in	ADP
ejpam-5901	257	7	which	which	PRON
ejpam-5901	257	8	for	for	ADP
ejpam-5901	257	9	φ1	φ1	NOUN
ejpam-5901	257	10	<	<	X
ejpam-5901	257	11	1	1	NUM
ejpam-5901	257	12	and	and	CCONJ
ejpam-5901	257	13	as	as	ADP
ejpam-5901	257	14	n	n	NUM
ejpam-5901	257	15	→	→	SYM
ejpam-5901	257	16	∞	∞	PROPN
ejpam-5901	257	17	,	,	PUNCT
ejpam-5901	257	18	we	we	PRON
ejpam-5901	257	19	have	have	VERB
ejpam-5901	257	20	sn	sn	PROPN
ejpam-5901	257	21	→	→	SYM
ejpam-5901	257	22	s.	s.	PROPN
ejpam-5901	257	23	similarly	similarly	ADV
ejpam-5901	257	24	∥z2n(t)∥	∥z2n(t)∥	PROPN
ejpam-5901	257	25	≤	≤	NOUN
ejpam-5901	257	26	[	[	PUNCT
ejpam-5901	257	27	ϱ1ϱ2γ(ϱ2	ϱ1ϱ2γ(ϱ2	NOUN
ejpam-5901	257	28	)	)	PUNCT
ejpam-5901	257	29	b∗(ϱ1)γ	b∗(ϱ1)γ	PROPN
ejpam-5901	257	30	(	(	PUNCT
ejpam-5901	257	31	ϱ1	ϱ1	NOUN
ejpam-5901	257	32	+	+	CCONJ
ejpam-5901	257	33	ϱ2	ϱ2	NOUN
ejpam-5901	257	34	)	)	PUNCT
ejpam-5901	257	35	+	+	CCONJ
ejpam-5901	257	36	ϱ2	ϱ2	PROPN
ejpam-5901	257	37	(	(	PUNCT
ejpam-5901	257	38	1−	1−	NUM
ejpam-5901	257	39	ϱ1	ϱ1	NOUN
ejpam-5901	257	40	)	)	PUNCT
ejpam-5901	257	41	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	257	42	)	)	PUNCT
ejpam-5901	257	43	]	]	PUNCT
ejpam-5901	258	1	n	n	X
ejpam-5901	258	2	φn	φn	ADP
ejpam-5901	258	3	2	2	NUM
ejpam-5901	258	4	∥c1−c∥	∥c1−c∥	VERB
ejpam-5901	258	5	,	,	PUNCT
ejpam-5901	258	6	∥z3n(t)∥	∥z3n(t)∥	PROPN
ejpam-5901	258	7	≤	≤	NOUN
ejpam-5901	258	8	[	[	PUNCT
ejpam-5901	258	9	ϱ1ϱ2γ(ϱ2	ϱ1ϱ2γ(ϱ2	NOUN
ejpam-5901	258	10	)	)	PUNCT
ejpam-5901	258	11	b∗(ϱ1)γ	b∗(ϱ1)γ	PROPN
ejpam-5901	258	12	(	(	PUNCT
ejpam-5901	258	13	ϱ1	ϱ1	NOUN
ejpam-5901	258	14	+	+	CCONJ
ejpam-5901	258	15	ϱ2	ϱ2	NOUN
ejpam-5901	258	16	)	)	PUNCT
ejpam-5901	259	1	+	+	CCONJ
ejpam-5901	259	2	ϱ2	ϱ2	PROPN
ejpam-5901	259	3	(	(	PUNCT
ejpam-5901	259	4	1−	1−	NUM
ejpam-5901	259	5	ϱ1	ϱ1	NOUN
ejpam-5901	259	6	)	)	PUNCT
ejpam-5901	259	7	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	259	8	)	)	PUNCT
ejpam-5901	259	9	]	]	PUNCT
ejpam-5901	260	1	n	n	X
ejpam-5901	260	2	φn	φn	ADV
ejpam-5901	260	3	3	3	NUM
ejpam-5901	260	4	∥i1−	∥i1−	PROPN
ejpam-5901	260	5	i∥	i∥	INTJ
ejpam-5901	260	6	,	,	PUNCT
ejpam-5901	260	7	∥z4n(t)∥	∥z4n(t)∥	PROPN
ejpam-5901	260	8	≤	≤	NOUN
ejpam-5901	260	9	[	[	PUNCT
ejpam-5901	260	10	ϱ1ϱ2γ(ϱ2	ϱ1ϱ2γ(ϱ2	NOUN
ejpam-5901	260	11	)	)	PUNCT
ejpam-5901	260	12	b∗(ϱ1)γ	b∗(ϱ1)γ	PROPN
ejpam-5901	260	13	(	(	PUNCT
ejpam-5901	260	14	ϱ1	ϱ1	NOUN
ejpam-5901	260	15	+	+	CCONJ
ejpam-5901	260	16	ϱ2	ϱ2	NOUN
ejpam-5901	260	17	)	)	PUNCT
ejpam-5901	260	18	+	+	CCONJ
ejpam-5901	260	19	ϱ2	ϱ2	PROPN
ejpam-5901	260	20	(	(	PUNCT
ejpam-5901	260	21	1−	1−	NUM
ejpam-5901	260	22	ϱ1	ϱ1	NOUN
ejpam-5901	260	23	)	)	PUNCT
ejpam-5901	260	24	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	260	25	)	)	PUNCT
ejpam-5901	260	26	]	]	PUNCT
ejpam-5901	260	27	n	n	CCONJ
ejpam-5901	260	28	φn	φn	ADP
ejpam-5901	260	29	4∥r1−r	4∥r1−r	PRON
ejpam-5901	260	30	∥.	∥.	X
ejpam-5901	260	31	when	when	SCONJ
ejpam-5901	260	32	n	n	X
ejpam-5901	260	33	→	→	SYM
ejpam-5901	260	34	∞	∞	PROPN
ejpam-5901	260	35	,	,	PUNCT
ejpam-5901	260	36	then	then	ADV
ejpam-5901	260	37	zin	zin	INTJ
ejpam-5901	260	38	(	(	PUNCT
ejpam-5901	260	39	tin	tin	NOUN
ejpam-5901	260	40	→	→	SYM
ejpam-5901	260	41	0	0	NUM
ejpam-5901	260	42	,	,	PUNCT
ejpam-5901	260	43	i	i	PRON
ejpam-5901	260	44	∈	∈	PROPN
ejpam-5901	260	45	n4	n4	PROPN
ejpam-5901	260	46	,	,	PUNCT
ejpam-5901	260	47	for	for	ADP
ejpam-5901	260	48	φi	φi	ADV
ejpam-5901	260	49	<	<	X
ejpam-5901	260	50	1	1	NUM
ejpam-5901	260	51	,	,	PUNCT
ejpam-5901	260	52	(	(	PUNCT
ejpam-5901	260	53	i	i	NOUN
ejpam-5901	260	54	=	=	NOUN
ejpam-5901	260	55	1	1	NUM
ejpam-5901	260	56	,	,	PUNCT
ejpam-5901	260	57	.	.	PUNCT
ejpam-5901	260	58	.	.	PUNCT
ejpam-5901	260	59	.	.	PUNCT
ejpam-5901	261	1	,	,	PUNCT
ejpam-5901	261	2	4	4	NUM
ejpam-5901	261	3	)	)	PUNCT
ejpam-5901	261	4	.	.	PUNCT
ejpam-5901	262	1	ultimately	ultimately	ADV
ejpam-5901	262	2	,	,	PUNCT
ejpam-5901	262	3	the	the	DET
ejpam-5901	262	4	ff	ff	NOUN
ejpam-5901	262	5	pneumonia	pneumonia	NOUN
ejpam-5901	262	6	system	system	NOUN
ejpam-5901	262	7	(	(	PUNCT
ejpam-5901	262	8	2	2	X
ejpam-5901	262	9	)	)	PUNCT
ejpam-5901	262	10	has	have	VERB
ejpam-5901	262	11	a	a	DET
ejpam-5901	262	12	solution	solution	NOUN
ejpam-5901	262	13	.	.	PUNCT
ejpam-5901	263	1	5	5	X
ejpam-5901	263	2	.	.	X
ejpam-5901	263	3	uniqueness	uniqueness	NOUN
ejpam-5901	263	4	of	of	ADP
ejpam-5901	263	5	the	the	DET
ejpam-5901	263	6	model	model	NOUN
ejpam-5901	263	7	solutions	solution	NOUN
ejpam-5901	263	8	lemma	lemma	PROPN
ejpam-5901	263	9	3	3	X
ejpam-5901	263	10	.	.	NOUN
ejpam-5901	263	11	model	model	NOUN
ejpam-5901	263	12	(	(	PUNCT
ejpam-5901	263	13	2	2	X
ejpam-5901	263	14	)	)	PUNCT
ejpam-5901	263	15	has	have	VERB
ejpam-5901	263	16	a	a	DET
ejpam-5901	263	17	unique	unique	ADJ
ejpam-5901	263	18	solution	solution	NOUN
ejpam-5901	263	19	if	if	SCONJ
ejpam-5901	263	20	the	the	DET
ejpam-5901	263	21	inequality	inequality	NOUN
ejpam-5901	263	22	is	be	AUX
ejpam-5901	263	23	satisfied:(ϱ2(1−	satisfied:(ϱ2(1−	ADJ
ejpam-5901	263	24	ϱ1	ϱ1	NOUN
ejpam-5901	263	25	)	)	PUNCT
ejpam-5901	264	1	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	264	2	)	)	PUNCT
ejpam-5901	265	1	+	+	CCONJ
ejpam-5901	265	2	ϱ1ϱ2γ(ϱ2	ϱ1ϱ2γ(ϱ2	NOUN
ejpam-5901	265	3	)	)	PUNCT
ejpam-5901	265	4	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	PUNCT
ejpam-5901	266	1	+	+	NUM
ejpam-5901	266	2	ϱ2	ϱ2	NOUN
ejpam-5901	266	3	)	)	PUNCT
ejpam-5901	266	4	)	)	PUNCT
ejpam-5901	267	1	φi	φi	ADP
ejpam-5901	267	2	≤	≤	NUM
ejpam-5901	267	3	1	1	NUM
ejpam-5901	267	4	,	,	PUNCT
ejpam-5901	267	5	for	for	ADP
ejpam-5901	267	6	i	i	PROPN
ejpam-5901	267	7	=	=	SYM
ejpam-5901	267	8	1	1	NUM
ejpam-5901	267	9	,	,	PUNCT
ejpam-5901	267	10	2	2	NUM
ejpam-5901	267	11	,	,	PUNCT
ejpam-5901	267	12	3	3	NUM
ejpam-5901	267	13	,	,	PUNCT
ejpam-5901	267	14	4	4	NUM
ejpam-5901	267	15	.	.	PUNCT
ejpam-5901	267	16	s.	s.	PROPN
ejpam-5901	267	17	saber	saber	PROPN
ejpam-5901	267	18	,	,	PUNCT
ejpam-5901	267	19	a.	a.	NOUN
ejpam-5901	267	20	a.	a.	NOUN
ejpam-5901	267	21	alahmari	alahmari	PROPN
ejpam-5901	267	22	/	/	SYM
ejpam-5901	267	23	eur	eur	PROPN
ejpam-5901	267	24	.	.	PUNCT
ejpam-5901	268	1	j.	j.	PROPN
ejpam-5901	268	2	pure	pure	PROPN
ejpam-5901	268	3	appl	appl	PROPN
ejpam-5901	268	4	.	.	PROPN
ejpam-5901	268	5	math	math	PROPN
ejpam-5901	268	6	,	,	PUNCT
ejpam-5901	268	7	18	18	NUM
ejpam-5901	268	8	(	(	PUNCT
ejpam-5901	268	9	2	2	NUM
ejpam-5901	268	10	)	)	PUNCT
ejpam-5901	268	11	(	(	PUNCT
ejpam-5901	268	12	2025	2025	NUM
ejpam-5901	268	13	)	)	PUNCT
ejpam-5901	268	14	,	,	PUNCT
ejpam-5901	268	15	5901	5901	NUM
ejpam-5901	268	16	12	12	NUM
ejpam-5901	268	17	of	of	ADP
ejpam-5901	268	18	23	23	NUM
ejpam-5901	268	19	proof	proof	NOUN
ejpam-5901	268	20	.	.	PUNCT
ejpam-5901	268	21	suppose	suppose	VERB
ejpam-5901	268	22	that	that	SCONJ
ejpam-5901	268	23	there	there	PRON
ejpam-5901	268	24	is	be	VERB
ejpam-5901	268	25	another	another	DET
ejpam-5901	268	26	solution	solution	NOUN
ejpam-5901	268	27	to	to	ADP
ejpam-5901	268	28	the	the	DET
ejpam-5901	268	29	fractal	fractal	ADJ
ejpam-5901	268	30	-	-	PUNCT
ejpam-5901	268	31	fractional	fractional	ADJ
ejpam-5901	268	32	epidemiological	epidemiological	ADJ
ejpam-5901	268	33	model	model	NOUN
ejpam-5901	268	34	(	(	PUNCT
ejpam-5901	268	35	2	2	NUM
ejpam-5901	268	36	)	)	PUNCT
ejpam-5901	268	37	,	,	PUNCT
ejpam-5901	268	38	and	and	CCONJ
ejpam-5901	268	39	we	we	PRON
ejpam-5901	268	40	can	can	AUX
ejpam-5901	268	41	compute	compute	VERB
ejpam-5901	268	42	the	the	DET
ejpam-5901	268	43	value	value	NOUN
ejpam-5901	268	44	for	for	ADP
ejpam-5901	268	45	s̃(t	s̃(t	PROPN
ejpam-5901	268	46	)	)	PUNCT
ejpam-5901	268	47	,	,	PUNCT
ejpam-5901	268	48	c̃(t	c̃(t	PROPN
ejpam-5901	268	49	)	)	PUNCT
ejpam-5901	268	50	,	,	PUNCT
ejpam-5901	268	51	ĩ(t	ĩ(t	PROPN
ejpam-5901	268	52	)	)	PUNCT
ejpam-5901	268	53	,	,	PUNCT
ejpam-5901	268	54	r̃(t	r̃(t	PROPN
ejpam-5901	268	55	)	)	PUNCT
ejpam-5901	268	56	using	use	VERB
ejpam-5901	268	57	that	that	DET
ejpam-5901	268	58	solution	solution	NOUN
ejpam-5901	268	59	,	,	PUNCT
ejpam-5901	268	60	so	so	SCONJ
ejpam-5901	268	61	that	that	SCONJ
ejpam-5901	268	62	the	the	DET
ejpam-5901	268	63	value	value	NOUN
ejpam-5901	268	64	for	for	ADP
ejpam-5901	268	65	s̃(t	s̃(t	PROPN
ejpam-5901	268	66	)	)	PUNCT
ejpam-5901	268	67	=	=	PUNCT
ejpam-5901	269	1	ϱ2(1−	ϱ2(1−	PROPN
ejpam-5901	269	2	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	269	3	ϱ2−1	ϱ2−1	ADP
ejpam-5901	269	4	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	269	5	)	)	PUNCT
ejpam-5901	269	6	w1(t	w1(t	PROPN
ejpam-5901	269	7	,	,	PUNCT
ejpam-5901	269	8	s̃(t	s̃(t	PROPN
ejpam-5901	269	9	)	)	PUNCT
ejpam-5901	269	10	)	)	PUNCT
ejpam-5901	270	1	+	+	CCONJ
ejpam-5901	270	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	270	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	270	4	)	)	PUNCT
ejpam-5901	270	5	∫	∫	PROPN
ejpam-5901	270	6	t	t	PROPN
ejpam-5901	270	7	0	0	NUM
ejpam-5901	271	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	271	2	ϵ)ϱ1−1w1(ϵ	ϵ)ϱ1−1w1(ϵ	PROPN
ejpam-5901	271	3	,	,	PUNCT
ejpam-5901	271	4	s̃(ϵ))dϵ	s̃(ϵ))dϵ	PROPN
ejpam-5901	271	5	,	,	PUNCT
ejpam-5901	271	6	c̃(t	c̃(t	PROPN
ejpam-5901	271	7	)	)	PUNCT
ejpam-5901	271	8	=	=	PUNCT
ejpam-5901	272	1	ϱ2(1−	ϱ2(1−	PROPN
ejpam-5901	272	2	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	272	3	ϱ2−1	ϱ2−1	ADP
ejpam-5901	272	4	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	272	5	)	)	PUNCT
ejpam-5901	272	6	w2(t	w2(t	PROPN
ejpam-5901	272	7	,	,	PUNCT
ejpam-5901	272	8	c̃(t	c̃(t	PROPN
ejpam-5901	272	9	)	)	PUNCT
ejpam-5901	272	10	)	)	PUNCT
ejpam-5901	273	1	+	+	CCONJ
ejpam-5901	273	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	273	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	273	4	)	)	PUNCT
ejpam-5901	273	5	∫	∫	PROPN
ejpam-5901	273	6	t	t	PROPN
ejpam-5901	273	7	0	0	NUM
ejpam-5901	274	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	274	2	ϵ)ϱ1−1w2(ϵ	ϵ)ϱ1−1w2(ϵ	NOUN
ejpam-5901	274	3	,	,	PUNCT
ejpam-5901	274	4	c̃(ϵ))dϵ	c̃(ϵ))dϵ	NOUN
ejpam-5901	274	5	,	,	PUNCT
ejpam-5901	274	6	ĩ(t	ĩ(t	PROPN
ejpam-5901	274	7	)	)	PUNCT
ejpam-5901	274	8	=	=	PUNCT
ejpam-5901	275	1	ϱ2(1−	ϱ2(1−	PROPN
ejpam-5901	275	2	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	275	3	ϱ2−1	ϱ2−1	ADP
ejpam-5901	275	4	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	275	5	)	)	PUNCT
ejpam-5901	275	6	w3(t	w3(t	PROPN
ejpam-5901	275	7	,	,	PUNCT
ejpam-5901	275	8	ĩ(t	ĩ(t	PROPN
ejpam-5901	275	9	)	)	PUNCT
ejpam-5901	275	10	)	)	PUNCT
ejpam-5901	276	1	+	+	CCONJ
ejpam-5901	276	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	276	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	276	4	)	)	PUNCT
ejpam-5901	276	5	∫	∫	PROPN
ejpam-5901	276	6	t	t	PROPN
ejpam-5901	276	7	0	0	NUM
ejpam-5901	277	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	277	2	ϵ)ϱ1−1w3(ϵ	ϵ)ϱ1−1w3(ϵ	NOUN
ejpam-5901	277	3	,	,	PUNCT
ejpam-5901	277	4	ĩ(ϵ))dϵ	ĩ(ϵ))dϵ	NUM
ejpam-5901	277	5	,	,	PUNCT
ejpam-5901	277	6	r̃(t	r̃(t	PROPN
ejpam-5901	277	7	)	)	PUNCT
ejpam-5901	277	8	=	=	PUNCT
ejpam-5901	278	1	ϱ2(1−	ϱ2(1−	PROPN
ejpam-5901	278	2	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	278	3	ϱ2−1	ϱ2−1	ADP
ejpam-5901	278	4	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	278	5	)	)	PUNCT
ejpam-5901	278	6	w4(t	w4(t	PROPN
ejpam-5901	278	7	,	,	PUNCT
ejpam-5901	278	8	r̃(t	r̃(t	PROPN
ejpam-5901	278	9	)	)	PUNCT
ejpam-5901	278	10	)	)	PUNCT
ejpam-5901	279	1	+	+	CCONJ
ejpam-5901	279	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	279	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	279	4	)	)	PUNCT
ejpam-5901	279	5	∫	∫	PROPN
ejpam-5901	279	6	t	t	PROPN
ejpam-5901	279	7	0	0	NUM
ejpam-5901	280	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	280	2	ϵ)ϱ1−1w4(ϵ	ϵ)ϱ1−1w4(ϵ	NOUN
ejpam-5901	280	3	,	,	PUNCT
ejpam-5901	280	4	r̃(ϵ))dϵ.	r̃(ϵ))dϵ.	NOUN
ejpam-5901	280	5	here	here	ADV
ejpam-5901	280	6	,	,	PUNCT
ejpam-5901	280	7	we	we	PRON
ejpam-5901	280	8	take	take	VERB
ejpam-5901	280	9	the	the	DET
ejpam-5901	280	10	norm	norm	NOUN
ejpam-5901	280	11	of	of	ADP
ejpam-5901	280	12	the	the	DET
ejpam-5901	280	13	difference	difference	NOUN
ejpam-5901	280	14	between	between	ADP
ejpam-5901	280	15	s(t	s(t	PROPN
ejpam-5901	280	16	)	)	PUNCT
ejpam-5901	280	17	and	and	CCONJ
ejpam-5901	280	18	s̃(t	s̃(t	PROPN
ejpam-5901	280	19	)	)	PUNCT
ejpam-5901	280	20	as	as	SCONJ
ejpam-5901	280	21	the	the	DET
ejpam-5901	280	22	difference	difference	NOUN
ejpam-5901	280	23	between	between	ADP
ejpam-5901	280	24	pair	pair	NOUN
ejpam-5901	280	25	s(t	s(t	PROPN
ejpam-5901	280	26	)	)	PUNCT
ejpam-5901	280	27	and	and	CCONJ
ejpam-5901	280	28	s̃(t	s̃(t	PROPN
ejpam-5901	280	29	)	)	PUNCT
ejpam-5901	280	30	as	as	SCONJ
ejpam-5901	280	31	follows	follow	VERB
ejpam-5901	280	32	:	:	PUNCT
ejpam-5901	280	33	∥	∥	PROPN
ejpam-5901	280	34	s(t)−	s(t)−	PROPN
ejpam-5901	280	35	s̃(t)∥	s̃(t)∥	NOUN
ejpam-5901	280	36	=	=	SYM
ejpam-5901	280	37	∥ϱ2(1−	∥ϱ2(1−	NUM
ejpam-5901	280	38	ϱ1)t	ϱ1)t	NOUN
ejpam-5901	280	39	ϱ2−1	ϱ2−1	ADP
ejpam-5901	280	40	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	280	41	)	)	PUNCT
ejpam-5901	280	42	(	(	PUNCT
ejpam-5901	280	43	w1(t	w1(t	PROPN
ejpam-5901	280	44	,	,	PUNCT
ejpam-5901	280	45	s(t))−w1(t	s(t))−w1(t	NUM
ejpam-5901	280	46	,	,	PUNCT
ejpam-5901	280	47	s̃(t	s̃(t	PROPN
ejpam-5901	280	48	)	)	PUNCT
ejpam-5901	280	49	)	)	PUNCT
ejpam-5901	280	50	)	)	PUNCT
ejpam-5901	281	1	+	+	CCONJ
ejpam-5901	281	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	281	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	281	4	)	)	PUNCT
ejpam-5901	281	5	∫	∫	PROPN
ejpam-5901	281	6	t	t	PROPN
ejpam-5901	281	7	0	0	NUM
ejpam-5901	282	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	282	2	ϵ)ϱ1−1(w1(ϵ	ϵ)ϱ1−1(w1(ϵ	PROPN
ejpam-5901	282	3	,	,	PUNCT
ejpam-5901	282	4	s(ϵ))−w1(ϵ	s(ϵ))−w1(ϵ	NOUN
ejpam-5901	282	5	,	,	PUNCT
ejpam-5901	282	6	s̃(ϵ)))dϵ∥	s̃(ϵ)))dϵ∥	PROPN
ejpam-5901	282	7	≤	≤	PROPN
ejpam-5901	282	8	ϱ2(1−	ϱ2(1−	VERB
ejpam-5901	282	9	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	282	10	ϱ2−1	ϱ2−1	ADP
ejpam-5901	282	11	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	282	12	)	)	PUNCT
ejpam-5901	282	13	∥w1(t	∥w1(t	ADJ
ejpam-5901	282	14	,	,	PUNCT
ejpam-5901	282	15	s(t))−w1(t	s(t))−w1(t	NUM
ejpam-5901	282	16	,	,	PUNCT
ejpam-5901	282	17	s̃(t))∥	s̃(t))∥	PROPN
ejpam-5901	282	18	+	+	CCONJ
ejpam-5901	282	19	ϱ1ϱ2	ϱ1ϱ2	PROPN
ejpam-5901	282	20	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	282	21	)	)	PUNCT
ejpam-5901	282	22	∫	∫	PROPN
ejpam-5901	283	1	t	t	PROPN
ejpam-5901	283	2	0	0	NUM
ejpam-5901	283	3	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	283	4	ϵ)ϱ1−1∥w1(ϵ	ϵ)ϱ1−1∥w1(ϵ	PROPN
ejpam-5901	283	5	,	,	PUNCT
ejpam-5901	283	6	s(ϵ))−w1(ϵ	s(ϵ))−w1(ϵ	NOUN
ejpam-5901	283	7	,	,	PUNCT
ejpam-5901	283	8	s̃(ϵ))∥dϵ	s̃(ϵ))∥dϵ	ADJ
ejpam-5901	283	9	≤	≤	NOUN
ejpam-5901	283	10	ϱ2(1−	ϱ2(1−	VERB
ejpam-5901	283	11	ϱ1)t2	ϱ1)t2	PROPN
ejpam-5901	283	12	−	−	PROPN
ejpam-5901	283	13	1	1	NUM
ejpam-5901	283	14	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	283	15	)	)	PUNCT
ejpam-5901	283	16	φ1∥s	φ1∥s	NOUN
ejpam-5901	283	17	−	−	PROPN
ejpam-5901	283	18	s̃∥	s̃∥	PUNCT
ejpam-5901	283	19	+	+	CCONJ
ejpam-5901	283	20	ϱ1ϱ2	ϱ1ϱ2	PROPN
ejpam-5901	283	21	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	283	22	)	)	PUNCT
ejpam-5901	283	23	∫	∫	PROPN
ejpam-5901	284	1	t	t	PROPN
ejpam-5901	284	2	0	0	NUM
ejpam-5901	285	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	285	2	ϵ)ϱ1−1φ1∥s	ϵ)ϱ1−1φ1∥s	PROPN
ejpam-5901	286	1	−	−	PROPN
ejpam-5901	286	2	s̃∥dϵ	s̃∥dϵ	PROPN
ejpam-5901	286	3	≤	≤	NUM
ejpam-5901	286	4	(	(	PUNCT
ejpam-5901	286	5	ϱ2(1−	ϱ2(1−	ADJ
ejpam-5901	286	6	ϱ1	ϱ1	NOUN
ejpam-5901	286	7	)	)	PUNCT
ejpam-5901	287	1	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	287	2	)	)	PUNCT
ejpam-5901	288	1	+	+	CCONJ
ejpam-5901	288	2	ϱ1ϱ2γ(ϱ2	ϱ1ϱ2γ(ϱ2	NOUN
ejpam-5901	288	3	)	)	PUNCT
ejpam-5901	288	4	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	PUNCT
ejpam-5901	289	1	+	+	NUM
ejpam-5901	289	2	ϱ2	ϱ2	NOUN
ejpam-5901	289	3	)	)	PUNCT
ejpam-5901	289	4	)	)	PUNCT
ejpam-5901	289	5	φ1∥s	φ1∥s	NOUN
ejpam-5901	289	6	−	−	PROPN
ejpam-5901	289	7	s̃∥.	s̃∥.	X
ejpam-5901	289	8	the	the	DET
ejpam-5901	289	9	inequality	inequality	NOUN
ejpam-5901	289	10	above	above	ADV
ejpam-5901	289	11	can	can	AUX
ejpam-5901	289	12	be	be	AUX
ejpam-5901	289	13	further	far	ADV
ejpam-5901	289	14	simplified	simplify	VERB
ejpam-5901	289	15	in	in	ADP
ejpam-5901	289	16	the	the	DET
ejpam-5901	289	17	following	following	ADJ
ejpam-5901	289	18	way	way	NOUN
ejpam-5901	289	19	:	:	PUNCT
ejpam-5901	289	20	[	[	PUNCT
ejpam-5901	289	21	1−	1−	NUM
ejpam-5901	289	22	(	(	PUNCT
ejpam-5901	289	23	ϱ2(1−	ϱ2(1−	ADJ
ejpam-5901	289	24	ϱ1	ϱ1	NOUN
ejpam-5901	289	25	)	)	PUNCT
ejpam-5901	290	1	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	290	2	)	)	PUNCT
ejpam-5901	291	1	+	+	CCONJ
ejpam-5901	291	2	ϱ1ϱ2γ(ϱ2	ϱ1ϱ2γ(ϱ2	NOUN
ejpam-5901	291	3	)	)	PUNCT
ejpam-5901	291	4	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	PUNCT
ejpam-5901	292	1	+	+	NUM
ejpam-5901	292	2	ϱ2	ϱ2	NOUN
ejpam-5901	292	3	)	)	PUNCT
ejpam-5901	292	4	)	)	PUNCT
ejpam-5901	293	1	ϱ1	ϱ1	NOUN
ejpam-5901	293	2	]	]	PUNCT
ejpam-5901	294	1	∥s	∥s	PROPN
ejpam-5901	294	2	−	−	PROPN
ejpam-5901	294	3	s̃∥	s̃∥	PUNCT
ejpam-5901	294	4	≤	≤	NOUN
ejpam-5901	294	5	0	0	NUM
ejpam-5901	294	6	.	.	PUNCT
ejpam-5901	295	1	based	base	VERB
ejpam-5901	295	2	on	on	ADP
ejpam-5901	295	3	this	this	DET
ejpam-5901	295	4	inequality	inequality	NOUN
ejpam-5901	295	5	,	,	PUNCT
ejpam-5901	295	6	we	we	PRON
ejpam-5901	295	7	can	can	AUX
ejpam-5901	295	8	write	write	VERB
ejpam-5901	295	9	that	that	DET
ejpam-5901	295	10	∥s	∥s	NOUN
ejpam-5901	295	11	−	−	PROPN
ejpam-5901	295	12	s̃∥	s̃∥	PUNCT
ejpam-5901	295	13	=	=	SYM
ejpam-5901	295	14	0	0	X
ejpam-5901	295	15	.	.	PUNCT
ejpam-5901	296	1	it	it	PRON
ejpam-5901	296	2	then	then	ADV
ejpam-5901	296	3	follows	follow	VERB
ejpam-5901	296	4	that	that	DET
ejpam-5901	296	5	s	s	PART
ejpam-5901	296	6	=	=	PUNCT
ejpam-5901	296	7	s̃.	s̃.	PROPN
ejpam-5901	296	8	similarly	similarly	ADV
ejpam-5901	296	9	,	,	PUNCT
ejpam-5901	296	10	one	one	PRON
ejpam-5901	296	11	can	can	AUX
ejpam-5901	296	12	obtain	obtain	VERB
ejpam-5901	296	13	c	c	NOUN
ejpam-5901	296	14	=	=	SYM
ejpam-5901	296	15	c̃	c̃	PROPN
ejpam-5901	296	16	,	,	PUNCT
ejpam-5901	296	17	i	i	PRON
ejpam-5901	296	18	=	=	PUNCT
ejpam-5901	296	19	ĩ	ĩ	PROPN
ejpam-5901	296	20	,	,	PUNCT
ejpam-5901	296	21	and	and	CCONJ
ejpam-5901	296	22	r	r	NOUN
ejpam-5901	296	23	=	=	SYM
ejpam-5901	296	24	r̃	r̃	NOUN
ejpam-5901	296	25	by	by	ADP
ejpam-5901	296	26	repeating	repeat	VERB
ejpam-5901	296	27	this	this	DET
ejpam-5901	296	28	process	process	NOUN
ejpam-5901	296	29	.	.	PUNCT
ejpam-5901	297	1	this	this	PRON
ejpam-5901	297	2	completes	complete	VERB
ejpam-5901	297	3	the	the	DET
ejpam-5901	297	4	proof	proof	NOUN
ejpam-5901	297	5	.	.	PUNCT
ejpam-5901	298	1	6	6	X
ejpam-5901	298	2	.	.	X
ejpam-5901	298	3	stability	stability	NOUN
ejpam-5901	298	4	analysis	analysis	NOUN
ejpam-5901	298	5	when	when	SCONJ
ejpam-5901	298	6	i	i	PRON
ejpam-5901	298	7	=	=	SYM
ejpam-5901	298	8	c	c	NOUN
ejpam-5901	298	9	=	=	SYM
ejpam-5901	298	10	0	0	PROPN
ejpam-5901	298	11	,	,	PUNCT
ejpam-5901	298	12	one	one	NOUN
ejpam-5901	298	13	obtains	obtain	VERB
ejpam-5901	298	14	the	the	DET
ejpam-5901	298	15	disease	disease	NOUN
ejpam-5901	298	16	-	-	PUNCT
ejpam-5901	298	17	free	free	ADJ
ejpam-5901	298	18	equilibrium	equilibrium	NOUN
ejpam-5901	298	19	point	point	NOUN
ejpam-5901	298	20	e0	e0	PROPN
ejpam-5901	298	21	=	=	PUNCT
ejpam-5901	298	22	(	(	PUNCT
ejpam-5901	298	23	πµ	πµ	PROPN
ejpam-5901	298	24	,	,	PUNCT
ejpam-5901	298	25	0	0	NUM
ejpam-5901	298	26	,	,	PUNCT
ejpam-5901	298	27	0	0	NUM
ejpam-5901	298	28	,	,	PUNCT
ejpam-5901	298	29	0	0	NUM
ejpam-5901	298	30	)	)	PUNCT
ejpam-5901	298	31	.	.	PUNCT
ejpam-5901	299	1	for	for	ADP
ejpam-5901	299	2	i∗	i∗	NOUN
ejpam-5901	299	3	>	>	X
ejpam-5901	299	4	0	0	NUM
ejpam-5901	299	5	,	,	PUNCT
ejpam-5901	299	6	and	and	CCONJ
ejpam-5901	299	7	taking	take	VERB
ejpam-5901	299	8	ff−abdϱ1,ϱ2	ff−abdϱ1,ϱ2	PROPN
ejpam-5901	299	9	t	t	PROPN
ejpam-5901	299	10	s(t	s(t	PROPN
ejpam-5901	299	11	)	)	PUNCT
ejpam-5901	299	12	=	=	SYM
ejpam-5901	299	13	0	0	NUM
ejpam-5901	299	14	,	,	PUNCT
ejpam-5901	299	15	ff−abdϱ1,ϱ2	ff−abdϱ1,ϱ2	PROPN
ejpam-5901	299	16	t	t	PROPN
ejpam-5901	299	17	c(t	c(t	PROPN
ejpam-5901	299	18	)	)	PUNCT
ejpam-5901	299	19	=	=	SYM
ejpam-5901	299	20	0	0	NUM
ejpam-5901	299	21	,	,	PUNCT
ejpam-5901	299	22	ff−abdϱ1,ϱ2	ff−abdϱ1,ϱ2	PROPN
ejpam-5901	299	23	t	t	PROPN
ejpam-5901	299	24	i(t	i(t	PROPN
ejpam-5901	299	25	)	)	PUNCT
ejpam-5901	299	26	=	=	SYM
ejpam-5901	299	27	0	0	PROPN
ejpam-5901	299	28	,	,	PUNCT
ejpam-5901	299	29	s.	s.	PROPN
ejpam-5901	299	30	saber	saber	PROPN
ejpam-5901	299	31	,	,	PUNCT
ejpam-5901	299	32	a.	a.	NOUN
ejpam-5901	299	33	a.	a.	NOUN
ejpam-5901	299	34	alahmari	alahmari	PROPN
ejpam-5901	299	35	/	/	SYM
ejpam-5901	299	36	eur	eur	PROPN
ejpam-5901	299	37	.	.	PUNCT
ejpam-5901	300	1	j.	j.	PROPN
ejpam-5901	300	2	pure	pure	PROPN
ejpam-5901	300	3	appl	appl	PROPN
ejpam-5901	300	4	.	.	PROPN
ejpam-5901	300	5	math	math	PROPN
ejpam-5901	300	6	,	,	PUNCT
ejpam-5901	300	7	18	18	NUM
ejpam-5901	300	8	(	(	PUNCT
ejpam-5901	300	9	2	2	NUM
ejpam-5901	300	10	)	)	PUNCT
ejpam-5901	300	11	(	(	PUNCT
ejpam-5901	300	12	2025	2025	NUM
ejpam-5901	300	13	)	)	PUNCT
ejpam-5901	300	14	,	,	PUNCT
ejpam-5901	300	15	5901	5901	NUM
ejpam-5901	300	16	13	13	NUM
ejpam-5901	300	17	of	of	ADP
ejpam-5901	300	18	23	23	NUM
ejpam-5901	300	19	ff−abdϱ1,ϱ2	ff−abdϱ1,ϱ2	NOUN
ejpam-5901	300	20	t	t	PROPN
ejpam-5901	300	21	r(t	r(t	NOUN
ejpam-5901	300	22	)	)	PUNCT
ejpam-5901	300	23	=	=	SYM
ejpam-5901	301	1	0	0	X
ejpam-5901	301	2	.	.	PUNCT
ejpam-5901	302	1	with	with	ADP
ejpam-5901	302	2	ℓ1	ℓ1	NOUN
ejpam-5901	302	3	=	=	SYM
ejpam-5901	302	4	ϑπ+(1−ϑ)(π+β+µ	ϑπ+(1−ϑ)(π+β+µ	PROPN
ejpam-5901	302	5	)	)	PUNCT
ejpam-5901	302	6	(	(	PUNCT
ejpam-5901	302	7	µ+τ+σ	µ+τ+σ	NOUN
ejpam-5901	302	8	)	)	PUNCT
ejpam-5901	302	9	,	,	PUNCT
ejpam-5901	302	10	one	one	PRON
ejpam-5901	302	11	obtains	obtain	VERB
ejpam-5901	302	12	the	the	DET
ejpam-5901	302	13	endemic	endemic	ADJ
ejpam-5901	302	14	equilibrium	equilibrium	NOUN
ejpam-5901	302	15	point	point	NOUN
ejpam-5901	302	16	e∗	e∗	NOUN
ejpam-5901	302	17	=	=	SYM
ejpam-5901	302	18	(	(	PUNCT
ejpam-5901	302	19	s∗,c∗	s∗,c∗	PROPN
ejpam-5901	302	20	,	,	PUNCT
ejpam-5901	302	21	i∗,r∗	i∗,r∗	PROPN
ejpam-5901	302	22	)	)	PUNCT
ejpam-5901	302	23	,	,	PUNCT
ejpam-5901	302	24	with	with	ADP
ejpam-5901	302	25	s∗	s∗	PROPN
ejpam-5901	302	26	=	=	SYM
ejpam-5901	302	27	n(π+β+µ	n(π+β+µ	NOUN
ejpam-5901	302	28	)	)	PUNCT
ejpam-5901	303	1	ℓ1+ϖ	ℓ1+ϖ	ADP
ejpam-5901	303	2	,	,	PUNCT
ejpam-5901	303	3	c∗	c∗	PROPN
ejpam-5901	303	4	=	=	SYM
ejpam-5901	303	5	(	(	PUNCT
ejpam-5901	303	6	µ+η)(π(ℓ1+ϖ)−µn(π+β+µ	µ+η)(π(ℓ1+ϖ)−µn(π+β+µ	PROPN
ejpam-5901	303	7	)	)	PUNCT
ejpam-5901	303	8	)	)	PUNCT
ejpam-5901	303	9	(	(	PUNCT
ejpam-5901	303	10	ℓ1+ϖ)(δ(π+β+µ)(µ+η)−η(ϱ2+τℓ1	ℓ1+ϖ)(δ(π+β+µ)(µ+η)−η(ϱ2+τℓ1	PROPN
ejpam-5901	303	11	)	)	PUNCT
ejpam-5901	303	12	)	)	PUNCT
ejpam-5901	303	13	,	,	PUNCT
ejpam-5901	303	14	i∗	i∗	NOUN
ejpam-5901	303	15	=	=	SYM
ejpam-5901	303	16	ℓ1(µ+η)(π(ℓ1+ϖ)−µn(π+β+µ	ℓ1(µ+η)(π(ℓ1+ϖ)−µn(π+β+µ	PROPN
ejpam-5901	303	17	)	)	PUNCT
ejpam-5901	303	18	)	)	PUNCT
ejpam-5901	303	19	(	(	PUNCT
ejpam-5901	303	20	ℓ1+ϖ)(δ(π+β+µ)(µ+η)−η(ϱ2+τℓ1	ℓ1+ϖ)(δ(π+β+µ)(µ+η)−η(ϱ2+τℓ1	PROPN
ejpam-5901	303	21	)	)	PUNCT
ejpam-5901	303	22	)	)	PUNCT
ejpam-5901	303	23	,	,	PUNCT
ejpam-5901	303	24	r∗	r∗	PROPN
ejpam-5901	303	25	=	=	SYM
ejpam-5901	303	26	(	(	PUNCT
ejpam-5901	303	27	ϱ2+τℓ1)(π(ℓ1+ϖ)−µn(π+β+µ	ϱ2+τℓ1)(π(ℓ1+ϖ)−µn(π+β+µ	NUM
ejpam-5901	303	28	)	)	PUNCT
ejpam-5901	303	29	)	)	PUNCT
ejpam-5901	303	30	(	(	PUNCT
ejpam-5901	303	31	ℓ1+ϖ)(δ(π+β+µ)(µ+η)−η(ϱ2+τℓ1	ℓ1+ϖ)(δ(π+β+µ)(µ+η)−η(ϱ2+τℓ1	PROPN
ejpam-5901	303	32	)	)	PUNCT
ejpam-5901	303	33	)	)	PUNCT
ejpam-5901	303	34	.	.	PUNCT
ejpam-5901	304	1	according	accord	VERB
ejpam-5901	304	2	to	to	ADP
ejpam-5901	304	3	[	[	X
ejpam-5901	304	4	53	53	NUM
ejpam-5901	304	5	]	]	PUNCT
ejpam-5901	304	6	,	,	PUNCT
ejpam-5901	304	7	the	the	DET
ejpam-5901	304	8	basic	basic	ADJ
ejpam-5901	304	9	reproduction	reproduction	NOUN
ejpam-5901	304	10	number	number	NOUN
ejpam-5901	304	11	of	of	ADP
ejpam-5901	304	12	the	the	DET
ejpam-5901	304	13	fractal	fractal	ADJ
ejpam-5901	304	14	-	-	PUNCT
ejpam-5901	304	15	fractional	fractional	ADJ
ejpam-5901	304	16	model	model	NOUN
ejpam-5901	304	17	(	(	PUNCT
ejpam-5901	304	18	2	2	NUM
ejpam-5901	304	19	)	)	PUNCT
ejpam-5901	304	20	is	be	AUX
ejpam-5901	304	21	r0	r0	NOUN
ejpam-5901	304	22	=	=	SYM
ejpam-5901	304	23	(	(	PUNCT
ejpam-5901	304	24	ϖϑ(µ+	ϖϑ(µ+	PROPN
ejpam-5901	304	25	τ	τ	PROPN
ejpam-5901	304	26	+	+	PROPN
ejpam-5901	304	27	σ	σ	PROPN
ejpam-5901	304	28	)	)	PUNCT
ejpam-5901	304	29	+	+	CCONJ
ejpam-5901	304	30	(	(	PUNCT
ejpam-5901	304	31	1−	1−	NUM
ejpam-5901	304	32	ϑ)((πϖ	ϑ)((πϖ	ADJ
ejpam-5901	304	33	+	+	CCONJ
ejpam-5901	304	34	(	(	PUNCT
ejpam-5901	304	35	π	π	X
ejpam-5901	304	36	+	+	X
ejpam-5901	304	37	β	β	X
ejpam-5901	304	38	+	+	CCONJ
ejpam-5901	304	39	µ)))δ	µ)))δ	PROPN
ejpam-5901	304	40	s0	s0	PROPN
ejpam-5901	304	41	n(π	n(π	PROPN
ejpam-5901	304	42	+	+	CCONJ
ejpam-5901	304	43	β	β	X
ejpam-5901	304	44	+	+	CCONJ
ejpam-5901	304	45	µ)(µ+	µ)(µ+	X
ejpam-5901	304	46	τ	τ	PROPN
ejpam-5901	304	47	+	+	PROPN
ejpam-5901	304	48	σ	σ	PROPN
ejpam-5901	304	49	)	)	PUNCT
ejpam-5901	304	50	.	.	PUNCT
ejpam-5901	305	1	hence	hence	ADV
ejpam-5901	305	2	according	accord	VERB
ejpam-5901	305	3	to	to	ADP
ejpam-5901	305	4	the	the	DET
ejpam-5901	305	5	routh	routh	PROPN
ejpam-5901	305	6	-	-	PUNCT
ejpam-5901	305	7	hurwitz	hurwitz	PROPN
ejpam-5901	305	8	criteria	criterion	NOUN
ejpam-5901	305	9	and	and	CCONJ
ejpam-5901	305	10	as	as	ADP
ejpam-5901	305	11	in	in	ADP
ejpam-5901	305	12	[	[	PUNCT
ejpam-5901	305	13	62	62	NUM
ejpam-5901	305	14	]	]	PUNCT
ejpam-5901	305	15	,	,	PUNCT
ejpam-5901	305	16	we	we	PRON
ejpam-5901	305	17	have	have	VERB
ejpam-5901	305	18	two	two	NUM
ejpam-5901	305	19	cases	case	NOUN
ejpam-5901	305	20	:	:	PUNCT
ejpam-5901	305	21	(	(	PUNCT
ejpam-5901	305	22	i	i	NOUN
ejpam-5901	305	23	)	)	PUNCT
ejpam-5901	305	24	the	the	DET
ejpam-5901	305	25	pneumonia	pneumonia	NOUN
ejpam-5901	305	26	trivial	trivial	ADJ
ejpam-5901	305	27	equilibrium	equilibrium	NOUN
ejpam-5901	305	28	,	,	PUNCT
ejpam-5901	305	29	denoted	denote	VERB
ejpam-5901	305	30	by	by	ADP
ejpam-5901	305	31	e0	e0	PROPN
ejpam-5901	305	32	=	=	PUNCT
ejpam-5901	305	33	(	(	PUNCT
ejpam-5901	305	34	0	0	NUM
ejpam-5901	305	35	,	,	PUNCT
ejpam-5901	305	36	0	0	NUM
ejpam-5901	305	37	,	,	PUNCT
ejpam-5901	305	38	0	0	NUM
ejpam-5901	305	39	,	,	PUNCT
ejpam-5901	305	40	0	0	NUM
ejpam-5901	305	41	)	)	PUNCT
ejpam-5901	305	42	,	,	PUNCT
ejpam-5901	305	43	is	be	AUX
ejpam-5901	305	44	stable	stable	ADJ
ejpam-5901	305	45	locally	locally	ADV
ejpam-5901	305	46	asymptoticallyin	asymptoticallyin	PROPN
ejpam-5901	306	1	if	if	SCONJ
ejpam-5901	306	2	r0	r0	NOUN
ejpam-5901	306	3	<	<	X
ejpam-5901	306	4	1	1	NUM
ejpam-5901	306	5	,	,	PUNCT
ejpam-5901	306	6	but	but	CCONJ
ejpam-5901	306	7	it	it	PRON
ejpam-5901	306	8	is	be	AUX
ejpam-5901	306	9	unstable	unstable	ADJ
ejpam-5901	306	10	if	if	SCONJ
ejpam-5901	306	11	r0	r0	NOUN
ejpam-5901	306	12	>	>	X
ejpam-5901	306	13	1	1	NUM
ejpam-5901	306	14	.	.	PUNCT
ejpam-5901	306	15	(	(	PUNCT
ejpam-5901	306	16	ii	ii	NOUN
ejpam-5901	306	17	)	)	PUNCT
ejpam-5901	306	18	the	the	DET
ejpam-5901	306	19	equilibrium	equilibrium	NOUN
ejpam-5901	306	20	point	point	NOUN
ejpam-5901	306	21	e1	e1	NOUN
ejpam-5901	306	22	=	=	SYM
ejpam-5901	306	23	(	(	PUNCT
ejpam-5901	306	24	πµ	πµ	PROPN
ejpam-5901	306	25	,	,	PUNCT
ejpam-5901	306	26	0	0	NUM
ejpam-5901	306	27	,	,	PUNCT
ejpam-5901	306	28	0	0	NUM
ejpam-5901	306	29	,	,	PUNCT
ejpam-5901	306	30	0	0	NUM
ejpam-5901	306	31	)	)	PUNCT
ejpam-5901	306	32	of	of	ADP
ejpam-5901	306	33	the	the	DET
ejpam-5901	306	34	nonlinear	nonlinear	ADJ
ejpam-5901	306	35	atangana	atangana	PROPN
ejpam-5901	306	36	-	-	PUNCT
ejpam-5901	306	37	baleanu	baleanu	ADJ
ejpam-5901	306	38	fractalfractional	fractalfractional	ADJ
ejpam-5901	306	39	scir	scir	PROPN
ejpam-5901	306	40	model	model	NOUN
ejpam-5901	306	41	(	(	PUNCT
ejpam-5901	306	42	2	2	NUM
ejpam-5901	306	43	)	)	PUNCT
ejpam-5901	306	44	is	be	AUX
ejpam-5901	306	45	locally	locally	ADV
ejpam-5901	306	46	asymptotically	asymptotically	ADV
ejpam-5901	306	47	stable	stable	ADJ
ejpam-5901	306	48	if	if	SCONJ
ejpam-5901	306	49	r0	r0	NOUN
ejpam-5901	306	50	<	<	X
ejpam-5901	306	51	1	1	NUM
ejpam-5901	306	52	.	.	PUNCT
ejpam-5901	306	53	(	(	PUNCT
ejpam-5901	306	54	iii	iii	X
ejpam-5901	306	55	)	)	PUNCT
ejpam-5901	306	56	the	the	DET
ejpam-5901	306	57	equilibrium	equilibrium	NOUN
ejpam-5901	306	58	point	point	NOUN
ejpam-5901	306	59	e2	e2	PROPN
ejpam-5901	306	60	=	=	SYM
ejpam-5901	306	61	(	(	PUNCT
ejpam-5901	306	62	s∗,c∗	s∗,c∗	PROPN
ejpam-5901	306	63	,	,	PUNCT
ejpam-5901	306	64	i∗,r∗	i∗,r∗	PROPN
ejpam-5901	306	65	)	)	PUNCT
ejpam-5901	306	66	of	of	ADP
ejpam-5901	306	67	the	the	DET
ejpam-5901	306	68	nonlinear	nonlinear	ADJ
ejpam-5901	306	69	atangana	atangana	PROPN
ejpam-5901	306	70	-	-	PUNCT
ejpam-5901	306	71	baleanu	baleanu	ADJ
ejpam-5901	306	72	fractal	fractal	ADJ
ejpam-5901	306	73	-	-	PUNCT
ejpam-5901	306	74	fractional	fractional	ADJ
ejpam-5901	306	75	scir	scir	PROPN
ejpam-5901	306	76	model	model	NOUN
ejpam-5901	306	77	(	(	PUNCT
ejpam-5901	306	78	2	2	NUM
ejpam-5901	306	79	)	)	PUNCT
ejpam-5901	306	80	is	be	AUX
ejpam-5901	306	81	locally	locally	ADV
ejpam-5901	306	82	asymptotically	asymptotically	ADV
ejpam-5901	306	83	stable	stable	ADJ
ejpam-5901	306	84	if	if	SCONJ
ejpam-5901	306	85	r0	r0	NOUN
ejpam-5901	306	86	>	>	X
ejpam-5901	306	87	1	1	X
ejpam-5901	306	88	.	.	PUNCT
ejpam-5901	306	89	definition	definition	NOUN
ejpam-5901	306	90	3	3	NUM
ejpam-5901	306	91	(	(	PUNCT
ejpam-5901	306	92	[	[	X
ejpam-5901	306	93	63	63	NUM
ejpam-5901	306	94	]	]	PUNCT
ejpam-5901	306	95	,	,	PUNCT
ejpam-5901	306	96	[	[	X
ejpam-5901	306	97	64	64	NUM
ejpam-5901	306	98	]	]	SYM
ejpam-5901	306	99	)	)	PUNCT
ejpam-5901	306	100	.	.	PUNCT
ejpam-5901	307	1	model	model	NOUN
ejpam-5901	307	2	(	(	PUNCT
ejpam-5901	307	3	2	2	X
ejpam-5901	307	4	)	)	PUNCT
ejpam-5901	307	5	is	be	AUX
ejpam-5901	307	6	hyers	hyer	NOUN
ejpam-5901	307	7	-	-	PUNCT
ejpam-5901	307	8	ulam	ulam	X
ejpam-5901	307	9	stable	stable	ADJ
ejpam-5901	307	10	if	if	SCONJ
ejpam-5901	307	11	vi	vi	PROPN
ejpam-5901	307	12	>	>	X
ejpam-5901	307	13	0	0	PUNCT
ejpam-5901	308	1	for	for	ADP
ejpam-5901	308	2	i	i	PROPN
ejpam-5901	308	3	∈	∈	PROPN
ejpam-5901	309	1	n4	n4	PROPN
ejpam-5901	309	2	i	i	PRON
ejpam-5901	309	3	,	,	PUNCT
ejpam-5901	309	4	satisfying	satisfy	VERB
ejpam-5901	309	5	for	for	ADP
ejpam-5901	309	6	every	every	DET
ejpam-5901	309	7	δi	δi	PROPN
ejpam-5901	309	8	,	,	PUNCT
ejpam-5901	309	9	i	i	PRON
ejpam-5901	309	10	∈	∈	PROPN
ejpam-5901	310	1	n4	n4	PROPN
ejpam-5901	311	1	i	i	PRON
ejpam-5901	311	2	|s(t)−	|s(t)−	PROPN
ejpam-5901	311	3	ϱ2(1−	ϱ2(1−	NOUN
ejpam-5901	311	4	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	311	5	ϱ2−1	ϱ2−1	ADP
ejpam-5901	311	6	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	311	7	)	)	PUNCT
ejpam-5901	311	8	w1(t	w1(t	PROPN
ejpam-5901	311	9	,	,	PUNCT
ejpam-5901	311	10	s(t))−	s(t))−	NOUN
ejpam-5901	311	11	ϱ1ϱ2	ϱ1ϱ2	PUNCT
ejpam-5901	311	12	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	311	13	)	)	PUNCT
ejpam-5901	311	14	∫	∫	PROPN
ejpam-5901	312	1	t	t	PROPN
ejpam-5901	312	2	0	0	NUM
ejpam-5901	313	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	313	2	ϵ)ϱ1−1w1(ϵ	ϵ)ϱ1−1w1(ϵ	PROPN
ejpam-5901	313	3	,	,	PUNCT
ejpam-5901	313	4	s(ϵ))dϵ|	s(ϵ))dϵ|	ADJ
ejpam-5901	313	5	≤	≤	NUM
ejpam-5901	313	6	δ1	δ1	NOUN
ejpam-5901	313	7	,	,	PUNCT
ejpam-5901	313	8	|c(t)−	|c(t)−	PROPN
ejpam-5901	313	9	ϱ2(1−	ϱ2(1−	PROPN
ejpam-5901	313	10	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	313	11	ϱ2−1	ϱ2−1	ADP
ejpam-5901	313	12	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	313	13	)	)	PUNCT
ejpam-5901	313	14	w2(t	w2(t	PROPN
ejpam-5901	313	15	,	,	PUNCT
ejpam-5901	313	16	c(t))−	c(t))−	NOUN
ejpam-5901	313	17	ϱ1ϱ2	ϱ1ϱ2	PROPN
ejpam-5901	313	18	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	313	19	)	)	PUNCT
ejpam-5901	314	1	∫	∫	PROPN
ejpam-5901	315	1	t	t	PROPN
ejpam-5901	315	2	0	0	NUM
ejpam-5901	316	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	316	2	ϵ)ϱ1−1w2(ϵ	ϵ)ϱ1−1w2(ϵ	NOUN
ejpam-5901	316	3	,	,	PUNCT
ejpam-5901	316	4	c(ϵ))dϵ|	c(ϵ))dϵ|	VERB
ejpam-5901	316	5	≤	≤	NUM
ejpam-5901	316	6	δ2	δ2	VERB
ejpam-5901	316	7	,	,	PUNCT
ejpam-5901	316	8	|	|	ADV
ejpam-5901	316	9	i(t)−	i(t)−	PROPN
ejpam-5901	316	10	ϱ2(1−	ϱ2(1−	VERB
ejpam-5901	316	11	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	316	12	ϱ2−1	ϱ2−1	ADP
ejpam-5901	316	13	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	316	14	)	)	PUNCT
ejpam-5901	316	15	w3(t	w3(t	PROPN
ejpam-5901	316	16	,	,	PUNCT
ejpam-5901	316	17	i(t))−	i(t))−	NOUN
ejpam-5901	316	18	ϱ1ϱ2	ϱ1ϱ2	NOUN
ejpam-5901	316	19	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	316	20	)	)	PUNCT
ejpam-5901	316	21	∫	∫	PROPN
ejpam-5901	317	1	t	t	PROPN
ejpam-5901	317	2	0	0	NUM
ejpam-5901	318	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	318	2	ϵ)ϱ1−1w3(ϵ	ϵ)ϱ1−1w3(ϵ	NOUN
ejpam-5901	318	3	,	,	PUNCT
ejpam-5901	318	4	i(ϵ))dϵ|	i(ϵ))dϵ|	NOUN
ejpam-5901	318	5	≤	≤	PROPN
ejpam-5901	318	6	δ3	δ3	PROPN
ejpam-5901	318	7	,	,	PUNCT
ejpam-5901	318	8	|r(t)−	|r(t)−	PROPN
ejpam-5901	318	9	ϱ2(1−	ϱ2(1−	VERB
ejpam-5901	318	10	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	318	11	ϱ2−1	ϱ2−1	ADP
ejpam-5901	318	12	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	318	13	)	)	PUNCT
ejpam-5901	318	14	w4(t	w4(t	PROPN
ejpam-5901	318	15	,	,	PUNCT
ejpam-5901	318	16	r(t))−	r(t))−	NOUN
ejpam-5901	318	17	ϱ1ϱ2	ϱ1ϱ2	PROPN
ejpam-5901	318	18	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	318	19	)	)	PUNCT
ejpam-5901	319	1	∫	∫	PROPN
ejpam-5901	319	2	t	t	PROPN
ejpam-5901	319	3	0	0	NUM
ejpam-5901	320	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	320	2	ϵ)ϱ1−1w4(ϵ	ϵ)ϱ1−1w4(ϵ	NOUN
ejpam-5901	320	3	,	,	PUNCT
ejpam-5901	320	4	r(ϵ))dϵ|	r(ϵ))dϵ|	ADJ
ejpam-5901	320	5	≤	≤	NOUN
ejpam-5901	320	6	δ4	δ4	NOUN
ejpam-5901	320	7	.	.	PUNCT
ejpam-5901	321	1	several	several	ADJ
ejpam-5901	321	2	approximate	approximate	ADJ
ejpam-5901	321	3	solutions	solution	NOUN
ejpam-5901	321	4	(	(	PUNCT
ejpam-5901	321	5	s1(t),c1(t	s1(t),c1(t	ADJ
ejpam-5901	321	6	)	)	PUNCT
ejpam-5901	321	7	,	,	PUNCT
ejpam-5901	321	8	i1(t),r1(t	i1(t),r1(t	PROPN
ejpam-5901	321	9	)	)	PUNCT
ejpam-5901	321	10	)	)	PUNCT
ejpam-5901	321	11	to	to	ADP
ejpam-5901	321	12	the	the	DET
ejpam-5901	321	13	model	model	NOUN
ejpam-5901	321	14	problem	problem	NOUN
ejpam-5901	321	15	(	(	PUNCT
ejpam-5901	321	16	2	2	X
ejpam-5901	321	17	)	)	PUNCT
ejpam-5901	321	18	are	be	AUX
ejpam-5901	321	19	available	available	ADJ
ejpam-5901	321	20	,	,	PUNCT
ejpam-5901	321	21	with	with	ADP
ejpam-5901	321	22	the	the	DET
ejpam-5901	321	23	following	follow	VERB
ejpam-5901	321	24	integral	integral	ADJ
ejpam-5901	321	25	equations	equation	NOUN
ejpam-5901	321	26	satisfying	satisfy	VERB
ejpam-5901	321	27	their	their	PRON
ejpam-5901	321	28	terms	term	NOUN
ejpam-5901	321	29	s1(t	s1(t	PART
ejpam-5901	321	30	)	)	PUNCT
ejpam-5901	321	31	=	=	PUNCT
ejpam-5901	321	32	ϱ2(1−	ϱ2(1−	PROPN
ejpam-5901	321	33	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	321	34	ϱ2−1	ϱ2−1	ADP
ejpam-5901	321	35	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	321	36	)	)	PUNCT
ejpam-5901	321	37	w1(t	w1(t	PROPN
ejpam-5901	321	38	,	,	PUNCT
ejpam-5901	321	39	s1(t	s1(t	X
ejpam-5901	321	40	)	)	PUNCT
ejpam-5901	321	41	)	)	PUNCT
ejpam-5901	322	1	+	+	CCONJ
ejpam-5901	322	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	322	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	322	4	)	)	PUNCT
ejpam-5901	322	5	∫	∫	PROPN
ejpam-5901	322	6	t	t	PROPN
ejpam-5901	322	7	0	0	NUM
ejpam-5901	323	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	323	2	ϵ)ϱ1−1w1(ϵ,s1(ϵ))dϵ	ϵ)ϱ1−1w1(ϵ,s1(ϵ))dϵ	PUNCT
ejpam-5901	324	1	c1(t	c1(t	NOUN
ejpam-5901	324	2	)	)	PUNCT
ejpam-5901	324	3	=	=	PUNCT
ejpam-5901	324	4	ϱ2(1−	ϱ2(1−	PROPN
ejpam-5901	324	5	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	324	6	ϱ2−1	ϱ2−1	ADP
ejpam-5901	324	7	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	324	8	)	)	PUNCT
ejpam-5901	324	9	w2(t	w2(t	PROPN
ejpam-5901	324	10	,	,	PUNCT
ejpam-5901	324	11	c1(t	c1(t	NOUN
ejpam-5901	324	12	)	)	PUNCT
ejpam-5901	324	13	)	)	PUNCT
ejpam-5901	325	1	+	+	CCONJ
ejpam-5901	325	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	325	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	325	4	)	)	PUNCT
ejpam-5901	325	5	∫	∫	PROPN
ejpam-5901	325	6	t	t	PROPN
ejpam-5901	325	7	0	0	NUM
ejpam-5901	326	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	326	2	ϵ)ϱ1−1w2(ϵ,c1(ϵ))dϵ	ϵ)ϱ1−1w2(ϵ,c1(ϵ))dϵ	PROPN
ejpam-5901	326	3	,	,	PUNCT
ejpam-5901	326	4	i1(t	i1(t	X
ejpam-5901	326	5	)	)	PUNCT
ejpam-5901	326	6	=	=	SYM
ejpam-5901	326	7	ϱ2(1−	ϱ2(1−	PROPN
ejpam-5901	326	8	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	326	9	ϱ2−1	ϱ2−1	ADP
ejpam-5901	326	10	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	326	11	)	)	PUNCT
ejpam-5901	326	12	w1(t	w1(t	PROPN
ejpam-5901	326	13	,	,	PUNCT
ejpam-5901	326	14	s1(t	s1(t	X
ejpam-5901	326	15	)	)	PUNCT
ejpam-5901	326	16	)	)	PUNCT
ejpam-5901	327	1	+	+	CCONJ
ejpam-5901	327	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	327	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	327	4	)	)	PUNCT
ejpam-5901	327	5	∫	∫	PROPN
ejpam-5901	327	6	t	t	PROPN
ejpam-5901	327	7	0	0	NUM
ejpam-5901	328	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	328	2	ϵ)ϱ1−1w3(ϵ	ϵ)ϱ1−1w3(ϵ	NOUN
ejpam-5901	328	3	,	,	PUNCT
ejpam-5901	328	4	i1(ϵ))dϵ	i1(ϵ))dϵ	NOUN
ejpam-5901	328	5	,	,	PUNCT
ejpam-5901	328	6	r1(t	r1(t	PROPN
ejpam-5901	328	7	)	)	PUNCT
ejpam-5901	328	8	=	=	SYM
ejpam-5901	328	9	ϱ2(1−	ϱ2(1−	PROPN
ejpam-5901	328	10	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	328	11	ϱ2−1	ϱ2−1	ADP
ejpam-5901	328	12	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	328	13	)	)	PUNCT
ejpam-5901	328	14	w4(t	w4(t	PROPN
ejpam-5901	328	15	,	,	PUNCT
ejpam-5901	328	16	r1(t	r1(t	PROPN
ejpam-5901	328	17	)	)	PUNCT
ejpam-5901	328	18	)	)	PUNCT
ejpam-5901	329	1	+	+	CCONJ
ejpam-5901	329	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	329	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	329	4	)	)	PUNCT
ejpam-5901	329	5	∫	∫	PROPN
ejpam-5901	329	6	t	t	PROPN
ejpam-5901	329	7	0	0	NUM
ejpam-5901	330	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	330	2	ϵ)ϱ1−1w4(ϵ,r1(ϵ))dϵ	ϵ)ϱ1−1w4(ϵ,r1(ϵ))dϵ	PROPN
ejpam-5901	330	3	,	,	PUNCT
ejpam-5901	330	4	such	such	ADJ
ejpam-5901	330	5	that	that	PRON
ejpam-5901	330	6	|s(t)−	|s(t)−	NUM
ejpam-5901	330	7	s1(t)|	s1(t)|	PROPN
ejpam-5901	330	8	≤	≤	NUM
ejpam-5901	330	9	τ1δ1	τ1δ1	NOUN
ejpam-5901	330	10	,	,	PUNCT
ejpam-5901	330	11	|	|	ADV
ejpam-5901	330	12	i(t)−	i(t)−	PROPN
ejpam-5901	330	13	i1(t)|	i1(t)|	PROPN
ejpam-5901	330	14	≤	≤	PROPN
ejpam-5901	330	15	τ2δ2	τ2δ2	PROPN
ejpam-5901	330	16	,	,	PUNCT
ejpam-5901	330	17	|s(t)−	|s(t)−	PROPN
ejpam-5901	330	18	s1(t)|	s1(t)|	NOUN
ejpam-5901	330	19	≤	≤	ADJ
ejpam-5901	330	20	τ3δ3	τ3δ3	PUNCT
ejpam-5901	330	21	,	,	PUNCT
ejpam-5901	330	22	|	|	ADV
ejpam-5901	330	23	i(t)−	i(t)−	PROPN
ejpam-5901	330	24	i1(t)|	i1(t)|	PROPN
ejpam-5901	330	25	≤	≤	PROPN
ejpam-5901	330	26	τ4δ4	τ4δ4	X
ejpam-5901	330	27	.	.	PUNCT
ejpam-5901	331	1	(	(	PUNCT
ejpam-5901	331	2	4	4	X
ejpam-5901	331	3	)	)	PUNCT
ejpam-5901	331	4	s.	s.	PROPN
ejpam-5901	331	5	saber	saber	PROPN
ejpam-5901	331	6	,	,	PUNCT
ejpam-5901	331	7	a.	a.	NOUN
ejpam-5901	331	8	a.	a.	NOUN
ejpam-5901	331	9	alahmari	alahmari	PROPN
ejpam-5901	331	10	/	/	SYM
ejpam-5901	331	11	eur	eur	PROPN
ejpam-5901	331	12	.	.	PUNCT
ejpam-5901	332	1	j.	j.	PROPN
ejpam-5901	332	2	pure	pure	PROPN
ejpam-5901	332	3	appl	appl	PROPN
ejpam-5901	332	4	.	.	PROPN
ejpam-5901	332	5	math	math	PROPN
ejpam-5901	332	6	,	,	PUNCT
ejpam-5901	332	7	18	18	NUM
ejpam-5901	332	8	(	(	PUNCT
ejpam-5901	332	9	2	2	NUM
ejpam-5901	332	10	)	)	PUNCT
ejpam-5901	332	11	(	(	PUNCT
ejpam-5901	332	12	2025	2025	NUM
ejpam-5901	332	13	)	)	PUNCT
ejpam-5901	332	14	,	,	PUNCT
ejpam-5901	332	15	5901	5901	NUM
ejpam-5901	332	16	14	14	NUM
ejpam-5901	332	17	of	of	ADP
ejpam-5901	332	18	23	23	NUM
ejpam-5901	332	19	theorem	theorem	NOUN
ejpam-5901	332	20	1	1	NUM
ejpam-5901	332	21	.	.	PUNCT
ejpam-5901	333	1	if	if	SCONJ
ejpam-5901	333	2	(	(	PUNCT
ejpam-5901	333	3	4	4	X
ejpam-5901	333	4	)	)	PUNCT
ejpam-5901	333	5	is	be	AUX
ejpam-5901	333	6	true	true	ADJ
ejpam-5901	333	7	,	,	PUNCT
ejpam-5901	333	8	then	then	ADV
ejpam-5901	333	9	model	model	NOUN
ejpam-5901	333	10	(	(	PUNCT
ejpam-5901	333	11	2	2	X
ejpam-5901	333	12	)	)	PUNCT
ejpam-5901	333	13	satisfies	satisfy	VERB
ejpam-5901	333	14	the	the	DET
ejpam-5901	333	15	hyers	hyers	PROPN
ejpam-5901	333	16	-	-	PUNCT
ejpam-5901	333	17	ulam	ulam	PROPN
ejpam-5901	333	18	stability	stability	NOUN
ejpam-5901	333	19	condition	condition	NOUN
ejpam-5901	333	20	.	.	PUNCT
ejpam-5901	334	1	proof	proof	NOUN
ejpam-5901	334	2	.	.	PUNCT
ejpam-5901	335	1	based	base	VERB
ejpam-5901	335	2	on	on	ADP
ejpam-5901	335	3	the	the	DET
ejpam-5901	335	4	results	result	NOUN
ejpam-5901	335	5	of	of	ADP
ejpam-5901	335	6	lemma	lemma	PROPN
ejpam-5901	335	7	1	1	NUM
ejpam-5901	335	8	,	,	PUNCT
ejpam-5901	335	9	we	we	PRON
ejpam-5901	335	10	can	can	AUX
ejpam-5901	335	11	conclude	conclude	VERB
ejpam-5901	335	12	the	the	DET
ejpam-5901	335	13	following	following	NOUN
ejpam-5901	335	14	:	:	PUNCT
ejpam-5901	335	15	|s(t)−	|s(t)−	PROPN
ejpam-5901	335	16	s1(t)|	s1(t)|	NOUN
ejpam-5901	335	17	=	=	SYM
ejpam-5901	335	18	∣∣∣ϱ2(1−	∣∣∣ϱ2(1−	PROPN
ejpam-5901	335	19	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	335	20	ϱ2−1	ϱ2−1	ADP
ejpam-5901	335	21	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	335	22	)	)	PUNCT
ejpam-5901	335	23	(	(	PUNCT
ejpam-5901	335	24	w1(t	w1(t	PROPN
ejpam-5901	335	25	,	,	PUNCT
ejpam-5901	335	26	s(t))−w1(t	s(t))−w1(t	NUM
ejpam-5901	335	27	,	,	PUNCT
ejpam-5901	335	28	s1(t	s1(t	PROPN
ejpam-5901	335	29	)	)	PUNCT
ejpam-5901	335	30	)	)	PUNCT
ejpam-5901	335	31	)	)	PUNCT
ejpam-5901	336	1	+	+	CCONJ
ejpam-5901	336	2	ϱ1ϱ2	ϱ1ϱ2	X
ejpam-5901	336	3	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	336	4	)	)	PUNCT
ejpam-5901	336	5	∫	∫	PROPN
ejpam-5901	336	6	t	t	PROPN
ejpam-5901	336	7	0	0	NUM
ejpam-5901	337	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	337	2	ϵ)ϱ1−1(w1(ϵ	ϵ)ϱ1−1(w1(ϵ	PROPN
ejpam-5901	337	3	,	,	PUNCT
ejpam-5901	337	4	s(ϵ))−w1(ϵ	s(ϵ))−w1(ϵ	NOUN
ejpam-5901	337	5	,	,	PUNCT
ejpam-5901	337	6	s1(ϵ)))dϵ	s1(ϵ)))dϵ	X
ejpam-5901	337	7	∣∣∣	∣∣∣	NOUN
ejpam-5901	337	8	≤	≤	NUM
ejpam-5901	337	9	ϱ2(1−	ϱ2(1−	NOUN
ejpam-5901	337	10	ϱ1)t	ϱ1)t	PROPN
ejpam-5901	337	11	ϱ2−1	ϱ2−1	ADP
ejpam-5901	337	12	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	337	13	)	)	PUNCT
ejpam-5901	337	14	η1∥s	η1∥s	NOUN
ejpam-5901	337	15	−	−	PROPN
ejpam-5901	337	16	s1∥	s1∥	PROPN
ejpam-5901	337	17	+	+	CCONJ
ejpam-5901	337	18	ϱ1ϱ2	ϱ1ϱ2	PROPN
ejpam-5901	337	19	b∗(ϱ1)γ(ϱ1	b∗(ϱ1)γ(ϱ1	NUM
ejpam-5901	337	20	)	)	PUNCT
ejpam-5901	337	21	∫	∫	PROPN
ejpam-5901	338	1	t	t	PROPN
ejpam-5901	338	2	0	0	NUM
ejpam-5901	339	1	ϵϱ2−1(t−	ϵϱ2−1(t−	PROPN
ejpam-5901	340	1	ϵ)ϱ1−1η1∥s	ϵ)ϱ1−1η1∥s	NOUN
ejpam-5901	341	1	−	−	NOUN
ejpam-5901	342	1	s1∥dϵ	s1∥dϵ	ADJ
ejpam-5901	342	2	≤	≤	NUM
ejpam-5901	342	3	(	(	PUNCT
ejpam-5901	342	4	ϱ2(1−	ϱ2(1−	ADJ
ejpam-5901	342	5	ϱ1	ϱ1	NOUN
ejpam-5901	342	6	)	)	PUNCT
ejpam-5901	342	7	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	342	8	)	)	PUNCT
ejpam-5901	343	1	+	+	PUNCT
ejpam-5901	343	2	ϱ1ϱ2γ(ϱ2	ϱ1ϱ2γ(ϱ2	NOUN
ejpam-5901	343	3	)	)	PUNCT
ejpam-5901	343	4	b∗(η1)γ(ϱ1	b∗(η1)γ(ϱ1	NOUN
ejpam-5901	344	1	+	+	SYM
ejpam-5901	344	2	ϱ2	ϱ2	NOUN
ejpam-5901	344	3	)	)	PUNCT
ejpam-5901	344	4	)	)	PUNCT
ejpam-5901	345	1	η1∥s	η1∥s	NOUN
ejpam-5901	345	2	−	−	PROPN
ejpam-5901	346	1	s1∥.	s1∥.	ADP
ejpam-5901	346	2	now	now	ADV
ejpam-5901	346	3	,	,	PUNCT
ejpam-5901	346	4	let	let	VERB
ejpam-5901	346	5	η1	η1	NOUN
ejpam-5901	346	6	=	=	SYM
ejpam-5901	346	7	δ1	δ1	NOUN
ejpam-5901	346	8	,	,	PUNCT
ejpam-5901	346	9	(	(	PUNCT
ejpam-5901	346	10	ϱ2(1−ϱ1	ϱ2(1−ϱ1	PROPN
ejpam-5901	346	11	)	)	PUNCT
ejpam-5901	346	12	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	346	13	)	)	PUNCT
ejpam-5901	347	1	+	+	CCONJ
ejpam-5901	347	2	ϱ1ϱ2γ(ϱ2	ϱ1ϱ2γ(ϱ2	ADJ
ejpam-5901	347	3	)	)	PUNCT
ejpam-5901	347	4	b∗(ϱ1)γ(ϱ1+ϱ2	b∗(ϱ1)γ(ϱ1+ϱ2	PROPN
ejpam-5901	347	5	)	)	PUNCT
ejpam-5901	347	6	)	)	PUNCT
ejpam-5901	348	1	∥s	∥s	NOUN
ejpam-5901	348	2	−	−	NOUN
ejpam-5901	348	3	s1∥	s1∥	NOUN
ejpam-5901	348	4	=	=	SYM
ejpam-5901	348	5	τ1	τ1	NOUN
ejpam-5901	348	6	.	.	PUNCT
ejpam-5901	349	1	then	then	ADV
ejpam-5901	349	2	we	we	PRON
ejpam-5901	349	3	have	have	VERB
ejpam-5901	349	4	|s(t)−	|s(t)−	NUM
ejpam-5901	349	5	s1(t)|	s1(t)|	PROPN
ejpam-5901	349	6	≤	≤	NUM
ejpam-5901	349	7	τ1δ1	τ1δ1	NOUN
ejpam-5901	349	8	.	.	PUNCT
ejpam-5901	350	1	similarly	similarly	ADV
ejpam-5901	350	2	,	,	PUNCT
ejpam-5901	350	3	one	one	PRON
ejpam-5901	350	4	obtains	obtain	VERB
ejpam-5901	350	5	|c(t)−	|c(t)−	PROPN
ejpam-5901	350	6	c1(t)|	c1(t)|	ADV
ejpam-5901	350	7	≤	≤	NOUN
ejpam-5901	350	8	τ2δ2	τ2δ2	PUNCT
ejpam-5901	350	9	,	,	PUNCT
ejpam-5901	350	10	with	with	ADP
ejpam-5901	350	11	η2	η2	PROPN
ejpam-5901	350	12	=	=	SYM
ejpam-5901	350	13	δ2	δ2	VERB
ejpam-5901	350	14	,	,	PUNCT
ejpam-5901	350	15	(	(	PUNCT
ejpam-5901	350	16	ϱ2(1−ϱ1	ϱ2(1−ϱ1	PROPN
ejpam-5901	350	17	)	)	PUNCT
ejpam-5901	350	18	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	350	19	)	)	PUNCT
ejpam-5901	351	1	+	+	CCONJ
ejpam-5901	351	2	ϱ1ϱ2γ(ϱ2	ϱ1ϱ2γ(ϱ2	ADJ
ejpam-5901	351	3	)	)	PUNCT
ejpam-5901	351	4	b∗(ϱ1)γ(ϱ1+ϱ2	b∗(ϱ1)γ(ϱ1+ϱ2	NUM
ejpam-5901	351	5	)	)	PUNCT
ejpam-5901	351	6	)	)	PUNCT
ejpam-5901	352	1	∥c	∥c	PRON
ejpam-5901	352	2	−	−	NOUN
ejpam-5901	352	3	c1∥	c1∥	NOUN
ejpam-5901	352	4	=	=	SYM
ejpam-5901	352	5	τ2	τ2	PROPN
ejpam-5901	352	6	.	.	PUNCT
ejpam-5901	353	1	also	also	ADV
ejpam-5901	353	2	|	|	ADV
ejpam-5901	353	3	i(t)−	i(t)−	PROPN
ejpam-5901	353	4	i1(t)|	i1(t)|	PROPN
ejpam-5901	353	5	≤	≤	ADJ
ejpam-5901	353	6	τ3δ3	τ3δ3	PUNCT
ejpam-5901	353	7	,	,	PUNCT
ejpam-5901	353	8	with	with	ADP
ejpam-5901	353	9	η3	η3	PROPN
ejpam-5901	353	10	=	=	SYM
ejpam-5901	353	11	δ3	δ3	PROPN
ejpam-5901	353	12	,	,	PUNCT
ejpam-5901	353	13	(	(	PUNCT
ejpam-5901	353	14	ϱ2(1−ϱ1	ϱ2(1−ϱ1	PROPN
ejpam-5901	353	15	)	)	PUNCT
ejpam-5901	353	16	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	353	17	)	)	PUNCT
ejpam-5901	354	1	+	+	CCONJ
ejpam-5901	354	2	ϱ1ϱ2γ(ϱ2	ϱ1ϱ2γ(ϱ2	ADJ
ejpam-5901	354	3	)	)	PUNCT
ejpam-5901	354	4	b∗(ϱ1)γ(ϱ1+ϱ2	b∗(ϱ1)γ(ϱ1+ϱ2	NUM
ejpam-5901	354	5	)	)	PUNCT
ejpam-5901	354	6	)	)	PUNCT
ejpam-5901	355	1	∥	∥	PUNCT
ejpam-5901	356	1	i−i1∥	i−i1∥	NUM
ejpam-5901	356	2	=	=	NOUN
ejpam-5901	356	3	τ3	τ3	NOUN
ejpam-5901	356	4	.	.	PUNCT
ejpam-5901	357	1	also	also	ADV
ejpam-5901	357	2	|r(t)−	|r(t)−	AUX
ejpam-5901	357	3	r1(t)|	r1(t)|	VERB
ejpam-5901	357	4	≤	≤	NUM
ejpam-5901	357	5	τ4δ4	τ4δ4	PUNCT
ejpam-5901	357	6	,	,	PUNCT
ejpam-5901	357	7	with	with	ADP
ejpam-5901	357	8	η4	η4	ADJ
ejpam-5901	357	9	=	=	SYM
ejpam-5901	357	10	δ4	δ4	PROPN
ejpam-5901	357	11	,	,	PUNCT
ejpam-5901	357	12	(	(	PUNCT
ejpam-5901	357	13	ϱ2(1−ϱ1	ϱ2(1−ϱ1	PROPN
ejpam-5901	357	14	)	)	PUNCT
ejpam-5901	357	15	b∗(ϱ1	b∗(ϱ1	PROPN
ejpam-5901	357	16	)	)	PUNCT
ejpam-5901	358	1	+	+	CCONJ
ejpam-5901	358	2	ϱ1ϱ2γ(ϱ2	ϱ1ϱ2γ(ϱ2	ADJ
ejpam-5901	358	3	)	)	PUNCT
ejpam-5901	358	4	b∗(ϱ1)γ(ϱ1+ϱ2	b∗(ϱ1)γ(ϱ1+ϱ2	NUM
ejpam-5901	358	5	)	)	PUNCT
ejpam-5901	358	6	)	)	PUNCT
ejpam-5901	359	1	∥r−	∥r−	PRON
ejpam-5901	359	2	r1∥	r1∥	NOUN
ejpam-5901	359	3	=	=	SYM
ejpam-5901	359	4	τ4	τ4	PROPN
ejpam-5901	359	5	.	.	PUNCT
ejpam-5901	360	1	7	7	X
ejpam-5901	360	2	.	.	X
ejpam-5901	360	3	fractal	fractal	ADJ
ejpam-5901	360	4	-	-	PUNCT
ejpam-5901	360	5	fractional	fractional	ADJ
ejpam-5901	360	6	atangana	atangana	PROPN
ejpam-5901	360	7	-	-	PUNCT
ejpam-5901	360	8	baleanu	baleanu	PROPN
ejpam-5901	360	9	scheme	scheme	NOUN
ejpam-5901	360	10	the	the	DET
ejpam-5901	360	11	antangana	antangana	ADJ
ejpam-5901	360	12	-	-	PUNCT
ejpam-5901	360	13	baleanu	baleanu	ADJ
ejpam-5901	360	14	integral	integral	ADJ
ejpam-5901	360	15	gives	give	VERB
ejpam-5901	360	16	us	we	PRON
ejpam-5901	360	17	ψ(t	ψ(t	PROPN
ejpam-5901	360	18	)	)	PUNCT
ejpam-5901	360	19	=	=	PUNCT
ejpam-5901	361	1	ψ(0	ψ(0	X
ejpam-5901	361	2	)	)	PUNCT
ejpam-5901	362	1	+	+	CCONJ
ejpam-5901	362	2	1−	1−	NUM
ejpam-5901	362	3	ϱ1	ϱ1	NOUN
ejpam-5901	362	4	ℏ(ϱ1	ℏ(ϱ1	NOUN
ejpam-5901	362	5	)	)	PUNCT
ejpam-5901	362	6	ξ(t	ξ(t	NOUN
ejpam-5901	362	7	,	,	PUNCT
ejpam-5901	362	8	ψ(t	ψ(t	PROPN
ejpam-5901	362	9	)	)	PUNCT
ejpam-5901	362	10	)	)	PUNCT
ejpam-5901	363	1	+	+	CCONJ
ejpam-5901	363	2	ϱ1	ϱ1	NOUN
ejpam-5901	363	3	ℏ(ϱ1)γ(ϱ1	ℏ(ϱ1)γ(ϱ1	NOUN
ejpam-5901	363	4	)	)	PUNCT
ejpam-5901	363	5	∫	∫	PROPN
ejpam-5901	363	6	t	t	PROPN
ejpam-5901	363	7	0	0	NUM
ejpam-5901	364	1	(	(	PUNCT
ejpam-5901	364	2	t−	t−	PROPN
ejpam-5901	364	3	ϵ)ϱ1−1ϵϱ2−1ξ(ϵ,ψ(ϵ))dϵ.	ϵ)ϱ1−1ϵϱ2−1ξ(ϵ,ψ(ϵ))dϵ.	NOUN
ejpam-5901	364	4	replacing	replace	VERB
ejpam-5901	364	5	t	t	NOUN
ejpam-5901	364	6	by	by	ADP
ejpam-5901	364	7	tn+1	tn+1	NOUN
ejpam-5901	364	8	we	we	PRON
ejpam-5901	364	9	have	have	VERB
ejpam-5901	364	10	ψn+1	ψn+1	NOUN
ejpam-5901	364	11	=	=	SYM
ejpam-5901	364	12	ψ(0	ψ(0	NOUN
ejpam-5901	364	13	)	)	PUNCT
ejpam-5901	365	1	+	+	CCONJ
ejpam-5901	365	2	1−	1−	NUM
ejpam-5901	365	3	ϱ1	ϱ1	NOUN
ejpam-5901	365	4	ℏ(ϱ1	ℏ(ϱ1	NOUN
ejpam-5901	365	5	)	)	PUNCT
ejpam-5901	366	1	ξ	ξ	PROPN
ejpam-5901	366	2	(	(	PUNCT
ejpam-5901	366	3	tn+1,ψ(t	tn+1,ψ(t	NOUN
ejpam-5901	366	4	)	)	PUNCT
ejpam-5901	366	5	)	)	PUNCT
ejpam-5901	367	1	+	+	CCONJ
ejpam-5901	367	2	ϱ1	ϱ1	NOUN
ejpam-5901	367	3	ℏ(ϱ1)γ(ϱ1	ℏ(ϱ1)γ(ϱ1	NOUN
ejpam-5901	367	4	)	)	PUNCT
ejpam-5901	367	5	∫	∫	PROPN
ejpam-5901	367	6	tn+1	tn+1	PROPN
ejpam-5901	367	7	0	0	NUM
ejpam-5901	367	8	(	(	PUNCT
ejpam-5901	367	9	tn+1	tn+1	PROPN
ejpam-5901	367	10	−	−	NOUN
ejpam-5901	368	1	ϵ)ϱ1−1	ϵ)ϱ1−1	ADJ
ejpam-5901	368	2	ϵϱ2−1ξ(ϵ,ψ(ϵ))dϵ.	ϵϱ2−1ξ(ϵ,ψ(ϵ))dϵ.	NUM
ejpam-5901	368	3	s.	s.	PROPN
ejpam-5901	368	4	saber	saber	PROPN
ejpam-5901	368	5	,	,	PUNCT
ejpam-5901	368	6	a.	a.	NOUN
ejpam-5901	368	7	a.	a.	NOUN
ejpam-5901	368	8	alahmari	alahmari	PROPN
ejpam-5901	368	9	/	/	SYM
ejpam-5901	368	10	eur	eur	PROPN
ejpam-5901	368	11	.	.	PUNCT
ejpam-5901	369	1	j.	j.	PROPN
ejpam-5901	369	2	pure	pure	PROPN
ejpam-5901	369	3	appl	appl	PROPN
ejpam-5901	369	4	.	.	PROPN
ejpam-5901	369	5	math	math	PROPN
ejpam-5901	369	6	,	,	PUNCT
ejpam-5901	369	7	18	18	NUM
ejpam-5901	369	8	(	(	PUNCT
ejpam-5901	369	9	2	2	NUM
ejpam-5901	369	10	)	)	PUNCT
ejpam-5901	369	11	(	(	PUNCT
ejpam-5901	369	12	2025	2025	NUM
ejpam-5901	369	13	)	)	PUNCT
ejpam-5901	369	14	,	,	PUNCT
ejpam-5901	369	15	5901	5901	NUM
ejpam-5901	369	16	15	15	NUM
ejpam-5901	369	17	of	of	ADP
ejpam-5901	369	18	23	23	NUM
ejpam-5901	369	19	application	application	NOUN
ejpam-5901	369	20	of	of	ADP
ejpam-5901	369	21	the	the	DET
ejpam-5901	369	22	two	two	NUM
ejpam-5901	369	23	-	-	PUNCT
ejpam-5901	369	24	step	step	NOUN
ejpam-5901	369	25	lagrange	lagrange	NOUN
ejpam-5901	369	26	polynomial	polynomial	ADJ
ejpam-5901	369	27	yields	yield	NOUN
ejpam-5901	369	28	ξ(t	ξ(t	NOUN
ejpam-5901	369	29	,	,	PUNCT
ejpam-5901	369	30	(	(	PUNCT
ejpam-5901	369	31	y	y	NOUN
ejpam-5901	369	32	,	,	PUNCT
ejpam-5901	369	33	ψ(t	ψ(t	PROPN
ejpam-5901	369	34	)	)	PUNCT
ejpam-5901	369	35	)	)	PUNCT
ejpam-5901	370	1	=	=	SYM
ejpam-5901	370	2	(	(	PUNCT
ejpam-5901	370	3	y	y	PROPN
ejpam-5901	370	4	−	−	PROPN
ejpam-5901	370	5	tϵ−1	tϵ−1	PROPN
ejpam-5901	370	6	)	)	PUNCT
ejpam-5901	370	7	ξ(t	ξ(t	PROPN
ejpam-5901	370	8	,	,	PUNCT
ejpam-5901	370	9	(	(	PUNCT
ejpam-5901	370	10	tϵ,ψ(tϵ	tϵ,ψ(tϵ	NOUN
ejpam-5901	370	11	)	)	PUNCT
ejpam-5901	370	12	)	)	PUNCT
ejpam-5901	371	1	tϵ	tϵ	ADP
ejpam-5901	371	2	−	−	PROPN
ejpam-5901	371	3	tϵ−1	tϵ−1	NOUN
ejpam-5901	371	4	−	−	PROPN
ejpam-5901	372	1	(	(	PUNCT
ejpam-5901	372	2	y	y	PROPN
ejpam-5901	372	3	−	−	PROPN
ejpam-5901	372	4	tϵ	tϵ	NOUN
ejpam-5901	372	5	)	)	PUNCT
ejpam-5901	372	6	ξ	ξ	PROPN
ejpam-5901	372	7	(	(	PUNCT
ejpam-5901	372	8	tϵ−1,ψ(tϵ−1	tϵ−1,ψ(tϵ−1	X
ejpam-5901	372	9	)	)	PUNCT
ejpam-5901	372	10	tϵ	tϵ	NOUN
ejpam-5901	372	11	−	−	PROPN
ejpam-5901	372	12	tϵ−1	tϵ−1	PROPN
ejpam-5901	372	13	=	=	SYM
ejpam-5901	372	14	ξ(t	ξ(t	PROPN
ejpam-5901	372	15	,	,	PUNCT
ejpam-5901	372	16	(	(	PUNCT
ejpam-5901	372	17	tϵ,ψ(tϵ	tϵ,ψ(tϵ	NOUN
ejpam-5901	372	18	)	)	PUNCT
ejpam-5901	372	19	)	)	PUNCT
ejpam-5901	373	1	(	(	PUNCT
ejpam-5901	373	2	x−	x−	PROPN
ejpam-5901	373	3	tϵ−1	tϵ−1	PROPN
ejpam-5901	373	4	)	)	PUNCT
ejpam-5901	373	5	tϵ	tϵ	NOUN
ejpam-5901	373	6	−	−	PROPN
ejpam-5901	373	7	tϵ−1	tϵ−1	PROPN
ejpam-5901	373	8	−	−	PROPN
ejpam-5901	373	9	ξ	ξ	PROPN
ejpam-5901	373	10	(	(	PUNCT
ejpam-5901	373	11	tϵ−1,ψ(tϵ−1	tϵ−1,ψ(tϵ−1	NUM
ejpam-5901	373	12	)	)	PUNCT
ejpam-5901	373	13	(	(	PUNCT
ejpam-5901	373	14	y	y	PROPN
ejpam-5901	373	15	−	−	PROPN
ejpam-5901	373	16	tϵ	tϵ	NOUN
ejpam-5901	373	17	)	)	PUNCT
ejpam-5901	373	18	tϵ	tϵ	NOUN
ejpam-5901	373	19	−	−	PROPN
ejpam-5901	373	20	tϵ−1	tϵ−1	PROPN
ejpam-5901	373	21	=	=	SYM
ejpam-5901	373	22	ξ(t	ξ(t	PROPN
ejpam-5901	373	23	,	,	PUNCT
ejpam-5901	373	24	(	(	PUNCT
ejpam-5901	373	25	tϵ,ψ(tϵ	tϵ,ψ(tϵ	NOUN
ejpam-5901	373	26	)	)	PUNCT
ejpam-5901	373	27	)	)	PUNCT
ejpam-5901	374	1	(	(	PUNCT
ejpam-5901	374	2	y	y	PROPN
ejpam-5901	374	3	−	−	PROPN
ejpam-5901	374	4	tϵ−1	tϵ−1	PROPN
ejpam-5901	374	5	)	)	PUNCT
ejpam-5901	374	6	h	h	NOUN
ejpam-5901	374	7	−	−	PROPN
ejpam-5901	374	8	ξ	ξ	PROPN
ejpam-5901	374	9	(	(	PUNCT
ejpam-5901	374	10	tϵ−1,ψ(tϵ−1	tϵ−1,ψ(tϵ−1	NUM
ejpam-5901	374	11	)	)	PUNCT
ejpam-5901	374	12	(	(	PUNCT
ejpam-5901	374	13	y	y	PROPN
ejpam-5901	374	14	−	−	PROPN
ejpam-5901	374	15	tϵ	tϵ	NOUN
ejpam-5901	374	16	)	)	PUNCT
ejpam-5901	374	17	h	h	NOUN
ejpam-5901	374	18	.	.	PUNCT
ejpam-5901	375	1	using	use	VERB
ejpam-5901	375	2	the	the	DET
ejpam-5901	375	3	lagrange	lagrange	NOUN
ejpam-5901	375	4	polynomial	polynomial	NOUN
ejpam-5901	375	5	,	,	PUNCT
ejpam-5901	375	6	we	we	PRON
ejpam-5901	375	7	obtain	obtain	VERB
ejpam-5901	375	8	ψn+1	ψn+1	NOUN
ejpam-5901	375	9	=	=	SYM
ejpam-5901	375	10	ψ(0	ψ(0	NOUN
ejpam-5901	375	11	)	)	PUNCT
ejpam-5901	376	1	+	+	CCONJ
ejpam-5901	376	2	1−	1−	NUM
ejpam-5901	376	3	ϱ1	ϱ1	NOUN
ejpam-5901	376	4	ℏ(ϱ1	ℏ(ϱ1	NOUN
ejpam-5901	376	5	)	)	PUNCT
ejpam-5901	376	6	ξ(t	ξ(t	NOUN
ejpam-5901	376	7	,	,	PUNCT
ejpam-5901	376	8	(	(	PUNCT
ejpam-5901	376	9	tn	tn	NOUN
ejpam-5901	376	10	,	,	PUNCT
ejpam-5901	376	11	ψ(tn	ψ(tn	ADV
ejpam-5901	376	12	)	)	PUNCT
ejpam-5901	376	13	)	)	PUNCT
ejpam-5901	377	1	+	+	CCONJ
ejpam-5901	377	2	ϱ1	ϱ1	NOUN
ejpam-5901	377	3	ℏ(ϱ1)γ(ϱ1	ℏ(ϱ1)γ(ϱ1	NOUN
ejpam-5901	377	4	)	)	PUNCT
ejpam-5901	377	5	n∑	n∑	NOUN
ejpam-5901	377	6	ϵ=1	ϵ=1	NUM
ejpam-5901	377	7	(	(	PUNCT
ejpam-5901	377	8	ξ(t	ξ(t	NOUN
ejpam-5901	377	9	,	,	PUNCT
ejpam-5901	377	10	(	(	PUNCT
ejpam-5901	377	11	tϵ,ψ(tϵ	tϵ,ψ(tϵ	NOUN
ejpam-5901	377	12	)	)	PUNCT
ejpam-5901	377	13	)	)	PUNCT
ejpam-5901	378	1	h	h	NOUN
ejpam-5901	378	2	∫	∫	PROPN
ejpam-5901	379	1	tϵ+1	tϵ+1	NUM
ejpam-5901	380	1	tϵ	tϵ	NOUN
ejpam-5901	380	2	(	(	PUNCT
ejpam-5901	380	3	ϵ−	ϵ−	PROPN
ejpam-5901	380	4	tϵ	tϵ	NOUN
ejpam-5901	380	5	−	−	PROPN
ejpam-5901	380	6	1	1	NUM
ejpam-5901	380	7	)	)	PUNCT
ejpam-5901	380	8	(	(	PUNCT
ejpam-5901	380	9	tn+1	tn+1	NUM
ejpam-5901	380	10	−	−	NOUN
ejpam-5901	380	11	ϵ)ϱ1−1	ϵ)ϱ1−1	ADJ
ejpam-5901	380	12	dϵ	dϵ	ADP
ejpam-5901	380	13	−ξ(t	−ξ(t	NOUN
ejpam-5901	380	14	,	,	PUNCT
ejpam-5901	380	15	(	(	PUNCT
ejpam-5901	380	16	tϵ−1,ψ(tϵ−1	tϵ−1,ψ(tϵ−1	NOUN
ejpam-5901	380	17	)	)	PUNCT
ejpam-5901	380	18	)	)	PUNCT
ejpam-5901	381	1	h	h	NOUN
ejpam-5901	381	2	∫	∫	PROPN
ejpam-5901	381	3	tn+1	tn+1	NUM
ejpam-5901	381	4	tϵ	tϵ	INTJ
ejpam-5901	381	5	(	(	PUNCT
ejpam-5901	381	6	ϵ−	ϵ−	NOUN
ejpam-5901	381	7	tϵ	tϵ	NOUN
ejpam-5901	381	8	)	)	PUNCT
ejpam-5901	381	9	(	(	PUNCT
ejpam-5901	381	10	tn+1	tn+1	NUM
ejpam-5901	381	11	−	−	NOUN
ejpam-5901	381	12	ϵ)ϱ1−1	ϵ)ϱ1−1	ADJ
ejpam-5901	381	13	dϵ	dϵ	PROPN
ejpam-5901	381	14	)	)	PUNCT
ejpam-5901	381	15	.	.	PUNCT
ejpam-5901	382	1	now	now	ADV
ejpam-5901	382	2	solving	solve	VERB
ejpam-5901	382	3	the	the	DET
ejpam-5901	382	4	integral	integral	ADJ
ejpam-5901	382	5	we	we	PRON
ejpam-5901	382	6	get	get	VERB
ejpam-5901	382	7	ψn+1	ψn+1	NOUN
ejpam-5901	382	8	=	=	SYM
ejpam-5901	382	9	ψ(0	ψ(0	NOUN
ejpam-5901	382	10	)	)	PUNCT
ejpam-5901	383	1	+	+	CCONJ
ejpam-5901	383	2	1−	1−	NUM
ejpam-5901	383	3	ϱ1	ϱ1	NOUN
ejpam-5901	383	4	ℏ(ϱ1	ℏ(ϱ1	NOUN
ejpam-5901	383	5	)	)	PUNCT
ejpam-5901	383	6	ξ(t	ξ(t	NOUN
ejpam-5901	383	7	,	,	PUNCT
ejpam-5901	383	8	(	(	PUNCT
ejpam-5901	383	9	tn	tn	NOUN
ejpam-5901	383	10	,	,	PUNCT
ejpam-5901	383	11	ψ(tn	ψ(tn	ADV
ejpam-5901	383	12	)	)	PUNCT
ejpam-5901	383	13	)	)	PUNCT
ejpam-5901	384	1	+	+	NUM
ejpam-5901	384	2	ϱ1h	ϱ1h	ADP
ejpam-5901	384	3	ϱ1	ϱ1	NOUN
ejpam-5901	384	4	γ	γ	X
ejpam-5901	384	5	(	(	PUNCT
ejpam-5901	384	6	ϱ1	ϱ1	NOUN
ejpam-5901	384	7	+	+	CCONJ
ejpam-5901	384	8	2	2	X
ejpam-5901	384	9	)	)	PUNCT
ejpam-5901	384	10	×	×	NOUN
ejpam-5901	384	11	n∑	n∑	NOUN
ejpam-5901	384	12	ϵ=1	ϵ=1	PUNCT
ejpam-5901	385	1	[	[	X
ejpam-5901	385	2	ξ(t	ξ(t	NOUN
ejpam-5901	385	3	,	,	PUNCT
ejpam-5901	385	4	(	(	PUNCT
ejpam-5901	385	5	tϵ,ψ(tϵ	tϵ,ψ(tϵ	NOUN
ejpam-5901	385	6	)	)	PUNCT
ejpam-5901	385	7	)	)	PUNCT
ejpam-5901	385	8	(	(	PUNCT
ejpam-5901	385	9	(	(	PUNCT
ejpam-5901	385	10	n−	n−	NOUN
ejpam-5901	385	11	ϵ+	ϵ+	PUNCT
ejpam-5901	385	12	1)ϱ1	1)ϱ1	NUM
ejpam-5901	385	13	(	(	PUNCT
ejpam-5901	385	14	n−	n−	NOUN
ejpam-5901	385	15	ϵ+	ϵ+	PUNCT
ejpam-5901	385	16	2	2	NUM
ejpam-5901	385	17	+	+	CCONJ
ejpam-5901	385	18	ϱ1	ϱ1	NOUN
ejpam-5901	385	19	)	)	PUNCT
ejpam-5901	385	20	−(n−	−(n−	VERB
ejpam-5901	385	21	ϵ)ϱ1	ϵ)ϱ1	PROPN
ejpam-5901	385	22	(	(	PUNCT
ejpam-5901	385	23	n−	n−	NOUN
ejpam-5901	385	24	ϵ+	ϵ+	X
ejpam-5901	385	25	2	2	NUM
ejpam-5901	385	26	+	+	NUM
ejpam-5901	385	27	2ϱ1	2ϱ1	NUM
ejpam-5901	385	28	)	)	PUNCT
ejpam-5901	385	29	)	)	PUNCT
ejpam-5901	385	30	−ξ(t	−ξ(t	NOUN
ejpam-5901	385	31	,	,	PUNCT
ejpam-5901	385	32	(	(	PUNCT
ejpam-5901	385	33	tϵ−1,ψϵ−1	tϵ−1,ψϵ−1	ADP
ejpam-5901	385	34	)	)	PUNCT
ejpam-5901	385	35	(	(	PUNCT
ejpam-5901	385	36	(	(	PUNCT
ejpam-5901	385	37	n−	n−	NOUN
ejpam-5901	385	38	ϵ+	ϵ+	X
ejpam-5901	385	39	1)ϱ1	1)ϱ1	NUM
ejpam-5901	385	40	+	+	PROPN
ejpam-5901	385	41	1	1	NUM
ejpam-5901	385	42	−	−	NOUN
ejpam-5901	385	43	(	(	PUNCT
ejpam-5901	385	44	n−	n−	NOUN
ejpam-5901	385	45	ϵ+	ϵ+	PUNCT
ejpam-5901	385	46	1	1	NUM
ejpam-5901	385	47	+	+	CCONJ
ejpam-5901	385	48	ϱ1	ϱ1	NOUN
ejpam-5901	385	49	)	)	PUNCT
ejpam-5901	385	50	(	(	PUNCT
ejpam-5901	385	51	n−	n−	NOUN
ejpam-5901	385	52	ϵ)ϱ1	ϵ)ϱ1	PROPN
ejpam-5901	385	53	)	)	PUNCT
ejpam-5901	385	54	]	]	PUNCT
ejpam-5901	385	55	.	.	PUNCT
ejpam-5901	386	1	now	now	ADV
ejpam-5901	386	2	replacing	replace	VERB
ejpam-5901	386	3	the	the	DET
ejpam-5901	386	4	value	value	NOUN
ejpam-5901	386	5	of	of	ADP
ejpam-5901	386	6	ξ(y	ξ(y	PROPN
ejpam-5901	386	7	,	,	PUNCT
ejpam-5901	386	8	ψ(t	ψ(t	PROPN
ejpam-5901	386	9	)	)	PUNCT
ejpam-5901	386	10	)	)	PUNCT
ejpam-5901	387	1	we	we	PRON
ejpam-5901	387	2	get	get	VERB
ejpam-5901	387	3	ψn+1	ψn+1	NOUN
ejpam-5901	387	4	=	=	SYM
ejpam-5901	387	5	ψ(0	ψ(0	NOUN
ejpam-5901	387	6	)	)	PUNCT
ejpam-5901	388	1	+	+	X
ejpam-5901	388	2	ϱ2	ϱ2	PROPN
ejpam-5901	388	3	t	t	NOUN
ejpam-5901	388	4	ϱ2−1	ϱ2−1	NOUN
ejpam-5901	388	5	1−	1−	NUM
ejpam-5901	388	6	ϱ1	ϱ1	PROPN
ejpam-5901	388	7	ℏ(ϱ1	ℏ(ϱ1	NOUN
ejpam-5901	388	8	)	)	PUNCT
ejpam-5901	389	1	υ	υ	NOUN
ejpam-5901	389	2	(	(	PUNCT
ejpam-5901	389	3	tϵ,ψ(tϵ	tϵ,ψ(tϵ	NOUN
ejpam-5901	389	4	)	)	PUNCT
ejpam-5901	389	5	)	)	PUNCT
ejpam-5901	390	1	+	+	CCONJ
ejpam-5901	390	2	ϱ2	ϱ2	PROPN
ejpam-5901	390	3	t	t	PROPN
ejpam-5901	390	4	ϱ2−1	ϱ2−1	NOUN
ejpam-5901	390	5	ϱ1h	ϱ1h	ADP
ejpam-5901	390	6	ϱ1	ϱ1	PROPN
ejpam-5901	390	7	γ	γ	X
ejpam-5901	390	8	(	(	PUNCT
ejpam-5901	390	9	ϱ1	ϱ1	NOUN
ejpam-5901	390	10	+	+	CCONJ
ejpam-5901	390	11	2	2	X
ejpam-5901	390	12	)	)	PUNCT
ejpam-5901	390	13	×	×	NOUN
ejpam-5901	390	14	n∑	n∑	NOUN
ejpam-5901	390	15	ϵ=1	ϵ=1	PUNCT
ejpam-5901	391	1	[	[	X
ejpam-5901	391	2	υ	υ	X
ejpam-5901	391	3	(	(	PUNCT
ejpam-5901	391	4	tϵ,ψ(tϵ	tϵ,ψ(tϵ	NOUN
ejpam-5901	391	5	)	)	PUNCT
ejpam-5901	391	6	)	)	PUNCT
ejpam-5901	391	7	(	(	PUNCT
ejpam-5901	391	8	(	(	PUNCT
ejpam-5901	391	9	n+	n+	X
ejpam-5901	391	10	1−	1−	NUM
ejpam-5901	391	11	ϵ)ϱ1	ϵ)ϱ1	PROPN
ejpam-5901	391	12	(	(	PUNCT
ejpam-5901	391	13	n−	n−	NOUN
ejpam-5901	391	14	ϵ+	ϵ+	PUNCT
ejpam-5901	391	15	2	2	NUM
ejpam-5901	391	16	+	+	CCONJ
ejpam-5901	391	17	ϱ1	ϱ1	NOUN
ejpam-5901	391	18	)	)	PUNCT
ejpam-5901	391	19	−(n−	−(n−	VERB
ejpam-5901	391	20	ϵ)ϱ1	ϵ)ϱ1	PROPN
ejpam-5901	391	21	(	(	PUNCT
ejpam-5901	391	22	n−	n−	NOUN
ejpam-5901	391	23	ϵ+	ϵ+	X
ejpam-5901	391	24	2	2	NUM
ejpam-5901	391	25	+	+	NUM
ejpam-5901	391	26	2ϱ1	2ϱ1	NUM
ejpam-5901	391	27	)	)	PUNCT
ejpam-5901	391	28	)	)	PUNCT
ejpam-5901	391	29	−υ(tϵ−1,ψϵ−1	−υ(tϵ−1,ψϵ−1	PROPN
ejpam-5901	391	30	)	)	PUNCT
ejpam-5901	391	31	(	(	PUNCT
ejpam-5901	391	32	(	(	PUNCT
ejpam-5901	391	33	n−	n−	NOUN
ejpam-5901	391	34	ϵ+	ϵ+	X
ejpam-5901	391	35	1)ϱ1	1)ϱ1	NUM
ejpam-5901	391	36	+	+	PROPN
ejpam-5901	391	37	1	1	NUM
ejpam-5901	391	38	−	−	NOUN
ejpam-5901	391	39	(	(	PUNCT
ejpam-5901	391	40	n−	n−	NOUN
ejpam-5901	391	41	ϵ+	ϵ+	PUNCT
ejpam-5901	391	42	1	1	NUM
ejpam-5901	391	43	+	+	CCONJ
ejpam-5901	391	44	ϱ1	ϱ1	NOUN
ejpam-5901	391	45	)	)	PUNCT
ejpam-5901	391	46	(	(	PUNCT
ejpam-5901	391	47	n−	n−	NOUN
ejpam-5901	391	48	ϵ)ϱ1	ϵ)ϱ1	PROPN
ejpam-5901	391	49	)	)	PUNCT
ejpam-5901	391	50	]	]	PUNCT
ejpam-5901	391	51	.	.	PUNCT
ejpam-5901	392	1	therefore	therefore	ADV
ejpam-5901	392	2	,	,	PUNCT
ejpam-5901	392	3	the	the	DET
ejpam-5901	392	4	above	above	ADJ
ejpam-5901	392	5	system	system	NOUN
ejpam-5901	392	6	’s	’s	PART
ejpam-5901	392	7	numerical	numerical	ADJ
ejpam-5901	392	8	scheme	scheme	NOUN
ejpam-5901	392	9	is	be	AUX
ejpam-5901	392	10	sn+1	sn+1	NOUN
ejpam-5901	392	11	=	=	SYM
ejpam-5901	392	12	s(0	s(0	PROPN
ejpam-5901	392	13	)	)	PUNCT
ejpam-5901	392	14	+	+	SYM
ejpam-5901	392	15	ϱ2	ϱ2	PROPN
ejpam-5901	392	16	t	t	NOUN
ejpam-5901	392	17	ϱ2−1	ϱ2−1	NOUN
ejpam-5901	392	18	1−	1−	NUM
ejpam-5901	392	19	ϱ1	ϱ1	PROPN
ejpam-5901	392	20	ℏ(ϱ1	ℏ(ϱ1	NOUN
ejpam-5901	392	21	)	)	PUNCT
ejpam-5901	392	22	w1	w1	NOUN
ejpam-5901	392	23	(	(	PUNCT
ejpam-5901	392	24	tϵ,s	tϵ,s	X
ejpam-5901	392	25	(	(	PUNCT
ejpam-5901	392	26	tϵ	tϵ	NOUN
ejpam-5901	392	27	)	)	PUNCT
ejpam-5901	392	28	)	)	PUNCT
ejpam-5901	393	1	+	+	CCONJ
ejpam-5901	393	2	ϱ2	ϱ2	PROPN
ejpam-5901	393	3	t	t	PROPN
ejpam-5901	393	4	ϱ2−1	ϱ2−1	NOUN
ejpam-5901	393	5	ϱ1h	ϱ1h	ADP
ejpam-5901	393	6	ϱ1	ϱ1	PROPN
ejpam-5901	393	7	γ	γ	X
ejpam-5901	393	8	(	(	PUNCT
ejpam-5901	393	9	ϱ1	ϱ1	NOUN
ejpam-5901	393	10	+	+	CCONJ
ejpam-5901	393	11	2	2	X
ejpam-5901	393	12	)	)	PUNCT
ejpam-5901	393	13	×	×	NOUN
ejpam-5901	393	14	n∑	n∑	NOUN
ejpam-5901	393	15	ϵ=1	ϵ=1	PUNCT
ejpam-5901	394	1	[	[	X
ejpam-5901	394	2	w1	w1	NOUN
ejpam-5901	394	3	(	(	PUNCT
ejpam-5901	394	4	tϵ	tϵ	NOUN
ejpam-5901	394	5	,	,	PUNCT
ejpam-5901	394	6	s	s	PART
ejpam-5901	394	7	(	(	PUNCT
ejpam-5901	394	8	tϵ	tϵ	NOUN
ejpam-5901	394	9	)	)	PUNCT
ejpam-5901	394	10	)	)	PUNCT
ejpam-5901	394	11	(	(	PUNCT
ejpam-5901	394	12	(	(	PUNCT
ejpam-5901	394	13	n−	n−	NOUN
ejpam-5901	394	14	ϵ+	ϵ+	PUNCT
ejpam-5901	394	15	1)ϱ1	1)ϱ1	NUM
ejpam-5901	394	16	(	(	PUNCT
ejpam-5901	394	17	n−	n−	NOUN
ejpam-5901	394	18	ϵ+	ϵ+	PUNCT
ejpam-5901	394	19	2	2	NUM
ejpam-5901	394	20	+	+	CCONJ
ejpam-5901	394	21	ϱ1	ϱ1	NOUN
ejpam-5901	394	22	)	)	PUNCT
ejpam-5901	394	23	−(n−	−(n−	VERB
ejpam-5901	394	24	ϵ)ϱ1	ϵ)ϱ1	PROPN
ejpam-5901	394	25	(	(	PUNCT
ejpam-5901	394	26	n−	n−	NOUN
ejpam-5901	394	27	ϵ+	ϵ+	X
ejpam-5901	394	28	2	2	NUM
ejpam-5901	394	29	+	+	NUM
ejpam-5901	394	30	2ϱ1	2ϱ1	NUM
ejpam-5901	394	31	)	)	PUNCT
ejpam-5901	394	32	)	)	PUNCT
ejpam-5901	395	1	−w1	−w1	INTJ
ejpam-5901	395	2	(	(	PUNCT
ejpam-5901	395	3	tϵ−1	tϵ−1	PROPN
ejpam-5901	395	4	,	,	PUNCT
ejpam-5901	395	5	sϵ−1	sϵ−1	NOUN
ejpam-5901	395	6	)	)	PUNCT
ejpam-5901	395	7	(	(	PUNCT
ejpam-5901	395	8	(	(	PUNCT
ejpam-5901	395	9	n−	n−	NOUN
ejpam-5901	395	10	ϵ+	ϵ+	X
ejpam-5901	395	11	1)ϱ1	1)ϱ1	NUM
ejpam-5901	395	12	+	+	PROPN
ejpam-5901	395	13	1	1	NUM
ejpam-5901	395	14	−	−	NOUN
ejpam-5901	395	15	(	(	PUNCT
ejpam-5901	395	16	n−	n−	NOUN
ejpam-5901	395	17	ϵ+	ϵ+	PUNCT
ejpam-5901	395	18	1	1	NUM
ejpam-5901	395	19	+	+	CCONJ
ejpam-5901	395	20	ϱ1	ϱ1	NOUN
ejpam-5901	395	21	)	)	PUNCT
ejpam-5901	395	22	(	(	PUNCT
ejpam-5901	395	23	n−	n−	NOUN
ejpam-5901	395	24	ϵ)ϱ1	ϵ)ϱ1	PROPN
ejpam-5901	395	25	)	)	PUNCT
ejpam-5901	395	26	]	]	PUNCT
ejpam-5901	395	27	,	,	PUNCT
ejpam-5901	395	28	s.	s.	PROPN
ejpam-5901	395	29	saber	saber	PROPN
ejpam-5901	395	30	,	,	PUNCT
ejpam-5901	395	31	a.	a.	NOUN
ejpam-5901	395	32	a.	a.	NOUN
ejpam-5901	395	33	alahmari	alahmari	PROPN
ejpam-5901	395	34	/	/	SYM
ejpam-5901	395	35	eur	eur	PROPN
ejpam-5901	395	36	.	.	PUNCT
ejpam-5901	396	1	j.	j.	PROPN
ejpam-5901	396	2	pure	pure	PROPN
ejpam-5901	396	3	appl	appl	PROPN
ejpam-5901	396	4	.	.	PROPN
ejpam-5901	396	5	math	math	PROPN
ejpam-5901	396	6	,	,	PUNCT
ejpam-5901	396	7	18	18	NUM
ejpam-5901	396	8	(	(	PUNCT
ejpam-5901	396	9	2	2	NUM
ejpam-5901	396	10	)	)	PUNCT
ejpam-5901	396	11	(	(	PUNCT
ejpam-5901	396	12	2025	2025	NUM
ejpam-5901	396	13	)	)	PUNCT
ejpam-5901	396	14	,	,	PUNCT
ejpam-5901	396	15	5901	5901	NUM
ejpam-5901	396	16	16	16	NUM
ejpam-5901	396	17	of	of	ADP
ejpam-5901	396	18	23	23	NUM
ejpam-5901	396	19	cn+1	cn+1	NUM
ejpam-5901	396	20	=	=	SYM
ejpam-5901	396	21	c(0	c(0	NOUN
ejpam-5901	396	22	)	)	PUNCT
ejpam-5901	397	1	+	+	CCONJ
ejpam-5901	397	2	ϱ2	ϱ2	PROPN
ejpam-5901	397	3	t	t	NOUN
ejpam-5901	397	4	ϱ2−1	ϱ2−1	NOUN
ejpam-5901	397	5	1−	1−	NUM
ejpam-5901	397	6	ϱ1	ϱ1	PROPN
ejpam-5901	397	7	ℏ(ϱ1	ℏ(ϱ1	NOUN
ejpam-5901	397	8	)	)	PUNCT
ejpam-5901	397	9	w2	w2	NOUN
ejpam-5901	397	10	(	(	PUNCT
ejpam-5901	397	11	tϵ,c	tϵ,c	X
ejpam-5901	397	12	(	(	PUNCT
ejpam-5901	397	13	tϵ	tϵ	NOUN
ejpam-5901	397	14	)	)	PUNCT
ejpam-5901	397	15	)	)	PUNCT
ejpam-5901	398	1	+	+	CCONJ
ejpam-5901	398	2	ϱ2	ϱ2	PROPN
ejpam-5901	398	3	t	t	PROPN
ejpam-5901	398	4	ϱ2−1	ϱ2−1	NOUN
ejpam-5901	398	5	ϱ1h	ϱ1h	ADP
ejpam-5901	398	6	ϱ1	ϱ1	PROPN
ejpam-5901	398	7	γ	γ	X
ejpam-5901	398	8	(	(	PUNCT
ejpam-5901	398	9	ϱ1	ϱ1	NOUN
ejpam-5901	398	10	+	+	CCONJ
ejpam-5901	398	11	2	2	X
ejpam-5901	398	12	)	)	PUNCT
ejpam-5901	398	13	×	×	NOUN
ejpam-5901	398	14	n∑	n∑	NOUN
ejpam-5901	398	15	ϵ=1	ϵ=1	PUNCT
ejpam-5901	399	1	[	[	X
ejpam-5901	399	2	w2	w2	NOUN
ejpam-5901	399	3	(	(	PUNCT
ejpam-5901	399	4	tϵ,c	tϵ,c	X
ejpam-5901	399	5	(	(	PUNCT
ejpam-5901	399	6	tϵ	tϵ	NOUN
ejpam-5901	399	7	)	)	PUNCT
ejpam-5901	399	8	)	)	PUNCT
ejpam-5901	399	9	(	(	PUNCT
ejpam-5901	399	10	(	(	PUNCT
ejpam-5901	399	11	n−	n−	NOUN
ejpam-5901	399	12	ϵ+	ϵ+	PUNCT
ejpam-5901	399	13	1)ϱ1	1)ϱ1	NUM
ejpam-5901	399	14	(	(	PUNCT
ejpam-5901	399	15	n−	n−	NOUN
ejpam-5901	399	16	ϵ+	ϵ+	PUNCT
ejpam-5901	399	17	2	2	NUM
ejpam-5901	399	18	+	+	CCONJ
ejpam-5901	399	19	ϱ1	ϱ1	NOUN
ejpam-5901	399	20	)	)	PUNCT
ejpam-5901	399	21	−(n−	−(n−	VERB
ejpam-5901	399	22	ϵ)ϱ1	ϵ)ϱ1	PROPN
ejpam-5901	399	23	(	(	PUNCT
ejpam-5901	399	24	n−	n−	NOUN
ejpam-5901	399	25	ϵ+	ϵ+	X
ejpam-5901	399	26	2	2	NUM
ejpam-5901	399	27	+	+	SYM
ejpam-5901	399	28	2ϱ1	2ϱ1	NUM
ejpam-5901	399	29	)	)	PUNCT
ejpam-5901	399	30	)	)	PUNCT
ejpam-5901	400	1	−w2	−w2	PROPN
ejpam-5901	400	2	(	(	PUNCT
ejpam-5901	400	3	tϵ−1,cϵ−1	tϵ−1,cϵ−1	PROPN
ejpam-5901	400	4	)	)	PUNCT
ejpam-5901	400	5	(	(	PUNCT
ejpam-5901	400	6	(	(	PUNCT
ejpam-5901	400	7	n−	n−	NOUN
ejpam-5901	400	8	ϵ+	ϵ+	X
ejpam-5901	400	9	1)ϱ1	1)ϱ1	NUM
ejpam-5901	400	10	+	+	PROPN
ejpam-5901	400	11	1	1	NUM
ejpam-5901	400	12	−	−	NOUN
ejpam-5901	400	13	(	(	PUNCT
ejpam-5901	400	14	n−	n−	NOUN
ejpam-5901	400	15	ϵ+	ϵ+	PUNCT
ejpam-5901	400	16	1	1	NUM
ejpam-5901	400	17	+	+	CCONJ
ejpam-5901	400	18	ϱ1	ϱ1	NOUN
ejpam-5901	400	19	)	)	PUNCT
ejpam-5901	400	20	(	(	PUNCT
ejpam-5901	400	21	n−	n−	NOUN
ejpam-5901	400	22	ϵ)ϱ1	ϵ)ϱ1	PROPN
ejpam-5901	400	23	)	)	PUNCT
ejpam-5901	400	24	]	]	PUNCT
ejpam-5901	400	25	,	,	PUNCT
ejpam-5901	400	26	in+1	in+1	X
ejpam-5901	400	27	=	=	SYM
ejpam-5901	400	28	i(0	i(0	PROPN
ejpam-5901	400	29	)	)	PUNCT
ejpam-5901	401	1	+	+	PUNCT
ejpam-5901	401	2	ϱ2	ϱ2	PROPN
ejpam-5901	401	3	t	t	NOUN
ejpam-5901	401	4	ϱ2−1	ϱ2−1	NOUN
ejpam-5901	401	5	1−	1−	NUM
ejpam-5901	401	6	ϱ1	ϱ1	PROPN
ejpam-5901	401	7	ℏ(ϱ1	ℏ(ϱ1	NOUN
ejpam-5901	401	8	)	)	PUNCT
ejpam-5901	401	9	w3	w3	PROPN
ejpam-5901	401	10	(	(	PUNCT
ejpam-5901	401	11	tϵ	tϵ	NOUN
ejpam-5901	401	12	,	,	PUNCT
ejpam-5901	401	13	i	i	PRON
ejpam-5901	401	14	(	(	PUNCT
ejpam-5901	401	15	tϵ	tϵ	NOUN
ejpam-5901	401	16	)	)	PUNCT
ejpam-5901	401	17	)	)	PUNCT
ejpam-5901	402	1	+	+	CCONJ
ejpam-5901	402	2	ϱ2	ϱ2	PROPN
ejpam-5901	402	3	t	t	PROPN
ejpam-5901	402	4	ϱ2−1	ϱ2−1	NOUN
ejpam-5901	402	5	ϱ1h	ϱ1h	ADP
ejpam-5901	402	6	ϱ1	ϱ1	PROPN
ejpam-5901	402	7	γ	γ	X
ejpam-5901	402	8	(	(	PUNCT
ejpam-5901	402	9	ϱ1	ϱ1	NOUN
ejpam-5901	402	10	+	+	CCONJ
ejpam-5901	402	11	2	2	X
ejpam-5901	402	12	)	)	PUNCT
ejpam-5901	402	13	×	×	NOUN
ejpam-5901	402	14	n∑	n∑	NOUN
ejpam-5901	402	15	ϵ=1	ϵ=1	PUNCT
ejpam-5901	403	1	[	[	X
ejpam-5901	403	2	w3	w3	PROPN
ejpam-5901	403	3	(	(	PUNCT
ejpam-5901	403	4	tϵ	tϵ	NOUN
ejpam-5901	403	5	,	,	PUNCT
ejpam-5901	403	6	i	i	PRON
ejpam-5901	403	7	(	(	PUNCT
ejpam-5901	403	8	tϵ	tϵ	NOUN
ejpam-5901	403	9	)	)	PUNCT
ejpam-5901	403	10	)	)	PUNCT
ejpam-5901	403	11	(	(	PUNCT
ejpam-5901	403	12	(	(	PUNCT
ejpam-5901	403	13	n−	n−	NOUN
ejpam-5901	403	14	ϵ+	ϵ+	PUNCT
ejpam-5901	403	15	1)ϱ1	1)ϱ1	NUM
ejpam-5901	403	16	(	(	PUNCT
ejpam-5901	403	17	n−	n−	NOUN
ejpam-5901	403	18	ϵ+	ϵ+	PUNCT
ejpam-5901	403	19	2	2	NUM
ejpam-5901	403	20	+	+	CCONJ
ejpam-5901	403	21	ϱ1	ϱ1	NOUN
ejpam-5901	403	22	)	)	PUNCT
ejpam-5901	403	23	−(n−	−(n−	VERB
ejpam-5901	403	24	ϵ)ϱ1	ϵ)ϱ1	PROPN
ejpam-5901	403	25	(	(	PUNCT
ejpam-5901	403	26	n−	n−	NOUN
ejpam-5901	403	27	ϵ+	ϵ+	X
ejpam-5901	403	28	2	2	NUM
ejpam-5901	403	29	+	+	NUM
ejpam-5901	403	30	2ϱ1	2ϱ1	NUM
ejpam-5901	403	31	)	)	PUNCT
ejpam-5901	403	32	)	)	PUNCT
ejpam-5901	404	1	−w3	−w3	PROPN
ejpam-5901	404	2	(	(	PUNCT
ejpam-5901	404	3	tϵ−1	tϵ−1	PROPN
ejpam-5901	404	4	,	,	PUNCT
ejpam-5901	404	5	iϵ−1	iϵ−1	PROPN
ejpam-5901	404	6	)	)	PUNCT
ejpam-5901	404	7	(	(	PUNCT
ejpam-5901	404	8	(	(	PUNCT
ejpam-5901	404	9	n−	n−	NOUN
ejpam-5901	404	10	ϵ+	ϵ+	X
ejpam-5901	404	11	1)ϱ1	1)ϱ1	NUM
ejpam-5901	404	12	+	+	PROPN
ejpam-5901	404	13	1	1	NUM
ejpam-5901	404	14	−	−	NOUN
ejpam-5901	404	15	(	(	PUNCT
ejpam-5901	404	16	n−	n−	NOUN
ejpam-5901	404	17	ϵ+	ϵ+	PUNCT
ejpam-5901	404	18	1	1	NUM
ejpam-5901	404	19	+	+	CCONJ
ejpam-5901	404	20	ϱ1	ϱ1	NOUN
ejpam-5901	404	21	)	)	PUNCT
ejpam-5901	404	22	(	(	PUNCT
ejpam-5901	404	23	n−	n−	NOUN
ejpam-5901	404	24	ϵ)ϱ1	ϵ)ϱ1	PROPN
ejpam-5901	404	25	)	)	PUNCT
ejpam-5901	404	26	]	]	PUNCT
ejpam-5901	404	27	,	,	PUNCT
ejpam-5901	404	28	rn+1	rn+1	X
ejpam-5901	404	29	=	=	SYM
ejpam-5901	404	30	r(0	r(0	PROPN
ejpam-5901	404	31	)	)	PUNCT
ejpam-5901	405	1	+	+	SYM
ejpam-5901	405	2	ϱ2	ϱ2	PROPN
ejpam-5901	405	3	t	t	NOUN
ejpam-5901	405	4	ϱ2−1	ϱ2−1	NOUN
ejpam-5901	405	5	1−	1−	NUM
ejpam-5901	405	6	ϱ1	ϱ1	PROPN
ejpam-5901	405	7	ℏ(ϱ1	ℏ(ϱ1	NOUN
ejpam-5901	405	8	)	)	PUNCT
ejpam-5901	405	9	w4	w4	NOUN
ejpam-5901	405	10	(	(	PUNCT
ejpam-5901	405	11	tϵ,r(tϵ	tϵ,r(tϵ	NOUN
ejpam-5901	405	12	)	)	PUNCT
ejpam-5901	405	13	)	)	PUNCT
ejpam-5901	406	1	+	+	CCONJ
ejpam-5901	406	2	ϱ2	ϱ2	PROPN
ejpam-5901	406	3	t	t	PROPN
ejpam-5901	406	4	ϱ2−1	ϱ2−1	NOUN
ejpam-5901	406	5	ϱ1h	ϱ1h	ADP
ejpam-5901	406	6	ϱ1	ϱ1	PROPN
ejpam-5901	406	7	γ	γ	X
ejpam-5901	406	8	(	(	PUNCT
ejpam-5901	406	9	ϱ1	ϱ1	NOUN
ejpam-5901	406	10	+	+	CCONJ
ejpam-5901	406	11	2	2	X
ejpam-5901	406	12	)	)	PUNCT
ejpam-5901	406	13	×	×	NOUN
ejpam-5901	406	14	n∑	n∑	NOUN
ejpam-5901	406	15	ϵ=1	ϵ=1	PUNCT
ejpam-5901	407	1	[	[	X
ejpam-5901	407	2	w4	w4	NOUN
ejpam-5901	407	3	(	(	PUNCT
ejpam-5901	407	4	tϵ,r(tϵ	tϵ,r(tϵ	NOUN
ejpam-5901	407	5	)	)	PUNCT
ejpam-5901	407	6	)	)	PUNCT
ejpam-5901	407	7	(	(	PUNCT
ejpam-5901	407	8	(	(	PUNCT
ejpam-5901	407	9	n−	n−	NOUN
ejpam-5901	407	10	ϵ+	ϵ+	PUNCT
ejpam-5901	407	11	1)ϱ1	1)ϱ1	NUM
ejpam-5901	407	12	(	(	PUNCT
ejpam-5901	407	13	n−	n−	NOUN
ejpam-5901	407	14	ϵ+	ϵ+	PUNCT
ejpam-5901	407	15	2	2	NUM
ejpam-5901	407	16	+	+	CCONJ
ejpam-5901	407	17	ϱ1	ϱ1	NOUN
ejpam-5901	407	18	)	)	PUNCT
ejpam-5901	407	19	−(n−	−(n−	VERB
ejpam-5901	407	20	ϵ)ϱ1	ϵ)ϱ1	PROPN
ejpam-5901	407	21	(	(	PUNCT
ejpam-5901	407	22	n−	n−	NOUN
ejpam-5901	407	23	ϵ+	ϵ+	X
ejpam-5901	407	24	2	2	NUM
ejpam-5901	407	25	+	+	NUM
ejpam-5901	407	26	2ϱ1	2ϱ1	NUM
ejpam-5901	407	27	)	)	PUNCT
ejpam-5901	407	28	)	)	PUNCT
ejpam-5901	408	1	−w4	−w4	NOUN
ejpam-5901	408	2	(	(	PUNCT
ejpam-5901	408	3	tϵ−1,rϵ−1	tϵ−1,rϵ−1	NOUN
ejpam-5901	408	4	)	)	PUNCT
ejpam-5901	408	5	(	(	PUNCT
ejpam-5901	408	6	(	(	PUNCT
ejpam-5901	408	7	n−	n−	NOUN
ejpam-5901	408	8	ϵ+	ϵ+	X
ejpam-5901	408	9	1)ϱ1	1)ϱ1	NUM
ejpam-5901	408	10	+	+	PROPN
ejpam-5901	408	11	1	1	NUM
ejpam-5901	408	12	−	−	NOUN
ejpam-5901	408	13	(	(	PUNCT
ejpam-5901	408	14	n−	n−	NOUN
ejpam-5901	408	15	ϵ+	ϵ+	PUNCT
ejpam-5901	408	16	1	1	NUM
ejpam-5901	408	17	+	+	CCONJ
ejpam-5901	408	18	ϱ1	ϱ1	NOUN
ejpam-5901	408	19	)	)	PUNCT
ejpam-5901	408	20	(	(	PUNCT
ejpam-5901	408	21	n−	n−	NOUN
ejpam-5901	408	22	ϵ)ϱ1	ϵ)ϱ1	PROPN
ejpam-5901	408	23	)	)	PUNCT
ejpam-5901	408	24	]	]	PUNCT
ejpam-5901	408	25	.	.	PUNCT
ejpam-5901	409	1	7.1	7.1	NUM
ejpam-5901	409	2	.	.	PUNCT
ejpam-5901	410	1	numerical	numerical	ADJ
ejpam-5901	410	2	simulations	simulation	NOUN
ejpam-5901	410	3	and	and	CCONJ
ejpam-5901	410	4	discussion	discussion	NOUN
ejpam-5901	410	5	detailed	detailed	ADJ
ejpam-5901	410	6	computations	computation	NOUN
ejpam-5901	410	7	of	of	ADP
ejpam-5901	410	8	model	model	NOUN
ejpam-5901	410	9	(	(	PUNCT
ejpam-5901	410	10	2	2	NUM
ejpam-5901	410	11	)	)	PUNCT
ejpam-5901	410	12	with	with	ADP
ejpam-5901	410	13	a	a	DET
ejpam-5901	410	14	particular	particular	ADJ
ejpam-5901	410	15	formulation	formulation	NOUN
ejpam-5901	410	16	are	be	AUX
ejpam-5901	410	17	presented	present	VERB
ejpam-5901	410	18	here	here	ADV
ejpam-5901	410	19	.	.	PUNCT
ejpam-5901	411	1	the	the	DET
ejpam-5901	411	2	numerical	numerical	ADJ
ejpam-5901	411	3	values	value	NOUN
ejpam-5901	411	4	are	be	AUX
ejpam-5901	411	5	given	give	VERB
ejpam-5901	411	6	from	from	ADP
ejpam-5901	411	7	[	[	X
ejpam-5901	411	8	62	62	NUM
ejpam-5901	411	9	]	]	SYM
ejpam-5901	411	10	:	:	PUNCT
ejpam-5901	411	11	s(0	s(0	PROPN
ejpam-5901	411	12	)	)	PUNCT
ejpam-5901	411	13	=	=	SYM
ejpam-5901	411	14	0.9	0.9	NUM
ejpam-5901	411	15	,	,	PUNCT
ejpam-5901	411	16	c(0	c(0	NOUN
ejpam-5901	411	17	)	)	PUNCT
ejpam-5901	411	18	=	=	SYM
ejpam-5901	411	19	0.2	0.2	NUM
ejpam-5901	411	20	,	,	PUNCT
ejpam-5901	411	21	i(0	i(0	PROPN
ejpam-5901	411	22	)	)	PUNCT
ejpam-5901	411	23	=	=	SYM
ejpam-5901	411	24	0.3	0.3	NUM
ejpam-5901	411	25	,	,	PUNCT
ejpam-5901	411	26	r(0	r(0	PROPN
ejpam-5901	411	27	)	)	PUNCT
ejpam-5901	411	28	=	=	PUNCT
ejpam-5901	411	29	0.1	0.1	NUM
ejpam-5901	411	30	.	.	PUNCT
ejpam-5901	412	1	the	the	DET
ejpam-5901	412	2	following	follow	VERB
ejpam-5901	412	3	figures	figure	NOUN
ejpam-5901	412	4	provide	provide	VERB
ejpam-5901	412	5	a	a	DET
ejpam-5901	412	6	numerical	numerical	ADJ
ejpam-5901	412	7	description	description	NOUN
ejpam-5901	412	8	of	of	ADP
ejpam-5901	412	9	the	the	DET
ejpam-5901	412	10	model	model	NOUN
ejpam-5901	412	11	.	.	PUNCT
ejpam-5901	413	1	fig	fig	NOUN
ejpam-5901	413	2	.	.	PUNCT
ejpam-5901	414	1	1	1	NUM
ejpam-5901	414	2	is	be	AUX
ejpam-5901	414	3	a	a	DET
ejpam-5901	414	4	description	description	NOUN
ejpam-5901	414	5	of	of	ADP
ejpam-5901	414	6	the	the	DET
ejpam-5901	414	7	numerical	numerical	ADJ
ejpam-5901	414	8	data	datum	NOUN
ejpam-5901	414	9	for	for	ADP
ejpam-5901	414	10	the	the	DET
ejpam-5901	414	11	s(t	s(t	PROPN
ejpam-5901	414	12	)	)	PUNCT
ejpam-5901	414	13	.	.	PUNCT
ejpam-5901	415	1	the	the	DET
ejpam-5901	415	2	numerical	numerical	ADJ
ejpam-5901	415	3	simulations	simulation	NOUN
ejpam-5901	415	4	presented	present	VERB
ejpam-5901	415	5	in	in	ADP
ejpam-5901	415	6	the	the	DET
ejpam-5901	415	7	figures	figure	NOUN
ejpam-5901	415	8	highlight	highlight	VERB
ejpam-5901	415	9	the	the	DET
ejpam-5901	415	10	impact	impact	NOUN
ejpam-5901	415	11	of	of	ADP
ejpam-5901	415	12	fractalfractional	fractalfractional	ADJ
ejpam-5901	415	13	operators	operator	NOUN
ejpam-5901	415	14	on	on	ADP
ejpam-5901	415	15	the	the	DET
ejpam-5901	415	16	dynamics	dynamic	NOUN
ejpam-5901	415	17	of	of	ADP
ejpam-5901	415	18	pneumonia	pneumonia	NOUN
ejpam-5901	415	19	transmission	transmission	NOUN
ejpam-5901	415	20	.	.	PUNCT
ejpam-5901	416	1	the	the	DET
ejpam-5901	416	2	variations	variation	NOUN
ejpam-5901	416	3	in	in	ADP
ejpam-5901	416	4	the	the	DET
ejpam-5901	416	5	fractional	fractional	ADJ
ejpam-5901	416	6	orders	order	NOUN
ejpam-5901	416	7	demonstrate	demonstrate	VERB
ejpam-5901	416	8	the	the	DET
ejpam-5901	416	9	flexibility	flexibility	NOUN
ejpam-5901	416	10	and	and	CCONJ
ejpam-5901	416	11	accuracy	accuracy	NOUN
ejpam-5901	416	12	of	of	ADP
ejpam-5901	416	13	the	the	DET
ejpam-5901	416	14	fractal	fractal	ADJ
ejpam-5901	416	15	-	-	PUNCT
ejpam-5901	416	16	fractional	fractional	ADJ
ejpam-5901	416	17	approach	approach	NOUN
ejpam-5901	416	18	in	in	ADP
ejpam-5901	416	19	capturing	capture	VERB
ejpam-5901	416	20	different	different	ADJ
ejpam-5901	416	21	dynamical	dynamical	ADJ
ejpam-5901	416	22	behaviors	behavior	NOUN
ejpam-5901	416	23	,	,	PUNCT
ejpam-5901	416	24	as	as	SCONJ
ejpam-5901	416	25	compared	compare	VERB
ejpam-5901	416	26	to	to	ADP
ejpam-5901	416	27	the	the	DET
ejpam-5901	416	28	classical	classical	ADJ
ejpam-5901	416	29	integer	integer	NOUN
ejpam-5901	416	30	-	-	PUNCT
ejpam-5901	416	31	order	order	NOUN
ejpam-5901	416	32	models	model	NOUN
ejpam-5901	416	33	.	.	PUNCT
ejpam-5901	417	1	in	in	ADP
ejpam-5901	417	2	figure	figure	NOUN
ejpam-5901	417	3	1	1	NUM
ejpam-5901	417	4	,	,	PUNCT
ejpam-5901	417	5	the	the	DET
ejpam-5901	417	6	dynamics	dynamic	NOUN
ejpam-5901	417	7	of	of	ADP
ejpam-5901	417	8	the	the	DET
ejpam-5901	417	9	susceptible	susceptible	ADJ
ejpam-5901	417	10	population	population	NOUN
ejpam-5901	417	11	s(t	s(t	PROPN
ejpam-5901	417	12	)	)	PUNCT
ejpam-5901	417	13	show	show	VERB
ejpam-5901	417	14	an	an	DET
ejpam-5901	417	15	initial	initial	ADJ
ejpam-5901	417	16	increase	increase	NOUN
ejpam-5901	417	17	,	,	PUNCT
ejpam-5901	417	18	reflecting	reflect	VERB
ejpam-5901	417	19	the	the	DET
ejpam-5901	417	20	recruitment	recruitment	NOUN
ejpam-5901	417	21	rate	rate	NOUN
ejpam-5901	417	22	into	into	ADP
ejpam-5901	417	23	the	the	DET
ejpam-5901	417	24	susceptible	susceptible	ADJ
ejpam-5901	417	25	class	class	NOUN
ejpam-5901	417	26	,	,	PUNCT
ejpam-5901	417	27	followed	follow	VERB
ejpam-5901	417	28	by	by	ADP
ejpam-5901	417	29	stabilization	stabilization	NOUN
ejpam-5901	417	30	.	.	PUNCT
ejpam-5901	418	1	this	this	DET
ejpam-5901	418	2	behavior	behavior	NOUN
ejpam-5901	418	3	is	be	AUX
ejpam-5901	418	4	consistent	consistent	ADJ
ejpam-5901	418	5	across	across	ADP
ejpam-5901	418	6	different	different	ADJ
ejpam-5901	418	7	fractional	fractional	ADJ
ejpam-5901	418	8	orders	order	NOUN
ejpam-5901	418	9	,	,	PUNCT
ejpam-5901	418	10	emphasizing	emphasize	VERB
ejpam-5901	418	11	the	the	DET
ejpam-5901	418	12	robustness	robustness	NOUN
ejpam-5901	418	13	of	of	ADP
ejpam-5901	418	14	the	the	DET
ejpam-5901	418	15	model	model	NOUN
ejpam-5901	418	16	in	in	ADP
ejpam-5901	418	17	predicting	predict	VERB
ejpam-5901	418	18	long	long	ADJ
ejpam-5901	418	19	-	-	PUNCT
ejpam-5901	418	20	term	term	NOUN
ejpam-5901	418	21	stability	stability	NOUN
ejpam-5901	418	22	.	.	PUNCT
ejpam-5901	419	1	this	this	DET
ejpam-5901	419	2	figure	figure	NOUN
ejpam-5901	419	3	illustrates	illustrate	VERB
ejpam-5901	419	4	the	the	DET
ejpam-5901	419	5	evolution	evolution	NOUN
ejpam-5901	419	6	of	of	ADP
ejpam-5901	419	7	the	the	DET
ejpam-5901	419	8	susceptible	susceptible	ADJ
ejpam-5901	419	9	population	population	NOUN
ejpam-5901	419	10	over	over	ADP
ejpam-5901	419	11	time	time	NOUN
ejpam-5901	419	12	for	for	ADP
ejpam-5901	419	13	different	different	ADJ
ejpam-5901	419	14	fractional	fractional	ADJ
ejpam-5901	419	15	orders	order	NOUN
ejpam-5901	419	16	.	.	PUNCT
ejpam-5901	420	1	the	the	DET
ejpam-5901	420	2	population	population	NOUN
ejpam-5901	420	3	initially	initially	ADV
ejpam-5901	420	4	increases	increase	VERB
ejpam-5901	420	5	due	due	ADJ
ejpam-5901	420	6	to	to	ADP
ejpam-5901	420	7	recruitment	recruitment	NOUN
ejpam-5901	420	8	into	into	ADP
ejpam-5901	420	9	the	the	DET
ejpam-5901	420	10	susceptible	susceptible	ADJ
ejpam-5901	420	11	class	class	NOUN
ejpam-5901	420	12	and	and	CCONJ
ejpam-5901	420	13	then	then	ADV
ejpam-5901	420	14	stabilizes	stabilize	VERB
ejpam-5901	420	15	.	.	PUNCT
ejpam-5901	421	1	higher	high	ADJ
ejpam-5901	421	2	fractional	fractional	ADJ
ejpam-5901	421	3	orders	order	NOUN
ejpam-5901	421	4	(	(	PUNCT
ejpam-5901	421	5	α	α	NOUN
ejpam-5901	421	6	≈	≈	PROPN
ejpam-5901	421	7	1	1	NUM
ejpam-5901	421	8	)	)	PUNCT
ejpam-5901	421	9	exhibit	exhibit	NOUN
ejpam-5901	421	10	behavior	behavior	NOUN
ejpam-5901	421	11	similar	similar	ADJ
ejpam-5901	421	12	to	to	ADP
ejpam-5901	421	13	classical	classical	ADJ
ejpam-5901	421	14	models	model	NOUN
ejpam-5901	421	15	,	,	PUNCT
ejpam-5901	421	16	whereas	whereas	SCONJ
ejpam-5901	421	17	lower	low	ADJ
ejpam-5901	421	18	orders	order	NOUN
ejpam-5901	421	19	introduce	introduce	VERB
ejpam-5901	421	20	stronger	strong	ADJ
ejpam-5901	421	21	memory	memory	NOUN
ejpam-5901	421	22	effects	effect	NOUN
ejpam-5901	421	23	,	,	PUNCT
ejpam-5901	421	24	altering	alter	VERB
ejpam-5901	421	25	the	the	DET
ejpam-5901	421	26	system	system	NOUN
ejpam-5901	421	27	’s	’s	PART
ejpam-5901	421	28	response	response	NOUN
ejpam-5901	421	29	.	.	PUNCT
ejpam-5901	422	1	figure	figure	NOUN
ejpam-5901	422	2	2	2	NUM
ejpam-5901	422	3	illustrates	illustrate	VERB
ejpam-5901	422	4	the	the	DET
ejpam-5901	422	5	behavior	behavior	NOUN
ejpam-5901	422	6	of	of	ADP
ejpam-5901	422	7	the	the	DET
ejpam-5901	422	8	carrier	carrier	NOUN
ejpam-5901	422	9	population	population	NOUN
ejpam-5901	422	10	c(t	c(t	PROPN
ejpam-5901	422	11	)	)	PUNCT
ejpam-5901	422	12	,	,	PUNCT
ejpam-5901	422	13	which	which	PRON
ejpam-5901	422	14	exhibits	exhibit	VERB
ejpam-5901	422	15	an	an	DET
ejpam-5901	422	16	early	early	ADJ
ejpam-5901	422	17	decline	decline	NOUN
ejpam-5901	422	18	before	before	ADP
ejpam-5901	422	19	stabilizing	stabilize	VERB
ejpam-5901	422	20	.	.	PUNCT
ejpam-5901	423	1	this	this	DET
ejpam-5901	423	2	decline	decline	NOUN
ejpam-5901	423	3	suggests	suggest	VERB
ejpam-5901	423	4	that	that	SCONJ
ejpam-5901	423	5	carriers	carrier	NOUN
ejpam-5901	423	6	either	either	CCONJ
ejpam-5901	423	7	progress	progress	VERB
ejpam-5901	423	8	to	to	ADP
ejpam-5901	423	9	the	the	DET
ejpam-5901	423	10	infected	infected	ADJ
ejpam-5901	423	11	class	class	NOUN
ejpam-5901	423	12	or	or	CCONJ
ejpam-5901	423	13	recover	recover	NOUN
ejpam-5901	423	14	due	due	ADP
ejpam-5901	423	15	to	to	ADP
ejpam-5901	423	16	treatment	treatment	NOUN
ejpam-5901	423	17	or	or	CCONJ
ejpam-5901	423	18	natural	natural	ADJ
ejpam-5901	423	19	immunity	immunity	NOUN
ejpam-5901	423	20	.	.	PUNCT
ejpam-5901	424	1	the	the	DET
ejpam-5901	424	2	rate	rate	NOUN
ejpam-5901	424	3	of	of	ADP
ejpam-5901	424	4	change	change	NOUN
ejpam-5901	424	5	is	be	AUX
ejpam-5901	424	6	influenced	influence	VERB
ejpam-5901	424	7	by	by	ADP
ejpam-5901	424	8	the	the	DET
ejpam-5901	424	9	fractional	fractional	ADJ
ejpam-5901	424	10	order	order	NOUN
ejpam-5901	424	11	,	,	PUNCT
ejpam-5901	424	12	indicating	indicate	VERB
ejpam-5901	424	13	the	the	DET
ejpam-5901	424	14	significance	significance	NOUN
ejpam-5901	424	15	of	of	ADP
ejpam-5901	424	16	memory	memory	NOUN
ejpam-5901	424	17	effects	effect	NOUN
ejpam-5901	424	18	in	in	ADP
ejpam-5901	424	19	disease	disease	NOUN
ejpam-5901	424	20	progression	progression	NOUN
ejpam-5901	424	21	.	.	PUNCT
ejpam-5901	425	1	the	the	DET
ejpam-5901	425	2	dynamics	dynamic	NOUN
ejpam-5901	425	3	of	of	ADP
ejpam-5901	425	4	carriers	carrier	NOUN
ejpam-5901	425	5	,	,	PUNCT
ejpam-5901	425	6	who	who	PRON
ejpam-5901	425	7	are	be	AUX
ejpam-5901	425	8	infected	infect	VERB
ejpam-5901	425	9	but	but	CCONJ
ejpam-5901	425	10	asymptomatic	asymptomatic	ADJ
ejpam-5901	425	11	,	,	PUNCT
ejpam-5901	425	12	are	be	AUX
ejpam-5901	425	13	displayed	display	VERB
ejpam-5901	425	14	.	.	PUNCT
ejpam-5901	426	1	the	the	DET
ejpam-5901	426	2	carrier	carrier	NOUN
ejpam-5901	426	3	population	population	NOUN
ejpam-5901	426	4	declines	decline	VERB
ejpam-5901	426	5	over	over	ADP
ejpam-5901	426	6	time	time	NOUN
ejpam-5901	426	7	,	,	PUNCT
ejpam-5901	426	8	s.	s.	PROPN
ejpam-5901	426	9	saber	saber	PROPN
ejpam-5901	426	10	,	,	PUNCT
ejpam-5901	426	11	a.	a.	NOUN
ejpam-5901	426	12	a.	a.	NOUN
ejpam-5901	426	13	alahmari	alahmari	PROPN
ejpam-5901	426	14	/	/	SYM
ejpam-5901	426	15	eur	eur	PROPN
ejpam-5901	426	16	.	.	PUNCT
ejpam-5901	427	1	j.	j.	PROPN
ejpam-5901	427	2	pure	pure	PROPN
ejpam-5901	427	3	appl	appl	PROPN
ejpam-5901	427	4	.	.	PROPN
ejpam-5901	427	5	math	math	PROPN
ejpam-5901	427	6	,	,	PUNCT
ejpam-5901	427	7	18	18	NUM
ejpam-5901	427	8	(	(	PUNCT
ejpam-5901	427	9	2	2	NUM
ejpam-5901	427	10	)	)	PUNCT
ejpam-5901	427	11	(	(	PUNCT
ejpam-5901	427	12	2025	2025	NUM
ejpam-5901	427	13	)	)	PUNCT
ejpam-5901	427	14	,	,	PUNCT
ejpam-5901	427	15	5901	5901	NUM
ejpam-5901	427	16	17	17	NUM
ejpam-5901	427	17	of	of	ADP
ejpam-5901	427	18	23	23	NUM
ejpam-5901	427	19	indicating	indicate	VERB
ejpam-5901	427	20	progression	progression	NOUN
ejpam-5901	427	21	to	to	ADP
ejpam-5901	427	22	the	the	DET
ejpam-5901	427	23	infected	infected	ADJ
ejpam-5901	427	24	class	class	NOUN
ejpam-5901	427	25	or	or	CCONJ
ejpam-5901	427	26	recovery	recovery	NOUN
ejpam-5901	427	27	.	.	PUNCT
ejpam-5901	428	1	lower	low	ADJ
ejpam-5901	428	2	fractional	fractional	ADJ
ejpam-5901	428	3	orders	order	NOUN
ejpam-5901	428	4	slow	slow	VERB
ejpam-5901	428	5	down	down	ADP
ejpam-5901	428	6	the	the	DET
ejpam-5901	428	7	decline	decline	NOUN
ejpam-5901	428	8	,	,	PUNCT
ejpam-5901	428	9	showing	show	VERB
ejpam-5901	428	10	the	the	DET
ejpam-5901	428	11	influence	influence	NOUN
ejpam-5901	428	12	of	of	ADP
ejpam-5901	428	13	memory	memory	NOUN
ejpam-5901	428	14	effects	effect	NOUN
ejpam-5901	428	15	on	on	ADP
ejpam-5901	428	16	disease	disease	NOUN
ejpam-5901	428	17	transmission	transmission	NOUN
ejpam-5901	428	18	.	.	PUNCT
ejpam-5901	429	1	figure	figure	NOUN
ejpam-5901	429	2	shows	show	VERB
ejpam-5901	429	3	the	the	DET
ejpam-5901	429	4	infected	infected	ADJ
ejpam-5901	429	5	population	population	NOUN
ejpam-5901	429	6	i(t	i(t	PROPN
ejpam-5901	429	7	)	)	PUNCT
ejpam-5901	429	8	,	,	PUNCT
ejpam-5901	429	9	which	which	PRON
ejpam-5901	429	10	initially	initially	ADV
ejpam-5901	429	11	increases	increase	VERB
ejpam-5901	429	12	before	before	ADP
ejpam-5901	429	13	declining	decline	VERB
ejpam-5901	429	14	and	and	CCONJ
ejpam-5901	429	15	stabilizing	stabilizing	NOUN
ejpam-5901	429	16	.	.	PUNCT
ejpam-5901	430	1	the	the	DET
ejpam-5901	430	2	infected	infected	ADJ
ejpam-5901	430	3	class	class	NOUN
ejpam-5901	430	4	dynamics	dynamic	NOUN
ejpam-5901	430	5	are	be	AUX
ejpam-5901	430	6	particularly	particularly	ADV
ejpam-5901	430	7	sensitive	sensitive	ADJ
ejpam-5901	430	8	to	to	ADP
ejpam-5901	430	9	changes	change	NOUN
ejpam-5901	430	10	in	in	ADP
ejpam-5901	430	11	fractional	fractional	ADJ
ejpam-5901	430	12	orders	order	NOUN
ejpam-5901	430	13	,	,	PUNCT
ejpam-5901	430	14	as	as	SCONJ
ejpam-5901	430	15	lower	low	ADJ
ejpam-5901	430	16	orders	order	NOUN
ejpam-5901	430	17	lead	lead	VERB
ejpam-5901	430	18	to	to	ADP
ejpam-5901	430	19	faster	fast	ADJ
ejpam-5901	430	20	stabilization	stabilization	NOUN
ejpam-5901	430	21	.	.	PUNCT
ejpam-5901	431	1	this	this	DET
ejpam-5901	431	2	result	result	NOUN
ejpam-5901	431	3	reflects	reflect	VERB
ejpam-5901	431	4	the	the	DET
ejpam-5901	431	5	importance	importance	NOUN
ejpam-5901	431	6	of	of	ADP
ejpam-5901	431	7	fractional	fractional	ADJ
ejpam-5901	431	8	derivatives	derivative	NOUN
ejpam-5901	431	9	in	in	ADP
ejpam-5901	431	10	modeling	model	VERB
ejpam-5901	431	11	the	the	DET
ejpam-5901	431	12	memory	memory	NOUN
ejpam-5901	431	13	and	and	CCONJ
ejpam-5901	431	14	long	long	ADJ
ejpam-5901	431	15	-	-	PUNCT
ejpam-5901	431	16	term	term	NOUN
ejpam-5901	431	17	effects	effect	NOUN
ejpam-5901	431	18	of	of	ADP
ejpam-5901	431	19	the	the	DET
ejpam-5901	431	20	infection	infection	NOUN
ejpam-5901	431	21	process	process	NOUN
ejpam-5901	431	22	.	.	PUNCT
ejpam-5901	432	1	the	the	DET
ejpam-5901	432	2	number	number	NOUN
ejpam-5901	432	3	of	of	ADP
ejpam-5901	432	4	infected	infect	VERB
ejpam-5901	432	5	individuals	individual	NOUN
ejpam-5901	432	6	initially	initially	ADV
ejpam-5901	432	7	rises	rise	VERB
ejpam-5901	432	8	,	,	PUNCT
ejpam-5901	432	9	peaks	peak	NOUN
ejpam-5901	432	10	,	,	PUNCT
ejpam-5901	432	11	and	and	CCONJ
ejpam-5901	432	12	then	then	ADV
ejpam-5901	432	13	declines	decline	VERB
ejpam-5901	432	14	as	as	SCONJ
ejpam-5901	432	15	people	people	NOUN
ejpam-5901	432	16	recover	recover	VERB
ejpam-5901	432	17	or	or	CCONJ
ejpam-5901	432	18	die	die	VERB
ejpam-5901	432	19	.	.	PUNCT
ejpam-5901	433	1	fractional	fractional	ADJ
ejpam-5901	433	2	models	model	NOUN
ejpam-5901	433	3	exhibit	exhibit	VERB
ejpam-5901	433	4	smoother	smooth	ADJ
ejpam-5901	433	5	transitions	transition	NOUN
ejpam-5901	433	6	and	and	CCONJ
ejpam-5901	433	7	prolonged	prolonged	ADJ
ejpam-5901	433	8	infection	infection	NOUN
ejpam-5901	433	9	durations	duration	NOUN
ejpam-5901	433	10	compared	compare	VERB
ejpam-5901	433	11	to	to	ADP
ejpam-5901	433	12	classical	classical	ADJ
ejpam-5901	433	13	integer	integer	NOUN
ejpam-5901	433	14	-	-	PUNCT
ejpam-5901	433	15	order	order	NOUN
ejpam-5901	433	16	models	model	NOUN
ejpam-5901	433	17	.	.	PUNCT
ejpam-5901	434	1	the	the	DET
ejpam-5901	434	2	choice	choice	NOUN
ejpam-5901	434	3	of	of	ADP
ejpam-5901	434	4	fractional	fractional	ADJ
ejpam-5901	434	5	order	order	NOUN
ejpam-5901	434	6	significantly	significantly	ADV
ejpam-5901	434	7	affects	affect	VERB
ejpam-5901	434	8	the	the	DET
ejpam-5901	434	9	persistence	persistence	NOUN
ejpam-5901	434	10	of	of	ADP
ejpam-5901	434	11	the	the	DET
ejpam-5901	434	12	disease	disease	NOUN
ejpam-5901	434	13	within	within	ADP
ejpam-5901	434	14	the	the	DET
ejpam-5901	434	15	population	population	NOUN
ejpam-5901	434	16	.	.	PUNCT
ejpam-5901	435	1	the	the	DET
ejpam-5901	435	2	recovered	recover	VERB
ejpam-5901	435	3	population	population	NOUN
ejpam-5901	435	4	r(t	r(t	NOUN
ejpam-5901	435	5	)	)	PUNCT
ejpam-5901	435	6	,	,	PUNCT
ejpam-5901	435	7	depicted	depict	VERB
ejpam-5901	435	8	in	in	ADP
ejpam-5901	435	9	figure	figure	NOUN
ejpam-5901	435	10	4	4	NUM
ejpam-5901	435	11	,	,	PUNCT
ejpam-5901	435	12	increases	increase	VERB
ejpam-5901	435	13	significantly	significantly	ADV
ejpam-5901	435	14	during	during	ADP
ejpam-5901	435	15	the	the	DET
ejpam-5901	435	16	initial	initial	ADJ
ejpam-5901	435	17	days	day	NOUN
ejpam-5901	435	18	before	before	ADP
ejpam-5901	435	19	reaching	reach	VERB
ejpam-5901	435	20	stability	stability	NOUN
ejpam-5901	435	21	.	.	PUNCT
ejpam-5901	436	1	this	this	DET
ejpam-5901	436	2	trend	trend	NOUN
ejpam-5901	436	3	aligns	align	VERB
ejpam-5901	436	4	with	with	ADP
ejpam-5901	436	5	the	the	DET
ejpam-5901	436	6	natural	natural	ADJ
ejpam-5901	436	7	progression	progression	NOUN
ejpam-5901	436	8	of	of	ADP
ejpam-5901	436	9	recovery	recovery	NOUN
ejpam-5901	436	10	in	in	ADP
ejpam-5901	436	11	the	the	DET
ejpam-5901	436	12	population	population	NOUN
ejpam-5901	436	13	.	.	PUNCT
ejpam-5901	437	1	the	the	DET
ejpam-5901	437	2	stabilization	stabilization	NOUN
ejpam-5901	437	3	of	of	ADP
ejpam-5901	437	4	all	all	DET
ejpam-5901	437	5	compartments	compartment	NOUN
ejpam-5901	437	6	over	over	ADP
ejpam-5901	437	7	time	time	NOUN
ejpam-5901	437	8	underlines	underline	VERB
ejpam-5901	437	9	the	the	DET
ejpam-5901	437	10	equilibrium	equilibrium	NOUN
ejpam-5901	437	11	behavior	behavior	NOUN
ejpam-5901	437	12	predicted	predict	VERB
ejpam-5901	437	13	by	by	ADP
ejpam-5901	437	14	the	the	DET
ejpam-5901	437	15	model	model	NOUN
ejpam-5901	437	16	.	.	PUNCT
ejpam-5901	438	1	the	the	DET
ejpam-5901	438	2	recovered	recovered	ADJ
ejpam-5901	438	3	population	population	NOUN
ejpam-5901	438	4	increases	increase	VERB
ejpam-5901	438	5	in	in	ADP
ejpam-5901	438	6	the	the	DET
ejpam-5901	438	7	early	early	ADJ
ejpam-5901	438	8	stages	stage	NOUN
ejpam-5901	438	9	and	and	CCONJ
ejpam-5901	438	10	eventually	eventually	ADV
ejpam-5901	438	11	stabilizes	stabilize	VERB
ejpam-5901	438	12	.	.	PUNCT
ejpam-5901	439	1	higher	high	ADJ
ejpam-5901	439	2	fractional	fractional	ADJ
ejpam-5901	439	3	orders	order	NOUN
ejpam-5901	439	4	lead	lead	VERB
ejpam-5901	439	5	to	to	ADP
ejpam-5901	439	6	a	a	DET
ejpam-5901	439	7	quicker	quick	ADJ
ejpam-5901	439	8	stabilization	stabilization	NOUN
ejpam-5901	439	9	of	of	ADP
ejpam-5901	439	10	the	the	DET
ejpam-5901	439	11	recovered	recovered	ADJ
ejpam-5901	439	12	class	class	NOUN
ejpam-5901	439	13	,	,	PUNCT
ejpam-5901	439	14	whereas	whereas	SCONJ
ejpam-5901	439	15	lower	low	ADJ
ejpam-5901	439	16	orders	order	NOUN
ejpam-5901	439	17	suggest	suggest	VERB
ejpam-5901	439	18	prolonged	prolonged	ADJ
ejpam-5901	439	19	memory	memory	NOUN
ejpam-5901	439	20	effects	effect	NOUN
ejpam-5901	439	21	and	and	CCONJ
ejpam-5901	439	22	delayed	delay	VERB
ejpam-5901	439	23	recovery	recovery	NOUN
ejpam-5901	439	24	.	.	PUNCT
ejpam-5901	440	1	figures	figure	VERB
ejpam-5901	440	2	5–7	5–7	PRON
ejpam-5901	440	3	provide	provide	VERB
ejpam-5901	440	4	a	a	DET
ejpam-5901	440	5	comprehensive	comprehensive	ADJ
ejpam-5901	440	6	comparison	comparison	NOUN
ejpam-5901	440	7	of	of	ADP
ejpam-5901	440	8	the	the	DET
ejpam-5901	440	9	solutions	solution	NOUN
ejpam-5901	440	10	for	for	ADP
ejpam-5901	440	11	all	all	DET
ejpam-5901	440	12	compartments	compartment	NOUN
ejpam-5901	440	13	under	under	ADP
ejpam-5901	440	14	varying	vary	VERB
ejpam-5901	440	15	fractional	fractional	ADJ
ejpam-5901	440	16	orders	order	NOUN
ejpam-5901	440	17	.	.	PUNCT
ejpam-5901	441	1	these	these	DET
ejpam-5901	441	2	figures	figure	NOUN
ejpam-5901	441	3	demonstrate	demonstrate	VERB
ejpam-5901	441	4	that	that	SCONJ
ejpam-5901	441	5	as	as	SCONJ
ejpam-5901	441	6	the	the	DET
ejpam-5901	441	7	fractional	fractional	ADJ
ejpam-5901	441	8	orders	order	NOUN
ejpam-5901	441	9	approach	approach	VERB
ejpam-5901	441	10	1.0	1.0	NUM
ejpam-5901	441	11	,	,	PUNCT
ejpam-5901	441	12	the	the	DET
ejpam-5901	441	13	solutions	solution	NOUN
ejpam-5901	441	14	converge	converge	VERB
ejpam-5901	441	15	to	to	ADP
ejpam-5901	441	16	the	the	DET
ejpam-5901	441	17	classical	classical	ADJ
ejpam-5901	441	18	case	case	NOUN
ejpam-5901	441	19	,	,	PUNCT
ejpam-5901	441	20	validating	validate	VERB
ejpam-5901	441	21	the	the	DET
ejpam-5901	441	22	model	model	NOUN
ejpam-5901	441	23	’s	’s	PART
ejpam-5901	441	24	ability	ability	NOUN
ejpam-5901	441	25	to	to	PART
ejpam-5901	441	26	replicate	replicate	VERB
ejpam-5901	441	27	traditional	traditional	ADJ
ejpam-5901	441	28	integer	integer	NOUN
ejpam-5901	441	29	-	-	PUNCT
ejpam-5901	441	30	order	order	NOUN
ejpam-5901	441	31	dynamics	dynamic	NOUN
ejpam-5901	441	32	while	while	SCONJ
ejpam-5901	441	33	offering	offer	VERB
ejpam-5901	441	34	greater	great	ADJ
ejpam-5901	441	35	flexibility	flexibility	NOUN
ejpam-5901	441	36	.	.	PUNCT
ejpam-5901	442	1	these	these	DET
ejpam-5901	442	2	figures	figure	NOUN
ejpam-5901	442	3	provide	provide	VERB
ejpam-5901	442	4	a	a	DET
ejpam-5901	442	5	comparative	comparative	ADJ
ejpam-5901	442	6	analysis	analysis	NOUN
ejpam-5901	442	7	of	of	ADP
ejpam-5901	442	8	all	all	DET
ejpam-5901	442	9	compartments	compartment	NOUN
ejpam-5901	442	10	(	(	PUNCT
ejpam-5901	442	11	s(t	s(t	PROPN
ejpam-5901	442	12	)	)	PUNCT
ejpam-5901	442	13	,	,	PUNCT
ejpam-5901	442	14	c(t	c(t	PROPN
ejpam-5901	442	15	)	)	PUNCT
ejpam-5901	442	16	,	,	PUNCT
ejpam-5901	442	17	i(t	i(t	PROPN
ejpam-5901	442	18	)	)	PUNCT
ejpam-5901	442	19	,	,	PUNCT
ejpam-5901	442	20	r(t	r(t	NOUN
ejpam-5901	442	21	)	)	PUNCT
ejpam-5901	442	22	)	)	PUNCT
ejpam-5901	442	23	under	under	ADP
ejpam-5901	442	24	varying	vary	VERB
ejpam-5901	442	25	fractional	fractional	ADJ
ejpam-5901	442	26	orders	order	NOUN
ejpam-5901	442	27	.	.	PUNCT
ejpam-5901	443	1	as	as	SCONJ
ejpam-5901	443	2	the	the	DET
ejpam-5901	443	3	fractional	fractional	ADJ
ejpam-5901	443	4	order	order	NOUN
ejpam-5901	443	5	approaches	approach	VERB
ejpam-5901	443	6	1	1	NUM
ejpam-5901	443	7	,	,	PUNCT
ejpam-5901	443	8	the	the	DET
ejpam-5901	443	9	system	system	NOUN
ejpam-5901	443	10	’s	’s	PART
ejpam-5901	443	11	behavior	behavior	NOUN
ejpam-5901	443	12	aligns	align	VERB
ejpam-5901	443	13	with	with	ADP
ejpam-5901	443	14	classical	classical	ADJ
ejpam-5901	443	15	integer	integer	NOUN
ejpam-5901	443	16	-	-	PUNCT
ejpam-5901	443	17	order	order	NOUN
ejpam-5901	443	18	models	model	NOUN
ejpam-5901	443	19	.	.	PUNCT
ejpam-5901	444	1	fractional	fractional	ADJ
ejpam-5901	444	2	models	model	NOUN
ejpam-5901	444	3	allow	allow	VERB
ejpam-5901	444	4	greater	great	ADJ
ejpam-5901	444	5	flexibility	flexibility	NOUN
ejpam-5901	444	6	in	in	ADP
ejpam-5901	444	7	capturing	capture	VERB
ejpam-5901	444	8	real	real	ADJ
ejpam-5901	444	9	-	-	PUNCT
ejpam-5901	444	10	world	world	NOUN
ejpam-5901	444	11	disease	disease	NOUN
ejpam-5901	444	12	dynamics	dynamic	NOUN
ejpam-5901	444	13	,	,	PUNCT
ejpam-5901	444	14	incorporating	incorporate	VERB
ejpam-5901	444	15	memory	memory	NOUN
ejpam-5901	444	16	effects	effect	NOUN
ejpam-5901	444	17	and	and	CCONJ
ejpam-5901	444	18	population	population	NOUN
ejpam-5901	444	19	heterogeneity	heterogeneity	NOUN
ejpam-5901	444	20	.	.	PUNCT
ejpam-5901	445	1	overall	overall	ADV
ejpam-5901	445	2	,	,	PUNCT
ejpam-5901	445	3	the	the	DET
ejpam-5901	445	4	results	result	NOUN
ejpam-5901	445	5	emphasize	emphasize	VERB
ejpam-5901	445	6	the	the	DET
ejpam-5901	445	7	utility	utility	NOUN
ejpam-5901	445	8	of	of	ADP
ejpam-5901	445	9	the	the	DET
ejpam-5901	445	10	fractal	fractal	ADJ
ejpam-5901	445	11	-	-	PUNCT
ejpam-5901	445	12	fractional	fractional	ADJ
ejpam-5901	445	13	operators	operator	NOUN
ejpam-5901	445	14	in	in	ADP
ejpam-5901	445	15	accurately	accurately	ADV
ejpam-5901	445	16	modeling	model	VERB
ejpam-5901	445	17	complex	complex	ADJ
ejpam-5901	445	18	real	real	ADJ
ejpam-5901	445	19	-	-	PUNCT
ejpam-5901	445	20	world	world	NOUN
ejpam-5901	445	21	phenomena	phenomenon	NOUN
ejpam-5901	445	22	,	,	PUNCT
ejpam-5901	445	23	such	such	ADJ
ejpam-5901	445	24	as	as	ADP
ejpam-5901	445	25	pneumonia	pneumonia	NOUN
ejpam-5901	445	26	transmission	transmission	NOUN
ejpam-5901	445	27	.	.	PUNCT
ejpam-5901	446	1	the	the	DET
ejpam-5901	446	2	ability	ability	NOUN
ejpam-5901	446	3	to	to	PART
ejpam-5901	446	4	vary	vary	VERB
ejpam-5901	446	5	the	the	DET
ejpam-5901	446	6	fractional	fractional	ADJ
ejpam-5901	446	7	orders	order	NOUN
ejpam-5901	446	8	allows	allow	VERB
ejpam-5901	446	9	for	for	ADP
ejpam-5901	446	10	a	a	DET
ejpam-5901	446	11	better	well	ADJ
ejpam-5901	446	12	understanding	understanding	NOUN
ejpam-5901	446	13	of	of	ADP
ejpam-5901	446	14	the	the	DET
ejpam-5901	446	15	disease	disease	NOUN
ejpam-5901	446	16	dynamics	dynamic	NOUN
ejpam-5901	446	17	under	under	ADP
ejpam-5901	446	18	different	different	ADJ
ejpam-5901	446	19	scenarios	scenario	NOUN
ejpam-5901	446	20	,	,	PUNCT
ejpam-5901	446	21	including	include	VERB
ejpam-5901	446	22	memory	memory	NOUN
ejpam-5901	446	23	effects	effect	NOUN
ejpam-5901	446	24	and	and	CCONJ
ejpam-5901	446	25	heterogeneous	heterogeneous	ADJ
ejpam-5901	446	26	population	population	NOUN
ejpam-5901	446	27	behaviors	behavior	NOUN
ejpam-5901	446	28	.	.	PUNCT
ejpam-5901	447	1	these	these	DET
ejpam-5901	447	2	insights	insight	NOUN
ejpam-5901	447	3	can	can	AUX
ejpam-5901	447	4	be	be	AUX
ejpam-5901	447	5	instrumental	instrumental	ADJ
ejpam-5901	447	6	in	in	ADP
ejpam-5901	447	7	optimizing	optimize	VERB
ejpam-5901	447	8	intervention	intervention	NOUN
ejpam-5901	447	9	strategies	strategy	NOUN
ejpam-5901	447	10	,	,	PUNCT
ejpam-5901	447	11	such	such	ADJ
ejpam-5901	447	12	as	as	ADP
ejpam-5901	447	13	vaccination	vaccination	NOUN
ejpam-5901	447	14	and	and	CCONJ
ejpam-5901	447	15	treatment	treatment	NOUN
ejpam-5901	447	16	programs	program	NOUN
ejpam-5901	447	17	.	.	PUNCT
ejpam-5901	448	1	future	future	ADJ
ejpam-5901	448	2	work	work	NOUN
ejpam-5901	448	3	could	could	AUX
ejpam-5901	448	4	focus	focus	VERB
ejpam-5901	448	5	on	on	ADP
ejpam-5901	448	6	incorporating	incorporate	VERB
ejpam-5901	448	7	environmental	environmental	ADJ
ejpam-5901	448	8	and	and	CCONJ
ejpam-5901	448	9	social	social	ADJ
ejpam-5901	448	10	factors	factor	NOUN
ejpam-5901	448	11	,	,	PUNCT
ejpam-5901	448	12	which	which	PRON
ejpam-5901	448	13	play	play	VERB
ejpam-5901	448	14	a	a	DET
ejpam-5901	448	15	critical	critical	ADJ
ejpam-5901	448	16	role	role	NOUN
ejpam-5901	448	17	in	in	ADP
ejpam-5901	448	18	the	the	DET
ejpam-5901	448	19	spread	spread	NOUN
ejpam-5901	448	20	and	and	CCONJ
ejpam-5901	448	21	treatment	treatment	NOUN
ejpam-5901	448	22	of	of	ADP
ejpam-5901	448	23	pneumonia	pneumonia	NOUN
ejpam-5901	448	24	,	,	PUNCT
ejpam-5901	448	25	to	to	PART
ejpam-5901	448	26	further	far	ADV
ejpam-5901	448	27	enhance	enhance	VERB
ejpam-5901	448	28	the	the	DET
ejpam-5901	448	29	model	model	NOUN
ejpam-5901	448	30	’s	’s	PART
ejpam-5901	448	31	applicability	applicability	NOUN
ejpam-5901	448	32	.	.	PUNCT
ejpam-5901	449	1	8	8	X
ejpam-5901	449	2	.	.	PUNCT
ejpam-5901	449	3	conclusions	conclusion	NOUN
ejpam-5901	449	4	this	this	DET
ejpam-5901	449	5	study	study	NOUN
ejpam-5901	449	6	explored	explore	VERB
ejpam-5901	449	7	a	a	DET
ejpam-5901	449	8	pneumonia	pneumonia	NOUN
ejpam-5901	449	9	transmission	transmission	NOUN
ejpam-5901	449	10	model	model	NOUN
ejpam-5901	449	11	using	use	VERB
ejpam-5901	449	12	fractal	fractal	ADJ
ejpam-5901	449	13	-	-	PUNCT
ejpam-5901	449	14	fractional	fractional	ADJ
ejpam-5901	449	15	derivatives	derivative	NOUN
ejpam-5901	449	16	,	,	PUNCT
ejpam-5901	449	17	demonstrating	demonstrate	VERB
ejpam-5901	449	18	the	the	DET
ejpam-5901	449	19	utility	utility	NOUN
ejpam-5901	449	20	of	of	ADP
ejpam-5901	449	21	these	these	DET
ejpam-5901	449	22	operators	operator	NOUN
ejpam-5901	449	23	in	in	ADP
ejpam-5901	449	24	capturing	capture	VERB
ejpam-5901	449	25	disease	disease	NOUN
ejpam-5901	449	26	spread	spread	VERB
ejpam-5901	449	27	dynamics	dynamic	NOUN
ejpam-5901	449	28	.	.	PUNCT
ejpam-5901	450	1	the	the	DET
ejpam-5901	450	2	numerical	numerical	ADJ
ejpam-5901	450	3	simulations	simulation	NOUN
ejpam-5901	450	4	revealed	reveal	VERB
ejpam-5901	450	5	how	how	SCONJ
ejpam-5901	450	6	varying	vary	VERB
ejpam-5901	450	7	the	the	DET
ejpam-5901	450	8	fractional	fractional	ADJ
ejpam-5901	450	9	orders	order	NOUN
ejpam-5901	450	10	influence	influence	VERB
ejpam-5901	450	11	the	the	DET
ejpam-5901	450	12	behavior	behavior	NOUN
ejpam-5901	450	13	of	of	ADP
ejpam-5901	450	14	the	the	DET
ejpam-5901	450	15	model	model	NOUN
ejpam-5901	450	16	compartments	compartment	NOUN
ejpam-5901	450	17	,	,	PUNCT
ejpam-5901	450	18	including	include	VERB
ejpam-5901	450	19	susceptible	susceptible	ADJ
ejpam-5901	450	20	,	,	PUNCT
ejpam-5901	450	21	carrier	carrier	NOUN
ejpam-5901	450	22	,	,	PUNCT
ejpam-5901	450	23	infected	infect	VERB
ejpam-5901	450	24	,	,	PUNCT
ejpam-5901	450	25	and	and	CCONJ
ejpam-5901	450	26	recovered	recovered	ADJ
ejpam-5901	450	27	populations	population	NOUN
ejpam-5901	450	28	.	.	PUNCT
ejpam-5901	451	1	by	by	ADP
ejpam-5901	451	2	incorporating	incorporate	VERB
ejpam-5901	451	3	long	long	ADJ
ejpam-5901	451	4	-	-	PUNCT
ejpam-5901	451	5	memory	memory	NOUN
ejpam-5901	451	6	effects	effect	NOUN
ejpam-5901	451	7	and	and	CCONJ
ejpam-5901	451	8	heterogeneous	heterogeneous	ADJ
ejpam-5901	451	9	responses	response	NOUN
ejpam-5901	451	10	,	,	PUNCT
ejpam-5901	451	11	the	the	DET
ejpam-5901	451	12	fractal	fractal	ADJ
ejpam-5901	451	13	-	-	PUNCT
ejpam-5901	451	14	fractional	fractional	ADJ
ejpam-5901	451	15	model	model	NOUN
ejpam-5901	451	16	provides	provide	VERB
ejpam-5901	451	17	a	a	DET
ejpam-5901	451	18	more	more	ADV
ejpam-5901	451	19	accurate	accurate	ADJ
ejpam-5901	451	20	and	and	CCONJ
ejpam-5901	451	21	flexible	flexible	ADJ
ejpam-5901	451	22	framework	framework	NOUN
ejpam-5901	451	23	than	than	ADP
ejpam-5901	451	24	traditional	traditional	ADJ
ejpam-5901	451	25	integer	integer	NOUN
ejpam-5901	451	26	-	-	PUNCT
ejpam-5901	451	27	order	order	NOUN
ejpam-5901	451	28	models	model	NOUN
ejpam-5901	451	29	.	.	PUNCT
ejpam-5901	452	1	the	the	DET
ejpam-5901	452	2	results	result	NOUN
ejpam-5901	452	3	showed	show	VERB
ejpam-5901	452	4	that	that	SCONJ
ejpam-5901	452	5	as	as	SCONJ
ejpam-5901	452	6	fractional	fractional	ADJ
ejpam-5901	452	7	orders	order	NOUN
ejpam-5901	452	8	approach	approach	VERB
ejpam-5901	452	9	1	1	NUM
ejpam-5901	452	10	,	,	PUNCT
ejpam-5901	452	11	the	the	DET
ejpam-5901	452	12	solutions	solution	NOUN
ejpam-5901	452	13	converge	converge	VERB
ejpam-5901	452	14	to	to	ADP
ejpam-5901	452	15	the	the	DET
ejpam-5901	452	16	classical	classical	ADJ
ejpam-5901	452	17	case	case	NOUN
ejpam-5901	452	18	.	.	PUNCT
ejpam-5901	453	1	as	as	ADP
ejpam-5901	453	2	a	a	DET
ejpam-5901	453	3	result	result	NOUN
ejpam-5901	453	4	,	,	PUNCT
ejpam-5901	453	5	fractional	fractional	ADJ
ejpam-5901	453	6	calculus	calculus	NOUN
ejpam-5901	453	7	is	be	AUX
ejpam-5901	453	8	compatible	compatible	ADJ
ejpam-5901	453	9	s.	s.	PROPN
ejpam-5901	453	10	saber	saber	PROPN
ejpam-5901	453	11	,	,	PUNCT
ejpam-5901	453	12	a.	a.	NOUN
ejpam-5901	453	13	a.	a.	NOUN
ejpam-5901	453	14	alahmari	alahmari	PROPN
ejpam-5901	453	15	/	/	SYM
ejpam-5901	453	16	eur	eur	PROPN
ejpam-5901	453	17	.	.	PUNCT
ejpam-5901	454	1	j.	j.	PROPN
ejpam-5901	454	2	pure	pure	PROPN
ejpam-5901	454	3	appl	appl	PROPN
ejpam-5901	454	4	.	.	PROPN
ejpam-5901	454	5	math	math	PROPN
ejpam-5901	454	6	,	,	PUNCT
ejpam-5901	454	7	18	18	NUM
ejpam-5901	454	8	(	(	PUNCT
ejpam-5901	454	9	2	2	NUM
ejpam-5901	454	10	)	)	PUNCT
ejpam-5901	454	11	(	(	PUNCT
ejpam-5901	454	12	2025	2025	NUM
ejpam-5901	454	13	)	)	PUNCT
ejpam-5901	454	14	,	,	PUNCT
ejpam-5901	454	15	5901	5901	NUM
ejpam-5901	454	16	18	18	NUM
ejpam-5901	454	17	of	of	ADP
ejpam-5901	454	18	23	23	NUM
ejpam-5901	454	19	0	0	NUM
ejpam-5901	454	20	10	10	NUM
ejpam-5901	454	21	20	20	NUM
ejpam-5901	454	22	30	30	NUM
ejpam-5901	454	23	40	40	NUM
ejpam-5901	454	24	50	50	NUM
ejpam-5901	454	25	60	60	NUM
ejpam-5901	454	26	time	time	NOUN
ejpam-5901	454	27	0.9	0.9	NUM
ejpam-5901	454	28	0.92	0.92	NUM
ejpam-5901	454	29	0.94	0.94	NUM
ejpam-5901	454	30	0.96	0.96	NUM
ejpam-5901	454	31	0.98	0.98	NUM
ejpam-5901	454	32	1	1	NUM
ejpam-5901	454	33	1.02	1.02	NUM
ejpam-5901	454	34	s	s	NOUN
ejpam-5901	454	35	(	(	PUNCT
ejpam-5901	454	36	t	t	PROPN
ejpam-5901	454	37	)	)	PUNCT
ejpam-5901	455	1	fo	fo	ADP
ejpam-5901	455	2	r	r	NOUN
ejpam-5901	455	3	o	o	NOUN
ejpam-5901	455	4	rd	rd	NOUN
ejpam-5901	455	5	e	e	NOUN
ejpam-5901	455	6	rs	rs	PROPN
ejpam-5901	455	7	1	1	NUM
ejpam-5901	455	8	,	,	PUNCT
ejpam-5901	455	9	0	0	NUM
ejpam-5901	455	10	.9	.9	NUM
ejpam-5901	455	11	5	5	NUM
ejpam-5901	455	12	,	,	PUNCT
ejpam-5901	455	13	0	0	NUM
ejpam-5901	455	14	.9	.9	NUM
ejpam-5901	455	15	,	,	PUNCT
ejpam-5901	455	16	0	0	NUM
ejpam-5901	455	17	.8	.8	NUM
ejpam-5901	455	18	5	5	NUM
ejpam-5901	455	19	s	s	VERB
ejpam-5901	455	20	at	at	ADP
ejpam-5901	455	21	order	order	NOUN
ejpam-5901	455	22	1	1	NUM
ejpam-5901	455	23	s	s	VERB
ejpam-5901	455	24	at	at	ADP
ejpam-5901	455	25	order	order	NOUN
ejpam-5901	455	26	0.95	0.95	NUM
ejpam-5901	455	27	s	s	NOUN
ejpam-5901	455	28	at	at	ADP
ejpam-5901	455	29	order	order	NOUN
ejpam-5901	455	30	0.90	0.90	NUM
ejpam-5901	455	31	s	s	VERB
ejpam-5901	455	32	at	at	ADP
ejpam-5901	455	33	order	order	NOUN
ejpam-5901	455	34	0.85	0.85	NUM
ejpam-5901	455	35	s	s	X
ejpam-5901	455	36	at	at	ADP
ejpam-5901	455	37	order	order	NOUN
ejpam-5901	455	38	0.8	0.8	NUM
ejpam-5901	455	39	figure	figure	NOUN
ejpam-5901	455	40	1	1	NUM
ejpam-5901	455	41	:	:	PUNCT
ejpam-5901	455	42	susceptible	susceptible	ADJ
ejpam-5901	455	43	class	class	NOUN
ejpam-5901	455	44	for	for	ADP
ejpam-5901	455	45	the	the	DET
ejpam-5901	455	46	different	different	ADJ
ejpam-5901	455	47	fractional	fractional	ADJ
ejpam-5901	455	48	orders	order	NOUN
ejpam-5901	455	49	of	of	ADP
ejpam-5901	455	50	the	the	DET
ejpam-5901	455	51	model	model	NOUN
ejpam-5901	455	52	(	(	PUNCT
ejpam-5901	455	53	2	2	NUM
ejpam-5901	455	54	)	)	PUNCT
ejpam-5901	455	55	.	.	PUNCT
ejpam-5901	456	1	0	0	NUM
ejpam-5901	456	2	10	10	NUM
ejpam-5901	456	3	20	20	NUM
ejpam-5901	456	4	30	30	NUM
ejpam-5901	456	5	40	40	NUM
ejpam-5901	456	6	50	50	NUM
ejpam-5901	456	7	60	60	NUM
ejpam-5901	456	8	time	time	NOUN
ejpam-5901	456	9	0	0	NUM
ejpam-5901	457	1	0.02	0.02	NUM
ejpam-5901	457	2	0.04	0.04	NUM
ejpam-5901	457	3	0.06	0.06	NUM
ejpam-5901	457	4	0.08	0.08	NUM
ejpam-5901	457	5	0.1	0.1	NUM
ejpam-5901	457	6	0.12	0.12	NUM
ejpam-5901	457	7	0.14	0.14	NUM
ejpam-5901	457	8	0.16	0.16	NUM
ejpam-5901	457	9	0.18	0.18	NUM
ejpam-5901	457	10	0.2	0.2	NUM
ejpam-5901	457	11	c	c	NOUN
ejpam-5901	457	12	(	(	PUNCT
ejpam-5901	457	13	t	t	PROPN
ejpam-5901	457	14	)	)	PUNCT
ejpam-5901	458	1	fo	fo	ADP
ejpam-5901	458	2	r	r	NOUN
ejpam-5901	458	3	o	o	NOUN
ejpam-5901	458	4	rd	rd	NOUN
ejpam-5901	458	5	e	e	NOUN
ejpam-5901	458	6	rs	rs	PROPN
ejpam-5901	458	7	1	1	NUM
ejpam-5901	458	8	,	,	PUNCT
ejpam-5901	458	9	0	0	NUM
ejpam-5901	458	10	.9	.9	NUM
ejpam-5901	458	11	5	5	NUM
ejpam-5901	458	12	,	,	PUNCT
ejpam-5901	458	13	0	0	NUM
ejpam-5901	458	14	.9	.9	NUM
ejpam-5901	458	15	,	,	PUNCT
ejpam-5901	458	16	0	0	NUM
ejpam-5901	458	17	.8	.8	NUM
ejpam-5901	458	18	5	5	NUM
ejpam-5901	458	19	c	c	NOUN
ejpam-5901	458	20	at	at	ADP
ejpam-5901	458	21	order	order	NOUN
ejpam-5901	458	22	1	1	NUM
ejpam-5901	458	23	c	c	NOUN
ejpam-5901	458	24	at	at	ADP
ejpam-5901	458	25	order	order	NOUN
ejpam-5901	458	26	0.95	0.95	NUM
ejpam-5901	458	27	c	c	NOUN
ejpam-5901	458	28	at	at	ADP
ejpam-5901	458	29	order	order	NOUN
ejpam-5901	458	30	0.90	0.90	NUM
ejpam-5901	458	31	c	c	NOUN
ejpam-5901	458	32	at	at	ADP
ejpam-5901	458	33	order	order	NOUN
ejpam-5901	458	34	0.85	0.85	NUM
ejpam-5901	458	35	c	c	NOUN
ejpam-5901	458	36	at	at	ADP
ejpam-5901	458	37	order	order	NOUN
ejpam-5901	458	38	0.8	0.8	NUM
ejpam-5901	458	39	figure	figure	NOUN
ejpam-5901	458	40	2	2	NUM
ejpam-5901	458	41	:	:	PUNCT
ejpam-5901	458	42	c(t	c(t	PROPN
ejpam-5901	458	43	)	)	PUNCT
ejpam-5901	458	44	class	class	NOUN
ejpam-5901	458	45	for	for	ADP
ejpam-5901	458	46	the	the	DET
ejpam-5901	458	47	different	different	ADJ
ejpam-5901	458	48	fractional	fractional	ADJ
ejpam-5901	458	49	orders	order	NOUN
ejpam-5901	458	50	of	of	ADP
ejpam-5901	458	51	the	the	DET
ejpam-5901	458	52	model	model	NOUN
ejpam-5901	458	53	(	(	PUNCT
ejpam-5901	458	54	2	2	NUM
ejpam-5901	458	55	)	)	PUNCT
ejpam-5901	458	56	.	.	PUNCT
ejpam-5901	459	1	0	0	NUM
ejpam-5901	459	2	10	10	NUM
ejpam-5901	459	3	20	20	NUM
ejpam-5901	459	4	30	30	NUM
ejpam-5901	459	5	40	40	NUM
ejpam-5901	459	6	50	50	NUM
ejpam-5901	459	7	60	60	NUM
ejpam-5901	459	8	time	time	NOUN
ejpam-5901	459	9	0	0	NUM
ejpam-5901	459	10	0.05	0.05	NUM
ejpam-5901	459	11	0.1	0.1	NUM
ejpam-5901	459	12	0.15	0.15	NUM
ejpam-5901	459	13	0.2	0.2	NUM
ejpam-5901	459	14	0.25	0.25	NUM
ejpam-5901	459	15	0.3	0.3	NUM
ejpam-5901	460	1	i	i	PROPN
ejpam-5901	460	2	(	(	PUNCT
ejpam-5901	460	3	t	t	PROPN
ejpam-5901	460	4	)	)	PUNCT
ejpam-5901	460	5	f	f	NOUN
ejpam-5901	461	1	o	o	NOUN
ejpam-5901	461	2	r	r	X
ejpam-5901	461	3	o	o	NOUN
ejpam-5901	461	4	rd	rd	NOUN
ejpam-5901	461	5	e	e	NOUN
ejpam-5901	461	6	rs	rs	PROPN
ejpam-5901	461	7	1	1	NUM
ejpam-5901	461	8	,	,	PUNCT
ejpam-5901	461	9	0	0	NUM
ejpam-5901	461	10	.9	.9	NUM
ejpam-5901	461	11	5	5	NUM
ejpam-5901	461	12	,	,	PUNCT
ejpam-5901	461	13	0	0	NUM
ejpam-5901	461	14	.9	.9	NUM
ejpam-5901	461	15	,	,	PUNCT
ejpam-5901	461	16	0	0	NUM
ejpam-5901	461	17	.8	.8	NUM
ejpam-5901	461	18	5	5	NUM
ejpam-5901	462	1	i	i	PRON
ejpam-5901	462	2	at	at	ADP
ejpam-5901	462	3	order	order	NOUN
ejpam-5901	462	4	1	1	NUM
ejpam-5901	462	5	i	i	PRON
ejpam-5901	462	6	at	at	ADP
ejpam-5901	462	7	order	order	NOUN
ejpam-5901	462	8	0.95	0.95	NUM
ejpam-5901	462	9	i	i	PRON
ejpam-5901	462	10	at	at	ADP
ejpam-5901	462	11	order	order	NOUN
ejpam-5901	462	12	0.90	0.90	NUM
ejpam-5901	462	13	i	i	PRON
ejpam-5901	462	14	at	at	ADP
ejpam-5901	462	15	order	order	NOUN
ejpam-5901	462	16	0.85	0.85	NUM
ejpam-5901	462	17	i	i	PRON
ejpam-5901	462	18	at	at	ADP
ejpam-5901	462	19	order	order	NOUN
ejpam-5901	462	20	0.8	0.8	NUM
ejpam-5901	462	21	figure	figure	NOUN
ejpam-5901	462	22	3	3	NUM
ejpam-5901	462	23	:	:	PUNCT
ejpam-5901	462	24	infected	infected	ADJ
ejpam-5901	462	25	class	class	NOUN
ejpam-5901	462	26	for	for	ADP
ejpam-5901	462	27	the	the	DET
ejpam-5901	462	28	different	different	ADJ
ejpam-5901	462	29	fractional	fractional	ADJ
ejpam-5901	462	30	orders	order	NOUN
ejpam-5901	462	31	of	of	ADP
ejpam-5901	462	32	the	the	DET
ejpam-5901	462	33	model	model	NOUN
ejpam-5901	462	34	(	(	PUNCT
ejpam-5901	462	35	2	2	NUM
ejpam-5901	462	36	)	)	PUNCT
ejpam-5901	462	37	.	.	PUNCT
ejpam-5901	463	1	0	0	NUM
ejpam-5901	463	2	10	10	NUM
ejpam-5901	463	3	20	20	NUM
ejpam-5901	463	4	30	30	NUM
ejpam-5901	463	5	40	40	NUM
ejpam-5901	463	6	50	50	NUM
ejpam-5901	463	7	60	60	NUM
ejpam-5901	463	8	time	time	NOUN
ejpam-5901	463	9	0	0	NUM
ejpam-5901	464	1	0.02	0.02	NUM
ejpam-5901	464	2	0.04	0.04	NUM
ejpam-5901	464	3	0.06	0.06	NUM
ejpam-5901	464	4	0.08	0.08	NUM
ejpam-5901	464	5	0.1	0.1	NUM
ejpam-5901	464	6	0.12	0.12	NUM
ejpam-5901	464	7	0.14	0.14	NUM
ejpam-5901	464	8	0.16	0.16	NUM
ejpam-5901	464	9	0.18	0.18	NUM
ejpam-5901	464	10	r	r	NOUN
ejpam-5901	464	11	(	(	PUNCT
ejpam-5901	464	12	t	t	PROPN
ejpam-5901	464	13	)	)	PUNCT
ejpam-5901	465	1	fo	fo	ADP
ejpam-5901	465	2	r	r	NOUN
ejpam-5901	465	3	o	o	NOUN
ejpam-5901	465	4	rd	rd	NOUN
ejpam-5901	465	5	e	e	NOUN
ejpam-5901	465	6	rs	rs	PROPN
ejpam-5901	465	7	1	1	NUM
ejpam-5901	465	8	,	,	PUNCT
ejpam-5901	465	9	0	0	NUM
ejpam-5901	465	10	.9	.9	NUM
ejpam-5901	465	11	5	5	NUM
ejpam-5901	465	12	,	,	PUNCT
ejpam-5901	465	13	0	0	NUM
ejpam-5901	465	14	.9	.9	NUM
ejpam-5901	465	15	,	,	PUNCT
ejpam-5901	465	16	0	0	NUM
ejpam-5901	465	17	.8	.8	NUM
ejpam-5901	465	18	5	5	NUM
ejpam-5901	465	19	r	r	NOUN
ejpam-5901	465	20	at	at	ADP
ejpam-5901	465	21	order	order	NOUN
ejpam-5901	465	22	1	1	NUM
ejpam-5901	465	23	r	r	NOUN
ejpam-5901	466	1	at	at	ADP
ejpam-5901	466	2	order	order	NOUN
ejpam-5901	466	3	0.95	0.95	NUM
ejpam-5901	466	4	r	r	NOUN
ejpam-5901	466	5	at	at	ADP
ejpam-5901	466	6	order	order	NOUN
ejpam-5901	466	7	0.90	0.90	NUM
ejpam-5901	466	8	r	r	NOUN
ejpam-5901	466	9	at	at	ADP
ejpam-5901	466	10	order	order	NOUN
ejpam-5901	466	11	0.85	0.85	NUM
ejpam-5901	466	12	r	r	NOUN
ejpam-5901	466	13	at	at	ADP
ejpam-5901	466	14	order	order	NOUN
ejpam-5901	466	15	0.8	0.8	NUM
ejpam-5901	466	16	figure	figure	NOUN
ejpam-5901	466	17	4	4	NUM
ejpam-5901	466	18	:	:	PUNCT
ejpam-5901	466	19	r(t	r(t	NOUN
ejpam-5901	466	20	)	)	PUNCT
ejpam-5901	466	21	class	class	NOUN
ejpam-5901	466	22	for	for	ADP
ejpam-5901	466	23	the	the	DET
ejpam-5901	466	24	different	different	ADJ
ejpam-5901	466	25	fractional	fractional	ADJ
ejpam-5901	466	26	orders	order	NOUN
ejpam-5901	466	27	of	of	ADP
ejpam-5901	466	28	the	the	DET
ejpam-5901	466	29	model	model	NOUN
ejpam-5901	466	30	(	(	PUNCT
ejpam-5901	466	31	2	2	NUM
ejpam-5901	466	32	)	)	PUNCT
ejpam-5901	466	33	.	.	PUNCT
ejpam-5901	467	1	with	with	ADP
ejpam-5901	467	2	conventional	conventional	ADJ
ejpam-5901	467	3	approaches	approach	NOUN
ejpam-5901	467	4	.	.	PUNCT
ejpam-5901	468	1	the	the	DET
ejpam-5901	468	2	stabilization	stabilization	NOUN
ejpam-5901	468	3	of	of	ADP
ejpam-5901	468	4	all	all	DET
ejpam-5901	468	5	compartments	compartment	NOUN
ejpam-5901	468	6	over	over	ADP
ejpam-5901	468	7	time	time	NOUN
ejpam-5901	468	8	indicates	indicate	VERB
ejpam-5901	468	9	equilibrium	equilibrium	NOUN
ejpam-5901	468	10	points	point	NOUN
ejpam-5901	468	11	and	and	CCONJ
ejpam-5901	468	12	supports	support	VERB
ejpam-5901	468	13	the	the	DET
ejpam-5901	468	14	model	model	NOUN
ejpam-5901	468	15	’s	’s	PART
ejpam-5901	468	16	effectiveness	effectiveness	NOUN
ejpam-5901	468	17	in	in	ADP
ejpam-5901	468	18	predicting	predict	VERB
ejpam-5901	468	19	disease	disease	NOUN
ejpam-5901	468	20	dynamics	dynamic	NOUN
ejpam-5901	468	21	.	.	PUNCT
ejpam-5901	469	1	this	this	DET
ejpam-5901	469	2	study	study	NOUN
ejpam-5901	469	3	emphasizes	emphasize	VERB
ejpam-5901	469	4	the	the	DET
ejpam-5901	469	5	importance	importance	NOUN
ejpam-5901	469	6	of	of	ADP
ejpam-5901	469	7	fractional	fractional	ADJ
ejpam-5901	469	8	-	-	PUNCT
ejpam-5901	469	9	order	order	NOUN
ejpam-5901	469	10	modeling	modeling	NOUN
ejpam-5901	469	11	in	in	ADP
ejpam-5901	469	12	understanding	understand	VERB
ejpam-5901	469	13	real	real	ADJ
ejpam-5901	469	14	-	-	PUNCT
ejpam-5901	469	15	world	world	NOUN
ejpam-5901	469	16	phenomena	phenomenon	NOUN
ejpam-5901	469	17	like	like	ADP
ejpam-5901	469	18	pneumonia	pneumonia	NOUN
ejpam-5901	469	19	transmission	transmission	NOUN
ejpam-5901	469	20	.	.	PUNCT
ejpam-5901	470	1	by	by	ADP
ejpam-5901	470	2	adjusting	adjust	VERB
ejpam-5901	470	3	fractional	fractional	ADJ
ejpam-5901	470	4	orders	order	NOUN
ejpam-5901	470	5	,	,	PUNCT
ejpam-5901	470	6	the	the	DET
ejpam-5901	470	7	model	model	NOUN
ejpam-5901	470	8	can	can	AUX
ejpam-5901	470	9	account	account	VERB
ejpam-5901	470	10	for	for	ADP
ejpam-5901	470	11	diverse	diverse	ADJ
ejpam-5901	470	12	population	population	NOUN
ejpam-5901	470	13	behaviors	behavior	NOUN
ejpam-5901	470	14	.	.	PUNCT
ejpam-5901	471	1	this	this	PRON
ejpam-5901	471	2	offers	offer	VERB
ejpam-5901	471	3	valuable	valuable	ADJ
ejpam-5901	471	4	insights	insight	NOUN
ejpam-5901	471	5	into	into	ADP
ejpam-5901	471	6	the	the	DET
ejpam-5901	471	7	effects	effect	NOUN
ejpam-5901	471	8	of	of	ADP
ejpam-5901	471	9	interventions	intervention	NOUN
ejpam-5901	471	10	such	such	ADJ
ejpam-5901	471	11	as	as	ADP
ejpam-5901	471	12	vaccination	vaccination	NOUN
ejpam-5901	471	13	and	and	CCONJ
ejpam-5901	471	14	treatment	treatment	NOUN
ejpam-5901	471	15	strategies	strategy	NOUN
ejpam-5901	471	16	.	.	PUNCT
ejpam-5901	472	1	future	future	ADJ
ejpam-5901	472	2	work	work	NOUN
ejpam-5901	472	3	should	should	AUX
ejpam-5901	472	4	consider	consider	VERB
ejpam-5901	472	5	environmental	environmental	ADJ
ejpam-5901	472	6	and	and	CCONJ
ejpam-5901	472	7	social	social	ADJ
ejpam-5901	472	8	factors	factor	NOUN
ejpam-5901	472	9	,	,	PUNCT
ejpam-5901	472	10	such	such	ADJ
ejpam-5901	472	11	as	as	ADP
ejpam-5901	472	12	air	air	NOUN
ejpam-5901	472	13	quality	quality	NOUN
ejpam-5901	472	14	,	,	PUNCT
ejpam-5901	472	15	temperature	temperature	NOUN
ejpam-5901	472	16	,	,	PUNCT
ejpam-5901	472	17	and	and	CCONJ
ejpam-5901	472	18	population	population	NOUN
ejpam-5901	472	19	density	density	NOUN
ejpam-5901	472	20	.	.	PUNCT
ejpam-5901	473	1	this	this	PRON
ejpam-5901	473	2	will	will	AUX
ejpam-5901	473	3	further	far	ADV
ejpam-5901	473	4	refine	refine	VERB
ejpam-5901	473	5	the	the	DET
ejpam-5901	473	6	model	model	NOUN
ejpam-5901	473	7	and	and	CCONJ
ejpam-5901	473	8	enhance	enhance	VERB
ejpam-5901	473	9	its	its	PRON
ejpam-5901	473	10	applicability	applicability	NOUN
ejpam-5901	473	11	.	.	PUNCT
ejpam-5901	474	1	the	the	DET
ejpam-5901	474	2	proposed	propose	VERB
ejpam-5901	474	3	method	method	NOUN
ejpam-5901	474	4	could	could	AUX
ejpam-5901	474	5	also	also	ADV
ejpam-5901	474	6	be	be	AUX
ejpam-5901	474	7	compared	compare	VERB
ejpam-5901	474	8	with	with	ADP
ejpam-5901	474	9	other	other	ADJ
ejpam-5901	474	10	numerical	numerical	ADJ
ejpam-5901	474	11	schemes	scheme	NOUN
ejpam-5901	474	12	for	for	ADP
ejpam-5901	474	13	a	a	DET
ejpam-5901	474	14	deeper	deep	ADJ
ejpam-5901	474	15	understanding	understanding	NOUN
ejpam-5901	474	16	of	of	ADP
ejpam-5901	474	17	its	its	PRON
ejpam-5901	474	18	robustness	robustness	NOUN
ejpam-5901	474	19	and	and	CCONJ
ejpam-5901	474	20	computational	computational	ADJ
ejpam-5901	474	21	efficiency	efficiency	NOUN
ejpam-5901	474	22	.	.	PUNCT
ejpam-5901	475	1	the	the	DET
ejpam-5901	475	2	fractal	fractal	ADJ
ejpam-5901	475	3	-	-	PUNCT
ejpam-5901	475	4	fractional	fractional	ADJ
ejpam-5901	475	5	approach	approach	NOUN
ejpam-5901	475	6	has	have	VERB
ejpam-5901	475	7	significant	significant	ADJ
ejpam-5901	475	8	potential	potential	NOUN
ejpam-5901	475	9	for	for	ADP
ejpam-5901	475	10	improving	improve	VERB
ejpam-5901	475	11	disease	disease	NOUN
ejpam-5901	475	12	modeling	modeling	NOUN
ejpam-5901	475	13	and	and	CCONJ
ejpam-5901	475	14	public	public	ADJ
ejpam-5901	475	15	health	health	NOUN
ejpam-5901	475	16	decisions	decision	NOUN
ejpam-5901	475	17	.	.	PUNCT
ejpam-5901	476	1	s.	s.	PROPN
ejpam-5901	476	2	saber	saber	PROPN
ejpam-5901	476	3	,	,	PUNCT
ejpam-5901	476	4	a.	a.	NOUN
ejpam-5901	476	5	a.	a.	NOUN
ejpam-5901	476	6	alahmari	alahmari	PROPN
ejpam-5901	476	7	/	/	SYM
ejpam-5901	476	8	eur	eur	PROPN
ejpam-5901	476	9	.	.	PUNCT
ejpam-5901	477	1	j.	j.	PROPN
ejpam-5901	477	2	pure	pure	PROPN
ejpam-5901	477	3	appl	appl	PROPN
ejpam-5901	477	4	.	.	PROPN
ejpam-5901	477	5	math	math	PROPN
ejpam-5901	477	6	,	,	PUNCT
ejpam-5901	477	7	18	18	NUM
ejpam-5901	477	8	(	(	PUNCT
ejpam-5901	477	9	2	2	NUM
ejpam-5901	477	10	)	)	PUNCT
ejpam-5901	477	11	(	(	PUNCT
ejpam-5901	477	12	2025	2025	NUM
ejpam-5901	477	13	)	)	PUNCT
ejpam-5901	477	14	,	,	PUNCT
ejpam-5901	477	15	5901	5901	NUM
ejpam-5901	477	16	19	19	NUM
ejpam-5901	477	17	of	of	ADP
ejpam-5901	477	18	23	23	NUM
ejpam-5901	477	19	0	0	NUM
ejpam-5901	477	20	10	10	NUM
ejpam-5901	477	21	20	20	NUM
ejpam-5901	477	22	30	30	NUM
ejpam-5901	477	23	40	40	NUM
ejpam-5901	477	24	50	50	NUM
ejpam-5901	477	25	60	60	NUM
ejpam-5901	477	26	time	time	NOUN
ejpam-5901	477	27	0	0	NUM
ejpam-5901	477	28	0.2	0.2	NUM
ejpam-5901	477	29	0.4	0.4	NUM
ejpam-5901	477	30	0.6	0.6	NUM
ejpam-5901	477	31	0.8	0.8	NUM
ejpam-5901	477	32	1	1	NUM
ejpam-5901	477	33	1.2	1.2	NUM
ejpam-5901	477	34	n	n	NUM
ejpam-5901	477	35	u	u	NOUN
ejpam-5901	477	36	m	m	NOUN
ejpam-5901	477	37	e	e	NOUN
ejpam-5901	477	38	ri	ri	NOUN
ejpam-5901	477	39	c	c	PROPN
ejpam-5901	477	40	a	a	DET
ejpam-5901	477	41	l	l	NOUN
ejpam-5901	477	42	s	s	PART
ejpam-5901	477	43	o	o	X
ejpam-5901	477	44	lu	lu	NOUN
ejpam-5901	477	45	ti	ti	NOUN
ejpam-5901	477	46	o	o	NOUN
ejpam-5901	478	1	n	n	NOUN
ejpam-5901	478	2	f	f	NOUN
ejpam-5901	478	3	o	o	NOUN
ejpam-5901	478	4	r	r	X
ejpam-5901	478	5	o	o	NOUN
ejpam-5901	478	6	rd	rd	NOUN
ejpam-5901	478	7	e	e	NOUN
ejpam-5901	478	8	r	r	NOUN
ejpam-5901	478	9	=	=	SYM
ejpam-5901	478	10	1	1	NUM
ejpam-5901	478	11	.0	.0	NUM
ejpam-5901	478	12	.	.	PUNCT
ejpam-5901	479	1	s	s	VERB
ejpam-5901	479	2	at	at	ADP
ejpam-5901	479	3	order	order	NOUN
ejpam-5901	479	4	=	=	SYM
ejpam-5901	479	5	1	1	NUM
ejpam-5901	479	6	c	c	NOUN
ejpam-5901	479	7	at	at	ADP
ejpam-5901	479	8	order	order	NOUN
ejpam-5901	479	9	=	=	SYM
ejpam-5901	479	10	1	1	NUM
ejpam-5901	480	1	i	i	PRON
ejpam-5901	480	2	at	at	ADP
ejpam-5901	480	3	order	order	NOUN
ejpam-5901	480	4	=	=	SYM
ejpam-5901	480	5	1	1	NUM
ejpam-5901	480	6	r	r	NOUN
ejpam-5901	480	7	at	at	ADP
ejpam-5901	480	8	order	order	NOUN
ejpam-5901	480	9	=	=	SYM
ejpam-5901	480	10	1	1	NUM
ejpam-5901	480	11	figure	figure	NOUN
ejpam-5901	480	12	5	5	NUM
ejpam-5901	480	13	:	:	PUNCT
ejpam-5901	480	14	time	time	NOUN
ejpam-5901	480	15	series	series	NOUN
ejpam-5901	480	16	of	of	ADP
ejpam-5901	480	17	s(t	s(t	PROPN
ejpam-5901	480	18	)	)	PUNCT
ejpam-5901	480	19	,	,	PUNCT
ejpam-5901	480	20	c(t	c(t	PROPN
ejpam-5901	480	21	)	)	PUNCT
ejpam-5901	480	22	,	,	PUNCT
ejpam-5901	480	23	i(t	i(t	PROPN
ejpam-5901	480	24	)	)	PUNCT
ejpam-5901	480	25	,	,	PUNCT
ejpam-5901	480	26	and	and	CCONJ
ejpam-5901	480	27	r(t	r(t	NOUN
ejpam-5901	480	28	)	)	PUNCT
ejpam-5901	480	29	using	use	VERB
ejpam-5901	480	30	fractal	fractal	ADJ
ejpam-5901	480	31	fractional	fractional	ADJ
ejpam-5901	480	32	methods	method	NOUN
ejpam-5901	480	33	in	in	ADP
ejpam-5901	480	34	the	the	DET
ejpam-5901	480	35	sense	sense	NOUN
ejpam-5901	480	36	of	of	ADP
ejpam-5901	480	37	atanganabaleanu	atanganabaleanu	NOUN
ejpam-5901	480	38	operators	operator	NOUN
ejpam-5901	480	39	for	for	ADP
ejpam-5901	480	40	ϱ1	ϱ1	NOUN
ejpam-5901	480	41	=	=	SYM
ejpam-5901	480	42	1	1	NUM
ejpam-5901	480	43	,	,	PUNCT
ejpam-5901	480	44	ϱ2	ϱ2	NOUN
ejpam-5901	480	45	=	=	NOUN
ejpam-5901	480	46	1	1	NUM
ejpam-5901	480	47	.	.	NOUN
ejpam-5901	480	48	0	0	NUM
ejpam-5901	480	49	10	10	NUM
ejpam-5901	480	50	20	20	NUM
ejpam-5901	480	51	30	30	NUM
ejpam-5901	480	52	40	40	NUM
ejpam-5901	480	53	50	50	NUM
ejpam-5901	480	54	60	60	NUM
ejpam-5901	480	55	time	time	NOUN
ejpam-5901	480	56	0	0	NUM
ejpam-5901	480	57	0.1	0.1	NUM
ejpam-5901	480	58	0.2	0.2	NUM
ejpam-5901	480	59	0.3	0.3	NUM
ejpam-5901	480	60	0.4	0.4	NUM
ejpam-5901	480	61	0.5	0.5	NUM
ejpam-5901	480	62	0.6	0.6	NUM
ejpam-5901	480	63	0.7	0.7	NUM
ejpam-5901	480	64	0.8	0.8	NUM
ejpam-5901	480	65	0.9	0.9	NUM
ejpam-5901	480	66	1	1	NUM
ejpam-5901	480	67	n	n	NUM
ejpam-5901	480	68	u	u	NOUN
ejpam-5901	480	69	m	m	NOUN
ejpam-5901	480	70	e	e	NOUN
ejpam-5901	480	71	ri	ri	NOUN
ejpam-5901	480	72	c	c	PROPN
ejpam-5901	480	73	a	a	DET
ejpam-5901	480	74	l	l	NOUN
ejpam-5901	480	75	s	s	PART
ejpam-5901	480	76	o	o	X
ejpam-5901	480	77	lu	lu	NOUN
ejpam-5901	480	78	ti	ti	NOUN
ejpam-5901	480	79	o	o	NOUN
ejpam-5901	481	1	n	n	NOUN
ejpam-5901	482	1	f	f	NOUN
ejpam-5901	482	2	o	o	NOUN
ejpam-5901	482	3	r	r	X
ejpam-5901	482	4	o	o	NOUN
ejpam-5901	482	5	rd	rd	NOUN
ejpam-5901	483	1	e	e	NOUN
ejpam-5901	483	2	r	r	NOUN
ejpam-5901	483	3	=	=	SYM
ejpam-5901	483	4	0	0	NUM
ejpam-5901	483	5	.9	.9	NUM
ejpam-5901	483	6	5	5	NUM
ejpam-5901	483	7	.	.	PUNCT
ejpam-5901	484	1	s	s	VERB
ejpam-5901	484	2	at	at	ADP
ejpam-5901	484	3	order	order	NOUN
ejpam-5901	484	4	=	=	SYM
ejpam-5901	484	5	0.95	0.95	NUM
ejpam-5901	484	6	c	c	NOUN
ejpam-5901	484	7	at	at	ADP
ejpam-5901	484	8	order	order	NOUN
ejpam-5901	484	9	=	=	PUNCT
ejpam-5901	484	10	0.95	0.95	NUM
ejpam-5901	484	11	i	i	PRON
ejpam-5901	484	12	at	at	ADP
ejpam-5901	484	13	order	order	NOUN
ejpam-5901	484	14	=	=	NOUN
ejpam-5901	484	15	0.95	0.95	NUM
ejpam-5901	484	16	r	r	NOUN
ejpam-5901	484	17	at	at	ADP
ejpam-5901	484	18	order	order	NOUN
ejpam-5901	484	19	=	=	SYM
ejpam-5901	484	20	0.95	0.95	NUM
ejpam-5901	484	21	figure	figure	NOUN
ejpam-5901	484	22	6	6	NUM
ejpam-5901	484	23	:	:	PUNCT
ejpam-5901	484	24	time	time	NOUN
ejpam-5901	484	25	series	series	NOUN
ejpam-5901	484	26	of	of	ADP
ejpam-5901	484	27	s(t	s(t	PROPN
ejpam-5901	484	28	)	)	PUNCT
ejpam-5901	484	29	,	,	PUNCT
ejpam-5901	484	30	c(t	c(t	PROPN
ejpam-5901	484	31	)	)	PUNCT
ejpam-5901	484	32	,	,	PUNCT
ejpam-5901	484	33	i(t	i(t	PROPN
ejpam-5901	484	34	)	)	PUNCT
ejpam-5901	484	35	,	,	PUNCT
ejpam-5901	484	36	and	and	CCONJ
ejpam-5901	484	37	r(t	r(t	NOUN
ejpam-5901	484	38	)	)	PUNCT
ejpam-5901	484	39	using	use	VERB
ejpam-5901	484	40	fractal	fractal	ADJ
ejpam-5901	484	41	fractional	fractional	ADJ
ejpam-5901	484	42	methods	method	NOUN
ejpam-5901	484	43	in	in	ADP
ejpam-5901	484	44	the	the	DET
ejpam-5901	484	45	sense	sense	NOUN
ejpam-5901	484	46	of	of	ADP
ejpam-5901	484	47	atanganabaleanu	atanganabaleanu	NOUN
ejpam-5901	484	48	operators	operator	NOUN
ejpam-5901	484	49	for	for	ADP
ejpam-5901	484	50	ϱ1	ϱ1	NOUN
ejpam-5901	484	51	=	=	NOUN
ejpam-5901	484	52	0.95	0.95	NUM
ejpam-5901	484	53	,	,	PUNCT
ejpam-5901	484	54	ϱ2	ϱ2	NOUN
ejpam-5901	484	55	=	=	NOUN
ejpam-5901	484	56	0.95	0.95	NUM
ejpam-5901	484	57	.	.	PUNCT
ejpam-5901	485	1	π	π	PROPN
ejpam-5901	485	2	the	the	DET
ejpam-5901	485	3	recruitment	recruitment	NOUN
ejpam-5901	485	4	rate	rate	NOUN
ejpam-5901	485	5	into	into	ADP
ejpam-5901	485	6	susceptible	susceptible	ADJ
ejpam-5901	485	7	population	population	NOUN
ejpam-5901	485	8	per	per	ADP
ejpam-5901	485	9	capita	capita	NOUN
ejpam-5901	485	10	0.5	0.5	NUM
ejpam-5901	485	11	δ	δ	NOUN
ejpam-5901	485	12	the	the	DET
ejpam-5901	485	13	rate	rate	NOUN
ejpam-5901	485	14	of	of	ADP
ejpam-5901	485	15	transmission	transmission	NOUN
ejpam-5901	485	16	2.5	2.5	NUM
ejpam-5901	485	17	ϖ	ϖ	NOUN
ejpam-5901	485	18	represents	represent	VERB
ejpam-5901	485	19	the	the	DET
ejpam-5901	485	20	rate	rate	NOUN
ejpam-5901	485	21	of	of	ADP
ejpam-5901	485	22	treated	treat	VERB
ejpam-5901	485	23	individuals	individual	NOUN
ejpam-5901	485	24	having	having	AUX
ejpam-5901	485	25	vaccinated	vaccinate	VERB
ejpam-5901	485	26	0.1124	0.1124	NUM
ejpam-5901	485	27	µ	µ	PRON
ejpam-5901	485	28	the	the	DET
ejpam-5901	485	29	natural	natural	ADJ
ejpam-5901	485	30	mortality	mortality	NOUN
ejpam-5901	485	31	rate	rate	NOUN
ejpam-5901	485	32	of	of	ADP
ejpam-5901	485	33	individuals	individual	NOUN
ejpam-5901	485	34	per	per	ADP
ejpam-5901	485	35	capita	capita	NOUN
ejpam-5901	485	36	0.5	0.5	NUM
ejpam-5901	485	37	η	η	NOUN
ejpam-5901	485	38	average	average	ADJ
ejpam-5901	485	39	time	time	NOUN
ejpam-5901	485	40	symptomatic	symptomatic	ADJ
ejpam-5901	485	41	infectious	infectious	ADJ
ejpam-5901	485	42	have	have	VERB
ejpam-5901	485	43	symptoms	symptom	NOUN
ejpam-5901	485	44	0.00641	0.00641	NUM
ejpam-5901	485	45	m	m	NOUN
ejpam-5901	485	46	the	the	DET
ejpam-5901	485	47	recovery	recovery	NOUN
ejpam-5901	485	48	rate	rate	NOUN
ejpam-5901	485	49	of	of	ADP
ejpam-5901	485	50	carriers	carrier	NOUN
ejpam-5901	485	51	per	per	ADP
ejpam-5901	485	52	capita	capita	NOUN
ejpam-5901	485	53	0.515	0.515	NUM
ejpam-5901	485	54	π	π	NOUN
ejpam-5901	485	55	the	the	DET
ejpam-5901	485	56	rate	rate	NOUN
ejpam-5901	485	57	of	of	ADP
ejpam-5901	485	58	developing	develop	VERB
ejpam-5901	485	59	symptoms	symptom	NOUN
ejpam-5901	485	60	by	by	ADP
ejpam-5901	485	61	carriers	carrier	NOUN
ejpam-5901	485	62	0.7096	0.7096	NUM
ejpam-5901	485	63	ϑ	ϑ	X
ejpam-5901	485	64	the	the	DET
ejpam-5901	485	65	proportion	proportion	NOUN
ejpam-5901	485	66	of	of	ADP
ejpam-5901	485	67	susceptible	susceptible	ADJ
ejpam-5901	485	68	individuals	individual	NOUN
ejpam-5901	485	69	who	who	PRON
ejpam-5901	485	70	joins	join	VERB
ejpam-5901	485	71	the	the	DET
ejpam-5901	485	72	carriers	carrier	NOUN
ejpam-5901	485	73	0.563	0.563	NUM
ejpam-5901	485	74	τ	τ	X
ejpam-5901	485	75	the	the	DET
ejpam-5901	485	76	recovery	recovery	NOUN
ejpam-5901	485	77	rate	rate	NOUN
ejpam-5901	485	78	of	of	ADP
ejpam-5901	485	79	individuals	individual	NOUN
ejpam-5901	485	80	who	who	PRON
ejpam-5901	485	81	are	be	AUX
ejpam-5901	485	82	infected	infect	VERB
ejpam-5901	485	83	of	of	ADP
ejpam-5901	485	84	pneumonia	pneumonia	NOUN
ejpam-5901	485	85	per	per	ADP
ejpam-5901	485	86	capita	capita	NOUN
ejpam-5901	485	87	0.641	0.641	NUM
ejpam-5901	485	88	σ	σ	NOUN
ejpam-5901	485	89	birth	birth	NOUN
ejpam-5901	485	90	rate	rate	NOUN
ejpam-5901	485	91	per	per	ADP
ejpam-5901	485	92	capita	capita	NOUN
ejpam-5901	485	93	of	of	ADP
ejpam-5901	485	94	the	the	DET
ejpam-5901	485	95	human	human	ADJ
ejpam-5901	485	96	population	population	NOUN
ejpam-5901	485	97	affected	affect	VERB
ejpam-5901	485	98	by	by	ADP
ejpam-5901	485	99	disease	disease	NOUN
ejpam-5901	485	100	0.53	0.53	NUM
ejpam-5901	485	101	table	table	NOUN
ejpam-5901	485	102	1	1	NUM
ejpam-5901	485	103	:	:	PUNCT
ejpam-5901	485	104	the	the	DET
ejpam-5901	485	105	values	value	NOUN
ejpam-5901	485	106	of	of	ADP
ejpam-5901	485	107	parameters	parameter	NOUN
ejpam-5901	485	108	and	and	CCONJ
ejpam-5901	485	109	initial	initial	ADJ
ejpam-5901	485	110	populations	population	NOUN
ejpam-5901	485	111	in	in	ADP
ejpam-5901	485	112	this	this	DET
ejpam-5901	485	113	study	study	NOUN
ejpam-5901	485	114	are	be	AUX
ejpam-5901	485	115	obtained	obtain	VERB
ejpam-5901	485	116	from	from	ADP
ejpam-5901	485	117	the	the	PRON
ejpam-5901	485	118	who	who	PRON
ejpam-5901	485	119	situation	situation	NOUN
ejpam-5901	485	120	report	report	NOUN
ejpam-5901	485	121	(	(	PUNCT
ejpam-5901	485	122	the	the	DET
ejpam-5901	485	123	national	national	PROPN
ejpam-5901	485	124	health	health	PROPN
ejpam-5901	485	125	commission	commission	PROPN
ejpam-5901	485	126	of	of	ADP
ejpam-5901	485	127	the	the	DET
ejpam-5901	485	128	republic	republic	NOUN
ejpam-5901	485	129	of	of	ADP
ejpam-5901	485	130	china	china	PROPN
ejpam-5901	485	131	)	)	PUNCT
ejpam-5901	485	132	presented	present	VERB
ejpam-5901	485	133	in	in	ADP
ejpam-5901	485	134	[	[	X
ejpam-5901	485	135	62	62	NUM
ejpam-5901	485	136	]	]	PUNCT
ejpam-5901	485	137	.	.	PUNCT
ejpam-5901	486	1	https://doi.org/10.32604/cmc.2022.020732	https://doi.org/10.32604/cmc.2022.020732	ADJ
ejpam-5901	486	2	acknowledgment	acknowledgment	NOUN
ejpam-5901	486	3	the	the	DET
ejpam-5901	486	4	authors	author	NOUN
ejpam-5901	486	5	extend	extend	VERB
ejpam-5901	486	6	their	their	PRON
ejpam-5901	486	7	appreciation	appreciation	NOUN
ejpam-5901	486	8	to	to	ADP
ejpam-5901	486	9	umm	umm	INTJ
ejpam-5901	486	10	al	al	PROPN
ejpam-5901	486	11	-	-	PUNCT
ejpam-5901	486	12	qura	qura	PROPN
ejpam-5901	486	13	university	university	PROPN
ejpam-5901	486	14	,	,	PUNCT
ejpam-5901	486	15	saudi	saudi	PROPN
ejpam-5901	486	16	arabia	arabia	PROPN
ejpam-5901	486	17	for	for	ADP
ejpam-5901	486	18	funding	fund	VERB
ejpam-5901	486	19	this	this	DET
ejpam-5901	486	20	research	research	NOUN
ejpam-5901	486	21	work	work	NOUN
ejpam-5901	486	22	through	through	ADP
ejpam-5901	486	23	grant	grant	NOUN
ejpam-5901	486	24	number	number	NOUN
ejpam-5901	486	25	:	:	PUNCT
ejpam-5901	487	1	25uqu4220004gssr02	25uqu4220004gssr02	X
ejpam-5901	487	2	.	.	X
ejpam-5901	488	1	funding	fund	VERB
ejpam-5901	488	2	this	this	DET
ejpam-5901	488	3	research	research	NOUN
ejpam-5901	488	4	work	work	NOUN
ejpam-5901	488	5	was	be	AUX
ejpam-5901	488	6	funded	fund	VERB
ejpam-5901	488	7	by	by	ADP
ejpam-5901	488	8	umm	umm	INTJ
ejpam-5901	488	9	al	al	PROPN
ejpam-5901	488	10	-	-	PUNCT
ejpam-5901	488	11	qura	qura	PROPN
ejpam-5901	488	12	university	university	NOUN
ejpam-5901	488	13	,	,	PUNCT
ejpam-5901	488	14	saudi	saudi	PROPN
ejpam-5901	488	15	arabia	arabia	PROPN
ejpam-5901	488	16	under	under	ADP
ejpam-5901	488	17	grant	grant	NOUN
ejpam-5901	488	18	number	number	NOUN
ejpam-5901	488	19	:	:	PUNCT
ejpam-5901	489	1	25uqu4220004gssr02	25uqu4220004gssr02	NUM
ejpam-5901	489	2	.	.	PUNCT
ejpam-5901	489	3	data	datum	NOUN
ejpam-5901	489	4	availability	availability	NOUN
ejpam-5901	489	5	all	all	DET
ejpam-5901	489	6	data	datum	NOUN
ejpam-5901	489	7	is	be	AUX
ejpam-5901	489	8	included	include	VERB
ejpam-5901	489	9	in	in	ADP
ejpam-5901	489	10	the	the	DET
ejpam-5901	489	11	manuscript	manuscript	NOUN
ejpam-5901	489	12	.	.	PUNCT
ejpam-5901	490	1	https://doi.org/10.32604/cmc.2022.020732	https://doi.org/10.32604/cmc.2022.020732	ADJ
ejpam-5901	490	2	s.	s.	PROPN
ejpam-5901	490	3	saber	saber	PROPN
ejpam-5901	490	4	,	,	PUNCT
ejpam-5901	490	5	a.	a.	NOUN
ejpam-5901	490	6	a.	a.	NOUN
ejpam-5901	490	7	alahmari	alahmari	PROPN
ejpam-5901	490	8	/	/	SYM
ejpam-5901	490	9	eur	eur	PROPN
ejpam-5901	490	10	.	.	PUNCT
ejpam-5901	491	1	j.	j.	PROPN
ejpam-5901	491	2	pure	pure	PROPN
ejpam-5901	491	3	appl	appl	PROPN
ejpam-5901	491	4	.	.	PROPN
ejpam-5901	491	5	math	math	PROPN
ejpam-5901	491	6	,	,	PUNCT
ejpam-5901	491	7	18	18	NUM
ejpam-5901	491	8	(	(	PUNCT
ejpam-5901	491	9	2	2	NUM
ejpam-5901	491	10	)	)	PUNCT
ejpam-5901	491	11	(	(	PUNCT
ejpam-5901	491	12	2025	2025	NUM
ejpam-5901	491	13	)	)	PUNCT
ejpam-5901	491	14	,	,	PUNCT
ejpam-5901	491	15	5901	5901	NUM
ejpam-5901	491	16	20	20	NUM
ejpam-5901	491	17	of	of	ADP
ejpam-5901	491	18	23	23	NUM
ejpam-5901	491	19	references	reference	NOUN
ejpam-5901	491	20	[	[	X
ejpam-5901	491	21	1	1	NUM
ejpam-5901	491	22	]	]	PUNCT
ejpam-5901	491	23	j.	j.	PROPN
ejpam-5901	491	24	ong’ala	ong’ala	PROPN
ejpam-5901	491	25	,	,	PUNCT
ejpam-5901	491	26	p.	p.	NOUN
ejpam-5901	491	27	oleche	oleche	NOUN
ejpam-5901	491	28	,	,	PUNCT
ejpam-5901	491	29	and	and	CCONJ
ejpam-5901	492	1	j.y.t	j.y.t	PROPN
ejpam-5901	492	2	.	.	PUNCT
ejpam-5901	492	3	mugisha	mugisha	PROPN
ejpam-5901	492	4	.	.	PUNCT
ejpam-5901	493	1	mathematical	mathematical	ADJ
ejpam-5901	493	2	model	model	NOUN
ejpam-5901	493	3	for	for	ADP
ejpam-5901	493	4	pneumonia	pneumonia	NOUN
ejpam-5901	493	5	dynamics	dynamic	NOUN
ejpam-5901	493	6	with	with	ADP
ejpam-5901	493	7	carriers	carrier	NOUN
ejpam-5901	493	8	.	.	PUNCT
ejpam-5901	494	1	int	int	NOUN
ejpam-5901	494	2	.	.	PUNCT
ejpam-5901	495	1	j.	j.	PROPN
ejpam-5901	495	2	math	math	PROPN
ejpam-5901	495	3	.	.	PUNCT
ejpam-5901	496	1	anal	anal	PROPN
ejpam-5901	496	2	.	.	PROPN
ejpam-5901	496	3	,	,	PUNCT
ejpam-5901	496	4	7(50):2457–2473	7(50):2457–2473	NUM
ejpam-5901	496	5	,	,	PUNCT
ejpam-5901	496	6	2013	2013	NUM
ejpam-5901	496	7	.	.	PUNCT
ejpam-5901	497	1	[	[	X
ejpam-5901	497	2	2	2	X
ejpam-5901	497	3	]	]	X
ejpam-5901	497	4	e.	e.	PROPN
ejpam-5901	497	5	mochan	mochan	PROPN
ejpam-5901	497	6	,	,	PUNCT
ejpam-5901	497	7	d.	d.	PROPN
ejpam-5901	497	8	swigon	swigon	PROPN
ejpam-5901	497	9	,	,	PUNCT
ejpam-5901	497	10	g.	g.	PROPN
ejpam-5901	497	11	ermentrout	ermentrout	PROPN
ejpam-5901	497	12	,	,	PUNCT
ejpam-5901	497	13	s.	s.	PROPN
ejpam-5901	497	14	luken	luken	VERB
ejpam-5901	497	15	,	,	PUNCT
ejpam-5901	497	16	and	and	CCONJ
ejpam-5901	497	17	g.a	g.a	PROPN
ejpam-5901	497	18	.	.	PROPN
ejpam-5901	497	19	clermont	clermont	PROPN
ejpam-5901	497	20	.	.	PUNCT
ejpam-5901	498	1	mathematical	mathematical	ADJ
ejpam-5901	498	2	model	model	NOUN
ejpam-5901	498	3	of	of	ADP
ejpam-5901	498	4	intrahost	intrahost	ADJ
ejpam-5901	498	5	pneumococcal	pneumococcal	ADJ
ejpam-5901	498	6	pneumonia	pneumonia	NOUN
ejpam-5901	498	7	infection	infection	NOUN
ejpam-5901	498	8	dynamics	dynamic	NOUN
ejpam-5901	498	9	in	in	ADP
ejpam-5901	498	10	murine	murine	ADJ
ejpam-5901	498	11	strains	strain	NOUN
ejpam-5901	498	12	.	.	PUNCT
ejpam-5901	499	1	j.	j.	PROPN
ejpam-5901	499	2	theor	theor	PROPN
ejpam-5901	499	3	.	.	PUNCT
ejpam-5901	500	1	biol	biol	PROPN
ejpam-5901	500	2	.	.	PUNCT
ejpam-5901	500	3	,	,	PUNCT
ejpam-5901	500	4	353:44–54	353:44–54	NUM
ejpam-5901	500	5	,	,	PUNCT
ejpam-5901	500	6	2014	2014	NUM
ejpam-5901	500	7	.	.	PUNCT
ejpam-5901	501	1	[	[	X
ejpam-5901	501	2	3	3	NUM
ejpam-5901	501	3	]	]	X
ejpam-5901	501	4	g.l	g.l	PROPN
ejpam-5901	501	5	.	.	PROPN
ejpam-5901	501	6	drusano	drusano	PROPN
ejpam-5901	501	7	,	,	PUNCT
ejpam-5901	501	8	w.	w.	PROPN
ejpam-5901	501	9	liu	liu	PROPN
ejpam-5901	501	10	,	,	PUNCT
ejpam-5901	501	11	s.	s.	PROPN
ejpam-5901	501	12	fikes	fikes	PROPN
ejpam-5901	501	13	,	,	PUNCT
ejpam-5901	501	14	r.	r.	PROPN
ejpam-5901	501	15	cirz	cirz	PROPN
ejpam-5901	501	16	,	,	PUNCT
ejpam-5901	501	17	n.	n.	NOUN
ejpam-5901	501	18	robbins	robbins	PROPN
ejpam-5901	501	19	,	,	PUNCT
ejpam-5901	501	20	s.	s.	PROPN
ejpam-5901	501	21	kurhanewicz	kurhanewicz	PROPN
ejpam-5901	501	22	,	,	PUNCT
ejpam-5901	501	23	and	and	CCONJ
ejpam-5901	501	24	a.	a.	PROPN
ejpam-5901	501	25	louie	louie	PROPN
ejpam-5901	501	26	.	.	PUNCT
ejpam-5901	502	1	interaction	interaction	NOUN
ejpam-5901	502	2	of	of	ADP
ejpam-5901	502	3	drugand	drugand	NOUN
ejpam-5901	502	4	granulocyte	granulocyte	NOUN
ejpam-5901	502	5	-	-	PUNCT
ejpam-5901	502	6	mediated	mediate	VERB
ejpam-5901	502	7	killing	killing	NOUN
ejpam-5901	502	8	of	of	ADP
ejpam-5901	502	9	pseudomonas	pseudomona	NOUN
ejpam-5901	502	10	aeruginosa	aeruginosa	NOUN
ejpam-5901	502	11	in	in	ADP
ejpam-5901	502	12	a	a	DET
ejpam-5901	502	13	murine	murine	ADJ
ejpam-5901	502	14	pneumonia	pneumonia	NOUN
ejpam-5901	502	15	model	model	NOUN
ejpam-5901	502	16	.	.	PUNCT
ejpam-5901	503	1	j.	j.	PROPN
ejpam-5901	503	2	infect	infect	PROPN
ejpam-5901	503	3	.	.	PUNCT
ejpam-5901	504	1	dis	dis	PROPN
ejpam-5901	504	2	.	.	PROPN
ejpam-5901	504	3	,	,	PUNCT
ejpam-5901	504	4	210(8):1319–1324	210(8):1319–1324	NUM
ejpam-5901	504	5	,	,	PUNCT
ejpam-5901	504	6	2014	2014	NUM
ejpam-5901	504	7	.	.	PUNCT
ejpam-5901	505	1	[	[	X
ejpam-5901	505	2	4	4	NUM
ejpam-5901	505	3	]	]	X
ejpam-5901	505	4	e.j	e.j	PROPN
ejpam-5901	505	5	.	.	PROPN
ejpam-5901	505	6	ndelwa	ndelwa	PROPN
ejpam-5901	505	7	,	,	PUNCT
ejpam-5901	505	8	m.	m.	NOUN
ejpam-5901	505	9	kgosimore	kgosimore	PROPN
ejpam-5901	505	10	,	,	PUNCT
ejpam-5901	505	11	e.s	e.s	PROPN
ejpam-5901	505	12	.	.	PROPN
ejpam-5901	505	13	massawe	massawe	PROPN
ejpam-5901	505	14	,	,	PUNCT
ejpam-5901	505	15	and	and	CCONJ
ejpam-5901	505	16	l.	l.	PROPN
ejpam-5901	505	17	namkinga	namkinga	PROPN
ejpam-5901	505	18	.	.	PUNCT
ejpam-5901	506	1	mathematical	mathematical	ADJ
ejpam-5901	506	2	modelling	modelling	NOUN
ejpam-5901	506	3	and	and	CCONJ
ejpam-5901	506	4	analysis	analysis	NOUN
ejpam-5901	506	5	of	of	ADP
ejpam-5901	506	6	treatment	treatment	NOUN
ejpam-5901	506	7	and	and	CCONJ
ejpam-5901	506	8	screening	screening	NOUN
ejpam-5901	506	9	of	of	ADP
ejpam-5901	506	10	pneumonia	pneumonia	NOUN
ejpam-5901	506	11	.	.	PUNCT
ejpam-5901	507	1	math	math	NOUN
ejpam-5901	507	2	.	.	PUNCT
ejpam-5901	508	1	theory	theory	NOUN
ejpam-5901	508	2	model	model	PROPN
ejpam-5901	508	3	.	.	PUNCT
ejpam-5901	508	4	,	,	PUNCT
ejpam-5901	508	5	5(10):21–39	5(10):21–39	NUM
ejpam-5901	508	6	,	,	PUNCT
ejpam-5901	508	7	2015	2015	NUM
ejpam-5901	508	8	.	.	PUNCT
ejpam-5901	509	1	[	[	X
ejpam-5901	509	2	5	5	X
ejpam-5901	509	3	]	]	PUNCT
ejpam-5901	509	4	k.	k.	PROPN
ejpam-5901	509	5	kosasih	kosasih	PROPN
ejpam-5901	509	6	,	,	PUNCT
ejpam-5901	509	7	u.r	u.r	PROPN
ejpam-5901	509	8	.	.	PROPN
ejpam-5901	509	9	abeyratne	abeyratne	PROPN
ejpam-5901	509	10	,	,	PUNCT
ejpam-5901	509	11	v.	v.	CCONJ
ejpam-5901	509	12	swarnkar	swarnkar	NOUN
ejpam-5901	509	13	,	,	PUNCT
ejpam-5901	509	14	and	and	CCONJ
ejpam-5901	509	15	r.	r.	PROPN
ejpam-5901	509	16	triasih	triasih	PROPN
ejpam-5901	509	17	.	.	PUNCT
ejpam-5901	510	1	wavelet	wavelet	PROPN
ejpam-5901	510	2	augmented	augment	VERB
ejpam-5901	510	3	cough	cough	NOUN
ejpam-5901	510	4	analysis	analysis	NOUN
ejpam-5901	510	5	for	for	ADP
ejpam-5901	510	6	rapid	rapid	ADJ
ejpam-5901	510	7	childhood	childhood	NOUN
ejpam-5901	510	8	pneumonia	pneumonia	NOUN
ejpam-5901	510	9	diagnosis	diagnosis	NOUN
ejpam-5901	510	10	.	.	PUNCT
ejpam-5901	511	1	ieee	ieee	PROPN
ejpam-5901	511	2	trans	trans	PROPN
ejpam-5901	511	3	.	.	PROPN
ejpam-5901	511	4	biomed	biome	VERB
ejpam-5901	511	5	.	.	PUNCT
ejpam-5901	512	1	eng	eng	PROPN
ejpam-5901	512	2	.	.	PROPN
ejpam-5901	512	3	,	,	PUNCT
ejpam-5901	512	4	62(4):1185–1194	62(4):1185–1194	NUM
ejpam-5901	512	5	,	,	PUNCT
ejpam-5901	512	6	2015	2015	NUM
ejpam-5901	512	7	.	.	PUNCT
ejpam-5901	513	1	[	[	X
ejpam-5901	513	2	6	6	NUM
ejpam-5901	513	3	]	]	PUNCT
ejpam-5901	513	4	a.c.g	a.c.g	NOUN
ejpam-5901	513	5	.	.	PUNCT
ejpam-5901	513	6	césar	césar	PROPN
ejpam-5901	513	7	,	,	PUNCT
ejpam-5901	513	8	l.f.c	l.f.c	PROPN
ejpam-5901	513	9	.	.	PROPN
ejpam-5901	513	10	nascimento	nascimento	PROPN
ejpam-5901	513	11	,	,	PUNCT
ejpam-5901	513	12	k.c.c	k.c.c	PROPN
ejpam-5901	513	13	.	.	PUNCT
ejpam-5901	513	14	mantovani	mantovani	PROPN
ejpam-5901	513	15	,	,	PUNCT
ejpam-5901	513	16	and	and	CCONJ
ejpam-5901	513	17	l.c.p	l.c.p	NOUN
ejpam-5901	513	18	.	.	PUNCT
ejpam-5901	513	19	vieira	vieira	PROPN
ejpam-5901	513	20	.	.	PUNCT
ejpam-5901	514	1	fine	fine	ADJ
ejpam-5901	514	2	particulate	particulate	NOUN
ejpam-5901	514	3	matter	matter	NOUN
ejpam-5901	514	4	estimated	estimate	VERB
ejpam-5901	514	5	by	by	ADP
ejpam-5901	514	6	mathematical	mathematical	ADJ
ejpam-5901	514	7	model	model	NOUN
ejpam-5901	514	8	and	and	CCONJ
ejpam-5901	514	9	hospitalisations	hospitalisation	NOUN
ejpam-5901	514	10	for	for	ADP
ejpam-5901	514	11	pneumonia	pneumonia	NOUN
ejpam-5901	514	12	and	and	CCONJ
ejpam-5901	514	13	asthma	asthma	NOUN
ejpam-5901	514	14	in	in	ADP
ejpam-5901	514	15	children	child	NOUN
ejpam-5901	514	16	.	.	PUNCT
ejpam-5901	515	1	rev	rev	PROPN
ejpam-5901	515	2	.	.	PROPN
ejpam-5901	515	3	paul	paul	PROPN
ejpam-5901	515	4	.	.	PUNCT
ejpam-5901	516	1	pediatr	pediatr	PROPN
ejpam-5901	516	2	.	.	PUNCT
ejpam-5901	517	1	(	(	PUNCT
ejpam-5901	517	2	engl	engl	PROPN
ejpam-5901	517	3	.	.	PUNCT
ejpam-5901	518	1	ed	ed	NOUN
ejpam-5901	518	2	.	.	PUNCT
ejpam-5901	518	3	)	)	PUNCT
ejpam-5901	518	4	,	,	PUNCT
ejpam-5901	519	1	34(1):18–23	34(1):18–23	NUM
ejpam-5901	519	2	,	,	PUNCT
ejpam-5901	519	3	2016	2016	NUM
ejpam-5901	519	4	.	.	PUNCT
ejpam-5901	520	1	[	[	X
ejpam-5901	520	2	7	7	X
ejpam-5901	520	3	]	]	X
ejpam-5901	520	4	c.	c.	PROPN
ejpam-5901	520	5	marchello	marchello	PROPN
ejpam-5901	520	6	,	,	PUNCT
ejpam-5901	520	7	a.p	a.p	PROPN
ejpam-5901	520	8	.	.	PROPN
ejpam-5901	520	9	dale	dale	PROPN
ejpam-5901	520	10	,	,	PUNCT
ejpam-5901	520	11	t.n	t.n	PROPN
ejpam-5901	520	12	.	.	PROPN
ejpam-5901	520	13	thai	thai	PROPN
ejpam-5901	520	14	,	,	PUNCT
ejpam-5901	520	15	d.s	d.s	PROPN
ejpam-5901	520	16	.	.	PROPN
ejpam-5901	520	17	han	han	PROPN
ejpam-5901	520	18	,	,	PUNCT
ejpam-5901	520	19	and	and	CCONJ
ejpam-5901	520	20	m.h	m.h	PROPN
ejpam-5901	520	21	.	.	PROPN
ejpam-5901	520	22	ebell	ebell	NOUN
ejpam-5901	520	23	.	.	PUNCT
ejpam-5901	521	1	prevalence	prevalence	NOUN
ejpam-5901	521	2	of	of	ADP
ejpam-5901	521	3	atypical	atypical	ADJ
ejpam-5901	521	4	pathogens	pathogen	NOUN
ejpam-5901	521	5	in	in	ADP
ejpam-5901	521	6	patients	patient	NOUN
ejpam-5901	521	7	with	with	ADP
ejpam-5901	521	8	cough	cough	NOUN
ejpam-5901	521	9	and	and	CCONJ
ejpam-5901	521	10	community	community	NOUN
ejpam-5901	521	11	-	-	PUNCT
ejpam-5901	521	12	acquired	acquire	VERB
ejpam-5901	521	13	pneumonia	pneumonia	NOUN
ejpam-5901	521	14	:	:	PUNCT
ejpam-5901	521	15	a	a	DET
ejpam-5901	521	16	metaanalysis	metaanalysis	NOUN
ejpam-5901	521	17	.	.	PUNCT
ejpam-5901	522	1	ann	ann	PROPN
ejpam-5901	522	2	.	.	PUNCT
ejpam-5901	522	3	fam	fam	PROPN
ejpam-5901	522	4	.	.	PUNCT
ejpam-5901	522	5	med	med	PROPN
ejpam-5901	522	6	.	.	PROPN
ejpam-5901	522	7	,	,	PUNCT
ejpam-5901	522	8	14(6):552–566	14(6):552–566	PROPN
ejpam-5901	522	9	,	,	PUNCT
ejpam-5901	522	10	2016	2016	NUM
ejpam-5901	522	11	.	.	PUNCT
ejpam-5901	523	1	[	[	X
ejpam-5901	523	2	8	8	NUM
ejpam-5901	523	3	]	]	X
ejpam-5901	523	4	y.h	y.h	PROPN
ejpam-5901	523	5	.	.	PROPN
ejpam-5901	523	6	cheng	cheng	PROPN
ejpam-5901	523	7	,	,	PUNCT
ejpam-5901	523	8	s.h	s.h	PROPN
ejpam-5901	523	9	.	.	PUNCT
ejpam-5901	523	10	you	you	PRON
ejpam-5901	523	11	,	,	PUNCT
ejpam-5901	523	12	y.j	y.j	PROPN
ejpam-5901	523	13	.	.	PUNCT
ejpam-5901	523	14	lin	lin	PROPN
ejpam-5901	523	15	,	,	PUNCT
ejpam-5901	523	16	s.c	s.c	PROPN
ejpam-5901	523	17	.	.	PROPN
ejpam-5901	523	18	chen	chen	PROPN
ejpam-5901	523	19	,	,	PUNCT
ejpam-5901	524	1	w.y	w.y	PROPN
ejpam-5901	524	2	.	.	PUNCT
ejpam-5901	524	3	chen	chen	PROPN
ejpam-5901	524	4	,	,	PUNCT
ejpam-5901	524	5	w.c	w.c	PROPN
ejpam-5901	524	6	.	.	PROPN
ejpam-5901	524	7	chou	chou	PROPN
ejpam-5901	524	8	,	,	PUNCT
ejpam-5901	524	9	and	and	CCONJ
ejpam-5901	524	10	c.m	c.m	PROPN
ejpam-5901	524	11	.	.	PROPN
ejpam-5901	524	12	liao	liao	PROPN
ejpam-5901	524	13	.	.	PROPN
ejpam-5901	525	1	mathematical	mathematical	ADJ
ejpam-5901	525	2	modeling	modeling	NOUN
ejpam-5901	525	3	of	of	ADP
ejpam-5901	525	4	post	post	ADJ
ejpam-5901	525	5	coinfection	coinfection	NOUN
ejpam-5901	525	6	with	with	ADP
ejpam-5901	525	7	influenza	influenza	NOUN
ejpam-5901	525	8	a	a	DET
ejpam-5901	525	9	virus	virus	NOUN
ejpam-5901	525	10	and	and	CCONJ
ejpam-5901	525	11	streptococcus	streptococcus	VERB
ejpam-5901	525	12	pneumoniae	pneumoniae	NOUN
ejpam-5901	525	13	,	,	PUNCT
ejpam-5901	525	14	with	with	ADP
ejpam-5901	525	15	implications	implication	NOUN
ejpam-5901	525	16	for	for	ADP
ejpam-5901	525	17	pneumonia	pneumonia	NOUN
ejpam-5901	525	18	and	and	CCONJ
ejpam-5901	525	19	copd	copd	NOUN
ejpam-5901	525	20	-	-	PUNCT
ejpam-5901	525	21	risk	risk	NOUN
ejpam-5901	525	22	assessment	assessment	NOUN
ejpam-5901	525	23	.	.	PUNCT
ejpam-5901	526	1	int	int	NOUN
ejpam-5901	526	2	.	.	PUNCT
ejpam-5901	527	1	j.	j.	PROPN
ejpam-5901	527	2	chronic	chronic	PROPN
ejpam-5901	527	3	obstr	obstr	PROPN
ejpam-5901	527	4	.	.	PUNCT
ejpam-5901	528	1	pulm	pulm	NOUN
ejpam-5901	528	2	.	.	PUNCT
ejpam-5901	529	1	dis	dis	PROPN
ejpam-5901	529	2	.	.	PROPN
ejpam-5901	529	3	,	,	PUNCT
ejpam-5901	529	4	12:1973–1988	12:1973–1988	NUM
ejpam-5901	529	5	,	,	PUNCT
ejpam-5901	529	6	2017	2017	NUM
ejpam-5901	529	7	.	.	PUNCT
ejpam-5901	530	1	[	[	X
ejpam-5901	530	2	9	9	NUM
ejpam-5901	530	3	]	]	PUNCT
ejpam-5901	530	4	k.	k.	NOUN
ejpam-5901	530	5	kosasih	kosasih	PROPN
ejpam-5901	530	6	and	and	CCONJ
ejpam-5901	530	7	u.	u.	PROPN
ejpam-5901	530	8	abeyratne	abeyratne	PROPN
ejpam-5901	530	9	.	.	PUNCT
ejpam-5901	531	1	exhaustive	exhaustive	ADJ
ejpam-5901	531	2	mathematical	mathematical	ADJ
ejpam-5901	531	3	analysis	analysis	NOUN
ejpam-5901	531	4	of	of	ADP
ejpam-5901	531	5	simple	simple	ADJ
ejpam-5901	531	6	clinical	clinical	ADJ
ejpam-5901	531	7	measurements	measurement	NOUN
ejpam-5901	531	8	for	for	ADP
ejpam-5901	531	9	childhood	childhood	ADJ
ejpam-5901	531	10	pneumonia	pneumonia	NOUN
ejpam-5901	531	11	diagnosis	diagnosis	NOUN
ejpam-5901	531	12	.	.	PUNCT
ejpam-5901	532	1	world	world	NOUN
ejpam-5901	532	2	j.	j.	PROPN
ejpam-5901	532	3	pediatr	pediatr	PROPN
ejpam-5901	532	4	.	.	PROPN
ejpam-5901	532	5	,	,	PUNCT
ejpam-5901	532	6	13(5):446–456	13(5):446–456	PROPN
ejpam-5901	532	7	,	,	PUNCT
ejpam-5901	532	8	2017	2017	NUM
ejpam-5901	532	9	.	.	PUNCT
ejpam-5901	533	1	[	[	X
ejpam-5901	533	2	10	10	NUM
ejpam-5901	533	3	]	]	X
ejpam-5901	533	4	g.t	g.t	PROPN
ejpam-5901	533	5	.	.	PROPN
ejpam-5901	533	6	tilahun	tilahun	PROPN
ejpam-5901	533	7	,	,	PUNCT
ejpam-5901	533	8	o.d	o.d	PROPN
ejpam-5901	533	9	.	.	PROPN
ejpam-5901	533	10	makinde	makinde	PROPN
ejpam-5901	533	11	,	,	PUNCT
ejpam-5901	533	12	and	and	CCONJ
ejpam-5901	533	13	d.	d.	PROPN
ejpam-5901	533	14	malonza	malonza	PROPN
ejpam-5901	533	15	.	.	PUNCT
ejpam-5901	534	1	modelling	modelling	NOUN
ejpam-5901	534	2	and	and	CCONJ
ejpam-5901	534	3	optimal	optimal	ADJ
ejpam-5901	534	4	control	control	NOUN
ejpam-5901	534	5	of	of	ADP
ejpam-5901	534	6	pneumonia	pneumonia	NOUN
ejpam-5901	534	7	disease	disease	NOUN
ejpam-5901	534	8	with	with	ADP
ejpam-5901	534	9	cost	cost	NOUN
ejpam-5901	534	10	-	-	PUNCT
ejpam-5901	534	11	effective	effective	ADJ
ejpam-5901	534	12	strategies	strategy	NOUN
ejpam-5901	534	13	.	.	PUNCT
ejpam-5901	535	1	j.	j.	PROPN
ejpam-5901	535	2	biol	biol	PROPN
ejpam-5901	535	3	.	.	PUNCT
ejpam-5901	536	1	dyn	dyn	PROPN
ejpam-5901	536	2	.	.	PUNCT
ejpam-5901	536	3	,	,	PUNCT
ejpam-5901	536	4	11(2):400–426	11(2):400–426	NUM
ejpam-5901	536	5	,	,	PUNCT
ejpam-5901	536	6	2017	2017	NUM
ejpam-5901	536	7	.	.	PUNCT
ejpam-5901	537	1	[	[	X
ejpam-5901	537	2	11	11	NUM
ejpam-5901	537	3	]	]	X
ejpam-5901	537	4	g.t	g.t	PROPN
ejpam-5901	537	5	.	.	PROPN
ejpam-5901	537	6	tilahun	tilahun	PROPN
ejpam-5901	537	7	,	,	PUNCT
ejpam-5901	537	8	o.d	o.d	PROPN
ejpam-5901	537	9	.	.	PROPN
ejpam-5901	537	10	makinde	makinde	PROPN
ejpam-5901	537	11	,	,	PUNCT
ejpam-5901	537	12	and	and	CCONJ
ejpam-5901	537	13	d.	d.	PROPN
ejpam-5901	537	14	malonza	malonza	PROPN
ejpam-5901	537	15	.	.	PUNCT
ejpam-5901	538	1	co	co	NOUN
ejpam-5901	539	1	-	-	NOUN
ejpam-5901	539	2	dynamics	dynamic	NOUN
ejpam-5901	539	3	of	of	ADP
ejpam-5901	539	4	pneumonia	pneumonia	NOUN
ejpam-5901	539	5	and	and	CCONJ
ejpam-5901	539	6	typhoid	typhoid	NOUN
ejpam-5901	539	7	fever	fever	NOUN
ejpam-5901	539	8	diseases	disease	NOUN
ejpam-5901	539	9	with	with	ADP
ejpam-5901	539	10	cost	cost	NOUN
ejpam-5901	539	11	-	-	PUNCT
ejpam-5901	539	12	effective	effective	ADJ
ejpam-5901	539	13	optimal	optimal	ADJ
ejpam-5901	539	14	control	control	NOUN
ejpam-5901	539	15	analysis	analysis	NOUN
ejpam-5901	539	16	.	.	PUNCT
ejpam-5901	540	1	appl	appl	PROPN
ejpam-5901	540	2	.	.	PROPN
ejpam-5901	540	3	math	math	PROPN
ejpam-5901	540	4	.	.	PUNCT
ejpam-5901	541	1	comput	comput	NOUN
ejpam-5901	541	2	.	.	PUNCT
ejpam-5901	541	3	,	,	PUNCT
ejpam-5901	541	4	316:438–459	316:438–459	PROPN
ejpam-5901	541	5	,	,	PUNCT
ejpam-5901	541	6	2018	2018	NUM
ejpam-5901	541	7	.	.	PUNCT
ejpam-5901	542	1	[	[	X
ejpam-5901	542	2	12	12	NUM
ejpam-5901	542	3	]	]	PUNCT
ejpam-5901	542	4	m.	m.	NOUN
ejpam-5901	542	5	raj	raj	PROPN
ejpam-5901	542	6	,	,	PUNCT
ejpam-5901	542	7	m.	m.	PROPN
ejpam-5901	542	8	reddy	reddy	PROPN
ejpam-5901	542	9	,	,	PUNCT
ejpam-5901	542	10	m.	m.	NOUN
ejpam-5901	542	11	mufeed	mufeed	PROPN
ejpam-5901	542	12	,	,	PUNCT
ejpam-5901	542	13	and	and	CCONJ
ejpam-5901	542	14	s.	s.	PROPN
ejpam-5901	542	15	karthika	karthika	PROPN
ejpam-5901	542	16	.	.	PUNCT
ejpam-5901	543	1	hmm	hmm	PROPN
ejpam-5901	543	2	based	base	VERB
ejpam-5901	543	3	cough	cough	NOUN
ejpam-5901	543	4	sound	sound	NOUN
ejpam-5901	543	5	analysis	analysis	NOUN
ejpam-5901	543	6	for	for	ADP
ejpam-5901	543	7	classifying	classify	VERB
ejpam-5901	543	8	asthma	asthma	NOUN
ejpam-5901	543	9	and	and	CCONJ
ejpam-5901	543	10	pneumonia	pneumonia	NOUN
ejpam-5901	543	11	in	in	ADP
ejpam-5901	543	12	paediatric	paediatric	ADJ
ejpam-5901	543	13	population	population	NOUN
ejpam-5901	543	14	.	.	PUNCT
ejpam-5901	544	1	international	international	ADJ
ejpam-5901	544	2	journal	journal	NOUN
ejpam-5901	544	3	of	of	ADP
ejpam-5901	544	4	pure	pure	ADJ
ejpam-5901	544	5	and	and	CCONJ
ejpam-5901	544	6	applied	applied	ADJ
ejpam-5901	544	7	mathematics	mathematic	NOUN
ejpam-5901	544	8	,	,	PUNCT
ejpam-5901	544	9	118(18):609–616	118(18):609–616	PROPN
ejpam-5901	544	10	,	,	PUNCT
ejpam-5901	544	11	2018	2018	NUM
ejpam-5901	544	12	.	.	PUNCT
ejpam-5901	545	1	[	[	X
ejpam-5901	545	2	13	13	NUM
ejpam-5901	545	3	]	]	PUNCT
ejpam-5901	545	4	m.	m.	NOUN
ejpam-5901	545	5	kizito	kizito	PROPN
ejpam-5901	545	6	and	and	CCONJ
ejpam-5901	545	7	j.	j.	PROPN
ejpam-5901	545	8	tumwiine	tumwiine	PROPN
ejpam-5901	545	9	.	.	PUNCT
ejpam-5901	546	1	a	a	DET
ejpam-5901	546	2	mathematical	mathematical	ADJ
ejpam-5901	546	3	model	model	NOUN
ejpam-5901	546	4	of	of	ADP
ejpam-5901	546	5	treatment	treatment	NOUN
ejpam-5901	546	6	and	and	CCONJ
ejpam-5901	546	7	vaccination	vaccination	NOUN
ejpam-5901	546	8	interventions	intervention	NOUN
ejpam-5901	546	9	of	of	ADP
ejpam-5901	546	10	pneumococcal	pneumococcal	ADJ
ejpam-5901	546	11	pneumonia	pneumonia	NOUN
ejpam-5901	546	12	infection	infection	NOUN
ejpam-5901	546	13	dynamics	dynamic	NOUN
ejpam-5901	546	14	.	.	PUNCT
ejpam-5901	547	1	journal	journal	NOUN
ejpam-5901	547	2	of	of	ADP
ejpam-5901	547	3	applied	apply	VERB
ejpam-5901	547	4	mathematics	mathematic	NOUN
ejpam-5901	547	5	,	,	PUNCT
ejpam-5901	547	6	2018	2018	NUM
ejpam-5901	547	7	.	.	PUNCT
ejpam-5901	548	1	[	[	X
ejpam-5901	548	2	14	14	NUM
ejpam-5901	548	3	]	]	X
ejpam-5901	548	4	f.k	f.k	PROPN
ejpam-5901	548	5	.	.	PROPN
ejpam-5901	548	6	mbabazi	mbabazi	PROPN
ejpam-5901	548	7	,	,	PUNCT
ejpam-5901	548	8	j.y.t	j.y.t	PROPN
ejpam-5901	548	9	.	.	PUNCT
ejpam-5901	548	10	mugisha	mugisha	PROPN
ejpam-5901	548	11	,	,	PUNCT
ejpam-5901	548	12	and	and	CCONJ
ejpam-5901	548	13	m.	m.	NOUN
ejpam-5901	548	14	kimathi	kimathi	PROPN
ejpam-5901	548	15	.	.	PUNCT
ejpam-5901	549	1	modeling	model	VERB
ejpam-5901	549	2	the	the	DET
ejpam-5901	549	3	within	within	ADP
ejpam-5901	549	4	-	-	PUNCT
ejpam-5901	549	5	host	host	NOUN
ejpam-5901	549	6	coinfection	coinfection	NOUN
ejpam-5901	549	7	of	of	ADP
ejpam-5901	549	8	influenza	influenza	NOUN
ejpam-5901	549	9	a	a	DET
ejpam-5901	549	10	virus	virus	NOUN
ejpam-5901	549	11	and	and	CCONJ
ejpam-5901	549	12	pneumococcus	pneumococcus	NOUN
ejpam-5901	549	13	.	.	PUNCT
ejpam-5901	550	1	applied	apply	VERB
ejpam-5901	550	2	mathematics	mathematic	NOUN
ejpam-5901	550	3	and	and	CCONJ
ejpam-5901	550	4	computation	computation	NOUN
ejpam-5901	550	5	,	,	PUNCT
ejpam-5901	550	6	339:488–506	339:488–506	NUM
ejpam-5901	550	7	,	,	PUNCT
ejpam-5901	550	8	2018	2018	NUM
ejpam-5901	550	9	.	.	PUNCT
ejpam-5901	551	1	s.	s.	PROPN
ejpam-5901	551	2	saber	saber	PROPN
ejpam-5901	551	3	,	,	PUNCT
ejpam-5901	551	4	a.	a.	NOUN
ejpam-5901	551	5	a.	a.	NOUN
ejpam-5901	551	6	alahmari	alahmari	PROPN
ejpam-5901	551	7	/	/	SYM
ejpam-5901	551	8	eur	eur	PROPN
ejpam-5901	551	9	.	.	PUNCT
ejpam-5901	552	1	j.	j.	PROPN
ejpam-5901	552	2	pure	pure	PROPN
ejpam-5901	552	3	appl	appl	PROPN
ejpam-5901	552	4	.	.	PROPN
ejpam-5901	552	5	math	math	PROPN
ejpam-5901	552	6	,	,	PUNCT
ejpam-5901	552	7	18	18	NUM
ejpam-5901	552	8	(	(	PUNCT
ejpam-5901	552	9	2	2	NUM
ejpam-5901	552	10	)	)	PUNCT
ejpam-5901	552	11	(	(	PUNCT
ejpam-5901	552	12	2025	2025	NUM
ejpam-5901	552	13	)	)	PUNCT
ejpam-5901	552	14	,	,	PUNCT
ejpam-5901	552	15	5901	5901	NUM
ejpam-5901	552	16	21	21	NUM
ejpam-5901	552	17	of	of	ADP
ejpam-5901	552	18	23	23	NUM
ejpam-5901	552	19	[	[	SYM
ejpam-5901	552	20	15	15	NUM
ejpam-5901	552	21	]	]	X
ejpam-5901	552	22	g.t	g.t	PROPN
ejpam-5901	552	23	.	.	PROPN
ejpam-5901	552	24	tilahun	tilahun	PROPN
ejpam-5901	552	25	.	.	PUNCT
ejpam-5901	553	1	optimal	optimal	ADJ
ejpam-5901	553	2	control	control	NOUN
ejpam-5901	553	3	analysis	analysis	NOUN
ejpam-5901	553	4	of	of	ADP
ejpam-5901	553	5	pneumonia	pneumonia	NOUN
ejpam-5901	553	6	and	and	CCONJ
ejpam-5901	553	7	meningitis	meningitis	NOUN
ejpam-5901	553	8	coinfection	coinfection	NOUN
ejpam-5901	553	9	.	.	PUNCT
ejpam-5901	554	1	computational	computational	ADJ
ejpam-5901	554	2	and	and	CCONJ
ejpam-5901	554	3	mathematical	mathematical	ADJ
ejpam-5901	554	4	methods	method	NOUN
ejpam-5901	554	5	in	in	ADP
ejpam-5901	554	6	medicine	medicine	NOUN
ejpam-5901	554	7	,	,	PUNCT
ejpam-5901	554	8	pages	page	NOUN
ejpam-5901	554	9	1–15	1–15	PROPN
ejpam-5901	554	10	,	,	PUNCT
ejpam-5901	554	11	2019	2019	NUM
ejpam-5901	554	12	.	.	PUNCT
ejpam-5901	555	1	[	[	X
ejpam-5901	555	2	16	16	NUM
ejpam-5901	555	3	]	]	X
ejpam-5901	555	4	g.t	g.t	PROPN
ejpam-5901	555	5	.	.	PROPN
ejpam-5901	555	6	tilahun	tilahun	PROPN
ejpam-5901	555	7	.	.	PUNCT
ejpam-5901	556	1	modeling	model	VERB
ejpam-5901	556	2	co	co	NOUN
ejpam-5901	556	3	-	-	NOUN
ejpam-5901	556	4	dynamics	dynamic	NOUN
ejpam-5901	556	5	of	of	ADP
ejpam-5901	556	6	pneumonia	pneumonia	NOUN
ejpam-5901	556	7	and	and	CCONJ
ejpam-5901	556	8	meningitis	meningitis	NOUN
ejpam-5901	556	9	diseases	disease	NOUN
ejpam-5901	556	10	.	.	PUNCT
ejpam-5901	557	1	advances	advance	NOUN
ejpam-5901	557	2	in	in	ADP
ejpam-5901	557	3	differential	differential	ADJ
ejpam-5901	557	4	equations	equation	NOUN
ejpam-5901	557	5	,	,	PUNCT
ejpam-5901	557	6	2019(1):1	2019(1):1	PROPN
ejpam-5901	557	7	,	,	PUNCT
ejpam-5901	557	8	2019	2019	NUM
ejpam-5901	557	9	.	.	PUNCT
ejpam-5901	558	1	[	[	X
ejpam-5901	558	2	17	17	NUM
ejpam-5901	558	3	]	]	X
ejpam-5901	558	4	i.m	i.m	PROPN
ejpam-5901	558	5	.	.	PUNCT
ejpam-5901	558	6	diah	diah	PROPN
ejpam-5901	558	7	and	and	CCONJ
ejpam-5901	558	8	n.	n.	PROPN
ejpam-5901	558	9	aziz	aziz	PROPN
ejpam-5901	558	10	.	.	PUNCT
ejpam-5901	559	1	stochastic	stochastic	ADJ
ejpam-5901	559	2	modelling	modelling	NOUN
ejpam-5901	559	3	for	for	ADP
ejpam-5901	559	4	pneumonia	pneumonia	NOUN
ejpam-5901	559	5	incidence	incidence	NOUN
ejpam-5901	559	6	:	:	PUNCT
ejpam-5901	559	7	a	a	DET
ejpam-5901	559	8	conceptual	conceptual	ADJ
ejpam-5901	559	9	framework	framework	NOUN
ejpam-5901	559	10	.	.	PUNCT
ejpam-5901	560	1	in	in	ADP
ejpam-5901	560	2	aip	aip	PROPN
ejpam-5901	560	3	conference	conference	NOUN
ejpam-5901	560	4	proceedings	proceeding	NOUN
ejpam-5901	560	5	,	,	PUNCT
ejpam-5901	560	6	volume	volume	NOUN
ejpam-5901	560	7	1	1	NUM
ejpam-5901	560	8	,	,	PUNCT
ejpam-5901	560	9	pages	page	NOUN
ejpam-5901	560	10	1–3	1–3	NUM
ejpam-5901	560	11	.	.	PUNCT
ejpam-5901	560	12	aip	aip	PROPN
ejpam-5901	560	13	,	,	PUNCT
ejpam-5901	560	14	new	new	PROPN
ejpam-5901	560	15	york	york	PROPN
ejpam-5901	560	16	,	,	PUNCT
ejpam-5901	560	17	2019	2019	NUM
ejpam-5901	560	18	.	.	PUNCT
ejpam-5901	561	1	[	[	X
ejpam-5901	561	2	18	18	NUM
ejpam-5901	561	3	]	]	X
ejpam-5901	561	4	f.k	f.k	PROPN
ejpam-5901	561	5	.	.	PROPN
ejpam-5901	561	6	mbabazi	mbabazi	PROPN
ejpam-5901	561	7	,	,	PUNCT
ejpam-5901	561	8	j.y	j.y	PROPN
ejpam-5901	561	9	.	.	PROPN
ejpam-5901	561	10	mugisha	mugisha	PROPN
ejpam-5901	561	11	,	,	PUNCT
ejpam-5901	561	12	and	and	CCONJ
ejpam-5901	561	13	m.	m.	PROPN
ejpam-5901	561	14	kimathi	kimathi	PROPN
ejpam-5901	561	15	.	.	PUNCT
ejpam-5901	562	1	hopf	hopf	ADJ
ejpam-5901	562	2	-	-	PUNCT
ejpam-5901	562	3	bifurcation	bifurcation	NOUN
ejpam-5901	562	4	analysis	analysis	NOUN
ejpam-5901	562	5	of	of	ADP
ejpam-5901	562	6	pneumococcal	pneumococcal	ADJ
ejpam-5901	562	7	pneumonia	pneumonia	NOUN
ejpam-5901	562	8	with	with	ADP
ejpam-5901	562	9	time	time	NOUN
ejpam-5901	562	10	delays	delay	NOUN
ejpam-5901	562	11	.	.	PUNCT
ejpam-5901	563	1	abstract	abstract	ADJ
ejpam-5901	563	2	and	and	CCONJ
ejpam-5901	563	3	applied	apply	VERB
ejpam-5901	563	4	analysis	analysis	NOUN
ejpam-5901	563	5	,	,	PUNCT
ejpam-5901	563	6	2019(1):1	2019(1):1	PROPN
ejpam-5901	563	7	,	,	PUNCT
ejpam-5901	563	8	2019	2019	NUM
ejpam-5901	563	9	.	.	PUNCT
ejpam-5901	564	1	[	[	X
ejpam-5901	564	2	19	19	NUM
ejpam-5901	564	3	]	]	X
ejpam-5901	564	4	d.	d.	PROPN
ejpam-5901	564	5	otoo	otoo	PROPN
ejpam-5901	564	6	,	,	PUNCT
ejpam-5901	564	7	p.	p.	PROPN
ejpam-5901	564	8	opoku	opoku	PROPN
ejpam-5901	564	9	,	,	PUNCT
ejpam-5901	564	10	s.	s.	PROPN
ejpam-5901	564	11	charles	charles	PROPN
ejpam-5901	564	12	,	,	PUNCT
ejpam-5901	564	13	and	and	CCONJ
ejpam-5901	564	14	a.p	a.p	PROPN
ejpam-5901	564	15	.	.	PROPN
ejpam-5901	564	16	kingsley	kingsley	PROPN
ejpam-5901	564	17	.	.	PUNCT
ejpam-5901	565	1	deterministic	deterministic	ADJ
ejpam-5901	565	2	epidemic	epidemic	NOUN
ejpam-5901	565	3	model	model	NOUN
ejpam-5901	565	4	for	for	ADP
ejpam-5901	565	5	(	(	PUNCT
ejpam-5901	565	6	svcsycasyir	svcsycasyir	NOUN
ejpam-5901	565	7	)	)	PUNCT
ejpam-5901	565	8	pneumonia	pneumonia	NOUN
ejpam-5901	565	9	dynamics	dynamic	NOUN
ejpam-5901	565	10	,	,	PUNCT
ejpam-5901	565	11	with	with	ADP
ejpam-5901	565	12	vaccination	vaccination	NOUN
ejpam-5901	565	13	and	and	CCONJ
ejpam-5901	565	14	temporal	temporal	ADJ
ejpam-5901	565	15	immunity	immunity	NOUN
ejpam-5901	565	16	.	.	PUNCT
ejpam-5901	566	1	infectious	infectious	ADJ
ejpam-5901	566	2	disease	disease	NOUN
ejpam-5901	566	3	modelling	modelling	NOUN
ejpam-5901	566	4	,	,	PUNCT
ejpam-5901	566	5	5:42–60	5:42–60	NUM
ejpam-5901	566	6	,	,	PUNCT
ejpam-5901	566	7	2020	2020	NUM
ejpam-5901	566	8	.	.	PUNCT
ejpam-5901	567	1	[	[	X
ejpam-5901	567	2	20	20	NUM
ejpam-5901	567	3	]	]	X
ejpam-5901	567	4	o.c	o.c	PROPN
ejpam-5901	567	5	.	.	PROPN
ejpam-5901	567	6	zephaniah	zephaniah	PROPN
ejpam-5901	567	7	,	,	PUNCT
ejpam-5901	567	8	u.i.r	u.i.r	NOUN
ejpam-5901	567	9	.	.	PUNCT
ejpam-5901	567	10	nwaugonma	nwaugonma	PROPN
ejpam-5901	567	11	,	,	PUNCT
ejpam-5901	567	12	i.s	i.s	PROPN
ejpam-5901	567	13	.	.	PROPN
ejpam-5901	567	14	chioma	chioma	PROPN
ejpam-5901	567	15	,	,	PUNCT
ejpam-5901	567	16	and	and	CCONJ
ejpam-5901	567	17	o.	o.	PROPN
ejpam-5901	567	18	adrew	adrew	PROPN
ejpam-5901	567	19	.	.	PUNCT
ejpam-5901	568	1	a	a	DET
ejpam-5901	568	2	mathematical	mathematical	ADJ
ejpam-5901	568	3	model	model	NOUN
ejpam-5901	568	4	and	and	CCONJ
ejpam-5901	568	5	analysis	analysis	NOUN
ejpam-5901	568	6	of	of	ADP
ejpam-5901	568	7	an	an	DET
ejpam-5901	568	8	sveir	sveir	ADJ
ejpam-5901	568	9	model	model	NOUN
ejpam-5901	568	10	for	for	ADP
ejpam-5901	568	11	streptococcus	streptococcus	ADJ
ejpam-5901	568	12	pneumonia	pneumonia	NOUN
ejpam-5901	568	13	with	with	ADP
ejpam-5901	568	14	saturated	saturate	VERB
ejpam-5901	568	15	incidence	incidence	NOUN
ejpam-5901	568	16	force	force	NOUN
ejpam-5901	568	17	of	of	ADP
ejpam-5901	568	18	infection	infection	NOUN
ejpam-5901	568	19	.	.	PUNCT
ejpam-5901	569	1	mathematical	mathematical	ADJ
ejpam-5901	569	2	modelling	modelling	NOUN
ejpam-5901	569	3	and	and	CCONJ
ejpam-5901	569	4	applications	application	NOUN
ejpam-5901	569	5	,	,	PUNCT
ejpam-5901	569	6	5(1):16	5(1):16	NUM
ejpam-5901	569	7	,	,	PUNCT
ejpam-5901	569	8	2020	2020	NUM
ejpam-5901	569	9	.	.	PUNCT
ejpam-5901	570	1	[	[	X
ejpam-5901	570	2	21	21	NUM
ejpam-5901	570	3	]	]	X
ejpam-5901	570	4	w.k	w.k	PROPN
ejpam-5901	570	5	.	.	PROPN
ejpam-5901	570	6	ming	ming	PROPN
ejpam-5901	570	7	,	,	PUNCT
ejpam-5901	570	8	j.	j.	PROPN
ejpam-5901	570	9	huang	huang	PROPN
ejpam-5901	570	10	,	,	PUNCT
ejpam-5901	570	11	and	and	CCONJ
ejpam-5901	570	12	c.j	c.j	PROPN
ejpam-5901	570	13	.	.	PROPN
ejpam-5901	570	14	zhang	zhang	PROPN
ejpam-5901	570	15	.	.	PUNCT
ejpam-5901	571	1	breaking	break	VERB
ejpam-5901	571	2	down	down	ADP
ejpam-5901	571	3	of	of	ADP
ejpam-5901	571	4	healthcare	healthcare	NOUN
ejpam-5901	571	5	system	system	NOUN
ejpam-5901	571	6	:	:	PUNCT
ejpam-5901	571	7	mathematical	mathematical	ADJ
ejpam-5901	571	8	modelling	modelling	NOUN
ejpam-5901	571	9	for	for	ADP
ejpam-5901	571	10	controlling	control	VERB
ejpam-5901	571	11	the	the	DET
ejpam-5901	571	12	novel	novel	ADJ
ejpam-5901	571	13	coronavirus	coronavirus	NOUN
ejpam-5901	571	14	(	(	PUNCT
ejpam-5901	571	15	2019	2019	NUM
ejpam-5901	571	16	-	-	PUNCT
ejpam-5901	571	17	ncov	ncov	NOUN
ejpam-5901	571	18	)	)	PUNCT
ejpam-5901	571	19	outbreak	outbreak	NOUN
ejpam-5901	571	20	in	in	ADP
ejpam-5901	571	21	wuhan	wuhan	PROPN
ejpam-5901	571	22	,	,	PUNCT
ejpam-5901	571	23	china	china	PROPN
ejpam-5901	571	24	.	.	PUNCT
ejpam-5901	572	1	biorxiv	biorxiv	PROPN
ejpam-5901	572	2	,	,	PUNCT
ejpam-5901	572	3	1:1–18	1:1–18	NUM
ejpam-5901	572	4	,	,	PUNCT
ejpam-5901	572	5	2020	2020	NUM
ejpam-5901	572	6	.	.	PUNCT
ejpam-5901	573	1	[	[	X
ejpam-5901	573	2	22	22	NUM
ejpam-5901	573	3	]	]	X
ejpam-5901	573	4	s.m	s.m	PROPN
ejpam-5901	573	5	.	.	PROPN
ejpam-5901	573	6	jung	jung	PROPN
ejpam-5901	573	7	,	,	PUNCT
ejpam-5901	573	8	r.	r.	PROPN
ejpam-5901	573	9	kinoshita	kinoshita	PROPN
ejpam-5901	573	10	,	,	PUNCT
ejpam-5901	573	11	r.n	r.n	PROPN
ejpam-5901	573	12	.	.	PROPN
ejpam-5901	573	13	thompson	thompson	PROPN
ejpam-5901	573	14	,	,	PUNCT
ejpam-5901	573	15	n.m	n.m	PROPN
ejpam-5901	573	16	.	.	PROPN
ejpam-5901	573	17	linton	linton	PROPN
ejpam-5901	573	18	,	,	PUNCT
ejpam-5901	573	19	y.	y.	PROPN
ejpam-5901	573	20	yang	yang	PROPN
ejpam-5901	573	21	,	,	PUNCT
ejpam-5901	573	22	a.r	a.r	PROPN
ejpam-5901	573	23	.	.	PROPN
ejpam-5901	573	24	akhmetzhanov	akhmetzhanov	PROPN
ejpam-5901	573	25	,	,	PUNCT
ejpam-5901	573	26	and	and	CCONJ
ejpam-5901	573	27	h.	h.	PROPN
ejpam-5901	573	28	nishiura	nishiura	PROPN
ejpam-5901	573	29	.	.	PUNCT
ejpam-5901	574	1	epidemiological	epidemiological	ADJ
ejpam-5901	574	2	identification	identification	NOUN
ejpam-5901	574	3	of	of	ADP
ejpam-5901	574	4	a	a	DET
ejpam-5901	574	5	novel	novel	ADJ
ejpam-5901	574	6	pathogen	pathogen	NOUN
ejpam-5901	574	7	in	in	ADP
ejpam-5901	574	8	realtime	realtime	NOUN
ejpam-5901	574	9	:	:	PUNCT
ejpam-5901	574	10	analysis	analysis	NOUN
ejpam-5901	574	11	of	of	ADP
ejpam-5901	574	12	the	the	DET
ejpam-5901	574	13	atypical	atypical	ADJ
ejpam-5901	574	14	pneumonia	pneumonia	NOUN
ejpam-5901	574	15	outbreak	outbreak	NOUN
ejpam-5901	574	16	in	in	ADP
ejpam-5901	574	17	wuhan	wuhan	PROPN
ejpam-5901	574	18	,	,	PUNCT
ejpam-5901	574	19	china	china	PROPN
ejpam-5901	574	20	,	,	PUNCT
ejpam-5901	574	21	2019—2020	2019—2020	NUM
ejpam-5901	574	22	.	.	PUNCT
ejpam-5901	574	23	journal	journal	NOUN
ejpam-5901	574	24	of	of	ADP
ejpam-5901	574	25	clinical	clinical	ADJ
ejpam-5901	574	26	medicine	medicine	NOUN
ejpam-5901	574	27	,	,	PUNCT
ejpam-5901	574	28	9(3):1–18	9(3):1–18	NUM
ejpam-5901	574	29	,	,	PUNCT
ejpam-5901	574	30	2020	2020	NUM
ejpam-5901	574	31	.	.	PUNCT
ejpam-5901	575	1	[	[	X
ejpam-5901	575	2	23	23	NUM
ejpam-5901	575	3	]	]	X
ejpam-5901	575	4	n.m	n.m	PROPN
ejpam-5901	575	5	.	.	PROPN
ejpam-5901	575	6	wafula	wafula	PROPN
ejpam-5901	575	7	,	,	PUNCT
ejpam-5901	575	8	b.o	b.o	PROPN
ejpam-5901	575	9	.	.	PROPN
ejpam-5901	575	10	kwach	kwach	PROPN
ejpam-5901	575	11	,	,	PUNCT
ejpam-5901	575	12	and	and	CCONJ
ejpam-5901	575	13	v.n	v.n	PROPN
ejpam-5901	575	14	.	.	PROPN
ejpam-5901	575	15	marani	marani	PROPN
ejpam-5901	575	16	.	.	PUNCT
ejpam-5901	576	1	mathematical	mathematical	ADJ
ejpam-5901	576	2	modeling	modeling	NOUN
ejpam-5901	576	3	and	and	CCONJ
ejpam-5901	576	4	optimal	optimal	ADJ
ejpam-5901	576	5	control	control	NOUN
ejpam-5901	576	6	for	for	ADP
ejpam-5901	576	7	controlling	control	VERB
ejpam-5901	576	8	pneumonia	pneumonia	NOUN
ejpam-5901	576	9	-	-	PUNCT
ejpam-5901	576	10	hiv	hiv	PROPN
ejpam-5901	576	11	coinfection	coinfection	NOUN
ejpam-5901	576	12	.	.	PUNCT
ejpam-5901	577	1	international	international	ADJ
ejpam-5901	577	2	journal	journal	NOUN
ejpam-5901	577	3	of	of	ADP
ejpam-5901	577	4	innovative	innovative	ADJ
ejpam-5901	577	5	research	research	NOUN
ejpam-5901	577	6	and	and	CCONJ
ejpam-5901	577	7	development	development	NOUN
ejpam-5901	577	8	,	,	PUNCT
ejpam-5901	577	9	10(1):138–144	10(1):138–144	NUM
ejpam-5901	577	10	,	,	PUNCT
ejpam-5901	577	11	2021	2021	NUM
ejpam-5901	577	12	.	.	PUNCT
ejpam-5901	578	1	[	[	X
ejpam-5901	578	2	24	24	NUM
ejpam-5901	578	3	]	]	X
ejpam-5901	578	4	k.i	k.i	PROPN
ejpam-5901	578	5	.	.	PUNCT
ejpam-5901	578	6	ouwatobi	ouwatobi	PROPN
ejpam-5901	578	7	and	and	CCONJ
ejpam-5901	578	8	l.m	l.m	PROPN
ejpam-5901	578	9	.	.	PROPN
ejpam-5901	578	10	erinle	erinle	PROPN
ejpam-5901	578	11	-	-	PUNCT
ejpam-5901	578	12	ibrahim	ibrahim	PROPN
ejpam-5901	578	13	.	.	PUNCT
ejpam-5901	579	1	mathematical	mathematical	ADJ
ejpam-5901	579	2	modeling	modeling	NOUN
ejpam-5901	579	3	of	of	ADP
ejpam-5901	579	4	pneumonia	pneumonia	NOUN
ejpam-5901	579	5	dynamics	dynamic	NOUN
ejpam-5901	579	6	of	of	ADP
ejpam-5901	579	7	children	child	NOUN
ejpam-5901	579	8	under	under	ADP
ejpam-5901	579	9	the	the	DET
ejpam-5901	579	10	age	age	NOUN
ejpam-5901	579	11	of	of	ADP
ejpam-5901	579	12	five	five	NUM
ejpam-5901	579	13	.	.	PUNCT
ejpam-5901	580	1	research	research	NOUN
ejpam-5901	580	2	square	square	PROPN
ejpam-5901	580	3	,	,	PUNCT
ejpam-5901	580	4	1:1–16	1:1–16	NUM
ejpam-5901	580	5	,	,	PUNCT
ejpam-5901	580	6	2021	2021	NUM
ejpam-5901	580	7	.	.	PUNCT
ejpam-5901	581	1	[	[	X
ejpam-5901	581	2	25	25	NUM
ejpam-5901	581	3	]	]	PUNCT
ejpam-5901	581	4	sayed	sayed	PROPN
ejpam-5901	581	5	saber	saber	PROPN
ejpam-5901	581	6	,	,	PUNCT
ejpam-5901	581	7	azza	azza	PROPN
ejpam-5901	581	8	m.	m.	PROPN
ejpam-5901	581	9	alghamdi	alghamdi	PROPN
ejpam-5901	581	10	,	,	PUNCT
ejpam-5901	581	11	ghada	ghada	PROPN
ejpam-5901	581	12	a.	a.	PROPN
ejpam-5901	581	13	ahmed	ahmed	PROPN
ejpam-5901	581	14	,	,	PUNCT
ejpam-5901	581	15	and	and	CCONJ
ejpam-5901	581	16	khulud	khulud	PROPN
ejpam-5901	581	17	m.	m.	PROPN
ejpam-5901	581	18	alshehri	alshehri	PROPN
ejpam-5901	581	19	.	.	PUNCT
ejpam-5901	582	1	mathematical	mathematical	ADJ
ejpam-5901	582	2	modelling	modelling	NOUN
ejpam-5901	582	3	and	and	CCONJ
ejpam-5901	582	4	optimal	optimal	ADJ
ejpam-5901	582	5	control	control	NOUN
ejpam-5901	582	6	of	of	ADP
ejpam-5901	582	7	pneumonia	pneumonia	NOUN
ejpam-5901	582	8	disease	disease	NOUN
ejpam-5901	582	9	in	in	ADP
ejpam-5901	582	10	sheep	sheep	NOUN
ejpam-5901	582	11	and	and	CCONJ
ejpam-5901	582	12	goats	goat	NOUN
ejpam-5901	582	13	in	in	ADP
ejpam-5901	582	14	al	al	PROPN
ejpam-5901	582	15	-	-	PUNCT
ejpam-5901	582	16	baha	baha	PROPN
ejpam-5901	582	17	region	region	NOUN
ejpam-5901	582	18	with	with	ADP
ejpam-5901	582	19	cost	cost	NOUN
ejpam-5901	582	20	-	-	PUNCT
ejpam-5901	582	21	effective	effective	ADJ
ejpam-5901	582	22	strategies	strategy	NOUN
ejpam-5901	582	23	.	.	PUNCT
ejpam-5901	583	1	aims	aim	VERB
ejpam-5901	583	2	mathematics	mathematic	NOUN
ejpam-5901	583	3	,	,	PUNCT
ejpam-5901	583	4	7(7):12011–12049	7(7):12011–12049	PROPN
ejpam-5901	583	5	,	,	PUNCT
ejpam-5901	583	6	2022	2022	NUM
ejpam-5901	583	7	.	.	PUNCT
ejpam-5901	584	1	[	[	X
ejpam-5901	584	2	26	26	NUM
ejpam-5901	584	3	]	]	X
ejpam-5901	584	4	n.	n.	NOUN
ejpam-5901	584	5	almutairi	almutairi	PROPN
ejpam-5901	584	6	,	,	PUNCT
ejpam-5901	584	7	s.	s.	PROPN
ejpam-5901	584	8	saber	saber	PROPN
ejpam-5901	584	9	,	,	PUNCT
ejpam-5901	584	10	and	and	CCONJ
ejpam-5901	584	11	a.	a.	NOUN
ejpam-5901	584	12	hijaz	hijaz	PROPN
ejpam-5901	584	13	.	.	PUNCT
ejpam-5901	585	1	the	the	DET
ejpam-5901	585	2	fractal	fractal	ADJ
ejpam-5901	585	3	-	-	PUNCT
ejpam-5901	585	4	fractional	fractional	ADJ
ejpam-5901	585	5	atangana	atangana	NOUN
ejpam-5901	585	6	-	-	PUNCT
ejpam-5901	585	7	baleanu	baleanu	NOUN
ejpam-5901	585	8	operator	operator	NOUN
ejpam-5901	585	9	for	for	ADP
ejpam-5901	585	10	pneumonia	pneumonia	NOUN
ejpam-5901	585	11	disease	disease	NOUN
ejpam-5901	585	12	:	:	PUNCT
ejpam-5901	585	13	stability	stability	NOUN
ejpam-5901	585	14	,	,	PUNCT
ejpam-5901	585	15	statistical	statistical	ADJ
ejpam-5901	585	16	and	and	CCONJ
ejpam-5901	585	17	numerical	numerical	ADJ
ejpam-5901	585	18	analyses	analysis	NOUN
ejpam-5901	585	19	.	.	PUNCT
ejpam-5901	586	1	aims	aim	VERB
ejpam-5901	586	2	mathematics	mathematic	NOUN
ejpam-5901	586	3	,	,	PUNCT
ejpam-5901	586	4	8(12):29382–29410	8(12):29382–29410	NUM
ejpam-5901	586	5	,	,	PUNCT
ejpam-5901	586	6	2023	2023	NUM
ejpam-5901	586	7	.	.	PUNCT
ejpam-5901	587	1	[	[	X
ejpam-5901	587	2	27	27	NUM
ejpam-5901	587	3	]	]	X
ejpam-5901	587	4	muhammad	muhammad	PROPN
ejpam-5901	587	5	naveed	naveed	PROPN
ejpam-5901	587	6	,	,	PUNCT
ejpam-5901	587	7	dumitru	dumitru	PROPN
ejpam-5901	587	8	baleanu	baleanu	PROPN
ejpam-5901	587	9	,	,	PUNCT
ejpam-5901	587	10	ali	ali	PROPN
ejpam-5901	587	11	raza	raza	PROPN
ejpam-5901	587	12	,	,	PUNCT
ejpam-5901	587	13	et	et	PROPN
ejpam-5901	587	14	al	al	PROPN
ejpam-5901	587	15	.	.	PUNCT
ejpam-5901	588	1	modeling	model	VERB
ejpam-5901	588	2	the	the	DET
ejpam-5901	588	3	transmission	transmission	NOUN
ejpam-5901	588	4	dynamics	dynamic	NOUN
ejpam-5901	588	5	of	of	ADP
ejpam-5901	588	6	delayed	delay	VERB
ejpam-5901	588	7	pneumonia	pneumonia	NOUN
ejpam-5901	588	8	-	-	PUNCT
ejpam-5901	588	9	like	like	ADJ
ejpam-5901	588	10	diseases	disease	NOUN
ejpam-5901	588	11	with	with	ADP
ejpam-5901	588	12	a	a	DET
ejpam-5901	588	13	sensitivity	sensitivity	NOUN
ejpam-5901	588	14	of	of	ADP
ejpam-5901	588	15	parameters	parameter	NOUN
ejpam-5901	588	16	.	.	PUNCT
ejpam-5901	589	1	advances	advance	NOUN
ejpam-5901	589	2	in	in	ADP
ejpam-5901	589	3	difference	difference	NOUN
ejpam-5901	589	4	equations	equation	NOUN
ejpam-5901	589	5	,	,	PUNCT
ejpam-5901	589	6	2021:468	2021:468	NOUN
ejpam-5901	589	7	,	,	PUNCT
ejpam-5901	589	8	2021	2021	NUM
ejpam-5901	589	9	.	.	PUNCT
ejpam-5901	590	1	[	[	X
ejpam-5901	590	2	28	28	NUM
ejpam-5901	590	3	]	]	X
ejpam-5901	590	4	h.	h.	PROPN
ejpam-5901	590	5	jafari	jafari	PROPN
ejpam-5901	590	6	,	,	PUNCT
ejpam-5901	590	7	h.	h.	PROPN
ejpam-5901	590	8	k.	k.	PROPN
ejpam-5901	590	9	jassim	jassim	PROPN
ejpam-5901	590	10	,	,	PUNCT
ejpam-5901	590	11	and	and	CCONJ
ejpam-5901	590	12	j.	j.	PROPN
ejpam-5901	590	13	vahidi	vahidi	PROPN
ejpam-5901	590	14	.	.	PUNCT
ejpam-5901	591	1	reduced	reduce	VERB
ejpam-5901	591	2	differential	differential	ADJ
ejpam-5901	591	3	transform	transform	NOUN
ejpam-5901	591	4	and	and	CCONJ
ejpam-5901	591	5	variational	variational	ADJ
ejpam-5901	591	6	iteration	iteration	NOUN
ejpam-5901	591	7	methods	method	NOUN
ejpam-5901	591	8	for	for	ADP
ejpam-5901	591	9	3d	3d	PROPN
ejpam-5901	591	10	diffusion	diffusion	NOUN
ejpam-5901	591	11	model	model	NOUN
ejpam-5901	591	12	in	in	ADP
ejpam-5901	591	13	fractal	fractal	ADJ
ejpam-5901	591	14	heat	heat	NOUN
ejpam-5901	591	15	transfer	transfer	NOUN
ejpam-5901	591	16	within	within	ADP
ejpam-5901	591	17	local	local	ADJ
ejpam-5901	591	18	fractional	fractional	ADJ
ejpam-5901	591	19	operators	operator	NOUN
ejpam-5901	591	20	.	.	PUNCT
ejpam-5901	592	1	thermal	thermal	ADJ
ejpam-5901	592	2	science	science	NOUN
ejpam-5901	592	3	,	,	PUNCT
ejpam-5901	592	4	22	22	NUM
ejpam-5901	592	5	:	:	PUNCT
ejpam-5901	592	6	s301	s301	PROPN
ejpam-5901	592	7	–	–	PUNCT
ejpam-5901	592	8	s307	s307	PROPN
ejpam-5901	592	9	,	,	PUNCT
ejpam-5901	592	10	2018	2018	NUM
ejpam-5901	592	11	.	.	PUNCT
ejpam-5901	593	1	[	[	X
ejpam-5901	593	2	29	29	NUM
ejpam-5901	593	3	]	]	X
ejpam-5901	593	4	d.	d.	PROPN
ejpam-5901	593	5	baleanu	baleanu	PROPN
ejpam-5901	593	6	and	and	CCONJ
ejpam-5901	593	7	h.	h.	PROPN
ejpam-5901	593	8	k.	k.	PROPN
ejpam-5901	593	9	jassim	jassim	PROPN
ejpam-5901	593	10	.	.	PUNCT
ejpam-5901	594	1	a	a	DET
ejpam-5901	594	2	modification	modification	NOUN
ejpam-5901	594	3	fractional	fractional	ADJ
ejpam-5901	594	4	homotopy	homotopy	NOUN
ejpam-5901	594	5	perturbation	perturbation	NOUN
ejpam-5901	594	6	method	method	NOUN
ejpam-5901	594	7	for	for	ADP
ejpam-5901	594	8	solving	solve	VERB
ejpam-5901	594	9	helmholtz	helmholtz	NOUN
ejpam-5901	594	10	and	and	CCONJ
ejpam-5901	594	11	coupled	couple	VERB
ejpam-5901	594	12	helmholtz	helmholtz	NOUN
ejpam-5901	594	13	equations	equation	NOUN
ejpam-5901	594	14	on	on	ADP
ejpam-5901	594	15	cantor	cantor	NOUN
ejpam-5901	594	16	sets	set	NOUN
ejpam-5901	594	17	.	.	PUNCT
ejpam-5901	595	1	fractal	fractal	PROPN
ejpam-5901	595	2	s.	s.	PROPN
ejpam-5901	595	3	saber	saber	PROPN
ejpam-5901	595	4	,	,	PUNCT
ejpam-5901	595	5	a.	a.	NOUN
ejpam-5901	595	6	a.	a.	NOUN
ejpam-5901	595	7	alahmari	alahmari	PROPN
ejpam-5901	595	8	/	/	SYM
ejpam-5901	595	9	eur	eur	PROPN
ejpam-5901	595	10	.	.	PUNCT
ejpam-5901	596	1	j.	j.	PROPN
ejpam-5901	596	2	pure	pure	PROPN
ejpam-5901	596	3	appl	appl	PROPN
ejpam-5901	596	4	.	.	PROPN
ejpam-5901	596	5	math	math	PROPN
ejpam-5901	596	6	,	,	PUNCT
ejpam-5901	596	7	18	18	NUM
ejpam-5901	596	8	(	(	PUNCT
ejpam-5901	596	9	2	2	NUM
ejpam-5901	596	10	)	)	PUNCT
ejpam-5901	596	11	(	(	PUNCT
ejpam-5901	596	12	2025	2025	NUM
ejpam-5901	596	13	)	)	PUNCT
ejpam-5901	596	14	,	,	PUNCT
ejpam-5901	596	15	5901	5901	NUM
ejpam-5901	596	16	22	22	NUM
ejpam-5901	596	17	of	of	ADP
ejpam-5901	596	18	23	23	NUM
ejpam-5901	596	19	and	and	CCONJ
ejpam-5901	596	20	fractional	fractional	ADJ
ejpam-5901	596	21	,	,	PUNCT
ejpam-5901	596	22	3(30):1–8	3(30):1–8	NOUN
ejpam-5901	596	23	,	,	PUNCT
ejpam-5901	596	24	2019	2019	NUM
ejpam-5901	596	25	.	.	PUNCT
ejpam-5901	597	1	[	[	X
ejpam-5901	597	2	30	30	NUM
ejpam-5901	597	3	]	]	X
ejpam-5901	597	4	y.	y.	NOUN
ejpam-5901	597	5	chatibi	chatibi	PROPN
ejpam-5901	597	6	,	,	PUNCT
ejpam-5901	597	7	e.h	e.h	PROPN
ejpam-5901	597	8	.	.	PROPN
ejpam-5901	597	9	el	el	PROPN
ejpam-5901	597	10	kinani	kinani	PROPN
ejpam-5901	597	11	,	,	PUNCT
ejpam-5901	597	12	and	and	CCONJ
ejpam-5901	597	13	a.	a.	NOUN
ejpam-5901	597	14	ouhadan	ouhadan	PROPN
ejpam-5901	597	15	.	.	PUNCT
ejpam-5901	598	1	variational	variational	ADJ
ejpam-5901	598	2	calculus	calculus	NOUN
ejpam-5901	598	3	involving	involve	VERB
ejpam-5901	598	4	nonlocal	nonlocal	ADJ
ejpam-5901	598	5	fractional	fractional	ADJ
ejpam-5901	598	6	derivative	derivative	NOUN
ejpam-5901	598	7	with	with	ADP
ejpam-5901	598	8	mittag	mittag	ADJ
ejpam-5901	598	9	–	–	PUNCT
ejpam-5901	598	10	leffler	leffler	ADJ
ejpam-5901	598	11	kernel	kernel	NOUN
ejpam-5901	598	12	.	.	PUNCT
ejpam-5901	599	1	chaos	chaos	NOUN
ejpam-5901	599	2	,	,	PUNCT
ejpam-5901	599	3	solitons	soliton	NOUN
ejpam-5901	599	4	&	&	CCONJ
ejpam-5901	599	5	fractals	fractal	NOUN
ejpam-5901	599	6	,	,	PUNCT
ejpam-5901	599	7	118:117	118:117	NUM
ejpam-5901	599	8	–	–	PUNCT
ejpam-5901	599	9	121	121	NUM
ejpam-5901	599	10	,	,	PUNCT
ejpam-5901	599	11	2019	2019	NUM
ejpam-5901	599	12	.	.	PUNCT
ejpam-5901	600	1	[	[	X
ejpam-5901	600	2	31	31	NUM
ejpam-5901	600	3	]	]	X
ejpam-5901	600	4	y.	y.	NOUN
ejpam-5901	600	5	chatibi	chatibi	PROPN
ejpam-5901	600	6	.	.	PUNCT
ejpam-5901	601	1	analytical	analytical	ADJ
ejpam-5901	601	2	solutions	solution	NOUN
ejpam-5901	601	3	of	of	ADP
ejpam-5901	601	4	virus	virus	NOUN
ejpam-5901	601	5	propagation	propagation	NOUN
ejpam-5901	601	6	model	model	NOUN
ejpam-5901	601	7	in	in	ADP
ejpam-5901	601	8	blockchain	blockchain	PROPN
ejpam-5901	601	9	networks	network	NOUN
ejpam-5901	601	10	.	.	PUNCT
ejpam-5901	602	1	quaestiones	quaestione	NOUN
ejpam-5901	602	2	mathematicae	mathematicae	PROPN
ejpam-5901	602	3	,	,	PUNCT
ejpam-5901	602	4	47(11):2153–2161	47(11):2153–2161	PROPN
ejpam-5901	602	5	,	,	PUNCT
ejpam-5901	602	6	2024	2024	NUM
ejpam-5901	602	7	.	.	PUNCT
ejpam-5901	603	1	[	[	X
ejpam-5901	603	2	32	32	NUM
ejpam-5901	603	3	]	]	PUNCT
ejpam-5901	603	4	p.	p.	NOUN
ejpam-5901	603	5	arena	arena	NOUN
ejpam-5901	603	6	,	,	PUNCT
ejpam-5901	603	7	r.	r.	PROPN
ejpam-5901	603	8	caponetto	caponetto	PROPN
ejpam-5901	603	9	,	,	PUNCT
ejpam-5901	603	10	l.	l.	PROPN
ejpam-5901	603	11	fortuna	fortuna	PROPN
ejpam-5901	603	12	,	,	PUNCT
ejpam-5901	603	13	and	and	CCONJ
ejpam-5901	603	14	d.	d.	PROPN
ejpam-5901	603	15	porto	porto	PROPN
ejpam-5901	603	16	.	.	PUNCT
ejpam-5901	604	1	nonlinear	nonlinear	ADJ
ejpam-5901	604	2	noninteger	noninteger	PROPN
ejpam-5901	604	3	order	order	NOUN
ejpam-5901	604	4	circuits	circuit	NOUN
ejpam-5901	604	5	and	and	CCONJ
ejpam-5901	604	6	systems	system	NOUN
ejpam-5901	604	7	.	.	PUNCT
ejpam-5901	605	1	world	world	PROPN
ejpam-5901	605	2	scientific	scientific	PROPN
ejpam-5901	605	3	,	,	PUNCT
ejpam-5901	605	4	singapore	singapore	PROPN
ejpam-5901	605	5	,	,	PUNCT
ejpam-5901	605	6	2000	2000	NUM
ejpam-5901	605	7	.	.	PUNCT
ejpam-5901	606	1	[	[	X
ejpam-5901	606	2	33	33	NUM
ejpam-5901	606	3	]	]	PUNCT
ejpam-5901	606	4	k.	k.	PROPN
ejpam-5901	606	5	s.	s.	PROPN
ejpam-5901	606	6	nisar	nisar	PROPN
ejpam-5901	606	7	,	,	PUNCT
ejpam-5901	606	8	m.	m.	NOUN
ejpam-5901	606	9	farman	farman	PROPN
ejpam-5901	606	10	,	,	PUNCT
ejpam-5901	606	11	m.	m.	PROPN
ejpam-5901	606	12	abdel	abdel	PROPN
ejpam-5901	606	13	-	-	PUNCT
ejpam-5901	606	14	aty	aty	PROPN
ejpam-5901	606	15	,	,	PUNCT
ejpam-5901	606	16	and	and	CCONJ
ejpam-5901	606	17	c.	c.	PROPN
ejpam-5901	606	18	ravichandran	ravichandran	NOUN
ejpam-5901	606	19	.	.	PUNCT
ejpam-5901	607	1	a	a	DET
ejpam-5901	607	2	review	review	NOUN
ejpam-5901	607	3	of	of	ADP
ejpam-5901	607	4	fractionalorder	fractionalorder	NOUN
ejpam-5901	607	5	models	model	NOUN
ejpam-5901	607	6	for	for	ADP
ejpam-5901	607	7	plant	plant	NOUN
ejpam-5901	607	8	epidemiology	epidemiology	NOUN
ejpam-5901	607	9	.	.	PUNCT
ejpam-5901	608	1	progr	progr	NOUN
ejpam-5901	608	2	.	.	PUNCT
ejpam-5901	609	1	fract	fract	PROPN
ejpam-5901	609	2	.	.	PUNCT
ejpam-5901	610	1	differ	differ	VERB
ejpam-5901	610	2	.	.	PUNCT
ejpam-5901	611	1	appl	appl	PROPN
ejpam-5901	611	2	.	.	PROPN
ejpam-5901	611	3	,	,	PUNCT
ejpam-5901	611	4	10:489–521	10:489–521	PROPN
ejpam-5901	611	5	,	,	PUNCT
ejpam-5901	611	6	2024	2024	NUM
ejpam-5901	611	7	.	.	PUNCT
ejpam-5901	612	1	[	[	X
ejpam-5901	612	2	34	34	NUM
ejpam-5901	612	3	]	]	X
ejpam-5901	612	4	e.	e.	PROPN
ejpam-5901	612	5	ahmed	ahmed	PROPN
ejpam-5901	612	6	and	and	CCONJ
ejpam-5901	612	7	a.	a.	PROPN
ejpam-5901	612	8	s.	s.	PROPN
ejpam-5901	612	9	elgazzar	elgazzar	PROPN
ejpam-5901	612	10	.	.	PUNCT
ejpam-5901	613	1	on	on	ADP
ejpam-5901	613	2	fractional	fractional	ADJ
ejpam-5901	613	3	order	order	NOUN
ejpam-5901	613	4	differential	differential	ADJ
ejpam-5901	613	5	equations	equation	NOUN
ejpam-5901	613	6	model	model	NOUN
ejpam-5901	613	7	for	for	ADP
ejpam-5901	613	8	nonlocal	nonlocal	ADJ
ejpam-5901	613	9	epidemics	epidemic	NOUN
ejpam-5901	613	10	.	.	PUNCT
ejpam-5901	614	1	physica	physica	PROPN
ejpam-5901	614	2	a	a	PRON
ejpam-5901	614	3	,	,	PUNCT
ejpam-5901	614	4	379:607–614	379:607–614	NUM
ejpam-5901	614	5	,	,	PUNCT
ejpam-5901	614	6	2007	2007	NUM
ejpam-5901	614	7	.	.	PUNCT
ejpam-5901	615	1	[	[	X
ejpam-5901	615	2	35	35	NUM
ejpam-5901	615	3	]	]	X
ejpam-5901	615	4	w.	w.	PROPN
ejpam-5901	615	5	li	li	PROPN
ejpam-5901	615	6	,	,	PUNCT
ejpam-5901	615	7	y.	y.	PROPN
ejpam-5901	615	8	wang	wang	PROPN
ejpam-5901	615	9	,	,	PUNCT
ejpam-5901	615	10	j.	j.	PROPN
ejpam-5901	615	11	cao	cao	PROPN
ejpam-5901	615	12	,	,	PUNCT
ejpam-5901	615	13	and	and	CCONJ
ejpam-5901	615	14	m.	m.	PROPN
ejpam-5901	615	15	abdel	abdel	PROPN
ejpam-5901	615	16	-	-	PUNCT
ejpam-5901	615	17	aty	aty	PROPN
ejpam-5901	615	18	.	.	PUNCT
ejpam-5901	615	19	dynamics	dynamic	NOUN
ejpam-5901	615	20	and	and	CCONJ
ejpam-5901	615	21	backward	backward	ADJ
ejpam-5901	615	22	bifurcations	bifurcation	NOUN
ejpam-5901	615	23	of	of	ADP
ejpam-5901	615	24	sei	sei	ADJ
ejpam-5901	615	25	tuberculosis	tuberculosis	NOUN
ejpam-5901	615	26	models	model	NOUN
ejpam-5901	615	27	in	in	ADP
ejpam-5901	615	28	homogeneous	homogeneous	ADJ
ejpam-5901	615	29	and	and	CCONJ
ejpam-5901	615	30	heterogeneous	heterogeneous	ADJ
ejpam-5901	615	31	populations	population	NOUN
ejpam-5901	615	32	.	.	PUNCT
ejpam-5901	616	1	j.	j.	PROPN
ejpam-5901	616	2	math	math	PROPN
ejpam-5901	616	3	.	.	PUNCT
ejpam-5901	617	1	anal	anal	PROPN
ejpam-5901	617	2	.	.	PUNCT
ejpam-5901	617	3	appl	appl	PROPN
ejpam-5901	617	4	.	.	PROPN
ejpam-5901	617	5	,	,	PUNCT
ejpam-5901	617	6	543:128924	543:128924	NUM
ejpam-5901	617	7	,	,	PUNCT
ejpam-5901	617	8	2025	2025	NUM
ejpam-5901	617	9	.	.	PUNCT
ejpam-5901	618	1	[	[	X
ejpam-5901	618	2	36	36	NUM
ejpam-5901	618	3	]	]	PUNCT
ejpam-5901	618	4	k.	k.	PROPN
ejpam-5901	618	5	s.	s.	PROPN
ejpam-5901	618	6	nisar	nisar	PROPN
ejpam-5901	618	7	,	,	PUNCT
ejpam-5901	618	8	m.	m.	NOUN
ejpam-5901	618	9	farman	farman	PROPN
ejpam-5901	618	10	,	,	PUNCT
ejpam-5901	618	11	m.	m.	PROPN
ejpam-5901	618	12	abdel	abdel	PROPN
ejpam-5901	618	13	-	-	PUNCT
ejpam-5901	618	14	aty	aty	PROPN
ejpam-5901	618	15	,	,	PUNCT
ejpam-5901	618	16	and	and	CCONJ
ejpam-5901	618	17	c.	c.	PROPN
ejpam-5901	618	18	ravichandran	ravichandran	NOUN
ejpam-5901	618	19	.	.	PUNCT
ejpam-5901	619	1	a	a	DET
ejpam-5901	619	2	review	review	NOUN
ejpam-5901	619	3	of	of	ADP
ejpam-5901	619	4	fractional	fractional	ADJ
ejpam-5901	619	5	order	order	NOUN
ejpam-5901	619	6	epidemic	epidemic	NOUN
ejpam-5901	619	7	models	model	NOUN
ejpam-5901	619	8	for	for	ADP
ejpam-5901	619	9	life	life	NOUN
ejpam-5901	619	10	sciences	science	NOUN
ejpam-5901	619	11	problems	problem	NOUN
ejpam-5901	619	12	:	:	PUNCT
ejpam-5901	619	13	past	past	ADJ
ejpam-5901	619	14	,	,	PUNCT
ejpam-5901	619	15	present	present	ADJ
ejpam-5901	619	16	and	and	CCONJ
ejpam-5901	619	17	future	future	NOUN
ejpam-5901	619	18	.	.	PUNCT
ejpam-5901	620	1	alexandria	alexandria	PROPN
ejpam-5901	620	2	eng	eng	PROPN
ejpam-5901	620	3	.	.	PUNCT
ejpam-5901	621	1	j.	j.	PROPN
ejpam-5901	621	2	,	,	PUNCT
ejpam-5901	621	3	95:283–305	95:283–305	PROPN
ejpam-5901	621	4	,	,	PUNCT
ejpam-5901	621	5	2024	2024	NUM
ejpam-5901	621	6	.	.	PUNCT
ejpam-5901	622	1	[	[	X
ejpam-5901	622	2	37	37	NUM
ejpam-5901	622	3	]	]	PUNCT
ejpam-5901	622	4	r.	r.	NOUN
ejpam-5901	622	5	hilfer	hilfer	PROPN
ejpam-5901	622	6	.	.	PUNCT
ejpam-5901	623	1	applications	application	NOUN
ejpam-5901	623	2	of	of	ADP
ejpam-5901	623	3	fractional	fractional	ADJ
ejpam-5901	623	4	calculus	calculus	NOUN
ejpam-5901	623	5	in	in	ADP
ejpam-5901	623	6	physics	physics	PROPN
ejpam-5901	623	7	.	.	PUNCT
ejpam-5901	624	1	world	world	PROPN
ejpam-5901	624	2	scientific	scientific	PROPN
ejpam-5901	624	3	,	,	PUNCT
ejpam-5901	624	4	singapore	singapore	PROPN
ejpam-5901	624	5	,	,	PUNCT
ejpam-5901	624	6	2000	2000	NUM
ejpam-5901	624	7	.	.	PUNCT
ejpam-5901	625	1	[	[	X
ejpam-5901	625	2	38	38	NUM
ejpam-5901	625	3	]	]	PUNCT
ejpam-5901	625	4	s.	s.	PROPN
ejpam-5901	625	5	saber	saber	PROPN
ejpam-5901	625	6	.	.	PUNCT
ejpam-5901	626	1	control	control	NOUN
ejpam-5901	626	2	of	of	ADP
ejpam-5901	626	3	chaos	chaos	NOUN
ejpam-5901	626	4	in	in	ADP
ejpam-5901	626	5	the	the	DET
ejpam-5901	626	6	burke	burke	PROPN
ejpam-5901	626	7	-	-	PUNCT
ejpam-5901	626	8	shaw	shaw	PROPN
ejpam-5901	626	9	system	system	NOUN
ejpam-5901	626	10	of	of	ADP
ejpam-5901	626	11	fractal	fractal	ADJ
ejpam-5901	626	12	-	-	PUNCT
ejpam-5901	626	13	fractional	fractional	ADJ
ejpam-5901	626	14	order	order	NOUN
ejpam-5901	626	15	in	in	ADP
ejpam-5901	626	16	the	the	DET
ejpam-5901	626	17	sense	sense	NOUN
ejpam-5901	626	18	of	of	ADP
ejpam-5901	626	19	caputo	caputo	PROPN
ejpam-5901	626	20	-	-	PUNCT
ejpam-5901	626	21	fabrizio	fabrizio	PROPN
ejpam-5901	626	22	.	.	PUNCT
ejpam-5901	627	1	j.	j.	PROPN
ejpam-5901	627	2	appl	appl	PROPN
ejpam-5901	627	3	.	.	PROPN
ejpam-5901	627	4	math	math	PROPN
ejpam-5901	627	5	.	.	PUNCT
ejpam-5901	628	1	comput	comput	NOUN
ejpam-5901	628	2	.	.	PUNCT
ejpam-5901	629	1	mech	mech	PROPN
ejpam-5901	629	2	.	.	PROPN
ejpam-5901	629	3	,	,	PUNCT
ejpam-5901	629	4	23:83–96	23:83–96	PROPN
ejpam-5901	629	5	,	,	PUNCT
ejpam-5901	629	6	2024	2024	NUM
ejpam-5901	629	7	.	.	PUNCT
ejpam-5901	630	1	[	[	X
ejpam-5901	630	2	39	39	NUM
ejpam-5901	630	3	]	]	PUNCT
ejpam-5901	630	4	t.	t.	PROPN
ejpam-5901	630	5	yan	yan	PROPN
ejpam-5901	630	6	et	et	PROPN
ejpam-5901	630	7	al	al	PROPN
ejpam-5901	630	8	.	.	PUNCT
ejpam-5901	631	1	analysis	analysis	NOUN
ejpam-5901	631	2	of	of	ADP
ejpam-5901	631	3	a	a	DET
ejpam-5901	631	4	lorenz	lorenz	PROPN
ejpam-5901	631	5	model	model	NOUN
ejpam-5901	631	6	using	use	VERB
ejpam-5901	631	7	adomian	adomian	NOUN
ejpam-5901	631	8	decomposition	decomposition	NOUN
ejpam-5901	631	9	and	and	CCONJ
ejpam-5901	631	10	fractalfractional	fractalfractional	ADJ
ejpam-5901	631	11	operators	operator	NOUN
ejpam-5901	631	12	.	.	PUNCT
ejpam-5901	632	1	thermal	thermal	ADJ
ejpam-5901	632	2	sci	sci	PROPN
ejpam-5901	632	3	.	.	PROPN
ejpam-5901	632	4	,	,	PUNCT
ejpam-5901	632	5	8(6b):5001–5009	8(6b):5001–5009	NUM
ejpam-5901	632	6	,	,	PUNCT
ejpam-5901	632	7	2024	2024	NUM
ejpam-5901	632	8	.	.	PUNCT
ejpam-5901	633	1	[	[	X
ejpam-5901	633	2	40	40	NUM
ejpam-5901	633	3	]	]	PUNCT
ejpam-5901	633	4	a.	a.	NOUN
ejpam-5901	633	5	alsulami	alsulami	PROPN
ejpam-5901	633	6	et	et	PROPN
ejpam-5901	633	7	al	al	PROPN
ejpam-5901	633	8	.	.	PROPN
ejpam-5901	633	9	controlled	control	VERB
ejpam-5901	633	10	chaos	chaos	NOUN
ejpam-5901	633	11	of	of	ADP
ejpam-5901	633	12	a	a	DET
ejpam-5901	633	13	fractal	fractal	ADJ
ejpam-5901	633	14	–	–	PUNCT
ejpam-5901	633	15	fractional	fractional	ADJ
ejpam-5901	633	16	newton	newton	NOUN
ejpam-5901	633	17	-	-	PUNCT
ejpam-5901	633	18	leipnik	leipnik	NOUN
ejpam-5901	633	19	system	system	NOUN
ejpam-5901	633	20	.	.	PUNCT
ejpam-5901	634	1	thermal	thermal	ADJ
ejpam-5901	634	2	sci	sci	PROPN
ejpam-5901	634	3	.	.	PROPN
ejpam-5901	634	4	,	,	PUNCT
ejpam-5901	634	5	28(6b):5153–5160	28(6b):5153–5160	NUM
ejpam-5901	634	6	,	,	PUNCT
ejpam-5901	634	7	2024	2024	NUM
ejpam-5901	634	8	.	.	PUNCT
ejpam-5901	635	1	[	[	X
ejpam-5901	635	2	41	41	NUM
ejpam-5901	635	3	]	]	PUNCT
ejpam-5901	635	4	m.	m.	NOUN
ejpam-5901	635	5	alhazmi	alhazmi	PROPN
ejpam-5901	635	6	et	et	PROPN
ejpam-5901	635	7	al	al	PROPN
ejpam-5901	635	8	.	.	PROPN
ejpam-5901	635	9	numerical	numerical	PROPN
ejpam-5901	635	10	approximation	approximation	NOUN
ejpam-5901	635	11	method	method	NOUN
ejpam-5901	635	12	and	and	CCONJ
ejpam-5901	635	13	chaos	chaos	NOUN
ejpam-5901	635	14	for	for	ADP
ejpam-5901	635	15	a	a	DET
ejpam-5901	635	16	chaotic	chaotic	ADJ
ejpam-5901	635	17	system	system	NOUN
ejpam-5901	635	18	in	in	ADP
ejpam-5901	635	19	sense	sense	NOUN
ejpam-5901	635	20	of	of	ADP
ejpam-5901	635	21	caputo	caputo	PROPN
ejpam-5901	635	22	-	-	PUNCT
ejpam-5901	635	23	fabrizio	fabrizio	PROPN
ejpam-5901	635	24	operator	operator	NOUN
ejpam-5901	635	25	.	.	PUNCT
ejpam-5901	636	1	thermal	thermal	ADJ
ejpam-5901	636	2	sci	sci	PROPN
ejpam-5901	636	3	.	.	PROPN
ejpam-5901	636	4	,	,	PUNCT
ejpam-5901	636	5	28(6b):5161–5168	28(6b):5161–5168	NUM
ejpam-5901	636	6	,	,	PUNCT
ejpam-5901	636	7	2024	2024	NUM
ejpam-5901	636	8	.	.	PUNCT
ejpam-5901	637	1	[	[	X
ejpam-5901	637	2	42	42	NUM
ejpam-5901	637	3	]	]	X
ejpam-5901	637	4	n.	n.	NOUN
ejpam-5901	637	5	almutairi	almutairi	PROPN
ejpam-5901	637	6	and	and	CCONJ
ejpam-5901	637	7	s.	s.	PROPN
ejpam-5901	637	8	saber	saber	PROPN
ejpam-5901	637	9	.	.	PUNCT
ejpam-5901	638	1	existence	existence	NOUN
ejpam-5901	638	2	of	of	ADP
ejpam-5901	638	3	chaos	chaos	NOUN
ejpam-5901	638	4	and	and	CCONJ
ejpam-5901	638	5	the	the	DET
ejpam-5901	638	6	approximate	approximate	ADJ
ejpam-5901	638	7	solution	solution	NOUN
ejpam-5901	638	8	of	of	ADP
ejpam-5901	638	9	the	the	DET
ejpam-5901	638	10	lorenz	lorenz	PROPN
ejpam-5901	638	11	–	–	PUNCT
ejpam-5901	638	12	lü–chen	lü–chen	NOUN
ejpam-5901	638	13	system	system	NOUN
ejpam-5901	638	14	with	with	ADP
ejpam-5901	638	15	the	the	DET
ejpam-5901	638	16	caputo	caputo	PROPN
ejpam-5901	638	17	fractional	fractional	PROPN
ejpam-5901	638	18	operator	operator	NOUN
ejpam-5901	638	19	.	.	PUNCT
ejpam-5901	639	1	aip	aip	PROPN
ejpam-5901	639	2	adv	adv	PROPN
ejpam-5901	639	3	.	.	PROPN
ejpam-5901	639	4	,	,	PUNCT
ejpam-5901	639	5	14:015112	14:015112	NUM
ejpam-5901	639	6	,	,	PUNCT
ejpam-5901	639	7	2024	2024	NUM
ejpam-5901	639	8	.	.	PUNCT
ejpam-5901	640	1	[	[	X
ejpam-5901	640	2	43	43	NUM
ejpam-5901	640	3	]	]	X
ejpam-5901	640	4	n.	n.	NOUN
ejpam-5901	640	5	almutairi	almutairi	PROPN
ejpam-5901	640	6	and	and	CCONJ
ejpam-5901	640	7	s.	s.	PROPN
ejpam-5901	640	8	saber	saber	PROPN
ejpam-5901	640	9	.	.	PUNCT
ejpam-5901	641	1	on	on	ADP
ejpam-5901	641	2	chaos	chaos	NOUN
ejpam-5901	641	3	control	control	NOUN
ejpam-5901	641	4	of	of	ADP
ejpam-5901	641	5	nonlinear	nonlinear	PROPN
ejpam-5901	641	6	fractional	fractional	PROPN
ejpam-5901	641	7	newton	newton	PROPN
ejpam-5901	641	8	-	-	PUNCT
ejpam-5901	641	9	leipnik	leipnik	NOUN
ejpam-5901	641	10	system	system	NOUN
ejpam-5901	641	11	via	via	ADP
ejpam-5901	641	12	fractional	fractional	PROPN
ejpam-5901	641	13	caputo	caputo	PROPN
ejpam-5901	641	14	-	-	PUNCT
ejpam-5901	641	15	fabrizio	fabrizio	PROPN
ejpam-5901	641	16	derivatives	derivative	NOUN
ejpam-5901	641	17	.	.	PUNCT
ejpam-5901	642	1	sci	sci	PROPN
ejpam-5901	642	2	.	.	PROPN
ejpam-5901	642	3	rep	rep	PROPN
ejpam-5901	642	4	.	.	PROPN
ejpam-5901	642	5	,	,	PUNCT
ejpam-5901	642	6	13:22726	13:22726	NUM
ejpam-5901	642	7	,	,	PUNCT
ejpam-5901	642	8	2023	2023	NUM
ejpam-5901	642	9	.	.	PUNCT
ejpam-5901	643	1	[	[	X
ejpam-5901	643	2	44	44	NUM
ejpam-5901	643	3	]	]	X
ejpam-5901	643	4	n.	n.	NOUN
ejpam-5901	643	5	almutairi	almutairi	PROPN
ejpam-5901	643	6	and	and	CCONJ
ejpam-5901	643	7	s.	s.	PROPN
ejpam-5901	643	8	saber	saber	PROPN
ejpam-5901	643	9	.	.	PUNCT
ejpam-5901	644	1	chaos	chaos	NOUN
ejpam-5901	644	2	control	control	NOUN
ejpam-5901	644	3	and	and	CCONJ
ejpam-5901	644	4	numerical	numerical	ADJ
ejpam-5901	644	5	solution	solution	NOUN
ejpam-5901	644	6	of	of	ADP
ejpam-5901	644	7	time	time	NOUN
ejpam-5901	644	8	-	-	PUNCT
ejpam-5901	644	9	varying	vary	VERB
ejpam-5901	644	10	fractional	fractional	ADJ
ejpam-5901	644	11	newton	newton	PROPN
ejpam-5901	644	12	-	-	PUNCT
ejpam-5901	644	13	leipnik	leipnik	NOUN
ejpam-5901	644	14	system	system	NOUN
ejpam-5901	644	15	using	use	VERB
ejpam-5901	644	16	fractional	fractional	ADJ
ejpam-5901	644	17	atangana	atangana	PROPN
ejpam-5901	644	18	-	-	PUNCT
ejpam-5901	644	19	baleanu	baleanu	ADJ
ejpam-5901	644	20	derivatives	derivative	NOUN
ejpam-5901	644	21	.	.	PUNCT
ejpam-5901	645	1	aims	aim	VERB
ejpam-5901	645	2	mathematics	mathematic	NOUN
ejpam-5901	645	3	,	,	PUNCT
ejpam-5901	645	4	8(11):25863–25887	8(11):25863–25887	NUM
ejpam-5901	645	5	,	,	PUNCT
ejpam-5901	645	6	2023	2023	NUM
ejpam-5901	645	7	.	.	PUNCT
ejpam-5901	646	1	[	[	X
ejpam-5901	646	2	45	45	NUM
ejpam-5901	646	3	]	]	X
ejpam-5901	646	4	n.	n.	NOUN
ejpam-5901	646	5	almutairi	almutairi	PROPN
ejpam-5901	646	6	and	and	CCONJ
ejpam-5901	646	7	s.	s.	PROPN
ejpam-5901	646	8	saber	saber	PROPN
ejpam-5901	646	9	.	.	PUNCT
ejpam-5901	647	1	application	application	NOUN
ejpam-5901	647	2	of	of	ADP
ejpam-5901	647	3	a	a	DET
ejpam-5901	647	4	time	time	NOUN
ejpam-5901	647	5	-	-	PUNCT
ejpam-5901	647	6	fractal	fractal	ADJ
ejpam-5901	647	7	fractional	fractional	ADJ
ejpam-5901	647	8	derivative	derivative	NOUN
ejpam-5901	647	9	with	with	ADP
ejpam-5901	647	10	a	a	DET
ejpam-5901	647	11	power	power	NOUN
ejpam-5901	647	12	-	-	PUNCT
ejpam-5901	647	13	law	law	NOUN
ejpam-5901	647	14	kernel	kernel	NOUN
ejpam-5901	647	15	to	to	ADP
ejpam-5901	647	16	the	the	DET
ejpam-5901	647	17	burke	burke	PROPN
ejpam-5901	647	18	-	-	PUNCT
ejpam-5901	647	19	shaw	shaw	PROPN
ejpam-5901	647	20	system	system	NOUN
ejpam-5901	647	21	based	base	VERB
ejpam-5901	647	22	on	on	ADP
ejpam-5901	647	23	newton	newton	PROPN
ejpam-5901	647	24	’s	’s	PART
ejpam-5901	647	25	interpolation	interpolation	NOUN
ejpam-5901	647	26	polynomials	polynomial	NOUN
ejpam-5901	647	27	.	.	PUNCT
ejpam-5901	648	1	methodsx	methodsx	PROPN
ejpam-5901	648	2	,	,	PUNCT
ejpam-5901	648	3	12:102510	12:102510	NUM
ejpam-5901	648	4	,	,	PUNCT
ejpam-5901	648	5	december	december	PROPN
ejpam-5901	648	6	2023	2023	NUM
ejpam-5901	648	7	.	.	PUNCT
ejpam-5901	649	1	[	[	X
ejpam-5901	649	2	46	46	NUM
ejpam-5901	649	3	]	]	X
ejpam-5901	649	4	khalid	khalid	PROPN
ejpam-5901	649	5	i.a	i.a	PROPN
ejpam-5901	649	6	.	.	PROPN
ejpam-5901	649	7	ahmed	ahmed	PROPN
ejpam-5901	649	8	,	,	PUNCT
ejpam-5901	649	9	haroon	haroon	PROPN
ejpam-5901	649	10	d.s	d.s	PROPN
ejpam-5901	649	11	.	.	PROPN
ejpam-5901	649	12	adam	adam	PROPN
ejpam-5901	649	13	,	,	PUNCT
ejpam-5901	649	14	najat	najat	PROPN
ejpam-5901	649	15	almutairi	almutairi	NOUN
ejpam-5901	649	16	,	,	PUNCT
ejpam-5901	649	17	and	and	CCONJ
ejpam-5901	649	18	sayed	say	VERB
ejpam-5901	649	19	saber	saber	PROPN
ejpam-5901	649	20	.	.	PUNCT
ejpam-5901	650	1	analytical	analytical	ADJ
ejpam-5901	650	2	solutions	solution	NOUN
ejpam-5901	650	3	for	for	ADP
ejpam-5901	650	4	a	a	DET
ejpam-5901	650	5	class	class	NOUN
ejpam-5901	650	6	of	of	ADP
ejpam-5901	650	7	variable	variable	ADJ
ejpam-5901	650	8	-	-	PUNCT
ejpam-5901	650	9	order	order	NOUN
ejpam-5901	650	10	fractional	fractional	ADJ
ejpam-5901	650	11	liu	liu	PROPN
ejpam-5901	650	12	system	system	NOUN
ejpam-5901	650	13	under	under	ADP
ejpam-5901	650	14	time	time	NOUN
ejpam-5901	650	15	-	-	PUNCT
ejpam-5901	650	16	dependent	dependent	ADJ
ejpam-5901	650	17	variable	variable	ADJ
ejpam-5901	650	18	coefficients	coefficient	NOUN
ejpam-5901	650	19	.	.	PUNCT
ejpam-5901	651	1	results	result	VERB
ejpam-5901	651	2	phys	phy	NOUN
ejpam-5901	651	3	.	.	PUNCT
ejpam-5901	651	4	,	,	PUNCT
ejpam-5901	651	5	56:107311	56:107311	NUM
ejpam-5901	651	6	,	,	PUNCT
ejpam-5901	651	7	2024	2024	NUM
ejpam-5901	651	8	.	.	PUNCT
ejpam-5901	652	1	[	[	X
ejpam-5901	652	2	47	47	NUM
ejpam-5901	652	3	]	]	X
ejpam-5901	652	4	r.	r.	PROPN
ejpam-5901	652	5	l.	l.	PROPN
ejpam-5901	652	6	bagley	bagley	PROPN
ejpam-5901	652	7	and	and	CCONJ
ejpam-5901	652	8	r.	r.	PROPN
ejpam-5901	652	9	a.	a.	PROPN
ejpam-5901	652	10	calico	calico	PROPN
ejpam-5901	652	11	.	.	PUNCT
ejpam-5901	653	1	fractional	fractional	ADJ
ejpam-5901	653	2	order	order	NOUN
ejpam-5901	653	3	state	state	NOUN
ejpam-5901	653	4	equations	equation	NOUN
ejpam-5901	653	5	for	for	ADP
ejpam-5901	653	6	the	the	DET
ejpam-5901	653	7	control	control	NOUN
ejpam-5901	653	8	of	of	ADP
ejpam-5901	653	9	s.	s.	PROPN
ejpam-5901	653	10	saber	saber	PROPN
ejpam-5901	653	11	,	,	PUNCT
ejpam-5901	653	12	a.	a.	NOUN
ejpam-5901	653	13	a.	a.	NOUN
ejpam-5901	653	14	alahmari	alahmari	PROPN
ejpam-5901	653	15	/	/	SYM
ejpam-5901	653	16	eur	eur	PROPN
ejpam-5901	653	17	.	.	PUNCT
ejpam-5901	654	1	j.	j.	PROPN
ejpam-5901	654	2	pure	pure	PROPN
ejpam-5901	654	3	appl	appl	PROPN
ejpam-5901	654	4	.	.	PROPN
ejpam-5901	654	5	math	math	PROPN
ejpam-5901	654	6	,	,	PUNCT
ejpam-5901	654	7	18	18	NUM
ejpam-5901	654	8	(	(	PUNCT
ejpam-5901	654	9	2	2	NUM
ejpam-5901	654	10	)	)	PUNCT
ejpam-5901	654	11	(	(	PUNCT
ejpam-5901	654	12	2025	2025	NUM
ejpam-5901	654	13	)	)	PUNCT
ejpam-5901	654	14	,	,	PUNCT
ejpam-5901	654	15	5901	5901	NUM
ejpam-5901	654	16	23	23	NUM
ejpam-5901	654	17	of	of	ADP
ejpam-5901	654	18	23	23	NUM
ejpam-5901	654	19	viscoelastically	viscoelastically	ADV
ejpam-5901	654	20	damped	damp	VERB
ejpam-5901	654	21	structures	structure	NOUN
ejpam-5901	654	22	.	.	PUNCT
ejpam-5901	655	1	j.	j.	PROPN
ejpam-5901	655	2	guid	guid	PROPN
ejpam-5901	655	3	.	.	PUNCT
ejpam-5901	656	1	control	control	PROPN
ejpam-5901	656	2	dyn	dyn	PROPN
ejpam-5901	656	3	.	.	PUNCT
ejpam-5901	656	4	,	,	PUNCT
ejpam-5901	656	5	14:304–311	14:304–311	NUM
ejpam-5901	656	6	,	,	PUNCT
ejpam-5901	656	7	1991	1991	NUM
ejpam-5901	656	8	.	.	PUNCT
ejpam-5901	657	1	[	[	X
ejpam-5901	657	2	48	48	NUM
ejpam-5901	657	3	]	]	X
ejpam-5901	657	4	o.	o.	PROPN
ejpam-5901	657	5	heaviside	heaviside	PROPN
ejpam-5901	657	6	.	.	PUNCT
ejpam-5901	658	1	electromagnetic	electromagnetic	ADJ
ejpam-5901	658	2	theory	theory	NOUN
ejpam-5901	658	3	.	.	PUNCT
ejpam-5901	659	1	chelsea	chelsea	PROPN
ejpam-5901	659	2	,	,	PUNCT
ejpam-5901	659	3	new	new	PROPN
ejpam-5901	659	4	york	york	PROPN
ejpam-5901	659	5	,	,	PUNCT
ejpam-5901	659	6	1971	1971	NUM
ejpam-5901	659	7	.	.	PUNCT
ejpam-5901	660	1	[	[	X
ejpam-5901	660	2	49	49	NUM
ejpam-5901	660	3	]	]	PUNCT
ejpam-5901	660	4	d.	d.	PROPN
ejpam-5901	660	5	kusnezov	kusnezov	PROPN
ejpam-5901	660	6	,	,	PUNCT
ejpam-5901	660	7	a.	a.	PROPN
ejpam-5901	660	8	bulgac	bulgac	PROPN
ejpam-5901	660	9	,	,	PUNCT
ejpam-5901	660	10	and	and	CCONJ
ejpam-5901	660	11	g.	g.	PROPN
ejpam-5901	660	12	d.	d.	PROPN
ejpam-5901	660	13	dang	dang	PROPN
ejpam-5901	660	14	.	.	PUNCT
ejpam-5901	661	1	quantum	quantum	ADJ
ejpam-5901	661	2	levy	levy	NOUN
ejpam-5901	661	3	processes	process	NOUN
ejpam-5901	661	4	and	and	CCONJ
ejpam-5901	661	5	fractional	fractional	ADJ
ejpam-5901	661	6	kinetics	kinetic	NOUN
ejpam-5901	661	7	.	.	PUNCT
ejpam-5901	662	1	phys	phy	NOUN
ejpam-5901	662	2	.	.	PUNCT
ejpam-5901	663	1	rev	rev	PROPN
ejpam-5901	663	2	.	.	PROPN
ejpam-5901	663	3	lett	lett	PROPN
ejpam-5901	663	4	.	.	PROPN
ejpam-5901	663	5	,	,	PUNCT
ejpam-5901	663	6	82:1136	82:1136	NUM
ejpam-5901	663	7	,	,	PUNCT
ejpam-5901	663	8	1999	1999	NUM
ejpam-5901	663	9	.	.	PUNCT
ejpam-5901	664	1	[	[	X
ejpam-5901	664	2	50	50	NUM
ejpam-5901	664	3	]	]	PUNCT
ejpam-5901	664	4	h.	h.	PROPN
ejpam-5901	664	5	a.	a.	PROPN
ejpam-5901	664	6	hammad	hammad	PROPN
ejpam-5901	664	7	,	,	PUNCT
ejpam-5901	664	8	m.	m.	NOUN
ejpam-5901	664	9	qasymeh	qasymeh	NOUN
ejpam-5901	664	10	,	,	PUNCT
ejpam-5901	664	11	and	and	CCONJ
ejpam-5901	664	12	m.	m.	PROPN
ejpam-5901	664	13	abdel	abdel	PROPN
ejpam-5901	664	14	-	-	PUNCT
ejpam-5901	664	15	aty	aty	PROPN
ejpam-5901	664	16	.	.	PROPN
ejpam-5901	664	17	existence	existence	NOUN
ejpam-5901	664	18	and	and	CCONJ
ejpam-5901	664	19	stability	stability	NOUN
ejpam-5901	664	20	results	result	VERB
ejpam-5901	664	21	for	for	ADP
ejpam-5901	664	22	a	a	DET
ejpam-5901	664	23	langevin	langevin	ADJ
ejpam-5901	664	24	system	system	NOUN
ejpam-5901	664	25	with	with	ADP
ejpam-5901	664	26	caputo	caputo	PROPN
ejpam-5901	664	27	–	–	PUNCT
ejpam-5901	664	28	hadamard	hadamard	ADJ
ejpam-5901	664	29	fractional	fractional	ADJ
ejpam-5901	664	30	operators	operator	NOUN
ejpam-5901	664	31	.	.	PUNCT
ejpam-5901	665	1	int	int	NOUN
ejpam-5901	665	2	.	.	PUNCT
ejpam-5901	666	1	j.	j.	PROPN
ejpam-5901	666	2	geom	geom	PROPN
ejpam-5901	666	3	.	.	PUNCT
ejpam-5901	667	1	methods	methods	PROPN
ejpam-5901	667	2	mod	mod	PROPN
ejpam-5901	667	3	.	.	PUNCT
ejpam-5901	668	1	phys	phy	NOUN
ejpam-5901	668	2	.	.	PUNCT
ejpam-5901	668	3	,	,	PUNCT
ejpam-5901	668	4	21:2450218	21:2450218	NOUN
ejpam-5901	668	5	,	,	PUNCT
ejpam-5901	668	6	2024	2024	NUM
ejpam-5901	668	7	.	.	PUNCT
ejpam-5901	669	1	[	[	X
ejpam-5901	669	2	51	51	NUM
ejpam-5901	669	3	]	]	PUNCT
ejpam-5901	669	4	k.	k.	PROPN
ejpam-5901	669	5	tornheim	tornheim	PROPN
ejpam-5901	669	6	.	.	PUNCT
ejpam-5901	670	1	are	be	AUX
ejpam-5901	670	2	metabolic	metabolic	NOUN
ejpam-5901	670	3	oscillations	oscillation	NOUN
ejpam-5901	670	4	responsible	responsible	ADJ
ejpam-5901	670	5	for	for	ADP
ejpam-5901	670	6	normal	normal	ADJ
ejpam-5901	670	7	oscillatory	oscillatory	ADJ
ejpam-5901	670	8	insulin	insulin	NOUN
ejpam-5901	670	9	secretion	secretion	NOUN
ejpam-5901	670	10	?	?	PUNCT
ejpam-5901	671	1	diabetes	diabete	NOUN
ejpam-5901	671	2	,	,	PUNCT
ejpam-5901	671	3	46(9):1375–1380	46(9):1375–1380	NOUN
ejpam-5901	671	4	,	,	PUNCT
ejpam-5901	671	5	1997	1997	NUM
ejpam-5901	671	6	.	.	PUNCT
ejpam-5901	672	1	[	[	X
ejpam-5901	672	2	52	52	NUM
ejpam-5901	672	3	]	]	PUNCT
ejpam-5901	672	4	s.	s.	PROPN
ejpam-5901	672	5	saber	saber	PROPN
ejpam-5901	672	6	et	et	PROPN
ejpam-5901	672	7	al	al	PROPN
ejpam-5901	672	8	.	.	PUNCT
ejpam-5901	673	1	a	a	DET
ejpam-5901	673	2	mathematical	mathematical	ADJ
ejpam-5901	673	3	model	model	NOUN
ejpam-5901	673	4	of	of	ADP
ejpam-5901	673	5	glucose	glucose	NOUN
ejpam-5901	673	6	-	-	PUNCT
ejpam-5901	673	7	insulin	insulin	NOUN
ejpam-5901	673	8	interaction	interaction	NOUN
ejpam-5901	673	9	with	with	ADP
ejpam-5901	673	10	time	time	NOUN
ejpam-5901	673	11	delay	delay	NOUN
ejpam-5901	673	12	.	.	PUNCT
ejpam-5901	674	1	j	j	PROPN
ejpam-5901	674	2	appl	appl	PROPN
ejpam-5901	674	3	computat	computat	PROPN
ejpam-5901	674	4	math	math	PROPN
ejpam-5901	674	5	,	,	PUNCT
ejpam-5901	674	6	7(3	7(3	NUM
ejpam-5901	674	7	)	)	PUNCT
ejpam-5901	674	8	,	,	PUNCT
ejpam-5901	674	9	2018	2018	NUM
ejpam-5901	674	10	.	.	PUNCT
ejpam-5901	675	1	[	[	X
ejpam-5901	675	2	53	53	NUM
ejpam-5901	675	3	]	]	PUNCT
ejpam-5901	675	4	m.	m.	NOUN
ejpam-5901	675	5	h.	h.	PROPN
ejpam-5901	675	6	alshehri	alshehri	PROPN
ejpam-5901	675	7	et	et	PROPN
ejpam-5901	675	8	al	al	PROPN
ejpam-5901	675	9	.	.	PUNCT
ejpam-5901	676	1	a	a	DET
ejpam-5901	676	2	caputo	caputo	PROPN
ejpam-5901	676	3	(	(	PUNCT
ejpam-5901	676	4	discretization	discretization	NOUN
ejpam-5901	676	5	)	)	PUNCT
ejpam-5901	676	6	fractional	fractional	ADJ
ejpam-5901	676	7	-	-	PUNCT
ejpam-5901	676	8	order	order	NOUN
ejpam-5901	676	9	model	model	NOUN
ejpam-5901	676	10	of	of	ADP
ejpam-5901	676	11	glucoseinsulin	glucoseinsulin	PROPN
ejpam-5901	676	12	interaction	interaction	NOUN
ejpam-5901	676	13	:	:	PUNCT
ejpam-5901	676	14	numerical	numerical	ADJ
ejpam-5901	676	15	solution	solution	NOUN
ejpam-5901	676	16	and	and	CCONJ
ejpam-5901	676	17	comparisons	comparison	NOUN
ejpam-5901	676	18	with	with	ADP
ejpam-5901	676	19	experimental	experimental	ADJ
ejpam-5901	676	20	data	datum	NOUN
ejpam-5901	676	21	.	.	PUNCT
ejpam-5901	677	1	j.	j.	PROPN
ejpam-5901	677	2	taibah	taibah	PROPN
ejpam-5901	677	3	univ	univ	PROPN
ejpam-5901	677	4	.	.	PUNCT
ejpam-5901	678	1	sci	sci	PROPN
ejpam-5901	678	2	.	.	PROPN
ejpam-5901	678	3	,	,	PUNCT
ejpam-5901	678	4	15:26–36	15:26–36	NUM
ejpam-5901	678	5	,	,	PUNCT
ejpam-5901	678	6	2021	2021	NUM
ejpam-5901	678	7	.	.	PUNCT
ejpam-5901	679	1	[	[	X
ejpam-5901	679	2	54	54	NUM
ejpam-5901	679	3	]	]	PUNCT
ejpam-5901	679	4	s.	s.	PROPN
ejpam-5901	679	5	saber	saber	PROPN
ejpam-5901	679	6	and	and	CCONJ
ejpam-5901	679	7	a.	a.	NOUN
ejpam-5901	679	8	alalyani	alalyani	PROPN
ejpam-5901	679	9	.	.	PUNCT
ejpam-5901	680	1	stability	stability	NOUN
ejpam-5901	680	2	analysis	analysis	NOUN
ejpam-5901	680	3	and	and	CCONJ
ejpam-5901	680	4	numerical	numerical	ADJ
ejpam-5901	680	5	simulations	simulation	NOUN
ejpam-5901	680	6	of	of	ADP
ejpam-5901	680	7	ivgtt	ivgtt	PROPN
ejpam-5901	680	8	glucoseinsulin	glucoseinsulin	PROPN
ejpam-5901	680	9	interaction	interaction	NOUN
ejpam-5901	680	10	models	model	NOUN
ejpam-5901	680	11	with	with	ADP
ejpam-5901	680	12	two	two	NUM
ejpam-5901	680	13	time	time	NOUN
ejpam-5901	680	14	delays	delay	NOUN
ejpam-5901	680	15	.	.	PUNCT
ejpam-5901	681	1	math	math	NOUN
ejpam-5901	681	2	.	.	PUNCT
ejpam-5901	682	1	model	model	PROPN
ejpam-5901	682	2	.	.	PUNCT
ejpam-5901	683	1	anal	anal	PROPN
ejpam-5901	683	2	.	.	PUNCT
ejpam-5901	683	3	,	,	PUNCT
ejpam-5901	683	4	27:383–407	27:383–407	PROPN
ejpam-5901	683	5	,	,	PUNCT
ejpam-5901	683	6	2022	2022	NUM
ejpam-5901	683	7	.	.	PUNCT
ejpam-5901	684	1	[	[	X
ejpam-5901	684	2	55	55	NUM
ejpam-5901	684	3	]	]	PUNCT
ejpam-5901	684	4	m.	m.	NOUN
ejpam-5901	684	5	h.	h.	PROPN
ejpam-5901	684	6	alshehri	alshehri	PROPN
ejpam-5901	684	7	,	,	PUNCT
ejpam-5901	684	8	s.	s.	PROPN
ejpam-5901	684	9	saber	saber	PROPN
ejpam-5901	684	10	,	,	PUNCT
ejpam-5901	684	11	and	and	CCONJ
ejpam-5901	684	12	f.	f.	PROPN
ejpam-5901	684	13	z.	z.	PROPN
ejpam-5901	684	14	duraihem	duraihem	PROPN
ejpam-5901	684	15	.	.	PUNCT
ejpam-5901	685	1	dynamical	dynamical	ADJ
ejpam-5901	685	2	analysis	analysis	NOUN
ejpam-5901	685	3	of	of	ADP
ejpam-5901	685	4	fractional	fractional	ADJ
ejpam-5901	685	5	-	-	PUNCT
ejpam-5901	685	6	order	order	NOUN
ejpam-5901	685	7	of	of	ADP
ejpam-5901	685	8	ivgtt	ivgtt	ADJ
ejpam-5901	685	9	glucose	glucose	NOUN
ejpam-5901	685	10	–	–	PUNCT
ejpam-5901	685	11	insulin	insulin	NOUN
ejpam-5901	685	12	interaction	interaction	NOUN
ejpam-5901	685	13	.	.	PUNCT
ejpam-5901	686	1	int	int	NOUN
ejpam-5901	686	2	.	.	PUNCT
ejpam-5901	687	1	j.	j.	PROPN
ejpam-5901	687	2	nonlin	nonlin	PROPN
ejpam-5901	687	3	.	.	PUNCT
ejpam-5901	688	1	sci	sci	PROPN
ejpam-5901	688	2	.	.	PUNCT
ejpam-5901	689	1	num	num	PROPN
ejpam-5901	689	2	.	.	PROPN
ejpam-5901	689	3	,	,	PUNCT
ejpam-5901	689	4	24:1123–1140	24:1123–1140	NUM
ejpam-5901	689	5	,	,	PUNCT
ejpam-5901	689	6	2023	2023	NUM
ejpam-5901	689	7	.	.	PUNCT
ejpam-5901	690	1	[	[	X
ejpam-5901	690	2	56	56	NUM
ejpam-5901	690	3	]	]	PUNCT
ejpam-5901	690	4	k.	k.	PROPN
ejpam-5901	690	5	i.	i.	PROPN
ejpam-5901	690	6	a.	a.	PROPN
ejpam-5901	690	7	ahmed	ahmed	PROPN
ejpam-5901	690	8	et	et	PROPN
ejpam-5901	690	9	al	al	PROPN
ejpam-5901	690	10	.	.	PUNCT
ejpam-5901	691	1	a	a	DET
ejpam-5901	691	2	comprehensive	comprehensive	ADJ
ejpam-5901	691	3	investigation	investigation	NOUN
ejpam-5901	691	4	of	of	ADP
ejpam-5901	691	5	fractional	fractional	ADJ
ejpam-5901	691	6	glucose	glucose	NOUN
ejpam-5901	691	7	-	-	PUNCT
ejpam-5901	691	8	insulin	insulin	NOUN
ejpam-5901	691	9	dynamics	dynamic	NOUN
ejpam-5901	691	10	:	:	PUNCT
ejpam-5901	691	11	existence	existence	NOUN
ejpam-5901	691	12	,	,	PUNCT
ejpam-5901	691	13	stability	stability	NOUN
ejpam-5901	691	14	,	,	PUNCT
ejpam-5901	691	15	and	and	CCONJ
ejpam-5901	691	16	numerical	numerical	ADJ
ejpam-5901	691	17	comparisons	comparison	NOUN
ejpam-5901	691	18	using	use	VERB
ejpam-5901	691	19	residual	residual	ADJ
ejpam-5901	691	20	power	power	NOUN
ejpam-5901	691	21	series	series	NOUN
ejpam-5901	691	22	and	and	CCONJ
ejpam-5901	691	23	generalized	generalized	ADJ
ejpam-5901	691	24	runge	runge	NOUN
ejpam-5901	691	25	-	-	PUNCT
ejpam-5901	691	26	kutta	kutta	NOUN
ejpam-5901	691	27	methods	method	NOUN
ejpam-5901	691	28	.	.	PUNCT
ejpam-5901	692	1	journal	journal	PROPN
ejpam-5901	692	2	of	of	ADP
ejpam-5901	692	3	taibah	taibah	PROPN
ejpam-5901	692	4	university	university	PROPN
ejpam-5901	692	5	for	for	ADP
ejpam-5901	692	6	science	science	NOUN
ejpam-5901	692	7	,	,	PUNCT
ejpam-5901	692	8	19(1	19(1	NUM
ejpam-5901	692	9	)	)	PUNCT
ejpam-5901	692	10	,	,	PUNCT
ejpam-5901	692	11	2025	2025	NUM
ejpam-5901	692	12	.	.	PUNCT
ejpam-5901	693	1	[	[	X
ejpam-5901	693	2	57	57	NUM
ejpam-5901	693	3	]	]	PUNCT
ejpam-5901	693	4	a.	a.	NOUN
ejpam-5901	693	5	atangana	atangana	PROPN
ejpam-5901	693	6	.	.	PUNCT
ejpam-5901	694	1	fractal	fractal	ADJ
ejpam-5901	694	2	-	-	PUNCT
ejpam-5901	694	3	fractional	fractional	ADJ
ejpam-5901	694	4	differentiation	differentiation	NOUN
ejpam-5901	694	5	and	and	CCONJ
ejpam-5901	694	6	integration	integration	NOUN
ejpam-5901	694	7	:	:	PUNCT
ejpam-5901	694	8	connecting	connect	VERB
ejpam-5901	694	9	fractal	fractal	ADJ
ejpam-5901	694	10	calculus	calculus	NOUN
ejpam-5901	694	11	and	and	CCONJ
ejpam-5901	694	12	fractional	fractional	ADJ
ejpam-5901	694	13	calculus	calculus	NOUN
ejpam-5901	694	14	to	to	PART
ejpam-5901	694	15	predict	predict	VERB
ejpam-5901	694	16	complex	complex	ADJ
ejpam-5901	694	17	systems	system	NOUN
ejpam-5901	694	18	.	.	PUNCT
ejpam-5901	695	1	chaos	chaos	NOUN
ejpam-5901	695	2	solitons	soliton	NOUN
ejpam-5901	695	3	fractals	fractal	NOUN
ejpam-5901	695	4	,	,	PUNCT
ejpam-5901	695	5	102:396–406	102:396–406	NUM
ejpam-5901	695	6	,	,	PUNCT
ejpam-5901	695	7	2017	2017	NUM
ejpam-5901	695	8	.	.	PUNCT
ejpam-5901	696	1	[	[	X
ejpam-5901	696	2	58	58	NUM
ejpam-5901	696	3	]	]	PUNCT
ejpam-5901	696	4	k.	k.	PROPN
ejpam-5901	696	5	i.	i.	PROPN
ejpam-5901	696	6	a.	a.	PROPN
ejpam-5901	696	7	ahmed	ahmed	PROPN
ejpam-5901	696	8	,	,	PUNCT
ejpam-5901	696	9	h.	h.	PROPN
ejpam-5901	696	10	d.	d.	PROPN
ejpam-5901	696	11	s.	s.	PROPN
ejpam-5901	696	12	adam	adam	PROPN
ejpam-5901	696	13	,	,	PUNCT
ejpam-5901	696	14	and	and	CCONJ
ejpam-5901	696	15	s.	s.	PROPN
ejpam-5901	696	16	saber	saber	PROPN
ejpam-5901	696	17	.	.	PUNCT
ejpam-5901	697	1	different	different	ADJ
ejpam-5901	697	2	strategies	strategy	NOUN
ejpam-5901	697	3	for	for	ADP
ejpam-5901	697	4	diabetes	diabetes	NOUN
ejpam-5901	697	5	by	by	ADP
ejpam-5901	697	6	mathematical	mathematical	ADJ
ejpam-5901	697	7	modeling	modeling	NOUN
ejpam-5901	697	8	:	:	PUNCT
ejpam-5901	697	9	applications	application	NOUN
ejpam-5901	697	10	of	of	ADP
ejpam-5901	697	11	fractal	fractal	ADJ
ejpam-5901	697	12	-	-	PUNCT
ejpam-5901	697	13	fractional	fractional	ADJ
ejpam-5901	697	14	derivatives	derivative	NOUN
ejpam-5901	697	15	in	in	ADP
ejpam-5901	697	16	the	the	DET
ejpam-5901	697	17	sense	sense	NOUN
ejpam-5901	697	18	of	of	ADP
ejpam-5901	697	19	atangana	atangana	PROPN
ejpam-5901	697	20	-	-	PUNCT
ejpam-5901	697	21	baleanu	baleanu	PROPN
ejpam-5901	697	22	.	.	PUNCT
ejpam-5901	698	1	results	result	NOUN
ejpam-5901	698	2	in	in	ADP
ejpam-5901	698	3	physics	physics	NOUN
ejpam-5901	698	4	,	,	PUNCT
ejpam-5901	698	5	26:106892	26:106892	NUM
ejpam-5901	698	6	,	,	PUNCT
ejpam-5901	698	7	2023	2023	NUM
ejpam-5901	698	8	.	.	PUNCT
ejpam-5901	699	1	[	[	X
ejpam-5901	699	2	59	59	NUM
ejpam-5901	699	3	]	]	PUNCT
ejpam-5901	699	4	k.	k.	PROPN
ejpam-5901	699	5	i.	i.	PROPN
ejpam-5901	699	6	a.	a.	PROPN
ejpam-5901	699	7	ahmed	ahmed	PROPN
ejpam-5901	699	8	et	et	PROPN
ejpam-5901	699	9	al	al	PROPN
ejpam-5901	699	10	.	.	PUNCT
ejpam-5901	700	1	different	different	ADJ
ejpam-5901	700	2	strategies	strategy	NOUN
ejpam-5901	700	3	for	for	ADP
ejpam-5901	700	4	diabetes	diabetes	NOUN
ejpam-5901	700	5	by	by	ADP
ejpam-5901	700	6	mathematical	mathematical	ADJ
ejpam-5901	700	7	modeling	modeling	NOUN
ejpam-5901	700	8	:	:	PUNCT
ejpam-5901	700	9	modified	modify	VERB
ejpam-5901	700	10	minimal	minimal	ADJ
ejpam-5901	700	11	model	model	NOUN
ejpam-5901	700	12	.	.	PUNCT
ejpam-5901	701	1	alexandria	alexandria	PROPN
ejpam-5901	701	2	engineering	engineering	PROPN
ejpam-5901	701	3	journal	journal	PROPN
ejpam-5901	701	4	,	,	PUNCT
ejpam-5901	701	5	80:74–87	80:74–87	NUM
ejpam-5901	701	6	,	,	PUNCT
ejpam-5901	701	7	2023	2023	NUM
ejpam-5901	701	8	.	.	PUNCT
ejpam-5901	702	1	[	[	X
ejpam-5901	702	2	60	60	NUM
ejpam-5901	702	3	]	]	X
ejpam-5901	702	4	h.	h.	PROPN
ejpam-5901	702	5	khan	khan	PROPN
ejpam-5901	702	6	,	,	PUNCT
ejpam-5901	702	7	j.	j.	PROPN
ejpam-5901	702	8	alzabut	alzabut	PROPN
ejpam-5901	702	9	,	,	PUNCT
ejpam-5901	702	10	a.	a.	NOUN
ejpam-5901	702	11	shah	shah	PROPN
ejpam-5901	702	12	,	,	PUNCT
ejpam-5901	702	13	et	et	PROPN
ejpam-5901	702	14	al	al	PROPN
ejpam-5901	702	15	.	.	PUNCT
ejpam-5901	703	1	a	a	DET
ejpam-5901	703	2	study	study	NOUN
ejpam-5901	703	3	on	on	ADP
ejpam-5901	703	4	the	the	DET
ejpam-5901	703	5	fractal	fractal	ADJ
ejpam-5901	703	6	-	-	PUNCT
ejpam-5901	703	7	fractional	fractional	ADJ
ejpam-5901	703	8	tobacco	tobacco	NOUN
ejpam-5901	703	9	smoking	smoking	NOUN
ejpam-5901	703	10	model	model	NOUN
ejpam-5901	703	11	.	.	PUNCT
ejpam-5901	704	1	aims	aim	VERB
ejpam-5901	704	2	math	math	NOUN
ejpam-5901	704	3	.	.	PUNCT
ejpam-5901	704	4	,	,	PUNCT
ejpam-5901	704	5	7:13887–13909	7:13887–13909	NUM
ejpam-5901	704	6	,	,	PUNCT
ejpam-5901	704	7	2022	2022	NUM
ejpam-5901	704	8	.	.	PUNCT
ejpam-5901	705	1	[	[	X
ejpam-5901	705	2	61	61	NUM
ejpam-5901	705	3	]	]	X
ejpam-5901	705	4	h.	h.	PROPN
ejpam-5901	705	5	khan	khan	PROPN
ejpam-5901	705	6	,	,	PUNCT
ejpam-5901	705	7	a.h	a.h	PROPN
ejpam-5901	705	8	.	.	PROPN
ejpam-5901	705	9	rajpar	rajpar	PROPN
ejpam-5901	705	10	,	,	PUNCT
ejpam-5901	705	11	j.	j.	PROPN
ejpam-5901	705	12	alzabut	alzabut	PROPN
ejpam-5901	705	13	,	,	PUNCT
ejpam-5901	705	14	et	et	PROPN
ejpam-5901	705	15	al	al	PROPN
ejpam-5901	705	16	.	.	PROPN
ejpam-5901	706	1	on	on	ADP
ejpam-5901	706	2	a	a	DET
ejpam-5901	706	3	fractal	fractal	ADJ
ejpam-5901	706	4	–	–	PUNCT
ejpam-5901	706	5	fractional	fractional	ADJ
ejpam-5901	706	6	-	-	PUNCT
ejpam-5901	706	7	based	base	VERB
ejpam-5901	706	8	modeling	modeling	NOUN
ejpam-5901	706	9	for	for	ADP
ejpam-5901	706	10	influenza	influenza	NOUN
ejpam-5901	706	11	and	and	CCONJ
ejpam-5901	706	12	its	its	PRON
ejpam-5901	706	13	analytical	analytical	ADJ
ejpam-5901	706	14	results	result	NOUN
ejpam-5901	706	15	.	.	PUNCT
ejpam-5901	707	1	qual	qual	X
ejpam-5901	707	2	.	.	PROPN
ejpam-5901	707	3	theory	theory	NOUN
ejpam-5901	707	4	dyn	dyn	PROPN
ejpam-5901	707	5	.	.	PUNCT
ejpam-5901	708	1	syst	syst	PROPN
ejpam-5901	708	2	.	.	PROPN
ejpam-5901	708	3	,	,	PUNCT
ejpam-5901	708	4	23:70	23:70	NUM
ejpam-5901	708	5	,	,	PUNCT
ejpam-5901	708	6	2024	2024	NUM
ejpam-5901	708	7	.	.	PUNCT
ejpam-5901	709	1	[	[	X
ejpam-5901	709	2	62	62	NUM
ejpam-5901	709	3	]	]	PUNCT
ejpam-5901	709	4	kamaledin	kamaledin	ADJ
ejpam-5901	709	5	abodayeh	abodayeh	PROPN
ejpam-5901	709	6	,	,	PUNCT
ejpam-5901	709	7	ali	ali	PROPN
ejpam-5901	709	8	raza	raza	PROPN
ejpam-5901	709	9	,	,	PUNCT
ejpam-5901	709	10	muhammad	muhammad	PROPN
ejpam-5901	709	11	rafiq	rafiq	PROPN
ejpam-5901	709	12	,	,	PUNCT
ejpam-5901	709	13	et	et	PROPN
ejpam-5901	709	14	al	al	PROPN
ejpam-5901	709	15	.	.	PUNCT
ejpam-5901	710	1	analysis	analysis	NOUN
ejpam-5901	710	2	of	of	ADP
ejpam-5901	710	3	pneumonia	pneumonia	NOUN
ejpam-5901	710	4	model	model	NOUN
ejpam-5901	710	5	via	via	ADP
ejpam-5901	710	6	efficient	efficient	ADJ
ejpam-5901	710	7	computing	computing	NOUN
ejpam-5901	710	8	techniques	technique	NOUN
ejpam-5901	710	9	.	.	PUNCT
ejpam-5901	711	1	computers	computer	NOUN
ejpam-5901	711	2	,	,	PUNCT
ejpam-5901	711	3	materials	material	NOUN
ejpam-5901	711	4	&	&	CCONJ
ejpam-5901	711	5	continua	continua	PROPN
ejpam-5901	711	6	,	,	PUNCT
ejpam-5901	711	7	70(3):6073–6088	70(3):6073–6088	NUM
ejpam-5901	711	8	,	,	PUNCT
ejpam-5901	711	9	2022	2022	NUM
ejpam-5901	711	10	.	.	PUNCT
ejpam-5901	712	1	[	[	X
ejpam-5901	712	2	63	63	NUM
ejpam-5901	712	3	]	]	SYM
ejpam-5901	712	4	s.m	s.m	PROPN
ejpam-5901	712	5	.	.	PUNCT
ejpam-5901	712	6	ulam	ulam	PROPN
ejpam-5901	712	7	.	.	PUNCT
ejpam-5901	713	1	a	a	DET
ejpam-5901	713	2	collection	collection	NOUN
ejpam-5901	713	3	of	of	ADP
ejpam-5901	713	4	mathematical	mathematical	ADJ
ejpam-5901	713	5	problems	problem	NOUN
ejpam-5901	713	6	.	.	PUNCT
ejpam-5901	714	1	interscience	interscience	NOUN
ejpam-5901	714	2	publ	publ	PROPN
ejpam-5901	714	3	.	.	PUNCT
ejpam-5901	715	1	,	,	PUNCT
ejpam-5901	715	2	new	new	PROPN
ejpam-5901	715	3	york	york	PROPN
ejpam-5901	715	4	,	,	PUNCT
ejpam-5901	715	5	1960	1960	NUM
ejpam-5901	715	6	.	.	PUNCT
ejpam-5901	716	1	[	[	X
ejpam-5901	716	2	64	64	NUM
ejpam-5901	716	3	]	]	X
ejpam-5901	716	4	stanislaw	stanislaw	PROPN
ejpam-5901	716	5	m	m	PROPN
ejpam-5901	716	6	ulam	ulam	PROPN
ejpam-5901	716	7	.	.	PUNCT
ejpam-5901	716	8	problems	problem	NOUN
ejpam-5901	716	9	in	in	ADP
ejpam-5901	716	10	modern	modern	ADJ
ejpam-5901	716	11	mathematics	mathematic	NOUN
ejpam-5901	716	12	.	.	PUNCT
ejpam-5901	717	1	courier	courier	NOUN
ejpam-5901	717	2	corporation	corporation	NOUN
ejpam-5901	717	3	,	,	PUNCT
ejpam-5901	717	4	2004	2004	NUM
ejpam-5901	717	5	.	.	PUNCT