id	sid	tid	token	lemma	pos
ejpam-5387	1	1	european	european	PROPN
ejpam-5387	1	2	journal	journal	PROPN
ejpam-5387	1	3	of	of	ADP
ejpam-5387	1	4	pure	pure	ADJ
ejpam-5387	1	5	and	and	CCONJ
ejpam-5387	1	6	applied	apply	VERB
ejpam-5387	1	7	mathematics	mathematic	NOUN
ejpam-5387	1	8	vol	vol	NOUN
ejpam-5387	1	9	.	.	PROPN
ejpam-5387	2	1	17	17	NUM
ejpam-5387	2	2	,	,	PUNCT
ejpam-5387	2	3	no	no	INTJ
ejpam-5387	2	4	.	.	NOUN
ejpam-5387	2	5	4	4	NUM
ejpam-5387	2	6	,	,	PUNCT
ejpam-5387	2	7	2024	2024	NUM
ejpam-5387	2	8	,	,	PUNCT
ejpam-5387	2	9	2706	2706	NUM
ejpam-5387	2	10	-	-	SYM
ejpam-5387	2	11	2719	2719	NUM
ejpam-5387	2	12	issn	issn	VERB
ejpam-5387	2	13	1307	1307	NUM
ejpam-5387	2	14	-	-	SYM
ejpam-5387	2	15	5543	5543	NUM
ejpam-5387	2	16	–	–	PUNCT
ejpam-5387	3	1	ejpam.com	ejpam.com	X
ejpam-5387	3	2	published	publish	VERB
ejpam-5387	3	3	by	by	ADP
ejpam-5387	3	4	new	new	PROPN
ejpam-5387	3	5	york	york	PROPN
ejpam-5387	3	6	business	business	PROPN
ejpam-5387	3	7	global	global	PROPN
ejpam-5387	3	8	efficient	efficient	ADJ
ejpam-5387	3	9	numerical	numerical	ADJ
ejpam-5387	3	10	solutions	solution	NOUN
ejpam-5387	3	11	for	for	ADP
ejpam-5387	3	12	breast	breast	NOUN
ejpam-5387	3	13	cancer	cancer	NOUN
ejpam-5387	3	14	model	model	NOUN
ejpam-5387	3	15	taghreed	taghreed	NOUN
ejpam-5387	3	16	a.	a.	NOUN
ejpam-5387	3	17	assiri	assiri	PROPN
ejpam-5387	3	18	mathematics	mathematics	PROPN
ejpam-5387	3	19	department	department	PROPN
ejpam-5387	3	20	,	,	PUNCT
ejpam-5387	3	21	faculty	faculty	NOUN
ejpam-5387	3	22	of	of	ADP
ejpam-5387	3	23	sciences	science	NOUN
ejpam-5387	3	24	,	,	PUNCT
ejpam-5387	3	25	umm	umm	INTJ
ejpam-5387	3	26	al	al	PROPN
ejpam-5387	3	27	-	-	PUNCT
ejpam-5387	3	28	qura	qura	PROPN
ejpam-5387	3	29	university	university	PROPN
ejpam-5387	3	30	,	,	PUNCT
ejpam-5387	3	31	makkah	makkah	PROPN
ejpam-5387	3	32	,	,	PUNCT
ejpam-5387	3	33	saudi	saudi	PROPN
ejpam-5387	3	34	arabia	arabia	PROPN
ejpam-5387	3	35	abstract	abstract	NOUN
ejpam-5387	3	36	.	.	PUNCT
ejpam-5387	4	1	we	we	PRON
ejpam-5387	4	2	know	know	VERB
ejpam-5387	4	3	that	that	PRON
ejpam-5387	4	4	mathematical	mathematical	ADJ
ejpam-5387	4	5	modeling	modeling	NOUN
ejpam-5387	4	6	is	be	AUX
ejpam-5387	4	7	a	a	DET
ejpam-5387	4	8	serious	serious	ADJ
ejpam-5387	4	9	agent	agent	NOUN
ejpam-5387	4	10	to	to	PART
ejpam-5387	4	11	realize	realize	VERB
ejpam-5387	4	12	the	the	DET
ejpam-5387	4	13	dynamics	dynamic	NOUN
ejpam-5387	4	14	of	of	ADP
ejpam-5387	4	15	breast	breast	NOUN
ejpam-5387	4	16	cancer	cancer	NOUN
ejpam-5387	4	17	development	development	NOUN
ejpam-5387	4	18	,	,	PUNCT
ejpam-5387	4	19	spread	spread	VERB
ejpam-5387	4	20	,	,	PUNCT
ejpam-5387	4	21	and	and	CCONJ
ejpam-5387	4	22	educe	educe	VERB
ejpam-5387	4	23	new	new	ADJ
ejpam-5387	4	24	therapeutic	therapeutic	ADJ
ejpam-5387	4	25	approaches	approach	NOUN
ejpam-5387	4	26	.	.	PUNCT
ejpam-5387	5	1	the	the	DET
ejpam-5387	5	2	main	main	ADJ
ejpam-5387	5	3	target	target	NOUN
ejpam-5387	5	4	of	of	ADP
ejpam-5387	5	5	this	this	DET
ejpam-5387	5	6	study	study	NOUN
ejpam-5387	5	7	is	be	AUX
ejpam-5387	5	8	to	to	PART
ejpam-5387	5	9	use	use	VERB
ejpam-5387	5	10	simpson	simpson	PROPN
ejpam-5387	5	11	’s	’s	PART
ejpam-5387	5	12	1/3	1/3	NUM
ejpam-5387	5	13	rule	rule	NOUN
ejpam-5387	5	14	as	as	ADP
ejpam-5387	5	15	an	an	DET
ejpam-5387	5	16	efficient	efficient	ADJ
ejpam-5387	5	17	numerical	numerical	ADJ
ejpam-5387	5	18	scheme	scheme	NOUN
ejpam-5387	5	19	for	for	ADP
ejpam-5387	5	20	integration	integration	NOUN
ejpam-5387	5	21	to	to	PART
ejpam-5387	5	22	numerically	numerically	ADV
ejpam-5387	5	23	treat	treat	VERB
ejpam-5387	5	24	the	the	DET
ejpam-5387	5	25	obtained	obtain	VERB
ejpam-5387	5	26	fractional	fractional	ADJ
ejpam-5387	5	27	integral	integral	ADJ
ejpam-5387	5	28	equations	equation	NOUN
ejpam-5387	5	29	and	and	CCONJ
ejpam-5387	5	30	reduce	reduce	VERB
ejpam-5387	5	31	them	they	PRON
ejpam-5387	5	32	to	to	ADP
ejpam-5387	5	33	a	a	DET
ejpam-5387	5	34	set	set	NOUN
ejpam-5387	5	35	of	of	ADP
ejpam-5387	5	36	algebraic	algebraic	ADJ
ejpam-5387	5	37	equations	equation	NOUN
ejpam-5387	5	38	.	.	PUNCT
ejpam-5387	6	1	the	the	DET
ejpam-5387	6	2	fractional	fractional	ADJ
ejpam-5387	6	3	derivatives	derivative	NOUN
ejpam-5387	6	4	here	here	ADV
ejpam-5387	6	5	are	be	AUX
ejpam-5387	6	6	taken	take	VERB
ejpam-5387	6	7	in	in	ADP
ejpam-5387	6	8	the	the	DET
ejpam-5387	6	9	caputo	caputo	PROPN
ejpam-5387	6	10	-	-	PUNCT
ejpam-5387	6	11	fabrizio	fabrizio	PROPN
ejpam-5387	6	12	(	(	PUNCT
ejpam-5387	6	13	cf	cf	NOUN
ejpam-5387	6	14	)	)	PUNCT
ejpam-5387	6	15	sense	sense	NOUN
ejpam-5387	6	16	.	.	PUNCT
ejpam-5387	7	1	particular	particular	ADJ
ejpam-5387	7	2	assurance	assurance	NOUN
ejpam-5387	7	3	is	be	AUX
ejpam-5387	7	4	located	locate	VERB
ejpam-5387	7	5	on	on	ADP
ejpam-5387	7	6	elucidating	elucidate	VERB
ejpam-5387	7	7	the	the	DET
ejpam-5387	7	8	error	error	NOUN
ejpam-5387	7	9	analysis	analysis	NOUN
ejpam-5387	7	10	of	of	ADP
ejpam-5387	7	11	the	the	DET
ejpam-5387	7	12	given	give	VERB
ejpam-5387	7	13	scheme	scheme	NOUN
ejpam-5387	7	14	.	.	PUNCT
ejpam-5387	8	1	the	the	DET
ejpam-5387	8	2	results	result	NOUN
ejpam-5387	8	3	acquired	acquire	VERB
ejpam-5387	8	4	by	by	ADP
ejpam-5387	8	5	implementing	implement	VERB
ejpam-5387	8	6	the	the	DET
ejpam-5387	8	7	runge	runge	NOUN
ejpam-5387	8	8	-	-	PUNCT
ejpam-5387	8	9	kutta	kutta	NOUN
ejpam-5387	8	10	method	method	NOUN
ejpam-5387	8	11	(	(	PUNCT
ejpam-5387	8	12	rk4	rk4	NOUN
ejpam-5387	8	13	m	m	NOUN
ejpam-5387	8	14	)	)	PUNCT
ejpam-5387	8	15	are	be	AUX
ejpam-5387	8	16	compared	compare	VERB
ejpam-5387	8	17	to	to	ADP
ejpam-5387	8	18	those	those	PRON
ejpam-5387	8	19	obtained	obtain	VERB
ejpam-5387	8	20	using	use	VERB
ejpam-5387	8	21	the	the	DET
ejpam-5387	8	22	achieved	achieve	VERB
ejpam-5387	8	23	results	result	NOUN
ejpam-5387	8	24	.	.	PUNCT
ejpam-5387	9	1	the	the	DET
ejpam-5387	9	2	results	result	NOUN
ejpam-5387	9	3	explain	explain	VERB
ejpam-5387	9	4	that	that	SCONJ
ejpam-5387	9	5	the	the	DET
ejpam-5387	9	6	implemented	implement	VERB
ejpam-5387	9	7	scheme	scheme	NOUN
ejpam-5387	9	8	offers	offer	VERB
ejpam-5387	9	9	a	a	DET
ejpam-5387	9	10	precise	precise	ADJ
ejpam-5387	9	11	and	and	CCONJ
ejpam-5387	9	12	effective	effective	ADJ
ejpam-5387	9	13	agent	agent	NOUN
ejpam-5387	9	14	for	for	ADP
ejpam-5387	9	15	simulating	simulate	VERB
ejpam-5387	9	16	this	this	DET
ejpam-5387	9	17	model	model	NOUN
ejpam-5387	9	18	.	.	PUNCT
ejpam-5387	10	1	the	the	DET
ejpam-5387	10	2	primary	primary	ADJ
ejpam-5387	10	3	benefit	benefit	NOUN
ejpam-5387	10	4	of	of	ADP
ejpam-5387	10	5	the	the	DET
ejpam-5387	10	6	implemented	implement	VERB
ejpam-5387	10	7	method	method	NOUN
ejpam-5387	10	8	is	be	AUX
ejpam-5387	10	9	that	that	SCONJ
ejpam-5387	10	10	it	it	PRON
ejpam-5387	10	11	relies	rely	VERB
ejpam-5387	10	12	on	on	ADP
ejpam-5387	10	13	a	a	DET
ejpam-5387	10	14	small	small	ADJ
ejpam-5387	10	15	number	number	NOUN
ejpam-5387	10	16	of	of	ADP
ejpam-5387	10	17	uncomplicated	uncomplicated	ADJ
ejpam-5387	10	18	steps	step	NOUN
ejpam-5387	10	19	and	and	CCONJ
ejpam-5387	10	20	does	do	AUX
ejpam-5387	10	21	not	not	PART
ejpam-5387	10	22	have	have	VERB
ejpam-5387	10	23	long	long	ADJ
ejpam-5387	10	24	-	-	PUNCT
ejpam-5387	10	25	term	term	NOUN
ejpam-5387	10	26	effects	effect	NOUN
ejpam-5387	10	27	.	.	PUNCT
ejpam-5387	11	1	2020	2020	NUM
ejpam-5387	11	2	mathematics	mathematic	NOUN
ejpam-5387	11	3	subject	subject	NOUN
ejpam-5387	11	4	classifications	classification	NOUN
ejpam-5387	11	5	:	:	PUNCT
ejpam-5387	11	6	34a12	34a12	NUM
ejpam-5387	11	7	,	,	PUNCT
ejpam-5387	11	8	41a30	41a30	NUM
ejpam-5387	11	9	,	,	PUNCT
ejpam-5387	11	10	26c10	26c10	NUM
ejpam-5387	11	11	,	,	PUNCT
ejpam-5387	11	12	47h10	47h10	NUM
ejpam-5387	11	13	,	,	PUNCT
ejpam-5387	11	14	65n20	65n20	NUM
ejpam-5387	11	15	key	key	ADJ
ejpam-5387	11	16	words	word	NOUN
ejpam-5387	11	17	and	and	CCONJ
ejpam-5387	11	18	phrases	phrase	NOUN
ejpam-5387	11	19	:	:	PUNCT
ejpam-5387	11	20	breast	breast	NOUN
ejpam-5387	11	21	cancer	cancer	NOUN
ejpam-5387	11	22	,	,	PUNCT
ejpam-5387	11	23	caputo	caputo	PROPN
ejpam-5387	11	24	-	-	PUNCT
ejpam-5387	11	25	fabrizio	fabrizio	PROPN
ejpam-5387	11	26	fractional	fractional	PROPN
ejpam-5387	11	27	derivative	derivative	ADJ
ejpam-5387	11	28	,	,	PUNCT
ejpam-5387	11	29	numerical	numerical	ADJ
ejpam-5387	11	30	integration	integration	NOUN
ejpam-5387	11	31	,	,	PUNCT
ejpam-5387	11	32	rk4	rk4	PROPN
ejpam-5387	11	33	m	m	VERB
ejpam-5387	11	34	1	1	NUM
ejpam-5387	11	35	.	.	PUNCT
ejpam-5387	11	36	introduction	introduction	NOUN
ejpam-5387	11	37	breast	breast	NOUN
ejpam-5387	11	38	cancer	cancer	NOUN
ejpam-5387	11	39	(	(	PUNCT
ejpam-5387	11	40	bc	bc	PROPN
ejpam-5387	11	41	)	)	PUNCT
ejpam-5387	11	42	is	be	AUX
ejpam-5387	11	43	described	describe	VERB
ejpam-5387	11	44	and	and	CCONJ
ejpam-5387	11	45	defined	define	VERB
ejpam-5387	11	46	as	as	ADP
ejpam-5387	11	47	a	a	DET
ejpam-5387	11	48	disease	disease	NOUN
ejpam-5387	11	49	condition	condition	NOUN
ejpam-5387	11	50	resulting	result	VERB
ejpam-5387	11	51	from	from	ADP
ejpam-5387	11	52	the	the	DET
ejpam-5387	11	53	uncontrolled	uncontrolled	ADJ
ejpam-5387	11	54	proliferation	proliferation	NOUN
ejpam-5387	11	55	of	of	ADP
ejpam-5387	11	56	cells	cell	NOUN
ejpam-5387	11	57	inside	inside	ADP
ejpam-5387	11	58	the	the	DET
ejpam-5387	11	59	breast	breast	NOUN
ejpam-5387	11	60	tissue	tissue	NOUN
ejpam-5387	11	61	.	.	PUNCT
ejpam-5387	12	1	through	through	ADP
ejpam-5387	12	2	the	the	DET
ejpam-5387	12	3	data	datum	NOUN
ejpam-5387	12	4	supplied	supply	VERB
ejpam-5387	12	5	by	by	ADP
ejpam-5387	12	6	the	the	DET
ejpam-5387	12	7	world	world	PROPN
ejpam-5387	12	8	health	health	PROPN
ejpam-5387	12	9	organization	organization	NOUN
ejpam-5387	12	10	(	(	PUNCT
ejpam-5387	12	11	who	who	PRON
ejpam-5387	12	12	)	)	PUNCT
ejpam-5387	12	13	on	on	ADP
ejpam-5387	12	14	the	the	DET
ejpam-5387	12	15	global	global	ADJ
ejpam-5387	12	16	burden	burden	NOUN
ejpam-5387	12	17	of	of	ADP
ejpam-5387	12	18	cancer	cancer	NOUN
ejpam-5387	12	19	,	,	PUNCT
ejpam-5387	12	20	we	we	PRON
ejpam-5387	12	21	can	can	AUX
ejpam-5387	12	22	find	find	VERB
ejpam-5387	12	23	that	that	SCONJ
ejpam-5387	12	24	the	the	DET
ejpam-5387	12	25	bc	bc	PROPN
ejpam-5387	12	26	has	have	VERB
ejpam-5387	12	27	the	the	DET
ejpam-5387	12	28	highest	high	ADJ
ejpam-5387	12	29	prevalence	prevalence	NOUN
ejpam-5387	12	30	rate	rate	NOUN
ejpam-5387	12	31	when	when	SCONJ
ejpam-5387	12	32	assorted	assort	VERB
ejpam-5387	12	33	to	to	ADP
ejpam-5387	12	34	other	other	ADJ
ejpam-5387	12	35	types	type	NOUN
ejpam-5387	12	36	of	of	ADP
ejpam-5387	12	37	cancer	cancer	NOUN
ejpam-5387	12	38	[	[	X
ejpam-5387	12	39	8	8	NUM
ejpam-5387	12	40	]	]	PUNCT
ejpam-5387	12	41	.	.	PUNCT
ejpam-5387	13	1	globally	globally	ADV
ejpam-5387	13	2	,	,	PUNCT
ejpam-5387	13	3	through	through	ADP
ejpam-5387	13	4	surveys	survey	NOUN
ejpam-5387	13	5	conducted	conduct	VERB
ejpam-5387	13	6	by	by	ADP
ejpam-5387	13	7	who	who	PRON
ejpam-5387	13	8	,	,	PUNCT
ejpam-5387	13	9	which	which	PRON
ejpam-5387	13	10	ranked	rank	VERB
ejpam-5387	13	11	bc	bc	PROPN
ejpam-5387	13	12	in	in	ADP
ejpam-5387	13	13	2004	2004	NUM
ejpam-5387	13	14	as	as	ADP
ejpam-5387	13	15	the	the	DET
ejpam-5387	13	16	second	second	ADJ
ejpam-5387	13	17	most	most	ADV
ejpam-5387	13	18	widespread	widespread	ADJ
ejpam-5387	13	19	form	form	NOUN
ejpam-5387	13	20	of	of	ADP
ejpam-5387	13	21	cancer	cancer	NOUN
ejpam-5387	13	22	,	,	PUNCT
ejpam-5387	13	23	we	we	PRON
ejpam-5387	13	24	find	find	VERB
ejpam-5387	13	25	that	that	SCONJ
ejpam-5387	13	26	it	it	PRON
ejpam-5387	13	27	represents	represent	VERB
ejpam-5387	13	28	a	a	DET
ejpam-5387	13	29	major	major	ADJ
ejpam-5387	13	30	potential	potential	ADJ
ejpam-5387	13	31	threat	threat	NOUN
ejpam-5387	13	32	to	to	ADP
ejpam-5387	13	33	women	woman	NOUN
ejpam-5387	13	34	,	,	PUNCT
ejpam-5387	13	35	as	as	SCONJ
ejpam-5387	13	36	it	it	PRON
ejpam-5387	13	37	influenced	influence	VERB
ejpam-5387	13	38	approximately	approximately	ADV
ejpam-5387	13	39	(	(	PUNCT
ejpam-5387	13	40	8	8	NUM
ejpam-5387	13	41	-	-	SYM
ejpam-5387	13	42	9)%	9)%	NUM
ejpam-5387	13	43	of	of	ADP
ejpam-5387	13	44	women	woman	NOUN
ejpam-5387	13	45	worldwide	worldwide	ADV
ejpam-5387	14	1	[	[	X
ejpam-5387	14	2	1	1	NUM
ejpam-5387	14	3	]	]	PUNCT
ejpam-5387	14	4	.	.	PUNCT
ejpam-5387	15	1	despite	despite	SCONJ
ejpam-5387	15	2	all	all	DET
ejpam-5387	15	3	these	these	DET
ejpam-5387	15	4	meditations	meditation	NOUN
ejpam-5387	15	5	and	and	CCONJ
ejpam-5387	15	6	numerous	numerous	ADJ
ejpam-5387	15	7	fulfillments	fulfillment	NOUN
ejpam-5387	15	8	,	,	PUNCT
ejpam-5387	15	9	the	the	DET
ejpam-5387	15	10	exact	exact	ADJ
ejpam-5387	15	11	reason	reason	NOUN
ejpam-5387	15	12	of	of	ADP
ejpam-5387	15	13	bc	bc	PROPN
ejpam-5387	15	14	is	be	AUX
ejpam-5387	15	15	still	still	ADV
ejpam-5387	15	16	mysterious	mysterious	ADJ
ejpam-5387	15	17	.	.	PUNCT
ejpam-5387	16	1	it	it	PRON
ejpam-5387	16	2	was	be	AUX
ejpam-5387	16	3	also	also	ADV
ejpam-5387	16	4	directly	directly	ADV
ejpam-5387	16	5	responsible	responsible	ADJ
ejpam-5387	16	6	for	for	ADP
ejpam-5387	16	7	the	the	DET
ejpam-5387	16	8	deaths	death	NOUN
ejpam-5387	16	9	of	of	ADP
ejpam-5387	16	10	685,000	685,000	NUM
ejpam-5387	16	11	people	people	NOUN
ejpam-5387	16	12	in	in	ADP
ejpam-5387	16	13	2020	2020	NUM
ejpam-5387	16	14	,	,	PUNCT
ejpam-5387	16	15	out	out	ADP
ejpam-5387	16	16	of	of	ADP
ejpam-5387	16	17	2.3	2.3	NUM
ejpam-5387	16	18	million	million	NUM
ejpam-5387	16	19	women	woman	NOUN
ejpam-5387	16	20	affected	affect	VERB
ejpam-5387	16	21	,	,	PUNCT
ejpam-5387	16	22	as	as	SCONJ
ejpam-5387	16	23	indicated	indicate	VERB
ejpam-5387	16	24	by	by	ADP
ejpam-5387	16	25	the	the	DET
ejpam-5387	16	26	diagnosis	diagnosis	NOUN
ejpam-5387	16	27	of	of	ADP
ejpam-5387	16	28	7.8	7.8	NUM
ejpam-5387	16	29	million	million	NUM
ejpam-5387	16	30	women	woman	NOUN
ejpam-5387	16	31	during	during	ADP
ejpam-5387	16	32	the	the	DET
ejpam-5387	16	33	previous	previous	ADJ
ejpam-5387	16	34	5	5	NUM
ejpam-5387	16	35	-	-	PUNCT
ejpam-5387	16	36	years	year	NOUN
ejpam-5387	16	37	.	.	PUNCT
ejpam-5387	17	1	breast	breast	NOUN
ejpam-5387	17	2	cancer	cancer	NOUN
ejpam-5387	17	3	is	be	AUX
ejpam-5387	17	4	most	most	ADV
ejpam-5387	17	5	common	common	ADJ
ejpam-5387	17	6	in	in	ADP
ejpam-5387	17	7	women	woman	NOUN
ejpam-5387	17	8	after	after	ADP
ejpam-5387	17	9	puberty	puberty	NOUN
ejpam-5387	17	10	and	and	CCONJ
ejpam-5387	17	11	its	its	PRON
ejpam-5387	17	12	incidence	incidence	NOUN
ejpam-5387	17	13	increases	increase	VERB
ejpam-5387	17	14	with	with	ADP
ejpam-5387	17	15	age	age	NOUN
ejpam-5387	17	16	[	[	X
ejpam-5387	17	17	1	1	NUM
ejpam-5387	17	18	]	]	PUNCT
ejpam-5387	17	19	.	.	PUNCT
ejpam-5387	18	1	based	base	VERB
ejpam-5387	18	2	on	on	ADP
ejpam-5387	18	3	all	all	PRON
ejpam-5387	18	4	of	of	ADP
ejpam-5387	18	5	the	the	DET
ejpam-5387	18	6	above	above	ADJ
ejpam-5387	18	7	considerations	consideration	NOUN
ejpam-5387	18	8	,	,	PUNCT
ejpam-5387	18	9	we	we	PRON
ejpam-5387	18	10	emphasize	emphasize	VERB
ejpam-5387	18	11	the	the	DET
ejpam-5387	18	12	need	need	NOUN
ejpam-5387	18	13	for	for	ADP
ejpam-5387	18	14	an	an	DET
ejpam-5387	18	15	aggregate	aggregate	ADJ
ejpam-5387	18	16	understanding	understanding	NOUN
ejpam-5387	18	17	of	of	ADP
ejpam-5387	18	18	the	the	DET
ejpam-5387	18	19	epidemiology	epidemiology	NOUN
ejpam-5387	18	20	of	of	ADP
ejpam-5387	18	21	bc	bc	PROPN
ejpam-5387	18	22	and	and	CCONJ
ejpam-5387	18	23	its	its	PRON
ejpam-5387	18	24	effects	effect	NOUN
ejpam-5387	18	25	on	on	ADP
ejpam-5387	18	26	women	woman	NOUN
ejpam-5387	18	27	’s	’s	PART
ejpam-5387	18	28	health	health	NOUN
ejpam-5387	18	29	,	,	PUNCT
ejpam-5387	18	30	as	as	SCONJ
ejpam-5387	18	31	it	it	PRON
ejpam-5387	18	32	is	be	AUX
ejpam-5387	18	33	of	of	ADP
ejpam-5387	18	34	doi	doi	NOUN
ejpam-5387	18	35	:	:	PUNCT
ejpam-5387	18	36	https://doi.org/10.29020/nybg.ejpam.v17i4.5387	https://doi.org/10.29020/nybg.ejpam.v17i4.5387	PRON
ejpam-5387	18	37	email	email	NOUN
ejpam-5387	18	38	address	address	NOUN
ejpam-5387	18	39	:	:	PUNCT
ejpam-5387	18	40	taassiri@uqu.edu.sa	taassiri@uqu.edu.sa	PROPN
ejpam-5387	18	41	(	(	PUNCT
ejpam-5387	18	42	t.	t.	NOUN
ejpam-5387	18	43	a.	a.	NOUN
ejpam-5387	18	44	assiri	assiri	PROPN
ejpam-5387	18	45	)	)	PUNCT
ejpam-5387	18	46	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5387	18	47	2706	2706	NUM
ejpam-5387	19	1	copyright	copyright	NOUN
ejpam-5387	19	2	:	:	PUNCT
ejpam-5387	19	3	©	©	PROPN
ejpam-5387	19	4	2024	2024	NUM
ejpam-5387	19	5	the	the	DET
ejpam-5387	19	6	author(s	author(s	NOUN
ejpam-5387	19	7	)	)	PUNCT
ejpam-5387	19	8	.	.	PUNCT
ejpam-5387	20	1	(	(	PUNCT
ejpam-5387	20	2	cc	cc	NOUN
ejpam-5387	20	3	by	by	ADP
ejpam-5387	20	4	-	-	PUNCT
ejpam-5387	20	5	nc	nc	PROPN
ejpam-5387	20	6	4.0	4.0	NUM
ejpam-5387	20	7	)	)	PUNCT
ejpam-5387	20	8	t.	t.	NOUN
ejpam-5387	20	9	a.	a.	NOUN
ejpam-5387	20	10	assiri	assiri	PROPN
ejpam-5387	20	11	/	/	SYM
ejpam-5387	20	12	eur	eur	PROPN
ejpam-5387	20	13	.	.	PUNCT
ejpam-5387	21	1	j.	j.	PROPN
ejpam-5387	21	2	pure	pure	PROPN
ejpam-5387	21	3	appl	appl	PROPN
ejpam-5387	21	4	.	.	PROPN
ejpam-5387	21	5	math	math	PROPN
ejpam-5387	21	6	,	,	PUNCT
ejpam-5387	21	7	17	17	NUM
ejpam-5387	21	8	(	(	PUNCT
ejpam-5387	21	9	4	4	NUM
ejpam-5387	21	10	)	)	PUNCT
ejpam-5387	21	11	(	(	PUNCT
ejpam-5387	21	12	2024	2024	NUM
ejpam-5387	21	13	)	)	PUNCT
ejpam-5387	21	14	,	,	PUNCT
ejpam-5387	21	15	2706	2706	NUM
ejpam-5387	21	16	-	-	SYM
ejpam-5387	21	17	2719	2719	NUM
ejpam-5387	21	18	2707	2707	NUM
ejpam-5387	21	19	great	great	ADJ
ejpam-5387	21	20	importance	importance	NOUN
ejpam-5387	21	21	in	in	ADP
ejpam-5387	21	22	improving	improve	VERB
ejpam-5387	21	23	effective	effective	ADJ
ejpam-5387	21	24	preventive	preventive	ADJ
ejpam-5387	21	25	and	and	CCONJ
ejpam-5387	21	26	therapeutic	therapeutic	ADJ
ejpam-5387	21	27	methods	method	NOUN
ejpam-5387	21	28	all	all	ADV
ejpam-5387	21	29	over	over	ADP
ejpam-5387	21	30	the	the	DET
ejpam-5387	21	31	world	world	NOUN
ejpam-5387	21	32	(	(	PUNCT
ejpam-5387	21	33	[	[	X
ejpam-5387	21	34	11	11	NUM
ejpam-5387	21	35	]	]	PUNCT
ejpam-5387	21	36	,	,	PUNCT
ejpam-5387	21	37	[	[	X
ejpam-5387	21	38	21	21	NUM
ejpam-5387	21	39	]	]	PUNCT
ejpam-5387	21	40	)	)	PUNCT
ejpam-5387	21	41	.	.	PUNCT
ejpam-5387	22	1	scientists	scientist	NOUN
ejpam-5387	22	2	are	be	AUX
ejpam-5387	22	3	currently	currently	ADV
ejpam-5387	22	4	studying	study	VERB
ejpam-5387	22	5	more	more	ADV
ejpam-5387	22	6	effective	effective	ADJ
ejpam-5387	22	7	fractional	fractional	ADJ
ejpam-5387	22	8	operators	operator	NOUN
ejpam-5387	22	9	(	(	PUNCT
ejpam-5387	22	10	[	[	X
ejpam-5387	22	11	5]-[23	5]-[23	NOUN
ejpam-5387	22	12	]	]	PUNCT
ejpam-5387	22	13	)	)	PUNCT
ejpam-5387	22	14	.	.	PUNCT
ejpam-5387	23	1	in	in	ADP
ejpam-5387	23	2	order	order	NOUN
ejpam-5387	23	3	to	to	PART
ejpam-5387	23	4	address	address	VERB
ejpam-5387	23	5	the	the	DET
ejpam-5387	23	6	issue	issue	NOUN
ejpam-5387	23	7	of	of	ADP
ejpam-5387	23	8	singularity	singularity	NOUN
ejpam-5387	23	9	and	and	CCONJ
ejpam-5387	23	10	achieve	achieve	VERB
ejpam-5387	23	11	accurate	accurate	ADJ
ejpam-5387	23	12	and	and	CCONJ
ejpam-5387	23	13	reliable	reliable	ADJ
ejpam-5387	23	14	modeling	modeling	NOUN
ejpam-5387	23	15	outcomes	outcome	NOUN
ejpam-5387	23	16	,	,	PUNCT
ejpam-5387	23	17	a	a	DET
ejpam-5387	23	18	more	more	ADV
ejpam-5387	23	19	effective	effective	ADJ
ejpam-5387	23	20	cf	cf	NOUN
ejpam-5387	23	21	fractional	fractional	ADJ
ejpam-5387	23	22	derivative	derivative	NOUN
ejpam-5387	23	23	has	have	AUX
ejpam-5387	23	24	been	be	AUX
ejpam-5387	23	25	developed	develop	VERB
ejpam-5387	23	26	.	.	PUNCT
ejpam-5387	24	1	this	this	DET
ejpam-5387	24	2	derivative	derivative	NOUN
ejpam-5387	24	3	incorporates	incorporate	VERB
ejpam-5387	24	4	a	a	DET
ejpam-5387	24	5	non	non	ADJ
ejpam-5387	24	6	-	-	ADJ
ejpam-5387	24	7	singular	singular	ADJ
ejpam-5387	24	8	kernel	kernel	NOUN
ejpam-5387	24	9	,	,	PUNCT
ejpam-5387	24	10	as	as	SCONJ
ejpam-5387	24	11	proposed	propose	VERB
ejpam-5387	24	12	by	by	ADP
ejpam-5387	24	13	caputo	caputo	PROPN
ejpam-5387	24	14	and	and	CCONJ
ejpam-5387	24	15	fabrizio	fabrizio	PROPN
ejpam-5387	24	16	,	,	PUNCT
ejpam-5387	24	17	leading	lead	VERB
ejpam-5387	24	18	to	to	ADP
ejpam-5387	24	19	improved	improved	ADJ
ejpam-5387	24	20	efficiency	efficiency	NOUN
ejpam-5387	24	21	and	and	CCONJ
ejpam-5387	24	22	robustness	robustness	NOUN
ejpam-5387	24	23	in	in	ADP
ejpam-5387	24	24	recent	recent	ADJ
ejpam-5387	24	25	years	year	NOUN
ejpam-5387	24	26	.	.	PUNCT
ejpam-5387	25	1	the	the	DET
ejpam-5387	25	2	use	use	NOUN
ejpam-5387	25	3	of	of	ADP
ejpam-5387	25	4	laplace	laplace	NOUN
ejpam-5387	25	5	transformation	transformation	NOUN
ejpam-5387	25	6	to	to	PART
ejpam-5387	25	7	convert	convert	VERB
ejpam-5387	25	8	it	it	PRON
ejpam-5387	25	9	to	to	ADP
ejpam-5387	25	10	integer	integer	NOUN
ejpam-5387	25	11	power	power	NOUN
ejpam-5387	25	12	is	be	AUX
ejpam-5387	25	13	regarded	regard	VERB
ejpam-5387	25	14	as	as	ADP
ejpam-5387	25	15	a	a	DET
ejpam-5387	25	16	constructive	constructive	ADJ
ejpam-5387	25	17	method	method	NOUN
ejpam-5387	25	18	.	.	PUNCT
ejpam-5387	26	1	consequently	consequently	ADV
ejpam-5387	26	2	,	,	PUNCT
ejpam-5387	26	3	in	in	ADP
ejpam-5387	26	4	some	some	DET
ejpam-5387	26	5	scenarios	scenario	NOUN
ejpam-5387	26	6	,	,	PUNCT
ejpam-5387	26	7	we	we	PRON
ejpam-5387	26	8	can	can	AUX
ejpam-5387	26	9	readily	readily	ADV
ejpam-5387	26	10	compute	compute	VERB
ejpam-5387	26	11	the	the	DET
ejpam-5387	26	12	precise	precise	ADJ
ejpam-5387	26	13	solution	solution	NOUN
ejpam-5387	26	14	.	.	PUNCT
ejpam-5387	27	1	the	the	DET
ejpam-5387	27	2	citation	citation	NOUN
ejpam-5387	27	3	for	for	ADP
ejpam-5387	27	4	this	this	DET
ejpam-5387	27	5	information	information	NOUN
ejpam-5387	27	6	is	be	AUX
ejpam-5387	27	7	[	[	X
ejpam-5387	27	8	6	6	NUM
ejpam-5387	27	9	]	]	PUNCT
ejpam-5387	27	10	.	.	PUNCT
ejpam-5387	28	1	the	the	DET
ejpam-5387	28	2	paper	paper	NOUN
ejpam-5387	28	3	[	[	X
ejpam-5387	28	4	16	16	NUM
ejpam-5387	28	5	]	]	PUNCT
ejpam-5387	28	6	explores	explore	VERB
ejpam-5387	28	7	the	the	DET
ejpam-5387	28	8	examination	examination	NOUN
ejpam-5387	28	9	of	of	ADP
ejpam-5387	28	10	fractional	fractional	ADJ
ejpam-5387	28	11	operators	operator	NOUN
ejpam-5387	28	12	and	and	CCONJ
ejpam-5387	28	13	presents	present	VERB
ejpam-5387	28	14	novel	novel	ADJ
ejpam-5387	28	15	characteristics	characteristic	NOUN
ejpam-5387	28	16	associated	associate	VERB
ejpam-5387	28	17	with	with	ADP
ejpam-5387	28	18	them	they	PRON
ejpam-5387	28	19	.	.	PUNCT
ejpam-5387	29	1	fractional	fractional	ADJ
ejpam-5387	29	2	derivatives	derivative	NOUN
ejpam-5387	29	3	have	have	AUX
ejpam-5387	29	4	acquired	acquire	VERB
ejpam-5387	29	5	increasing	increase	VERB
ejpam-5387	29	6	leverage	leverage	NOUN
ejpam-5387	29	7	in	in	ADP
ejpam-5387	29	8	the	the	DET
ejpam-5387	29	9	last	last	ADJ
ejpam-5387	29	10	few	few	ADJ
ejpam-5387	29	11	years	year	NOUN
ejpam-5387	29	12	,	,	PUNCT
ejpam-5387	29	13	as	as	SCONJ
ejpam-5387	29	14	they	they	PRON
ejpam-5387	29	15	have	have	AUX
ejpam-5387	29	16	greatly	greatly	ADV
ejpam-5387	29	17	contributed	contribute	VERB
ejpam-5387	29	18	to	to	ADP
ejpam-5387	29	19	presenting	present	VERB
ejpam-5387	29	20	the	the	DET
ejpam-5387	29	21	most	most	ADV
ejpam-5387	29	22	difficult	difficult	ADJ
ejpam-5387	29	23	mathematical	mathematical	ADJ
ejpam-5387	29	24	models	model	NOUN
ejpam-5387	29	25	in	in	ADP
ejpam-5387	29	26	a	a	DET
ejpam-5387	29	27	clearer	clear	ADJ
ejpam-5387	29	28	and	and	CCONJ
ejpam-5387	29	29	more	more	ADV
ejpam-5387	29	30	comprehensive	comprehensive	ADJ
ejpam-5387	29	31	manner	manner	NOUN
ejpam-5387	29	32	,	,	PUNCT
ejpam-5387	29	33	which	which	PRON
ejpam-5387	29	34	in	in	ADP
ejpam-5387	29	35	turn	turn	NOUN
ejpam-5387	29	36	has	have	AUX
ejpam-5387	29	37	helped	help	VERB
ejpam-5387	29	38	researchers	researcher	NOUN
ejpam-5387	29	39	to	to	PART
ejpam-5387	29	40	obtain	obtain	VERB
ejpam-5387	29	41	more	more	ADV
ejpam-5387	29	42	accurate	accurate	ADJ
ejpam-5387	29	43	solutions	solution	NOUN
ejpam-5387	29	44	to	to	ADP
ejpam-5387	29	45	such	such	ADJ
ejpam-5387	29	46	models	model	NOUN
ejpam-5387	29	47	by	by	ADP
ejpam-5387	29	48	applying	apply	VERB
ejpam-5387	29	49	appropriate	appropriate	ADJ
ejpam-5387	29	50	numerical	numerical	ADJ
ejpam-5387	29	51	and	and	CCONJ
ejpam-5387	29	52	approximate	approximate	ADJ
ejpam-5387	29	53	methods	method	NOUN
ejpam-5387	29	54	.	.	PUNCT
ejpam-5387	30	1	the	the	DET
ejpam-5387	30	2	fundamental	fundamental	ADJ
ejpam-5387	30	3	focus	focus	NOUN
ejpam-5387	30	4	of	of	ADP
ejpam-5387	30	5	the	the	DET
ejpam-5387	30	6	research	research	NOUN
ejpam-5387	30	7	[	[	X
ejpam-5387	30	8	13	13	NUM
ejpam-5387	30	9	]	]	PUNCT
ejpam-5387	30	10	is	be	AUX
ejpam-5387	30	11	the	the	DET
ejpam-5387	30	12	monotonicity	monotonicity	NOUN
ejpam-5387	30	13	theorem	theorem	NOUN
ejpam-5387	30	14	for	for	ADP
ejpam-5387	30	15	fractional	fractional	ADJ
ejpam-5387	30	16	differential	differential	ADJ
ejpam-5387	30	17	equations	equation	NOUN
ejpam-5387	30	18	(	(	PUNCT
ejpam-5387	30	19	fdes	fde	NOUN
ejpam-5387	30	20	)	)	PUNCT
ejpam-5387	30	21	in	in	ADP
ejpam-5387	30	22	the	the	DET
ejpam-5387	30	23	caputo	caputo	PROPN
ejpam-5387	30	24	form	form	NOUN
ejpam-5387	30	25	.	.	PUNCT
ejpam-5387	31	1	a	a	DET
ejpam-5387	31	2	study	study	NOUN
ejpam-5387	31	3	[	[	X
ejpam-5387	31	4	18	18	NUM
ejpam-5387	31	5	]	]	PUNCT
ejpam-5387	31	6	has	have	AUX
ejpam-5387	31	7	devised	devise	VERB
ejpam-5387	31	8	a	a	DET
ejpam-5387	31	9	highly	highly	ADV
ejpam-5387	31	10	effective	effective	ADJ
ejpam-5387	31	11	numerical	numerical	ADJ
ejpam-5387	31	12	technique	technique	NOUN
ejpam-5387	31	13	,	,	PUNCT
ejpam-5387	31	14	known	know	VERB
ejpam-5387	31	15	as	as	ADP
ejpam-5387	31	16	the	the	DET
ejpam-5387	31	17	iterative	iterative	NOUN
ejpam-5387	31	18	reproducing	reproduce	VERB
ejpam-5387	31	19	kernel	kernel	NOUN
ejpam-5387	31	20	algorithm	algorithm	PROPN
ejpam-5387	31	21	,	,	PUNCT
ejpam-5387	31	22	for	for	ADP
ejpam-5387	31	23	computing	compute	VERB
ejpam-5387	31	24	approximate	approximate	ADJ
ejpam-5387	31	25	solutions	solution	NOUN
ejpam-5387	31	26	to	to	ADP
ejpam-5387	31	27	fractional	fractional	ADJ
ejpam-5387	31	28	riccati	riccati	PROPN
ejpam-5387	31	29	and	and	CCONJ
ejpam-5387	31	30	bernoulli	bernoulli	PROPN
ejpam-5387	31	31	des	des	PROPN
ejpam-5387	31	32	while	while	SCONJ
ejpam-5387	31	33	considering	consider	VERB
ejpam-5387	31	34	the	the	DET
ejpam-5387	31	35	cf	cf	NOUN
ejpam-5387	31	36	-	-	PUNCT
ejpam-5387	31	37	derivative	derivative	NOUN
ejpam-5387	31	38	.	.	PUNCT
ejpam-5387	32	1	furthermore	furthermore	ADV
ejpam-5387	32	2	,	,	PUNCT
ejpam-5387	32	3	a	a	DET
ejpam-5387	32	4	work	work	NOUN
ejpam-5387	32	5	conducted	conduct	VERB
ejpam-5387	32	6	in	in	ADP
ejpam-5387	32	7	[	[	X
ejpam-5387	32	8	7	7	NUM
ejpam-5387	32	9	]	]	PUNCT
ejpam-5387	32	10	has	have	AUX
ejpam-5387	32	11	examined	examine	VERB
ejpam-5387	32	12	the	the	DET
ejpam-5387	32	13	intricate	intricate	ADJ
ejpam-5387	32	14	dynamics	dynamic	NOUN
ejpam-5387	32	15	of	of	ADP
ejpam-5387	32	16	the	the	DET
ejpam-5387	32	17	omicron	omicron	PROPN
ejpam-5387	32	18	variant	variant	NOUN
ejpam-5387	32	19	of	of	ADP
ejpam-5387	32	20	covid-19	covid-19	PROPN
ejpam-5387	32	21	by	by	ADP
ejpam-5387	32	22	employing	employ	VERB
ejpam-5387	32	23	cf	cf	NOUN
ejpam-5387	32	24	-	-	PUNCT
ejpam-5387	32	25	fractional	fractional	ADJ
ejpam-5387	32	26	operators	operator	NOUN
ejpam-5387	32	27	,	,	PUNCT
ejpam-5387	32	28	and	and	CCONJ
ejpam-5387	32	29	others	other	NOUN
ejpam-5387	33	1	[	[	X
ejpam-5387	33	2	25	25	NUM
ejpam-5387	33	3	]	]	PUNCT
ejpam-5387	33	4	.	.	PUNCT
ejpam-5387	34	1	in	in	ADP
ejpam-5387	34	2	addition	addition	NOUN
ejpam-5387	34	3	,	,	PUNCT
ejpam-5387	34	4	a	a	DET
ejpam-5387	34	5	numerical	numerical	ADJ
ejpam-5387	34	6	method	method	NOUN
ejpam-5387	34	7	is	be	AUX
ejpam-5387	34	8	created	create	VERB
ejpam-5387	34	9	that	that	PRON
ejpam-5387	34	10	includes	include	VERB
ejpam-5387	34	11	an	an	DET
ejpam-5387	34	12	exponential	exponential	ADJ
ejpam-5387	34	13	law	law	NOUN
ejpam-5387	34	14	kernel	kernel	NOUN
ejpam-5387	34	15	to	to	PART
ejpam-5387	34	16	analyze	analyze	VERB
ejpam-5387	34	17	and	and	CCONJ
ejpam-5387	34	18	model	model	VERB
ejpam-5387	34	19	the	the	DET
ejpam-5387	34	20	spread	spread	NOUN
ejpam-5387	34	21	of	of	ADP
ejpam-5387	34	22	the	the	DET
ejpam-5387	34	23	infection	infection	NOUN
ejpam-5387	34	24	.	.	PUNCT
ejpam-5387	35	1	many	many	ADJ
ejpam-5387	35	2	mathematicians	mathematician	NOUN
ejpam-5387	35	3	find	find	VERB
ejpam-5387	35	4	it	it	PRON
ejpam-5387	35	5	challenging	challenge	VERB
ejpam-5387	35	6	to	to	PART
ejpam-5387	35	7	create	create	VERB
ejpam-5387	35	8	numerical	numerical	ADJ
ejpam-5387	35	9	and	and	CCONJ
ejpam-5387	35	10	approximate	approximate	ADJ
ejpam-5387	35	11	solutions	solution	NOUN
ejpam-5387	35	12	for	for	ADP
ejpam-5387	35	13	the	the	DET
ejpam-5387	35	14	fdes	fde	NOUN
ejpam-5387	35	15	(	(	PUNCT
ejpam-5387	35	16	[	[	X
ejpam-5387	35	17	3]-[14	3]-[14	NUM
ejpam-5387	35	18	]	]	NUM
ejpam-5387	35	19	)	)	PUNCT
ejpam-5387	35	20	.	.	PUNCT
ejpam-5387	36	1	the	the	DET
ejpam-5387	36	2	adams	adams	PROPN
ejpam-5387	36	3	-	-	PUNCT
ejpam-5387	36	4	bashforth	bashforth	NOUN
ejpam-5387	36	5	method	method	NOUN
ejpam-5387	36	6	,	,	PUNCT
ejpam-5387	36	7	incorporating	incorporate	VERB
ejpam-5387	36	8	the	the	DET
ejpam-5387	36	9	cf	cf	NOUN
ejpam-5387	36	10	operator	operator	NOUN
ejpam-5387	36	11	,	,	PUNCT
ejpam-5387	36	12	is	be	AUX
ejpam-5387	36	13	formulated	formulate	VERB
ejpam-5387	36	14	in	in	ADP
ejpam-5387	36	15	[	[	X
ejpam-5387	36	16	22	22	NUM
ejpam-5387	36	17	]	]	PUNCT
ejpam-5387	36	18	.	.	PUNCT
ejpam-5387	37	1	this	this	DET
ejpam-5387	37	2	method	method	NOUN
ejpam-5387	37	3	involves	involve	VERB
ejpam-5387	37	4	three	three	NUM
ejpam-5387	37	5	steps	step	NOUN
ejpam-5387	37	6	and	and	CCONJ
ejpam-5387	37	7	can	can	AUX
ejpam-5387	37	8	be	be	AUX
ejpam-5387	37	9	used	use	VERB
ejpam-5387	37	10	to	to	PART
ejpam-5387	37	11	solve	solve	VERB
ejpam-5387	37	12	both	both	DET
ejpam-5387	37	13	linear	linear	ADJ
ejpam-5387	37	14	/	/	SYM
ejpam-5387	37	15	nonlinear	nonlinear	ADJ
ejpam-5387	37	16	fdes	fde	NOUN
ejpam-5387	37	17	.	.	PUNCT
ejpam-5387	38	1	additionally	additionally	ADV
ejpam-5387	38	2	,	,	PUNCT
ejpam-5387	38	3	it	it	PRON
ejpam-5387	38	4	possesses	possess	VERB
ejpam-5387	38	5	diverse	diverse	ADJ
ejpam-5387	38	6	uses	use	NOUN
ejpam-5387	38	7	in	in	ADP
ejpam-5387	38	8	resolving	resolve	VERB
ejpam-5387	38	9	chaotic	chaotic	ADJ
ejpam-5387	38	10	systems	system	NOUN
ejpam-5387	38	11	with	with	ADP
ejpam-5387	38	12	fractional	fractional	ADJ
ejpam-5387	38	13	orders	order	NOUN
ejpam-5387	38	14	.	.	PUNCT
ejpam-5387	39	1	the	the	DET
ejpam-5387	39	2	authors	author	NOUN
ejpam-5387	39	3	of	of	ADP
ejpam-5387	39	4	[	[	X
ejpam-5387	39	5	12	12	NUM
ejpam-5387	39	6	]	]	PUNCT
ejpam-5387	39	7	have	have	AUX
ejpam-5387	39	8	developed	develop	VERB
ejpam-5387	39	9	a	a	DET
ejpam-5387	39	10	trapezoidal	trapezoidal	ADJ
ejpam-5387	39	11	strategy	strategy	NOUN
ejpam-5387	39	12	to	to	PART
ejpam-5387	39	13	solve	solve	VERB
ejpam-5387	39	14	the	the	DET
ejpam-5387	39	15	fdes	fde	NOUN
ejpam-5387	39	16	efficiently	efficiently	ADV
ejpam-5387	39	17	.	.	PUNCT
ejpam-5387	40	1	this	this	DET
ejpam-5387	40	2	scheme	scheme	NOUN
ejpam-5387	40	3	utilizes	utilize	VERB
ejpam-5387	40	4	the	the	DET
ejpam-5387	40	5	cf	cf	NOUN
ejpam-5387	40	6	operator	operator	NOUN
ejpam-5387	40	7	and	and	CCONJ
ejpam-5387	40	8	achieves	achieve	VERB
ejpam-5387	40	9	a	a	DET
ejpam-5387	40	10	convergence	convergence	NOUN
ejpam-5387	40	11	order	order	NOUN
ejpam-5387	40	12	of	of	ADP
ejpam-5387	40	13	two	two	NUM
ejpam-5387	40	14	.	.	PUNCT
ejpam-5387	41	1	additionally	additionally	ADV
ejpam-5387	41	2	,	,	PUNCT
ejpam-5387	41	3	the	the	DET
ejpam-5387	41	4	convergence	convergence	NOUN
ejpam-5387	41	5	and	and	CCONJ
ejpam-5387	41	6	stability	stability	NOUN
ejpam-5387	41	7	of	of	ADP
ejpam-5387	41	8	this	this	DET
ejpam-5387	41	9	technique	technique	NOUN
ejpam-5387	41	10	have	have	AUX
ejpam-5387	41	11	been	be	AUX
ejpam-5387	41	12	thoroughly	thoroughly	ADV
ejpam-5387	41	13	investigated	investigate	VERB
ejpam-5387	41	14	.	.	PUNCT
ejpam-5387	42	1	inspired	inspire	VERB
ejpam-5387	42	2	by	by	ADP
ejpam-5387	42	3	this	this	DET
ejpam-5387	42	4	research	research	NOUN
ejpam-5387	42	5	,	,	PUNCT
ejpam-5387	42	6	we	we	PRON
ejpam-5387	42	7	devised	devise	VERB
ejpam-5387	42	8	simpson	simpson	PROPN
ejpam-5387	42	9	’s	’s	PART
ejpam-5387	42	10	1/3	1/3	NUM
ejpam-5387	42	11	scheme	scheme	NOUN
ejpam-5387	42	12	for	for	ADP
ejpam-5387	42	13	solving	solve	VERB
ejpam-5387	42	14	fdes	fde	NOUN
ejpam-5387	42	15	.	.	PUNCT
ejpam-5387	43	1	this	this	DET
ejpam-5387	43	2	method	method	NOUN
ejpam-5387	43	3	achieves	achieve	VERB
ejpam-5387	43	4	a	a	DET
ejpam-5387	43	5	high	high	ADJ
ejpam-5387	43	6	level	level	NOUN
ejpam-5387	43	7	of	of	ADP
ejpam-5387	43	8	accuracy	accuracy	NOUN
ejpam-5387	43	9	,	,	PUNCT
ejpam-5387	43	10	with	with	ADP
ejpam-5387	43	11	an	an	DET
ejpam-5387	43	12	order	order	NOUN
ejpam-5387	43	13	of	of	ADP
ejpam-5387	43	14	four	four	NUM
ejpam-5387	43	15	,	,	PUNCT
ejpam-5387	43	16	as	as	SCONJ
ejpam-5387	43	17	detailed	detailed	ADJ
ejpam-5387	43	18	in	in	ADP
ejpam-5387	43	19	our	our	PRON
ejpam-5387	43	20	work	work	NOUN
ejpam-5387	43	21	.	.	PUNCT
ejpam-5387	44	1	the	the	DET
ejpam-5387	44	2	proposed	propose	VERB
ejpam-5387	44	3	fractional	fractional	PROPN
ejpam-5387	44	4	simpson	simpson	PROPN
ejpam-5387	44	5	’s	’s	PART
ejpam-5387	44	6	1/3	1/3	NUM
ejpam-5387	44	7	approach	approach	NOUN
ejpam-5387	44	8	offers	offer	VERB
ejpam-5387	44	9	superior	superior	ADJ
ejpam-5387	44	10	accuracy	accuracy	NOUN
ejpam-5387	44	11	compared	compare	VERB
ejpam-5387	44	12	to	to	ADP
ejpam-5387	44	13	current	current	ADJ
ejpam-5387	44	14	methods	method	NOUN
ejpam-5387	44	15	and	and	CCONJ
ejpam-5387	44	16	is	be	AUX
ejpam-5387	44	17	straightforward	straightforward	ADJ
ejpam-5387	44	18	to	to	PART
ejpam-5387	44	19	implement	implement	VERB
ejpam-5387	44	20	.	.	PUNCT
ejpam-5387	45	1	the	the	DET
ejpam-5387	45	2	novelty	novelty	NOUN
ejpam-5387	45	3	in	in	ADP
ejpam-5387	45	4	the	the	DET
ejpam-5387	45	5	current	current	ADJ
ejpam-5387	45	6	research	research	NOUN
ejpam-5387	45	7	is	be	AUX
ejpam-5387	45	8	the	the	DET
ejpam-5387	45	9	attempt	attempt	NOUN
ejpam-5387	45	10	to	to	PART
ejpam-5387	45	11	reach	reach	VERB
ejpam-5387	45	12	numerical	numerical	ADJ
ejpam-5387	45	13	simulations	simulation	NOUN
ejpam-5387	45	14	(	(	PUNCT
ejpam-5387	45	15	through	through	ADP
ejpam-5387	45	16	a	a	DET
ejpam-5387	45	17	good	good	ADJ
ejpam-5387	45	18	numerical	numerical	ADJ
ejpam-5387	45	19	method	method	NOUN
ejpam-5387	45	20	)	)	PUNCT
ejpam-5387	45	21	to	to	PART
ejpam-5387	45	22	study	study	VERB
ejpam-5387	45	23	the	the	DET
ejpam-5387	45	24	important	important	ADJ
ejpam-5387	45	25	system	system	NOUN
ejpam-5387	45	26	under	under	ADP
ejpam-5387	45	27	consideration	consideration	NOUN
ejpam-5387	45	28	which	which	PRON
ejpam-5387	45	29	is	be	AUX
ejpam-5387	45	30	of	of	ADP
ejpam-5387	45	31	interest	interest	NOUN
ejpam-5387	45	32	to	to	ADP
ejpam-5387	45	33	many	many	ADJ
ejpam-5387	45	34	researchers	researcher	NOUN
ejpam-5387	45	35	,	,	PUNCT
ejpam-5387	45	36	so	so	SCONJ
ejpam-5387	45	37	we	we	PRON
ejpam-5387	45	38	presented	present	VERB
ejpam-5387	45	39	by	by	ADP
ejpam-5387	45	40	shedding	shed	VERB
ejpam-5387	45	41	some	some	DET
ejpam-5387	45	42	light	light	NOUN
ejpam-5387	45	43	on	on	ADP
ejpam-5387	45	44	the	the	DET
ejpam-5387	45	45	convergence	convergence	NOUN
ejpam-5387	45	46	and	and	CCONJ
ejpam-5387	45	47	calculating	calculate	VERB
ejpam-5387	45	48	the	the	DET
ejpam-5387	45	49	resulting	result	VERB
ejpam-5387	45	50	error	error	NOUN
ejpam-5387	45	51	as	as	ADV
ejpam-5387	45	52	well	well	ADV
ejpam-5387	45	53	as	as	ADP
ejpam-5387	45	54	comparisons	comparison	NOUN
ejpam-5387	45	55	with	with	ADP
ejpam-5387	45	56	the	the	DET
ejpam-5387	45	57	same	same	ADJ
ejpam-5387	45	58	method	method	NOUN
ejpam-5387	45	59	but	but	CCONJ
ejpam-5387	45	60	in	in	ADP
ejpam-5387	45	61	a	a	DET
ejpam-5387	45	62	less	less	ADV
ejpam-5387	45	63	accurate	accurate	ADJ
ejpam-5387	45	64	case	case	NOUN
ejpam-5387	45	65	and	and	CCONJ
ejpam-5387	45	66	finally	finally	ADV
ejpam-5387	45	67	the	the	DET
ejpam-5387	45	68	effect	effect	NOUN
ejpam-5387	45	69	of	of	ADP
ejpam-5387	45	70	the	the	DET
ejpam-5387	45	71	parameters	parameter	NOUN
ejpam-5387	45	72	in	in	ADP
ejpam-5387	45	73	the	the	DET
ejpam-5387	45	74	system	system	NOUN
ejpam-5387	45	75	on	on	ADP
ejpam-5387	45	76	the	the	DET
ejpam-5387	45	77	behavior	behavior	NOUN
ejpam-5387	45	78	of	of	ADP
ejpam-5387	45	79	the	the	DET
ejpam-5387	45	80	solution	solution	NOUN
ejpam-5387	45	81	to	to	PART
ejpam-5387	45	82	provide	provide	VERB
ejpam-5387	45	83	recommendations	recommendation	NOUN
ejpam-5387	45	84	that	that	PRON
ejpam-5387	45	85	can	can	AUX
ejpam-5387	45	86	be	be	AUX
ejpam-5387	45	87	used	use	VERB
ejpam-5387	45	88	by	by	ADP
ejpam-5387	45	89	those	those	PRON
ejpam-5387	45	90	interested	interested	ADJ
ejpam-5387	45	91	in	in	ADP
ejpam-5387	45	92	studying	study	VERB
ejpam-5387	45	93	this	this	DET
ejpam-5387	45	94	model	model	NOUN
ejpam-5387	45	95	medically	medically	ADV
ejpam-5387	45	96	or	or	CCONJ
ejpam-5387	45	97	industrially	industrially	ADV
ejpam-5387	45	98	.	.	PUNCT
ejpam-5387	46	1	this	this	DET
ejpam-5387	46	2	work	work	NOUN
ejpam-5387	46	3	is	be	AUX
ejpam-5387	46	4	devoted	devote	VERB
ejpam-5387	46	5	to	to	ADP
ejpam-5387	46	6	giving	give	VERB
ejpam-5387	46	7	a	a	DET
ejpam-5387	46	8	numerical	numerical	ADJ
ejpam-5387	46	9	solution	solution	NOUN
ejpam-5387	46	10	for	for	ADP
ejpam-5387	46	11	the	the	DET
ejpam-5387	46	12	fractional	fractional	PROPN
ejpam-5387	46	13	bc	bc	PROPN
ejpam-5387	46	14	model	model	PROPN
ejpam-5387	46	15	.	.	PUNCT
ejpam-5387	47	1	this	this	PRON
ejpam-5387	47	2	is	be	AUX
ejpam-5387	47	3	by	by	ADP
ejpam-5387	47	4	using	use	VERB
ejpam-5387	47	5	the	the	DET
ejpam-5387	47	6	simpson	simpson	PROPN
ejpam-5387	47	7	’s	’s	PART
ejpam-5387	47	8	1	1	NUM
ejpam-5387	47	9	3	3	NUM
ejpam-5387	47	10	rule	rule	NOUN
ejpam-5387	47	11	for	for	ADP
ejpam-5387	47	12	cf	cf	NOUN
ejpam-5387	47	13	-	-	PUNCT
ejpam-5387	47	14	fractional	fractional	ADJ
ejpam-5387	47	15	integral	integral	ADJ
ejpam-5387	47	16	.	.	PUNCT
ejpam-5387	48	1	the	the	DET
ejpam-5387	48	2	outline	outline	NOUN
ejpam-5387	48	3	of	of	ADP
ejpam-5387	48	4	the	the	DET
ejpam-5387	48	5	paper	paper	NOUN
ejpam-5387	48	6	is	be	AUX
ejpam-5387	48	7	given	give	VERB
ejpam-5387	48	8	as	as	SCONJ
ejpam-5387	48	9	follows	follow	VERB
ejpam-5387	48	10	:	:	PUNCT
ejpam-5387	48	11	section	section	NOUN
ejpam-5387	48	12	2	2	NUM
ejpam-5387	48	13	,	,	PUNCT
ejpam-5387	48	14	presents	present	VERB
ejpam-5387	48	15	some	some	DET
ejpam-5387	48	16	basic	basic	ADJ
ejpam-5387	48	17	concepts	concept	NOUN
ejpam-5387	48	18	t.	t.	PROPN
ejpam-5387	48	19	a.	a.	PROPN
ejpam-5387	48	20	assiri	assiri	PROPN
ejpam-5387	48	21	/	/	SYM
ejpam-5387	48	22	eur	eur	PROPN
ejpam-5387	48	23	.	.	PUNCT
ejpam-5387	49	1	j.	j.	PROPN
ejpam-5387	49	2	pure	pure	PROPN
ejpam-5387	49	3	appl	appl	PROPN
ejpam-5387	49	4	.	.	PROPN
ejpam-5387	49	5	math	math	PROPN
ejpam-5387	49	6	,	,	PUNCT
ejpam-5387	49	7	17	17	NUM
ejpam-5387	49	8	(	(	PUNCT
ejpam-5387	49	9	4	4	NUM
ejpam-5387	49	10	)	)	PUNCT
ejpam-5387	49	11	(	(	PUNCT
ejpam-5387	49	12	2024	2024	NUM
ejpam-5387	49	13	)	)	PUNCT
ejpam-5387	49	14	,	,	PUNCT
ejpam-5387	49	15	2706	2706	NUM
ejpam-5387	49	16	-	-	SYM
ejpam-5387	49	17	2719	2719	NUM
ejpam-5387	49	18	2708	2708	NUM
ejpam-5387	49	19	of	of	ADP
ejpam-5387	49	20	fractional	fractional	ADJ
ejpam-5387	49	21	calculus	calculus	NOUN
ejpam-5387	49	22	in	in	ADP
ejpam-5387	49	23	sense	sense	NOUN
ejpam-5387	49	24	of	of	ADP
ejpam-5387	49	25	the	the	DET
ejpam-5387	49	26	caputo	caputo	PROPN
ejpam-5387	49	27	and	and	CCONJ
ejpam-5387	49	28	fabrizio	fabrizio	PROPN
ejpam-5387	49	29	.	.	PUNCT
ejpam-5387	50	1	section	section	PROPN
ejpam-5387	50	2	3	3	NUM
ejpam-5387	50	3	,	,	PUNCT
ejpam-5387	50	4	describes	describe	VERB
ejpam-5387	50	5	the	the	DET
ejpam-5387	50	6	breast	breast	NOUN
ejpam-5387	50	7	cancer	cancer	NOUN
ejpam-5387	50	8	system	system	NOUN
ejpam-5387	50	9	in	in	ADP
ejpam-5387	50	10	its	its	PRON
ejpam-5387	50	11	fractional	fractional	ADJ
ejpam-5387	50	12	form	form	NOUN
ejpam-5387	50	13	.	.	PUNCT
ejpam-5387	51	1	section	section	NOUN
ejpam-5387	51	2	4	4	NUM
ejpam-5387	51	3	,	,	PUNCT
ejpam-5387	51	4	derives	derive	VERB
ejpam-5387	51	5	the	the	DET
ejpam-5387	51	6	simpson’s-13	simpson’s-13	NOUN
ejpam-5387	51	7	rule	rule	NOUN
ejpam-5387	51	8	for	for	ADP
ejpam-5387	51	9	cffractional	cffractional	ADJ
ejpam-5387	51	10	integral	integral	ADJ
ejpam-5387	51	11	.	.	PUNCT
ejpam-5387	52	1	section	section	NOUN
ejpam-5387	52	2	5	5	NUM
ejpam-5387	52	3	,	,	PUNCT
ejpam-5387	52	4	outlines	outline	VERB
ejpam-5387	52	5	a	a	DET
ejpam-5387	52	6	numerical	numerical	ADJ
ejpam-5387	52	7	implementation	implementation	NOUN
ejpam-5387	52	8	for	for	ADP
ejpam-5387	52	9	solving	solve	VERB
ejpam-5387	52	10	the	the	DET
ejpam-5387	52	11	model	model	NOUN
ejpam-5387	52	12	under	under	ADP
ejpam-5387	52	13	study	study	NOUN
ejpam-5387	52	14	.	.	PUNCT
ejpam-5387	53	1	section	section	NOUN
ejpam-5387	53	2	6	6	NUM
ejpam-5387	53	3	,	,	PUNCT
ejpam-5387	53	4	presents	present	VERB
ejpam-5387	53	5	a	a	DET
ejpam-5387	53	6	numerical	numerical	ADJ
ejpam-5387	53	7	simulation	simulation	NOUN
ejpam-5387	53	8	for	for	ADP
ejpam-5387	53	9	the	the	DET
ejpam-5387	53	10	model	model	NOUN
ejpam-5387	53	11	under	under	ADP
ejpam-5387	53	12	study	study	NOUN
ejpam-5387	53	13	.	.	PUNCT
ejpam-5387	54	1	section	section	NOUN
ejpam-5387	54	2	7	7	NUM
ejpam-5387	54	3	,	,	PUNCT
ejpam-5387	54	4	gives	give	VERB
ejpam-5387	54	5	the	the	DET
ejpam-5387	54	6	conclusions	conclusion	NOUN
ejpam-5387	54	7	and	and	CCONJ
ejpam-5387	54	8	remarks	remark	NOUN
ejpam-5387	54	9	.	.	PUNCT
ejpam-5387	55	1	2	2	X
ejpam-5387	55	2	.	.	X
ejpam-5387	55	3	preliminaries	preliminary	NOUN
ejpam-5387	55	4	mathematical	mathematical	ADJ
ejpam-5387	55	5	models	model	NOUN
ejpam-5387	55	6	using	use	VERB
ejpam-5387	55	7	more	more	ADV
ejpam-5387	55	8	accurate	accurate	ADJ
ejpam-5387	55	9	fractional	fractional	ADJ
ejpam-5387	55	10	derivatives	derivative	NOUN
ejpam-5387	55	11	(	(	PUNCT
ejpam-5387	55	12	fds	fds	NOUN
ejpam-5387	55	13	)	)	PUNCT
ejpam-5387	55	14	have	have	AUX
ejpam-5387	55	15	been	be	AUX
ejpam-5387	55	16	used	use	VERB
ejpam-5387	55	17	by	by	ADP
ejpam-5387	55	18	taking	take	VERB
ejpam-5387	55	19	advantage	advantage	NOUN
ejpam-5387	55	20	of	of	ADP
ejpam-5387	55	21	a	a	DET
ejpam-5387	55	22	non	non	ADJ
ejpam-5387	55	23	-	-	ADJ
ejpam-5387	55	24	singular	singular	ADJ
ejpam-5387	55	25	kernel	kernel	NOUN
ejpam-5387	55	26	.	.	PUNCT
ejpam-5387	56	1	this	this	DET
ejpam-5387	56	2	approach	approach	NOUN
ejpam-5387	56	3	enhances	enhance	VERB
ejpam-5387	56	4	the	the	DET
ejpam-5387	56	5	system	system	NOUN
ejpam-5387	56	6	’s	’s	PART
ejpam-5387	56	7	ability	ability	NOUN
ejpam-5387	56	8	to	to	PART
ejpam-5387	56	9	accurately	accurately	ADV
ejpam-5387	56	10	represent	represent	VERB
ejpam-5387	56	11	and	and	CCONJ
ejpam-5387	56	12	capture	capture	VERB
ejpam-5387	56	13	memory	memory	NOUN
ejpam-5387	56	14	effects	effect	NOUN
ejpam-5387	56	15	.	.	PUNCT
ejpam-5387	57	1	in	in	ADP
ejpam-5387	57	2	2015	2015	NUM
ejpam-5387	57	3	,	,	PUNCT
ejpam-5387	57	4	caputo	caputo	PROPN
ejpam-5387	57	5	and	and	CCONJ
ejpam-5387	57	6	fabrizio	fabrizio	PROPN
ejpam-5387	57	7	successfully	successfully	ADV
ejpam-5387	57	8	introduced	introduce	VERB
ejpam-5387	57	9	cf	cf	NOUN
ejpam-5387	57	10	-	-	PUNCT
ejpam-5387	57	11	fd	fd	NOUN
ejpam-5387	57	12	by	by	ADP
ejpam-5387	57	13	substituting	substitute	VERB
ejpam-5387	57	14	the	the	DET
ejpam-5387	57	15	singular	singular	ADJ
ejpam-5387	57	16	kernel	kernel	NOUN
ejpam-5387	57	17	(	(	PUNCT
ejpam-5387	57	18	t	t	PROPN
ejpam-5387	57	19	−	−	PROPN
ejpam-5387	57	20	τ)−γ	τ)−γ	PUNCT
ejpam-5387	57	21	with	with	ADP
ejpam-5387	57	22	e	e	NOUN
ejpam-5387	57	23	(	(	PUNCT
ejpam-5387	57	24	−γ(t−τ	−γ(t−τ	NOUN
ejpam-5387	57	25	)	)	PUNCT
ejpam-5387	57	26	1−γ	1−γ	NUM
ejpam-5387	57	27	)	)	PUNCT
ejpam-5387	57	28	in	in	ADP
ejpam-5387	57	29	the	the	DET
ejpam-5387	57	30	caputo	caputo	PROPN
ejpam-5387	57	31	derivative	derivative	NOUN
ejpam-5387	58	1	[	[	X
ejpam-5387	58	2	6	6	NUM
ejpam-5387	58	3	]	]	PUNCT
ejpam-5387	58	4	.	.	PUNCT
ejpam-5387	59	1	here	here	ADV
ejpam-5387	59	2	,	,	PUNCT
ejpam-5387	59	3	we	we	PRON
ejpam-5387	59	4	will	will	AUX
ejpam-5387	59	5	provide	provide	VERB
ejpam-5387	59	6	a	a	DET
ejpam-5387	59	7	succinct	succinct	ADJ
ejpam-5387	59	8	overview	overview	NOUN
ejpam-5387	59	9	of	of	ADP
ejpam-5387	59	10	fundamental	fundamental	ADJ
ejpam-5387	59	11	definitions	definition	NOUN
ejpam-5387	59	12	pertaining	pertain	VERB
ejpam-5387	59	13	to	to	ADP
ejpam-5387	59	14	fractional	fractional	ADJ
ejpam-5387	59	15	calculus	calculus	NOUN
ejpam-5387	59	16	involving	involve	VERB
ejpam-5387	59	17	a	a	DET
ejpam-5387	59	18	non	non	ADJ
ejpam-5387	59	19	-	-	ADJ
ejpam-5387	59	20	singular	singular	ADJ
ejpam-5387	59	21	kernel	kernel	NOUN
ejpam-5387	59	22	.	.	PUNCT
ejpam-5387	60	1	definition	definition	NOUN
ejpam-5387	60	2	1	1	NUM
ejpam-5387	60	3	.	.	PUNCT
ejpam-5387	61	1	for	for	ADP
ejpam-5387	61	2	ψ(t	ψ(t	PROPN
ejpam-5387	61	3	)	)	PUNCT
ejpam-5387	61	4	∈	∈	PROPN
ejpam-5387	61	5	h1(0	h1(0	PROPN
ejpam-5387	61	6	,	,	PUNCT
ejpam-5387	61	7	a	a	PRON
ejpam-5387	61	8	)	)	PUNCT
ejpam-5387	61	9	,	,	PUNCT
ejpam-5387	61	10	0	0	PUNCT
ejpam-5387	61	11	<	<	X
ejpam-5387	61	12	γ	γ	X
ejpam-5387	61	13	<	<	X
ejpam-5387	61	14	1	1	NUM
ejpam-5387	61	15	.	.	PUNCT
ejpam-5387	62	1	then	then	ADV
ejpam-5387	62	2	the	the	DET
ejpam-5387	62	3	cf	cf	NOUN
ejpam-5387	62	4	-	-	PUNCT
ejpam-5387	62	5	fd	fd	NOUN
ejpam-5387	62	6	cfdγψ(t	cfdγψ(t	NOUN
ejpam-5387	62	7	)	)	PUNCT
ejpam-5387	62	8	and	and	CCONJ
ejpam-5387	62	9	cf	cf	X
ejpam-5387	62	10	fractional	fractional	ADJ
ejpam-5387	62	11	integral	integral	ADJ
ejpam-5387	62	12	cf	cf	NOUN
ejpam-5387	62	13	iγψ(t	iγψ(t	PROPN
ejpam-5387	62	14	)	)	PUNCT
ejpam-5387	62	15	,	,	PUNCT
ejpam-5387	62	16	respectively	respectively	ADV
ejpam-5387	62	17	are	be	AUX
ejpam-5387	62	18	defined	define	VERB
ejpam-5387	62	19	by	by	ADP
ejpam-5387	62	20	:	:	PUNCT
ejpam-5387	62	21	cfdγψ(t	cfdγψ(t	NOUN
ejpam-5387	62	22	)	)	PUNCT
ejpam-5387	62	23	:	:	PUNCT
ejpam-5387	62	24	=	=	SYM
ejpam-5387	62	25	1	1	NUM
ejpam-5387	62	26	1−	1−	NUM
ejpam-5387	62	27	γ	γ	PROPN
ejpam-5387	62	28	∫	∫	PROPN
ejpam-5387	62	29	t	t	PROPN
ejpam-5387	62	30	0	0	NUM
ejpam-5387	62	31	exp	exp	NOUN
ejpam-5387	62	32	[	[	PUNCT
ejpam-5387	62	33	−	−	PROPN
ejpam-5387	62	34	γ	γ	NOUN
ejpam-5387	62	35	1−	1−	NUM
ejpam-5387	62	36	γ	γ	X
ejpam-5387	62	37	(	(	PUNCT
ejpam-5387	62	38	t−	t−	PROPN
ejpam-5387	62	39	τ	τ	PROPN
ejpam-5387	62	40	)	)	PUNCT
ejpam-5387	62	41	]	]	PUNCT
ejpam-5387	63	1	ψ̇(τ)dτ	ψ̇(τ)dτ	INTJ
ejpam-5387	63	2	,	,	PUNCT
ejpam-5387	63	3	cf	cf	X
ejpam-5387	63	4	iγψ(t	iγψ(t	PROPN
ejpam-5387	63	5	)	)	PUNCT
ejpam-5387	63	6	:	:	PUNCT
ejpam-5387	63	7	=	=	SYM
ejpam-5387	63	8	(	(	PUNCT
ejpam-5387	63	9	1−	1−	NUM
ejpam-5387	63	10	γ)ψ(t	γ)ψ(t	PROPN
ejpam-5387	63	11	)	)	PUNCT
ejpam-5387	64	1	+	+	CCONJ
ejpam-5387	64	2	γ	γ	PROPN
ejpam-5387	64	3	∫	∫	PROPN
ejpam-5387	64	4	t	t	PROPN
ejpam-5387	64	5	0	0	NUM
ejpam-5387	64	6	ψ(τ)dτ	ψ(τ)dτ	PROPN
ejpam-5387	64	7	.	.	PUNCT
ejpam-5387	65	1	(	(	PUNCT
ejpam-5387	65	2	1	1	NUM
ejpam-5387	65	3	)	)	PUNCT
ejpam-5387	65	4	3	3	NUM
ejpam-5387	65	5	.	.	X
ejpam-5387	66	1	formulation	formulation	NOUN
ejpam-5387	66	2	of	of	ADP
ejpam-5387	66	3	the	the	DET
ejpam-5387	66	4	model	model	NOUN
ejpam-5387	66	5	as	as	SCONJ
ejpam-5387	66	6	mentioned	mention	VERB
ejpam-5387	66	7	above	above	ADV
ejpam-5387	66	8	,	,	PUNCT
ejpam-5387	66	9	the	the	DET
ejpam-5387	66	10	mathematical	mathematical	ADJ
ejpam-5387	66	11	modeling	modeling	NOUN
ejpam-5387	66	12	of	of	ADP
ejpam-5387	66	13	the	the	DET
ejpam-5387	66	14	bc	bc	PROPN
ejpam-5387	66	15	or	or	CCONJ
ejpam-5387	66	16	any	any	DET
ejpam-5387	66	17	other	other	ADJ
ejpam-5387	66	18	biological	biological	ADJ
ejpam-5387	66	19	phenomena	phenomenon	NOUN
ejpam-5387	66	20	has	have	AUX
ejpam-5387	66	21	been	be	AUX
ejpam-5387	66	22	an	an	DET
ejpam-5387	66	23	important	important	ADJ
ejpam-5387	66	24	tool	tool	NOUN
ejpam-5387	66	25	for	for	ADP
ejpam-5387	66	26	understanding	understand	VERB
ejpam-5387	66	27	the	the	DET
ejpam-5387	66	28	dynamics	dynamic	NOUN
ejpam-5387	66	29	of	of	ADP
ejpam-5387	66	30	tumor	tumor	NOUN
ejpam-5387	66	31	growth	growth	NOUN
ejpam-5387	66	32	in	in	ADP
ejpam-5387	66	33	the	the	DET
ejpam-5387	66	34	treatment	treatment	NOUN
ejpam-5387	66	35	process	process	NOUN
ejpam-5387	66	36	and	and	CCONJ
ejpam-5387	66	37	solving	solve	VERB
ejpam-5387	66	38	epidemiological	epidemiological	ADJ
ejpam-5387	66	39	problems	problem	NOUN
ejpam-5387	66	40	.	.	PUNCT
ejpam-5387	67	1	this	this	PRON
ejpam-5387	67	2	is	be	AUX
ejpam-5387	67	3	evident	evident	ADJ
ejpam-5387	67	4	from	from	ADP
ejpam-5387	67	5	the	the	DET
ejpam-5387	67	6	studies	study	NOUN
ejpam-5387	67	7	previously	previously	ADV
ejpam-5387	67	8	done	do	VERB
ejpam-5387	67	9	in	in	ADP
ejpam-5387	67	10	[	[	X
ejpam-5387	67	11	19	19	NUM
ejpam-5387	67	12	]	]	PUNCT
ejpam-5387	67	13	.	.	PUNCT
ejpam-5387	68	1	despite	despite	SCONJ
ejpam-5387	68	2	the	the	DET
ejpam-5387	68	3	large	large	ADJ
ejpam-5387	68	4	number	number	NOUN
ejpam-5387	68	5	of	of	ADP
ejpam-5387	68	6	studies	study	NOUN
ejpam-5387	68	7	,	,	PUNCT
ejpam-5387	68	8	none	none	NOUN
ejpam-5387	68	9	of	of	ADP
ejpam-5387	68	10	the	the	DET
ejpam-5387	68	11	proposed	propose	VERB
ejpam-5387	68	12	mathematical	mathematical	ADJ
ejpam-5387	68	13	models	model	NOUN
ejpam-5387	68	14	included	include	VERB
ejpam-5387	68	15	a	a	DET
ejpam-5387	68	16	diet	diet	NOUN
ejpam-5387	68	17	(	(	PUNCT
ejpam-5387	68	18	ketogenic	ketogenic	ADJ
ejpam-5387	68	19	diet	diet	NOUN
ejpam-5387	68	20	)	)	PUNCT
ejpam-5387	68	21	.	.	PUNCT
ejpam-5387	69	1	therefore	therefore	ADV
ejpam-5387	69	2	,	,	PUNCT
ejpam-5387	69	3	oak	oak	AUX
ejpam-5387	69	4	et	et	PROPN
ejpam-5387	69	5	al	al	PROPN
ejpam-5387	69	6	.	.	PROPN
ejpam-5387	69	7	developed	develop	VERB
ejpam-5387	69	8	the	the	DET
ejpam-5387	69	9	model	model	NOUN
ejpam-5387	69	10	in	in	ADP
ejpam-5387	69	11	[	[	X
ejpam-5387	69	12	20	20	NUM
ejpam-5387	69	13	]	]	PUNCT
ejpam-5387	69	14	,	,	PUNCT
ejpam-5387	69	15	to	to	PART
ejpam-5387	69	16	include	include	VERB
ejpam-5387	69	17	some	some	PRON
ejpam-5387	69	18	of	of	ADP
ejpam-5387	69	19	the	the	DET
ejpam-5387	69	20	control	control	NOUN
ejpam-5387	69	21	factors	factor	NOUN
ejpam-5387	69	22	such	such	ADJ
ejpam-5387	69	23	as	as	ADP
ejpam-5387	69	24	immune	immune	ADJ
ejpam-5387	69	25	booster	booster	NOUN
ejpam-5387	69	26	,	,	PUNCT
ejpam-5387	69	27	anticancer	anticancer	NOUN
ejpam-5387	69	28	drug	drug	NOUN
ejpam-5387	69	29	,	,	PUNCT
ejpam-5387	69	30	and	and	CCONJ
ejpam-5387	69	31	ketogenic	ketogenic	ADJ
ejpam-5387	69	32	diet	diet	NOUN
ejpam-5387	69	33	,	,	PUNCT
ejpam-5387	69	34	in	in	ADP
ejpam-5387	69	35	order	order	NOUN
ejpam-5387	69	36	to	to	PART
ejpam-5387	69	37	confirm	confirm	VERB
ejpam-5387	69	38	that	that	SCONJ
ejpam-5387	69	39	there	there	PRON
ejpam-5387	69	40	is	be	VERB
ejpam-5387	69	41	an	an	DET
ejpam-5387	69	42	interaction	interaction	NOUN
ejpam-5387	69	43	between	between	ADP
ejpam-5387	69	44	cells	cell	NOUN
ejpam-5387	69	45	due	due	ADP
ejpam-5387	69	46	to	to	ADP
ejpam-5387	69	47	the	the	DET
ejpam-5387	69	48	variation	variation	NOUN
ejpam-5387	69	49	in	in	ADP
ejpam-5387	69	50	the	the	DET
ejpam-5387	69	51	tumor	tumor	NOUN
ejpam-5387	69	52	cell	cell	NOUN
ejpam-5387	69	53	dna	dna	NOUN
ejpam-5387	70	1	[	[	X
ejpam-5387	70	2	9	9	NUM
ejpam-5387	70	3	]	]	PUNCT
ejpam-5387	70	4	.	.	PUNCT
ejpam-5387	71	1	we	we	PRON
ejpam-5387	71	2	study	study	VERB
ejpam-5387	71	3	the	the	DET
ejpam-5387	71	4	following	follow	VERB
ejpam-5387	71	5	fractional	fractional	ADJ
ejpam-5387	71	6	forms	form	NOUN
ejpam-5387	71	7	of	of	ADP
ejpam-5387	71	8	breast	breast	NOUN
ejpam-5387	71	9	cancer	cancer	NOUN
ejpam-5387	71	10	(	(	PUNCT
ejpam-5387	71	11	[	[	X
ejpam-5387	71	12	2	2	NUM
ejpam-5387	71	13	]	]	PUNCT
ejpam-5387	71	14	,	,	PUNCT
ejpam-5387	71	15	[	[	X
ejpam-5387	71	16	24	24	NUM
ejpam-5387	71	17	]	]	PUNCT
ejpam-5387	71	18	):	):	PUNCT
ejpam-5387	71	19	cfdνψ1(t	cfdνψ1(t	NOUN
ejpam-5387	71	20	)	)	PUNCT
ejpam-5387	72	1	=	=	PUNCT
ejpam-5387	72	2	λ1	λ1	PROPN
ejpam-5387	72	3	ψ1(t	ψ1(t	PROPN
ejpam-5387	72	4	)	)	PUNCT
ejpam-5387	72	5	(	(	PUNCT
ejpam-5387	72	6	p1	p1	PROPN
ejpam-5387	72	7	−	−	PROPN
ejpam-5387	72	8	β1ψ1(t)−	β1ψ1(t)−	PROPN
ejpam-5387	72	9	α1	α1	PROPN
ejpam-5387	72	10	ψ2(t))−	ψ2(t))−	NUM
ejpam-5387	72	11	(	(	PUNCT
ejpam-5387	72	12	1−	1−	NUM
ejpam-5387	72	13	p)θ1	p)θ1	PROPN
ejpam-5387	72	14	ψ1(t)ψ4(t	ψ1(t)ψ4(t	NOUN
ejpam-5387	72	15	)	)	PUNCT
ejpam-5387	72	16	,	,	PUNCT
ejpam-5387	72	17	cfdνψ2(t	cfdνψ2(t	NOUN
ejpam-5387	72	18	)	)	PUNCT
ejpam-5387	73	1	=	=	SYM
ejpam-5387	73	2	λ2	λ2	NUM
ejpam-5387	73	3	ψ2(t	ψ2(t	PROPN
ejpam-5387	73	4	)	)	PUNCT
ejpam-5387	73	5	(	(	PUNCT
ejpam-5387	73	6	p2d−	p2d−	NOUN
ejpam-5387	73	7	β2ψ2(t)−	β2ψ2(t)−	SYM
ejpam-5387	73	8	α2ψ3(t))−	α2ψ3(t))−	PROPN
ejpam-5387	73	9	κψ2(t	κψ2(t	NOUN
ejpam-5387	73	10	)	)	PUNCT
ejpam-5387	73	11	+	+	CCONJ
ejpam-5387	73	12	(	(	PUNCT
ejpam-5387	73	13	1−	1−	NUM
ejpam-5387	73	14	p)θ1ψ1(t	p)θ1ψ1(t	X
ejpam-5387	73	15	)	)	PUNCT
ejpam-5387	73	16	+	+	CCONJ
ejpam-5387	73	17	ψ2(t)ψ4(t	ψ2(t)ψ4(t	ADJ
ejpam-5387	73	18	)	)	PUNCT
ejpam-5387	73	19	,	,	PUNCT
ejpam-5387	73	20	cfdνψ3(t	cfdνψ3(t	PROPN
ejpam-5387	73	21	)	)	PUNCT
ejpam-5387	74	1	=	=	SYM
ejpam-5387	74	2	σρ+	σρ+	NOUN
ejpam-5387	75	1	λ1	λ1	PROPN
ejpam-5387	75	2	ψ3(t	ψ3(t	PROPN
ejpam-5387	75	3	)	)	PUNCT
ejpam-5387	75	4	(	(	PUNCT
ejpam-5387	75	5	p3	p3	PROPN
ejpam-5387	75	6	−	−	PROPN
ejpam-5387	75	7	β3	β3	PROPN
ejpam-5387	75	8	−	−	PROPN
ejpam-5387	75	9	α3ψ2(t))−	α3ψ2(t))−	NUM
ejpam-5387	75	10	(	(	PUNCT
ejpam-5387	75	11	1−	1−	NUM
ejpam-5387	75	12	p)θ2ψ3(t)ψ4(t	p)θ2ψ3(t)ψ4(t	NOUN
ejpam-5387	75	13	)	)	PUNCT
ejpam-5387	75	14	,	,	PUNCT
ejpam-5387	75	15	cfdνψ4(t	cfdνψ4(t	PROPN
ejpam-5387	75	16	)	)	PUNCT
ejpam-5387	75	17	=	=	SYM
ejpam-5387	75	18	α4ψ4(t	α4ψ4(t	X
ejpam-5387	75	19	)	)	PUNCT
ejpam-5387	75	20	+	+	CCONJ
ejpam-5387	75	21	ϱ(1−	ϱ(1−	PROPN
ejpam-5387	75	22	p	p	X
ejpam-5387	75	23	)	)	PUNCT
ejpam-5387	75	24	,	,	PUNCT
ejpam-5387	75	25	(	(	PUNCT
ejpam-5387	75	26	2	2	X
ejpam-5387	75	27	)	)	PUNCT
ejpam-5387	75	28	t.	t.	NOUN
ejpam-5387	75	29	a.	a.	NOUN
ejpam-5387	75	30	assiri	assiri	PROPN
ejpam-5387	75	31	/	/	SYM
ejpam-5387	75	32	eur	eur	PROPN
ejpam-5387	75	33	.	.	PUNCT
ejpam-5387	76	1	j.	j.	PROPN
ejpam-5387	76	2	pure	pure	PROPN
ejpam-5387	76	3	appl	appl	PROPN
ejpam-5387	76	4	.	.	PROPN
ejpam-5387	76	5	math	math	PROPN
ejpam-5387	76	6	,	,	PUNCT
ejpam-5387	76	7	17	17	NUM
ejpam-5387	76	8	(	(	PUNCT
ejpam-5387	76	9	4	4	NUM
ejpam-5387	76	10	)	)	PUNCT
ejpam-5387	76	11	(	(	PUNCT
ejpam-5387	76	12	2024	2024	NUM
ejpam-5387	76	13	)	)	PUNCT
ejpam-5387	76	14	,	,	PUNCT
ejpam-5387	76	15	2706	2706	NUM
ejpam-5387	76	16	-	-	SYM
ejpam-5387	76	17	2719	2719	NUM
ejpam-5387	76	18	2709	2709	NUM
ejpam-5387	76	19	the	the	DET
ejpam-5387	76	20	corresponding	corresponding	ADJ
ejpam-5387	76	21	i.cs	i.cs	PROPN
ejpam-5387	76	22	of	of	ADP
ejpam-5387	76	23	this	this	DET
ejpam-5387	76	24	model	model	NOUN
ejpam-5387	76	25	are	be	AUX
ejpam-5387	76	26	taken	take	VERB
ejpam-5387	76	27	as	as	SCONJ
ejpam-5387	76	28	follows	follow	VERB
ejpam-5387	76	29	:	:	PUNCT
ejpam-5387	76	30	ψ1(0	ψ1(0	PROPN
ejpam-5387	76	31	)	)	PUNCT
ejpam-5387	76	32	=	=	PRON
ejpam-5387	77	1	ψ̂0	ψ̂0	ADJ
ejpam-5387	77	2	1	1	NUM
ejpam-5387	77	3	,	,	PUNCT
ejpam-5387	77	4	ψ2(0	ψ2(0	NOUN
ejpam-5387	77	5	)	)	PUNCT
ejpam-5387	77	6	=	=	PUNCT
ejpam-5387	78	1	ψ̂0	ψ̂0	PROPN
ejpam-5387	78	2	2	2	NUM
ejpam-5387	78	3	,	,	PUNCT
ejpam-5387	78	4	ψ3(0	ψ3(0	PROPN
ejpam-5387	78	5	)	)	PUNCT
ejpam-5387	78	6	=	=	SYM
ejpam-5387	79	1	ψ̂0	ψ̂0	PROPN
ejpam-5387	79	2	3	3	NUM
ejpam-5387	79	3	,	,	PUNCT
ejpam-5387	79	4	ψ4(0	ψ4(0	NOUN
ejpam-5387	79	5	)	)	PUNCT
ejpam-5387	79	6	=	=	SYM
ejpam-5387	79	7	ψ̂0	ψ̂0	PROPN
ejpam-5387	80	1	4	4	X
ejpam-5387	80	2	.	.	PUNCT
ejpam-5387	80	3	the	the	DET
ejpam-5387	80	4	description	description	NOUN
ejpam-5387	80	5	of	of	ADP
ejpam-5387	80	6	the	the	DET
ejpam-5387	80	7	meaning	meaning	NOUN
ejpam-5387	80	8	of	of	ADP
ejpam-5387	80	9	the	the	DET
ejpam-5387	80	10	included	include	VERB
ejpam-5387	80	11	parameters	parameter	NOUN
ejpam-5387	80	12	(	(	PUNCT
ejpam-5387	80	13	∈	∈	PROPN
ejpam-5387	80	14	r+	r+	NOUN
ejpam-5387	80	15	)	)	PUNCT
ejpam-5387	80	16	of	of	ADP
ejpam-5387	80	17	the	the	DET
ejpam-5387	80	18	system	system	NOUN
ejpam-5387	80	19	(	(	PUNCT
ejpam-5387	80	20	2	2	NUM
ejpam-5387	80	21	)	)	PUNCT
ejpam-5387	80	22	,	,	PUNCT
ejpam-5387	80	23	will	will	AUX
ejpam-5387	80	24	give	give	VERB
ejpam-5387	80	25	in	in	ADP
ejpam-5387	80	26	the	the	DET
ejpam-5387	80	27	table	table	NOUN
ejpam-5387	80	28	1	1	NUM
ejpam-5387	80	29	[	[	X
ejpam-5387	80	30	20	20	NUM
ejpam-5387	80	31	]	]	PUNCT
ejpam-5387	80	32	.	.	PUNCT
ejpam-5387	81	1	the	the	DET
ejpam-5387	81	2	stability	stability	NOUN
ejpam-5387	81	3	analysis	analysis	NOUN
ejpam-5387	81	4	,	,	PUNCT
ejpam-5387	81	5	equilibrium	equilibrium	NOUN
ejpam-5387	81	6	points	point	NOUN
ejpam-5387	81	7	,	,	PUNCT
ejpam-5387	81	8	existence	existence	NOUN
ejpam-5387	81	9	,	,	PUNCT
ejpam-5387	81	10	&	&	CCONJ
ejpam-5387	81	11	uniqueness	uniqueness	NOUN
ejpam-5387	81	12	,	,	PUNCT
ejpam-5387	81	13	of	of	ADP
ejpam-5387	81	14	the	the	DET
ejpam-5387	81	15	system	system	NOUN
ejpam-5387	81	16	under	under	ADP
ejpam-5387	81	17	consideration	consideration	NOUN
ejpam-5387	81	18	are	be	AUX
ejpam-5387	81	19	given	give	VERB
ejpam-5387	81	20	in	in	ADP
ejpam-5387	81	21	[	[	X
ejpam-5387	81	22	24	24	NUM
ejpam-5387	81	23	]	]	PUNCT
ejpam-5387	81	24	.	.	PUNCT
ejpam-5387	82	1	table	table	NOUN
ejpam-5387	82	2	1	1	NUM
ejpam-5387	82	3	:	:	PUNCT
ejpam-5387	82	4	the	the	DET
ejpam-5387	82	5	description	description	NOUN
ejpam-5387	82	6	of	of	ADP
ejpam-5387	82	7	the	the	DET
ejpam-5387	82	8	included	include	VERB
ejpam-5387	82	9	variables	variable	NOUN
ejpam-5387	82	10	of	of	ADP
ejpam-5387	82	11	the	the	DET
ejpam-5387	82	12	system	system	NOUN
ejpam-5387	82	13	(	(	PUNCT
ejpam-5387	82	14	2	2	NUM
ejpam-5387	82	15	)	)	PUNCT
ejpam-5387	82	16	.	.	PUNCT
ejpam-5387	83	1	symbol	symbol	NOUN
ejpam-5387	83	2	description	description	NOUN
ejpam-5387	83	3	ψ1(t	ψ1(t	PART
ejpam-5387	83	4	)	)	PUNCT
ejpam-5387	83	5	normal	normal	ADJ
ejpam-5387	83	6	cell	cell	NOUN
ejpam-5387	83	7	population	population	NOUN
ejpam-5387	83	8	ψ2(t	ψ2(t	NOUN
ejpam-5387	83	9	)	)	PUNCT
ejpam-5387	83	10	luminal	luminal	ADJ
ejpam-5387	83	11	type	type	NOUN
ejpam-5387	83	12	tumor	tumor	NOUN
ejpam-5387	83	13	cells	cell	NOUN
ejpam-5387	83	14	ψ3(t	ψ3(t	NOUN
ejpam-5387	83	15	)	)	PUNCT
ejpam-5387	83	16	class	class	NOUN
ejpam-5387	83	17	of	of	ADP
ejpam-5387	83	18	immune	immune	ADJ
ejpam-5387	83	19	response	response	NOUN
ejpam-5387	83	20	ψ4(t	ψ4(t	NOUN
ejpam-5387	83	21	)	)	PUNCT
ejpam-5387	83	22	estrogen	estrogen	NOUN
ejpam-5387	83	23	compartment	compartment	NOUN
ejpam-5387	83	24	λ1	λ1	ADJ
ejpam-5387	83	25	growth	growth	NOUN
ejpam-5387	83	26	rate	rate	NOUN
ejpam-5387	83	27	of	of	ADP
ejpam-5387	83	28	ψ1	ψ1	ADJ
ejpam-5387	83	29	λ2	λ2	NOUN
ejpam-5387	83	30	growth	growth	NOUN
ejpam-5387	83	31	rate	rate	NOUN
ejpam-5387	83	32	of	of	ADP
ejpam-5387	83	33	ψ2	ψ2	NOUN
ejpam-5387	83	34	pi	pi	NOUN
ejpam-5387	83	35	carrying	carry	VERB
ejpam-5387	83	36	capacity	capacity	NOUN
ejpam-5387	83	37	of	of	ADP
ejpam-5387	83	38	ψi	ψi	NOUN
ejpam-5387	83	39	,	,	PUNCT
ejpam-5387	83	40	i	i	PRON
ejpam-5387	83	41	=	=	NOUN
ejpam-5387	83	42	1	1	NUM
ejpam-5387	83	43	,	,	PUNCT
ejpam-5387	83	44	2	2	NUM
ejpam-5387	83	45	,	,	PUNCT
ejpam-5387	83	46	3	3	NUM
ejpam-5387	83	47	(	(	PUNCT
ejpam-5387	83	48	1−	1−	NUM
ejpam-5387	83	49	p	p	NOUN
ejpam-5387	83	50	)	)	PUNCT
ejpam-5387	83	51	effectiveness	effectiveness	NOUN
ejpam-5387	83	52	of	of	ADP
ejpam-5387	83	53	anti	anti	ADJ
ejpam-5387	83	54	-	-	ADJ
ejpam-5387	83	55	cancer	cancer	ADJ
ejpam-5387	83	56	drugs	drug	NOUN
ejpam-5387	83	57	ϱ	ϱ	ADP
ejpam-5387	83	58	process	process	NOUN
ejpam-5387	83	59	of	of	ADP
ejpam-5387	83	60	constantly	constantly	ADV
ejpam-5387	83	61	replenishing	replenish	VERB
ejpam-5387	83	62	excess	excess	ADJ
ejpam-5387	83	63	estrogen	estrogen	NOUN
ejpam-5387	83	64	α1	α1	PROPN
ejpam-5387	83	65	inhibition	inhibition	NOUN
ejpam-5387	83	66	rate	rate	NOUN
ejpam-5387	83	67	of	of	ADP
ejpam-5387	83	68	ψ1(t	ψ1(t	NOUN
ejpam-5387	83	69	)	)	PUNCT
ejpam-5387	83	70	α2	α2	ADJ
ejpam-5387	83	71	rate	rate	NOUN
ejpam-5387	83	72	of	of	ADP
ejpam-5387	83	73	the	the	DET
ejpam-5387	83	74	effectiveness	effectiveness	NOUN
ejpam-5387	83	75	of	of	ADP
ejpam-5387	83	76	the	the	DET
ejpam-5387	83	77	immune	immune	ADJ
ejpam-5387	83	78	system	system	NOUN
ejpam-5387	83	79	to	to	ADP
ejpam-5387	83	80	the	the	DET
ejpam-5387	83	81	tumor	tumor	NOUN
ejpam-5387	83	82	cells	cell	NOUN
ejpam-5387	83	83	α3	α3	ADJ
ejpam-5387	83	84	rate	rate	NOUN
ejpam-5387	83	85	of	of	ADP
ejpam-5387	83	86	interaction	interaction	NOUN
ejpam-5387	83	87	between	between	ADP
ejpam-5387	83	88	ψ2(t	ψ2(t	PROPN
ejpam-5387	83	89	)	)	PUNCT
ejpam-5387	83	90	and	and	CCONJ
ejpam-5387	83	91	ψ3(t	ψ3(t	NOUN
ejpam-5387	83	92	)	)	PUNCT
ejpam-5387	83	93	θ1	θ1	NOUN
ejpam-5387	83	94	tumor	tumor	NOUN
ejpam-5387	83	95	formation	formation	NOUN
ejpam-5387	83	96	rate	rate	NOUN
ejpam-5387	83	97	resulting	result	VERB
ejpam-5387	83	98	from	from	ADP
ejpam-5387	83	99	dna	dna	PROPN
ejpam-5387	83	100	mutation	mutation	NOUN
ejpam-5387	83	101	caused	cause	VERB
ejpam-5387	83	102	by	by	ADP
ejpam-5387	83	103	the	the	DET
ejpam-5387	83	104	presence	presence	NOUN
ejpam-5387	83	105	of	of	ADP
ejpam-5387	83	106	excess	excess	ADJ
ejpam-5387	83	107	estrogen	estrogen	NOUN
ejpam-5387	83	108	θ2	θ2	ADP
ejpam-5387	83	109	immune	immune	ADJ
ejpam-5387	83	110	suppression	suppression	NOUN
ejpam-5387	83	111	rate	rate	NOUN
ejpam-5387	83	112	βi	βi	ADP
ejpam-5387	83	113	logistic	logistic	ADJ
ejpam-5387	83	114	rate	rate	NOUN
ejpam-5387	83	115	of	of	ADP
ejpam-5387	83	116	ψi	ψi	NOUN
ejpam-5387	83	117	,	,	PUNCT
ejpam-5387	83	118	i	i	PRON
ejpam-5387	83	119	=	=	NOUN
ejpam-5387	83	120	1	1	NUM
ejpam-5387	83	121	,	,	PUNCT
ejpam-5387	83	122	2	2	NUM
ejpam-5387	83	123	,	,	PUNCT
ejpam-5387	83	124	3	3	NUM
ejpam-5387	83	125	d	d	NOUN
ejpam-5387	83	126	ketogenic	ketogenic	ADJ
ejpam-5387	83	127	diet	diet	NOUN
ejpam-5387	83	128	4	4	NUM
ejpam-5387	83	129	.	.	PUNCT
ejpam-5387	84	1	derivation	derivation	NOUN
ejpam-5387	84	2	simpson’s-1/3	simpson’s-1/3	NUM
ejpam-5387	84	3	rule	rule	NOUN
ejpam-5387	84	4	for	for	ADP
ejpam-5387	84	5	cf	cf	NOUN
ejpam-5387	84	6	-	-	PUNCT
ejpam-5387	84	7	fractional	fractional	ADJ
ejpam-5387	84	8	integral	integral	ADJ
ejpam-5387	84	9	this	this	DET
ejpam-5387	84	10	section	section	NOUN
ejpam-5387	84	11	presents	present	VERB
ejpam-5387	84	12	the	the	DET
ejpam-5387	84	13	formulation	formulation	NOUN
ejpam-5387	84	14	of	of	ADP
ejpam-5387	84	15	the	the	DET
ejpam-5387	84	16	fractional	fractional	ADJ
ejpam-5387	84	17	simpson’s-1/3	simpson’s-1/3	NUM
ejpam-5387	84	18	rule	rule	NOUN
ejpam-5387	84	19	(	(	PUNCT
ejpam-5387	84	20	fsr	fsr	PROPN
ejpam-5387	84	21	)	)	PUNCT
ejpam-5387	84	22	for	for	ADP
ejpam-5387	84	23	solving	solve	VERB
ejpam-5387	84	24	cf	cf	NOUN
ejpam-5387	84	25	-	-	PUNCT
ejpam-5387	84	26	fdes	fde	NOUN
ejpam-5387	84	27	[	[	X
ejpam-5387	84	28	4	4	NUM
ejpam-5387	84	29	]	]	PUNCT
ejpam-5387	84	30	.	.	PUNCT
ejpam-5387	85	1	considering	consider	VERB
ejpam-5387	85	2	the	the	DET
ejpam-5387	85	3	subsequent	subsequent	ADJ
ejpam-5387	85	4	γ	γ	NOUN
ejpam-5387	85	5	-	-	PUNCT
ejpam-5387	85	6	order	order	NOUN
ejpam-5387	85	7	fde	fde	NOUN
ejpam-5387	85	8	:	:	PUNCT
ejpam-5387	85	9	cfdγu(t	cfdγu(t	VERB
ejpam-5387	85	10	)	)	PUNCT
ejpam-5387	85	11	=	=	SYM
ejpam-5387	85	12	f(u(t	f(u(t	PROPN
ejpam-5387	85	13	)	)	PUNCT
ejpam-5387	85	14	)	)	PUNCT
ejpam-5387	85	15	,	,	PUNCT
ejpam-5387	85	16	u(0	u(0	PROPN
ejpam-5387	85	17	)	)	PUNCT
ejpam-5387	85	18	=	=	PUNCT
ejpam-5387	85	19	u0	u0	ADJ
ejpam-5387	85	20	,	,	PUNCT
ejpam-5387	85	21	(	(	PUNCT
ejpam-5387	85	22	3	3	NUM
ejpam-5387	85	23	)	)	PUNCT
ejpam-5387	85	24	whereas	whereas	SCONJ
ejpam-5387	85	25	f	f	PROPN
ejpam-5387	85	26	∈	∈	PROPN
ejpam-5387	85	27	c[0	c[0	PROPN
ejpam-5387	85	28	,	,	PUNCT
ejpam-5387	85	29	t	t	X
ejpam-5387	85	30	]	]	PUNCT
ejpam-5387	85	31	and	and	CCONJ
ejpam-5387	85	32	satisfies	satisfy	VERB
ejpam-5387	85	33	the	the	DET
ejpam-5387	85	34	lipschitz	lipschitz	NOUN
ejpam-5387	85	35	condition	condition	NOUN
ejpam-5387	85	36	:	:	PUNCT
ejpam-5387	85	37	|f	|f	PROPN
ejpam-5387	85	38	(	(	PUNCT
ejpam-5387	85	39	u(t1))−	u(t1))−	NOUN
ejpam-5387	85	40	f	f	X
ejpam-5387	85	41	(	(	PUNCT
ejpam-5387	85	42	u(t2	u(t2	NOUN
ejpam-5387	85	43	)	)	PUNCT
ejpam-5387	85	44	)	)	PUNCT
ejpam-5387	86	1	|	|	ADV
ejpam-5387	86	2	≤	≤	X
ejpam-5387	86	3	ϵ	ϵ	X
ejpam-5387	86	4	|u(t1)−	|u(t1)−	PROPN
ejpam-5387	86	5	u(t2)|	u(t2)|	PROPN
ejpam-5387	86	6	,	,	PUNCT
ejpam-5387	86	7	ϵ	ϵ	X
ejpam-5387	86	8	>	>	X
ejpam-5387	86	9	0	0	NUM
ejpam-5387	86	10	.	.	PUNCT
ejpam-5387	87	1	(	(	PUNCT
ejpam-5387	87	2	4	4	X
ejpam-5387	87	3	)	)	PUNCT
ejpam-5387	87	4	applying	apply	VERB
ejpam-5387	87	5	cf	cf	NOUN
ejpam-5387	87	6	-	-	PUNCT
ejpam-5387	87	7	fractional	fractional	ADJ
ejpam-5387	87	8	integral	integral	ADJ
ejpam-5387	87	9	operator	operator	NOUN
ejpam-5387	87	10	on	on	ADP
ejpam-5387	87	11	the	the	DET
ejpam-5387	87	12	ivp	ivp	NOUN
ejpam-5387	87	13	(	(	PUNCT
ejpam-5387	87	14	3	3	NUM
ejpam-5387	87	15	)	)	PUNCT
ejpam-5387	87	16	and	and	CCONJ
ejpam-5387	87	17	applying	apply	VERB
ejpam-5387	87	18	proposition	proposition	NOUN
ejpam-5387	87	19	3	3	NUM
ejpam-5387	87	20	in	in	ADP
ejpam-5387	87	21	[	[	X
ejpam-5387	87	22	2	2	NUM
ejpam-5387	87	23	]	]	PUNCT
ejpam-5387	87	24	and	and	CCONJ
ejpam-5387	87	25	formula	formula	NOUN
ejpam-5387	87	26	(	(	PUNCT
ejpam-5387	87	27	1	1	NUM
ejpam-5387	87	28	)	)	PUNCT
ejpam-5387	87	29	,	,	PUNCT
ejpam-5387	87	30	we	we	PRON
ejpam-5387	87	31	get	get	VERB
ejpam-5387	87	32	:	:	PUNCT
ejpam-5387	87	33	u(t	u(t	NOUN
ejpam-5387	87	34	)	)	PUNCT
ejpam-5387	87	35	=	=	PUNCT
ejpam-5387	88	1	u0	u0	ADJ
ejpam-5387	88	2	+	+	CCONJ
ejpam-5387	88	3	cf	cf	NOUN
ejpam-5387	88	4	iγf	iγf	NOUN
ejpam-5387	88	5	(	(	PUNCT
ejpam-5387	88	6	u(t	u(t	PROPN
ejpam-5387	88	7	)	)	PUNCT
ejpam-5387	88	8	)	)	PUNCT
ejpam-5387	89	1	=	=	PUNCT
ejpam-5387	89	2	u0	u0	ADJ
ejpam-5387	89	3	+	+	X
ejpam-5387	89	4	(	(	PUNCT
ejpam-5387	89	5	1−	1−	NUM
ejpam-5387	89	6	γ)f(u(t	γ)f(u(t	NOUN
ejpam-5387	89	7	)	)	PUNCT
ejpam-5387	89	8	)	)	PUNCT
ejpam-5387	90	1	+	+	CCONJ
ejpam-5387	90	2	γ	γ	PROPN
ejpam-5387	90	3	∫	∫	PROPN
ejpam-5387	90	4	t	t	PROPN
ejpam-5387	90	5	0	0	NUM
ejpam-5387	90	6	f(u(s))ds	f(u(s))ds	PROPN
ejpam-5387	90	7	.	.	PUNCT
ejpam-5387	91	1	(	(	PUNCT
ejpam-5387	91	2	5	5	X
ejpam-5387	91	3	)	)	PUNCT
ejpam-5387	91	4	t.	t.	NOUN
ejpam-5387	91	5	a.	a.	NOUN
ejpam-5387	91	6	assiri	assiri	PROPN
ejpam-5387	91	7	/	/	SYM
ejpam-5387	91	8	eur	eur	PROPN
ejpam-5387	91	9	.	.	PUNCT
ejpam-5387	92	1	j.	j.	PROPN
ejpam-5387	92	2	pure	pure	PROPN
ejpam-5387	92	3	appl	appl	PROPN
ejpam-5387	92	4	.	.	PROPN
ejpam-5387	92	5	math	math	PROPN
ejpam-5387	92	6	,	,	PUNCT
ejpam-5387	92	7	17	17	NUM
ejpam-5387	92	8	(	(	PUNCT
ejpam-5387	92	9	4	4	NUM
ejpam-5387	92	10	)	)	PUNCT
ejpam-5387	92	11	(	(	PUNCT
ejpam-5387	92	12	2024	2024	NUM
ejpam-5387	92	13	)	)	PUNCT
ejpam-5387	92	14	,	,	PUNCT
ejpam-5387	92	15	2706	2706	NUM
ejpam-5387	92	16	-	-	SYM
ejpam-5387	92	17	2719	2719	NUM
ejpam-5387	92	18	2710	2710	NUM
ejpam-5387	92	19	theorem	theorem	NOUN
ejpam-5387	92	20	1	1	NUM
ejpam-5387	92	21	.	.	PUNCT
ejpam-5387	93	1	[	[	X
ejpam-5387	93	2	17	17	NUM
ejpam-5387	93	3	]	]	PUNCT
ejpam-5387	93	4	let	let	VERB
ejpam-5387	93	5	us	we	PRON
ejpam-5387	93	6	assume	assume	VERB
ejpam-5387	93	7	a	a	DET
ejpam-5387	93	8	continuous	continuous	ADJ
ejpam-5387	93	9	function	function	NOUN
ejpam-5387	93	10	f	f	NOUN
ejpam-5387	93	11	:	:	PUNCT
ejpam-5387	94	1	[	[	X
ejpam-5387	94	2	0	0	NUM
ejpam-5387	94	3	,	,	PUNCT
ejpam-5387	94	4	t	t	X
ejpam-5387	94	5	]	]	PUNCT
ejpam-5387	94	6	×	×	NOUN
ejpam-5387	94	7	r	r	NOUN
ejpam-5387	94	8	→	→	SYM
ejpam-5387	94	9	r	r	NOUN
ejpam-5387	94	10	with	with	ADP
ejpam-5387	94	11	γ	γ	X
ejpam-5387	94	12	∈	∈	PROPN
ejpam-5387	94	13	(	(	PUNCT
ejpam-5387	94	14	0	0	NUM
ejpam-5387	94	15	,	,	PUNCT
ejpam-5387	94	16	1	1	NUM
ejpam-5387	94	17	)	)	PUNCT
ejpam-5387	94	18	that	that	PRON
ejpam-5387	94	19	satisfies	satisfy	VERB
ejpam-5387	94	20	the	the	DET
ejpam-5387	94	21	criterion	criterion	NOUN
ejpam-5387	94	22	(	(	PUNCT
ejpam-5387	94	23	4	4	NUM
ejpam-5387	94	24	)	)	PUNCT
ejpam-5387	94	25	.	.	PUNCT
ejpam-5387	95	1	then	then	ADV
ejpam-5387	95	2	the	the	DET
ejpam-5387	95	3	ivp	ivp	X
ejpam-5387	95	4	(	(	PUNCT
ejpam-5387	95	5	3	3	X
ejpam-5387	95	6	)	)	PUNCT
ejpam-5387	95	7	has	have	VERB
ejpam-5387	95	8	a	a	DET
ejpam-5387	95	9	unique	unique	ADJ
ejpam-5387	95	10	solution	solution	NOUN
ejpam-5387	95	11	on	on	ADP
ejpam-5387	95	12	c[0	c[0	PROPN
ejpam-5387	95	13	,	,	PUNCT
ejpam-5387	95	14	t	t	X
ejpam-5387	95	15	]	]	PUNCT
ejpam-5387	95	16	under	under	ADP
ejpam-5387	95	17	the	the	DET
ejpam-5387	95	18	condition	condition	NOUN
ejpam-5387	95	19	:	:	PUNCT
ejpam-5387	95	20	(	(	PUNCT
ejpam-5387	95	21	2(1−	2(1−	NUM
ejpam-5387	95	22	γ	γ	X
ejpam-5387	95	23	)	)	PUNCT
ejpam-5387	96	1	+	+	NUM
ejpam-5387	96	2	2γ	2γ	NUM
ejpam-5387	96	3	t	t	NOUN
ejpam-5387	96	4	)	)	PUNCT
ejpam-5387	96	5	ϵ	ϵ	X
ejpam-5387	96	6	(	(	PUNCT
ejpam-5387	96	7	2−	2−	NUM
ejpam-5387	96	8	γ	γ	NOUN
ejpam-5387	96	9	)	)	PUNCT
ejpam-5387	96	10	<	<	X
ejpam-5387	96	11	1	1	X
ejpam-5387	96	12	.	.	PUNCT
ejpam-5387	96	13	initially	initially	ADV
ejpam-5387	96	14	,	,	PUNCT
ejpam-5387	96	15	we	we	PRON
ejpam-5387	96	16	will	will	AUX
ejpam-5387	96	17	employ	employ	VERB
ejpam-5387	96	18	a	a	DET
ejpam-5387	96	19	quadratic	quadratic	ADJ
ejpam-5387	96	20	polynomial	polynomial	ADJ
ejpam-5387	96	21	p2	p2	NOUN
ejpam-5387	96	22	to	to	PART
ejpam-5387	96	23	estimate	estimate	VERB
ejpam-5387	96	24	the	the	DET
ejpam-5387	96	25	integral	integral	ADJ
ejpam-5387	96	26	function	function	NOUN
ejpam-5387	96	27	f	f	PROPN
ejpam-5387	96	28	in	in	ADP
ejpam-5387	96	29	equation	equation	NOUN
ejpam-5387	96	30	(	(	PUNCT
ejpam-5387	96	31	5	5	NUM
ejpam-5387	96	32	)	)	PUNCT
ejpam-5387	96	33	.	.	PUNCT
ejpam-5387	97	1	the	the	DET
ejpam-5387	97	2	function	function	NOUN
ejpam-5387	97	3	will	will	AUX
ejpam-5387	97	4	be	be	AUX
ejpam-5387	97	5	assessed	assess	VERB
ejpam-5387	97	6	at	at	ADP
ejpam-5387	97	7	t0	t0	PROPN
ejpam-5387	97	8	,	,	PUNCT
ejpam-5387	97	9	t1	t1	NOUN
ejpam-5387	97	10	,	,	PUNCT
ejpam-5387	97	11	and	and	CCONJ
ejpam-5387	97	12	t2	t2	NOUN
ejpam-5387	97	13	,	,	PUNCT
ejpam-5387	97	14	where	where	SCONJ
ejpam-5387	97	15	t0	t0	PROPN
ejpam-5387	97	16	is	be	AUX
ejpam-5387	97	17	less	less	ADJ
ejpam-5387	97	18	than	than	ADP
ejpam-5387	97	19	t1	t1	NOUN
ejpam-5387	97	20	,	,	PUNCT
ejpam-5387	97	21	and	and	CCONJ
ejpam-5387	97	22	t1	t1	NOUN
ejpam-5387	97	23	is	be	AUX
ejpam-5387	97	24	less	less	ADJ
ejpam-5387	97	25	than	than	ADP
ejpam-5387	97	26	t2	t2	NOUN
ejpam-5387	97	27	.	.	PUNCT
ejpam-5387	98	1	the	the	DET
ejpam-5387	98	2	interval	interval	NOUN
ejpam-5387	98	3	is	be	AUX
ejpam-5387	98	4	partitioned	partition	VERB
ejpam-5387	98	5	into	into	ADP
ejpam-5387	98	6	two	two	NUM
ejpam-5387	98	7	subintervals	subinterval	NOUN
ejpam-5387	98	8	,	,	PUNCT
ejpam-5387	98	9	denoted	denote	VERB
ejpam-5387	98	10	as	as	ADP
ejpam-5387	98	11	t1−	t1−	NOUN
ejpam-5387	98	12	t0	t0	NOUN
ejpam-5387	99	1	=	=	SYM
ejpam-5387	99	2	t2−	t2−	PROPN
ejpam-5387	99	3	t1	t1	NOUN
ejpam-5387	99	4	=	=	SYM
ejpam-5387	99	5	h	h	NOUN
ejpam-5387	99	6	,	,	PUNCT
ejpam-5387	99	7	resulting	result	VERB
ejpam-5387	99	8	in	in	ADP
ejpam-5387	99	9	a	a	DET
ejpam-5387	99	10	combined	combine	VERB
ejpam-5387	99	11	width	width	NOUN
ejpam-5387	99	12	of	of	ADP
ejpam-5387	99	13	2h	2h	NUM
ejpam-5387	99	14	.	.	PUNCT
ejpam-5387	100	1	the	the	DET
ejpam-5387	100	2	integration	integration	NOUN
ejpam-5387	100	3	of	of	ADP
ejpam-5387	100	4	the	the	DET
ejpam-5387	100	5	quadratic	quadratic	ADJ
ejpam-5387	100	6	polynomial	polynomial	ADJ
ejpam-5387	100	7	p2	p2	NOUN
ejpam-5387	100	8	can	can	AUX
ejpam-5387	100	9	be	be	AUX
ejpam-5387	100	10	computed	compute	VERB
ejpam-5387	100	11	as	as	SCONJ
ejpam-5387	100	12	follows	follow	VERB
ejpam-5387	100	13	:	:	PUNCT
ejpam-5387	100	14	i2f(u(t	i2f(u(t	NOUN
ejpam-5387	100	15	)	)	PUNCT
ejpam-5387	100	16	)	)	PUNCT
ejpam-5387	101	1	=	=	SYM
ejpam-5387	101	2	∫	∫	PROPN
ejpam-5387	101	3	b	b	PROPN
ejpam-5387	101	4	a	a	DET
ejpam-5387	101	5	f(u(t))dt	f(u(t))dt	NOUN
ejpam-5387	102	1	≈	≈	PROPN
ejpam-5387	102	2	∫	∫	PROPN
ejpam-5387	102	3	t2	t2	PROPN
ejpam-5387	102	4	t0	t0	PROPN
ejpam-5387	102	5	p2(u(t))dt	p2(u(t))dt	PUNCT
ejpam-5387	103	1	=	=	SYM
ejpam-5387	103	2	∫	∫	PROPN
ejpam-5387	103	3	t2	t2	PROPN
ejpam-5387	103	4	t0	t0	PROPN
ejpam-5387	103	5			PROPN
ejpam-5387	103	6	2∑	2∑	NUM
ejpam-5387	103	7	j=0	j=0	PROPN
ejpam-5387	103	8	lj(t	lj(t	PUNCT
ejpam-5387	103	9	)	)	PUNCT
ejpam-5387	103	10	f	f	PROPN
ejpam-5387	103	11	(	(	PUNCT
ejpam-5387	103	12	u	u	NOUN
ejpam-5387	103	13	(	(	PUNCT
ejpam-5387	103	14	tj	tj	NOUN
ejpam-5387	103	15	)	)	PUNCT
ejpam-5387	103	16	)	)	PUNCT
ejpam-5387	103	17			NOUN
ejpam-5387	103	18	dt	dt	PROPN
ejpam-5387	103	19	,	,	PUNCT
ejpam-5387	103	20	where	where	SCONJ
ejpam-5387	103	21	the	the	DET
ejpam-5387	103	22	second	second	ADJ
ejpam-5387	103	23	-	-	PUNCT
ejpam-5387	103	24	order	order	NOUN
ejpam-5387	103	25	lagrange	lagrange	NOUN
ejpam-5387	103	26	polynomials	polynomial	NOUN
ejpam-5387	103	27	l0(t	l0(t	NOUN
ejpam-5387	103	28	)	)	PUNCT
ejpam-5387	103	29	,	,	PUNCT
ejpam-5387	103	30	l1(t	l1(t	PROPN
ejpam-5387	103	31	)	)	PUNCT
ejpam-5387	103	32	,	,	PUNCT
ejpam-5387	103	33	and	and	CCONJ
ejpam-5387	103	34	l2(t	l2(t	PROPN
ejpam-5387	103	35	)	)	PUNCT
ejpam-5387	103	36	are	be	AUX
ejpam-5387	103	37	defined	define	VERB
ejpam-5387	103	38	as	as	SCONJ
ejpam-5387	103	39	follows	follow	VERB
ejpam-5387	103	40	:	:	PUNCT
ejpam-5387	103	41	lj(t	lj(t	PUNCT
ejpam-5387	103	42	)	)	PUNCT
ejpam-5387	104	1	=	=	SYM
ejpam-5387	105	1	2∏	2∏	NUM
ejpam-5387	105	2	i=0	i=0	PROPN
ejpam-5387	105	3	,	,	PUNCT
ejpam-5387	105	4	i	i	PRON
ejpam-5387	105	5	̸=	̸=	PROPN
ejpam-5387	105	6	j	j	PROPN
ejpam-5387	105	7	(	(	PUNCT
ejpam-5387	105	8	t−	t−	PROPN
ejpam-5387	105	9	ti	ti	NOUN
ejpam-5387	105	10	)	)	PUNCT
ejpam-5387	105	11	(	(	PUNCT
ejpam-5387	105	12	tj	tj	NOUN
ejpam-5387	105	13	−	−	NOUN
ejpam-5387	105	14	ti	ti	NOUN
ejpam-5387	105	15	)	)	PUNCT
ejpam-5387	105	16	.	.	PUNCT
ejpam-5387	106	1	integrating	integrate	VERB
ejpam-5387	106	2	the	the	DET
ejpam-5387	106	3	first	first	ADJ
ejpam-5387	106	4	interpolant	interpolant	NOUN
ejpam-5387	106	5	function	function	NOUN
ejpam-5387	106	6	l0(t	l0(t	PROPN
ejpam-5387	106	7	)	)	PUNCT
ejpam-5387	106	8	,	,	PUNCT
ejpam-5387	106	9	by	by	ADP
ejpam-5387	106	10	taking	take	VERB
ejpam-5387	106	11	h	h	NOUN
ejpam-5387	106	12	=	=	NOUN
ejpam-5387	106	13	t2−t0	t2−t0	NUM
ejpam-5387	106	14	2	2	NUM
ejpam-5387	106	15	and	and	CCONJ
ejpam-5387	106	16	substituting	substitute	VERB
ejpam-5387	106	17	”	"	PUNCT
ejpam-5387	106	18	t	t	PROPN
ejpam-5387	106	19	=	=	PUNCT
ejpam-5387	106	20	s+	s+	NUM
ejpam-5387	106	21	t0	t0	PROPN
ejpam-5387	106	22	”	"	PUNCT
ejpam-5387	106	23	,	,	PUNCT
ejpam-5387	106	24	gives	give	VERB
ejpam-5387	106	25	us:∫	us:∫	ADP
ejpam-5387	106	26	t2	t2	NOUN
ejpam-5387	106	27	t0	t0	PROPN
ejpam-5387	106	28	l0(t)dt	l0(t)dt	X
ejpam-5387	107	1	=	=	SYM
ejpam-5387	107	2	1	1	NUM
ejpam-5387	107	3	2h2	2h2	NUM
ejpam-5387	107	4	∫	∫	PROPN
ejpam-5387	107	5	t0	t0	PROPN
ejpam-5387	108	1	+	+	PROPN
ejpam-5387	108	2	2h	2h	NUM
ejpam-5387	108	3	t0	t0	NOUN
ejpam-5387	108	4	(	(	PUNCT
ejpam-5387	108	5	t−	t−	PROPN
ejpam-5387	108	6	t1	t1	NOUN
ejpam-5387	108	7	)	)	PUNCT
ejpam-5387	108	8	(	(	PUNCT
ejpam-5387	108	9	t−	t−	PROPN
ejpam-5387	108	10	t2	t2	NOUN
ejpam-5387	108	11	)	)	PUNCT
ejpam-5387	108	12	dt	dt	NOUN
ejpam-5387	109	1	=	=	NOUN
ejpam-5387	109	2	1	1	NUM
ejpam-5387	109	3	2h2	2h2	NUM
ejpam-5387	109	4	∫	∫	PROPN
ejpam-5387	109	5	2h	2h	NUM
ejpam-5387	109	6	0	0	PUNCT
ejpam-5387	109	7	(	(	PUNCT
ejpam-5387	109	8	s+	s+	NUM
ejpam-5387	109	9	t0	t0	PROPN
ejpam-5387	109	10	−	−	PROPN
ejpam-5387	109	11	t2	t2	PROPN
ejpam-5387	109	12	)	)	PUNCT
ejpam-5387	109	13	(	(	PUNCT
ejpam-5387	109	14	s+	s+	NUM
ejpam-5387	110	1	t0	t0	PROPN
ejpam-5387	110	2	−	−	PROPN
ejpam-5387	110	3	t1	t1	NOUN
ejpam-5387	110	4	)	)	PUNCT
ejpam-5387	110	5	ds	ds	NOUN
ejpam-5387	110	6	=	=	SYM
ejpam-5387	110	7	1	1	NUM
ejpam-5387	110	8	2h2	2h2	NUM
ejpam-5387	110	9	∫	∫	PROPN
ejpam-5387	110	10	2h	2h	NUM
ejpam-5387	110	11	0	0	PUNCT
ejpam-5387	110	12	(	(	PUNCT
ejpam-5387	110	13	s−	s−	PROPN
ejpam-5387	110	14	2h)(s−	2h)(s−	NUM
ejpam-5387	110	15	h)ds	h)ds	PROPN
ejpam-5387	110	16	=	=	SYM
ejpam-5387	110	17	h	h	NOUN
ejpam-5387	110	18	3	3	NUM
ejpam-5387	110	19	.	.	PUNCT
ejpam-5387	111	1	after	after	ADP
ejpam-5387	111	2	making	make	VERB
ejpam-5387	111	3	some	some	DET
ejpam-5387	111	4	simplifications	simplification	NOUN
ejpam-5387	111	5	to	to	ADP
ejpam-5387	111	6	the	the	DET
ejpam-5387	111	7	rest	rest	NOUN
ejpam-5387	111	8	of	of	ADP
ejpam-5387	111	9	the	the	DET
ejpam-5387	111	10	terms	term	NOUN
ejpam-5387	111	11	,	,	PUNCT
ejpam-5387	111	12	we	we	PRON
ejpam-5387	111	13	have	have	VERB
ejpam-5387	111	14	the	the	DET
ejpam-5387	111	15	following	follow	VERB
ejpam-5387	111	16	:	:	PUNCT
ejpam-5387	111	17	i2(f	i2(f	X
ejpam-5387	111	18	)	)	PUNCT
ejpam-5387	111	19	=	=	SYM
ejpam-5387	111	20	h	h	NOUN
ejpam-5387	111	21	3	3	NUM
ejpam-5387	112	1	[	[	X
ejpam-5387	112	2	f	f	X
ejpam-5387	112	3	(	(	PUNCT
ejpam-5387	112	4	u	u	PROPN
ejpam-5387	112	5	(	(	PUNCT
ejpam-5387	112	6	t0	t0	NOUN
ejpam-5387	112	7	)	)	PUNCT
ejpam-5387	112	8	)	)	PUNCT
ejpam-5387	113	1	+	+	CCONJ
ejpam-5387	113	2	4f	4f	NUM
ejpam-5387	113	3	(	(	PUNCT
ejpam-5387	113	4	u	u	NOUN
ejpam-5387	113	5	(	(	PUNCT
ejpam-5387	113	6	t1	t1	NOUN
ejpam-5387	113	7	)	)	PUNCT
ejpam-5387	113	8	)	)	PUNCT
ejpam-5387	114	1	+	+	CCONJ
ejpam-5387	114	2	f	f	X
ejpam-5387	114	3	(	(	PUNCT
ejpam-5387	114	4	u	u	NOUN
ejpam-5387	114	5	(	(	PUNCT
ejpam-5387	114	6	t2	t2	PROPN
ejpam-5387	114	7	)	)	PUNCT
ejpam-5387	114	8	)	)	PUNCT
ejpam-5387	114	9	]	]	PUNCT
ejpam-5387	114	10	.	.	PUNCT
ejpam-5387	115	1	using	use	VERB
ejpam-5387	115	2	eq.(5	eq.(5	NOUN
ejpam-5387	115	3	)	)	PUNCT
ejpam-5387	115	4	,	,	PUNCT
ejpam-5387	115	5	we	we	PRON
ejpam-5387	115	6	get	get	VERB
ejpam-5387	115	7	:	:	PUNCT
ejpam-5387	115	8	u	u	NOUN
ejpam-5387	115	9	(	(	PUNCT
ejpam-5387	115	10	tn	tn	NOUN
ejpam-5387	115	11	)	)	PUNCT
ejpam-5387	115	12	=	=	PUNCT
ejpam-5387	116	1	u0	u0	ADJ
ejpam-5387	116	2	+	+	X
ejpam-5387	116	3	(	(	PUNCT
ejpam-5387	116	4	1−	1−	NUM
ejpam-5387	116	5	γ)f	γ)f	NOUN
ejpam-5387	116	6	(	(	PUNCT
ejpam-5387	116	7	u	u	NOUN
ejpam-5387	116	8	(	(	PUNCT
ejpam-5387	116	9	tn	tn	NOUN
ejpam-5387	116	10	)	)	PUNCT
ejpam-5387	116	11	)	)	PUNCT
ejpam-5387	117	1	+	+	CCONJ
ejpam-5387	117	2	h	h	NOUN
ejpam-5387	117	3	3	3	NUM
ejpam-5387	118	1	[	[	X
ejpam-5387	118	2	f	f	X
ejpam-5387	118	3	(	(	PUNCT
ejpam-5387	118	4	u	u	PROPN
ejpam-5387	118	5	(	(	PUNCT
ejpam-5387	118	6	t0	t0	NOUN
ejpam-5387	118	7	)	)	PUNCT
ejpam-5387	118	8	)	)	PUNCT
ejpam-5387	119	1	+	+	CCONJ
ejpam-5387	119	2	4f	4f	NUM
ejpam-5387	119	3	(	(	PUNCT
ejpam-5387	119	4	u	u	NOUN
ejpam-5387	119	5	(	(	PUNCT
ejpam-5387	119	6	t1	t1	NOUN
ejpam-5387	119	7	)	)	PUNCT
ejpam-5387	119	8	)	)	PUNCT
ejpam-5387	120	1	+	+	CCONJ
ejpam-5387	120	2	f	f	X
ejpam-5387	120	3	(	(	PUNCT
ejpam-5387	120	4	u	u	NOUN
ejpam-5387	120	5	(	(	PUNCT
ejpam-5387	120	6	t2	t2	PROPN
ejpam-5387	120	7	)	)	PUNCT
ejpam-5387	120	8	)	)	PUNCT
ejpam-5387	120	9	]	]	PUNCT
ejpam-5387	120	10	,	,	PUNCT
ejpam-5387	120	11	n	n	NOUN
ejpam-5387	120	12	=	=	SYM
ejpam-5387	120	13	0	0	NUM
ejpam-5387	120	14	,	,	PUNCT
ejpam-5387	120	15	1	1	NUM
ejpam-5387	120	16	,	,	PUNCT
ejpam-5387	120	17	2	2	NUM
ejpam-5387	120	18	.	.	PUNCT
ejpam-5387	120	19	to	to	PART
ejpam-5387	120	20	improve	improve	VERB
ejpam-5387	120	21	the	the	DET
ejpam-5387	120	22	accuracy	accuracy	NOUN
ejpam-5387	120	23	of	of	ADP
ejpam-5387	120	24	numerical	numerical	ADJ
ejpam-5387	120	25	integration	integration	NOUN
ejpam-5387	120	26	,	,	PUNCT
ejpam-5387	120	27	we	we	PRON
ejpam-5387	120	28	partition	partition	VERB
ejpam-5387	120	29	[	[	X
ejpam-5387	120	30	a	a	X
ejpam-5387	120	31	,	,	PUNCT
ejpam-5387	120	32	b	b	NOUN
ejpam-5387	120	33	]	]	X
ejpam-5387	120	34	to	to	ADP
ejpam-5387	120	35	n	n	PRON
ejpam-5387	120	36	sub	sub	NOUN
ejpam-5387	120	37	-	-	NOUN
ejpam-5387	120	38	intervals	interval	NOUN
ejpam-5387	120	39	as	as	SCONJ
ejpam-5387	120	40	follows	follow	VERB
ejpam-5387	120	41	:	:	PUNCT
ejpam-5387	120	42	for	for	ADP
ejpam-5387	120	43	any	any	DET
ejpam-5387	120	44	even	even	ADJ
ejpam-5387	120	45	number	number	NOUN
ejpam-5387	120	46	n	n	CCONJ
ejpam-5387	120	47	≥	≥	NOUN
ejpam-5387	120	48	2	2	NUM
ejpam-5387	120	49	,	,	PUNCT
ejpam-5387	120	50	we	we	PRON
ejpam-5387	120	51	establish	establish	VERB
ejpam-5387	120	52	the	the	DET
ejpam-5387	120	53	following	follow	VERB
ejpam-5387	120	54	definitions	definition	NOUN
ejpam-5387	120	55	:	:	PUNCT
ejpam-5387	120	56	h	h	NOUN
ejpam-5387	120	57	=	=	PUNCT
ejpam-5387	120	58	b−	b−	PROPN
ejpam-5387	120	59	a	a	PRON
ejpam-5387	120	60	n	n	NOUN
ejpam-5387	120	61	=	=	SYM
ejpam-5387	120	62	tk+1	tk+1	NUM
ejpam-5387	120	63	−	−	PROPN
ejpam-5387	120	64	tk	tk	PROPN
ejpam-5387	120	65	,	,	PUNCT
ejpam-5387	120	66	k	k	PROPN
ejpam-5387	120	67	=	=	SYM
ejpam-5387	120	68	0	0	NUM
ejpam-5387	120	69	,	,	PUNCT
ejpam-5387	120	70	1	1	NUM
ejpam-5387	120	71	,	,	PUNCT
ejpam-5387	120	72	2	2	NUM
ejpam-5387	120	73	,	,	PUNCT
ejpam-5387	120	74	.	.	PUNCT
ejpam-5387	120	75	.	.	PUNCT
ejpam-5387	121	1	.	.	PUNCT
ejpam-5387	122	1	,	,	PUNCT
ejpam-5387	122	2	n.	n.	PROPN
ejpam-5387	122	3	t.	t.	PROPN
ejpam-5387	122	4	a.	a.	PROPN
ejpam-5387	122	5	assiri	assiri	PROPN
ejpam-5387	122	6	/	/	SYM
ejpam-5387	122	7	eur	eur	PROPN
ejpam-5387	122	8	.	.	PUNCT
ejpam-5387	123	1	j.	j.	PROPN
ejpam-5387	123	2	pure	pure	PROPN
ejpam-5387	123	3	appl	appl	PROPN
ejpam-5387	123	4	.	.	PROPN
ejpam-5387	123	5	math	math	PROPN
ejpam-5387	123	6	,	,	PUNCT
ejpam-5387	123	7	17	17	NUM
ejpam-5387	123	8	(	(	PUNCT
ejpam-5387	123	9	4	4	NUM
ejpam-5387	123	10	)	)	PUNCT
ejpam-5387	123	11	(	(	PUNCT
ejpam-5387	123	12	2024	2024	NUM
ejpam-5387	123	13	)	)	PUNCT
ejpam-5387	123	14	,	,	PUNCT
ejpam-5387	123	15	2706	2706	NUM
ejpam-5387	123	16	-	-	SYM
ejpam-5387	123	17	2719	2719	NUM
ejpam-5387	123	18	2711	2711	NUM
ejpam-5387	123	19	now	now	ADV
ejpam-5387	123	20	,	,	PUNCT
ejpam-5387	123	21	by	by	ADP
ejpam-5387	123	22	using	use	VERB
ejpam-5387	123	23	the	the	DET
ejpam-5387	123	24	quadrature	quadrature	NOUN
ejpam-5387	123	25	rule	rule	NOUN
ejpam-5387	123	26	for	for	ADP
ejpam-5387	123	27	each	each	DET
ejpam-5387	123	28	pair	pair	NOUN
ejpam-5387	123	29	of	of	ADP
ejpam-5387	123	30	subintervals	subinterval	NOUN
ejpam-5387	123	31	and	and	CCONJ
ejpam-5387	123	32	implementing	implement	VERB
ejpam-5387	123	33	the	the	DET
ejpam-5387	123	34	simpson’s-1/3	simpson’s-1/3	ADJ
ejpam-5387	123	35	rule	rule	NOUN
ejpam-5387	123	36	to	to	ADP
ejpam-5387	123	37	each	each	PRON
ejpam-5387	123	38	of	of	ADP
ejpam-5387	123	39	[	[	PUNCT
ejpam-5387	123	40	t2k	t2k	PROPN
ejpam-5387	123	41	,	,	PUNCT
ejpam-5387	123	42	t2(k+1	t2(k+1	PROPN
ejpam-5387	123	43	)	)	PUNCT
ejpam-5387	123	44	]	]	PUNCT
ejpam-5387	123	45	,	,	PUNCT
ejpam-5387	123	46	k	k	X
ejpam-5387	123	47	=	=	SYM
ejpam-5387	123	48	0	0	NUM
ejpam-5387	123	49	,	,	PUNCT
ejpam-5387	123	50	1	1	NUM
ejpam-5387	123	51	,	,	PUNCT
ejpam-5387	123	52	2	2	NUM
ejpam-5387	123	53	,	,	PUNCT
ejpam-5387	123	54	.	.	PUNCT
ejpam-5387	123	55	.	.	PUNCT
ejpam-5387	124	1	.	.	PUNCT
ejpam-5387	125	1	,	,	PUNCT
ejpam-5387	125	2	n−2	n−2	PROPN
ejpam-5387	125	3	2	2	NUM
ejpam-5387	125	4	,	,	PUNCT
ejpam-5387	125	5	we	we	PRON
ejpam-5387	125	6	can	can	AUX
ejpam-5387	125	7	appoint	appoint	VERB
ejpam-5387	125	8	the	the	DET
ejpam-5387	125	9	following	follow	VERB
ejpam-5387	125	10	formula	formula	NOUN
ejpam-5387	125	11	:	:	PUNCT
ejpam-5387	125	12	in(f	in(f	X
ejpam-5387	125	13	)	)	PUNCT
ejpam-5387	126	1	=	=	SYM
ejpam-5387	126	2	n−2	n−2	PROPN
ejpam-5387	126	3	2∑	2∑	X
ejpam-5387	126	4	k=0	k=0	PROPN
ejpam-5387	126	5	∫	∫	PROPN
ejpam-5387	127	1	t2k+2	t2k+2	PROPN
ejpam-5387	127	2	t2k	t2k	NOUN
ejpam-5387	127	3	f(u(t))dt	f(u(t))dt	NOUN
ejpam-5387	128	1	=	=	SYM
ejpam-5387	128	2	n−2	n−2	PROPN
ejpam-5387	128	3	2∑	2∑	NUM
ejpam-5387	128	4	k=0	k=0	PROPN
ejpam-5387	128	5	(	(	PUNCT
ejpam-5387	128	6	h	h	NOUN
ejpam-5387	128	7	3	3	NUM
ejpam-5387	129	1	[	[	X
ejpam-5387	129	2	f	f	X
ejpam-5387	129	3	(	(	PUNCT
ejpam-5387	129	4	u	u	PROPN
ejpam-5387	129	5	(	(	PUNCT
ejpam-5387	129	6	t2k	t2k	PROPN
ejpam-5387	129	7	)	)	PUNCT
ejpam-5387	129	8	)	)	PUNCT
ejpam-5387	130	1	+	+	CCONJ
ejpam-5387	130	2	4f	4f	NUM
ejpam-5387	130	3	(	(	PUNCT
ejpam-5387	130	4	u	u	NOUN
ejpam-5387	130	5	(	(	PUNCT
ejpam-5387	130	6	t2k+1	t2k+1	NOUN
ejpam-5387	130	7	)	)	PUNCT
ejpam-5387	130	8	)	)	PUNCT
ejpam-5387	131	1	+	+	CCONJ
ejpam-5387	131	2	f	f	X
ejpam-5387	131	3	(	(	PUNCT
ejpam-5387	131	4	u	u	NOUN
ejpam-5387	131	5	(	(	PUNCT
ejpam-5387	131	6	t2k+2	t2k+2	NOUN
ejpam-5387	131	7	)	)	PUNCT
ejpam-5387	131	8	)	)	PUNCT
ejpam-5387	131	9	]	]	PUNCT
ejpam-5387	131	10	)	)	PUNCT
ejpam-5387	131	11	.	.	PUNCT
ejpam-5387	132	1	by	by	ADP
ejpam-5387	132	2	referring	refer	VERB
ejpam-5387	132	3	un	un	PROPN
ejpam-5387	132	4	as	as	ADP
ejpam-5387	132	5	the	the	DET
ejpam-5387	132	6	approximate	approximate	ADJ
ejpam-5387	132	7	solution	solution	NOUN
ejpam-5387	132	8	of	of	ADP
ejpam-5387	132	9	u	u	PROPN
ejpam-5387	132	10	(	(	PUNCT
ejpam-5387	132	11	tn	tn	PROPN
ejpam-5387	132	12	)	)	PUNCT
ejpam-5387	132	13	and	and	CCONJ
ejpam-5387	132	14	using	use	VERB
ejpam-5387	132	15	eq.(5	eq.(5	NOUN
ejpam-5387	132	16	)	)	PUNCT
ejpam-5387	132	17	,	,	PUNCT
ejpam-5387	132	18	we	we	PRON
ejpam-5387	132	19	can	can	AUX
ejpam-5387	132	20	write	write	VERB
ejpam-5387	132	21	the	the	DET
ejpam-5387	132	22	fsr	fsr	PROPN
ejpam-5387	132	23	for	for	ADP
ejpam-5387	132	24	the	the	DET
ejpam-5387	132	25	cf	cf	NOUN
ejpam-5387	132	26	-	-	PUNCT
ejpam-5387	132	27	fde	fde	NOUN
ejpam-5387	132	28	(	(	PUNCT
ejpam-5387	132	29	3	3	NUM
ejpam-5387	132	30	)	)	PUNCT
ejpam-5387	132	31	,	,	PUNCT
ejpam-5387	132	32	for	for	ADP
ejpam-5387	132	33	n	n	NOUN
ejpam-5387	132	34	=	=	SYM
ejpam-5387	132	35	0[1](m−	0[1](m−	NUM
ejpam-5387	132	36	1	1	NUM
ejpam-5387	132	37	):	):	PUNCT
ejpam-5387	132	38	un+1	un+1	PROPN
ejpam-5387	132	39	=	=	SYM
ejpam-5387	132	40	u0+(1−γ)f	u0+(1−γ)f	PROPN
ejpam-5387	132	41	(	(	PUNCT
ejpam-5387	132	42	un+1)+γ	un+1)+γ	PROPN
ejpam-5387	132	43	h	h	PROPN
ejpam-5387	132	44	3	3	NUM
ejpam-5387	132	45	f	f	PUNCT
ejpam-5387	132	46	(	(	PUNCT
ejpam-5387	132	47	u	u	PROPN
ejpam-5387	132	48	(	(	PUNCT
ejpam-5387	132	49	t0	t0	NOUN
ejpam-5387	132	50	)	)	PUNCT
ejpam-5387	132	51	)	)	PUNCT
ejpam-5387	133	1	+	+	CCONJ
ejpam-5387	133	2	4	4	NUM
ejpam-5387	133	3	n∑	n∑	NOUN
ejpam-5387	133	4	i=2,4,6	i=2,4,6	NUM
ejpam-5387	133	5	f	f	X
ejpam-5387	133	6	(	(	PUNCT
ejpam-5387	133	7	u	u	NOUN
ejpam-5387	133	8	(	(	PUNCT
ejpam-5387	133	9	ti	ti	NOUN
ejpam-5387	133	10	)	)	PUNCT
ejpam-5387	133	11	)	)	PUNCT
ejpam-5387	134	1	+	+	CCONJ
ejpam-5387	134	2	2	2	NUM
ejpam-5387	134	3	n−1∑	n−1∑	PROPN
ejpam-5387	134	4	j=1,3,5	j=1,3,5	NUM
ejpam-5387	134	5	f	f	X
ejpam-5387	134	6	(	(	PUNCT
ejpam-5387	134	7	u	u	NOUN
ejpam-5387	134	8	(	(	PUNCT
ejpam-5387	134	9	tj	tj	NOUN
ejpam-5387	134	10	)	)	PUNCT
ejpam-5387	134	11	)	)	PUNCT
ejpam-5387	135	1	+	+	CCONJ
ejpam-5387	135	2	f	f	X
ejpam-5387	135	3	(	(	PUNCT
ejpam-5387	135	4	u	u	NOUN
ejpam-5387	135	5	(	(	PUNCT
ejpam-5387	135	6	tn+1	tn+1	NOUN
ejpam-5387	135	7	)	)	PUNCT
ejpam-5387	135	8	)	)	PUNCT
ejpam-5387	135	9			NOUN
ejpam-5387	135	10	.	.	PUNCT
ejpam-5387	136	1	this	this	DET
ejpam-5387	136	2	formula	formula	NOUN
ejpam-5387	136	3	can	can	AUX
ejpam-5387	136	4	be	be	AUX
ejpam-5387	136	5	rewritten	rewrite	VERB
ejpam-5387	136	6	in	in	ADP
ejpam-5387	136	7	a	a	DET
ejpam-5387	136	8	compact	compact	ADJ
ejpam-5387	136	9	form	form	NOUN
ejpam-5387	136	10	as	as	SCONJ
ejpam-5387	136	11	follows	follow	VERB
ejpam-5387	136	12	:	:	PUNCT
ejpam-5387	137	1	un+1	un+1	PROPN
ejpam-5387	137	2	=	=	PUNCT
ejpam-5387	137	3	u0	u0	PROPN
ejpam-5387	137	4	+	+	X
ejpam-5387	137	5	(	(	PUNCT
ejpam-5387	137	6	1−	1−	NUM
ejpam-5387	137	7	γ)f	γ)f	ADJ
ejpam-5387	137	8	(	(	PUNCT
ejpam-5387	137	9	un+1	un+1	NOUN
ejpam-5387	137	10	)	)	PUNCT
ejpam-5387	137	11	+	+	CCONJ
ejpam-5387	137	12	γh	γh	ADP
ejpam-5387	137	13	n+1∑	n+1∑	PROPN
ejpam-5387	137	14	r=0	r=0	PROPN
ejpam-5387	137	15	ξrf	ξrf	NOUN
ejpam-5387	137	16	(	(	PUNCT
ejpam-5387	137	17	ur	ur	INTJ
ejpam-5387	137	18	)	)	PUNCT
ejpam-5387	137	19	,	,	PUNCT
ejpam-5387	137	20	n	n	NOUN
ejpam-5387	137	21	=	=	SYM
ejpam-5387	137	22	0	0	NUM
ejpam-5387	137	23	,	,	PUNCT
ejpam-5387	137	24	1	1	NUM
ejpam-5387	137	25	,	,	PUNCT
ejpam-5387	137	26	2	2	NUM
ejpam-5387	137	27	,	,	PUNCT
ejpam-5387	137	28	.	.	PUNCT
ejpam-5387	137	29	.	.	PUNCT
ejpam-5387	137	30	.	.	PUNCT
ejpam-5387	138	1	,	,	PUNCT
ejpam-5387	138	2	m−	m−	PROPN
ejpam-5387	138	3	1	1	NUM
ejpam-5387	138	4	,	,	PUNCT
ejpam-5387	138	5	(	(	PUNCT
ejpam-5387	138	6	6	6	NUM
ejpam-5387	138	7	)	)	PUNCT
ejpam-5387	138	8	where	where	SCONJ
ejpam-5387	138	9	ξr	ξr	PRON
ejpam-5387	138	10	are	be	AUX
ejpam-5387	138	11	the	the	DET
ejpam-5387	138	12	weights	weight	NOUN
ejpam-5387	138	13	of	of	ADP
ejpam-5387	138	14	the	the	DET
ejpam-5387	138	15	fsr	fsr	PROPN
ejpam-5387	138	16	and	and	CCONJ
ejpam-5387	138	17	defined	define	VERB
ejpam-5387	138	18	as	as	ADP
ejpam-5387	138	19	:	:	PUNCT
ejpam-5387	138	20	ξr	ξr	X
ejpam-5387	138	21	=	=	SYM
ejpam-5387	138	22			PROPN
ejpam-5387	138	23	1/3	1/3	NUM
ejpam-5387	138	24	,	,	PUNCT
ejpam-5387	138	25	r	r	NOUN
ejpam-5387	138	26	=	=	SYM
ejpam-5387	138	27	0	0	NUM
ejpam-5387	138	28	,	,	PUNCT
ejpam-5387	138	29	n+	n+	PUNCT
ejpam-5387	138	30	1	1	NUM
ejpam-5387	138	31	,	,	PUNCT
ejpam-5387	138	32	2/3	2/3	NUM
ejpam-5387	138	33	,	,	PUNCT
ejpam-5387	138	34	r	r	NOUN
ejpam-5387	138	35	=	=	SYM
ejpam-5387	138	36	1	1	NUM
ejpam-5387	138	37	,	,	PUNCT
ejpam-5387	138	38	3	3	NUM
ejpam-5387	138	39	,	,	PUNCT
ejpam-5387	138	40	5	5	NUM
ejpam-5387	138	41	,	,	PUNCT
ejpam-5387	138	42	.	.	PUNCT
ejpam-5387	138	43	.	.	PUNCT
ejpam-5387	139	1	.	.	PUNCT
ejpam-5387	140	1	,	,	PUNCT
ejpam-5387	140	2	4/3	4/3	NUM
ejpam-5387	140	3	,	,	PUNCT
ejpam-5387	140	4	r	r	NOUN
ejpam-5387	140	5	=	=	SYM
ejpam-5387	140	6	2	2	NUM
ejpam-5387	140	7	,	,	PUNCT
ejpam-5387	140	8	4	4	NUM
ejpam-5387	140	9	,	,	PUNCT
ejpam-5387	140	10	6	6	NUM
ejpam-5387	140	11	,	,	PUNCT
ejpam-5387	140	12	.	.	PUNCT
ejpam-5387	140	13	.	.	PUNCT
ejpam-5387	140	14	.	.	PUNCT
ejpam-5387	140	15	.	.	PUNCT
ejpam-5387	141	1	lemma	lemma	PROPN
ejpam-5387	141	2	1	1	NUM
ejpam-5387	141	3	.	.	PUNCT
ejpam-5387	142	1	[	[	X
ejpam-5387	142	2	4	4	X
ejpam-5387	142	3	]	]	PUNCT
ejpam-5387	142	4	suppose	suppose	VERB
ejpam-5387	142	5	that	that	SCONJ
ejpam-5387	142	6	f(u(t	f(u(t	PROPN
ejpam-5387	142	7	)	)	PUNCT
ejpam-5387	142	8	)	)	PUNCT
ejpam-5387	143	1	∈	∈	PROPN
ejpam-5387	143	2	c4([a	c4([a	PROPN
ejpam-5387	143	3	,	,	PUNCT
ejpam-5387	143	4	b	b	NOUN
ejpam-5387	143	5	]	]	X
ejpam-5387	143	6	)	)	PUNCT
ejpam-5387	143	7	,	,	PUNCT
ejpam-5387	143	8	then	then	ADV
ejpam-5387	143	9	the	the	DET
ejpam-5387	143	10	error	error	NOUN
ejpam-5387	143	11	of	of	ADP
ejpam-5387	143	12	numerical	numerical	ADJ
ejpam-5387	143	13	scheme	scheme	NOUN
ejpam-5387	143	14	(	(	PUNCT
ejpam-5387	143	15	6	6	NUM
ejpam-5387	143	16	)	)	PUNCT
ejpam-5387	143	17	is	be	AUX
ejpam-5387	143	18	estimated	estimate	VERB
ejpam-5387	143	19	by	by	ADP
ejpam-5387	143	20	:	:	PUNCT
ejpam-5387	144	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5387	144	2	∫	∫	PROPN
ejpam-5387	144	3	tn+1	tn+1	PROPN
ejpam-5387	144	4	t0	t0	PROPN
ejpam-5387	144	5	f(u(s))ds−	f(u(s))ds−	X
ejpam-5387	144	6	γh	γh	ADP
ejpam-5387	144	7	n+1∑	n+1∑	PROPN
ejpam-5387	144	8	i=0	i=0	PROPN
ejpam-5387	144	9	ξif	ξif	X
ejpam-5387	144	10	(	(	PUNCT
ejpam-5387	144	11	u(ti	u(ti	NOUN
ejpam-5387	144	12	)	)	PUNCT
ejpam-5387	144	13	)	)	PUNCT
ejpam-5387	145	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5387	145	2	≤	≤	ADJ
ejpam-5387	145	3	h4	h4	NOUN
ejpam-5387	145	4	,	,	PUNCT
ejpam-5387	145	5	where	where	SCONJ
ejpam-5387	145	6	ĉ	ĉ	ADV
ejpam-5387	145	7	=	=	SYM
ejpam-5387	145	8	(	(	PUNCT
ejpam-5387	145	9	b−a)f	b−a)f	PROPN
ejpam-5387	145	10	(	(	PUNCT
ejpam-5387	145	11	4)(ζ	4)(ζ	PROPN
ejpam-5387	145	12	)	)	PUNCT
ejpam-5387	145	13	180	180	NUM
ejpam-5387	145	14	,	,	PUNCT
ejpam-5387	145	15	for	for	ADP
ejpam-5387	145	16	some	some	PRON
ejpam-5387	145	17	constant	constant	ADJ
ejpam-5387	145	18	a	a	PRON
ejpam-5387	145	19	<	<	X
ejpam-5387	145	20	ζ	ζ	NOUN
ejpam-5387	145	21	<	<	X
ejpam-5387	145	22	b	b	PROPN
ejpam-5387	145	23	,	,	PUNCT
ejpam-5387	145	24	h	h	NOUN
ejpam-5387	145	25	=	=	NOUN
ejpam-5387	145	26	b−a	b−a	NOUN
ejpam-5387	145	27	n	n	NOUN
ejpam-5387	145	28	,	,	PUNCT
ejpam-5387	145	29	and	and	CCONJ
ejpam-5387	145	30	tk	tk	X
ejpam-5387	145	31	=	=	PUNCT
ejpam-5387	145	32	a	a	PROPN
ejpam-5387	145	33	+	+	X
ejpam-5387	145	34	hk	hk	PROPN
ejpam-5387	145	35	,	,	PUNCT
ejpam-5387	145	36	k	k	PROPN
ejpam-5387	145	37	=	=	SYM
ejpam-5387	145	38	0	0	NUM
ejpam-5387	145	39	,	,	PUNCT
ejpam-5387	145	40	1	1	NUM
ejpam-5387	145	41	,	,	PUNCT
ejpam-5387	145	42	.	.	PUNCT
ejpam-5387	145	43	.	.	PUNCT
ejpam-5387	145	44	.	.	PUNCT
ejpam-5387	146	1	,	,	PUNCT
ejpam-5387	146	2	n+	n+	PUNCT
ejpam-5387	147	1	1	1	X
ejpam-5387	147	2	.	.	PUNCT
ejpam-5387	147	3	the	the	DET
ejpam-5387	147	4	stability	stability	NOUN
ejpam-5387	147	5	and	and	CCONJ
ejpam-5387	147	6	error	error	NOUN
ejpam-5387	147	7	analysis	analysis	NOUN
ejpam-5387	147	8	of	of	ADP
ejpam-5387	147	9	the	the	DET
ejpam-5387	147	10	regulated	regulate	VERB
ejpam-5387	147	11	numerical	numerical	ADJ
ejpam-5387	147	12	scheme	scheme	NOUN
ejpam-5387	147	13	are	be	AUX
ejpam-5387	147	14	investigated	investigate	VERB
ejpam-5387	147	15	and	and	CCONJ
ejpam-5387	147	16	proved	prove	VERB
ejpam-5387	147	17	meanwhile	meanwhile	ADV
ejpam-5387	147	18	the	the	DET
ejpam-5387	147	19	following	follow	VERB
ejpam-5387	147	20	theorems	theorem	NOUN
ejpam-5387	147	21	[	[	X
ejpam-5387	147	22	4	4	NUM
ejpam-5387	147	23	]	]	PUNCT
ejpam-5387	147	24	.	.	PUNCT
ejpam-5387	148	1	theorem	theorem	NOUN
ejpam-5387	148	2	2	2	NUM
ejpam-5387	148	3	.	.	PUNCT
ejpam-5387	149	1	the	the	DET
ejpam-5387	149	2	newly	newly	ADV
ejpam-5387	149	3	designed	design	VERB
ejpam-5387	149	4	fractional	fractional	ADJ
ejpam-5387	149	5	numerical	numerical	ADJ
ejpam-5387	149	6	technique	technique	NOUN
ejpam-5387	149	7	(	(	PUNCT
ejpam-5387	149	8	6	6	NUM
ejpam-5387	149	9	)	)	PUNCT
ejpam-5387	149	10	exhibits	exhibit	VERB
ejpam-5387	149	11	conditional	conditional	ADJ
ejpam-5387	149	12	stability	stability	NOUN
ejpam-5387	149	13	.	.	PUNCT
ejpam-5387	150	1	proof	proof	NOUN
ejpam-5387	150	2	.	.	PUNCT
ejpam-5387	151	1	the	the	DET
ejpam-5387	151	2	proof	proof	NOUN
ejpam-5387	151	3	of	of	ADP
ejpam-5387	151	4	this	this	DET
ejpam-5387	151	5	theorem	theorem	NOUN
ejpam-5387	151	6	can	can	AUX
ejpam-5387	151	7	be	be	AUX
ejpam-5387	151	8	found	find	VERB
ejpam-5387	151	9	on	on	ADP
ejpam-5387	151	10	[	[	X
ejpam-5387	151	11	4	4	NUM
ejpam-5387	151	12	]	]	PUNCT
ejpam-5387	151	13	.	.	PUNCT
ejpam-5387	152	1	t.	t.	PROPN
ejpam-5387	152	2	a.	a.	PROPN
ejpam-5387	152	3	assiri	assiri	PROPN
ejpam-5387	152	4	/	/	SYM
ejpam-5387	152	5	eur	eur	PROPN
ejpam-5387	152	6	.	.	PUNCT
ejpam-5387	153	1	j.	j.	PROPN
ejpam-5387	153	2	pure	pure	PROPN
ejpam-5387	153	3	appl	appl	PROPN
ejpam-5387	153	4	.	.	PROPN
ejpam-5387	153	5	math	math	PROPN
ejpam-5387	153	6	,	,	PUNCT
ejpam-5387	153	7	17	17	NUM
ejpam-5387	153	8	(	(	PUNCT
ejpam-5387	153	9	4	4	NUM
ejpam-5387	153	10	)	)	PUNCT
ejpam-5387	153	11	(	(	PUNCT
ejpam-5387	153	12	2024	2024	NUM
ejpam-5387	153	13	)	)	PUNCT
ejpam-5387	153	14	,	,	PUNCT
ejpam-5387	153	15	2706	2706	NUM
ejpam-5387	153	16	-	-	SYM
ejpam-5387	153	17	2719	2719	NUM
ejpam-5387	153	18	2712	2712	NUM
ejpam-5387	153	19	theorem	theorem	NOUN
ejpam-5387	153	20	3	3	NUM
ejpam-5387	153	21	.	.	PUNCT
ejpam-5387	154	1	the	the	DET
ejpam-5387	154	2	recently	recently	ADV
ejpam-5387	154	3	developed	develop	VERB
ejpam-5387	154	4	fractional	fractional	ADJ
ejpam-5387	154	5	numerical	numerical	ADJ
ejpam-5387	154	6	method	method	PROPN
ejpam-5387	154	7	exhibits	exhibit	VERB
ejpam-5387	154	8	conditional	conditional	ADJ
ejpam-5387	154	9	convergence	convergence	NOUN
ejpam-5387	154	10	of	of	ADP
ejpam-5387	154	11	order	order	NOUN
ejpam-5387	154	12	4	4	NUM
ejpam-5387	154	13	,	,	PUNCT
ejpam-5387	154	14	as	as	SCONJ
ejpam-5387	154	15	stated	state	VERB
ejpam-5387	154	16	in	in	ADP
ejpam-5387	154	17	equation	equation	NOUN
ejpam-5387	154	18	(	(	PUNCT
ejpam-5387	154	19	6	6	NUM
ejpam-5387	154	20	)	)	PUNCT
ejpam-5387	154	21	.	.	PUNCT
ejpam-5387	155	1	∥u	∥u	PROPN
ejpam-5387	155	2	(	(	PUNCT
ejpam-5387	155	3	tn+1)−	tn+1)−	PROPN
ejpam-5387	155	4	un+1∥	un+1∥	PROPN
ejpam-5387	155	5	≤	≤	PROPN
ejpam-5387	155	6	ch4	ch4	PROPN
ejpam-5387	155	7	,	,	PUNCT
ejpam-5387	155	8	where	where	SCONJ
ejpam-5387	155	9	c	c	NOUN
ejpam-5387	155	10	=	=	SYM
ejpam-5387	155	11	γĉ	γĉ	PROPN
ejpam-5387	155	12	ch	ch	NOUN
ejpam-5387	155	13	.	.	PUNCT
ejpam-5387	155	14	proof	proof	NOUN
ejpam-5387	155	15	.	.	PUNCT
ejpam-5387	156	1	the	the	DET
ejpam-5387	156	2	proof	proof	NOUN
ejpam-5387	156	3	of	of	ADP
ejpam-5387	156	4	this	this	DET
ejpam-5387	156	5	criterion	criterion	NOUN
ejpam-5387	156	6	can	can	AUX
ejpam-5387	156	7	be	be	AUX
ejpam-5387	156	8	found	find	VERB
ejpam-5387	156	9	on	on	ADP
ejpam-5387	156	10	[	[	X
ejpam-5387	156	11	4	4	NUM
ejpam-5387	156	12	]	]	PUNCT
ejpam-5387	156	13	.	.	PUNCT
ejpam-5387	157	1	5	5	X
ejpam-5387	157	2	.	.	X
ejpam-5387	157	3	numerical	numerical	ADJ
ejpam-5387	157	4	implementation	implementation	NOUN
ejpam-5387	157	5	here	here	ADV
ejpam-5387	157	6	in	in	ADP
ejpam-5387	157	7	this	this	DET
ejpam-5387	157	8	section	section	NOUN
ejpam-5387	157	9	,	,	PUNCT
ejpam-5387	157	10	we	we	PRON
ejpam-5387	157	11	will	will	AUX
ejpam-5387	157	12	try	try	VERB
ejpam-5387	157	13	to	to	PART
ejpam-5387	157	14	treat	treat	VERB
ejpam-5387	157	15	the	the	DET
ejpam-5387	157	16	shortcomings	shortcoming	NOUN
ejpam-5387	157	17	of	of	ADP
ejpam-5387	157	18	the	the	DET
ejpam-5387	157	19	existing	exist	VERB
ejpam-5387	157	20	numerical	numerical	ADJ
ejpam-5387	157	21	methods	method	NOUN
ejpam-5387	157	22	,	,	PUNCT
ejpam-5387	157	23	which	which	PRON
ejpam-5387	157	24	are	be	AUX
ejpam-5387	157	25	represented	represent	VERB
ejpam-5387	157	26	by	by	ADP
ejpam-5387	157	27	the	the	DET
ejpam-5387	157	28	slow	slow	ADJ
ejpam-5387	157	29	convergence	convergence	NOUN
ejpam-5387	157	30	of	of	ADP
ejpam-5387	157	31	most	most	ADJ
ejpam-5387	157	32	of	of	ADP
ejpam-5387	157	33	them	they	PRON
ejpam-5387	157	34	when	when	SCONJ
ejpam-5387	157	35	solving	solve	VERB
ejpam-5387	157	36	this	this	DET
ejpam-5387	157	37	type	type	NOUN
ejpam-5387	157	38	of	of	ADP
ejpam-5387	157	39	problem	problem	NOUN
ejpam-5387	157	40	,	,	PUNCT
ejpam-5387	157	41	which	which	PRON
ejpam-5387	157	42	in	in	ADP
ejpam-5387	157	43	turn	turn	NOUN
ejpam-5387	157	44	leads	lead	VERB
ejpam-5387	157	45	to	to	ADP
ejpam-5387	157	46	inaccurate	inaccurate	ADJ
ejpam-5387	157	47	approximations	approximation	NOUN
ejpam-5387	157	48	(	(	PUNCT
ejpam-5387	157	49	[	[	X
ejpam-5387	157	50	14	14	NUM
ejpam-5387	157	51	]	]	PUNCT
ejpam-5387	157	52	,	,	PUNCT
ejpam-5387	157	53	[	[	X
ejpam-5387	157	54	15	15	NUM
ejpam-5387	157	55	]	]	NUM
ejpam-5387	157	56	)	)	PUNCT
ejpam-5387	157	57	.	.	PUNCT
ejpam-5387	158	1	for	for	ADP
ejpam-5387	158	2	this	this	PRON
ejpam-5387	158	3	,	,	PUNCT
ejpam-5387	158	4	we	we	PRON
ejpam-5387	158	5	will	will	AUX
ejpam-5387	158	6	use	use	VERB
ejpam-5387	158	7	the	the	DET
ejpam-5387	158	8	fsr	fsr	PROPN
ejpam-5387	158	9	for	for	ADP
ejpam-5387	158	10	numerical	numerical	ADJ
ejpam-5387	158	11	integration	integration	NOUN
ejpam-5387	158	12	to	to	PART
ejpam-5387	158	13	calculate	calculate	VERB
ejpam-5387	158	14	the	the	DET
ejpam-5387	158	15	resulting	result	VERB
ejpam-5387	158	16	integral	integral	ADJ
ejpam-5387	158	17	in	in	ADP
ejpam-5387	158	18	the	the	DET
ejpam-5387	158	19	system	system	NOUN
ejpam-5387	158	20	of	of	ADP
ejpam-5387	158	21	integral	integral	ADJ
ejpam-5387	158	22	equations	equation	NOUN
ejpam-5387	158	23	obtained	obtain	VERB
ejpam-5387	158	24	from	from	ADP
ejpam-5387	158	25	the	the	DET
ejpam-5387	158	26	same	same	ADJ
ejpam-5387	158	27	system	system	NOUN
ejpam-5387	158	28	of	of	ADP
ejpam-5387	158	29	fdes	fde	NOUN
ejpam-5387	158	30	under	under	ADP
ejpam-5387	158	31	study	study	NOUN
ejpam-5387	158	32	.	.	PUNCT
ejpam-5387	159	1	now	now	ADV
ejpam-5387	159	2	,	,	PUNCT
ejpam-5387	159	3	we	we	PRON
ejpam-5387	159	4	will	will	AUX
ejpam-5387	159	5	numerically	numerically	ADV
ejpam-5387	159	6	treat	treat	VERB
ejpam-5387	159	7	the	the	DET
ejpam-5387	159	8	bc	bc	PROPN
ejpam-5387	159	9	system	system	NOUN
ejpam-5387	159	10	in	in	ADP
ejpam-5387	159	11	its	its	PRON
ejpam-5387	159	12	fractional	fractional	ADJ
ejpam-5387	159	13	form	form	NOUN
ejpam-5387	159	14	by	by	ADP
ejpam-5387	159	15	creating	create	VERB
ejpam-5387	159	16	a	a	DET
ejpam-5387	159	17	numerical	numerical	ADJ
ejpam-5387	159	18	scheme	scheme	NOUN
ejpam-5387	159	19	of	of	ADP
ejpam-5387	159	20	it	it	PRON
ejpam-5387	159	21	.	.	PUNCT
ejpam-5387	160	1	for	for	ADP
ejpam-5387	160	2	this	this	DET
ejpam-5387	160	3	purpose	purpose	NOUN
ejpam-5387	160	4	,	,	PUNCT
ejpam-5387	160	5	let	let	VERB
ejpam-5387	160	6	us	we	PRON
ejpam-5387	160	7	reformulate	reformulate	VERB
ejpam-5387	160	8	the	the	DET
ejpam-5387	160	9	system	system	NOUN
ejpam-5387	160	10	(	(	PUNCT
ejpam-5387	160	11	2	2	NUM
ejpam-5387	160	12	)	)	PUNCT
ejpam-5387	160	13	in	in	ADP
ejpam-5387	160	14	an	an	DET
ejpam-5387	160	15	operator	operator	NOUN
ejpam-5387	160	16	form	form	NOUN
ejpam-5387	160	17	as	as	SCONJ
ejpam-5387	160	18	follows	follow	VERB
ejpam-5387	160	19	:	:	PUNCT
ejpam-5387	160	20	cfdν	cfdν	NOUN
ejpam-5387	160	21	ψ̄(t	ψ̄(t	ADJ
ejpam-5387	160	22	)	)	PUNCT
ejpam-5387	160	23	=	=	SYM
ejpam-5387	160	24	f(ψ̄(t	f(ψ̄(t	NOUN
ejpam-5387	160	25	)	)	PUNCT
ejpam-5387	160	26	,	,	PUNCT
ejpam-5387	160	27	t	t	PROPN
ejpam-5387	160	28	)	)	PUNCT
ejpam-5387	160	29	,	,	PUNCT
ejpam-5387	160	30	(	(	PUNCT
ejpam-5387	160	31	7	7	X
ejpam-5387	160	32	)	)	PUNCT
ejpam-5387	160	33	where	where	SCONJ
ejpam-5387	160	34	ψ̄(t	ψ̄(t	ADJ
ejpam-5387	160	35	)	)	PUNCT
ejpam-5387	160	36	=	=	PUNCT
ejpam-5387	161	1	[	[	X
ejpam-5387	161	2	ψ1(t	ψ1(t	NOUN
ejpam-5387	161	3	)	)	PUNCT
ejpam-5387	161	4	,	,	PUNCT
ejpam-5387	161	5	ψ2(t	ψ2(t	PROPN
ejpam-5387	161	6	)	)	PUNCT
ejpam-5387	161	7	,	,	PUNCT
ejpam-5387	161	8	ψ3(t	ψ3(t	PROPN
ejpam-5387	161	9	)	)	PUNCT
ejpam-5387	161	10	,	,	PUNCT
ejpam-5387	161	11	ψ4(t	ψ4(t	PROPN
ejpam-5387	161	12	)	)	PUNCT
ejpam-5387	161	13	]	]	PUNCT
ejpam-5387	162	1	t	t	PROPN
ejpam-5387	162	2	,	,	PUNCT
ejpam-5387	162	3	f(ψ̄(t	f(ψ̄(t	PROPN
ejpam-5387	162	4	)	)	PUNCT
ejpam-5387	162	5	,	,	PUNCT
ejpam-5387	162	6	t	t	PROPN
ejpam-5387	162	7	)	)	PUNCT
ejpam-5387	162	8	=	=	PUNCT
ejpam-5387	163	1	[	[	X
ejpam-5387	163	2	f1	f1	NOUN
ejpam-5387	163	3	,	,	PUNCT
ejpam-5387	163	4	f2	f2	PROPN
ejpam-5387	163	5	,	,	PUNCT
ejpam-5387	163	6	f3	f3	PROPN
ejpam-5387	163	7	,	,	PUNCT
ejpam-5387	163	8	f4	f4	PROPN
ejpam-5387	163	9	]	]	X
ejpam-5387	163	10	t	t	NOUN
ejpam-5387	163	11	,	,	PUNCT
ejpam-5387	163	12	ψ̄(0	ψ̄(0	PUNCT
ejpam-5387	163	13	)	)	PUNCT
ejpam-5387	164	1	=	=	NOUN
ejpam-5387	165	1	[	[	X
ejpam-5387	165	2	ψ̂0	ψ̂0	X
ejpam-5387	165	3	1	1	NUM
ejpam-5387	165	4	,	,	PUNCT
ejpam-5387	165	5	ψ̂	ψ̂	ADV
ejpam-5387	165	6	0	0	NUM
ejpam-5387	165	7	2	2	NUM
ejpam-5387	165	8	,	,	PUNCT
ejpam-5387	165	9	ψ̂	ψ̂	ADV
ejpam-5387	165	10	0	0	NUM
ejpam-5387	165	11	3	3	NUM
ejpam-5387	165	12	,	,	PUNCT
ejpam-5387	165	13	ψ̂	ψ̂	ADV
ejpam-5387	165	14	0	0	NUM
ejpam-5387	165	15	4	4	NUM
ejpam-5387	165	16	]	]	X
ejpam-5387	165	17	t	t	NOUN
ejpam-5387	165	18	,	,	PUNCT
ejpam-5387	165	19	(	(	PUNCT
ejpam-5387	165	20	8)	8)	NUM
ejpam-5387	165	21	where	where	SCONJ
ejpam-5387	165	22	each	each	DET
ejpam-5387	165	23	one	one	NUM
ejpam-5387	165	24	of	of	ADP
ejpam-5387	165	25	the	the	DET
ejpam-5387	165	26	functions	function	NOUN
ejpam-5387	165	27	fi(ψ1	fi(ψ1	NOUN
ejpam-5387	165	28	,	,	PUNCT
ejpam-5387	165	29	ψ2	ψ2	NOUN
ejpam-5387	165	30	,	,	PUNCT
ejpam-5387	165	31	ψ3	ψ3	NOUN
ejpam-5387	165	32	,	,	PUNCT
ejpam-5387	165	33	ψ4	ψ4	PROPN
ejpam-5387	165	34	,	,	PUNCT
ejpam-5387	165	35	t	t	PROPN
ejpam-5387	165	36	)	)	PUNCT
ejpam-5387	165	37	,	,	PUNCT
ejpam-5387	165	38	i	i	PRON
ejpam-5387	165	39	=	=	PUNCT
ejpam-5387	165	40	1(1)4	1(1)4	PROPN
ejpam-5387	165	41	is	be	AUX
ejpam-5387	165	42	defined	define	VERB
ejpam-5387	165	43	in	in	ADP
ejpam-5387	165	44	the	the	DET
ejpam-5387	165	45	rhs	rhs	PROPN
ejpam-5387	165	46	of	of	ADP
ejpam-5387	165	47	the	the	DET
ejpam-5387	165	48	four	four	NUM
ejpam-5387	165	49	equations	equation	NOUN
ejpam-5387	165	50	in	in	ADP
ejpam-5387	165	51	(	(	PUNCT
ejpam-5387	165	52	2	2	NUM
ejpam-5387	165	53	)	)	PUNCT
ejpam-5387	165	54	,	,	PUNCT
ejpam-5387	165	55	respectively	respectively	ADV
ejpam-5387	165	56	.	.	PUNCT
ejpam-5387	166	1	applying	apply	VERB
ejpam-5387	166	2	cf	cf	NOUN
ejpam-5387	166	3	-	-	PUNCT
ejpam-5387	166	4	fractional	fractional	ADJ
ejpam-5387	166	5	integral	integral	ADJ
ejpam-5387	166	6	operator	operator	NOUN
ejpam-5387	166	7	on	on	ADP
ejpam-5387	166	8	the	the	DET
ejpam-5387	166	9	model	model	NOUN
ejpam-5387	166	10	(	(	PUNCT
ejpam-5387	166	11	7	7	NUM
ejpam-5387	166	12	)	)	PUNCT
ejpam-5387	166	13	and	and	CCONJ
ejpam-5387	166	14	implementing	implement	VERB
ejpam-5387	166	15	proposition	proposition	NOUN
ejpam-5387	166	16	3	3	NUM
ejpam-5387	166	17	in	in	ADP
ejpam-5387	166	18	[	[	X
ejpam-5387	166	19	2	2	NUM
ejpam-5387	166	20	]	]	PUNCT
ejpam-5387	166	21	and	and	CCONJ
ejpam-5387	166	22	formula	formula	NOUN
ejpam-5387	166	23	(	(	PUNCT
ejpam-5387	166	24	1	1	NUM
ejpam-5387	166	25	)	)	PUNCT
ejpam-5387	166	26	,	,	PUNCT
ejpam-5387	166	27	we	we	PRON
ejpam-5387	166	28	get	get	VERB
ejpam-5387	166	29	:	:	PUNCT
ejpam-5387	166	30	ψ̄(t	ψ̄(t	X
ejpam-5387	166	31	)	)	PUNCT
ejpam-5387	166	32	=	=	PUNCT
ejpam-5387	166	33	ψ̄(0	ψ̄(0	X
ejpam-5387	166	34	)	)	PUNCT
ejpam-5387	167	1	+	+	CCONJ
ejpam-5387	167	2	cf	cf	X
ejpam-5387	167	3	iν	iν	NOUN
ejpam-5387	167	4	f(ψ̄(t	f(ψ̄(t	NOUN
ejpam-5387	167	5	)	)	PUNCT
ejpam-5387	167	6	,	,	PUNCT
ejpam-5387	167	7	t	t	PROPN
ejpam-5387	167	8	)	)	PUNCT
ejpam-5387	167	9	=	=	PUNCT
ejpam-5387	167	10	ψ̄(0	ψ̄(0	PUNCT
ejpam-5387	167	11	)	)	PUNCT
ejpam-5387	168	1	+	+	CCONJ
ejpam-5387	168	2	(	(	PUNCT
ejpam-5387	168	3	1−	1−	NUM
ejpam-5387	168	4	ν)f(ψ̄(t	ν)f(ψ̄(t	NUM
ejpam-5387	168	5	)	)	PUNCT
ejpam-5387	168	6	,	,	PUNCT
ejpam-5387	168	7	t	t	PROPN
ejpam-5387	168	8	)	)	PUNCT
ejpam-5387	169	1	+	+	NUM
ejpam-5387	169	2	ν	ν	X
ejpam-5387	169	3	∫	∫	PROPN
ejpam-5387	169	4	t	t	PROPN
ejpam-5387	169	5	0	0	NUM
ejpam-5387	169	6	f(ψ̄(s	f(ψ̄(s	PROPN
ejpam-5387	169	7	)	)	PUNCT
ejpam-5387	169	8	,	,	PUNCT
ejpam-5387	170	1	s)ds	s)ds	PROPN
ejpam-5387	170	2	.	.	PROPN
ejpam-5387	171	1	(	(	PUNCT
ejpam-5387	171	2	9	9	X
ejpam-5387	171	3	)	)	PUNCT
ejpam-5387	171	4	applying	apply	VERB
ejpam-5387	171	5	the	the	DET
ejpam-5387	171	6	derived	derive	VERB
ejpam-5387	171	7	fsr	fsr	NOUN
ejpam-5387	171	8	for	for	ADP
ejpam-5387	171	9	the	the	DET
ejpam-5387	171	10	integration	integration	NOUN
ejpam-5387	171	11	on	on	ADP
ejpam-5387	171	12	the	the	DET
ejpam-5387	171	13	rhs	rhs	PROPN
ejpam-5387	171	14	of	of	ADP
ejpam-5387	171	15	(	(	PUNCT
ejpam-5387	171	16	9	9	NUM
ejpam-5387	171	17	)	)	PUNCT
ejpam-5387	171	18	,	,	PUNCT
ejpam-5387	171	19	to	to	PART
ejpam-5387	171	20	get	get	VERB
ejpam-5387	171	21	the	the	DET
ejpam-5387	171	22	following	follow	VERB
ejpam-5387	171	23	numerical	numerical	ADJ
ejpam-5387	171	24	scheme	scheme	NOUN
ejpam-5387	171	25	as	as	SCONJ
ejpam-5387	171	26	constructed	construct	VERB
ejpam-5387	171	27	in	in	ADP
ejpam-5387	171	28	the	the	DET
ejpam-5387	171	29	formula	formula	NOUN
ejpam-5387	171	30	(	(	PUNCT
ejpam-5387	171	31	6	6	NUM
ejpam-5387	171	32	):	):	PUNCT
ejpam-5387	171	33	ψ̄n+1	ψ̄n+1	NOUN
ejpam-5387	171	34	=	=	PUNCT
ejpam-5387	171	35	ψ̄(0	ψ̄(0	PUNCT
ejpam-5387	171	36	)	)	PUNCT
ejpam-5387	172	1	+	+	CCONJ
ejpam-5387	172	2	(	(	PUNCT
ejpam-5387	172	3	1−	1−	NUM
ejpam-5387	172	4	ν)f(ψ̄n+1	ν)f(ψ̄n+1	PROPN
ejpam-5387	172	5	,	,	PUNCT
ejpam-5387	172	6	tn+1	tn+1	NOUN
ejpam-5387	172	7	)	)	PUNCT
ejpam-5387	173	1	+	+	NUM
ejpam-5387	173	2	ν	ν	PROPN
ejpam-5387	173	3	h	h	NOUN
ejpam-5387	173	4	n+1∑	n+1∑	PROPN
ejpam-5387	173	5	r=0	r=0	PROPN
ejpam-5387	173	6	ξr	ξr	PROPN
ejpam-5387	173	7	f(ψ̄r	f(ψ̄r	NOUN
ejpam-5387	173	8	,	,	PUNCT
ejpam-5387	173	9	tr	tr	VERB
ejpam-5387	173	10	)	)	PUNCT
ejpam-5387	173	11	,	,	PUNCT
ejpam-5387	173	12	n	n	NOUN
ejpam-5387	173	13	=	=	SYM
ejpam-5387	173	14	0	0	NUM
ejpam-5387	173	15	,	,	PUNCT
ejpam-5387	173	16	1	1	NUM
ejpam-5387	173	17	,	,	PUNCT
ejpam-5387	173	18	2	2	NUM
ejpam-5387	173	19	,	,	PUNCT
ejpam-5387	173	20	.	.	PUNCT
ejpam-5387	173	21	.	.	PUNCT
ejpam-5387	173	22	.	.	PUNCT
ejpam-5387	174	1	,	,	PUNCT
ejpam-5387	174	2	m−	m−	PROPN
ejpam-5387	174	3	1	1	NUM
ejpam-5387	174	4	,	,	PUNCT
ejpam-5387	174	5	(	(	PUNCT
ejpam-5387	174	6	10	10	NUM
ejpam-5387	174	7	)	)	PUNCT
ejpam-5387	174	8	where	where	SCONJ
ejpam-5387	174	9	the	the	DET
ejpam-5387	174	10	weights	weight	NOUN
ejpam-5387	174	11	ξr	ξr	NOUN
ejpam-5387	174	12	,	,	PUNCT
ejpam-5387	174	13	r	r	NOUN
ejpam-5387	174	14	=	=	SYM
ejpam-5387	174	15	0	0	NUM
ejpam-5387	174	16	,	,	PUNCT
ejpam-5387	174	17	1	1	NUM
ejpam-5387	174	18	,	,	PUNCT
ejpam-5387	174	19	...	...	PUNCT
ejpam-5387	174	20	,	,	PUNCT
ejpam-5387	174	21	n+	n+	ADP
ejpam-5387	174	22	1	1	NUM
ejpam-5387	174	23	of	of	ADP
ejpam-5387	174	24	the	the	DET
ejpam-5387	174	25	fsr	fsr	NOUN
ejpam-5387	174	26	are	be	AUX
ejpam-5387	174	27	defined	define	VERB
ejpam-5387	174	28	in	in	ADP
ejpam-5387	174	29	(	(	PUNCT
ejpam-5387	174	30	6	6	NUM
ejpam-5387	174	31	)	)	PUNCT
ejpam-5387	174	32	.	.	PUNCT
ejpam-5387	175	1	so	so	ADV
ejpam-5387	175	2	,	,	PUNCT
ejpam-5387	175	3	the	the	DET
ejpam-5387	175	4	system	system	NOUN
ejpam-5387	175	5	given	give	VERB
ejpam-5387	175	6	in	in	ADP
ejpam-5387	175	7	(	(	PUNCT
ejpam-5387	175	8	10	10	NUM
ejpam-5387	175	9	)	)	PUNCT
ejpam-5387	175	10	transforms	transform	VERB
ejpam-5387	175	11	to	to	ADP
ejpam-5387	175	12	an	an	DET
ejpam-5387	175	13	algebraic	algebraic	ADJ
ejpam-5387	175	14	equations	equation	NOUN
ejpam-5387	175	15	system	system	NOUN
ejpam-5387	175	16	as	as	SCONJ
ejpam-5387	175	17	follows	follow	VERB
ejpam-5387	175	18	:	:	PUNCT
ejpam-5387	175	19	ψk	ψk	VERB
ejpam-5387	175	20	,	,	PUNCT
ejpam-5387	175	21	n+1	n+1	PROPN
ejpam-5387	175	22	=	=	SYM
ejpam-5387	175	23	ψk,0	ψk,0	PROPN
ejpam-5387	175	24	+	+	CCONJ
ejpam-5387	175	25	(	(	PUNCT
ejpam-5387	175	26	1−	1−	NUM
ejpam-5387	175	27	ν)fk(ψ1,n+1	ν)fk(ψ1,n+1	PROPN
ejpam-5387	175	28	,	,	PUNCT
ejpam-5387	175	29	ψ2,n+1	ψ2,n+1	PROPN
ejpam-5387	175	30	,	,	PUNCT
ejpam-5387	175	31	ψ3,n+1	ψ3,n+1	PROPN
ejpam-5387	175	32	,	,	PUNCT
ejpam-5387	175	33	ψ4,n+1	ψ4,n+1	PROPN
ejpam-5387	175	34	,	,	PUNCT
ejpam-5387	175	35	tn+1	tn+1	NOUN
ejpam-5387	175	36	)	)	PUNCT
ejpam-5387	176	1	+	+	NUM
ejpam-5387	176	2	ν	ν	PROPN
ejpam-5387	176	3	h	h	NOUN
ejpam-5387	176	4	n+1∑	n+1∑	PROPN
ejpam-5387	176	5	r=0	r=0	PROPN
ejpam-5387	176	6	ξr	ξr	ADP
ejpam-5387	176	7	fk(ψ1,r	fk(ψ1,r	PROPN
ejpam-5387	176	8	,	,	PUNCT
ejpam-5387	176	9	ψ2,r	ψ2,r	PROPN
ejpam-5387	176	10	,	,	PUNCT
ejpam-5387	176	11	ψ3,r	ψ3,r	PROPN
ejpam-5387	176	12	,	,	PUNCT
ejpam-5387	176	13	ψ4,r	ψ4,r	PROPN
ejpam-5387	176	14	,	,	PUNCT
ejpam-5387	176	15	tr	tr	VERB
ejpam-5387	176	16	)	)	PUNCT
ejpam-5387	176	17	,	,	PUNCT
ejpam-5387	177	1	k	k	X
ejpam-5387	177	2	=	=	PUNCT
ejpam-5387	177	3	1(1)4	1(1)4	ADJ
ejpam-5387	177	4	,	,	PUNCT
ejpam-5387	177	5	where	where	SCONJ
ejpam-5387	177	6	the	the	DET
ejpam-5387	177	7	functions	function	NOUN
ejpam-5387	177	8	fk	fk	INTJ
ejpam-5387	177	9	are	be	AUX
ejpam-5387	177	10	defined	define	VERB
ejpam-5387	177	11	in	in	ADP
ejpam-5387	177	12	(	(	PUNCT
ejpam-5387	177	13	8)	8)	NUM
ejpam-5387	177	14	.	.	PUNCT
ejpam-5387	177	15	t.	t.	PROPN
ejpam-5387	177	16	a.	a.	PROPN
ejpam-5387	177	17	assiri	assiri	PROPN
ejpam-5387	177	18	/	/	SYM
ejpam-5387	177	19	eur	eur	PROPN
ejpam-5387	177	20	.	.	PUNCT
ejpam-5387	178	1	j.	j.	PROPN
ejpam-5387	178	2	pure	pure	PROPN
ejpam-5387	178	3	appl	appl	PROPN
ejpam-5387	178	4	.	.	PROPN
ejpam-5387	178	5	math	math	PROPN
ejpam-5387	178	6	,	,	PUNCT
ejpam-5387	178	7	17	17	NUM
ejpam-5387	178	8	(	(	PUNCT
ejpam-5387	178	9	4	4	NUM
ejpam-5387	178	10	)	)	PUNCT
ejpam-5387	178	11	(	(	PUNCT
ejpam-5387	178	12	2024	2024	NUM
ejpam-5387	178	13	)	)	PUNCT
ejpam-5387	178	14	,	,	PUNCT
ejpam-5387	178	15	2706	2706	NUM
ejpam-5387	178	16	-	-	SYM
ejpam-5387	178	17	2719	2719	NUM
ejpam-5387	178	18	2713	2713	NUM
ejpam-5387	178	19	6	6	NUM
ejpam-5387	178	20	.	.	PUNCT
ejpam-5387	179	1	experimental	experimental	ADJ
ejpam-5387	179	2	results	result	NOUN
ejpam-5387	179	3	now	now	ADV
ejpam-5387	179	4	,	,	PUNCT
ejpam-5387	179	5	we	we	PRON
ejpam-5387	179	6	are	be	AUX
ejpam-5387	179	7	going	go	VERB
ejpam-5387	179	8	to	to	PART
ejpam-5387	179	9	test	test	VERB
ejpam-5387	179	10	the	the	DET
ejpam-5387	179	11	precision	precision	NOUN
ejpam-5387	179	12	of	of	ADP
ejpam-5387	179	13	the	the	DET
ejpam-5387	179	14	resulting	result	VERB
ejpam-5387	179	15	numerical	numerical	ADJ
ejpam-5387	179	16	scheme	scheme	NOUN
ejpam-5387	179	17	by	by	ADP
ejpam-5387	179	18	introducing	introduce	VERB
ejpam-5387	179	19	numerical	numerical	ADJ
ejpam-5387	179	20	simulation	simulation	NOUN
ejpam-5387	179	21	on	on	ADP
ejpam-5387	179	22	some	some	DET
ejpam-5387	179	23	cases	case	NOUN
ejpam-5387	179	24	in	in	ADP
ejpam-5387	179	25	[	[	X
ejpam-5387	179	26	0	0	NUM
ejpam-5387	179	27	,	,	PUNCT
ejpam-5387	179	28	3	3	NUM
ejpam-5387	179	29	]	]	PUNCT
ejpam-5387	179	30	for	for	ADP
ejpam-5387	179	31	the	the	DET
ejpam-5387	179	32	proposed	propose	VERB
ejpam-5387	179	33	model	model	NOUN
ejpam-5387	179	34	(	(	PUNCT
ejpam-5387	179	35	2	2	NUM
ejpam-5387	179	36	)	)	PUNCT
ejpam-5387	179	37	.	.	PUNCT
ejpam-5387	180	1	the	the	DET
ejpam-5387	180	2	behavior	behavior	NOUN
ejpam-5387	180	3	of	of	ADP
ejpam-5387	180	4	ψk(t	ψk(t	NOUN
ejpam-5387	180	5	)	)	PUNCT
ejpam-5387	180	6	,	,	PUNCT
ejpam-5387	180	7	k	k	PROPN
ejpam-5387	180	8	=	=	SYM
ejpam-5387	180	9	1	1	NUM
ejpam-5387	180	10	,	,	PUNCT
ejpam-5387	180	11	2	2	NUM
ejpam-5387	180	12	,	,	PUNCT
ejpam-5387	180	13	3	3	NUM
ejpam-5387	180	14	,	,	PUNCT
ejpam-5387	180	15	4	4	NUM
ejpam-5387	180	16	are	be	AUX
ejpam-5387	180	17	presented	present	VERB
ejpam-5387	180	18	in	in	ADP
ejpam-5387	180	19	figures	figure	NOUN
ejpam-5387	180	20	1	1	NUM
ejpam-5387	180	21	-	-	SYM
ejpam-5387	180	22	5	5	NUM
ejpam-5387	180	23	at	at	ADP
ejpam-5387	180	24	different	different	ADJ
ejpam-5387	180	25	values	value	NOUN
ejpam-5387	180	26	of	of	ADP
ejpam-5387	180	27	some	some	DET
ejpam-5387	180	28	parameters	parameter	NOUN
ejpam-5387	180	29	(	(	PUNCT
ejpam-5387	180	30	ν	ν	NOUN
ejpam-5387	180	31	,	,	PUNCT
ejpam-5387	180	32	ϱ	ϱ	ADP
ejpam-5387	180	33	,	,	PUNCT
ejpam-5387	180	34	p	p	X
ejpam-5387	180	35	,	,	PUNCT
ejpam-5387	180	36	m	m	PROPN
ejpam-5387	180	37	)	)	PUNCT
ejpam-5387	180	38	.	.	PUNCT
ejpam-5387	181	1	we	we	PRON
ejpam-5387	181	2	approach	approach	VERB
ejpam-5387	181	3	the	the	DET
ejpam-5387	181	4	system	system	NOUN
ejpam-5387	181	5	under	under	ADP
ejpam-5387	181	6	study	study	NOUN
ejpam-5387	181	7	(	(	PUNCT
ejpam-5387	181	8	2	2	NUM
ejpam-5387	181	9	)	)	PUNCT
ejpam-5387	181	10	with	with	ADP
ejpam-5387	181	11	the	the	DET
ejpam-5387	181	12	following	follow	VERB
ejpam-5387	181	13	values	value	NOUN
ejpam-5387	181	14	for	for	ADP
ejpam-5387	181	15	the	the	DET
ejpam-5387	181	16	parameters	parameter	NOUN
ejpam-5387	181	17	contained	contain	VERB
ejpam-5387	181	18	in	in	ADP
ejpam-5387	181	19	it	it	PRON
ejpam-5387	181	20	[	[	X
ejpam-5387	181	21	10	10	NUM
ejpam-5387	181	22	]	]	X
ejpam-5387	181	23	:	:	PUNCT
ejpam-5387	181	24	θ1	θ1	NOUN
ejpam-5387	181	25	=	=	SYM
ejpam-5387	181	26	0.2	0.2	NUM
ejpam-5387	181	27	,	,	PUNCT
ejpam-5387	181	28	θ2	θ2	ADV
ejpam-5387	181	29	=	=	NOUN
ejpam-5387	181	30	0.02	0.02	NUM
ejpam-5387	181	31	,	,	PUNCT
ejpam-5387	181	32	λ1	λ1	PROPN
ejpam-5387	181	33	=	=	SYM
ejpam-5387	181	34	0.3	0.3	NUM
ejpam-5387	181	35	,	,	PUNCT
ejpam-5387	181	36	λ2	λ2	NOUN
ejpam-5387	181	37	=	=	PUNCT
ejpam-5387	181	38	0.4	0.4	NUM
ejpam-5387	181	39	,	,	PUNCT
ejpam-5387	181	40	d	d	X
ejpam-5387	181	41	=	=	SYM
ejpam-5387	181	42	0.5	0.5	NUM
ejpam-5387	181	43	,	,	PUNCT
ejpam-5387	181	44	α1	α1	PROPN
ejpam-5387	181	45	=	=	SYM
ejpam-5387	181	46	6×	6×	NOUN
ejpam-5387	181	47	10−8	10−8	NUM
ejpam-5387	181	48	,	,	PUNCT
ejpam-5387	181	49	α2	α2	PROPN
ejpam-5387	181	50	=	=	SYM
ejpam-5387	181	51	3×	3×	NUM
ejpam-5387	181	52	10−7	10−7	NUM
ejpam-5387	181	53	,	,	PUNCT
ejpam-5387	181	54	α3	α3	PROPN
ejpam-5387	181	55	=	=	SYM
ejpam-5387	181	56	1×10−7	1×10−7	NUM
ejpam-5387	181	57	,	,	PUNCT
ejpam-5387	181	58	α4	α4	NOUN
ejpam-5387	181	59	=	=	SYM
ejpam-5387	181	60	0.97	0.97	NUM
ejpam-5387	181	61	,	,	PUNCT
ejpam-5387	181	62	ρ	ρ	PROPN
ejpam-5387	181	63	=	=	NOUN
ejpam-5387	181	64	0.01	0.01	NUM
ejpam-5387	181	65	,	,	PUNCT
ejpam-5387	181	66	κ	κ	X
ejpam-5387	181	67	=	=	SYM
ejpam-5387	181	68	2	2	NUM
ejpam-5387	181	69	,	,	PUNCT
ejpam-5387	181	70	β1	β1	PROPN
ejpam-5387	181	71	=	=	PUNCT
ejpam-5387	181	72	0.15	0.15	NUM
ejpam-5387	181	73	,	,	PUNCT
ejpam-5387	181	74	β2	β2	NOUN
ejpam-5387	181	75	=	=	NOUN
ejpam-5387	181	76	0.7	0.7	NUM
ejpam-5387	181	77	,	,	PUNCT
ejpam-5387	181	78	β3	β3	ADJ
ejpam-5387	181	79	=	=	NOUN
ejpam-5387	181	80	0.1	0.1	NUM
ejpam-5387	181	81	,	,	PUNCT
ejpam-5387	181	82	p	p	NOUN
ejpam-5387	181	83	=	=	NOUN
ejpam-5387	181	84	0.5	0.5	NUM
ejpam-5387	181	85	,	,	PUNCT
ejpam-5387	181	86	σ	σ	NOUN
ejpam-5387	181	87	=	=	SYM
ejpam-5387	181	88	0.1	0.1	NUM
ejpam-5387	181	89	,	,	PUNCT
ejpam-5387	181	90	p1	p1	NOUN
ejpam-5387	181	91	=	=	NOUN
ejpam-5387	181	92	0.1	0.1	NUM
ejpam-5387	181	93	,	,	PUNCT
ejpam-5387	181	94	p2	p2	X
ejpam-5387	181	95	=	=	SYM
ejpam-5387	181	96	0.2	0.2	NUM
ejpam-5387	181	97	,	,	PUNCT
ejpam-5387	181	98	p3	p3	PROPN
ejpam-5387	181	99	=	=	PUNCT
ejpam-5387	181	100	0.3	0.3	NUM
ejpam-5387	181	101	,	,	PUNCT
ejpam-5387	181	102	ϱ	ϱ	X
ejpam-5387	181	103	=	=	PUNCT
ejpam-5387	181	104	0.8	0.8	NUM
ejpam-5387	181	105	,	,	PUNCT
ejpam-5387	181	106	with	with	ADP
ejpam-5387	181	107	the	the	DET
ejpam-5387	181	108	initial	initial	ADJ
ejpam-5387	181	109	conditions	condition	NOUN
ejpam-5387	181	110	(	(	PUNCT
ejpam-5387	181	111	i.cs	i.cs	NOUN
ejpam-5387	181	112	)	)	PUNCT
ejpam-5387	181	113	ψi(0	ψi(0	PROPN
ejpam-5387	181	114	)	)	PUNCT
ejpam-5387	181	115	=	=	NOUN
ejpam-5387	181	116	0.2	0.2	NUM
ejpam-5387	181	117	,	,	PUNCT
ejpam-5387	181	118	i	i	PRON
ejpam-5387	181	119	=	=	NOUN
ejpam-5387	181	120	1	1	NUM
ejpam-5387	181	121	,	,	PUNCT
ejpam-5387	181	122	2	2	NUM
ejpam-5387	181	123	,	,	PUNCT
ejpam-5387	181	124	3	3	NUM
ejpam-5387	181	125	,	,	PUNCT
ejpam-5387	181	126	4	4	NUM
ejpam-5387	181	127	.	.	NUM
ejpam-5387	181	128	figures	figure	NOUN
ejpam-5387	181	129	1	1	NUM
ejpam-5387	181	130	-	-	SYM
ejpam-5387	181	131	5	5	NUM
ejpam-5387	181	132	display	display	VERB
ejpam-5387	181	133	a	a	DET
ejpam-5387	181	134	numerical	numerical	ADJ
ejpam-5387	181	135	simulation	simulation	NOUN
ejpam-5387	181	136	for	for	ADP
ejpam-5387	181	137	the	the	DET
ejpam-5387	181	138	system	system	NOUN
ejpam-5387	181	139	under	under	ADP
ejpam-5387	181	140	investigation	investigation	NOUN
ejpam-5387	181	141	by	by	ADP
ejpam-5387	181	142	applying	apply	VERB
ejpam-5387	181	143	the	the	DET
ejpam-5387	181	144	given	give	VERB
ejpam-5387	181	145	procedure	procedure	NOUN
ejpam-5387	181	146	.	.	PUNCT
ejpam-5387	182	1	(	(	PUNCT
ejpam-5387	182	2	i	i	NOUN
ejpam-5387	182	3	)	)	PUNCT
ejpam-5387	182	4	figure	figure	VERB
ejpam-5387	182	5	1	1	NUM
ejpam-5387	182	6	outlines	outline	VERB
ejpam-5387	182	7	the	the	DET
ejpam-5387	182	8	solution	solution	NOUN
ejpam-5387	182	9	via	via	ADP
ejpam-5387	182	10	various	various	ADJ
ejpam-5387	182	11	values	value	NOUN
ejpam-5387	182	12	of	of	ADP
ejpam-5387	182	13	ν	ν	NOUN
ejpam-5387	182	14	=	=	SYM
ejpam-5387	182	15	1.0	1.0	NUM
ejpam-5387	182	16	,	,	PUNCT
ejpam-5387	182	17	0.95	0.95	NUM
ejpam-5387	182	18	,	,	PUNCT
ejpam-5387	182	19	0.85	0.85	NUM
ejpam-5387	182	20	,	,	PUNCT
ejpam-5387	182	21	0.75	0.75	NUM
ejpam-5387	182	22	,	,	PUNCT
ejpam-5387	182	23	at	at	ADP
ejpam-5387	182	24	h	h	NOUN
ejpam-5387	182	25	=	=	NOUN
ejpam-5387	182	26	0.01	0.01	NUM
ejpam-5387	182	27	.	.	PUNCT
ejpam-5387	183	1	(	(	PUNCT
ejpam-5387	183	2	ii	ii	NOUN
ejpam-5387	183	3	)	)	PUNCT
ejpam-5387	183	4	figure	figure	NOUN
ejpam-5387	183	5	2	2	NUM
ejpam-5387	183	6	gives	give	VERB
ejpam-5387	183	7	the	the	DET
ejpam-5387	183	8	solution	solution	NOUN
ejpam-5387	183	9	for	for	ADP
ejpam-5387	183	10	distinct	distinct	ADJ
ejpam-5387	183	11	values	value	NOUN
ejpam-5387	183	12	of	of	ADP
ejpam-5387	183	13	m	m	NOUN
ejpam-5387	183	14	=	=	SYM
ejpam-5387	183	15	5	5	NUM
ejpam-5387	183	16	,	,	PUNCT
ejpam-5387	183	17	10	10	NUM
ejpam-5387	183	18	,	,	PUNCT
ejpam-5387	183	19	15	15	NUM
ejpam-5387	183	20	.	.	PUNCT
ejpam-5387	184	1	(	(	PUNCT
ejpam-5387	184	2	iii	iii	X
ejpam-5387	184	3	)	)	PUNCT
ejpam-5387	184	4	figure	figure	NOUN
ejpam-5387	184	5	3	3	NUM
ejpam-5387	184	6	shows	show	VERB
ejpam-5387	184	7	the	the	DET
ejpam-5387	184	8	solution	solution	NOUN
ejpam-5387	184	9	for	for	ADP
ejpam-5387	184	10	distinct	distinct	ADJ
ejpam-5387	184	11	values	value	NOUN
ejpam-5387	184	12	of	of	ADP
ejpam-5387	184	13	the	the	DET
ejpam-5387	184	14	estrogen	estrogen	NOUN
ejpam-5387	184	15	source	source	NOUN
ejpam-5387	184	16	rate	rate	NOUN
ejpam-5387	184	17	ϱ	ϱ	NOUN
ejpam-5387	184	18	=	=	SYM
ejpam-5387	184	19	0.8	0.8	NUM
ejpam-5387	184	20	,	,	PUNCT
ejpam-5387	184	21	1.4	1.4	NUM
ejpam-5387	184	22	,	,	PUNCT
ejpam-5387	184	23	2.0	2.0	NUM
ejpam-5387	184	24	,	,	PUNCT
ejpam-5387	184	25	2.6	2.6	NUM
ejpam-5387	184	26	.	.	PUNCT
ejpam-5387	185	1	(	(	PUNCT
ejpam-5387	185	2	iv	iv	X
ejpam-5387	185	3	)	)	PUNCT
ejpam-5387	185	4	figure	figure	NOUN
ejpam-5387	185	5	4	4	NUM
ejpam-5387	185	6	depicts	depict	VERB
ejpam-5387	185	7	the	the	DET
ejpam-5387	185	8	effect	effect	NOUN
ejpam-5387	185	9	of	of	ADP
ejpam-5387	185	10	p	p	NOUN
ejpam-5387	185	11	(=	(=	NUM
ejpam-5387	185	12	0.25	0.25	NUM
ejpam-5387	185	13	,	,	PUNCT
ejpam-5387	185	14	0.5	0.5	NUM
ejpam-5387	185	15	,	,	PUNCT
ejpam-5387	185	16	0.75	0.75	NUM
ejpam-5387	185	17	,	,	PUNCT
ejpam-5387	185	18	1.0	1.0	NUM
ejpam-5387	185	19	)	)	PUNCT
ejpam-5387	185	20	on	on	ADP
ejpam-5387	185	21	the	the	DET
ejpam-5387	185	22	approximate	approximate	ADJ
ejpam-5387	185	23	solution	solution	NOUN
ejpam-5387	185	24	.	.	PUNCT
ejpam-5387	186	1	(	(	PUNCT
ejpam-5387	186	2	v	v	NOUN
ejpam-5387	186	3	)	)	PUNCT
ejpam-5387	186	4	figure	figure	NOUN
ejpam-5387	186	5	5	5	NUM
ejpam-5387	186	6	presents	present	VERB
ejpam-5387	186	7	a	a	DET
ejpam-5387	186	8	comparison	comparison	NOUN
ejpam-5387	186	9	between	between	ADP
ejpam-5387	186	10	the	the	DET
ejpam-5387	186	11	solution	solution	NOUN
ejpam-5387	186	12	created	create	VERB
ejpam-5387	186	13	by	by	ADP
ejpam-5387	186	14	the	the	DET
ejpam-5387	186	15	obtained	obtain	VERB
ejpam-5387	186	16	approach	approach	NOUN
ejpam-5387	186	17	with	with	ADP
ejpam-5387	186	18	that	that	DET
ejpam-5387	186	19	numerical	numerical	ADJ
ejpam-5387	186	20	solution	solution	NOUN
ejpam-5387	186	21	by	by	ADP
ejpam-5387	186	22	implementing	implement	VERB
ejpam-5387	186	23	rk4	rk4	NOUN
ejpam-5387	186	24	m	m	NOUN
ejpam-5387	186	25	[	[	X
ejpam-5387	186	26	14	14	NUM
ejpam-5387	186	27	]	]	PUNCT
ejpam-5387	186	28	with	with	ADP
ejpam-5387	186	29	the	the	DET
ejpam-5387	186	30	same	same	ADJ
ejpam-5387	186	31	parameters	parameter	NOUN
ejpam-5387	186	32	and	and	CCONJ
ejpam-5387	186	33	i.cs	i.cs	PROPN
ejpam-5387	186	34	.	.	PUNCT
ejpam-5387	187	1	the	the	DET
ejpam-5387	187	2	behavior	behavior	NOUN
ejpam-5387	187	3	of	of	ADP
ejpam-5387	187	4	the	the	DET
ejpam-5387	187	5	approximate	approximate	ADJ
ejpam-5387	187	6	solution	solution	NOUN
ejpam-5387	187	7	is	be	AUX
ejpam-5387	187	8	based	base	VERB
ejpam-5387	187	9	on	on	ADP
ejpam-5387	187	10	ν	ν	PROPN
ejpam-5387	187	11	,	,	PUNCT
ejpam-5387	187	12	m	m	PROPN
ejpam-5387	187	13	,	,	PUNCT
ejpam-5387	187	14	ϱ	ϱ	ADP
ejpam-5387	187	15	,	,	PUNCT
ejpam-5387	187	16	p	p	X
ejpam-5387	187	17	,	,	PUNCT
ejpam-5387	187	18	as	as	SCONJ
ejpam-5387	187	19	shown	show	VERB
ejpam-5387	187	20	in	in	ADP
ejpam-5387	187	21	figures	figure	NOUN
ejpam-5387	187	22	1	1	NUM
ejpam-5387	187	23	-	-	SYM
ejpam-5387	187	24	4	4	NUM
ejpam-5387	187	25	,	,	PUNCT
ejpam-5387	187	26	respectively	respectively	ADV
ejpam-5387	187	27	.	.	PUNCT
ejpam-5387	188	1	from	from	ADP
ejpam-5387	188	2	figures	figure	NOUN
ejpam-5387	188	3	3	3	NUM
ejpam-5387	188	4	and	and	CCONJ
ejpam-5387	188	5	4	4	NUM
ejpam-5387	188	6	,	,	PUNCT
ejpam-5387	188	7	we	we	PRON
ejpam-5387	188	8	can	can	AUX
ejpam-5387	188	9	confirm	confirm	VERB
ejpam-5387	188	10	that	that	SCONJ
ejpam-5387	188	11	the	the	DET
ejpam-5387	188	12	behavior	behavior	NOUN
ejpam-5387	188	13	of	of	ADP
ejpam-5387	188	14	the	the	DET
ejpam-5387	188	15	solution	solution	NOUN
ejpam-5387	188	16	consists	consist	VERB
ejpam-5387	188	17	with	with	ADP
ejpam-5387	188	18	the	the	DET
ejpam-5387	188	19	nature	nature	NOUN
ejpam-5387	188	20	effect	effect	NOUN
ejpam-5387	188	21	of	of	ADP
ejpam-5387	188	22	the	the	DET
ejpam-5387	188	23	parameters	parameter	NOUN
ejpam-5387	188	24	ϱ	ϱ	VERB
ejpam-5387	188	25	,	,	PUNCT
ejpam-5387	188	26	and	and	CCONJ
ejpam-5387	188	27	p	p	X
ejpam-5387	188	28	,	,	PUNCT
ejpam-5387	188	29	respectively	respectively	ADV
ejpam-5387	188	30	.	.	PUNCT
ejpam-5387	189	1	from	from	ADP
ejpam-5387	189	2	figures	figure	NOUN
ejpam-5387	189	3	2	2	NUM
ejpam-5387	189	4	and	and	CCONJ
ejpam-5387	189	5	5	5	NUM
ejpam-5387	189	6	,	,	PUNCT
ejpam-5387	189	7	we	we	PRON
ejpam-5387	189	8	can	can	AUX
ejpam-5387	189	9	point	point	VERB
ejpam-5387	189	10	out	out	ADP
ejpam-5387	189	11	that	that	SCONJ
ejpam-5387	189	12	the	the	DET
ejpam-5387	189	13	proposed	propose	VERB
ejpam-5387	189	14	method	method	NOUN
ejpam-5387	189	15	has	have	AUX
ejpam-5387	189	16	been	be	AUX
ejpam-5387	189	17	well	well	ADV
ejpam-5387	189	18	implemented	implement	VERB
ejpam-5387	189	19	to	to	PART
ejpam-5387	189	20	solve	solve	VERB
ejpam-5387	189	21	the	the	DET
ejpam-5387	189	22	model	model	NOUN
ejpam-5387	189	23	under	under	ADP
ejpam-5387	189	24	study	study	NOUN
ejpam-5387	189	25	.	.	PUNCT
ejpam-5387	190	1	hence	hence	ADV
ejpam-5387	190	2	,	,	PUNCT
ejpam-5387	190	3	we	we	PRON
ejpam-5387	190	4	can	can	AUX
ejpam-5387	190	5	verify	verify	VERB
ejpam-5387	190	6	that	that	SCONJ
ejpam-5387	190	7	the	the	DET
ejpam-5387	190	8	expected	expect	VERB
ejpam-5387	190	9	behavior	behavior	NOUN
ejpam-5387	190	10	of	of	ADP
ejpam-5387	190	11	the	the	DET
ejpam-5387	190	12	disease	disease	NOUN
ejpam-5387	190	13	has	have	AUX
ejpam-5387	190	14	been	be	AUX
ejpam-5387	190	15	obtained	obtain	VERB
ejpam-5387	190	16	,	,	PUNCT
ejpam-5387	190	17	which	which	PRON
ejpam-5387	190	18	means	mean	VERB
ejpam-5387	190	19	that	that	SCONJ
ejpam-5387	190	20	we	we	PRON
ejpam-5387	190	21	have	have	AUX
ejpam-5387	190	22	provided	provide	VERB
ejpam-5387	190	23	an	an	DET
ejpam-5387	190	24	evident	evident	ADJ
ejpam-5387	190	25	simulation	simulation	NOUN
ejpam-5387	190	26	of	of	ADP
ejpam-5387	190	27	the	the	DET
ejpam-5387	190	28	proposed	propose	VERB
ejpam-5387	190	29	system	system	NOUN
ejpam-5387	190	30	that	that	PRON
ejpam-5387	190	31	can	can	AUX
ejpam-5387	190	32	be	be	AUX
ejpam-5387	190	33	used	use	VERB
ejpam-5387	190	34	by	by	ADP
ejpam-5387	190	35	the	the	DET
ejpam-5387	190	36	relevant	relevant	ADJ
ejpam-5387	190	37	authorities	authority	NOUN
ejpam-5387	190	38	to	to	PART
ejpam-5387	190	39	treat	treat	VERB
ejpam-5387	190	40	this	this	DET
ejpam-5387	190	41	deadly	deadly	ADJ
ejpam-5387	190	42	cancer	cancer	NOUN
ejpam-5387	190	43	.	.	PUNCT
ejpam-5387	191	1	t.	t.	PROPN
ejpam-5387	191	2	a.	a.	PROPN
ejpam-5387	191	3	assiri	assiri	PROPN
ejpam-5387	191	4	/	/	SYM
ejpam-5387	191	5	eur	eur	PROPN
ejpam-5387	191	6	.	.	PUNCT
ejpam-5387	192	1	j.	j.	PROPN
ejpam-5387	192	2	pure	pure	PROPN
ejpam-5387	192	3	appl	appl	PROPN
ejpam-5387	192	4	.	.	PROPN
ejpam-5387	192	5	math	math	PROPN
ejpam-5387	192	6	,	,	PUNCT
ejpam-5387	192	7	17	17	NUM
ejpam-5387	192	8	(	(	PUNCT
ejpam-5387	192	9	4	4	NUM
ejpam-5387	192	10	)	)	PUNCT
ejpam-5387	192	11	(	(	PUNCT
ejpam-5387	192	12	2024	2024	NUM
ejpam-5387	192	13	)	)	PUNCT
ejpam-5387	192	14	,	,	PUNCT
ejpam-5387	192	15	2706	2706	NUM
ejpam-5387	192	16	-	-	SYM
ejpam-5387	192	17	2719	2719	NUM
ejpam-5387	192	18	2714	2714	NUM
ejpam-5387	192	19	figure	figure	NOUN
ejpam-5387	192	20	1	1	NUM
ejpam-5387	192	21	.	.	PUNCT
ejpam-5387	193	1	the	the	DET
ejpam-5387	193	2	solution	solution	NOUN
ejpam-5387	193	3	ψi(t	ψi(t	PUNCT
ejpam-5387	193	4	)	)	PUNCT
ejpam-5387	193	5	via	via	ADP
ejpam-5387	193	6	various	various	ADJ
ejpam-5387	193	7	values	value	NOUN
ejpam-5387	193	8	of	of	ADP
ejpam-5387	193	9	ν	ν	PROPN
ejpam-5387	193	10	.	.	PUNCT
ejpam-5387	193	11	figure	figure	NOUN
ejpam-5387	193	12	2	2	NUM
ejpam-5387	193	13	.	.	PUNCT
ejpam-5387	194	1	the	the	DET
ejpam-5387	194	2	solution	solution	NOUN
ejpam-5387	194	3	ψi(t	ψi(t	PUNCT
ejpam-5387	194	4	)	)	PUNCT
ejpam-5387	194	5	via	via	ADP
ejpam-5387	194	6	various	various	ADJ
ejpam-5387	194	7	values	value	NOUN
ejpam-5387	194	8	of	of	ADP
ejpam-5387	194	9	m.	m.	NOUN
ejpam-5387	194	10	t.	t.	PROPN
ejpam-5387	194	11	a.	a.	PROPN
ejpam-5387	194	12	assiri	assiri	PROPN
ejpam-5387	194	13	/	/	SYM
ejpam-5387	194	14	eur	eur	PROPN
ejpam-5387	194	15	.	.	PUNCT
ejpam-5387	195	1	j.	j.	PROPN
ejpam-5387	195	2	pure	pure	PROPN
ejpam-5387	195	3	appl	appl	PROPN
ejpam-5387	195	4	.	.	PROPN
ejpam-5387	195	5	math	math	PROPN
ejpam-5387	195	6	,	,	PUNCT
ejpam-5387	195	7	17	17	NUM
ejpam-5387	195	8	(	(	PUNCT
ejpam-5387	195	9	4	4	NUM
ejpam-5387	195	10	)	)	PUNCT
ejpam-5387	195	11	(	(	PUNCT
ejpam-5387	195	12	2024	2024	NUM
ejpam-5387	195	13	)	)	PUNCT
ejpam-5387	195	14	,	,	PUNCT
ejpam-5387	195	15	2706	2706	NUM
ejpam-5387	195	16	-	-	SYM
ejpam-5387	195	17	2719	2719	NUM
ejpam-5387	195	18	2715	2715	NUM
ejpam-5387	195	19	figure	figure	NOUN
ejpam-5387	195	20	3	3	NUM
ejpam-5387	195	21	.	.	PUNCT
ejpam-5387	196	1	the	the	DET
ejpam-5387	196	2	solution	solution	NOUN
ejpam-5387	196	3	ψi(t	ψi(t	PUNCT
ejpam-5387	196	4	)	)	PUNCT
ejpam-5387	196	5	via	via	ADP
ejpam-5387	196	6	various	various	ADJ
ejpam-5387	196	7	values	value	NOUN
ejpam-5387	196	8	of	of	ADP
ejpam-5387	196	9	ϱ.	ϱ.	NOUN
ejpam-5387	196	10	t.	t.	PROPN
ejpam-5387	196	11	a.	a.	PROPN
ejpam-5387	196	12	assiri	assiri	PROPN
ejpam-5387	196	13	/	/	SYM
ejpam-5387	196	14	eur	eur	PROPN
ejpam-5387	196	15	.	.	PUNCT
ejpam-5387	197	1	j.	j.	PROPN
ejpam-5387	197	2	pure	pure	PROPN
ejpam-5387	197	3	appl	appl	PROPN
ejpam-5387	197	4	.	.	PROPN
ejpam-5387	197	5	math	math	PROPN
ejpam-5387	197	6	,	,	PUNCT
ejpam-5387	197	7	17	17	NUM
ejpam-5387	197	8	(	(	PUNCT
ejpam-5387	197	9	4	4	NUM
ejpam-5387	197	10	)	)	PUNCT
ejpam-5387	197	11	(	(	PUNCT
ejpam-5387	197	12	2024	2024	NUM
ejpam-5387	197	13	)	)	PUNCT
ejpam-5387	197	14	,	,	PUNCT
ejpam-5387	197	15	2706	2706	NUM
ejpam-5387	197	16	-	-	SYM
ejpam-5387	197	17	2719	2719	NUM
ejpam-5387	197	18	2716	2716	NUM
ejpam-5387	197	19	figure	figure	NOUN
ejpam-5387	197	20	4	4	NUM
ejpam-5387	197	21	.	.	PUNCT
ejpam-5387	198	1	the	the	DET
ejpam-5387	198	2	solution	solution	NOUN
ejpam-5387	198	3	ψi(t	ψi(t	PUNCT
ejpam-5387	198	4	)	)	PUNCT
ejpam-5387	198	5	via	via	ADP
ejpam-5387	198	6	various	various	ADJ
ejpam-5387	198	7	values	value	NOUN
ejpam-5387	198	8	of	of	ADP
ejpam-5387	198	9	p.	p.	NOUN
ejpam-5387	198	10	figure	figure	NOUN
ejpam-5387	198	11	5	5	NUM
ejpam-5387	198	12	.	.	PUNCT
ejpam-5387	198	13	comparison	comparison	NOUN
ejpam-5387	198	14	the	the	DET
ejpam-5387	198	15	solution	solution	NOUN
ejpam-5387	198	16	obtained	obtain	VERB
ejpam-5387	198	17	by	by	ADP
ejpam-5387	198	18	proposed	propose	VERB
ejpam-5387	198	19	method	method	NOUN
ejpam-5387	198	20	and	and	CCONJ
ejpam-5387	198	21	rk4	rk4	NOUN
ejpam-5387	198	22	m.	m.	NOUN
ejpam-5387	198	23	references	reference	VERB
ejpam-5387	198	24	2717	2717	NUM
ejpam-5387	198	25	7	7	NUM
ejpam-5387	198	26	.	.	PUNCT
ejpam-5387	198	27	conclusions	conclusion	NOUN
ejpam-5387	198	28	and	and	CCONJ
ejpam-5387	198	29	remarks	remark	VERB
ejpam-5387	198	30	this	this	DET
ejpam-5387	198	31	study	study	NOUN
ejpam-5387	198	32	aims	aim	VERB
ejpam-5387	198	33	to	to	PART
ejpam-5387	198	34	utilize	utilize	VERB
ejpam-5387	198	35	an	an	DET
ejpam-5387	198	36	efficient	efficient	ADJ
ejpam-5387	198	37	and	and	CCONJ
ejpam-5387	198	38	accurate	accurate	ADJ
ejpam-5387	198	39	method	method	NOUN
ejpam-5387	198	40	to	to	PART
ejpam-5387	198	41	gain	gain	VERB
ejpam-5387	198	42	numerical	numerical	ADJ
ejpam-5387	198	43	solutions	solution	NOUN
ejpam-5387	198	44	for	for	ADP
ejpam-5387	198	45	the	the	DET
ejpam-5387	198	46	cf	cf	NOUN
ejpam-5387	198	47	-	-	PUNCT
ejpam-5387	198	48	fractional	fractional	ADJ
ejpam-5387	198	49	bc	bc	PROPN
ejpam-5387	198	50	mathematical	mathematical	PROPN
ejpam-5387	198	51	system	system	NOUN
ejpam-5387	198	52	.	.	PUNCT
ejpam-5387	199	1	simpson	simpson	PROPN
ejpam-5387	199	2	’s	’s	PART
ejpam-5387	199	3	rule	rule	NOUN
ejpam-5387	199	4	1/3	1/3	NUM
ejpam-5387	199	5	was	be	AUX
ejpam-5387	199	6	applied	apply	VERB
ejpam-5387	199	7	in	in	ADP
ejpam-5387	199	8	its	its	PRON
ejpam-5387	199	9	fractional	fractional	ADJ
ejpam-5387	199	10	form	form	NOUN
ejpam-5387	199	11	in	in	ADP
ejpam-5387	199	12	computing	compute	VERB
ejpam-5387	199	13	the	the	DET
ejpam-5387	199	14	resulting	result	VERB
ejpam-5387	199	15	integral	integral	ADJ
ejpam-5387	199	16	within	within	ADP
ejpam-5387	199	17	the	the	DET
ejpam-5387	199	18	system	system	NOUN
ejpam-5387	199	19	of	of	ADP
ejpam-5387	199	20	fractional	fractional	ADJ
ejpam-5387	199	21	integral	integral	ADJ
ejpam-5387	199	22	equations	equation	NOUN
ejpam-5387	199	23	corresponding	correspond	VERB
ejpam-5387	199	24	to	to	ADP
ejpam-5387	199	25	the	the	DET
ejpam-5387	199	26	fdes	fde	NOUN
ejpam-5387	199	27	expressing	express	VERB
ejpam-5387	199	28	mathematically	mathematically	ADV
ejpam-5387	199	29	the	the	DET
ejpam-5387	199	30	bc	bc	PROPN
ejpam-5387	199	31	model	model	NOUN
ejpam-5387	199	32	to	to	PART
ejpam-5387	199	33	achieve	achieve	VERB
ejpam-5387	199	34	fourth	fourth	ADJ
ejpam-5387	199	35	-	-	PUNCT
ejpam-5387	199	36	order	order	NOUN
ejpam-5387	199	37	accuracy	accuracy	NOUN
ejpam-5387	199	38	for	for	ADP
ejpam-5387	199	39	the	the	DET
ejpam-5387	199	40	resulting	result	VERB
ejpam-5387	199	41	solutions	solution	NOUN
ejpam-5387	199	42	.	.	PUNCT
ejpam-5387	200	1	this	this	DET
ejpam-5387	200	2	study	study	NOUN
ejpam-5387	200	3	utilized	utilize	VERB
ejpam-5387	200	4	several	several	ADJ
ejpam-5387	200	5	values	value	NOUN
ejpam-5387	200	6	of	of	ADP
ejpam-5387	200	7	the	the	DET
ejpam-5387	200	8	fractional	fractional	ADJ
ejpam-5387	200	9	order	order	NOUN
ejpam-5387	200	10	ν	ν	NOUN
ejpam-5387	200	11	and	and	CCONJ
ejpam-5387	200	12	ϱ	ϱ	VERB
ejpam-5387	200	13	,	,	PUNCT
ejpam-5387	200	14	m	m	PROPN
ejpam-5387	200	15	,	,	PUNCT
ejpam-5387	200	16	p	p	X
ejpam-5387	200	17	to	to	PART
ejpam-5387	200	18	derive	derive	VERB
ejpam-5387	200	19	solutions	solution	NOUN
ejpam-5387	200	20	for	for	ADP
ejpam-5387	200	21	the	the	DET
ejpam-5387	200	22	model	model	NOUN
ejpam-5387	200	23	being	be	AUX
ejpam-5387	200	24	examined	examine	VERB
ejpam-5387	200	25	.	.	PUNCT
ejpam-5387	201	1	also	also	ADV
ejpam-5387	201	2	,	,	PUNCT
ejpam-5387	201	3	we	we	PRON
ejpam-5387	201	4	have	have	AUX
ejpam-5387	201	5	determined	determine	VERB
ejpam-5387	201	6	that	that	SCONJ
ejpam-5387	201	7	the	the	DET
ejpam-5387	201	8	proposed	propose	VERB
ejpam-5387	201	9	approach	approach	NOUN
ejpam-5387	201	10	is	be	AUX
ejpam-5387	201	11	remarkably	remarkably	ADV
ejpam-5387	201	12	effective	effective	ADJ
ejpam-5387	201	13	in	in	ADP
ejpam-5387	201	14	analyzing	analyze	VERB
ejpam-5387	201	15	this	this	DET
ejpam-5387	201	16	system	system	NOUN
ejpam-5387	201	17	.	.	PUNCT
ejpam-5387	202	1	furthermore	furthermore	ADV
ejpam-5387	202	2	,	,	PUNCT
ejpam-5387	202	3	reducing	reduce	VERB
ejpam-5387	202	4	the	the	DET
ejpam-5387	202	5	value	value	NOUN
ejpam-5387	202	6	of	of	ADP
ejpam-5387	202	7	h	h	NOUN
ejpam-5387	202	8	allows	allow	VERB
ejpam-5387	202	9	us	we	PRON
ejpam-5387	202	10	to	to	PART
ejpam-5387	202	11	control	control	VERB
ejpam-5387	202	12	the	the	DET
ejpam-5387	202	13	accuracy	accuracy	NOUN
ejpam-5387	202	14	of	of	ADP
ejpam-5387	202	15	the	the	DET
ejpam-5387	202	16	numerical	numerical	ADJ
ejpam-5387	202	17	solution	solution	NOUN
ejpam-5387	202	18	.	.	PUNCT
ejpam-5387	203	1	from	from	ADP
ejpam-5387	203	2	the	the	DET
ejpam-5387	203	3	obtained	obtain	VERB
ejpam-5387	203	4	solutions	solution	NOUN
ejpam-5387	203	5	,	,	PUNCT
ejpam-5387	203	6	we	we	PRON
ejpam-5387	203	7	can	can	AUX
ejpam-5387	203	8	confirm	confirm	VERB
ejpam-5387	203	9	that	that	SCONJ
ejpam-5387	203	10	the	the	DET
ejpam-5387	203	11	offered	offer	VERB
ejpam-5387	203	12	approach	approach	NOUN
ejpam-5387	203	13	is	be	AUX
ejpam-5387	203	14	surprisingly	surprisingly	ADV
ejpam-5387	203	15	successful	successful	ADJ
ejpam-5387	203	16	in	in	ADP
ejpam-5387	203	17	simulating	simulate	VERB
ejpam-5387	203	18	the	the	DET
ejpam-5387	203	19	bcmodel	bcmodel	NOUN
ejpam-5387	203	20	,	,	PUNCT
ejpam-5387	203	21	as	as	ADV
ejpam-5387	203	22	well	well	ADV
ejpam-5387	203	23	as	as	ADP
ejpam-5387	203	24	demonstrating	demonstrate	VERB
ejpam-5387	203	25	the	the	DET
ejpam-5387	203	26	accuracy	accuracy	NOUN
ejpam-5387	203	27	and	and	CCONJ
ejpam-5387	203	28	computational	computational	ADJ
ejpam-5387	203	29	effectiveness	effectiveness	NOUN
ejpam-5387	203	30	of	of	ADP
ejpam-5387	203	31	this	this	DET
ejpam-5387	203	32	method	method	NOUN
ejpam-5387	203	33	.	.	PUNCT
ejpam-5387	204	1	finally	finally	ADV
ejpam-5387	204	2	,	,	PUNCT
ejpam-5387	204	3	the	the	DET
ejpam-5387	204	4	present	present	ADJ
ejpam-5387	204	5	study	study	NOUN
ejpam-5387	204	6	may	may	AUX
ejpam-5387	204	7	contribute	contribute	VERB
ejpam-5387	204	8	to	to	ADP
ejpam-5387	204	9	providing	provide	VERB
ejpam-5387	204	10	more	more	ADV
ejpam-5387	204	11	robust	robust	ADJ
ejpam-5387	204	12	physical	physical	ADJ
ejpam-5387	204	13	explanations	explanation	NOUN
ejpam-5387	204	14	for	for	ADP
ejpam-5387	204	15	future	future	ADJ
ejpam-5387	204	16	theoretical	theoretical	ADJ
ejpam-5387	204	17	and	and	CCONJ
ejpam-5387	204	18	computational	computational	ADJ
ejpam-5387	204	19	studies	study	NOUN
ejpam-5387	204	20	on	on	ADP
ejpam-5387	204	21	the	the	DET
ejpam-5387	204	22	same	same	ADJ
ejpam-5387	204	23	topic	topic	NOUN
ejpam-5387	204	24	.	.	PUNCT
ejpam-5387	205	1	references	reference	NOUN
ejpam-5387	205	2	[	[	X
ejpam-5387	205	3	1	1	NUM
ejpam-5387	205	4	]	]	PUNCT
ejpam-5387	205	5	breast	breast	NOUN
ejpam-5387	205	6	cancer	cancer	NOUN
ejpam-5387	205	7	.	.	PUNCT
ejpam-5387	206	1	https://www.who.int/news-room/fact-sheets/detail/	https://www.who.int/news-room/fact-sheets/detail/	NOUN
ejpam-5387	206	2	breast	breast	NOUN
ejpam-5387	206	3	-	-	PUNCT
ejpam-5387	206	4	cancer	cancer	NOUN
ejpam-5387	206	5	.	.	PUNCT
ejpam-5387	207	1	accessed	access	VERB
ejpam-5387	207	2	:	:	PUNCT
ejpam-5387	207	3	15	15	NUM
ejpam-5387	207	4	july	july	PROPN
ejpam-5387	207	5	2023	2023	NUM
ejpam-5387	207	6	.	.	PUNCT
ejpam-5387	208	1	[	[	X
ejpam-5387	208	2	2	2	X
ejpam-5387	208	3	]	]	PUNCT
ejpam-5387	208	4	t.	t.	NOUN
ejpam-5387	208	5	abdeljawad	abdeljawad	PROPN
ejpam-5387	208	6	and	and	CCONJ
ejpam-5387	208	7	d.	d.	PROPN
ejpam-5387	208	8	baleanu	baleanu	PROPN
ejpam-5387	208	9	.	.	PUNCT
ejpam-5387	209	1	on	on	ADP
ejpam-5387	209	2	fractional	fractional	ADJ
ejpam-5387	209	3	derivatives	derivative	NOUN
ejpam-5387	209	4	with	with	ADP
ejpam-5387	209	5	exponential	exponential	ADJ
ejpam-5387	209	6	kernel	kernel	NOUN
ejpam-5387	209	7	and	and	CCONJ
ejpam-5387	209	8	their	their	PRON
ejpam-5387	209	9	discrete	discrete	ADJ
ejpam-5387	209	10	versions	version	NOUN
ejpam-5387	209	11	.	.	PUNCT
ejpam-5387	210	1	rep	rep	PROPN
ejpam-5387	210	2	.	.	PROPN
ejpam-5387	210	3	math	math	PROPN
ejpam-5387	210	4	.	.	PUNCT
ejpam-5387	211	1	phys	phy	NOUN
ejpam-5387	211	2	.	.	PUNCT
ejpam-5387	211	3	,	,	PUNCT
ejpam-5387	211	4	80:11–27	80:11–27	NUM
ejpam-5387	211	5	,	,	PUNCT
ejpam-5387	211	6	2017	2017	NUM
ejpam-5387	211	7	.	.	PUNCT
ejpam-5387	212	1	[	[	X
ejpam-5387	212	2	3	3	X
ejpam-5387	212	3	]	]	PUNCT
ejpam-5387	212	4	m.	m.	NOUN
ejpam-5387	212	5	adel	adel	PROPN
ejpam-5387	212	6	,	,	PUNCT
ejpam-5387	212	7	m.	m.	NOUN
ejpam-5387	212	8	m.	m.	NOUN
ejpam-5387	212	9	khader	khader	PROPN
ejpam-5387	212	10	,	,	PUNCT
ejpam-5387	212	11	t.	t.	PROPN
ejpam-5387	212	12	a.	a.	NOUN
ejpam-5387	212	13	assiri	assiri	PROPN
ejpam-5387	212	14	,	,	PUNCT
ejpam-5387	212	15	and	and	CCONJ
ejpam-5387	212	16	w.	w.	PROPN
ejpam-5387	212	17	kaleel	kaleel	PROPN
ejpam-5387	212	18	.	.	PUNCT
ejpam-5387	213	1	numerical	numerical	PROPN
ejpam-5387	213	2	simulation	simulation	PROPN
ejpam-5387	213	3	for	for	ADP
ejpam-5387	213	4	covid-19	covid-19	PROPN
ejpam-5387	213	5	model	model	NOUN
ejpam-5387	213	6	using	use	VERB
ejpam-5387	213	7	a	a	DET
ejpam-5387	213	8	multidomain	multidomain	ADJ
ejpam-5387	213	9	spectral	spectral	ADJ
ejpam-5387	213	10	relaxation	relaxation	NOUN
ejpam-5387	213	11	technique	technique	NOUN
ejpam-5387	213	12	.	.	PUNCT
ejpam-5387	214	1	symmetry	symmetry	NOUN
ejpam-5387	214	2	,	,	PUNCT
ejpam-5387	214	3	15:1–15	15:1–15	NUM
ejpam-5387	214	4	,	,	PUNCT
ejpam-5387	214	5	2023	2023	NUM
ejpam-5387	214	6	.	.	PUNCT
ejpam-5387	215	1	[	[	X
ejpam-5387	215	2	4	4	X
ejpam-5387	215	3	]	]	PUNCT
ejpam-5387	215	4	s.	s.	PROPN
ejpam-5387	215	5	arshad	arshad	PROPN
ejpam-5387	215	6	,	,	PUNCT
ejpam-5387	215	7	i.	i.	PROPN
ejpam-5387	215	8	saleem	saleem	PROPN
ejpam-5387	215	9	,	,	PUNCT
ejpam-5387	215	10	a.	a.	NOUN
ejpam-5387	215	11	akgul	akgul	PROPN
ejpam-5387	215	12	,	,	PUNCT
ejpam-5387	215	13	j.	j.	PROPN
ejpam-5387	215	14	huang	huang	PROPN
ejpam-5387	215	15	,	,	PUNCT
ejpam-5387	215	16	y.	y.	PROPN
ejpam-5387	215	17	tang	tang	PROPN
ejpam-5387	215	18	,	,	PUNCT
ejpam-5387	215	19	and	and	CCONJ
ejpam-5387	215	20	s.	s.	PROPN
ejpam-5387	215	21	m.	m.	PROPN
ejpam-5387	215	22	eldin	eldin	PROPN
ejpam-5387	215	23	.	.	PUNCT
ejpam-5387	216	1	a	a	DET
ejpam-5387	216	2	novel	novel	ADJ
ejpam-5387	216	3	numerical	numerical	ADJ
ejpam-5387	216	4	method	method	NOUN
ejpam-5387	216	5	for	for	ADP
ejpam-5387	216	6	solving	solve	VERB
ejpam-5387	216	7	the	the	DET
ejpam-5387	216	8	caputo	caputo	PROPN
ejpam-5387	216	9	-	-	PUNCT
ejpam-5387	216	10	fabrizio	fabrizio	PROPN
ejpam-5387	216	11	fractional	fractional	ADJ
ejpam-5387	216	12	differential	differential	NOUN
ejpam-5387	216	13	equation	equation	NOUN
ejpam-5387	216	14	.	.	PUNCT
ejpam-5387	217	1	aims	aim	VERB
ejpam-5387	217	2	mathematics	mathematic	NOUN
ejpam-5387	217	3	,	,	PUNCT
ejpam-5387	217	4	8:9535–9556	8:9535–9556	NUM
ejpam-5387	217	5	,	,	PUNCT
ejpam-5387	217	6	2022	2022	NUM
ejpam-5387	217	7	.	.	PUNCT
ejpam-5387	218	1	[	[	X
ejpam-5387	218	2	5	5	NUM
ejpam-5387	218	3	]	]	PUNCT
ejpam-5387	218	4	a.	a.	NOUN
ejpam-5387	218	5	ait	ait	PROPN
ejpam-5387	218	6	brahim	brahim	PROPN
ejpam-5387	218	7	,	,	PUNCT
ejpam-5387	218	8	j.	j.	PROPN
ejpam-5387	218	9	el	el	PROPN
ejpam-5387	218	10	ghordaf	ghordaf	PROPN
ejpam-5387	218	11	,	,	PUNCT
ejpam-5387	218	12	a.	a.	PROPN
ejpam-5387	218	13	el	el	PROPN
ejpam-5387	218	14	hajaji	hajaji	PROPN
ejpam-5387	218	15	,	,	PUNCT
ejpam-5387	218	16	k.	k.	PROPN
ejpam-5387	218	17	hilal	hilal	PROPN
ejpam-5387	218	18	,	,	PUNCT
ejpam-5387	218	19	and	and	CCONJ
ejpam-5387	218	20	j.	j.	PROPN
ejpam-5387	218	21	e.	e.	PROPN
ejpam-5387	218	22	n.	n.	PROPN
ejpam-5387	218	23	valdes	valdes	PROPN
ejpam-5387	218	24	.	.	PUNCT
ejpam-5387	219	1	a	a	DET
ejpam-5387	219	2	comparative	comparative	ADJ
ejpam-5387	219	3	analysis	analysis	NOUN
ejpam-5387	219	4	of	of	ADP
ejpam-5387	219	5	conformable	conformable	ADJ
ejpam-5387	219	6	,	,	PUNCT
ejpam-5387	219	7	non	non	ADJ
ejpam-5387	219	8	-	-	ADJ
ejpam-5387	219	9	conformable	conformable	ADJ
ejpam-5387	219	10	,	,	PUNCT
ejpam-5387	219	11	riemann	riemann	PROPN
ejpam-5387	219	12	-	-	PUNCT
ejpam-5387	219	13	liouville	liouville	NOUN
ejpam-5387	219	14	,	,	PUNCT
ejpam-5387	219	15	and	and	CCONJ
ejpam-5387	219	16	caputo	caputo	PROPN
ejpam-5387	219	17	fractional	fractional	ADJ
ejpam-5387	219	18	derivatives	derivative	NOUN
ejpam-5387	219	19	.	.	PUNCT
ejpam-5387	220	1	eur	eur	PROPN
ejpam-5387	220	2	.	.	PUNCT
ejpam-5387	221	1	j.	j.	PROPN
ejpam-5387	221	2	of	of	ADP
ejpam-5387	221	3	pure	pure	ADJ
ejpam-5387	221	4	and	and	CCONJ
ejpam-5387	221	5	appl	appl	ADJ
ejpam-5387	221	6	.	.	PUNCT
ejpam-5387	222	1	maths	maths	PROPN
ejpam-5387	222	2	.	.	PUNCT
ejpam-5387	222	3	,	,	PUNCT
ejpam-5387	222	4	17:1842–1854	17:1842–1854	NUM
ejpam-5387	222	5	,	,	PUNCT
ejpam-5387	222	6	2024	2024	NUM
ejpam-5387	222	7	.	.	PUNCT
ejpam-5387	223	1	[	[	X
ejpam-5387	223	2	6	6	NUM
ejpam-5387	223	3	]	]	PUNCT
ejpam-5387	223	4	m.	m.	NOUN
ejpam-5387	223	5	caputo	caputo	PROPN
ejpam-5387	223	6	and	and	CCONJ
ejpam-5387	223	7	m.	m.	PROPN
ejpam-5387	223	8	fabrizio	fabrizio	PROPN
ejpam-5387	223	9	.	.	PUNCT
ejpam-5387	224	1	a	a	DET
ejpam-5387	224	2	new	new	ADJ
ejpam-5387	224	3	definition	definition	NOUN
ejpam-5387	224	4	of	of	ADP
ejpam-5387	224	5	fractional	fractional	ADJ
ejpam-5387	224	6	derivative	derivative	NOUN
ejpam-5387	224	7	without	without	ADP
ejpam-5387	224	8	singular	singular	ADJ
ejpam-5387	224	9	kernel	kernel	PROPN
ejpam-5387	224	10	.	.	PUNCT
ejpam-5387	225	1	progr	progr	NOUN
ejpam-5387	225	2	.	.	PUNCT
ejpam-5387	226	1	fract	fract	PROPN
ejpam-5387	226	2	.	.	PUNCT
ejpam-5387	227	1	differ	differ	VERB
ejpam-5387	227	2	.	.	PUNCT
ejpam-5387	228	1	appl	appl	PROPN
ejpam-5387	228	2	.	.	PROPN
ejpam-5387	228	3	,	,	PUNCT
ejpam-5387	228	4	1:73–85	1:73–85	NUM
ejpam-5387	228	5	,	,	PUNCT
ejpam-5387	228	6	2015	2015	NUM
ejpam-5387	228	7	.	.	PUNCT
ejpam-5387	229	1	[	[	X
ejpam-5387	229	2	7	7	X
ejpam-5387	229	3	]	]	X
ejpam-5387	229	4	m.	m.	NOUN
ejpam-5387	229	5	farman	farman	PROPN
ejpam-5387	229	6	,	,	PUNCT
ejpam-5387	229	7	h.	h.	PROPN
ejpam-5387	229	8	besbes	besbes	PROPN
ejpam-5387	229	9	,	,	PUNCT
ejpam-5387	229	10	k.	k.	PROPN
ejpam-5387	229	11	s.	s.	PROPN
ejpam-5387	229	12	nisar	nisar	PROPN
ejpam-5387	229	13	,	,	PUNCT
ejpam-5387	229	14	and	and	CCONJ
ejpam-5387	229	15	m.	m.	NOUN
ejpam-5387	229	16	omri	omri	PROPN
ejpam-5387	229	17	.	.	PUNCT
ejpam-5387	230	1	analysis	analysis	NOUN
ejpam-5387	230	2	and	and	CCONJ
ejpam-5387	230	3	dynamical	dynamical	ADJ
ejpam-5387	230	4	transmission	transmission	NOUN
ejpam-5387	230	5	of	of	ADP
ejpam-5387	230	6	covid-19	covid-19	PROPN
ejpam-5387	230	7	model	model	NOUN
ejpam-5387	230	8	by	by	ADP
ejpam-5387	230	9	using	use	VERB
ejpam-5387	230	10	caputo	caputo	PROPN
ejpam-5387	230	11	-	-	PUNCT
ejpam-5387	230	12	fabrizio	fabrizio	PROPN
ejpam-5387	230	13	derivative	derivative	NOUN
ejpam-5387	230	14	.	.	PUNCT
ejpam-5387	231	1	alex	alex	PROPN
ejpam-5387	231	2	.	.	PUNCT
ejpam-5387	232	1	eng	eng	PROPN
ejpam-5387	232	2	.	.	PUNCT
ejpam-5387	233	1	j.	j.	PROPN
ejpam-5387	233	2	,	,	PUNCT
ejpam-5387	233	3	66:597–606	66:597–606	PROPN
ejpam-5387	233	4	,	,	PUNCT
ejpam-5387	233	5	2023	2023	NUM
ejpam-5387	233	6	.	.	PUNCT
ejpam-5387	234	1	[	[	X
ejpam-5387	234	2	8	8	NUM
ejpam-5387	234	3	]	]	X
ejpam-5387	234	4	m.	m.	NOUN
ejpam-5387	234	5	fathoni	fathoni	NOUN
ejpam-5387	234	6	,	,	PUNCT
ejpam-5387	234	7	g.	g.	PROPN
ejpam-5387	234	8	gunardi	gunardi	PROPN
ejpam-5387	234	9	,	,	PUNCT
ejpam-5387	234	10	f.	f.	PROPN
ejpam-5387	234	11	a.	a.	PROPN
ejpam-5387	234	12	kusumo	kusumo	PROPN
ejpam-5387	234	13	,	,	PUNCT
ejpam-5387	234	14	and	and	CCONJ
ejpam-5387	234	15	s.	s.	PROPN
ejpam-5387	234	16	h.	h.	PROPN
ejpam-5387	234	17	hutajulu	hutajulu	PROPN
ejpam-5387	234	18	.	.	PUNCT
ejpam-5387	235	1	mathematical	mathematical	ADJ
ejpam-5387	235	2	model	model	NOUN
ejpam-5387	235	3	analysis	analysis	NOUN
ejpam-5387	235	4	of	of	ADP
ejpam-5387	235	5	breast	breast	NOUN
ejpam-5387	235	6	cancer	cancer	NOUN
ejpam-5387	235	7	stages	stage	NOUN
ejpam-5387	235	8	with	with	ADP
ejpam-5387	235	9	side	side	ADJ
ejpam-5387	235	10	effects	effect	NOUN
ejpam-5387	235	11	on	on	ADP
ejpam-5387	235	12	the	the	DET
ejpam-5387	235	13	heart	heart	NOUN
ejpam-5387	235	14	in	in	ADP
ejpam-5387	235	15	chemotherapy	chemotherapy	NOUN
ejpam-5387	235	16	pareferences	pareference	NOUN
ejpam-5387	235	17	2718	2718	NUM
ejpam-5387	235	18	tients	tient	NOUN
ejpam-5387	235	19	.	.	PUNCT
ejpam-5387	236	1	in	in	ADP
ejpam-5387	236	2	proceedings	proceeding	NOUN
ejpam-5387	236	3	of	of	ADP
ejpam-5387	236	4	the	the	DET
ejpam-5387	236	5	aip	aip	PROPN
ejpam-5387	236	6	conference	conference	NOUN
ejpam-5387	236	7	proceedings	proceeding	NOUN
ejpam-5387	236	8	,	,	PUNCT
ejpam-5387	236	9	yogyakarta	yogyakarta	PROPN
ejpam-5387	236	10	,	,	PUNCT
ejpam-5387	236	11	indonesia	indonesia	PROPN
ejpam-5387	236	12	,	,	PUNCT
ejpam-5387	236	13	29	29	NUM
ejpam-5387	236	14	july–1	july–1	NOUN
ejpam-5387	236	15	august	august	PROPN
ejpam-5387	236	16	2019	2019	NUM
ejpam-5387	236	17	,	,	PUNCT
ejpam-5387	236	18	2019	2019	NUM
ejpam-5387	236	19	.	.	PUNCT
ejpam-5387	237	1	aip	aip	PROPN
ejpam-5387	237	2	publishing	publishing	PROPN
ejpam-5387	237	3	.	.	PUNCT
ejpam-5387	238	1	[	[	X
ejpam-5387	238	2	9	9	NUM
ejpam-5387	238	3	]	]	PUNCT
ejpam-5387	238	4	m.	m.	NOUN
ejpam-5387	238	5	a.	a.	PROPN
ejpam-5387	238	6	hajji	hajji	PROPN
ejpam-5387	238	7	and	and	CCONJ
ejpam-5387	238	8	q.	q.	PROPN
ejpam-5387	238	9	al	al	PROPN
ejpam-5387	238	10	-	-	PUNCT
ejpam-5387	238	11	mdallal	mdallal	PROPN
ejpam-5387	238	12	.	.	PUNCT
ejpam-5387	239	1	numerical	numerical	ADJ
ejpam-5387	239	2	simulations	simulation	NOUN
ejpam-5387	239	3	of	of	ADP
ejpam-5387	239	4	a	a	DET
ejpam-5387	239	5	delay	delay	NOUN
ejpam-5387	239	6	model	model	NOUN
ejpam-5387	239	7	for	for	ADP
ejpam-5387	239	8	immune	immune	ADJ
ejpam-5387	239	9	system	system	NOUN
ejpam-5387	239	10	-	-	PUNCT
ejpam-5387	239	11	tumor	tumor	NOUN
ejpam-5387	239	12	interaction	interaction	NOUN
ejpam-5387	239	13	.	.	PUNCT
ejpam-5387	240	1	sultan	sultan	PROPN
ejpam-5387	240	2	qaboos	qaboos	PROPN
ejpam-5387	240	3	univ	univ	PROPN
ejpam-5387	240	4	.	.	PUNCT
ejpam-5387	241	1	j.	j.	PROPN
ejpam-5387	241	2	sci	sci	PROPN
ejpam-5387	241	3	.	.	PROPN
ejpam-5387	241	4	,	,	PUNCT
ejpam-5387	241	5	23:19–31	23:19–31	NUM
ejpam-5387	241	6	,	,	PUNCT
ejpam-5387	241	7	2018	2018	NUM
ejpam-5387	241	8	.	.	PUNCT
ejpam-5387	242	1	[	[	X
ejpam-5387	242	2	10	10	NUM
ejpam-5387	242	3	]	]	PUNCT
ejpam-5387	242	4	m.	m.	NOUN
ejpam-5387	242	5	a.	a.	PROPN
ejpam-5387	242	6	hammad	hammad	PROPN
ejpam-5387	242	7	,	,	PUNCT
ejpam-5387	242	8	i.	i.	PROPN
ejpam-5387	242	9	h.	h.	PROPN
ejpam-5387	242	10	jebril	jebril	PROPN
ejpam-5387	242	11	,	,	PUNCT
ejpam-5387	242	12	s.	s.	PROPN
ejpam-5387	242	13	alshorm	alshorm	PROPN
ejpam-5387	242	14	,	,	PUNCT
ejpam-5387	242	15	i.	i.	PROPN
ejpam-5387	242	16	m.	m.	PROPN
ejpam-5387	242	17	batiha	batiha	PROPN
ejpam-5387	242	18	,	,	PUNCT
ejpam-5387	242	19	and	and	CCONJ
ejpam-5387	242	20	n.	n.	PROPN
ejpam-5387	242	21	a.	a.	PROPN
ejpam-5387	242	22	hammad	hammad	PROPN
ejpam-5387	242	23	.	.	PROPN
ejpam-5387	243	1	numerical	numerical	ADJ
ejpam-5387	243	2	solution	solution	NOUN
ejpam-5387	243	3	for	for	ADP
ejpam-5387	243	4	a	a	DET
ejpam-5387	243	5	fractional	fractional	ADJ
ejpam-5387	243	6	-	-	PUNCT
ejpam-5387	243	7	order	order	NOUN
ejpam-5387	243	8	mathematical	mathematical	ADJ
ejpam-5387	243	9	model	model	NOUN
ejpam-5387	243	10	of	of	ADP
ejpam-5387	243	11	immune	immune	NOUN
ejpam-5387	243	12	-	-	PUNCT
ejpam-5387	243	13	chemotherapeutic	chemotherapeutic	NOUN
ejpam-5387	243	14	treatment	treatment	NOUN
ejpam-5387	243	15	for	for	ADP
ejpam-5387	243	16	breast	breast	NOUN
ejpam-5387	243	17	cancer	cancer	NOUN
ejpam-5387	243	18	using	use	VERB
ejpam-5387	243	19	the	the	DET
ejpam-5387	243	20	modified	modify	VERB
ejpam-5387	243	21	fractional	fractional	ADJ
ejpam-5387	243	22	formula	formula	NOUN
ejpam-5387	243	23	.	.	PUNCT
ejpam-5387	244	1	int	int	NOUN
ejpam-5387	244	2	.	.	PUNCT
ejpam-5387	245	1	j.	j.	PROPN
ejpam-5387	245	2	anal	anal	PROPN
ejpam-5387	245	3	.	.	PUNCT
ejpam-5387	246	1	appl	appl	PROPN
ejpam-5387	246	2	.	.	PROPN
ejpam-5387	246	3	,	,	PUNCT
ejpam-5387	246	4	21:1–9	21:1–9	NUM
ejpam-5387	246	5	,	,	PUNCT
ejpam-5387	246	6	2023	2023	NUM
ejpam-5387	246	7	.	.	PUNCT
ejpam-5387	247	1	[	[	X
ejpam-5387	247	2	11	11	NUM
ejpam-5387	247	3	]	]	PUNCT
ejpam-5387	247	4	m.	m.	NOUN
ejpam-5387	247	5	idrees	idree	NOUN
ejpam-5387	247	6	,	,	PUNCT
ejpam-5387	247	7	a.	a.	PROPN
ejpam-5387	247	8	s.	s.	PROPN
ejpam-5387	247	9	alnahdi	alnahdi	PROPN
ejpam-5387	247	10	,	,	PUNCT
ejpam-5387	247	11	and	and	CCONJ
ejpam-5387	247	12	m.	m.	PROPN
ejpam-5387	247	13	b.	b.	PROPN
ejpam-5387	247	14	jeelani	jeelani	PROPN
ejpam-5387	247	15	.	.	PUNCT
ejpam-5387	248	1	mathematical	mathematical	ADJ
ejpam-5387	248	2	modeling	modeling	NOUN
ejpam-5387	248	3	of	of	ADP
ejpam-5387	248	4	breast	breast	NOUN
ejpam-5387	248	5	cancer	cancer	NOUN
ejpam-5387	248	6	based	base	VERB
ejpam-5387	248	7	on	on	ADP
ejpam-5387	248	8	the	the	DET
ejpam-5387	248	9	caputo	caputo	PROPN
ejpam-5387	248	10	-	-	PUNCT
ejpam-5387	248	11	fabrizio	fabrizio	PROPN
ejpam-5387	248	12	fractal	fractal	ADJ
ejpam-5387	248	13	-	-	PUNCT
ejpam-5387	248	14	fractional	fractional	ADJ
ejpam-5387	248	15	derivative	derivative	NOUN
ejpam-5387	248	16	.	.	PUNCT
ejpam-5387	249	1	fractal	fractal	PROPN
ejpam-5387	249	2	and	and	CCONJ
ejpam-5387	249	3	fractional	fractional	ADJ
ejpam-5387	249	4	,	,	PUNCT
ejpam-5387	249	5	7:1–14	7:1–14	NUM
ejpam-5387	249	6	,	,	PUNCT
ejpam-5387	249	7	2023	2023	NUM
ejpam-5387	249	8	.	.	PUNCT
ejpam-5387	250	1	[	[	X
ejpam-5387	250	2	12	12	NUM
ejpam-5387	250	3	]	]	PUNCT
ejpam-5387	250	4	a.	a.	NOUN
ejpam-5387	250	5	jajarmi	jajarmi	PROPN
ejpam-5387	250	6	,	,	PUNCT
ejpam-5387	250	7	s.	s.	PROPN
ejpam-5387	250	8	arshad	arshad	PROPN
ejpam-5387	250	9	,	,	PUNCT
ejpam-5387	250	10	and	and	CCONJ
ejpam-5387	250	11	d.	d.	PROPN
ejpam-5387	250	12	baleanu	baleanu	PROPN
ejpam-5387	250	13	.	.	PUNCT
ejpam-5387	251	1	a	a	DET
ejpam-5387	251	2	new	new	ADJ
ejpam-5387	251	3	fractional	fractional	ADJ
ejpam-5387	251	4	modeling	modeling	NOUN
ejpam-5387	251	5	and	and	CCONJ
ejpam-5387	251	6	control	control	NOUN
ejpam-5387	251	7	strategy	strategy	NOUN
ejpam-5387	251	8	for	for	ADP
ejpam-5387	251	9	the	the	DET
ejpam-5387	251	10	outbreak	outbreak	NOUN
ejpam-5387	251	11	of	of	ADP
ejpam-5387	251	12	dengue	dengue	NOUN
ejpam-5387	251	13	fever	fever	NOUN
ejpam-5387	251	14	.	.	PUNCT
ejpam-5387	252	1	physica	physica	PROPN
ejpam-5387	252	2	a	a	DET
ejpam-5387	252	3	,	,	PUNCT
ejpam-5387	252	4	535:1–10	535:1–10	NUM
ejpam-5387	252	5	,	,	PUNCT
ejpam-5387	252	6	2019	2019	NUM
ejpam-5387	252	7	.	.	PUNCT
ejpam-5387	253	1	[	[	X
ejpam-5387	253	2	13	13	NUM
ejpam-5387	253	3	]	]	PUNCT
ejpam-5387	253	4	t.	t.	NOUN
ejpam-5387	253	5	jin	jin	PROPN
ejpam-5387	253	6	and	and	CCONJ
ejpam-5387	253	7	x.	x.	PROPN
ejpam-5387	253	8	yang	yang	PROPN
ejpam-5387	253	9	.	.	PUNCT
ejpam-5387	254	1	monotonicity	monotonicity	PROPN
ejpam-5387	254	2	theorem	theorem	VERB
ejpam-5387	254	3	for	for	ADP
ejpam-5387	254	4	the	the	DET
ejpam-5387	254	5	uncertain	uncertain	ADJ
ejpam-5387	254	6	fractional	fractional	ADJ
ejpam-5387	254	7	differential	differential	ADJ
ejpam-5387	254	8	equation	equation	NOUN
ejpam-5387	254	9	and	and	CCONJ
ejpam-5387	254	10	application	application	NOUN
ejpam-5387	254	11	to	to	ADP
ejpam-5387	254	12	uncertain	uncertain	ADJ
ejpam-5387	254	13	financial	financial	ADJ
ejpam-5387	254	14	market	market	NOUN
ejpam-5387	254	15	.	.	PUNCT
ejpam-5387	255	1	math	math	NOUN
ejpam-5387	255	2	.	.	PUNCT
ejpam-5387	256	1	comput	comput	NOUN
ejpam-5387	256	2	.	.	PUNCT
ejpam-5387	257	1	simulat	simulat	NOUN
ejpam-5387	257	2	.	.	PUNCT
ejpam-5387	257	3	,	,	PUNCT
ejpam-5387	257	4	190:03–221	190:03–221	NUM
ejpam-5387	257	5	,	,	PUNCT
ejpam-5387	257	6	2021	2021	NUM
ejpam-5387	257	7	.	.	PUNCT
ejpam-5387	258	1	[	[	X
ejpam-5387	258	2	14	14	NUM
ejpam-5387	258	3	]	]	PUNCT
ejpam-5387	258	4	m.	m.	NOUN
ejpam-5387	258	5	m.	m.	NOUN
ejpam-5387	258	6	khader	khader	PROPN
ejpam-5387	258	7	and	and	CCONJ
ejpam-5387	258	8	m.	m.	PROPN
ejpam-5387	258	9	adel	adel	PROPN
ejpam-5387	258	10	.	.	PUNCT
ejpam-5387	259	1	modeling	modeling	NOUN
ejpam-5387	259	2	and	and	CCONJ
ejpam-5387	259	3	numerical	numerical	PROPN
ejpam-5387	259	4	simulation	simulation	NOUN
ejpam-5387	259	5	for	for	ADP
ejpam-5387	259	6	covering	cover	VERB
ejpam-5387	259	7	the	the	DET
ejpam-5387	259	8	fractional	fractional	ADJ
ejpam-5387	259	9	covid-19	covid-19	PROPN
ejpam-5387	259	10	model	model	NOUN
ejpam-5387	259	11	using	use	VERB
ejpam-5387	259	12	spectral	spectral	ADJ
ejpam-5387	259	13	collocation	collocation	NOUN
ejpam-5387	259	14	-	-	PUNCT
ejpam-5387	259	15	optimization	optimization	NOUN
ejpam-5387	259	16	algorithms	algorithm	NOUN
ejpam-5387	259	17	.	.	PUNCT
ejpam-5387	260	1	fractal	fractal	ADJ
ejpam-5387	260	2	fract	fract	PROPN
ejpam-5387	260	3	.	.	PUNCT
ejpam-5387	260	4	,	,	PUNCT
ejpam-5387	260	5	6:1–19	6:1–19	NUM
ejpam-5387	260	6	,	,	PUNCT
ejpam-5387	260	7	2022	2022	NUM
ejpam-5387	260	8	.	.	PUNCT
ejpam-5387	261	1	[	[	X
ejpam-5387	261	2	15	15	NUM
ejpam-5387	261	3	]	]	X
ejpam-5387	261	4	m.	m.	NOUN
ejpam-5387	261	5	m.	m.	NOUN
ejpam-5387	261	6	khader	khader	PROPN
ejpam-5387	261	7	,	,	PUNCT
ejpam-5387	261	8	n.	n.	PROPN
ejpam-5387	261	9	h.	h.	PROPN
ejpam-5387	261	10	sweilam	sweilam	PROPN
ejpam-5387	261	11	,	,	PUNCT
ejpam-5387	261	12	a.	a.	PROPN
ejpam-5387	261	13	m.	m.	PROPN
ejpam-5387	261	14	s.	s.	PROPN
ejpam-5387	261	15	mahdy	mahdy	PROPN
ejpam-5387	261	16	,	,	PUNCT
ejpam-5387	261	17	and	and	CCONJ
ejpam-5387	261	18	n.	n.	PROPN
ejpam-5387	261	19	k.	k.	PROPN
ejpam-5387	261	20	a.	a.	PROPN
ejpam-5387	261	21	moniem	moniem	PROPN
ejpam-5387	261	22	.	.	PUNCT
ejpam-5387	262	1	numerical	numerical	PROPN
ejpam-5387	262	2	simulation	simulation	PROPN
ejpam-5387	262	3	for	for	ADP
ejpam-5387	262	4	the	the	DET
ejpam-5387	262	5	fractional	fractional	PROPN
ejpam-5387	262	6	sirc	sirc	PROPN
ejpam-5387	262	7	model	model	NOUN
ejpam-5387	262	8	and	and	CCONJ
ejpam-5387	262	9	influenza	influenza	NOUN
ejpam-5387	262	10	a.	a.	NOUN
ejpam-5387	262	11	appl	appl	PROPN
ejpam-5387	262	12	.	.	PROPN
ejpam-5387	263	1	math	math	PROPN
ejpam-5387	263	2	.	.	PUNCT
ejpam-5387	264	1	inf	inf	PROPN
ejpam-5387	264	2	.	.	PUNCT
ejpam-5387	265	1	sci	sci	PROPN
ejpam-5387	265	2	.	.	PROPN
ejpam-5387	265	3	,	,	PUNCT
ejpam-5387	265	4	8:1029–1036	8:1029–1036	NOUN
ejpam-5387	265	5	,	,	PUNCT
ejpam-5387	265	6	2014	2014	NUM
ejpam-5387	265	7	.	.	PUNCT
ejpam-5387	266	1	[	[	X
ejpam-5387	266	2	16	16	NUM
ejpam-5387	266	3	]	]	PUNCT
ejpam-5387	266	4	j.	j.	PROPN
ejpam-5387	266	5	rong	rong	PROPN
ejpam-5387	266	6	loh	loh	PROPN
ejpam-5387	266	7	,	,	PUNCT
ejpam-5387	266	8	a.	a.	NOUN
ejpam-5387	266	9	isah	isah	PROPN
ejpam-5387	266	10	,	,	PUNCT
ejpam-5387	266	11	c.	c.	PROPN
ejpam-5387	266	12	phang	phang	PROPN
ejpam-5387	266	13	,	,	PUNCT
ejpam-5387	266	14	and	and	CCONJ
ejpam-5387	266	15	y.	y.	PROPN
ejpam-5387	266	16	t.	t.	PROPN
ejpam-5387	266	17	toh	toh	PROPN
ejpam-5387	266	18	.	.	PUNCT
ejpam-5387	267	1	on	on	ADP
ejpam-5387	267	2	the	the	DET
ejpam-5387	267	3	new	new	ADJ
ejpam-5387	267	4	properties	property	NOUN
ejpam-5387	267	5	of	of	ADP
ejpam-5387	267	6	caputofabrizio	caputofabrizio	NOUN
ejpam-5387	267	7	operator	operator	NOUN
ejpam-5387	267	8	and	and	CCONJ
ejpam-5387	267	9	its	its	PRON
ejpam-5387	267	10	application	application	NOUN
ejpam-5387	267	11	in	in	ADP
ejpam-5387	267	12	deriving	derive	VERB
ejpam-5387	267	13	shifted	shift	VERB
ejpam-5387	267	14	legendre	legendre	PROPN
ejpam-5387	267	15	operational	operational	ADJ
ejpam-5387	267	16	matrix	matrix	NOUN
ejpam-5387	267	17	.	.	PUNCT
ejpam-5387	268	1	appl	appl	PROPN
ejpam-5387	268	2	.	.	PUNCT
ejpam-5387	269	1	numer	numer	PROPN
ejpam-5387	269	2	.	.	PUNCT
ejpam-5387	269	3	math	math	PROPN
ejpam-5387	269	4	.	.	PUNCT
ejpam-5387	269	5	,	,	PUNCT
ejpam-5387	269	6	132:138–153	132:138–153	NUM
ejpam-5387	269	7	,	,	PUNCT
ejpam-5387	269	8	2018	2018	NUM
ejpam-5387	269	9	.	.	PUNCT
ejpam-5387	270	1	[	[	X
ejpam-5387	270	2	17	17	NUM
ejpam-5387	270	3	]	]	X
ejpam-5387	270	4	j.	j.	PROPN
ejpam-5387	270	5	losada	losada	PROPN
ejpam-5387	270	6	and	and	CCONJ
ejpam-5387	270	7	j.	j.	PROPN
ejpam-5387	270	8	j.	j.	PROPN
ejpam-5387	270	9	nieto	nieto	PROPN
ejpam-5387	270	10	.	.	PUNCT
ejpam-5387	271	1	properties	property	NOUN
ejpam-5387	271	2	of	of	ADP
ejpam-5387	271	3	a	a	DET
ejpam-5387	271	4	new	new	ADJ
ejpam-5387	271	5	fractional	fractional	ADJ
ejpam-5387	271	6	derivative	derivative	NOUN
ejpam-5387	271	7	without	without	ADP
ejpam-5387	271	8	singular	singular	ADJ
ejpam-5387	271	9	kernel	kernel	PROPN
ejpam-5387	271	10	.	.	PUNCT
ejpam-5387	272	1	progr	progr	NOUN
ejpam-5387	272	2	.	.	PUNCT
ejpam-5387	273	1	fract	fract	PROPN
ejpam-5387	273	2	.	.	PUNCT
ejpam-5387	274	1	differ	differ	VERB
ejpam-5387	274	2	.	.	PUNCT
ejpam-5387	275	1	appl	appl	PROPN
ejpam-5387	275	2	.	.	PROPN
ejpam-5387	275	3	,	,	PUNCT
ejpam-5387	275	4	1:87–92	1:87–92	NUM
ejpam-5387	275	5	,	,	PUNCT
ejpam-5387	275	6	2015	2015	NUM
ejpam-5387	275	7	.	.	PUNCT
ejpam-5387	276	1	[	[	X
ejpam-5387	276	2	18	18	NUM
ejpam-5387	276	3	]	]	X
ejpam-5387	276	4	s.	s.	PROPN
ejpam-5387	276	5	momani	momani	PROPN
ejpam-5387	276	6	,	,	PUNCT
ejpam-5387	276	7	n.	n.	PROPN
ejpam-5387	276	8	djeddi	djeddi	PROPN
ejpam-5387	276	9	,	,	PUNCT
ejpam-5387	276	10	m.	m.	NOUN
ejpam-5387	276	11	al	al	PROPN
ejpam-5387	276	12	-	-	PUNCT
ejpam-5387	276	13	smadi	smadi	NOUN
ejpam-5387	276	14	,	,	PUNCT
ejpam-5387	276	15	and	and	CCONJ
ejpam-5387	276	16	s.	s.	PROPN
ejpam-5387	276	17	al	al	PROPN
ejpam-5387	276	18	-	-	PUNCT
ejpam-5387	276	19	omari	omari	PROPN
ejpam-5387	276	20	.	.	PUNCT
ejpam-5387	277	1	numerical	numerical	PROPN
ejpam-5387	277	2	investigation	investigation	PROPN
ejpam-5387	277	3	for	for	ADP
ejpam-5387	277	4	caputo	caputo	PROPN
ejpam-5387	277	5	-	-	PUNCT
ejpam-5387	277	6	fabrizio	fabrizio	PROPN
ejpam-5387	277	7	fractional	fractional	PROPN
ejpam-5387	277	8	riccati	riccati	PROPN
ejpam-5387	277	9	and	and	CCONJ
ejpam-5387	277	10	bernoulli	bernoulli	PROPN
ejpam-5387	277	11	equations	equation	NOUN
ejpam-5387	277	12	using	use	VERB
ejpam-5387	277	13	iterative	iterative	NOUN
ejpam-5387	277	14	reproducing	reproduce	VERB
ejpam-5387	277	15	kernel	kernel	NOUN
ejpam-5387	277	16	method	method	NOUN
ejpam-5387	277	17	.	.	PUNCT
ejpam-5387	278	1	appl	appl	PROPN
ejpam-5387	278	2	.	.	PUNCT
ejpam-5387	279	1	numer	numer	PROPN
ejpam-5387	279	2	.	.	PUNCT
ejpam-5387	279	3	math	math	PROPN
ejpam-5387	279	4	.	.	PUNCT
ejpam-5387	279	5	,	,	PUNCT
ejpam-5387	279	6	170:418–434	170:418–434	NUM
ejpam-5387	279	7	,	,	PUNCT
ejpam-5387	279	8	2021	2021	NUM
ejpam-5387	279	9	.	.	PUNCT
ejpam-5387	280	1	[	[	X
ejpam-5387	280	2	19	19	NUM
ejpam-5387	280	3	]	]	X
ejpam-5387	280	4	c.	c.	PROPN
ejpam-5387	280	5	mufudza	mufudza	PROPN
ejpam-5387	280	6	,	,	PUNCT
ejpam-5387	280	7	s.	s.	PROPN
ejpam-5387	280	8	walter	walter	PROPN
ejpam-5387	280	9	,	,	PUNCT
ejpam-5387	280	10	and	and	CCONJ
ejpam-5387	280	11	e.	e.	PROPN
ejpam-5387	280	12	t.	t.	PROPN
ejpam-5387	280	13	chiyaka	chiyaka	PROPN
ejpam-5387	280	14	.	.	PUNCT
ejpam-5387	281	1	assessing	assess	VERB
ejpam-5387	281	2	the	the	DET
ejpam-5387	281	3	effects	effect	NOUN
ejpam-5387	281	4	of	of	ADP
ejpam-5387	281	5	estrogen	estrogen	NOUN
ejpam-5387	281	6	on	on	ADP
ejpam-5387	281	7	the	the	DET
ejpam-5387	281	8	dynamics	dynamic	NOUN
ejpam-5387	281	9	of	of	ADP
ejpam-5387	281	10	chemo	chemo	NOUN
ejpam-5387	281	11	-	-	PUNCT
ejpam-5387	281	12	virotherapy	virotherapy	NOUN
ejpam-5387	281	13	cancer	cancer	NOUN
ejpam-5387	281	14	.	.	PUNCT
ejpam-5387	282	1	comput	comput	NOUN
ejpam-5387	282	2	.	.	PUNCT
ejpam-5387	283	1	math	math	NOUN
ejpam-5387	283	2	.	.	PUNCT
ejpam-5387	284	1	methods	method	NOUN
ejpam-5387	284	2	med	me	VERB
ejpam-5387	284	3	.	.	PROPN
ejpam-5387	284	4	,	,	PUNCT
ejpam-5387	284	5	473572:1–15	473572:1–15	NUM
ejpam-5387	284	6	,	,	PUNCT
ejpam-5387	284	7	2012	2012	NUM
ejpam-5387	284	8	.	.	PUNCT
ejpam-5387	285	1	[	[	X
ejpam-5387	285	2	20	20	NUM
ejpam-5387	285	3	]	]	PUNCT
ejpam-5387	285	4	s.	s.	PROPN
ejpam-5387	285	5	i.	i.	PROPN
ejpam-5387	285	6	oke	oke	PROPN
ejpam-5387	285	7	,	,	PUNCT
ejpam-5387	285	8	m.	m.	PROPN
ejpam-5387	285	9	b.	b.	PROPN
ejpam-5387	285	10	matadi	matadi	PROPN
ejpam-5387	285	11	,	,	PUNCT
ejpam-5387	285	12	and	and	CCONJ
ejpam-5387	285	13	s.	s.	PROPN
ejpam-5387	285	14	s.	s.	PROPN
ejpam-5387	285	15	xulu	xulu	VERB
ejpam-5387	285	16	.	.	PUNCT
ejpam-5387	286	1	optimal	optimal	ADJ
ejpam-5387	286	2	control	control	NOUN
ejpam-5387	286	3	analysis	analysis	NOUN
ejpam-5387	286	4	of	of	ADP
ejpam-5387	286	5	a	a	DET
ejpam-5387	286	6	mathematical	mathematical	ADJ
ejpam-5387	286	7	model	model	NOUN
ejpam-5387	286	8	for	for	ADP
ejpam-5387	286	9	breast	breast	NOUN
ejpam-5387	286	10	cancer	cancer	NOUN
ejpam-5387	286	11	.	.	PUNCT
ejpam-5387	287	1	math	math	NOUN
ejpam-5387	287	2	.	.	PUNCT
ejpam-5387	288	1	comput	comput	NOUN
ejpam-5387	288	2	.	.	PUNCT
ejpam-5387	289	1	appl	appl	PROPN
ejpam-5387	289	2	.	.	PROPN
ejpam-5387	289	3	,	,	PUNCT
ejpam-5387	289	4	21:1–16	21:1–16	NUM
ejpam-5387	289	5	,	,	PUNCT
ejpam-5387	289	6	2018	2018	NUM
ejpam-5387	289	7	.	.	PUNCT
ejpam-5387	290	1	references	reference	NOUN
ejpam-5387	290	2	2719	2719	NUM
ejpam-5387	290	3	[	[	X
ejpam-5387	290	4	21	21	NUM
ejpam-5387	290	5	]	]	X
ejpam-5387	290	6	f.	f.	PROPN
ejpam-5387	290	7	okose	okose	PROPN
ejpam-5387	290	8	,	,	PUNCT
ejpam-5387	290	9	m.	m.	NOUN
ejpam-5387	290	10	t.	t.	PROPN
ejpam-5387	290	11	senel	senel	PROPN
ejpam-5387	290	12	,	,	PUNCT
ejpam-5387	290	13	and	and	CCONJ
ejpam-5387	290	14	r.	r.	PROPN
ejpam-5387	290	15	habbireeh	habbireeh	PROPN
ejpam-5387	290	16	.	.	PUNCT
ejpam-5387	291	1	fractional	fractional	ADJ
ejpam-5387	291	2	-	-	PUNCT
ejpam-5387	291	3	order	order	NOUN
ejpam-5387	291	4	mathematical	mathematical	ADJ
ejpam-5387	291	5	modeling	modeling	NOUN
ejpam-5387	291	6	of	of	ADP
ejpam-5387	291	7	cancer	cancer	NOUN
ejpam-5387	291	8	cells	cell	NOUN
ejpam-5387	291	9	-	-	PUNCT
ejpam-5387	291	10	cancer	cancer	NOUN
ejpam-5387	291	11	stem	stem	NOUN
ejpam-5387	291	12	cells	cell	NOUN
ejpam-5387	291	13	-	-	PUNCT
ejpam-5387	291	14	immune	immune	ADJ
ejpam-5387	291	15	system	system	NOUN
ejpam-5387	291	16	interaction	interaction	NOUN
ejpam-5387	291	17	with	with	ADP
ejpam-5387	291	18	chemotherapy	chemotherapy	NOUN
ejpam-5387	291	19	.	.	PUNCT
ejpam-5387	292	1	math	math	PROPN
ejpam-5387	292	2	.	.	PUNCT
ejpam-5387	293	1	model	model	PROPN
ejpam-5387	293	2	.	.	PUNCT
ejpam-5387	294	1	numer	numer	PROPN
ejpam-5387	294	2	.	.	PUNCT
ejpam-5387	295	1	simul	simul	PROPN
ejpam-5387	295	2	.	.	PUNCT
ejpam-5387	295	3	appl	appl	PROPN
ejpam-5387	295	4	.	.	PROPN
ejpam-5387	295	5	,	,	PUNCT
ejpam-5387	295	6	1:67–83	1:67–83	NUM
ejpam-5387	295	7	,	,	PUNCT
ejpam-5387	295	8	2021	2021	NUM
ejpam-5387	295	9	.	.	PUNCT
ejpam-5387	296	1	[	[	X
ejpam-5387	296	2	22	22	NUM
ejpam-5387	296	3	]	]	PUNCT
ejpam-5387	296	4	k.	k.	PROPN
ejpam-5387	296	5	m.	m.	PROPN
ejpam-5387	296	6	owolabi	owolabi	NOUN
ejpam-5387	296	7	and	and	CCONJ
ejpam-5387	296	8	a.	a.	NOUN
ejpam-5387	296	9	atangana	atangana	PROPN
ejpam-5387	296	10	.	.	PUNCT
ejpam-5387	297	1	analysis	analysis	NOUN
ejpam-5387	297	2	and	and	CCONJ
ejpam-5387	297	3	application	application	NOUN
ejpam-5387	297	4	of	of	ADP
ejpam-5387	297	5	new	new	ADJ
ejpam-5387	297	6	fractional	fractional	ADJ
ejpam-5387	297	7	adamsbashforth	adamsbashforth	NOUN
ejpam-5387	297	8	scheme	scheme	NOUN
ejpam-5387	297	9	with	with	ADP
ejpam-5387	297	10	caputo	caputo	PROPN
ejpam-5387	297	11	-	-	PUNCT
ejpam-5387	297	12	fabrizio	fabrizio	PROPN
ejpam-5387	297	13	derivative	derivative	NOUN
ejpam-5387	297	14	.	.	PUNCT
ejpam-5387	298	1	chaos	chaos	NOUN
ejpam-5387	298	2	soliton	soliton	NOUN
ejpam-5387	298	3	fract	fract	NOUN
ejpam-5387	298	4	.	.	PUNCT
ejpam-5387	298	5	,	,	PUNCT
ejpam-5387	298	6	105:111	105:111	NUM
ejpam-5387	298	7	–	–	PUNCT
ejpam-5387	298	8	119	119	NUM
ejpam-5387	298	9	,	,	PUNCT
ejpam-5387	298	10	2017	2017	NUM
ejpam-5387	298	11	.	.	PUNCT
ejpam-5387	299	1	[	[	X
ejpam-5387	299	2	23	23	NUM
ejpam-5387	299	3	]	]	PUNCT
ejpam-5387	299	4	m.	m.	NOUN
ejpam-5387	299	5	a.	a.	PROPN
ejpam-5387	299	6	rois	rois	PROPN
ejpam-5387	299	7	,	,	PUNCT
ejpam-5387	299	8	fatmawati	fatmawati	NOUN
ejpam-5387	299	9	,	,	PUNCT
ejpam-5387	299	10	and	and	CCONJ
ejpam-5387	299	11	c.	c.	PROPN
ejpam-5387	299	12	alfiniyah	alfiniyah	PROPN
ejpam-5387	299	13	.	.	PUNCT
ejpam-5387	300	1	optimal	optimal	ADJ
ejpam-5387	300	2	control	control	NOUN
ejpam-5387	300	3	of	of	ADP
ejpam-5387	300	4	covid-19	covid-19	PROPN
ejpam-5387	300	5	model	model	NOUN
ejpam-5387	300	6	with	with	ADP
ejpam-5387	300	7	partial	partial	ADJ
ejpam-5387	300	8	comorbidity	comorbidity	NOUN
ejpam-5387	300	9	sub	sub	NOUN
ejpam-5387	300	10	-	-	NOUN
ejpam-5387	300	11	populations	population	NOUN
ejpam-5387	300	12	and	and	CCONJ
ejpam-5387	300	13	two	two	NUM
ejpam-5387	300	14	isolation	isolation	NOUN
ejpam-5387	300	15	treatments	treatment	NOUN
ejpam-5387	300	16	in	in	ADP
ejpam-5387	300	17	indonesia	indonesia	PROPN
ejpam-5387	300	18	.	.	PUNCT
ejpam-5387	301	1	eur	eur	PROPN
ejpam-5387	301	2	.	.	PUNCT
ejpam-5387	302	1	j.	j.	PROPN
ejpam-5387	302	2	of	of	ADP
ejpam-5387	302	3	pure	pure	ADJ
ejpam-5387	302	4	and	and	CCONJ
ejpam-5387	302	5	appl	appl	ADJ
ejpam-5387	302	6	.	.	PUNCT
ejpam-5387	303	1	maths	maths	PROPN
ejpam-5387	303	2	.	.	PUNCT
ejpam-5387	303	3	,	,	PUNCT
ejpam-5387	303	4	16:523–537	16:523–537	PROPN
ejpam-5387	303	5	,	,	PUNCT
ejpam-5387	303	6	2023	2023	NUM
ejpam-5387	303	7	.	.	PUNCT
ejpam-5387	304	1	[	[	X
ejpam-5387	304	2	24	24	NUM
ejpam-5387	304	3	]	]	X
ejpam-5387	304	4	a	a	PRON
ejpam-5387	304	5	.	.	PUNCT
ejpam-5387	304	6	yousef	yousef	PROPN
ejpam-5387	304	7	,	,	PUNCT
ejpam-5387	304	8	f.	f.	PROPN
ejpam-5387	304	9	bozkurt	bozkurt	PROPN
ejpam-5387	304	10	,	,	PUNCT
ejpam-5387	304	11	and	and	CCONJ
ejpam-5387	304	12	t.	t.	PROPN
ejpam-5387	304	13	abdeljawad	abdeljawad	NOUN
ejpam-5387	304	14	.	.	PUNCT
ejpam-5387	305	1	mathematical	mathematical	ADJ
ejpam-5387	305	2	modeling	modeling	NOUN
ejpam-5387	305	3	of	of	ADP
ejpam-5387	305	4	the	the	DET
ejpam-5387	305	5	immunechemotherapeutic	immunechemotherapeutic	ADJ
ejpam-5387	305	6	treatment	treatment	NOUN
ejpam-5387	305	7	of	of	ADP
ejpam-5387	305	8	breast	breast	NOUN
ejpam-5387	305	9	cancer	cancer	NOUN
ejpam-5387	305	10	under	under	ADP
ejpam-5387	305	11	some	some	DET
ejpam-5387	305	12	control	control	NOUN
ejpam-5387	305	13	parameters	parameter	NOUN
ejpam-5387	305	14	.	.	PUNCT
ejpam-5387	306	1	adva	adva	PROPN
ejpam-5387	306	2	.	.	PUNCT
ejpam-5387	307	1	differ	differ	VERB
ejpam-5387	307	2	.	.	PUNCT
ejpam-5387	308	1	equs	equs	PROPN
ejpam-5387	308	2	.	.	PROPN
ejpam-5387	308	3	,	,	PUNCT
ejpam-5387	308	4	696:1–25	696:1–25	NUM
ejpam-5387	308	5	,	,	PUNCT
ejpam-5387	308	6	2020	2020	NUM
ejpam-5387	308	7	.	.	PUNCT
ejpam-5387	309	1	[	[	X
ejpam-5387	309	2	25	25	NUM
ejpam-5387	309	3	]	]	PUNCT
ejpam-5387	309	4	t.	t.	PROPN
ejpam-5387	309	5	zhang	zhang	PROPN
ejpam-5387	309	6	and	and	CCONJ
ejpam-5387	309	7	y.	y.	PROPN
ejpam-5387	309	8	li	li	PROPN
ejpam-5387	309	9	.	.	PROPN
ejpam-5387	309	10	exponential	exponential	PROPN
ejpam-5387	309	11	euler	euler	PROPN
ejpam-5387	309	12	scheme	scheme	NOUN
ejpam-5387	309	13	of	of	ADP
ejpam-5387	309	14	multi	multi	ADJ
ejpam-5387	309	15	-	-	ADJ
ejpam-5387	309	16	delay	delay	ADJ
ejpam-5387	309	17	caputo	caputo	PROPN
ejpam-5387	309	18	-	-	PUNCT
ejpam-5387	309	19	fabrizio	fabrizio	PROPN
ejpam-5387	309	20	fractional	fractional	ADJ
ejpam-5387	309	21	-	-	PUNCT
ejpam-5387	309	22	order	order	NOUN
ejpam-5387	309	23	differential	differential	ADJ
ejpam-5387	309	24	equations	equation	NOUN
ejpam-5387	309	25	.	.	PUNCT
ejpam-5387	310	1	appl	appl	PROPN
ejpam-5387	310	2	.	.	PROPN
ejpam-5387	310	3	math	math	PROPN
ejpam-5387	310	4	.	.	PUNCT
ejpam-5387	311	1	lett	lett	PROPN
ejpam-5387	311	2	.	.	PROPN
ejpam-5387	311	3	,	,	PUNCT
ejpam-5387	311	4	124:1–15	124:1–15	NUM
ejpam-5387	311	5	,	,	PUNCT
ejpam-5387	311	6	2022	2022	NUM
ejpam-5387	311	7	.	.	PUNCT