id	sid	tid	token	lemma	pos
ejpam-5442	1	1	european	european	PROPN
ejpam-5442	1	2	journal	journal	PROPN
ejpam-5442	1	3	of	of	ADP
ejpam-5442	1	4	pure	pure	ADJ
ejpam-5442	1	5	and	and	CCONJ
ejpam-5442	1	6	applied	apply	VERB
ejpam-5442	1	7	mathematics	mathematic	NOUN
ejpam-5442	1	8	vol	vol	NOUN
ejpam-5442	1	9	.	.	PROPN
ejpam-5442	2	1	17	17	NUM
ejpam-5442	2	2	,	,	PUNCT
ejpam-5442	2	3	no	no	INTJ
ejpam-5442	2	4	.	.	NOUN
ejpam-5442	2	5	4	4	NUM
ejpam-5442	2	6	,	,	PUNCT
ejpam-5442	2	7	2024	2024	NUM
ejpam-5442	2	8	,	,	PUNCT
ejpam-5442	2	9	3277	3277	NUM
ejpam-5442	2	10	-	-	SYM
ejpam-5442	2	11	3290	3290	NUM
ejpam-5442	2	12	issn	issn	PROPN
ejpam-5442	2	13	1307	1307	NUM
ejpam-5442	2	14	-	-	SYM
ejpam-5442	2	15	5543	5543	NUM
ejpam-5442	2	16	–	–	PUNCT
ejpam-5442	2	17	ejpam.com	ejpam.com	X
ejpam-5442	2	18	published	publish	VERB
ejpam-5442	2	19	by	by	ADP
ejpam-5442	2	20	new	new	PROPN
ejpam-5442	2	21	york	york	PROPN
ejpam-5442	2	22	business	business	PROPN
ejpam-5442	2	23	global	global	PROPN
ejpam-5442	2	24	numerical	numerical	ADJ
ejpam-5442	2	25	treatment	treatment	NOUN
ejpam-5442	2	26	for	for	ADP
ejpam-5442	2	27	the	the	DET
ejpam-5442	2	28	caputo	caputo	PROPN
ejpam-5442	2	29	-	-	PUNCT
ejpam-5442	2	30	fabrizio	fabrizio	PROPN
ejpam-5442	2	31	fractional	fractional	ADJ
ejpam-5442	2	32	smoking	smoking	NOUN
ejpam-5442	2	33	model	model	NOUN
ejpam-5442	2	34	using	use	VERB
ejpam-5442	2	35	an	an	DET
ejpam-5442	2	36	efficient	efficient	ADJ
ejpam-5442	2	37	numerical	numerical	ADJ
ejpam-5442	2	38	technique	technique	NOUN
ejpam-5442	2	39	mohamed	mohamed	PROPN
ejpam-5442	2	40	adel1,∗	adel1,∗	PROPN
ejpam-5442	2	41	,	,	PUNCT
ejpam-5442	2	42	mohamed	mohamed	PROPN
ejpam-5442	2	43	m.	m.	PROPN
ejpam-5442	2	44	khader2,3	khader2,3	PROPN
ejpam-5442	2	45	,	,	PUNCT
ejpam-5442	2	46	najla	najla	ADJ
ejpam-5442	2	47	a.	a.	PROPN
ejpam-5442	2	48	mohammed4	mohammed4	PROPN
ejpam-5442	2	49	1	1	NUM
ejpam-5442	2	50	department	department	NOUN
ejpam-5442	2	51	of	of	ADP
ejpam-5442	2	52	mathematics	mathematic	NOUN
ejpam-5442	2	53	,	,	PUNCT
ejpam-5442	2	54	faculty	faculty	NOUN
ejpam-5442	2	55	of	of	ADP
ejpam-5442	2	56	science	science	NOUN
ejpam-5442	2	57	,	,	PUNCT
ejpam-5442	2	58	islamic	islamic	PROPN
ejpam-5442	2	59	university	university	PROPN
ejpam-5442	2	60	of	of	ADP
ejpam-5442	2	61	madinah	madinah	PROPN
ejpam-5442	2	62	,	,	PUNCT
ejpam-5442	2	63	medina	medina	PROPN
ejpam-5442	2	64	,	,	PUNCT
ejpam-5442	2	65	saudi	saudi	PROPN
ejpam-5442	2	66	arabia	arabia	PROPN
ejpam-5442	2	67	2	2	NUM
ejpam-5442	2	68	department	department	NOUN
ejpam-5442	2	69	of	of	ADP
ejpam-5442	2	70	mathematics	mathematic	NOUN
ejpam-5442	2	71	and	and	CCONJ
ejpam-5442	2	72	statistics	statistic	NOUN
ejpam-5442	2	73	,	,	PUNCT
ejpam-5442	2	74	college	college	NOUN
ejpam-5442	2	75	of	of	ADP
ejpam-5442	2	76	science	science	NOUN
ejpam-5442	2	77	,	,	PUNCT
ejpam-5442	2	78	imam	imam	PROPN
ejpam-5442	2	79	mohammad	mohammad	PROPN
ejpam-5442	2	80	ibn	ibn	PROPN
ejpam-5442	2	81	saud	saud	PROPN
ejpam-5442	2	82	islamic	islamic	PROPN
ejpam-5442	2	83	university	university	PROPN
ejpam-5442	2	84	(	(	PUNCT
ejpam-5442	2	85	imsiu	imsiu	PROPN
ejpam-5442	2	86	)	)	PUNCT
ejpam-5442	2	87	,	,	PUNCT
ejpam-5442	2	88	riyadh	riyadh	PROPN
ejpam-5442	2	89	,	,	PUNCT
ejpam-5442	2	90	saudi	saudi	PROPN
ejpam-5442	2	91	arabia	arabia	PROPN
ejpam-5442	2	92	3	3	NUM
ejpam-5442	2	93	department	department	NOUN
ejpam-5442	2	94	of	of	ADP
ejpam-5442	2	95	mathematics	mathematic	NOUN
ejpam-5442	2	96	,	,	PUNCT
ejpam-5442	2	97	faculty	faculty	NOUN
ejpam-5442	2	98	of	of	ADP
ejpam-5442	2	99	science	science	NOUN
ejpam-5442	2	100	,	,	PUNCT
ejpam-5442	2	101	benha	benha	VERB
ejpam-5442	2	102	university	university	NOUN
ejpam-5442	2	103	,	,	PUNCT
ejpam-5442	2	104	benha	benha	NOUN
ejpam-5442	2	105	,	,	PUNCT
ejpam-5442	2	106	egypt	egypt	PROPN
ejpam-5442	2	107	4	4	NUM
ejpam-5442	2	108	mathemtaics	mathemtaics	PROPN
ejpam-5442	2	109	department	department	NOUN
ejpam-5442	2	110	,	,	PUNCT
ejpam-5442	2	111	faculty	faculty	NOUN
ejpam-5442	2	112	of	of	ADP
ejpam-5442	2	113	sciences	science	NOUN
ejpam-5442	2	114	,	,	PUNCT
ejpam-5442	2	115	umm	umm	INTJ
ejpam-5442	2	116	al	al	PROPN
ejpam-5442	2	117	-	-	PUNCT
ejpam-5442	2	118	qura	qura	PROPN
ejpam-5442	2	119	university	university	PROPN
ejpam-5442	2	120	,	,	PUNCT
ejpam-5442	2	121	makkah	makkah	PROPN
ejpam-5442	2	122	,	,	PUNCT
ejpam-5442	2	123	saudi	saudi	PROPN
ejpam-5442	2	124	arabia	arabia	PROPN
ejpam-5442	2	125	abstract	abstract	NOUN
ejpam-5442	2	126	.	.	PUNCT
ejpam-5442	3	1	smoking	smoking	NOUN
ejpam-5442	3	2	is	be	AUX
ejpam-5442	3	3	a	a	DET
ejpam-5442	3	4	prevalent	prevalent	ADJ
ejpam-5442	3	5	social	social	ADJ
ejpam-5442	3	6	behavior	behavior	NOUN
ejpam-5442	3	7	widely	widely	ADV
ejpam-5442	3	8	practiced	practice	VERB
ejpam-5442	3	9	worldwide	worldwide	ADV
ejpam-5442	3	10	,	,	PUNCT
ejpam-5442	3	11	especially	especially	ADV
ejpam-5442	3	12	in	in	ADP
ejpam-5442	3	13	settings	setting	NOUN
ejpam-5442	3	14	such	such	ADJ
ejpam-5442	3	15	as	as	ADP
ejpam-5442	3	16	schools	school	NOUN
ejpam-5442	3	17	and	and	CCONJ
ejpam-5442	3	18	some	some	DET
ejpam-5442	3	19	significant	significant	ADJ
ejpam-5442	3	20	gatherings	gathering	NOUN
ejpam-5442	3	21	.	.	PUNCT
ejpam-5442	4	1	based	base	VERB
ejpam-5442	4	2	on	on	ADP
ejpam-5442	4	3	the	the	DET
ejpam-5442	4	4	world	world	PROPN
ejpam-5442	4	5	health	health	NOUN
ejpam-5442	4	6	organization	organization	NOUN
ejpam-5442	4	7	(	(	PUNCT
ejpam-5442	4	8	who	who	PRON
ejpam-5442	4	9	)	)	PUNCT
ejpam-5442	4	10	,	,	PUNCT
ejpam-5442	4	11	smoking	smoking	NOUN
ejpam-5442	4	12	is	be	AUX
ejpam-5442	4	13	the	the	DET
ejpam-5442	4	14	third	third	ADJ
ejpam-5442	4	15	leading	lead	VERB
ejpam-5442	4	16	source	source	NOUN
ejpam-5442	4	17	of	of	ADP
ejpam-5442	4	18	human	human	ADJ
ejpam-5442	4	19	mortality	mortality	NOUN
ejpam-5442	4	20	and	and	CCONJ
ejpam-5442	4	21	the	the	DET
ejpam-5442	4	22	primary	primary	ADJ
ejpam-5442	4	23	preventable	preventable	ADJ
ejpam-5442	4	24	cause	cause	NOUN
ejpam-5442	4	25	of	of	ADP
ejpam-5442	4	26	disease	disease	NOUN
ejpam-5442	4	27	.	.	PUNCT
ejpam-5442	5	1	this	this	DET
ejpam-5442	5	2	study	study	NOUN
ejpam-5442	5	3	introduces	introduce	VERB
ejpam-5442	5	4	a	a	DET
ejpam-5442	5	5	highly	highly	ADV
ejpam-5442	5	6	efficient	efficient	ADJ
ejpam-5442	5	7	simulation	simulation	NOUN
ejpam-5442	5	8	technique	technique	NOUN
ejpam-5442	5	9	to	to	PART
ejpam-5442	5	10	analyze	analyze	VERB
ejpam-5442	5	11	and	and	CCONJ
ejpam-5442	5	12	solve	solve	VERB
ejpam-5442	5	13	the	the	DET
ejpam-5442	5	14	caputo	caputo	PROPN
ejpam-5442	5	15	-	-	PUNCT
ejpam-5442	5	16	fabrizio	fabrizio	PROPN
ejpam-5442	5	17	(	(	PUNCT
ejpam-5442	5	18	cf	cf	NOUN
ejpam-5442	5	19	)	)	PUNCT
ejpam-5442	5	20	fractional	fractional	ADJ
ejpam-5442	5	21	smoking	smoking	NOUN
ejpam-5442	5	22	model	model	NOUN
ejpam-5442	5	23	.	.	PUNCT
ejpam-5442	6	1	we	we	PRON
ejpam-5442	6	2	numerically	numerically	ADV
ejpam-5442	6	3	solve	solve	VERB
ejpam-5442	6	4	the	the	DET
ejpam-5442	6	5	fractional	fractional	ADJ
ejpam-5442	6	6	integral	integral	ADJ
ejpam-5442	6	7	equations	equation	NOUN
ejpam-5442	6	8	(	(	PUNCT
ejpam-5442	6	9	fies	fie	NOUN
ejpam-5442	6	10	)	)	PUNCT
ejpam-5442	6	11	with	with	ADP
ejpam-5442	6	12	simpson	simpson	PROPN
ejpam-5442	6	13	’s	’s	PART
ejpam-5442	6	14	1/3	1/3	NUM
ejpam-5442	6	15	rule	rule	NOUN
ejpam-5442	6	16	,	,	PUNCT
ejpam-5442	6	17	an	an	DET
ejpam-5442	6	18	effective	effective	ADJ
ejpam-5442	6	19	numerical	numerical	ADJ
ejpam-5442	6	20	integration	integration	NOUN
ejpam-5442	6	21	technique	technique	NOUN
ejpam-5442	6	22	.	.	PUNCT
ejpam-5442	7	1	we	we	PRON
ejpam-5442	7	2	concentrate	concentrate	VERB
ejpam-5442	7	3	on	on	ADP
ejpam-5442	7	4	clarifying	clarify	VERB
ejpam-5442	7	5	the	the	DET
ejpam-5442	7	6	stability	stability	NOUN
ejpam-5442	7	7	/	/	SYM
ejpam-5442	7	8	convergence	convergence	NOUN
ejpam-5442	7	9	of	of	ADP
ejpam-5442	7	10	the	the	DET
ejpam-5442	7	11	proposed	propose	VERB
ejpam-5442	7	12	strategy	strategy	NOUN
ejpam-5442	7	13	.	.	PUNCT
ejpam-5442	8	1	we	we	PRON
ejpam-5442	8	2	juxtapose	juxtapose	VERB
ejpam-5442	8	3	the	the	DET
ejpam-5442	8	4	outcomes	outcome	NOUN
ejpam-5442	8	5	derived	derive	VERB
ejpam-5442	8	6	using	use	VERB
ejpam-5442	8	7	the	the	DET
ejpam-5442	8	8	runge	runge	NOUN
ejpam-5442	8	9	-	-	PUNCT
ejpam-5442	8	10	kutta	kutta	NOUN
ejpam-5442	8	11	method	method	NOUN
ejpam-5442	8	12	(	(	PUNCT
ejpam-5442	8	13	rk4	rk4	NOUN
ejpam-5442	8	14	)	)	PUNCT
ejpam-5442	8	15	with	with	ADP
ejpam-5442	8	16	those	those	PRON
ejpam-5442	8	17	obtained	obtain	VERB
ejpam-5442	8	18	through	through	ADP
ejpam-5442	8	19	the	the	DET
ejpam-5442	8	20	implemented	implement	VERB
ejpam-5442	8	21	methodology	methodology	NOUN
ejpam-5442	8	22	.	.	PUNCT
ejpam-5442	9	1	the	the	DET
ejpam-5442	9	2	findings	finding	NOUN
ejpam-5442	9	3	indicate	indicate	VERB
ejpam-5442	9	4	that	that	SCONJ
ejpam-5442	9	5	the	the	DET
ejpam-5442	9	6	used	use	VERB
ejpam-5442	9	7	technique	technique	NOUN
ejpam-5442	9	8	provides	provide	VERB
ejpam-5442	9	9	a	a	DET
ejpam-5442	9	10	simple	simple	ADJ
ejpam-5442	9	11	and	and	CCONJ
ejpam-5442	9	12	efficient	efficient	ADJ
ejpam-5442	9	13	instrument	instrument	NOUN
ejpam-5442	9	14	for	for	ADP
ejpam-5442	9	15	simulating	simulate	VERB
ejpam-5442	9	16	the	the	DET
ejpam-5442	9	17	solution	solution	NOUN
ejpam-5442	9	18	of	of	ADP
ejpam-5442	9	19	these	these	DET
ejpam-5442	9	20	models	model	NOUN
ejpam-5442	9	21	.	.	PUNCT
ejpam-5442	10	1	the	the	DET
ejpam-5442	10	2	principal	principal	ADJ
ejpam-5442	10	3	advantage	advantage	NOUN
ejpam-5442	10	4	of	of	ADP
ejpam-5442	10	5	the	the	DET
ejpam-5442	10	6	proposed	propose	VERB
ejpam-5442	10	7	method	method	NOUN
ejpam-5442	10	8	is	be	AUX
ejpam-5442	10	9	its	its	PRON
ejpam-5442	10	10	dependence	dependence	NOUN
ejpam-5442	10	11	on	on	ADP
ejpam-5442	10	12	a	a	DET
ejpam-5442	10	13	limited	limited	ADJ
ejpam-5442	10	14	number	number	NOUN
ejpam-5442	10	15	of	of	ADP
ejpam-5442	10	16	straightforward	straightforward	ADJ
ejpam-5442	10	17	steps	step	NOUN
ejpam-5442	10	18	,	,	PUNCT
ejpam-5442	10	19	devoid	devoid	ADJ
ejpam-5442	10	20	of	of	ADP
ejpam-5442	10	21	long	long	ADJ
ejpam-5442	10	22	-	-	PUNCT
ejpam-5442	10	23	term	term	NOUN
ejpam-5442	10	24	consequences	consequence	NOUN
ejpam-5442	10	25	or	or	CCONJ
ejpam-5442	10	26	reliance	reliance	NOUN
ejpam-5442	10	27	on	on	ADP
ejpam-5442	10	28	a	a	DET
ejpam-5442	10	29	perturbation	perturbation	NOUN
ejpam-5442	10	30	parameter	parameter	NOUN
ejpam-5442	10	31	.	.	PUNCT
ejpam-5442	11	1	2020	2020	NUM
ejpam-5442	11	2	mathematics	mathematic	NOUN
ejpam-5442	11	3	subject	subject	NOUN
ejpam-5442	11	4	classifications	classification	NOUN
ejpam-5442	11	5	:	:	PUNCT
ejpam-5442	11	6	34a12	34a12	NUM
ejpam-5442	11	7	,	,	PUNCT
ejpam-5442	11	8	41a30	41a30	NUM
ejpam-5442	11	9	,	,	PUNCT
ejpam-5442	11	10	47h10	47h10	NUM
ejpam-5442	11	11	,	,	PUNCT
ejpam-5442	11	12	65n20	65n20	NUM
ejpam-5442	11	13	.	.	PUNCT
ejpam-5442	12	1	key	key	ADJ
ejpam-5442	12	2	words	word	NOUN
ejpam-5442	12	3	and	and	CCONJ
ejpam-5442	12	4	phrases	phrase	NOUN
ejpam-5442	12	5	:	:	PUNCT
ejpam-5442	12	6	smoking	smoking	NOUN
ejpam-5442	12	7	model	model	NOUN
ejpam-5442	12	8	,	,	PUNCT
ejpam-5442	12	9	caputo	caputo	PROPN
ejpam-5442	12	10	-	-	PUNCT
ejpam-5442	12	11	fabrizio	fabrizio	PROPN
ejpam-5442	12	12	fractional	fractional	PROPN
ejpam-5442	12	13	derivative	derivative	ADJ
ejpam-5442	12	14	,	,	PUNCT
ejpam-5442	12	15	numerical	numerical	ADJ
ejpam-5442	12	16	integration	integration	NOUN
ejpam-5442	12	17	,	,	PUNCT
ejpam-5442	12	18	rk4	rk4	NOUN
ejpam-5442	12	19	method	method	NOUN
ejpam-5442	12	20	1	1	NUM
ejpam-5442	12	21	.	.	PUNCT
ejpam-5442	13	1	introduction	introduction	NOUN
ejpam-5442	13	2	according	accord	VERB
ejpam-5442	13	3	to	to	ADP
ejpam-5442	13	4	a	a	DET
ejpam-5442	13	5	report	report	NOUN
ejpam-5442	13	6	by	by	ADP
ejpam-5442	13	7	the	the	PRON
ejpam-5442	13	8	who	who	PRON
ejpam-5442	13	9	,	,	PUNCT
ejpam-5442	13	10	many	many	ADJ
ejpam-5442	13	11	smokers	smoker	NOUN
ejpam-5442	13	12	pass	pass	VERB
ejpam-5442	13	13	away	away	ADV
ejpam-5442	13	14	in	in	ADP
ejpam-5442	13	15	their	their	PRON
ejpam-5442	13	16	prime	prime	ADJ
ejpam-5442	13	17	years	year	NOUN
ejpam-5442	13	18	.	.	PUNCT
ejpam-5442	14	1	more	more	ADJ
ejpam-5442	14	2	than	than	ADP
ejpam-5442	14	3	5	5	NUM
ejpam-5442	14	4	million	million	NUM
ejpam-5442	14	5	deaths	death	NOUN
ejpam-5442	14	6	globally	globally	ADV
ejpam-5442	14	7	occur	occur	VERB
ejpam-5442	14	8	each	each	DET
ejpam-5442	14	9	year	year	NOUN
ejpam-5442	14	10	as	as	ADP
ejpam-5442	14	11	a	a	DET
ejpam-5442	14	12	result	result	NOUN
ejpam-5442	14	13	of	of	ADP
ejpam-5442	14	14	smoking	smoking	NOUN
ejpam-5442	14	15	’s	’s	PART
ejpam-5442	14	16	effects	effect	NOUN
ejpam-5442	14	17	on	on	ADP
ejpam-5442	14	18	various	various	ADJ
ejpam-5442	14	19	body	body	NOUN
ejpam-5442	14	20	processes	process	NOUN
ejpam-5442	14	21	;	;	PUNCT
ejpam-5442	14	22	by	by	ADP
ejpam-5442	14	23	2030	2030	NUM
ejpam-5442	14	24	,	,	PUNCT
ejpam-5442	14	25	this	this	DET
ejpam-5442	14	26	number	number	NOUN
ejpam-5442	14	27	could	could	AUX
ejpam-5442	14	28	increase	increase	VERB
ejpam-5442	14	29	to	to	ADP
ejpam-5442	14	30	8	8	NUM
ejpam-5442	14	31	million	million	NUM
ejpam-5442	14	32	(	(	PUNCT
ejpam-5442	14	33	[	[	X
ejpam-5442	14	34	23	23	NUM
ejpam-5442	14	35	]	]	PUNCT
ejpam-5442	14	36	,	,	PUNCT
ejpam-5442	14	37	[	[	X
ejpam-5442	14	38	27	27	NUM
ejpam-5442	14	39	]	]	NUM
ejpam-5442	14	40	)	)	PUNCT
ejpam-5442	14	41	.	.	PUNCT
ejpam-5442	15	1	smokers	smoker	NOUN
ejpam-5442	15	2	are	be	AUX
ejpam-5442	15	3	70	70	NUM
ejpam-5442	15	4	%	%	NOUN
ejpam-5442	15	5	more	more	ADV
ejpam-5442	15	6	likely	likely	ADJ
ejpam-5442	15	7	to	to	PART
ejpam-5442	15	8	experience	experience	VERB
ejpam-5442	15	9	a	a	DET
ejpam-5442	15	10	heart	heart	NOUN
ejpam-5442	15	11	attack	attack	NOUN
ejpam-5442	15	12	compared	compare	VERB
ejpam-5442	15	13	to	to	ADP
ejpam-5442	15	14	non	non	NOUN
ejpam-5442	15	15	-	-	NOUN
ejpam-5442	15	16	smokers	smoker	NOUN
ejpam-5442	15	17	.	.	PUNCT
ejpam-5442	16	1	lung	lung	NOUN
ejpam-5442	16	2	∗corresponding	∗corresponde	VERB
ejpam-5442	16	3	author	author	NOUN
ejpam-5442	16	4	.	.	PUNCT
ejpam-5442	17	1	doi	doi	NOUN
ejpam-5442	17	2	:	:	PUNCT
ejpam-5442	17	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5442	https://doi.org/10.29020/nybg.ejpam.v17i4.5442	PROPN
ejpam-5442	17	4	email	email	NOUN
ejpam-5442	17	5	addresses	address	NOUN
ejpam-5442	17	6	:	:	PUNCT
ejpam-5442	17	7	m.adel@iu.edu.sa	m.adel@iu.edu.sa	PROPN
ejpam-5442	17	8	or	or	CCONJ
ejpam-5442	17	9	adel@sci.cu.edu.eg	adel@sci.cu.edu.eg	PROPN
ejpam-5442	17	10	(	(	PUNCT
ejpam-5442	17	11	m.	m.	NOUN
ejpam-5442	17	12	adel	adel	PROPN
ejpam-5442	17	13	)	)	PUNCT
ejpam-5442	17	14	,	,	PUNCT
ejpam-5442	17	15	mmkhader@imamu.edu.sa	mmkhader@imamu.edu.sa	PROPN
ejpam-5442	17	16	(	(	PUNCT
ejpam-5442	17	17	m.	m.	NOUN
ejpam-5442	17	18	m.	m.	NOUN
ejpam-5442	17	19	khader	khader	PROPN
ejpam-5442	17	20	)	)	PUNCT
ejpam-5442	17	21	,	,	PUNCT
ejpam-5442	17	22	namohammed@uqu.edu.sa	namohammed@uqu.edu.sa	PROPN
ejpam-5442	17	23	(	(	PUNCT
ejpam-5442	17	24	n.	n.	PROPN
ejpam-5442	17	25	a.	a.	PROPN
ejpam-5442	17	26	mohammed	mohammed	PROPN
ejpam-5442	17	27	)	)	PUNCT
ejpam-5442	17	28	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5442	18	1	3277	3277	NUM
ejpam-5442	19	1	copyright	copyright	NOUN
ejpam-5442	19	2	:	:	PUNCT
ejpam-5442	19	3	©	©	PROPN
ejpam-5442	19	4	2024	2024	NUM
ejpam-5442	19	5	the	the	DET
ejpam-5442	19	6	author(s	author(s	NOUN
ejpam-5442	19	7	)	)	PUNCT
ejpam-5442	19	8	.	.	PUNCT
ejpam-5442	20	1	(	(	PUNCT
ejpam-5442	20	2	cc	cc	NOUN
ejpam-5442	20	3	by	by	ADP
ejpam-5442	20	4	-	-	PUNCT
ejpam-5442	20	5	nc	nc	PROPN
ejpam-5442	20	6	4.0	4.0	NUM
ejpam-5442	20	7	)	)	PUNCT
ejpam-5442	20	8	m.	m.	NOUN
ejpam-5442	20	9	adel	adel	PROPN
ejpam-5442	20	10	,	,	PUNCT
ejpam-5442	20	11	m.	m.	NOUN
ejpam-5442	20	12	m.	m.	NOUN
ejpam-5442	20	13	khader	khader	PROPN
ejpam-5442	20	14	,	,	PUNCT
ejpam-5442	20	15	n.	n.	PROPN
ejpam-5442	20	16	a.	a.	PROPN
ejpam-5442	20	17	mohammed	mohammed	PROPN
ejpam-5442	20	18	/	/	SYM
ejpam-5442	20	19	eur	eur	PROPN
ejpam-5442	20	20	.	.	PUNCT
ejpam-5442	21	1	j.	j.	PROPN
ejpam-5442	21	2	pure	pure	PROPN
ejpam-5442	21	3	appl	appl	PROPN
ejpam-5442	21	4	.	.	PROPN
ejpam-5442	21	5	math	math	PROPN
ejpam-5442	21	6	,	,	PUNCT
ejpam-5442	21	7	17	17	NUM
ejpam-5442	21	8	(	(	PUNCT
ejpam-5442	21	9	4	4	NUM
ejpam-5442	21	10	)	)	PUNCT
ejpam-5442	21	11	(	(	PUNCT
ejpam-5442	21	12	2024	2024	NUM
ejpam-5442	21	13	)	)	PUNCT
ejpam-5442	21	14	,	,	PUNCT
ejpam-5442	21	15	3277	3277	NUM
ejpam-5442	21	16	-	-	SYM
ejpam-5442	21	17	3290	3290	NUM
ejpam-5442	21	18	3278	3278	NUM
ejpam-5442	21	19	cancer	cancer	NOUN
ejpam-5442	21	20	occurs	occur	VERB
ejpam-5442	21	21	10	10	NUM
ejpam-5442	21	22	%	%	NOUN
ejpam-5442	21	23	more	more	ADV
ejpam-5442	21	24	frequently	frequently	ADV
ejpam-5442	21	25	in	in	ADP
ejpam-5442	21	26	smokers	smoker	NOUN
ejpam-5442	21	27	than	than	ADP
ejpam-5442	21	28	in	in	ADP
ejpam-5442	21	29	non	non	ADJ
ejpam-5442	21	30	-	-	NOUN
ejpam-5442	21	31	smokers	smoker	NOUN
ejpam-5442	21	32	.	.	PUNCT
ejpam-5442	22	1	smokers	smoker	NOUN
ejpam-5442	22	2	often	often	ADV
ejpam-5442	22	3	live	live	VERB
ejpam-5442	22	4	10	10	NUM
ejpam-5442	22	5	to	to	PART
ejpam-5442	22	6	13	13	NUM
ejpam-5442	22	7	years	year	NOUN
ejpam-5442	22	8	less	less	ADJ
ejpam-5442	22	9	than	than	SCONJ
ejpam-5442	22	10	others	other	NOUN
ejpam-5442	22	11	do	do	VERB
ejpam-5442	22	12	.	.	PUNCT
ejpam-5442	23	1	researchers	researcher	NOUN
ejpam-5442	23	2	work	work	VERB
ejpam-5442	23	3	to	to	PART
ejpam-5442	23	4	extend	extend	VERB
ejpam-5442	23	5	people	people	NOUN
ejpam-5442	23	6	’s	’s	PART
ejpam-5442	23	7	lives	life	NOUN
ejpam-5442	23	8	to	to	PART
ejpam-5442	23	9	reduce	reduce	VERB
ejpam-5442	23	10	smoking	smoking	NOUN
ejpam-5442	23	11	.	.	PUNCT
ejpam-5442	24	1	to	to	PART
ejpam-5442	24	2	best	well	ADV
ejpam-5442	24	3	explain	explain	VERB
ejpam-5442	24	4	cigarette	cigarette	NOUN
ejpam-5442	24	5	smoking	smoking	NOUN
ejpam-5442	24	6	,	,	PUNCT
ejpam-5442	24	7	many	many	ADJ
ejpam-5442	24	8	academics	academic	NOUN
ejpam-5442	24	9	have	have	AUX
ejpam-5442	24	10	investigated	investigate	VERB
ejpam-5442	24	11	several	several	ADJ
ejpam-5442	24	12	efficient	efficient	ADJ
ejpam-5442	24	13	smoking	smoking	NOUN
ejpam-5442	24	14	models	model	NOUN
ejpam-5442	24	15	.	.	PUNCT
ejpam-5442	25	1	they	they	PRON
ejpam-5442	25	2	categorize	categorize	VERB
ejpam-5442	25	3	individuals	individual	NOUN
ejpam-5442	25	4	as	as	ADP
ejpam-5442	25	5	potential	potential	ADJ
ejpam-5442	25	6	,	,	PUNCT
ejpam-5442	25	7	chain	chain	NOUN
ejpam-5442	25	8	,	,	PUNCT
ejpam-5442	25	9	or	or	CCONJ
ejpam-5442	25	10	permanently	permanently	ADV
ejpam-5442	25	11	abstinent	abstinent	ADJ
ejpam-5442	25	12	smokers	smoker	NOUN
ejpam-5442	25	13	.	.	PUNCT
ejpam-5442	26	1	probably	probably	ADV
ejpam-5442	26	2	around	around	ADP
ejpam-5442	26	3	1997	1997	NUM
ejpam-5442	26	4	[	[	X
ejpam-5442	26	5	12	12	NUM
ejpam-5442	26	6	]	]	PUNCT
ejpam-5442	26	7	,	,	PUNCT
ejpam-5442	26	8	the	the	DET
ejpam-5442	26	9	smoking	smoking	NOUN
ejpam-5442	26	10	mathematical	mathematical	ADJ
ejpam-5442	26	11	model	model	NOUN
ejpam-5442	26	12	came	come	VERB
ejpam-5442	26	13	into	into	ADP
ejpam-5442	26	14	existence	existence	NOUN
ejpam-5442	26	15	.	.	PUNCT
ejpam-5442	27	1	more	more	ADV
ejpam-5442	27	2	recently	recently	ADV
ejpam-5442	27	3	,	,	PUNCT
ejpam-5442	27	4	in	in	ADP
ejpam-5442	27	5	2007	2007	NUM
ejpam-5442	27	6	,	,	PUNCT
ejpam-5442	27	7	a	a	DET
ejpam-5442	27	8	survey	survey	NOUN
ejpam-5442	27	9	conducted	conduct	VERB
ejpam-5442	27	10	in	in	ADP
ejpam-5442	27	11	korea	korea	PROPN
ejpam-5442	27	12	by	by	ADP
ejpam-5442	27	13	ham	ham	PROPN
ejpam-5442	28	1	[	[	X
ejpam-5442	28	2	14	14	NUM
ejpam-5442	28	3	]	]	PUNCT
ejpam-5442	28	4	recorded	record	VERB
ejpam-5442	28	5	the	the	DET
ejpam-5442	28	6	various	various	ADJ
ejpam-5442	28	7	stages	stage	NOUN
ejpam-5442	28	8	and	and	CCONJ
ejpam-5442	28	9	practices	practice	NOUN
ejpam-5442	28	10	of	of	ADP
ejpam-5442	28	11	smoking	smoke	VERB
ejpam-5442	28	12	among	among	ADP
ejpam-5442	28	13	students	student	NOUN
ejpam-5442	28	14	.	.	PUNCT
ejpam-5442	29	1	liu	liu	PROPN
ejpam-5442	29	2	et	et	PROPN
ejpam-5442	29	3	al	al	PROPN
ejpam-5442	29	4	.	.	PUNCT
ejpam-5442	30	1	[	[	X
ejpam-5442	30	2	20	20	NUM
ejpam-5442	30	3	]	]	PUNCT
ejpam-5442	30	4	in	in	ADP
ejpam-5442	30	5	2008	2008	NUM
ejpam-5442	30	6	refined	refined	ADJ
ejpam-5442	30	7	ham	ham	PROPN
ejpam-5442	30	8	’s	’s	PART
ejpam-5442	30	9	model	model	NOUN
ejpam-5442	30	10	to	to	PART
ejpam-5442	30	11	incorporate	incorporate	VERB
ejpam-5442	30	12	a	a	DET
ejpam-5442	30	13	new	new	ADJ
ejpam-5442	30	14	category	category	NOUN
ejpam-5442	30	15	of	of	ADP
ejpam-5442	30	16	temporarily	temporarily	ADV
ejpam-5442	30	17	abstaining	abstain	VERB
ejpam-5442	30	18	smokers	smoker	NOUN
ejpam-5442	30	19	.	.	PUNCT
ejpam-5442	31	1	in	in	ADP
ejpam-5442	31	2	[	[	X
ejpam-5442	31	3	14	14	NUM
ejpam-5442	31	4	]	]	PUNCT
ejpam-5442	31	5	,	,	PUNCT
ejpam-5442	31	6	the	the	DET
ejpam-5442	31	7	authors	author	NOUN
ejpam-5442	31	8	enhanced	enhance	VERB
ejpam-5442	31	9	an	an	DET
ejpam-5442	31	10	integer	integer	NOUN
ejpam-5442	31	11	-	-	PUNCT
ejpam-5442	31	12	order	order	NOUN
ejpam-5442	31	13	model	model	NOUN
ejpam-5442	31	14	by	by	ADP
ejpam-5442	31	15	incorporating	incorporate	VERB
ejpam-5442	31	16	a	a	DET
ejpam-5442	31	17	novel	novel	ADJ
ejpam-5442	31	18	category	category	NOUN
ejpam-5442	31	19	of	of	ADP
ejpam-5442	31	20	infrequent	infrequent	ADJ
ejpam-5442	31	21	smokers	smoker	NOUN
ejpam-5442	31	22	and	and	CCONJ
ejpam-5442	31	23	a	a	DET
ejpam-5442	31	24	dynamic	dynamic	ADJ
ejpam-5442	31	25	interaction	interaction	NOUN
ejpam-5442	31	26	.	.	PUNCT
ejpam-5442	32	1	the	the	DET
ejpam-5442	32	2	smoking	smoking	NOUN
ejpam-5442	32	3	models	model	NOUN
ejpam-5442	32	4	have	have	AUX
ejpam-5442	32	5	also	also	ADV
ejpam-5442	32	6	been	be	AUX
ejpam-5442	32	7	provided	provide	VERB
ejpam-5442	32	8	by	by	ADP
ejpam-5442	32	9	several	several	ADJ
ejpam-5442	32	10	authors	author	NOUN
ejpam-5442	32	11	in	in	ADP
ejpam-5442	32	12	integer	integer	NOUN
ejpam-5442	32	13	and	and	CCONJ
ejpam-5442	32	14	fractional	fractional	ADJ
ejpam-5442	32	15	orders	order	NOUN
ejpam-5442	32	16	[	[	X
ejpam-5442	32	17	10	10	NUM
ejpam-5442	32	18	]	]	PUNCT
ejpam-5442	32	19	.	.	PUNCT
ejpam-5442	33	1	in	in	ADP
ejpam-5442	33	2	the	the	DET
ejpam-5442	33	3	last	last	ADJ
ejpam-5442	33	4	few	few	ADJ
ejpam-5442	33	5	years	year	NOUN
ejpam-5442	33	6	,	,	PUNCT
ejpam-5442	33	7	there	there	PRON
ejpam-5442	33	8	are	be	VERB
ejpam-5442	33	9	many	many	ADJ
ejpam-5442	33	10	novel	novel	ADJ
ejpam-5442	33	11	techniques	technique	NOUN
ejpam-5442	33	12	and	and	CCONJ
ejpam-5442	33	13	topics	topic	NOUN
ejpam-5442	33	14	have	have	AUX
ejpam-5442	33	15	been	be	AUX
ejpam-5442	33	16	presented	present	VERB
ejpam-5442	33	17	in	in	ADP
ejpam-5442	33	18	the	the	DET
ejpam-5442	33	19	field	field	NOUN
ejpam-5442	33	20	of	of	ADP
ejpam-5442	33	21	fractional	fractional	ADJ
ejpam-5442	33	22	analysis	analysis	NOUN
ejpam-5442	33	23	,	,	PUNCT
ejpam-5442	33	24	for	for	ADP
ejpam-5442	33	25	example	example	NOUN
ejpam-5442	33	26	,	,	PUNCT
ejpam-5442	33	27	a	a	DET
ejpam-5442	33	28	study	study	NOUN
ejpam-5442	33	29	of	of	ADP
ejpam-5442	33	30	the	the	DET
ejpam-5442	33	31	susceptible	susceptible	ADJ
ejpam-5442	33	32	-	-	PUNCT
ejpam-5442	33	33	infected	infect	VERB
ejpam-5442	33	34	-	-	PUNCT
ejpam-5442	33	35	recovered	recover	VERB
ejpam-5442	33	36	epidemiological	epidemiological	ADJ
ejpam-5442	33	37	model	model	NOUN
ejpam-5442	33	38	for	for	ADP
ejpam-5442	33	39	pediatric	pediatric	ADJ
ejpam-5442	33	40	diseases	disease	NOUN
ejpam-5442	33	41	is	be	AUX
ejpam-5442	33	42	performed	perform	VERB
ejpam-5442	33	43	by	by	ADP
ejpam-5442	33	44	implementing	implement	VERB
ejpam-5442	33	45	the	the	DET
ejpam-5442	33	46	q	q	NOUN
ejpam-5442	33	47	-	-	PUNCT
ejpam-5442	33	48	homotopy	homotopy	NOUN
ejpam-5442	33	49	analysis	analysis	NOUN
ejpam-5442	33	50	transform	transform	NOUN
ejpam-5442	33	51	technique	technique	NOUN
ejpam-5442	33	52	(	(	PUNCT
ejpam-5442	33	53	hatm	hatm	ADJ
ejpam-5442	33	54	)	)	PUNCT
ejpam-5442	34	1	[	[	X
ejpam-5442	34	2	25	25	NUM
ejpam-5442	34	3	]	]	PUNCT
ejpam-5442	34	4	,	,	PUNCT
ejpam-5442	34	5	as	as	SCONJ
ejpam-5442	34	6	previously	previously	ADV
ejpam-5442	34	7	employed	employ	VERB
ejpam-5442	34	8	by	by	ADP
ejpam-5442	34	9	the	the	DET
ejpam-5442	34	10	authors	author	NOUN
ejpam-5442	34	11	in	in	ADP
ejpam-5442	34	12	[	[	X
ejpam-5442	34	13	26	26	NUM
ejpam-5442	34	14	]	]	PUNCT
ejpam-5442	34	15	to	to	PART
ejpam-5442	34	16	numerically	numerically	ADV
ejpam-5442	34	17	solve	solve	VERB
ejpam-5442	34	18	fractional	fractional	ADJ
ejpam-5442	34	19	burger	burger	NOUN
ejpam-5442	34	20	’s	’s	PART
ejpam-5442	34	21	equations	equation	NOUN
ejpam-5442	34	22	.	.	PUNCT
ejpam-5442	35	1	linear	linear	ADJ
ejpam-5442	35	2	,	,	PUNCT
ejpam-5442	35	3	nonlinear	nonlinear	ADJ
ejpam-5442	35	4	,	,	PUNCT
ejpam-5442	35	5	fractional	fractional	ADJ
ejpam-5442	35	6	,	,	PUNCT
ejpam-5442	35	7	and	and	CCONJ
ejpam-5442	35	8	fuzzy	fuzzy	ADJ
ejpam-5442	35	9	stochastic	stochastic	ADJ
ejpam-5442	35	10	problems	problem	NOUN
ejpam-5442	35	11	discussed	discuss	VERB
ejpam-5442	35	12	in	in	ADP
ejpam-5442	35	13	(	(	PUNCT
ejpam-5442	35	14	[	[	X
ejpam-5442	35	15	4	4	NUM
ejpam-5442	35	16	]	]	PUNCT
ejpam-5442	35	17	,	,	PUNCT
ejpam-5442	36	1	[	[	X
ejpam-5442	36	2	7	7	NUM
ejpam-5442	36	3	]	]	NUM
ejpam-5442	36	4	)	)	PUNCT
ejpam-5442	36	5	.	.	PUNCT
ejpam-5442	37	1	there	there	PRON
ejpam-5442	37	2	are	be	VERB
ejpam-5442	37	3	many	many	ADJ
ejpam-5442	37	4	real	real	ADJ
ejpam-5442	37	5	-	-	PUNCT
ejpam-5442	37	6	life	life	NOUN
ejpam-5442	37	7	problems	problem	NOUN
ejpam-5442	37	8	were	be	AUX
ejpam-5442	37	9	discussed	discuss	VERB
ejpam-5442	37	10	recently	recently	ADV
ejpam-5442	37	11	in	in	ADP
ejpam-5442	37	12	many	many	ADJ
ejpam-5442	37	13	scientific	scientific	ADJ
ejpam-5442	37	14	papers	paper	NOUN
ejpam-5442	37	15	,	,	PUNCT
ejpam-5442	37	16	for	for	ADP
ejpam-5442	37	17	example	example	NOUN
ejpam-5442	37	18	,	,	PUNCT
ejpam-5442	37	19	the	the	DET
ejpam-5442	37	20	mathematical	mathematical	ADJ
ejpam-5442	37	21	fractional	fractional	ADJ
ejpam-5442	37	22	-	-	PUNCT
ejpam-5442	37	23	order	order	NOUN
ejpam-5442	37	24	model	model	NOUN
ejpam-5442	37	25	of	of	ADP
ejpam-5442	37	26	a	a	DET
ejpam-5442	37	27	novel	novel	ADJ
ejpam-5442	37	28	coronavirus	coronavirus	NOUN
ejpam-5442	37	29	’s	’s	PART
ejpam-5442	37	30	caputo	caputo	PROPN
ejpam-5442	37	31	growth	growth	PROPN
ejpam-5442	37	32	was	be	AUX
ejpam-5442	37	33	examined	examine	VERB
ejpam-5442	37	34	in	in	ADP
ejpam-5442	37	35	[	[	X
ejpam-5442	37	36	2	2	NUM
ejpam-5442	37	37	]	]	PUNCT
ejpam-5442	37	38	.	.	PUNCT
ejpam-5442	38	1	also	also	ADV
ejpam-5442	38	2	,	,	PUNCT
ejpam-5442	38	3	there	there	PRON
ejpam-5442	38	4	are	be	VERB
ejpam-5442	38	5	many	many	ADJ
ejpam-5442	38	6	theoretical	theoretical	ADJ
ejpam-5442	38	7	studies	study	NOUN
ejpam-5442	38	8	that	that	PRON
ejpam-5442	38	9	support	support	VERB
ejpam-5442	38	10	the	the	DET
ejpam-5442	38	11	numerical	numerical	ADJ
ejpam-5442	38	12	techniques	technique	NOUN
ejpam-5442	38	13	,	,	PUNCT
ejpam-5442	38	14	for	for	ADP
ejpam-5442	38	15	example	example	NOUN
ejpam-5442	38	16	,	,	PUNCT
ejpam-5442	38	17	the	the	DET
ejpam-5442	38	18	existence	existence	NOUN
ejpam-5442	38	19	,	,	PUNCT
ejpam-5442	38	20	uniqueness	uniqueness	NOUN
ejpam-5442	38	21	,	,	PUNCT
ejpam-5442	38	22	and	and	CCONJ
ejpam-5442	38	23	synchronization	synchronization	NOUN
ejpam-5442	38	24	of	of	ADP
ejpam-5442	38	25	a	a	DET
ejpam-5442	38	26	discrete	discrete	ADJ
ejpam-5442	38	27	-	-	PUNCT
ejpam-5442	38	28	time	time	NOUN
ejpam-5442	38	29	fractional	fractional	ADJ
ejpam-5442	38	30	tumor	tumor	NOUN
ejpam-5442	38	31	growth	growth	NOUN
ejpam-5442	38	32	model	model	NOUN
ejpam-5442	38	33	,	,	PUNCT
ejpam-5442	38	34	along	along	ADP
ejpam-5442	38	35	with	with	ADP
ejpam-5442	38	36	numerical	numerical	ADJ
ejpam-5442	38	37	discoveries	discovery	NOUN
ejpam-5442	38	38	and	and	CCONJ
ejpam-5442	38	39	essential	essential	ADJ
ejpam-5442	38	40	criteria	criterion	NOUN
ejpam-5442	38	41	for	for	ADP
ejpam-5442	38	42	a	a	DET
ejpam-5442	38	43	modified	modify	VERB
ejpam-5442	38	44	-	-	PUNCT
ejpam-5442	38	45	abc	abc	NOUN
ejpam-5442	38	46	fractional	fractional	ADJ
ejpam-5442	38	47	order	order	NOUN
ejpam-5442	38	48	smoking	smoking	NOUN
ejpam-5442	38	49	model	model	NOUN
ejpam-5442	38	50	solution	solution	NOUN
ejpam-5442	38	51	,	,	PUNCT
ejpam-5442	38	52	were	be	AUX
ejpam-5442	38	53	delineated	delineate	VERB
ejpam-5442	38	54	in	in	ADP
ejpam-5442	38	55	(	(	PUNCT
ejpam-5442	38	56	[	[	X
ejpam-5442	38	57	3]-[5	3]-[5	NUM
ejpam-5442	38	58	]	]	X
ejpam-5442	38	59	)	)	PUNCT
ejpam-5442	38	60	.	.	PUNCT
ejpam-5442	39	1	scientists	scientist	NOUN
ejpam-5442	39	2	are	be	AUX
ejpam-5442	39	3	currently	currently	ADV
ejpam-5442	39	4	studying	study	VERB
ejpam-5442	39	5	more	more	ADV
ejpam-5442	39	6	effective	effective	ADJ
ejpam-5442	39	7	fractional	fractional	ADJ
ejpam-5442	39	8	operators	operator	NOUN
ejpam-5442	39	9	.	.	PUNCT
ejpam-5442	40	1	in	in	ADP
ejpam-5442	40	2	order	order	NOUN
ejpam-5442	40	3	to	to	PART
ejpam-5442	40	4	address	address	VERB
ejpam-5442	40	5	the	the	DET
ejpam-5442	40	6	issue	issue	NOUN
ejpam-5442	40	7	of	of	ADP
ejpam-5442	40	8	singularity	singularity	NOUN
ejpam-5442	40	9	and	and	CCONJ
ejpam-5442	40	10	achieve	achieve	VERB
ejpam-5442	40	11	accurate	accurate	ADJ
ejpam-5442	40	12	and	and	CCONJ
ejpam-5442	40	13	reliable	reliable	ADJ
ejpam-5442	40	14	modeling	modeling	NOUN
ejpam-5442	40	15	outcomes	outcome	NOUN
ejpam-5442	40	16	,	,	PUNCT
ejpam-5442	40	17	an	an	DET
ejpam-5442	40	18	enhanced	enhanced	ADJ
ejpam-5442	40	19	fractional	fractional	ADJ
ejpam-5442	40	20	-	-	PUNCT
ejpam-5442	40	21	order	order	NOUN
ejpam-5442	40	22	caputo	caputo	PROPN
ejpam-5442	40	23	-	-	PUNCT
ejpam-5442	40	24	fabrizio	fabrizio	PROPN
ejpam-5442	40	25	derivative	derivative	NOUN
ejpam-5442	40	26	has	have	AUX
ejpam-5442	40	27	been	be	AUX
ejpam-5442	40	28	formulated	formulate	VERB
ejpam-5442	40	29	.	.	PUNCT
ejpam-5442	41	1	this	this	DET
ejpam-5442	41	2	derivative	derivative	NOUN
ejpam-5442	41	3	incorporates	incorporate	VERB
ejpam-5442	41	4	a	a	DET
ejpam-5442	41	5	non	non	ADJ
ejpam-5442	41	6	-	-	ADJ
ejpam-5442	41	7	singular	singular	ADJ
ejpam-5442	41	8	kernel	kernel	NOUN
ejpam-5442	41	9	,	,	PUNCT
ejpam-5442	41	10	as	as	SCONJ
ejpam-5442	41	11	proposed	propose	VERB
ejpam-5442	41	12	by	by	ADP
ejpam-5442	41	13	caputo	caputo	PROPN
ejpam-5442	41	14	and	and	CCONJ
ejpam-5442	41	15	fabrizio	fabrizio	PROPN
ejpam-5442	41	16	,	,	PUNCT
ejpam-5442	41	17	leading	lead	VERB
ejpam-5442	41	18	to	to	ADP
ejpam-5442	41	19	improved	improved	ADJ
ejpam-5442	41	20	efficiency	efficiency	NOUN
ejpam-5442	41	21	and	and	CCONJ
ejpam-5442	41	22	robustness	robustness	NOUN
ejpam-5442	41	23	in	in	ADP
ejpam-5442	41	24	recent	recent	ADJ
ejpam-5442	41	25	years	year	NOUN
ejpam-5442	41	26	.	.	PUNCT
ejpam-5442	42	1	the	the	DET
ejpam-5442	42	2	use	use	NOUN
ejpam-5442	42	3	of	of	ADP
ejpam-5442	42	4	laplace	laplace	NOUN
ejpam-5442	42	5	transformation	transformation	NOUN
ejpam-5442	42	6	to	to	PART
ejpam-5442	42	7	convert	convert	VERB
ejpam-5442	42	8	it	it	PRON
ejpam-5442	42	9	to	to	ADP
ejpam-5442	42	10	integer	integer	NOUN
ejpam-5442	42	11	power	power	NOUN
ejpam-5442	42	12	is	be	AUX
ejpam-5442	42	13	regarded	regard	VERB
ejpam-5442	42	14	as	as	ADP
ejpam-5442	42	15	a	a	DET
ejpam-5442	42	16	constructive	constructive	ADJ
ejpam-5442	42	17	method	method	NOUN
ejpam-5442	42	18	.	.	PUNCT
ejpam-5442	43	1	consequently	consequently	ADV
ejpam-5442	43	2	,	,	PUNCT
ejpam-5442	43	3	in	in	ADP
ejpam-5442	43	4	some	some	DET
ejpam-5442	43	5	scenarios	scenario	NOUN
ejpam-5442	43	6	,	,	PUNCT
ejpam-5442	43	7	we	we	PRON
ejpam-5442	43	8	can	can	AUX
ejpam-5442	43	9	readily	readily	ADV
ejpam-5442	43	10	compute	compute	VERB
ejpam-5442	43	11	the	the	DET
ejpam-5442	43	12	precise	precise	ADJ
ejpam-5442	43	13	solution	solution	NOUN
ejpam-5442	43	14	.	.	PUNCT
ejpam-5442	44	1	the	the	DET
ejpam-5442	44	2	citation	citation	NOUN
ejpam-5442	44	3	for	for	ADP
ejpam-5442	44	4	this	this	DET
ejpam-5442	44	5	information	information	NOUN
ejpam-5442	44	6	is	be	AUX
ejpam-5442	44	7	[	[	X
ejpam-5442	44	8	9	9	NUM
ejpam-5442	44	9	]	]	PUNCT
ejpam-5442	44	10	.	.	PUNCT
ejpam-5442	45	1	the	the	DET
ejpam-5442	45	2	paper	paper	NOUN
ejpam-5442	45	3	[	[	X
ejpam-5442	45	4	21	21	NUM
ejpam-5442	45	5	]	]	PUNCT
ejpam-5442	45	6	explores	explore	VERB
ejpam-5442	45	7	the	the	DET
ejpam-5442	45	8	examination	examination	NOUN
ejpam-5442	45	9	of	of	ADP
ejpam-5442	45	10	fractional	fractional	ADJ
ejpam-5442	45	11	operators	operator	NOUN
ejpam-5442	45	12	and	and	CCONJ
ejpam-5442	45	13	presents	present	VERB
ejpam-5442	45	14	novel	novel	ADJ
ejpam-5442	45	15	characteristics	characteristic	NOUN
ejpam-5442	45	16	associated	associate	VERB
ejpam-5442	45	17	with	with	ADP
ejpam-5442	45	18	them	they	PRON
ejpam-5442	45	19	.	.	PUNCT
ejpam-5442	46	1	unlike	unlike	ADP
ejpam-5442	46	2	traditional	traditional	ADJ
ejpam-5442	46	3	integer	integer	NOUN
ejpam-5442	46	4	derivatives	derivative	NOUN
ejpam-5442	46	5	,	,	PUNCT
ejpam-5442	46	6	fractionalorder	fractionalorder	ADJ
ejpam-5442	46	7	derivatives	derivative	NOUN
ejpam-5442	46	8	have	have	AUX
ejpam-5442	46	9	emerged	emerge	VERB
ejpam-5442	46	10	as	as	ADP
ejpam-5442	46	11	significant	significant	ADJ
ejpam-5442	46	12	solutions	solution	NOUN
ejpam-5442	46	13	to	to	ADP
ejpam-5442	46	14	intricate	intricate	ADJ
ejpam-5442	46	15	situations	situation	NOUN
ejpam-5442	46	16	in	in	ADP
ejpam-5442	46	17	recent	recent	ADJ
ejpam-5442	46	18	years	year	NOUN
ejpam-5442	46	19	.	.	PUNCT
ejpam-5442	47	1	in	in	ADP
ejpam-5442	47	2	the	the	DET
ejpam-5442	47	3	paper	paper	NOUN
ejpam-5442	47	4	[	[	X
ejpam-5442	47	5	19	19	NUM
ejpam-5442	47	6	]	]	X
ejpam-5442	47	7	,	,	PUNCT
ejpam-5442	47	8	a	a	DET
ejpam-5442	47	9	new	new	ADJ
ejpam-5442	47	10	and	and	CCONJ
ejpam-5442	47	11	effective	effective	ADJ
ejpam-5442	47	12	model	model	NOUN
ejpam-5442	47	13	for	for	ADP
ejpam-5442	47	14	uncertain	uncertain	ADJ
ejpam-5442	47	15	fractional	fractional	ADJ
ejpam-5442	47	16	currency	currency	NOUN
ejpam-5442	47	17	is	be	AUX
ejpam-5442	47	18	established	establish	VERB
ejpam-5442	47	19	.	.	PUNCT
ejpam-5442	48	1	the	the	DET
ejpam-5442	48	2	solution	solution	NOUN
ejpam-5442	48	3	to	to	ADP
ejpam-5442	48	4	the	the	DET
ejpam-5442	48	5	fractional	fractional	ADJ
ejpam-5442	48	6	differential	differential	ADJ
ejpam-5442	48	7	equations	equation	NOUN
ejpam-5442	48	8	(	(	PUNCT
ejpam-5442	48	9	fdes	fde	NOUN
ejpam-5442	48	10	)	)	PUNCT
ejpam-5442	48	11	is	be	AUX
ejpam-5442	48	12	calculated	calculate	VERB
ejpam-5442	48	13	using	use	VERB
ejpam-5442	48	14	the	the	DET
ejpam-5442	48	15	caputo	caputo	PROPN
ejpam-5442	48	16	derivative	derivative	NOUN
ejpam-5442	48	17	,	,	PUNCT
ejpam-5442	48	18	with	with	ADP
ejpam-5442	48	19	the	the	DET
ejpam-5442	48	20	mittag	mittag	ADJ
ejpam-5442	48	21	-	-	PUNCT
ejpam-5442	48	22	leffler	leffler	NOUN
ejpam-5442	48	23	function	function	NOUN
ejpam-5442	48	24	being	be	AUX
ejpam-5442	48	25	employed	employ	VERB
ejpam-5442	48	26	.	.	PUNCT
ejpam-5442	49	1	the	the	DET
ejpam-5442	49	2	study	study	NOUN
ejpam-5442	49	3	[	[	X
ejpam-5442	49	4	28	28	NUM
ejpam-5442	49	5	]	]	X
ejpam-5442	49	6	looks	look	VERB
ejpam-5442	49	7	at	at	ADP
ejpam-5442	49	8	how	how	SCONJ
ejpam-5442	49	9	to	to	PART
ejpam-5442	49	10	use	use	VERB
ejpam-5442	49	11	the	the	DET
ejpam-5442	49	12	cf	cf	NOUN
ejpam-5442	49	13	operator	operator	NOUN
ejpam-5442	49	14	to	to	PART
ejpam-5442	49	15	find	find	VERB
ejpam-5442	49	16	analytical	analytical	ADJ
ejpam-5442	49	17	solutions	solution	NOUN
ejpam-5442	49	18	for	for	ADP
ejpam-5442	49	19	fractional	fractional	ADJ
ejpam-5442	49	20	volterra	volterra	NOUN
ejpam-5442	49	21	integral	integral	ADJ
ejpam-5442	49	22	-	-	PUNCT
ejpam-5442	49	23	differential	differential	NOUN
ejpam-5442	49	24	equations	equation	NOUN
ejpam-5442	49	25	.	.	PUNCT
ejpam-5442	50	1	furthermore	furthermore	ADV
ejpam-5442	50	2	,	,	PUNCT
ejpam-5442	50	3	a	a	DET
ejpam-5442	50	4	work	work	NOUN
ejpam-5442	50	5	conducted	conduct	VERB
ejpam-5442	50	6	in	in	ADP
ejpam-5442	50	7	[	[	X
ejpam-5442	50	8	11	11	NUM
ejpam-5442	50	9	]	]	PUNCT
ejpam-5442	50	10	has	have	AUX
ejpam-5442	50	11	examined	examine	VERB
ejpam-5442	50	12	the	the	DET
ejpam-5442	50	13	intricate	intricate	ADJ
ejpam-5442	50	14	dynamics	dynamic	NOUN
ejpam-5442	50	15	of	of	ADP
ejpam-5442	50	16	the	the	DET
ejpam-5442	50	17	omicron	omicron	PROPN
ejpam-5442	50	18	variant	variant	NOUN
ejpam-5442	50	19	of	of	ADP
ejpam-5442	50	20	covid-19	covid-19	PROPN
ejpam-5442	50	21	by	by	ADP
ejpam-5442	50	22	employing	employ	VERB
ejpam-5442	50	23	cf	cf	NOUN
ejpam-5442	50	24	-	-	PUNCT
ejpam-5442	50	25	fractional	fractional	ADJ
ejpam-5442	50	26	operators	operator	NOUN
ejpam-5442	50	27	.	.	PUNCT
ejpam-5442	51	1	in	in	ADP
ejpam-5442	51	2	addition	addition	NOUN
ejpam-5442	51	3	,	,	PUNCT
ejpam-5442	51	4	a	a	DET
ejpam-5442	51	5	numerical	numerical	ADJ
ejpam-5442	51	6	method	method	NOUN
ejpam-5442	51	7	is	be	AUX
ejpam-5442	51	8	created	create	VERB
ejpam-5442	51	9	that	that	PRON
ejpam-5442	51	10	includes	include	VERB
ejpam-5442	51	11	an	an	DET
ejpam-5442	51	12	exponential	exponential	ADJ
ejpam-5442	51	13	law	law	NOUN
ejpam-5442	51	14	kernel	kernel	NOUN
ejpam-5442	51	15	to	to	PART
ejpam-5442	51	16	analyze	analyze	VERB
ejpam-5442	51	17	and	and	CCONJ
ejpam-5442	51	18	model	model	VERB
ejpam-5442	51	19	the	the	DET
ejpam-5442	51	20	spread	spread	NOUN
ejpam-5442	51	21	of	of	ADP
ejpam-5442	51	22	the	the	DET
ejpam-5442	51	23	infection	infection	NOUN
ejpam-5442	51	24	.	.	PUNCT
ejpam-5442	52	1	many	many	ADJ
ejpam-5442	52	2	mathematicians	mathematician	NOUN
ejpam-5442	52	3	found	find	VERB
ejpam-5442	52	4	a	a	DET
ejpam-5442	52	5	challenging	challenging	NOUN
ejpam-5442	52	6	to	to	PART
ejpam-5442	52	7	create	create	VERB
ejpam-5442	52	8	numerical	numerical	ADJ
ejpam-5442	52	9	and	and	CCONJ
ejpam-5442	52	10	analytical	analytical	ADJ
ejpam-5442	52	11	solutions	solution	NOUN
ejpam-5442	52	12	for	for	ADP
ejpam-5442	52	13	the	the	DET
ejpam-5442	52	14	fdes	fde	NOUN
ejpam-5442	52	15	.	.	PUNCT
ejpam-5442	53	1	due	due	ADP
ejpam-5442	53	2	to	to	ADP
ejpam-5442	53	3	the	the	DET
ejpam-5442	53	4	lack	lack	NOUN
ejpam-5442	53	5	of	of	ADP
ejpam-5442	53	6	accurate	accurate	ADJ
ejpam-5442	53	7	solutions	solution	NOUN
ejpam-5442	53	8	for	for	ADP
ejpam-5442	53	9	many	many	ADJ
ejpam-5442	53	10	physical	physical	ADJ
ejpam-5442	53	11	problems	problem	NOUN
ejpam-5442	53	12	with	with	ADP
ejpam-5442	53	13	m.	m.	PROPN
ejpam-5442	53	14	adel	adel	PROPN
ejpam-5442	53	15	,	,	PUNCT
ejpam-5442	53	16	m.	m.	NOUN
ejpam-5442	53	17	m.	m.	NOUN
ejpam-5442	53	18	khader	khader	PROPN
ejpam-5442	53	19	,	,	PUNCT
ejpam-5442	53	20	n.	n.	PROPN
ejpam-5442	53	21	a.	a.	PROPN
ejpam-5442	53	22	mohammed	mohammed	PROPN
ejpam-5442	53	23	/	/	SYM
ejpam-5442	53	24	eur	eur	PROPN
ejpam-5442	53	25	.	.	PUNCT
ejpam-5442	54	1	j.	j.	PROPN
ejpam-5442	54	2	pure	pure	PROPN
ejpam-5442	54	3	appl	appl	PROPN
ejpam-5442	54	4	.	.	PROPN
ejpam-5442	54	5	math	math	PROPN
ejpam-5442	54	6	,	,	PUNCT
ejpam-5442	54	7	17	17	NUM
ejpam-5442	54	8	(	(	PUNCT
ejpam-5442	54	9	4	4	NUM
ejpam-5442	54	10	)	)	PUNCT
ejpam-5442	54	11	(	(	PUNCT
ejpam-5442	54	12	2024	2024	NUM
ejpam-5442	54	13	)	)	PUNCT
ejpam-5442	54	14	,	,	PUNCT
ejpam-5442	54	15	3277	3277	NUM
ejpam-5442	54	16	-	-	SYM
ejpam-5442	54	17	3290	3290	NUM
ejpam-5442	54	18	3279	3279	NUM
ejpam-5442	54	19	fractional	fractional	ADJ
ejpam-5442	54	20	models	model	NOUN
ejpam-5442	55	1	,	,	PUNCT
ejpam-5442	55	2	some	some	DET
ejpam-5442	55	3	academics	academic	NOUN
ejpam-5442	55	4	have	have	AUX
ejpam-5442	55	5	shown	show	VERB
ejpam-5442	55	6	a	a	DET
ejpam-5442	55	7	strong	strong	ADJ
ejpam-5442	55	8	interest	interest	NOUN
ejpam-5442	55	9	in	in	ADP
ejpam-5442	55	10	developing	develop	VERB
ejpam-5442	55	11	numerical	numerical	ADJ
ejpam-5442	55	12	solutions	solution	NOUN
ejpam-5442	55	13	for	for	ADP
ejpam-5442	55	14	the	the	DET
ejpam-5442	55	15	fdes	fde	NOUN
ejpam-5442	55	16	(	(	PUNCT
ejpam-5442	55	17	[	[	X
ejpam-5442	55	18	16],[17	16],[17	PROPN
ejpam-5442	55	19	]	]	X
ejpam-5442	55	20	)	)	PUNCT
ejpam-5442	55	21	.	.	PUNCT
ejpam-5442	56	1	the	the	DET
ejpam-5442	56	2	adams	adams	PROPN
ejpam-5442	56	3	-	-	PUNCT
ejpam-5442	56	4	bashforth	bashforth	NOUN
ejpam-5442	56	5	method	method	NOUN
ejpam-5442	56	6	,	,	PUNCT
ejpam-5442	56	7	incorporating	incorporate	VERB
ejpam-5442	56	8	the	the	DET
ejpam-5442	56	9	cf	cf	NOUN
ejpam-5442	56	10	operator	operator	NOUN
ejpam-5442	56	11	,	,	PUNCT
ejpam-5442	56	12	is	be	AUX
ejpam-5442	56	13	formulated	formulate	VERB
ejpam-5442	56	14	in	in	ADP
ejpam-5442	56	15	[	[	X
ejpam-5442	56	16	24	24	NUM
ejpam-5442	56	17	]	]	PUNCT
ejpam-5442	56	18	.	.	PUNCT
ejpam-5442	57	1	this	this	DET
ejpam-5442	57	2	method	method	NOUN
ejpam-5442	57	3	involves	involve	VERB
ejpam-5442	57	4	three	three	NUM
ejpam-5442	57	5	steps	step	NOUN
ejpam-5442	57	6	and	and	CCONJ
ejpam-5442	57	7	can	can	AUX
ejpam-5442	57	8	be	be	AUX
ejpam-5442	57	9	used	use	VERB
ejpam-5442	57	10	to	to	PART
ejpam-5442	57	11	solve	solve	VERB
ejpam-5442	57	12	both	both	CCONJ
ejpam-5442	57	13	linear	linear	ADJ
ejpam-5442	57	14	and	and	CCONJ
ejpam-5442	57	15	nonlinear	nonlinear	ADJ
ejpam-5442	57	16	fdes	fde	NOUN
ejpam-5442	57	17	.	.	PUNCT
ejpam-5442	58	1	additionally	additionally	ADV
ejpam-5442	58	2	,	,	PUNCT
ejpam-5442	58	3	it	it	PRON
ejpam-5442	58	4	possesses	possess	VERB
ejpam-5442	58	5	diverse	diverse	ADJ
ejpam-5442	58	6	uses	use	NOUN
ejpam-5442	58	7	in	in	ADP
ejpam-5442	58	8	resolving	resolve	VERB
ejpam-5442	58	9	chaotic	chaotic	ADJ
ejpam-5442	58	10	systems	system	NOUN
ejpam-5442	58	11	with	with	ADP
ejpam-5442	58	12	fractional	fractional	ADJ
ejpam-5442	58	13	orders	order	NOUN
ejpam-5442	58	14	.	.	PUNCT
ejpam-5442	59	1	the	the	DET
ejpam-5442	59	2	authors	author	NOUN
ejpam-5442	59	3	[	[	X
ejpam-5442	59	4	15	15	NUM
ejpam-5442	59	5	]	]	PUNCT
ejpam-5442	59	6	have	have	AUX
ejpam-5442	59	7	developed	develop	VERB
ejpam-5442	59	8	a	a	DET
ejpam-5442	59	9	trapezoidal	trapezoidal	ADJ
ejpam-5442	59	10	approach	approach	NOUN
ejpam-5442	59	11	for	for	ADP
ejpam-5442	59	12	the	the	DET
ejpam-5442	59	13	effective	effective	ADJ
ejpam-5442	59	14	resolution	resolution	NOUN
ejpam-5442	59	15	of	of	ADP
ejpam-5442	59	16	fractional	fractional	ADJ
ejpam-5442	59	17	differential	differential	ADJ
ejpam-5442	59	18	equations	equation	NOUN
ejpam-5442	59	19	(	(	PUNCT
ejpam-5442	59	20	fdes	fde	NOUN
ejpam-5442	59	21	)	)	PUNCT
ejpam-5442	59	22	.	.	PUNCT
ejpam-5442	60	1	this	this	DET
ejpam-5442	60	2	technique	technique	NOUN
ejpam-5442	60	3	utilizes	utilize	VERB
ejpam-5442	60	4	the	the	DET
ejpam-5442	60	5	cf	cf	NOUN
ejpam-5442	60	6	operator	operator	NOUN
ejpam-5442	60	7	and	and	CCONJ
ejpam-5442	60	8	achieves	achieve	VERB
ejpam-5442	60	9	a	a	DET
ejpam-5442	60	10	convergence	convergence	NOUN
ejpam-5442	60	11	order	order	NOUN
ejpam-5442	60	12	of	of	ADP
ejpam-5442	60	13	two	two	NUM
ejpam-5442	60	14	.	.	PUNCT
ejpam-5442	61	1	moreover	moreover	ADV
ejpam-5442	61	2	,	,	PUNCT
ejpam-5442	61	3	the	the	DET
ejpam-5442	61	4	convergence	convergence	NOUN
ejpam-5442	61	5	and	and	CCONJ
ejpam-5442	61	6	stability	stability	NOUN
ejpam-5442	61	7	of	of	ADP
ejpam-5442	61	8	this	this	DET
ejpam-5442	61	9	scheme	scheme	NOUN
ejpam-5442	61	10	have	have	AUX
ejpam-5442	61	11	been	be	AUX
ejpam-5442	61	12	thoroughly	thoroughly	ADV
ejpam-5442	61	13	investigated	investigate	VERB
ejpam-5442	61	14	.	.	PUNCT
ejpam-5442	62	1	here	here	ADV
ejpam-5442	62	2	in	in	ADP
ejpam-5442	62	3	this	this	DET
ejpam-5442	62	4	research	research	NOUN
ejpam-5442	62	5	,	,	PUNCT
ejpam-5442	62	6	we	we	PRON
ejpam-5442	62	7	implement	implement	VERB
ejpam-5442	62	8	simpson	simpson	PROPN
ejpam-5442	62	9	’s	’s	PART
ejpam-5442	62	10	1/3	1/3	NUM
ejpam-5442	62	11	approach	approach	NOUN
ejpam-5442	62	12	for	for	ADP
ejpam-5442	62	13	addressing	address	VERB
ejpam-5442	62	14	the	the	DET
ejpam-5442	62	15	fdes	fde	NOUN
ejpam-5442	62	16	via	via	ADP
ejpam-5442	62	17	the	the	DET
ejpam-5442	62	18	cf	cf	NOUN
ejpam-5442	62	19	-	-	PUNCT
ejpam-5442	62	20	derivative	derivative	NOUN
ejpam-5442	62	21	.	.	PUNCT
ejpam-5442	63	1	this	this	DET
ejpam-5442	63	2	method	method	NOUN
ejpam-5442	63	3	achieves	achieve	VERB
ejpam-5442	63	4	a	a	DET
ejpam-5442	63	5	high	high	ADJ
ejpam-5442	63	6	level	level	NOUN
ejpam-5442	63	7	of	of	ADP
ejpam-5442	63	8	accuracy	accuracy	NOUN
ejpam-5442	63	9	,	,	PUNCT
ejpam-5442	63	10	with	with	ADP
ejpam-5442	63	11	an	an	DET
ejpam-5442	63	12	order	order	NOUN
ejpam-5442	63	13	of	of	ADP
ejpam-5442	63	14	four	four	NUM
ejpam-5442	63	15	,	,	PUNCT
ejpam-5442	63	16	as	as	SCONJ
ejpam-5442	63	17	detailed	detailed	ADJ
ejpam-5442	63	18	in	in	ADP
ejpam-5442	63	19	our	our	PRON
ejpam-5442	63	20	work	work	NOUN
ejpam-5442	63	21	.	.	PUNCT
ejpam-5442	64	1	the	the	DET
ejpam-5442	64	2	proposed	propose	VERB
ejpam-5442	64	3	fractional	fractional	PROPN
ejpam-5442	64	4	simpson	simpson	PROPN
ejpam-5442	64	5	’s	’s	PART
ejpam-5442	64	6	1/3	1/3	NUM
ejpam-5442	64	7	approach	approach	NOUN
ejpam-5442	64	8	offers	offer	VERB
ejpam-5442	64	9	superior	superior	ADJ
ejpam-5442	64	10	accuracy	accuracy	NOUN
ejpam-5442	64	11	compared	compare	VERB
ejpam-5442	64	12	to	to	ADP
ejpam-5442	64	13	current	current	ADJ
ejpam-5442	64	14	methods	method	NOUN
ejpam-5442	64	15	and	and	CCONJ
ejpam-5442	64	16	is	be	AUX
ejpam-5442	64	17	straightforward	straightforward	ADJ
ejpam-5442	64	18	to	to	PART
ejpam-5442	64	19	implement	implement	VERB
ejpam-5442	64	20	.	.	PUNCT
ejpam-5442	65	1	the	the	DET
ejpam-5442	65	2	manuscript	manuscript	NOUN
ejpam-5442	65	3	is	be	AUX
ejpam-5442	65	4	structured	structure	VERB
ejpam-5442	65	5	as	as	SCONJ
ejpam-5442	65	6	follows	follow	VERB
ejpam-5442	65	7	:	:	PUNCT
ejpam-5442	65	8	section	section	NOUN
ejpam-5442	65	9	2	2	NUM
ejpam-5442	65	10	provides	provide	VERB
ejpam-5442	65	11	the	the	DET
ejpam-5442	65	12	first	first	ADJ
ejpam-5442	65	13	knowledge	knowledge	NOUN
ejpam-5442	65	14	concerning	concern	VERB
ejpam-5442	65	15	fractional	fractional	ADJ
ejpam-5442	65	16	order	order	NOUN
ejpam-5442	65	17	integrals	integral	NOUN
ejpam-5442	65	18	and	and	CCONJ
ejpam-5442	65	19	derivatives	derivative	NOUN
ejpam-5442	65	20	.	.	PUNCT
ejpam-5442	66	1	section	section	NOUN
ejpam-5442	66	2	3	3	NUM
ejpam-5442	66	3	delineates	delineate	VERB
ejpam-5442	66	4	the	the	DET
ejpam-5442	66	5	smoking	smoking	NOUN
ejpam-5442	66	6	system	system	NOUN
ejpam-5442	66	7	and	and	CCONJ
ejpam-5442	66	8	its	its	PRON
ejpam-5442	66	9	cf	cf	NOUN
ejpam-5442	66	10	-	-	PUNCT
ejpam-5442	66	11	fractional	fractional	ADJ
ejpam-5442	66	12	representation	representation	NOUN
ejpam-5442	66	13	.	.	PUNCT
ejpam-5442	67	1	section	section	NOUN
ejpam-5442	67	2	4	4	NUM
ejpam-5442	67	3	delineates	delineate	VERB
ejpam-5442	67	4	the	the	DET
ejpam-5442	67	5	derivation	derivation	NOUN
ejpam-5442	67	6	of	of	ADP
ejpam-5442	67	7	simpson	simpson	PROPN
ejpam-5442	67	8	’s	’s	PART
ejpam-5442	67	9	1/3	1/3	NUM
ejpam-5442	67	10	rule	rule	NOUN
ejpam-5442	67	11	for	for	ADP
ejpam-5442	67	12	the	the	DET
ejpam-5442	67	13	cf	cf	NOUN
ejpam-5442	67	14	-	-	PUNCT
ejpam-5442	67	15	fractional	fractional	ADJ
ejpam-5442	67	16	integral	integral	ADJ
ejpam-5442	67	17	.	.	PUNCT
ejpam-5442	67	18	section	section	NOUN
ejpam-5442	67	19	5	5	NUM
ejpam-5442	67	20	gives	give	VERB
ejpam-5442	67	21	the	the	DET
ejpam-5442	67	22	convergence	convergence	NOUN
ejpam-5442	67	23	analysis	analysis	NOUN
ejpam-5442	67	24	of	of	ADP
ejpam-5442	67	25	the	the	DET
ejpam-5442	67	26	proposed	propose	VERB
ejpam-5442	67	27	method	method	NOUN
ejpam-5442	67	28	.	.	PUNCT
ejpam-5442	68	1	section	section	NOUN
ejpam-5442	68	2	6	6	NUM
ejpam-5442	68	3	outlines	outline	VERB
ejpam-5442	68	4	the	the	DET
ejpam-5442	68	5	numerical	numerical	ADJ
ejpam-5442	68	6	implementation	implementation	NOUN
ejpam-5442	68	7	of	of	ADP
ejpam-5442	68	8	the	the	DET
ejpam-5442	68	9	proposed	propose	VERB
ejpam-5442	68	10	strategy	strategy	NOUN
ejpam-5442	68	11	for	for	ADP
ejpam-5442	68	12	addressing	address	VERB
ejpam-5442	68	13	the	the	DET
ejpam-5442	68	14	smoking	smoking	NOUN
ejpam-5442	68	15	system	system	NOUN
ejpam-5442	68	16	.	.	PUNCT
ejpam-5442	69	1	section	section	NOUN
ejpam-5442	69	2	7	7	NUM
ejpam-5442	69	3	presents	present	VERB
ejpam-5442	69	4	the	the	DET
ejpam-5442	69	5	results	result	NOUN
ejpam-5442	69	6	and	and	CCONJ
ejpam-5442	69	7	discussions	discussion	NOUN
ejpam-5442	69	8	of	of	ADP
ejpam-5442	69	9	the	the	DET
ejpam-5442	69	10	numerical	numerical	PROPN
ejpam-5442	69	11	simulation	simulation	PROPN
ejpam-5442	69	12	,	,	PUNCT
ejpam-5442	69	13	while	while	SCONJ
ejpam-5442	69	14	section	section	NOUN
ejpam-5442	69	15	8	8	NUM
ejpam-5442	69	16	provides	provide	VERB
ejpam-5442	69	17	the	the	DET
ejpam-5442	69	18	conclusions	conclusion	NOUN
ejpam-5442	69	19	.	.	PUNCT
ejpam-5442	70	1	2	2	X
ejpam-5442	70	2	.	.	NUM
ejpam-5442	70	3	preliminaries	preliminary	NOUN
ejpam-5442	70	4	fractional	fractional	ADJ
ejpam-5442	70	5	derivatives	derivative	NOUN
ejpam-5442	70	6	have	have	AUX
ejpam-5442	70	7	been	be	AUX
ejpam-5442	70	8	accurately	accurately	ADV
ejpam-5442	70	9	defined	define	VERB
ejpam-5442	70	10	by	by	ADP
ejpam-5442	70	11	mathematical	mathematical	ADJ
ejpam-5442	70	12	models	model	NOUN
ejpam-5442	70	13	employing	employ	VERB
ejpam-5442	70	14	a	a	DET
ejpam-5442	70	15	non	non	ADJ
ejpam-5442	70	16	-	-	ADJ
ejpam-5442	70	17	singular	singular	ADJ
ejpam-5442	70	18	kernel	kernel	NOUN
ejpam-5442	70	19	have	have	AUX
ejpam-5442	70	20	accurately	accurately	ADV
ejpam-5442	70	21	defined	define	VERB
ejpam-5442	70	22	fractional	fractional	ADJ
ejpam-5442	70	23	derivatives	derivative	NOUN
ejpam-5442	70	24	.	.	PUNCT
ejpam-5442	71	1	this	this	DET
ejpam-5442	71	2	method	method	NOUN
ejpam-5442	71	3	improves	improve	VERB
ejpam-5442	71	4	the	the	DET
ejpam-5442	71	5	system	system	NOUN
ejpam-5442	71	6	’s	’s	PART
ejpam-5442	71	7	capacity	capacity	NOUN
ejpam-5442	71	8	to	to	PART
ejpam-5442	71	9	precisely	precisely	ADV
ejpam-5442	71	10	depict	depict	VERB
ejpam-5442	71	11	and	and	CCONJ
ejpam-5442	71	12	record	record	NOUN
ejpam-5442	71	13	memory	memory	NOUN
ejpam-5442	71	14	effects	effect	NOUN
ejpam-5442	71	15	.	.	PUNCT
ejpam-5442	72	1	this	this	DET
ejpam-5442	72	2	definition	definition	NOUN
ejpam-5442	72	3	is	be	AUX
ejpam-5442	72	4	the	the	DET
ejpam-5442	72	5	most	most	ADV
ejpam-5442	72	6	significant	significant	ADJ
ejpam-5442	72	7	one	one	NUM
ejpam-5442	72	8	employed	employ	VERB
ejpam-5442	72	9	in	in	ADP
ejpam-5442	72	10	the	the	DET
ejpam-5442	72	11	development	development	NOUN
ejpam-5442	72	12	of	of	ADP
ejpam-5442	72	13	fractional	fractional	ADJ
ejpam-5442	72	14	calculus	calculus	NOUN
ejpam-5442	72	15	theory	theory	NOUN
ejpam-5442	72	16	[	[	X
ejpam-5442	72	17	9	9	NUM
ejpam-5442	72	18	]	]	PUNCT
ejpam-5442	72	19	.	.	PUNCT
ejpam-5442	73	1	this	this	DET
ejpam-5442	73	2	part	part	NOUN
ejpam-5442	73	3	provides	provide	VERB
ejpam-5442	73	4	a	a	DET
ejpam-5442	73	5	succinct	succinct	ADJ
ejpam-5442	73	6	overview	overview	NOUN
ejpam-5442	73	7	of	of	ADP
ejpam-5442	73	8	the	the	DET
ejpam-5442	73	9	fundamental	fundamental	ADJ
ejpam-5442	73	10	definitions	definition	NOUN
ejpam-5442	73	11	of	of	ADP
ejpam-5442	73	12	fractional	fractional	ADJ
ejpam-5442	73	13	calculus	calculus	NOUN
ejpam-5442	73	14	involving	involve	VERB
ejpam-5442	73	15	a	a	DET
ejpam-5442	73	16	non	non	ADJ
ejpam-5442	73	17	-	-	ADJ
ejpam-5442	73	18	singular	singular	ADJ
ejpam-5442	73	19	kernel	kernel	NOUN
ejpam-5442	73	20	.	.	PUNCT
ejpam-5442	74	1	definition	definition	NOUN
ejpam-5442	74	2	1	1	NUM
ejpam-5442	74	3	.	.	PUNCT
ejpam-5442	75	1	[	[	X
ejpam-5442	75	2	9	9	NUM
ejpam-5442	75	3	]	]	PUNCT
ejpam-5442	75	4	for	for	ADP
ejpam-5442	75	5	ψ(t	ψ(t	PROPN
ejpam-5442	75	6	)	)	PUNCT
ejpam-5442	75	7	∈	∈	PROPN
ejpam-5442	75	8	h1(0	h1(0	PROPN
ejpam-5442	75	9	,	,	PUNCT
ejpam-5442	75	10	a	a	PRON
ejpam-5442	75	11	)	)	PUNCT
ejpam-5442	75	12	,	,	PUNCT
ejpam-5442	75	13	0	0	PUNCT
ejpam-5442	75	14	<	<	X
ejpam-5442	75	15	γ	γ	X
ejpam-5442	75	16	<	<	X
ejpam-5442	75	17	1	1	NUM
ejpam-5442	75	18	.	.	PUNCT
ejpam-5442	76	1	then	then	ADV
ejpam-5442	76	2	the	the	DET
ejpam-5442	76	3	cf	cf	NOUN
ejpam-5442	76	4	fractional	fractional	ADJ
ejpam-5442	76	5	derivative	derivative	ADJ
ejpam-5442	76	6	cfdγψ(t	cfdγψ(t	NOUN
ejpam-5442	76	7	)	)	PUNCT
ejpam-5442	76	8	and	and	CCONJ
ejpam-5442	76	9	its	its	PRON
ejpam-5442	76	10	fi	fi	NOUN
ejpam-5442	76	11	cf	cf	NOUN
ejpam-5442	76	12	iγψ(t	iγψ(t	PROPN
ejpam-5442	76	13	)	)	PUNCT
ejpam-5442	76	14	,	,	PUNCT
ejpam-5442	76	15	respectively	respectively	ADV
ejpam-5442	76	16	are	be	AUX
ejpam-5442	76	17	given	give	VERB
ejpam-5442	76	18	as	as	SCONJ
ejpam-5442	76	19	follows	follow	VERB
ejpam-5442	76	20	:	:	PUNCT
ejpam-5442	76	21	cfdγψ(t	cfdγψ(t	NOUN
ejpam-5442	76	22	)	)	PUNCT
ejpam-5442	76	23	:	:	PUNCT
ejpam-5442	76	24	=	=	SYM
ejpam-5442	76	25	1	1	NUM
ejpam-5442	76	26	1−	1−	NUM
ejpam-5442	76	27	γ	γ	PROPN
ejpam-5442	76	28	∫	∫	PROPN
ejpam-5442	76	29	t	t	PROPN
ejpam-5442	76	30	0	0	NUM
ejpam-5442	76	31	exp	exp	NOUN
ejpam-5442	76	32	[	[	PUNCT
ejpam-5442	76	33	−	−	PROPN
ejpam-5442	76	34	γ	γ	NOUN
ejpam-5442	76	35	1−	1−	NUM
ejpam-5442	76	36	γ	γ	X
ejpam-5442	76	37	(	(	PUNCT
ejpam-5442	76	38	t−	t−	PROPN
ejpam-5442	76	39	τ	τ	PROPN
ejpam-5442	76	40	)	)	PUNCT
ejpam-5442	76	41	]	]	PUNCT
ejpam-5442	76	42	ψ̇(τ)dτ	ψ̇(τ)dτ	INTJ
ejpam-5442	76	43	,	,	PUNCT
ejpam-5442	76	44	cf	cf	X
ejpam-5442	76	45	iγψ(t	iγψ(t	PROPN
ejpam-5442	76	46	)	)	PUNCT
ejpam-5442	76	47	:	:	PUNCT
ejpam-5442	76	48	=	=	SYM
ejpam-5442	76	49	(	(	PUNCT
ejpam-5442	76	50	1−	1−	NUM
ejpam-5442	76	51	γ)ψ(t	γ)ψ(t	PROPN
ejpam-5442	76	52	)	)	PUNCT
ejpam-5442	77	1	+	+	CCONJ
ejpam-5442	77	2	γ	γ	PROPN
ejpam-5442	77	3	∫	∫	PROPN
ejpam-5442	77	4	t	t	PROPN
ejpam-5442	77	5	0	0	NUM
ejpam-5442	77	6	ψ(τ)dτ	ψ(τ)dτ	PROPN
ejpam-5442	77	7	.	.	PUNCT
ejpam-5442	78	1	(	(	PUNCT
ejpam-5442	78	2	1	1	NUM
ejpam-5442	78	3	)	)	PUNCT
ejpam-5442	78	4	3	3	NUM
ejpam-5442	78	5	.	.	X
ejpam-5442	79	1	description	description	NOUN
ejpam-5442	79	2	of	of	ADP
ejpam-5442	79	3	the	the	DET
ejpam-5442	79	4	fractional	fractional	ADJ
ejpam-5442	79	5	smoking	smoking	NOUN
ejpam-5442	79	6	system	system	NOUN
ejpam-5442	79	7	now	now	ADV
ejpam-5442	79	8	,	,	PUNCT
ejpam-5442	79	9	the	the	DET
ejpam-5442	79	10	suggested	suggest	VERB
ejpam-5442	79	11	approach	approach	NOUN
ejpam-5442	79	12	to	to	ADP
ejpam-5442	79	13	solving	solve	VERB
ejpam-5442	79	14	the	the	DET
ejpam-5442	79	15	fractional	fractional	ADJ
ejpam-5442	79	16	smoking	smoking	NOUN
ejpam-5442	79	17	model	model	NOUN
ejpam-5442	79	18	will	will	AUX
ejpam-5442	79	19	be	be	AUX
ejpam-5442	79	20	put	put	VERB
ejpam-5442	79	21	into	into	ADP
ejpam-5442	79	22	practice	practice	NOUN
ejpam-5442	79	23	.	.	PUNCT
ejpam-5442	80	1	because	because	SCONJ
ejpam-5442	80	2	mathematical	mathematical	ADJ
ejpam-5442	80	3	modeling	modeling	NOUN
ejpam-5442	80	4	has	have	AUX
ejpam-5442	80	5	been	be	AUX
ejpam-5442	80	6	an	an	DET
ejpam-5442	80	7	important	important	ADJ
ejpam-5442	80	8	tool	tool	NOUN
ejpam-5442	80	9	for	for	ADP
ejpam-5442	80	10	pandemic	pandemic	ADJ
ejpam-5442	80	11	grasp	grasp	NOUN
ejpam-5442	80	12	m.	m.	NOUN
ejpam-5442	80	13	adel	adel	PROPN
ejpam-5442	80	14	,	,	PUNCT
ejpam-5442	80	15	m.	m.	NOUN
ejpam-5442	80	16	m.	m.	NOUN
ejpam-5442	80	17	khader	khader	PROPN
ejpam-5442	80	18	,	,	PUNCT
ejpam-5442	80	19	n.	n.	PROPN
ejpam-5442	80	20	a.	a.	PROPN
ejpam-5442	80	21	mohammed	mohammed	PROPN
ejpam-5442	80	22	/	/	SYM
ejpam-5442	80	23	eur	eur	PROPN
ejpam-5442	80	24	.	.	PUNCT
ejpam-5442	81	1	j.	j.	PROPN
ejpam-5442	81	2	pure	pure	PROPN
ejpam-5442	81	3	appl	appl	PROPN
ejpam-5442	81	4	.	.	PROPN
ejpam-5442	81	5	math	math	PROPN
ejpam-5442	81	6	,	,	PUNCT
ejpam-5442	81	7	17	17	NUM
ejpam-5442	81	8	(	(	PUNCT
ejpam-5442	81	9	4	4	NUM
ejpam-5442	81	10	)	)	PUNCT
ejpam-5442	81	11	(	(	PUNCT
ejpam-5442	81	12	2024	2024	NUM
ejpam-5442	81	13	)	)	PUNCT
ejpam-5442	81	14	,	,	PUNCT
ejpam-5442	81	15	3277	3277	NUM
ejpam-5442	81	16	-	-	SYM
ejpam-5442	81	17	3290	3290	NUM
ejpam-5442	81	18	3280	3280	NUM
ejpam-5442	81	19	in	in	ADP
ejpam-5442	81	20	recent	recent	ADJ
ejpam-5442	81	21	decades	decade	NOUN
ejpam-5442	81	22	[	[	X
ejpam-5442	81	23	13	13	NUM
ejpam-5442	81	24	]	]	PUNCT
ejpam-5442	82	1	,	,	PUNCT
ejpam-5442	82	2	we	we	PRON
ejpam-5442	82	3	can	can	AUX
ejpam-5442	82	4	use	use	VERB
ejpam-5442	82	5	it	it	PRON
ejpam-5442	82	6	to	to	PART
ejpam-5442	82	7	stop	stop	VERB
ejpam-5442	82	8	the	the	DET
ejpam-5442	82	9	spread	spread	NOUN
ejpam-5442	82	10	of	of	ADP
ejpam-5442	82	11	tobacco	tobacco	NOUN
ejpam-5442	82	12	usage	usage	NOUN
ejpam-5442	82	13	.	.	PUNCT
ejpam-5442	83	1	the	the	DET
ejpam-5442	83	2	current	current	ADJ
ejpam-5442	83	3	study	study	NOUN
ejpam-5442	83	4	incorporates	incorporate	VERB
ejpam-5442	83	5	the	the	DET
ejpam-5442	83	6	improved	improved	ADJ
ejpam-5442	83	7	smoking	smoking	NOUN
ejpam-5442	83	8	model	model	NOUN
ejpam-5442	83	9	,	,	PUNCT
ejpam-5442	83	10	which	which	PRON
ejpam-5442	83	11	involves	involve	VERB
ejpam-5442	83	12	the	the	DET
ejpam-5442	83	13	cf	cf	NOUN
ejpam-5442	83	14	-	-	PUNCT
ejpam-5442	83	15	fractional	fractional	ADJ
ejpam-5442	83	16	derivative	derivative	NOUN
ejpam-5442	83	17	,	,	PUNCT
ejpam-5442	83	18	to	to	PART
ejpam-5442	83	19	enhance	enhance	VERB
ejpam-5442	83	20	the	the	DET
ejpam-5442	83	21	understanding	understanding	NOUN
ejpam-5442	83	22	of	of	ADP
ejpam-5442	83	23	both	both	DET
ejpam-5442	83	24	qualitative	qualitative	ADJ
ejpam-5442	83	25	and	and	CCONJ
ejpam-5442	83	26	numerical	numerical	ADJ
ejpam-5442	83	27	analysis	analysis	NOUN
ejpam-5442	83	28	[	[	X
ejpam-5442	83	29	6	6	NUM
ejpam-5442	83	30	]	]	PUNCT
ejpam-5442	83	31	.	.	PUNCT
ejpam-5442	84	1	cfdϱψ1(t	cfdϱψ1(t	VERB
ejpam-5442	84	2	)	)	PUNCT
ejpam-5442	85	1	=	=	SYM
ejpam-5442	85	2	σ	σ	NOUN
ejpam-5442	85	3	−	−	NOUN
ejpam-5442	85	4	ℓ1	ℓ1	NOUN
ejpam-5442	85	5	ψ1(t)ψ2(t	ψ1(t)ψ2(t	NOUN
ejpam-5442	85	6	)	)	PUNCT
ejpam-5442	85	7	+	+	CCONJ
ejpam-5442	85	8	γ	γ	X
ejpam-5442	85	9	ψ4(t)−	ψ4(t)−	PROPN
ejpam-5442	85	10	β	β	X
ejpam-5442	85	11	ψ1(t	ψ1(t	PROPN
ejpam-5442	85	12	)	)	PUNCT
ejpam-5442	85	13	,	,	PUNCT
ejpam-5442	85	14	ψ1(0	ψ1(0	PROPN
ejpam-5442	85	15	)	)	PUNCT
ejpam-5442	85	16	=	=	PUNCT
ejpam-5442	86	1	ψ0	ψ0	ADJ
ejpam-5442	86	2	1	1	NUM
ejpam-5442	86	3	,	,	PUNCT
ejpam-5442	86	4	cfdϱψ2(t	cfdϱψ2(t	NOUN
ejpam-5442	86	5	)	)	PUNCT
ejpam-5442	86	6	=	=	PUNCT
ejpam-5442	87	1	ℓ1	ℓ1	VERB
ejpam-5442	87	2	ψ1(t)ψ2(t)−	ψ1(t)ψ2(t)−	PROPN
ejpam-5442	87	3	ℓ2	ℓ2	PROPN
ejpam-5442	87	4	ψ2(t)ψ3(t)−	ψ2(t)ψ3(t)−	PROPN
ejpam-5442	87	5	(	(	PUNCT
ejpam-5442	87	6	σ1	σ1	PROPN
ejpam-5442	87	7	+	+	CCONJ
ejpam-5442	87	8	β)ψ2(t	β)ψ2(t	PROPN
ejpam-5442	87	9	)	)	PUNCT
ejpam-5442	87	10	,	,	PUNCT
ejpam-5442	87	11	ψ2(0	ψ2(0	NOUN
ejpam-5442	87	12	)	)	PUNCT
ejpam-5442	87	13	=	=	PUNCT
ejpam-5442	88	1	ψ0	ψ0	ADJ
ejpam-5442	88	2	2	2	NUM
ejpam-5442	88	3	,	,	PUNCT
ejpam-5442	88	4	cfdϱψ3(t	cfdϱψ3(t	ADV
ejpam-5442	88	5	)	)	PUNCT
ejpam-5442	89	1	=	=	SYM
ejpam-5442	89	2	ℓ2	ℓ2	PROPN
ejpam-5442	89	3	ψ2(t)ψ3(t)−	ψ2(t)ψ3(t)−	PROPN
ejpam-5442	89	4	(	(	PUNCT
ejpam-5442	89	5	θ	θ	PROPN
ejpam-5442	89	6	+	+	CCONJ
ejpam-5442	89	7	σ2	σ2	PROPN
ejpam-5442	89	8	+	+	CCONJ
ejpam-5442	89	9	β)ψ3(t	β)ψ3(t	NOUN
ejpam-5442	89	10	)	)	PUNCT
ejpam-5442	89	11	)	)	PUNCT
ejpam-5442	89	12	,	,	PUNCT
ejpam-5442	89	13	ψ3(0	ψ3(0	PROPN
ejpam-5442	89	14	)	)	PUNCT
ejpam-5442	89	15	=	=	PUNCT
ejpam-5442	89	16	ψ0	ψ0	ADJ
ejpam-5442	89	17	3	3	NUM
ejpam-5442	89	18	,	,	PUNCT
ejpam-5442	89	19	cfdϱψ4(t	cfdϱψ4(t	ADJ
ejpam-5442	89	20	)	)	PUNCT
ejpam-5442	89	21	=	=	SYM
ejpam-5442	89	22	θ	θ	X
ejpam-5442	89	23	ψ3(t)−	ψ3(t)−	PUNCT
ejpam-5442	89	24	(	(	PUNCT
ejpam-5442	89	25	α+	α+	X
ejpam-5442	89	26	β	β	X
ejpam-5442	89	27	+	+	CCONJ
ejpam-5442	89	28	γ)ψ4(t	γ)ψ4(t	PROPN
ejpam-5442	89	29	)	)	PUNCT
ejpam-5442	89	30	,	,	PUNCT
ejpam-5442	89	31	ψ4(0	ψ4(0	NOUN
ejpam-5442	89	32	)	)	PUNCT
ejpam-5442	89	33	=	=	SYM
ejpam-5442	89	34	ψ0	ψ0	ADJ
ejpam-5442	89	35	4	4	NUM
ejpam-5442	89	36	,	,	PUNCT
ejpam-5442	89	37	cfdϱψ5(t	cfdϱψ5(t	NUM
ejpam-5442	89	38	)	)	PUNCT
ejpam-5442	89	39	=	=	SYM
ejpam-5442	89	40	αψ4(t)−	αψ4(t)−	PROPN
ejpam-5442	89	41	β	β	X
ejpam-5442	89	42	ψ5(t	ψ5(t	NOUN
ejpam-5442	89	43	)	)	PUNCT
ejpam-5442	89	44	,	,	PUNCT
ejpam-5442	89	45	ψ5(0	ψ5(0	NOUN
ejpam-5442	89	46	)	)	PUNCT
ejpam-5442	89	47	=	=	SYM
ejpam-5442	90	1	ψ0	ψ0	ADJ
ejpam-5442	90	2	5	5	NUM
ejpam-5442	90	3	.	.	PUNCT
ejpam-5442	91	1	(	(	PUNCT
ejpam-5442	91	2	2	2	X
ejpam-5442	91	3	)	)	PUNCT
ejpam-5442	91	4	this	this	DET
ejpam-5442	91	5	concept	concept	NOUN
ejpam-5442	91	6	classifies	classify	VERB
ejpam-5442	91	7	the	the	DET
ejpam-5442	91	8	total	total	ADJ
ejpam-5442	91	9	population	population	NOUN
ejpam-5442	91	10	into	into	ADP
ejpam-5442	91	11	5	5	NUM
ejpam-5442	91	12	categories	category	NOUN
ejpam-5442	91	13	,	,	PUNCT
ejpam-5442	91	14	denoted	denote	VERB
ejpam-5442	91	15	as	as	ADP
ejpam-5442	91	16	ψ1	ψ1	NOUN
ejpam-5442	91	17	,	,	PUNCT
ejpam-5442	91	18	ψ2	ψ2	NOUN
ejpam-5442	91	19	,	,	PUNCT
ejpam-5442	91	20	ψ3	ψ3	NOUN
ejpam-5442	91	21	,	,	PUNCT
ejpam-5442	91	22	ψ4	ψ4	NOUN
ejpam-5442	91	23	,	,	PUNCT
ejpam-5442	91	24	and	and	CCONJ
ejpam-5442	91	25	ψ5	ψ5	PROPN
ejpam-5442	91	26	,	,	PUNCT
ejpam-5442	91	27	representing	represent	VERB
ejpam-5442	91	28	vulnerable	vulnerable	ADJ
ejpam-5442	91	29	smokers	smoker	NOUN
ejpam-5442	91	30	,	,	PUNCT
ejpam-5442	91	31	individuals	individual	NOUN
ejpam-5442	91	32	who	who	PRON
ejpam-5442	91	33	ingest	ingest	VERB
ejpam-5442	91	34	tobacco	tobacco	NOUN
ejpam-5442	91	35	,	,	PUNCT
ejpam-5442	91	36	occasional	occasional	ADJ
ejpam-5442	91	37	smokers	smoker	NOUN
ejpam-5442	91	38	,	,	PUNCT
ejpam-5442	91	39	regular	regular	ADJ
ejpam-5442	91	40	smokers	smoker	NOUN
ejpam-5442	91	41	,	,	PUNCT
ejpam-5442	91	42	and	and	CCONJ
ejpam-5442	91	43	individuals	individual	NOUN
ejpam-5442	91	44	who	who	PRON
ejpam-5442	91	45	have	have	AUX
ejpam-5442	91	46	quit	quit	VERB
ejpam-5442	91	47	smoking	smoking	NOUN
ejpam-5442	91	48	at	at	ADP
ejpam-5442	91	49	a	a	DET
ejpam-5442	91	50	specific	specific	ADJ
ejpam-5442	91	51	time	time	NOUN
ejpam-5442	91	52	.	.	PUNCT
ejpam-5442	92	1	the	the	DET
ejpam-5442	92	2	description	description	NOUN
ejpam-5442	92	3	of	of	ADP
ejpam-5442	92	4	the	the	DET
ejpam-5442	92	5	constants	constant	NOUN
ejpam-5442	92	6	in	in	ADP
ejpam-5442	92	7	the	the	DET
ejpam-5442	92	8	system	system	NOUN
ejpam-5442	92	9	(	(	PUNCT
ejpam-5442	92	10	2	2	X
ejpam-5442	92	11	)	)	PUNCT
ejpam-5442	92	12	are	be	AUX
ejpam-5442	92	13	stated	state	VERB
ejpam-5442	92	14	as	as	SCONJ
ejpam-5442	92	15	follows	follow	VERB
ejpam-5442	92	16	:	:	PUNCT
ejpam-5442	92	17	(	(	PUNCT
ejpam-5442	92	18	i	i	NOUN
ejpam-5442	92	19	)	)	PUNCT
ejpam-5442	92	20	σ	σ	PROPN
ejpam-5442	92	21	is	be	AUX
ejpam-5442	92	22	the	the	DET
ejpam-5442	92	23	rate	rate	NOUN
ejpam-5442	92	24	at	at	ADP
ejpam-5442	92	25	which	which	PRON
ejpam-5442	92	26	individuals	individual	NOUN
ejpam-5442	92	27	are	be	AUX
ejpam-5442	92	28	recruited	recruit	VERB
ejpam-5442	92	29	through	through	ADP
ejpam-5442	92	30	migration	migration	NOUN
ejpam-5442	92	31	or	or	CCONJ
ejpam-5442	92	32	birth	birth	NOUN
ejpam-5442	92	33	;	;	PUNCT
ejpam-5442	92	34	(	(	PUNCT
ejpam-5442	92	35	ii	ii	NOUN
ejpam-5442	92	36	)	)	PUNCT
ejpam-5442	92	37	ℓ1	ℓ1	NOUN
ejpam-5442	92	38	is	be	AUX
ejpam-5442	92	39	the	the	DET
ejpam-5442	92	40	rate	rate	NOUN
ejpam-5442	92	41	at	at	ADP
ejpam-5442	92	42	which	which	PRON
ejpam-5442	92	43	the	the	DET
ejpam-5442	92	44	vulnerable	vulnerable	ADJ
ejpam-5442	92	45	population	population	NOUN
ejpam-5442	92	46	transitions	transition	NOUN
ejpam-5442	92	47	into	into	ADP
ejpam-5442	92	48	the	the	DET
ejpam-5442	92	49	snuffing	snuff	VERB
ejpam-5442	92	50	class	class	NOUN
ejpam-5442	92	51	;	;	PUNCT
ejpam-5442	92	52	(	(	PUNCT
ejpam-5442	92	53	iii	iii	X
ejpam-5442	92	54	)	)	PUNCT
ejpam-5442	92	55	ℓ2	ℓ2	NOUN
ejpam-5442	92	56	is	be	AUX
ejpam-5442	92	57	the	the	DET
ejpam-5442	92	58	frequency	frequency	NOUN
ejpam-5442	92	59	of	of	ADP
ejpam-5442	92	60	snuffing	snuff	VERB
ejpam-5442	92	61	increases	increase	NOUN
ejpam-5442	92	62	among	among	ADP
ejpam-5442	92	63	occasional	occasional	ADJ
ejpam-5442	92	64	smokers	smoker	NOUN
ejpam-5442	92	65	;	;	PUNCT
ejpam-5442	92	66	(	(	PUNCT
ejpam-5442	92	67	iv	iv	X
ejpam-5442	92	68	)	)	PUNCT
ejpam-5442	92	69	θ	θ	PROPN
ejpam-5442	92	70	is	be	AUX
ejpam-5442	92	71	the	the	DET
ejpam-5442	92	72	conversion	conversion	NOUN
ejpam-5442	92	73	rate	rate	NOUN
ejpam-5442	92	74	of	of	ADP
ejpam-5442	92	75	occasional	occasional	ADJ
ejpam-5442	92	76	smokers	smoker	NOUN
ejpam-5442	92	77	transitioning	transition	VERB
ejpam-5442	92	78	to	to	ADP
ejpam-5442	92	79	regular	regular	ADJ
ejpam-5442	92	80	smoking	smoking	NOUN
ejpam-5442	92	81	;	;	PUNCT
ejpam-5442	92	82	(	(	PUNCT
ejpam-5442	92	83	v	v	NOUN
ejpam-5442	92	84	)	)	PUNCT
ejpam-5442	92	85	α	α	PROPN
ejpam-5442	92	86	,	,	PUNCT
ejpam-5442	92	87	β	β	X
ejpam-5442	92	88	,	,	PUNCT
ejpam-5442	92	89	γ	γ	NOUN
ejpam-5442	92	90	are	be	AUX
ejpam-5442	92	91	the	the	DET
ejpam-5442	92	92	rates	rate	NOUN
ejpam-5442	92	93	of	of	ADP
ejpam-5442	92	94	departure	departure	NOUN
ejpam-5442	92	95	,	,	PUNCT
ejpam-5442	92	96	natural	natural	ADJ
ejpam-5442	92	97	mortality	mortality	NOUN
ejpam-5442	92	98	,	,	PUNCT
ejpam-5442	92	99	and	and	CCONJ
ejpam-5442	92	100	recovery	recovery	NOUN
ejpam-5442	92	101	,	,	PUNCT
ejpam-5442	92	102	respectively	respectively	ADV
ejpam-5442	92	103	;	;	PUNCT
ejpam-5442	92	104	(	(	PUNCT
ejpam-5442	92	105	vi	vi	NOUN
ejpam-5442	92	106	)	)	PUNCT
ejpam-5442	92	107	σ1	σ1	PROPN
ejpam-5442	92	108	,	,	PUNCT
ejpam-5442	92	109	σ2	σ2	PROPN
ejpam-5442	92	110	are	be	AUX
ejpam-5442	92	111	the	the	DET
ejpam-5442	92	112	mortality	mortality	NOUN
ejpam-5442	92	113	rate	rate	NOUN
ejpam-5442	92	114	among	among	ADP
ejpam-5442	92	115	individuals	individual	NOUN
ejpam-5442	92	116	who	who	PRON
ejpam-5442	92	117	use	use	VERB
ejpam-5442	92	118	snuff	snuff	NOUN
ejpam-5442	92	119	and	and	CCONJ
ejpam-5442	92	120	the	the	DET
ejpam-5442	92	121	mortality	mortality	NOUN
ejpam-5442	92	122	rate	rate	NOUN
ejpam-5442	92	123	caused	cause	VERB
ejpam-5442	92	124	by	by	ADP
ejpam-5442	92	125	smoking	smoking	NOUN
ejpam-5442	92	126	,	,	PUNCT
ejpam-5442	92	127	respectively	respectively	ADV
ejpam-5442	92	128	.	.	PUNCT
ejpam-5442	93	1	4	4	X
ejpam-5442	93	2	.	.	X
ejpam-5442	93	3	derivation	derivation	NOUN
ejpam-5442	93	4	simpson’s-1/3	simpson’s-1/3	NUM
ejpam-5442	93	5	rule	rule	NOUN
ejpam-5442	93	6	for	for	ADP
ejpam-5442	93	7	cf	cf	NOUN
ejpam-5442	93	8	-	-	PUNCT
ejpam-5442	93	9	fractional	fractional	ADJ
ejpam-5442	93	10	integral	integral	ADJ
ejpam-5442	93	11	this	this	DET
ejpam-5442	93	12	section	section	NOUN
ejpam-5442	93	13	presents	present	VERB
ejpam-5442	93	14	the	the	DET
ejpam-5442	93	15	formulation	formulation	NOUN
ejpam-5442	93	16	of	of	ADP
ejpam-5442	93	17	the	the	DET
ejpam-5442	93	18	fractional	fractional	ADJ
ejpam-5442	93	19	simpson’s-1/3	simpson’s-1/3	ADJ
ejpam-5442	93	20	strategy	strategy	NOUN
ejpam-5442	93	21	(	(	PUNCT
ejpam-5442	93	22	fsr	fsr	PROPN
ejpam-5442	93	23	)	)	PUNCT
ejpam-5442	93	24	for	for	ADP
ejpam-5442	93	25	solving	solve	VERB
ejpam-5442	93	26	cf	cf	NOUN
ejpam-5442	93	27	-	-	PUNCT
ejpam-5442	93	28	fdes	fde	NOUN
ejpam-5442	93	29	[	[	X
ejpam-5442	93	30	8	8	NUM
ejpam-5442	93	31	]	]	PUNCT
ejpam-5442	93	32	.	.	PUNCT
ejpam-5442	94	1	this	this	DET
ejpam-5442	94	2	aim	aim	NOUN
ejpam-5442	94	3	will	will	AUX
ejpam-5442	94	4	be	be	AUX
ejpam-5442	94	5	achieved	achieve	VERB
ejpam-5442	94	6	through	through	ADP
ejpam-5442	94	7	the	the	DET
ejpam-5442	94	8	following	follow	VERB
ejpam-5442	94	9	steps	step	NOUN
ejpam-5442	94	10	:	:	PUNCT
ejpam-5442	94	11	(	(	PUNCT
ejpam-5442	94	12	i	i	NOUN
ejpam-5442	94	13	)	)	PUNCT
ejpam-5442	94	14	considering	consider	VERB
ejpam-5442	94	15	the	the	DET
ejpam-5442	94	16	subsequent	subsequent	ADJ
ejpam-5442	94	17	γ	γ	NOUN
ejpam-5442	94	18	-	-	PUNCT
ejpam-5442	94	19	order	order	NOUN
ejpam-5442	94	20	ivp	ivp	NOUN
ejpam-5442	94	21	:	:	PUNCT
ejpam-5442	94	22	cfdγu(t	cfdγu(t	ADJ
ejpam-5442	94	23	)	)	PUNCT
ejpam-5442	94	24	=	=	SYM
ejpam-5442	94	25	f(u(t	f(u(t	PROPN
ejpam-5442	94	26	)	)	PUNCT
ejpam-5442	94	27	)	)	PUNCT
ejpam-5442	94	28	,	,	PUNCT
ejpam-5442	94	29	u(0	u(0	PROPN
ejpam-5442	94	30	)	)	PUNCT
ejpam-5442	94	31	=	=	PUNCT
ejpam-5442	95	1	u0	u0	ADJ
ejpam-5442	95	2	.	.	PUNCT
ejpam-5442	96	1	(	(	PUNCT
ejpam-5442	96	2	3	3	NUM
ejpam-5442	96	3	)	)	PUNCT
ejpam-5442	96	4	(	(	PUNCT
ejpam-5442	96	5	ii	ii	NOUN
ejpam-5442	96	6	)	)	PUNCT
ejpam-5442	96	7	applying	apply	VERB
ejpam-5442	96	8	the	the	DET
ejpam-5442	96	9	cf	cf	NOUN
ejpam-5442	96	10	-	-	PUNCT
ejpam-5442	96	11	fractional	fractional	ADJ
ejpam-5442	96	12	integral	integral	ADJ
ejpam-5442	96	13	operator	operator	NOUN
ejpam-5442	96	14	on	on	ADP
ejpam-5442	96	15	the	the	DET
ejpam-5442	96	16	ivp	ivp	NOUN
ejpam-5442	96	17	(	(	PUNCT
ejpam-5442	96	18	3	3	NUM
ejpam-5442	96	19	)	)	PUNCT
ejpam-5442	96	20	and	and	CCONJ
ejpam-5442	96	21	applying	apply	VERB
ejpam-5442	96	22	proposition	proposition	NOUN
ejpam-5442	96	23	3	3	NUM
ejpam-5442	96	24	in	in	ADP
ejpam-5442	96	25	[	[	X
ejpam-5442	96	26	1	1	NUM
ejpam-5442	96	27	]	]	PUNCT
ejpam-5442	96	28	and	and	CCONJ
ejpam-5442	96	29	formula	formula	NOUN
ejpam-5442	96	30	(	(	PUNCT
ejpam-5442	96	31	1	1	NUM
ejpam-5442	96	32	)	)	PUNCT
ejpam-5442	96	33	,	,	PUNCT
ejpam-5442	96	34	we	we	PRON
ejpam-5442	96	35	get	get	VERB
ejpam-5442	96	36	:	:	PUNCT
ejpam-5442	96	37	u(t	u(t	NOUN
ejpam-5442	96	38	)	)	PUNCT
ejpam-5442	96	39	=	=	PUNCT
ejpam-5442	97	1	u0	u0	ADJ
ejpam-5442	97	2	+	+	CCONJ
ejpam-5442	97	3	cf	cf	NOUN
ejpam-5442	97	4	iγf	iγf	NOUN
ejpam-5442	97	5	(	(	PUNCT
ejpam-5442	97	6	u(t	u(t	PROPN
ejpam-5442	97	7	)	)	PUNCT
ejpam-5442	97	8	)	)	PUNCT
ejpam-5442	98	1	=	=	PUNCT
ejpam-5442	98	2	u0	u0	ADJ
ejpam-5442	98	3	+	+	X
ejpam-5442	98	4	(	(	PUNCT
ejpam-5442	98	5	1−	1−	NUM
ejpam-5442	98	6	γ)f(u(t	γ)f(u(t	NOUN
ejpam-5442	98	7	)	)	PUNCT
ejpam-5442	98	8	)	)	PUNCT
ejpam-5442	99	1	+	+	CCONJ
ejpam-5442	99	2	γ	γ	PROPN
ejpam-5442	99	3	∫	∫	PROPN
ejpam-5442	99	4	t	t	PROPN
ejpam-5442	99	5	0	0	NUM
ejpam-5442	99	6	f(u(s))ds	f(u(s))ds	PROPN
ejpam-5442	99	7	.	.	PUNCT
ejpam-5442	100	1	(	(	PUNCT
ejpam-5442	100	2	4	4	NUM
ejpam-5442	100	3	)	)	PUNCT
ejpam-5442	100	4	(	(	PUNCT
ejpam-5442	100	5	iii	iii	NOUN
ejpam-5442	100	6	)	)	PUNCT
ejpam-5442	100	7	initially	initially	ADV
ejpam-5442	100	8	,	,	PUNCT
ejpam-5442	100	9	we	we	PRON
ejpam-5442	100	10	will	will	AUX
ejpam-5442	100	11	employ	employ	VERB
ejpam-5442	100	12	a	a	DET
ejpam-5442	100	13	quadratic	quadratic	ADJ
ejpam-5442	100	14	polynomial	polynomial	ADJ
ejpam-5442	100	15	p2	p2	NOUN
ejpam-5442	100	16	to	to	PART
ejpam-5442	100	17	estimate	estimate	VERB
ejpam-5442	100	18	the	the	DET
ejpam-5442	100	19	integral	integral	ADJ
ejpam-5442	100	20	function	function	NOUN
ejpam-5442	100	21	f	f	PROPN
ejpam-5442	100	22	in	in	ADP
ejpam-5442	100	23	equation	equation	NOUN
ejpam-5442	100	24	(	(	PUNCT
ejpam-5442	100	25	4	4	NUM
ejpam-5442	100	26	)	)	PUNCT
ejpam-5442	100	27	.	.	PUNCT
ejpam-5442	101	1	the	the	DET
ejpam-5442	101	2	function	function	NOUN
ejpam-5442	101	3	will	will	AUX
ejpam-5442	101	4	be	be	AUX
ejpam-5442	101	5	assessed	assess	VERB
ejpam-5442	101	6	at	at	ADP
ejpam-5442	101	7	t0	t0	PROPN
ejpam-5442	101	8	,	,	PUNCT
ejpam-5442	101	9	t1	t1	NOUN
ejpam-5442	101	10	,	,	PUNCT
ejpam-5442	101	11	and	and	CCONJ
ejpam-5442	101	12	t2	t2	NOUN
ejpam-5442	101	13	,	,	PUNCT
ejpam-5442	101	14	where	where	SCONJ
ejpam-5442	101	15	t0	t0	PROPN
ejpam-5442	101	16	is	be	AUX
ejpam-5442	101	17	less	less	ADJ
ejpam-5442	101	18	than	than	ADP
ejpam-5442	101	19	m.	m.	PROPN
ejpam-5442	101	20	adel	adel	PROPN
ejpam-5442	101	21	,	,	PUNCT
ejpam-5442	101	22	m.	m.	NOUN
ejpam-5442	101	23	m.	m.	NOUN
ejpam-5442	101	24	khader	khader	PROPN
ejpam-5442	101	25	,	,	PUNCT
ejpam-5442	101	26	n.	n.	PROPN
ejpam-5442	101	27	a.	a.	PROPN
ejpam-5442	101	28	mohammed	mohammed	PROPN
ejpam-5442	101	29	/	/	SYM
ejpam-5442	101	30	eur	eur	PROPN
ejpam-5442	101	31	.	.	PUNCT
ejpam-5442	102	1	j.	j.	PROPN
ejpam-5442	102	2	pure	pure	PROPN
ejpam-5442	102	3	appl	appl	PROPN
ejpam-5442	102	4	.	.	PROPN
ejpam-5442	102	5	math	math	PROPN
ejpam-5442	102	6	,	,	PUNCT
ejpam-5442	102	7	17	17	NUM
ejpam-5442	102	8	(	(	PUNCT
ejpam-5442	102	9	4	4	NUM
ejpam-5442	102	10	)	)	PUNCT
ejpam-5442	102	11	(	(	PUNCT
ejpam-5442	102	12	2024	2024	NUM
ejpam-5442	102	13	)	)	PUNCT
ejpam-5442	102	14	,	,	PUNCT
ejpam-5442	102	15	3277	3277	NUM
ejpam-5442	102	16	-	-	SYM
ejpam-5442	102	17	3290	3290	NUM
ejpam-5442	102	18	3281	3281	NUM
ejpam-5442	102	19	t1	t1	NOUN
ejpam-5442	102	20	and	and	CCONJ
ejpam-5442	102	21	t1	t1	NOUN
ejpam-5442	102	22	is	be	AUX
ejpam-5442	102	23	less	less	ADJ
ejpam-5442	102	24	than	than	ADP
ejpam-5442	102	25	t2	t2	NOUN
ejpam-5442	102	26	.	.	PUNCT
ejpam-5442	103	1	the	the	DET
ejpam-5442	103	2	interval	interval	NOUN
ejpam-5442	103	3	is	be	AUX
ejpam-5442	103	4	partitioned	partition	VERB
ejpam-5442	103	5	into	into	ADP
ejpam-5442	103	6	two	two	NUM
ejpam-5442	103	7	subintervals	subinterval	NOUN
ejpam-5442	103	8	,	,	PUNCT
ejpam-5442	103	9	denoted	denote	VERB
ejpam-5442	103	10	as	as	ADP
ejpam-5442	103	11	t1	t1	NOUN
ejpam-5442	103	12	−	−	PROPN
ejpam-5442	103	13	t0	t0	PROPN
ejpam-5442	103	14	=	=	SYM
ejpam-5442	103	15	t2	t2	PROPN
ejpam-5442	103	16	−	−	PROPN
ejpam-5442	103	17	t1	t1	NOUN
ejpam-5442	103	18	=	=	SYM
ejpam-5442	103	19	h	h	NOUN
ejpam-5442	103	20	,	,	PUNCT
ejpam-5442	103	21	resulting	result	VERB
ejpam-5442	103	22	in	in	ADP
ejpam-5442	103	23	a	a	DET
ejpam-5442	103	24	combined	combine	VERB
ejpam-5442	103	25	width	width	NOUN
ejpam-5442	103	26	of	of	ADP
ejpam-5442	103	27	2h	2h	NUM
ejpam-5442	103	28	.	.	PUNCT
ejpam-5442	104	1	the	the	DET
ejpam-5442	104	2	integration	integration	NOUN
ejpam-5442	104	3	of	of	ADP
ejpam-5442	104	4	the	the	DET
ejpam-5442	104	5	quadratic	quadratic	ADJ
ejpam-5442	104	6	polynomial	polynomial	ADJ
ejpam-5442	104	7	p2	p2	NOUN
ejpam-5442	104	8	can	can	AUX
ejpam-5442	104	9	be	be	AUX
ejpam-5442	104	10	computed	compute	VERB
ejpam-5442	104	11	as	as	SCONJ
ejpam-5442	104	12	follows	follow	VERB
ejpam-5442	104	13	:	:	PUNCT
ejpam-5442	104	14	i2f(u(t	i2f(u(t	NOUN
ejpam-5442	104	15	)	)	PUNCT
ejpam-5442	104	16	)	)	PUNCT
ejpam-5442	105	1	=	=	SYM
ejpam-5442	105	2	∫	∫	PROPN
ejpam-5442	105	3	b	b	PROPN
ejpam-5442	105	4	a	a	DET
ejpam-5442	105	5	f(u(t))dt	f(u(t))dt	NOUN
ejpam-5442	106	1	≈	≈	PROPN
ejpam-5442	106	2	∫	∫	PROPN
ejpam-5442	106	3	t2	t2	PROPN
ejpam-5442	106	4	t0	t0	PROPN
ejpam-5442	106	5	p2(u(t))dt	p2(u(t))dt	PUNCT
ejpam-5442	107	1	=	=	SYM
ejpam-5442	107	2	∫	∫	PROPN
ejpam-5442	107	3	t2	t2	PROPN
ejpam-5442	107	4	t0	t0	PROPN
ejpam-5442	107	5			PROPN
ejpam-5442	107	6	2∑	2∑	NUM
ejpam-5442	107	7	j=0	j=0	PROPN
ejpam-5442	107	8	lj(t	lj(t	PUNCT
ejpam-5442	107	9	)	)	PUNCT
ejpam-5442	107	10	f	f	PROPN
ejpam-5442	107	11	(	(	PUNCT
ejpam-5442	107	12	u	u	NOUN
ejpam-5442	107	13	(	(	PUNCT
ejpam-5442	107	14	tj	tj	NOUN
ejpam-5442	107	15	)	)	PUNCT
ejpam-5442	107	16	)	)	PUNCT
ejpam-5442	107	17			NOUN
ejpam-5442	107	18	dt	dt	PROPN
ejpam-5442	107	19	,	,	PUNCT
ejpam-5442	107	20	where	where	SCONJ
ejpam-5442	107	21	the	the	DET
ejpam-5442	107	22	second	second	ADJ
ejpam-5442	107	23	-	-	PUNCT
ejpam-5442	107	24	order	order	NOUN
ejpam-5442	107	25	lagrange	lagrange	NOUN
ejpam-5442	107	26	polynomials	polynomial	NOUN
ejpam-5442	107	27	l0(t	l0(t	NOUN
ejpam-5442	107	28	)	)	PUNCT
ejpam-5442	107	29	,	,	PUNCT
ejpam-5442	107	30	l1(t	l1(t	PROPN
ejpam-5442	107	31	)	)	PUNCT
ejpam-5442	107	32	,	,	PUNCT
ejpam-5442	107	33	and	and	CCONJ
ejpam-5442	107	34	l2(t	l2(t	PROPN
ejpam-5442	107	35	)	)	PUNCT
ejpam-5442	107	36	are	be	AUX
ejpam-5442	107	37	defined	define	VERB
ejpam-5442	107	38	as	as	SCONJ
ejpam-5442	107	39	follows	follow	VERB
ejpam-5442	107	40	:	:	PUNCT
ejpam-5442	107	41	lj(t	lj(t	PUNCT
ejpam-5442	107	42	)	)	PUNCT
ejpam-5442	108	1	=	=	SYM
ejpam-5442	109	1	2∏	2∏	NUM
ejpam-5442	109	2	i=0	i=0	PROPN
ejpam-5442	109	3	,	,	PUNCT
ejpam-5442	109	4	i	i	PRON
ejpam-5442	109	5	̸=	̸=	PROPN
ejpam-5442	109	6	j	j	PROPN
ejpam-5442	109	7	(	(	PUNCT
ejpam-5442	109	8	t−	t−	PROPN
ejpam-5442	109	9	ti	ti	NOUN
ejpam-5442	109	10	)	)	PUNCT
ejpam-5442	109	11	(	(	PUNCT
ejpam-5442	109	12	tj	tj	NOUN
ejpam-5442	109	13	−	−	NOUN
ejpam-5442	109	14	ti	ti	NOUN
ejpam-5442	109	15	)	)	PUNCT
ejpam-5442	109	16	.	.	PUNCT
ejpam-5442	110	1	(	(	PUNCT
ejpam-5442	110	2	iv	iv	X
ejpam-5442	110	3	)	)	PUNCT
ejpam-5442	110	4	integrating	integrate	VERB
ejpam-5442	110	5	the	the	DET
ejpam-5442	110	6	first	first	ADJ
ejpam-5442	110	7	interpolant	interpolant	NOUN
ejpam-5442	110	8	function	function	NOUN
ejpam-5442	110	9	l0(t	l0(t	PROPN
ejpam-5442	110	10	)	)	PUNCT
ejpam-5442	110	11	,	,	PUNCT
ejpam-5442	110	12	by	by	ADP
ejpam-5442	110	13	taking	take	VERB
ejpam-5442	110	14	h	h	NOUN
ejpam-5442	110	15	=	=	NOUN
ejpam-5442	110	16	t2−t0	t2−t0	NUM
ejpam-5442	110	17	2	2	NUM
ejpam-5442	110	18	and	and	CCONJ
ejpam-5442	110	19	substituting	substitute	VERB
ejpam-5442	110	20	”	"	PUNCT
ejpam-5442	110	21	t	t	PROPN
ejpam-5442	110	22	=	=	PUNCT
ejpam-5442	110	23	s+	s+	NUM
ejpam-5442	110	24	t0	t0	PROPN
ejpam-5442	110	25	”	"	PUNCT
ejpam-5442	110	26	,	,	PUNCT
ejpam-5442	110	27	gives	give	VERB
ejpam-5442	110	28	us:∫	us:∫	ADP
ejpam-5442	110	29	t2	t2	NOUN
ejpam-5442	110	30	t0	t0	PROPN
ejpam-5442	110	31	l0(t)dt	l0(t)dt	X
ejpam-5442	111	1	=	=	SYM
ejpam-5442	111	2	1	1	NUM
ejpam-5442	111	3	2h2	2h2	NUM
ejpam-5442	111	4	∫	∫	PROPN
ejpam-5442	111	5	t0	t0	PROPN
ejpam-5442	112	1	+	+	PROPN
ejpam-5442	112	2	2h	2h	NUM
ejpam-5442	112	3	t0	t0	NOUN
ejpam-5442	112	4	(	(	PUNCT
ejpam-5442	112	5	t−	t−	PROPN
ejpam-5442	112	6	t1	t1	NOUN
ejpam-5442	112	7	)	)	PUNCT
ejpam-5442	112	8	(	(	PUNCT
ejpam-5442	112	9	t−	t−	PROPN
ejpam-5442	112	10	t2	t2	NOUN
ejpam-5442	112	11	)	)	PUNCT
ejpam-5442	112	12	dt	dt	NOUN
ejpam-5442	113	1	=	=	NOUN
ejpam-5442	113	2	1	1	NUM
ejpam-5442	113	3	2h2	2h2	NUM
ejpam-5442	113	4	∫	∫	PROPN
ejpam-5442	113	5	2h	2h	NUM
ejpam-5442	113	6	0	0	PUNCT
ejpam-5442	113	7	(	(	PUNCT
ejpam-5442	113	8	s+	s+	NUM
ejpam-5442	113	9	t0	t0	PROPN
ejpam-5442	113	10	−	−	PROPN
ejpam-5442	113	11	t2	t2	PROPN
ejpam-5442	113	12	)	)	PUNCT
ejpam-5442	113	13	(	(	PUNCT
ejpam-5442	113	14	s+	s+	NUM
ejpam-5442	114	1	t0	t0	PROPN
ejpam-5442	114	2	−	−	PROPN
ejpam-5442	114	3	t1	t1	NOUN
ejpam-5442	114	4	)	)	PUNCT
ejpam-5442	114	5	ds	ds	NOUN
ejpam-5442	114	6	=	=	SYM
ejpam-5442	114	7	1	1	NUM
ejpam-5442	114	8	2h2	2h2	NUM
ejpam-5442	114	9	∫	∫	PROPN
ejpam-5442	114	10	2h	2h	NUM
ejpam-5442	114	11	0	0	PUNCT
ejpam-5442	114	12	(	(	PUNCT
ejpam-5442	114	13	s−	s−	PROPN
ejpam-5442	114	14	2h)(s−	2h)(s−	NUM
ejpam-5442	114	15	h)ds	h)ds	PROPN
ejpam-5442	114	16	=	=	SYM
ejpam-5442	114	17	h	h	NOUN
ejpam-5442	114	18	3	3	NUM
ejpam-5442	114	19	.	.	PUNCT
ejpam-5442	115	1	after	after	ADP
ejpam-5442	115	2	making	make	VERB
ejpam-5442	115	3	some	some	DET
ejpam-5442	115	4	simplifications	simplification	NOUN
ejpam-5442	115	5	to	to	ADP
ejpam-5442	115	6	the	the	DET
ejpam-5442	115	7	rest	rest	NOUN
ejpam-5442	115	8	of	of	ADP
ejpam-5442	115	9	the	the	DET
ejpam-5442	115	10	terms	term	NOUN
ejpam-5442	115	11	,	,	PUNCT
ejpam-5442	115	12	we	we	PRON
ejpam-5442	115	13	have	have	VERB
ejpam-5442	115	14	the	the	DET
ejpam-5442	115	15	following	follow	VERB
ejpam-5442	115	16	:	:	PUNCT
ejpam-5442	115	17	i2(f	i2(f	X
ejpam-5442	115	18	)	)	PUNCT
ejpam-5442	115	19	=	=	SYM
ejpam-5442	115	20	h	h	NOUN
ejpam-5442	115	21	3	3	NUM
ejpam-5442	116	1	[	[	X
ejpam-5442	116	2	f	f	X
ejpam-5442	116	3	(	(	PUNCT
ejpam-5442	116	4	u	u	PROPN
ejpam-5442	116	5	(	(	PUNCT
ejpam-5442	116	6	t0	t0	NOUN
ejpam-5442	116	7	)	)	PUNCT
ejpam-5442	116	8	)	)	PUNCT
ejpam-5442	117	1	+	+	CCONJ
ejpam-5442	117	2	4f	4f	NUM
ejpam-5442	117	3	(	(	PUNCT
ejpam-5442	117	4	u	u	NOUN
ejpam-5442	117	5	(	(	PUNCT
ejpam-5442	117	6	t1	t1	NOUN
ejpam-5442	117	7	)	)	PUNCT
ejpam-5442	117	8	)	)	PUNCT
ejpam-5442	118	1	+	+	CCONJ
ejpam-5442	118	2	f	f	X
ejpam-5442	118	3	(	(	PUNCT
ejpam-5442	118	4	u	u	NOUN
ejpam-5442	118	5	(	(	PUNCT
ejpam-5442	118	6	t2	t2	PROPN
ejpam-5442	118	7	)	)	PUNCT
ejpam-5442	118	8	)	)	PUNCT
ejpam-5442	118	9	]	]	PUNCT
ejpam-5442	118	10	.	.	PUNCT
ejpam-5442	119	1	(	(	PUNCT
ejpam-5442	119	2	v	v	NOUN
ejpam-5442	119	3	)	)	PUNCT
ejpam-5442	119	4	by	by	ADP
ejpam-5442	119	5	substituting	substitute	VERB
ejpam-5442	119	6	in	in	ADP
ejpam-5442	119	7	the	the	DET
ejpam-5442	119	8	equation	equation	NOUN
ejpam-5442	119	9	(	(	PUNCT
ejpam-5442	119	10	4	4	NUM
ejpam-5442	119	11	)	)	PUNCT
ejpam-5442	119	12	,	,	PUNCT
ejpam-5442	119	13	we	we	PRON
ejpam-5442	119	14	get	get	VERB
ejpam-5442	119	15	:	:	PUNCT
ejpam-5442	119	16	u	u	NOUN
ejpam-5442	119	17	(	(	PUNCT
ejpam-5442	119	18	tn	tn	NOUN
ejpam-5442	119	19	)	)	PUNCT
ejpam-5442	119	20	=	=	SYM
ejpam-5442	119	21	u0+(1−γ)f	u0+(1−γ)f	PROPN
ejpam-5442	119	22	(	(	PUNCT
ejpam-5442	119	23	u	u	NOUN
ejpam-5442	119	24	(	(	PUNCT
ejpam-5442	119	25	tn))+	tn))+	NOUN
ejpam-5442	119	26	h	h	NOUN
ejpam-5442	119	27	3	3	NUM
ejpam-5442	119	28	γ	γ	X
ejpam-5442	119	29	[	[	X
ejpam-5442	119	30	f	f	X
ejpam-5442	119	31	(	(	PUNCT
ejpam-5442	119	32	u	u	PROPN
ejpam-5442	119	33	(	(	PUNCT
ejpam-5442	119	34	t0	t0	NOUN
ejpam-5442	119	35	)	)	PUNCT
ejpam-5442	119	36	)	)	PUNCT
ejpam-5442	120	1	+	+	CCONJ
ejpam-5442	120	2	4f	4f	NUM
ejpam-5442	120	3	(	(	PUNCT
ejpam-5442	120	4	u	u	NOUN
ejpam-5442	120	5	(	(	PUNCT
ejpam-5442	120	6	t1	t1	NOUN
ejpam-5442	120	7	)	)	PUNCT
ejpam-5442	120	8	)	)	PUNCT
ejpam-5442	121	1	+	+	CCONJ
ejpam-5442	121	2	f	f	X
ejpam-5442	121	3	(	(	PUNCT
ejpam-5442	121	4	u	u	NOUN
ejpam-5442	121	5	(	(	PUNCT
ejpam-5442	121	6	t2	t2	PROPN
ejpam-5442	121	7	)	)	PUNCT
ejpam-5442	121	8	)	)	PUNCT
ejpam-5442	121	9	]	]	PUNCT
ejpam-5442	121	10	,	,	PUNCT
ejpam-5442	121	11	n	n	NOUN
ejpam-5442	121	12	=	=	SYM
ejpam-5442	121	13	0	0	NUM
ejpam-5442	121	14	,	,	PUNCT
ejpam-5442	121	15	1	1	NUM
ejpam-5442	121	16	,	,	PUNCT
ejpam-5442	121	17	2	2	NUM
ejpam-5442	121	18	.	.	PUNCT
ejpam-5442	121	19	(	(	PUNCT
ejpam-5442	121	20	vi	vi	NOUN
ejpam-5442	121	21	)	)	PUNCT
ejpam-5442	121	22	to	to	PART
ejpam-5442	121	23	improve	improve	VERB
ejpam-5442	121	24	the	the	DET
ejpam-5442	121	25	accuracy	accuracy	NOUN
ejpam-5442	121	26	of	of	ADP
ejpam-5442	121	27	numerical	numerical	ADJ
ejpam-5442	121	28	integration	integration	NOUN
ejpam-5442	121	29	,	,	PUNCT
ejpam-5442	121	30	we	we	PRON
ejpam-5442	121	31	partition	partition	VERB
ejpam-5442	121	32	[	[	X
ejpam-5442	121	33	a	a	X
ejpam-5442	121	34	,	,	PUNCT
ejpam-5442	121	35	b	b	NOUN
ejpam-5442	121	36	]	]	X
ejpam-5442	121	37	to	to	ADP
ejpam-5442	121	38	n	n	PROPN
ejpam-5442	121	39	subintervals	subinterval	NOUN
ejpam-5442	121	40	as	as	SCONJ
ejpam-5442	121	41	follows	follow	VERB
ejpam-5442	121	42	:	:	PUNCT
ejpam-5442	121	43	for	for	ADP
ejpam-5442	121	44	any	any	DET
ejpam-5442	121	45	even	even	ADJ
ejpam-5442	121	46	number	number	NOUN
ejpam-5442	121	47	n	n	CCONJ
ejpam-5442	121	48	≥	≥	NOUN
ejpam-5442	121	49	2	2	NUM
ejpam-5442	121	50	,	,	PUNCT
ejpam-5442	121	51	we	we	PRON
ejpam-5442	121	52	establish	establish	VERB
ejpam-5442	121	53	the	the	DET
ejpam-5442	121	54	following	follow	VERB
ejpam-5442	121	55	definitions	definition	NOUN
ejpam-5442	121	56	:	:	PUNCT
ejpam-5442	121	57	h	h	NOUN
ejpam-5442	121	58	=	=	PUNCT
ejpam-5442	121	59	b−	b−	PROPN
ejpam-5442	121	60	a	a	PRON
ejpam-5442	121	61	n	n	NOUN
ejpam-5442	121	62	=	=	SYM
ejpam-5442	121	63	tk+1	tk+1	NUM
ejpam-5442	121	64	−	−	PROPN
ejpam-5442	121	65	tk	tk	PROPN
ejpam-5442	121	66	,	,	PUNCT
ejpam-5442	121	67	k	k	PROPN
ejpam-5442	121	68	=	=	SYM
ejpam-5442	121	69	0	0	NUM
ejpam-5442	121	70	,	,	PUNCT
ejpam-5442	121	71	1	1	NUM
ejpam-5442	121	72	,	,	PUNCT
ejpam-5442	121	73	2	2	NUM
ejpam-5442	121	74	,	,	PUNCT
ejpam-5442	121	75	.	.	PUNCT
ejpam-5442	121	76	.	.	PUNCT
ejpam-5442	122	1	.	.	PUNCT
ejpam-5442	123	1	,	,	PUNCT
ejpam-5442	123	2	n.	n.	PROPN
ejpam-5442	123	3	now	now	ADV
ejpam-5442	123	4	,	,	PUNCT
ejpam-5442	123	5	by	by	ADP
ejpam-5442	123	6	using	use	VERB
ejpam-5442	123	7	the	the	DET
ejpam-5442	123	8	quadrature	quadrature	NOUN
ejpam-5442	123	9	rule	rule	NOUN
ejpam-5442	123	10	for	for	ADP
ejpam-5442	123	11	each	each	DET
ejpam-5442	123	12	pair	pair	NOUN
ejpam-5442	123	13	of	of	ADP
ejpam-5442	123	14	subintervals	subinterval	NOUN
ejpam-5442	123	15	and	and	CCONJ
ejpam-5442	123	16	implementing	implement	VERB
ejpam-5442	123	17	the	the	DET
ejpam-5442	123	18	simpson’s-1/3	simpson’s-1/3	ADJ
ejpam-5442	123	19	rule	rule	NOUN
ejpam-5442	123	20	to	to	ADP
ejpam-5442	123	21	each	each	PRON
ejpam-5442	123	22	[	[	PUNCT
ejpam-5442	123	23	t2k	t2k	PROPN
ejpam-5442	123	24	,	,	PUNCT
ejpam-5442	123	25	t2(k+1	t2(k+1	PROPN
ejpam-5442	123	26	)	)	PUNCT
ejpam-5442	123	27	]	]	PUNCT
ejpam-5442	123	28	,	,	PUNCT
ejpam-5442	123	29	k	k	X
ejpam-5442	123	30	=	=	SYM
ejpam-5442	123	31	0	0	NUM
ejpam-5442	123	32	,	,	PUNCT
ejpam-5442	123	33	1	1	NUM
ejpam-5442	123	34	,	,	PUNCT
ejpam-5442	123	35	2	2	NUM
ejpam-5442	123	36	,	,	PUNCT
ejpam-5442	123	37	.	.	PUNCT
ejpam-5442	123	38	.	.	PUNCT
ejpam-5442	124	1	.	.	PUNCT
ejpam-5442	125	1	,	,	PUNCT
ejpam-5442	125	2	n−2	n−2	PROPN
ejpam-5442	125	3	2	2	NUM
ejpam-5442	125	4	,	,	PUNCT
ejpam-5442	125	5	we	we	PRON
ejpam-5442	125	6	can	can	AUX
ejpam-5442	125	7	appoint	appoint	VERB
ejpam-5442	125	8	the	the	DET
ejpam-5442	125	9	following	follow	VERB
ejpam-5442	125	10	formula	formula	NOUN
ejpam-5442	125	11	:	:	PUNCT
ejpam-5442	125	12	in(f	in(f	X
ejpam-5442	125	13	)	)	PUNCT
ejpam-5442	126	1	=	=	SYM
ejpam-5442	126	2	n−2	n−2	PROPN
ejpam-5442	126	3	2∑	2∑	X
ejpam-5442	126	4	k=0	k=0	PROPN
ejpam-5442	126	5	∫	∫	PROPN
ejpam-5442	127	1	t2k+2	t2k+2	PROPN
ejpam-5442	127	2	t2k	t2k	NOUN
ejpam-5442	127	3	f(u(t))dt	f(u(t))dt	NOUN
ejpam-5442	128	1	=	=	SYM
ejpam-5442	128	2	n−2	n−2	PROPN
ejpam-5442	128	3	2∑	2∑	NUM
ejpam-5442	128	4	k=0	k=0	PROPN
ejpam-5442	128	5	(	(	PUNCT
ejpam-5442	128	6	h	h	NOUN
ejpam-5442	128	7	3	3	NUM
ejpam-5442	129	1	[	[	X
ejpam-5442	129	2	f	f	X
ejpam-5442	129	3	(	(	PUNCT
ejpam-5442	129	4	u	u	PROPN
ejpam-5442	129	5	(	(	PUNCT
ejpam-5442	129	6	t2k	t2k	PROPN
ejpam-5442	129	7	)	)	PUNCT
ejpam-5442	129	8	)	)	PUNCT
ejpam-5442	130	1	+	+	CCONJ
ejpam-5442	130	2	4f	4f	NUM
ejpam-5442	130	3	(	(	PUNCT
ejpam-5442	130	4	u	u	NOUN
ejpam-5442	130	5	(	(	PUNCT
ejpam-5442	130	6	t2k+1	t2k+1	NOUN
ejpam-5442	130	7	)	)	PUNCT
ejpam-5442	130	8	)	)	PUNCT
ejpam-5442	131	1	+	+	CCONJ
ejpam-5442	131	2	f	f	X
ejpam-5442	131	3	(	(	PUNCT
ejpam-5442	131	4	u	u	NOUN
ejpam-5442	131	5	(	(	PUNCT
ejpam-5442	131	6	t2k+2	t2k+2	NOUN
ejpam-5442	131	7	)	)	PUNCT
ejpam-5442	131	8	)	)	PUNCT
ejpam-5442	131	9	]	]	PUNCT
ejpam-5442	131	10	)	)	PUNCT
ejpam-5442	131	11	.	.	PUNCT
ejpam-5442	132	1	m.	m.	PROPN
ejpam-5442	132	2	adel	adel	PROPN
ejpam-5442	132	3	,	,	PUNCT
ejpam-5442	132	4	m.	m.	NOUN
ejpam-5442	132	5	m.	m.	NOUN
ejpam-5442	132	6	khader	khader	PROPN
ejpam-5442	132	7	,	,	PUNCT
ejpam-5442	132	8	n.	n.	PROPN
ejpam-5442	132	9	a.	a.	PROPN
ejpam-5442	132	10	mohammed	mohammed	PROPN
ejpam-5442	132	11	/	/	SYM
ejpam-5442	132	12	eur	eur	PROPN
ejpam-5442	132	13	.	.	PUNCT
ejpam-5442	133	1	j.	j.	PROPN
ejpam-5442	133	2	pure	pure	PROPN
ejpam-5442	133	3	appl	appl	PROPN
ejpam-5442	133	4	.	.	PROPN
ejpam-5442	133	5	math	math	PROPN
ejpam-5442	133	6	,	,	PUNCT
ejpam-5442	133	7	17	17	NUM
ejpam-5442	133	8	(	(	PUNCT
ejpam-5442	133	9	4	4	NUM
ejpam-5442	133	10	)	)	PUNCT
ejpam-5442	133	11	(	(	PUNCT
ejpam-5442	133	12	2024	2024	NUM
ejpam-5442	133	13	)	)	PUNCT
ejpam-5442	133	14	,	,	PUNCT
ejpam-5442	133	15	3277	3277	NUM
ejpam-5442	133	16	-	-	SYM
ejpam-5442	133	17	3290	3290	NUM
ejpam-5442	133	18	3282	3282	NUM
ejpam-5442	133	19	(	(	PUNCT
ejpam-5442	133	20	vii	vii	PROPN
ejpam-5442	133	21	)	)	PUNCT
ejpam-5442	133	22	by	by	ADP
ejpam-5442	133	23	referring	refer	VERB
ejpam-5442	133	24	uj	uj	PROPN
ejpam-5442	133	25	as	as	ADP
ejpam-5442	133	26	the	the	DET
ejpam-5442	133	27	approximate	approximate	ADJ
ejpam-5442	133	28	solution	solution	NOUN
ejpam-5442	133	29	of	of	ADP
ejpam-5442	133	30	u	u	PROPN
ejpam-5442	133	31	(	(	PUNCT
ejpam-5442	133	32	tj	tj	NOUN
ejpam-5442	133	33	)	)	PUNCT
ejpam-5442	133	34	and	and	CCONJ
ejpam-5442	133	35	using	use	VERB
ejpam-5442	133	36	eq.(4	eq.(4	PRON
ejpam-5442	133	37	)	)	PUNCT
ejpam-5442	134	1	,	,	PUNCT
ejpam-5442	134	2	we	we	PRON
ejpam-5442	134	3	can	can	AUX
ejpam-5442	134	4	write	write	VERB
ejpam-5442	134	5	the	the	DET
ejpam-5442	134	6	fsr	fsr	PROPN
ejpam-5442	134	7	for	for	ADP
ejpam-5442	134	8	the	the	DET
ejpam-5442	134	9	cf	cf	NOUN
ejpam-5442	134	10	-	-	PUNCT
ejpam-5442	134	11	fde	fde	NOUN
ejpam-5442	134	12	(	(	PUNCT
ejpam-5442	134	13	3	3	NUM
ejpam-5442	134	14	)	)	PUNCT
ejpam-5442	134	15	,	,	PUNCT
ejpam-5442	134	16	for	for	ADP
ejpam-5442	134	17	j	j	PROPN
ejpam-5442	134	18	=	=	PUNCT
ejpam-5442	134	19	0(1)(n−	0(1)(n−	VERB
ejpam-5442	135	1	1	1	NUM
ejpam-5442	135	2	):	):	PUNCT
ejpam-5442	135	3	uj+1	uj+1	X
ejpam-5442	135	4	=	=	PUNCT
ejpam-5442	135	5	u0	u0	NOUN
ejpam-5442	135	6	+	+	CCONJ
ejpam-5442	135	7	(	(	PUNCT
ejpam-5442	135	8	1−	1−	NUM
ejpam-5442	135	9	γ)f	γ)f	ADJ
ejpam-5442	135	10	(	(	PUNCT
ejpam-5442	135	11	uj+1	uj+1	NUM
ejpam-5442	135	12	)	)	PUNCT
ejpam-5442	135	13	+	+	CCONJ
ejpam-5442	136	1	γ	γ	X
ejpam-5442	136	2	h	h	NOUN
ejpam-5442	136	3	3	3	NUM
ejpam-5442	136	4	[	[	PUNCT
ejpam-5442	136	5	f	f	X
ejpam-5442	136	6	(	(	PUNCT
ejpam-5442	136	7	u	u	PROPN
ejpam-5442	136	8	(	(	PUNCT
ejpam-5442	136	9	t0	t0	NOUN
ejpam-5442	136	10	)	)	PUNCT
ejpam-5442	136	11	)	)	PUNCT
ejpam-5442	137	1	+	+	CCONJ
ejpam-5442	137	2	4	4	NUM
ejpam-5442	137	3	j∑	j∑	NOUN
ejpam-5442	137	4	i=2,4,6	i=2,4,6	NUM
ejpam-5442	137	5	f	f	X
ejpam-5442	137	6	(	(	PUNCT
ejpam-5442	137	7	u	u	NOUN
ejpam-5442	137	8	(	(	PUNCT
ejpam-5442	137	9	ti	ti	NOUN
ejpam-5442	137	10	)	)	PUNCT
ejpam-5442	137	11	)	)	PUNCT
ejpam-5442	138	1	+	+	CCONJ
ejpam-5442	138	2	2	2	NUM
ejpam-5442	138	3	j−1∑	j−1∑	NOUN
ejpam-5442	138	4	j=1,3,5	j=1,3,5	X
ejpam-5442	138	5	f	f	X
ejpam-5442	138	6	(	(	PUNCT
ejpam-5442	138	7	u	u	NOUN
ejpam-5442	138	8	(	(	PUNCT
ejpam-5442	138	9	tj	tj	NOUN
ejpam-5442	138	10	)	)	PUNCT
ejpam-5442	138	11	)	)	PUNCT
ejpam-5442	139	1	+	+	CCONJ
ejpam-5442	139	2	f	f	X
ejpam-5442	139	3	(	(	PUNCT
ejpam-5442	139	4	u	u	NOUN
ejpam-5442	139	5	(	(	PUNCT
ejpam-5442	139	6	tj+1	tj+1	PROPN
ejpam-5442	139	7	)	)	PUNCT
ejpam-5442	139	8	)	)	PUNCT
ejpam-5442	139	9	]	]	PUNCT
ejpam-5442	139	10	.	.	PUNCT
ejpam-5442	140	1	this	this	DET
ejpam-5442	140	2	formula	formula	NOUN
ejpam-5442	140	3	can	can	AUX
ejpam-5442	140	4	be	be	AUX
ejpam-5442	140	5	rewritten	rewrite	VERB
ejpam-5442	140	6	in	in	ADP
ejpam-5442	140	7	a	a	DET
ejpam-5442	140	8	compact	compact	ADJ
ejpam-5442	140	9	form	form	NOUN
ejpam-5442	140	10	as	as	SCONJ
ejpam-5442	140	11	follows	follow	VERB
ejpam-5442	140	12	:	:	PUNCT
ejpam-5442	140	13	uj+1	uj+1	NUM
ejpam-5442	140	14	=	=	PUNCT
ejpam-5442	140	15	u0	u0	ADJ
ejpam-5442	140	16	+	+	CCONJ
ejpam-5442	140	17	(	(	PUNCT
ejpam-5442	140	18	1−	1−	NUM
ejpam-5442	140	19	γ	γ	X
ejpam-5442	140	20	)	)	PUNCT
ejpam-5442	140	21	f	f	NOUN
ejpam-5442	140	22	(	(	PUNCT
ejpam-5442	140	23	uj+1	uj+1	PROPN
ejpam-5442	140	24	)	)	PUNCT
ejpam-5442	140	25	+	+	CCONJ
ejpam-5442	140	26	γ	γ	PROPN
ejpam-5442	140	27	h	h	NOUN
ejpam-5442	140	28	j+1∑	j+1∑	PROPN
ejpam-5442	140	29	r=0	r=0	PROPN
ejpam-5442	140	30	ξr	ξr	PROPN
ejpam-5442	140	31	f	f	PROPN
ejpam-5442	140	32	(	(	PUNCT
ejpam-5442	140	33	ur	ur	INTJ
ejpam-5442	140	34	)	)	PUNCT
ejpam-5442	140	35	,	,	PUNCT
ejpam-5442	140	36	j	j	PROPN
ejpam-5442	141	1	=	=	SYM
ejpam-5442	141	2	0	0	NUM
ejpam-5442	141	3	,	,	PUNCT
ejpam-5442	141	4	1	1	NUM
ejpam-5442	141	5	,	,	PUNCT
ejpam-5442	141	6	2	2	NUM
ejpam-5442	141	7	,	,	PUNCT
ejpam-5442	141	8	.	.	PUNCT
ejpam-5442	141	9	.	.	PUNCT
ejpam-5442	142	1	.	.	PUNCT
ejpam-5442	143	1	,	,	PUNCT
ejpam-5442	143	2	n−	n−	NOUN
ejpam-5442	143	3	1	1	NUM
ejpam-5442	143	4	,	,	PUNCT
ejpam-5442	143	5	(	(	PUNCT
ejpam-5442	143	6	5	5	NUM
ejpam-5442	143	7	)	)	PUNCT
ejpam-5442	143	8	where	where	SCONJ
ejpam-5442	143	9	ξr	ξr	PROPN
ejpam-5442	143	10	are	be	AUX
ejpam-5442	143	11	the	the	DET
ejpam-5442	143	12	weights	weight	NOUN
ejpam-5442	143	13	of	of	ADP
ejpam-5442	143	14	the	the	DET
ejpam-5442	143	15	fsr	fsr	NOUN
ejpam-5442	143	16	and	and	CCONJ
ejpam-5442	143	17	are	be	AUX
ejpam-5442	143	18	defined	define	VERB
ejpam-5442	143	19	as	as	ADP
ejpam-5442	143	20	:	:	PUNCT
ejpam-5442	143	21	ξr	ξr	X
ejpam-5442	143	22	=	=	SYM
ejpam-5442	143	23			PROPN
ejpam-5442	143	24	1/3	1/3	NUM
ejpam-5442	143	25	,	,	PUNCT
ejpam-5442	143	26	r	r	NOUN
ejpam-5442	143	27	=	=	SYM
ejpam-5442	143	28	0	0	NUM
ejpam-5442	143	29	,	,	PUNCT
ejpam-5442	143	30	n+	n+	PUNCT
ejpam-5442	143	31	1	1	NUM
ejpam-5442	143	32	,	,	PUNCT
ejpam-5442	143	33	2/3	2/3	NUM
ejpam-5442	143	34	,	,	PUNCT
ejpam-5442	143	35	r	r	NOUN
ejpam-5442	143	36	=	=	SYM
ejpam-5442	143	37	1	1	NUM
ejpam-5442	143	38	,	,	PUNCT
ejpam-5442	143	39	3	3	NUM
ejpam-5442	143	40	,	,	PUNCT
ejpam-5442	143	41	5	5	NUM
ejpam-5442	143	42	,	,	PUNCT
ejpam-5442	143	43	.	.	PUNCT
ejpam-5442	143	44	.	.	PUNCT
ejpam-5442	144	1	.	.	PUNCT
ejpam-5442	145	1	,	,	PUNCT
ejpam-5442	145	2	4/3	4/3	NUM
ejpam-5442	145	3	,	,	PUNCT
ejpam-5442	145	4	r	r	NOUN
ejpam-5442	145	5	=	=	SYM
ejpam-5442	145	6	2	2	NUM
ejpam-5442	145	7	,	,	PUNCT
ejpam-5442	145	8	4	4	NUM
ejpam-5442	145	9	,	,	PUNCT
ejpam-5442	145	10	6	6	NUM
ejpam-5442	145	11	,	,	PUNCT
ejpam-5442	145	12	.	.	PUNCT
ejpam-5442	145	13	.	.	PUNCT
ejpam-5442	145	14	.	.	PUNCT
ejpam-5442	145	15	.	.	PUNCT
ejpam-5442	146	1	5	5	X
ejpam-5442	146	2	.	.	X
ejpam-5442	146	3	convergence	convergence	NOUN
ejpam-5442	146	4	analysis	analysis	NOUN
ejpam-5442	146	5	in	in	ADP
ejpam-5442	146	6	this	this	DET
ejpam-5442	146	7	section	section	NOUN
ejpam-5442	146	8	,	,	PUNCT
ejpam-5442	146	9	we	we	PRON
ejpam-5442	146	10	are	be	AUX
ejpam-5442	146	11	going	go	VERB
ejpam-5442	146	12	to	to	PART
ejpam-5442	146	13	collect	collect	VERB
ejpam-5442	146	14	some	some	DET
ejpam-5442	146	15	theorems	theorem	NOUN
ejpam-5442	146	16	concerning	concern	VERB
ejpam-5442	146	17	the	the	DET
ejpam-5442	146	18	stability	stability	NOUN
ejpam-5442	146	19	and	and	CCONJ
ejpam-5442	146	20	error	error	NOUN
ejpam-5442	146	21	analysis	analysis	NOUN
ejpam-5442	146	22	of	of	ADP
ejpam-5442	146	23	the	the	DET
ejpam-5442	146	24	given	give	VERB
ejpam-5442	146	25	ivp	ivp	PROPN
ejpam-5442	146	26	(	(	PUNCT
ejpam-5442	146	27	3	3	NUM
ejpam-5442	146	28	)	)	PUNCT
ejpam-5442	146	29	,	,	PUNCT
ejpam-5442	146	30	and	and	CCONJ
ejpam-5442	146	31	the	the	DET
ejpam-5442	146	32	regulated	regulated	ADJ
ejpam-5442	146	33	numerical	numerical	ADJ
ejpam-5442	146	34	scheme	scheme	NOUN
ejpam-5442	146	35	which	which	PRON
ejpam-5442	146	36	investigated	investigate	VERB
ejpam-5442	146	37	and	and	CCONJ
ejpam-5442	146	38	proved	prove	VERB
ejpam-5442	146	39	in	in	ADP
ejpam-5442	146	40	(	(	PUNCT
ejpam-5442	146	41	[	[	X
ejpam-5442	146	42	8	8	NUM
ejpam-5442	146	43	]	]	PUNCT
ejpam-5442	146	44	,	,	PUNCT
ejpam-5442	146	45	[	[	X
ejpam-5442	146	46	22	22	NUM
ejpam-5442	146	47	]	]	PUNCT
ejpam-5442	146	48	)	)	PUNCT
ejpam-5442	146	49	.	.	PUNCT
ejpam-5442	147	1	theorem	theorem	NOUN
ejpam-5442	147	2	1	1	NUM
ejpam-5442	147	3	.	.	PUNCT
ejpam-5442	148	1	[	[	X
ejpam-5442	148	2	22	22	NUM
ejpam-5442	148	3	]	]	PUNCT
ejpam-5442	148	4	let	let	VERB
ejpam-5442	148	5	us	we	PRON
ejpam-5442	148	6	assume	assume	VERB
ejpam-5442	148	7	a	a	DET
ejpam-5442	148	8	continuous	continuous	ADJ
ejpam-5442	148	9	function	function	NOUN
ejpam-5442	148	10	f	f	NOUN
ejpam-5442	148	11	:	:	PUNCT
ejpam-5442	149	1	[	[	X
ejpam-5442	149	2	0	0	NUM
ejpam-5442	149	3	,	,	PUNCT
ejpam-5442	149	4	t	t	X
ejpam-5442	149	5	]	]	PUNCT
ejpam-5442	149	6	×	×	NOUN
ejpam-5442	149	7	r	r	NOUN
ejpam-5442	149	8	→	→	SYM
ejpam-5442	149	9	r	r	NOUN
ejpam-5442	149	10	with	with	ADP
ejpam-5442	149	11	γ	γ	X
ejpam-5442	149	12	∈	∈	PROPN
ejpam-5442	149	13	(	(	PUNCT
ejpam-5442	149	14	0	0	NUM
ejpam-5442	149	15	,	,	PUNCT
ejpam-5442	149	16	1	1	NUM
ejpam-5442	149	17	)	)	PUNCT
ejpam-5442	149	18	that	that	PRON
ejpam-5442	149	19	satisfies	satisfy	VERB
ejpam-5442	149	20	the	the	DET
ejpam-5442	149	21	lipschitz	lipschitz	NOUN
ejpam-5442	149	22	condition	condition	NOUN
ejpam-5442	149	23	:	:	PUNCT
ejpam-5442	149	24	|f	|f	PROPN
ejpam-5442	149	25	(	(	PUNCT
ejpam-5442	149	26	u(t1))−	u(t1))−	NOUN
ejpam-5442	149	27	f	f	X
ejpam-5442	149	28	(	(	PUNCT
ejpam-5442	149	29	u(t2	u(t2	NOUN
ejpam-5442	149	30	)	)	PUNCT
ejpam-5442	149	31	)	)	PUNCT
ejpam-5442	150	1	|	|	ADV
ejpam-5442	150	2	≤	≤	X
ejpam-5442	150	3	ϵ	ϵ	X
ejpam-5442	150	4	|u(t1)−	|u(t1)−	PROPN
ejpam-5442	150	5	u(t2)|	u(t2)|	PROPN
ejpam-5442	150	6	,	,	PUNCT
ejpam-5442	150	7	ϵ	ϵ	X
ejpam-5442	150	8	>	>	X
ejpam-5442	150	9	0	0	NUM
ejpam-5442	150	10	.	.	PUNCT
ejpam-5442	151	1	(	(	PUNCT
ejpam-5442	151	2	6	6	NUM
ejpam-5442	151	3	)	)	PUNCT
ejpam-5442	151	4	then	then	ADV
ejpam-5442	151	5	the	the	DET
ejpam-5442	151	6	ivp	ivp	X
ejpam-5442	151	7	(	(	PUNCT
ejpam-5442	151	8	3	3	X
ejpam-5442	151	9	)	)	PUNCT
ejpam-5442	151	10	has	have	VERB
ejpam-5442	151	11	a	a	DET
ejpam-5442	151	12	unique	unique	ADJ
ejpam-5442	151	13	solution	solution	NOUN
ejpam-5442	151	14	on	on	ADP
ejpam-5442	151	15	c[0	c[0	PROPN
ejpam-5442	151	16	,	,	PUNCT
ejpam-5442	151	17	t	t	X
ejpam-5442	151	18	]	]	PUNCT
ejpam-5442	151	19	under	under	ADP
ejpam-5442	151	20	the	the	DET
ejpam-5442	151	21	condition	condition	NOUN
ejpam-5442	151	22	:	:	PUNCT
ejpam-5442	151	23	(	(	PUNCT
ejpam-5442	151	24	2(1−	2(1−	NUM
ejpam-5442	151	25	γ	γ	X
ejpam-5442	151	26	)	)	PUNCT
ejpam-5442	152	1	+	+	NUM
ejpam-5442	152	2	2γ	2γ	NUM
ejpam-5442	152	3	t	t	NOUN
ejpam-5442	152	4	)	)	PUNCT
ejpam-5442	152	5	ϵ	ϵ	X
ejpam-5442	152	6	(	(	PUNCT
ejpam-5442	152	7	2−	2−	NUM
ejpam-5442	152	8	γ	γ	NOUN
ejpam-5442	152	9	)	)	PUNCT
ejpam-5442	152	10	<	<	X
ejpam-5442	152	11	1	1	X
ejpam-5442	152	12	.	.	PUNCT
ejpam-5442	153	1	lemma	lemma	PROPN
ejpam-5442	153	2	1	1	X
ejpam-5442	153	3	.	.	PUNCT
ejpam-5442	153	4	suppose	suppose	VERB
ejpam-5442	153	5	that	that	SCONJ
ejpam-5442	153	6	f(u(t	f(u(t	PROPN
ejpam-5442	153	7	)	)	PUNCT
ejpam-5442	153	8	)	)	PUNCT
ejpam-5442	154	1	∈	∈	PROPN
ejpam-5442	154	2	c4([a	c4([a	PROPN
ejpam-5442	154	3	,	,	PUNCT
ejpam-5442	154	4	b	b	NOUN
ejpam-5442	154	5	]	]	X
ejpam-5442	154	6	)	)	PUNCT
ejpam-5442	154	7	,	,	PUNCT
ejpam-5442	154	8	then	then	ADV
ejpam-5442	154	9	the	the	DET
ejpam-5442	154	10	error	error	NOUN
ejpam-5442	154	11	of	of	ADP
ejpam-5442	154	12	numerical	numerical	ADJ
ejpam-5442	154	13	scheme	scheme	NOUN
ejpam-5442	154	14	(	(	PUNCT
ejpam-5442	154	15	5	5	NUM
ejpam-5442	154	16	)	)	PUNCT
ejpam-5442	154	17	is	be	AUX
ejpam-5442	154	18	estimated	estimate	VERB
ejpam-5442	154	19	by	by	ADP
ejpam-5442	154	20	:	:	PUNCT
ejpam-5442	155	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5442	155	2	∫	∫	PROPN
ejpam-5442	155	3	tn+1	tn+1	PROPN
ejpam-5442	155	4	t0	t0	PROPN
ejpam-5442	155	5	f(u(s))ds−	f(u(s))ds−	X
ejpam-5442	155	6	γh	γh	ADP
ejpam-5442	155	7	n+1∑	n+1∑	PROPN
ejpam-5442	155	8	i=0	i=0	PROPN
ejpam-5442	155	9	ξif	ξif	X
ejpam-5442	155	10	(	(	PUNCT
ejpam-5442	155	11	u(ti	u(ti	NOUN
ejpam-5442	155	12	)	)	PUNCT
ejpam-5442	155	13	)	)	PUNCT
ejpam-5442	156	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5442	156	2	≤	≤	ADJ
ejpam-5442	156	3	h4	h4	NOUN
ejpam-5442	156	4	,	,	PUNCT
ejpam-5442	156	5	where	where	SCONJ
ejpam-5442	156	6	ĉ	ĉ	ADV
ejpam-5442	156	7	=	=	SYM
ejpam-5442	156	8	(	(	PUNCT
ejpam-5442	156	9	b−a)f	b−a)f	PROPN
ejpam-5442	156	10	(	(	PUNCT
ejpam-5442	156	11	4)(ζ	4)(ζ	PROPN
ejpam-5442	156	12	)	)	PUNCT
ejpam-5442	156	13	180	180	NUM
ejpam-5442	156	14	,	,	PUNCT
ejpam-5442	156	15	for	for	ADP
ejpam-5442	156	16	some	some	PRON
ejpam-5442	156	17	constant	constant	ADJ
ejpam-5442	156	18	a	a	PRON
ejpam-5442	156	19	<	<	X
ejpam-5442	156	20	ζ	ζ	NOUN
ejpam-5442	156	21	<	<	X
ejpam-5442	156	22	b	b	PROPN
ejpam-5442	156	23	,	,	PUNCT
ejpam-5442	156	24	h	h	NOUN
ejpam-5442	156	25	=	=	NOUN
ejpam-5442	156	26	b−a	b−a	NOUN
ejpam-5442	156	27	n	n	NOUN
ejpam-5442	156	28	,	,	PUNCT
ejpam-5442	156	29	and	and	CCONJ
ejpam-5442	156	30	tk	tk	X
ejpam-5442	156	31	=	=	PUNCT
ejpam-5442	156	32	a	a	PROPN
ejpam-5442	156	33	+	+	X
ejpam-5442	156	34	hk	hk	PROPN
ejpam-5442	156	35	,	,	PUNCT
ejpam-5442	156	36	k	k	PROPN
ejpam-5442	156	37	=	=	SYM
ejpam-5442	156	38	0	0	NUM
ejpam-5442	156	39	,	,	PUNCT
ejpam-5442	156	40	1	1	NUM
ejpam-5442	156	41	,	,	PUNCT
ejpam-5442	156	42	.	.	PUNCT
ejpam-5442	156	43	.	.	PUNCT
ejpam-5442	156	44	.	.	PUNCT
ejpam-5442	157	1	,	,	PUNCT
ejpam-5442	157	2	n+	n+	PUNCT
ejpam-5442	158	1	1	1	X
ejpam-5442	158	2	.	.	PUNCT
ejpam-5442	158	3	the	the	DET
ejpam-5442	158	4	stability	stability	NOUN
ejpam-5442	158	5	and	and	CCONJ
ejpam-5442	158	6	error	error	NOUN
ejpam-5442	158	7	analysis	analysis	NOUN
ejpam-5442	158	8	of	of	ADP
ejpam-5442	158	9	the	the	DET
ejpam-5442	158	10	regulated	regulate	VERB
ejpam-5442	158	11	numerical	numerical	ADJ
ejpam-5442	158	12	scheme	scheme	NOUN
ejpam-5442	158	13	are	be	AUX
ejpam-5442	158	14	investigated	investigate	VERB
ejpam-5442	158	15	and	and	CCONJ
ejpam-5442	158	16	proved	prove	VERB
ejpam-5442	158	17	meanwhile	meanwhile	ADV
ejpam-5442	158	18	the	the	DET
ejpam-5442	158	19	following	follow	VERB
ejpam-5442	158	20	theorems	theorem	NOUN
ejpam-5442	158	21	[	[	X
ejpam-5442	158	22	8	8	NUM
ejpam-5442	158	23	]	]	PUNCT
ejpam-5442	158	24	.	.	PUNCT
ejpam-5442	159	1	m.	m.	PROPN
ejpam-5442	159	2	adel	adel	PROPN
ejpam-5442	159	3	,	,	PUNCT
ejpam-5442	159	4	m.	m.	NOUN
ejpam-5442	159	5	m.	m.	NOUN
ejpam-5442	159	6	khader	khader	PROPN
ejpam-5442	159	7	,	,	PUNCT
ejpam-5442	159	8	n.	n.	PROPN
ejpam-5442	159	9	a.	a.	PROPN
ejpam-5442	159	10	mohammed	mohammed	PROPN
ejpam-5442	159	11	/	/	SYM
ejpam-5442	159	12	eur	eur	PROPN
ejpam-5442	159	13	.	.	PUNCT
ejpam-5442	160	1	j.	j.	PROPN
ejpam-5442	160	2	pure	pure	PROPN
ejpam-5442	160	3	appl	appl	PROPN
ejpam-5442	160	4	.	.	PROPN
ejpam-5442	160	5	math	math	PROPN
ejpam-5442	160	6	,	,	PUNCT
ejpam-5442	160	7	17	17	NUM
ejpam-5442	160	8	(	(	PUNCT
ejpam-5442	160	9	4	4	NUM
ejpam-5442	160	10	)	)	PUNCT
ejpam-5442	160	11	(	(	PUNCT
ejpam-5442	160	12	2024	2024	NUM
ejpam-5442	160	13	)	)	PUNCT
ejpam-5442	160	14	,	,	PUNCT
ejpam-5442	160	15	3277	3277	NUM
ejpam-5442	160	16	-	-	SYM
ejpam-5442	160	17	3290	3290	NUM
ejpam-5442	160	18	3283	3283	NUM
ejpam-5442	160	19	theorem	theorem	NOUN
ejpam-5442	160	20	2	2	NUM
ejpam-5442	160	21	.	.	PUNCT
ejpam-5442	161	1	the	the	DET
ejpam-5442	161	2	newly	newly	ADV
ejpam-5442	161	3	designed	design	VERB
ejpam-5442	161	4	fractional	fractional	ADJ
ejpam-5442	161	5	numerical	numerical	ADJ
ejpam-5442	161	6	technique	technique	NOUN
ejpam-5442	161	7	(	(	PUNCT
ejpam-5442	161	8	5	5	NUM
ejpam-5442	161	9	)	)	PUNCT
ejpam-5442	161	10	exhibits	exhibit	VERB
ejpam-5442	161	11	conditional	conditional	ADJ
ejpam-5442	161	12	stability	stability	NOUN
ejpam-5442	161	13	.	.	PUNCT
ejpam-5442	162	1	theorem	theorem	VERB
ejpam-5442	162	2	3	3	NUM
ejpam-5442	162	3	.	.	PUNCT
ejpam-5442	163	1	the	the	DET
ejpam-5442	163	2	recently	recently	ADV
ejpam-5442	163	3	developed	develop	VERB
ejpam-5442	163	4	fractional	fractional	ADJ
ejpam-5442	163	5	numerical	numerical	ADJ
ejpam-5442	163	6	method	method	PROPN
ejpam-5442	163	7	exhibits	exhibit	VERB
ejpam-5442	163	8	conditional	conditional	ADJ
ejpam-5442	163	9	convergence	convergence	NOUN
ejpam-5442	163	10	of	of	ADP
ejpam-5442	163	11	order	order	NOUN
ejpam-5442	163	12	four	four	NUM
ejpam-5442	163	13	,	,	PUNCT
ejpam-5442	163	14	as	as	SCONJ
ejpam-5442	163	15	stated	state	VERB
ejpam-5442	163	16	in	in	ADP
ejpam-5442	163	17	the	the	DET
ejpam-5442	163	18	equation	equation	NOUN
ejpam-5442	163	19	(	(	PUNCT
ejpam-5442	163	20	5	5	NUM
ejpam-5442	163	21	):	):	PUNCT
ejpam-5442	163	22	∥u	∥u	PROPN
ejpam-5442	163	23	(	(	PUNCT
ejpam-5442	163	24	tn+1)−	tn+1)−	PROPN
ejpam-5442	163	25	un+1∥	un+1∥	PROPN
ejpam-5442	163	26	≤	≤	PROPN
ejpam-5442	163	27	ch4	ch4	PROPN
ejpam-5442	163	28	,	,	PUNCT
ejpam-5442	163	29	where	where	SCONJ
ejpam-5442	163	30	c	c	NOUN
ejpam-5442	163	31	=	=	SYM
ejpam-5442	163	32	γĉ	γĉ	PROPN
ejpam-5442	163	33	ch	ch	NOUN
ejpam-5442	163	34	.	.	PROPN
ejpam-5442	163	35	6	6	NUM
ejpam-5442	163	36	.	.	X
ejpam-5442	164	1	numerical	numerical	ADJ
ejpam-5442	164	2	implementation	implementation	NOUN
ejpam-5442	164	3	most	most	ADJ
ejpam-5442	164	4	of	of	ADP
ejpam-5442	164	5	the	the	DET
ejpam-5442	164	6	existing	exist	VERB
ejpam-5442	164	7	numerical	numerical	ADJ
ejpam-5442	164	8	methods	method	NOUN
ejpam-5442	164	9	converge	converge	VERB
ejpam-5442	164	10	slowly	slowly	ADV
ejpam-5442	164	11	for	for	ADP
ejpam-5442	164	12	this	this	DET
ejpam-5442	164	13	kind	kind	NOUN
ejpam-5442	164	14	of	of	ADP
ejpam-5442	164	15	problem	problem	NOUN
ejpam-5442	164	16	and	and	CCONJ
ejpam-5442	164	17	this	this	DET
ejpam-5442	164	18	results	result	NOUN
ejpam-5442	164	19	in	in	ADP
ejpam-5442	164	20	inaccurate	inaccurate	ADJ
ejpam-5442	164	21	approximations	approximation	NOUN
ejpam-5442	164	22	.	.	PUNCT
ejpam-5442	165	1	in	in	ADP
ejpam-5442	165	2	this	this	DET
ejpam-5442	165	3	work	work	NOUN
ejpam-5442	165	4	,	,	PUNCT
ejpam-5442	165	5	the	the	DET
ejpam-5442	165	6	discretized	discretized	ADJ
ejpam-5442	165	7	system	system	NOUN
ejpam-5442	165	8	of	of	ADP
ejpam-5442	165	9	cffractional	cffractional	ADJ
ejpam-5442	165	10	differential	differential	ADJ
ejpam-5442	165	11	equations	equation	NOUN
ejpam-5442	165	12	is	be	AUX
ejpam-5442	165	13	numerically	numerically	ADV
ejpam-5442	165	14	integrated	integrate	VERB
ejpam-5442	165	15	using	use	VERB
ejpam-5442	165	16	simpson	simpson	PROPN
ejpam-5442	165	17	’s	’s	PART
ejpam-5442	165	18	1/3	1/3	NUM
ejpam-5442	165	19	technique	technique	NOUN
ejpam-5442	165	20	.	.	PUNCT
ejpam-5442	166	1	we	we	PRON
ejpam-5442	166	2	will	will	AUX
ejpam-5442	166	3	develop	develop	VERB
ejpam-5442	166	4	a	a	DET
ejpam-5442	166	5	numerical	numerical	ADJ
ejpam-5442	166	6	method	method	NOUN
ejpam-5442	166	7	to	to	PART
ejpam-5442	166	8	illustrate	illustrate	VERB
ejpam-5442	166	9	the	the	DET
ejpam-5442	166	10	numerical	numerical	ADJ
ejpam-5442	166	11	behavior	behavior	NOUN
ejpam-5442	166	12	of	of	ADP
ejpam-5442	166	13	the	the	DET
ejpam-5442	166	14	cf	cf	NOUN
ejpam-5442	166	15	fractional	fractional	ADJ
ejpam-5442	166	16	smoking	smoking	NOUN
ejpam-5442	166	17	system	system	NOUN
ejpam-5442	166	18	.	.	PUNCT
ejpam-5442	167	1	to	to	ADP
ejpam-5442	167	2	this	this	DET
ejpam-5442	167	3	end	end	NOUN
ejpam-5442	167	4	,	,	PUNCT
ejpam-5442	167	5	let	let	VERB
ejpam-5442	167	6	us	we	PRON
ejpam-5442	167	7	revisit	revisit	VERB
ejpam-5442	167	8	the	the	DET
ejpam-5442	167	9	model	model	NOUN
ejpam-5442	167	10	presented	present	VERB
ejpam-5442	167	11	in	in	ADP
ejpam-5442	167	12	(	(	PUNCT
ejpam-5442	167	13	2	2	NUM
ejpam-5442	167	14	):	):	PUNCT
ejpam-5442	167	15	cfdϱ	cfdϱ	ADJ
ejpam-5442	167	16	ψ̄(t	ψ̄(t	NOUN
ejpam-5442	168	1	)	)	PUNCT
ejpam-5442	168	2	=	=	SYM
ejpam-5442	168	3	f(ψ̄(t	f(ψ̄(t	NOUN
ejpam-5442	168	4	)	)	PUNCT
ejpam-5442	168	5	,	,	PUNCT
ejpam-5442	168	6	t	t	PROPN
ejpam-5442	168	7	)	)	PUNCT
ejpam-5442	168	8	,	,	PUNCT
ejpam-5442	168	9	(	(	PUNCT
ejpam-5442	168	10	7	7	X
ejpam-5442	168	11	)	)	PUNCT
ejpam-5442	168	12	where	where	SCONJ
ejpam-5442	168	13	ψ̄(t	ψ̄(t	ADJ
ejpam-5442	168	14	)	)	PUNCT
ejpam-5442	168	15	=	=	PUNCT
ejpam-5442	169	1	[	[	X
ejpam-5442	169	2	ψ1(t	ψ1(t	NOUN
ejpam-5442	169	3	)	)	PUNCT
ejpam-5442	169	4	,	,	PUNCT
ejpam-5442	169	5	ψ2(t	ψ2(t	PROPN
ejpam-5442	169	6	)	)	PUNCT
ejpam-5442	169	7	,	,	PUNCT
ejpam-5442	169	8	ψ3(t	ψ3(t	PROPN
ejpam-5442	169	9	)	)	PUNCT
ejpam-5442	169	10	,	,	PUNCT
ejpam-5442	169	11	ψ4(t	ψ4(t	PROPN
ejpam-5442	169	12	)	)	PUNCT
ejpam-5442	169	13	,	,	PUNCT
ejpam-5442	169	14	ψ5(t	ψ5(t	NOUN
ejpam-5442	169	15	)	)	PUNCT
ejpam-5442	169	16	]	]	PUNCT
ejpam-5442	169	17	t	t	X
ejpam-5442	169	18	,	,	PUNCT
ejpam-5442	169	19	ψ̄(0	ψ̄(0	PUNCT
ejpam-5442	169	20	)	)	PUNCT
ejpam-5442	169	21	=	=	PUNCT
ejpam-5442	170	1	[	[	X
ejpam-5442	170	2	ψ1(0	ψ1(0	PROPN
ejpam-5442	170	3	)	)	PUNCT
ejpam-5442	170	4	,	,	PUNCT
ejpam-5442	170	5	ψ2(0	ψ2(0	PROPN
ejpam-5442	170	6	)	)	PUNCT
ejpam-5442	170	7	,	,	PUNCT
ejpam-5442	170	8	ψ3(0	ψ3(0	PROPN
ejpam-5442	170	9	)	)	PUNCT
ejpam-5442	170	10	,	,	PUNCT
ejpam-5442	170	11	ψ4(0	ψ4(0	NOUN
ejpam-5442	170	12	)	)	PUNCT
ejpam-5442	170	13	,	,	PUNCT
ejpam-5442	170	14	ψ5(0	ψ5(0	NOUN
ejpam-5442	170	15	)	)	PUNCT
ejpam-5442	170	16	]	]	PUNCT
ejpam-5442	171	1	t	t	NOUN
ejpam-5442	171	2	,	,	PUNCT
ejpam-5442	171	3	f(ψ̄(t	f(ψ̄(t	PROPN
ejpam-5442	171	4	)	)	PUNCT
ejpam-5442	171	5	,	,	PUNCT
ejpam-5442	171	6	t	t	X
ejpam-5442	171	7	)	)	PUNCT
ejpam-5442	171	8	=	=	X
ejpam-5442	172	1			NOUN
ejpam-5442	172	2	f1(ψ1	f1(ψ1	NOUN
ejpam-5442	172	3	,	,	PUNCT
ejpam-5442	172	4	ψ2	ψ2	NOUN
ejpam-5442	172	5	,	,	PUNCT
ejpam-5442	172	6	ψ3	ψ3	NOUN
ejpam-5442	172	7	,	,	PUNCT
ejpam-5442	172	8	ψ4	ψ4	PROPN
ejpam-5442	172	9	,	,	PUNCT
ejpam-5442	172	10	ψ5	ψ5	PROPN
ejpam-5442	172	11	,	,	PUNCT
ejpam-5442	172	12	t	t	NOUN
ejpam-5442	172	13	)	)	PUNCT
ejpam-5442	172	14	f2(ψ1	f2(ψ1	NOUN
ejpam-5442	172	15	,	,	PUNCT
ejpam-5442	172	16	ψ2	ψ2	NOUN
ejpam-5442	172	17	,	,	PUNCT
ejpam-5442	172	18	ψ3	ψ3	NOUN
ejpam-5442	172	19	,	,	PUNCT
ejpam-5442	172	20	ψ4	ψ4	PROPN
ejpam-5442	172	21	,	,	PUNCT
ejpam-5442	172	22	ψ5	ψ5	PROPN
ejpam-5442	172	23	,	,	PUNCT
ejpam-5442	172	24	t	t	PROPN
ejpam-5442	172	25	)	)	PUNCT
ejpam-5442	172	26	f3(ψ1	f3(ψ1	NOUN
ejpam-5442	172	27	,	,	PUNCT
ejpam-5442	172	28	ψ2	ψ2	NOUN
ejpam-5442	172	29	,	,	PUNCT
ejpam-5442	172	30	ψ3	ψ3	NOUN
ejpam-5442	172	31	,	,	PUNCT
ejpam-5442	172	32	ψ4	ψ4	PROPN
ejpam-5442	172	33	,	,	PUNCT
ejpam-5442	172	34	ψ5	ψ5	PROPN
ejpam-5442	172	35	,	,	PUNCT
ejpam-5442	172	36	t	t	NOUN
ejpam-5442	172	37	)	)	PUNCT
ejpam-5442	172	38	f4(ψ1	f4(ψ1	NOUN
ejpam-5442	172	39	,	,	PUNCT
ejpam-5442	172	40	ψ2	ψ2	NOUN
ejpam-5442	172	41	,	,	PUNCT
ejpam-5442	172	42	ψ3	ψ3	NOUN
ejpam-5442	172	43	,	,	PUNCT
ejpam-5442	172	44	ψ4	ψ4	PROPN
ejpam-5442	172	45	,	,	PUNCT
ejpam-5442	172	46	ψ5	ψ5	PROPN
ejpam-5442	172	47	,	,	PUNCT
ejpam-5442	172	48	t	t	PROPN
ejpam-5442	172	49	)	)	PUNCT
ejpam-5442	172	50	f5(ψ1	f5(ψ1	NOUN
ejpam-5442	172	51	,	,	PUNCT
ejpam-5442	172	52	ψ2	ψ2	NOUN
ejpam-5442	172	53	,	,	PUNCT
ejpam-5442	172	54	ψ3	ψ3	NOUN
ejpam-5442	172	55	,	,	PUNCT
ejpam-5442	172	56	ψ4	ψ4	PROPN
ejpam-5442	172	57	,	,	PUNCT
ejpam-5442	172	58	ψ5	ψ5	PROPN
ejpam-5442	172	59	,	,	PUNCT
ejpam-5442	172	60	t	t	NOUN
ejpam-5442	172	61	)	)	PUNCT
ejpam-5442	172	62			NOUN
ejpam-5442	173	1	=	=	SYM
ejpam-5442	173	2			NOUN
ejpam-5442	173	3	σ	σ	NOUN
ejpam-5442	173	4	−	−	NOUN
ejpam-5442	173	5	ℓ1	ℓ1	NOUN
ejpam-5442	173	6	ψ1(t)ψ2(t	ψ1(t)ψ2(t	NOUN
ejpam-5442	173	7	)	)	PUNCT
ejpam-5442	174	1	+	+	CCONJ
ejpam-5442	174	2	γ	γ	X
ejpam-5442	174	3	ψ4(t)−	ψ4(t)−	PROPN
ejpam-5442	174	4	β	β	X
ejpam-5442	174	5	ψ1(t	ψ1(t	PROPN
ejpam-5442	174	6	)	)	PUNCT
ejpam-5442	174	7	ℓ1	ℓ1	NOUN
ejpam-5442	174	8	ψ1(t)ψ2(t)−	ψ1(t)ψ2(t)−	PROPN
ejpam-5442	174	9	ℓ2	ℓ2	PROPN
ejpam-5442	174	10	ψ2(t)ψ3(t)−	ψ2(t)ψ3(t)−	PROPN
ejpam-5442	174	11	(	(	PUNCT
ejpam-5442	174	12	σ1	σ1	PROPN
ejpam-5442	174	13	+	+	CCONJ
ejpam-5442	174	14	β)ψ2(t	β)ψ2(t	NOUN
ejpam-5442	174	15	)	)	PUNCT
ejpam-5442	174	16	ℓ2	ℓ2	PROPN
ejpam-5442	174	17	ψ2(t)ψ3(t)−	ψ2(t)ψ3(t)−	PROPN
ejpam-5442	174	18	(	(	PUNCT
ejpam-5442	174	19	ψ	ψ	X
ejpam-5442	174	20	+	+	X
ejpam-5442	174	21	σ2	σ2	NOUN
ejpam-5442	174	22	+	+	CCONJ
ejpam-5442	174	23	β)ψ3(t	β)ψ3(t	PROPN
ejpam-5442	174	24	)	)	PUNCT
ejpam-5442	174	25	θ	θ	PROPN
ejpam-5442	174	26	ψ3(t)−	ψ3(t)−	PROPN
ejpam-5442	174	27	(	(	PUNCT
ejpam-5442	174	28	α+	α+	X
ejpam-5442	174	29	β	β	X
ejpam-5442	174	30	+	+	SYM
ejpam-5442	174	31	γ)ψ4(t	γ)ψ4(t	PROPN
ejpam-5442	174	32	)	)	PUNCT
ejpam-5442	174	33	αψ4(t)−	αψ4(t)−	PROPN
ejpam-5442	174	34	β	β	X
ejpam-5442	174	35	ψ5(t	ψ5(t	NOUN
ejpam-5442	174	36	)	)	PUNCT
ejpam-5442	174	37			NOUN
ejpam-5442	174	38	.	.	PUNCT
ejpam-5442	175	1	(	(	PUNCT
ejpam-5442	175	2	8)	8)	NUM
ejpam-5442	175	3	applying	apply	VERB
ejpam-5442	175	4	the	the	DET
ejpam-5442	175	5	cf	cf	NOUN
ejpam-5442	175	6	fractional	fractional	ADJ
ejpam-5442	175	7	integral	integral	ADJ
ejpam-5442	175	8	operator	operator	NOUN
ejpam-5442	175	9	on	on	ADP
ejpam-5442	175	10	eq.(7	eq.(7	NOUN
ejpam-5442	175	11	)	)	PUNCT
ejpam-5442	175	12	and	and	CCONJ
ejpam-5442	175	13	using	use	VERB
ejpam-5442	175	14	proposition	proposition	NOUN
ejpam-5442	175	15	3	3	NUM
ejpam-5442	175	16	in	in	ADP
ejpam-5442	175	17	[	[	X
ejpam-5442	175	18	1	1	NUM
ejpam-5442	175	19	]	]	PUNCT
ejpam-5442	175	20	and	and	CCONJ
ejpam-5442	175	21	formula	formula	NOUN
ejpam-5442	175	22	(	(	PUNCT
ejpam-5442	175	23	1	1	NUM
ejpam-5442	175	24	)	)	PUNCT
ejpam-5442	175	25	,	,	PUNCT
ejpam-5442	175	26	we	we	PRON
ejpam-5442	175	27	get	get	VERB
ejpam-5442	175	28	:	:	PUNCT
ejpam-5442	175	29	ψ̄(t	ψ̄(t	X
ejpam-5442	175	30	)	)	PUNCT
ejpam-5442	175	31	=	=	PUNCT
ejpam-5442	175	32	ψ̄(0	ψ̄(0	PUNCT
ejpam-5442	175	33	)	)	PUNCT
ejpam-5442	176	1	+	+	CCONJ
ejpam-5442	176	2	cf	cf	NOUN
ejpam-5442	176	3	iϱ	iϱ	NOUN
ejpam-5442	176	4	f(ψ̄(t	f(ψ̄(t	PROPN
ejpam-5442	176	5	)	)	PUNCT
ejpam-5442	176	6	,	,	PUNCT
ejpam-5442	176	7	t	t	PROPN
ejpam-5442	176	8	)	)	PUNCT
ejpam-5442	176	9	=	=	PUNCT
ejpam-5442	176	10	ψ̄(0	ψ̄(0	PUNCT
ejpam-5442	176	11	)	)	PUNCT
ejpam-5442	177	1	+	+	CCONJ
ejpam-5442	177	2	(	(	PUNCT
ejpam-5442	177	3	1−	1−	NUM
ejpam-5442	177	4	ϱ)f(ψ̄(t	ϱ)f(ψ̄(t	NUM
ejpam-5442	177	5	)	)	PUNCT
ejpam-5442	177	6	,	,	PUNCT
ejpam-5442	177	7	t	t	PROPN
ejpam-5442	177	8	)	)	PUNCT
ejpam-5442	177	9	+	+	CCONJ
ejpam-5442	177	10	ϱ	ϱ	ADP
ejpam-5442	177	11	∫	∫	PROPN
ejpam-5442	177	12	t	t	PROPN
ejpam-5442	177	13	0	0	NUM
ejpam-5442	177	14	f(ψ̄(s	f(ψ̄(s	PROPN
ejpam-5442	177	15	)	)	PUNCT
ejpam-5442	177	16	,	,	PUNCT
ejpam-5442	178	1	s)ds	s)ds	PROPN
ejpam-5442	178	2	.	.	PROPN
ejpam-5442	179	1	(	(	PUNCT
ejpam-5442	179	2	9	9	X
ejpam-5442	179	3	)	)	PUNCT
ejpam-5442	179	4	applying	apply	VERB
ejpam-5442	179	5	the	the	DET
ejpam-5442	179	6	derived	derive	VERB
ejpam-5442	179	7	simpson’s-1/3	simpson’s-1/3	NUM
ejpam-5442	179	8	rule	rule	NOUN
ejpam-5442	179	9	for	for	ADP
ejpam-5442	179	10	the	the	DET
ejpam-5442	179	11	integration	integration	NOUN
ejpam-5442	179	12	on	on	ADP
ejpam-5442	179	13	the	the	DET
ejpam-5442	179	14	rhs	rhs	PROPN
ejpam-5442	179	15	of	of	ADP
ejpam-5442	179	16	(	(	PUNCT
ejpam-5442	179	17	9	9	NUM
ejpam-5442	179	18	)	)	PUNCT
ejpam-5442	179	19	,	,	PUNCT
ejpam-5442	179	20	to	to	PART
ejpam-5442	179	21	get	get	VERB
ejpam-5442	179	22	the	the	DET
ejpam-5442	179	23	following	follow	VERB
ejpam-5442	179	24	numerical	numerical	ADJ
ejpam-5442	179	25	scheme	scheme	NOUN
ejpam-5442	179	26	as	as	SCONJ
ejpam-5442	179	27	constructed	construct	VERB
ejpam-5442	179	28	in	in	ADP
ejpam-5442	179	29	the	the	DET
ejpam-5442	179	30	formula	formula	NOUN
ejpam-5442	179	31	(	(	PUNCT
ejpam-5442	179	32	5	5	NUM
ejpam-5442	179	33	):	):	PUNCT
ejpam-5442	179	34	ψ̄j+1	ψ̄j+1	NOUN
ejpam-5442	179	35	=	=	SYM
ejpam-5442	179	36	ψ̄(0)+(1−ϱ)f(ψ̄j+1	ψ̄(0)+(1−ϱ)f(ψ̄j+1	NOUN
ejpam-5442	179	37	,	,	PUNCT
ejpam-5442	179	38	tj+1)+ϱ	tj+1)+ϱ	PUNCT
ejpam-5442	179	39	h	h	NOUN
ejpam-5442	179	40	j+1∑	j+1∑	PROPN
ejpam-5442	179	41	r=0	r=0	PROPN
ejpam-5442	179	42	ξr	ξr	PROPN
ejpam-5442	179	43	f(ψ̄r	f(ψ̄r	NOUN
ejpam-5442	179	44	,	,	PUNCT
ejpam-5442	179	45	tr	tr	VERB
ejpam-5442	179	46	)	)	PUNCT
ejpam-5442	179	47	,	,	PUNCT
ejpam-5442	179	48	j	j	PROPN
ejpam-5442	179	49	=	=	SYM
ejpam-5442	179	50	0	0	NUM
ejpam-5442	179	51	,	,	PUNCT
ejpam-5442	179	52	1	1	NUM
ejpam-5442	179	53	,	,	PUNCT
ejpam-5442	179	54	2	2	NUM
ejpam-5442	179	55	,	,	PUNCT
ejpam-5442	179	56	.	.	PUNCT
ejpam-5442	179	57	.	.	PUNCT
ejpam-5442	180	1	.	.	PUNCT
ejpam-5442	181	1	,	,	PUNCT
ejpam-5442	181	2	n−1	n−1	PROPN
ejpam-5442	181	3	,	,	PUNCT
ejpam-5442	181	4	(	(	PUNCT
ejpam-5442	181	5	10	10	NUM
ejpam-5442	181	6	)	)	PUNCT
ejpam-5442	181	7	where	where	SCONJ
ejpam-5442	181	8	the	the	DET
ejpam-5442	181	9	weights	weight	NOUN
ejpam-5442	181	10	ξr	ξr	NOUN
ejpam-5442	181	11	,	,	PUNCT
ejpam-5442	181	12	r	r	NOUN
ejpam-5442	181	13	=	=	SYM
ejpam-5442	181	14	0	0	NUM
ejpam-5442	181	15	,	,	PUNCT
ejpam-5442	181	16	1	1	NUM
ejpam-5442	181	17	,	,	PUNCT
ejpam-5442	181	18	...	...	PUNCT
ejpam-5442	181	19	,	,	PUNCT
ejpam-5442	181	20	j	j	PROPN
ejpam-5442	182	1	+	+	CCONJ
ejpam-5442	182	2	1	1	NUM
ejpam-5442	182	3	of	of	ADP
ejpam-5442	182	4	the	the	DET
ejpam-5442	182	5	fractional	fractional	ADJ
ejpam-5442	182	6	simpson’s-1/3	simpson’s-1/3	ADJ
ejpam-5442	182	7	rule	rule	NOUN
ejpam-5442	182	8	are	be	AUX
ejpam-5442	182	9	defined	define	VERB
ejpam-5442	182	10	in	in	ADP
ejpam-5442	182	11	(	(	PUNCT
ejpam-5442	182	12	7	7	NUM
ejpam-5442	182	13	)	)	PUNCT
ejpam-5442	182	14	.	.	PUNCT
ejpam-5442	183	1	m.	m.	PROPN
ejpam-5442	183	2	adel	adel	PROPN
ejpam-5442	183	3	,	,	PUNCT
ejpam-5442	183	4	m.	m.	NOUN
ejpam-5442	183	5	m.	m.	NOUN
ejpam-5442	183	6	khader	khader	PROPN
ejpam-5442	183	7	,	,	PUNCT
ejpam-5442	183	8	n.	n.	PROPN
ejpam-5442	183	9	a.	a.	PROPN
ejpam-5442	183	10	mohammed	mohammed	PROPN
ejpam-5442	183	11	/	/	SYM
ejpam-5442	183	12	eur	eur	PROPN
ejpam-5442	183	13	.	.	PUNCT
ejpam-5442	184	1	j.	j.	PROPN
ejpam-5442	184	2	pure	pure	PROPN
ejpam-5442	184	3	appl	appl	PROPN
ejpam-5442	184	4	.	.	PROPN
ejpam-5442	184	5	math	math	PROPN
ejpam-5442	184	6	,	,	PUNCT
ejpam-5442	184	7	17	17	NUM
ejpam-5442	184	8	(	(	PUNCT
ejpam-5442	184	9	4	4	NUM
ejpam-5442	184	10	)	)	PUNCT
ejpam-5442	184	11	(	(	PUNCT
ejpam-5442	184	12	2024	2024	NUM
ejpam-5442	184	13	)	)	PUNCT
ejpam-5442	184	14	,	,	PUNCT
ejpam-5442	184	15	3277	3277	NUM
ejpam-5442	184	16	-	-	SYM
ejpam-5442	184	17	3290	3290	NUM
ejpam-5442	184	18	3284	3284	NUM
ejpam-5442	184	19	so	so	ADV
ejpam-5442	184	20	,	,	PUNCT
ejpam-5442	184	21	the	the	DET
ejpam-5442	184	22	system	system	NOUN
ejpam-5442	184	23	given	give	VERB
ejpam-5442	184	24	in	in	ADP
ejpam-5442	184	25	(	(	PUNCT
ejpam-5442	184	26	2	2	NUM
ejpam-5442	184	27	)	)	PUNCT
ejpam-5442	184	28	transforms	transform	VERB
ejpam-5442	184	29	into	into	ADP
ejpam-5442	184	30	a	a	DET
ejpam-5442	184	31	system	system	NOUN
ejpam-5442	184	32	of	of	ADP
ejpam-5442	184	33	algebraic	algebraic	ADJ
ejpam-5442	184	34	equations	equation	NOUN
ejpam-5442	184	35	as	as	SCONJ
ejpam-5442	184	36	follows	follow	VERB
ejpam-5442	184	37	(	(	PUNCT
ejpam-5442	184	38	for	for	ADP
ejpam-5442	184	39	j	j	PROPN
ejpam-5442	184	40	=	=	SYM
ejpam-5442	184	41	0	0	NUM
ejpam-5442	184	42	,	,	PUNCT
ejpam-5442	184	43	1	1	NUM
ejpam-5442	184	44	,	,	PUNCT
ejpam-5442	184	45	2	2	NUM
ejpam-5442	184	46	,	,	PUNCT
ejpam-5442	184	47	.	.	PUNCT
ejpam-5442	184	48	.	.	PUNCT
ejpam-5442	185	1	.	.	PUNCT
ejpam-5442	186	1	,	,	PUNCT
ejpam-5442	186	2	n−	n−	NOUN
ejpam-5442	186	3	1	1	NUM
ejpam-5442	186	4	):	):	PUNCT
ejpam-5442	186	5	ψk	ψk	VERB
ejpam-5442	186	6	,	,	PUNCT
ejpam-5442	186	7	j+1	j+1	PROPN
ejpam-5442	186	8	=	=	PUNCT
ejpam-5442	186	9	ψk,0	ψk,0	PROPN
ejpam-5442	187	1	+	+	CCONJ
ejpam-5442	187	2	(	(	PUNCT
ejpam-5442	187	3	1−	1−	NUM
ejpam-5442	187	4	ϱ)fk(ψ1,j+1	ϱ)fk(ψ1,j+1	NOUN
ejpam-5442	187	5	,	,	PUNCT
ejpam-5442	187	6	ψ2,j+1	ψ2,j+1	PROPN
ejpam-5442	187	7	,	,	PUNCT
ejpam-5442	187	8	ψ3,j+1	ψ3,j+1	PROPN
ejpam-5442	187	9	,	,	PUNCT
ejpam-5442	187	10	ψ4,j+1	ψ4,j+1	PROPN
ejpam-5442	187	11	,	,	PUNCT
ejpam-5442	187	12	ψ5,j+1	ψ5,j+1	PROPN
ejpam-5442	187	13	,	,	PUNCT
ejpam-5442	187	14	tj+1	tj+1	PROPN
ejpam-5442	187	15	)	)	PUNCT
ejpam-5442	187	16	+	+	CCONJ
ejpam-5442	187	17	ϱ	ϱ	PROPN
ejpam-5442	187	18	h	h	NOUN
ejpam-5442	187	19	j+1∑	j+1∑	PROPN
ejpam-5442	187	20	r=0	r=0	PROPN
ejpam-5442	188	1	ξr	ξr	ADP
ejpam-5442	188	2	fk(ψ1,r	fk(ψ1,r	PROPN
ejpam-5442	188	3	,	,	PUNCT
ejpam-5442	188	4	ψ2,r	ψ2,r	PROPN
ejpam-5442	188	5	,	,	PUNCT
ejpam-5442	188	6	ψ3,r	ψ3,r	PROPN
ejpam-5442	188	7	,	,	PUNCT
ejpam-5442	188	8	ψ4,r	ψ4,r	PROPN
ejpam-5442	188	9	,	,	PUNCT
ejpam-5442	188	10	ψ5,r	ψ5,r	PROPN
ejpam-5442	188	11	,	,	PUNCT
ejpam-5442	188	12	tr	tr	VERB
ejpam-5442	188	13	)	)	PUNCT
ejpam-5442	188	14	,	,	PUNCT
ejpam-5442	188	15	k	k	PROPN
ejpam-5442	188	16	=	=	SYM
ejpam-5442	188	17	1(1)5	1(1)5	NUM
ejpam-5442	188	18	,	,	PUNCT
ejpam-5442	188	19	(	(	PUNCT
ejpam-5442	188	20	11	11	NUM
ejpam-5442	188	21	)	)	PUNCT
ejpam-5442	188	22	where	where	SCONJ
ejpam-5442	188	23	the	the	DET
ejpam-5442	188	24	functions	function	NOUN
ejpam-5442	188	25	fk	fk	INTJ
ejpam-5442	188	26	are	be	AUX
ejpam-5442	188	27	defined	define	VERB
ejpam-5442	188	28	in	in	ADP
ejpam-5442	188	29	(	(	PUNCT
ejpam-5442	188	30	8)	8)	NUM
ejpam-5442	188	31	.	.	NOUN
ejpam-5442	188	32	7	7	NUM
ejpam-5442	188	33	.	.	X
ejpam-5442	188	34	numerical	numerical	PROPN
ejpam-5442	188	35	simulation	simulation	PROPN
ejpam-5442	188	36	this	this	DET
ejpam-5442	188	37	section	section	NOUN
ejpam-5442	188	38	aims	aim	VERB
ejpam-5442	188	39	to	to	PART
ejpam-5442	188	40	evaluate	evaluate	VERB
ejpam-5442	188	41	the	the	DET
ejpam-5442	188	42	efficacy	efficacy	NOUN
ejpam-5442	188	43	of	of	ADP
ejpam-5442	188	44	the	the	DET
ejpam-5442	188	45	suggested	suggest	VERB
ejpam-5442	188	46	approach	approach	NOUN
ejpam-5442	188	47	by	by	ADP
ejpam-5442	188	48	simulating	simulate	VERB
ejpam-5442	188	49	a	a	DET
ejpam-5442	188	50	solution	solution	NOUN
ejpam-5442	188	51	throughout	throughout	ADP
ejpam-5442	188	52	the	the	DET
ejpam-5442	188	53	interval	interval	NOUN
ejpam-5442	188	54	[	[	X
ejpam-5442	188	55	0	0	NUM
ejpam-5442	188	56	,	,	PUNCT
ejpam-5442	188	57	50	50	NUM
ejpam-5442	188	58	]	]	PUNCT
ejpam-5442	188	59	,	,	PUNCT
ejpam-5442	188	60	whereby	whereby	SCONJ
ejpam-5442	188	61	we	we	PRON
ejpam-5442	188	62	examine	examine	VERB
ejpam-5442	188	63	the	the	DET
ejpam-5442	188	64	system	system	NOUN
ejpam-5442	188	65	(	(	PUNCT
ejpam-5442	188	66	2	2	NUM
ejpam-5442	188	67	)	)	PUNCT
ejpam-5442	188	68	with	with	ADP
ejpam-5442	188	69	varying	vary	VERB
ejpam-5442	188	70	values	value	NOUN
ejpam-5442	188	71	of	of	ADP
ejpam-5442	188	72	ϱ	ϱ	PROPN
ejpam-5442	188	73	,	,	PUNCT
ejpam-5442	188	74	β	β	X
ejpam-5442	188	75	,	,	PUNCT
ejpam-5442	188	76	and	and	CCONJ
ejpam-5442	188	77	distinct	distinct	ADJ
ejpam-5442	188	78	initial	initial	ADJ
ejpam-5442	188	79	solutions	solution	NOUN
ejpam-5442	188	80	(	(	PUNCT
ejpam-5442	188	81	i.cs	i.cs	NOUN
ejpam-5442	188	82	)	)	PUNCT
ejpam-5442	189	1	[	[	X
ejpam-5442	189	2	18	18	NUM
ejpam-5442	189	3	]	]	PUNCT
ejpam-5442	189	4	.	.	PUNCT
ejpam-5442	190	1	in	in	ADP
ejpam-5442	190	2	all	all	DET
ejpam-5442	190	3	figures	figure	NOUN
ejpam-5442	190	4	,	,	PUNCT
ejpam-5442	190	5	we	we	PRON
ejpam-5442	190	6	utilize	utilize	VERB
ejpam-5442	190	7	identical	identical	ADJ
ejpam-5442	190	8	quantities	quantity	NOUN
ejpam-5442	190	9	for	for	ADP
ejpam-5442	190	10	the	the	DET
ejpam-5442	190	11	following	following	ADJ
ejpam-5442	190	12	constants	constant	NOUN
ejpam-5442	190	13	:	:	PUNCT
ejpam-5442	190	14	σ	σ	NOUN
ejpam-5442	190	15	=	=	SYM
ejpam-5442	190	16	0.1	0.1	NUM
ejpam-5442	190	17	,	,	PUNCT
ejpam-5442	190	18	θ	θ	X
ejpam-5442	190	19	=	=	PUNCT
ejpam-5442	190	20	α	α	X
ejpam-5442	190	21	=	=	NOUN
ejpam-5442	190	22	0.05	0.05	NUM
ejpam-5442	190	23	,	,	PUNCT
ejpam-5442	190	24	ℓ1	ℓ1	NOUN
ejpam-5442	190	25	=	=	SYM
ejpam-5442	190	26	γ	γ	X
ejpam-5442	190	27	=	=	SYM
ejpam-5442	190	28	σ1	σ1	PROPN
ejpam-5442	190	29	=	=	PROPN
ejpam-5442	190	30	σ2	σ2	PROPN
ejpam-5442	190	31	=	=	NOUN
ejpam-5442	190	32	0.003	0.003	NUM
ejpam-5442	190	33	,	,	PUNCT
ejpam-5442	190	34	ℓ2	ℓ2	NOUN
ejpam-5442	190	35	=	=	PUNCT
ejpam-5442	190	36	β	β	X
ejpam-5442	190	37	=	=	SYM
ejpam-5442	190	38	0.002	0.002	NUM
ejpam-5442	190	39	.	.	PUNCT
ejpam-5442	191	1	we	we	PRON
ejpam-5442	191	2	examine	examine	VERB
ejpam-5442	191	3	the	the	DET
ejpam-5442	191	4	subsequent	subsequent	ADJ
ejpam-5442	191	5	two	two	NUM
ejpam-5442	191	6	scenarios	scenario	NOUN
ejpam-5442	191	7	about	about	ADP
ejpam-5442	191	8	the	the	DET
ejpam-5442	191	9	i.cs	i.cs	NOUN
ejpam-5442	191	10	:	:	PUNCT
ejpam-5442	191	11	(	(	PUNCT
ejpam-5442	191	12	i	i	NOUN
ejpam-5442	191	13	)	)	PUNCT
ejpam-5442	191	14	small	small	ADJ
ejpam-5442	191	15	values	value	NOUN
ejpam-5442	191	16	:	:	PUNCT
ejpam-5442	191	17	ψ0	ψ0	PROPN
ejpam-5442	191	18	1	1	NUM
ejpam-5442	191	19	=	=	SYM
ejpam-5442	191	20	40	40	NUM
ejpam-5442	191	21	,	,	PUNCT
ejpam-5442	191	22	ψ0	ψ0	ADV
ejpam-5442	191	23	2	2	NUM
ejpam-5442	191	24	=	=	SYM
ejpam-5442	191	25	30	30	NUM
ejpam-5442	191	26	,	,	PUNCT
ejpam-5442	191	27	ψ0	ψ0	NOUN
ejpam-5442	191	28	3	3	NUM
ejpam-5442	191	29	=	=	SYM
ejpam-5442	191	30	20	20	NUM
ejpam-5442	191	31	,	,	PUNCT
ejpam-5442	191	32	ψ0	ψ0	ADV
ejpam-5442	191	33	4	4	NUM
ejpam-5442	191	34	=	=	SYM
ejpam-5442	191	35	10	10	NUM
ejpam-5442	191	36	,	,	PUNCT
ejpam-5442	191	37	ψ0	ψ0	ADV
ejpam-5442	191	38	5	5	NUM
ejpam-5442	191	39	=	=	SYM
ejpam-5442	191	40	5	5	NUM
ejpam-5442	191	41	;	;	PUNCT
ejpam-5442	191	42	(	(	PUNCT
ejpam-5442	191	43	ii	ii	NOUN
ejpam-5442	191	44	)	)	PUNCT
ejpam-5442	191	45	large	large	ADJ
ejpam-5442	191	46	values	value	NOUN
ejpam-5442	191	47	:	:	PUNCT
ejpam-5442	191	48	ψ0	ψ0	PROPN
ejpam-5442	191	49	1	1	NUM
ejpam-5442	191	50	=	=	SYM
ejpam-5442	191	51	75	75	NUM
ejpam-5442	191	52	,	,	PUNCT
ejpam-5442	191	53	ψ0	ψ0	NOUN
ejpam-5442	191	54	2	2	NUM
ejpam-5442	191	55	=	=	SYM
ejpam-5442	191	56	60	60	NUM
ejpam-5442	191	57	,	,	PUNCT
ejpam-5442	191	58	ψ0	ψ0	NOUN
ejpam-5442	191	59	3	3	NUM
ejpam-5442	191	60	=	=	SYM
ejpam-5442	191	61	45	45	NUM
ejpam-5442	191	62	,	,	PUNCT
ejpam-5442	191	63	ψ0	ψ0	ADV
ejpam-5442	191	64	4	4	NUM
ejpam-5442	191	65	=	=	SYM
ejpam-5442	191	66	30	30	NUM
ejpam-5442	191	67	,	,	PUNCT
ejpam-5442	191	68	ψ0	ψ0	ADV
ejpam-5442	191	69	5	5	NUM
ejpam-5442	191	70	=	=	SYM
ejpam-5442	191	71	15	15	NUM
ejpam-5442	191	72	.	.	PUNCT
ejpam-5442	192	1	furthermore	furthermore	ADV
ejpam-5442	192	2	,	,	PUNCT
ejpam-5442	192	3	we	we	PRON
ejpam-5442	192	4	provide	provide	VERB
ejpam-5442	192	5	a	a	DET
ejpam-5442	192	6	comparison	comparison	NOUN
ejpam-5442	192	7	of	of	ADP
ejpam-5442	192	8	the	the	DET
ejpam-5442	192	9	findings	finding	NOUN
ejpam-5442	192	10	derived	derive	VERB
ejpam-5442	192	11	from	from	ADP
ejpam-5442	192	12	the	the	DET
ejpam-5442	192	13	suggested	suggest	VERB
ejpam-5442	192	14	technique	technique	NOUN
ejpam-5442	192	15	with	with	ADP
ejpam-5442	192	16	those	those	PRON
ejpam-5442	192	17	given	give	VERB
ejpam-5442	192	18	by	by	ADP
ejpam-5442	192	19	using	use	VERB
ejpam-5442	192	20	the	the	DET
ejpam-5442	192	21	rk4	rk4	NOUN
ejpam-5442	192	22	method	method	NOUN
ejpam-5442	192	23	to	to	PART
ejpam-5442	192	24	assess	assess	VERB
ejpam-5442	192	25	the	the	DET
ejpam-5442	192	26	quality	quality	NOUN
ejpam-5442	192	27	and	and	CCONJ
ejpam-5442	192	28	accuracy	accuracy	NOUN
ejpam-5442	192	29	of	of	ADP
ejpam-5442	192	30	the	the	DET
ejpam-5442	192	31	given	give	VERB
ejpam-5442	192	32	scheme	scheme	NOUN
ejpam-5442	192	33	.	.	PUNCT
ejpam-5442	193	1	the	the	DET
ejpam-5442	193	2	numerical	numerical	ADJ
ejpam-5442	193	3	results	result	NOUN
ejpam-5442	193	4	obtained	obtain	VERB
ejpam-5442	193	5	for	for	ADP
ejpam-5442	193	6	the	the	DET
ejpam-5442	193	7	analyzed	analyze	VERB
ejpam-5442	193	8	model	model	NOUN
ejpam-5442	193	9	using	use	VERB
ejpam-5442	193	10	the	the	DET
ejpam-5442	193	11	introduced	introduce	VERB
ejpam-5442	193	12	numerical	numerical	ADJ
ejpam-5442	193	13	scheme	scheme	NOUN
ejpam-5442	193	14	are	be	AUX
ejpam-5442	193	15	presented	present	VERB
ejpam-5442	193	16	in	in	ADP
ejpam-5442	193	17	figures	figure	NOUN
ejpam-5442	193	18	1	1	NUM
ejpam-5442	193	19	-	-	SYM
ejpam-5442	193	20	3	3	NUM
ejpam-5442	193	21	.	.	PUNCT
ejpam-5442	194	1	(	(	PUNCT
ejpam-5442	194	2	i	i	NOUN
ejpam-5442	194	3	)	)	PUNCT
ejpam-5442	194	4	figure	figure	NOUN
ejpam-5442	194	5	1	1	NUM
ejpam-5442	194	6	illustrates	illustrate	VERB
ejpam-5442	194	7	the	the	DET
ejpam-5442	194	8	numerical	numerical	ADJ
ejpam-5442	194	9	solution	solution	NOUN
ejpam-5442	194	10	for	for	ADP
ejpam-5442	194	11	diverse	diverse	ADJ
ejpam-5442	194	12	values	value	NOUN
ejpam-5442	194	13	of	of	ADP
ejpam-5442	194	14	ϱ	ϱ	NOUN
ejpam-5442	194	15	=	=	SYM
ejpam-5442	194	16	1.0	1.0	NUM
ejpam-5442	194	17	,	,	PUNCT
ejpam-5442	194	18	0.95	0.95	NUM
ejpam-5442	194	19	,	,	PUNCT
ejpam-5442	194	20	0.85	0.85	NUM
ejpam-5442	194	21	,	,	PUNCT
ejpam-5442	194	22	0.75	0.75	NUM
ejpam-5442	194	23	,	,	PUNCT
ejpam-5442	194	24	with	with	ADP
ejpam-5442	194	25	h	h	NOUN
ejpam-5442	194	26	=	=	NOUN
ejpam-5442	194	27	0.1	0.1	NUM
ejpam-5442	194	28	,	,	PUNCT
ejpam-5442	194	29	under	under	ADP
ejpam-5442	194	30	the	the	DET
ejpam-5442	194	31	small	small	ADJ
ejpam-5442	194	32	values	value	NOUN
ejpam-5442	194	33	of	of	ADP
ejpam-5442	194	34	the	the	DET
ejpam-5442	194	35	i.cs	i.cs	NOUN
ejpam-5442	194	36	.	.	PUNCT
ejpam-5442	195	1	(	(	PUNCT
ejpam-5442	195	2	ii	ii	NOUN
ejpam-5442	195	3	)	)	PUNCT
ejpam-5442	195	4	figure	figure	NOUN
ejpam-5442	195	5	2	2	NUM
ejpam-5442	195	6	illustrates	illustrate	VERB
ejpam-5442	195	7	a	a	DET
ejpam-5442	195	8	comparison	comparison	NOUN
ejpam-5442	195	9	of	of	ADP
ejpam-5442	195	10	the	the	DET
ejpam-5442	195	11	results	result	NOUN
ejpam-5442	195	12	derived	derive	VERB
ejpam-5442	195	13	from	from	ADP
ejpam-5442	195	14	the	the	DET
ejpam-5442	195	15	proposed	propose	VERB
ejpam-5442	195	16	technique	technique	NOUN
ejpam-5442	195	17	against	against	ADP
ejpam-5442	195	18	those	those	PRON
ejpam-5442	195	19	obtained	obtain	VERB
ejpam-5442	195	20	using	use	VERB
ejpam-5442	195	21	the	the	DET
ejpam-5442	195	22	rk4	rk4	NOUN
ejpam-5442	195	23	method	method	NOUN
ejpam-5442	195	24	at	at	ADP
ejpam-5442	195	25	(	(	PUNCT
ejpam-5442	195	26	ϱ	ϱ	NOUN
ejpam-5442	195	27	=	=	NOUN
ejpam-5442	195	28	1	1	NUM
ejpam-5442	195	29	)	)	PUNCT
ejpam-5442	195	30	with	with	ADP
ejpam-5442	195	31	h	h	NOUN
ejpam-5442	195	32	=	=	NOUN
ejpam-5442	195	33	0.1	0.1	NUM
ejpam-5442	195	34	under	under	ADP
ejpam-5442	195	35	the	the	DET
ejpam-5442	195	36	small	small	ADJ
ejpam-5442	195	37	values	value	NOUN
ejpam-5442	195	38	of	of	ADP
ejpam-5442	195	39	the	the	DET
ejpam-5442	195	40	i.cs	i.cs	NOUN
ejpam-5442	195	41	.	.	PUNCT
ejpam-5442	196	1	(	(	PUNCT
ejpam-5442	196	2	iii	iii	X
ejpam-5442	196	3	)	)	PUNCT
ejpam-5442	196	4	figure	figure	NOUN
ejpam-5442	196	5	3	3	NUM
ejpam-5442	196	6	examines	examine	VERB
ejpam-5442	196	7	the	the	DET
ejpam-5442	196	8	impact	impact	NOUN
ejpam-5442	196	9	of	of	ADP
ejpam-5442	196	10	the	the	DET
ejpam-5442	196	11	natural	natural	ADJ
ejpam-5442	196	12	death	death	NOUN
ejpam-5442	196	13	rate	rate	NOUN
ejpam-5442	196	14	on	on	ADP
ejpam-5442	196	15	the	the	DET
ejpam-5442	196	16	system	system	NOUN
ejpam-5442	196	17	,	,	PUNCT
ejpam-5442	196	18	utilizing	utilize	VERB
ejpam-5442	196	19	various	various	ADJ
ejpam-5442	196	20	values	value	NOUN
ejpam-5442	196	21	of	of	ADP
ejpam-5442	196	22	β	β	X
ejpam-5442	196	23	=	=	SYM
ejpam-5442	196	24	0.002	0.002	NUM
ejpam-5442	196	25	,	,	PUNCT
ejpam-5442	196	26	0.004	0.004	NUM
ejpam-5442	196	27	,	,	PUNCT
ejpam-5442	196	28	0.006	0.006	NUM
ejpam-5442	196	29	,	,	PUNCT
ejpam-5442	196	30	0.008	0.008	NUM
ejpam-5442	196	31	,	,	PUNCT
ejpam-5442	196	32	at	at	ADP
ejpam-5442	196	33	ϱ	ϱ	NOUN
ejpam-5442	196	34	=	=	SYM
ejpam-5442	196	35	0.93	0.93	NUM
ejpam-5442	196	36	,	,	PUNCT
ejpam-5442	196	37	h	h	NOUN
ejpam-5442	196	38	=	=	NOUN
ejpam-5442	196	39	0.1	0.1	NUM
ejpam-5442	196	40	,	,	PUNCT
ejpam-5442	196	41	under	under	ADP
ejpam-5442	196	42	the	the	DET
ejpam-5442	196	43	large	large	ADJ
ejpam-5442	196	44	values	value	NOUN
ejpam-5442	196	45	of	of	ADP
ejpam-5442	196	46	the	the	DET
ejpam-5442	196	47	i.cs	i.cs	NOUN
ejpam-5442	196	48	.	.	PUNCT
ejpam-5442	196	49	by	by	ADP
ejpam-5442	196	50	looking	look	VERB
ejpam-5442	196	51	closely	closely	ADV
ejpam-5442	196	52	at	at	ADP
ejpam-5442	196	53	these	these	DET
ejpam-5442	196	54	three	three	NUM
ejpam-5442	196	55	figures	figure	NOUN
ejpam-5442	196	56	,	,	PUNCT
ejpam-5442	196	57	we	we	PRON
ejpam-5442	196	58	can	can	AUX
ejpam-5442	196	59	assert	assert	VERB
ejpam-5442	196	60	and	and	CCONJ
ejpam-5442	196	61	confirm	confirm	VERB
ejpam-5442	196	62	that	that	SCONJ
ejpam-5442	196	63	the	the	DET
ejpam-5442	196	64	numerical	numerical	ADJ
ejpam-5442	196	65	solution	solution	NOUN
ejpam-5442	196	66	is	be	AUX
ejpam-5442	196	67	based	base	VERB
ejpam-5442	196	68	on	on	ADP
ejpam-5442	196	69	the	the	DET
ejpam-5442	196	70	different	different	ADJ
ejpam-5442	196	71	values	value	NOUN
ejpam-5442	196	72	of	of	ADP
ejpam-5442	196	73	ϱ	ϱ	PROPN
ejpam-5442	196	74	,	,	PUNCT
ejpam-5442	196	75	h	h	NOUN
ejpam-5442	196	76	,	,	PUNCT
ejpam-5442	196	77	and	and	CCONJ
ejpam-5442	196	78	β	β	X
ejpam-5442	196	79	;	;	PUNCT
ejpam-5442	196	80	and	and	CCONJ
ejpam-5442	196	81	it	it	PRON
ejpam-5442	196	82	is	be	AUX
ejpam-5442	196	83	a	a	DET
ejpam-5442	196	84	clear	clear	ADJ
ejpam-5442	196	85	indication	indication	NOUN
ejpam-5442	196	86	that	that	SCONJ
ejpam-5442	196	87	the	the	DET
ejpam-5442	196	88	presented	present	VERB
ejpam-5442	196	89	numerical	numerical	ADJ
ejpam-5442	196	90	scheme	scheme	NOUN
ejpam-5442	196	91	has	have	AUX
ejpam-5442	196	92	been	be	AUX
ejpam-5442	196	93	well	well	ADV
ejpam-5442	196	94	-	-	PUNCT
ejpam-5442	196	95	implemented	implement	VERB
ejpam-5442	196	96	for	for	ADP
ejpam-5442	196	97	solving	solve	VERB
ejpam-5442	196	98	the	the	DET
ejpam-5442	196	99	suggested	suggest	VERB
ejpam-5442	196	100	system	system	NOUN
ejpam-5442	196	101	in	in	ADP
ejpam-5442	196	102	its	its	PRON
ejpam-5442	196	103	fractional	fractional	ADJ
ejpam-5442	196	104	form	form	NOUN
ejpam-5442	196	105	and	and	CCONJ
ejpam-5442	196	106	with	with	ADP
ejpam-5442	196	107	this	this	DET
ejpam-5442	196	108	type	type	NOUN
ejpam-5442	196	109	of	of	ADP
ejpam-5442	196	110	derivatives	derivative	NOUN
ejpam-5442	196	111	with	with	ADP
ejpam-5442	196	112	small	small	ADJ
ejpam-5442	196	113	and	and	CCONJ
ejpam-5442	196	114	large	large	ADJ
ejpam-5442	196	115	values	value	NOUN
ejpam-5442	196	116	of	of	ADP
ejpam-5442	196	117	the	the	DET
ejpam-5442	196	118	fractional	fractional	ADJ
ejpam-5442	196	119	order	order	NOUN
ejpam-5442	196	120	.	.	PUNCT
ejpam-5442	197	1	m.	m.	NOUN
ejpam-5442	197	2	adel	adel	PROPN
ejpam-5442	197	3	,	,	PUNCT
ejpam-5442	197	4	m.	m.	NOUN
ejpam-5442	197	5	m.	m.	NOUN
ejpam-5442	197	6	khader	khader	PROPN
ejpam-5442	197	7	,	,	PUNCT
ejpam-5442	197	8	n.	n.	PROPN
ejpam-5442	197	9	a.	a.	PROPN
ejpam-5442	197	10	mohammed	mohammed	PROPN
ejpam-5442	197	11	/	/	SYM
ejpam-5442	197	12	eur	eur	PROPN
ejpam-5442	197	13	.	.	PUNCT
ejpam-5442	198	1	j.	j.	PROPN
ejpam-5442	198	2	pure	pure	PROPN
ejpam-5442	198	3	appl	appl	PROPN
ejpam-5442	198	4	.	.	PROPN
ejpam-5442	198	5	math	math	PROPN
ejpam-5442	198	6	,	,	PUNCT
ejpam-5442	198	7	17	17	NUM
ejpam-5442	198	8	(	(	PUNCT
ejpam-5442	198	9	4	4	NUM
ejpam-5442	198	10	)	)	PUNCT
ejpam-5442	198	11	(	(	PUNCT
ejpam-5442	198	12	2024	2024	NUM
ejpam-5442	198	13	)	)	PUNCT
ejpam-5442	198	14	,	,	PUNCT
ejpam-5442	198	15	3277	3277	NUM
ejpam-5442	198	16	-	-	SYM
ejpam-5442	198	17	3290	3290	NUM
ejpam-5442	198	18	3285	3285	NUM
ejpam-5442	198	19	fig	fig	NOUN
ejpam-5442	198	20	.	.	PUNCT
ejpam-5442	199	1	1	1	NUM
ejpam-5442	199	2	:	:	PUNCT
ejpam-5442	199	3	the	the	DET
ejpam-5442	199	4	approximate	approximate	ADJ
ejpam-5442	199	5	solution	solution	NOUN
ejpam-5442	199	6	ψi(t	ψi(t	NOUN
ejpam-5442	199	7	)	)	PUNCT
ejpam-5442	199	8	,	,	PUNCT
ejpam-5442	199	9	i	i	PRON
ejpam-5442	199	10	=	=	NOUN
ejpam-5442	199	11	1	1	NUM
ejpam-5442	199	12	,	,	PUNCT
ejpam-5442	199	13	2	2	NUM
ejpam-5442	199	14	,	,	PUNCT
ejpam-5442	199	15	3	3	NUM
ejpam-5442	199	16	,	,	PUNCT
ejpam-5442	199	17	4	4	NUM
ejpam-5442	199	18	,	,	PUNCT
ejpam-5442	199	19	5	5	NUM
ejpam-5442	199	20	against	against	ADP
ejpam-5442	199	21	distinct	distinct	ADJ
ejpam-5442	199	22	values	value	NOUN
ejpam-5442	199	23	of	of	ADP
ejpam-5442	199	24	ϱ	ϱ	NOUN
ejpam-5442	199	25	with	with	ADP
ejpam-5442	199	26	small	small	ADJ
ejpam-5442	199	27	initial	initial	ADJ
ejpam-5442	199	28	values	value	NOUN
ejpam-5442	199	29	.	.	PUNCT
ejpam-5442	200	1	m.	m.	NOUN
ejpam-5442	200	2	adel	adel	PROPN
ejpam-5442	200	3	,	,	PUNCT
ejpam-5442	200	4	m.	m.	NOUN
ejpam-5442	200	5	m.	m.	NOUN
ejpam-5442	200	6	khader	khader	PROPN
ejpam-5442	200	7	,	,	PUNCT
ejpam-5442	200	8	n.	n.	PROPN
ejpam-5442	200	9	a.	a.	PROPN
ejpam-5442	200	10	mohammed	mohammed	PROPN
ejpam-5442	200	11	/	/	SYM
ejpam-5442	200	12	eur	eur	PROPN
ejpam-5442	200	13	.	.	PUNCT
ejpam-5442	201	1	j.	j.	PROPN
ejpam-5442	201	2	pure	pure	PROPN
ejpam-5442	201	3	appl	appl	PROPN
ejpam-5442	201	4	.	.	PROPN
ejpam-5442	201	5	math	math	PROPN
ejpam-5442	201	6	,	,	PUNCT
ejpam-5442	201	7	17	17	NUM
ejpam-5442	201	8	(	(	PUNCT
ejpam-5442	201	9	4	4	NUM
ejpam-5442	201	10	)	)	PUNCT
ejpam-5442	201	11	(	(	PUNCT
ejpam-5442	201	12	2024	2024	NUM
ejpam-5442	201	13	)	)	PUNCT
ejpam-5442	201	14	,	,	PUNCT
ejpam-5442	201	15	3277	3277	NUM
ejpam-5442	201	16	-	-	SYM
ejpam-5442	201	17	3290	3290	NUM
ejpam-5442	201	18	3286	3286	NUM
ejpam-5442	201	19	fig	fig	NOUN
ejpam-5442	201	20	.	.	PUNCT
ejpam-5442	202	1	2	2	NUM
ejpam-5442	202	2	:	:	PUNCT
ejpam-5442	202	3	the	the	DET
ejpam-5442	202	4	solution	solution	NOUN
ejpam-5442	202	5	ψi(t	ψi(t	NOUN
ejpam-5442	202	6	)	)	PUNCT
ejpam-5442	202	7	,	,	PUNCT
ejpam-5442	202	8	i	i	PRON
ejpam-5442	202	9	=	=	NOUN
ejpam-5442	202	10	1	1	NUM
ejpam-5442	202	11	,	,	PUNCT
ejpam-5442	202	12	2	2	NUM
ejpam-5442	202	13	,	,	PUNCT
ejpam-5442	202	14	3	3	NUM
ejpam-5442	202	15	,	,	PUNCT
ejpam-5442	202	16	4	4	NUM
ejpam-5442	202	17	,	,	PUNCT
ejpam-5442	202	18	5	5	NUM
ejpam-5442	202	19	by	by	ADP
ejpam-5442	202	20	the	the	DET
ejpam-5442	202	21	present	present	ADJ
ejpam-5442	202	22	and	and	CCONJ
ejpam-5442	202	23	rk4	rk4	NOUN
ejpam-5442	202	24	methods	method	NOUN
ejpam-5442	202	25	ϱ	ϱ	ADP
ejpam-5442	202	26	=	=	SYM
ejpam-5442	202	27	1	1	PROPN
ejpam-5442	202	28	.	.	PUNCT
ejpam-5442	202	29	m.	m.	NOUN
ejpam-5442	202	30	adel	adel	PROPN
ejpam-5442	202	31	,	,	PUNCT
ejpam-5442	202	32	m.	m.	NOUN
ejpam-5442	202	33	m.	m.	NOUN
ejpam-5442	202	34	khader	khader	PROPN
ejpam-5442	202	35	,	,	PUNCT
ejpam-5442	202	36	n.	n.	PROPN
ejpam-5442	202	37	a.	a.	PROPN
ejpam-5442	202	38	mohammed	mohammed	PROPN
ejpam-5442	202	39	/	/	SYM
ejpam-5442	202	40	eur	eur	PROPN
ejpam-5442	202	41	.	.	PUNCT
ejpam-5442	203	1	j.	j.	PROPN
ejpam-5442	203	2	pure	pure	PROPN
ejpam-5442	203	3	appl	appl	PROPN
ejpam-5442	203	4	.	.	PROPN
ejpam-5442	203	5	math	math	PROPN
ejpam-5442	203	6	,	,	PUNCT
ejpam-5442	203	7	17	17	NUM
ejpam-5442	203	8	(	(	PUNCT
ejpam-5442	203	9	4	4	NUM
ejpam-5442	203	10	)	)	PUNCT
ejpam-5442	203	11	(	(	PUNCT
ejpam-5442	203	12	2024	2024	NUM
ejpam-5442	203	13	)	)	PUNCT
ejpam-5442	203	14	,	,	PUNCT
ejpam-5442	203	15	3277	3277	NUM
ejpam-5442	203	16	-	-	SYM
ejpam-5442	203	17	3290	3290	NUM
ejpam-5442	203	18	3287	3287	NUM
ejpam-5442	203	19	fig	fig	NOUN
ejpam-5442	203	20	.	.	PUNCT
ejpam-5442	204	1	3	3	NUM
ejpam-5442	204	2	:	:	PUNCT
ejpam-5442	204	3	the	the	DET
ejpam-5442	204	4	effect	effect	NOUN
ejpam-5442	204	5	of	of	ADP
ejpam-5442	204	6	β	β	PRON
ejpam-5442	204	7	on	on	ADP
ejpam-5442	204	8	the	the	DET
ejpam-5442	204	9	approximate	approximate	ADJ
ejpam-5442	204	10	solution	solution	NOUN
ejpam-5442	204	11	ψi(t	ψi(t	NOUN
ejpam-5442	204	12	)	)	PUNCT
ejpam-5442	204	13	,	,	PUNCT
ejpam-5442	204	14	i	i	PRON
ejpam-5442	204	15	=	=	NOUN
ejpam-5442	204	16	1	1	NUM
ejpam-5442	204	17	,	,	PUNCT
ejpam-5442	204	18	2	2	NUM
ejpam-5442	204	19	,	,	PUNCT
ejpam-5442	204	20	3	3	NUM
ejpam-5442	204	21	,	,	PUNCT
ejpam-5442	204	22	4	4	NUM
ejpam-5442	204	23	,	,	PUNCT
ejpam-5442	204	24	5	5	NUM
ejpam-5442	204	25	.	.	NOUN
ejpam-5442	204	26	8	8	NUM
ejpam-5442	204	27	.	.	PUNCT
ejpam-5442	205	1	conclusions	conclusion	NOUN
ejpam-5442	205	2	and	and	CCONJ
ejpam-5442	205	3	discussions	discussion	NOUN
ejpam-5442	205	4	this	this	DET
ejpam-5442	205	5	study	study	NOUN
ejpam-5442	205	6	seeks	seek	VERB
ejpam-5442	205	7	to	to	PART
ejpam-5442	205	8	apply	apply	VERB
ejpam-5442	205	9	fractional	fractional	ADJ
ejpam-5442	205	10	calculus	calculus	NOUN
ejpam-5442	205	11	tools	tool	NOUN
ejpam-5442	205	12	and	and	CCONJ
ejpam-5442	205	13	techniques	technique	NOUN
ejpam-5442	205	14	to	to	PART
ejpam-5442	205	15	derive	derive	VERB
ejpam-5442	205	16	numerical	numerical	ADJ
ejpam-5442	205	17	solutions	solution	NOUN
ejpam-5442	205	18	for	for	ADP
ejpam-5442	205	19	the	the	DET
ejpam-5442	205	20	smoking	smoking	NOUN
ejpam-5442	205	21	mathematical	mathematical	ADJ
ejpam-5442	205	22	system	system	NOUN
ejpam-5442	205	23	,	,	PUNCT
ejpam-5442	205	24	utilizing	utilize	VERB
ejpam-5442	205	25	the	the	DET
ejpam-5442	205	26	cf	cf	NOUN
ejpam-5442	205	27	-	-	PUNCT
ejpam-5442	205	28	fractional	fractional	ADJ
ejpam-5442	205	29	derivative	derivative	ADJ
ejpam-5442	205	30	operator	operator	NOUN
ejpam-5442	205	31	.	.	PUNCT
ejpam-5442	206	1	the	the	DET
ejpam-5442	206	2	numerical	numerical	ADJ
ejpam-5442	206	3	evaluation	evaluation	NOUN
ejpam-5442	206	4	of	of	ADP
ejpam-5442	206	5	the	the	DET
ejpam-5442	206	6	conversion	conversion	NOUN
ejpam-5442	206	7	system	system	NOUN
ejpam-5442	206	8	for	for	ADP
ejpam-5442	206	9	fractional	fractional	ADJ
ejpam-5442	206	10	integral	integral	ADJ
ejpam-5442	206	11	equations	equation	NOUN
ejpam-5442	206	12	is	be	AUX
ejpam-5442	206	13	conducted	conduct	VERB
ejpam-5442	206	14	utilizing	utilize	VERB
ejpam-5442	206	15	simpson	simpson	PROPN
ejpam-5442	206	16	’s	’s	PART
ejpam-5442	206	17	1/3	1/3	NUM
ejpam-5442	206	18	formula	formula	NOUN
ejpam-5442	206	19	,	,	PUNCT
ejpam-5442	206	20	attaining	attain	VERB
ejpam-5442	206	21	fourth	fourth	ADJ
ejpam-5442	206	22	-	-	PUNCT
ejpam-5442	206	23	order	order	NOUN
ejpam-5442	206	24	accuracy	accuracy	NOUN
ejpam-5442	206	25	.	.	PUNCT
ejpam-5442	207	1	this	this	DET
ejpam-5442	207	2	study	study	NOUN
ejpam-5442	207	3	employed	employ	VERB
ejpam-5442	207	4	various	various	ADJ
ejpam-5442	207	5	values	value	NOUN
ejpam-5442	207	6	of	of	ADP
ejpam-5442	207	7	the	the	DET
ejpam-5442	207	8	fractional	fractional	ADJ
ejpam-5442	207	9	order	order	NOUN
ejpam-5442	207	10	ϱ	ϱ	ADP
ejpam-5442	207	11	and	and	CCONJ
ejpam-5442	207	12	a	a	DET
ejpam-5442	207	13	step	step	NOUN
ejpam-5442	207	14	size	size	NOUN
ejpam-5442	207	15	of	of	ADP
ejpam-5442	207	16	h	h	NOUN
ejpam-5442	207	17	=	=	NOUN
ejpam-5442	207	18	0.1	0.1	NUM
ejpam-5442	207	19	to	to	PART
ejpam-5442	207	20	obtain	obtain	VERB
ejpam-5442	207	21	solureferences	solureference	NOUN
ejpam-5442	207	22	3288	3288	NUM
ejpam-5442	207	23	tions	tion	NOUN
ejpam-5442	207	24	for	for	ADP
ejpam-5442	207	25	the	the	DET
ejpam-5442	207	26	mathematical	mathematical	ADJ
ejpam-5442	207	27	model	model	NOUN
ejpam-5442	207	28	under	under	ADP
ejpam-5442	207	29	investigation	investigation	NOUN
ejpam-5442	207	30	.	.	PUNCT
ejpam-5442	208	1	furthermore	furthermore	ADV
ejpam-5442	208	2	,	,	PUNCT
ejpam-5442	208	3	we	we	PRON
ejpam-5442	208	4	have	have	AUX
ejpam-5442	208	5	ascertained	ascertain	VERB
ejpam-5442	208	6	that	that	SCONJ
ejpam-5442	208	7	the	the	DET
ejpam-5442	208	8	suggested	suggest	VERB
ejpam-5442	208	9	methodology	methodology	NOUN
ejpam-5442	208	10	is	be	AUX
ejpam-5442	208	11	exceptionally	exceptionally	ADV
ejpam-5442	208	12	proficient	proficient	ADJ
ejpam-5442	208	13	in	in	ADP
ejpam-5442	208	14	evaluating	evaluate	VERB
ejpam-5442	208	15	this	this	DET
ejpam-5442	208	16	mathematical	mathematical	ADJ
ejpam-5442	208	17	model	model	NOUN
ejpam-5442	208	18	.	.	PUNCT
ejpam-5442	209	1	furthermore	furthermore	ADV
ejpam-5442	209	2	,	,	PUNCT
ejpam-5442	209	3	reducing	reduce	VERB
ejpam-5442	209	4	the	the	DET
ejpam-5442	209	5	value	value	NOUN
ejpam-5442	209	6	of	of	ADP
ejpam-5442	209	7	h	h	NOUN
ejpam-5442	209	8	allows	allow	VERB
ejpam-5442	209	9	us	we	PRON
ejpam-5442	209	10	to	to	PART
ejpam-5442	209	11	control	control	VERB
ejpam-5442	209	12	the	the	DET
ejpam-5442	209	13	accuracy	accuracy	NOUN
ejpam-5442	209	14	of	of	ADP
ejpam-5442	209	15	the	the	DET
ejpam-5442	209	16	numerical	numerical	ADJ
ejpam-5442	209	17	solutions	solution	NOUN
ejpam-5442	209	18	.	.	PUNCT
ejpam-5442	210	1	in	in	ADP
ejpam-5442	210	2	conclusion	conclusion	NOUN
ejpam-5442	210	3	,	,	PUNCT
ejpam-5442	210	4	we	we	PRON
ejpam-5442	210	5	have	have	AUX
ejpam-5442	210	6	found	find	VERB
ejpam-5442	210	7	that	that	SCONJ
ejpam-5442	210	8	using	use	VERB
ejpam-5442	210	9	the	the	DET
ejpam-5442	210	10	cf	cf	NOUN
ejpam-5442	210	11	-	-	PUNCT
ejpam-5442	210	12	fractional	fractional	ADJ
ejpam-5442	210	13	derivative	derivative	ADJ
ejpam-5442	210	14	operator	operator	NOUN
ejpam-5442	210	15	makes	make	VERB
ejpam-5442	210	16	the	the	DET
ejpam-5442	210	17	mathematical	mathematical	ADJ
ejpam-5442	210	18	model	model	NOUN
ejpam-5442	210	19	under	under	ADP
ejpam-5442	210	20	study	study	NOUN
ejpam-5442	210	21	in	in	ADP
ejpam-5442	210	22	this	this	DET
ejpam-5442	210	23	research	research	NOUN
ejpam-5442	210	24	more	more	ADV
ejpam-5442	210	25	suitable	suitable	ADJ
ejpam-5442	210	26	for	for	ADP
ejpam-5442	210	27	numerical	numerical	ADJ
ejpam-5442	210	28	simulations	simulation	NOUN
ejpam-5442	210	29	.	.	PUNCT
ejpam-5442	211	1	the	the	DET
ejpam-5442	211	2	rk4	rk4	NOUN
ejpam-5442	211	3	technique	technique	NOUN
ejpam-5442	211	4	produces	produce	VERB
ejpam-5442	211	5	similar	similar	ADJ
ejpam-5442	211	6	graphical	graphical	ADJ
ejpam-5442	211	7	findings	finding	NOUN
ejpam-5442	211	8	and	and	CCONJ
ejpam-5442	211	9	results	result	NOUN
ejpam-5442	211	10	.	.	PUNCT
ejpam-5442	212	1	furthermore	furthermore	ADV
ejpam-5442	212	2	,	,	PUNCT
ejpam-5442	212	3	our	our	PRON
ejpam-5442	212	4	research	research	NOUN
ejpam-5442	212	5	reveals	reveal	VERB
ejpam-5442	212	6	the	the	DET
ejpam-5442	212	7	precise	precise	ADJ
ejpam-5442	212	8	and	and	CCONJ
ejpam-5442	212	9	efficient	efficient	ADJ
ejpam-5442	212	10	nature	nature	NOUN
ejpam-5442	212	11	of	of	ADP
ejpam-5442	212	12	the	the	DET
ejpam-5442	212	13	suggested	suggest	VERB
ejpam-5442	212	14	approach	approach	NOUN
ejpam-5442	212	15	.	.	PUNCT
ejpam-5442	213	1	in	in	ADP
ejpam-5442	213	2	future	future	ADJ
ejpam-5442	213	3	studies	study	NOUN
ejpam-5442	213	4	,	,	PUNCT
ejpam-5442	213	5	we	we	PRON
ejpam-5442	213	6	want	want	VERB
ejpam-5442	213	7	to	to	PART
ejpam-5442	213	8	utilize	utilize	VERB
ejpam-5442	213	9	the	the	DET
ejpam-5442	213	10	same	same	ADJ
ejpam-5442	213	11	model	model	NOUN
ejpam-5442	213	12	as	as	ADP
ejpam-5442	213	13	a	a	DET
ejpam-5442	213	14	generalization	generalization	NOUN
ejpam-5442	213	15	of	of	ADP
ejpam-5442	213	16	the	the	DET
ejpam-5442	213	17	current	current	ADJ
ejpam-5442	213	18	work	work	NOUN
ejpam-5442	213	19	but	but	CCONJ
ejpam-5442	213	20	with	with	ADP
ejpam-5442	213	21	varying	vary	VERB
ejpam-5442	213	22	types	type	NOUN
ejpam-5442	213	23	of	of	ADP
ejpam-5442	213	24	fractional	fractional	ADJ
ejpam-5442	213	25	derivatives	derivative	NOUN
ejpam-5442	213	26	.	.	PUNCT
ejpam-5442	214	1	acknowledgements	acknowledgement	NOUN
ejpam-5442	214	2	the	the	DET
ejpam-5442	214	3	researchers	researcher	NOUN
ejpam-5442	214	4	wish	wish	VERB
ejpam-5442	214	5	to	to	PART
ejpam-5442	214	6	extend	extend	VERB
ejpam-5442	214	7	their	their	PRON
ejpam-5442	214	8	sincere	sincere	ADJ
ejpam-5442	214	9	gratitude	gratitude	NOUN
ejpam-5442	214	10	to	to	ADP
ejpam-5442	214	11	the	the	DET
ejpam-5442	214	12	deanship	deanship	NOUN
ejpam-5442	214	13	of	of	ADP
ejpam-5442	214	14	scientific	scientific	ADJ
ejpam-5442	214	15	research	research	NOUN
ejpam-5442	214	16	at	at	ADP
ejpam-5442	214	17	the	the	DET
ejpam-5442	214	18	islamic	islamic	PROPN
ejpam-5442	214	19	university	university	PROPN
ejpam-5442	214	20	of	of	ADP
ejpam-5442	214	21	madinah	madinah	PROPN
ejpam-5442	214	22	for	for	ADP
ejpam-5442	214	23	the	the	DET
ejpam-5442	214	24	support	support	NOUN
ejpam-5442	214	25	provided	provide	VERB
ejpam-5442	214	26	to	to	ADP
ejpam-5442	214	27	the	the	DET
ejpam-5442	214	28	postpublishing	postpublishe	VERB
ejpam-5442	214	29	program	program	NOUN
ejpam-5442	214	30	.	.	PUNCT
ejpam-5442	215	1	references	reference	NOUN
ejpam-5442	215	2	[	[	X
ejpam-5442	215	3	1	1	X
ejpam-5442	215	4	]	]	PUNCT
ejpam-5442	215	5	t.	t.	NOUN
ejpam-5442	215	6	abdeljawad	abdeljawad	PROPN
ejpam-5442	215	7	and	and	CCONJ
ejpam-5442	215	8	d.	d.	PROPN
ejpam-5442	215	9	baleanu	baleanu	PROPN
ejpam-5442	215	10	.	.	PUNCT
ejpam-5442	216	1	on	on	ADP
ejpam-5442	216	2	fractional	fractional	ADJ
ejpam-5442	216	3	derivatives	derivative	NOUN
ejpam-5442	216	4	with	with	ADP
ejpam-5442	216	5	exponential	exponential	ADJ
ejpam-5442	216	6	kernel	kernel	NOUN
ejpam-5442	216	7	and	and	CCONJ
ejpam-5442	216	8	their	their	PRON
ejpam-5442	216	9	discrete	discrete	ADJ
ejpam-5442	216	10	versions	version	NOUN
ejpam-5442	216	11	.	.	PUNCT
ejpam-5442	217	1	reports	report	NOUN
ejpam-5442	217	2	on	on	ADP
ejpam-5442	217	3	mathematical	mathematical	ADJ
ejpam-5442	217	4	physics	physics	NOUN
ejpam-5442	217	5	,	,	PUNCT
ejpam-5442	217	6	80:11–27	80:11–27	NUM
ejpam-5442	217	7	,	,	PUNCT
ejpam-5442	217	8	2017	2017	NUM
ejpam-5442	217	9	.	.	PUNCT
ejpam-5442	218	1	[	[	X
ejpam-5442	218	2	2	2	NUM
ejpam-5442	218	3	]	]	PUNCT
ejpam-5442	218	4	k.	k.	PROPN
ejpam-5442	218	5	abuasbeh	abuasbeh	PROPN
ejpam-5442	218	6	,	,	PUNCT
ejpam-5442	218	7	r.	r.	PROPN
ejpam-5442	218	8	shafqat	shafqat	PROPN
ejpam-5442	218	9	,	,	PUNCT
ejpam-5442	218	10	a.	a.	NOUN
ejpam-5442	218	11	alsinai	alsinai	PROPN
ejpam-5442	218	12	,	,	PUNCT
ejpam-5442	218	13	and	and	CCONJ
ejpam-5442	218	14	m.	m.	NOUN
ejpam-5442	218	15	awadalla	awadalla	PROPN
ejpam-5442	218	16	.	.	PUNCT
ejpam-5442	219	1	analysis	analysis	NOUN
ejpam-5442	219	2	of	of	ADP
ejpam-5442	219	3	the	the	DET
ejpam-5442	219	4	mathematical	mathematical	ADJ
ejpam-5442	219	5	modeling	modeling	NOUN
ejpam-5442	219	6	of	of	ADP
ejpam-5442	219	7	covid-19	covid-19	PROPN
ejpam-5442	219	8	by	by	ADP
ejpam-5442	219	9	using	use	VERB
ejpam-5442	219	10	a	a	DET
ejpam-5442	219	11	mild	mild	ADJ
ejpam-5442	219	12	solution	solution	NOUN
ejpam-5442	219	13	with	with	ADP
ejpam-5442	219	14	delay	delay	PROPN
ejpam-5442	219	15	caputo	caputo	PROPN
ejpam-5442	219	16	operator	operator	PROPN
ejpam-5442	219	17	.	.	PUNCT
ejpam-5442	219	18	symmetry	symmetry	PROPN
ejpam-5442	219	19	,	,	PUNCT
ejpam-5442	219	20	15:286	15:286	NUM
ejpam-5442	219	21	,	,	PUNCT
ejpam-5442	219	22	2023	2023	NUM
ejpam-5442	219	23	.	.	PUNCT
ejpam-5442	220	1	[	[	X
ejpam-5442	220	2	3	3	X
ejpam-5442	220	3	]	]	PUNCT
ejpam-5442	220	4	w.	w.	PROPN
ejpam-5442	220	5	al	al	PROPN
ejpam-5442	220	6	-	-	PUNCT
ejpam-5442	220	7	sadi	sadi	PROPN
ejpam-5442	220	8	,	,	PUNCT
ejpam-5442	220	9	z.	z.	PROPN
ejpam-5442	220	10	wei	wei	PROPN
ejpam-5442	220	11	,	,	PUNCT
ejpam-5442	220	12	t.	t.	PROPN
ejpam-5442	220	13	q.	q.	PROPN
ejpam-5442	220	14	s.	s.	PROPN
ejpam-5442	220	15	abdullah	abdullah	PROPN
ejpam-5442	220	16	,	,	PUNCT
ejpam-5442	220	17	a.	a.	NOUN
ejpam-5442	220	18	alkhazzan	alkhazzan	PROPN
ejpam-5442	220	19	,	,	PUNCT
ejpam-5442	220	20	and	and	CCONJ
ejpam-5442	220	21	j.	j.	PROPN
ejpam-5442	220	22	f.	f.	PROPN
ejpam-5442	220	23	gomez	gomez	PROPN
ejpam-5442	220	24	-	-	PUNCT
ejpam-5442	220	25	aguilar	aguilar	PROPN
ejpam-5442	220	26	.	.	PUNCT
ejpam-5442	221	1	dynamical	dynamical	ADJ
ejpam-5442	221	2	and	and	CCONJ
ejpam-5442	221	3	numerical	numerical	ADJ
ejpam-5442	221	4	analysis	analysis	NOUN
ejpam-5442	221	5	of	of	ADP
ejpam-5442	221	6	the	the	DET
ejpam-5442	221	7	hepatitis	hepatitis	PROPN
ejpam-5442	221	8	b	b	PROPN
ejpam-5442	221	9	virus	virus	NOUN
ejpam-5442	221	10	treatment	treatment	NOUN
ejpam-5442	221	11	model	model	NOUN
ejpam-5442	221	12	through	through	ADP
ejpam-5442	221	13	fractal	fractal	ADJ
ejpam-5442	221	14	-	-	PUNCT
ejpam-5442	221	15	fractional	fractional	ADJ
ejpam-5442	221	16	derivative	derivative	NOUN
ejpam-5442	221	17	.	.	PUNCT
ejpam-5442	222	1	mathematical	mathematical	ADJ
ejpam-5442	222	2	methods	method	NOUN
ejpam-5442	222	3	in	in	ADP
ejpam-5442	222	4	the	the	DET
ejpam-5442	222	5	applied	apply	VERB
ejpam-5442	222	6	sciences	science	NOUN
ejpam-5442	222	7	,	,	PUNCT
ejpam-5442	222	8	5:1–19	5:1–19	NUM
ejpam-5442	222	9	,	,	PUNCT
ejpam-5442	222	10	2024	2024	NUM
ejpam-5442	222	11	.	.	PUNCT
ejpam-5442	223	1	[	[	X
ejpam-5442	223	2	4	4	NUM
ejpam-5442	223	3	]	]	X
ejpam-5442	223	4	m.	m.	NOUN
ejpam-5442	223	5	alqhtani	alqhtani	PROPN
ejpam-5442	223	6	,	,	PUNCT
ejpam-5442	223	7	j.	j.	PROPN
ejpam-5442	223	8	f.	f.	PROPN
ejpam-5442	223	9	gomez	gomez	PROPN
ejpam-5442	223	10	aguilar	aguilar	PROPN
ejpam-5442	223	11	,	,	PUNCT
ejpam-5442	223	12	k.	k.	PROPN
ejpam-5442	223	13	m.	m.	PROPN
ejpam-5442	223	14	saad	saad	PROPN
ejpam-5442	223	15	,	,	PUNCT
ejpam-5442	223	16	z.	z.	PROPN
ejpam-5442	223	17	sabir	sabir	PROPN
ejpam-5442	223	18	,	,	PUNCT
ejpam-5442	223	19	and	and	CCONJ
ejpam-5442	223	20	e.	e.	PROPN
ejpam-5442	223	21	p.	p.	PROPN
ejpam-5442	223	22	careta	careta	PROPN
ejpam-5442	223	23	.	.	PUNCT
ejpam-5442	224	1	a	a	DET
ejpam-5442	224	2	scale	scale	NOUN
ejpam-5442	224	3	conjugate	conjugate	ADJ
ejpam-5442	224	4	neural	neural	ADJ
ejpam-5442	224	5	network	network	NOUN
ejpam-5442	224	6	learning	learning	NOUN
ejpam-5442	224	7	process	process	NOUN
ejpam-5442	224	8	for	for	ADP
ejpam-5442	224	9	the	the	DET
ejpam-5442	224	10	nonlinear	nonlinear	ADJ
ejpam-5442	224	11	malaria	malaria	PROPN
ejpam-5442	224	12	disease	disease	NOUN
ejpam-5442	224	13	model	model	NOUN
ejpam-5442	224	14	.	.	PUNCT
ejpam-5442	225	1	aims	aim	VERB
ejpam-5442	225	2	mathematics	mathematic	NOUN
ejpam-5442	225	3	,	,	PUNCT
ejpam-5442	225	4	89:21106–2122	89:21106–2122	NUM
ejpam-5442	225	5	,	,	PUNCT
ejpam-5442	225	6	2023	2023	NUM
ejpam-5442	225	7	.	.	PUNCT
ejpam-5442	226	1	[	[	X
ejpam-5442	226	2	5	5	X
ejpam-5442	226	3	]	]	PUNCT
ejpam-5442	226	4	j.	j.	PROPN
ejpam-5442	226	5	alzabut	alzabut	PROPN
ejpam-5442	226	6	,	,	PUNCT
ejpam-5442	226	7	r.	r.	PROPN
ejpam-5442	226	8	dhineshbabu	dhineshbabu	PROPN
ejpam-5442	226	9	,	,	PUNCT
ejpam-5442	226	10	a.	a.	PROPN
ejpam-5442	226	11	g.	g.	PROPN
ejpam-5442	226	12	m.	m.	PROPN
ejpam-5442	226	13	selvam	selvam	PROPN
ejpam-5442	226	14	,	,	PUNCT
ejpam-5442	226	15	j.	j.	PROPN
ejpam-5442	226	16	f.	f.	PROPN
ejpam-5442	226	17	gomez	gomez	PROPN
ejpam-5442	226	18	-	-	PUNCT
ejpam-5442	226	19	aguilar	aguilar	PROPN
ejpam-5442	226	20	,	,	PUNCT
ejpam-5442	226	21	and	and	CCONJ
ejpam-5442	226	22	h.	h.	PROPN
ejpam-5442	226	23	khan	khan	PROPN
ejpam-5442	226	24	.	.	PUNCT
ejpam-5442	227	1	existence	existence	NOUN
ejpam-5442	227	2	,	,	PUNCT
ejpam-5442	227	3	uniqueness	uniqueness	NOUN
ejpam-5442	227	4	and	and	CCONJ
ejpam-5442	227	5	synchronization	synchronization	NOUN
ejpam-5442	227	6	of	of	ADP
ejpam-5442	227	7	a	a	DET
ejpam-5442	227	8	fractional	fractional	ADJ
ejpam-5442	227	9	tumor	tumor	NOUN
ejpam-5442	227	10	growth	growth	NOUN
ejpam-5442	227	11	model	model	NOUN
ejpam-5442	227	12	in	in	ADP
ejpam-5442	227	13	discrete	discrete	ADJ
ejpam-5442	227	14	time	time	NOUN
ejpam-5442	227	15	with	with	ADP
ejpam-5442	227	16	numerical	numerical	ADJ
ejpam-5442	227	17	results	result	NOUN
ejpam-5442	227	18	.	.	PUNCT
ejpam-5442	228	1	results	result	NOUN
ejpam-5442	228	2	in	in	ADP
ejpam-5442	228	3	physics	physics	NOUN
ejpam-5442	228	4	,	,	PUNCT
ejpam-5442	228	5	54:107030	54:107030	NUM
ejpam-5442	228	6	,	,	PUNCT
ejpam-5442	228	7	2023	2023	NUM
ejpam-5442	228	8	.	.	PUNCT
ejpam-5442	229	1	[	[	X
ejpam-5442	229	2	6	6	NUM
ejpam-5442	229	3	]	]	X
ejpam-5442	229	4	y.	y.	PROPN
ejpam-5442	229	5	n.	n.	PROPN
ejpam-5442	229	6	anjam	anjam	PROPN
ejpam-5442	229	7	,	,	PUNCT
ejpam-5442	229	8	r.	r.	PROPN
ejpam-5442	229	9	shafqat	shafqat	PROPN
ejpam-5442	229	10	,	,	PUNCT
ejpam-5442	229	11	i.	i.	PROPN
ejpam-5442	229	12	e.	e.	PROPN
ejpam-5442	229	13	sarris	sarris	PROPN
ejpam-5442	229	14	,	,	PUNCT
ejpam-5442	229	15	m.	m.	NOUN
ejpam-5442	229	16	rahma	rahma	PROPN
ejpam-5442	229	17	,	,	PUNCT
ejpam-5442	229	18	s.	s.	PROPN
ejpam-5442	229	19	touseef	touseef	PROPN
ejpam-5442	229	20	,	,	PUNCT
ejpam-5442	229	21	and	and	CCONJ
ejpam-5442	229	22	m.	m.	PROPN
ejpam-5442	229	23	arshad	arshad	PROPN
ejpam-5442	229	24	.	.	PUNCT
ejpam-5442	230	1	a	a	DET
ejpam-5442	230	2	fractional	fractional	ADJ
ejpam-5442	230	3	order	order	NOUN
ejpam-5442	230	4	investigation	investigation	NOUN
ejpam-5442	230	5	of	of	ADP
ejpam-5442	230	6	the	the	DET
ejpam-5442	230	7	smoking	smoking	NOUN
ejpam-5442	230	8	model	model	NOUN
ejpam-5442	230	9	using	use	VERB
ejpam-5442	230	10	the	the	DET
ejpam-5442	230	11	caputo	caputo	PROPN
ejpam-5442	230	12	-	-	PUNCT
ejpam-5442	230	13	fabrizio	fabrizio	PROPN
ejpam-5442	230	14	differential	differential	NOUN
ejpam-5442	230	15	operator	operator	NOUN
ejpam-5442	230	16	.	.	PUNCT
ejpam-5442	231	1	fractal	fractal	ADJ
ejpam-5442	231	2	fract	fract	PROPN
ejpam-5442	231	3	.	.	PUNCT
ejpam-5442	231	4	,	,	PUNCT
ejpam-5442	231	5	623:1–18	623:1–18	NUM
ejpam-5442	231	6	,	,	PUNCT
ejpam-5442	231	7	2022	2022	NUM
ejpam-5442	231	8	.	.	PUNCT
ejpam-5442	232	1	[	[	X
ejpam-5442	232	2	7	7	X
ejpam-5442	232	3	]	]	X
ejpam-5442	232	4	h.	h.	PROPN
ejpam-5442	232	5	m.	m.	PROPN
ejpam-5442	232	6	arshad	arshad	PROPN
ejpam-5442	232	7	and	and	CCONJ
ejpam-5442	232	8	r.	r.	PROPN
ejpam-5442	232	9	shafqat	shafqat	PROPN
ejpam-5442	232	10	.	.	PUNCT
ejpam-5442	233	1	approximating	approximate	VERB
ejpam-5442	233	2	solutions	solution	NOUN
ejpam-5442	233	3	of	of	ADP
ejpam-5442	233	4	fuzzy	fuzzy	ADJ
ejpam-5442	233	5	stochastic	stochastic	ADJ
ejpam-5442	233	6	fractional	fractional	ADJ
ejpam-5442	233	7	integro	integro	ADJ
ejpam-5442	233	8	-	-	PUNCT
ejpam-5442	233	9	evolution	evolution	NOUN
ejpam-5442	233	10	equations	equation	NOUN
ejpam-5442	233	11	with	with	ADP
ejpam-5442	233	12	the	the	DET
ejpam-5442	233	13	averaging	averaging	NOUN
ejpam-5442	233	14	principle	principle	NOUN
ejpam-5442	233	15	:	:	PUNCT
ejpam-5442	233	16	theory	theory	NOUN
ejpam-5442	233	17	and	and	CCONJ
ejpam-5442	233	18	applications	application	NOUN
ejpam-5442	233	19	.	.	PUNCT
ejpam-5442	234	1	international	international	ADJ
ejpam-5442	234	2	journal	journal	NOUN
ejpam-5442	234	3	of	of	ADP
ejpam-5442	234	4	advancements	advancement	NOUN
ejpam-5442	234	5	in	in	ADP
ejpam-5442	234	6	mathematics	mathematic	NOUN
ejpam-5442	234	7	,	,	PUNCT
ejpam-5442	234	8	22:150–163	22:150–163	NUM
ejpam-5442	234	9	,	,	PUNCT
ejpam-5442	234	10	2022	2022	NUM
ejpam-5442	234	11	.	.	PUNCT
ejpam-5442	235	1	references	reference	NOUN
ejpam-5442	235	2	3289	3289	NUM
ejpam-5442	236	1	[	[	X
ejpam-5442	236	2	8	8	NUM
ejpam-5442	236	3	]	]	PUNCT
ejpam-5442	236	4	s.	s.	PROPN
ejpam-5442	236	5	arshad	arshad	PROPN
ejpam-5442	236	6	,	,	PUNCT
ejpam-5442	236	7	i.	i.	PROPN
ejpam-5442	236	8	saleem	saleem	PROPN
ejpam-5442	236	9	,	,	PUNCT
ejpam-5442	236	10	a.	a.	PROPN
ejpam-5442	236	11	akgül	akgül	PROPN
ejpam-5442	236	12	,	,	PUNCT
ejpam-5442	236	13	j.	j.	PROPN
ejpam-5442	236	14	huang	huang	PROPN
ejpam-5442	236	15	,	,	PUNCT
ejpam-5442	236	16	y.	y.	PROPN
ejpam-5442	236	17	tang	tang	PROPN
ejpam-5442	236	18	,	,	PUNCT
ejpam-5442	236	19	and	and	CCONJ
ejpam-5442	236	20	s.	s.	PROPN
ejpam-5442	236	21	m.	m.	PROPN
ejpam-5442	236	22	eldin	eldin	PROPN
ejpam-5442	236	23	.	.	PUNCT
ejpam-5442	237	1	a	a	DET
ejpam-5442	237	2	novel	novel	ADJ
ejpam-5442	237	3	numerical	numerical	ADJ
ejpam-5442	237	4	method	method	NOUN
ejpam-5442	237	5	for	for	ADP
ejpam-5442	237	6	solving	solve	VERB
ejpam-5442	237	7	the	the	DET
ejpam-5442	237	8	caputo	caputo	PROPN
ejpam-5442	237	9	-	-	PUNCT
ejpam-5442	237	10	fabrizio	fabrizio	PROPN
ejpam-5442	237	11	fractional	fractional	ADJ
ejpam-5442	237	12	differential	differential	NOUN
ejpam-5442	237	13	equation	equation	NOUN
ejpam-5442	237	14	.	.	PUNCT
ejpam-5442	238	1	aims	aim	VERB
ejpam-5442	238	2	mathematics	mathematic	NOUN
ejpam-5442	238	3	,	,	PUNCT
ejpam-5442	238	4	84:9535–9556	84:9535–9556	NUM
ejpam-5442	238	5	,	,	PUNCT
ejpam-5442	238	6	2022	2022	NUM
ejpam-5442	238	7	.	.	PUNCT
ejpam-5442	239	1	[	[	X
ejpam-5442	239	2	9	9	NUM
ejpam-5442	239	3	]	]	PUNCT
ejpam-5442	239	4	m.	m.	NOUN
ejpam-5442	239	5	caputo	caputo	PROPN
ejpam-5442	239	6	and	and	CCONJ
ejpam-5442	239	7	m.	m.	PROPN
ejpam-5442	239	8	fabrizio	fabrizio	PROPN
ejpam-5442	239	9	.	.	PUNCT
ejpam-5442	240	1	a	a	DET
ejpam-5442	240	2	new	new	ADJ
ejpam-5442	240	3	definition	definition	NOUN
ejpam-5442	240	4	of	of	ADP
ejpam-5442	240	5	fractional	fractional	ADJ
ejpam-5442	240	6	derivative	derivative	NOUN
ejpam-5442	240	7	without	without	ADP
ejpam-5442	240	8	singular	singular	ADJ
ejpam-5442	240	9	kernel	kernel	PROPN
ejpam-5442	240	10	.	.	PUNCT
ejpam-5442	241	1	progr	progr	NOUN
ejpam-5442	241	2	.	.	PUNCT
ejpam-5442	242	1	fract	fract	PROPN
ejpam-5442	242	2	.	.	PUNCT
ejpam-5442	243	1	differ	differ	VERB
ejpam-5442	243	2	.	.	PUNCT
ejpam-5442	244	1	appl	appl	PROPN
ejpam-5442	244	2	.	.	PROPN
ejpam-5442	244	3	,	,	PUNCT
ejpam-5442	244	4	1:73–85	1:73–85	NUM
ejpam-5442	244	5	,	,	PUNCT
ejpam-5442	244	6	2015	2015	NUM
ejpam-5442	244	7	.	.	PUNCT
ejpam-5442	245	1	[	[	X
ejpam-5442	245	2	10	10	NUM
ejpam-5442	245	3	]	]	X
ejpam-5442	245	4	v.	v.	CCONJ
ejpam-5442	245	5	s.	s.	PROPN
ejpam-5442	245	6	erturk	erturk	PROPN
ejpam-5442	245	7	,	,	PUNCT
ejpam-5442	245	8	g.	g.	PROPN
ejpam-5442	245	9	zaman	zaman	PROPN
ejpam-5442	245	10	,	,	PUNCT
ejpam-5442	245	11	and	and	CCONJ
ejpam-5442	245	12	s.	s.	PROPN
ejpam-5442	245	13	momani	momani	PROPN
ejpam-5442	245	14	.	.	PUNCT
ejpam-5442	246	1	a	a	DET
ejpam-5442	246	2	numeric	numeric	ADJ
ejpam-5442	246	3	analytic	analytic	ADJ
ejpam-5442	246	4	method	method	NOUN
ejpam-5442	246	5	for	for	ADP
ejpam-5442	246	6	approximating	approximate	VERB
ejpam-5442	246	7	a	a	DET
ejpam-5442	246	8	giving	giving	NOUN
ejpam-5442	246	9	up	up	ADP
ejpam-5442	246	10	smoking	smoking	NOUN
ejpam-5442	246	11	model	model	NOUN
ejpam-5442	246	12	containing	contain	VERB
ejpam-5442	246	13	fractional	fractional	ADJ
ejpam-5442	246	14	derivatives	derivative	NOUN
ejpam-5442	246	15	.	.	PUNCT
ejpam-5442	247	1	comput	comput	NOUN
ejpam-5442	247	2	.	.	PUNCT
ejpam-5442	248	1	math	math	NOUN
ejpam-5442	248	2	.	.	PUNCT
ejpam-5442	249	1	appl	appl	PROPN
ejpam-5442	249	2	.	.	PROPN
ejpam-5442	249	3	,	,	PUNCT
ejpam-5442	249	4	64:3068–3074	64:3068–3074	NOUN
ejpam-5442	249	5	,	,	PUNCT
ejpam-5442	249	6	2012	2012	NUM
ejpam-5442	249	7	.	.	PUNCT
ejpam-5442	250	1	[	[	X
ejpam-5442	250	2	11	11	NUM
ejpam-5442	250	3	]	]	PUNCT
ejpam-5442	250	4	m.	m.	NOUN
ejpam-5442	250	5	farman	farman	PROPN
ejpam-5442	250	6	,	,	PUNCT
ejpam-5442	250	7	h.	h.	PROPN
ejpam-5442	250	8	besbes	besbes	PROPN
ejpam-5442	250	9	,	,	PUNCT
ejpam-5442	250	10	k.	k.	PROPN
ejpam-5442	250	11	s.	s.	PROPN
ejpam-5442	250	12	nisar	nisar	PROPN
ejpam-5442	250	13	,	,	PUNCT
ejpam-5442	250	14	and	and	CCONJ
ejpam-5442	250	15	m.	m.	NOUN
ejpam-5442	250	16	omri	omri	PROPN
ejpam-5442	250	17	.	.	PUNCT
ejpam-5442	251	1	analysis	analysis	NOUN
ejpam-5442	251	2	and	and	CCONJ
ejpam-5442	251	3	dynamical	dynamical	ADJ
ejpam-5442	251	4	transmission	transmission	NOUN
ejpam-5442	251	5	of	of	ADP
ejpam-5442	251	6	the	the	DET
ejpam-5442	251	7	covid-19	covid-19	PROPN
ejpam-5442	251	8	model	model	NOUN
ejpam-5442	251	9	by	by	ADP
ejpam-5442	251	10	using	use	VERB
ejpam-5442	251	11	caputo	caputo	PROPN
ejpam-5442	251	12	-	-	PUNCT
ejpam-5442	251	13	fabrizio	fabrizio	PROPN
ejpam-5442	251	14	derivative	derivative	NOUN
ejpam-5442	251	15	.	.	PUNCT
ejpam-5442	252	1	alexandria	alexandria	PROPN
ejpam-5442	252	2	engineering	engineering	PROPN
ejpam-5442	252	3	journal	journal	PROPN
ejpam-5442	252	4	,	,	PUNCT
ejpam-5442	252	5	66:597–606	66:597–606	NUM
ejpam-5442	252	6	,	,	PUNCT
ejpam-5442	252	7	2023	2023	NUM
ejpam-5442	252	8	.	.	PUNCT
ejpam-5442	253	1	[	[	X
ejpam-5442	253	2	12	12	NUM
ejpam-5442	253	3	]	]	X
ejpam-5442	253	4	c.	c.	PROPN
ejpam-5442	253	5	c.	c.	PROPN
ejpam-5442	253	6	garsow	garsow	PROPN
ejpam-5442	253	7	,	,	PUNCT
ejpam-5442	253	8	g.	g.	PROPN
ejpam-5442	253	9	j.	j.	PROPN
ejpam-5442	253	10	salivia	salivia	PROPN
ejpam-5442	253	11	,	,	PUNCT
ejpam-5442	253	12	and	and	CCONJ
ejpam-5442	253	13	a.	a.	PROPN
ejpam-5442	253	14	r.	r.	PROPN
ejpam-5442	253	15	herrera	herrera	PROPN
ejpam-5442	253	16	.	.	PUNCT
ejpam-5442	254	1	mathematical	mathematical	ADJ
ejpam-5442	254	2	models	model	NOUN
ejpam-5442	254	3	for	for	ADP
ejpam-5442	254	4	dynamics	dynamic	NOUN
ejpam-5442	254	5	of	of	ADP
ejpam-5442	254	6	tobacco	tobacco	NOUN
ejpam-5442	254	7	use	use	NOUN
ejpam-5442	254	8	,	,	PUNCT
ejpam-5442	254	9	recovery	recovery	NOUN
ejpam-5442	254	10	and	and	CCONJ
ejpam-5442	254	11	relapse	relapse	NOUN
ejpam-5442	254	12	.	.	PUNCT
ejpam-5442	255	1	technical	technical	ADJ
ejpam-5442	255	2	report	report	PROPN
ejpam-5442	255	3	,	,	PUNCT
ejpam-5442	255	4	cornell	cornell	PROPN
ejpam-5442	255	5	university	university	PROPN
ejpam-5442	255	6	,	,	PUNCT
ejpam-5442	255	7	london	london	PROPN
ejpam-5442	255	8	,	,	PUNCT
ejpam-5442	255	9	uk	uk	PROPN
ejpam-5442	255	10	,	,	PUNCT
ejpam-5442	255	11	2000	2000	NUM
ejpam-5442	255	12	.	.	PUNCT
ejpam-5442	256	1	[	[	X
ejpam-5442	256	2	13	13	NUM
ejpam-5442	256	3	]	]	SYM
ejpam-5442	256	4	i.	i.	PROPN
ejpam-5442	256	5	goldenberg	goldenberg	PROPN
ejpam-5442	256	6	,	,	PUNCT
ejpam-5442	256	7	m.	m.	NOUN
ejpam-5442	256	8	jonas	jonas	PROPN
ejpam-5442	256	9	,	,	PUNCT
ejpam-5442	256	10	a.	a.	PROPN
ejpam-5442	256	11	tenenbaum	tenenbaum	PROPN
ejpam-5442	256	12	,	,	PUNCT
ejpam-5442	256	13	v.	v.	ADP
ejpam-5442	256	14	boyko	boyko	NOUN
ejpam-5442	256	15	,	,	PUNCT
ejpam-5442	256	16	s.	s.	PROPN
ejpam-5442	256	17	matetzky	matetzky	PROPN
ejpam-5442	256	18	,	,	PUNCT
ejpam-5442	256	19	a.	a.	PROPN
ejpam-5442	256	20	shotan	shotan	PROPN
ejpam-5442	256	21	,	,	PUNCT
ejpam-5442	256	22	s.	s.	PROPN
ejpam-5442	256	23	behar	behar	PROPN
ejpam-5442	256	24	,	,	PUNCT
ejpam-5442	256	25	and	and	CCONJ
ejpam-5442	256	26	h.	h.	PROPN
ejpam-5442	256	27	r.	r.	PROPN
ejpam-5442	256	28	reiss	reiss	PROPN
ejpam-5442	256	29	.	.	PROPN
ejpam-5442	256	30	bezafibrate	bezafibrate	PROPN
ejpam-5442	256	31	infarction	infarction	NOUN
ejpam-5442	256	32	prevention	prevention	NOUN
ejpam-5442	256	33	study	study	NOUN
ejpam-5442	256	34	group	group	NOUN
ejpam-5442	256	35	:	:	PUNCT
ejpam-5442	256	36	current	current	ADJ
ejpam-5442	256	37	smoking	smoking	NOUN
ejpam-5442	256	38	,	,	PUNCT
ejpam-5442	256	39	smoking	smoking	NOUN
ejpam-5442	256	40	cessation	cessation	NOUN
ejpam-5442	256	41	,	,	PUNCT
ejpam-5442	256	42	and	and	CCONJ
ejpam-5442	256	43	the	the	DET
ejpam-5442	256	44	risk	risk	NOUN
ejpam-5442	256	45	of	of	ADP
ejpam-5442	256	46	sudden	sudden	ADJ
ejpam-5442	256	47	cardiac	cardiac	ADJ
ejpam-5442	256	48	death	death	NOUN
ejpam-5442	256	49	in	in	ADP
ejpam-5442	256	50	patients	patient	NOUN
ejpam-5442	256	51	with	with	ADP
ejpam-5442	256	52	coronary	coronary	ADJ
ejpam-5442	256	53	artery	artery	NOUN
ejpam-5442	256	54	disease	disease	NOUN
ejpam-5442	256	55	.	.	PUNCT
ejpam-5442	257	1	arch	arch	PROPN
ejpam-5442	257	2	.	.	PUNCT
ejpam-5442	258	1	int	int	NOUN
ejpam-5442	258	2	.	.	PUNCT
ejpam-5442	259	1	med	med	PROPN
ejpam-5442	259	2	.	.	PROPN
ejpam-5442	259	3	,	,	PUNCT
ejpam-5442	259	4	163:2301–2305	163:2301–2305	NUM
ejpam-5442	259	5	,	,	PUNCT
ejpam-5442	259	6	2003	2003	NUM
ejpam-5442	259	7	.	.	PUNCT
ejpam-5442	260	1	[	[	X
ejpam-5442	260	2	14	14	NUM
ejpam-5442	260	3	]	]	X
ejpam-5442	260	4	o.	o.	PROPN
ejpam-5442	260	5	k.	k.	PROPN
ejpam-5442	260	6	ham	ham	PROPN
ejpam-5442	260	7	.	.	PUNCT
ejpam-5442	261	1	stages	stage	NOUN
ejpam-5442	261	2	and	and	CCONJ
ejpam-5442	261	3	processes	process	NOUN
ejpam-5442	261	4	of	of	ADP
ejpam-5442	261	5	smoking	smoking	NOUN
ejpam-5442	261	6	cessation	cessation	NOUN
ejpam-5442	261	7	among	among	ADP
ejpam-5442	261	8	adolescents	adolescent	NOUN
ejpam-5442	261	9	.	.	PUNCT
ejpam-5442	262	1	west	west	PROPN
ejpam-5442	262	2	.	.	PUNCT
ejpam-5442	263	1	j.	j.	PROPN
ejpam-5442	263	2	nurs	nurs	PROPN
ejpam-5442	263	3	.	.	PUNCT
ejpam-5442	264	1	res	re	NOUN
ejpam-5442	264	2	.	.	PROPN
ejpam-5442	264	3	,	,	PUNCT
ejpam-5442	264	4	29:301–315	29:301–315	NUM
ejpam-5442	264	5	,	,	PUNCT
ejpam-5442	264	6	2007	2007	NUM
ejpam-5442	264	7	.	.	PUNCT
ejpam-5442	265	1	[	[	X
ejpam-5442	265	2	15	15	NUM
ejpam-5442	265	3	]	]	X
ejpam-5442	265	4	a.	a.	NOUN
ejpam-5442	265	5	jajarmi	jajarmi	PROPN
ejpam-5442	265	6	,	,	PUNCT
ejpam-5442	265	7	s.	s.	PROPN
ejpam-5442	265	8	arshad	arshad	PROPN
ejpam-5442	265	9	,	,	PUNCT
ejpam-5442	265	10	and	and	CCONJ
ejpam-5442	265	11	d.	d.	PROPN
ejpam-5442	265	12	baleanu	baleanu	PROPN
ejpam-5442	265	13	.	.	PUNCT
ejpam-5442	266	1	a	a	DET
ejpam-5442	266	2	new	new	ADJ
ejpam-5442	266	3	fractional	fractional	ADJ
ejpam-5442	266	4	modeling	modeling	NOUN
ejpam-5442	266	5	and	and	CCONJ
ejpam-5442	266	6	control	control	NOUN
ejpam-5442	266	7	strategy	strategy	NOUN
ejpam-5442	266	8	for	for	ADP
ejpam-5442	266	9	the	the	DET
ejpam-5442	266	10	outbreak	outbreak	NOUN
ejpam-5442	266	11	of	of	ADP
ejpam-5442	266	12	dengue	dengue	NOUN
ejpam-5442	266	13	fever	fever	NOUN
ejpam-5442	266	14	.	.	PUNCT
ejpam-5442	267	1	physica	physica	PROPN
ejpam-5442	267	2	a	a	DET
ejpam-5442	267	3	,	,	PUNCT
ejpam-5442	267	4	535:1–10	535:1–10	NUM
ejpam-5442	267	5	,	,	PUNCT
ejpam-5442	267	6	2019	2019	NUM
ejpam-5442	267	7	.	.	PUNCT
ejpam-5442	268	1	[	[	X
ejpam-5442	268	2	16	16	NUM
ejpam-5442	268	3	]	]	PUNCT
ejpam-5442	268	4	m.	m.	NOUN
ejpam-5442	268	5	m.	m.	NOUN
ejpam-5442	268	6	khader	khader	PROPN
ejpam-5442	268	7	and	and	CCONJ
ejpam-5442	268	8	k.	k.	PROPN
ejpam-5442	268	9	m.	m.	PROPN
ejpam-5442	268	10	abualnaja	abualnaja	PROPN
ejpam-5442	268	11	.	.	PUNCT
ejpam-5442	269	1	galerkin	galerkin	ADJ
ejpam-5442	269	2	-	-	PUNCT
ejpam-5442	269	3	fem	fem	NOUN
ejpam-5442	269	4	for	for	ADP
ejpam-5442	269	5	obtaining	obtain	VERB
ejpam-5442	269	6	the	the	DET
ejpam-5442	269	7	numerical	numerical	ADJ
ejpam-5442	269	8	solution	solution	NOUN
ejpam-5442	269	9	of	of	ADP
ejpam-5442	269	10	the	the	DET
ejpam-5442	269	11	linear	linear	PROPN
ejpam-5442	269	12	fractional	fractional	PROPN
ejpam-5442	269	13	klein	klein	PROPN
ejpam-5442	269	14	-	-	PUNCT
ejpam-5442	269	15	gordon	gordon	PROPN
ejpam-5442	269	16	equation	equation	NOUN
ejpam-5442	269	17	.	.	PUNCT
ejpam-5442	270	1	journal	journal	PROPN
ejpam-5442	270	2	of	of	ADP
ejpam-5442	270	3	applied	apply	VERB
ejpam-5442	270	4	analysis	analysis	NOUN
ejpam-5442	270	5	and	and	CCONJ
ejpam-5442	270	6	computation	computation	NOUN
ejpam-5442	270	7	,	,	PUNCT
ejpam-5442	270	8	9:261–270	9:261–270	NUM
ejpam-5442	270	9	,	,	PUNCT
ejpam-5442	270	10	2019	2019	NUM
ejpam-5442	270	11	.	.	PUNCT
ejpam-5442	271	1	[	[	X
ejpam-5442	271	2	17	17	NUM
ejpam-5442	271	3	]	]	PUNCT
ejpam-5442	271	4	m.	m.	NOUN
ejpam-5442	271	5	m.	m.	NOUN
ejpam-5442	271	6	khader	khader	PROPN
ejpam-5442	271	7	and	and	CCONJ
ejpam-5442	271	8	m.	m.	PROPN
ejpam-5442	271	9	adel	adel	PROPN
ejpam-5442	271	10	.	.	PUNCT
ejpam-5442	272	1	modeling	modeling	NOUN
ejpam-5442	272	2	and	and	CCONJ
ejpam-5442	272	3	numerical	numerical	PROPN
ejpam-5442	272	4	simulation	simulation	NOUN
ejpam-5442	272	5	for	for	ADP
ejpam-5442	272	6	covering	cover	VERB
ejpam-5442	272	7	the	the	DET
ejpam-5442	272	8	fractional	fractional	ADJ
ejpam-5442	272	9	covid-19	covid-19	PROPN
ejpam-5442	272	10	model	model	NOUN
ejpam-5442	272	11	using	use	VERB
ejpam-5442	272	12	spectral	spectral	ADJ
ejpam-5442	272	13	collocation	collocation	NOUN
ejpam-5442	272	14	-	-	PUNCT
ejpam-5442	272	15	optimization	optimization	NOUN
ejpam-5442	272	16	algorithms	algorithm	NOUN
ejpam-5442	272	17	.	.	PUNCT
ejpam-5442	273	1	fractal	fractal	ADJ
ejpam-5442	273	2	and	and	CCONJ
ejpam-5442	273	3	fractional	fractional	ADJ
ejpam-5442	273	4	,	,	PUNCT
ejpam-5442	273	5	6363:1–19	6363:1–19	NUM
ejpam-5442	273	6	,	,	PUNCT
ejpam-5442	273	7	2022	2022	NUM
ejpam-5442	273	8	.	.	PUNCT
ejpam-5442	274	1	[	[	X
ejpam-5442	274	2	18	18	NUM
ejpam-5442	274	3	]	]	PUNCT
ejpam-5442	274	4	m.	m.	NOUN
ejpam-5442	274	5	m.	m.	NOUN
ejpam-5442	274	6	khader	khader	PROPN
ejpam-5442	274	7	and	and	CCONJ
ejpam-5442	274	8	a.	a.	PROPN
ejpam-5442	274	9	h.	h.	PROPN
ejpam-5442	274	10	tedjani	tedjani	PROPN
ejpam-5442	274	11	.	.	PUNCT
ejpam-5442	275	1	numerical	numerical	PROPN
ejpam-5442	275	2	simulation	simulation	PROPN
ejpam-5442	275	3	for	for	ADP
ejpam-5442	275	4	the	the	DET
ejpam-5442	275	5	fractional	fractional	ADJ
ejpam-5442	275	6	-	-	PUNCT
ejpam-5442	275	7	order	order	NOUN
ejpam-5442	275	8	smoking	smoking	NOUN
ejpam-5442	275	9	model	model	NOUN
ejpam-5442	275	10	using	use	VERB
ejpam-5442	275	11	a	a	DET
ejpam-5442	275	12	spectral	spectral	ADJ
ejpam-5442	275	13	collocation	collocation	NOUN
ejpam-5442	275	14	method	method	NOUN
ejpam-5442	275	15	based	base	VERB
ejpam-5442	275	16	on	on	ADP
ejpam-5442	275	17	the	the	DET
ejpam-5442	275	18	gegenbauer	gegenbauer	NOUN
ejpam-5442	275	19	wavelet	wavelet	NOUN
ejpam-5442	275	20	polynomials	polynomial	NOUN
ejpam-5442	275	21	.	.	PUNCT
ejpam-5442	276	1	journal	journal	NOUN
ejpam-5442	276	2	of	of	ADP
ejpam-5442	276	3	applied	apply	VERB
ejpam-5442	276	4	analysis	analysis	NOUN
ejpam-5442	276	5	and	and	CCONJ
ejpam-5442	276	6	computation	computation	NOUN
ejpam-5442	276	7	,	,	PUNCT
ejpam-5442	276	8	14:847–863	14:847–863	NUM
ejpam-5442	276	9	,	,	PUNCT
ejpam-5442	276	10	2024	2024	NUM
ejpam-5442	276	11	.	.	PUNCT
ejpam-5442	277	1	[	[	X
ejpam-5442	277	2	19	19	NUM
ejpam-5442	277	3	]	]	PUNCT
ejpam-5442	277	4	q.	q.	PROPN
ejpam-5442	277	5	liu	liu	PROPN
ejpam-5442	277	6	,	,	PUNCT
ejpam-5442	277	7	t.	t.	PROPN
ejpam-5442	277	8	jin	jin	PROPN
ejpam-5442	277	9	,	,	PUNCT
ejpam-5442	277	10	m.	m.	PROPN
ejpam-5442	277	11	zhu	zhu	PROPN
ejpam-5442	277	12	,	,	PUNCT
ejpam-5442	277	13	c.	c.	PROPN
ejpam-5442	277	14	tian	tian	PROPN
ejpam-5442	277	15	,	,	PUNCT
ejpam-5442	277	16	f.	f.	PROPN
ejpam-5442	277	17	li	li	PROPN
ejpam-5442	277	18	,	,	PUNCT
ejpam-5442	277	19	and	and	CCONJ
ejpam-5442	277	20	d.	d.	PROPN
ejpam-5442	277	21	jiang	jiang	PROPN
ejpam-5442	277	22	.	.	PUNCT
ejpam-5442	278	1	uncertain	uncertain	ADJ
ejpam-5442	278	2	currency	currency	NOUN
ejpam-5442	278	3	option	option	NOUN
ejpam-5442	278	4	pricing	pricing	NOUN
ejpam-5442	278	5	based	base	VERB
ejpam-5442	278	6	on	on	ADP
ejpam-5442	278	7	the	the	DET
ejpam-5442	278	8	fractional	fractional	ADJ
ejpam-5442	278	9	differential	differential	ADJ
ejpam-5442	278	10	equation	equation	NOUN
ejpam-5442	278	11	in	in	ADP
ejpam-5442	278	12	the	the	DET
ejpam-5442	278	13	caputo	caputo	PROPN
ejpam-5442	278	14	sense	sense	NOUN
ejpam-5442	278	15	.	.	PUNCT
ejpam-5442	279	1	fractal	fractal	ADJ
ejpam-5442	279	2	fract	fract	PROPN
ejpam-5442	279	3	.	.	PUNCT
ejpam-5442	279	4	,	,	PUNCT
ejpam-5442	279	5	6:407–412	6:407–412	NUM
ejpam-5442	279	6	,	,	PUNCT
ejpam-5442	279	7	2022	2022	NUM
ejpam-5442	279	8	.	.	PUNCT
ejpam-5442	280	1	references	reference	NOUN
ejpam-5442	280	2	3290	3290	NUM
ejpam-5442	281	1	[	[	X
ejpam-5442	281	2	20	20	NUM
ejpam-5442	281	3	]	]	PUNCT
ejpam-5442	281	4	t.	t.	PROPN
ejpam-5442	281	5	liu	liu	PROPN
ejpam-5442	281	6	,	,	PUNCT
ejpam-5442	281	7	t.	t.	PROPN
ejpam-5442	281	8	j.	j.	PROPN
ejpam-5442	281	9	deiss	deiss	PROPN
ejpam-5442	281	10	,	,	PUNCT
ejpam-5442	281	11	m.	m.	PROPN
ejpam-5442	281	12	w.	w.	PROPN
ejpam-5442	281	13	lippi	lippi	PROPN
ejpam-5442	281	14	,	,	PUNCT
ejpam-5442	281	15	a.	a.	PROPN
ejpam-5442	281	16	jauregui	jauregui	PROPN
ejpam-5442	281	17	,	,	PUNCT
ejpam-5442	281	18	k.	k.	PROPN
ejpam-5442	281	19	vessel	vessel	PROPN
ejpam-5442	281	20	,	,	PUNCT
ejpam-5442	281	21	s.	s.	PROPN
ejpam-5442	281	22	ke	ke	PROPN
ejpam-5442	281	23	,	,	PUNCT
ejpam-5442	281	24	a.	a.	NOUN
ejpam-5442	281	25	belzer	belzer	PROPN
ejpam-5442	281	26	,	,	PUNCT
ejpam-5442	281	27	h.	h.	PROPN
ejpam-5442	281	28	zhuo	zhuo	PROPN
ejpam-5442	281	29	,	,	PUNCT
ejpam-5442	281	30	k.	k.	PROPN
ejpam-5442	281	31	n.	n.	PROPN
ejpam-5442	281	32	kangelaris	kangelaris	PROPN
ejpam-5442	281	33	,	,	PUNCT
ejpam-5442	281	34	and	and	CCONJ
ejpam-5442	281	35	a.	a.	PROPN
ejpam-5442	281	36	d.	d.	PROPN
ejpam-5442	281	37	gomez	gomez	PROPN
ejpam-5442	281	38	et	et	PROPN
ejpam-5442	282	1	al	al	PROPN
ejpam-5442	282	2	.	.	PROPN
ejpam-5442	282	3	alternative	alternative	ADJ
ejpam-5442	282	4	tobacco	tobacco	NOUN
ejpam-5442	282	5	product	product	NOUN
ejpam-5442	282	6	use	use	NOUN
ejpam-5442	282	7	in	in	ADP
ejpam-5442	282	8	critically	critically	ADV
ejpam-5442	282	9	ill	ill	ADJ
ejpam-5442	282	10	patients	patient	NOUN
ejpam-5442	282	11	.	.	PUNCT
ejpam-5442	283	1	int	int	NOUN
ejpam-5442	283	2	.	.	PUNCT
ejpam-5442	284	1	j.	j.	PROPN
ejpam-5442	284	2	environ	environ	PROPN
ejpam-5442	284	3	.	.	PUNCT
ejpam-5442	285	1	res	re	NOUN
ejpam-5442	285	2	.	.	PUNCT
ejpam-5442	286	1	public	public	ADJ
ejpam-5442	286	2	health	health	NOUN
ejpam-5442	286	3	,	,	PUNCT
ejpam-5442	286	4	17:1–15	17:1–15	NUM
ejpam-5442	286	5	,	,	PUNCT
ejpam-5442	286	6	2020	2020	NUM
ejpam-5442	286	7	.	.	PUNCT
ejpam-5442	287	1	[	[	X
ejpam-5442	287	2	21	21	NUM
ejpam-5442	287	3	]	]	X
ejpam-5442	287	4	j.	j.	PROPN
ejpam-5442	287	5	rong	rong	PROPN
ejpam-5442	287	6	loh	loh	PROPN
ejpam-5442	287	7	,	,	PUNCT
ejpam-5442	287	8	a.	a.	NOUN
ejpam-5442	287	9	isah	isah	PROPN
ejpam-5442	287	10	,	,	PUNCT
ejpam-5442	287	11	c.	c.	PROPN
ejpam-5442	287	12	phang	phang	PROPN
ejpam-5442	287	13	,	,	PUNCT
ejpam-5442	287	14	and	and	CCONJ
ejpam-5442	287	15	y.	y.	PROPN
ejpam-5442	287	16	t.	t.	PROPN
ejpam-5442	287	17	toh	toh	PROPN
ejpam-5442	287	18	.	.	PUNCT
ejpam-5442	288	1	on	on	ADP
ejpam-5442	288	2	the	the	DET
ejpam-5442	288	3	new	new	ADJ
ejpam-5442	288	4	properties	property	NOUN
ejpam-5442	288	5	of	of	ADP
ejpam-5442	288	6	caputofabrizio	caputofabrizio	NOUN
ejpam-5442	288	7	operator	operator	NOUN
ejpam-5442	288	8	and	and	CCONJ
ejpam-5442	288	9	its	its	PRON
ejpam-5442	288	10	application	application	NOUN
ejpam-5442	288	11	in	in	ADP
ejpam-5442	288	12	deriving	derive	VERB
ejpam-5442	288	13	shifted	shift	VERB
ejpam-5442	288	14	legendre	legendre	PROPN
ejpam-5442	288	15	operational	operational	ADJ
ejpam-5442	288	16	matrix	matrix	NOUN
ejpam-5442	288	17	.	.	PUNCT
ejpam-5442	289	1	appl	appl	PROPN
ejpam-5442	289	2	.	.	PUNCT
ejpam-5442	290	1	numer	numer	PROPN
ejpam-5442	290	2	.	.	PUNCT
ejpam-5442	290	3	math	math	PROPN
ejpam-5442	290	4	.	.	PUNCT
ejpam-5442	290	5	,	,	PUNCT
ejpam-5442	290	6	132:138–153	132:138–153	NUM
ejpam-5442	290	7	,	,	PUNCT
ejpam-5442	290	8	2018	2018	NUM
ejpam-5442	290	9	.	.	PUNCT
ejpam-5442	291	1	[	[	X
ejpam-5442	291	2	22	22	NUM
ejpam-5442	291	3	]	]	X
ejpam-5442	291	4	j.	j.	PROPN
ejpam-5442	291	5	losada	losada	PROPN
ejpam-5442	291	6	and	and	CCONJ
ejpam-5442	291	7	j.	j.	PROPN
ejpam-5442	291	8	j.	j.	PROPN
ejpam-5442	291	9	nieto	nieto	PROPN
ejpam-5442	291	10	.	.	PUNCT
ejpam-5442	292	1	properties	property	NOUN
ejpam-5442	292	2	of	of	ADP
ejpam-5442	292	3	a	a	DET
ejpam-5442	292	4	new	new	ADJ
ejpam-5442	292	5	fractional	fractional	ADJ
ejpam-5442	292	6	derivative	derivative	NOUN
ejpam-5442	292	7	without	without	ADP
ejpam-5442	292	8	singular	singular	ADJ
ejpam-5442	292	9	kernel	kernel	PROPN
ejpam-5442	292	10	.	.	PUNCT
ejpam-5442	293	1	progr	progr	NOUN
ejpam-5442	293	2	.	.	PUNCT
ejpam-5442	294	1	fract	fract	PROPN
ejpam-5442	294	2	.	.	PUNCT
ejpam-5442	295	1	differ	differ	VERB
ejpam-5442	295	2	.	.	PUNCT
ejpam-5442	296	1	appl	appl	PROPN
ejpam-5442	296	2	.	.	PROPN
ejpam-5442	296	3	,	,	PUNCT
ejpam-5442	296	4	1:87–92	1:87–92	NUM
ejpam-5442	296	5	,	,	PUNCT
ejpam-5442	296	6	2015	2015	NUM
ejpam-5442	296	7	.	.	PUNCT
ejpam-5442	297	1	[	[	X
ejpam-5442	297	2	23	23	NUM
ejpam-5442	297	3	]	]	PUNCT
ejpam-5442	297	4	world	world	NOUN
ejpam-5442	297	5	health	health	NOUN
ejpam-5442	297	6	organisation	organisation	NOUN
ejpam-5442	297	7	.	.	PUNCT
ejpam-5442	298	1	monitoring	monitor	VERB
ejpam-5442	298	2	tobacco	tobacco	NOUN
ejpam-5442	298	3	use	use	NOUN
ejpam-5442	298	4	and	and	CCONJ
ejpam-5442	298	5	prevention	prevention	NOUN
ejpam-5442	298	6	policies	policy	NOUN
ejpam-5442	298	7	.	.	PUNCT
ejpam-5442	299	1	executive	executive	ADJ
ejpam-5442	299	2	summary	summary	NOUN
ejpam-5442	299	3	.	.	PUNCT
ejpam-5442	300	1	world	world	NOUN
ejpam-5442	300	2	health	health	PROPN
ejpam-5442	300	3	organisation	organisation	NOUN
ejpam-5442	300	4	,	,	PUNCT
ejpam-5442	300	5	2017	2017	NUM
ejpam-5442	300	6	.	.	PUNCT
ejpam-5442	301	1	[	[	X
ejpam-5442	301	2	24	24	NUM
ejpam-5442	301	3	]	]	PUNCT
ejpam-5442	301	4	k.	k.	PROPN
ejpam-5442	301	5	m.	m.	PROPN
ejpam-5442	301	6	owolabi	owolabi	NOUN
ejpam-5442	301	7	and	and	CCONJ
ejpam-5442	301	8	a.	a.	NOUN
ejpam-5442	301	9	atangana	atangana	PROPN
ejpam-5442	301	10	.	.	PUNCT
ejpam-5442	302	1	analysis	analysis	NOUN
ejpam-5442	302	2	and	and	CCONJ
ejpam-5442	302	3	application	application	NOUN
ejpam-5442	302	4	of	of	ADP
ejpam-5442	302	5	new	new	ADJ
ejpam-5442	302	6	fractional	fractional	ADJ
ejpam-5442	302	7	adamsbashforth	adamsbashforth	NOUN
ejpam-5442	302	8	scheme	scheme	NOUN
ejpam-5442	302	9	with	with	ADP
ejpam-5442	302	10	caputo	caputo	PROPN
ejpam-5442	302	11	-	-	PUNCT
ejpam-5442	302	12	fabrizio	fabrizio	PROPN
ejpam-5442	302	13	derivative	derivative	NOUN
ejpam-5442	302	14	.	.	PUNCT
ejpam-5442	303	1	chaos	chaos	NOUN
ejpam-5442	303	2	solitons	soliton	NOUN
ejpam-5442	303	3	fract	fract	NOUN
ejpam-5442	303	4	.	.	PUNCT
ejpam-5442	303	5	,	,	PUNCT
ejpam-5442	303	6	105:111	105:111	NUM
ejpam-5442	303	7	–	–	PUNCT
ejpam-5442	303	8	119	119	NUM
ejpam-5442	303	9	,	,	PUNCT
ejpam-5442	303	10	2017	2017	NUM
ejpam-5442	303	11	.	.	PUNCT
ejpam-5442	304	1	[	[	X
ejpam-5442	304	2	25	25	NUM
ejpam-5442	304	3	]	]	X
ejpam-5442	304	4	p.	p.	NOUN
ejpam-5442	304	5	veeresha	veeresha	PROPN
ejpam-5442	304	6	,	,	PUNCT
ejpam-5442	304	7	e.	e.	PROPN
ejpam-5442	304	8	ilhan	ilhan	PROPN
ejpam-5442	304	9	,	,	PUNCT
ejpam-5442	304	10	d.	d.	PROPN
ejpam-5442	304	11	g.	g.	PROPN
ejpam-5442	304	12	prakasha	prakasha	PROPN
ejpam-5442	304	13	,	,	PUNCT
ejpam-5442	304	14	and	and	CCONJ
ejpam-5442	304	15	h.	h.	PROPN
ejpam-5442	304	16	m.	m.	PROPN
ejpam-5442	304	17	baskonus	baskonus	PROPN
ejpam-5442	304	18	.	.	PUNCT
ejpam-5442	305	1	a	a	DET
ejpam-5442	305	2	new	new	ADJ
ejpam-5442	305	3	numerical	numerical	ADJ
ejpam-5442	305	4	investigation	investigation	NOUN
ejpam-5442	305	5	of	of	ADP
ejpam-5442	305	6	fractional	fractional	ADJ
ejpam-5442	305	7	order	order	NOUN
ejpam-5442	305	8	susceptible	susceptible	ADJ
ejpam-5442	305	9	-	-	PUNCT
ejpam-5442	305	10	infected	infect	VERB
ejpam-5442	305	11	-	-	PUNCT
ejpam-5442	305	12	recovered	recover	VERB
ejpam-5442	305	13	epidemic	epidemic	NOUN
ejpam-5442	305	14	model	model	NOUN
ejpam-5442	305	15	of	of	ADP
ejpam-5442	305	16	childhood	childhood	NOUN
ejpam-5442	305	17	disease	disease	NOUN
ejpam-5442	305	18	.	.	PUNCT
ejpam-5442	306	1	alexandria	alexandria	PROPN
ejpam-5442	306	2	engineering	engineering	PROPN
ejpam-5442	306	3	journal	journal	PROPN
ejpam-5442	306	4	,	,	PUNCT
ejpam-5442	306	5	61:1747–1756	61:1747–1756	NUM
ejpam-5442	306	6	,	,	PUNCT
ejpam-5442	306	7	2022	2022	NUM
ejpam-5442	306	8	.	.	PUNCT
ejpam-5442	307	1	[	[	X
ejpam-5442	307	2	26	26	NUM
ejpam-5442	307	3	]	]	X
ejpam-5442	307	4	p.	p.	NOUN
ejpam-5442	307	5	veeresha	veeresha	PROPN
ejpam-5442	307	6	and	and	CCONJ
ejpam-5442	307	7	d.	d.	PROPN
ejpam-5442	307	8	g.	g.	PROPN
ejpam-5442	307	9	prakasha	prakasha	PROPN
ejpam-5442	307	10	.	.	PUNCT
ejpam-5442	308	1	a	a	DET
ejpam-5442	308	2	novel	novel	ADJ
ejpam-5442	308	3	technique	technique	NOUN
ejpam-5442	308	4	for	for	ADP
ejpam-5442	308	5	(	(	PUNCT
ejpam-5442	308	6	2n+1)-dimensional	2n+1)-dimensional	NUM
ejpam-5442	308	7	timefractional	timefractional	NOUN
ejpam-5442	308	8	coupled	couple	VERB
ejpam-5442	308	9	burgers	burger	NOUN
ejpam-5442	308	10	equations	equation	NOUN
ejpam-5442	308	11	.	.	PUNCT
ejpam-5442	309	1	alexandria	alexandria	PROPN
ejpam-5442	309	2	engineering	engineering	PROPN
ejpam-5442	309	3	journal	journal	PROPN
ejpam-5442	309	4	,	,	PUNCT
ejpam-5442	309	5	166:324–345	166:324–345	NUM
ejpam-5442	309	6	,	,	PUNCT
ejpam-5442	309	7	2019	2019	NUM
ejpam-5442	309	8	.	.	PUNCT
ejpam-5442	310	1	[	[	X
ejpam-5442	310	2	27	27	NUM
ejpam-5442	310	3	]	]	PUNCT
ejpam-5442	310	4	a.	a.	NOUN
ejpam-5442	310	5	yildirum	yildirum	NOUN
ejpam-5442	310	6	and	and	CCONJ
ejpam-5442	310	7	y.	y.	PROPN
ejpam-5442	310	8	cherruault	cherruault	PROPN
ejpam-5442	310	9	.	.	PUNCT
ejpam-5442	311	1	analytical	analytical	ADJ
ejpam-5442	311	2	approximate	approximate	ADJ
ejpam-5442	311	3	solution	solution	NOUN
ejpam-5442	311	4	of	of	ADP
ejpam-5442	311	5	a	a	DET
ejpam-5442	311	6	sir	sir	NOUN
ejpam-5442	311	7	epidemic	epidemic	NOUN
ejpam-5442	311	8	model	model	NOUN
ejpam-5442	311	9	with	with	ADP
ejpam-5442	311	10	constant	constant	ADJ
ejpam-5442	311	11	vaccination	vaccination	NOUN
ejpam-5442	311	12	strategy	strategy	NOUN
ejpam-5442	311	13	by	by	ADP
ejpam-5442	311	14	homotopy	homotopy	NOUN
ejpam-5442	311	15	perturbation	perturbation	NOUN
ejpam-5442	311	16	method	method	NOUN
ejpam-5442	311	17	.	.	PUNCT
ejpam-5442	312	1	emerald	emerald	NOUN
ejpam-5442	312	2	,	,	PUNCT
ejpam-5442	312	3	38:1566–1581	38:1566–1581	NUM
ejpam-5442	312	4	,	,	PUNCT
ejpam-5442	312	5	2009	2009	NUM
ejpam-5442	312	6	.	.	PUNCT
ejpam-5442	313	1	[	[	X
ejpam-5442	313	2	28	28	NUM
ejpam-5442	313	3	]	]	X
ejpam-5442	313	4	f.	f.	PROPN
ejpam-5442	313	5	youbi	youbi	PROPN
ejpam-5442	313	6	,	,	PUNCT
ejpam-5442	313	7	s.	s.	PROPN
ejpam-5442	313	8	momani	momani	PROPN
ejpam-5442	313	9	,	,	PUNCT
ejpam-5442	313	10	s.	s.	PROPN
ejpam-5442	313	11	hasan	hasan	PROPN
ejpam-5442	313	12	,	,	PUNCT
ejpam-5442	313	13	and	and	CCONJ
ejpam-5442	313	14	m.	m.	PROPN
ejpam-5442	313	15	al	al	PROPN
ejpam-5442	313	16	-	-	PUNCT
ejpam-5442	313	17	smadi	smadi	NOUN
ejpam-5442	313	18	.	.	PUNCT
ejpam-5442	314	1	effective	effective	ADJ
ejpam-5442	314	2	numerical	numerical	ADJ
ejpam-5442	314	3	technique	technique	NOUN
ejpam-5442	314	4	for	for	ADP
ejpam-5442	314	5	nonlinear	nonlinear	ADJ
ejpam-5442	314	6	caputo	caputo	PROPN
ejpam-5442	314	7	-	-	PUNCT
ejpam-5442	314	8	fabrizio	fabrizio	PROPN
ejpam-5442	314	9	systems	system	NOUN
ejpam-5442	314	10	of	of	ADP
ejpam-5442	314	11	fractional	fractional	PROPN
ejpam-5442	314	12	volterra	volterra	PROPN
ejpam-5442	314	13	integro	integro	PROPN
ejpam-5442	314	14	-	-	PUNCT
ejpam-5442	314	15	differential	differential	NOUN
ejpam-5442	314	16	equations	equation	NOUN
ejpam-5442	314	17	in	in	ADP
ejpam-5442	314	18	hilbert	hilbert	PROPN
ejpam-5442	314	19	space	space	NOUN
ejpam-5442	314	20	.	.	PUNCT
ejpam-5442	315	1	alexandria	alexandria	PROPN
ejpam-5442	315	2	engineering	engineering	PROPN
ejpam-5442	315	3	journal	journal	PROPN
ejpam-5442	315	4	,	,	PUNCT
ejpam-5442	315	5	61:1778–1786	61:1778–1786	PROPN
ejpam-5442	315	6	,	,	PUNCT
ejpam-5442	315	7	2022	2022	NUM
ejpam-5442	315	8	.	.	PUNCT