id	sid	tid	token	lemma	pos
ejpam-5924	1	1	european	european	PROPN
ejpam-5924	1	2	journal	journal	PROPN
ejpam-5924	1	3	of	of	ADP
ejpam-5924	1	4	pure	pure	ADJ
ejpam-5924	1	5	and	and	CCONJ
ejpam-5924	1	6	applied	applied	ADJ
ejpam-5924	1	7	mathematics	mathematic	NOUN
ejpam-5924	1	8	2025	2025	NUM
ejpam-5924	1	9	,	,	PUNCT
ejpam-5924	1	10	vol	vol	NOUN
ejpam-5924	1	11	.	.	PROPN
ejpam-5924	1	12	18	18	NUM
ejpam-5924	1	13	,	,	PUNCT
ejpam-5924	1	14	issue	issue	NOUN
ejpam-5924	1	15	2	2	NUM
ejpam-5924	1	16	,	,	PUNCT
ejpam-5924	1	17	article	article	NOUN
ejpam-5924	1	18	number	number	NOUN
ejpam-5924	1	19	5924	5924	NUM
ejpam-5924	1	20	issn	issn	VERB
ejpam-5924	1	21	1307	1307	NUM
ejpam-5924	1	22	-	-	SYM
ejpam-5924	1	23	5543	5543	NUM
ejpam-5924	1	24	–	–	PUNCT
ejpam-5924	1	25	ejpam.com	ejpam.com	X
ejpam-5924	1	26	published	publish	VERB
ejpam-5924	1	27	by	by	ADP
ejpam-5924	1	28	new	new	PROPN
ejpam-5924	1	29	york	york	PROPN
ejpam-5924	1	30	business	business	PROPN
ejpam-5924	1	31	global	global	ADJ
ejpam-5924	1	32	computational	computational	ADJ
ejpam-5924	1	33	methods	method	NOUN
ejpam-5924	1	34	,	,	PUNCT
ejpam-5924	1	35	existence	existence	NOUN
ejpam-5924	1	36	and	and	CCONJ
ejpam-5924	1	37	uniqueness	uniqueness	NOUN
ejpam-5924	1	38	for	for	ADP
ejpam-5924	1	39	solving	solve	VERB
ejpam-5924	1	40	2	2	NUM
ejpam-5924	1	41	-	-	PUNCT
ejpam-5924	1	42	d	d	ADJ
ejpam-5924	1	43	fractional	fractional	ADJ
ejpam-5924	1	44	nonlinear	nonlinear	ADJ
ejpam-5924	1	45	fredholm	fredholm	NOUN
ejpam-5924	1	46	integro	integro	ADJ
ejpam-5924	1	47	-	-	PUNCT
ejpam-5924	1	48	differential	differential	NOUN
ejpam-5924	1	49	equation	equation	NOUN
ejpam-5924	1	50	abeer	abeer	PROPN
ejpam-5924	1	51	m.	m.	PROPN
ejpam-5924	2	1	al	al	PROPN
ejpam-5924	2	2	-	-	PUNCT
ejpam-5924	2	3	bugami1,∗	bugami1,∗	NOUN
ejpam-5924	2	4	,	,	PUNCT
ejpam-5924	2	5	nuha	nuha	NOUN
ejpam-5924	2	6	a.	a.	PROPN
ejpam-5924	2	7	alharbi1	alharbi1	PROPN
ejpam-5924	2	8	,	,	PUNCT
ejpam-5924	2	9	amr	amr	PROPN
ejpam-5924	2	10	m.	m.	NOUN
ejpam-5924	2	11	s.	s.	PROPN
ejpam-5924	2	12	mahdy1	mahdy1	PROPN
ejpam-5924	2	13	1	1	NUM
ejpam-5924	2	14	department	department	NOUN
ejpam-5924	2	15	of	of	ADP
ejpam-5924	2	16	mathematics	mathematic	NOUN
ejpam-5924	2	17	and	and	CCONJ
ejpam-5924	2	18	statistics	statistic	NOUN
ejpam-5924	2	19	,	,	PUNCT
ejpam-5924	2	20	college	college	NOUN
ejpam-5924	2	21	of	of	ADP
ejpam-5924	2	22	science	science	PROPN
ejpam-5924	2	23	,	,	PUNCT
ejpam-5924	2	24	taif	taif	PROPN
ejpam-5924	2	25	university	university	PROPN
ejpam-5924	2	26	,	,	PUNCT
ejpam-5924	2	27	p.o	p.o	PROPN
ejpam-5924	2	28	.	.	PROPN
ejpam-5924	2	29	box	box	PROPN
ejpam-5924	2	30	11099	11099	NUM
ejpam-5924	2	31	,	,	PUNCT
ejpam-5924	2	32	taif	taif	PROPN
ejpam-5924	2	33	21944	21944	NUM
ejpam-5924	2	34	,	,	PUNCT
ejpam-5924	2	35	saudi	saudi	PROPN
ejpam-5924	2	36	arabia	arabia	PROPN
ejpam-5924	2	37	abstract	abstract	NOUN
ejpam-5924	2	38	.	.	PUNCT
ejpam-5924	3	1	in	in	ADP
ejpam-5924	3	2	this	this	DET
ejpam-5924	3	3	paper	paper	NOUN
ejpam-5924	3	4	,	,	PUNCT
ejpam-5924	3	5	we	we	PRON
ejpam-5924	3	6	have	have	AUX
ejpam-5924	3	7	investigated	investigate	VERB
ejpam-5924	3	8	the	the	DET
ejpam-5924	3	9	two	two	NUM
ejpam-5924	3	10	-	-	PUNCT
ejpam-5924	3	11	dimensional	dimensional	ADJ
ejpam-5924	3	12	fractional	fractional	ADJ
ejpam-5924	3	13	nonlinear	nonlinear	ADJ
ejpam-5924	3	14	fredholm	fredholm	NOUN
ejpam-5924	3	15	integro	integro	ADJ
ejpam-5924	3	16	-	-	PUNCT
ejpam-5924	3	17	differential	differential	NOUN
ejpam-5924	3	18	equation	equation	NOUN
ejpam-5924	3	19	(	(	PUNCT
ejpam-5924	3	20	tdfnfi	tdfnfi	NOUN
ejpam-5924	3	21	-	-	PUNCT
ejpam-5924	3	22	de	de	NOUN
ejpam-5924	3	23	)	)	PUNCT
ejpam-5924	3	24	.	.	PUNCT
ejpam-5924	4	1	these	these	DET
ejpam-5924	4	2	equations	equation	NOUN
ejpam-5924	4	3	are	be	AUX
ejpam-5924	4	4	used	use	VERB
ejpam-5924	4	5	in	in	ADP
ejpam-5924	4	6	many	many	ADJ
ejpam-5924	4	7	fields	field	NOUN
ejpam-5924	4	8	,	,	PUNCT
ejpam-5924	4	9	including	include	VERB
ejpam-5924	4	10	particle	particle	NOUN
ejpam-5924	4	11	dynamics	dynamic	NOUN
ejpam-5924	4	12	in	in	ADP
ejpam-5924	4	13	physics	physics	NOUN
ejpam-5924	4	14	,	,	PUNCT
ejpam-5924	4	15	biology	biology	NOUN
ejpam-5924	4	16	,	,	PUNCT
ejpam-5924	4	17	and	and	CCONJ
ejpam-5924	4	18	control	control	NOUN
ejpam-5924	4	19	theory	theory	NOUN
ejpam-5924	4	20	.	.	PUNCT
ejpam-5924	5	1	we	we	PRON
ejpam-5924	5	2	have	have	AUX
ejpam-5924	5	3	developed	develop	VERB
ejpam-5924	5	4	an	an	DET
ejpam-5924	5	5	effective	effective	ADJ
ejpam-5924	5	6	combined	combined	ADJ
ejpam-5924	5	7	approach	approach	NOUN
ejpam-5924	5	8	in	in	ADP
ejpam-5924	5	9	our	our	PRON
ejpam-5924	5	10	work	work	NOUN
ejpam-5924	5	11	that	that	PRON
ejpam-5924	5	12	uses	use	VERB
ejpam-5924	5	13	homotopy	homotopy	VERB
ejpam-5924	5	14	analysis	analysis	NOUN
ejpam-5924	5	15	(	(	PUNCT
ejpam-5924	5	16	ham	ham	NOUN
ejpam-5924	5	17	)	)	PUNCT
ejpam-5924	5	18	and	and	CCONJ
ejpam-5924	5	19	the	the	DET
ejpam-5924	5	20	adomian	adomian	NOUN
ejpam-5924	5	21	decomposition	decomposition	NOUN
ejpam-5924	5	22	method	method	NOUN
ejpam-5924	5	23	(	(	PUNCT
ejpam-5924	5	24	adm	adm	PROPN
ejpam-5924	5	25	)	)	PUNCT
ejpam-5924	5	26	to	to	PART
ejpam-5924	5	27	solve	solve	VERB
ejpam-5924	5	28	fractional	fractional	ADJ
ejpam-5924	5	29	integro	integro	ADJ
ejpam-5924	5	30	-	-	PUNCT
ejpam-5924	5	31	differential	differential	NOUN
ejpam-5924	5	32	equations	equation	NOUN
ejpam-5924	5	33	in	in	ADP
ejpam-5924	5	34	two	two	NUM
ejpam-5924	5	35	dimensions	dimension	NOUN
ejpam-5924	5	36	.	.	PUNCT
ejpam-5924	6	1	numerical	numerical	ADJ
ejpam-5924	6	2	experiment	experiment	NOUN
ejpam-5924	6	3	results	result	NOUN
ejpam-5924	6	4	show	show	VERB
ejpam-5924	6	5	the	the	DET
ejpam-5924	6	6	effectiveness	effectiveness	NOUN
ejpam-5924	6	7	of	of	ADP
ejpam-5924	6	8	our	our	PRON
ejpam-5924	6	9	recently	recently	ADV
ejpam-5924	6	10	created	create	VERB
ejpam-5924	6	11	technique	technique	NOUN
ejpam-5924	6	12	.	.	PUNCT
ejpam-5924	7	1	we	we	PRON
ejpam-5924	7	2	prove	prove	VERB
ejpam-5924	7	3	the	the	DET
ejpam-5924	7	4	existence	existence	NOUN
ejpam-5924	7	5	and	and	CCONJ
ejpam-5924	7	6	uniqueness	uniqueness	NOUN
ejpam-5924	7	7	of	of	ADP
ejpam-5924	7	8	the	the	DET
ejpam-5924	7	9	exact	exact	ADJ
ejpam-5924	7	10	solution	solution	NOUN
ejpam-5924	7	11	.	.	PUNCT
ejpam-5924	8	1	to	to	PART
ejpam-5924	8	2	illustrate	illustrate	VERB
ejpam-5924	8	3	the	the	DET
ejpam-5924	8	4	numerical	numerical	ADJ
ejpam-5924	8	5	effectiveness	effectiveness	NOUN
ejpam-5924	8	6	of	of	ADP
ejpam-5924	8	7	the	the	DET
ejpam-5924	8	8	suggested	suggest	VERB
ejpam-5924	8	9	approach	approach	NOUN
ejpam-5924	8	10	,	,	PUNCT
ejpam-5924	8	11	we	we	PRON
ejpam-5924	8	12	provide	provide	VERB
ejpam-5924	8	13	a	a	DET
ejpam-5924	8	14	number	number	NOUN
ejpam-5924	8	15	of	of	ADP
ejpam-5924	8	16	numerical	numerical	ADJ
ejpam-5924	8	17	examples	example	NOUN
ejpam-5924	8	18	.	.	PUNCT
ejpam-5924	9	1	the	the	DET
ejpam-5924	9	2	suggested	suggest	VERB
ejpam-5924	9	3	approach	approach	NOUN
ejpam-5924	9	4	is	be	AUX
ejpam-5924	9	5	accurate	accurate	ADJ
ejpam-5924	9	6	and	and	CCONJ
ejpam-5924	9	7	applicable	applicable	ADJ
ejpam-5924	9	8	to	to	ADP
ejpam-5924	9	9	various	various	ADJ
ejpam-5924	9	10	nonlinear	nonlinear	ADJ
ejpam-5924	9	11	issues	issue	NOUN
ejpam-5924	9	12	in	in	ADP
ejpam-5924	9	13	science	science	NOUN
ejpam-5924	9	14	,	,	PUNCT
ejpam-5924	9	15	according	accord	VERB
ejpam-5924	9	16	to	to	ADP
ejpam-5924	9	17	theoretical	theoretical	ADJ
ejpam-5924	9	18	and	and	CCONJ
ejpam-5924	9	19	numerical	numerical	ADJ
ejpam-5924	9	20	results	result	NOUN
ejpam-5924	9	21	.	.	PUNCT
ejpam-5924	10	1	2020	2020	NUM
ejpam-5924	10	2	mathematics	mathematic	NOUN
ejpam-5924	10	3	subject	subject	NOUN
ejpam-5924	10	4	classifications	classification	NOUN
ejpam-5924	10	5	:	:	PUNCT
ejpam-5924	10	6	45j05	45j05	NUM
ejpam-5924	10	7	,	,	PUNCT
ejpam-5924	10	8	45g10	45g10	NUM
ejpam-5924	10	9	,	,	PUNCT
ejpam-5924	10	10	26a33	26a33	NUM
ejpam-5924	10	11	,	,	PUNCT
ejpam-5924	10	12	35r11	35r11	NUM
ejpam-5924	10	13	,	,	PUNCT
ejpam-5924	10	14	65r20	65r20	NUM
ejpam-5924	10	15	,	,	PUNCT
ejpam-5924	10	16	65l10	65l10	NUM
ejpam-5924	10	17	key	key	ADJ
ejpam-5924	10	18	words	word	NOUN
ejpam-5924	10	19	and	and	CCONJ
ejpam-5924	10	20	phrases	phrase	NOUN
ejpam-5924	10	21	:	:	PUNCT
ejpam-5924	10	22	tdfnfi	tdfnfi	ADJ
ejpam-5924	10	23	-	-	PUNCT
ejpam-5924	10	24	de	de	ADJ
ejpam-5924	10	25	,	,	PUNCT
ejpam-5924	10	26	existence	existence	NOUN
ejpam-5924	10	27	and	and	CCONJ
ejpam-5924	10	28	uniqueness	uniqueness	NOUN
ejpam-5924	10	29	,	,	PUNCT
ejpam-5924	10	30	adm	adm	PROPN
ejpam-5924	10	31	,	,	PUNCT
ejpam-5924	10	32	ham	ham	NOUN
ejpam-5924	10	33	1	1	NUM
ejpam-5924	10	34	.	.	PUNCT
ejpam-5924	11	1	introduction	introduction	NOUN
ejpam-5924	11	2	integral	integral	ADJ
ejpam-5924	11	3	equations	equation	NOUN
ejpam-5924	11	4	are	be	AUX
ejpam-5924	11	5	used	use	VERB
ejpam-5924	11	6	in	in	ADP
ejpam-5924	11	7	many	many	ADJ
ejpam-5924	11	8	different	different	ADJ
ejpam-5924	11	9	fields	field	NOUN
ejpam-5924	11	10	,	,	PUNCT
ejpam-5924	11	11	such	such	ADJ
ejpam-5924	11	12	as	as	ADP
ejpam-5924	11	13	continuous	continuous	ADJ
ejpam-5924	11	14	mechanical	mechanical	ADJ
ejpam-5924	11	15	engineering	engineering	NOUN
ejpam-5924	11	16	,	,	PUNCT
ejpam-5924	11	17	potential	potential	ADJ
ejpam-5924	11	18	concept	concept	NOUN
ejpam-5924	11	19	,	,	PUNCT
ejpam-5924	11	20	geophysics	geophysic	NOUN
ejpam-5924	11	21	,	,	PUNCT
ejpam-5924	11	22	electricity	electricity	NOUN
ejpam-5924	11	23	and	and	CCONJ
ejpam-5924	11	24	magnetism	magnetism	NOUN
ejpam-5924	11	25	,	,	PUNCT
ejpam-5924	11	26	kinetic	kinetic	ADJ
ejpam-5924	11	27	theory	theory	NOUN
ejpam-5924	11	28	of	of	ADP
ejpam-5924	11	29	gasses	gas	NOUN
ejpam-5924	11	30	,	,	PUNCT
ejpam-5924	11	31	hereditary	hereditary	ADJ
ejpam-5924	11	32	phenomena	phenomenon	NOUN
ejpam-5924	11	33	in	in	ADP
ejpam-5924	11	34	biology	biology	NOUN
ejpam-5924	11	35	and	and	CCONJ
ejpam-5924	11	36	physics	physics	NOUN
ejpam-5924	11	37	,	,	PUNCT
ejpam-5924	11	38	quantum	quantum	NOUN
ejpam-5924	11	39	mechanics	mechanic	NOUN
ejpam-5924	11	40	,	,	PUNCT
ejpam-5924	11	41	radiation	radiation	NOUN
ejpam-5924	11	42	,	,	PUNCT
ejpam-5924	11	43	optimisation	optimisation	NOUN
ejpam-5924	11	44	,	,	PUNCT
ejpam-5924	11	45	which	which	PRON
ejpam-5924	11	46	includes	include	VERB
ejpam-5924	11	47	optimal	optimal	ADJ
ejpam-5924	11	48	system	system	NOUN
ejpam-5924	11	49	design	design	NOUN
ejpam-5924	11	50	,	,	PUNCT
ejpam-5924	11	51	theory	theory	NOUN
ejpam-5924	11	52	of	of	ADP
ejpam-5924	11	53	communication	communication	NOUN
ejpam-5924	11	54	,	,	PUNCT
ejpam-5924	11	55	economics	economic	NOUN
ejpam-5924	11	56	of	of	ADP
ejpam-5924	11	57	mathematics	mathematic	NOUN
ejpam-5924	11	58	,	,	PUNCT
ejpam-5924	11	59	genetics	genetic	NOUN
ejpam-5924	11	60	of	of	ADP
ejpam-5924	11	61	populations	population	NOUN
ejpam-5924	11	62	,	,	PUNCT
ejpam-5924	11	63	medical	medical	ADJ
ejpam-5924	11	64	procedures	procedure	NOUN
ejpam-5924	11	65	,	,	PUNCT
ejpam-5924	11	66	computational	computational	ADJ
ejpam-5924	11	67	problems	problem	NOUN
ejpam-5924	11	68	of	of	ADP
ejpam-5924	11	69	radiative	radiative	ADJ
ejpam-5924	11	70	equilibrium	equilibrium	NOUN
ejpam-5924	11	71	,	,	PUNCT
ejpam-5924	11	72	the	the	DET
ejpam-5924	11	73	particle	particle	NOUN
ejpam-5924	11	74	transport	transport	NOUN
ejpam-5924	11	75	problems	problem	NOUN
ejpam-5924	11	76	of	of	ADP
ejpam-5924	11	77	the	the	DET
ejpam-5924	11	78	fields	field	NOUN
ejpam-5924	11	79	of	of	ADP
ejpam-5924	11	80	a	a	PRON
ejpam-5924	11	81	and	and	CCONJ
ejpam-5924	11	82	reactor	reactor	NOUN
ejpam-5924	11	83	principle	principle	NOUN
ejpam-5924	11	84	,	,	PUNCT
ejpam-5924	11	85	acoustics	acoustic	NOUN
ejpam-5924	11	86	,	,	PUNCT
ejpam-5924	11	87	steady	steady	ADJ
ejpam-5924	11	88	state	state	NOUN
ejpam-5924	11	89	heat	heat	NOUN
ejpam-5924	11	90	conduction	conduction	NOUN
ejpam-5924	11	91	,	,	PUNCT
ejpam-5924	11	92	and	and	CCONJ
ejpam-5924	11	93	radiative	radiative	ADJ
ejpam-5924	11	94	heat	heat	NOUN
ejpam-5924	11	95	transfer	transfer	NOUN
ejpam-5924	11	96	troubles	trouble	NOUN
ejpam-5924	11	97	.	.	PUNCT
ejpam-5924	12	1	fredholm	fredholm	VERB
ejpam-5924	12	2	integral	integral	ADJ
ejpam-5924	12	3	equation	equation	NOUN
ejpam-5924	12	4	is	be	AUX
ejpam-5924	12	5	one	one	NUM
ejpam-5924	12	6	of	of	ADP
ejpam-5924	12	7	the	the	DET
ejpam-5924	12	8	most	most	ADV
ejpam-5924	12	9	important	important	ADJ
ejpam-5924	12	10	integral	integral	ADJ
ejpam-5924	12	11	equations	equation	NOUN
ejpam-5924	12	12	.	.	PUNCT
ejpam-5924	13	1	singh	singh	PROPN
ejpam-5924	13	2	and	and	CCONJ
ejpam-5924	13	3	pippal	pippal	ADJ
ejpam-5924	13	4	[	[	X
ejpam-5924	13	5	1	1	NUM
ejpam-5924	13	6	]	]	PUNCT
ejpam-5924	13	7	utilized	utilize	VERB
ejpam-5924	13	8	the	the	DET
ejpam-5924	13	9	shehu	shehu	NOUN
ejpam-5924	13	10	transform	transform	VERB
ejpam-5924	13	11	combined	combine	VERB
ejpam-5924	13	12	with	with	ADP
ejpam-5924	13	13	the	the	DET
ejpam-5924	13	14	adomian	adomian	NOUN
ejpam-5924	13	15	polynomial	polynomial	NOUN
ejpam-5924	13	16	to	to	PART
ejpam-5924	13	17	solve	solve	VERB
ejpam-5924	13	18	effectively	effectively	ADV
ejpam-5924	13	19	nonlinear	nonlinear	ADJ
ejpam-5924	13	20	fractional	fractional	ADJ
ejpam-5924	13	21	differential	differential	ADJ
ejpam-5924	13	22	equations	equation	NOUN
ejpam-5924	13	23	.	.	PUNCT
ejpam-5924	14	1	additionally	additionally	ADV
ejpam-5924	14	2	,	,	PUNCT
ejpam-5924	14	3	ali	ali	PROPN
ejpam-5924	14	4	et	et	PROPN
ejpam-5924	14	5	al	al	PROPN
ejpam-5924	14	6	.	.	PUNCT
ejpam-5924	15	1	[	[	X
ejpam-5924	15	2	2	2	X
ejpam-5924	15	3	]	]	PUNCT
ejpam-5924	15	4	presented	present	VERB
ejpam-5924	15	5	a	a	DET
ejpam-5924	15	6	numerical	numerical	ADJ
ejpam-5924	15	7	solution	solution	NOUN
ejpam-5924	15	8	for	for	ADP
ejpam-5924	15	9	fractional	fractional	ADJ
ejpam-5924	15	10	integro	integro	ADJ
ejpam-5924	15	11	-	-	PUNCT
ejpam-5924	15	12	differential	differential	NOUN
ejpam-5924	15	13	equations	equation	NOUN
ejpam-5924	15	14	with	with	ADP
ejpam-5924	15	15	a	a	DET
ejpam-5924	15	16	linear	linear	ADJ
ejpam-5924	15	17	functional	functional	ADJ
ejpam-5924	15	18	argument	argument	NOUN
ejpam-5924	15	19	,	,	PUNCT
ejpam-5924	15	20	∗corresponding	∗corresponde	VERB
ejpam-5924	15	21	author	author	NOUN
ejpam-5924	15	22	.	.	PUNCT
ejpam-5924	16	1	doi	doi	NOUN
ejpam-5924	16	2	:	:	PUNCT
ejpam-5924	16	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5924	https://doi.org/10.29020/nybg.ejpam.v18i2.5924	NOUN
ejpam-5924	16	4	email	email	NOUN
ejpam-5924	16	5	addresses	address	VERB
ejpam-5924	16	6	:	:	PUNCT
ejpam-5924	16	7	abeer101aa@yahoo.com	abeer101aa@yahoo.com	PROPN
ejpam-5924	16	8	(	(	PUNCT
ejpam-5924	16	9	a.	a.	PROPN
ejpam-5924	16	10	al	al	PROPN
ejpam-5924	16	11	-	-	PUNCT
ejpam-5924	16	12	bugami	bugami	NOUN
ejpam-5924	16	13	)	)	PUNCT
ejpam-5924	16	14	,	,	PUNCT
ejpam-5924	16	15	noha1231@hotmail.com	noha1231@hotmail.com	X
ejpam-5924	17	1	(	(	PUNCT
ejpam-5924	17	2	n.	n.	NOUN
ejpam-5924	17	3	alharbi	alharbi	PROPN
ejpam-5924	17	4	)	)	PUNCT
ejpam-5924	17	5	,	,	PUNCT
ejpam-5924	17	6	amr	amr	NOUN
ejpam-5924	17	7	mahdy85@yahoo.com	mahdy85@yahoo.com	PROPN
ejpam-5924	17	8	(	(	PUNCT
ejpam-5924	17	9	a.	a.	NOUN
ejpam-5924	17	10	mahdy	mahdy	NOUN
ejpam-5924	17	11	)	)	PUNCT
ejpam-5924	17	12	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5924	18	1	1	1	NUM
ejpam-5924	18	2	copyright	copyright	NOUN
ejpam-5924	18	3	:	:	PUNCT
ejpam-5924	18	4	©	©	PROPN
ejpam-5924	18	5	2025	2025	NUM
ejpam-5924	18	6	the	the	DET
ejpam-5924	18	7	author(s	author(s	NOUN
ejpam-5924	18	8	)	)	PUNCT
ejpam-5924	18	9	.	.	PUNCT
ejpam-5924	19	1	(	(	PUNCT
ejpam-5924	19	2	cc	cc	NOUN
ejpam-5924	19	3	by	by	ADP
ejpam-5924	19	4	-	-	PUNCT
ejpam-5924	19	5	nc	nc	PROPN
ejpam-5924	19	6	4.0	4.0	NUM
ejpam-5924	19	7	)	)	PUNCT
ejpam-5924	19	8	a.	a.	NOUN
ejpam-5924	19	9	m.	m.	NOUN
ejpam-5924	19	10	al	al	PROPN
ejpam-5924	19	11	-	-	PUNCT
ejpam-5924	19	12	bugami	bugami	NOUN
ejpam-5924	19	13	,	,	PUNCT
ejpam-5924	19	14	n.	n.	NOUN
ejpam-5924	19	15	a.	a.	NOUN
ejpam-5924	19	16	alharbi	alharbi	PROPN
ejpam-5924	19	17	,	,	PUNCT
ejpam-5924	19	18	a.	a.	NOUN
ejpam-5924	19	19	m.	m.	PROPN
ejpam-5924	19	20	s.	s.	PROPN
ejpam-5924	19	21	mahdy	mahdy	PROPN
ejpam-5924	19	22	/	/	SYM
ejpam-5924	19	23	eur	eur	PROPN
ejpam-5924	19	24	.	.	PUNCT
ejpam-5924	20	1	j.	j.	PROPN
ejpam-5924	20	2	pure	pure	PROPN
ejpam-5924	20	3	appl	appl	PROPN
ejpam-5924	20	4	.	.	PROPN
ejpam-5924	20	5	math	math	PROPN
ejpam-5924	20	6	,	,	PUNCT
ejpam-5924	20	7	18	18	NUM
ejpam-5924	20	8	(	(	PUNCT
ejpam-5924	20	9	2	2	NUM
ejpam-5924	20	10	)	)	PUNCT
ejpam-5924	20	11	(	(	PUNCT
ejpam-5924	20	12	2025	2025	NUM
ejpam-5924	20	13	)	)	PUNCT
ejpam-5924	20	14	,	,	PUNCT
ejpam-5924	20	15	5924	5924	NUM
ejpam-5924	20	16	2	2	NUM
ejpam-5924	20	17	of	of	ADP
ejpam-5924	20	18	14	14	NUM
ejpam-5924	20	19	employing	employ	VERB
ejpam-5924	20	20	chebyshev	chebyshev	NOUN
ejpam-5924	20	21	serious	serious	ADJ
ejpam-5924	20	22	for	for	ADP
ejpam-5924	20	23	increased	increase	VERB
ejpam-5924	20	24	precision	precision	NOUN
ejpam-5924	20	25	.	.	PUNCT
ejpam-5924	21	1	oyedepo	oyedepo	NOUN
ejpam-5924	21	2	et	et	PROPN
ejpam-5924	21	3	al	al	PROPN
ejpam-5924	21	4	.	.	PUNCT
ejpam-5924	22	1	[	[	X
ejpam-5924	22	2	3	3	X
ejpam-5924	22	3	]	]	PUNCT
ejpam-5924	22	4	contributed	contribute	VERB
ejpam-5924	22	5	a	a	DET
ejpam-5924	22	6	competitional	competitional	ADJ
ejpam-5924	22	7	algorithm	algorithm	NOUN
ejpam-5924	22	8	specifically	specifically	ADV
ejpam-5924	22	9	designed	design	VERB
ejpam-5924	22	10	for	for	ADP
ejpam-5924	22	11	fractional	fractional	ADJ
ejpam-5924	22	12	fredholm	fredholm	NOUN
ejpam-5924	22	13	integro	integro	ADJ
ejpam-5924	22	14	-	-	PUNCT
ejpam-5924	22	15	differential	differential	NOUN
ejpam-5924	22	16	equations	equation	NOUN
ejpam-5924	22	17	,	,	PUNCT
ejpam-5924	22	18	providing	provide	VERB
ejpam-5924	22	19	a	a	DET
ejpam-5924	22	20	robot	robot	NOUN
ejpam-5924	22	21	and	and	CCONJ
ejpam-5924	22	22	efficacious	efficacious	ADJ
ejpam-5924	22	23	method	method	NOUN
ejpam-5924	22	24	for	for	ADP
ejpam-5924	22	25	tackling	tackle	VERB
ejpam-5924	22	26	these	these	DET
ejpam-5924	22	27	complex	complex	ADJ
ejpam-5924	22	28	problems	problem	NOUN
ejpam-5924	22	29	.	.	PUNCT
ejpam-5924	23	1	moreover	moreover	ADV
ejpam-5924	23	2	,	,	PUNCT
ejpam-5924	23	3	toma	toma	PROPN
ejpam-5924	23	4	and	and	CCONJ
ejpam-5924	23	5	postavaru	postavaru	NOUN
ejpam-5924	24	1	[	[	X
ejpam-5924	24	2	4	4	NUM
ejpam-5924	24	3	]	]	PUNCT
ejpam-5924	24	4	proposed	propose	VERB
ejpam-5924	24	5	a	a	DET
ejpam-5924	24	6	numerical	numerical	ADJ
ejpam-5924	24	7	method	method	NOUN
ejpam-5924	24	8	for	for	ADP
ejpam-5924	24	9	solving	solve	VERB
ejpam-5924	24	10	fractional	fractional	ADJ
ejpam-5924	24	11	fredholm	fredholm	NOUN
ejpam-5924	24	12	integro	integro	ADJ
ejpam-5924	24	13	-	-	PUNCT
ejpam-5924	24	14	differential	differential	NOUN
ejpam-5924	24	15	equations	equation	NOUN
ejpam-5924	24	16	with	with	ADP
ejpam-5924	24	17	a	a	DET
ejpam-5924	24	18	focus	focus	NOUN
ejpam-5924	24	19	on	on	ADP
ejpam-5924	24	20	enhancing	enhance	VERB
ejpam-5924	24	21	accuracy	accuracy	NOUN
ejpam-5924	24	22	.	.	PUNCT
ejpam-5924	25	1	abdou	abdou	PROPN
ejpam-5924	25	2	et	et	PROPN
ejpam-5924	25	3	al	al	PROPN
ejpam-5924	25	4	.	.	PROPN
ejpam-5924	25	5	is	be	AUX
ejpam-5924	25	6	performed	perform	VERB
ejpam-5924	25	7	a	a	DET
ejpam-5924	25	8	comprehensive	comprehensive	ADJ
ejpam-5924	25	9	analysis	analysis	NOUN
ejpam-5924	25	10	of	of	ADP
ejpam-5924	25	11	the	the	DET
ejpam-5924	25	12	convergence	convergence	NOUN
ejpam-5924	25	13	into	into	ADP
ejpam-5924	25	14	that	that	DET
ejpam-5924	25	15	adomian	adomian	NOUN
ejpam-5924	25	16	’s	’s	PART
ejpam-5924	25	17	method	method	NOUN
ejpam-5924	25	18	when	when	SCONJ
ejpam-5924	25	19	applied	apply	VERB
ejpam-5924	25	20	to	to	ADP
ejpam-5924	25	21	nonlinear	nonlinear	ADJ
ejpam-5924	25	22	equations	equation	NOUN
ejpam-5924	25	23	in	in	ADP
ejpam-5924	25	24	[	[	X
ejpam-5924	25	25	5	5	NUM
ejpam-5924	25	26	]	]	PUNCT
ejpam-5924	25	27	.	.	PUNCT
ejpam-5924	26	1	abbaoui	abbaoui	NOUN
ejpam-5924	26	2	and	and	CCONJ
ejpam-5924	26	3	cherruault	cherruault	NOUN
ejpam-5924	27	1	[	[	X
ejpam-5924	27	2	6	6	NUM
ejpam-5924	27	3	]	]	PUNCT
ejpam-5924	27	4	also	also	ADV
ejpam-5924	27	5	performed	perform	VERB
ejpam-5924	27	6	a	a	DET
ejpam-5924	27	7	comprehensive	comprehensive	ADJ
ejpam-5924	27	8	analysis	analysis	NOUN
ejpam-5924	27	9	of	of	ADP
ejpam-5924	27	10	the	the	DET
ejpam-5924	27	11	convergence	convergence	NOUN
ejpam-5924	27	12	into	into	ADP
ejpam-5924	27	13	that	that	DET
ejpam-5924	27	14	adomian	adomian	NOUN
ejpam-5924	27	15	’s	’s	PART
ejpam-5924	27	16	method	method	NOUN
ejpam-5924	27	17	when	when	SCONJ
ejpam-5924	27	18	applied	apply	VERB
ejpam-5924	27	19	to	to	ADP
ejpam-5924	27	20	nonlinear	nonlinear	ADJ
ejpam-5924	27	21	equations	equation	NOUN
ejpam-5924	27	22	.	.	PUNCT
ejpam-5924	28	1	behiry	behiry	NOUN
ejpam-5924	28	2	et	et	PROPN
ejpam-5924	28	3	al	al	PROPN
ejpam-5924	28	4	.	.	PUNCT
ejpam-5924	29	1	[	[	X
ejpam-5924	29	2	7	7	NUM
ejpam-5924	29	3	]	]	PUNCT
ejpam-5924	29	4	developed	develop	VERB
ejpam-5924	29	5	a	a	DET
ejpam-5924	29	6	new	new	ADJ
ejpam-5924	29	7	algorithm	algorithm	NOUN
ejpam-5924	29	8	for	for	ADP
ejpam-5924	29	9	the	the	DET
ejpam-5924	29	10	decomposition	decomposition	NOUN
ejpam-5924	29	11	solution	solution	NOUN
ejpam-5924	29	12	of	of	ADP
ejpam-5924	29	13	nonlinear	nonlinear	ADJ
ejpam-5924	29	14	differential	differential	ADJ
ejpam-5924	29	15	equations	equation	NOUN
ejpam-5924	29	16	,	,	PUNCT
ejpam-5924	29	17	further	far	ADV
ejpam-5924	29	18	advancing	advance	VERB
ejpam-5924	29	19	the	the	DET
ejpam-5924	29	20	method	method	NOUN
ejpam-5924	29	21	.	.	PUNCT
ejpam-5924	30	1	tair	tair	NOUN
ejpam-5924	30	2	et	et	PROPN
ejpam-5924	30	3	al	al	PROPN
ejpam-5924	30	4	.	.	PUNCT
ejpam-5924	31	1	[	[	X
ejpam-5924	31	2	8	8	NUM
ejpam-5924	31	3	]	]	PUNCT
ejpam-5924	31	4	explored	explore	VERB
ejpam-5924	31	5	two	two	NUM
ejpam-5924	31	6	numerical	numerical	ADJ
ejpam-5924	31	7	techniques	technique	NOUN
ejpam-5924	31	8	for	for	ADP
ejpam-5924	31	9	solving	solve	VERB
ejpam-5924	31	10	the	the	DET
ejpam-5924	31	11	linear	linear	ADJ
ejpam-5924	31	12	integro	integro	ADJ
ejpam-5924	31	13	-	-	PUNCT
ejpam-5924	31	14	differential	differential	NOUN
ejpam-5924	31	15	fredholm	fredholm	NOUN
ejpam-5924	31	16	equation	equation	NOUN
ejpam-5924	31	17	with	with	ADP
ejpam-5924	31	18	a	a	DET
ejpam-5924	31	19	weakly	weakly	ADJ
ejpam-5924	31	20	singular	singular	ADJ
ejpam-5924	31	21	kernel	kernel	NOUN
ejpam-5924	31	22	,	,	PUNCT
ejpam-5924	31	23	while	while	SCONJ
ejpam-5924	31	24	al	al	PROPN
ejpam-5924	31	25	-	-	PUNCT
ejpam-5924	31	26	bugami	bugami	NOUN
ejpam-5924	32	1	[	[	X
ejpam-5924	32	2	9	9	NUM
ejpam-5924	32	3	]	]	PUNCT
ejpam-5924	32	4	focused	focus	VERB
ejpam-5924	32	5	on	on	ADP
ejpam-5924	32	6	two	two	NUM
ejpam-5924	32	7	-	-	PUNCT
ejpam-5924	32	8	dimensional	dimensional	ADJ
ejpam-5924	32	9	fredholm	fredholm	NOUN
ejpam-5924	32	10	integro	integro	ADJ
ejpam-5924	32	11	-	-	PUNCT
ejpam-5924	32	12	differential	differential	NOUN
ejpam-5924	32	13	equations	equation	NOUN
ejpam-5924	32	14	with	with	ADP
ejpam-5924	32	15	singular	singular	ADJ
ejpam-5924	32	16	kernels	kernel	NOUN
ejpam-5924	32	17	,	,	PUNCT
ejpam-5924	32	18	providing	provide	VERB
ejpam-5924	32	19	accurate	accurate	ADJ
ejpam-5924	32	20	numerical	numerical	ADJ
ejpam-5924	32	21	method	method	NOUN
ejpam-5924	32	22	for	for	ADP
ejpam-5924	32	23	their	their	PRON
ejpam-5924	32	24	solution	solution	NOUN
ejpam-5924	32	25	.	.	PUNCT
ejpam-5924	33	1	abbaszadeh	abbaszadeh	PROPN
ejpam-5924	33	2	et	et	PROPN
ejpam-5924	33	3	al	al	PROPN
ejpam-5924	33	4	.	.	PUNCT
ejpam-5924	34	1	[	[	X
ejpam-5924	34	2	10	10	NUM
ejpam-5924	34	3	]	]	PUNCT
ejpam-5924	34	4	employed	employ	VERB
ejpam-5924	34	5	legendre	legendre	PROPN
ejpam-5924	34	6	wavelets	wavelet	NOUN
ejpam-5924	34	7	to	to	PART
ejpam-5924	34	8	solve	solve	VERB
ejpam-5924	34	9	fractional	fractional	ADJ
ejpam-5924	34	10	fredholm	fredholm	NOUN
ejpam-5924	34	11	integro	integro	ADJ
ejpam-5924	34	12	-	-	PUNCT
ejpam-5924	34	13	differential	differential	NOUN
ejpam-5924	34	14	equations	equation	NOUN
ejpam-5924	34	15	,	,	PUNCT
ejpam-5924	34	16	while	while	SCONJ
ejpam-5924	34	17	rawashdeh	rawashdeh	PROPN
ejpam-5924	34	18	et	et	PROPN
ejpam-5924	34	19	al	al	PROPN
ejpam-5924	34	20	.	.	PUNCT
ejpam-5924	35	1	[	[	X
ejpam-5924	35	2	11	11	NUM
ejpam-5924	35	3	]	]	PUNCT
ejpam-5924	35	4	provided	provide	VERB
ejpam-5924	35	5	a	a	DET
ejpam-5924	35	6	detailed	detailed	ADJ
ejpam-5924	35	7	convergence	convergence	NOUN
ejpam-5924	35	8	analysis	analysis	NOUN
ejpam-5924	35	9	for	for	ADP
ejpam-5924	35	10	the	the	DET
ejpam-5924	35	11	fractional	fractional	ADJ
ejpam-5924	35	12	decomposition	decomposition	NOUN
ejpam-5924	35	13	method	method	NOUN
ejpam-5924	35	14	as	as	SCONJ
ejpam-5924	35	15	applied	apply	VERB
ejpam-5924	35	16	to	to	ADP
ejpam-5924	35	17	nonlinear	nonlinear	ADJ
ejpam-5924	35	18	fractional	fractional	ADJ
ejpam-5924	35	19	fredholm	fredholm	NOUN
ejpam-5924	35	20	integro	integro	ADJ
ejpam-5924	35	21	-	-	PUNCT
ejpam-5924	35	22	differential	differential	NOUN
ejpam-5924	35	23	equations	equation	NOUN
ejpam-5924	35	24	.	.	PUNCT
ejpam-5924	36	1	li	li	PROPN
ejpam-5924	36	2	and	and	CCONJ
ejpam-5924	36	3	pang	pang	PROPN
ejpam-5924	36	4	[	[	X
ejpam-5924	36	5	12	12	NUM
ejpam-5924	36	6	]	]	PUNCT
ejpam-5924	36	7	]	]	PUNCT
ejpam-5924	36	8	expanded	expand	VERB
ejpam-5924	36	9	the	the	DET
ejpam-5924	36	10	application	application	NOUN
ejpam-5924	36	11	of	of	ADP
ejpam-5924	36	12	the	the	DET
ejpam-5924	36	13	adm	adm	PROPN
ejpam-5924	36	14	to	to	ADP
ejpam-5924	36	15	nonlinear	nonlinear	ADJ
ejpam-5924	36	16	systems	system	NOUN
ejpam-5924	36	17	.	.	PUNCT
ejpam-5924	37	1	in	in	ADP
ejpam-5924	37	2	addition	addition	NOUN
ejpam-5924	37	3	,	,	PUNCT
ejpam-5924	37	4	momani	momani	NOUN
ejpam-5924	37	5	and	and	CCONJ
ejpam-5924	37	6	noor	noor	PROPN
ejpam-5924	37	7	[	[	X
ejpam-5924	37	8	13	13	NUM
ejpam-5924	37	9	]	]	PUNCT
ejpam-5924	37	10	developed	develop	VERB
ejpam-5924	37	11	numerical	numerical	ADJ
ejpam-5924	37	12	techniques	technique	NOUN
ejpam-5924	37	13	to	to	PART
ejpam-5924	37	14	solve	solve	VERB
ejpam-5924	37	15	fractional	fractional	ADJ
ejpam-5924	37	16	integro	integro	ADJ
ejpam-5924	37	17	-	-	PUNCT
ejpam-5924	37	18	differential	differential	NOUN
ejpam-5924	37	19	equations	equation	NOUN
ejpam-5924	37	20	of	of	ADP
ejpam-5924	37	21	fourth	fourth	ADJ
ejpam-5924	37	22	order	order	NOUN
ejpam-5924	37	23	.	.	PUNCT
ejpam-5924	38	1	in	in	ADP
ejpam-5924	38	2	the	the	DET
ejpam-5924	38	3	realm	realm	NOUN
ejpam-5924	38	4	of	of	ADP
ejpam-5924	38	5	two	two	NUM
ejpam-5924	38	6	-	-	PUNCT
ejpam-5924	38	7	dimensional	dimensional	ADJ
ejpam-5924	38	8	nonlinear	nonlinear	ADJ
ejpam-5924	38	9	fredholm	fredholm	NOUN
ejpam-5924	38	10	integro	integro	ADJ
ejpam-5924	38	11	-	-	PUNCT
ejpam-5924	38	12	differential	differential	NOUN
ejpam-5924	38	13	equations	equation	NOUN
ejpam-5924	38	14	,	,	PUNCT
ejpam-5924	38	15	al	al	PROPN
ejpam-5924	38	16	-	-	PUNCT
ejpam-5924	38	17	bugami	bugami	NOUN
ejpam-5924	39	1	[	[	X
ejpam-5924	39	2	14	14	NUM
ejpam-5924	39	3	]	]	PUNCT
ejpam-5924	39	4	presented	present	VERB
ejpam-5924	39	5	effective	effective	ADJ
ejpam-5924	39	6	numerical	numerical	ADJ
ejpam-5924	39	7	solutions	solution	NOUN
ejpam-5924	39	8	.	.	PUNCT
ejpam-5924	40	1	additionally	additionally	ADV
ejpam-5924	40	2	,	,	PUNCT
ejpam-5924	40	3	hasan	hasan	PROPN
ejpam-5924	40	4	[	[	X
ejpam-5924	40	5	15	15	NUM
ejpam-5924	40	6	]	]	PUNCT
ejpam-5924	40	7	applied	apply	VERB
ejpam-5924	40	8	the	the	DET
ejpam-5924	40	9	(	(	PUNCT
ejpam-5924	40	10	adm	adm	PROPN
ejpam-5924	40	11	)	)	PUNCT
ejpam-5924	40	12	to	to	ADP
ejpam-5924	40	13	nonlinear	nonlinear	ADJ
ejpam-5924	40	14	systems	system	NOUN
ejpam-5924	40	15	involving	involve	VERB
ejpam-5924	40	16	fractional	fractional	ADJ
ejpam-5924	40	17	fredholm	fredholm	NOUN
ejpam-5924	40	18	integro	integro	ADJ
ejpam-5924	40	19	-	-	PUNCT
ejpam-5924	40	20	differential	differential	NOUN
ejpam-5924	40	21	equations	equation	NOUN
ejpam-5924	40	22	.	.	PUNCT
ejpam-5924	41	1	we	we	PRON
ejpam-5924	41	2	will	will	AUX
ejpam-5924	41	3	use	use	VERB
ejpam-5924	41	4	the	the	DET
ejpam-5924	41	5	ham	ham	NOUN
ejpam-5924	41	6	and	and	CCONJ
ejpam-5924	41	7	adm	adm	NOUN
ejpam-5924	41	8	for	for	ADP
ejpam-5924	41	9	dealing	deal	VERB
ejpam-5924	41	10	with	with	ADP
ejpam-5924	41	11	the	the	DET
ejpam-5924	41	12	(	(	PUNCT
ejpam-5924	41	13	tdfnfi	tdfnfi	ADJ
ejpam-5924	41	14	-	-	PUNCT
ejpam-5924	41	15	de	de	NOUN
ejpam-5924	41	16	)	)	PUNCT
ejpam-5924	41	17	in	in	ADP
ejpam-5924	41	18	this	this	DET
ejpam-5924	41	19	study	study	NOUN
ejpam-5924	41	20	.	.	PUNCT
ejpam-5924	42	1	the	the	DET
ejpam-5924	42	2	tdfnfi	tdfnfi	ADJ
ejpam-5924	42	3	-	-	PUNCT
ejpam-5924	42	4	de	de	ADJ
ejpam-5924	42	5	form	form	NOUN
ejpam-5924	42	6	will	will	AUX
ejpam-5924	42	7	evaluate	evaluate	VERB
ejpam-5924	42	8	.	.	PUNCT
ejpam-5924	43	1	dαu(s	dαu(s	PROPN
ejpam-5924	43	2	,	,	PUNCT
ejpam-5924	43	3	t	t	PROPN
ejpam-5924	43	4	)	)	PUNCT
ejpam-5924	43	5	=	=	PUNCT
ejpam-5924	43	6	f(s	f(s	PROPN
ejpam-5924	43	7	,	,	PUNCT
ejpam-5924	43	8	t	t	PROPN
ejpam-5924	43	9	)	)	PUNCT
ejpam-5924	43	10	+	+	CCONJ
ejpam-5924	44	1	λ	λ	PROPN
ejpam-5924	44	2	∫	∫	PROPN
ejpam-5924	44	3	b	b	PROPN
ejpam-5924	44	4	a	a	DET
ejpam-5924	44	5	∫	∫	PROPN
ejpam-5924	44	6	d	d	X
ejpam-5924	44	7	c	c	PROPN
ejpam-5924	44	8	k(s	k(s	PROPN
ejpam-5924	44	9	,	,	PUNCT
ejpam-5924	44	10	t	t	PROPN
ejpam-5924	44	11	,	,	PUNCT
ejpam-5924	44	12	τ	τ	PROPN
ejpam-5924	44	13	,	,	PUNCT
ejpam-5924	44	14	ξ)γ(τ	ξ)γ(τ	PROPN
ejpam-5924	44	15	,	,	PUNCT
ejpam-5924	44	16	ξ	ξ	PROPN
ejpam-5924	44	17	,	,	PUNCT
ejpam-5924	44	18	dαu(τ	dαu(τ	PROPN
ejpam-5924	44	19	,	,	PUNCT
ejpam-5924	44	20	ξ))dτdξ	ξ))dτdξ	NOUN
ejpam-5924	44	21	,	,	PUNCT
ejpam-5924	44	22	(	(	PUNCT
ejpam-5924	44	23	1	1	X
ejpam-5924	44	24	)	)	PUNCT
ejpam-5924	44	25	where	where	SCONJ
ejpam-5924	44	26	u(s	u(s	ADJ
ejpam-5924	44	27	,	,	PUNCT
ejpam-5924	44	28	t	t	PROPN
ejpam-5924	44	29	)	)	PUNCT
ejpam-5924	44	30	is	be	AUX
ejpam-5924	44	31	an	an	DET
ejpam-5924	44	32	unknown	unknown	ADJ
ejpam-5924	44	33	function	function	NOUN
ejpam-5924	44	34	,	,	PUNCT
ejpam-5924	44	35	f(s	f(s	ADV
ejpam-5924	44	36	,	,	PUNCT
ejpam-5924	44	37	t),k(s	t),k(s	ADV
ejpam-5924	44	38	,	,	PUNCT
ejpam-5924	44	39	t	t	PROPN
ejpam-5924	44	40	,	,	PUNCT
ejpam-5924	44	41	τ	τ	PROPN
ejpam-5924	44	42	,	,	PUNCT
ejpam-5924	44	43	ξ	ξ	X
ejpam-5924	44	44	)	)	PUNCT
ejpam-5924	44	45	are	be	AUX
ejpam-5924	44	46	given	give	VERB
ejpam-5924	44	47	functions	function	NOUN
ejpam-5924	44	48	,	,	PUNCT
ejpam-5924	44	49	and	and	CCONJ
ejpam-5924	44	50	λ	λ	PROPN
ejpam-5924	44	51	is	be	AUX
ejpam-5924	44	52	parameter	parameter	NOUN
ejpam-5924	44	53	.	.	PUNCT
ejpam-5924	45	1	also	also	ADV
ejpam-5924	45	2	0	0	PUNCT
ejpam-5924	45	3	<	<	X
ejpam-5924	45	4	α	α	PROPN
ejpam-5924	45	5	≤	≤	NUM
ejpam-5924	45	6	1	1	NUM
ejpam-5924	45	7	and	and	CCONJ
ejpam-5924	45	8	(	(	PUNCT
ejpam-5924	45	9	s	s	PROPN
ejpam-5924	45	10	,	,	PUNCT
ejpam-5924	45	11	t	t	PROPN
ejpam-5924	45	12	)	)	PUNCT
ejpam-5924	45	13	∈	∈	PROPN
ejpam-5924	45	14	ω	ω	NUM
ejpam-5924	45	15	=	=	PUNCT
ejpam-5924	46	1	[	[	X
ejpam-5924	46	2	a	a	DET
ejpam-5924	46	3	,	,	PUNCT
ejpam-5924	46	4	b]×	b]×	NOUN
ejpam-5924	47	1	[	[	X
ejpam-5924	47	2	c	c	X
ejpam-5924	47	3	,	,	PUNCT
ejpam-5924	47	4	d	d	X
ejpam-5924	47	5	]	]	X
ejpam-5924	47	6	.	.	PUNCT
ejpam-5924	48	1	2	2	X
ejpam-5924	48	2	.	.	X
ejpam-5924	48	3	the	the	DET
ejpam-5924	48	4	existence	existence	NOUN
ejpam-5924	48	5	and	and	CCONJ
ejpam-5924	48	6	uniqueness	uniqueness	NOUN
ejpam-5924	48	7	theorem	theorem	ADJ
ejpam-5924	48	8	1	1	NUM
ejpam-5924	48	9	.	.	PUNCT
ejpam-5924	49	1	let	let	VERB
ejpam-5924	49	2	(	(	PUNCT
ejpam-5924	49	3	m	m	NOUN
ejpam-5924	49	4	,	,	PUNCT
ejpam-5924	49	5	d	d	NOUN
ejpam-5924	49	6	)	)	PUNCT
ejpam-5924	49	7	be	be	AUX
ejpam-5924	49	8	a	a	DET
ejpam-5924	49	9	metric	metric	ADJ
ejpam-5924	49	10	space	space	NOUN
ejpam-5924	49	11	with	with	ADP
ejpam-5924	49	12	m̸=	m̸=	PROPN
ejpam-5924	49	13	∅.	∅.	AUX
ejpam-5924	49	14	suppose	suppose	VERB
ejpam-5924	49	15	m	m	AUX
ejpam-5924	49	16	̸=	̸=	PROPN
ejpam-5924	49	17	∅	∅	NOUN
ejpam-5924	49	18	is	be	AUX
ejpam-5924	49	19	complete	complete	ADJ
ejpam-5924	49	20	and	and	CCONJ
ejpam-5924	49	21	let	let	VERB
ejpam-5924	49	22	i	i	PRON
ejpam-5924	49	23	:	:	PUNCT
ejpam-5924	49	24	m	m	VERB
ejpam-5924	49	25	→	→	NOUN
ejpam-5924	49	26	m	m	AUX
ejpam-5924	49	27	be	be	AUX
ejpam-5924	49	28	contraction	contraction	NOUN
ejpam-5924	49	29	mapping	mapping	NOUN
ejpam-5924	49	30	.	.	PUNCT
ejpam-5924	50	1	then	then	ADV
ejpam-5924	50	2	,	,	PUNCT
ejpam-5924	50	3	i	i	PRON
ejpam-5924	50	4	has	have	VERB
ejpam-5924	50	5	exactly	exactly	ADV
ejpam-5924	50	6	one	one	NUM
ejpam-5924	50	7	fixed	fix	VERB
ejpam-5924	50	8	point	point	NOUN
ejpam-5924	50	9	.	.	PUNCT
ejpam-5924	51	1	furthermore	furthermore	ADV
ejpam-5924	51	2	,	,	PUNCT
ejpam-5924	51	3	we	we	PRON
ejpam-5924	51	4	can	can	AUX
ejpam-5924	51	5	express	express	VERB
ejpam-5924	51	6	the	the	DET
ejpam-5924	51	7	equation	equation	NOUN
ejpam-5924	51	8	in	in	ADP
ejpam-5924	51	9	(	(	PUNCT
ejpam-5924	51	10	1	1	NUM
ejpam-5924	51	11	)	)	PUNCT
ejpam-5924	51	12	in	in	ADP
ejpam-5924	51	13	the	the	DET
ejpam-5924	51	14	form	form	NOUN
ejpam-5924	51	15	of	of	ADP
ejpam-5924	51	16	an	an	DET
ejpam-5924	51	17	integral	integral	ADJ
ejpam-5924	51	18	operator	operator	NOUN
ejpam-5924	51	19	as	as	SCONJ
ejpam-5924	51	20	follows	follow	VERB
ejpam-5924	51	21	:	:	PUNCT
ejpam-5924	51	22	t̃dαu(s	t̃dαu(s	ADJ
ejpam-5924	51	23	,	,	PUNCT
ejpam-5924	51	24	t	t	PROPN
ejpam-5924	51	25	)	)	PUNCT
ejpam-5924	51	26	=	=	PUNCT
ejpam-5924	51	27	f(s	f(s	PROPN
ejpam-5924	51	28	,	,	PUNCT
ejpam-5924	51	29	t	t	PROPN
ejpam-5924	51	30	)	)	PUNCT
ejpam-5924	52	1	+	+	CCONJ
ejpam-5924	52	2	tdαu(s	tdαu(s	NUM
ejpam-5924	52	3	,	,	PUNCT
ejpam-5924	52	4	t	t	PROPN
ejpam-5924	52	5	)	)	PUNCT
ejpam-5924	52	6	,	,	PUNCT
ejpam-5924	52	7	(	(	PUNCT
ejpam-5924	52	8	2	2	X
ejpam-5924	52	9	)	)	PUNCT
ejpam-5924	52	10	where	where	SCONJ
ejpam-5924	52	11	tdαu(s	tdαu(s	NOUN
ejpam-5924	52	12	,	,	PUNCT
ejpam-5924	52	13	t	t	PROPN
ejpam-5924	52	14	)	)	PUNCT
ejpam-5924	52	15	=	=	PUNCT
ejpam-5924	53	1	λ	λ	X
ejpam-5924	53	2	∫	∫	PROPN
ejpam-5924	53	3	b	b	PROPN
ejpam-5924	53	4	a	a	DET
ejpam-5924	53	5	∫	∫	PROPN
ejpam-5924	53	6	d	d	X
ejpam-5924	53	7	c	c	PROPN
ejpam-5924	53	8	k(s	k(s	PROPN
ejpam-5924	53	9	,	,	PUNCT
ejpam-5924	53	10	t	t	PROPN
ejpam-5924	53	11	,	,	PUNCT
ejpam-5924	53	12	τ	τ	PROPN
ejpam-5924	53	13	,	,	PUNCT
ejpam-5924	53	14	ξ)γ(τ	ξ)γ(τ	PROPN
ejpam-5924	53	15	,	,	PUNCT
ejpam-5924	53	16	ξ	ξ	PROPN
ejpam-5924	53	17	,	,	PUNCT
ejpam-5924	53	18	dαu(τ	dαu(τ	PROPN
ejpam-5924	53	19	,	,	PUNCT
ejpam-5924	53	20	ξ))dτdξ	ξ))dτdξ	NOUN
ejpam-5924	53	21	.	.	PUNCT
ejpam-5924	54	1	(	(	PUNCT
ejpam-5924	54	2	3	3	X
ejpam-5924	54	3	)	)	PUNCT
ejpam-5924	54	4	also	also	ADV
ejpam-5924	54	5	assume	assume	VERB
ejpam-5924	54	6	the	the	DET
ejpam-5924	54	7	following	follow	VERB
ejpam-5924	54	8	conditions	condition	NOUN
ejpam-5924	54	9	:	:	PUNCT
ejpam-5924	54	10	a.	a.	NOUN
ejpam-5924	54	11	m.	m.	PROPN
ejpam-5924	54	12	al	al	PROPN
ejpam-5924	54	13	-	-	PUNCT
ejpam-5924	54	14	bugami	bugami	NOUN
ejpam-5924	54	15	,	,	PUNCT
ejpam-5924	54	16	n.	n.	NOUN
ejpam-5924	54	17	a.	a.	NOUN
ejpam-5924	54	18	alharbi	alharbi	PROPN
ejpam-5924	54	19	,	,	PUNCT
ejpam-5924	54	20	a.	a.	NOUN
ejpam-5924	54	21	m.	m.	PROPN
ejpam-5924	54	22	s.	s.	PROPN
ejpam-5924	54	23	mahdy	mahdy	PROPN
ejpam-5924	54	24	/	/	SYM
ejpam-5924	54	25	eur	eur	PROPN
ejpam-5924	54	26	.	.	PUNCT
ejpam-5924	55	1	j.	j.	PROPN
ejpam-5924	55	2	pure	pure	PROPN
ejpam-5924	55	3	appl	appl	PROPN
ejpam-5924	55	4	.	.	PROPN
ejpam-5924	55	5	math	math	PROPN
ejpam-5924	55	6	,	,	PUNCT
ejpam-5924	55	7	18	18	NUM
ejpam-5924	55	8	(	(	PUNCT
ejpam-5924	55	9	2	2	NUM
ejpam-5924	55	10	)	)	PUNCT
ejpam-5924	55	11	(	(	PUNCT
ejpam-5924	55	12	2025	2025	NUM
ejpam-5924	55	13	)	)	PUNCT
ejpam-5924	55	14	,	,	PUNCT
ejpam-5924	55	15	5924	5924	NUM
ejpam-5924	55	16	3	3	NUM
ejpam-5924	55	17	of	of	ADP
ejpam-5924	55	18	14	14	NUM
ejpam-5924	55	19	(	(	PUNCT
ejpam-5924	55	20	i	i	NOUN
ejpam-5924	55	21	)	)	PUNCT
ejpam-5924	55	22	k(s	k(s	PROPN
ejpam-5924	55	23	,	,	PUNCT
ejpam-5924	55	24	t	t	PROPN
ejpam-5924	55	25	,	,	PUNCT
ejpam-5924	55	26	τ	τ	PROPN
ejpam-5924	55	27	,	,	PUNCT
ejpam-5924	55	28	ξ	ξ	X
ejpam-5924	55	29	)	)	PUNCT
ejpam-5924	55	30	satisfies	satisfy	VERB
ejpam-5924	55	31	|k(s	|k(s	PROPN
ejpam-5924	55	32	,	,	PUNCT
ejpam-5924	55	33	t	t	PROPN
ejpam-5924	55	34	,	,	PUNCT
ejpam-5924	55	35	τ	τ	PROPN
ejpam-5924	55	36	,	,	PUNCT
ejpam-5924	55	37	ξ)|	ξ)|	ADJ
ejpam-5924	55	38	≤	≤	NUM
ejpam-5924	55	39	κ	κ	NOUN
ejpam-5924	55	40	,	,	PUNCT
ejpam-5924	55	41	where	where	SCONJ
ejpam-5924	55	42	κ	κ	NOUN
ejpam-5924	55	43	is	be	AUX
ejpam-5924	55	44	a	a	DET
ejpam-5924	55	45	constant	constant	ADJ
ejpam-5924	55	46	.	.	PUNCT
ejpam-5924	56	1	(	(	PUNCT
ejpam-5924	56	2	ii	ii	NOUN
ejpam-5924	56	3	)	)	PUNCT
ejpam-5924	56	4	f(s	f(s	PROPN
ejpam-5924	56	5	,	,	PUNCT
ejpam-5924	56	6	t	t	PROPN
ejpam-5924	56	7	)	)	PUNCT
ejpam-5924	56	8	is	be	AUX
ejpam-5924	56	9	continuous	continuous	ADJ
ejpam-5924	56	10	in	in	ADP
ejpam-5924	56	11	c[a	c[a	NUM
ejpam-5924	56	12	,	,	PUNCT
ejpam-5924	56	13	b]×	b]×	VERB
ejpam-5924	56	14	c[c	c[c	NOUN
ejpam-5924	56	15	,	,	PUNCT
ejpam-5924	56	16	d	d	X
ejpam-5924	56	17	]	]	X
ejpam-5924	56	18	,	,	PUNCT
ejpam-5924	56	19	with	with	ADP
ejpam-5924	56	20	its	its	PRON
ejpam-5924	56	21	norm	norm	NOUN
ejpam-5924	56	22	defined	define	VERB
ejpam-5924	56	23	as	as	ADP
ejpam-5924	56	24	:	:	PUNCT
ejpam-5924	56	25	||f(s	||f(s	NOUN
ejpam-5924	56	26	,	,	PUNCT
ejpam-5924	56	27	t)||	t)||	NOUN
ejpam-5924	56	28	=	=	PUNCT
ejpam-5924	57	1	[	[	X
ejpam-5924	57	2	∫	∫	X
ejpam-5924	57	3	b	b	X
ejpam-5924	57	4	a	a	DET
ejpam-5924	57	5	∫	∫	PROPN
ejpam-5924	57	6	d	d	X
ejpam-5924	57	7	c	c	PROPN
ejpam-5924	57	8	|f(s	|f(s	PROPN
ejpam-5924	57	9	,	,	PUNCT
ejpam-5924	57	10	t)|2dsdt	t)|2dsdt	X
ejpam-5924	57	11	]	]	PUNCT
ejpam-5924	57	12	1	1	NUM
ejpam-5924	57	13	2	2	NUM
ejpam-5924	57	14	=	=	SYM
ejpam-5924	57	15	v	v	NOUN
ejpam-5924	57	16	,	,	PUNCT
ejpam-5924	57	17	where	where	SCONJ
ejpam-5924	57	18	v	v	NOUN
ejpam-5924	57	19	is	be	AUX
ejpam-5924	57	20	a	a	DET
ejpam-5924	57	21	constant	constant	ADJ
ejpam-5924	57	22	.	.	PUNCT
ejpam-5924	58	1	(	(	PUNCT
ejpam-5924	58	2	iii	iii	X
ejpam-5924	58	3	)	)	PUNCT
ejpam-5924	58	4	the	the	DET
ejpam-5924	58	5	continuous	continuous	ADJ
ejpam-5924	58	6	function	function	NOUN
ejpam-5924	58	7	γ(s	γ(s	PROPN
ejpam-5924	58	8	,	,	PUNCT
ejpam-5924	58	9	t	t	PROPN
ejpam-5924	58	10	,	,	PUNCT
ejpam-5924	58	11	dαu(s	dαu(s	PROPN
ejpam-5924	58	12	,	,	PUNCT
ejpam-5924	58	13	t	t	PROPN
ejpam-5924	58	14	)	)	PUNCT
ejpam-5924	58	15	)	)	PUNCT
ejpam-5924	58	16	satisfies	satisfy	VERB
ejpam-5924	58	17	the	the	DET
ejpam-5924	58	18	following	follow	VERB
ejpam-5924	58	19	conditions	condition	NOUN
ejpam-5924	58	20	for	for	ADP
ejpam-5924	58	21	some	some	DET
ejpam-5924	58	22	constant	constant	ADJ
ejpam-5924	58	23	g	g	PROPN
ejpam-5924	58	24	>	>	X
ejpam-5924	58	25	g1	g1	PROPN
ejpam-5924	58	26	>	>	X
ejpam-5924	58	27	m	m	PROPN
ejpam-5924	58	28	,	,	PUNCT
ejpam-5924	58	29	g	g	PROPN
ejpam-5924	58	30	>	>	X
ejpam-5924	58	31	m	m	PROPN
ejpam-5924	58	32	:	:	PUNCT
ejpam-5924	58	33	i.	i.	PROPN
ejpam-5924	58	34	[	[	PUNCT
ejpam-5924	58	35	∫	∫	PROPN
ejpam-5924	58	36	b	b	PROPN
ejpam-5924	58	37	a	a	DET
ejpam-5924	58	38	∫	∫	PROPN
ejpam-5924	59	1	d	d	X
ejpam-5924	59	2	c	c	PROPN
ejpam-5924	59	3	|γ(s	|γ(s	PROPN
ejpam-5924	59	4	,	,	PUNCT
ejpam-5924	59	5	t	t	PROPN
ejpam-5924	59	6	,	,	PUNCT
ejpam-5924	59	7	dαu(s	dαu(s	PROPN
ejpam-5924	59	8	,	,	PUNCT
ejpam-5924	59	9	t))|2dsdt	t))|2dsdt	NOUN
ejpam-5924	59	10	]	]	PUNCT
ejpam-5924	59	11	1	1	NUM
ejpam-5924	59	12	2	2	NUM
ejpam-5924	59	13	≤	≤	NUM
ejpam-5924	59	14	g1||dαu(s	g1||dαu(s	PROPN
ejpam-5924	59	15	,	,	PUNCT
ejpam-5924	59	16	t)||	t)||	PROPN
ejpam-5924	59	17	.	.	PUNCT
ejpam-5924	59	18	ii	ii	PROPN
ejpam-5924	59	19	.	.	PUNCT
ejpam-5924	60	1	|γ(s	|γ(s	PROPN
ejpam-5924	60	2	,	,	PUNCT
ejpam-5924	60	3	t	t	PROPN
ejpam-5924	60	4	,	,	PUNCT
ejpam-5924	60	5	dαu1(s	dαu1(	NOUN
ejpam-5924	60	6	,	,	PUNCT
ejpam-5924	60	7	t))−	t))−	NOUN
ejpam-5924	60	8	γ(s	γ(s	PROPN
ejpam-5924	60	9	,	,	PUNCT
ejpam-5924	60	10	t	t	PROPN
ejpam-5924	60	11	,	,	PUNCT
ejpam-5924	60	12	dαu2(s	dαu2(s	NOUN
ejpam-5924	60	13	,	,	PUNCT
ejpam-5924	60	14	t))|	t))|	PROPN
ejpam-5924	60	15	≤	≤	PROPN
ejpam-5924	60	16	m(s	m(s	PROPN
ejpam-5924	60	17	,	,	PUNCT
ejpam-5924	60	18	t	t	PROPN
ejpam-5924	60	19	)	)	PUNCT
ejpam-5924	60	20	·	·	PUNCT
ejpam-5924	60	21	|dαu1(s	|dαu1(	VERB
ejpam-5924	60	22	,	,	PUNCT
ejpam-5924	60	23	t)−dαu2(s	t)−dαu2(s	NOUN
ejpam-5924	60	24	,	,	PUNCT
ejpam-5924	60	25	t)|	t)|	NOUN
ejpam-5924	60	26	,	,	PUNCT
ejpam-5924	60	27	where	where	SCONJ
ejpam-5924	60	28	∥m(s	∥m(s	NOUN
ejpam-5924	60	29	,	,	PUNCT
ejpam-5924	60	30	t)∥	t)∥	PUNCT
ejpam-5924	60	31	=	=	SYM
ejpam-5924	61	1	m	m	VERB
ejpam-5924	61	2	and	and	CCONJ
ejpam-5924	61	3	m	m	VERB
ejpam-5924	61	4	is	be	AUX
ejpam-5924	61	5	a	a	DET
ejpam-5924	61	6	constant	constant	ADJ
ejpam-5924	61	7	.	.	PUNCT
ejpam-5924	62	1	(	(	PUNCT
ejpam-5924	62	2	iv	iv	X
ejpam-5924	62	3	)	)	PUNCT
ejpam-5924	62	4	the	the	DET
ejpam-5924	62	5	unknown	unknown	ADJ
ejpam-5924	62	6	function	function	NOUN
ejpam-5924	62	7	dαu(s	dαu(s	PROPN
ejpam-5924	62	8	,	,	PUNCT
ejpam-5924	62	9	t	t	PROPN
ejpam-5924	62	10	)	)	PUNCT
ejpam-5924	62	11	behaves	behave	VERB
ejpam-5924	62	12	similarly	similarly	ADV
ejpam-5924	62	13	to	to	ADP
ejpam-5924	62	14	the	the	DET
ejpam-5924	62	15	given	give	VERB
ejpam-5924	62	16	function	function	NOUN
ejpam-5924	62	17	f(s	f(s	PROPN
ejpam-5924	62	18	,	,	PUNCT
ejpam-5924	62	19	t	t	PROPN
ejpam-5924	62	20	)	)	PUNCT
ejpam-5924	62	21	in	in	ADP
ejpam-5924	62	22	c[a	c[a	NUM
ejpam-5924	62	23	,	,	PUNCT
ejpam-5924	62	24	b]×	b]×	VERB
ejpam-5924	62	25	c[c	c[c	NOUN
ejpam-5924	62	26	,	,	PUNCT
ejpam-5924	62	27	d	d	X
ejpam-5924	62	28	]	]	X
ejpam-5924	62	29	,	,	PUNCT
ejpam-5924	62	30	with	with	ADP
ejpam-5924	62	31	its	its	PRON
ejpam-5924	62	32	norm	norm	NOUN
ejpam-5924	62	33	defined	define	VERB
ejpam-5924	62	34	as	as	ADP
ejpam-5924	62	35	:	:	PUNCT
ejpam-5924	62	36	∥dαu(s	∥dαu(s	NUM
ejpam-5924	62	37	,	,	PUNCT
ejpam-5924	62	38	t)∥	t)∥	PUNCT
ejpam-5924	62	39	=	=	PUNCT
ejpam-5924	63	1	[	[	X
ejpam-5924	63	2	∫	∫	X
ejpam-5924	63	3	b	b	X
ejpam-5924	63	4	a	a	DET
ejpam-5924	63	5	∫	∫	PROPN
ejpam-5924	63	6	d	d	X
ejpam-5924	63	7	c	c	PROPN
ejpam-5924	63	8	|dαu(s	|dαu(s	PROPN
ejpam-5924	63	9	,	,	PUNCT
ejpam-5924	63	10	t)|2dsdt	t)|2dsdt	X
ejpam-5924	63	11	]	]	PUNCT
ejpam-5924	63	12	1	1	NUM
ejpam-5924	63	13	2	2	NUM
ejpam-5924	63	14	.	.	PUNCT
ejpam-5924	63	15	theorem	theorem	NOUN
ejpam-5924	63	16	2	2	NUM
ejpam-5924	63	17	.	.	PUNCT
ejpam-5924	64	1	if	if	SCONJ
ejpam-5924	64	2	the	the	DET
ejpam-5924	64	3	first	first	ADJ
ejpam-5924	64	4	three	three	NUM
ejpam-5924	64	5	conditions	condition	NOUN
ejpam-5924	64	6	are	be	AUX
ejpam-5924	64	7	satisfied	satisfied	ADJ
ejpam-5924	64	8	,	,	PUNCT
ejpam-5924	64	9	then	then	ADV
ejpam-5924	64	10	eq	eq	ADJ
ejpam-5924	64	11	(	(	PUNCT
ejpam-5924	64	12	1	1	X
ejpam-5924	64	13	)	)	PUNCT
ejpam-5924	64	14	has	have	VERB
ejpam-5924	64	15	a	a	DET
ejpam-5924	64	16	unique	unique	ADJ
ejpam-5924	64	17	solution	solution	NOUN
ejpam-5924	64	18	in	in	ADP
ejpam-5924	64	19	c[a	c[a	NUM
ejpam-5924	64	20	,	,	PUNCT
ejpam-5924	64	21	b]×	b]×	VERB
ejpam-5924	64	22	c[c	c[c	NOUN
ejpam-5924	64	23	,	,	PUNCT
ejpam-5924	64	24	d	d	X
ejpam-5924	64	25	]	]	X
ejpam-5924	64	26	.	.	PUNCT
ejpam-5924	65	1	lemma	lemma	PROPN
ejpam-5924	65	2	1	1	NUM
ejpam-5924	65	3	.	.	PUNCT
ejpam-5924	66	1	the	the	DET
ejpam-5924	66	2	space	space	NOUN
ejpam-5924	66	3	c[a	c[a	NOUN
ejpam-5924	66	4	,	,	PUNCT
ejpam-5924	66	5	b]×c[c	b]×c[c	NOUN
ejpam-5924	66	6	,	,	PUNCT
ejpam-5924	66	7	d	d	X
ejpam-5924	66	8	]	]	X
ejpam-5924	66	9	is	be	AUX
ejpam-5924	66	10	mapped	map	VERB
ejpam-5924	66	11	into	into	ADP
ejpam-5924	66	12	itself	itself	PRON
ejpam-5924	66	13	by	by	ADP
ejpam-5924	66	14	the	the	DET
ejpam-5924	66	15	operator	operator	NOUN
ejpam-5924	66	16	t̃	t̃	PROPN
ejpam-5924	66	17	defined	define	VERB
ejpam-5924	66	18	by	by	ADP
ejpam-5924	66	19	(	(	PUNCT
ejpam-5924	66	20	2	2	NUM
ejpam-5924	66	21	)	)	PUNCT
ejpam-5924	66	22	under	under	ADP
ejpam-5924	66	23	the	the	DET
ejpam-5924	66	24	conditions	condition	NOUN
ejpam-5924	66	25	(	(	PUNCT
ejpam-5924	66	26	1)–(3	1)–(3	NUM
ejpam-5924	66	27	-	-	NOUN
ejpam-5924	66	28	i	i	PRON
ejpam-5924	66	29	)	)	PUNCT
ejpam-5924	66	30	.	.	PUNCT
ejpam-5924	67	1	proof	proof	NOUN
ejpam-5924	67	2	.	.	PUNCT
ejpam-5924	68	1	using	use	VERB
ejpam-5924	68	2	equation	equation	NOUN
ejpam-5924	68	3	(	(	PUNCT
ejpam-5924	68	4	2	2	NUM
ejpam-5924	68	5	)	)	PUNCT
ejpam-5924	68	6	and	and	CCONJ
ejpam-5924	68	7	(	(	PUNCT
ejpam-5924	68	8	3	3	NUM
ejpam-5924	68	9	)	)	PUNCT
ejpam-5924	68	10	,	,	PUNCT
ejpam-5924	68	11	we	we	PRON
ejpam-5924	68	12	have	have	VERB
ejpam-5924	68	13	:	:	PUNCT
ejpam-5924	68	14	∥t̃dαu(s	∥t̃dαu(s	ADJ
ejpam-5924	68	15	,	,	PUNCT
ejpam-5924	68	16	t)∥	t)∥	NUM
ejpam-5924	68	17	≤	≤	NUM
ejpam-5924	68	18	∥f(s	∥f(	NOUN
ejpam-5924	68	19	,	,	PUNCT
ejpam-5924	68	20	t)∥+	t)∥+	ADJ
ejpam-5924	68	21	|λ|	|λ|	NOUN
ejpam-5924	68	22	∥∥∥∥∫	∥∥∥∥∫	NOUN
ejpam-5924	68	23	b	b	PROPN
ejpam-5924	68	24	a	a	DET
ejpam-5924	68	25	∫	∫	PROPN
ejpam-5924	68	26	d	d	X
ejpam-5924	68	27	c	c	PROPN
ejpam-5924	68	28	|k(s	|k(s	PROPN
ejpam-5924	68	29	,	,	PUNCT
ejpam-5924	68	30	t	t	PROPN
ejpam-5924	68	31	,	,	PUNCT
ejpam-5924	68	32	τ	τ	PROPN
ejpam-5924	68	33	,	,	PUNCT
ejpam-5924	68	34	ξ)||γ(τ	ξ)||γ(τ	NOUN
ejpam-5924	68	35	,	,	PUNCT
ejpam-5924	68	36	ξ	ξ	PROPN
ejpam-5924	68	37	,	,	PUNCT
ejpam-5924	68	38	dαu(τ	dαu(τ	PROPN
ejpam-5924	68	39	,	,	PUNCT
ejpam-5924	68	40	ξ))|dτdξ	ξ))|dτdξ	NOUN
ejpam-5924	68	41	∥∥∥∥	∥∥∥∥	NUM
ejpam-5924	68	42	,	,	PUNCT
ejpam-5924	68	43	(	(	PUNCT
ejpam-5924	68	44	4	4	NUM
ejpam-5924	68	45	)	)	PUNCT
ejpam-5924	68	46	by	by	ADP
ejpam-5924	68	47	applying	apply	VERB
ejpam-5924	68	48	condition	condition	NOUN
ejpam-5924	68	49	(	(	PUNCT
ejpam-5924	68	50	2	2	NUM
ejpam-5924	68	51	)	)	PUNCT
ejpam-5924	68	52	,	,	PUNCT
ejpam-5924	68	53	it	it	PRON
ejpam-5924	68	54	follows	follow	VERB
ejpam-5924	68	55	that	that	SCONJ
ejpam-5924	68	56	:	:	PUNCT
ejpam-5924	68	57	∥t̃dαu(s	∥t̃dαu(s	NUM
ejpam-5924	68	58	,	,	PUNCT
ejpam-5924	68	59	t)∥	t)∥	NUM
ejpam-5924	68	60	≤	≤	NOUN
ejpam-5924	68	61	v	v	X
ejpam-5924	68	62	+	+	X
ejpam-5924	68	63	|λ|	|λ|	NOUN
ejpam-5924	68	64	·	·	PUNCT
ejpam-5924	68	65	[	[	PUNCT
ejpam-5924	68	66	|k(s	|k(s	PROPN
ejpam-5924	68	67	,	,	PUNCT
ejpam-5924	68	68	t	t	PROPN
ejpam-5924	68	69	,	,	PUNCT
ejpam-5924	68	70	τ	τ	PROPN
ejpam-5924	68	71	,	,	PUNCT
ejpam-5924	68	72	ξ)|	ξ)|	NOUN
ejpam-5924	68	73	]	]	X
ejpam-5924	68	74	[	[	PUNCT
ejpam-5924	68	75	∫	∫	PROPN
ejpam-5924	68	76	b	b	PROPN
ejpam-5924	68	77	a	a	DET
ejpam-5924	68	78	∫	∫	PROPN
ejpam-5924	68	79	d	d	X
ejpam-5924	68	80	c	c	PROPN
ejpam-5924	68	81	|γ(s	|γ(s	PROPN
ejpam-5924	68	82	,	,	PUNCT
ejpam-5924	68	83	t	t	PROPN
ejpam-5924	68	84	,	,	PUNCT
ejpam-5924	68	85	dαu(s	dαu(s	PROPN
ejpam-5924	68	86	,	,	PUNCT
ejpam-5924	68	87	t))|2dsdt	t))|2dsdt	NOUN
ejpam-5924	68	88	]	]	PUNCT
ejpam-5924	68	89	1	1	NUM
ejpam-5924	68	90	2	2	NUM
ejpam-5924	68	91	,	,	PUNCT
ejpam-5924	68	92	(	(	PUNCT
ejpam-5924	68	93	5	5	X
ejpam-5924	68	94	)	)	PUNCT
ejpam-5924	68	95	using	use	VERB
ejpam-5924	68	96	conditions	condition	NOUN
ejpam-5924	68	97	(	(	PUNCT
ejpam-5924	68	98	1	1	NUM
ejpam-5924	68	99	)	)	PUNCT
ejpam-5924	68	100	and	and	CCONJ
ejpam-5924	68	101	(	(	PUNCT
ejpam-5924	68	102	3	3	NUM
ejpam-5924	68	103	-	-	PUNCT
ejpam-5924	68	104	i	i	NOUN
ejpam-5924	68	105	)	)	PUNCT
ejpam-5924	68	106	,	,	PUNCT
ejpam-5924	68	107	we	we	PRON
ejpam-5924	68	108	can	can	AUX
ejpam-5924	68	109	estimate	estimate	VERB
ejpam-5924	68	110	:	:	PUNCT
ejpam-5924	68	111	∥t̃dαu(s	∥t̃dαu(s	NUM
ejpam-5924	68	112	,	,	PUNCT
ejpam-5924	68	113	t)∥	t)∥	NUM
ejpam-5924	68	114	≤	≤	NOUN
ejpam-5924	68	115	v	v	NOUN
ejpam-5924	68	116	+	+	CCONJ
ejpam-5924	68	117	δ∥dαu(s	δ∥dαu(s	ADJ
ejpam-5924	68	118	,	,	PUNCT
ejpam-5924	68	119	t)∥	t)∥	PROPN
ejpam-5924	68	120	,	,	PUNCT
ejpam-5924	68	121	when	when	SCONJ
ejpam-5924	68	122	δ	δ	PROPN
ejpam-5924	68	123	=	=	SYM
ejpam-5924	68	124	|λ|κg	|λ|κg	PROPN
ejpam-5924	68	125	.	.	PUNCT
ejpam-5924	69	1	hence	hence	ADV
ejpam-5924	69	2	,	,	PUNCT
ejpam-5924	69	3	this	this	DET
ejpam-5924	69	4	inequality	inequality	NOUN
ejpam-5924	69	5	(	(	PUNCT
ejpam-5924	69	6	2	2	NUM
ejpam-5924	69	7	)	)	PUNCT
ejpam-5924	69	8	confirms	confirm	VERB
ejpam-5924	69	9	that	that	SCONJ
ejpam-5924	69	10	the	the	DET
ejpam-5924	69	11	operator	operator	NOUN
ejpam-5924	69	12	t̃	t̃	PROPN
ejpam-5924	69	13	is	be	AUX
ejpam-5924	69	14	bounded	bound	VERB
ejpam-5924	69	15	,	,	PUNCT
ejpam-5924	69	16	with	with	ADP
ejpam-5924	69	17	:	:	PUNCT
ejpam-5924	69	18	∥t̃dαu(s	∥t̃dαu(s	ADJ
ejpam-5924	69	19	,	,	PUNCT
ejpam-5924	69	20	t)∥	t)∥	PROPN
ejpam-5924	69	21	≤	≤	NUM
ejpam-5924	69	22	δ∥dαu(s	δ∥dαu(s	X
ejpam-5924	69	23	,	,	PUNCT
ejpam-5924	69	24	t)∥.	t)∥.	PRON
ejpam-5924	69	25	a.	a.	NOUN
ejpam-5924	69	26	m.	m.	NOUN
ejpam-5924	69	27	al	al	PROPN
ejpam-5924	69	28	-	-	PUNCT
ejpam-5924	69	29	bugami	bugami	NOUN
ejpam-5924	69	30	,	,	PUNCT
ejpam-5924	69	31	n.	n.	NOUN
ejpam-5924	69	32	a.	a.	NOUN
ejpam-5924	69	33	alharbi	alharbi	PROPN
ejpam-5924	69	34	,	,	PUNCT
ejpam-5924	69	35	a.	a.	NOUN
ejpam-5924	69	36	m.	m.	PROPN
ejpam-5924	69	37	s.	s.	PROPN
ejpam-5924	69	38	mahdy	mahdy	PROPN
ejpam-5924	69	39	/	/	SYM
ejpam-5924	69	40	eur	eur	PROPN
ejpam-5924	69	41	.	.	PUNCT
ejpam-5924	70	1	j.	j.	PROPN
ejpam-5924	70	2	pure	pure	PROPN
ejpam-5924	70	3	appl	appl	PROPN
ejpam-5924	70	4	.	.	PROPN
ejpam-5924	70	5	math	math	PROPN
ejpam-5924	70	6	,	,	PUNCT
ejpam-5924	70	7	18	18	NUM
ejpam-5924	70	8	(	(	PUNCT
ejpam-5924	70	9	2	2	NUM
ejpam-5924	70	10	)	)	PUNCT
ejpam-5924	70	11	(	(	PUNCT
ejpam-5924	70	12	2025	2025	NUM
ejpam-5924	70	13	)	)	PUNCT
ejpam-5924	70	14	,	,	PUNCT
ejpam-5924	70	15	5924	5924	NUM
ejpam-5924	70	16	4	4	NUM
ejpam-5924	70	17	of	of	ADP
ejpam-5924	70	18	14	14	NUM
ejpam-5924	70	19	lemma	lemma	PROPN
ejpam-5924	70	20	2	2	NUM
ejpam-5924	70	21	.	.	PUNCT
ejpam-5924	71	1	the	the	DET
ejpam-5924	71	2	operator	operator	NOUN
ejpam-5924	71	3	t̃	t̃	PROPN
ejpam-5924	71	4	is	be	AUX
ejpam-5924	71	5	a	a	DET
ejpam-5924	71	6	contraction	contraction	NOUN
ejpam-5924	71	7	on	on	ADP
ejpam-5924	71	8	the	the	DET
ejpam-5924	71	9	banach	banach	NOUN
ejpam-5924	71	10	space	space	NOUN
ejpam-5924	71	11	c[a	c[a	NOUN
ejpam-5924	71	12	,	,	PUNCT
ejpam-5924	71	13	b	b	X
ejpam-5924	71	14	]	]	X
ejpam-5924	71	15	×	×	NOUN
ejpam-5924	71	16	c[c	c[c	NOUN
ejpam-5924	71	17	,	,	PUNCT
ejpam-5924	71	18	d	d	X
ejpam-5924	71	19	]	]	X
ejpam-5924	71	20	,	,	PUNCT
ejpam-5924	71	21	if	if	SCONJ
ejpam-5924	71	22	conditions	condition	NOUN
ejpam-5924	71	23	(	(	PUNCT
ejpam-5924	71	24	1	1	NUM
ejpam-5924	71	25	)	)	PUNCT
ejpam-5924	71	26	and	and	CCONJ
ejpam-5924	71	27	(	(	PUNCT
ejpam-5924	71	28	3	3	NUM
ejpam-5924	71	29	-	-	PUNCT
ejpam-5924	71	30	ii	ii	NOUN
ejpam-5924	71	31	)	)	PUNCT
ejpam-5924	71	32	are	be	AUX
ejpam-5924	71	33	satisfied	satisfied	ADJ
ejpam-5924	71	34	.	.	PUNCT
ejpam-5924	72	1	proof	proof	NOUN
ejpam-5924	72	2	.	.	PUNCT
ejpam-5924	73	1	suppose	suppose	VERB
ejpam-5924	73	2	we	we	PRON
ejpam-5924	73	3	have	have	VERB
ejpam-5924	73	4	two	two	NUM
ejpam-5924	73	5	unknown	unknown	ADJ
ejpam-5924	73	6	function	function	NOUN
ejpam-5924	73	7	dαu1(s	dαu1(	NOUN
ejpam-5924	73	8	,	,	PUNCT
ejpam-5924	73	9	t	t	PROPN
ejpam-5924	73	10	)	)	PUNCT
ejpam-5924	73	11	and	and	CCONJ
ejpam-5924	73	12	dαu2(s	dαu2(s	NOUN
ejpam-5924	73	13	,	,	PUNCT
ejpam-5924	73	14	t	t	PROPN
ejpam-5924	73	15	)	)	PUNCT
ejpam-5924	73	16	in	in	ADP
ejpam-5924	73	17	c[a	c[a	NUM
ejpam-5924	73	18	,	,	PUNCT
ejpam-5924	73	19	b]×	b]×	VERB
ejpam-5924	73	20	c[c	c[c	NOUN
ejpam-5924	73	21	,	,	PUNCT
ejpam-5924	73	22	d	d	X
ejpam-5924	73	23	]	]	X
ejpam-5924	73	24	,	,	PUNCT
ejpam-5924	73	25	we	we	PRON
ejpam-5924	73	26	can	can	AUX
ejpam-5924	73	27	apply	apply	VERB
ejpam-5924	73	28	equations	equation	NOUN
ejpam-5924	73	29	(	(	PUNCT
ejpam-5924	73	30	2	2	NUM
ejpam-5924	73	31	)	)	PUNCT
ejpam-5924	73	32	and	and	CCONJ
ejpam-5924	73	33	(	(	PUNCT
ejpam-5924	73	34	3	3	X
ejpam-5924	73	35	)	)	PUNCT
ejpam-5924	73	36	to	to	PART
ejpam-5924	73	37	obtain	obtain	VERB
ejpam-5924	73	38	:	:	PUNCT
ejpam-5924	73	39	∥(t̃dαu1	∥(t̃dαu1	NOUN
ejpam-5924	73	40	−	−	PROPN
ejpam-5924	73	41	t̃dαu2)(s	t̃dαu2)(s	NOUN
ejpam-5924	73	42	,	,	PUNCT
ejpam-5924	73	43	t)∥	t)∥	NUM
ejpam-5924	73	44	≤	≤	NUM
ejpam-5924	73	45	|λ|	|λ|	PROPN
ejpam-5924	73	46	∥∥∥∥∫	∥∥∥∥∫	VERB
ejpam-5924	73	47	b	b	PROPN
ejpam-5924	73	48	a	a	DET
ejpam-5924	73	49	∫	∫	PROPN
ejpam-5924	73	50	d	d	X
ejpam-5924	73	51	c	c	PROPN
ejpam-5924	73	52	|k(s	|k(s	PROPN
ejpam-5924	73	53	,	,	PUNCT
ejpam-5924	73	54	t	t	PROPN
ejpam-5924	73	55	,	,	PUNCT
ejpam-5924	73	56	τ	τ	PROPN
ejpam-5924	73	57	,	,	PUNCT
ejpam-5924	73	58	ξ)|	ξ)|	PROPN
ejpam-5924	73	59	·	·	SYM
ejpam-5924	73	60	|γ(τ	|γ(τ	PROPN
ejpam-5924	73	61	,	,	PUNCT
ejpam-5924	73	62	ξ	ξ	PROPN
ejpam-5924	73	63	,	,	PUNCT
ejpam-5924	73	64	dαu1(τ	dαu1(τ	NOUN
ejpam-5924	73	65	,	,	PUNCT
ejpam-5924	73	66	ξ))−	ξ))−	ADJ
ejpam-5924	73	67	γ(τ	γ(τ	PROPN
ejpam-5924	73	68	,	,	PUNCT
ejpam-5924	73	69	ξ	ξ	PROPN
ejpam-5924	73	70	,	,	PUNCT
ejpam-5924	73	71	dαu2(τ	dαu2(τ	NUM
ejpam-5924	73	72	,	,	PUNCT
ejpam-5924	73	73	ξ))|dτdξ	ξ))|dτdξ	ADP
ejpam-5924	73	74	∥∥∥∥	∥∥∥∥	NUM
ejpam-5924	73	75	,	,	PUNCT
ejpam-5924	73	76	by	by	ADP
ejpam-5924	73	77	using	use	VERB
ejpam-5924	73	78	condition	condition	NOUN
ejpam-5924	73	79	(	(	PUNCT
ejpam-5924	73	80	3	3	NUM
ejpam-5924	73	81	-	-	PUNCT
ejpam-5924	73	82	ii	ii	NOUN
ejpam-5924	73	83	)	)	PUNCT
ejpam-5924	73	84	,	,	PUNCT
ejpam-5924	73	85	we	we	PRON
ejpam-5924	73	86	get	get	VERB
ejpam-5924	73	87	:	:	PUNCT
ejpam-5924	73	88	∥(t̃dαu1	∥(t̃dαu1	NOUN
ejpam-5924	73	89	−	−	PROPN
ejpam-5924	73	90	t̃dαu2)(s	t̃dαu2)(s	NOUN
ejpam-5924	73	91	,	,	PUNCT
ejpam-5924	73	92	t)∥	t)∥	NUM
ejpam-5924	73	93	≤	≤	NUM
ejpam-5924	73	94	|λ|	|λ|	X
ejpam-5924	73	95	·	·	PUNCT
ejpam-5924	73	96	[	[	PUNCT
ejpam-5924	73	97	|k(s	|k(s	PROPN
ejpam-5924	73	98	,	,	PUNCT
ejpam-5924	73	99	t	t	PROPN
ejpam-5924	73	100	,	,	PUNCT
ejpam-5924	73	101	τ	τ	PROPN
ejpam-5924	73	102	,	,	PUNCT
ejpam-5924	73	103	ξ)|	ξ)|	X
ejpam-5924	73	104	]	]	PUNCT
ejpam-5924	73	105	·	·	PUNCT
ejpam-5924	73	106	[	[	PUNCT
ejpam-5924	73	107	∫	∫	PROPN
ejpam-5924	73	108	b	b	PROPN
ejpam-5924	73	109	a	a	DET
ejpam-5924	73	110	∫	∫	PROPN
ejpam-5924	73	111	d	d	X
ejpam-5924	73	112	c	c	PROPN
ejpam-5924	73	113	m2(s	m2(s	PROPN
ejpam-5924	73	114	,	,	PUNCT
ejpam-5924	73	115	t)|dαu1(τ	t)|dαu1(τ	NOUN
ejpam-5924	73	116	,	,	PUNCT
ejpam-5924	73	117	ξ)−dαu1(τ	ξ)−dαu1(τ	NOUN
ejpam-5924	73	118	,	,	PUNCT
ejpam-5924	73	119	ξ)|2dτdξ	ξ)|2dτdξ	NUM
ejpam-5924	73	120	]	]	PUNCT
ejpam-5924	73	121	1	1	NUM
ejpam-5924	73	122	2	2	NUM
ejpam-5924	73	123	.	.	PUNCT
ejpam-5924	74	1	thus	thus	ADV
ejpam-5924	74	2	,	,	PUNCT
ejpam-5924	74	3	we	we	PRON
ejpam-5924	74	4	conclude	conclude	VERB
ejpam-5924	74	5	:	:	PUNCT
ejpam-5924	74	6	∥(t̃dαu1	∥(t̃dαu1	NOUN
ejpam-5924	74	7	−	−	PROPN
ejpam-5924	74	8	t̃dαu2)(s	t̃dαu2)(s	NOUN
ejpam-5924	74	9	,	,	PUNCT
ejpam-5924	74	10	t)∥	t)∥	NUM
ejpam-5924	74	11	≤	≤	NUM
ejpam-5924	74	12	δ∥dαu1(s	δ∥dαu1(s	ADJ
ejpam-5924	74	13	,	,	PUNCT
ejpam-5924	74	14	t)−dαu2(s	t)−dαu2(s	NOUN
ejpam-5924	74	15	,	,	PUNCT
ejpam-5924	74	16	t)∥.	t)∥.	PRON
ejpam-5924	74	17	3	3	NUM
ejpam-5924	74	18	.	.	PUNCT
ejpam-5924	75	1	adm	adm	NOUN
ejpam-5924	75	2	in	in	ADP
ejpam-5924	75	3	this	this	DET
ejpam-5924	75	4	section	section	NOUN
ejpam-5924	75	5	,	,	PUNCT
ejpam-5924	75	6	we	we	PRON
ejpam-5924	75	7	will	will	AUX
ejpam-5924	75	8	address	address	VERB
ejpam-5924	75	9	the	the	DET
ejpam-5924	75	10	tdfnfi	tdfnfi	ADV
ejpam-5924	75	11	-	-	PUNCT
ejpam-5924	75	12	de	de	NOUN
ejpam-5924	75	13	using	use	VERB
ejpam-5924	75	14	adm	adm	PROPN
ejpam-5924	75	15	.	.	PUNCT
ejpam-5924	76	1	let	let	VERB
ejpam-5924	76	2	’s	’s	NOUN
ejpam-5924	76	3	consider	consider	VERB
ejpam-5924	76	4	(	(	PUNCT
ejpam-5924	76	5	1	1	NUM
ejpam-5924	76	6	)	)	PUNCT
ejpam-5924	76	7	,	,	PUNCT
ejpam-5924	76	8	in	in	ADP
ejpam-5924	76	9	witch	witch	NOUN
ejpam-5924	76	10	f(s	f(s	PROPN
ejpam-5924	76	11	,	,	PUNCT
ejpam-5924	76	12	t	t	PROPN
ejpam-5924	76	13	)	)	PUNCT
ejpam-5924	76	14	is	be	AUX
ejpam-5924	76	15	a	a	DET
ejpam-5924	76	16	function	function	NOUN
ejpam-5924	76	17	that	that	PRON
ejpam-5924	76	18	is	be	AUX
ejpam-5924	76	19	bounded	bound	VERB
ejpam-5924	76	20	,	,	PUNCT
ejpam-5924	76	21	and	and	CCONJ
ejpam-5924	76	22	for	for	SCONJ
ejpam-5924	76	23	all	all	DET
ejpam-5924	76	24	(	(	PUNCT
ejpam-5924	76	25	s	s	PROPN
ejpam-5924	76	26	,	,	PUNCT
ejpam-5924	76	27	t	t	PROPN
ejpam-5924	76	28	)	)	PUNCT
ejpam-5924	76	29	belongs	belong	VERB
ejpam-5924	76	30	to	to	ADP
ejpam-5924	76	31	the	the	DET
ejpam-5924	76	32	set	set	NOUN
ejpam-5924	76	33	ω	ω	PROPN
ejpam-5924	76	34	=	=	PUNCT
ejpam-5924	77	1	[	[	X
ejpam-5924	77	2	a	a	X
ejpam-5924	77	3	,	,	PUNCT
ejpam-5924	77	4	b	b	NOUN
ejpam-5924	77	5	]	]	X
ejpam-5924	77	6	×	×	NOUN
ejpam-5924	77	7	[	[	X
ejpam-5924	77	8	c	c	X
ejpam-5924	77	9	,	,	PUNCT
ejpam-5924	77	10	d	d	NOUN
ejpam-5924	77	11	]	]	X
ejpam-5924	77	12	.	.	PUNCT
ejpam-5924	78	1	the	the	DET
ejpam-5924	78	2	kernel	kernel	PROPN
ejpam-5924	78	3	|k(s	|k(s	PROPN
ejpam-5924	78	4	,	,	PUNCT
ejpam-5924	78	5	t	t	PROPN
ejpam-5924	78	6	,	,	PUNCT
ejpam-5924	78	7	τ	τ	PROPN
ejpam-5924	78	8	,	,	PUNCT
ejpam-5924	78	9	ξ)|	ξ)|	ADJ
ejpam-5924	78	10	≤	≤	NUM
ejpam-5924	78	11	κ	κ	NOUN
ejpam-5924	78	12	.	.	PUNCT
ejpam-5924	79	1	the	the	DET
ejpam-5924	79	2	nonlinear	nonlinear	ADJ
ejpam-5924	79	3	term	term	NOUN
ejpam-5924	79	4	γ(τ	γ(τ	PROPN
ejpam-5924	79	5	,	,	PUNCT
ejpam-5924	79	6	ξ	ξ	PROPN
ejpam-5924	79	7	,	,	PUNCT
ejpam-5924	79	8	dαu(τ	dαu(τ	PROPN
ejpam-5924	79	9	,	,	PUNCT
ejpam-5924	79	10	ξ	ξ	NOUN
ejpam-5924	79	11	)	)	PUNCT
ejpam-5924	79	12	)	)	PUNCT
ejpam-5924	79	13	is	be	AUX
ejpam-5924	79	14	lipchitz	lipchitz	NOUN
ejpam-5924	79	15	continuous	continuous	ADJ
ejpam-5924	79	16	and	and	CCONJ
ejpam-5924	79	17	satisfies	satisfy	VERB
ejpam-5924	79	18	the	the	DET
ejpam-5924	79	19	following	follow	VERB
ejpam-5924	79	20	condition	condition	NOUN
ejpam-5924	79	21	:	:	PUNCT
ejpam-5924	79	22	|γ(dαu)−	|γ(dαu)−	DET
ejpam-5924	79	23	γ(dαũ)|	γ(dαũ)|	PROPN
ejpam-5924	79	24	≤	≤	NOUN
ejpam-5924	79	25	l|dαu−dαũ|	l|dαu−dαũ|	NOUN
ejpam-5924	79	26	.	.	PUNCT
ejpam-5924	80	1	we	we	PRON
ejpam-5924	80	2	define	define	VERB
ejpam-5924	80	3	the	the	DET
ejpam-5924	80	4	space	space	NOUN
ejpam-5924	80	5	c[a	c[a	NOUN
ejpam-5924	80	6	,	,	PUNCT
ejpam-5924	80	7	b	b	X
ejpam-5924	80	8	]	]	X
ejpam-5924	80	9	×	×	NOUN
ejpam-5924	80	10	c[c	c[c	NOUN
ejpam-5924	80	11	,	,	PUNCT
ejpam-5924	80	12	d	d	X
ejpam-5924	80	13	]	]	X
ejpam-5924	80	14	,	,	PUNCT
ejpam-5924	80	15	continuous	continuous	ADJ
ejpam-5924	80	16	functions	function	NOUN
ejpam-5924	80	17	on	on	ADP
ejpam-5924	80	18	the	the	DET
ejpam-5924	80	19	rectangle	rectangle	NOUN
ejpam-5924	80	20	[	[	X
ejpam-5924	80	21	a	a	X
ejpam-5924	80	22	,	,	PUNCT
ejpam-5924	80	23	b	b	NOUN
ejpam-5924	80	24	]	]	X
ejpam-5924	80	25	×	×	NOUN
ejpam-5924	81	1	[	[	X
ejpam-5924	81	2	c	c	X
ejpam-5924	81	3	,	,	PUNCT
ejpam-5924	81	4	d	d	X
ejpam-5924	81	5	]	]	X
ejpam-5924	81	6	,	,	PUNCT
ejpam-5924	81	7	with	with	ADP
ejpam-5924	81	8	the	the	DET
ejpam-5924	81	9	associated	associated	ADJ
ejpam-5924	81	10	distance	distance	NOUN
ejpam-5924	81	11	function	function	NOUN
ejpam-5924	81	12	d∗(dαũ	d∗(dαũ	NOUN
ejpam-5924	81	13	,	,	PUNCT
ejpam-5924	81	14	dαu	dαu	NOUN
ejpam-5924	81	15	)	)	PUNCT
ejpam-5924	81	16	defined	define	VERB
ejpam-5924	81	17	by	by	ADP
ejpam-5924	81	18	:	:	PUNCT
ejpam-5924	81	19	d∗(dαũ	d∗(dαũ	NOUN
ejpam-5924	81	20	,	,	PUNCT
ejpam-5924	81	21	dαu	dαu	ADJ
ejpam-5924	81	22	)	)	PUNCT
ejpam-5924	81	23	=	=	SYM
ejpam-5924	81	24	max	max	X
ejpam-5924	81	25	(	(	PUNCT
ejpam-5924	81	26	s	s	PROPN
ejpam-5924	81	27	,	,	PUNCT
ejpam-5924	81	28	t)∈ω	t)∈ω	X
ejpam-5924	81	29	|dαũ(s	|dαũ(s	PROPN
ejpam-5924	81	30	,	,	PUNCT
ejpam-5924	81	31	t)−dαu(s	t)−dαu(s	ADJ
ejpam-5924	81	32	,	,	PUNCT
ejpam-5924	81	33	t)|	t)|	NOUN
ejpam-5924	81	34	.	.	PUNCT
ejpam-5924	82	1	(	(	PUNCT
ejpam-5924	82	2	6	6	NUM
ejpam-5924	82	3	)	)	PUNCT
ejpam-5924	82	4	the	the	DET
ejpam-5924	82	5	unknown	unknown	ADJ
ejpam-5924	82	6	function	function	NOUN
ejpam-5924	82	7	dαu(s	dαu(s	PROPN
ejpam-5924	82	8	,	,	PUNCT
ejpam-5924	82	9	t	t	PROPN
ejpam-5924	82	10	)	)	PUNCT
ejpam-5924	82	11	is	be	AUX
ejpam-5924	82	12	assumed	assume	VERB
ejpam-5924	82	13	to	to	PART
ejpam-5924	82	14	have	have	VERB
ejpam-5924	82	15	the	the	DET
ejpam-5924	82	16	series	series	NOUN
ejpam-5924	82	17	form	form	NOUN
ejpam-5924	82	18	:	:	PUNCT
ejpam-5924	82	19	dαu(s	dαu(s	PROPN
ejpam-5924	82	20	,	,	PUNCT
ejpam-5924	82	21	t	t	PROPN
ejpam-5924	82	22	)	)	PUNCT
ejpam-5924	82	23	=	=	PUNCT
ejpam-5924	83	1	∞∑	∞∑	PRON
ejpam-5924	83	2	n=0	n=0	NUM
ejpam-5924	83	3	dαun(s	dαun(s	PROPN
ejpam-5924	83	4	,	,	PUNCT
ejpam-5924	83	5	t	t	PROPN
ejpam-5924	83	6	)	)	PUNCT
ejpam-5924	83	7	.	.	PUNCT
ejpam-5924	84	1	(	(	PUNCT
ejpam-5924	84	2	7	7	X
ejpam-5924	84	3	)	)	PUNCT
ejpam-5924	84	4	the	the	DET
ejpam-5924	84	5	nonlinear	nonlinear	ADJ
ejpam-5924	84	6	term	term	NOUN
ejpam-5924	84	7	γ(τ	γ(τ	PROPN
ejpam-5924	84	8	,	,	PUNCT
ejpam-5924	84	9	ξ	ξ	PROPN
ejpam-5924	84	10	,	,	PUNCT
ejpam-5924	84	11	dαu(τ	dαu(τ	PROPN
ejpam-5924	84	12	,	,	PUNCT
ejpam-5924	84	13	ξ	ξ	NOUN
ejpam-5924	84	14	)	)	PUNCT
ejpam-5924	84	15	)	)	PUNCT
ejpam-5924	84	16	in	in	ADP
ejpam-5924	84	17	(	(	PUNCT
ejpam-5924	84	18	1	1	X
ejpam-5924	84	19	)	)	PUNCT
ejpam-5924	84	20	is	be	AUX
ejpam-5924	84	21	similarly	similarly	ADV
ejpam-5924	84	22	decomposed	decompose	VERB
ejpam-5924	84	23	into	into	ADP
ejpam-5924	84	24	an	an	DET
ejpam-5924	84	25	infinite	infinite	ADJ
ejpam-5924	84	26	series	series	NOUN
ejpam-5924	84	27	:	:	PUNCT
ejpam-5924	84	28	γ(τ	γ(τ	PROPN
ejpam-5924	84	29	,	,	PUNCT
ejpam-5924	84	30	ξ	ξ	PROPN
ejpam-5924	84	31	,	,	PUNCT
ejpam-5924	84	32	dαu(s	dαu(s	PROPN
ejpam-5924	84	33	,	,	PUNCT
ejpam-5924	84	34	t	t	PROPN
ejpam-5924	84	35	)	)	PUNCT
ejpam-5924	84	36	)	)	PUNCT
ejpam-5924	85	1	=	=	PUNCT
ejpam-5924	86	1	∞∑	∞∑	PRON
ejpam-5924	86	2	n=0	n=0	PROPN
ejpam-5924	86	3	anun(s	anun(s	PROPN
ejpam-5924	86	4	,	,	PUNCT
ejpam-5924	86	5	t	t	PROPN
ejpam-5924	86	6	)	)	PUNCT
ejpam-5924	86	7	,	,	PUNCT
ejpam-5924	86	8	(	(	PUNCT
ejpam-5924	86	9	8)	8)	NUM
ejpam-5924	86	10	a.	a.	NOUN
ejpam-5924	86	11	m.	m.	NOUN
ejpam-5924	86	12	al	al	PROPN
ejpam-5924	86	13	-	-	PUNCT
ejpam-5924	86	14	bugami	bugami	NOUN
ejpam-5924	86	15	,	,	PUNCT
ejpam-5924	86	16	n.	n.	NOUN
ejpam-5924	86	17	a.	a.	NOUN
ejpam-5924	86	18	alharbi	alharbi	PROPN
ejpam-5924	86	19	,	,	PUNCT
ejpam-5924	86	20	a.	a.	NOUN
ejpam-5924	86	21	m.	m.	PROPN
ejpam-5924	86	22	s.	s.	PROPN
ejpam-5924	86	23	mahdy	mahdy	PROPN
ejpam-5924	86	24	/	/	SYM
ejpam-5924	86	25	eur	eur	PROPN
ejpam-5924	86	26	.	.	PUNCT
ejpam-5924	87	1	j.	j.	PROPN
ejpam-5924	87	2	pure	pure	PROPN
ejpam-5924	87	3	appl	appl	PROPN
ejpam-5924	87	4	.	.	PROPN
ejpam-5924	87	5	math	math	PROPN
ejpam-5924	87	6	,	,	PUNCT
ejpam-5924	87	7	18	18	NUM
ejpam-5924	87	8	(	(	PUNCT
ejpam-5924	87	9	2	2	NUM
ejpam-5924	87	10	)	)	PUNCT
ejpam-5924	87	11	(	(	PUNCT
ejpam-5924	87	12	2025	2025	NUM
ejpam-5924	87	13	)	)	PUNCT
ejpam-5924	87	14	,	,	PUNCT
ejpam-5924	87	15	5924	5924	NUM
ejpam-5924	87	16	5	5	NUM
ejpam-5924	87	17	of	of	ADP
ejpam-5924	87	18	14	14	NUM
ejpam-5924	87	19	where	where	SCONJ
ejpam-5924	87	20	the	the	DET
ejpam-5924	87	21	traditional	traditional	ADJ
ejpam-5924	87	22	form	form	NOUN
ejpam-5924	87	23	of	of	ADP
ejpam-5924	87	24	the	the	DET
ejpam-5924	87	25	adomian	adomian	NOUN
ejpam-5924	87	26	polynomials	polynomial	VERB
ejpam-5924	87	27	an	an	PRON
ejpam-5924	87	28	is	be	AUX
ejpam-5924	87	29	[	[	X
ejpam-5924	87	30	16][17	16][17	NUM
ejpam-5924	87	31	]	]	PUNCT
ejpam-5924	87	32	given	give	VERB
ejpam-5924	87	33	by	by	ADP
ejpam-5924	87	34	:	:	PUNCT
ejpam-5924	87	35	an	an	DET
ejpam-5924	87	36	=	=	SYM
ejpam-5924	87	37	1	1	NUM
ejpam-5924	87	38	n	n	NOUN
ejpam-5924	87	39	!	!	PUNCT
ejpam-5924	88	1	[	[	PUNCT
ejpam-5924	88	2	dn	dn	PROPN
ejpam-5924	88	3	dλn	dλn	PROPN
ejpam-5924	88	4	γ	γ	X
ejpam-5924	88	5	(	(	PUNCT
ejpam-5924	88	6	∞∑	∞∑	PROPN
ejpam-5924	88	7	i=0	i=0	PROPN
ejpam-5924	88	8	λidαui)]λ=0	λidαui)]λ=0	PROPN
ejpam-5924	88	9	.	.	PUNCT
ejpam-5924	88	10	(	(	PUNCT
ejpam-5924	88	11	9	9	NUM
ejpam-5924	88	12	)	)	PUNCT
ejpam-5924	88	13	another	another	DET
ejpam-5924	88	14	formulation	formulation	NOUN
ejpam-5924	88	15	of	of	ADP
ejpam-5924	88	16	the	the	DET
ejpam-5924	88	17	adomian	adomian	NOUN
ejpam-5924	88	18	polynomials	polynomial	NOUN
ejpam-5924	88	19	is	be	AUX
ejpam-5924	88	20	expressed	express	VERB
ejpam-5924	88	21	as	as	ADP
ejpam-5924	88	22	:	:	PUNCT
ejpam-5924	88	23	an	an	PRON
ejpam-5924	88	24	=	=	PUNCT
ejpam-5924	88	25	γ(sn)−	γ(sn)−	X
ejpam-5924	88	26	n−1∑	n−1∑	PROPN
ejpam-5924	88	27	i=0	i=0	PROPN
ejpam-5924	88	28	ai	ai	VERB
ejpam-5924	88	29	,	,	PUNCT
ejpam-5924	88	30	(	(	PUNCT
ejpam-5924	88	31	10	10	NUM
ejpam-5924	88	32	)	)	PUNCT
ejpam-5924	88	33	where	where	SCONJ
ejpam-5924	88	34	sn	sn	PROPN
ejpam-5924	88	35	is	be	AUX
ejpam-5924	88	36	defined	define	VERB
ejpam-5924	88	37	by	by	ADP
ejpam-5924	88	38	:	:	PUNCT
ejpam-5924	88	39	sn	sn	PROPN
ejpam-5924	88	40	=	=	SYM
ejpam-5924	88	41	n∑	n∑	PROPN
ejpam-5924	88	42	i=0	i=0	PROPN
ejpam-5924	88	43	dαui(s	dαui(s	PROPN
ejpam-5924	88	44	,	,	PUNCT
ejpam-5924	88	45	t	t	PROPN
ejpam-5924	88	46	)	)	PUNCT
ejpam-5924	88	47	.	.	PUNCT
ejpam-5924	89	1	(	(	PUNCT
ejpam-5924	89	2	11	11	NUM
ejpam-5924	89	3	)	)	PUNCT
ejpam-5924	89	4	by	by	ADP
ejpam-5924	89	5	applying	apply	VERB
ejpam-5924	89	6	the	the	DET
ejpam-5924	89	7	adomian	adomian	NOUN
ejpam-5924	89	8	decomposition	decomposition	NOUN
ejpam-5924	89	9	method	method	NOUN
ejpam-5924	89	10	to	to	ADP
ejpam-5924	89	11	equation	equation	NOUN
ejpam-5924	89	12	(	(	PUNCT
ejpam-5924	89	13	1	1	NUM
ejpam-5924	89	14	)	)	PUNCT
ejpam-5924	89	15	,	,	PUNCT
ejpam-5924	89	16	we	we	PRON
ejpam-5924	89	17	obtain	obtain	VERB
ejpam-5924	89	18	the	the	DET
ejpam-5924	89	19	solution	solution	NOUN
ejpam-5924	89	20	in	in	ADP
ejpam-5924	89	21	series	series	NOUN
ejpam-5924	89	22	form	form	NOUN
ejpam-5924	89	23	:	:	PUNCT
ejpam-5924	89	24	dαu(s	dαu(s	PROPN
ejpam-5924	89	25	,	,	PUNCT
ejpam-5924	89	26	t	t	PROPN
ejpam-5924	89	27	)	)	PUNCT
ejpam-5924	89	28	=	=	PUNCT
ejpam-5924	90	1	∞∑	∞∑	PRON
ejpam-5924	90	2	n=0	n=0	NUM
ejpam-5924	90	3	dαun(s	dαun(s	PROPN
ejpam-5924	90	4	,	,	PUNCT
ejpam-5924	90	5	t	t	PROPN
ejpam-5924	90	6	)	)	PUNCT
ejpam-5924	90	7	,	,	PUNCT
ejpam-5924	90	8	(	(	PUNCT
ejpam-5924	90	9	12	12	NUM
ejpam-5924	90	10	)	)	PUNCT
ejpam-5924	90	11	where	where	SCONJ
ejpam-5924	90	12	dαu0(s	dαu0(s	NUM
ejpam-5924	90	13	,	,	PUNCT
ejpam-5924	90	14	t	t	PROPN
ejpam-5924	90	15	)	)	PUNCT
ejpam-5924	90	16	=	=	PUNCT
ejpam-5924	90	17	f(s	f(s	PROPN
ejpam-5924	90	18	,	,	PUNCT
ejpam-5924	90	19	t	t	PROPN
ejpam-5924	90	20	)	)	PUNCT
ejpam-5924	90	21	,	,	PUNCT
ejpam-5924	90	22	dαui(s	dαui(s	PROPN
ejpam-5924	90	23	,	,	PUNCT
ejpam-5924	90	24	t	t	PROPN
ejpam-5924	90	25	)	)	PUNCT
ejpam-5924	90	26	=	=	PUNCT
ejpam-5924	91	1	λ	λ	X
ejpam-5924	91	2	∫	∫	PROPN
ejpam-5924	91	3	b	b	PROPN
ejpam-5924	91	4	a	a	DET
ejpam-5924	91	5	∫	∫	PROPN
ejpam-5924	91	6	d	d	X
ejpam-5924	91	7	c	c	PROPN
ejpam-5924	91	8	k(s	k(s	PROPN
ejpam-5924	91	9	,	,	PUNCT
ejpam-5924	91	10	t	t	PROPN
ejpam-5924	91	11	,	,	PUNCT
ejpam-5924	91	12	τ	τ	PROPN
ejpam-5924	91	13	,	,	PUNCT
ejpam-5924	91	14	ξ)ai−1dτdξ	ξ)ai−1dτdξ	NOUN
ejpam-5924	91	15	,	,	PUNCT
ejpam-5924	91	16	i	i	PRON
ejpam-5924	91	17	≥	≥	VERB
ejpam-5924	91	18	1	1	NUM
ejpam-5924	91	19	.	.	PUNCT
ejpam-5924	91	20	(	(	PUNCT
ejpam-5924	91	21	13	13	NUM
ejpam-5924	91	22	)	)	SYM
ejpam-5924	91	23	4	4	NUM
ejpam-5924	91	24	.	.	X
ejpam-5924	92	1	ham	ham	NOUN
ejpam-5924	92	2	in	in	ADP
ejpam-5924	92	3	this	this	DET
ejpam-5924	92	4	section	section	NOUN
ejpam-5924	92	5	,	,	PUNCT
ejpam-5924	92	6	we	we	PRON
ejpam-5924	92	7	aim	aim	VERB
ejpam-5924	92	8	to	to	PART
ejpam-5924	92	9	solve	solve	VERB
ejpam-5924	92	10	the	the	DET
ejpam-5924	92	11	nonlinear	nonlinear	ADJ
ejpam-5924	92	12	(	(	PUNCT
ejpam-5924	92	13	fnt	fnt	NOUN
ejpam-5924	92	14	-	-	PUNCT
ejpam-5924	92	15	dfide	dfide	NOUN
ejpam-5924	92	16	)	)	PUNCT
ejpam-5924	92	17	using	use	VERB
ejpam-5924	92	18	the	the	DET
ejpam-5924	92	19	homotopy	homotopy	NOUN
ejpam-5924	92	20	analysis	analysis	NOUN
ejpam-5924	92	21	method	method	NOUN
ejpam-5924	92	22	(	(	PUNCT
ejpam-5924	92	23	ham	ham	NOUN
ejpam-5924	92	24	)	)	PUNCT
ejpam-5924	92	25	.	.	PUNCT
ejpam-5924	93	1	this	this	DET
ejpam-5924	93	2	approach	approach	NOUN
ejpam-5924	93	3	is	be	AUX
ejpam-5924	93	4	novel	novel	ADJ
ejpam-5924	93	5	because	because	SCONJ
ejpam-5924	93	6	,	,	PUNCT
ejpam-5924	93	7	to	to	ADP
ejpam-5924	93	8	the	the	DET
ejpam-5924	93	9	best	good	ADJ
ejpam-5924	93	10	of	of	ADP
ejpam-5924	93	11	our	our	PRON
ejpam-5924	93	12	knowledge	knowledge	NOUN
ejpam-5924	93	13	,	,	PUNCT
ejpam-5924	93	14	previous	previous	ADJ
ejpam-5924	93	15	studies	study	NOUN
ejpam-5924	93	16	have	have	AUX
ejpam-5924	93	17	primarily	primarily	ADV
ejpam-5924	93	18	applied	apply	VERB
ejpam-5924	93	19	ham	ham	NOUN
ejpam-5924	93	20	to	to	PART
ejpam-5924	93	21	solve	solve	VERB
ejpam-5924	93	22	two	two	NUM
ejpam-5924	93	23	-	-	PUNCT
ejpam-5924	93	24	dimensional	dimensional	ADJ
ejpam-5924	93	25	fractional	fractional	ADJ
ejpam-5924	93	26	integrodifferential	integrodifferential	ADJ
ejpam-5924	93	27	equations	equation	NOUN
ejpam-5924	93	28	.	.	PUNCT
ejpam-5924	94	1	consider	consider	VERB
ejpam-5924	94	2	(	(	PUNCT
ejpam-5924	94	3	1	1	NUM
ejpam-5924	94	4	)	)	PUNCT
ejpam-5924	94	5	,	,	PUNCT
ejpam-5924	94	6	where	where	SCONJ
ejpam-5924	94	7	k(s	k(s	PROPN
ejpam-5924	94	8	,	,	PUNCT
ejpam-5924	94	9	t	t	PROPN
ejpam-5924	94	10	,	,	PUNCT
ejpam-5924	94	11	τ	τ	PROPN
ejpam-5924	94	12	,	,	PUNCT
ejpam-5924	94	13	ξ	ξ	X
ejpam-5924	94	14	)	)	PUNCT
ejpam-5924	94	15	and	and	CCONJ
ejpam-5924	94	16	f(s	f(s	PROPN
ejpam-5924	94	17	,	,	PUNCT
ejpam-5924	94	18	t	t	PROPN
ejpam-5924	94	19	)	)	PUNCT
ejpam-5924	94	20	are	be	AUX
ejpam-5924	94	21	known	know	VERB
ejpam-5924	94	22	functions	function	NOUN
ejpam-5924	94	23	,	,	PUNCT
ejpam-5924	94	24	and	and	CCONJ
ejpam-5924	95	1	γ(τ	γ(τ	PROPN
ejpam-5924	95	2	,	,	PUNCT
ejpam-5924	95	3	ξ	ξ	PROPN
ejpam-5924	95	4	,	,	PUNCT
ejpam-5924	95	5	dαu(τ	dαu(τ	PROPN
ejpam-5924	95	6	,	,	PUNCT
ejpam-5924	95	7	ξ	ξ	NOUN
ejpam-5924	95	8	)	)	PUNCT
ejpam-5924	95	9	)	)	PUNCT
ejpam-5924	95	10	is	be	AUX
ejpam-5924	95	11	a	a	DET
ejpam-5924	95	12	known	know	VERB
ejpam-5924	95	13	nonlinear	nonlinear	ADJ
ejpam-5924	95	14	function	function	NOUN
ejpam-5924	95	15	of	of	ADP
ejpam-5924	95	16	dαu	dαu	NOUN
ejpam-5924	95	17	.	.	PUNCT
ejpam-5924	96	1	to	to	PART
ejpam-5924	96	2	describe	describe	VERB
ejpam-5924	96	3	the	the	DET
ejpam-5924	96	4	method	method	NOUN
ejpam-5924	96	5	,	,	PUNCT
ejpam-5924	96	6	we	we	PRON
ejpam-5924	96	7	define	define	VERB
ejpam-5924	96	8	the	the	DET
ejpam-5924	96	9	nonlinear	nonlinear	ADJ
ejpam-5924	96	10	operator	operator	NOUN
ejpam-5924	96	11	n	n	NOUN
ejpam-5924	96	12	:	:	PUNCT
ejpam-5924	96	13	n	n	PROPN
ejpam-5924	97	1	[	[	X
ejpam-5924	97	2	dαu	dαu	X
ejpam-5924	97	3	]	]	X
ejpam-5924	97	4	=	=	SYM
ejpam-5924	97	5	dαu(x	dαu(x	PROPN
ejpam-5924	97	6	,	,	PUNCT
ejpam-5924	97	7	t)−	t)−	PROPN
ejpam-5924	97	8	f(x	f(x	PROPN
ejpam-5924	97	9	,	,	PUNCT
ejpam-5924	97	10	t)−	t)−	PROPN
ejpam-5924	97	11	∫	∫	PROPN
ejpam-5924	98	1	b	b	PROPN
ejpam-5924	98	2	a	a	DET
ejpam-5924	98	3	∫	∫	PROPN
ejpam-5924	98	4	d	d	X
ejpam-5924	98	5	c	c	PROPN
ejpam-5924	98	6	k(x	k(x	PROPN
ejpam-5924	98	7	,	,	PUNCT
ejpam-5924	98	8	t	t	PROPN
ejpam-5924	98	9	,	,	PUNCT
ejpam-5924	98	10	τ	τ	PROPN
ejpam-5924	98	11	,	,	PUNCT
ejpam-5924	98	12	ξ)γ(τ	ξ)γ(τ	PROPN
ejpam-5924	98	13	,	,	PUNCT
ejpam-5924	98	14	ξ	ξ	PROPN
ejpam-5924	98	15	,	,	PUNCT
ejpam-5924	98	16	dαu(τ	dαu(τ	PROPN
ejpam-5924	98	17	,	,	PUNCT
ejpam-5924	98	18	ξ))dτdξ	ξ))dτdξ	SYM
ejpam-5924	98	19	=	=	SYM
ejpam-5924	98	20	0	0	PROPN
ejpam-5924	98	21	.	.	PUNCT
ejpam-5924	99	1	(	(	PUNCT
ejpam-5924	99	2	14	14	NUM
ejpam-5924	99	3	)	)	PUNCT
ejpam-5924	99	4	let	let	VERB
ejpam-5924	99	5	dαu0(s	dαu0(s	NUM
ejpam-5924	99	6	,	,	PUNCT
ejpam-5924	99	7	t	t	PROPN
ejpam-5924	99	8	)	)	PUNCT
ejpam-5924	99	9	denote	denote	VERB
ejpam-5924	99	10	an	an	DET
ejpam-5924	99	11	initial	initial	ADJ
ejpam-5924	99	12	guess	guess	NOUN
ejpam-5924	99	13	for	for	ADP
ejpam-5924	99	14	the	the	DET
ejpam-5924	99	15	exact	exact	ADJ
ejpam-5924	99	16	solution	solution	NOUN
ejpam-5924	99	17	u(s	u(s	PROPN
ejpam-5924	99	18	,	,	PUNCT
ejpam-5924	99	19	t	t	PROPN
ejpam-5924	99	20	)	)	PUNCT
ejpam-5924	99	21	,	,	PUNCT
ejpam-5924	99	22	and	and	CCONJ
ejpam-5924	99	23	choose	choose	VERB
ejpam-5924	99	24	a	a	DET
ejpam-5924	99	25	non	non	ADJ
ejpam-5924	99	26	-	-	ADJ
ejpam-5924	99	27	zero	zero	ADJ
ejpam-5924	99	28	auxiliary	auxiliary	ADJ
ejpam-5924	99	29	parameter	parameter	NOUN
ejpam-5924	99	30	h	h	NOUN
ejpam-5924	99	31	̸=	̸=	PROPN
ejpam-5924	99	32	0	0	NUM
ejpam-5924	99	33	,	,	PUNCT
ejpam-5924	99	34	an	an	DET
ejpam-5924	99	35	auxiliary	auxiliary	ADJ
ejpam-5924	99	36	function	function	NOUN
ejpam-5924	99	37	h(s	h(s	PROPN
ejpam-5924	99	38	,	,	PUNCT
ejpam-5924	99	39	t	t	PROPN
ejpam-5924	99	40	)	)	PUNCT
ejpam-5924	99	41	,	,	PUNCT
ejpam-5924	99	42	and	and	CCONJ
ejpam-5924	99	43	linear	linear	ADJ
ejpam-5924	99	44	operator	operator	NOUN
ejpam-5924	99	45	l	l	NOUN
ejpam-5924	99	46	,	,	PUNCT
ejpam-5924	99	47	such	such	ADJ
ejpam-5924	99	48	that	that	SCONJ
ejpam-5924	99	49	l[e(s	l[e(s	PROPN
ejpam-5924	99	50	,	,	PUNCT
ejpam-5924	99	51	t	t	PROPN
ejpam-5924	99	52	)	)	PUNCT
ejpam-5924	99	53	]	]	PUNCT
ejpam-5924	100	1	=	=	PUNCT
ejpam-5924	100	2	0	0	PUNCT
ejpam-5924	100	3	whenever	whenever	SCONJ
ejpam-5924	100	4	e(s	e(s	PROPN
ejpam-5924	100	5	,	,	PUNCT
ejpam-5924	100	6	t	t	PROPN
ejpam-5924	100	7	)	)	PUNCT
ejpam-5924	100	8	=	=	NOUN
ejpam-5924	100	9	0	0	X
ejpam-5924	100	10	.	.	PUNCT
ejpam-5924	101	1	for	for	ADP
ejpam-5924	101	2	p	p	PROPN
ejpam-5924	101	3	∈	∈	PROPN
ejpam-5924	102	1	[	[	X
ejpam-5924	102	2	0	0	NUM
ejpam-5924	102	3	,	,	PUNCT
ejpam-5924	102	4	1	1	NUM
ejpam-5924	102	5	]	]	PUNCT
ejpam-5924	102	6	,	,	PUNCT
ejpam-5924	102	7	we	we	PRON
ejpam-5924	102	8	construct	construct	VERB
ejpam-5924	102	9	the	the	DET
ejpam-5924	102	10	following	follow	VERB
ejpam-5924	102	11	homotopy	homotopy	NOUN
ejpam-5924	102	12	:	:	PUNCT
ejpam-5924	102	13	(	(	PUNCT
ejpam-5924	102	14	1−	1−	NUM
ejpam-5924	102	15	p)[ϕ(s	p)[ϕ(s	X
ejpam-5924	102	16	,	,	PUNCT
ejpam-5924	102	17	t	t	PROPN
ejpam-5924	102	18	;	;	PUNCT
ejpam-5924	102	19	p)−dαu0(x	p)−dαu0(x	PROPN
ejpam-5924	102	20	,	,	PUNCT
ejpam-5924	102	21	t)]−	t)]−	ADV
ejpam-5924	102	22	phh(s	phh(s	NOUN
ejpam-5924	102	23	,	,	PUNCT
ejpam-5924	102	24	t)n	t)n	PUNCT
ejpam-5924	103	1	[	[	X
ejpam-5924	103	2	ϕ(s	ϕ(s	PROPN
ejpam-5924	103	3	,	,	PUNCT
ejpam-5924	103	4	t	t	PROPN
ejpam-5924	103	5	;	;	PUNCT
ejpam-5924	103	6	p	p	X
ejpam-5924	103	7	)	)	PUNCT
ejpam-5924	103	8	]	]	PUNCT
ejpam-5924	103	9	=	=	SYM
ejpam-5924	103	10	h[ϕ(s	h[ϕ(s	X
ejpam-5924	103	11	,	,	PUNCT
ejpam-5924	103	12	t	t	PROPN
ejpam-5924	103	13	;	;	PUNCT
ejpam-5924	103	14	p);dαu0(s	p);dαu0(s	PROPN
ejpam-5924	103	15	,	,	PUNCT
ejpam-5924	103	16	t	t	PROPN
ejpam-5924	103	17	)	)	PUNCT
ejpam-5924	103	18	,	,	PUNCT
ejpam-5924	103	19	h(s	h(s	PROPN
ejpam-5924	103	20	,	,	PUNCT
ejpam-5924	103	21	t	t	PROPN
ejpam-5924	103	22	)	)	PUNCT
ejpam-5924	103	23	,	,	PUNCT
ejpam-5924	103	24	h	h	NOUN
ejpam-5924	103	25	,	,	PUNCT
ejpam-5924	103	26	p	p	X
ejpam-5924	103	27	]	]	X
ejpam-5924	103	28	.	.	PUNCT
ejpam-5924	104	1	(	(	PUNCT
ejpam-5924	104	2	15	15	NUM
ejpam-5924	104	3	)	)	PUNCT
ejpam-5924	104	4	a.	a.	NOUN
ejpam-5924	104	5	m.	m.	NOUN
ejpam-5924	104	6	al	al	PROPN
ejpam-5924	104	7	-	-	PUNCT
ejpam-5924	104	8	bugami	bugami	NOUN
ejpam-5924	104	9	,	,	PUNCT
ejpam-5924	104	10	n.	n.	NOUN
ejpam-5924	104	11	a.	a.	NOUN
ejpam-5924	104	12	alharbi	alharbi	PROPN
ejpam-5924	104	13	,	,	PUNCT
ejpam-5924	104	14	a.	a.	NOUN
ejpam-5924	104	15	m.	m.	PROPN
ejpam-5924	104	16	s.	s.	PROPN
ejpam-5924	104	17	mahdy	mahdy	PROPN
ejpam-5924	104	18	/	/	SYM
ejpam-5924	104	19	eur	eur	PROPN
ejpam-5924	104	20	.	.	PUNCT
ejpam-5924	105	1	j.	j.	PROPN
ejpam-5924	105	2	pure	pure	PROPN
ejpam-5924	105	3	appl	appl	PROPN
ejpam-5924	105	4	.	.	PROPN
ejpam-5924	105	5	math	math	PROPN
ejpam-5924	105	6	,	,	PUNCT
ejpam-5924	105	7	18	18	NUM
ejpam-5924	105	8	(	(	PUNCT
ejpam-5924	105	9	2	2	NUM
ejpam-5924	105	10	)	)	PUNCT
ejpam-5924	105	11	(	(	PUNCT
ejpam-5924	105	12	2025	2025	NUM
ejpam-5924	105	13	)	)	PUNCT
ejpam-5924	105	14	,	,	PUNCT
ejpam-5924	105	15	5924	5924	NUM
ejpam-5924	105	16	6	6	NUM
ejpam-5924	105	17	of	of	ADP
ejpam-5924	105	18	14	14	NUM
ejpam-5924	105	19	it	it	PRON
ejpam-5924	105	20	is	be	AUX
ejpam-5924	105	21	important	important	ADJ
ejpam-5924	105	22	to	to	PART
ejpam-5924	105	23	emphasize	emphasize	VERB
ejpam-5924	105	24	that	that	SCONJ
ejpam-5924	105	25	we	we	PRON
ejpam-5924	105	26	have	have	VERB
ejpam-5924	105	27	significant	significant	ADJ
ejpam-5924	105	28	flexibility	flexibility	NOUN
ejpam-5924	105	29	in	in	ADP
ejpam-5924	105	30	choosing	choose	VERB
ejpam-5924	105	31	the	the	DET
ejpam-5924	105	32	initial	initial	ADJ
ejpam-5924	105	33	guess	guess	NOUN
ejpam-5924	105	34	dαu0(s	dαu0(s	NUM
ejpam-5924	105	35	,	,	PUNCT
ejpam-5924	105	36	t	t	PROPN
ejpam-5924	105	37	)	)	PUNCT
ejpam-5924	105	38	,	,	PUNCT
ejpam-5924	105	39	the	the	DET
ejpam-5924	105	40	auxiliary	auxiliary	ADJ
ejpam-5924	105	41	linear	linear	ADJ
ejpam-5924	105	42	operator	operator	NOUN
ejpam-5924	105	43	l	l	NOUN
ejpam-5924	105	44	,	,	PUNCT
ejpam-5924	105	45	the	the	DET
ejpam-5924	105	46	non	non	ADJ
ejpam-5924	105	47	-	-	ADJ
ejpam-5924	105	48	zero	zero	NUM
ejpam-5924	105	49	parameter	parameter	NOUN
ejpam-5924	105	50	h	h	NOUN
ejpam-5924	105	51	,	,	PUNCT
ejpam-5924	105	52	and	and	CCONJ
ejpam-5924	105	53	the	the	DET
ejpam-5924	105	54	auxiliary	auxiliary	ADJ
ejpam-5924	105	55	function	function	NOUN
ejpam-5924	105	56	h(s	h(s	PROPN
ejpam-5924	105	57	,	,	PUNCT
ejpam-5924	105	58	t	t	PROPN
ejpam-5924	105	59	)	)	PUNCT
ejpam-5924	105	60	.	.	PUNCT
ejpam-5924	106	1	additionally	additionally	ADV
ejpam-5924	106	2	,	,	PUNCT
ejpam-5924	106	3	let	let	VERB
ejpam-5924	106	4	h̃	h̃	PRON
ejpam-5924	106	5	be	be	AUX
ejpam-5924	106	6	a	a	DET
ejpam-5924	106	7	secondary	secondary	ADJ
ejpam-5924	106	8	auxiliary	auxiliary	ADJ
ejpam-5924	106	9	function	function	NOUN
ejpam-5924	106	10	that	that	PRON
ejpam-5924	106	11	ensures	ensure	VERB
ejpam-5924	106	12	the	the	DET
ejpam-5924	106	13	homotopy	homotopy	NOUN
ejpam-5924	106	14	satisfies	satisfy	VERB
ejpam-5924	106	15	the	the	DET
ejpam-5924	106	16	condition	condition	NOUN
ejpam-5924	106	17	:	:	PUNCT
ejpam-5924	106	18	h̃[ϕ(s	h̃[ϕ(s	PROPN
ejpam-5924	106	19	,	,	PUNCT
ejpam-5924	106	20	t	t	PROPN
ejpam-5924	106	21	;	;	PUNCT
ejpam-5924	106	22	p);dαu0(s	p);dαu0(s	PROPN
ejpam-5924	106	23	,	,	PUNCT
ejpam-5924	106	24	t	t	PROPN
ejpam-5924	106	25	)	)	PUNCT
ejpam-5924	106	26	,	,	PUNCT
ejpam-5924	106	27	h(s	h(s	PROPN
ejpam-5924	106	28	,	,	PUNCT
ejpam-5924	106	29	t	t	PROPN
ejpam-5924	106	30	)	)	PUNCT
ejpam-5924	106	31	,	,	PUNCT
ejpam-5924	106	32	h	h	NOUN
ejpam-5924	106	33	,	,	PUNCT
ejpam-5924	106	34	p	p	X
ejpam-5924	106	35	]	]	X
ejpam-5924	106	36	=	=	SYM
ejpam-5924	106	37	0	0	X
ejpam-5924	106	38	.	.	PUNCT
ejpam-5924	107	1	(	(	PUNCT
ejpam-5924	107	2	16	16	NUM
ejpam-5924	107	3	)	)	PUNCT
ejpam-5924	107	4	thus	thus	ADV
ejpam-5924	107	5	,	,	PUNCT
ejpam-5924	107	6	the	the	DET
ejpam-5924	107	7	homotopy	homotopy	NOUN
ejpam-5924	107	8	equation	equation	NOUN
ejpam-5924	107	9	can	can	AUX
ejpam-5924	107	10	be	be	AUX
ejpam-5924	107	11	written	write	VERB
ejpam-5924	107	12	as	as	ADP
ejpam-5924	107	13	:	:	PUNCT
ejpam-5924	107	14	(	(	PUNCT
ejpam-5924	107	15	1−	1−	NUM
ejpam-5924	107	16	p)[ϕ(s	p)[ϕ(s	X
ejpam-5924	107	17	,	,	PUNCT
ejpam-5924	107	18	t	t	PROPN
ejpam-5924	107	19	;	;	PUNCT
ejpam-5924	107	20	p)−dαu0(x	p)−dαu0(x	PROPN
ejpam-5924	107	21	,	,	PUNCT
ejpam-5924	107	22	t	t	PROPN
ejpam-5924	107	23	)	)	PUNCT
ejpam-5924	107	24	]	]	PUNCT
ejpam-5924	108	1	=	=	PUNCT
ejpam-5924	108	2	phh(s	phh(s	PROPN
ejpam-5924	108	3	,	,	PUNCT
ejpam-5924	108	4	t)n	t)n	PUNCT
ejpam-5924	109	1	[	[	X
ejpam-5924	109	2	ϕ(s	ϕ(s	PROPN
ejpam-5924	109	3	,	,	PUNCT
ejpam-5924	109	4	t	t	PROPN
ejpam-5924	109	5	;	;	PUNCT
ejpam-5924	109	6	p	p	X
ejpam-5924	109	7	)	)	PUNCT
ejpam-5924	109	8	]	]	PUNCT
ejpam-5924	109	9	,	,	PUNCT
ejpam-5924	109	10	(	(	PUNCT
ejpam-5924	109	11	17	17	NUM
ejpam-5924	109	12	)	)	PUNCT
ejpam-5924	109	13	when	when	SCONJ
ejpam-5924	109	14	p	p	NOUN
ejpam-5924	109	15	=	=	NOUN
ejpam-5924	109	16	0	0	NUM
ejpam-5924	109	17	,	,	PUNCT
ejpam-5924	109	18	from	from	ADP
ejpam-5924	109	19	equation	equation	NOUN
ejpam-5924	109	20	(	(	PUNCT
ejpam-5924	109	21	17	17	NUM
ejpam-5924	109	22	)	)	PUNCT
ejpam-5924	109	23	,	,	PUNCT
ejpam-5924	109	24	we	we	PRON
ejpam-5924	109	25	get	get	VERB
ejpam-5924	109	26	:	:	PUNCT
ejpam-5924	109	27	ϕ(s	ϕ(s	PROPN
ejpam-5924	109	28	,	,	PUNCT
ejpam-5924	109	29	t	t	PROPN
ejpam-5924	109	30	;	;	PUNCT
ejpam-5924	109	31	p	p	X
ejpam-5924	109	32	)	)	PUNCT
ejpam-5924	109	33	=	=	SYM
ejpam-5924	109	34	dαu0(s	dαu0(s	NUM
ejpam-5924	109	35	,	,	PUNCT
ejpam-5924	109	36	t	t	PROPN
ejpam-5924	109	37	)	)	PUNCT
ejpam-5924	109	38	.	.	PUNCT
ejpam-5924	110	1	(	(	PUNCT
ejpam-5924	110	2	18	18	NUM
ejpam-5924	110	3	)	)	PUNCT
ejpam-5924	110	4	furthermore	furthermore	ADV
ejpam-5924	110	5	,	,	PUNCT
ejpam-5924	110	6	when	when	SCONJ
ejpam-5924	110	7	p	p	NOUN
ejpam-5924	110	8	=	=	NOUN
ejpam-5924	110	9	1	1	NUM
ejpam-5924	110	10	and	and	CCONJ
ejpam-5924	110	11	h	h	NOUN
ejpam-5924	110	12	̸=	̸=	PROPN
ejpam-5924	110	13	0	0	NUM
ejpam-5924	110	14	,	,	PUNCT
ejpam-5924	110	15	h(s	h(s	PROPN
ejpam-5924	110	16	,	,	PUNCT
ejpam-5924	110	17	t	t	PROPN
ejpam-5924	110	18	)	)	PUNCT
ejpam-5924	110	19	̸=	̸=	PROPN
ejpam-5924	110	20	0	0	NUM
ejpam-5924	110	21	,	,	PUNCT
ejpam-5924	110	22	equation	equation	NOUN
ejpam-5924	110	23	(	(	PUNCT
ejpam-5924	110	24	17	17	NUM
ejpam-5924	110	25	)	)	PUNCT
ejpam-5924	110	26	becomes	become	VERB
ejpam-5924	110	27	:	:	PUNCT
ejpam-5924	110	28	ϕ(s	ϕ(s	PROPN
ejpam-5924	110	29	,	,	PUNCT
ejpam-5924	110	30	t	t	PROPN
ejpam-5924	110	31	;	;	PUNCT
ejpam-5924	110	32	1	1	X
ejpam-5924	110	33	)	)	PUNCT
ejpam-5924	110	34	=	=	SYM
ejpam-5924	111	1	dαu(s	dαu(s	PROPN
ejpam-5924	111	2	,	,	PUNCT
ejpam-5924	111	3	t	t	PROPN
ejpam-5924	111	4	)	)	PUNCT
ejpam-5924	111	5	.	.	PUNCT
ejpam-5924	112	1	(	(	PUNCT
ejpam-5924	112	2	19	19	NUM
ejpam-5924	112	3	)	)	PUNCT
ejpam-5924	112	4	if	if	SCONJ
ejpam-5924	112	5	we	we	PRON
ejpam-5924	112	6	observe	observe	VERB
ejpam-5924	112	7	the	the	DET
ejpam-5924	112	8	value	value	NOUN
ejpam-5924	112	9	of	of	ADP
ejpam-5924	112	10	p	p	NOUN
ejpam-5924	112	11	from	from	ADP
ejpam-5924	112	12	0	0	NUM
ejpam-5924	112	13	to	to	PART
ejpam-5924	112	14	1	1	NUM
ejpam-5924	112	15	m	m	NOUN
ejpam-5924	112	16	the	the	DET
ejpam-5924	112	17	embedding	embed	VERB
ejpam-5924	112	18	parameter	parameter	NOUN
ejpam-5924	112	19	gradually	gradually	ADV
ejpam-5924	112	20	increases	increase	VERB
ejpam-5924	112	21	for	for	ADP
ejpam-5924	112	22	ϕ(s	ϕ(s	PROPN
ejpam-5924	112	23	,	,	PUNCT
ejpam-5924	112	24	t	t	PROPN
ejpam-5924	112	25	;	;	PUNCT
ejpam-5924	112	26	p	p	X
ejpam-5924	112	27	)	)	PUNCT
ejpam-5924	112	28	in	in	ADP
ejpam-5924	112	29	equations	equation	NOUN
ejpam-5924	112	30	(	(	PUNCT
ejpam-5924	112	31	1	1	NUM
ejpam-5924	112	32	)	)	PUNCT
ejpam-5924	112	33	and	and	CCONJ
ejpam-5924	112	34	(	(	PUNCT
ejpam-5924	112	35	19	19	NUM
ejpam-5924	112	36	)	)	PUNCT
ejpam-5924	112	37	,	,	PUNCT
ejpam-5924	112	38	such	such	ADJ
ejpam-5924	112	39	that	that	SCONJ
ejpam-5924	112	40	it	it	PRON
ejpam-5924	112	41	begins	begin	VERB
ejpam-5924	112	42	from	from	ADP
ejpam-5924	112	43	the	the	DET
ejpam-5924	112	44	initial	initial	ADJ
ejpam-5924	112	45	approximation	approximation	NOUN
ejpam-5924	112	46	and	and	CCONJ
ejpam-5924	112	47	reaches	reach	VERB
ejpam-5924	112	48	the	the	DET
ejpam-5924	112	49	exact	exact	ADJ
ejpam-5924	112	50	solution	solution	NOUN
ejpam-5924	112	51	.	.	PUNCT
ejpam-5924	113	1	we	we	PRON
ejpam-5924	113	2	refer	refer	VERB
ejpam-5924	113	3	to	to	ADP
ejpam-5924	113	4	this	this	DET
ejpam-5924	113	5	change	change	NOUN
ejpam-5924	113	6	in	in	ADP
ejpam-5924	113	7	homotopy	homotopy	NOUN
ejpam-5924	113	8	deformation	deformation	NOUN
ejpam-5924	113	9	,	,	PUNCT
ejpam-5924	113	10	and	and	CCONJ
ejpam-5924	113	11	we	we	PRON
ejpam-5924	113	12	can	can	AUX
ejpam-5924	113	13	be	be	AUX
ejpam-5924	113	14	expressed	express	VERB
ejpam-5924	113	15	in	in	ADP
ejpam-5924	113	16	the	the	DET
ejpam-5924	113	17	following	follow	VERB
ejpam-5924	113	18	form	form	NOUN
ejpam-5924	113	19	:	:	PUNCT
ejpam-5924	113	20	ϕ(s	ϕ(s	PROPN
ejpam-5924	113	21	,	,	PUNCT
ejpam-5924	113	22	t	t	PROPN
ejpam-5924	113	23	;	;	PUNCT
ejpam-5924	113	24	p	p	X
ejpam-5924	113	25	)	)	PUNCT
ejpam-5924	113	26	=	=	SYM
ejpam-5924	113	27	dαu0(x	dαu0(x	NOUN
ejpam-5924	113	28	,	,	PUNCT
ejpam-5924	113	29	t	t	PROPN
ejpam-5924	113	30	)	)	PUNCT
ejpam-5924	114	1	+	+	CCONJ
ejpam-5924	114	2	∞∑	∞∑	NUM
ejpam-5924	114	3	r=1	r=1	NOUN
ejpam-5924	114	4	dαur(s	dαur(s	NOUN
ejpam-5924	114	5	,	,	PUNCT
ejpam-5924	114	6	t)p	t)p	NOUN
ejpam-5924	114	7	r.	r.	NOUN
ejpam-5924	114	8	(	(	PUNCT
ejpam-5924	114	9	20	20	NUM
ejpam-5924	114	10	)	)	PUNCT
ejpam-5924	114	11	here	here	ADV
ejpam-5924	114	12	,	,	PUNCT
ejpam-5924	114	13	ur(s	ur(s	PROPN
ejpam-5924	114	14	,	,	PUNCT
ejpam-5924	114	15	t	t	PROPN
ejpam-5924	114	16	)	)	PUNCT
ejpam-5924	114	17	is	be	AUX
ejpam-5924	114	18	given	give	VERB
ejpam-5924	114	19	by	by	ADP
ejpam-5924	114	20	:	:	PUNCT
ejpam-5924	114	21	dαur(s	dαur(s	PROPN
ejpam-5924	114	22	,	,	PUNCT
ejpam-5924	114	23	t	t	PROPN
ejpam-5924	114	24	)	)	PUNCT
ejpam-5924	114	25	=	=	SYM
ejpam-5924	115	1	1	1	NUM
ejpam-5924	115	2	r	r	NOUN
ejpam-5924	115	3	!	!	PUNCT
ejpam-5924	116	1	∂ϕ(s	∂ϕ(s	PROPN
ejpam-5924	116	2	,	,	PUNCT
ejpam-5924	116	3	t	t	PROPN
ejpam-5924	116	4	;	;	PUNCT
ejpam-5924	116	5	p	p	X
ejpam-5924	116	6	)	)	PUNCT
ejpam-5924	116	7	∂pr	∂pr	PROPN
ejpam-5924	116	8	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5924	116	9	p=0	p=0	PROPN
ejpam-5924	116	10	(	(	PUNCT
ejpam-5924	116	11	21	21	NUM
ejpam-5924	116	12	)	)	PUNCT
ejpam-5924	116	13	based	base	VERB
ejpam-5924	116	14	on	on	ADP
ejpam-5924	116	15	these	these	DET
ejpam-5924	116	16	assumptions	assumption	NOUN
ejpam-5924	116	17	,	,	PUNCT
ejpam-5924	116	18	we	we	PRON
ejpam-5924	116	19	can	can	AUX
ejpam-5924	116	20	write	write	VERB
ejpam-5924	116	21	the	the	DET
ejpam-5924	116	22	exact	exact	ADJ
ejpam-5924	116	23	solution	solution	NOUN
ejpam-5924	116	24	as	as	ADP
ejpam-5924	116	25	:	:	PUNCT
ejpam-5924	116	26	dαu(s	dαu(s	PROPN
ejpam-5924	116	27	,	,	PUNCT
ejpam-5924	116	28	t	t	PROPN
ejpam-5924	116	29	)	)	PUNCT
ejpam-5924	116	30	=	=	SYM
ejpam-5924	116	31	ϕ(s	ϕ(s	PROPN
ejpam-5924	116	32	,	,	PUNCT
ejpam-5924	116	33	t	t	PROPN
ejpam-5924	116	34	;	;	PUNCT
ejpam-5924	116	35	1	1	X
ejpam-5924	116	36	)	)	PUNCT
ejpam-5924	116	37	=	=	SYM
ejpam-5924	116	38	dαu0(s	dαu0(s	NUM
ejpam-5924	116	39	,	,	PUNCT
ejpam-5924	116	40	t	t	PROPN
ejpam-5924	116	41	)	)	PUNCT
ejpam-5924	116	42	+	+	CCONJ
ejpam-5924	117	1	∞∑	∞∑	NUM
ejpam-5924	117	2	r=1	r=1	NOUN
ejpam-5924	117	3	dαur(s	dαur(s	NOUN
ejpam-5924	117	4	,	,	PUNCT
ejpam-5924	117	5	t)p	t)p	NOUN
ejpam-5924	117	6	(	(	PUNCT
ejpam-5924	117	7	22	22	NUM
ejpam-5924	117	8	)	)	PUNCT
ejpam-5924	117	9	thus	thus	ADV
ejpam-5924	117	10	,	,	PUNCT
ejpam-5924	117	11	the	the	DET
ejpam-5924	117	12	sequence	sequence	NOUN
ejpam-5924	117	13	of	of	ADP
ejpam-5924	117	14	approximations	approximation	NOUN
ejpam-5924	117	15	for	for	ADP
ejpam-5924	117	16	dαu(s	dαu(s	PROPN
ejpam-5924	117	17	,	,	PUNCT
ejpam-5924	117	18	t	t	PROPN
ejpam-5924	117	19	)	)	PUNCT
ejpam-5924	117	20	can	can	AUX
ejpam-5924	117	21	be	be	AUX
ejpam-5924	117	22	expressed	express	VERB
ejpam-5924	117	23	as	as	ADP
ejpam-5924	117	24	:	:	PUNCT
ejpam-5924	117	25	dαūn(s	dαūn(s	NOUN
ejpam-5924	117	26	,	,	PUNCT
ejpam-5924	117	27	t	t	PROPN
ejpam-5924	117	28	)	)	PUNCT
ejpam-5924	117	29	=	=	PRON
ejpam-5924	117	30	{	{	PUNCT
ejpam-5924	117	31	dαu0(s	dαu0(s	NUM
ejpam-5924	117	32	,	,	PUNCT
ejpam-5924	117	33	t	t	PROPN
ejpam-5924	117	34	)	)	PUNCT
ejpam-5924	117	35	,	,	PUNCT
ejpam-5924	117	36	d	d	PROPN
ejpam-5924	117	37	αu1(s	αu1(s	PROPN
ejpam-5924	117	38	,	,	PUNCT
ejpam-5924	117	39	t	t	PROPN
ejpam-5924	117	40	)	)	PUNCT
ejpam-5924	117	41	,	,	PUNCT
ejpam-5924	117	42	....	....	PUNCT
ejpam-5924	117	43	,	,	PUNCT
ejpam-5924	117	44	d	d	PROPN
ejpam-5924	117	45	αun(s	αun(s	PROPN
ejpam-5924	117	46	,	,	PUNCT
ejpam-5924	117	47	t	t	PROPN
ejpam-5924	117	48	)	)	PUNCT
ejpam-5924	117	49	}	}	PUNCT
ejpam-5924	117	50	(	(	PUNCT
ejpam-5924	117	51	23	23	NUM
ejpam-5924	117	52	)	)	PUNCT
ejpam-5924	117	53	the	the	DET
ejpam-5924	117	54	zero	zero	NUM
ejpam-5924	117	55	-	-	PUNCT
ejpam-5924	117	56	order	order	NOUN
ejpam-5924	117	57	deformation	deformation	NOUN
ejpam-5924	117	58	equation	equation	NOUN
ejpam-5924	117	59	(	(	PUNCT
ejpam-5924	117	60	21	21	NUM
ejpam-5924	117	61	)	)	PUNCT
ejpam-5924	117	62	,	,	PUNCT
ejpam-5924	117	63	in	in	ADP
ejpam-5924	117	64	accordance	accordance	NOUN
ejpam-5924	117	65	with	with	ADP
ejpam-5924	117	66	equation	equation	NOUN
ejpam-5924	117	67	(	(	PUNCT
ejpam-5924	117	68	17	17	NUM
ejpam-5924	117	69	)	)	PUNCT
ejpam-5924	117	70	,	,	PUNCT
ejpam-5924	117	71	can	can	AUX
ejpam-5924	117	72	be	be	AUX
ejpam-5924	117	73	used	use	VERB
ejpam-5924	117	74	to	to	PART
ejpam-5924	117	75	construct	construct	VERB
ejpam-5924	117	76	the	the	DET
ejpam-5924	117	77	governing	govern	VERB
ejpam-5924	117	78	equation	equation	NOUN
ejpam-5924	117	79	of	of	ADP
ejpam-5924	117	80	dαum(s	dαum(s	PROPN
ejpam-5924	117	81	,	,	PUNCT
ejpam-5924	117	82	t	t	PROPN
ejpam-5924	117	83	)	)	PUNCT
ejpam-5924	117	84	.	.	PUNCT
ejpam-5924	118	1	the	the	DET
ejpam-5924	118	2	called	call	VERB
ejpam-5924	118	3	mth	mth	NOUN
ejpam-5924	118	4	-	-	PUNCT
ejpam-5924	118	5	order	order	NOUN
ejpam-5924	118	6	deformation	deformation	NOUN
ejpam-5924	118	7	equation	equation	NOUN
ejpam-5924	118	8	gets	get	VERB
ejpam-5924	118	9	by	by	ADP
ejpam-5924	118	10	differentiating	differentiate	VERB
ejpam-5924	118	11	the	the	DET
ejpam-5924	118	12	zero	zero	NUM
ejpam-5924	118	13	-	-	PUNCT
ejpam-5924	118	14	order	order	NOUN
ejpam-5924	118	15	deformation	deformation	NOUN
ejpam-5924	118	16	equation	equation	NOUN
ejpam-5924	118	17	(	(	PUNCT
ejpam-5924	118	18	17	17	NUM
ejpam-5924	118	19	)	)	PUNCT
ejpam-5924	118	20	r	r	NOUN
ejpam-5924	118	21	times	time	NOUN
ejpam-5924	118	22	with	with	ADP
ejpam-5924	118	23	regard	regard	NOUN
ejpam-5924	118	24	to	to	ADP
ejpam-5924	118	25	p	p	PRON
ejpam-5924	118	26	,	,	PUNCT
ejpam-5924	118	27	dividing	divide	VERB
ejpam-5924	118	28	the	the	DET
ejpam-5924	118	29	result	result	NOUN
ejpam-5924	118	30	by	by	ADP
ejpam-5924	118	31	r	r	NOUN
ejpam-5924	118	32	!	!	PUNCT
ejpam-5924	118	33	,	,	PUNCT
ejpam-5924	118	34	and	and	CCONJ
ejpam-5924	118	35	setting	set	VERB
ejpam-5924	118	36	r	r	NOUN
ejpam-5924	118	37	=	=	SYM
ejpam-5924	118	38	0	0	X
ejpam-5924	118	39	.	.	PUNCT
ejpam-5924	119	1	besed	bese	VERB
ejpam-5924	119	2	on	on	ADP
ejpam-5924	119	3	equation	equation	NOUN
ejpam-5924	119	4	(	(	PUNCT
ejpam-5924	119	5	21	21	NUM
ejpam-5924	119	6	)	)	PUNCT
ejpam-5924	119	7	,	,	PUNCT
ejpam-5924	119	8	the	the	DET
ejpam-5924	119	9	governing	govern	VERB
ejpam-5924	119	10	equation	equation	NOUN
ejpam-5924	119	11	for	for	ADP
ejpam-5924	119	12	dαum(s	dαum(s	PROPN
ejpam-5924	119	13	,	,	PUNCT
ejpam-5924	119	14	t	t	PROPN
ejpam-5924	119	15	)	)	PUNCT
ejpam-5924	119	16	can	can	AUX
ejpam-5924	119	17	be	be	AUX
ejpam-5924	119	18	derived	derive	VERB
ejpam-5924	119	19	from	from	ADP
ejpam-5924	119	20	the	the	DET
ejpam-5924	119	21	zero	zero	NUM
ejpam-5924	119	22	-	-	PUNCT
ejpam-5924	119	23	order	order	NOUN
ejpam-5924	119	24	deformation	deformation	NOUN
ejpam-5924	119	25	equation	equation	NOUN
ejpam-5924	119	26	(	(	PUNCT
ejpam-5924	119	27	17	17	NUM
ejpam-5924	119	28	)	)	PUNCT
ejpam-5924	119	29	.	.	PUNCT
ejpam-5924	120	1	by	by	ADP
ejpam-5924	120	2	differentiating	differentiate	VERB
ejpam-5924	120	3	equation	equation	NOUN
ejpam-5924	120	4	(	(	PUNCT
ejpam-5924	120	5	17	17	NUM
ejpam-5924	120	6	)	)	PUNCT
ejpam-5924	120	7	r	r	NOUN
ejpam-5924	120	8	times	time	NOUN
ejpam-5924	120	9	with	with	ADP
ejpam-5924	120	10	a.	a.	PROPN
ejpam-5924	120	11	m.	m.	PROPN
ejpam-5924	120	12	al	al	PROPN
ejpam-5924	120	13	-	-	PUNCT
ejpam-5924	120	14	bugami	bugami	NOUN
ejpam-5924	120	15	,	,	PUNCT
ejpam-5924	120	16	n.	n.	NOUN
ejpam-5924	120	17	a.	a.	NOUN
ejpam-5924	120	18	alharbi	alharbi	PROPN
ejpam-5924	120	19	,	,	PUNCT
ejpam-5924	120	20	a.	a.	NOUN
ejpam-5924	120	21	m.	m.	PROPN
ejpam-5924	120	22	s.	s.	PROPN
ejpam-5924	120	23	mahdy	mahdy	PROPN
ejpam-5924	120	24	/	/	SYM
ejpam-5924	120	25	eur	eur	PROPN
ejpam-5924	120	26	.	.	PUNCT
ejpam-5924	121	1	j.	j.	PROPN
ejpam-5924	121	2	pure	pure	PROPN
ejpam-5924	121	3	appl	appl	PROPN
ejpam-5924	121	4	.	.	PROPN
ejpam-5924	121	5	math	math	PROPN
ejpam-5924	121	6	,	,	PUNCT
ejpam-5924	121	7	18	18	NUM
ejpam-5924	121	8	(	(	PUNCT
ejpam-5924	121	9	2	2	NUM
ejpam-5924	121	10	)	)	PUNCT
ejpam-5924	121	11	(	(	PUNCT
ejpam-5924	121	12	2025	2025	NUM
ejpam-5924	121	13	)	)	PUNCT
ejpam-5924	121	14	,	,	PUNCT
ejpam-5924	121	15	5924	5924	NUM
ejpam-5924	121	16	7	7	NUM
ejpam-5924	121	17	of	of	ADP
ejpam-5924	121	18	14	14	NUM
ejpam-5924	121	19	respect	respect	NOUN
ejpam-5924	121	20	to	to	ADP
ejpam-5924	121	21	r	r	NOUN
ejpam-5924	121	22	,	,	PUNCT
ejpam-5924	121	23	then	then	ADV
ejpam-5924	121	24	dividing	divide	VERB
ejpam-5924	121	25	by	by	ADP
ejpam-5924	121	26	r	r	NOUN
ejpam-5924	121	27	!	!	PUNCT
ejpam-5924	122	1	and	and	CCONJ
ejpam-5924	122	2	setting	set	VERB
ejpam-5924	122	3	p	p	X
ejpam-5924	122	4	=	=	SYM
ejpam-5924	122	5	0	0	NUM
ejpam-5924	122	6	,	,	PUNCT
ejpam-5924	122	7	we	we	PRON
ejpam-5924	122	8	obtain	obtain	VERB
ejpam-5924	122	9	the	the	DET
ejpam-5924	122	10	mth	mth	NOUN
ejpam-5924	122	11	-	-	PUNCT
ejpam-5924	122	12	order	order	NOUN
ejpam-5924	122	13	deformation	deformation	NOUN
ejpam-5924	122	14	equation	equation	NOUN
ejpam-5924	122	15	as	as	SCONJ
ejpam-5924	122	16	follows	follow	VERB
ejpam-5924	122	17	:	:	PUNCT
ejpam-5924	122	18	l[dαur(s	l[dαur(s	ADJ
ejpam-5924	122	19	,	,	PUNCT
ejpam-5924	122	20	t)−	t)−	PROPN
ejpam-5924	122	21	σrd	σrd	NOUN
ejpam-5924	122	22	αur−1(s	αur−1(s	NUM
ejpam-5924	122	23	,	,	PUNCT
ejpam-5924	122	24	t	t	PROPN
ejpam-5924	122	25	)	)	PUNCT
ejpam-5924	122	26	]	]	PUNCT
ejpam-5924	123	1	=	=	SYM
ejpam-5924	123	2	hh(s	hh(s	X
ejpam-5924	123	3	,	,	PUNCT
ejpam-5924	123	4	t)j	t)j	X
ejpam-5924	123	5	(	(	PUNCT
ejpam-5924	123	6	dαūr−1(s	dαūr−1(s	PROPN
ejpam-5924	123	7	,	,	PUNCT
ejpam-5924	123	8	t	t	NOUN
ejpam-5924	123	9	)	)	PUNCT
ejpam-5924	123	10	)	)	PUNCT
ejpam-5924	123	11	dαur(0	dαur(0	PROPN
ejpam-5924	123	12	,	,	PUNCT
ejpam-5924	123	13	0	0	NUM
ejpam-5924	123	14	)	)	PUNCT
ejpam-5924	123	15	=	=	SYM
ejpam-5924	123	16	0	0	PUNCT
ejpam-5924	123	17	(	(	PUNCT
ejpam-5924	123	18	24	24	NUM
ejpam-5924	123	19	)	)	PUNCT
ejpam-5924	124	1	where	where	SCONJ
ejpam-5924	124	2	j	j	PROPN
ejpam-5924	124	3	(	(	PUNCT
ejpam-5924	124	4	dαūr−1(s	dαūr−1(s	PROPN
ejpam-5924	124	5	,	,	PUNCT
ejpam-5924	124	6	t	t	NOUN
ejpam-5924	124	7	)	)	PUNCT
ejpam-5924	124	8	)	)	PUNCT
ejpam-5924	125	1	=	=	SYM
ejpam-5924	126	1	1	1	NUM
ejpam-5924	127	1	(	(	PUNCT
ejpam-5924	127	2	r	r	NOUN
ejpam-5924	127	3	−	−	NOUN
ejpam-5924	127	4	1	1	NUM
ejpam-5924	127	5	)	)	PUNCT
ejpam-5924	127	6	!	!	PUNCT
ejpam-5924	128	1	∂r−1n	∂r−1n	PROPN
ejpam-5924	129	1	[	[	X
ejpam-5924	129	2	ϕ(s	ϕ(s	PROPN
ejpam-5924	129	3	,	,	PUNCT
ejpam-5924	129	4	t	t	PROPN
ejpam-5924	129	5	;	;	PUNCT
ejpam-5924	129	6	p	p	X
ejpam-5924	129	7	)	)	PUNCT
ejpam-5924	129	8	]	]	PUNCT
ejpam-5924	130	1	∂pr−1	∂pr−1	PROPN
ejpam-5924	130	2	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5924	130	3	p=0	p=0	PROPN
ejpam-5924	130	4	(	(	PUNCT
ejpam-5924	130	5	25	25	NUM
ejpam-5924	130	6	)	)	PUNCT
ejpam-5924	130	7	and	and	CCONJ
ejpam-5924	130	8	the	the	DET
ejpam-5924	130	9	condition	condition	NOUN
ejpam-5924	130	10	σr	σr	PROPN
ejpam-5924	130	11	is	be	AUX
ejpam-5924	130	12	defined	define	VERB
ejpam-5924	130	13	as	as	ADP
ejpam-5924	130	14	:	:	PUNCT
ejpam-5924	130	15	σr	σr	PROPN
ejpam-5924	130	16	=	=	PUNCT
ejpam-5924	130	17			X
ejpam-5924	130	18	0	0	NUM
ejpam-5924	130	19	(	(	PUNCT
ejpam-5924	130	20	r	r	NOUN
ejpam-5924	130	21	≤	≤	NUM
ejpam-5924	130	22	0	0	NUM
ejpam-5924	130	23	)	)	PUNCT
ejpam-5924	130	24	1	1	NUM
ejpam-5924	130	25	(	(	PUNCT
ejpam-5924	130	26	r	r	NOUN
ejpam-5924	130	27	>	>	X
ejpam-5924	130	28	0	0	NUM
ejpam-5924	130	29	)	)	PUNCT
ejpam-5924	130	30	(	(	PUNCT
ejpam-5924	130	31	26	26	NUM
ejpam-5924	130	32	)	)	PUNCT
ejpam-5924	130	33	5	5	NUM
ejpam-5924	130	34	.	.	PUNCT
ejpam-5924	130	35	numerical	numerical	PROPN
ejpam-5924	130	36	applications	application	NOUN
ejpam-5924	130	37	application	application	NOUN
ejpam-5924	130	38	1	1	NUM
ejpam-5924	130	39	.	.	PUNCT
ejpam-5924	130	40	consider	consider	VERB
ejpam-5924	130	41	the	the	DET
ejpam-5924	130	42	following	follow	VERB
ejpam-5924	130	43	caputo	caputo	PROPN
ejpam-5924	130	44	fractional	fractional	PROPN
ejpam-5924	130	45	linear	linear	PROPN
ejpam-5924	130	46	fredholm	fredholm	PROPN
ejpam-5924	130	47	integro	integro	ADJ
ejpam-5924	130	48	-	-	PUNCT
ejpam-5924	130	49	differential	differential	NOUN
ejpam-5924	130	50	equation	equation	NOUN
ejpam-5924	130	51	d0.5u(s	d0.5u(s	PROPN
ejpam-5924	130	52	,	,	PUNCT
ejpam-5924	130	53	t	t	PROPN
ejpam-5924	130	54	)	)	PUNCT
ejpam-5924	130	55	=	=	PUNCT
ejpam-5924	131	1	2.256758334	2.256758334	NUM
ejpam-5924	131	2	s	s	PART
ejpam-5924	131	3	√	√	NOUN
ejpam-5924	131	4	t−	t−	PROPN
ejpam-5924	131	5	0.6790610904	0.6790610904	NUM
ejpam-5924	131	6	+	+	CCONJ
ejpam-5924	131	7	∫	∫	PROPN
ejpam-5924	131	8	1	1	NUM
ejpam-5924	131	9	0	0	NUM
ejpam-5924	131	10	∫	∫	PROPN
ejpam-5924	131	11	1	1	NUM
ejpam-5924	131	12	0	0	NUM
ejpam-5924	131	13	√	√	PROPN
ejpam-5924	131	14	τξ	τξ	PRON
ejpam-5924	131	15	d0.5u(τ	d0.5u(τ	PROPN
ejpam-5924	131	16	,	,	PUNCT
ejpam-5924	131	17	ξ)dτdξ	ξ)dτdξ	PROPN
ejpam-5924	131	18	(	(	PUNCT
ejpam-5924	131	19	27	27	NUM
ejpam-5924	131	20	)	)	PUNCT
ejpam-5924	131	21	the	the	DET
ejpam-5924	131	22	exact	exact	ADJ
ejpam-5924	131	23	solution	solution	NOUN
ejpam-5924	131	24	u(s	u(s	PROPN
ejpam-5924	131	25	,	,	PUNCT
ejpam-5924	131	26	t	t	PROPN
ejpam-5924	131	27	)	)	PUNCT
ejpam-5924	131	28	=	=	PUNCT
ejpam-5924	132	1	2.256758334	2.256758334	NUM
ejpam-5924	132	2	s	s	NOUN
ejpam-5924	132	3	√	√	NOUN
ejpam-5924	132	4	t	t	NOUN
ejpam-5924	132	5	.	.	PUNCT
ejpam-5924	133	1	table	table	NOUN
ejpam-5924	133	2	1	1	NUM
ejpam-5924	133	3	:	:	PUNCT
ejpam-5924	133	4	numerical	numerical	ADJ
ejpam-5924	133	5	results	result	NOUN
ejpam-5924	133	6	and	and	CCONJ
ejpam-5924	133	7	absolute	absolute	ADJ
ejpam-5924	133	8	error	error	NOUN
ejpam-5924	133	9	values	value	NOUN
ejpam-5924	133	10	using	use	VERB
ejpam-5924	133	11	(	(	PUNCT
ejpam-5924	133	12	adm	adm	PROPN
ejpam-5924	133	13	)	)	PUNCT
ejpam-5924	133	14	and	and	CCONJ
ejpam-5924	133	15	(	(	PUNCT
ejpam-5924	133	16	ham	ham	PROPN
ejpam-5924	133	17	)	)	PUNCT
ejpam-5924	133	18	,	,	PUNCT
ejpam-5924	133	19	n	n	NOUN
ejpam-5924	133	20	=	=	SYM
ejpam-5924	133	21	10	10	NUM
ejpam-5924	133	22	,	,	PUNCT
ejpam-5924	133	23	at	at	ADP
ejpam-5924	133	24	fractional	fractional	ADJ
ejpam-5924	133	25	order	order	NOUN
ejpam-5924	133	26	α	α	NOUN
ejpam-5924	133	27	=	=	SYM
ejpam-5924	133	28	0.5	0.5	NUM
ejpam-5924	133	29	in	in	ADP
ejpam-5924	133	30	application	application	NOUN
ejpam-5924	133	31	1	1	NUM
ejpam-5924	133	32	.	.	PUNCT
ejpam-5924	134	1	s	s	PROPN
ejpam-5924	134	2	t	t	PROPN
ejpam-5924	134	3	uexact	uexact	ADJ
ejpam-5924	134	4	adm	adm	PROPN
ejpam-5924	134	5	ham	ham	PROPN
ejpam-5924	134	6	uadm	uadm	PROPN
ejpam-5924	134	7	erroradm	erroradm	PROPN
ejpam-5924	134	8	uham	uham	PROPN
ejpam-5924	134	9	errorham	errorham	PROPN
ejpam-5924	134	10	0.0	0.0	NUM
ejpam-5924	134	11	0.0	0.0	NUM
ejpam-5924	134	12	0	0	NUM
ejpam-5924	134	13	0	0	NUM
ejpam-5924	134	14	0	0	NUM
ejpam-5924	135	1	4×	4×	NOUN
ejpam-5924	135	2	10−8	10−8	NUM
ejpam-5924	135	3	4×	4×	NOUN
ejpam-5924	136	1	10−8	10−8	NUM
ejpam-5924	136	2	0.1	0.1	NUM
ejpam-5924	136	3	0.1	0.1	NUM
ejpam-5924	136	4	0.07136496464	0.07136496464	NUM
ejpam-5924	137	1	0.07136496464	0.07136496464	NUM
ejpam-5924	137	2	0	0	NUM
ejpam-5924	137	3	0.07136500464	0.07136500464	NUM
ejpam-5924	137	4	4.000×	4.000×	NUM
ejpam-5924	137	5	10−8	10−8	NUM
ejpam-5924	137	6	0.2	0.2	NUM
ejpam-5924	137	7	0.2	0.2	NUM
ejpam-5924	137	8	0.2018506018	0.2018506018	NUM
ejpam-5924	137	9	0.2018506017	0.2018506017	NUM
ejpam-5924	137	10	1×	1×	NUM
ejpam-5924	137	11	10−10	10−10	NUM
ejpam-5924	137	12	0.2018506417	0.2018506417	NUM
ejpam-5924	137	13	3.99×	3.99×	NUM
ejpam-5924	137	14	10−8	10−8	NUM
ejpam-5924	137	15	0.3	0.3	NUM
ejpam-5924	137	16	0.3	0.3	NUM
ejpam-5924	137	17	0.3708232338	0.3708232338	NUM
ejpam-5924	137	18	0.3708232338	0.3708232338	NUM
ejpam-5924	137	19	0	0	NUM
ejpam-5924	137	20	0.3708232738	0.3708232738	NUM
ejpam-5924	137	21	4.00×	4.00×	NUM
ejpam-5924	137	22	10−8	10−8	NUM
ejpam-5924	137	23	0.4	0.4	NUM
ejpam-5924	137	24	0.4	0.4	NUM
ejpam-5924	137	25	0.5709197172	0.5709197172	NUM
ejpam-5924	137	26	0.5709197171	0.5709197171	NUM
ejpam-5924	137	27	1×	1×	NUM
ejpam-5924	137	28	10−10	10−10	NUM
ejpam-5924	137	29	0.5709197571	0.5709197571	NUM
ejpam-5924	138	1	3.99×	3.99×	NUM
ejpam-5924	138	2	10−8	10−8	NUM
ejpam-5924	138	3	0.5	0.5	NUM
ejpam-5924	138	4	0.5	0.5	NUM
ejpam-5924	138	5	0.797884561	0.797884561	NUM
ejpam-5924	138	6	0.7978845608	0.7978845608	NUM
ejpam-5924	138	7	2×	2×	NUM
ejpam-5924	138	8	10−10	10−10	NUM
ejpam-5924	138	9	0.7978846008	0.7978846008	NUM
ejpam-5924	138	10	3.98×	3.98×	NUM
ejpam-5924	138	11	10−8	10−8	NUM
ejpam-5924	138	12	0.6	0.6	NUM
ejpam-5924	138	13	0.6	0.6	NUM
ejpam-5924	138	14	1.048846493	1.048846493	NUM
ejpam-5924	138	15	1.048846493	1.048846493	NUM
ejpam-5924	138	16	0	0	NUM
ejpam-5924	139	1	1.048846533	1.048846533	NUM
ejpam-5924	139	2	4.0×	4.0×	NUM
ejpam-5924	139	3	10−8	10−8	NUM
ejpam-5924	139	4	0.7	0.7	NUM
ejpam-5924	139	5	0.7	0.7	NUM
ejpam-5924	139	6	1.321697642	1.321697642	NUM
ejpam-5924	139	7	1.321697641	1.321697641	NUM
ejpam-5924	139	8	1×	1×	NUM
ejpam-5924	139	9	10−9	10−9	NUM
ejpam-5924	139	10	1.321697681	1.321697681	NUM
ejpam-5924	139	11	3.9×	3.9×	PROPN
ejpam-5924	139	12	10−8	10−8	NUM
ejpam-5924	139	13	0.8	0.8	NUM
ejpam-5924	139	14	0.8	0.8	NUM
ejpam-5924	139	15	1.614804814	1.614804814	NUM
ejpam-5924	139	16	1.614804814	1.614804814	NUM
ejpam-5924	139	17	0	0	NUM
ejpam-5924	139	18	1.614804854	1.614804854	NUM
ejpam-5924	139	19	4.0×	4.0×	NUM
ejpam-5924	139	20	10−8	10−8	NUM
ejpam-5924	139	21	0.9	0.9	NUM
ejpam-5924	139	22	0.9	0.9	NUM
ejpam-5924	139	23	1.926854045	1.926854045	NUM
ejpam-5924	139	24	1.926854045	1.926854045	NUM
ejpam-5924	139	25	0	0	NUM
ejpam-5924	139	26	1.926854085	1.926854085	NUM
ejpam-5924	139	27	4.0×	4.0×	NUM
ejpam-5924	139	28	10−8	10−8	NUM
ejpam-5924	139	29	1.0	1.0	NUM
ejpam-5924	139	30	1.0	1.0	NUM
ejpam-5924	139	31	2.256758334	2.256758334	NUM
ejpam-5924	139	32	2.256758334	2.256758334	NUM
ejpam-5924	139	33	0	0	NUM
ejpam-5924	139	34	2.256758374	2.256758374	NUM
ejpam-5924	139	35	4.0×	4.0×	NUM
ejpam-5924	139	36	10−8	10−8	NUM
ejpam-5924	139	37	a.	a.	NOUN
ejpam-5924	139	38	m.	m.	NOUN
ejpam-5924	139	39	al	al	PROPN
ejpam-5924	139	40	-	-	PUNCT
ejpam-5924	139	41	bugami	bugami	NOUN
ejpam-5924	139	42	,	,	PUNCT
ejpam-5924	139	43	n.	n.	NOUN
ejpam-5924	139	44	a.	a.	NOUN
ejpam-5924	139	45	alharbi	alharbi	PROPN
ejpam-5924	139	46	,	,	PUNCT
ejpam-5924	139	47	a.	a.	NOUN
ejpam-5924	139	48	m.	m.	PROPN
ejpam-5924	139	49	s.	s.	PROPN
ejpam-5924	139	50	mahdy	mahdy	PROPN
ejpam-5924	139	51	/	/	SYM
ejpam-5924	139	52	eur	eur	PROPN
ejpam-5924	139	53	.	.	PUNCT
ejpam-5924	140	1	j.	j.	PROPN
ejpam-5924	140	2	pure	pure	PROPN
ejpam-5924	140	3	appl	appl	PROPN
ejpam-5924	140	4	.	.	PROPN
ejpam-5924	140	5	math	math	PROPN
ejpam-5924	140	6	,	,	PUNCT
ejpam-5924	140	7	18	18	NUM
ejpam-5924	140	8	(	(	PUNCT
ejpam-5924	140	9	2	2	NUM
ejpam-5924	140	10	)	)	PUNCT
ejpam-5924	140	11	(	(	PUNCT
ejpam-5924	140	12	2025	2025	NUM
ejpam-5924	140	13	)	)	PUNCT
ejpam-5924	140	14	,	,	PUNCT
ejpam-5924	140	15	5924	5924	NUM
ejpam-5924	140	16	8	8	NUM
ejpam-5924	140	17	of	of	ADP
ejpam-5924	140	18	14	14	NUM
ejpam-5924	140	19	figure	figure	NOUN
ejpam-5924	140	20	1	1	NUM
ejpam-5924	140	21	:	:	PUNCT
ejpam-5924	140	22	exact	exact	ADJ
ejpam-5924	140	23	solution	solution	NOUN
ejpam-5924	140	24	of	of	ADP
ejpam-5924	140	25	(	(	PUNCT
ejpam-5924	140	26	adm	adm	PROPN
ejpam-5924	140	27	)	)	PUNCT
ejpam-5924	140	28	for	for	ADP
ejpam-5924	140	29	α	α	NOUN
ejpam-5924	140	30	=	=	SYM
ejpam-5924	140	31	0.5	0.5	NUM
ejpam-5924	140	32	in	in	ADP
ejpam-5924	140	33	application	application	NOUN
ejpam-5924	140	34	1	1	NUM
ejpam-5924	140	35	figure	figure	NOUN
ejpam-5924	140	36	2	2	NUM
ejpam-5924	140	37	:	:	PUNCT
ejpam-5924	140	38	approximate	approximate	ADJ
ejpam-5924	140	39	solution	solution	NOUN
ejpam-5924	140	40	of	of	ADP
ejpam-5924	140	41	(	(	PUNCT
ejpam-5924	140	42	adm	adm	PROPN
ejpam-5924	140	43	)	)	PUNCT
ejpam-5924	140	44	for	for	ADP
ejpam-5924	140	45	α	α	NOUN
ejpam-5924	140	46	=	=	SYM
ejpam-5924	140	47	0.5	0.5	NUM
ejpam-5924	140	48	in	in	ADP
ejpam-5924	140	49	application	application	NOUN
ejpam-5924	140	50	1	1	NUM
ejpam-5924	140	51	figure	figure	NOUN
ejpam-5924	140	52	3	3	NUM
ejpam-5924	140	53	:	:	PUNCT
ejpam-5924	140	54	exact	exact	ADJ
ejpam-5924	140	55	solution	solution	NOUN
ejpam-5924	140	56	of	of	ADP
ejpam-5924	140	57	(	(	PUNCT
ejpam-5924	140	58	ham	ham	NOUN
ejpam-5924	140	59	)	)	PUNCT
ejpam-5924	140	60	for	for	ADP
ejpam-5924	140	61	α	α	NOUN
ejpam-5924	140	62	=	=	SYM
ejpam-5924	140	63	0.5	0.5	NUM
ejpam-5924	140	64	in	in	ADP
ejpam-5924	140	65	application	application	NOUN
ejpam-5924	140	66	1	1	NUM
ejpam-5924	140	67	figure	figure	NOUN
ejpam-5924	140	68	4	4	NUM
ejpam-5924	140	69	:	:	PUNCT
ejpam-5924	140	70	approximate	approximate	ADJ
ejpam-5924	140	71	solution	solution	NOUN
ejpam-5924	140	72	of	of	ADP
ejpam-5924	140	73	(	(	PUNCT
ejpam-5924	140	74	ham	ham	NOUN
ejpam-5924	140	75	)	)	PUNCT
ejpam-5924	140	76	for	for	ADP
ejpam-5924	140	77	α	α	NOUN
ejpam-5924	140	78	=	=	SYM
ejpam-5924	140	79	0.5	0.5	NUM
ejpam-5924	140	80	in	in	ADP
ejpam-5924	140	81	application	application	NOUN
ejpam-5924	140	82	1	1	NUM
ejpam-5924	140	83	application	application	NOUN
ejpam-5924	140	84	2	2	NUM
ejpam-5924	140	85	.	.	PUNCT
ejpam-5924	140	86	consider	consider	VERB
ejpam-5924	140	87	the	the	DET
ejpam-5924	140	88	following	follow	VERB
ejpam-5924	140	89	caputo	caputo	PROPN
ejpam-5924	140	90	fractional	fractional	PROPN
ejpam-5924	140	91	linear	linear	PROPN
ejpam-5924	140	92	fredholm	fredholm	PROPN
ejpam-5924	140	93	integro	integro	ADJ
ejpam-5924	140	94	-	-	PUNCT
ejpam-5924	140	95	differential	differential	NOUN
ejpam-5924	140	96	equation	equation	NOUN
ejpam-5924	140	97	d0.8u(s	d0.8u(s	PROPN
ejpam-5924	140	98	,	,	PUNCT
ejpam-5924	140	99	t	t	PROPN
ejpam-5924	140	100	)	)	PUNCT
ejpam-5924	140	101	=	=	SYM
ejpam-5924	140	102	2.178248842	2.178248842	NUM
ejpam-5924	140	103	st1/5	st1/5	NOUN
ejpam-5924	140	104	−	−	ADP
ejpam-5924	140	105	0.8324154416	0.8324154416	NUM
ejpam-5924	140	106	+	+	CCONJ
ejpam-5924	140	107	∫	∫	PROPN
ejpam-5924	140	108	1	1	NUM
ejpam-5924	140	109	0	0	NUM
ejpam-5924	140	110	∫	∫	PROPN
ejpam-5924	140	111	1	1	NUM
ejpam-5924	140	112	0	0	NUM
ejpam-5924	140	113	√	√	PROPN
ejpam-5924	140	114	τξ	τξ	ADJ
ejpam-5924	140	115	d0.8u(τ	d0.8u(τ	PROPN
ejpam-5924	140	116	,	,	PUNCT
ejpam-5924	140	117	ξ)dτdξ	ξ)dτdξ	PROPN
ejpam-5924	140	118	(	(	PUNCT
ejpam-5924	140	119	28	28	NUM
ejpam-5924	140	120	)	)	PUNCT
ejpam-5924	140	121	the	the	DET
ejpam-5924	140	122	exact	exact	ADJ
ejpam-5924	140	123	solution	solution	NOUN
ejpam-5924	140	124	is	be	AUX
ejpam-5924	140	125	u(s	u(s	ADJ
ejpam-5924	140	126	,	,	PUNCT
ejpam-5924	140	127	t	t	NOUN
ejpam-5924	140	128	)	)	PUNCT
ejpam-5924	140	129	=	=	SYM
ejpam-5924	141	1	2.178248842	2.178248842	NUM
ejpam-5924	141	2	st1/5	st1/5	NOUN
ejpam-5924	141	3	.	.	PUNCT
ejpam-5924	141	4	a.	a.	PROPN
ejpam-5924	141	5	m.	m.	PROPN
ejpam-5924	141	6	al	al	PROPN
ejpam-5924	141	7	-	-	PUNCT
ejpam-5924	141	8	bugami	bugami	NOUN
ejpam-5924	141	9	,	,	PUNCT
ejpam-5924	141	10	n.	n.	NOUN
ejpam-5924	141	11	a.	a.	NOUN
ejpam-5924	141	12	alharbi	alharbi	PROPN
ejpam-5924	141	13	,	,	PUNCT
ejpam-5924	141	14	a.	a.	NOUN
ejpam-5924	141	15	m.	m.	PROPN
ejpam-5924	141	16	s.	s.	PROPN
ejpam-5924	141	17	mahdy	mahdy	PROPN
ejpam-5924	141	18	/	/	SYM
ejpam-5924	141	19	eur	eur	PROPN
ejpam-5924	141	20	.	.	PUNCT
ejpam-5924	142	1	j.	j.	PROPN
ejpam-5924	142	2	pure	pure	PROPN
ejpam-5924	142	3	appl	appl	PROPN
ejpam-5924	142	4	.	.	PROPN
ejpam-5924	142	5	math	math	PROPN
ejpam-5924	142	6	,	,	PUNCT
ejpam-5924	142	7	18	18	NUM
ejpam-5924	142	8	(	(	PUNCT
ejpam-5924	142	9	2	2	NUM
ejpam-5924	142	10	)	)	PUNCT
ejpam-5924	142	11	(	(	PUNCT
ejpam-5924	142	12	2025	2025	NUM
ejpam-5924	142	13	)	)	PUNCT
ejpam-5924	142	14	,	,	PUNCT
ejpam-5924	142	15	5924	5924	NUM
ejpam-5924	142	16	9	9	NUM
ejpam-5924	142	17	of	of	ADP
ejpam-5924	142	18	14	14	NUM
ejpam-5924	142	19	table	table	NOUN
ejpam-5924	142	20	2	2	NUM
ejpam-5924	142	21	:	:	PUNCT
ejpam-5924	142	22	numerical	numerical	ADJ
ejpam-5924	142	23	results	result	NOUN
ejpam-5924	142	24	and	and	CCONJ
ejpam-5924	142	25	absolute	absolute	ADJ
ejpam-5924	142	26	error	error	NOUN
ejpam-5924	142	27	values	value	NOUN
ejpam-5924	142	28	using	use	VERB
ejpam-5924	142	29	(	(	PUNCT
ejpam-5924	142	30	adm	adm	PROPN
ejpam-5924	142	31	)	)	PUNCT
ejpam-5924	142	32	and	and	CCONJ
ejpam-5924	142	33	(	(	PUNCT
ejpam-5924	142	34	ham	ham	PROPN
ejpam-5924	142	35	)	)	PUNCT
ejpam-5924	142	36	,	,	PUNCT
ejpam-5924	142	37	n	n	NOUN
ejpam-5924	142	38	=	=	SYM
ejpam-5924	142	39	10	10	NUM
ejpam-5924	142	40	,	,	PUNCT
ejpam-5924	142	41	at	at	ADP
ejpam-5924	142	42	fractional	fractional	ADJ
ejpam-5924	142	43	order	order	NOUN
ejpam-5924	142	44	α	α	NOUN
ejpam-5924	142	45	=	=	NOUN
ejpam-5924	142	46	0.8	0.8	NUM
ejpam-5924	142	47	in	in	ADP
ejpam-5924	142	48	application	application	NOUN
ejpam-5924	142	49	2	2	NUM
ejpam-5924	142	50	.	.	PUNCT
ejpam-5924	142	51	s	s	PROPN
ejpam-5924	142	52	t	t	PROPN
ejpam-5924	142	53	uexact	uexact	ADJ
ejpam-5924	142	54	adm	adm	PROPN
ejpam-5924	142	55	ham	ham	PROPN
ejpam-5924	142	56	uadm	uadm	PROPN
ejpam-5924	142	57	erroradm	erroradm	PROPN
ejpam-5924	142	58	uham	uham	PROPN
ejpam-5924	142	59	errorham	errorham	PROPN
ejpam-5924	142	60	0.0	0.0	NUM
ejpam-5924	142	61	0.0	0.0	NUM
ejpam-5924	142	62	0	0	NUM
ejpam-5924	142	63	0	0	NUM
ejpam-5924	142	64	0	0	NUM
ejpam-5924	143	1	3×	3×	NUM
ejpam-5924	143	2	10−8	10−8	NUM
ejpam-5924	143	3	3×	3×	NUM
ejpam-5924	143	4	10−8	10−8	NUM
ejpam-5924	143	5	0.1	0.1	NUM
ejpam-5924	143	6	0.1	0.1	NUM
ejpam-5924	143	7	0.1374382105	0.1374382105	NUM
ejpam-5924	143	8	0.1374382105	0.1374382105	NUM
ejpam-5924	143	9	0	0	NUM
ejpam-5924	143	10	0.1374382405	0.1374382405	NUM
ejpam-5924	143	11	3.00×	3.00×	NUM
ejpam-5924	143	12	10−8	10−8	NUM
ejpam-5924	143	13	0.2	0.2	NUM
ejpam-5924	143	14	0.2	0.2	NUM
ejpam-5924	143	15	0.3157500926	0.3157500926	NUM
ejpam-5924	143	16	0.3157500925	0.3157500925	NUM
ejpam-5924	143	17	1×	1×	NUM
ejpam-5924	143	18	10−10	10−10	NUM
ejpam-5924	143	19	0.3157501225	0.3157501225	NUM
ejpam-5924	143	20	2.99×	2.99×	NUM
ejpam-5924	143	21	10−8	10−8	NUM
ejpam-5924	143	22	0.3	0.3	NUM
ejpam-5924	143	23	0.3	0.3	NUM
ejpam-5924	143	24	0.5136330933	0.5136330933	NUM
ejpam-5924	143	25	0.5136330933	0.5136330933	NUM
ejpam-5924	143	26	0	0	NUM
ejpam-5924	143	27	0.5136331233	0.5136331233	NUM
ejpam-5924	143	28	3.00×	3.00×	NUM
ejpam-5924	143	29	10−8	10−8	NUM
ejpam-5924	143	30	0.4	0.4	NUM
ejpam-5924	143	31	0.4	0.4	NUM
ejpam-5924	143	32	0.725403224	0.725403224	NUM
ejpam-5924	143	33	0.7254032241	0.7254032241	NUM
ejpam-5924	143	34	1×	1×	NUM
ejpam-5924	143	35	10−10	10−10	NUM
ejpam-5924	143	36	0.7254032541	0.7254032541	NUM
ejpam-5924	143	37	3.01×	3.01×	NUM
ejpam-5924	143	38	10−8	10−8	NUM
ejpam-5924	143	39	0.5	0.5	NUM
ejpam-5924	143	40	0.5	0.5	NUM
ejpam-5924	143	41	0.948137878	0.948137878	NUM
ejpam-5924	143	42	0.9481378781	0.9481378781	NUM
ejpam-5924	143	43	1×	1×	NUM
ejpam-5924	143	44	10−10	10−10	NUM
ejpam-5924	143	45	0.9481379081	0.9481379081	NUM
ejpam-5924	144	1	3.01×	3.01×	NUM
ejpam-5924	144	2	10−8	10−8	NUM
ejpam-5924	144	3	0.6	0.6	NUM
ejpam-5924	144	4	0.6	0.6	NUM
ejpam-5924	144	5	1.180018979	1.180018979	NUM
ejpam-5924	144	6	1.180018979	1.180018979	NUM
ejpam-5924	144	7	0	0	NUM
ejpam-5924	144	8	1.180019009	1.180019009	NUM
ejpam-5924	144	9	3.0×	3.0×	NUM
ejpam-5924	144	10	10−8	10−8	NUM
ejpam-5924	144	11	0.7	0.7	NUM
ejpam-5924	144	12	0.7	0.7	NUM
ejpam-5924	144	13	1.419793357	1.419793357	NUM
ejpam-5924	144	14	1.419793357	1.419793357	NUM
ejpam-5924	144	15	0	0	NUM
ejpam-5924	144	16	1.419793387	1.419793387	NUM
ejpam-5924	144	17	3.0×	3.0×	NUM
ejpam-5924	144	18	10−8	10−8	NUM
ejpam-5924	145	1	0.8	0.8	NUM
ejpam-5924	145	2	0.8	0.8	NUM
ejpam-5924	145	3	1.666538980	1.666538980	NUM
ejpam-5924	145	4	1.666538980	1.666538980	NUM
ejpam-5924	145	5	0	0	NUM
ejpam-5924	145	6	1.666539010	1.666539010	NUM
ejpam-5924	145	7	3.0×	3.0×	NUM
ejpam-5924	145	8	10−8	10−8	NUM
ejpam-5924	145	9	0.9	0.9	NUM
ejpam-5924	145	10	0.9	0.9	NUM
ejpam-5924	145	11	1.919545908	1.919545908	NUM
ejpam-5924	145	12	1.919545908	1.919545908	NUM
ejpam-5924	145	13	0	0	NUM
ejpam-5924	145	14	1.919545938	1.919545938	NUM
ejpam-5924	145	15	3.0×	3.0×	NUM
ejpam-5924	145	16	10−8	10−8	NUM
ejpam-5924	145	17	1.0	1.0	NUM
ejpam-5924	145	18	1.0	1.0	NUM
ejpam-5924	145	19	2.178248842	2.178248842	NUM
ejpam-5924	145	20	2.178248842	2.178248842	NUM
ejpam-5924	145	21	0	0	NUM
ejpam-5924	145	22	2.178248872	2.178248872	NUM
ejpam-5924	145	23	3.0×	3.0×	NUM
ejpam-5924	145	24	10−8	10−8	NUM
ejpam-5924	145	25	figure	figure	NOUN
ejpam-5924	145	26	5	5	NUM
ejpam-5924	145	27	:	:	PUNCT
ejpam-5924	145	28	exact	exact	ADJ
ejpam-5924	145	29	solution	solution	NOUN
ejpam-5924	145	30	of	of	ADP
ejpam-5924	145	31	(	(	PUNCT
ejpam-5924	145	32	adm	adm	PROPN
ejpam-5924	145	33	)	)	PUNCT
ejpam-5924	145	34	for	for	ADP
ejpam-5924	145	35	α	α	NOUN
ejpam-5924	145	36	=	=	SYM
ejpam-5924	145	37	0.8	0.8	NUM
ejpam-5924	145	38	in	in	ADP
ejpam-5924	145	39	application	application	NOUN
ejpam-5924	145	40	2	2	NUM
ejpam-5924	145	41	figure	figure	NOUN
ejpam-5924	145	42	6	6	NUM
ejpam-5924	145	43	:	:	PUNCT
ejpam-5924	145	44	approximate	approximate	ADJ
ejpam-5924	145	45	solution	solution	NOUN
ejpam-5924	145	46	of	of	ADP
ejpam-5924	145	47	(	(	PUNCT
ejpam-5924	145	48	adm	adm	PROPN
ejpam-5924	145	49	)	)	PUNCT
ejpam-5924	145	50	for	for	ADP
ejpam-5924	145	51	α	α	NOUN
ejpam-5924	145	52	=	=	SYM
ejpam-5924	145	53	0.8	0.8	NUM
ejpam-5924	145	54	in	in	ADP
ejpam-5924	145	55	application	application	NOUN
ejpam-5924	145	56	2	2	NUM
ejpam-5924	145	57	a.	a.	NOUN
ejpam-5924	145	58	m.	m.	NOUN
ejpam-5924	145	59	al	al	PROPN
ejpam-5924	145	60	-	-	PUNCT
ejpam-5924	145	61	bugami	bugami	NOUN
ejpam-5924	145	62	,	,	PUNCT
ejpam-5924	145	63	n.	n.	NOUN
ejpam-5924	145	64	a.	a.	NOUN
ejpam-5924	145	65	alharbi	alharbi	PROPN
ejpam-5924	145	66	,	,	PUNCT
ejpam-5924	145	67	a.	a.	NOUN
ejpam-5924	145	68	m.	m.	PROPN
ejpam-5924	145	69	s.	s.	PROPN
ejpam-5924	145	70	mahdy	mahdy	PROPN
ejpam-5924	145	71	/	/	SYM
ejpam-5924	145	72	eur	eur	PROPN
ejpam-5924	145	73	.	.	PUNCT
ejpam-5924	146	1	j.	j.	PROPN
ejpam-5924	146	2	pure	pure	PROPN
ejpam-5924	146	3	appl	appl	PROPN
ejpam-5924	146	4	.	.	PROPN
ejpam-5924	146	5	math	math	PROPN
ejpam-5924	146	6	,	,	PUNCT
ejpam-5924	146	7	18	18	NUM
ejpam-5924	146	8	(	(	PUNCT
ejpam-5924	146	9	2	2	NUM
ejpam-5924	146	10	)	)	PUNCT
ejpam-5924	146	11	(	(	PUNCT
ejpam-5924	146	12	2025	2025	NUM
ejpam-5924	146	13	)	)	PUNCT
ejpam-5924	146	14	,	,	PUNCT
ejpam-5924	146	15	5924	5924	NUM
ejpam-5924	146	16	10	10	NUM
ejpam-5924	146	17	of	of	ADP
ejpam-5924	146	18	14	14	NUM
ejpam-5924	146	19	figure	figure	NOUN
ejpam-5924	146	20	7	7	NUM
ejpam-5924	146	21	:	:	PUNCT
ejpam-5924	146	22	exact	exact	ADJ
ejpam-5924	146	23	solution	solution	NOUN
ejpam-5924	146	24	of	of	ADP
ejpam-5924	146	25	(	(	PUNCT
ejpam-5924	146	26	ham	ham	NOUN
ejpam-5924	146	27	)	)	PUNCT
ejpam-5924	146	28	for	for	ADP
ejpam-5924	146	29	α	α	NOUN
ejpam-5924	146	30	=	=	SYM
ejpam-5924	146	31	0.8	0.8	NUM
ejpam-5924	146	32	in	in	ADP
ejpam-5924	146	33	application	application	NOUN
ejpam-5924	146	34	2	2	NUM
ejpam-5924	146	35	figure	figure	NOUN
ejpam-5924	146	36	8	8	NUM
ejpam-5924	146	37	:	:	PUNCT
ejpam-5924	146	38	approximate	approximate	ADJ
ejpam-5924	146	39	solution	solution	NOUN
ejpam-5924	146	40	of	of	ADP
ejpam-5924	146	41	(	(	PUNCT
ejpam-5924	146	42	ham	ham	NOUN
ejpam-5924	146	43	)	)	PUNCT
ejpam-5924	146	44	for	for	ADP
ejpam-5924	146	45	α	α	NOUN
ejpam-5924	146	46	=	=	SYM
ejpam-5924	146	47	0.8	0.8	NUM
ejpam-5924	146	48	in	in	ADP
ejpam-5924	146	49	application	application	NOUN
ejpam-5924	146	50	2	2	NUM
ejpam-5924	146	51	application	application	NOUN
ejpam-5924	146	52	3	3	NUM
ejpam-5924	146	53	.	.	PUNCT
ejpam-5924	146	54	consider	consider	VERB
ejpam-5924	146	55	the	the	DET
ejpam-5924	146	56	following	follow	VERB
ejpam-5924	146	57	caputo	caputo	PROPN
ejpam-5924	146	58	fractional	fractional	PROPN
ejpam-5924	146	59	nonlinear	nonlinear	PROPN
ejpam-5924	146	60	fredholm	fredholm	NOUN
ejpam-5924	146	61	integrodifferential	integrodifferential	ADJ
ejpam-5924	146	62	equation	equation	NOUN
ejpam-5924	146	63	d0.5u(s	d0.5u(s	PROPN
ejpam-5924	146	64	,	,	PUNCT
ejpam-5924	146	65	t	t	PROPN
ejpam-5924	146	66	)	)	PUNCT
ejpam-5924	146	67	=	=	PUNCT
ejpam-5924	147	1	2.256758334	2.256758334	NUM
ejpam-5924	147	2	s	s	PART
ejpam-5924	147	3	√	√	NOUN
ejpam-5924	147	4	t−	t−	PROPN
ejpam-5924	147	5	1.235153476	1.235153476	NUM
ejpam-5924	147	6	+	+	CCONJ
ejpam-5924	147	7	∫	∫	PROPN
ejpam-5924	147	8	1	1	NUM
ejpam-5924	147	9	0	0	NUM
ejpam-5924	147	10	∫	∫	PROPN
ejpam-5924	147	11	1	1	NUM
ejpam-5924	147	12	0	0	NUM
ejpam-5924	147	13	√	√	PROPN
ejpam-5924	147	14	τξ	τξ	X
ejpam-5924	147	15	(	(	PUNCT
ejpam-5924	147	16	d0.5u(τ	d0.5u(τ	ADJ
ejpam-5924	147	17	,	,	PUNCT
ejpam-5924	147	18	ξ))2	ξ))2	NOUN
ejpam-5924	147	19	dτdξ	dτdξ	NOUN
ejpam-5924	147	20	(	(	PUNCT
ejpam-5924	147	21	29	29	NUM
ejpam-5924	147	22	)	)	PUNCT
ejpam-5924	147	23	the	the	DET
ejpam-5924	147	24	exact	exact	ADJ
ejpam-5924	147	25	solution	solution	NOUN
ejpam-5924	147	26	is	be	AUX
ejpam-5924	147	27	u(s	u(s	ADJ
ejpam-5924	147	28	,	,	PUNCT
ejpam-5924	147	29	t	t	NOUN
ejpam-5924	147	30	)	)	PUNCT
ejpam-5924	147	31	=	=	PUNCT
ejpam-5924	148	1	2.256758334	2.256758334	NUM
ejpam-5924	148	2	s	s	PART
ejpam-5924	148	3	√	√	NOUN
ejpam-5924	148	4	t.	t.	PROPN
ejpam-5924	148	5	s	s	PROPN
ejpam-5924	148	6	t	t	PROPN
ejpam-5924	148	7	uexact	uexact	ADJ
ejpam-5924	148	8	adm	adm	PROPN
ejpam-5924	148	9	ham	ham	PROPN
ejpam-5924	148	10	uadm	uadm	PROPN
ejpam-5924	148	11	erroradm	erroradm	PROPN
ejpam-5924	148	12	uham	uham	PROPN
ejpam-5924	148	13	errorham	errorham	PROPN
ejpam-5924	148	14	0.0	0.0	NUM
ejpam-5924	148	15	0.0	0.0	NUM
ejpam-5924	148	16	0	0	NUM
ejpam-5924	148	17	0	0	NUM
ejpam-5924	148	18	0	0	NUM
ejpam-5924	149	1	−2×	−2×	NOUN
ejpam-5924	149	2	10−8	10−8	NUM
ejpam-5924	149	3	2×	2×	NUM
ejpam-5924	149	4	10−8	10−8	NUM
ejpam-5924	150	1	0.1	0.1	NUM
ejpam-5924	150	2	0.1	0.1	NUM
ejpam-5924	150	3	0.07136496464	0.07136496464	NUM
ejpam-5924	150	4	0.07136496464	0.07136496464	NUM
ejpam-5924	150	5	0	0	NUM
ejpam-5924	150	6	0.07136494464	0.07136494464	NUM
ejpam-5924	150	7	2.000×	2.000×	NUM
ejpam-5924	151	1	10−8	10−8	NUM
ejpam-5924	151	2	0.2	0.2	NUM
ejpam-5924	151	3	0.2	0.2	NUM
ejpam-5924	151	4	0.2018506018	0.2018506018	NUM
ejpam-5924	151	5	0.2018506017	0.2018506017	NUM
ejpam-5924	151	6	1×	1×	NUM
ejpam-5924	151	7	10−10	10−10	NUM
ejpam-5924	151	8	0.2018505817	0.2018505817	NUM
ejpam-5924	151	9	2.01×	2.01×	NUM
ejpam-5924	151	10	10−8	10−8	NUM
ejpam-5924	151	11	0.3	0.3	NUM
ejpam-5924	151	12	0.3	0.3	NUM
ejpam-5924	151	13	0.3708232338	0.3708232338	NUM
ejpam-5924	151	14	0.3708232338	0.3708232338	NUM
ejpam-5924	151	15	0	0	NUM
ejpam-5924	152	1	0.3708232138	0.3708232138	NUM
ejpam-5924	152	2	2.00×	2.00×	NUM
ejpam-5924	152	3	10−8	10−8	NUM
ejpam-5924	152	4	0.4	0.4	NUM
ejpam-5924	152	5	0.4	0.4	NUM
ejpam-5924	152	6	0.5709197172	0.5709197172	NUM
ejpam-5924	152	7	0.5709197171	0.5709197171	NUM
ejpam-5924	152	8	1×	1×	NUM
ejpam-5924	152	9	10−10	10−10	NUM
ejpam-5924	152	10	0.5709196971	0.5709196971	NUM
ejpam-5924	152	11	2.01×	2.01×	NUM
ejpam-5924	152	12	10−8	10−8	NUM
ejpam-5924	152	13	0.5	0.5	NUM
ejpam-5924	152	14	0.5	0.5	NUM
ejpam-5924	152	15	0.797884561	0.797884561	NUM
ejpam-5924	152	16	0.7978845608	0.7978845608	NUM
ejpam-5924	152	17	2×	2×	NUM
ejpam-5924	152	18	10−10	10−10	NUM
ejpam-5924	152	19	0.7978845408	0.7978845408	NUM
ejpam-5924	153	1	2.02×	2.02×	NUM
ejpam-5924	153	2	10−8	10−8	NUM
ejpam-5924	153	3	0.6	0.6	NUM
ejpam-5924	153	4	0.6	0.6	NUM
ejpam-5924	153	5	1.048846493	1.048846493	NUM
ejpam-5924	153	6	1.048846493	1.048846493	NUM
ejpam-5924	153	7	0	0	NUM
ejpam-5924	153	8	1.048846473	1.048846473	NUM
ejpam-5924	153	9	2.0×	2.0×	NUM
ejpam-5924	153	10	10−8	10−8	NUM
ejpam-5924	153	11	0.7	0.7	NUM
ejpam-5924	153	12	0.7	0.7	NUM
ejpam-5924	153	13	1.321697642	1.321697642	NUM
ejpam-5924	153	14	1.321697641	1.321697641	NUM
ejpam-5924	153	15	1×	1×	NUM
ejpam-5924	153	16	10−9	10−9	NUM
ejpam-5924	153	17	1.321697621	1.321697621	NUM
ejpam-5924	153	18	2.1×	2.1×	NUM
ejpam-5924	153	19	10−8	10−8	NUM
ejpam-5924	153	20	0.8	0.8	NUM
ejpam-5924	153	21	0.8	0.8	NUM
ejpam-5924	153	22	1.614804814	1.614804814	NUM
ejpam-5924	153	23	1.614804814	1.614804814	NUM
ejpam-5924	153	24	0	0	NUM
ejpam-5924	154	1	1.614804794	1.614804794	NUM
ejpam-5924	154	2	2.0×	2.0×	NUM
ejpam-5924	154	3	10−8	10−8	NUM
ejpam-5924	154	4	0.9	0.9	NUM
ejpam-5924	154	5	0.9	0.9	NUM
ejpam-5924	154	6	1.926854045	1.926854045	NUM
ejpam-5924	154	7	1.926854045	1.926854045	NUM
ejpam-5924	154	8	0	0	NUM
ejpam-5924	154	9	1.926854025	1.926854025	NUM
ejpam-5924	154	10	2.0×	2.0×	NUM
ejpam-5924	154	11	10−8	10−8	NUM
ejpam-5924	154	12	1.0	1.0	NUM
ejpam-5924	154	13	1.0	1.0	NUM
ejpam-5924	154	14	2.256758334	2.256758334	NUM
ejpam-5924	154	15	2.256758334	2.256758334	NUM
ejpam-5924	154	16	0	0	NUM
ejpam-5924	154	17	2.256758314	2.256758314	NUM
ejpam-5924	154	18	2.0×	2.0×	NUM
ejpam-5924	154	19	10−8	10−8	NUM
ejpam-5924	154	20	table	table	NOUN
ejpam-5924	154	21	3	3	NUM
ejpam-5924	154	22	:	:	PUNCT
ejpam-5924	154	23	numerical	numerical	ADJ
ejpam-5924	154	24	results	result	NOUN
ejpam-5924	154	25	and	and	CCONJ
ejpam-5924	154	26	absolute	absolute	ADJ
ejpam-5924	154	27	error	error	NOUN
ejpam-5924	154	28	values	value	NOUN
ejpam-5924	154	29	using	use	VERB
ejpam-5924	154	30	(	(	PUNCT
ejpam-5924	154	31	adm	adm	PROPN
ejpam-5924	154	32	)	)	PUNCT
ejpam-5924	154	33	and	and	CCONJ
ejpam-5924	154	34	(	(	PUNCT
ejpam-5924	154	35	ham	ham	PROPN
ejpam-5924	154	36	)	)	PUNCT
ejpam-5924	154	37	,	,	PUNCT
ejpam-5924	154	38	n	n	NOUN
ejpam-5924	154	39	=	=	SYM
ejpam-5924	154	40	10	10	NUM
ejpam-5924	154	41	,	,	PUNCT
ejpam-5924	154	42	at	at	ADP
ejpam-5924	154	43	fractional	fractional	ADJ
ejpam-5924	154	44	order	order	NOUN
ejpam-5924	154	45	α	α	NOUN
ejpam-5924	154	46	=	=	SYM
ejpam-5924	154	47	0.5	0.5	NUM
ejpam-5924	154	48	in	in	ADP
ejpam-5924	154	49	application	application	NOUN
ejpam-5924	154	50	3	3	NUM
ejpam-5924	154	51	.	.	PUNCT
ejpam-5924	154	52	a.	a.	PROPN
ejpam-5924	154	53	m.	m.	PROPN
ejpam-5924	155	1	al	al	PROPN
ejpam-5924	155	2	-	-	PUNCT
ejpam-5924	155	3	bugami	bugami	NOUN
ejpam-5924	155	4	,	,	PUNCT
ejpam-5924	155	5	n.	n.	NOUN
ejpam-5924	155	6	a.	a.	NOUN
ejpam-5924	155	7	alharbi	alharbi	PROPN
ejpam-5924	155	8	,	,	PUNCT
ejpam-5924	155	9	a.	a.	NOUN
ejpam-5924	155	10	m.	m.	PROPN
ejpam-5924	155	11	s.	s.	PROPN
ejpam-5924	155	12	mahdy	mahdy	PROPN
ejpam-5924	155	13	/	/	SYM
ejpam-5924	155	14	eur	eur	PROPN
ejpam-5924	155	15	.	.	PUNCT
ejpam-5924	156	1	j.	j.	PROPN
ejpam-5924	156	2	pure	pure	PROPN
ejpam-5924	156	3	appl	appl	PROPN
ejpam-5924	156	4	.	.	PROPN
ejpam-5924	156	5	math	math	PROPN
ejpam-5924	156	6	,	,	PUNCT
ejpam-5924	156	7	18	18	NUM
ejpam-5924	156	8	(	(	PUNCT
ejpam-5924	156	9	2	2	NUM
ejpam-5924	156	10	)	)	PUNCT
ejpam-5924	156	11	(	(	PUNCT
ejpam-5924	156	12	2025	2025	NUM
ejpam-5924	156	13	)	)	PUNCT
ejpam-5924	156	14	,	,	PUNCT
ejpam-5924	156	15	5924	5924	NUM
ejpam-5924	156	16	11	11	NUM
ejpam-5924	156	17	of	of	ADP
ejpam-5924	156	18	14	14	NUM
ejpam-5924	156	19	figure	figure	NOUN
ejpam-5924	156	20	9	9	NUM
ejpam-5924	156	21	:	:	PUNCT
ejpam-5924	156	22	exact	exact	ADJ
ejpam-5924	156	23	solution	solution	NOUN
ejpam-5924	156	24	of	of	ADP
ejpam-5924	156	25	(	(	PUNCT
ejpam-5924	156	26	adm	adm	PROPN
ejpam-5924	156	27	)	)	PUNCT
ejpam-5924	156	28	for	for	ADP
ejpam-5924	156	29	α	α	NOUN
ejpam-5924	156	30	=	=	SYM
ejpam-5924	156	31	0.5	0.5	NUM
ejpam-5924	156	32	in	in	ADP
ejpam-5924	156	33	application	application	NOUN
ejpam-5924	156	34	3	3	NUM
ejpam-5924	156	35	figure	figure	NOUN
ejpam-5924	156	36	10	10	NUM
ejpam-5924	156	37	:	:	PUNCT
ejpam-5924	156	38	approximate	approximate	ADJ
ejpam-5924	156	39	solution	solution	NOUN
ejpam-5924	156	40	of	of	ADP
ejpam-5924	156	41	(	(	PUNCT
ejpam-5924	156	42	adm	adm	PROPN
ejpam-5924	156	43	)	)	PUNCT
ejpam-5924	156	44	for	for	ADP
ejpam-5924	156	45	α	α	NOUN
ejpam-5924	156	46	=	=	SYM
ejpam-5924	156	47	0.5	0.5	NUM
ejpam-5924	156	48	in	in	ADP
ejpam-5924	156	49	application	application	NOUN
ejpam-5924	156	50	3	3	NUM
ejpam-5924	156	51	figure	figure	NOUN
ejpam-5924	156	52	11	11	NUM
ejpam-5924	156	53	:	:	PUNCT
ejpam-5924	156	54	exact	exact	ADJ
ejpam-5924	156	55	solution	solution	NOUN
ejpam-5924	156	56	of	of	ADP
ejpam-5924	156	57	(	(	PUNCT
ejpam-5924	156	58	ham	ham	NOUN
ejpam-5924	156	59	)	)	PUNCT
ejpam-5924	156	60	for	for	ADP
ejpam-5924	156	61	α	α	NOUN
ejpam-5924	156	62	=	=	SYM
ejpam-5924	156	63	0.5	0.5	NUM
ejpam-5924	156	64	in	in	ADP
ejpam-5924	156	65	application	application	NOUN
ejpam-5924	156	66	3	3	NUM
ejpam-5924	156	67	figure	figure	NOUN
ejpam-5924	156	68	12	12	NUM
ejpam-5924	156	69	:	:	PUNCT
ejpam-5924	156	70	approximate	approximate	ADJ
ejpam-5924	156	71	solution	solution	NOUN
ejpam-5924	156	72	of	of	ADP
ejpam-5924	156	73	(	(	PUNCT
ejpam-5924	156	74	ham	ham	NOUN
ejpam-5924	156	75	)	)	PUNCT
ejpam-5924	156	76	for	for	ADP
ejpam-5924	156	77	α	α	NOUN
ejpam-5924	156	78	=	=	SYM
ejpam-5924	156	79	0.5	0.5	NUM
ejpam-5924	156	80	in	in	ADP
ejpam-5924	156	81	application	application	NOUN
ejpam-5924	156	82	3	3	NUM
ejpam-5924	156	83	application	application	NOUN
ejpam-5924	156	84	4	4	NUM
ejpam-5924	156	85	.	.	PUNCT
ejpam-5924	156	86	consider	consider	VERB
ejpam-5924	156	87	the	the	DET
ejpam-5924	156	88	following	follow	VERB
ejpam-5924	156	89	caputo	caputo	PROPN
ejpam-5924	156	90	fractional	fractional	PROPN
ejpam-5924	156	91	nonlinear	nonlinear	PROPN
ejpam-5924	156	92	fredholm	fredholm	NOUN
ejpam-5924	156	93	integrodifferential	integrodifferential	ADJ
ejpam-5924	156	94	equation	equation	NOUN
ejpam-5924	156	95	d0.8u(s	d0.8u(s	PROPN
ejpam-5924	156	96	,	,	PUNCT
ejpam-5924	156	97	t	t	PROPN
ejpam-5924	156	98	)	)	PUNCT
ejpam-5924	156	99	=	=	SYM
ejpam-5924	156	100	2.178248842	2.178248842	NUM
ejpam-5924	156	101	st1/5	st1/5	NOUN
ejpam-5924	156	102	−	−	ADP
ejpam-5924	156	103	1.631364025	1.631364025	NUM
ejpam-5924	156	104	+	+	CCONJ
ejpam-5924	156	105	∫	∫	PROPN
ejpam-5924	156	106	1	1	NUM
ejpam-5924	156	107	0	0	NUM
ejpam-5924	156	108	∫	∫	PROPN
ejpam-5924	156	109	1	1	NUM
ejpam-5924	156	110	0	0	NUM
ejpam-5924	156	111	√	√	PROPN
ejpam-5924	156	112	τξ	τξ	X
ejpam-5924	156	113	(	(	PUNCT
ejpam-5924	156	114	d0.8u(τ	d0.8u(τ	PROPN
ejpam-5924	156	115	,	,	PUNCT
ejpam-5924	156	116	ξ))2	ξ))2	NOUN
ejpam-5924	156	117	dτdξ	dτdξ	NOUN
ejpam-5924	156	118	(	(	PUNCT
ejpam-5924	156	119	30	30	NUM
ejpam-5924	156	120	)	)	PUNCT
ejpam-5924	156	121	the	the	DET
ejpam-5924	156	122	exact	exact	ADJ
ejpam-5924	156	123	solution	solution	NOUN
ejpam-5924	156	124	is	be	AUX
ejpam-5924	156	125	u(s	u(s	ADJ
ejpam-5924	156	126	,	,	PUNCT
ejpam-5924	156	127	t	t	NOUN
ejpam-5924	156	128	)	)	PUNCT
ejpam-5924	156	129	=	=	PUNCT
ejpam-5924	156	130	2.178248842	2.178248842	NUM
ejpam-5924	156	131	s	s	NOUN
ejpam-5924	156	132	t1/5	t1/5	NOUN
ejpam-5924	156	133	.	.	PUNCT
ejpam-5924	157	1	a.	a.	PROPN
ejpam-5924	157	2	m.	m.	PROPN
ejpam-5924	157	3	al	al	PROPN
ejpam-5924	157	4	-	-	PUNCT
ejpam-5924	157	5	bugami	bugami	NOUN
ejpam-5924	157	6	,	,	PUNCT
ejpam-5924	157	7	n.	n.	NOUN
ejpam-5924	157	8	a.	a.	NOUN
ejpam-5924	157	9	alharbi	alharbi	PROPN
ejpam-5924	157	10	,	,	PUNCT
ejpam-5924	157	11	a.	a.	NOUN
ejpam-5924	157	12	m.	m.	PROPN
ejpam-5924	157	13	s.	s.	PROPN
ejpam-5924	157	14	mahdy	mahdy	PROPN
ejpam-5924	157	15	/	/	SYM
ejpam-5924	157	16	eur	eur	PROPN
ejpam-5924	157	17	.	.	PUNCT
ejpam-5924	158	1	j.	j.	PROPN
ejpam-5924	158	2	pure	pure	PROPN
ejpam-5924	158	3	appl	appl	PROPN
ejpam-5924	158	4	.	.	PROPN
ejpam-5924	158	5	math	math	PROPN
ejpam-5924	158	6	,	,	PUNCT
ejpam-5924	158	7	18	18	NUM
ejpam-5924	158	8	(	(	PUNCT
ejpam-5924	158	9	2	2	NUM
ejpam-5924	158	10	)	)	PUNCT
ejpam-5924	158	11	(	(	PUNCT
ejpam-5924	158	12	2025	2025	NUM
ejpam-5924	158	13	)	)	PUNCT
ejpam-5924	158	14	,	,	PUNCT
ejpam-5924	158	15	5924	5924	NUM
ejpam-5924	158	16	12	12	NUM
ejpam-5924	158	17	of	of	ADP
ejpam-5924	158	18	14	14	NUM
ejpam-5924	158	19	table	table	NOUN
ejpam-5924	158	20	4	4	NUM
ejpam-5924	158	21	:	:	PUNCT
ejpam-5924	158	22	numerical	numerical	ADJ
ejpam-5924	158	23	results	result	NOUN
ejpam-5924	158	24	and	and	CCONJ
ejpam-5924	158	25	absolute	absolute	ADJ
ejpam-5924	158	26	error	error	NOUN
ejpam-5924	158	27	values	value	NOUN
ejpam-5924	158	28	using	use	VERB
ejpam-5924	158	29	(	(	PUNCT
ejpam-5924	158	30	adm	adm	PROPN
ejpam-5924	158	31	)	)	PUNCT
ejpam-5924	158	32	and	and	CCONJ
ejpam-5924	158	33	(	(	PUNCT
ejpam-5924	158	34	ham	ham	PROPN
ejpam-5924	158	35	)	)	PUNCT
ejpam-5924	158	36	,	,	PUNCT
ejpam-5924	158	37	n	n	NOUN
ejpam-5924	158	38	=	=	SYM
ejpam-5924	158	39	10	10	NUM
ejpam-5924	158	40	,	,	PUNCT
ejpam-5924	158	41	at	at	ADP
ejpam-5924	158	42	fractional	fractional	ADJ
ejpam-5924	158	43	order	order	NOUN
ejpam-5924	158	44	α	α	NOUN
ejpam-5924	158	45	=	=	NOUN
ejpam-5924	158	46	0.8	0.8	NUM
ejpam-5924	158	47	in	in	ADP
ejpam-5924	158	48	application	application	NOUN
ejpam-5924	158	49	4	4	NUM
ejpam-5924	158	50	.	.	PUNCT
ejpam-5924	158	51	s	s	PROPN
ejpam-5924	158	52	t	t	PROPN
ejpam-5924	158	53	uexact	uexact	ADJ
ejpam-5924	158	54	adm	adm	PROPN
ejpam-5924	158	55	ham	ham	PROPN
ejpam-5924	158	56	uadm	uadm	PROPN
ejpam-5924	158	57	erroradm	erroradm	PROPN
ejpam-5924	158	58	uham	uham	PROPN
ejpam-5924	158	59	errorham	errorham	PROPN
ejpam-5924	158	60	0.0	0.0	NUM
ejpam-5924	158	61	0.0	0.0	NUM
ejpam-5924	158	62	0	0	NUM
ejpam-5924	158	63	0	0	NUM
ejpam-5924	158	64	0	0	NUM
ejpam-5924	159	1	−5.5×	−5.5×	NOUN
ejpam-5924	159	2	10−8	10−8	NUM
ejpam-5924	160	1	5.5×	5.5×	NUM
ejpam-5924	160	2	10−8	10−8	NUM
ejpam-5924	160	3	0.1	0.1	NUM
ejpam-5924	160	4	0.1	0.1	NUM
ejpam-5924	161	1	0.1374382105	0.1374382105	NUM
ejpam-5924	161	2	0.1374382105	0.1374382105	NUM
ejpam-5924	161	3	0	0	NUM
ejpam-5924	161	4	0.1374381555	0.1374381555	NUM
ejpam-5924	162	1	5.50×	5.50×	NUM
ejpam-5924	162	2	10−8	10−8	NUM
ejpam-5924	162	3	0.2	0.2	NUM
ejpam-5924	162	4	0.2	0.2	NUM
ejpam-5924	162	5	0.3157500926	0.3157500926	NUM
ejpam-5924	162	6	0.3157500925	0.3157500925	NUM
ejpam-5924	162	7	1×	1×	NUM
ejpam-5924	162	8	10−10	10−10	NUM
ejpam-5924	162	9	0.3157500375	0.3157500375	NUM
ejpam-5924	163	1	5.51×	5.51×	NUM
ejpam-5924	163	2	10−8	10−8	NUM
ejpam-5924	163	3	0.3	0.3	NUM
ejpam-5924	163	4	0.3	0.3	NUM
ejpam-5924	163	5	0.5136330933	0.5136330933	NUM
ejpam-5924	163	6	0.5136330933	0.5136330933	NUM
ejpam-5924	163	7	0	0	NUM
ejpam-5924	163	8	0.5136330383	0.5136330383	NUM
ejpam-5924	163	9	5.50×	5.50×	NUM
ejpam-5924	163	10	10−8	10−8	NUM
ejpam-5924	163	11	0.4	0.4	NUM
ejpam-5924	163	12	0.4	0.4	NUM
ejpam-5924	163	13	0.725403224	0.725403224	NUM
ejpam-5924	163	14	0.7254032241	0.7254032241	NUM
ejpam-5924	163	15	1×	1×	NUM
ejpam-5924	163	16	10−10	10−10	NUM
ejpam-5924	163	17	0.7254031691	0.7254031691	NUM
ejpam-5924	163	18	5.49×	5.49×	NUM
ejpam-5924	163	19	10−8	10−8	NUM
ejpam-5924	163	20	0.5	0.5	NUM
ejpam-5924	163	21	0.5	0.5	NUM
ejpam-5924	163	22	0.948137878	0.948137878	NUM
ejpam-5924	163	23	0.9481378781	0.9481378781	NUM
ejpam-5924	163	24	1×	1×	NUM
ejpam-5924	163	25	10−10	10−10	NUM
ejpam-5924	163	26	0.9481378231	0.9481378231	NUM
ejpam-5924	163	27	5.49×	5.49×	NUM
ejpam-5924	164	1	10−8	10−8	NUM
ejpam-5924	164	2	0.6	0.6	NUM
ejpam-5924	164	3	0.6	0.6	NUM
ejpam-5924	164	4	1.180018979	1.180018979	NUM
ejpam-5924	164	5	1.180018979	1.180018979	NUM
ejpam-5924	164	6	0	0	NUM
ejpam-5924	164	7	1.180018924	1.180018924	NUM
ejpam-5924	164	8	5.5×	5.5×	NUM
ejpam-5924	164	9	10−8	10−8	NUM
ejpam-5924	164	10	0.7	0.7	NUM
ejpam-5924	164	11	0.7	0.7	NUM
ejpam-5924	164	12	1.419793357	1.419793357	NUM
ejpam-5924	164	13	1.419793357	1.419793357	NUM
ejpam-5924	164	14	0	0	NUM
ejpam-5924	164	15	1.419793302	1.419793302	NUM
ejpam-5924	164	16	5.5×	5.5×	NUM
ejpam-5924	164	17	10−8	10−8	NUM
ejpam-5924	164	18	0.8	0.8	NUM
ejpam-5924	164	19	0.8	0.8	NUM
ejpam-5924	164	20	1.66653898	1.66653898	NUM
ejpam-5924	164	21	1.66653898	1.66653898	NUM
ejpam-5924	164	22	0	0	NUM
ejpam-5924	164	23	1.666538925	1.666538925	NUM
ejpam-5924	164	24	5.5×	5.5×	NUM
ejpam-5924	164	25	10−8	10−8	NUM
ejpam-5924	164	26	0.9	0.9	NUM
ejpam-5924	164	27	0.9	0.9	NUM
ejpam-5924	164	28	1.919545908	1.919545908	NUM
ejpam-5924	164	29	1.919545908	1.919545908	NUM
ejpam-5924	164	30	0	0	NUM
ejpam-5924	164	31	1.919545853	1.919545853	NUM
ejpam-5924	164	32	5.5×	5.5×	NUM
ejpam-5924	164	33	10−8	10−8	NUM
ejpam-5924	164	34	1.0	1.0	NUM
ejpam-5924	164	35	1.0	1.0	NUM
ejpam-5924	164	36	2.178248842	2.178248842	NUM
ejpam-5924	164	37	2.178248842	2.178248842	NUM
ejpam-5924	164	38	0	0	NUM
ejpam-5924	164	39	2.178248787	2.178248787	NUM
ejpam-5924	164	40	5.5×	5.5×	NUM
ejpam-5924	164	41	10−8	10−8	NUM
ejpam-5924	164	42	figure	figure	NOUN
ejpam-5924	164	43	13	13	NUM
ejpam-5924	164	44	:	:	PUNCT
ejpam-5924	164	45	exact	exact	ADJ
ejpam-5924	164	46	solution	solution	NOUN
ejpam-5924	164	47	of	of	ADP
ejpam-5924	164	48	(	(	PUNCT
ejpam-5924	164	49	adm	adm	PROPN
ejpam-5924	164	50	)	)	PUNCT
ejpam-5924	164	51	for	for	ADP
ejpam-5924	164	52	α	α	NOUN
ejpam-5924	164	53	=	=	SYM
ejpam-5924	164	54	0.8	0.8	NUM
ejpam-5924	164	55	in	in	ADP
ejpam-5924	164	56	application	application	NOUN
ejpam-5924	164	57	4	4	NUM
ejpam-5924	164	58	figure	figure	NOUN
ejpam-5924	164	59	14	14	NUM
ejpam-5924	164	60	:	:	PUNCT
ejpam-5924	164	61	approximate	approximate	ADJ
ejpam-5924	164	62	solution	solution	NOUN
ejpam-5924	164	63	of	of	ADP
ejpam-5924	164	64	(	(	PUNCT
ejpam-5924	164	65	adm	adm	PROPN
ejpam-5924	164	66	)	)	PUNCT
ejpam-5924	164	67	for	for	ADP
ejpam-5924	164	68	α	α	NOUN
ejpam-5924	164	69	=	=	SYM
ejpam-5924	164	70	0.8	0.8	NUM
ejpam-5924	164	71	in	in	ADP
ejpam-5924	164	72	application	application	NOUN
ejpam-5924	164	73	4	4	NUM
ejpam-5924	164	74	a.	a.	NOUN
ejpam-5924	164	75	m.	m.	NOUN
ejpam-5924	164	76	al	al	PROPN
ejpam-5924	164	77	-	-	PUNCT
ejpam-5924	164	78	bugami	bugami	NOUN
ejpam-5924	164	79	,	,	PUNCT
ejpam-5924	164	80	n.	n.	NOUN
ejpam-5924	164	81	a.	a.	NOUN
ejpam-5924	164	82	alharbi	alharbi	PROPN
ejpam-5924	164	83	,	,	PUNCT
ejpam-5924	164	84	a.	a.	NOUN
ejpam-5924	164	85	m.	m.	PROPN
ejpam-5924	164	86	s.	s.	PROPN
ejpam-5924	164	87	mahdy	mahdy	PROPN
ejpam-5924	164	88	/	/	SYM
ejpam-5924	164	89	eur	eur	PROPN
ejpam-5924	164	90	.	.	PUNCT
ejpam-5924	165	1	j.	j.	PROPN
ejpam-5924	165	2	pure	pure	PROPN
ejpam-5924	165	3	appl	appl	PROPN
ejpam-5924	165	4	.	.	PROPN
ejpam-5924	165	5	math	math	PROPN
ejpam-5924	165	6	,	,	PUNCT
ejpam-5924	165	7	18	18	NUM
ejpam-5924	165	8	(	(	PUNCT
ejpam-5924	165	9	2	2	NUM
ejpam-5924	165	10	)	)	PUNCT
ejpam-5924	165	11	(	(	PUNCT
ejpam-5924	165	12	2025	2025	NUM
ejpam-5924	165	13	)	)	PUNCT
ejpam-5924	165	14	,	,	PUNCT
ejpam-5924	165	15	5924	5924	NUM
ejpam-5924	165	16	13	13	NUM
ejpam-5924	165	17	of	of	ADP
ejpam-5924	165	18	14	14	NUM
ejpam-5924	165	19	figure	figure	NOUN
ejpam-5924	165	20	15	15	NUM
ejpam-5924	165	21	:	:	PUNCT
ejpam-5924	165	22	exact	exact	ADJ
ejpam-5924	165	23	solution	solution	NOUN
ejpam-5924	165	24	of	of	ADP
ejpam-5924	165	25	(	(	PUNCT
ejpam-5924	165	26	ham	ham	NOUN
ejpam-5924	165	27	)	)	PUNCT
ejpam-5924	165	28	for	for	ADP
ejpam-5924	165	29	α	α	NOUN
ejpam-5924	165	30	=	=	SYM
ejpam-5924	165	31	0.8	0.8	NUM
ejpam-5924	165	32	in	in	ADP
ejpam-5924	165	33	application	application	NOUN
ejpam-5924	165	34	4	4	NUM
ejpam-5924	165	35	figure	figure	NOUN
ejpam-5924	165	36	16	16	NUM
ejpam-5924	165	37	:	:	PUNCT
ejpam-5924	165	38	approximate	approximate	ADJ
ejpam-5924	165	39	solution	solution	NOUN
ejpam-5924	165	40	of	of	ADP
ejpam-5924	165	41	(	(	PUNCT
ejpam-5924	165	42	ham	ham	NOUN
ejpam-5924	165	43	)	)	PUNCT
ejpam-5924	165	44	for	for	ADP
ejpam-5924	165	45	α	α	NOUN
ejpam-5924	165	46	=	=	SYM
ejpam-5924	165	47	0.8	0.8	NUM
ejpam-5924	165	48	in	in	ADP
ejpam-5924	165	49	application	application	NOUN
ejpam-5924	165	50	4	4	NUM
ejpam-5924	165	51	6	6	NUM
ejpam-5924	165	52	.	.	PUNCT
ejpam-5924	166	1	conclusion	conclusion	NOUN
ejpam-5924	166	2	from	from	ADP
ejpam-5924	166	3	the	the	DET
ejpam-5924	166	4	previous	previous	ADJ
ejpam-5924	166	5	study	study	NOUN
ejpam-5924	166	6	,	,	PUNCT
ejpam-5924	166	7	we	we	PRON
ejpam-5924	166	8	concluded	conclude	VERB
ejpam-5924	166	9	the	the	DET
ejpam-5924	166	10	following	following	NOUN
ejpam-5924	166	11	:	:	PUNCT
ejpam-5924	166	12	as	as	ADP
ejpam-5924	166	13	s	s	PROPN
ejpam-5924	166	14	,	,	PUNCT
ejpam-5924	166	15	t	t	PROPN
ejpam-5924	166	16	are	be	AUX
ejpam-5924	166	17	increasing	increase	VERB
ejpam-5924	166	18	in	in	ADP
ejpam-5924	166	19	[	[	X
ejpam-5924	166	20	0	0	NUM
ejpam-5924	166	21	,	,	PUNCT
ejpam-5924	166	22	1]×[0	1]×[0	NUM
ejpam-5924	166	23	,	,	PUNCT
ejpam-5924	166	24	1	1	NUM
ejpam-5924	166	25	]	]	PUNCT
ejpam-5924	166	26	the	the	DET
ejpam-5924	166	27	error	error	NOUN
ejpam-5924	166	28	for	for	ADP
ejpam-5924	166	29	(	(	PUNCT
ejpam-5924	166	30	adm	adm	PROPN
ejpam-5924	166	31	)	)	PUNCT
ejpam-5924	166	32	is	be	AUX
ejpam-5924	166	33	increasing	increase	VERB
ejpam-5924	166	34	and	and	CCONJ
ejpam-5924	166	35	for	for	ADP
ejpam-5924	166	36	(	(	PUNCT
ejpam-5924	166	37	ham	ham	NOUN
ejpam-5924	166	38	)	)	PUNCT
ejpam-5924	166	39	is	be	AUX
ejpam-5924	166	40	remain	remain	VERB
ejpam-5924	166	41	constant	constant	ADJ
ejpam-5924	166	42	at	at	ADP
ejpam-5924	166	43	108	108	NUM
ejpam-5924	166	44	.	.	PUNCT
ejpam-5924	167	1	in	in	ADP
ejpam-5924	167	2	nonlinear	nonlinear	ADJ
ejpam-5924	167	3	case	case	NOUN
ejpam-5924	167	4	the	the	DET
ejpam-5924	167	5	using	use	VERB
ejpam-5924	167	6	0.8	0.8	NUM
ejpam-5924	167	7	is	be	AUX
ejpam-5924	167	8	a	a	DET
ejpam-5924	167	9	smaller	small	ADJ
ejpam-5924	167	10	than	than	ADP
ejpam-5924	167	11	by	by	ADP
ejpam-5924	167	12	0.5	0.5	NUM
ejpam-5924	167	13	.	.	PUNCT
ejpam-5924	168	1	the	the	DET
ejpam-5924	168	2	error	error	NOUN
ejpam-5924	168	3	using	use	VERB
ejpam-5924	168	4	0.8	0.8	NUM
ejpam-5924	168	5	is	be	AUX
ejpam-5924	168	6	it	it	PRON
ejpam-5924	168	7	smaller	small	ADJ
ejpam-5924	168	8	than	than	ADP
ejpam-5924	168	9	in	in	ADP
ejpam-5924	168	10	(	(	PUNCT
ejpam-5924	168	11	adm	adm	PROPN
ejpam-5924	168	12	)	)	PUNCT
ejpam-5924	168	13	and	and	CCONJ
ejpam-5924	168	14	(	(	PUNCT
ejpam-5924	168	15	ham),(adm	ham),(adm	ADV
ejpam-5924	168	16	)	)	PUNCT
ejpam-5924	168	17	using	use	VERB
ejpam-5924	168	18	0.8	0.8	NUM
ejpam-5924	168	19	is	be	AUX
ejpam-5924	168	20	more	more	ADV
ejpam-5924	168	21	accurate	accurate	ADJ
ejpam-5924	168	22	than	than	ADP
ejpam-5924	168	23	using	use	VERB
ejpam-5924	168	24	0.5	0.5	NUM
ejpam-5924	168	25	.	.	PUNCT
ejpam-5924	169	1	at	at	ADP
ejpam-5924	169	2	n	n	NOUN
ejpam-5924	169	3	=	=	NUM
ejpam-5924	169	4	10	10	NUM
ejpam-5924	169	5	the	the	DET
ejpam-5924	169	6	error	error	NOUN
ejpam-5924	169	7	is	be	AUX
ejpam-5924	169	8	decreasing	decrease	VERB
ejpam-5924	169	9	in	in	ADP
ejpam-5924	169	10	linear	linear	NOUN
ejpam-5924	169	11	and	and	CCONJ
ejpam-5924	169	12	nonlinear	nonlinear	VERB
ejpam-5924	169	13	case.when	case.when	SCONJ
ejpam-5924	169	14	using	use	VERB
ejpam-5924	169	15	the	the	DET
ejpam-5924	169	16	same	same	ADJ
ejpam-5924	169	17	fractional	fractional	ADJ
ejpam-5924	169	18	order	order	NOUN
ejpam-5924	169	19	(	(	PUNCT
ejpam-5924	169	20	adm	adm	PROPN
ejpam-5924	169	21	)	)	PUNCT
ejpam-5924	169	22	and	and	CCONJ
ejpam-5924	169	23	(	(	PUNCT
ejpam-5924	169	24	ham	ham	NOUN
ejpam-5924	169	25	)	)	PUNCT
ejpam-5924	169	26	,	,	PUNCT
ejpam-5924	169	27	exactly	exactly	ADV
ejpam-5924	169	28	the	the	DET
ejpam-5924	169	29	same	same	ADJ
ejpam-5924	169	30	error	error	NOUN
ejpam-5924	169	31	,	,	PUNCT
ejpam-5924	169	32	but	but	CCONJ
ejpam-5924	169	33	using	use	VERB
ejpam-5924	169	34	fractional	fractional	ADJ
ejpam-5924	169	35	order	order	NOUN
ejpam-5924	169	36	0.8	0.8	NUM
ejpam-5924	169	37	,	,	PUNCT
ejpam-5924	169	38	(	(	PUNCT
ejpam-5924	169	39	adm	adm	PROPN
ejpam-5924	169	40	)	)	PUNCT
ejpam-5924	169	41	convergences	convergence	NOUN
ejpam-5924	169	42	faster	fast	ADV
ejpam-5924	169	43	than	than	ADP
ejpam-5924	169	44	(	(	PUNCT
ejpam-5924	169	45	ham	ham	NOUN
ejpam-5924	169	46	)	)	PUNCT
ejpam-5924	169	47	.	.	PUNCT
ejpam-5924	170	1	the	the	DET
ejpam-5924	170	2	error	error	NOUN
ejpam-5924	170	3	decreases	decrease	VERB
ejpam-5924	170	4	when	when	SCONJ
ejpam-5924	170	5	the	the	DET
ejpam-5924	170	6	fractional	fractional	ADJ
ejpam-5924	170	7	order	order	NOUN
ejpam-5924	170	8	of	of	ADP
ejpam-5924	170	9	(	(	PUNCT
ejpam-5924	170	10	adm	adm	PROPN
ejpam-5924	170	11	)	)	PUNCT
ejpam-5924	170	12	increases	increase	NOUN
ejpam-5924	170	13	and	and	CCONJ
ejpam-5924	170	14	the	the	DET
ejpam-5924	170	15	error	error	NOUN
ejpam-5924	170	16	for	for	ADP
ejpam-5924	170	17	(	(	PUNCT
ejpam-5924	170	18	ham	ham	NOUN
ejpam-5924	170	19	)	)	PUNCT
ejpam-5924	170	20	remains	remain	VERB
ejpam-5924	170	21	the	the	DET
ejpam-5924	170	22	same	same	ADJ
ejpam-5924	170	23	.	.	PUNCT
ejpam-5924	171	1	when	when	SCONJ
ejpam-5924	171	2	the	the	DET
ejpam-5924	171	3	fractional	fractional	ADJ
ejpam-5924	171	4	order	order	NOUN
ejpam-5924	171	5	of	of	ADP
ejpam-5924	171	6	(	(	PUNCT
ejpam-5924	171	7	adm	adm	PROPN
ejpam-5924	171	8	)	)	PUNCT
ejpam-5924	171	9	is	be	AUX
ejpam-5924	171	10	0.8	0.8	NUM
ejpam-5924	171	11	,	,	PUNCT
ejpam-5924	171	12	the	the	DET
ejpam-5924	171	13	error	error	NOUN
ejpam-5924	171	14	increases	increase	NOUN
ejpam-5924	171	15	,	,	PUNCT
ejpam-5924	171	16	whereas	whereas	SCONJ
ejpam-5924	171	17	when	when	SCONJ
ejpam-5924	171	18	the	the	DET
ejpam-5924	171	19	fractional	fractional	ADJ
ejpam-5924	171	20	order	order	NOUN
ejpam-5924	171	21	is	be	AUX
ejpam-5924	171	22	0.8	0.8	NUM
ejpam-5924	171	23	,	,	PUNCT
ejpam-5924	171	24	the	the	DET
ejpam-5924	171	25	error	error	NOUN
ejpam-5924	171	26	decreases	decrease	VERB
ejpam-5924	171	27	.	.	PUNCT
ejpam-5924	172	1	the	the	DET
ejpam-5924	172	2	maple	maple	NOUN
ejpam-5924	172	3	program	program	NOUN
ejpam-5924	172	4	was	be	AUX
ejpam-5924	172	5	used	use	VERB
ejpam-5924	172	6	to	to	PART
ejpam-5924	172	7	write	write	VERB
ejpam-5924	172	8	the	the	DET
ejpam-5924	172	9	codes	code	NOUN
ejpam-5924	172	10	.	.	PUNCT
ejpam-5924	173	1	future	future	ADJ
ejpam-5924	173	2	work	work	NOUN
ejpam-5924	173	3	.	.	PUNCT
ejpam-5924	174	1	other	other	ADJ
ejpam-5924	174	2	methods	method	NOUN
ejpam-5924	174	3	,	,	PUNCT
ejpam-5924	174	4	such	such	ADJ
ejpam-5924	174	5	as	as	ADP
ejpam-5924	174	6	the	the	DET
ejpam-5924	174	7	homomtopy	homomtopy	NOUN
ejpam-5924	174	8	perturbation	perturbation	NOUN
ejpam-5924	174	9	method	method	NOUN
ejpam-5924	174	10	,	,	PUNCT
ejpam-5924	174	11	the	the	DET
ejpam-5924	174	12	galerkin	galerkin	ADJ
ejpam-5924	174	13	method	method	NOUN
ejpam-5924	174	14	,	,	PUNCT
ejpam-5924	174	15	the	the	DET
ejpam-5924	174	16	collocation	collocation	NOUN
ejpam-5924	174	17	method	method	NOUN
ejpam-5924	174	18	and	and	CCONJ
ejpam-5924	174	19	chypechev	chypechev	ADJ
ejpam-5924	174	20	polynomial	polynomial	ADJ
ejpam-5924	174	21	,	,	PUNCT
ejpam-5924	174	22	will	will	AUX
ejpam-5924	174	23	be	be	AUX
ejpam-5924	174	24	used	use	VERB
ejpam-5924	174	25	to	to	PART
ejpam-5924	174	26	solve	solve	VERB
ejpam-5924	174	27	the	the	DET
ejpam-5924	174	28	tdfnfi	tdfnfi	NOUN
ejpam-5924	174	29	-	-	PUNCT
ejpam-5924	174	30	de	de	NOUN
ejpam-5924	174	31	,	,	PUNCT
ejpam-5924	174	32	and	and	CCONJ
ejpam-5924	174	33	compare	compare	VERB
ejpam-5924	174	34	with	with	ADP
ejpam-5924	174	35	adm	adm	PROPN
ejpam-5924	174	36	and	and	CCONJ
ejpam-5924	174	37	ham	ham	PROPN
ejpam-5924	174	38	.	.	PUNCT
ejpam-5924	175	1	references	reference	NOUN
ejpam-5924	175	2	[	[	X
ejpam-5924	175	3	1	1	NUM
ejpam-5924	175	4	]	]	PUNCT
ejpam-5924	175	5	amandeep	amandeep	NOUN
ejpam-5924	175	6	singh	singh	PROPN
ejpam-5924	175	7	and	and	CCONJ
ejpam-5924	175	8	sarita	sarita	PROPN
ejpam-5924	175	9	pippal	pippal	NOUN
ejpam-5924	175	10	.	.	PUNCT
ejpam-5924	176	1	solving	solve	VERB
ejpam-5924	176	2	nonlinear	nonlinear	ADJ
ejpam-5924	176	3	fractional	fractional	ADJ
ejpam-5924	176	4	differential	differential	NOUN
ejpam-5924	176	5	equations	equation	NOUN
ejpam-5924	176	6	by	by	ADP
ejpam-5924	176	7	using	use	VERB
ejpam-5924	176	8	shehu	shehu	NOUN
ejpam-5924	176	9	transform	transform	VERB
ejpam-5924	176	10	and	and	CCONJ
ejpam-5924	176	11	adomian	adomian	NOUN
ejpam-5924	176	12	polynomials	polynomial	NOUN
ejpam-5924	176	13	.	.	PUNCT
ejpam-5924	177	1	pages	page	NOUN
ejpam-5924	177	2	797–816	797–816	NUM
ejpam-5924	177	3	,	,	PUNCT
ejpam-5924	177	4	2024	2024	NUM
ejpam-5924	177	5	.	.	PUNCT
ejpam-5924	178	1	[	[	X
ejpam-5924	178	2	2	2	X
ejpam-5924	178	3	]	]	X
ejpam-5924	178	4	khalid	khalid	PROPN
ejpam-5924	178	5	k	k	PROPN
ejpam-5924	178	6	ali	ali	PROPN
ejpam-5924	178	7	,	,	PUNCT
ejpam-5924	178	8	mohamed	mohame	VERB
ejpam-5924	178	9	a	a	DET
ejpam-5924	178	10	abd	abd	PROPN
ejpam-5924	178	11	el	el	PROPN
ejpam-5924	178	12	salam	salam	PROPN
ejpam-5924	178	13	,	,	PUNCT
ejpam-5924	178	14	emad	emad	PROPN
ejpam-5924	178	15	mh	mh	PROPN
ejpam-5924	178	16	mohamed	mohamed	PROPN
ejpam-5924	178	17	,	,	PUNCT
ejpam-5924	178	18	bessem	bessem	NOUN
ejpam-5924	178	19	samet	samet	NOUN
ejpam-5924	178	20	,	,	PUNCT
ejpam-5924	178	21	sunil	sunil	PROPN
ejpam-5924	178	22	kumar	kumar	PROPN
ejpam-5924	178	23	,	,	PUNCT
ejpam-5924	178	24	and	and	CCONJ
ejpam-5924	178	25	ms	ms	PROPN
ejpam-5924	178	26	osman	osman	PROPN
ejpam-5924	178	27	.	.	PUNCT
ejpam-5924	179	1	numerical	numerical	ADJ
ejpam-5924	179	2	solution	solution	NOUN
ejpam-5924	179	3	for	for	ADP
ejpam-5924	179	4	generalized	generalized	ADJ
ejpam-5924	179	5	nonlinear	nonlinear	ADJ
ejpam-5924	179	6	fractional	fractional	ADJ
ejpam-5924	179	7	integro	integro	ADJ
ejpam-5924	179	8	-	-	PUNCT
ejpam-5924	179	9	differential	differential	NOUN
ejpam-5924	179	10	equations	equation	NOUN
ejpam-5924	179	11	with	with	ADP
ejpam-5924	179	12	linear	linear	ADJ
ejpam-5924	179	13	functional	functional	ADJ
ejpam-5924	179	14	arguments	argument	NOUN
ejpam-5924	179	15	using	use	VERB
ejpam-5924	179	16	chebyshev	chebyshev	NOUN
ejpam-5924	179	17	series	series	NOUN
ejpam-5924	179	18	.	.	PUNCT
ejpam-5924	180	1	2020:494	2020:494	NUM
ejpam-5924	180	2	,	,	PUNCT
ejpam-5924	180	3	2020	2020	NUM
ejpam-5924	180	4	.	.	PUNCT
ejpam-5924	181	1	[	[	X
ejpam-5924	181	2	3	3	X
ejpam-5924	181	3	]	]	PUNCT
ejpam-5924	181	4	taiye	taiye	PRON
ejpam-5924	181	5	oyedepo	oyedepo	NOUN
ejpam-5924	181	6	,	,	PUNCT
ejpam-5924	181	7	christie	christie	PROPN
ejpam-5924	181	8	yemisi	yemisi	PROPN
ejpam-5924	181	9	ishola	ishola	PROPN
ejpam-5924	181	10	,	,	PUNCT
ejpam-5924	181	11	adam	adam	PROPN
ejpam-5924	181	12	ajimoti	ajimoti	PROPN
ejpam-5924	181	13	ishaq	ishaq	PROPN
ejpam-5924	181	14	,	,	PUNCT
ejpam-5924	181	15	abdullahi	abdullahi	PROPN
ejpam-5924	181	16	muhammed	muhammed	PROPN
ejpam-5924	181	17	a.	a.	PROPN
ejpam-5924	181	18	m.	m.	PROPN
ejpam-5924	181	19	al	al	PROPN
ejpam-5924	181	20	-	-	PUNCT
ejpam-5924	181	21	bugami	bugami	NOUN
ejpam-5924	181	22	,	,	PUNCT
ejpam-5924	181	23	n.	n.	NOUN
ejpam-5924	181	24	a.	a.	NOUN
ejpam-5924	181	25	alharbi	alharbi	PROPN
ejpam-5924	181	26	,	,	PUNCT
ejpam-5924	181	27	a.	a.	NOUN
ejpam-5924	181	28	m.	m.	PROPN
ejpam-5924	181	29	s.	s.	PROPN
ejpam-5924	181	30	mahdy	mahdy	PROPN
ejpam-5924	181	31	/	/	SYM
ejpam-5924	181	32	eur	eur	PROPN
ejpam-5924	181	33	.	.	PUNCT
ejpam-5924	182	1	j.	j.	PROPN
ejpam-5924	182	2	pure	pure	PROPN
ejpam-5924	182	3	appl	appl	PROPN
ejpam-5924	182	4	.	.	PROPN
ejpam-5924	182	5	math	math	PROPN
ejpam-5924	182	6	,	,	PUNCT
ejpam-5924	182	7	18	18	NUM
ejpam-5924	182	8	(	(	PUNCT
ejpam-5924	182	9	2	2	NUM
ejpam-5924	182	10	)	)	PUNCT
ejpam-5924	182	11	(	(	PUNCT
ejpam-5924	182	12	2025	2025	NUM
ejpam-5924	182	13	)	)	PUNCT
ejpam-5924	182	14	,	,	PUNCT
ejpam-5924	182	15	5924	5924	NUM
ejpam-5924	182	16	14	14	NUM
ejpam-5924	182	17	of	of	ADP
ejpam-5924	182	18	14	14	NUM
ejpam-5924	182	19	ayinde	ayinde	NOUN
ejpam-5924	182	20	,	,	PUNCT
ejpam-5924	182	21	and	and	CCONJ
ejpam-5924	182	22	olalekan	olalekan	PROPN
ejpam-5924	182	23	lukman	lukman	PROPN
ejpam-5924	182	24	ahmed	ahmed	PROPN
ejpam-5924	182	25	.	.	PUNCT
ejpam-5924	183	1	computational	computational	ADJ
ejpam-5924	183	2	algorithm	algorithm	NOUN
ejpam-5924	183	3	for	for	ADP
ejpam-5924	183	4	fractional	fractional	ADJ
ejpam-5924	183	5	fredholm	fredholm	NOUN
ejpam-5924	183	6	integro	integro	ADJ
ejpam-5924	183	7	-	-	PUNCT
ejpam-5924	183	8	differential	differential	NOUN
ejpam-5924	183	9	equations	equation	NOUN
ejpam-5924	183	10	.	.	PUNCT
ejpam-5924	184	1	17(1	17(1	NUM
ejpam-5924	184	2	)	)	PUNCT
ejpam-5924	184	3	,	,	PUNCT
ejpam-5924	184	4	2023	2023	NUM
ejpam-5924	184	5	.	.	PUNCT
ejpam-5924	185	1	[	[	X
ejpam-5924	185	2	4	4	X
ejpam-5924	185	3	]	]	PUNCT
ejpam-5924	185	4	antonela	antonela	NOUN
ejpam-5924	185	5	toma	toma	PROPN
ejpam-5924	185	6	and	and	CCONJ
ejpam-5924	185	7	octavian	octavian	ADJ
ejpam-5924	185	8	postavaru	postavaru	NOUN
ejpam-5924	185	9	.	.	PUNCT
ejpam-5924	186	1	a	a	DET
ejpam-5924	186	2	numerical	numerical	ADJ
ejpam-5924	186	3	method	method	NOUN
ejpam-5924	186	4	to	to	PART
ejpam-5924	186	5	solve	solve	VERB
ejpam-5924	186	6	fractional	fractional	ADJ
ejpam-5924	186	7	fredholm	fredholm	NOUN
ejpam-5924	186	8	-	-	PUNCT
ejpam-5924	186	9	volterra	volterra	NOUN
ejpam-5924	186	10	integro	integro	PROPN
ejpam-5924	186	11	-	-	PUNCT
ejpam-5924	186	12	differential	differential	NOUN
ejpam-5924	186	13	equations	equation	NOUN
ejpam-5924	186	14	.	.	PUNCT
ejpam-5924	187	1	68:469–478	68:469–478	NOUN
ejpam-5924	187	2	,	,	PUNCT
ejpam-5924	187	3	2023	2023	NUM
ejpam-5924	187	4	.	.	PUNCT
ejpam-5924	188	1	[	[	X
ejpam-5924	188	2	5	5	NUM
ejpam-5924	188	3	]	]	X
ejpam-5924	188	4	m	m	VERB
ejpam-5924	188	5	a	a	DET
ejpam-5924	188	6	abdou	abdou	NOUN
ejpam-5924	188	7	,	,	PUNCT
ejpam-5924	189	1	i	i	PROPN
ejpam-5924	189	2	l	l	PROPN
ejpam-5924	189	3	el	el	PROPN
ejpam-5924	189	4	-	-	PUNCT
ejpam-5924	189	5	kalla	kalla	PROPN
ejpam-5924	189	6	,	,	PUNCT
ejpam-5924	189	7	and	and	CCONJ
ejpam-5924	189	8	a	a	DET
ejpam-5924	189	9	m	m	PROPN
ejpam-5924	189	10	al	al	PROPN
ejpam-5924	189	11	-	-	PUNCT
ejpam-5924	189	12	bugami	bugami	NOUN
ejpam-5924	189	13	.	.	PUNCT
ejpam-5924	190	1	new	new	ADJ
ejpam-5924	190	2	approach	approach	NOUN
ejpam-5924	190	3	for	for	ADP
ejpam-5924	190	4	convergence	convergence	NOUN
ejpam-5924	190	5	of	of	ADP
ejpam-5924	190	6	the	the	DET
ejpam-5924	190	7	series	series	NOUN
ejpam-5924	190	8	solution	solution	NOUN
ejpam-5924	190	9	to	to	ADP
ejpam-5924	190	10	a	a	DET
ejpam-5924	190	11	class	class	NOUN
ejpam-5924	190	12	of	of	ADP
ejpam-5924	190	13	nonlinear	nonlinear	PROPN
ejpam-5924	190	14	hammerstein	hammerstein	PROPN
ejpam-5924	190	15	integral	integral	ADJ
ejpam-5924	190	16	equations	equation	NOUN
ejpam-5924	190	17	.	.	PUNCT
ejpam-5924	191	1	3(4):261–269	3(4):261–269	NUM
ejpam-5924	191	2	,	,	PUNCT
ejpam-5924	191	3	2011	2011	NUM
ejpam-5924	191	4	.	.	PUNCT
ejpam-5924	192	1	[	[	X
ejpam-5924	192	2	6	6	NUM
ejpam-5924	192	3	]	]	PUNCT
ejpam-5924	192	4	k.	k.	PROPN
ejpam-5924	192	5	abbaoui	abbaoui	PROPN
ejpam-5924	192	6	and	and	CCONJ
ejpam-5924	192	7	y.	y.	PROPN
ejpam-5924	192	8	cherruault	cherruault	PROPN
ejpam-5924	192	9	.	.	PUNCT
ejpam-5924	193	1	convergence	convergence	NOUN
ejpam-5924	193	2	of	of	ADP
ejpam-5924	193	3	adomian	adomian	NOUN
ejpam-5924	193	4	’s	’s	PART
ejpam-5924	193	5	method	method	NOUN
ejpam-5924	193	6	applied	apply	VERB
ejpam-5924	193	7	to	to	ADP
ejpam-5924	193	8	nonlinear	nonlinear	ADJ
ejpam-5924	193	9	equations	equation	NOUN
ejpam-5924	193	10	.	.	PUNCT
ejpam-5924	194	1	20(9):69–73	20(9):69–73	NUM
ejpam-5924	194	2	,	,	PUNCT
ejpam-5924	194	3	1994	1994	NUM
ejpam-5924	194	4	.	.	PUNCT
ejpam-5924	195	1	[	[	X
ejpam-5924	195	2	7	7	X
ejpam-5924	195	3	]	]	X
ejpam-5924	195	4	s.h	s.h	PROPN
ejpam-5924	195	5	.	.	PROPN
ejpam-5924	195	6	behiry	behiry	PROPN
ejpam-5924	195	7	,	,	PUNCT
ejpam-5924	195	8	h.	h.	PROPN
ejpam-5924	195	9	hashish	hashish	PROPN
ejpam-5924	195	10	,	,	PUNCT
ejpam-5924	195	11	i.l	i.l	PROPN
ejpam-5924	195	12	.	.	PROPN
ejpam-5924	196	1	el	el	PROPN
ejpam-5924	196	2	-	-	PUNCT
ejpam-5924	196	3	kalla	kalla	PROPN
ejpam-5924	196	4	,	,	PUNCT
ejpam-5924	196	5	and	and	CCONJ
ejpam-5924	196	6	a.	a.	NOUN
ejpam-5924	196	7	elsaid	elsaid	PROPN
ejpam-5924	196	8	.	.	PUNCT
ejpam-5924	197	1	a	a	DET
ejpam-5924	197	2	new	new	ADJ
ejpam-5924	197	3	algorithm	algorithm	NOUN
ejpam-5924	197	4	for	for	ADP
ejpam-5924	197	5	the	the	DET
ejpam-5924	197	6	decomposition	decomposition	NOUN
ejpam-5924	197	7	solution	solution	NOUN
ejpam-5924	197	8	of	of	ADP
ejpam-5924	197	9	nonlinear	nonlinear	ADJ
ejpam-5924	197	10	differential	differential	ADJ
ejpam-5924	197	11	equations	equation	NOUN
ejpam-5924	197	12	.	.	PUNCT
ejpam-5924	198	1	54(4):459–466	54(4):459–466	NUM
ejpam-5924	198	2	,	,	PUNCT
ejpam-5924	198	3	2007	2007	NUM
ejpam-5924	198	4	.	.	PUNCT
ejpam-5924	199	1	[	[	X
ejpam-5924	199	2	8	8	NUM
ejpam-5924	199	3	]	]	X
ejpam-5924	199	4	boutheina	boutheina	PROPN
ejpam-5924	199	5	tair	tair	PROPN
ejpam-5924	199	6	,	,	PUNCT
ejpam-5924	199	7	sami	sami	PROPN
ejpam-5924	199	8	segni	segni	PROPN
ejpam-5924	199	9	,	,	PUNCT
ejpam-5924	199	10	hamza	hamza	NOUN
ejpam-5924	199	11	guebbai	guebbai	NOUN
ejpam-5924	199	12	,	,	PUNCT
ejpam-5924	199	13	and	and	CCONJ
ejpam-5924	199	14	mourad	mourad	PROPN
ejpam-5924	199	15	ghait	ghait	PROPN
ejpam-5924	199	16	.	.	PUNCT
ejpam-5924	200	1	two	two	NUM
ejpam-5924	200	2	numerical	numerical	ADJ
ejpam-5924	200	3	treatments	treatment	NOUN
ejpam-5924	200	4	for	for	ADP
ejpam-5924	200	5	solving	solve	VERB
ejpam-5924	200	6	the	the	DET
ejpam-5924	200	7	linear	linear	ADJ
ejpam-5924	200	8	integro	integro	ADJ
ejpam-5924	200	9	-	-	PUNCT
ejpam-5924	200	10	differential	differential	NOUN
ejpam-5924	200	11	fredholm	fredholm	NOUN
ejpam-5924	200	12	equation	equation	NOUN
ejpam-5924	200	13	with	with	ADP
ejpam-5924	200	14	a	a	DET
ejpam-5924	200	15	weakly	weakly	ADJ
ejpam-5924	200	16	singular	singular	ADJ
ejpam-5924	200	17	kernel	kernel	NOUN
ejpam-5924	200	18	.	.	PUNCT
ejpam-5924	201	1	23(2):117–136	23(2):117–136	NUM
ejpam-5924	201	2	,	,	PUNCT
ejpam-5924	201	3	2022	2022	NUM
ejpam-5924	201	4	.	.	PUNCT
ejpam-5924	202	1	[	[	X
ejpam-5924	202	2	9	9	NUM
ejpam-5924	202	3	]	]	X
ejpam-5924	202	4	abeer	abeer	PROPN
ejpam-5924	202	5	m.	m.	PROPN
ejpam-5924	202	6	al	al	PROPN
ejpam-5924	202	7	-	-	PUNCT
ejpam-5924	202	8	bugami	bugami	NOUN
ejpam-5924	202	9	.	.	PUNCT
ejpam-5924	203	1	two	two	NUM
ejpam-5924	203	2	-	-	PUNCT
ejpam-5924	203	3	dimensional	dimensional	ADJ
ejpam-5924	203	4	fredholm	fredholm	NOUN
ejpam-5924	203	5	integro	integro	ADJ
ejpam-5924	203	6	-	-	PUNCT
ejpam-5924	203	7	differential	differential	NOUN
ejpam-5924	203	8	equation	equation	NOUN
ejpam-5924	203	9	with	with	ADP
ejpam-5924	203	10	singular	singular	ADJ
ejpam-5924	203	11	kernel	kernel	NOUN
ejpam-5924	203	12	and	and	CCONJ
ejpam-5924	203	13	its	its	PRON
ejpam-5924	203	14	numerical	numerical	ADJ
ejpam-5924	203	15	solutions	solution	NOUN
ejpam-5924	203	16	.	.	PUNCT
ejpam-5924	204	1	2022(2501947):1–8	2022(2501947):1–8	NUM
ejpam-5924	204	2	,	,	PUNCT
ejpam-5924	204	3	2022	2022	NUM
ejpam-5924	204	4	.	.	PUNCT
ejpam-5924	205	1	[	[	X
ejpam-5924	205	2	10	10	NUM
ejpam-5924	205	3	]	]	X
ejpam-5924	205	4	d	d	X
ejpam-5924	205	5	abbaszadeh	abbaszadeh	NOUN
ejpam-5924	205	6	,	,	PUNCT
ejpam-5924	205	7	m	m	VERB
ejpam-5924	205	8	tavassoli	tavassoli	PROPN
ejpam-5924	205	9	kajani	kajani	PROPN
ejpam-5924	205	10	,	,	PUNCT
ejpam-5924	205	11	m	m	VERB
ejpam-5924	205	12	momeni	momeni	ADJ
ejpam-5924	205	13	,	,	PUNCT
ejpam-5924	205	14	m	m	VERB
ejpam-5924	205	15	zahraei	zahraei	ADJ
ejpam-5924	205	16	,	,	PUNCT
ejpam-5924	205	17	and	and	CCONJ
ejpam-5924	205	18	m	m	PROPN
ejpam-5924	205	19	maleki	maleki	NOUN
ejpam-5924	205	20	.	.	PUNCT
ejpam-5924	206	1	solving	solve	VERB
ejpam-5924	206	2	fractional	fractional	ADJ
ejpam-5924	206	3	fredholm	fredholm	NOUN
ejpam-5924	206	4	integro	integro	ADJ
ejpam-5924	206	5	–	–	PUNCT
ejpam-5924	206	6	differential	differential	ADJ
ejpam-5924	206	7	equations	equation	NOUN
ejpam-5924	206	8	using	use	VERB
ejpam-5924	206	9	legendre	legendre	PROPN
ejpam-5924	206	10	wavelets	wavelet	NOUN
ejpam-5924	206	11	.	.	PUNCT
ejpam-5924	207	1	166:168	166:168	NOUN
ejpam-5924	207	2	–	–	PUNCT
ejpam-5924	207	3	185	185	NUM
ejpam-5924	207	4	,	,	PUNCT
ejpam-5924	207	5	2021	2021	NUM
ejpam-5924	207	6	.	.	PUNCT
ejpam-5924	208	1	[	[	X
ejpam-5924	208	2	11	11	NUM
ejpam-5924	208	3	]	]	X
ejpam-5924	208	4	mahmoud	mahmoud	PROPN
ejpam-5924	208	5	s	s	PART
ejpam-5924	208	6	rawashdeh	rawashdeh	NOUN
ejpam-5924	208	7	,	,	PUNCT
ejpam-5924	208	8	hala	hala	PROPN
ejpam-5924	208	9	abedalqader	abedalqader	NOUN
ejpam-5924	208	10	,	,	PUNCT
ejpam-5924	208	11	and	and	CCONJ
ejpam-5924	208	12	nazek	nazek	VERB
ejpam-5924	208	13	a	a	DET
ejpam-5924	208	14	obeidat	obeidat	NOUN
ejpam-5924	208	15	.	.	PUNCT
ejpam-5924	209	1	convergence	convergence	NOUN
ejpam-5924	209	2	analysis	analysis	NOUN
ejpam-5924	209	3	for	for	ADP
ejpam-5924	209	4	the	the	DET
ejpam-5924	209	5	fractional	fractional	ADJ
ejpam-5924	209	6	decomposition	decomposition	NOUN
ejpam-5924	209	7	method	method	NOUN
ejpam-5924	209	8	applied	apply	VERB
ejpam-5924	209	9	to	to	ADP
ejpam-5924	209	10	class	class	NOUN
ejpam-5924	209	11	of	of	ADP
ejpam-5924	209	12	nonlinear	nonlinear	ADJ
ejpam-5924	209	13	fractional	fractional	ADJ
ejpam-5924	209	14	fredholm	fredholm	NOUN
ejpam-5924	209	15	integro	integro	ADJ
ejpam-5924	209	16	-	-	PUNCT
ejpam-5924	209	17	differential	differential	NOUN
ejpam-5924	209	18	equation	equation	NOUN
ejpam-5924	209	19	.	.	PUNCT
ejpam-5924	210	1	17:174830262211511	17:174830262211511	NUM
ejpam-5924	210	2	,	,	PUNCT
ejpam-5924	210	3	2023	2023	NUM
ejpam-5924	210	4	.	.	PUNCT
ejpam-5924	211	1	[	[	X
ejpam-5924	211	2	12	12	NUM
ejpam-5924	211	3	]	]	PUNCT
ejpam-5924	211	4	wenjin	wenjin	PROPN
ejpam-5924	211	5	li	li	PROPN
ejpam-5924	211	6	and	and	CCONJ
ejpam-5924	211	7	yanni	yanni	PROPN
ejpam-5924	211	8	pang	pang	PROPN
ejpam-5924	211	9	.	.	PUNCT
ejpam-5924	212	1	application	application	NOUN
ejpam-5924	212	2	of	of	ADP
ejpam-5924	212	3	adomian	adomian	ADJ
ejpam-5924	212	4	decomposition	decomposition	NOUN
ejpam-5924	212	5	method	method	NOUN
ejpam-5924	212	6	to	to	ADP
ejpam-5924	212	7	nonlinear	nonlinear	ADJ
ejpam-5924	212	8	systems	system	NOUN
ejpam-5924	212	9	.	.	PUNCT
ejpam-5924	213	1	2020(1):67	2020(1):67	NUM
ejpam-5924	213	2	,	,	PUNCT
ejpam-5924	213	3	2020	2020	NUM
ejpam-5924	213	4	.	.	PUNCT
ejpam-5924	214	1	[	[	X
ejpam-5924	214	2	13	13	NUM
ejpam-5924	214	3	]	]	SYM
ejpam-5924	214	4	shaher	shaher	ADJ
ejpam-5924	214	5	momani	momani	PROPN
ejpam-5924	214	6	and	and	CCONJ
ejpam-5924	214	7	muhammad	muhammad	PROPN
ejpam-5924	214	8	aslam	aslam	PROPN
ejpam-5924	214	9	noor	noor	PROPN
ejpam-5924	214	10	.	.	PUNCT
ejpam-5924	215	1	numerical	numerical	ADJ
ejpam-5924	215	2	methods	method	NOUN
ejpam-5924	215	3	for	for	ADP
ejpam-5924	215	4	fourth	fourth	ADJ
ejpam-5924	215	5	-	-	PUNCT
ejpam-5924	215	6	order	order	NOUN
ejpam-5924	215	7	fractional	fractional	ADJ
ejpam-5924	215	8	integro	integro	ADJ
ejpam-5924	215	9	-	-	PUNCT
ejpam-5924	215	10	differential	differential	NOUN
ejpam-5924	215	11	equations	equation	NOUN
ejpam-5924	215	12	.	.	PUNCT
ejpam-5924	216	1	182(1):754–760	182(1):754–760	NUM
ejpam-5924	216	2	,	,	PUNCT
ejpam-5924	216	3	2006	2006	NUM
ejpam-5924	216	4	.	.	PUNCT
ejpam-5924	217	1	[	[	X
ejpam-5924	217	2	14	14	NUM
ejpam-5924	217	3	]	]	PUNCT
ejpam-5924	217	4	a.	a.	NOUN
ejpam-5924	217	5	m.	m.	PROPN
ejpam-5924	217	6	al	al	PROPN
ejpam-5924	217	7	-	-	PUNCT
ejpam-5924	217	8	bugami	bugami	NOUN
ejpam-5924	217	9	.	.	PUNCT
ejpam-5924	218	1	nonlinear	nonlinear	ADJ
ejpam-5924	218	2	fredholm	fredholm	PROPN
ejpam-5924	218	3	integro	integro	ADJ
ejpam-5924	218	4	-	-	PUNCT
ejpam-5924	218	5	differential	differential	NOUN
ejpam-5924	218	6	equation	equation	NOUN
ejpam-5924	218	7	in	in	ADP
ejpam-5924	218	8	two	two	NUM
ejpam-5924	218	9	-	-	PUNCT
ejpam-5924	218	10	dimensional	dimensional	ADJ
ejpam-5924	218	11	and	and	CCONJ
ejpam-5924	218	12	its	its	PRON
ejpam-5924	218	13	numerical	numerical	ADJ
ejpam-5924	218	14	solutions	solution	NOUN
ejpam-5924	218	15	.	.	PUNCT
ejpam-5924	218	16	6(10):10383–10394	6(10):10383–10394	NUM
ejpam-5924	218	17	,	,	PUNCT
ejpam-5924	218	18	2021	2021	NUM
ejpam-5924	218	19	.	.	PUNCT
ejpam-5924	219	1	[	[	X
ejpam-5924	219	2	15	15	NUM
ejpam-5924	219	3	]	]	X
ejpam-5924	219	4	nabaa	nabaa	PROPN
ejpam-5924	219	5	n	n	PROPN
ejpam-5924	219	6	hasan	hasan	PROPN
ejpam-5924	219	7	.	.	PUNCT
ejpam-5924	220	1	adomian	adomian	PROPN
ejpam-5924	220	2	decomposition	decomposition	NOUN
ejpam-5924	220	3	method	method	NOUN
ejpam-5924	220	4	applied	apply	VERB
ejpam-5924	220	5	to	to	ADP
ejpam-5924	220	6	nonlinear	nonlinear	ADJ
ejpam-5924	220	7	system	system	NOUN
ejpam-5924	220	8	of	of	ADP
ejpam-5924	220	9	fractional	fractional	ADJ
ejpam-5924	220	10	fredholm	fredholm	NOUN
ejpam-5924	220	11	integro	integro	ADJ
ejpam-5924	220	12	-	-	PUNCT
ejpam-5924	220	13	differential	differential	NOUN
ejpam-5924	220	14	equations	equation	NOUN
ejpam-5924	220	15	.	.	PUNCT
ejpam-5924	221	1	24(5	24(5	NUM
ejpam-5924	221	2	)	)	PUNCT
ejpam-5924	221	3	,	,	PUNCT
ejpam-5924	221	4	2013	2013	NUM
ejpam-5924	221	5	.	.	PUNCT
ejpam-5924	222	1	[	[	X
ejpam-5924	222	2	16	16	NUM
ejpam-5924	222	3	]	]	X
ejpam-5924	222	4	i.l	i.l	PROPN
ejpam-5924	222	5	.	.	PROPN
ejpam-5924	222	6	el	el	PROPN
ejpam-5924	222	7	-	-	PUNCT
ejpam-5924	222	8	kalla	kalla	PROPN
ejpam-5924	222	9	.	.	PUNCT
ejpam-5924	223	1	new	new	ADJ
ejpam-5924	223	2	results	result	NOUN
ejpam-5924	223	3	on	on	ADP
ejpam-5924	223	4	the	the	DET
ejpam-5924	223	5	analytic	analytic	ADJ
ejpam-5924	223	6	summation	summation	NOUN
ejpam-5924	223	7	of	of	ADP
ejpam-5924	223	8	adomian	adomian	PROPN
ejpam-5924	223	9	series	series	NOUN
ejpam-5924	223	10	for	for	ADP
ejpam-5924	223	11	some	some	DET
ejpam-5924	223	12	classes	class	NOUN
ejpam-5924	223	13	of	of	ADP
ejpam-5924	223	14	differential	differential	ADJ
ejpam-5924	223	15	and	and	CCONJ
ejpam-5924	223	16	integral	integral	ADJ
ejpam-5924	223	17	equations	equation	NOUN
ejpam-5924	223	18	.	.	PUNCT
ejpam-5924	224	1	217(8):3756–3763	217(8):3756–3763	NUM
ejpam-5924	224	2	,	,	PUNCT
ejpam-5924	224	3	2010	2010	NUM
ejpam-5924	224	4	.	.	PUNCT
ejpam-5924	225	1	[	[	X
ejpam-5924	225	2	17	17	NUM
ejpam-5924	225	3	]	]	X
ejpam-5924	225	4	i.l	i.l	PROPN
ejpam-5924	225	5	.	.	PROPN
ejpam-5924	225	6	el	el	PROPN
ejpam-5924	225	7	-	-	PUNCT
ejpam-5924	225	8	kalla	kalla	PROPN
ejpam-5924	225	9	.	.	PUNCT
ejpam-5924	226	1	piece	piece	NOUN
ejpam-5924	226	2	-	-	PUNCT
ejpam-5924	226	3	wise	wise	ADJ
ejpam-5924	226	4	continuous	continuous	ADJ
ejpam-5924	226	5	solution	solution	NOUN
ejpam-5924	226	6	to	to	ADP
ejpam-5924	226	7	a	a	DET
ejpam-5924	226	8	class	class	NOUN
ejpam-5924	226	9	of	of	ADP
ejpam-5924	226	10	nonlinear	nonlinear	ADJ
ejpam-5924	226	11	boundary	boundary	ADJ
ejpam-5924	226	12	value	value	NOUN
ejpam-5924	226	13	problems	problem	NOUN
ejpam-5924	226	14	.	.	PUNCT
ejpam-5924	227	1	4(2):325–331	4(2):325–331	NUM
ejpam-5924	227	2	,	,	PUNCT
ejpam-5924	227	3	2013	2013	NUM
ejpam-5924	227	4	.	.	PUNCT