id	sid	tid	token	lemma	pos
ejpam-6865	1	1	european	european	PROPN
ejpam-6865	1	2	journal	journal	PROPN
ejpam-6865	1	3	of	of	ADP
ejpam-6865	1	4	pure	pure	ADJ
ejpam-6865	1	5	and	and	CCONJ
ejpam-6865	1	6	applied	applied	ADJ
ejpam-6865	1	7	mathematics	mathematic	NOUN
ejpam-6865	1	8	2025	2025	NUM
ejpam-6865	1	9	,	,	PUNCT
ejpam-6865	1	10	vol	vol	NOUN
ejpam-6865	1	11	.	.	PROPN
ejpam-6865	1	12	18	18	NUM
ejpam-6865	1	13	,	,	PUNCT
ejpam-6865	1	14	issue	issue	NOUN
ejpam-6865	1	15	4	4	NUM
ejpam-6865	1	16	,	,	PUNCT
ejpam-6865	1	17	article	article	NOUN
ejpam-6865	1	18	number	number	NOUN
ejpam-6865	1	19	6865	6865	NUM
ejpam-6865	1	20	issn	issn	PROPN
ejpam-6865	1	21	1307	1307	NUM
ejpam-6865	1	22	-	-	SYM
ejpam-6865	1	23	5543	5543	NUM
ejpam-6865	1	24	–	–	PUNCT
ejpam-6865	1	25	ejpam.com	ejpam.com	X
ejpam-6865	1	26	published	publish	VERB
ejpam-6865	1	27	by	by	ADP
ejpam-6865	1	28	new	new	PROPN
ejpam-6865	1	29	york	york	PROPN
ejpam-6865	1	30	business	business	PROPN
ejpam-6865	1	31	global	global	PROPN
ejpam-6865	1	32	two	two	NUM
ejpam-6865	1	33	numerical	numerical	ADJ
ejpam-6865	1	34	approaches	approach	NOUN
ejpam-6865	1	35	to	to	ADP
ejpam-6865	1	36	solving	solve	VERB
ejpam-6865	1	37	fractional	fractional	ADJ
ejpam-6865	1	38	differential	differential	ADJ
ejpam-6865	1	39	equations	equation	NOUN
ejpam-6865	1	40	with	with	ADP
ejpam-6865	1	41	a	a	DET
ejpam-6865	1	42	generalized	generalized	ADJ
ejpam-6865	1	43	mittag	mittag	ADJ
ejpam-6865	1	44	–	–	PUNCT
ejpam-6865	1	45	leffler	leffl	ADJ
ejpam-6865	1	46	kernel	kernel	NOUN
ejpam-6865	1	47	using	use	VERB
ejpam-6865	1	48	bernstein	bernstein	PROPN
ejpam-6865	1	49	polynomials	polynomials	PROPN
ejpam-6865	1	50	shreen	shreen	PROPN
ejpam-6865	1	51	tamimi1	tamimi1	PROPN
ejpam-6865	1	52	,	,	PUNCT
ejpam-6865	1	53	a.	a.	PROPN
ejpam-6865	1	54	k.	k.	PROPN
ejpam-6865	1	55	alomari2,∗	alomari2,∗	PROPN
ejpam-6865	1	56	,	,	PUNCT
ejpam-6865	1	57	m.	m.	NOUN
ejpam-6865	1	58	alaroud1	alaroud1	PROPN
ejpam-6865	1	59	1	1	NUM
ejpam-6865	1	60	department	department	NOUN
ejpam-6865	1	61	of	of	ADP
ejpam-6865	1	62	mathematics	mathematic	NOUN
ejpam-6865	1	63	,	,	PUNCT
ejpam-6865	1	64	faculty	faculty	NOUN
ejpam-6865	1	65	of	of	ADP
ejpam-6865	1	66	science	science	NOUN
ejpam-6865	1	67	,	,	PUNCT
ejpam-6865	1	68	yarmouk	yarmouk	CCONJ
ejpam-6865	1	69	university	university	NOUN
ejpam-6865	1	70	,	,	PUNCT
ejpam-6865	1	71	211	211	NUM
ejpam-6865	1	72	-	-	SYM
ejpam-6865	1	73	63	63	NUM
ejpam-6865	1	74	irbid	irbid	NOUN
ejpam-6865	1	75	,	,	PUNCT
ejpam-6865	1	76	jordan	jordan	PROPN
ejpam-6865	1	77	2	2	NUM
ejpam-6865	1	78	department	department	NOUN
ejpam-6865	1	79	of	of	ADP
ejpam-6865	1	80	mathematics	mathematic	NOUN
ejpam-6865	1	81	,	,	PUNCT
ejpam-6865	1	82	faculty	faculty	NOUN
ejpam-6865	1	83	of	of	ADP
ejpam-6865	1	84	science	science	NOUN
ejpam-6865	1	85	,	,	PUNCT
ejpam-6865	1	86	islamic	islamic	PROPN
ejpam-6865	1	87	university	university	PROPN
ejpam-6865	1	88	of	of	ADP
ejpam-6865	1	89	madinah	madinah	PROPN
ejpam-6865	1	90	,	,	PUNCT
ejpam-6865	1	91	42351	42351	NUM
ejpam-6865	1	92	,	,	PUNCT
ejpam-6865	1	93	madinah	madinah	PROPN
ejpam-6865	1	94	,	,	PUNCT
ejpam-6865	1	95	saudi	saudi	PROPN
ejpam-6865	1	96	arabia	arabia	PROPN
ejpam-6865	1	97	abstract	abstract	NOUN
ejpam-6865	1	98	.	.	PUNCT
ejpam-6865	2	1	this	this	DET
ejpam-6865	2	2	paper	paper	NOUN
ejpam-6865	2	3	presents	present	VERB
ejpam-6865	2	4	a	a	DET
ejpam-6865	2	5	solution	solution	NOUN
ejpam-6865	2	6	to	to	ADP
ejpam-6865	2	7	fractional	fractional	ADJ
ejpam-6865	2	8	differential	differential	ADJ
ejpam-6865	2	9	equations	equation	NOUN
ejpam-6865	2	10	containing	contain	VERB
ejpam-6865	2	11	three	three	NUM
ejpam-6865	2	12	parameters	parameter	NOUN
ejpam-6865	2	13	,	,	PUNCT
ejpam-6865	2	14	utilizing	utilize	VERB
ejpam-6865	2	15	bernstein	bernstein	PROPN
ejpam-6865	2	16	polynomials	polynomial	NOUN
ejpam-6865	2	17	through	through	ADP
ejpam-6865	2	18	two	two	NUM
ejpam-6865	2	19	efficient	efficient	ADJ
ejpam-6865	2	20	computational	computational	ADJ
ejpam-6865	2	21	approaches	approach	NOUN
ejpam-6865	2	22	.	.	PUNCT
ejpam-6865	3	1	in	in	ADP
ejpam-6865	3	2	the	the	DET
ejpam-6865	3	3	first	first	ADJ
ejpam-6865	3	4	approach	approach	NOUN
ejpam-6865	3	5	,	,	PUNCT
ejpam-6865	3	6	the	the	DET
ejpam-6865	3	7	solution	solution	NOUN
ejpam-6865	3	8	is	be	AUX
ejpam-6865	3	9	expressed	express	VERB
ejpam-6865	3	10	as	as	ADP
ejpam-6865	3	11	a	a	DET
ejpam-6865	3	12	linear	linear	ADJ
ejpam-6865	3	13	combination	combination	NOUN
ejpam-6865	3	14	of	of	ADP
ejpam-6865	3	15	bernstein	bernstein	PROPN
ejpam-6865	3	16	polynomials	polynomials	PROPN
ejpam-6865	3	17	.	.	PUNCT
ejpam-6865	4	1	in	in	ADP
ejpam-6865	4	2	contrast	contrast	NOUN
ejpam-6865	4	3	,	,	PUNCT
ejpam-6865	4	4	in	in	ADP
ejpam-6865	4	5	the	the	DET
ejpam-6865	4	6	second	second	NOUN
ejpam-6865	4	7	,	,	PUNCT
ejpam-6865	4	8	the	the	DET
ejpam-6865	4	9	fractional	fractional	ADJ
ejpam-6865	4	10	derivative	derivative	NOUN
ejpam-6865	4	11	itself	itself	PRON
ejpam-6865	4	12	is	be	AUX
ejpam-6865	4	13	represented	represent	VERB
ejpam-6865	4	14	in	in	ADP
ejpam-6865	4	15	terms	term	NOUN
ejpam-6865	4	16	of	of	ADP
ejpam-6865	4	17	bernstein	bernstein	PROPN
ejpam-6865	4	18	polynomials	polynomials	PROPN
ejpam-6865	4	19	.	.	PUNCT
ejpam-6865	5	1	the	the	DET
ejpam-6865	5	2	key	key	ADJ
ejpam-6865	5	3	properties	property	NOUN
ejpam-6865	5	4	of	of	ADP
ejpam-6865	5	5	both	both	DET
ejpam-6865	5	6	algorithms	algorithm	NOUN
ejpam-6865	5	7	are	be	AUX
ejpam-6865	5	8	derived	derive	VERB
ejpam-6865	5	9	and	and	CCONJ
ejpam-6865	5	10	analyzed	analyze	VERB
ejpam-6865	5	11	.	.	PUNCT
ejpam-6865	6	1	the	the	DET
ejpam-6865	6	2	generalized	generalize	VERB
ejpam-6865	6	3	atangana	atangana	PROPN
ejpam-6865	6	4	baleanu	baleanu	PROPN
ejpam-6865	6	5	caputo	caputo	PROPN
ejpam-6865	6	6	definition	definition	NOUN
ejpam-6865	6	7	of	of	ADP
ejpam-6865	6	8	fractional	fractional	ADJ
ejpam-6865	6	9	derivative	derivative	NOUN
ejpam-6865	6	10	that	that	PRON
ejpam-6865	6	11	uses	use	VERB
ejpam-6865	6	12	the	the	DET
ejpam-6865	6	13	mittag	mittag	ADJ
ejpam-6865	6	14	-	-	PUNCT
ejpam-6865	6	15	leffler	leffler	NOUN
ejpam-6865	6	16	function	function	NOUN
ejpam-6865	6	17	as	as	ADP
ejpam-6865	6	18	the	the	DET
ejpam-6865	6	19	kernel	kernel	NOUN
ejpam-6865	6	20	of	of	ADP
ejpam-6865	6	21	the	the	DET
ejpam-6865	6	22	integration	integration	NOUN
ejpam-6865	6	23	form	form	NOUN
ejpam-6865	6	24	of	of	ADP
ejpam-6865	6	25	the	the	DET
ejpam-6865	6	26	fractional	fractional	ADJ
ejpam-6865	6	27	derivative	derivative	NOUN
ejpam-6865	6	28	,	,	PUNCT
ejpam-6865	6	29	characterized	characterize	VERB
ejpam-6865	6	30	by	by	ADP
ejpam-6865	6	31	three	three	NUM
ejpam-6865	6	32	tunable	tunable	ADJ
ejpam-6865	6	33	parameters	parameter	NOUN
ejpam-6865	6	34	,	,	PUNCT
ejpam-6865	6	35	is	be	AUX
ejpam-6865	6	36	adopted	adopt	VERB
ejpam-6865	6	37	throughout	throughout	ADP
ejpam-6865	6	38	this	this	DET
ejpam-6865	6	39	study	study	NOUN
ejpam-6865	6	40	.	.	PUNCT
ejpam-6865	7	1	those	those	DET
ejpam-6865	7	2	parameters	parameter	NOUN
ejpam-6865	7	3	can	can	AUX
ejpam-6865	7	4	adjust	adjust	VERB
ejpam-6865	7	5	the	the	DET
ejpam-6865	7	6	existence	existence	NOUN
ejpam-6865	7	7	and	and	CCONJ
ejpam-6865	7	8	the	the	DET
ejpam-6865	7	9	behavior	behavior	NOUN
ejpam-6865	7	10	of	of	ADP
ejpam-6865	7	11	the	the	DET
ejpam-6865	7	12	solution	solution	NOUN
ejpam-6865	7	13	for	for	ADP
ejpam-6865	7	14	the	the	DET
ejpam-6865	7	15	fractional	fractional	ADJ
ejpam-6865	7	16	derivative	derivative	ADJ
ejpam-6865	7	17	equations	equation	NOUN
ejpam-6865	7	18	.	.	PUNCT
ejpam-6865	8	1	a	a	DET
ejpam-6865	8	2	set	set	NOUN
ejpam-6865	8	3	of	of	ADP
ejpam-6865	8	4	initial	initial	ADJ
ejpam-6865	8	5	value	value	NOUN
ejpam-6865	8	6	problems	problem	NOUN
ejpam-6865	8	7	,	,	PUNCT
ejpam-6865	8	8	including	include	VERB
ejpam-6865	8	9	both	both	CCONJ
ejpam-6865	8	10	linear	linear	ADJ
ejpam-6865	8	11	and	and	CCONJ
ejpam-6865	8	12	nonlinear	nonlinear	ADJ
ejpam-6865	8	13	fractional	fractional	ADJ
ejpam-6865	8	14	differential	differential	NOUN
ejpam-6865	8	15	equations	equation	NOUN
ejpam-6865	8	16	,	,	PUNCT
ejpam-6865	8	17	are	be	AUX
ejpam-6865	8	18	solved	solve	VERB
ejpam-6865	8	19	using	use	VERB
ejpam-6865	8	20	the	the	DET
ejpam-6865	8	21	suggested	suggest	VERB
ejpam-6865	8	22	approaches	approach	NOUN
ejpam-6865	8	23	.	.	PUNCT
ejpam-6865	9	1	the	the	DET
ejpam-6865	9	2	solution	solution	NOUN
ejpam-6865	9	3	profiles	profile	NOUN
ejpam-6865	9	4	illustrate	illustrate	VERB
ejpam-6865	9	5	the	the	DET
ejpam-6865	9	6	performance	performance	NOUN
ejpam-6865	9	7	of	of	ADP
ejpam-6865	9	8	the	the	DET
ejpam-6865	9	9	numerical	numerical	ADJ
ejpam-6865	9	10	solutions	solution	NOUN
ejpam-6865	9	11	and	and	CCONJ
ejpam-6865	9	12	the	the	DET
ejpam-6865	9	13	impact	impact	NOUN
ejpam-6865	9	14	of	of	ADP
ejpam-6865	9	15	the	the	DET
ejpam-6865	9	16	atangana	atangana	PROPN
ejpam-6865	9	17	baleanu	baleanu	PROPN
ejpam-6865	9	18	caputo	caputo	PROPN
ejpam-6865	9	19	definition	definition	NOUN
ejpam-6865	9	20	on	on	ADP
ejpam-6865	9	21	the	the	DET
ejpam-6865	9	22	obtained	obtain	VERB
ejpam-6865	9	23	findings	finding	NOUN
ejpam-6865	9	24	,	,	PUNCT
ejpam-6865	9	25	demonstrating	demonstrate	VERB
ejpam-6865	9	26	that	that	SCONJ
ejpam-6865	9	27	bernstein	bernstein	PROPN
ejpam-6865	9	28	polynomials	polynomial	NOUN
ejpam-6865	9	29	provide	provide	VERB
ejpam-6865	9	30	improved	improved	ADJ
ejpam-6865	9	31	accuracy	accuracy	NOUN
ejpam-6865	9	32	and	and	CCONJ
ejpam-6865	9	33	efficiency	efficiency	NOUN
ejpam-6865	9	34	in	in	ADP
ejpam-6865	9	35	extracting	extract	VERB
ejpam-6865	9	36	solutions	solution	NOUN
ejpam-6865	9	37	for	for	ADP
ejpam-6865	9	38	the	the	DET
ejpam-6865	9	39	considered	consider	VERB
ejpam-6865	9	40	fractional	fractional	ADJ
ejpam-6865	9	41	models	model	NOUN
ejpam-6865	9	42	.	.	PUNCT
ejpam-6865	10	1	the	the	DET
ejpam-6865	10	2	computational	computational	ADJ
ejpam-6865	10	3	simulation	simulation	NOUN
ejpam-6865	10	4	of	of	ADP
ejpam-6865	10	5	this	this	DET
ejpam-6865	10	6	comparative	comparative	ADJ
ejpam-6865	10	7	analysis	analysis	NOUN
ejpam-6865	10	8	reveals	reveal	VERB
ejpam-6865	10	9	that	that	SCONJ
ejpam-6865	10	10	the	the	DET
ejpam-6865	10	11	second	second	ADJ
ejpam-6865	10	12	approach	approach	NOUN
ejpam-6865	10	13	yields	yield	VERB
ejpam-6865	10	14	higher	high	ADJ
ejpam-6865	10	15	accuracy	accuracy	NOUN
ejpam-6865	10	16	with	with	ADP
ejpam-6865	10	17	smaller	small	ADJ
ejpam-6865	10	18	absolute	absolute	ADJ
ejpam-6865	10	19	errors	error	NOUN
ejpam-6865	10	20	and	and	CCONJ
ejpam-6865	10	21	additionally	additionally	ADV
ejpam-6865	10	22	provides	provide	VERB
ejpam-6865	10	23	insight	insight	NOUN
ejpam-6865	10	24	into	into	ADP
ejpam-6865	10	25	the	the	DET
ejpam-6865	10	26	existence	existence	NOUN
ejpam-6865	10	27	of	of	ADP
ejpam-6865	10	28	solutions	solution	NOUN
ejpam-6865	10	29	,	,	PUNCT
ejpam-6865	10	30	as	as	SCONJ
ejpam-6865	10	31	illustrated	illustrate	VERB
ejpam-6865	10	32	through	through	ADP
ejpam-6865	10	33	the	the	DET
ejpam-6865	10	34	studied	study	VERB
ejpam-6865	10	35	fractional	fractional	ADJ
ejpam-6865	10	36	models	model	NOUN
ejpam-6865	10	37	.	.	PUNCT
ejpam-6865	11	1	2020	2020	NUM
ejpam-6865	11	2	mathematics	mathematic	NOUN
ejpam-6865	11	3	subject	subject	NOUN
ejpam-6865	11	4	classifications	classification	NOUN
ejpam-6865	11	5	:	:	PUNCT
ejpam-6865	11	6	26a33	26a33	NUM
ejpam-6865	11	7	,	,	PUNCT
ejpam-6865	11	8	41a30	41a30	NUM
ejpam-6865	11	9	,	,	PUNCT
ejpam-6865	11	10	65n12	65n12	NUM
ejpam-6865	11	11	,	,	PUNCT
ejpam-6865	11	12	33c45	33c45	NUM
ejpam-6865	11	13	,	,	PUNCT
ejpam-6865	11	14	33e12	33e12	NUM
ejpam-6865	11	15	,	,	PUNCT
ejpam-6865	11	16	65n22	65n22	NUM
ejpam-6865	11	17	key	key	ADJ
ejpam-6865	11	18	words	word	NOUN
ejpam-6865	11	19	and	and	CCONJ
ejpam-6865	11	20	phrases	phrase	NOUN
ejpam-6865	11	21	:	:	PUNCT
ejpam-6865	11	22	generalized	generalized	ADJ
ejpam-6865	11	23	abc	abc	PROPN
ejpam-6865	11	24	fractional	fractional	PROPN
ejpam-6865	11	25	derivative	derivative	ADJ
ejpam-6865	11	26	,	,	PUNCT
ejpam-6865	11	27	generalized	generalize	VERB
ejpam-6865	11	28	mittag	mittag	ADJ
ejpam-6865	11	29	-	-	PUNCT
ejpam-6865	11	30	leffler	leffler	NOUN
ejpam-6865	11	31	kernel	kernel	NOUN
ejpam-6865	11	32	,	,	PUNCT
ejpam-6865	11	33	bernstein	bernstein	PROPN
ejpam-6865	11	34	polynomials	polynomials	PROPN
ejpam-6865	11	35	,	,	PUNCT
ejpam-6865	11	36	riemann	riemann	PROPN
ejpam-6865	11	37	-	-	PUNCT
ejpam-6865	11	38	liouville	liouville	VERB
ejpam-6865	11	39	fractional	fractional	ADJ
ejpam-6865	11	40	derivative	derivative	ADJ
ejpam-6865	11	41	,	,	PUNCT
ejpam-6865	11	42	fractional	fractional	ADJ
ejpam-6865	11	43	calculus	calculus	NOUN
ejpam-6865	11	44	,	,	PUNCT
ejpam-6865	11	45	ab	ab	PROPN
ejpam-6865	11	46	fractional	fractional	ADJ
ejpam-6865	11	47	integral	integral	ADJ
ejpam-6865	11	48	∗corresponding	∗corresponde	VERB
ejpam-6865	11	49	author	author	NOUN
ejpam-6865	11	50	.	.	PUNCT
ejpam-6865	12	1	doi	doi	NOUN
ejpam-6865	12	2	:	:	PUNCT
ejpam-6865	12	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6865	https://doi.org/10.29020/nybg.ejpam.v18i4.6865	ADJ
ejpam-6865	12	4	email	email	NOUN
ejpam-6865	12	5	addresses	address	NOUN
ejpam-6865	12	6	:	:	PUNCT
ejpam-6865	12	7	shreentamimi25@gmail.com	shreentamimi25@gmail.com	PROPN
ejpam-6865	12	8	(	(	PUNCT
ejpam-6865	12	9	s.	s.	PROPN
ejpam-6865	12	10	tamimi	tamimi	PROPN
ejpam-6865	12	11	)	)	PUNCT
ejpam-6865	12	12	,	,	PUNCT
ejpam-6865	12	13	abdomari2008@yahoo.com	abdomari2008@yahoo.com	X
ejpam-6865	13	1	(	(	PUNCT
ejpam-6865	13	2	a.	a.	PROPN
ejpam-6865	13	3	k.	k.	PROPN
ejpam-6865	13	4	alomari	alomari	PROPN
ejpam-6865	13	5	)	)	PUNCT
ejpam-6865	13	6	,	,	PUNCT
ejpam-6865	13	7	mohammad.alaroud@yu.edu.jo	mohammad.alaroud@yu.edu.jo	NOUN
ejpam-6865	13	8	(	(	PUNCT
ejpam-6865	13	9	m.	m.	NOUN
ejpam-6865	13	10	alaroud	alaroud	PROPN
ejpam-6865	13	11	)	)	PUNCT
ejpam-6865	13	12	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6865	14	1	1	1	NUM
ejpam-6865	14	2	copyright	copyright	NOUN
ejpam-6865	14	3	:	:	PUNCT
ejpam-6865	14	4	©	©	PROPN
ejpam-6865	14	5	2025	2025	NUM
ejpam-6865	14	6	the	the	DET
ejpam-6865	14	7	author(s	author(s	NOUN
ejpam-6865	14	8	)	)	PUNCT
ejpam-6865	14	9	.	.	PUNCT
ejpam-6865	15	1	(	(	PUNCT
ejpam-6865	15	2	cc	cc	NOUN
ejpam-6865	15	3	by	by	ADP
ejpam-6865	15	4	-	-	PUNCT
ejpam-6865	15	5	nc	nc	PROPN
ejpam-6865	15	6	4.0	4.0	NUM
ejpam-6865	15	7	)	)	PUNCT
ejpam-6865	15	8	s.	s.	PROPN
ejpam-6865	15	9	tamimi	tamimi	PROPN
ejpam-6865	15	10	,	,	PUNCT
ejpam-6865	15	11	a.	a.	PROPN
ejpam-6865	15	12	k.	k.	PROPN
ejpam-6865	15	13	alomari	alomari	PROPN
ejpam-6865	15	14	,	,	PUNCT
ejpam-6865	15	15	m.	m.	NOUN
ejpam-6865	15	16	alaroud	alaroud	PROPN
ejpam-6865	15	17	/	/	SYM
ejpam-6865	15	18	eur	eur	PROPN
ejpam-6865	15	19	.	.	PUNCT
ejpam-6865	16	1	j.	j.	PROPN
ejpam-6865	16	2	pure	pure	PROPN
ejpam-6865	16	3	appl	appl	PROPN
ejpam-6865	16	4	.	.	PROPN
ejpam-6865	16	5	math	math	PROPN
ejpam-6865	16	6	,	,	PUNCT
ejpam-6865	16	7	18	18	NUM
ejpam-6865	16	8	(	(	PUNCT
ejpam-6865	16	9	4	4	NUM
ejpam-6865	16	10	)	)	PUNCT
ejpam-6865	16	11	(	(	PUNCT
ejpam-6865	16	12	2025	2025	NUM
ejpam-6865	16	13	)	)	PUNCT
ejpam-6865	16	14	,	,	PUNCT
ejpam-6865	16	15	6865	6865	NUM
ejpam-6865	16	16	2	2	NUM
ejpam-6865	16	17	of	of	ADP
ejpam-6865	16	18	19	19	NUM
ejpam-6865	16	19	1	1	NUM
ejpam-6865	16	20	.	.	PUNCT
ejpam-6865	17	1	introduction	introduction	NOUN
ejpam-6865	17	2	differential	differential	NOUN
ejpam-6865	17	3	equations	equation	NOUN
ejpam-6865	17	4	are	be	AUX
ejpam-6865	17	5	one	one	NUM
ejpam-6865	17	6	of	of	ADP
ejpam-6865	17	7	the	the	DET
ejpam-6865	17	8	most	most	ADV
ejpam-6865	17	9	used	use	VERB
ejpam-6865	17	10	for	for	ADP
ejpam-6865	17	11	modeling	model	VERB
ejpam-6865	17	12	real	real	ADJ
ejpam-6865	17	13	-	-	PUNCT
ejpam-6865	17	14	life	life	NOUN
ejpam-6865	17	15	phenomena	phenomenon	NOUN
ejpam-6865	17	16	that	that	PRON
ejpam-6865	17	17	are	be	AUX
ejpam-6865	17	18	based	base	VERB
ejpam-6865	17	19	on	on	ADP
ejpam-6865	17	20	calculating	calculate	VERB
ejpam-6865	17	21	the	the	DET
ejpam-6865	17	22	changes	change	NOUN
ejpam-6865	17	23	of	of	ADP
ejpam-6865	17	24	the	the	DET
ejpam-6865	17	25	systems	system	NOUN
ejpam-6865	17	26	based	base	VERB
ejpam-6865	17	27	on	on	ADP
ejpam-6865	17	28	dimensions	dimension	NOUN
ejpam-6865	17	29	or	or	CCONJ
ejpam-6865	17	30	time	time	NOUN
ejpam-6865	17	31	.	.	PUNCT
ejpam-6865	18	1	replacing	replace	VERB
ejpam-6865	18	2	the	the	DET
ejpam-6865	18	3	standard	standard	ADJ
ejpam-6865	18	4	derivatives	derivative	NOUN
ejpam-6865	18	5	with	with	ADP
ejpam-6865	18	6	fractional	fractional	ADJ
ejpam-6865	18	7	ones	one	NOUN
ejpam-6865	18	8	will	will	AUX
ejpam-6865	18	9	enrich	enrich	VERB
ejpam-6865	18	10	the	the	DET
ejpam-6865	18	11	problem	problem	NOUN
ejpam-6865	18	12	with	with	ADP
ejpam-6865	18	13	several	several	ADJ
ejpam-6865	18	14	parameters	parameter	NOUN
ejpam-6865	18	15	that	that	PRON
ejpam-6865	18	16	can	can	AUX
ejpam-6865	18	17	be	be	AUX
ejpam-6865	18	18	fitted	fit	VERB
ejpam-6865	18	19	to	to	ADP
ejpam-6865	18	20	real	real	ADJ
ejpam-6865	18	21	data	datum	NOUN
ejpam-6865	18	22	[	[	X
ejpam-6865	18	23	1	1	NUM
ejpam-6865	18	24	,	,	PUNCT
ejpam-6865	18	25	2	2	NUM
ejpam-6865	18	26	]	]	PUNCT
ejpam-6865	18	27	.	.	PUNCT
ejpam-6865	19	1	most	most	ADJ
ejpam-6865	19	2	of	of	ADP
ejpam-6865	19	3	those	those	DET
ejpam-6865	19	4	fractional	fractional	ADJ
ejpam-6865	19	5	derivatives(fds	derivatives(fds	NOUN
ejpam-6865	19	6	)	)	PUNCT
ejpam-6865	19	7	are	be	AUX
ejpam-6865	19	8	close	close	ADJ
ejpam-6865	19	9	to	to	ADP
ejpam-6865	19	10	the	the	DET
ejpam-6865	19	11	standard	standard	ADJ
ejpam-6865	19	12	one	one	NUM
ejpam-6865	19	13	in	in	ADP
ejpam-6865	19	14	the	the	DET
ejpam-6865	19	15	case	case	NOUN
ejpam-6865	19	16	of	of	ADP
ejpam-6865	19	17	an	an	DET
ejpam-6865	19	18	integer	integer	NOUN
ejpam-6865	19	19	derivative	derivative	NOUN
ejpam-6865	19	20	.	.	PUNCT
ejpam-6865	20	1	fractional	fractional	ADJ
ejpam-6865	20	2	order	order	NOUN
ejpam-6865	20	3	calculus	calculus	NOUN
ejpam-6865	20	4	has	have	AUX
ejpam-6865	20	5	garnered	garner	VERB
ejpam-6865	20	6	significant	significant	ADJ
ejpam-6865	20	7	interest	interest	NOUN
ejpam-6865	20	8	in	in	ADP
ejpam-6865	20	9	both	both	CCONJ
ejpam-6865	20	10	theoretical	theoretical	ADJ
ejpam-6865	20	11	and	and	CCONJ
ejpam-6865	20	12	applied	apply	VERB
ejpam-6865	20	13	sciences	science	NOUN
ejpam-6865	20	14	over	over	ADP
ejpam-6865	20	15	the	the	DET
ejpam-6865	20	16	past	past	ADJ
ejpam-6865	20	17	twenty	twenty	NUM
ejpam-6865	20	18	years	year	NOUN
ejpam-6865	20	19	.	.	PUNCT
ejpam-6865	21	1	diverse	diverse	ADJ
ejpam-6865	21	2	kinds	kind	NOUN
ejpam-6865	21	3	of	of	ADP
ejpam-6865	21	4	fractional	fractional	ADJ
ejpam-6865	21	5	operators	operator	NOUN
ejpam-6865	21	6	have	have	AUX
ejpam-6865	21	7	been	be	AUX
ejpam-6865	21	8	introduced	introduce	VERB
ejpam-6865	21	9	,	,	PUNCT
ejpam-6865	21	10	such	such	ADJ
ejpam-6865	21	11	as	as	ADP
ejpam-6865	21	12	grunwald	grunwald	NOUN
ejpam-6865	21	13	-	-	PUNCT
ejpam-6865	21	14	letnikov	letnikov	NOUN
ejpam-6865	21	15	,	,	PUNCT
ejpam-6865	21	16	riemann	riemann	PROPN
ejpam-6865	21	17	-	-	PUNCT
ejpam-6865	21	18	liouville	liouville	NOUN
ejpam-6865	21	19	(	(	PUNCT
ejpam-6865	21	20	r	r	NOUN
ejpam-6865	21	21	-	-	PUNCT
ejpam-6865	21	22	l	l	NOUN
ejpam-6865	21	23	)	)	PUNCT
ejpam-6865	21	24	,	,	PUNCT
ejpam-6865	21	25	riesz	riesz	PROPN
ejpam-6865	21	26	,	,	PUNCT
ejpam-6865	21	27	caputo	caputo	PROPN
ejpam-6865	21	28	,	,	PUNCT
ejpam-6865	21	29	and	and	CCONJ
ejpam-6865	21	30	atangana	atangana	PROPN
ejpam-6865	21	31	baleanu	baleanu	PROPN
ejpam-6865	21	32	caputo	caputo	PROPN
ejpam-6865	21	33	(	(	PUNCT
ejpam-6865	21	34	abc	abc	PROPN
ejpam-6865	21	35	)	)	PUNCT
ejpam-6865	21	36	fds	fds	NOUN
ejpam-6865	21	37	.	.	PUNCT
ejpam-6865	22	1	[	[	X
ejpam-6865	22	2	3–5	3–5	NOUN
ejpam-6865	22	3	]	]	PUNCT
ejpam-6865	22	4	,	,	PUNCT
ejpam-6865	22	5	and	and	CCONJ
ejpam-6865	22	6	have	have	AUX
ejpam-6865	22	7	been	be	AUX
ejpam-6865	22	8	thoroughly	thoroughly	ADV
ejpam-6865	22	9	studied	study	VERB
ejpam-6865	22	10	as	as	ADP
ejpam-6865	22	11	worthy	worthy	ADJ
ejpam-6865	22	12	tools	tool	NOUN
ejpam-6865	22	13	for	for	ADP
ejpam-6865	22	14	depicting	depict	VERB
ejpam-6865	22	15	genetic	genetic	ADJ
ejpam-6865	22	16	features	feature	NOUN
ejpam-6865	22	17	,	,	PUNCT
ejpam-6865	22	18	memory	memory	NOUN
ejpam-6865	22	19	influences	influence	NOUN
ejpam-6865	22	20	,	,	PUNCT
ejpam-6865	22	21	and	and	CCONJ
ejpam-6865	22	22	material	material	NOUN
ejpam-6865	22	23	convey	convey	NOUN
ejpam-6865	22	24	procedures	procedure	NOUN
ejpam-6865	22	25	in	in	ADP
ejpam-6865	22	26	a	a	DET
ejpam-6865	22	27	variety	variety	NOUN
ejpam-6865	22	28	of	of	ADP
ejpam-6865	22	29	applied	apply	VERB
ejpam-6865	22	30	mathematics	mathematic	NOUN
ejpam-6865	22	31	,	,	PUNCT
ejpam-6865	22	32	engineering	engineering	NOUN
ejpam-6865	22	33	[	[	X
ejpam-6865	22	34	6	6	NUM
ejpam-6865	22	35	]	]	PUNCT
ejpam-6865	22	36	,	,	PUNCT
ejpam-6865	22	37	and	and	CCONJ
ejpam-6865	22	38	physics	physics	NOUN
ejpam-6865	22	39	disciplines	discipline	NOUN
ejpam-6865	22	40	,	,	PUNCT
ejpam-6865	22	41	including	include	VERB
ejpam-6865	22	42	dynamics	dynamic	NOUN
ejpam-6865	22	43	,	,	PUNCT
ejpam-6865	22	44	elasticity	elasticity	NOUN
ejpam-6865	22	45	,	,	PUNCT
ejpam-6865	22	46	control	control	NOUN
ejpam-6865	22	47	theory	theory	NOUN
ejpam-6865	22	48	,	,	PUNCT
ejpam-6865	22	49	and	and	CCONJ
ejpam-6865	22	50	mechanics	mechanic	NOUN
ejpam-6865	22	51	.	.	PUNCT
ejpam-6865	23	1	the	the	DET
ejpam-6865	23	2	calculus	calculus	NOUN
ejpam-6865	23	3	of	of	ADP
ejpam-6865	23	4	variations	variation	NOUN
ejpam-6865	23	5	is	be	AUX
ejpam-6865	23	6	a	a	DET
ejpam-6865	23	7	further	further	ADJ
ejpam-6865	23	8	discipline	discipline	NOUN
ejpam-6865	23	9	in	in	ADP
ejpam-6865	23	10	which	which	PRON
ejpam-6865	23	11	fractional	fractional	ADJ
ejpam-6865	23	12	order	order	NOUN
ejpam-6865	23	13	calculus	calculus	NOUN
ejpam-6865	23	14	has	have	AUX
ejpam-6865	23	15	shown	show	VERB
ejpam-6865	23	16	great	great	ADJ
ejpam-6865	23	17	utility	utility	NOUN
ejpam-6865	23	18	(	(	PUNCT
ejpam-6865	23	19	see	see	VERB
ejpam-6865	23	20	[	[	X
ejpam-6865	23	21	7	7	NUM
ejpam-6865	23	22	,	,	PUNCT
ejpam-6865	23	23	8	8	NUM
ejpam-6865	23	24	]	]	NUM
ejpam-6865	23	25	)	)	PUNCT
ejpam-6865	23	26	.	.	PUNCT
ejpam-6865	24	1	here	here	ADV
ejpam-6865	24	2	,	,	PUNCT
ejpam-6865	24	3	fds	fds	NOUN
ejpam-6865	24	4	are	be	AUX
ejpam-6865	24	5	used	use	VERB
ejpam-6865	24	6	to	to	PART
ejpam-6865	24	7	model	model	VERB
ejpam-6865	24	8	functionals	functional	NOUN
ejpam-6865	24	9	rather	rather	ADV
ejpam-6865	24	10	than	than	ADP
ejpam-6865	24	11	a	a	DET
ejpam-6865	24	12	path	path	NOUN
ejpam-6865	24	13	’s	’s	PART
ejpam-6865	24	14	first	first	ADJ
ejpam-6865	24	15	-	-	PUNCT
ejpam-6865	24	16	order	order	NOUN
ejpam-6865	24	17	derivative	derivative	NOUN
ejpam-6865	24	18	.	.	PUNCT
ejpam-6865	25	1	this	this	PRON
ejpam-6865	25	2	is	be	AUX
ejpam-6865	25	3	often	often	ADV
ejpam-6865	25	4	the	the	DET
ejpam-6865	25	5	case	case	NOUN
ejpam-6865	25	6	in	in	ADP
ejpam-6865	25	7	many	many	ADJ
ejpam-6865	25	8	mathematical	mathematical	ADJ
ejpam-6865	25	9	or	or	CCONJ
ejpam-6865	25	10	engineering	engineering	NOUN
ejpam-6865	25	11	challenges	challenge	NOUN
ejpam-6865	25	12	,	,	PUNCT
ejpam-6865	25	13	providing	provide	VERB
ejpam-6865	25	14	a	a	DET
ejpam-6865	25	15	more	more	ADV
ejpam-6865	25	16	accurate	accurate	ADJ
ejpam-6865	25	17	quantification	quantification	NOUN
ejpam-6865	25	18	of	of	ADP
ejpam-6865	25	19	physical	physical	ADJ
ejpam-6865	25	20	processes	process	NOUN
ejpam-6865	25	21	.	.	PUNCT
ejpam-6865	26	1	a	a	DET
ejpam-6865	26	2	great	great	ADJ
ejpam-6865	26	3	deal	deal	NOUN
ejpam-6865	26	4	of	of	ADP
ejpam-6865	26	5	work	work	NOUN
ejpam-6865	26	6	has	have	AUX
ejpam-6865	26	7	been	be	AUX
ejpam-6865	26	8	done	do	VERB
ejpam-6865	26	9	on	on	ADP
ejpam-6865	26	10	the	the	DET
ejpam-6865	26	11	fractional	fractional	ADJ
ejpam-6865	26	12	order	order	NOUN
ejpam-6865	26	13	calculus	calculus	NOUN
ejpam-6865	26	14	of	of	ADP
ejpam-6865	26	15	variations	variation	NOUN
ejpam-6865	26	16	(	(	PUNCT
ejpam-6865	26	17	e.g.	e.g.	ADV
ejpam-6865	26	18	,	,	PUNCT
ejpam-6865	26	19	sun	sun	PROPN
ejpam-6865	26	20	et	et	PROPN
ejpam-6865	26	21	al	al	PROPN
ejpam-6865	26	22	.	.	PUNCT
ejpam-6865	27	1	[	[	X
ejpam-6865	27	2	9	9	NUM
ejpam-6865	27	3	]	]	PUNCT
ejpam-6865	27	4	,	,	PUNCT
ejpam-6865	27	5	agrawal	agrawal	PROPN
ejpam-6865	28	1	[	[	X
ejpam-6865	28	2	10	10	NUM
ejpam-6865	28	3	]	]	PUNCT
ejpam-6865	28	4	,	,	PUNCT
ejpam-6865	28	5	atanackovic	atanackovic	PROPN
ejpam-6865	28	6	et	et	PROPN
ejpam-6865	28	7	al	al	PROPN
ejpam-6865	28	8	.	.	PUNCT
ejpam-6865	29	1	[	[	X
ejpam-6865	29	2	11	11	NUM
ejpam-6865	29	3	]	]	SYM
ejpam-6865	29	4	araz	araz	NOUN
ejpam-6865	29	5	and	and	CCONJ
ejpam-6865	29	6	çetin	çetin	NOUN
ejpam-6865	29	7	[	[	X
ejpam-6865	29	8	12	12	NUM
ejpam-6865	29	9	]	]	PUNCT
ejpam-6865	29	10	,	,	PUNCT
ejpam-6865	29	11	arik	arik	PROPN
ejpam-6865	29	12	and	and	CCONJ
ejpam-6865	29	13	araz	araz	NOUN
ejpam-6865	30	1	[	[	X
ejpam-6865	30	2	13	13	NUM
ejpam-6865	30	3	]	]	PUNCT
ejpam-6865	30	4	,	,	PUNCT
ejpam-6865	30	5	jahan	jahan	PROPN
ejpam-6865	30	6	et	et	PROPN
ejpam-6865	30	7	al	al	PROPN
ejpam-6865	30	8	.	.	PUNCT
ejpam-6865	31	1	[	[	X
ejpam-6865	31	2	14	14	NUM
ejpam-6865	31	3	]	]	PUNCT
ejpam-6865	31	4	and	and	CCONJ
ejpam-6865	31	5	almeida	almeida	PROPN
ejpam-6865	31	6	and	and	CCONJ
ejpam-6865	31	7	torres	torre	VERB
ejpam-6865	31	8	[	[	X
ejpam-6865	31	9	15	15	NUM
ejpam-6865	31	10	]	]	PUNCT
ejpam-6865	31	11	)	)	PUNCT
ejpam-6865	31	12	.	.	PUNCT
ejpam-6865	32	1	although	although	SCONJ
ejpam-6865	32	2	the	the	DET
ejpam-6865	32	3	fractional	fractional	ADJ
ejpam-6865	32	4	order	order	NOUN
ejpam-6865	32	5	calculus	calculus	NOUN
ejpam-6865	32	6	of	of	ADP
ejpam-6865	32	7	variations	variation	NOUN
ejpam-6865	32	8	literature	literature	NOUN
ejpam-6865	32	9	is	be	AUX
ejpam-6865	32	10	currently	currently	ADV
ejpam-6865	32	11	extensive	extensive	ADJ
ejpam-6865	32	12	,	,	PUNCT
ejpam-6865	32	13	further	further	ADJ
ejpam-6865	32	14	investigation	investigation	NOUN
ejpam-6865	32	15	is	be	AUX
ejpam-6865	32	16	still	still	ADV
ejpam-6865	32	17	necessary	necessary	ADJ
ejpam-6865	32	18	.	.	PUNCT
ejpam-6865	33	1	fds	fds	NOUN
ejpam-6865	33	2	can	can	AUX
ejpam-6865	33	3	be	be	AUX
ejpam-6865	33	4	constructed	construct	VERB
ejpam-6865	33	5	using	use	VERB
ejpam-6865	33	6	various	various	ADJ
ejpam-6865	33	7	techniques	technique	NOUN
ejpam-6865	33	8	that	that	PRON
ejpam-6865	33	9	do	do	AUX
ejpam-6865	33	10	not	not	PART
ejpam-6865	33	11	always	always	ADV
ejpam-6865	33	12	yield	yield	VERB
ejpam-6865	33	13	the	the	DET
ejpam-6865	33	14	same	same	ADJ
ejpam-6865	33	15	result	result	NOUN
ejpam-6865	33	16	.	.	PUNCT
ejpam-6865	34	1	some	some	PRON
ejpam-6865	34	2	of	of	ADP
ejpam-6865	34	3	these	these	PRON
ejpam-6865	34	4	are	be	AUX
ejpam-6865	34	5	defined	define	VERB
ejpam-6865	34	6	using	use	VERB
ejpam-6865	34	7	a	a	DET
ejpam-6865	34	8	fractional	fractional	ADJ
ejpam-6865	34	9	integral	integral	NOUN
ejpam-6865	34	10	.	.	PUNCT
ejpam-6865	35	1	due	due	ADP
ejpam-6865	35	2	to	to	ADP
ejpam-6865	35	3	definition	definition	NOUN
ejpam-6865	35	4	incompatibility	incompatibility	NOUN
ejpam-6865	35	5	,	,	PUNCT
ejpam-6865	35	6	it	it	PRON
ejpam-6865	35	7	is	be	AUX
ejpam-6865	35	8	usually	usually	ADV
ejpam-6865	35	9	necessary	necessary	ADJ
ejpam-6865	35	10	to	to	PART
ejpam-6865	35	11	be	be	AUX
ejpam-6865	35	12	explicit	explicit	ADJ
ejpam-6865	35	13	about	about	ADP
ejpam-6865	35	14	which	which	DET
ejpam-6865	35	15	definition	definition	NOUN
ejpam-6865	35	16	is	be	AUX
ejpam-6865	35	17	utilized	utilize	VERB
ejpam-6865	35	18	,	,	PUNCT
ejpam-6865	35	19	even	even	ADV
ejpam-6865	35	20	for	for	ADP
ejpam-6865	35	21	smooth	smooth	ADJ
ejpam-6865	35	22	functions	function	NOUN
ejpam-6865	35	23	.	.	PUNCT
ejpam-6865	36	1	the	the	DET
ejpam-6865	36	2	nonlocal	nonlocal	ADJ
ejpam-6865	36	3	fd	fd	PROPN
ejpam-6865	36	4	takes	take	VERB
ejpam-6865	36	5	the	the	DET
ejpam-6865	36	6	memory	memory	NOUN
ejpam-6865	36	7	of	of	ADP
ejpam-6865	36	8	the	the	DET
ejpam-6865	36	9	function	function	NOUN
ejpam-6865	36	10	into	into	ADP
ejpam-6865	36	11	account	account	NOUN
ejpam-6865	36	12	and	and	CCONJ
ejpam-6865	36	13	is	be	AUX
ejpam-6865	36	14	formed	form	VERB
ejpam-6865	36	15	based	base	VERB
ejpam-6865	36	16	on	on	ADP
ejpam-6865	36	17	the	the	DET
ejpam-6865	36	18	integration	integration	NOUN
ejpam-6865	36	19	of	of	ADP
ejpam-6865	36	20	a	a	DET
ejpam-6865	36	21	kernel	kernel	NOUN
ejpam-6865	36	22	and	and	CCONJ
ejpam-6865	36	23	the	the	DET
ejpam-6865	36	24	function	function	NOUN
ejpam-6865	36	25	or	or	CCONJ
ejpam-6865	36	26	its	its	PRON
ejpam-6865	36	27	standard	standard	ADJ
ejpam-6865	36	28	derivative	derivative	NOUN
ejpam-6865	36	29	.	.	PUNCT
ejpam-6865	37	1	several	several	ADJ
ejpam-6865	37	2	kernels	kernel	NOUN
ejpam-6865	37	3	are	be	AUX
ejpam-6865	37	4	used	use	VERB
ejpam-6865	37	5	to	to	PART
ejpam-6865	37	6	formulate	formulate	VERB
ejpam-6865	37	7	these	these	DET
ejpam-6865	37	8	kinds	kind	NOUN
ejpam-6865	37	9	of	of	ADP
ejpam-6865	37	10	fds	fds	NOUN
ejpam-6865	37	11	,	,	PUNCT
ejpam-6865	37	12	and	and	CCONJ
ejpam-6865	37	13	singular	singular	NOUN
ejpam-6865	37	14	and	and	CCONJ
ejpam-6865	37	15	non	non	ADJ
ejpam-6865	37	16	-	-	ADJ
ejpam-6865	37	17	singular	singular	ADJ
ejpam-6865	37	18	are	be	AUX
ejpam-6865	37	19	investigated	investigate	VERB
ejpam-6865	37	20	[	[	X
ejpam-6865	37	21	16	16	NUM
ejpam-6865	37	22	,	,	PUNCT
ejpam-6865	37	23	17	17	NUM
ejpam-6865	37	24	]	]	PUNCT
ejpam-6865	37	25	.	.	PUNCT
ejpam-6865	38	1	each	each	DET
ejpam-6865	38	2	kernel	kernel	PROPN
ejpam-6865	38	3	plays	play	VERB
ejpam-6865	38	4	a	a	DET
ejpam-6865	38	5	significant	significant	ADJ
ejpam-6865	38	6	role	role	NOUN
ejpam-6865	38	7	in	in	ADP
ejpam-6865	38	8	the	the	DET
ejpam-6865	38	9	behavior	behavior	NOUN
ejpam-6865	38	10	of	of	ADP
ejpam-6865	38	11	the	the	DET
ejpam-6865	38	12	solution	solution	NOUN
ejpam-6865	38	13	.	.	PUNCT
ejpam-6865	39	1	the	the	DET
ejpam-6865	39	2	nonsingular	nonsingular	PROPN
ejpam-6865	39	3	fd	fd	PROPN
ejpam-6865	39	4	employed	employ	VERB
ejpam-6865	39	5	several	several	ADJ
ejpam-6865	39	6	kernels	kernel	NOUN
ejpam-6865	39	7	,	,	PUNCT
ejpam-6865	39	8	including	include	VERB
ejpam-6865	39	9	the	the	DET
ejpam-6865	39	10	exponential	exponential	ADJ
ejpam-6865	39	11	function	function	NOUN
ejpam-6865	39	12	and	and	CCONJ
ejpam-6865	39	13	the	the	DET
ejpam-6865	39	14	mittagleffler	mittagleffler	NOUN
ejpam-6865	39	15	function	function	NOUN
ejpam-6865	39	16	.	.	PUNCT
ejpam-6865	40	1	one	one	NUM
ejpam-6865	40	2	of	of	ADP
ejpam-6865	40	3	the	the	DET
ejpam-6865	40	4	main	main	ADJ
ejpam-6865	40	5	disadvantages	disadvantage	NOUN
ejpam-6865	40	6	of	of	ADP
ejpam-6865	40	7	using	use	VERB
ejpam-6865	40	8	those	those	DET
ejpam-6865	40	9	kinds	kind	NOUN
ejpam-6865	40	10	is	be	AUX
ejpam-6865	40	11	the	the	DET
ejpam-6865	40	12	lack	lack	NOUN
ejpam-6865	40	13	of	of	ADP
ejpam-6865	40	14	a	a	DET
ejpam-6865	40	15	solution	solution	NOUN
ejpam-6865	40	16	,	,	PUNCT
ejpam-6865	40	17	even	even	ADV
ejpam-6865	40	18	for	for	ADP
ejpam-6865	40	19	a	a	DET
ejpam-6865	40	20	simple	simple	ADJ
ejpam-6865	40	21	one	one	NUM
ejpam-6865	40	22	.	.	PUNCT
ejpam-6865	41	1	so	so	ADV
ejpam-6865	41	2	,	,	PUNCT
ejpam-6865	41	3	the	the	DET
ejpam-6865	41	4	use	use	NOUN
ejpam-6865	41	5	of	of	ADP
ejpam-6865	41	6	the	the	DET
ejpam-6865	41	7	mittag	mittag	ADJ
ejpam-6865	41	8	-	-	PUNCT
ejpam-6865	41	9	leffler	leffler	NOUN
ejpam-6865	41	10	function	function	NOUN
ejpam-6865	41	11	can	can	AUX
ejpam-6865	41	12	overcome	overcome	VERB
ejpam-6865	41	13	this	this	DET
ejpam-6865	41	14	limitation	limitation	NOUN
ejpam-6865	41	15	and	and	CCONJ
ejpam-6865	41	16	enrich	enrich	VERB
ejpam-6865	41	17	the	the	DET
ejpam-6865	41	18	solution	solution	NOUN
ejpam-6865	41	19	parameter	parameter	NOUN
ejpam-6865	41	20	[	[	X
ejpam-6865	41	21	18	18	NUM
ejpam-6865	41	22	]	]	PUNCT
ejpam-6865	41	23	.	.	PUNCT
ejpam-6865	42	1	several	several	ADJ
ejpam-6865	42	2	methods	method	NOUN
ejpam-6865	42	3	are	be	AUX
ejpam-6865	42	4	used	use	VERB
ejpam-6865	42	5	to	to	PART
ejpam-6865	42	6	solve	solve	VERB
ejpam-6865	42	7	the	the	DET
ejpam-6865	42	8	fractional	fractional	ADJ
ejpam-6865	42	9	differential	differential	ADJ
ejpam-6865	42	10	equations	equation	NOUN
ejpam-6865	42	11	(	(	PUNCT
ejpam-6865	42	12	fdes	fde	NOUN
ejpam-6865	42	13	)	)	PUNCT
ejpam-6865	42	14	in	in	ADP
ejpam-6865	42	15	the	the	DET
ejpam-6865	42	16	sense	sense	NOUN
ejpam-6865	42	17	of	of	ADP
ejpam-6865	42	18	the	the	DET
ejpam-6865	42	19	mittag	mittag	ADJ
ejpam-6865	42	20	-	-	PUNCT
ejpam-6865	42	21	leffler	leffler	NOUN
ejpam-6865	42	22	kernel	kernel	NOUN
ejpam-6865	42	23	,	,	PUNCT
ejpam-6865	42	24	such	such	ADJ
ejpam-6865	42	25	as	as	ADP
ejpam-6865	42	26	pure	pure	ADJ
ejpam-6865	42	27	numerical	numerical	ADJ
ejpam-6865	42	28	methods	method	NOUN
ejpam-6865	42	29	based	base	VERB
ejpam-6865	42	30	on	on	ADP
ejpam-6865	42	31	adams	adams	PROPN
ejpam-6865	42	32	bashforth	bashforth	PROPN
ejpam-6865	42	33	techniques	technique	NOUN
ejpam-6865	42	34	[	[	X
ejpam-6865	42	35	19	19	NUM
ejpam-6865	42	36	,	,	PUNCT
ejpam-6865	42	37	20	20	NUM
ejpam-6865	42	38	]	]	PUNCT
ejpam-6865	42	39	or	or	CCONJ
ejpam-6865	42	40	midpoint	midpoint	NOUN
ejpam-6865	42	41	method	method	NOUN
ejpam-6865	42	42	[	[	X
ejpam-6865	42	43	21	21	NUM
ejpam-6865	42	44	]	]	PUNCT
ejpam-6865	42	45	,	,	PUNCT
ejpam-6865	42	46	approximate	approximate	ADJ
ejpam-6865	42	47	analytic	analytic	ADJ
ejpam-6865	42	48	methods	method	NOUN
ejpam-6865	42	49	such	such	ADJ
ejpam-6865	42	50	as	as	ADP
ejpam-6865	42	51	homotopy	homotopy	NOUN
ejpam-6865	42	52	analysis	analysis	NOUN
ejpam-6865	42	53	method	method	NOUN
ejpam-6865	43	1	[	[	X
ejpam-6865	43	2	22	22	NUM
ejpam-6865	43	3	]	]	PUNCT
ejpam-6865	43	4	,	,	PUNCT
ejpam-6865	43	5	legendre	legendre	PROPN
ejpam-6865	43	6	polynomials	polynomial	VERB
ejpam-6865	43	7	[	[	X
ejpam-6865	43	8	23	23	NUM
ejpam-6865	43	9	]	]	PUNCT
ejpam-6865	43	10	,	,	PUNCT
ejpam-6865	43	11	bernstein	bernstein	PROPN
ejpam-6865	43	12	polynomials	polynomials	PROPN
ejpam-6865	43	13	[	[	X
ejpam-6865	43	14	24	24	NUM
ejpam-6865	43	15	,	,	PUNCT
ejpam-6865	43	16	25	25	NUM
ejpam-6865	43	17	]	]	PUNCT
ejpam-6865	43	18	and	and	CCONJ
ejpam-6865	43	19	other	other	ADJ
ejpam-6865	43	20	collocation	collocation	NOUN
ejpam-6865	43	21	method	method	NOUN
ejpam-6865	43	22	based	base	VERB
ejpam-6865	43	23	on	on	ADP
ejpam-6865	43	24	bell	bell	PROPN
ejpam-6865	43	25	wavelets	wavelet	NOUN
ejpam-6865	43	26	[	[	X
ejpam-6865	43	27	26	26	NUM
ejpam-6865	43	28	]	]	PUNCT
ejpam-6865	43	29	.	.	PUNCT
ejpam-6865	44	1	the	the	DET
ejpam-6865	44	2	methods	method	NOUN
ejpam-6865	44	3	that	that	PRON
ejpam-6865	44	4	are	be	AUX
ejpam-6865	44	5	based	base	VERB
ejpam-6865	44	6	on	on	ADP
ejpam-6865	44	7	orthogonal	orthogonal	ADJ
ejpam-6865	44	8	polynomials	polynomial	NOUN
ejpam-6865	44	9	,	,	PUNCT
ejpam-6865	44	10	such	such	ADJ
ejpam-6865	44	11	as	as	ADP
ejpam-6865	44	12	legendre	legendre	PROPN
ejpam-6865	44	13	or	or	CCONJ
ejpam-6865	44	14	bernstein	bernstein	PROPN
ejpam-6865	44	15	,	,	PUNCT
ejpam-6865	44	16	usually	usually	ADV
ejpam-6865	44	17	approximate	approximate	VERB
ejpam-6865	44	18	the	the	DET
ejpam-6865	44	19	solution	solution	NOUN
ejpam-6865	44	20	by	by	ADP
ejpam-6865	44	21	polynomials	polynomial	NOUN
ejpam-6865	44	22	with	with	ADP
ejpam-6865	44	23	integer	integer	NOUN
ejpam-6865	44	24	powers	power	NOUN
ejpam-6865	44	25	.	.	PUNCT
ejpam-6865	45	1	this	this	PRON
ejpam-6865	45	2	may	may	AUX
ejpam-6865	45	3	lead	lead	VERB
ejpam-6865	45	4	to	to	ADP
ejpam-6865	45	5	missing	miss	VERB
ejpam-6865	45	6	the	the	DET
ejpam-6865	45	7	effects	effect	NOUN
ejpam-6865	45	8	of	of	ADP
ejpam-6865	45	9	the	the	DET
ejpam-6865	45	10	fractional	fractional	ADJ
ejpam-6865	45	11	order	order	NOUN
ejpam-6865	45	12	.	.	PUNCT
ejpam-6865	46	1	so	so	ADV
ejpam-6865	46	2	,	,	PUNCT
ejpam-6865	46	3	our	our	PRON
ejpam-6865	46	4	motivations	motivation	NOUN
ejpam-6865	46	5	are	be	AUX
ejpam-6865	46	6	to	to	PART
ejpam-6865	46	7	build	build	VERB
ejpam-6865	46	8	a	a	DET
ejpam-6865	46	9	new	new	ADJ
ejpam-6865	46	10	algorithm	algorithm	NOUN
ejpam-6865	46	11	based	base	VERB
ejpam-6865	46	12	on	on	ADP
ejpam-6865	46	13	the	the	DET
ejpam-6865	46	14	orthogonal	orthogonal	ADJ
ejpam-6865	46	15	polynomials	polynomial	NOUN
ejpam-6865	46	16	that	that	PRON
ejpam-6865	46	17	observes	observe	VERB
ejpam-6865	46	18	the	the	DET
ejpam-6865	46	19	effects	effect	NOUN
ejpam-6865	46	20	of	of	ADP
ejpam-6865	46	21	fractional	fractional	ADJ
ejpam-6865	46	22	power	power	NOUN
ejpam-6865	46	23	solution	solution	NOUN
ejpam-6865	46	24	and	and	CCONJ
ejpam-6865	46	25	compares	compare	VERB
ejpam-6865	46	26	our	our	PRON
ejpam-6865	46	27	results	result	NOUN
ejpam-6865	46	28	with	with	ADP
ejpam-6865	46	29	the	the	DET
ejpam-6865	46	30	standard	standard	ADJ
ejpam-6865	46	31	one	one	NUM
ejpam-6865	46	32	.	.	PUNCT
ejpam-6865	47	1	this	this	DET
ejpam-6865	47	2	work	work	NOUN
ejpam-6865	47	3	will	will	AUX
ejpam-6865	47	4	established	establish	VERB
ejpam-6865	47	5	a	a	DET
ejpam-6865	47	6	general	general	ADJ
ejpam-6865	47	7	s.	s.	PROPN
ejpam-6865	47	8	tamimi	tamimi	PROPN
ejpam-6865	47	9	,	,	PUNCT
ejpam-6865	47	10	a.	a.	PROPN
ejpam-6865	47	11	k.	k.	PROPN
ejpam-6865	47	12	alomari	alomari	PROPN
ejpam-6865	47	13	,	,	PUNCT
ejpam-6865	47	14	m.	m.	NOUN
ejpam-6865	47	15	alaroud	alaroud	PROPN
ejpam-6865	47	16	/	/	SYM
ejpam-6865	47	17	eur	eur	PROPN
ejpam-6865	47	18	.	.	PUNCT
ejpam-6865	48	1	j.	j.	PROPN
ejpam-6865	48	2	pure	pure	PROPN
ejpam-6865	48	3	appl	appl	PROPN
ejpam-6865	48	4	.	.	PROPN
ejpam-6865	48	5	math	math	PROPN
ejpam-6865	48	6	,	,	PUNCT
ejpam-6865	48	7	18	18	NUM
ejpam-6865	48	8	(	(	PUNCT
ejpam-6865	48	9	4	4	NUM
ejpam-6865	48	10	)	)	PUNCT
ejpam-6865	48	11	(	(	PUNCT
ejpam-6865	48	12	2025	2025	NUM
ejpam-6865	48	13	)	)	PUNCT
ejpam-6865	48	14	,	,	PUNCT
ejpam-6865	48	15	6865	6865	NUM
ejpam-6865	48	16	3	3	NUM
ejpam-6865	48	17	of	of	ADP
ejpam-6865	48	18	19	19	NUM
ejpam-6865	48	19	framework	framework	NOUN
ejpam-6865	48	20	for	for	ADP
ejpam-6865	48	21	solving	solving	NOUN
ejpam-6865	48	22	of	of	ADP
ejpam-6865	48	23	fde	fde	NOUN
ejpam-6865	48	24	with	with	ADP
ejpam-6865	48	25	mittag	mittag	ADJ
ejpam-6865	48	26	-	-	PUNCT
ejpam-6865	48	27	leffler	leffler	NOUN
ejpam-6865	48	28	function	function	NOUN
ejpam-6865	48	29	of	of	ADP
ejpam-6865	48	30	three	three	NUM
ejpam-6865	48	31	parameters	parameter	NOUN
ejpam-6865	48	32	kernel	kernel	PROPN
ejpam-6865	48	33	based	base	VERB
ejpam-6865	48	34	on	on	ADP
ejpam-6865	48	35	the	the	DET
ejpam-6865	48	36	bernstein	bernstein	PROPN
ejpam-6865	48	37	polynomials	polynomial	NOUN
ejpam-6865	48	38	in	in	ADP
ejpam-6865	48	39	two	two	NUM
ejpam-6865	48	40	approaches	approach	NOUN
ejpam-6865	48	41	,	,	PUNCT
ejpam-6865	48	42	the	the	DET
ejpam-6865	48	43	first	first	ADJ
ejpam-6865	48	44	one	one	NUM
ejpam-6865	48	45	by	by	ADP
ejpam-6865	48	46	assuming	assume	VERB
ejpam-6865	48	47	the	the	DET
ejpam-6865	48	48	solution	solution	NOUN
ejpam-6865	48	49	as	as	ADP
ejpam-6865	48	50	a	a	DET
ejpam-6865	48	51	linear	linear	ADJ
ejpam-6865	48	52	combinations	combination	NOUN
ejpam-6865	48	53	of	of	ADP
ejpam-6865	48	54	the	the	DET
ejpam-6865	48	55	polynomial	polynomial	NOUN
ejpam-6865	48	56	and	and	CCONJ
ejpam-6865	48	57	the	the	DET
ejpam-6865	48	58	second	second	ADJ
ejpam-6865	48	59	one	one	NUM
ejpam-6865	48	60	by	by	ADP
ejpam-6865	48	61	assuming	assume	VERB
ejpam-6865	48	62	the	the	DET
ejpam-6865	48	63	fractional	fractional	ADJ
ejpam-6865	48	64	derivative	derivative	NOUN
ejpam-6865	48	65	is	be	AUX
ejpam-6865	48	66	the	the	DET
ejpam-6865	48	67	linear	linear	ADJ
ejpam-6865	48	68	combinations	combination	NOUN
ejpam-6865	48	69	of	of	ADP
ejpam-6865	48	70	the	the	DET
ejpam-6865	48	71	derivative	derivative	NOUN
ejpam-6865	48	72	which	which	PRON
ejpam-6865	48	73	leads	lead	VERB
ejpam-6865	48	74	to	to	ADP
ejpam-6865	48	75	the	the	DET
ejpam-6865	48	76	solution	solution	NOUN
ejpam-6865	48	77	forms	form	NOUN
ejpam-6865	48	78	that	that	PRON
ejpam-6865	48	79	depends	depend	VERB
ejpam-6865	48	80	on	on	ADP
ejpam-6865	48	81	,	,	PUNCT
ejpam-6865	48	82	the	the	DET
ejpam-6865	48	83	fractional	fractional	ADJ
ejpam-6865	48	84	parameters	parameter	NOUN
ejpam-6865	48	85	.	.	PUNCT
ejpam-6865	49	1	the	the	DET
ejpam-6865	49	2	experimental	experimental	ADJ
ejpam-6865	49	3	results	result	NOUN
ejpam-6865	49	4	proved	prove	VERB
ejpam-6865	49	5	that	that	SCONJ
ejpam-6865	49	6	the	the	DET
ejpam-6865	49	7	second	second	ADJ
ejpam-6865	49	8	approach	approach	NOUN
ejpam-6865	49	9	is	be	AUX
ejpam-6865	49	10	more	more	ADV
ejpam-6865	49	11	accurate	accurate	ADJ
ejpam-6865	49	12	and	and	CCONJ
ejpam-6865	49	13	gives	give	VERB
ejpam-6865	49	14	an	an	DET
ejpam-6865	49	15	explicit	explicit	ADJ
ejpam-6865	49	16	solution	solution	NOUN
ejpam-6865	49	17	based	base	VERB
ejpam-6865	49	18	on	on	ADP
ejpam-6865	49	19	independent	independent	ADJ
ejpam-6865	49	20	parameters	parameter	NOUN
ejpam-6865	49	21	of	of	ADP
ejpam-6865	49	22	powers	power	NOUN
ejpam-6865	49	23	of	of	ADP
ejpam-6865	49	24	the	the	DET
ejpam-6865	49	25	fractional	fractional	ADJ
ejpam-6865	49	26	parameters	parameter	NOUN
ejpam-6865	49	27	.	.	PUNCT
ejpam-6865	50	1	moreover	moreover	ADV
ejpam-6865	50	2	,	,	PUNCT
ejpam-6865	50	3	clear	clear	ADJ
ejpam-6865	50	4	steps	step	NOUN
ejpam-6865	50	5	for	for	ADP
ejpam-6865	50	6	both	both	DET
ejpam-6865	50	7	approaches	approach	NOUN
ejpam-6865	50	8	are	be	AUX
ejpam-6865	50	9	established	establish	VERB
ejpam-6865	50	10	in	in	ADP
ejpam-6865	50	11	an	an	DET
ejpam-6865	50	12	easy	easy	ADJ
ejpam-6865	50	13	-	-	PUNCT
ejpam-6865	50	14	to	to	ADP
ejpam-6865	50	15	-	-	PUNCT
ejpam-6865	50	16	compute	compute	NOUN
ejpam-6865	50	17	manner	manner	NOUN
ejpam-6865	50	18	.	.	PUNCT
ejpam-6865	51	1	the	the	DET
ejpam-6865	51	2	paper	paper	NOUN
ejpam-6865	51	3	is	be	AUX
ejpam-6865	51	4	organized	organize	VERB
ejpam-6865	51	5	as	as	SCONJ
ejpam-6865	51	6	follows	follow	VERB
ejpam-6865	51	7	:	:	PUNCT
ejpam-6865	51	8	in	in	ADP
ejpam-6865	51	9	section	section	NOUN
ejpam-6865	51	10	2	2	NUM
ejpam-6865	51	11	,	,	PUNCT
ejpam-6865	51	12	we	we	PRON
ejpam-6865	51	13	proposed	propose	VERB
ejpam-6865	51	14	definitions	definition	NOUN
ejpam-6865	51	15	and	and	CCONJ
ejpam-6865	51	16	theories	theory	NOUN
ejpam-6865	51	17	,	,	PUNCT
ejpam-6865	51	18	along	along	ADP
ejpam-6865	51	19	with	with	ADP
ejpam-6865	51	20	their	their	PRON
ejpam-6865	51	21	proofs	proof	NOUN
ejpam-6865	51	22	,	,	PUNCT
ejpam-6865	51	23	that	that	SCONJ
ejpam-6865	51	24	we	we	PRON
ejpam-6865	51	25	needed	need	VERB
ejpam-6865	51	26	for	for	ADP
ejpam-6865	51	27	this	this	DET
ejpam-6865	51	28	paper	paper	NOUN
ejpam-6865	51	29	.	.	PUNCT
ejpam-6865	52	1	in	in	ADP
ejpam-6865	52	2	section	section	NOUN
ejpam-6865	52	3	3	3	NUM
ejpam-6865	52	4	,	,	PUNCT
ejpam-6865	52	5	we	we	PRON
ejpam-6865	52	6	illustrate	illustrate	VERB
ejpam-6865	52	7	the	the	DET
ejpam-6865	52	8	definition	definition	NOUN
ejpam-6865	52	9	and	and	CCONJ
ejpam-6865	52	10	some	some	DET
ejpam-6865	52	11	properties	property	NOUN
ejpam-6865	52	12	of	of	ADP
ejpam-6865	52	13	the	the	DET
ejpam-6865	52	14	bernstein	bernstein	PROPN
ejpam-6865	52	15	polynomials	polynomials	PROPN
ejpam-6865	52	16	,	,	PUNCT
ejpam-6865	52	17	and	and	CCONJ
ejpam-6865	52	18	we	we	PRON
ejpam-6865	52	19	find	find	VERB
ejpam-6865	52	20	the	the	DET
ejpam-6865	52	21	abc	abc	PROPN
ejpam-6865	52	22	fractional	fractional	PROPN
ejpam-6865	52	23	derivative	derivative	NOUN
ejpam-6865	52	24	for	for	ADP
ejpam-6865	52	25	the	the	DET
ejpam-6865	52	26	bernstein	bernstein	PROPN
ejpam-6865	52	27	polynomials	polynomials	PROPN
ejpam-6865	52	28	.	.	PUNCT
ejpam-6865	53	1	in	in	ADP
ejpam-6865	53	2	section	section	NOUN
ejpam-6865	53	3	four	four	NUM
ejpam-6865	53	4	,	,	PUNCT
ejpam-6865	53	5	we	we	PRON
ejpam-6865	53	6	presented	present	VERB
ejpam-6865	53	7	the	the	DET
ejpam-6865	53	8	procedure	procedure	NOUN
ejpam-6865	53	9	of	of	ADP
ejpam-6865	53	10	two	two	NUM
ejpam-6865	53	11	approaches	approach	NOUN
ejpam-6865	53	12	for	for	ADP
ejpam-6865	53	13	solving	solve	VERB
ejpam-6865	53	14	fractional	fractional	ADJ
ejpam-6865	53	15	-	-	PUNCT
ejpam-6865	53	16	order	order	NOUN
ejpam-6865	53	17	problems	problem	NOUN
ejpam-6865	53	18	and	and	CCONJ
ejpam-6865	53	19	showed	show	VERB
ejpam-6865	53	20	the	the	DET
ejpam-6865	53	21	numerical	numerical	ADJ
ejpam-6865	53	22	results	result	NOUN
ejpam-6865	53	23	.	.	PUNCT
ejpam-6865	54	1	in	in	ADP
ejpam-6865	54	2	the	the	DET
ejpam-6865	54	3	fifth	fifth	ADJ
ejpam-6865	54	4	section	section	NOUN
ejpam-6865	54	5	,	,	PUNCT
ejpam-6865	54	6	we	we	PRON
ejpam-6865	54	7	discussed	discuss	VERB
ejpam-6865	54	8	the	the	DET
ejpam-6865	54	9	numerical	numerical	ADJ
ejpam-6865	54	10	results	result	NOUN
ejpam-6865	54	11	for	for	ADP
ejpam-6865	54	12	the	the	DET
ejpam-6865	54	13	examples	example	NOUN
ejpam-6865	54	14	.	.	PUNCT
ejpam-6865	55	1	in	in	ADP
ejpam-6865	55	2	section	section	NOUN
ejpam-6865	55	3	6	6	NUM
ejpam-6865	55	4	,	,	PUNCT
ejpam-6865	55	5	we	we	PRON
ejpam-6865	55	6	discussed	discuss	VERB
ejpam-6865	55	7	and	and	CCONJ
ejpam-6865	55	8	compared	compare	VERB
ejpam-6865	55	9	the	the	DET
ejpam-6865	55	10	two	two	NUM
ejpam-6865	55	11	approaches	approach	NOUN
ejpam-6865	55	12	for	for	ADP
ejpam-6865	55	13	all	all	DET
ejpam-6865	55	14	the	the	DET
ejpam-6865	55	15	presented	present	VERB
ejpam-6865	55	16	examples	example	NOUN
ejpam-6865	55	17	.	.	PUNCT
ejpam-6865	56	1	the	the	DET
ejpam-6865	56	2	conclusions	conclusion	NOUN
ejpam-6865	56	3	are	be	AUX
ejpam-6865	56	4	presented	present	VERB
ejpam-6865	56	5	in	in	ADP
ejpam-6865	56	6	section	section	NOUN
ejpam-6865	56	7	7	7	NUM
ejpam-6865	56	8	.	.	NOUN
ejpam-6865	56	9	2	2	NUM
ejpam-6865	56	10	.	.	NOUN
ejpam-6865	56	11	basic	basic	ADJ
ejpam-6865	56	12	definitions	definition	NOUN
ejpam-6865	56	13	and	and	CCONJ
ejpam-6865	56	14	theorems	theorem	NOUN
ejpam-6865	56	15	this	this	DET
ejpam-6865	56	16	section	section	NOUN
ejpam-6865	56	17	presents	present	VERB
ejpam-6865	56	18	the	the	DET
ejpam-6865	56	19	definition	definition	NOUN
ejpam-6865	56	20	of	of	ADP
ejpam-6865	56	21	the	the	DET
ejpam-6865	56	22	left	leave	VERB
ejpam-6865	56	23	abc	abc	PROPN
ejpam-6865	56	24	fd	fd	PROPN
ejpam-6865	56	25	with	with	ADP
ejpam-6865	56	26	kernel	kernel	PROPN
ejpam-6865	56	27	eγ	eγ	ADP
ejpam-6865	56	28	α,µ(λ	α,µ(λ	PROPN
ejpam-6865	56	29	,	,	PUNCT
ejpam-6865	56	30	t	t	PROPN
ejpam-6865	56	31	)	)	PUNCT
ejpam-6865	56	32	,	,	PUNCT
ejpam-6865	56	33	and	and	CCONJ
ejpam-6865	56	34	we	we	PRON
ejpam-6865	56	35	define	define	VERB
ejpam-6865	56	36	the	the	DET
ejpam-6865	56	37	left	left	ADJ
ejpam-6865	56	38	ab	ab	PROPN
ejpam-6865	56	39	fractional	fractional	ADJ
ejpam-6865	56	40	integral	integral	ADJ
ejpam-6865	56	41	and	and	CCONJ
ejpam-6865	56	42	some	some	DET
ejpam-6865	56	43	properties	property	NOUN
ejpam-6865	56	44	.	.	PUNCT
ejpam-6865	57	1	the	the	DET
ejpam-6865	57	2	r	r	NOUN
ejpam-6865	57	3	-	-	PUNCT
ejpam-6865	57	4	l	l	NOUN
ejpam-6865	57	5	fractional	fractional	ADJ
ejpam-6865	57	6	integral	integral	ADJ
ejpam-6865	57	7	of	of	ADP
ejpam-6865	57	8	order	order	NOUN
ejpam-6865	57	9	n	n	PRON
ejpam-6865	57	10	−	−	NOUN
ejpam-6865	57	11	α	α	PRON
ejpam-6865	57	12	where	where	SCONJ
ejpam-6865	57	13	α	α	X
ejpam-6865	57	14	,	,	PUNCT
ejpam-6865	57	15	a	a	PRON
ejpam-6865	57	16	,	,	PUNCT
ejpam-6865	57	17	t	t	PROPN
ejpam-6865	57	18	∈	∈	PROPN
ejpam-6865	57	19	r	r	NOUN
ejpam-6865	57	20	and	and	CCONJ
ejpam-6865	57	21	n	n	CCONJ
ejpam-6865	57	22	−	−	PROPN
ejpam-6865	57	23	1	1	NUM
ejpam-6865	57	24	<	<	X
ejpam-6865	57	25	α	α	X
ejpam-6865	57	26	<	<	X
ejpam-6865	57	27	n	n	X
ejpam-6865	57	28	from	from	ADP
ejpam-6865	57	29	the	the	DET
ejpam-6865	57	30	left	left	NOUN
ejpam-6865	57	31	and	and	CCONJ
ejpam-6865	57	32	right	right	ADJ
ejpam-6865	57	33	respectively	respectively	ADV
ejpam-6865	57	34	are	be	AUX
ejpam-6865	57	35	defined	define	VERB
ejpam-6865	57	36	as	as	ADP
ejpam-6865	57	37	[	[	X
ejpam-6865	57	38	27	27	NUM
ejpam-6865	57	39	]	]	NUM
ejpam-6865	57	40	:	:	PUNCT
ejpam-6865	57	41	ain−α	ain−α	PROPN
ejpam-6865	57	42	t	t	PROPN
ejpam-6865	57	43	f(t	f(t	PROPN
ejpam-6865	57	44	)	)	PUNCT
ejpam-6865	57	45	=	=	SYM
ejpam-6865	57	46	1	1	NUM
ejpam-6865	57	47	γ(n−	γ(n−	PROPN
ejpam-6865	57	48	α	α	NOUN
ejpam-6865	57	49	)	)	PUNCT
ejpam-6865	57	50	∫	∫	PROPN
ejpam-6865	58	1	t	t	PROPN
ejpam-6865	58	2	a	a	X
ejpam-6865	58	3	(	(	PUNCT
ejpam-6865	58	4	t−	t−	PROPN
ejpam-6865	58	5	s)n−α−1f(s)ds	s)n−α−1f(s)ds	NOUN
ejpam-6865	58	6	,	,	PUNCT
ejpam-6865	58	7	(	(	PUNCT
ejpam-6865	58	8	1	1	X
ejpam-6865	58	9	)	)	PUNCT
ejpam-6865	58	10	tin−α	tin−α	NOUN
ejpam-6865	58	11	b	b	NOUN
ejpam-6865	58	12	f(t	f(t	PROPN
ejpam-6865	58	13	)	)	PUNCT
ejpam-6865	58	14	=	=	SYM
ejpam-6865	58	15	1	1	NUM
ejpam-6865	58	16	γ(n−	γ(n−	PROPN
ejpam-6865	58	17	α	α	NOUN
ejpam-6865	58	18	)	)	PUNCT
ejpam-6865	58	19	∫	∫	PROPN
ejpam-6865	58	20	b	b	PROPN
ejpam-6865	58	21	t	t	PROPN
ejpam-6865	58	22	(	(	PUNCT
ejpam-6865	58	23	t−	t−	PROPN
ejpam-6865	58	24	s)n−α−1f(s)ds	s)n−α−1f(s)ds	NOUN
ejpam-6865	58	25	.	.	PUNCT
ejpam-6865	59	1	(	(	PUNCT
ejpam-6865	59	2	2	2	X
ejpam-6865	59	3	)	)	PUNCT
ejpam-6865	59	4	the	the	DET
ejpam-6865	59	5	r	r	NOUN
ejpam-6865	59	6	-	-	PUNCT
ejpam-6865	59	7	l	l	NOUN
ejpam-6865	59	8	fd	fd	NOUN
ejpam-6865	59	9	from	from	ADP
ejpam-6865	59	10	the	the	DET
ejpam-6865	59	11	left	left	NOUN
ejpam-6865	59	12	and	and	CCONJ
ejpam-6865	59	13	right	right	ADJ
ejpam-6865	59	14	,	,	PUNCT
ejpam-6865	59	15	respectively	respectively	ADV
ejpam-6865	59	16	,	,	PUNCT
ejpam-6865	59	17	are	be	AUX
ejpam-6865	59	18	defined	define	VERB
ejpam-6865	59	19	as	as	ADP
ejpam-6865	59	20	[	[	X
ejpam-6865	59	21	28	28	NUM
ejpam-6865	59	22	]	]	X
ejpam-6865	59	23	:	:	PUNCT
ejpam-6865	59	24	adα	adα	PROPN
ejpam-6865	59	25	t	t	PROPN
ejpam-6865	59	26	f(t	f(t	PROPN
ejpam-6865	59	27	)	)	PUNCT
ejpam-6865	60	1	=	=	PUNCT
ejpam-6865	60	2	dn	dn	PROPN
ejpam-6865	60	3	dtn	dtn	PROPN
ejpam-6865	60	4	ad−(n−α	ad−(n−α	PROPN
ejpam-6865	60	5	)	)	PUNCT
ejpam-6865	60	6	t	t	PROPN
ejpam-6865	60	7	f(t	f(t	PROPN
ejpam-6865	60	8	)	)	PUNCT
ejpam-6865	61	1	=	=	PUNCT
ejpam-6865	61	2	dn	dn	PROPN
ejpam-6865	61	3	dtn	dtn	PROPN
ejpam-6865	61	4	(	(	PUNCT
ejpam-6865	61	5	ain−α	ain−α	NOUN
ejpam-6865	61	6	t	t	PROPN
ejpam-6865	61	7	f(t	f(t	PROPN
ejpam-6865	61	8	)	)	PUNCT
ejpam-6865	61	9	)	)	PUNCT
ejpam-6865	61	10	,	,	PUNCT
ejpam-6865	61	11	(	(	PUNCT
ejpam-6865	61	12	3	3	X
ejpam-6865	61	13	)	)	PUNCT
ejpam-6865	61	14	tdα	tdα	PROPN
ejpam-6865	61	15	b	b	X
ejpam-6865	61	16	f(t	f(t	PROPN
ejpam-6865	61	17	)	)	PUNCT
ejpam-6865	61	18	=	=	PUNCT
ejpam-6865	61	19	dn	dn	PROPN
ejpam-6865	61	20	dtn	dtn	PROPN
ejpam-6865	61	21	td	td	PROPN
ejpam-6865	61	22	−(n−α	−(n−α	NOUN
ejpam-6865	61	23	)	)	PUNCT
ejpam-6865	61	24	b	b	NOUN
ejpam-6865	61	25	f(t	f(t	NOUN
ejpam-6865	61	26	)	)	PUNCT
ejpam-6865	61	27	=	=	PUNCT
ejpam-6865	61	28	dn	dn	PROPN
ejpam-6865	61	29	dtn	dtn	PROPN
ejpam-6865	61	30	(	(	PUNCT
ejpam-6865	61	31	tin−α	tin−α	NOUN
ejpam-6865	61	32	b	b	PRON
ejpam-6865	61	33	f(t	f(t	NOUN
ejpam-6865	61	34	)	)	PUNCT
ejpam-6865	61	35	)	)	PUNCT
ejpam-6865	61	36	.	.	PUNCT
ejpam-6865	62	1	(	(	PUNCT
ejpam-6865	62	2	4	4	X
ejpam-6865	62	3	)	)	PUNCT
ejpam-6865	62	4	the	the	DET
ejpam-6865	62	5	caputo	caputo	PROPN
ejpam-6865	62	6	fd	fd	PROPN
ejpam-6865	62	7	for	for	ADP
ejpam-6865	62	8	n−	n−	NOUN
ejpam-6865	62	9	1	1	NUM
ejpam-6865	62	10	<	<	X
ejpam-6865	62	11	α	α	PROPN
ejpam-6865	62	12	≤	≤	PUNCT
ejpam-6865	62	13	n	n	CCONJ
ejpam-6865	62	14	is	be	AUX
ejpam-6865	62	15	defined	define	VERB
ejpam-6865	62	16	as	as	ADP
ejpam-6865	62	17	[	[	X
ejpam-6865	62	18	29	29	NUM
ejpam-6865	62	19	]	]	NUM
ejpam-6865	62	20	:	:	PUNCT
ejpam-6865	62	21	cdα	cdα	NOUN
ejpam-6865	62	22	af(t	af(t	PUNCT
ejpam-6865	62	23	)	)	PUNCT
ejpam-6865	63	1	=	=	SYM
ejpam-6865	63	2	1	1	NUM
ejpam-6865	63	3	γ(n−	γ(n−	PROPN
ejpam-6865	63	4	α	α	NOUN
ejpam-6865	63	5	)	)	PUNCT
ejpam-6865	63	6	∫	∫	PROPN
ejpam-6865	63	7	t	t	PROPN
ejpam-6865	63	8	a	a	PRON
ejpam-6865	63	9	(	(	PUNCT
ejpam-6865	63	10	t−	t−	PROPN
ejpam-6865	63	11	s)n−α−1f	s)n−α−1f	PROPN
ejpam-6865	63	12	(	(	PUNCT
ejpam-6865	63	13	n)(s)ds	n)(s)ds	NOUN
ejpam-6865	63	14	.	.	PUNCT
ejpam-6865	64	1	(	(	PUNCT
ejpam-6865	64	2	5	5	X
ejpam-6865	64	3	)	)	PUNCT
ejpam-6865	64	4	s.	s.	PROPN
ejpam-6865	64	5	tamimi	tamimi	PROPN
ejpam-6865	64	6	,	,	PUNCT
ejpam-6865	64	7	a.	a.	PROPN
ejpam-6865	64	8	k.	k.	PROPN
ejpam-6865	64	9	alomari	alomari	PROPN
ejpam-6865	64	10	,	,	PUNCT
ejpam-6865	64	11	m.	m.	NOUN
ejpam-6865	64	12	alaroud	alaroud	PROPN
ejpam-6865	64	13	/	/	SYM
ejpam-6865	64	14	eur	eur	PROPN
ejpam-6865	64	15	.	.	PUNCT
ejpam-6865	65	1	j.	j.	PROPN
ejpam-6865	65	2	pure	pure	PROPN
ejpam-6865	65	3	appl	appl	PROPN
ejpam-6865	65	4	.	.	PROPN
ejpam-6865	65	5	math	math	PROPN
ejpam-6865	65	6	,	,	PUNCT
ejpam-6865	65	7	18	18	NUM
ejpam-6865	65	8	(	(	PUNCT
ejpam-6865	65	9	4	4	NUM
ejpam-6865	65	10	)	)	PUNCT
ejpam-6865	65	11	(	(	PUNCT
ejpam-6865	65	12	2025	2025	NUM
ejpam-6865	65	13	)	)	PUNCT
ejpam-6865	65	14	,	,	PUNCT
ejpam-6865	65	15	6865	6865	NUM
ejpam-6865	65	16	4	4	NUM
ejpam-6865	65	17	of	of	ADP
ejpam-6865	65	18	19	19	NUM
ejpam-6865	65	19	definition	definition	NOUN
ejpam-6865	65	20	1	1	NUM
ejpam-6865	65	21	.	.	PUNCT
ejpam-6865	66	1	[	[	X
ejpam-6865	66	2	22	22	NUM
ejpam-6865	66	3	]	]	PUNCT
ejpam-6865	66	4	the	the	DET
ejpam-6865	66	5	fd	fd	PROPN
ejpam-6865	66	6	in	in	ADP
ejpam-6865	66	7	the	the	DET
ejpam-6865	66	8	sense	sense	NOUN
ejpam-6865	66	9	of	of	ADP
ejpam-6865	66	10	generalized	generalized	ADJ
ejpam-6865	66	11	abc	abc	PROPN
ejpam-6865	66	12	with	with	ADP
ejpam-6865	66	13	kernel	kernel	PROPN
ejpam-6865	66	14	eγ	eγ	ADP
ejpam-6865	66	15	α,µ(λ	α,µ(λ	PROPN
ejpam-6865	66	16	,	,	PUNCT
ejpam-6865	66	17	t	t	PROPN
ejpam-6865	66	18	)	)	PUNCT
ejpam-6865	66	19	is	be	AUX
ejpam-6865	66	20	given	give	VERB
ejpam-6865	66	21	by	by	ADP
ejpam-6865	66	22	(	(	PUNCT
ejpam-6865	66	23	abc	abc	PROPN
ejpam-6865	66	24	a	a	DET
ejpam-6865	66	25	dα,µ,γf)(x	dα,µ,γf)(x	PROPN
ejpam-6865	66	26	)	)	PUNCT
ejpam-6865	66	27	=	=	SYM
ejpam-6865	66	28	m(α1	m(α1	NOUN
ejpam-6865	66	29	)	)	PUNCT
ejpam-6865	66	30	1−	1−	NUM
ejpam-6865	66	31	α1	α1	PROPN
ejpam-6865	66	32	∫	∫	PROPN
ejpam-6865	66	33	x	x	X
ejpam-6865	66	34	a	a	PRON
ejpam-6865	66	35	eγ	eγ	PRON
ejpam-6865	66	36	α1,µ(λ	α1,µ(λ	NOUN
ejpam-6865	66	37	,	,	PUNCT
ejpam-6865	66	38	x−	x−	PROPN
ejpam-6865	66	39	t)f	t)f	X
ejpam-6865	66	40	(	(	PUNCT
ejpam-6865	66	41	n+1)(t)dt	n+1)(t)dt	PROPN
ejpam-6865	66	42	,	,	PUNCT
ejpam-6865	66	43	(	(	PUNCT
ejpam-6865	66	44	6	6	NUM
ejpam-6865	66	45	)	)	PUNCT
ejpam-6865	66	46	and	and	CCONJ
ejpam-6865	66	47	(	(	PUNCT
ejpam-6865	66	48	abcdα,µ,γ	abcdα,µ,γ	PROPN
ejpam-6865	66	49	b	b	PROPN
ejpam-6865	66	50	f)(x	f)(x	NOUN
ejpam-6865	66	51	)	)	PUNCT
ejpam-6865	66	52	=	=	SYM
ejpam-6865	66	53	−m(α1	−m(α1	NOUN
ejpam-6865	66	54	)	)	PUNCT
ejpam-6865	66	55	1−	1−	NUM
ejpam-6865	66	56	α1	α1	PROPN
ejpam-6865	67	1	∫	∫	PROPN
ejpam-6865	67	2	b	b	PROPN
ejpam-6865	67	3	x	x	PROPN
ejpam-6865	67	4	eγ	eγ	ADP
ejpam-6865	67	5	α1,µ(λ	α1,µ(λ	PROPN
ejpam-6865	67	6	,	,	PUNCT
ejpam-6865	67	7	x−	x−	PROPN
ejpam-6865	67	8	t)f	t)f	X
ejpam-6865	67	9	(	(	PUNCT
ejpam-6865	67	10	n+1)(t)dt	n+1)(t)dt	PROPN
ejpam-6865	67	11	,	,	PUNCT
ejpam-6865	67	12	(	(	PUNCT
ejpam-6865	67	13	7	7	X
ejpam-6865	67	14	)	)	PUNCT
ejpam-6865	67	15	where	where	SCONJ
ejpam-6865	67	16	m(α1	m(α1	NOUN
ejpam-6865	67	17	)	)	PUNCT
ejpam-6865	67	18	is	be	AUX
ejpam-6865	67	19	a	a	DET
ejpam-6865	67	20	function	function	NOUN
ejpam-6865	67	21	of	of	ADP
ejpam-6865	67	22	the	the	DET
ejpam-6865	67	23	nationalization	nationalization	NOUN
ejpam-6865	67	24	with	with	ADP
ejpam-6865	67	25	m(0)=m(1)=1	m(0)=m(1)=1	PROPN
ejpam-6865	67	26	and	and	CCONJ
ejpam-6865	67	27	n	n	ADV
ejpam-6865	67	28	<	<	X
ejpam-6865	67	29	α	α	PRON
ejpam-6865	67	30	≤	≤	NUM
ejpam-6865	67	31	n+	n+	PUNCT
ejpam-6865	68	1	1	1	NUM
ejpam-6865	68	2	,	,	PUNCT
ejpam-6865	68	3	n	n	PRON
ejpam-6865	68	4	∈	∈	PROPN
ejpam-6865	68	5	{	{	PUNCT
ejpam-6865	68	6	0	0	NUM
ejpam-6865	68	7	,	,	PUNCT
ejpam-6865	68	8	1	1	NUM
ejpam-6865	68	9	,	,	PUNCT
ejpam-6865	68	10	2	2	NUM
ejpam-6865	68	11	,	,	PUNCT
ejpam-6865	68	12	...	...	PUNCT
ejpam-6865	68	13	}	}	PUNCT
ejpam-6865	68	14	,	,	PUNCT
ejpam-6865	68	15	λ	λ	X
ejpam-6865	68	16	=	=	SYM
ejpam-6865	68	17	−	−	PROPN
ejpam-6865	68	18	α1	α1	PROPN
ejpam-6865	68	19	1−	1−	NUM
ejpam-6865	68	20	α1	α1	PROPN
ejpam-6865	68	21	,	,	PUNCT
ejpam-6865	68	22	α1	α1	PROPN
ejpam-6865	68	23	=	=	SYM
ejpam-6865	68	24	α−	α−	ADP
ejpam-6865	68	25	n	n	CCONJ
ejpam-6865	68	26	,	,	PUNCT
ejpam-6865	68	27	µ	µ	X
ejpam-6865	68	28	>	>	X
ejpam-6865	68	29	0	0	NUM
ejpam-6865	68	30	and	and	CCONJ
ejpam-6865	68	31	γ	γ	PROPN
ejpam-6865	68	32	∈	∈	PROPN
ejpam-6865	68	33	r	r	NOUN
ejpam-6865	68	34	,	,	PUNCT
ejpam-6865	68	35	where	where	SCONJ
ejpam-6865	68	36	eγ	eγ	ADP
ejpam-6865	68	37	α1,µ(λ	α1,µ(λ	PROPN
ejpam-6865	68	38	,	,	PUNCT
ejpam-6865	68	39	x−	x−	PROPN
ejpam-6865	68	40	t	t	PROPN
ejpam-6865	68	41	)	)	PUNCT
ejpam-6865	68	42	=	=	PUNCT
ejpam-6865	69	1	∞∑	∞∑	NUM
ejpam-6865	69	2	k=0	k=0	PROPN
ejpam-6865	69	3	(	(	PUNCT
ejpam-6865	69	4	γ)k	γ)k	X
ejpam-6865	69	5	k!γ(α1k	k!γ(α1k	PROPN
ejpam-6865	69	6	+	+	CCONJ
ejpam-6865	69	7	µ	µ	NOUN
ejpam-6865	69	8	)	)	PUNCT
ejpam-6865	69	9	λk(x−	λk(x−	ADV
ejpam-6865	69	10	t)α1k+µ−1	t)α1k+µ−1	VERB
ejpam-6865	69	11	,	,	PUNCT
ejpam-6865	69	12	(	(	PUNCT
ejpam-6865	69	13	8)	8)	NUM
ejpam-6865	69	14	and	and	CCONJ
ejpam-6865	69	15	(	(	PUNCT
ejpam-6865	69	16	γ)k	γ)k	X
ejpam-6865	69	17	=	=	SYM
ejpam-6865	69	18	γ(γ	γ(γ	PROPN
ejpam-6865	69	19	+	+	CCONJ
ejpam-6865	69	20	1)(γ	1)(γ	NUM
ejpam-6865	69	21	+	+	NUM
ejpam-6865	69	22	2)	2)	NUM
ejpam-6865	69	23	...	...	PUNCT
ejpam-6865	69	24	(γ	(γ	PROPN
ejpam-6865	70	1	+	+	CCONJ
ejpam-6865	70	2	k	k	X
ejpam-6865	70	3	−	−	NOUN
ejpam-6865	71	1	1	1	NUM
ejpam-6865	71	2	)	)	PUNCT
ejpam-6865	71	3	;	;	PUNCT
ejpam-6865	71	4	k	k	PROPN
ejpam-6865	71	5	∈	∈	PROPN
ejpam-6865	71	6	n.	n.	PROPN
ejpam-6865	71	7	theorem	theorem	VERB
ejpam-6865	71	8	1	1	NUM
ejpam-6865	71	9	.	.	PUNCT
ejpam-6865	72	1	[	[	X
ejpam-6865	72	2	30	30	NUM
ejpam-6865	72	3	]	]	PUNCT
ejpam-6865	72	4	”	"	PUNCT
ejpam-6865	72	5	the	the	DET
ejpam-6865	72	6	generalized	generalize	VERB
ejpam-6865	72	7	fd	fd	PROPN
ejpam-6865	72	8	with	with	ADP
ejpam-6865	72	9	generalized	generalized	ADJ
ejpam-6865	72	10	mittag	mittag	ADJ
ejpam-6865	72	11	-	-	PUNCT
ejpam-6865	72	12	leffler	leffler	NOUN
ejpam-6865	72	13	kernel	kernel	NOUN
ejpam-6865	72	14	of	of	ADP
ejpam-6865	72	15	xβ	xβ	PROPN
ejpam-6865	72	16	(	(	PUNCT
ejpam-6865	72	17	β	β	X
ejpam-6865	72	18	>	>	X
ejpam-6865	72	19	n	n	CCONJ
ejpam-6865	72	20	)	)	PUNCT
ejpam-6865	72	21	of	of	ADP
ejpam-6865	72	22	order	order	NOUN
ejpam-6865	72	23	α	α	NOUN
ejpam-6865	72	24	(	(	PUNCT
ejpam-6865	72	25	n	n	X
ejpam-6865	72	26	<	<	X
ejpam-6865	72	27	α	α	PROPN
ejpam-6865	72	28	5	5	NUM
ejpam-6865	72	29	n+	n+	SYM
ejpam-6865	72	30	1	1	NUM
ejpam-6865	72	31	)	)	PUNCT
ejpam-6865	72	32	is	be	AUX
ejpam-6865	72	33	given	give	VERB
ejpam-6865	72	34	,	,	PUNCT
ejpam-6865	72	35	for	for	ADP
ejpam-6865	72	36	µ	µ	NOUN
ejpam-6865	72	37	>	>	SYM
ejpam-6865	72	38	0	0	NUM
ejpam-6865	72	39	and	and	CCONJ
ejpam-6865	72	40	α1	α1	PROPN
ejpam-6865	72	41	=	=	SYM
ejpam-6865	72	42	α−	α−	ADP
ejpam-6865	72	43	n	n	PROPN
ejpam-6865	72	44	(	(	PUNCT
ejpam-6865	72	45	n0	n0	NUM
ejpam-6865	72	46	)	)	PUNCT
ejpam-6865	72	47	,	,	PUNCT
ejpam-6865	72	48	by	by	ADP
ejpam-6865	72	49	abc	abc	PROPN
ejpam-6865	72	50	0d	0d	X
ejpam-6865	72	51	α,µ,γxβ	α,µ,γxβ	PROPN
ejpam-6865	72	52	=	=	PUNCT
ejpam-6865	73	1	m(α1)γ(β	m(α1)γ(β	PROPN
ejpam-6865	73	2	+	+	NUM
ejpam-6865	73	3	1	1	NUM
ejpam-6865	73	4	)	)	PUNCT
ejpam-6865	73	5	1−	1−	NUM
ejpam-6865	73	6	α1	α1	PROPN
ejpam-6865	73	7	∞∑	∞∑	PROPN
ejpam-6865	73	8	k=0	k=0	PROPN
ejpam-6865	73	9	λk(γ)kx	λk(γ)kx	VERB
ejpam-6865	73	10	α1k+µ+β−n−1	α1k+µ+β−n−1	PROPN
ejpam-6865	74	1	k	k	NOUN
ejpam-6865	74	2	!	!	PUNCT
ejpam-6865	74	3	γ(α1k	γ(α1k	NOUN
ejpam-6865	74	4	+	+	NUM
ejpam-6865	74	5	β	β	X
ejpam-6865	74	6	+	+	NUM
ejpam-6865	74	7	µ−	µ−	PROPN
ejpam-6865	74	8	n	n	CCONJ
ejpam-6865	74	9	)	)	PUNCT
ejpam-6865	74	10	(	(	PUNCT
ejpam-6865	74	11	9	9	X
ejpam-6865	74	12	)	)	PUNCT
ejpam-6865	74	13	=	=	VERB
ejpam-6865	75	1	m(α1)γ(β	m(α1)γ(β	PROPN
ejpam-6865	76	1	+	+	ADJ
ejpam-6865	76	2	1	1	NUM
ejpam-6865	76	3	)	)	PUNCT
ejpam-6865	76	4	1−	1−	NUM
ejpam-6865	76	5	α1	α1	PROPN
ejpam-6865	76	6	eγ	eγ	ADP
ejpam-6865	76	7	α1,µ+β−n(λ	α1,µ+β−n(λ	PROPN
ejpam-6865	76	8	,	,	PUNCT
ejpam-6865	76	9	x	x	NOUN
ejpam-6865	76	10	)	)	PUNCT
ejpam-6865	76	11	.	.	PUNCT
ejpam-6865	76	12	”	"	PUNCT
ejpam-6865	77	1	(	(	PUNCT
ejpam-6865	77	2	10	10	NUM
ejpam-6865	77	3	)	)	PUNCT
ejpam-6865	77	4	theorem	theorem	NOUN
ejpam-6865	77	5	2	2	NUM
ejpam-6865	77	6	.	.	PUNCT
ejpam-6865	78	1	[	[	X
ejpam-6865	78	2	18	18	NUM
ejpam-6865	78	3	]	]	PUNCT
ejpam-6865	78	4	”	"	PUNCT
ejpam-6865	78	5	let	let	VERB
ejpam-6865	78	6	f	f	PROPN
ejpam-6865	78	7	∈	∈	PROPN
ejpam-6865	78	8	cn+1	cn+1	VERB
ejpam-6865	79	1	[	[	X
ejpam-6865	79	2	0	0	NUM
ejpam-6865	79	3	,	,	PUNCT
ejpam-6865	79	4	1	1	NUM
ejpam-6865	79	5	]	]	PUNCT
ejpam-6865	79	6	.	.	PUNCT
ejpam-6865	80	1	the	the	DET
ejpam-6865	80	2	laplace	laplace	NOUN
ejpam-6865	80	3	transform	transform	NOUN
ejpam-6865	80	4	of	of	ADP
ejpam-6865	80	5	the	the	DET
ejpam-6865	80	6	abc	abc	PROPN
ejpam-6865	80	7	-	-	PUNCT
ejpam-6865	80	8	fd	fd	PROPN
ejpam-6865	80	9	with	with	ADP
ejpam-6865	80	10	kernel	kernel	PROPN
ejpam-6865	80	11	eγ	eγ	ADP
ejpam-6865	80	12	α,µ(λ	α,µ(λ	PROPN
ejpam-6865	80	13	,	,	PUNCT
ejpam-6865	80	14	t	t	PROPN
ejpam-6865	80	15	)	)	PUNCT
ejpam-6865	80	16	for	for	ADP
ejpam-6865	80	17	n	n	X
ejpam-6865	80	18	<	<	X
ejpam-6865	80	19	α	α	X
ejpam-6865	80	20	<	<	X
ejpam-6865	80	21	n+	n+	X
ejpam-6865	80	22	1	1	NUM
ejpam-6865	80	23	,	,	PUNCT
ejpam-6865	80	24	µ	µ	X
ejpam-6865	80	25	>	>	X
ejpam-6865	80	26	0	0	PROPN
ejpam-6865	80	27	,	,	PUNCT
ejpam-6865	80	28	γ	γ	NOUN
ejpam-6865	80	29	=	=	SYM
ejpam-6865	80	30	1	1	NUM
ejpam-6865	80	31	and	and	CCONJ
ejpam-6865	80	32	λ	λ	X
ejpam-6865	80	33	=	=	PRON
ejpam-6865	80	34	−α1	−α1	VERB
ejpam-6865	80	35	1−α1	1−α1	NUM
ejpam-6865	80	36	is	be	AUX
ejpam-6865	80	37	given	give	VERB
ejpam-6865	80	38	by	by	ADP
ejpam-6865	80	39	l	l	NOUN
ejpam-6865	80	40	[	[	PUNCT
ejpam-6865	80	41	(	(	PUNCT
ejpam-6865	80	42	abc	abc	PROPN
ejpam-6865	80	43	0	0	NUM
ejpam-6865	80	44	dα,µ,γf)(x	dα,µ,γf)(x	PROPN
ejpam-6865	80	45	)	)	PUNCT
ejpam-6865	80	46	]	]	PUNCT
ejpam-6865	81	1	(	(	PUNCT
ejpam-6865	81	2	s	s	X
ejpam-6865	81	3	)	)	PUNCT
ejpam-6865	81	4	=	=	SYM
ejpam-6865	81	5	m(α1	m(α1	NOUN
ejpam-6865	81	6	)	)	PUNCT
ejpam-6865	81	7	1−	1−	NUM
ejpam-6865	81	8	α1	α1	PROPN
ejpam-6865	81	9	(	(	PUNCT
ejpam-6865	81	10	1−	1−	NUM
ejpam-6865	81	11	λs−α)−1sn+1−µf	λs−α)−1sn+1−µf	PROPN
ejpam-6865	81	12	(	(	PUNCT
ejpam-6865	81	13	s	s	NOUN
ejpam-6865	81	14	)	)	PUNCT
ejpam-6865	81	15	.	.	PUNCT
ejpam-6865	81	16	”	"	PUNCT
ejpam-6865	82	1	(	(	PUNCT
ejpam-6865	82	2	11	11	NUM
ejpam-6865	82	3	)	)	PUNCT
ejpam-6865	82	4	proposition	proposition	NOUN
ejpam-6865	82	5	1	1	NUM
ejpam-6865	82	6	.	.	PUNCT
ejpam-6865	83	1	[	[	X
ejpam-6865	83	2	31	31	NUM
ejpam-6865	83	3	]	]	PUNCT
ejpam-6865	83	4	let	let	VERB
ejpam-6865	83	5	m(α1	m(α1	NOUN
ejpam-6865	83	6	)	)	PUNCT
ejpam-6865	83	7	1−	1−	NUM
ejpam-6865	83	8	α1	α1	PROPN
ejpam-6865	83	9	(	(	PUNCT
ejpam-6865	83	10	1−	1−	NUM
ejpam-6865	83	11	λs−α)−1sn+1−µf	λs−α)−1sn+1−µf	PROPN
ejpam-6865	83	12	(	(	PUNCT
ejpam-6865	83	13	s	s	X
ejpam-6865	83	14	)	)	PUNCT
ejpam-6865	83	15	=	=	PUNCT
ejpam-6865	83	16	u(s	u(s	PROPN
ejpam-6865	83	17	)	)	PUNCT
ejpam-6865	83	18	,	,	PUNCT
ejpam-6865	83	19	(	(	PUNCT
ejpam-6865	83	20	12	12	NUM
ejpam-6865	83	21	)	)	PUNCT
ejpam-6865	83	22	then	then	ADV
ejpam-6865	83	23	f	f	X
ejpam-6865	83	24	(	(	PUNCT
ejpam-6865	83	25	s	s	X
ejpam-6865	83	26	)	)	PUNCT
ejpam-6865	83	27	=	=	SYM
ejpam-6865	83	28	1−	1−	NUM
ejpam-6865	83	29	α1	α1	PROPN
ejpam-6865	83	30	m(α1	m(α1	NOUN
ejpam-6865	83	31	)	)	PUNCT
ejpam-6865	83	32	sµ−(n+1)u(s	sµ−(n+1)u(s	NOUN
ejpam-6865	83	33	)	)	PUNCT
ejpam-6865	84	1	+	+	CCONJ
ejpam-6865	84	2	α1	α1	PROPN
ejpam-6865	84	3	m(α1	m(α1	NOUN
ejpam-6865	84	4	)	)	PUNCT
ejpam-6865	84	5	sµ−(n+1)−αu(s	sµ−(n+1)−αu(s	PROPN
ejpam-6865	84	6	)	)	PUNCT
ejpam-6865	84	7	,	,	PUNCT
ejpam-6865	84	8	(	(	PUNCT
ejpam-6865	84	9	13	13	NUM
ejpam-6865	84	10	)	)	PUNCT
ejpam-6865	84	11	by	by	ADP
ejpam-6865	84	12	applying	apply	VERB
ejpam-6865	84	13	the	the	DET
ejpam-6865	84	14	inverse	inverse	NOUN
ejpam-6865	84	15	laplace	laplace	NOUN
ejpam-6865	84	16	transform	transform	NOUN
ejpam-6865	84	17	to	to	ADP
ejpam-6865	84	18	both	both	DET
ejpam-6865	84	19	sides	side	NOUN
ejpam-6865	84	20	,	,	PUNCT
ejpam-6865	84	21	we	we	PRON
ejpam-6865	84	22	have	have	VERB
ejpam-6865	84	23	f(t	f(t	NOUN
ejpam-6865	84	24	)	)	PUNCT
ejpam-6865	84	25	=	=	SYM
ejpam-6865	84	26	1−	1−	NUM
ejpam-6865	84	27	α1	α1	PROPN
ejpam-6865	84	28	m(α1	m(α1	NOUN
ejpam-6865	84	29	)	)	PUNCT
ejpam-6865	84	30	in+1−µu(t	in+1−µu(t	PROPN
ejpam-6865	84	31	)	)	PUNCT
ejpam-6865	84	32	+	+	NUM
ejpam-6865	84	33	α1	α1	PROPN
ejpam-6865	84	34	m(α1	m(α1	NOUN
ejpam-6865	84	35	)	)	PUNCT
ejpam-6865	84	36	in+1−µ+αu(t	in+1−µ+αu(t	VERB
ejpam-6865	84	37	)	)	PUNCT
ejpam-6865	84	38	.	.	PUNCT
ejpam-6865	85	1	(	(	PUNCT
ejpam-6865	85	2	14	14	NUM
ejpam-6865	85	3	)	)	PUNCT
ejpam-6865	85	4	s.	s.	PROPN
ejpam-6865	85	5	tamimi	tamimi	PROPN
ejpam-6865	85	6	,	,	PUNCT
ejpam-6865	85	7	a.	a.	PROPN
ejpam-6865	85	8	k.	k.	PROPN
ejpam-6865	85	9	alomari	alomari	PROPN
ejpam-6865	85	10	,	,	PUNCT
ejpam-6865	85	11	m.	m.	NOUN
ejpam-6865	85	12	alaroud	alaroud	PROPN
ejpam-6865	85	13	/	/	SYM
ejpam-6865	85	14	eur	eur	PROPN
ejpam-6865	85	15	.	.	PUNCT
ejpam-6865	86	1	j.	j.	PROPN
ejpam-6865	86	2	pure	pure	PROPN
ejpam-6865	86	3	appl	appl	PROPN
ejpam-6865	86	4	.	.	PROPN
ejpam-6865	86	5	math	math	PROPN
ejpam-6865	86	6	,	,	PUNCT
ejpam-6865	86	7	18	18	NUM
ejpam-6865	86	8	(	(	PUNCT
ejpam-6865	86	9	4	4	NUM
ejpam-6865	86	10	)	)	PUNCT
ejpam-6865	86	11	(	(	PUNCT
ejpam-6865	86	12	2025	2025	NUM
ejpam-6865	86	13	)	)	PUNCT
ejpam-6865	86	14	,	,	PUNCT
ejpam-6865	86	15	6865	6865	NUM
ejpam-6865	86	16	5	5	NUM
ejpam-6865	86	17	of	of	ADP
ejpam-6865	86	18	19	19	NUM
ejpam-6865	86	19	definition	definition	NOUN
ejpam-6865	86	20	2	2	NUM
ejpam-6865	86	21	.	.	PUNCT
ejpam-6865	87	1	the	the	DET
ejpam-6865	87	2	left	left	ADJ
ejpam-6865	87	3	ab	ab	PROPN
ejpam-6865	87	4	fractional	fractional	ADJ
ejpam-6865	87	5	integral	integral	ADJ
ejpam-6865	87	6	for	for	ADP
ejpam-6865	87	7	n	n	X
ejpam-6865	87	8	<	<	X
ejpam-6865	87	9	α	α	X
ejpam-6865	87	10	<	<	X
ejpam-6865	87	11	n+1	n+1	PROPN
ejpam-6865	87	12	,	,	PUNCT
ejpam-6865	87	13	µ	µ	X
ejpam-6865	87	14	>	>	SYM
ejpam-6865	87	15	0	0	NUM
ejpam-6865	87	16	and	and	CCONJ
ejpam-6865	87	17	γ	γ	X
ejpam-6865	87	18	=	=	SYM
ejpam-6865	87	19	1	1	NUM
ejpam-6865	87	20	is	be	AUX
ejpam-6865	87	21	given	give	VERB
ejpam-6865	87	22	by	by	ADP
ejpam-6865	87	23	(	(	PUNCT
ejpam-6865	87	24	ab	ab	PROPN
ejpam-6865	87	25	a	a	DET
ejpam-6865	87	26	iα,µ,γf)(x	iα,µ,γf)(x	PROPN
ejpam-6865	87	27	)	)	PUNCT
ejpam-6865	87	28	=	=	PUNCT
ejpam-6865	88	1	γ∑	γ∑	PROPN
ejpam-6865	88	2	i=0	i=0	PROPN
ejpam-6865	88	3	(	(	PUNCT
ejpam-6865	88	4	γ	γ	X
ejpam-6865	88	5	i	i	PROPN
ejpam-6865	88	6	)	)	PUNCT
ejpam-6865	88	7	αi	αi	VERB
ejpam-6865	88	8	1	1	NUM
ejpam-6865	88	9	m(α1)(1−	m(α1)(1−	PROPN
ejpam-6865	88	10	α1)i−1	α1)i−1	PROPN
ejpam-6865	88	11	(	(	PUNCT
ejpam-6865	88	12	rl	rl	VERB
ejpam-6865	88	13	a	a	DET
ejpam-6865	88	14	iαi−µ+n+1f)(x	iαi−µ+n+1f)(x	PROPN
ejpam-6865	88	15	)	)	PUNCT
ejpam-6865	88	16	,	,	PUNCT
ejpam-6865	88	17	(	(	PUNCT
ejpam-6865	88	18	15	15	NUM
ejpam-6865	88	19	)	)	PUNCT
ejpam-6865	88	20	where	where	SCONJ
ejpam-6865	88	21	(	(	PUNCT
ejpam-6865	88	22	rl	rl	ADP
ejpam-6865	88	23	a	a	DET
ejpam-6865	88	24	iαi−µ+n+1f)(x	iαi−µ+n+1f)(x	PROPN
ejpam-6865	88	25	)	)	PUNCT
ejpam-6865	88	26	is	be	AUX
ejpam-6865	88	27	the	the	DET
ejpam-6865	88	28	rl	rl	PROPN
ejpam-6865	88	29	fractional	fractional	ADJ
ejpam-6865	88	30	integral	integral	ADJ
ejpam-6865	88	31	of	of	ADP
ejpam-6865	88	32	order	order	NOUN
ejpam-6865	88	33	αi−	αi−	NUM
ejpam-6865	88	34	µ+	µ+	X
ejpam-6865	88	35	n+	n+	NUM
ejpam-6865	88	36	1	1	NUM
ejpam-6865	88	37	.	.	X
ejpam-6865	88	38	theorem	theorem	NOUN
ejpam-6865	88	39	3	3	NUM
ejpam-6865	88	40	.	.	X
ejpam-6865	88	41	for	for	ADP
ejpam-6865	88	42	n	n	X
ejpam-6865	88	43	<	<	X
ejpam-6865	88	44	α	α	X
ejpam-6865	88	45	<	<	X
ejpam-6865	88	46	n+	n+	X
ejpam-6865	88	47	1	1	NUM
ejpam-6865	88	48	,	,	PUNCT
ejpam-6865	88	49	µ	µ	X
ejpam-6865	88	50	>	>	SYM
ejpam-6865	88	51	0	0	NUM
ejpam-6865	88	52	and	and	CCONJ
ejpam-6865	88	53	γ	γ	X
ejpam-6865	88	54	=	=	SYM
ejpam-6865	88	55	1	1	NUM
ejpam-6865	88	56	,	,	PUNCT
ejpam-6865	88	57	we	we	PRON
ejpam-6865	88	58	conclude	conclude	VERB
ejpam-6865	88	59	that	that	SCONJ
ejpam-6865	88	60	ab	ab	PROPN
ejpam-6865	88	61	a	a	DET
ejpam-6865	88	62	iα,µ,γaabcdα,µ,γu(t	iα,µ,γaabcdα,µ,γu(t	NUM
ejpam-6865	88	63	)	)	PUNCT
ejpam-6865	88	64	=	=	SYM
ejpam-6865	89	1	u(t)−	u(t)−	PROPN
ejpam-6865	89	2	u(a)−	u(a)−	ADV
ejpam-6865	89	3	(	(	PUNCT
ejpam-6865	89	4	t−	t−	PROPN
ejpam-6865	89	5	a)u′(a)−	a)u′(a)−	NOUN
ejpam-6865	89	6	·	·	PUNCT
ejpam-6865	89	7	·	·	PUNCT
ejpam-6865	89	8	·	·	PUNCT
ejpam-6865	89	9	−	−	PROPN
ejpam-6865	89	10	(	(	PUNCT
ejpam-6865	89	11	t−	t−	X
ejpam-6865	89	12	a)n−1	a)n−1	ADJ
ejpam-6865	89	13	(	(	PUNCT
ejpam-6865	89	14	n−	n−	NOUN
ejpam-6865	89	15	1	1	NUM
ejpam-6865	89	16	)	)	PUNCT
ejpam-6865	89	17	!	!	PUNCT
ejpam-6865	90	1	un−1(a)−	un−1(a)−	PROPN
ejpam-6865	90	2	(	(	PUNCT
ejpam-6865	90	3	t−	t−	PROPN
ejpam-6865	90	4	a)n	a)n	NOUN
ejpam-6865	90	5	n	n	CCONJ
ejpam-6865	90	6	!	!	PUNCT
ejpam-6865	90	7	un(a	un(a	PROPN
ejpam-6865	90	8	)	)	PUNCT
ejpam-6865	90	9	,	,	PUNCT
ejpam-6865	90	10	(	(	PUNCT
ejpam-6865	90	11	16	16	NUM
ejpam-6865	90	12	)	)	PUNCT
ejpam-6865	90	13	where	where	SCONJ
ejpam-6865	90	14	n	n	NUM
ejpam-6865	90	15	∈	∈	PROPN
ejpam-6865	90	16	n.	n.	NOUN
ejpam-6865	90	17	proof	proof	NOUN
ejpam-6865	90	18	.	.	PUNCT
ejpam-6865	91	1	by	by	ADP
ejpam-6865	91	2	applying	apply	VERB
ejpam-6865	91	3	the	the	DET
ejpam-6865	91	4	operator	operator	NOUN
ejpam-6865	91	5	ab	ab	PROPN
ejpam-6865	91	6	a	a	DET
ejpam-6865	91	7	iα,µ,γ	iα,µ,γ	PROPN
ejpam-6865	91	8	in	in	ADP
ejpam-6865	91	9	definition	definition	NOUN
ejpam-6865	91	10	2	2	NUM
ejpam-6865	91	11	on	on	ADP
ejpam-6865	91	12	the	the	DET
ejpam-6865	91	13	derivative	derivative	ADJ
ejpam-6865	91	14	dα,µ,γu(t	dα,µ,γu(t	PROPN
ejpam-6865	91	15	)	)	PUNCT
ejpam-6865	91	16	,	,	PUNCT
ejpam-6865	91	17	we	we	PRON
ejpam-6865	91	18	have	have	VERB
ejpam-6865	91	19	ab	ab	PROPN
ejpam-6865	91	20	a	a	DET
ejpam-6865	91	21	iα,µ,γabc	iα,µ,γabc	PROPN
ejpam-6865	91	22	a	a	DET
ejpam-6865	91	23	dα,µ,γu(t	dα,µ,γu(t	NOUN
ejpam-6865	91	24	)	)	PUNCT
ejpam-6865	91	25	=	=	SYM
ejpam-6865	91	26	1−	1−	NUM
ejpam-6865	91	27	α1	α1	PROPN
ejpam-6865	91	28	m(α1	m(α1	NOUN
ejpam-6865	91	29	)	)	PUNCT
ejpam-6865	91	30	rl	rl	ADP
ejpam-6865	91	31	a	a	DET
ejpam-6865	91	32	in+1−µ	in+1−µ	NOUN
ejpam-6865	91	33	(	(	PUNCT
ejpam-6865	91	34	abc	abc	PROPN
ejpam-6865	91	35	a	a	DET
ejpam-6865	91	36	dα,µ,γu)(t	dα,µ,γu)(t	PROPN
ejpam-6865	91	37	)	)	PUNCT
ejpam-6865	91	38	+	+	NUM
ejpam-6865	91	39	α1	α1	PROPN
ejpam-6865	91	40	m(α1	m(α1	NOUN
ejpam-6865	91	41	)	)	PUNCT
ejpam-6865	91	42	rl	rl	ADP
ejpam-6865	91	43	a	a	DET
ejpam-6865	91	44	in+1−µ+α	in+1−µ+α	PROPN
ejpam-6865	91	45	(	(	PUNCT
ejpam-6865	91	46	abc	abc	PROPN
ejpam-6865	91	47	a	a	DET
ejpam-6865	91	48	dα,µ,γu)(t	dα,µ,γu)(t	PROPN
ejpam-6865	91	49	)	)	PUNCT
ejpam-6865	91	50	,	,	PUNCT
ejpam-6865	91	51	=	=	SYM
ejpam-6865	92	1	∞∑	∞∑	PROPN
ejpam-6865	92	2	k=0	k=0	PROPN
ejpam-6865	92	3	λkrl	λkrl	VERB
ejpam-6865	92	4	a	a	DET
ejpam-6865	92	5	iα1k+n+1u(n+1)(t)−	iα1k+n+1u(n+1)(t)−	PROPN
ejpam-6865	92	6	∞∑	∞∑	PROPN
ejpam-6865	92	7	k=0	k=0	AUX
ejpam-6865	92	8	λkrl	λkrl	VERB
ejpam-6865	92	9	a	a	DET
ejpam-6865	92	10	iα1k+α+n+1u(n+1)(t	iα1k+α+n+1u(n+1)(t	NOUN
ejpam-6865	92	11	)	)	PUNCT
ejpam-6865	92	12	,	,	PUNCT
ejpam-6865	92	13	=	=	PUNCT
ejpam-6865	92	14	∞∑	∞∑	NUM
ejpam-6865	92	15	k=0	k=0	PUNCT
ejpam-6865	92	16	λk	λk	ADP
ejpam-6865	92	17	1	1	NUM
ejpam-6865	92	18	γ(α1k	γ(α1k	NOUN
ejpam-6865	92	19	+	+	CCONJ
ejpam-6865	92	20	n+	n+	X
ejpam-6865	92	21	1	1	NUM
ejpam-6865	92	22	)	)	PUNCT
ejpam-6865	92	23	·	·	PUNCT
ejpam-6865	93	1	∫	∫	PROPN
ejpam-6865	94	1	x	x	PUNCT
ejpam-6865	94	2	a	a	PRON
ejpam-6865	94	3	(	(	PUNCT
ejpam-6865	94	4	x−	x−	PROPN
ejpam-6865	94	5	t)α1k+nu(n+1)(t)dt	t)α1k+nu(n+1)(t)dt	NOUN
ejpam-6865	94	6	−	−	PROPN
ejpam-6865	95	1	∞∑	∞∑	ADJ
ejpam-6865	95	2	k=0	k=0	PROPN
ejpam-6865	95	3	λk+1	λk+1	PRON
ejpam-6865	95	4	γ(α1k	γ(α1k	NOUN
ejpam-6865	95	5	+	+	CCONJ
ejpam-6865	95	6	α+	α+	X
ejpam-6865	95	7	n+	n+	NUM
ejpam-6865	95	8	1	1	NUM
ejpam-6865	95	9	)	)	PUNCT
ejpam-6865	95	10	·	·	PUNCT
ejpam-6865	95	11	∫	∫	PROPN
ejpam-6865	96	1	x	x	PUNCT
ejpam-6865	96	2	a	a	PRON
ejpam-6865	96	3	(	(	PUNCT
ejpam-6865	96	4	x−	x−	PROPN
ejpam-6865	96	5	t)α1k+α+nu(n+1)(t)dt	t)α1k+α+nu(n+1)(t)dt	PROPN
ejpam-6865	96	6	,	,	PUNCT
ejpam-6865	96	7	=	=	SYM
ejpam-6865	96	8	∫	∫	PROPN
ejpam-6865	96	9	x	x	X
ejpam-6865	96	10	a	a	PRON
ejpam-6865	96	11	(	(	PUNCT
ejpam-6865	96	12	eα1,n+1(λ	eα1,n+1(λ	PROPN
ejpam-6865	96	13	,	,	PUNCT
ejpam-6865	96	14	x−	x−	PROPN
ejpam-6865	96	15	t)−	t)−	PROPN
ejpam-6865	96	16	λeα1,α+n+1(λ	λeα1,α+n+1(λ	PROPN
ejpam-6865	96	17	,	,	PUNCT
ejpam-6865	96	18	x−	x−	PROPN
ejpam-6865	96	19	t))u(n+1)(t)dt	t))u(n+1)(t)dt	NOUN
ejpam-6865	96	20	,	,	PUNCT
ejpam-6865	96	21	=	=	SYM
ejpam-6865	96	22	1	1	NUM
ejpam-6865	96	23	γ(n+	γ(n+	NUM
ejpam-6865	96	24	1	1	NUM
ejpam-6865	96	25	)	)	PUNCT
ejpam-6865	96	26	∫	∫	NOUN
ejpam-6865	97	1	x	x	X
ejpam-6865	97	2	a	a	DET
ejpam-6865	97	3	(	(	PUNCT
ejpam-6865	97	4	x−	x−	PROPN
ejpam-6865	97	5	t)nu(n+1)(t)dt	t)nu(n+1)(t)dt	PROPN
ejpam-6865	97	6	,	,	PUNCT
ejpam-6865	97	7	=	=	SYM
ejpam-6865	97	8	u(t)−	u(t)−	PROPN
ejpam-6865	98	1	u(a)−	u(a)−	ADV
ejpam-6865	98	2	(	(	PUNCT
ejpam-6865	98	3	t−	t−	PROPN
ejpam-6865	98	4	a)u′(a)−	a)u′(a)−	NOUN
ejpam-6865	98	5	·	·	PUNCT
ejpam-6865	98	6	·	·	PUNCT
ejpam-6865	98	7	·	·	PUNCT
ejpam-6865	98	8	−	−	PROPN
ejpam-6865	98	9	(	(	PUNCT
ejpam-6865	98	10	t−	t−	X
ejpam-6865	98	11	a)n−1	a)n−1	ADJ
ejpam-6865	98	12	(	(	PUNCT
ejpam-6865	98	13	n−	n−	NOUN
ejpam-6865	98	14	1	1	NUM
ejpam-6865	98	15	)	)	PUNCT
ejpam-6865	98	16	!	!	PUNCT
ejpam-6865	99	1	u(n−1)(a)−	u(n−1)(a)−	ADP
ejpam-6865	99	2	(	(	PUNCT
ejpam-6865	99	3	t−	t−	PROPN
ejpam-6865	99	4	a)n	a)n	NOUN
ejpam-6865	99	5	n	n	CCONJ
ejpam-6865	99	6	!	!	PUNCT
ejpam-6865	99	7	u(n)(a	u(n)(a	NOUN
ejpam-6865	99	8	)	)	PUNCT
ejpam-6865	99	9	.	.	PUNCT
ejpam-6865	100	1	3	3	X
ejpam-6865	100	2	.	.	X
ejpam-6865	100	3	the	the	DET
ejpam-6865	100	4	bernstein	bernstein	PROPN
ejpam-6865	100	5	polynomials	polynomial	NOUN
ejpam-6865	100	6	and	and	CCONJ
ejpam-6865	100	7	the	the	DET
ejpam-6865	100	8	abc	abc	PROPN
ejpam-6865	100	9	fds	fds	PROPN
ejpam-6865	100	10	definition	definition	NOUN
ejpam-6865	100	11	3	3	NUM
ejpam-6865	100	12	.	.	PUNCT
ejpam-6865	101	1	[	[	X
ejpam-6865	101	2	32	32	NUM
ejpam-6865	101	3	]	]	PUNCT
ejpam-6865	101	4	bernstein	bernstein	PROPN
ejpam-6865	101	5	polynomials	polynomials	PROPN
ejpam-6865	101	6	is	be	AUX
ejpam-6865	101	7	a	a	DET
ejpam-6865	101	8	linear	linear	ADJ
ejpam-6865	101	9	combination	combination	NOUN
ejpam-6865	101	10	of	of	ADP
ejpam-6865	101	11	(	(	PUNCT
ejpam-6865	101	12	l	l	NOUN
ejpam-6865	101	13	+	+	NOUN
ejpam-6865	101	14	1	1	X
ejpam-6865	101	15	)	)	PUNCT
ejpam-6865	101	16	terms	term	NOUN
ejpam-6865	101	17	which	which	PRON
ejpam-6865	101	18	is	be	AUX
ejpam-6865	101	19	defined	define	VERB
ejpam-6865	101	20	as	as	ADP
ejpam-6865	101	21	one	one	NUM
ejpam-6865	101	22	dimension	dimension	NOUN
ejpam-6865	101	23	of	of	ADP
ejpam-6865	101	24	degree	degree	NOUN
ejpam-6865	101	25	l	l	NOUN
ejpam-6865	101	26	on	on	ADP
ejpam-6865	101	27	[	[	X
ejpam-6865	101	28	0	0	NUM
ejpam-6865	101	29	,	,	PUNCT
ejpam-6865	101	30	1	1	NUM
ejpam-6865	101	31	]	]	PUNCT
ejpam-6865	101	32	as	as	ADP
ejpam-6865	101	33	s.	s.	PROPN
ejpam-6865	101	34	tamimi	tamimi	PROPN
ejpam-6865	101	35	,	,	PUNCT
ejpam-6865	101	36	a.	a.	PROPN
ejpam-6865	101	37	k.	k.	PROPN
ejpam-6865	101	38	alomari	alomari	PROPN
ejpam-6865	101	39	,	,	PUNCT
ejpam-6865	101	40	m.	m.	NOUN
ejpam-6865	101	41	alaroud	alaroud	PROPN
ejpam-6865	101	42	/	/	SYM
ejpam-6865	101	43	eur	eur	PROPN
ejpam-6865	101	44	.	.	PUNCT
ejpam-6865	102	1	j.	j.	PROPN
ejpam-6865	102	2	pure	pure	PROPN
ejpam-6865	102	3	appl	appl	PROPN
ejpam-6865	102	4	.	.	PROPN
ejpam-6865	102	5	math	math	PROPN
ejpam-6865	102	6	,	,	PUNCT
ejpam-6865	102	7	18	18	NUM
ejpam-6865	102	8	(	(	PUNCT
ejpam-6865	102	9	4	4	NUM
ejpam-6865	102	10	)	)	PUNCT
ejpam-6865	102	11	(	(	PUNCT
ejpam-6865	102	12	2025	2025	NUM
ejpam-6865	102	13	)	)	PUNCT
ejpam-6865	102	14	,	,	PUNCT
ejpam-6865	102	15	6865	6865	NUM
ejpam-6865	102	16	6	6	NUM
ejpam-6865	102	17	of	of	ADP
ejpam-6865	102	18	19	19	NUM
ejpam-6865	102	19	bv	bv	PROPN
ejpam-6865	102	20	,	,	PUNCT
ejpam-6865	102	21	l(z	l(z	PROPN
ejpam-6865	102	22	)	)	PUNCT
ejpam-6865	102	23	=	=	PRON
ejpam-6865	103	1	(	(	PUNCT
ejpam-6865	103	2	l	l	NOUN
ejpam-6865	103	3	v	v	NOUN
ejpam-6865	103	4	)	)	PUNCT
ejpam-6865	103	5	zi(1−	zi(1−	PROPN
ejpam-6865	103	6	z)l−v	z)l−v	NOUN
ejpam-6865	103	7	,	,	PUNCT
ejpam-6865	103	8	v	v	NOUN
ejpam-6865	103	9	=	=	SYM
ejpam-6865	103	10	0	0	NUM
ejpam-6865	103	11	,	,	PUNCT
ejpam-6865	103	12	...	...	PUNCT
ejpam-6865	103	13	,	,	PUNCT
ejpam-6865	103	14	l	l	NOUN
ejpam-6865	103	15	,	,	PUNCT
ejpam-6865	103	16	(	(	PUNCT
ejpam-6865	103	17	17	17	NUM
ejpam-6865	103	18	)	)	PUNCT
ejpam-6865	103	19	or	or	CCONJ
ejpam-6865	103	20	bv	bv	PROPN
ejpam-6865	103	21	,	,	PUNCT
ejpam-6865	103	22	l(z	l(z	PROPN
ejpam-6865	103	23	)	)	PUNCT
ejpam-6865	103	24	=	=	PRON
ejpam-6865	104	1	(	(	PUNCT
ejpam-6865	104	2	l	l	NOUN
ejpam-6865	104	3	v	v	X
ejpam-6865	104	4	)	)	PUNCT
ejpam-6865	104	5	zv	zv	NOUN
ejpam-6865	104	6	l−v∑	l−v∑	PROPN
ejpam-6865	104	7	s=0	s=0	PROPN
ejpam-6865	104	8	(	(	PUNCT
ejpam-6865	104	9	−1)s	−1)s	X
ejpam-6865	104	10	(	(	PUNCT
ejpam-6865	104	11	l	l	NOUN
ejpam-6865	104	12	−	−	PROPN
ejpam-6865	104	13	v	v	NOUN
ejpam-6865	104	14	s	s	PART
ejpam-6865	104	15	)	)	PUNCT
ejpam-6865	104	16	zs	zs	NOUN
ejpam-6865	104	17	=	=	SYM
ejpam-6865	104	18	l−v∑	l−v∑	PROPN
ejpam-6865	105	1	s=0	s=0	X
ejpam-6865	105	2	(	(	PUNCT
ejpam-6865	105	3	−1)s	−1)s	X
ejpam-6865	105	4	(	(	PUNCT
ejpam-6865	105	5	l	l	NOUN
ejpam-6865	105	6	v	v	NOUN
ejpam-6865	105	7	)	)	PUNCT
ejpam-6865	105	8	(	(	PUNCT
ejpam-6865	105	9	l	l	NOUN
ejpam-6865	105	10	−	−	PROPN
ejpam-6865	105	11	v	v	NOUN
ejpam-6865	105	12	s	s	NOUN
ejpam-6865	105	13	)	)	PUNCT
ejpam-6865	105	14	zs+v	zs+v	NOUN
ejpam-6865	105	15	,	,	PUNCT
ejpam-6865	105	16	v	v	NOUN
ejpam-6865	105	17	=	=	SYM
ejpam-6865	105	18	0	0	NUM
ejpam-6865	105	19	,	,	PUNCT
ejpam-6865	105	20	...	...	PUNCT
ejpam-6865	105	21	,	,	PUNCT
ejpam-6865	105	22	l.	l.	PROPN
ejpam-6865	105	23	theorem	theorem	VERB
ejpam-6865	105	24	4	4	NUM
ejpam-6865	105	25	.	.	PUNCT
ejpam-6865	106	1	the	the	DET
ejpam-6865	106	2	fd	fd	PROPN
ejpam-6865	106	3	with	with	ADP
ejpam-6865	106	4	generalized	generalized	ADJ
ejpam-6865	106	5	mittag	mittag	ADJ
ejpam-6865	106	6	-	-	PUNCT
ejpam-6865	106	7	leffler	leffler	NOUN
ejpam-6865	106	8	kernel	kernel	NOUN
ejpam-6865	106	9	for	for	ADP
ejpam-6865	106	10	bernstein	bernstein	PROPN
ejpam-6865	106	11	polynomial	polynomial	PROPN
ejpam-6865	106	12	using	use	VERB
ejpam-6865	106	13	for	for	ADP
ejpam-6865	106	14	n	n	X
ejpam-6865	106	15	<	<	X
ejpam-6865	106	16	α	α	PROPN
ejpam-6865	106	17	≤	≤	NUM
ejpam-6865	106	18	n+	n+	PUNCT
ejpam-6865	106	19	1	1	NUM
ejpam-6865	106	20	,	,	PUNCT
ejpam-6865	106	21	α1	α1	PROPN
ejpam-6865	106	22	=	=	SYM
ejpam-6865	106	23	α−	α−	ADP
ejpam-6865	106	24	n	n	PRON
ejpam-6865	106	25	where	where	SCONJ
ejpam-6865	106	26	n	n	X
ejpam-6865	106	27	∈	∈	PROPN
ejpam-6865	106	28	n0	n0	PROPN
ejpam-6865	106	29	,	,	PUNCT
ejpam-6865	106	30	µ	µ	X
ejpam-6865	106	31	>	>	X
ejpam-6865	106	32	0	0	NUM
ejpam-6865	106	33	and	and	CCONJ
ejpam-6865	106	34	γ	γ	PROPN
ejpam-6865	106	35	∈	∈	PROPN
ejpam-6865	106	36	n	n	PART
ejpam-6865	106	37	is	be	AUX
ejpam-6865	106	38	given	give	VERB
ejpam-6865	106	39	by	by	ADP
ejpam-6865	106	40	abc	abc	PROPN
ejpam-6865	106	41	0	0	PROPN
ejpam-6865	106	42	dα,µ,γbv	dα,µ,γbv	PROPN
ejpam-6865	106	43	,	,	PUNCT
ejpam-6865	106	44	l(z	l(z	X
ejpam-6865	106	45	)	)	PUNCT
ejpam-6865	106	46	=	=	PUNCT
ejpam-6865	107	1	l−v∑	l−v∑	NUM
ejpam-6865	107	2	s	s	X
ejpam-6865	107	3	=	=	X
ejpam-6865	107	4	dαe−v	dαe−v	PROPN
ejpam-6865	107	5	(	(	PUNCT
ejpam-6865	107	6	−1)s	−1)s	X
ejpam-6865	107	7	(	(	PUNCT
ejpam-6865	107	8	l	l	NOUN
ejpam-6865	107	9	v	v	NOUN
ejpam-6865	107	10	)	)	PUNCT
ejpam-6865	107	11	(	(	PUNCT
ejpam-6865	107	12	l	l	NOUN
ejpam-6865	107	13	−	−	PROPN
ejpam-6865	107	14	v	v	PROPN
ejpam-6865	107	15	s	s	NOUN
ejpam-6865	107	16	)	)	PUNCT
ejpam-6865	107	17	m(α1	m(α1	NOUN
ejpam-6865	107	18	)	)	PUNCT
ejpam-6865	107	19	1−	1−	NUM
ejpam-6865	107	20	α1	α1	PROPN
ejpam-6865	107	21	γ(s+	γ(s+	VERB
ejpam-6865	107	22	v+1)eγ	v+1)eγ	PROPN
ejpam-6865	107	23	α1,µ+s+v−n(λ	α1,µ+s+v−n(λ	PROPN
ejpam-6865	107	24	,	,	PUNCT
ejpam-6865	107	25	z	z	NOUN
ejpam-6865	107	26	)	)	PUNCT
ejpam-6865	107	27	.	.	PUNCT
ejpam-6865	108	1	(	(	PUNCT
ejpam-6865	108	2	18	18	NUM
ejpam-6865	108	3	)	)	PUNCT
ejpam-6865	108	4	proof	proof	NOUN
ejpam-6865	108	5	.	.	PUNCT
ejpam-6865	109	1	using	use	VERB
ejpam-6865	109	2	theorem	theorem	NOUN
ejpam-6865	109	3	1	1	NUM
ejpam-6865	109	4	,	,	PUNCT
ejpam-6865	109	5	we	we	PRON
ejpam-6865	109	6	have	have	VERB
ejpam-6865	109	7	abc	abc	PROPN
ejpam-6865	109	8	0	0	PROPN
ejpam-6865	109	9	dα,µ,γbv	dα,µ,γbv	PROPN
ejpam-6865	109	10	,	,	PUNCT
ejpam-6865	109	11	l(z	l(z	X
ejpam-6865	109	12	)	)	PUNCT
ejpam-6865	110	1	=	=	SYM
ejpam-6865	110	2	abc	abc	PROPN
ejpam-6865	110	3	0	0	X
ejpam-6865	110	4	dα,µ,γ	dα,µ,γ	PROPN
ejpam-6865	110	5	(	(	PUNCT
ejpam-6865	110	6	l−v∑	l−v∑	PROPN
ejpam-6865	110	7	s=0	s=0	X
ejpam-6865	110	8	(	(	PUNCT
ejpam-6865	110	9	−1)s	−1)s	X
ejpam-6865	110	10	(	(	PUNCT
ejpam-6865	110	11	l	l	NOUN
ejpam-6865	110	12	v	v	NOUN
ejpam-6865	110	13	)	)	PUNCT
ejpam-6865	110	14	(	(	PUNCT
ejpam-6865	110	15	l	l	NOUN
ejpam-6865	110	16	−	−	PROPN
ejpam-6865	110	17	v	v	NOUN
ejpam-6865	110	18	s	s	NOUN
ejpam-6865	110	19	)	)	PUNCT
ejpam-6865	110	20	zs+v	zs+v	NOUN
ejpam-6865	110	21	)	)	PUNCT
ejpam-6865	111	1	=	=	SYM
ejpam-6865	112	1	l−v∑	l−v∑	PROPN
ejpam-6865	112	2	s=0	s=0	X
ejpam-6865	112	3	(	(	PUNCT
ejpam-6865	112	4	−1)s	−1)s	X
ejpam-6865	112	5	(	(	PUNCT
ejpam-6865	112	6	l	l	NOUN
ejpam-6865	112	7	v	v	NOUN
ejpam-6865	112	8	)	)	PUNCT
ejpam-6865	112	9	(	(	PUNCT
ejpam-6865	112	10	l	l	NOUN
ejpam-6865	112	11	−	−	PROPN
ejpam-6865	112	12	v	v	PROPN
ejpam-6865	112	13	s	s	PART
ejpam-6865	112	14	)	)	PUNCT
ejpam-6865	112	15	abc	abc	PROPN
ejpam-6865	112	16	0	0	NUM
ejpam-6865	113	1	dα,µ,γzs+v	dα,µ,γzs+v	PROPN
ejpam-6865	113	2	=	=	PRON
ejpam-6865	114	1	l−v∑	l−v∑	NUM
ejpam-6865	114	2	s	s	X
ejpam-6865	114	3	=	=	X
ejpam-6865	114	4	dαe−v	dαe−v	PROPN
ejpam-6865	114	5	(	(	PUNCT
ejpam-6865	114	6	−1)s	−1)s	X
ejpam-6865	114	7	(	(	PUNCT
ejpam-6865	114	8	l	l	NOUN
ejpam-6865	114	9	v	v	NOUN
ejpam-6865	114	10	)	)	PUNCT
ejpam-6865	114	11	(	(	PUNCT
ejpam-6865	114	12	l	l	NOUN
ejpam-6865	114	13	−	−	PROPN
ejpam-6865	114	14	v	v	PROPN
ejpam-6865	114	15	s	s	NOUN
ejpam-6865	114	16	)	)	PUNCT
ejpam-6865	114	17	m(α1	m(α1	NOUN
ejpam-6865	114	18	)	)	PUNCT
ejpam-6865	114	19	1−	1−	NUM
ejpam-6865	114	20	α1	α1	PROPN
ejpam-6865	114	21	γ(s+	γ(s+	VERB
ejpam-6865	114	22	v	v	ADP
ejpam-6865	114	23	+	+	PROPN
ejpam-6865	114	24	1)eγ	1)eγ	PROPN
ejpam-6865	114	25	α1,µ+s+v−n(λ	α1,µ+s+v−n(λ	PROPN
ejpam-6865	114	26	,	,	PUNCT
ejpam-6865	114	27	z	z	NOUN
ejpam-6865	114	28	)	)	PUNCT
ejpam-6865	114	29	.	.	PUNCT
ejpam-6865	115	1	4	4	X
ejpam-6865	115	2	.	.	X
ejpam-6865	115	3	solutions	solution	NOUN
ejpam-6865	115	4	approach	approach	VERB
ejpam-6865	115	5	this	this	DET
ejpam-6865	115	6	section	section	NOUN
ejpam-6865	115	7	shows	show	VERB
ejpam-6865	115	8	the	the	DET
ejpam-6865	115	9	procedure	procedure	NOUN
ejpam-6865	115	10	for	for	ADP
ejpam-6865	115	11	solving	solve	VERB
ejpam-6865	115	12	fdes	fde	NOUN
ejpam-6865	115	13	with	with	ADP
ejpam-6865	115	14	a	a	DET
ejpam-6865	115	15	generalized	generalized	ADJ
ejpam-6865	115	16	mittag	mittag	ADJ
ejpam-6865	115	17	-	-	PUNCT
ejpam-6865	115	18	leffler	leffler	NOUN
ejpam-6865	115	19	kernel	kernel	NOUN
ejpam-6865	115	20	using	use	VERB
ejpam-6865	115	21	bernstein	bernstein	PROPN
ejpam-6865	115	22	polynomials	polynomial	NOUN
ejpam-6865	115	23	.	.	PUNCT
ejpam-6865	116	1	mainly	mainly	ADV
ejpam-6865	116	2	,	,	PUNCT
ejpam-6865	116	3	we	we	PRON
ejpam-6865	116	4	built	build	VERB
ejpam-6865	116	5	two	two	NUM
ejpam-6865	116	6	algorithms	algorithm	NOUN
ejpam-6865	116	7	,	,	PUNCT
ejpam-6865	116	8	the	the	DET
ejpam-6865	116	9	first	first	ADJ
ejpam-6865	116	10	one	one	NOUN
ejpam-6865	116	11	assumes	assume	VERB
ejpam-6865	116	12	the	the	DET
ejpam-6865	116	13	solution	solution	NOUN
ejpam-6865	116	14	is	be	AUX
ejpam-6865	116	15	a	a	DET
ejpam-6865	116	16	linear	linear	ADJ
ejpam-6865	116	17	combination	combination	NOUN
ejpam-6865	116	18	of	of	ADP
ejpam-6865	116	19	bernstein	bernstein	PROPN
ejpam-6865	116	20	polynomials	polynomials	PROPN
ejpam-6865	116	21	.	.	PUNCT
ejpam-6865	117	1	in	in	ADP
ejpam-6865	117	2	contrast	contrast	NOUN
ejpam-6865	117	3	,	,	PUNCT
ejpam-6865	117	4	the	the	DET
ejpam-6865	117	5	second	second	ADJ
ejpam-6865	117	6	approach	approach	NOUN
ejpam-6865	117	7	assumes	assume	VERB
ejpam-6865	117	8	that	that	SCONJ
ejpam-6865	117	9	the	the	DET
ejpam-6865	117	10	fd	fd	PROPN
ejpam-6865	117	11	is	be	AUX
ejpam-6865	117	12	a	a	DET
ejpam-6865	117	13	linear	linear	ADJ
ejpam-6865	117	14	combination	combination	NOUN
ejpam-6865	117	15	.	.	PUNCT
ejpam-6865	118	1	consider	consider	VERB
ejpam-6865	118	2	the	the	DET
ejpam-6865	118	3	fde	fde	PROPN
ejpam-6865	118	4	abc	abc	PROPN
ejpam-6865	118	5	a	a	DET
ejpam-6865	118	6	dα,µ,γ	dα,µ,γ	PROPN
ejpam-6865	118	7	t	t	PROPN
ejpam-6865	118	8	u(t	u(t	PROPN
ejpam-6865	118	9	)	)	PUNCT
ejpam-6865	118	10	=	=	SYM
ejpam-6865	118	11	f(u(t	f(u(t	PROPN
ejpam-6865	118	12	)	)	PUNCT
ejpam-6865	118	13	,	,	PUNCT
ejpam-6865	118	14	t	t	PROPN
ejpam-6865	118	15	)	)	PUNCT
ejpam-6865	118	16	,	,	PUNCT
ejpam-6865	118	17	a	a	DET
ejpam-6865	118	18	≤	≤	NUM
ejpam-6865	118	19	t	t	NOUN
ejpam-6865	118	20	≤	≤	NUM
ejpam-6865	118	21	b	b	PROPN
ejpam-6865	118	22	,	,	PUNCT
ejpam-6865	118	23	(	(	PUNCT
ejpam-6865	118	24	19	19	NUM
ejpam-6865	118	25	)	)	PUNCT
ejpam-6865	118	26	with	with	ADP
ejpam-6865	118	27	initial	initial	ADJ
ejpam-6865	118	28	condition	condition	NOUN
ejpam-6865	118	29	u(a	u(a	NOUN
ejpam-6865	118	30	)	)	PUNCT
ejpam-6865	118	31	=	=	SYM
ejpam-6865	119	1	c	c	X
ejpam-6865	119	2	,	,	PUNCT
ejpam-6865	119	3	(	(	PUNCT
ejpam-6865	119	4	20	20	NUM
ejpam-6865	119	5	)	)	PUNCT
ejpam-6865	119	6	s.	s.	PROPN
ejpam-6865	119	7	tamimi	tamimi	PROPN
ejpam-6865	119	8	,	,	PUNCT
ejpam-6865	119	9	a.	a.	PROPN
ejpam-6865	119	10	k.	k.	PROPN
ejpam-6865	119	11	alomari	alomari	PROPN
ejpam-6865	119	12	,	,	PUNCT
ejpam-6865	119	13	m.	m.	NOUN
ejpam-6865	119	14	alaroud	alaroud	PROPN
ejpam-6865	119	15	/	/	SYM
ejpam-6865	119	16	eur	eur	PROPN
ejpam-6865	119	17	.	.	PUNCT
ejpam-6865	120	1	j.	j.	PROPN
ejpam-6865	120	2	pure	pure	PROPN
ejpam-6865	120	3	appl	appl	PROPN
ejpam-6865	120	4	.	.	PROPN
ejpam-6865	120	5	math	math	PROPN
ejpam-6865	120	6	,	,	PUNCT
ejpam-6865	120	7	18	18	NUM
ejpam-6865	120	8	(	(	PUNCT
ejpam-6865	120	9	4	4	NUM
ejpam-6865	120	10	)	)	PUNCT
ejpam-6865	120	11	(	(	PUNCT
ejpam-6865	120	12	2025	2025	NUM
ejpam-6865	120	13	)	)	PUNCT
ejpam-6865	120	14	,	,	PUNCT
ejpam-6865	120	15	6865	6865	NUM
ejpam-6865	120	16	7	7	NUM
ejpam-6865	120	17	of	of	ADP
ejpam-6865	120	18	19	19	NUM
ejpam-6865	120	19	where	where	SCONJ
ejpam-6865	120	20	n	n	ADP
ejpam-6865	120	21	<	<	X
ejpam-6865	120	22	α	α	X
ejpam-6865	120	23	≤	≤	NUM
ejpam-6865	120	24	n+	n+	PUNCT
ejpam-6865	120	25	1	1	NUM
ejpam-6865	120	26	,	,	PUNCT
ejpam-6865	120	27	µ	µ	X
ejpam-6865	120	28	>	>	SYM
ejpam-6865	120	29	0	0	NUM
ejpam-6865	120	30	and	and	CCONJ
ejpam-6865	120	31	γ	γ	PROPN
ejpam-6865	120	32	∈	∈	PROPN
ejpam-6865	120	33	n.	n.	PROPN
ejpam-6865	120	34	approach	approach	NOUN
ejpam-6865	120	35	1	1	NUM
ejpam-6865	120	36	.	.	PUNCT
ejpam-6865	121	1	this	this	DET
ejpam-6865	121	2	approach	approach	NOUN
ejpam-6865	121	3	was	be	AUX
ejpam-6865	121	4	introduced	introduce	VERB
ejpam-6865	121	5	in	in	ADP
ejpam-6865	121	6	[	[	X
ejpam-6865	121	7	22	22	NUM
ejpam-6865	121	8	]	]	PUNCT
ejpam-6865	121	9	,	,	PUNCT
ejpam-6865	121	10	it	it	PRON
ejpam-6865	121	11	based	base	VERB
ejpam-6865	121	12	on	on	ADP
ejpam-6865	121	13	the	the	DET
ejpam-6865	121	14	following	follow	VERB
ejpam-6865	121	15	steps	step	NOUN
ejpam-6865	121	16	.	.	PUNCT
ejpam-6865	122	1	u(t	u(t	NOUN
ejpam-6865	122	2	)	)	PUNCT
ejpam-6865	122	3	=	=	PUNCT
ejpam-6865	122	4	l∑	l∑	ADP
ejpam-6865	122	5	v=0	v=0	PUNCT
ejpam-6865	122	6	cvbv	cvbv	PROPN
ejpam-6865	122	7	,	,	PUNCT
ejpam-6865	122	8	l(t	l(t	PROPN
ejpam-6865	122	9	)	)	PUNCT
ejpam-6865	122	10	.	.	PUNCT
ejpam-6865	123	1	(	(	PUNCT
ejpam-6865	123	2	21	21	NUM
ejpam-6865	123	3	)	)	PUNCT
ejpam-6865	123	4	applying	apply	VERB
ejpam-6865	123	5	the	the	DET
ejpam-6865	123	6	abc	abc	PROPN
ejpam-6865	123	7	-	-	PUNCT
ejpam-6865	123	8	fd	fd	PROPN
ejpam-6865	123	9	on	on	ADP
ejpam-6865	123	10	both	both	DET
ejpam-6865	123	11	sides	side	NOUN
ejpam-6865	123	12	of	of	ADP
ejpam-6865	123	13	equation	equation	NOUN
ejpam-6865	123	14	(	(	PUNCT
ejpam-6865	123	15	19	19	NUM
ejpam-6865	123	16	)	)	PUNCT
ejpam-6865	123	17	to	to	PART
ejpam-6865	123	18	get	get	VERB
ejpam-6865	123	19	(	(	PUNCT
ejpam-6865	123	20	abc	abc	PROPN
ejpam-6865	123	21	a	a	DET
ejpam-6865	123	22	dα,µ,γu(t	dα,µ,γu(t	NOUN
ejpam-6865	123	23	)	)	PUNCT
ejpam-6865	123	24	)	)	PUNCT
ejpam-6865	124	1	=	=	PUNCT
ejpam-6865	125	1	l∑	l∑	ADP
ejpam-6865	125	2	v=0	v=0	X
ejpam-6865	125	3	cv	cv	PROPN
ejpam-6865	125	4	l−v∑	l−v∑	PROPN
ejpam-6865	125	5	s=0	s=0	PROPN
ejpam-6865	125	6	(	(	PUNCT
ejpam-6865	125	7	−1)s	−1)s	X
ejpam-6865	125	8	(	(	PUNCT
ejpam-6865	125	9	l	l	NOUN
ejpam-6865	125	10	v	v	NOUN
ejpam-6865	125	11	)	)	PUNCT
ejpam-6865	125	12	(	(	PUNCT
ejpam-6865	125	13	l	l	NOUN
ejpam-6865	125	14	−	−	PROPN
ejpam-6865	125	15	v	v	NOUN
ejpam-6865	125	16	s	s	NOUN
ejpam-6865	125	17	)	)	PUNCT
ejpam-6865	125	18	(	(	PUNCT
ejpam-6865	125	19	abc	abc	PROPN
ejpam-6865	125	20	a	a	DET
ejpam-6865	125	21	dα,µ,γts+v	dα,µ,γts+v	PROPN
ejpam-6865	125	22	)	)	PUNCT
ejpam-6865	125	23	.	.	PUNCT
ejpam-6865	126	1	(	(	PUNCT
ejpam-6865	126	2	22	22	NUM
ejpam-6865	126	3	)	)	PUNCT
ejpam-6865	126	4	according	accord	VERB
ejpam-6865	126	5	to	to	ADP
ejpam-6865	126	6	theorem	theorem	NOUN
ejpam-6865	126	7	(	(	PUNCT
ejpam-6865	126	8	3	3	NUM
ejpam-6865	126	9	)	)	PUNCT
ejpam-6865	126	10	,	,	PUNCT
ejpam-6865	126	11	we	we	PRON
ejpam-6865	126	12	have	have	VERB
ejpam-6865	126	13	(	(	PUNCT
ejpam-6865	126	14	abc	abc	PROPN
ejpam-6865	126	15	a	a	DET
ejpam-6865	126	16	dα,µ,γu(t	dα,µ,γu(t	NOUN
ejpam-6865	126	17	)	)	PUNCT
ejpam-6865	126	18	)	)	PUNCT
ejpam-6865	127	1	=	=	PUNCT
ejpam-6865	128	1	l∑	l∑	ADP
ejpam-6865	128	2	v=0	v=0	X
ejpam-6865	129	1	cv	cv	NOUN
ejpam-6865	129	2	l−v∑	l−v∑	PROPN
ejpam-6865	129	3	s	s	PROPN
ejpam-6865	129	4	=	=	X
ejpam-6865	129	5	dαe−v	dαe−v	PROPN
ejpam-6865	129	6	(	(	PUNCT
ejpam-6865	129	7	−1)s	−1)s	X
ejpam-6865	129	8	(	(	PUNCT
ejpam-6865	129	9	l	l	NOUN
ejpam-6865	129	10	v	v	NOUN
ejpam-6865	129	11	)	)	PUNCT
ejpam-6865	129	12	(	(	PUNCT
ejpam-6865	129	13	l	l	NOUN
ejpam-6865	129	14	−	−	PROPN
ejpam-6865	129	15	v	v	PROPN
ejpam-6865	129	16	s	s	NOUN
ejpam-6865	129	17	)	)	PUNCT
ejpam-6865	129	18	×	×	NOUN
ejpam-6865	129	19	m(α1	m(α1	NOUN
ejpam-6865	129	20	)	)	PUNCT
ejpam-6865	129	21	1−	1−	NUM
ejpam-6865	129	22	α1	α1	PROPN
ejpam-6865	129	23	γ(s+	γ(s+	VERB
ejpam-6865	129	24	v	v	ADP
ejpam-6865	129	25	+	+	NOUN
ejpam-6865	129	26	1)eγ	1)eγ	PROPN
ejpam-6865	129	27	α1,µ+s+v−n(λ	α1,µ+s+v−n(λ	PROPN
ejpam-6865	129	28	,	,	PUNCT
ejpam-6865	129	29	t	t	PROPN
ejpam-6865	129	30	)	)	PUNCT
ejpam-6865	129	31	,	,	PUNCT
ejpam-6865	129	32	(	(	PUNCT
ejpam-6865	129	33	23	23	NUM
ejpam-6865	129	34	)	)	PUNCT
ejpam-6865	129	35	then	then	ADV
ejpam-6865	129	36	equation	equation	NOUN
ejpam-6865	129	37	(	(	PUNCT
ejpam-6865	129	38	19	19	NUM
ejpam-6865	129	39	)	)	PUNCT
ejpam-6865	129	40	gives	give	VERB
ejpam-6865	129	41	l∑	l∑	PUNCT
ejpam-6865	129	42	v=0	v=0	NOUN
ejpam-6865	129	43	cv	cv	PROPN
ejpam-6865	129	44	0	0	PUNCT
ejpam-6865	130	1	abcdα,µ,γ	abcdα,µ,γ	PROPN
ejpam-6865	130	2	t	t	PROPN
ejpam-6865	130	3	bv	bv	PROPN
ejpam-6865	130	4	,	,	PUNCT
ejpam-6865	130	5	l(t	l(t	PROPN
ejpam-6865	130	6	)	)	PUNCT
ejpam-6865	131	1	=	=	SYM
ejpam-6865	131	2	f	f	X
ejpam-6865	131	3	(	(	PUNCT
ejpam-6865	131	4	l∑	l∑	ADP
ejpam-6865	131	5	v=0	v=0	VERB
ejpam-6865	131	6	cvbv	cvbv	PROPN
ejpam-6865	131	7	,	,	PUNCT
ejpam-6865	131	8	l(t	l(t	PROPN
ejpam-6865	131	9	)	)	PUNCT
ejpam-6865	131	10	,	,	PUNCT
ejpam-6865	131	11	t	t	PROPN
ejpam-6865	131	12	)	)	PUNCT
ejpam-6865	131	13	l∑	l∑	PUNCT
ejpam-6865	132	1	v=0	v=0	VERB
ejpam-6865	132	2	cv	cv	NOUN
ejpam-6865	132	3	l−v∑	l−v∑	PROPN
ejpam-6865	132	4	s	s	PROPN
ejpam-6865	132	5	=	=	X
ejpam-6865	132	6	dαe−v	dαe−v	PROPN
ejpam-6865	132	7	(	(	PUNCT
ejpam-6865	132	8	−1)s	−1)s	X
ejpam-6865	132	9	(	(	PUNCT
ejpam-6865	132	10	l	l	NOUN
ejpam-6865	132	11	v	v	NOUN
ejpam-6865	132	12	)	)	PUNCT
ejpam-6865	132	13	(	(	PUNCT
ejpam-6865	132	14	l	l	NOUN
ejpam-6865	132	15	−	−	PROPN
ejpam-6865	132	16	v	v	PROPN
ejpam-6865	132	17	s	s	NOUN
ejpam-6865	132	18	)	)	PUNCT
ejpam-6865	132	19	m(α1	m(α1	NOUN
ejpam-6865	132	20	)	)	PUNCT
ejpam-6865	132	21	1−	1−	NUM
ejpam-6865	132	22	α1	α1	PROPN
ejpam-6865	132	23	γ(s+	γ(s+	VERB
ejpam-6865	132	24	v	v	ADP
ejpam-6865	132	25	+	+	NOUN
ejpam-6865	132	26	1)×	1)×	NUM
ejpam-6865	132	27	eγ	eγ	ADP
ejpam-6865	132	28	α1,µ+s+v−n(λ	α1,µ+s+v−n(λ	PROPN
ejpam-6865	132	29	,	,	PUNCT
ejpam-6865	132	30	t	t	PROPN
ejpam-6865	132	31	)	)	PUNCT
ejpam-6865	133	1	=	=	SYM
ejpam-6865	133	2	f	f	X
ejpam-6865	133	3	(	(	PUNCT
ejpam-6865	133	4	l∑	l∑	ADP
ejpam-6865	133	5	v=0	v=0	VERB
ejpam-6865	133	6	cvbv	cvbv	PROPN
ejpam-6865	133	7	,	,	PUNCT
ejpam-6865	133	8	l(t	l(t	PROPN
ejpam-6865	133	9	)	)	PUNCT
ejpam-6865	133	10	,	,	PUNCT
ejpam-6865	133	11	t	t	PROPN
ejpam-6865	133	12	)	)	PUNCT
ejpam-6865	133	13	,	,	PUNCT
ejpam-6865	133	14	(	(	PUNCT
ejpam-6865	133	15	24	24	NUM
ejpam-6865	133	16	)	)	PUNCT
ejpam-6865	133	17	and	and	CCONJ
ejpam-6865	133	18	the	the	DET
ejpam-6865	133	19	initial	initial	ADJ
ejpam-6865	133	20	condition	condition	NOUN
ejpam-6865	133	21	gives	give	VERB
ejpam-6865	133	22	l∑	l∑	NOUN
ejpam-6865	133	23	v=0	v=0	ADP
ejpam-6865	133	24	cvbv	cvbv	PROPN
ejpam-6865	133	25	,	,	PUNCT
ejpam-6865	133	26	l(a	l(a	PROPN
ejpam-6865	133	27	)	)	PUNCT
ejpam-6865	133	28	=	=	SYM
ejpam-6865	133	29	c.	c.	NOUN
ejpam-6865	133	30	(	(	PUNCT
ejpam-6865	133	31	25	25	NUM
ejpam-6865	133	32	)	)	PUNCT
ejpam-6865	133	33	now	now	ADV
ejpam-6865	133	34	,	,	PUNCT
ejpam-6865	133	35	substitute	substitute	PROPN
ejpam-6865	133	36	t	t	NOUN
ejpam-6865	133	37	=	=	SYM
ejpam-6865	133	38	tv	tv	NOUN
ejpam-6865	133	39	in	in	ADP
ejpam-6865	133	40	equation	equation	NOUN
ejpam-6865	133	41	(	(	PUNCT
ejpam-6865	133	42	24	24	NUM
ejpam-6865	133	43	)	)	PUNCT
ejpam-6865	133	44	for	for	ADP
ejpam-6865	133	45	v	v	NOUN
ejpam-6865	133	46	=	=	SYM
ejpam-6865	133	47	1	1	NUM
ejpam-6865	133	48	,	,	PUNCT
ejpam-6865	133	49	2	2	NUM
ejpam-6865	133	50	,	,	PUNCT
ejpam-6865	133	51	..	..	PUNCT
ejpam-6865	133	52	,	,	PUNCT
ejpam-6865	133	53	l	l	NOUN
ejpam-6865	133	54	,	,	PUNCT
ejpam-6865	133	55	then	then	ADV
ejpam-6865	133	56	we	we	PRON
ejpam-6865	133	57	have	have	VERB
ejpam-6865	133	58	l	l	NOUN
ejpam-6865	133	59	nonlinear	nonlinear	ADJ
ejpam-6865	133	60	equations	equation	NOUN
ejpam-6865	133	61	and	and	CCONJ
ejpam-6865	133	62	using	use	VERB
ejpam-6865	133	63	equation	equation	NOUN
ejpam-6865	133	64	(	(	PUNCT
ejpam-6865	133	65	25	25	NUM
ejpam-6865	133	66	)	)	PUNCT
ejpam-6865	133	67	,	,	PUNCT
ejpam-6865	133	68	then	then	ADV
ejpam-6865	133	69	(	(	PUNCT
ejpam-6865	133	70	l	l	NOUN
ejpam-6865	133	71	+	+	NOUN
ejpam-6865	133	72	1	1	NUM
ejpam-6865	133	73	)	)	PUNCT
ejpam-6865	133	74	of	of	ADP
ejpam-6865	133	75	nonlinear	nonlinear	ADJ
ejpam-6865	133	76	equations	equation	NOUN
ejpam-6865	133	77	are	be	AUX
ejpam-6865	133	78	generated	generate	VERB
ejpam-6865	133	79	.	.	PUNCT
ejpam-6865	134	1	by	by	ADP
ejpam-6865	134	2	solving	solve	VERB
ejpam-6865	134	3	those	those	DET
ejpam-6865	134	4	equations	equation	NOUN
ejpam-6865	134	5	,	,	PUNCT
ejpam-6865	134	6	we	we	PRON
ejpam-6865	134	7	determined	determine	VERB
ejpam-6865	134	8	the	the	DET
ejpam-6865	134	9	cv	cv	PROPN
ejpam-6865	134	10	for	for	ADP
ejpam-6865	134	11	v	v	NOUN
ejpam-6865	134	12	=	=	SYM
ejpam-6865	134	13	0	0	NUM
ejpam-6865	134	14	,	,	PUNCT
ejpam-6865	134	15	1	1	NUM
ejpam-6865	134	16	,	,	PUNCT
ejpam-6865	134	17	...	...	PUNCT
ejpam-6865	134	18	,	,	PUNCT
ejpam-6865	134	19	l.	l.	PROPN
ejpam-6865	134	20	as	as	ADP
ejpam-6865	134	21	a	a	DET
ejpam-6865	134	22	result	result	NOUN
ejpam-6865	134	23	,	,	PUNCT
ejpam-6865	134	24	the	the	DET
ejpam-6865	134	25	approximate	approximate	ADJ
ejpam-6865	134	26	solution	solution	NOUN
ejpam-6865	134	27	u(t	u(t	NOUN
ejpam-6865	134	28	)	)	PUNCT
ejpam-6865	134	29	can	can	AUX
ejpam-6865	134	30	be	be	AUX
ejpam-6865	134	31	calculated	calculate	VERB
ejpam-6865	134	32	.	.	PUNCT
ejpam-6865	135	1	approach	approach	NOUN
ejpam-6865	135	2	2	2	NUM
ejpam-6865	135	3	.	.	PUNCT
ejpam-6865	136	1	assume	assume	VERB
ejpam-6865	136	2	abc	abc	PROPN
ejpam-6865	136	3	a	a	DET
ejpam-6865	136	4	dα,µ,γ	dα,µ,γ	PROPN
ejpam-6865	136	5	t	t	PROPN
ejpam-6865	136	6	u(t	u(t	PROPN
ejpam-6865	136	7	)	)	PUNCT
ejpam-6865	136	8	=	=	PUNCT
ejpam-6865	136	9	l∑	l∑	ADP
ejpam-6865	136	10	v=0	v=0	PUNCT
ejpam-6865	136	11	cvbv	cvbv	PROPN
ejpam-6865	136	12	,	,	PUNCT
ejpam-6865	136	13	l(t	l(t	PROPN
ejpam-6865	136	14	)	)	PUNCT
ejpam-6865	136	15	.	.	PUNCT
ejpam-6865	137	1	(	(	PUNCT
ejpam-6865	137	2	26	26	NUM
ejpam-6865	137	3	)	)	PUNCT
ejpam-6865	137	4	s.	s.	PROPN
ejpam-6865	137	5	tamimi	tamimi	PROPN
ejpam-6865	137	6	,	,	PUNCT
ejpam-6865	137	7	a.	a.	PROPN
ejpam-6865	137	8	k.	k.	PROPN
ejpam-6865	137	9	alomari	alomari	PROPN
ejpam-6865	137	10	,	,	PUNCT
ejpam-6865	137	11	m.	m.	NOUN
ejpam-6865	137	12	alaroud	alaroud	PROPN
ejpam-6865	137	13	/	/	SYM
ejpam-6865	137	14	eur	eur	PROPN
ejpam-6865	137	15	.	.	PUNCT
ejpam-6865	138	1	j.	j.	PROPN
ejpam-6865	138	2	pure	pure	PROPN
ejpam-6865	138	3	appl	appl	PROPN
ejpam-6865	138	4	.	.	PROPN
ejpam-6865	138	5	math	math	PROPN
ejpam-6865	138	6	,	,	PUNCT
ejpam-6865	138	7	18	18	NUM
ejpam-6865	138	8	(	(	PUNCT
ejpam-6865	138	9	4	4	NUM
ejpam-6865	138	10	)	)	PUNCT
ejpam-6865	138	11	(	(	PUNCT
ejpam-6865	138	12	2025	2025	NUM
ejpam-6865	138	13	)	)	PUNCT
ejpam-6865	138	14	,	,	PUNCT
ejpam-6865	138	15	6865	6865	NUM
ejpam-6865	138	16	8	8	NUM
ejpam-6865	138	17	of	of	ADP
ejpam-6865	138	18	19	19	NUM
ejpam-6865	138	19	then	then	ADV
ejpam-6865	138	20	,	,	PUNCT
ejpam-6865	138	21	apply	apply	VERB
ejpam-6865	138	22	the	the	DET
ejpam-6865	138	23	abc	abc	PROPN
ejpam-6865	138	24	fractional	fractional	ADJ
ejpam-6865	138	25	integral	integral	ADJ
ejpam-6865	138	26	operator	operator	NOUN
ejpam-6865	138	27	on	on	ADP
ejpam-6865	138	28	equation	equation	NOUN
ejpam-6865	138	29	(	(	PUNCT
ejpam-6865	138	30	26	26	NUM
ejpam-6865	138	31	)	)	PUNCT
ejpam-6865	138	32	to	to	PART
ejpam-6865	138	33	get	get	VERB
ejpam-6865	138	34	ab	ab	PROPN
ejpam-6865	138	35	a	a	DET
ejpam-6865	138	36	iα,µ,γabc	iα,µ,γabc	PROPN
ejpam-6865	138	37	a	a	DET
ejpam-6865	138	38	dα,µ,γ	dα,µ,γ	PROPN
ejpam-6865	138	39	t	t	PROPN
ejpam-6865	138	40	u(t	u(t	PROPN
ejpam-6865	138	41	)	)	PUNCT
ejpam-6865	138	42	=	=	PUNCT
ejpam-6865	139	1	l∑	l∑	ADP
ejpam-6865	139	2	v=0	v=0	X
ejpam-6865	139	3	cv	cv	PROPN
ejpam-6865	139	4	ab	ab	PROPN
ejpam-6865	139	5	a	a	DET
ejpam-6865	139	6	iα,µ,γbv	iα,µ,γbv	PROPN
ejpam-6865	139	7	,	,	PUNCT
ejpam-6865	139	8	l(t	l(t	PROPN
ejpam-6865	139	9	)	)	PUNCT
ejpam-6865	139	10	.	.	PUNCT
ejpam-6865	140	1	(	(	PUNCT
ejpam-6865	140	2	27	27	NUM
ejpam-6865	140	3	)	)	PUNCT
ejpam-6865	140	4	using	use	VERB
ejpam-6865	140	5	definition	definition	NOUN
ejpam-6865	140	6	(	(	PUNCT
ejpam-6865	140	7	2	2	NUM
ejpam-6865	140	8	)	)	PUNCT
ejpam-6865	140	9	,	,	PUNCT
ejpam-6865	140	10	theorem	theorem	X
ejpam-6865	140	11	(	(	PUNCT
ejpam-6865	140	12	2	2	NUM
ejpam-6865	140	13	)	)	PUNCT
ejpam-6865	140	14	,	,	PUNCT
ejpam-6865	140	15	and	and	CCONJ
ejpam-6865	140	16	equation	equation	NOUN
ejpam-6865	140	17	(	(	PUNCT
ejpam-6865	140	18	13	13	NUM
ejpam-6865	140	19	)	)	PUNCT
ejpam-6865	140	20	,	,	PUNCT
ejpam-6865	140	21	we	we	PRON
ejpam-6865	140	22	have	have	VERB
ejpam-6865	140	23	u(t)−	u(t)−	PROPN
ejpam-6865	140	24	u(a)−	u(a)−	ADV
ejpam-6865	140	25	·	·	PUNCT
ejpam-6865	140	26	·	·	PUNCT
ejpam-6865	140	27	·	·	PUNCT
ejpam-6865	141	1	−	−	PUNCT
ejpam-6865	141	2	(	(	PUNCT
ejpam-6865	141	3	t−	t−	PROPN
ejpam-6865	141	4	a)n	a)n	NOUN
ejpam-6865	141	5	n	n	CCONJ
ejpam-6865	141	6	!	!	PUNCT
ejpam-6865	141	7	u(n)(a	u(n)(a	NUM
ejpam-6865	141	8	)	)	PUNCT
ejpam-6865	141	9	=	=	SYM
ejpam-6865	142	1	l∑	l∑	ADP
ejpam-6865	142	2	v=0	v=0	PUNCT
ejpam-6865	142	3	cv	cv	PROPN
ejpam-6865	142	4	l−v∑	l−v∑	PROPN
ejpam-6865	142	5	s=0	s=0	PROPN
ejpam-6865	142	6	(	(	PUNCT
ejpam-6865	142	7	−1)s	−1)s	X
ejpam-6865	142	8	(	(	PUNCT
ejpam-6865	142	9	l	l	NOUN
ejpam-6865	142	10	v	v	NOUN
ejpam-6865	142	11	)	)	PUNCT
ejpam-6865	142	12	(	(	PUNCT
ejpam-6865	142	13	l	l	NOUN
ejpam-6865	142	14	−	−	PROPN
ejpam-6865	142	15	v	v	NOUN
ejpam-6865	142	16	s	s	PART
ejpam-6865	142	17	)	)	PUNCT
ejpam-6865	142	18	γ∑	γ∑	ADP
ejpam-6865	143	1	r=0	r=0	PROPN
ejpam-6865	143	2	(	(	PUNCT
ejpam-6865	143	3	γ	γ	NOUN
ejpam-6865	143	4	r	r	NOUN
ejpam-6865	143	5	)	)	PUNCT
ejpam-6865	143	6	αr	αr	PROPN
ejpam-6865	143	7	(	(	PUNCT
ejpam-6865	143	8	1−	1−	NUM
ejpam-6865	143	9	α)r−1	α)r−1	NUM
ejpam-6865	143	10	×	×	NOUN
ejpam-6865	143	11	rl	rl	VERB
ejpam-6865	143	12	a	a	DET
ejpam-6865	143	13	iαr−µ+n+1ts+v	iαr−µ+n+1ts+v	PROPN
ejpam-6865	143	14	,	,	PUNCT
ejpam-6865	143	15	(	(	PUNCT
ejpam-6865	143	16	28	28	NUM
ejpam-6865	143	17	)	)	PUNCT
ejpam-6865	143	18	where	where	SCONJ
ejpam-6865	143	19	rl	rl	ADP
ejpam-6865	143	20	a	a	DET
ejpam-6865	143	21	iαr−µ+n+1	iαr−µ+n+1	NOUN
ejpam-6865	143	22	is	be	AUX
ejpam-6865	143	23	the	the	DET
ejpam-6865	143	24	left	leave	VERB
ejpam-6865	143	25	rl	rl	ADP
ejpam-6865	143	26	fractional	fractional	ADJ
ejpam-6865	143	27	integral	integral	ADJ
ejpam-6865	143	28	of	of	ADP
ejpam-6865	143	29	order	order	NOUN
ejpam-6865	143	30	αr−µ+n+1	αr−µ+n+1	NUM
ejpam-6865	143	31	which	which	PRON
ejpam-6865	143	32	is	be	AUX
ejpam-6865	143	33	defined	define	VERB
ejpam-6865	143	34	in	in	ADP
ejpam-6865	143	35	equation	equation	NOUN
ejpam-6865	143	36	(	(	PUNCT
ejpam-6865	143	37	1	1	NUM
ejpam-6865	143	38	)	)	PUNCT
ejpam-6865	143	39	.	.	PUNCT
ejpam-6865	144	1	we	we	PRON
ejpam-6865	144	2	assume	assume	VERB
ejpam-6865	144	3	abc	abc	PROPN
ejpam-6865	144	4	0	0	PROPN
ejpam-6865	144	5	dα,µ,γ	dα,µ,γ	PROPN
ejpam-6865	144	6	t	t	PROPN
ejpam-6865	144	7	u(t	u(t	PROPN
ejpam-6865	144	8	)	)	PUNCT
ejpam-6865	144	9	=	=	PUNCT
ejpam-6865	145	1	l∑	l∑	ADP
ejpam-6865	145	2	v=0	v=0	PUNCT
ejpam-6865	145	3	cvbv	cvbv	PROPN
ejpam-6865	145	4	,	,	PUNCT
ejpam-6865	145	5	l(t	l(t	PROPN
ejpam-6865	145	6	)	)	PUNCT
ejpam-6865	145	7	,	,	PUNCT
ejpam-6865	145	8	(	(	PUNCT
ejpam-6865	145	9	29	29	NUM
ejpam-6865	145	10	)	)	PUNCT
ejpam-6865	145	11	then	then	ADV
ejpam-6865	145	12	(	(	PUNCT
ejpam-6865	145	13	19	19	NUM
ejpam-6865	145	14	)	)	PUNCT
ejpam-6865	145	15	gives	give	VERB
ejpam-6865	145	16	l∑	l∑	NOUN
ejpam-6865	145	17	v=0	v=0	ADP
ejpam-6865	145	18	cvbv	cvbv	PROPN
ejpam-6865	145	19	,	,	PUNCT
ejpam-6865	145	20	l(t	l(t	PROPN
ejpam-6865	145	21	)	)	PUNCT
ejpam-6865	146	1	=	=	SYM
ejpam-6865	146	2	f	f	X
ejpam-6865	146	3	(	(	PUNCT
ejpam-6865	146	4	l∑	l∑	NOUN
ejpam-6865	146	5	v=0	v=0	PROPN
ejpam-6865	146	6	cv	cv	PROPN
ejpam-6865	146	7	abiα,µ,γbv	abiα,µ,γbv	NOUN
ejpam-6865	146	8	,	,	PUNCT
ejpam-6865	146	9	l(t	l(t	PROPN
ejpam-6865	146	10	)	)	PUNCT
ejpam-6865	146	11	+	+	CCONJ
ejpam-6865	146	12	u(a	u(a	NOUN
ejpam-6865	146	13	)	)	PUNCT
ejpam-6865	146	14	+	+	CCONJ
ejpam-6865	146	15	·	·	PUNCT
ejpam-6865	146	16	·	·	PUNCT
ejpam-6865	146	17	·	·	PUNCT
ejpam-6865	146	18	+	+	CCONJ
ejpam-6865	146	19	(	(	PUNCT
ejpam-6865	146	20	t−	t−	PROPN
ejpam-6865	146	21	a)n	a)n	NOUN
ejpam-6865	146	22	n	n	CCONJ
ejpam-6865	146	23	!	!	PUNCT
ejpam-6865	146	24	un(a	un(a	PROPN
ejpam-6865	146	25	)	)	PUNCT
ejpam-6865	146	26	,	,	PUNCT
ejpam-6865	146	27	t	t	PROPN
ejpam-6865	146	28	)	)	PUNCT
ejpam-6865	146	29	,	,	PUNCT
ejpam-6865	146	30	(	(	PUNCT
ejpam-6865	146	31	30	30	NUM
ejpam-6865	146	32	)	)	PUNCT
ejpam-6865	146	33	and	and	CCONJ
ejpam-6865	146	34	the	the	DET
ejpam-6865	146	35	initial	initial	ADJ
ejpam-6865	146	36	condition	condition	NOUN
ejpam-6865	146	37	gives	give	VERB
ejpam-6865	146	38	l∑	l∑	PUNCT
ejpam-6865	146	39	v=0	v=0	PROPN
ejpam-6865	146	40	cv	cv	PROPN
ejpam-6865	146	41	abiα,µ,γbv	abiα,µ,γbv	PROPN
ejpam-6865	146	42	,	,	PUNCT
ejpam-6865	146	43	l(a	l(a	PROPN
ejpam-6865	146	44	)	)	PUNCT
ejpam-6865	146	45	=	=	SYM
ejpam-6865	146	46	0	0	X
ejpam-6865	146	47	.	.	PUNCT
ejpam-6865	146	48	(	(	PUNCT
ejpam-6865	146	49	31	31	NUM
ejpam-6865	146	50	)	)	PUNCT
ejpam-6865	146	51	now	now	ADV
ejpam-6865	146	52	,	,	PUNCT
ejpam-6865	146	53	substitute	substitute	PROPN
ejpam-6865	146	54	t	t	NOUN
ejpam-6865	146	55	=	=	SYM
ejpam-6865	146	56	tv	tv	NOUN
ejpam-6865	146	57	in	in	ADP
ejpam-6865	146	58	equation	equation	NOUN
ejpam-6865	146	59	(	(	PUNCT
ejpam-6865	146	60	30	30	NUM
ejpam-6865	146	61	)	)	PUNCT
ejpam-6865	146	62	for	for	ADP
ejpam-6865	146	63	v	v	NOUN
ejpam-6865	146	64	=	=	SYM
ejpam-6865	146	65	1	1	NUM
ejpam-6865	146	66	,	,	PUNCT
ejpam-6865	146	67	2	2	NUM
ejpam-6865	146	68	,	,	PUNCT
ejpam-6865	146	69	..	..	PUNCT
ejpam-6865	146	70	,	,	PUNCT
ejpam-6865	146	71	l	l	NOUN
ejpam-6865	146	72	,	,	PUNCT
ejpam-6865	146	73	then	then	ADV
ejpam-6865	146	74	we	we	PRON
ejpam-6865	146	75	have	have	VERB
ejpam-6865	146	76	l	l	NOUN
ejpam-6865	146	77	nonlinear	nonlinear	ADJ
ejpam-6865	146	78	equations	equation	NOUN
ejpam-6865	146	79	and	and	CCONJ
ejpam-6865	146	80	using	use	VERB
ejpam-6865	146	81	equation	equation	NOUN
ejpam-6865	146	82	(	(	PUNCT
ejpam-6865	146	83	31	31	NUM
ejpam-6865	146	84	)	)	PUNCT
ejpam-6865	146	85	,	,	PUNCT
ejpam-6865	146	86	then	then	ADV
ejpam-6865	146	87	(	(	PUNCT
ejpam-6865	146	88	l	l	NOUN
ejpam-6865	146	89	+	+	NOUN
ejpam-6865	146	90	1	1	NUM
ejpam-6865	146	91	)	)	PUNCT
ejpam-6865	146	92	of	of	ADP
ejpam-6865	146	93	nonlinear	nonlinear	ADJ
ejpam-6865	146	94	equations	equation	NOUN
ejpam-6865	146	95	are	be	AUX
ejpam-6865	146	96	generated	generate	VERB
ejpam-6865	146	97	.	.	PUNCT
ejpam-6865	147	1	by	by	ADP
ejpam-6865	147	2	solving	solve	VERB
ejpam-6865	147	3	those	those	DET
ejpam-6865	147	4	equations	equation	NOUN
ejpam-6865	147	5	using	use	VERB
ejpam-6865	147	6	newton	newton	PROPN
ejpam-6865	147	7	’s	’s	PART
ejpam-6865	147	8	iterative	iterative	NOUN
ejpam-6865	147	9	methods	method	NOUN
ejpam-6865	147	10	,	,	PUNCT
ejpam-6865	147	11	we	we	PRON
ejpam-6865	147	12	determined	determine	VERB
ejpam-6865	147	13	the	the	DET
ejpam-6865	147	14	cv	cv	PROPN
ejpam-6865	147	15	for	for	ADP
ejpam-6865	147	16	v	v	NOUN
ejpam-6865	147	17	=	=	SYM
ejpam-6865	147	18	0	0	NUM
ejpam-6865	147	19	,	,	PUNCT
ejpam-6865	147	20	1	1	NUM
ejpam-6865	147	21	,	,	PUNCT
ejpam-6865	147	22	...	...	PUNCT
ejpam-6865	147	23	,	,	PUNCT
ejpam-6865	147	24	l.	l.	PROPN
ejpam-6865	147	25	as	as	ADP
ejpam-6865	147	26	a	a	DET
ejpam-6865	147	27	result	result	NOUN
ejpam-6865	147	28	,	,	PUNCT
ejpam-6865	147	29	the	the	DET
ejpam-6865	147	30	approximate	approximate	ADJ
ejpam-6865	147	31	solution	solution	NOUN
ejpam-6865	147	32	can	can	AUX
ejpam-6865	147	33	be	be	AUX
ejpam-6865	147	34	calculated	calculate	VERB
ejpam-6865	147	35	.	.	PUNCT
ejpam-6865	148	1	5	5	X
ejpam-6865	148	2	.	.	X
ejpam-6865	148	3	illustrative	illustrative	ADJ
ejpam-6865	148	4	examples	example	NOUN
ejpam-6865	148	5	using	use	VERB
ejpam-6865	148	6	the	the	DET
ejpam-6865	148	7	two	two	NUM
ejpam-6865	148	8	proposed	propose	VERB
ejpam-6865	148	9	methods	method	NOUN
ejpam-6865	148	10	in	in	ADP
ejpam-6865	148	11	this	this	DET
ejpam-6865	148	12	section	section	NOUN
ejpam-6865	148	13	,	,	PUNCT
ejpam-6865	148	14	we	we	PRON
ejpam-6865	148	15	show	show	VERB
ejpam-6865	148	16	the	the	DET
ejpam-6865	148	17	schemes	scheme	NOUN
ejpam-6865	148	18	of	of	ADP
ejpam-6865	148	19	the	the	DET
ejpam-6865	148	20	three	three	NUM
ejpam-6865	148	21	fractional	fractional	ADJ
ejpam-6865	148	22	order	order	NOUN
ejpam-6865	148	23	initial	initial	ADJ
ejpam-6865	148	24	value	value	NOUN
ejpam-6865	148	25	problems	problem	NOUN
ejpam-6865	148	26	with	with	ADP
ejpam-6865	148	27	the	the	DET
ejpam-6865	148	28	help	help	NOUN
ejpam-6865	148	29	of	of	ADP
ejpam-6865	148	30	the	the	DET
ejpam-6865	148	31	bernstein	bernstein	PROPN
ejpam-6865	148	32	polynomial	polynomial	PROPN
ejpam-6865	148	33	using	use	VERB
ejpam-6865	148	34	two	two	NUM
ejpam-6865	148	35	approaches	approach	NOUN
ejpam-6865	148	36	.	.	PUNCT
ejpam-6865	149	1	s.	s.	PROPN
ejpam-6865	149	2	tamimi	tamimi	PROPN
ejpam-6865	149	3	,	,	PUNCT
ejpam-6865	149	4	a.	a.	PROPN
ejpam-6865	149	5	k.	k.	PROPN
ejpam-6865	149	6	alomari	alomari	PROPN
ejpam-6865	149	7	,	,	PUNCT
ejpam-6865	149	8	m.	m.	NOUN
ejpam-6865	149	9	alaroud	alaroud	PROPN
ejpam-6865	149	10	/	/	SYM
ejpam-6865	149	11	eur	eur	PROPN
ejpam-6865	149	12	.	.	PUNCT
ejpam-6865	150	1	j.	j.	PROPN
ejpam-6865	150	2	pure	pure	PROPN
ejpam-6865	150	3	appl	appl	PROPN
ejpam-6865	150	4	.	.	PROPN
ejpam-6865	150	5	math	math	PROPN
ejpam-6865	150	6	,	,	PUNCT
ejpam-6865	150	7	18	18	NUM
ejpam-6865	150	8	(	(	PUNCT
ejpam-6865	150	9	4	4	NUM
ejpam-6865	150	10	)	)	PUNCT
ejpam-6865	150	11	(	(	PUNCT
ejpam-6865	150	12	2025	2025	NUM
ejpam-6865	150	13	)	)	PUNCT
ejpam-6865	150	14	,	,	PUNCT
ejpam-6865	150	15	6865	6865	NUM
ejpam-6865	150	16	9	9	NUM
ejpam-6865	150	17	of	of	ADP
ejpam-6865	150	18	19	19	NUM
ejpam-6865	150	19	example	example	NOUN
ejpam-6865	150	20	1	1	NUM
ejpam-6865	150	21	consider	consider	VERB
ejpam-6865	150	22	the	the	DET
ejpam-6865	150	23	following	follow	VERB
ejpam-6865	150	24	fde	fde	PROPN
ejpam-6865	150	25	[	[	X
ejpam-6865	150	26	22	22	NUM
ejpam-6865	150	27	]	]	PUNCT
ejpam-6865	150	28	:	:	PUNCT
ejpam-6865	150	29	abc	abc	PROPN
ejpam-6865	150	30	0	0	NUM
ejpam-6865	150	31	dα,µ,γ	dα,µ,γ	PROPN
ejpam-6865	150	32	t	t	PROPN
ejpam-6865	150	33	u(t	u(t	PROPN
ejpam-6865	150	34	)	)	PUNCT
ejpam-6865	150	35	=	=	SYM
ejpam-6865	150	36	t2	t2	NOUN
ejpam-6865	150	37	,	,	PUNCT
ejpam-6865	150	38	u(0	u(0	PROPN
ejpam-6865	150	39	)	)	PUNCT
ejpam-6865	150	40	=	=	SYM
ejpam-6865	150	41	0	0	NUM
ejpam-6865	150	42	,	,	PUNCT
ejpam-6865	150	43	(	(	PUNCT
ejpam-6865	150	44	32	32	NUM
ejpam-6865	150	45	)	)	PUNCT
ejpam-6865	150	46	where	where	SCONJ
ejpam-6865	150	47	γ	γ	PROPN
ejpam-6865	150	48	,	,	PUNCT
ejpam-6865	150	49	µ	µ	NUM
ejpam-6865	150	50	,	,	PUNCT
ejpam-6865	150	51	α	α	PROPN
ejpam-6865	150	52	∈	∈	PROPN
ejpam-6865	150	53	r	r	PROPN
ejpam-6865	150	54	,	,	PUNCT
ejpam-6865	150	55	µ	µ	X
ejpam-6865	150	56	>	>	X
ejpam-6865	150	57	0	0	NUM
ejpam-6865	150	58	,	,	PUNCT
ejpam-6865	150	59	and	and	CCONJ
ejpam-6865	150	60	0	0	NUM
ejpam-6865	150	61	<	<	X
ejpam-6865	150	62	α	α	X
ejpam-6865	150	63	<	<	X
ejpam-6865	150	64	1	1	NUM
ejpam-6865	150	65	.	.	PUNCT
ejpam-6865	150	66	by	by	ADP
ejpam-6865	150	67	applying	apply	VERB
ejpam-6865	150	68	the	the	DET
ejpam-6865	150	69	operator	operator	NOUN
ejpam-6865	150	70	0abiα,µ,γ	0abiα,µ,γ	NUM
ejpam-6865	150	71	on	on	ADP
ejpam-6865	150	72	the	the	DET
ejpam-6865	150	73	equation	equation	NOUN
ejpam-6865	150	74	(	(	PUNCT
ejpam-6865	150	75	32	32	NUM
ejpam-6865	150	76	)	)	PUNCT
ejpam-6865	150	77	,	,	PUNCT
ejpam-6865	150	78	and	and	CCONJ
ejpam-6865	150	79	using	use	VERB
ejpam-6865	150	80	theorem	theorem	NOUN
ejpam-6865	150	81	3	3	NUM
ejpam-6865	150	82	,	,	PUNCT
ejpam-6865	150	83	the	the	DET
ejpam-6865	150	84	exact	exact	ADJ
ejpam-6865	150	85	solution	solution	NOUN
ejpam-6865	150	86	is	be	AUX
ejpam-6865	150	87	u(t)=	u(t)=	NOUN
ejpam-6865	150	88			X
ejpam-6865	150	89	∑γ	∑γ	ADV
ejpam-6865	150	90	i=0	i=0	PROPN
ejpam-6865	150	91	(	(	PUNCT
ejpam-6865	150	92	γ	γ	X
ejpam-6865	150	93	i	i	PROPN
ejpam-6865	150	94	)	)	PUNCT
ejpam-6865	150	95	2(1−α)1−iαitαi−µ+3	2(1−α)1−iαitαi−µ+3	NUM
ejpam-6865	150	96	m(α)(αi−µ+4	m(α)(αi−µ+4	NOUN
ejpam-6865	150	97	)	)	PUNCT
ejpam-6865	151	1	+	+	CCONJ
ejpam-6865	151	2	(	(	PUNCT
ejpam-6865	151	3	1−α)t2	1−α)t2	NUM
ejpam-6865	151	4	m(α	m(α	PROPN
ejpam-6865	151	5	)	)	PUNCT
ejpam-6865	151	6	,	,	PUNCT
ejpam-6865	151	7	µ	µ	X
ejpam-6865	151	8	≥	≥	NOUN
ejpam-6865	151	9	1	1	NUM
ejpam-6865	151	10	∑γ	∑γ	PROPN
ejpam-6865	151	11	i=0	i=0	PROPN
ejpam-6865	151	12	(	(	PUNCT
ejpam-6865	151	13	γ	γ	X
ejpam-6865	151	14	i	i	PROPN
ejpam-6865	151	15	)	)	PUNCT
ejpam-6865	151	16	2(1−α)1−iαitαi−µ+3	2(1−α)1−iαitαi−µ+3	NUM
ejpam-6865	151	17	m(α)(αi−µ+4	m(α)(αi−µ+4	NOUN
ejpam-6865	151	18	)	)	PUNCT
ejpam-6865	151	19	+	+	CCONJ
ejpam-6865	151	20	2(1−α)t3−µ	2(1−α)t3−µ	NUM
ejpam-6865	151	21	m(α)γ(4−µ	m(α)γ(4−µ	NUM
ejpam-6865	151	22	)	)	PUNCT
ejpam-6865	151	23	,	,	PUNCT
ejpam-6865	151	24	µ	µ	X
ejpam-6865	151	25	<	<	X
ejpam-6865	151	26	1	1	NUM
ejpam-6865	151	27	.	.	X
ejpam-6865	151	28	approach	approach	NOUN
ejpam-6865	151	29	1	1	NUM
ejpam-6865	151	30	:	:	PUNCT
ejpam-6865	151	31	this	this	DET
ejpam-6865	151	32	approach	approach	NOUN
ejpam-6865	151	33	was	be	AUX
ejpam-6865	151	34	introduced	introduce	VERB
ejpam-6865	151	35	in	in	ADP
ejpam-6865	151	36	[	[	X
ejpam-6865	151	37	22	22	NUM
ejpam-6865	151	38	]	]	PUNCT
ejpam-6865	151	39	that	that	PRON
ejpam-6865	151	40	is	be	AUX
ejpam-6865	151	41	based	base	VERB
ejpam-6865	151	42	on	on	ADP
ejpam-6865	151	43	the	the	DET
ejpam-6865	151	44	following	follow	VERB
ejpam-6865	151	45	steps	step	NOUN
ejpam-6865	151	46	.	.	PUNCT
ejpam-6865	152	1	step	step	NOUN
ejpam-6865	152	2	1	1	NUM
ejpam-6865	152	3	we	we	PRON
ejpam-6865	152	4	can	can	AUX
ejpam-6865	152	5	approximate	approximate	VERB
ejpam-6865	152	6	u(t	u(t	NOUN
ejpam-6865	152	7	)	)	PUNCT
ejpam-6865	152	8	as	as	ADP
ejpam-6865	152	9	:	:	PUNCT
ejpam-6865	152	10	u(t	u(t	NOUN
ejpam-6865	152	11	)	)	PUNCT
ejpam-6865	152	12	=	=	PUNCT
ejpam-6865	152	13	m∑	m∑	CCONJ
ejpam-6865	152	14	i=0	i=0	ADJ
ejpam-6865	152	15	cibi	cibi	NOUN
ejpam-6865	152	16	,	,	PUNCT
ejpam-6865	152	17	m(t	m(t	NOUN
ejpam-6865	152	18	)	)	PUNCT
ejpam-6865	152	19	.	.	PUNCT
ejpam-6865	153	1	(	(	PUNCT
ejpam-6865	153	2	33	33	NUM
ejpam-6865	153	3	)	)	PUNCT
ejpam-6865	153	4	step	step	NOUN
ejpam-6865	153	5	2	2	NUM
ejpam-6865	153	6	using	use	VERB
ejpam-6865	153	7	(	(	PUNCT
ejpam-6865	153	8	18	18	NUM
ejpam-6865	153	9	)	)	PUNCT
ejpam-6865	153	10	for	for	ADP
ejpam-6865	153	11	(	(	PUNCT
ejpam-6865	153	12	32	32	NUM
ejpam-6865	153	13	)	)	PUNCT
ejpam-6865	153	14	,	,	PUNCT
ejpam-6865	153	15	we	we	PRON
ejpam-6865	153	16	have	have	VERB
ejpam-6865	153	17	m∑	m∑	VERB
ejpam-6865	153	18	i=0	i=0	VERB
ejpam-6865	153	19	m−i∑	m−i∑	NOUN
ejpam-6865	154	1	k	k	X
ejpam-6865	154	2	=	=	PROPN
ejpam-6865	154	3	dαe−i	dαe−i	PROPN
ejpam-6865	154	4	ci(−1)k	ci(−1)k	PROPN
ejpam-6865	154	5	(	(	PUNCT
ejpam-6865	154	6	m	m	VERB
ejpam-6865	154	7	i	i	NOUN
ejpam-6865	154	8	)	)	PUNCT
ejpam-6865	154	9	(	(	PUNCT
ejpam-6865	154	10	m−	m−	PROPN
ejpam-6865	154	11	i	i	PROPN
ejpam-6865	154	12	k	k	NOUN
ejpam-6865	154	13	)	)	PUNCT
ejpam-6865	154	14	m(α1	m(α1	NOUN
ejpam-6865	154	15	)	)	PUNCT
ejpam-6865	154	16	1−	1−	NUM
ejpam-6865	154	17	α1	α1	PROPN
ejpam-6865	154	18	γ(k	γ(k	PROPN
ejpam-6865	154	19	+	+	PRON
ejpam-6865	154	20	i+	i+	NUM
ejpam-6865	154	21	1)eγ	1)eγ	NUM
ejpam-6865	154	22	α1,µ+k+i(λ	α1,µ+k+i(λ	NUM
ejpam-6865	154	23	,	,	PUNCT
ejpam-6865	154	24	t	t	PROPN
ejpam-6865	154	25	)	)	PUNCT
ejpam-6865	154	26	=	=	SYM
ejpam-6865	154	27	t2	t2	NOUN
ejpam-6865	154	28	.	.	PUNCT
ejpam-6865	155	1	(	(	PUNCT
ejpam-6865	155	2	34	34	NUM
ejpam-6865	155	3	)	)	PUNCT
ejpam-6865	155	4	step	step	NOUN
ejpam-6865	155	5	3	3	NUM
ejpam-6865	155	6	the	the	DET
ejpam-6865	155	7	initial	initial	ADJ
ejpam-6865	155	8	condition	condition	NOUN
ejpam-6865	155	9	gives	give	VERB
ejpam-6865	155	10	:	:	PUNCT
ejpam-6865	155	11	m∑	m∑	ADV
ejpam-6865	155	12	i=0	i=0	ADJ
ejpam-6865	155	13	cibi	cibi	NOUN
ejpam-6865	155	14	,	,	PUNCT
ejpam-6865	155	15	m(0	m(0	NOUN
ejpam-6865	155	16	)	)	PUNCT
ejpam-6865	155	17	=	=	SYM
ejpam-6865	155	18	u(0	u(0	PROPN
ejpam-6865	155	19	)	)	PUNCT
ejpam-6865	155	20	.	.	PUNCT
ejpam-6865	156	1	(	(	PUNCT
ejpam-6865	156	2	35	35	NUM
ejpam-6865	156	3	)	)	PUNCT
ejpam-6865	156	4	then	then	ADV
ejpam-6865	156	5	we	we	PRON
ejpam-6865	156	6	have	have	VERB
ejpam-6865	156	7	c0	c0	NOUN
ejpam-6865	156	8	=	=	SYM
ejpam-6865	156	9	0	0	X
ejpam-6865	156	10	.	.	X
ejpam-6865	157	1	step	step	NOUN
ejpam-6865	157	2	4	4	NUM
ejpam-6865	157	3	now	now	ADV
ejpam-6865	157	4	,	,	PUNCT
ejpam-6865	157	5	substitute	substitute	ADJ
ejpam-6865	157	6	collection	collection	NOUN
ejpam-6865	157	7	points	point	NOUN
ejpam-6865	157	8	in	in	ADP
ejpam-6865	157	9	equation	equation	NOUN
ejpam-6865	157	10	(	(	PUNCT
ejpam-6865	157	11	34	34	NUM
ejpam-6865	157	12	)	)	PUNCT
ejpam-6865	157	13	to	to	PART
ejpam-6865	157	14	have	have	VERB
ejpam-6865	157	15	a	a	DET
ejpam-6865	157	16	system	system	NOUN
ejpam-6865	157	17	of	of	ADP
ejpam-6865	157	18	linear	linear	PROPN
ejpam-6865	157	19	equations	equation	NOUN
ejpam-6865	157	20	,	,	PUNCT
ejpam-6865	157	21	then	then	ADV
ejpam-6865	157	22	by	by	ADP
ejpam-6865	157	23	solving	solve	VERB
ejpam-6865	157	24	these	these	DET
ejpam-6865	157	25	equations	equation	NOUN
ejpam-6865	157	26	we	we	PRON
ejpam-6865	157	27	get	get	VERB
ejpam-6865	157	28	ci	ci	NOUN
ejpam-6865	157	29	for	for	ADP
ejpam-6865	157	30	i	i	PROPN
ejpam-6865	157	31	=	=	NOUN
ejpam-6865	157	32	1	1	NUM
ejpam-6865	157	33	,	,	PUNCT
ejpam-6865	157	34	·	·	PUNCT
ejpam-6865	157	35	·	·	PUNCT
ejpam-6865	157	36	·	·	PUNCT
ejpam-6865	157	37	,	,	PUNCT
ejpam-6865	157	38	m.	m.	NOUN
ejpam-6865	157	39	step	step	NOUN
ejpam-6865	157	40	5	5	NUM
ejpam-6865	157	41	finally	finally	ADV
ejpam-6865	157	42	,	,	PUNCT
ejpam-6865	157	43	substitute	substitute	VERB
ejpam-6865	157	44	the	the	DET
ejpam-6865	157	45	values	value	NOUN
ejpam-6865	157	46	of	of	ADP
ejpam-6865	157	47	ci	ci	NOUN
ejpam-6865	157	48	in	in	ADP
ejpam-6865	157	49	equation	equation	NOUN
ejpam-6865	157	50	(	(	PUNCT
ejpam-6865	157	51	33	33	NUM
ejpam-6865	157	52	)	)	PUNCT
ejpam-6865	157	53	to	to	PART
ejpam-6865	157	54	obtain	obtain	VERB
ejpam-6865	157	55	the	the	DET
ejpam-6865	157	56	solution	solution	NOUN
ejpam-6865	157	57	of	of	ADP
ejpam-6865	157	58	(	(	PUNCT
ejpam-6865	157	59	32	32	NUM
ejpam-6865	157	60	)	)	PUNCT
ejpam-6865	157	61	using	use	VERB
ejpam-6865	157	62	the	the	DET
ejpam-6865	157	63	first	first	ADJ
ejpam-6865	157	64	approach	approach	NOUN
ejpam-6865	157	65	.	.	PUNCT
ejpam-6865	158	1	the	the	DET
ejpam-6865	158	2	residual	residual	ADJ
ejpam-6865	158	3	error	error	NOUN
ejpam-6865	158	4	function	function	NOUN
ejpam-6865	158	5	(	(	PUNCT
ejpam-6865	158	6	ref	ref	NOUN
ejpam-6865	158	7	)	)	PUNCT
ejpam-6865	158	8	for	for	ADP
ejpam-6865	158	9	(	(	PUNCT
ejpam-6865	158	10	32	32	NUM
ejpam-6865	158	11	)	)	PUNCT
ejpam-6865	158	12	can	can	AUX
ejpam-6865	158	13	be	be	AUX
ejpam-6865	158	14	defined	define	VERB
ejpam-6865	158	15	as	as	ADP
ejpam-6865	158	16	:	:	PUNCT
ejpam-6865	158	17	ref	ref	NOUN
ejpam-6865	158	18	(	(	PUNCT
ejpam-6865	158	19	t	t	NOUN
ejpam-6865	158	20	)	)	PUNCT
ejpam-6865	158	21	=	=	NOUN
ejpam-6865	158	22	abc	abc	PROPN
ejpam-6865	158	23	0	0	PROPN
ejpam-6865	158	24	dα,µ,γ	dα,µ,γ	PROPN
ejpam-6865	158	25	t	t	PROPN
ejpam-6865	158	26	u(t)−	u(t)−	PROPN
ejpam-6865	158	27	t2	t2	PROPN
ejpam-6865	158	28	.	.	PUNCT
ejpam-6865	159	1	(	(	PUNCT
ejpam-6865	159	2	36	36	NUM
ejpam-6865	159	3	)	)	PUNCT
ejpam-6865	159	4	in	in	ADP
ejpam-6865	159	5	figure	figure	NOUN
ejpam-6865	159	6	1	1	NUM
ejpam-6865	159	7	,	,	PUNCT
ejpam-6865	159	8	we	we	PRON
ejpam-6865	159	9	plot	plot	VERB
ejpam-6865	159	10	the	the	DET
ejpam-6865	159	11	present	present	ADJ
ejpam-6865	159	12	solution	solution	NOUN
ejpam-6865	159	13	of	of	ADP
ejpam-6865	159	14	example	example	NOUN
ejpam-6865	159	15	1	1	NUM
ejpam-6865	159	16	using	use	VERB
ejpam-6865	159	17	the	the	DET
ejpam-6865	159	18	first	first	ADJ
ejpam-6865	159	19	approach	approach	NOUN
ejpam-6865	159	20	with	with	ADP
ejpam-6865	159	21	several	several	ADJ
ejpam-6865	159	22	s.	s.	PROPN
ejpam-6865	159	23	tamimi	tamimi	PROPN
ejpam-6865	159	24	,	,	PUNCT
ejpam-6865	159	25	a.	a.	PROPN
ejpam-6865	159	26	k.	k.	PROPN
ejpam-6865	159	27	alomari	alomari	PROPN
ejpam-6865	159	28	,	,	PUNCT
ejpam-6865	159	29	m.	m.	NOUN
ejpam-6865	159	30	alaroud	alaroud	PROPN
ejpam-6865	159	31	/	/	SYM
ejpam-6865	159	32	eur	eur	PROPN
ejpam-6865	159	33	.	.	PUNCT
ejpam-6865	160	1	j.	j.	PROPN
ejpam-6865	160	2	pure	pure	PROPN
ejpam-6865	160	3	appl	appl	PROPN
ejpam-6865	160	4	.	.	PROPN
ejpam-6865	160	5	math	math	PROPN
ejpam-6865	160	6	,	,	PUNCT
ejpam-6865	160	7	18	18	NUM
ejpam-6865	160	8	(	(	PUNCT
ejpam-6865	160	9	4	4	NUM
ejpam-6865	160	10	)	)	PUNCT
ejpam-6865	160	11	(	(	PUNCT
ejpam-6865	160	12	2025	2025	NUM
ejpam-6865	160	13	)	)	PUNCT
ejpam-6865	160	14	,	,	PUNCT
ejpam-6865	160	15	6865	6865	NUM
ejpam-6865	160	16	10	10	NUM
ejpam-6865	160	17	of	of	ADP
ejpam-6865	160	18	19	19	NUM
ejpam-6865	160	19	α=0.3	α=0.3	ADV
ejpam-6865	160	20	α=0.5	α=0.5	ADJ
ejpam-6865	160	21	α=0.7	α=0.7	NOUN
ejpam-6865	160	22	0.0	0.0	NUM
ejpam-6865	160	23	0.2	0.2	NUM
ejpam-6865	160	24	0.4	0.4	NUM
ejpam-6865	160	25	0.6	0.6	NUM
ejpam-6865	160	26	0.8	0.8	NUM
ejpam-6865	160	27	1.0	1.0	NUM
ejpam-6865	160	28	0.0	0.0	NUM
ejpam-6865	160	29	0.2	0.2	NUM
ejpam-6865	160	30	0.4	0.4	NUM
ejpam-6865	160	31	0.6	0.6	NUM
ejpam-6865	160	32	0.8	0.8	NUM
ejpam-6865	160	33	1.0	1.0	NUM
ejpam-6865	160	34	1.2	1.2	NUM
ejpam-6865	160	35	t	t	NOUN
ejpam-6865	160	36	u	u	PROPN
ejpam-6865	160	37	(	(	PUNCT
ejpam-6865	160	38	t	t	NOUN
ejpam-6865	160	39	)	)	PUNCT
ejpam-6865	160	40	figure	figure	NOUN
ejpam-6865	160	41	1	1	NUM
ejpam-6865	160	42	:	:	PUNCT
ejpam-6865	160	43	the	the	DET
ejpam-6865	160	44	approximate	approximate	ADJ
ejpam-6865	160	45	solutions	solution	NOUN
ejpam-6865	160	46	of	of	ADP
ejpam-6865	160	47	example	example	NOUN
ejpam-6865	160	48	1	1	NUM
ejpam-6865	160	49	using	use	VERB
ejpam-6865	160	50	the	the	DET
ejpam-6865	160	51	first	first	ADJ
ejpam-6865	160	52	approach	approach	NOUN
ejpam-6865	160	53	with	with	ADP
ejpam-6865	160	54	several	several	ADJ
ejpam-6865	160	55	values	value	NOUN
ejpam-6865	160	56	of	of	ADP
ejpam-6865	160	57	α	α	NOUN
ejpam-6865	160	58	and	and	CCONJ
ejpam-6865	160	59	µ=1	µ=1	X
ejpam-6865	160	60	and	and	CCONJ
ejpam-6865	160	61	γ=2	γ=2	NOUN
ejpam-6865	160	62	.	.	PUNCT
ejpam-6865	161	1	α	α	PROPN
ejpam-6865	161	2	0.3	0.3	NUM
ejpam-6865	161	3	α	α	NOUN
ejpam-6865	161	4	0.5	0.5	NUM
ejpam-6865	161	5	α	α	NOUN
ejpam-6865	161	6	0.7	0.7	NUM
ejpam-6865	161	7	0.0	0.0	NUM
ejpam-6865	161	8	0.2	0.2	NUM
ejpam-6865	161	9	0.4	0.4	NUM
ejpam-6865	161	10	0.6	0.6	NUM
ejpam-6865	161	11	0.8	0.8	NUM
ejpam-6865	161	12	1.0	1.0	NUM
ejpam-6865	161	13	0.0	0.0	NUM
ejpam-6865	161	14	0.1	0.1	NUM
ejpam-6865	161	15	0.2	0.2	NUM
ejpam-6865	161	16	0.3	0.3	NUM
ejpam-6865	161	17	0.4	0.4	NUM
ejpam-6865	161	18	t	t	PROPN
ejpam-6865	161	19	u	u	PROPN
ejpam-6865	161	20	(	(	PUNCT
ejpam-6865	161	21	a	a	DET
ejpam-6865	161	22	p	p	X
ejpam-6865	161	23	p	p	X
ejpam-6865	161	24	ro	ro	X
ejpam-6865	161	25	x	x	PROPN
ejpam-6865	161	26	i	i	PRON
ejpam-6865	161	27	m	m	VERB
ejpam-6865	161	28	at	at	ADP
ejpam-6865	161	29	e	e	NOUN
ejpam-6865	161	30	)	)	PUNCT
ejpam-6865	161	31	u	u	NOUN
ejpam-6865	161	32	(	(	PUNCT
ejpam-6865	161	33	e	e	NOUN
ejpam-6865	161	34	x	x	PROPN
ejpam-6865	161	35	ac	ac	PROPN
ejpam-6865	161	36	t	t	PROPN
ejpam-6865	161	37	)	)	PUNCT
ejpam-6865	161	38			PROPN
ejpam-6865	161	39	figure	figure	NOUN
ejpam-6865	161	40	2	2	NUM
ejpam-6865	161	41	:	:	PUNCT
ejpam-6865	161	42	absolute	absolute	ADJ
ejpam-6865	161	43	error	error	NOUN
ejpam-6865	161	44	using	use	VERB
ejpam-6865	161	45	the	the	DET
ejpam-6865	161	46	first	first	ADJ
ejpam-6865	161	47	approach	approach	NOUN
ejpam-6865	161	48	with	with	ADP
ejpam-6865	161	49	several	several	ADJ
ejpam-6865	161	50	values	value	NOUN
ejpam-6865	161	51	of	of	ADP
ejpam-6865	161	52	α	α	NOUN
ejpam-6865	161	53	and	and	CCONJ
ejpam-6865	161	54	fixed	fix	VERB
ejpam-6865	161	55	value	value	NOUN
ejpam-6865	161	56	of	of	ADP
ejpam-6865	161	57	µ	µ	NOUN
ejpam-6865	161	58	and	and	CCONJ
ejpam-6865	161	59	γ	γ	PROPN
ejpam-6865	161	60	.	.	PROPN
ejpam-6865	161	61	values	value	NOUN
ejpam-6865	161	62	of	of	ADP
ejpam-6865	161	63	α	α	NOUN
ejpam-6865	161	64	and	and	CCONJ
ejpam-6865	161	65	fixed	fix	VERB
ejpam-6865	161	66	µ	µ	X
ejpam-6865	161	67	=	=	SYM
ejpam-6865	161	68	1	1	NUM
ejpam-6865	161	69	,	,	PUNCT
ejpam-6865	161	70	γ	γ	NOUN
ejpam-6865	161	71	=	=	SYM
ejpam-6865	161	72	1	1	X
ejpam-6865	161	73	.	.	PUNCT
ejpam-6865	161	74	figure	figure	NOUN
ejpam-6865	161	75	2	2	NUM
ejpam-6865	161	76	presents	present	VERB
ejpam-6865	161	77	the	the	DET
ejpam-6865	161	78	absolute	absolute	ADJ
ejpam-6865	161	79	error	error	NOUN
ejpam-6865	161	80	of	of	ADP
ejpam-6865	161	81	example	example	NOUN
ejpam-6865	161	82	1	1	NUM
ejpam-6865	161	83	using	use	VERB
ejpam-6865	161	84	the	the	DET
ejpam-6865	161	85	first	first	ADJ
ejpam-6865	161	86	approach	approach	NOUN
ejpam-6865	161	87	for	for	ADP
ejpam-6865	161	88	several	several	ADJ
ejpam-6865	161	89	values	value	NOUN
ejpam-6865	161	90	of	of	ADP
ejpam-6865	161	91	α	α	NOUN
ejpam-6865	161	92	and	and	CCONJ
ejpam-6865	161	93	fixed	fix	VERB
ejpam-6865	161	94	µ	µ	X
ejpam-6865	161	95	=	=	SYM
ejpam-6865	161	96	1	1	NUM
ejpam-6865	161	97	,	,	PUNCT
ejpam-6865	161	98	γ	γ	NOUN
ejpam-6865	161	99	=	=	SYM
ejpam-6865	161	100	2	2	NUM
ejpam-6865	161	101	.	.	PUNCT
ejpam-6865	162	1	the	the	DET
ejpam-6865	162	2	solutions	solution	NOUN
ejpam-6865	162	3	using	use	VERB
ejpam-6865	162	4	approach	approach	NOUN
ejpam-6865	162	5	1	1	NUM
ejpam-6865	162	6	are	be	AUX
ejpam-6865	162	7	the	the	DET
ejpam-6865	162	8	same	same	ADJ
ejpam-6865	162	9	in	in	ADP
ejpam-6865	162	10	[	[	X
ejpam-6865	162	11	22	22	NUM
ejpam-6865	162	12	]	]	PUNCT
ejpam-6865	162	13	.	.	PUNCT
ejpam-6865	163	1	approach	approach	NOUN
ejpam-6865	163	2	2	2	NUM
ejpam-6865	163	3	:	:	PUNCT
ejpam-6865	163	4	step	step	NOUN
ejpam-6865	163	5	1	1	NUM
ejpam-6865	163	6	let	let	VERB
ejpam-6865	163	7	abc	abc	PROPN
ejpam-6865	163	8	0	0	PROPN
ejpam-6865	163	9	dα,µ,γ	dα,µ,γ	PROPN
ejpam-6865	163	10	t	t	PROPN
ejpam-6865	163	11	u(t	u(t	PROPN
ejpam-6865	163	12	)	)	PUNCT
ejpam-6865	163	13	=	=	PUNCT
ejpam-6865	163	14	m∑	m∑	CCONJ
ejpam-6865	163	15	i=0	i=0	ADJ
ejpam-6865	163	16	cibi	cibi	NOUN
ejpam-6865	163	17	,	,	PUNCT
ejpam-6865	163	18	m(t	m(t	NOUN
ejpam-6865	163	19	)	)	PUNCT
ejpam-6865	163	20	.	.	PUNCT
ejpam-6865	164	1	(	(	PUNCT
ejpam-6865	164	2	37	37	NUM
ejpam-6865	164	3	)	)	PUNCT
ejpam-6865	164	4	step	step	NOUN
ejpam-6865	164	5	2	2	NUM
ejpam-6865	164	6	by	by	ADP
ejpam-6865	164	7	substituting	substitute	VERB
ejpam-6865	164	8	equation	equation	NOUN
ejpam-6865	164	9	(	(	PUNCT
ejpam-6865	164	10	37	37	NUM
ejpam-6865	164	11	)	)	PUNCT
ejpam-6865	164	12	in	in	ADP
ejpam-6865	164	13	equation	equation	NOUN
ejpam-6865	164	14	(	(	PUNCT
ejpam-6865	164	15	32	32	NUM
ejpam-6865	164	16	)	)	PUNCT
ejpam-6865	164	17	,	,	PUNCT
ejpam-6865	164	18	we	we	PRON
ejpam-6865	164	19	have	have	VERB
ejpam-6865	164	20	m∑	m∑	NOUN
ejpam-6865	164	21	i=0	i=0	ADJ
ejpam-6865	164	22	cibi	cibi	NOUN
ejpam-6865	164	23	,	,	PUNCT
ejpam-6865	164	24	m(t	m(t	NOUN
ejpam-6865	164	25	)	)	PUNCT
ejpam-6865	164	26	=	=	SYM
ejpam-6865	164	27	t2	t2	NOUN
ejpam-6865	164	28	.	.	PUNCT
ejpam-6865	165	1	(	(	PUNCT
ejpam-6865	165	2	38	38	NUM
ejpam-6865	165	3	)	)	PUNCT
ejpam-6865	165	4	step	step	NOUN
ejpam-6865	165	5	3	3	NUM
ejpam-6865	165	6	the	the	DET
ejpam-6865	165	7	initial	initial	ADJ
ejpam-6865	165	8	condition	condition	NOUN
ejpam-6865	165	9	m∑	m∑	VERB
ejpam-6865	165	10	i=0	i=0	PROPN
ejpam-6865	165	11	ci	ci	PROPN
ejpam-6865	165	12	ab	ab	PROPN
ejpam-6865	165	13	0	0	PROPN
ejpam-6865	165	14	iα,µ,γbi	iα,µ,γbi	PROPN
ejpam-6865	165	15	,	,	PUNCT
ejpam-6865	165	16	m(0	m(0	PROPN
ejpam-6865	165	17	)	)	PUNCT
ejpam-6865	165	18	+	+	PROPN
ejpam-6865	166	1	u(0	u(0	NOUN
ejpam-6865	166	2	)	)	PUNCT
ejpam-6865	166	3	=	=	SYM
ejpam-6865	166	4	u(0	u(0	PROPN
ejpam-6865	166	5	)	)	PUNCT
ejpam-6865	166	6	,	,	PUNCT
ejpam-6865	166	7	(	(	PUNCT
ejpam-6865	166	8	39	39	NUM
ejpam-6865	166	9	)	)	PUNCT
ejpam-6865	166	10	s.	s.	PROPN
ejpam-6865	166	11	tamimi	tamimi	PROPN
ejpam-6865	166	12	,	,	PUNCT
ejpam-6865	166	13	a.	a.	PROPN
ejpam-6865	166	14	k.	k.	PROPN
ejpam-6865	166	15	alomari	alomari	PROPN
ejpam-6865	166	16	,	,	PUNCT
ejpam-6865	166	17	m.	m.	NOUN
ejpam-6865	166	18	alaroud	alaroud	PROPN
ejpam-6865	166	19	/	/	SYM
ejpam-6865	166	20	eur	eur	PROPN
ejpam-6865	166	21	.	.	PUNCT
ejpam-6865	167	1	j.	j.	PROPN
ejpam-6865	167	2	pure	pure	PROPN
ejpam-6865	167	3	appl	appl	PROPN
ejpam-6865	167	4	.	.	PROPN
ejpam-6865	167	5	math	math	PROPN
ejpam-6865	167	6	,	,	PUNCT
ejpam-6865	167	7	18	18	NUM
ejpam-6865	167	8	(	(	PUNCT
ejpam-6865	167	9	4	4	NUM
ejpam-6865	167	10	)	)	PUNCT
ejpam-6865	167	11	(	(	PUNCT
ejpam-6865	167	12	2025	2025	NUM
ejpam-6865	167	13	)	)	PUNCT
ejpam-6865	167	14	,	,	PUNCT
ejpam-6865	167	15	6865	6865	NUM
ejpam-6865	167	16	11	11	NUM
ejpam-6865	167	17	of	of	ADP
ejpam-6865	167	18	19	19	NUM
ejpam-6865	167	19	gives	give	VERB
ejpam-6865	167	20	c0	c0	NOUN
ejpam-6865	167	21	=	=	PROPN
ejpam-6865	167	22	0	0	X
ejpam-6865	167	23	.	.	PUNCT
ejpam-6865	168	1	(	(	PUNCT
ejpam-6865	168	2	40	40	NUM
ejpam-6865	168	3	)	)	PUNCT
ejpam-6865	168	4	step	step	NOUN
ejpam-6865	168	5	4	4	NUM
ejpam-6865	168	6	we	we	PRON
ejpam-6865	168	7	apply	apply	VERB
ejpam-6865	168	8	the	the	DET
ejpam-6865	168	9	left	left	ADJ
ejpam-6865	168	10	ab	ab	PROPN
ejpam-6865	168	11	fractional	fractional	ADJ
ejpam-6865	168	12	integral	integral	ADJ
ejpam-6865	168	13	of	of	ADP
ejpam-6865	168	14	equation	equation	NOUN
ejpam-6865	168	15	(	(	PUNCT
ejpam-6865	168	16	19	19	NUM
ejpam-6865	168	17	)	)	PUNCT
ejpam-6865	168	18	using	use	VERB
ejpam-6865	168	19	equation	equation	NOUN
ejpam-6865	168	20	(	(	PUNCT
ejpam-6865	168	21	16	16	NUM
ejpam-6865	168	22	)	)	PUNCT
ejpam-6865	168	23	,	,	PUNCT
ejpam-6865	168	24	to	to	PART
ejpam-6865	168	25	have	have	VERB
ejpam-6865	168	26	u(t)−	u(t)−	PROPN
ejpam-6865	168	27	u(0	u(0	PROPN
ejpam-6865	168	28	)	)	PUNCT
ejpam-6865	168	29	=	=	PUNCT
ejpam-6865	169	1	m∑	m∑	CCONJ
ejpam-6865	169	2	i=0	i=0	PROPN
ejpam-6865	169	3	ci	ci	PROPN
ejpam-6865	169	4	(	(	PUNCT
ejpam-6865	169	5	m	m	VERB
ejpam-6865	169	6	i	i	NOUN
ejpam-6865	169	7	)	)	PUNCT
ejpam-6865	170	1	m−i∑	m−i∑	ADP
ejpam-6865	170	2	k=0	k=0	PROPN
ejpam-6865	170	3	(	(	PUNCT
ejpam-6865	170	4	−1)k	−1)k	PROPN
ejpam-6865	170	5	(	(	PUNCT
ejpam-6865	170	6	m−	m−	PROPN
ejpam-6865	170	7	i	i	PROPN
ejpam-6865	170	8	k	k	PROPN
ejpam-6865	170	9	)	)	PUNCT
ejpam-6865	170	10	γ∑	γ∑	PROPN
ejpam-6865	170	11	n=0	n=0	PROPN
ejpam-6865	170	12	(	(	PUNCT
ejpam-6865	170	13	γ	γ	PROPN
ejpam-6865	170	14	n	n	ADJ
ejpam-6865	170	15	)	)	PUNCT
ejpam-6865	170	16	αn	αn	NOUN
ejpam-6865	170	17	m(1−	m(1−	PROPN
ejpam-6865	170	18	α)n−1	α)n−1	PROPN
ejpam-6865	170	19	×	×	PROPN
ejpam-6865	170	20	γ(k	γ(k	PROPN
ejpam-6865	170	21	+	+	CCONJ
ejpam-6865	170	22	i+	i+	NUM
ejpam-6865	170	23	1	1	NUM
ejpam-6865	170	24	)	)	PUNCT
ejpam-6865	170	25	γ(αn+	γ(αn+	ADP
ejpam-6865	170	26	k	k	PROPN
ejpam-6865	171	1	+	+	CCONJ
ejpam-6865	171	2	i−	i−	PROPN
ejpam-6865	171	3	µ+	µ+	PRON
ejpam-6865	171	4	2	2	NUM
ejpam-6865	171	5	)	)	PUNCT
ejpam-6865	171	6	×	×	NOUN
ejpam-6865	171	7	tαn+k+i−µ+1	tαn+k+i−µ+1	NOUN
ejpam-6865	171	8	.	.	PUNCT
ejpam-6865	172	1	(	(	PUNCT
ejpam-6865	172	2	41	41	NUM
ejpam-6865	172	3	)	)	PUNCT
ejpam-6865	172	4	step	step	NOUN
ejpam-6865	172	5	5	5	NUM
ejpam-6865	172	6	now	now	ADV
ejpam-6865	172	7	,	,	PUNCT
ejpam-6865	172	8	at	at	ADP
ejpam-6865	172	9	collecation	collecation	NOUN
ejpam-6865	172	10	points	point	NOUN
ejpam-6865	172	11	tr	tr	NOUN
ejpam-6865	172	12	we	we	PRON
ejpam-6865	172	13	have	have	VERB
ejpam-6865	172	14	equation	equation	NOUN
ejpam-6865	172	15	(	(	PUNCT
ejpam-6865	172	16	38	38	NUM
ejpam-6865	172	17	)	)	PUNCT
ejpam-6865	172	18	in	in	ADP
ejpam-6865	172	19	this	this	DET
ejpam-6865	172	20	form	form	NOUN
ejpam-6865	172	21	:	:	PUNCT
ejpam-6865	172	22	m∑	m∑	PUNCT
ejpam-6865	172	23	i=0	i=0	ADJ
ejpam-6865	172	24	cibi	cibi	NOUN
ejpam-6865	172	25	,	,	PUNCT
ejpam-6865	172	26	m(tr)−	m(tr)−	NOUN
ejpam-6865	172	27	t2r	t2r	X
ejpam-6865	172	28	=	=	NOUN
ejpam-6865	172	29	0	0	X
ejpam-6865	172	30	.	.	PUNCT
ejpam-6865	173	1	(	(	PUNCT
ejpam-6865	173	2	42	42	NUM
ejpam-6865	173	3	)	)	PUNCT
ejpam-6865	173	4	step	step	NOUN
ejpam-6865	173	5	6	6	NUM
ejpam-6865	173	6	from	from	ADP
ejpam-6865	173	7	equation	equation	NOUN
ejpam-6865	173	8	(	(	PUNCT
ejpam-6865	173	9	42	42	NUM
ejpam-6865	173	10	)	)	PUNCT
ejpam-6865	173	11	,	,	PUNCT
ejpam-6865	173	12	we	we	PRON
ejpam-6865	173	13	have	have	VERB
ejpam-6865	173	14	a	a	DET
ejpam-6865	173	15	system	system	NOUN
ejpam-6865	173	16	of	of	ADP
ejpam-6865	173	17	linear	linear	PROPN
ejpam-6865	173	18	equations	equation	NOUN
ejpam-6865	173	19	.	.	PUNCT
ejpam-6865	174	1	by	by	ADP
ejpam-6865	174	2	solving	solve	VERB
ejpam-6865	174	3	these	these	DET
ejpam-6865	174	4	equations	equation	NOUN
ejpam-6865	174	5	,	,	PUNCT
ejpam-6865	174	6	we	we	PRON
ejpam-6865	174	7	get	get	VERB
ejpam-6865	174	8	ci	ci	NOUN
ejpam-6865	174	9	for	for	ADP
ejpam-6865	174	10	i	i	PROPN
ejpam-6865	174	11	=	=	NOUN
ejpam-6865	174	12	1	1	NUM
ejpam-6865	174	13	,	,	PUNCT
ejpam-6865	174	14	·	·	PUNCT
ejpam-6865	174	15	·	·	PUNCT
ejpam-6865	174	16	·	·	PUNCT
ejpam-6865	174	17	,	,	PUNCT
ejpam-6865	174	18	m.	m.	NOUN
ejpam-6865	174	19	finally	finally	ADV
ejpam-6865	174	20	,	,	PUNCT
ejpam-6865	174	21	substitute	substitute	NOUN
ejpam-6865	174	22	ci	ci	PROPN
ejpam-6865	174	23	in	in	ADP
ejpam-6865	174	24	equation	equation	NOUN
ejpam-6865	174	25	(	(	PUNCT
ejpam-6865	174	26	41	41	NUM
ejpam-6865	174	27	)	)	PUNCT
ejpam-6865	174	28	to	to	PART
ejpam-6865	174	29	obtain	obtain	VERB
ejpam-6865	174	30	the	the	DET
ejpam-6865	174	31	approximate	approximate	ADJ
ejpam-6865	174	32	solution	solution	NOUN
ejpam-6865	174	33	of	of	ADP
ejpam-6865	174	34	equation	equation	NOUN
ejpam-6865	174	35	(	(	PUNCT
ejpam-6865	174	36	32	32	NUM
ejpam-6865	174	37	)	)	PUNCT
ejpam-6865	174	38	.	.	PUNCT
ejpam-6865	175	1	in	in	ADP
ejpam-6865	175	2	figure	figure	NOUN
ejpam-6865	175	3	3	3	NUM
ejpam-6865	175	4	and	and	CCONJ
ejpam-6865	175	5	figure	figure	VERB
ejpam-6865	175	6	4	4	NUM
ejpam-6865	175	7	,	,	PUNCT
ejpam-6865	175	8	we	we	PRON
ejpam-6865	175	9	plot	plot	VERB
ejpam-6865	175	10	the	the	DET
ejpam-6865	175	11	approximate	approximate	ADJ
ejpam-6865	175	12	solutions	solution	NOUN
ejpam-6865	175	13	and	and	CCONJ
ejpam-6865	175	14	the	the	DET
ejpam-6865	175	15	absolute	absolute	ADJ
ejpam-6865	175	16	error	error	NOUN
ejpam-6865	175	17	of	of	ADP
ejpam-6865	175	18	example	example	NOUN
ejpam-6865	175	19	1	1	NUM
ejpam-6865	175	20	using	use	VERB
ejpam-6865	175	21	the	the	DET
ejpam-6865	175	22	second	second	ADJ
ejpam-6865	175	23	approach	approach	NOUN
ejpam-6865	175	24	for	for	ADP
ejpam-6865	175	25	several	several	ADJ
ejpam-6865	175	26	values	value	NOUN
ejpam-6865	175	27	of	of	ADP
ejpam-6865	175	28	α	α	NOUN
ejpam-6865	175	29	and	and	CCONJ
ejpam-6865	175	30	fixed	fix	VERB
ejpam-6865	175	31	µ	µ	X
ejpam-6865	175	32	=	=	SYM
ejpam-6865	175	33	1	1	NUM
ejpam-6865	175	34	,	,	PUNCT
ejpam-6865	175	35	γ	γ	NOUN
ejpam-6865	175	36	=	=	SYM
ejpam-6865	175	37	2	2	NUM
ejpam-6865	175	38	and	and	CCONJ
ejpam-6865	175	39	in	in	ADP
ejpam-6865	175	40	table	table	NOUN
ejpam-6865	175	41	1	1	NUM
ejpam-6865	175	42	,	,	PUNCT
ejpam-6865	175	43	we	we	PRON
ejpam-6865	175	44	calculate	calculate	VERB
ejpam-6865	175	45	the	the	DET
ejpam-6865	175	46	approximate	approximate	ADJ
ejpam-6865	175	47	solutions	solution	NOUN
ejpam-6865	175	48	for	for	ADP
ejpam-6865	175	49	several	several	ADJ
ejpam-6865	175	50	values	value	NOUN
ejpam-6865	175	51	of	of	ADP
ejpam-6865	175	52	α	α	NOUN
ejpam-6865	175	53	at	at	ADP
ejpam-6865	175	54	various	various	ADJ
ejpam-6865	175	55	values	value	NOUN
ejpam-6865	175	56	of	of	ADP
ejpam-6865	175	57	t.	t.	NOUN
ejpam-6865	175	58	α=0.3	α=0.3	ADV
ejpam-6865	175	59	α=0.5	α=0.5	ADJ
ejpam-6865	175	60	α=0.7	α=0.7	NOUN
ejpam-6865	175	61	0.0	0.0	NUM
ejpam-6865	175	62	0.2	0.2	NUM
ejpam-6865	175	63	0.4	0.4	NUM
ejpam-6865	175	64	0.6	0.6	NUM
ejpam-6865	175	65	0.8	0.8	NUM
ejpam-6865	175	66	1.0	1.0	NUM
ejpam-6865	175	67	0.0	0.0	NUM
ejpam-6865	175	68	0.2	0.2	NUM
ejpam-6865	175	69	0.4	0.4	NUM
ejpam-6865	175	70	0.6	0.6	NUM
ejpam-6865	175	71	0.8	0.8	NUM
ejpam-6865	175	72	1.0	1.0	NUM
ejpam-6865	175	73	1.2	1.2	NUM
ejpam-6865	175	74	t	t	NOUN
ejpam-6865	175	75	u	u	PROPN
ejpam-6865	175	76	(	(	PUNCT
ejpam-6865	175	77	t	t	NOUN
ejpam-6865	175	78	)	)	PUNCT
ejpam-6865	175	79	figure	figure	NOUN
ejpam-6865	175	80	3	3	NUM
ejpam-6865	175	81	:	:	PUNCT
ejpam-6865	175	82	the	the	DET
ejpam-6865	175	83	approximate	approximate	ADJ
ejpam-6865	175	84	solutions	solution	NOUN
ejpam-6865	175	85	using	use	VERB
ejpam-6865	175	86	the	the	DET
ejpam-6865	175	87	second	second	ADJ
ejpam-6865	175	88	approach	approach	NOUN
ejpam-6865	175	89	with	with	ADP
ejpam-6865	175	90	several	several	ADJ
ejpam-6865	175	91	values	value	NOUN
ejpam-6865	175	92	of	of	ADP
ejpam-6865	175	93	α	α	NOUN
ejpam-6865	175	94	and	and	CCONJ
ejpam-6865	175	95	µ=1	µ=1	X
ejpam-6865	175	96	and	and	CCONJ
ejpam-6865	175	97	γ=2	γ=2	PROPN
ejpam-6865	175	98	.	.	PUNCT
ejpam-6865	176	1	s.	s.	PROPN
ejpam-6865	176	2	tamimi	tamimi	PROPN
ejpam-6865	176	3	,	,	PUNCT
ejpam-6865	176	4	a.	a.	PROPN
ejpam-6865	176	5	k.	k.	PROPN
ejpam-6865	176	6	alomari	alomari	PROPN
ejpam-6865	176	7	,	,	PUNCT
ejpam-6865	176	8	m.	m.	NOUN
ejpam-6865	176	9	alaroud	alaroud	PROPN
ejpam-6865	176	10	/	/	SYM
ejpam-6865	176	11	eur	eur	PROPN
ejpam-6865	176	12	.	.	PUNCT
ejpam-6865	177	1	j.	j.	PROPN
ejpam-6865	177	2	pure	pure	PROPN
ejpam-6865	177	3	appl	appl	PROPN
ejpam-6865	177	4	.	.	PROPN
ejpam-6865	177	5	math	math	PROPN
ejpam-6865	177	6	,	,	PUNCT
ejpam-6865	177	7	18	18	NUM
ejpam-6865	177	8	(	(	PUNCT
ejpam-6865	177	9	4	4	NUM
ejpam-6865	177	10	)	)	PUNCT
ejpam-6865	177	11	(	(	PUNCT
ejpam-6865	177	12	2025	2025	NUM
ejpam-6865	177	13	)	)	PUNCT
ejpam-6865	177	14	,	,	PUNCT
ejpam-6865	177	15	6865	6865	NUM
ejpam-6865	177	16	12	12	NUM
ejpam-6865	177	17	of	of	ADP
ejpam-6865	177	18	19	19	NUM
ejpam-6865	177	19	α	α	NOUN
ejpam-6865	177	20	0.3	0.3	NUM
ejpam-6865	177	21	α	α	NOUN
ejpam-6865	177	22	0.5	0.5	NUM
ejpam-6865	177	23	α	α	NOUN
ejpam-6865	177	24	0.7	0.7	NUM
ejpam-6865	177	25	0.0	0.0	NUM
ejpam-6865	177	26	0.2	0.2	NUM
ejpam-6865	177	27	0.4	0.4	NUM
ejpam-6865	177	28	0.6	0.6	NUM
ejpam-6865	177	29	0.8	0.8	NUM
ejpam-6865	177	30	1.0	1.0	NUM
ejpam-6865	177	31	0	0	NUM
ejpam-6865	177	32	1.×	1.×	NUM
ejpam-6865	177	33	10	10	NUM
ejpam-6865	177	34	-	-	SYM
ejpam-6865	177	35	16	16	NUM
ejpam-6865	177	36	2.×	2.×	NUM
ejpam-6865	177	37	10	10	NUM
ejpam-6865	177	38	-	-	SYM
ejpam-6865	177	39	16	16	NUM
ejpam-6865	177	40	3.×	3.×	NUM
ejpam-6865	177	41	10	10	NUM
ejpam-6865	177	42	-	-	SYM
ejpam-6865	177	43	16	16	NUM
ejpam-6865	177	44	4.×	4.×	NUM
ejpam-6865	177	45	10	10	NUM
ejpam-6865	177	46	-	-	SYM
ejpam-6865	177	47	16	16	NUM
ejpam-6865	177	48	5.×	5.×	NUM
ejpam-6865	177	49	10	10	NUM
ejpam-6865	177	50	-	-	SYM
ejpam-6865	177	51	16	16	NUM
ejpam-6865	177	52	6.×	6.×	NUM
ejpam-6865	177	53	10	10	NUM
ejpam-6865	177	54	-	-	SYM
ejpam-6865	177	55	16	16	NUM
ejpam-6865	177	56	7.×	7.×	NUM
ejpam-6865	177	57	10	10	NUM
ejpam-6865	177	58	-	-	SYM
ejpam-6865	177	59	16	16	NUM
ejpam-6865	177	60	t	t	NOUN
ejpam-6865	177	61	u	u	PROPN
ejpam-6865	177	62	(	(	PUNCT
ejpam-6865	177	63	a	a	DET
ejpam-6865	177	64	p	p	X
ejpam-6865	177	65	p	p	X
ejpam-6865	177	66	ro	ro	X
ejpam-6865	177	67	x	x	PROPN
ejpam-6865	177	68	i	i	PRON
ejpam-6865	177	69	m	m	VERB
ejpam-6865	177	70	at	at	ADP
ejpam-6865	177	71	e	e	NOUN
ejpam-6865	177	72	)	)	PUNCT
ejpam-6865	177	73	u	u	NOUN
ejpam-6865	177	74	(	(	PUNCT
ejpam-6865	177	75	e	e	NOUN
ejpam-6865	177	76	x	x	PROPN
ejpam-6865	177	77	ac	ac	PROPN
ejpam-6865	177	78	t	t	PROPN
ejpam-6865	177	79	)	)	PUNCT
ejpam-6865	177	80	figure	figure	NOUN
ejpam-6865	177	81	4	4	NUM
ejpam-6865	177	82	:	:	PUNCT
ejpam-6865	177	83	the	the	DET
ejpam-6865	177	84	absolute	absolute	ADJ
ejpam-6865	177	85	error	error	NOUN
ejpam-6865	177	86	between	between	ADP
ejpam-6865	177	87	exact	exact	ADJ
ejpam-6865	177	88	and	and	CCONJ
ejpam-6865	177	89	approximate	approximate	ADJ
ejpam-6865	177	90	solutions	solution	NOUN
ejpam-6865	177	91	using	use	VERB
ejpam-6865	177	92	the	the	DET
ejpam-6865	177	93	second	second	ADJ
ejpam-6865	177	94	approach	approach	NOUN
ejpam-6865	177	95	with	with	ADP
ejpam-6865	177	96	several	several	ADJ
ejpam-6865	177	97	values	value	NOUN
ejpam-6865	177	98	of	of	ADP
ejpam-6865	177	99	α	α	NOUN
ejpam-6865	177	100	and	and	CCONJ
ejpam-6865	177	101	a	a	DET
ejpam-6865	177	102	fixed	fix	VERB
ejpam-6865	177	103	value	value	NOUN
ejpam-6865	177	104	of	of	ADP
ejpam-6865	177	105	µ	µ	NOUN
ejpam-6865	177	106	and	and	CCONJ
ejpam-6865	177	107	γ	γ	PROPN
ejpam-6865	177	108	.	.	PROPN
ejpam-6865	177	109	table	table	NOUN
ejpam-6865	177	110	1	1	NUM
ejpam-6865	177	111	:	:	PUNCT
ejpam-6865	177	112	the	the	DET
ejpam-6865	177	113	approximate	approximate	ADJ
ejpam-6865	177	114	solutions	solution	NOUN
ejpam-6865	177	115	for	for	ADP
ejpam-6865	177	116	example	example	NOUN
ejpam-6865	177	117	1	1	NUM
ejpam-6865	177	118	using	use	VERB
ejpam-6865	177	119	the	the	DET
ejpam-6865	177	120	second	second	ADJ
ejpam-6865	177	121	approach	approach	NOUN
ejpam-6865	177	122	for	for	ADP
ejpam-6865	177	123	several	several	ADJ
ejpam-6865	177	124	values	value	NOUN
ejpam-6865	177	125	of	of	ADP
ejpam-6865	177	126	α	α	NOUN
ejpam-6865	177	127	.	.	PUNCT
ejpam-6865	178	1	t	t	PROPN
ejpam-6865	178	2	α	α	PROPN
ejpam-6865	178	3	α	α	NOUN
ejpam-6865	178	4	=	=	PUNCT
ejpam-6865	178	5	0.3	0.3	NUM
ejpam-6865	178	6	α	α	NOUN
ejpam-6865	178	7	=	=	SYM
ejpam-6865	178	8	0.5	0.5	NUM
ejpam-6865	178	9	α	α	NOUN
ejpam-6865	178	10	=	=	NOUN
ejpam-6865	178	11	0.7	0.7	NUM
ejpam-6865	178	12	α	α	NOUN
ejpam-6865	178	13	=	=	SYM
ejpam-6865	178	14	0.9	0.9	NUM
ejpam-6865	178	15	0.3	0.3	NUM
ejpam-6865	178	16	0.094069	0.094069	NUM
ejpam-6865	178	17	0.0791659	0.0791659	NUM
ejpam-6865	178	18	0.058388	0.058388	NUM
ejpam-6865	178	19	0.039047	0.039047	NUM
ejpam-6865	178	20	0.5	0.5	NUM
ejpam-6865	178	21	0.277218	0.277218	NUM
ejpam-6865	178	22	0.252218	0.252218	NUM
ejpam-6865	178	23	0.208848	0.208848	NUM
ejpam-6865	178	24	0.181213	0.181213	NUM
ejpam-6865	178	25	0.7	0.7	NUM
ejpam-6865	178	26	0.567254	0.567254	NUM
ejpam-6865	178	27	0.548884	0.548884	NUM
ejpam-6865	178	28	0.499127	0.499127	NUM
ejpam-6865	178	29	0.524649	0.524649	NUM
ejpam-6865	178	30	1	1	NUM
ejpam-6865	178	31	1.216373	1.216373	NUM
ejpam-6865	178	32	1.268468	1.268468	NUM
ejpam-6865	178	33	1.293638	1.293638	NUM
ejpam-6865	178	34	1.687511	1.687511	NUM
ejpam-6865	178	35	example	example	NOUN
ejpam-6865	178	36	2	2	NUM
ejpam-6865	178	37	consider	consider	VERB
ejpam-6865	178	38	the	the	DET
ejpam-6865	178	39	following	follow	VERB
ejpam-6865	178	40	nonlinear	nonlinear	ADJ
ejpam-6865	178	41	fde	fde	PROPN
ejpam-6865	178	42	:	:	PUNCT
ejpam-6865	178	43	abc	abc	PROPN
ejpam-6865	178	44	0	0	NUM
ejpam-6865	178	45	dα,µ,γu(t	dα,µ,γu(t	PROPN
ejpam-6865	178	46	)	)	PUNCT
ejpam-6865	179	1	=	=	SYM
ejpam-6865	179	2	u2(t)−	u2(t)−	PROPN
ejpam-6865	179	3	u(t	u(t	PROPN
ejpam-6865	179	4	)	)	PUNCT
ejpam-6865	179	5	,	,	PUNCT
ejpam-6865	179	6	u(0	u(0	PROPN
ejpam-6865	179	7	)	)	PUNCT
ejpam-6865	179	8	=	=	SYM
ejpam-6865	179	9	0.5	0.5	NUM
ejpam-6865	179	10	,	,	PUNCT
ejpam-6865	179	11	(	(	PUNCT
ejpam-6865	179	12	43	43	NUM
ejpam-6865	179	13	)	)	PUNCT
ejpam-6865	179	14	where	where	SCONJ
ejpam-6865	179	15	0	0	NUM
ejpam-6865	179	16	<	<	X
ejpam-6865	179	17	α	α	X
ejpam-6865	179	18	<	<	X
ejpam-6865	179	19	1	1	NUM
ejpam-6865	179	20	and	and	CCONJ
ejpam-6865	179	21	µ	µ	NOUN
ejpam-6865	179	22	=	=	SYM
ejpam-6865	179	23	γ	γ	X
ejpam-6865	179	24	=	=	SYM
ejpam-6865	179	25	1	1	NUM
ejpam-6865	179	26	,	,	PUNCT
ejpam-6865	179	27	and	and	CCONJ
ejpam-6865	179	28	the	the	DET
ejpam-6865	179	29	exact	exact	ADJ
ejpam-6865	179	30	solution	solution	NOUN
ejpam-6865	179	31	at	at	ADP
ejpam-6865	179	32	α	α	NOUN
ejpam-6865	179	33	=	=	SYM
ejpam-6865	179	34	1	1	NUM
ejpam-6865	179	35	is	be	AUX
ejpam-6865	179	36	u(t	u(t	NOUN
ejpam-6865	179	37	)	)	PUNCT
ejpam-6865	179	38	=	=	SYM
ejpam-6865	180	1	1	1	NUM
ejpam-6865	180	2	et	et	NOUN
ejpam-6865	180	3	+	+	NOUN
ejpam-6865	180	4	1	1	NUM
ejpam-6865	180	5	.	.	PUNCT
ejpam-6865	181	1	(	(	PUNCT
ejpam-6865	181	2	44	44	NUM
ejpam-6865	181	3	)	)	PUNCT
ejpam-6865	181	4	approach	approach	NOUN
ejpam-6865	181	5	1	1	NUM
ejpam-6865	181	6	:	:	PUNCT
ejpam-6865	181	7	we	we	PRON
ejpam-6865	181	8	solve	solve	VERB
ejpam-6865	181	9	this	this	DET
ejpam-6865	181	10	example	example	NOUN
ejpam-6865	181	11	using	use	VERB
ejpam-6865	181	12	the	the	DET
ejpam-6865	181	13	first	first	ADJ
ejpam-6865	181	14	approach	approach	NOUN
ejpam-6865	181	15	,	,	PUNCT
ejpam-6865	181	16	then	then	ADV
ejpam-6865	181	17	equation	equation	NOUN
ejpam-6865	181	18	(	(	PUNCT
ejpam-6865	181	19	43	43	NUM
ejpam-6865	181	20	)	)	PUNCT
ejpam-6865	181	21	becomes	become	VERB
ejpam-6865	181	22	m∑	m∑	ADJ
ejpam-6865	181	23	i=0	i=0	PROPN
ejpam-6865	181	24	ci	ci	NOUN
ejpam-6865	182	1	m−i∑	m−i∑	ADJ
ejpam-6865	182	2	k	k	X
ejpam-6865	182	3	=	=	PRON
ejpam-6865	182	4	dαe−i	dαe−i	PROPN
ejpam-6865	182	5	(	(	PUNCT
ejpam-6865	182	6	−1)k	−1)k	PROPN
ejpam-6865	182	7	(	(	PUNCT
ejpam-6865	182	8	m	m	VERB
ejpam-6865	182	9	i	i	NOUN
ejpam-6865	182	10	)	)	PUNCT
ejpam-6865	182	11	(	(	PUNCT
ejpam-6865	182	12	m−	m−	PROPN
ejpam-6865	182	13	i	i	PROPN
ejpam-6865	182	14	k	k	NOUN
ejpam-6865	182	15	)	)	PUNCT
ejpam-6865	182	16	m(α1	m(α1	NOUN
ejpam-6865	182	17	)	)	PUNCT
ejpam-6865	182	18	1−	1−	NUM
ejpam-6865	182	19	α1	α1	PROPN
ejpam-6865	182	20	γ(k	γ(k	PROPN
ejpam-6865	182	21	+	+	PRON
ejpam-6865	182	22	i+	i+	NUM
ejpam-6865	182	23	1)eγ	1)eγ	NUM
ejpam-6865	182	24	α1,µ+k+i(λ	α1,µ+k+i(λ	NUM
ejpam-6865	182	25	,	,	PUNCT
ejpam-6865	182	26	t	t	PROPN
ejpam-6865	182	27	)	)	PUNCT
ejpam-6865	182	28	=(	=(	NOUN
ejpam-6865	182	29	m∑	m∑	CCONJ
ejpam-6865	182	30	i=0	i=0	ADJ
ejpam-6865	182	31	cibi	cibi	NOUN
ejpam-6865	182	32	,	,	PUNCT
ejpam-6865	182	33	m(t	m(t	NOUN
ejpam-6865	182	34	)	)	PUNCT
ejpam-6865	182	35	)	)	PUNCT
ejpam-6865	182	36	2	2	NUM
ejpam-6865	182	37	−	−	NOUN
ejpam-6865	182	38	m∑	m∑	CCONJ
ejpam-6865	182	39	i=0	i=0	ADJ
ejpam-6865	182	40	cibi	cibi	NOUN
ejpam-6865	182	41	,	,	PUNCT
ejpam-6865	182	42	m(t	m(t	NOUN
ejpam-6865	182	43	)	)	PUNCT
ejpam-6865	182	44	,	,	PUNCT
ejpam-6865	182	45	(	(	PUNCT
ejpam-6865	182	46	45	45	NUM
ejpam-6865	182	47	)	)	PUNCT
ejpam-6865	182	48	the	the	DET
ejpam-6865	182	49	initial	initial	ADJ
ejpam-6865	182	50	condition	condition	NOUN
ejpam-6865	182	51	gives	give	VERB
ejpam-6865	182	52	c0	c0	NOUN
ejpam-6865	182	53	=	=	PROPN
ejpam-6865	182	54	0.5	0.5	NUM
ejpam-6865	182	55	.	.	PUNCT
ejpam-6865	183	1	(	(	PUNCT
ejpam-6865	183	2	46	46	NUM
ejpam-6865	183	3	)	)	PUNCT
ejpam-6865	183	4	s.	s.	PROPN
ejpam-6865	183	5	tamimi	tamimi	PROPN
ejpam-6865	183	6	,	,	PUNCT
ejpam-6865	183	7	a.	a.	PROPN
ejpam-6865	183	8	k.	k.	PROPN
ejpam-6865	183	9	alomari	alomari	PROPN
ejpam-6865	183	10	,	,	PUNCT
ejpam-6865	183	11	m.	m.	NOUN
ejpam-6865	183	12	alaroud	alaroud	PROPN
ejpam-6865	183	13	/	/	SYM
ejpam-6865	183	14	eur	eur	PROPN
ejpam-6865	183	15	.	.	PUNCT
ejpam-6865	184	1	j.	j.	PROPN
ejpam-6865	184	2	pure	pure	PROPN
ejpam-6865	184	3	appl	appl	PROPN
ejpam-6865	184	4	.	.	PROPN
ejpam-6865	184	5	math	math	PROPN
ejpam-6865	184	6	,	,	PUNCT
ejpam-6865	184	7	18	18	NUM
ejpam-6865	184	8	(	(	PUNCT
ejpam-6865	184	9	4	4	NUM
ejpam-6865	184	10	)	)	PUNCT
ejpam-6865	184	11	(	(	PUNCT
ejpam-6865	184	12	2025	2025	NUM
ejpam-6865	184	13	)	)	PUNCT
ejpam-6865	184	14	,	,	PUNCT
ejpam-6865	184	15	6865	6865	NUM
ejpam-6865	184	16	13	13	NUM
ejpam-6865	184	17	of	of	ADP
ejpam-6865	184	18	19	19	NUM
ejpam-6865	184	19	when	when	SCONJ
ejpam-6865	184	20	we	we	PRON
ejpam-6865	184	21	apply	apply	VERB
ejpam-6865	184	22	m+	m+	NUM
ejpam-6865	184	23	1−	1−	NUM
ejpam-6865	184	24	dαe	dαe	NOUN
ejpam-6865	184	25	points	point	NOUN
ejpam-6865	184	26	in	in	ADP
ejpam-6865	184	27	equation	equation	NOUN
ejpam-6865	184	28	(	(	PUNCT
ejpam-6865	184	29	45	45	NUM
ejpam-6865	184	30	)	)	PUNCT
ejpam-6865	184	31	,	,	PUNCT
ejpam-6865	184	32	we	we	PRON
ejpam-6865	184	33	have	have	VERB
ejpam-6865	184	34	m	m	PROPN
ejpam-6865	184	35	nonlinear	nonlinear	ADJ
ejpam-6865	184	36	equations	equation	NOUN
ejpam-6865	184	37	,	,	PUNCT
ejpam-6865	184	38	then	then	ADV
ejpam-6865	184	39	m	m	PROPN
ejpam-6865	184	40	of	of	ADP
ejpam-6865	184	41	nonlinear	nonlinear	ADJ
ejpam-6865	184	42	equations	equation	NOUN
ejpam-6865	184	43	are	be	AUX
ejpam-6865	184	44	generated	generate	VERB
ejpam-6865	184	45	.	.	PUNCT
ejpam-6865	185	1	by	by	ADP
ejpam-6865	185	2	solving	solve	VERB
ejpam-6865	185	3	those	those	DET
ejpam-6865	185	4	equations	equation	NOUN
ejpam-6865	185	5	,	,	PUNCT
ejpam-6865	185	6	we	we	PRON
ejpam-6865	185	7	determined	determine	VERB
ejpam-6865	185	8	the	the	DET
ejpam-6865	185	9	ci	ci	NOUN
ejpam-6865	185	10	for	for	ADP
ejpam-6865	185	11	i	i	PROPN
ejpam-6865	185	12	=	=	NOUN
ejpam-6865	185	13	1	1	NUM
ejpam-6865	185	14	,	,	PUNCT
ejpam-6865	185	15	...	...	PUNCT
ejpam-6865	185	16	,	,	PUNCT
ejpam-6865	185	17	m.	m.	NOUN
ejpam-6865	185	18	as	as	ADP
ejpam-6865	185	19	a	a	DET
ejpam-6865	185	20	result	result	NOUN
ejpam-6865	185	21	,	,	PUNCT
ejpam-6865	185	22	the	the	DET
ejpam-6865	185	23	approximate	approximate	ADJ
ejpam-6865	185	24	solution	solution	NOUN
ejpam-6865	185	25	u(t	u(t	NOUN
ejpam-6865	185	26	)	)	PUNCT
ejpam-6865	185	27	can	can	AUX
ejpam-6865	185	28	be	be	AUX
ejpam-6865	185	29	calculated	calculate	VERB
ejpam-6865	185	30	.	.	PUNCT
ejpam-6865	186	1	we	we	PRON
ejpam-6865	186	2	plot	plot	VERB
ejpam-6865	186	3	the	the	DET
ejpam-6865	186	4	residual	residual	ADJ
ejpam-6865	186	5	error	error	NOUN
ejpam-6865	186	6	function	function	NOUN
ejpam-6865	186	7	(	(	PUNCT
ejpam-6865	186	8	ref	ref	NOUN
ejpam-6865	186	9	)	)	PUNCT
ejpam-6865	186	10	for	for	ADP
ejpam-6865	186	11	the	the	DET
ejpam-6865	186	12	approximate	approximate	ADJ
ejpam-6865	186	13	solution	solution	NOUN
ejpam-6865	186	14	of	of	ADP
ejpam-6865	186	15	example	example	NOUN
ejpam-6865	186	16	2	2	NUM
ejpam-6865	186	17	using	use	VERB
ejpam-6865	186	18	the	the	DET
ejpam-6865	186	19	first	first	ADJ
ejpam-6865	186	20	approach	approach	NOUN
ejpam-6865	186	21	with	with	ADP
ejpam-6865	186	22	α	α	PROPN
ejpam-6865	186	23	→	→	SYM
ejpam-6865	186	24	1	1	NUM
ejpam-6865	186	25	and	and	CCONJ
ejpam-6865	186	26	µ	µ	X
ejpam-6865	186	27	=	=	SYM
ejpam-6865	186	28	γ	γ	X
ejpam-6865	186	29	=	=	SYM
ejpam-6865	186	30	1	1	NUM
ejpam-6865	186	31	in	in	ADP
ejpam-6865	186	32	figure	figure	NOUN
ejpam-6865	186	33	5	5	NUM
ejpam-6865	186	34	.	.	PUNCT
ejpam-6865	187	1	the	the	DET
ejpam-6865	187	2	solutions	solution	NOUN
ejpam-6865	187	3	using	use	VERB
ejpam-6865	187	4	approach	approach	NOUN
ejpam-6865	187	5	1	1	NUM
ejpam-6865	187	6	are	be	AUX
ejpam-6865	187	7	the	the	DET
ejpam-6865	187	8	same	same	ADJ
ejpam-6865	187	9	in	in	ADP
ejpam-6865	187	10	[	[	X
ejpam-6865	187	11	22	22	NUM
ejpam-6865	187	12	]	]	PUNCT
ejpam-6865	187	13	.	.	PUNCT
ejpam-6865	188	1	0.0	0.0	NUM
ejpam-6865	188	2	0.2	0.2	NUM
ejpam-6865	188	3	0.4	0.4	NUM
ejpam-6865	188	4	0.6	0.6	NUM
ejpam-6865	188	5	0.8	0.8	NUM
ejpam-6865	188	6	1.0	1.0	NUM
ejpam-6865	188	7	0.00000	0.00000	NUM
ejpam-6865	188	8	0.00001	0.00001	NUM
ejpam-6865	188	9	0.00002	0.00002	NUM
ejpam-6865	188	10	0.00003	0.00003	NUM
ejpam-6865	188	11	0.00004	0.00004	NUM
ejpam-6865	188	12	0.00005	0.00005	NUM
ejpam-6865	188	13	0.00006	0.00006	NUM
ejpam-6865	188	14	0.00007	0.00007	NUM
ejpam-6865	188	15	t	t	NOUN
ejpam-6865	188	16	r	r	NOUN
ejpam-6865	188	17	e	e	NOUN
ejpam-6865	188	18	f	f	PROPN
ejpam-6865	188	19	figure	figure	NOUN
ejpam-6865	188	20	5	5	NUM
ejpam-6865	188	21	:	:	PUNCT
ejpam-6865	188	22	the	the	DET
ejpam-6865	188	23	ref	ref	NOUN
ejpam-6865	188	24	of	of	ADP
ejpam-6865	188	25	example	example	NOUN
ejpam-6865	188	26	2	2	NUM
ejpam-6865	188	27	using	use	VERB
ejpam-6865	188	28	the	the	DET
ejpam-6865	188	29	first	first	ADJ
ejpam-6865	188	30	approach	approach	NOUN
ejpam-6865	188	31	.	.	PUNCT
ejpam-6865	189	1	approach	approach	NOUN
ejpam-6865	189	2	2	2	NUM
ejpam-6865	189	3	:	:	PUNCT
ejpam-6865	189	4	when	when	SCONJ
ejpam-6865	189	5	we	we	PRON
ejpam-6865	189	6	solve	solve	VERB
ejpam-6865	189	7	using	use	VERB
ejpam-6865	189	8	the	the	DET
ejpam-6865	189	9	second	second	ADJ
ejpam-6865	189	10	approach	approach	NOUN
ejpam-6865	189	11	,	,	PUNCT
ejpam-6865	189	12	then	then	ADV
ejpam-6865	189	13	equation	equation	NOUN
ejpam-6865	189	14	(	(	PUNCT
ejpam-6865	189	15	43	43	NUM
ejpam-6865	189	16	)	)	PUNCT
ejpam-6865	189	17	becomes	become	VERB
ejpam-6865	189	18	m∑	m∑	ADJ
ejpam-6865	189	19	i=0	i=0	ADJ
ejpam-6865	189	20	cibi	cibi	NOUN
ejpam-6865	189	21	,	,	PUNCT
ejpam-6865	189	22	m(t	m(t	NOUN
ejpam-6865	189	23	)	)	PUNCT
ejpam-6865	189	24	=	=	SYM
ejpam-6865	190	1	(	(	PUNCT
ejpam-6865	190	2	m∑	m∑	INTJ
ejpam-6865	190	3	i=0	i=0	PROPN
ejpam-6865	190	4	ci	ci	PROPN
ejpam-6865	190	5	abiα,µ,γbi	abiα,µ,γbi	NOUN
ejpam-6865	190	6	,	,	PUNCT
ejpam-6865	190	7	m(t	m(t	NOUN
ejpam-6865	190	8	)	)	PUNCT
ejpam-6865	191	1	+	+	CCONJ
ejpam-6865	191	2	0.5	0.5	NUM
ejpam-6865	191	3	)	)	SYM
ejpam-6865	191	4	2	2	NUM
ejpam-6865	191	5	−	−	PROPN
ejpam-6865	191	6	(	(	PUNCT
ejpam-6865	191	7	m∑	m∑	CCONJ
ejpam-6865	191	8	i=0	i=0	PROPN
ejpam-6865	191	9	ci	ci	PROPN
ejpam-6865	191	10	abiα,µ,γbi	abiα,µ,γbi	NOUN
ejpam-6865	191	11	,	,	PUNCT
ejpam-6865	191	12	m(t	m(t	NOUN
ejpam-6865	191	13	)	)	PUNCT
ejpam-6865	191	14	+	+	CCONJ
ejpam-6865	191	15	0.5	0.5	NUM
ejpam-6865	191	16	)	)	PUNCT
ejpam-6865	191	17	,	,	PUNCT
ejpam-6865	191	18	(	(	PUNCT
ejpam-6865	191	19	47	47	NUM
ejpam-6865	191	20	)	)	PUNCT
ejpam-6865	191	21	and	and	CCONJ
ejpam-6865	191	22	the	the	DET
ejpam-6865	191	23	initial	initial	ADJ
ejpam-6865	191	24	condition	condition	NOUN
ejpam-6865	191	25	gives	give	VERB
ejpam-6865	191	26	c0	c0	NOUN
ejpam-6865	191	27	=	=	PUNCT
ejpam-6865	191	28	0	0	X
ejpam-6865	191	29	.	.	PUNCT
ejpam-6865	192	1	(	(	PUNCT
ejpam-6865	192	2	48	48	NUM
ejpam-6865	192	3	)	)	PUNCT
ejpam-6865	192	4	when	when	SCONJ
ejpam-6865	192	5	we	we	PRON
ejpam-6865	192	6	apply	apply	VERB
ejpam-6865	192	7	m+	m+	NUM
ejpam-6865	192	8	1−	1−	NUM
ejpam-6865	192	9	dαe	dαe	NOUN
ejpam-6865	192	10	points	point	NOUN
ejpam-6865	192	11	in	in	ADP
ejpam-6865	192	12	equation	equation	NOUN
ejpam-6865	192	13	(	(	PUNCT
ejpam-6865	192	14	47	47	NUM
ejpam-6865	192	15	)	)	PUNCT
ejpam-6865	192	16	,	,	PUNCT
ejpam-6865	192	17	we	we	PRON
ejpam-6865	192	18	have	have	VERB
ejpam-6865	192	19	m	m	PROPN
ejpam-6865	192	20	nonlinear	nonlinear	ADJ
ejpam-6865	192	21	equations	equation	NOUN
ejpam-6865	192	22	then	then	ADV
ejpam-6865	192	23	m	m	PROPN
ejpam-6865	192	24	of	of	ADP
ejpam-6865	192	25	nonlinear	nonlinear	ADJ
ejpam-6865	192	26	equations	equation	NOUN
ejpam-6865	192	27	are	be	AUX
ejpam-6865	192	28	generated	generate	VERB
ejpam-6865	192	29	.	.	PUNCT
ejpam-6865	193	1	by	by	ADP
ejpam-6865	193	2	solving	solve	VERB
ejpam-6865	193	3	those	those	DET
ejpam-6865	193	4	equations	equation	NOUN
ejpam-6865	193	5	,	,	PUNCT
ejpam-6865	193	6	we	we	PRON
ejpam-6865	193	7	determined	determine	VERB
ejpam-6865	193	8	the	the	DET
ejpam-6865	193	9	ci	ci	NOUN
ejpam-6865	193	10	for	for	ADP
ejpam-6865	193	11	i	i	PROPN
ejpam-6865	193	12	=	=	NOUN
ejpam-6865	193	13	1	1	NUM
ejpam-6865	193	14	,	,	PUNCT
ejpam-6865	193	15	...	...	PUNCT
ejpam-6865	193	16	,	,	PUNCT
ejpam-6865	193	17	m.	m.	NOUN
ejpam-6865	193	18	as	as	ADP
ejpam-6865	193	19	a	a	DET
ejpam-6865	193	20	result	result	NOUN
ejpam-6865	193	21	,	,	PUNCT
ejpam-6865	193	22	the	the	DET
ejpam-6865	193	23	approximate	approximate	ADJ
ejpam-6865	193	24	solution	solution	NOUN
ejpam-6865	193	25	u(t	u(t	NOUN
ejpam-6865	193	26	)	)	PUNCT
ejpam-6865	193	27	can	can	AUX
ejpam-6865	193	28	be	be	AUX
ejpam-6865	193	29	calculated	calculate	VERB
ejpam-6865	193	30	.	.	PUNCT
ejpam-6865	194	1	then	then	ADV
ejpam-6865	194	2	the	the	DET
ejpam-6865	194	3	ref	ref	NOUN
ejpam-6865	194	4	is	be	AUX
ejpam-6865	194	5	as	as	SCONJ
ejpam-6865	194	6	follows	follow	VERB
ejpam-6865	194	7	ref	ref	NOUN
ejpam-6865	194	8	(	(	PUNCT
ejpam-6865	194	9	t	t	NOUN
ejpam-6865	194	10	)	)	PUNCT
ejpam-6865	195	1	=	=	NOUN
ejpam-6865	195	2	abc	abc	PROPN
ejpam-6865	195	3	0	0	PUNCT
ejpam-6865	195	4	dα,µ,γu(t)−	dα,µ,γu(t)−	X
ejpam-6865	195	5	u2(t	u2(t	PROPN
ejpam-6865	195	6	)	)	PUNCT
ejpam-6865	195	7	+	+	CCONJ
ejpam-6865	195	8	u(t	u(t	NOUN
ejpam-6865	195	9	)	)	PUNCT
ejpam-6865	195	10	,	,	PUNCT
ejpam-6865	195	11	(	(	PUNCT
ejpam-6865	195	12	49	49	NUM
ejpam-6865	195	13	)	)	PUNCT
ejpam-6865	195	14	which	which	PRON
ejpam-6865	195	15	is	be	AUX
ejpam-6865	195	16	ploted	plot	VERB
ejpam-6865	195	17	in	in	ADP
ejpam-6865	195	18	6	6	NUM
ejpam-6865	195	19	.	.	PUNCT
ejpam-6865	196	1	now	now	ADV
ejpam-6865	196	2	,	,	PUNCT
ejpam-6865	196	3	in	in	ADP
ejpam-6865	196	4	figure	figure	NOUN
ejpam-6865	196	5	7	7	NUM
ejpam-6865	196	6	,	,	PUNCT
ejpam-6865	196	7	we	we	PRON
ejpam-6865	196	8	plot	plot	VERB
ejpam-6865	196	9	the	the	DET
ejpam-6865	196	10	exact	exact	NOUN
ejpam-6865	196	11	(	(	PUNCT
ejpam-6865	196	12	for	for	ADP
ejpam-6865	196	13	α	α	NOUN
ejpam-6865	196	14	=	=	SYM
ejpam-6865	196	15	1	1	NUM
ejpam-6865	196	16	)	)	PUNCT
ejpam-6865	196	17	and	and	CCONJ
ejpam-6865	196	18	approximate	approximate	ADJ
ejpam-6865	196	19	solution	solution	NOUN
ejpam-6865	196	20	for	for	ADP
ejpam-6865	196	21	(	(	PUNCT
ejpam-6865	196	22	α	α	NOUN
ejpam-6865	196	23	=	=	NOUN
ejpam-6865	196	24	0.5	0.5	NUM
ejpam-6865	196	25	)	)	PUNCT
ejpam-6865	196	26	using	use	VERB
ejpam-6865	196	27	the	the	DET
ejpam-6865	196	28	second	second	ADJ
ejpam-6865	196	29	approach	approach	NOUN
ejpam-6865	196	30	that	that	PRON
ejpam-6865	196	31	expresses	express	VERB
ejpam-6865	196	32	that	that	SCONJ
ejpam-6865	196	33	the	the	DET
ejpam-6865	196	34	solution	solution	NOUN
ejpam-6865	196	35	does	do	AUX
ejpam-6865	196	36	not	not	PART
ejpam-6865	196	37	exist	exist	VERB
ejpam-6865	196	38	.	.	PUNCT
ejpam-6865	197	1	the	the	DET
ejpam-6865	197	2	conclusion	conclusion	NOUN
ejpam-6865	197	3	in	in	ADP
ejpam-6865	197	4	this	this	DET
ejpam-6865	197	5	example	example	NOUN
ejpam-6865	197	6	demonstrates	demonstrate	VERB
ejpam-6865	197	7	the	the	DET
ejpam-6865	197	8	results	result	NOUN
ejpam-6865	197	9	given	give	VERB
ejpam-6865	197	10	in	in	ADP
ejpam-6865	197	11	[	[	PUNCT
ejpam-6865	197	12	33	33	NUM
ejpam-6865	197	13	]	]	PUNCT
ejpam-6865	197	14	;	;	PUNCT
ejpam-6865	197	15	the	the	DET
ejpam-6865	197	16	fde	fde	PROPN
ejpam-6865	197	17	abc	abc	PROPN
ejpam-6865	197	18	0	0	PUNCT
ejpam-6865	197	19	dα,1,1u(t	dα,1,1u(t	PROPN
ejpam-6865	197	20	)	)	PUNCT
ejpam-6865	198	1	=	=	SYM
ejpam-6865	198	2	u2(t)−	u2(t)−	PROPN
ejpam-6865	198	3	u(t	u(t	PROPN
ejpam-6865	198	4	)	)	PUNCT
ejpam-6865	198	5	,	,	PUNCT
ejpam-6865	198	6	u(0	u(0	PROPN
ejpam-6865	198	7	)	)	PUNCT
ejpam-6865	198	8	=	=	SYM
ejpam-6865	198	9	0.5	0.5	NUM
ejpam-6865	198	10	,	,	PUNCT
ejpam-6865	198	11	has	have	VERB
ejpam-6865	198	12	a	a	DET
ejpam-6865	198	13	nontrivial	nontrivial	ADJ
ejpam-6865	198	14	solution	solution	NOUN
ejpam-6865	198	15	only	only	ADV
ejpam-6865	198	16	if	if	SCONJ
ejpam-6865	198	17	u2(0)−	u2(0)−	PROPN
ejpam-6865	198	18	u(0	u(0	NOUN
ejpam-6865	198	19	)	)	PUNCT
ejpam-6865	198	20	=	=	SYM
ejpam-6865	198	21	0	0	X
ejpam-6865	198	22	.	.	PUNCT
ejpam-6865	198	23	example	example	NOUN
ejpam-6865	198	24	3	3	NUM
ejpam-6865	198	25	s.	s.	PROPN
ejpam-6865	198	26	tamimi	tamimi	PROPN
ejpam-6865	198	27	,	,	PUNCT
ejpam-6865	198	28	a.	a.	PROPN
ejpam-6865	198	29	k.	k.	PROPN
ejpam-6865	198	30	alomari	alomari	PROPN
ejpam-6865	198	31	,	,	PUNCT
ejpam-6865	198	32	m.	m.	NOUN
ejpam-6865	198	33	alaroud	alaroud	PROPN
ejpam-6865	198	34	/	/	SYM
ejpam-6865	198	35	eur	eur	PROPN
ejpam-6865	198	36	.	.	PUNCT
ejpam-6865	199	1	j.	j.	PROPN
ejpam-6865	199	2	pure	pure	PROPN
ejpam-6865	199	3	appl	appl	PROPN
ejpam-6865	199	4	.	.	PROPN
ejpam-6865	199	5	math	math	PROPN
ejpam-6865	199	6	,	,	PUNCT
ejpam-6865	199	7	18	18	NUM
ejpam-6865	199	8	(	(	PUNCT
ejpam-6865	199	9	4	4	NUM
ejpam-6865	199	10	)	)	PUNCT
ejpam-6865	199	11	(	(	PUNCT
ejpam-6865	199	12	2025	2025	NUM
ejpam-6865	199	13	)	)	PUNCT
ejpam-6865	199	14	,	,	PUNCT
ejpam-6865	199	15	6865	6865	NUM
ejpam-6865	199	16	14	14	NUM
ejpam-6865	199	17	of	of	ADP
ejpam-6865	199	18	19	19	NUM
ejpam-6865	199	19	0.0	0.0	NUM
ejpam-6865	199	20	0.2	0.2	NUM
ejpam-6865	199	21	0.4	0.4	NUM
ejpam-6865	199	22	0.6	0.6	NUM
ejpam-6865	200	1	0.8	0.8	NUM
ejpam-6865	200	2	1.0	1.0	NUM
ejpam-6865	200	3	0	0	NUM
ejpam-6865	201	1	2.×	2.×	NUM
ejpam-6865	201	2	10	10	NUM
ejpam-6865	201	3	-	-	SYM
ejpam-6865	201	4	6	6	NUM
ejpam-6865	201	5	4.×	4.×	NUM
ejpam-6865	201	6	10	10	NUM
ejpam-6865	201	7	-	-	SYM
ejpam-6865	201	8	6	6	NUM
ejpam-6865	201	9	6.×	6.×	NUM
ejpam-6865	201	10	10	10	NUM
ejpam-6865	201	11	-	-	SYM
ejpam-6865	201	12	6	6	NUM
ejpam-6865	201	13	8.×	8.×	PROPN
ejpam-6865	201	14	10	10	NUM
ejpam-6865	201	15	-	-	SYM
ejpam-6865	201	16	6	6	NUM
ejpam-6865	201	17	t	t	NOUN
ejpam-6865	201	18	r	r	NOUN
ejpam-6865	201	19	e	e	NOUN
ejpam-6865	201	20	f	f	PROPN
ejpam-6865	201	21	figure	figure	VERB
ejpam-6865	201	22	6	6	NUM
ejpam-6865	201	23	:	:	PUNCT
ejpam-6865	201	24	the	the	DET
ejpam-6865	201	25	ref	ref	NOUN
ejpam-6865	201	26	of	of	ADP
ejpam-6865	201	27	example	example	NOUN
ejpam-6865	201	28	2	2	NUM
ejpam-6865	201	29	using	use	VERB
ejpam-6865	201	30	the	the	DET
ejpam-6865	201	31	second	second	ADJ
ejpam-6865	201	32	approach	approach	NOUN
ejpam-6865	201	33	.	.	PUNCT
ejpam-6865	202	1	approximate	approximate	ADJ
ejpam-6865	202	2	exact	exact	ADJ
ejpam-6865	202	3	0.0	0.0	NUM
ejpam-6865	202	4	0.2	0.2	NUM
ejpam-6865	202	5	0.4	0.4	NUM
ejpam-6865	202	6	0.6	0.6	NUM
ejpam-6865	202	7	0.8	0.8	NUM
ejpam-6865	202	8	1.0	1.0	NUM
ejpam-6865	202	9	0.30	0.30	NUM
ejpam-6865	202	10	0.35	0.35	NUM
ejpam-6865	202	11	0.40	0.40	NUM
ejpam-6865	202	12	0.45	0.45	NUM
ejpam-6865	202	13	0.50	0.50	NUM
ejpam-6865	202	14	t	t	NOUN
ejpam-6865	202	15	u	u	PROPN
ejpam-6865	202	16	(	(	PUNCT
ejpam-6865	202	17	t	t	NOUN
ejpam-6865	202	18	)	)	PUNCT
ejpam-6865	202	19	figure	figure	NOUN
ejpam-6865	202	20	7	7	NUM
ejpam-6865	202	21	:	:	PUNCT
ejpam-6865	202	22	the	the	DET
ejpam-6865	202	23	exact	exact	ADJ
ejpam-6865	202	24	solution	solution	NOUN
ejpam-6865	202	25	and	and	CCONJ
ejpam-6865	202	26	approximate	approximate	ADJ
ejpam-6865	202	27	solutions	solution	NOUN
ejpam-6865	202	28	using	use	VERB
ejpam-6865	202	29	the	the	DET
ejpam-6865	202	30	second	second	ADJ
ejpam-6865	202	31	approach	approach	NOUN
ejpam-6865	202	32	with	with	ADP
ejpam-6865	202	33	α	α	PROPN
ejpam-6865	202	34	=	=	SYM
ejpam-6865	202	35	0.5	0.5	NUM
ejpam-6865	202	36	,	,	PUNCT
ejpam-6865	202	37	µ	µ	NOUN
ejpam-6865	202	38	=	=	SYM
ejpam-6865	202	39	1	1	NUM
ejpam-6865	202	40	,	,	PUNCT
ejpam-6865	202	41	and	and	CCONJ
ejpam-6865	202	42	γ	γ	X
ejpam-6865	202	43	=	=	SYM
ejpam-6865	202	44	1	1	NUM
ejpam-6865	202	45	.	.	PUNCT
ejpam-6865	203	1	in	in	ADP
ejpam-6865	203	2	this	this	DET
ejpam-6865	203	3	example	example	NOUN
ejpam-6865	203	4	,	,	PUNCT
ejpam-6865	203	5	we	we	PRON
ejpam-6865	203	6	investigate	investigate	VERB
ejpam-6865	203	7	the	the	DET
ejpam-6865	203	8	fde	fde	NOUN
ejpam-6865	203	9	by	by	ADP
ejpam-6865	203	10	applying	apply	VERB
ejpam-6865	203	11	the	the	DET
ejpam-6865	203	12	second	second	ADJ
ejpam-6865	203	13	approach	approach	NOUN
ejpam-6865	203	14	for	for	ADP
ejpam-6865	203	15	1	1	NUM
ejpam-6865	203	16	<	<	X
ejpam-6865	203	17	α	α	PROPN
ejpam-6865	203	18	≤	≤	NUM
ejpam-6865	203	19	2	2	NUM
ejpam-6865	203	20	.	.	PUNCT
ejpam-6865	203	21	consider	consider	VERB
ejpam-6865	203	22	the	the	DET
ejpam-6865	203	23	following	follow	VERB
ejpam-6865	203	24	fde	fde	PROPN
ejpam-6865	203	25	:	:	PUNCT
ejpam-6865	203	26	abc	abc	PROPN
ejpam-6865	203	27	0	0	PROPN
ejpam-6865	203	28	dα,µ,γ	dα,µ,γ	PROPN
ejpam-6865	203	29	t	t	PROPN
ejpam-6865	203	30	u(t	u(t	PROPN
ejpam-6865	203	31	)	)	PUNCT
ejpam-6865	204	1	+	+	CCONJ
ejpam-6865	204	2	u(t	u(t	NOUN
ejpam-6865	204	3	)	)	PUNCT
ejpam-6865	204	4	=	=	SYM
ejpam-6865	204	5	0	0	NUM
ejpam-6865	204	6	,	,	PUNCT
ejpam-6865	204	7	u(0	u(0	NOUN
ejpam-6865	204	8	)	)	PUNCT
ejpam-6865	204	9	=	=	SYM
ejpam-6865	204	10	0	0	NUM
ejpam-6865	204	11	and	and	CCONJ
ejpam-6865	204	12	u′(0	u′(0	PROPN
ejpam-6865	204	13	)	)	PUNCT
ejpam-6865	204	14	=	=	SYM
ejpam-6865	204	15	1	1	NUM
ejpam-6865	204	16	,	,	PUNCT
ejpam-6865	204	17	(	(	PUNCT
ejpam-6865	204	18	50	50	NUM
ejpam-6865	204	19	)	)	PUNCT
ejpam-6865	204	20	which	which	PRON
ejpam-6865	204	21	has	have	VERB
ejpam-6865	204	22	an	an	DET
ejpam-6865	204	23	exact	exact	ADJ
ejpam-6865	204	24	solution	solution	NOUN
ejpam-6865	204	25	for	for	ADP
ejpam-6865	204	26	α	α	NOUN
ejpam-6865	204	27	=	=	SYM
ejpam-6865	204	28	2	2	NUM
ejpam-6865	204	29	u(t	u(t	NOUN
ejpam-6865	204	30	)	)	PUNCT
ejpam-6865	204	31	=	=	SYM
ejpam-6865	204	32	sin(t	sin(t	PROPN
ejpam-6865	204	33	)	)	PUNCT
ejpam-6865	204	34	.	.	PUNCT
ejpam-6865	205	1	(	(	PUNCT
ejpam-6865	205	2	51	51	NUM
ejpam-6865	205	3	)	)	PUNCT
ejpam-6865	205	4	let	let	VERB
ejpam-6865	205	5	abc	abc	PROPN
ejpam-6865	205	6	0	0	NUM
ejpam-6865	205	7	dα,µ,γu(t	dα,µ,γu(t	PROPN
ejpam-6865	205	8	)	)	PUNCT
ejpam-6865	206	1	=	=	PUNCT
ejpam-6865	206	2	m∑	m∑	CCONJ
ejpam-6865	206	3	i=0	i=0	ADJ
ejpam-6865	206	4	cibi	cibi	NOUN
ejpam-6865	206	5	,	,	PUNCT
ejpam-6865	206	6	m(t	m(t	NOUN
ejpam-6865	206	7	)	)	PUNCT
ejpam-6865	206	8	.	.	PUNCT
ejpam-6865	207	1	(	(	PUNCT
ejpam-6865	207	2	52	52	NUM
ejpam-6865	207	3	)	)	PUNCT
ejpam-6865	207	4	by	by	ADP
ejpam-6865	207	5	applying	apply	VERB
ejpam-6865	207	6	the	the	DET
ejpam-6865	207	7	left	left	ADJ
ejpam-6865	207	8	ab	ab	PROPN
ejpam-6865	207	9	fractional	fractional	ADJ
ejpam-6865	207	10	integral	integral	ADJ
ejpam-6865	207	11	on	on	ADP
ejpam-6865	207	12	equation	equation	NOUN
ejpam-6865	207	13	(	(	PUNCT
ejpam-6865	207	14	52	52	NUM
ejpam-6865	207	15	)	)	PUNCT
ejpam-6865	207	16	,	,	PUNCT
ejpam-6865	207	17	we	we	PRON
ejpam-6865	207	18	get	get	VERB
ejpam-6865	207	19	u(t	u(t	NOUN
ejpam-6865	207	20	)	)	PUNCT
ejpam-6865	208	1	=	=	PUNCT
ejpam-6865	208	2	m∑	m∑	CCONJ
ejpam-6865	208	3	i=0	i=0	PROPN
ejpam-6865	208	4	ci	ci	PROPN
ejpam-6865	208	5	(	(	PUNCT
ejpam-6865	208	6	m	m	VERB
ejpam-6865	208	7	i	i	NOUN
ejpam-6865	208	8	)	)	PUNCT
ejpam-6865	208	9	m−i∑	m−i∑	ADP
ejpam-6865	208	10	k=0	k=0	PROPN
ejpam-6865	208	11	(	(	PUNCT
ejpam-6865	208	12	−1)k	−1)k	PROPN
ejpam-6865	208	13	(	(	PUNCT
ejpam-6865	208	14	m−	m−	PROPN
ejpam-6865	208	15	i	i	PROPN
ejpam-6865	208	16	k	k	PROPN
ejpam-6865	208	17	)	)	PUNCT
ejpam-6865	208	18	γ∑	γ∑	PROPN
ejpam-6865	209	1	s=0	s=0	PROPN
ejpam-6865	209	2	(	(	PUNCT
ejpam-6865	209	3	γ	γ	X
ejpam-6865	209	4	s	s	PART
ejpam-6865	209	5	)	)	PUNCT
ejpam-6865	209	6	αs	αs	ADP
ejpam-6865	209	7	1	1	NUM
ejpam-6865	209	8	(	(	PUNCT
ejpam-6865	209	9	1−	1−	NUM
ejpam-6865	209	10	α1)s−1	α1)s−1	PROPN
ejpam-6865	209	11	×	×	PROPN
ejpam-6865	209	12	γ(k	γ(k	PROPN
ejpam-6865	209	13	+	+	CCONJ
ejpam-6865	209	14	i+	i+	NUM
ejpam-6865	209	15	1	1	NUM
ejpam-6865	209	16	)	)	PUNCT
ejpam-6865	209	17	γ(αs−	γ(αs−	PUNCT
ejpam-6865	209	18	µ+	µ+	X
ejpam-6865	209	19	k	k	X
ejpam-6865	209	20	+	+	X
ejpam-6865	209	21	i+	i+	NOUN
ejpam-6865	209	22	3	3	NUM
ejpam-6865	209	23	)	)	PUNCT
ejpam-6865	209	24	tαs−µ+k+i+2	tαs−µ+k+i+2	X
ejpam-6865	210	1	+	+	CCONJ
ejpam-6865	210	2	u(0	u(0	NOUN
ejpam-6865	210	3	)	)	PUNCT
ejpam-6865	210	4	+	+	SYM
ejpam-6865	211	1	tu′(0	tu′(0	NOUN
ejpam-6865	211	2	)	)	PUNCT
ejpam-6865	211	3	,	,	PUNCT
ejpam-6865	211	4	(	(	PUNCT
ejpam-6865	211	5	53	53	NUM
ejpam-6865	211	6	)	)	PUNCT
ejpam-6865	211	7	s.	s.	PROPN
ejpam-6865	211	8	tamimi	tamimi	PROPN
ejpam-6865	211	9	,	,	PUNCT
ejpam-6865	211	10	a.	a.	PROPN
ejpam-6865	211	11	k.	k.	PROPN
ejpam-6865	211	12	alomari	alomari	PROPN
ejpam-6865	211	13	,	,	PUNCT
ejpam-6865	211	14	m.	m.	NOUN
ejpam-6865	211	15	alaroud	alaroud	PROPN
ejpam-6865	211	16	/	/	SYM
ejpam-6865	211	17	eur	eur	PROPN
ejpam-6865	211	18	.	.	PUNCT
ejpam-6865	212	1	j.	j.	PROPN
ejpam-6865	212	2	pure	pure	PROPN
ejpam-6865	212	3	appl	appl	PROPN
ejpam-6865	212	4	.	.	PROPN
ejpam-6865	212	5	math	math	PROPN
ejpam-6865	212	6	,	,	PUNCT
ejpam-6865	212	7	18	18	NUM
ejpam-6865	212	8	(	(	PUNCT
ejpam-6865	212	9	4	4	NUM
ejpam-6865	212	10	)	)	PUNCT
ejpam-6865	212	11	(	(	PUNCT
ejpam-6865	212	12	2025	2025	NUM
ejpam-6865	212	13	)	)	PUNCT
ejpam-6865	212	14	,	,	PUNCT
ejpam-6865	212	15	6865	6865	NUM
ejpam-6865	212	16	15	15	NUM
ejpam-6865	212	17	of	of	ADP
ejpam-6865	212	18	19	19	NUM
ejpam-6865	212	19	then	then	ADV
ejpam-6865	212	20	u(t	u(t	NOUN
ejpam-6865	212	21	)	)	PUNCT
ejpam-6865	212	22	=	=	PUNCT
ejpam-6865	212	23	m∑	m∑	CCONJ
ejpam-6865	212	24	i=0	i=0	PROPN
ejpam-6865	212	25	ci	ci	PROPN
ejpam-6865	212	26	(	(	PUNCT
ejpam-6865	212	27	m	m	VERB
ejpam-6865	212	28	i	i	NOUN
ejpam-6865	212	29	)	)	PUNCT
ejpam-6865	213	1	m−i∑	m−i∑	ADP
ejpam-6865	213	2	k=0	k=0	PROPN
ejpam-6865	213	3	(	(	PUNCT
ejpam-6865	213	4	−1)k	−1)k	PROPN
ejpam-6865	213	5	(	(	PUNCT
ejpam-6865	213	6	m−	m−	PROPN
ejpam-6865	213	7	i	i	PROPN
ejpam-6865	213	8	k	k	PROPN
ejpam-6865	213	9	)	)	PUNCT
ejpam-6865	213	10	γ∑	γ∑	PROPN
ejpam-6865	214	1	s=0	s=0	PROPN
ejpam-6865	214	2	(	(	PUNCT
ejpam-6865	214	3	γ	γ	X
ejpam-6865	214	4	s	s	PART
ejpam-6865	214	5	)	)	PUNCT
ejpam-6865	214	6	αs	αs	ADP
ejpam-6865	214	7	1	1	NUM
ejpam-6865	214	8	(	(	PUNCT
ejpam-6865	214	9	1−	1−	NUM
ejpam-6865	214	10	α1)s−1	α1)s−1	PROPN
ejpam-6865	214	11	×	×	PROPN
ejpam-6865	214	12	γ(k	γ(k	PROPN
ejpam-6865	214	13	+	+	CCONJ
ejpam-6865	214	14	i+	i+	NUM
ejpam-6865	214	15	1	1	NUM
ejpam-6865	214	16	)	)	PUNCT
ejpam-6865	214	17	γ(αs−	γ(αs−	PUNCT
ejpam-6865	214	18	µ+	µ+	X
ejpam-6865	214	19	k	k	X
ejpam-6865	214	20	+	+	X
ejpam-6865	214	21	i+	i+	NOUN
ejpam-6865	214	22	3	3	NUM
ejpam-6865	214	23	)	)	PUNCT
ejpam-6865	214	24	tαs−µ+k+i+2	tαs−µ+k+i+2	PROPN
ejpam-6865	215	1	+	+	NUM
ejpam-6865	215	2	t	t	PROPN
ejpam-6865	215	3	,	,	PUNCT
ejpam-6865	215	4	(	(	PUNCT
ejpam-6865	215	5	54	54	NUM
ejpam-6865	215	6	)	)	PUNCT
ejpam-6865	215	7	and	and	CCONJ
ejpam-6865	215	8	u′(t	u′(t	NOUN
ejpam-6865	215	9	)	)	PUNCT
ejpam-6865	216	1	=	=	PUNCT
ejpam-6865	216	2	m∑	m∑	CCONJ
ejpam-6865	216	3	i=0	i=0	PROPN
ejpam-6865	216	4	ci	ci	PROPN
ejpam-6865	216	5	(	(	PUNCT
ejpam-6865	216	6	m	m	VERB
ejpam-6865	216	7	i	i	NOUN
ejpam-6865	216	8	)	)	PUNCT
ejpam-6865	216	9	m−i∑	m−i∑	ADP
ejpam-6865	216	10	k=0	k=0	PROPN
ejpam-6865	216	11	(	(	PUNCT
ejpam-6865	216	12	−1)k	−1)k	PROPN
ejpam-6865	216	13	(	(	PUNCT
ejpam-6865	216	14	m−	m−	PROPN
ejpam-6865	216	15	i	i	PROPN
ejpam-6865	216	16	k	k	PROPN
ejpam-6865	216	17	)	)	PUNCT
ejpam-6865	216	18	γ∑	γ∑	PROPN
ejpam-6865	217	1	s=0	s=0	PROPN
ejpam-6865	217	2	(	(	PUNCT
ejpam-6865	217	3	γ	γ	X
ejpam-6865	217	4	s	s	PART
ejpam-6865	217	5	)	)	PUNCT
ejpam-6865	217	6	αs	αs	ADP
ejpam-6865	217	7	1	1	NUM
ejpam-6865	217	8	(	(	PUNCT
ejpam-6865	217	9	1−	1−	NUM
ejpam-6865	217	10	α1)s−1	α1)s−1	PROPN
ejpam-6865	217	11	×	×	PROPN
ejpam-6865	217	12	γ(k	γ(k	PROPN
ejpam-6865	217	13	+	+	CCONJ
ejpam-6865	217	14	i+	i+	NUM
ejpam-6865	217	15	1	1	NUM
ejpam-6865	217	16	)	)	PUNCT
ejpam-6865	217	17	γ(αs−	γ(αs−	PUNCT
ejpam-6865	217	18	µ+	µ+	X
ejpam-6865	217	19	k	k	X
ejpam-6865	217	20	+	+	X
ejpam-6865	217	21	i+	i+	NUM
ejpam-6865	217	22	2	2	NUM
ejpam-6865	217	23	)	)	PUNCT
ejpam-6865	217	24	tαs−µ+k+i+1	tαs−µ+k+i+1	NOUN
ejpam-6865	218	1	+	+	NOUN
ejpam-6865	218	2	1	1	NUM
ejpam-6865	218	3	.	.	PUNCT
ejpam-6865	218	4	(	(	PUNCT
ejpam-6865	218	5	55	55	NUM
ejpam-6865	218	6	)	)	PUNCT
ejpam-6865	218	7	by	by	ADP
ejpam-6865	218	8	substituting	substitute	VERB
ejpam-6865	218	9	t	t	NOUN
ejpam-6865	218	10	=	=	SYM
ejpam-6865	218	11	0	0	NUM
ejpam-6865	218	12	in	in	ADP
ejpam-6865	218	13	equation	equation	NOUN
ejpam-6865	218	14	(	(	PUNCT
ejpam-6865	218	15	55	55	NUM
ejpam-6865	218	16	)	)	PUNCT
ejpam-6865	218	17	,	,	PUNCT
ejpam-6865	218	18	we	we	PRON
ejpam-6865	218	19	have	have	VERB
ejpam-6865	218	20	c0	c0	NOUN
ejpam-6865	218	21	=	=	SYM
ejpam-6865	218	22	0	0	X
ejpam-6865	218	23	.	.	PUNCT
ejpam-6865	219	1	(	(	PUNCT
ejpam-6865	219	2	56	56	NUM
ejpam-6865	219	3	)	)	PUNCT
ejpam-6865	219	4	now	now	ADV
ejpam-6865	219	5	,	,	PUNCT
ejpam-6865	219	6	when	when	SCONJ
ejpam-6865	219	7	we	we	PRON
ejpam-6865	219	8	apply	apply	VERB
ejpam-6865	219	9	m+	m+	NUM
ejpam-6865	219	10	1−	1−	NUM
ejpam-6865	219	11	dαe	dαe	NOUN
ejpam-6865	219	12	points	point	NOUN
ejpam-6865	219	13	in	in	ADP
ejpam-6865	219	14	equation	equation	NOUN
ejpam-6865	219	15	(	(	PUNCT
ejpam-6865	219	16	50	50	NUM
ejpam-6865	219	17	)	)	PUNCT
ejpam-6865	219	18	,	,	PUNCT
ejpam-6865	219	19	we	we	PRON
ejpam-6865	219	20	have	have	VERB
ejpam-6865	219	21	a	a	DET
ejpam-6865	219	22	system	system	NOUN
ejpam-6865	219	23	of	of	ADP
ejpam-6865	219	24	equations	equation	NOUN
ejpam-6865	219	25	,	,	PUNCT
ejpam-6865	219	26	then	then	ADV
ejpam-6865	219	27	by	by	ADP
ejpam-6865	219	28	solving	solve	VERB
ejpam-6865	219	29	this	this	DET
ejpam-6865	219	30	system	system	NOUN
ejpam-6865	219	31	we	we	PRON
ejpam-6865	219	32	get	get	VERB
ejpam-6865	219	33	the	the	DET
ejpam-6865	219	34	values	value	NOUN
ejpam-6865	219	35	of	of	ADP
ejpam-6865	219	36	ci	ci	NOUN
ejpam-6865	219	37	for	for	ADP
ejpam-6865	219	38	i	i	PROPN
ejpam-6865	219	39	=	=	NOUN
ejpam-6865	219	40	1	1	NUM
ejpam-6865	219	41	,	,	PUNCT
ejpam-6865	219	42	·	·	PUNCT
ejpam-6865	219	43	·	·	PUNCT
ejpam-6865	219	44	·	·	PUNCT
ejpam-6865	219	45	,	,	PUNCT
ejpam-6865	219	46	m.	m.	NOUN
ejpam-6865	219	47	then	then	ADV
ejpam-6865	219	48	the	the	DET
ejpam-6865	219	49	ref	ref	NOUN
ejpam-6865	219	50	is	be	AUX
ejpam-6865	219	51	ref	ref	NOUN
ejpam-6865	219	52	(	(	PUNCT
ejpam-6865	219	53	t	t	NOUN
ejpam-6865	219	54	)	)	PUNCT
ejpam-6865	220	1	=	=	NOUN
ejpam-6865	220	2	abc	abc	PROPN
ejpam-6865	220	3	0	0	NUM
ejpam-6865	220	4	dα,µ,γu(t	dα,µ,γu(t	PROPN
ejpam-6865	220	5	)	)	PUNCT
ejpam-6865	221	1	+	+	CCONJ
ejpam-6865	221	2	u(t	u(t	NOUN
ejpam-6865	221	3	)	)	PUNCT
ejpam-6865	221	4	.	.	PUNCT
ejpam-6865	222	1	(	(	PUNCT
ejpam-6865	222	2	57	57	NUM
ejpam-6865	222	3	)	)	PUNCT
ejpam-6865	222	4	in	in	ADP
ejpam-6865	222	5	figure	figure	NOUN
ejpam-6865	222	6	8	8	NUM
ejpam-6865	222	7	,	,	PUNCT
ejpam-6865	222	8	we	we	PRON
ejpam-6865	222	9	plot	plot	VERB
ejpam-6865	222	10	the	the	DET
ejpam-6865	222	11	ref	ref	NOUN
ejpam-6865	222	12	for	for	ADP
ejpam-6865	222	13	the	the	DET
ejpam-6865	222	14	approximate	approximate	ADJ
ejpam-6865	222	15	solution	solution	NOUN
ejpam-6865	222	16	using	use	VERB
ejpam-6865	222	17	the	the	DET
ejpam-6865	222	18	second	second	ADJ
ejpam-6865	222	19	approach	approach	NOUN
ejpam-6865	222	20	of	of	ADP
ejpam-6865	222	21	example	example	NOUN
ejpam-6865	222	22	3	3	NUM
ejpam-6865	222	23	with	with	ADP
ejpam-6865	222	24	several	several	ADJ
ejpam-6865	222	25	values	value	NOUN
ejpam-6865	222	26	of	of	ADP
ejpam-6865	222	27	α	α	NOUN
ejpam-6865	222	28	and	and	CCONJ
ejpam-6865	222	29	fixed	fix	VERB
ejpam-6865	222	30	µ	µ	X
ejpam-6865	222	31	=	=	SYM
ejpam-6865	222	32	γ	γ	X
ejpam-6865	222	33	=	=	SYM
ejpam-6865	222	34	1	1	NUM
ejpam-6865	222	35	.	.	PUNCT
ejpam-6865	222	36	also	also	ADV
ejpam-6865	222	37	in	in	ADP
ejpam-6865	222	38	table	table	NOUN
ejpam-6865	222	39	2	2	NUM
ejpam-6865	222	40	,	,	PUNCT
ejpam-6865	222	41	we	we	PRON
ejpam-6865	222	42	calculate	calculate	VERB
ejpam-6865	222	43	the	the	DET
ejpam-6865	222	44	approximate	approximate	ADJ
ejpam-6865	222	45	solutions	solution	NOUN
ejpam-6865	222	46	with	with	ADP
ejpam-6865	222	47	several	several	ADJ
ejpam-6865	222	48	values	value	NOUN
ejpam-6865	222	49	of	of	ADP
ejpam-6865	222	50	α	α	NOUN
ejpam-6865	222	51	at	at	ADP
ejpam-6865	222	52	various	various	ADJ
ejpam-6865	222	53	points	point	NOUN
ejpam-6865	222	54	of	of	ADP
ejpam-6865	222	55	t.	t.	PROPN
ejpam-6865	222	56	α=1.8	α=1.8	PROPN
ejpam-6865	222	57	α=1.6	α=1.6	PROPN
ejpam-6865	222	58	α=1.4	α=1.4	VERB
ejpam-6865	222	59	0.0	0.0	NUM
ejpam-6865	222	60	0.2	0.2	NUM
ejpam-6865	222	61	0.4	0.4	NUM
ejpam-6865	222	62	0.6	0.6	NUM
ejpam-6865	222	63	0.8	0.8	NUM
ejpam-6865	222	64	1.0	1.0	NUM
ejpam-6865	222	65	0.000000	0.000000	NUM
ejpam-6865	222	66	5.×	5.×	NUM
ejpam-6865	222	67	10	10	NUM
ejpam-6865	222	68	-	-	SYM
ejpam-6865	222	69	6	6	NUM
ejpam-6865	222	70	0.000010	0.000010	NUM
ejpam-6865	222	71	0.000015	0.000015	NUM
ejpam-6865	222	72	t	t	NOUN
ejpam-6865	222	73	r	r	NOUN
ejpam-6865	222	74	e	e	NOUN
ejpam-6865	222	75	f	f	PROPN
ejpam-6865	222	76	figure	figure	NOUN
ejpam-6865	222	77	8	8	NUM
ejpam-6865	222	78	:	:	PUNCT
ejpam-6865	222	79	the	the	DET
ejpam-6865	222	80	ref	ref	NOUN
ejpam-6865	222	81	for	for	ADP
ejpam-6865	222	82	the	the	DET
ejpam-6865	222	83	approximate	approximate	ADJ
ejpam-6865	222	84	solutions	solution	NOUN
ejpam-6865	222	85	with	with	ADP
ejpam-6865	222	86	several	several	ADJ
ejpam-6865	222	87	values	value	NOUN
ejpam-6865	222	88	of	of	ADP
ejpam-6865	222	89	α	α	NOUN
ejpam-6865	222	90	and	and	CCONJ
ejpam-6865	222	91	fixed	fix	VERB
ejpam-6865	222	92	µ=γ=1	µ=γ=1	PROPN
ejpam-6865	222	93	.	.	PUNCT
ejpam-6865	223	1	now	now	ADV
ejpam-6865	223	2	,	,	PUNCT
ejpam-6865	223	3	we	we	PRON
ejpam-6865	223	4	show	show	VERB
ejpam-6865	223	5	the	the	DET
ejpam-6865	223	6	ref	ref	NOUN
ejpam-6865	223	7	of	of	ADP
ejpam-6865	223	8	the	the	DET
ejpam-6865	223	9	approximate	approximate	ADJ
ejpam-6865	223	10	solution	solution	NOUN
ejpam-6865	223	11	using	use	VERB
ejpam-6865	223	12	the	the	DET
ejpam-6865	223	13	second	second	ADJ
ejpam-6865	223	14	approach	approach	NOUN
ejpam-6865	223	15	for	for	ADP
ejpam-6865	223	16	example	example	NOUN
ejpam-6865	223	17	3	3	NUM
ejpam-6865	223	18	with	with	ADP
ejpam-6865	223	19	several	several	ADJ
ejpam-6865	223	20	values	value	NOUN
ejpam-6865	223	21	of	of	ADP
ejpam-6865	223	22	µ	µ	NOUN
ejpam-6865	223	23	and	and	CCONJ
ejpam-6865	223	24	α	α	NOUN
ejpam-6865	223	25	=	=	SYM
ejpam-6865	223	26	1.8	1.8	NUM
ejpam-6865	223	27	,	,	PUNCT
ejpam-6865	223	28	γ	γ	NOUN
ejpam-6865	223	29	=	=	SYM
ejpam-6865	223	30	1	1	NUM
ejpam-6865	223	31	in	in	ADP
ejpam-6865	223	32	figure	figure	NOUN
ejpam-6865	223	33	9	9	NUM
ejpam-6865	223	34	.	.	PUNCT
ejpam-6865	224	1	s.	s.	PROPN
ejpam-6865	224	2	tamimi	tamimi	PROPN
ejpam-6865	224	3	,	,	PUNCT
ejpam-6865	224	4	a.	a.	PROPN
ejpam-6865	224	5	k.	k.	PROPN
ejpam-6865	224	6	alomari	alomari	PROPN
ejpam-6865	224	7	,	,	PUNCT
ejpam-6865	224	8	m.	m.	NOUN
ejpam-6865	224	9	alaroud	alaroud	PROPN
ejpam-6865	224	10	/	/	SYM
ejpam-6865	224	11	eur	eur	PROPN
ejpam-6865	224	12	.	.	PUNCT
ejpam-6865	225	1	j.	j.	PROPN
ejpam-6865	225	2	pure	pure	PROPN
ejpam-6865	225	3	appl	appl	PROPN
ejpam-6865	225	4	.	.	PROPN
ejpam-6865	225	5	math	math	PROPN
ejpam-6865	225	6	,	,	PUNCT
ejpam-6865	225	7	18	18	NUM
ejpam-6865	225	8	(	(	PUNCT
ejpam-6865	225	9	4	4	NUM
ejpam-6865	225	10	)	)	PUNCT
ejpam-6865	225	11	(	(	PUNCT
ejpam-6865	225	12	2025	2025	NUM
ejpam-6865	225	13	)	)	PUNCT
ejpam-6865	225	14	,	,	PUNCT
ejpam-6865	225	15	6865	6865	NUM
ejpam-6865	225	16	16	16	NUM
ejpam-6865	225	17	of	of	ADP
ejpam-6865	225	18	19	19	NUM
ejpam-6865	225	19	table	table	NOUN
ejpam-6865	225	20	2	2	NUM
ejpam-6865	225	21	:	:	PUNCT
ejpam-6865	225	22	the	the	DET
ejpam-6865	225	23	approximate	approximate	ADJ
ejpam-6865	225	24	solutions	solution	NOUN
ejpam-6865	225	25	for	for	ADP
ejpam-6865	225	26	example	example	NOUN
ejpam-6865	225	27	3	3	NUM
ejpam-6865	225	28	using	use	VERB
ejpam-6865	225	29	the	the	DET
ejpam-6865	225	30	second	second	ADJ
ejpam-6865	225	31	approach	approach	NOUN
ejpam-6865	225	32	for	for	ADP
ejpam-6865	225	33	several	several	ADJ
ejpam-6865	225	34	values	value	NOUN
ejpam-6865	225	35	of	of	ADP
ejpam-6865	225	36	α	α	NOUN
ejpam-6865	225	37	.	.	PUNCT
ejpam-6865	226	1	t	t	PROPN
ejpam-6865	226	2	α	α	NOUN
ejpam-6865	226	3	α	α	NOUN
ejpam-6865	226	4	=	=	NOUN
ejpam-6865	226	5	1.2	1.2	NUM
ejpam-6865	226	6	α	α	NOUN
ejpam-6865	226	7	=	=	SYM
ejpam-6865	226	8	1.4	1.4	NUM
ejpam-6865	226	9	α	α	NOUN
ejpam-6865	226	10	=	=	SYM
ejpam-6865	226	11	1.6	1.6	NUM
ejpam-6865	226	12	α	α	NOUN
ejpam-6865	226	13	=	=	SYM
ejpam-6865	226	14	1.8	1.8	NUM
ejpam-6865	226	15	0.2	0.2	NUM
ejpam-6865	226	16	0.19866936	0.19866936	NUM
ejpam-6865	226	17	0.19866934	0.19866934	NUM
ejpam-6865	226	18	0.19866933	0.19866933	NUM
ejpam-6865	226	19	0.19866933	0.19866933	NUM
ejpam-6865	226	20	0.5	0.5	NUM
ejpam-6865	226	21	0.47942562	0.47942562	NUM
ejpam-6865	226	22	0.47942557	0.47942557	NUM
ejpam-6865	226	23	0.47942555	0.47942555	NUM
ejpam-6865	226	24	0.47942554	0.47942554	NUM
ejpam-6865	226	25	0.8	0.8	NUM
ejpam-6865	226	26	0.71735621	0.71735621	NUM
ejpam-6865	226	27	0.71735615	0.71735615	NUM
ejpam-6865	226	28	0.71735611	0.71735611	NUM
ejpam-6865	226	29	0.71735609	0.71735609	NUM
ejpam-6865	226	30	1	1	NUM
ejpam-6865	226	31	0.84147113	0.84147113	NUM
ejpam-6865	226	32	0.84147105	0.84147105	NUM
ejpam-6865	226	33	0.84147101	0.84147101	NUM
ejpam-6865	226	34	0.84147099	0.84147099	NUM
ejpam-6865	226	35	μ=0.4	μ=0.4	NOUN
ejpam-6865	226	36	μ=0.5	μ=0.5	NUM
ejpam-6865	226	37	μ=0.9	μ=0.9	NOUN
ejpam-6865	226	38	0.0	0.0	NUM
ejpam-6865	226	39	0.2	0.2	NUM
ejpam-6865	226	40	0.4	0.4	NUM
ejpam-6865	226	41	0.6	0.6	NUM
ejpam-6865	226	42	0.8	0.8	NUM
ejpam-6865	226	43	1.0	1.0	NUM
ejpam-6865	226	44	0.00000	0.00000	NUM
ejpam-6865	226	45	0.00001	0.00001	NUM
ejpam-6865	226	46	0.00002	0.00002	NUM
ejpam-6865	226	47	0.00003	0.00003	NUM
ejpam-6865	226	48	0.00004	0.00004	NUM
ejpam-6865	226	49	0.00005	0.00005	NUM
ejpam-6865	226	50	0.00006	0.00006	NUM
ejpam-6865	226	51	0.00007	0.00007	NUM
ejpam-6865	226	52	t	t	NOUN
ejpam-6865	226	53	r	r	NOUN
ejpam-6865	226	54	e	e	NOUN
ejpam-6865	226	55	f	f	PROPN
ejpam-6865	226	56	figure	figure	NOUN
ejpam-6865	226	57	9	9	NUM
ejpam-6865	226	58	:	:	PUNCT
ejpam-6865	226	59	the	the	PRON
ejpam-6865	226	60	about	about	ADP
ejpam-6865	226	61	ref	ref	NOUN
ejpam-6865	226	62	of	of	ADP
ejpam-6865	226	63	the	the	DET
ejpam-6865	226	64	approximate	approximate	ADJ
ejpam-6865	226	65	solutions	solution	NOUN
ejpam-6865	226	66	with	with	ADP
ejpam-6865	226	67	α	α	PROPN
ejpam-6865	226	68	=	=	SYM
ejpam-6865	226	69	1.8	1.8	NUM
ejpam-6865	226	70	,	,	PUNCT
ejpam-6865	226	71	γ	γ	NOUN
ejpam-6865	226	72	=	=	SYM
ejpam-6865	226	73	1	1	NUM
ejpam-6865	226	74	and	and	CCONJ
ejpam-6865	226	75	several	several	ADJ
ejpam-6865	226	76	values	value	NOUN
ejpam-6865	226	77	of	of	ADP
ejpam-6865	226	78	µ.	µ.	NOUN
ejpam-6865	226	79	6	6	NUM
ejpam-6865	226	80	.	.	PUNCT
ejpam-6865	227	1	discussions	discussion	NOUN
ejpam-6865	227	2	in	in	ADP
ejpam-6865	227	3	example	example	NOUN
ejpam-6865	227	4	1	1	NUM
ejpam-6865	227	5	,	,	PUNCT
ejpam-6865	227	6	the	the	DET
ejpam-6865	227	7	comparison	comparison	NOUN
ejpam-6865	227	8	between	between	ADP
ejpam-6865	227	9	the	the	DET
ejpam-6865	227	10	solutions	solution	NOUN
ejpam-6865	227	11	using	use	VERB
ejpam-6865	227	12	the	the	DET
ejpam-6865	227	13	first	first	ADJ
ejpam-6865	227	14	approach	approach	NOUN
ejpam-6865	227	15	is	be	AUX
ejpam-6865	227	16	shown	show	VERB
ejpam-6865	227	17	in	in	ADP
ejpam-6865	227	18	figure	figure	NOUN
ejpam-6865	227	19	1	1	NUM
ejpam-6865	227	20	.	.	PUNCT
ejpam-6865	227	21	as	as	SCONJ
ejpam-6865	227	22	shown	show	VERB
ejpam-6865	227	23	,	,	PUNCT
ejpam-6865	227	24	there	there	PRON
ejpam-6865	227	25	is	be	VERB
ejpam-6865	227	26	a	a	DET
ejpam-6865	227	27	significant	significant	ADJ
ejpam-6865	227	28	dispersion	dispersion	NOUN
ejpam-6865	227	29	in	in	ADP
ejpam-6865	227	30	the	the	DET
ejpam-6865	227	31	results	result	NOUN
ejpam-6865	227	32	when	when	SCONJ
ejpam-6865	227	33	the	the	DET
ejpam-6865	227	34	values	value	NOUN
ejpam-6865	227	35	of	of	ADP
ejpam-6865	227	36	α	α	PROPN
ejpam-6865	227	37	are	be	AUX
ejpam-6865	227	38	changed	change	VERB
ejpam-6865	227	39	.	.	PUNCT
ejpam-6865	228	1	figure	figure	NOUN
ejpam-6865	228	2	2	2	NUM
ejpam-6865	228	3	illustrates	illustrate	VERB
ejpam-6865	228	4	the	the	DET
ejpam-6865	228	5	approximate	approximate	ADJ
ejpam-6865	228	6	solution	solution	NOUN
ejpam-6865	228	7	for	for	ADP
ejpam-6865	228	8	various	various	ADJ
ejpam-6865	228	9	values	value	NOUN
ejpam-6865	228	10	of	of	ADP
ejpam-6865	228	11	the	the	DET
ejpam-6865	228	12	fractional	fractional	ADJ
ejpam-6865	228	13	parameters	parameter	NOUN
ejpam-6865	228	14	.	.	PUNCT
ejpam-6865	229	1	as	as	SCONJ
ejpam-6865	229	2	shown	show	VERB
ejpam-6865	229	3	,	,	PUNCT
ejpam-6865	229	4	the	the	DET
ejpam-6865	229	5	three	three	NUM
ejpam-6865	229	6	curves	curve	NOUN
ejpam-6865	229	7	are	be	AUX
ejpam-6865	229	8	very	very	ADV
ejpam-6865	229	9	close	close	ADJ
ejpam-6865	229	10	to	to	ADP
ejpam-6865	229	11	each	each	DET
ejpam-6865	229	12	other	other	ADJ
ejpam-6865	229	13	,	,	PUNCT
ejpam-6865	229	14	indicating	indicate	VERB
ejpam-6865	229	15	that	that	SCONJ
ejpam-6865	229	16	this	this	DET
ejpam-6865	229	17	method	method	NOUN
ejpam-6865	229	18	is	be	AUX
ejpam-6865	229	19	more	more	ADV
ejpam-6865	229	20	reliable	reliable	ADJ
ejpam-6865	229	21	and	and	CCONJ
ejpam-6865	229	22	accurate	accurate	ADJ
ejpam-6865	229	23	.	.	PUNCT
ejpam-6865	230	1	the	the	DET
ejpam-6865	230	2	absolute	absolute	ADJ
ejpam-6865	230	3	error	error	NOUN
ejpam-6865	230	4	for	for	ADP
ejpam-6865	230	5	the	the	DET
ejpam-6865	230	6	first	first	ADJ
ejpam-6865	230	7	and	and	CCONJ
ejpam-6865	230	8	second	second	ADJ
ejpam-6865	230	9	approaches	approach	NOUN
ejpam-6865	230	10	is	be	AUX
ejpam-6865	230	11	displayed	display	VERB
ejpam-6865	230	12	in	in	ADP
ejpam-6865	230	13	figures	figure	NOUN
ejpam-6865	230	14	3	3	NUM
ejpam-6865	230	15	and	and	CCONJ
ejpam-6865	230	16	4	4	NUM
ejpam-6865	230	17	,	,	PUNCT
ejpam-6865	230	18	respectively	respectively	ADV
ejpam-6865	230	19	.	.	PUNCT
ejpam-6865	231	1	as	as	SCONJ
ejpam-6865	231	2	shown	show	VERB
ejpam-6865	231	3	,	,	PUNCT
ejpam-6865	231	4	the	the	DET
ejpam-6865	231	5	second	second	ADJ
ejpam-6865	231	6	approach	approach	NOUN
ejpam-6865	231	7	gives	give	VERB
ejpam-6865	231	8	a	a	DET
ejpam-6865	231	9	better	well	ADJ
ejpam-6865	231	10	residual	residual	ADJ
ejpam-6865	231	11	error	error	NOUN
ejpam-6865	231	12	than	than	ADP
ejpam-6865	231	13	the	the	DET
ejpam-6865	231	14	first	first	ADJ
ejpam-6865	231	15	approach	approach	NOUN
ejpam-6865	231	16	.	.	PUNCT
ejpam-6865	232	1	in	in	ADP
ejpam-6865	232	2	contrast	contrast	NOUN
ejpam-6865	232	3	,	,	PUNCT
ejpam-6865	232	4	the	the	DET
ejpam-6865	232	5	second	second	ADJ
ejpam-6865	232	6	approach	approach	NOUN
ejpam-6865	232	7	yields	yield	VERB
ejpam-6865	232	8	a	a	DET
ejpam-6865	232	9	very	very	ADV
ejpam-6865	232	10	small	small	ADJ
ejpam-6865	232	11	error	error	NOUN
ejpam-6865	232	12	that	that	PRON
ejpam-6865	232	13	tends	tend	VERB
ejpam-6865	232	14	to	to	ADP
ejpam-6865	232	15	10−15	10−15	NUM
ejpam-6865	232	16	compared	compare	VERB
ejpam-6865	232	17	to	to	ADP
ejpam-6865	232	18	the	the	DET
ejpam-6865	232	19	first	first	ADJ
ejpam-6865	232	20	approach	approach	NOUN
ejpam-6865	232	21	.	.	PUNCT
ejpam-6865	233	1	for	for	ADP
ejpam-6865	233	2	example	example	NOUN
ejpam-6865	233	3	2	2	NUM
ejpam-6865	233	4	,	,	PUNCT
ejpam-6865	233	5	the	the	DET
ejpam-6865	233	6	same	same	ADJ
ejpam-6865	233	7	trend	trend	NOUN
ejpam-6865	233	8	has	have	AUX
ejpam-6865	233	9	been	be	AUX
ejpam-6865	233	10	observed	observe	VERB
ejpam-6865	233	11	;	;	PUNCT
ejpam-6865	233	12	the	the	DET
ejpam-6865	233	13	residual	residual	ADJ
ejpam-6865	233	14	errors	error	NOUN
ejpam-6865	233	15	are	be	AUX
ejpam-6865	233	16	plotted	plot	VERB
ejpam-6865	233	17	in	in	ADP
ejpam-6865	233	18	figures	figure	NOUN
ejpam-6865	233	19	5	5	NUM
ejpam-6865	233	20	and	and	CCONJ
ejpam-6865	233	21	6	6	NUM
ejpam-6865	233	22	for	for	ADP
ejpam-6865	233	23	the	the	DET
ejpam-6865	233	24	first	first	ADJ
ejpam-6865	233	25	and	and	CCONJ
ejpam-6865	233	26	second	second	ADJ
ejpam-6865	233	27	approaches	approach	NOUN
ejpam-6865	233	28	,	,	PUNCT
ejpam-6865	233	29	respectively	respectively	ADV
ejpam-6865	233	30	.	.	PUNCT
ejpam-6865	234	1	as	as	SCONJ
ejpam-6865	234	2	shown	show	VERB
ejpam-6865	234	3	,	,	PUNCT
ejpam-6865	234	4	the	the	DET
ejpam-6865	234	5	error	error	NOUN
ejpam-6865	234	6	in	in	ADP
ejpam-6865	234	7	the	the	DET
ejpam-6865	234	8	second	second	ADJ
ejpam-6865	234	9	approach	approach	NOUN
ejpam-6865	234	10	was	be	AUX
ejpam-6865	234	11	significantly	significantly	ADV
ejpam-6865	234	12	lower	low	ADJ
ejpam-6865	234	13	than	than	ADP
ejpam-6865	234	14	that	that	PRON
ejpam-6865	234	15	in	in	ADP
ejpam-6865	234	16	the	the	DET
ejpam-6865	234	17	first	first	ADJ
ejpam-6865	234	18	approach	approach	NOUN
ejpam-6865	234	19	,	,	PUNCT
ejpam-6865	234	20	indicating	indicate	VERB
ejpam-6865	234	21	that	that	SCONJ
ejpam-6865	234	22	the	the	DET
ejpam-6865	234	23	second	second	ADJ
ejpam-6865	234	24	approach	approach	NOUN
ejpam-6865	234	25	is	be	AUX
ejpam-6865	234	26	more	more	ADV
ejpam-6865	234	27	accurate	accurate	ADJ
ejpam-6865	234	28	and	and	CCONJ
ejpam-6865	234	29	yields	yield	VERB
ejpam-6865	234	30	reliable	reliable	ADJ
ejpam-6865	234	31	results	result	NOUN
ejpam-6865	234	32	.	.	PUNCT
ejpam-6865	235	1	figure	figure	VERB
ejpam-6865	235	2	7	7	NUM
ejpam-6865	235	3	shows	show	VERB
ejpam-6865	235	4	that	that	SCONJ
ejpam-6865	235	5	the	the	DET
ejpam-6865	235	6	solution	solution	NOUN
ejpam-6865	235	7	does	do	AUX
ejpam-6865	235	8	not	not	PART
ejpam-6865	235	9	exist	exist	VERB
ejpam-6865	235	10	with	with	ADP
ejpam-6865	235	11	α	α	NOUN
ejpam-6865	235	12	=	=	SYM
ejpam-6865	235	13	0.5	0.5	NUM
ejpam-6865	235	14	and	and	CCONJ
ejpam-6865	235	15	µ	µ	X
ejpam-6865	235	16	=	=	SYM
ejpam-6865	235	17	γ	γ	X
ejpam-6865	235	18	=	=	SYM
ejpam-6865	235	19	1	1	NUM
ejpam-6865	235	20	using	use	VERB
ejpam-6865	235	21	the	the	DET
ejpam-6865	235	22	second	second	ADJ
ejpam-6865	235	23	approach	approach	NOUN
ejpam-6865	235	24	,	,	PUNCT
ejpam-6865	235	25	which	which	PRON
ejpam-6865	235	26	agrees	agree	VERB
ejpam-6865	235	27	with	with	ADP
ejpam-6865	235	28	the	the	DET
ejpam-6865	235	29	theoretical	theoretical	ADJ
ejpam-6865	235	30	results	result	NOUN
ejpam-6865	235	31	in	in	ADP
ejpam-6865	235	32	[	[	X
ejpam-6865	235	33	33	33	NUM
ejpam-6865	235	34	]	]	PUNCT
ejpam-6865	235	35	.	.	PUNCT
ejpam-6865	236	1	in	in	ADP
ejpam-6865	236	2	example	example	NOUN
ejpam-6865	236	3	3	3	NUM
ejpam-6865	236	4	,	,	PUNCT
ejpam-6865	236	5	the	the	DET
ejpam-6865	236	6	absolute	absolute	ADJ
ejpam-6865	236	7	residual	residual	ADJ
ejpam-6865	236	8	error	error	NOUN
ejpam-6865	236	9	in	in	ADP
ejpam-6865	236	10	figure	figure	NOUN
ejpam-6865	236	11	8	8	NUM
ejpam-6865	236	12	decreases	decrease	NOUN
ejpam-6865	236	13	when	when	SCONJ
ejpam-6865	236	14	the	the	DET
ejpam-6865	236	15	α	α	PROPN
ejpam-6865	236	16	value	value	NOUN
ejpam-6865	236	17	increases	increase	NOUN
ejpam-6865	236	18	and	and	CCONJ
ejpam-6865	236	19	when	when	SCONJ
ejpam-6865	236	20	it	it	PRON
ejpam-6865	236	21	becomes	become	VERB
ejpam-6865	236	22	close	close	ADJ
ejpam-6865	236	23	to	to	ADP
ejpam-6865	236	24	an	an	DET
ejpam-6865	236	25	integer	integer	NOUN
ejpam-6865	236	26	number	number	NOUN
ejpam-6865	236	27	for	for	ADP
ejpam-6865	236	28	fixing	fix	VERB
ejpam-6865	236	29	the	the	DET
ejpam-6865	236	30	µ	µ	NOUN
ejpam-6865	236	31	and	and	CCONJ
ejpam-6865	236	32	γ	γ	PROPN
ejpam-6865	236	33	.	.	PROPN
ejpam-6865	236	34	figure	figure	NOUN
ejpam-6865	236	35	9	9	NUM
ejpam-6865	236	36	shows	show	VERB
ejpam-6865	236	37	the	the	DET
ejpam-6865	236	38	absolute	absolute	ADJ
ejpam-6865	236	39	residual	residual	ADJ
ejpam-6865	236	40	error	error	NOUN
ejpam-6865	236	41	when	when	SCONJ
ejpam-6865	236	42	the	the	DET
ejpam-6865	236	43	µ	µ	NOUN
ejpam-6865	236	44	is	be	AUX
ejpam-6865	236	45	varying	vary	VERB
ejpam-6865	236	46	;	;	PUNCT
ejpam-6865	236	47	as	as	SCONJ
ejpam-6865	236	48	indicated	indicate	VERB
ejpam-6865	236	49	,	,	PUNCT
ejpam-6865	236	50	the	the	DET
ejpam-6865	236	51	error	error	NOUN
ejpam-6865	236	52	decreases	decrease	VERB
ejpam-6865	236	53	as	as	ADP
ejpam-6865	236	54	the	the	DET
ejpam-6865	236	55	µ	µ	NOUN
ejpam-6865	236	56	increases	increase	NOUN
ejpam-6865	236	57	,	,	PUNCT
ejpam-6865	236	58	and	and	CCONJ
ejpam-6865	236	59	the	the	DET
ejpam-6865	236	60	error	error	NOUN
ejpam-6865	236	61	becomes	become	VERB
ejpam-6865	236	62	minimum	minimum	NOUN
ejpam-6865	236	63	when	when	SCONJ
ejpam-6865	236	64	the	the	DET
ejpam-6865	236	65	value	value	NOUN
ejpam-6865	236	66	of	of	ADP
ejpam-6865	236	67	µ	µ	NOUN
ejpam-6865	236	68	is	be	AUX
ejpam-6865	236	69	close	close	ADJ
ejpam-6865	236	70	to	to	ADP
ejpam-6865	236	71	one	one	NUM
ejpam-6865	236	72	.	.	PUNCT
ejpam-6865	237	1	s.	s.	PROPN
ejpam-6865	237	2	tamimi	tamimi	PROPN
ejpam-6865	237	3	,	,	PUNCT
ejpam-6865	237	4	a.	a.	PROPN
ejpam-6865	237	5	k.	k.	PROPN
ejpam-6865	237	6	alomari	alomari	PROPN
ejpam-6865	237	7	,	,	PUNCT
ejpam-6865	237	8	m.	m.	NOUN
ejpam-6865	237	9	alaroud	alaroud	PROPN
ejpam-6865	237	10	/	/	SYM
ejpam-6865	237	11	eur	eur	PROPN
ejpam-6865	237	12	.	.	PUNCT
ejpam-6865	238	1	j.	j.	PROPN
ejpam-6865	238	2	pure	pure	PROPN
ejpam-6865	238	3	appl	appl	PROPN
ejpam-6865	238	4	.	.	PROPN
ejpam-6865	238	5	math	math	PROPN
ejpam-6865	238	6	,	,	PUNCT
ejpam-6865	238	7	18	18	NUM
ejpam-6865	238	8	(	(	PUNCT
ejpam-6865	238	9	4	4	NUM
ejpam-6865	238	10	)	)	PUNCT
ejpam-6865	238	11	(	(	PUNCT
ejpam-6865	238	12	2025	2025	NUM
ejpam-6865	238	13	)	)	PUNCT
ejpam-6865	238	14	,	,	PUNCT
ejpam-6865	238	15	6865	6865	NUM
ejpam-6865	238	16	17	17	NUM
ejpam-6865	238	17	of	of	ADP
ejpam-6865	238	18	19	19	NUM
ejpam-6865	238	19	7	7	NUM
ejpam-6865	238	20	.	.	PUNCT
ejpam-6865	239	1	conclusions	conclusion	NOUN
ejpam-6865	239	2	in	in	ADP
ejpam-6865	239	3	this	this	DET
ejpam-6865	239	4	study	study	NOUN
ejpam-6865	239	5	,	,	PUNCT
ejpam-6865	239	6	we	we	PRON
ejpam-6865	239	7	built	build	VERB
ejpam-6865	239	8	two	two	NUM
ejpam-6865	239	9	frameworks	framework	NOUN
ejpam-6865	239	10	for	for	ADP
ejpam-6865	239	11	solving	solve	VERB
ejpam-6865	239	12	fdes	fde	NOUN
ejpam-6865	239	13	in	in	ADP
ejpam-6865	239	14	the	the	DET
ejpam-6865	239	15	sense	sense	NOUN
ejpam-6865	239	16	of	of	ADP
ejpam-6865	239	17	abc	abc	PROPN
ejpam-6865	239	18	-	-	PUNCT
ejpam-6865	239	19	fd	fd	PROPN
ejpam-6865	239	20	with	with	ADP
ejpam-6865	239	21	generalized	generalized	ADJ
ejpam-6865	239	22	mittag	mittag	ADJ
ejpam-6865	239	23	-	-	PUNCT
ejpam-6865	239	24	leffler	leffler	NOUN
ejpam-6865	239	25	function	function	NOUN
ejpam-6865	239	26	by	by	ADP
ejpam-6865	239	27	investigating	investigate	VERB
ejpam-6865	239	28	the	the	DET
ejpam-6865	239	29	use	use	NOUN
ejpam-6865	239	30	of	of	ADP
ejpam-6865	239	31	bernstein	bernstein	PROPN
ejpam-6865	239	32	polynomials	polynomials	PROPN
ejpam-6865	239	33	,	,	PUNCT
ejpam-6865	239	34	where	where	SCONJ
ejpam-6865	239	35	the	the	DET
ejpam-6865	239	36	first	first	ADJ
ejpam-6865	239	37	approach	approach	NOUN
ejpam-6865	239	38	,	,	PUNCT
ejpam-6865	239	39	suppose	suppose	VERB
ejpam-6865	239	40	y(t	y(t	NOUN
ejpam-6865	239	41	)	)	PUNCT
ejpam-6865	240	1	=	=	PUNCT
ejpam-6865	240	2	m∑	m∑	CCONJ
ejpam-6865	240	3	i=0	i=0	PROPN
ejpam-6865	240	4	ci	ci	PROPN
ejpam-6865	240	5	(	(	PUNCT
ejpam-6865	240	6	m	m	VERB
ejpam-6865	240	7	i	i	NOUN
ejpam-6865	240	8	)	)	PUNCT
ejpam-6865	240	9	m−i∑	m−i∑	ADP
ejpam-6865	240	10	k=0	k=0	PROPN
ejpam-6865	240	11	(	(	PUNCT
ejpam-6865	240	12	−1)k	−1)k	PROPN
ejpam-6865	240	13	(	(	PUNCT
ejpam-6865	240	14	m−	m−	PROPN
ejpam-6865	240	15	i	i	PROPN
ejpam-6865	240	16	k	k	PROPN
ejpam-6865	240	17	)	)	PUNCT
ejpam-6865	240	18	tk+i	tk+i	NOUN
ejpam-6865	240	19	.	.	PUNCT
ejpam-6865	241	1	while	while	SCONJ
ejpam-6865	241	2	,	,	PUNCT
ejpam-6865	241	3	the	the	DET
ejpam-6865	241	4	second	second	ADJ
ejpam-6865	241	5	approach	approach	NOUN
ejpam-6865	241	6	,	,	PUNCT
ejpam-6865	241	7	suppose	suppose	VERB
ejpam-6865	241	8	(	(	PUNCT
ejpam-6865	241	9	abc	abc	PROPN
ejpam-6865	241	10	0	0	NUM
ejpam-6865	241	11	dα,µ,γy)(t	dα,µ,γy)(t	PROPN
ejpam-6865	241	12	)	)	PUNCT
ejpam-6865	241	13	=	=	PUNCT
ejpam-6865	242	1	m∑	m∑	CCONJ
ejpam-6865	242	2	i=0	i=0	PROPN
ejpam-6865	242	3	ci	ci	PROPN
ejpam-6865	242	4	(	(	PUNCT
ejpam-6865	242	5	m	m	VERB
ejpam-6865	242	6	i	i	NOUN
ejpam-6865	242	7	)	)	PUNCT
ejpam-6865	243	1	m−i∑	m−i∑	ADP
ejpam-6865	243	2	k=0	k=0	PROPN
ejpam-6865	243	3	(	(	PUNCT
ejpam-6865	243	4	−1)k	−1)k	PROPN
ejpam-6865	243	5	(	(	PUNCT
ejpam-6865	243	6	m−	m−	PROPN
ejpam-6865	243	7	i	i	PROPN
ejpam-6865	243	8	k	k	PROPN
ejpam-6865	243	9	)	)	PUNCT
ejpam-6865	244	1	tk+i	tk+i	NOUN
ejpam-6865	244	2	.	.	PUNCT
ejpam-6865	245	1	when	when	SCONJ
ejpam-6865	245	2	we	we	PRON
ejpam-6865	245	3	concluded	conclude	VERB
ejpam-6865	245	4	that	that	SCONJ
ejpam-6865	245	5	the	the	DET
ejpam-6865	245	6	analytic	analytic	ADJ
ejpam-6865	245	7	solution	solution	NOUN
ejpam-6865	245	8	using	use	VERB
ejpam-6865	245	9	the	the	DET
ejpam-6865	245	10	second	second	ADJ
ejpam-6865	245	11	approach	approach	NOUN
ejpam-6865	245	12	was	be	AUX
ejpam-6865	245	13	closer	close	ADJ
ejpam-6865	245	14	to	to	ADP
ejpam-6865	245	15	the	the	DET
ejpam-6865	245	16	exact	exact	ADJ
ejpam-6865	245	17	solution	solution	NOUN
ejpam-6865	245	18	and	and	CCONJ
ejpam-6865	245	19	had	have	VERB
ejpam-6865	245	20	better	well	ADJ
ejpam-6865	245	21	accuracy	accuracy	NOUN
ejpam-6865	245	22	compared	compare	VERB
ejpam-6865	245	23	with	with	ADP
ejpam-6865	245	24	the	the	DET
ejpam-6865	245	25	first	first	ADJ
ejpam-6865	245	26	approach	approach	NOUN
ejpam-6865	245	27	,	,	PUNCT
ejpam-6865	245	28	we	we	PRON
ejpam-6865	245	29	noticed	notice	VERB
ejpam-6865	245	30	that	that	SCONJ
ejpam-6865	245	31	the	the	DET
ejpam-6865	245	32	absolute	absolute	ADJ
ejpam-6865	245	33	error	error	NOUN
ejpam-6865	245	34	was	be	AUX
ejpam-6865	245	35	very	very	ADV
ejpam-6865	245	36	small	small	ADJ
ejpam-6865	245	37	for	for	ADP
ejpam-6865	245	38	the	the	DET
ejpam-6865	245	39	second	second	ADJ
ejpam-6865	245	40	approach	approach	NOUN
ejpam-6865	245	41	in	in	ADP
ejpam-6865	245	42	all	all	DET
ejpam-6865	245	43	the	the	DET
ejpam-6865	245	44	given	give	VERB
ejpam-6865	245	45	examples	example	NOUN
ejpam-6865	245	46	.	.	PUNCT
ejpam-6865	246	1	also	also	ADV
ejpam-6865	246	2	,	,	PUNCT
ejpam-6865	246	3	the	the	DET
ejpam-6865	246	4	main	main	ADJ
ejpam-6865	246	5	feature	feature	NOUN
ejpam-6865	246	6	of	of	ADP
ejpam-6865	246	7	the	the	DET
ejpam-6865	246	8	second	second	ADJ
ejpam-6865	246	9	approach	approach	NOUN
ejpam-6865	246	10	is	be	AUX
ejpam-6865	246	11	capable	capable	ADJ
ejpam-6865	246	12	of	of	ADP
ejpam-6865	246	13	identifying	identify	VERB
ejpam-6865	246	14	whether	whether	SCONJ
ejpam-6865	246	15	an	an	DET
ejpam-6865	246	16	approximate	approximate	ADJ
ejpam-6865	246	17	solution	solution	NOUN
ejpam-6865	246	18	exists	exist	VERB
ejpam-6865	246	19	or	or	CCONJ
ejpam-6865	246	20	not	not	PART
ejpam-6865	246	21	.	.	PUNCT
ejpam-6865	247	1	in	in	ADP
ejpam-6865	247	2	contrast	contrast	NOUN
ejpam-6865	247	3	,	,	PUNCT
ejpam-6865	247	4	approach	approach	NOUN
ejpam-6865	247	5	1	1	NUM
ejpam-6865	247	6	lacks	lack	VERB
ejpam-6865	247	7	this	this	DET
ejpam-6865	247	8	capability	capability	NOUN
ejpam-6865	247	9	,	,	PUNCT
ejpam-6865	247	10	as	as	SCONJ
ejpam-6865	247	11	noted	note	VERB
ejpam-6865	247	12	in	in	ADP
ejpam-6865	247	13	example	example	NOUN
ejpam-6865	248	1	2	2	NUM
ejpam-6865	248	2	.	.	PUNCT
ejpam-6865	248	3	therefore	therefore	ADV
ejpam-6865	248	4	,	,	PUNCT
ejpam-6865	248	5	the	the	DET
ejpam-6865	248	6	present	present	ADJ
ejpam-6865	248	7	approaches	approach	NOUN
ejpam-6865	248	8	can	can	AUX
ejpam-6865	248	9	be	be	AUX
ejpam-6865	248	10	investigated	investigate	VERB
ejpam-6865	248	11	for	for	ADP
ejpam-6865	248	12	more	more	ADJ
ejpam-6865	248	13	complex	complex	ADJ
ejpam-6865	248	14	problems	problem	NOUN
ejpam-6865	248	15	,	,	PUNCT
ejpam-6865	248	16	such	such	ADJ
ejpam-6865	248	17	as	as	ADP
ejpam-6865	248	18	boundary	boundary	ADJ
ejpam-6865	248	19	value	value	NOUN
ejpam-6865	248	20	problems	problem	NOUN
ejpam-6865	248	21	or	or	CCONJ
ejpam-6865	248	22	integro	integro	ADJ
ejpam-6865	248	23	-	-	PUNCT
ejpam-6865	248	24	differential	differential	NOUN
ejpam-6865	248	25	equations	equation	NOUN
ejpam-6865	248	26	.	.	PUNCT
ejpam-6865	249	1	references	reference	NOUN
ejpam-6865	249	2	[	[	X
ejpam-6865	249	3	1	1	NUM
ejpam-6865	249	4	]	]	PUNCT
ejpam-6865	249	5	a.	a.	NOUN
ejpam-6865	249	6	a.	a.	NOUN
ejpam-6865	249	7	kilbas	kilbas	PROPN
ejpam-6865	249	8	,	,	PUNCT
ejpam-6865	249	9	h.	h.	PROPN
ejpam-6865	249	10	m.	m.	PROPN
ejpam-6865	249	11	srivastava	srivastava	PROPN
ejpam-6865	249	12	,	,	PUNCT
ejpam-6865	249	13	and	and	CCONJ
ejpam-6865	249	14	j.	j.	PROPN
ejpam-6865	249	15	j.	j.	PROPN
ejpam-6865	249	16	trujillo	trujillo	PROPN
ejpam-6865	249	17	.	.	PUNCT
ejpam-6865	249	18	theory	theory	NOUN
ejpam-6865	249	19	and	and	CCONJ
ejpam-6865	249	20	applications	application	NOUN
ejpam-6865	249	21	of	of	ADP
ejpam-6865	249	22	fractional	fractional	ADJ
ejpam-6865	249	23	differential	differential	ADJ
ejpam-6865	249	24	equations	equation	NOUN
ejpam-6865	249	25	,	,	PUNCT
ejpam-6865	249	26	volume	volume	NOUN
ejpam-6865	249	27	204	204	NUM
ejpam-6865	249	28	of	of	ADP
ejpam-6865	249	29	north	north	NOUN
ejpam-6865	249	30	-	-	PUNCT
ejpam-6865	249	31	holland	holland	PROPN
ejpam-6865	249	32	mathematics	mathematics	PROPN
ejpam-6865	249	33	studies	study	NOUN
ejpam-6865	249	34	.	.	PUNCT
ejpam-6865	250	1	elsevier	elsevier	NOUN
ejpam-6865	250	2	,	,	PUNCT
ejpam-6865	250	3	2006	2006	NUM
ejpam-6865	250	4	.	.	PUNCT
ejpam-6865	251	1	[	[	X
ejpam-6865	251	2	2	2	X
ejpam-6865	251	3	]	]	PUNCT
ejpam-6865	251	4	s.	s.	PROPN
ejpam-6865	251	5	sahoo	sahoo	PROPN
ejpam-6865	251	6	.	.	PUNCT
ejpam-6865	251	7	fractional	fractional	ADJ
ejpam-6865	251	8	differential	differential	ADJ
ejpam-6865	251	9	equations	equation	NOUN
ejpam-6865	251	10	and	and	CCONJ
ejpam-6865	251	11	their	their	PRON
ejpam-6865	251	12	applications	application	NOUN
ejpam-6865	251	13	to	to	ADP
ejpam-6865	251	14	real	real	ADJ
ejpam-6865	251	15	-	-	PUNCT
ejpam-6865	251	16	world	world	NOUN
ejpam-6865	251	17	problems	problem	NOUN
ejpam-6865	251	18	.	.	PUNCT
ejpam-6865	252	1	mathematical	mathematical	ADJ
ejpam-6865	252	2	examples	example	NOUN
ejpam-6865	252	3	and	and	CCONJ
ejpam-6865	252	4	methods	method	NOUN
ejpam-6865	252	5	in	in	ADP
ejpam-6865	252	6	applied	applied	ADJ
ejpam-6865	252	7	sciences	science	NOUN
ejpam-6865	252	8	,	,	PUNCT
ejpam-6865	252	9	29(12):2193–2212	29(12):2193–2212	NUM
ejpam-6865	252	10	,	,	PUNCT
ejpam-6865	252	11	2019	2019	NUM
ejpam-6865	252	12	.	.	PUNCT
ejpam-6865	253	1	[	[	X
ejpam-6865	253	2	3	3	X
ejpam-6865	253	3	]	]	X
ejpam-6865	253	4	g.	g.	PROPN
ejpam-6865	253	5	sales	sales	PROPN
ejpam-6865	253	6	teodoro	teodoro	PROPN
ejpam-6865	253	7	,	,	PUNCT
ejpam-6865	253	8	j.	j.	PROPN
ejpam-6865	253	9	a.	a.	PROPN
ejpam-6865	253	10	tenreiro	tenreiro	PROPN
ejpam-6865	253	11	machado	machado	PROPN
ejpam-6865	253	12	,	,	PUNCT
ejpam-6865	253	13	and	and	CCONJ
ejpam-6865	253	14	e.	e.	PROPN
ejpam-6865	253	15	capelas	capelas	PROPN
ejpam-6865	253	16	de	de	PROPN
ejpam-6865	253	17	oliveira	oliveira	PROPN
ejpam-6865	253	18	.	.	PUNCT
ejpam-6865	254	1	a	a	DET
ejpam-6865	254	2	review	review	NOUN
ejpam-6865	254	3	of	of	ADP
ejpam-6865	254	4	definitions	definition	NOUN
ejpam-6865	254	5	of	of	ADP
ejpam-6865	254	6	fractional	fractional	ADJ
ejpam-6865	254	7	derivatives	derivative	NOUN
ejpam-6865	254	8	and	and	CCONJ
ejpam-6865	254	9	other	other	ADJ
ejpam-6865	254	10	operators	operator	NOUN
ejpam-6865	254	11	.	.	PUNCT
ejpam-6865	255	1	journal	journal	NOUN
ejpam-6865	255	2	of	of	ADP
ejpam-6865	255	3	computational	computational	ADJ
ejpam-6865	255	4	physics	physics	NOUN
ejpam-6865	255	5	,	,	PUNCT
ejpam-6865	255	6	388:195–208	388:195–208	NUM
ejpam-6865	255	7	,	,	PUNCT
ejpam-6865	255	8	2019	2019	NUM
ejpam-6865	255	9	.	.	PUNCT
ejpam-6865	256	1	[	[	X
ejpam-6865	256	2	4	4	X
ejpam-6865	256	3	]	]	PUNCT
ejpam-6865	256	4	p.	p.	NOUN
ejpam-6865	256	5	yadav	yadav	PROPN
ejpam-6865	256	6	,	,	PUNCT
ejpam-6865	256	7	s.	s.	PROPN
ejpam-6865	256	8	jahan	jahan	PROPN
ejpam-6865	256	9	,	,	PUNCT
ejpam-6865	256	10	and	and	CCONJ
ejpam-6865	256	11	k.	k.	PROPN
ejpam-6865	256	12	s.	s.	PROPN
ejpam-6865	256	13	nisar	nisar	PROPN
ejpam-6865	256	14	.	.	PUNCT
ejpam-6865	257	1	fractional	fractional	ADJ
ejpam-6865	257	2	order	order	NOUN
ejpam-6865	257	3	mathematical	mathematical	ADJ
ejpam-6865	257	4	model	model	NOUN
ejpam-6865	257	5	of	of	ADP
ejpam-6865	257	6	ebola	ebola	PROPN
ejpam-6865	257	7	virus	virus	NOUN
ejpam-6865	257	8	under	under	ADP
ejpam-6865	257	9	atangana	atangana	PROPN
ejpam-6865	257	10	–	–	PUNCT
ejpam-6865	257	11	baleanu	baleanu	PROPN
ejpam-6865	257	12	–	–	PUNCT
ejpam-6865	257	13	caputo	caputo	NOUN
ejpam-6865	257	14	operator	operator	NOUN
ejpam-6865	257	15	.	.	PUNCT
ejpam-6865	258	1	results	result	NOUN
ejpam-6865	258	2	in	in	ADP
ejpam-6865	258	3	control	control	NOUN
ejpam-6865	258	4	and	and	CCONJ
ejpam-6865	258	5	optimization	optimization	NOUN
ejpam-6865	258	6	,	,	PUNCT
ejpam-6865	258	7	13:100332	13:100332	NUM
ejpam-6865	258	8	,	,	PUNCT
ejpam-6865	258	9	2023	2023	NUM
ejpam-6865	258	10	.	.	PUNCT
ejpam-6865	259	1	[	[	X
ejpam-6865	259	2	5	5	X
ejpam-6865	259	3	]	]	PUNCT
ejpam-6865	259	4	s.	s.	PROPN
ejpam-6865	259	5	ahmed	ahmed	PROPN
ejpam-6865	259	6	,	,	PUNCT
ejpam-6865	259	7	s.	s.	PROPN
ejpam-6865	259	8	jahan	jahan	PROPN
ejpam-6865	259	9	,	,	PUNCT
ejpam-6865	259	10	and	and	CCONJ
ejpam-6865	259	11	k.	k.	PROPN
ejpam-6865	259	12	s.	s.	PROPN
ejpam-6865	259	13	nisar	nisar	PROPN
ejpam-6865	259	14	.	.	PUNCT
ejpam-6865	260	1	a	a	DET
ejpam-6865	260	2	fractional	fractional	ADJ
ejpam-6865	260	3	model	model	NOUN
ejpam-6865	260	4	for	for	ADP
ejpam-6865	260	5	the	the	DET
ejpam-6865	260	6	dynamics	dynamic	NOUN
ejpam-6865	260	7	of	of	ADP
ejpam-6865	260	8	covid-19	covid-19	PROPN
ejpam-6865	260	9	using	use	VERB
ejpam-6865	260	10	atangana	atangana	PROPN
ejpam-6865	260	11	-	-	PUNCT
ejpam-6865	260	12	baleanu	baleanu	ADJ
ejpam-6865	260	13	fractional	fractional	ADJ
ejpam-6865	260	14	operators	operator	NOUN
ejpam-6865	260	15	.	.	PUNCT
ejpam-6865	261	1	journal	journal	NOUN
ejpam-6865	261	2	of	of	ADP
ejpam-6865	261	3	mathematics	mathematic	NOUN
ejpam-6865	261	4	and	and	CCONJ
ejpam-6865	261	5	computer	computer	NOUN
ejpam-6865	261	6	science	science	NOUN
ejpam-6865	261	7	,	,	PUNCT
ejpam-6865	261	8	39(2):233–248	39(2):233–248	NUM
ejpam-6865	261	9	,	,	PUNCT
ejpam-6865	261	10	2025	2025	NUM
ejpam-6865	261	11	.	.	PUNCT
ejpam-6865	262	1	[	[	X
ejpam-6865	262	2	6	6	NUM
ejpam-6865	262	3	]	]	PUNCT
ejpam-6865	262	4	p.	p.	NOUN
ejpam-6865	262	5	yadav	yadav	PROPN
ejpam-6865	262	6	,	,	PUNCT
ejpam-6865	262	7	s.	s.	PROPN
ejpam-6865	262	8	jahan	jahan	PROPN
ejpam-6865	262	9	,	,	PUNCT
ejpam-6865	262	10	and	and	CCONJ
ejpam-6865	262	11	k.	k.	PROPN
ejpam-6865	262	12	s.	s.	PROPN
ejpam-6865	262	13	nisar	nisar	PROPN
ejpam-6865	262	14	.	.	PUNCT
ejpam-6865	262	15	shifted	shift	VERB
ejpam-6865	262	16	fractional	fractional	ADJ
ejpam-6865	262	17	order	order	NOUN
ejpam-6865	262	18	gegenbauer	gegenbauer	NOUN
ejpam-6865	262	19	wavelets	wavelet	NOUN
ejpam-6865	262	20	method	method	NOUN
ejpam-6865	262	21	for	for	ADP
ejpam-6865	262	22	solving	solve	VERB
ejpam-6865	262	23	electrical	electrical	ADJ
ejpam-6865	262	24	circuits	circuit	NOUN
ejpam-6865	262	25	model	model	NOUN
ejpam-6865	262	26	of	of	ADP
ejpam-6865	262	27	fractional	fractional	ADJ
ejpam-6865	262	28	order	order	NOUN
ejpam-6865	262	29	.	.	PUNCT
ejpam-6865	263	1	ain	ain	PROPN
ejpam-6865	263	2	shams	sham	VERB
ejpam-6865	263	3	engineering	engineering	NOUN
ejpam-6865	263	4	journal	journal	NOUN
ejpam-6865	263	5	,	,	PUNCT
ejpam-6865	263	6	14(11):102544	14(11):102544	NUM
ejpam-6865	263	7	,	,	PUNCT
ejpam-6865	263	8	2023	2023	NUM
ejpam-6865	263	9	.	.	PUNCT
ejpam-6865	264	1	[	[	X
ejpam-6865	264	2	7	7	X
ejpam-6865	264	3	]	]	X
ejpam-6865	264	4	r.	r.	PROPN
ejpam-6865	264	5	almeida	almeida	PROPN
ejpam-6865	264	6	,	,	PUNCT
ejpam-6865	264	7	s.	s.	PROPN
ejpam-6865	264	8	pooseh	pooseh	PROPN
ejpam-6865	264	9	,	,	PUNCT
ejpam-6865	264	10	and	and	CCONJ
ejpam-6865	264	11	d.	d.	PROPN
ejpam-6865	264	12	f.	f.	PROPN
ejpam-6865	264	13	m.	m.	PROPN
ejpam-6865	264	14	torres	torre	VERB
ejpam-6865	264	15	.	.	PUNCT
ejpam-6865	265	1	computational	computational	ADJ
ejpam-6865	265	2	methods	method	NOUN
ejpam-6865	265	3	in	in	ADP
ejpam-6865	265	4	the	the	DET
ejpam-6865	265	5	fractional	fractional	ADJ
ejpam-6865	265	6	calculus	calculus	NOUN
ejpam-6865	265	7	of	of	ADP
ejpam-6865	265	8	variations	variation	NOUN
ejpam-6865	265	9	.	.	PUNCT
ejpam-6865	266	1	world	world	NOUN
ejpam-6865	266	2	scientific	scientific	ADJ
ejpam-6865	266	3	publishing	publishing	NOUN
ejpam-6865	266	4	company	company	NOUN
ejpam-6865	266	5	,	,	PUNCT
ejpam-6865	266	6	2015	2015	NUM
ejpam-6865	266	7	.	.	PUNCT
ejpam-6865	267	1	s.	s.	PROPN
ejpam-6865	267	2	tamimi	tamimi	PROPN
ejpam-6865	267	3	,	,	PUNCT
ejpam-6865	267	4	a.	a.	PROPN
ejpam-6865	267	5	k.	k.	PROPN
ejpam-6865	267	6	alomari	alomari	PROPN
ejpam-6865	267	7	,	,	PUNCT
ejpam-6865	267	8	m.	m.	NOUN
ejpam-6865	267	9	alaroud	alaroud	PROPN
ejpam-6865	267	10	/	/	SYM
ejpam-6865	267	11	eur	eur	PROPN
ejpam-6865	267	12	.	.	PUNCT
ejpam-6865	268	1	j.	j.	PROPN
ejpam-6865	268	2	pure	pure	PROPN
ejpam-6865	268	3	appl	appl	PROPN
ejpam-6865	268	4	.	.	PROPN
ejpam-6865	268	5	math	math	PROPN
ejpam-6865	268	6	,	,	PUNCT
ejpam-6865	268	7	18	18	NUM
ejpam-6865	268	8	(	(	PUNCT
ejpam-6865	268	9	4	4	NUM
ejpam-6865	268	10	)	)	PUNCT
ejpam-6865	268	11	(	(	PUNCT
ejpam-6865	268	12	2025	2025	NUM
ejpam-6865	268	13	)	)	PUNCT
ejpam-6865	268	14	,	,	PUNCT
ejpam-6865	268	15	6865	6865	NUM
ejpam-6865	268	16	18	18	NUM
ejpam-6865	268	17	of	of	ADP
ejpam-6865	268	18	19	19	NUM
ejpam-6865	268	19	[	[	SYM
ejpam-6865	268	20	8	8	NUM
ejpam-6865	268	21	]	]	PUNCT
ejpam-6865	268	22	a.	a.	PROPN
ejpam-6865	268	23	b.	b.	PROPN
ejpam-6865	268	24	malinowska	malinowska	PROPN
ejpam-6865	268	25	,	,	PUNCT
ejpam-6865	268	26	t.	t.	NOUN
ejpam-6865	268	27	odzijewicz	odzijewicz	NOUN
ejpam-6865	268	28	,	,	PUNCT
ejpam-6865	268	29	and	and	CCONJ
ejpam-6865	268	30	d.	d.	PROPN
ejpam-6865	268	31	f.	f.	PROPN
ejpam-6865	268	32	m.	m.	PROPN
ejpam-6865	268	33	torres	torres	PROPN
ejpam-6865	268	34	.	.	PUNCT
ejpam-6865	269	1	fractional	fractional	ADJ
ejpam-6865	269	2	calculus	calculus	NOUN
ejpam-6865	269	3	.	.	PUNCT
ejpam-6865	270	1	in	in	ADP
ejpam-6865	270	2	advanced	advanced	ADJ
ejpam-6865	270	3	methods	method	NOUN
ejpam-6865	270	4	in	in	ADP
ejpam-6865	270	5	the	the	DET
ejpam-6865	270	6	fractional	fractional	ADJ
ejpam-6865	270	7	calculus	calculus	NOUN
ejpam-6865	270	8	of	of	ADP
ejpam-6865	270	9	variations	variation	NOUN
ejpam-6865	270	10	,	,	PUNCT
ejpam-6865	270	11	pages	page	NOUN
ejpam-6865	270	12	7–21	7–21	PROPN
ejpam-6865	270	13	.	.	PUNCT
ejpam-6865	271	1	springer	springer	NOUN
ejpam-6865	271	2	international	international	ADJ
ejpam-6865	271	3	publishing	publishing	NOUN
ejpam-6865	271	4	,	,	PUNCT
ejpam-6865	271	5	cham	cham	NOUN
ejpam-6865	271	6	,	,	PUNCT
ejpam-6865	271	7	2015	2015	NUM
ejpam-6865	271	8	.	.	PUNCT
ejpam-6865	272	1	[	[	X
ejpam-6865	272	2	9	9	NUM
ejpam-6865	272	3	]	]	X
ejpam-6865	272	4	h.	h.	PROPN
ejpam-6865	272	5	sun	sun	PROPN
ejpam-6865	272	6	,	,	PUNCT
ejpam-6865	272	7	y.	y.	PROPN
ejpam-6865	272	8	zhang	zhang	PROPN
ejpam-6865	272	9	,	,	PUNCT
ejpam-6865	272	10	d.	d.	PROPN
ejpam-6865	272	11	baleanu	baleanu	PROPN
ejpam-6865	272	12	,	,	PUNCT
ejpam-6865	272	13	w.	w.	PROPN
ejpam-6865	272	14	chen	chen	PROPN
ejpam-6865	272	15	,	,	PUNCT
ejpam-6865	272	16	and	and	CCONJ
ejpam-6865	272	17	y.	y.	PROPN
ejpam-6865	272	18	chen	chen	PROPN
ejpam-6865	272	19	.	.	PUNCT
ejpam-6865	273	1	a	a	DET
ejpam-6865	273	2	new	new	ADJ
ejpam-6865	273	3	collection	collection	NOUN
ejpam-6865	273	4	of	of	ADP
ejpam-6865	273	5	realworld	realworld	PROPN
ejpam-6865	273	6	applications	application	NOUN
ejpam-6865	273	7	of	of	ADP
ejpam-6865	273	8	fractional	fractional	ADJ
ejpam-6865	273	9	calculus	calculus	NOUN
ejpam-6865	273	10	in	in	ADP
ejpam-6865	273	11	science	science	NOUN
ejpam-6865	273	12	and	and	CCONJ
ejpam-6865	273	13	engineering	engineering	NOUN
ejpam-6865	273	14	.	.	PUNCT
ejpam-6865	274	1	communications	communication	NOUN
ejpam-6865	274	2	in	in	ADP
ejpam-6865	274	3	nonlinear	nonlinear	ADJ
ejpam-6865	274	4	science	science	NOUN
ejpam-6865	274	5	and	and	CCONJ
ejpam-6865	274	6	numerical	numerical	PROPN
ejpam-6865	274	7	simulation	simulation	PROPN
ejpam-6865	274	8	,	,	PUNCT
ejpam-6865	274	9	64:213–231	64:213–231	NUM
ejpam-6865	274	10	,	,	PUNCT
ejpam-6865	274	11	2018	2018	NUM
ejpam-6865	274	12	.	.	PUNCT
ejpam-6865	275	1	[	[	X
ejpam-6865	275	2	10	10	NUM
ejpam-6865	275	3	]	]	X
ejpam-6865	275	4	o.	o.	PROPN
ejpam-6865	275	5	p.	p.	PROPN
ejpam-6865	275	6	agrawal	agrawal	PROPN
ejpam-6865	275	7	.	.	PUNCT
ejpam-6865	276	1	fractional	fractional	ADJ
ejpam-6865	276	2	variational	variational	ADJ
ejpam-6865	276	3	calculus	calculus	NOUN
ejpam-6865	276	4	in	in	ADP
ejpam-6865	276	5	terms	term	NOUN
ejpam-6865	276	6	of	of	ADP
ejpam-6865	276	7	riesz	riesz	ADJ
ejpam-6865	276	8	fractional	fractional	ADJ
ejpam-6865	276	9	derivatives	derivative	NOUN
ejpam-6865	276	10	.	.	PUNCT
ejpam-6865	277	1	journal	journal	PROPN
ejpam-6865	277	2	of	of	ADP
ejpam-6865	277	3	physics	physics	PROPN
ejpam-6865	277	4	a	a	PRON
ejpam-6865	277	5	:	:	PUNCT
ejpam-6865	277	6	mathematical	mathematical	ADJ
ejpam-6865	277	7	and	and	CCONJ
ejpam-6865	277	8	theoretical	theoretical	ADJ
ejpam-6865	277	9	,	,	PUNCT
ejpam-6865	277	10	40(24):6287–6303	40(24):6287–6303	NOUN
ejpam-6865	277	11	,	,	PUNCT
ejpam-6865	277	12	2007	2007	NUM
ejpam-6865	277	13	.	.	PUNCT
ejpam-6865	278	1	[	[	X
ejpam-6865	278	2	11	11	NUM
ejpam-6865	278	3	]	]	PUNCT
ejpam-6865	278	4	t.	t.	PROPN
ejpam-6865	278	5	m.	m.	PROPN
ejpam-6865	278	6	atanacković	atanacković	PROPN
ejpam-6865	278	7	,	,	PUNCT
ejpam-6865	278	8	s.	s.	PROPN
ejpam-6865	278	9	konjik	konjik	PROPN
ejpam-6865	278	10	,	,	PUNCT
ejpam-6865	278	11	and	and	CCONJ
ejpam-6865	278	12	s.	s.	PROPN
ejpam-6865	278	13	pilipović	pilipović	PROPN
ejpam-6865	278	14	.	.	PUNCT
ejpam-6865	279	1	variational	variational	ADJ
ejpam-6865	279	2	problems	problem	NOUN
ejpam-6865	279	3	with	with	ADP
ejpam-6865	279	4	fractional	fractional	ADJ
ejpam-6865	279	5	derivatives	derivative	NOUN
ejpam-6865	279	6	:	:	PUNCT
ejpam-6865	279	7	euler	euler	NOUN
ejpam-6865	279	8	-	-	PUNCT
ejpam-6865	279	9	lagrange	lagrange	PROPN
ejpam-6865	279	10	equations	equation	NOUN
ejpam-6865	279	11	.	.	PUNCT
ejpam-6865	280	1	journal	journal	PROPN
ejpam-6865	280	2	of	of	ADP
ejpam-6865	280	3	physics	physics	PROPN
ejpam-6865	280	4	a	a	PRON
ejpam-6865	280	5	:	:	PUNCT
ejpam-6865	280	6	mathematical	mathematical	ADJ
ejpam-6865	280	7	and	and	CCONJ
ejpam-6865	280	8	theoretical	theoretical	ADJ
ejpam-6865	280	9	,	,	PUNCT
ejpam-6865	280	10	41(9):095201	41(9):095201	NUM
ejpam-6865	280	11	,	,	PUNCT
ejpam-6865	280	12	2008	2008	NUM
ejpam-6865	280	13	.	.	PUNCT
ejpam-6865	281	1	[	[	X
ejpam-6865	281	2	12	12	NUM
ejpam-6865	281	3	]	]	X
ejpam-6865	281	4	s.	s.	PROPN
ejpam-6865	281	5	i̇.	i̇.	PROPN
ejpam-6865	281	6	araz	araz	PROPN
ejpam-6865	281	7	and	and	CCONJ
ejpam-6865	281	8	m.	m.	NOUN
ejpam-6865	281	9	a.	a.	PROPN
ejpam-6865	281	10	çetin	çetin	PROPN
ejpam-6865	281	11	.	.	PUNCT
ejpam-6865	282	1	fractal	fractal	ADJ
ejpam-6865	282	2	-	-	PUNCT
ejpam-6865	282	3	fractional	fractional	ADJ
ejpam-6865	282	4	modeling	modeling	NOUN
ejpam-6865	282	5	of	of	ADP
ejpam-6865	282	6	the	the	DET
ejpam-6865	282	7	covid-19	covid-19	PROPN
ejpam-6865	282	8	spread	spread	VERB
ejpam-6865	282	9	with	with	ADP
ejpam-6865	282	10	deterministic	deterministic	ADJ
ejpam-6865	282	11	and	and	CCONJ
ejpam-6865	282	12	stochastic	stochastic	ADJ
ejpam-6865	282	13	approaches	approach	NOUN
ejpam-6865	282	14	.	.	PUNCT
ejpam-6865	283	1	international	international	ADJ
ejpam-6865	283	2	journal	journal	PROPN
ejpam-6865	283	3	of	of	ADP
ejpam-6865	283	4	applied	applied	ADJ
ejpam-6865	283	5	and	and	CCONJ
ejpam-6865	283	6	computational	computational	ADJ
ejpam-6865	283	7	mathematics	mathematic	NOUN
ejpam-6865	283	8	,	,	PUNCT
ejpam-6865	283	9	11(1):4	11(1):4	PROPN
ejpam-6865	283	10	,	,	PUNCT
ejpam-6865	283	11	2025	2025	NUM
ejpam-6865	283	12	.	.	PUNCT
ejpam-6865	284	1	[	[	X
ejpam-6865	284	2	13	13	NUM
ejpam-6865	284	3	]	]	PUNCT
ejpam-6865	284	4	i̇.	i̇.	NOUN
ejpam-6865	284	5	a.	a.	NOUN
ejpam-6865	284	6	arık	arık	PROPN
ejpam-6865	284	7	and	and	CCONJ
ejpam-6865	284	8	s.	s.	PROPN
ejpam-6865	284	9	i̇.	i̇.	PROPN
ejpam-6865	284	10	araz	araz	NOUN
ejpam-6865	284	11	.	.	PUNCT
ejpam-6865	285	1	crossover	crossover	ADP
ejpam-6865	285	2	behaviors	behavior	NOUN
ejpam-6865	285	3	via	via	ADP
ejpam-6865	285	4	piecewise	piecewise	NOUN
ejpam-6865	285	5	concept	concept	NOUN
ejpam-6865	285	6	:	:	PUNCT
ejpam-6865	285	7	a	a	DET
ejpam-6865	285	8	model	model	NOUN
ejpam-6865	285	9	of	of	ADP
ejpam-6865	285	10	tumor	tumor	NOUN
ejpam-6865	285	11	growth	growth	NOUN
ejpam-6865	285	12	and	and	CCONJ
ejpam-6865	285	13	its	its	PRON
ejpam-6865	285	14	response	response	NOUN
ejpam-6865	285	15	to	to	PART
ejpam-6865	285	16	radiotherapy	radiotherapy	VERB
ejpam-6865	285	17	.	.	PUNCT
ejpam-6865	286	1	results	result	NOUN
ejpam-6865	286	2	in	in	ADP
ejpam-6865	286	3	physics	physics	NOUN
ejpam-6865	286	4	,	,	PUNCT
ejpam-6865	286	5	41:105894	41:105894	NUM
ejpam-6865	286	6	,	,	PUNCT
ejpam-6865	286	7	2022	2022	NUM
ejpam-6865	286	8	.	.	PUNCT
ejpam-6865	287	1	[	[	X
ejpam-6865	287	2	14	14	NUM
ejpam-6865	287	3	]	]	X
ejpam-6865	287	4	s.	s.	PROPN
ejpam-6865	287	5	jahan	jahan	PROPN
ejpam-6865	287	6	,	,	PUNCT
ejpam-6865	287	7	s.	s.	PROPN
ejpam-6865	287	8	ahmed	ahmed	PROPN
ejpam-6865	287	9	,	,	PUNCT
ejpam-6865	287	10	p.	p.	NOUN
ejpam-6865	287	11	yadav	yadav	PROPN
ejpam-6865	287	12	,	,	PUNCT
ejpam-6865	287	13	and	and	CCONJ
ejpam-6865	287	14	k.	k.	PROPN
ejpam-6865	287	15	s.	s.	PROPN
ejpam-6865	287	16	nisar	nisar	PROPN
ejpam-6865	287	17	.	.	PUNCT
ejpam-6865	288	1	fibonacci	fibonacci	PROPN
ejpam-6865	288	2	wavelet	wavelet	PROPN
ejpam-6865	288	3	method	method	NOUN
ejpam-6865	288	4	for	for	ADP
ejpam-6865	288	5	the	the	DET
ejpam-6865	288	6	numerical	numerical	ADJ
ejpam-6865	288	7	solution	solution	NOUN
ejpam-6865	288	8	of	of	ADP
ejpam-6865	288	9	a	a	DET
ejpam-6865	288	10	fractional	fractional	ADJ
ejpam-6865	288	11	relaxation	relaxation	NOUN
ejpam-6865	288	12	–	–	PUNCT
ejpam-6865	288	13	oscillation	oscillation	NOUN
ejpam-6865	288	14	model	model	NOUN
ejpam-6865	288	15	.	.	PUNCT
ejpam-6865	289	1	partial	partial	ADJ
ejpam-6865	289	2	differential	differential	ADJ
ejpam-6865	289	3	equations	equation	NOUN
ejpam-6865	289	4	in	in	ADP
ejpam-6865	289	5	applied	applied	ADJ
ejpam-6865	289	6	mathematics	mathematic	NOUN
ejpam-6865	289	7	,	,	PUNCT
ejpam-6865	289	8	8:100568	8:100568	NUM
ejpam-6865	289	9	,	,	PUNCT
ejpam-6865	289	10	2023	2023	NUM
ejpam-6865	289	11	.	.	PUNCT
ejpam-6865	290	1	[	[	X
ejpam-6865	290	2	15	15	NUM
ejpam-6865	290	3	]	]	X
ejpam-6865	290	4	r.	r.	PROPN
ejpam-6865	290	5	almeida	almeida	PROPN
ejpam-6865	290	6	and	and	CCONJ
ejpam-6865	290	7	d.	d.	PROPN
ejpam-6865	290	8	f.	f.	PROPN
ejpam-6865	290	9	m.	m.	PROPN
ejpam-6865	290	10	torres	torres	PROPN
ejpam-6865	290	11	.	.	PUNCT
ejpam-6865	291	1	fractional	fractional	ADJ
ejpam-6865	291	2	variational	variational	ADJ
ejpam-6865	291	3	calculus	calculus	NOUN
ejpam-6865	291	4	for	for	ADP
ejpam-6865	291	5	non	non	ADJ
ejpam-6865	291	6	-	-	ADJ
ejpam-6865	291	7	differentiable	differentiable	ADJ
ejpam-6865	291	8	functions	function	NOUN
ejpam-6865	291	9	.	.	PUNCT
ejpam-6865	292	1	computers	computer	NOUN
ejpam-6865	292	2	&	&	CCONJ
ejpam-6865	292	3	mathematics	mathematics	PROPN
ejpam-6865	292	4	with	with	ADP
ejpam-6865	292	5	applications	application	NOUN
ejpam-6865	292	6	,	,	PUNCT
ejpam-6865	292	7	61(10):3097–3104	61(10):3097–3104	PROPN
ejpam-6865	292	8	,	,	PUNCT
ejpam-6865	292	9	2011	2011	NUM
ejpam-6865	292	10	.	.	PUNCT
ejpam-6865	293	1	[	[	X
ejpam-6865	293	2	16	16	NUM
ejpam-6865	293	3	]	]	PUNCT
ejpam-6865	293	4	s.	s.	PROPN
ejpam-6865	293	5	kumar	kumar	PROPN
ejpam-6865	293	6	,	,	PUNCT
ejpam-6865	293	7	j.	j.	PROPN
ejpam-6865	293	8	cao	cao	PROPN
ejpam-6865	293	9	,	,	PUNCT
ejpam-6865	293	10	and	and	CCONJ
ejpam-6865	293	11	m.	m.	PROPN
ejpam-6865	293	12	abdel	abdel	PROPN
ejpam-6865	293	13	-	-	PUNCT
ejpam-6865	293	14	aty	aty	PROPN
ejpam-6865	293	15	.	.	PUNCT
ejpam-6865	294	1	a	a	DET
ejpam-6865	294	2	novel	novel	ADJ
ejpam-6865	294	3	mathematical	mathematical	ADJ
ejpam-6865	294	4	approach	approach	NOUN
ejpam-6865	294	5	of	of	ADP
ejpam-6865	294	6	covid-19	covid-19	PROPN
ejpam-6865	294	7	with	with	ADP
ejpam-6865	294	8	non	non	ADJ
ejpam-6865	294	9	-	-	ADJ
ejpam-6865	294	10	singular	singular	ADJ
ejpam-6865	294	11	fractional	fractional	ADJ
ejpam-6865	294	12	derivative	derivative	NOUN
ejpam-6865	294	13	.	.	PUNCT
ejpam-6865	295	1	chaos	chaos	NOUN
ejpam-6865	295	2	,	,	PUNCT
ejpam-6865	295	3	solitons	soliton	NOUN
ejpam-6865	295	4	&	&	CCONJ
ejpam-6865	295	5	fractals	fractal	NOUN
ejpam-6865	295	6	,	,	PUNCT
ejpam-6865	295	7	139:110048	139:110048	NUM
ejpam-6865	295	8	,	,	PUNCT
ejpam-6865	295	9	2020	2020	NUM
ejpam-6865	295	10	.	.	PUNCT
ejpam-6865	296	1	[	[	X
ejpam-6865	296	2	17	17	NUM
ejpam-6865	296	3	]	]	X
ejpam-6865	296	4	c.	c.	PROPN
ejpam-6865	296	5	li	li	PROPN
ejpam-6865	296	6	,	,	PUNCT
ejpam-6865	296	7	l.	l.	PROPN
ejpam-6865	296	8	zheng	zheng	PROPN
ejpam-6865	296	9	,	,	PUNCT
ejpam-6865	296	10	and	and	CCONJ
ejpam-6865	296	11	d.	d.	PROPN
ejpam-6865	296	12	wang	wang	PROPN
ejpam-6865	296	13	.	.	PUNCT
ejpam-6865	296	14	hydro	hydro	NOUN
ejpam-6865	296	15	-	-	PUNCT
ejpam-6865	296	16	thermo	thermo	NOUN
ejpam-6865	296	17	-	-	PUNCT
ejpam-6865	296	18	mechanical	mechanical	ADJ
ejpam-6865	296	19	transient	transient	ADJ
ejpam-6865	296	20	response	response	NOUN
ejpam-6865	296	21	for	for	ADP
ejpam-6865	296	22	a	a	DET
ejpam-6865	296	23	cylindrical	cylindrical	ADJ
ejpam-6865	296	24	unlined	unlined	ADJ
ejpam-6865	296	25	tunnel	tunnel	NOUN
ejpam-6865	296	26	in	in	ADP
ejpam-6865	296	27	poroelastic	poroelastic	ADJ
ejpam-6865	296	28	medium	medium	NOUN
ejpam-6865	296	29	based	base	VERB
ejpam-6865	296	30	on	on	ADP
ejpam-6865	296	31	non	non	ADJ
ejpam-6865	296	32	-	-	ADJ
ejpam-6865	296	33	singular	singular	ADJ
ejpam-6865	296	34	fractional	fractional	ADJ
ejpam-6865	296	35	derivatives	derivative	NOUN
ejpam-6865	296	36	.	.	PUNCT
ejpam-6865	297	1	journal	journal	NOUN
ejpam-6865	297	2	of	of	ADP
ejpam-6865	297	3	vibration	vibration	NOUN
ejpam-6865	297	4	engineering	engineering	NOUN
ejpam-6865	297	5	&	&	CCONJ
ejpam-6865	297	6	technologies	technology	NOUN
ejpam-6865	297	7	,	,	PUNCT
ejpam-6865	297	8	13(1):5	13(1):5	PROPN
ejpam-6865	297	9	,	,	PUNCT
ejpam-6865	297	10	2025	2025	NUM
ejpam-6865	297	11	.	.	PUNCT
ejpam-6865	298	1	[	[	X
ejpam-6865	298	2	18	18	NUM
ejpam-6865	298	3	]	]	PUNCT
ejpam-6865	298	4	t.	t.	NOUN
ejpam-6865	298	5	abdeljawad	abdeljawad	PROPN
ejpam-6865	298	6	and	and	CCONJ
ejpam-6865	298	7	d.	d.	PROPN
ejpam-6865	298	8	baleanu	baleanu	PROPN
ejpam-6865	298	9	.	.	PUNCT
ejpam-6865	299	1	on	on	ADP
ejpam-6865	299	2	fractional	fractional	ADJ
ejpam-6865	299	3	derivatives	derivative	NOUN
ejpam-6865	299	4	with	with	ADP
ejpam-6865	299	5	generalized	generalized	ADJ
ejpam-6865	299	6	mittagleffler	mittagleffler	NOUN
ejpam-6865	299	7	kernels	kernel	NOUN
ejpam-6865	299	8	.	.	PUNCT
ejpam-6865	300	1	advances	advance	NOUN
ejpam-6865	300	2	in	in	ADP
ejpam-6865	300	3	difference	difference	NOUN
ejpam-6865	300	4	equations	equation	NOUN
ejpam-6865	300	5	,	,	PUNCT
ejpam-6865	300	6	2018(1):1–15	2018(1):1–15	NOUN
ejpam-6865	300	7	,	,	PUNCT
ejpam-6865	300	8	2018	2018	NUM
ejpam-6865	300	9	.	.	PUNCT
ejpam-6865	301	1	[	[	X
ejpam-6865	301	2	19	19	NUM
ejpam-6865	301	3	]	]	PUNCT
ejpam-6865	301	4	k.	k.	PROPN
ejpam-6865	301	5	boulehmi	boulehmi	PROPN
ejpam-6865	301	6	.	.	PUNCT
ejpam-6865	302	1	a	a	DET
ejpam-6865	302	2	novel	novel	ADJ
ejpam-6865	302	3	numerical	numerical	ADJ
ejpam-6865	302	4	scheme	scheme	NOUN
ejpam-6865	302	5	for	for	ADP
ejpam-6865	302	6	fractional	fractional	ADJ
ejpam-6865	302	7	bernoulli	bernoulli	NOUN
ejpam-6865	302	8	equations	equation	NOUN
ejpam-6865	302	9	and	and	CCONJ
ejpam-6865	302	10	the	the	DET
ejpam-6865	302	11	rössler	rössler	NOUN
ejpam-6865	302	12	example	example	NOUN
ejpam-6865	302	13	:	:	PUNCT
ejpam-6865	302	14	a	a	DET
ejpam-6865	302	15	comparative	comparative	ADJ
ejpam-6865	302	16	analysis	analysis	NOUN
ejpam-6865	302	17	using	use	VERB
ejpam-6865	302	18	atangana	atangana	PROPN
ejpam-6865	302	19	-	-	PUNCT
ejpam-6865	302	20	baleanu	baleanu	PROPN
ejpam-6865	302	21	caputo	caputo	PROPN
ejpam-6865	302	22	fractional	fractional	PROPN
ejpam-6865	302	23	derivative	derivative	PROPN
ejpam-6865	302	24	.	.	PUNCT
ejpam-6865	303	1	european	european	PROPN
ejpam-6865	303	2	journal	journal	PROPN
ejpam-6865	303	3	of	of	ADP
ejpam-6865	303	4	pure	pure	ADJ
ejpam-6865	303	5	and	and	CCONJ
ejpam-6865	303	6	applied	applied	ADJ
ejpam-6865	303	7	mathematics	mathematic	NOUN
ejpam-6865	303	8	,	,	PUNCT
ejpam-6865	303	9	17(1):445–461	17(1):445–461	NUM
ejpam-6865	303	10	,	,	PUNCT
ejpam-6865	303	11	2024	2024	NUM
ejpam-6865	303	12	.	.	PUNCT
ejpam-6865	304	1	[	[	X
ejpam-6865	304	2	20	20	NUM
ejpam-6865	304	3	]	]	PUNCT
ejpam-6865	304	4	a.	a.	PROPN
ejpam-6865	304	5	b.	b.	PROPN
ejpam-6865	304	6	alzahrani	alzahrani	PROPN
ejpam-6865	304	7	,	,	PUNCT
ejpam-6865	304	8	r.	r.	PROPN
ejpam-6865	304	9	saadeh	saadeh	PROPN
ejpam-6865	304	10	,	,	PUNCT
ejpam-6865	304	11	m.	m.	NOUN
ejpam-6865	304	12	a.	a.	PROPN
ejpam-6865	304	13	abdoon	abdoon	PROPN
ejpam-6865	304	14	,	,	PUNCT
ejpam-6865	304	15	m.	m.	NOUN
ejpam-6865	304	16	elbadri	elbadri	PROPN
ejpam-6865	304	17	,	,	PUNCT
ejpam-6865	304	18	m.	m.	NOUN
ejpam-6865	304	19	berir	berir	NOUN
ejpam-6865	304	20	,	,	PUNCT
ejpam-6865	304	21	and	and	CCONJ
ejpam-6865	304	22	a.	a.	NOUN
ejpam-6865	304	23	qazza	qazza	PROPN
ejpam-6865	304	24	.	.	PUNCT
ejpam-6865	305	1	effective	effective	ADJ
ejpam-6865	305	2	methods	method	NOUN
ejpam-6865	305	3	for	for	ADP
ejpam-6865	305	4	numerical	numerical	ADJ
ejpam-6865	305	5	analysis	analysis	NOUN
ejpam-6865	305	6	of	of	ADP
ejpam-6865	305	7	the	the	DET
ejpam-6865	305	8	simplest	simple	ADJ
ejpam-6865	305	9	chaotic	chaotic	ADJ
ejpam-6865	305	10	circuit	circuit	NOUN
ejpam-6865	305	11	example	example	NOUN
ejpam-6865	305	12	with	with	ADP
ejpam-6865	305	13	atangana	atangana	PROPN
ejpam-6865	305	14	–	–	PUNCT
ejpam-6865	305	15	baleanu	baleanu	PROPN
ejpam-6865	305	16	caputo	caputo	PROPN
ejpam-6865	305	17	fractional	fractional	PROPN
ejpam-6865	305	18	derivative	derivative	PROPN
ejpam-6865	305	19	.	.	PUNCT
ejpam-6865	306	1	journal	journal	PROPN
ejpam-6865	306	2	of	of	ADP
ejpam-6865	306	3	engineering	engineering	NOUN
ejpam-6865	306	4	mathematics	mathematic	NOUN
ejpam-6865	306	5	,	,	PUNCT
ejpam-6865	306	6	144(1):9	144(1):9	NUM
ejpam-6865	306	7	,	,	PUNCT
ejpam-6865	306	8	2024	2024	NUM
ejpam-6865	306	9	.	.	PUNCT
ejpam-6865	307	1	[	[	X
ejpam-6865	307	2	21	21	NUM
ejpam-6865	307	3	]	]	PUNCT
ejpam-6865	307	4	m.	m.	NOUN
ejpam-6865	307	5	a.	a.	NOUN
ejpam-6865	307	6	boubekeur	boubekeur	PROPN
ejpam-6865	307	7	,	,	PUNCT
ejpam-6865	307	8	s.	s.	PROPN
ejpam-6865	307	9	boulaaras	boulaaras	PROPN
ejpam-6865	307	10	,	,	PUNCT
ejpam-6865	307	11	and	and	CCONJ
ejpam-6865	307	12	s.	s.	PROPN
ejpam-6865	307	13	i.	i.	PROPN
ejpam-6865	307	14	araz	araz	PROPN
ejpam-6865	307	15	.	.	PUNCT
ejpam-6865	308	1	successive	successive	ADJ
ejpam-6865	308	2	midpoint	midpoint	NOUN
ejpam-6865	308	3	method	method	NOUN
ejpam-6865	308	4	for	for	ADP
ejpam-6865	308	5	fractional	fractional	ADJ
ejpam-6865	308	6	differential	differential	ADJ
ejpam-6865	308	7	equations	equation	NOUN
ejpam-6865	308	8	with	with	ADP
ejpam-6865	308	9	nonlocal	nonlocal	ADJ
ejpam-6865	308	10	kernels	kernel	NOUN
ejpam-6865	308	11	:	:	PUNCT
ejpam-6865	308	12	error	error	NOUN
ejpam-6865	308	13	analysis	analysis	NOUN
ejpam-6865	308	14	,	,	PUNCT
ejpam-6865	308	15	stability	stability	NOUN
ejpam-6865	308	16	,	,	PUNCT
ejpam-6865	308	17	and	and	CCONJ
ejpam-6865	308	18	applications	application	NOUN
ejpam-6865	308	19	.	.	PUNCT
ejpam-6865	309	1	open	open	ADJ
ejpam-6865	309	2	physics	physics	PROPN
ejpam-6865	309	3	,	,	PUNCT
ejpam-6865	309	4	23(1):20250203	23(1):20250203	NUM
ejpam-6865	309	5	,	,	PUNCT
ejpam-6865	309	6	2025	2025	NUM
ejpam-6865	309	7	.	.	PUNCT
ejpam-6865	310	1	[	[	X
ejpam-6865	310	2	22	22	NUM
ejpam-6865	310	3	]	]	PUNCT
ejpam-6865	310	4	a.	a.	NOUN
ejpam-6865	310	5	k.	k.	PROPN
ejpam-6865	310	6	alomari	alomari	PROPN
ejpam-6865	310	7	,	,	PUNCT
ejpam-6865	310	8	t.	t.	PROPN
ejpam-6865	310	9	abdeljawad	abdeljawad	PROPN
ejpam-6865	310	10	,	,	PUNCT
ejpam-6865	310	11	d.	d.	PROPN
ejpam-6865	310	12	baleanu	baleanu	PROPN
ejpam-6865	310	13	,	,	PUNCT
ejpam-6865	310	14	k.	k.	PROPN
ejpam-6865	310	15	m.	m.	PROPN
ejpam-6865	310	16	saad	saad	PROPN
ejpam-6865	310	17	,	,	PUNCT
ejpam-6865	310	18	and	and	CCONJ
ejpam-6865	310	19	q.	q.	PROPN
ejpam-6865	310	20	m.	m.	PROPN
ejpam-6865	310	21	al	al	PROPN
ejpam-6865	310	22	-	-	PUNCT
ejpam-6865	310	23	mdallal	mdallal	PROPN
ejpam-6865	310	24	.	.	PUNCT
ejpam-6865	311	1	numerical	numerical	ADJ
ejpam-6865	311	2	solutions	solution	NOUN
ejpam-6865	311	3	of	of	ADP
ejpam-6865	311	4	fractional	fractional	ADJ
ejpam-6865	311	5	parabolic	parabolic	ADJ
ejpam-6865	311	6	equations	equation	NOUN
ejpam-6865	311	7	with	with	ADP
ejpam-6865	311	8	generalized	generalized	ADJ
ejpam-6865	311	9	mittag	mittag	ADJ
ejpam-6865	311	10	–	–	PUNCT
ejpam-6865	311	11	leffler	leffler	NOUN
ejpam-6865	311	12	kernels	kernel	NOUN
ejpam-6865	311	13	.	.	PUNCT
ejpam-6865	312	1	numerical	numerical	ADJ
ejpam-6865	312	2	methods	method	NOUN
ejpam-6865	312	3	for	for	ADP
ejpam-6865	312	4	partial	partial	ADJ
ejpam-6865	312	5	differential	differential	NOUN
ejpam-6865	312	6	equations	equation	NOUN
ejpam-6865	312	7	,	,	PUNCT
ejpam-6865	312	8	pages	page	NOUN
ejpam-6865	312	9	1–13	1–13	NOUN
ejpam-6865	312	10	,	,	PUNCT
ejpam-6865	312	11	2020	2020	NUM
ejpam-6865	312	12	.	.	PUNCT
ejpam-6865	313	1	[	[	X
ejpam-6865	313	2	23	23	NUM
ejpam-6865	313	3	]	]	PUNCT
ejpam-6865	313	4	s.	s.	PROPN
ejpam-6865	313	5	zhagharian	zhagharian	PROPN
ejpam-6865	313	6	,	,	PUNCT
ejpam-6865	313	7	m.	m.	NOUN
ejpam-6865	313	8	h.	h.	PROPN
ejpam-6865	313	9	heydari	heydari	PROPN
ejpam-6865	313	10	,	,	PUNCT
ejpam-6865	313	11	and	and	CCONJ
ejpam-6865	313	12	m.	m.	PROPN
ejpam-6865	313	13	razzaghi	razzaghi	PROPN
ejpam-6865	313	14	.	.	PUNCT
ejpam-6865	314	1	piecewise	piecewise	PROPN
ejpam-6865	314	2	fractional	fractional	PROPN
ejpam-6865	314	3	legendre	legendre	PROPN
ejpam-6865	314	4	functions	function	NOUN
ejpam-6865	314	5	for	for	ADP
ejpam-6865	314	6	nonlinear	nonlinear	ADJ
ejpam-6865	314	7	fractional	fractional	ADJ
ejpam-6865	314	8	optimal	optimal	ADJ
ejpam-6865	314	9	control	control	NOUN
ejpam-6865	314	10	problems	problem	NOUN
ejpam-6865	314	11	with	with	ADP
ejpam-6865	314	12	abc	abc	PROPN
ejpam-6865	314	13	fractional	fractional	PROPN
ejpam-6865	314	14	derivative	derivative	PROPN
ejpam-6865	314	15	s.	s.	PROPN
ejpam-6865	314	16	tamimi	tamimi	PROPN
ejpam-6865	314	17	,	,	PUNCT
ejpam-6865	314	18	a.	a.	PROPN
ejpam-6865	314	19	k.	k.	PROPN
ejpam-6865	314	20	alomari	alomari	PROPN
ejpam-6865	314	21	,	,	PUNCT
ejpam-6865	314	22	m.	m.	NOUN
ejpam-6865	314	23	alaroud	alaroud	PROPN
ejpam-6865	314	24	/	/	SYM
ejpam-6865	314	25	eur	eur	PROPN
ejpam-6865	314	26	.	.	PUNCT
ejpam-6865	315	1	j.	j.	PROPN
ejpam-6865	315	2	pure	pure	PROPN
ejpam-6865	315	3	appl	appl	PROPN
ejpam-6865	315	4	.	.	PROPN
ejpam-6865	315	5	math	math	PROPN
ejpam-6865	315	6	,	,	PUNCT
ejpam-6865	315	7	18	18	NUM
ejpam-6865	315	8	(	(	PUNCT
ejpam-6865	315	9	4	4	NUM
ejpam-6865	315	10	)	)	PUNCT
ejpam-6865	315	11	(	(	PUNCT
ejpam-6865	315	12	2025	2025	NUM
ejpam-6865	315	13	)	)	PUNCT
ejpam-6865	315	14	,	,	PUNCT
ejpam-6865	315	15	6865	6865	NUM
ejpam-6865	315	16	19	19	NUM
ejpam-6865	315	17	of	of	ADP
ejpam-6865	315	18	19	19	NUM
ejpam-6865	315	19	and	and	CCONJ
ejpam-6865	315	20	non‐smooth	non‐smooth	NOUN
ejpam-6865	315	21	solutions	solution	NOUN
ejpam-6865	315	22	.	.	PUNCT
ejpam-6865	316	1	asian	asian	ADJ
ejpam-6865	316	2	journal	journal	PROPN
ejpam-6865	316	3	of	of	ADP
ejpam-6865	316	4	control	control	NOUN
ejpam-6865	316	5	,	,	PUNCT
ejpam-6865	316	6	26(1):490–503	26(1):490–503	NUM
ejpam-6865	316	7	,	,	PUNCT
ejpam-6865	316	8	2024	2024	NUM
ejpam-6865	316	9	.	.	PUNCT
ejpam-6865	317	1	[	[	X
ejpam-6865	317	2	24	24	NUM
ejpam-6865	317	3	]	]	PUNCT
ejpam-6865	317	4	a.	a.	NOUN
ejpam-6865	317	5	k.	k.	PROPN
ejpam-6865	317	6	alomari	alomari	PROPN
ejpam-6865	317	7	,	,	PUNCT
ejpam-6865	317	8	a.	a.	PROPN
ejpam-6865	317	9	r.	r.	PROPN
ejpam-6865	317	10	al	al	PROPN
ejpam-6865	317	11	-	-	PUNCT
ejpam-6865	317	12	shatnawi	shatnawi	PROPN
ejpam-6865	317	13	,	,	PUNCT
ejpam-6865	317	14	a.	a.	NOUN
ejpam-6865	317	15	almalki	almalki	ADV
ejpam-6865	317	16	,	,	PUNCT
ejpam-6865	317	17	and	and	CCONJ
ejpam-6865	317	18	n.	n.	PROPN
ejpam-6865	317	19	anakira	anakira	PROPN
ejpam-6865	317	20	.	.	PUNCT
ejpam-6865	318	1	bernstein	bernstein	PROPN
ejpam-6865	318	2	polynomials	polynomial	VERB
ejpam-6865	318	3	for	for	ADP
ejpam-6865	318	4	solving	solve	VERB
ejpam-6865	318	5	fractional	fractional	ADJ
ejpam-6865	318	6	differential	differential	ADJ
ejpam-6865	318	7	equations	equation	NOUN
ejpam-6865	318	8	with	with	ADP
ejpam-6865	318	9	two	two	NUM
ejpam-6865	318	10	parameters	parameter	NOUN
ejpam-6865	318	11	.	.	PUNCT
ejpam-6865	319	1	european	european	ADJ
ejpam-6865	319	2	journal	journal	PROPN
ejpam-6865	319	3	of	of	ADP
ejpam-6865	319	4	pure	pure	ADJ
ejpam-6865	319	5	and	and	CCONJ
ejpam-6865	319	6	applied	applied	ADJ
ejpam-6865	319	7	mathematics	mathematic	NOUN
ejpam-6865	319	8	,	,	PUNCT
ejpam-6865	319	9	17(4):3539–3556	17(4):3539–3556	NUM
ejpam-6865	319	10	,	,	PUNCT
ejpam-6865	319	11	2024	2024	NUM
ejpam-6865	319	12	.	.	PUNCT
ejpam-6865	320	1	[	[	X
ejpam-6865	320	2	25	25	NUM
ejpam-6865	320	3	]	]	PUNCT
ejpam-6865	320	4	s.	s.	PROPN
ejpam-6865	320	5	a.	a.	PROPN
ejpam-6865	320	6	t.	t.	PROPN
ejpam-6865	320	7	algazaa	algazaa	PROPN
ejpam-6865	320	8	and	and	CCONJ
ejpam-6865	320	9	j.	j.	PROPN
ejpam-6865	320	10	saeidian	saeidian	PROPN
ejpam-6865	320	11	.	.	PUNCT
ejpam-6865	321	1	solving	solve	VERB
ejpam-6865	321	2	nonlinear	nonlinear	ADJ
ejpam-6865	321	3	multi	multi	ADJ
ejpam-6865	321	4	-	-	ADJ
ejpam-6865	321	5	order	order	ADJ
ejpam-6865	321	6	fractional	fractional	ADJ
ejpam-6865	321	7	differential	differential	NOUN
ejpam-6865	321	8	equations	equation	NOUN
ejpam-6865	321	9	using	use	VERB
ejpam-6865	321	10	bernstein	bernstein	PROPN
ejpam-6865	321	11	polynomials	polynomials	PROPN
ejpam-6865	321	12	.	.	PUNCT
ejpam-6865	322	1	ieee	ieee	NOUN
ejpam-6865	322	2	access	access	NOUN
ejpam-6865	322	3	,	,	PUNCT
ejpam-6865	322	4	11:128032–128043	11:128032–128043	NUM
ejpam-6865	322	5	,	,	PUNCT
ejpam-6865	322	6	2023	2023	NUM
ejpam-6865	322	7	.	.	PUNCT
ejpam-6865	323	1	[	[	X
ejpam-6865	323	2	26	26	NUM
ejpam-6865	323	3	]	]	PUNCT
ejpam-6865	323	4	p.	p.	NOUN
ejpam-6865	323	5	yadav	yadav	PROPN
ejpam-6865	323	6	and	and	CCONJ
ejpam-6865	323	7	s.	s.	PROPN
ejpam-6865	323	8	jahan	jahan	PROPN
ejpam-6865	323	9	.	.	PUNCT
ejpam-6865	324	1	bell	bell	PROPN
ejpam-6865	324	2	wavelet	wavelet	NOUN
ejpam-6865	324	3	-	-	PUNCT
ejpam-6865	324	4	based	base	VERB
ejpam-6865	324	5	numerical	numerical	ADJ
ejpam-6865	324	6	algorithm	algorithm	NOUN
ejpam-6865	324	7	for	for	ADP
ejpam-6865	324	8	fractional	fractional	ADJ
ejpam-6865	324	9	-	-	PUNCT
ejpam-6865	324	10	order	order	NOUN
ejpam-6865	324	11	(	(	PUNCT
ejpam-6865	324	12	1	1	NUM
ejpam-6865	324	13	+	+	NOUN
ejpam-6865	324	14	1)-dimensional	1)-dimensional	ADJ
ejpam-6865	324	15	telegraph	telegraph	NOUN
ejpam-6865	324	16	equations	equation	NOUN
ejpam-6865	324	17	involving	involve	VERB
ejpam-6865	324	18	derivative	derivative	NOUN
ejpam-6865	324	19	in	in	ADP
ejpam-6865	324	20	caputo	caputo	PROPN
ejpam-6865	324	21	sense	sense	NOUN
ejpam-6865	324	22	.	.	PUNCT
ejpam-6865	325	1	international	international	ADJ
ejpam-6865	325	2	journal	journal	PROPN
ejpam-6865	325	3	of	of	ADP
ejpam-6865	325	4	dynamics	dynamic	NOUN
ejpam-6865	325	5	and	and	CCONJ
ejpam-6865	325	6	control	control	NOUN
ejpam-6865	325	7	,	,	PUNCT
ejpam-6865	325	8	13(2):71	13(2):71	NUM
ejpam-6865	325	9	,	,	PUNCT
ejpam-6865	325	10	2025	2025	NUM
ejpam-6865	325	11	.	.	PUNCT
ejpam-6865	326	1	[	[	X
ejpam-6865	326	2	27	27	NUM
ejpam-6865	326	3	]	]	PUNCT
ejpam-6865	326	4	a.	a.	NOUN
ejpam-6865	326	5	atangana	atangana	PROPN
ejpam-6865	326	6	and	and	CCONJ
ejpam-6865	326	7	j.	j.	PROPN
ejpam-6865	326	8	f.	f.	PROPN
ejpam-6865	326	9	gómez‐aguilar	gómez‐aguilar	PROPN
ejpam-6865	326	10	.	.	PUNCT
ejpam-6865	327	1	numerical	numerical	PROPN
ejpam-6865	327	2	approximation	approximation	NOUN
ejpam-6865	327	3	of	of	ADP
ejpam-6865	327	4	riemann‐liouville	riemann‐liouville	NOUN
ejpam-6865	327	5	definition	definition	NOUN
ejpam-6865	327	6	of	of	ADP
ejpam-6865	327	7	fractional	fractional	ADJ
ejpam-6865	327	8	derivative	derivative	NOUN
ejpam-6865	327	9	:	:	PUNCT
ejpam-6865	327	10	from	from	ADP
ejpam-6865	327	11	riemann‐liouville	riemann‐liouville	NOUN
ejpam-6865	327	12	to	to	ADP
ejpam-6865	327	13	atangana‐baleanu	atangana‐baleanu	PRON
ejpam-6865	327	14	.	.	PUNCT
ejpam-6865	328	1	numerical	numerical	ADJ
ejpam-6865	328	2	methods	method	NOUN
ejpam-6865	328	3	for	for	ADP
ejpam-6865	328	4	partial	partial	ADJ
ejpam-6865	328	5	differential	differential	NOUN
ejpam-6865	328	6	equations	equation	NOUN
ejpam-6865	328	7	,	,	PUNCT
ejpam-6865	328	8	34(5):1502–1523	34(5):1502–1523	NUM
ejpam-6865	328	9	,	,	PUNCT
ejpam-6865	328	10	2018	2018	NUM
ejpam-6865	328	11	.	.	PUNCT
ejpam-6865	329	1	[	[	X
ejpam-6865	329	2	28	28	NUM
ejpam-6865	329	3	]	]	X
ejpam-6865	330	1	p.	p.	NOUN
ejpam-6865	330	2	o.	o.	PROPN
ejpam-6865	331	1	mohammed	mohammed	PROPN
ejpam-6865	331	2	.	.	PUNCT
ejpam-6865	332	1	hermite‐hadamard	hermite‐hadamard	PROPN
ejpam-6865	332	2	inequalities	inequality	NOUN
ejpam-6865	332	3	for	for	ADP
ejpam-6865	332	4	riemann‐liouville	riemann‐liouville	NOUN
ejpam-6865	332	5	fractional	fractional	ADJ
ejpam-6865	332	6	integrals	integral	NOUN
ejpam-6865	332	7	of	of	ADP
ejpam-6865	332	8	a	a	DET
ejpam-6865	332	9	convex	convex	NOUN
ejpam-6865	332	10	function	function	NOUN
ejpam-6865	332	11	with	with	ADP
ejpam-6865	332	12	respect	respect	NOUN
ejpam-6865	332	13	to	to	ADP
ejpam-6865	332	14	a	a	DET
ejpam-6865	332	15	monotone	monotone	ADJ
ejpam-6865	332	16	function	function	NOUN
ejpam-6865	332	17	.	.	PUNCT
ejpam-6865	333	1	mathematical	mathematical	ADJ
ejpam-6865	333	2	methods	method	NOUN
ejpam-6865	333	3	in	in	ADP
ejpam-6865	333	4	the	the	DET
ejpam-6865	333	5	applied	apply	VERB
ejpam-6865	333	6	sciences	science	NOUN
ejpam-6865	333	7	,	,	PUNCT
ejpam-6865	333	8	44(3):2314–2324	44(3):2314–2324	NUM
ejpam-6865	333	9	,	,	PUNCT
ejpam-6865	333	10	2019	2019	NUM
ejpam-6865	333	11	.	.	PUNCT
ejpam-6865	334	1	[	[	X
ejpam-6865	334	2	29	29	NUM
ejpam-6865	334	3	]	]	PUNCT
ejpam-6865	334	4	a.	a.	NOUN
ejpam-6865	334	5	padder	padder	NOUN
ejpam-6865	334	6	,	,	PUNCT
ejpam-6865	334	7	l.	l.	PROPN
ejpam-6865	334	8	almutairi	almutairi	PROPN
ejpam-6865	334	9	,	,	PUNCT
ejpam-6865	334	10	s.	s.	PROPN
ejpam-6865	334	11	qureshi	qureshi	PROPN
ejpam-6865	334	12	,	,	PUNCT
ejpam-6865	334	13	a.	a.	PROPN
ejpam-6865	334	14	soomro	soomro	PROPN
ejpam-6865	334	15	,	,	PUNCT
ejpam-6865	334	16	a.	a.	PROPN
ejpam-6865	334	17	afroz	afroz	PROPN
ejpam-6865	334	18	,	,	PUNCT
ejpam-6865	334	19	e.	e.	PROPN
ejpam-6865	334	20	hincal	hincal	PROPN
ejpam-6865	334	21	,	,	PUNCT
ejpam-6865	334	22	and	and	CCONJ
ejpam-6865	334	23	a.	a.	NOUN
ejpam-6865	334	24	tassaddiq	tassaddiq	NOUN
ejpam-6865	334	25	.	.	PUNCT
ejpam-6865	335	1	dynamical	dynamical	ADJ
ejpam-6865	335	2	analysis	analysis	NOUN
ejpam-6865	335	3	of	of	ADP
ejpam-6865	335	4	generalized	generalized	ADJ
ejpam-6865	335	5	tumor	tumor	NOUN
ejpam-6865	335	6	example	example	NOUN
ejpam-6865	335	7	with	with	ADP
ejpam-6865	335	8	caputo	caputo	PROPN
ejpam-6865	335	9	fractional	fractional	ADJ
ejpam-6865	335	10	-	-	PUNCT
ejpam-6865	335	11	order	order	NOUN
ejpam-6865	335	12	derivative	derivative	NOUN
ejpam-6865	335	13	.	.	PUNCT
ejpam-6865	336	1	fractal	fractal	PROPN
ejpam-6865	336	2	and	and	CCONJ
ejpam-6865	336	3	fractional	fractional	ADJ
ejpam-6865	336	4	,	,	PUNCT
ejpam-6865	336	5	7(3):258	7(3):258	NUM
ejpam-6865	336	6	,	,	PUNCT
ejpam-6865	336	7	2023	2023	NUM
ejpam-6865	336	8	.	.	PUNCT
ejpam-6865	337	1	[	[	X
ejpam-6865	337	2	30	30	NUM
ejpam-6865	337	3	]	]	X
ejpam-6865	337	4	h.	h.	PROPN
ejpam-6865	337	5	m.	m.	PROPN
ejpam-6865	337	6	srivastava	srivastava	PROPN
ejpam-6865	337	7	,	,	PUNCT
ejpam-6865	337	8	a.	a.	PROPN
ejpam-6865	337	9	k.	k.	PROPN
ejpam-6865	337	10	n.	n.	PROPN
ejpam-6865	337	11	alomari	alomari	PROPN
ejpam-6865	337	12	,	,	PUNCT
ejpam-6865	337	13	k.	k.	PROPN
ejpam-6865	337	14	m.	m.	PROPN
ejpam-6865	337	15	saad	saad	PROPN
ejpam-6865	337	16	,	,	PUNCT
ejpam-6865	337	17	and	and	CCONJ
ejpam-6865	337	18	w.	w.	PROPN
ejpam-6865	337	19	m.	m.	PROPN
ejpam-6865	337	20	hamanah	hamanah	PROPN
ejpam-6865	337	21	.	.	PUNCT
ejpam-6865	338	1	some	some	DET
ejpam-6865	338	2	dynamical	dynamical	ADJ
ejpam-6865	338	3	examples	example	NOUN
ejpam-6865	338	4	involving	involve	VERB
ejpam-6865	338	5	fractional	fractional	ADJ
ejpam-6865	338	6	-	-	PUNCT
ejpam-6865	338	7	order	order	NOUN
ejpam-6865	338	8	derivatives	derivative	NOUN
ejpam-6865	338	9	with	with	ADP
ejpam-6865	338	10	the	the	DET
ejpam-6865	338	11	mittag	mittag	ADJ
ejpam-6865	338	12	-	-	PUNCT
ejpam-6865	338	13	leffler	leffler	NOUN
ejpam-6865	338	14	type	type	NOUN
ejpam-6865	338	15	kernels	kernel	NOUN
ejpam-6865	338	16	and	and	CCONJ
ejpam-6865	338	17	their	their	PRON
ejpam-6865	338	18	applications	application	NOUN
ejpam-6865	338	19	based	base	VERB
ejpam-6865	338	20	upon	upon	SCONJ
ejpam-6865	338	21	the	the	DET
ejpam-6865	338	22	legendre	legendre	PROPN
ejpam-6865	338	23	spectral	spectral	ADJ
ejpam-6865	338	24	collocation	collocation	NOUN
ejpam-6865	338	25	method	method	NOUN
ejpam-6865	338	26	.	.	PUNCT
ejpam-6865	339	1	fractal	fractal	ADJ
ejpam-6865	339	2	and	and	CCONJ
ejpam-6865	339	3	fractional	fractional	ADJ
ejpam-6865	339	4	,	,	PUNCT
ejpam-6865	339	5	5(3):131	5(3):131	NUM
ejpam-6865	339	6	,	,	PUNCT
ejpam-6865	339	7	2021	2021	NUM
ejpam-6865	339	8	.	.	PUNCT
ejpam-6865	340	1	[	[	X
ejpam-6865	340	2	31	31	NUM
ejpam-6865	340	3	]	]	PUNCT
ejpam-6865	340	4	t.	t.	PROPN
ejpam-6865	340	5	abdeljawad	abdeljawad	NOUN
ejpam-6865	340	6	.	.	PUNCT
ejpam-6865	341	1	fractional	fractional	ADJ
ejpam-6865	341	2	difference	difference	NOUN
ejpam-6865	341	3	operators	operator	NOUN
ejpam-6865	341	4	with	with	ADP
ejpam-6865	341	5	discrete	discrete	ADJ
ejpam-6865	341	6	generalized	generalize	VERB
ejpam-6865	341	7	mittag	mittag	ADJ
ejpam-6865	341	8	–	–	PUNCT
ejpam-6865	341	9	leffler	leffler	ADJ
ejpam-6865	341	10	kernels	kernel	NOUN
ejpam-6865	341	11	.	.	PUNCT
ejpam-6865	342	1	chaos	chaos	NOUN
ejpam-6865	342	2	,	,	PUNCT
ejpam-6865	342	3	solitons	soliton	NOUN
ejpam-6865	342	4	&	&	CCONJ
ejpam-6865	342	5	fractals	fractal	NOUN
ejpam-6865	342	6	,	,	PUNCT
ejpam-6865	342	7	126:315–324	126:315–324	NUM
ejpam-6865	342	8	,	,	PUNCT
ejpam-6865	342	9	2019	2019	NUM
ejpam-6865	342	10	.	.	PUNCT
ejpam-6865	343	1	[	[	X
ejpam-6865	343	2	32	32	NUM
ejpam-6865	343	3	]	]	PUNCT
ejpam-6865	343	4	h.	h.	PROPN
ejpam-6865	343	5	m.	m.	PROPN
ejpam-6865	343	6	ahmed	ahmed	PROPN
ejpam-6865	343	7	.	.	PUNCT
ejpam-6865	344	1	numerical	numerical	PROPN
ejpam-6865	344	2	solutions	solution	NOUN
ejpam-6865	344	3	of	of	ADP
ejpam-6865	344	4	high	high	ADJ
ejpam-6865	344	5	-	-	PUNCT
ejpam-6865	344	6	order	order	NOUN
ejpam-6865	344	7	differential	differential	ADJ
ejpam-6865	344	8	equations	equation	NOUN
ejpam-6865	344	9	with	with	ADP
ejpam-6865	344	10	polynomial	polynomial	ADJ
ejpam-6865	344	11	coefficients	coefficient	NOUN
ejpam-6865	344	12	using	use	VERB
ejpam-6865	344	13	a	a	DET
ejpam-6865	344	14	bernstein	bernstein	PROPN
ejpam-6865	344	15	polynomial	polynomial	ADJ
ejpam-6865	344	16	basis	basis	NOUN
ejpam-6865	344	17	.	.	PUNCT
ejpam-6865	345	1	mediterranean	mediterranean	PROPN
ejpam-6865	345	2	journal	journal	PROPN
ejpam-6865	345	3	of	of	ADP
ejpam-6865	345	4	mathematics	mathematic	NOUN
ejpam-6865	345	5	,	,	PUNCT
ejpam-6865	345	6	20(6):303	20(6):303	NUM
ejpam-6865	345	7	,	,	PUNCT
ejpam-6865	345	8	2023	2023	NUM
ejpam-6865	345	9	.	.	PUNCT
ejpam-6865	346	1	[	[	X
ejpam-6865	346	2	33	33	NUM
ejpam-6865	346	3	]	]	PUNCT
ejpam-6865	346	4	k.	k.	PROPN
ejpam-6865	346	5	diethelm	diethelm	PROPN
ejpam-6865	346	6	,	,	PUNCT
ejpam-6865	346	7	r.	r.	PROPN
ejpam-6865	346	8	garrappa	garrappa	PROPN
ejpam-6865	346	9	,	,	PUNCT
ejpam-6865	346	10	a.	a.	NOUN
ejpam-6865	346	11	giusti	giusti	NOUN
ejpam-6865	346	12	,	,	PUNCT
ejpam-6865	346	13	and	and	CCONJ
ejpam-6865	346	14	m.	m.	NOUN
ejpam-6865	346	15	stynes	styne	NOUN
ejpam-6865	346	16	.	.	PUNCT
ejpam-6865	347	1	why	why	SCONJ
ejpam-6865	347	2	fractional	fractional	ADJ
ejpam-6865	347	3	derivatives	derivative	NOUN
ejpam-6865	347	4	with	with	ADP
ejpam-6865	347	5	nonsingular	nonsingular	ADJ
ejpam-6865	347	6	kernels	kernel	NOUN
ejpam-6865	347	7	should	should	AUX
ejpam-6865	347	8	not	not	PART
ejpam-6865	347	9	be	be	AUX
ejpam-6865	347	10	used	use	VERB
ejpam-6865	347	11	.	.	PUNCT
ejpam-6865	348	1	fractional	fractional	ADJ
ejpam-6865	348	2	calculus	calculus	NOUN
ejpam-6865	348	3	and	and	CCONJ
ejpam-6865	348	4	applied	apply	VERB
ejpam-6865	348	5	analysis	analysis	NOUN
ejpam-6865	348	6	,	,	PUNCT
ejpam-6865	348	7	23(3):610–634	23(3):610–634	PROPN
ejpam-6865	348	8	,	,	PUNCT
ejpam-6865	348	9	2020	2020	NUM
ejpam-6865	348	10	.	.	PUNCT