id	sid	tid	token	lemma	pos
ejpam-6982	1	1	european	european	PROPN
ejpam-6982	1	2	journal	journal	PROPN
ejpam-6982	1	3	of	of	ADP
ejpam-6982	1	4	pure	pure	ADJ
ejpam-6982	1	5	and	and	CCONJ
ejpam-6982	1	6	applied	applied	ADJ
ejpam-6982	1	7	mathematics	mathematic	NOUN
ejpam-6982	1	8	2025	2025	NUM
ejpam-6982	1	9	,	,	PUNCT
ejpam-6982	1	10	vol	vol	NOUN
ejpam-6982	1	11	.	.	PROPN
ejpam-6982	1	12	18	18	NUM
ejpam-6982	1	13	,	,	PUNCT
ejpam-6982	1	14	issue	issue	NOUN
ejpam-6982	1	15	4	4	NUM
ejpam-6982	1	16	,	,	PUNCT
ejpam-6982	1	17	article	article	NOUN
ejpam-6982	1	18	number	number	NOUN
ejpam-6982	1	19	6982	6982	NUM
ejpam-6982	1	20	issn	issn	PROPN
ejpam-6982	1	21	1307	1307	NUM
ejpam-6982	1	22	-	-	SYM
ejpam-6982	1	23	5543	5543	NUM
ejpam-6982	1	24	–	–	PUNCT
ejpam-6982	1	25	ejpam.com	ejpam.com	X
ejpam-6982	1	26	published	publish	VERB
ejpam-6982	1	27	by	by	ADP
ejpam-6982	1	28	new	new	PROPN
ejpam-6982	1	29	york	york	PROPN
ejpam-6982	1	30	business	business	PROPN
ejpam-6982	1	31	global	global	ADJ
ejpam-6982	1	32	qualitative	qualitative	ADJ
ejpam-6982	1	33	study	study	NOUN
ejpam-6982	1	34	on	on	ADP
ejpam-6982	1	35	semi	semi	ADJ
ejpam-6982	1	36	-	-	ADJ
ejpam-6982	1	37	analytical	analytical	ADJ
ejpam-6982	1	38	methods	method	NOUN
ejpam-6982	1	39	for	for	ADP
ejpam-6982	1	40	solving	solve	VERB
ejpam-6982	1	41	nonlinear	nonlinear	ADJ
ejpam-6982	1	42	time	time	NOUN
ejpam-6982	1	43	-	-	PUNCT
ejpam-6982	1	44	fractional	fractional	ADJ
ejpam-6982	1	45	partial	partial	ADJ
ejpam-6982	1	46	differential	differential	NOUN
ejpam-6982	1	47	equations	equation	NOUN
ejpam-6982	1	48	alaa	alaa	PROPN
ejpam-6982	1	49	mohammad	mohammad	PROPN
ejpam-6982	1	50	alhammad1	alhammad1	PROPN
ejpam-6982	1	51	,	,	PUNCT
ejpam-6982	1	52	abdulkafi	abdulkafi	PROPN
ejpam-6982	1	53	mohammed	mohammed	PROPN
ejpam-6982	1	54	saeed1,∗	saeed1,∗	PROPN
ejpam-6982	1	55	1	1	NUM
ejpam-6982	1	56	department	department	NOUN
ejpam-6982	1	57	of	of	ADP
ejpam-6982	1	58	mathematics	mathematic	NOUN
ejpam-6982	1	59	,	,	PUNCT
ejpam-6982	1	60	college	college	NOUN
ejpam-6982	1	61	of	of	ADP
ejpam-6982	1	62	science	science	NOUN
ejpam-6982	1	63	,	,	PUNCT
ejpam-6982	1	64	qassim	qassim	PROPN
ejpam-6982	1	65	university	university	PROPN
ejpam-6982	1	66	,	,	PUNCT
ejpam-6982	1	67	buraydah	buraydah	NOUN
ejpam-6982	1	68	51452	51452	NUM
ejpam-6982	1	69	,	,	PUNCT
ejpam-6982	1	70	saudi	saudi	PROPN
ejpam-6982	1	71	arabia	arabia	PROPN
ejpam-6982	1	72	abstract	abstract	NOUN
ejpam-6982	1	73	.	.	PUNCT
ejpam-6982	2	1	this	this	DET
ejpam-6982	2	2	paper	paper	NOUN
ejpam-6982	2	3	focuses	focus	VERB
ejpam-6982	2	4	on	on	ADP
ejpam-6982	2	5	finding	find	VERB
ejpam-6982	2	6	semi	semi	ADJ
ejpam-6982	2	7	-	-	ADJ
ejpam-6982	2	8	analytical	analytical	ADJ
ejpam-6982	2	9	solutions	solution	NOUN
ejpam-6982	2	10	of	of	ADP
ejpam-6982	2	11	nonlinear	nonlinear	ADJ
ejpam-6982	2	12	partial	partial	ADJ
ejpam-6982	2	13	differential	differential	ADJ
ejpam-6982	2	14	equations	equation	NOUN
ejpam-6982	2	15	of	of	ADP
ejpam-6982	2	16	fractional	fractional	ADJ
ejpam-6982	2	17	order	order	NOUN
ejpam-6982	2	18	by	by	ADP
ejpam-6982	2	19	using	use	VERB
ejpam-6982	2	20	four	four	NUM
ejpam-6982	2	21	techniques	technique	NOUN
ejpam-6982	2	22	such	such	ADJ
ejpam-6982	2	23	as	as	ADP
ejpam-6982	2	24	sumudu	sumudu	NOUN
ejpam-6982	2	25	decomposition	decomposition	NOUN
ejpam-6982	2	26	,	,	PUNCT
ejpam-6982	2	27	natural	natural	ADJ
ejpam-6982	2	28	decomposition	decomposition	NOUN
ejpam-6982	2	29	,	,	PUNCT
ejpam-6982	2	30	adomian	adomian	NOUN
ejpam-6982	2	31	decomposition	decomposition	NOUN
ejpam-6982	2	32	and	and	CCONJ
ejpam-6982	2	33	modified	modify	VERB
ejpam-6982	2	34	laplace	laplace	NOUN
ejpam-6982	2	35	variational	variational	ADJ
ejpam-6982	2	36	iteration	iteration	NOUN
ejpam-6982	2	37	methods	method	NOUN
ejpam-6982	2	38	.	.	PUNCT
ejpam-6982	3	1	the	the	DET
ejpam-6982	3	2	fractional	fractional	ADJ
ejpam-6982	3	3	derivatives	derivative	NOUN
ejpam-6982	3	4	are	be	AUX
ejpam-6982	3	5	described	describe	VERB
ejpam-6982	3	6	in	in	ADP
ejpam-6982	3	7	the	the	DET
ejpam-6982	3	8	caputo	caputo	PROPN
ejpam-6982	3	9	sense	sense	NOUN
ejpam-6982	3	10	.	.	PUNCT
ejpam-6982	4	1	in	in	ADP
ejpam-6982	4	2	these	these	DET
ejpam-6982	4	3	methods	method	NOUN
ejpam-6982	4	4	,	,	PUNCT
ejpam-6982	4	5	the	the	DET
ejpam-6982	4	6	solution	solution	NOUN
ejpam-6982	4	7	manifests	manifest	VERB
ejpam-6982	4	8	as	as	ADP
ejpam-6982	4	9	a	a	DET
ejpam-6982	4	10	convergent	convergent	NOUN
ejpam-6982	4	11	series	series	NOUN
ejpam-6982	4	12	with	with	ADP
ejpam-6982	4	13	conveniently	conveniently	ADV
ejpam-6982	4	14	computable	computable	ADJ
ejpam-6982	4	15	components	component	NOUN
ejpam-6982	4	16	.	.	PUNCT
ejpam-6982	5	1	numerical	numerical	ADJ
ejpam-6982	5	2	results	result	NOUN
ejpam-6982	5	3	show	show	VERB
ejpam-6982	5	4	that	that	SCONJ
ejpam-6982	5	5	the	the	DET
ejpam-6982	5	6	four	four	NUM
ejpam-6982	5	7	approaches	approach	NOUN
ejpam-6982	5	8	are	be	AUX
ejpam-6982	5	9	easy	easy	ADJ
ejpam-6982	5	10	to	to	PART
ejpam-6982	5	11	implement	implement	VERB
ejpam-6982	5	12	and	and	CCONJ
ejpam-6982	5	13	accurate	accurate	ADJ
ejpam-6982	5	14	when	when	SCONJ
ejpam-6982	5	15	applied	apply	VERB
ejpam-6982	5	16	to	to	ADP
ejpam-6982	5	17	partial	partial	ADJ
ejpam-6982	5	18	differential	differential	ADJ
ejpam-6982	5	19	equations	equation	NOUN
ejpam-6982	5	20	of	of	ADP
ejpam-6982	5	21	fractional	fractional	ADJ
ejpam-6982	5	22	order	order	NOUN
ejpam-6982	5	23	,	,	PUNCT
ejpam-6982	5	24	although	although	SCONJ
ejpam-6982	5	25	there	there	PRON
ejpam-6982	5	26	are	be	VERB
ejpam-6982	5	27	some	some	DET
ejpam-6982	5	28	distinct	distinct	ADJ
ejpam-6982	5	29	differences	difference	NOUN
ejpam-6982	5	30	between	between	ADP
ejpam-6982	5	31	the	the	DET
ejpam-6982	5	32	methods	method	NOUN
ejpam-6982	5	33	studied	study	VERB
ejpam-6982	5	34	,	,	PUNCT
ejpam-6982	5	35	which	which	PRON
ejpam-6982	5	36	depend	depend	VERB
ejpam-6982	5	37	on	on	ADP
ejpam-6982	5	38	the	the	DET
ejpam-6982	5	39	nature	nature	NOUN
ejpam-6982	5	40	of	of	ADP
ejpam-6982	5	41	the	the	DET
ejpam-6982	5	42	equations	equation	NOUN
ejpam-6982	5	43	and	and	CCONJ
ejpam-6982	5	44	the	the	DET
ejpam-6982	5	45	conditions	condition	NOUN
ejpam-6982	5	46	associated	associate	VERB
ejpam-6982	5	47	with	with	ADP
ejpam-6982	5	48	them	they	PRON
ejpam-6982	5	49	.	.	PUNCT
ejpam-6982	6	1	2020	2020	NUM
ejpam-6982	6	2	mathematics	mathematic	NOUN
ejpam-6982	6	3	subject	subject	NOUN
ejpam-6982	6	4	classifications	classification	NOUN
ejpam-6982	6	5	:	:	PUNCT
ejpam-6982	6	6	35b45	35b45	NUM
ejpam-6982	6	7	,	,	PUNCT
ejpam-6982	6	8	35d30	35d30	NUM
ejpam-6982	6	9	,	,	PUNCT
ejpam-6982	6	10	35d35	35d35	NUM
ejpam-6982	6	11	key	key	ADJ
ejpam-6982	6	12	words	word	NOUN
ejpam-6982	6	13	and	and	CCONJ
ejpam-6982	6	14	phrases	phrase	NOUN
ejpam-6982	6	15	:	:	PUNCT
ejpam-6982	6	16	nonlinear	nonlinear	ADJ
ejpam-6982	6	17	partial	partial	ADJ
ejpam-6982	6	18	differential	differential	NOUN
ejpam-6982	6	19	equations	equation	NOUN
ejpam-6982	6	20	,	,	PUNCT
ejpam-6982	6	21	adomian	adomian	NOUN
ejpam-6982	6	22	decomposition	decomposition	NOUN
ejpam-6982	6	23	method	method	NOUN
ejpam-6982	6	24	,	,	PUNCT
ejpam-6982	6	25	modified	modify	VERB
ejpam-6982	6	26	variational	variational	ADJ
ejpam-6982	6	27	iteration	iteration	NOUN
ejpam-6982	6	28	laplace	laplace	NOUN
ejpam-6982	6	29	transform	transform	NOUN
ejpam-6982	6	30	method	method	NOUN
ejpam-6982	6	31	1	1	NUM
ejpam-6982	6	32	.	.	PUNCT
ejpam-6982	7	1	introduction	introduction	NOUN
ejpam-6982	7	2	fractional	fractional	ADJ
ejpam-6982	7	3	calculus	calculus	NOUN
ejpam-6982	7	4	is	be	AUX
ejpam-6982	7	5	a	a	DET
ejpam-6982	7	6	field	field	NOUN
ejpam-6982	7	7	of	of	ADP
ejpam-6982	7	8	mathematics	mathematic	NOUN
ejpam-6982	7	9	study	study	NOUN
ejpam-6982	7	10	that	that	PRON
ejpam-6982	7	11	grows	grow	VERB
ejpam-6982	7	12	out	out	ADP
ejpam-6982	7	13	of	of	ADP
ejpam-6982	7	14	the	the	DET
ejpam-6982	7	15	traditional	traditional	ADJ
ejpam-6982	7	16	definitions	definition	NOUN
ejpam-6982	7	17	of	of	ADP
ejpam-6982	7	18	calculus	calculus	NOUN
ejpam-6982	7	19	integral	integral	ADJ
ejpam-6982	7	20	and	and	CCONJ
ejpam-6982	7	21	derivative	derivative	ADJ
ejpam-6982	7	22	operators	operator	NOUN
ejpam-6982	7	23	in	in	ADP
ejpam-6982	7	24	much	much	ADV
ejpam-6982	7	25	the	the	DET
ejpam-6982	7	26	same	same	ADJ
ejpam-6982	7	27	way	way	NOUN
ejpam-6982	7	28	frictional	frictional	ADJ
ejpam-6982	7	29	are	be	AUX
ejpam-6982	7	30	an	an	DET
ejpam-6982	7	31	outgrowth	outgrowth	NOUN
ejpam-6982	7	32	of	of	ADP
ejpam-6982	7	33	exponents	exponent	NOUN
ejpam-6982	7	34	with	with	ADP
ejpam-6982	7	35	integer	integer	NOUN
ejpam-6982	7	36	values	value	NOUN
ejpam-6982	7	37	.	.	PUNCT
ejpam-6982	8	1	fractional	fractional	ADJ
ejpam-6982	8	2	calculus	calculus	NOUN
ejpam-6982	8	3	has	have	AUX
ejpam-6982	8	4	been	be	AUX
ejpam-6982	8	5	part	part	NOUN
ejpam-6982	8	6	of	of	ADP
ejpam-6982	8	7	mathematics	mathematic	NOUN
ejpam-6982	8	8	and	and	CCONJ
ejpam-6982	8	9	science	science	NOUN
ejpam-6982	8	10	literature	literature	NOUN
ejpam-6982	8	11	for	for	ADP
ejpam-6982	8	12	more	more	ADJ
ejpam-6982	8	13	than	than	ADP
ejpam-6982	8	14	three	three	NUM
ejpam-6982	8	15	centuries	century	NOUN
ejpam-6982	8	16	.	.	PUNCT
ejpam-6982	9	1	it	it	PRON
ejpam-6982	9	2	has	have	AUX
ejpam-6982	9	3	been	be	AUX
ejpam-6982	9	4	used	use	VERB
ejpam-6982	9	5	to	to	PART
ejpam-6982	9	6	model	model	VERB
ejpam-6982	9	7	physical	physical	ADJ
ejpam-6982	9	8	and	and	CCONJ
ejpam-6982	9	9	engineering	engineering	NOUN
ejpam-6982	9	10	processes	process	NOUN
ejpam-6982	9	11	that	that	PRON
ejpam-6982	9	12	are	be	AUX
ejpam-6982	9	13	found	find	VERB
ejpam-6982	9	14	to	to	PART
ejpam-6982	9	15	be	be	AUX
ejpam-6982	9	16	best	well	ADV
ejpam-6982	9	17	described	describe	VERB
ejpam-6982	9	18	by	by	ADP
ejpam-6982	9	19	fractional	fractional	ADJ
ejpam-6982	9	20	differential	differential	ADJ
ejpam-6982	9	21	equations	equation	NOUN
ejpam-6982	10	1	[	[	X
ejpam-6982	10	2	1–4	1–4	X
ejpam-6982	10	3	]	]	PUNCT
ejpam-6982	10	4	.	.	PUNCT
ejpam-6982	11	1	recent	recent	ADJ
ejpam-6982	11	2	research	research	NOUN
ejpam-6982	11	3	has	have	AUX
ejpam-6982	11	4	studied	study	VERB
ejpam-6982	11	5	the	the	DET
ejpam-6982	11	6	applications	application	NOUN
ejpam-6982	11	7	of	of	ADP
ejpam-6982	11	8	fractional	fractional	ADJ
ejpam-6982	11	9	calculus	calculus	NOUN
ejpam-6982	11	10	in	in	ADP
ejpam-6982	11	11	several	several	ADJ
ejpam-6982	11	12	domains	domain	NOUN
ejpam-6982	11	13	,	,	PUNCT
ejpam-6982	11	14	including	include	VERB
ejpam-6982	11	15	fractional	fractional	ADJ
ejpam-6982	11	16	-	-	PUNCT
ejpam-6982	11	17	order	order	NOUN
ejpam-6982	11	18	epidemic	epidemic	NOUN
ejpam-6982	11	19	models	model	NOUN
ejpam-6982	11	20	[	[	X
ejpam-6982	11	21	5	5	NUM
ejpam-6982	11	22	]	]	PUNCT
ejpam-6982	11	23	,	,	PUNCT
ejpam-6982	11	24	fractional	fractional	ADJ
ejpam-6982	11	25	-	-	PUNCT
ejpam-6982	11	26	order	order	NOUN
ejpam-6982	11	27	optimal	optimal	ADJ
ejpam-6982	11	28	control	control	NOUN
ejpam-6982	11	29	problem	problem	NOUN
ejpam-6982	11	30	[	[	X
ejpam-6982	11	31	6	6	NUM
ejpam-6982	11	32	]	]	PUNCT
ejpam-6982	11	33	.	.	PUNCT
ejpam-6982	12	1	most	most	ADJ
ejpam-6982	12	2	phenomena	phenomenon	NOUN
ejpam-6982	12	3	in	in	ADP
ejpam-6982	12	4	nature	nature	NOUN
ejpam-6982	12	5	are	be	AUX
ejpam-6982	12	6	described	describe	VERB
ejpam-6982	12	7	by	by	ADP
ejpam-6982	12	8	nonlinear	nonlinear	ADJ
ejpam-6982	12	9	differential	differential	ADJ
ejpam-6982	12	10	equations	equation	NOUN
ejpam-6982	12	11	.	.	PUNCT
ejpam-6982	13	1	therefore	therefore	ADV
ejpam-6982	13	2	,	,	PUNCT
ejpam-6982	13	3	scientists	scientist	NOUN
ejpam-6982	13	4	in	in	ADP
ejpam-6982	13	5	different	different	ADJ
ejpam-6982	13	6	branches	branch	NOUN
ejpam-6982	13	7	of	of	ADP
ejpam-6982	13	8	science	science	NOUN
ejpam-6982	13	9	try	try	VERB
ejpam-6982	13	10	to	to	PART
ejpam-6982	13	11	solve	solve	VERB
ejpam-6982	13	12	them	they	PRON
ejpam-6982	13	13	.	.	PUNCT
ejpam-6982	14	1	but	but	CCONJ
ejpam-6982	14	2	because	because	SCONJ
ejpam-6982	14	3	of	of	ADP
ejpam-6982	14	4	the	the	DET
ejpam-6982	14	5	nonlinear	nonlinear	ADJ
ejpam-6982	14	6	part	part	NOUN
ejpam-6982	14	7	of	of	ADP
ejpam-6982	14	8	these	these	DET
ejpam-6982	14	9	groups	group	NOUN
ejpam-6982	14	10	of	of	ADP
ejpam-6982	14	11	equations	equation	NOUN
ejpam-6982	14	12	,	,	PUNCT
ejpam-6982	14	13	finding	find	VERB
ejpam-6982	14	14	an	an	DET
ejpam-6982	14	15	exact	exact	ADJ
ejpam-6982	14	16	solution	solution	NOUN
ejpam-6982	14	17	is	be	AUX
ejpam-6982	14	18	not	not	PART
ejpam-6982	14	19	easy	easy	ADJ
ejpam-6982	14	20	[	[	X
ejpam-6982	14	21	7	7	NUM
ejpam-6982	14	22	]	]	SYM
ejpam-6982	14	23	.	.	PUNCT
ejpam-6982	15	1	approximation	approximation	NOUN
ejpam-6982	15	2	and	and	CCONJ
ejpam-6982	15	3	numerical	numerical	ADJ
ejpam-6982	15	4	techniques	technique	NOUN
ejpam-6982	15	5	must	must	AUX
ejpam-6982	15	6	be	be	AUX
ejpam-6982	15	7	used	use	VERB
ejpam-6982	15	8	.	.	PUNCT
ejpam-6982	16	1	the	the	DET
ejpam-6982	16	2	adomian	adomian	NOUN
ejpam-6982	16	3	decomposition	decomposition	NOUN
ejpam-6982	16	4	method	method	NOUN
ejpam-6982	17	1	[	[	X
ejpam-6982	17	2	8–11	8–11	NOUN
ejpam-6982	17	3	]	]	PUNCT
ejpam-6982	17	4	,	,	PUNCT
ejpam-6982	17	5	the	the	DET
ejpam-6982	17	6	sumudu	sumudu	NOUN
ejpam-6982	17	7	decomposition	decomposition	NOUN
ejpam-6982	17	8	method	method	NOUN
ejpam-6982	17	9	[	[	X
ejpam-6982	17	10	12	12	NUM
ejpam-6982	17	11	]	]	PUNCT
ejpam-6982	17	12	,	,	PUNCT
ejpam-6982	17	13	the	the	DET
ejpam-6982	17	14	natural	natural	ADJ
ejpam-6982	17	15	∗corresponding	∗corresponde	VERB
ejpam-6982	17	16	author	author	NOUN
ejpam-6982	17	17	.	.	PUNCT
ejpam-6982	18	1	doi	doi	NOUN
ejpam-6982	18	2	:	:	PUNCT
ejpam-6982	18	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6982	https://doi.org/10.29020/nybg.ejpam.v18i4.6982	NOUN
ejpam-6982	18	4	email	email	NOUN
ejpam-6982	18	5	addresses	address	NOUN
ejpam-6982	18	6	:	:	PUNCT
ejpam-6982	18	7	451214285@qu.edu.sa	451214285@qu.edu.sa	NUM
ejpam-6982	18	8	(	(	PUNCT
ejpam-6982	18	9	a.	a.	NOUN
ejpam-6982	18	10	m.	m.	NOUN
ejpam-6982	18	11	alhammad	alhammad	PROPN
ejpam-6982	18	12	)	)	PUNCT
ejpam-6982	18	13	,	,	PUNCT
ejpam-6982	18	14	abdulkafi.ahmed@qu.edu.sa	abdulkafi.ahmed@qu.edu.sa	PROPN
ejpam-6982	18	15	(	(	PUNCT
ejpam-6982	18	16	a.	a.	PROPN
ejpam-6982	18	17	m.	m.	PROPN
ejpam-6982	18	18	saeed	saeed	PROPN
ejpam-6982	18	19	)	)	PUNCT
ejpam-6982	18	20	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6982	18	21	1	1	NUM
ejpam-6982	18	22	copyright	copyright	NOUN
ejpam-6982	18	23	:	:	PUNCT
ejpam-6982	19	1	©	©	PROPN
ejpam-6982	19	2	2025	2025	NUM
ejpam-6982	19	3	the	the	DET
ejpam-6982	19	4	author(s	author(s	NOUN
ejpam-6982	19	5	)	)	PUNCT
ejpam-6982	19	6	.	.	PUNCT
ejpam-6982	20	1	(	(	PUNCT
ejpam-6982	20	2	cc	cc	NOUN
ejpam-6982	20	3	by	by	ADP
ejpam-6982	20	4	-	-	PUNCT
ejpam-6982	20	5	nc	nc	PROPN
ejpam-6982	20	6	4.0	4.0	NUM
ejpam-6982	20	7	)	)	PUNCT
ejpam-6982	20	8	a.	a.	NOUN
ejpam-6982	20	9	m.	m.	NOUN
ejpam-6982	20	10	alhammad	alhammad	PROPN
ejpam-6982	20	11	,	,	PUNCT
ejpam-6982	20	12	a.	a.	NOUN
ejpam-6982	20	13	m.	m.	PROPN
ejpam-6982	20	14	saeed	saeed	PROPN
ejpam-6982	20	15	/	/	SYM
ejpam-6982	20	16	eur	eur	PROPN
ejpam-6982	20	17	.	.	PUNCT
ejpam-6982	21	1	j.	j.	PROPN
ejpam-6982	21	2	pure	pure	PROPN
ejpam-6982	21	3	appl	appl	PROPN
ejpam-6982	21	4	.	.	PROPN
ejpam-6982	21	5	math	math	PROPN
ejpam-6982	21	6	,	,	PUNCT
ejpam-6982	21	7	18	18	NUM
ejpam-6982	21	8	(	(	PUNCT
ejpam-6982	21	9	4	4	NUM
ejpam-6982	21	10	)	)	PUNCT
ejpam-6982	21	11	(	(	PUNCT
ejpam-6982	21	12	2025	2025	NUM
ejpam-6982	21	13	)	)	PUNCT
ejpam-6982	21	14	,	,	PUNCT
ejpam-6982	21	15	6982	6982	NUM
ejpam-6982	21	16	2	2	NUM
ejpam-6982	21	17	of	of	ADP
ejpam-6982	21	18	22	22	NUM
ejpam-6982	21	19	decomposition	decomposition	NOUN
ejpam-6982	21	20	method	method	NOUN
ejpam-6982	21	21	[	[	X
ejpam-6982	21	22	13	13	NUM
ejpam-6982	21	23	]	]	PUNCT
ejpam-6982	21	24	and	and	CCONJ
ejpam-6982	21	25	modified	modify	VERB
ejpam-6982	21	26	laplace	laplace	NOUN
ejpam-6982	21	27	variational	variational	ADJ
ejpam-6982	21	28	iteration	iteration	NOUN
ejpam-6982	21	29	method	method	NOUN
ejpam-6982	22	1	[	[	X
ejpam-6982	22	2	14	14	NUM
ejpam-6982	22	3	]	]	PUNCT
ejpam-6982	22	4	are	be	AUX
ejpam-6982	22	5	relatively	relatively	ADV
ejpam-6982	22	6	new	new	ADJ
ejpam-6982	22	7	approaches	approach	NOUN
ejpam-6982	22	8	to	to	PART
ejpam-6982	22	9	provide	provide	VERB
ejpam-6982	22	10	an	an	DET
ejpam-6982	22	11	analytical	analytical	ADJ
ejpam-6982	22	12	approximation	approximation	NOUN
ejpam-6982	22	13	to	to	ADP
ejpam-6982	22	14	linear	linear	ADJ
ejpam-6982	22	15	and	and	CCONJ
ejpam-6982	22	16	nonlinear	nonlinear	ADJ
ejpam-6982	22	17	problems	problem	NOUN
ejpam-6982	22	18	,	,	PUNCT
ejpam-6982	22	19	and	and	CCONJ
ejpam-6982	22	20	they	they	PRON
ejpam-6982	22	21	are	be	AUX
ejpam-6982	22	22	particularly	particularly	ADV
ejpam-6982	22	23	valuable	valuable	ADJ
ejpam-6982	22	24	as	as	ADP
ejpam-6982	22	25	tools	tool	NOUN
ejpam-6982	22	26	for	for	ADP
ejpam-6982	22	27	scientists	scientist	NOUN
ejpam-6982	22	28	and	and	CCONJ
ejpam-6982	22	29	applied	apply	VERB
ejpam-6982	22	30	mathematicians	mathematician	NOUN
ejpam-6982	22	31	.	.	PUNCT
ejpam-6982	23	1	for	for	ADP
ejpam-6982	23	2	nonlinear	nonlinear	ADJ
ejpam-6982	23	3	models	model	NOUN
ejpam-6982	23	4	,	,	PUNCT
ejpam-6982	23	5	the	the	DET
ejpam-6982	23	6	previous	previous	ADJ
ejpam-6982	23	7	methods	method	NOUN
ejpam-6982	23	8	have	have	AUX
ejpam-6982	23	9	shown	show	VERB
ejpam-6982	23	10	dependable	dependable	ADJ
ejpam-6982	23	11	results	result	NOUN
ejpam-6982	23	12	and	and	CCONJ
ejpam-6982	23	13	give	give	VERB
ejpam-6982	23	14	analytical	analytical	ADJ
ejpam-6982	23	15	approximations	approximation	NOUN
ejpam-6982	23	16	solutions	solution	NOUN
ejpam-6982	23	17	that	that	PRON
ejpam-6982	23	18	converge	converge	VERB
ejpam-6982	23	19	very	very	ADV
ejpam-6982	23	20	rapidly	rapidly	ADV
ejpam-6982	23	21	.	.	PUNCT
ejpam-6982	24	1	this	this	DET
ejpam-6982	24	2	paper	paper	NOUN
ejpam-6982	24	3	is	be	AUX
ejpam-6982	24	4	organized	organize	VERB
ejpam-6982	24	5	as	as	SCONJ
ejpam-6982	24	6	follows	follow	VERB
ejpam-6982	24	7	:	:	PUNCT
ejpam-6982	24	8	section	section	NOUN
ejpam-6982	24	9	2	2	NUM
ejpam-6982	24	10	provides	provide	VERB
ejpam-6982	24	11	a	a	DET
ejpam-6982	24	12	brief	brief	ADJ
ejpam-6982	24	13	overview	overview	NOUN
ejpam-6982	24	14	of	of	ADP
ejpam-6982	24	15	basic	basic	ADJ
ejpam-6982	24	16	concept	concept	NOUN
ejpam-6982	24	17	of	of	ADP
ejpam-6982	24	18	fraction	fraction	NOUN
ejpam-6982	24	19	calculus	calculus	NOUN
ejpam-6982	24	20	.	.	PUNCT
ejpam-6982	25	1	section	section	NOUN
ejpam-6982	25	2	3	3	NUM
ejpam-6982	25	3	presents	present	VERB
ejpam-6982	25	4	the	the	DET
ejpam-6982	25	5	description	description	NOUN
ejpam-6982	25	6	of	of	ADP
ejpam-6982	25	7	proposed	propose	VERB
ejpam-6982	25	8	transformations	transformation	NOUN
ejpam-6982	25	9	methods	method	NOUN
ejpam-6982	25	10	and	and	CCONJ
ejpam-6982	25	11	the	the	DET
ejpam-6982	25	12	analysis	analysis	NOUN
ejpam-6982	25	13	of	of	ADP
ejpam-6982	25	14	these	these	DET
ejpam-6982	25	15	methods	method	NOUN
ejpam-6982	25	16	given	give	VERB
ejpam-6982	25	17	by	by	ADP
ejpam-6982	25	18	section	section	NOUN
ejpam-6982	25	19	4	4	NUM
ejpam-6982	25	20	.	.	PUNCT
ejpam-6982	25	21	section	section	NOUN
ejpam-6982	25	22	5	5	NUM
ejpam-6982	25	23	includes	include	VERB
ejpam-6982	25	24	the	the	DET
ejpam-6982	25	25	numerical	numerical	ADJ
ejpam-6982	25	26	experiments	experiment	NOUN
ejpam-6982	25	27	and	and	CCONJ
ejpam-6982	25	28	the	the	DET
ejpam-6982	25	29	comparison	comparison	NOUN
ejpam-6982	25	30	among	among	ADP
ejpam-6982	25	31	these	these	DET
ejpam-6982	25	32	methods	method	NOUN
ejpam-6982	25	33	.	.	PUNCT
ejpam-6982	26	1	the	the	DET
ejpam-6982	26	2	paper	paper	NOUN
ejpam-6982	26	3	ends	end	VERB
ejpam-6982	26	4	with	with	ADP
ejpam-6982	26	5	conclusion	conclusion	NOUN
ejpam-6982	26	6	and	and	CCONJ
ejpam-6982	26	7	final	final	ADJ
ejpam-6982	26	8	remarks	remark	NOUN
ejpam-6982	26	9	.	.	PUNCT
ejpam-6982	27	1	2	2	X
ejpam-6982	27	2	.	.	X
ejpam-6982	27	3	basic	basic	ADJ
ejpam-6982	27	4	concept	concept	NOUN
ejpam-6982	27	5	of	of	ADP
ejpam-6982	27	6	fractional	fractional	ADJ
ejpam-6982	27	7	calculus	calculus	NOUN
ejpam-6982	27	8	this	this	DET
ejpam-6982	27	9	section	section	NOUN
ejpam-6982	27	10	is	be	AUX
ejpam-6982	27	11	devoted	devote	VERB
ejpam-6982	27	12	to	to	ADP
ejpam-6982	27	13	a	a	DET
ejpam-6982	27	14	description	description	NOUN
ejpam-6982	27	15	of	of	ADP
ejpam-6982	27	16	the	the	DET
ejpam-6982	27	17	basic	basic	ADJ
ejpam-6982	27	18	ideas	idea	NOUN
ejpam-6982	27	19	of	of	ADP
ejpam-6982	27	20	fractional	fractional	ADJ
ejpam-6982	27	21	calculus	calculus	NOUN
ejpam-6982	27	22	,	,	PUNCT
ejpam-6982	27	23	which	which	PRON
ejpam-6982	27	24	are	be	AUX
ejpam-6982	27	25	essential	essential	ADJ
ejpam-6982	27	26	to	to	ADP
ejpam-6982	27	27	comprehending	comprehend	VERB
ejpam-6982	27	28	complex	complex	ADJ
ejpam-6982	27	29	systems	system	NOUN
ejpam-6982	27	30	,	,	PUNCT
ejpam-6982	27	31	and	and	CCONJ
ejpam-6982	27	32	explores	explore	VERB
ejpam-6982	27	33	the	the	DET
ejpam-6982	27	34	fundamental	fundamental	ADJ
ejpam-6982	27	35	meanings	meaning	NOUN
ejpam-6982	27	36	of	of	ADP
ejpam-6982	27	37	integrals	integral	NOUN
ejpam-6982	27	38	and	and	CCONJ
ejpam-6982	27	39	fractional	fractional	ADJ
ejpam-6982	27	40	derivatives	derivative	NOUN
ejpam-6982	27	41	,	,	PUNCT
ejpam-6982	27	42	as	as	ADV
ejpam-6982	27	43	well	well	ADV
ejpam-6982	27	44	as	as	ADP
ejpam-6982	27	45	their	their	PRON
ejpam-6982	27	46	different	different	ADJ
ejpam-6982	27	47	forms	form	NOUN
ejpam-6982	27	48	and	and	CCONJ
ejpam-6982	27	49	use	use	NOUN
ejpam-6982	27	50	.	.	PUNCT
ejpam-6982	28	1	definition	definition	NOUN
ejpam-6982	28	2	1	1	NUM
ejpam-6982	28	3	.	.	PUNCT
ejpam-6982	29	1	[	[	X
ejpam-6982	29	2	8	8	NUM
ejpam-6982	29	3	]	]	X
ejpam-6982	29	4	a	a	DET
ejpam-6982	29	5	real	real	ADJ
ejpam-6982	29	6	function	function	NOUN
ejpam-6982	29	7	f(x	f(x	PROPN
ejpam-6982	29	8	)	)	PUNCT
ejpam-6982	29	9	,	,	PUNCT
ejpam-6982	29	10	x	x	X
ejpam-6982	29	11	>	>	X
ejpam-6982	29	12	0	0	NUM
ejpam-6982	29	13	,	,	PUNCT
ejpam-6982	29	14	is	be	AUX
ejpam-6982	29	15	siaid	siaid	VERB
ejpam-6982	29	16	to	to	PART
ejpam-6982	29	17	be	be	AUX
ejpam-6982	29	18	in	in	ADP
ejpam-6982	29	19	the	the	DET
ejpam-6982	29	20	space	space	NOUN
ejpam-6982	29	21	cµ	cµ	NOUN
ejpam-6982	29	22	,	,	PUNCT
ejpam-6982	29	23	µ	µ	X
ejpam-6982	29	24	∈	∈	NOUN
ejpam-6982	29	25	r	r	NOUN
ejpam-6982	29	26	if	if	SCONJ
ejpam-6982	29	27	there	there	PRON
ejpam-6982	29	28	exists	exist	VERB
ejpam-6982	29	29	a	a	DET
ejpam-6982	29	30	real	real	ADJ
ejpam-6982	29	31	number	number	NOUN
ejpam-6982	29	32	p	p	NOUN
ejpam-6982	29	33	(	(	PUNCT
ejpam-6982	29	34	>	>	X
ejpam-6982	29	35	µ	µ	NUM
ejpam-6982	29	36	)	)	PUNCT
ejpam-6982	29	37	,	,	PUNCT
ejpam-6982	30	1	such	such	ADJ
ejpam-6982	30	2	that	that	SCONJ
ejpam-6982	30	3	f(x	f(x	NOUN
ejpam-6982	30	4	)	)	PUNCT
ejpam-6982	30	5	=	=	SYM
ejpam-6982	30	6	xpf1(x	xpf1(x	NUM
ejpam-6982	30	7	)	)	PUNCT
ejpam-6982	30	8	∈	∈	NOUN
ejpam-6982	30	9	c[0,∞	c[0,∞	NUM
ejpam-6982	30	10	)	)	PUNCT
ejpam-6982	30	11	,	,	PUNCT
ejpam-6982	30	12	and	and	CCONJ
ejpam-6982	30	13	it	it	PRON
ejpam-6982	30	14	is	be	AUX
ejpam-6982	30	15	said	say	VERB
ejpam-6982	30	16	to	to	PART
ejpam-6982	30	17	be	be	AUX
ejpam-6982	30	18	in	in	ADP
ejpam-6982	30	19	the	the	DET
ejpam-6982	30	20	space	space	NOUN
ejpam-6982	30	21	cm	cm	PROPN
ejpam-6982	30	22	µ	µ	PROPN
ejpam-6982	30	23	iff	iff	PROPN
ejpam-6982	30	24	fm	fm	PROPN
ejpam-6982	30	25	∈	∈	PROPN
ejpam-6982	30	26	cµ,m	cµ,m	X
ejpam-6982	30	27	∈	∈	PROPN
ejpam-6982	30	28	n	n	X
ejpam-6982	30	29	.	.	PUNCT
ejpam-6982	31	1	definition	definition	NOUN
ejpam-6982	31	2	2	2	NUM
ejpam-6982	31	3	.	.	PUNCT
ejpam-6982	32	1	[	[	X
ejpam-6982	32	2	8	8	NUM
ejpam-6982	32	3	]	]	PUNCT
ejpam-6982	32	4	the	the	DET
ejpam-6982	32	5	riemann	riemann	PROPN
ejpam-6982	32	6	-	-	PUNCT
ejpam-6982	32	7	liouville	liouville	VERB
ejpam-6982	32	8	fractional	fractional	ADJ
ejpam-6982	32	9	integral	integral	ADJ
ejpam-6982	32	10	operator	operator	NOUN
ejpam-6982	32	11	of	of	ADP
ejpam-6982	32	12	order	order	NOUN
ejpam-6982	32	13	α	α	PROPN
ejpam-6982	32	14	≥	≥	NOUN
ejpam-6982	32	15	µ	µ	NOUN
ejpam-6982	32	16	,	,	PUNCT
ejpam-6982	32	17	of	of	ADP
ejpam-6982	32	18	function	function	NOUN
ejpam-6982	32	19	f	f	PROPN
ejpam-6982	32	20	∈	∈	PROPN
ejpam-6982	32	21	cµ	cµ	PROPN
ejpam-6982	32	22	,	,	PUNCT
ejpam-6982	32	23	µ	µ	PRON
ejpam-6982	32	24	≥	≥	NOUN
ejpam-6982	32	25	−1	−1	NOUN
ejpam-6982	32	26	,	,	PUNCT
ejpam-6982	32	27	is	be	AUX
ejpam-6982	32	28	defined	define	VERB
ejpam-6982	32	29	as	as	ADP
ejpam-6982	32	30	jαf(x	jαf(x	PROPN
ejpam-6982	32	31	)	)	PUNCT
ejpam-6982	32	32	=	=	PRON
ejpam-6982	32	33	{	{	PUNCT
ejpam-6982	32	34	1	1	NUM
ejpam-6982	32	35	γ(α	γ(α	NOUN
ejpam-6982	32	36	)	)	PUNCT
ejpam-6982	32	37	∫	∫	PROPN
ejpam-6982	33	1	x	x	X
ejpam-6982	33	2	a	a	DET
ejpam-6982	33	3	(	(	PUNCT
ejpam-6982	33	4	x−	x−	PROPN
ejpam-6982	33	5	t)α−1f(t)dt	t)α−1f(t)dt	PROPN
ejpam-6982	33	6	,	,	PUNCT
ejpam-6982	33	7	α	α	PROPN
ejpam-6982	33	8	>	>	X
ejpam-6982	33	9	0	0	PROPN
ejpam-6982	33	10	,	,	PUNCT
ejpam-6982	33	11	x	x	X
ejpam-6982	33	12	>	>	X
ejpam-6982	33	13	0	0	PROPN
ejpam-6982	33	14	,	,	PUNCT
ejpam-6982	33	15	f(x	f(x	PROPN
ejpam-6982	33	16	)	)	PUNCT
ejpam-6982	33	17	,	,	PUNCT
ejpam-6982	33	18	α	α	X
ejpam-6982	33	19	=	=	SYM
ejpam-6982	33	20	0	0	X
ejpam-6982	33	21	.	.	PUNCT
ejpam-6982	34	1	we	we	PRON
ejpam-6982	34	2	mention	mention	VERB
ejpam-6982	34	3	only	only	ADV
ejpam-6982	34	4	the	the	DET
ejpam-6982	34	5	following	follow	VERB
ejpam-6982	34	6	properties	property	NOUN
ejpam-6982	34	7	of	of	ADP
ejpam-6982	34	8	the	the	DET
ejpam-6982	34	9	operator	operator	NOUN
ejpam-6982	34	10	jα	jα	PROPN
ejpam-6982	34	11	.	.	PROPN
ejpam-6982	34	12	for	for	ADP
ejpam-6982	34	13	function	function	NOUN
ejpam-6982	34	14	f	f	PROPN
ejpam-6982	34	15	∈	∈	PROPN
ejpam-6982	34	16	cµ	cµ	PROPN
ejpam-6982	34	17	,	,	PUNCT
ejpam-6982	34	18	µ	µ	X
ejpam-6982	34	19	≥	≥	NOUN
ejpam-6982	34	20	−1	−1	NOUN
ejpam-6982	34	21	,	,	PUNCT
ejpam-6982	34	22	α	α	X
ejpam-6982	34	23	,	,	PUNCT
ejpam-6982	34	24	β	β	X
ejpam-6982	34	25	≥	≥	NOUN
ejpam-6982	34	26	0	0	NUM
ejpam-6982	34	27	and	and	CCONJ
ejpam-6982	34	28	γ	γ	X
ejpam-6982	34	29	>	>	X
ejpam-6982	34	30	−1	−1	NOUN
ejpam-6982	34	31	(	(	PUNCT
ejpam-6982	34	32	i	i	NOUN
ejpam-6982	34	33	)	)	PUNCT
ejpam-6982	34	34	jαjβf(x	jαjβf(x	PROPN
ejpam-6982	34	35	)	)	PUNCT
ejpam-6982	34	36	=	=	SYM
ejpam-6982	34	37	jα+βf(x	jα+βf(x	PROPN
ejpam-6982	34	38	)	)	PUNCT
ejpam-6982	34	39	,	,	PUNCT
ejpam-6982	34	40	(	(	PUNCT
ejpam-6982	34	41	ii	ii	NOUN
ejpam-6982	34	42	)	)	PUNCT
ejpam-6982	34	43	jαjβf(x	jαjβf(x	PROPN
ejpam-6982	34	44	)	)	PUNCT
ejpam-6982	35	1	=	=	SYM
ejpam-6982	35	2	jβjαf(x	jβjαf(x	PROPN
ejpam-6982	35	3	)	)	PUNCT
ejpam-6982	35	4	,	,	PUNCT
ejpam-6982	35	5	(	(	PUNCT
ejpam-6982	35	6	iii	iii	X
ejpam-6982	35	7	)	)	PUNCT
ejpam-6982	35	8	jαxγ	jαxγ	NOUN
ejpam-6982	35	9	=	=	PUNCT
ejpam-6982	35	10	γ(γ+1	γ(γ+1	NUM
ejpam-6982	35	11	)	)	PUNCT
ejpam-6982	35	12	γ(α+γ+1)x	γ(α+γ+1)x	ADP
ejpam-6982	35	13	α+γ	α+γ	NUM
ejpam-6982	35	14	.	.	PUNCT
ejpam-6982	36	1	the	the	DET
ejpam-6982	36	2	riemann	riemann	PROPN
ejpam-6982	36	3	-	-	PUNCT
ejpam-6982	36	4	liouville	liouville	VERB
ejpam-6982	36	5	derivative	derivative	NOUN
ejpam-6982	36	6	exhibits	exhibit	VERB
ejpam-6982	36	7	certain	certain	ADJ
ejpam-6982	36	8	drawbacks	drawback	NOUN
ejpam-6982	36	9	for	for	ADP
ejpam-6982	36	10	modeling	model	VERB
ejpam-6982	36	11	real	real	ADJ
ejpam-6982	36	12	-	-	PUNCT
ejpam-6982	36	13	world	world	NOUN
ejpam-6982	36	14	occurrences	occurrence	NOUN
ejpam-6982	36	15	using	use	VERB
ejpam-6982	36	16	fractional	fractional	ADJ
ejpam-6982	36	17	differential	differential	ADJ
ejpam-6982	36	18	equations	equation	NOUN
ejpam-6982	36	19	,	,	PUNCT
ejpam-6982	36	20	as	as	SCONJ
ejpam-6982	36	21	noted	note	VERB
ejpam-6982	36	22	in	in	ADP
ejpam-6982	36	23	[	[	X
ejpam-6982	36	24	8	8	NUM
ejpam-6982	36	25	,	,	PUNCT
ejpam-6982	36	26	12	12	NUM
ejpam-6982	36	27	]	]	PUNCT
ejpam-6982	36	28	.	.	PUNCT
ejpam-6982	37	1	consequently	consequently	ADV
ejpam-6982	37	2	,	,	PUNCT
ejpam-6982	37	3	we	we	PRON
ejpam-6982	37	4	will	will	AUX
ejpam-6982	37	5	now	now	ADV
ejpam-6982	37	6	provide	provide	VERB
ejpam-6982	37	7	a	a	DET
ejpam-6982	37	8	modified	modify	VERB
ejpam-6982	37	9	fractional	fractional	ADJ
ejpam-6982	37	10	differentiation	differentiation	NOUN
ejpam-6982	37	11	operator	operator	NOUN
ejpam-6982	37	12	dα	dα	NOUN
ejpam-6982	37	13	.	.	PROPN
ejpam-6982	37	14	presented	present	VERB
ejpam-6982	37	15	by	by	ADP
ejpam-6982	37	16	caputo	caputo	PROPN
ejpam-6982	37	17	in	in	ADP
ejpam-6982	37	18	his	his	PRON
ejpam-6982	37	19	study	study	NOUN
ejpam-6982	37	20	of	of	ADP
ejpam-6982	37	21	viscoelasticity	viscoelasticity	NOUN
ejpam-6982	37	22	theory	theory	NOUN
ejpam-6982	37	23	[	[	X
ejpam-6982	37	24	15	15	NUM
ejpam-6982	37	25	]	]	PUNCT
ejpam-6982	37	26	.	.	PUNCT
ejpam-6982	38	1	definition	definition	NOUN
ejpam-6982	38	2	3	3	NUM
ejpam-6982	38	3	.	.	PUNCT
ejpam-6982	39	1	[	[	X
ejpam-6982	39	2	12	12	NUM
ejpam-6982	39	3	]	]	PUNCT
ejpam-6982	39	4	for	for	SCONJ
ejpam-6982	39	5	m	m	NOUN
ejpam-6982	39	6	to	to	PART
ejpam-6982	39	7	be	be	AUX
ejpam-6982	39	8	the	the	DET
ejpam-6982	39	9	smallest	small	ADJ
ejpam-6982	39	10	integer	integer	NOUN
ejpam-6982	39	11	that	that	PRON
ejpam-6982	39	12	exceeds	exceed	VERB
ejpam-6982	39	13	α	α	PROPN
ejpam-6982	39	14	,	,	PUNCT
ejpam-6982	39	15	the	the	DET
ejpam-6982	39	16	caputo	caputo	PROPN
ejpam-6982	39	17	fractional	fractional	ADJ
ejpam-6982	39	18	derivatives	derivative	NOUN
ejpam-6982	39	19	of	of	ADP
ejpam-6982	39	20	order	order	NOUN
ejpam-6982	39	21	α	α	PROPN
ejpam-6982	39	22	>	>	X
ejpam-6982	39	23	0	0	NUM
ejpam-6982	39	24	is	be	AUX
ejpam-6982	39	25	defined	define	VERB
ejpam-6982	39	26	as	as	ADP
ejpam-6982	39	27	:	:	PUNCT
ejpam-6982	39	28	dαf(x	dαf(x	PROPN
ejpam-6982	39	29	,	,	PUNCT
ejpam-6982	39	30	t	t	PROPN
ejpam-6982	39	31	)	)	PUNCT
ejpam-6982	39	32	=	=	SYM
ejpam-6982	39	33	dαf(x	dαf(x	PROPN
ejpam-6982	39	34	,	,	PUNCT
ejpam-6982	39	35	t	t	PROPN
ejpam-6982	39	36	)	)	PUNCT
ejpam-6982	39	37	dtα	dtα	NOUN
ejpam-6982	39	38	=	=	NOUN
ejpam-6982	39	39	{	{	PUNCT
ejpam-6982	39	40	1	1	NUM
ejpam-6982	39	41	γ(m−α	γ(m−α	NOUN
ejpam-6982	39	42	)	)	PUNCT
ejpam-6982	40	1	∫	∫	PROPN
ejpam-6982	40	2	t	t	PROPN
ejpam-6982	40	3	0	0	NUM
ejpam-6982	40	4	(	(	PUNCT
ejpam-6982	40	5	t−	t−	PROPN
ejpam-6982	40	6	τ)m−α−1	τ)m−α−1	PROPN
ejpam-6982	40	7	d	d	PRON
ejpam-6982	40	8	mf(x	mf(x	PROPN
ejpam-6982	40	9	,	,	PUNCT
ejpam-6982	40	10	τ	τ	NOUN
ejpam-6982	40	11	)	)	PUNCT
ejpam-6982	40	12	dτm	dτm	NOUN
ejpam-6982	40	13	,	,	PUNCT
ejpam-6982	40	14	m−	m−	PROPN
ejpam-6982	40	15	1	1	NUM
ejpam-6982	40	16	<	<	X
ejpam-6982	40	17	α	α	PROPN
ejpam-6982	40	18	≤	≤	NUM
ejpam-6982	40	19	m	m	VERB
ejpam-6982	40	20	dmf(x	dmf(x	PROPN
ejpam-6982	40	21	,	,	PUNCT
ejpam-6982	40	22	t	t	PROPN
ejpam-6982	40	23	)	)	PUNCT
ejpam-6982	40	24	dtm	dtm	PROPN
ejpam-6982	40	25	,	,	PUNCT
ejpam-6982	40	26	α	α	NOUN
ejpam-6982	40	27	=	=	SYM
ejpam-6982	40	28	m,∈	m,∈	PROPN
ejpam-6982	40	29	n	n	NOUN
ejpam-6982	40	30	a.	a.	NOUN
ejpam-6982	40	31	m.	m.	NOUN
ejpam-6982	40	32	alhammad	alhammad	PROPN
ejpam-6982	40	33	,	,	PUNCT
ejpam-6982	40	34	a.	a.	NOUN
ejpam-6982	40	35	m.	m.	PROPN
ejpam-6982	40	36	saeed	saeed	PROPN
ejpam-6982	40	37	/	/	SYM
ejpam-6982	40	38	eur	eur	PROPN
ejpam-6982	40	39	.	.	PUNCT
ejpam-6982	41	1	j.	j.	PROPN
ejpam-6982	41	2	pure	pure	PROPN
ejpam-6982	41	3	appl	appl	PROPN
ejpam-6982	41	4	.	.	PROPN
ejpam-6982	41	5	math	math	PROPN
ejpam-6982	41	6	,	,	PUNCT
ejpam-6982	41	7	18	18	NUM
ejpam-6982	41	8	(	(	PUNCT
ejpam-6982	41	9	4	4	NUM
ejpam-6982	41	10	)	)	PUNCT
ejpam-6982	41	11	(	(	PUNCT
ejpam-6982	41	12	2025	2025	NUM
ejpam-6982	41	13	)	)	PUNCT
ejpam-6982	41	14	,	,	PUNCT
ejpam-6982	41	15	6982	6982	NUM
ejpam-6982	41	16	3	3	NUM
ejpam-6982	41	17	of	of	ADP
ejpam-6982	41	18	22	22	NUM
ejpam-6982	41	19	one	one	NUM
ejpam-6982	41	20	may	may	AUX
ejpam-6982	41	21	refer	refer	VERB
ejpam-6982	41	22	to	to	ADP
ejpam-6982	41	23	the	the	DET
ejpam-6982	41	24	cited	cite	VERB
ejpam-6982	41	25	sources	source	NOUN
ejpam-6982	41	26	for	for	ADP
ejpam-6982	41	27	the	the	DET
ejpam-6982	41	28	mathematical	mathematical	ADJ
ejpam-6982	41	29	characteristics	characteristic	NOUN
ejpam-6982	41	30	of	of	ADP
ejpam-6982	41	31	fractional	fractional	ADJ
ejpam-6982	41	32	derivatives	derivative	NOUN
ejpam-6982	41	33	and	and	CCONJ
ejpam-6982	41	34	integrals	integral	NOUN
ejpam-6982	41	35	.	.	PUNCT
ejpam-6982	42	1	in	in	ADP
ejpam-6982	42	2	section	section	NOUN
ejpam-6982	42	3	5	5	NUM
ejpam-6982	42	4	,	,	PUNCT
ejpam-6982	42	5	we	we	PRON
ejpam-6982	42	6	demonstrate	demonstrate	VERB
ejpam-6982	42	7	the	the	DET
ejpam-6982	42	8	application	application	NOUN
ejpam-6982	42	9	of	of	ADP
ejpam-6982	42	10	semi	semi	ADJ
ejpam-6982	42	11	-	-	ADJ
ejpam-6982	42	12	analytical	analytical	ADJ
ejpam-6982	42	13	methods	method	NOUN
ejpam-6982	42	14	for	for	ADP
ejpam-6982	42	15	solving	solve	VERB
ejpam-6982	42	16	known	know	VERB
ejpam-6982	42	17	and	and	CCONJ
ejpam-6982	42	18	commonly	commonly	ADV
ejpam-6982	42	19	encountered	encounter	VERB
ejpam-6982	42	20	categories	category	NOUN
ejpam-6982	42	21	of	of	ADP
ejpam-6982	42	22	fractional	fractional	ADJ
ejpam-6982	42	23	partial	partial	ADJ
ejpam-6982	42	24	differential	differential	NOUN
ejpam-6982	42	25	equations	equation	NOUN
ejpam-6982	42	26	(	(	PUNCT
ejpam-6982	42	27	fpdes	fpdes	PROPN
ejpam-6982	42	28	)	)	PUNCT
ejpam-6982	42	29	,	,	PUNCT
ejpam-6982	42	30	such	such	ADJ
ejpam-6982	42	31	as	as	ADP
ejpam-6982	42	32	nonlinear	nonlinear	ADJ
ejpam-6982	42	33	time	time	NOUN
ejpam-6982	42	34	-	-	PUNCT
ejpam-6982	42	35	fractional	fractional	ADJ
ejpam-6982	42	36	advection	advection	NOUN
ejpam-6982	42	37	partial	partial	ADJ
ejpam-6982	42	38	differential	differential	NOUN
ejpam-6982	42	39	equation	equation	NOUN
ejpam-6982	42	40	and	and	CCONJ
ejpam-6982	42	41	nonlinear	nonlinear	ADJ
ejpam-6982	42	42	time	time	NOUN
ejpam-6982	42	43	-	-	PUNCT
ejpam-6982	42	44	fractional	fractional	ADJ
ejpam-6982	42	45	hyperbolic	hyperbolic	ADJ
ejpam-6982	42	46	partial	partial	ADJ
ejpam-6982	42	47	differential	differential	NOUN
ejpam-6982	42	48	equation	equation	NOUN
ejpam-6982	42	49	.	.	PUNCT
ejpam-6982	43	1	3	3	X
ejpam-6982	43	2	.	.	X
ejpam-6982	43	3	the	the	DET
ejpam-6982	43	4	proposed	propose	VERB
ejpam-6982	43	5	transformations	transformation	NOUN
ejpam-6982	43	6	methods	method	NOUN
ejpam-6982	43	7	there	there	PRON
ejpam-6982	43	8	are	be	VERB
ejpam-6982	43	9	several	several	ADJ
ejpam-6982	43	10	integral	integral	ADJ
ejpam-6982	43	11	transformations	transformation	NOUN
ejpam-6982	43	12	available	available	ADJ
ejpam-6982	43	13	for	for	ADP
ejpam-6982	43	14	solving	solve	VERB
ejpam-6982	43	15	fractional	fractional	ADJ
ejpam-6982	43	16	differential	differential	ADJ
ejpam-6982	43	17	equations	equation	NOUN
ejpam-6982	43	18	.	.	PUNCT
ejpam-6982	44	1	the	the	DET
ejpam-6982	44	2	laplace	laplace	NOUN
ejpam-6982	44	3	transform	transform	NOUN
ejpam-6982	44	4	is	be	AUX
ejpam-6982	44	5	the	the	DET
ejpam-6982	44	6	most	most	ADV
ejpam-6982	44	7	extensively	extensively	ADV
ejpam-6982	44	8	utilized	utilize	VERB
ejpam-6982	44	9	.	.	PUNCT
ejpam-6982	45	1	the	the	DET
ejpam-6982	45	2	core	core	ADJ
ejpam-6982	45	3	idea	idea	NOUN
ejpam-6982	45	4	behind	behind	ADP
ejpam-6982	45	5	the	the	DET
ejpam-6982	45	6	laplace	laplace	NOUN
ejpam-6982	45	7	transforms	transform	VERB
ejpam-6982	45	8	is	be	AUX
ejpam-6982	45	9	mopping	mop	VERB
ejpam-6982	45	10	of	of	ADP
ejpam-6982	45	11	a	a	DET
ejpam-6982	45	12	time	time	NOUN
ejpam-6982	45	13	-	-	PUNCT
ejpam-6982	45	14	domain	domain	NOUN
ejpam-6982	45	15	function	function	NOUN
ejpam-6982	45	16	f(t	f(t	NOUN
ejpam-6982	45	17	)	)	PUNCT
ejpam-6982	45	18	into	into	ADP
ejpam-6982	45	19	an	an	DET
ejpam-6982	45	20	s	s	NOUN
ejpam-6982	45	21	-	-	PUNCT
ejpam-6982	45	22	domain	domain	NOUN
ejpam-6982	45	23	function	function	NOUN
ejpam-6982	45	24	f	f	PROPN
ejpam-6982	45	25	(	(	PUNCT
ejpam-6982	45	26	s	s	X
ejpam-6982	45	27	)	)	PUNCT
ejpam-6982	45	28	using	use	VERB
ejpam-6982	45	29	an	an	DET
ejpam-6982	45	30	integral	integral	ADJ
ejpam-6982	45	31	transformation	transformation	NOUN
ejpam-6982	45	32	.	.	PUNCT
ejpam-6982	46	1	by	by	ADP
ejpam-6982	46	2	this	this	PRON
ejpam-6982	46	3	,	,	PUNCT
ejpam-6982	46	4	differentiation	differentiation	NOUN
ejpam-6982	46	5	and	and	CCONJ
ejpam-6982	46	6	integration	integration	NOUN
ejpam-6982	46	7	operations	operation	NOUN
ejpam-6982	46	8	in	in	ADP
ejpam-6982	46	9	the	the	DET
ejpam-6982	46	10	time	time	NOUN
ejpam-6982	46	11	domain	domain	NOUN
ejpam-6982	46	12	are	be	AUX
ejpam-6982	46	13	made	make	VERB
ejpam-6982	46	14	equivalent	equivalent	ADJ
ejpam-6982	46	15	to	to	ADP
ejpam-6982	46	16	multiplication	multiplication	NOUN
ejpam-6982	46	17	and	and	CCONJ
ejpam-6982	46	18	division	division	NOUN
ejpam-6982	46	19	by	by	ADP
ejpam-6982	46	20	s	s	PRON
ejpam-6982	46	21	in	in	ADP
ejpam-6982	46	22	the	the	DET
ejpam-6982	46	23	laplace	laplace	NOUN
ejpam-6982	46	24	domain	domain	NOUN
ejpam-6982	46	25	[	[	X
ejpam-6982	46	26	16	16	NUM
ejpam-6982	46	27	,	,	PUNCT
ejpam-6982	46	28	17	17	NUM
ejpam-6982	46	29	]	]	PUNCT
ejpam-6982	46	30	.	.	PUNCT
ejpam-6982	47	1	in	in	ADP
ejpam-6982	47	2	the	the	DET
ejpam-6982	47	3	sumudu	sumudu	NOUN
ejpam-6982	47	4	transform	transform	NOUN
ejpam-6982	47	5	,	,	PUNCT
ejpam-6982	47	6	the	the	DET
ejpam-6982	47	7	differentiation	differentiation	NOUN
ejpam-6982	47	8	and	and	CCONJ
ejpam-6982	47	9	integration	integration	NOUN
ejpam-6982	47	10	operations	operation	NOUN
ejpam-6982	47	11	in	in	ADP
ejpam-6982	47	12	the	the	DET
ejpam-6982	47	13	t	t	NOUN
ejpam-6982	47	14	-	-	PUNCT
ejpam-6982	47	15	domain	domain	NOUN
ejpam-6982	47	16	are	be	AUX
ejpam-6982	47	17	made	make	VERB
ejpam-6982	47	18	equivalent	equivalent	ADJ
ejpam-6982	47	19	to	to	ADP
ejpam-6982	47	20	division	division	NOUN
ejpam-6982	47	21	and	and	CCONJ
ejpam-6982	47	22	multiplication	multiplication	NOUN
ejpam-6982	47	23	by	by	ADP
ejpam-6982	47	24	u	u	NOUN
ejpam-6982	47	25	in	in	ADP
ejpam-6982	47	26	a	a	DET
ejpam-6982	47	27	u	u	NOUN
ejpam-6982	47	28	-	-	NOUN
ejpam-6982	47	29	domain	domain	NOUN
ejpam-6982	47	30	.	.	PUNCT
ejpam-6982	48	1	this	this	PRON
ejpam-6982	48	2	makes	make	VERB
ejpam-6982	48	3	it	it	PRON
ejpam-6982	48	4	possible	possible	ADJ
ejpam-6982	48	5	to	to	PART
ejpam-6982	48	6	treat	treat	VERB
ejpam-6982	48	7	the	the	DET
ejpam-6982	48	8	variable	variable	ADJ
ejpam-6982	48	9	u	u	NOUN
ejpam-6982	48	10	and	and	CCONJ
ejpam-6982	48	11	transformed	transform	VERB
ejpam-6982	48	12	function	function	NOUN
ejpam-6982	48	13	f(u	f(u	PROPN
ejpam-6982	48	14	)	)	PUNCT
ejpam-6982	48	15	as	as	ADP
ejpam-6982	48	16	replicas	replica	NOUN
ejpam-6982	48	17	of	of	ADP
ejpam-6982	48	18	t	t	PROPN
ejpam-6982	48	19	and	and	CCONJ
ejpam-6982	48	20	f(t	f(t	NOUN
ejpam-6982	48	21	)	)	PUNCT
ejpam-6982	48	22	,	,	PUNCT
ejpam-6982	48	23	respectively	respectively	ADV
ejpam-6982	48	24	.	.	PUNCT
ejpam-6982	49	1	it	it	PRON
ejpam-6982	49	2	is	be	AUX
ejpam-6982	49	3	even	even	ADV
ejpam-6982	49	4	possible	possible	ADJ
ejpam-6982	49	5	to	to	PART
ejpam-6982	49	6	express	express	VERB
ejpam-6982	49	7	them	they	PRON
ejpam-6982	49	8	in	in	ADP
ejpam-6982	49	9	the	the	DET
ejpam-6982	49	10	same	same	ADJ
ejpam-6982	49	11	engineering	engineering	NOUN
ejpam-6982	49	12	units	unit	NOUN
ejpam-6982	49	13	as	as	ADP
ejpam-6982	49	14	t	t	PROPN
ejpam-6982	49	15	and	and	CCONJ
ejpam-6982	49	16	f(t	f(t	NOUN
ejpam-6982	49	17	)	)	PUNCT
ejpam-6982	49	18	so	so	SCONJ
ejpam-6982	49	19	that	that	SCONJ
ejpam-6982	49	20	the	the	DET
ejpam-6982	49	21	consistency	consistency	NOUN
ejpam-6982	49	22	of	of	ADP
ejpam-6982	49	23	units	unit	NOUN
ejpam-6982	49	24	in	in	ADP
ejpam-6982	49	25	a	a	DET
ejpam-6982	49	26	differential	differential	ADJ
ejpam-6982	49	27	equation	equation	NOUN
ejpam-6982	49	28	describing	describe	VERB
ejpam-6982	49	29	a	a	DET
ejpam-6982	49	30	physical	physical	ADJ
ejpam-6982	49	31	process	process	NOUN
ejpam-6982	49	32	can	can	AUX
ejpam-6982	49	33	be	be	AUX
ejpam-6982	49	34	maintained	maintain	VERB
ejpam-6982	49	35	even	even	ADV
ejpam-6982	49	36	after	after	ADP
ejpam-6982	49	37	the	the	DET
ejpam-6982	49	38	transformation	transformation	NOUN
ejpam-6982	49	39	[	[	X
ejpam-6982	49	40	16	16	NUM
ejpam-6982	49	41	]	]	PUNCT
ejpam-6982	49	42	.	.	PUNCT
ejpam-6982	50	1	the	the	DET
ejpam-6982	50	2	natural	natural	ADJ
ejpam-6982	50	3	transform	transform	NOUN
ejpam-6982	50	4	is	be	AUX
ejpam-6982	50	5	derived	derive	VERB
ejpam-6982	50	6	from	from	ADP
ejpam-6982	50	7	the	the	DET
ejpam-6982	50	8	fourier	fourier	NOUN
ejpam-6982	50	9	integral	integral	NOUN
ejpam-6982	50	10	,	,	PUNCT
ejpam-6982	50	11	and	and	CCONJ
ejpam-6982	50	12	it	it	PRON
ejpam-6982	50	13	converges	converge	VERB
ejpam-6982	50	14	to	to	ADP
ejpam-6982	50	15	the	the	DET
ejpam-6982	50	16	laplace	laplace	NOUN
ejpam-6982	50	17	transform	transform	NOUN
ejpam-6982	50	18	and	and	CCONJ
ejpam-6982	50	19	the	the	DET
ejpam-6982	50	20	sumudu	sumudu	NOUN
ejpam-6982	50	21	transform	transform	NOUN
ejpam-6982	50	22	[	[	X
ejpam-6982	50	23	18	18	NUM
ejpam-6982	50	24	]	]	PUNCT
ejpam-6982	50	25	.	.	PUNCT
ejpam-6982	51	1	definition	definition	NOUN
ejpam-6982	51	2	4	4	NUM
ejpam-6982	51	3	.	.	PUNCT
ejpam-6982	52	1	[	[	X
ejpam-6982	52	2	19	19	NUM
ejpam-6982	52	3	]	]	PUNCT
ejpam-6982	52	4	the	the	DET
ejpam-6982	52	5	laplace	laplace	NOUN
ejpam-6982	52	6	transform	transform	NOUN
ejpam-6982	52	7	of	of	ADP
ejpam-6982	52	8	f(t	f(t	NOUN
ejpam-6982	52	9	):	):	PUNCT
ejpam-6982	52	10	l[f(t	l[f(t	NOUN
ejpam-6982	52	11	)	)	PUNCT
ejpam-6982	52	12	]	]	PUNCT
ejpam-6982	53	1	=	=	SYM
ejpam-6982	53	2	f	f	X
ejpam-6982	53	3	(	(	PUNCT
ejpam-6982	53	4	s	s	X
ejpam-6982	53	5	)	)	PUNCT
ejpam-6982	53	6	=	=	SYM
ejpam-6982	53	7	∫	∫	PROPN
ejpam-6982	53	8	∞	∞	NUM
ejpam-6982	53	9	0	0	NUM
ejpam-6982	54	1	e−stf(t)dt	e−stf(t)dt	PROPN
ejpam-6982	54	2	definition	definition	NOUN
ejpam-6982	54	3	5	5	NUM
ejpam-6982	54	4	.	.	PUNCT
ejpam-6982	55	1	[	[	X
ejpam-6982	55	2	12	12	NUM
ejpam-6982	55	3	]	]	PUNCT
ejpam-6982	55	4	the	the	DET
ejpam-6982	55	5	sumudu	sumudu	NOUN
ejpam-6982	55	6	transform	transform	VERB
ejpam-6982	55	7	over	over	ADP
ejpam-6982	55	8	the	the	DET
ejpam-6982	55	9	following	follow	VERB
ejpam-6982	55	10	set	set	NOUN
ejpam-6982	55	11	of	of	ADP
ejpam-6982	55	12	functions	function	NOUN
ejpam-6982	55	13	a	a	PRON
ejpam-6982	55	14	=	=	X
ejpam-6982	55	15	{	{	PUNCT
ejpam-6982	55	16	f(t	f(t	PROPN
ejpam-6982	55	17	)	)	PUNCT
ejpam-6982	55	18	∣∣∣∣∃m	∣∣∣∣∃m	NOUN
ejpam-6982	55	19	,	,	PUNCT
ejpam-6982	55	20	τ1	τ1	NOUN
ejpam-6982	55	21	,	,	PUNCT
ejpam-6982	55	22	τ2	τ2	NOUN
ejpam-6982	55	23	>	>	X
ejpam-6982	55	24	0	0	NUM
ejpam-6982	55	25	,	,	PUNCT
ejpam-6982	55	26	|f(t)|	|f(t)|	ADJ
ejpam-6982	55	27	<	<	X
ejpam-6982	55	28	me	i	PRON
ejpam-6982	55	29	|t|	|t|	ADJ
ejpam-6982	55	30	tj	tj	INTJ
ejpam-6982	55	31	,	,	PUNCT
ejpam-6982	55	32	if	if	SCONJ
ejpam-6982	55	33	t	t	PROPN
ejpam-6982	55	34	∈	∈	PROPN
ejpam-6982	55	35	(	(	PUNCT
ejpam-6982	55	36	−1)j	−1)j	NOUN
ejpam-6982	55	37	×	×	NOUN
ejpam-6982	56	1	[	[	X
ejpam-6982	56	2	0,∞	0,∞	NOUN
ejpam-6982	56	3	)	)	PUNCT
ejpam-6982	56	4	}	}	PUNCT
ejpam-6982	56	5	,	,	PUNCT
ejpam-6982	56	6	is	be	AUX
ejpam-6982	56	7	defined	define	VERB
ejpam-6982	56	8	as	as	ADP
ejpam-6982	56	9	,	,	PUNCT
ejpam-6982	56	10	for	for	ADP
ejpam-6982	56	11	u	u	PROPN
ejpam-6982	56	12	∈	∈	PROPN
ejpam-6982	56	13	(	(	PUNCT
ejpam-6982	56	14	τ1	τ1	NOUN
ejpam-6982	56	15	,	,	PUNCT
ejpam-6982	56	16	τ2	τ2	NOUN
ejpam-6982	56	17	)	)	PUNCT
ejpam-6982	56	18	,	,	PUNCT
ejpam-6982	56	19	we	we	PRON
ejpam-6982	56	20	have	have	VERB
ejpam-6982	56	21	s[f(t	s[f(t	NOUN
ejpam-6982	56	22	)	)	PUNCT
ejpam-6982	56	23	]	]	PUNCT
ejpam-6982	57	1	=	=	PUNCT
ejpam-6982	57	2	g(u	g(u	X
ejpam-6982	57	3	)	)	PUNCT
ejpam-6982	57	4	=	=	SYM
ejpam-6982	58	1	∫	∫	PROPN
ejpam-6982	58	2	∞	∞	NUM
ejpam-6982	58	3	0	0	PUNCT
ejpam-6982	59	1	f(ut)e−tdt	f(ut)e−tdt	PROPN
ejpam-6982	59	2	=	=	SYM
ejpam-6982	60	1	∫	∫	PROPN
ejpam-6982	60	2	∞	∞	NUM
ejpam-6982	60	3	0	0	NUM
ejpam-6982	60	4	1	1	NUM
ejpam-6982	60	5	u	u	NOUN
ejpam-6982	60	6	e−	e−	PROPN
ejpam-6982	60	7	t	t	PROPN
ejpam-6982	60	8	u	u	NOUN
ejpam-6982	60	9	f(t)dt	f(t)dt	PROPN
ejpam-6982	60	10	.	.	PROPN
ejpam-6982	60	11	definition	definition	NOUN
ejpam-6982	60	12	6	6	NUM
ejpam-6982	60	13	.	.	PUNCT
ejpam-6982	61	1	[	[	X
ejpam-6982	61	2	18	18	NUM
ejpam-6982	61	3	]	]	X
ejpam-6982	61	4	the	the	DET
ejpam-6982	61	5	natural	natural	ADJ
ejpam-6982	61	6	transform	transform	NOUN
ejpam-6982	61	7	over	over	ADP
ejpam-6982	61	8	the	the	DET
ejpam-6982	61	9	following	follow	VERB
ejpam-6982	61	10	set	set	NOUN
ejpam-6982	61	11	of	of	ADP
ejpam-6982	61	12	functions	function	NOUN
ejpam-6982	61	13	a	a	DET
ejpam-6982	61	14	=	=	X
ejpam-6982	61	15	{	{	PUNCT
ejpam-6982	61	16	f(t	f(t	PROPN
ejpam-6982	61	17	)	)	PUNCT
ejpam-6982	61	18	∣∣∣∣∃m	∣∣∣∣∃m	NOUN
ejpam-6982	61	19	,	,	PUNCT
ejpam-6982	61	20	τ1	τ1	NOUN
ejpam-6982	61	21	,	,	PUNCT
ejpam-6982	61	22	τ2	τ2	NOUN
ejpam-6982	61	23	>	>	X
ejpam-6982	61	24	0	0	NUM
ejpam-6982	61	25	,	,	PUNCT
ejpam-6982	61	26	|f(t)|	|f(t)|	ADJ
ejpam-6982	61	27	<	<	X
ejpam-6982	61	28	me	i	PRON
ejpam-6982	61	29	t	t	PROPN
ejpam-6982	61	30	tj	tj	INTJ
ejpam-6982	61	31	,	,	PUNCT
ejpam-6982	61	32	if	if	SCONJ
ejpam-6982	61	33	t	t	PROPN
ejpam-6982	61	34	∈	∈	PROPN
ejpam-6982	61	35	(	(	PUNCT
ejpam-6982	61	36	−1)j	−1)j	NOUN
ejpam-6982	61	37	×	×	NOUN
ejpam-6982	62	1	[	[	X
ejpam-6982	62	2	0,∞	0,∞	NOUN
ejpam-6982	62	3	)	)	PUNCT
ejpam-6982	62	4	}	}	PUNCT
ejpam-6982	62	5	,	,	PUNCT
ejpam-6982	62	6	is	be	AUX
ejpam-6982	62	7	defined	define	VERB
ejpam-6982	62	8	as	as	ADP
ejpam-6982	62	9	n[f(t	n[f(t	NOUN
ejpam-6982	62	10	)	)	PUNCT
ejpam-6982	62	11	]	]	PUNCT
ejpam-6982	63	1	=	=	PUNCT
ejpam-6982	63	2	r(s	r(s	NUM
ejpam-6982	63	3	,	,	PUNCT
ejpam-6982	63	4	u	u	NOUN
ejpam-6982	63	5	)	)	PUNCT
ejpam-6982	63	6	=	=	SYM
ejpam-6982	64	1	∫	∫	PROPN
ejpam-6982	64	2	∞	∞	PROPN
ejpam-6982	64	3	0	0	NUM
ejpam-6982	65	1	e−stf(ut)dt	e−stf(ut)dt	PROPN
ejpam-6982	65	2	,	,	PUNCT
ejpam-6982	65	3	s	s	PART
ejpam-6982	65	4	>	>	X
ejpam-6982	65	5	0	0	PROPN
ejpam-6982	65	6	,	,	PUNCT
ejpam-6982	65	7	u	u	NOUN
ejpam-6982	65	8	>	>	X
ejpam-6982	65	9	0	0	NUM
ejpam-6982	65	10	.	.	PUNCT
ejpam-6982	65	11	a.	a.	PROPN
ejpam-6982	65	12	m.	m.	PROPN
ejpam-6982	65	13	alhammad	alhammad	PROPN
ejpam-6982	65	14	,	,	PUNCT
ejpam-6982	65	15	a.	a.	NOUN
ejpam-6982	65	16	m.	m.	PROPN
ejpam-6982	65	17	saeed	saeed	PROPN
ejpam-6982	65	18	/	/	SYM
ejpam-6982	65	19	eur	eur	PROPN
ejpam-6982	65	20	.	.	PUNCT
ejpam-6982	66	1	j.	j.	PROPN
ejpam-6982	66	2	pure	pure	PROPN
ejpam-6982	66	3	appl	appl	PROPN
ejpam-6982	66	4	.	.	PROPN
ejpam-6982	66	5	math	math	PROPN
ejpam-6982	66	6	,	,	PUNCT
ejpam-6982	66	7	18	18	NUM
ejpam-6982	66	8	(	(	PUNCT
ejpam-6982	66	9	4	4	NUM
ejpam-6982	66	10	)	)	PUNCT
ejpam-6982	66	11	(	(	PUNCT
ejpam-6982	66	12	2025	2025	NUM
ejpam-6982	66	13	)	)	PUNCT
ejpam-6982	66	14	,	,	PUNCT
ejpam-6982	66	15	6982	6982	NUM
ejpam-6982	66	16	4	4	NUM
ejpam-6982	66	17	of	of	ADP
ejpam-6982	66	18	22	22	NUM
ejpam-6982	66	19	remark	remark	NOUN
ejpam-6982	66	20	1	1	NUM
ejpam-6982	66	21	.	.	PUNCT
ejpam-6982	67	1	if	if	SCONJ
ejpam-6982	67	2	s[f(t	s[f(t	NUM
ejpam-6982	67	3	)	)	PUNCT
ejpam-6982	67	4	]	]	PUNCT
ejpam-6982	68	1	=	=	PUNCT
ejpam-6982	68	2	g(u	g(u	PROPN
ejpam-6982	68	3	)	)	PUNCT
ejpam-6982	68	4	,	,	PUNCT
ejpam-6982	68	5	l[f(t	l[f(t	PROPN
ejpam-6982	68	6	)	)	PUNCT
ejpam-6982	68	7	]	]	PUNCT
ejpam-6982	69	1	=	=	SYM
ejpam-6982	69	2	f	f	X
ejpam-6982	69	3	(	(	PUNCT
ejpam-6982	69	4	s	s	NOUN
ejpam-6982	69	5	)	)	PUNCT
ejpam-6982	69	6	and	and	CCONJ
ejpam-6982	69	7	n[f(t	n[f(t	NOUN
ejpam-6982	69	8	)	)	PUNCT
ejpam-6982	69	9	]	]	PUNCT
ejpam-6982	70	1	=	=	PUNCT
ejpam-6982	70	2	r(s	r(s	NUM
ejpam-6982	70	3	,	,	PUNCT
ejpam-6982	70	4	u	u	NOUN
ejpam-6982	70	5	)	)	PUNCT
ejpam-6982	70	6	,	,	PUNCT
ejpam-6982	70	7	then	then	ADV
ejpam-6982	70	8	the	the	DET
ejpam-6982	70	9	relationship	relationship	NOUN
ejpam-6982	70	10	between	between	ADP
ejpam-6982	70	11	sumudu	sumudu	NOUN
ejpam-6982	70	12	and	and	CCONJ
ejpam-6982	70	13	laplace	laplace	NOUN
ejpam-6982	70	14	transforms	transform	VERB
ejpam-6982	70	15	[	[	PUNCT
ejpam-6982	70	16	20	20	NUM
ejpam-6982	70	17	]	]	PUNCT
ejpam-6982	70	18	:	:	PUNCT
ejpam-6982	70	19	the	the	DET
ejpam-6982	70	20	transformations	transformation	NOUN
ejpam-6982	70	21	are	be	AUX
ejpam-6982	70	22	connected	connect	VERB
ejpam-6982	70	23	via	via	ADP
ejpam-6982	70	24	a	a	DET
ejpam-6982	70	25	change	change	NOUN
ejpam-6982	70	26	of	of	ADP
ejpam-6982	70	27	variables	variable	NOUN
ejpam-6982	70	28	:	:	PUNCT
ejpam-6982	70	29	•	•	NUM
ejpam-6982	70	30	g(u	g(u	PROPN
ejpam-6982	70	31	)	)	PUNCT
ejpam-6982	70	32	=	=	SYM
ejpam-6982	70	33	1	1	NUM
ejpam-6982	70	34	uf	uf	NOUN
ejpam-6982	70	35	(	(	PUNCT
ejpam-6982	70	36	1	1	NUM
ejpam-6982	70	37	u	u	NOUN
ejpam-6982	70	38	)	)	PUNCT
ejpam-6982	70	39	.	.	PUNCT
ejpam-6982	71	1	equivalently	equivalently	ADV
ejpam-6982	71	2	:	:	PUNCT
ejpam-6982	71	3	•	•	NUM
ejpam-6982	71	4	f	f	X
ejpam-6982	71	5	(	(	PUNCT
ejpam-6982	71	6	s	s	X
ejpam-6982	71	7	)	)	PUNCT
ejpam-6982	71	8	=	=	SYM
ejpam-6982	71	9	1	1	NUM
ejpam-6982	71	10	sg	sg	NOUN
ejpam-6982	71	11	(	(	PUNCT
ejpam-6982	71	12	1	1	NUM
ejpam-6982	71	13	s	s	NOUN
ejpam-6982	71	14	)	)	PUNCT
ejpam-6982	71	15	,	,	PUNCT
ejpam-6982	71	16	where	where	SCONJ
ejpam-6982	71	17	s	s	VERB
ejpam-6982	71	18	=	=	SYM
ejpam-6982	71	19	1	1	NUM
ejpam-6982	71	20	u	u	NOUN
ejpam-6982	71	21	and	and	CCONJ
ejpam-6982	71	22	u	u	NOUN
ejpam-6982	71	23	=	=	NOUN
ejpam-6982	71	24	1	1	NUM
ejpam-6982	71	25	s	s	NOUN
ejpam-6982	71	26	.	.	PUNCT
ejpam-6982	71	27	relationship	relationship	NOUN
ejpam-6982	71	28	between	between	ADP
ejpam-6982	71	29	sumudu	sumudu	NOUN
ejpam-6982	71	30	and	and	CCONJ
ejpam-6982	71	31	natural	natural	ADJ
ejpam-6982	71	32	transforms	transform	NOUN
ejpam-6982	71	33	[	[	X
ejpam-6982	71	34	18	18	NUM
ejpam-6982	71	35	]	]	X
ejpam-6982	71	36	:	:	PUNCT
ejpam-6982	71	37	r(s	r(s	NUM
ejpam-6982	71	38	,	,	PUNCT
ejpam-6982	71	39	u	u	NOUN
ejpam-6982	71	40	)	)	PUNCT
ejpam-6982	71	41	=	=	SYM
ejpam-6982	71	42	1	1	NUM
ejpam-6982	71	43	s	s	NOUN
ejpam-6982	71	44	g	g	NOUN
ejpam-6982	71	45	(	(	PUNCT
ejpam-6982	71	46	u	u	NOUN
ejpam-6982	71	47	s	s	PROPN
ejpam-6982	71	48	)	)	PUNCT
ejpam-6982	71	49	.	.	PUNCT
ejpam-6982	72	1	relationship	relationship	NOUN
ejpam-6982	72	2	between	between	ADP
ejpam-6982	72	3	natural	natural	ADJ
ejpam-6982	72	4	and	and	CCONJ
ejpam-6982	72	5	laplace	laplace	NOUN
ejpam-6982	72	6	transforms	transform	VERB
ejpam-6982	72	7	[	[	X
ejpam-6982	72	8	18	18	NUM
ejpam-6982	72	9	]	]	X
ejpam-6982	72	10	:	:	PUNCT
ejpam-6982	72	11	r(s	r(s	NUM
ejpam-6982	72	12	,	,	PUNCT
ejpam-6982	72	13	u	u	NOUN
ejpam-6982	72	14	)	)	PUNCT
ejpam-6982	72	15	=	=	SYM
ejpam-6982	72	16	1	1	NUM
ejpam-6982	72	17	u	u	NOUN
ejpam-6982	72	18	f	f	X
ejpam-6982	72	19	(	(	PUNCT
ejpam-6982	72	20	s	s	NOUN
ejpam-6982	72	21	u	u	NOUN
ejpam-6982	72	22	)	)	PUNCT
ejpam-6982	72	23	.	.	PUNCT
ejpam-6982	73	1	definition	definition	NOUN
ejpam-6982	73	2	7	7	NUM
ejpam-6982	73	3	.	.	PUNCT
ejpam-6982	74	1	[	[	X
ejpam-6982	74	2	19	19	NUM
ejpam-6982	74	3	]	]	PUNCT
ejpam-6982	74	4	the	the	DET
ejpam-6982	74	5	laplace	laplace	NOUN
ejpam-6982	74	6	transform	transform	NOUN
ejpam-6982	74	7	of	of	ADP
ejpam-6982	74	8	the	the	DET
ejpam-6982	74	9	caputo	caputo	PROPN
ejpam-6982	74	10	fractional	fractional	PROPN
ejpam-6982	74	11	derivative	derivative	NOUN
ejpam-6982	74	12	is	be	AUX
ejpam-6982	74	13	defined	define	VERB
ejpam-6982	74	14	as	as	ADP
ejpam-6982	74	15	l	l	PROPN
ejpam-6982	74	16	[	[	X
ejpam-6982	74	17	dαf(x	dαf(x	PROPN
ejpam-6982	74	18	)	)	PUNCT
ejpam-6982	74	19	]	]	PUNCT
ejpam-6982	75	1	=	=	SYM
ejpam-6982	75	2	sαl[f(x)]−	sαl[f(x)]−	PROPN
ejpam-6982	75	3	m−1∑	m−1∑	PROPN
ejpam-6982	75	4	k=0	k=0	PROPN
ejpam-6982	75	5	sα−k−1fk(0	sα−k−1fk(0	PROPN
ejpam-6982	75	6	)	)	PUNCT
ejpam-6982	75	7	,	,	PUNCT
ejpam-6982	75	8	m−	m−	PROPN
ejpam-6982	75	9	1	1	NUM
ejpam-6982	75	10	<	<	X
ejpam-6982	75	11	α	α	PROPN
ejpam-6982	75	12	≤	≤	NUM
ejpam-6982	75	13	m	m	PROPN
ejpam-6982	75	14	definition	definition	NOUN
ejpam-6982	75	15	8	8	NUM
ejpam-6982	75	16	.	.	PUNCT
ejpam-6982	76	1	[	[	X
ejpam-6982	76	2	12	12	NUM
ejpam-6982	76	3	]	]	PUNCT
ejpam-6982	76	4	the	the	DET
ejpam-6982	76	5	sumudo	sumudo	PROPN
ejpam-6982	76	6	transform	transform	NOUN
ejpam-6982	76	7	of	of	ADP
ejpam-6982	76	8	the	the	DET
ejpam-6982	76	9	caputo	caputo	PROPN
ejpam-6982	76	10	fractional	fractional	PROPN
ejpam-6982	76	11	derivative	derivative	NOUN
ejpam-6982	76	12	is	be	AUX
ejpam-6982	76	13	defined	define	VERB
ejpam-6982	76	14	as	as	ADP
ejpam-6982	76	15	s	s	PRON
ejpam-6982	76	16	[	[	X
ejpam-6982	76	17	dα	dα	ADP
ejpam-6982	76	18	t	t	PROPN
ejpam-6982	76	19	f(x	f(x	PROPN
ejpam-6982	76	20	,	,	PUNCT
ejpam-6982	76	21	t	t	PROPN
ejpam-6982	76	22	)	)	PUNCT
ejpam-6982	76	23	]	]	PUNCT
ejpam-6982	77	1	=	=	PUNCT
ejpam-6982	77	2	s[f(x	s[f(x	PROPN
ejpam-6982	77	3	,	,	PUNCT
ejpam-6982	77	4	t	t	PROPN
ejpam-6982	77	5	)	)	PUNCT
ejpam-6982	77	6	]	]	PUNCT
ejpam-6982	78	1	uα	uα	PROPN
ejpam-6982	78	2	−	−	PROPN
ejpam-6982	78	3	m−1∑	m−1∑	PRON
ejpam-6982	78	4	k=0	k=0	PROPN
ejpam-6982	78	5	fk(x	fk(x	PROPN
ejpam-6982	78	6	,	,	PUNCT
ejpam-6982	78	7	0	0	X
ejpam-6982	78	8	)	)	PUNCT
ejpam-6982	78	9	uα−k	uα−k	NOUN
ejpam-6982	78	10	,	,	PUNCT
ejpam-6982	78	11	m−	m−	PROPN
ejpam-6982	78	12	1	1	NUM
ejpam-6982	78	13	<	<	X
ejpam-6982	78	14	α	α	PROPN
ejpam-6982	78	15	≤	≤	NUM
ejpam-6982	78	16	m	m	PROPN
ejpam-6982	78	17	definition	definition	NOUN
ejpam-6982	78	18	9	9	NUM
ejpam-6982	78	19	.	.	PUNCT
ejpam-6982	79	1	[	[	X
ejpam-6982	79	2	21	21	NUM
ejpam-6982	79	3	]	]	X
ejpam-6982	79	4	the	the	DET
ejpam-6982	79	5	natural	natural	ADJ
ejpam-6982	79	6	transform	transform	NOUN
ejpam-6982	79	7	of	of	ADP
ejpam-6982	79	8	the	the	DET
ejpam-6982	79	9	caputo	caputo	PROPN
ejpam-6982	79	10	fractional	fractional	PROPN
ejpam-6982	79	11	derivative	derivative	NOUN
ejpam-6982	79	12	is	be	AUX
ejpam-6982	79	13	defined	define	VERB
ejpam-6982	79	14	as	as	ADP
ejpam-6982	79	15	n	n	PROPN
ejpam-6982	79	16	[	[	X
ejpam-6982	79	17	dαf(x	dαf(x	PROPN
ejpam-6982	79	18	)	)	PUNCT
ejpam-6982	79	19	]	]	PUNCT
ejpam-6982	80	1	=	=	PUNCT
ejpam-6982	80	2	sα	sα	ADJ
ejpam-6982	80	3	uα	uα	PROPN
ejpam-6982	80	4	n[f(x)]−	n[f(x)]−	PROPN
ejpam-6982	80	5	m−1∑	m−1∑	DET
ejpam-6982	80	6	k=0	k=0	PROPN
ejpam-6982	80	7	sα−(k+1	sα−(k+1	PROPN
ejpam-6982	80	8	)	)	PUNCT
ejpam-6982	80	9	uα−k	uα−k	PROPN
ejpam-6982	80	10	fk(0	fk(0	PROPN
ejpam-6982	80	11	)	)	PUNCT
ejpam-6982	80	12	,	,	PUNCT
ejpam-6982	80	13	m−	m−	PROPN
ejpam-6982	80	14	1	1	NUM
ejpam-6982	80	15	<	<	X
ejpam-6982	80	16	α	α	PROPN
ejpam-6982	80	17	≤	≤	NUM
ejpam-6982	80	18	m	m	VERB
ejpam-6982	80	19	4	4	NUM
ejpam-6982	80	20	.	.	PUNCT
ejpam-6982	81	1	analysis	analysis	NOUN
ejpam-6982	81	2	of	of	ADP
ejpam-6982	81	3	methods	method	NOUN
ejpam-6982	81	4	the	the	DET
ejpam-6982	81	5	aim	aim	NOUN
ejpam-6982	81	6	of	of	ADP
ejpam-6982	81	7	this	this	DET
ejpam-6982	81	8	section	section	NOUN
ejpam-6982	81	9	is	be	AUX
ejpam-6982	81	10	to	to	PART
ejpam-6982	81	11	discuss	discuss	VERB
ejpam-6982	81	12	the	the	DET
ejpam-6982	81	13	use	use	NOUN
ejpam-6982	81	14	of	of	ADP
ejpam-6982	81	15	the	the	DET
ejpam-6982	81	16	transform	transform	NOUN
ejpam-6982	81	17	algorithm	algorithm	NOUN
ejpam-6982	81	18	for	for	ADP
ejpam-6982	81	19	nonlinear	nonlinear	ADJ
ejpam-6982	81	20	partial	partial	ADJ
ejpam-6982	81	21	fractional	fractional	ADJ
ejpam-6982	81	22	differential	differential	NOUN
ejpam-6982	81	23	equations	equation	NOUN
ejpam-6982	81	24	.	.	PUNCT
ejpam-6982	82	1	we	we	PRON
ejpam-6982	82	2	consider	consider	VERB
ejpam-6982	82	3	the	the	DET
ejpam-6982	82	4	following	follow	VERB
ejpam-6982	82	5	time	time	NOUN
ejpam-6982	82	6	-	-	PUNCT
ejpam-6982	82	7	fractional	fractional	ADJ
ejpam-6982	82	8	partial	partial	ADJ
ejpam-6982	82	9	differential	differential	NOUN
ejpam-6982	82	10	equation	equation	NOUN
ejpam-6982	82	11	[	[	X
ejpam-6982	82	12	8	8	NUM
ejpam-6982	82	13	]	]	PUNCT
ejpam-6982	82	14	:	:	PUNCT
ejpam-6982	82	15	dα	dα	PROPN
ejpam-6982	82	16	t	t	PROPN
ejpam-6982	82	17	u(x	u(x	PROPN
ejpam-6982	82	18	,	,	PUNCT
ejpam-6982	82	19	t	t	PROPN
ejpam-6982	82	20	)	)	PUNCT
ejpam-6982	83	1	=	=	SYM
ejpam-6982	83	2	f	f	PROPN
ejpam-6982	83	3	(	(	PUNCT
ejpam-6982	83	4	u	u	NOUN
ejpam-6982	83	5	,	,	PUNCT
ejpam-6982	83	6	ux	ux	PROPN
ejpam-6982	83	7	,	,	PUNCT
ejpam-6982	83	8	uxx	uxx	PROPN
ejpam-6982	83	9	)	)	PUNCT
ejpam-6982	83	10	+	+	CCONJ
ejpam-6982	84	1	g(x	g(x	PROPN
ejpam-6982	84	2	,	,	PUNCT
ejpam-6982	84	3	t	t	PROPN
ejpam-6982	84	4	)	)	PUNCT
ejpam-6982	84	5	,	,	PUNCT
ejpam-6982	84	6	m−	m−	PROPN
ejpam-6982	84	7	1	1	NUM
ejpam-6982	84	8	<	<	X
ejpam-6982	84	9	α	α	PROPN
ejpam-6982	84	10	≤	≤	NUM
ejpam-6982	84	11	m	m	ADP
ejpam-6982	84	12	,	,	PUNCT
ejpam-6982	84	13	(	(	PUNCT
ejpam-6982	84	14	1	1	X
ejpam-6982	84	15	)	)	PUNCT
ejpam-6982	84	16	where	where	SCONJ
ejpam-6982	84	17	dα	dα	ADP
ejpam-6982	84	18	t	t	PROPN
ejpam-6982	84	19	=	=	PUNCT
ejpam-6982	84	20	dα	dα	PRON
ejpam-6982	84	21	dtα	dtα	NOUN
ejpam-6982	84	22	is	be	AUX
ejpam-6982	84	23	the	the	DET
ejpam-6982	84	24	caputo	caputo	PROPN
ejpam-6982	84	25	fractional	fractional	PROPN
ejpam-6982	84	26	derivative	derivative	NOUN
ejpam-6982	84	27	of	of	ADP
ejpam-6982	84	28	order	order	NOUN
ejpam-6982	84	29	α	α	NOUN
ejpam-6982	84	30	,	,	PUNCT
ejpam-6982	84	31	m	m	PROPN
ejpam-6982	84	32	∈	∈	PROPN
ejpam-6982	84	33	n	n	CCONJ
ejpam-6982	84	34	,	,	PUNCT
ejpam-6982	84	35	f	f	PROPN
ejpam-6982	84	36	is	be	AUX
ejpam-6982	84	37	a	a	DET
ejpam-6982	84	38	nonlinear	nonlinear	ADJ
ejpam-6982	84	39	function	function	NOUN
ejpam-6982	84	40	and	and	CCONJ
ejpam-6982	84	41	g	g	NOUN
ejpam-6982	84	42	is	be	AUX
ejpam-6982	84	43	the	the	DET
ejpam-6982	84	44	source	source	NOUN
ejpam-6982	84	45	function	function	NOUN
ejpam-6982	84	46	.	.	PUNCT
ejpam-6982	85	1	the	the	DET
ejpam-6982	85	2	initial	initial	ADJ
ejpam-6982	85	3	and	and	CCONJ
ejpam-6982	85	4	boundary	boundary	ADJ
ejpam-6982	85	5	conditions	condition	NOUN
ejpam-6982	85	6	associated	associate	VERB
ejpam-6982	85	7	with	with	ADP
ejpam-6982	85	8	(	(	PUNCT
ejpam-6982	85	9	1	1	X
ejpam-6982	85	10	)	)	PUNCT
ejpam-6982	85	11	are	be	AUX
ejpam-6982	85	12	of	of	ADP
ejpam-6982	85	13	the	the	DET
ejpam-6982	85	14	form	form	NOUN
ejpam-6982	85	15	u(x	u(x	NOUN
ejpam-6982	85	16	,	,	PUNCT
ejpam-6982	85	17	0	0	NUM
ejpam-6982	85	18	)	)	PUNCT
ejpam-6982	85	19	=	=	SYM
ejpam-6982	85	20	h(x	h(x	PROPN
ejpam-6982	85	21	)	)	PUNCT
ejpam-6982	85	22	,	,	PUNCT
ejpam-6982	85	23	0	0	NUM
ejpam-6982	85	24	<	<	X
ejpam-6982	85	25	α	α	PROPN
ejpam-6982	85	26	≤	≤	ADJ
ejpam-6982	85	27	1	1	NUM
ejpam-6982	85	28	u(x	u(x	NOUN
ejpam-6982	85	29	,	,	PUNCT
ejpam-6982	85	30	t	t	NOUN
ejpam-6982	85	31	)	)	PUNCT
ejpam-6982	85	32	→	→	SYM
ejpam-6982	85	33	0	0	NUM
ejpam-6982	86	1	as	as	ADP
ejpam-6982	86	2	|x|	|x|	PROPN
ejpam-6982	86	3	→	→	SYM
ejpam-6982	86	4	∞	∞	PROPN
ejpam-6982	86	5	,	,	PUNCT
ejpam-6982	86	6	t	t	X
ejpam-6982	86	7	>	>	X
ejpam-6982	86	8	0	0	NUM
ejpam-6982	86	9	,	,	PUNCT
ejpam-6982	86	10	(	(	PUNCT
ejpam-6982	86	11	2	2	X
ejpam-6982	86	12	)	)	PUNCT
ejpam-6982	86	13	a.	a.	NOUN
ejpam-6982	86	14	m.	m.	NOUN
ejpam-6982	86	15	alhammad	alhammad	PROPN
ejpam-6982	86	16	,	,	PUNCT
ejpam-6982	86	17	a.	a.	NOUN
ejpam-6982	86	18	m.	m.	PROPN
ejpam-6982	86	19	saeed	saeed	PROPN
ejpam-6982	86	20	/	/	SYM
ejpam-6982	86	21	eur	eur	PROPN
ejpam-6982	86	22	.	.	PUNCT
ejpam-6982	87	1	j.	j.	PROPN
ejpam-6982	87	2	pure	pure	PROPN
ejpam-6982	87	3	appl	appl	PROPN
ejpam-6982	87	4	.	.	PROPN
ejpam-6982	87	5	math	math	PROPN
ejpam-6982	87	6	,	,	PUNCT
ejpam-6982	87	7	18	18	NUM
ejpam-6982	87	8	(	(	PUNCT
ejpam-6982	87	9	4	4	NUM
ejpam-6982	87	10	)	)	PUNCT
ejpam-6982	87	11	(	(	PUNCT
ejpam-6982	87	12	2025	2025	NUM
ejpam-6982	87	13	)	)	PUNCT
ejpam-6982	87	14	,	,	PUNCT
ejpam-6982	87	15	6982	6982	NUM
ejpam-6982	87	16	5	5	NUM
ejpam-6982	87	17	of	of	ADP
ejpam-6982	87	18	22	22	NUM
ejpam-6982	87	19	and	and	CCONJ
ejpam-6982	87	20	u(x	u(x	NOUN
ejpam-6982	87	21	,	,	PUNCT
ejpam-6982	87	22	0	0	NUM
ejpam-6982	87	23	)	)	PUNCT
ejpam-6982	87	24	=	=	SYM
ejpam-6982	87	25	h(x	h(x	PROPN
ejpam-6982	87	26	)	)	PUNCT
ejpam-6982	87	27	,	,	PUNCT
ejpam-6982	87	28	du(x	du(x	ADV
ejpam-6982	87	29	,	,	PUNCT
ejpam-6982	87	30	0	0	NUM
ejpam-6982	87	31	)	)	PUNCT
ejpam-6982	87	32	dt	dt	NOUN
ejpam-6982	87	33	=	=	SYM
ejpam-6982	87	34	k(x	k(x	PROPN
ejpam-6982	87	35	)	)	PUNCT
ejpam-6982	87	36	,	,	PUNCT
ejpam-6982	87	37	1	1	NUM
ejpam-6982	87	38	<	<	X
ejpam-6982	87	39	α	α	PROPN
ejpam-6982	87	40	≤	≤	ADJ
ejpam-6982	87	41	2	2	NUM
ejpam-6982	87	42	u(x	u(x	NOUN
ejpam-6982	87	43	,	,	PUNCT
ejpam-6982	87	44	t	t	NOUN
ejpam-6982	87	45	)	)	PUNCT
ejpam-6982	87	46	→	→	SYM
ejpam-6982	87	47	0	0	NUM
ejpam-6982	88	1	as	as	ADP
ejpam-6982	88	2	|x|	|x|	PROPN
ejpam-6982	88	3	→	→	SYM
ejpam-6982	88	4	∞	∞	PROPN
ejpam-6982	88	5	,	,	PUNCT
ejpam-6982	88	6	t	t	X
ejpam-6982	88	7	>	>	X
ejpam-6982	88	8	0	0	NUM
ejpam-6982	88	9	.	.	PUNCT
ejpam-6982	89	1	(	(	PUNCT
ejpam-6982	89	2	3	3	X
ejpam-6982	89	3	)	)	PUNCT
ejpam-6982	89	4	the	the	DET
ejpam-6982	89	5	decomposition	decomposition	NOUN
ejpam-6982	89	6	method	method	NOUN
ejpam-6982	89	7	requires	require	VERB
ejpam-6982	89	8	that	that	SCONJ
ejpam-6982	89	9	the	the	DET
ejpam-6982	89	10	nonlinear	nonlinear	ADJ
ejpam-6982	89	11	fractional	fractional	ADJ
ejpam-6982	89	12	differential	differential	NOUN
ejpam-6982	89	13	eq	eq	ADJ
ejpam-6982	89	14	.	.	PUNCT
ejpam-6982	90	1	(	(	PUNCT
ejpam-6982	90	2	1	1	X
ejpam-6982	90	3	)	)	PUNCT
ejpam-6982	90	4	be	be	AUX
ejpam-6982	90	5	expressed	express	VERB
ejpam-6982	90	6	in	in	ADP
ejpam-6982	90	7	terms	term	NOUN
ejpam-6982	90	8	of	of	ADP
ejpam-6982	90	9	operator	operator	NOUN
ejpam-6982	90	10	form	form	NOUN
ejpam-6982	90	11	as	as	ADP
ejpam-6982	90	12	dα	dα	PROPN
ejpam-6982	90	13	t	t	PROPN
ejpam-6982	90	14	u(x	u(x	PROPN
ejpam-6982	90	15	,	,	PUNCT
ejpam-6982	90	16	t	t	PROPN
ejpam-6982	90	17	)	)	PUNCT
ejpam-6982	90	18	+	+	CCONJ
ejpam-6982	90	19	lu(x	lu(x	NOUN
ejpam-6982	90	20	,	,	PUNCT
ejpam-6982	90	21	t	t	PROPN
ejpam-6982	90	22	)	)	PUNCT
ejpam-6982	90	23	+	+	NOUN
ejpam-6982	90	24	nu(x	nu(x	NOUN
ejpam-6982	90	25	,	,	PUNCT
ejpam-6982	90	26	t	t	NOUN
ejpam-6982	90	27	)	)	PUNCT
ejpam-6982	90	28	=	=	SYM
ejpam-6982	91	1	g(x	g(x	PROPN
ejpam-6982	91	2	,	,	PUNCT
ejpam-6982	91	3	t	t	PROPN
ejpam-6982	91	4	)	)	PUNCT
ejpam-6982	91	5	,	,	PUNCT
ejpam-6982	91	6	x	x	X
ejpam-6982	91	7	>	>	X
ejpam-6982	91	8	0	0	NUM
ejpam-6982	91	9	,	,	PUNCT
ejpam-6982	91	10	(	(	PUNCT
ejpam-6982	91	11	4	4	X
ejpam-6982	91	12	)	)	PUNCT
ejpam-6982	91	13	where	where	SCONJ
ejpam-6982	91	14	l	l	NOUN
ejpam-6982	91	15	is	be	AUX
ejpam-6982	91	16	a	a	DET
ejpam-6982	91	17	linear	linear	ADJ
ejpam-6982	91	18	operator	operator	NOUN
ejpam-6982	91	19	,	,	PUNCT
ejpam-6982	91	20	which	which	PRON
ejpam-6982	91	21	might	might	AUX
ejpam-6982	91	22	include	include	VERB
ejpam-6982	91	23	other	other	ADJ
ejpam-6982	91	24	fractional	fractional	ADJ
ejpam-6982	91	25	derivatives	derivative	NOUN
ejpam-6982	91	26	of	of	ADP
ejpam-6982	91	27	order	order	NOUN
ejpam-6982	91	28	less	less	ADJ
ejpam-6982	91	29	than	than	ADP
ejpam-6982	91	30	α	α	PROPN
ejpam-6982	91	31	,	,	PUNCT
ejpam-6982	91	32	n	n	X
ejpam-6982	91	33	is	be	AUX
ejpam-6982	91	34	a	a	DET
ejpam-6982	91	35	nonlinear	nonlinear	ADJ
ejpam-6982	91	36	operator	operator	NOUN
ejpam-6982	91	37	that	that	PRON
ejpam-6982	91	38	might	might	AUX
ejpam-6982	91	39	also	also	ADV
ejpam-6982	91	40	include	include	VERB
ejpam-6982	91	41	other	other	ADJ
ejpam-6982	91	42	fractional	fractional	ADJ
ejpam-6982	91	43	derivatives	derivative	NOUN
ejpam-6982	91	44	of	of	ADP
ejpam-6982	91	45	order	order	NOUN
ejpam-6982	91	46	less	less	ADJ
ejpam-6982	91	47	than	than	ADP
ejpam-6982	91	48	α	α	NOUN
ejpam-6982	91	49	,	,	PUNCT
ejpam-6982	91	50	g(x	g(x	PROPN
ejpam-6982	91	51	,	,	PUNCT
ejpam-6982	91	52	t	t	PROPN
ejpam-6982	91	53	)	)	PUNCT
ejpam-6982	91	54	and	and	CCONJ
ejpam-6982	91	55	dα	dα	PROPN
ejpam-6982	91	56	t	t	NOUN
ejpam-6982	91	57	are	be	AUX
ejpam-6982	91	58	defined	define	VERB
ejpam-6982	91	59	as	as	ADP
ejpam-6982	91	60	in	in	ADP
ejpam-6982	91	61	eq	eq	NOUN
ejpam-6982	91	62	.	.	PUNCT
ejpam-6982	92	1	(	(	PUNCT
ejpam-6982	92	2	1	1	NUM
ejpam-6982	92	3	)	)	PUNCT
ejpam-6982	92	4	.	.	PUNCT
ejpam-6982	93	1	4.1	4.1	NUM
ejpam-6982	93	2	.	.	PUNCT
ejpam-6982	93	3	adomian	adomian	NOUN
ejpam-6982	93	4	decomposition	decomposition	NOUN
ejpam-6982	93	5	and	and	CCONJ
ejpam-6982	93	6	transform	transform	NOUN
ejpam-6982	93	7	-	-	PUNCT
ejpam-6982	93	8	based	base	VERB
ejpam-6982	93	9	variants	variant	NOUN
ejpam-6982	93	10	although	although	SCONJ
ejpam-6982	93	11	the	the	DET
ejpam-6982	93	12	adomian	adomian	NOUN
ejpam-6982	93	13	decomposition	decomposition	NOUN
ejpam-6982	93	14	method	method	NOUN
ejpam-6982	93	15	,	,	PUNCT
ejpam-6982	93	16	the	the	DET
ejpam-6982	93	17	sumudu	sumudu	NOUN
ejpam-6982	93	18	decomposition	decomposition	NOUN
ejpam-6982	93	19	method	method	NOUN
ejpam-6982	93	20	,	,	PUNCT
ejpam-6982	93	21	and	and	CCONJ
ejpam-6982	93	22	the	the	DET
ejpam-6982	93	23	natural	natural	ADJ
ejpam-6982	93	24	decomposition	decomposition	NOUN
ejpam-6982	93	25	method	method	NOUN
ejpam-6982	93	26	apply	apply	VERB
ejpam-6982	93	27	different	different	ADJ
ejpam-6982	93	28	integral	integral	ADJ
ejpam-6982	93	29	transforms	transform	NOUN
ejpam-6982	93	30	in	in	ADP
ejpam-6982	93	31	their	their	PRON
ejpam-6982	93	32	formulations	formulation	NOUN
ejpam-6982	93	33	,	,	PUNCT
ejpam-6982	93	34	the	the	DET
ejpam-6982	93	35	obtained	obtain	VERB
ejpam-6982	93	36	decomposition	decomposition	NOUN
ejpam-6982	93	37	components	component	NOUN
ejpam-6982	93	38	and	and	CCONJ
ejpam-6982	93	39	numerical	numerical	ADJ
ejpam-6982	93	40	results	result	NOUN
ejpam-6982	93	41	are	be	AUX
ejpam-6982	93	42	identical	identical	ADJ
ejpam-6982	93	43	for	for	ADP
ejpam-6982	93	44	all	all	DET
ejpam-6982	93	45	the	the	DET
ejpam-6982	93	46	considered	consider	VERB
ejpam-6982	93	47	problems	problem	NOUN
ejpam-6982	93	48	.	.	PUNCT
ejpam-6982	94	1	adomian	adomian	NOUN
ejpam-6982	94	2	decomposition	decomposition	NOUN
ejpam-6982	94	3	method	method	NOUN
ejpam-6982	94	4	:	:	PUNCT
ejpam-6982	94	5	applying	apply	VERB
ejpam-6982	94	6	the	the	DET
ejpam-6982	94	7	operator	operator	NOUN
ejpam-6982	94	8	jα	jα	NOUN
ejpam-6982	94	9	,	,	PUNCT
ejpam-6982	94	10	the	the	DET
ejpam-6982	94	11	inverse	inverse	NOUN
ejpam-6982	94	12	of	of	ADP
ejpam-6982	94	13	the	the	DET
ejpam-6982	94	14	operator	operator	NOUN
ejpam-6982	94	15	dα	dα	ADP
ejpam-6982	94	16	t	t	PROPN
ejpam-6982	94	17	,	,	PUNCT
ejpam-6982	94	18	to	to	ADP
ejpam-6982	94	19	both	both	DET
ejpam-6982	94	20	sides	side	NOUN
ejpam-6982	94	21	of	of	ADP
ejpam-6982	94	22	eq	eq	PROPN
ejpam-6982	94	23	.	.	PUNCT
ejpam-6982	95	1	(	(	PUNCT
ejpam-6982	95	2	4	4	X
ejpam-6982	95	3	)	)	PUNCT
ejpam-6982	95	4	yields	yield	NOUN
ejpam-6982	96	1	[	[	X
ejpam-6982	96	2	8	8	NUM
ejpam-6982	96	3	]	]	SYM
ejpam-6982	96	4	:	:	PUNCT
ejpam-6982	96	5	u(x	u(x	PROPN
ejpam-6982	96	6	,	,	PUNCT
ejpam-6982	96	7	t	t	PROPN
ejpam-6982	96	8	)	)	PUNCT
ejpam-6982	96	9	=	=	SYM
ejpam-6982	97	1	m−1∑	m−1∑	PROPN
ejpam-6982	97	2	k=0	k=0	PROPN
ejpam-6982	97	3	dku	dku	PROPN
ejpam-6982	97	4	dtk	dtk	PROPN
ejpam-6982	97	5	(	(	PUNCT
ejpam-6982	97	6	x	x	X
ejpam-6982	97	7	,	,	PUNCT
ejpam-6982	97	8	0	0	NUM
ejpam-6982	97	9	+	+	NUM
ejpam-6982	97	10	)	)	PUNCT
ejpam-6982	97	11	tk	tk	PROPN
ejpam-6982	98	1	k	k	NOUN
ejpam-6982	98	2	!	!	PUNCT
ejpam-6982	99	1	+	+	CCONJ
ejpam-6982	99	2	jαg(x	jαg(x	PROPN
ejpam-6982	99	3	,	,	PUNCT
ejpam-6982	99	4	t)−	t)−	PROPN
ejpam-6982	99	5	jα[lu(x	jα[lu(x	PROPN
ejpam-6982	99	6	,	,	PUNCT
ejpam-6982	99	7	t	t	PROPN
ejpam-6982	99	8	)	)	PUNCT
ejpam-6982	99	9	+	+	NOUN
ejpam-6982	99	10	nu(x	nu(x	NOUN
ejpam-6982	99	11	,	,	PUNCT
ejpam-6982	99	12	t	t	PROPN
ejpam-6982	99	13	)	)	PUNCT
ejpam-6982	99	14	]	]	PUNCT
ejpam-6982	99	15	.	.	PUNCT
ejpam-6982	100	1	(	(	PUNCT
ejpam-6982	100	2	5	5	X
ejpam-6982	100	3	)	)	PUNCT
ejpam-6982	100	4	the	the	DET
ejpam-6982	100	5	adomian	adomian	NOUN
ejpam-6982	100	6	decomposition	decomposition	NOUN
ejpam-6982	100	7	method	method	NOUN
ejpam-6982	100	8	suggests	suggest	VERB
ejpam-6982	100	9	that	that	SCONJ
ejpam-6982	100	10	the	the	DET
ejpam-6982	100	11	solution	solution	NOUN
ejpam-6982	100	12	u(x	u(x	VERB
ejpam-6982	100	13	,	,	PUNCT
ejpam-6982	100	14	t	t	PROPN
ejpam-6982	100	15	)	)	PUNCT
ejpam-6982	100	16	be	be	AUX
ejpam-6982	100	17	decomposed	decompose	VERB
ejpam-6982	100	18	into	into	ADP
ejpam-6982	100	19	an	an	DET
ejpam-6982	100	20	infinite	infinite	ADJ
ejpam-6982	100	21	series	series	NOUN
ejpam-6982	100	22	of	of	ADP
ejpam-6982	100	23	components	component	NOUN
ejpam-6982	100	24	.	.	PUNCT
ejpam-6982	101	1	u(x	u(x	NOUN
ejpam-6982	101	2	,	,	PUNCT
ejpam-6982	101	3	t	t	PROPN
ejpam-6982	101	4	)	)	PUNCT
ejpam-6982	101	5	=	=	PUNCT
ejpam-6982	102	1	∞∑	∞∑	PRON
ejpam-6982	102	2	n=0	n=0	NUM
ejpam-6982	102	3	un(x	un(x	NUM
ejpam-6982	102	4	,	,	PUNCT
ejpam-6982	102	5	t	t	PROPN
ejpam-6982	102	6	)	)	PUNCT
ejpam-6982	102	7	.	.	PUNCT
ejpam-6982	103	1	(	(	PUNCT
ejpam-6982	103	2	6	6	NUM
ejpam-6982	103	3	)	)	PUNCT
ejpam-6982	103	4	and	and	CCONJ
ejpam-6982	103	5	the	the	DET
ejpam-6982	103	6	nonlinear	nonlinear	ADJ
ejpam-6982	103	7	function	function	NOUN
ejpam-6982	103	8	in	in	ADP
ejpam-6982	103	9	eq	eq	ADP
ejpam-6982	103	10	.	.	PUNCT
ejpam-6982	104	1	(	(	PUNCT
ejpam-6982	104	2	5	5	NUM
ejpam-6982	104	3	)	)	PUNCT
ejpam-6982	104	4	is	be	AUX
ejpam-6982	104	5	decomposed	decompose	VERB
ejpam-6982	104	6	as	as	SCONJ
ejpam-6982	104	7	follows	follow	VERB
ejpam-6982	104	8	:	:	PUNCT
ejpam-6982	104	9	nu	nu	NOUN
ejpam-6982	104	10	=	=	PUNCT
ejpam-6982	105	1	∞∑	∞∑	PROPN
ejpam-6982	105	2	n=0	n=0	PROPN
ejpam-6982	105	3	an	an	PRON
ejpam-6982	105	4	,	,	PUNCT
ejpam-6982	105	5	(	(	PUNCT
ejpam-6982	105	6	7	7	X
ejpam-6982	105	7	)	)	PUNCT
ejpam-6982	105	8	here	here	ADV
ejpam-6982	105	9	an	an	PRON
ejpam-6982	105	10	are	be	AUX
ejpam-6982	105	11	the	the	DET
ejpam-6982	105	12	so	so	ADV
ejpam-6982	105	13	-	-	PUNCT
ejpam-6982	105	14	called	call	VERB
ejpam-6982	105	15	adomian	adomian	NOUN
ejpam-6982	105	16	polynomials	polynomial	NOUN
ejpam-6982	105	17	.	.	PUNCT
ejpam-6982	106	1	the	the	DET
ejpam-6982	106	2	general	general	ADJ
ejpam-6982	106	3	form	form	NOUN
ejpam-6982	106	4	of	of	ADP
ejpam-6982	106	5	the	the	DET
ejpam-6982	106	6	formula	formula	NOUN
ejpam-6982	106	7	for	for	ADP
ejpam-6982	106	8	an	an	DET
ejpam-6982	106	9	adomian	adomian	NOUN
ejpam-6982	106	10	polynomials	polynomial	NOUN
ejpam-6982	106	11	is	be	AUX
ejpam-6982	106	12	an	an	DET
ejpam-6982	106	13	=	=	SYM
ejpam-6982	106	14	1	1	NUM
ejpam-6982	106	15	n	n	NOUN
ejpam-6982	106	16	!	!	PUNCT
ejpam-6982	107	1	[	[	PUNCT
ejpam-6982	107	2	dn	dn	PROPN
ejpam-6982	107	3	dλn	dλn	PROPN
ejpam-6982	107	4	n	n	CCONJ
ejpam-6982	107	5	(	(	PUNCT
ejpam-6982	107	6	n∑	n∑	PROPN
ejpam-6982	107	7	k=0	k=0	PROPN
ejpam-6982	107	8	λkuk	λkuk	PROPN
ejpam-6982	107	9	)	)	PUNCT
ejpam-6982	107	10	]	]	PUNCT
ejpam-6982	108	1	λ=0	λ=0	X
ejpam-6982	108	2	.	.	PUNCT
ejpam-6982	109	1	(	(	PUNCT
ejpam-6982	109	2	8)	8)	NUM
ejpam-6982	109	3	the	the	DET
ejpam-6982	109	4	adomian	adomian	NOUN
ejpam-6982	109	5	polynomial	polynomial	NOUN
ejpam-6982	109	6	an	an	PRON
ejpam-6982	109	7	can	can	AUX
ejpam-6982	109	8	be	be	AUX
ejpam-6982	109	9	calculated	calculate	VERB
ejpam-6982	109	10	for	for	ADP
ejpam-6982	109	11	all	all	DET
ejpam-6982	109	12	forms	form	NOUN
ejpam-6982	109	13	of	of	ADP
ejpam-6982	109	14	nonlinearity	nonlinearity	NOUN
ejpam-6982	109	15	according	accord	VERB
ejpam-6982	109	16	to	to	ADP
ejpam-6982	109	17	specific	specific	ADJ
ejpam-6982	109	18	algorithms	algorithm	NOUN
ejpam-6982	109	19	constructed	construct	VERB
ejpam-6982	109	20	by	by	ADP
ejpam-6982	109	21	adomian	adomian	NOUN
ejpam-6982	109	22	[	[	X
ejpam-6982	109	23	9	9	NUM
ejpam-6982	109	24	]	]	PUNCT
ejpam-6982	109	25	.	.	PUNCT
ejpam-6982	110	1	a.	a.	PROPN
ejpam-6982	110	2	m.	m.	PROPN
ejpam-6982	110	3	alhammad	alhammad	PROPN
ejpam-6982	110	4	,	,	PUNCT
ejpam-6982	110	5	a.	a.	NOUN
ejpam-6982	110	6	m.	m.	PROPN
ejpam-6982	110	7	saeed	saeed	PROPN
ejpam-6982	110	8	/	/	SYM
ejpam-6982	110	9	eur	eur	PROPN
ejpam-6982	110	10	.	.	PUNCT
ejpam-6982	111	1	j.	j.	PROPN
ejpam-6982	111	2	pure	pure	PROPN
ejpam-6982	111	3	appl	appl	PROPN
ejpam-6982	111	4	.	.	PROPN
ejpam-6982	111	5	math	math	PROPN
ejpam-6982	111	6	,	,	PUNCT
ejpam-6982	111	7	18	18	NUM
ejpam-6982	111	8	(	(	PUNCT
ejpam-6982	111	9	4	4	NUM
ejpam-6982	111	10	)	)	PUNCT
ejpam-6982	111	11	(	(	PUNCT
ejpam-6982	111	12	2025	2025	NUM
ejpam-6982	111	13	)	)	PUNCT
ejpam-6982	111	14	,	,	PUNCT
ejpam-6982	111	15	6982	6982	NUM
ejpam-6982	111	16	6	6	NUM
ejpam-6982	111	17	of	of	ADP
ejpam-6982	111	18	22	22	NUM
ejpam-6982	111	19	substituting	substitute	VERB
ejpam-6982	111	20	the	the	DET
ejpam-6982	111	21	series	series	NOUN
ejpam-6982	111	22	of	of	ADP
ejpam-6982	111	23	decompositions	decomposition	NOUN
ejpam-6982	111	24	(	(	PUNCT
ejpam-6982	111	25	6	6	NUM
ejpam-6982	111	26	)	)	PUNCT
ejpam-6982	111	27	and	and	CCONJ
ejpam-6982	111	28	(	(	PUNCT
ejpam-6982	111	29	7	7	X
ejpam-6982	111	30	)	)	PUNCT
ejpam-6982	111	31	into	into	ADP
ejpam-6982	111	32	both	both	DET
ejpam-6982	111	33	sides	side	NOUN
ejpam-6982	111	34	of	of	ADP
ejpam-6982	111	35	(	(	PUNCT
ejpam-6982	111	36	5	5	NUM
ejpam-6982	111	37	)	)	PUNCT
ejpam-6982	111	38	gives	give	VERB
ejpam-6982	111	39	.	.	PUNCT
ejpam-6982	112	1	∞∑	∞∑	PRON
ejpam-6982	112	2	n=0	n=0	NUM
ejpam-6982	112	3	un(x	un(x	NUM
ejpam-6982	112	4	,	,	PUNCT
ejpam-6982	112	5	t	t	PROPN
ejpam-6982	112	6	)	)	PUNCT
ejpam-6982	112	7	=	=	SYM
ejpam-6982	113	1	m−1∑	m−1∑	PROPN
ejpam-6982	113	2	k=0	k=0	PROPN
ejpam-6982	113	3	dku	dku	PROPN
ejpam-6982	113	4	dtk	dtk	PROPN
ejpam-6982	113	5	(	(	PUNCT
ejpam-6982	113	6	x	x	X
ejpam-6982	113	7	,	,	PUNCT
ejpam-6982	113	8	0	0	NUM
ejpam-6982	113	9	+	+	NUM
ejpam-6982	113	10	)	)	PUNCT
ejpam-6982	113	11	tk	tk	PROPN
ejpam-6982	114	1	k	k	NOUN
ejpam-6982	114	2	!	!	PUNCT
ejpam-6982	115	1	+	+	CCONJ
ejpam-6982	116	1	jαg(x	jαg(x	PROPN
ejpam-6982	116	2	,	,	PUNCT
ejpam-6982	116	3	t)−	t)−	PROPN
ejpam-6982	116	4	jα	jα	X
ejpam-6982	116	5	[	[	PUNCT
ejpam-6982	116	6	l	l	X
ejpam-6982	116	7	(	(	PUNCT
ejpam-6982	116	8	∞∑	∞∑	PROPN
ejpam-6982	116	9	n=0	n=0	NUM
ejpam-6982	116	10	un(x	un(x	NUM
ejpam-6982	116	11	,	,	PUNCT
ejpam-6982	116	12	t	t	PROPN
ejpam-6982	116	13	)	)	PUNCT
ejpam-6982	116	14	)	)	PUNCT
ejpam-6982	117	1	+	+	CCONJ
ejpam-6982	118	1	∞∑	∞∑	NUM
ejpam-6982	118	2	n=0	n=0	PUNCT
ejpam-6982	118	3	an	an	PRON
ejpam-6982	118	4	]	]	PUNCT
ejpam-6982	118	5	.	.	PUNCT
ejpam-6982	119	1	(	(	PUNCT
ejpam-6982	119	2	9	9	NUM
ejpam-6982	119	3	)	)	PUNCT
ejpam-6982	119	4	from	from	ADP
ejpam-6982	119	5	this	this	DET
ejpam-6982	119	6	equation	equation	NOUN
ejpam-6982	119	7	,	,	PUNCT
ejpam-6982	119	8	the	the	DET
ejpam-6982	119	9	iterates	iterate	NOUN
ejpam-6982	119	10	are	be	AUX
ejpam-6982	119	11	determined	determine	VERB
ejpam-6982	119	12	by	by	ADP
ejpam-6982	119	13	the	the	DET
ejpam-6982	119	14	following	follow	VERB
ejpam-6982	119	15	recursive	recursive	ADJ
ejpam-6982	119	16	way	way	NOUN
ejpam-6982	119	17	.	.	PUNCT
ejpam-6982	120	1	u0(x	u0(x	ADP
ejpam-6982	120	2	,	,	PUNCT
ejpam-6982	120	3	t	t	PROPN
ejpam-6982	120	4	)	)	PUNCT
ejpam-6982	120	5	=	=	SYM
ejpam-6982	121	1	m−1∑	m−1∑	PROPN
ejpam-6982	121	2	k=0	k=0	PROPN
ejpam-6982	121	3	dku	dku	PROPN
ejpam-6982	121	4	dtk	dtk	PROPN
ejpam-6982	121	5	(	(	PUNCT
ejpam-6982	121	6	x	x	X
ejpam-6982	121	7	,	,	PUNCT
ejpam-6982	121	8	0	0	NUM
ejpam-6982	121	9	+	+	NUM
ejpam-6982	121	10	)	)	PUNCT
ejpam-6982	121	11	tk	tk	PROPN
ejpam-6982	122	1	k	k	NOUN
ejpam-6982	122	2	!	!	PUNCT
ejpam-6982	123	1	+	+	CCONJ
ejpam-6982	124	1	jαg(x	jαg(x	PROPN
ejpam-6982	124	2	,	,	PUNCT
ejpam-6982	124	3	t	t	PROPN
ejpam-6982	124	4	)	)	PUNCT
ejpam-6982	124	5	,	,	PUNCT
ejpam-6982	124	6	u1(x	u1(x	PROPN
ejpam-6982	124	7	,	,	PUNCT
ejpam-6982	124	8	t	t	PROPN
ejpam-6982	124	9	)	)	PUNCT
ejpam-6982	124	10	=	=	SYM
ejpam-6982	125	1	−jα	−jα	X
ejpam-6982	126	1	[	[	X
ejpam-6982	126	2	lu0	lu0	NOUN
ejpam-6982	126	3	+	+	NOUN
ejpam-6982	126	4	a0	a0	NOUN
ejpam-6982	126	5	]	]	PUNCT
ejpam-6982	126	6	,	,	PUNCT
ejpam-6982	126	7	u2(x	u2(x	PROPN
ejpam-6982	126	8	,	,	PUNCT
ejpam-6982	126	9	t	t	PROPN
ejpam-6982	126	10	)	)	PUNCT
ejpam-6982	126	11	=	=	SYM
ejpam-6982	126	12	−jα	−jα	X
ejpam-6982	127	1	[	[	X
ejpam-6982	127	2	lu1	lu1	X
ejpam-6982	127	3	+	+	NOUN
ejpam-6982	127	4	a1	a1	NOUN
ejpam-6982	127	5	]	]	PUNCT
ejpam-6982	127	6	,	,	PUNCT
ejpam-6982	127	7	...	...	PUNCT
ejpam-6982	128	1	un+1(x	un+1(x	ADJ
ejpam-6982	128	2	,	,	PUNCT
ejpam-6982	128	3	t	t	PROPN
ejpam-6982	128	4	)	)	PUNCT
ejpam-6982	128	5	=	=	SYM
ejpam-6982	129	1	−jα	−jα	X
ejpam-6982	130	1	[	[	X
ejpam-6982	130	2	lun	lun	X
ejpam-6982	131	1	+	+	NOUN
ejpam-6982	131	2	an	an	X
ejpam-6982	131	3	]	]	X
ejpam-6982	131	4	.	.	PUNCT
ejpam-6982	132	1	(	(	PUNCT
ejpam-6982	132	2	10	10	NUM
ejpam-6982	132	3	)	)	PUNCT
ejpam-6982	132	4	finally	finally	ADV
ejpam-6982	132	5	,	,	PUNCT
ejpam-6982	132	6	we	we	PRON
ejpam-6982	132	7	approximate	approximate	VERB
ejpam-6982	132	8	the	the	DET
ejpam-6982	132	9	solution	solution	NOUN
ejpam-6982	132	10	u(x	u(x	NOUN
ejpam-6982	132	11	,	,	PUNCT
ejpam-6982	132	12	t	t	PROPN
ejpam-6982	132	13	)	)	PUNCT
ejpam-6982	132	14	by	by	ADP
ejpam-6982	132	15	the	the	DET
ejpam-6982	132	16	truncated	truncated	ADJ
ejpam-6982	132	17	series	series	NOUN
ejpam-6982	132	18	.	.	PUNCT
ejpam-6982	133	1	ϕn	ϕn	INTJ
ejpam-6982	133	2	(	(	PUNCT
ejpam-6982	133	3	x	x	PROPN
ejpam-6982	133	4	,	,	PUNCT
ejpam-6982	133	5	t	t	PROPN
ejpam-6982	133	6	)	)	PUNCT
ejpam-6982	133	7	=	=	PRON
ejpam-6982	133	8	n−1∑	n−1∑	PROPN
ejpam-6982	133	9	n=0	n=0	NUM
ejpam-6982	133	10	un(x	un(x	NUM
ejpam-6982	133	11	,	,	PUNCT
ejpam-6982	133	12	t	t	PROPN
ejpam-6982	133	13	)	)	PUNCT
ejpam-6982	133	14	and	and	CCONJ
ejpam-6982	133	15	lim	lim	PROPN
ejpam-6982	133	16	n→∞	n→∞	PROPN
ejpam-6982	134	1	ϕn	ϕn	INTJ
ejpam-6982	134	2	(	(	PUNCT
ejpam-6982	134	3	x	x	PROPN
ejpam-6982	134	4	,	,	PUNCT
ejpam-6982	134	5	t	t	PROPN
ejpam-6982	134	6	)	)	PUNCT
ejpam-6982	134	7	=	=	SYM
ejpam-6982	134	8	u(x	u(x	PROPN
ejpam-6982	134	9	,	,	PUNCT
ejpam-6982	134	10	t	t	PROPN
ejpam-6982	134	11	)	)	PUNCT
ejpam-6982	134	12	.	.	PUNCT
ejpam-6982	135	1	(	(	PUNCT
ejpam-6982	135	2	11	11	NUM
ejpam-6982	135	3	)	)	PUNCT
ejpam-6982	135	4	sumudu	sumudu	NOUN
ejpam-6982	135	5	decomposition	decomposition	NOUN
ejpam-6982	135	6	method	method	NOUN
ejpam-6982	135	7	:	:	PUNCT
ejpam-6982	135	8	applying	apply	VERB
ejpam-6982	135	9	the	the	DET
ejpam-6982	135	10	sumudu	sumudu	NOUN
ejpam-6982	135	11	transform	transform	NOUN
ejpam-6982	135	12	on	on	ADP
ejpam-6982	135	13	both	both	DET
ejpam-6982	135	14	sides	side	NOUN
ejpam-6982	135	15	of	of	ADP
ejpam-6982	135	16	eq	eq	PROPN
ejpam-6982	135	17	.	.	PUNCT
ejpam-6982	136	1	(	(	PUNCT
ejpam-6982	136	2	4	4	X
ejpam-6982	136	3	)	)	PUNCT
ejpam-6982	136	4	yields	yield	NOUN
ejpam-6982	136	5	[	[	X
ejpam-6982	136	6	12	12	NUM
ejpam-6982	136	7	]	]	X
ejpam-6982	136	8	s	s	X
ejpam-6982	137	1	[	[	X
ejpam-6982	137	2	dα	dα	ADP
ejpam-6982	137	3	t	t	PROPN
ejpam-6982	137	4	u(x	u(x	PROPN
ejpam-6982	137	5	,	,	PUNCT
ejpam-6982	137	6	t	t	PROPN
ejpam-6982	137	7	)	)	PUNCT
ejpam-6982	137	8	]	]	PUNCT
ejpam-6982	138	1	=	=	PUNCT
ejpam-6982	138	2	s[g(x	s[g(x	NOUN
ejpam-6982	138	3	,	,	PUNCT
ejpam-6982	138	4	t)−	t)−	PROPN
ejpam-6982	138	5	lu(x	lu(x	NOUN
ejpam-6982	138	6	,	,	PUNCT
ejpam-6982	138	7	t)−nu(x	t)−nu(x	PROPN
ejpam-6982	138	8	,	,	PUNCT
ejpam-6982	138	9	t	t	PROPN
ejpam-6982	138	10	)	)	PUNCT
ejpam-6982	138	11	]	]	PUNCT
ejpam-6982	138	12	.	.	PUNCT
ejpam-6982	139	1	(	(	PUNCT
ejpam-6982	139	2	12	12	NUM
ejpam-6982	139	3	)	)	PUNCT
ejpam-6982	139	4	using	use	VERB
ejpam-6982	139	5	the	the	DET
ejpam-6982	139	6	differentiation	differentiation	NOUN
ejpam-6982	139	7	property	property	NOUN
ejpam-6982	139	8	of	of	ADP
ejpam-6982	139	9	the	the	DET
ejpam-6982	139	10	sumudu	sumudu	NOUN
ejpam-6982	139	11	transform	transform	NOUN
ejpam-6982	139	12	for	for	ADP
ejpam-6982	139	13	caputo	caputo	PROPN
ejpam-6982	139	14	,	,	PUNCT
ejpam-6982	139	15	we	we	PRON
ejpam-6982	139	16	get	get	VERB
ejpam-6982	139	17	u−αs[u(x	u−αs[u(x	PROPN
ejpam-6982	139	18	,	,	PUNCT
ejpam-6982	139	19	t)]−	t)]−	NOUN
ejpam-6982	139	20	m−1∑	m−1∑	NUM
ejpam-6982	139	21	k=0	k=0	PROPN
ejpam-6982	139	22	u−(α−k)uk(x.0	u−(α−k)uk(x.0	PROPN
ejpam-6982	139	23	)	)	PUNCT
ejpam-6982	139	24	=	=	SYM
ejpam-6982	139	25	s[g(x	s[g(x	NOUN
ejpam-6982	139	26	,	,	PUNCT
ejpam-6982	139	27	t)−	t)−	PROPN
ejpam-6982	139	28	lu(x	lu(x	NOUN
ejpam-6982	139	29	,	,	PUNCT
ejpam-6982	139	30	t)−nu(x	t)−nu(x	PROPN
ejpam-6982	139	31	,	,	PUNCT
ejpam-6982	139	32	t	t	PROPN
ejpam-6982	139	33	)	)	PUNCT
ejpam-6982	139	34	]	]	PUNCT
ejpam-6982	139	35	.	.	PUNCT
ejpam-6982	140	1	(	(	PUNCT
ejpam-6982	140	2	13	13	NUM
ejpam-6982	140	3	)	)	PUNCT
ejpam-6982	140	4	simplify	simplify	NOUN
ejpam-6982	140	5	,	,	PUNCT
ejpam-6982	140	6	we	we	PRON
ejpam-6982	140	7	get	get	VERB
ejpam-6982	140	8	.	.	PUNCT
ejpam-6982	141	1	u(x	u(x	NOUN
ejpam-6982	141	2	,	,	PUNCT
ejpam-6982	141	3	t	t	PROPN
ejpam-6982	141	4	)	)	PUNCT
ejpam-6982	141	5	=	=	SYM
ejpam-6982	142	1	m−1∑	m−1∑	PROPN
ejpam-6982	142	2	k=0	k=0	PROPN
ejpam-6982	142	3	u(k)fk(x	u(k)fk(x	ADJ
ejpam-6982	142	4	)	)	PUNCT
ejpam-6982	143	1	+	+	CCONJ
ejpam-6982	143	2	s−1	s−1	PROPN
ejpam-6982	143	3	(	(	PUNCT
ejpam-6982	143	4	uαs[g(x	uαs[g(x	ADV
ejpam-6982	143	5	,	,	PUNCT
ejpam-6982	143	6	t)])−	t)])−	ADJ
ejpam-6982	143	7	s−1	s−1	PROPN
ejpam-6982	143	8	(	(	PUNCT
ejpam-6982	143	9	uαs[lu(x	uαs[lu(x	NOUN
ejpam-6982	143	10	,	,	PUNCT
ejpam-6982	143	11	t	t	PROPN
ejpam-6982	143	12	)	)	PUNCT
ejpam-6982	143	13	+	+	NUM
ejpam-6982	143	14	nu(x	nu(x	PROPN
ejpam-6982	143	15	,	,	PUNCT
ejpam-6982	143	16	t	t	PROPN
ejpam-6982	143	17	)	)	PUNCT
ejpam-6982	143	18	]	]	PUNCT
ejpam-6982	143	19	)	)	PUNCT
ejpam-6982	143	20	.	.	PUNCT
ejpam-6982	144	1	(	(	PUNCT
ejpam-6982	144	2	14	14	X
ejpam-6982	144	3	)	)	PUNCT
ejpam-6982	144	4	substituting	substitute	VERB
ejpam-6982	144	5	the	the	DET
ejpam-6982	144	6	series	series	NOUN
ejpam-6982	144	7	of	of	ADP
ejpam-6982	144	8	decompositions	decomposition	NOUN
ejpam-6982	144	9	(	(	PUNCT
ejpam-6982	144	10	6	6	NUM
ejpam-6982	144	11	)	)	PUNCT
ejpam-6982	144	12	and	and	CCONJ
ejpam-6982	144	13	(	(	PUNCT
ejpam-6982	144	14	7	7	X
ejpam-6982	144	15	)	)	PUNCT
ejpam-6982	144	16	into	into	ADP
ejpam-6982	144	17	both	both	DET
ejpam-6982	144	18	sides	side	NOUN
ejpam-6982	144	19	of	of	ADP
ejpam-6982	144	20	(	(	PUNCT
ejpam-6982	144	21	5	5	NUM
ejpam-6982	144	22	)	)	PUNCT
ejpam-6982	144	23	gives	give	VERB
ejpam-6982	144	24	,	,	PUNCT
ejpam-6982	144	25	∞∑	∞∑	PRON
ejpam-6982	144	26	n=0	n=0	NOUN
ejpam-6982	144	27	un(x	un(x	NUM
ejpam-6982	144	28	,	,	PUNCT
ejpam-6982	144	29	t	t	PROPN
ejpam-6982	144	30	)	)	PUNCT
ejpam-6982	144	31	=	=	SYM
ejpam-6982	145	1	m−1∑	m−1∑	PROPN
ejpam-6982	145	2	k=0	k=0	PROPN
ejpam-6982	145	3	u(k)fk(x	u(k)fk(x	ADJ
ejpam-6982	145	4	)	)	PUNCT
ejpam-6982	146	1	+	+	CCONJ
ejpam-6982	146	2	s−1	s−1	PROPN
ejpam-6982	146	3	(	(	PUNCT
ejpam-6982	146	4	uαs[g(x	uαs[g(x	PROPN
ejpam-6982	146	5	,	,	PUNCT
ejpam-6982	146	6	t	t	PROPN
ejpam-6982	146	7	)	)	PUNCT
ejpam-6982	146	8	]	]	PUNCT
ejpam-6982	146	9	)	)	PUNCT
ejpam-6982	146	10	−	−	PROPN
ejpam-6982	147	1	s−1	s−1	PROPN
ejpam-6982	147	2	[	[	PUNCT
ejpam-6982	147	3	uαs	uαs	PROPN
ejpam-6982	147	4	(	(	PUNCT
ejpam-6982	147	5	l	l	X
ejpam-6982	147	6	(	(	PUNCT
ejpam-6982	147	7	∞∑	∞∑	PROPN
ejpam-6982	147	8	n=0	n=0	NUM
ejpam-6982	147	9	un(x	un(x	NUM
ejpam-6982	147	10	,	,	PUNCT
ejpam-6982	147	11	t	t	PROPN
ejpam-6982	147	12	)	)	PUNCT
ejpam-6982	147	13	)	)	PUNCT
ejpam-6982	148	1	+	+	CCONJ
ejpam-6982	149	1	∞∑	∞∑	NUM
ejpam-6982	149	2	n=0	n=0	NUM
ejpam-6982	149	3	an	an	PRON
ejpam-6982	149	4	)	)	PUNCT
ejpam-6982	149	5	]	]	PUNCT
ejpam-6982	149	6	,	,	PUNCT
ejpam-6982	149	7	(	(	PUNCT
ejpam-6982	149	8	15	15	NUM
ejpam-6982	149	9	)	)	PUNCT
ejpam-6982	149	10	where	where	SCONJ
ejpam-6982	149	11	an	an	DET
ejpam-6982	149	12	defined	define	VERB
ejpam-6982	149	13	in	in	ADP
ejpam-6982	149	14	eq	eq	ADP
ejpam-6982	149	15	.	.	PUNCT
ejpam-6982	150	1	(	(	PUNCT
ejpam-6982	150	2	8)	8)	NUM
ejpam-6982	150	3	.	.	PUNCT
ejpam-6982	150	4	a.	a.	NOUN
ejpam-6982	150	5	m.	m.	PROPN
ejpam-6982	150	6	alhammad	alhammad	PROPN
ejpam-6982	150	7	,	,	PUNCT
ejpam-6982	150	8	a.	a.	NOUN
ejpam-6982	150	9	m.	m.	PROPN
ejpam-6982	150	10	saeed	saeed	PROPN
ejpam-6982	150	11	/	/	SYM
ejpam-6982	150	12	eur	eur	PROPN
ejpam-6982	150	13	.	.	PUNCT
ejpam-6982	151	1	j.	j.	PROPN
ejpam-6982	151	2	pure	pure	PROPN
ejpam-6982	151	3	appl	appl	PROPN
ejpam-6982	151	4	.	.	PROPN
ejpam-6982	151	5	math	math	PROPN
ejpam-6982	151	6	,	,	PUNCT
ejpam-6982	151	7	18	18	NUM
ejpam-6982	151	8	(	(	PUNCT
ejpam-6982	151	9	4	4	NUM
ejpam-6982	151	10	)	)	PUNCT
ejpam-6982	151	11	(	(	PUNCT
ejpam-6982	151	12	2025	2025	NUM
ejpam-6982	151	13	)	)	PUNCT
ejpam-6982	151	14	,	,	PUNCT
ejpam-6982	151	15	6982	6982	NUM
ejpam-6982	151	16	7	7	NUM
ejpam-6982	151	17	of	of	ADP
ejpam-6982	151	18	22	22	NUM
ejpam-6982	151	19	on	on	ADP
ejpam-6982	151	20	comparing	compare	VERB
ejpam-6982	151	21	both	both	DET
ejpam-6982	151	22	sides	side	NOUN
ejpam-6982	151	23	of	of	ADP
ejpam-6982	151	24	the	the	DET
ejpam-6982	151	25	eq	eq	NOUN
ejpam-6982	151	26	.	.	PUNCT
ejpam-6982	151	27	(	(	PUNCT
ejpam-6982	151	28	15	15	NUM
ejpam-6982	151	29	)	)	PUNCT
ejpam-6982	151	30	,	,	PUNCT
ejpam-6982	151	31	we	we	PRON
ejpam-6982	151	32	get	get	VERB
ejpam-6982	151	33	u0(x	u0(x	ADP
ejpam-6982	151	34	,	,	PUNCT
ejpam-6982	151	35	t	t	PROPN
ejpam-6982	151	36	)	)	PUNCT
ejpam-6982	151	37	=	=	SYM
ejpam-6982	152	1	m−1∑	m−1∑	PROPN
ejpam-6982	152	2	k=0	k=0	PROPN
ejpam-6982	152	3	u(k)fk(x	u(k)fk(x	ADJ
ejpam-6982	152	4	)	)	PUNCT
ejpam-6982	153	1	+	+	CCONJ
ejpam-6982	153	2	s−1	s−1	PROPN
ejpam-6982	153	3	(	(	PUNCT
ejpam-6982	153	4	uαs[g(x	uαs[g(x	PROPN
ejpam-6982	153	5	,	,	PUNCT
ejpam-6982	153	6	t	t	PROPN
ejpam-6982	153	7	)	)	PUNCT
ejpam-6982	153	8	]	]	PUNCT
ejpam-6982	153	9	)	)	PUNCT
ejpam-6982	153	10	,	,	PUNCT
ejpam-6982	153	11	u1(x	u1(x	PROPN
ejpam-6982	153	12	,	,	PUNCT
ejpam-6982	153	13	t	t	PROPN
ejpam-6982	153	14	)	)	PUNCT
ejpam-6982	153	15	=	=	PUNCT
ejpam-6982	153	16	−s−1	−s−1	NUM
ejpam-6982	153	17	(	(	PUNCT
ejpam-6982	153	18	uαs	uαs	X
ejpam-6982	153	19	[	[	X
ejpam-6982	153	20	lu0	lu0	NOUN
ejpam-6982	153	21	+	+	SYM
ejpam-6982	153	22	a0	a0	NOUN
ejpam-6982	153	23	]	]	X
ejpam-6982	153	24	)	)	PUNCT
ejpam-6982	153	25	,	,	PUNCT
ejpam-6982	153	26	u2(x	u2(x	PROPN
ejpam-6982	153	27	,	,	PUNCT
ejpam-6982	153	28	t	t	PROPN
ejpam-6982	153	29	)	)	PUNCT
ejpam-6982	153	30	=	=	PUNCT
ejpam-6982	153	31	−s−1	−s−1	NUM
ejpam-6982	153	32	(	(	PUNCT
ejpam-6982	153	33	uαs	uαs	X
ejpam-6982	154	1	[	[	X
ejpam-6982	154	2	lu1	lu1	VERB
ejpam-6982	154	3	+	+	VERB
ejpam-6982	154	4	a1	a1	NOUN
ejpam-6982	154	5	]	]	X
ejpam-6982	154	6	)	)	PUNCT
ejpam-6982	154	7	,	,	PUNCT
ejpam-6982	154	8	...	...	PUNCT
ejpam-6982	155	1	un+1(x	un+1(x	ADJ
ejpam-6982	155	2	,	,	PUNCT
ejpam-6982	155	3	t	t	PROPN
ejpam-6982	155	4	)	)	PUNCT
ejpam-6982	155	5	=	=	PUNCT
ejpam-6982	156	1	−s−1	−s−1	NUM
ejpam-6982	156	2	(	(	PUNCT
ejpam-6982	156	3	uαs	uαs	PROPN
ejpam-6982	157	1	[	[	X
ejpam-6982	157	2	lun	lun	X
ejpam-6982	158	1	+	+	NOUN
ejpam-6982	158	2	an	an	DET
ejpam-6982	158	3	]	]	X
ejpam-6982	158	4	)	)	PUNCT
ejpam-6982	158	5	,	,	PUNCT
ejpam-6982	159	1	n	n	X
ejpam-6982	159	2	≥	≥	NOUN
ejpam-6982	159	3	1	1	NUM
ejpam-6982	159	4	.	.	PUNCT
ejpam-6982	160	1	(	(	PUNCT
ejpam-6982	160	2	16	16	NUM
ejpam-6982	160	3	)	)	PUNCT
ejpam-6982	160	4	finally	finally	ADV
ejpam-6982	160	5	,	,	PUNCT
ejpam-6982	160	6	we	we	PRON
ejpam-6982	160	7	approximate	approximate	VERB
ejpam-6982	160	8	the	the	DET
ejpam-6982	160	9	solution	solution	NOUN
ejpam-6982	160	10	u(x	u(x	NOUN
ejpam-6982	160	11	,	,	PUNCT
ejpam-6982	160	12	t	t	PROPN
ejpam-6982	160	13	)	)	PUNCT
ejpam-6982	160	14	by	by	ADP
ejpam-6982	160	15	the	the	DET
ejpam-6982	160	16	truncated	truncated	ADJ
ejpam-6982	160	17	series	series	NOUN
ejpam-6982	160	18	.	.	PUNCT
ejpam-6982	161	1	ϕn	ϕn	INTJ
ejpam-6982	161	2	(	(	PUNCT
ejpam-6982	161	3	x	x	PROPN
ejpam-6982	161	4	,	,	PUNCT
ejpam-6982	161	5	t	t	PROPN
ejpam-6982	161	6	)	)	PUNCT
ejpam-6982	161	7	=	=	PRON
ejpam-6982	161	8	n−1∑	n−1∑	PROPN
ejpam-6982	161	9	n=0	n=0	NUM
ejpam-6982	161	10	un(x	un(x	NUM
ejpam-6982	161	11	,	,	PUNCT
ejpam-6982	161	12	t	t	PROPN
ejpam-6982	161	13	)	)	PUNCT
ejpam-6982	161	14	and	and	CCONJ
ejpam-6982	161	15	lim	lim	PROPN
ejpam-6982	161	16	n→∞	n→∞	PROPN
ejpam-6982	162	1	ϕn	ϕn	INTJ
ejpam-6982	162	2	(	(	PUNCT
ejpam-6982	162	3	x	x	PROPN
ejpam-6982	162	4	,	,	PUNCT
ejpam-6982	162	5	t	t	PROPN
ejpam-6982	162	6	)	)	PUNCT
ejpam-6982	162	7	=	=	SYM
ejpam-6982	162	8	u(x	u(x	PROPN
ejpam-6982	162	9	,	,	PUNCT
ejpam-6982	162	10	t	t	PROPN
ejpam-6982	162	11	)	)	PUNCT
ejpam-6982	162	12	.	.	PUNCT
ejpam-6982	163	1	(	(	PUNCT
ejpam-6982	163	2	17	17	NUM
ejpam-6982	163	3	)	)	PUNCT
ejpam-6982	163	4	natural	natural	ADJ
ejpam-6982	163	5	decomposition	decomposition	NOUN
ejpam-6982	163	6	method	method	NOUN
ejpam-6982	163	7	:	:	PUNCT
ejpam-6982	163	8	we	we	PRON
ejpam-6982	163	9	apply	apply	VERB
ejpam-6982	163	10	the	the	DET
ejpam-6982	163	11	natural	natural	ADJ
ejpam-6982	163	12	transform	transform	NOUN
ejpam-6982	163	13	on	on	ADP
ejpam-6982	163	14	both	both	DET
ejpam-6982	163	15	sides	side	NOUN
ejpam-6982	163	16	of	of	ADP
ejpam-6982	163	17	eq	eq	PROPN
ejpam-6982	163	18	.	.	PUNCT
ejpam-6982	164	1	(	(	PUNCT
ejpam-6982	164	2	4	4	NUM
ejpam-6982	164	3	)	)	PUNCT
ejpam-6982	164	4	,	,	PUNCT
ejpam-6982	164	5	which	which	PRON
ejpam-6982	164	6	yields	yield	VERB
ejpam-6982	164	7	[	[	X
ejpam-6982	164	8	13	13	NUM
ejpam-6982	164	9	]	]	PUNCT
ejpam-6982	164	10	.	.	PUNCT
ejpam-6982	165	1	n	n	PRON
ejpam-6982	166	1	[	[	X
ejpam-6982	166	2	dα	dα	PRON
ejpam-6982	166	3	t	t	PROPN
ejpam-6982	166	4	u(x	u(x	PROPN
ejpam-6982	166	5	,	,	PUNCT
ejpam-6982	166	6	t	t	PROPN
ejpam-6982	166	7	)	)	PUNCT
ejpam-6982	166	8	]	]	PUNCT
ejpam-6982	167	1	=	=	PUNCT
ejpam-6982	167	2	n[g(x	n[g(x	X
ejpam-6982	167	3	,	,	PUNCT
ejpam-6982	167	4	t)−	t)−	PROPN
ejpam-6982	167	5	lu(x	lu(x	NOUN
ejpam-6982	167	6	,	,	PUNCT
ejpam-6982	167	7	t)−nu(x	t)−nu(x	PROPN
ejpam-6982	167	8	,	,	PUNCT
ejpam-6982	167	9	t	t	PROPN
ejpam-6982	167	10	)	)	PUNCT
ejpam-6982	167	11	]	]	PUNCT
ejpam-6982	167	12	.	.	PUNCT
ejpam-6982	168	1	(	(	PUNCT
ejpam-6982	168	2	18	18	NUM
ejpam-6982	168	3	)	)	PUNCT
ejpam-6982	168	4	using	use	VERB
ejpam-6982	168	5	the	the	DET
ejpam-6982	168	6	differentiation	differentiation	NOUN
ejpam-6982	168	7	property	property	NOUN
ejpam-6982	168	8	of	of	ADP
ejpam-6982	168	9	the	the	DET
ejpam-6982	168	10	natural	natural	ADJ
ejpam-6982	168	11	transform	transform	NOUN
ejpam-6982	168	12	for	for	ADP
ejpam-6982	168	13	caputo	caputo	PROPN
ejpam-6982	168	14	,	,	PUNCT
ejpam-6982	168	15	we	we	PRON
ejpam-6982	168	16	get	get	VERB
ejpam-6982	168	17	sα	sα	ADV
ejpam-6982	168	18	uα	uα	ADP
ejpam-6982	168	19	n[u(x	n[u(x	NOUN
ejpam-6982	168	20	,	,	PUNCT
ejpam-6982	168	21	t)]−	t)]−	NOUN
ejpam-6982	168	22	m−1∑	m−1∑	NUM
ejpam-6982	168	23	k=0	k=0	PROPN
ejpam-6982	168	24	sα−(k+1	sα−(k+1	PROPN
ejpam-6982	168	25	)	)	PUNCT
ejpam-6982	168	26	uα−k	uα−k	NOUN
ejpam-6982	168	27	uk(x	uk(x	ADP
ejpam-6982	168	28	,	,	PUNCT
ejpam-6982	168	29	0	0	NUM
ejpam-6982	168	30	)	)	PUNCT
ejpam-6982	168	31	=	=	PUNCT
ejpam-6982	169	1	n[g(x	n[g(x	NOUN
ejpam-6982	169	2	,	,	PUNCT
ejpam-6982	169	3	t)−	t)−	PROPN
ejpam-6982	169	4	lu(x	lu(x	NOUN
ejpam-6982	169	5	,	,	PUNCT
ejpam-6982	169	6	t)−nu(x	t)−nu(x	PROPN
ejpam-6982	169	7	,	,	PUNCT
ejpam-6982	169	8	t	t	PROPN
ejpam-6982	169	9	)	)	PUNCT
ejpam-6982	169	10	]	]	PUNCT
ejpam-6982	169	11	.	.	PUNCT
ejpam-6982	170	1	(	(	PUNCT
ejpam-6982	170	2	19	19	NUM
ejpam-6982	170	3	)	)	PUNCT
ejpam-6982	170	4	simplify	simplify	NOUN
ejpam-6982	170	5	,	,	PUNCT
ejpam-6982	170	6	we	we	PRON
ejpam-6982	170	7	get	get	VERB
ejpam-6982	170	8	u(x	u(x	NOUN
ejpam-6982	170	9	,	,	PUNCT
ejpam-6982	170	10	t	t	NOUN
ejpam-6982	170	11	)	)	PUNCT
ejpam-6982	170	12	=	=	SYM
ejpam-6982	171	1	m−1∑	m−1∑	PROPN
ejpam-6982	171	2	k=0	k=0	PROPN
ejpam-6982	171	3	s−(k+1	s−(k+1	PROPN
ejpam-6982	171	4	)	)	PUNCT
ejpam-6982	171	5	u−k	u−k	NOUN
ejpam-6982	171	6	uk(x	uk(x	ADP
ejpam-6982	171	7	,	,	PUNCT
ejpam-6982	171	8	0	0	NUM
ejpam-6982	171	9	)	)	PUNCT
ejpam-6982	172	1	+	+	CCONJ
ejpam-6982	172	2	n−1	n−1	PROPN
ejpam-6982	172	3	(	(	PUNCT
ejpam-6982	172	4	uα	uα	PROPN
ejpam-6982	172	5	sα	sα	ADV
ejpam-6982	172	6	n[g(x	n[g(x	X
ejpam-6982	172	7	,	,	PUNCT
ejpam-6982	172	8	t	t	PROPN
ejpam-6982	172	9	)	)	PUNCT
ejpam-6982	172	10	]	]	PUNCT
ejpam-6982	172	11	)	)	PUNCT
ejpam-6982	173	1	−	−	PROPN
ejpam-6982	173	2	n−1	n−1	PROPN
ejpam-6982	173	3	(	(	PUNCT
ejpam-6982	173	4	uα	uα	PROPN
ejpam-6982	173	5	sα	sα	PROPN
ejpam-6982	173	6	n[lu(x	n[lu(x	PROPN
ejpam-6982	173	7	,	,	PUNCT
ejpam-6982	173	8	t	t	PROPN
ejpam-6982	173	9	)	)	PUNCT
ejpam-6982	173	10	+	+	NOUN
ejpam-6982	173	11	nu(x	nu(x	NOUN
ejpam-6982	173	12	,	,	PUNCT
ejpam-6982	173	13	t	t	PROPN
ejpam-6982	173	14	)	)	PUNCT
ejpam-6982	173	15	]	]	PUNCT
ejpam-6982	173	16	)	)	PUNCT
ejpam-6982	173	17	.	.	PUNCT
ejpam-6982	174	1	(	(	PUNCT
ejpam-6982	174	2	20	20	NUM
ejpam-6982	174	3	)	)	PUNCT
ejpam-6982	174	4	substitution	substitution	NOUN
ejpam-6982	174	5	the	the	DET
ejpam-6982	174	6	decomposition	decomposition	NOUN
ejpam-6982	174	7	series	series	NOUN
ejpam-6982	174	8	(	(	PUNCT
ejpam-6982	174	9	6	6	NUM
ejpam-6982	174	10	)	)	PUNCT
ejpam-6982	174	11	and	and	CCONJ
ejpam-6982	174	12	(	(	PUNCT
ejpam-6982	174	13	7	7	X
ejpam-6982	174	14	)	)	PUNCT
ejpam-6982	174	15	into	into	ADP
ejpam-6982	174	16	both	both	DET
ejpam-6982	174	17	sides	side	NOUN
ejpam-6982	174	18	of	of	ADP
ejpam-6982	174	19	(	(	PUNCT
ejpam-6982	174	20	20	20	NUM
ejpam-6982	174	21	)	)	PUNCT
ejpam-6982	174	22	gives	give	VERB
ejpam-6982	174	23	.	.	PUNCT
ejpam-6982	175	1	∞∑	∞∑	DET
ejpam-6982	175	2	n=0	n=0	NUM
ejpam-6982	175	3	un(x	un(x	NUM
ejpam-6982	175	4	,	,	PUNCT
ejpam-6982	175	5	t	t	PROPN
ejpam-6982	175	6	)	)	PUNCT
ejpam-6982	175	7	=	=	SYM
ejpam-6982	175	8	m−1∑	m−1∑	PROPN
ejpam-6982	175	9	k=0	k=0	PROPN
ejpam-6982	175	10	s−(k+1	s−(k+1	PROPN
ejpam-6982	175	11	)	)	PUNCT
ejpam-6982	175	12	u−k	u−k	NOUN
ejpam-6982	175	13	uk(x	uk(x	ADP
ejpam-6982	175	14	,	,	PUNCT
ejpam-6982	175	15	0	0	NUM
ejpam-6982	175	16	)	)	PUNCT
ejpam-6982	176	1	+	+	CCONJ
ejpam-6982	176	2	n−1	n−1	PROPN
ejpam-6982	176	3	(	(	PUNCT
ejpam-6982	176	4	uα	uα	PROPN
ejpam-6982	176	5	sα	sα	ADV
ejpam-6982	176	6	n[g(x	n[g(x	X
ejpam-6982	176	7	,	,	PUNCT
ejpam-6982	176	8	t	t	PROPN
ejpam-6982	176	9	)	)	PUNCT
ejpam-6982	176	10	]	]	PUNCT
ejpam-6982	176	11	)	)	PUNCT
ejpam-6982	177	1	−	−	PROPN
ejpam-6982	177	2	n−1	n−1	PROPN
ejpam-6982	177	3	[	[	PUNCT
ejpam-6982	177	4	uα	uα	X
ejpam-6982	177	5	sα	sα	VERB
ejpam-6982	177	6	n	n	PROPN
ejpam-6982	177	7	(	(	PUNCT
ejpam-6982	177	8	l	l	X
ejpam-6982	177	9	(	(	PUNCT
ejpam-6982	177	10	∞∑	∞∑	PROPN
ejpam-6982	177	11	n=0	n=0	NUM
ejpam-6982	177	12	un(x	un(x	NUM
ejpam-6982	177	13	,	,	PUNCT
ejpam-6982	177	14	t	t	PROPN
ejpam-6982	177	15	)	)	PUNCT
ejpam-6982	177	16	)	)	PUNCT
ejpam-6982	178	1	+	+	CCONJ
ejpam-6982	179	1	∞∑	∞∑	NUM
ejpam-6982	179	2	n=0	n=0	NUM
ejpam-6982	179	3	an	an	PRON
ejpam-6982	179	4	)	)	PUNCT
ejpam-6982	179	5	]	]	PUNCT
ejpam-6982	179	6	.	.	PUNCT
ejpam-6982	180	1	(	(	PUNCT
ejpam-6982	180	2	21	21	NUM
ejpam-6982	180	3	)	)	PUNCT
ejpam-6982	180	4	where	where	SCONJ
ejpam-6982	180	5	an	an	DET
ejpam-6982	180	6	defined	define	VERB
ejpam-6982	180	7	in	in	ADP
ejpam-6982	180	8	eq	eq	ADP
ejpam-6982	180	9	.	.	PUNCT
ejpam-6982	181	1	(	(	PUNCT
ejpam-6982	181	2	8)	8)	NUM
ejpam-6982	181	3	.	.	PUNCT
ejpam-6982	181	4	from	from	ADP
ejpam-6982	181	5	this	this	DET
ejpam-6982	181	6	equation	equation	NOUN
ejpam-6982	181	7	,	,	PUNCT
ejpam-6982	181	8	the	the	DET
ejpam-6982	181	9	iterates	iterate	NOUN
ejpam-6982	181	10	are	be	AUX
ejpam-6982	181	11	determined	determine	VERB
ejpam-6982	181	12	by	by	ADP
ejpam-6982	181	13	the	the	DET
ejpam-6982	181	14	following	follow	VERB
ejpam-6982	181	15	recursive	recursive	ADJ
ejpam-6982	181	16	way	way	NOUN
ejpam-6982	181	17	u0(x	u0(x	SYM
ejpam-6982	181	18	,	,	PUNCT
ejpam-6982	181	19	t	t	PROPN
ejpam-6982	181	20	)	)	PUNCT
ejpam-6982	181	21	=	=	SYM
ejpam-6982	182	1	m−1∑	m−1∑	PROPN
ejpam-6982	182	2	k=0	k=0	PROPN
ejpam-6982	182	3	s−(k+1	s−(k+1	PROPN
ejpam-6982	182	4	)	)	PUNCT
ejpam-6982	182	5	u−k	u−k	NOUN
ejpam-6982	182	6	uk(x	uk(x	ADP
ejpam-6982	182	7	,	,	PUNCT
ejpam-6982	182	8	0	0	NUM
ejpam-6982	182	9	)	)	PUNCT
ejpam-6982	183	1	+	+	CCONJ
ejpam-6982	183	2	n−1	n−1	PROPN
ejpam-6982	183	3	(	(	PUNCT
ejpam-6982	183	4	uα	uα	PROPN
ejpam-6982	183	5	sα	sα	ADV
ejpam-6982	183	6	n[g(x	n[g(x	X
ejpam-6982	183	7	,	,	PUNCT
ejpam-6982	183	8	t	t	PROPN
ejpam-6982	183	9	)	)	PUNCT
ejpam-6982	183	10	]	]	PUNCT
ejpam-6982	183	11	)	)	PUNCT
ejpam-6982	183	12	,	,	PUNCT
ejpam-6982	183	13	a.	a.	NOUN
ejpam-6982	183	14	m.	m.	NOUN
ejpam-6982	183	15	alhammad	alhammad	PROPN
ejpam-6982	183	16	,	,	PUNCT
ejpam-6982	183	17	a.	a.	NOUN
ejpam-6982	183	18	m.	m.	PROPN
ejpam-6982	183	19	saeed	saeed	PROPN
ejpam-6982	183	20	/	/	SYM
ejpam-6982	183	21	eur	eur	PROPN
ejpam-6982	183	22	.	.	PUNCT
ejpam-6982	184	1	j.	j.	PROPN
ejpam-6982	184	2	pure	pure	PROPN
ejpam-6982	184	3	appl	appl	PROPN
ejpam-6982	184	4	.	.	PROPN
ejpam-6982	184	5	math	math	PROPN
ejpam-6982	184	6	,	,	PUNCT
ejpam-6982	184	7	18	18	NUM
ejpam-6982	184	8	(	(	PUNCT
ejpam-6982	184	9	4	4	NUM
ejpam-6982	184	10	)	)	PUNCT
ejpam-6982	184	11	(	(	PUNCT
ejpam-6982	184	12	2025	2025	NUM
ejpam-6982	184	13	)	)	PUNCT
ejpam-6982	184	14	,	,	PUNCT
ejpam-6982	184	15	6982	6982	NUM
ejpam-6982	184	16	8	8	NUM
ejpam-6982	184	17	of	of	ADP
ejpam-6982	184	18	22	22	NUM
ejpam-6982	184	19	u1(x	u1(x	PROPN
ejpam-6982	184	20	,	,	PUNCT
ejpam-6982	184	21	t	t	PROPN
ejpam-6982	184	22	)	)	PUNCT
ejpam-6982	184	23	=	=	SYM
ejpam-6982	184	24	−n−1	−n−1	NUM
ejpam-6982	184	25	(	(	PUNCT
ejpam-6982	184	26	uα	uα	NOUN
ejpam-6982	184	27	sα	sα	VERB
ejpam-6982	184	28	n	n	PROPN
ejpam-6982	185	1	[	[	X
ejpam-6982	185	2	lu0	lu0	NOUN
ejpam-6982	185	3	+	+	NOUN
ejpam-6982	185	4	a0	a0	NOUN
ejpam-6982	185	5	]	]	PUNCT
ejpam-6982	185	6	)	)	PUNCT
ejpam-6982	185	7	,	,	PUNCT
ejpam-6982	185	8	u2(x	u2(x	PROPN
ejpam-6982	185	9	,	,	PUNCT
ejpam-6982	185	10	t	t	PROPN
ejpam-6982	185	11	)	)	PUNCT
ejpam-6982	186	1	=	=	SYM
ejpam-6982	186	2	−n−1	−n−1	NUM
ejpam-6982	187	1	(	(	PUNCT
ejpam-6982	187	2	uα	uα	AUX
ejpam-6982	187	3	sα	sα	VERB
ejpam-6982	187	4	n	n	PROPN
ejpam-6982	187	5	[	[	X
ejpam-6982	187	6	lu1	lu1	VERB
ejpam-6982	187	7	+	+	NOUN
ejpam-6982	187	8	a1	a1	NOUN
ejpam-6982	187	9	]	]	PUNCT
ejpam-6982	187	10	)	)	PUNCT
ejpam-6982	187	11	,	,	PUNCT
ejpam-6982	187	12	(	(	PUNCT
ejpam-6982	187	13	22	22	NUM
ejpam-6982	187	14	)	)	PUNCT
ejpam-6982	187	15	...	...	PUNCT
ejpam-6982	188	1	un+1(x	un+1(x	PROPN
ejpam-6982	188	2	,	,	PUNCT
ejpam-6982	188	3	t	t	PROPN
ejpam-6982	188	4	)	)	PUNCT
ejpam-6982	188	5	=	=	SYM
ejpam-6982	188	6	−n−1	−n−1	NUM
ejpam-6982	188	7	(	(	PUNCT
ejpam-6982	188	8	uα	uα	NOUN
ejpam-6982	188	9	sα	sα	VERB
ejpam-6982	188	10	n	n	PROPN
ejpam-6982	189	1	[	[	X
ejpam-6982	189	2	lun	lun	X
ejpam-6982	190	1	+	+	NOUN
ejpam-6982	190	2	an	an	X
ejpam-6982	190	3	]	]	X
ejpam-6982	190	4	)	)	PUNCT
ejpam-6982	190	5	,	,	PUNCT
ejpam-6982	190	6	n	n	X
ejpam-6982	190	7	≥	≥	NOUN
ejpam-6982	190	8	1	1	NUM
ejpam-6982	190	9	.	.	PUNCT
ejpam-6982	191	1	finally	finally	ADV
ejpam-6982	191	2	,	,	PUNCT
ejpam-6982	191	3	we	we	PRON
ejpam-6982	191	4	approximate	approximate	VERB
ejpam-6982	191	5	the	the	DET
ejpam-6982	191	6	analytical	analytical	ADJ
ejpam-6982	191	7	solution	solution	NOUN
ejpam-6982	191	8	u(x	u(x	NOUN
ejpam-6982	191	9	,	,	PUNCT
ejpam-6982	191	10	t	t	PROPN
ejpam-6982	191	11	)	)	PUNCT
ejpam-6982	191	12	by	by	ADP
ejpam-6982	191	13	truncated	truncated	ADJ
ejpam-6982	191	14	series	series	NOUN
ejpam-6982	191	15	:	:	PUNCT
ejpam-6982	191	16	ϕn	ϕn	X
ejpam-6982	191	17	(	(	PUNCT
ejpam-6982	191	18	x	x	PROPN
ejpam-6982	191	19	,	,	PUNCT
ejpam-6982	191	20	t	t	PROPN
ejpam-6982	191	21	)	)	PUNCT
ejpam-6982	191	22	=	=	PRON
ejpam-6982	192	1	n−1∑	n−1∑	PROPN
ejpam-6982	192	2	n=0	n=0	NUM
ejpam-6982	192	3	un(x	un(x	NUM
ejpam-6982	192	4	,	,	PUNCT
ejpam-6982	192	5	t	t	PROPN
ejpam-6982	192	6	)	)	PUNCT
ejpam-6982	192	7	and	and	CCONJ
ejpam-6982	192	8	lim	lim	PROPN
ejpam-6982	192	9	n→∞	n→∞	PROPN
ejpam-6982	193	1	ϕn	ϕn	INTJ
ejpam-6982	193	2	(	(	PUNCT
ejpam-6982	193	3	x	x	PROPN
ejpam-6982	193	4	,	,	PUNCT
ejpam-6982	193	5	t	t	PROPN
ejpam-6982	193	6	)	)	PUNCT
ejpam-6982	193	7	=	=	SYM
ejpam-6982	193	8	u(x	u(x	PROPN
ejpam-6982	193	9	,	,	PUNCT
ejpam-6982	193	10	t	t	PROPN
ejpam-6982	193	11	)	)	PUNCT
ejpam-6982	193	12	.	.	PUNCT
ejpam-6982	194	1	4.2	4.2	NUM
ejpam-6982	194	2	.	.	PUNCT
ejpam-6982	194	3	modified	modify	VERB
ejpam-6982	194	4	laplace	laplace	PROPN
ejpam-6982	194	5	variational	variational	ADJ
ejpam-6982	194	6	iteration	iteration	NOUN
ejpam-6982	194	7	method	method	NOUN
ejpam-6982	194	8	the	the	DET
ejpam-6982	194	9	new	new	ADJ
ejpam-6982	194	10	tactic	tactic	NOUN
ejpam-6982	194	11	of	of	ADP
ejpam-6982	194	12	modified	modify	VERB
ejpam-6982	194	13	laplace	laplace	NOUN
ejpam-6982	194	14	variation	variation	NOUN
ejpam-6982	194	15	iteration	iteration	NOUN
ejpam-6982	194	16	technique	technique	NOUN
ejpam-6982	194	17	is	be	AUX
ejpam-6982	194	18	applied	apply	VERB
ejpam-6982	194	19	as	as	SCONJ
ejpam-6982	194	20	follows	follow	VERB
ejpam-6982	194	21	.	.	PUNCT
ejpam-6982	195	1	we	we	PRON
ejpam-6982	195	2	apply	apply	VERB
ejpam-6982	195	3	laplace	laplace	NOUN
ejpam-6982	195	4	transform	transform	NOUN
ejpam-6982	195	5	on	on	ADP
ejpam-6982	195	6	both	both	DET
ejpam-6982	195	7	sides	side	NOUN
ejpam-6982	195	8	of	of	ADP
ejpam-6982	195	9	eq	eq	PROPN
ejpam-6982	195	10	.	.	PUNCT
ejpam-6982	196	1	(	(	PUNCT
ejpam-6982	196	2	4	4	X
ejpam-6982	196	3	)	)	PUNCT
ejpam-6982	196	4	yields	yield	NOUN
ejpam-6982	196	5	[	[	X
ejpam-6982	196	6	14	14	NUM
ejpam-6982	196	7	]	]	PUNCT
ejpam-6982	196	8	.	.	PUNCT
ejpam-6982	197	1	l	l	PUNCT
ejpam-6982	198	1	[	[	X
ejpam-6982	198	2	dα	dα	ADP
ejpam-6982	198	3	t	t	PROPN
ejpam-6982	198	4	u(x	u(x	PROPN
ejpam-6982	198	5	,	,	PUNCT
ejpam-6982	198	6	t	t	PROPN
ejpam-6982	198	7	)	)	PUNCT
ejpam-6982	198	8	]	]	PUNCT
ejpam-6982	198	9	=	=	SYM
ejpam-6982	198	10	l[g(x	l[g(x	X
ejpam-6982	198	11	,	,	PUNCT
ejpam-6982	198	12	t)−	t)−	PROPN
ejpam-6982	198	13	lu(x	lu(x	NOUN
ejpam-6982	198	14	,	,	PUNCT
ejpam-6982	198	15	t)−nu(x	t)−nu(x	PROPN
ejpam-6982	198	16	,	,	PUNCT
ejpam-6982	198	17	t	t	PROPN
ejpam-6982	198	18	)	)	PUNCT
ejpam-6982	198	19	]	]	PUNCT
ejpam-6982	198	20	.	.	PUNCT
ejpam-6982	199	1	(	(	PUNCT
ejpam-6982	199	2	23	23	NUM
ejpam-6982	199	3	)	)	PUNCT
ejpam-6982	199	4	using	use	VERB
ejpam-6982	199	5	the	the	DET
ejpam-6982	199	6	differentiation	differentiation	NOUN
ejpam-6982	199	7	property	property	NOUN
ejpam-6982	199	8	of	of	ADP
ejpam-6982	199	9	laplace	laplace	NOUN
ejpam-6982	199	10	transform	transform	NOUN
ejpam-6982	199	11	for	for	ADP
ejpam-6982	199	12	caputo	caputo	PROPN
ejpam-6982	199	13	,	,	PUNCT
ejpam-6982	199	14	we	we	PRON
ejpam-6982	199	15	get	get	AUX
ejpam-6982	199	16	sαl[u(x	sαl[u(x	NOUN
ejpam-6982	199	17	,	,	PUNCT
ejpam-6982	199	18	t)]−	t)]−	ADJ
ejpam-6982	199	19	m−1∑	m−1∑	PRON
ejpam-6982	199	20	k=0	k=0	PROPN
ejpam-6982	199	21	s(α−k−1)uk(x	s(α−k−1)uk(x	NOUN
ejpam-6982	199	22	,	,	PUNCT
ejpam-6982	199	23	0	0	NUM
ejpam-6982	199	24	)	)	PUNCT
ejpam-6982	199	25	=	=	SYM
ejpam-6982	200	1	l[g(x	l[g(x	X
ejpam-6982	200	2	,	,	PUNCT
ejpam-6982	200	3	t)−nu(x	t)−nu(x	PROPN
ejpam-6982	200	4	,	,	PUNCT
ejpam-6982	200	5	t	t	PROPN
ejpam-6982	200	6	)	)	PUNCT
ejpam-6982	200	7	]	]	PUNCT
ejpam-6982	200	8	,	,	PUNCT
ejpam-6982	200	9	(	(	PUNCT
ejpam-6982	200	10	24	24	NUM
ejpam-6982	200	11	)	)	PUNCT
ejpam-6982	200	12	u(x	u(x	NOUN
ejpam-6982	200	13	,	,	PUNCT
ejpam-6982	200	14	s	s	X
ejpam-6982	200	15	)	)	PUNCT
ejpam-6982	200	16	=	=	SYM
ejpam-6982	200	17	h(x	h(x	PROPN
ejpam-6982	200	18	)	)	PUNCT
ejpam-6982	200	19	s	s	PART
ejpam-6982	200	20	+	+	NUM
ejpam-6982	200	21	k(x	k(x	PROPN
ejpam-6982	200	22	)	)	PUNCT
ejpam-6982	200	23	s2	s2	NOUN
ejpam-6982	200	24	+	+	CCONJ
ejpam-6982	201	1	l	l	NOUN
ejpam-6982	201	2	sα	sα	NOUN
ejpam-6982	202	1	[	[	X
ejpam-6982	202	2	g(x	g(x	NOUN
ejpam-6982	202	3	,	,	PUNCT
ejpam-6982	202	4	t)]−	t)]−	NOUN
ejpam-6982	202	5	l	l	PROPN
ejpam-6982	202	6	sα	sα	PROPN
ejpam-6982	203	1	[	[	X
ejpam-6982	203	2	nu(x	nu(x	ADP
ejpam-6982	203	3	,	,	PUNCT
ejpam-6982	203	4	t	t	PROPN
ejpam-6982	203	5	)	)	PUNCT
ejpam-6982	203	6	]	]	PUNCT
ejpam-6982	203	7	,	,	PUNCT
ejpam-6982	203	8	(	(	PUNCT
ejpam-6982	203	9	25	25	NUM
ejpam-6982	203	10	)	)	PUNCT
ejpam-6982	203	11	u(x	u(x	PROPN
ejpam-6982	203	12	,	,	PUNCT
ejpam-6982	203	13	t	t	NOUN
ejpam-6982	203	14	)	)	PUNCT
ejpam-6982	203	15	=	=	SYM
ejpam-6982	203	16	f(x	f(x	PROPN
ejpam-6982	203	17	,	,	PUNCT
ejpam-6982	203	18	t)−	t)−	PROPN
ejpam-6982	203	19	l−1	l−1	PROPN
ejpam-6982	203	20	[	[	PUNCT
ejpam-6982	203	21	l	l	NOUN
ejpam-6982	203	22	sα	sα	NOUN
ejpam-6982	204	1	[	[	X
ejpam-6982	204	2	nu(x	nu(x	ADP
ejpam-6982	204	3	,	,	PUNCT
ejpam-6982	204	4	t	t	PROPN
ejpam-6982	204	5	)	)	PUNCT
ejpam-6982	204	6	]	]	PUNCT
ejpam-6982	204	7	]	]	PUNCT
ejpam-6982	204	8	.	.	PUNCT
ejpam-6982	205	1	(	(	PUNCT
ejpam-6982	205	2	26	26	NUM
ejpam-6982	205	3	)	)	PUNCT
ejpam-6982	205	4	differentiating	differentiate	VERB
ejpam-6982	205	5	the	the	DET
ejpam-6982	205	6	results	result	NOUN
ejpam-6982	205	7	obtained	obtain	VERB
ejpam-6982	205	8	above	above	ADV
ejpam-6982	205	9	with	with	ADP
ejpam-6982	205	10	respect	respect	NOUN
ejpam-6982	205	11	to	to	ADP
ejpam-6982	205	12	α	α	PRON
ejpam-6982	205	13	,	,	PUNCT
ejpam-6982	205	14	we	we	PRON
ejpam-6982	205	15	then	then	ADV
ejpam-6982	205	16	get	get	VERB
ejpam-6982	205	17	the	the	DET
ejpam-6982	205	18	value	value	NOUN
ejpam-6982	205	19	of	of	ADP
ejpam-6982	205	20	the	the	DET
ejpam-6982	205	21	general	general	ADJ
ejpam-6982	205	22	lagrange	lagrange	PROPN
ejpam-6982	205	23	multiplier	multiplier	ADV
ejpam-6982	205	24	,	,	PUNCT
ejpam-6982	205	25	for	for	ADP
ejpam-6982	205	26	the	the	DET
ejpam-6982	205	27	correction	correction	NOUN
ejpam-6982	205	28	functional	functional	ADJ
ejpam-6982	205	29	iterative	iterative	NOUN
ejpam-6982	205	30	formula	formula	NOUN
ejpam-6982	205	31	to	to	PART
ejpam-6982	205	32	equal	equal	VERB
ejpam-6982	205	33	one	one	NUM
ejpam-6982	205	34	.	.	PUNCT
ejpam-6982	206	1	du(x	du(x	PROPN
ejpam-6982	206	2	,	,	PUNCT
ejpam-6982	206	3	t	t	PROPN
ejpam-6982	206	4	)	)	PUNCT
ejpam-6982	206	5	dt	dt	NOUN
ejpam-6982	206	6	=	=	SYM
ejpam-6982	207	1	df(x	df(x	PROPN
ejpam-6982	207	2	,	,	PUNCT
ejpam-6982	207	3	t	t	PROPN
ejpam-6982	207	4	)	)	PUNCT
ejpam-6982	207	5	dt	dt	PUNCT
ejpam-6982	208	1	−	−	PROPN
ejpam-6982	209	1	d	d	INTJ
ejpam-6982	209	2	dt	dt	X
ejpam-6982	209	3	l−1	l−1	PROPN
ejpam-6982	209	4	[	[	PUNCT
ejpam-6982	209	5	l	l	NOUN
ejpam-6982	209	6	sα	sα	NOUN
ejpam-6982	210	1	[	[	X
ejpam-6982	210	2	nu(x	nu(x	ADP
ejpam-6982	210	3	,	,	PUNCT
ejpam-6982	210	4	t	t	PROPN
ejpam-6982	210	5	)	)	PUNCT
ejpam-6982	210	6	]	]	PUNCT
ejpam-6982	210	7	]	]	PUNCT
ejpam-6982	210	8	.	.	PUNCT
ejpam-6982	211	1	(	(	PUNCT
ejpam-6982	211	2	27	27	NUM
ejpam-6982	211	3	)	)	PUNCT
ejpam-6982	211	4	therefore	therefore	ADV
ejpam-6982	211	5	,	,	PUNCT
ejpam-6982	211	6	equation	equation	NOUN
ejpam-6982	211	7	(	(	PUNCT
ejpam-6982	211	8	27	27	NUM
ejpam-6982	211	9	)	)	PUNCT
ejpam-6982	211	10	can	can	AUX
ejpam-6982	211	11	be	be	AUX
ejpam-6982	211	12	put	put	VERB
ejpam-6982	211	13	above	above	ADV
ejpam-6982	211	14	in	in	ADP
ejpam-6982	211	15	the	the	DET
ejpam-6982	211	16	following	follow	VERB
ejpam-6982	211	17	formula	formula	NOUN
ejpam-6982	211	18	:	:	PUNCT
ejpam-6982	211	19	un+1(x	un+1(x	ADJ
ejpam-6982	211	20	,	,	PUNCT
ejpam-6982	211	21	t	t	PROPN
ejpam-6982	211	22	)	)	PUNCT
ejpam-6982	211	23	=	=	SYM
ejpam-6982	212	1	un(x	un(x	X
ejpam-6982	212	2	,	,	PUNCT
ejpam-6982	212	3	t	t	PROPN
ejpam-6982	212	4	)	)	PUNCT
ejpam-6982	213	1	+	+	CCONJ
ejpam-6982	213	2	∫	∫	PROPN
ejpam-6982	213	3	t	t	NOUN
ejpam-6982	213	4	0	0	NUM
ejpam-6982	214	1	λ	λ	PROPN
ejpam-6982	214	2	[	[	PUNCT
ejpam-6982	214	3	dun(x	dun(x	PROPN
ejpam-6982	214	4	,	,	PUNCT
ejpam-6982	214	5	y	y	NOUN
ejpam-6982	214	6	)	)	PUNCT
ejpam-6982	214	7	dy	dy	NOUN
ejpam-6982	214	8	−	−	PROPN
ejpam-6982	214	9	df(x	df(x	NOUN
ejpam-6982	214	10	,	,	PUNCT
ejpam-6982	214	11	y	y	NOUN
ejpam-6982	214	12	)	)	PUNCT
ejpam-6982	214	13	dy	dy	NOUN
ejpam-6982	215	1	+	+	CCONJ
ejpam-6982	215	2	d	d	PROPN
ejpam-6982	215	3	dy	dy	NOUN
ejpam-6982	215	4	l−1	l−1	PROPN
ejpam-6982	215	5	[	[	PUNCT
ejpam-6982	215	6	l	l	NOUN
ejpam-6982	215	7	sα	sα	NOUN
ejpam-6982	216	1	[	[	X
ejpam-6982	216	2	nun(x	nun(x	PROPN
ejpam-6982	216	3	,	,	PUNCT
ejpam-6982	216	4	y	y	NOUN
ejpam-6982	216	5	)	)	PUNCT
ejpam-6982	216	6	]	]	PUNCT
ejpam-6982	217	1	]	]	X
ejpam-6982	217	2	]	]	X
ejpam-6982	217	3	dy	dy	X
ejpam-6982	217	4	.	.	PUNCT
ejpam-6982	218	1	(	(	PUNCT
ejpam-6982	218	2	28	28	NUM
ejpam-6982	218	3	)	)	PUNCT
ejpam-6982	218	4	the	the	DET
ejpam-6982	218	5	general	general	ADJ
ejpam-6982	218	6	lagrange	lagrange	PROPN
ejpam-6982	218	7	multiplier	multiplier	ADV
ejpam-6982	218	8	for	for	ADP
ejpam-6982	218	9	equation	equation	NOUN
ejpam-6982	218	10	(	(	PUNCT
ejpam-6982	218	11	28	28	NUM
ejpam-6982	218	12	)	)	PUNCT
ejpam-6982	218	13	can	can	AUX
ejpam-6982	218	14	be	be	AUX
ejpam-6982	218	15	identified	identify	VERB
ejpam-6982	218	16	optimally	optimally	ADV
ejpam-6982	218	17	via	via	ADP
ejpam-6982	218	18	variation	variation	NOUN
ejpam-6982	218	19	theory	theory	NOUN
ejpam-6982	218	20	to	to	PART
ejpam-6982	218	21	get	get	VERB
ejpam-6982	218	22	1	1	NUM
ejpam-6982	218	23	+	+	CCONJ
ejpam-6982	218	24	λ|y	λ|y	NOUN
ejpam-6982	218	25	=	=	NOUN
ejpam-6982	218	26	t	t	NOUN
ejpam-6982	218	27	=	=	SYM
ejpam-6982	218	28	0	0	NUM
ejpam-6982	218	29	,	,	PUNCT
ejpam-6982	218	30	λ|y	λ|y	NOUN
ejpam-6982	219	1	=	=	NOUN
ejpam-6982	219	2	t	t	NOUN
ejpam-6982	219	3	=	=	SYM
ejpam-6982	219	4	−1	−1	NOUN
ejpam-6982	219	5	.	.	PUNCT
ejpam-6982	219	6	a.	a.	PROPN
ejpam-6982	219	7	m.	m.	PROPN
ejpam-6982	219	8	alhammad	alhammad	PROPN
ejpam-6982	219	9	,	,	PUNCT
ejpam-6982	219	10	a.	a.	NOUN
ejpam-6982	219	11	m.	m.	PROPN
ejpam-6982	219	12	saeed	saeed	PROPN
ejpam-6982	219	13	/	/	SYM
ejpam-6982	219	14	eur	eur	PROPN
ejpam-6982	219	15	.	.	PUNCT
ejpam-6982	220	1	j.	j.	PROPN
ejpam-6982	220	2	pure	pure	PROPN
ejpam-6982	220	3	appl	appl	PROPN
ejpam-6982	220	4	.	.	PROPN
ejpam-6982	220	5	math	math	PROPN
ejpam-6982	220	6	,	,	PUNCT
ejpam-6982	220	7	18	18	NUM
ejpam-6982	220	8	(	(	PUNCT
ejpam-6982	220	9	4	4	NUM
ejpam-6982	220	10	)	)	PUNCT
ejpam-6982	220	11	(	(	PUNCT
ejpam-6982	220	12	2025	2025	NUM
ejpam-6982	220	13	)	)	PUNCT
ejpam-6982	220	14	,	,	PUNCT
ejpam-6982	220	15	6982	6982	NUM
ejpam-6982	220	16	9	9	NUM
ejpam-6982	220	17	of	of	ADP
ejpam-6982	220	18	22	22	NUM
ejpam-6982	220	19	substituting	substitute	VERB
ejpam-6982	220	20	λ	λ	NOUN
ejpam-6982	220	21	=	=	PUNCT
ejpam-6982	220	22	−1	−1	NOUN
ejpam-6982	220	23	into	into	ADP
ejpam-6982	220	24	equation	equation	NOUN
ejpam-6982	220	25	(	(	PUNCT
ejpam-6982	220	26	28	28	NUM
ejpam-6982	220	27	)	)	PUNCT
ejpam-6982	220	28	we	we	PRON
ejpam-6982	220	29	get	get	VERB
ejpam-6982	220	30	the	the	DET
ejpam-6982	220	31	iterative	iterative	NOUN
ejpam-6982	220	32	formula	formula	NOUN
ejpam-6982	220	33	n	n	NOUN
ejpam-6982	220	34	=	=	SYM
ejpam-6982	220	35	1	1	NUM
ejpam-6982	220	36	,	,	PUNCT
ejpam-6982	220	37	2	2	NUM
ejpam-6982	220	38	,	,	PUNCT
ejpam-6982	220	39	·	·	PUNCT
ejpam-6982	220	40	·	·	PUNCT
ejpam-6982	220	41	·	·	PUNCT
ejpam-6982	220	42	follows	follow	VERB
ejpam-6982	220	43	:	:	PUNCT
ejpam-6982	220	44	un+1(x	un+1(x	ADJ
ejpam-6982	220	45	,	,	PUNCT
ejpam-6982	220	46	t	t	PROPN
ejpam-6982	220	47	)	)	PUNCT
ejpam-6982	220	48	=	=	SYM
ejpam-6982	221	1	un(x	un(x	X
ejpam-6982	221	2	,	,	PUNCT
ejpam-6982	221	3	t)−	t)−	PROPN
ejpam-6982	221	4	∫	∫	PROPN
ejpam-6982	222	1	t	t	NOUN
ejpam-6982	222	2	0	0	NUM
ejpam-6982	223	1	[	[	PUNCT
ejpam-6982	223	2	dun(x	dun(x	PROPN
ejpam-6982	223	3	,	,	PUNCT
ejpam-6982	223	4	y	y	NOUN
ejpam-6982	223	5	)	)	PUNCT
ejpam-6982	223	6	dy	dy	NOUN
ejpam-6982	223	7	−	−	PROPN
ejpam-6982	223	8	df(x	df(x	NOUN
ejpam-6982	223	9	,	,	PUNCT
ejpam-6982	223	10	y	y	NOUN
ejpam-6982	223	11	)	)	PUNCT
ejpam-6982	223	12	dy	dy	NOUN
ejpam-6982	224	1	+	+	CCONJ
ejpam-6982	224	2	d	d	PROPN
ejpam-6982	224	3	dy	dy	NOUN
ejpam-6982	224	4	l−1	l−1	PROPN
ejpam-6982	224	5	[	[	PUNCT
ejpam-6982	224	6	l	l	NOUN
ejpam-6982	224	7	sα	sα	NOUN
ejpam-6982	225	1	[	[	X
ejpam-6982	225	2	nun(x	nun(x	PROPN
ejpam-6982	225	3	,	,	PUNCT
ejpam-6982	225	4	y	y	NOUN
ejpam-6982	225	5	)	)	PUNCT
ejpam-6982	225	6	]	]	PUNCT
ejpam-6982	226	1	]	]	X
ejpam-6982	226	2	]	]	X
ejpam-6982	226	3	dy	dy	X
ejpam-6982	226	4	.	.	PUNCT
ejpam-6982	227	1	(	(	PUNCT
ejpam-6982	227	2	29	29	NUM
ejpam-6982	227	3	)	)	PUNCT
ejpam-6982	227	4	equation	equation	NOUN
ejpam-6982	227	5	(	(	PUNCT
ejpam-6982	227	6	29	29	NUM
ejpam-6982	227	7	)	)	PUNCT
ejpam-6982	227	8	is	be	AUX
ejpam-6982	227	9	the	the	DET
ejpam-6982	227	10	new	new	ADJ
ejpam-6982	227	11	modified	modify	VERB
ejpam-6982	227	12	function	function	NOUN
ejpam-6982	227	13	of	of	ADP
ejpam-6982	227	14	the	the	DET
ejpam-6982	227	15	laplace	laplace	NOUN
ejpam-6982	227	16	transform	transform	NOUN
ejpam-6982	227	17	and	and	CCONJ
ejpam-6982	227	18	variational	variational	ADJ
ejpam-6982	227	19	iteration	iteration	NOUN
ejpam-6982	227	20	method	method	NOUN
ejpam-6982	227	21	.	.	PUNCT
ejpam-6982	228	1	start	start	VERB
ejpam-6982	228	2	with	with	ADP
ejpam-6982	228	3	the	the	DET
ejpam-6982	228	4	initial	initial	ADJ
ejpam-6982	228	5	iteration	iteration	NOUN
ejpam-6982	228	6	u(x	u(x	NOUN
ejpam-6982	228	7	,	,	PUNCT
ejpam-6982	228	8	t	t	NOUN
ejpam-6982	228	9	)	)	PUNCT
ejpam-6982	228	10	=	=	SYM
ejpam-6982	228	11	u(x	u(x	NOUN
ejpam-6982	228	12	,	,	PUNCT
ejpam-6982	228	13	0	0	NUM
ejpam-6982	228	14	)	)	PUNCT
ejpam-6982	228	15	.	.	PUNCT
ejpam-6982	229	1	the	the	DET
ejpam-6982	229	2	exact	exact	ADJ
ejpam-6982	229	3	solution	solution	NOUN
ejpam-6982	229	4	is	be	AUX
ejpam-6982	229	5	present	present	ADJ
ejpam-6982	229	6	as	as	ADP
ejpam-6982	229	7	the	the	DET
ejpam-6982	229	8	sequent	sequent	NOUN
ejpam-6982	229	9	approximation	approximation	NOUN
ejpam-6982	229	10	un+1(x	un+1(x	PROPN
ejpam-6982	229	11	,	,	PUNCT
ejpam-6982	229	12	t	t	PROPN
ejpam-6982	229	13	)	)	PUNCT
ejpam-6982	229	14	,	,	PUNCT
ejpam-6982	229	15	n	n	NOUN
ejpam-6982	229	16	=	=	SYM
ejpam-6982	229	17	1	1	NUM
ejpam-6982	229	18	,	,	PUNCT
ejpam-6982	229	19	2	2	NUM
ejpam-6982	229	20	,	,	PUNCT
ejpam-6982	229	21	·	·	PUNCT
ejpam-6982	229	22	·	·	PUNCT
ejpam-6982	229	23	·	·	PUNCT
ejpam-6982	229	24	.	.	PUNCT
ejpam-6982	230	1	in	in	ADP
ejpam-6982	230	2	other	other	ADJ
ejpam-6982	230	3	words	word	NOUN
ejpam-6982	230	4	,	,	PUNCT
ejpam-6982	230	5	u(x	u(x	PROPN
ejpam-6982	230	6	,	,	PUNCT
ejpam-6982	230	7	t	t	NOUN
ejpam-6982	230	8	)	)	PUNCT
ejpam-6982	230	9	=	=	VERB
ejpam-6982	230	10	lim	lim	PROPN
ejpam-6982	230	11	n→∞	n→∞	NUM
ejpam-6982	230	12	un(x	un(x	PROPN
ejpam-6982	230	13	,	,	PUNCT
ejpam-6982	230	14	t	t	PROPN
ejpam-6982	230	15	)	)	PUNCT
ejpam-6982	230	16	.	.	PUNCT
ejpam-6982	231	1	5	5	X
ejpam-6982	231	2	.	.	NOUN
ejpam-6982	231	3	numerical	numerical	ADJ
ejpam-6982	231	4	experiments	experiment	NOUN
ejpam-6982	231	5	and	and	CCONJ
ejpam-6982	231	6	discussion	discussion	NOUN
ejpam-6982	231	7	of	of	ADP
ejpam-6982	231	8	results	result	NOUN
ejpam-6982	231	9	in	in	ADP
ejpam-6982	231	10	this	this	DET
ejpam-6982	231	11	section	section	NOUN
ejpam-6982	231	12	,	,	PUNCT
ejpam-6982	231	13	we	we	PRON
ejpam-6982	231	14	shall	shall	AUX
ejpam-6982	231	15	illustrate	illustrate	VERB
ejpam-6982	231	16	the	the	DET
ejpam-6982	231	17	four	four	NUM
ejpam-6982	231	18	techniques	technique	NOUN
ejpam-6982	231	19	by	by	ADP
ejpam-6982	231	20	several	several	ADJ
ejpam-6982	231	21	examples	example	NOUN
ejpam-6982	231	22	.	.	PUNCT
ejpam-6982	232	1	these	these	DET
ejpam-6982	232	2	examples	example	NOUN
ejpam-6982	232	3	are	be	AUX
ejpam-6982	232	4	somewhat	somewhat	ADV
ejpam-6982	232	5	artificial	artificial	ADJ
ejpam-6982	232	6	in	in	ADP
ejpam-6982	232	7	the	the	DET
ejpam-6982	232	8	sense	sense	NOUN
ejpam-6982	232	9	that	that	SCONJ
ejpam-6982	232	10	the	the	DET
ejpam-6982	232	11	exact	exact	ADJ
ejpam-6982	232	12	answer	answer	NOUN
ejpam-6982	232	13	,	,	PUNCT
ejpam-6982	232	14	for	for	ADP
ejpam-6982	232	15	the	the	DET
ejpam-6982	232	16	special	special	ADJ
ejpam-6982	232	17	cases	case	NOUN
ejpam-6982	232	18	α	α	X
ejpam-6982	232	19	=	=	SYM
ejpam-6982	232	20	1	1	NUM
ejpam-6982	232	21	,	,	PUNCT
ejpam-6982	232	22	α	α	NOUN
ejpam-6982	232	23	=	=	SYM
ejpam-6982	232	24	2	2	NUM
ejpam-6982	232	25	is	be	AUX
ejpam-6982	232	26	known	know	VERB
ejpam-6982	232	27	in	in	ADP
ejpam-6982	232	28	advance	advance	NOUN
ejpam-6982	232	29	,	,	PUNCT
ejpam-6982	232	30	and	and	CCONJ
ejpam-6982	232	31	the	the	DET
ejpam-6982	232	32	initial	initial	ADJ
ejpam-6982	232	33	and	and	CCONJ
ejpam-6982	232	34	boundary	boundary	ADJ
ejpam-6982	232	35	conditions	condition	NOUN
ejpam-6982	232	36	are	be	AUX
ejpam-6982	232	37	directly	directly	ADV
ejpam-6982	232	38	taken	take	VERB
ejpam-6982	232	39	from	from	ADP
ejpam-6982	232	40	this	this	DET
ejpam-6982	232	41	answer	answer	NOUN
ejpam-6982	232	42	.	.	PUNCT
ejpam-6982	233	1	nonetheless	nonetheless	ADV
ejpam-6982	233	2	,	,	PUNCT
ejpam-6982	233	3	such	such	DET
ejpam-6982	233	4	an	an	DET
ejpam-6982	233	5	approach	approach	NOUN
ejpam-6982	233	6	is	be	AUX
ejpam-6982	233	7	needed	need	VERB
ejpam-6982	233	8	to	to	PART
ejpam-6982	233	9	evaluate	evaluate	VERB
ejpam-6982	233	10	the	the	DET
ejpam-6982	233	11	accuracy	accuracy	NOUN
ejpam-6982	233	12	of	of	ADP
ejpam-6982	233	13	the	the	DET
ejpam-6982	233	14	analytical	analytical	ADJ
ejpam-6982	233	15	techniques	technique	NOUN
ejpam-6982	233	16	and	and	CCONJ
ejpam-6982	233	17	to	to	PART
ejpam-6982	233	18	examine	examine	VERB
ejpam-6982	233	19	the	the	DET
ejpam-6982	233	20	effect	effect	NOUN
ejpam-6982	233	21	of	of	ADP
ejpam-6982	233	22	varying	vary	VERB
ejpam-6982	233	23	the	the	DET
ejpam-6982	233	24	order	order	NOUN
ejpam-6982	233	25	of	of	ADP
ejpam-6982	233	26	the	the	DET
ejpam-6982	233	27	timefractional	timefractional	ADJ
ejpam-6982	233	28	derivative	derivative	NOUN
ejpam-6982	233	29	on	on	ADP
ejpam-6982	233	30	the	the	DET
ejpam-6982	233	31	behavior	behavior	NOUN
ejpam-6982	233	32	of	of	ADP
ejpam-6982	233	33	the	the	DET
ejpam-6982	233	34	solution	solution	NOUN
ejpam-6982	233	35	.	.	PUNCT
ejpam-6982	234	1	all	all	DET
ejpam-6982	234	2	the	the	DET
ejpam-6982	234	3	results	result	NOUN
ejpam-6982	234	4	are	be	AUX
ejpam-6982	234	5	calculated	calculate	VERB
ejpam-6982	234	6	by	by	ADP
ejpam-6982	234	7	using	use	VERB
ejpam-6982	234	8	the	the	DET
ejpam-6982	234	9	software	software	NOUN
ejpam-6982	234	10	matlab	matlab	PROPN
ejpam-6982	234	11	.	.	PUNCT
ejpam-6982	234	12	example	example	NOUN
ejpam-6982	235	1	1	1	NUM
ejpam-6982	235	2	.	.	X
ejpam-6982	235	3	consider	consider	VERB
ejpam-6982	235	4	the	the	DET
ejpam-6982	235	5	nonlinear	nonlinear	ADJ
ejpam-6982	235	6	time	time	NOUN
ejpam-6982	235	7	-	-	PUNCT
ejpam-6982	235	8	fractional	fractional	ADJ
ejpam-6982	235	9	advection	advection	NOUN
ejpam-6982	235	10	partial	partial	ADJ
ejpam-6982	235	11	differential	differential	NOUN
ejpam-6982	235	12	equation	equation	NOUN
ejpam-6982	235	13	.	.	PUNCT
ejpam-6982	236	1	dαu(x	dαu(x	NOUN
ejpam-6982	236	2	,	,	PUNCT
ejpam-6982	236	3	t	t	PROPN
ejpam-6982	236	4	)	)	PUNCT
ejpam-6982	237	1	+	+	CCONJ
ejpam-6982	237	2	u(x	u(x	NOUN
ejpam-6982	237	3	,	,	PUNCT
ejpam-6982	237	4	t)ux(x	t)ux(x	ADJ
ejpam-6982	237	5	,	,	PUNCT
ejpam-6982	237	6	t	t	PROPN
ejpam-6982	237	7	)	)	PUNCT
ejpam-6982	238	1	=	=	SYM
ejpam-6982	238	2	x+	x+	PROPN
ejpam-6982	238	3	xt2	xt2	PROPN
ejpam-6982	238	4	,	,	PUNCT
ejpam-6982	238	5	t	t	PROPN
ejpam-6982	238	6	>	>	X
ejpam-6982	238	7	0	0	PROPN
ejpam-6982	238	8	,	,	PUNCT
ejpam-6982	238	9	x	x	X
ejpam-6982	238	10	∈	∈	PROPN
ejpam-6982	238	11	r	r	NOUN
ejpam-6982	238	12	,	,	PUNCT
ejpam-6982	238	13	0	0	NUM
ejpam-6982	238	14	<	<	X
ejpam-6982	238	15	α	α	PROPN
ejpam-6982	238	16	≤	≤	NUM
ejpam-6982	238	17	1	1	NUM
ejpam-6982	238	18	,	,	PUNCT
ejpam-6982	238	19	(	(	PUNCT
ejpam-6982	238	20	30	30	NUM
ejpam-6982	238	21	)	)	PUNCT
ejpam-6982	238	22	subject	subject	NOUN
ejpam-6982	238	23	to	to	ADP
ejpam-6982	238	24	the	the	DET
ejpam-6982	238	25	initial	initial	ADJ
ejpam-6982	238	26	condition	condition	NOUN
ejpam-6982	238	27	u(x	u(x	NOUN
ejpam-6982	238	28	,	,	PUNCT
ejpam-6982	238	29	0	0	NUM
ejpam-6982	238	30	)	)	PUNCT
ejpam-6982	238	31	=	=	SYM
ejpam-6982	238	32	0	0	X
ejpam-6982	238	33	.	.	PUNCT
ejpam-6982	239	1	(	(	PUNCT
ejpam-6982	239	2	31	31	NUM
ejpam-6982	239	3	)	)	PUNCT
ejpam-6982	239	4	the	the	DET
ejpam-6982	239	5	values	value	NOUN
ejpam-6982	239	6	of	of	ADP
ejpam-6982	239	7	α	α	NOUN
ejpam-6982	239	8	=	=	SYM
ejpam-6982	239	9	1	1	NUM
ejpam-6982	239	10	is	be	AUX
ejpam-6982	239	11	the	the	DET
ejpam-6982	239	12	only	only	ADJ
ejpam-6982	239	13	case	case	NOUN
ejpam-6982	239	14	for	for	ADP
ejpam-6982	239	15	which	which	PRON
ejpam-6982	239	16	we	we	PRON
ejpam-6982	239	17	know	know	VERB
ejpam-6982	239	18	the	the	DET
ejpam-6982	239	19	exact	exact	ADJ
ejpam-6982	239	20	solution	solution	NOUN
ejpam-6982	239	21	u(x	u(x	NOUN
ejpam-6982	239	22	,	,	PUNCT
ejpam-6982	239	23	t	t	PROPN
ejpam-6982	239	24	)	)	PUNCT
ejpam-6982	239	25	=	=	SYM
ejpam-6982	240	1	xt	xt	PROPN
ejpam-6982	240	2	.	.	PUNCT
ejpam-6982	240	3	to	to	PART
ejpam-6982	240	4	solve	solve	VERB
ejpam-6982	240	5	the	the	DET
ejpam-6982	240	6	problem	problem	NOUN
ejpam-6982	240	7	using	use	VERB
ejpam-6982	240	8	the	the	DET
ejpam-6982	240	9	decomposition	decomposition	NOUN
ejpam-6982	240	10	method	method	NOUN
ejpam-6982	240	11	[	[	X
ejpam-6982	240	12	8	8	NUM
ejpam-6982	240	13	]	]	PUNCT
ejpam-6982	240	14	,	,	PUNCT
ejpam-6982	240	15	we	we	PRON
ejpam-6982	240	16	simply	simply	ADV
ejpam-6982	240	17	substitute	substitute	VERB
ejpam-6982	240	18	(	(	PUNCT
ejpam-6982	240	19	30	30	NUM
ejpam-6982	240	20	)	)	PUNCT
ejpam-6982	240	21	and	and	CCONJ
ejpam-6982	240	22	the	the	DET
ejpam-6982	240	23	initial	initial	ADJ
ejpam-6982	240	24	conditions	condition	NOUN
ejpam-6982	240	25	(	(	PUNCT
ejpam-6982	240	26	31	31	NUM
ejpam-6982	240	27	)	)	PUNCT
ejpam-6982	240	28	into	into	ADP
ejpam-6982	240	29	(	(	PUNCT
ejpam-6982	240	30	10	10	NUM
ejpam-6982	240	31	)	)	PUNCT
ejpam-6982	240	32	,	,	PUNCT
ejpam-6982	240	33	to	to	PART
ejpam-6982	240	34	obtain	obtain	VERB
ejpam-6982	240	35	the	the	DET
ejpam-6982	240	36	following	follow	VERB
ejpam-6982	240	37	recurrence	recurrence	NOUN
ejpam-6982	240	38	relation	relation	NOUN
ejpam-6982	240	39	.	.	PUNCT
ejpam-6982	241	1	u0(x	u0(x	PROPN
ejpam-6982	241	2	,	,	PUNCT
ejpam-6982	241	3	t	t	PROPN
ejpam-6982	241	4	)	)	PUNCT
ejpam-6982	241	5	=	=	SYM
ejpam-6982	241	6	u(x	u(x	NOUN
ejpam-6982	241	7	,	,	PUNCT
ejpam-6982	241	8	0	0	NUM
ejpam-6982	241	9	)	)	PUNCT
ejpam-6982	242	1	+	+	CCONJ
ejpam-6982	242	2	jα	jα	NOUN
ejpam-6982	242	3	(	(	PUNCT
ejpam-6982	242	4	x+	x+	X
ejpam-6982	242	5	xt2	xt2	PROPN
ejpam-6982	242	6	)	)	PUNCT
ejpam-6982	243	1	=	=	PUNCT
ejpam-6982	243	2	x	x	X
ejpam-6982	243	3	(	(	PUNCT
ejpam-6982	243	4	tα	tα	ADP
ejpam-6982	243	5	γ(α+	γ(α+	DET
ejpam-6982	243	6	1	1	NUM
ejpam-6982	243	7	)	)	PUNCT
ejpam-6982	244	1	+	+	NUM
ejpam-6982	244	2	2tα+2	2tα+2	NUM
ejpam-6982	244	3	γ(α+	γ(α+	DET
ejpam-6982	244	4	3	3	NUM
ejpam-6982	244	5	)	)	PUNCT
ejpam-6982	244	6	)	)	PUNCT
ejpam-6982	245	1	,	,	PUNCT
ejpam-6982	245	2	un+1(x	un+1(x	PROPN
ejpam-6982	245	3	,	,	PUNCT
ejpam-6982	245	4	t	t	PROPN
ejpam-6982	245	5	)	)	PUNCT
ejpam-6982	245	6	=	=	SYM
ejpam-6982	245	7	−jα	−jα	X
ejpam-6982	246	1	[	[	X
ejpam-6982	246	2	an	an	X
ejpam-6982	246	3	]	]	X
ejpam-6982	246	4	,	,	PUNCT
ejpam-6982	246	5	n	n	X
ejpam-6982	246	6	≥	≥	NOUN
ejpam-6982	246	7	0	0	NUM
ejpam-6982	246	8	.	.	PUNCT
ejpam-6982	247	1	(	(	PUNCT
ejpam-6982	247	2	32	32	NUM
ejpam-6982	247	3	)	)	PUNCT
ejpam-6982	247	4	where	where	SCONJ
ejpam-6982	247	5	an	an	PRON
ejpam-6982	247	6	are	be	AUX
ejpam-6982	247	7	the	the	DET
ejpam-6982	247	8	adomian	adomian	NOUN
ejpam-6982	247	9	polynomials	polynomial	NOUN
ejpam-6982	247	10	for	for	ADP
ejpam-6982	247	11	the	the	DET
ejpam-6982	247	12	nonlinear	nonlinear	ADJ
ejpam-6982	247	13	function	function	NOUN
ejpam-6982	247	14	n	n	NOUN
ejpam-6982	247	15	=	=	SYM
ejpam-6982	247	16	u(x	u(x	NOUN
ejpam-6982	247	17	,	,	PUNCT
ejpam-6982	247	18	t)ux(x	t)ux(x	ADV
ejpam-6982	247	19	,	,	PUNCT
ejpam-6982	247	20	t	t	PROPN
ejpam-6982	247	21	)	)	PUNCT
ejpam-6982	247	22	.	.	PUNCT
ejpam-6982	248	1	the	the	DET
ejpam-6982	248	2	few	few	ADJ
ejpam-6982	248	3	components	component	NOUN
ejpam-6982	248	4	of	of	ADP
ejpam-6982	248	5	adomian	adomian	NOUN
ejpam-6982	248	6	polynomials	polynomial	NOUN
ejpam-6982	248	7	,	,	PUNCT
ejpam-6982	248	8	are	be	AUX
ejpam-6982	248	9	given	give	VERB
ejpam-6982	248	10	by	by	ADP
ejpam-6982	248	11	[	[	PUNCT
ejpam-6982	248	12	9	9	NUM
ejpam-6982	248	13	]	]	SYM
ejpam-6982	248	14	:	:	PUNCT
ejpam-6982	248	15	a0	a0	PROPN
ejpam-6982	248	16	=	=	SYM
ejpam-6982	248	17	u0u0x	u0u0x	NUM
ejpam-6982	248	18	,	,	PUNCT
ejpam-6982	248	19	a1	a1	NOUN
ejpam-6982	248	20	=	=	PUNCT
ejpam-6982	248	21	u0xu1	u0xu1	NOUN
ejpam-6982	248	22	+	+	CCONJ
ejpam-6982	248	23	u0u1x	u0u1x	NUM
ejpam-6982	248	24	,	,	PUNCT
ejpam-6982	248	25	a2	a2	PROPN
ejpam-6982	248	26	=	=	SYM
ejpam-6982	248	27	u0xu2	u0xu2	PROPN
ejpam-6982	248	28	+	+	CCONJ
ejpam-6982	248	29	u1xu1	u1xu1	NOUN
ejpam-6982	248	30	+	+	CCONJ
ejpam-6982	248	31	u2xu0	u2xu0	NOUN
ejpam-6982	248	32	,	,	PUNCT
ejpam-6982	248	33	(	(	PUNCT
ejpam-6982	248	34	33	33	NUM
ejpam-6982	248	35	)	)	PUNCT
ejpam-6982	248	36	and	and	CCONJ
ejpam-6982	248	37	we	we	PRON
ejpam-6982	248	38	can	can	AUX
ejpam-6982	248	39	continue	continue	VERB
ejpam-6982	248	40	the	the	DET
ejpam-6982	248	41	calculations	calculation	NOUN
ejpam-6982	248	42	to	to	PART
ejpam-6982	248	43	find	find	VERB
ejpam-6982	248	44	a3	a3	NOUN
ejpam-6982	248	45	and	and	CCONJ
ejpam-6982	248	46	so	so	ADV
ejpam-6982	248	47	on	on	ADV
ejpam-6982	248	48	by	by	ADP
ejpam-6982	248	49	the	the	DET
ejpam-6982	248	50	same	same	ADJ
ejpam-6982	248	51	manner	manner	NOUN
ejpam-6982	248	52	.	.	PUNCT
ejpam-6982	249	1	a.	a.	NOUN
ejpam-6982	249	2	m.	m.	PROPN
ejpam-6982	249	3	alhammad	alhammad	PROPN
ejpam-6982	249	4	,	,	PUNCT
ejpam-6982	249	5	a.	a.	NOUN
ejpam-6982	249	6	m.	m.	PROPN
ejpam-6982	249	7	saeed	saeed	PROPN
ejpam-6982	249	8	/	/	SYM
ejpam-6982	249	9	eur	eur	PROPN
ejpam-6982	249	10	.	.	PUNCT
ejpam-6982	250	1	j.	j.	PROPN
ejpam-6982	250	2	pure	pure	PROPN
ejpam-6982	250	3	appl	appl	PROPN
ejpam-6982	250	4	.	.	PROPN
ejpam-6982	250	5	math	math	PROPN
ejpam-6982	250	6	,	,	PUNCT
ejpam-6982	250	7	18	18	NUM
ejpam-6982	250	8	(	(	PUNCT
ejpam-6982	250	9	4	4	NUM
ejpam-6982	250	10	)	)	PUNCT
ejpam-6982	250	11	(	(	PUNCT
ejpam-6982	250	12	2025	2025	NUM
ejpam-6982	250	13	)	)	PUNCT
ejpam-6982	250	14	,	,	PUNCT
ejpam-6982	250	15	6982	6982	NUM
ejpam-6982	250	16	10	10	NUM
ejpam-6982	250	17	of	of	ADP
ejpam-6982	250	18	22	22	NUM
ejpam-6982	250	19	in	in	ADP
ejpam-6982	250	20	view	view	NOUN
ejpam-6982	250	21	of	of	ADP
ejpam-6982	250	22	(	(	PUNCT
ejpam-6982	250	23	32	32	NUM
ejpam-6982	250	24	)	)	PUNCT
ejpam-6982	250	25	,	,	PUNCT
ejpam-6982	250	26	the	the	DET
ejpam-6982	250	27	first	first	ADJ
ejpam-6982	250	28	few	few	ADJ
ejpam-6982	250	29	components	component	NOUN
ejpam-6982	250	30	of	of	ADP
ejpam-6982	250	31	the	the	DET
ejpam-6982	250	32	decomposition	decomposition	NOUN
ejpam-6982	250	33	series	series	NOUN
ejpam-6982	250	34	are	be	AUX
ejpam-6982	250	35	derived	derive	VERB
ejpam-6982	250	36	as	as	SCONJ
ejpam-6982	250	37	follows	follow	VERB
ejpam-6982	250	38	u0(x	u0(x	PRON
ejpam-6982	250	39	,	,	PUNCT
ejpam-6982	250	40	t	t	PROPN
ejpam-6982	250	41	)	)	PUNCT
ejpam-6982	251	1	=	=	NOUN
ejpam-6982	251	2	x	x	X
ejpam-6982	251	3	(	(	PUNCT
ejpam-6982	251	4	tα	tα	ADP
ejpam-6982	251	5	γ(α+	γ(α+	DET
ejpam-6982	251	6	1	1	NUM
ejpam-6982	251	7	)	)	PUNCT
ejpam-6982	251	8	+	+	NUM
ejpam-6982	251	9	2tα+2	2tα+2	NUM
ejpam-6982	251	10	γ(α+	γ(α+	DET
ejpam-6982	251	11	3	3	NUM
ejpam-6982	251	12	)	)	PUNCT
ejpam-6982	251	13	)	)	PUNCT
ejpam-6982	251	14	,	,	PUNCT
ejpam-6982	251	15	(	(	PUNCT
ejpam-6982	251	16	34	34	NUM
ejpam-6982	251	17	)	)	PUNCT
ejpam-6982	251	18	u1(x	u1(x	PROPN
ejpam-6982	251	19	,	,	PUNCT
ejpam-6982	251	20	t	t	PROPN
ejpam-6982	251	21	)	)	PUNCT
ejpam-6982	252	1	=	=	NOUN
ejpam-6982	252	2	−	−	NOUN
ejpam-6982	252	3	x	x	SYM
ejpam-6982	252	4	[	[	PUNCT
ejpam-6982	252	5	γ(2α+	γ(2α+	PROPN
ejpam-6982	252	6	1)t3α	1)t3α	X
ejpam-6982	252	7	γ(α+	γ(α+	PRON
ejpam-6982	252	8	1)2γ(3α+	1)2γ(3α+	NUM
ejpam-6982	252	9	1	1	NUM
ejpam-6982	252	10	)	)	PUNCT
ejpam-6982	252	11	+	+	CCONJ
ejpam-6982	252	12	4γ(2α+	4γ(2α+	NUM
ejpam-6982	252	13	3)t3α+2	3)t3α+2	NUM
ejpam-6982	252	14	γ(α+	γ(α+	PRON
ejpam-6982	252	15	1)γ(α+	1)γ(α+	PROPN
ejpam-6982	252	16	3)γ(3α+	3)γ(3α+	NUM
ejpam-6982	252	17	3	3	NUM
ejpam-6982	252	18	)	)	PUNCT
ejpam-6982	252	19	+	+	CCONJ
ejpam-6982	252	20	4γ(2α+	4γ(2α+	NUM
ejpam-6982	252	21	5)t3α+4	5)t3α+4	NUM
ejpam-6982	252	22	γ(α+	γ(α+	ADJ
ejpam-6982	252	23	3)2γ(3α+	3)2γ(3α+	NUM
ejpam-6982	252	24	5	5	NUM
ejpam-6982	252	25	)	)	PUNCT
ejpam-6982	252	26	]	]	PUNCT
ejpam-6982	252	27	,	,	PUNCT
ejpam-6982	252	28	(	(	PUNCT
ejpam-6982	252	29	35	35	NUM
ejpam-6982	252	30	)	)	PUNCT
ejpam-6982	252	31	u2(x	u2(x	PROPN
ejpam-6982	252	32	,	,	PUNCT
ejpam-6982	252	33	t	t	PROPN
ejpam-6982	252	34	)	)	PUNCT
ejpam-6982	252	35	=	=	NOUN
ejpam-6982	253	1	2x	2x	NOUN
ejpam-6982	253	2	[	[	PUNCT
ejpam-6982	253	3	γ(2α+	γ(2α+	X
ejpam-6982	253	4	1)γ(4α+	1)γ(4α+	NUM
ejpam-6982	253	5	1)t5α	1)t5α	NUM
ejpam-6982	253	6	γ(α+	γ(α+	ADP
ejpam-6982	253	7	1)3γ(3α+	1)3γ(3α+	NUM
ejpam-6982	253	8	1)γ(5α+	1)γ(5α+	NUM
ejpam-6982	253	9	1	1	NUM
ejpam-6982	253	10	)	)	PUNCT
ejpam-6982	253	11	+	+	CCONJ
ejpam-6982	253	12	8γ(2α+	8γ(2α+	NUM
ejpam-6982	253	13	5)γ(4α+	5)γ(4α+	NOUN
ejpam-6982	253	14	7)t5α+6	7)t5α+6	X
ejpam-6982	253	15	γ(α+	γ(α+	PRON
ejpam-6982	253	16	3)3γ(3α+	3)3γ(3α+	NUM
ejpam-6982	253	17	5)γ(5α+	5)γ(5α+	NUM
ejpam-6982	253	18	7	7	NUM
ejpam-6982	253	19	)	)	PUNCT
ejpam-6982	253	20	+	+	CCONJ
ejpam-6982	253	21	.	.	PUNCT
ejpam-6982	253	22	.	.	PUNCT
ejpam-6982	253	23	.	.	PUNCT
ejpam-6982	253	24	]	]	PUNCT
ejpam-6982	253	25	.	.	PUNCT
ejpam-6982	254	1	(	(	PUNCT
ejpam-6982	254	2	36	36	NUM
ejpam-6982	254	3	)	)	PUNCT
ejpam-6982	254	4	and	and	CCONJ
ejpam-6982	254	5	soon	soon	ADV
ejpam-6982	254	6	,	,	PUNCT
ejpam-6982	254	7	in	in	ADP
ejpam-6982	254	8	this	this	DET
ejpam-6982	254	9	manner	manner	NOUN
ejpam-6982	254	10	the	the	DET
ejpam-6982	254	11	rest	rest	NOUN
ejpam-6982	254	12	of	of	ADP
ejpam-6982	254	13	components	component	NOUN
ejpam-6982	254	14	of	of	ADP
ejpam-6982	254	15	the	the	DET
ejpam-6982	254	16	decomposition	decomposition	NOUN
ejpam-6982	254	17	series	series	NOUN
ejpam-6982	254	18	can	can	AUX
ejpam-6982	254	19	be	be	AUX
ejpam-6982	254	20	obtained	obtain	VERB
ejpam-6982	254	21	.	.	PUNCT
ejpam-6982	255	1	the	the	DET
ejpam-6982	255	2	first	first	ADJ
ejpam-6982	255	3	three	three	NUM
ejpam-6982	255	4	terms	term	NOUN
ejpam-6982	255	5	of	of	ADP
ejpam-6982	255	6	the	the	DET
ejpam-6982	255	7	decomposition	decomposition	NOUN
ejpam-6982	255	8	series	series	NOUN
ejpam-6982	255	9	(	(	PUNCT
ejpam-6982	255	10	6	6	NUM
ejpam-6982	255	11	)	)	PUNCT
ejpam-6982	255	12	are	be	AUX
ejpam-6982	255	13	given	give	VERB
ejpam-6982	255	14	by	by	ADP
ejpam-6982	255	15	u(x	u(x	NOUN
ejpam-6982	255	16	,	,	PUNCT
ejpam-6982	255	17	t	t	NOUN
ejpam-6982	255	18	)	)	PUNCT
ejpam-6982	255	19	=	=	SYM
ejpam-6982	256	1	x	x	PUNCT
ejpam-6982	256	2	[	[	PUNCT
ejpam-6982	256	3	tα	tα	ADP
ejpam-6982	256	4	γ(α+	γ(α+	DET
ejpam-6982	256	5	1	1	NUM
ejpam-6982	256	6	)	)	PUNCT
ejpam-6982	256	7	+	+	NUM
ejpam-6982	256	8	2tα+2	2tα+2	NUM
ejpam-6982	256	9	γ(α+	γ(α+	DET
ejpam-6982	256	10	3	3	NUM
ejpam-6982	256	11	)	)	PUNCT
ejpam-6982	256	12	−	−	PROPN
ejpam-6982	257	1	γ(2α+	γ(2α+	PROPN
ejpam-6982	257	2	1)t3α	1)t3α	PROPN
ejpam-6982	257	3	γ(α+	γ(α+	PRON
ejpam-6982	257	4	1)2γ(3α+	1)2γ(3α+	NUM
ejpam-6982	257	5	1	1	NUM
ejpam-6982	257	6	)	)	PUNCT
ejpam-6982	257	7	−	−	PROPN
ejpam-6982	257	8	4γ(2α+	4γ(2α+	NUM
ejpam-6982	257	9	3)t3α+2	3)t3α+2	NUM
ejpam-6982	258	1	γ(α+	γ(α+	DET
ejpam-6982	258	2	1)γ(α+	1)γ(α+	PROPN
ejpam-6982	258	3	3)γ(3α+	3)γ(3α+	NUM
ejpam-6982	258	4	3	3	NUM
ejpam-6982	258	5	)	)	PUNCT
ejpam-6982	258	6	−	−	NOUN
ejpam-6982	258	7	4γ(2α+	4γ(2α+	NUM
ejpam-6982	259	1	5)t3α+4	5)t3α+4	NUM
ejpam-6982	259	2	γ(α+	γ(α+	ADJ
ejpam-6982	259	3	3)2γ(3α+	3)2γ(3α+	NUM
ejpam-6982	259	4	5	5	NUM
ejpam-6982	259	5	)	)	PUNCT
ejpam-6982	259	6	+	+	CCONJ
ejpam-6982	259	7	γ(2α+	γ(2α+	PROPN
ejpam-6982	259	8	1)γ(4α+	1)γ(4α+	NUM
ejpam-6982	259	9	1)t5α	1)t5α	NUM
ejpam-6982	259	10	γ(α+	γ(α+	ADP
ejpam-6982	259	11	1)3γ(3α+	1)3γ(3α+	NUM
ejpam-6982	259	12	1)γ(5α+	1)γ(5α+	NUM
ejpam-6982	259	13	1	1	NUM
ejpam-6982	259	14	)	)	PUNCT
ejpam-6982	259	15	+	+	PUNCT
ejpam-6982	259	16	·	·	PUNCT
ejpam-6982	259	17	·	·	PUNCT
ejpam-6982	259	18	·	·	PUNCT
ejpam-6982	259	19	]	]	PUNCT
ejpam-6982	259	20	.	.	PUNCT
ejpam-6982	260	1	(	(	PUNCT
ejpam-6982	260	2	37	37	NUM
ejpam-6982	260	3	)	)	PUNCT
ejpam-6982	260	4	to	to	PART
ejpam-6982	260	5	solve	solve	VERB
ejpam-6982	260	6	the	the	DET
ejpam-6982	260	7	problem	problem	NOUN
ejpam-6982	260	8	using	use	VERB
ejpam-6982	260	9	the	the	DET
ejpam-6982	260	10	sumudu	sumudu	NOUN
ejpam-6982	260	11	decomposition	decomposition	NOUN
ejpam-6982	260	12	method	method	NOUN
ejpam-6982	260	13	,	,	PUNCT
ejpam-6982	260	14	we	we	PRON
ejpam-6982	260	15	simply	simply	ADV
ejpam-6982	260	16	substitute	substitute	VERB
ejpam-6982	260	17	(	(	PUNCT
ejpam-6982	260	18	30	30	NUM
ejpam-6982	260	19	)	)	PUNCT
ejpam-6982	260	20	and	and	CCONJ
ejpam-6982	260	21	the	the	DET
ejpam-6982	260	22	initial	initial	ADJ
ejpam-6982	260	23	conditions	condition	NOUN
ejpam-6982	260	24	(	(	PUNCT
ejpam-6982	260	25	31	31	NUM
ejpam-6982	260	26	)	)	PUNCT
ejpam-6982	260	27	into	into	ADP
ejpam-6982	260	28	(	(	PUNCT
ejpam-6982	260	29	16	16	NUM
ejpam-6982	260	30	)	)	PUNCT
ejpam-6982	260	31	,	,	PUNCT
ejpam-6982	260	32	to	to	PART
ejpam-6982	260	33	obtain	obtain	VERB
ejpam-6982	260	34	the	the	DET
ejpam-6982	260	35	following	follow	VERB
ejpam-6982	260	36	recurrence	recurrence	NOUN
ejpam-6982	260	37	relation	relation	NOUN
ejpam-6982	260	38	u0(x	u0(x	PROPN
ejpam-6982	260	39	,	,	PUNCT
ejpam-6982	260	40	t	t	PROPN
ejpam-6982	260	41	)	)	PUNCT
ejpam-6982	260	42	=	=	SYM
ejpam-6982	261	1	m−1∑	m−1∑	PROPN
ejpam-6982	261	2	k=0	k=0	PROPN
ejpam-6982	261	3	u(k)fk(x	u(k)fk(x	ADJ
ejpam-6982	261	4	)	)	PUNCT
ejpam-6982	262	1	+	+	CCONJ
ejpam-6982	262	2	s−1	s−1	PROPN
ejpam-6982	262	3	(	(	PUNCT
ejpam-6982	262	4	uαs	uαs	PROPN
ejpam-6982	262	5	[	[	PUNCT
ejpam-6982	262	6	x+	x+	X
ejpam-6982	262	7	xt2	xt2	PROPN
ejpam-6982	262	8	]	]	PUNCT
ejpam-6982	262	9	)	)	PUNCT
ejpam-6982	263	1	=	=	PUNCT
ejpam-6982	263	2	x	x	X
ejpam-6982	263	3	(	(	PUNCT
ejpam-6982	263	4	tα	tα	ADP
ejpam-6982	263	5	γ(α+	γ(α+	DET
ejpam-6982	263	6	1	1	NUM
ejpam-6982	263	7	)	)	PUNCT
ejpam-6982	263	8	+	+	NUM
ejpam-6982	263	9	2tα+2	2tα+2	NUM
ejpam-6982	263	10	γ(α+	γ(α+	DET
ejpam-6982	263	11	3	3	NUM
ejpam-6982	263	12	)	)	PUNCT
ejpam-6982	263	13	)	)	PUNCT
ejpam-6982	263	14	,	,	PUNCT
ejpam-6982	263	15	un+1(x	un+1(x	PROPN
ejpam-6982	263	16	,	,	PUNCT
ejpam-6982	263	17	t	t	PROPN
ejpam-6982	263	18	)	)	PUNCT
ejpam-6982	263	19	=	=	PUNCT
ejpam-6982	264	1	−s−1	−s−1	NUM
ejpam-6982	264	2	(	(	PUNCT
ejpam-6982	264	3	uαs	uαs	X
ejpam-6982	265	1	[	[	X
ejpam-6982	265	2	an	an	X
ejpam-6982	265	3	]	]	X
ejpam-6982	265	4	)	)	PUNCT
ejpam-6982	265	5	,	,	PUNCT
ejpam-6982	266	1	n	n	X
ejpam-6982	266	2	≥	≥	NOUN
ejpam-6982	266	3	1	1	NUM
ejpam-6982	266	4	.	.	PUNCT
ejpam-6982	267	1	(	(	PUNCT
ejpam-6982	267	2	38	38	NUM
ejpam-6982	267	3	)	)	PUNCT
ejpam-6982	267	4	the	the	DET
ejpam-6982	267	5	few	few	ADJ
ejpam-6982	267	6	components	component	NOUN
ejpam-6982	267	7	of	of	ADP
ejpam-6982	267	8	adomian	adomian	NOUN
ejpam-6982	267	9	polynomials	polynomial	NOUN
ejpam-6982	267	10	show	show	VERB
ejpam-6982	267	11	in	in	ADP
ejpam-6982	267	12	(	(	PUNCT
ejpam-6982	267	13	33	33	NUM
ejpam-6982	267	14	)	)	PUNCT
ejpam-6982	267	15	.	.	PUNCT
ejpam-6982	268	1	in	in	ADP
ejpam-6982	268	2	view	view	NOUN
ejpam-6982	268	3	of	of	ADP
ejpam-6982	268	4	(	(	PUNCT
ejpam-6982	268	5	38	38	NUM
ejpam-6982	268	6	)	)	PUNCT
ejpam-6982	268	7	,	,	PUNCT
ejpam-6982	268	8	the	the	DET
ejpam-6982	268	9	first	first	ADJ
ejpam-6982	268	10	few	few	ADJ
ejpam-6982	268	11	components	component	NOUN
ejpam-6982	268	12	of	of	ADP
ejpam-6982	268	13	the	the	DET
ejpam-6982	268	14	decomposition	decomposition	NOUN
ejpam-6982	268	15	series	series	NOUN
ejpam-6982	268	16	are	be	AUX
ejpam-6982	268	17	derived	derive	VERB
ejpam-6982	268	18	as	as	ADP
ejpam-6982	268	19	in	in	ADP
ejpam-6982	268	20	equations	equation	NOUN
ejpam-6982	268	21	(	(	PUNCT
ejpam-6982	268	22	35	35	NUM
ejpam-6982	268	23	)	)	PUNCT
ejpam-6982	268	24	and	and	CCONJ
ejpam-6982	268	25	(	(	PUNCT
ejpam-6982	268	26	36	36	NUM
ejpam-6982	268	27	)	)	PUNCT
ejpam-6982	268	28	and	and	CCONJ
ejpam-6982	268	29	so	so	ADV
ejpam-6982	268	30	on	on	ADV
ejpam-6982	268	31	,	,	PUNCT
ejpam-6982	268	32	in	in	ADP
ejpam-6982	268	33	this	this	DET
ejpam-6982	268	34	manner	manner	NOUN
ejpam-6982	268	35	the	the	DET
ejpam-6982	268	36	rest	rest	NOUN
ejpam-6982	268	37	of	of	ADP
ejpam-6982	268	38	components	component	NOUN
ejpam-6982	268	39	of	of	ADP
ejpam-6982	268	40	the	the	DET
ejpam-6982	268	41	sumudu	sumudu	NOUN
ejpam-6982	268	42	decomposition	decomposition	NOUN
ejpam-6982	268	43	series	series	NOUN
ejpam-6982	268	44	can	can	AUX
ejpam-6982	268	45	be	be	AUX
ejpam-6982	268	46	obtained	obtain	VERB
ejpam-6982	268	47	.	.	PUNCT
ejpam-6982	269	1	the	the	DET
ejpam-6982	269	2	first	first	ADJ
ejpam-6982	269	3	three	three	NUM
ejpam-6982	269	4	terms	term	NOUN
ejpam-6982	269	5	of	of	ADP
ejpam-6982	269	6	the	the	DET
ejpam-6982	269	7	decomposition	decomposition	NOUN
ejpam-6982	269	8	series	series	NOUN
ejpam-6982	269	9	are	be	AUX
ejpam-6982	269	10	given	give	VERB
ejpam-6982	269	11	by	by	ADP
ejpam-6982	269	12	u(x	u(x	NOUN
ejpam-6982	269	13	,	,	PUNCT
ejpam-6982	269	14	t)as	t)as	PROPN
ejpam-6982	269	15	written	write	VERB
ejpam-6982	269	16	in	in	ADP
ejpam-6982	269	17	equation	equation	NOUN
ejpam-6982	269	18	(	(	PUNCT
ejpam-6982	269	19	37	37	NUM
ejpam-6982	269	20	)	)	PUNCT
ejpam-6982	269	21	.	.	PUNCT
ejpam-6982	270	1	to	to	PART
ejpam-6982	270	2	solve	solve	VERB
ejpam-6982	270	3	the	the	DET
ejpam-6982	270	4	problem	problem	NOUN
ejpam-6982	270	5	using	use	VERB
ejpam-6982	270	6	the	the	DET
ejpam-6982	270	7	natural	natural	ADJ
ejpam-6982	270	8	decomposition	decomposition	NOUN
ejpam-6982	270	9	method	method	NOUN
ejpam-6982	270	10	,	,	PUNCT
ejpam-6982	270	11	we	we	PRON
ejpam-6982	270	12	simply	simply	ADV
ejpam-6982	270	13	substitute	substitute	VERB
ejpam-6982	270	14	(	(	PUNCT
ejpam-6982	270	15	30	30	NUM
ejpam-6982	270	16	)	)	PUNCT
ejpam-6982	270	17	and	and	CCONJ
ejpam-6982	270	18	the	the	DET
ejpam-6982	270	19	initial	initial	ADJ
ejpam-6982	270	20	conditions	condition	NOUN
ejpam-6982	270	21	(	(	PUNCT
ejpam-6982	270	22	31	31	NUM
ejpam-6982	270	23	)	)	PUNCT
ejpam-6982	270	24	into	into	ADP
ejpam-6982	270	25	(	(	PUNCT
ejpam-6982	270	26	22	22	NUM
ejpam-6982	270	27	)	)	PUNCT
ejpam-6982	270	28	,	,	PUNCT
ejpam-6982	270	29	to	to	PART
ejpam-6982	270	30	obtain	obtain	VERB
ejpam-6982	270	31	the	the	DET
ejpam-6982	270	32	following	follow	VERB
ejpam-6982	270	33	recurrence	recurrence	NOUN
ejpam-6982	270	34	relation	relation	NOUN
ejpam-6982	270	35	.	.	PUNCT
ejpam-6982	271	1	u0(x	u0(x	PROPN
ejpam-6982	271	2	,	,	PUNCT
ejpam-6982	271	3	t	t	PROPN
ejpam-6982	271	4	)	)	PUNCT
ejpam-6982	271	5	=	=	SYM
ejpam-6982	272	1	m−1∑	m−1∑	PROPN
ejpam-6982	272	2	k=0	k=0	PROPN
ejpam-6982	272	3	s−(k+1	s−(k+1	PROPN
ejpam-6982	272	4	)	)	PUNCT
ejpam-6982	272	5	u−k	u−k	NOUN
ejpam-6982	272	6	uk(x	uk(x	ADP
ejpam-6982	272	7	,	,	PUNCT
ejpam-6982	272	8	0	0	NUM
ejpam-6982	272	9	)	)	PUNCT
ejpam-6982	273	1	+	+	CCONJ
ejpam-6982	273	2	n−1	n−1	PROPN
ejpam-6982	273	3	(	(	PUNCT
ejpam-6982	273	4	uα	uα	PROPN
ejpam-6982	273	5	sα	sα	ADV
ejpam-6982	273	6	n[g(x	n[g(x	X
ejpam-6982	273	7	,	,	PUNCT
ejpam-6982	273	8	t	t	PROPN
ejpam-6982	273	9	)	)	PUNCT
ejpam-6982	273	10	]	]	PUNCT
ejpam-6982	273	11	)	)	PUNCT
ejpam-6982	274	1	=	=	PUNCT
ejpam-6982	274	2	x	x	X
ejpam-6982	274	3	(	(	PUNCT
ejpam-6982	274	4	tα	tα	ADP
ejpam-6982	274	5	γ(α+	γ(α+	DET
ejpam-6982	274	6	1	1	NUM
ejpam-6982	274	7	)	)	PUNCT
ejpam-6982	274	8	+	+	NUM
ejpam-6982	274	9	2tα+2	2tα+2	NUM
ejpam-6982	274	10	γ(α+	γ(α+	DET
ejpam-6982	274	11	3	3	NUM
ejpam-6982	274	12	)	)	PUNCT
ejpam-6982	274	13	)	)	PUNCT
ejpam-6982	275	1	,	,	PUNCT
ejpam-6982	275	2	un+1(x	un+1(x	PROPN
ejpam-6982	275	3	,	,	PUNCT
ejpam-6982	275	4	t	t	PROPN
ejpam-6982	275	5	)	)	PUNCT
ejpam-6982	275	6	=	=	SYM
ejpam-6982	275	7	−n−1	−n−1	NUM
ejpam-6982	276	1	(	(	PUNCT
ejpam-6982	276	2	uα	uα	NOUN
ejpam-6982	276	3	sα	sα	VERB
ejpam-6982	276	4	n	n	PROPN
ejpam-6982	277	1	[	[	X
ejpam-6982	277	2	an	an	X
ejpam-6982	277	3	]	]	X
ejpam-6982	277	4	)	)	PUNCT
ejpam-6982	277	5	,	,	PUNCT
ejpam-6982	277	6	n	n	X
ejpam-6982	277	7	≥	≥	NOUN
ejpam-6982	277	8	1	1	NUM
ejpam-6982	277	9	.	.	PUNCT
ejpam-6982	278	1	(	(	PUNCT
ejpam-6982	278	2	39	39	NUM
ejpam-6982	278	3	)	)	PUNCT
ejpam-6982	278	4	in	in	ADP
ejpam-6982	278	5	view	view	NOUN
ejpam-6982	278	6	of	of	ADP
ejpam-6982	278	7	(	(	PUNCT
ejpam-6982	278	8	39	39	NUM
ejpam-6982	278	9	)	)	PUNCT
ejpam-6982	278	10	,	,	PUNCT
ejpam-6982	278	11	the	the	DET
ejpam-6982	278	12	first	first	ADJ
ejpam-6982	278	13	few	few	ADJ
ejpam-6982	278	14	components	component	NOUN
ejpam-6982	278	15	of	of	ADP
ejpam-6982	278	16	the	the	DET
ejpam-6982	278	17	decomposition	decomposition	NOUN
ejpam-6982	278	18	series	series	NOUN
ejpam-6982	278	19	are	be	AUX
ejpam-6982	278	20	derived	derive	VERB
ejpam-6982	278	21	as	as	ADP
ejpam-6982	278	22	in	in	ADP
ejpam-6982	278	23	equations	equation	NOUN
ejpam-6982	278	24	(	(	PUNCT
ejpam-6982	278	25	35	35	NUM
ejpam-6982	278	26	)	)	PUNCT
ejpam-6982	278	27	and	and	CCONJ
ejpam-6982	278	28	(	(	PUNCT
ejpam-6982	278	29	36	36	NUM
ejpam-6982	278	30	)	)	PUNCT
ejpam-6982	278	31	and	and	CCONJ
ejpam-6982	278	32	so	so	ADV
ejpam-6982	278	33	on	on	ADV
ejpam-6982	278	34	,	,	PUNCT
ejpam-6982	278	35	in	in	ADP
ejpam-6982	278	36	this	this	DET
ejpam-6982	278	37	manner	manner	NOUN
ejpam-6982	278	38	the	the	DET
ejpam-6982	278	39	rest	rest	NOUN
ejpam-6982	278	40	of	of	ADP
ejpam-6982	278	41	components	component	NOUN
ejpam-6982	278	42	of	of	ADP
ejpam-6982	278	43	the	the	DET
ejpam-6982	278	44	natural	natural	ADJ
ejpam-6982	278	45	a.	a.	NOUN
ejpam-6982	278	46	m.	m.	NOUN
ejpam-6982	278	47	alhammad	alhammad	PROPN
ejpam-6982	278	48	,	,	PUNCT
ejpam-6982	278	49	a.	a.	NOUN
ejpam-6982	278	50	m.	m.	PROPN
ejpam-6982	278	51	saeed	saeed	PROPN
ejpam-6982	278	52	/	/	SYM
ejpam-6982	278	53	eur	eur	PROPN
ejpam-6982	278	54	.	.	PUNCT
ejpam-6982	279	1	j.	j.	PROPN
ejpam-6982	279	2	pure	pure	PROPN
ejpam-6982	279	3	appl	appl	PROPN
ejpam-6982	279	4	.	.	PROPN
ejpam-6982	279	5	math	math	PROPN
ejpam-6982	279	6	,	,	PUNCT
ejpam-6982	279	7	18	18	NUM
ejpam-6982	279	8	(	(	PUNCT
ejpam-6982	279	9	4	4	NUM
ejpam-6982	279	10	)	)	PUNCT
ejpam-6982	279	11	(	(	PUNCT
ejpam-6982	279	12	2025	2025	NUM
ejpam-6982	279	13	)	)	PUNCT
ejpam-6982	279	14	,	,	PUNCT
ejpam-6982	279	15	6982	6982	NUM
ejpam-6982	279	16	11	11	NUM
ejpam-6982	279	17	of	of	ADP
ejpam-6982	279	18	22	22	NUM
ejpam-6982	279	19	decomposition	decomposition	NOUN
ejpam-6982	279	20	series	series	NOUN
ejpam-6982	279	21	can	can	AUX
ejpam-6982	279	22	be	be	AUX
ejpam-6982	279	23	obtained	obtain	VERB
ejpam-6982	279	24	.	.	PUNCT
ejpam-6982	280	1	the	the	DET
ejpam-6982	280	2	first	first	ADJ
ejpam-6982	280	3	three	three	NUM
ejpam-6982	280	4	terms	term	NOUN
ejpam-6982	280	5	of	of	ADP
ejpam-6982	280	6	the	the	DET
ejpam-6982	280	7	decomposition	decomposition	NOUN
ejpam-6982	280	8	series	series	NOUN
ejpam-6982	280	9	are	be	AUX
ejpam-6982	280	10	given	give	VERB
ejpam-6982	280	11	by	by	ADP
ejpam-6982	280	12	u(x	u(x	NOUN
ejpam-6982	280	13	,	,	PUNCT
ejpam-6982	280	14	t	t	PROPN
ejpam-6982	280	15	)	)	PUNCT
ejpam-6982	280	16	as	as	SCONJ
ejpam-6982	280	17	written	write	VERB
ejpam-6982	280	18	in	in	ADP
ejpam-6982	280	19	equation	equation	NOUN
ejpam-6982	280	20	(	(	PUNCT
ejpam-6982	280	21	37	37	NUM
ejpam-6982	280	22	)	)	PUNCT
ejpam-6982	280	23	.	.	PUNCT
ejpam-6982	281	1	to	to	PART
ejpam-6982	281	2	solve	solve	VERB
ejpam-6982	281	3	the	the	DET
ejpam-6982	281	4	problem	problem	NOUN
ejpam-6982	281	5	using	use	VERB
ejpam-6982	281	6	the	the	DET
ejpam-6982	281	7	modified	modify	VERB
ejpam-6982	281	8	laplace	laplace	NOUN
ejpam-6982	281	9	variational	variational	ADJ
ejpam-6982	281	10	iteration	iteration	NOUN
ejpam-6982	281	11	method	method	NOUN
ejpam-6982	281	12	[	[	X
ejpam-6982	281	13	14	14	NUM
ejpam-6982	281	14	]	]	PUNCT
ejpam-6982	281	15	,	,	PUNCT
ejpam-6982	281	16	by	by	ADP
ejpam-6982	281	17	enforcement	enforcement	NOUN
ejpam-6982	281	18	of	of	ADP
ejpam-6982	281	19	the	the	DET
ejpam-6982	281	20	laplace	laplace	NOUN
ejpam-6982	281	21	transform	transform	NOUN
ejpam-6982	281	22	to	to	ADP
ejpam-6982	281	23	the	the	DET
ejpam-6982	281	24	sides	side	NOUN
ejpam-6982	281	25	of	of	ADP
ejpam-6982	281	26	equation	equation	NOUN
ejpam-6982	281	27	(	(	PUNCT
ejpam-6982	281	28	30	30	NUM
ejpam-6982	281	29	)	)	PUNCT
ejpam-6982	281	30	and	and	CCONJ
ejpam-6982	281	31	using	use	VERB
ejpam-6982	281	32	the	the	DET
ejpam-6982	281	33	initial	initial	ADJ
ejpam-6982	281	34	conditions	condition	NOUN
ejpam-6982	281	35	(	(	PUNCT
ejpam-6982	281	36	31	31	NUM
ejpam-6982	281	37	)	)	PUNCT
ejpam-6982	281	38	,	,	PUNCT
ejpam-6982	281	39	we	we	PRON
ejpam-6982	281	40	get	get	VERB
ejpam-6982	281	41	u(x	u(x	NOUN
ejpam-6982	281	42	,	,	PUNCT
ejpam-6982	281	43	s	s	X
ejpam-6982	281	44	)	)	PUNCT
ejpam-6982	281	45	=	=	PUNCT
ejpam-6982	282	1	x	x	PUNCT
ejpam-6982	282	2	s1+α	s1+α	ADP
ejpam-6982	282	3	+	+	NOUN
ejpam-6982	282	4	2x	2x	NUM
ejpam-6982	282	5	s3+α	s3+α	VERB
ejpam-6982	282	6	−	−	PROPN
ejpam-6982	282	7	(	(	PUNCT
ejpam-6982	282	8	1	1	NUM
ejpam-6982	282	9	sα	sα	ADJ
ejpam-6982	282	10	l	l	PROPN
ejpam-6982	282	11	(	(	PUNCT
ejpam-6982	282	12	u(x	u(x	NOUN
ejpam-6982	282	13	,	,	PUNCT
ejpam-6982	282	14	t)ux(x	t)ux(x	ADJ
ejpam-6982	282	15	,	,	PUNCT
ejpam-6982	282	16	t	t	PROPN
ejpam-6982	282	17	)	)	PUNCT
ejpam-6982	282	18	)	)	PUNCT
ejpam-6982	282	19	)	)	PUNCT
ejpam-6982	282	20	.	.	PUNCT
ejpam-6982	283	1	(	(	PUNCT
ejpam-6982	283	2	40	40	NUM
ejpam-6982	283	3	)	)	PUNCT
ejpam-6982	283	4	taking	take	VERB
ejpam-6982	283	5	the	the	DET
ejpam-6982	283	6	inverse	inverse	NOUN
ejpam-6982	283	7	laplace	laplace	NOUN
ejpam-6982	283	8	transform	transform	NOUN
ejpam-6982	283	9	to	to	ADP
ejpam-6982	283	10	the	the	DET
ejpam-6982	283	11	sides	side	NOUN
ejpam-6982	283	12	of	of	ADP
ejpam-6982	283	13	equation	equation	NOUN
ejpam-6982	283	14	(	(	PUNCT
ejpam-6982	283	15	40	40	NUM
ejpam-6982	283	16	)	)	PUNCT
ejpam-6982	283	17	,	,	PUNCT
ejpam-6982	283	18	we	we	PRON
ejpam-6982	283	19	obtain	obtain	VERB
ejpam-6982	283	20	u(x	u(x	NOUN
ejpam-6982	283	21	,	,	PUNCT
ejpam-6982	283	22	t	t	PROPN
ejpam-6982	283	23	)	)	PUNCT
ejpam-6982	283	24	=	=	PUNCT
ejpam-6982	284	1	xtα	xtα	PUNCT
ejpam-6982	285	1	γ(1	γ(1	PROPN
ejpam-6982	285	2	+	+	CCONJ
ejpam-6982	285	3	α	α	X
ejpam-6982	285	4	)	)	PUNCT
ejpam-6982	285	5	+	+	CCONJ
ejpam-6982	286	1	2xtα+2	2xtα+2	NUM
ejpam-6982	286	2	γ(α+	γ(α+	DET
ejpam-6982	286	3	3	3	NUM
ejpam-6982	286	4	)	)	PUNCT
ejpam-6982	286	5	−	−	PROPN
ejpam-6982	287	1	l−1	l−1	PROPN
ejpam-6982	287	2	(	(	PUNCT
ejpam-6982	287	3	1	1	NUM
ejpam-6982	287	4	sα	sα	ADJ
ejpam-6982	287	5	l	l	PROPN
ejpam-6982	287	6	(	(	PUNCT
ejpam-6982	287	7	u(x	u(x	NOUN
ejpam-6982	287	8	,	,	PUNCT
ejpam-6982	287	9	t)ux(x	t)ux(x	ADJ
ejpam-6982	287	10	,	,	PUNCT
ejpam-6982	287	11	t	t	PROPN
ejpam-6982	287	12	)	)	PUNCT
ejpam-6982	287	13	)	)	PUNCT
ejpam-6982	287	14	)	)	PUNCT
ejpam-6982	287	15	.	.	PUNCT
ejpam-6982	288	1	(	(	PUNCT
ejpam-6982	288	2	41	41	NUM
ejpam-6982	288	3	)	)	PUNCT
ejpam-6982	288	4	now	now	ADV
ejpam-6982	288	5	the	the	DET
ejpam-6982	288	6	new	new	ADJ
ejpam-6982	288	7	tactic	tactic	NOUN
ejpam-6982	288	8	of	of	ADP
ejpam-6982	288	9	the	the	DET
ejpam-6982	288	10	modified	modify	VERB
ejpam-6982	288	11	laplace	laplace	NOUN
ejpam-6982	288	12	variational	variational	ADJ
ejpam-6982	288	13	iteration	iteration	NOUN
ejpam-6982	288	14	technique	technique	NOUN
ejpam-6982	288	15	is	be	AUX
ejpam-6982	288	16	instituted	institute	VERB
ejpam-6982	288	17	on	on	ADP
ejpam-6982	288	18	(	(	PUNCT
ejpam-6982	288	19	27	27	NUM
ejpam-6982	288	20	)	)	PUNCT
ejpam-6982	288	21	from	from	ADP
ejpam-6982	288	22	equation	equation	NOUN
ejpam-6982	288	23	(	(	PUNCT
ejpam-6982	288	24	41	41	NUM
ejpam-6982	288	25	)	)	PUNCT
ejpam-6982	288	26	,	,	PUNCT
ejpam-6982	288	27	and	and	CCONJ
ejpam-6982	288	28	we	we	PRON
ejpam-6982	288	29	get	get	VERB
ejpam-6982	288	30	du(x	du(x	NOUN
ejpam-6982	288	31	,	,	PUNCT
ejpam-6982	288	32	t	t	PROPN
ejpam-6982	288	33	)	)	PUNCT
ejpam-6982	288	34	dt	dt	NOUN
ejpam-6982	289	1	=	=	PUNCT
ejpam-6982	289	2	d	d	X
ejpam-6982	289	3	dt	dt	X
ejpam-6982	289	4	(	(	PUNCT
ejpam-6982	289	5	xtα	xtα	X
ejpam-6982	290	1	γ(1	γ(1	PROPN
ejpam-6982	290	2	+	+	CCONJ
ejpam-6982	290	3	α	α	NOUN
ejpam-6982	290	4	)	)	PUNCT
ejpam-6982	290	5	)	)	PUNCT
ejpam-6982	291	1	+	+	CCONJ
ejpam-6982	292	1	d	d	X
ejpam-6982	292	2	dt	dt	X
ejpam-6982	292	3	(	(	PUNCT
ejpam-6982	292	4	2xtα+2	2xtα+2	NUM
ejpam-6982	292	5	γ(α+	γ(α+	DET
ejpam-6982	292	6	3	3	NUM
ejpam-6982	292	7	)	)	PUNCT
ejpam-6982	292	8	)	)	PUNCT
ejpam-6982	292	9	−	−	PROPN
ejpam-6982	293	1	d	d	INTJ
ejpam-6982	293	2	dt	dt	X
ejpam-6982	293	3	(	(	PUNCT
ejpam-6982	293	4	l−1	l−1	PROPN
ejpam-6982	293	5	(	(	PUNCT
ejpam-6982	293	6	1	1	NUM
ejpam-6982	293	7	sα	sα	ADJ
ejpam-6982	293	8	l	l	PROPN
ejpam-6982	293	9	(	(	PUNCT
ejpam-6982	293	10	u(x	u(x	NOUN
ejpam-6982	293	11	,	,	PUNCT
ejpam-6982	293	12	t)ux(x	t)ux(x	ADJ
ejpam-6982	293	13	,	,	PUNCT
ejpam-6982	293	14	t	t	PROPN
ejpam-6982	293	15	)	)	PUNCT
ejpam-6982	293	16	)	)	PUNCT
ejpam-6982	293	17	)	)	PUNCT
ejpam-6982	293	18	)	)	PUNCT
ejpam-6982	293	19	.	.	PUNCT
ejpam-6982	294	1	(	(	PUNCT
ejpam-6982	294	2	42	42	X
ejpam-6982	294	3	)	)	PUNCT
ejpam-6982	294	4	we	we	PRON
ejpam-6982	294	5	simply	simply	ADV
ejpam-6982	294	6	substitute	substitute	VERB
ejpam-6982	294	7	equation	equation	NOUN
ejpam-6982	294	8	(	(	PUNCT
ejpam-6982	294	9	42	42	NUM
ejpam-6982	294	10	)	)	PUNCT
ejpam-6982	294	11	and	and	CCONJ
ejpam-6982	294	12	the	the	DET
ejpam-6982	294	13	initial	initial	ADJ
ejpam-6982	294	14	condition	condition	NOUN
ejpam-6982	294	15	equation	equation	NOUN
ejpam-6982	294	16	(	(	PUNCT
ejpam-6982	294	17	31	31	NUM
ejpam-6982	294	18	)	)	PUNCT
ejpam-6982	294	19	into	into	ADP
ejpam-6982	294	20	equation	equation	NOUN
ejpam-6982	294	21	(	(	PUNCT
ejpam-6982	294	22	29	29	NUM
ejpam-6982	294	23	)	)	PUNCT
ejpam-6982	294	24	,	,	PUNCT
ejpam-6982	294	25	by	by	ADP
ejpam-6982	294	26	the	the	DET
ejpam-6982	294	27	new	new	ADJ
ejpam-6982	294	28	modified	modify	VERB
ejpam-6982	294	29	function	function	NOUN
ejpam-6982	294	30	,	,	PUNCT
ejpam-6982	294	31	we	we	PRON
ejpam-6982	294	32	find	find	VERB
ejpam-6982	294	33	u0(x	u0(x	PRON
ejpam-6982	294	34	,	,	PUNCT
ejpam-6982	294	35	t	t	PROPN
ejpam-6982	294	36	)	)	PUNCT
ejpam-6982	294	37	=	=	SYM
ejpam-6982	294	38	u(x	u(x	NOUN
ejpam-6982	294	39	,	,	PUNCT
ejpam-6982	294	40	0	0	NUM
ejpam-6982	294	41	)	)	PUNCT
ejpam-6982	294	42	=	=	SYM
ejpam-6982	294	43	0	0	PUNCT
ejpam-6982	295	1	u1(x	u1(x	ADJ
ejpam-6982	295	2	,	,	PUNCT
ejpam-6982	295	3	t	t	PROPN
ejpam-6982	295	4	)	)	PUNCT
ejpam-6982	295	5	=	=	SYM
ejpam-6982	295	6	xtα	xtα	PUNCT
ejpam-6982	296	1	γ(1	γ(1	PROPN
ejpam-6982	296	2	+	+	CCONJ
ejpam-6982	296	3	α	α	X
ejpam-6982	296	4	)	)	PUNCT
ejpam-6982	296	5	+	+	CCONJ
ejpam-6982	297	1	2xtα+2	2xtα+2	NUM
ejpam-6982	297	2	γ(α+	γ(α+	DET
ejpam-6982	297	3	3	3	NUM
ejpam-6982	297	4	)	)	PUNCT
ejpam-6982	297	5	u2(x	u2(x	PROPN
ejpam-6982	297	6	,	,	PUNCT
ejpam-6982	297	7	t	t	PROPN
ejpam-6982	297	8	)	)	PUNCT
ejpam-6982	297	9	=	=	SYM
ejpam-6982	298	1	xtα	xtα	PUNCT
ejpam-6982	299	1	γ(1	γ(1	PROPN
ejpam-6982	299	2	+	+	CCONJ
ejpam-6982	299	3	α	α	X
ejpam-6982	299	4	)	)	PUNCT
ejpam-6982	299	5	+	+	CCONJ
ejpam-6982	300	1	2xtα+2	2xtα+2	NUM
ejpam-6982	300	2	γ(α+	γ(α+	DET
ejpam-6982	300	3	3	3	NUM
ejpam-6982	300	4	)	)	PUNCT
ejpam-6982	300	5	−	−	PROPN
ejpam-6982	301	1	(	(	PUNCT
ejpam-6982	301	2	γ(1	γ(1	PROPN
ejpam-6982	301	3	+	+	CCONJ
ejpam-6982	301	4	2α)xt3α	2α)xt3α	NUM
ejpam-6982	301	5	γ(1	γ(1	NOUN
ejpam-6982	301	6	+	+	PUNCT
ejpam-6982	301	7	α)2γ(3α+	α)2γ(3α+	NOUN
ejpam-6982	301	8	1	1	NUM
ejpam-6982	301	9	)	)	PUNCT
ejpam-6982	301	10	)	)	PUNCT
ejpam-6982	302	1	−	−	PROPN
ejpam-6982	303	1	4xγ(2α+	4xγ(2α+	NUM
ejpam-6982	303	2	3)t3α+2	3)t3α+2	ADJ
ejpam-6982	303	3	γ(1	γ(1	PROPN
ejpam-6982	303	4	+	+	CCONJ
ejpam-6982	303	5	α)γ(α+	α)γ(α+	NUM
ejpam-6982	303	6	3)γ(3α+	3)γ(3α+	NUM
ejpam-6982	303	7	3	3	NUM
ejpam-6982	303	8	)	)	PUNCT
ejpam-6982	304	1	−	−	PROPN
ejpam-6982	304	2	4xγ(2α+	4xγ(2α+	PROPN
ejpam-6982	305	1	5)t3α+4	5)t3α+4	NOUN
ejpam-6982	305	2	γ(α+	γ(α+	X
ejpam-6982	305	3	3)2γ(3α+	3)2γ(3α+	NUM
ejpam-6982	305	4	5	5	NUM
ejpam-6982	305	5	)	)	PUNCT
ejpam-6982	305	6	.	.	PUNCT
ejpam-6982	306	1	tables	table	NOUN
ejpam-6982	306	2	(	(	PUNCT
ejpam-6982	306	3	1	1	NUM
ejpam-6982	306	4	,	,	PUNCT
ejpam-6982	306	5	2	2	NUM
ejpam-6982	306	6	,	,	PUNCT
ejpam-6982	306	7	3	3	X
ejpam-6982	306	8	)	)	PUNCT
ejpam-6982	306	9	show	show	VERB
ejpam-6982	306	10	the	the	DET
ejpam-6982	306	11	approximate	approximate	ADJ
ejpam-6982	306	12	solutions	solution	NOUN
ejpam-6982	306	13	for	for	ADP
ejpam-6982	306	14	eq	eq	PROPN
ejpam-6982	306	15	.	.	PUNCT
ejpam-6982	307	1	(	(	PUNCT
ejpam-6982	307	2	30	30	NUM
ejpam-6982	307	3	)	)	PUNCT
ejpam-6982	307	4	obtained	obtain	VERB
ejpam-6982	307	5	for	for	ADP
ejpam-6982	307	6	different	different	ADJ
ejpam-6982	307	7	values	value	NOUN
ejpam-6982	307	8	of	of	ADP
ejpam-6982	307	9	a	a	PRON
ejpam-6982	307	10	using	use	VERB
ejpam-6982	307	11	the	the	DET
ejpam-6982	307	12	decomposition	decomposition	NOUN
ejpam-6982	307	13	method	method	NOUN
ejpam-6982	307	14	,	,	PUNCT
ejpam-6982	307	15	sumudu	sumudu	NOUN
ejpam-6982	307	16	decomposition	decomposition	NOUN
ejpam-6982	307	17	method	method	NOUN
ejpam-6982	307	18	,	,	PUNCT
ejpam-6982	307	19	natural	natural	ADJ
ejpam-6982	307	20	decomposition	decomposition	NOUN
ejpam-6982	307	21	method	method	NOUN
ejpam-6982	307	22	,	,	PUNCT
ejpam-6982	307	23	adomian	adomian	NOUN
ejpam-6982	307	24	decomposition	decomposition	NOUN
ejpam-6982	307	25	method	method	NOUN
ejpam-6982	307	26	,	,	PUNCT
ejpam-6982	307	27	and	and	CCONJ
ejpam-6982	307	28	modified	modify	VERB
ejpam-6982	307	29	laplace	laplace	NOUN
ejpam-6982	307	30	variational	variational	ADJ
ejpam-6982	307	31	iteration	iteration	NOUN
ejpam-6982	307	32	.	.	PUNCT
ejpam-6982	308	1	it	it	PRON
ejpam-6982	308	2	is	be	AUX
ejpam-6982	308	3	to	to	PART
ejpam-6982	308	4	be	be	AUX
ejpam-6982	308	5	noted	note	VERB
ejpam-6982	308	6	that	that	SCONJ
ejpam-6982	308	7	only	only	ADV
ejpam-6982	308	8	three	three	NUM
ejpam-6982	308	9	terms	term	NOUN
ejpam-6982	308	10	of	of	ADP
ejpam-6982	308	11	this	this	DET
ejpam-6982	308	12	decomposition	decomposition	NOUN
ejpam-6982	308	13	series	series	NOUN
ejpam-6982	308	14	and	and	CCONJ
ejpam-6982	308	15	the	the	DET
ejpam-6982	308	16	modified	modified	ADJ
ejpam-6982	308	17	laplace	laplace	NOUN
ejpam-6982	308	18	variational	variational	ADJ
ejpam-6982	308	19	iteration	iteration	NOUN
ejpam-6982	308	20	were	be	AUX
ejpam-6982	308	21	used	use	VERB
ejpam-6982	308	22	in	in	ADP
ejpam-6982	308	23	evaluating	evaluate	VERB
ejpam-6982	308	24	the	the	DET
ejpam-6982	308	25	approximate	approximate	ADJ
ejpam-6982	308	26	solutions	solution	NOUN
ejpam-6982	308	27	for	for	ADP
ejpam-6982	308	28	obtaining	obtain	VERB
ejpam-6982	308	29	the	the	DET
ejpam-6982	308	30	results	result	NOUN
ejpam-6982	308	31	.	.	PUNCT
ejpam-6982	309	1	the	the	DET
ejpam-6982	309	2	accuracy	accuracy	NOUN
ejpam-6982	309	3	can	can	AUX
ejpam-6982	309	4	be	be	AUX
ejpam-6982	309	5	improved	improve	VERB
ejpam-6982	309	6	by	by	ADP
ejpam-6982	309	7	computing	compute	VERB
ejpam-6982	309	8	more	more	ADJ
ejpam-6982	309	9	terms	term	NOUN
ejpam-6982	309	10	of	of	ADP
ejpam-6982	309	11	the	the	DET
ejpam-6982	309	12	approximate	approximate	ADJ
ejpam-6982	309	13	solution	solution	NOUN
ejpam-6982	309	14	.	.	PUNCT
ejpam-6982	310	1	a.	a.	NOUN
ejpam-6982	310	2	m.	m.	PROPN
ejpam-6982	310	3	alhammad	alhammad	PROPN
ejpam-6982	310	4	,	,	PUNCT
ejpam-6982	310	5	a.	a.	NOUN
ejpam-6982	310	6	m.	m.	PROPN
ejpam-6982	310	7	saeed	saeed	PROPN
ejpam-6982	310	8	/	/	SYM
ejpam-6982	310	9	eur	eur	PROPN
ejpam-6982	310	10	.	.	PUNCT
ejpam-6982	311	1	j.	j.	PROPN
ejpam-6982	311	2	pure	pure	PROPN
ejpam-6982	311	3	appl	appl	PROPN
ejpam-6982	311	4	.	.	PROPN
ejpam-6982	311	5	math	math	PROPN
ejpam-6982	311	6	,	,	PUNCT
ejpam-6982	311	7	18	18	NUM
ejpam-6982	311	8	(	(	PUNCT
ejpam-6982	311	9	4	4	NUM
ejpam-6982	311	10	)	)	PUNCT
ejpam-6982	311	11	(	(	PUNCT
ejpam-6982	311	12	2025	2025	NUM
ejpam-6982	311	13	)	)	PUNCT
ejpam-6982	311	14	,	,	PUNCT
ejpam-6982	311	15	6982	6982	NUM
ejpam-6982	311	16	12	12	NUM
ejpam-6982	311	17	of	of	ADP
ejpam-6982	311	18	22	22	NUM
ejpam-6982	311	19	table	table	NOUN
ejpam-6982	311	20	1	1	NUM
ejpam-6982	311	21	:	:	PUNCT
ejpam-6982	311	22	numerical	numerical	ADJ
ejpam-6982	311	23	values	value	NOUN
ejpam-6982	311	24	when	when	SCONJ
ejpam-6982	311	25	α	α	PROPN
ejpam-6982	311	26	=	=	NOUN
ejpam-6982	311	27	0.5	0.5	NUM
ejpam-6982	311	28	for	for	ADP
ejpam-6982	311	29	eq	eq	NOUN
ejpam-6982	311	30	.	.	PUNCT
ejpam-6982	311	31	(	(	PUNCT
ejpam-6982	311	32	30	30	NUM
ejpam-6982	311	33	)	)	PUNCT
ejpam-6982	311	34	.	.	PUNCT
ejpam-6982	312	1	t	t	NOUN
ejpam-6982	312	2	x	x	PUNCT
ejpam-6982	312	3	uadm	uadm	PROPN
ejpam-6982	312	4	undm	undm	PROPN
ejpam-6982	312	5	−	−	ADP
ejpam-6982	312	6	usdm	usdm	PROPN
ejpam-6982	312	7	umlvim	umlvim	ADJ
ejpam-6982	312	8	0.2	0.2	NUM
ejpam-6982	312	9	0.25	0.25	NUM
ejpam-6982	312	10	0.1128438450	0.1128438450	NUM
ejpam-6982	312	11	0.1128438450	0.1128438450	NUM
ejpam-6982	312	12	0.1067989518	0.1067989518	NUM
ejpam-6982	312	13	0.5	0.5	NUM
ejpam-6982	312	14	0.2256876900	0.2256876900	NUM
ejpam-6982	312	15	0.2256876900	0.2256876900	NUM
ejpam-6982	312	16	0.2135979036	0.2135979036	NUM
ejpam-6982	312	17	0.75	0.75	NUM
ejpam-6982	312	18	0.3385315349	0.3385315349	NUM
ejpam-6982	312	19	0.3385315349	0.3385315349	NUM
ejpam-6982	312	20	0.3203968554	0.3203968554	NUM
ejpam-6982	312	21	1	1	NUM
ejpam-6982	312	22	0.4513753799	0.4513753799	NUM
ejpam-6982	312	23	0.4513753799	0.4513753799	NUM
ejpam-6982	312	24	0.4271958072	0.4271958072	NUM
ejpam-6982	312	25	0.4	0.4	NUM
ejpam-6982	312	26	0.25	0.25	NUM
ejpam-6982	312	27	0.1640101327	0.1640101327	NUM
ejpam-6982	312	28	0.1640101327	0.1640101327	NUM
ejpam-6982	312	29	0.1257268756	0.1257268756	NUM
ejpam-6982	312	30	0.5	0.5	NUM
ejpam-6982	312	31	0.3280202655	0.3280202655	NUM
ejpam-6982	313	1	0.3280202655	0.3280202655	NUM
ejpam-6982	313	2	0.2514537512	0.2514537512	NUM
ejpam-6982	313	3	0.75	0.75	NUM
ejpam-6982	313	4	0.4920303982	0.4920303982	NUM
ejpam-6982	313	5	0.4920303982	0.4920303982	NUM
ejpam-6982	313	6	0.3771806267	0.3771806267	NUM
ejpam-6982	313	7	1	1	NUM
ejpam-6982	313	8	0.6560405310	0.6560405310	NUM
ejpam-6982	313	9	0.6560405310	0.6560405310	NUM
ejpam-6982	313	10	0.5029075023	0.5029075023	NUM
ejpam-6982	313	11	0.6	0.6	NUM
ejpam-6982	313	12	0.25	0.25	NUM
ejpam-6982	313	13	0.2440592839	0.2440592839	NUM
ejpam-6982	313	14	0.2440592839	0.2440592839	NUM
ejpam-6982	313	15	0.1176010458	0.1176010458	NUM
ejpam-6982	313	16	0.5	0.5	NUM
ejpam-6982	313	17	0.4881185678	0.4881185678	NUM
ejpam-6982	313	18	0.4881185678	0.4881185678	NUM
ejpam-6982	313	19	0.2352020917	0.2352020917	NUM
ejpam-6982	313	20	0.75	0.75	NUM
ejpam-6982	313	21	0.7321778516	0.7321778516	NUM
ejpam-6982	313	22	0.7321778516	0.7321778516	NUM
ejpam-6982	313	23	0.3528031375	0.3528031375	NUM
ejpam-6982	313	24	1	1	NUM
ejpam-6982	313	25	0.9762371355	0.9762371355	NUM
ejpam-6982	313	26	0.9762371355	0.9762371355	NUM
ejpam-6982	313	27	0.4704041833	0.4704041833	NUM
ejpam-6982	313	28	table	table	NOUN
ejpam-6982	313	29	2	2	NUM
ejpam-6982	313	30	:	:	PUNCT
ejpam-6982	313	31	numerical	numerical	ADJ
ejpam-6982	313	32	values	value	NOUN
ejpam-6982	313	33	when	when	SCONJ
ejpam-6982	313	34	α	α	X
ejpam-6982	313	35	=	=	PROPN
ejpam-6982	313	36	0.75	0.75	NUM
ejpam-6982	313	37	for	for	ADP
ejpam-6982	313	38	eq	eq	PROPN
ejpam-6982	313	39	.	.	PUNCT
ejpam-6982	313	40	(	(	PUNCT
ejpam-6982	313	41	30	30	NUM
ejpam-6982	313	42	)	)	PUNCT
ejpam-6982	313	43	.	.	PUNCT
ejpam-6982	314	1	t	t	NOUN
ejpam-6982	314	2	x	x	PUNCT
ejpam-6982	314	3	uadm	uadm	PROPN
ejpam-6982	314	4	undm	undm	PROPN
ejpam-6982	314	5	−	−	ADP
ejpam-6982	314	6	usdm	usdm	PROPN
ejpam-6982	314	7	umlvim	umlvim	ADJ
ejpam-6982	314	8	0.2	0.2	NUM
ejpam-6982	314	9	0.25	0.25	NUM
ejpam-6982	314	10	0.0787870110	0.0787870110	NUM
ejpam-6982	314	11	0.0787870110	0.0787870110	NUM
ejpam-6982	314	12	0.0784882208	0.0784882208	NUM
ejpam-6982	314	13	0.5	0.5	NUM
ejpam-6982	314	14	0.1575740220	0.1575740220	NUM
ejpam-6982	314	15	0.1575740220	0.1575740220	NUM
ejpam-6982	315	1	0.1569764416	0.1569764416	NUM
ejpam-6982	315	2	0.75	0.75	NUM
ejpam-6982	315	3	0.2363610330	0.2363610330	NUM
ejpam-6982	315	4	0.2363610330	0.2363610330	NUM
ejpam-6982	315	5	0.2354646624	0.2354646624	NUM
ejpam-6982	315	6	1	1	NUM
ejpam-6982	315	7	0.3151480440	0.3151480440	NUM
ejpam-6982	315	8	0.3151480440	0.3151480440	NUM
ejpam-6982	315	9	0.3139528832	0.3139528832	NUM
ejpam-6982	315	10	0.4	0.4	NUM
ejpam-6982	315	11	0.25	0.25	NUM
ejpam-6982	315	12	0.1289407026	0.1289407026	NUM
ejpam-6982	315	13	0.1289407026	0.1289407026	NUM
ejpam-6982	315	14	0.1245800056	0.1245800056	NUM
ejpam-6982	315	15	0.5	0.5	NUM
ejpam-6982	315	16	0.2578814051	0.2578814051	NUM
ejpam-6982	315	17	0.2578814051	0.2578814051	NUM
ejpam-6982	315	18	0.2491600112	0.2491600112	NUM
ejpam-6982	315	19	0.75	0.75	NUM
ejpam-6982	315	20	0.3868221077	0.3868221077	NUM
ejpam-6982	315	21	0.3868221077	0.3868221077	NUM
ejpam-6982	315	22	0.3737400168	0.3737400168	NUM
ejpam-6982	315	23	1	1	NUM
ejpam-6982	315	24	0.5157628102	0.5157628102	NUM
ejpam-6982	315	25	0.5157628102	0.5157628102	NUM
ejpam-6982	315	26	0.4983200224	0.4983200224	NUM
ejpam-6982	315	27	0.6	0.6	NUM
ejpam-6982	315	28	0.25	0.25	NUM
ejpam-6982	315	29	0.1772526142	0.1772526142	NUM
ejpam-6982	315	30	0.1772526142	0.1772526142	NUM
ejpam-6982	315	31	0.1544935814	0.1544935814	NUM
ejpam-6982	315	32	0.5	0.5	NUM
ejpam-6982	315	33	0.3545052283	0.3545052283	NUM
ejpam-6982	315	34	0.3545052283	0.3545052283	NUM
ejpam-6982	315	35	0.3089871628	0.3089871628	NUM
ejpam-6982	315	36	0.75	0.75	NUM
ejpam-6982	315	37	0.5317578425	0.5317578425	NUM
ejpam-6982	315	38	0.5317578425	0.5317578425	NUM
ejpam-6982	315	39	0.4634807443	0.4634807443	NUM
ejpam-6982	315	40	1	1	NUM
ejpam-6982	315	41	0.7090104566	0.7090104566	NUM
ejpam-6982	315	42	0.7090104566	0.7090104566	NUM
ejpam-6982	315	43	0.6179743257	0.6179743257	NUM
ejpam-6982	315	44	table	table	NOUN
ejpam-6982	315	45	3	3	NUM
ejpam-6982	315	46	:	:	PUNCT
ejpam-6982	315	47	numerical	numerical	ADJ
ejpam-6982	315	48	values	value	NOUN
ejpam-6982	315	49	when	when	SCONJ
ejpam-6982	315	50	α	α	PROPN
ejpam-6982	315	51	=	=	NOUN
ejpam-6982	315	52	1	1	NUM
ejpam-6982	315	53	for	for	ADP
ejpam-6982	315	54	eq	eq	PROPN
ejpam-6982	315	55	.	.	PUNCT
ejpam-6982	315	56	(	(	PUNCT
ejpam-6982	315	57	30	30	NUM
ejpam-6982	315	58	)	)	PUNCT
ejpam-6982	315	59	.	.	PUNCT
ejpam-6982	316	1	t	t	NOUN
ejpam-6982	316	2	x	x	PUNCT
ejpam-6982	316	3	uadm	uadm	PROPN
ejpam-6982	316	4	undm	undm	PROPN
ejpam-6982	316	5	−	−	ADP
ejpam-6982	316	6	usdm	usdm	VERB
ejpam-6982	316	7	umlvim	umlvim	ADJ
ejpam-6982	316	8	uexact	uexact	ADJ
ejpam-6982	316	9	0.2	0.2	NUM
ejpam-6982	316	10	0.25	0.25	NUM
ejpam-6982	316	11	0.0500001744	0.0500001744	NUM
ejpam-6982	316	12	0.0500001744	0.0500001744	NUM
ejpam-6982	316	13	0.0499892825	0.0499892825	NUM
ejpam-6982	316	14	0.0500000000	0.0500000000	NUM
ejpam-6982	316	15	0.5	0.5	NUM
ejpam-6982	316	16	0.1000003488	0.1000003488	NUM
ejpam-6982	316	17	0.1000003488	0.1000003488	NUM
ejpam-6982	316	18	0.0999785651	0.0999785651	NUM
ejpam-6982	316	19	0.1000000000	0.1000000000	NUM
ejpam-6982	316	20	0.75	0.75	NUM
ejpam-6982	316	21	0.1500005233	0.1500005233	NUM
ejpam-6982	316	22	0.1500005233	0.1500005233	NUM
ejpam-6982	316	23	0.1499678476	0.1499678476	NUM
ejpam-6982	316	24	0.1500000000	0.1500000000	NUM
ejpam-6982	316	25	1	1	NUM
ejpam-6982	316	26	0.2000006977	0.2000006977	NUM
ejpam-6982	316	27	0.2000006977	0.2000006977	NUM
ejpam-6982	316	28	0.1999571302	0.1999571302	NUM
ejpam-6982	316	29	0.2000000000	0.2000000000	NUM
ejpam-6982	316	30	0.4	0.4	NUM
ejpam-6982	316	31	0.25	0.25	NUM
ejpam-6982	316	32	0.1000229939	0.1000229939	NUM
ejpam-6982	316	33	0.1000229939	0.1000229939	NUM
ejpam-6982	316	34	0.0996521651	0.0996521651	NUM
ejpam-6982	316	35	0.1000000000	0.1000000000	NUM
ejpam-6982	316	36	0.5	0.5	NUM
ejpam-6982	316	37	0.2000459878	0.2000459878	NUM
ejpam-6982	316	38	0.2000459878	0.2000459878	NUM
ejpam-6982	316	39	0.1993043302	0.1993043302	NUM
ejpam-6982	316	40	0.2000000000	0.2000000000	NUM
ejpam-6982	316	41	0.75	0.75	NUM
ejpam-6982	316	42	0.3000689818	0.3000689818	NUM
ejpam-6982	316	43	0.3000689818	0.3000689818	NUM
ejpam-6982	316	44	0.2989564952	0.2989564952	NUM
ejpam-6982	316	45	0.3000000000	0.3000000000	NUM
ejpam-6982	316	46	1	1	NUM
ejpam-6982	316	47	0.4000919757	0.4000919757	NUM
ejpam-6982	316	48	0.4000919757	0.4000919757	NUM
ejpam-6982	316	49	0.3986086603	0.3986086603	NUM
ejpam-6982	316	50	0.4000000000	0.4000000000	NUM
ejpam-6982	316	51	0.6	0.6	NUM
ejpam-6982	316	52	0.25	0.25	NUM
ejpam-6982	316	53	0.1504123340	0.1504123340	NUM
ejpam-6982	316	54	0.1504123340	0.1504123340	NUM
ejpam-6982	316	55	0.1472969143	0.1472969143	NUM
ejpam-6982	316	56	0.1500000000	0.1500000000	NUM
ejpam-6982	316	57	0.5	0.5	NUM
ejpam-6982	316	58	0.3008246680	0.3008246680	NUM
ejpam-6982	316	59	0.3008246680	0.3008246680	NUM
ejpam-6982	316	60	0.2945938286	0.2945938286	NUM
ejpam-6982	316	61	0.3000000000	0.3000000000	NUM
ejpam-6982	316	62	0.75	0.75	NUM
ejpam-6982	316	63	0.4512370020	0.4512370020	NUM
ejpam-6982	316	64	0.4512370020	0.4512370020	NUM
ejpam-6982	316	65	0.4418907429	0.4418907429	NUM
ejpam-6982	316	66	0.4500000000	0.4500000000	NUM
ejpam-6982	316	67	1	1	NUM
ejpam-6982	316	68	0.6016493361	0.6016493361	NUM
ejpam-6982	316	69	0.6016493361	0.6016493361	NUM
ejpam-6982	316	70	0.5891876571	0.5891876571	NUM
ejpam-6982	316	71	0.6000000000	0.6000000000	NUM
ejpam-6982	316	72	a.	a.	NOUN
ejpam-6982	316	73	m.	m.	NOUN
ejpam-6982	316	74	alhammad	alhammad	PROPN
ejpam-6982	316	75	,	,	PUNCT
ejpam-6982	316	76	a.	a.	NOUN
ejpam-6982	316	77	m.	m.	PROPN
ejpam-6982	316	78	saeed	saeed	PROPN
ejpam-6982	316	79	/	/	SYM
ejpam-6982	316	80	eur	eur	PROPN
ejpam-6982	316	81	.	.	PUNCT
ejpam-6982	317	1	j.	j.	PROPN
ejpam-6982	317	2	pure	pure	PROPN
ejpam-6982	317	3	appl	appl	PROPN
ejpam-6982	317	4	.	.	PROPN
ejpam-6982	317	5	math	math	PROPN
ejpam-6982	317	6	,	,	PUNCT
ejpam-6982	317	7	18	18	NUM
ejpam-6982	317	8	(	(	PUNCT
ejpam-6982	317	9	4	4	NUM
ejpam-6982	317	10	)	)	PUNCT
ejpam-6982	317	11	(	(	PUNCT
ejpam-6982	317	12	2025	2025	NUM
ejpam-6982	317	13	)	)	PUNCT
ejpam-6982	317	14	,	,	PUNCT
ejpam-6982	317	15	6982	6982	NUM
ejpam-6982	317	16	13	13	NUM
ejpam-6982	317	17	of	of	ADP
ejpam-6982	317	18	22	22	NUM
ejpam-6982	317	19	table	table	NOUN
ejpam-6982	317	20	(	(	PUNCT
ejpam-6982	317	21	4	4	NUM
ejpam-6982	317	22	)	)	PUNCT
ejpam-6982	317	23	shows	show	VERB
ejpam-6982	317	24	the	the	DET
ejpam-6982	317	25	absolute	absolute	ADJ
ejpam-6982	317	26	error	error	NOUN
ejpam-6982	317	27	between	between	ADP
ejpam-6982	317	28	the	the	DET
ejpam-6982	317	29	exact	exact	ADJ
ejpam-6982	317	30	and	and	CCONJ
ejpam-6982	317	31	approximate	approximate	ADJ
ejpam-6982	317	32	solutions	solution	NOUN
ejpam-6982	317	33	for	for	ADP
ejpam-6982	317	34	eq	eq	PROPN
ejpam-6982	317	35	.	.	PUNCT
ejpam-6982	318	1	(	(	PUNCT
ejpam-6982	318	2	30	30	NUM
ejpam-6982	318	3	)	)	PUNCT
ejpam-6982	318	4	produced	produce	VERB
ejpam-6982	318	5	using	use	VERB
ejpam-6982	318	6	adomian	adomian	NOUN
ejpam-6982	318	7	decomposition	decomposition	NOUN
ejpam-6982	318	8	method	method	NOUN
ejpam-6982	318	9	and	and	CCONJ
ejpam-6982	318	10	modified	modify	VERB
ejpam-6982	318	11	laplace	laplace	NOUN
ejpam-6982	318	12	variational	variational	ADJ
ejpam-6982	318	13	iteration	iteration	NOUN
ejpam-6982	318	14	method	method	NOUN
ejpam-6982	318	15	.	.	PUNCT
ejpam-6982	319	1	the	the	DET
ejpam-6982	319	2	results	result	NOUN
ejpam-6982	319	3	are	be	AUX
ejpam-6982	319	4	computed	compute	VERB
ejpam-6982	319	5	after	after	ADP
ejpam-6982	319	6	applying	apply	VERB
ejpam-6982	319	7	three	three	NUM
ejpam-6982	319	8	iterations	iteration	NOUN
ejpam-6982	319	9	of	of	ADP
ejpam-6982	319	10	each	each	DET
ejpam-6982	319	11	method	method	NOUN
ejpam-6982	319	12	for	for	ADP
ejpam-6982	319	13	various	various	ADJ
ejpam-6982	319	14	values	value	NOUN
ejpam-6982	319	15	.	.	PUNCT
ejpam-6982	320	1	table	table	NOUN
ejpam-6982	320	2	4	4	NUM
ejpam-6982	320	3	:	:	PUNCT
ejpam-6982	320	4	the	the	DET
ejpam-6982	320	5	absolute	absolute	ADJ
ejpam-6982	320	6	error	error	NOUN
ejpam-6982	320	7	for	for	ADP
ejpam-6982	320	8	α	α	NOUN
ejpam-6982	320	9	=	=	SYM
ejpam-6982	320	10	1	1	NUM
ejpam-6982	320	11	for	for	ADP
ejpam-6982	320	12	eq	eq	PROPN
ejpam-6982	320	13	.	.	PUNCT
ejpam-6982	321	1	(	(	PUNCT
ejpam-6982	321	2	30	30	NUM
ejpam-6982	321	3	)	)	PUNCT
ejpam-6982	321	4	.	.	PUNCT
ejpam-6982	322	1	t	t	NOUN
ejpam-6982	322	2	x	x	PUNCT
ejpam-6982	322	3	uadm	uadm	NOUN
ejpam-6982	322	4	umlvim	umlvim	NOUN
ejpam-6982	322	5	0.2	0.2	NUM
ejpam-6982	322	6	0.25	0.25	NUM
ejpam-6982	322	7	0.0000001744	0.0000001744	NUM
ejpam-6982	322	8	0.0000107175	0.0000107175	NUM
ejpam-6982	322	9	0.5	0.5	NUM
ejpam-6982	322	10	0.0000003488	0.0000003488	NUM
ejpam-6982	322	11	0.0000214349	0.0000214349	NUM
ejpam-6982	322	12	0.75	0.75	NUM
ejpam-6982	322	13	0.0000005233	0.0000005233	NUM
ejpam-6982	322	14	0.0000321524	0.0000321524	NUM
ejpam-6982	322	15	1	1	NUM
ejpam-6982	322	16	0.0000006977	0.0000006977	NUM
ejpam-6982	322	17	0.0000428698	0.0000428698	NUM
ejpam-6982	322	18	0.4	0.4	NUM
ejpam-6982	322	19	0.25	0.25	NUM
ejpam-6982	322	20	0.0000229939	0.0000229939	NUM
ejpam-6982	322	21	0.0003478349	0.0003478349	NUM
ejpam-6982	322	22	0.5	0.5	NUM
ejpam-6982	322	23	0.0000459878	0.0000459878	NUM
ejpam-6982	322	24	0.0006956698	0.0006956698	NUM
ejpam-6982	322	25	0.75	0.75	NUM
ejpam-6982	322	26	0.0000689818	0.0000689818	NUM
ejpam-6982	322	27	0.0010435048	0.0010435048	NUM
ejpam-6982	322	28	1	1	NUM
ejpam-6982	322	29	0.0000919757	0.0000919757	NUM
ejpam-6982	322	30	0.0013913397	0.0013913397	NUM
ejpam-6982	322	31	0.6	0.6	NUM
ejpam-6982	322	32	0.25	0.25	NUM
ejpam-6982	322	33	0.0004123340	0.0004123340	NUM
ejpam-6982	322	34	0.0027030857	0.0027030857	NUM
ejpam-6982	322	35	0.5	0.5	NUM
ejpam-6982	322	36	0.0008246680	0.0008246680	NUM
ejpam-6982	322	37	0.0054061714	0.0054061714	NUM
ejpam-6982	322	38	0.75	0.75	NUM
ejpam-6982	322	39	0.0012370020	0.0012370020	NUM
ejpam-6982	322	40	0.0081092571	0.0081092571	NUM
ejpam-6982	322	41	1	1	NUM
ejpam-6982	322	42	0.0016493361	0.0016493361	NUM
ejpam-6982	322	43	0.0108123429	0.0108123429	NUM
ejpam-6982	322	44	figure	figure	NOUN
ejpam-6982	322	45	1	1	NUM
ejpam-6982	322	46	:	:	PUNCT
ejpam-6982	322	47	comparison	comparison	NOUN
ejpam-6982	322	48	of	of	ADP
ejpam-6982	322	49	adm	adm	PROPN
ejpam-6982	322	50	and	and	CCONJ
ejpam-6982	322	51	mlvim	mlvim	VERB
ejpam-6982	322	52	solution	solution	NOUN
ejpam-6982	322	53	for	for	ADP
ejpam-6982	322	54	the	the	DET
ejpam-6982	322	55	first	first	ADJ
ejpam-6982	322	56	three	three	NUM
ejpam-6982	322	57	approximations	approximation	NOUN
ejpam-6982	322	58	α	α	X
ejpam-6982	322	59	=	=	SYM
ejpam-6982	322	60	0.5	0.5	NUM
ejpam-6982	322	61	,	,	PUNCT
ejpam-6982	322	62	t	t	NOUN
ejpam-6982	322	63	=	=	NUM
ejpam-6982	322	64	0.2	0.2	NUM
ejpam-6982	322	65	,	,	PUNCT
ejpam-6982	322	66	with	with	ADP
ejpam-6982	322	67	x	x	X
ejpam-6982	323	1	=	=	SYM
ejpam-6982	323	2	0	0	NUM
ejpam-6982	323	3	:	:	SYM
ejpam-6982	323	4	1	1	NUM
ejpam-6982	323	5	,	,	PUNCT
ejpam-6982	323	6	for	for	ADP
ejpam-6982	323	7	equation	equation	NOUN
ejpam-6982	323	8	(	(	PUNCT
ejpam-6982	323	9	30	30	NUM
ejpam-6982	323	10	)	)	PUNCT
ejpam-6982	323	11	.	.	PUNCT
ejpam-6982	323	12	a.	a.	PROPN
ejpam-6982	323	13	m.	m.	PROPN
ejpam-6982	323	14	alhammad	alhammad	PROPN
ejpam-6982	323	15	,	,	PUNCT
ejpam-6982	323	16	a.	a.	NOUN
ejpam-6982	323	17	m.	m.	PROPN
ejpam-6982	323	18	saeed	saeed	PROPN
ejpam-6982	323	19	/	/	SYM
ejpam-6982	323	20	eur	eur	PROPN
ejpam-6982	323	21	.	.	PUNCT
ejpam-6982	324	1	j.	j.	PROPN
ejpam-6982	324	2	pure	pure	PROPN
ejpam-6982	324	3	appl	appl	PROPN
ejpam-6982	324	4	.	.	PROPN
ejpam-6982	324	5	math	math	PROPN
ejpam-6982	324	6	,	,	PUNCT
ejpam-6982	324	7	18	18	NUM
ejpam-6982	324	8	(	(	PUNCT
ejpam-6982	324	9	4	4	NUM
ejpam-6982	324	10	)	)	PUNCT
ejpam-6982	324	11	(	(	PUNCT
ejpam-6982	324	12	2025	2025	NUM
ejpam-6982	324	13	)	)	PUNCT
ejpam-6982	324	14	,	,	PUNCT
ejpam-6982	324	15	6982	6982	NUM
ejpam-6982	324	16	14	14	NUM
ejpam-6982	324	17	of	of	ADP
ejpam-6982	324	18	22	22	NUM
ejpam-6982	324	19	figure	figure	NOUN
ejpam-6982	324	20	2	2	NUM
ejpam-6982	324	21	:	:	PUNCT
ejpam-6982	324	22	comparison	comparison	NOUN
ejpam-6982	324	23	of	of	ADP
ejpam-6982	324	24	adm	adm	PROPN
ejpam-6982	324	25	and	and	CCONJ
ejpam-6982	324	26	mlvim	mlvim	VERB
ejpam-6982	324	27	solution	solution	NOUN
ejpam-6982	324	28	for	for	ADP
ejpam-6982	324	29	the	the	DET
ejpam-6982	324	30	first	first	ADJ
ejpam-6982	324	31	three	three	NUM
ejpam-6982	324	32	approximations	approximation	NOUN
ejpam-6982	324	33	α	α	NOUN
ejpam-6982	324	34	=	=	SYM
ejpam-6982	324	35	1	1	NUM
ejpam-6982	324	36	,	,	PUNCT
ejpam-6982	324	37	t	t	NOUN
ejpam-6982	324	38	=	=	SYM
ejpam-6982	324	39	0.6	0.6	NUM
ejpam-6982	324	40	,	,	PUNCT
ejpam-6982	324	41	with	with	ADP
ejpam-6982	324	42	x	x	X
ejpam-6982	325	1	=	=	SYM
ejpam-6982	325	2	0	0	NUM
ejpam-6982	325	3	:	:	SYM
ejpam-6982	325	4	1	1	NUM
ejpam-6982	325	5	,	,	PUNCT
ejpam-6982	325	6	for	for	ADP
ejpam-6982	325	7	equation	equation	NOUN
ejpam-6982	325	8	(	(	PUNCT
ejpam-6982	325	9	30	30	NUM
ejpam-6982	325	10	)	)	PUNCT
ejpam-6982	325	11	.	.	PUNCT
ejpam-6982	326	1	figure	figure	VERB
ejpam-6982	326	2	3	3	NUM
ejpam-6982	326	3	:	:	PUNCT
ejpam-6982	326	4	comparison	comparison	NOUN
ejpam-6982	326	5	of	of	ADP
ejpam-6982	326	6	the	the	DET
ejpam-6982	326	7	absolute	absolute	ADJ
ejpam-6982	326	8	error	error	NOUN
ejpam-6982	326	9	between	between	ADP
ejpam-6982	326	10	the	the	DET
ejpam-6982	326	11	adm	adm	PROPN
ejpam-6982	326	12	and	and	CCONJ
ejpam-6982	326	13	mlvim	mlvim	VERB
ejpam-6982	326	14	solution	solution	NOUN
ejpam-6982	326	15	for	for	ADP
ejpam-6982	326	16	the	the	DET
ejpam-6982	326	17	first	first	ADJ
ejpam-6982	326	18	three	three	NUM
ejpam-6982	326	19	approximations	approximation	NOUN
ejpam-6982	326	20	α	α	NOUN
ejpam-6982	326	21	=	=	SYM
ejpam-6982	326	22	1	1	NUM
ejpam-6982	326	23	,	,	PUNCT
ejpam-6982	326	24	t	t	NOUN
ejpam-6982	326	25	=	=	SYM
ejpam-6982	326	26	0.6	0.6	NUM
ejpam-6982	326	27	,	,	PUNCT
ejpam-6982	326	28	with	with	ADP
ejpam-6982	326	29	x	x	X
ejpam-6982	327	1	=	=	SYM
ejpam-6982	327	2	0	0	NUM
ejpam-6982	327	3	:	:	SYM
ejpam-6982	327	4	1	1	NUM
ejpam-6982	327	5	,	,	PUNCT
ejpam-6982	327	6	for	for	ADP
ejpam-6982	327	7	eq	eq	NOUN
ejpam-6982	327	8	.	.	PUNCT
ejpam-6982	327	9	(	(	PUNCT
ejpam-6982	327	10	30	30	NUM
ejpam-6982	327	11	)	)	PUNCT
ejpam-6982	327	12	.	.	PUNCT
ejpam-6982	327	13	example	example	NOUN
ejpam-6982	328	1	2	2	NUM
ejpam-6982	328	2	.	.	X
ejpam-6982	328	3	consider	consider	VERB
ejpam-6982	328	4	the	the	DET
ejpam-6982	328	5	nonlinear	nonlinear	ADJ
ejpam-6982	328	6	time	time	NOUN
ejpam-6982	328	7	-	-	PUNCT
ejpam-6982	328	8	fractional	fractional	ADJ
ejpam-6982	328	9	hyperbolic	hyperbolic	ADJ
ejpam-6982	328	10	partial	partial	ADJ
ejpam-6982	328	11	differential	differential	NOUN
ejpam-6982	328	12	equation	equation	NOUN
ejpam-6982	328	13	.	.	PUNCT
ejpam-6982	329	1	dαu(x	dαu(x	NOUN
ejpam-6982	329	2	,	,	PUNCT
ejpam-6982	329	3	t	t	PROPN
ejpam-6982	329	4	)	)	PUNCT
ejpam-6982	329	5	=	=	PUNCT
ejpam-6982	330	1	d	d	X
ejpam-6982	330	2	dx	dx	PROPN
ejpam-6982	330	3	(	(	PUNCT
ejpam-6982	330	4	u(x	u(x	PROPN
ejpam-6982	330	5	,	,	PUNCT
ejpam-6982	330	6	t	t	NOUN
ejpam-6982	330	7	)	)	PUNCT
ejpam-6982	330	8	u(x	u(x	PROPN
ejpam-6982	330	9	,	,	PUNCT
ejpam-6982	330	10	t	t	PROPN
ejpam-6982	330	11	)	)	PUNCT
ejpam-6982	330	12	dx	dx	PROPN
ejpam-6982	330	13	)	)	PUNCT
ejpam-6982	330	14	,	,	PUNCT
ejpam-6982	330	15	t	t	X
ejpam-6982	330	16	>	>	X
ejpam-6982	330	17	0	0	PROPN
ejpam-6982	330	18	,	,	PUNCT
ejpam-6982	330	19	x	x	X
ejpam-6982	330	20	∈	∈	PROPN
ejpam-6982	330	21	r	r	NOUN
ejpam-6982	330	22	,	,	PUNCT
ejpam-6982	330	23	1	1	NUM
ejpam-6982	330	24	<	<	X
ejpam-6982	330	25	α	α	PROPN
ejpam-6982	330	26	≤	≤	NUM
ejpam-6982	330	27	2	2	NUM
ejpam-6982	330	28	,	,	PUNCT
ejpam-6982	330	29	(	(	PUNCT
ejpam-6982	330	30	43	43	NUM
ejpam-6982	330	31	)	)	PUNCT
ejpam-6982	330	32	a.	a.	NOUN
ejpam-6982	330	33	m.	m.	NOUN
ejpam-6982	330	34	alhammad	alhammad	PROPN
ejpam-6982	330	35	,	,	PUNCT
ejpam-6982	330	36	a.	a.	NOUN
ejpam-6982	330	37	m.	m.	PROPN
ejpam-6982	330	38	saeed	saeed	PROPN
ejpam-6982	330	39	/	/	SYM
ejpam-6982	330	40	eur	eur	PROPN
ejpam-6982	330	41	.	.	PUNCT
ejpam-6982	331	1	j.	j.	PROPN
ejpam-6982	331	2	pure	pure	PROPN
ejpam-6982	331	3	appl	appl	PROPN
ejpam-6982	331	4	.	.	PROPN
ejpam-6982	331	5	math	math	PROPN
ejpam-6982	331	6	,	,	PUNCT
ejpam-6982	331	7	18	18	NUM
ejpam-6982	331	8	(	(	PUNCT
ejpam-6982	331	9	4	4	NUM
ejpam-6982	331	10	)	)	PUNCT
ejpam-6982	331	11	(	(	PUNCT
ejpam-6982	331	12	2025	2025	NUM
ejpam-6982	331	13	)	)	PUNCT
ejpam-6982	331	14	,	,	PUNCT
ejpam-6982	331	15	6982	6982	NUM
ejpam-6982	331	16	15	15	NUM
ejpam-6982	331	17	of	of	ADP
ejpam-6982	331	18	22	22	NUM
ejpam-6982	331	19	subject	subject	NOUN
ejpam-6982	331	20	to	to	ADP
ejpam-6982	331	21	the	the	DET
ejpam-6982	331	22	initial	initial	ADJ
ejpam-6982	331	23	condition	condition	NOUN
ejpam-6982	331	24	u(x	u(x	NOUN
ejpam-6982	331	25	,	,	PUNCT
ejpam-6982	331	26	0	0	NUM
ejpam-6982	331	27	)	)	PUNCT
ejpam-6982	331	28	=	=	SYM
ejpam-6982	331	29	x2	x2	PROPN
ejpam-6982	331	30	,	,	PUNCT
ejpam-6982	331	31	ut(x	ut(x	NOUN
ejpam-6982	331	32	,	,	PUNCT
ejpam-6982	331	33	0	0	NUM
ejpam-6982	331	34	)	)	PUNCT
ejpam-6982	331	35	=	=	SYM
ejpam-6982	332	1	−2x2	−2x2	PROPN
ejpam-6982	332	2	.	.	PUNCT
ejpam-6982	333	1	(	(	PUNCT
ejpam-6982	333	2	44	44	NUM
ejpam-6982	333	3	)	)	PUNCT
ejpam-6982	333	4	the	the	DET
ejpam-6982	333	5	values	value	NOUN
ejpam-6982	333	6	of	of	ADP
ejpam-6982	333	7	α	α	NOUN
ejpam-6982	333	8	=	=	SYM
ejpam-6982	333	9	2	2	NUM
ejpam-6982	333	10	is	be	AUX
ejpam-6982	333	11	the	the	DET
ejpam-6982	333	12	only	only	ADJ
ejpam-6982	333	13	case	case	NOUN
ejpam-6982	333	14	for	for	ADP
ejpam-6982	333	15	which	which	PRON
ejpam-6982	333	16	we	we	PRON
ejpam-6982	333	17	know	know	VERB
ejpam-6982	333	18	the	the	DET
ejpam-6982	333	19	exact	exact	ADJ
ejpam-6982	333	20	solution	solution	NOUN
ejpam-6982	333	21	u(x	u(x	NOUN
ejpam-6982	333	22	,	,	PUNCT
ejpam-6982	333	23	t	t	NOUN
ejpam-6982	333	24	)	)	PUNCT
ejpam-6982	333	25	=	=	PUNCT
ejpam-6982	334	1	(	(	PUNCT
ejpam-6982	334	2	x	x	SYM
ejpam-6982	334	3	t+	t+	NOUN
ejpam-6982	334	4	1	1	NUM
ejpam-6982	334	5	)	)	SYM
ejpam-6982	334	6	2	2	NUM
ejpam-6982	334	7	.	.	PUNCT
ejpam-6982	335	1	to	to	PART
ejpam-6982	335	2	solve	solve	VERB
ejpam-6982	335	3	the	the	DET
ejpam-6982	335	4	problem	problem	NOUN
ejpam-6982	335	5	using	use	VERB
ejpam-6982	335	6	the	the	DET
ejpam-6982	335	7	decomposition	decomposition	NOUN
ejpam-6982	335	8	method	method	NOUN
ejpam-6982	335	9	[	[	X
ejpam-6982	335	10	8	8	NUM
ejpam-6982	335	11	]	]	PUNCT
ejpam-6982	335	12	,	,	PUNCT
ejpam-6982	335	13	we	we	PRON
ejpam-6982	335	14	simply	simply	ADV
ejpam-6982	335	15	substitute	substitute	VERB
ejpam-6982	335	16	(	(	PUNCT
ejpam-6982	335	17	43	43	NUM
ejpam-6982	335	18	)	)	PUNCT
ejpam-6982	335	19	and	and	CCONJ
ejpam-6982	335	20	the	the	DET
ejpam-6982	335	21	initial	initial	ADJ
ejpam-6982	335	22	conditions	condition	NOUN
ejpam-6982	335	23	(	(	PUNCT
ejpam-6982	335	24	44	44	NUM
ejpam-6982	335	25	)	)	PUNCT
ejpam-6982	335	26	into	into	ADP
ejpam-6982	335	27	(	(	PUNCT
ejpam-6982	335	28	10	10	NUM
ejpam-6982	335	29	)	)	PUNCT
ejpam-6982	335	30	,	,	PUNCT
ejpam-6982	335	31	to	to	PART
ejpam-6982	335	32	obtain	obtain	VERB
ejpam-6982	335	33	the	the	DET
ejpam-6982	335	34	following	follow	VERB
ejpam-6982	335	35	recurrence	recurrence	NOUN
ejpam-6982	335	36	relation	relation	NOUN
ejpam-6982	335	37	.	.	PUNCT
ejpam-6982	336	1	u0(x	u0(x	PROPN
ejpam-6982	336	2	,	,	PUNCT
ejpam-6982	336	3	t	t	PROPN
ejpam-6982	336	4	)	)	PUNCT
ejpam-6982	336	5	=	=	SYM
ejpam-6982	336	6	u(x	u(x	NOUN
ejpam-6982	336	7	,	,	PUNCT
ejpam-6982	336	8	0	0	NUM
ejpam-6982	336	9	)	)	PUNCT
ejpam-6982	337	1	+	+	CCONJ
ejpam-6982	337	2	jα	jα	NOUN
ejpam-6982	337	3	(	(	PUNCT
ejpam-6982	337	4	x+	x+	X
ejpam-6982	337	5	xt2	xt2	PROPN
ejpam-6982	337	6	)	)	PUNCT
ejpam-6982	338	1	=	=	PUNCT
ejpam-6982	338	2	x	x	X
ejpam-6982	338	3	(	(	PUNCT
ejpam-6982	338	4	tα	tα	ADP
ejpam-6982	338	5	γ(α+	γ(α+	DET
ejpam-6982	338	6	1	1	NUM
ejpam-6982	338	7	)	)	PUNCT
ejpam-6982	339	1	+	+	NUM
ejpam-6982	339	2	2tα+2	2tα+2	NUM
ejpam-6982	339	3	γ(α+	γ(α+	DET
ejpam-6982	339	4	3	3	NUM
ejpam-6982	339	5	)	)	PUNCT
ejpam-6982	339	6	)	)	PUNCT
ejpam-6982	340	1	,	,	PUNCT
ejpam-6982	340	2	un+1(x	un+1(x	PROPN
ejpam-6982	340	3	,	,	PUNCT
ejpam-6982	340	4	t	t	PROPN
ejpam-6982	340	5	)	)	PUNCT
ejpam-6982	340	6	=	=	PUNCT
ejpam-6982	341	1	jα	jα	X
ejpam-6982	342	1	[	[	X
ejpam-6982	342	2	an	an	X
ejpam-6982	342	3	]	]	X
ejpam-6982	342	4	,	,	PUNCT
ejpam-6982	342	5	n	n	X
ejpam-6982	342	6	≥	≥	NOUN
ejpam-6982	342	7	0	0	NUM
ejpam-6982	342	8	,	,	PUNCT
ejpam-6982	342	9	(	(	PUNCT
ejpam-6982	342	10	45	45	NUM
ejpam-6982	342	11	)	)	PUNCT
ejpam-6982	342	12	where	where	SCONJ
ejpam-6982	342	13	an	an	PRON
ejpam-6982	342	14	are	be	AUX
ejpam-6982	342	15	the	the	DET
ejpam-6982	342	16	adomian	adomian	NOUN
ejpam-6982	342	17	polynomials	polynomial	NOUN
ejpam-6982	342	18	for	for	ADP
ejpam-6982	342	19	the	the	DET
ejpam-6982	342	20	nonlinear	nonlinear	ADJ
ejpam-6982	342	21	function	function	NOUN
ejpam-6982	342	22	n	n	NOUN
ejpam-6982	342	23	=	=	SYM
ejpam-6982	342	24	u(x	u(x	NOUN
ejpam-6982	342	25	,	,	PUNCT
ejpam-6982	342	26	t)ux(x	t)ux(x	ADV
ejpam-6982	342	27	,	,	PUNCT
ejpam-6982	342	28	t	t	PROPN
ejpam-6982	342	29	)	)	PUNCT
ejpam-6982	342	30	,	,	PUNCT
ejpam-6982	342	31	the	the	DET
ejpam-6982	342	32	few	few	ADJ
ejpam-6982	342	33	components	component	NOUN
ejpam-6982	342	34	of	of	ADP
ejpam-6982	342	35	adomian	adomian	NOUN
ejpam-6982	342	36	polynomials	polynomial	NOUN
ejpam-6982	342	37	,	,	PUNCT
ejpam-6982	342	38	are	be	AUX
ejpam-6982	342	39	given	give	VERB
ejpam-6982	342	40	by	by	ADP
ejpam-6982	342	41	[	[	PUNCT
ejpam-6982	342	42	9	9	NUM
ejpam-6982	342	43	]	]	X
ejpam-6982	342	44	a0	a0	NOUN
ejpam-6982	342	45	=	=	SYM
ejpam-6982	342	46	u0u0x	u0u0x	NUM
ejpam-6982	342	47	a1	a1	NOUN
ejpam-6982	342	48	=	=	SYM
ejpam-6982	342	49	u0xu1	u0xu1	NOUN
ejpam-6982	342	50	+	+	CCONJ
ejpam-6982	342	51	u0u1x	u0u1x	NUM
ejpam-6982	342	52	,	,	PUNCT
ejpam-6982	342	53	a2	a2	PROPN
ejpam-6982	342	54	=	=	SYM
ejpam-6982	342	55	u0xu2	u0xu2	PROPN
ejpam-6982	342	56	+	+	CCONJ
ejpam-6982	342	57	u1xu1	u1xu1	NOUN
ejpam-6982	342	58	+	+	CCONJ
ejpam-6982	342	59	u2xu0	u2xu0	NOUN
ejpam-6982	342	60	,	,	PUNCT
ejpam-6982	342	61	(	(	PUNCT
ejpam-6982	342	62	46	46	NUM
ejpam-6982	342	63	)	)	PUNCT
ejpam-6982	342	64	and	and	CCONJ
ejpam-6982	342	65	we	we	PRON
ejpam-6982	342	66	can	can	AUX
ejpam-6982	342	67	continue	continue	VERB
ejpam-6982	342	68	the	the	DET
ejpam-6982	342	69	calculations	calculation	NOUN
ejpam-6982	342	70	to	to	PART
ejpam-6982	342	71	find	find	VERB
ejpam-6982	342	72	a3	a3	NOUN
ejpam-6982	342	73	and	and	CCONJ
ejpam-6982	342	74	so	so	ADV
ejpam-6982	342	75	on	on	ADV
ejpam-6982	342	76	by	by	ADP
ejpam-6982	342	77	the	the	DET
ejpam-6982	342	78	same	same	ADJ
ejpam-6982	342	79	manner	manner	NOUN
ejpam-6982	342	80	.	.	PUNCT
ejpam-6982	343	1	in	in	ADP
ejpam-6982	343	2	view	view	NOUN
ejpam-6982	343	3	of	of	ADP
ejpam-6982	343	4	(	(	PUNCT
ejpam-6982	343	5	45	45	NUM
ejpam-6982	343	6	)	)	PUNCT
ejpam-6982	343	7	,	,	PUNCT
ejpam-6982	343	8	the	the	DET
ejpam-6982	343	9	first	first	ADJ
ejpam-6982	343	10	few	few	ADJ
ejpam-6982	343	11	components	component	NOUN
ejpam-6982	343	12	of	of	ADP
ejpam-6982	343	13	the	the	DET
ejpam-6982	343	14	decomposition	decomposition	NOUN
ejpam-6982	343	15	series	series	NOUN
ejpam-6982	343	16	are	be	AUX
ejpam-6982	343	17	derived	derive	VERB
ejpam-6982	343	18	as	as	SCONJ
ejpam-6982	343	19	follows	follow	VERB
ejpam-6982	343	20	u0(x	u0(x	PRON
ejpam-6982	343	21	,	,	PUNCT
ejpam-6982	343	22	t	t	PROPN
ejpam-6982	343	23	)	)	PUNCT
ejpam-6982	343	24	=	=	PUNCT
ejpam-6982	344	1	x2(1−	x2(1−	PROPN
ejpam-6982	344	2	2	2	NUM
ejpam-6982	344	3	t	t	NOUN
ejpam-6982	344	4	)	)	PUNCT
ejpam-6982	344	5	,	,	PUNCT
ejpam-6982	344	6	u1(x	u1(x	PROPN
ejpam-6982	344	7	,	,	PUNCT
ejpam-6982	344	8	t	t	PROPN
ejpam-6982	344	9	)	)	PUNCT
ejpam-6982	344	10	=	=	SYM
ejpam-6982	344	11	6x2	6x2	NUM
ejpam-6982	344	12	(	(	PUNCT
ejpam-6982	344	13	tα	tα	ADP
ejpam-6982	344	14	γ(α+	γ(α+	PRON
ejpam-6982	344	15	1	1	NUM
ejpam-6982	344	16	)	)	PUNCT
ejpam-6982	344	17	−	−	NOUN
ejpam-6982	344	18	4tα+1	4tα+1	NUM
ejpam-6982	344	19	γ(α+	γ(α+	DET
ejpam-6982	344	20	2	2	NUM
ejpam-6982	344	21	)	)	PUNCT
ejpam-6982	344	22	+	+	NUM
ejpam-6982	344	23	8tα+2	8tα+2	NUM
ejpam-6982	344	24	γ(α+	γ(α+	DET
ejpam-6982	344	25	3	3	NUM
ejpam-6982	344	26	)	)	PUNCT
ejpam-6982	344	27	)	)	PUNCT
ejpam-6982	344	28	,	,	PUNCT
ejpam-6982	344	29	(	(	PUNCT
ejpam-6982	344	30	47	47	NUM
ejpam-6982	344	31	)	)	PUNCT
ejpam-6982	344	32	u2(x	u2(x	PROPN
ejpam-6982	344	33	,	,	PUNCT
ejpam-6982	344	34	t	t	PROPN
ejpam-6982	344	35	)	)	PUNCT
ejpam-6982	345	1	=	=	SYM
ejpam-6982	345	2	72x2	72x2	NUM
ejpam-6982	345	3	(	(	PUNCT
ejpam-6982	345	4	t2α	t2α	NUM
ejpam-6982	345	5	γ(2α+	γ(2α+	NOUN
ejpam-6982	345	6	1	1	NUM
ejpam-6982	345	7	)	)	PUNCT
ejpam-6982	345	8	−	−	PROPN
ejpam-6982	345	9	4t2α+1	4t2α+1	NUM
ejpam-6982	345	10	γ(2α+	γ(2α+	NOUN
ejpam-6982	345	11	2	2	NUM
ejpam-6982	345	12	)	)	PUNCT
ejpam-6982	345	13	+	+	NUM
ejpam-6982	345	14	8t2α+2	8t2α+2	NUM
ejpam-6982	345	15	γ(2α+	γ(2α+	NOUN
ejpam-6982	345	16	3	3	NUM
ejpam-6982	345	17	)	)	PUNCT
ejpam-6982	345	18	−	−	PROPN
ejpam-6982	346	1	2γ(α+	2γ(α+	NUM
ejpam-6982	346	2	2)t2α+1	2)t2α+1	NOUN
ejpam-6982	346	3	γ(α+	γ(α+	DET
ejpam-6982	346	4	1)γ(2α+	1)γ(2α+	ADJ
ejpam-6982	346	5	2	2	NUM
ejpam-6982	346	6	)	)	PUNCT
ejpam-6982	346	7	,	,	PUNCT
ejpam-6982	347	1	+	+	CCONJ
ejpam-6982	347	2	8γ(α+	8γ(α+	NUM
ejpam-6982	347	3	3)t2α+2	3)t2α+2	NUM
ejpam-6982	347	4	γ(α+	γ(α+	DET
ejpam-6982	347	5	2)γ(2α+	2)γ(2α+	ADJ
ejpam-6982	347	6	3	3	NUM
ejpam-6982	347	7	)	)	PUNCT
ejpam-6982	347	8	−	−	PROPN
ejpam-6982	347	9	16γ(α+	16γ(α+	NUM
ejpam-6982	347	10	4)t2α+3	4)t2α+3	PROPN
ejpam-6982	347	11	γ(α+	γ(α+	DET
ejpam-6982	347	12	3)γ(2α+	3)γ(2α+	NUM
ejpam-6982	347	13	4	4	NUM
ejpam-6982	347	14	)	)	PUNCT
ejpam-6982	347	15	)	)	PUNCT
ejpam-6982	347	16	.	.	PUNCT
ejpam-6982	348	1	(	(	PUNCT
ejpam-6982	348	2	48	48	NUM
ejpam-6982	348	3	)	)	PUNCT
ejpam-6982	348	4	and	and	CCONJ
ejpam-6982	348	5	soon	soon	ADV
ejpam-6982	348	6	,	,	PUNCT
ejpam-6982	348	7	in	in	ADP
ejpam-6982	348	8	this	this	DET
ejpam-6982	348	9	manner	manner	NOUN
ejpam-6982	348	10	the	the	DET
ejpam-6982	348	11	rest	rest	NOUN
ejpam-6982	348	12	of	of	ADP
ejpam-6982	348	13	components	component	NOUN
ejpam-6982	348	14	of	of	ADP
ejpam-6982	348	15	the	the	DET
ejpam-6982	348	16	decomposition	decomposition	NOUN
ejpam-6982	348	17	series	series	NOUN
ejpam-6982	348	18	can	can	AUX
ejpam-6982	348	19	be	be	AUX
ejpam-6982	348	20	obtained	obtain	VERB
ejpam-6982	348	21	.	.	PUNCT
ejpam-6982	349	1	the	the	DET
ejpam-6982	349	2	first	first	ADJ
ejpam-6982	349	3	three	three	NUM
ejpam-6982	349	4	terms	term	NOUN
ejpam-6982	349	5	of	of	ADP
ejpam-6982	349	6	the	the	DET
ejpam-6982	349	7	decomposition	decomposition	NOUN
ejpam-6982	349	8	series	series	NOUN
ejpam-6982	349	9	(	(	PUNCT
ejpam-6982	349	10	6	6	NUM
ejpam-6982	349	11	)	)	PUNCT
ejpam-6982	349	12	are	be	AUX
ejpam-6982	349	13	given	give	VERB
ejpam-6982	349	14	by	by	ADP
ejpam-6982	349	15	.	.	PUNCT
ejpam-6982	350	1	u(x	u(x	PROPN
ejpam-6982	350	2	,	,	PUNCT
ejpam-6982	350	3	t	t	NOUN
ejpam-6982	350	4	)	)	PUNCT
ejpam-6982	351	1	=	=	NOUN
ejpam-6982	351	2	x2(1−	x2(1−	PROPN
ejpam-6982	351	3	2	2	NUM
ejpam-6982	351	4	t	t	NOUN
ejpam-6982	351	5	)	)	PUNCT
ejpam-6982	351	6	+	+	CCONJ
ejpam-6982	351	7	6x2	6x2	NUM
ejpam-6982	351	8	(	(	PUNCT
ejpam-6982	351	9	tα	tα	ADP
ejpam-6982	351	10	γ(α+	γ(α+	PRON
ejpam-6982	351	11	1	1	NUM
ejpam-6982	351	12	)	)	PUNCT
ejpam-6982	351	13	−	−	NOUN
ejpam-6982	351	14	4tα+1	4tα+1	NUM
ejpam-6982	351	15	γ(α+	γ(α+	DET
ejpam-6982	351	16	2	2	NUM
ejpam-6982	351	17	)	)	PUNCT
ejpam-6982	351	18	+	+	NUM
ejpam-6982	351	19	8tα+2	8tα+2	NUM
ejpam-6982	351	20	γ(α+	γ(α+	DET
ejpam-6982	351	21	3	3	NUM
ejpam-6982	351	22	)	)	PUNCT
ejpam-6982	351	23	)	)	PUNCT
ejpam-6982	352	1	+	+	CCONJ
ejpam-6982	352	2	72x2	72x2	NUM
ejpam-6982	352	3	(	(	PUNCT
ejpam-6982	352	4	t2α	t2α	NUM
ejpam-6982	352	5	γ(2α+	γ(2α+	NOUN
ejpam-6982	352	6	1	1	NUM
ejpam-6982	352	7	)	)	PUNCT
ejpam-6982	352	8	−	−	PROPN
ejpam-6982	352	9	4t2α+1	4t2α+1	NUM
ejpam-6982	352	10	γ(2α+	γ(2α+	NOUN
ejpam-6982	352	11	2	2	NUM
ejpam-6982	352	12	)	)	PUNCT
ejpam-6982	352	13	+	+	NUM
ejpam-6982	352	14	·	·	PUNCT
ejpam-6982	352	15	·	·	PUNCT
ejpam-6982	352	16	·	·	PUNCT
ejpam-6982	352	17	)	)	PUNCT
ejpam-6982	352	18	.	.	PUNCT
ejpam-6982	353	1	(	(	PUNCT
ejpam-6982	353	2	49	49	NUM
ejpam-6982	353	3	)	)	PUNCT
ejpam-6982	353	4	to	to	PART
ejpam-6982	353	5	solve	solve	VERB
ejpam-6982	353	6	the	the	DET
ejpam-6982	353	7	problem	problem	NOUN
ejpam-6982	353	8	using	use	VERB
ejpam-6982	353	9	the	the	DET
ejpam-6982	353	10	sumudu	sumudu	NOUN
ejpam-6982	353	11	decomposition	decomposition	NOUN
ejpam-6982	353	12	method	method	NOUN
ejpam-6982	353	13	[	[	X
ejpam-6982	353	14	12	12	NUM
ejpam-6982	353	15	]	]	PUNCT
ejpam-6982	353	16	,	,	PUNCT
ejpam-6982	353	17	we	we	PRON
ejpam-6982	353	18	simply	simply	ADV
ejpam-6982	353	19	substitute	substitute	VERB
ejpam-6982	353	20	(	(	PUNCT
ejpam-6982	353	21	43	43	NUM
ejpam-6982	353	22	)	)	PUNCT
ejpam-6982	353	23	and	and	CCONJ
ejpam-6982	353	24	the	the	DET
ejpam-6982	353	25	initial	initial	ADJ
ejpam-6982	353	26	conditions	condition	NOUN
ejpam-6982	353	27	(	(	PUNCT
ejpam-6982	353	28	44	44	NUM
ejpam-6982	353	29	)	)	PUNCT
ejpam-6982	353	30	into	into	ADP
ejpam-6982	353	31	(	(	PUNCT
ejpam-6982	353	32	16	16	NUM
ejpam-6982	353	33	)	)	PUNCT
ejpam-6982	353	34	,	,	PUNCT
ejpam-6982	353	35	to	to	PART
ejpam-6982	353	36	obtain	obtain	VERB
ejpam-6982	353	37	the	the	DET
ejpam-6982	353	38	following	follow	VERB
ejpam-6982	353	39	recurrence	recurrence	NOUN
ejpam-6982	353	40	relation	relation	NOUN
ejpam-6982	353	41	u0(x	u0(x	PROPN
ejpam-6982	353	42	,	,	PUNCT
ejpam-6982	353	43	t	t	PROPN
ejpam-6982	353	44	)	)	PUNCT
ejpam-6982	353	45	=	=	PUNCT
ejpam-6982	354	1	x2(1−	x2(1−	PROPN
ejpam-6982	354	2	2	2	NUM
ejpam-6982	354	3	t	t	NOUN
ejpam-6982	354	4	)	)	PUNCT
ejpam-6982	354	5	un+1(x	un+1(x	PROPN
ejpam-6982	354	6	,	,	PUNCT
ejpam-6982	354	7	t	t	PROPN
ejpam-6982	354	8	)	)	PUNCT
ejpam-6982	354	9	=	=	SYM
ejpam-6982	355	1	s−1	s−1	PROPN
ejpam-6982	355	2	(	(	PUNCT
ejpam-6982	355	3	uαs	uαs	PROPN
ejpam-6982	356	1	[	[	X
ejpam-6982	356	2	an	an	X
ejpam-6982	356	3	]	]	X
ejpam-6982	356	4	)	)	PUNCT
ejpam-6982	356	5	,	,	PUNCT
ejpam-6982	357	1	n	n	X
ejpam-6982	357	2	≥	≥	NOUN
ejpam-6982	357	3	1	1	NUM
ejpam-6982	357	4	.	.	PUNCT
ejpam-6982	358	1	(	(	PUNCT
ejpam-6982	358	2	50	50	NUM
ejpam-6982	358	3	)	)	PUNCT
ejpam-6982	358	4	a.	a.	NOUN
ejpam-6982	358	5	m.	m.	NOUN
ejpam-6982	358	6	alhammad	alhammad	PROPN
ejpam-6982	358	7	,	,	PUNCT
ejpam-6982	358	8	a.	a.	NOUN
ejpam-6982	358	9	m.	m.	PROPN
ejpam-6982	358	10	saeed	saeed	PROPN
ejpam-6982	358	11	/	/	SYM
ejpam-6982	358	12	eur	eur	PROPN
ejpam-6982	358	13	.	.	PUNCT
ejpam-6982	359	1	j.	j.	PROPN
ejpam-6982	359	2	pure	pure	PROPN
ejpam-6982	359	3	appl	appl	PROPN
ejpam-6982	359	4	.	.	PROPN
ejpam-6982	359	5	math	math	PROPN
ejpam-6982	359	6	,	,	PUNCT
ejpam-6982	359	7	18	18	NUM
ejpam-6982	359	8	(	(	PUNCT
ejpam-6982	359	9	4	4	NUM
ejpam-6982	359	10	)	)	PUNCT
ejpam-6982	359	11	(	(	PUNCT
ejpam-6982	359	12	2025	2025	NUM
ejpam-6982	359	13	)	)	PUNCT
ejpam-6982	359	14	,	,	PUNCT
ejpam-6982	359	15	6982	6982	NUM
ejpam-6982	359	16	16	16	NUM
ejpam-6982	359	17	of	of	ADP
ejpam-6982	359	18	22	22	NUM
ejpam-6982	359	19	in	in	ADP
ejpam-6982	359	20	view	view	NOUN
ejpam-6982	359	21	of	of	ADP
ejpam-6982	359	22	(	(	PUNCT
ejpam-6982	359	23	50	50	NUM
ejpam-6982	359	24	)	)	PUNCT
ejpam-6982	359	25	,	,	PUNCT
ejpam-6982	359	26	the	the	DET
ejpam-6982	359	27	first	first	ADJ
ejpam-6982	359	28	few	few	ADJ
ejpam-6982	359	29	components	component	NOUN
ejpam-6982	359	30	of	of	ADP
ejpam-6982	359	31	the	the	DET
ejpam-6982	359	32	decomposition	decomposition	NOUN
ejpam-6982	359	33	series	series	NOUN
ejpam-6982	359	34	are	be	AUX
ejpam-6982	359	35	derived	derive	VERB
ejpam-6982	359	36	as	as	SCONJ
ejpam-6982	359	37	follows	follow	VERB
ejpam-6982	359	38	u0(x	u0(x	PRON
ejpam-6982	359	39	,	,	PUNCT
ejpam-6982	359	40	t	t	PROPN
ejpam-6982	359	41	)	)	PUNCT
ejpam-6982	360	1	=	=	NOUN
ejpam-6982	360	2	x2(1−	x2(1−	PROPN
ejpam-6982	360	3	2	2	NUM
ejpam-6982	360	4	t	t	NOUN
ejpam-6982	360	5	)	)	PUNCT
ejpam-6982	360	6	,	,	PUNCT
ejpam-6982	360	7	where	where	SCONJ
ejpam-6982	360	8	u1(x	u1(x	NOUN
ejpam-6982	360	9	,	,	PUNCT
ejpam-6982	360	10	t	t	PROPN
ejpam-6982	360	11	)	)	PUNCT
ejpam-6982	360	12	and	and	CCONJ
ejpam-6982	360	13	u2(x	u2(x	PROPN
ejpam-6982	360	14	,	,	PUNCT
ejpam-6982	360	15	t	t	PROPN
ejpam-6982	360	16	)	)	PUNCT
ejpam-6982	360	17	as	as	SCONJ
ejpam-6982	360	18	written	write	VERB
ejpam-6982	360	19	in	in	ADP
ejpam-6982	360	20	equations	equation	NOUN
ejpam-6982	360	21	(	(	PUNCT
ejpam-6982	360	22	47	47	NUM
ejpam-6982	360	23	)	)	PUNCT
ejpam-6982	360	24	and	and	CCONJ
ejpam-6982	360	25	(	(	PUNCT
ejpam-6982	360	26	48	48	NUM
ejpam-6982	360	27	)	)	PUNCT
ejpam-6982	360	28	and	and	CCONJ
ejpam-6982	360	29	soon	soon	ADV
ejpam-6982	360	30	,	,	PUNCT
ejpam-6982	360	31	in	in	ADP
ejpam-6982	360	32	this	this	DET
ejpam-6982	360	33	manner	manner	NOUN
ejpam-6982	360	34	the	the	DET
ejpam-6982	360	35	rest	rest	NOUN
ejpam-6982	360	36	of	of	ADP
ejpam-6982	360	37	components	component	NOUN
ejpam-6982	360	38	of	of	ADP
ejpam-6982	360	39	the	the	DET
ejpam-6982	360	40	decomposition	decomposition	NOUN
ejpam-6982	360	41	series	series	NOUN
ejpam-6982	360	42	can	can	AUX
ejpam-6982	360	43	be	be	AUX
ejpam-6982	360	44	obtained	obtain	VERB
ejpam-6982	360	45	.	.	PUNCT
ejpam-6982	361	1	the	the	DET
ejpam-6982	361	2	first	first	ADJ
ejpam-6982	361	3	three	three	NUM
ejpam-6982	361	4	terms	term	NOUN
ejpam-6982	361	5	of	of	ADP
ejpam-6982	361	6	the	the	DET
ejpam-6982	361	7	decomposition	decomposition	NOUN
ejpam-6982	361	8	series	series	NOUN
ejpam-6982	361	9	(	(	PUNCT
ejpam-6982	361	10	6	6	NUM
ejpam-6982	361	11	)	)	PUNCT
ejpam-6982	361	12	are	be	AUX
ejpam-6982	361	13	given	give	VERB
ejpam-6982	361	14	by	by	ADP
ejpam-6982	361	15	u(x	u(x	NOUN
ejpam-6982	361	16	,	,	PUNCT
ejpam-6982	361	17	t	t	PROPN
ejpam-6982	361	18	)	)	PUNCT
ejpam-6982	361	19	=	=	SYM
ejpam-6982	361	20	eq.(49	eq.(49	PROPN
ejpam-6982	361	21	)	)	PUNCT
ejpam-6982	361	22	.	.	PUNCT
ejpam-6982	362	1	to	to	PART
ejpam-6982	362	2	solve	solve	VERB
ejpam-6982	362	3	the	the	DET
ejpam-6982	362	4	problem	problem	NOUN
ejpam-6982	362	5	using	use	VERB
ejpam-6982	362	6	the	the	DET
ejpam-6982	362	7	natural	natural	ADJ
ejpam-6982	362	8	decomposition	decomposition	NOUN
ejpam-6982	362	9	method	method	NOUN
ejpam-6982	362	10	,	,	PUNCT
ejpam-6982	362	11	we	we	PRON
ejpam-6982	362	12	simply	simply	ADV
ejpam-6982	362	13	substitute	substitute	VERB
ejpam-6982	362	14	(	(	PUNCT
ejpam-6982	362	15	43	43	NUM
ejpam-6982	362	16	)	)	PUNCT
ejpam-6982	362	17	and	and	CCONJ
ejpam-6982	362	18	the	the	DET
ejpam-6982	362	19	initial	initial	ADJ
ejpam-6982	362	20	conditions	condition	NOUN
ejpam-6982	362	21	(	(	PUNCT
ejpam-6982	362	22	44	44	NUM
ejpam-6982	362	23	)	)	PUNCT
ejpam-6982	362	24	into	into	ADP
ejpam-6982	362	25	(	(	PUNCT
ejpam-6982	362	26	22	22	NUM
ejpam-6982	362	27	)	)	PUNCT
ejpam-6982	362	28	,	,	PUNCT
ejpam-6982	362	29	to	to	PART
ejpam-6982	362	30	obtain	obtain	VERB
ejpam-6982	362	31	the	the	DET
ejpam-6982	362	32	following	follow	VERB
ejpam-6982	362	33	recurrence	recurrence	NOUN
ejpam-6982	362	34	relation	relation	NOUN
ejpam-6982	362	35	u0(x	u0(x	PROPN
ejpam-6982	362	36	,	,	PUNCT
ejpam-6982	362	37	t	t	PROPN
ejpam-6982	362	38	)	)	PUNCT
ejpam-6982	362	39	=	=	PUNCT
ejpam-6982	363	1	x2(1−	x2(1−	PROPN
ejpam-6982	363	2	2	2	NUM
ejpam-6982	363	3	t	t	NOUN
ejpam-6982	363	4	)	)	PUNCT
ejpam-6982	363	5	,	,	PUNCT
ejpam-6982	363	6	un+1(x	un+1(x	PROPN
ejpam-6982	363	7	,	,	PUNCT
ejpam-6982	363	8	t	t	PROPN
ejpam-6982	363	9	)	)	PUNCT
ejpam-6982	364	1	=	=	SYM
ejpam-6982	364	2	n−1	n−1	PROPN
ejpam-6982	364	3	(	(	PUNCT
ejpam-6982	364	4	uα	uα	PROPN
ejpam-6982	364	5	sα	sα	VERB
ejpam-6982	364	6	n	n	PROPN
ejpam-6982	364	7	[	[	X
ejpam-6982	364	8	an	an	X
ejpam-6982	364	9	]	]	X
ejpam-6982	364	10	)	)	PUNCT
ejpam-6982	364	11	,	,	PUNCT
ejpam-6982	364	12	n	n	X
ejpam-6982	364	13	≥	≥	NOUN
ejpam-6982	364	14	1	1	NUM
ejpam-6982	364	15	.	.	PUNCT
ejpam-6982	364	16	(	(	PUNCT
ejpam-6982	364	17	51	51	NUM
ejpam-6982	364	18	)	)	PUNCT
ejpam-6982	364	19	in	in	ADP
ejpam-6982	364	20	view	view	NOUN
ejpam-6982	364	21	of	of	ADP
ejpam-6982	364	22	(	(	PUNCT
ejpam-6982	364	23	51	51	NUM
ejpam-6982	364	24	)	)	PUNCT
ejpam-6982	364	25	,	,	PUNCT
ejpam-6982	364	26	the	the	DET
ejpam-6982	364	27	first	first	ADJ
ejpam-6982	364	28	few	few	ADJ
ejpam-6982	364	29	components	component	NOUN
ejpam-6982	364	30	of	of	ADP
ejpam-6982	364	31	the	the	DET
ejpam-6982	364	32	decomposition	decomposition	NOUN
ejpam-6982	364	33	series	series	NOUN
ejpam-6982	364	34	are	be	AUX
ejpam-6982	364	35	derived	derive	VERB
ejpam-6982	364	36	as	as	SCONJ
ejpam-6982	364	37	follows	follow	VERB
ejpam-6982	364	38	u0(x	u0(x	PRON
ejpam-6982	364	39	,	,	PUNCT
ejpam-6982	364	40	t	t	PROPN
ejpam-6982	364	41	)	)	PUNCT
ejpam-6982	365	1	=	=	NOUN
ejpam-6982	365	2	x2(1−	x2(1−	PROPN
ejpam-6982	365	3	2	2	NUM
ejpam-6982	365	4	t	t	NOUN
ejpam-6982	365	5	)	)	PUNCT
ejpam-6982	365	6	,	,	PUNCT
ejpam-6982	365	7	where	where	SCONJ
ejpam-6982	365	8	u1(x	u1(x	NOUN
ejpam-6982	365	9	,	,	PUNCT
ejpam-6982	365	10	t	t	PROPN
ejpam-6982	365	11	)	)	PUNCT
ejpam-6982	365	12	and	and	CCONJ
ejpam-6982	365	13	u2(x	u2(x	PROPN
ejpam-6982	365	14	,	,	PUNCT
ejpam-6982	365	15	t	t	PROPN
ejpam-6982	365	16	)	)	PUNCT
ejpam-6982	365	17	as	as	SCONJ
ejpam-6982	365	18	written	write	VERB
ejpam-6982	365	19	in	in	ADP
ejpam-6982	365	20	equations	equation	NOUN
ejpam-6982	365	21	(	(	PUNCT
ejpam-6982	365	22	47	47	NUM
ejpam-6982	365	23	)	)	PUNCT
ejpam-6982	365	24	and	and	CCONJ
ejpam-6982	365	25	(	(	PUNCT
ejpam-6982	365	26	48	48	NUM
ejpam-6982	365	27	)	)	PUNCT
ejpam-6982	365	28	and	and	CCONJ
ejpam-6982	365	29	soon	soon	ADV
ejpam-6982	365	30	,	,	PUNCT
ejpam-6982	365	31	in	in	ADP
ejpam-6982	365	32	this	this	DET
ejpam-6982	365	33	manner	manner	NOUN
ejpam-6982	365	34	the	the	DET
ejpam-6982	365	35	rest	rest	NOUN
ejpam-6982	365	36	of	of	ADP
ejpam-6982	365	37	components	component	NOUN
ejpam-6982	365	38	of	of	ADP
ejpam-6982	365	39	the	the	DET
ejpam-6982	365	40	decomposition	decomposition	NOUN
ejpam-6982	365	41	series	series	NOUN
ejpam-6982	365	42	can	can	AUX
ejpam-6982	365	43	be	be	AUX
ejpam-6982	365	44	obtained	obtain	VERB
ejpam-6982	365	45	.	.	PUNCT
ejpam-6982	366	1	the	the	DET
ejpam-6982	366	2	first	first	ADJ
ejpam-6982	366	3	three	three	NUM
ejpam-6982	366	4	terms	term	NOUN
ejpam-6982	366	5	of	of	ADP
ejpam-6982	366	6	the	the	DET
ejpam-6982	366	7	decomposition	decomposition	NOUN
ejpam-6982	366	8	series	series	NOUN
ejpam-6982	366	9	(	(	PUNCT
ejpam-6982	366	10	6	6	NUM
ejpam-6982	366	11	)	)	PUNCT
ejpam-6982	366	12	are	be	AUX
ejpam-6982	366	13	given	give	VERB
ejpam-6982	366	14	by	by	ADP
ejpam-6982	366	15	u(x	u(x	NOUN
ejpam-6982	366	16	,	,	PUNCT
ejpam-6982	366	17	t	t	PROPN
ejpam-6982	366	18	)	)	PUNCT
ejpam-6982	366	19	as	as	SCONJ
ejpam-6982	366	20	written	write	VERB
ejpam-6982	366	21	in	in	ADP
ejpam-6982	366	22	equation	equation	NOUN
ejpam-6982	366	23	(	(	PUNCT
ejpam-6982	366	24	49	49	NUM
ejpam-6982	366	25	)	)	PUNCT
ejpam-6982	366	26	.	.	PUNCT
ejpam-6982	367	1	to	to	PART
ejpam-6982	367	2	solve	solve	VERB
ejpam-6982	367	3	the	the	DET
ejpam-6982	367	4	problem	problem	NOUN
ejpam-6982	367	5	using	use	VERB
ejpam-6982	367	6	the	the	DET
ejpam-6982	367	7	modified	modify	VERB
ejpam-6982	367	8	laplace	laplace	NOUN
ejpam-6982	367	9	variational	variational	ADJ
ejpam-6982	367	10	iteration	iteration	NOUN
ejpam-6982	367	11	method	method	NOUN
ejpam-6982	367	12	[	[	X
ejpam-6982	367	13	14	14	NUM
ejpam-6982	367	14	]	]	PUNCT
ejpam-6982	367	15	,	,	PUNCT
ejpam-6982	367	16	by	by	ADP
ejpam-6982	367	17	enforcement	enforcement	NOUN
ejpam-6982	367	18	of	of	ADP
ejpam-6982	367	19	the	the	DET
ejpam-6982	367	20	laplace	laplace	NOUN
ejpam-6982	367	21	transform	transform	NOUN
ejpam-6982	367	22	to	to	ADP
ejpam-6982	367	23	the	the	DET
ejpam-6982	367	24	sides	side	NOUN
ejpam-6982	367	25	of	of	ADP
ejpam-6982	367	26	equation	equation	NOUN
ejpam-6982	367	27	(	(	PUNCT
ejpam-6982	367	28	43	43	NUM
ejpam-6982	367	29	)	)	PUNCT
ejpam-6982	367	30	and	and	CCONJ
ejpam-6982	367	31	using	use	VERB
ejpam-6982	367	32	the	the	DET
ejpam-6982	367	33	initial	initial	ADJ
ejpam-6982	367	34	conditions	condition	NOUN
ejpam-6982	367	35	(	(	PUNCT
ejpam-6982	367	36	44	44	NUM
ejpam-6982	367	37	)	)	PUNCT
ejpam-6982	367	38	,	,	PUNCT
ejpam-6982	367	39	we	we	PRON
ejpam-6982	367	40	get	get	VERB
ejpam-6982	367	41	sαl[u(x	sαl[u(x	NOUN
ejpam-6982	367	42	,	,	PUNCT
ejpam-6982	367	43	t)]−	t)]−	PRON
ejpam-6982	367	44	sα−1x2	sα−1x2	VERB
ejpam-6982	367	45	+	+	X
ejpam-6982	367	46	2sα−2x2	2sα−2x2	NOUN
ejpam-6982	367	47	=	=	SYM
ejpam-6982	367	48	l	l	NOUN
ejpam-6982	367	49	(	(	PUNCT
ejpam-6982	367	50	d	d	X
ejpam-6982	367	51	dx	dx	PROPN
ejpam-6982	367	52	(	(	PUNCT
ejpam-6982	367	53	u(x	u(x	PROPN
ejpam-6982	367	54	,	,	PUNCT
ejpam-6982	367	55	t	t	NOUN
ejpam-6982	367	56	)	)	PUNCT
ejpam-6982	367	57	u(x	u(x	PROPN
ejpam-6982	367	58	,	,	PUNCT
ejpam-6982	367	59	t	t	PROPN
ejpam-6982	367	60	)	)	PUNCT
ejpam-6982	367	61	dx	dx	PROPN
ejpam-6982	367	62	)	)	PUNCT
ejpam-6982	367	63	)	)	PUNCT
ejpam-6982	367	64	,	,	PUNCT
ejpam-6982	367	65	l[u(x	l[u(x	NOUN
ejpam-6982	367	66	,	,	PUNCT
ejpam-6982	367	67	t	t	PROPN
ejpam-6982	367	68	)	)	PUNCT
ejpam-6982	367	69	]	]	PUNCT
ejpam-6982	368	1	=	=	PUNCT
ejpam-6982	368	2	x2	x2	PROPN
ejpam-6982	368	3	s	s	PART
ejpam-6982	368	4	−	−	PROPN
ejpam-6982	368	5	2x2	2x2	NUM
ejpam-6982	368	6	s2	s2	PROPN
ejpam-6982	368	7	+	+	CCONJ
ejpam-6982	368	8	s−αl	s−αl	PROPN
ejpam-6982	368	9	(	(	PUNCT
ejpam-6982	368	10	d	d	X
ejpam-6982	368	11	dx	dx	PROPN
ejpam-6982	368	12	(	(	PUNCT
ejpam-6982	368	13	u(x	u(x	PROPN
ejpam-6982	368	14	,	,	PUNCT
ejpam-6982	368	15	t	t	NOUN
ejpam-6982	368	16	)	)	PUNCT
ejpam-6982	368	17	u(x	u(x	PROPN
ejpam-6982	368	18	,	,	PUNCT
ejpam-6982	368	19	t	t	PROPN
ejpam-6982	368	20	)	)	PUNCT
ejpam-6982	368	21	dx	dx	PROPN
ejpam-6982	368	22	)	)	PUNCT
ejpam-6982	368	23	)	)	PUNCT
ejpam-6982	368	24	,	,	PUNCT
ejpam-6982	368	25	u(x	u(x	PROPN
ejpam-6982	368	26	,	,	PUNCT
ejpam-6982	368	27	s	s	NOUN
ejpam-6982	368	28	)	)	PUNCT
ejpam-6982	368	29	=	=	SYM
ejpam-6982	369	1	x2	x2	PROPN
ejpam-6982	369	2	s	s	PART
ejpam-6982	369	3	−	−	PROPN
ejpam-6982	369	4	2x2	2x2	NUM
ejpam-6982	369	5	s2	s2	NOUN
ejpam-6982	369	6	+	+	CCONJ
ejpam-6982	369	7	(	(	PUNCT
ejpam-6982	369	8	1	1	NUM
ejpam-6982	369	9	sα	sα	ADJ
ejpam-6982	369	10	l	l	PROPN
ejpam-6982	369	11	(	(	PUNCT
ejpam-6982	369	12	u(x	u(x	NOUN
ejpam-6982	369	13	,	,	PUNCT
ejpam-6982	369	14	t)ux(x	t)ux(x	ADJ
ejpam-6982	369	15	,	,	PUNCT
ejpam-6982	369	16	t	t	PROPN
ejpam-6982	369	17	)	)	PUNCT
ejpam-6982	369	18	)	)	PUNCT
ejpam-6982	369	19	)	)	PUNCT
ejpam-6982	369	20	.	.	PUNCT
ejpam-6982	370	1	(	(	PUNCT
ejpam-6982	370	2	52	52	X
ejpam-6982	370	3	)	)	PUNCT
ejpam-6982	370	4	taking	take	VERB
ejpam-6982	370	5	the	the	DET
ejpam-6982	370	6	inverse	inverse	NOUN
ejpam-6982	370	7	laplace	laplace	NOUN
ejpam-6982	370	8	transform	transform	NOUN
ejpam-6982	370	9	to	to	ADP
ejpam-6982	370	10	the	the	DET
ejpam-6982	370	11	sides	side	NOUN
ejpam-6982	370	12	of	of	ADP
ejpam-6982	370	13	equation	equation	NOUN
ejpam-6982	370	14	(	(	PUNCT
ejpam-6982	370	15	52	52	NUM
ejpam-6982	370	16	)	)	PUNCT
ejpam-6982	370	17	,	,	PUNCT
ejpam-6982	370	18	we	we	PRON
ejpam-6982	370	19	obtain	obtain	VERB
ejpam-6982	370	20	u(x	u(x	NOUN
ejpam-6982	370	21	,	,	PUNCT
ejpam-6982	370	22	t	t	NOUN
ejpam-6982	370	23	)	)	PUNCT
ejpam-6982	370	24	=	=	SYM
ejpam-6982	371	1	x2	x2	NUM
ejpam-6982	372	1	−	−	PROPN
ejpam-6982	372	2	2x2t+	2x2t+	NUM
ejpam-6982	372	3	l−1	l−1	PROPN
ejpam-6982	372	4	(	(	PUNCT
ejpam-6982	372	5	s−αl	s−αl	PROPN
ejpam-6982	372	6	(	(	PUNCT
ejpam-6982	372	7	d	d	X
ejpam-6982	372	8	dx	dx	PROPN
ejpam-6982	372	9	(	(	PUNCT
ejpam-6982	372	10	u(x	u(x	PROPN
ejpam-6982	372	11	,	,	PUNCT
ejpam-6982	372	12	t	t	NOUN
ejpam-6982	372	13	)	)	PUNCT
ejpam-6982	372	14	u(x	u(x	PROPN
ejpam-6982	372	15	,	,	PUNCT
ejpam-6982	372	16	t	t	PROPN
ejpam-6982	372	17	)	)	PUNCT
ejpam-6982	372	18	dx	dx	PROPN
ejpam-6982	372	19	)	)	PUNCT
ejpam-6982	372	20	)	)	PUNCT
ejpam-6982	372	21	)	)	PUNCT
ejpam-6982	372	22	.	.	PUNCT
ejpam-6982	373	1	(	(	PUNCT
ejpam-6982	373	2	53	53	NUM
ejpam-6982	373	3	)	)	PUNCT
ejpam-6982	373	4	now	now	ADV
ejpam-6982	373	5	the	the	DET
ejpam-6982	373	6	new	new	ADJ
ejpam-6982	373	7	tactic	tactic	NOUN
ejpam-6982	373	8	of	of	ADP
ejpam-6982	373	9	the	the	DET
ejpam-6982	373	10	modified	modify	VERB
ejpam-6982	373	11	laplace	laplace	NOUN
ejpam-6982	373	12	variational	variational	ADJ
ejpam-6982	373	13	iteration	iteration	NOUN
ejpam-6982	373	14	technique	technique	NOUN
ejpam-6982	373	15	is	be	AUX
ejpam-6982	373	16	instituted	institute	VERB
ejpam-6982	373	17	on	on	ADP
ejpam-6982	373	18	(	(	PUNCT
ejpam-6982	373	19	27	27	NUM
ejpam-6982	373	20	)	)	PUNCT
ejpam-6982	373	21	from	from	ADP
ejpam-6982	373	22	equation	equation	NOUN
ejpam-6982	373	23	(	(	PUNCT
ejpam-6982	373	24	53	53	NUM
ejpam-6982	373	25	)	)	PUNCT
ejpam-6982	373	26	,	,	PUNCT
ejpam-6982	373	27	and	and	CCONJ
ejpam-6982	373	28	we	we	PRON
ejpam-6982	373	29	get	get	VERB
ejpam-6982	373	30	du(x	du(x	NOUN
ejpam-6982	373	31	,	,	PUNCT
ejpam-6982	373	32	t	t	PROPN
ejpam-6982	373	33	)	)	PUNCT
ejpam-6982	373	34	dt	dt	NOUN
ejpam-6982	374	1	=	=	PUNCT
ejpam-6982	374	2	d	d	NOUN
ejpam-6982	374	3	dt	dt	X
ejpam-6982	375	1	(	(	PUNCT
ejpam-6982	375	2	x2	x2	INTJ
ejpam-6982	375	3	−	−	PROPN
ejpam-6982	375	4	2x2	2x2	NUM
ejpam-6982	375	5	t	t	PROPN
ejpam-6982	375	6	)	)	PUNCT
ejpam-6982	376	1	+	+	CCONJ
ejpam-6982	376	2	d	d	X
ejpam-6982	376	3	dt	dt	X
ejpam-6982	376	4	(	(	PUNCT
ejpam-6982	376	5	l−1	l−1	PROPN
ejpam-6982	376	6	(	(	PUNCT
ejpam-6982	376	7	1	1	NUM
ejpam-6982	376	8	sα	sα	ADJ
ejpam-6982	376	9	l	l	PROPN
ejpam-6982	376	10	(	(	PUNCT
ejpam-6982	376	11	u(x	u(x	NOUN
ejpam-6982	376	12	,	,	PUNCT
ejpam-6982	376	13	t)ux(x	t)ux(x	ADJ
ejpam-6982	376	14	,	,	PUNCT
ejpam-6982	376	15	t	t	PROPN
ejpam-6982	376	16	)	)	PUNCT
ejpam-6982	376	17	)	)	PUNCT
ejpam-6982	376	18	)	)	PUNCT
ejpam-6982	376	19	)	)	PUNCT
ejpam-6982	376	20	.	.	PUNCT
ejpam-6982	377	1	(	(	PUNCT
ejpam-6982	377	2	54	54	NUM
ejpam-6982	377	3	)	)	PUNCT
ejpam-6982	377	4	a.	a.	NOUN
ejpam-6982	377	5	m.	m.	NOUN
ejpam-6982	377	6	alhammad	alhammad	PROPN
ejpam-6982	377	7	,	,	PUNCT
ejpam-6982	377	8	a.	a.	NOUN
ejpam-6982	377	9	m.	m.	PROPN
ejpam-6982	377	10	saeed	saeed	PROPN
ejpam-6982	377	11	/	/	SYM
ejpam-6982	377	12	eur	eur	PROPN
ejpam-6982	377	13	.	.	PUNCT
ejpam-6982	378	1	j.	j.	PROPN
ejpam-6982	378	2	pure	pure	PROPN
ejpam-6982	378	3	appl	appl	PROPN
ejpam-6982	378	4	.	.	PROPN
ejpam-6982	378	5	math	math	PROPN
ejpam-6982	378	6	,	,	PUNCT
ejpam-6982	378	7	18	18	NUM
ejpam-6982	378	8	(	(	PUNCT
ejpam-6982	378	9	4	4	NUM
ejpam-6982	378	10	)	)	PUNCT
ejpam-6982	378	11	(	(	PUNCT
ejpam-6982	378	12	2025	2025	NUM
ejpam-6982	378	13	)	)	PUNCT
ejpam-6982	378	14	,	,	PUNCT
ejpam-6982	378	15	6982	6982	NUM
ejpam-6982	378	16	17	17	NUM
ejpam-6982	378	17	of	of	ADP
ejpam-6982	378	18	22	22	NUM
ejpam-6982	378	19	we	we	PRON
ejpam-6982	378	20	simply	simply	ADV
ejpam-6982	378	21	substitute	substitute	VERB
ejpam-6982	378	22	equation	equation	NOUN
ejpam-6982	378	23	(	(	PUNCT
ejpam-6982	378	24	54	54	NUM
ejpam-6982	378	25	)	)	PUNCT
ejpam-6982	378	26	and	and	CCONJ
ejpam-6982	378	27	the	the	DET
ejpam-6982	378	28	initial	initial	ADJ
ejpam-6982	378	29	condition	condition	NOUN
ejpam-6982	378	30	equation	equation	NOUN
ejpam-6982	378	31	(	(	PUNCT
ejpam-6982	378	32	44	44	NUM
ejpam-6982	378	33	)	)	PUNCT
ejpam-6982	378	34	into	into	ADP
ejpam-6982	378	35	equation	equation	NOUN
ejpam-6982	378	36	(	(	PUNCT
ejpam-6982	378	37	29	29	NUM
ejpam-6982	378	38	)	)	PUNCT
ejpam-6982	378	39	;	;	PUNCT
ejpam-6982	378	40	by	by	ADP
ejpam-6982	378	41	the	the	DET
ejpam-6982	378	42	new	new	ADJ
ejpam-6982	378	43	modified	modify	VERB
ejpam-6982	378	44	function	function	NOUN
ejpam-6982	378	45	,	,	PUNCT
ejpam-6982	378	46	we	we	PRON
ejpam-6982	378	47	find	find	VERB
ejpam-6982	378	48	u0(x	u0(x	PRON
ejpam-6982	378	49	,	,	PUNCT
ejpam-6982	378	50	t	t	PROPN
ejpam-6982	378	51	)	)	PUNCT
ejpam-6982	379	1	=	=	NOUN
ejpam-6982	379	2	x2(1−	x2(1−	PROPN
ejpam-6982	379	3	2	2	NUM
ejpam-6982	379	4	t	t	NOUN
ejpam-6982	379	5	)	)	PUNCT
ejpam-6982	379	6	,	,	PUNCT
ejpam-6982	379	7	u1(x	u1(x	PROPN
ejpam-6982	379	8	,	,	PUNCT
ejpam-6982	379	9	t	t	PROPN
ejpam-6982	379	10	)	)	PUNCT
ejpam-6982	379	11	=	=	NOUN
ejpam-6982	379	12	x2(1−	x2(1−	PROPN
ejpam-6982	379	13	2	2	NUM
ejpam-6982	379	14	t	t	NOUN
ejpam-6982	379	15	)	)	PUNCT
ejpam-6982	379	16	+	+	CCONJ
ejpam-6982	379	17	6x2tα	6x2tα	NUM
ejpam-6982	379	18	γ(α+	γ(α+	DET
ejpam-6982	379	19	1	1	NUM
ejpam-6982	379	20	)	)	PUNCT
ejpam-6982	379	21	−	−	PROPN
ejpam-6982	379	22	24x2tα+1	24x2tα+1	NUM
ejpam-6982	380	1	γ(α+	γ(α+	DET
ejpam-6982	380	2	2	2	NUM
ejpam-6982	380	3	)	)	PUNCT
ejpam-6982	380	4	+	+	CCONJ
ejpam-6982	380	5	48x2tα+2	48x2tα+2	NUM
ejpam-6982	380	6	γ(α+	γ(α+	DET
ejpam-6982	380	7	3	3	NUM
ejpam-6982	380	8	)	)	PUNCT
ejpam-6982	380	9	,	,	PUNCT
ejpam-6982	380	10	u2(x	u2(x	PROPN
ejpam-6982	380	11	,	,	PUNCT
ejpam-6982	380	12	t	t	PROPN
ejpam-6982	380	13	)	)	PUNCT
ejpam-6982	381	1	=	=	NOUN
ejpam-6982	381	2	x2(1−	x2(1−	PROPN
ejpam-6982	381	3	2	2	NUM
ejpam-6982	381	4	t	t	NOUN
ejpam-6982	381	5	)	)	PUNCT
ejpam-6982	381	6	+	+	CCONJ
ejpam-6982	381	7	6x2	6x2	NUM
ejpam-6982	381	8	(	(	PUNCT
ejpam-6982	381	9	tα	tα	ADP
ejpam-6982	381	10	γ(α+	γ(α+	PRON
ejpam-6982	381	11	1	1	NUM
ejpam-6982	381	12	)	)	PUNCT
ejpam-6982	381	13	−	−	NOUN
ejpam-6982	381	14	3tα+1	3tα+1	NUM
ejpam-6982	381	15	γ(α+	γ(α+	DET
ejpam-6982	381	16	2	2	NUM
ejpam-6982	381	17	)	)	PUNCT
ejpam-6982	381	18	+	+	NUM
ejpam-6982	382	1	4tα+2	4tα+2	NUM
ejpam-6982	382	2	γ(α+	γ(α+	DET
ejpam-6982	382	3	3	3	NUM
ejpam-6982	382	4	)	)	PUNCT
ejpam-6982	382	5	+	+	NUM
ejpam-6982	382	6	12t2α	12t2α	NUM
ejpam-6982	382	7	γ(2α+	γ(2α+	NOUN
ejpam-6982	382	8	1	1	NUM
ejpam-6982	382	9	)	)	PUNCT
ejpam-6982	382	10	·	·	PUNCT
ejpam-6982	382	11	·	·	PUNCT
ejpam-6982	382	12	·	·	PUNCT
ejpam-6982	382	13	)	)	PUNCT
ejpam-6982	382	14	tables	table	NOUN
ejpam-6982	382	15	(	(	PUNCT
ejpam-6982	382	16	5	5	NUM
ejpam-6982	382	17	,	,	PUNCT
ejpam-6982	382	18	6	6	NUM
ejpam-6982	382	19	,	,	PUNCT
ejpam-6982	382	20	7	7	X
ejpam-6982	382	21	)	)	PUNCT
ejpam-6982	382	22	show	show	VERB
ejpam-6982	382	23	the	the	DET
ejpam-6982	382	24	approximate	approximate	ADJ
ejpam-6982	382	25	solutions	solution	NOUN
ejpam-6982	382	26	for	for	ADP
ejpam-6982	382	27	eq	eq	PROPN
ejpam-6982	382	28	.	.	PUNCT
ejpam-6982	383	1	(	(	PUNCT
ejpam-6982	383	2	43	43	NUM
ejpam-6982	383	3	)	)	PUNCT
ejpam-6982	383	4	obtained	obtain	VERB
ejpam-6982	383	5	for	for	ADP
ejpam-6982	383	6	different	different	ADJ
ejpam-6982	383	7	values	value	NOUN
ejpam-6982	383	8	of	of	ADP
ejpam-6982	383	9	a	a	PRON
ejpam-6982	383	10	using	use	VERB
ejpam-6982	383	11	the	the	DET
ejpam-6982	383	12	decomposition	decomposition	NOUN
ejpam-6982	383	13	method	method	NOUN
ejpam-6982	383	14	sumudu	sumudu	NOUN
ejpam-6982	383	15	decomposition	decomposition	NOUN
ejpam-6982	383	16	method	method	NOUN
ejpam-6982	383	17	,	,	PUNCT
ejpam-6982	383	18	natural	natural	ADJ
ejpam-6982	383	19	decomposition	decomposition	NOUN
ejpam-6982	383	20	method	method	NOUN
ejpam-6982	383	21	,	,	PUNCT
ejpam-6982	383	22	adomian	adomian	NOUN
ejpam-6982	383	23	decomposition	decomposition	NOUN
ejpam-6982	383	24	method	method	NOUN
ejpam-6982	383	25	and	and	CCONJ
ejpam-6982	383	26	modified	modify	VERB
ejpam-6982	383	27	laplace	laplace	NOUN
ejpam-6982	383	28	variational	variational	ADJ
ejpam-6982	383	29	iteration	iteration	NOUN
ejpam-6982	383	30	.	.	PUNCT
ejpam-6982	384	1	it	it	PRON
ejpam-6982	384	2	is	be	AUX
ejpam-6982	384	3	to	to	PART
ejpam-6982	384	4	be	be	AUX
ejpam-6982	384	5	noted	note	VERB
ejpam-6982	384	6	that	that	SCONJ
ejpam-6982	384	7	only	only	ADV
ejpam-6982	384	8	three	three	NUM
ejpam-6982	384	9	terms	term	NOUN
ejpam-6982	384	10	of	of	ADP
ejpam-6982	384	11	this	this	DET
ejpam-6982	384	12	decomposition	decomposition	NOUN
ejpam-6982	384	13	series	series	NOUN
ejpam-6982	384	14	and	and	CCONJ
ejpam-6982	384	15	the	the	DET
ejpam-6982	384	16	modified	modified	ADJ
ejpam-6982	384	17	laplace	laplace	NOUN
ejpam-6982	384	18	variational	variational	ADJ
ejpam-6982	384	19	iteration	iteration	NOUN
ejpam-6982	384	20	were	be	AUX
ejpam-6982	384	21	used	use	VERB
ejpam-6982	384	22	in	in	ADP
ejpam-6982	384	23	evaluating	evaluate	VERB
ejpam-6982	384	24	the	the	DET
ejpam-6982	384	25	approximate	approximate	ADJ
ejpam-6982	384	26	solutions	solution	NOUN
ejpam-6982	384	27	for	for	ADP
ejpam-6982	384	28	table	table	NOUN
ejpam-6982	384	29	(	(	PUNCT
ejpam-6982	384	30	5	5	NUM
ejpam-6982	384	31	,	,	PUNCT
ejpam-6982	384	32	6	6	NUM
ejpam-6982	384	33	,	,	PUNCT
ejpam-6982	384	34	7	7	NUM
ejpam-6982	384	35	)	)	PUNCT
ejpam-6982	384	36	.	.	PUNCT
ejpam-6982	385	1	the	the	DET
ejpam-6982	385	2	accuracy	accuracy	NOUN
ejpam-6982	385	3	can	can	AUX
ejpam-6982	385	4	be	be	AUX
ejpam-6982	385	5	improved	improve	VERB
ejpam-6982	385	6	by	by	ADP
ejpam-6982	385	7	computing	compute	VERB
ejpam-6982	385	8	more	more	ADJ
ejpam-6982	385	9	terms	term	NOUN
ejpam-6982	385	10	of	of	ADP
ejpam-6982	385	11	the	the	DET
ejpam-6982	385	12	approximate	approximate	ADJ
ejpam-6982	385	13	solution	solution	NOUN
ejpam-6982	385	14	table	table	NOUN
ejpam-6982	385	15	5	5	NUM
ejpam-6982	385	16	:	:	PUNCT
ejpam-6982	385	17	numerical	numerical	ADJ
ejpam-6982	385	18	values	value	NOUN
ejpam-6982	385	19	when	when	SCONJ
ejpam-6982	385	20	α	α	X
ejpam-6982	385	21	=	=	NOUN
ejpam-6982	385	22	1.5	1.5	NUM
ejpam-6982	385	23	for	for	ADP
ejpam-6982	385	24	eq	eq	NOUN
ejpam-6982	385	25	.	.	PUNCT
ejpam-6982	386	1	(	(	PUNCT
ejpam-6982	386	2	43	43	NUM
ejpam-6982	386	3	)	)	PUNCT
ejpam-6982	386	4	.	.	PUNCT
ejpam-6982	387	1	t	t	NOUN
ejpam-6982	387	2	x	x	PUNCT
ejpam-6982	387	3	uadm	uadm	PROPN
ejpam-6982	387	4	undm	undm	PROPN
ejpam-6982	387	5	−	−	ADP
ejpam-6982	387	6	usdm	usdm	PROPN
ejpam-6982	387	7	umlvim	umlvim	ADJ
ejpam-6982	387	8	0.2	0.2	NUM
ejpam-6982	387	9	0.25	0.25	NUM
ejpam-6982	387	10	0.0592832468	0.0592832468	NUM
ejpam-6982	387	11	0.0592832468	0.0592832468	NUM
ejpam-6982	387	12	0.0596734742	0.0596734742	NUM
ejpam-6982	387	13	0.5	0.5	NUM
ejpam-6982	387	14	0.2371329870	0.2371329870	NUM
ejpam-6982	387	15	0.2371329870	0.2371329870	NUM
ejpam-6982	387	16	0.2386938966	0.2386938966	NUM
ejpam-6982	387	17	0.75	0.75	NUM
ejpam-6982	387	18	0.5335492208	0.5335492208	NUM
ejpam-6982	387	19	0.5335492208	0.5335492208	NUM
ejpam-6982	387	20	0.5370612674	0.5370612674	NUM
ejpam-6982	387	21	1	1	NUM
ejpam-6982	387	22	0.9485319481	0.9485319481	NUM
ejpam-6982	387	23	0.9485319481	0.9485319481	NUM
ejpam-6982	387	24	0.9547755866	0.9547755866	NUM
ejpam-6982	387	25	0.4	0.4	NUM
ejpam-6982	387	26	0.25	0.25	NUM
ejpam-6982	388	1	0.0654118621	0.0654118621	NUM
ejpam-6982	388	2	0.0654118621	0.0654118621	NUM
ejpam-6982	388	3	0.0708846937	0.0708846937	NUM
ejpam-6982	388	4	0.5	0.5	NUM
ejpam-6982	388	5	0.2616474484	0.2616474484	NUM
ejpam-6982	388	6	0.2616474484	0.2616474484	NUM
ejpam-6982	388	7	0.2835387748	0.2835387748	NUM
ejpam-6982	388	8	0.75	0.75	NUM
ejpam-6982	388	9	0.5887067589	0.5887067589	NUM
ejpam-6982	388	10	0.5887067589	0.5887067589	NUM
ejpam-6982	388	11	0.6379622433	0.6379622433	NUM
ejpam-6982	388	12	1	1	NUM
ejpam-6982	388	13	1.0465897936	1.0465897936	NUM
ejpam-6982	388	14	1.0465897936	1.0465897936	NUM
ejpam-6982	388	15	1.1341550992	1.1341550992	NUM
ejpam-6982	388	16	0.6	0.6	NUM
ejpam-6982	388	17	0.25	0.25	NUM
ejpam-6982	388	18	0.0631775739	0.0631775739	NUM
ejpam-6982	388	19	0.0631775739	0.0631775739	NUM
ejpam-6982	388	20	0.0846789648	0.0846789648	NUM
ejpam-6982	388	21	0.5	0.5	NUM
ejpam-6982	388	22	0.2527102956	0.2527102956	NUM
ejpam-6982	388	23	0.2527102956	0.2527102956	NUM
ejpam-6982	388	24	0.3387158594	0.3387158594	NUM
ejpam-6982	388	25	0.75	0.75	NUM
ejpam-6982	388	26	0.5685981652	0.5685981652	NUM
ejpam-6982	388	27	0.5685981652	0.5685981652	NUM
ejpam-6982	388	28	0.7621106836	0.7621106836	NUM
ejpam-6982	388	29	1	1	NUM
ejpam-6982	388	30	1.0108411825	1.0108411825	NUM
ejpam-6982	388	31	1.0108411825	1.0108411825	NUM
ejpam-6982	388	32	1.3548634375	1.3548634375	NUM
ejpam-6982	388	33	a.	a.	NOUN
ejpam-6982	388	34	m.	m.	NOUN
ejpam-6982	388	35	alhammad	alhammad	PROPN
ejpam-6982	388	36	,	,	PUNCT
ejpam-6982	388	37	a.	a.	NOUN
ejpam-6982	388	38	m.	m.	PROPN
ejpam-6982	388	39	saeed	saeed	PROPN
ejpam-6982	388	40	/	/	SYM
ejpam-6982	388	41	eur	eur	PROPN
ejpam-6982	388	42	.	.	PUNCT
ejpam-6982	389	1	j.	j.	PROPN
ejpam-6982	389	2	pure	pure	PROPN
ejpam-6982	389	3	appl	appl	PROPN
ejpam-6982	389	4	.	.	PROPN
ejpam-6982	389	5	math	math	PROPN
ejpam-6982	389	6	,	,	PUNCT
ejpam-6982	389	7	18	18	NUM
ejpam-6982	389	8	(	(	PUNCT
ejpam-6982	389	9	4	4	NUM
ejpam-6982	389	10	)	)	PUNCT
ejpam-6982	389	11	(	(	PUNCT
ejpam-6982	389	12	2025	2025	NUM
ejpam-6982	389	13	)	)	PUNCT
ejpam-6982	389	14	,	,	PUNCT
ejpam-6982	389	15	6982	6982	NUM
ejpam-6982	389	16	18	18	NUM
ejpam-6982	389	17	of	of	ADP
ejpam-6982	389	18	22	22	NUM
ejpam-6982	389	19	table	table	NOUN
ejpam-6982	389	20	6	6	NUM
ejpam-6982	389	21	:	:	PUNCT
ejpam-6982	389	22	numerical	numerical	ADJ
ejpam-6982	389	23	values	value	NOUN
ejpam-6982	389	24	when	when	SCONJ
ejpam-6982	389	25	α	α	X
ejpam-6982	389	26	=	=	PROPN
ejpam-6982	389	27	1.75	1.75	NUM
ejpam-6982	389	28	for	for	ADP
ejpam-6982	389	29	eq	eq	PROPN
ejpam-6982	389	30	.	.	PUNCT
ejpam-6982	390	1	(	(	PUNCT
ejpam-6982	390	2	43	43	NUM
ejpam-6982	390	3	)	)	PUNCT
ejpam-6982	390	4	.	.	PUNCT
ejpam-6982	391	1	t	t	NOUN
ejpam-6982	391	2	x	x	PUNCT
ejpam-6982	391	3	uadm	uadm	PROPN
ejpam-6982	391	4	undm	undm	PROPN
ejpam-6982	391	5	−	−	ADP
ejpam-6982	391	6	usdm	usdm	PROPN
ejpam-6982	391	7	umlvim	umlvim	ADJ
ejpam-6982	392	1	0.2	0.2	NUM
ejpam-6982	392	2	0.25	0.25	NUM
ejpam-6982	392	3	0.0487012403	0.0487012403	NUM
ejpam-6982	392	4	0.0487012403	0.0487012403	NUM
ejpam-6982	392	5	0.0487471818	0.0487471818	NUM
ejpam-6982	392	6	0.5	0.5	NUM
ejpam-6982	392	7	0.1948049610	0.1948049610	NUM
ejpam-6982	392	8	0.1948049610	0.1948049610	NUM
ejpam-6982	392	9	0.1949887272	0.1949887272	NUM
ejpam-6982	392	10	0.75	0.75	NUM
ejpam-6982	392	11	0.4383111623	0.4383111623	NUM
ejpam-6982	392	12	0.4383111623	0.4383111623	NUM
ejpam-6982	392	13	0.4387246362	0.4387246362	NUM
ejpam-6982	392	14	1	1	NUM
ejpam-6982	392	15	0.7792198441	0.7792198441	NUM
ejpam-6982	392	16	0.7792198441	0.7792198441	NUM
ejpam-6982	392	17	0.7799549088	0.7799549088	NUM
ejpam-6982	392	18	0.4	0.4	NUM
ejpam-6982	392	19	0.25	0.25	NUM
ejpam-6982	392	20	0.0437480416	0.0437480416	NUM
ejpam-6982	392	21	0.0437480416	0.0437480416	NUM
ejpam-6982	392	22	0.0448869280	0.0448869280	NUM
ejpam-6982	392	23	0.5	0.5	NUM
ejpam-6982	392	24	0.1749921662	0.1749921662	NUM
ejpam-6982	392	25	0.1749921662	0.1749921662	NUM
ejpam-6982	392	26	0.1795477122	0.1795477122	NUM
ejpam-6982	392	27	0.75	0.75	NUM
ejpam-6982	392	28	0.3937323741	0.3937323741	NUM
ejpam-6982	392	29	0.3937323741	0.3937323741	NUM
ejpam-6982	392	30	0.4039823524	0.4039823524	NUM
ejpam-6982	392	31	1	1	NUM
ejpam-6982	392	32	0.6999686650	0.6999686650	NUM
ejpam-6982	392	33	0.6999686650	0.6999686650	NUM
ejpam-6982	392	34	0.7181908488	0.7181908488	NUM
ejpam-6982	392	35	0.6	0.6	NUM
ejpam-6982	392	36	0.25	0.25	NUM
ejpam-6982	392	37	0.0381836436	0.0381836436	NUM
ejpam-6982	392	38	0.0381836436	0.0381836436	NUM
ejpam-6982	392	39	0.0445168272	0.0445168272	NUM
ejpam-6982	392	40	0.5	0.5	NUM
ejpam-6982	392	41	0.1527345746	0.1527345746	NUM
ejpam-6982	392	42	0.1527345746	0.1527345746	NUM
ejpam-6982	392	43	0.1780673088	0.1780673088	NUM
ejpam-6982	392	44	0.75	0.75	NUM
ejpam-6982	392	45	0.3436527928	0.3436527928	NUM
ejpam-6982	392	46	0.3436527928	0.3436527928	NUM
ejpam-6982	392	47	0.4006514448	0.4006514448	NUM
ejpam-6982	392	48	1	1	NUM
ejpam-6982	392	49	0.610938298	0.610938298	NUM
ejpam-6982	392	50	0.610938298	0.610938298	NUM
ejpam-6982	392	51	0.7122692353	0.7122692353	NUM
ejpam-6982	392	52	table	table	NOUN
ejpam-6982	392	53	7	7	NUM
ejpam-6982	392	54	:	:	PUNCT
ejpam-6982	392	55	numerical	numerical	ADJ
ejpam-6982	392	56	values	value	NOUN
ejpam-6982	392	57	when	when	SCONJ
ejpam-6982	392	58	α	α	PROPN
ejpam-6982	392	59	=	=	SYM
ejpam-6982	392	60	2	2	NUM
ejpam-6982	392	61	for	for	ADP
ejpam-6982	392	62	eq	eq	NOUN
ejpam-6982	392	63	.	.	PUNCT
ejpam-6982	393	1	(	(	PUNCT
ejpam-6982	393	2	43	43	NUM
ejpam-6982	393	3	)	)	PUNCT
ejpam-6982	393	4	.	.	PUNCT
ejpam-6982	394	1	t	t	NOUN
ejpam-6982	394	2	x	x	PUNCT
ejpam-6982	394	3	uadm	uadm	PROPN
ejpam-6982	394	4	undm	undm	PROPN
ejpam-6982	394	5	−	−	ADP
ejpam-6982	394	6	usdm	usdm	VERB
ejpam-6982	394	7	umlvim	umlvim	ADJ
ejpam-6982	394	8	uexact	uexact	ADJ
ejpam-6982	394	9	0.2	0.2	NUM
ejpam-6982	394	10	0.25	0.25	NUM
ejpam-6982	394	11	0.0433950857	0.0433950857	NUM
ejpam-6982	394	12	0.0433950857	0.0433950857	NUM
ejpam-6982	394	13	0.0433999819	0.0433999819	NUM
ejpam-6982	394	14	0.0434027778	0.0434027778	NUM
ejpam-6982	394	15	0.5	0.5	NUM
ejpam-6982	394	16	0.1735803429	0.1735803429	NUM
ejpam-6982	394	17	0.1735803429	0.1735803429	NUM
ejpam-6982	394	18	0.1735999276	0.1735999276	NUM
ejpam-6982	394	19	0.1736111111	0.1736111111	NUM
ejpam-6982	394	20	0.75	0.75	NUM
ejpam-6982	394	21	0.3905557714	0.3905557714	NUM
ejpam-6982	394	22	0.3905557714	0.3905557714	NUM
ejpam-6982	394	23	0.3905998371	0.3905998371	NUM
ejpam-6982	394	24	0.3906250000	0.3906250000	NUM
ejpam-6982	394	25	1	1	NUM
ejpam-6982	394	26	0.6943213714	0.6943213714	NUM
ejpam-6982	394	27	0.6943213714	0.6943213714	NUM
ejpam-6982	394	28	0.6943997104	0.6943997104	NUM
ejpam-6982	394	29	0.6944444444	0.6944444444	NUM
ejpam-6982	394	30	0.4	0.4	NUM
ejpam-6982	394	31	0.25	0.25	NUM
ejpam-6982	394	32	0.0315669714	0.0315669714	NUM
ejpam-6982	394	33	0.0315669714	0.0315669714	NUM
ejpam-6982	394	34	0.0317794680	0.0317794680	NUM
ejpam-6982	394	35	0.0318877551	0.0318877551	NUM
ejpam-6982	394	36	0.5	0.5	NUM
ejpam-6982	394	37	0.1262678857	0.1262678857	NUM
ejpam-6982	394	38	0.1262678857	0.1262678857	NUM
ejpam-6982	394	39	0.1271178720	0.1271178720	NUM
ejpam-6982	394	40	0.1275510204	0.1275510204	NUM
ejpam-6982	394	41	0.75	0.75	NUM
ejpam-6982	394	42	0.2841027429	0.2841027429	NUM
ejpam-6982	394	43	0.2841027429	0.2841027429	NUM
ejpam-6982	394	44	0.2860152121	0.2860152121	NUM
ejpam-6982	395	1	0.2869897959	0.2869897959	NUM
ejpam-6982	395	2	1	1	NUM
ejpam-6982	395	3	0.5050715429	0.5050715429	NUM
ejpam-6982	395	4	0.5050715429	0.5050715429	NUM
ejpam-6982	395	5	0.5084714881	0.5084714881	NUM
ejpam-6982	395	6	0.5102040816	0.5102040816	NUM
ejpam-6982	395	7	0.6	0.6	NUM
ejpam-6982	395	8	0.25	0.25	NUM
ejpam-6982	395	9	0.0220044571	0.0220044571	NUM
ejpam-6982	395	10	0.0220044571	0.0220044571	NUM
ejpam-6982	395	11	0.0236648775	0.0236648775	NUM
ejpam-6982	395	12	0.0244140625	0.0244140625	NUM
ejpam-6982	395	13	0.5	0.5	NUM
ejpam-6982	395	14	0.0880178286	0.0880178286	NUM
ejpam-6982	395	15	0.0880178286	0.0880178286	VERB
ejpam-6982	395	16	0.0946595101	0.0946595101	NUM
ejpam-6982	395	17	0.0976562500	0.0976562500	NUM
ejpam-6982	395	18	0.75	0.75	NUM
ejpam-6982	395	19	0.1980401143	0.1980401143	NUM
ejpam-6982	395	20	0.1980401143	0.1980401143	NUM
ejpam-6982	395	21	0.2129838978	0.2129838978	NUM
ejpam-6982	395	22	0.2197265625	0.2197265625	NUM
ejpam-6982	395	23	1	1	NUM
ejpam-6982	395	24	0.3520713143	0.3520713143	NUM
ejpam-6982	395	25	0.3520713143	0.3520713143	NUM
ejpam-6982	395	26	0.3786380405	0.3786380405	NUM
ejpam-6982	395	27	0.3906250000	0.3906250000	NUM
ejpam-6982	395	28	table	table	NOUN
ejpam-6982	395	29	(	(	PUNCT
ejpam-6982	395	30	8)	8)	NUM
ejpam-6982	395	31	shows	show	VERB
ejpam-6982	395	32	the	the	DET
ejpam-6982	395	33	absolute	absolute	ADJ
ejpam-6982	395	34	error	error	NOUN
ejpam-6982	395	35	between	between	ADP
ejpam-6982	395	36	the	the	DET
ejpam-6982	395	37	exact	exact	ADJ
ejpam-6982	395	38	and	and	CCONJ
ejpam-6982	395	39	approximate	approximate	ADJ
ejpam-6982	395	40	solutions	solution	NOUN
ejpam-6982	395	41	for	for	ADP
ejpam-6982	395	42	eq	eq	PROPN
ejpam-6982	395	43	.	.	PUNCT
ejpam-6982	396	1	(	(	PUNCT
ejpam-6982	396	2	43	43	NUM
ejpam-6982	396	3	)	)	PUNCT
ejpam-6982	396	4	produced	produce	VERB
ejpam-6982	396	5	using	use	VERB
ejpam-6982	396	6	adomian	adomian	NOUN
ejpam-6982	396	7	decomposition	decomposition	NOUN
ejpam-6982	396	8	method	method	NOUN
ejpam-6982	396	9	and	and	CCONJ
ejpam-6982	396	10	modified	modify	VERB
ejpam-6982	396	11	laplace	laplace	NOUN
ejpam-6982	396	12	variational	variational	ADJ
ejpam-6982	396	13	iteration	iteration	NOUN
ejpam-6982	396	14	method	method	NOUN
ejpam-6982	396	15	.	.	PUNCT
ejpam-6982	397	1	the	the	DET
ejpam-6982	397	2	results	result	NOUN
ejpam-6982	397	3	are	be	AUX
ejpam-6982	397	4	computed	compute	VERB
ejpam-6982	397	5	after	after	ADP
ejpam-6982	397	6	applying	apply	VERB
ejpam-6982	397	7	three	three	NUM
ejpam-6982	397	8	iterations	iteration	NOUN
ejpam-6982	397	9	of	of	ADP
ejpam-6982	397	10	each	each	DET
ejpam-6982	397	11	method	method	NOUN
ejpam-6982	397	12	for	for	ADP
ejpam-6982	397	13	various	various	ADJ
ejpam-6982	397	14	values	value	NOUN
ejpam-6982	397	15	.	.	PUNCT
ejpam-6982	398	1	a.	a.	NOUN
ejpam-6982	398	2	m.	m.	PROPN
ejpam-6982	398	3	alhammad	alhammad	PROPN
ejpam-6982	398	4	,	,	PUNCT
ejpam-6982	398	5	a.	a.	NOUN
ejpam-6982	398	6	m.	m.	PROPN
ejpam-6982	398	7	saeed	saeed	PROPN
ejpam-6982	398	8	/	/	SYM
ejpam-6982	398	9	eur	eur	PROPN
ejpam-6982	398	10	.	.	PUNCT
ejpam-6982	399	1	j.	j.	PROPN
ejpam-6982	399	2	pure	pure	PROPN
ejpam-6982	399	3	appl	appl	PROPN
ejpam-6982	399	4	.	.	PROPN
ejpam-6982	399	5	math	math	PROPN
ejpam-6982	399	6	,	,	PUNCT
ejpam-6982	399	7	18	18	NUM
ejpam-6982	399	8	(	(	PUNCT
ejpam-6982	399	9	4	4	NUM
ejpam-6982	399	10	)	)	PUNCT
ejpam-6982	399	11	(	(	PUNCT
ejpam-6982	399	12	2025	2025	NUM
ejpam-6982	399	13	)	)	PUNCT
ejpam-6982	399	14	,	,	PUNCT
ejpam-6982	399	15	6982	6982	NUM
ejpam-6982	399	16	19	19	NUM
ejpam-6982	399	17	of	of	ADP
ejpam-6982	399	18	22	22	NUM
ejpam-6982	399	19	table	table	NOUN
ejpam-6982	399	20	8	8	NUM
ejpam-6982	399	21	:	:	PUNCT
ejpam-6982	399	22	the	the	DET
ejpam-6982	399	23	absolute	absolute	ADJ
ejpam-6982	399	24	error	error	NOUN
ejpam-6982	399	25	for	for	ADP
ejpam-6982	399	26	α	α	NOUN
ejpam-6982	399	27	=	=	SYM
ejpam-6982	399	28	2	2	NUM
ejpam-6982	399	29	for	for	ADP
ejpam-6982	399	30	eq	eq	NOUN
ejpam-6982	399	31	.	.	PUNCT
ejpam-6982	400	1	(	(	PUNCT
ejpam-6982	400	2	43	43	NUM
ejpam-6982	400	3	)	)	PUNCT
ejpam-6982	400	4	.	.	PUNCT
ejpam-6982	401	1	t	t	NOUN
ejpam-6982	401	2	x	x	PUNCT
ejpam-6982	401	3	uadm	uadm	NOUN
ejpam-6982	401	4	umlvim	umlvim	NOUN
ejpam-6982	401	5	0.2	0.2	NUM
ejpam-6982	401	6	0.25	0.25	NUM
ejpam-6982	401	7	0.0000076921	0.0000076921	NUM
ejpam-6982	401	8	0.0000027959	0.0000027959	NUM
ejpam-6982	401	9	0.5	0.5	NUM
ejpam-6982	401	10	0.0000307682	0.0000307682	NUM
ejpam-6982	401	11	0.0000111835	0.0000111835	NUM
ejpam-6982	401	12	0.75	0.75	NUM
ejpam-6982	401	13	0.0000692286	0.0000692286	NUM
ejpam-6982	401	14	0.0000251629	0.0000251629	NUM
ejpam-6982	401	15	1	1	NUM
ejpam-6982	401	16	0.0001230730	0.0001230730	NUM
ejpam-6982	401	17	0.0000447341	0.0000447341	NUM
ejpam-6982	401	18	0.4	0.4	NUM
ejpam-6982	401	19	0.25	0.25	NUM
ejpam-6982	401	20	0.0003207837	0.0003207837	NUM
ejpam-6982	401	21	0.0001082871	0.0001082871	NUM
ejpam-6982	401	22	0.5	0.5	NUM
ejpam-6982	401	23	0.0012831347	0.0012831347	NUM
ejpam-6982	401	24	0.0004331484	0.0004331484	NUM
ejpam-6982	401	25	0.75	0.75	NUM
ejpam-6982	401	26	0.0028870530	0.0028870530	NUM
ejpam-6982	401	27	0.0009745838	0.0009745838	NUM
ejpam-6982	401	28	1	1	NUM
ejpam-6982	401	29	0.0051325387	0.0051325387	NUM
ejpam-6982	402	1	0.0017325935	0.0017325935	NUM
ejpam-6982	402	2	0.6	0.6	NUM
ejpam-6982	402	3	0.25	0.25	NUM
ejpam-6982	402	4	0.0024096054	0.0024096054	NUM
ejpam-6982	402	5	0.0007491850	0.0007491850	NUM
ejpam-6982	402	6	0.5	0.5	NUM
ejpam-6982	402	7	0.0096384214	0.0096384214	NUM
ejpam-6982	402	8	0.0029967399	0.0029967399	NUM
ejpam-6982	402	9	0.75	0.75	NUM
ejpam-6982	402	10	0.0216864482	0.0216864482	NUM
ejpam-6982	402	11	0.0067426647	0.0067426647	NUM
ejpam-6982	402	12	1	1	NUM
ejpam-6982	402	13	0.0385536857	0.0385536857	NUM
ejpam-6982	402	14	0.0119869595	0.0119869595	NUM
ejpam-6982	402	15	figure	figure	NOUN
ejpam-6982	402	16	4	4	NUM
ejpam-6982	402	17	:	:	PUNCT
ejpam-6982	402	18	comparison	comparison	NOUN
ejpam-6982	402	19	of	of	ADP
ejpam-6982	402	20	adm	adm	PROPN
ejpam-6982	402	21	and	and	CCONJ
ejpam-6982	402	22	mlvim	mlvim	VERB
ejpam-6982	402	23	solution	solution	NOUN
ejpam-6982	402	24	for	for	ADP
ejpam-6982	402	25	the	the	DET
ejpam-6982	402	26	first	first	ADJ
ejpam-6982	402	27	three	three	NUM
ejpam-6982	402	28	approximations	approximation	NOUN
ejpam-6982	402	29	α	α	NOUN
ejpam-6982	402	30	=	=	SYM
ejpam-6982	402	31	1.5	1.5	NUM
ejpam-6982	402	32	,	,	PUNCT
ejpam-6982	402	33	t	t	NOUN
ejpam-6982	402	34	=	=	NUM
ejpam-6982	402	35	0.4	0.4	NUM
ejpam-6982	402	36	,	,	PUNCT
ejpam-6982	402	37	with	with	ADP
ejpam-6982	402	38	x	x	X
ejpam-6982	403	1	=	=	SYM
ejpam-6982	403	2	0	0	NUM
ejpam-6982	403	3	:	:	SYM
ejpam-6982	403	4	1	1	NUM
ejpam-6982	403	5	,	,	PUNCT
ejpam-6982	403	6	for	for	ADP
ejpam-6982	403	7	equation	equation	NOUN
ejpam-6982	403	8	(	(	PUNCT
ejpam-6982	403	9	43	43	NUM
ejpam-6982	403	10	)	)	PUNCT
ejpam-6982	403	11	.	.	PUNCT
ejpam-6982	404	1	a.	a.	PROPN
ejpam-6982	404	2	m.	m.	PROPN
ejpam-6982	404	3	alhammad	alhammad	PROPN
ejpam-6982	404	4	,	,	PUNCT
ejpam-6982	404	5	a.	a.	NOUN
ejpam-6982	404	6	m.	m.	PROPN
ejpam-6982	404	7	saeed	saeed	PROPN
ejpam-6982	404	8	/	/	SYM
ejpam-6982	404	9	eur	eur	PROPN
ejpam-6982	404	10	.	.	PUNCT
ejpam-6982	405	1	j.	j.	PROPN
ejpam-6982	405	2	pure	pure	PROPN
ejpam-6982	405	3	appl	appl	PROPN
ejpam-6982	405	4	.	.	PROPN
ejpam-6982	405	5	math	math	PROPN
ejpam-6982	405	6	,	,	PUNCT
ejpam-6982	405	7	18	18	NUM
ejpam-6982	405	8	(	(	PUNCT
ejpam-6982	405	9	4	4	NUM
ejpam-6982	405	10	)	)	PUNCT
ejpam-6982	405	11	(	(	PUNCT
ejpam-6982	405	12	2025	2025	NUM
ejpam-6982	405	13	)	)	PUNCT
ejpam-6982	405	14	,	,	PUNCT
ejpam-6982	405	15	6982	6982	NUM
ejpam-6982	405	16	20	20	NUM
ejpam-6982	405	17	of	of	ADP
ejpam-6982	405	18	22	22	NUM
ejpam-6982	405	19	figure	figure	NOUN
ejpam-6982	405	20	5	5	NUM
ejpam-6982	405	21	:	:	PUNCT
ejpam-6982	405	22	comparison	comparison	NOUN
ejpam-6982	405	23	of	of	ADP
ejpam-6982	405	24	adm	adm	PROPN
ejpam-6982	405	25	and	and	CCONJ
ejpam-6982	405	26	mlvim	mlvim	VERB
ejpam-6982	405	27	solution	solution	NOUN
ejpam-6982	405	28	for	for	ADP
ejpam-6982	405	29	the	the	DET
ejpam-6982	405	30	first	first	ADJ
ejpam-6982	405	31	three	three	NUM
ejpam-6982	405	32	approximations	approximation	NOUN
ejpam-6982	405	33	α	α	NOUN
ejpam-6982	405	34	=	=	SYM
ejpam-6982	405	35	2	2	NUM
ejpam-6982	405	36	,	,	PUNCT
ejpam-6982	405	37	t	t	NOUN
ejpam-6982	405	38	=	=	SYM
ejpam-6982	405	39	0.6	0.6	NUM
ejpam-6982	405	40	,	,	PUNCT
ejpam-6982	405	41	with	with	ADP
ejpam-6982	405	42	x	x	X
ejpam-6982	406	1	=	=	SYM
ejpam-6982	406	2	0	0	NUM
ejpam-6982	406	3	:	:	SYM
ejpam-6982	406	4	1	1	NUM
ejpam-6982	406	5	,	,	PUNCT
ejpam-6982	406	6	for	for	ADP
ejpam-6982	406	7	equation	equation	NOUN
ejpam-6982	406	8	(	(	PUNCT
ejpam-6982	406	9	43	43	NUM
ejpam-6982	406	10	)	)	PUNCT
ejpam-6982	406	11	.	.	PUNCT
ejpam-6982	407	1	figure	figure	VERB
ejpam-6982	407	2	6	6	NUM
ejpam-6982	407	3	:	:	PUNCT
ejpam-6982	407	4	comparison	comparison	NOUN
ejpam-6982	407	5	of	of	ADP
ejpam-6982	407	6	the	the	DET
ejpam-6982	407	7	absolute	absolute	ADJ
ejpam-6982	407	8	error	error	NOUN
ejpam-6982	407	9	between	between	ADP
ejpam-6982	407	10	the	the	DET
ejpam-6982	407	11	adm	adm	PROPN
ejpam-6982	407	12	and	and	CCONJ
ejpam-6982	407	13	mlvim	mlvim	VERB
ejpam-6982	407	14	solution	solution	NOUN
ejpam-6982	407	15	for	for	ADP
ejpam-6982	407	16	the	the	DET
ejpam-6982	407	17	first	first	ADJ
ejpam-6982	407	18	three	three	NUM
ejpam-6982	407	19	approximations	approximation	NOUN
ejpam-6982	407	20	α	α	NOUN
ejpam-6982	407	21	=	=	SYM
ejpam-6982	407	22	2	2	NUM
ejpam-6982	407	23	,	,	PUNCT
ejpam-6982	407	24	t	t	NOUN
ejpam-6982	407	25	=	=	SYM
ejpam-6982	407	26	0.6	0.6	NUM
ejpam-6982	407	27	,	,	PUNCT
ejpam-6982	407	28	with	with	ADP
ejpam-6982	407	29	x	x	X
ejpam-6982	408	1	=	=	SYM
ejpam-6982	408	2	0	0	NUM
ejpam-6982	408	3	:	:	SYM
ejpam-6982	408	4	1	1	NUM
ejpam-6982	408	5	,	,	PUNCT
ejpam-6982	408	6	for	for	ADP
ejpam-6982	408	7	eq	eq	NOUN
ejpam-6982	408	8	.	.	PUNCT
ejpam-6982	408	9	(	(	PUNCT
ejpam-6982	408	10	43	43	NUM
ejpam-6982	408	11	)	)	PUNCT
ejpam-6982	408	12	.	.	PUNCT
ejpam-6982	409	1	6	6	X
ejpam-6982	409	2	.	.	X
ejpam-6982	409	3	conclusions	conclusion	NOUN
ejpam-6982	409	4	the	the	DET
ejpam-6982	409	5	main	main	ADJ
ejpam-6982	409	6	objective	objective	NOUN
ejpam-6982	409	7	of	of	ADP
ejpam-6982	409	8	this	this	DET
ejpam-6982	409	9	article	article	NOUN
ejpam-6982	409	10	was	be	AUX
ejpam-6982	409	11	to	to	PART
ejpam-6982	409	12	investigate	investigate	VERB
ejpam-6982	409	13	an	an	DET
ejpam-6982	409	14	accurate	accurate	ADJ
ejpam-6982	409	15	approximate	approximate	ADJ
ejpam-6982	409	16	solutions	solution	NOUN
ejpam-6982	409	17	for	for	ADP
ejpam-6982	409	18	nonlinear	nonlinear	ADJ
ejpam-6982	409	19	partial	partial	ADJ
ejpam-6982	409	20	differential	differential	ADJ
ejpam-6982	409	21	equations	equation	NOUN
ejpam-6982	409	22	of	of	ADP
ejpam-6982	409	23	fractional	fractional	ADJ
ejpam-6982	409	24	order	order	NOUN
ejpam-6982	409	25	.	.	PUNCT
ejpam-6982	410	1	this	this	DET
ejpam-6982	410	2	goal	goal	NOUN
ejpam-6982	410	3	was	be	AUX
ejpam-6982	410	4	achieved	achieve	VERB
ejpam-6982	410	5	by	by	ADP
ejpam-6982	410	6	applying	apply	VERB
ejpam-6982	410	7	the	the	DET
ejpam-6982	410	8	modified	modify	VERB
ejpam-6982	410	9	laplace	laplace	NOUN
ejpam-6982	410	10	variational	variational	ADJ
ejpam-6982	410	11	iteration	iteration	NOUN
ejpam-6982	410	12	method	method	NOUN
ejpam-6982	410	13	and	and	CCONJ
ejpam-6982	410	14	three	three	NUM
ejpam-6982	410	15	variants	variant	NOUN
ejpam-6982	410	16	of	of	ADP
ejpam-6982	410	17	the	the	DET
ejpam-6982	410	18	adomian	adomian	NOUN
ejpam-6982	410	19	decomposition	decomposition	NOUN
ejpam-6982	410	20	method	method	NOUN
ejpam-6982	410	21	(	(	PUNCT
ejpam-6982	410	22	adm	adm	PROPN
ejpam-6982	410	23	):	):	PUNCT
ejpam-6982	410	24	the	the	DET
ejpam-6982	410	25	standard	standard	PROPN
ejpam-6982	410	26	adm	adm	PROPN
ejpam-6982	410	27	,	,	PUNCT
ejpam-6982	410	28	adm	adm	PROPN
ejpam-6982	410	29	with	with	ADP
ejpam-6982	410	30	the	the	DET
ejpam-6982	410	31	sumudu	sumudu	NOUN
ejpam-6982	410	32	transform	transform	NOUN
ejpam-6982	410	33	,	,	PUNCT
ejpam-6982	410	34	and	and	CCONJ
ejpam-6982	410	35	the	the	DET
ejpam-6982	410	36	natural	natural	ADJ
ejpam-6982	410	37	adm	adm	PROPN
ejpam-6982	410	38	.	.	PUNCT
ejpam-6982	411	1	all	all	DET
ejpam-6982	411	2	these	these	DET
ejpam-6982	411	3	methods	method	NOUN
ejpam-6982	411	4	yield	yield	VERB
ejpam-6982	411	5	solutions	solution	NOUN
ejpam-6982	411	6	expressed	express	VERB
ejpam-6982	411	7	as	as	ADP
ejpam-6982	411	8	convergent	convergent	NOUN
ejpam-6982	411	9	series	series	NOUN
ejpam-6982	411	10	that	that	PRON
ejpam-6982	411	11	are	be	AUX
ejpam-6982	411	12	straightforward	straightforward	ADJ
ejpam-6982	411	13	to	to	PART
ejpam-6982	411	14	compute	compute	VERB
ejpam-6982	411	15	.	.	PUNCT
ejpam-6982	412	1	there	there	PRON
ejpam-6982	412	2	are	be	VERB
ejpam-6982	412	3	two	two	NUM
ejpam-6982	412	4	key	key	ADJ
ejpam-6982	412	5	observations	observation	NOUN
ejpam-6982	412	6	to	to	PART
ejpam-6982	412	7	highlight	highlight	VERB
ejpam-6982	412	8	.	.	PUNCT
ejpam-6982	413	1	first	first	ADV
ejpam-6982	413	2	,	,	PUNCT
ejpam-6982	413	3	all	all	DET
ejpam-6982	413	4	three	three	NUM
ejpam-6982	413	5	variants	variant	NOUN
ejpam-6982	413	6	of	of	ADP
ejpam-6982	413	7	the	the	DET
ejpam-6982	413	8	adomian	adomian	NOUN
ejpam-6982	413	9	decomposition	decomposition	NOUN
ejpam-6982	413	10	method	method	NOUN
ejpam-6982	413	11	(	(	PUNCT
ejpam-6982	413	12	adm)—the	adm)—the	DET
ejpam-6982	413	13	standard	standard	PROPN
ejpam-6982	413	14	adm	adm	PROPN
ejpam-6982	413	15	,	,	PUNCT
ejpam-6982	413	16	adm	adm	PROPN
ejpam-6982	413	17	with	with	ADP
ejpam-6982	413	18	the	the	DET
ejpam-6982	413	19	sumudu	sumudu	NOUN
ejpam-6982	413	20	transform	transform	NOUN
ejpam-6982	413	21	,	,	PUNCT
ejpam-6982	413	22	and	and	CCONJ
ejpam-6982	413	23	the	the	DET
ejpam-6982	413	24	natural	natural	ADJ
ejpam-6982	413	25	adm	adm	PROPN
ejpam-6982	413	26	—	—	PUNCT
ejpam-6982	413	27	yielded	yield	VERB
ejpam-6982	413	28	identical	identical	ADJ
ejpam-6982	413	29	numerical	numerical	ADJ
ejpam-6982	413	30	solutions	solution	NOUN
ejpam-6982	413	31	and	and	CCONJ
ejpam-6982	413	32	convergence	convergence	NOUN
ejpam-6982	413	33	rates	rate	NOUN
ejpam-6982	413	34	.	.	PUNCT
ejpam-6982	414	1	this	this	PRON
ejpam-6982	414	2	demonstrates	demonstrate	VERB
ejpam-6982	414	3	their	their	PRON
ejpam-6982	414	4	equivalence	equivalence	NOUN
ejpam-6982	414	5	in	in	ADP
ejpam-6982	414	6	a.	a.	NOUN
ejpam-6982	414	7	m.	m.	NOUN
ejpam-6982	414	8	alhammad	alhammad	PROPN
ejpam-6982	414	9	,	,	PUNCT
ejpam-6982	414	10	a.	a.	NOUN
ejpam-6982	414	11	m.	m.	PROPN
ejpam-6982	414	12	saeed	saeed	PROPN
ejpam-6982	414	13	/	/	SYM
ejpam-6982	414	14	eur	eur	PROPN
ejpam-6982	414	15	.	.	PUNCT
ejpam-6982	415	1	j.	j.	PROPN
ejpam-6982	415	2	pure	pure	PROPN
ejpam-6982	415	3	appl	appl	PROPN
ejpam-6982	415	4	.	.	PROPN
ejpam-6982	415	5	math	math	PROPN
ejpam-6982	415	6	,	,	PUNCT
ejpam-6982	415	7	18	18	NUM
ejpam-6982	415	8	(	(	PUNCT
ejpam-6982	415	9	4	4	NUM
ejpam-6982	415	10	)	)	PUNCT
ejpam-6982	415	11	(	(	PUNCT
ejpam-6982	415	12	2025	2025	NUM
ejpam-6982	415	13	)	)	PUNCT
ejpam-6982	415	14	,	,	PUNCT
ejpam-6982	415	15	6982	6982	NUM
ejpam-6982	415	16	21	21	NUM
ejpam-6982	415	17	of	of	ADP
ejpam-6982	415	18	22	22	NUM
ejpam-6982	415	19	both	both	CCONJ
ejpam-6982	415	20	accuracy	accuracy	NOUN
ejpam-6982	415	21	and	and	CCONJ
ejpam-6982	415	22	efficiency	efficiency	NOUN
ejpam-6982	415	23	for	for	ADP
ejpam-6982	415	24	the	the	DET
ejpam-6982	415	25	cases	case	NOUN
ejpam-6982	415	26	studied	study	VERB
ejpam-6982	415	27	.	.	PUNCT
ejpam-6982	416	1	therefore	therefore	ADV
ejpam-6982	416	2	,	,	PUNCT
ejpam-6982	416	3	the	the	DET
ejpam-6982	416	4	choice	choice	NOUN
ejpam-6982	416	5	among	among	ADP
ejpam-6982	416	6	them	they	PRON
ejpam-6982	416	7	can	can	AUX
ejpam-6982	416	8	primarily	primarily	ADV
ejpam-6982	416	9	depend	depend	VERB
ejpam-6982	416	10	on	on	ADP
ejpam-6982	416	11	ease	ease	NOUN
ejpam-6982	416	12	of	of	ADP
ejpam-6982	416	13	implementation	implementation	NOUN
ejpam-6982	416	14	,	,	PUNCT
ejpam-6982	416	15	although	although	SCONJ
ejpam-6982	416	16	differences	difference	NOUN
ejpam-6982	416	17	may	may	AUX
ejpam-6982	416	18	emerge	emerge	VERB
ejpam-6982	416	19	for	for	ADP
ejpam-6982	416	20	more	more	ADJ
ejpam-6982	416	21	complex	complex	ADJ
ejpam-6982	416	22	problems	problem	NOUN
ejpam-6982	416	23	.	.	PUNCT
ejpam-6982	417	1	second	second	ADJ
ejpam-6982	417	2	,	,	PUNCT
ejpam-6982	417	3	in	in	ADP
ejpam-6982	417	4	example	example	NOUN
ejpam-6982	417	5	1	1	NUM
ejpam-6982	417	6	,	,	PUNCT
ejpam-6982	417	7	the	the	DET
ejpam-6982	417	8	decomposition	decomposition	NOUN
ejpam-6982	417	9	method	method	NOUN
ejpam-6982	417	10	provided	provide	VERB
ejpam-6982	417	11	a	a	DET
ejpam-6982	417	12	faster	fast	ADV
ejpam-6982	417	13	-	-	PUNCT
ejpam-6982	417	14	converging	converge	VERB
ejpam-6982	417	15	approximate	approximate	ADJ
ejpam-6982	417	16	solution	solution	NOUN
ejpam-6982	417	17	than	than	ADP
ejpam-6982	417	18	the	the	DET
ejpam-6982	417	19	modified	modify	VERB
ejpam-6982	417	20	laplace	laplace	NOUN
ejpam-6982	417	21	variational	variational	ADJ
ejpam-6982	417	22	iteration	iteration	NOUN
ejpam-6982	417	23	method	method	NOUN
ejpam-6982	417	24	.	.	PUNCT
ejpam-6982	418	1	conversely	conversely	ADV
ejpam-6982	418	2	,	,	PUNCT
ejpam-6982	418	3	in	in	ADP
ejpam-6982	418	4	example	example	NOUN
ejpam-6982	418	5	2	2	NUM
ejpam-6982	418	6	,	,	PUNCT
ejpam-6982	418	7	the	the	DET
ejpam-6982	418	8	modified	modify	VERB
ejpam-6982	418	9	laplace	laplace	NOUN
ejpam-6982	418	10	variational	variational	ADJ
ejpam-6982	418	11	iteration	iteration	NOUN
ejpam-6982	418	12	method	method	NOUN
ejpam-6982	418	13	showed	show	VERB
ejpam-6982	418	14	faster	fast	ADJ
ejpam-6982	418	15	convergence	convergence	NOUN
ejpam-6982	418	16	toward	toward	ADP
ejpam-6982	418	17	the	the	DET
ejpam-6982	418	18	exact	exact	ADJ
ejpam-6982	418	19	solution	solution	NOUN
ejpam-6982	418	20	than	than	ADP
ejpam-6982	418	21	the	the	DET
ejpam-6982	418	22	decomposition	decomposition	NOUN
ejpam-6982	418	23	method	method	NOUN
ejpam-6982	418	24	.	.	PUNCT
ejpam-6982	419	1	hence	hence	ADV
ejpam-6982	419	2	,	,	PUNCT
ejpam-6982	419	3	the	the	DET
ejpam-6982	419	4	accuracy	accuracy	NOUN
ejpam-6982	419	5	and	and	CCONJ
ejpam-6982	419	6	performance	performance	NOUN
ejpam-6982	419	7	of	of	ADP
ejpam-6982	419	8	these	these	DET
ejpam-6982	419	9	methods	method	NOUN
ejpam-6982	419	10	depend	depend	VERB
ejpam-6982	419	11	on	on	ADP
ejpam-6982	419	12	the	the	DET
ejpam-6982	419	13	specific	specific	ADJ
ejpam-6982	419	14	nonlinear	nonlinear	ADJ
ejpam-6982	419	15	fractional	fractional	ADJ
ejpam-6982	419	16	differential	differential	ADJ
ejpam-6982	419	17	equation	equation	NOUN
ejpam-6982	419	18	under	under	ADP
ejpam-6982	419	19	consideration	consideration	NOUN
ejpam-6982	419	20	.	.	PUNCT
ejpam-6982	420	1	both	both	DET
ejpam-6982	420	2	approaches	approach	NOUN
ejpam-6982	420	3	can	can	AUX
ejpam-6982	420	4	thus	thus	ADV
ejpam-6982	420	5	serve	serve	VERB
ejpam-6982	420	6	as	as	ADP
ejpam-6982	420	7	effective	effective	ADJ
ejpam-6982	420	8	alternatives	alternative	NOUN
ejpam-6982	420	9	for	for	ADP
ejpam-6982	420	10	solving	solve	VERB
ejpam-6982	420	11	fractional	fractional	ADJ
ejpam-6982	420	12	partial	partial	ADJ
ejpam-6982	420	13	differential	differential	NOUN
ejpam-6982	420	14	equations	equation	NOUN
ejpam-6982	420	15	.	.	PUNCT
ejpam-6982	421	1	these	these	DET
ejpam-6982	421	2	findings	finding	NOUN
ejpam-6982	421	3	are	be	AUX
ejpam-6982	421	4	consistent	consistent	ADJ
ejpam-6982	421	5	with	with	ADP
ejpam-6982	421	6	previously	previously	ADV
ejpam-6982	421	7	reported	report	VERB
ejpam-6982	421	8	results	result	NOUN
ejpam-6982	421	9	[	[	X
ejpam-6982	421	10	8	8	NUM
ejpam-6982	421	11	,	,	PUNCT
ejpam-6982	421	12	14	14	NUM
ejpam-6982	421	13	]	]	PUNCT
ejpam-6982	421	14	.	.	PUNCT
ejpam-6982	422	1	the	the	DET
ejpam-6982	422	2	future	future	ADJ
ejpam-6982	422	3	work	work	NOUN
ejpam-6982	422	4	of	of	ADP
ejpam-6982	422	5	this	this	DET
ejpam-6982	422	6	study	study	NOUN
ejpam-6982	422	7	can	can	AUX
ejpam-6982	422	8	be	be	AUX
ejpam-6982	422	9	extended	extend	VERB
ejpam-6982	422	10	in	in	ADP
ejpam-6982	422	11	several	several	ADJ
ejpam-6982	422	12	directions	direction	NOUN
ejpam-6982	422	13	such	such	ADJ
ejpam-6982	422	14	that	that	DET
ejpam-6982	422	15	application	application	NOUN
ejpam-6982	422	16	to	to	ADP
ejpam-6982	422	17	higher	higher	ADV
ejpam-6982	422	18	-	-	PUNCT
ejpam-6982	422	19	dimensional	dimensional	ADJ
ejpam-6982	422	20	problems	problem	NOUN
ejpam-6982	422	21	and	and	CCONJ
ejpam-6982	422	22	extend	extend	VERB
ejpam-6982	422	23	the	the	DET
ejpam-6982	422	24	methods	method	NOUN
ejpam-6982	422	25	to	to	ADP
ejpam-6982	422	26	equations	equation	NOUN
ejpam-6982	422	27	involving	involve	VERB
ejpam-6982	422	28	variable	variable	ADJ
ejpam-6982	422	29	fractional	fractional	ADJ
ejpam-6982	422	30	orders	order	NOUN
ejpam-6982	422	31	and	and	CCONJ
ejpam-6982	422	32	coupled	couple	VERB
ejpam-6982	422	33	fractional	fractional	ADJ
ejpam-6982	422	34	operators	operator	NOUN
ejpam-6982	422	35	.	.	PUNCT
ejpam-6982	423	1	acknowledgements	acknowledgement	NOUN
ejpam-6982	423	2	the	the	DET
ejpam-6982	423	3	authors	author	NOUN
ejpam-6982	423	4	thank	thank	VERB
ejpam-6982	423	5	the	the	DET
ejpam-6982	423	6	anonymous	anonymous	ADJ
ejpam-6982	423	7	reviewers	reviewer	NOUN
ejpam-6982	423	8	for	for	ADP
ejpam-6982	423	9	their	their	PRON
ejpam-6982	423	10	insightful	insightful	ADJ
ejpam-6982	423	11	suggestions	suggestion	NOUN
ejpam-6982	423	12	,	,	PUNCT
ejpam-6982	423	13	which	which	PRON
ejpam-6982	423	14	have	have	AUX
ejpam-6982	423	15	greatly	greatly	ADV
ejpam-6982	423	16	improved	improve	VERB
ejpam-6982	423	17	the	the	DET
ejpam-6982	423	18	quality	quality	NOUN
ejpam-6982	423	19	of	of	ADP
ejpam-6982	423	20	the	the	DET
ejpam-6982	423	21	manuscript	manuscript	NOUN
ejpam-6982	423	22	.	.	PUNCT
ejpam-6982	424	1	references	reference	NOUN
ejpam-6982	424	2	[	[	X
ejpam-6982	424	3	1	1	NUM
ejpam-6982	424	4	]	]	X
ejpam-6982	424	5	mehdi	mehdi	ADJ
ejpam-6982	424	6	dalir	dalir	NOUN
ejpam-6982	424	7	and	and	CCONJ
ejpam-6982	424	8	majid	majid	PROPN
ejpam-6982	424	9	bashour	bashour	PROPN
ejpam-6982	424	10	.	.	PUNCT
ejpam-6982	425	1	applications	application	NOUN
ejpam-6982	425	2	of	of	ADP
ejpam-6982	425	3	fractional	fractional	ADJ
ejpam-6982	425	4	calculus	calculus	NOUN
ejpam-6982	425	5	.	.	PUNCT
ejpam-6982	426	1	applied	apply	VERB
ejpam-6982	426	2	mathematical	mathematical	ADJ
ejpam-6982	426	3	sciences	sciences	PROPN
ejpam-6982	426	4	,	,	PUNCT
ejpam-6982	426	5	4(21):1021–1032	4(21):1021–1032	NUM
ejpam-6982	426	6	,	,	PUNCT
ejpam-6982	426	7	2010	2010	NUM
ejpam-6982	426	8	.	.	PUNCT
ejpam-6982	427	1	[	[	X
ejpam-6982	427	2	2	2	X
ejpam-6982	427	3	]	]	PUNCT
ejpam-6982	427	4	bruce	bruce	PROPN
ejpam-6982	427	5	j	j	PROPN
ejpam-6982	427	6	west	west	PROPN
ejpam-6982	427	7	.	.	PUNCT
ejpam-6982	428	1	colloquium	colloquium	NOUN
ejpam-6982	428	2	:	:	PUNCT
ejpam-6982	428	3	fractional	fractional	ADJ
ejpam-6982	428	4	calculus	calculus	NOUN
ejpam-6982	428	5	view	view	NOUN
ejpam-6982	428	6	of	of	ADP
ejpam-6982	428	7	complexity	complexity	NOUN
ejpam-6982	428	8	:	:	PUNCT
ejpam-6982	428	9	a	a	DET
ejpam-6982	428	10	tutorial	tutorial	NOUN
ejpam-6982	428	11	.	.	PUNCT
ejpam-6982	429	1	reviews	review	NOUN
ejpam-6982	429	2	of	of	ADP
ejpam-6982	429	3	modern	modern	ADJ
ejpam-6982	429	4	physics	physic	NOUN
ejpam-6982	429	5	,	,	PUNCT
ejpam-6982	429	6	86(4):1169–1186	86(4):1169–1186	NUM
ejpam-6982	429	7	,	,	PUNCT
ejpam-6982	429	8	2014	2014	NUM
ejpam-6982	429	9	.	.	PUNCT
ejpam-6982	430	1	[	[	X
ejpam-6982	430	2	3	3	X
ejpam-6982	430	3	]	]	X
ejpam-6982	430	4	shantanu	shantanu	PROPN
ejpam-6982	430	5	das	das	PROPN
ejpam-6982	430	6	.	.	PUNCT
ejpam-6982	430	7	functional	functional	ADJ
ejpam-6982	430	8	fractional	fractional	ADJ
ejpam-6982	430	9	calculus	calculus	NOUN
ejpam-6982	430	10	,	,	PUNCT
ejpam-6982	430	11	volume	volume	NOUN
ejpam-6982	430	12	1	1	NUM
ejpam-6982	430	13	.	.	PUNCT
ejpam-6982	430	14	springer	springer	NOUN
ejpam-6982	430	15	,	,	PUNCT
ejpam-6982	430	16	2011	2011	NUM
ejpam-6982	430	17	.	.	PUNCT
ejpam-6982	431	1	[	[	X
ejpam-6982	431	2	4	4	NUM
ejpam-6982	431	3	]	]	PUNCT
ejpam-6982	431	4	francesco	francesco	PROPN
ejpam-6982	431	5	mainardi	mainardi	PROPN
ejpam-6982	431	6	.	.	PUNCT
ejpam-6982	432	1	fractional	fractional	ADJ
ejpam-6982	432	2	calculus	calculus	NOUN
ejpam-6982	432	3	:	:	PUNCT
ejpam-6982	432	4	theory	theory	NOUN
ejpam-6982	432	5	and	and	CCONJ
ejpam-6982	432	6	applications	application	NOUN
ejpam-6982	432	7	,	,	PUNCT
ejpam-6982	432	8	2018	2018	NUM
ejpam-6982	432	9	.	.	PUNCT
ejpam-6982	433	1	[	[	X
ejpam-6982	433	2	5	5	X
ejpam-6982	433	3	]	]	PUNCT
ejpam-6982	433	4	ahmed	ahmed	PROPN
ejpam-6982	433	5	m	m	PROPN
ejpam-6982	433	6	yousef	yousef	PROPN
ejpam-6982	433	7	,	,	PUNCT
ejpam-6982	433	8	saad	saad	PROPN
ejpam-6982	433	9	z	z	PROPN
ejpam-6982	433	10	rida	rida	PROPN
ejpam-6982	433	11	,	,	PUNCT
ejpam-6982	433	12	yassein	yassein	PROPN
ejpam-6982	433	13	gh	gh	PROPN
ejpam-6982	433	14	gouda	gouda	NOUN
ejpam-6982	433	15	,	,	PUNCT
ejpam-6982	433	16	and	and	CCONJ
ejpam-6982	433	17	asmaa	asmaa	PROPN
ejpam-6982	433	18	s	s	PROPN
ejpam-6982	433	19	zaki	zaki	PROPN
ejpam-6982	433	20	.	.	PUNCT
ejpam-6982	434	1	on	on	ADP
ejpam-6982	434	2	dynamics	dynamic	NOUN
ejpam-6982	434	3	of	of	ADP
ejpam-6982	434	4	a	a	DET
ejpam-6982	434	5	fractional	fractional	ADJ
ejpam-6982	434	6	-	-	PUNCT
ejpam-6982	434	7	order	order	NOUN
ejpam-6982	434	8	sirs	sir	NOUN
ejpam-6982	434	9	epidemic	epidemic	NOUN
ejpam-6982	434	10	model	model	NOUN
ejpam-6982	434	11	with	with	ADP
ejpam-6982	434	12	standard	standard	ADJ
ejpam-6982	434	13	incidence	incidence	NOUN
ejpam-6982	434	14	rate	rate	NOUN
ejpam-6982	434	15	and	and	CCONJ
ejpam-6982	434	16	its	its	PRON
ejpam-6982	434	17	discretization	discretization	NOUN
ejpam-6982	434	18	.	.	PUNCT
ejpam-6982	435	1	progress	progress	NOUN
ejpam-6982	435	2	in	in	ADP
ejpam-6982	435	3	fractional	fractional	ADJ
ejpam-6982	435	4	differentiation	differentiation	NOUN
ejpam-6982	435	5	&	&	CCONJ
ejpam-6982	435	6	applications	application	NOUN
ejpam-6982	435	7	,	,	PUNCT
ejpam-6982	435	8	5(4):297–306	5(4):297–306	NUM
ejpam-6982	435	9	,	,	PUNCT
ejpam-6982	435	10	2019	2019	NUM
ejpam-6982	435	11	.	.	PUNCT
ejpam-6982	436	1	[	[	X
ejpam-6982	436	2	6	6	NUM
ejpam-6982	436	3	]	]	X
ejpam-6982	436	4	abella	abella	PROPN
ejpam-6982	436	5	el	el	PROPN
ejpam-6982	436	6	kabouss	kabouss	PROPN
ejpam-6982	436	7	and	and	CCONJ
ejpam-6982	436	8	abdelhak	abdelhak	PROPN
ejpam-6982	436	9	bouhamed	bouhame	VERB
ejpam-6982	436	10	.	.	PUNCT
ejpam-6982	437	1	regional	regional	ADJ
ejpam-6982	437	2	fractional	fractional	ADJ
ejpam-6982	437	3	optimal	optimal	ADJ
ejpam-6982	437	4	control	control	NOUN
ejpam-6982	437	5	problem	problem	NOUN
ejpam-6982	437	6	of	of	ADP
ejpam-6982	437	7	a	a	DET
ejpam-6982	437	8	bilinear	bilinear	NOUN
ejpam-6982	437	9	reaction	reaction	NOUN
ejpam-6982	437	10	diffusion	diffusion	NOUN
ejpam-6982	437	11	equation	equation	NOUN
ejpam-6982	437	12	using	use	VERB
ejpam-6982	437	13	distributed	distribute	VERB
ejpam-6982	437	14	bounded	bound	VERB
ejpam-6982	437	15	controls	control	NOUN
ejpam-6982	437	16	.	.	PUNCT
ejpam-6982	438	1	progr	progr	NOUN
ejpam-6982	438	2	.	.	PUNCT
ejpam-6982	439	1	fract	fract	PROPN
ejpam-6982	439	2	.	.	PUNCT
ejpam-6982	440	1	differ	differ	VERB
ejpam-6982	440	2	.	.	PUNCT
ejpam-6982	441	1	appl	appl	PROPN
ejpam-6982	441	2	.	.	PROPN
ejpam-6982	441	3	,	,	PUNCT
ejpam-6982	441	4	10(4):537–544	10(4):537–544	PROPN
ejpam-6982	441	5	,	,	PUNCT
ejpam-6982	441	6	2024	2024	NUM
ejpam-6982	441	7	.	.	PUNCT
ejpam-6982	442	1	[	[	X
ejpam-6982	442	2	7	7	X
ejpam-6982	442	3	]	]	X
ejpam-6982	442	4	hassan	hassan	PROPN
ejpam-6982	442	5	eltayeb	eltayeb	PROPN
ejpam-6982	442	6	and	and	CCONJ
ejpam-6982	442	7	adem	adem	PROPN
ejpam-6982	442	8	kılıçman	kılıçman	PROPN
ejpam-6982	442	9	.	.	PUNCT
ejpam-6982	443	1	application	application	NOUN
ejpam-6982	443	2	of	of	ADP
ejpam-6982	443	3	sumudu	sumudu	NOUN
ejpam-6982	443	4	decomposition	decomposition	NOUN
ejpam-6982	443	5	method	method	NOUN
ejpam-6982	443	6	to	to	PART
ejpam-6982	443	7	solve	solve	VERB
ejpam-6982	443	8	nonlinear	nonlinear	ADJ
ejpam-6982	443	9	system	system	NOUN
ejpam-6982	443	10	of	of	ADP
ejpam-6982	443	11	partial	partial	ADJ
ejpam-6982	443	12	differential	differential	ADJ
ejpam-6982	443	13	equations	equation	NOUN
ejpam-6982	443	14	.	.	PUNCT
ejpam-6982	444	1	in	in	ADP
ejpam-6982	444	2	abstract	abstract	ADJ
ejpam-6982	444	3	and	and	CCONJ
ejpam-6982	444	4	applied	apply	VERB
ejpam-6982	444	5	analysis	analysis	NOUN
ejpam-6982	444	6	,	,	PUNCT
ejpam-6982	444	7	volume	volume	NOUN
ejpam-6982	444	8	2012	2012	NUM
ejpam-6982	444	9	,	,	PUNCT
ejpam-6982	444	10	page	page	NOUN
ejpam-6982	444	11	412948	412948	NUM
ejpam-6982	444	12	.	.	PUNCT
ejpam-6982	445	1	wiley	wiley	PROPN
ejpam-6982	445	2	online	online	PROPN
ejpam-6982	445	3	library	library	PROPN
ejpam-6982	445	4	,	,	PUNCT
ejpam-6982	445	5	2012	2012	NUM
ejpam-6982	445	6	.	.	PUNCT
ejpam-6982	446	1	[	[	X
ejpam-6982	446	2	8	8	NUM
ejpam-6982	446	3	]	]	X
ejpam-6982	446	4	zaid	zaid	ADJ
ejpam-6982	446	5	odibat	odibat	NOUN
ejpam-6982	446	6	and	and	CCONJ
ejpam-6982	446	7	shaher	shaher	PROPN
ejpam-6982	446	8	momani	momani	PROPN
ejpam-6982	446	9	.	.	PUNCT
ejpam-6982	447	1	numerical	numerical	ADJ
ejpam-6982	447	2	methods	method	NOUN
ejpam-6982	447	3	for	for	ADP
ejpam-6982	447	4	nonlinear	nonlinear	ADJ
ejpam-6982	447	5	partial	partial	ADJ
ejpam-6982	447	6	differential	differential	ADJ
ejpam-6982	447	7	equations	equation	NOUN
ejpam-6982	447	8	of	of	ADP
ejpam-6982	447	9	fractional	fractional	ADJ
ejpam-6982	447	10	order	order	NOUN
ejpam-6982	447	11	.	.	PUNCT
ejpam-6982	448	1	applied	apply	VERB
ejpam-6982	448	2	mathematical	mathematical	ADJ
ejpam-6982	448	3	modelling	modelling	NOUN
ejpam-6982	448	4	,	,	PUNCT
ejpam-6982	448	5	32(1):28–39	32(1):28–39	NUM
ejpam-6982	448	6	,	,	PUNCT
ejpam-6982	448	7	2008	2008	NUM
ejpam-6982	448	8	.	.	PUNCT
ejpam-6982	449	1	[	[	X
ejpam-6982	449	2	9	9	NUM
ejpam-6982	449	3	]	]	X
ejpam-6982	449	4	abdul	abdul	PROPN
ejpam-6982	449	5	-	-	PUNCT
ejpam-6982	449	6	majid	majid	PROPN
ejpam-6982	449	7	wazwaz	wazwaz	NOUN
ejpam-6982	449	8	.	.	PUNCT
ejpam-6982	450	1	a	a	DET
ejpam-6982	450	2	new	new	ADJ
ejpam-6982	450	3	algorithm	algorithm	NOUN
ejpam-6982	450	4	for	for	ADP
ejpam-6982	450	5	calculating	calculate	VERB
ejpam-6982	450	6	adomian	adomian	NOUN
ejpam-6982	450	7	polynomials	polynomial	NOUN
ejpam-6982	450	8	for	for	ADP
ejpam-6982	450	9	nonlinear	nonlinear	ADJ
ejpam-6982	450	10	operators	operator	NOUN
ejpam-6982	450	11	.	.	PUNCT
ejpam-6982	451	1	applied	apply	VERB
ejpam-6982	451	2	mathematics	mathematic	NOUN
ejpam-6982	451	3	and	and	CCONJ
ejpam-6982	451	4	computation	computation	NOUN
ejpam-6982	451	5	,	,	PUNCT
ejpam-6982	451	6	111(1):33–51	111(1):33–51	NUM
ejpam-6982	451	7	,	,	PUNCT
ejpam-6982	451	8	2000	2000	NUM
ejpam-6982	451	9	.	.	PUNCT
ejpam-6982	452	1	[	[	X
ejpam-6982	452	2	10	10	NUM
ejpam-6982	452	3	]	]	X
ejpam-6982	452	4	varsha	varsha	PROPN
ejpam-6982	452	5	daftardar	daftardar	NOUN
ejpam-6982	452	6	-	-	PUNCT
ejpam-6982	452	7	gejji	gejji	NOUN
ejpam-6982	452	8	and	and	CCONJ
ejpam-6982	452	9	hossein	hossein	PROPN
ejpam-6982	452	10	jafari	jafari	PROPN
ejpam-6982	452	11	.	.	PUNCT
ejpam-6982	453	1	adomian	adomian	PROPN
ejpam-6982	453	2	decomposition	decomposition	NOUN
ejpam-6982	453	3	:	:	PUNCT
ejpam-6982	453	4	a	a	DET
ejpam-6982	453	5	tool	tool	NOUN
ejpam-6982	453	6	for	for	ADP
ejpam-6982	453	7	solving	solve	VERB
ejpam-6982	453	8	a.	a.	NOUN
ejpam-6982	453	9	m.	m.	NOUN
ejpam-6982	453	10	alhammad	alhammad	PROPN
ejpam-6982	453	11	,	,	PUNCT
ejpam-6982	453	12	a.	a.	NOUN
ejpam-6982	453	13	m.	m.	PROPN
ejpam-6982	453	14	saeed	saeed	PROPN
ejpam-6982	453	15	/	/	SYM
ejpam-6982	453	16	eur	eur	PROPN
ejpam-6982	453	17	.	.	PUNCT
ejpam-6982	454	1	j.	j.	PROPN
ejpam-6982	454	2	pure	pure	PROPN
ejpam-6982	454	3	appl	appl	PROPN
ejpam-6982	454	4	.	.	PROPN
ejpam-6982	454	5	math	math	PROPN
ejpam-6982	454	6	,	,	PUNCT
ejpam-6982	454	7	18	18	NUM
ejpam-6982	454	8	(	(	PUNCT
ejpam-6982	454	9	4	4	NUM
ejpam-6982	454	10	)	)	PUNCT
ejpam-6982	454	11	(	(	PUNCT
ejpam-6982	454	12	2025	2025	NUM
ejpam-6982	454	13	)	)	PUNCT
ejpam-6982	454	14	,	,	PUNCT
ejpam-6982	454	15	6982	6982	NUM
ejpam-6982	454	16	22	22	NUM
ejpam-6982	454	17	of	of	ADP
ejpam-6982	454	18	22	22	NUM
ejpam-6982	454	19	a	a	DET
ejpam-6982	454	20	system	system	NOUN
ejpam-6982	454	21	of	of	ADP
ejpam-6982	454	22	fractional	fractional	ADJ
ejpam-6982	454	23	differential	differential	ADJ
ejpam-6982	454	24	equations	equation	NOUN
ejpam-6982	454	25	.	.	PUNCT
ejpam-6982	455	1	journal	journal	PROPN
ejpam-6982	455	2	of	of	ADP
ejpam-6982	455	3	mathematical	mathematical	ADJ
ejpam-6982	455	4	analysis	analysis	NOUN
ejpam-6982	455	5	and	and	CCONJ
ejpam-6982	455	6	applications	application	NOUN
ejpam-6982	455	7	,	,	PUNCT
ejpam-6982	455	8	301(2):508–518	301(2):508–518	NUM
ejpam-6982	455	9	,	,	PUNCT
ejpam-6982	455	10	2005	2005	NUM
ejpam-6982	455	11	.	.	PUNCT
ejpam-6982	456	1	[	[	X
ejpam-6982	456	2	11	11	NUM
ejpam-6982	456	3	]	]	X
ejpam-6982	456	4	george	george	PROPN
ejpam-6982	456	5	adomian	adomian	PROPN
ejpam-6982	456	6	.	.	PUNCT
ejpam-6982	457	1	a	a	DET
ejpam-6982	457	2	review	review	NOUN
ejpam-6982	457	3	of	of	ADP
ejpam-6982	457	4	the	the	DET
ejpam-6982	457	5	decomposition	decomposition	NOUN
ejpam-6982	457	6	method	method	NOUN
ejpam-6982	457	7	in	in	ADP
ejpam-6982	457	8	applied	applied	ADJ
ejpam-6982	457	9	mathematics	mathematic	NOUN
ejpam-6982	457	10	.	.	PUNCT
ejpam-6982	458	1	journal	journal	PROPN
ejpam-6982	458	2	of	of	ADP
ejpam-6982	458	3	mathematical	mathematical	ADJ
ejpam-6982	458	4	analysis	analysis	NOUN
ejpam-6982	458	5	and	and	CCONJ
ejpam-6982	458	6	applications	application	NOUN
ejpam-6982	458	7	,	,	PUNCT
ejpam-6982	458	8	135(2):501–544	135(2):501–544	NUM
ejpam-6982	458	9	,	,	PUNCT
ejpam-6982	458	10	1988	1988	NUM
ejpam-6982	458	11	.	.	PUNCT
ejpam-6982	459	1	[	[	X
ejpam-6982	459	2	12	12	NUM
ejpam-6982	459	3	]	]	X
ejpam-6982	459	4	kamel	kamel	PROPN
ejpam-6982	459	5	al	al	PROPN
ejpam-6982	459	6	-	-	PUNCT
ejpam-6982	459	7	khaled	khaled	PROPN
ejpam-6982	459	8	.	.	PUNCT
ejpam-6982	460	1	numerical	numerical	ADJ
ejpam-6982	460	2	solution	solution	NOUN
ejpam-6982	460	3	of	of	ADP
ejpam-6982	460	4	time	time	NOUN
ejpam-6982	460	5	-	-	PUNCT
ejpam-6982	460	6	fractional	fractional	ADJ
ejpam-6982	460	7	partial	partial	ADJ
ejpam-6982	460	8	differential	differential	NOUN
ejpam-6982	460	9	equations	equation	NOUN
ejpam-6982	460	10	using	use	VERB
ejpam-6982	460	11	sumudu	sumudu	NOUN
ejpam-6982	460	12	decomposition	decomposition	NOUN
ejpam-6982	460	13	method	method	NOUN
ejpam-6982	460	14	.	.	PUNCT
ejpam-6982	461	1	rom	rom	PROPN
ejpam-6982	461	2	.	.	PUNCT
ejpam-6982	462	1	j.	j.	PROPN
ejpam-6982	462	2	phys	phys	PROPN
ejpam-6982	462	3	,	,	PUNCT
ejpam-6982	462	4	60(1	60(1	PROPN
ejpam-6982	462	5	-	-	SYM
ejpam-6982	462	6	2):99–110	2):99–110	NUM
ejpam-6982	462	7	,	,	PUNCT
ejpam-6982	462	8	2015	2015	NUM
ejpam-6982	462	9	.	.	PUNCT
ejpam-6982	463	1	[	[	X
ejpam-6982	463	2	13	13	NUM
ejpam-6982	463	3	]	]	PUNCT
ejpam-6982	463	4	rasool	rasool	NOUN
ejpam-6982	463	5	shah	shah	NOUN
ejpam-6982	463	6	,	,	PUNCT
ejpam-6982	463	7	hassan	hassan	PROPN
ejpam-6982	463	8	khan	khan	PROPN
ejpam-6982	463	9	,	,	PUNCT
ejpam-6982	463	10	saima	saima	PROPN
ejpam-6982	463	11	mustafa	mustafa	PROPN
ejpam-6982	463	12	,	,	PUNCT
ejpam-6982	463	13	poom	poom	NOUN
ejpam-6982	463	14	kumam	kumam	NOUN
ejpam-6982	463	15	,	,	PUNCT
ejpam-6982	463	16	and	and	CCONJ
ejpam-6982	463	17	muhammad	muhammad	PROPN
ejpam-6982	463	18	arif	arif	PROPN
ejpam-6982	463	19	.	.	PUNCT
ejpam-6982	464	1	analytical	analytical	ADJ
ejpam-6982	464	2	solutions	solution	NOUN
ejpam-6982	464	3	of	of	ADP
ejpam-6982	464	4	fractional	fractional	ADJ
ejpam-6982	464	5	-	-	PUNCT
ejpam-6982	464	6	order	order	NOUN
ejpam-6982	464	7	diffusion	diffusion	NOUN
ejpam-6982	464	8	equations	equation	NOUN
ejpam-6982	464	9	by	by	ADP
ejpam-6982	464	10	natural	natural	ADJ
ejpam-6982	464	11	transform	transform	NOUN
ejpam-6982	464	12	decomposition	decomposition	NOUN
ejpam-6982	464	13	method	method	NOUN
ejpam-6982	464	14	.	.	PUNCT
ejpam-6982	465	1	entropy	entropy	PROPN
ejpam-6982	465	2	,	,	PUNCT
ejpam-6982	465	3	21(6):557	21(6):557	NUM
ejpam-6982	465	4	,	,	PUNCT
ejpam-6982	465	5	2019	2019	NUM
ejpam-6982	465	6	.	.	PUNCT
ejpam-6982	466	1	[	[	X
ejpam-6982	466	2	14	14	NUM
ejpam-6982	466	3	]	]	X
ejpam-6982	466	4	mohamed	mohamed	PROPN
ejpam-6982	466	5	z	z	PROPN
ejpam-6982	466	6	mohamed	mohamed	PROPN
ejpam-6982	466	7	,	,	PUNCT
ejpam-6982	466	8	tarig	tarig	PROPN
ejpam-6982	466	9	m	m	VERB
ejpam-6982	466	10	elzaki	elzaki	NOUN
ejpam-6982	466	11	,	,	PUNCT
ejpam-6982	466	12	mohamed	mohamed	PROPN
ejpam-6982	466	13	s	s	PROPN
ejpam-6982	466	14	algolam	algolam	PROPN
ejpam-6982	466	15	,	,	PUNCT
ejpam-6982	466	16	eltaib	eltaib	NOUN
ejpam-6982	466	17	m	m	PROPN
ejpam-6982	466	18	abd	abd	PROPN
ejpam-6982	466	19	elmohmoud	elmohmoud	ADJ
ejpam-6982	466	20	,	,	PUNCT
ejpam-6982	466	21	and	and	CCONJ
ejpam-6982	466	22	amjad	amjad	PROPN
ejpam-6982	466	23	e	e	PROPN
ejpam-6982	466	24	hamza	hamza	PROPN
ejpam-6982	466	25	.	.	PUNCT
ejpam-6982	467	1	new	new	ADJ
ejpam-6982	467	2	modified	modify	VERB
ejpam-6982	467	3	variational	variational	ADJ
ejpam-6982	467	4	iteration	iteration	NOUN
ejpam-6982	467	5	laplace	laplace	NOUN
ejpam-6982	467	6	transform	transform	NOUN
ejpam-6982	467	7	method	method	NOUN
ejpam-6982	467	8	compares	compare	VERB
ejpam-6982	467	9	laplace	laplace	NOUN
ejpam-6982	467	10	adomian	adomian	NOUN
ejpam-6982	467	11	decomposition	decomposition	NOUN
ejpam-6982	467	12	method	method	NOUN
ejpam-6982	467	13	for	for	ADP
ejpam-6982	467	14	solution	solution	NOUN
ejpam-6982	467	15	time	time	NOUN
ejpam-6982	467	16	-	-	PUNCT
ejpam-6982	467	17	partial	partial	ADJ
ejpam-6982	467	18	fractional	fractional	ADJ
ejpam-6982	467	19	differential	differential	ADJ
ejpam-6982	467	20	equations	equation	NOUN
ejpam-6982	467	21	.	.	PUNCT
ejpam-6982	468	1	journal	journal	PROPN
ejpam-6982	468	2	of	of	ADP
ejpam-6982	468	3	applied	apply	VERB
ejpam-6982	468	4	mathematics	mathematic	NOUN
ejpam-6982	468	5	,	,	PUNCT
ejpam-6982	468	6	2021(1):6662645	2021(1):6662645	NUM
ejpam-6982	468	7	,	,	PUNCT
ejpam-6982	468	8	2021	2021	NUM
ejpam-6982	468	9	.	.	PUNCT
ejpam-6982	469	1	[	[	X
ejpam-6982	469	2	15	15	NUM
ejpam-6982	469	3	]	]	X
ejpam-6982	469	4	michele	michele	PROPN
ejpam-6982	469	5	caputo	caputo	PROPN
ejpam-6982	469	6	.	.	PROPN
ejpam-6982	470	1	linear	linear	PROPN
ejpam-6982	470	2	models	model	NOUN
ejpam-6982	470	3	of	of	ADP
ejpam-6982	470	4	dissipation	dissipation	NOUN
ejpam-6982	470	5	whose	whose	DET
ejpam-6982	470	6	q	q	NOUN
ejpam-6982	470	7	is	be	AUX
ejpam-6982	470	8	almost	almost	ADV
ejpam-6982	470	9	frequency	frequency	ADJ
ejpam-6982	470	10	independent	independent	ADJ
ejpam-6982	470	11	—	—	PUNCT
ejpam-6982	470	12	ii	ii	NOUN
ejpam-6982	470	13	.	.	PUNCT
ejpam-6982	470	14	geophysical	geophysical	ADJ
ejpam-6982	470	15	journal	journal	PROPN
ejpam-6982	470	16	international	international	PROPN
ejpam-6982	470	17	,	,	PUNCT
ejpam-6982	470	18	13(5):529–539	13(5):529–539	NUM
ejpam-6982	470	19	,	,	PUNCT
ejpam-6982	470	20	1967	1967	NUM
ejpam-6982	470	21	.	.	PUNCT
ejpam-6982	471	1	[	[	X
ejpam-6982	471	2	16	16	NUM
ejpam-6982	471	3	]	]	X
ejpam-6982	471	4	george	george	PROPN
ejpam-6982	471	5	k	k	PROPN
ejpam-6982	471	6	watugala	watugala	PROPN
ejpam-6982	471	7	.	.	PUNCT
ejpam-6982	472	1	sumudu	sumudu	NOUN
ejpam-6982	472	2	transform	transform	NOUN
ejpam-6982	472	3	:	:	PUNCT
ejpam-6982	472	4	a	a	DET
ejpam-6982	472	5	new	new	ADJ
ejpam-6982	472	6	integral	integral	ADJ
ejpam-6982	472	7	transform	transform	NOUN
ejpam-6982	472	8	to	to	PART
ejpam-6982	472	9	solve	solve	VERB
ejpam-6982	472	10	differential	differential	ADJ
ejpam-6982	472	11	equations	equation	NOUN
ejpam-6982	472	12	and	and	CCONJ
ejpam-6982	472	13	control	control	NOUN
ejpam-6982	472	14	engineering	engineering	NOUN
ejpam-6982	472	15	problems	problem	NOUN
ejpam-6982	472	16	.	.	PUNCT
ejpam-6982	473	1	integrated	integrated	ADJ
ejpam-6982	473	2	education	education	NOUN
ejpam-6982	473	3	,	,	PUNCT
ejpam-6982	473	4	24(1):35–43	24(1):35–43	NUM
ejpam-6982	473	5	,	,	PUNCT
ejpam-6982	473	6	1993	1993	NUM
ejpam-6982	473	7	.	.	PUNCT
ejpam-6982	474	1	[	[	X
ejpam-6982	474	2	17	17	NUM
ejpam-6982	474	3	]	]	X
ejpam-6982	474	4	phil	phil	PROPN
ejpam-6982	474	5	pg	pg	PROPN
ejpam-6982	474	6	dyke	dyke	PROPN
ejpam-6982	474	7	and	and	CCONJ
ejpam-6982	474	8	pp	pp	ADP
ejpam-6982	474	9	dyke	dyke	ADJ
ejpam-6982	474	10	.	.	PUNCT
ejpam-6982	475	1	an	an	DET
ejpam-6982	475	2	introduction	introduction	NOUN
ejpam-6982	475	3	to	to	ADP
ejpam-6982	475	4	laplace	laplace	NOUN
ejpam-6982	475	5	transforms	transform	VERB
ejpam-6982	475	6	and	and	CCONJ
ejpam-6982	475	7	fourier	fouri	ADJ
ejpam-6982	475	8	series	series	NOUN
ejpam-6982	475	9	,	,	PUNCT
ejpam-6982	475	10	volume	volume	NOUN
ejpam-6982	475	11	517	517	NUM
ejpam-6982	475	12	.	.	PUNCT
ejpam-6982	475	13	springer	springer	NOUN
ejpam-6982	475	14	,	,	PUNCT
ejpam-6982	475	15	2001	2001	NUM
ejpam-6982	475	16	.	.	PUNCT
ejpam-6982	476	1	[	[	X
ejpam-6982	476	2	18	18	NUM
ejpam-6982	476	3	]	]	X
ejpam-6982	476	4	fethi	fethi	PROPN
ejpam-6982	476	5	bin	bin	NOUN
ejpam-6982	476	6	muhammed	muhamme	VERB
ejpam-6982	476	7	belgacem	belgacem	NOUN
ejpam-6982	476	8	and	and	CCONJ
ejpam-6982	476	9	r	r	PROPN
ejpam-6982	476	10	silambarasan	silambarasan	NOUN
ejpam-6982	476	11	.	.	PUNCT
ejpam-6982	477	1	theory	theory	NOUN
ejpam-6982	477	2	of	of	ADP
ejpam-6982	477	3	natural	natural	ADJ
ejpam-6982	477	4	transform	transform	NOUN
ejpam-6982	477	5	.	.	PUNCT
ejpam-6982	478	1	math	math	NOUN
ejpam-6982	478	2	.	.	PUNCT
ejpam-6982	479	1	engg	engg	PROPN
ejpam-6982	479	2	.	.	PUNCT
ejpam-6982	480	1	sci	sci	PROPN
ejpam-6982	480	2	.	.	PUNCT
ejpam-6982	480	3	aeros	aero	NOUN
ejpam-6982	480	4	,	,	PUNCT
ejpam-6982	480	5	3:99–124	3:99–124	NUM
ejpam-6982	480	6	,	,	PUNCT
ejpam-6982	480	7	2012	2012	NUM
ejpam-6982	480	8	.	.	PUNCT
ejpam-6982	481	1	[	[	X
ejpam-6982	481	2	19	19	NUM
ejpam-6982	481	3	]	]	X
ejpam-6982	481	4	hossein	hossein	PROPN
ejpam-6982	481	5	jafari	jafari	PROPN
ejpam-6982	481	6	,	,	PUNCT
ejpam-6982	481	7	chaudry	chaudry	PROPN
ejpam-6982	481	8	masood	masood	PROPN
ejpam-6982	481	9	khalique	khalique	PROPN
ejpam-6982	481	10	,	,	PUNCT
ejpam-6982	481	11	and	and	CCONJ
ejpam-6982	481	12	m	m	PROPN
ejpam-6982	481	13	nazari	nazari	PROPN
ejpam-6982	481	14	.	.	PUNCT
ejpam-6982	482	1	application	application	NOUN
ejpam-6982	482	2	of	of	ADP
ejpam-6982	482	3	the	the	DET
ejpam-6982	482	4	laplace	laplace	NOUN
ejpam-6982	482	5	decomposition	decomposition	NOUN
ejpam-6982	482	6	method	method	NOUN
ejpam-6982	482	7	for	for	ADP
ejpam-6982	482	8	solving	solve	VERB
ejpam-6982	482	9	linear	linear	NOUN
ejpam-6982	482	10	and	and	CCONJ
ejpam-6982	482	11	nonlinear	nonlinear	ADJ
ejpam-6982	482	12	fractional	fractional	ADJ
ejpam-6982	482	13	diffusion	diffusion	NOUN
ejpam-6982	482	14	–	–	PUNCT
ejpam-6982	482	15	wave	wave	NOUN
ejpam-6982	482	16	equations	equation	NOUN
ejpam-6982	482	17	.	.	PUNCT
ejpam-6982	483	1	applied	apply	VERB
ejpam-6982	483	2	mathematics	mathematics	NOUN
ejpam-6982	483	3	letters	letter	NOUN
ejpam-6982	483	4	,	,	PUNCT
ejpam-6982	483	5	24(11):1799–1805	24(11):1799–1805	NUM
ejpam-6982	483	6	,	,	PUNCT
ejpam-6982	483	7	2011	2011	NUM
ejpam-6982	483	8	.	.	PUNCT
ejpam-6982	484	1	[	[	X
ejpam-6982	484	2	20	20	NUM
ejpam-6982	484	3	]	]	X
ejpam-6982	484	4	rashmi	rashmi	PROPN
ejpam-6982	484	5	mishra	mishra	PROPN
ejpam-6982	484	6	,	,	PUNCT
ejpam-6982	484	7	sudhanshu	sudhanshu	NOUN
ejpam-6982	484	8	aggarwal	aggarwal	PROPN
ejpam-6982	484	9	,	,	PUNCT
ejpam-6982	484	10	lokesh	lokesh	PROPN
ejpam-6982	484	11	chaudhary	chaudhary	PROPN
ejpam-6982	484	12	,	,	PUNCT
ejpam-6982	484	13	and	and	CCONJ
ejpam-6982	484	14	anuj	anuj	PROPN
ejpam-6982	484	15	kumar	kumar	PROPN
ejpam-6982	484	16	.	.	PROPN
ejpam-6982	484	17	relationship	relationship	NOUN
ejpam-6982	484	18	between	between	ADP
ejpam-6982	484	19	sumudu	sumudu	NOUN
ejpam-6982	484	20	and	and	CCONJ
ejpam-6982	484	21	some	some	DET
ejpam-6982	484	22	efficient	efficient	ADJ
ejpam-6982	484	23	integral	integral	ADJ
ejpam-6982	484	24	transforms	transform	NOUN
ejpam-6982	484	25	.	.	PUNCT
ejpam-6982	485	1	international	international	ADJ
ejpam-6982	485	2	journal	journal	NOUN
ejpam-6982	485	3	of	of	ADP
ejpam-6982	485	4	innovative	innovative	ADJ
ejpam-6982	485	5	technology	technology	NOUN
ejpam-6982	485	6	and	and	CCONJ
ejpam-6982	485	7	exploring	explore	VERB
ejpam-6982	485	8	engineering	engineering	NOUN
ejpam-6982	485	9	,	,	PUNCT
ejpam-6982	485	10	9(3):153–159	9(3):153–159	NUM
ejpam-6982	485	11	,	,	PUNCT
ejpam-6982	485	12	2020	2020	NUM
ejpam-6982	485	13	.	.	PUNCT
ejpam-6982	486	1	[	[	X
ejpam-6982	486	2	21	21	NUM
ejpam-6982	486	3	]	]	X
ejpam-6982	486	4	ali	ali	PROPN
ejpam-6982	486	5	khalouta	khalouta	PROPN
ejpam-6982	486	6	and	and	CCONJ
ejpam-6982	486	7	abdelouahab	abdelouahab	PROPN
ejpam-6982	486	8	kadem	kadem	PROPN
ejpam-6982	486	9	.	.	PUNCT
ejpam-6982	487	1	fractional	fractional	ADJ
ejpam-6982	487	2	natural	natural	ADJ
ejpam-6982	487	3	decomposition	decomposition	NOUN
ejpam-6982	487	4	method	method	NOUN
ejpam-6982	487	5	for	for	ADP
ejpam-6982	487	6	solving	solve	VERB
ejpam-6982	487	7	a	a	DET
ejpam-6982	487	8	certain	certain	ADJ
ejpam-6982	487	9	class	class	NOUN
ejpam-6982	487	10	of	of	ADP
ejpam-6982	487	11	nonlinear	nonlinear	ADJ
ejpam-6982	487	12	time	time	NOUN
ejpam-6982	487	13	-	-	PUNCT
ejpam-6982	487	14	fractional	fractional	ADJ
ejpam-6982	487	15	wave	wave	NOUN
ejpam-6982	487	16	-	-	PUNCT
ejpam-6982	487	17	like	like	ADJ
ejpam-6982	487	18	equations	equation	NOUN
ejpam-6982	487	19	with	with	ADP
ejpam-6982	487	20	variable	variable	ADJ
ejpam-6982	487	21	coefficients	coefficient	NOUN
ejpam-6982	487	22	.	.	PUNCT
ejpam-6982	488	1	acta	acta	PROPN
ejpam-6982	488	2	univ	univ	PROPN
ejpam-6982	488	3	.	.	PUNCT
ejpam-6982	489	1	sapientiae	sapientiae	PROPN
ejpam-6982	489	2	math	math	PROPN
ejpam-6982	489	3	,	,	PUNCT
ejpam-6982	489	4	11(1):99–116	11(1):99–116	NUM
ejpam-6982	489	5	,	,	PUNCT
ejpam-6982	489	6	2019	2019	NUM
ejpam-6982	489	7	.	.	PUNCT