id	sid	tid	token	lemma	pos
ejpam-5476	1	1	european	european	PROPN
ejpam-5476	1	2	journal	journal	PROPN
ejpam-5476	1	3	of	of	ADP
ejpam-5476	1	4	pure	pure	ADJ
ejpam-5476	1	5	and	and	CCONJ
ejpam-5476	1	6	applied	apply	VERB
ejpam-5476	1	7	mathematics	mathematic	NOUN
ejpam-5476	1	8	vol	vol	NOUN
ejpam-5476	1	9	.	.	PROPN
ejpam-5476	2	1	17	17	NUM
ejpam-5476	2	2	,	,	PUNCT
ejpam-5476	2	3	no	no	INTJ
ejpam-5476	2	4	.	.	NOUN
ejpam-5476	2	5	4	4	NUM
ejpam-5476	2	6	,	,	PUNCT
ejpam-5476	2	7	2024	2024	NUM
ejpam-5476	2	8	,	,	PUNCT
ejpam-5476	2	9	3539	3539	NUM
ejpam-5476	2	10	-	-	SYM
ejpam-5476	2	11	3556	3556	NUM
ejpam-5476	2	12	issn	issn	PROPN
ejpam-5476	2	13	1307	1307	NUM
ejpam-5476	2	14	-	-	SYM
ejpam-5476	2	15	5543	5543	NUM
ejpam-5476	2	16	–	–	PUNCT
ejpam-5476	3	1	ejpam.com	ejpam.com	X
ejpam-5476	3	2	published	publish	VERB
ejpam-5476	3	3	by	by	ADP
ejpam-5476	3	4	new	new	PROPN
ejpam-5476	3	5	york	york	PROPN
ejpam-5476	3	6	business	business	PROPN
ejpam-5476	3	7	global	global	PROPN
ejpam-5476	3	8	bernstein	bernstein	PROPN
ejpam-5476	3	9	polynomials	polynomial	NOUN
ejpam-5476	3	10	for	for	ADP
ejpam-5476	3	11	solving	solve	VERB
ejpam-5476	3	12	fractional	fractional	ADJ
ejpam-5476	3	13	differential	differential	ADJ
ejpam-5476	3	14	equations	equation	NOUN
ejpam-5476	3	15	with	with	ADP
ejpam-5476	3	16	two	two	NUM
ejpam-5476	3	17	parameters	parameter	NOUN
ejpam-5476	3	18	a.k	a.k	PROPN
ejpam-5476	3	19	.	.	PROPN
ejpam-5476	3	20	alomari1	alomari1	PROPN
ejpam-5476	3	21	,	,	PUNCT
ejpam-5476	3	22	abdul	abdul	PROPN
ejpam-5476	3	23	rhman	rhman	PROPN
ejpam-5476	3	24	al	al	PROPN
ejpam-5476	3	25	-	-	PUNCT
ejpam-5476	3	26	shatnawi1	shatnawi1	PROPN
ejpam-5476	3	27	,	,	PUNCT
ejpam-5476	3	28	adel	adel	PROPN
ejpam-5476	3	29	almalki2	almalki2	PROPN
ejpam-5476	3	30	,	,	PUNCT
ejpam-5476	3	31	nidal	nidal	ADJ
ejpam-5476	3	32	anakira3,4,∗	anakira3,4,∗	ADJ
ejpam-5476	3	33	1	1	NUM
ejpam-5476	3	34	department	department	NOUN
ejpam-5476	3	35	of	of	ADP
ejpam-5476	3	36	mathematics	mathematic	NOUN
ejpam-5476	3	37	,	,	PUNCT
ejpam-5476	3	38	yarmouk	yarmouk	CCONJ
ejpam-5476	3	39	university	university	NOUN
ejpam-5476	3	40	,	,	PUNCT
ejpam-5476	3	41	irbid	irbid	PROPN
ejpam-5476	3	42	,	,	PUNCT
ejpam-5476	3	43	jordan	jordan	PROPN
ejpam-5476	3	44	2	2	NUM
ejpam-5476	3	45	al	al	PROPN
ejpam-5476	3	46	-	-	PUNCT
ejpam-5476	3	47	gunfudah	gunfudah	PROPN
ejpam-5476	3	48	university	university	PROPN
ejpam-5476	3	49	college	college	NOUN
ejpam-5476	3	50	,	,	PUNCT
ejpam-5476	3	51	umm	umm	INTJ
ejpam-5476	3	52	alqura	alqura	NOUN
ejpam-5476	3	53	university	university	PROPN
ejpam-5476	3	54	,	,	PUNCT
ejpam-5476	3	55	mecca	mecca	PROPN
ejpam-5476	3	56	21955	21955	NUM
ejpam-5476	3	57	,	,	PUNCT
ejpam-5476	3	58	saudi	saudi	PROPN
ejpam-5476	3	59	arabia	arabia	PROPN
ejpam-5476	3	60	3	3	NUM
ejpam-5476	3	61	faculty	faculty	NOUN
ejpam-5476	3	62	of	of	ADP
ejpam-5476	3	63	education	education	NOUN
ejpam-5476	3	64	and	and	CCONJ
ejpam-5476	3	65	arts	art	NOUN
ejpam-5476	3	66	,	,	PUNCT
ejpam-5476	3	67	sohar	sohar	PROPN
ejpam-5476	3	68	university	university	PROPN
ejpam-5476	3	69	,	,	PUNCT
ejpam-5476	3	70	sohar	sohar	PROPN
ejpam-5476	3	71	3111	3111	PROPN
ejpam-5476	3	72	,	,	PUNCT
ejpam-5476	3	73	oman	oman	NOUN
ejpam-5476	3	74	4	4	NUM
ejpam-5476	3	75	jadara	jadara	PROPN
ejpam-5476	3	76	university	university	PROPN
ejpam-5476	3	77	research	research	NOUN
ejpam-5476	3	78	center	center	NOUN
ejpam-5476	3	79	,	,	PUNCT
ejpam-5476	3	80	jadara	jadara	PROPN
ejpam-5476	3	81	university	university	PROPN
ejpam-5476	3	82	,	,	PUNCT
ejpam-5476	3	83	jordan	jordan	PROPN
ejpam-5476	3	84	abstract	abstract	PROPN
ejpam-5476	3	85	.	.	PUNCT
ejpam-5476	4	1	this	this	DET
ejpam-5476	4	2	work	work	NOUN
ejpam-5476	4	3	presents	present	VERB
ejpam-5476	4	4	a	a	DET
ejpam-5476	4	5	general	general	ADJ
ejpam-5476	4	6	framework	framework	NOUN
ejpam-5476	4	7	for	for	ADP
ejpam-5476	4	8	solving	solve	VERB
ejpam-5476	4	9	generalized	generalize	VERB
ejpam-5476	4	10	fractional	fractional	ADJ
ejpam-5476	4	11	differential	differential	ADJ
ejpam-5476	4	12	equations	equation	NOUN
ejpam-5476	4	13	based	base	VERB
ejpam-5476	4	14	on	on	ADP
ejpam-5476	4	15	operational	operational	ADJ
ejpam-5476	4	16	matrices	matrix	NOUN
ejpam-5476	4	17	of	of	ADP
ejpam-5476	4	18	the	the	DET
ejpam-5476	4	19	generalized	generalized	ADJ
ejpam-5476	4	20	bernstein	bernstein	PROPN
ejpam-5476	4	21	polynomials	polynomial	NOUN
ejpam-5476	4	22	.	.	PUNCT
ejpam-5476	5	1	this	this	DET
ejpam-5476	5	2	method	method	NOUN
ejpam-5476	5	3	effectively	effectively	ADV
ejpam-5476	5	4	obtains	obtain	VERB
ejpam-5476	5	5	approximate	approximate	ADJ
ejpam-5476	5	6	analytical	analytical	ADJ
ejpam-5476	5	7	solutions	solution	NOUN
ejpam-5476	5	8	of	of	ADP
ejpam-5476	5	9	many	many	ADJ
ejpam-5476	5	10	fractional	fractional	ADJ
ejpam-5476	5	11	differential	differential	ADJ
ejpam-5476	5	12	equations	equation	NOUN
ejpam-5476	5	13	.	.	PUNCT
ejpam-5476	6	1	the	the	DET
ejpam-5476	6	2	generalized	generalized	ADJ
ejpam-5476	6	3	fractional	fractional	ADJ
ejpam-5476	6	4	derivative	derivative	NOUN
ejpam-5476	6	5	of	of	ADP
ejpam-5476	6	6	the	the	DET
ejpam-5476	6	7	caputo	caputo	PROPN
ejpam-5476	6	8	type	type	NOUN
ejpam-5476	6	9	with	with	ADP
ejpam-5476	6	10	two	two	NUM
ejpam-5476	6	11	parameters	parameter	NOUN
ejpam-5476	6	12	and	and	CCONJ
ejpam-5476	6	13	its	its	PRON
ejpam-5476	6	14	properties	property	NOUN
ejpam-5476	6	15	are	be	AUX
ejpam-5476	6	16	studied	study	VERB
ejpam-5476	6	17	.	.	PUNCT
ejpam-5476	7	1	using	use	VERB
ejpam-5476	7	2	orthonormal	orthonormal	ADJ
ejpam-5476	7	3	bernstein	bernstein	NOUN
ejpam-5476	7	4	polynomials	polynomial	NOUN
ejpam-5476	7	5	has	have	AUX
ejpam-5476	7	6	led	lead	VERB
ejpam-5476	7	7	to	to	ADP
ejpam-5476	7	8	the	the	DET
ejpam-5476	7	9	development	development	NOUN
ejpam-5476	7	10	of	of	ADP
ejpam-5476	7	11	fractional	fractional	ADJ
ejpam-5476	7	12	polynomials	polynomial	NOUN
ejpam-5476	7	13	,	,	PUNCT
ejpam-5476	7	14	which	which	PRON
ejpam-5476	7	15	offer	offer	VERB
ejpam-5476	7	16	an	an	DET
ejpam-5476	7	17	approximate	approximate	ADJ
ejpam-5476	7	18	solution	solution	NOUN
ejpam-5476	7	19	for	for	ADP
ejpam-5476	7	20	ordinary	ordinary	ADJ
ejpam-5476	7	21	fractional	fractional	ADJ
ejpam-5476	7	22	differential	differential	ADJ
ejpam-5476	7	23	equations	equation	NOUN
ejpam-5476	7	24	.	.	PUNCT
ejpam-5476	8	1	the	the	DET
ejpam-5476	8	2	approach	approach	NOUN
ejpam-5476	8	3	employs	employ	VERB
ejpam-5476	8	4	the	the	DET
ejpam-5476	8	5	generalized	generalize	VERB
ejpam-5476	8	6	orthogonal	orthogonal	ADJ
ejpam-5476	8	7	bernstein	bernstein	PROPN
ejpam-5476	8	8	polynomials	polynomials	PROPN
ejpam-5476	8	9	(	(	PUNCT
ejpam-5476	8	10	fobps	fobps	NOUN
ejpam-5476	8	11	)	)	PUNCT
ejpam-5476	8	12	and	and	CCONJ
ejpam-5476	8	13	constructs	construct	VERB
ejpam-5476	8	14	their	their	PRON
ejpam-5476	8	15	operational	operational	ADJ
ejpam-5476	8	16	matrices	matrix	NOUN
ejpam-5476	8	17	for	for	ADP
ejpam-5476	8	18	fractional	fractional	ADJ
ejpam-5476	8	19	integration	integration	NOUN
ejpam-5476	8	20	and	and	CCONJ
ejpam-5476	8	21	derivative	derivative	NOUN
ejpam-5476	8	22	in	in	ADP
ejpam-5476	8	23	the	the	DET
ejpam-5476	8	24	generalized	generalize	VERB
ejpam-5476	8	25	caputo	caputo	PROPN
ejpam-5476	8	26	sense	sense	NOUN
ejpam-5476	8	27	to	to	PART
ejpam-5476	8	28	achieve	achieve	VERB
ejpam-5476	8	29	this	this	DET
ejpam-5476	8	30	objective	objective	NOUN
ejpam-5476	8	31	.	.	PUNCT
ejpam-5476	9	1	operational	operational	ADJ
ejpam-5476	9	2	matrices	matrix	NOUN
ejpam-5476	9	3	convert	convert	VERB
ejpam-5476	9	4	ordinary	ordinary	ADJ
ejpam-5476	9	5	differential	differential	ADJ
ejpam-5476	9	6	equations	equation	NOUN
ejpam-5476	9	7	into	into	ADP
ejpam-5476	9	8	a	a	DET
ejpam-5476	9	9	system	system	NOUN
ejpam-5476	9	10	of	of	ADP
ejpam-5476	9	11	algebraic	algebraic	ADJ
ejpam-5476	9	12	equations	equation	NOUN
ejpam-5476	9	13	,	,	PUNCT
ejpam-5476	9	14	which	which	PRON
ejpam-5476	9	15	can	can	AUX
ejpam-5476	9	16	be	be	AUX
ejpam-5476	9	17	solved	solve	VERB
ejpam-5476	9	18	using	use	VERB
ejpam-5476	9	19	newton	newton	PROPN
ejpam-5476	9	20	’s	’s	PART
ejpam-5476	9	21	method	method	NOUN
ejpam-5476	9	22	.	.	PUNCT
ejpam-5476	10	1	the	the	DET
ejpam-5476	10	2	convergence	convergence	NOUN
ejpam-5476	10	3	analysis	analysis	NOUN
ejpam-5476	10	4	and	and	CCONJ
ejpam-5476	10	5	error	error	NOUN
ejpam-5476	10	6	estimate	estimate	NOUN
ejpam-5476	10	7	associated	associate	VERB
ejpam-5476	10	8	with	with	ADP
ejpam-5476	10	9	the	the	DET
ejpam-5476	10	10	proposed	propose	VERB
ejpam-5476	10	11	problem	problem	NOUN
ejpam-5476	10	12	have	have	AUX
ejpam-5476	10	13	been	be	AUX
ejpam-5476	10	14	investigated	investigate	VERB
ejpam-5476	10	15	using	use	VERB
ejpam-5476	10	16	the	the	DET
ejpam-5476	10	17	approximation	approximation	NOUN
ejpam-5476	10	18	of	of	ADP
ejpam-5476	10	19	generalized	generalized	ADJ
ejpam-5476	10	20	orthogonal	orthogonal	ADJ
ejpam-5476	10	21	bernstein	bernstein	PROPN
ejpam-5476	10	22	polynomials	polynomials	PROPN
ejpam-5476	10	23	(	(	PUNCT
ejpam-5476	10	24	fobps	fobps	PROPN
ejpam-5476	10	25	)	)	PUNCT
ejpam-5476	10	26	.	.	PUNCT
ejpam-5476	11	1	the	the	DET
ejpam-5476	11	2	effect	effect	NOUN
ejpam-5476	11	3	of	of	ADP
ejpam-5476	11	4	the	the	DET
ejpam-5476	11	5	new	new	ADJ
ejpam-5476	11	6	parameters	parameter	NOUN
ejpam-5476	11	7	of	of	ADP
ejpam-5476	11	8	the	the	DET
ejpam-5476	11	9	fractional	fractional	ADJ
ejpam-5476	11	10	derivative	derivative	NOUN
ejpam-5476	11	11	is	be	AUX
ejpam-5476	11	12	presented	present	VERB
ejpam-5476	11	13	in	in	ADP
ejpam-5476	11	14	several	several	ADJ
ejpam-5476	11	15	examples	example	NOUN
ejpam-5476	11	16	.	.	PUNCT
ejpam-5476	12	1	finally	finally	ADV
ejpam-5476	12	2	,	,	PUNCT
ejpam-5476	12	3	several	several	ADJ
ejpam-5476	12	4	examples	example	NOUN
ejpam-5476	12	5	are	be	AUX
ejpam-5476	12	6	included	include	VERB
ejpam-5476	12	7	to	to	PART
ejpam-5476	12	8	clarify	clarify	VERB
ejpam-5476	12	9	the	the	DET
ejpam-5476	12	10	proposed	propose	VERB
ejpam-5476	12	11	technique	technique	NOUN
ejpam-5476	12	12	’s	’s	PART
ejpam-5476	12	13	validity	validity	NOUN
ejpam-5476	12	14	,	,	PUNCT
ejpam-5476	12	15	efficiency	efficiency	NOUN
ejpam-5476	12	16	,	,	PUNCT
ejpam-5476	12	17	and	and	CCONJ
ejpam-5476	12	18	applicability	applicability	NOUN
ejpam-5476	12	19	via	via	ADP
ejpam-5476	12	20	generalized	generalize	VERB
ejpam-5476	12	21	orthogonal	orthogonal	ADJ
ejpam-5476	12	22	bernstein	bernstein	PROPN
ejpam-5476	12	23	polynomials	polynomials	PROPN
ejpam-5476	12	24	(	(	PUNCT
ejpam-5476	12	25	fobps	fobps	NOUN
ejpam-5476	12	26	)	)	PUNCT
ejpam-5476	12	27	approximation	approximation	NOUN
ejpam-5476	12	28	.	.	PUNCT
ejpam-5476	13	1	2020	2020	NUM
ejpam-5476	13	2	mathematics	mathematic	NOUN
ejpam-5476	13	3	subject	subject	NOUN
ejpam-5476	13	4	classifications	classification	NOUN
ejpam-5476	13	5	:	:	PUNCT
ejpam-5476	13	6	26a33	26a33	NUM
ejpam-5476	13	7	,	,	PUNCT
ejpam-5476	13	8	11cxx	11cxx	PRON
ejpam-5476	13	9	,	,	PUNCT
ejpam-5476	13	10	34a08	34a08	DET
ejpam-5476	13	11	key	key	ADJ
ejpam-5476	13	12	words	word	NOUN
ejpam-5476	13	13	and	and	CCONJ
ejpam-5476	13	14	phrases	phrase	NOUN
ejpam-5476	13	15	:	:	PUNCT
ejpam-5476	13	16	generalized	generalized	ADJ
ejpam-5476	13	17	fractional	fractional	ADJ
ejpam-5476	13	18	derivative	derivative	NOUN
ejpam-5476	13	19	,	,	PUNCT
ejpam-5476	13	20	bernstein	bernstein	PROPN
ejpam-5476	13	21	polynomials	polynomials	PROPN
ejpam-5476	13	22	,	,	PUNCT
ejpam-5476	13	23	operational	operational	ADJ
ejpam-5476	13	24	matrices	matrix	NOUN
ejpam-5476	13	25	,	,	PUNCT
ejpam-5476	13	26	riccati	riccati	NOUN
ejpam-5476	13	27	equation	equation	NOUN
ejpam-5476	13	28	1	1	NUM
ejpam-5476	13	29	.	.	PUNCT
ejpam-5476	14	1	introduction	introduction	NOUN
ejpam-5476	14	2	differential	differential	NOUN
ejpam-5476	14	3	equations	equation	NOUN
ejpam-5476	14	4	are	be	AUX
ejpam-5476	14	5	an	an	DET
ejpam-5476	14	6	essential	essential	ADJ
ejpam-5476	14	7	tool	tool	NOUN
ejpam-5476	14	8	for	for	ADP
ejpam-5476	14	9	modeling	model	VERB
ejpam-5476	14	10	several	several	ADJ
ejpam-5476	14	11	phenomena	phenomenon	NOUN
ejpam-5476	14	12	in	in	ADP
ejpam-5476	14	13	sciences	science	NOUN
ejpam-5476	14	14	,	,	PUNCT
ejpam-5476	14	15	engineers	engineer	NOUN
ejpam-5476	14	16	,	,	PUNCT
ejpam-5476	14	17	and	and	CCONJ
ejpam-5476	14	18	other	other	ADJ
ejpam-5476	14	19	fields	field	NOUN
ejpam-5476	14	20	[	[	X
ejpam-5476	14	21	16	16	NUM
ejpam-5476	14	22	]	]	PUNCT
ejpam-5476	14	23	.	.	PUNCT
ejpam-5476	15	1	studying	study	VERB
ejpam-5476	15	2	this	this	DET
ejpam-5476	15	3	topic	topic	NOUN
ejpam-5476	15	4	will	will	AUX
ejpam-5476	15	5	help	help	VERB
ejpam-5476	15	6	the	the	DET
ejpam-5476	15	7	researchers	researcher	NOUN
ejpam-5476	15	8	to	to	PART
ejpam-5476	15	9	understand	understand	VERB
ejpam-5476	15	10	those	those	DET
ejpam-5476	15	11	models	model	NOUN
ejpam-5476	15	12	.	.	PUNCT
ejpam-5476	16	1	generalizing	generalize	VERB
ejpam-5476	16	2	this	this	DET
ejpam-5476	16	3	topic	topic	NOUN
ejpam-5476	16	4	from	from	ADP
ejpam-5476	16	5	natural	natural	ADJ
ejpam-5476	16	6	to	to	ADP
ejpam-5476	16	7	fractional	fractional	ADJ
ejpam-5476	16	8	derivatives	derivative	NOUN
ejpam-5476	16	9	will	will	AUX
ejpam-5476	16	10	help	help	VERB
ejpam-5476	16	11	the	the	DET
ejpam-5476	16	12	∗corresponding	∗corresponding	NOUN
ejpam-5476	16	13	author	author	NOUN
ejpam-5476	16	14	.	.	PUNCT
ejpam-5476	17	1	doi	doi	NOUN
ejpam-5476	17	2	:	:	PUNCT
ejpam-5476	17	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5476	https://doi.org/10.29020/nybg.ejpam.v17i4.5476	NOUN
ejpam-5476	17	4	email	email	NOUN
ejpam-5476	17	5	addresses	address	NOUN
ejpam-5476	17	6	:	:	PUNCT
ejpam-5476	17	7	abdalkareem@yu.edu.jo	abdalkareem@yu.edu.jo	ADJ
ejpam-5476	17	8	(	(	PUNCT
ejpam-5476	17	9	a.k	a.k	PROPN
ejpam-5476	17	10	.	.	PROPN
ejpam-5476	17	11	aloimari	aloimari	PROPN
ejpam-5476	17	12	)	)	PUNCT
ejpam-5476	17	13	,	,	PUNCT
ejpam-5476	17	14	abd1997shatnawi@gmail.com	abd1997shatnawi@gmail.com	PROPN
ejpam-5476	17	15	(	(	PUNCT
ejpam-5476	17	16	a.r	a.r	PROPN
ejpam-5476	17	17	.	.	PROPN
ejpam-5476	17	18	al	al	PROPN
ejpam-5476	17	19	-	-	PUNCT
ejpam-5476	17	20	shatnawi	shatnawi	PROPN
ejpam-5476	17	21	)	)	PUNCT
ejpam-5476	17	22	,	,	PUNCT
ejpam-5476	17	23	aaamalki@uqu.edu.sa	aaamalki@uqu.edu.sa	PROPN
ejpam-5476	17	24	(	(	PUNCT
ejpam-5476	17	25	a.	a.	PROPN
ejpam-5476	17	26	almalki	almalki	ADV
ejpam-5476	17	27	)	)	PUNCT
ejpam-5476	17	28	,	,	PUNCT
ejpam-5476	17	29	nanakira@su.edu.om	nanakira@su.edu.om	PROPN
ejpam-5476	17	30	(	(	PUNCT
ejpam-5476	17	31	n.	n.	PROPN
ejpam-5476	17	32	anakira	anakira	PROPN
ejpam-5476	17	33	)	)	PUNCT
ejpam-5476	17	34	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5476	18	1	3539	3539	NUM
ejpam-5476	18	2	copyright	copyright	NOUN
ejpam-5476	18	3	:	:	PUNCT
ejpam-5476	18	4	©	©	PROPN
ejpam-5476	18	5	2024	2024	NUM
ejpam-5476	18	6	the	the	DET
ejpam-5476	18	7	author(s	author(s	NOUN
ejpam-5476	18	8	)	)	PUNCT
ejpam-5476	18	9	.	.	PUNCT
ejpam-5476	19	1	(	(	PUNCT
ejpam-5476	19	2	cc	cc	NOUN
ejpam-5476	19	3	by	by	ADP
ejpam-5476	19	4	-	-	PUNCT
ejpam-5476	19	5	nc	nc	PROPN
ejpam-5476	19	6	4.0	4.0	NUM
ejpam-5476	19	7	)	)	PUNCT
ejpam-5476	19	8	n.	n.	PROPN
ejpam-5476	19	9	anakira	anakira	PROPN
ejpam-5476	19	10	et	et	PROPN
ejpam-5476	19	11	al	al	PROPN
ejpam-5476	19	12	.	.	PUNCT
ejpam-5476	19	13	/	/	SYM
ejpam-5476	19	14	eur	eur	PROPN
ejpam-5476	19	15	.	.	PUNCT
ejpam-5476	20	1	j.	j.	PROPN
ejpam-5476	20	2	pure	pure	PROPN
ejpam-5476	20	3	appl	appl	PROPN
ejpam-5476	20	4	.	.	PROPN
ejpam-5476	20	5	math	math	PROPN
ejpam-5476	20	6	,	,	PUNCT
ejpam-5476	20	7	17	17	NUM
ejpam-5476	20	8	(	(	PUNCT
ejpam-5476	20	9	4	4	NUM
ejpam-5476	20	10	)	)	PUNCT
ejpam-5476	20	11	(	(	PUNCT
ejpam-5476	20	12	2024	2024	NUM
ejpam-5476	20	13	)	)	PUNCT
ejpam-5476	20	14	,	,	PUNCT
ejpam-5476	20	15	3539	3539	NUM
ejpam-5476	20	16	-	-	SYM
ejpam-5476	20	17	3556	3556	NUM
ejpam-5476	20	18	3540	3540	NUM
ejpam-5476	20	19	researcher	researcher	NOUN
ejpam-5476	20	20	fit	fit	VERB
ejpam-5476	20	21	their	their	PRON
ejpam-5476	20	22	actual	actual	ADJ
ejpam-5476	20	23	data	datum	NOUN
ejpam-5476	20	24	within	within	ADP
ejpam-5476	20	25	the	the	DET
ejpam-5476	20	26	expected	expect	VERB
ejpam-5476	20	27	results	result	NOUN
ejpam-5476	20	28	using	use	VERB
ejpam-5476	20	29	a	a	DET
ejpam-5476	20	30	nonstandard	nonstandard	ADJ
ejpam-5476	20	31	derivative	derivative	NOUN
ejpam-5476	20	32	[	[	X
ejpam-5476	20	33	4	4	NUM
ejpam-5476	20	34	]	]	PUNCT
ejpam-5476	20	35	.	.	PUNCT
ejpam-5476	21	1	in	in	ADP
ejpam-5476	21	2	1695	1695	NUM
ejpam-5476	21	3	,	,	PUNCT
ejpam-5476	21	4	a	a	DET
ejpam-5476	21	5	new	new	ADJ
ejpam-5476	21	6	concept	concept	NOUN
ejpam-5476	21	7	of	of	ADP
ejpam-5476	21	8	differential	differential	ADJ
ejpam-5476	21	9	equations	equation	NOUN
ejpam-5476	21	10	appeared	appear	VERB
ejpam-5476	21	11	,	,	PUNCT
ejpam-5476	21	12	fractional	fractional	ADJ
ejpam-5476	21	13	differential	differential	ADJ
ejpam-5476	21	14	equations	equation	NOUN
ejpam-5476	21	15	,	,	PUNCT
ejpam-5476	21	16	and	and	CCONJ
ejpam-5476	21	17	it	it	PRON
ejpam-5476	21	18	became	become	VERB
ejpam-5476	21	19	the	the	DET
ejpam-5476	21	20	subject	subject	NOUN
ejpam-5476	21	21	of	of	ADP
ejpam-5476	21	22	interest	interest	NOUN
ejpam-5476	21	23	to	to	ADP
ejpam-5476	21	24	many	many	ADJ
ejpam-5476	21	25	scientists	scientist	NOUN
ejpam-5476	21	26	.	.	PUNCT
ejpam-5476	22	1	several	several	ADJ
ejpam-5476	22	2	fractional	fractional	ADJ
ejpam-5476	22	3	derivative	derivative	ADJ
ejpam-5476	22	4	models	model	NOUN
ejpam-5476	22	5	have	have	AUX
ejpam-5476	22	6	been	be	AUX
ejpam-5476	22	7	introduced	introduce	VERB
ejpam-5476	22	8	,	,	PUNCT
ejpam-5476	22	9	such	such	ADJ
ejpam-5476	22	10	as	as	ADP
ejpam-5476	22	11	leibnitz	leibnitz	PROPN
ejpam-5476	22	12	,	,	PUNCT
ejpam-5476	22	13	euler	euler	PROPN
ejpam-5476	22	14	,	,	PUNCT
ejpam-5476	22	15	fourier	fourier	NOUN
ejpam-5476	22	16	,	,	PUNCT
ejpam-5476	22	17	abel	abel	PROPN
ejpam-5476	22	18	,	,	PUNCT
ejpam-5476	22	19	liouville	liouville	PROPN
ejpam-5476	22	20	,	,	PUNCT
ejpam-5476	22	21	riemann	riemann	PROPN
ejpam-5476	22	22	,	,	PUNCT
ejpam-5476	22	23	and	and	CCONJ
ejpam-5476	22	24	hadamard	hadamard	ADJ
ejpam-5476	23	1	[	[	X
ejpam-5476	23	2	12	12	NUM
ejpam-5476	23	3	,	,	PUNCT
ejpam-5476	23	4	13	13	NUM
ejpam-5476	23	5	,	,	PUNCT
ejpam-5476	23	6	18	18	NUM
ejpam-5476	23	7	,	,	PUNCT
ejpam-5476	23	8	19	19	NUM
ejpam-5476	23	9	,	,	PUNCT
ejpam-5476	23	10	42	42	NUM
ejpam-5476	23	11	]	]	PUNCT
ejpam-5476	23	12	.	.	PUNCT
ejpam-5476	24	1	the	the	DET
ejpam-5476	24	2	difference	difference	NOUN
ejpam-5476	24	3	between	between	ADP
ejpam-5476	24	4	them	they	PRON
ejpam-5476	24	5	is	be	AUX
ejpam-5476	24	6	the	the	DET
ejpam-5476	24	7	kernel	kernel	NOUN
ejpam-5476	24	8	that	that	PRON
ejpam-5476	24	9	used	use	VERB
ejpam-5476	24	10	[	[	X
ejpam-5476	24	11	1	1	NUM
ejpam-5476	24	12	,	,	PUNCT
ejpam-5476	24	13	2	2	NUM
ejpam-5476	24	14	,	,	PUNCT
ejpam-5476	24	15	6	6	NUM
ejpam-5476	24	16	,	,	PUNCT
ejpam-5476	24	17	11	11	NUM
ejpam-5476	24	18	,	,	PUNCT
ejpam-5476	24	19	14	14	NUM
ejpam-5476	24	20	]	]	PUNCT
ejpam-5476	24	21	.	.	PUNCT
ejpam-5476	25	1	the	the	DET
ejpam-5476	25	2	researchers	researcher	NOUN
ejpam-5476	25	3	have	have	AUX
ejpam-5476	25	4	studied	study	VERB
ejpam-5476	25	5	these	these	DET
ejpam-5476	25	6	new	new	ADJ
ejpam-5476	25	7	fractional	fractional	ADJ
ejpam-5476	25	8	operators	operator	NOUN
ejpam-5476	25	9	by	by	ADP
ejpam-5476	25	10	introducing	introduce	VERB
ejpam-5476	25	11	new	new	ADJ
ejpam-5476	25	12	definitions	definition	NOUN
ejpam-5476	25	13	and	and	CCONJ
ejpam-5476	25	14	discussing	discuss	VERB
ejpam-5476	25	15	their	their	PRON
ejpam-5476	25	16	important	important	ADJ
ejpam-5476	25	17	properties	property	NOUN
ejpam-5476	25	18	.	.	PUNCT
ejpam-5476	26	1	these	these	DET
ejpam-5476	26	2	definitions	definition	NOUN
ejpam-5476	26	3	have	have	VERB
ejpam-5476	26	4	applications	application	NOUN
ejpam-5476	26	5	in	in	ADP
ejpam-5476	26	6	various	various	ADJ
ejpam-5476	26	7	fields	field	NOUN
ejpam-5476	26	8	,	,	PUNCT
ejpam-5476	26	9	such	such	ADJ
ejpam-5476	26	10	as	as	ADP
ejpam-5476	26	11	physics	physics	NOUN
ejpam-5476	26	12	[	[	X
ejpam-5476	26	13	3	3	NUM
ejpam-5476	26	14	]	]	PUNCT
ejpam-5476	26	15	,	,	PUNCT
ejpam-5476	26	16	dynamical	dynamical	ADJ
ejpam-5476	26	17	systems	system	NOUN
ejpam-5476	26	18	,	,	PUNCT
ejpam-5476	26	19	engineering	engineering	NOUN
ejpam-5476	26	20	[	[	X
ejpam-5476	26	21	29	29	NUM
ejpam-5476	26	22	]	]	PUNCT
ejpam-5476	26	23	,	,	PUNCT
ejpam-5476	26	24	mechanics	mechanic	NOUN
ejpam-5476	26	25	,	,	PUNCT
ejpam-5476	26	26	signal	signal	ADJ
ejpam-5476	26	27	processing	processing	NOUN
ejpam-5476	26	28	,	,	PUNCT
ejpam-5476	26	29	images	image	NOUN
ejpam-5476	26	30	,	,	PUNCT
ejpam-5476	26	31	and	and	CCONJ
ejpam-5476	26	32	control	control	NOUN
ejpam-5476	26	33	theory	theory	NOUN
ejpam-5476	26	34	[	[	X
ejpam-5476	26	35	34	34	NUM
ejpam-5476	26	36	]	]	PUNCT
ejpam-5476	26	37	.	.	PUNCT
ejpam-5476	27	1	definition	definition	NOUN
ejpam-5476	27	2	1.1	1.1	NUM
ejpam-5476	27	3	.	.	PUNCT
ejpam-5476	28	1	the	the	DET
ejpam-5476	28	2	riemann	riemann	PROPN
ejpam-5476	28	3	-	-	PUNCT
ejpam-5476	28	4	liouville	liouville	VERB
ejpam-5476	28	5	fractional	fractional	ADJ
ejpam-5476	28	6	integral	integral	ADJ
ejpam-5476	28	7	of	of	ADP
ejpam-5476	28	8	order	order	NOUN
ejpam-5476	28	9	α	α	PROPN
ejpam-5476	28	10	>	>	X
ejpam-5476	28	11	0	0	NUM
ejpam-5476	28	12	is	be	AUX
ejpam-5476	28	13	defined	define	VERB
ejpam-5476	28	14	by	by	ADP
ejpam-5476	28	15	iα+a	iα+a	PROPN
ejpam-5476	28	16	=	=	SYM
ejpam-5476	28	17	1	1	NUM
ejpam-5476	28	18	γ(α	γ(α	NOUN
ejpam-5476	28	19	)	)	PUNCT
ejpam-5476	29	1	∫	∫	PROPN
ejpam-5476	29	2	t	t	PROPN
ejpam-5476	29	3	a	a	PRON
ejpam-5476	29	4	(	(	PUNCT
ejpam-5476	29	5	t−	t−	PROPN
ejpam-5476	29	6	s)α−1f(s)ds	s)α−1f(s)ds	PROPN
ejpam-5476	29	7	,	,	PUNCT
ejpam-5476	29	8	t	t	PROPN
ejpam-5476	29	9	>	>	X
ejpam-5476	29	10	a	a	DET
ejpam-5476	29	11	(	(	PUNCT
ejpam-5476	29	12	1	1	NUM
ejpam-5476	29	13	)	)	PUNCT
ejpam-5476	29	14	using	use	VERB
ejpam-5476	29	15	this	this	DET
ejpam-5476	29	16	definition	definition	NOUN
ejpam-5476	29	17	of	of	ADP
ejpam-5476	29	18	fractional	fractional	ADJ
ejpam-5476	29	19	integration	integration	NOUN
ejpam-5476	29	20	,	,	PUNCT
ejpam-5476	29	21	the	the	DET
ejpam-5476	29	22	riemann	riemann	PROPN
ejpam-5476	29	23	-	-	PUNCT
ejpam-5476	29	24	liouville	liouville	VERB
ejpam-5476	29	25	derivative	derivative	NOUN
ejpam-5476	29	26	and	and	CCONJ
ejpam-5476	29	27	the	the	DET
ejpam-5476	29	28	caputo	caputo	PROPN
ejpam-5476	29	29	fractional	fractional	PROPN
ejpam-5476	29	30	derivative	derivative	NOUN
ejpam-5476	29	31	of	of	ADP
ejpam-5476	29	32	order	order	NOUN
ejpam-5476	29	33	α	α	PROPN
ejpam-5476	29	34	>	>	X
ejpam-5476	29	35	0	0	NUM
ejpam-5476	29	36	are	be	AUX
ejpam-5476	29	37	defined	define	VERB
ejpam-5476	29	38	by	by	ADP
ejpam-5476	29	39	:	:	PUNCT
ejpam-5476	29	40	rdα	rdα	NOUN
ejpam-5476	29	41	a	a	DET
ejpam-5476	29	42	f(t	f(t	PROPN
ejpam-5476	29	43	)	)	PUNCT
ejpam-5476	29	44	=	=	SYM
ejpam-5476	29	45	1	1	NUM
ejpam-5476	29	46	γ(m−	γ(m−	PROPN
ejpam-5476	29	47	α	α	NOUN
ejpam-5476	29	48	)	)	PUNCT
ejpam-5476	29	49	dm	dm	PROPN
ejpam-5476	29	50	dtm	dtm	PROPN
ejpam-5476	29	51	(	(	PUNCT
ejpam-5476	29	52	∫	∫	PROPN
ejpam-5476	29	53	t	t	PROPN
ejpam-5476	29	54	a	a	X
ejpam-5476	29	55	(	(	PUNCT
ejpam-5476	29	56	t−	t−	PROPN
ejpam-5476	29	57	s)m−α−1f(s)ds	s)m−α−1f(s)ds	NOUN
ejpam-5476	29	58	)	)	PUNCT
ejpam-5476	29	59	(	(	PUNCT
ejpam-5476	29	60	2	2	X
ejpam-5476	29	61	)	)	PUNCT
ejpam-5476	29	62	cdα	cdα	NOUN
ejpam-5476	29	63	a+f(t	a+f(t	NOUN
ejpam-5476	29	64	)	)	PUNCT
ejpam-5476	29	65	=	=	SYM
ejpam-5476	29	66	1	1	NUM
ejpam-5476	29	67	γ(m−	γ(m−	PROPN
ejpam-5476	29	68	α	α	NUM
ejpam-5476	29	69	)	)	PUNCT
ejpam-5476	29	70	∫	∫	PROPN
ejpam-5476	29	71	t	t	PROPN
ejpam-5476	29	72	a	a	PRON
ejpam-5476	29	73	(	(	PUNCT
ejpam-5476	29	74	t−	t−	PROPN
ejpam-5476	29	75	s)m−α−1f	s)m−α−1f	PROPN
ejpam-5476	29	76	(	(	PUNCT
ejpam-5476	29	77	m)(s)ds	m)(s)ds	PROPN
ejpam-5476	29	78	(	(	PUNCT
ejpam-5476	29	79	3	3	NUM
ejpam-5476	29	80	)	)	PUNCT
ejpam-5476	29	81	respectively	respectively	ADV
ejpam-5476	29	82	,	,	PUNCT
ejpam-5476	29	83	where	where	SCONJ
ejpam-5476	29	84	m−	m−	PROPN
ejpam-5476	29	85	1	1	NUM
ejpam-5476	29	86	<	<	X
ejpam-5476	29	87	α	α	PROPN
ejpam-5476	29	88	≤	≤	NUM
ejpam-5476	29	89	m	m	PROPN
ejpam-5476	29	90	,	,	PUNCT
ejpam-5476	29	91	and	and	CCONJ
ejpam-5476	29	92	m	m	PROPN
ejpam-5476	29	93	∈	∈	PROPN
ejpam-5476	29	94	n.	n.	NOUN
ejpam-5476	30	1	the	the	DET
ejpam-5476	30	2	caputo	caputo	PROPN
ejpam-5476	30	3	definition	definition	NOUN
ejpam-5476	30	4	is	be	AUX
ejpam-5476	30	5	one	one	NUM
ejpam-5476	30	6	of	of	ADP
ejpam-5476	30	7	the	the	DET
ejpam-5476	30	8	most	most	ADV
ejpam-5476	30	9	important	important	ADJ
ejpam-5476	30	10	definitions	definition	NOUN
ejpam-5476	30	11	used	use	VERB
ejpam-5476	30	12	to	to	PART
ejpam-5476	30	13	treat	treat	VERB
ejpam-5476	30	14	many	many	ADJ
ejpam-5476	30	15	physical	physical	ADJ
ejpam-5476	30	16	problems	problem	NOUN
ejpam-5476	30	17	related	relate	VERB
ejpam-5476	30	18	to	to	ADP
ejpam-5476	30	19	fractional	fractional	ADJ
ejpam-5476	30	20	calculus	calculus	NOUN
ejpam-5476	30	21	,	,	PUNCT
ejpam-5476	30	22	due	due	ADP
ejpam-5476	30	23	to	to	ADP
ejpam-5476	30	24	its	its	PRON
ejpam-5476	30	25	properties	property	NOUN
ejpam-5476	30	26	similar	similar	ADJ
ejpam-5476	30	27	to	to	ADP
ejpam-5476	30	28	those	those	PRON
ejpam-5476	30	29	of	of	ADP
ejpam-5476	30	30	ordinary	ordinary	ADJ
ejpam-5476	30	31	derivatives	derivative	NOUN
ejpam-5476	30	32	.	.	PUNCT
ejpam-5476	31	1	the	the	DET
ejpam-5476	31	2	fractional	fractional	ADJ
ejpam-5476	31	3	integral	integral	NOUN
ejpam-5476	31	4	of	of	ADP
ejpam-5476	31	5	the	the	DET
ejpam-5476	31	6	fractional	fractional	ADJ
ejpam-5476	31	7	derivative	derivative	NOUN
ejpam-5476	31	8	is	be	AUX
ejpam-5476	31	9	given	give	VERB
ejpam-5476	31	10	by	by	ADP
ejpam-5476	31	11	iαad	iαad	NOUN
ejpam-5476	31	12	α	α	NOUN
ejpam-5476	31	13	a+f(t	a+f(t	NUM
ejpam-5476	31	14	)	)	PUNCT
ejpam-5476	31	15	=	=	SYM
ejpam-5476	31	16	f(t)−	f(t)−	PROPN
ejpam-5476	31	17	m−1∑	m−1∑	PROPN
ejpam-5476	31	18	n=0	n=0	PROPN
ejpam-5476	31	19	f	f	X
ejpam-5476	31	20	(	(	PUNCT
ejpam-5476	31	21	k)(a	k)(a	NOUN
ejpam-5476	31	22	)	)	PUNCT
ejpam-5476	31	23	k	k	NOUN
ejpam-5476	31	24	!	!	PUNCT
ejpam-5476	32	1	(	(	PUNCT
ejpam-5476	32	2	t−	t−	PROPN
ejpam-5476	32	3	a)k	a)k	ADJ
ejpam-5476	32	4	,	,	PUNCT
ejpam-5476	32	5	t	t	PROPN
ejpam-5476	32	6	>	>	X
ejpam-5476	32	7	0	0	NUM
ejpam-5476	32	8	.	.	PUNCT
ejpam-5476	33	1	(	(	PUNCT
ejpam-5476	33	2	4	4	X
ejpam-5476	33	3	)	)	PUNCT
ejpam-5476	33	4	a	a	DET
ejpam-5476	33	5	generalized	generalized	ADJ
ejpam-5476	33	6	form	form	NOUN
ejpam-5476	33	7	of	of	ADP
ejpam-5476	33	8	the	the	DET
ejpam-5476	33	9	fractional	fractional	ADJ
ejpam-5476	33	10	derivative	derivative	NOUN
ejpam-5476	33	11	is	be	AUX
ejpam-5476	33	12	with	with	ADP
ejpam-5476	33	13	two	two	NUM
ejpam-5476	33	14	parameters	parameter	NOUN
ejpam-5476	33	15	recently	recently	ADV
ejpam-5476	33	16	presented	present	VERB
ejpam-5476	33	17	by	by	ADP
ejpam-5476	33	18	udita	udita	PROPN
ejpam-5476	33	19	n.	n.	PROPN
ejpam-5476	33	20	katugampola	katugampola	PROPN
ejpam-5476	34	1	[	[	X
ejpam-5476	34	2	23	23	NUM
ejpam-5476	34	3	]	]	PUNCT
ejpam-5476	34	4	,	,	PUNCT
ejpam-5476	34	5	and	and	CCONJ
ejpam-5476	34	6	odibat	odibat	NOUN
ejpam-5476	34	7	and	and	CCONJ
ejpam-5476	34	8	baleanu	baleanu	NOUN
ejpam-5476	35	1	[	[	X
ejpam-5476	35	2	41	41	NUM
ejpam-5476	35	3	]	]	PUNCT
ejpam-5476	35	4	.	.	PUNCT
ejpam-5476	36	1	the	the	DET
ejpam-5476	36	2	new	new	ADJ
ejpam-5476	36	3	version	version	NOUN
ejpam-5476	36	4	of	of	ADP
ejpam-5476	36	5	the	the	DET
ejpam-5476	36	6	derivative	derivative	NOUN
ejpam-5476	36	7	contains	contain	VERB
ejpam-5476	36	8	two	two	NUM
ejpam-5476	36	9	parameters	parameter	NOUN
ejpam-5476	36	10	;	;	PUNCT
ejpam-5476	36	11	thus	thus	ADV
ejpam-5476	36	12	,	,	PUNCT
ejpam-5476	36	13	the	the	DET
ejpam-5476	36	14	solution	solution	NOUN
ejpam-5476	36	15	of	of	ADP
ejpam-5476	36	16	the	the	DET
ejpam-5476	36	17	fractional	fractional	ADJ
ejpam-5476	36	18	differential	differential	NOUN
ejpam-5476	36	19	equation	equation	NOUN
ejpam-5476	36	20	depends	depend	VERB
ejpam-5476	36	21	on	on	ADP
ejpam-5476	36	22	those	those	DET
ejpam-5476	36	23	parameters	parameter	NOUN
ejpam-5476	36	24	.	.	PUNCT
ejpam-5476	37	1	in	in	ADP
ejpam-5476	37	2	this	this	DET
ejpam-5476	37	3	paper	paper	NOUN
ejpam-5476	37	4	,	,	PUNCT
ejpam-5476	37	5	we	we	PRON
ejpam-5476	37	6	will	will	AUX
ejpam-5476	37	7	use	use	VERB
ejpam-5476	37	8	odibat	odibat	NOUN
ejpam-5476	37	9	and	and	CCONJ
ejpam-5476	37	10	baleanu	baleanu	ADJ
ejpam-5476	37	11	definitions	definition	NOUN
ejpam-5476	37	12	.	.	PUNCT
ejpam-5476	38	1	definition	definition	NOUN
ejpam-5476	38	2	1.2	1.2	NUM
ejpam-5476	38	3	.	.	PUNCT
ejpam-5476	39	1	the	the	DET
ejpam-5476	39	2	generalized	generalized	ADJ
ejpam-5476	39	3	fractional	fractional	ADJ
ejpam-5476	39	4	derivative	derivative	NOUN
ejpam-5476	39	5	of	of	ADP
ejpam-5476	39	6	a	a	DET
ejpam-5476	39	7	continues	continue	NOUN
ejpam-5476	39	8	function	function	NOUN
ejpam-5476	39	9	f	f	PROPN
ejpam-5476	39	10	is	be	AUX
ejpam-5476	39	11	dα	dα	NOUN
ejpam-5476	39	12	,	,	PUNCT
ejpam-5476	39	13	ρ	ρ	PROPN
ejpam-5476	39	14	a+	a+	PUNCT
ejpam-5476	39	15	f	f	NOUN
ejpam-5476	39	16	of	of	ADP
ejpam-5476	39	17	order	order	NOUN
ejpam-5476	39	18	α	α	X
ejpam-5476	39	19	>	>	X
ejpam-5476	39	20	0	0	NUM
ejpam-5476	39	21	,	,	PUNCT
ejpam-5476	39	22	and	and	CCONJ
ejpam-5476	39	23	ρ	ρ	NOUN
ejpam-5476	39	24	>	>	X
ejpam-5476	39	25	0	0	NUM
ejpam-5476	39	26	can	can	AUX
ejpam-5476	39	27	be	be	AUX
ejpam-5476	39	28	written	write	VERB
ejpam-5476	39	29	as	as	ADP
ejpam-5476	39	30	dα	dα	PROPN
ejpam-5476	39	31	,	,	PUNCT
ejpam-5476	39	32	ρ	ρ	NOUN
ejpam-5476	39	33	a+	a+	PUNCT
ejpam-5476	39	34	f(t	f(t	PROPN
ejpam-5476	39	35	)	)	PUNCT
ejpam-5476	40	1	=	=	PUNCT
ejpam-5476	40	2	ρα−m+1	ρα−m+1	PROPN
ejpam-5476	40	3	γ(m−	γ(m−	PROPN
ejpam-5476	40	4	α	α	NOUN
ejpam-5476	40	5	)	)	PUNCT
ejpam-5476	40	6	∫	∫	PROPN
ejpam-5476	40	7	t	t	PROPN
ejpam-5476	40	8	a	a	DET
ejpam-5476	40	9	sρ−1(tρ	sρ−1(tρ	NUM
ejpam-5476	40	10	−	−	PROPN
ejpam-5476	40	11	sρ)m−α−1(s1−ρ	sρ)m−α−1(s1−ρ	NOUN
ejpam-5476	40	12	d	d	X
ejpam-5476	40	13	ds	ds	ADJ
ejpam-5476	40	14	)	)	PUNCT
ejpam-5476	40	15	mf(s)ds	mf(s)ds	NOUN
ejpam-5476	40	16	,	,	PUNCT
ejpam-5476	40	17	(	(	PUNCT
ejpam-5476	40	18	5	5	NUM
ejpam-5476	40	19	)	)	PUNCT
ejpam-5476	40	20	where	where	SCONJ
ejpam-5476	40	21	a	a	DET
ejpam-5476	40	22	>	>	X
ejpam-5476	40	23	0	0	NUM
ejpam-5476	40	24	,	,	PUNCT
ejpam-5476	40	25	ρ	ρ	PROPN
ejpam-5476	40	26	>	>	X
ejpam-5476	40	27	0	0	PROPN
ejpam-5476	40	28	,	,	PUNCT
ejpam-5476	40	29	m−	m−	PROPN
ejpam-5476	40	30	1	1	NUM
ejpam-5476	40	31	<	<	X
ejpam-5476	40	32	α	α	PROPN
ejpam-5476	40	33	≤	≤	NUM
ejpam-5476	40	34	m	m	PROPN
ejpam-5476	40	35	,	,	PUNCT
ejpam-5476	40	36	and	and	CCONJ
ejpam-5476	40	37	m	m	PROPN
ejpam-5476	40	38	∈	∈	PROPN
ejpam-5476	40	39	n.	n.	PROPN
ejpam-5476	40	40	n.	n.	PROPN
ejpam-5476	40	41	anakira	anakira	PROPN
ejpam-5476	40	42	et	et	PROPN
ejpam-5476	40	43	al	al	PROPN
ejpam-5476	40	44	.	.	PUNCT
ejpam-5476	40	45	/	/	SYM
ejpam-5476	40	46	eur	eur	PROPN
ejpam-5476	40	47	.	.	PUNCT
ejpam-5476	41	1	j.	j.	PROPN
ejpam-5476	41	2	pure	pure	PROPN
ejpam-5476	41	3	appl	appl	PROPN
ejpam-5476	41	4	.	.	PROPN
ejpam-5476	41	5	math	math	PROPN
ejpam-5476	41	6	,	,	PUNCT
ejpam-5476	41	7	17	17	NUM
ejpam-5476	41	8	(	(	PUNCT
ejpam-5476	41	9	4	4	NUM
ejpam-5476	41	10	)	)	PUNCT
ejpam-5476	41	11	(	(	PUNCT
ejpam-5476	41	12	2024	2024	NUM
ejpam-5476	41	13	)	)	PUNCT
ejpam-5476	41	14	,	,	PUNCT
ejpam-5476	41	15	3539	3539	NUM
ejpam-5476	41	16	-	-	SYM
ejpam-5476	41	17	3556	3556	NUM
ejpam-5476	41	18	3541	3541	NUM
ejpam-5476	41	19	this	this	DET
ejpam-5476	41	20	generalization	generalization	NOUN
ejpam-5476	41	21	has	have	AUX
ejpam-5476	41	22	investigated	investigate	VERB
ejpam-5476	41	23	several	several	ADJ
ejpam-5476	41	24	applications	application	NOUN
ejpam-5476	41	25	.	.	PUNCT
ejpam-5476	42	1	for	for	ADP
ejpam-5476	42	2	example	example	NOUN
ejpam-5476	42	3	,	,	PUNCT
ejpam-5476	42	4	kumar	kumar	PROPN
ejpam-5476	42	5	et	et	PROPN
ejpam-5476	42	6	al	al	PROPN
ejpam-5476	42	7	.	.	PUNCT
ejpam-5476	43	1	[	[	X
ejpam-5476	43	2	28	28	NUM
ejpam-5476	43	3	]	]	PUNCT
ejpam-5476	43	4	introduced	introduce	VERB
ejpam-5476	43	5	the	the	DET
ejpam-5476	43	6	solution	solution	NOUN
ejpam-5476	43	7	of	of	ADP
ejpam-5476	43	8	the	the	DET
ejpam-5476	43	9	coronavirus	coronavirus	NOUN
ejpam-5476	43	10	disease	disease	NOUN
ejpam-5476	43	11	model	model	NOUN
ejpam-5476	43	12	in	in	ADP
ejpam-5476	43	13	brazil	brazil	PROPN
ejpam-5476	43	14	via	via	ADP
ejpam-5476	43	15	the	the	DET
ejpam-5476	43	16	new	new	ADJ
ejpam-5476	43	17	definition	definition	NOUN
ejpam-5476	43	18	.	.	PUNCT
ejpam-5476	44	1	the	the	DET
ejpam-5476	44	2	solution	solution	NOUN
ejpam-5476	44	3	of	of	ADP
ejpam-5476	44	4	influences	influence	NOUN
ejpam-5476	44	5	infection	infection	NOUN
ejpam-5476	44	6	dynamics	dynamic	NOUN
ejpam-5476	44	7	for	for	ADP
ejpam-5476	44	8	a	a	DET
ejpam-5476	44	9	butterfly	butterfly	NOUN
ejpam-5476	44	10	pathogen	pathogen	NOUN
ejpam-5476	44	11	and	and	CCONJ
ejpam-5476	44	12	covid-19	covid-19	PROPN
ejpam-5476	44	13	model	model	NOUN
ejpam-5476	44	14	restively	restively	ADV
ejpam-5476	44	15	are	be	AUX
ejpam-5476	44	16	presented	present	VERB
ejpam-5476	44	17	by	by	ADP
ejpam-5476	44	18	kumar	kumar	PROPN
ejpam-5476	44	19	and	and	CCONJ
ejpam-5476	44	20	erturk	erturk	PROPN
ejpam-5476	45	1	[	[	X
ejpam-5476	45	2	20	20	NUM
ejpam-5476	45	3	,	,	PUNCT
ejpam-5476	45	4	27	27	NUM
ejpam-5476	45	5	]	]	PUNCT
ejpam-5476	45	6	respectively	respectively	ADV
ejpam-5476	45	7	.	.	PUNCT
ejpam-5476	46	1	there	there	PRON
ejpam-5476	46	2	is	be	VERB
ejpam-5476	46	3	now	now	ADV
ejpam-5476	46	4	no	no	DET
ejpam-5476	46	5	research	research	NOUN
ejpam-5476	46	6	paper	paper	NOUN
ejpam-5476	46	7	handling	handle	VERB
ejpam-5476	46	8	the	the	DET
ejpam-5476	46	9	approximations	approximation	NOUN
ejpam-5476	46	10	of	of	ADP
ejpam-5476	46	11	the	the	DET
ejpam-5476	46	12	solution	solution	NOUN
ejpam-5476	46	13	using	use	VERB
ejpam-5476	46	14	analytical	analytical	ADJ
ejpam-5476	46	15	methods	method	NOUN
ejpam-5476	46	16	.	.	PUNCT
ejpam-5476	47	1	one	one	NUM
ejpam-5476	47	2	of	of	ADP
ejpam-5476	47	3	the	the	DET
ejpam-5476	47	4	essential	essential	ADJ
ejpam-5476	47	5	main	main	ADJ
ejpam-5476	47	6	branches	branch	NOUN
ejpam-5476	47	7	of	of	ADP
ejpam-5476	47	8	numerical	numerical	ADJ
ejpam-5476	47	9	analysis	analysis	NOUN
ejpam-5476	47	10	is	be	AUX
ejpam-5476	47	11	approximation	approximation	NOUN
ejpam-5476	47	12	.	.	PUNCT
ejpam-5476	48	1	polynomials	polynomial	NOUN
ejpam-5476	48	2	are	be	AUX
ejpam-5476	48	3	useful	useful	ADJ
ejpam-5476	48	4	mathematical	mathematical	ADJ
ejpam-5476	48	5	tools	tool	NOUN
ejpam-5476	48	6	that	that	PRON
ejpam-5476	48	7	are	be	AUX
ejpam-5476	48	8	easily	easily	ADV
ejpam-5476	48	9	defined	define	VERB
ejpam-5476	48	10	,	,	PUNCT
ejpam-5476	48	11	characterized	characterize	VERB
ejpam-5476	48	12	,	,	PUNCT
ejpam-5476	48	13	combined	combine	VERB
ejpam-5476	48	14	,	,	PUNCT
ejpam-5476	48	15	derived	derive	VERB
ejpam-5476	48	16	,	,	PUNCT
ejpam-5476	48	17	and	and	CCONJ
ejpam-5476	48	18	grouped	group	VERB
ejpam-5476	48	19	to	to	PART
ejpam-5476	48	20	form	form	VERB
ejpam-5476	48	21	curves	curve	NOUN
ejpam-5476	48	22	that	that	PRON
ejpam-5476	48	23	can	can	AUX
ejpam-5476	48	24	approximate	approximate	VERB
ejpam-5476	48	25	any	any	DET
ejpam-5476	48	26	function	function	NOUN
ejpam-5476	48	27	to	to	ADP
ejpam-5476	48	28	any	any	DET
ejpam-5476	48	29	required	required	ADJ
ejpam-5476	48	30	precision	precision	NOUN
ejpam-5476	48	31	.	.	PUNCT
ejpam-5476	49	1	also	also	ADV
ejpam-5476	49	2	,	,	PUNCT
ejpam-5476	49	3	different	different	ADJ
ejpam-5476	49	4	bases	basis	NOUN
ejpam-5476	49	5	can	can	AUX
ejpam-5476	49	6	characterize	characterize	VERB
ejpam-5476	49	7	the	the	DET
ejpam-5476	49	8	polynomials	polynomial	NOUN
ejpam-5476	49	9	.	.	PUNCT
ejpam-5476	50	1	each	each	DET
ejpam-5476	50	2	basis	basis	NOUN
ejpam-5476	50	3	type	type	NOUN
ejpam-5476	50	4	possesses	possess	VERB
ejpam-5476	50	5	unique	unique	ADJ
ejpam-5476	50	6	strengths	strength	NOUN
ejpam-5476	50	7	,	,	PUNCT
ejpam-5476	50	8	including	include	VERB
ejpam-5476	50	9	the	the	DET
ejpam-5476	50	10	monomial	monomial	ADJ
ejpam-5476	50	11	power	power	NOUN
ejpam-5476	50	12	,	,	PUNCT
ejpam-5476	50	13	jacobi	jacobi	PROPN
ejpam-5476	50	14	,	,	PUNCT
ejpam-5476	50	15	bernstein	bernstein	PROPN
ejpam-5476	50	16	,	,	PUNCT
ejpam-5476	50	17	and	and	CCONJ
ejpam-5476	50	18	hermite	hermite	ADJ
ejpam-5476	50	19	forms	form	NOUN
ejpam-5476	50	20	.	.	PUNCT
ejpam-5476	51	1	a	a	DET
ejpam-5476	51	2	wide	wide	ADJ
ejpam-5476	51	3	range	range	NOUN
ejpam-5476	51	4	of	of	ADP
ejpam-5476	51	5	problems	problem	NOUN
ejpam-5476	51	6	can	can	AUX
ejpam-5476	51	7	be	be	AUX
ejpam-5476	51	8	effectively	effectively	ADV
ejpam-5476	51	9	addressed	address	VERB
ejpam-5476	51	10	by	by	ADP
ejpam-5476	51	11	selecting	select	VERB
ejpam-5476	51	12	the	the	DET
ejpam-5476	51	13	appropriate	appropriate	ADJ
ejpam-5476	51	14	basis	basis	NOUN
ejpam-5476	51	15	,	,	PUNCT
ejpam-5476	51	16	and	and	CCONJ
ejpam-5476	51	17	various	various	ADJ
ejpam-5476	51	18	complexities	complexity	NOUN
ejpam-5476	51	19	can	can	AUX
ejpam-5476	51	20	be	be	AUX
ejpam-5476	51	21	mitigated	mitigate	VERB
ejpam-5476	51	22	or	or	CCONJ
ejpam-5476	51	23	eliminated	eliminate	VERB
ejpam-5476	51	24	.	.	PUNCT
ejpam-5476	52	1	one	one	NUM
ejpam-5476	52	2	of	of	ADP
ejpam-5476	52	3	those	those	DET
ejpam-5476	52	4	polynomials	polynomial	NOUN
ejpam-5476	52	5	is	be	AUX
ejpam-5476	52	6	bernstein	bernstein	PROPN
ejpam-5476	52	7	polynomials	polynomial	NOUN
ejpam-5476	52	8	,	,	PUNCT
ejpam-5476	52	9	which	which	PRON
ejpam-5476	52	10	are	be	AUX
ejpam-5476	52	11	widely	widely	ADV
ejpam-5476	52	12	used	use	VERB
ejpam-5476	52	13	to	to	PART
ejpam-5476	52	14	approximate	approximate	VERB
ejpam-5476	52	15	the	the	DET
ejpam-5476	52	16	solutions	solution	NOUN
ejpam-5476	52	17	of	of	ADP
ejpam-5476	52	18	ordinary	ordinary	ADJ
ejpam-5476	52	19	and	and	CCONJ
ejpam-5476	52	20	fractional	fractional	ADJ
ejpam-5476	52	21	differential	differential	ADJ
ejpam-5476	52	22	equations	equation	NOUN
ejpam-5476	52	23	[	[	X
ejpam-5476	52	24	32	32	NUM
ejpam-5476	52	25	,	,	PUNCT
ejpam-5476	52	26	35	35	NUM
ejpam-5476	52	27	,	,	PUNCT
ejpam-5476	52	28	39	39	NUM
ejpam-5476	52	29	,	,	PUNCT
ejpam-5476	52	30	40	40	NUM
ejpam-5476	52	31	]	]	PUNCT
ejpam-5476	52	32	.	.	PUNCT
ejpam-5476	53	1	the	the	DET
ejpam-5476	53	2	method	method	NOUN
ejpam-5476	53	3	assumes	assume	VERB
ejpam-5476	53	4	the	the	DET
ejpam-5476	53	5	solution	solution	NOUN
ejpam-5476	53	6	can	can	AUX
ejpam-5476	53	7	be	be	AUX
ejpam-5476	53	8	approximated	approximate	VERB
ejpam-5476	53	9	via	via	ADP
ejpam-5476	53	10	a	a	DET
ejpam-5476	53	11	linear	linear	ADJ
ejpam-5476	53	12	combination	combination	NOUN
ejpam-5476	53	13	of	of	ADP
ejpam-5476	53	14	bernstein	bernstein	PROPN
ejpam-5476	53	15	polynomials	polynomials	PROPN
ejpam-5476	53	16	.	.	PUNCT
ejpam-5476	54	1	those	those	DET
ejpam-5476	54	2	polynomials	polynomial	NOUN
ejpam-5476	54	3	have	have	AUX
ejpam-5476	54	4	been	be	AUX
ejpam-5476	54	5	used	use	VERB
ejpam-5476	54	6	to	to	PART
ejpam-5476	54	7	solve	solve	VERB
ejpam-5476	54	8	several	several	ADJ
ejpam-5476	54	9	linear	linear	ADJ
ejpam-5476	54	10	and	and	CCONJ
ejpam-5476	54	11	nonlinear	nonlinear	ADJ
ejpam-5476	54	12	fractional	fractional	ADJ
ejpam-5476	54	13	differential	differential	ADJ
ejpam-5476	54	14	equations	equation	NOUN
ejpam-5476	54	15	such	such	ADJ
ejpam-5476	54	16	as	as	ADP
ejpam-5476	54	17	khan	khan	PROPN
ejpam-5476	54	18	et	et	PROPN
ejpam-5476	54	19	al	al	PROPN
ejpam-5476	54	20	.	.	PUNCT
ejpam-5476	55	1	[	[	X
ejpam-5476	55	2	25	25	NUM
ejpam-5476	55	3	]	]	PUNCT
ejpam-5476	55	4	solved	solve	VERB
ejpam-5476	55	5	brusselator	brusselator	NOUN
ejpam-5476	55	6	system	system	NOUN
ejpam-5476	55	7	,	,	PUNCT
ejpam-5476	55	8	mirzaee	mirzaee	PROPN
ejpam-5476	55	9	,	,	PUNCT
ejpam-5476	55	10	and	and	CCONJ
ejpam-5476	55	11	alipour	alipour	ADJ
ejpam-5476	55	12	[	[	X
ejpam-5476	55	13	30	30	NUM
ejpam-5476	55	14	]	]	X
ejpam-5476	55	15	solved	solved	PROPN
ejpam-5476	55	16	volterra	volterra	PROPN
ejpam-5476	55	17	integro	integro	PROPN
ejpam-5476	55	18	-	-	PUNCT
ejpam-5476	55	19	differential	differential	NOUN
ejpam-5476	55	20	equations	equation	NOUN
ejpam-5476	55	21	and	and	CCONJ
ejpam-5476	55	22	others	other	NOUN
ejpam-5476	56	1	[	[	X
ejpam-5476	56	2	7–10	7–10	NUM
ejpam-5476	56	3	,	,	PUNCT
ejpam-5476	56	4	17	17	NUM
ejpam-5476	56	5	,	,	PUNCT
ejpam-5476	56	6	21	21	NUM
ejpam-5476	56	7	,	,	PUNCT
ejpam-5476	56	8	22	22	NUM
ejpam-5476	56	9	,	,	PUNCT
ejpam-5476	56	10	24	24	NUM
ejpam-5476	56	11	,	,	PUNCT
ejpam-5476	56	12	33	33	NUM
ejpam-5476	56	13	,	,	PUNCT
ejpam-5476	56	14	36–38	36–38	NUM
ejpam-5476	56	15	,	,	PUNCT
ejpam-5476	56	16	43	43	NUM
ejpam-5476	56	17	]	]	PUNCT
ejpam-5476	56	18	.	.	PUNCT
ejpam-5476	57	1	up	up	ADP
ejpam-5476	57	2	to	to	ADP
ejpam-5476	57	3	now	now	ADV
ejpam-5476	57	4	,	,	PUNCT
ejpam-5476	57	5	bernstein	bernstein	PROPN
ejpam-5476	57	6	polynomials	polynomial	NOUN
ejpam-5476	57	7	do	do	AUX
ejpam-5476	57	8	not	not	PART
ejpam-5476	57	9	use	use	VERB
ejpam-5476	57	10	to	to	PART
ejpam-5476	57	11	approximate	approximate	VERB
ejpam-5476	57	12	the	the	DET
ejpam-5476	57	13	generalized	generalized	ADJ
ejpam-5476	57	14	caputo	caputo	NOUN
ejpam-5476	57	15	-	-	PUNCT
ejpam-5476	57	16	type	type	NOUN
ejpam-5476	57	17	fractional	fractional	ADJ
ejpam-5476	57	18	derivative.this	derivative.this	PRON
ejpam-5476	57	19	work	work	NOUN
ejpam-5476	57	20	will	will	AUX
ejpam-5476	57	21	build	build	VERB
ejpam-5476	57	22	this	this	DET
ejpam-5476	57	23	algorithm	algorithm	NOUN
ejpam-5476	57	24	.	.	PUNCT
ejpam-5476	58	1	unlike	unlike	ADP
ejpam-5476	58	2	other	other	ADJ
ejpam-5476	58	3	methods	method	NOUN
ejpam-5476	58	4	,	,	PUNCT
ejpam-5476	58	5	the	the	DET
ejpam-5476	58	6	algorithm	algorithm	NOUN
ejpam-5476	58	7	does	do	AUX
ejpam-5476	58	8	not	not	PART
ejpam-5476	58	9	need	need	VERB
ejpam-5476	58	10	to	to	PART
ejpam-5476	58	11	select	select	VERB
ejpam-5476	58	12	an	an	DET
ejpam-5476	58	13	initial	initial	ADJ
ejpam-5476	58	14	guess	guess	NOUN
ejpam-5476	58	15	like	like	ADP
ejpam-5476	58	16	other	other	ADJ
ejpam-5476	58	17	methods	method	NOUN
ejpam-5476	58	18	or	or	CCONJ
ejpam-5476	58	19	use	use	VERB
ejpam-5476	58	20	help	help	NOUN
ejpam-5476	58	21	from	from	ADP
ejpam-5476	58	22	other	other	ADJ
ejpam-5476	58	23	techniques	technique	NOUN
ejpam-5476	58	24	.	.	PUNCT
ejpam-5476	59	1	it	it	PRON
ejpam-5476	59	2	can	can	AUX
ejpam-5476	59	3	be	be	AUX
ejpam-5476	59	4	used	use	VERB
ejpam-5476	59	5	directly	directly	ADV
ejpam-5476	59	6	to	to	PART
ejpam-5476	59	7	solve	solve	VERB
ejpam-5476	59	8	the	the	DET
ejpam-5476	59	9	problem	problem	NOUN
ejpam-5476	59	10	.	.	PUNCT
ejpam-5476	60	1	finding	find	VERB
ejpam-5476	60	2	the	the	DET
ejpam-5476	60	3	approximate	approximate	ADJ
ejpam-5476	60	4	analytic	analytic	ADJ
ejpam-5476	60	5	solution	solution	NOUN
ejpam-5476	60	6	based	base	VERB
ejpam-5476	60	7	on	on	ADP
ejpam-5476	60	8	the	the	DET
ejpam-5476	60	9	orthogonal	orthogonal	ADJ
ejpam-5476	60	10	polynomials	polynomial	NOUN
ejpam-5476	60	11	for	for	ADP
ejpam-5476	60	12	fde	fde	NOUN
ejpam-5476	60	13	of	of	ADP
ejpam-5476	60	14	generalized	generalized	ADJ
ejpam-5476	60	15	form	form	NOUN
ejpam-5476	60	16	will	will	AUX
ejpam-5476	60	17	help	help	VERB
ejpam-5476	60	18	the	the	DET
ejpam-5476	60	19	scientist	scientist	NOUN
ejpam-5476	60	20	fit	fit	VERB
ejpam-5476	60	21	their	their	PRON
ejpam-5476	60	22	real	real	ADJ
ejpam-5476	60	23	data	datum	NOUN
ejpam-5476	60	24	of	of	ADP
ejpam-5476	60	25	the	the	DET
ejpam-5476	60	26	model	model	NOUN
ejpam-5476	60	27	with	with	ADP
ejpam-5476	60	28	several	several	ADJ
ejpam-5476	60	29	parameters	parameter	NOUN
ejpam-5476	60	30	that	that	PRON
ejpam-5476	60	31	make	make	VERB
ejpam-5476	60	32	it	it	PRON
ejpam-5476	60	33	easy	easy	ADJ
ejpam-5476	60	34	to	to	PART
ejpam-5476	60	35	differentiate	differentiate	VERB
ejpam-5476	60	36	,	,	PUNCT
ejpam-5476	60	37	integrate	integrate	VERB
ejpam-5476	60	38	,	,	PUNCT
ejpam-5476	60	39	and	and	CCONJ
ejpam-5476	60	40	analyze	analyze	VERB
ejpam-5476	60	41	the	the	DET
ejpam-5476	60	42	models	model	NOUN
ejpam-5476	60	43	.	.	PUNCT
ejpam-5476	61	1	the	the	DET
ejpam-5476	61	2	main	main	ADJ
ejpam-5476	61	3	objective	objective	NOUN
ejpam-5476	61	4	of	of	ADP
ejpam-5476	61	5	this	this	DET
ejpam-5476	61	6	work	work	NOUN
ejpam-5476	61	7	is	be	AUX
ejpam-5476	61	8	to	to	PART
ejpam-5476	61	9	build	build	VERB
ejpam-5476	61	10	a	a	DET
ejpam-5476	61	11	convergent	convergent	NOUN
ejpam-5476	61	12	numerical	numerical	ADJ
ejpam-5476	61	13	algorithm	algorithm	NOUN
ejpam-5476	61	14	for	for	ADP
ejpam-5476	61	15	solving	solve	VERB
ejpam-5476	61	16	the	the	DET
ejpam-5476	61	17	fractional	fractional	ADJ
ejpam-5476	61	18	differential	differential	ADJ
ejpam-5476	61	19	equation	equation	NOUN
ejpam-5476	61	20	(	(	PUNCT
ejpam-5476	61	21	fde	fde	PROPN
ejpam-5476	61	22	)	)	PUNCT
ejpam-5476	61	23	with	with	ADP
ejpam-5476	61	24	two	two	NUM
ejpam-5476	61	25	parameters	parameter	NOUN
ejpam-5476	61	26	in	in	ADP
ejpam-5476	61	27	terms	term	NOUN
ejpam-5476	61	28	of	of	ADP
ejpam-5476	61	29	an	an	DET
ejpam-5476	61	30	analytic	analytic	ADJ
ejpam-5476	61	31	approach	approach	NOUN
ejpam-5476	61	32	.	.	PUNCT
ejpam-5476	62	1	in	in	ADP
ejpam-5476	62	2	this	this	DET
ejpam-5476	62	3	paper	paper	NOUN
ejpam-5476	62	4	,	,	PUNCT
ejpam-5476	62	5	we	we	PRON
ejpam-5476	62	6	utilized	utilize	VERB
ejpam-5476	62	7	the	the	DET
ejpam-5476	62	8	operational	operational	ADJ
ejpam-5476	62	9	matrix	matrix	NOUN
ejpam-5476	62	10	of	of	ADP
ejpam-5476	62	11	fdes	fde	NOUN
ejpam-5476	62	12	to	to	PART
ejpam-5476	62	13	solve	solve	VERB
ejpam-5476	62	14	the	the	DET
ejpam-5476	62	15	fractional	fractional	ADJ
ejpam-5476	62	16	model	model	NOUN
ejpam-5476	62	17	of	of	ADP
ejpam-5476	62	18	differential	differential	ADJ
ejpam-5476	62	19	equations	equation	NOUN
ejpam-5476	62	20	.	.	PUNCT
ejpam-5476	63	1	by	by	ADP
ejpam-5476	63	2	employing	employ	VERB
ejpam-5476	63	3	an	an	DET
ejpam-5476	63	4	operational	operational	ADJ
ejpam-5476	63	5	matrix	matrix	NOUN
ejpam-5476	63	6	,	,	PUNCT
ejpam-5476	63	7	we	we	PRON
ejpam-5476	63	8	transform	transform	VERB
ejpam-5476	63	9	the	the	DET
ejpam-5476	63	10	fractional	fractional	ADJ
ejpam-5476	63	11	differential	differential	ADJ
ejpam-5476	63	12	equation	equation	NOUN
ejpam-5476	63	13	into	into	ADP
ejpam-5476	63	14	a	a	DET
ejpam-5476	63	15	set	set	NOUN
ejpam-5476	63	16	of	of	ADP
ejpam-5476	63	17	linear	linear	PROPN
ejpam-5476	63	18	or	or	CCONJ
ejpam-5476	63	19	nonlinear	nonlinear	ADJ
ejpam-5476	63	20	algebraic	algebraic	ADJ
ejpam-5476	63	21	equations	equation	NOUN
ejpam-5476	63	22	.	.	PUNCT
ejpam-5476	64	1	solving	solve	VERB
ejpam-5476	64	2	this	this	DET
ejpam-5476	64	3	system	system	NOUN
ejpam-5476	64	4	yields	yield	VERB
ejpam-5476	64	5	an	an	DET
ejpam-5476	64	6	approximate	approximate	ADJ
ejpam-5476	64	7	solution	solution	NOUN
ejpam-5476	64	8	for	for	ADP
ejpam-5476	64	9	the	the	DET
ejpam-5476	64	10	original	original	ADJ
ejpam-5476	64	11	equation.the	equation.the	DET
ejpam-5476	64	12	algorithm	algorithm	NOUN
ejpam-5476	64	13	can	can	AUX
ejpam-5476	64	14	give	give	VERB
ejpam-5476	64	15	the	the	DET
ejpam-5476	64	16	best	good	ADJ
ejpam-5476	64	17	approximation	approximation	NOUN
ejpam-5476	64	18	solution	solution	NOUN
ejpam-5476	64	19	to	to	ADP
ejpam-5476	64	20	linear	linear	NOUN
ejpam-5476	64	21	and	and	CCONJ
ejpam-5476	64	22	nonlinear	nonlinear	ADJ
ejpam-5476	64	23	fde	fde	NOUN
ejpam-5476	64	24	in	in	ADP
ejpam-5476	64	25	two	two	NUM
ejpam-5476	64	26	parameters	parameter	NOUN
ejpam-5476	64	27	,	,	PUNCT
ejpam-5476	64	28	as	as	SCONJ
ejpam-5476	64	29	increases	increase	VERB
ejpam-5476	64	30	the	the	DET
ejpam-5476	64	31	degree	degree	NOUN
ejpam-5476	64	32	of	of	ADP
ejpam-5476	64	33	the	the	DET
ejpam-5476	64	34	polynomial	polynomial	ADJ
ejpam-5476	64	35	the	the	DET
ejpam-5476	64	36	solution	solution	NOUN
ejpam-5476	64	37	converges	converge	VERB
ejpam-5476	64	38	to	to	ADP
ejpam-5476	64	39	the	the	DET
ejpam-5476	64	40	exact	exact	ADJ
ejpam-5476	64	41	one	one	NUM
ejpam-5476	64	42	.	.	PUNCT
ejpam-5476	65	1	2	2	X
ejpam-5476	65	2	.	.	X
ejpam-5476	65	3	bernstein	bernstein	PROPN
ejpam-5476	65	4	polynomials	polynomials	PROPN
ejpam-5476	65	5	bernstein	bernstein	PROPN
ejpam-5476	65	6	polynomials	polynomial	NOUN
ejpam-5476	65	7	are	be	AUX
ejpam-5476	65	8	one	one	NUM
ejpam-5476	65	9	of	of	ADP
ejpam-5476	65	10	the	the	DET
ejpam-5476	65	11	most	most	ADV
ejpam-5476	65	12	important	important	ADJ
ejpam-5476	65	13	groups	group	NOUN
ejpam-5476	65	14	of	of	ADP
ejpam-5476	65	15	polynomials	polynomial	NOUN
ejpam-5476	65	16	because	because	SCONJ
ejpam-5476	65	17	they	they	PRON
ejpam-5476	65	18	have	have	VERB
ejpam-5476	65	19	many	many	ADJ
ejpam-5476	65	20	properties	property	NOUN
ejpam-5476	65	21	such	such	ADJ
ejpam-5476	65	22	as	as	ADP
ejpam-5476	65	23	continuity	continuity	NOUN
ejpam-5476	65	24	and	and	CCONJ
ejpam-5476	65	25	base	base	NOUN
ejpam-5476	65	26	group	group	NOUN
ejpam-5476	65	27	unit	unit	NOUN
ejpam-5476	65	28	of	of	ADP
ejpam-5476	65	29	b	b	PROPN
ejpam-5476	65	30	polynomials	polynomial	NOUN
ejpam-5476	65	31	over	over	ADP
ejpam-5476	65	32	the	the	DET
ejpam-5476	65	33	period	period	NOUN
ejpam-5476	65	34	[	[	X
ejpam-5476	65	35	0	0	NUM
ejpam-5476	65	36	,	,	PUNCT
ejpam-5476	65	37	r	r	NOUN
ejpam-5476	65	38	]	]	PUNCT
ejpam-5476	65	39	.	.	PUNCT
ejpam-5476	66	1	at	at	ADP
ejpam-5476	66	2	x	x	X
ejpam-5476	66	3	=	=	SYM
ejpam-5476	66	4	0	0	NUM
ejpam-5476	66	5	the	the	DET
ejpam-5476	66	6	bases	basis	NOUN
ejpam-5476	66	7	of	of	ADP
ejpam-5476	66	8	the	the	DET
ejpam-5476	66	9	bernstein	bernstein	PROPN
ejpam-5476	66	10	polynomial	polynomial	PROPN
ejpam-5476	66	11	disappear	disappear	VERB
ejpam-5476	66	12	except	except	SCONJ
ejpam-5476	66	13	for	for	ADP
ejpam-5476	66	14	the	the	DET
ejpam-5476	66	15	first	first	ADJ
ejpam-5476	66	16	polynomial	polynomial	NOUN
ejpam-5476	66	17	,	,	PUNCT
ejpam-5476	66	18	which	which	PRON
ejpam-5476	66	19	is	be	AUX
ejpam-5476	66	20	equal	equal	ADJ
ejpam-5476	66	21	to	to	ADP
ejpam-5476	66	22	1	1	NUM
ejpam-5476	66	23	,	,	PUNCT
ejpam-5476	66	24	and	and	CCONJ
ejpam-5476	66	25	at	at	ADP
ejpam-5476	66	26	x	x	X
ejpam-5476	66	27	=	=	NOUN
ejpam-5476	66	28	r	r	NOUN
ejpam-5476	66	29	these	these	DET
ejpam-5476	66	30	polynomials	polynomial	NOUN
ejpam-5476	66	31	disappear	disappear	VERB
ejpam-5476	66	32	except	except	SCONJ
ejpam-5476	66	33	for	for	ADP
ejpam-5476	66	34	the	the	DET
ejpam-5476	66	35	last	last	ADJ
ejpam-5476	66	36	polynomial	polynomial	NOUN
ejpam-5476	66	37	,	,	PUNCT
ejpam-5476	66	38	which	which	PRON
ejpam-5476	66	39	also	also	ADV
ejpam-5476	66	40	equals	equal	VERB
ejpam-5476	66	41	1	1	NUM
ejpam-5476	66	42	during	during	ADP
ejpam-5476	66	43	the	the	DET
ejpam-5476	66	44	interval	interval	NOUN
ejpam-5476	66	45	[	[	X
ejpam-5476	66	46	0	0	NUM
ejpam-5476	66	47	,	,	PUNCT
ejpam-5476	66	48	r	r	NOUN
ejpam-5476	66	49	]	]	PUNCT
ejpam-5476	66	50	.	.	PUNCT
ejpam-5476	67	1	this	this	DET
ejpam-5476	67	2	property	property	NOUN
ejpam-5476	67	3	is	be	AUX
ejpam-5476	67	4	important	important	ADJ
ejpam-5476	67	5	for	for	ADP
ejpam-5476	67	6	increasing	increase	VERB
ejpam-5476	67	7	the	the	DET
ejpam-5476	67	8	flexibility	flexibility	NOUN
ejpam-5476	67	9	to	to	PART
ejpam-5476	67	10	enforce	enforce	VERB
ejpam-5476	67	11	boundary	boundary	ADJ
ejpam-5476	67	12	conditions	condition	NOUN
ejpam-5476	67	13	at	at	ADP
ejpam-5476	67	14	interval	interval	NOUN
ejpam-5476	67	15	endpoints	endpoint	NOUN
ejpam-5476	67	16	.	.	PUNCT
ejpam-5476	68	1	it	it	PRON
ejpam-5476	68	2	also	also	ADV
ejpam-5476	68	3	ensures	ensure	VERB
ejpam-5476	68	4	that	that	SCONJ
ejpam-5476	68	5	the	the	DET
ejpam-5476	68	6	sum	sum	NOUN
ejpam-5476	68	7	at	at	ADP
ejpam-5476	68	8	any	any	DET
ejpam-5476	68	9	point	point	NOUN
ejpam-5476	68	10	x	x	PUNCT
ejpam-5476	68	11	of	of	ADP
ejpam-5476	68	12	all	all	DET
ejpam-5476	68	13	bernstein	bernstein	PROPN
ejpam-5476	68	14	polynomials	polynomial	NOUN
ejpam-5476	68	15	is	be	AUX
ejpam-5476	68	16	unity	unity	NOUN
ejpam-5476	68	17	.	.	PUNCT
ejpam-5476	69	1	n.	n.	PROPN
ejpam-5476	69	2	anakira	anakira	PROPN
ejpam-5476	69	3	et	et	PROPN
ejpam-5476	69	4	al	al	PROPN
ejpam-5476	69	5	.	.	PUNCT
ejpam-5476	69	6	/	/	SYM
ejpam-5476	69	7	eur	eur	PROPN
ejpam-5476	69	8	.	.	PUNCT
ejpam-5476	70	1	j.	j.	PROPN
ejpam-5476	70	2	pure	pure	PROPN
ejpam-5476	70	3	appl	appl	PROPN
ejpam-5476	70	4	.	.	PROPN
ejpam-5476	70	5	math	math	PROPN
ejpam-5476	70	6	,	,	PUNCT
ejpam-5476	70	7	17	17	NUM
ejpam-5476	70	8	(	(	PUNCT
ejpam-5476	70	9	4	4	NUM
ejpam-5476	70	10	)	)	PUNCT
ejpam-5476	70	11	(	(	PUNCT
ejpam-5476	70	12	2024	2024	NUM
ejpam-5476	70	13	)	)	PUNCT
ejpam-5476	70	14	,	,	PUNCT
ejpam-5476	70	15	3539	3539	NUM
ejpam-5476	70	16	-	-	SYM
ejpam-5476	70	17	3556	3556	NUM
ejpam-5476	70	18	3542	3542	NUM
ejpam-5476	70	19	definition	definition	NOUN
ejpam-5476	70	20	2.1	2.1	NUM
ejpam-5476	70	21	.	.	PUNCT
ejpam-5476	71	1	the	the	DET
ejpam-5476	71	2	b	b	NOUN
ejpam-5476	71	3	-	-	PUNCT
ejpam-5476	71	4	polynomial	polynomial	ADJ
ejpam-5476	71	5	of	of	ADP
ejpam-5476	71	6	n	n	CCONJ
ejpam-5476	71	7	-	-	PUNCT
ejpam-5476	71	8	th	th	VERB
ejpam-5476	71	9	degree	degree	NOUN
ejpam-5476	71	10	are	be	AUX
ejpam-5476	71	11	defined	define	VERB
ejpam-5476	71	12	on	on	ADP
ejpam-5476	71	13	the	the	DET
ejpam-5476	71	14	interval	interval	NOUN
ejpam-5476	71	15	[	[	X
ejpam-5476	71	16	0	0	NUM
ejpam-5476	71	17	,	,	PUNCT
ejpam-5476	71	18	1	1	NUM
ejpam-5476	71	19	]	]	PUNCT
ejpam-5476	71	20	as	as	ADP
ejpam-5476	71	21	[	[	X
ejpam-5476	71	22	15	15	NUM
ejpam-5476	71	23	]	]	PUNCT
ejpam-5476	71	24	bi	bi	NOUN
ejpam-5476	71	25	,	,	PUNCT
ejpam-5476	71	26	n(t	n(t	PROPN
ejpam-5476	71	27	)	)	PUNCT
ejpam-5476	71	28	=	=	PUNCT
ejpam-5476	71	29	(	(	PUNCT
ejpam-5476	71	30	n	n	NOUN
ejpam-5476	71	31	i	i	NOUN
ejpam-5476	71	32	)	)	PUNCT
ejpam-5476	72	1	(	(	PUNCT
ejpam-5476	72	2	1−	1−	NUM
ejpam-5476	72	3	t)n−iti	t)n−iti	PROPN
ejpam-5476	72	4	,	,	PUNCT
ejpam-5476	72	5	(	(	PUNCT
ejpam-5476	72	6	6	6	X
ejpam-5476	72	7	)	)	PUNCT
ejpam-5476	72	8	bernstein	bernstein	PROPN
ejpam-5476	72	9	polynomials	polynomial	NOUN
ejpam-5476	72	10	are	be	AUX
ejpam-5476	72	11	considered	consider	VERB
ejpam-5476	72	12	positive	positive	ADJ
ejpam-5476	72	13	,	,	PUNCT
ejpam-5476	72	14	forming	form	VERB
ejpam-5476	72	15	the	the	DET
ejpam-5476	72	16	unit	unit	NOUN
ejpam-5476	72	17	for	for	ADP
ejpam-5476	72	18	every	every	DET
ejpam-5476	72	19	real	real	NOUN
ejpam-5476	72	20	x	x	NOUN
ejpam-5476	72	21	that	that	PRON
ejpam-5476	72	22	belongs	belong	VERB
ejpam-5476	72	23	to	to	ADP
ejpam-5476	72	24	the	the	DET
ejpam-5476	72	25	period	period	NOUN
ejpam-5476	72	26	[	[	X
ejpam-5476	72	27	0	0	NUM
ejpam-5476	72	28	,	,	PUNCT
ejpam-5476	72	29	1	1	NUM
ejpam-5476	72	30	]	]	PUNCT
ejpam-5476	72	31	,	,	PUNCT
ejpam-5476	72	32	which	which	PRON
ejpam-5476	72	33	can	can	AUX
ejpam-5476	72	34	be	be	AUX
ejpam-5476	72	35	proved	prove	VERB
ejpam-5476	72	36	easily	easily	ADV
ejpam-5476	72	37	.	.	PUNCT
ejpam-5476	73	1	these	these	DET
ejpam-5476	73	2	polynomials	polynomial	NOUN
ejpam-5476	73	3	can	can	AUX
ejpam-5476	73	4	be	be	AUX
ejpam-5476	73	5	written	write	VERB
ejpam-5476	73	6	in	in	ADP
ejpam-5476	73	7	terms	term	NOUN
ejpam-5476	73	8	of	of	ADP
ejpam-5476	73	9	the	the	DET
ejpam-5476	73	10	linear	linear	ADJ
ejpam-5476	73	11	combination	combination	NOUN
ejpam-5476	73	12	of	of	ADP
ejpam-5476	73	13	the	the	DET
ejpam-5476	73	14	basic	basic	ADJ
ejpam-5476	73	15	functions	function	NOUN
ejpam-5476	73	16	by	by	ADP
ejpam-5476	73	17	using	use	VERB
ejpam-5476	73	18	the	the	DET
ejpam-5476	73	19	binomial	binomial	ADJ
ejpam-5476	73	20	expansion	expansion	NOUN
ejpam-5476	73	21	of	of	ADP
ejpam-5476	73	22	(	(	PUNCT
ejpam-5476	73	23	1−	1−	NUM
ejpam-5476	73	24	t)n−i	t)n−i	ADV
ejpam-5476	73	25	,	,	PUNCT
ejpam-5476	73	26	as	as	ADP
ejpam-5476	73	27	:	:	PUNCT
ejpam-5476	73	28	bi	bi	NOUN
ejpam-5476	73	29	,	,	PUNCT
ejpam-5476	73	30	n(t	n(t	PROPN
ejpam-5476	73	31	)	)	PUNCT
ejpam-5476	73	32	=	=	PUNCT
ejpam-5476	73	33	(	(	PUNCT
ejpam-5476	73	34	n	n	NOUN
ejpam-5476	73	35	i	i	NOUN
ejpam-5476	73	36	)	)	PUNCT
ejpam-5476	74	1	(	(	PUNCT
ejpam-5476	74	2	1−	1−	NUM
ejpam-5476	74	3	t)n−iti	t)n−iti	PROPN
ejpam-5476	74	4	,	,	PUNCT
ejpam-5476	74	5	=	=	PUNCT
ejpam-5476	74	6	(	(	PUNCT
ejpam-5476	74	7	n	n	X
ejpam-5476	74	8	i	i	PRON
ejpam-5476	74	9	)	)	PUNCT
ejpam-5476	74	10	ti	ti	PROPN
ejpam-5476	74	11	(	(	PUNCT
ejpam-5476	74	12	n−i∑	n−i∑	X
ejpam-5476	74	13	k=0	k=0	PROPN
ejpam-5476	74	14	(	(	PUNCT
ejpam-5476	74	15	−1)k	−1)k	PROPN
ejpam-5476	74	16	(	(	PUNCT
ejpam-5476	74	17	n−	n−	VERB
ejpam-5476	74	18	i	i	NOUN
ejpam-5476	74	19	k	k	PROPN
ejpam-5476	74	20	)	)	PUNCT
ejpam-5476	74	21	tk	tk	PROPN
ejpam-5476	74	22	)	)	PUNCT
ejpam-5476	74	23	,	,	PUNCT
ejpam-5476	74	24	=	=	SYM
ejpam-5476	74	25	n−i∑	n−i∑	DET
ejpam-5476	74	26	k=0	k=0	PROPN
ejpam-5476	74	27	(	(	PUNCT
ejpam-5476	74	28	−1)k	−1)k	PROPN
ejpam-5476	74	29	(	(	PUNCT
ejpam-5476	74	30	n	n	NOUN
ejpam-5476	74	31	i	i	PRON
ejpam-5476	74	32	)	)	PUNCT
ejpam-5476	74	33	(	(	PUNCT
ejpam-5476	74	34	n−	n−	NOUN
ejpam-5476	74	35	i	i	NOUN
ejpam-5476	74	36	k	k	PROPN
ejpam-5476	74	37	)	)	PUNCT
ejpam-5476	74	38	tk+i	tk+i	NOUN
ejpam-5476	74	39	,	,	PUNCT
ejpam-5476	74	40	i	i	PRON
ejpam-5476	74	41	=	=	NOUN
ejpam-5476	74	42	1	1	NUM
ejpam-5476	74	43	,	,	PUNCT
ejpam-5476	74	44	2	2	NUM
ejpam-5476	74	45	,	,	PUNCT
ejpam-5476	74	46	..	..	PUNCT
ejpam-5476	74	47	,	,	PUNCT
ejpam-5476	74	48	n.	n.	PROPN
ejpam-5476	74	49	definition	definition	NOUN
ejpam-5476	74	50	2.2	2.2	NUM
ejpam-5476	74	51	.	.	PUNCT
ejpam-5476	75	1	the	the	DET
ejpam-5476	75	2	orthonormal	orthonormal	PROPN
ejpam-5476	75	3	bernstein	bernstein	PROPN
ejpam-5476	75	4	polynomial	polynomial	PROPN
ejpam-5476	75	5	(	(	PUNCT
ejpam-5476	75	6	obps	obps	NOUN
ejpam-5476	75	7	)	)	PUNCT
ejpam-5476	75	8	on	on	ADP
ejpam-5476	75	9	the	the	DET
ejpam-5476	75	10	interval	interval	NOUN
ejpam-5476	75	11	[	[	X
ejpam-5476	75	12	0	0	NUM
ejpam-5476	75	13	,	,	PUNCT
ejpam-5476	75	14	1	1	NUM
ejpam-5476	75	15	]	]	PUNCT
ejpam-5476	75	16	of	of	ADP
ejpam-5476	75	17	degree	degree	NOUN
ejpam-5476	75	18	n	n	CCONJ
ejpam-5476	75	19	in	in	ADP
ejpam-5476	75	20	terms	term	NOUN
ejpam-5476	75	21	of	of	ADP
ejpam-5476	75	22	original	original	ADJ
ejpam-5476	75	23	orthonormal	orthonormal	ADJ
ejpam-5476	75	24	bernstein	bernstein	PROPN
ejpam-5476	75	25	basis	basis	NOUN
ejpam-5476	75	26	functions	function	NOUN
ejpam-5476	75	27	can	can	AUX
ejpam-5476	75	28	be	be	AUX
ejpam-5476	75	29	defined	define	VERB
ejpam-5476	75	30	as	as	ADP
ejpam-5476	75	31	[	[	X
ejpam-5476	75	32	31	31	NUM
ejpam-5476	75	33	]	]	SYM
ejpam-5476	75	34	ϕi	ϕi	ADP
ejpam-5476	75	35	,	,	PUNCT
ejpam-5476	75	36	n(s	n(s	PROPN
ejpam-5476	75	37	)	)	PUNCT
ejpam-5476	75	38	=	=	SYM
ejpam-5476	76	1	√	√	PROPN
ejpam-5476	76	2	2(n−	2(n−	NUM
ejpam-5476	76	3	i	i	NOUN
ejpam-5476	76	4	)	)	PUNCT
ejpam-5476	77	1	+	+	CCONJ
ejpam-5476	77	2	1	1	NUM
ejpam-5476	77	3	i∑	i∑	PROPN
ejpam-5476	77	4	k=0	k=0	PROPN
ejpam-5476	77	5	(	(	PUNCT
ejpam-5476	77	6	−1)k	−1)k	PROPN
ejpam-5476	77	7	(	(	PUNCT
ejpam-5476	77	8	2n+1−k	2n+1−k	NOUN
ejpam-5476	77	9	i−k	i−k	NOUN
ejpam-5476	77	10	)	)	PUNCT
ejpam-5476	77	11	(	(	PUNCT
ejpam-5476	77	12	i	i	NOUN
ejpam-5476	77	13	k	k	PROPN
ejpam-5476	77	14	)	)	PUNCT
ejpam-5476	77	15	(	(	PUNCT
ejpam-5476	77	16	n−k	n−k	NOUN
ejpam-5476	77	17	i−k	i−k	NOUN
ejpam-5476	77	18	)	)	PUNCT
ejpam-5476	77	19	bi−k	bi−k	NOUN
ejpam-5476	77	20	,	,	PUNCT
ejpam-5476	77	21	n−k(s	n−k(s	NOUN
ejpam-5476	77	22	)	)	PUNCT
ejpam-5476	77	23	,	,	PUNCT
ejpam-5476	77	24	(	(	PUNCT
ejpam-5476	77	25	7	7	X
ejpam-5476	77	26	)	)	PUNCT
ejpam-5476	77	27	where	where	SCONJ
ejpam-5476	77	28	bi	bi	NOUN
ejpam-5476	77	29	,	,	PUNCT
ejpam-5476	77	30	n(s	n(s	X
ejpam-5476	77	31	)	)	PUNCT
ejpam-5476	77	32	=	=	SYM
ejpam-5476	77	33	n−i∑	n−i∑	DET
ejpam-5476	77	34	k=0	k=0	PROPN
ejpam-5476	77	35	(	(	PUNCT
ejpam-5476	77	36	−1)k	−1)k	PROPN
ejpam-5476	77	37	(	(	PUNCT
ejpam-5476	77	38	n	n	NOUN
ejpam-5476	77	39	i	i	PRON
ejpam-5476	77	40	)	)	PUNCT
ejpam-5476	77	41	(	(	PUNCT
ejpam-5476	77	42	n−	n−	NOUN
ejpam-5476	77	43	i	i	NOUN
ejpam-5476	77	44	k	k	NOUN
ejpam-5476	77	45	)	)	PUNCT
ejpam-5476	77	46	si+k	si+k	PROPN
ejpam-5476	77	47	.	.	PUNCT
ejpam-5476	78	1	(	(	PUNCT
ejpam-5476	78	2	8)	8)	NUM
ejpam-5476	78	3	definition	definition	NOUN
ejpam-5476	78	4	2.3	2.3	NUM
ejpam-5476	78	5	.	.	PUNCT
ejpam-5476	79	1	fractional	fractional	ADJ
ejpam-5476	79	2	orthonormal	orthonormal	ADJ
ejpam-5476	79	3	bernstein	bernstein	PROPN
ejpam-5476	79	4	polynomials	polynomials	PROPN
ejpam-5476	79	5	(	(	PUNCT
ejpam-5476	79	6	fobps	fobps	NOUN
ejpam-5476	79	7	)	)	PUNCT
ejpam-5476	79	8	are	be	AUX
ejpam-5476	79	9	derived	derive	VERB
ejpam-5476	79	10	by	by	ADP
ejpam-5476	79	11	transforming	transform	VERB
ejpam-5476	79	12	s	s	PRON
ejpam-5476	79	13	to	to	ADP
ejpam-5476	79	14	tv	tv	NOUN
ejpam-5476	79	15	,	,	PUNCT
ejpam-5476	79	16	where	where	SCONJ
ejpam-5476	79	17	(	(	PUNCT
ejpam-5476	79	18	v	v	NOUN
ejpam-5476	79	19	>	>	X
ejpam-5476	79	20	0	0	NUM
ejpam-5476	79	21	)	)	PUNCT
ejpam-5476	79	22	,	,	PUNCT
ejpam-5476	79	23	using	use	VERB
ejpam-5476	79	24	the	the	DET
ejpam-5476	79	25	foundation	foundation	NOUN
ejpam-5476	79	26	of	of	ADP
ejpam-5476	79	27	obps	obps	NOUN
ejpam-5476	79	28	.	.	PUNCT
ejpam-5476	80	1	these	these	DET
ejpam-5476	80	2	fobps	fobps	NOUN
ejpam-5476	80	3	are	be	AUX
ejpam-5476	80	4	represented	represent	VERB
ejpam-5476	80	5	as	as	ADP
ejpam-5476	80	6	ϕv	ϕv	ADP
ejpam-5476	80	7	i	i	PROPN
ejpam-5476	80	8	,	,	PUNCT
ejpam-5476	80	9	n(t	n(t	PROPN
ejpam-5476	80	10	)	)	PUNCT
ejpam-5476	80	11	for	for	ADP
ejpam-5476	80	12	i	i	PROPN
ejpam-5476	80	13	=	=	NOUN
ejpam-5476	80	14	0	0	NUM
ejpam-5476	80	15	,	,	PUNCT
ejpam-5476	80	16	.	.	PUNCT
ejpam-5476	80	17	.	.	PUNCT
ejpam-5476	81	1	.	.	PUNCT
ejpam-5476	82	1	,	,	PUNCT
ejpam-5476	82	2	n.	n.	VERB
ejpam-5476	82	3	the	the	DET
ejpam-5476	82	4	analytical	analytical	ADJ
ejpam-5476	82	5	expression	expression	NOUN
ejpam-5476	82	6	of	of	ADP
ejpam-5476	82	7	fobps	fobps	NOUN
ejpam-5476	82	8	can	can	AUX
ejpam-5476	82	9	be	be	AUX
ejpam-5476	82	10	obtained	obtain	VERB
ejpam-5476	82	11	through	through	ADP
ejpam-5476	82	12	the	the	DET
ejpam-5476	82	13	following	follow	VERB
ejpam-5476	82	14	formula	formula	NOUN
ejpam-5476	82	15	[	[	X
ejpam-5476	82	16	31	31	NUM
ejpam-5476	82	17	]	]	X
ejpam-5476	82	18	:	:	PUNCT
ejpam-5476	83	1	ϕv	ϕv	ADP
ejpam-5476	83	2	i	i	PRON
ejpam-5476	83	3	,	,	PUNCT
ejpam-5476	83	4	n(t	n(t	PROPN
ejpam-5476	83	5	)	)	PUNCT
ejpam-5476	83	6	=	=	SYM
ejpam-5476	84	1	√	√	PROPN
ejpam-5476	84	2	2(n−	2(n−	NUM
ejpam-5476	84	3	i	i	NOUN
ejpam-5476	84	4	)	)	PUNCT
ejpam-5476	85	1	+	+	CCONJ
ejpam-5476	85	2	1(1−	1(1−	X
ejpam-5476	85	3	tv)n−i	tv)n−i	ADP
ejpam-5476	85	4	i∑	i∑	NUM
ejpam-5476	85	5	k=0	k=0	PROPN
ejpam-5476	85	6	(	(	PUNCT
ejpam-5476	85	7	−1)k	−1)k	PROPN
ejpam-5476	85	8	(	(	PUNCT
ejpam-5476	85	9	2n+	2n+	NUM
ejpam-5476	85	10	1−	1−	NUM
ejpam-5476	85	11	k	k	PROPN
ejpam-5476	85	12	i−	i−	PROPN
ejpam-5476	85	13	k	k	PROPN
ejpam-5476	85	14	)	)	PUNCT
ejpam-5476	85	15	(	(	PUNCT
ejpam-5476	85	16	i	i	NOUN
ejpam-5476	85	17	k	k	PROPN
ejpam-5476	85	18	)	)	PUNCT
ejpam-5476	85	19	tv(i−k	tv(i−k	PROPN
ejpam-5476	85	20	)	)	PUNCT
ejpam-5476	85	21	,	,	PUNCT
ejpam-5476	85	22	(	(	PUNCT
ejpam-5476	85	23	9	9	X
ejpam-5476	85	24	)	)	PUNCT
ejpam-5476	85	25	for	for	ADP
ejpam-5476	85	26	i	i	PROPN
ejpam-5476	85	27	=	=	SYM
ejpam-5476	85	28	0	0	NUM
ejpam-5476	85	29	,	,	PUNCT
ejpam-5476	85	30	1	1	NUM
ejpam-5476	85	31	,	,	PUNCT
ejpam-5476	85	32	·	·	PUNCT
ejpam-5476	85	33	·	·	PUNCT
ejpam-5476	85	34	·	·	PUNCT
ejpam-5476	85	35	,	,	PUNCT
ejpam-5476	85	36	n.	n.	PROPN
ejpam-5476	85	37	now	now	ADV
ejpam-5476	85	38	we	we	PRON
ejpam-5476	85	39	define	define	VERB
ejpam-5476	85	40	ϕv(t	ϕv(t	PRON
ejpam-5476	85	41	)	)	PUNCT
ejpam-5476	85	42	be	be	AUX
ejpam-5476	85	43	a	a	DET
ejpam-5476	85	44	set	set	NOUN
ejpam-5476	85	45	of	of	ADP
ejpam-5476	85	46	fobps	fobps	NOUN
ejpam-5476	85	47	of	of	ADP
ejpam-5476	85	48	degree	degree	NOUN
ejpam-5476	85	49	n	n	CCONJ
ejpam-5476	85	50	as	as	ADP
ejpam-5476	85	51	:	:	PUNCT
ejpam-5476	85	52	ϕv(t	ϕv(t	X
ejpam-5476	85	53	)	)	PUNCT
ejpam-5476	86	1	=	=	PUNCT
ejpam-5476	87	1	[	[	X
ejpam-5476	87	2	ϕv	ϕv	NOUN
ejpam-5476	87	3	0,n(t	0,n(t	NUM
ejpam-5476	87	4	)	)	PUNCT
ejpam-5476	87	5	,	,	PUNCT
ejpam-5476	87	6	ϕ	ϕ	NOUN
ejpam-5476	87	7	v	v	ADP
ejpam-5476	87	8	1,n(t	1,n(t	NUM
ejpam-5476	87	9	)	)	PUNCT
ejpam-5476	87	10	,	,	PUNCT
ejpam-5476	87	11	·	·	PUNCT
ejpam-5476	87	12	·	·	PUNCT
ejpam-5476	87	13	·	·	PUNCT
ejpam-5476	87	14	,	,	PUNCT
ejpam-5476	87	15	ϕv	ϕv	ADP
ejpam-5476	87	16	n	n	CCONJ
ejpam-5476	87	17	,	,	PUNCT
ejpam-5476	87	18	n(t	n(t	PROPN
ejpam-5476	87	19	)	)	PUNCT
ejpam-5476	87	20	]	]	PUNCT
ejpam-5476	88	1	t	t	PROPN
ejpam-5476	88	2	,	,	PUNCT
ejpam-5476	88	3	(	(	PUNCT
ejpam-5476	88	4	10	10	NUM
ejpam-5476	88	5	)	)	PUNCT
ejpam-5476	88	6	where	where	SCONJ
ejpam-5476	88	7	ϕv	ϕv	ADP
ejpam-5476	88	8	i	i	PRON
ejpam-5476	88	9	,	,	PUNCT
ejpam-5476	88	10	n(t	n(t	PROPN
ejpam-5476	88	11	)	)	PUNCT
ejpam-5476	88	12	for	for	ADP
ejpam-5476	88	13	i	i	PROPN
ejpam-5476	88	14	=	=	NOUN
ejpam-5476	88	15	0	0	NUM
ejpam-5476	88	16	,	,	PUNCT
ejpam-5476	88	17	.	.	PUNCT
ejpam-5476	88	18	.	.	PUNCT
ejpam-5476	88	19	.	.	PUNCT
ejpam-5476	89	1	,	,	PUNCT
ejpam-5476	89	2	n	n	PRON
ejpam-5476	89	3	are	be	AUX
ejpam-5476	89	4	fobps	fobps	NOUN
ejpam-5476	89	5	defined	define	VERB
ejpam-5476	89	6	in	in	ADP
ejpam-5476	89	7	equation	equation	NOUN
ejpam-5476	89	8	(	(	PUNCT
ejpam-5476	89	9	9	9	NUM
ejpam-5476	89	10	)	)	PUNCT
ejpam-5476	89	11	,	,	PUNCT
ejpam-5476	89	12	and	and	CCONJ
ejpam-5476	89	13	its	its	PRON
ejpam-5476	89	14	matrix	matrix	NOUN
ejpam-5476	89	15	form	form	NOUN
ejpam-5476	89	16	as	as	ADP
ejpam-5476	89	17	:	:	PUNCT
ejpam-5476	89	18	ϕv(t	ϕv(t	X
ejpam-5476	89	19	)	)	PUNCT
ejpam-5476	89	20	=	=	PUNCT
ejpam-5476	90	1	at	at	ADP
ejpam-5476	90	2	v	v	NUM
ejpam-5476	90	3	n	n	CCONJ
ejpam-5476	90	4	(	(	PUNCT
ejpam-5476	90	5	t	t	PROPN
ejpam-5476	90	6	)	)	PUNCT
ejpam-5476	90	7	,	,	PUNCT
ejpam-5476	90	8	(	(	PUNCT
ejpam-5476	90	9	11	11	NUM
ejpam-5476	90	10	)	)	PUNCT
ejpam-5476	90	11	where	where	SCONJ
ejpam-5476	90	12	t	t	PROPN
ejpam-5476	90	13	v	v	NOUN
ejpam-5476	90	14	n	n	PROPN
ejpam-5476	90	15	(	(	PUNCT
ejpam-5476	90	16	t	t	NOUN
ejpam-5476	90	17	)	)	PUNCT
ejpam-5476	90	18	=	=	PUNCT
ejpam-5476	91	1	[	[	X
ejpam-5476	91	2	1	1	NUM
ejpam-5476	91	3	,	,	PUNCT
ejpam-5476	91	4	tv	tv	NOUN
ejpam-5476	91	5	,	,	PUNCT
ejpam-5476	91	6	t2v	t2v	NOUN
ejpam-5476	91	7	,	,	PUNCT
ejpam-5476	91	8	·	·	PUNCT
ejpam-5476	91	9	·	·	PUNCT
ejpam-5476	91	10	·	·	PUNCT
ejpam-5476	91	11	,	,	PUNCT
ejpam-5476	91	12	tnv	tnv	NOUN
ejpam-5476	91	13	]	]	PUNCT
ejpam-5476	91	14	,	,	PUNCT
ejpam-5476	91	15	(	(	PUNCT
ejpam-5476	91	16	12	12	NUM
ejpam-5476	91	17	)	)	PUNCT
ejpam-5476	91	18	n.	n.	NOUN
ejpam-5476	91	19	anakira	anakira	PROPN
ejpam-5476	91	20	et	et	PROPN
ejpam-5476	91	21	al	al	PROPN
ejpam-5476	91	22	.	.	PUNCT
ejpam-5476	91	23	/	/	SYM
ejpam-5476	91	24	eur	eur	PROPN
ejpam-5476	91	25	.	.	PUNCT
ejpam-5476	92	1	j.	j.	PROPN
ejpam-5476	92	2	pure	pure	PROPN
ejpam-5476	92	3	appl	appl	PROPN
ejpam-5476	92	4	.	.	PROPN
ejpam-5476	92	5	math	math	PROPN
ejpam-5476	92	6	,	,	PUNCT
ejpam-5476	92	7	17	17	NUM
ejpam-5476	92	8	(	(	PUNCT
ejpam-5476	92	9	4	4	NUM
ejpam-5476	92	10	)	)	PUNCT
ejpam-5476	92	11	(	(	PUNCT
ejpam-5476	92	12	2024	2024	NUM
ejpam-5476	92	13	)	)	PUNCT
ejpam-5476	92	14	,	,	PUNCT
ejpam-5476	92	15	3539	3539	NUM
ejpam-5476	92	16	-	-	SYM
ejpam-5476	92	17	3556	3556	NUM
ejpam-5476	92	18	3543	3543	NUM
ejpam-5476	92	19	and	and	CCONJ
ejpam-5476	92	20	a	a	PRON
ejpam-5476	92	21	=	=	PRON
ejpam-5476	93	1	[	[	X
ejpam-5476	93	2	ai	ai	NOUN
ejpam-5476	93	3	,	,	PUNCT
ejpam-5476	93	4	j	j	PROPN
ejpam-5476	93	5	]	]	PUNCT
ejpam-5476	93	6	is	be	AUX
ejpam-5476	93	7	(	(	PUNCT
ejpam-5476	93	8	n+	n+	NUM
ejpam-5476	93	9	1)×	1)×	NUM
ejpam-5476	93	10	(	(	PUNCT
ejpam-5476	93	11	n+	n+	NOUN
ejpam-5476	93	12	1	1	NUM
ejpam-5476	93	13	)	)	PUNCT
ejpam-5476	93	14	matrix	matrix	NOUN
ejpam-5476	93	15	where	where	SCONJ
ejpam-5476	93	16	its	its	PRON
ejpam-5476	93	17	elements	element	NOUN
ejpam-5476	93	18	are	be	AUX
ejpam-5476	93	19	ai.j	ai.j	NOUN
ejpam-5476	93	20	=	=	SYM
ejpam-5476	93	21	√	√	PROPN
ejpam-5476	93	22	2(n−	2(n−	NUM
ejpam-5476	93	23	i	i	NOUN
ejpam-5476	93	24	)	)	PUNCT
ejpam-5476	94	1	+	+	CCONJ
ejpam-5476	94	2	1	1	NUM
ejpam-5476	94	3	min{i	min{i	NOUN
ejpam-5476	94	4	,	,	PUNCT
ejpam-5476	94	5	j}∑	j}∑	PROPN
ejpam-5476	94	6	k	k	NOUN
ejpam-5476	94	7	=	=	SYM
ejpam-5476	94	8	max{0,j−n+i	max{0,j−n+i	ADJ
ejpam-5476	94	9	}	}	PUNCT
ejpam-5476	94	10	mi	mi	NOUN
ejpam-5476	94	11	,	,	PUNCT
ejpam-5476	94	12	j−kni	j−kni	NOUN
ejpam-5476	94	13	,	,	PUNCT
ejpam-5476	94	14	k	k	PROPN
ejpam-5476	94	15	,	,	PUNCT
ejpam-5476	94	16	i	i	PRON
ejpam-5476	94	17	,	,	PUNCT
ejpam-5476	94	18	j	j	PROPN
ejpam-5476	94	19	=	=	SYM
ejpam-5476	94	20	0	0	NUM
ejpam-5476	94	21	,	,	PUNCT
ejpam-5476	94	22	1	1	NUM
ejpam-5476	94	23	,	,	PUNCT
ejpam-5476	94	24	2	2	NUM
ejpam-5476	94	25	,	,	PUNCT
ejpam-5476	94	26	·	·	PUNCT
ejpam-5476	94	27	·	·	PUNCT
ejpam-5476	94	28	·	·	PUNCT
ejpam-5476	94	29	,	,	PUNCT
ejpam-5476	94	30	n	n	X
ejpam-5476	94	31	(	(	PUNCT
ejpam-5476	94	32	13	13	NUM
ejpam-5476	94	33	)	)	PUNCT
ejpam-5476	94	34	where	where	SCONJ
ejpam-5476	94	35	mi	mi	PROPN
ejpam-5476	94	36	,	,	PUNCT
ejpam-5476	94	37	j	j	PROPN
ejpam-5476	94	38	and	and	CCONJ
ejpam-5476	94	39	ni	ni	PROPN
ejpam-5476	94	40	,	,	PUNCT
ejpam-5476	94	41	j	j	PROPN
ejpam-5476	94	42	are	be	AUX
ejpam-5476	94	43	defined	define	VERB
ejpam-5476	94	44	as	as	SCONJ
ejpam-5476	94	45	follows	follow	VERB
ejpam-5476	94	46	:	:	PUNCT
ejpam-5476	94	47	mi	mi	PROPN
ejpam-5476	94	48	,	,	PUNCT
ejpam-5476	94	49	j	j	PROPN
ejpam-5476	94	50	=	=	PRON
ejpam-5476	94	51	(	(	PUNCT
ejpam-5476	94	52	−1)j	−1)j	X
ejpam-5476	94	53	(	(	PUNCT
ejpam-5476	94	54	n−i	n−i	PROPN
ejpam-5476	94	55	j	j	PROPN
ejpam-5476	94	56	)	)	PUNCT
ejpam-5476	94	57	,	,	PUNCT
ejpam-5476	94	58	j	j	PROPN
ejpam-5476	94	59	=	=	SYM
ejpam-5476	94	60	0	0	NUM
ejpam-5476	94	61	,	,	PUNCT
ejpam-5476	94	62	1	1	NUM
ejpam-5476	94	63	,	,	PUNCT
ejpam-5476	94	64	·	·	PUNCT
ejpam-5476	94	65	·	·	PUNCT
ejpam-5476	94	66	·	·	PUNCT
ejpam-5476	94	67	,	,	PUNCT
ejpam-5476	94	68	n−	n−	NOUN
ejpam-5476	94	69	i	i	PROPN
ejpam-5476	94	70	,	,	PUNCT
ejpam-5476	94	71	ni	ni	PROPN
ejpam-5476	94	72	,	,	PUNCT
ejpam-5476	94	73	j	j	NOUN
ejpam-5476	94	74	=	=	PRON
ejpam-5476	94	75	(	(	PUNCT
ejpam-5476	94	76	−1)i−j	−1)i−j	PROPN
ejpam-5476	94	77	(	(	PUNCT
ejpam-5476	94	78	2n+1−i+j	2n+1−i+j	NUM
ejpam-5476	94	79	j	j	NOUN
ejpam-5476	94	80	)	)	PUNCT
ejpam-5476	94	81	(	(	PUNCT
ejpam-5476	94	82	i	i	PROPN
ejpam-5476	94	83	i−j	i−j	PROPN
ejpam-5476	94	84	)	)	PUNCT
ejpam-5476	94	85	,	,	PUNCT
ejpam-5476	94	86	j	j	PROPN
ejpam-5476	94	87	=	=	SYM
ejpam-5476	94	88	0	0	NUM
ejpam-5476	94	89	,	,	PUNCT
ejpam-5476	94	90	1	1	NUM
ejpam-5476	94	91	,	,	PUNCT
ejpam-5476	94	92	·	·	PUNCT
ejpam-5476	94	93	·	·	PUNCT
ejpam-5476	94	94	·	·	PUNCT
ejpam-5476	94	95	,	,	PUNCT
ejpam-5476	94	96	i.	i.	NOUN
ejpam-5476	94	97	.	.	PUNCT
ejpam-5476	95	1	2.1	2.1	NUM
ejpam-5476	95	2	.	.	PUNCT
ejpam-5476	95	3	approximation	approximation	NOUN
ejpam-5476	95	4	of	of	ADP
ejpam-5476	95	5	function	function	NOUN
ejpam-5476	95	6	for	for	ADP
ejpam-5476	95	7	fobps	fobps	NOUN
ejpam-5476	95	8	the	the	DET
ejpam-5476	95	9	set	set	NOUN
ejpam-5476	95	10	of	of	ADP
ejpam-5476	95	11	bernstein	bernstein	PROPN
ejpam-5476	95	12	polynomials	polynomials	PROPN
ejpam-5476	95	13	{	{	PUNCT
ejpam-5476	95	14	b0,m	b0,m	PROPN
ejpam-5476	95	15	,	,	PUNCT
ejpam-5476	95	16	b1,m	b1,m	PROPN
ejpam-5476	95	17	,	,	PUNCT
ejpam-5476	95	18	·	·	PUNCT
ejpam-5476	95	19	·	·	PUNCT
ejpam-5476	95	20	·	·	PUNCT
ejpam-5476	95	21	,	,	PUNCT
ejpam-5476	95	22	bm	bm	PROPN
ejpam-5476	95	23	,	,	PUNCT
ejpam-5476	95	24	m	m	VERB
ejpam-5476	95	25	}	}	PUNCT
ejpam-5476	95	26	in	in	ADP
ejpam-5476	95	27	hilbert	hilbert	PROPN
ejpam-5476	95	28	space	space	PROPN
ejpam-5476	95	29	l2[0	l2[0	PROPN
ejpam-5476	95	30	,	,	PUNCT
ejpam-5476	95	31	1	1	NUM
ejpam-5476	95	32	]	]	PUNCT
ejpam-5476	95	33	is	be	AUX
ejpam-5476	95	34	a	a	DET
ejpam-5476	95	35	complete	complete	ADJ
ejpam-5476	95	36	basis	basis	NOUN
ejpam-5476	96	1	[	[	X
ejpam-5476	96	2	26	26	NUM
ejpam-5476	96	3	]	]	PUNCT
ejpam-5476	96	4	.	.	PUNCT
ejpam-5476	97	1	therefore	therefore	ADV
ejpam-5476	97	2	,	,	PUNCT
ejpam-5476	97	3	the	the	DET
ejpam-5476	97	4	set	set	NOUN
ejpam-5476	97	5	of	of	ADP
ejpam-5476	97	6	fobps	fobps	NOUN
ejpam-5476	97	7	{	{	PUNCT
ejpam-5476	97	8	ϕ0,m	ϕ0,m	PROPN
ejpam-5476	97	9	,	,	PUNCT
ejpam-5476	97	10	ϕ1,m	ϕ1,m	PROPN
ejpam-5476	97	11	,	,	PUNCT
ejpam-5476	97	12	·	·	PUNCT
ejpam-5476	97	13	·	·	PUNCT
ejpam-5476	97	14	·	·	PUNCT
ejpam-5476	97	15	,	,	PUNCT
ejpam-5476	97	16	ϕm	ϕm	INTJ
ejpam-5476	97	17	,	,	PUNCT
ejpam-5476	97	18	m	m	VERB
ejpam-5476	97	19	}	}	PUNCT
ejpam-5476	97	20	is	be	AUX
ejpam-5476	97	21	a	a	DET
ejpam-5476	97	22	complete	complete	ADJ
ejpam-5476	97	23	basis	basis	NOUN
ejpam-5476	97	24	in	in	ADP
ejpam-5476	97	25	hilbert	hilbert	PROPN
ejpam-5476	97	26	space	space	PROPN
ejpam-5476	97	27	l2[0	l2[0	PROPN
ejpam-5476	97	28	,	,	PUNCT
ejpam-5476	97	29	1	1	NUM
ejpam-5476	97	30	]	]	PUNCT
ejpam-5476	97	31	.	.	PUNCT
ejpam-5476	98	1	so	so	ADV
ejpam-5476	98	2	any	any	DET
ejpam-5476	98	3	function	function	NOUN
ejpam-5476	98	4	f(t	f(t	NOUN
ejpam-5476	98	5	)	)	PUNCT
ejpam-5476	98	6	in	in	ADP
ejpam-5476	98	7	hilbert	hilbert	PROPN
ejpam-5476	98	8	space	space	PROPN
ejpam-5476	98	9	l2[0	l2[0	PROPN
ejpam-5476	98	10	,	,	PUNCT
ejpam-5476	98	11	1	1	NUM
ejpam-5476	98	12	]	]	PUNCT
ejpam-5476	98	13	can	can	AUX
ejpam-5476	98	14	be	be	AUX
ejpam-5476	98	15	represented	represent	VERB
ejpam-5476	98	16	by	by	ADP
ejpam-5476	98	17	fobps	fobps	NOUN
ejpam-5476	98	18	as	as	ADP
ejpam-5476	98	19	f(t	f(t	NOUN
ejpam-5476	98	20	)	)	PUNCT
ejpam-5476	98	21	≃	≃	VERB
ejpam-5476	98	22	m∑	m∑	ADP
ejpam-5476	98	23	0	0	NUM
ejpam-5476	98	24	ciϕi	ciϕi	NOUN
ejpam-5476	98	25	,	,	PUNCT
ejpam-5476	98	26	m(t	m(t	NOUN
ejpam-5476	98	27	)	)	PUNCT
ejpam-5476	98	28	=	=	SYM
ejpam-5476	98	29	ctϕ(t	ctϕ(t	PROPN
ejpam-5476	98	30	)	)	PUNCT
ejpam-5476	98	31	(	(	PUNCT
ejpam-5476	98	32	14	14	NUM
ejpam-5476	98	33	)	)	PUNCT
ejpam-5476	98	34	where	where	SCONJ
ejpam-5476	98	35	ϕt	ϕt	PROPN
ejpam-5476	98	36	(	(	PUNCT
ejpam-5476	98	37	t	t	PROPN
ejpam-5476	98	38	)	)	PUNCT
ejpam-5476	98	39	=	=	PUNCT
ejpam-5476	99	1	[	[	X
ejpam-5476	99	2	ϕ0,m	ϕ0,m	PROPN
ejpam-5476	99	3	,	,	PUNCT
ejpam-5476	99	4	ϕ1,m	ϕ1,m	PROPN
ejpam-5476	99	5	,	,	PUNCT
ejpam-5476	99	6	·	·	PUNCT
ejpam-5476	99	7	·	·	PUNCT
ejpam-5476	99	8	·	·	PUNCT
ejpam-5476	99	9	,	,	PUNCT
ejpam-5476	99	10	ϕm	ϕm	INTJ
ejpam-5476	99	11	,	,	PUNCT
ejpam-5476	99	12	m	m	PROPN
ejpam-5476	99	13	]	]	PUNCT
ejpam-5476	99	14	and	and	CCONJ
ejpam-5476	99	15	ct	ct	NOUN
ejpam-5476	99	16	=	=	PUNCT
ejpam-5476	100	1	[	[	X
ejpam-5476	100	2	c1	c1	PROPN
ejpam-5476	100	3	,	,	PUNCT
ejpam-5476	100	4	c2	c2	PROPN
ejpam-5476	100	5	,	,	PUNCT
ejpam-5476	100	6	·	·	PUNCT
ejpam-5476	100	7	·	·	PUNCT
ejpam-5476	100	8	·	·	PUNCT
ejpam-5476	100	9	,	,	PUNCT
ejpam-5476	100	10	cm	cm	NOUN
ejpam-5476	100	11	]	]	PUNCT
ejpam-5476	100	12	.	.	PUNCT
ejpam-5476	101	1	the	the	DET
ejpam-5476	101	2	vector	vector	NOUN
ejpam-5476	101	3	c	c	PROPN
ejpam-5476	101	4	can	can	AUX
ejpam-5476	101	5	be	be	AUX
ejpam-5476	101	6	obtained	obtain	VERB
ejpam-5476	101	7	by	by	ADP
ejpam-5476	101	8	ct	ct	PROPN
ejpam-5476	101	9	⟨ϕv(t	⟨ϕv(t	PROPN
ejpam-5476	101	10	)	)	PUNCT
ejpam-5476	101	11	,	,	PUNCT
ejpam-5476	101	12	ϕv(t)⟩w(t	ϕv(t)⟩w(t	NOUN
ejpam-5476	101	13	)	)	PUNCT
ejpam-5476	101	14	=	=	SYM
ejpam-5476	102	1	⟨f(t	⟨f(t	X
ejpam-5476	102	2	)	)	PUNCT
ejpam-5476	102	3	,	,	PUNCT
ejpam-5476	102	4	ϕv(t)⟩w(t	ϕv(t)⟩w(t	NOUN
ejpam-5476	102	5	)	)	PUNCT
ejpam-5476	102	6	,	,	PUNCT
ejpam-5476	102	7	(	(	PUNCT
ejpam-5476	102	8	15	15	NUM
ejpam-5476	102	9	)	)	PUNCT
ejpam-5476	102	10	but	but	CCONJ
ejpam-5476	102	11	ϕ(t	ϕ(t	NUM
ejpam-5476	102	12	)	)	PUNCT
ejpam-5476	102	13	are	be	AUX
ejpam-5476	102	14	orthogonal	orthogonal	ADJ
ejpam-5476	102	15	with	with	ADP
ejpam-5476	102	16	respect	respect	NOUN
ejpam-5476	102	17	to	to	ADP
ejpam-5476	102	18	the	the	DET
ejpam-5476	102	19	weight	weight	NOUN
ejpam-5476	102	20	function	function	NOUN
ejpam-5476	102	21	w(t	w(t	PROPN
ejpam-5476	102	22	)	)	PUNCT
ejpam-5476	102	23	,	,	PUNCT
ejpam-5476	102	24	so	so	CCONJ
ejpam-5476	102	25	equation	equation	NOUN
ejpam-5476	102	26	(	(	PUNCT
ejpam-5476	102	27	15	15	NUM
ejpam-5476	102	28	)	)	PUNCT
ejpam-5476	102	29	becomes	become	VERB
ejpam-5476	102	30	ct	ct	NOUN
ejpam-5476	102	31	=	=	PUNCT
ejpam-5476	102	32	v⟨f(t	v⟨f(t	NOUN
ejpam-5476	102	33	)	)	PUNCT
ejpam-5476	102	34	,	,	PUNCT
ejpam-5476	102	35	ϕv(t)⟩w(t	ϕv(t)⟩w(t	NOUN
ejpam-5476	102	36	)	)	PUNCT
ejpam-5476	102	37	.	.	PUNCT
ejpam-5476	103	1	(	(	PUNCT
ejpam-5476	103	2	16	16	NUM
ejpam-5476	103	3	)	)	PUNCT
ejpam-5476	103	4	3	3	NUM
ejpam-5476	103	5	.	.	X
ejpam-5476	103	6	generalized	generalize	VERB
ejpam-5476	103	7	caputo	caputo	PROPN
ejpam-5476	103	8	-	-	PUNCT
ejpam-5476	103	9	type	type	NOUN
ejpam-5476	103	10	fractional	fractional	ADJ
ejpam-5476	103	11	derivatives	derivative	NOUN
ejpam-5476	103	12	definition	definition	NOUN
ejpam-5476	103	13	3.1	3.1	NUM
ejpam-5476	103	14	.	.	PUNCT
ejpam-5476	104	1	the	the	DET
ejpam-5476	104	2	generalized	generalized	ADJ
ejpam-5476	104	3	fractional	fractional	ADJ
ejpam-5476	104	4	integral	integral	NOUN
ejpam-5476	104	5	of	of	ADP
ejpam-5476	104	6	a	a	DET
ejpam-5476	104	7	continues	continue	NOUN
ejpam-5476	104	8	function	function	NOUN
ejpam-5476	104	9	f	f	PROPN
ejpam-5476	104	10	is	be	AUX
ejpam-5476	104	11	iα	iα	ADJ
ejpam-5476	104	12	,	,	PUNCT
ejpam-5476	104	13	ρa+	ρa+	ADJ
ejpam-5476	104	14	f	f	NOUN
ejpam-5476	104	15	of	of	ADP
ejpam-5476	104	16	order	order	NOUN
ejpam-5476	104	17	α	α	X
ejpam-5476	104	18	>	>	X
ejpam-5476	104	19	0	0	NUM
ejpam-5476	104	20	,	,	PUNCT
ejpam-5476	104	21	and	and	CCONJ
ejpam-5476	104	22	ρ	ρ	NOUN
ejpam-5476	104	23	>	>	X
ejpam-5476	104	24	0	0	NUM
ejpam-5476	104	25	can	can	AUX
ejpam-5476	104	26	be	be	AUX
ejpam-5476	104	27	written	write	VERB
ejpam-5476	104	28	as	as	ADP
ejpam-5476	104	29	[	[	X
ejpam-5476	104	30	41	41	NUM
ejpam-5476	104	31	]	]	PUNCT
ejpam-5476	104	32	.	.	PUNCT
ejpam-5476	105	1	iα	iα	PROPN
ejpam-5476	105	2	,	,	PUNCT
ejpam-5476	105	3	ρa+	ρa+	ADJ
ejpam-5476	105	4	f(t	f(t	NOUN
ejpam-5476	105	5	)	)	PUNCT
ejpam-5476	105	6	=	=	SYM
ejpam-5476	105	7	ρ1−α	ρ1−α	ADJ
ejpam-5476	105	8	γ(α	γ(α	NOUN
ejpam-5476	105	9	)	)	PUNCT
ejpam-5476	105	10	∫	∫	PROPN
ejpam-5476	106	1	t	t	PROPN
ejpam-5476	106	2	a	a	DET
ejpam-5476	106	3	sρ−1(tρ	sρ−1(tρ	PROPN
ejpam-5476	106	4	−	−	PROPN
ejpam-5476	106	5	sρ)α−1f(s)ds	sρ)α−1f(s)ds	PROPN
ejpam-5476	106	6	.	.	PUNCT
ejpam-5476	107	1	(	(	PUNCT
ejpam-5476	107	2	17	17	NUM
ejpam-5476	107	3	)	)	PUNCT
ejpam-5476	107	4	odibat	odibat	NOUN
ejpam-5476	107	5	and	and	CCONJ
ejpam-5476	107	6	baleanu	baleanu	NOUN
ejpam-5476	107	7	were	be	AUX
ejpam-5476	107	8	able	able	ADJ
ejpam-5476	107	9	to	to	PART
ejpam-5476	107	10	determine	determine	VERB
ejpam-5476	107	11	the	the	DET
ejpam-5476	107	12	relationship	relationship	NOUN
ejpam-5476	107	13	between	between	ADP
ejpam-5476	107	14	the	the	DET
ejpam-5476	107	15	generalized	generalized	ADJ
ejpam-5476	107	16	fractional	fractional	ADJ
ejpam-5476	107	17	integral	integral	ADJ
ejpam-5476	107	18	given	give	VERB
ejpam-5476	107	19	in	in	ADP
ejpam-5476	107	20	(	(	PUNCT
ejpam-5476	107	21	17	17	NUM
ejpam-5476	107	22	)	)	PUNCT
ejpam-5476	107	23	and	and	CCONJ
ejpam-5476	107	24	the	the	DET
ejpam-5476	107	25	given	give	VERB
ejpam-5476	107	26	generalized	generalize	VERB
ejpam-5476	107	27	fractional	fractional	ADJ
ejpam-5476	107	28	derivative	derivative	NOUN
ejpam-5476	107	29	given	give	VERB
ejpam-5476	107	30	in	in	ADP
ejpam-5476	107	31	(	(	PUNCT
ejpam-5476	107	32	5	5	NUM
ejpam-5476	107	33	)	)	PUNCT
ejpam-5476	107	34	as	as	ADP
ejpam-5476	107	35	[	[	X
ejpam-5476	107	36	41	41	NUM
ejpam-5476	107	37	]	]	PUNCT
ejpam-5476	107	38	:	:	PUNCT
ejpam-5476	107	39	iα	iα	PROPN
ejpam-5476	107	40	,	,	PUNCT
ejpam-5476	107	41	ρ	ρ	PROPN
ejpam-5476	107	42	a+	a+	PUNCT
ejpam-5476	107	43	dα	dα	PROPN
ejpam-5476	107	44	,	,	PUNCT
ejpam-5476	107	45	ρ	ρ	NOUN
ejpam-5476	107	46	a+	a+	PUNCT
ejpam-5476	107	47	f(t	f(t	PROPN
ejpam-5476	107	48	)	)	PUNCT
ejpam-5476	107	49	=	=	SYM
ejpam-5476	107	50	f(t)−	f(t)−	PROPN
ejpam-5476	107	51	m−1∑	m−1∑	NUM
ejpam-5476	107	52	n=0	n=0	PROPN
ejpam-5476	107	53	1	1	NUM
ejpam-5476	107	54	ρnn	ρnn	NOUN
ejpam-5476	107	55	!	!	PUNCT
ejpam-5476	108	1	(	(	PUNCT
ejpam-5476	108	2	tρ	tρ	INTJ
ejpam-5476	108	3	−	−	PROPN
ejpam-5476	108	4	aρ)n[(x1−ρ	aρ)n[(x1−ρ	PROPN
ejpam-5476	108	5	d	d	PROPN
ejpam-5476	108	6	dx	dx	PROPN
ejpam-5476	108	7	)	)	PUNCT
ejpam-5476	108	8	nf(x)]|x	nf(x)]|x	PROPN
ejpam-5476	109	1	=	=	SYM
ejpam-5476	109	2	a	a	NOUN
ejpam-5476	109	3	,	,	PUNCT
ejpam-5476	109	4	(	(	PUNCT
ejpam-5476	109	5	18	18	NUM
ejpam-5476	109	6	)	)	PUNCT
ejpam-5476	109	7	n.	n.	NOUN
ejpam-5476	109	8	anakira	anakira	PROPN
ejpam-5476	109	9	et	et	PROPN
ejpam-5476	109	10	al	al	PROPN
ejpam-5476	109	11	.	.	PUNCT
ejpam-5476	109	12	/	/	SYM
ejpam-5476	109	13	eur	eur	PROPN
ejpam-5476	109	14	.	.	PUNCT
ejpam-5476	110	1	j.	j.	PROPN
ejpam-5476	110	2	pure	pure	PROPN
ejpam-5476	110	3	appl	appl	PROPN
ejpam-5476	110	4	.	.	PROPN
ejpam-5476	110	5	math	math	PROPN
ejpam-5476	110	6	,	,	PUNCT
ejpam-5476	110	7	17	17	NUM
ejpam-5476	110	8	(	(	PUNCT
ejpam-5476	110	9	4	4	NUM
ejpam-5476	110	10	)	)	PUNCT
ejpam-5476	110	11	(	(	PUNCT
ejpam-5476	110	12	2024	2024	NUM
ejpam-5476	110	13	)	)	PUNCT
ejpam-5476	110	14	,	,	PUNCT
ejpam-5476	110	15	3539	3539	NUM
ejpam-5476	110	16	-	-	SYM
ejpam-5476	110	17	3556	3556	NUM
ejpam-5476	110	18	3544	3544	NUM
ejpam-5476	110	19	where	where	SCONJ
ejpam-5476	110	20	0	0	X
ejpam-5476	110	21	<	<	X
ejpam-5476	110	22	α	α	X
ejpam-5476	110	23	≤	≤	PUNCT
ejpam-5476	110	24	m	m	PROPN
ejpam-5476	110	25	,	,	PUNCT
ejpam-5476	110	26	ρ	ρ	PROPN
ejpam-5476	110	27	>	>	X
ejpam-5476	110	28	0	0	PROPN
ejpam-5476	110	29	and	and	CCONJ
ejpam-5476	110	30	a	a	DET
ejpam-5476	110	31	≥	≥	NOUN
ejpam-5476	110	32	0	0	NUM
ejpam-5476	110	33	.	.	PUNCT
ejpam-5476	111	1	in	in	ADP
ejpam-5476	111	2	the	the	DET
ejpam-5476	111	3	following	following	NOUN
ejpam-5476	111	4	,	,	PUNCT
ejpam-5476	111	5	we	we	PRON
ejpam-5476	111	6	will	will	AUX
ejpam-5476	111	7	show	show	VERB
ejpam-5476	111	8	some	some	DET
ejpam-5476	111	9	theorems	theorem	NOUN
ejpam-5476	111	10	and	and	CCONJ
ejpam-5476	111	11	essential	essential	ADJ
ejpam-5476	111	12	properties	property	NOUN
ejpam-5476	111	13	of	of	ADP
ejpam-5476	111	14	generalized	generalized	ADJ
ejpam-5476	111	15	fractional	fractional	ADJ
ejpam-5476	111	16	derivatives	derivative	NOUN
ejpam-5476	111	17	and	and	CCONJ
ejpam-5476	111	18	integrals	integral	NOUN
ejpam-5476	111	19	with	with	ADP
ejpam-5476	111	20	two	two	NUM
ejpam-5476	111	21	parameters	parameter	NOUN
ejpam-5476	111	22	that	that	SCONJ
ejpam-5476	111	23	we	we	PRON
ejpam-5476	111	24	will	will	AUX
ejpam-5476	111	25	need	need	VERB
ejpam-5476	111	26	in	in	ADP
ejpam-5476	111	27	the	the	DET
ejpam-5476	111	28	next	next	ADJ
ejpam-5476	111	29	section	section	NOUN
ejpam-5476	111	30	.	.	PUNCT
ejpam-5476	112	1	(	(	PUNCT
ejpam-5476	112	2	i	i	NOUN
ejpam-5476	112	3	)	)	PUNCT
ejpam-5476	112	4	iα	iα	PROPN
ejpam-5476	112	5	,	,	PUNCT
ejpam-5476	112	6	ρ0	ρ0	PROPN
ejpam-5476	112	7	c	c	NOUN
ejpam-5476	112	8	=	=	SYM
ejpam-5476	112	9	c	c	NOUN
ejpam-5476	112	10	ρ−α	ρ−α	NOUN
ejpam-5476	112	11	γ(α+1	γ(α+1	NOUN
ejpam-5476	112	12	)	)	PUNCT
ejpam-5476	112	13	t	t	PROPN
ejpam-5476	112	14	αρ	αρ	PROPN
ejpam-5476	112	15	.	.	PUNCT
ejpam-5476	113	1	(	(	PUNCT
ejpam-5476	113	2	ii	ii	NOUN
ejpam-5476	113	3	)	)	PUNCT
ejpam-5476	113	4	iα	iα	PROPN
ejpam-5476	113	5	,	,	PUNCT
ejpam-5476	113	6	ρ0	ρ0	PROPN
ejpam-5476	113	7	tβ	tβ	PROPN
ejpam-5476	113	8	=	=	PUNCT
ejpam-5476	113	9	ρ−αγ(1+β	ρ−αγ(1+β	PROPN
ejpam-5476	113	10	ρ	ρ	NOUN
ejpam-5476	113	11	)	)	PUNCT
ejpam-5476	114	1	γ(1+β	γ(1+β	PROPN
ejpam-5476	114	2	ρ	ρ	NUM
ejpam-5476	115	1	+	+	PROPN
ejpam-5476	115	2	α	α	NOUN
ejpam-5476	115	3	)	)	PUNCT
ejpam-5476	115	4	tβ+αρ	tβ+αρ	NOUN
ejpam-5476	115	5	.	.	PUNCT
ejpam-5476	115	6	(	(	PUNCT
ejpam-5476	115	7	iii	iii	NOUN
ejpam-5476	115	8	)	)	PUNCT
ejpam-5476	115	9	iα	iα	NOUN
ejpam-5476	115	10	,	,	PUNCT
ejpam-5476	115	11	ρa	ρa	PART
ejpam-5476	116	1	[	[	X
ejpam-5476	116	2	cf(t	cf(t	NOUN
ejpam-5476	116	3	)	)	PUNCT
ejpam-5476	116	4	+	+	CCONJ
ejpam-5476	116	5	g(t	g(t	NOUN
ejpam-5476	116	6	)	)	PUNCT
ejpam-5476	116	7	]	]	PUNCT
ejpam-5476	116	8	=	=	SYM
ejpam-5476	116	9	ciα	ciα	PROPN
ejpam-5476	116	10	,	,	PUNCT
ejpam-5476	116	11	ρa	ρa	PRON
ejpam-5476	116	12	f(t	f(t	NOUN
ejpam-5476	116	13	)	)	PUNCT
ejpam-5476	117	1	+	+	CCONJ
ejpam-5476	117	2	iα	iα	ADJ
ejpam-5476	117	3	,	,	PUNCT
ejpam-5476	117	4	ρa	ρa	PRON
ejpam-5476	117	5	g(t	g(t	PROPN
ejpam-5476	117	6	)	)	PUNCT
ejpam-5476	117	7	.	.	PUNCT
ejpam-5476	118	1	(	(	PUNCT
ejpam-5476	118	2	iv	iv	X
ejpam-5476	118	3	)	)	PUNCT
ejpam-5476	118	4	dα	dα	PROPN
ejpam-5476	118	5	,	,	PUNCT
ejpam-5476	118	6	ρ	ρ	PROPN
ejpam-5476	118	7	a+	a+	PUNCT
ejpam-5476	118	8	c	c	NOUN
ejpam-5476	118	9	=	=	SYM
ejpam-5476	118	10	0	0	PROPN
ejpam-5476	118	11	.	.	PUNCT
ejpam-5476	119	1	(	(	PUNCT
ejpam-5476	119	2	v	v	NOUN
ejpam-5476	119	3	)	)	PUNCT
ejpam-5476	119	4	dα	dα	PROPN
ejpam-5476	119	5	,	,	PUNCT
ejpam-5476	119	6	ρ	ρ	PROPN
ejpam-5476	119	7	0	0	NUM
ejpam-5476	119	8	tβ	tβ	NOUN
ejpam-5476	119	9	=	=	PUNCT
ejpam-5476	119	10	{	{	PUNCT
ejpam-5476	119	11	0	0	NUM
ejpam-5476	119	12	:	:	PUNCT
ejpam-5476	119	13	β	β	X
ejpam-5476	119	14	<	<	X
ejpam-5476	119	15	m	m	PROPN
ejpam-5476	119	16	,	,	PUNCT
ejpam-5476	119	17	m−	m−	PROPN
ejpam-5476	119	18	1	1	NUM
ejpam-5476	119	19	≤	≤	NUM
ejpam-5476	120	1	α	α	PRON
ejpam-5476	120	2	<	<	X
ejpam-5476	120	3	m	m	VERB
ejpam-5476	120	4	ρα−mγ(β+1)γ(β+ρ−mρ	ρα−mγ(β+1)γ(β+ρ−mρ	NOUN
ejpam-5476	120	5	ρ	ρ	NOUN
ejpam-5476	120	6	)	)	PUNCT
ejpam-5476	120	7	γ(β−m+1)γ(m−α+β+ρ−mρ	γ(β−m+1)γ(m−α+β+ρ−mρ	PROPN
ejpam-5476	120	8	ρ	ρ	PROPN
ejpam-5476	120	9	)	)	PUNCT
ejpam-5476	120	10	tβ−αρ	tβ−αρ	NOUN
ejpam-5476	120	11	:	:	PUNCT
ejpam-5476	120	12	otherwise	otherwise	ADV
ejpam-5476	120	13	.	.	PUNCT
ejpam-5476	121	1	(	(	PUNCT
ejpam-5476	121	2	vi	vi	X
ejpam-5476	121	3	)	)	PUNCT
ejpam-5476	121	4	dα	dα	PROPN
ejpam-5476	121	5	,	,	PUNCT
ejpam-5476	121	6	ρ	ρ	PROPN
ejpam-5476	121	7	a	a	PRON
ejpam-5476	122	1	[	[	X
ejpam-5476	122	2	cf(t	cf(t	X
ejpam-5476	122	3	)	)	PUNCT
ejpam-5476	123	1	+	+	CCONJ
ejpam-5476	123	2	g(t	g(t	NOUN
ejpam-5476	123	3	)	)	PUNCT
ejpam-5476	123	4	]	]	PUNCT
ejpam-5476	124	1	=	=	PUNCT
ejpam-5476	124	2	cdα	cdα	PROPN
ejpam-5476	124	3	,	,	PUNCT
ejpam-5476	124	4	ρ	ρ	PROPN
ejpam-5476	124	5	a+	a+	PUNCT
ejpam-5476	124	6	f(t	f(t	PROPN
ejpam-5476	124	7	)	)	PUNCT
ejpam-5476	125	1	+	+	SYM
ejpam-5476	125	2	dα	dα	ADJ
ejpam-5476	125	3	,	,	PUNCT
ejpam-5476	125	4	ρ	ρ	PROPN
ejpam-5476	125	5	a+	a+	PUNCT
ejpam-5476	125	6	g(t	g(t	PROPN
ejpam-5476	125	7	)	)	PUNCT
ejpam-5476	125	8	.	.	PUNCT
ejpam-5476	126	1	4	4	X
ejpam-5476	126	2	.	.	NUM
ejpam-5476	126	3	generalized	generalize	VERB
ejpam-5476	126	4	operational	operational	ADJ
ejpam-5476	126	5	matrix	matrix	NOUN
ejpam-5476	126	6	of	of	ADP
ejpam-5476	126	7	orthogonal	orthogonal	ADJ
ejpam-5476	126	8	bernstein	bernstein	PROPN
ejpam-5476	126	9	polynomials	polynomial	VERB
ejpam-5476	126	10	the	the	DET
ejpam-5476	126	11	main	main	ADJ
ejpam-5476	126	12	objective	objective	NOUN
ejpam-5476	126	13	of	of	ADP
ejpam-5476	126	14	this	this	DET
ejpam-5476	126	15	section	section	NOUN
ejpam-5476	126	16	is	be	AUX
ejpam-5476	126	17	to	to	PART
ejpam-5476	126	18	derive	derive	VERB
ejpam-5476	126	19	the	the	DET
ejpam-5476	126	20	fobps	fobps	NOUN
ejpam-5476	126	21	operational	operational	ADJ
ejpam-5476	126	22	matrices	matrix	NOUN
ejpam-5476	126	23	for	for	ADP
ejpam-5476	126	24	generalized	generalized	ADJ
ejpam-5476	126	25	caputo	caputo	PROPN
ejpam-5476	126	26	fractional	fractional	ADJ
ejpam-5476	126	27	derivatives	derivative	NOUN
ejpam-5476	126	28	.	.	PUNCT
ejpam-5476	127	1	we	we	PRON
ejpam-5476	127	2	derive	derive	VERB
ejpam-5476	127	3	the	the	DET
ejpam-5476	127	4	fobps	fobps	NOUN
ejpam-5476	127	5	operational	operational	ADJ
ejpam-5476	127	6	matrices	matrix	NOUN
ejpam-5476	127	7	of	of	ADP
ejpam-5476	127	8	fractional	fractional	ADJ
ejpam-5476	127	9	integration	integration	NOUN
ejpam-5476	127	10	and	and	CCONJ
ejpam-5476	127	11	derivative	derivative	NOUN
ejpam-5476	127	12	,	,	PUNCT
ejpam-5476	127	13	the	the	DET
ejpam-5476	127	14	identities	identity	NOUN
ejpam-5476	127	15	,	,	PUNCT
ejpam-5476	127	16	and	and	CCONJ
ejpam-5476	127	17	zero	zero	NUM
ejpam-5476	127	18	matrices	matrix	NOUN
ejpam-5476	127	19	of	of	ADP
ejpam-5476	127	20	order	order	NOUN
ejpam-5476	127	21	(	(	PUNCT
ejpam-5476	127	22	n+1	n+1	NOUN
ejpam-5476	127	23	)	)	PUNCT
ejpam-5476	127	24	are	be	AUX
ejpam-5476	127	25	i	i	PRON
ejpam-5476	127	26	and	and	CCONJ
ejpam-5476	127	27	o	o	NOUN
ejpam-5476	127	28	,	,	PUNCT
ejpam-5476	127	29	respectively	respectively	ADV
ejpam-5476	127	30	.	.	PUNCT
ejpam-5476	128	1	4.1	4.1	NUM
ejpam-5476	128	2	.	.	PUNCT
ejpam-5476	128	3	operational	operational	ADJ
ejpam-5476	128	4	matrix	matrix	NOUN
ejpam-5476	128	5	of	of	ADP
ejpam-5476	128	6	fractional	fractional	ADJ
ejpam-5476	128	7	integration	integration	NOUN
ejpam-5476	128	8	based	base	VERB
ejpam-5476	128	9	on	on	ADP
ejpam-5476	128	10	fobps	fobps	NOUN
ejpam-5476	128	11	the	the	DET
ejpam-5476	128	12	generalized	generalized	ADJ
ejpam-5476	128	13	fractional	fractional	ADJ
ejpam-5476	128	14	integral	integral	ADJ
ejpam-5476	128	15	of	of	ADP
ejpam-5476	128	16	ϕv(t	ϕv(t	NOUN
ejpam-5476	128	17	)	)	PUNCT
ejpam-5476	128	18	is	be	AUX
ejpam-5476	128	19	defined	define	VERB
ejpam-5476	128	20	as	as	ADP
ejpam-5476	128	21	:	:	PUNCT
ejpam-5476	128	22	iα	iα	NOUN
ejpam-5476	128	23	,	,	PUNCT
ejpam-5476	128	24	ρϕv(t	ρϕv(t	NOUN
ejpam-5476	128	25	)	)	PUNCT
ejpam-5476	128	26	=	=	SYM
ejpam-5476	128	27	iα	iα	PROPN
ejpam-5476	128	28	,	,	PUNCT
ejpam-5476	128	29	ρ	ρ	PROPN
ejpam-5476	128	30	,	,	PUNCT
ejpam-5476	128	31	vϕv(t	vϕv(t	PROPN
ejpam-5476	128	32	)	)	PUNCT
ejpam-5476	128	33	,	,	PUNCT
ejpam-5476	128	34	(	(	PUNCT
ejpam-5476	128	35	19	19	NUM
ejpam-5476	128	36	)	)	PUNCT
ejpam-5476	128	37	where	where	SCONJ
ejpam-5476	128	38	iα	iα	PROPN
ejpam-5476	128	39	,	,	PUNCT
ejpam-5476	128	40	ρ	ρ	PROPN
ejpam-5476	128	41	,	,	PUNCT
ejpam-5476	128	42	v	v	NOUN
ejpam-5476	128	43	is	be	AUX
ejpam-5476	128	44	called	call	VERB
ejpam-5476	128	45	the	the	DET
ejpam-5476	128	46	operational	operational	ADJ
ejpam-5476	128	47	matrix	matrix	NOUN
ejpam-5476	128	48	of	of	ADP
ejpam-5476	128	49	generalized	generalized	ADJ
ejpam-5476	128	50	fractional	fractional	ADJ
ejpam-5476	128	51	integration	integration	NOUN
ejpam-5476	128	52	of	of	ADP
ejpam-5476	128	53	order	order	NOUN
ejpam-5476	128	54	α	α	X
ejpam-5476	128	55	>	>	X
ejpam-5476	128	56	0	0	PROPN
ejpam-5476	128	57	,	,	PUNCT
ejpam-5476	128	58	ρ	ρ	PROPN
ejpam-5476	128	59	>	>	X
ejpam-5476	128	60	0	0	NUM
ejpam-5476	128	61	.	.	PUNCT
ejpam-5476	128	62	from	from	ADP
ejpam-5476	128	63	equation	equation	NOUN
ejpam-5476	128	64	(	(	PUNCT
ejpam-5476	128	65	11	11	NUM
ejpam-5476	128	66	)	)	PUNCT
ejpam-5476	128	67	and	and	CCONJ
ejpam-5476	128	68	the	the	DET
ejpam-5476	128	69	properties	property	NOUN
ejpam-5476	128	70	of	of	ADP
ejpam-5476	128	71	the	the	DET
ejpam-5476	128	72	operator	operator	NOUN
ejpam-5476	128	73	iα	iα	PROPN
ejpam-5476	128	74	,	,	PUNCT
ejpam-5476	128	75	ρ	ρ	PROPN
ejpam-5476	128	76	we	we	PRON
ejpam-5476	128	77	get	get	VERB
ejpam-5476	128	78	.	.	PUNCT
ejpam-5476	129	1	iα	iα	VERB
ejpam-5476	129	2	,	,	PUNCT
ejpam-5476	129	3	ρϕv(t	ρϕv(t	NOUN
ejpam-5476	129	4	)	)	PUNCT
ejpam-5476	129	5	=	=	SYM
ejpam-5476	129	6	iα	iα	PROPN
ejpam-5476	129	7	,	,	PUNCT
ejpam-5476	129	8	ρat	ρat	PROPN
ejpam-5476	129	9	v	v	NOUN
ejpam-5476	129	10	n	n	PROPN
ejpam-5476	129	11	(	(	PUNCT
ejpam-5476	129	12	t	t	PROPN
ejpam-5476	129	13	)	)	PUNCT
ejpam-5476	129	14	=	=	SYM
ejpam-5476	129	15	aiα	aiα	PROPN
ejpam-5476	129	16	,	,	PUNCT
ejpam-5476	129	17	ρ(t	ρ(t	PROPN
ejpam-5476	129	18	v	v	ADP
ejpam-5476	129	19	n	n	PROPN
ejpam-5476	129	20	(	(	PUNCT
ejpam-5476	129	21	t	t	PROPN
ejpam-5476	129	22	)	)	PUNCT
ejpam-5476	129	23	)	)	PUNCT
ejpam-5476	130	1	=	=	SYM
ejpam-5476	130	2	a[iα	a[iα	PROPN
ejpam-5476	130	3	,	,	PUNCT
ejpam-5476	130	4	ρ1	ρ1	NOUN
ejpam-5476	130	5	,	,	PUNCT
ejpam-5476	130	6	iα	iα	NOUN
ejpam-5476	130	7	,	,	PUNCT
ejpam-5476	130	8	ρtv	ρtv	PROPN
ejpam-5476	130	9	,	,	PUNCT
ejpam-5476	130	10	·	·	PUNCT
ejpam-5476	130	11	·	·	PUNCT
ejpam-5476	130	12	·	·	PUNCT
ejpam-5476	130	13	,	,	PUNCT
ejpam-5476	130	14	iα	iα	ADP
ejpam-5476	130	15	,	,	PUNCT
ejpam-5476	130	16	ρtnv]t	ρtnv]t	ADJ
ejpam-5476	130	17	,	,	PUNCT
ejpam-5476	130	18	=	=	PUNCT
ejpam-5476	130	19	a[ρ	a[ρ	X
ejpam-5476	130	20	−αγ[1	−αγ[1	PROPN
ejpam-5476	130	21	]	]	X
ejpam-5476	130	22	γ[1+α	γ[1+α	X
ejpam-5476	130	23	]	]	X
ejpam-5476	130	24	t	t	PROPN
ejpam-5476	130	25	αρ	αρ	PROPN
ejpam-5476	130	26	,	,	PUNCT
ejpam-5476	130	27	ρ−α	ρ−α	PROPN
ejpam-5476	130	28	γ[1	γ[1	PROPN
ejpam-5476	130	29	+	+	PROPN
ejpam-5476	130	30	v	v	ADP
ejpam-5476	130	31	ρ	ρ	NOUN
ejpam-5476	130	32	]	]	PUNCT
ejpam-5476	131	1	γ[1+α+	γ[1+α+	NOUN
ejpam-5476	131	2	v	v	ADP
ejpam-5476	131	3	ρ	ρ	PROPN
ejpam-5476	131	4	]	]	PUNCT
ejpam-5476	131	5	t	t	PROPN
ejpam-5476	131	6	v+αρ	v+αρ	VERB
ejpam-5476	131	7	,	,	PUNCT
ejpam-5476	131	8	·	·	PUNCT
ejpam-5476	131	9	·	·	PUNCT
ejpam-5476	131	10	·	·	PUNCT
ejpam-5476	131	11	,	,	PUNCT
ejpam-5476	131	12	ρ−α	ρ−α	NOUN
ejpam-5476	131	13	γ[1+nv	γ[1+nv	X
ejpam-5476	131	14	ρ	ρ	PROPN
ejpam-5476	131	15	]	]	PUNCT
ejpam-5476	131	16	γ[1+α+nv	γ[1+α+nv	NOUN
ejpam-5476	131	17	ρ	ρ	PROPN
ejpam-5476	131	18	]	]	PUNCT
ejpam-5476	131	19	t	t	PROPN
ejpam-5476	131	20	nv+αρ]t	nv+αρ]t	PROPN
ejpam-5476	131	21	,	,	PUNCT
ejpam-5476	131	22	=	=	SYM
ejpam-5476	131	23	abt̄	abt̄	NOUN
ejpam-5476	131	24	v	v	ADP
ejpam-5476	131	25	n	n	PROPN
ejpam-5476	131	26	(	(	PUNCT
ejpam-5476	131	27	t	t	PROPN
ejpam-5476	131	28	)	)	PUNCT
ejpam-5476	131	29	.	.	PUNCT
ejpam-5476	132	1	(	(	PUNCT
ejpam-5476	132	2	20	20	NUM
ejpam-5476	132	3	)	)	PUNCT
ejpam-5476	132	4	where	where	SCONJ
ejpam-5476	132	5	b	b	X
ejpam-5476	133	1	=	=	PUNCT
ejpam-5476	134	1	[	[	X
ejpam-5476	134	2	bi	bi	NOUN
ejpam-5476	134	3	,	,	PUNCT
ejpam-5476	134	4	j	j	PROPN
ejpam-5476	134	5	]	]	PUNCT
ejpam-5476	134	6	is	be	AUX
ejpam-5476	134	7	an	an	DET
ejpam-5476	134	8	(	(	PUNCT
ejpam-5476	134	9	n+	n+	NUM
ejpam-5476	134	10	1)×	1)×	NUM
ejpam-5476	134	11	(	(	PUNCT
ejpam-5476	134	12	n+	n+	NOUN
ejpam-5476	134	13	1	1	NUM
ejpam-5476	134	14	)	)	PUNCT
ejpam-5476	134	15	matrix	matrix	NOUN
ejpam-5476	134	16	,	,	PUNCT
ejpam-5476	134	17	and	and	CCONJ
ejpam-5476	134	18	for	for	ADP
ejpam-5476	134	19	i	i	PROPN
ejpam-5476	134	20	,	,	PUNCT
ejpam-5476	134	21	j	j	PROPN
ejpam-5476	134	22	=	=	SYM
ejpam-5476	134	23	0	0	PROPN
ejpam-5476	134	24	,	,	PUNCT
ejpam-5476	134	25	.	.	PUNCT
ejpam-5476	134	26	.	.	PUNCT
ejpam-5476	135	1	.	.	PUNCT
ejpam-5476	136	1	,	,	PUNCT
ejpam-5476	136	2	n	n	CCONJ
ejpam-5476	136	3	,	,	PUNCT
ejpam-5476	136	4	the	the	DET
ejpam-5476	136	5	bi	bi	NOUN
ejpam-5476	136	6	,	,	PUNCT
ejpam-5476	136	7	j	j	PROPN
ejpam-5476	136	8	is	be	AUX
ejpam-5476	136	9	given	give	VERB
ejpam-5476	136	10	by	by	ADP
ejpam-5476	136	11	:	:	PUNCT
ejpam-5476	136	12	bij	bij	VERB
ejpam-5476	136	13	=	=	PUNCT
ejpam-5476	136	14			PUNCT
ejpam-5476	136	15	ρ−α	ρ−α	NOUN
ejpam-5476	136	16	γ[1	γ[1	PROPN
ejpam-5476	136	17	+	+	PROPN
ejpam-5476	136	18	iv	iv	NUM
ejpam-5476	136	19	ρ	ρ	NOUN
ejpam-5476	136	20	]	]	PUNCT
ejpam-5476	136	21	γ[1+α+	γ[1+α+	NOUN
ejpam-5476	136	22	iv	iv	NUM
ejpam-5476	136	23	ρ	ρ	NOUN
ejpam-5476	136	24	]	]	PUNCT
ejpam-5476	136	25	:	:	PUNCT
ejpam-5476	136	26	i	i	PRON
ejpam-5476	136	27	=	=	PUNCT
ejpam-5476	136	28	j	j	PROPN
ejpam-5476	136	29	0	0	NUM
ejpam-5476	136	30	:	:	PUNCT
ejpam-5476	136	31	otherwise	otherwise	ADV
ejpam-5476	136	32	(	(	PUNCT
ejpam-5476	136	33	21	21	NUM
ejpam-5476	136	34	)	)	PUNCT
ejpam-5476	136	35	n.	n.	PROPN
ejpam-5476	136	36	anakira	anakira	PROPN
ejpam-5476	136	37	et	et	PROPN
ejpam-5476	136	38	al	al	PROPN
ejpam-5476	136	39	.	.	PUNCT
ejpam-5476	136	40	/	/	SYM
ejpam-5476	136	41	eur	eur	PROPN
ejpam-5476	136	42	.	.	PUNCT
ejpam-5476	137	1	j.	j.	PROPN
ejpam-5476	137	2	pure	pure	PROPN
ejpam-5476	137	3	appl	appl	PROPN
ejpam-5476	137	4	.	.	PROPN
ejpam-5476	137	5	math	math	PROPN
ejpam-5476	137	6	,	,	PUNCT
ejpam-5476	137	7	17	17	NUM
ejpam-5476	137	8	(	(	PUNCT
ejpam-5476	137	9	4	4	NUM
ejpam-5476	137	10	)	)	PUNCT
ejpam-5476	137	11	(	(	PUNCT
ejpam-5476	137	12	2024	2024	NUM
ejpam-5476	137	13	)	)	PUNCT
ejpam-5476	137	14	,	,	PUNCT
ejpam-5476	137	15	3539	3539	NUM
ejpam-5476	137	16	-	-	SYM
ejpam-5476	137	17	3556	3556	NUM
ejpam-5476	137	18	3545	3545	NUM
ejpam-5476	137	19	and	and	CCONJ
ejpam-5476	137	20	t̄	t̄	PROPN
ejpam-5476	137	21	v	v	PROPN
ejpam-5476	137	22	n	n	PROPN
ejpam-5476	137	23	(	(	PUNCT
ejpam-5476	137	24	t	t	NOUN
ejpam-5476	137	25	)	)	PUNCT
ejpam-5476	137	26	=	=	PUNCT
ejpam-5476	138	1	[	[	X
ejpam-5476	138	2	tαρ	tαρ	NOUN
ejpam-5476	138	3	,	,	PUNCT
ejpam-5476	138	4	·	·	PUNCT
ejpam-5476	138	5	·	·	PUNCT
ejpam-5476	138	6	·	·	PUNCT
ejpam-5476	138	7	,	,	PUNCT
ejpam-5476	138	8	tnv+αρ]t	tnv+αρ]t	PROPN
ejpam-5476	138	9	.	.	PUNCT
ejpam-5476	139	1	(	(	PUNCT
ejpam-5476	139	2	22	22	NUM
ejpam-5476	139	3	)	)	PUNCT
ejpam-5476	139	4	now	now	ADV
ejpam-5476	139	5	,	,	PUNCT
ejpam-5476	139	6	we	we	PRON
ejpam-5476	139	7	approximate	approximate	VERB
ejpam-5476	139	8	tiv+αρ	tiv+αρ	NOUN
ejpam-5476	139	9	for	for	ADP
ejpam-5476	139	10	i	i	PRON
ejpam-5476	139	11	=	=	SYM
ejpam-5476	139	12	0	0	NUM
ejpam-5476	139	13	,	,	PUNCT
ejpam-5476	139	14	1	1	NUM
ejpam-5476	139	15	,	,	PUNCT
ejpam-5476	139	16	.	.	PUNCT
ejpam-5476	139	17	.	.	PUNCT
ejpam-5476	140	1	.	.	PUNCT
ejpam-5476	141	1	,	,	PUNCT
ejpam-5476	141	2	n	n	CCONJ
ejpam-5476	141	3	,	,	PUNCT
ejpam-5476	141	4	in	in	ADP
ejpam-5476	141	5	terms	term	NOUN
ejpam-5476	141	6	of	of	ADP
ejpam-5476	141	7	fobps	fobps	NOUN
ejpam-5476	141	8	as	as	ADP
ejpam-5476	141	9	tiv+αρ	tiv+αρ	NOUN
ejpam-5476	141	10	≃	≃	VERB
ejpam-5476	141	11	et	et	NOUN
ejpam-5476	141	12	i	i	PROPN
ejpam-5476	141	13	ϕ	ϕ	PROPN
ejpam-5476	141	14	v(t	v(t	PROPN
ejpam-5476	141	15	)	)	PUNCT
ejpam-5476	141	16	,	,	PUNCT
ejpam-5476	141	17	(	(	PUNCT
ejpam-5476	141	18	23	23	NUM
ejpam-5476	141	19	)	)	PUNCT
ejpam-5476	141	20	where	where	SCONJ
ejpam-5476	141	21	ei	ei	NOUN
ejpam-5476	141	22	=	=	SYM
ejpam-5476	141	23	v	v	NUM
ejpam-5476	141	24	∫	∫	PROPN
ejpam-5476	141	25	1	1	NUM
ejpam-5476	141	26	0	0	NUM
ejpam-5476	141	27	tiv+αρϕv(t)w(t)dt	tiv+αρϕv(t)w(t)dt	NOUN
ejpam-5476	141	28	,	,	PUNCT
ejpam-5476	141	29	=	=	NOUN
ejpam-5476	141	30	v	v	NUM
ejpam-5476	141	31	[	[	X
ejpam-5476	141	32	∫	∫	PROPN
ejpam-5476	141	33	1	1	NUM
ejpam-5476	141	34	0	0	NUM
ejpam-5476	141	35	tiv+αρϕv	tiv+αρϕv	PROPN
ejpam-5476	141	36	0,n(t)t	0,n(t)t	PROPN
ejpam-5476	141	37	v−1dt	v−1dt	PROPN
ejpam-5476	141	38	,	,	PUNCT
ejpam-5476	141	39	·	·	PUNCT
ejpam-5476	141	40	·	·	PUNCT
ejpam-5476	141	41	·	·	PUNCT
ejpam-5476	141	42	,	,	PUNCT
ejpam-5476	141	43	∫	∫	PROPN
ejpam-5476	142	1	1	1	NUM
ejpam-5476	142	2	0	0	NUM
ejpam-5476	142	3	tiv+αρϕv	tiv+αρϕv	PROPN
ejpam-5476	142	4	n	n	CCONJ
ejpam-5476	142	5	,	,	PUNCT
ejpam-5476	142	6	n(t)t	n(t)t	PROPN
ejpam-5476	142	7	v−1dt	v−1dt	NOUN
ejpam-5476	142	8	]	]	X
ejpam-5476	142	9	t	t	PROPN
ejpam-5476	142	10	.	.	PUNCT
ejpam-5476	143	1	we	we	PRON
ejpam-5476	143	2	will	will	AUX
ejpam-5476	143	3	define	define	VERB
ejpam-5476	143	4	a	a	DET
ejpam-5476	143	5	new	new	ADJ
ejpam-5476	143	6	matrix	matrix	NOUN
ejpam-5476	143	7	of	of	ADP
ejpam-5476	143	8	order	order	NOUN
ejpam-5476	143	9	(	(	PUNCT
ejpam-5476	143	10	n	n	NOUN
ejpam-5476	143	11	+	+	CCONJ
ejpam-5476	143	12	1	1	NUM
ejpam-5476	143	13	)	)	PUNCT
ejpam-5476	143	14	×	×	NOUN
ejpam-5476	143	15	(	(	PUNCT
ejpam-5476	143	16	n	n	NOUN
ejpam-5476	143	17	+	+	NUM
ejpam-5476	143	18	1	1	NUM
ejpam-5476	143	19	)	)	PUNCT
ejpam-5476	143	20	denoted	denote	VERB
ejpam-5476	143	21	e	e	X
ejpam-5476	143	22	=	=	PUNCT
ejpam-5476	144	1	[	[	X
ejpam-5476	144	2	eij	eij	X
ejpam-5476	144	3	]	]	PUNCT
ejpam-5476	144	4	where	where	SCONJ
ejpam-5476	144	5	ei	ei	PROPN
ejpam-5476	144	6	,	,	PUNCT
ejpam-5476	144	7	j	j	PROPN
ejpam-5476	144	8	is	be	AUX
ejpam-5476	144	9	given	give	VERB
ejpam-5476	144	10	by	by	ADP
ejpam-5476	144	11	:	:	PUNCT
ejpam-5476	144	12	eij	eij	PROPN
ejpam-5476	144	13	=	=	SYM
ejpam-5476	144	14	√	√	PROPN
ejpam-5476	144	15	2(n−	2(n−	NUM
ejpam-5476	144	16	j	j	NOUN
ejpam-5476	144	17	)	)	PUNCT
ejpam-5476	145	1	+	+	CCONJ
ejpam-5476	145	2	1	1	NUM
ejpam-5476	145	3	j∑	j∑	NOUN
ejpam-5476	145	4	k=0	k=0	PROPN
ejpam-5476	145	5	(	(	PUNCT
ejpam-5476	145	6	−1)k	−1)k	PROPN
ejpam-5476	145	7	(	(	PUNCT
ejpam-5476	145	8	2n+	2n+	NUM
ejpam-5476	145	9	1−	1−	NUM
ejpam-5476	146	1	k	k	PROPN
ejpam-5476	146	2	j	j	PROPN
ejpam-5476	146	3	−	−	PROPN
ejpam-5476	146	4	k	k	PROPN
ejpam-5476	146	5	)	)	PUNCT
ejpam-5476	146	6	(	(	PUNCT
ejpam-5476	146	7	j	j	PROPN
ejpam-5476	146	8	k	k	PROPN
ejpam-5476	146	9	)	)	PUNCT
ejpam-5476	146	10	γ[i+	γ[i+	PROPN
ejpam-5476	146	11	j	j	PROPN
ejpam-5476	147	1	+	+	CCONJ
ejpam-5476	147	2	αρ	αρ	PROPN
ejpam-5476	147	3	v	v	ADP
ejpam-5476	147	4	−	−	PROPN
ejpam-5476	147	5	k	k	PROPN
ejpam-5476	148	1	+	+	NOUN
ejpam-5476	148	2	1]γ[n−	1]γ[n−	NUM
ejpam-5476	148	3	j	j	NOUN
ejpam-5476	148	4	+	+	CCONJ
ejpam-5476	148	5	1	1	X
ejpam-5476	148	6	]	]	PUNCT
ejpam-5476	148	7	γ[i+	γ[i+	PROPN
ejpam-5476	148	8	n+	n+	PUNCT
ejpam-5476	148	9	αρ	αρ	NOUN
ejpam-5476	148	10	v	v	ADP
ejpam-5476	148	11	−	−	PROPN
ejpam-5476	149	1	k	k	PROPN
ejpam-5476	150	1	+	+	PROPN
ejpam-5476	150	2	2	2	NUM
ejpam-5476	150	3	]	]	PUNCT
ejpam-5476	150	4	.	.	PUNCT
ejpam-5476	151	1	(	(	PUNCT
ejpam-5476	151	2	24	24	NUM
ejpam-5476	151	3	)	)	PUNCT
ejpam-5476	151	4	we	we	PRON
ejpam-5476	151	5	have	have	AUX
ejpam-5476	151	6	iα	iα	VERB
ejpam-5476	151	7	,	,	PUNCT
ejpam-5476	151	8	ρϕv(t	ρϕv(t	NOUN
ejpam-5476	151	9	)	)	PUNCT
ejpam-5476	151	10	=	=	SYM
ejpam-5476	151	11	abetϕv(t	abetϕv(t	PROPN
ejpam-5476	151	12	)	)	PUNCT
ejpam-5476	151	13	(	(	PUNCT
ejpam-5476	151	14	25	25	NUM
ejpam-5476	151	15	)	)	PUNCT
ejpam-5476	152	1	so	so	ADV
ejpam-5476	152	2	,	,	PUNCT
ejpam-5476	152	3	iα	iα	PROPN
ejpam-5476	152	4	,	,	PUNCT
ejpam-5476	152	5	ρ	ρ	PROPN
ejpam-5476	152	6	,	,	PUNCT
ejpam-5476	152	7	v	v	NOUN
ejpam-5476	152	8	=	=	PUNCT
ejpam-5476	152	9	abet	abet	ADJ
ejpam-5476	152	10	.	.	PUNCT
ejpam-5476	153	1	4.2	4.2	NUM
ejpam-5476	153	2	.	.	PUNCT
ejpam-5476	153	3	operational	operational	ADJ
ejpam-5476	153	4	matrix	matrix	NOUN
ejpam-5476	153	5	of	of	ADP
ejpam-5476	153	6	fractional	fractional	ADJ
ejpam-5476	153	7	differentiation	differentiation	NOUN
ejpam-5476	153	8	based	base	VERB
ejpam-5476	153	9	on	on	ADP
ejpam-5476	153	10	fobps	fobps	NOUN
ejpam-5476	153	11	the	the	DET
ejpam-5476	153	12	generalized	generalize	VERB
ejpam-5476	153	13	fractional	fractional	ADJ
ejpam-5476	153	14	differential	differential	NOUN
ejpam-5476	153	15	of	of	ADP
ejpam-5476	153	16	ϕv(t	ϕv(t	NOUN
ejpam-5476	153	17	)	)	PUNCT
ejpam-5476	153	18	is	be	AUX
ejpam-5476	153	19	defined	define	VERB
ejpam-5476	153	20	as	as	ADP
ejpam-5476	153	21	:	:	PUNCT
ejpam-5476	153	22	dα	dα	NUM
ejpam-5476	153	23	,	,	PUNCT
ejpam-5476	153	24	ρ	ρ	PROPN
ejpam-5476	153	25	t	t	NOUN
ejpam-5476	153	26	ϕv(t	ϕv(t	PUNCT
ejpam-5476	153	27	)	)	PUNCT
ejpam-5476	154	1	=	=	SYM
ejpam-5476	154	2	dα	dα	PROPN
ejpam-5476	154	3	,	,	PUNCT
ejpam-5476	154	4	ρ	ρ	PROPN
ejpam-5476	154	5	,	,	PUNCT
ejpam-5476	154	6	vϕv(t	vϕv(t	PROPN
ejpam-5476	154	7	)	)	PUNCT
ejpam-5476	154	8	.	.	PUNCT
ejpam-5476	155	1	(	(	PUNCT
ejpam-5476	155	2	26	26	NUM
ejpam-5476	155	3	)	)	PUNCT
ejpam-5476	155	4	where	where	SCONJ
ejpam-5476	155	5	dα	dα	ADP
ejpam-5476	155	6	,	,	PUNCT
ejpam-5476	155	7	ρ	ρ	PROPN
ejpam-5476	155	8	,	,	PUNCT
ejpam-5476	155	9	v	v	NOUN
ejpam-5476	155	10	is	be	AUX
ejpam-5476	155	11	called	call	VERB
ejpam-5476	155	12	the	the	DET
ejpam-5476	155	13	operational	operational	ADJ
ejpam-5476	155	14	matrix	matrix	NOUN
ejpam-5476	155	15	of	of	ADP
ejpam-5476	155	16	generalized	generalized	ADJ
ejpam-5476	155	17	fractional	fractional	ADJ
ejpam-5476	155	18	differential	differential	NOUN
ejpam-5476	155	19	of	of	ADP
ejpam-5476	155	20	order	order	NOUN
ejpam-5476	155	21	α	α	X
ejpam-5476	155	22	>	>	X
ejpam-5476	155	23	0	0	PROPN
ejpam-5476	155	24	,	,	PUNCT
ejpam-5476	155	25	ρ	ρ	PROPN
ejpam-5476	155	26	>	>	X
ejpam-5476	155	27	0	0	NUM
ejpam-5476	155	28	.	.	PUNCT
ejpam-5476	156	1	from	from	ADP
ejpam-5476	156	2	equation	equation	NOUN
ejpam-5476	156	3	(	(	PUNCT
ejpam-5476	156	4	11	11	NUM
ejpam-5476	156	5	)	)	PUNCT
ejpam-5476	156	6	and	and	CCONJ
ejpam-5476	156	7	the	the	DET
ejpam-5476	156	8	properties	property	NOUN
ejpam-5476	156	9	of	of	ADP
ejpam-5476	156	10	the	the	DET
ejpam-5476	156	11	operator	operator	NOUN
ejpam-5476	156	12	dα	dα	VERB
ejpam-5476	156	13	,	,	PUNCT
ejpam-5476	156	14	ρ	ρ	PROPN
ejpam-5476	156	15	t	t	NOUN
ejpam-5476	156	16	we	we	PRON
ejpam-5476	156	17	get	get	VERB
ejpam-5476	156	18	.	.	PUNCT
ejpam-5476	157	1	dα	dα	X
ejpam-5476	157	2	,	,	PUNCT
ejpam-5476	157	3	ρ	ρ	PROPN
ejpam-5476	157	4	t	t	NOUN
ejpam-5476	157	5	ϕv(t	ϕv(t	PUNCT
ejpam-5476	157	6	)	)	PUNCT
ejpam-5476	158	1	=	=	SYM
ejpam-5476	158	2	dα	dα	PROPN
ejpam-5476	158	3	,	,	PUNCT
ejpam-5476	158	4	ρ	ρ	PROPN
ejpam-5476	158	5	t	t	NOUN
ejpam-5476	158	6	at	at	ADP
ejpam-5476	158	7	v	v	NUM
ejpam-5476	158	8	n	n	CCONJ
ejpam-5476	158	9	(	(	PUNCT
ejpam-5476	158	10	t	t	NOUN
ejpam-5476	158	11	)	)	PUNCT
ejpam-5476	158	12	=	=	NOUN
ejpam-5476	158	13	adα	adα	PROPN
ejpam-5476	158	14	,	,	PUNCT
ejpam-5476	158	15	ρ	ρ	PROPN
ejpam-5476	158	16	t	t	PROPN
ejpam-5476	158	17	(	(	PUNCT
ejpam-5476	158	18	t	t	PROPN
ejpam-5476	158	19	v	v	PROPN
ejpam-5476	158	20	n	n	PROPN
ejpam-5476	158	21	(	(	PUNCT
ejpam-5476	158	22	t	t	PROPN
ejpam-5476	158	23	)	)	PUNCT
ejpam-5476	158	24	)	)	PUNCT
ejpam-5476	159	1	=	=	PUNCT
ejpam-5476	159	2	a[dα	a[dα	PROPN
ejpam-5476	159	3	,	,	PUNCT
ejpam-5476	159	4	ρ	ρ	PROPN
ejpam-5476	159	5	t	t	PROPN
ejpam-5476	159	6	1	1	NUM
ejpam-5476	159	7	,	,	PUNCT
ejpam-5476	159	8	dα	dα	X
ejpam-5476	159	9	,	,	PUNCT
ejpam-5476	159	10	ρ	ρ	PROPN
ejpam-5476	159	11	t	t	PROPN
ejpam-5476	159	12	tv	tv	NOUN
ejpam-5476	159	13	,	,	PUNCT
ejpam-5476	159	14	·	·	PUNCT
ejpam-5476	159	15	·	·	PUNCT
ejpam-5476	159	16	·	·	PUNCT
ejpam-5476	159	17	,	,	PUNCT
ejpam-5476	159	18	dα	dα	X
ejpam-5476	159	19	,	,	PUNCT
ejpam-5476	159	20	ρ	ρ	PROPN
ejpam-5476	159	21	t	t	NOUN
ejpam-5476	159	22	tnv]t	tnv]t	X
ejpam-5476	159	23	,	,	PUNCT
ejpam-5476	159	24	=	=	SYM
ejpam-5476	159	25	a[0	a[0	PROPN
ejpam-5476	159	26	,	,	PUNCT
ejpam-5476	159	27	ρ−1+α	ρ−1+α	PROPN
ejpam-5476	159	28	γ[1+v]γ	γ[1+v]γ	PROPN
ejpam-5476	159	29	[	[	PUNCT
ejpam-5476	159	30	v+ρ−1ρ	v+ρ−1ρ	PROPN
ejpam-5476	159	31	ρ	ρ	X
ejpam-5476	159	32	]	]	PUNCT
ejpam-5476	159	33	γ[v]γ[1−α+	γ[v]γ[1−α+	PROPN
ejpam-5476	159	34	v	v	NUM
ejpam-5476	159	35	ρ	ρ	X
ejpam-5476	159	36	]	]	PUNCT
ejpam-5476	159	37	tv−αρ	tv−αρ	NOUN
ejpam-5476	159	38	,	,	PUNCT
ejpam-5476	159	39	·	·	PUNCT
ejpam-5476	159	40	·	·	PUNCT
ejpam-5476	159	41	·	·	PUNCT
ejpam-5476	159	42	,	,	PUNCT
ejpam-5476	159	43	ρ−1+α	ρ−1+α	PROPN
ejpam-5476	159	44	γ[1+nv]γ[nv	γ[1+nv]γ[nv	NOUN
ejpam-5476	159	45	ρ	ρ	X
ejpam-5476	159	46	]	]	PUNCT
ejpam-5476	159	47	γ[n]γ[1−α+n	γ[n]γ[1−α+n	NOUN
ejpam-5476	159	48	ρ	ρ	PROPN
ejpam-5476	159	49	]	]	PUNCT
ejpam-5476	159	50	t	t	X
ejpam-5476	159	51	nv−αρ]t	nv−αρ]t	NOUN
ejpam-5476	159	52	,	,	PUNCT
ejpam-5476	159	53	=	=	SYM
ejpam-5476	159	54	abt̄	abt̄	NOUN
ejpam-5476	159	55	v	v	ADP
ejpam-5476	159	56	n	n	PROPN
ejpam-5476	159	57	(	(	PUNCT
ejpam-5476	159	58	t	t	PROPN
ejpam-5476	159	59	)	)	PUNCT
ejpam-5476	159	60	.	.	PUNCT
ejpam-5476	160	1	(	(	PUNCT
ejpam-5476	160	2	27	27	NUM
ejpam-5476	160	3	)	)	PUNCT
ejpam-5476	160	4	where	where	SCONJ
ejpam-5476	160	5	b	b	X
ejpam-5476	160	6	=	=	PUNCT
ejpam-5476	161	1	[	[	X
ejpam-5476	161	2	bi	bi	NOUN
ejpam-5476	161	3	,	,	PUNCT
ejpam-5476	161	4	j	j	PROPN
ejpam-5476	161	5	]	]	PUNCT
ejpam-5476	161	6	is	be	AUX
ejpam-5476	161	7	an	an	DET
ejpam-5476	161	8	(	(	PUNCT
ejpam-5476	161	9	n	n	NOUN
ejpam-5476	161	10	+	+	NOUN
ejpam-5476	161	11	1	1	NUM
ejpam-5476	161	12	)	)	PUNCT
ejpam-5476	161	13	×	×	NOUN
ejpam-5476	161	14	(	(	PUNCT
ejpam-5476	161	15	n	n	NOUN
ejpam-5476	161	16	+	+	CCONJ
ejpam-5476	161	17	1	1	NUM
ejpam-5476	161	18	)	)	PUNCT
ejpam-5476	161	19	matrix	matrix	NOUN
ejpam-5476	161	20	,	,	PUNCT
ejpam-5476	161	21	and	and	CCONJ
ejpam-5476	161	22	for	for	ADP
ejpam-5476	161	23	i	i	PROPN
ejpam-5476	161	24	,	,	PUNCT
ejpam-5476	161	25	j	j	PROPN
ejpam-5476	161	26	=	=	SYM
ejpam-5476	161	27	0	0	NUM
ejpam-5476	161	28	,	,	PUNCT
ejpam-5476	161	29	1	1	NUM
ejpam-5476	161	30	,	,	PUNCT
ejpam-5476	161	31	.	.	PUNCT
ejpam-5476	161	32	.	.	PUNCT
ejpam-5476	162	1	.	.	PUNCT
ejpam-5476	163	1	,	,	PUNCT
ejpam-5476	163	2	n	n	CCONJ
ejpam-5476	163	3	,	,	PUNCT
ejpam-5476	163	4	the	the	DET
ejpam-5476	163	5	bi	bi	NOUN
ejpam-5476	163	6	,	,	PUNCT
ejpam-5476	163	7	j	j	PROPN
ejpam-5476	163	8	is	be	AUX
ejpam-5476	163	9	given	give	VERB
ejpam-5476	163	10	by	by	ADP
ejpam-5476	163	11	:	:	PUNCT
ejpam-5476	163	12	bij	bij	NOUN
ejpam-5476	163	13	=	=	PUNCT
ejpam-5476	163	14			PROPN
ejpam-5476	163	15	ρ−1+α	ρ−1+α	PROPN
ejpam-5476	164	1	γ[1+iv]γ	γ[1+iv]γ	X
ejpam-5476	164	2	[	[	PUNCT
ejpam-5476	164	3	iv	iv	NUM
ejpam-5476	164	4	ρ	ρ	NOUN
ejpam-5476	164	5	]	]	PUNCT
ejpam-5476	164	6	γ[iv]γ[1−α+	γ[iv]γ[1−α+	PROPN
ejpam-5476	165	1	i	i	PRON
ejpam-5476	165	2	ρ	ρ	X
ejpam-5476	165	3	]	]	PUNCT
ejpam-5476	166	1	:	:	PUNCT
ejpam-5476	166	2	i	i	PRON
ejpam-5476	166	3	=	=	PUNCT
ejpam-5476	166	4	j	j	PROPN
ejpam-5476	166	5	̸=	̸=	PROPN
ejpam-5476	166	6	0	0	NUM
ejpam-5476	166	7	0	0	NUM
ejpam-5476	166	8	:	:	PUNCT
ejpam-5476	166	9	otherwise	otherwise	ADV
ejpam-5476	166	10	(	(	PUNCT
ejpam-5476	166	11	28	28	NUM
ejpam-5476	166	12	)	)	PUNCT
ejpam-5476	166	13	n.	n.	NOUN
ejpam-5476	166	14	anakira	anakira	PROPN
ejpam-5476	166	15	et	et	PROPN
ejpam-5476	166	16	al	al	PROPN
ejpam-5476	166	17	.	.	PUNCT
ejpam-5476	166	18	/	/	SYM
ejpam-5476	166	19	eur	eur	PROPN
ejpam-5476	166	20	.	.	PUNCT
ejpam-5476	167	1	j.	j.	PROPN
ejpam-5476	167	2	pure	pure	PROPN
ejpam-5476	167	3	appl	appl	PROPN
ejpam-5476	167	4	.	.	PROPN
ejpam-5476	167	5	math	math	PROPN
ejpam-5476	167	6	,	,	PUNCT
ejpam-5476	167	7	17	17	NUM
ejpam-5476	167	8	(	(	PUNCT
ejpam-5476	167	9	4	4	NUM
ejpam-5476	167	10	)	)	PUNCT
ejpam-5476	167	11	(	(	PUNCT
ejpam-5476	167	12	2024	2024	NUM
ejpam-5476	167	13	)	)	PUNCT
ejpam-5476	167	14	,	,	PUNCT
ejpam-5476	167	15	3539	3539	NUM
ejpam-5476	167	16	-	-	SYM
ejpam-5476	167	17	3556	3556	NUM
ejpam-5476	167	18	3546	3546	NUM
ejpam-5476	167	19	and	and	CCONJ
ejpam-5476	167	20	t̄	t̄	PROPN
ejpam-5476	167	21	v	v	PROPN
ejpam-5476	167	22	n	n	PROPN
ejpam-5476	167	23	(	(	PUNCT
ejpam-5476	167	24	t	t	NOUN
ejpam-5476	167	25	)	)	PUNCT
ejpam-5476	167	26	=	=	PUNCT
ejpam-5476	168	1	[	[	X
ejpam-5476	168	2	0	0	NUM
ejpam-5476	168	3	,	,	PUNCT
ejpam-5476	168	4	tv−αρ	tv−αρ	NOUN
ejpam-5476	168	5	,	,	PUNCT
ejpam-5476	168	6	·	·	PUNCT
ejpam-5476	168	7	·	·	PUNCT
ejpam-5476	168	8	·	·	PUNCT
ejpam-5476	168	9	,	,	PUNCT
ejpam-5476	168	10	tnv−αρ]t	tnv−αρ]t	PROPN
ejpam-5476	168	11	.	.	PUNCT
ejpam-5476	169	1	(	(	PUNCT
ejpam-5476	169	2	29	29	NUM
ejpam-5476	169	3	)	)	PUNCT
ejpam-5476	169	4	now	now	ADV
ejpam-5476	169	5	,	,	PUNCT
ejpam-5476	169	6	we	we	PRON
ejpam-5476	169	7	approximate	approximate	VERB
ejpam-5476	169	8	tiv−αρ	tiv−αρ	NOUN
ejpam-5476	169	9	for	for	ADP
ejpam-5476	169	10	i	i	PRON
ejpam-5476	169	11	=	=	NOUN
ejpam-5476	169	12	1	1	NUM
ejpam-5476	169	13	,	,	PUNCT
ejpam-5476	169	14	.	.	PUNCT
ejpam-5476	169	15	.	.	PUNCT
ejpam-5476	170	1	.	.	PUNCT
ejpam-5476	171	1	,	,	PUNCT
ejpam-5476	171	2	n	n	CCONJ
ejpam-5476	171	3	,	,	PUNCT
ejpam-5476	171	4	in	in	ADP
ejpam-5476	171	5	terms	term	NOUN
ejpam-5476	171	6	of	of	ADP
ejpam-5476	171	7	fobps	fobps	NOUN
ejpam-5476	171	8	as	as	SCONJ
ejpam-5476	171	9	tiv−αρ	tiv−αρ	NOUN
ejpam-5476	171	10	≃	≃	VERB
ejpam-5476	171	11	ēt	ēt	NOUN
ejpam-5476	171	12	i	i	PROPN
ejpam-5476	171	13	ϕ	ϕ	PROPN
ejpam-5476	171	14	v(t	v(t	PROPN
ejpam-5476	171	15	)	)	PUNCT
ejpam-5476	171	16	,	,	PUNCT
ejpam-5476	171	17	(	(	PUNCT
ejpam-5476	171	18	30	30	NUM
ejpam-5476	171	19	)	)	PUNCT
ejpam-5476	171	20	where	where	SCONJ
ejpam-5476	171	21	ēi	ēi	NOUN
ejpam-5476	171	22	=	=	SYM
ejpam-5476	171	23	v	v	NUM
ejpam-5476	171	24	∫	∫	PROPN
ejpam-5476	171	25	1	1	NUM
ejpam-5476	171	26	0	0	NUM
ejpam-5476	171	27	tiv−αρϕv(t)w(t)dt	tiv−αρϕv(t)w(t)dt	NOUN
ejpam-5476	172	1	,	,	PUNCT
ejpam-5476	172	2	=	=	NOUN
ejpam-5476	172	3	v	v	NUM
ejpam-5476	173	1	[	[	X
ejpam-5476	173	2	∫	∫	PROPN
ejpam-5476	173	3	1	1	NUM
ejpam-5476	173	4	0	0	NUM
ejpam-5476	173	5	tiv−αρϕv	tiv−αρϕv	PROPN
ejpam-5476	173	6	0,n(t)t	0,n(t)t	PROPN
ejpam-5476	173	7	v−1dt	v−1dt	NOUN
ejpam-5476	173	8	,	,	PUNCT
ejpam-5476	173	9	·	·	PUNCT
ejpam-5476	173	10	·	·	PUNCT
ejpam-5476	173	11	·	·	PUNCT
ejpam-5476	173	12	,	,	PUNCT
ejpam-5476	173	13	∫	∫	PROPN
ejpam-5476	173	14	1	1	NUM
ejpam-5476	173	15	0	0	NUM
ejpam-5476	173	16	tiv−αρϕv	tiv−αρϕv	PROPN
ejpam-5476	173	17	n	n	CCONJ
ejpam-5476	173	18	,	,	PUNCT
ejpam-5476	173	19	n(t)t	n(t)t	PROPN
ejpam-5476	173	20	v−1dt	v−1dt	NOUN
ejpam-5476	173	21	]	]	X
ejpam-5476	173	22	t	t	PROPN
ejpam-5476	173	23	.	.	PUNCT
ejpam-5476	174	1	now	now	ADV
ejpam-5476	174	2	,	,	PUNCT
ejpam-5476	174	3	ē	ē	ADV
ejpam-5476	174	4	can	can	AUX
ejpam-5476	174	5	be	be	AUX
ejpam-5476	174	6	written	write	VERB
ejpam-5476	174	7	as	as	ADP
ejpam-5476	174	8	(	(	PUNCT
ejpam-5476	174	9	n+	n+	NUM
ejpam-5476	174	10	1)×	1)×	NUM
ejpam-5476	174	11	(	(	PUNCT
ejpam-5476	174	12	n+	n+	NOUN
ejpam-5476	174	13	1	1	NUM
ejpam-5476	174	14	)	)	PUNCT
ejpam-5476	174	15	matrix	matrix	NOUN
ejpam-5476	174	16	in	in	ADP
ejpam-5476	174	17	the	the	DET
ejpam-5476	174	18	form	form	NOUN
ejpam-5476	174	19	ē	ē	ADV
ejpam-5476	174	20	=	=	PUNCT
ejpam-5476	175	1	[	[	X
ejpam-5476	175	2	ēij	ēij	X
ejpam-5476	175	3	]	]	PUNCT
ejpam-5476	175	4	where	where	SCONJ
ejpam-5476	175	5	:	:	PUNCT
ejpam-5476	175	6	ēij	ēij	PROPN
ejpam-5476	175	7	=	=	PUNCT
ejpam-5476	175	8	{	{	PUNCT
ejpam-5476	175	9	0	0	NUM
ejpam-5476	175	10	:	:	PUNCT
ejpam-5476	175	11	i	i	PRON
ejpam-5476	175	12	=	=	PUNCT
ejpam-5476	175	13	j	j	PROPN
ejpam-5476	175	14	=	=	SYM
ejpam-5476	175	15	0√	0√	PROPN
ejpam-5476	176	1	2(n−	2(n−	NUM
ejpam-5476	176	2	j	j	NOUN
ejpam-5476	176	3	)	)	PUNCT
ejpam-5476	177	1	+	+	CCONJ
ejpam-5476	177	2	1	1	NUM
ejpam-5476	177	3	∑j	∑j	NOUN
ejpam-5476	177	4	k=0(−1)k	k=0(−1)k	X
ejpam-5476	177	5	(	(	PUNCT
ejpam-5476	177	6	2n+1−k	2n+1−k	NUM
ejpam-5476	177	7	j−k	j−k	NOUN
ejpam-5476	177	8	)	)	PUNCT
ejpam-5476	177	9	(	(	PUNCT
ejpam-5476	177	10	j	j	PROPN
ejpam-5476	177	11	k	k	PROPN
ejpam-5476	177	12	)	)	PUNCT
ejpam-5476	177	13	γ[i+j−αρ	γ[i+j−αρ	NOUN
ejpam-5476	177	14	v	v	ADP
ejpam-5476	177	15	−k+1]γ[n−j+1	−k+1]γ[n−j+1	NOUN
ejpam-5476	177	16	]	]	PUNCT
ejpam-5476	177	17	γ[i+n−αρ	γ[i+n−αρ	X
ejpam-5476	177	18	v	v	PRON
ejpam-5476	177	19	−k+2	−k+2	NOUN
ejpam-5476	177	20	]	]	X
ejpam-5476	177	21	:	:	PUNCT
ejpam-5476	177	22	otherwise	otherwise	ADV
ejpam-5476	177	23	(	(	PUNCT
ejpam-5476	177	24	31	31	NUM
ejpam-5476	177	25	)	)	PUNCT
ejpam-5476	177	26	then	then	ADV
ejpam-5476	177	27	,	,	PUNCT
ejpam-5476	177	28	dα	dα	PROPN
ejpam-5476	177	29	,	,	PUNCT
ejpam-5476	177	30	ρ	ρ	PROPN
ejpam-5476	177	31	t	t	NOUN
ejpam-5476	177	32	ϕv(t	ϕv(t	PUNCT
ejpam-5476	177	33	)	)	PUNCT
ejpam-5476	177	34	=	=	PUNCT
ejpam-5476	177	35	abētϕv(t	abētϕv(t	NOUN
ejpam-5476	177	36	)	)	PUNCT
ejpam-5476	177	37	,	,	PUNCT
ejpam-5476	177	38	(	(	PUNCT
ejpam-5476	177	39	32	32	NUM
ejpam-5476	177	40	)	)	PUNCT
ejpam-5476	177	41	and	and	CCONJ
ejpam-5476	177	42	dα	dα	PROPN
ejpam-5476	177	43	,	,	PUNCT
ejpam-5476	177	44	ρ	ρ	NOUN
ejpam-5476	177	45	,	,	PUNCT
ejpam-5476	177	46	v	v	NOUN
ejpam-5476	177	47	=	=	SYM
ejpam-5476	178	1	abēt	abēt	NOUN
ejpam-5476	178	2	.	.	PUNCT
ejpam-5476	179	1	so	so	ADV
ejpam-5476	179	2	,	,	PUNCT
ejpam-5476	179	3	the	the	DET
ejpam-5476	179	4	generation	generation	NOUN
ejpam-5476	179	5	of	of	ADP
ejpam-5476	179	6	the	the	DET
ejpam-5476	179	7	above	above	ADJ
ejpam-5476	179	8	formula	formula	NOUN
ejpam-5476	179	9	can	can	AUX
ejpam-5476	179	10	be	be	AUX
ejpam-5476	179	11	given	give	VERB
ejpam-5476	179	12	by	by	ADP
ejpam-5476	179	13	diagram	diagram	NOUN
ejpam-5476	179	14	1	1	NUM
ejpam-5476	179	15	figure	figure	NOUN
ejpam-5476	179	16	1	1	NUM
ejpam-5476	179	17	:	:	PUNCT
ejpam-5476	179	18	operational	operational	ADJ
ejpam-5476	179	19	matrix	matrix	NOUN
ejpam-5476	179	20	of	of	ADP
ejpam-5476	179	21	fractional	fractional	ADJ
ejpam-5476	179	22	differentiation	differentiation	NOUN
ejpam-5476	179	23	.	.	PUNCT
ejpam-5476	180	1	n.	n.	PROPN
ejpam-5476	180	2	anakira	anakira	PROPN
ejpam-5476	180	3	et	et	PROPN
ejpam-5476	180	4	al	al	PROPN
ejpam-5476	180	5	.	.	PUNCT
ejpam-5476	180	6	/	/	SYM
ejpam-5476	180	7	eur	eur	PROPN
ejpam-5476	180	8	.	.	PUNCT
ejpam-5476	181	1	j.	j.	PROPN
ejpam-5476	181	2	pure	pure	PROPN
ejpam-5476	181	3	appl	appl	PROPN
ejpam-5476	181	4	.	.	PROPN
ejpam-5476	181	5	math	math	PROPN
ejpam-5476	181	6	,	,	PUNCT
ejpam-5476	181	7	17	17	NUM
ejpam-5476	181	8	(	(	PUNCT
ejpam-5476	181	9	4	4	NUM
ejpam-5476	181	10	)	)	PUNCT
ejpam-5476	181	11	(	(	PUNCT
ejpam-5476	181	12	2024	2024	NUM
ejpam-5476	181	13	)	)	PUNCT
ejpam-5476	181	14	,	,	PUNCT
ejpam-5476	181	15	3539	3539	NUM
ejpam-5476	181	16	-	-	SYM
ejpam-5476	181	17	3556	3556	NUM
ejpam-5476	181	18	3547	3547	NUM
ejpam-5476	181	19	5	5	NUM
ejpam-5476	181	20	.	.	PUNCT
ejpam-5476	182	1	convergence	convergence	NOUN
ejpam-5476	182	2	analysis	analysis	NOUN
ejpam-5476	182	3	and	and	CCONJ
ejpam-5476	182	4	error	error	NOUN
ejpam-5476	182	5	estimate	estimate	NOUN
ejpam-5476	182	6	in	in	ADP
ejpam-5476	182	7	this	this	DET
ejpam-5476	182	8	section	section	NOUN
ejpam-5476	182	9	,	,	PUNCT
ejpam-5476	182	10	we	we	PRON
ejpam-5476	182	11	provide	provide	VERB
ejpam-5476	182	12	the	the	DET
ejpam-5476	182	13	convergence	convergence	NOUN
ejpam-5476	182	14	theorem	theorem	NOUN
ejpam-5476	182	15	of	of	ADP
ejpam-5476	182	16	the	the	DET
ejpam-5476	182	17	method	method	NOUN
ejpam-5476	182	18	based	base	VERB
ejpam-5476	182	19	on	on	ADP
ejpam-5476	182	20	some	some	DET
ejpam-5476	182	21	existing	exist	VERB
ejpam-5476	182	22	results	result	NOUN
ejpam-5476	182	23	in	in	ADP
ejpam-5476	182	24	[	[	X
ejpam-5476	182	25	5	5	NUM
ejpam-5476	182	26	,	,	PUNCT
ejpam-5476	182	27	30	30	NUM
ejpam-5476	182	28	]	]	PUNCT
ejpam-5476	182	29	.	.	PUNCT
ejpam-5476	183	1	theorem	theorem	VERB
ejpam-5476	183	2	5.1	5.1	NUM
ejpam-5476	183	3	.	.	PUNCT
ejpam-5476	184	1	[	[	X
ejpam-5476	184	2	5	5	X
ejpam-5476	184	3	]	]	PUNCT
ejpam-5476	184	4	let	let	VERB
ejpam-5476	184	5	f	f	PRON
ejpam-5476	184	6	:	:	PUNCT
ejpam-5476	185	1	[	[	X
ejpam-5476	185	2	0	0	NUM
ejpam-5476	185	3	,	,	PUNCT
ejpam-5476	185	4	1	1	NUM
ejpam-5476	185	5	]	]	PUNCT
ejpam-5476	185	6	→	→	PUNCT
ejpam-5476	185	7	r	r	NOUN
ejpam-5476	185	8	such	such	ADJ
ejpam-5476	185	9	that	that	SCONJ
ejpam-5476	185	10	f	f	PROPN
ejpam-5476	185	11	∈	∈	PROPN
ejpam-5476	185	12	cn+1[0	cn+1[0	ADV
ejpam-5476	185	13	,	,	PUNCT
ejpam-5476	185	14	1	1	NUM
ejpam-5476	185	15	]	]	PUNCT
ejpam-5476	185	16	,	,	PUNCT
ejpam-5476	185	17	and	and	CCONJ
ejpam-5476	185	18	sn	sn	PROPN
ejpam-5476	185	19	=	=	PROPN
ejpam-5476	185	20	span{ϕv	span{ϕv	PROPN
ejpam-5476	185	21	0,n	0,n	PROPN
ejpam-5476	185	22	,	,	PUNCT
ejpam-5476	185	23	ϕ	ϕ	X
ejpam-5476	185	24	v	v	ADP
ejpam-5476	185	25	1,n	1,n	NUM
ejpam-5476	185	26	,	,	PUNCT
ejpam-5476	185	27	·	·	PUNCT
ejpam-5476	185	28	·	·	PUNCT
ejpam-5476	185	29	·	·	PUNCT
ejpam-5476	185	30	,	,	PUNCT
ejpam-5476	185	31	ϕv	ϕv	ADP
ejpam-5476	185	32	n	n	CCONJ
ejpam-5476	185	33	,	,	PUNCT
ejpam-5476	185	34	n	n	CCONJ
ejpam-5476	185	35	}	}	PUNCT
ejpam-5476	185	36	,	,	PUNCT
ejpam-5476	185	37	now	now	ADV
ejpam-5476	185	38	if	if	SCONJ
ejpam-5476	185	39	ktϕv	ktϕv	NOUN
ejpam-5476	185	40	be	be	VERB
ejpam-5476	185	41	the	the	DET
ejpam-5476	185	42	best	good	ADJ
ejpam-5476	185	43	approximation	approximation	NOUN
ejpam-5476	185	44	f	f	PROPN
ejpam-5476	185	45	out	out	ADP
ejpam-5476	185	46	of	of	ADP
ejpam-5476	185	47	sn	sn	NOUN
ejpam-5476	185	48	then	then	ADV
ejpam-5476	185	49	||f	||f	VERB
ejpam-5476	185	50	−ktϕv||2	−ktϕv||2	PROPN
ejpam-5476	185	51	≤	≤	ADV
ejpam-5476	185	52	c̄	c̄	PROPN
ejpam-5476	185	53	(	(	PUNCT
ejpam-5476	185	54	n+	n+	NUM
ejpam-5476	185	55	1)!2	1)!2	NUM
ejpam-5476	185	56	√	√	NOUN
ejpam-5476	185	57	2n+	2n+	NUM
ejpam-5476	185	58	1	1	NUM
ejpam-5476	185	59	,	,	PUNCT
ejpam-5476	185	60	(	(	PUNCT
ejpam-5476	185	61	33	33	NUM
ejpam-5476	185	62	)	)	PUNCT
ejpam-5476	185	63	where	where	SCONJ
ejpam-5476	185	64	c̄	c̄	PROPN
ejpam-5476	185	65	=	=	SYM
ejpam-5476	185	66	max	max	PROPN
ejpam-5476	185	67	t∈[0,1	t∈[0,1	PROPN
ejpam-5476	185	68	]	]	PUNCT
ejpam-5476	185	69	|f	|f	PROPN
ejpam-5476	186	1	(	(	PUNCT
ejpam-5476	186	2	n+1)(t)|	n+1)(t)|	PROPN
ejpam-5476	186	3	.	.	PUNCT
ejpam-5476	187	1	(	(	PUNCT
ejpam-5476	187	2	34	34	NUM
ejpam-5476	187	3	)	)	PUNCT
ejpam-5476	187	4	6	6	NUM
ejpam-5476	187	5	.	.	PUNCT
ejpam-5476	188	1	examples	example	NOUN
ejpam-5476	188	2	.	.	PUNCT
ejpam-5476	189	1	example	example	NOUN
ejpam-5476	190	1	1	1	NUM
ejpam-5476	190	2	.	.	X
ejpam-5476	190	3	consider	consider	VERB
ejpam-5476	190	4	the	the	DET
ejpam-5476	190	5	following	follow	VERB
ejpam-5476	190	6	linear	linear	ADJ
ejpam-5476	190	7	ordinary	ordinary	ADJ
ejpam-5476	190	8	differential	differential	ADJ
ejpam-5476	190	9	equation	equation	NOUN
ejpam-5476	190	10	on	on	ADP
ejpam-5476	190	11	[	[	X
ejpam-5476	190	12	0	0	NUM
ejpam-5476	190	13	,	,	PUNCT
ejpam-5476	190	14	1	1	NUM
ejpam-5476	190	15	]	]	PUNCT
ejpam-5476	190	16	.	.	PUNCT
ejpam-5476	191	1	dα	dα	X
ejpam-5476	191	2	,	,	PUNCT
ejpam-5476	191	3	ρ	ρ	PROPN
ejpam-5476	191	4	t	t	NOUN
ejpam-5476	191	5	u(t	u(t	PROPN
ejpam-5476	191	6	)	)	PUNCT
ejpam-5476	191	7	=	=	SYM
ejpam-5476	191	8	u(t	u(t	NOUN
ejpam-5476	191	9	)	)	PUNCT
ejpam-5476	192	1	+	+	NUM
ejpam-5476	192	2	t	t	PROPN
ejpam-5476	192	3	,	,	PUNCT
ejpam-5476	192	4	u(0	u(0	NOUN
ejpam-5476	192	5	)	)	PUNCT
ejpam-5476	192	6	=	=	SYM
ejpam-5476	192	7	1	1	NUM
ejpam-5476	192	8	,	,	PUNCT
ejpam-5476	192	9	0	0	NUM
ejpam-5476	192	10	<	<	X
ejpam-5476	192	11	α	α	PROPN
ejpam-5476	192	12	≤	≤	NUM
ejpam-5476	192	13	1	1	NUM
ejpam-5476	192	14	,	,	PUNCT
ejpam-5476	192	15	ρ	ρ	PROPN
ejpam-5476	192	16	>	>	X
ejpam-5476	192	17	0	0	PUNCT
ejpam-5476	193	1	(	(	PUNCT
ejpam-5476	193	2	35	35	NUM
ejpam-5476	193	3	)	)	PUNCT
ejpam-5476	193	4	when	when	SCONJ
ejpam-5476	193	5	α	α	NOUN
ejpam-5476	193	6	=	=	SYM
ejpam-5476	193	7	ρ	ρ	PROPN
ejpam-5476	193	8	=	=	SYM
ejpam-5476	193	9	1	1	NUM
ejpam-5476	193	10	,	,	PUNCT
ejpam-5476	193	11	the	the	DET
ejpam-5476	193	12	equation	equation	NOUN
ejpam-5476	193	13	has	have	VERB
ejpam-5476	193	14	exact	exact	ADJ
ejpam-5476	193	15	solution	solution	NOUN
ejpam-5476	193	16	u(t	u(t	NOUN
ejpam-5476	193	17	)	)	PUNCT
ejpam-5476	193	18	=	=	PUNCT
ejpam-5476	194	1	2e2	2e2	PROPN
ejpam-5476	194	2	t	t	NOUN
ejpam-5476	194	3	−	−	NOUN
ejpam-5476	194	4	t−	t−	PROPN
ejpam-5476	194	5	1	1	NUM
ejpam-5476	194	6	.	.	PUNCT
ejpam-5476	194	7	first	first	ADV
ejpam-5476	194	8	suppose	suppose	VERB
ejpam-5476	194	9	that	that	SCONJ
ejpam-5476	194	10	u(t	u(t	NOUN
ejpam-5476	194	11	)	)	PUNCT
ejpam-5476	194	12	=	=	SYM
ejpam-5476	194	13	ktϕv(t	ktϕv(t	NOUN
ejpam-5476	194	14	)	)	PUNCT
ejpam-5476	194	15	,	,	PUNCT
ejpam-5476	194	16	and	and	CCONJ
ejpam-5476	194	17	dα	dα	VERB
ejpam-5476	194	18	,	,	PUNCT
ejpam-5476	194	19	ρ	ρ	NOUN
ejpam-5476	194	20	0	0	SYM
ejpam-5476	194	21	u(t	u(t	NOUN
ejpam-5476	194	22	)	)	PUNCT
ejpam-5476	194	23	=	=	PUNCT
ejpam-5476	195	1	ktdα	ktdα	PROPN
ejpam-5476	195	2	,	,	PUNCT
ejpam-5476	195	3	ρϕv(t	ρϕv(t	NOUN
ejpam-5476	195	4	)	)	PUNCT
ejpam-5476	195	5	,	,	PUNCT
ejpam-5476	195	6	next	next	ADJ
ejpam-5476	195	7	write	write	PROPN
ejpam-5476	195	8	t	t	PROPN
ejpam-5476	195	9	in	in	ADP
ejpam-5476	195	10	term	term	NOUN
ejpam-5476	195	11	of	of	ADP
ejpam-5476	195	12	1d	1d	NUM
ejpam-5476	195	13	-	-	PUNCT
ejpam-5476	195	14	fobps	fobps	NOUN
ejpam-5476	195	15	as	as	ADP
ejpam-5476	195	16	t	t	PROPN
ejpam-5476	195	17	=	=	PUNCT
ejpam-5476	196	1	ctϕv(t),where	ctϕv(t),where	ADV
ejpam-5476	196	2	ct	ct	PROPN
ejpam-5476	196	3	=	=	SYM
ejpam-5476	196	4	v	v	NUM
ejpam-5476	196	5	∫	∫	PROPN
ejpam-5476	196	6	1	1	NUM
ejpam-5476	196	7	0	0	NUM
ejpam-5476	196	8	tϕv(t)tdt	tϕv(t)tdt	PROPN
ejpam-5476	196	9	.	.	PUNCT
ejpam-5476	197	1	(	(	PUNCT
ejpam-5476	197	2	36	36	NUM
ejpam-5476	197	3	)	)	PUNCT
ejpam-5476	197	4	we	we	PRON
ejpam-5476	197	5	can	can	AUX
ejpam-5476	197	6	construct	construct	VERB
ejpam-5476	197	7	n	n	DET
ejpam-5476	197	8	linear	linear	ADJ
ejpam-5476	197	9	equation	equation	NOUN
ejpam-5476	197	10	using∫	using∫	VERB
ejpam-5476	197	11	1	1	NUM
ejpam-5476	197	12	0	0	NUM
ejpam-5476	197	13	(	(	PUNCT
ejpam-5476	197	14	ktdα	ktdα	PROPN
ejpam-5476	197	15	,	,	PUNCT
ejpam-5476	197	16	ρ	ρ	PROPN
ejpam-5476	197	17	−kt	−kt	PROPN
ejpam-5476	197	18	−	−	PROPN
ejpam-5476	197	19	ct	ct	NOUN
ejpam-5476	197	20	)	)	PUNCT
ejpam-5476	197	21	ϕv(t)ti+1dt	ϕv(t)ti+1dt	PROPN
ejpam-5476	198	1	=	=	SYM
ejpam-5476	198	2	0	0	NUM
ejpam-5476	198	3	,	,	PUNCT
ejpam-5476	198	4	i	i	PRON
ejpam-5476	198	5	=	=	NOUN
ejpam-5476	198	6	0	0	NUM
ejpam-5476	198	7	,	,	PUNCT
ejpam-5476	198	8	1	1	NUM
ejpam-5476	198	9	,	,	PUNCT
ejpam-5476	198	10	·	·	PUNCT
ejpam-5476	198	11	·	·	PUNCT
ejpam-5476	198	12	·	·	PUNCT
ejpam-5476	198	13	n−	n−	NOUN
ejpam-5476	198	14	1	1	NUM
ejpam-5476	198	15	.	.	PUNCT
ejpam-5476	198	16	(	(	PUNCT
ejpam-5476	198	17	37	37	NUM
ejpam-5476	198	18	)	)	PUNCT
ejpam-5476	198	19	apply	apply	VERB
ejpam-5476	198	20	the	the	DET
ejpam-5476	198	21	initial	initial	ADJ
ejpam-5476	198	22	condition	condition	NOUN
ejpam-5476	198	23	u(0	u(0	NOUN
ejpam-5476	198	24	)	)	PUNCT
ejpam-5476	198	25	=	=	SYM
ejpam-5476	198	26	1	1	NUM
ejpam-5476	198	27	to	to	PART
ejpam-5476	198	28	get	get	VERB
ejpam-5476	198	29	ktϕv(0	ktϕv(0	NOUN
ejpam-5476	198	30	)	)	PUNCT
ejpam-5476	198	31	=	=	SYM
ejpam-5476	199	1	1	1	X
ejpam-5476	199	2	.	.	PUNCT
ejpam-5476	199	3	(	(	PUNCT
ejpam-5476	199	4	38	38	NUM
ejpam-5476	199	5	)	)	PUNCT
ejpam-5476	199	6	thus	thus	ADV
ejpam-5476	199	7	,	,	PUNCT
ejpam-5476	199	8	we	we	PRON
ejpam-5476	199	9	have	have	AUX
ejpam-5476	199	10	(	(	PUNCT
ejpam-5476	199	11	n+	n+	NOUN
ejpam-5476	199	12	1	1	X
ejpam-5476	199	13	)	)	PUNCT
ejpam-5476	199	14	equations	equation	NOUN
ejpam-5476	199	15	for	for	ADP
ejpam-5476	199	16	(	(	PUNCT
ejpam-5476	199	17	n+	n+	NOUN
ejpam-5476	199	18	1	1	NUM
ejpam-5476	199	19	)	)	PUNCT
ejpam-5476	199	20	unknown	unknown	ADJ
ejpam-5476	199	21	variables	variable	NOUN
ejpam-5476	199	22	of	of	ADP
ejpam-5476	199	23	the	the	DET
ejpam-5476	199	24	vector	vector	NOUN
ejpam-5476	199	25	k.	k.	PROPN
ejpam-5476	199	26	after	after	ADP
ejpam-5476	199	27	solving	solve	VERB
ejpam-5476	199	28	the	the	DET
ejpam-5476	199	29	linear	linear	ADJ
ejpam-5476	199	30	system	system	NOUN
ejpam-5476	199	31	,	,	PUNCT
ejpam-5476	199	32	we	we	PRON
ejpam-5476	199	33	can	can	AUX
ejpam-5476	199	34	calculate	calculate	VERB
ejpam-5476	199	35	the	the	DET
ejpam-5476	199	36	approximation	approximation	NOUN
ejpam-5476	199	37	solution	solution	NOUN
ejpam-5476	199	38	u(t	u(t	NOUN
ejpam-5476	199	39	)	)	PUNCT
ejpam-5476	199	40	.	.	PUNCT
ejpam-5476	200	1	figure	figure	NOUN
ejpam-5476	200	2	2	2	NUM
ejpam-5476	200	3	.	.	PUNCT
ejpam-5476	200	4	shows	show	VERB
ejpam-5476	200	5	the	the	DET
ejpam-5476	200	6	exact	exact	ADJ
ejpam-5476	200	7	solution	solution	NOUN
ejpam-5476	200	8	and	and	CCONJ
ejpam-5476	200	9	the	the	DET
ejpam-5476	200	10	approximate	approximate	ADJ
ejpam-5476	200	11	solutions	solution	NOUN
ejpam-5476	200	12	of	of	ADP
ejpam-5476	200	13	example	example	NOUN
ejpam-5476	200	14	1	1	NUM
ejpam-5476	200	15	for	for	ADP
ejpam-5476	200	16	α	α	NOUN
ejpam-5476	200	17	,	,	PUNCT
ejpam-5476	200	18	ρ	ρ	PROPN
ejpam-5476	200	19	=	=	SYM
ejpam-5476	200	20	1	1	NUM
ejpam-5476	200	21	,	,	PUNCT
ejpam-5476	200	22	v	v	NOUN
ejpam-5476	200	23	=	=	SYM
ejpam-5476	200	24	1	1	NUM
ejpam-5476	200	25	,	,	PUNCT
ejpam-5476	200	26	and	and	CCONJ
ejpam-5476	200	27	n	n	CCONJ
ejpam-5476	200	28	=	=	SYM
ejpam-5476	200	29	6	6	NUM
ejpam-5476	200	30	.	.	PUNCT
ejpam-5476	201	1	the	the	DET
ejpam-5476	201	2	absolute	absolute	ADJ
ejpam-5476	201	3	error	error	NOUN
ejpam-5476	201	4	between	between	ADP
ejpam-5476	201	5	the	the	DET
ejpam-5476	201	6	exact	exact	ADJ
ejpam-5476	201	7	solution	solution	NOUN
ejpam-5476	201	8	and	and	CCONJ
ejpam-5476	201	9	approximation	approximation	NOUN
ejpam-5476	201	10	solutions	solution	NOUN
ejpam-5476	201	11	of	of	ADP
ejpam-5476	201	12	example	example	NOUN
ejpam-5476	201	13	1	1	NUM
ejpam-5476	201	14	when	when	SCONJ
ejpam-5476	201	15	n	n	X
ejpam-5476	201	16	=	=	SYM
ejpam-5476	201	17	6	6	NUM
ejpam-5476	201	18	,	,	PUNCT
ejpam-5476	201	19	with	with	ADP
ejpam-5476	201	20	α	α	PROPN
ejpam-5476	201	21	,	,	PUNCT
ejpam-5476	201	22	ρ	ρ	PROPN
ejpam-5476	201	23	=	=	PROPN
ejpam-5476	201	24	,	,	PUNCT
ejpam-5476	201	25	and	and	CCONJ
ejpam-5476	201	26	v	v	NOUN
ejpam-5476	201	27	=	=	SYM
ejpam-5476	201	28	1	1	NUM
ejpam-5476	201	29	is	be	AUX
ejpam-5476	201	30	plotted	plot	VERB
ejpam-5476	201	31	in	in	ADP
ejpam-5476	201	32	figure	figure	NOUN
ejpam-5476	201	33	3	3	NUM
ejpam-5476	201	34	.	.	PUNCT
ejpam-5476	202	1	of	of	ADP
ejpam-5476	202	2	course	course	NOUN
ejpam-5476	202	3	,	,	PUNCT
ejpam-5476	202	4	by	by	ADP
ejpam-5476	202	5	increasing	increase	VERB
ejpam-5476	202	6	the	the	DET
ejpam-5476	202	7	value	value	NOUN
ejpam-5476	202	8	of	of	ADP
ejpam-5476	202	9	n	n	PROPN
ejpam-5476	202	10	of	of	ADP
ejpam-5476	202	11	fobps	fobps	NOUN
ejpam-5476	202	12	,	,	PUNCT
ejpam-5476	202	13	the	the	DET
ejpam-5476	202	14	approximate	approximate	ADJ
ejpam-5476	202	15	values	value	NOUN
ejpam-5476	202	16	of	of	ADP
ejpam-5476	202	17	u(t	u(t	NOUN
ejpam-5476	202	18	)	)	PUNCT
ejpam-5476	202	19	converge	converge	NOUN
ejpam-5476	202	20	to	to	ADP
ejpam-5476	202	21	the	the	DET
ejpam-5476	202	22	exact	exact	ADJ
ejpam-5476	202	23	solutions	solution	NOUN
ejpam-5476	202	24	.	.	PUNCT
ejpam-5476	203	1	figure	figure	NOUN
ejpam-5476	203	2	4	4	NUM
ejpam-5476	203	3	.	.	PUNCT
ejpam-5476	204	1	present	present	VERB
ejpam-5476	204	2	the	the	DET
ejpam-5476	204	3	solution	solution	NOUN
ejpam-5476	204	4	when	when	SCONJ
ejpam-5476	204	5	n	n	PROPN
ejpam-5476	204	6	=	=	SYM
ejpam-5476	204	7	6	6	NUM
ejpam-5476	204	8	,	,	PUNCT
ejpam-5476	204	9	ρ	ρ	PROPN
ejpam-5476	204	10	=	=	SYM
ejpam-5476	204	11	1	1	NUM
ejpam-5476	204	12	,	,	PUNCT
ejpam-5476	204	13	v	v	NOUN
ejpam-5476	204	14	=	=	SYM
ejpam-5476	204	15	1	1	NUM
ejpam-5476	204	16	,	,	PUNCT
ejpam-5476	204	17	and	and	CCONJ
ejpam-5476	204	18	different	different	ADJ
ejpam-5476	204	19	values	value	NOUN
ejpam-5476	204	20	of	of	ADP
ejpam-5476	204	21	α	α	NOUN
ejpam-5476	204	22	.	.	PUNCT
ejpam-5476	205	1	the	the	DET
ejpam-5476	205	2	effect	effect	NOUN
ejpam-5476	205	3	of	of	ADP
ejpam-5476	205	4	ρ	ρ	PROPN
ejpam-5476	205	5	is	be	AUX
ejpam-5476	205	6	presented	present	VERB
ejpam-5476	205	7	in	in	ADP
ejpam-5476	205	8	figure	figure	NOUN
ejpam-5476	205	9	?	?	PUNCT
ejpam-5476	205	10	?	?	PUNCT
ejpam-5476	205	11	.	.	PUNCT
ejpam-5476	206	1	the	the	DET
ejpam-5476	206	2	solution	solution	NOUN
ejpam-5476	206	3	does	do	AUX
ejpam-5476	206	4	not	not	PART
ejpam-5476	206	5	depend	depend	VERB
ejpam-5476	206	6	only	only	ADV
ejpam-5476	206	7	on	on	ADP
ejpam-5476	206	8	α	α	NOUN
ejpam-5476	206	9	but	but	CCONJ
ejpam-5476	206	10	also	also	ADV
ejpam-5476	206	11	on	on	ADP
ejpam-5476	206	12	ρ	ρ	NUM
ejpam-5476	206	13	.	.	PUNCT
ejpam-5476	207	1	the	the	DET
ejpam-5476	207	2	solution	solution	NOUN
ejpam-5476	207	3	for	for	ADP
ejpam-5476	207	4	different	different	ADJ
ejpam-5476	207	5	values	value	NOUN
ejpam-5476	207	6	of	of	ADP
ejpam-5476	207	7	α	α	PROPN
ejpam-5476	207	8	and	and	CCONJ
ejpam-5476	207	9	ρ	ρ	PROPN
ejpam-5476	207	10	is	be	AUX
ejpam-5476	207	11	presented	present	VERB
ejpam-5476	207	12	in	in	ADP
ejpam-5476	207	13	figure	figure	NOUN
ejpam-5476	207	14	n.	n.	PROPN
ejpam-5476	207	15	anakira	anakira	PROPN
ejpam-5476	207	16	et	et	PROPN
ejpam-5476	207	17	al	al	PROPN
ejpam-5476	207	18	.	.	PUNCT
ejpam-5476	207	19	/	/	SYM
ejpam-5476	207	20	eur	eur	PROPN
ejpam-5476	207	21	.	.	PUNCT
ejpam-5476	208	1	j.	j.	PROPN
ejpam-5476	208	2	pure	pure	PROPN
ejpam-5476	208	3	appl	appl	PROPN
ejpam-5476	208	4	.	.	PROPN
ejpam-5476	208	5	math	math	PROPN
ejpam-5476	208	6	,	,	PUNCT
ejpam-5476	208	7	17	17	NUM
ejpam-5476	208	8	(	(	PUNCT
ejpam-5476	208	9	4	4	NUM
ejpam-5476	208	10	)	)	PUNCT
ejpam-5476	208	11	(	(	PUNCT
ejpam-5476	208	12	2024	2024	NUM
ejpam-5476	208	13	)	)	PUNCT
ejpam-5476	208	14	,	,	PUNCT
ejpam-5476	208	15	3539	3539	NUM
ejpam-5476	208	16	-	-	SYM
ejpam-5476	208	17	3556	3556	NUM
ejpam-5476	208	18	3548	3548	NUM
ejpam-5476	208	19	uexact	uexact	ADJ
ejpam-5476	208	20	n=6	n=6	ADJ
ejpam-5476	208	21	0.0	0.0	NUM
ejpam-5476	208	22	0.2	0.2	NUM
ejpam-5476	208	23	0.4	0.4	NUM
ejpam-5476	208	24	0.6	0.6	NUM
ejpam-5476	208	25	0.8	0.8	NUM
ejpam-5476	208	26	1.0	1.0	NUM
ejpam-5476	208	27	0.0	0.0	NUM
ejpam-5476	208	28	0.5	0.5	NUM
ejpam-5476	208	29	1.0	1.0	NUM
ejpam-5476	208	30	1.5	1.5	NUM
ejpam-5476	208	31	2.0	2.0	NUM
ejpam-5476	208	32	2.5	2.5	NUM
ejpam-5476	208	33	3.0	3.0	NUM
ejpam-5476	208	34	3.5	3.5	NUM
ejpam-5476	208	35	t	t	NOUN
ejpam-5476	208	36	u	u	PROPN
ejpam-5476	208	37	(	(	PUNCT
ejpam-5476	208	38	t	t	NOUN
ejpam-5476	208	39	)	)	PUNCT
ejpam-5476	208	40	figure	figure	NOUN
ejpam-5476	208	41	2	2	NUM
ejpam-5476	208	42	:	:	PUNCT
ejpam-5476	208	43	the	the	DET
ejpam-5476	208	44	exact	exact	ADJ
ejpam-5476	208	45	solution	solution	NOUN
ejpam-5476	208	46	and	and	CCONJ
ejpam-5476	208	47	approximation	approximation	NOUN
ejpam-5476	208	48	solutions	solution	NOUN
ejpam-5476	208	49	for	for	ADP
ejpam-5476	208	50	example	example	NOUN
ejpam-5476	208	51	1	1	NUM
ejpam-5476	208	52	when	when	SCONJ
ejpam-5476	208	53	n	n	X
ejpam-5476	208	54	=	=	SYM
ejpam-5476	208	55	6	6	NUM
ejpam-5476	208	56	,	,	PUNCT
ejpam-5476	208	57	with	with	ADP
ejpam-5476	208	58	α	α	NOUN
ejpam-5476	208	59	=	=	SYM
ejpam-5476	208	60	1	1	NUM
ejpam-5476	208	61	,	,	PUNCT
ejpam-5476	208	62	ρ	ρ	NOUN
ejpam-5476	208	63	=	=	SYM
ejpam-5476	208	64	1	1	NUM
ejpam-5476	208	65	,	,	PUNCT
ejpam-5476	208	66	and	and	CCONJ
ejpam-5476	208	67	v	v	X
ejpam-5476	208	68	=	=	SYM
ejpam-5476	208	69	1	1	NUM
ejpam-5476	208	70	.	.	PUNCT
ejpam-5476	208	71	0.0	0.0	NUM
ejpam-5476	208	72	0.2	0.2	NUM
ejpam-5476	208	73	0.4	0.4	NUM
ejpam-5476	208	74	0.6	0.6	NUM
ejpam-5476	208	75	0.8	0.8	NUM
ejpam-5476	208	76	1.0	1.0	NUM
ejpam-5476	208	77	0	0	NUM
ejpam-5476	209	1	1.×	1.×	NUM
ejpam-5476	209	2	10	10	NUM
ejpam-5476	209	3	-	-	SYM
ejpam-5476	209	4	6	6	NUM
ejpam-5476	209	5	2.×	2.×	NUM
ejpam-5476	209	6	10	10	NUM
ejpam-5476	209	7	-	-	SYM
ejpam-5476	209	8	6	6	NUM
ejpam-5476	209	9	3.×	3.×	NUM
ejpam-5476	209	10	10	10	NUM
ejpam-5476	209	11	-	-	SYM
ejpam-5476	209	12	6	6	NUM
ejpam-5476	209	13	4.×	4.×	NUM
ejpam-5476	209	14	10	10	NUM
ejpam-5476	209	15	-	-	SYM
ejpam-5476	209	16	6	6	NUM
ejpam-5476	209	17	t	t	NOUN
ejpam-5476	209	18	a	a	PRON
ejpam-5476	209	19	bs	bs	NOUN
ejpam-5476	209	20	ol	ol	PROPN
ejpam-5476	209	21	ut	ut	PROPN
ejpam-5476	209	22	e	e	PROPN
ejpam-5476	209	23	e	e	PROPN
ejpam-5476	209	24	ro	ro	PROPN
ejpam-5476	209	25	rr	rr	AUX
ejpam-5476	209	26	figure	figure	VERB
ejpam-5476	209	27	3	3	NUM
ejpam-5476	209	28	:	:	PUNCT
ejpam-5476	209	29	the	the	DET
ejpam-5476	209	30	absolute	absolute	ADJ
ejpam-5476	209	31	error	error	NOUN
ejpam-5476	209	32	between	between	ADP
ejpam-5476	209	33	the	the	DET
ejpam-5476	209	34	exact	exact	ADJ
ejpam-5476	209	35	solution	solution	NOUN
ejpam-5476	209	36	and	and	CCONJ
ejpam-5476	209	37	approximation	approximation	NOUN
ejpam-5476	209	38	solutions	solution	NOUN
ejpam-5476	209	39	,	,	PUNCT
ejpam-5476	209	40	for	for	ADP
ejpam-5476	209	41	example	example	NOUN
ejpam-5476	209	42	,	,	PUNCT
ejpam-5476	209	43	1	1	NUM
ejpam-5476	209	44	when	when	SCONJ
ejpam-5476	209	45	α	α	NOUN
ejpam-5476	209	46	=	=	SYM
ejpam-5476	209	47	ρ	ρ	PROPN
ejpam-5476	209	48	=	=	SYM
ejpam-5476	209	49	1	1	NUM
ejpam-5476	209	50	,	,	PUNCT
ejpam-5476	209	51	and	and	CCONJ
ejpam-5476	209	52	v	v	X
ejpam-5476	209	53	=	=	SYM
ejpam-5476	209	54	1	1	NUM
ejpam-5476	209	55	,	,	PUNCT
ejpam-5476	209	56	for	for	ADP
ejpam-5476	209	57	n	n	NOUN
ejpam-5476	209	58	=	=	SYM
ejpam-5476	209	59	6	6	NUM
ejpam-5476	209	60	.	.	NOUN
ejpam-5476	209	61	6	6	NUM
ejpam-5476	209	62	.	.	PUNCT
ejpam-5476	210	1	it	it	PRON
ejpam-5476	210	2	is	be	AUX
ejpam-5476	210	3	worth	worth	ADJ
ejpam-5476	210	4	mentioning	mention	VERB
ejpam-5476	210	5	that	that	SCONJ
ejpam-5476	210	6	the	the	DET
ejpam-5476	210	7	solution	solution	NOUN
ejpam-5476	210	8	is	be	AUX
ejpam-5476	210	9	changed	change	VERB
ejpam-5476	210	10	for	for	SCONJ
ejpam-5476	210	11	every	every	DET
ejpam-5476	210	12	single	single	ADJ
ejpam-5476	210	13	value	value	NOUN
ejpam-5476	210	14	of	of	ADP
ejpam-5476	210	15	α	α	PROPN
ejpam-5476	210	16	and	and	CCONJ
ejpam-5476	210	17	ρ	ρ	PROPN
ejpam-5476	210	18	.	.	PROPN
ejpam-5476	210	19	table	table	NOUN
ejpam-5476	210	20	1	1	NUM
ejpam-5476	210	21	shown	show	VERB
ejpam-5476	210	22	approximate	approximate	ADJ
ejpam-5476	210	23	solutions	solution	NOUN
ejpam-5476	210	24	of	of	ADP
ejpam-5476	210	25	example	example	NOUN
ejpam-5476	210	26	1	1	NUM
ejpam-5476	210	27	when	when	SCONJ
ejpam-5476	210	28	t	t	NOUN
ejpam-5476	210	29	=	=	SYM
ejpam-5476	210	30	1	1	NUM
ejpam-5476	210	31	,	,	PUNCT
ejpam-5476	210	32	v	v	NOUN
ejpam-5476	210	33	=	=	SYM
ejpam-5476	210	34	1	1	NUM
ejpam-5476	210	35	,	,	PUNCT
ejpam-5476	210	36	and	and	CCONJ
ejpam-5476	210	37	different	different	ADJ
ejpam-5476	210	38	value	value	NOUN
ejpam-5476	210	39	of	of	ADP
ejpam-5476	210	40	α	α	PROPN
ejpam-5476	210	41	,	,	PUNCT
ejpam-5476	210	42	ρ	ρ	PROPN
ejpam-5476	210	43	.	.	PUNCT
ejpam-5476	211	1	finally	finally	ADV
ejpam-5476	211	2	,	,	PUNCT
ejpam-5476	211	3	we	we	PRON
ejpam-5476	211	4	note	note	VERB
ejpam-5476	211	5	that	that	SCONJ
ejpam-5476	211	6	the	the	DET
ejpam-5476	211	7	cpu	cpu	ADJ
ejpam-5476	211	8	time	time	NOUN
ejpam-5476	211	9	for	for	ADP
ejpam-5476	211	10	this	this	DET
ejpam-5476	211	11	example	example	NOUN
ejpam-5476	211	12	is	be	AUX
ejpam-5476	211	13	2.372s	2.372s	NUM
ejpam-5476	211	14	for	for	ADP
ejpam-5476	211	15	n	n	NOUN
ejpam-5476	211	16	=	=	NUM
ejpam-5476	211	17	6	6	NUM
ejpam-5476	211	18	using	use	VERB
ejpam-5476	211	19	mathematica	mathematica	PROPN
ejpam-5476	211	20	software	software	PROPN
ejpam-5476	211	21	.	.	PUNCT
ejpam-5476	212	1	example	example	NOUN
ejpam-5476	213	1	2	2	NUM
ejpam-5476	213	2	.	.	X
ejpam-5476	213	3	consider	consider	VERB
ejpam-5476	213	4	the	the	DET
ejpam-5476	213	5	following	follow	VERB
ejpam-5476	213	6	nonlinear	nonlinear	ADJ
ejpam-5476	213	7	riccati	riccati	PROPN
ejpam-5476	213	8	equation	equation	NOUN
ejpam-5476	213	9	on	on	ADP
ejpam-5476	213	10	[	[	X
ejpam-5476	213	11	0,1	0,1	NUM
ejpam-5476	213	12	]	]	PUNCT
ejpam-5476	213	13	,	,	PUNCT
ejpam-5476	213	14	with	with	ADP
ejpam-5476	213	15	a	a	DET
ejpam-5476	213	16	given	give	VERB
ejpam-5476	213	17	initial	initial	ADJ
ejpam-5476	213	18	condition	condition	NOUN
ejpam-5476	213	19	dα	dα	NOUN
ejpam-5476	213	20	,	,	PUNCT
ejpam-5476	213	21	ρ	ρ	NOUN
ejpam-5476	213	22	0	0	SYM
ejpam-5476	213	23	u(t	u(t	NOUN
ejpam-5476	213	24	)	)	PUNCT
ejpam-5476	213	25	=	=	SYM
ejpam-5476	213	26	2u(t)−	2u(t)−	NUM
ejpam-5476	213	27	u2(t	u2(t	NOUN
ejpam-5476	213	28	)	)	PUNCT
ejpam-5476	213	29	+	+	NUM
ejpam-5476	213	30	1	1	NUM
ejpam-5476	213	31	,	,	PUNCT
ejpam-5476	213	32	u(0	u(0	NOUN
ejpam-5476	213	33	)	)	PUNCT
ejpam-5476	213	34	=	=	SYM
ejpam-5476	213	35	0	0	NUM
ejpam-5476	213	36	,	,	PUNCT
ejpam-5476	213	37	0	0	NUM
ejpam-5476	213	38	<	<	X
ejpam-5476	213	39	α	α	PROPN
ejpam-5476	213	40	≤	≤	NUM
ejpam-5476	213	41	1	1	NUM
ejpam-5476	213	42	,	,	PUNCT
ejpam-5476	213	43	ρ	ρ	PROPN
ejpam-5476	213	44	>	>	X
ejpam-5476	213	45	0	0	NUM
ejpam-5476	213	46	.	.	PUNCT
ejpam-5476	214	1	(	(	PUNCT
ejpam-5476	214	2	39	39	NUM
ejpam-5476	214	3	)	)	PUNCT
ejpam-5476	214	4	the	the	DET
ejpam-5476	214	5	exact	exact	ADJ
ejpam-5476	214	6	solution	solution	NOUN
ejpam-5476	214	7	when	when	SCONJ
ejpam-5476	214	8	α	α	X
ejpam-5476	214	9	,	,	PUNCT
ejpam-5476	214	10	ρ	ρ	PROPN
ejpam-5476	214	11	=	=	SYM
ejpam-5476	214	12	1	1	NUM
ejpam-5476	214	13	is	be	AUX
ejpam-5476	214	14	u(t	u(t	NOUN
ejpam-5476	214	15	)	)	PUNCT
ejpam-5476	214	16	=	=	SYM
ejpam-5476	214	17	e2	e2	PROPN
ejpam-5476	214	18	√	√	NUM
ejpam-5476	214	19	2	2	NUM
ejpam-5476	214	20	t	t	NOUN
ejpam-5476	214	21	−	−	NOUN
ejpam-5476	214	22	1	1	NUM
ejpam-5476	214	23	−e2	−e2	NOUN
ejpam-5476	215	1	√	√	NOUN
ejpam-5476	215	2	2	2	NUM
ejpam-5476	215	3	t	t	NOUN
ejpam-5476	215	4	+	+	CCONJ
ejpam-5476	215	5	√	√	PROPN
ejpam-5476	215	6	2e2	2e2	NUM
ejpam-5476	215	7	√	√	PROPN
ejpam-5476	215	8	2	2	NUM
ejpam-5476	215	9	t	t	NOUN
ejpam-5476	215	10	+	+	NOUN
ejpam-5476	215	11	1	1	NUM
ejpam-5476	215	12	+	+	CCONJ
ejpam-5476	215	13	√	√	NUM
ejpam-5476	215	14	2	2	NUM
ejpam-5476	215	15	.	.	PUNCT
ejpam-5476	216	1	(	(	PUNCT
ejpam-5476	216	2	40	40	NUM
ejpam-5476	216	3	)	)	PUNCT
ejpam-5476	216	4	n.	n.	PROPN
ejpam-5476	216	5	anakira	anakira	PROPN
ejpam-5476	216	6	et	et	PROPN
ejpam-5476	216	7	al	al	PROPN
ejpam-5476	216	8	.	.	PUNCT
ejpam-5476	216	9	/	/	SYM
ejpam-5476	216	10	eur	eur	PROPN
ejpam-5476	216	11	.	.	PUNCT
ejpam-5476	217	1	j.	j.	PROPN
ejpam-5476	217	2	pure	pure	PROPN
ejpam-5476	217	3	appl	appl	PROPN
ejpam-5476	217	4	.	.	PROPN
ejpam-5476	217	5	math	math	PROPN
ejpam-5476	217	6	,	,	PUNCT
ejpam-5476	217	7	17	17	NUM
ejpam-5476	217	8	(	(	PUNCT
ejpam-5476	217	9	4	4	NUM
ejpam-5476	217	10	)	)	PUNCT
ejpam-5476	217	11	(	(	PUNCT
ejpam-5476	217	12	2024	2024	NUM
ejpam-5476	217	13	)	)	PUNCT
ejpam-5476	217	14	,	,	PUNCT
ejpam-5476	217	15	3539	3539	NUM
ejpam-5476	217	16	-	-	SYM
ejpam-5476	217	17	3556	3556	NUM
ejpam-5476	217	18	3549	3549	NUM
ejpam-5476	217	19	α=1	α=1	PUNCT
ejpam-5476	217	20	α=0.9	α=0.9	NOUN
ejpam-5476	217	21	α=0.75	α=0.75	ADJ
ejpam-5476	217	22	0.0	0.0	NUM
ejpam-5476	217	23	0.2	0.2	NUM
ejpam-5476	217	24	0.4	0.4	NUM
ejpam-5476	217	25	0.6	0.6	NUM
ejpam-5476	217	26	0.8	0.8	NUM
ejpam-5476	217	27	1.0	1.0	NUM
ejpam-5476	217	28	1.0	1.0	NUM
ejpam-5476	217	29	1.5	1.5	NUM
ejpam-5476	217	30	2.0	2.0	NUM
ejpam-5476	217	31	2.5	2.5	NUM
ejpam-5476	217	32	3.0	3.0	NUM
ejpam-5476	217	33	3.5	3.5	NUM
ejpam-5476	217	34	4.0	4.0	NUM
ejpam-5476	217	35	4.5	4.5	NUM
ejpam-5476	217	36	t	t	NOUN
ejpam-5476	217	37	u	u	PROPN
ejpam-5476	217	38	(	(	PUNCT
ejpam-5476	217	39	t	t	NOUN
ejpam-5476	217	40	)	)	PUNCT
ejpam-5476	217	41	figure	figure	NOUN
ejpam-5476	217	42	4	4	NUM
ejpam-5476	217	43	:	:	PUNCT
ejpam-5476	217	44	the	the	DET
ejpam-5476	217	45	approximate	approximate	ADJ
ejpam-5476	217	46	solution	solution	NOUN
ejpam-5476	217	47	for	for	ADP
ejpam-5476	217	48	example	example	NOUN
ejpam-5476	217	49	1	1	NUM
ejpam-5476	217	50	for	for	ADP
ejpam-5476	217	51	fixed	fix	VERB
ejpam-5476	217	52	n	n	NOUN
ejpam-5476	217	53	=	=	SYM
ejpam-5476	217	54	6	6	NUM
ejpam-5476	217	55	,	,	PUNCT
ejpam-5476	217	56	v	v	NOUN
ejpam-5476	217	57	=	=	SYM
ejpam-5476	217	58	1	1	NUM
ejpam-5476	217	59	,	,	PUNCT
ejpam-5476	217	60	ρ	ρ	NOUN
ejpam-5476	217	61	=	=	SYM
ejpam-5476	217	62	1	1	NUM
ejpam-5476	217	63	,	,	PUNCT
ejpam-5476	217	64	and	and	CCONJ
ejpam-5476	217	65	vary	vary	VERB
ejpam-5476	217	66	α	α	NUM
ejpam-5476	217	67	.	.	PUNCT
ejpam-5476	217	68	ρ=1	ρ=1	ADJ
ejpam-5476	217	69	ρ=0.9	ρ=0.9	NOUN
ejpam-5476	217	70	ρ=0.75	ρ=0.75	NOUN
ejpam-5476	217	71	0.0	0.0	NUM
ejpam-5476	217	72	0.2	0.2	NUM
ejpam-5476	217	73	0.4	0.4	NUM
ejpam-5476	217	74	0.6	0.6	NUM
ejpam-5476	217	75	0.8	0.8	NUM
ejpam-5476	217	76	1.0	1.0	NUM
ejpam-5476	217	77	1.0	1.0	NUM
ejpam-5476	217	78	1.5	1.5	NUM
ejpam-5476	217	79	2.0	2.0	NUM
ejpam-5476	217	80	2.5	2.5	NUM
ejpam-5476	217	81	3.0	3.0	NUM
ejpam-5476	217	82	3.5	3.5	NUM
ejpam-5476	217	83	t	t	NOUN
ejpam-5476	217	84	u	u	PROPN
ejpam-5476	217	85	(	(	PUNCT
ejpam-5476	217	86	t	t	NOUN
ejpam-5476	217	87	)	)	PUNCT
ejpam-5476	217	88	figure	figure	NOUN
ejpam-5476	217	89	5	5	NUM
ejpam-5476	217	90	:	:	PUNCT
ejpam-5476	217	91	the	the	DET
ejpam-5476	217	92	approximate	approximate	ADJ
ejpam-5476	217	93	solutions	solution	NOUN
ejpam-5476	217	94	for	for	ADP
ejpam-5476	217	95	example	example	NOUN
ejpam-5476	217	96	1	1	NUM
ejpam-5476	217	97	for	for	ADP
ejpam-5476	217	98	fixed	fix	VERB
ejpam-5476	217	99	n	n	NOUN
ejpam-5476	217	100	=	=	SYM
ejpam-5476	217	101	6	6	NUM
ejpam-5476	217	102	,	,	PUNCT
ejpam-5476	217	103	α	α	NOUN
ejpam-5476	217	104	=	=	SYM
ejpam-5476	217	105	1	1	NUM
ejpam-5476	217	106	,	,	PUNCT
ejpam-5476	217	107	v	v	NOUN
ejpam-5476	217	108	=	=	SYM
ejpam-5476	217	109	1	1	NUM
ejpam-5476	217	110	,	,	PUNCT
ejpam-5476	217	111	and	and	CCONJ
ejpam-5476	217	112	vary	vary	VERB
ejpam-5476	217	113	ρ	ρ	PROPN
ejpam-5476	217	114	.	.	PUNCT
ejpam-5476	218	1	α=1,ρ=1	α=1,ρ=1	NOUN
ejpam-5476	218	2	α=0.9,ρ=0.9	α=0.9,ρ=0.9	PUNCT
ejpam-5476	219	1	α=0.85,ρ=0.75	α=0.85,ρ=0.75	X
ejpam-5476	219	2	0.0	0.0	NUM
ejpam-5476	219	3	0.2	0.2	NUM
ejpam-5476	219	4	0.4	0.4	NUM
ejpam-5476	219	5	0.6	0.6	NUM
ejpam-5476	219	6	0.8	0.8	NUM
ejpam-5476	219	7	1.0	1.0	NUM
ejpam-5476	219	8	1.0	1.0	NUM
ejpam-5476	219	9	1.5	1.5	NUM
ejpam-5476	219	10	2.0	2.0	NUM
ejpam-5476	219	11	2.5	2.5	NUM
ejpam-5476	219	12	3.0	3.0	NUM
ejpam-5476	219	13	3.5	3.5	NUM
ejpam-5476	219	14	t	t	NOUN
ejpam-5476	219	15	u	u	PROPN
ejpam-5476	219	16	(	(	PUNCT
ejpam-5476	219	17	t	t	PROPN
ejpam-5476	219	18	)	)	PUNCT
ejpam-5476	219	19	figure	figure	NOUN
ejpam-5476	219	20	6	6	NUM
ejpam-5476	219	21	:	:	PUNCT
ejpam-5476	219	22	the	the	DET
ejpam-5476	219	23	approximation	approximation	NOUN
ejpam-5476	219	24	solutions	solution	NOUN
ejpam-5476	219	25	for	for	ADP
ejpam-5476	219	26	example	example	NOUN
ejpam-5476	219	27	1	1	NUM
ejpam-5476	219	28	for	for	ADP
ejpam-5476	219	29	fixed	fix	VERB
ejpam-5476	219	30	n	n	NOUN
ejpam-5476	219	31	=	=	SYM
ejpam-5476	219	32	6	6	NUM
ejpam-5476	219	33	,	,	PUNCT
ejpam-5476	219	34	v	v	NOUN
ejpam-5476	219	35	=	=	SYM
ejpam-5476	219	36	1	1	NUM
ejpam-5476	219	37	,	,	PUNCT
ejpam-5476	219	38	and	and	CCONJ
ejpam-5476	219	39	vary	vary	VERB
ejpam-5476	219	40	α	α	PROPN
ejpam-5476	219	41	,	,	PUNCT
ejpam-5476	219	42	ρ	ρ	PROPN
ejpam-5476	219	43	.	.	PUNCT
ejpam-5476	219	44	n.	n.	PROPN
ejpam-5476	219	45	anakira	anakira	PROPN
ejpam-5476	219	46	et	et	PROPN
ejpam-5476	219	47	al	al	PROPN
ejpam-5476	219	48	.	.	PUNCT
ejpam-5476	219	49	/	/	SYM
ejpam-5476	219	50	eur	eur	PROPN
ejpam-5476	219	51	.	.	PUNCT
ejpam-5476	220	1	j.	j.	PROPN
ejpam-5476	220	2	pure	pure	PROPN
ejpam-5476	220	3	appl	appl	PROPN
ejpam-5476	220	4	.	.	PROPN
ejpam-5476	220	5	math	math	PROPN
ejpam-5476	220	6	,	,	PUNCT
ejpam-5476	220	7	17	17	NUM
ejpam-5476	220	8	(	(	PUNCT
ejpam-5476	220	9	4	4	NUM
ejpam-5476	220	10	)	)	PUNCT
ejpam-5476	220	11	(	(	PUNCT
ejpam-5476	220	12	2024	2024	NUM
ejpam-5476	220	13	)	)	PUNCT
ejpam-5476	220	14	,	,	PUNCT
ejpam-5476	220	15	3539	3539	NUM
ejpam-5476	220	16	-	-	SYM
ejpam-5476	220	17	3556	3556	NUM
ejpam-5476	220	18	3550	3550	NUM
ejpam-5476	220	19	table	table	NOUN
ejpam-5476	220	20	1	1	NUM
ejpam-5476	220	21	:	:	PUNCT
ejpam-5476	220	22	approximate	approximate	ADJ
ejpam-5476	220	23	solutions	solution	NOUN
ejpam-5476	220	24	of	of	ADP
ejpam-5476	220	25	example	example	NOUN
ejpam-5476	220	26	1	1	NUM
ejpam-5476	220	27	when	when	SCONJ
ejpam-5476	220	28	t	t	NOUN
ejpam-5476	220	29	=	=	SYM
ejpam-5476	220	30	1	1	NUM
ejpam-5476	220	31	,	,	PUNCT
ejpam-5476	220	32	v	v	NOUN
ejpam-5476	220	33	=	=	SYM
ejpam-5476	220	34	1	1	NUM
ejpam-5476	220	35	,	,	PUNCT
ejpam-5476	220	36	and	and	CCONJ
ejpam-5476	220	37	different	different	ADJ
ejpam-5476	220	38	value	value	NOUN
ejpam-5476	220	39	of	of	ADP
ejpam-5476	220	40	α	α	PROPN
ejpam-5476	220	41	,	,	PUNCT
ejpam-5476	220	42	ρ	ρ	PROPN
ejpam-5476	220	43	n	n	NOUN
ejpam-5476	220	44	α	α	NOUN
ejpam-5476	220	45	=	=	SYM
ejpam-5476	220	46	1,ρ	1,ρ	NUM
ejpam-5476	220	47	=	=	SYM
ejpam-5476	220	48	1	1	NUM
ejpam-5476	220	49	α	α	NOUN
ejpam-5476	220	50	=	=	SYM
ejpam-5476	220	51	1,ρ	1,ρ	PROPN
ejpam-5476	220	52	=	=	SYM
ejpam-5476	220	53	0.9	0.9	NUM
ejpam-5476	220	54	α	α	NOUN
ejpam-5476	220	55	=	=	SYM
ejpam-5476	220	56	0.95,ρ	0.95,ρ	NUM
ejpam-5476	221	1	=	=	NUM
ejpam-5476	221	2	0.75	0.75	NUM
ejpam-5476	221	3	α	α	NOUN
ejpam-5476	221	4	=	=	PUNCT
ejpam-5476	221	5	0.9,ρ	0.9,ρ	NOUN
ejpam-5476	221	6	=	=	NUM
ejpam-5476	222	1	1.2	1.2	NUM
ejpam-5476	222	2	5	5	NUM
ejpam-5476	222	3	3.43666	3.43666	NUM
ejpam-5476	222	4	3.35715	3.35715	NUM
ejpam-5476	222	5	3.31114	3.31114	NUM
ejpam-5476	222	6	4.02278	4.02278	NUM
ejpam-5476	222	7	6	6	NUM
ejpam-5476	222	8	3.43656	3.43656	NUM
ejpam-5476	222	9	3.36259	3.36259	NUM
ejpam-5476	222	10	3.32984	3.32984	NUM
ejpam-5476	222	11	4.01898	4.01898	NUM
ejpam-5476	222	12	7	7	NUM
ejpam-5476	222	13	3.43656	3.43656	NUM
ejpam-5476	222	14	3.36669	3.36669	NUM
ejpam-5476	222	15	3.34406	3.34406	NUM
ejpam-5476	222	16	4.01691	4.01691	NUM
ejpam-5476	222	17	8	8	NUM
ejpam-5476	222	18	3.43656	3.43656	NUM
ejpam-5476	222	19	3.36986	3.36986	NUM
ejpam-5476	222	20	3.35519	3.35519	NUM
ejpam-5476	222	21	4.01535	4.01535	NUM
ejpam-5476	222	22	now	now	ADV
ejpam-5476	222	23	,	,	PUNCT
ejpam-5476	222	24	we	we	PRON
ejpam-5476	222	25	will	will	AUX
ejpam-5476	222	26	suppose	suppose	VERB
ejpam-5476	222	27	that	that	SCONJ
ejpam-5476	222	28	u(t	u(t	NOUN
ejpam-5476	222	29	)	)	PUNCT
ejpam-5476	222	30	=	=	SYM
ejpam-5476	222	31	ktϕv(t	ktϕv(t	NOUN
ejpam-5476	222	32	)	)	PUNCT
ejpam-5476	222	33	,	,	PUNCT
ejpam-5476	222	34	and	and	CCONJ
ejpam-5476	222	35	dα	dα	VERB
ejpam-5476	222	36	,	,	PUNCT
ejpam-5476	222	37	ρ	ρ	NOUN
ejpam-5476	222	38	0	0	SYM
ejpam-5476	222	39	u(t	u(t	NOUN
ejpam-5476	222	40	)	)	PUNCT
ejpam-5476	222	41	=	=	PUNCT
ejpam-5476	223	1	ktdα	ktdα	PROPN
ejpam-5476	223	2	,	,	PUNCT
ejpam-5476	223	3	ρ	ρ	PROPN
ejpam-5476	223	4	,	,	PUNCT
ejpam-5476	223	5	vϕv(t	vϕv(t	PROPN
ejpam-5476	223	6	)	)	PUNCT
ejpam-5476	223	7	,	,	PUNCT
ejpam-5476	223	8	next	next	ADV
ejpam-5476	223	9	we	we	PRON
ejpam-5476	223	10	write	write	VERB
ejpam-5476	223	11	1	1	NUM
ejpam-5476	223	12	in	in	ADP
ejpam-5476	223	13	term	term	NOUN
ejpam-5476	223	14	of	of	ADP
ejpam-5476	223	15	fobps	fobps	NOUN
ejpam-5476	223	16	as	as	ADP
ejpam-5476	223	17	1	1	NUM
ejpam-5476	223	18	=	=	SYM
ejpam-5476	223	19	ctϕv(t	ctϕv(t	NOUN
ejpam-5476	223	20	)	)	PUNCT
ejpam-5476	223	21	,	,	PUNCT
ejpam-5476	223	22	where	where	SCONJ
ejpam-5476	223	23	ct	ct	PROPN
ejpam-5476	223	24	=	=	SYM
ejpam-5476	223	25	v	v	NUM
ejpam-5476	223	26	∫	∫	PROPN
ejpam-5476	223	27	1	1	NUM
ejpam-5476	223	28	0	0	NUM
ejpam-5476	223	29	ϕv(t)dt	ϕv(t)dt	NOUN
ejpam-5476	223	30	.	.	PUNCT
ejpam-5476	224	1	(	(	PUNCT
ejpam-5476	224	2	41	41	NUM
ejpam-5476	224	3	)	)	PUNCT
ejpam-5476	224	4	substitute	substitute	NOUN
ejpam-5476	224	5	these	these	DET
ejpam-5476	224	6	assumptions	assumption	NOUN
ejpam-5476	224	7	into	into	ADP
ejpam-5476	224	8	the	the	DET
ejpam-5476	224	9	equation	equation	NOUN
ejpam-5476	224	10	39	39	NUM
ejpam-5476	224	11	.	.	PUNCT
ejpam-5476	225	1	thus	thus	ADV
ejpam-5476	225	2	we	we	PRON
ejpam-5476	225	3	get	get	VERB
ejpam-5476	225	4	ktdα	ktdα	PROPN
ejpam-5476	225	5	,	,	PUNCT
ejpam-5476	225	6	ρ	ρ	PROPN
ejpam-5476	225	7	,	,	PUNCT
ejpam-5476	225	8	vϕv(t)−	vϕv(t)−	PROPN
ejpam-5476	225	9	2ktϕv(t	2ktϕv(t	NUM
ejpam-5476	225	10	)	)	PUNCT
ejpam-5476	226	1	+	+	CCONJ
ejpam-5476	226	2	(	(	PUNCT
ejpam-5476	226	3	ktϕv	ktϕv	NOUN
ejpam-5476	226	4	(	(	PUNCT
ejpam-5476	226	5	t))2	t))2	PROPN
ejpam-5476	226	6	−	−	PROPN
ejpam-5476	226	7	ctϕv(t	ctϕv(t	PROPN
ejpam-5476	226	8	)	)	PUNCT
ejpam-5476	226	9	=	=	SYM
ejpam-5476	226	10	0	0	X
ejpam-5476	226	11	.	.	PUNCT
ejpam-5476	227	1	(	(	PUNCT
ejpam-5476	227	2	42	42	X
ejpam-5476	227	3	)	)	PUNCT
ejpam-5476	227	4	construct	construct	VERB
ejpam-5476	227	5	the	the	DET
ejpam-5476	227	6	n	n	PRON
ejpam-5476	227	7	equation	equation	NOUN
ejpam-5476	227	8	as	as	ADP
ejpam-5476	227	9	∫	∫	PROPN
ejpam-5476	227	10	1	1	NUM
ejpam-5476	227	11	0	0	NUM
ejpam-5476	228	1	[	[	X
ejpam-5476	228	2	ktdα	ktdα	PROPN
ejpam-5476	228	3	,	,	PUNCT
ejpam-5476	228	4	ρ	ρ	PROPN
ejpam-5476	228	5	,	,	PUNCT
ejpam-5476	228	6	vϕv(t)−	vϕv(t)−	PROPN
ejpam-5476	228	7	2ktϕv(t	2ktϕv(t	NUM
ejpam-5476	228	8	)	)	PUNCT
ejpam-5476	229	1	+	+	CCONJ
ejpam-5476	229	2	(	(	PUNCT
ejpam-5476	229	3	ktϕv	ktϕv	NOUN
ejpam-5476	229	4	(	(	PUNCT
ejpam-5476	229	5	t))2	t))2	PROPN
ejpam-5476	229	6	−	−	PROPN
ejpam-5476	229	7	ctϕv(t	ctϕv(t	NOUN
ejpam-5476	229	8	)	)	PUNCT
ejpam-5476	229	9	]	]	PUNCT
ejpam-5476	230	1	i+1	i+1	NUM
ejpam-5476	230	2	√	√	ADV
ejpam-5476	230	3	t	t	NOUN
ejpam-5476	230	4	=	=	SYM
ejpam-5476	230	5	0	0	NUM
ejpam-5476	230	6	,	,	PUNCT
ejpam-5476	230	7	i	i	PRON
ejpam-5476	230	8	=	=	NOUN
ejpam-5476	230	9	1	1	NUM
ejpam-5476	230	10	,	,	PUNCT
ejpam-5476	230	11	2	2	NUM
ejpam-5476	230	12	,	,	PUNCT
ejpam-5476	230	13	·	·	PUNCT
ejpam-5476	230	14	·	·	PUNCT
ejpam-5476	230	15	·	·	PUNCT
ejpam-5476	230	16	,	,	PUNCT
ejpam-5476	230	17	n	n	CCONJ
ejpam-5476	230	18	,	,	PUNCT
ejpam-5476	230	19	(	(	PUNCT
ejpam-5476	230	20	43	43	NUM
ejpam-5476	230	21	)	)	PUNCT
ejpam-5476	230	22	the	the	DET
ejpam-5476	230	23	initial	initial	ADJ
ejpam-5476	230	24	condition	condition	NOUN
ejpam-5476	230	25	gives	give	VERB
ejpam-5476	230	26	ktϕv(0	ktϕv(0	NOUN
ejpam-5476	230	27	)	)	PUNCT
ejpam-5476	231	1	=	=	SYM
ejpam-5476	231	2	0	0	X
ejpam-5476	231	3	.	.	PUNCT
ejpam-5476	232	1	(	(	PUNCT
ejpam-5476	232	2	44	44	NUM
ejpam-5476	232	3	)	)	PUNCT
ejpam-5476	232	4	thus	thus	ADV
ejpam-5476	232	5	,	,	PUNCT
ejpam-5476	232	6	we	we	PRON
ejpam-5476	232	7	have	have	VERB
ejpam-5476	232	8	(	(	PUNCT
ejpam-5476	232	9	n+1	n+1	NOUN
ejpam-5476	232	10	)	)	PUNCT
ejpam-5476	232	11	nonlinear	nonlinear	ADJ
ejpam-5476	232	12	equation	equation	NOUN
ejpam-5476	232	13	for	for	ADP
ejpam-5476	232	14	(	(	PUNCT
ejpam-5476	232	15	n+1	n+1	NOUN
ejpam-5476	232	16	)	)	PUNCT
ejpam-5476	232	17	unknown	unknown	ADJ
ejpam-5476	232	18	variable	variable	NOUN
ejpam-5476	232	19	of	of	ADP
ejpam-5476	232	20	vector	vector	PROPN
ejpam-5476	232	21	k.	k.	PROPN
ejpam-5476	232	22	after	after	ADP
ejpam-5476	232	23	solving	solve	VERB
ejpam-5476	232	24	the	the	DET
ejpam-5476	232	25	nonlinear	nonlinear	ADJ
ejpam-5476	232	26	system	system	NOUN
ejpam-5476	232	27	,	,	PUNCT
ejpam-5476	232	28	we	we	PRON
ejpam-5476	232	29	can	can	AUX
ejpam-5476	232	30	calculate	calculate	VERB
ejpam-5476	232	31	the	the	DET
ejpam-5476	232	32	approximation	approximation	NOUN
ejpam-5476	232	33	solution	solution	NOUN
ejpam-5476	232	34	.	.	PUNCT
ejpam-5476	233	1	uexact	uexact	ADJ
ejpam-5476	233	2	n=6	n=6	NOUN
ejpam-5476	233	3	0.0	0.0	NUM
ejpam-5476	233	4	0.2	0.2	NUM
ejpam-5476	233	5	0.4	0.4	NUM
ejpam-5476	233	6	0.6	0.6	NUM
ejpam-5476	233	7	0.8	0.8	NUM
ejpam-5476	233	8	1.0	1.0	NUM
ejpam-5476	233	9	0.0	0.0	NUM
ejpam-5476	233	10	0.5	0.5	NUM
ejpam-5476	233	11	1.0	1.0	NUM
ejpam-5476	233	12	1.5	1.5	NUM
ejpam-5476	233	13	t	t	NOUN
ejpam-5476	233	14	u	u	PROPN
ejpam-5476	233	15	(	(	PUNCT
ejpam-5476	233	16	t	t	NOUN
ejpam-5476	233	17	)	)	PUNCT
ejpam-5476	233	18	figure	figure	NOUN
ejpam-5476	233	19	7	7	NUM
ejpam-5476	233	20	:	:	PUNCT
ejpam-5476	233	21	the	the	DET
ejpam-5476	233	22	exact	exact	ADJ
ejpam-5476	233	23	solution	solution	NOUN
ejpam-5476	233	24	and	and	CCONJ
ejpam-5476	233	25	approximation	approximation	NOUN
ejpam-5476	233	26	solutions	solution	NOUN
ejpam-5476	233	27	for	for	ADP
ejpam-5476	233	28	example	example	NOUN
ejpam-5476	233	29	2	2	NUM
ejpam-5476	233	30	when	when	SCONJ
ejpam-5476	233	31	n	n	X
ejpam-5476	233	32	=	=	SYM
ejpam-5476	233	33	6	6	NUM
ejpam-5476	233	34	,	,	PUNCT
ejpam-5476	233	35	with	with	ADP
ejpam-5476	233	36	α	α	NOUN
ejpam-5476	233	37	=	=	SYM
ejpam-5476	233	38	1	1	NUM
ejpam-5476	233	39	,	,	PUNCT
ejpam-5476	233	40	ρ	ρ	NOUN
ejpam-5476	233	41	=	=	SYM
ejpam-5476	233	42	1	1	NUM
ejpam-5476	233	43	,	,	PUNCT
ejpam-5476	233	44	and	and	CCONJ
ejpam-5476	233	45	v	v	X
ejpam-5476	233	46	=	=	SYM
ejpam-5476	233	47	1	1	NUM
ejpam-5476	233	48	.	.	PUNCT
ejpam-5476	234	1	n.	n.	PROPN
ejpam-5476	234	2	anakira	anakira	PROPN
ejpam-5476	234	3	et	et	PROPN
ejpam-5476	234	4	al	al	PROPN
ejpam-5476	234	5	.	.	PUNCT
ejpam-5476	234	6	/	/	SYM
ejpam-5476	234	7	eur	eur	PROPN
ejpam-5476	234	8	.	.	PUNCT
ejpam-5476	235	1	j.	j.	PROPN
ejpam-5476	235	2	pure	pure	PROPN
ejpam-5476	235	3	appl	appl	PROPN
ejpam-5476	235	4	.	.	PROPN
ejpam-5476	235	5	math	math	PROPN
ejpam-5476	235	6	,	,	PUNCT
ejpam-5476	235	7	17	17	NUM
ejpam-5476	235	8	(	(	PUNCT
ejpam-5476	235	9	4	4	NUM
ejpam-5476	235	10	)	)	PUNCT
ejpam-5476	235	11	(	(	PUNCT
ejpam-5476	235	12	2024	2024	NUM
ejpam-5476	235	13	)	)	PUNCT
ejpam-5476	235	14	,	,	PUNCT
ejpam-5476	235	15	3539	3539	NUM
ejpam-5476	235	16	-	-	SYM
ejpam-5476	235	17	3556	3556	NUM
ejpam-5476	235	18	3551	3551	NUM
ejpam-5476	235	19	n=3	n=3	PUNCT
ejpam-5476	235	20	n=4	n=4	X
ejpam-5476	235	21	n=5	n=5	PRON
ejpam-5476	235	22	n=6	n=6	NOUN
ejpam-5476	235	23	0.0	0.0	NUM
ejpam-5476	235	24	0.2	0.2	NUM
ejpam-5476	235	25	0.4	0.4	NUM
ejpam-5476	235	26	0.6	0.6	NUM
ejpam-5476	235	27	0.8	0.8	NUM
ejpam-5476	235	28	1.0	1.0	NUM
ejpam-5476	235	29	0.000	0.000	NUM
ejpam-5476	235	30	0.001	0.001	NUM
ejpam-5476	235	31	0.002	0.002	NUM
ejpam-5476	235	32	0.003	0.003	NUM
ejpam-5476	235	33	0.004	0.004	NUM
ejpam-5476	235	34	0.005	0.005	NUM
ejpam-5476	235	35	0.006	0.006	NUM
ejpam-5476	235	36	0.007	0.007	NUM
ejpam-5476	235	37	t	t	PROPN
ejpam-5476	235	38	a	a	DET
ejpam-5476	235	39	bs	bs	NOUN
ejpam-5476	235	40	ol	ol	PROPN
ejpam-5476	235	41	ut	ut	PROPN
ejpam-5476	235	42	e	e	PROPN
ejpam-5476	235	43	e	e	PROPN
ejpam-5476	235	44	rr	rr	NOUN
ejpam-5476	235	45	or	or	CCONJ
ejpam-5476	235	46	figure	figure	VERB
ejpam-5476	235	47	8	8	NUM
ejpam-5476	235	48	:	:	PUNCT
ejpam-5476	235	49	the	the	DET
ejpam-5476	235	50	absolute	absolute	ADJ
ejpam-5476	235	51	error	error	NOUN
ejpam-5476	235	52	between	between	ADP
ejpam-5476	235	53	the	the	DET
ejpam-5476	235	54	exact	exact	ADJ
ejpam-5476	235	55	solution	solution	NOUN
ejpam-5476	235	56	and	and	CCONJ
ejpam-5476	235	57	approximate	approximate	ADJ
ejpam-5476	235	58	solution	solution	NOUN
ejpam-5476	235	59	,	,	PUNCT
ejpam-5476	235	60	for	for	ADP
ejpam-5476	235	61	example	example	NOUN
ejpam-5476	235	62	,	,	PUNCT
ejpam-5476	235	63	2	2	NUM
ejpam-5476	235	64	when	when	SCONJ
ejpam-5476	235	65	α	α	NOUN
ejpam-5476	235	66	=	=	SYM
ejpam-5476	235	67	1	1	NUM
ejpam-5476	235	68	,	,	PUNCT
ejpam-5476	235	69	ρ	ρ	NOUN
ejpam-5476	235	70	=	=	SYM
ejpam-5476	235	71	1	1	NUM
ejpam-5476	235	72	,	,	PUNCT
ejpam-5476	235	73	v	v	NOUN
ejpam-5476	235	74	=	=	SYM
ejpam-5476	235	75	1	1	NUM
ejpam-5476	235	76	and	and	CCONJ
ejpam-5476	235	77	vary	vary	VERB
ejpam-5476	235	78	n.	n.	PROPN
ejpam-5476	235	79	α=1	α=1	PUNCT
ejpam-5476	235	80	α=0.9	α=0.9	NOUN
ejpam-5476	235	81	α=0.75	α=0.75	ADJ
ejpam-5476	235	82	0.0	0.0	NUM
ejpam-5476	235	83	0.2	0.2	NUM
ejpam-5476	235	84	0.4	0.4	NUM
ejpam-5476	235	85	0.6	0.6	NUM
ejpam-5476	235	86	0.8	0.8	NUM
ejpam-5476	235	87	1.0	1.0	NUM
ejpam-5476	235	88	0.0	0.0	NUM
ejpam-5476	235	89	0.5	0.5	NUM
ejpam-5476	235	90	1.0	1.0	NUM
ejpam-5476	235	91	1.5	1.5	NUM
ejpam-5476	235	92	t	t	NOUN
ejpam-5476	235	93	u	u	PROPN
ejpam-5476	235	94	(	(	PUNCT
ejpam-5476	235	95	t	t	NOUN
ejpam-5476	235	96	)	)	PUNCT
ejpam-5476	235	97	figure	figure	NOUN
ejpam-5476	235	98	9	9	NUM
ejpam-5476	235	99	:	:	PUNCT
ejpam-5476	235	100	the	the	DET
ejpam-5476	235	101	approximation	approximation	NOUN
ejpam-5476	235	102	solutions	solution	NOUN
ejpam-5476	235	103	for	for	ADP
ejpam-5476	235	104	example	example	NOUN
ejpam-5476	235	105	2	2	NUM
ejpam-5476	235	106	for	for	ADP
ejpam-5476	235	107	fixed	fix	VERB
ejpam-5476	235	108	n	n	NOUN
ejpam-5476	235	109	=	=	SYM
ejpam-5476	235	110	4	4	NUM
ejpam-5476	235	111	,	,	PUNCT
ejpam-5476	235	112	ρ	ρ	PROPN
ejpam-5476	235	113	=	=	SYM
ejpam-5476	235	114	1	1	NUM
ejpam-5476	235	115	,	,	PUNCT
ejpam-5476	235	116	and	and	CCONJ
ejpam-5476	235	117	v	v	X
ejpam-5476	235	118	=	=	SYM
ejpam-5476	235	119	1	1	NUM
ejpam-5476	235	120	and	and	CCONJ
ejpam-5476	235	121	vary	vary	VERB
ejpam-5476	235	122	α	α	PROPN
ejpam-5476	235	123	.	.	PUNCT
ejpam-5476	235	124	figures	figure	NOUN
ejpam-5476	235	125	7	7	NUM
ejpam-5476	235	126	show	show	VERB
ejpam-5476	235	127	the	the	DET
ejpam-5476	235	128	exact	exact	ADJ
ejpam-5476	235	129	solution	solution	NOUN
ejpam-5476	235	130	together	together	ADV
ejpam-5476	235	131	with	with	ADP
ejpam-5476	235	132	the	the	DET
ejpam-5476	235	133	approximate	approximate	ADJ
ejpam-5476	235	134	solution	solution	NOUN
ejpam-5476	235	135	,	,	PUNCT
ejpam-5476	235	136	for	for	ADP
ejpam-5476	235	137	example	example	NOUN
ejpam-5476	235	138	,	,	PUNCT
ejpam-5476	235	139	2	2	NUM
ejpam-5476	235	140	when	when	SCONJ
ejpam-5476	235	141	n	n	X
ejpam-5476	235	142	=	=	SYM
ejpam-5476	235	143	6	6	NUM
ejpam-5476	235	144	,	,	PUNCT
ejpam-5476	235	145	and	and	CCONJ
ejpam-5476	235	146	the	the	DET
ejpam-5476	235	147	absolute	absolute	ADJ
ejpam-5476	235	148	error	error	NOUN
ejpam-5476	235	149	between	between	ADP
ejpam-5476	235	150	them	they	PRON
ejpam-5476	235	151	for	for	ADP
ejpam-5476	235	152	α	α	NOUN
ejpam-5476	235	153	,	,	PUNCT
ejpam-5476	235	154	ρ	ρ	PROPN
ejpam-5476	235	155	=	=	SYM
ejpam-5476	235	156	1	1	NUM
ejpam-5476	235	157	,	,	PUNCT
ejpam-5476	235	158	v	v	NOUN
ejpam-5476	235	159	=	=	SYM
ejpam-5476	235	160	1	1	NUM
ejpam-5476	235	161	,	,	PUNCT
ejpam-5476	235	162	and	and	CCONJ
ejpam-5476	235	163	different	different	ADJ
ejpam-5476	235	164	values	value	NOUN
ejpam-5476	235	165	of	of	ADP
ejpam-5476	235	166	n	n	NOUN
ejpam-5476	235	167	are	be	AUX
ejpam-5476	235	168	shown	show	VERB
ejpam-5476	235	169	in	in	ADP
ejpam-5476	235	170	figures	figure	NOUN
ejpam-5476	235	171	8	8	NUM
ejpam-5476	235	172	,	,	PUNCT
ejpam-5476	235	173	we	we	PRON
ejpam-5476	235	174	note	note	VERB
ejpam-5476	235	175	,	,	PUNCT
ejpam-5476	235	176	by	by	ADP
ejpam-5476	235	177	increasing	increase	VERB
ejpam-5476	235	178	the	the	DET
ejpam-5476	235	179	value	value	NOUN
ejpam-5476	235	180	of	of	ADP
ejpam-5476	235	181	n	n	PROPN
ejpam-5476	235	182	of	of	ADP
ejpam-5476	235	183	fobps	fobps	NOUN
ejpam-5476	235	184	,	,	PUNCT
ejpam-5476	235	185	the	the	DET
ejpam-5476	235	186	approximate	approximate	ADJ
ejpam-5476	235	187	solution	solution	NOUN
ejpam-5476	235	188	of	of	ADP
ejpam-5476	235	189	u(t	u(t	NOUN
ejpam-5476	235	190	)	)	PUNCT
ejpam-5476	235	191	converges	converge	NOUN
ejpam-5476	235	192	to	to	ADP
ejpam-5476	235	193	the	the	DET
ejpam-5476	235	194	exact	exact	ADJ
ejpam-5476	235	195	solutions	solution	NOUN
ejpam-5476	235	196	.	.	PUNCT
ejpam-5476	236	1	in	in	ADP
ejpam-5476	236	2	figure	figure	NOUN
ejpam-5476	236	3	9	9	NUM
ejpam-5476	236	4	,	,	PUNCT
ejpam-5476	236	5	we	we	PRON
ejpam-5476	236	6	plot	plot	VERB
ejpam-5476	236	7	the	the	DET
ejpam-5476	236	8	approximate	approximate	ADJ
ejpam-5476	236	9	solution	solution	NOUN
ejpam-5476	236	10	,	,	PUNCT
ejpam-5476	236	11	for	for	ADP
ejpam-5476	236	12	example	example	NOUN
ejpam-5476	236	13	,	,	PUNCT
ejpam-5476	236	14	2	2	NUM
ejpam-5476	236	15	when	when	SCONJ
ejpam-5476	236	16	n	n	X
ejpam-5476	236	17	=	=	SYM
ejpam-5476	236	18	4	4	NUM
ejpam-5476	236	19	,	,	PUNCT
ejpam-5476	236	20	ρ	ρ	PROPN
ejpam-5476	236	21	=	=	SYM
ejpam-5476	236	22	1	1	NUM
ejpam-5476	236	23	,	,	PUNCT
ejpam-5476	236	24	v	v	NOUN
ejpam-5476	236	25	=	=	SYM
ejpam-5476	236	26	1	1	NUM
ejpam-5476	236	27	,	,	PUNCT
ejpam-5476	236	28	and	and	CCONJ
ejpam-5476	236	29	different	different	ADJ
ejpam-5476	236	30	values	value	NOUN
ejpam-5476	236	31	of	of	ADP
ejpam-5476	236	32	α	α	NOUN
ejpam-5476	236	33	.	.	PUNCT
ejpam-5476	237	1	as	as	SCONJ
ejpam-5476	237	2	α	α	PROPN
ejpam-5476	237	3	approaches	approach	VERB
ejpam-5476	237	4	1	1	NUM
ejpam-5476	237	5	,	,	PUNCT
ejpam-5476	237	6	we	we	PRON
ejpam-5476	237	7	note	note	VERB
ejpam-5476	237	8	that	that	SCONJ
ejpam-5476	237	9	the	the	DET
ejpam-5476	237	10	approximate	approximate	ADJ
ejpam-5476	237	11	solution	solution	NOUN
ejpam-5476	237	12	converges	converge	VERB
ejpam-5476	237	13	to	to	ADP
ejpam-5476	237	14	the	the	DET
ejpam-5476	237	15	exact	exact	ADJ
ejpam-5476	237	16	solution	solution	NOUN
ejpam-5476	237	17	.	.	PUNCT
ejpam-5476	238	1	the	the	DET
ejpam-5476	238	2	approximate	approximate	ADJ
ejpam-5476	238	3	solution	solution	NOUN
ejpam-5476	238	4	for	for	ADP
ejpam-5476	238	5	example	example	NOUN
ejpam-5476	238	6	2	2	NUM
ejpam-5476	238	7	when	when	SCONJ
ejpam-5476	238	8	n	n	X
ejpam-5476	238	9	=	=	SYM
ejpam-5476	238	10	4	4	NUM
ejpam-5476	238	11	,	,	PUNCT
ejpam-5476	238	12	α	α	NOUN
ejpam-5476	238	13	=	=	SYM
ejpam-5476	238	14	1	1	NUM
ejpam-5476	238	15	,	,	PUNCT
ejpam-5476	238	16	v	v	NOUN
ejpam-5476	238	17	=	=	SYM
ejpam-5476	238	18	1	1	NUM
ejpam-5476	238	19	,	,	PUNCT
ejpam-5476	238	20	and	and	CCONJ
ejpam-5476	238	21	different	different	ADJ
ejpam-5476	238	22	value	value	NOUN
ejpam-5476	238	23	of	of	ADP
ejpam-5476	238	24	ρ	ρ	PROPN
ejpam-5476	238	25	are	be	AUX
ejpam-5476	238	26	shown	show	VERB
ejpam-5476	238	27	in	in	ADP
ejpam-5476	238	28	figure	figure	NOUN
ejpam-5476	238	29	10	10	NUM
ejpam-5476	238	30	.	.	PUNCT
ejpam-5476	239	1	the	the	DET
ejpam-5476	239	2	solution	solution	NOUN
ejpam-5476	239	3	does	do	AUX
ejpam-5476	239	4	not	not	PART
ejpam-5476	239	5	depend	depend	VERB
ejpam-5476	239	6	only	only	ADV
ejpam-5476	239	7	on	on	ADP
ejpam-5476	239	8	α	α	NOUN
ejpam-5476	239	9	but	but	CCONJ
ejpam-5476	239	10	also	also	ADV
ejpam-5476	239	11	on	on	ADP
ejpam-5476	239	12	ρ	ρ	NUM
ejpam-5476	239	13	.	.	PUNCT
ejpam-5476	240	1	the	the	DET
ejpam-5476	240	2	effect	effect	NOUN
ejpam-5476	240	3	of	of	ADP
ejpam-5476	240	4	changing	change	VERB
ejpam-5476	240	5	two	two	NUM
ejpam-5476	240	6	values	value	NOUN
ejpam-5476	240	7	of	of	ADP
ejpam-5476	240	8	α	α	PROPN
ejpam-5476	240	9	,	,	PUNCT
ejpam-5476	240	10	ρ	ρ	NOUN
ejpam-5476	240	11	for	for	ADP
ejpam-5476	240	12	changing	change	VERB
ejpam-5476	240	13	an	an	DET
ejpam-5476	240	14	approximate	approximate	ADJ
ejpam-5476	240	15	solution	solution	NOUN
ejpam-5476	240	16	for	for	ADP
ejpam-5476	240	17	example	example	NOUN
ejpam-5476	240	18	2	2	NUM
ejpam-5476	240	19	is	be	AUX
ejpam-5476	240	20	presented	present	VERB
ejpam-5476	240	21	in	in	ADP
ejpam-5476	240	22	figure	figure	NOUN
ejpam-5476	240	23	11	11	NUM
ejpam-5476	240	24	,	,	PUNCT
ejpam-5476	240	25	and	and	CCONJ
ejpam-5476	240	26	we	we	PRON
ejpam-5476	240	27	note	note	VERB
ejpam-5476	240	28	that	that	SCONJ
ejpam-5476	240	29	as	as	ADP
ejpam-5476	240	30	α	α	PROPN
ejpam-5476	240	31	,	,	PUNCT
ejpam-5476	240	32	ρ	ρ	PROPN
ejpam-5476	240	33	approaches	approach	VERB
ejpam-5476	240	34	1	1	NUM
ejpam-5476	240	35	,	,	PUNCT
ejpam-5476	240	36	the	the	DET
ejpam-5476	240	37	numerical	numerical	ADJ
ejpam-5476	240	38	solution	solution	NOUN
ejpam-5476	240	39	converges	converge	VERB
ejpam-5476	240	40	to	to	ADP
ejpam-5476	240	41	the	the	DET
ejpam-5476	240	42	exact	exact	ADJ
ejpam-5476	240	43	solution	solution	NOUN
ejpam-5476	240	44	.	.	PUNCT
ejpam-5476	241	1	table	table	NOUN
ejpam-5476	241	2	2	2	NUM
ejpam-5476	241	3	shows	show	VERB
ejpam-5476	241	4	approximate	approximate	ADJ
ejpam-5476	241	5	solutions	solution	NOUN
ejpam-5476	241	6	of	of	ADP
ejpam-5476	241	7	fractional	fractional	ADJ
ejpam-5476	241	8	riccati	riccati	NOUN
ejpam-5476	241	9	equation	equation	NOUN
ejpam-5476	241	10	when	when	SCONJ
ejpam-5476	241	11	t	t	PROPN
ejpam-5476	241	12	=	=	SYM
ejpam-5476	241	13	1	1	NUM
ejpam-5476	241	14	,	,	PUNCT
ejpam-5476	241	15	v	v	NOUN
ejpam-5476	241	16	=	=	SYM
ejpam-5476	241	17	1	1	NUM
ejpam-5476	241	18	,	,	PUNCT
ejpam-5476	241	19	and	and	CCONJ
ejpam-5476	241	20	different	different	ADJ
ejpam-5476	241	21	values	value	NOUN
ejpam-5476	241	22	of	of	ADP
ejpam-5476	241	23	α	α	PROPN
ejpam-5476	241	24	,	,	PUNCT
ejpam-5476	241	25	ρ	ρ	PROPN
ejpam-5476	241	26	.	.	PUNCT
ejpam-5476	242	1	it	it	PRON
ejpam-5476	242	2	is	be	AUX
ejpam-5476	242	3	clear	clear	ADJ
ejpam-5476	242	4	that	that	SCONJ
ejpam-5476	242	5	the	the	DET
ejpam-5476	242	6	solution	solution	NOUN
ejpam-5476	242	7	behaviors	behavior	NOUN
ejpam-5476	242	8	depend	depend	VERB
ejpam-5476	242	9	on	on	ADP
ejpam-5476	242	10	the	the	DET
ejpam-5476	242	11	two	two	NUM
ejpam-5476	242	12	fractional	fractional	ADJ
ejpam-5476	242	13	parameters	parameter	NOUN
ejpam-5476	242	14	which	which	PRON
ejpam-5476	242	15	give	give	VERB
ejpam-5476	242	16	the	the	DET
ejpam-5476	242	17	scientists	scientist	NOUN
ejpam-5476	242	18	a	a	DET
ejpam-5476	242	19	benefit	benefit	NOUN
ejpam-5476	242	20	in	in	ADP
ejpam-5476	242	21	choosing	choose	VERB
ejpam-5476	242	22	which	which	DET
ejpam-5476	242	23	one	one	PRON
ejpam-5476	242	24	can	can	AUX
ejpam-5476	242	25	fit	fit	VERB
ejpam-5476	242	26	the	the	DET
ejpam-5476	242	27	real	real	ADJ
ejpam-5476	242	28	data	datum	NOUN
ejpam-5476	242	29	n.	n.	PROPN
ejpam-5476	242	30	anakira	anakira	PROPN
ejpam-5476	242	31	et	et	PROPN
ejpam-5476	242	32	al	al	PROPN
ejpam-5476	242	33	.	.	PUNCT
ejpam-5476	242	34	/	/	SYM
ejpam-5476	242	35	eur	eur	PROPN
ejpam-5476	242	36	.	.	PUNCT
ejpam-5476	243	1	j.	j.	PROPN
ejpam-5476	243	2	pure	pure	PROPN
ejpam-5476	243	3	appl	appl	PROPN
ejpam-5476	243	4	.	.	PROPN
ejpam-5476	243	5	math	math	PROPN
ejpam-5476	243	6	,	,	PUNCT
ejpam-5476	243	7	17	17	NUM
ejpam-5476	243	8	(	(	PUNCT
ejpam-5476	243	9	4	4	NUM
ejpam-5476	243	10	)	)	PUNCT
ejpam-5476	243	11	(	(	PUNCT
ejpam-5476	243	12	2024	2024	NUM
ejpam-5476	243	13	)	)	PUNCT
ejpam-5476	243	14	,	,	PUNCT
ejpam-5476	243	15	3539	3539	NUM
ejpam-5476	243	16	-	-	SYM
ejpam-5476	243	17	3556	3556	NUM
ejpam-5476	243	18	3552	3552	NUM
ejpam-5476	243	19	ρ=1	ρ=1	ADJ
ejpam-5476	243	20	ρ=0.9	ρ=0.9	NOUN
ejpam-5476	243	21	ρ=0.85	ρ=0.85	NOUN
ejpam-5476	243	22	0.0	0.0	NUM
ejpam-5476	243	23	0.2	0.2	NUM
ejpam-5476	243	24	0.4	0.4	NUM
ejpam-5476	243	25	0.6	0.6	NUM
ejpam-5476	243	26	0.8	0.8	NUM
ejpam-5476	243	27	1.0	1.0	NUM
ejpam-5476	243	28	0.0	0.0	NUM
ejpam-5476	243	29	0.5	0.5	NUM
ejpam-5476	243	30	1.0	1.0	NUM
ejpam-5476	243	31	1.5	1.5	NUM
ejpam-5476	243	32	t	t	NOUN
ejpam-5476	243	33	u	u	PROPN
ejpam-5476	243	34	(	(	PUNCT
ejpam-5476	243	35	t	t	NOUN
ejpam-5476	243	36	)	)	PUNCT
ejpam-5476	243	37	figure	figure	NOUN
ejpam-5476	243	38	10	10	NUM
ejpam-5476	243	39	:	:	PUNCT
ejpam-5476	243	40	the	the	DET
ejpam-5476	243	41	approximation	approximation	NOUN
ejpam-5476	243	42	solutions	solution	NOUN
ejpam-5476	243	43	for	for	ADP
ejpam-5476	243	44	example	example	NOUN
ejpam-5476	243	45	2	2	NUM
ejpam-5476	243	46	for	for	ADP
ejpam-5476	243	47	fixed	fix	VERB
ejpam-5476	243	48	n	n	NOUN
ejpam-5476	243	49	=	=	SYM
ejpam-5476	243	50	4	4	NUM
ejpam-5476	243	51	,	,	PUNCT
ejpam-5476	243	52	α	α	NOUN
ejpam-5476	243	53	=	=	SYM
ejpam-5476	243	54	1	1	NUM
ejpam-5476	243	55	,	,	PUNCT
ejpam-5476	243	56	and	and	CCONJ
ejpam-5476	243	57	v	v	X
ejpam-5476	243	58	=	=	SYM
ejpam-5476	243	59	1	1	NUM
ejpam-5476	243	60	,	,	PUNCT
ejpam-5476	243	61	and	and	CCONJ
ejpam-5476	243	62	vary	vary	VERB
ejpam-5476	243	63	ρ	ρ	PROPN
ejpam-5476	243	64	.	.	PUNCT
ejpam-5476	244	1	α=1,ρ=1	α=1,ρ=1	PROPN
ejpam-5476	244	2	α=0.85,ρ=0.75	α=0.85,ρ=0.75	PROPN
ejpam-5476	244	3	α=0.95,ρ=0.75	α=0.95,ρ=0.75	ADJ
ejpam-5476	244	4	0.0	0.0	NUM
ejpam-5476	244	5	0.2	0.2	NUM
ejpam-5476	244	6	0.4	0.4	NUM
ejpam-5476	244	7	0.6	0.6	NUM
ejpam-5476	244	8	0.8	0.8	NUM
ejpam-5476	244	9	1.0	1.0	NUM
ejpam-5476	244	10	0.0	0.0	NUM
ejpam-5476	244	11	0.5	0.5	NUM
ejpam-5476	244	12	1.0	1.0	NUM
ejpam-5476	244	13	1.5	1.5	NUM
ejpam-5476	244	14	t	t	NOUN
ejpam-5476	244	15	u	u	PROPN
ejpam-5476	244	16	(	(	PUNCT
ejpam-5476	244	17	t	t	NOUN
ejpam-5476	244	18	)	)	PUNCT
ejpam-5476	244	19	figure	figure	NOUN
ejpam-5476	244	20	11	11	NUM
ejpam-5476	244	21	:	:	PUNCT
ejpam-5476	244	22	the	the	DET
ejpam-5476	244	23	approximation	approximation	NOUN
ejpam-5476	244	24	solutions	solution	NOUN
ejpam-5476	244	25	for	for	ADP
ejpam-5476	244	26	example	example	NOUN
ejpam-5476	244	27	2	2	NUM
ejpam-5476	244	28	for	for	ADP
ejpam-5476	244	29	fixed	fix	VERB
ejpam-5476	244	30	n	n	NOUN
ejpam-5476	244	31	=	=	SYM
ejpam-5476	244	32	4	4	NUM
ejpam-5476	244	33	,	,	PUNCT
ejpam-5476	244	34	and	and	CCONJ
ejpam-5476	244	35	v	v	X
ejpam-5476	244	36	=	=	SYM
ejpam-5476	244	37	1	1	NUM
ejpam-5476	244	38	and	and	CCONJ
ejpam-5476	244	39	vary	vary	VERB
ejpam-5476	244	40	α	α	PROPN
ejpam-5476	244	41	,	,	PUNCT
ejpam-5476	244	42	ρ	ρ	PROPN
ejpam-5476	244	43	.	.	PUNCT
ejpam-5476	245	1	more	more	ADV
ejpam-5476	245	2	accurately	accurately	ADV
ejpam-5476	245	3	.	.	PUNCT
ejpam-5476	246	1	7	7	X
ejpam-5476	246	2	.	.	X
ejpam-5476	246	3	conclusion	conclusion	NOUN
ejpam-5476	246	4	in	in	ADP
ejpam-5476	246	5	this	this	DET
ejpam-5476	246	6	paper	paper	NOUN
ejpam-5476	246	7	,	,	PUNCT
ejpam-5476	246	8	we	we	PRON
ejpam-5476	246	9	apply	apply	VERB
ejpam-5476	246	10	the	the	DET
ejpam-5476	246	11	method	method	NOUN
ejpam-5476	246	12	of	of	ADP
ejpam-5476	246	13	operational	operational	ADJ
ejpam-5476	246	14	matrices	matrix	NOUN
ejpam-5476	246	15	for	for	ADP
ejpam-5476	246	16	bernstein	bernstein	PROPN
ejpam-5476	246	17	polynomials	polynomial	NOUN
ejpam-5476	246	18	to	to	PART
ejpam-5476	246	19	solve	solve	VERB
ejpam-5476	246	20	the	the	DET
ejpam-5476	246	21	generalized	generalize	VERB
ejpam-5476	246	22	fractional	fractional	ADJ
ejpam-5476	246	23	differential	differential	NOUN
ejpam-5476	246	24	of	of	ADP
ejpam-5476	246	25	the	the	DET
ejpam-5476	246	26	caputo	caputo	PROPN
ejpam-5476	246	27	type	type	NOUN
ejpam-5476	246	28	with	with	ADP
ejpam-5476	246	29	two	two	NUM
ejpam-5476	246	30	parameters	parameter	NOUN
ejpam-5476	246	31	.	.	PUNCT
ejpam-5476	247	1	operational	operational	ADJ
ejpam-5476	247	2	matrices	matrix	NOUN
ejpam-5476	247	3	convert	convert	VERB
ejpam-5476	247	4	differential	differential	ADJ
ejpam-5476	247	5	equations	equation	NOUN
ejpam-5476	247	6	into	into	ADP
ejpam-5476	247	7	algebraic	algebraic	ADJ
ejpam-5476	247	8	equations	equation	NOUN
ejpam-5476	247	9	to	to	PART
ejpam-5476	247	10	calculate	calculate	VERB
ejpam-5476	247	11	approximate	approximate	ADJ
ejpam-5476	247	12	solutions	solution	NOUN
ejpam-5476	247	13	to	to	PART
ejpam-5476	247	14	linear	linear	VERB
ejpam-5476	247	15	and	and	CCONJ
ejpam-5476	247	16	nonlinear	nonlinear	ADJ
ejpam-5476	247	17	fractional	fractional	ADJ
ejpam-5476	247	18	differential	differential	ADJ
ejpam-5476	247	19	equations	equation	NOUN
ejpam-5476	247	20	.	.	PUNCT
ejpam-5476	248	1	the	the	DET
ejpam-5476	248	2	accuracy	accuracy	NOUN
ejpam-5476	248	3	of	of	ADP
ejpam-5476	248	4	the	the	DET
ejpam-5476	248	5	approximate	approximate	ADJ
ejpam-5476	248	6	solutions	solution	NOUN
ejpam-5476	248	7	was	be	AUX
ejpam-5476	248	8	verified	verify	VERB
ejpam-5476	248	9	by	by	ADP
ejpam-5476	248	10	comparing	compare	VERB
ejpam-5476	248	11	the	the	DET
ejpam-5476	248	12	approximate	approximate	ADJ
ejpam-5476	248	13	solutions	solution	NOUN
ejpam-5476	248	14	when	when	SCONJ
ejpam-5476	248	15	α	α	X
ejpam-5476	248	16	,	,	PUNCT
ejpam-5476	248	17	ρ	ρ	NOUN
ejpam-5476	248	18	=	=	SYM
ejpam-5476	248	19	1	1	NUM
ejpam-5476	248	20	,	,	PUNCT
ejpam-5476	248	21	and	and	CCONJ
ejpam-5476	248	22	v	v	X
ejpam-5476	248	23	=	=	SYM
ejpam-5476	248	24	1	1	NUM
ejpam-5476	248	25	with	with	ADP
ejpam-5476	248	26	the	the	DET
ejpam-5476	248	27	exact	exact	ADJ
ejpam-5476	248	28	solutions	solution	NOUN
ejpam-5476	248	29	in	in	ADP
ejpam-5476	248	30	the	the	DET
ejpam-5476	248	31	case	case	NOUN
ejpam-5476	248	32	of	of	ADP
ejpam-5476	248	33	linear	linear	PROPN
ejpam-5476	248	34	and	and	CCONJ
ejpam-5476	248	35	nonlinear	nonlinear	ADJ
ejpam-5476	248	36	equations	equation	NOUN
ejpam-5476	248	37	.	.	PUNCT
ejpam-5476	249	1	the	the	DET
ejpam-5476	249	2	method	method	NOUN
ejpam-5476	249	3	used	use	VERB
ejpam-5476	249	4	to	to	PART
ejpam-5476	249	5	analyze	analyze	VERB
ejpam-5476	249	6	and	and	CCONJ
ejpam-5476	249	7	solve	solve	VERB
ejpam-5476	249	8	fractional	fractional	ADJ
ejpam-5476	249	9	differential	differential	NOUN
ejpam-5476	249	10	equations	equation	NOUN
ejpam-5476	249	11	is	be	AUX
ejpam-5476	249	12	implemented	implement	VERB
ejpam-5476	249	13	.	.	PUNCT
ejpam-5476	250	1	the	the	DET
ejpam-5476	250	2	operational	operational	ADJ
ejpam-5476	250	3	matrices	matrix	NOUN
ejpam-5476	250	4	method	method	NOUN
ejpam-5476	250	5	is	be	AUX
ejpam-5476	250	6	effective	effective	ADJ
ejpam-5476	250	7	and	and	CCONJ
ejpam-5476	250	8	reveals	reveal	VERB
ejpam-5476	250	9	the	the	DET
ejpam-5476	250	10	existence	existence	NOUN
ejpam-5476	250	11	of	of	ADP
ejpam-5476	250	12	the	the	DET
ejpam-5476	250	13	approximate	approximate	ADJ
ejpam-5476	250	14	solution	solution	NOUN
ejpam-5476	250	15	.	.	PUNCT
ejpam-5476	251	1	from	from	ADP
ejpam-5476	251	2	the	the	DET
ejpam-5476	251	3	solved	solve	VERB
ejpam-5476	251	4	linear	linear	NOUN
ejpam-5476	251	5	and	and	CCONJ
ejpam-5476	251	6	nonlinear	nonlinear	ADJ
ejpam-5476	251	7	problems	problem	NOUN
ejpam-5476	251	8	,	,	PUNCT
ejpam-5476	251	9	it	it	PRON
ejpam-5476	251	10	was	be	AUX
ejpam-5476	251	11	found	find	VERB
ejpam-5476	251	12	that	that	SCONJ
ejpam-5476	251	13	the	the	DET
ejpam-5476	251	14	approximate	approximate	ADJ
ejpam-5476	251	15	solutions	solution	NOUN
ejpam-5476	251	16	obtained	obtain	VERB
ejpam-5476	251	17	using	use	VERB
ejpam-5476	251	18	the	the	DET
ejpam-5476	251	19	presented	present	VERB
ejpam-5476	251	20	algorithm	algorithm	NOUN
ejpam-5476	251	21	are	be	AUX
ejpam-5476	251	22	very	very	ADV
ejpam-5476	251	23	close	close	ADJ
ejpam-5476	251	24	to	to	ADP
ejpam-5476	251	25	the	the	DET
ejpam-5476	251	26	references	reference	NOUN
ejpam-5476	251	27	3553	3553	NUM
ejpam-5476	251	28	table	table	NOUN
ejpam-5476	251	29	2	2	NUM
ejpam-5476	251	30	:	:	PUNCT
ejpam-5476	251	31	approximate	approximate	ADJ
ejpam-5476	251	32	solutions	solution	NOUN
ejpam-5476	251	33	of	of	ADP
ejpam-5476	251	34	fractional	fractional	ADJ
ejpam-5476	251	35	riccati	riccati	NOUN
ejpam-5476	251	36	equation	equation	NOUN
ejpam-5476	252	1	when	when	SCONJ
ejpam-5476	252	2	t	t	PROPN
ejpam-5476	252	3	=	=	SYM
ejpam-5476	252	4	1	1	NUM
ejpam-5476	252	5	,	,	PUNCT
ejpam-5476	252	6	and	and	CCONJ
ejpam-5476	252	7	different	different	ADJ
ejpam-5476	252	8	values	value	NOUN
ejpam-5476	252	9	of	of	ADP
ejpam-5476	252	10	α	α	PROPN
ejpam-5476	252	11	,	,	PUNCT
ejpam-5476	252	12	ρ	ρ	PROPN
ejpam-5476	252	13	n	n	NOUN
ejpam-5476	252	14	α	α	NOUN
ejpam-5476	252	15	=	=	SYM
ejpam-5476	252	16	1,ρ	1,ρ	NUM
ejpam-5476	252	17	=	=	SYM
ejpam-5476	252	18	1	1	NUM
ejpam-5476	252	19	α	α	NOUN
ejpam-5476	252	20	=	=	SYM
ejpam-5476	252	21	1,ρ	1,ρ	PROPN
ejpam-5476	252	22	=	=	SYM
ejpam-5476	252	23	0.9	0.9	NUM
ejpam-5476	252	24	α	α	NOUN
ejpam-5476	252	25	=	=	SYM
ejpam-5476	252	26	0.95,ρ	0.95,ρ	NUM
ejpam-5476	252	27	=	=	NUM
ejpam-5476	252	28	0.75	0.75	NUM
ejpam-5476	252	29	α	α	NOUN
ejpam-5476	252	30	=	=	PUNCT
ejpam-5476	252	31	0.9,ρ	0.9,ρ	NOUN
ejpam-5476	253	1	=	=	NUM
ejpam-5476	253	2	1.2	1.2	NUM
ejpam-5476	253	3	3	3	NUM
ejpam-5476	253	4	1.69116	1.69116	NUM
ejpam-5476	253	5	1.68978	1.68978	NUM
ejpam-5476	253	6	1.70788	1.70788	NUM
ejpam-5476	253	7	1.79401	1.79401	NUM
ejpam-5476	253	8	4	4	NUM
ejpam-5476	253	9	1.6892	1.6892	NUM
ejpam-5476	253	10	1.68927	1.68927	NUM
ejpam-5476	253	11	1.70997	1.70997	NUM
ejpam-5476	253	12	1.78634	1.78634	NUM
ejpam-5476	253	13	5	5	NUM
ejpam-5476	253	14	1.68945	1.68945	NUM
ejpam-5476	253	15	1.68947	1.68947	NUM
ejpam-5476	253	16	1.7106	1.7106	NUM
ejpam-5476	253	17	1.78903	1.78903	NUM
ejpam-5476	253	18	6	6	NUM
ejpam-5476	253	19	1.68937	1.68937	NUM
ejpam-5476	253	20	1.68891	1.68891	NUM
ejpam-5476	253	21	1.71064	1.71064	NUM
ejpam-5476	253	22	1.79657	1.79657	NUM
ejpam-5476	253	23	exact	exact	ADJ
ejpam-5476	253	24	solutions	solution	NOUN
ejpam-5476	253	25	.	.	PUNCT
ejpam-5476	254	1	therefore	therefore	ADV
ejpam-5476	254	2	,	,	PUNCT
ejpam-5476	254	3	this	this	DET
ejpam-5476	254	4	study	study	NOUN
ejpam-5476	254	5	will	will	AUX
ejpam-5476	254	6	begin	begin	VERB
ejpam-5476	254	7	further	far	ADV
ejpam-5476	254	8	implementing	implement	VERB
ejpam-5476	254	9	and	and	CCONJ
ejpam-5476	254	10	investigating	investigate	VERB
ejpam-5476	254	11	generalized	generalized	ADJ
ejpam-5476	254	12	partial	partial	ADJ
ejpam-5476	254	13	caputo	caputo	PROPN
ejpam-5476	254	14	systems	systems	PROPN
ejpam-5476	254	15	.	.	PUNCT
ejpam-5476	255	1	physical	physical	ADJ
ejpam-5476	255	2	interpretation	interpretation	NOUN
ejpam-5476	255	3	of	of	ADP
ejpam-5476	255	4	the	the	DET
ejpam-5476	255	5	generalized	generalize	VERB
ejpam-5476	255	6	fractional	fractional	ADJ
ejpam-5476	255	7	differential	differential	NOUN
ejpam-5476	255	8	equations	equation	NOUN
ejpam-5476	255	9	can	can	AUX
ejpam-5476	255	10	also	also	ADV
ejpam-5476	255	11	be	be	AUX
ejpam-5476	255	12	investigated	investigate	VERB
ejpam-5476	255	13	in	in	ADP
ejpam-5476	255	14	the	the	DET
ejpam-5476	255	15	future	future	NOUN
ejpam-5476	255	16	.	.	PUNCT
ejpam-5476	256	1	references	reference	NOUN
ejpam-5476	256	2	[	[	X
ejpam-5476	256	3	1	1	X
ejpam-5476	256	4	]	]	PUNCT
ejpam-5476	256	5	t.	t.	NOUN
ejpam-5476	256	6	abdeljawad	abdeljawad	NOUN
ejpam-5476	256	7	and	and	CCONJ
ejpam-5476	256	8	q.	q.	PROPN
ejpam-5476	256	9	m.	m.	PROPN
ejpam-5476	256	10	al	al	PROPN
ejpam-5476	256	11	-	-	PUNCT
ejpam-5476	256	12	mdallal	mdallal	PROPN
ejpam-5476	256	13	.	.	PUNCT
ejpam-5476	257	1	discrete	discrete	VERB
ejpam-5476	257	2	mittag	mittag	ADJ
ejpam-5476	257	3	–	–	PUNCT
ejpam-5476	257	4	leffler	leffler	ADJ
ejpam-5476	257	5	kernel	kernel	NOUN
ejpam-5476	257	6	type	type	NOUN
ejpam-5476	257	7	fractional	fractional	ADJ
ejpam-5476	257	8	difference	difference	NOUN
ejpam-5476	257	9	initial	initial	ADJ
ejpam-5476	257	10	value	value	NOUN
ejpam-5476	257	11	problems	problem	NOUN
ejpam-5476	257	12	and	and	CCONJ
ejpam-5476	257	13	gronwall	gronwall	PROPN
ejpam-5476	257	14	’s	’s	PART
ejpam-5476	257	15	inequality	inequality	NOUN
ejpam-5476	257	16	.	.	PUNCT
ejpam-5476	258	1	j.	j.	PROPN
ejpam-5476	258	2	comput	comput	PROPN
ejpam-5476	258	3	.	.	PUNCT
ejpam-5476	259	1	appl	appl	PROPN
ejpam-5476	259	2	.	.	PROPN
ejpam-5476	259	3	math	math	PROPN
ejpam-5476	259	4	.	.	PUNCT
ejpam-5476	259	5	,	,	PUNCT
ejpam-5476	259	6	339:218–230	339:218–230	NUM
ejpam-5476	259	7	,	,	PUNCT
ejpam-5476	259	8	2018	2018	NUM
ejpam-5476	259	9	.	.	PUNCT
ejpam-5476	260	1	[	[	X
ejpam-5476	260	2	2	2	X
ejpam-5476	260	3	]	]	PUNCT
ejpam-5476	260	4	t.	t.	NOUN
ejpam-5476	260	5	abdeljawad	abdeljawad	PROPN
ejpam-5476	260	6	and	and	CCONJ
ejpam-5476	260	7	d.	d.	PROPN
ejpam-5476	260	8	baleanu	baleanu	PROPN
ejpam-5476	260	9	.	.	PUNCT
ejpam-5476	261	1	on	on	ADP
ejpam-5476	261	2	fractional	fractional	ADJ
ejpam-5476	261	3	derivatives	derivative	NOUN
ejpam-5476	261	4	with	with	ADP
ejpam-5476	261	5	generalized	generalized	ADJ
ejpam-5476	261	6	mittag	mittag	ADJ
ejpam-5476	261	7	–	–	PUNCT
ejpam-5476	261	8	leffler	leffler	ADJ
ejpam-5476	261	9	kernels	kernel	NOUN
ejpam-5476	261	10	.	.	PUNCT
ejpam-5476	262	1	adv	adv	PROPN
ejpam-5476	262	2	.	.	PUNCT
ejpam-5476	263	1	diff	diff	PROPN
ejpam-5476	263	2	.	.	PUNCT
ejpam-5476	264	1	equat	equat	PROPN
ejpam-5476	264	2	.	.	PUNCT
ejpam-5476	264	3	,	,	PUNCT
ejpam-5476	264	4	468	468	NUM
ejpam-5476	264	5	,	,	PUNCT
ejpam-5476	264	6	2018	2018	NUM
ejpam-5476	264	7	.	.	PUNCT
ejpam-5476	265	1	[	[	X
ejpam-5476	265	2	3	3	X
ejpam-5476	265	3	]	]	PUNCT
ejpam-5476	265	4	k.	k.	PROPN
ejpam-5476	265	5	a.	a.	PROPN
ejpam-5476	265	6	abro	abro	PROPN
ejpam-5476	265	7	,	,	PUNCT
ejpam-5476	265	8	a.	a.	PROPN
ejpam-5476	265	9	atangana	atangana	PROPN
ejpam-5476	265	10	,	,	PUNCT
ejpam-5476	265	11	and	and	CCONJ
ejpam-5476	265	12	j.	j.	PROPN
ejpam-5476	265	13	f.	f.	PROPN
ejpam-5476	265	14	gomez	gomez	PROPN
ejpam-5476	265	15	-	-	PUNCT
ejpam-5476	265	16	aguilar	aguilar	PROPN
ejpam-5476	265	17	.	.	PUNCT
ejpam-5476	266	1	ferromagnetic	ferromagnetic	ADJ
ejpam-5476	266	2	chaos	chaos	NOUN
ejpam-5476	266	3	in	in	ADP
ejpam-5476	266	4	thermal	thermal	ADJ
ejpam-5476	266	5	convection	convection	NOUN
ejpam-5476	266	6	of	of	ADP
ejpam-5476	266	7	fluid	fluid	NOUN
ejpam-5476	266	8	through	through	ADP
ejpam-5476	266	9	fractal	fractal	ADJ
ejpam-5476	266	10	–	–	PUNCT
ejpam-5476	266	11	fractional	fractional	ADJ
ejpam-5476	266	12	differentiations	differentiation	NOUN
ejpam-5476	266	13	.	.	PUNCT
ejpam-5476	267	1	journal	journal	NOUN
ejpam-5476	267	2	of	of	ADP
ejpam-5476	267	3	thermal	thermal	ADJ
ejpam-5476	267	4	analysis	analysis	NOUN
ejpam-5476	267	5	and	and	CCONJ
ejpam-5476	267	6	calorimetry	calorimetry	NOUN
ejpam-5476	267	7	,	,	PUNCT
ejpam-5476	267	8	147:8461–8473	147:8461–8473	NUM
ejpam-5476	267	9	,	,	PUNCT
ejpam-5476	267	10	2022	2022	NUM
ejpam-5476	267	11	.	.	PUNCT
ejpam-5476	268	1	[	[	X
ejpam-5476	268	2	4	4	NUM
ejpam-5476	268	3	]	]	PUNCT
ejpam-5476	268	4	r.	r.	PROPN
ejpam-5476	268	5	b.	b.	PROPN
ejpam-5476	268	6	albadarneh	albadarneh	PROPN
ejpam-5476	268	7	,	,	PUNCT
ejpam-5476	268	8	i.	i.	PROPN
ejpam-5476	268	9	batiha	batiha	PROPN
ejpam-5476	268	10	,	,	PUNCT
ejpam-5476	268	11	a.	a.	NOUN
ejpam-5476	268	12	k.	k.	PROPN
ejpam-5476	268	13	alomari	alomari	PROPN
ejpam-5476	268	14	,	,	PUNCT
ejpam-5476	268	15	and	and	CCONJ
ejpam-5476	268	16	n.	n.	PROPN
ejpam-5476	268	17	tahat	tahat	PROPN
ejpam-5476	268	18	.	.	PUNCT
ejpam-5476	269	1	numerical	numerical	ADJ
ejpam-5476	269	2	approach	approach	NOUN
ejpam-5476	269	3	for	for	ADP
ejpam-5476	269	4	approximating	approximate	VERB
ejpam-5476	269	5	the	the	DET
ejpam-5476	269	6	caputo	caputo	PROPN
ejpam-5476	269	7	fractional	fractional	ADJ
ejpam-5476	269	8	-	-	PUNCT
ejpam-5476	269	9	order	order	NOUN
ejpam-5476	269	10	derivative	derivative	ADJ
ejpam-5476	269	11	operator	operator	NOUN
ejpam-5476	269	12	.	.	PUNCT
ejpam-5476	270	1	aims	aim	VERB
ejpam-5476	270	2	mathematics	mathematic	NOUN
ejpam-5476	270	3	,	,	PUNCT
ejpam-5476	270	4	6(11):12743–12756	6(11):12743–12756	NUM
ejpam-5476	270	5	,	,	PUNCT
ejpam-5476	270	6	2021	2021	NUM
ejpam-5476	270	7	.	.	PUNCT
ejpam-5476	271	1	[	[	X
ejpam-5476	271	2	5	5	X
ejpam-5476	271	3	]	]	PUNCT
ejpam-5476	271	4	m.	m.	NOUN
ejpam-5476	271	5	alipour	alipour	ADJ
ejpam-5476	271	6	and	and	CCONJ
ejpam-5476	271	7	d.	d.	PROPN
ejpam-5476	271	8	rostamy	rostamy	PROPN
ejpam-5476	271	9	.	.	PUNCT
ejpam-5476	272	1	bernstein	bernstein	PROPN
ejpam-5476	272	2	polynomials	polynomial	VERB
ejpam-5476	272	3	for	for	ADP
ejpam-5476	272	4	solving	solve	VERB
ejpam-5476	272	5	abel	abel	NOUN
ejpam-5476	272	6	’s	’s	PART
ejpam-5476	272	7	integral	integral	ADJ
ejpam-5476	272	8	equation	equation	NOUN
ejpam-5476	272	9	.	.	PUNCT
ejpam-5476	273	1	journal	journal	NOUN
ejpam-5476	273	2	of	of	ADP
ejpam-5476	273	3	mathematics	mathematics	PROPN
ejpam-5476	273	4	and	and	CCONJ
ejpam-5476	273	5	computer	computer	NOUN
ejpam-5476	273	6	science	science	NOUN
ejpam-5476	273	7	,	,	PUNCT
ejpam-5476	273	8	3(4):403–412	3(4):403–412	NUM
ejpam-5476	273	9	,	,	PUNCT
ejpam-5476	273	10	2011	2011	NUM
ejpam-5476	273	11	.	.	PUNCT
ejpam-5476	274	1	[	[	X
ejpam-5476	274	2	6	6	NUM
ejpam-5476	274	3	]	]	PUNCT
ejpam-5476	274	4	b.	b.	PROPN
ejpam-5476	274	5	s.	s.	PROPN
ejpam-5476	274	6	t.	t.	PROPN
ejpam-5476	274	7	alkahtani	alkahtani	PROPN
ejpam-5476	274	8	.	.	PUNCT
ejpam-5476	275	1	atangana	atangana	PROPN
ejpam-5476	275	2	–	–	PUNCT
ejpam-5476	275	3	batogna	batogna	PROPN
ejpam-5476	275	4	numerical	numerical	ADJ
ejpam-5476	275	5	scheme	scheme	NOUN
ejpam-5476	275	6	applied	apply	VERB
ejpam-5476	275	7	on	on	ADP
ejpam-5476	275	8	a	a	DET
ejpam-5476	275	9	linear	linear	ADJ
ejpam-5476	275	10	and	and	CCONJ
ejpam-5476	275	11	non	non	ADJ
ejpam-5476	275	12	-	-	ADJ
ejpam-5476	275	13	linear	linear	ADJ
ejpam-5476	275	14	fractional	fractional	ADJ
ejpam-5476	275	15	differential	differential	NOUN
ejpam-5476	275	16	equation	equation	NOUN
ejpam-5476	275	17	.	.	PUNCT
ejpam-5476	276	1	eur	eur	ADJ
ejpam-5476	276	2	.	.	PUNCT
ejpam-5476	276	3	phys	phy	NOUN
ejpam-5476	276	4	.	.	PUNCT
ejpam-5476	277	1	j.	j.	PROPN
ejpam-5476	277	2	plus	plus	PROPN
ejpam-5476	277	3	,	,	PUNCT
ejpam-5476	277	4	133(3):111	133(3):111	NUM
ejpam-5476	277	5	,	,	PUNCT
ejpam-5476	277	6	2018	2018	NUM
ejpam-5476	277	7	.	.	PUNCT
ejpam-5476	278	1	[	[	X
ejpam-5476	278	2	7	7	X
ejpam-5476	278	3	]	]	PUNCT
ejpam-5476	278	4	s.	s.	PROPN
ejpam-5476	278	5	a.	a.	PROPN
ejpam-5476	278	6	altaie	altaie	PROPN
ejpam-5476	278	7	,	,	PUNCT
ejpam-5476	278	8	n.	n.	PROPN
ejpam-5476	278	9	anakira	anakira	PROPN
ejpam-5476	278	10	,	,	PUNCT
ejpam-5476	278	11	a.	a.	PROPN
ejpam-5476	278	12	jameel	jameel	PROPN
ejpam-5476	278	13	,	,	PUNCT
ejpam-5476	278	14	o.	o.	PROPN
ejpam-5476	278	15	ababneh	ababneh	PROPN
ejpam-5476	278	16	,	,	PUNCT
ejpam-5476	278	17	a.	a.	NOUN
ejpam-5476	278	18	qazza	qazza	PROPN
ejpam-5476	278	19	,	,	PUNCT
ejpam-5476	278	20	and	and	CCONJ
ejpam-5476	278	21	a.	a.	NOUN
ejpam-5476	278	22	k.	k.	PROPN
ejpam-5476	278	23	alomari	alomari	PROPN
ejpam-5476	278	24	.	.	PUNCT
ejpam-5476	279	1	homotopy	homotopy	VERB
ejpam-5476	279	2	analysis	analysis	NOUN
ejpam-5476	279	3	method	method	NOUN
ejpam-5476	279	4	analytical	analytical	ADJ
ejpam-5476	279	5	scheme	scheme	NOUN
ejpam-5476	279	6	for	for	ADP
ejpam-5476	279	7	developing	develop	VERB
ejpam-5476	279	8	a	a	DET
ejpam-5476	279	9	solution	solution	NOUN
ejpam-5476	279	10	to	to	ADP
ejpam-5476	279	11	partial	partial	ADJ
ejpam-5476	279	12	differential	differential	ADJ
ejpam-5476	279	13	equations	equation	NOUN
ejpam-5476	279	14	in	in	ADP
ejpam-5476	279	15	fuzzy	fuzzy	ADJ
ejpam-5476	279	16	environment	environment	NOUN
ejpam-5476	279	17	.	.	PUNCT
ejpam-5476	280	1	fractal	fractal	ADJ
ejpam-5476	280	2	and	and	CCONJ
ejpam-5476	280	3	fractional	fractional	ADJ
ejpam-5476	280	4	,	,	PUNCT
ejpam-5476	280	5	6(8):419	6(8):419	NUM
ejpam-5476	280	6	,	,	PUNCT
ejpam-5476	280	7	2022	2022	NUM
ejpam-5476	280	8	.	.	PUNCT
ejpam-5476	281	1	[	[	X
ejpam-5476	281	2	8	8	NUM
ejpam-5476	281	3	]	]	PUNCT
ejpam-5476	281	4	a.	a.	PROPN
ejpam-5476	281	5	b.	b.	PROPN
ejpam-5476	281	6	alzahrani	alzahrani	PROPN
ejpam-5476	281	7	,	,	PUNCT
ejpam-5476	281	8	r.	r.	PROPN
ejpam-5476	281	9	saadeh	saadeh	PROPN
ejpam-5476	281	10	,	,	PUNCT
ejpam-5476	281	11	m.	m.	NOUN
ejpam-5476	281	12	a.	a.	PROPN
ejpam-5476	281	13	abdoon	abdoon	PROPN
ejpam-5476	281	14	,	,	PUNCT
ejpam-5476	281	15	m.	m.	NOUN
ejpam-5476	281	16	elbadri	elbadri	PROPN
ejpam-5476	281	17	,	,	PUNCT
ejpam-5476	281	18	m.	m.	NOUN
ejpam-5476	281	19	berir	berir	NOUN
ejpam-5476	281	20	,	,	PUNCT
ejpam-5476	281	21	and	and	CCONJ
ejpam-5476	281	22	a.	a.	NOUN
ejpam-5476	281	23	qazza	qazza	PROPN
ejpam-5476	281	24	.	.	PUNCT
ejpam-5476	282	1	effective	effective	ADJ
ejpam-5476	282	2	methods	method	NOUN
ejpam-5476	282	3	for	for	ADP
ejpam-5476	282	4	numerical	numerical	ADJ
ejpam-5476	282	5	analysis	analysis	NOUN
ejpam-5476	282	6	of	of	ADP
ejpam-5476	282	7	the	the	DET
ejpam-5476	282	8	simplest	simple	ADJ
ejpam-5476	282	9	chaotic	chaotic	ADJ
ejpam-5476	282	10	circuit	circuit	NOUN
ejpam-5476	282	11	model	model	NOUN
ejpam-5476	282	12	with	with	ADP
ejpam-5476	282	13	atangana	atangana	PROPN
ejpam-5476	282	14	–	–	PUNCT
ejpam-5476	282	15	baleanu	baleanu	PROPN
ejpam-5476	282	16	caputo	caputo	PROPN
ejpam-5476	282	17	fractional	fractional	PROPN
ejpam-5476	282	18	derivative	derivative	PROPN
ejpam-5476	282	19	.	.	PUNCT
ejpam-5476	283	1	journal	journal	PROPN
ejpam-5476	283	2	of	of	ADP
ejpam-5476	283	3	engineering	engineering	NOUN
ejpam-5476	283	4	mathematics	mathematic	NOUN
ejpam-5476	283	5	,	,	PUNCT
ejpam-5476	283	6	144(1):9	144(1):9	NUM
ejpam-5476	283	7	,	,	PUNCT
ejpam-5476	283	8	2024	2024	NUM
ejpam-5476	283	9	.	.	PUNCT
ejpam-5476	284	1	[	[	X
ejpam-5476	284	2	9	9	NUM
ejpam-5476	284	3	]	]	X
ejpam-5476	284	4	n.	n.	PROPN
ejpam-5476	284	5	r.	r.	PROPN
ejpam-5476	284	6	anakira	anakira	PROPN
ejpam-5476	284	7	,	,	PUNCT
ejpam-5476	284	8	a.	a.	PROPN
ejpam-5476	284	9	h.	h.	PROPN
ejpam-5476	284	10	shather	shather	PROPN
ejpam-5476	284	11	,	,	PUNCT
ejpam-5476	284	12	a.	a.	PROPN
ejpam-5476	284	13	f.	f.	PROPN
ejpam-5476	284	14	jameel	jameel	PROPN
ejpam-5476	284	15	,	,	PUNCT
ejpam-5476	284	16	a.	a.	PROPN
ejpam-5476	284	17	k.	k.	PROPN
ejpam-5476	284	18	alomari	alomari	PROPN
ejpam-5476	284	19	,	,	PUNCT
ejpam-5476	284	20	and	and	CCONJ
ejpam-5476	284	21	a.	a.	NOUN
ejpam-5476	284	22	saaban	saaban	PROPN
ejpam-5476	284	23	.	.	PUNCT
ejpam-5476	285	1	direct	direct	ADJ
ejpam-5476	285	2	solution	solution	NOUN
ejpam-5476	285	3	of	of	ADP
ejpam-5476	285	4	uncertain	uncertain	ADJ
ejpam-5476	285	5	bratu	bratu	NOUN
ejpam-5476	285	6	initial	initial	ADJ
ejpam-5476	285	7	value	value	NOUN
ejpam-5476	285	8	problem	problem	NOUN
ejpam-5476	285	9	.	.	PUNCT
ejpam-5476	286	1	international	international	ADJ
ejpam-5476	286	2	journal	journal	NOUN
ejpam-5476	286	3	of	of	ADP
ejpam-5476	286	4	electrical	electrical	ADJ
ejpam-5476	286	5	and	and	CCONJ
ejpam-5476	286	6	computer	computer	NOUN
ejpam-5476	286	7	engineering	engineering	NOUN
ejpam-5476	286	8	,	,	PUNCT
ejpam-5476	286	9	9(6):5075	9(6):5075	NUM
ejpam-5476	286	10	,	,	PUNCT
ejpam-5476	286	11	2019	2019	NUM
ejpam-5476	286	12	.	.	PUNCT
ejpam-5476	287	1	references	reference	NOUN
ejpam-5476	287	2	3554	3554	NUM
ejpam-5476	287	3	[	[	X
ejpam-5476	287	4	10	10	NUM
ejpam-5476	287	5	]	]	X
ejpam-5476	287	6	e.	e.	PROPN
ejpam-5476	287	7	asl	asl	PROPN
ejpam-5476	287	8	,	,	PUNCT
ejpam-5476	287	9	j.	j.	PROPN
ejpam-5476	287	10	hengamian	hengamian	PROPN
ejpam-5476	287	11	,	,	PUNCT
ejpam-5476	287	12	saberi	saberi	PROPN
ejpam-5476	287	13	-	-	PUNCT
ejpam-5476	287	14	nadjafi	nadjafi	PROPN
ejpam-5476	287	15	,	,	PUNCT
ejpam-5476	287	16	and	and	CCONJ
ejpam-5476	287	17	m.	m.	PROPN
ejpam-5476	287	18	gachpazan	gachpazan	PROPN
ejpam-5476	287	19	.	.	PUNCT
ejpam-5476	288	1	numerical	numerical	ADJ
ejpam-5476	288	2	solution	solution	NOUN
ejpam-5476	288	3	of	of	ADP
ejpam-5476	288	4	fractional	fractional	ADJ
ejpam-5476	288	5	-	-	PUNCT
ejpam-5476	288	6	order	order	NOUN
ejpam-5476	288	7	population	population	NOUN
ejpam-5476	288	8	growth	growth	NOUN
ejpam-5476	288	9	model	model	NOUN
ejpam-5476	288	10	using	use	VERB
ejpam-5476	288	11	fractional	fractional	ADJ
ejpam-5476	288	12	-	-	PUNCT
ejpam-5476	288	13	order	order	NOUN
ejpam-5476	288	14	muntz	muntz	PROPN
ejpam-5476	288	15	–	–	PUNCT
ejpam-5476	288	16	legendre	legendre	NOUN
ejpam-5476	288	17	collocation	collocation	NOUN
ejpam-5476	288	18	method	method	NOUN
ejpam-5476	288	19	and	and	CCONJ
ejpam-5476	288	20	pade	pade	NOUN
ejpam-5476	288	21	–	–	PUNCT
ejpam-5476	288	22	approximants	approximant	NOUN
ejpam-5476	288	23	.	.	PUNCT
ejpam-5476	289	1	jordan	jordan	PROPN
ejpam-5476	289	2	journal	journal	PROPN
ejpam-5476	289	3	of	of	ADP
ejpam-5476	289	4	mathematics	mathematics	PROPN
ejpam-5476	289	5	and	and	CCONJ
ejpam-5476	289	6	statistics	statistic	NOUN
ejpam-5476	289	7	(	(	PUNCT
ejpam-5476	289	8	jjms	jjms	PROPN
ejpam-5476	289	9	)	)	PUNCT
ejpam-5476	289	10	,	,	PUNCT
ejpam-5476	289	11	15(1):157–175	15(1):157–175	PROPN
ejpam-5476	289	12	,	,	PUNCT
ejpam-5476	289	13	2022	2022	NUM
ejpam-5476	289	14	.	.	PUNCT
ejpam-5476	290	1	[	[	X
ejpam-5476	290	2	11	11	NUM
ejpam-5476	290	3	]	]	PUNCT
ejpam-5476	290	4	a.	a.	NOUN
ejpam-5476	290	5	atangana	atangana	PROPN
ejpam-5476	290	6	and	and	CCONJ
ejpam-5476	290	7	d.	d.	PROPN
ejpam-5476	290	8	baleanu	baleanu	PROPN
ejpam-5476	290	9	.	.	PUNCT
ejpam-5476	291	1	new	new	ADJ
ejpam-5476	291	2	fractional	fractional	ADJ
ejpam-5476	291	3	derivatives	derivative	NOUN
ejpam-5476	291	4	with	with	ADP
ejpam-5476	291	5	nonlocal	nonlocal	ADJ
ejpam-5476	291	6	and	and	CCONJ
ejpam-5476	291	7	nonsingular	nonsingular	ADJ
ejpam-5476	291	8	kernel	kernel	NOUN
ejpam-5476	291	9	,	,	PUNCT
ejpam-5476	291	10	theory	theory	NOUN
ejpam-5476	291	11	and	and	CCONJ
ejpam-5476	291	12	application	application	NOUN
ejpam-5476	291	13	to	to	PART
ejpam-5476	291	14	heat	heat	NOUN
ejpam-5476	291	15	transfer	transfer	NOUN
ejpam-5476	291	16	model	model	NOUN
ejpam-5476	291	17	.	.	PUNCT
ejpam-5476	292	1	2016	2016	NUM
ejpam-5476	292	2	.	.	PUNCT
ejpam-5476	293	1	[	[	X
ejpam-5476	293	2	12	12	NUM
ejpam-5476	293	3	]	]	PUNCT
ejpam-5476	293	4	a.	a.	NOUN
ejpam-5476	293	5	atangana	atangana	PROPN
ejpam-5476	293	6	and	and	CCONJ
ejpam-5476	293	7	j.	j.	PROPN
ejpam-5476	293	8	f.	f.	PROPN
ejpam-5476	293	9	gómez	gómez	PROPN
ejpam-5476	293	10	-	-	PUNCT
ejpam-5476	293	11	aguilar	aguilar	PROPN
ejpam-5476	293	12	.	.	PUNCT
ejpam-5476	294	1	a	a	DET
ejpam-5476	294	2	new	new	ADJ
ejpam-5476	294	3	derivative	derivative	NOUN
ejpam-5476	294	4	with	with	ADP
ejpam-5476	294	5	normal	normal	ADJ
ejpam-5476	294	6	distribution	distribution	NOUN
ejpam-5476	294	7	kernel	kernel	NOUN
ejpam-5476	294	8	:	:	PUNCT
ejpam-5476	294	9	theory	theory	NOUN
ejpam-5476	294	10	,	,	PUNCT
ejpam-5476	294	11	methods	method	NOUN
ejpam-5476	294	12	and	and	CCONJ
ejpam-5476	294	13	applications	application	NOUN
ejpam-5476	294	14	.	.	PUNCT
ejpam-5476	295	1	physica	physica	PROPN
ejpam-5476	295	2	a	a	DET
ejpam-5476	295	3	:	:	PUNCT
ejpam-5476	295	4	statistical	statistical	ADJ
ejpam-5476	295	5	mechanics	mechanic	NOUN
ejpam-5476	295	6	and	and	CCONJ
ejpam-5476	295	7	its	its	PRON
ejpam-5476	295	8	applications	application	NOUN
ejpam-5476	295	9	,	,	PUNCT
ejpam-5476	295	10	476:1–14	476:1–14	NUM
ejpam-5476	295	11	,	,	PUNCT
ejpam-5476	295	12	2017	2017	NUM
ejpam-5476	295	13	.	.	PUNCT
ejpam-5476	296	1	[	[	X
ejpam-5476	296	2	13	13	NUM
ejpam-5476	296	3	]	]	PUNCT
ejpam-5476	296	4	a.	a.	NOUN
ejpam-5476	296	5	atangana	atangana	PROPN
ejpam-5476	296	6	and	and	CCONJ
ejpam-5476	296	7	t.	t.	PROPN
ejpam-5476	296	8	mekkaoui	mekkaoui	PROPN
ejpam-5476	296	9	.	.	PUNCT
ejpam-5476	297	1	trinition	trinition	VERB
ejpam-5476	297	2	the	the	DET
ejpam-5476	297	3	complex	complex	ADJ
ejpam-5476	297	4	number	number	NOUN
ejpam-5476	297	5	with	with	ADP
ejpam-5476	297	6	two	two	NUM
ejpam-5476	297	7	imaginary	imaginary	ADJ
ejpam-5476	297	8	parts	part	NOUN
ejpam-5476	297	9	:	:	PUNCT
ejpam-5476	297	10	fractal	fractal	ADJ
ejpam-5476	297	11	,	,	PUNCT
ejpam-5476	297	12	chaos	chaos	NOUN
ejpam-5476	297	13	and	and	CCONJ
ejpam-5476	297	14	fractional	fractional	ADJ
ejpam-5476	297	15	calculus	calculus	NOUN
ejpam-5476	297	16	.	.	PUNCT
ejpam-5476	298	1	chaos	chaos	NOUN
ejpam-5476	298	2	solitons	soliton	NOUN
ejpam-5476	298	3	fractals	fractal	NOUN
ejpam-5476	298	4	,	,	PUNCT
ejpam-5476	298	5	128:366–381	128:366–381	NUM
ejpam-5476	298	6	,	,	PUNCT
ejpam-5476	298	7	2019	2019	NUM
ejpam-5476	298	8	.	.	PUNCT
ejpam-5476	299	1	[	[	X
ejpam-5476	299	2	14	14	NUM
ejpam-5476	299	3	]	]	X
ejpam-5476	299	4	o.	o.	PROPN
ejpam-5476	299	5	atangana	atangana	PROPN
ejpam-5476	299	6	and	and	CCONJ
ejpam-5476	299	7	m.	m.	PROPN
ejpam-5476	299	8	kolade	kolade	PROPN
ejpam-5476	299	9	.	.	PUNCT
ejpam-5476	300	1	new	new	ADJ
ejpam-5476	300	2	numerical	numerical	ADJ
ejpam-5476	300	3	approach	approach	NOUN
ejpam-5476	300	4	for	for	ADP
ejpam-5476	300	5	fractional	fractional	ADJ
ejpam-5476	300	6	differential	differential	ADJ
ejpam-5476	300	7	equations	equation	NOUN
ejpam-5476	300	8	.	.	PUNCT
ejpam-5476	301	1	math	math	NOUN
ejpam-5476	301	2	.	.	PUNCT
ejpam-5476	302	1	modell	modell	PROPN
ejpam-5476	302	2	.	.	PUNCT
ejpam-5476	302	3	natl	natl	PROPN
ejpam-5476	302	4	.	.	PUNCT
ejpam-5476	303	1	phenomena	phenomena	PROPN
ejpam-5476	303	2	,	,	PUNCT
ejpam-5476	303	3	13(1):3	13(1):3	PROPN
ejpam-5476	303	4	,	,	PUNCT
ejpam-5476	303	5	2018	2018	NUM
ejpam-5476	303	6	.	.	PUNCT
ejpam-5476	304	1	[	[	X
ejpam-5476	304	2	15	15	NUM
ejpam-5476	304	3	]	]	X
ejpam-5476	304	4	m.	m.	NOUN
ejpam-5476	304	5	i.	i.	PROPN
ejpam-5476	304	6	bhatti	bhatti	PROPN
ejpam-5476	304	7	and	and	CCONJ
ejpam-5476	304	8	p.	p.	PROPN
ejpam-5476	304	9	bracken	bracken	NOUN
ejpam-5476	304	10	.	.	PUNCT
ejpam-5476	305	1	solutions	solution	NOUN
ejpam-5476	305	2	of	of	ADP
ejpam-5476	305	3	differential	differential	ADJ
ejpam-5476	305	4	equations	equation	NOUN
ejpam-5476	305	5	in	in	ADP
ejpam-5476	305	6	a	a	DET
ejpam-5476	305	7	bernstein	bernstein	PROPN
ejpam-5476	305	8	polynomial	polynomial	PROPN
ejpam-5476	305	9	basis	basis	NOUN
ejpam-5476	305	10	.	.	PUNCT
ejpam-5476	306	1	journal	journal	NOUN
ejpam-5476	306	2	of	of	ADP
ejpam-5476	306	3	computational	computational	ADJ
ejpam-5476	306	4	and	and	CCONJ
ejpam-5476	306	5	applied	applied	ADJ
ejpam-5476	306	6	mathematics	mathematic	NOUN
ejpam-5476	306	7	,	,	PUNCT
ejpam-5476	306	8	205(1):272–280	205(1):272–280	NUM
ejpam-5476	306	9	,	,	PUNCT
ejpam-5476	306	10	2007	2007	NUM
ejpam-5476	306	11	.	.	PUNCT
ejpam-5476	307	1	[	[	X
ejpam-5476	307	2	16	16	NUM
ejpam-5476	307	3	]	]	X
ejpam-5476	307	4	william	william	PROPN
ejpam-5476	307	5	e.	e.	PROPN
ejpam-5476	307	6	boyce	boyce	PROPN
ejpam-5476	307	7	and	and	CCONJ
ejpam-5476	307	8	richard	richard	PROPN
ejpam-5476	307	9	c.	c.	PROPN
ejpam-5476	307	10	diprima	diprima	PROPN
ejpam-5476	307	11	.	.	PUNCT
ejpam-5476	308	1	elementary	elementary	PROPN
ejpam-5476	308	2	differential	differential	PROPN
ejpam-5476	308	3	equations	equation	NOUN
ejpam-5476	308	4	and	and	CCONJ
ejpam-5476	308	5	boundary	boundary	ADJ
ejpam-5476	308	6	value	value	NOUN
ejpam-5476	308	7	problems	problem	NOUN
ejpam-5476	308	8	.	.	PUNCT
ejpam-5476	309	1	wiley	wiley	PROPN
ejpam-5476	309	2	,	,	PUNCT
ejpam-5476	309	3	8th	8th	ADJ
ejpam-5476	309	4	edition	edition	NOUN
ejpam-5476	309	5	,	,	PUNCT
ejpam-5476	309	6	2004	2004	NUM
ejpam-5476	309	7	.	.	PUNCT
ejpam-5476	310	1	[	[	X
ejpam-5476	310	2	17	17	NUM
ejpam-5476	310	3	]	]	X
ejpam-5476	310	4	h.	h.	PROPN
ejpam-5476	310	5	b.	b.	PROPN
ejpam-5476	310	6	chethan	chethan	PROPN
ejpam-5476	310	7	,	,	PUNCT
ejpam-5476	310	8	r.	r.	PROPN
ejpam-5476	310	9	saadeh	saadeh	PROPN
ejpam-5476	310	10	,	,	PUNCT
ejpam-5476	310	11	d.	d.	PROPN
ejpam-5476	310	12	g.	g.	PROPN
ejpam-5476	310	13	prakasha	prakasha	PROPN
ejpam-5476	310	14	,	,	PUNCT
ejpam-5476	310	15	a.	a.	NOUN
ejpam-5476	310	16	qazza	qazza	PROPN
ejpam-5476	310	17	,	,	PUNCT
ejpam-5476	310	18	n.	n.	PROPN
ejpam-5476	310	19	s.	s.	PROPN
ejpam-5476	310	20	malagi	malagi	PROPN
ejpam-5476	310	21	,	,	PUNCT
ejpam-5476	310	22	m.	m.	PROPN
ejpam-5476	310	23	nagaraja	nagaraja	PROPN
ejpam-5476	310	24	,	,	PUNCT
ejpam-5476	310	25	and	and	CCONJ
ejpam-5476	310	26	d.	d.	PROPN
ejpam-5476	310	27	u.	u.	PROPN
ejpam-5476	310	28	sarwe	sarwe	PROPN
ejpam-5476	310	29	.	.	PUNCT
ejpam-5476	311	1	an	an	DET
ejpam-5476	311	2	efficient	efficient	ADJ
ejpam-5476	311	3	approximate	approximate	ADJ
ejpam-5476	311	4	analytical	analytical	ADJ
ejpam-5476	311	5	technique	technique	NOUN
ejpam-5476	311	6	for	for	ADP
ejpam-5476	311	7	the	the	DET
ejpam-5476	311	8	fractional	fractional	ADJ
ejpam-5476	311	9	model	model	NOUN
ejpam-5476	311	10	describing	describe	VERB
ejpam-5476	311	11	the	the	DET
ejpam-5476	311	12	solid	solid	ADJ
ejpam-5476	311	13	tumor	tumor	NOUN
ejpam-5476	311	14	invasion	invasion	NOUN
ejpam-5476	311	15	.	.	PUNCT
ejpam-5476	312	1	frontiers	frontier	NOUN
ejpam-5476	312	2	in	in	ADP
ejpam-5476	312	3	physics	physics	PROPN
ejpam-5476	312	4	,	,	PUNCT
ejpam-5476	312	5	12:1294506	12:1294506	NUM
ejpam-5476	312	6	,	,	PUNCT
ejpam-5476	312	7	2024	2024	NUM
ejpam-5476	312	8	.	.	PUNCT
ejpam-5476	313	1	[	[	X
ejpam-5476	313	2	18	18	NUM
ejpam-5476	313	3	]	]	X
ejpam-5476	313	4	s.	s.	PROPN
ejpam-5476	313	5	djennadi	djennadi	PROPN
ejpam-5476	313	6	,	,	PUNCT
ejpam-5476	313	7	n.	n.	NOUN
ejpam-5476	313	8	shawagfeh	shawagfeh	NOUN
ejpam-5476	313	9	,	,	PUNCT
ejpam-5476	313	10	m.	m.	NOUN
ejpam-5476	313	11	s.	s.	PROPN
ejpam-5476	313	12	osman	osman	PROPN
ejpam-5476	313	13	,	,	PUNCT
ejpam-5476	313	14	j.	j.	PROPN
ejpam-5476	313	15	f.	f.	PROPN
ejpam-5476	313	16	gómez	gómez	PROPN
ejpam-5476	313	17	-	-	PUNCT
ejpam-5476	313	18	aguilar	aguilar	ADJ
ejpam-5476	313	19	,	,	PUNCT
ejpam-5476	313	20	and	and	CCONJ
ejpam-5476	313	21	o.	o.	NOUN
ejpam-5476	313	22	a.	a.	NOUN
ejpam-5476	313	23	arqub	arqub	NOUN
ejpam-5476	313	24	.	.	PUNCT
ejpam-5476	314	1	the	the	DET
ejpam-5476	314	2	tikhonov	tikhonov	NOUN
ejpam-5476	314	3	regularization	regularization	NOUN
ejpam-5476	314	4	method	method	NOUN
ejpam-5476	314	5	for	for	ADP
ejpam-5476	314	6	the	the	DET
ejpam-5476	314	7	inverse	inverse	NOUN
ejpam-5476	314	8	source	source	NOUN
ejpam-5476	314	9	problem	problem	NOUN
ejpam-5476	314	10	of	of	ADP
ejpam-5476	314	11	time	time	NOUN
ejpam-5476	314	12	fractional	fractional	ADJ
ejpam-5476	314	13	heat	heat	NOUN
ejpam-5476	314	14	equation	equation	NOUN
ejpam-5476	314	15	in	in	ADP
ejpam-5476	314	16	the	the	DET
ejpam-5476	314	17	view	view	NOUN
ejpam-5476	314	18	of	of	ADP
ejpam-5476	314	19	abc	abc	PROPN
ejpam-5476	314	20	-	-	PUNCT
ejpam-5476	314	21	fractional	fractional	ADJ
ejpam-5476	314	22	technique	technique	NOUN
ejpam-5476	314	23	.	.	PUNCT
ejpam-5476	315	1	physica	physica	PROPN
ejpam-5476	315	2	scripta	scripta	PROPN
ejpam-5476	315	3	,	,	PUNCT
ejpam-5476	315	4	96(9):094006	96(9):094006	NUM
ejpam-5476	315	5	,	,	PUNCT
ejpam-5476	315	6	2021	2021	NUM
ejpam-5476	315	7	.	.	PUNCT
ejpam-5476	316	1	[	[	X
ejpam-5476	316	2	19	19	NUM
ejpam-5476	316	3	]	]	X
ejpam-5476	316	4	e.	e.	PROPN
ejpam-5476	316	5	r.	r.	PROPN
ejpam-5476	316	6	el	el	PROPN
ejpam-5476	316	7	-	-	PUNCT
ejpam-5476	316	8	zahar	zahar	PROPN
ejpam-5476	316	9	,	,	PUNCT
ejpam-5476	316	10	a.	a.	NOUN
ejpam-5476	316	11	m.	m.	NOUN
ejpam-5476	316	12	alotaibi	alotaibi	PROPN
ejpam-5476	316	13	,	,	PUNCT
ejpam-5476	316	14	a.	a.	PROPN
ejpam-5476	316	15	ebaid	ebaid	PROPN
ejpam-5476	316	16	,	,	PUNCT
ejpam-5476	316	17	a.	a.	PROPN
ejpam-5476	316	18	f.	f.	PROPN
ejpam-5476	316	19	aljohani	aljohani	PROPN
ejpam-5476	316	20	,	,	PUNCT
ejpam-5476	316	21	and	and	CCONJ
ejpam-5476	316	22	j.	j.	PROPN
ejpam-5476	316	23	g.	g.	PROPN
ejpam-5476	316	24	aguilar	aguilar	PROPN
ejpam-5476	316	25	.	.	PUNCT
ejpam-5476	317	1	the	the	DET
ejpam-5476	317	2	riemann	riemann	PROPN
ejpam-5476	317	3	–	–	PUNCT
ejpam-5476	317	4	liouville	liouville	VERB
ejpam-5476	317	5	fractional	fractional	ADJ
ejpam-5476	317	6	derivative	derivative	NOUN
ejpam-5476	317	7	for	for	ADP
ejpam-5476	317	8	ambartsumian	ambartsumian	ADJ
ejpam-5476	317	9	equation	equation	NOUN
ejpam-5476	317	10	.	.	PUNCT
ejpam-5476	318	1	results	result	NOUN
ejpam-5476	318	2	in	in	ADP
ejpam-5476	318	3	physics	physics	NOUN
ejpam-5476	318	4	,	,	PUNCT
ejpam-5476	318	5	19:103551	19:103551	NUM
ejpam-5476	318	6	,	,	PUNCT
ejpam-5476	318	7	2020	2020	NUM
ejpam-5476	318	8	.	.	PUNCT
ejpam-5476	319	1	[	[	X
ejpam-5476	319	2	20	20	NUM
ejpam-5476	319	3	]	]	PUNCT
ejpam-5476	319	4	v.	v.	CCONJ
ejpam-5476	319	5	s.	s.	PROPN
ejpam-5476	319	6	erturk	erturk	PROPN
ejpam-5476	319	7	and	and	CCONJ
ejpam-5476	319	8	p.	p.	PROPN
ejpam-5476	319	9	kumar	kumar	PROPN
ejpam-5476	319	10	.	.	PUNCT
ejpam-5476	320	1	solution	solution	NOUN
ejpam-5476	320	2	of	of	ADP
ejpam-5476	320	3	a	a	DET
ejpam-5476	320	4	covid-19	covid-19	PROPN
ejpam-5476	320	5	model	model	NOUN
ejpam-5476	320	6	via	via	ADP
ejpam-5476	320	7	new	new	ADJ
ejpam-5476	320	8	generalized	generalize	VERB
ejpam-5476	320	9	caputotype	caputotype	ADJ
ejpam-5476	320	10	fractional	fractional	ADJ
ejpam-5476	320	11	derivatives	derivative	NOUN
ejpam-5476	320	12	.	.	PUNCT
ejpam-5476	321	1	chaos	chaos	NOUN
ejpam-5476	321	2	,	,	PUNCT
ejpam-5476	321	3	solitons	soliton	NOUN
ejpam-5476	321	4	&	&	CCONJ
ejpam-5476	321	5	fractals	fractal	NOUN
ejpam-5476	321	6	,	,	PUNCT
ejpam-5476	321	7	139:110280	139:110280	NUM
ejpam-5476	321	8	,	,	PUNCT
ejpam-5476	321	9	2021	2021	NUM
ejpam-5476	321	10	.	.	PUNCT
ejpam-5476	322	1	[	[	X
ejpam-5476	322	2	21	21	NUM
ejpam-5476	322	3	]	]	PUNCT
ejpam-5476	322	4	m.	m.	NOUN
ejpam-5476	322	5	o.	o.	PROPN
ejpam-5476	322	6	h.	h.	PROPN
ejpam-5476	322	7	d.	d.	PROPN
ejpam-5476	322	8	irfan	irfan	PROPN
ejpam-5476	322	9	and	and	CCONJ
ejpam-5476	322	10	a.	a.	NOUN
ejpam-5476	322	11	shah	shah	PROPN
ejpam-5476	322	12	firdous	firdous	ADJ
ejpam-5476	322	13	.	.	PUNCT
ejpam-5476	323	1	numerical	numerical	ADJ
ejpam-5476	323	2	solution	solution	NOUN
ejpam-5476	323	3	of	of	ADP
ejpam-5476	323	4	bioheat	bioheat	ADJ
ejpam-5476	323	5	transfer	transfer	NOUN
ejpam-5476	323	6	model	model	NOUN
ejpam-5476	323	7	using	use	VERB
ejpam-5476	323	8	generalized	generalized	ADJ
ejpam-5476	323	9	wavelet	wavelet	NOUN
ejpam-5476	323	10	collocation	collocation	NOUN
ejpam-5476	323	11	method	method	NOUN
ejpam-5476	323	12	.	.	PUNCT
ejpam-5476	324	1	jordan	jordan	PROPN
ejpam-5476	324	2	journal	journal	PROPN
ejpam-5476	324	3	of	of	ADP
ejpam-5476	324	4	mathematics	mathematics	PROPN
ejpam-5476	324	5	and	and	CCONJ
ejpam-5476	324	6	statistics	statistic	NOUN
ejpam-5476	324	7	(	(	PUNCT
ejpam-5476	324	8	jjms	jjms	NOUN
ejpam-5476	324	9	)	)	PUNCT
ejpam-5476	324	10	,	,	PUNCT
ejpam-5476	324	11	15(2):211–229	15(2):211–229	PROPN
ejpam-5476	324	12	,	,	PUNCT
ejpam-5476	324	13	2022	2022	NUM
ejpam-5476	324	14	.	.	PUNCT
ejpam-5476	325	1	references	reference	NOUN
ejpam-5476	325	2	3555	3555	NUM
ejpam-5476	325	3	[	[	X
ejpam-5476	325	4	22	22	NUM
ejpam-5476	325	5	]	]	PUNCT
ejpam-5476	325	6	a.	a.	NOUN
ejpam-5476	325	7	jameela	jameela	PROPN
ejpam-5476	325	8	,	,	PUNCT
ejpam-5476	325	9	n.	n.	PROPN
ejpam-5476	325	10	r.	r.	PROPN
ejpam-5476	325	11	anakira	anakira	PROPN
ejpam-5476	325	12	,	,	PUNCT
ejpam-5476	325	13	a.	a.	PROPN
ejpam-5476	325	14	k.	k.	PROPN
ejpam-5476	325	15	alomari	alomari	PROPN
ejpam-5476	325	16	,	,	PUNCT
ejpam-5476	325	17	i.	i.	PROPN
ejpam-5476	325	18	hashim	hashim	PROPN
ejpam-5476	325	19	,	,	PUNCT
ejpam-5476	325	20	and	and	CCONJ
ejpam-5476	325	21	m.	m.	NOUN
ejpam-5476	325	22	a.	a.	NOUN
ejpam-5476	325	23	shakhatreh	shakhatreh	PROPN
ejpam-5476	325	24	.	.	PUNCT
ejpam-5476	326	1	numerical	numerical	ADJ
ejpam-5476	326	2	solution	solution	NOUN
ejpam-5476	326	3	of	of	ADP
ejpam-5476	326	4	n’th	n’th	ADJ
ejpam-5476	326	5	order	order	NOUN
ejpam-5476	326	6	fuzzy	fuzzy	ADJ
ejpam-5476	326	7	initial	initial	ADJ
ejpam-5476	326	8	value	value	NOUN
ejpam-5476	326	9	problems	problem	NOUN
ejpam-5476	326	10	by	by	ADP
ejpam-5476	326	11	six	six	NUM
ejpam-5476	326	12	stages	stage	NOUN
ejpam-5476	326	13	.	.	PUNCT
ejpam-5476	327	1	journal	journal	NOUN
ejpam-5476	327	2	of	of	ADP
ejpam-5476	327	3	nonlinear	nonlinear	PROPN
ejpam-5476	327	4	science	science	NOUN
ejpam-5476	327	5	applications	application	NOUN
ejpam-5476	327	6	,	,	PUNCT
ejpam-5476	327	7	9(2):627–640	9(2):627–640	NUM
ejpam-5476	327	8	,	,	PUNCT
ejpam-5476	327	9	2016	2016	NUM
ejpam-5476	327	10	.	.	PUNCT
ejpam-5476	328	1	[	[	X
ejpam-5476	328	2	23	23	NUM
ejpam-5476	328	3	]	]	PUNCT
ejpam-5476	328	4	udita	udita	PROPN
ejpam-5476	328	5	n.	n.	PROPN
ejpam-5476	328	6	katugampola	katugampola	PROPN
ejpam-5476	328	7	.	.	PUNCT
ejpam-5476	329	1	new	new	ADJ
ejpam-5476	329	2	approach	approach	NOUN
ejpam-5476	329	3	to	to	ADP
ejpam-5476	329	4	a	a	DET
ejpam-5476	329	5	generalized	generalized	ADJ
ejpam-5476	329	6	fractional	fractional	ADJ
ejpam-5476	329	7	integral	integral	ADJ
ejpam-5476	329	8	.	.	PUNCT
ejpam-5476	329	9	applied	apply	VERB
ejpam-5476	329	10	mathematics	mathematic	NOUN
ejpam-5476	329	11	and	and	CCONJ
ejpam-5476	329	12	computation	computation	NOUN
ejpam-5476	329	13	,	,	PUNCT
ejpam-5476	329	14	218:860–865	218:860–865	NUM
ejpam-5476	329	15	,	,	PUNCT
ejpam-5476	329	16	2011	2011	NUM
ejpam-5476	329	17	.	.	PUNCT
ejpam-5476	330	1	[	[	X
ejpam-5476	330	2	24	24	NUM
ejpam-5476	330	3	]	]	PUNCT
ejpam-5476	330	4	a.	a.	NOUN
ejpam-5476	330	5	kayedi	kayedi	PROPN
ejpam-5476	330	6	-	-	PUNCT
ejpam-5476	330	7	bardeh	bardeh	NOUN
ejpam-5476	330	8	,	,	PUNCT
ejpam-5476	330	9	m.	m.	NOUN
ejpam-5476	330	10	eslahchi	eslahchi	PROPN
ejpam-5476	330	11	,	,	PUNCT
ejpam-5476	330	12	and	and	CCONJ
ejpam-5476	330	13	m.	m.	NOUN
ejpam-5476	330	14	dehghan	dehghan	PROPN
ejpam-5476	330	15	.	.	PUNCT
ejpam-5476	331	1	a	a	DET
ejpam-5476	331	2	method	method	NOUN
ejpam-5476	331	3	for	for	ADP
ejpam-5476	331	4	obtaining	obtain	VERB
ejpam-5476	331	5	the	the	DET
ejpam-5476	331	6	operational	operational	ADJ
ejpam-5476	331	7	matrix	matrix	NOUN
ejpam-5476	331	8	of	of	ADP
ejpam-5476	331	9	fractional	fractional	ADJ
ejpam-5476	331	10	jacobi	jacobi	PROPN
ejpam-5476	331	11	functions	function	NOUN
ejpam-5476	331	12	and	and	CCONJ
ejpam-5476	331	13	applications	application	NOUN
ejpam-5476	331	14	.	.	PUNCT
ejpam-5476	332	1	journal	journal	NOUN
ejpam-5476	332	2	of	of	ADP
ejpam-5476	332	3	vibration	vibration	NOUN
ejpam-5476	332	4	and	and	CCONJ
ejpam-5476	332	5	control	control	NOUN
ejpam-5476	332	6	,	,	PUNCT
ejpam-5476	332	7	2012	2012	NUM
ejpam-5476	332	8	.	.	PUNCT
ejpam-5476	333	1	[	[	X
ejpam-5476	333	2	25	25	NUM
ejpam-5476	333	3	]	]	X
ejpam-5476	333	4	h.	h.	PROPN
ejpam-5476	333	5	khan	khan	PROPN
ejpam-5476	333	6	,	,	PUNCT
ejpam-5476	333	7	h.	h.	PROPN
ejpam-5476	333	8	jafari	jafari	PROPN
ejpam-5476	333	9	,	,	PUNCT
ejpam-5476	333	10	r.	r.	PROPN
ejpam-5476	333	11	a.	a.	PROPN
ejpam-5476	333	12	khan	khan	PROPN
ejpam-5476	333	13	,	,	PUNCT
ejpam-5476	333	14	h.	h.	PROPN
ejpam-5476	333	15	tajadodi	tajadodi	PROPN
ejpam-5476	333	16	,	,	PUNCT
ejpam-5476	333	17	and	and	CCONJ
ejpam-5476	333	18	s.	s.	PROPN
ejpam-5476	333	19	j.	j.	PROPN
ejpam-5476	333	20	johnston	johnston	PROPN
ejpam-5476	333	21	.	.	PUNCT
ejpam-5476	334	1	numerical	numerical	PROPN
ejpam-5476	334	2	solutions	solution	NOUN
ejpam-5476	334	3	of	of	ADP
ejpam-5476	334	4	the	the	DET
ejpam-5476	334	5	nonlinear	nonlinear	ADJ
ejpam-5476	334	6	fractional	fractional	ADJ
ejpam-5476	334	7	-	-	PUNCT
ejpam-5476	334	8	order	order	NOUN
ejpam-5476	334	9	brusselator	brusselator	NOUN
ejpam-5476	334	10	system	system	NOUN
ejpam-5476	334	11	by	by	ADP
ejpam-5476	334	12	bernstein	bernstein	PROPN
ejpam-5476	334	13	polynomials	polynomials	PROPN
ejpam-5476	334	14	.	.	PUNCT
ejpam-5476	335	1	the	the	DET
ejpam-5476	335	2	scientific	scientific	ADJ
ejpam-5476	335	3	world	world	NOUN
ejpam-5476	335	4	journal	journal	NOUN
ejpam-5476	335	5	,	,	PUNCT
ejpam-5476	335	6	2014	2014	NUM
ejpam-5476	335	7	.	.	PUNCT
ejpam-5476	336	1	[	[	X
ejpam-5476	336	2	26	26	NUM
ejpam-5476	336	3	]	]	X
ejpam-5476	336	4	h.	h.	PROPN
ejpam-5476	336	5	khan	khan	PROPN
ejpam-5476	336	6	,	,	PUNCT
ejpam-5476	336	7	h.	h.	PROPN
ejpam-5476	336	8	jafari	jafari	PROPN
ejpam-5476	336	9	,	,	PUNCT
ejpam-5476	336	10	r.	r.	PROPN
ejpam-5476	336	11	a.	a.	PROPN
ejpam-5476	336	12	khan	khan	PROPN
ejpam-5476	336	13	,	,	PUNCT
ejpam-5476	336	14	h.	h.	PROPN
ejpam-5476	336	15	tajadodi	tajadodi	PROPN
ejpam-5476	336	16	,	,	PUNCT
ejpam-5476	336	17	and	and	CCONJ
ejpam-5476	336	18	s.	s.	PROPN
ejpam-5476	336	19	j.	j.	PROPN
ejpam-5476	336	20	johnston	johnston	PROPN
ejpam-5476	336	21	.	.	PUNCT
ejpam-5476	337	1	numerical	numerical	PROPN
ejpam-5476	337	2	solutions	solution	NOUN
ejpam-5476	337	3	of	of	ADP
ejpam-5476	337	4	the	the	DET
ejpam-5476	337	5	nonlinear	nonlinear	ADJ
ejpam-5476	337	6	fractional	fractional	ADJ
ejpam-5476	337	7	-	-	PUNCT
ejpam-5476	337	8	order	order	NOUN
ejpam-5476	337	9	brusselator	brusselator	NOUN
ejpam-5476	337	10	system	system	NOUN
ejpam-5476	337	11	by	by	ADP
ejpam-5476	337	12	bernstein	bernstein	PROPN
ejpam-5476	337	13	polynomials	polynomials	PROPN
ejpam-5476	337	14	.	.	PUNCT
ejpam-5476	338	1	the	the	DET
ejpam-5476	338	2	scientific	scientific	ADJ
ejpam-5476	338	3	world	world	NOUN
ejpam-5476	338	4	journal	journal	NOUN
ejpam-5476	338	5	,	,	PUNCT
ejpam-5476	338	6	2014	2014	NUM
ejpam-5476	338	7	.	.	PUNCT
ejpam-5476	339	1	[	[	X
ejpam-5476	339	2	27	27	NUM
ejpam-5476	339	3	]	]	PUNCT
ejpam-5476	339	4	p.	p.	PROPN
ejpam-5476	339	5	kumar	kumar	PROPN
ejpam-5476	339	6	and	and	CCONJ
ejpam-5476	339	7	v.	v.	PROPN
ejpam-5476	339	8	s.	s.	PROPN
ejpam-5476	339	9	erturk	erturk	PROPN
ejpam-5476	339	10	.	.	PUNCT
ejpam-5476	340	1	environmental	environmental	ADJ
ejpam-5476	340	2	persistence	persistence	NOUN
ejpam-5476	340	3	influences	influence	VERB
ejpam-5476	340	4	infection	infection	NOUN
ejpam-5476	340	5	dynamics	dynamic	NOUN
ejpam-5476	340	6	for	for	ADP
ejpam-5476	340	7	a	a	DET
ejpam-5476	340	8	butterfly	butterfly	NOUN
ejpam-5476	340	9	pathogen	pathogen	NOUN
ejpam-5476	340	10	via	via	ADP
ejpam-5476	340	11	new	new	ADJ
ejpam-5476	340	12	generalized	generalize	VERB
ejpam-5476	340	13	caputo	caputo	PROPN
ejpam-5476	340	14	type	type	NOUN
ejpam-5476	340	15	fractional	fractional	ADJ
ejpam-5476	340	16	derivative	derivative	NOUN
ejpam-5476	340	17	.	.	PUNCT
ejpam-5476	341	1	chaos	chaos	NOUN
ejpam-5476	341	2	,	,	PUNCT
ejpam-5476	341	3	solitons	soliton	NOUN
ejpam-5476	341	4	&	&	CCONJ
ejpam-5476	341	5	fractals	fractal	NOUN
ejpam-5476	341	6	,	,	PUNCT
ejpam-5476	341	7	144:110672	144:110672	NUM
ejpam-5476	341	8	,	,	PUNCT
ejpam-5476	341	9	2021	2021	NUM
ejpam-5476	341	10	.	.	PUNCT
ejpam-5476	342	1	[	[	X
ejpam-5476	342	2	28	28	NUM
ejpam-5476	342	3	]	]	X
ejpam-5476	342	4	p.	p.	PROPN
ejpam-5476	342	5	kumar	kumar	PROPN
ejpam-5476	342	6	,	,	PUNCT
ejpam-5476	342	7	v.	v.	PROPN
ejpam-5476	342	8	s.	s.	PROPN
ejpam-5476	342	9	erturk	erturk	PROPN
ejpam-5476	342	10	,	,	PUNCT
ejpam-5476	342	11	h.	h.	PROPN
ejpam-5476	342	12	abboubakar	abboubakar	PROPN
ejpam-5476	342	13	,	,	PUNCT
ejpam-5476	342	14	and	and	CCONJ
ejpam-5476	342	15	k.	k.	PROPN
ejpam-5476	342	16	s.	s.	PROPN
ejpam-5476	342	17	nisar	nisar	PROPN
ejpam-5476	342	18	.	.	PUNCT
ejpam-5476	343	1	prediction	prediction	NOUN
ejpam-5476	343	2	studies	study	NOUN
ejpam-5476	343	3	of	of	ADP
ejpam-5476	343	4	the	the	DET
ejpam-5476	343	5	epidemic	epidemic	NOUN
ejpam-5476	343	6	peak	peak	NOUN
ejpam-5476	343	7	of	of	ADP
ejpam-5476	343	8	coronavirus	coronavirus	NOUN
ejpam-5476	343	9	disease	disease	NOUN
ejpam-5476	343	10	in	in	ADP
ejpam-5476	343	11	brazil	brazil	PROPN
ejpam-5476	343	12	via	via	ADP
ejpam-5476	343	13	new	new	ADJ
ejpam-5476	343	14	generalized	generalize	VERB
ejpam-5476	343	15	caputo	caputo	PROPN
ejpam-5476	343	16	type	type	NOUN
ejpam-5476	343	17	fractional	fractional	ADJ
ejpam-5476	343	18	derivatives	derivative	NOUN
ejpam-5476	343	19	.	.	PUNCT
ejpam-5476	344	1	alexandria	alexandria	PROPN
ejpam-5476	344	2	engineering	engineering	PROPN
ejpam-5476	344	3	journal	journal	PROPN
ejpam-5476	344	4	,	,	PUNCT
ejpam-5476	344	5	60(3):3189–3204	60(3):3189–3204	NUM
ejpam-5476	344	6	,	,	PUNCT
ejpam-5476	344	7	2021	2021	NUM
ejpam-5476	344	8	.	.	PUNCT
ejpam-5476	345	1	[	[	X
ejpam-5476	345	2	29	29	NUM
ejpam-5476	345	3	]	]	PUNCT
ejpam-5476	345	4	s.	s.	PROPN
ejpam-5476	345	5	kumar	kumar	PROPN
ejpam-5476	345	6	,	,	PUNCT
ejpam-5476	345	7	v.	v.	PROPN
ejpam-5476	345	8	gupta	gupta	PROPN
ejpam-5476	345	9	,	,	PUNCT
ejpam-5476	345	10	and	and	CCONJ
ejpam-5476	345	11	j.	j.	PROPN
ejpam-5476	345	12	f.	f.	PROPN
ejpam-5476	345	13	gómez	gómez	PROPN
ejpam-5476	345	14	-	-	PUNCT
ejpam-5476	345	15	aguilar	aguilar	PROPN
ejpam-5476	345	16	.	.	PUNCT
ejpam-5476	346	1	an	an	DET
ejpam-5476	346	2	efficient	efficient	ADJ
ejpam-5476	346	3	operational	operational	ADJ
ejpam-5476	346	4	matrix	matrix	NOUN
ejpam-5476	346	5	technique	technique	NOUN
ejpam-5476	346	6	to	to	PART
ejpam-5476	346	7	solve	solve	VERB
ejpam-5476	346	8	the	the	DET
ejpam-5476	346	9	fractional	fractional	ADJ
ejpam-5476	346	10	order	order	NOUN
ejpam-5476	346	11	non	non	ADJ
ejpam-5476	346	12	-	-	ADJ
ejpam-5476	346	13	local	local	ADJ
ejpam-5476	346	14	boundary	boundary	ADJ
ejpam-5476	346	15	value	value	NOUN
ejpam-5476	346	16	problems	problem	NOUN
ejpam-5476	346	17	.	.	PUNCT
ejpam-5476	347	1	journal	journal	PROPN
ejpam-5476	347	2	of	of	ADP
ejpam-5476	347	3	mathematical	mathematical	ADJ
ejpam-5476	347	4	chemistry	chemistry	NOUN
ejpam-5476	347	5	,	,	PUNCT
ejpam-5476	347	6	60(8):1463–1479	60(8):1463–1479	NUM
ejpam-5476	347	7	,	,	PUNCT
ejpam-5476	347	8	2022	2022	NUM
ejpam-5476	347	9	.	.	PUNCT
ejpam-5476	348	1	[	[	X
ejpam-5476	348	2	30	30	NUM
ejpam-5476	348	3	]	]	X
ejpam-5476	348	4	f.	f.	PROPN
ejpam-5476	348	5	mirzaee	mirzaee	PROPN
ejpam-5476	348	6	and	and	CCONJ
ejpam-5476	348	7	s.	s.	PROPN
ejpam-5476	348	8	alipour	alipour	PROPN
ejpam-5476	348	9	.	.	PUNCT
ejpam-5476	349	1	fractional	fractional	ADJ
ejpam-5476	349	2	-	-	PUNCT
ejpam-5476	349	3	order	order	NOUN
ejpam-5476	349	4	orthogonal	orthogonal	ADJ
ejpam-5476	349	5	bernstein	bernstein	PROPN
ejpam-5476	349	6	polynomials	polynomial	NOUN
ejpam-5476	349	7	for	for	ADP
ejpam-5476	349	8	numerical	numerical	ADJ
ejpam-5476	349	9	solution	solution	NOUN
ejpam-5476	349	10	of	of	ADP
ejpam-5476	349	11	nonlinear	nonlinear	ADJ
ejpam-5476	349	12	fractional	fractional	ADJ
ejpam-5476	349	13	partial	partial	ADJ
ejpam-5476	349	14	volterra	volterra	NOUN
ejpam-5476	349	15	integro	integro	PROPN
ejpam-5476	349	16	-	-	PUNCT
ejpam-5476	349	17	differential	differential	NOUN
ejpam-5476	349	18	equations	equation	NOUN
ejpam-5476	349	19	.	.	PUNCT
ejpam-5476	350	1	mathematical	mathematical	ADJ
ejpam-5476	350	2	methods	method	NOUN
ejpam-5476	350	3	in	in	ADP
ejpam-5476	350	4	the	the	DET
ejpam-5476	350	5	applied	apply	VERB
ejpam-5476	350	6	sciences	science	NOUN
ejpam-5476	350	7	,	,	PUNCT
ejpam-5476	350	8	42(6):1870–1893	42(6):1870–1893	NUM
ejpam-5476	350	9	,	,	PUNCT
ejpam-5476	350	10	2019	2019	NUM
ejpam-5476	350	11	.	.	PUNCT
ejpam-5476	351	1	[	[	X
ejpam-5476	351	2	31	31	NUM
ejpam-5476	351	3	]	]	PUNCT
ejpam-5476	351	4	f.	f.	PROPN
ejpam-5476	351	5	mirzaee	mirzaee	PROPN
ejpam-5476	351	6	and	and	CCONJ
ejpam-5476	351	7	s.	s.	PROPN
ejpam-5476	351	8	alipour	alipour	PROPN
ejpam-5476	351	9	.	.	PUNCT
ejpam-5476	352	1	fractional	fractional	ADJ
ejpam-5476	352	2	-	-	PUNCT
ejpam-5476	352	3	order	order	NOUN
ejpam-5476	352	4	orthogonal	orthogonal	ADJ
ejpam-5476	352	5	bernstein	bernstein	PROPN
ejpam-5476	352	6	polynomials	polynomial	NOUN
ejpam-5476	352	7	for	for	ADP
ejpam-5476	352	8	numerical	numerical	ADJ
ejpam-5476	352	9	solution	solution	NOUN
ejpam-5476	352	10	of	of	ADP
ejpam-5476	352	11	nonlinear	nonlinear	ADJ
ejpam-5476	352	12	fractional	fractional	ADJ
ejpam-5476	352	13	partial	partial	ADJ
ejpam-5476	352	14	volterra	volterra	NOUN
ejpam-5476	352	15	integro	integro	PROPN
ejpam-5476	352	16	-	-	PUNCT
ejpam-5476	352	17	differential	differential	NOUN
ejpam-5476	352	18	equations	equation	NOUN
ejpam-5476	352	19	.	.	PUNCT
ejpam-5476	353	1	mathematical	mathematical	ADJ
ejpam-5476	353	2	methods	method	NOUN
ejpam-5476	353	3	in	in	ADP
ejpam-5476	353	4	the	the	DET
ejpam-5476	353	5	applied	apply	VERB
ejpam-5476	353	6	sciences	science	NOUN
ejpam-5476	353	7	,	,	PUNCT
ejpam-5476	353	8	42(6):1870–1893	42(6):1870–1893	NUM
ejpam-5476	353	9	,	,	PUNCT
ejpam-5476	353	10	2019	2019	NUM
ejpam-5476	353	11	.	.	PUNCT
ejpam-5476	354	1	[	[	X
ejpam-5476	354	2	32	32	NUM
ejpam-5476	354	3	]	]	PUNCT
ejpam-5476	354	4	f.	f.	PROPN
ejpam-5476	354	5	mirzaee	mirzaee	PROPN
ejpam-5476	354	6	and	and	CCONJ
ejpam-5476	354	7	s.	s.	PROPN
ejpam-5476	354	8	alipour	alipour	PROPN
ejpam-5476	354	9	.	.	PUNCT
ejpam-5476	355	1	a	a	DET
ejpam-5476	355	2	hybrid	hybrid	ADJ
ejpam-5476	355	3	approach	approach	NOUN
ejpam-5476	355	4	of	of	ADP
ejpam-5476	355	5	nonlinear	nonlinear	ADJ
ejpam-5476	355	6	partial	partial	ADJ
ejpam-5476	355	7	mixed	mixed	ADJ
ejpam-5476	355	8	integrodifferential	integrodifferential	ADJ
ejpam-5476	355	9	equations	equation	NOUN
ejpam-5476	355	10	of	of	ADP
ejpam-5476	355	11	fractional	fractional	ADJ
ejpam-5476	355	12	order	order	NOUN
ejpam-5476	355	13	.	.	PUNCT
ejpam-5476	356	1	iranian	iranian	ADJ
ejpam-5476	356	2	journal	journal	PROPN
ejpam-5476	356	3	of	of	ADP
ejpam-5476	356	4	science	science	NOUN
ejpam-5476	356	5	and	and	CCONJ
ejpam-5476	356	6	technology	technology	NOUN
ejpam-5476	356	7	,	,	PUNCT
ejpam-5476	356	8	transactions	transaction	VERB
ejpam-5476	356	9	a	a	DET
ejpam-5476	356	10	:	:	PUNCT
ejpam-5476	356	11	science	science	NOUN
ejpam-5476	356	12	,	,	PUNCT
ejpam-5476	356	13	44(3	44(3	NOUN
ejpam-5476	356	14	)	)	PUNCT
ejpam-5476	356	15	,	,	PUNCT
ejpam-5476	356	16	2020	2020	NUM
ejpam-5476	356	17	.	.	PUNCT
ejpam-5476	357	1	[	[	X
ejpam-5476	357	2	33	33	NUM
ejpam-5476	357	3	]	]	PUNCT
ejpam-5476	357	4	f.	f.	PROPN
ejpam-5476	357	5	mirzaee	mirzaee	PROPN
ejpam-5476	357	6	,	,	PUNCT
ejpam-5476	357	7	s.	s.	PROPN
ejpam-5476	357	8	alipour	alipour	PROPN
ejpam-5476	357	9	,	,	PUNCT
ejpam-5476	357	10	and	and	CCONJ
ejpam-5476	357	11	n.	n.	PROPN
ejpam-5476	357	12	samadyar	samadyar	PROPN
ejpam-5476	357	13	.	.	PUNCT
ejpam-5476	358	1	a	a	DET
ejpam-5476	358	2	numerical	numerical	ADJ
ejpam-5476	358	3	approach	approach	NOUN
ejpam-5476	358	4	for	for	ADP
ejpam-5476	358	5	solving	solve	VERB
ejpam-5476	358	6	weakly	weakly	ADJ
ejpam-5476	358	7	singular	singular	ADJ
ejpam-5476	358	8	partial	partial	ADJ
ejpam-5476	358	9	integro	integro	ADJ
ejpam-5476	358	10	-	-	PUNCT
ejpam-5476	358	11	differential	differential	NOUN
ejpam-5476	358	12	equations	equation	NOUN
ejpam-5476	358	13	via	via	ADP
ejpam-5476	358	14	two	two	NUM
ejpam-5476	358	15	-	-	PUNCT
ejpam-5476	358	16	dimensional	dimensional	ADJ
ejpam-5476	358	17	-	-	PUNCT
ejpam-5476	358	18	orthonormal	orthonormal	ADJ
ejpam-5476	358	19	bernstein	bernstein	NOUN
ejpam-5476	358	20	polynomials	polynomial	NOUN
ejpam-5476	358	21	with	with	ADP
ejpam-5476	358	22	the	the	DET
ejpam-5476	358	23	convergence	convergence	NOUN
ejpam-5476	358	24	analysis	analysis	NOUN
ejpam-5476	358	25	.	.	PUNCT
ejpam-5476	359	1	numerical	numerical	ADJ
ejpam-5476	359	2	methods	method	NOUN
ejpam-5476	359	3	for	for	ADP
ejpam-5476	359	4	partial	partial	ADJ
ejpam-5476	359	5	differential	differential	NOUN
ejpam-5476	359	6	equations	equation	NOUN
ejpam-5476	359	7	,	,	PUNCT
ejpam-5476	359	8	35(2):615–637	35(2):615–637	NOUN
ejpam-5476	359	9	,	,	PUNCT
ejpam-5476	359	10	2019	2019	NUM
ejpam-5476	359	11	.	.	PUNCT
ejpam-5476	360	1	references	reference	NOUN
ejpam-5476	360	2	3556	3556	NUM
ejpam-5476	360	3	[	[	X
ejpam-5476	360	4	34	34	NUM
ejpam-5476	360	5	]	]	X
ejpam-5476	360	6	f.	f.	PROPN
ejpam-5476	360	7	mirzaee	mirzaee	PROPN
ejpam-5476	360	8	and	and	CCONJ
ejpam-5476	360	9	s.	s.	PROPN
ejpam-5476	360	10	f.	f.	PROPN
ejpam-5476	360	11	hoseini	hoseini	PROPN
ejpam-5476	360	12	.	.	PUNCT
ejpam-5476	360	13	hybrid	hybrid	ADJ
ejpam-5476	360	14	functions	function	NOUN
ejpam-5476	360	15	of	of	ADP
ejpam-5476	360	16	bernstein	bernstein	PROPN
ejpam-5476	360	17	polynomials	polynomials	PROPN
ejpam-5476	360	18	and	and	CCONJ
ejpam-5476	360	19	blockpulse	blockpulse	ADJ
ejpam-5476	360	20	functions	function	NOUN
ejpam-5476	360	21	for	for	ADP
ejpam-5476	360	22	solving	solve	VERB
ejpam-5476	360	23	optimal	optimal	ADJ
ejpam-5476	360	24	control	control	NOUN
ejpam-5476	360	25	of	of	ADP
ejpam-5476	360	26	the	the	DET
ejpam-5476	360	27	nonlinear	nonlinear	PROPN
ejpam-5476	360	28	volterra	volterra	PROPN
ejpam-5476	360	29	integral	integral	ADJ
ejpam-5476	360	30	equations	equation	NOUN
ejpam-5476	360	31	.	.	PUNCT
ejpam-5476	361	1	indagationes	indagatione	NOUN
ejpam-5476	361	2	mathematicae	mathematicae	PROPN
ejpam-5476	361	3	,	,	PUNCT
ejpam-5476	361	4	27(3):835–849	27(3):835–849	PROPN
ejpam-5476	361	5	,	,	PUNCT
ejpam-5476	361	6	2016	2016	NUM
ejpam-5476	361	7	.	.	PUNCT
ejpam-5476	362	1	[	[	X
ejpam-5476	362	2	35	35	NUM
ejpam-5476	362	3	]	]	X
ejpam-5476	362	4	f.	f.	PROPN
ejpam-5476	362	5	mirzaee	mirzaee	PROPN
ejpam-5476	362	6	,	,	PUNCT
ejpam-5476	362	7	s.	s.	PROPN
ejpam-5476	362	8	f.	f.	PROPN
ejpam-5476	362	9	hoseini	hoseini	PROPN
ejpam-5476	362	10	,	,	PUNCT
ejpam-5476	362	11	and	and	CCONJ
ejpam-5476	362	12	s.	s.	PROPN
ejpam-5476	362	13	alipour	alipour	PROPN
ejpam-5476	362	14	.	.	PUNCT
ejpam-5476	363	1	numerical	numerical	ADJ
ejpam-5476	363	2	solution	solution	NOUN
ejpam-5476	363	3	of	of	ADP
ejpam-5476	363	4	the	the	DET
ejpam-5476	363	5	spread	spread	NOUN
ejpam-5476	363	6	of	of	ADP
ejpam-5476	363	7	infectious	infectious	ADJ
ejpam-5476	363	8	diseases	disease	NOUN
ejpam-5476	363	9	mathematical	mathematical	ADJ
ejpam-5476	363	10	model	model	NOUN
ejpam-5476	363	11	based	base	VERB
ejpam-5476	363	12	on	on	ADP
ejpam-5476	363	13	shifted	shift	VERB
ejpam-5476	363	14	bernstein	bernstein	PROPN
ejpam-5476	363	15	polynomials	polynomials	PROPN
ejpam-5476	363	16	.	.	PUNCT
ejpam-5476	364	1	journal	journal	NOUN
ejpam-5476	364	2	of	of	ADP
ejpam-5476	364	3	new	new	ADJ
ejpam-5476	364	4	researches	research	NOUN
ejpam-5476	364	5	in	in	ADP
ejpam-5476	364	6	mathematics	mathematic	NOUN
ejpam-5476	364	7	,	,	PUNCT
ejpam-5476	364	8	6(24):29–38	6(24):29–38	NUM
ejpam-5476	364	9	,	,	PUNCT
ejpam-5476	364	10	2020	2020	NUM
ejpam-5476	364	11	.	.	PUNCT
ejpam-5476	365	1	[	[	X
ejpam-5476	365	2	36	36	NUM
ejpam-5476	365	3	]	]	X
ejpam-5476	365	4	f.	f.	PROPN
ejpam-5476	365	5	mirzaee	mirzaee	PROPN
ejpam-5476	365	6	and	and	CCONJ
ejpam-5476	365	7	n.	n.	PROPN
ejpam-5476	365	8	samadyar	samadyar	PROPN
ejpam-5476	365	9	.	.	PUNCT
ejpam-5476	366	1	application	application	NOUN
ejpam-5476	366	2	of	of	ADP
ejpam-5476	366	3	orthonormal	orthonormal	ADJ
ejpam-5476	366	4	bernstein	bernstein	PROPN
ejpam-5476	366	5	polynomials	polynomial	NOUN
ejpam-5476	366	6	to	to	PART
ejpam-5476	366	7	construct	construct	VERB
ejpam-5476	366	8	a	a	DET
ejpam-5476	366	9	efficient	efficient	ADJ
ejpam-5476	366	10	scheme	scheme	NOUN
ejpam-5476	366	11	for	for	ADP
ejpam-5476	366	12	solving	solve	VERB
ejpam-5476	366	13	fractional	fractional	ADJ
ejpam-5476	366	14	stochastic	stochastic	ADJ
ejpam-5476	366	15	integro	integro	ADJ
ejpam-5476	366	16	-	-	PUNCT
ejpam-5476	366	17	differential	differential	NOUN
ejpam-5476	366	18	equation	equation	NOUN
ejpam-5476	366	19	.	.	PUNCT
ejpam-5476	367	1	optik	optik	PROPN
ejpam-5476	367	2	,	,	PUNCT
ejpam-5476	367	3	132:262–273	132:262–273	NUM
ejpam-5476	367	4	,	,	PUNCT
ejpam-5476	367	5	2017	2017	NUM
ejpam-5476	367	6	.	.	PUNCT
ejpam-5476	368	1	[	[	X
ejpam-5476	368	2	37	37	NUM
ejpam-5476	368	3	]	]	X
ejpam-5476	368	4	f.	f.	PROPN
ejpam-5476	368	5	mirzaee	mirzaee	PROPN
ejpam-5476	368	6	and	and	CCONJ
ejpam-5476	368	7	n.	n.	PROPN
ejpam-5476	368	8	samadyar	samadyar	PROPN
ejpam-5476	368	9	.	.	PUNCT
ejpam-5476	369	1	parameters	parameter	NOUN
ejpam-5476	369	2	estimation	estimation	NOUN
ejpam-5476	369	3	of	of	ADP
ejpam-5476	369	4	hiv	hiv	PROPN
ejpam-5476	369	5	infection	infection	NOUN
ejpam-5476	369	6	model	model	NOUN
ejpam-5476	369	7	of	of	ADP
ejpam-5476	369	8	cd4	cd4	PROPN
ejpam-5476	369	9	+	+	PROPN
ejpam-5476	369	10	t	t	PROPN
ejpam-5476	369	11	-	-	PUNCT
ejpam-5476	369	12	cells	cell	NOUN
ejpam-5476	369	13	by	by	ADP
ejpam-5476	369	14	applying	apply	VERB
ejpam-5476	369	15	orthonormal	orthonormal	ADJ
ejpam-5476	369	16	bernstein	bernstein	PROPN
ejpam-5476	369	17	collocation	collocation	NOUN
ejpam-5476	369	18	method	method	NOUN
ejpam-5476	369	19	.	.	PUNCT
ejpam-5476	370	1	international	international	ADJ
ejpam-5476	370	2	journal	journal	NOUN
ejpam-5476	370	3	of	of	ADP
ejpam-5476	370	4	biomathematics	biomathematic	NOUN
ejpam-5476	370	5	,	,	PUNCT
ejpam-5476	370	6	11(02):1850020	11(02):1850020	NUM
ejpam-5476	370	7	,	,	PUNCT
ejpam-5476	370	8	2018	2018	NUM
ejpam-5476	370	9	.	.	PUNCT
ejpam-5476	371	1	[	[	X
ejpam-5476	371	2	38	38	NUM
ejpam-5476	371	3	]	]	PUNCT
ejpam-5476	371	4	f.	f.	PROPN
ejpam-5476	371	5	mirzaee	mirzaee	PROPN
ejpam-5476	371	6	and	and	CCONJ
ejpam-5476	371	7	n.	n.	PROPN
ejpam-5476	371	8	samadyar	samadyar	PROPN
ejpam-5476	371	9	.	.	PUNCT
ejpam-5476	372	1	numerical	numerical	ADJ
ejpam-5476	372	2	solution	solution	NOUN
ejpam-5476	372	3	based	base	VERB
ejpam-5476	372	4	on	on	ADP
ejpam-5476	372	5	two	two	NUM
ejpam-5476	372	6	-	-	PUNCT
ejpam-5476	372	7	dimensional	dimensional	ADJ
ejpam-5476	372	8	orthonormal	orthonormal	ADJ
ejpam-5476	372	9	bernstein	bernstein	NOUN
ejpam-5476	372	10	polynomials	polynomial	NOUN
ejpam-5476	372	11	for	for	ADP
ejpam-5476	372	12	solving	solve	VERB
ejpam-5476	372	13	some	some	DET
ejpam-5476	372	14	classes	class	NOUN
ejpam-5476	372	15	of	of	ADP
ejpam-5476	372	16	two	two	NUM
ejpam-5476	372	17	-	-	PUNCT
ejpam-5476	372	18	dimensional	dimensional	ADJ
ejpam-5476	372	19	nonlinear	nonlinear	ADJ
ejpam-5476	372	20	integral	integral	ADJ
ejpam-5476	372	21	equations	equation	NOUN
ejpam-5476	372	22	of	of	ADP
ejpam-5476	372	23	fractional	fractional	ADJ
ejpam-5476	372	24	order	order	NOUN
ejpam-5476	372	25	.	.	PUNCT
ejpam-5476	373	1	applied	apply	VERB
ejpam-5476	373	2	mathematics	mathematic	NOUN
ejpam-5476	373	3	and	and	CCONJ
ejpam-5476	373	4	computation	computation	NOUN
ejpam-5476	373	5	,	,	PUNCT
ejpam-5476	373	6	344:191	344:191	NUM
ejpam-5476	373	7	–	–	PUNCT
ejpam-5476	373	8	203	203	NUM
ejpam-5476	373	9	,	,	PUNCT
ejpam-5476	373	10	2019	2019	NUM
ejpam-5476	373	11	.	.	PUNCT
ejpam-5476	374	1	[	[	X
ejpam-5476	374	2	39	39	NUM
ejpam-5476	374	3	]	]	PUNCT
ejpam-5476	374	4	f.	f.	PROPN
ejpam-5476	374	5	mirzaee	mirzaee	PROPN
ejpam-5476	374	6	and	and	CCONJ
ejpam-5476	374	7	n.	n.	PROPN
ejpam-5476	374	8	samadyar	samadyar	PROPN
ejpam-5476	374	9	.	.	PUNCT
ejpam-5476	375	1	on	on	ADP
ejpam-5476	375	2	the	the	DET
ejpam-5476	375	3	numerical	numerical	ADJ
ejpam-5476	375	4	method	method	NOUN
ejpam-5476	375	5	for	for	ADP
ejpam-5476	375	6	solving	solve	VERB
ejpam-5476	375	7	a	a	DET
ejpam-5476	375	8	system	system	NOUN
ejpam-5476	375	9	of	of	ADP
ejpam-5476	375	10	nonlinear	nonlinear	ADJ
ejpam-5476	375	11	fractional	fractional	ADJ
ejpam-5476	375	12	ordinary	ordinary	ADJ
ejpam-5476	375	13	differential	differential	ADJ
ejpam-5476	375	14	equations	equation	NOUN
ejpam-5476	375	15	arising	arise	VERB
ejpam-5476	375	16	in	in	ADP
ejpam-5476	375	17	hiv	hiv	PROPN
ejpam-5476	375	18	infection	infection	NOUN
ejpam-5476	375	19	of	of	ADP
ejpam-5476	375	20	cd4	cd4	PROPN
ejpam-5476	375	21	t	t	PROPN
ejpam-5476	375	22	cells	cell	NOUN
ejpam-5476	375	23	.	.	PUNCT
ejpam-5476	376	1	iranian	iranian	ADJ
ejpam-5476	376	2	journal	journal	PROPN
ejpam-5476	376	3	of	of	ADP
ejpam-5476	376	4	science	science	NOUN
ejpam-5476	376	5	and	and	CCONJ
ejpam-5476	376	6	technology	technology	NOUN
ejpam-5476	376	7	,	,	PUNCT
ejpam-5476	376	8	transactions	transaction	VERB
ejpam-5476	376	9	a	a	DET
ejpam-5476	376	10	:	:	PUNCT
ejpam-5476	376	11	science	science	NOUN
ejpam-5476	376	12	,	,	PUNCT
ejpam-5476	376	13	43(3):1127	43(3):1127	NUM
ejpam-5476	376	14	–	–	PUNCT
ejpam-5476	376	15	1138	1138	NUM
ejpam-5476	376	16	,	,	PUNCT
ejpam-5476	376	17	2019	2019	NUM
ejpam-5476	376	18	.	.	PUNCT
ejpam-5476	377	1	[	[	X
ejpam-5476	377	2	40	40	NUM
ejpam-5476	377	3	]	]	PUNCT
ejpam-5476	377	4	f.	f.	PROPN
ejpam-5476	377	5	mirzaee	mirzaee	PROPN
ejpam-5476	377	6	,	,	PUNCT
ejpam-5476	377	7	n.	n.	PROPN
ejpam-5476	377	8	samadyar	samadyar	PROPN
ejpam-5476	377	9	,	,	PUNCT
ejpam-5476	377	10	and	and	CCONJ
ejpam-5476	377	11	s.	s.	PROPN
ejpam-5476	377	12	alipour	alipour	PROPN
ejpam-5476	377	13	.	.	PUNCT
ejpam-5476	378	1	numerical	numerical	ADJ
ejpam-5476	378	2	solution	solution	NOUN
ejpam-5476	378	3	of	of	ADP
ejpam-5476	378	4	high	high	ADJ
ejpam-5476	378	5	order	order	NOUN
ejpam-5476	378	6	linear	linear	NOUN
ejpam-5476	378	7	complex	complex	ADJ
ejpam-5476	378	8	differential	differential	ADJ
ejpam-5476	378	9	equations	equation	NOUN
ejpam-5476	378	10	via	via	ADP
ejpam-5476	378	11	complex	complex	ADJ
ejpam-5476	378	12	operational	operational	ADJ
ejpam-5476	378	13	matrix	matrix	NOUN
ejpam-5476	378	14	method	method	NOUN
ejpam-5476	378	15	.	.	PUNCT
ejpam-5476	379	1	sema	sema	PROPN
ejpam-5476	379	2	journal	journal	PROPN
ejpam-5476	379	3	,	,	PUNCT
ejpam-5476	379	4	76(1):1–13	76(1):1–13	NUM
ejpam-5476	379	5	,	,	PUNCT
ejpam-5476	379	6	2019	2019	NUM
ejpam-5476	379	7	.	.	PUNCT
ejpam-5476	380	1	[	[	X
ejpam-5476	380	2	41	41	NUM
ejpam-5476	380	3	]	]	PUNCT
ejpam-5476	380	4	z.	z.	PROPN
ejpam-5476	380	5	odibat	odibat	PROPN
ejpam-5476	380	6	and	and	CCONJ
ejpam-5476	380	7	d.	d.	PROPN
ejpam-5476	380	8	baleanu	baleanu	PROPN
ejpam-5476	380	9	.	.	PUNCT
ejpam-5476	381	1	numerical	numerical	PROPN
ejpam-5476	381	2	simulation	simulation	PROPN
ejpam-5476	381	3	of	of	ADP
ejpam-5476	381	4	initial	initial	ADJ
ejpam-5476	381	5	value	value	NOUN
ejpam-5476	381	6	problems	problem	NOUN
ejpam-5476	381	7	with	with	ADP
ejpam-5476	381	8	generalized	generalized	ADJ
ejpam-5476	381	9	caputo	caputo	NOUN
ejpam-5476	381	10	-	-	PUNCT
ejpam-5476	381	11	type	type	NOUN
ejpam-5476	381	12	fractional	fractional	ADJ
ejpam-5476	381	13	derivatives	derivative	NOUN
ejpam-5476	381	14	.	.	PUNCT
ejpam-5476	382	1	applied	apply	VERB
ejpam-5476	382	2	numerical	numerical	ADJ
ejpam-5476	382	3	mathematics	mathematic	NOUN
ejpam-5476	382	4	,	,	PUNCT
ejpam-5476	382	5	156:94	156:94	NUM
ejpam-5476	382	6	–	–	PUNCT
ejpam-5476	382	7	105	105	NUM
ejpam-5476	382	8	,	,	PUNCT
ejpam-5476	382	9	2020	2020	NUM
ejpam-5476	382	10	.	.	PUNCT
ejpam-5476	383	1	[	[	X
ejpam-5476	383	2	42	42	NUM
ejpam-5476	383	3	]	]	X
ejpam-5476	383	4	ndolane	ndolane	ADJ
ejpam-5476	383	5	sene	sene	PROPN
ejpam-5476	383	6	.	.	PUNCT
ejpam-5476	384	1	analytical	analytical	ADJ
ejpam-5476	384	2	solutions	solution	NOUN
ejpam-5476	384	3	of	of	ADP
ejpam-5476	384	4	hristov	hristov	ADJ
ejpam-5476	384	5	diffusion	diffusion	NOUN
ejpam-5476	384	6	equations	equation	NOUN
ejpam-5476	384	7	with	with	ADP
ejpam-5476	384	8	non	non	ADJ
ejpam-5476	384	9	-	-	ADJ
ejpam-5476	384	10	singular	singular	ADJ
ejpam-5476	384	11	fractional	fractional	ADJ
ejpam-5476	384	12	derivatives	derivative	NOUN
ejpam-5476	384	13	.	.	PUNCT
ejpam-5476	385	1	chaos	chaos	NOUN
ejpam-5476	385	2	:	:	PUNCT
ejpam-5476	385	3	an	an	DET
ejpam-5476	385	4	interdisciplinary	interdisciplinary	ADJ
ejpam-5476	385	5	journal	journal	NOUN
ejpam-5476	385	6	of	of	ADP
ejpam-5476	385	7	nonlinear	nonlinear	ADJ
ejpam-5476	385	8	science	science	NOUN
ejpam-5476	385	9	,	,	PUNCT
ejpam-5476	385	10	29(2):023112	29(2):023112	NUM
ejpam-5476	385	11	,	,	PUNCT
ejpam-5476	385	12	2019	2019	NUM
ejpam-5476	385	13	.	.	PUNCT
ejpam-5476	386	1	[	[	X
ejpam-5476	386	2	43	43	NUM
ejpam-5476	386	3	]	]	X
ejpam-5476	386	4	harendra	harendra	PROPN
ejpam-5476	386	5	singh	singh	PROPN
ejpam-5476	386	6	.	.	PUNCT
ejpam-5476	387	1	operational	operational	ADJ
ejpam-5476	387	2	matrix	matrix	NOUN
ejpam-5476	387	3	approach	approach	NOUN
ejpam-5476	387	4	for	for	ADP
ejpam-5476	387	5	approximate	approximate	ADJ
ejpam-5476	387	6	solution	solution	NOUN
ejpam-5476	387	7	of	of	ADP
ejpam-5476	387	8	fractional	fractional	ADJ
ejpam-5476	387	9	model	model	NOUN
ejpam-5476	387	10	of	of	ADP
ejpam-5476	387	11	bloch	bloch	PROPN
ejpam-5476	387	12	equation	equation	PROPN
ejpam-5476	387	13	.	.	PUNCT
ejpam-5476	388	1	journal	journal	PROPN
ejpam-5476	388	2	of	of	ADP
ejpam-5476	388	3	king	king	PROPN
ejpam-5476	388	4	saud	saud	PROPN
ejpam-5476	388	5	university	university	PROPN
ejpam-5476	388	6	science	science	NOUN
ejpam-5476	388	7	,	,	PUNCT
ejpam-5476	388	8	2016	2016	NUM
ejpam-5476	388	9	.	.	PUNCT