id	sid	tid	token	lemma	pos
ejpam-2672	1	1	european	european	PROPN
ejpam-2672	1	2	journal	journal	PROPN
ejpam-2672	1	3	of	of	ADP
ejpam-2672	1	4	pure	pure	ADJ
ejpam-2672	1	5	and	and	CCONJ
ejpam-2672	1	6	applied	apply	VERB
ejpam-2672	1	7	mathematics	mathematic	NOUN
ejpam-2672	1	8	vol	vol	NOUN
ejpam-2672	1	9	.	.	PROPN
ejpam-2672	2	1	10	10	NUM
ejpam-2672	2	2	,	,	PUNCT
ejpam-2672	2	3	no	no	INTJ
ejpam-2672	2	4	.	.	NOUN
ejpam-2672	2	5	3	3	NUM
ejpam-2672	2	6	,	,	PUNCT
ejpam-2672	2	7	2017	2017	NUM
ejpam-2672	2	8	,	,	PUNCT
ejpam-2672	2	9	586	586	NUM
ejpam-2672	2	10	-	-	SYM
ejpam-2672	2	11	601	601	NUM
ejpam-2672	2	12	issn	issn	PROPN
ejpam-2672	2	13	1307	1307	NUM
ejpam-2672	2	14	-	-	SYM
ejpam-2672	2	15	5543	5543	NUM
ejpam-2672	2	16	–	–	PUNCT
ejpam-2672	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2672	2	18	published	publish	VERB
ejpam-2672	2	19	by	by	ADP
ejpam-2672	2	20	new	new	PROPN
ejpam-2672	2	21	york	york	PROPN
ejpam-2672	2	22	business	business	PROPN
ejpam-2672	2	23	global	global	ADJ
ejpam-2672	2	24	analytical	analytical	ADJ
ejpam-2672	2	25	approximate	approximate	ADJ
ejpam-2672	2	26	solution	solution	NOUN
ejpam-2672	2	27	of	of	ADP
ejpam-2672	2	28	fractional	fractional	ADJ
ejpam-2672	2	29	wave	wave	NOUN
ejpam-2672	2	30	equation	equation	NOUN
ejpam-2672	2	31	by	by	ADP
ejpam-2672	2	32	the	the	DET
ejpam-2672	2	33	optimal	optimal	ADJ
ejpam-2672	2	34	homotopy	homotopy	NOUN
ejpam-2672	2	35	analysis	analysis	NOUN
ejpam-2672	2	36	method	method	NOUN
ejpam-2672	2	37	a.	a.	NOUN
ejpam-2672	2	38	elsaid1,∗	elsaid1,∗	PROPN
ejpam-2672	2	39	,	,	PUNCT
ejpam-2672	2	40	s.	s.	PROPN
ejpam-2672	2	41	shamseldeen1	shamseldeen1	PROPN
ejpam-2672	2	42	,	,	PUNCT
ejpam-2672	2	43	s.	s.	PROPN
ejpam-2672	2	44	madkour1	madkour1	NOUN
ejpam-2672	2	45	1	1	NUM
ejpam-2672	2	46	mathematics	mathematic	NOUN
ejpam-2672	2	47	and	and	CCONJ
ejpam-2672	2	48	engineering	engineering	NOUN
ejpam-2672	2	49	physics	physics	PROPN
ejpam-2672	2	50	department	department	PROPN
ejpam-2672	2	51	,	,	PUNCT
ejpam-2672	2	52	faculty	faculty	NOUN
ejpam-2672	2	53	of	of	ADP
ejpam-2672	2	54	engineering	engineer	VERB
ejpam-2672	2	55	mansoura	mansoura	PROPN
ejpam-2672	2	56	university	university	PROPN
ejpam-2672	2	57	,	,	PUNCT
ejpam-2672	2	58	egypt	egypt	PROPN
ejpam-2672	2	59	abstract	abstract	PROPN
ejpam-2672	2	60	.	.	PUNCT
ejpam-2672	3	1	in	in	ADP
ejpam-2672	3	2	this	this	DET
ejpam-2672	3	3	article	article	NOUN
ejpam-2672	3	4	,	,	PUNCT
ejpam-2672	3	5	we	we	PRON
ejpam-2672	3	6	study	study	VERB
ejpam-2672	3	7	the	the	DET
ejpam-2672	3	8	space	space	NOUN
ejpam-2672	3	9	-	-	PUNCT
ejpam-2672	3	10	fractional	fractional	ADJ
ejpam-2672	3	11	wave	wave	NOUN
ejpam-2672	3	12	equation	equation	NOUN
ejpam-2672	3	13	with	with	ADP
ejpam-2672	3	14	riesz	riesz	NOUN
ejpam-2672	3	15	fractional	fractional	ADJ
ejpam-2672	3	16	derivative	derivative	NOUN
ejpam-2672	3	17	.	.	PUNCT
ejpam-2672	4	1	the	the	DET
ejpam-2672	4	2	continuation	continuation	NOUN
ejpam-2672	4	3	of	of	ADP
ejpam-2672	4	4	the	the	DET
ejpam-2672	4	5	solution	solution	NOUN
ejpam-2672	4	6	of	of	ADP
ejpam-2672	4	7	this	this	DET
ejpam-2672	4	8	space	space	NOUN
ejpam-2672	4	9	-	-	PUNCT
ejpam-2672	4	10	fractional	fractional	ADJ
ejpam-2672	4	11	equation	equation	NOUN
ejpam-2672	4	12	to	to	ADP
ejpam-2672	4	13	the	the	DET
ejpam-2672	4	14	solution	solution	NOUN
ejpam-2672	4	15	of	of	ADP
ejpam-2672	4	16	the	the	DET
ejpam-2672	4	17	corresponding	corresponding	ADJ
ejpam-2672	4	18	integer	integer	NOUN
ejpam-2672	4	19	order	order	NOUN
ejpam-2672	4	20	equation	equation	NOUN
ejpam-2672	4	21	is	be	AUX
ejpam-2672	4	22	proved	prove	VERB
ejpam-2672	4	23	.	.	PUNCT
ejpam-2672	5	1	the	the	DET
ejpam-2672	5	2	series	series	NOUN
ejpam-2672	5	3	solution	solution	NOUN
ejpam-2672	5	4	is	be	AUX
ejpam-2672	5	5	obtained	obtain	VERB
ejpam-2672	5	6	based	base	VERB
ejpam-2672	5	7	on	on	ADP
ejpam-2672	5	8	properties	property	NOUN
ejpam-2672	5	9	of	of	ADP
ejpam-2672	5	10	riesz	riesz	VERB
ejpam-2672	5	11	fractional	fractional	ADJ
ejpam-2672	5	12	derivative	derivative	ADJ
ejpam-2672	5	13	operator	operator	NOUN
ejpam-2672	5	14	and	and	CCONJ
ejpam-2672	5	15	utilizing	utilize	VERB
ejpam-2672	5	16	the	the	DET
ejpam-2672	5	17	optimal	optimal	ADJ
ejpam-2672	5	18	homotopy	homotopy	NOUN
ejpam-2672	5	19	analysis	analysis	NOUN
ejpam-2672	5	20	method	method	NOUN
ejpam-2672	5	21	(	(	PUNCT
ejpam-2672	5	22	oham	oham	NOUN
ejpam-2672	5	23	)	)	PUNCT
ejpam-2672	5	24	.	.	PUNCT
ejpam-2672	6	1	numerical	numerical	ADJ
ejpam-2672	6	2	simulations	simulation	NOUN
ejpam-2672	6	3	are	be	AUX
ejpam-2672	6	4	presented	present	VERB
ejpam-2672	6	5	to	to	PART
ejpam-2672	6	6	validate	validate	VERB
ejpam-2672	6	7	the	the	DET
ejpam-2672	6	8	method	method	NOUN
ejpam-2672	6	9	and	and	CCONJ
ejpam-2672	6	10	to	to	PART
ejpam-2672	6	11	show	show	VERB
ejpam-2672	6	12	the	the	DET
ejpam-2672	6	13	effect	effect	NOUN
ejpam-2672	6	14	of	of	ADP
ejpam-2672	6	15	changing	change	VERB
ejpam-2672	6	16	the	the	DET
ejpam-2672	6	17	fractional	fractional	ADJ
ejpam-2672	6	18	derivative	derivative	ADJ
ejpam-2672	6	19	parameter	parameter	NOUN
ejpam-2672	6	20	on	on	ADP
ejpam-2672	6	21	the	the	DET
ejpam-2672	6	22	solution	solution	NOUN
ejpam-2672	6	23	behavior	behavior	NOUN
ejpam-2672	6	24	.	.	PUNCT
ejpam-2672	7	1	2010	2010	NUM
ejpam-2672	7	2	mathematics	mathematic	NOUN
ejpam-2672	7	3	subject	subject	NOUN
ejpam-2672	7	4	classifications	classification	NOUN
ejpam-2672	7	5	:	:	PUNCT
ejpam-2672	7	6	35l05	35l05	NUM
ejpam-2672	7	7	,	,	PUNCT
ejpam-2672	7	8	26a33	26a33	NUM
ejpam-2672	7	9	,	,	PUNCT
ejpam-2672	7	10	35c10	35c10	NUM
ejpam-2672	7	11	key	key	ADJ
ejpam-2672	7	12	words	word	NOUN
ejpam-2672	7	13	and	and	CCONJ
ejpam-2672	7	14	phrases	phrase	NOUN
ejpam-2672	7	15	:	:	PUNCT
ejpam-2672	7	16	space	space	NOUN
ejpam-2672	7	17	-	-	PUNCT
ejpam-2672	7	18	fractional	fractional	ADJ
ejpam-2672	7	19	wave	wave	NOUN
ejpam-2672	7	20	equation	equation	NOUN
ejpam-2672	7	21	,	,	PUNCT
ejpam-2672	7	22	riesz	riesz	NOUN
ejpam-2672	7	23	,	,	PUNCT
ejpam-2672	7	24	optimal	optimal	ADJ
ejpam-2672	7	25	homotopy	homotopy	NOUN
ejpam-2672	7	26	analysis	analysis	NOUN
ejpam-2672	7	27	method	method	NOUN
ejpam-2672	7	28	1	1	NUM
ejpam-2672	7	29	.	.	PUNCT
ejpam-2672	8	1	introduction	introduction	NOUN
ejpam-2672	8	2	fractional	fractional	ADJ
ejpam-2672	8	3	derivatives	derivative	NOUN
ejpam-2672	8	4	,	,	PUNCT
ejpam-2672	8	5	as	as	ADP
ejpam-2672	8	6	generalizations	generalization	NOUN
ejpam-2672	8	7	of	of	ADP
ejpam-2672	8	8	classical	classical	ADJ
ejpam-2672	8	9	integer	integer	NOUN
ejpam-2672	8	10	order	order	NOUN
ejpam-2672	8	11	derivatives	derivative	NOUN
ejpam-2672	8	12	,	,	PUNCT
ejpam-2672	8	13	are	be	AUX
ejpam-2672	8	14	increasingly	increasingly	ADV
ejpam-2672	8	15	used	use	VERB
ejpam-2672	8	16	to	to	PART
ejpam-2672	8	17	model	model	VERB
ejpam-2672	8	18	numerous	numerous	ADJ
ejpam-2672	8	19	problems	problem	NOUN
ejpam-2672	8	20	in	in	ADP
ejpam-2672	8	21	different	different	ADJ
ejpam-2672	8	22	fields	field	NOUN
ejpam-2672	8	23	of	of	ADP
ejpam-2672	8	24	applied	applied	ADJ
ejpam-2672	8	25	science	science	NOUN
ejpam-2672	8	26	.	.	PUNCT
ejpam-2672	9	1	in	in	ADP
ejpam-2672	9	2	recent	recent	ADJ
ejpam-2672	9	3	years	year	NOUN
ejpam-2672	9	4	,	,	PUNCT
ejpam-2672	9	5	the	the	DET
ejpam-2672	9	6	fractional	fractional	ADJ
ejpam-2672	9	7	derivative	derivative	ADJ
ejpam-2672	9	8	models	model	NOUN
ejpam-2672	9	9	are	be	AUX
ejpam-2672	9	10	developed	develop	VERB
ejpam-2672	9	11	to	to	PART
ejpam-2672	9	12	describe	describe	VERB
ejpam-2672	9	13	the	the	DET
ejpam-2672	9	14	dissipative	dissipative	ADJ
ejpam-2672	9	15	attenuation	attenuation	NOUN
ejpam-2672	9	16	in	in	ADP
ejpam-2672	9	17	complex	complex	ADJ
ejpam-2672	9	18	materials	material	NOUN
ejpam-2672	9	19	,	,	PUNCT
ejpam-2672	9	20	such	such	ADJ
ejpam-2672	9	21	as	as	ADP
ejpam-2672	9	22	anomalous	anomalous	ADJ
ejpam-2672	9	23	diffusion	diffusion	NOUN
ejpam-2672	10	1	[	[	X
ejpam-2672	10	2	12	12	NUM
ejpam-2672	10	3	]	]	PUNCT
ejpam-2672	10	4	and	and	CCONJ
ejpam-2672	11	1	[	[	X
ejpam-2672	11	2	15	15	NUM
ejpam-2672	11	3	]	]	X
ejpam-2672	11	4	,	,	PUNCT
ejpam-2672	11	5	viscoelastic	viscoelastic	NOUN
ejpam-2672	11	6	damping	damp	VERB
ejpam-2672	11	7	[	[	X
ejpam-2672	11	8	1	1	NUM
ejpam-2672	11	9	]	]	PUNCT
ejpam-2672	11	10	and	and	CCONJ
ejpam-2672	11	11	[	[	X
ejpam-2672	11	12	11	11	NUM
ejpam-2672	11	13	]	]	PUNCT
ejpam-2672	11	14	,	,	PUNCT
ejpam-2672	11	15	and	and	CCONJ
ejpam-2672	11	16	wave	wave	NOUN
ejpam-2672	11	17	propagation	propagation	NOUN
ejpam-2672	11	18	[	[	X
ejpam-2672	11	19	4	4	NUM
ejpam-2672	11	20	]	]	PUNCT
ejpam-2672	11	21	and	and	CCONJ
ejpam-2672	11	22	[	[	X
ejpam-2672	11	23	5	5	NUM
ejpam-2672	11	24	]	]	PUNCT
ejpam-2672	11	25	.	.	PUNCT
ejpam-2672	12	1	the	the	DET
ejpam-2672	12	2	operators	operator	NOUN
ejpam-2672	12	3	of	of	ADP
ejpam-2672	12	4	fractional	fractional	ADJ
ejpam-2672	12	5	differentiation	differentiation	NOUN
ejpam-2672	12	6	and	and	CCONJ
ejpam-2672	12	7	integration	integration	NOUN
ejpam-2672	12	8	are	be	AUX
ejpam-2672	12	9	also	also	ADV
ejpam-2672	12	10	used	use	VERB
ejpam-2672	12	11	for	for	ADP
ejpam-2672	12	12	extensions	extension	NOUN
ejpam-2672	12	13	of	of	ADP
ejpam-2672	12	14	the	the	DET
ejpam-2672	12	15	diffusion	diffusion	NOUN
ejpam-2672	12	16	and	and	CCONJ
ejpam-2672	12	17	wave	wave	NOUN
ejpam-2672	12	18	equations	equation	NOUN
ejpam-2672	12	19	[	[	X
ejpam-2672	12	20	13	13	NUM
ejpam-2672	12	21	]	]	PUNCT
ejpam-2672	12	22	and	and	CCONJ
ejpam-2672	12	23	[	[	X
ejpam-2672	12	24	14	14	NUM
ejpam-2672	12	25	]	]	PUNCT
ejpam-2672	12	26	.	.	PUNCT
ejpam-2672	13	1	studies	study	NOUN
ejpam-2672	13	2	have	have	AUX
ejpam-2672	13	3	been	be	AUX
ejpam-2672	13	4	devoted	devote	VERB
ejpam-2672	13	5	for	for	ADP
ejpam-2672	13	6	a	a	DET
ejpam-2672	13	7	type	type	NOUN
ejpam-2672	13	8	of	of	ADP
ejpam-2672	13	9	anomalous	anomalous	ADJ
ejpam-2672	13	10	diffusion	diffusion	NOUN
ejpam-2672	13	11	modeled	model	VERB
ejpam-2672	13	12	by	by	ADP
ejpam-2672	13	13	the	the	DET
ejpam-2672	13	14	fractional	fractional	ADJ
ejpam-2672	13	15	diffusion	diffusion	NOUN
ejpam-2672	13	16	equation	equation	NOUN
ejpam-2672	13	17	with	with	ADP
ejpam-2672	13	18	spatial	spatial	ADJ
ejpam-2672	13	19	riesz	riesz	NOUN
ejpam-2672	13	20	and	and	CCONJ
ejpam-2672	13	21	riesz	riesz	NOUN
ejpam-2672	13	22	-	-	PUNCT
ejpam-2672	13	23	feller	feller	NOUN
ejpam-2672	13	24	fractional	fractional	ADJ
ejpam-2672	13	25	derivatives	derivative	NOUN
ejpam-2672	13	26	[	[	X
ejpam-2672	13	27	6	6	NUM
ejpam-2672	13	28	]	]	PUNCT
ejpam-2672	13	29	and	and	CCONJ
ejpam-2672	13	30	[	[	X
ejpam-2672	13	31	8	8	NUM
ejpam-2672	13	32	]	]	PUNCT
ejpam-2672	13	33	.	.	PUNCT
ejpam-2672	14	1	yet	yet	ADV
ejpam-2672	14	2	,	,	PUNCT
ejpam-2672	14	3	few	few	ADJ
ejpam-2672	14	4	articles	article	NOUN
ejpam-2672	14	5	dealt	deal	VERB
ejpam-2672	14	6	with	with	ADP
ejpam-2672	14	7	applying	apply	VERB
ejpam-2672	14	8	iterative	iterative	NOUN
ejpam-2672	14	9	techniques	technique	NOUN
ejpam-2672	14	10	to	to	PART
ejpam-2672	14	11	riesz	riesz	VERB
ejpam-2672	14	12	fractional	fractional	ADJ
ejpam-2672	14	13	partial	partial	ADJ
ejpam-2672	14	14	differential	differential	NOUN
ejpam-2672	14	15	equations	equation	NOUN
ejpam-2672	14	16	(	(	PUNCT
ejpam-2672	14	17	fpdes	fpde	NOUN
ejpam-2672	14	18	)	)	PUNCT
ejpam-2672	14	19	.	.	PUNCT
ejpam-2672	15	1	this	this	PRON
ejpam-2672	15	2	is	be	AUX
ejpam-2672	15	3	due	due	ADJ
ejpam-2672	15	4	to	to	ADP
ejpam-2672	15	5	the	the	DET
ejpam-2672	15	6	difficulty	difficulty	NOUN
ejpam-2672	15	7	in	in	ADP
ejpam-2672	15	8	repeated	repeat	VERB
ejpam-2672	15	9	application	application	NOUN
ejpam-2672	15	10	of	of	ADP
ejpam-2672	15	11	riesz	riesz	PROPN
ejpam-2672	15	12	fractional	fractional	ADJ
ejpam-2672	15	13	derivative	derivative	NOUN
ejpam-2672	15	14	to	to	ADP
ejpam-2672	15	15	solution	solution	NOUN
ejpam-2672	15	16	components	component	NOUN
ejpam-2672	15	17	.	.	PUNCT
ejpam-2672	16	1	this	this	DET
ejpam-2672	16	2	work	work	NOUN
ejpam-2672	16	3	is	be	AUX
ejpam-2672	16	4	based	base	VERB
ejpam-2672	16	5	on	on	ADP
ejpam-2672	16	6	properties	property	NOUN
ejpam-2672	16	7	that	that	PRON
ejpam-2672	16	8	show	show	VERB
ejpam-2672	16	9	repetitive	repetitive	ADJ
ejpam-2672	16	10	behavior	behavior	NOUN
ejpam-2672	16	11	for	for	ADP
ejpam-2672	16	12	complex	complex	ADJ
ejpam-2672	16	13	exponential	exponential	ADJ
ejpam-2672	16	14	function	function	NOUN
ejpam-2672	16	15	,	,	PUNCT
ejpam-2672	16	16	hence	hence	ADV
ejpam-2672	16	17	sine	sine	VERB
ejpam-2672	16	18	and	and	CCONJ
ejpam-2672	16	19	cosine	cosine	NOUN
ejpam-2672	16	20	functions	function	NOUN
ejpam-2672	16	21	,	,	PUNCT
ejpam-2672	16	22	when	when	SCONJ
ejpam-2672	16	23	subjected	subject	VERB
ejpam-2672	16	24	to	to	ADP
ejpam-2672	16	25	the	the	DET
ejpam-2672	16	26	application	application	NOUN
ejpam-2672	16	27	of	of	ADP
ejpam-2672	16	28	riesz	riesz	PROPN
ejpam-2672	16	29	fractional	fractional	ADJ
ejpam-2672	16	30	derivative	derivative	ADJ
ejpam-2672	17	1	[	[	X
ejpam-2672	17	2	6	6	NUM
ejpam-2672	17	3	]	]	PUNCT
ejpam-2672	17	4	and	and	CCONJ
ejpam-2672	17	5	[	[	X
ejpam-2672	17	6	7	7	NUM
ejpam-2672	17	7	]	]	PUNCT
ejpam-2672	17	8	.	.	PUNCT
ejpam-2672	18	1	in	in	ADP
ejpam-2672	18	2	this	this	DET
ejpam-2672	18	3	work	work	NOUN
ejpam-2672	18	4	,	,	PUNCT
ejpam-2672	18	5	the	the	DET
ejpam-2672	18	6	motivation	motivation	NOUN
ejpam-2672	18	7	is	be	AUX
ejpam-2672	18	8	to	to	PART
ejpam-2672	18	9	establish	establish	VERB
ejpam-2672	18	10	the	the	DET
ejpam-2672	18	11	continuation	continuation	NOUN
ejpam-2672	18	12	of	of	ADP
ejpam-2672	18	13	the	the	DET
ejpam-2672	18	14	solution	solution	NOUN
ejpam-2672	18	15	of	of	ADP
ejpam-2672	18	16	the	the	DET
ejpam-2672	18	17	spacefractional	spacefractional	ADJ
ejpam-2672	18	18	wave	wave	NOUN
ejpam-2672	18	19	equation	equation	NOUN
ejpam-2672	18	20	with	with	ADP
ejpam-2672	18	21	spatial	spatial	ADJ
ejpam-2672	18	22	derivative	derivative	NOUN
ejpam-2672	18	23	in	in	ADP
ejpam-2672	18	24	riesz	riesz	PROPN
ejpam-2672	18	25	sense	sense	NOUN
ejpam-2672	18	26	to	to	ADP
ejpam-2672	18	27	the	the	DET
ejpam-2672	18	28	exact	exact	ADJ
ejpam-2672	18	29	solution	solution	NOUN
ejpam-2672	18	30	of	of	ADP
ejpam-2672	18	31	the	the	DET
ejpam-2672	18	32	∗corresponding	∗corresponde	VERB
ejpam-2672	18	33	author	author	NOUN
ejpam-2672	18	34	.	.	PUNCT
ejpam-2672	19	1	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2672	20	1	586	586	NUM
ejpam-2672	20	2	c	c	X
ejpam-2672	20	3	©	©	PROPN
ejpam-2672	20	4	2017	2017	NUM
ejpam-2672	20	5	ejpam	ejpam	NOUN
ejpam-2672	20	6	all	all	DET
ejpam-2672	20	7	rights	right	NOUN
ejpam-2672	20	8	reserved	reserve	VERB
ejpam-2672	20	9	.	.	PUNCT
ejpam-2672	21	1	a.	a.	PROPN
ejpam-2672	21	2	elsaid	elsaid	PROPN
ejpam-2672	21	3	,	,	PUNCT
ejpam-2672	21	4	s.	s.	PROPN
ejpam-2672	21	5	shamseldeen	shamseldeen	PROPN
ejpam-2672	21	6	,	,	PUNCT
ejpam-2672	21	7	s.	s.	PROPN
ejpam-2672	21	8	madkour	madkour	PROPN
ejpam-2672	21	9	/	/	SYM
ejpam-2672	21	10	eur	eur	PROPN
ejpam-2672	21	11	.	.	PUNCT
ejpam-2672	22	1	j.	j.	PROPN
ejpam-2672	22	2	pure	pure	PROPN
ejpam-2672	22	3	appl	appl	PROPN
ejpam-2672	22	4	.	.	PROPN
ejpam-2672	22	5	math	math	PROPN
ejpam-2672	22	6	,	,	PUNCT
ejpam-2672	22	7	10	10	NUM
ejpam-2672	22	8	(	(	PUNCT
ejpam-2672	22	9	3	3	NUM
ejpam-2672	22	10	)	)	PUNCT
ejpam-2672	22	11	(	(	PUNCT
ejpam-2672	22	12	2017	2017	NUM
ejpam-2672	22	13	)	)	PUNCT
ejpam-2672	22	14	,	,	PUNCT
ejpam-2672	22	15	586	586	NUM
ejpam-2672	22	16	-	-	SYM
ejpam-2672	22	17	601	601	NUM
ejpam-2672	22	18	587	587	NUM
ejpam-2672	22	19	corresponding	correspond	VERB
ejpam-2672	22	20	integer	integer	NOUN
ejpam-2672	22	21	-	-	PUNCT
ejpam-2672	22	22	order	order	NOUN
ejpam-2672	22	23	equation	equation	NOUN
ejpam-2672	22	24	as	as	ADP
ejpam-2672	22	25	the	the	DET
ejpam-2672	22	26	order	order	NOUN
ejpam-2672	22	27	of	of	ADP
ejpam-2672	22	28	the	the	DET
ejpam-2672	22	29	fractional	fractional	ADJ
ejpam-2672	22	30	derivative	derivative	ADJ
ejpam-2672	22	31	approaches	approach	VERB
ejpam-2672	22	32	its	its	PRON
ejpam-2672	22	33	integer	integer	NOUN
ejpam-2672	22	34	limit	limit	NOUN
ejpam-2672	22	35	.	.	PUNCT
ejpam-2672	23	1	this	this	DET
ejpam-2672	23	2	objective	objective	NOUN
ejpam-2672	23	3	is	be	AUX
ejpam-2672	23	4	carried	carry	VERB
ejpam-2672	23	5	out	out	ADP
ejpam-2672	23	6	theoretically	theoretically	ADV
ejpam-2672	23	7	then	then	ADV
ejpam-2672	23	8	via	via	ADP
ejpam-2672	23	9	approximate	approximate	ADJ
ejpam-2672	23	10	series	series	PROPN
ejpam-2672	23	11	solution	solution	NOUN
ejpam-2672	23	12	obtained	obtain	VERB
ejpam-2672	23	13	iteratively	iteratively	ADV
ejpam-2672	23	14	by	by	ADP
ejpam-2672	23	15	applying	apply	VERB
ejpam-2672	23	16	the	the	DET
ejpam-2672	23	17	optimal	optimal	ADJ
ejpam-2672	23	18	homotopy	homotopy	NOUN
ejpam-2672	23	19	analysis	analysis	NOUN
ejpam-2672	23	20	method	method	NOUN
ejpam-2672	23	21	(	(	PUNCT
ejpam-2672	23	22	oham	oham	NOUN
ejpam-2672	23	23	)	)	PUNCT
ejpam-2672	23	24	.	.	PUNCT
ejpam-2672	24	1	we	we	PRON
ejpam-2672	24	2	consider	consider	VERB
ejpam-2672	24	3	the	the	DET
ejpam-2672	24	4	space	space	NOUN
ejpam-2672	24	5	-	-	PUNCT
ejpam-2672	24	6	fractional	fractional	ADJ
ejpam-2672	24	7	wave	wave	NOUN
ejpam-2672	24	8	equation	equation	NOUN
ejpam-2672	24	9	of	of	ADP
ejpam-2672	24	10	the	the	DET
ejpam-2672	24	11	form	form	NOUN
ejpam-2672	24	12	∂2	∂2	NOUN
ejpam-2672	24	13	∂t2	∂t2	NOUN
ejpam-2672	24	14	u(x	u(x	NOUN
ejpam-2672	24	15	,	,	PUNCT
ejpam-2672	24	16	t	t	NOUN
ejpam-2672	24	17	)	)	PUNCT
ejpam-2672	24	18	=	=	PUNCT
ejpam-2672	25	1	rαxu(x	rαxu(x	PROPN
ejpam-2672	25	2	,	,	PUNCT
ejpam-2672	25	3	t	t	PROPN
ejpam-2672	25	4	)	)	PUNCT
ejpam-2672	26	1	+	+	NOUN
ejpam-2672	26	2	p	p	X
ejpam-2672	26	3	(	(	PUNCT
ejpam-2672	26	4	u	u	NOUN
ejpam-2672	26	5	)	)	PUNCT
ejpam-2672	26	6	,	,	PUNCT
ejpam-2672	26	7	−∞	−∞	PUNCT
ejpam-2672	26	8	<	<	X
ejpam-2672	26	9	x	x	X
ejpam-2672	26	10	<	<	X
ejpam-2672	26	11	∞	∞	PROPN
ejpam-2672	26	12	,	,	PUNCT
ejpam-2672	26	13	t	t	X
ejpam-2672	26	14	>	>	X
ejpam-2672	26	15	0	0	NUM
ejpam-2672	26	16	,	,	PUNCT
ejpam-2672	26	17	(	(	PUNCT
ejpam-2672	26	18	1	1	X
ejpam-2672	26	19	)	)	PUNCT
ejpam-2672	26	20	subject	subject	NOUN
ejpam-2672	26	21	to	to	ADP
ejpam-2672	26	22	the	the	DET
ejpam-2672	26	23	initial	initial	ADJ
ejpam-2672	26	24	conditions	condition	NOUN
ejpam-2672	26	25			PUNCT
ejpam-2672	26	26	u(x	u(x	NOUN
ejpam-2672	26	27	,	,	PUNCT
ejpam-2672	26	28	0	0	NUM
ejpam-2672	26	29	)	)	PUNCT
ejpam-2672	26	30	=	=	SYM
ejpam-2672	26	31	f1(x	f1(x	PROPN
ejpam-2672	26	32	)	)	PUNCT
ejpam-2672	26	33	,	,	PUNCT
ejpam-2672	26	34	∂	∂	NUM
ejpam-2672	26	35	∂tu(x	∂tu(x	NOUN
ejpam-2672	26	36	,	,	PUNCT
ejpam-2672	26	37	0	0	NUM
ejpam-2672	26	38	)	)	PUNCT
ejpam-2672	26	39	=	=	SYM
ejpam-2672	26	40	f2(x	f2(x	PROPN
ejpam-2672	26	41	)	)	PUNCT
ejpam-2672	26	42	.	.	PUNCT
ejpam-2672	27	1	(	(	PUNCT
ejpam-2672	27	2	2	2	X
ejpam-2672	27	3	)	)	PUNCT
ejpam-2672	27	4	where	where	SCONJ
ejpam-2672	27	5	rαx	rαx	NOUN
ejpam-2672	27	6	denotes	denote	VERB
ejpam-2672	27	7	the	the	DET
ejpam-2672	27	8	riesz	riesz	PROPN
ejpam-2672	27	9	fractional	fractional	ADJ
ejpam-2672	27	10	derivative	derivative	NOUN
ejpam-2672	27	11	(	(	PUNCT
ejpam-2672	27	12	in	in	ADP
ejpam-2672	27	13	space	space	NOUN
ejpam-2672	27	14	)	)	PUNCT
ejpam-2672	27	15	of	of	ADP
ejpam-2672	27	16	order	order	NOUN
ejpam-2672	27	17	α	α	NOUN
ejpam-2672	27	18	.	.	PUNCT
ejpam-2672	28	1	the	the	DET
ejpam-2672	28	2	parameter	parameter	NOUN
ejpam-2672	28	3	α	α	PROPN
ejpam-2672	28	4	is	be	AUX
ejpam-2672	28	5	restricted	restrict	VERB
ejpam-2672	28	6	to	to	ADP
ejpam-2672	28	7	the	the	DET
ejpam-2672	28	8	conditions	condition	NOUN
ejpam-2672	28	9	0	0	PUNCT
ejpam-2672	29	1	<	<	X
ejpam-2672	29	2	α	α	X
ejpam-2672	29	3	<	<	X
ejpam-2672	29	4	2	2	NUM
ejpam-2672	29	5	and	and	CCONJ
ejpam-2672	29	6	α	α	NOUN
ejpam-2672	29	7	6=	6=	ADP
ejpam-2672	29	8	1	1	NUM
ejpam-2672	29	9	.	.	PUNCT
ejpam-2672	30	1	the	the	DET
ejpam-2672	30	2	function	function	NOUN
ejpam-2672	30	3	p	p	NOUN
ejpam-2672	30	4	is	be	AUX
ejpam-2672	30	5	a	a	DET
ejpam-2672	30	6	continuous	continuous	ADJ
ejpam-2672	30	7	function	function	NOUN
ejpam-2672	30	8	in	in	ADP
ejpam-2672	30	9	u	u	NOUN
ejpam-2672	30	10	,	,	PUNCT
ejpam-2672	30	11	and	and	CCONJ
ejpam-2672	30	12	the	the	DET
ejpam-2672	30	13	two	two	NUM
ejpam-2672	30	14	functions	function	NOUN
ejpam-2672	30	15	f1	f1	NOUN
ejpam-2672	30	16	and	and	CCONJ
ejpam-2672	30	17	f2	f2	PROPN
ejpam-2672	30	18	are	be	AUX
ejpam-2672	30	19	functions	function	NOUN
ejpam-2672	30	20	in	in	ADP
ejpam-2672	30	21	the	the	DET
ejpam-2672	30	22	space	space	NOUN
ejpam-2672	30	23	of	of	ADP
ejpam-2672	30	24	integrable	integrable	ADJ
ejpam-2672	30	25	functions	function	NOUN
ejpam-2672	30	26	l1(−∞,∞	l1(−∞,∞	PROPN
ejpam-2672	30	27	)	)	PUNCT
ejpam-2672	30	28	.	.	PUNCT
ejpam-2672	31	1	this	this	DET
ejpam-2672	31	2	paper	paper	NOUN
ejpam-2672	31	3	is	be	AUX
ejpam-2672	31	4	organized	organize	VERB
ejpam-2672	31	5	as	as	SCONJ
ejpam-2672	31	6	follows	follow	VERB
ejpam-2672	31	7	.	.	PUNCT
ejpam-2672	32	1	in	in	ADP
ejpam-2672	32	2	section	section	NOUN
ejpam-2672	32	3	two	two	NUM
ejpam-2672	32	4	,	,	PUNCT
ejpam-2672	32	5	basic	basic	ADJ
ejpam-2672	32	6	definitions	definition	NOUN
ejpam-2672	32	7	of	of	ADP
ejpam-2672	32	8	fractional	fractional	ADJ
ejpam-2672	32	9	derivative	derivative	ADJ
ejpam-2672	32	10	operators	operator	NOUN
ejpam-2672	32	11	involved	involve	VERB
ejpam-2672	32	12	are	be	AUX
ejpam-2672	32	13	presented	present	VERB
ejpam-2672	32	14	.	.	PUNCT
ejpam-2672	33	1	proof	proof	NOUN
ejpam-2672	33	2	of	of	ADP
ejpam-2672	33	3	continuation	continuation	NOUN
ejpam-2672	33	4	of	of	ADP
ejpam-2672	33	5	solution	solution	NOUN
ejpam-2672	33	6	is	be	AUX
ejpam-2672	33	7	presented	present	VERB
ejpam-2672	33	8	in	in	ADP
ejpam-2672	33	9	section	section	NOUN
ejpam-2672	33	10	three	three	NUM
ejpam-2672	33	11	.	.	PUNCT
ejpam-2672	34	1	the	the	DET
ejpam-2672	34	2	oham	oham	NOUN
ejpam-2672	34	3	is	be	AUX
ejpam-2672	34	4	illustrated	illustrate	VERB
ejpam-2672	34	5	in	in	ADP
ejpam-2672	34	6	section	section	NOUN
ejpam-2672	34	7	four	four	NUM
ejpam-2672	34	8	.	.	PUNCT
ejpam-2672	35	1	in	in	ADP
ejpam-2672	35	2	section	section	NOUN
ejpam-2672	35	3	five	five	NUM
ejpam-2672	35	4	,	,	PUNCT
ejpam-2672	35	5	the	the	DET
ejpam-2672	35	6	results	result	NOUN
ejpam-2672	35	7	of	of	ADP
ejpam-2672	35	8	numerical	numerical	ADJ
ejpam-2672	35	9	experiments	experiment	NOUN
ejpam-2672	35	10	are	be	AUX
ejpam-2672	35	11	presented	present	VERB
ejpam-2672	35	12	,	,	PUNCT
ejpam-2672	35	13	considering	consider	VERB
ejpam-2672	35	14	the	the	DET
ejpam-2672	35	15	space	space	NOUN
ejpam-2672	35	16	fractional	fractional	ADJ
ejpam-2672	35	17	sine	sine	NOUN
ejpam-2672	35	18	-	-	PUNCT
ejpam-2672	35	19	gordan	gordan	PROPN
ejpam-2672	35	20	equation	equation	NOUN
ejpam-2672	35	21	.	.	PUNCT
ejpam-2672	36	1	section	section	NOUN
ejpam-2672	36	2	six	six	NUM
ejpam-2672	36	3	contains	contain	VERB
ejpam-2672	36	4	the	the	DET
ejpam-2672	36	5	conclusion	conclusion	NOUN
ejpam-2672	36	6	of	of	ADP
ejpam-2672	36	7	this	this	DET
ejpam-2672	36	8	work	work	NOUN
ejpam-2672	36	9	.	.	PUNCT
ejpam-2672	37	1	2	2	X
ejpam-2672	37	2	.	.	X
ejpam-2672	37	3	fractional	fractional	ADJ
ejpam-2672	37	4	derivatives	derivative	NOUN
ejpam-2672	37	5	and	and	CCONJ
ejpam-2672	37	6	integrals	integral	NOUN
ejpam-2672	37	7	definition	definition	NOUN
ejpam-2672	37	8	1	1	NUM
ejpam-2672	37	9	.	.	PUNCT
ejpam-2672	38	1	a	a	DET
ejpam-2672	38	2	real	real	ADJ
ejpam-2672	38	3	function	function	NOUN
ejpam-2672	38	4	f(x	f(x	PROPN
ejpam-2672	38	5	)	)	PUNCT
ejpam-2672	38	6	,	,	PUNCT
ejpam-2672	38	7	x	x	X
ejpam-2672	38	8	>	>	X
ejpam-2672	38	9	0	0	NUM
ejpam-2672	38	10	,	,	PUNCT
ejpam-2672	38	11	is	be	AUX
ejpam-2672	38	12	said	say	VERB
ejpam-2672	38	13	to	to	PART
ejpam-2672	38	14	be	be	AUX
ejpam-2672	38	15	in	in	ADP
ejpam-2672	38	16	the	the	DET
ejpam-2672	38	17	space	space	NOUN
ejpam-2672	38	18	cµ	cµ	NOUN
ejpam-2672	38	19	,	,	PUNCT
ejpam-2672	38	20	µ	µ	X
ejpam-2672	38	21	∈	∈	NOUN
ejpam-2672	38	22	r	r	NOUN
ejpam-2672	38	23	,	,	PUNCT
ejpam-2672	38	24	if	if	SCONJ
ejpam-2672	38	25	there	there	PRON
ejpam-2672	38	26	exists	exist	VERB
ejpam-2672	38	27	a	a	DET
ejpam-2672	38	28	real	real	ADJ
ejpam-2672	38	29	number	number	NOUN
ejpam-2672	38	30	p	p	PROPN
ejpam-2672	38	31	>	>	X
ejpam-2672	38	32	µ	µ	PROPN
ejpam-2672	38	33	,	,	PUNCT
ejpam-2672	38	34	such	such	ADJ
ejpam-2672	38	35	that	that	SCONJ
ejpam-2672	38	36	f(x	f(x	NOUN
ejpam-2672	38	37	)	)	PUNCT
ejpam-2672	38	38	=	=	SYM
ejpam-2672	39	1	xpf1(x	xpf1(x	NUM
ejpam-2672	39	2	)	)	PUNCT
ejpam-2672	39	3	,	,	PUNCT
ejpam-2672	39	4	where	where	SCONJ
ejpam-2672	39	5	f1(x	f1(x	NOUN
ejpam-2672	39	6	)	)	PUNCT
ejpam-2672	39	7	∈	∈	PROPN
ejpam-2672	39	8	c(0,∞	c(0,∞	NOUN
ejpam-2672	39	9	)	)	PUNCT
ejpam-2672	39	10	,	,	PUNCT
ejpam-2672	39	11	and	and	CCONJ
ejpam-2672	39	12	it	it	PRON
ejpam-2672	39	13	is	be	AUX
ejpam-2672	39	14	said	say	VERB
ejpam-2672	39	15	to	to	PART
ejpam-2672	39	16	be	be	AUX
ejpam-2672	39	17	in	in	ADP
ejpam-2672	39	18	the	the	DET
ejpam-2672	39	19	space	space	NOUN
ejpam-2672	39	20	cmµ	cmµ	NOUN
ejpam-2672	39	21	if	if	SCONJ
ejpam-2672	39	22	fm	fm	PROPN
ejpam-2672	39	23	∈	∈	PROPN
ejpam-2672	39	24	cµ	cµ	VERB
ejpam-2672	39	25	,	,	PUNCT
ejpam-2672	39	26	m	m	PROPN
ejpam-2672	39	27	∈	∈	NOUN
ejpam-2672	39	28	n.	n.	NOUN
ejpam-2672	39	29	definition	definition	NOUN
ejpam-2672	39	30	2	2	NUM
ejpam-2672	39	31	.	.	PUNCT
ejpam-2672	40	1	the	the	DET
ejpam-2672	40	2	riemann	riemann	PROPN
ejpam-2672	40	3	-	-	PUNCT
ejpam-2672	40	4	liouville	liouville	VERB
ejpam-2672	40	5	fractional	fractional	ADJ
ejpam-2672	40	6	integral	integral	ADJ
ejpam-2672	40	7	operator	operator	NOUN
ejpam-2672	40	8	of	of	ADP
ejpam-2672	40	9	order	order	NOUN
ejpam-2672	40	10	α	α	PRON
ejpam-2672	40	11	≥	≥	NOUN
ejpam-2672	40	12	0	0	NUM
ejpam-2672	40	13	of	of	ADP
ejpam-2672	40	14	a	a	DET
ejpam-2672	40	15	function	function	NOUN
ejpam-2672	40	16	f(x	f(x	PROPN
ejpam-2672	40	17	)	)	PUNCT
ejpam-2672	40	18	∈	∈	PROPN
ejpam-2672	40	19	cµ	cµ	PROPN
ejpam-2672	40	20	,	,	PUNCT
ejpam-2672	40	21	µ	µ	PRON
ejpam-2672	40	22	≥	≥	NOUN
ejpam-2672	40	23	−1	−1	NOUN
ejpam-2672	40	24	is	be	AUX
ejpam-2672	40	25	defined	define	VERB
ejpam-2672	40	26	as	as	PROPN
ejpam-2672	40	27	jαf(x	jαf(x	PROPN
ejpam-2672	40	28	)	)	PUNCT
ejpam-2672	40	29	=	=	SYM
ejpam-2672	40	30	1	1	NUM
ejpam-2672	40	31	γ(α	γ(α	NOUN
ejpam-2672	40	32	)	)	PUNCT
ejpam-2672	41	1	x∫	x∫	PROPN
ejpam-2672	41	2	0	0	NUM
ejpam-2672	42	1	(	(	PUNCT
ejpam-2672	42	2	x−	x−	PROPN
ejpam-2672	42	3	τ)α−1f(τ)dτ	τ)α−1f(τ)dτ	PROPN
ejpam-2672	42	4	,	,	PUNCT
ejpam-2672	42	5	α	α	PROPN
ejpam-2672	42	6	>	>	X
ejpam-2672	42	7	0	0	PROPN
ejpam-2672	42	8	,	,	PUNCT
ejpam-2672	42	9	x	x	X
ejpam-2672	42	10	>	>	X
ejpam-2672	42	11	0	0	NUM
ejpam-2672	42	12	,	,	PUNCT
ejpam-2672	42	13	j0f(x	j0f(x	NOUN
ejpam-2672	42	14	)	)	PUNCT
ejpam-2672	42	15	=	=	SYM
ejpam-2672	42	16	f(x	f(x	PROPN
ejpam-2672	42	17	)	)	PUNCT
ejpam-2672	42	18	.	.	PUNCT
ejpam-2672	43	1	(	(	PUNCT
ejpam-2672	43	2	3	3	X
ejpam-2672	43	3	)	)	PUNCT
ejpam-2672	43	4	definition	definition	NOUN
ejpam-2672	43	5	3	3	NUM
ejpam-2672	43	6	.	.	PUNCT
ejpam-2672	44	1	the	the	DET
ejpam-2672	44	2	fractional	fractional	ADJ
ejpam-2672	44	3	derivative	derivative	NOUN
ejpam-2672	44	4	in	in	ADP
ejpam-2672	44	5	riemann	riemann	PROPN
ejpam-2672	44	6	-	-	PUNCT
ejpam-2672	44	7	liouville	liouville	VERB
ejpam-2672	44	8	sense	sense	NOUN
ejpam-2672	44	9	of	of	ADP
ejpam-2672	44	10	f(x),m	f(x),m	NOUN
ejpam-2672	44	11	∈	∈	PROPN
ejpam-2672	44	12	n	n	CCONJ
ejpam-2672	44	13	,	,	PUNCT
ejpam-2672	44	14	x	x	PROPN
ejpam-2672	44	15	>	>	X
ejpam-2672	44	16	0	0	NUM
ejpam-2672	44	17	is	be	AUX
ejpam-2672	44	18	defined	define	VERB
ejpam-2672	44	19	as	as	ADP
ejpam-2672	44	20	dβ	dβ	ADJ
ejpam-2672	44	21	xf(t	xf(t	NOUN
ejpam-2672	44	22	)	)	PUNCT
ejpam-2672	44	23	=	=	PUNCT
ejpam-2672	45	1	dm	dm	NUM
ejpam-2672	45	2	dxm	dxm	PROPN
ejpam-2672	45	3	jm−βf(x	jm−βf(x	PROPN
ejpam-2672	45	4	)	)	PUNCT
ejpam-2672	45	5	,	,	PUNCT
ejpam-2672	45	6	m−	m−	PROPN
ejpam-2672	45	7	1	1	NUM
ejpam-2672	45	8	<	<	X
ejpam-2672	45	9	β	β	X
ejpam-2672	45	10	<	<	X
ejpam-2672	45	11	m.	m.	NOUN
ejpam-2672	45	12	(	(	PUNCT
ejpam-2672	45	13	4	4	X
ejpam-2672	45	14	)	)	PUNCT
ejpam-2672	45	15	definition	definition	NOUN
ejpam-2672	45	16	4	4	NUM
ejpam-2672	45	17	.	.	PUNCT
ejpam-2672	46	1	the	the	DET
ejpam-2672	46	2	fractional	fractional	ADJ
ejpam-2672	46	3	derivative	derivative	NOUN
ejpam-2672	46	4	in	in	ADP
ejpam-2672	46	5	caputo	caputo	PROPN
ejpam-2672	46	6	sense	sense	NOUN
ejpam-2672	46	7	of	of	ADP
ejpam-2672	46	8	f(x	f(x	PROPN
ejpam-2672	46	9	)	)	PUNCT
ejpam-2672	46	10	∈	∈	PROPN
ejpam-2672	46	11	cm−1	cm−1	NOUN
ejpam-2672	46	12	,	,	PUNCT
ejpam-2672	46	13	m	m	PROPN
ejpam-2672	46	14	∈	∈	PROPN
ejpam-2672	46	15	n	n	CCONJ
ejpam-2672	46	16	,	,	PUNCT
ejpam-2672	46	17	x	x	PROPN
ejpam-2672	46	18	>	>	X
ejpam-2672	46	19	0	0	NUM
ejpam-2672	46	20	is	be	AUX
ejpam-2672	46	21	defined	define	VERB
ejpam-2672	46	22	as	as	ADP
ejpam-2672	46	23	cdβ	cdβ	PROPN
ejpam-2672	46	24	xf(x	xf(x	NUM
ejpam-2672	46	25	)	)	PUNCT
ejpam-2672	47	1	=	=	PRON
ejpam-2672	47	2	{	{	PUNCT
ejpam-2672	47	3	jm−β	jm−β	PROPN
ejpam-2672	47	4	dm	dm	PROPN
ejpam-2672	47	5	dxm	dxm	PROPN
ejpam-2672	47	6	f(x	f(x	PROPN
ejpam-2672	47	7	)	)	PUNCT
ejpam-2672	47	8	,	,	PUNCT
ejpam-2672	47	9	m−	m−	PROPN
ejpam-2672	47	10	1	1	NUM
ejpam-2672	47	11	<	<	X
ejpam-2672	47	12	β	β	X
ejpam-2672	47	13	<	<	X
ejpam-2672	47	14	m	m	PROPN
ejpam-2672	47	15	,	,	PUNCT
ejpam-2672	47	16	dm	dm	PROPN
ejpam-2672	47	17	dxm	dxm	PROPN
ejpam-2672	47	18	f(x	f(x	PROPN
ejpam-2672	47	19	)	)	PUNCT
ejpam-2672	47	20	,	,	PUNCT
ejpam-2672	47	21	β	β	X
ejpam-2672	47	22	=	=	PUNCT
ejpam-2672	47	23	m.	m.	NOUN
ejpam-2672	47	24	(	(	PUNCT
ejpam-2672	47	25	5	5	NUM
ejpam-2672	47	26	)	)	PUNCT
ejpam-2672	47	27	a.	a.	NOUN
ejpam-2672	47	28	elsaid	elsaid	PROPN
ejpam-2672	47	29	,	,	PUNCT
ejpam-2672	47	30	s.	s.	PROPN
ejpam-2672	47	31	shamseldeen	shamseldeen	PROPN
ejpam-2672	47	32	,	,	PUNCT
ejpam-2672	47	33	s.	s.	PROPN
ejpam-2672	47	34	madkour	madkour	PROPN
ejpam-2672	47	35	/	/	SYM
ejpam-2672	47	36	eur	eur	PROPN
ejpam-2672	47	37	.	.	PUNCT
ejpam-2672	48	1	j.	j.	PROPN
ejpam-2672	48	2	pure	pure	PROPN
ejpam-2672	48	3	appl	appl	PROPN
ejpam-2672	48	4	.	.	PROPN
ejpam-2672	48	5	math	math	PROPN
ejpam-2672	48	6	,	,	PUNCT
ejpam-2672	48	7	10	10	NUM
ejpam-2672	48	8	(	(	PUNCT
ejpam-2672	48	9	3	3	NUM
ejpam-2672	48	10	)	)	PUNCT
ejpam-2672	48	11	(	(	PUNCT
ejpam-2672	48	12	2017	2017	NUM
ejpam-2672	48	13	)	)	PUNCT
ejpam-2672	48	14	,	,	PUNCT
ejpam-2672	48	15	586	586	NUM
ejpam-2672	48	16	-	-	SYM
ejpam-2672	48	17	601	601	NUM
ejpam-2672	48	18	588	588	NUM
ejpam-2672	48	19	definition	definition	NOUN
ejpam-2672	48	20	5	5	NUM
ejpam-2672	48	21	.	.	PUNCT
ejpam-2672	49	1	the	the	DET
ejpam-2672	49	2	riesz	riesz	PROPN
ejpam-2672	49	3	partial	partial	ADJ
ejpam-2672	49	4	fractional	fractional	ADJ
ejpam-2672	49	5	derivative	derivative	ADJ
ejpam-2672	49	6	rαx	rαx	NOUN
ejpam-2672	49	7	is	be	AUX
ejpam-2672	49	8	defined	define	VERB
ejpam-2672	49	9	as	as	ADP
ejpam-2672	49	10	[	[	X
ejpam-2672	49	11	8	8	NUM
ejpam-2672	49	12	]	]	SYM
ejpam-2672	49	13	rαxu(x	rαxu(x	NOUN
ejpam-2672	49	14	)	)	PUNCT
ejpam-2672	49	15	=	=	SYM
ejpam-2672	50	1	−	−	PROPN
ejpam-2672	50	2	1	1	NUM
ejpam-2672	50	3	2	2	NUM
ejpam-2672	50	4	cos(απ/2	cos(απ/2	PROPN
ejpam-2672	50	5	)	)	PUNCT
ejpam-2672	51	1	[	[	X
ejpam-2672	51	2	dα	dα	DET
ejpam-2672	51	3	+	+	NOUN
ejpam-2672	51	4	u(x	u(x	NOUN
ejpam-2672	51	5	)	)	PUNCT
ejpam-2672	52	1	+	+	ADJ
ejpam-2672	52	2	dα	dα	ADJ
ejpam-2672	52	3	−u(x	−u(x	NOUN
ejpam-2672	52	4	)	)	PUNCT
ejpam-2672	52	5	]	]	PUNCT
ejpam-2672	52	6	,	,	PUNCT
ejpam-2672	52	7	0	0	PUNCT
ejpam-2672	52	8	<	<	X
ejpam-2672	52	9	α	α	X
ejpam-2672	52	10	<	<	X
ejpam-2672	52	11	2	2	NUM
ejpam-2672	52	12	,	,	PUNCT
ejpam-2672	52	13	α	α	PROPN
ejpam-2672	52	14	6=	6=	ADP
ejpam-2672	52	15	1	1	NUM
ejpam-2672	52	16	(	(	PUNCT
ejpam-2672	52	17	6	6	NUM
ejpam-2672	52	18	)	)	PUNCT
ejpam-2672	52	19	where	where	SCONJ
ejpam-2672	52	20	dα	dα	ADJ
ejpam-2672	52	21	±u(x	±u(x	PROPN
ejpam-2672	52	22	)	)	PUNCT
ejpam-2672	52	23	are	be	AUX
ejpam-2672	52	24	the	the	DET
ejpam-2672	52	25	weyl	weyl	VERB
ejpam-2672	52	26	fractional	fractional	ADJ
ejpam-2672	52	27	derivatives	derivative	NOUN
ejpam-2672	52	28	dα	dα	ADJ
ejpam-2672	52	29	±u(x	±u(x	PROPN
ejpam-2672	52	30	)	)	PUNCT
ejpam-2672	52	31	=	=	PRON
ejpam-2672	52	32	{	{	PUNCT
ejpam-2672	52	33	±	±	NUM
ejpam-2672	52	34	d	d	NOUN
ejpam-2672	52	35	dxw	dxw	VERB
ejpam-2672	52	36	1−α	1−α	NUM
ejpam-2672	52	37	±	±	NUM
ejpam-2672	52	38	u(x	u(x	NOUN
ejpam-2672	52	39	)	)	PUNCT
ejpam-2672	52	40	,	,	PUNCT
ejpam-2672	52	41	0	0	NUM
ejpam-2672	52	42	<	<	X
ejpam-2672	52	43	α	α	X
ejpam-2672	52	44	<	<	X
ejpam-2672	52	45	1	1	NUM
ejpam-2672	52	46	d2	d2	PROPN
ejpam-2672	52	47	dx2	dx2	PROPN
ejpam-2672	52	48	w	w	PROPN
ejpam-2672	52	49	2−α	2−α	PROPN
ejpam-2672	52	50	±	±	NUM
ejpam-2672	52	51	u(x	u(x	NOUN
ejpam-2672	52	52	)	)	PUNCT
ejpam-2672	52	53	,	,	PUNCT
ejpam-2672	52	54	1	1	NUM
ejpam-2672	52	55	<	<	X
ejpam-2672	52	56	α	α	X
ejpam-2672	52	57	<	<	X
ejpam-2672	52	58	2	2	NUM
ejpam-2672	52	59	,	,	PUNCT
ejpam-2672	52	60	(	(	PUNCT
ejpam-2672	52	61	7	7	NUM
ejpam-2672	52	62	)	)	PUNCT
ejpam-2672	52	63	and	and	CCONJ
ejpam-2672	52	64	w	w	PROPN
ejpam-2672	52	65	β	β	X
ejpam-2672	52	66	±	±	NUM
ejpam-2672	52	67	denote	denote	VERB
ejpam-2672	52	68	the	the	DET
ejpam-2672	52	69	weyl	weyl	VERB
ejpam-2672	52	70	fractional	fractional	ADJ
ejpam-2672	52	71	integrals	integral	NOUN
ejpam-2672	52	72	of	of	ADP
ejpam-2672	52	73	order	order	NOUN
ejpam-2672	52	74	β	β	X
ejpam-2672	52	75	>	>	X
ejpam-2672	52	76	0	0	NUM
ejpam-2672	52	77	,	,	PUNCT
ejpam-2672	52	78	given	give	VERB
ejpam-2672	52	79	by	by	ADP
ejpam-2672	52	80	w	w	PROPN
ejpam-2672	52	81	β	β	PROPN
ejpam-2672	52	82	+	+	NOUN
ejpam-2672	52	83	u(x	u(x	NOUN
ejpam-2672	52	84	)	)	PUNCT
ejpam-2672	52	85	=	=	SYM
ejpam-2672	52	86	1	1	NUM
ejpam-2672	52	87	γ(β	γ(β	PROPN
ejpam-2672	52	88	)	)	PUNCT
ejpam-2672	53	1	x∫	x∫	PROPN
ejpam-2672	53	2	−∞	−∞	PUNCT
ejpam-2672	53	3	(	(	PUNCT
ejpam-2672	53	4	x−	x−	PROPN
ejpam-2672	53	5	z)β−1u(z)dz	z)β−1u(z)dz	PROPN
ejpam-2672	53	6	,	,	PUNCT
ejpam-2672	53	7	w	w	ADJ
ejpam-2672	53	8	β	β	NOUN
ejpam-2672	53	9	−u(x	−u(x	NOUN
ejpam-2672	53	10	)	)	PUNCT
ejpam-2672	53	11	=	=	SYM
ejpam-2672	53	12	1	1	NUM
ejpam-2672	53	13	γ(β	γ(β	PROPN
ejpam-2672	53	14	)	)	PUNCT
ejpam-2672	53	15	∞∫	∞∫	NOUN
ejpam-2672	53	16	x	x	SYM
ejpam-2672	53	17	(	(	PUNCT
ejpam-2672	53	18	z	z	NOUN
ejpam-2672	53	19	−	−	PROPN
ejpam-2672	53	20	x)β−1u(z)dz	x)β−1u(z)dz	PROPN
ejpam-2672	53	21	.	.	PUNCT
ejpam-2672	54	1	(	(	PUNCT
ejpam-2672	54	2	8)	8)	NUM
ejpam-2672	54	3	when	when	SCONJ
ejpam-2672	54	4	α	α	NOUN
ejpam-2672	54	5	=	=	NOUN
ejpam-2672	54	6	0	0	PUNCT
ejpam-2672	55	1	the	the	DET
ejpam-2672	55	2	weyl	weyl	VERB
ejpam-2672	55	3	fractional	fractional	ADJ
ejpam-2672	55	4	derivative	derivative	ADJ
ejpam-2672	55	5	degenerates	degenerate	NOUN
ejpam-2672	55	6	into	into	ADP
ejpam-2672	55	7	the	the	DET
ejpam-2672	55	8	identity	identity	NOUN
ejpam-2672	55	9	operator	operator	NOUN
ejpam-2672	55	10	d0	d0	NOUN
ejpam-2672	55	11	±u(x	±u(x	PROPN
ejpam-2672	55	12	)	)	PUNCT
ejpam-2672	55	13	=	=	SYM
ejpam-2672	55	14	u(x	u(x	PROPN
ejpam-2672	55	15	)	)	PUNCT
ejpam-2672	55	16	.	.	PUNCT
ejpam-2672	56	1	(	(	PUNCT
ejpam-2672	56	2	9	9	X
ejpam-2672	56	3	)	)	PUNCT
ejpam-2672	56	4	for	for	ADP
ejpam-2672	56	5	continuity	continuity	NOUN
ejpam-2672	56	6	we	we	PRON
ejpam-2672	56	7	have	have	VERB
ejpam-2672	56	8	d1	d1	NOUN
ejpam-2672	56	9	±u(x	±u(x	PROPN
ejpam-2672	56	10	)	)	PUNCT
ejpam-2672	57	1	=	=	SYM
ejpam-2672	57	2	±	±	NUM
ejpam-2672	57	3	d	d	NOUN
ejpam-2672	57	4	dx	dx	PROPN
ejpam-2672	57	5	u(x	u(x	PROPN
ejpam-2672	57	6	)	)	PUNCT
ejpam-2672	57	7	,	,	PUNCT
ejpam-2672	57	8	d2	d2	PROPN
ejpam-2672	57	9	±u(x	±u(x	PROPN
ejpam-2672	57	10	)	)	PUNCT
ejpam-2672	58	1	=	=	SYM
ejpam-2672	58	2	d2	d2	PROPN
ejpam-2672	58	3	dx2	dx2	PROPN
ejpam-2672	58	4	u(x	u(x	PROPN
ejpam-2672	58	5	)	)	PUNCT
ejpam-2672	58	6	.	.	PUNCT
ejpam-2672	59	1	(	(	PUNCT
ejpam-2672	59	2	10	10	NUM
ejpam-2672	59	3	)	)	PUNCT
ejpam-2672	59	4	evidently	evidently	ADV
ejpam-2672	59	5	,	,	PUNCT
ejpam-2672	59	6	in	in	ADP
ejpam-2672	59	7	case	case	NOUN
ejpam-2672	59	8	α	α	X
ejpam-2672	59	9	=	=	SYM
ejpam-2672	59	10	2	2	NUM
ejpam-2672	59	11	,	,	PUNCT
ejpam-2672	59	12	we	we	PRON
ejpam-2672	59	13	define	define	VERB
ejpam-2672	59	14	rαxu(x	rαxu(x	NOUN
ejpam-2672	59	15	)	)	PUNCT
ejpam-2672	59	16	=	=	SYM
ejpam-2672	59	17	d2	d2	PROPN
ejpam-2672	59	18	dx2	dx2	PROPN
ejpam-2672	59	19	u(x	u(x	PROPN
ejpam-2672	59	20	)	)	PUNCT
ejpam-2672	59	21	.	.	PUNCT
ejpam-2672	60	1	(	(	PUNCT
ejpam-2672	60	2	11	11	NUM
ejpam-2672	60	3	)	)	PUNCT
ejpam-2672	60	4	for	for	ADP
ejpam-2672	60	5	the	the	DET
ejpam-2672	60	6	case	case	NOUN
ejpam-2672	60	7	α	α	NOUN
ejpam-2672	60	8	=	=	SYM
ejpam-2672	60	9	1	1	NUM
ejpam-2672	60	10	we	we	PRON
ejpam-2672	60	11	have	have	VERB
ejpam-2672	60	12	r1	r1	NOUN
ejpam-2672	60	13	xu(x	xu(x	NOUN
ejpam-2672	60	14	)	)	PUNCT
ejpam-2672	60	15	=	=	PUNCT
ejpam-2672	61	1	d	d	NUM
ejpam-2672	61	2	dx	dx	PROPN
ejpam-2672	61	3	hu(x	hu(x	NUM
ejpam-2672	61	4	)	)	PUNCT
ejpam-2672	61	5	(	(	PUNCT
ejpam-2672	61	6	12	12	NUM
ejpam-2672	61	7	)	)	PUNCT
ejpam-2672	61	8	=	=	PUNCT
ejpam-2672	62	1	d	d	X
ejpam-2672	62	2	dx	dx	PROPN
ejpam-2672	62	3	1	1	NUM
ejpam-2672	62	4	π	π	PROPN
ejpam-2672	62	5	∞∫	∞∫	PROPN
ejpam-2672	62	6	−∞	−∞	ADP
ejpam-2672	62	7	u(z	u(z	NOUN
ejpam-2672	62	8	)	)	PUNCT
ejpam-2672	62	9	z	z	NOUN
ejpam-2672	62	10	−	−	NOUN
ejpam-2672	62	11	x	x	SYM
ejpam-2672	62	12	dz	dz	PROPN
ejpam-2672	62	13	,	,	PUNCT
ejpam-2672	62	14	(	(	PUNCT
ejpam-2672	62	15	13	13	NUM
ejpam-2672	62	16	)	)	PUNCT
ejpam-2672	62	17	where	where	SCONJ
ejpam-2672	62	18	h	h	NOUN
ejpam-2672	62	19	is	be	AUX
ejpam-2672	62	20	the	the	DET
ejpam-2672	62	21	hilbert	hilbert	NOUN
ejpam-2672	62	22	transform	transform	NOUN
ejpam-2672	62	23	and	and	CCONJ
ejpam-2672	62	24	the	the	DET
ejpam-2672	62	25	integral	integral	ADJ
ejpam-2672	62	26	is	be	AUX
ejpam-2672	62	27	understood	understand	VERB
ejpam-2672	62	28	in	in	ADP
ejpam-2672	62	29	the	the	DET
ejpam-2672	62	30	cauchy	cauchy	ADJ
ejpam-2672	62	31	principal	principal	ADJ
ejpam-2672	62	32	value	value	NOUN
ejpam-2672	62	33	sense	sense	NOUN
ejpam-2672	62	34	.	.	PUNCT
ejpam-2672	63	1	3	3	X
ejpam-2672	63	2	.	.	X
ejpam-2672	63	3	continuation	continuation	NOUN
ejpam-2672	63	4	of	of	ADP
ejpam-2672	63	5	the	the	DET
ejpam-2672	63	6	solution	solution	NOUN
ejpam-2672	63	7	in	in	ADP
ejpam-2672	63	8	this	this	DET
ejpam-2672	63	9	section	section	NOUN
ejpam-2672	63	10	,	,	PUNCT
ejpam-2672	63	11	we	we	PRON
ejpam-2672	63	12	prove	prove	VERB
ejpam-2672	63	13	the	the	DET
ejpam-2672	63	14	continuation	continuation	NOUN
ejpam-2672	63	15	of	of	ADP
ejpam-2672	63	16	the	the	DET
ejpam-2672	63	17	solution	solution	NOUN
ejpam-2672	63	18	to	to	ADP
ejpam-2672	63	19	fractional	fractional	ADJ
ejpam-2672	63	20	-	-	PUNCT
ejpam-2672	63	21	order	order	NOUN
ejpam-2672	63	22	wave	wave	NOUN
ejpam-2672	63	23	equation	equation	NOUN
ejpam-2672	63	24	with	with	ADP
ejpam-2672	63	25	riesz	riesz	PROPN
ejpam-2672	63	26	spatial	spatial	ADJ
ejpam-2672	63	27	derivative	derivative	NOUN
ejpam-2672	63	28	to	to	ADP
ejpam-2672	63	29	the	the	DET
ejpam-2672	63	30	solution	solution	NOUN
ejpam-2672	63	31	of	of	ADP
ejpam-2672	63	32	the	the	DET
ejpam-2672	63	33	corresponding	corresponding	ADJ
ejpam-2672	63	34	integer	integer	NOUN
ejpam-2672	63	35	-	-	PUNCT
ejpam-2672	63	36	order	order	NOUN
ejpam-2672	63	37	equation	equation	NOUN
ejpam-2672	63	38	.	.	PUNCT
ejpam-2672	64	1	a.	a.	PROPN
ejpam-2672	64	2	elsaid	elsaid	PROPN
ejpam-2672	64	3	,	,	PUNCT
ejpam-2672	64	4	s.	s.	PROPN
ejpam-2672	64	5	shamseldeen	shamseldeen	PROPN
ejpam-2672	64	6	,	,	PUNCT
ejpam-2672	64	7	s.	s.	PROPN
ejpam-2672	64	8	madkour	madkour	PROPN
ejpam-2672	64	9	/	/	SYM
ejpam-2672	64	10	eur	eur	PROPN
ejpam-2672	64	11	.	.	PUNCT
ejpam-2672	65	1	j.	j.	PROPN
ejpam-2672	65	2	pure	pure	PROPN
ejpam-2672	65	3	appl	appl	PROPN
ejpam-2672	65	4	.	.	PROPN
ejpam-2672	65	5	math	math	PROPN
ejpam-2672	65	6	,	,	PUNCT
ejpam-2672	65	7	10	10	NUM
ejpam-2672	65	8	(	(	PUNCT
ejpam-2672	65	9	3	3	NUM
ejpam-2672	65	10	)	)	PUNCT
ejpam-2672	65	11	(	(	PUNCT
ejpam-2672	65	12	2017	2017	NUM
ejpam-2672	65	13	)	)	PUNCT
ejpam-2672	65	14	,	,	PUNCT
ejpam-2672	65	15	586	586	NUM
ejpam-2672	65	16	-	-	SYM
ejpam-2672	65	17	601	601	NUM
ejpam-2672	65	18	589	589	NUM
ejpam-2672	65	19	theorem	theorem	NOUN
ejpam-2672	65	20	1	1	NUM
ejpam-2672	65	21	.	.	PUNCT
ejpam-2672	66	1	if	if	SCONJ
ejpam-2672	66	2	f1(x	f1(x	PROPN
ejpam-2672	66	3	)	)	PUNCT
ejpam-2672	66	4	and	and	CCONJ
ejpam-2672	66	5	f2(x	f2(x	NUM
ejpam-2672	66	6	)	)	PUNCT
ejpam-2672	66	7	are	be	AUX
ejpam-2672	66	8	functions	function	NOUN
ejpam-2672	66	9	in	in	ADP
ejpam-2672	66	10	the	the	DET
ejpam-2672	66	11	space	space	NOUN
ejpam-2672	66	12	of	of	ADP
ejpam-2672	66	13	integrable	integrable	ADJ
ejpam-2672	66	14	functions	function	NOUN
ejpam-2672	66	15	l1(−∞,∞	l1(−∞,∞	PROPN
ejpam-2672	66	16	)	)	PUNCT
ejpam-2672	66	17	,	,	PUNCT
ejpam-2672	66	18	then	then	ADV
ejpam-2672	66	19	the	the	DET
ejpam-2672	66	20	exact	exact	ADJ
ejpam-2672	66	21	solution	solution	NOUN
ejpam-2672	66	22	uα(x	uα(x	PROPN
ejpam-2672	66	23	,	,	PUNCT
ejpam-2672	66	24	t	t	PROPN
ejpam-2672	66	25	)	)	PUNCT
ejpam-2672	66	26	of	of	ADP
ejpam-2672	66	27	the	the	DET
ejpam-2672	66	28	space	space	NOUN
ejpam-2672	66	29	fractional	fractional	ADJ
ejpam-2672	66	30	wave	wave	NOUN
ejpam-2672	66	31	equation	equation	NOUN
ejpam-2672	66	32	∂2	∂2	NOUN
ejpam-2672	66	33	∂t2	∂t2	NOUN
ejpam-2672	66	34	u(x	u(x	NOUN
ejpam-2672	66	35	,	,	PUNCT
ejpam-2672	66	36	t	t	NOUN
ejpam-2672	66	37	)	)	PUNCT
ejpam-2672	66	38	=	=	PUNCT
ejpam-2672	67	1	rαxu(x	rαxu(x	PROPN
ejpam-2672	67	2	,	,	PUNCT
ejpam-2672	67	3	t	t	PROPN
ejpam-2672	67	4	)	)	PUNCT
ejpam-2672	67	5	,	,	PUNCT
ejpam-2672	67	6	−∞	−∞	PUNCT
ejpam-2672	67	7	<	<	X
ejpam-2672	67	8	x	x	X
ejpam-2672	67	9	<	<	X
ejpam-2672	67	10	∞	∞	PROPN
ejpam-2672	67	11	t	t	X
ejpam-2672	67	12	>	>	X
ejpam-2672	67	13	0	0	NUM
ejpam-2672	67	14	,	,	PUNCT
ejpam-2672	67	15	(	(	PUNCT
ejpam-2672	67	16	14	14	NUM
ejpam-2672	67	17	)	)	PUNCT
ejpam-2672	67	18	with	with	ADP
ejpam-2672	67	19	the	the	DET
ejpam-2672	67	20	initial	initial	ADJ
ejpam-2672	67	21	conditions	condition	NOUN
ejpam-2672	67	22			PUNCT
ejpam-2672	67	23	u(x	u(x	NOUN
ejpam-2672	67	24	,	,	PUNCT
ejpam-2672	67	25	0	0	NUM
ejpam-2672	67	26	)	)	PUNCT
ejpam-2672	67	27	=	=	SYM
ejpam-2672	67	28	f1(x	f1(x	PROPN
ejpam-2672	67	29	)	)	PUNCT
ejpam-2672	67	30	,	,	PUNCT
ejpam-2672	67	31	∂	∂	NUM
ejpam-2672	67	32	∂tu(x	∂tu(x	NOUN
ejpam-2672	67	33	,	,	PUNCT
ejpam-2672	67	34	0	0	NUM
ejpam-2672	67	35	)	)	PUNCT
ejpam-2672	67	36	=	=	SYM
ejpam-2672	67	37	f2(x	f2(x	PROPN
ejpam-2672	67	38	)	)	PUNCT
ejpam-2672	67	39	.	.	PUNCT
ejpam-2672	68	1	(	(	PUNCT
ejpam-2672	68	2	15	15	NUM
ejpam-2672	68	3	)	)	PUNCT
ejpam-2672	68	4	is	be	AUX
ejpam-2672	68	5	given	give	VERB
ejpam-2672	68	6	by	by	ADP
ejpam-2672	68	7	uα(x	uα(x	NOUN
ejpam-2672	68	8	,	,	PUNCT
ejpam-2672	68	9	t	t	PROPN
ejpam-2672	68	10	)	)	PUNCT
ejpam-2672	68	11	=	=	SYM
ejpam-2672	68	12	1	1	NUM
ejpam-2672	68	13	π	π	X
ejpam-2672	68	14	∞∫	∞∫	PROPN
ejpam-2672	68	15	−∞	−∞	ADP
ejpam-2672	68	16	∞∫	∞∫	PROPN
ejpam-2672	68	17	0	0	PUNCT
ejpam-2672	69	1	(	(	PUNCT
ejpam-2672	69	2	e2,1(−ωα	e2,1(−ωα	NOUN
ejpam-2672	69	3	t2)f1(v	t2)f1(v	NOUN
ejpam-2672	69	4	)	)	PUNCT
ejpam-2672	70	1	+	+	NUM
ejpam-2672	70	2	t	t	NOUN
ejpam-2672	70	3	e2,2(−ωα	e2,2(−ωα	NOUN
ejpam-2672	70	4	t2)f2(v	t2)f2(v	PROPN
ejpam-2672	70	5	)	)	PUNCT
ejpam-2672	70	6	)	)	PUNCT
ejpam-2672	71	1	cos(ω(x−	cos(ω(x−	NOUN
ejpam-2672	71	2	v))dωdv	v))dωdv	NOUN
ejpam-2672	71	3	(	(	PUNCT
ejpam-2672	71	4	16	16	NUM
ejpam-2672	71	5	)	)	PUNCT
ejpam-2672	71	6	where	where	SCONJ
ejpam-2672	71	7	eη	eη	NOUN
ejpam-2672	71	8	,	,	PUNCT
ejpam-2672	71	9	γ(z	γ(z	PROPN
ejpam-2672	71	10	)	)	PUNCT
ejpam-2672	71	11	is	be	AUX
ejpam-2672	71	12	the	the	DET
ejpam-2672	71	13	mittage	mittage	NOUN
ejpam-2672	71	14	leffler	leffl	ADJ
ejpam-2672	71	15	function	function	NOUN
ejpam-2672	71	16	defined	define	VERB
ejpam-2672	71	17	by	by	ADP
ejpam-2672	71	18	[	[	X
ejpam-2672	71	19	16	16	NUM
ejpam-2672	71	20	]	]	X
ejpam-2672	71	21	eη	eη	NOUN
ejpam-2672	71	22	,	,	PUNCT
ejpam-2672	71	23	γ(z	γ(z	PROPN
ejpam-2672	71	24	)	)	PUNCT
ejpam-2672	71	25	=	=	PUNCT
ejpam-2672	72	1	∞∑	∞∑	NUM
ejpam-2672	72	2	n=0	n=0	NUM
ejpam-2672	72	3	zn	zn	PROPN
ejpam-2672	72	4	γ(ηn+	γ(ηn+	X
ejpam-2672	72	5	γ	γ	PROPN
ejpam-2672	72	6	)	)	PUNCT
ejpam-2672	72	7	,	,	PUNCT
ejpam-2672	72	8	(	(	PUNCT
ejpam-2672	72	9	17	17	NUM
ejpam-2672	72	10	)	)	PUNCT
ejpam-2672	72	11	where	where	SCONJ
ejpam-2672	72	12	e2,1(−ωα	e2,1(−ωα	PROPN
ejpam-2672	72	13	t2	t2	PROPN
ejpam-2672	72	14	)	)	PUNCT
ejpam-2672	72	15	=	=	SYM
ejpam-2672	72	16	cos(ωα/2	cos(ωα/2	NUM
ejpam-2672	72	17	t	t	PROPN
ejpam-2672	72	18	)	)	PUNCT
ejpam-2672	72	19	,	,	PUNCT
ejpam-2672	72	20	(	(	PUNCT
ejpam-2672	72	21	18	18	NUM
ejpam-2672	72	22	)	)	PUNCT
ejpam-2672	72	23	e2,2(−ωα	e2,2(−ωα	NOUN
ejpam-2672	72	24	t2	t2	NOUN
ejpam-2672	72	25	)	)	PUNCT
ejpam-2672	72	26	=	=	PRON
ejpam-2672	72	27	sin(ωα/2	sin(ωα/2	NOUN
ejpam-2672	72	28	t	t	PROPN
ejpam-2672	72	29	)	)	PUNCT
ejpam-2672	72	30	ωα/2	ωα/2	NOUN
ejpam-2672	72	31	t	t	NOUN
ejpam-2672	72	32	.	.	PUNCT
ejpam-2672	73	1	(	(	PUNCT
ejpam-2672	73	2	19	19	NUM
ejpam-2672	73	3	)	)	PUNCT
ejpam-2672	73	4	theorem	theorem	NOUN
ejpam-2672	73	5	2	2	NUM
ejpam-2672	73	6	.	.	PUNCT
ejpam-2672	74	1	let	let	VERB
ejpam-2672	74	2	α	α	PRON
ejpam-2672	74	3	∈	∈	PROPN
ejpam-2672	74	4	(	(	PUNCT
ejpam-2672	74	5	1	1	NUM
ejpam-2672	74	6	,	,	PUNCT
ejpam-2672	74	7	2	2	NUM
ejpam-2672	74	8	)	)	PUNCT
ejpam-2672	74	9	,	,	PUNCT
ejpam-2672	74	10	f1(x	f1(x	PROPN
ejpam-2672	74	11	)	)	PUNCT
ejpam-2672	74	12	and	and	CCONJ
ejpam-2672	74	13	f2(x	f2(x	NUM
ejpam-2672	74	14	)	)	PUNCT
ejpam-2672	74	15	are	be	AUX
ejpam-2672	74	16	functions	function	NOUN
ejpam-2672	74	17	in	in	ADP
ejpam-2672	74	18	the	the	DET
ejpam-2672	74	19	space	space	NOUN
ejpam-2672	74	20	of	of	ADP
ejpam-2672	74	21	integrable	integrable	ADJ
ejpam-2672	74	22	functions	function	NOUN
ejpam-2672	74	23	l1(−∞,∞	l1(−∞,∞	PROPN
ejpam-2672	74	24	)	)	PUNCT
ejpam-2672	74	25	,	,	PUNCT
ejpam-2672	74	26	and	and	CCONJ
ejpam-2672	74	27	uα	uα	PROPN
ejpam-2672	74	28	displayed	display	VERB
ejpam-2672	74	29	in	in	ADP
ejpam-2672	74	30	(	(	PUNCT
ejpam-2672	74	31	16	16	NUM
ejpam-2672	74	32	)	)	PUNCT
ejpam-2672	74	33	be	be	AUX
ejpam-2672	74	34	the	the	DET
ejpam-2672	74	35	solution	solution	NOUN
ejpam-2672	74	36	of	of	ADP
ejpam-2672	74	37	the	the	DET
ejpam-2672	74	38	space	space	NOUN
ejpam-2672	74	39	-	-	PUNCT
ejpam-2672	74	40	fractional	fractional	ADJ
ejpam-2672	74	41	problem	problem	NOUN
ejpam-2672	74	42	(	(	PUNCT
ejpam-2672	74	43	14	14	NUM
ejpam-2672	74	44	-	-	SYM
ejpam-2672	74	45	15	15	NUM
ejpam-2672	74	46	)	)	PUNCT
ejpam-2672	74	47	,	,	PUNCT
ejpam-2672	74	48	then	then	ADV
ejpam-2672	74	49	lim	lim	PROPN
ejpam-2672	74	50	α→2	α→2	PUNCT
ejpam-2672	74	51	uα(x	uα(x	PROPN
ejpam-2672	74	52	,	,	PUNCT
ejpam-2672	74	53	t	t	PROPN
ejpam-2672	74	54	)	)	PUNCT
ejpam-2672	74	55	=	=	SYM
ejpam-2672	74	56	u(x	u(x	PROPN
ejpam-2672	74	57	,	,	PUNCT
ejpam-2672	74	58	t	t	PROPN
ejpam-2672	74	59	)	)	PUNCT
ejpam-2672	74	60	,	,	PUNCT
ejpam-2672	74	61	where	where	SCONJ
ejpam-2672	74	62	u(x	u(x	NOUN
ejpam-2672	74	63	,	,	PUNCT
ejpam-2672	74	64	t	t	PROPN
ejpam-2672	74	65	)	)	PUNCT
ejpam-2672	74	66	is	be	AUX
ejpam-2672	74	67	the	the	DET
ejpam-2672	74	68	exact	exact	ADJ
ejpam-2672	74	69	solution	solution	NOUN
ejpam-2672	74	70	of	of	ADP
ejpam-2672	74	71	the	the	DET
ejpam-2672	74	72	integer	integer	NOUN
ejpam-2672	74	73	-	-	PUNCT
ejpam-2672	74	74	order	order	NOUN
ejpam-2672	74	75	wave	wave	NOUN
ejpam-2672	74	76	equation	equation	NOUN
ejpam-2672	74	77	{	{	PUNCT
ejpam-2672	74	78	utt(x	utt(x	PROPN
ejpam-2672	74	79	,	,	PUNCT
ejpam-2672	74	80	t	t	PROPN
ejpam-2672	74	81	)	)	PUNCT
ejpam-2672	74	82	=	=	SYM
ejpam-2672	75	1	uxx(x	uxx(x	PROPN
ejpam-2672	75	2	,	,	PUNCT
ejpam-2672	75	3	t	t	PROPN
ejpam-2672	75	4	)	)	PUNCT
ejpam-2672	75	5	,	,	PUNCT
ejpam-2672	75	6	−∞	−∞	PUNCT
ejpam-2672	75	7	<	<	X
ejpam-2672	75	8	x	x	X
ejpam-2672	75	9	<	<	X
ejpam-2672	75	10	∞	∞	PROPN
ejpam-2672	75	11	,	,	PUNCT
ejpam-2672	75	12	t	t	X
ejpam-2672	75	13	>	>	X
ejpam-2672	75	14	0	0	NUM
ejpam-2672	75	15	,	,	PUNCT
ejpam-2672	75	16	u(x	u(x	NOUN
ejpam-2672	75	17	,	,	PUNCT
ejpam-2672	75	18	0	0	NUM
ejpam-2672	75	19	)	)	PUNCT
ejpam-2672	75	20	=	=	SYM
ejpam-2672	75	21	f1(x	f1(x	PROPN
ejpam-2672	75	22	)	)	PUNCT
ejpam-2672	75	23	,	,	PUNCT
ejpam-2672	75	24	ut(x	ut(x	NOUN
ejpam-2672	75	25	,	,	PUNCT
ejpam-2672	75	26	0	0	NUM
ejpam-2672	75	27	)	)	PUNCT
ejpam-2672	75	28	=	=	SYM
ejpam-2672	75	29	f2(x	f2(x	PROPN
ejpam-2672	75	30	)	)	PUNCT
ejpam-2672	75	31	.	.	PUNCT
ejpam-2672	76	1	(	(	PUNCT
ejpam-2672	76	2	20	20	X
ejpam-2672	76	3	)	)	PUNCT
ejpam-2672	76	4	proof	proof	NOUN
ejpam-2672	76	5	.	.	PUNCT
ejpam-2672	77	1	consider	consider	VERB
ejpam-2672	77	2	the	the	DET
ejpam-2672	77	3	set	set	NOUN
ejpam-2672	77	4	of	of	ADP
ejpam-2672	77	5	functions	function	NOUN
ejpam-2672	77	6	ϕn(ω	ϕn(ω	PUNCT
ejpam-2672	77	7	)	)	PUNCT
ejpam-2672	77	8	and	and	CCONJ
ejpam-2672	77	9	ψn(ω	ψn(ω	NOUN
ejpam-2672	77	10	)	)	PUNCT
ejpam-2672	77	11	for	for	ADP
ejpam-2672	77	12	ω	ω	PROPN
ejpam-2672	77	13	∈	∈	PROPN
ejpam-2672	77	14	(	(	PUNCT
ejpam-2672	77	15	0,∞	0,∞	NOUN
ejpam-2672	77	16	)	)	PUNCT
ejpam-2672	77	17	,	,	PUNCT
ejpam-2672	77	18	n	n	X
ejpam-2672	77	19	∈	∈	NOUN
ejpam-2672	77	20	n+	n+	PUNCT
ejpam-2672	77	21	by	by	ADP
ejpam-2672	77	22	ϕn(ω	ϕn(ω	NOUN
ejpam-2672	77	23	)	)	PUNCT
ejpam-2672	77	24	=	=	SYM
ejpam-2672	78	1	1	1	NUM
ejpam-2672	78	2	π	π	NOUN
ejpam-2672	78	3	e2,1(−ω2−	e2,1(−ω2−	NOUN
ejpam-2672	78	4	1	1	NUM
ejpam-2672	78	5	n+1	n+1	PROPN
ejpam-2672	78	6	t2	t2	NOUN
ejpam-2672	78	7	)	)	PUNCT
ejpam-2672	78	8	∞∫	∞∫	PROPN
ejpam-2672	78	9	−∞	−∞	ADP
ejpam-2672	78	10	f1(v	f1(v	PROPN
ejpam-2672	78	11	)	)	PUNCT
ejpam-2672	78	12	cos(ω(x−	cos(ω(x−	NOUN
ejpam-2672	78	13	v))dv	v))dv	NOUN
ejpam-2672	78	14	,	,	PUNCT
ejpam-2672	78	15	(	(	PUNCT
ejpam-2672	78	16	21	21	NUM
ejpam-2672	78	17	)	)	PUNCT
ejpam-2672	78	18	a.	a.	NOUN
ejpam-2672	78	19	elsaid	elsaid	PROPN
ejpam-2672	78	20	,	,	PUNCT
ejpam-2672	78	21	s.	s.	PROPN
ejpam-2672	78	22	shamseldeen	shamseldeen	PROPN
ejpam-2672	78	23	,	,	PUNCT
ejpam-2672	78	24	s.	s.	PROPN
ejpam-2672	78	25	madkour	madkour	PROPN
ejpam-2672	78	26	/	/	SYM
ejpam-2672	78	27	eur	eur	PROPN
ejpam-2672	78	28	.	.	PUNCT
ejpam-2672	79	1	j.	j.	PROPN
ejpam-2672	79	2	pure	pure	PROPN
ejpam-2672	79	3	appl	appl	PROPN
ejpam-2672	79	4	.	.	PROPN
ejpam-2672	79	5	math	math	PROPN
ejpam-2672	79	6	,	,	PUNCT
ejpam-2672	79	7	10	10	NUM
ejpam-2672	79	8	(	(	PUNCT
ejpam-2672	79	9	3	3	NUM
ejpam-2672	79	10	)	)	PUNCT
ejpam-2672	79	11	(	(	PUNCT
ejpam-2672	79	12	2017	2017	NUM
ejpam-2672	79	13	)	)	PUNCT
ejpam-2672	79	14	,	,	PUNCT
ejpam-2672	79	15	586	586	NUM
ejpam-2672	79	16	-	-	SYM
ejpam-2672	79	17	601	601	NUM
ejpam-2672	79	18	590	590	NUM
ejpam-2672	79	19	ψn(ω	ψn(ω	NOUN
ejpam-2672	79	20	)	)	PUNCT
ejpam-2672	79	21	=	=	SYM
ejpam-2672	80	1	1	1	NUM
ejpam-2672	80	2	π	π	NOUN
ejpam-2672	80	3	te2,2(−ω2−	te2,2(−ω2−	PROPN
ejpam-2672	80	4	1	1	NUM
ejpam-2672	80	5	n+1	n+1	PROPN
ejpam-2672	80	6	t2	t2	PROPN
ejpam-2672	80	7	)	)	PUNCT
ejpam-2672	80	8	∞∫	∞∫	PROPN
ejpam-2672	80	9	−∞	−∞	ADP
ejpam-2672	80	10	f2(v	f2(v	PROPN
ejpam-2672	80	11	)	)	PUNCT
ejpam-2672	80	12	cos(ω(x−	cos(ω(x−	NOUN
ejpam-2672	80	13	v))dv	v))dv	NOUN
ejpam-2672	80	14	.	.	PUNCT
ejpam-2672	81	1	(	(	PUNCT
ejpam-2672	81	2	22	22	NUM
ejpam-2672	81	3	)	)	PUNCT
ejpam-2672	81	4	these	these	DET
ejpam-2672	81	5	two	two	NUM
ejpam-2672	81	6	set	set	NOUN
ejpam-2672	81	7	of	of	ADP
ejpam-2672	81	8	functions	function	NOUN
ejpam-2672	81	9	satisfy	satisfy	NOUN
ejpam-2672	81	10	lebesgue	lebesgue	PROPN
ejpam-2672	81	11	dominated	dominate	VERB
ejpam-2672	81	12	convergence	convergence	NOUN
ejpam-2672	81	13	theorem	theorem	VERB
ejpam-2672	81	14	as	as	ADP
ejpam-2672	81	15	|ϕn(ω)|	|ϕn(ω)|	ADP
ejpam-2672	81	16	≤	≤	NUM
ejpam-2672	81	17	1	1	NUM
ejpam-2672	81	18	π	π	NOUN
ejpam-2672	81	19	∣∣∣e2,1(−ω2−	∣∣∣e2,1(−ω2−	VERB
ejpam-2672	81	20	1	1	NUM
ejpam-2672	81	21	n+1	n+1	PROPN
ejpam-2672	81	22	t2	t2	NOUN
ejpam-2672	81	23	)	)	PUNCT
ejpam-2672	81	24	∣∣∣	∣∣∣	NOUN
ejpam-2672	81	25	∞∫	∞∫	PROPN
ejpam-2672	81	26	−∞	−∞	ADP
ejpam-2672	81	27	|f1(v)|	|f1(v)|	PROPN
ejpam-2672	81	28	|cos(ω(x−	|cos(ω(x−	PROPN
ejpam-2672	81	29	v))|	v))|	PROPN
ejpam-2672	81	30	dv	dv	PROPN
ejpam-2672	81	31	,	,	PUNCT
ejpam-2672	81	32	≤	≤	NUM
ejpam-2672	81	33	1	1	NUM
ejpam-2672	81	34	π	π	NOUN
ejpam-2672	81	35	∣∣∣e2,1(−ω2−	∣∣∣e2,1(−ω2−	VERB
ejpam-2672	81	36	1	1	NUM
ejpam-2672	81	37	n+1	n+1	PROPN
ejpam-2672	81	38	t2	t2	NOUN
ejpam-2672	81	39	)	)	PUNCT
ejpam-2672	81	40	∣∣∣	∣∣∣	NOUN
ejpam-2672	81	41	∞∫	∞∫	PROPN
ejpam-2672	81	42	−∞	−∞	ADP
ejpam-2672	81	43	|f1(v)|	|f1(v)|	PROPN
ejpam-2672	81	44	dv	dv	PROPN
ejpam-2672	81	45	,	,	PUNCT
ejpam-2672	81	46	and	and	CCONJ
ejpam-2672	81	47	since	since	SCONJ
ejpam-2672	81	48	f1	f1	PROPN
ejpam-2672	81	49	∈	∈	PROPN
ejpam-2672	81	50	l1(−∞,∞	l1(−∞,∞	PROPN
ejpam-2672	81	51	)	)	PUNCT
ejpam-2672	81	52	,	,	PUNCT
ejpam-2672	81	53	there	there	PRON
ejpam-2672	81	54	exists	exist	VERB
ejpam-2672	81	55	m	m	VERB
ejpam-2672	81	56	>	>	X
ejpam-2672	81	57	0	0	NUM
ejpam-2672	82	1	such	such	ADJ
ejpam-2672	82	2	that	that	SCONJ
ejpam-2672	82	3	∞∫	∞∫	PROPN
ejpam-2672	82	4	−∞	−∞	ADP
ejpam-2672	82	5	|f1(v)|	|f1(v)|	ADJ
ejpam-2672	82	6	dv	dv	PROPN
ejpam-2672	82	7	<	<	X
ejpam-2672	82	8	m	m	PROPN
ejpam-2672	82	9	.	.	PUNCT
ejpam-2672	83	1	hence	hence	ADV
ejpam-2672	83	2	|ϕn(ω)|	|ϕn(ω)|	ADV
ejpam-2672	83	3	≤	≤	NUM
ejpam-2672	83	4	m	m	VERB
ejpam-2672	83	5	π	π	NOUN
ejpam-2672	83	6	∣∣∣e2,1(−ω2−	∣∣∣e2,1(−ω2−	PROPN
ejpam-2672	83	7	1	1	NUM
ejpam-2672	83	8	n+1	n+1	PROPN
ejpam-2672	83	9	t2	t2	NOUN
ejpam-2672	83	10	)	)	PUNCT
ejpam-2672	83	11	∣∣∣	∣∣∣	NOUN
ejpam-2672	83	12	.	.	PUNCT
ejpam-2672	84	1	(	(	PUNCT
ejpam-2672	84	2	23	23	NUM
ejpam-2672	84	3	)	)	PUNCT
ejpam-2672	84	4	from	from	ADP
ejpam-2672	84	5	[	[	X
ejpam-2672	84	6	16	16	NUM
ejpam-2672	84	7	]	]	X
ejpam-2672	84	8	theorem	theorem	NOUN
ejpam-2672	84	9	(	(	PUNCT
ejpam-2672	84	10	1.6	1.6	NUM
ejpam-2672	84	11	)	)	PUNCT
ejpam-2672	84	12	,	,	PUNCT
ejpam-2672	84	13	there	there	PRON
ejpam-2672	84	14	exits	exit	VERB
ejpam-2672	84	15	k1	k1	PROPN
ejpam-2672	84	16	>	>	X
ejpam-2672	84	17	0	0	NUM
ejpam-2672	85	1	such	such	ADJ
ejpam-2672	85	2	that	that	SCONJ
ejpam-2672	85	3	|eη	|eη	NOUN
ejpam-2672	85	4	,	,	PUNCT
ejpam-2672	85	5	γ(−z)|	γ(−z)|	ADJ
ejpam-2672	85	6	≤	≤	NUM
ejpam-2672	85	7	k1	k1	NOUN
ejpam-2672	85	8	1	1	NUM
ejpam-2672	85	9	+	+	NUM
ejpam-2672	85	10	|z|	|z|	NOUN
ejpam-2672	85	11	,	,	PUNCT
ejpam-2672	85	12	(	(	PUNCT
ejpam-2672	85	13	24	24	NUM
ejpam-2672	85	14	)	)	PUNCT
ejpam-2672	85	15	then	then	ADV
ejpam-2672	85	16	|ϕn(ω)|	|ϕn(ω)|	DET
ejpam-2672	85	17	≤	≤	NOUN
ejpam-2672	85	18	mk1	mk1	VERB
ejpam-2672	85	19	π	π	PROPN
ejpam-2672	85	20	1	1	NUM
ejpam-2672	85	21	1	1	NUM
ejpam-2672	85	22	+	+	NUM
ejpam-2672	85	23	∣∣∣ω2−	∣∣∣ω2−	VERB
ejpam-2672	85	24	1	1	NUM
ejpam-2672	85	25	n+1	n+1	PROPN
ejpam-2672	85	26	t2	t2	PROPN
ejpam-2672	85	27	∣∣∣	∣∣∣	NOUN
ejpam-2672	85	28	,	,	PUNCT
ejpam-2672	85	29	ω	ω	NUM
ejpam-2672	85	30	∈	∈	PROPN
ejpam-2672	85	31	(	(	PUNCT
ejpam-2672	85	32	0,∞	0,∞	NOUN
ejpam-2672	85	33	)	)	PUNCT
ejpam-2672	85	34	,	,	PUNCT
ejpam-2672	85	35	n	n	NOUN
ejpam-2672	85	36	=	=	SYM
ejpam-2672	85	37	1	1	NUM
ejpam-2672	85	38	,	,	PUNCT
ejpam-2672	85	39	2	2	NUM
ejpam-2672	85	40	,	,	PUNCT
ejpam-2672	85	41	...	...	PUNCT
ejpam-2672	85	42	(	(	PUNCT
ejpam-2672	85	43	25	25	NUM
ejpam-2672	85	44	)	)	PUNCT
ejpam-2672	85	45	for	for	ADP
ejpam-2672	85	46	bounded	bound	VERB
ejpam-2672	85	47	time	time	NOUN
ejpam-2672	85	48	interval	interval	NOUN
ejpam-2672	85	49	0	0	PUNCT
ejpam-2672	85	50	<	<	X
ejpam-2672	85	51	t	t	X
ejpam-2672	85	52	<	<	X
ejpam-2672	85	53	t	t	X
ejpam-2672	85	54	<	<	X
ejpam-2672	85	55	∞	∞	PROPN
ejpam-2672	85	56	,	,	PUNCT
ejpam-2672	85	57	there	there	PRON
ejpam-2672	85	58	exists	exist	VERB
ejpam-2672	85	59	k2(ρ	k2(ρ	PROPN
ejpam-2672	85	60	)	)	PUNCT
ejpam-2672	85	61	>	>	X
ejpam-2672	85	62	0	0	NUM
ejpam-2672	86	1	such	such	ADJ
ejpam-2672	86	2	that	that	SCONJ
ejpam-2672	86	3	|ϕn(ω)|	|ϕn(ω)|	PROPN
ejpam-2672	86	4	≤	≤	NOUN
ejpam-2672	86	5	g1(ω	g1(ω	NUM
ejpam-2672	86	6	)	)	PUNCT
ejpam-2672	86	7	=	=	SYM
ejpam-2672	86	8	k2(ρ	k2(ρ	PROPN
ejpam-2672	86	9	)	)	PUNCT
ejpam-2672	86	10	1	1	NUM
ejpam-2672	87	1	+	+	CCONJ
ejpam-2672	87	2	ω1+ρ	ω1+ρ	INTJ
ejpam-2672	87	3	,	,	PUNCT
ejpam-2672	87	4	ρ	ρ	PROPN
ejpam-2672	87	5	∈	∈	PROPN
ejpam-2672	87	6	(	(	PUNCT
ejpam-2672	87	7	0	0	NUM
ejpam-2672	87	8	,	,	PUNCT
ejpam-2672	87	9	0.5	0.5	NUM
ejpam-2672	87	10	)	)	PUNCT
ejpam-2672	87	11	,	,	PUNCT
ejpam-2672	87	12	and	and	CCONJ
ejpam-2672	87	13	g1(ω	g1(ω	X
ejpam-2672	87	14	)	)	PUNCT
ejpam-2672	87	15	∈	∈	PROPN
ejpam-2672	87	16	l1(0,∞	l1(0,∞	NOUN
ejpam-2672	87	17	)	)	PUNCT
ejpam-2672	87	18	since	since	SCONJ
ejpam-2672	87	19	∞∫	∞∫	PROPN
ejpam-2672	87	20	0	0	NUM
ejpam-2672	87	21	|g1(ω)|	|g1(ω)|	PUNCT
ejpam-2672	87	22	dω	dω	ADP
ejpam-2672	87	23	=	=	SYM
ejpam-2672	87	24	k2(ρ)γ	k2(ρ)γ	PROPN
ejpam-2672	87	25	(	(	PUNCT
ejpam-2672	87	26	ρ	ρ	PROPN
ejpam-2672	87	27	1	1	NUM
ejpam-2672	87	28	+	+	NUM
ejpam-2672	87	29	ρ	ρ	NOUN
ejpam-2672	87	30	)	)	PUNCT
ejpam-2672	88	1	γ(1	γ(1	NOUN
ejpam-2672	89	1	+	+	CCONJ
ejpam-2672	89	2	1	1	NUM
ejpam-2672	89	3	1	1	NUM
ejpam-2672	89	4	+	+	NUM
ejpam-2672	89	5	ρ	ρ	NUM
ejpam-2672	89	6	)	)	PUNCT
ejpam-2672	89	7	.	.	PUNCT
ejpam-2672	90	1	(	(	PUNCT
ejpam-2672	90	2	26	26	NUM
ejpam-2672	90	3	)	)	PUNCT
ejpam-2672	90	4	thus	thus	ADV
ejpam-2672	90	5	the	the	DET
ejpam-2672	90	6	set	set	NOUN
ejpam-2672	90	7	of	of	ADP
ejpam-2672	90	8	functions	function	NOUN
ejpam-2672	90	9	ϕn(ω	ϕn(ω	NUM
ejpam-2672	90	10	)	)	PUNCT
ejpam-2672	90	11	satisfy	satisfy	PROPN
ejpam-2672	90	12	lebesgue	lebesgue	PROPN
ejpam-2672	90	13	dominated	dominate	VERB
ejpam-2672	90	14	convergence	convergence	NOUN
ejpam-2672	90	15	theorem	theorem	VERB
ejpam-2672	90	16	.	.	PUNCT
ejpam-2672	91	1	following	follow	VERB
ejpam-2672	91	2	the	the	DET
ejpam-2672	91	3	same	same	ADJ
ejpam-2672	91	4	steps	step	NOUN
ejpam-2672	91	5	,	,	PUNCT
ejpam-2672	91	6	one	one	PRON
ejpam-2672	91	7	can	can	AUX
ejpam-2672	91	8	prove	prove	VERB
ejpam-2672	91	9	that	that	SCONJ
ejpam-2672	91	10	the	the	DET
ejpam-2672	91	11	set	set	NOUN
ejpam-2672	91	12	of	of	ADP
ejpam-2672	91	13	functions	function	NOUN
ejpam-2672	91	14	ψn(ω	ψn(ω	NOUN
ejpam-2672	91	15	)	)	PUNCT
ejpam-2672	91	16	satisfy	satisfy	PROPN
ejpam-2672	91	17	lebesgue	lebesgue	PROPN
ejpam-2672	91	18	dominated	dominate	VERB
ejpam-2672	91	19	convergence	convergence	NOUN
ejpam-2672	91	20	theorem	theorem	VERB
ejpam-2672	91	21	as	as	ADV
ejpam-2672	91	22	well	well	ADV
ejpam-2672	91	23	.	.	PUNCT
ejpam-2672	92	1	now	now	ADV
ejpam-2672	92	2	,	,	PUNCT
ejpam-2672	92	3	as	as	SCONJ
ejpam-2672	92	4	lim	lim	PROPN
ejpam-2672	92	5	n→∞	n→∞	NUM
ejpam-2672	92	6	ϕn(ω	ϕn(ω	PUNCT
ejpam-2672	92	7	)	)	PUNCT
ejpam-2672	92	8	=	=	SYM
ejpam-2672	92	9	1	1	NUM
ejpam-2672	92	10	π	π	NOUN
ejpam-2672	92	11	e2,1(−ω2t2	e2,1(−ω2t2	PROPN
ejpam-2672	92	12	)	)	PUNCT
ejpam-2672	92	13	∞∫	∞∫	PROPN
ejpam-2672	92	14	−∞	−∞	ADP
ejpam-2672	92	15	f1(v	f1(v	PROPN
ejpam-2672	92	16	)	)	PUNCT
ejpam-2672	92	17	cos(ω(x−	cos(ω(x−	NOUN
ejpam-2672	92	18	v))dv	v))dv	NOUN
ejpam-2672	92	19	,	,	PUNCT
ejpam-2672	92	20	(	(	PUNCT
ejpam-2672	92	21	27	27	NUM
ejpam-2672	92	22	)	)	PUNCT
ejpam-2672	92	23	a.	a.	NOUN
ejpam-2672	92	24	elsaid	elsaid	PROPN
ejpam-2672	92	25	,	,	PUNCT
ejpam-2672	92	26	s.	s.	PROPN
ejpam-2672	92	27	shamseldeen	shamseldeen	PROPN
ejpam-2672	92	28	,	,	PUNCT
ejpam-2672	92	29	s.	s.	PROPN
ejpam-2672	92	30	madkour	madkour	PROPN
ejpam-2672	92	31	/	/	SYM
ejpam-2672	92	32	eur	eur	PROPN
ejpam-2672	92	33	.	.	PUNCT
ejpam-2672	93	1	j.	j.	PROPN
ejpam-2672	93	2	pure	pure	PROPN
ejpam-2672	93	3	appl	appl	PROPN
ejpam-2672	93	4	.	.	PROPN
ejpam-2672	93	5	math	math	PROPN
ejpam-2672	93	6	,	,	PUNCT
ejpam-2672	93	7	10	10	NUM
ejpam-2672	93	8	(	(	PUNCT
ejpam-2672	93	9	3	3	NUM
ejpam-2672	93	10	)	)	PUNCT
ejpam-2672	93	11	(	(	PUNCT
ejpam-2672	93	12	2017	2017	NUM
ejpam-2672	93	13	)	)	PUNCT
ejpam-2672	93	14	,	,	PUNCT
ejpam-2672	93	15	586	586	NUM
ejpam-2672	93	16	-	-	SYM
ejpam-2672	93	17	601	601	NUM
ejpam-2672	93	18	591	591	NUM
ejpam-2672	93	19	lim	lim	PROPN
ejpam-2672	93	20	n→∞	n→∞	NUM
ejpam-2672	93	21	ψn(ω	ψn(ω	NOUN
ejpam-2672	93	22	)	)	PUNCT
ejpam-2672	93	23	=	=	SYM
ejpam-2672	93	24	1	1	NUM
ejpam-2672	93	25	π	π	NOUN
ejpam-2672	93	26	te2,2(−ω2t2	te2,2(−ω2t2	PROPN
ejpam-2672	93	27	)	)	PUNCT
ejpam-2672	93	28	∞∫	∞∫	PROPN
ejpam-2672	93	29	−∞	−∞	ADP
ejpam-2672	93	30	f2(v	f2(v	PROPN
ejpam-2672	93	31	)	)	PUNCT
ejpam-2672	93	32	cos(ω(x−	cos(ω(x−	NOUN
ejpam-2672	93	33	v))dv	v))dv	NOUN
ejpam-2672	93	34	.	.	PUNCT
ejpam-2672	94	1	(	(	PUNCT
ejpam-2672	94	2	28	28	NUM
ejpam-2672	94	3	)	)	PUNCT
ejpam-2672	94	4	then	then	ADV
ejpam-2672	94	5	setting	set	VERB
ejpam-2672	94	6	α	α	NOUN
ejpam-2672	94	7	=	=	PUNCT
ejpam-2672	94	8	2−	2−	NUM
ejpam-2672	94	9	1	1	NUM
ejpam-2672	94	10	n+1	n+1	PROPN
ejpam-2672	94	11	u2(x	u2(x	PROPN
ejpam-2672	94	12	,	,	PUNCT
ejpam-2672	94	13	t	t	PROPN
ejpam-2672	94	14	)	)	PUNCT
ejpam-2672	94	15	=	=	PROPN
ejpam-2672	94	16	lim	lim	PROPN
ejpam-2672	94	17	α→2	α→2	NOUN
ejpam-2672	94	18	uα(x	uα(x	PROPN
ejpam-2672	94	19	,	,	PUNCT
ejpam-2672	94	20	t	t	PROPN
ejpam-2672	94	21	)	)	PUNCT
ejpam-2672	95	1	=	=	VERB
ejpam-2672	95	2	lim	lim	PROPN
ejpam-2672	95	3	n→∞	n→∞	NUM
ejpam-2672	95	4	∞∫	∞∫	PROPN
ejpam-2672	95	5	0	0	NUM
ejpam-2672	96	1	[	[	X
ejpam-2672	96	2	ϕn(ω	ϕn(ω	NUM
ejpam-2672	96	3	)	)	PUNCT
ejpam-2672	97	1	+	+	NUM
ejpam-2672	98	1	ψn(ω)]dω	ψn(ω)]dω	PROPN
ejpam-2672	98	2	(	(	PUNCT
ejpam-2672	98	3	29	29	NUM
ejpam-2672	98	4	)	)	PUNCT
ejpam-2672	98	5	=	=	SYM
ejpam-2672	99	1	∞∫	∞∫	PROPN
ejpam-2672	99	2	0	0	NUM
ejpam-2672	100	1	lim	lim	PROPN
ejpam-2672	100	2	n→∞	n→∞	X
ejpam-2672	101	1	[	[	X
ejpam-2672	101	2	ϕn(ω	ϕn(ω	NUM
ejpam-2672	101	3	)	)	PUNCT
ejpam-2672	102	1	+	+	CCONJ
ejpam-2672	102	2	ψn(ω)]dω	ψn(ω)]dω	NOUN
ejpam-2672	102	3	,	,	PUNCT
ejpam-2672	102	4	(	(	PUNCT
ejpam-2672	102	5	30	30	NUM
ejpam-2672	102	6	)	)	PUNCT
ejpam-2672	102	7	which	which	PRON
ejpam-2672	102	8	yields	yield	VERB
ejpam-2672	102	9	u2(x	u2(x	PROPN
ejpam-2672	102	10	,	,	PUNCT
ejpam-2672	102	11	t	t	PROPN
ejpam-2672	102	12	)	)	PUNCT
ejpam-2672	102	13	=	=	SYM
ejpam-2672	102	14	1	1	NUM
ejpam-2672	102	15	π	π	X
ejpam-2672	102	16	∞∫	∞∫	PROPN
ejpam-2672	102	17	−∞	−∞	ADP
ejpam-2672	102	18	∞∫	∞∫	PROPN
ejpam-2672	102	19	0	0	NUM
ejpam-2672	102	20	(	(	PUNCT
ejpam-2672	102	21	cos(ω	cos(ω	PROPN
ejpam-2672	102	22	t)q1(v	t)q1(v	NOUN
ejpam-2672	102	23	)	)	PUNCT
ejpam-2672	102	24	+	+	CCONJ
ejpam-2672	102	25	sin(ω	sin(ω	PROPN
ejpam-2672	102	26	t	t	PROPN
ejpam-2672	102	27	)	)	PUNCT
ejpam-2672	102	28	ω	ω	PROPN
ejpam-2672	102	29	q2(v	q2(v	PROPN
ejpam-2672	102	30	)	)	PUNCT
ejpam-2672	102	31	)	)	PUNCT
ejpam-2672	102	32	cos(ω(x−	cos(ω(x−	NOUN
ejpam-2672	102	33	v))dωdv	v))dωdv	NOUN
ejpam-2672	102	34	,	,	PUNCT
ejpam-2672	102	35	which	which	PRON
ejpam-2672	102	36	is	be	AUX
ejpam-2672	102	37	the	the	DET
ejpam-2672	102	38	exact	exact	ADJ
ejpam-2672	102	39	solution	solution	NOUN
ejpam-2672	102	40	of	of	ADP
ejpam-2672	102	41	the	the	DET
ejpam-2672	102	42	integer	integer	NOUN
ejpam-2672	102	43	-	-	PUNCT
ejpam-2672	102	44	order	order	NOUN
ejpam-2672	102	45	wave	wave	NOUN
ejpam-2672	102	46	equation	equation	NOUN
ejpam-2672	102	47	(	(	PUNCT
ejpam-2672	102	48	20	20	NUM
ejpam-2672	102	49	)	)	PUNCT
ejpam-2672	102	50	.	.	PUNCT
ejpam-2672	103	1	4	4	X
ejpam-2672	103	2	.	.	X
ejpam-2672	103	3	optimal	optimal	ADJ
ejpam-2672	103	4	homotopy	homotopy	NOUN
ejpam-2672	103	5	analysis	analysis	NOUN
ejpam-2672	103	6	method	method	NOUN
ejpam-2672	103	7	(	(	PUNCT
ejpam-2672	103	8	oham	oham	NOUN
ejpam-2672	103	9	)	)	PUNCT
ejpam-2672	103	10	we	we	PRON
ejpam-2672	103	11	begin	begin	VERB
ejpam-2672	103	12	by	by	ADP
ejpam-2672	103	13	illustrating	illustrate	VERB
ejpam-2672	103	14	the	the	DET
ejpam-2672	103	15	classical	classical	ADJ
ejpam-2672	103	16	homotopy	homotopy	NOUN
ejpam-2672	103	17	analysis	analysis	NOUN
ejpam-2672	103	18	method	method	NOUN
ejpam-2672	103	19	(	(	PUNCT
ejpam-2672	103	20	ham	ham	NOUN
ejpam-2672	103	21	)	)	PUNCT
ejpam-2672	103	22	.	.	PUNCT
ejpam-2672	104	1	consider	consider	VERB
ejpam-2672	104	2	the	the	DET
ejpam-2672	104	3	following	follow	VERB
ejpam-2672	104	4	nonlinear	nonlinear	ADJ
ejpam-2672	104	5	equation	equation	NOUN
ejpam-2672	104	6	n	n	PRON
ejpam-2672	104	7	[	[	X
ejpam-2672	104	8	u(x	u(x	PROPN
ejpam-2672	104	9	,	,	PUNCT
ejpam-2672	104	10	t	t	PROPN
ejpam-2672	104	11	)	)	PUNCT
ejpam-2672	104	12	]	]	PUNCT
ejpam-2672	105	1	=	=	PUNCT
ejpam-2672	105	2	0	0	NUM
ejpam-2672	105	3	,	,	PUNCT
ejpam-2672	105	4	(	(	PUNCT
ejpam-2672	105	5	31	31	NUM
ejpam-2672	105	6	)	)	PUNCT
ejpam-2672	105	7	where	where	SCONJ
ejpam-2672	105	8	n	n	PRON
ejpam-2672	105	9	is	be	AUX
ejpam-2672	105	10	a	a	DET
ejpam-2672	105	11	nonlinear	nonlinear	ADJ
ejpam-2672	105	12	operator	operator	NOUN
ejpam-2672	105	13	,	,	PUNCT
ejpam-2672	105	14	u(x	u(x	PROPN
ejpam-2672	105	15	,	,	PUNCT
ejpam-2672	105	16	t	t	PROPN
ejpam-2672	105	17	)	)	PUNCT
ejpam-2672	105	18	is	be	AUX
ejpam-2672	105	19	the	the	DET
ejpam-2672	105	20	unknown	unknown	ADJ
ejpam-2672	105	21	function	function	NOUN
ejpam-2672	105	22	and	and	CCONJ
ejpam-2672	105	23	x	x	SYM
ejpam-2672	105	24	and	and	CCONJ
ejpam-2672	105	25	t	t	PROPN
ejpam-2672	105	26	denote	denote	VERB
ejpam-2672	105	27	spatial	spatial	ADJ
ejpam-2672	105	28	and	and	CCONJ
ejpam-2672	105	29	temporal	temporal	ADJ
ejpam-2672	105	30	independent	independent	ADJ
ejpam-2672	105	31	variables	variable	NOUN
ejpam-2672	105	32	,	,	PUNCT
ejpam-2672	105	33	respectively	respectively	ADV
ejpam-2672	105	34	.	.	PUNCT
ejpam-2672	106	1	by	by	ADP
ejpam-2672	106	2	generalizing	generalize	VERB
ejpam-2672	106	3	the	the	DET
ejpam-2672	106	4	traditional	traditional	ADJ
ejpam-2672	106	5	homotopy	homotopy	NOUN
ejpam-2672	106	6	method	method	NOUN
ejpam-2672	106	7	,	,	PUNCT
ejpam-2672	106	8	liao	liao	PROPN
ejpam-2672	107	1	[	[	X
ejpam-2672	107	2	9	9	NUM
ejpam-2672	107	3	]	]	PUNCT
ejpam-2672	107	4	constructs	construct	VERB
ejpam-2672	107	5	the	the	DET
ejpam-2672	107	6	so	so	ADV
ejpam-2672	107	7	-	-	PUNCT
ejpam-2672	107	8	called	call	VERB
ejpam-2672	107	9	zero	zero	NUM
ejpam-2672	107	10	-	-	PUNCT
ejpam-2672	107	11	order	order	NOUN
ejpam-2672	107	12	deformation	deformation	NOUN
ejpam-2672	107	13	equation	equation	NOUN
ejpam-2672	107	14	(	(	PUNCT
ejpam-2672	107	15	1−	1−	NUM
ejpam-2672	107	16	p)l[φ(x	p)l[φ(x	PROPN
ejpam-2672	107	17	,	,	PUNCT
ejpam-2672	107	18	t	t	PROPN
ejpam-2672	107	19	;	;	PUNCT
ejpam-2672	107	20	p)−	p)−	PROPN
ejpam-2672	107	21	u0(x	u0(x	PROPN
ejpam-2672	107	22	,	,	PUNCT
ejpam-2672	107	23	t	t	PROPN
ejpam-2672	107	24	)	)	PUNCT
ejpam-2672	107	25	]	]	PUNCT
ejpam-2672	108	1	=	=	PUNCT
ejpam-2672	108	2	p	p	X
ejpam-2672	108	3	~	~	PROPN
ejpam-2672	108	4	h(x	h(x	PROPN
ejpam-2672	108	5	,	,	PUNCT
ejpam-2672	108	6	t)n	t)n	PUNCT
ejpam-2672	109	1	[	[	X
ejpam-2672	109	2	φ(x	φ(x	PROPN
ejpam-2672	109	3	,	,	PUNCT
ejpam-2672	109	4	t	t	PROPN
ejpam-2672	109	5	;	;	PUNCT
ejpam-2672	109	6	p	p	X
ejpam-2672	109	7	)	)	PUNCT
ejpam-2672	109	8	]	]	PUNCT
ejpam-2672	109	9	,	,	PUNCT
ejpam-2672	109	10	(	(	PUNCT
ejpam-2672	109	11	32	32	NUM
ejpam-2672	109	12	)	)	PUNCT
ejpam-2672	109	13	where	where	SCONJ
ejpam-2672	109	14	p	p	PRON
ejpam-2672	109	15	∈	∈	PROPN
ejpam-2672	110	1	[	[	X
ejpam-2672	110	2	0	0	NUM
ejpam-2672	110	3	,	,	PUNCT
ejpam-2672	110	4	1	1	NUM
ejpam-2672	110	5	]	]	PUNCT
ejpam-2672	110	6	is	be	AUX
ejpam-2672	110	7	an	an	DET
ejpam-2672	110	8	embedding	embed	VERB
ejpam-2672	110	9	parameter	parameter	NOUN
ejpam-2672	110	10	,	,	PUNCT
ejpam-2672	110	11	~	~	PUNCT
ejpam-2672	110	12	is	be	AUX
ejpam-2672	110	13	a	a	DET
ejpam-2672	110	14	nonzero	nonzero	ADJ
ejpam-2672	110	15	auxiliary	auxiliary	ADJ
ejpam-2672	110	16	parameter	parameter	NOUN
ejpam-2672	110	17	,	,	PUNCT
ejpam-2672	110	18	h(x	h(x	PROPN
ejpam-2672	110	19	,	,	PUNCT
ejpam-2672	110	20	t	t	PROPN
ejpam-2672	110	21	)	)	PUNCT
ejpam-2672	110	22	is	be	AUX
ejpam-2672	110	23	an	an	DET
ejpam-2672	110	24	auxiliary	auxiliary	ADJ
ejpam-2672	110	25	function	function	NOUN
ejpam-2672	110	26	,	,	PUNCT
ejpam-2672	110	27	l	l	NOUN
ejpam-2672	110	28	is	be	AUX
ejpam-2672	110	29	an	an	DET
ejpam-2672	110	30	auxiliary	auxiliary	ADJ
ejpam-2672	110	31	linear	linear	NOUN
ejpam-2672	110	32	operator	operator	NOUN
ejpam-2672	110	33	,	,	PUNCT
ejpam-2672	110	34	u0(x	u0(x	PROPN
ejpam-2672	110	35	,	,	PUNCT
ejpam-2672	110	36	t	t	PROPN
ejpam-2672	110	37	)	)	PUNCT
ejpam-2672	110	38	is	be	AUX
ejpam-2672	110	39	an	an	DET
ejpam-2672	110	40	initial	initial	ADJ
ejpam-2672	110	41	guess	guess	NOUN
ejpam-2672	110	42	of	of	ADP
ejpam-2672	110	43	u(x	u(x	NOUN
ejpam-2672	110	44	,	,	PUNCT
ejpam-2672	110	45	t	t	PROPN
ejpam-2672	110	46	)	)	PUNCT
ejpam-2672	110	47	and	and	CCONJ
ejpam-2672	110	48	φ(x	φ(x	PROPN
ejpam-2672	110	49	,	,	PUNCT
ejpam-2672	110	50	t	t	PROPN
ejpam-2672	110	51	;	;	PUNCT
ejpam-2672	110	52	p	p	X
ejpam-2672	110	53	)	)	PUNCT
ejpam-2672	110	54	is	be	AUX
ejpam-2672	110	55	an	an	DET
ejpam-2672	110	56	unknown	unknown	ADJ
ejpam-2672	110	57	function	function	NOUN
ejpam-2672	110	58	.	.	PUNCT
ejpam-2672	111	1	obviously	obviously	ADV
ejpam-2672	111	2	,	,	PUNCT
ejpam-2672	111	3	when	when	SCONJ
ejpam-2672	111	4	p	p	PROPN
ejpam-2672	111	5	=	=	NOUN
ejpam-2672	111	6	0	0	PROPN
ejpam-2672	111	7	and	and	CCONJ
ejpam-2672	111	8	p	p	X
ejpam-2672	111	9	=	=	NOUN
ejpam-2672	111	10	1	1	NUM
ejpam-2672	111	11	,	,	PUNCT
ejpam-2672	111	12	we	we	PRON
ejpam-2672	111	13	have	have	VERB
ejpam-2672	111	14	φ(x	φ(x	NOUN
ejpam-2672	111	15	,	,	PUNCT
ejpam-2672	111	16	t	t	NOUN
ejpam-2672	111	17	;	;	PUNCT
ejpam-2672	111	18	0	0	NUM
ejpam-2672	111	19	)	)	PUNCT
ejpam-2672	111	20	=	=	SYM
ejpam-2672	111	21	u0(x	u0(x	PROPN
ejpam-2672	111	22	,	,	PUNCT
ejpam-2672	111	23	t	t	PROPN
ejpam-2672	111	24	)	)	PUNCT
ejpam-2672	111	25	,	,	PUNCT
ejpam-2672	111	26	φ(x	φ(x	PROPN
ejpam-2672	111	27	,	,	PUNCT
ejpam-2672	111	28	t	t	PROPN
ejpam-2672	111	29	;	;	PUNCT
ejpam-2672	111	30	1	1	X
ejpam-2672	111	31	)	)	PUNCT
ejpam-2672	111	32	=	=	SYM
ejpam-2672	111	33	u(x	u(x	NOUN
ejpam-2672	111	34	,	,	PUNCT
ejpam-2672	111	35	t	t	PROPN
ejpam-2672	111	36	)	)	PUNCT
ejpam-2672	111	37	,	,	PUNCT
ejpam-2672	111	38	respectively	respectively	ADV
ejpam-2672	111	39	.	.	PUNCT
ejpam-2672	112	1	thus	thus	ADV
ejpam-2672	112	2	,	,	PUNCT
ejpam-2672	112	3	as	as	SCONJ
ejpam-2672	112	4	p	p	NOUN
ejpam-2672	112	5	increases	increase	VERB
ejpam-2672	112	6	from	from	ADP
ejpam-2672	112	7	0	0	NUM
ejpam-2672	112	8	to	to	ADP
ejpam-2672	112	9	1	1	NUM
ejpam-2672	112	10	,	,	PUNCT
ejpam-2672	112	11	the	the	DET
ejpam-2672	112	12	solution	solution	NOUN
ejpam-2672	112	13	φ(x	φ(x	PROPN
ejpam-2672	112	14	,	,	PUNCT
ejpam-2672	112	15	t	t	PROPN
ejpam-2672	112	16	;	;	PUNCT
ejpam-2672	112	17	p	p	X
ejpam-2672	112	18	)	)	PUNCT
ejpam-2672	112	19	varies	vary	VERB
ejpam-2672	112	20	from	from	ADP
ejpam-2672	112	21	the	the	DET
ejpam-2672	112	22	initial	initial	ADJ
ejpam-2672	112	23	guess	guess	NOUN
ejpam-2672	112	24	u0(x	u0(x	SYM
ejpam-2672	112	25	,	,	PUNCT
ejpam-2672	112	26	t	t	PROPN
ejpam-2672	112	27	)	)	PUNCT
ejpam-2672	112	28	to	to	ADP
ejpam-2672	112	29	the	the	DET
ejpam-2672	112	30	solution	solution	NOUN
ejpam-2672	112	31	u(x	u(x	NOUN
ejpam-2672	112	32	,	,	PUNCT
ejpam-2672	112	33	t	t	PROPN
ejpam-2672	112	34	)	)	PUNCT
ejpam-2672	112	35	.	.	PUNCT
ejpam-2672	113	1	by	by	ADP
ejpam-2672	113	2	expanding	expand	VERB
ejpam-2672	113	3	φ(x	φ(x	PROPN
ejpam-2672	113	4	,	,	PUNCT
ejpam-2672	113	5	t	t	PROPN
ejpam-2672	113	6	;	;	PUNCT
ejpam-2672	113	7	p	p	X
ejpam-2672	113	8	)	)	PUNCT
ejpam-2672	113	9	in	in	ADP
ejpam-2672	113	10	taylor	taylor	PROPN
ejpam-2672	113	11	series	series	PROPN
ejpam-2672	113	12	with	with	ADP
ejpam-2672	113	13	respect	respect	NOUN
ejpam-2672	113	14	to	to	ADP
ejpam-2672	113	15	p	p	PRON
ejpam-2672	113	16	,	,	PUNCT
ejpam-2672	113	17	we	we	PRON
ejpam-2672	113	18	have	have	VERB
ejpam-2672	113	19	φ(x	φ(x	NOUN
ejpam-2672	113	20	,	,	PUNCT
ejpam-2672	113	21	t	t	PROPN
ejpam-2672	113	22	;	;	PUNCT
ejpam-2672	113	23	p	p	X
ejpam-2672	113	24	)	)	PUNCT
ejpam-2672	113	25	=	=	SYM
ejpam-2672	113	26	u0(x	u0(x	PROPN
ejpam-2672	113	27	,	,	PUNCT
ejpam-2672	113	28	t	t	PROPN
ejpam-2672	113	29	)	)	PUNCT
ejpam-2672	114	1	+	+	CCONJ
ejpam-2672	114	2	∞∑	∞∑	PROPN
ejpam-2672	114	3	m=1	m=1	X
ejpam-2672	114	4	um(x	um(x	PROPN
ejpam-2672	114	5	,	,	PUNCT
ejpam-2672	114	6	t)pm	t)pm	PROPN
ejpam-2672	114	7	,	,	PUNCT
ejpam-2672	114	8	(	(	PUNCT
ejpam-2672	114	9	33	33	NUM
ejpam-2672	114	10	)	)	PUNCT
ejpam-2672	114	11	a.	a.	NOUN
ejpam-2672	114	12	elsaid	elsaid	PROPN
ejpam-2672	114	13	,	,	PUNCT
ejpam-2672	114	14	s.	s.	PROPN
ejpam-2672	114	15	shamseldeen	shamseldeen	PROPN
ejpam-2672	114	16	,	,	PUNCT
ejpam-2672	114	17	s.	s.	PROPN
ejpam-2672	114	18	madkour	madkour	PROPN
ejpam-2672	114	19	/	/	SYM
ejpam-2672	114	20	eur	eur	PROPN
ejpam-2672	114	21	.	.	PUNCT
ejpam-2672	115	1	j.	j.	PROPN
ejpam-2672	115	2	pure	pure	PROPN
ejpam-2672	115	3	appl	appl	PROPN
ejpam-2672	115	4	.	.	PROPN
ejpam-2672	115	5	math	math	PROPN
ejpam-2672	115	6	,	,	PUNCT
ejpam-2672	115	7	10	10	NUM
ejpam-2672	115	8	(	(	PUNCT
ejpam-2672	115	9	3	3	NUM
ejpam-2672	115	10	)	)	PUNCT
ejpam-2672	115	11	(	(	PUNCT
ejpam-2672	115	12	2017	2017	NUM
ejpam-2672	115	13	)	)	PUNCT
ejpam-2672	115	14	,	,	PUNCT
ejpam-2672	115	15	586	586	NUM
ejpam-2672	115	16	-	-	SYM
ejpam-2672	115	17	601	601	NUM
ejpam-2672	115	18	592	592	NUM
ejpam-2672	115	19	where	where	SCONJ
ejpam-2672	115	20	um(x	um(x	NUM
ejpam-2672	115	21	,	,	PUNCT
ejpam-2672	115	22	t	t	PROPN
ejpam-2672	115	23	)	)	PUNCT
ejpam-2672	115	24	=	=	SYM
ejpam-2672	115	25	1	1	NUM
ejpam-2672	115	26	m	m	NOUN
ejpam-2672	115	27	!	!	PUNCT
ejpam-2672	116	1	∂mφ(x	∂mφ(x	PROPN
ejpam-2672	116	2	,	,	PUNCT
ejpam-2672	116	3	t	t	PROPN
ejpam-2672	116	4	;	;	PUNCT
ejpam-2672	116	5	p	p	X
ejpam-2672	116	6	)	)	PUNCT
ejpam-2672	116	7	∂pm	∂pm	PROPN
ejpam-2672	116	8	|p=0	|p=0	PROPN
ejpam-2672	116	9	.	.	PUNCT
ejpam-2672	117	1	(	(	PUNCT
ejpam-2672	117	2	34	34	NUM
ejpam-2672	117	3	)	)	PUNCT
ejpam-2672	117	4	if	if	SCONJ
ejpam-2672	117	5	the	the	DET
ejpam-2672	117	6	auxiliary	auxiliary	ADJ
ejpam-2672	117	7	linear	linear	NOUN
ejpam-2672	117	8	operator	operator	NOUN
ejpam-2672	117	9	,	,	PUNCT
ejpam-2672	117	10	the	the	DET
ejpam-2672	117	11	initial	initial	ADJ
ejpam-2672	117	12	guess	guess	NOUN
ejpam-2672	117	13	and	and	CCONJ
ejpam-2672	117	14	the	the	DET
ejpam-2672	117	15	auxiliary	auxiliary	ADJ
ejpam-2672	117	16	parameter	parameter	NOUN
ejpam-2672	117	17	~	~	PUNCT
ejpam-2672	117	18	and	and	CCONJ
ejpam-2672	117	19	the	the	DET
ejpam-2672	117	20	auxiliary	auxiliary	ADJ
ejpam-2672	117	21	function	function	NOUN
ejpam-2672	117	22	are	be	AUX
ejpam-2672	117	23	so	so	ADV
ejpam-2672	117	24	properly	properly	ADV
ejpam-2672	117	25	chosen	choose	VERB
ejpam-2672	117	26	,	,	PUNCT
ejpam-2672	117	27	then	then	ADV
ejpam-2672	117	28	,	,	PUNCT
ejpam-2672	117	29	as	as	SCONJ
ejpam-2672	117	30	proved	prove	VERB
ejpam-2672	117	31	by	by	ADP
ejpam-2672	117	32	liao	liao	PROPN
ejpam-2672	118	1	[	[	X
ejpam-2672	118	2	9	9	NUM
ejpam-2672	118	3	]	]	PUNCT
ejpam-2672	118	4	,	,	PUNCT
ejpam-2672	118	5	series	series	NOUN
ejpam-2672	118	6	(	(	PUNCT
ejpam-2672	118	7	33	33	NUM
ejpam-2672	118	8	)	)	PUNCT
ejpam-2672	118	9	converges	converge	VERB
ejpam-2672	118	10	at	at	ADP
ejpam-2672	118	11	p	p	NOUN
ejpam-2672	118	12	=	=	PROPN
ejpam-2672	118	13	1	1	NUM
ejpam-2672	118	14	and	and	CCONJ
ejpam-2672	118	15	one	one	NUM
ejpam-2672	118	16	has	have	VERB
ejpam-2672	118	17	u(x	u(x	NOUN
ejpam-2672	118	18	,	,	PUNCT
ejpam-2672	118	19	t	t	NOUN
ejpam-2672	118	20	)	)	PUNCT
ejpam-2672	118	21	=	=	SYM
ejpam-2672	118	22	u0(x	u0(x	PROPN
ejpam-2672	118	23	,	,	PUNCT
ejpam-2672	118	24	t	t	PROPN
ejpam-2672	118	25	)	)	PUNCT
ejpam-2672	118	26	+	+	CCONJ
ejpam-2672	119	1	∞∑	∞∑	PROPN
ejpam-2672	119	2	m=1	m=1	X
ejpam-2672	119	3	um(x	um(x	NUM
ejpam-2672	119	4	,	,	PUNCT
ejpam-2672	119	5	t	t	PROPN
ejpam-2672	119	6	)	)	PUNCT
ejpam-2672	119	7	(	(	PUNCT
ejpam-2672	119	8	35	35	NUM
ejpam-2672	119	9	)	)	PUNCT
ejpam-2672	119	10	which	which	PRON
ejpam-2672	119	11	must	must	AUX
ejpam-2672	119	12	be	be	AUX
ejpam-2672	119	13	one	one	NUM
ejpam-2672	119	14	of	of	ADP
ejpam-2672	119	15	solutions	solution	NOUN
ejpam-2672	119	16	of	of	ADP
ejpam-2672	119	17	the	the	DET
ejpam-2672	119	18	original	original	ADJ
ejpam-2672	119	19	nonlinear	nonlinear	ADJ
ejpam-2672	119	20	equation	equation	NOUN
ejpam-2672	119	21	,	,	PUNCT
ejpam-2672	119	22	as	as	SCONJ
ejpam-2672	119	23	proved	prove	VERB
ejpam-2672	119	24	by	by	ADP
ejpam-2672	119	25	liao	liao	PROPN
ejpam-2672	119	26	[	[	X
ejpam-2672	119	27	9	9	NUM
ejpam-2672	119	28	]	]	PUNCT
ejpam-2672	119	29	.	.	PUNCT
ejpam-2672	120	1	using	use	VERB
ejpam-2672	120	2	definition	definition	NOUN
ejpam-2672	120	3	(	(	PUNCT
ejpam-2672	120	4	34	34	NUM
ejpam-2672	120	5	)	)	PUNCT
ejpam-2672	120	6	,	,	PUNCT
ejpam-2672	120	7	the	the	DET
ejpam-2672	120	8	governing	govern	VERB
ejpam-2672	120	9	equation	equation	NOUN
ejpam-2672	120	10	of	of	ADP
ejpam-2672	120	11	the	the	DET
ejpam-2672	120	12	ham	ham	NOUN
ejpam-2672	120	13	can	can	AUX
ejpam-2672	120	14	be	be	AUX
ejpam-2672	120	15	deduced	deduce	VERB
ejpam-2672	120	16	from	from	ADP
ejpam-2672	120	17	the	the	DET
ejpam-2672	120	18	zero	zero	NUM
ejpam-2672	120	19	-	-	PUNCT
ejpam-2672	120	20	order	order	NOUN
ejpam-2672	120	21	deformation	deformation	NOUN
ejpam-2672	120	22	equation	equation	NOUN
ejpam-2672	120	23	(	(	PUNCT
ejpam-2672	120	24	32	32	NUM
ejpam-2672	120	25	)	)	PUNCT
ejpam-2672	120	26	as	as	SCONJ
ejpam-2672	120	27	follows	follow	VERB
ejpam-2672	120	28	.	.	PUNCT
ejpam-2672	121	1	define	define	VERB
ejpam-2672	121	2	the	the	DET
ejpam-2672	121	3	vector	vector	NOUN
ejpam-2672	121	4	−→u	−→u	ADP
ejpam-2672	121	5	n	n	NOUN
ejpam-2672	121	6	=	=	NUM
ejpam-2672	121	7	{	{	PUNCT
ejpam-2672	121	8	u0(x	u0(x	PROPN
ejpam-2672	121	9	,	,	PUNCT
ejpam-2672	121	10	t	t	PROPN
ejpam-2672	121	11	)	)	PUNCT
ejpam-2672	121	12	,	,	PUNCT
ejpam-2672	121	13	u1(x	u1(x	PROPN
ejpam-2672	121	14	,	,	PUNCT
ejpam-2672	121	15	t	t	PROPN
ejpam-2672	121	16	)	)	PUNCT
ejpam-2672	121	17	,	,	PUNCT
ejpam-2672	121	18	u2(x	u2(x	PROPN
ejpam-2672	121	19	,	,	PUNCT
ejpam-2672	121	20	t	t	PROPN
ejpam-2672	121	21	)	)	PUNCT
ejpam-2672	121	22	,	,	PUNCT
ejpam-2672	121	23	...	...	PUNCT
ejpam-2672	121	24	,	,	PUNCT
ejpam-2672	121	25	un(x	un(x	X
ejpam-2672	121	26	,	,	PUNCT
ejpam-2672	121	27	t	t	PROPN
ejpam-2672	121	28	)	)	PUNCT
ejpam-2672	121	29	}	}	PUNCT
ejpam-2672	121	30	(	(	PUNCT
ejpam-2672	121	31	36	36	NUM
ejpam-2672	121	32	)	)	PUNCT
ejpam-2672	121	33	from	from	ADP
ejpam-2672	121	34	equation	equation	NOUN
ejpam-2672	121	35	(	(	PUNCT
ejpam-2672	121	36	32	32	NUM
ejpam-2672	121	37	)	)	PUNCT
ejpam-2672	121	38	,	,	PUNCT
ejpam-2672	121	39	the	the	DET
ejpam-2672	121	40	so	so	ADV
ejpam-2672	121	41	-	-	PUNCT
ejpam-2672	121	42	called	call	VERB
ejpam-2672	121	43	m	m	VERB
ejpam-2672	121	44	th	th	NOUN
ejpam-2672	121	45	-	-	PUNCT
ejpam-2672	121	46	order	order	NOUN
ejpam-2672	121	47	deformation	deformation	NOUN
ejpam-2672	121	48	equation	equation	NOUN
ejpam-2672	121	49	is	be	AUX
ejpam-2672	121	50	given	give	VERB
ejpam-2672	121	51	by	by	ADP
ejpam-2672	121	52	l[um(x	l[um(x	PROPN
ejpam-2672	121	53	,	,	PUNCT
ejpam-2672	121	54	t)−	t)−	PROPN
ejpam-2672	121	55	χmum−1(x	χmum−1(x	NOUN
ejpam-2672	121	56	,	,	PUNCT
ejpam-2672	121	57	t	t	PROPN
ejpam-2672	121	58	)	)	PUNCT
ejpam-2672	121	59	]	]	PUNCT
ejpam-2672	122	1	=	=	SYM
ejpam-2672	122	2	~h(x	~h(x	NOUN
ejpam-2672	122	3	,	,	PUNCT
ejpam-2672	122	4	t)<m[−→u	t)<m[−→u	NOUN
ejpam-2672	122	5	m−1(x	m−1(x	NOUN
ejpam-2672	122	6	,	,	PUNCT
ejpam-2672	122	7	t	t	PROPN
ejpam-2672	122	8	)	)	PUNCT
ejpam-2672	122	9	]	]	PUNCT
ejpam-2672	122	10	,	,	PUNCT
ejpam-2672	122	11	(	(	PUNCT
ejpam-2672	122	12	37	37	NUM
ejpam-2672	122	13	)	)	PUNCT
ejpam-2672	122	14	where	where	SCONJ
ejpam-2672	122	15	<	<	X
ejpam-2672	122	16	m[−→u	m[−→u	ADP
ejpam-2672	122	17	m−1	m−1	PROPN
ejpam-2672	122	18	]	]	PUNCT
ejpam-2672	122	19	=	=	SYM
ejpam-2672	122	20	1	1	X
ejpam-2672	122	21	(	(	PUNCT
ejpam-2672	122	22	m−	m−	PROPN
ejpam-2672	122	23	1	1	NUM
ejpam-2672	122	24	)	)	PUNCT
ejpam-2672	122	25	!	!	PUNCT
ejpam-2672	123	1	∂m−1n	∂m−1n	PROPN
ejpam-2672	124	1	[	[	X
ejpam-2672	124	2	φ(x	φ(x	PROPN
ejpam-2672	124	3	,	,	PUNCT
ejpam-2672	124	4	t	t	PROPN
ejpam-2672	124	5	;	;	PUNCT
ejpam-2672	124	6	p	p	X
ejpam-2672	124	7	)	)	PUNCT
ejpam-2672	124	8	]	]	PUNCT
ejpam-2672	124	9	∂pm−1	∂pm−1	PROPN
ejpam-2672	124	10	|p=0	|p=0	PROPN
ejpam-2672	124	11	,	,	PUNCT
ejpam-2672	124	12	(	(	PUNCT
ejpam-2672	124	13	38	38	NUM
ejpam-2672	124	14	)	)	PUNCT
ejpam-2672	124	15	and	and	CCONJ
ejpam-2672	124	16	χm	χm	NOUN
ejpam-2672	124	17	=	=	SYM
ejpam-2672	124	18	{	{	PUNCT
ejpam-2672	124	19	0,m	0,m	INTJ
ejpam-2672	124	20	≤	≤	NUM
ejpam-2672	124	21	1	1	NUM
ejpam-2672	124	22	,	,	PUNCT
ejpam-2672	124	23	1,m	1,m	NOUN
ejpam-2672	124	24	>	>	X
ejpam-2672	124	25	1	1	X
ejpam-2672	124	26	.	.	PUNCT
ejpam-2672	124	27	(	(	PUNCT
ejpam-2672	124	28	39	39	NUM
ejpam-2672	124	29	)	)	PUNCT
ejpam-2672	124	30	applying	apply	VERB
ejpam-2672	124	31	the	the	DET
ejpam-2672	124	32	inverse	inverse	NOUN
ejpam-2672	124	33	operator	operator	NOUN
ejpam-2672	124	34	l−1	l−1	PROPN
ejpam-2672	124	35	to	to	ADP
ejpam-2672	124	36	both	both	DET
ejpam-2672	124	37	sides	side	NOUN
ejpam-2672	124	38	of	of	ADP
ejpam-2672	124	39	(	(	PUNCT
ejpam-2672	124	40	37	37	NUM
ejpam-2672	124	41	)	)	PUNCT
ejpam-2672	124	42	,	,	PUNCT
ejpam-2672	124	43	um(x	um(x	PROPN
ejpam-2672	124	44	,	,	PUNCT
ejpam-2672	124	45	t	t	PROPN
ejpam-2672	124	46	)	)	PUNCT
ejpam-2672	124	47	can	can	AUX
ejpam-2672	124	48	be	be	AUX
ejpam-2672	124	49	easily	easily	ADV
ejpam-2672	124	50	solved	solve	VERB
ejpam-2672	124	51	for	for	ADP
ejpam-2672	124	52	by	by	ADP
ejpam-2672	124	53	symbolic	symbolic	ADJ
ejpam-2672	124	54	computations	computation	NOUN
ejpam-2672	124	55	software	software	NOUN
ejpam-2672	124	56	.	.	PUNCT
ejpam-2672	125	1	the	the	DET
ejpam-2672	125	2	ham	ham	NOUN
ejpam-2672	125	3	has	have	AUX
ejpam-2672	125	4	been	be	AUX
ejpam-2672	125	5	successfully	successfully	ADV
ejpam-2672	125	6	applied	apply	VERB
ejpam-2672	125	7	to	to	PART
ejpam-2672	125	8	solve	solve	VERB
ejpam-2672	125	9	various	various	ADJ
ejpam-2672	125	10	classes	class	NOUN
ejpam-2672	125	11	of	of	ADP
ejpam-2672	125	12	equations	equation	NOUN
ejpam-2672	125	13	and	and	CCONJ
ejpam-2672	125	14	applied	apply	VERB
ejpam-2672	125	15	problems	problem	NOUN
ejpam-2672	125	16	[	[	X
ejpam-2672	125	17	3]-[2	3]-[2	X
ejpam-2672	125	18	]	]	X
ejpam-2672	125	19	.	.	PUNCT
ejpam-2672	126	1	in	in	ADP
ejpam-2672	126	2	the	the	DET
ejpam-2672	126	3	classical	classical	ADJ
ejpam-2672	126	4	ham	ham	NOUN
ejpam-2672	126	5	,	,	PUNCT
ejpam-2672	126	6	choosing	choose	VERB
ejpam-2672	126	7	the	the	DET
ejpam-2672	126	8	value	value	NOUN
ejpam-2672	126	9	of	of	ADP
ejpam-2672	126	10	parameter	parameter	NOUN
ejpam-2672	126	11	~	~	PUNCT
ejpam-2672	126	12	depends	depend	VERB
ejpam-2672	126	13	on	on	ADP
ejpam-2672	126	14	inspecting	inspect	VERB
ejpam-2672	126	15	the	the	DET
ejpam-2672	126	16	graph	graph	NOUN
ejpam-2672	126	17	of	of	ADP
ejpam-2672	126	18	the	the	DET
ejpam-2672	126	19	quantity	quantity	NOUN
ejpam-2672	126	20	of	of	ADP
ejpam-2672	126	21	interest	interest	NOUN
ejpam-2672	126	22	;	;	PUNCT
ejpam-2672	126	23	the	the	DET
ejpam-2672	126	24	solution	solution	NOUN
ejpam-2672	126	25	or	or	CCONJ
ejpam-2672	126	26	one	one	NUM
ejpam-2672	126	27	of	of	ADP
ejpam-2672	126	28	its	its	PRON
ejpam-2672	126	29	derivatives	derivative	NOUN
ejpam-2672	126	30	.	.	PUNCT
ejpam-2672	127	1	yet	yet	ADV
ejpam-2672	127	2	,	,	PUNCT
ejpam-2672	127	3	when	when	SCONJ
ejpam-2672	127	4	h(x	h(x	PROPN
ejpam-2672	127	5	,	,	PUNCT
ejpam-2672	127	6	t	t	PROPN
ejpam-2672	127	7	)	)	PUNCT
ejpam-2672	127	8	is	be	AUX
ejpam-2672	127	9	fixed	fix	VERB
ejpam-2672	127	10	,	,	PUNCT
ejpam-2672	127	11	it	it	PRON
ejpam-2672	127	12	is	be	AUX
ejpam-2672	127	13	obvious	obvious	ADJ
ejpam-2672	127	14	that	that	SCONJ
ejpam-2672	127	15	um(x	um(x	SYM
ejpam-2672	127	16	,	,	PUNCT
ejpam-2672	127	17	t	t	PROPN
ejpam-2672	127	18	)	)	PUNCT
ejpam-2672	127	19	contains	contain	VERB
ejpam-2672	127	20	only	only	ADV
ejpam-2672	127	21	one	one	NUM
ejpam-2672	127	22	control	control	NOUN
ejpam-2672	127	23	parameter	parameter	NOUN
ejpam-2672	127	24	~.	~.	PROPN
ejpam-2672	127	25	thus	thus	ADV
ejpam-2672	127	26	,	,	PUNCT
ejpam-2672	127	27	by	by	ADP
ejpam-2672	127	28	constructing	construct	VERB
ejpam-2672	127	29	a	a	DET
ejpam-2672	127	30	formula	formula	NOUN
ejpam-2672	127	31	for	for	ADP
ejpam-2672	127	32	the	the	DET
ejpam-2672	127	33	residual	residual	ADJ
ejpam-2672	127	34	error	error	NOUN
ejpam-2672	127	35	,	,	PUNCT
ejpam-2672	127	36	the	the	DET
ejpam-2672	127	37	oham	oham	ADJ
ejpam-2672	127	38	solution	solution	NOUN
ejpam-2672	127	39	is	be	AUX
ejpam-2672	127	40	obtained	obtain	VERB
ejpam-2672	127	41	by	by	ADP
ejpam-2672	127	42	choosing	choose	VERB
ejpam-2672	127	43	the	the	DET
ejpam-2672	127	44	value	value	NOUN
ejpam-2672	127	45	for	for	ADP
ejpam-2672	127	46	parameter	parameter	NOUN
ejpam-2672	127	47	~	~	PUNCT
ejpam-2672	127	48	that	that	PRON
ejpam-2672	127	49	minimizes	minimize	VERB
ejpam-2672	127	50	the	the	DET
ejpam-2672	127	51	error	error	NOUN
ejpam-2672	127	52	.	.	PUNCT
ejpam-2672	128	1	here	here	ADV
ejpam-2672	128	2	,	,	PUNCT
ejpam-2672	128	3	the	the	DET
ejpam-2672	128	4	averaged	average	VERB
ejpam-2672	128	5	residual	residual	ADJ
ejpam-2672	128	6	error	error	NOUN
ejpam-2672	128	7	defined	define	VERB
ejpam-2672	128	8	for	for	ADP
ejpam-2672	128	9	ordinary	ordinary	ADJ
ejpam-2672	128	10	differential	differential	ADJ
ejpam-2672	128	11	equations	equation	NOUN
ejpam-2672	128	12	in	in	ADP
ejpam-2672	128	13	[	[	X
ejpam-2672	128	14	10	10	NUM
ejpam-2672	128	15	]	]	PUNCT
ejpam-2672	128	16	is	be	AUX
ejpam-2672	128	17	generalized	generalize	VERB
ejpam-2672	128	18	to	to	ADP
ejpam-2672	128	19	the	the	DET
ejpam-2672	128	20	case	case	NOUN
ejpam-2672	128	21	of	of	ADP
ejpam-2672	128	22	two	two	NUM
ejpam-2672	128	23	variable	variable	ADJ
ejpam-2672	128	24	partial	partial	ADJ
ejpam-2672	128	25	differential	differential	NOUN
ejpam-2672	128	26	equations	equation	NOUN
ejpam-2672	128	27	in	in	ADP
ejpam-2672	128	28	the	the	DET
ejpam-2672	128	29	following	follow	VERB
ejpam-2672	128	30	form	form	NOUN
ejpam-2672	128	31	em(~	em(~	PROPN
ejpam-2672	128	32	)	)	PUNCT
ejpam-2672	128	33	=	=	SYM
ejpam-2672	128	34	1	1	NUM
ejpam-2672	128	35	mk	mk	NOUN
ejpam-2672	128	36	m∑	m∑	VERB
ejpam-2672	128	37	i=0	i=0	PROPN
ejpam-2672	128	38	k∑	k∑	PROPN
ejpam-2672	128	39	j=0	j=0	PROPN
ejpam-2672	128	40	[	[	PUNCT
ejpam-2672	128	41	n	n	CCONJ
ejpam-2672	128	42	m∑	m∑	CCONJ
ejpam-2672	128	43	n=0	n=0	PROPN
ejpam-2672	128	44	un	un	PROPN
ejpam-2672	128	45	(	(	PUNCT
ejpam-2672	128	46	i	i	PRON
ejpam-2672	128	47	m	m	VERB
ejpam-2672	128	48	,	,	PUNCT
ejpam-2672	128	49	j	j	PROPN
ejpam-2672	128	50	k	k	PROPN
ejpam-2672	128	51	)	)	PUNCT
ejpam-2672	129	1	]	]	SYM
ejpam-2672	129	2	2	2	NUM
ejpam-2672	129	3	,	,	PUNCT
ejpam-2672	129	4	(	(	PUNCT
ejpam-2672	129	5	40	40	NUM
ejpam-2672	129	6	)	)	PUNCT
ejpam-2672	129	7	which	which	PRON
ejpam-2672	129	8	is	be	AUX
ejpam-2672	129	9	a	a	DET
ejpam-2672	129	10	nonlinear	nonlinear	ADJ
ejpam-2672	129	11	algebraic	algebraic	ADJ
ejpam-2672	129	12	equation	equation	NOUN
ejpam-2672	129	13	of	of	ADP
ejpam-2672	129	14	one	one	NUM
ejpam-2672	129	15	unknown	unknown	NOUN
ejpam-2672	129	16	;	;	PUNCT
ejpam-2672	129	17	the	the	DET
ejpam-2672	129	18	convergence	convergence	NOUN
ejpam-2672	129	19	-	-	PUNCT
ejpam-2672	129	20	control	control	NOUN
ejpam-2672	129	21	parameter	parameter	NOUN
ejpam-2672	129	22	~.	~.	PUNCT
ejpam-2672	130	1	thus	thus	ADV
ejpam-2672	130	2	the	the	DET
ejpam-2672	130	3	optimal	optimal	ADJ
ejpam-2672	130	4	value	value	NOUN
ejpam-2672	130	5	of	of	ADP
ejpam-2672	130	6	~	~	PUNCT
ejpam-2672	130	7	is	be	AUX
ejpam-2672	130	8	determined	determine	VERB
ejpam-2672	130	9	by	by	ADP
ejpam-2672	130	10	the	the	DET
ejpam-2672	130	11	minimum	minimum	NOUN
ejpam-2672	130	12	of	of	ADP
ejpam-2672	130	13	the	the	DET
ejpam-2672	130	14	averaged	average	VERB
ejpam-2672	130	15	residual	residual	ADJ
ejpam-2672	130	16	error	error	NOUN
ejpam-2672	130	17	em	em	PRON
ejpam-2672	130	18	to	to	PART
ejpam-2672	130	19	ensure	ensure	VERB
ejpam-2672	130	20	the	the	DET
ejpam-2672	130	21	fast	fast	ADJ
ejpam-2672	130	22	convergence	convergence	NOUN
ejpam-2672	130	23	of	of	ADP
ejpam-2672	130	24	the	the	DET
ejpam-2672	130	25	homotopy	homotopy	NOUN
ejpam-2672	130	26	series	series	NOUN
ejpam-2672	130	27	.	.	PUNCT
ejpam-2672	131	1	to	to	PART
ejpam-2672	131	2	apply	apply	VERB
ejpam-2672	131	3	the	the	DET
ejpam-2672	131	4	oham	oham	ADJ
ejpam-2672	131	5	recursive	recursive	ADJ
ejpam-2672	131	6	technique	technique	NOUN
ejpam-2672	131	7	to	to	ADP
ejpam-2672	131	8	the	the	DET
ejpam-2672	131	9	problem	problem	NOUN
ejpam-2672	131	10	,	,	PUNCT
ejpam-2672	131	11	a	a	DET
ejpam-2672	131	12	repeated	repeat	VERB
ejpam-2672	131	13	evaluation	evaluation	NOUN
ejpam-2672	131	14	of	of	ADP
ejpam-2672	131	15	riesz	riesz	PROPN
ejpam-2672	131	16	fractional	fractional	ADJ
ejpam-2672	131	17	derivative	derivative	NOUN
ejpam-2672	131	18	to	to	ADP
ejpam-2672	131	19	solution	solution	NOUN
ejpam-2672	131	20	components	component	NOUN
ejpam-2672	131	21	is	be	AUX
ejpam-2672	131	22	needed	need	VERB
ejpam-2672	131	23	.	.	PUNCT
ejpam-2672	132	1	this	this	DET
ejpam-2672	132	2	obstacle	obstacle	NOUN
ejpam-2672	132	3	is	be	AUX
ejpam-2672	132	4	overcome	overcome	VERB
ejpam-2672	132	5	by	by	ADP
ejpam-2672	132	6	using	use	VERB
ejpam-2672	132	7	property	property	NOUN
ejpam-2672	132	8	of	of	ADP
ejpam-2672	132	9	riesz	riesz	PROPN
ejpam-2672	132	10	fractional	fractional	ADJ
ejpam-2672	132	11	derivative	derivative	NOUN
ejpam-2672	132	12	in	in	ADP
ejpam-2672	132	13	the	the	DET
ejpam-2672	132	14	following	follow	VERB
ejpam-2672	132	15	lemma	lemma	PROPN
ejpam-2672	132	16	.	.	PUNCT
ejpam-2672	133	1	a.	a.	PROPN
ejpam-2672	133	2	elsaid	elsaid	PROPN
ejpam-2672	133	3	,	,	PUNCT
ejpam-2672	133	4	s.	s.	PROPN
ejpam-2672	133	5	shamseldeen	shamseldeen	PROPN
ejpam-2672	133	6	,	,	PUNCT
ejpam-2672	133	7	s.	s.	PROPN
ejpam-2672	133	8	madkour	madkour	PROPN
ejpam-2672	133	9	/	/	SYM
ejpam-2672	133	10	eur	eur	PROPN
ejpam-2672	133	11	.	.	PUNCT
ejpam-2672	134	1	j.	j.	PROPN
ejpam-2672	134	2	pure	pure	PROPN
ejpam-2672	134	3	appl	appl	PROPN
ejpam-2672	134	4	.	.	PROPN
ejpam-2672	134	5	math	math	PROPN
ejpam-2672	134	6	,	,	PUNCT
ejpam-2672	134	7	10	10	NUM
ejpam-2672	134	8	(	(	PUNCT
ejpam-2672	134	9	3	3	NUM
ejpam-2672	134	10	)	)	PUNCT
ejpam-2672	134	11	(	(	PUNCT
ejpam-2672	134	12	2017	2017	NUM
ejpam-2672	134	13	)	)	PUNCT
ejpam-2672	134	14	,	,	PUNCT
ejpam-2672	134	15	586	586	NUM
ejpam-2672	134	16	-	-	SYM
ejpam-2672	134	17	601	601	NUM
ejpam-2672	134	18	593	593	NUM
ejpam-2672	134	19	lemma	lemma	PROPN
ejpam-2672	134	20	3	3	X
ejpam-2672	134	21	.	.	PUNCT
ejpam-2672	135	1	let	let	VERB
ejpam-2672	135	2	α	α	PRON
ejpam-2672	135	3	∈	∈	PROPN
ejpam-2672	135	4	(	(	PUNCT
ejpam-2672	135	5	0	0	NUM
ejpam-2672	135	6	,	,	PUNCT
ejpam-2672	135	7	2	2	NUM
ejpam-2672	135	8	)	)	PUNCT
ejpam-2672	135	9	,	,	PUNCT
ejpam-2672	135	10	α	α	PROPN
ejpam-2672	135	11	6=	6=	ADP
ejpam-2672	135	12	1	1	NUM
ejpam-2672	135	13	.	.	PUNCT
ejpam-2672	136	1	then	then	ADV
ejpam-2672	136	2	rαx(eiωx	rαx(eiωx	NUM
ejpam-2672	136	3	)	)	PUNCT
ejpam-2672	136	4	=	=	SYM
ejpam-2672	136	5	−ωαei(ωx	−ωαei(ωx	NUM
ejpam-2672	136	6	)	)	PUNCT
ejpam-2672	136	7	,	,	PUNCT
ejpam-2672	136	8	(	(	PUNCT
ejpam-2672	136	9	41	41	NUM
ejpam-2672	136	10	)	)	PUNCT
ejpam-2672	136	11	or	or	CCONJ
ejpam-2672	136	12	in	in	ADP
ejpam-2672	136	13	a	a	DET
ejpam-2672	136	14	trigonometric	trigonometric	ADJ
ejpam-2672	136	15	form	form	NOUN
ejpam-2672	136	16	rαx	rαx	NOUN
ejpam-2672	136	17	sin(ωx	sin(ωx	NUM
ejpam-2672	136	18	)	)	PUNCT
ejpam-2672	136	19	=	=	SYM
ejpam-2672	137	1	−ωα	−ωα	NOUN
ejpam-2672	137	2	sin(ωx	sin(ωx	NUM
ejpam-2672	137	3	)	)	PUNCT
ejpam-2672	137	4	,	,	PUNCT
ejpam-2672	137	5	(	(	PUNCT
ejpam-2672	137	6	42	42	X
ejpam-2672	137	7	)	)	PUNCT
ejpam-2672	137	8	rαx	rαx	NOUN
ejpam-2672	137	9	cos(ωx	cos(ωx	NOUN
ejpam-2672	137	10	)	)	PUNCT
ejpam-2672	137	11	=	=	SYM
ejpam-2672	137	12	−ωα	−ωα	PROPN
ejpam-2672	137	13	cos(ωx	cos(ωx	NOUN
ejpam-2672	137	14	)	)	PUNCT
ejpam-2672	137	15	.	.	PUNCT
ejpam-2672	138	1	(	(	PUNCT
ejpam-2672	138	2	43	43	NUM
ejpam-2672	138	3	)	)	PUNCT
ejpam-2672	138	4	proof	proof	NOUN
ejpam-2672	138	5	.	.	PUNCT
ejpam-2672	139	1	see	see	VERB
ejpam-2672	139	2	[	[	X
ejpam-2672	139	3	6	6	NUM
ejpam-2672	139	4	]	]	PUNCT
ejpam-2672	139	5	and	and	CCONJ
ejpam-2672	139	6	[	[	X
ejpam-2672	139	7	7	7	NUM
ejpam-2672	139	8	]	]	PUNCT
ejpam-2672	139	9	.	.	PUNCT
ejpam-2672	140	1	5	5	X
ejpam-2672	140	2	.	.	X
ejpam-2672	140	3	numerical	numerical	PROPN
ejpam-2672	140	4	simulation	simulation	PROPN
ejpam-2672	140	5	in	in	ADP
ejpam-2672	140	6	this	this	DET
ejpam-2672	140	7	section	section	NOUN
ejpam-2672	140	8	,	,	PUNCT
ejpam-2672	140	9	we	we	PRON
ejpam-2672	140	10	consider	consider	VERB
ejpam-2672	140	11	linear	linear	ADJ
ejpam-2672	140	12	and	and	CCONJ
ejpam-2672	140	13	nonlinear	nonlinear	ADJ
ejpam-2672	140	14	problems	problem	NOUN
ejpam-2672	140	15	to	to	PART
ejpam-2672	140	16	illustrate	illustrate	VERB
ejpam-2672	140	17	the	the	DET
ejpam-2672	140	18	efficiency	efficiency	NOUN
ejpam-2672	140	19	of	of	ADP
ejpam-2672	140	20	the	the	DET
ejpam-2672	140	21	method	method	NOUN
ejpam-2672	140	22	of	of	ADP
ejpam-2672	140	23	solution	solution	NOUN
ejpam-2672	140	24	to	to	ADP
ejpam-2672	140	25	this	this	DET
ejpam-2672	140	26	type	type	NOUN
ejpam-2672	140	27	of	of	ADP
ejpam-2672	140	28	problems	problem	NOUN
ejpam-2672	140	29	and	and	CCONJ
ejpam-2672	140	30	to	to	PART
ejpam-2672	140	31	illustrate	illustrate	VERB
ejpam-2672	140	32	the	the	DET
ejpam-2672	140	33	continuation	continuation	NOUN
ejpam-2672	140	34	of	of	ADP
ejpam-2672	140	35	the	the	DET
ejpam-2672	140	36	solution	solution	NOUN
ejpam-2672	140	37	we	we	PRON
ejpam-2672	140	38	proved	prove	VERB
ejpam-2672	140	39	in	in	ADP
ejpam-2672	140	40	section	section	NOUN
ejpam-2672	140	41	3	3	NUM
ejpam-2672	140	42	.	.	PUNCT
ejpam-2672	141	1	in	in	ADP
ejpam-2672	141	2	each	each	DET
ejpam-2672	141	3	problem	problem	NOUN
ejpam-2672	141	4	,	,	PUNCT
ejpam-2672	141	5	a	a	DET
ejpam-2672	141	6	table	table	NOUN
ejpam-2672	141	7	is	be	AUX
ejpam-2672	141	8	presented	present	VERB
ejpam-2672	141	9	to	to	PART
ejpam-2672	141	10	show	show	VERB
ejpam-2672	141	11	the	the	DET
ejpam-2672	141	12	estimated	estimate	VERB
ejpam-2672	141	13	values	value	NOUN
ejpam-2672	141	14	the	the	DET
ejpam-2672	141	15	optimal	optimal	ADJ
ejpam-2672	141	16	convergence	convergence	NOUN
ejpam-2672	141	17	control	control	NOUN
ejpam-2672	141	18	parameter	parameter	NOUN
ejpam-2672	141	19	~	~	PUNCT
ejpam-2672	141	20	and	and	CCONJ
ejpam-2672	141	21	the	the	DET
ejpam-2672	141	22	corresponding	corresponding	ADJ
ejpam-2672	141	23	residual	residual	ADJ
ejpam-2672	141	24	error	error	NOUN
ejpam-2672	141	25	em	em	PRON
ejpam-2672	141	26	at	at	ADP
ejpam-2672	141	27	different	different	ADJ
ejpam-2672	141	28	values	value	NOUN
ejpam-2672	141	29	of	of	ADP
ejpam-2672	141	30	the	the	DET
ejpam-2672	141	31	fractional	fractional	ADJ
ejpam-2672	141	32	derivative	derivative	ADJ
ejpam-2672	141	33	α	α	NOUN
ejpam-2672	141	34	.	.	PUNCT
ejpam-2672	142	1	these	these	DET
ejpam-2672	142	2	estimated	estimate	VERB
ejpam-2672	142	3	values	value	NOUN
ejpam-2672	142	4	are	be	AUX
ejpam-2672	142	5	calculated	calculate	VERB
ejpam-2672	142	6	via	via	ADP
ejpam-2672	142	7	minimizing	minimizing	NOUN
ejpam-2672	142	8	of	of	ADP
ejpam-2672	142	9	the	the	DET
ejpam-2672	142	10	averaged	average	VERB
ejpam-2672	142	11	residual	residual	ADJ
ejpam-2672	142	12	error	error	NOUN
ejpam-2672	142	13	em	em	PRON
ejpam-2672	142	14	displayed	display	VERB
ejpam-2672	142	15	in	in	ADP
ejpam-2672	142	16	(	(	PUNCT
ejpam-2672	142	17	40	40	NUM
ejpam-2672	142	18	)	)	PUNCT
ejpam-2672	142	19	in	in	ADP
ejpam-2672	142	20	the	the	DET
ejpam-2672	142	21	space	space	NOUN
ejpam-2672	142	22	domain	domain	NOUN
ejpam-2672	142	23	0	0	NUM
ejpam-2672	142	24	≤	≤	NUM
ejpam-2672	142	25	x	x	SYM
ejpam-2672	142	26	≤	≤	NOUN
ejpam-2672	142	27	2.0	2.0	NUM
ejpam-2672	142	28	and	and	CCONJ
ejpam-2672	142	29	the	the	DET
ejpam-2672	142	30	time	time	NOUN
ejpam-2672	142	31	interval	interval	NOUN
ejpam-2672	142	32	0	0	NUM
ejpam-2672	142	33	≤	≤	NUM
ejpam-2672	142	34	t	t	PROPN
ejpam-2672	142	35	≤	≤	NOUN
ejpam-2672	142	36	2.0	2.0	NUM
ejpam-2672	142	37	.	.	PUNCT
ejpam-2672	143	1	example	example	NOUN
ejpam-2672	143	2	1	1	NUM
ejpam-2672	143	3	.	.	X
ejpam-2672	144	1	consider	consider	VERB
ejpam-2672	144	2	problem	problem	NOUN
ejpam-2672	144	3	(	(	PUNCT
ejpam-2672	144	4	1	1	NUM
ejpam-2672	144	5	-	-	SYM
ejpam-2672	144	6	2	2	NUM
ejpam-2672	144	7	)	)	PUNCT
ejpam-2672	144	8	with	with	ADP
ejpam-2672	144	9	p(u	p(u	NOUN
ejpam-2672	144	10	)	)	PUNCT
ejpam-2672	144	11	=	=	SYM
ejpam-2672	144	12	u	u	NOUN
ejpam-2672	144	13	,	,	PUNCT
ejpam-2672	144	14	f1(x	f1(x	PROPN
ejpam-2672	144	15	)	)	PUNCT
ejpam-2672	144	16	=	=	SYM
ejpam-2672	144	17	sin(πx	sin(πx	X
ejpam-2672	144	18	/	/	SYM
ejpam-2672	144	19	a	a	NOUN
ejpam-2672	144	20	)	)	PUNCT
ejpam-2672	144	21	and	and	CCONJ
ejpam-2672	144	22	f2(x	f2(x	NUM
ejpam-2672	144	23	)	)	PUNCT
ejpam-2672	144	24	=	=	SYM
ejpam-2672	144	25	−	−	NOUN
ejpam-2672	144	26	sin(πx	sin(πx	X
ejpam-2672	144	27	/	/	SYM
ejpam-2672	144	28	a	a	NOUN
ejpam-2672	144	29	)	)	PUNCT
ejpam-2672	144	30	{	{	PUNCT
ejpam-2672	144	31	utt(x	utt(x	PROPN
ejpam-2672	144	32	,	,	PUNCT
ejpam-2672	144	33	t	t	PROPN
ejpam-2672	144	34	)	)	PUNCT
ejpam-2672	144	35	=	=	PUNCT
ejpam-2672	145	1	rαxu(x	rαxu(x	PROPN
ejpam-2672	145	2	,	,	PUNCT
ejpam-2672	145	3	t	t	PROPN
ejpam-2672	145	4	)	)	PUNCT
ejpam-2672	145	5	+	+	NUM
ejpam-2672	145	6	u	u	NOUN
ejpam-2672	145	7	,	,	PUNCT
ejpam-2672	145	8	−∞	−∞	X
ejpam-2672	145	9	<	<	X
ejpam-2672	145	10	x	x	X
ejpam-2672	145	11	<	<	X
ejpam-2672	145	12	∞	∞	PROPN
ejpam-2672	145	13	,	,	PUNCT
ejpam-2672	145	14	t	t	X
ejpam-2672	145	15	>	>	X
ejpam-2672	145	16	0	0	NUM
ejpam-2672	145	17	,	,	PUNCT
ejpam-2672	145	18	u(x	u(x	NOUN
ejpam-2672	145	19	,	,	PUNCT
ejpam-2672	145	20	0	0	NUM
ejpam-2672	145	21	)	)	PUNCT
ejpam-2672	145	22	=	=	SYM
ejpam-2672	145	23	sin(πx	sin(πx	X
ejpam-2672	145	24	/	/	SYM
ejpam-2672	145	25	a	a	NOUN
ejpam-2672	145	26	)	)	PUNCT
ejpam-2672	145	27	,	,	PUNCT
ejpam-2672	145	28	ut(x	ut(x	NOUN
ejpam-2672	145	29	,	,	PUNCT
ejpam-2672	145	30	0	0	NUM
ejpam-2672	145	31	)	)	PUNCT
ejpam-2672	145	32	=	=	SYM
ejpam-2672	145	33	sin(πx	sin(πx	X
ejpam-2672	145	34	/	/	SYM
ejpam-2672	145	35	a	a	NOUN
ejpam-2672	145	36	)	)	PUNCT
ejpam-2672	145	37	,	,	PUNCT
ejpam-2672	145	38	(	(	PUNCT
ejpam-2672	145	39	44	44	NUM
ejpam-2672	145	40	)	)	PUNCT
ejpam-2672	145	41	where	where	SCONJ
ejpam-2672	145	42	a	a	PRON
ejpam-2672	145	43	is	be	AUX
ejpam-2672	145	44	a	a	DET
ejpam-2672	145	45	real	real	ADV
ejpam-2672	145	46	constant	constant	ADJ
ejpam-2672	145	47	.	.	PUNCT
ejpam-2672	146	1	the	the	DET
ejpam-2672	146	2	auxiliary	auxiliary	ADJ
ejpam-2672	146	3	linear	linear	ADJ
ejpam-2672	146	4	operator	operator	NOUN
ejpam-2672	146	5	is	be	AUX
ejpam-2672	146	6	chosen	choose	VERB
ejpam-2672	146	7	as	as	ADP
ejpam-2672	146	8	l[φ	l[φ	X
ejpam-2672	146	9	]	]	PUNCT
ejpam-2672	146	10	=	=	SYM
ejpam-2672	146	11	∂2	∂2	NOUN
ejpam-2672	146	12	∂t2	∂t2	NOUN
ejpam-2672	146	13	(	(	PUNCT
ejpam-2672	146	14	φ	φ	NOUN
ejpam-2672	146	15	)	)	PUNCT
ejpam-2672	146	16	,	,	PUNCT
ejpam-2672	146	17	(	(	PUNCT
ejpam-2672	146	18	45	45	NUM
ejpam-2672	146	19	)	)	PUNCT
ejpam-2672	146	20	and	and	CCONJ
ejpam-2672	146	21	the	the	DET
ejpam-2672	146	22	nonlinear	nonlinear	ADJ
ejpam-2672	146	23	operator	operator	NOUN
ejpam-2672	146	24	n	n	NOUN
ejpam-2672	146	25	is	be	AUX
ejpam-2672	146	26	chosen	choose	VERB
ejpam-2672	146	27	as	as	ADP
ejpam-2672	146	28	n	n	PROPN
ejpam-2672	146	29	[	[	X
ejpam-2672	146	30	φ	φ	X
ejpam-2672	146	31	]	]	X
ejpam-2672	146	32	=	=	SYM
ejpam-2672	146	33	φtt	φtt	NOUN
ejpam-2672	146	34	−rαx(φ)−	−rαx(φ)−	PROPN
ejpam-2672	146	35	φ	φ	NOUN
ejpam-2672	146	36	.	.	PUNCT
ejpam-2672	147	1	(	(	PUNCT
ejpam-2672	147	2	46	46	NUM
ejpam-2672	147	3	)	)	PUNCT
ejpam-2672	147	4	the	the	DET
ejpam-2672	147	5	m	m	NOUN
ejpam-2672	147	6	th	th	ADJ
ejpam-2672	147	7	-	-	PUNCT
ejpam-2672	147	8	order	order	NOUN
ejpam-2672	147	9	deformation	deformation	NOUN
ejpam-2672	147	10	equation	equation	NOUN
ejpam-2672	147	11	,	,	PUNCT
ejpam-2672	147	12	with	with	ADP
ejpam-2672	147	13	h(x	h(x	PROPN
ejpam-2672	147	14	,	,	PUNCT
ejpam-2672	147	15	t	t	PROPN
ejpam-2672	147	16	)	)	PUNCT
ejpam-2672	147	17	=	=	SYM
ejpam-2672	147	18	1	1	NUM
ejpam-2672	147	19	,	,	PUNCT
ejpam-2672	147	20	for	for	ADP
ejpam-2672	147	21	this	this	DET
ejpam-2672	147	22	linear	linear	ADJ
ejpam-2672	147	23	problem	problem	NOUN
ejpam-2672	147	24	is	be	AUX
ejpam-2672	147	25	given	give	VERB
ejpam-2672	147	26	by	by	ADP
ejpam-2672	147	27	∂2	∂2	ADJ
ejpam-2672	147	28	∂t2	∂t2	NOUN
ejpam-2672	147	29	[	[	X
ejpam-2672	147	30	um(x	um(x	X
ejpam-2672	147	31	,	,	PUNCT
ejpam-2672	147	32	t)−	t)−	PROPN
ejpam-2672	147	33	χmum−1(x	χmum−1(x	NOUN
ejpam-2672	147	34	,	,	PUNCT
ejpam-2672	147	35	t	t	PROPN
ejpam-2672	147	36	)	)	PUNCT
ejpam-2672	147	37	]	]	PUNCT
ejpam-2672	148	1	=	=	PUNCT
ejpam-2672	148	2	~	~	PUNCT
ejpam-2672	148	3	(	(	PUNCT
ejpam-2672	148	4	∂2	∂2	NOUN
ejpam-2672	148	5	∂t2	∂t2	NOUN
ejpam-2672	148	6	(	(	PUNCT
ejpam-2672	148	7	um−1)−rαx(um−1)−	um−1)−rαx(um−1)−	PROPN
ejpam-2672	148	8	um−1	um−1	PROPN
ejpam-2672	148	9	)	)	PUNCT
ejpam-2672	148	10	,	,	PUNCT
ejpam-2672	148	11	(	(	PUNCT
ejpam-2672	148	12	47	47	NUM
ejpam-2672	148	13	)	)	PUNCT
ejpam-2672	148	14	a.	a.	NOUN
ejpam-2672	148	15	elsaid	elsaid	PROPN
ejpam-2672	148	16	,	,	PUNCT
ejpam-2672	148	17	s.	s.	PROPN
ejpam-2672	148	18	shamseldeen	shamseldeen	PROPN
ejpam-2672	148	19	,	,	PUNCT
ejpam-2672	148	20	s.	s.	PROPN
ejpam-2672	148	21	madkour	madkour	PROPN
ejpam-2672	148	22	/	/	SYM
ejpam-2672	148	23	eur	eur	PROPN
ejpam-2672	148	24	.	.	PUNCT
ejpam-2672	149	1	j.	j.	PROPN
ejpam-2672	149	2	pure	pure	PROPN
ejpam-2672	149	3	appl	appl	PROPN
ejpam-2672	149	4	.	.	PROPN
ejpam-2672	149	5	math	math	PROPN
ejpam-2672	149	6	,	,	PUNCT
ejpam-2672	149	7	10	10	NUM
ejpam-2672	149	8	(	(	PUNCT
ejpam-2672	149	9	3	3	NUM
ejpam-2672	149	10	)	)	PUNCT
ejpam-2672	149	11	(	(	PUNCT
ejpam-2672	149	12	2017	2017	NUM
ejpam-2672	149	13	)	)	PUNCT
ejpam-2672	149	14	,	,	PUNCT
ejpam-2672	149	15	586	586	NUM
ejpam-2672	149	16	-	-	SYM
ejpam-2672	149	17	601	601	NUM
ejpam-2672	149	18	594	594	NUM
ejpam-2672	149	19	with	with	ADP
ejpam-2672	149	20	u0(x	u0(x	PROPN
ejpam-2672	149	21	,	,	PUNCT
ejpam-2672	149	22	t	t	PROPN
ejpam-2672	149	23	)	)	PUNCT
ejpam-2672	149	24	=	=	SYM
ejpam-2672	149	25	f1(x	f1(x	PROPN
ejpam-2672	149	26	)	)	PUNCT
ejpam-2672	150	1	+	+	NUM
ejpam-2672	150	2	t	t	PROPN
ejpam-2672	150	3	f2(x	f2(x	PROPN
ejpam-2672	150	4	)	)	PUNCT
ejpam-2672	150	5	=	=	PUNCT
ejpam-2672	150	6	(	(	PUNCT
ejpam-2672	150	7	1−	1−	NUM
ejpam-2672	150	8	t	t	PROPN
ejpam-2672	150	9	)	)	PUNCT
ejpam-2672	150	10	sin(πx	sin(πx	NOUN
ejpam-2672	150	11	/	/	SYM
ejpam-2672	150	12	a	a	NOUN
ejpam-2672	150	13	)	)	PUNCT
ejpam-2672	150	14	(	(	PUNCT
ejpam-2672	150	15	48	48	NUM
ejpam-2672	150	16	)	)	PUNCT
ejpam-2672	150	17	the	the	DET
ejpam-2672	150	18	inverse	inverse	ADJ
ejpam-2672	150	19	integral	integral	ADJ
ejpam-2672	150	20	operator	operator	NOUN
ejpam-2672	150	21	is	be	AUX
ejpam-2672	150	22	applied	apply	VERB
ejpam-2672	150	23	to	to	ADP
ejpam-2672	150	24	both	both	DET
ejpam-2672	150	25	sides	side	NOUN
ejpam-2672	150	26	of	of	ADP
ejpam-2672	150	27	equation	equation	NOUN
ejpam-2672	150	28	(	(	PUNCT
ejpam-2672	150	29	47	47	NUM
ejpam-2672	150	30	)	)	PUNCT
ejpam-2672	150	31	to	to	PART
ejpam-2672	150	32	obtain	obtain	VERB
ejpam-2672	150	33	the	the	DET
ejpam-2672	150	34	series	series	NOUN
ejpam-2672	150	35	solution	solution	NOUN
ejpam-2672	150	36	terms	term	NOUN
ejpam-2672	150	37	.	.	PUNCT
ejpam-2672	151	1	the	the	DET
ejpam-2672	151	2	first	first	ADJ
ejpam-2672	151	3	three	three	NUM
ejpam-2672	151	4	terms	term	NOUN
ejpam-2672	151	5	are	be	AUX
ejpam-2672	151	6	given	give	VERB
ejpam-2672	151	7	by	by	ADP
ejpam-2672	151	8	u0	u0	ADJ
ejpam-2672	151	9	=	=	SYM
ejpam-2672	151	10	(	(	PUNCT
ejpam-2672	151	11	1−	1−	NUM
ejpam-2672	151	12	t	t	NOUN
ejpam-2672	151	13	)	)	PUNCT
ejpam-2672	151	14	sin	sin	NOUN
ejpam-2672	151	15	(	(	PUNCT
ejpam-2672	151	16	πx	πx	X
ejpam-2672	151	17	a	a	PRON
ejpam-2672	151	18	)	)	PUNCT
ejpam-2672	151	19	,	,	PUNCT
ejpam-2672	151	20	u1	u1	NOUN
ejpam-2672	151	21	=	=	SYM
ejpam-2672	151	22	−ht	−ht	VERB
ejpam-2672	151	23	2	2	NUM
ejpam-2672	151	24	6	6	NUM
ejpam-2672	151	25	(	(	PUNCT
ejpam-2672	151	26	−1	−1	NOUN
ejpam-2672	151	27	+	+	PUNCT
ejpam-2672	151	28	(	(	PUNCT
ejpam-2672	151	29	π	π	PROPN
ejpam-2672	151	30	a	a	X
ejpam-2672	151	31	)	)	PUNCT
ejpam-2672	151	32	α	α	NOUN
ejpam-2672	151	33	)	)	PUNCT
ejpam-2672	151	34	(	(	PUNCT
ejpam-2672	151	35	−3	−3	PROPN
ejpam-2672	151	36	+	+	NUM
ejpam-2672	151	37	t	t	NOUN
ejpam-2672	151	38	)	)	PUNCT
ejpam-2672	151	39	sin	sin	NOUN
ejpam-2672	151	40	(	(	PUNCT
ejpam-2672	151	41	πx	πx	NOUN
ejpam-2672	151	42	a	a	NOUN
ejpam-2672	151	43	)	)	PUNCT
ejpam-2672	151	44	,	,	PUNCT
ejpam-2672	151	45	u2	u2	NOUN
ejpam-2672	151	46	=	=	PUNCT
ejpam-2672	151	47	−	−	PROPN
ejpam-2672	151	48	ht	ht	INTJ
ejpam-2672	151	49	2	2	NUM
ejpam-2672	151	50	120	120	NUM
ejpam-2672	151	51	(	(	PUNCT
ejpam-2672	151	52	−1	−1	NOUN
ejpam-2672	151	53	+	+	PUNCT
ejpam-2672	151	54	(	(	PUNCT
ejpam-2672	151	55	π	π	PROPN
ejpam-2672	151	56	a	a	X
ejpam-2672	151	57	)	)	PUNCT
ejpam-2672	151	58	α	α	NOUN
ejpam-2672	151	59	)	)	PUNCT
ejpam-2672	151	60	(	(	PUNCT
ejpam-2672	151	61	20(−3	20(−3	NUM
ejpam-2672	151	62	+	+	SYM
ejpam-2672	151	63	t	t	NOUN
ejpam-2672	151	64	)	)	PUNCT
ejpam-2672	152	1	+	+	NUM
ejpam-2672	152	2	h	h	NOUN
ejpam-2672	152	3	(	(	PUNCT
ejpam-2672	152	4	−60	−60	NOUN
ejpam-2672	153	1	+	+	CCONJ
ejpam-2672	153	2	20t+	20t+	NUM
ejpam-2672	153	3	(	(	PUNCT
ejpam-2672	153	4	5−	5−	NUM
ejpam-2672	153	5	5	5	NUM
ejpam-2672	153	6	(	(	PUNCT
ejpam-2672	153	7	π	π	PROPN
ejpam-2672	153	8	a	a	X
ejpam-2672	153	9	)	)	PUNCT
ejpam-2672	153	10	α	α	NOUN
ejpam-2672	153	11	)	)	PUNCT
ejpam-2672	153	12	t2	t2	NOUN
ejpam-2672	153	13	+	+	CCONJ
ejpam-2672	153	14	(	(	PUNCT
ejpam-2672	153	15	−1	−1	NOUN
ejpam-2672	153	16	+	+	PUNCT
ejpam-2672	153	17	(	(	PUNCT
ejpam-2672	153	18	π	π	PROPN
ejpam-2672	153	19	a	a	X
ejpam-2672	153	20	)	)	PUNCT
ejpam-2672	153	21	α	α	NOUN
ejpam-2672	153	22	)	)	PUNCT
ejpam-2672	153	23	t3	t3	NOUN
ejpam-2672	153	24	)	)	PUNCT
ejpam-2672	153	25	)	)	PUNCT
ejpam-2672	153	26	sin	sin	NOUN
ejpam-2672	153	27	(	(	PUNCT
ejpam-2672	153	28	πx	πx	NOUN
ejpam-2672	153	29	a	a	PRON
ejpam-2672	153	30	)	)	PUNCT
ejpam-2672	153	31	.	.	PUNCT
ejpam-2672	154	1	table	table	NOUN
ejpam-2672	154	2	1	1	NUM
ejpam-2672	154	3	shows	show	VERB
ejpam-2672	154	4	the	the	DET
ejpam-2672	154	5	estimated	estimate	VERB
ejpam-2672	154	6	values	value	NOUN
ejpam-2672	154	7	of	of	ADP
ejpam-2672	154	8	the	the	DET
ejpam-2672	154	9	optimal	optimal	ADJ
ejpam-2672	154	10	convergence	convergence	NOUN
ejpam-2672	154	11	control	control	NOUN
ejpam-2672	154	12	parameter	parameter	NOUN
ejpam-2672	154	13	~	~	PUNCT
ejpam-2672	154	14	and	and	CCONJ
ejpam-2672	154	15	the	the	DET
ejpam-2672	154	16	corresponding	corresponding	ADJ
ejpam-2672	154	17	residual	residual	ADJ
ejpam-2672	154	18	error	error	NOUN
ejpam-2672	154	19	em	em	PRON
ejpam-2672	154	20	for	for	ADP
ejpam-2672	154	21	the	the	DET
ejpam-2672	154	22	linear	linear	ADJ
ejpam-2672	154	23	problem	problem	NOUN
ejpam-2672	154	24	displayed	display	VERB
ejpam-2672	154	25	in	in	ADP
ejpam-2672	154	26	(	(	PUNCT
ejpam-2672	154	27	44	44	NUM
ejpam-2672	154	28	)	)	PUNCT
ejpam-2672	154	29	at	at	ADP
ejpam-2672	154	30	different	different	ADJ
ejpam-2672	154	31	values	value	NOUN
ejpam-2672	154	32	of	of	ADP
ejpam-2672	154	33	the	the	DET
ejpam-2672	154	34	fractional	fractional	ADJ
ejpam-2672	154	35	derivative	derivative	ADJ
ejpam-2672	154	36	α	α	NOUN
ejpam-2672	154	37	in	in	ADP
ejpam-2672	154	38	the	the	DET
ejpam-2672	154	39	space	space	NOUN
ejpam-2672	154	40	domain	domain	NOUN
ejpam-2672	154	41	0	0	NUM
ejpam-2672	154	42	≤	≤	NUM
ejpam-2672	154	43	x	x	SYM
ejpam-2672	154	44	≤	≤	NOUN
ejpam-2672	154	45	2.0	2.0	NUM
ejpam-2672	154	46	and	and	CCONJ
ejpam-2672	154	47	the	the	DET
ejpam-2672	154	48	time	time	NOUN
ejpam-2672	154	49	interval	interval	NOUN
ejpam-2672	154	50	0	0	NUM
ejpam-2672	154	51	≤	≤	NUM
ejpam-2672	154	52	t	t	PROPN
ejpam-2672	154	53	≤	≤	NOUN
ejpam-2672	154	54	2.0	2.0	NUM
ejpam-2672	154	55	.	.	PUNCT
ejpam-2672	154	56	table	table	NOUN
ejpam-2672	154	57	1	1	NUM
ejpam-2672	154	58	:	:	PUNCT
ejpam-2672	154	59	the	the	DET
ejpam-2672	154	60	estimated	estimate	VERB
ejpam-2672	154	61	optimal	optimal	ADJ
ejpam-2672	154	62	convergence	convergence	NOUN
ejpam-2672	154	63	parameter	parameter	NOUN
ejpam-2672	154	64	~	~	PUNCT
ejpam-2672	154	65	and	and	CCONJ
ejpam-2672	154	66	the	the	DET
ejpam-2672	154	67	corresponding	corresponding	ADJ
ejpam-2672	154	68	residual	residual	ADJ
ejpam-2672	154	69	error	error	NOUN
ejpam-2672	154	70	em	em	PRON
ejpam-2672	154	71	for	for	ADP
ejpam-2672	154	72	0	0	NUM
ejpam-2672	154	73	≤	≤	NUM
ejpam-2672	154	74	x	x	SYM
ejpam-2672	154	75	≤	≤	NOUN
ejpam-2672	154	76	2.0	2.0	NUM
ejpam-2672	154	77	and	and	CCONJ
ejpam-2672	154	78	0	0	NUM
ejpam-2672	154	79	≤	≤	NUM
ejpam-2672	154	80	t	t	NOUN
ejpam-2672	154	81	≤	≤	NOUN
ejpam-2672	154	82	2.0	2.0	NUM
ejpam-2672	154	83	at	at	ADP
ejpam-2672	154	84	different	different	ADJ
ejpam-2672	154	85	fractional	fractional	ADJ
ejpam-2672	154	86	derivative	derivative	ADJ
ejpam-2672	154	87	α	α	NOUN
ejpam-2672	154	88	for	for	ADP
ejpam-2672	154	89	example	example	NOUN
ejpam-2672	154	90	(	(	PUNCT
ejpam-2672	154	91	1	1	NUM
ejpam-2672	154	92	)	)	PUNCT
ejpam-2672	154	93	.	.	PUNCT
ejpam-2672	155	1	α	α	X
ejpam-2672	155	2	~	~	PUNCT
ejpam-2672	155	3	em	em	PRON
ejpam-2672	155	4	optimal	optimal	ADJ
ejpam-2672	155	5	parameter	parameter	NOUN
ejpam-2672	155	6	residual	residual	ADJ
ejpam-2672	155	7	error	error	NOUN
ejpam-2672	155	8	1.7	1.7	NUM
ejpam-2672	155	9	−0.940496	−0.940496	NUM
ejpam-2672	155	10	1.12317e	1.12317e	NUM
ejpam-2672	155	11	−	−	NUM
ejpam-2672	155	12	5	5	NUM
ejpam-2672	155	13	1.8	1.8	NUM
ejpam-2672	155	14	−0.938046	−0.938046	NUM
ejpam-2672	155	15	8.19812e	8.19812e	NUM
ejpam-2672	155	16	−	−	NUM
ejpam-2672	155	17	5	5	NUM
ejpam-2672	155	18	1.9	1.9	NUM
ejpam-2672	155	19	−0.933025	−0.933025	NOUN
ejpam-2672	155	20	1.75198e	1.75198e	NUM
ejpam-2672	155	21	−	−	NOUN
ejpam-2672	155	22	4	4	NUM
ejpam-2672	155	23	2.0	2.0	NUM
ejpam-2672	156	1	−0.928713	−0.928713	PRON
ejpam-2672	156	2	3.51187e	3.51187e	NUM
ejpam-2672	156	3	−	−	PROPN
ejpam-2672	156	4	4	4	NUM
ejpam-2672	156	5	α	α	NOUN
ejpam-2672	156	6	=	=	NOUN
ejpam-2672	156	7	1.7	1.7	NUM
ejpam-2672	156	8	α	α	NOUN
ejpam-2672	156	9	=	=	PUNCT
ejpam-2672	156	10	1.9	1.9	NUM
ejpam-2672	156	11	α	α	NOUN
ejpam-2672	156	12	=	=	PUNCT
ejpam-2672	156	13	1.8	1.8	NUM
ejpam-2672	156	14	α	α	NOUN
ejpam-2672	156	15	=	=	SYM
ejpam-2672	156	16	2.0	2.0	NUM
ejpam-2672	156	17	0.5	0.5	NUM
ejpam-2672	156	18	1.0	1.0	NUM
ejpam-2672	156	19	1.5	1.5	NUM
ejpam-2672	156	20	2.0	2.0	NUM
ejpam-2672	156	21	x	x	SYM
ejpam-2672	156	22	0.02	0.02	NUM
ejpam-2672	156	23	0.04	0.04	NUM
ejpam-2672	156	24	0.06	0.06	NUM
ejpam-2672	156	25	0.08	0.08	NUM
ejpam-2672	156	26	uαhx,0.7l	uαhx,0.7l	PROPN
ejpam-2672	156	27	figure	figure	NOUN
ejpam-2672	156	28	1	1	NUM
ejpam-2672	156	29	:	:	PUNCT
ejpam-2672	156	30	the	the	DET
ejpam-2672	156	31	solution	solution	NOUN
ejpam-2672	156	32	of	of	ADP
ejpam-2672	156	33	(	(	PUNCT
ejpam-2672	156	34	44	44	NUM
ejpam-2672	156	35	)	)	PUNCT
ejpam-2672	156	36	at	at	ADP
ejpam-2672	156	37	t	t	NOUN
ejpam-2672	156	38	=	=	SYM
ejpam-2672	156	39	0.5	0.5	NUM
ejpam-2672	156	40	,	,	PUNCT
ejpam-2672	156	41	0	0	NUM
ejpam-2672	156	42	≤	≤	NUM
ejpam-2672	156	43	x	x	SYM
ejpam-2672	156	44	≤	≤	NUM
ejpam-2672	156	45	2	2	NUM
ejpam-2672	156	46	and	and	CCONJ
ejpam-2672	156	47	different	different	ADJ
ejpam-2672	156	48	values	value	NOUN
ejpam-2672	156	49	of	of	ADP
ejpam-2672	156	50	the	the	DET
ejpam-2672	156	51	fractional	fractional	ADJ
ejpam-2672	156	52	order	order	NOUN
ejpam-2672	156	53	α	α	NOUN
ejpam-2672	156	54	=	=	SYM
ejpam-2672	156	55	1.7	1.7	NUM
ejpam-2672	156	56	,	,	PUNCT
ejpam-2672	156	57	1.8	1.8	NUM
ejpam-2672	156	58	,	,	PUNCT
ejpam-2672	156	59	1.9	1.9	NUM
ejpam-2672	156	60	and	and	CCONJ
ejpam-2672	156	61	2.0	2.0	NUM
ejpam-2672	156	62	.	.	PUNCT
ejpam-2672	157	1	the	the	DET
ejpam-2672	157	2	series	series	NOUN
ejpam-2672	157	3	solution	solution	NOUN
ejpam-2672	157	4	is	be	AUX
ejpam-2672	157	5	obtained	obtain	VERB
ejpam-2672	157	6	by	by	ADP
ejpam-2672	157	7	u	u	NOUN
ejpam-2672	157	8	=	=	X
ejpam-2672	157	9	u0	u0	X
ejpam-2672	157	10	+	+	NOUN
ejpam-2672	157	11	u1	u1	NOUN
ejpam-2672	157	12	+	+	NOUN
ejpam-2672	157	13	u2	u2	NOUN
ejpam-2672	157	14	+	+	NOUN
ejpam-2672	157	15	u3	u3	NOUN
ejpam-2672	157	16	+	+	CCONJ
ejpam-2672	157	17	.....	.....	PUNCT
ejpam-2672	157	18	figures	figure	NOUN
ejpam-2672	157	19	(	(	PUNCT
ejpam-2672	157	20	1	1	NUM
ejpam-2672	157	21	)	)	PUNCT
ejpam-2672	157	22	and	and	CCONJ
ejpam-2672	157	23	(	(	PUNCT
ejpam-2672	157	24	2	2	X
ejpam-2672	157	25	)	)	PUNCT
ejpam-2672	157	26	show	show	VERB
ejpam-2672	157	27	the	the	DET
ejpam-2672	157	28	effect	effect	NOUN
ejpam-2672	157	29	of	of	ADP
ejpam-2672	157	30	the	the	DET
ejpam-2672	157	31	fractional	fractional	ADJ
ejpam-2672	157	32	order	order	NOUN
ejpam-2672	157	33	derivative	derivative	ADJ
ejpam-2672	157	34	α	α	NOUN
ejpam-2672	157	35	on	on	ADP
ejpam-2672	157	36	the	the	DET
ejpam-2672	157	37	behavior	behavior	NOUN
ejpam-2672	157	38	of	of	ADP
ejpam-2672	157	39	the	the	DET
ejpam-2672	157	40	solution	solution	NOUN
ejpam-2672	157	41	at	at	ADP
ejpam-2672	157	42	fixed	fix	VERB
ejpam-2672	157	43	time	time	NOUN
ejpam-2672	157	44	a.	a.	PROPN
ejpam-2672	157	45	elsaid	elsaid	PROPN
ejpam-2672	157	46	,	,	PUNCT
ejpam-2672	157	47	s.	s.	PROPN
ejpam-2672	157	48	shamseldeen	shamseldeen	PROPN
ejpam-2672	157	49	,	,	PUNCT
ejpam-2672	157	50	s.	s.	PROPN
ejpam-2672	157	51	madkour	madkour	PROPN
ejpam-2672	157	52	/	/	SYM
ejpam-2672	157	53	eur	eur	PROPN
ejpam-2672	157	54	.	.	PUNCT
ejpam-2672	158	1	j.	j.	PROPN
ejpam-2672	158	2	pure	pure	PROPN
ejpam-2672	158	3	appl	appl	PROPN
ejpam-2672	158	4	.	.	PROPN
ejpam-2672	158	5	math	math	PROPN
ejpam-2672	158	6	,	,	PUNCT
ejpam-2672	158	7	10	10	NUM
ejpam-2672	158	8	(	(	PUNCT
ejpam-2672	158	9	3	3	NUM
ejpam-2672	158	10	)	)	PUNCT
ejpam-2672	158	11	(	(	PUNCT
ejpam-2672	158	12	2017	2017	NUM
ejpam-2672	158	13	)	)	PUNCT
ejpam-2672	158	14	,	,	PUNCT
ejpam-2672	158	15	586	586	NUM
ejpam-2672	158	16	-	-	SYM
ejpam-2672	158	17	601	601	NUM
ejpam-2672	158	18	595	595	NUM
ejpam-2672	158	19	α	α	NOUN
ejpam-2672	158	20	=	=	NOUN
ejpam-2672	158	21	1.7	1.7	NUM
ejpam-2672	158	22	α	α	NOUN
ejpam-2672	158	23	=	=	PUNCT
ejpam-2672	158	24	1.8	1.8	NUM
ejpam-2672	158	25	α	α	NOUN
ejpam-2672	158	26	=	=	VERB
ejpam-2672	158	27	2.0	2.0	NUM
ejpam-2672	158	28	α	α	NOUN
ejpam-2672	158	29	=	=	SYM
ejpam-2672	158	30	1.9	1.9	NUM
ejpam-2672	158	31	0.5	0.5	NUM
ejpam-2672	158	32	1.0	1.0	NUM
ejpam-2672	158	33	1.5	1.5	NUM
ejpam-2672	158	34	2.0	2.0	NUM
ejpam-2672	158	35	x	x	SYM
ejpam-2672	158	36	-0.4	-0.4	PROPN
ejpam-2672	158	37	-0.3	-0.3	PROPN
ejpam-2672	158	38	-0.2	-0.2	PROPN
ejpam-2672	158	39	-0.1	-0.1	PROPN
ejpam-2672	158	40	uαhx,1.0l	uαhx,1.0l	NOUN
ejpam-2672	158	41	figure	figure	NOUN
ejpam-2672	158	42	2	2	NUM
ejpam-2672	158	43	:	:	PUNCT
ejpam-2672	158	44	the	the	DET
ejpam-2672	158	45	solution	solution	NOUN
ejpam-2672	158	46	of	of	ADP
ejpam-2672	158	47	(	(	PUNCT
ejpam-2672	158	48	44	44	NUM
ejpam-2672	158	49	)	)	PUNCT
ejpam-2672	158	50	at	at	ADP
ejpam-2672	158	51	t	t	NOUN
ejpam-2672	158	52	=	=	SYM
ejpam-2672	158	53	1.0	1.0	NUM
ejpam-2672	158	54	,	,	PUNCT
ejpam-2672	158	55	0	0	NUM
ejpam-2672	158	56	≤	≤	NUM
ejpam-2672	158	57	x	x	SYM
ejpam-2672	158	58	≤	≤	NUM
ejpam-2672	158	59	2	2	NUM
ejpam-2672	158	60	and	and	CCONJ
ejpam-2672	158	61	different	different	ADJ
ejpam-2672	158	62	values	value	NOUN
ejpam-2672	158	63	of	of	ADP
ejpam-2672	158	64	the	the	DET
ejpam-2672	158	65	fractional	fractional	ADJ
ejpam-2672	158	66	order	order	NOUN
ejpam-2672	158	67	α	α	NOUN
ejpam-2672	158	68	=	=	SYM
ejpam-2672	158	69	1.7	1.7	NUM
ejpam-2672	158	70	,	,	PUNCT
ejpam-2672	158	71	1.8	1.8	NUM
ejpam-2672	158	72	,	,	PUNCT
ejpam-2672	158	73	1.9	1.9	NUM
ejpam-2672	158	74	and	and	CCONJ
ejpam-2672	158	75	2.0	2.0	NUM
ejpam-2672	158	76	.	.	PUNCT
ejpam-2672	159	1	t	t	PROPN
ejpam-2672	159	2	=	=	NUM
ejpam-2672	159	3	0.5	0.5	NUM
ejpam-2672	159	4	t	t	NOUN
ejpam-2672	159	5	=	=	SYM
ejpam-2672	159	6	1.0	1.0	NUM
ejpam-2672	159	7	t	t	NOUN
ejpam-2672	159	8	=	=	SYM
ejpam-2672	159	9	0.0	0.0	NUM
ejpam-2672	159	10	t	t	NOUN
ejpam-2672	159	11	=	=	SYM
ejpam-2672	159	12	1.5	1.5	NUM
ejpam-2672	159	13	0.5	0.5	NUM
ejpam-2672	159	14	1.0	1.0	NUM
ejpam-2672	159	15	1.5	1.5	NUM
ejpam-2672	159	16	2.0	2.0	NUM
ejpam-2672	159	17	x	x	SYM
ejpam-2672	159	18	-1.0	-1.0	PROPN
ejpam-2672	159	19	-0.5	-0.5	NUM
ejpam-2672	159	20	0.5	0.5	NUM
ejpam-2672	159	21	1.0	1.0	NUM
ejpam-2672	159	22	u1.9hx	u1.9hx	NOUN
ejpam-2672	159	23	,	,	PUNCT
ejpam-2672	159	24	tl	tl	PROPN
ejpam-2672	159	25	figure	figure	VERB
ejpam-2672	159	26	3	3	NUM
ejpam-2672	159	27	:	:	PUNCT
ejpam-2672	159	28	the	the	DET
ejpam-2672	159	29	solution	solution	NOUN
ejpam-2672	159	30	of	of	ADP
ejpam-2672	159	31	(	(	PUNCT
ejpam-2672	159	32	44	44	NUM
ejpam-2672	159	33	)	)	PUNCT
ejpam-2672	159	34	at	at	ADP
ejpam-2672	159	35	different	different	ADJ
ejpam-2672	159	36	times	time	NOUN
ejpam-2672	159	37	t	t	NOUN
ejpam-2672	159	38	=	=	SYM
ejpam-2672	159	39	0.0	0.0	NUM
ejpam-2672	159	40	,	,	PUNCT
ejpam-2672	159	41	0.5	0.5	NUM
ejpam-2672	159	42	,	,	PUNCT
ejpam-2672	159	43	1.0	1.0	NUM
ejpam-2672	159	44	,	,	PUNCT
ejpam-2672	159	45	and	and	CCONJ
ejpam-2672	159	46	1.5	1.5	NUM
ejpam-2672	159	47	,	,	PUNCT
ejpam-2672	159	48	0	0	NUM
ejpam-2672	159	49	≤	≤	NUM
ejpam-2672	159	50	x	x	SYM
ejpam-2672	159	51	≤	≤	NUM
ejpam-2672	159	52	2	2	NUM
ejpam-2672	159	53	and	and	CCONJ
ejpam-2672	159	54	the	the	DET
ejpam-2672	159	55	fractional	fractional	ADJ
ejpam-2672	159	56	order	order	NOUN
ejpam-2672	159	57	α	α	NOUN
ejpam-2672	159	58	=	=	SYM
ejpam-2672	159	59	1.9	1.9	NUM
ejpam-2672	159	60	.	.	PUNCT
ejpam-2672	160	1	t	t	PROPN
ejpam-2672	160	2	=	=	NUM
ejpam-2672	160	3	0.5	0.5	NUM
ejpam-2672	160	4	and	and	CCONJ
ejpam-2672	160	5	t	t	NOUN
ejpam-2672	160	6	=	=	SYM
ejpam-2672	160	7	1.0	1.0	NUM
ejpam-2672	160	8	,	,	PUNCT
ejpam-2672	160	9	respectively	respectively	ADV
ejpam-2672	160	10	,	,	PUNCT
ejpam-2672	160	11	while	while	SCONJ
ejpam-2672	160	12	figure	figure	NOUN
ejpam-2672	160	13	(	(	PUNCT
ejpam-2672	160	14	3	3	NUM
ejpam-2672	160	15	)	)	PUNCT
ejpam-2672	160	16	illustrates	illustrate	VERB
ejpam-2672	160	17	the	the	DET
ejpam-2672	160	18	temporal	temporal	ADJ
ejpam-2672	160	19	behavior	behavior	NOUN
ejpam-2672	160	20	of	of	ADP
ejpam-2672	160	21	the	the	DET
ejpam-2672	160	22	solution	solution	NOUN
ejpam-2672	160	23	at	at	ADP
ejpam-2672	160	24	a	a	DET
ejpam-2672	160	25	fixed	fix	VERB
ejpam-2672	160	26	fractional	fractional	ADJ
ejpam-2672	160	27	order	order	NOUN
ejpam-2672	160	28	,	,	PUNCT
ejpam-2672	160	29	α	α	NOUN
ejpam-2672	160	30	=	=	SYM
ejpam-2672	160	31	1.9	1.9	NUM
ejpam-2672	160	32	.	.	PUNCT
ejpam-2672	161	1	the	the	DET
ejpam-2672	161	2	plots	plot	NOUN
ejpam-2672	161	3	represent	represent	VERB
ejpam-2672	161	4	the	the	DET
ejpam-2672	161	5	sum	sum	NOUN
ejpam-2672	161	6	of	of	ADP
ejpam-2672	161	7	the	the	DET
ejpam-2672	161	8	first	first	ADJ
ejpam-2672	161	9	four	four	NUM
ejpam-2672	161	10	terms	term	NOUN
ejpam-2672	161	11	(	(	PUNCT
ejpam-2672	161	12	u0	u0	ADJ
ejpam-2672	161	13	to	to	ADP
ejpam-2672	161	14	u3	u3	NOUN
ejpam-2672	161	15	)	)	PUNCT
ejpam-2672	161	16	in	in	ADP
ejpam-2672	161	17	the	the	DET
ejpam-2672	161	18	oham	oham	NOUN
ejpam-2672	161	19	series	series	NOUN
ejpam-2672	161	20	when	when	SCONJ
ejpam-2672	161	21	a	a	DET
ejpam-2672	161	22	=	=	SYM
ejpam-2672	161	23	2.0	2.0	NUM
ejpam-2672	161	24	example	example	NOUN
ejpam-2672	161	25	2	2	NUM
ejpam-2672	161	26	.	.	X
ejpam-2672	161	27	consider	consider	VERB
ejpam-2672	161	28	problem	problem	NOUN
ejpam-2672	161	29	(	(	PUNCT
ejpam-2672	161	30	1	1	NUM
ejpam-2672	161	31	-	-	SYM
ejpam-2672	161	32	2	2	NUM
ejpam-2672	161	33	)	)	PUNCT
ejpam-2672	161	34	with	with	ADP
ejpam-2672	161	35	p	p	PROPN
ejpam-2672	161	36	(	(	PUNCT
ejpam-2672	161	37	u	u	NOUN
ejpam-2672	161	38	)	)	PUNCT
ejpam-2672	161	39	=	=	SYM
ejpam-2672	161	40	u	u	PROPN
ejpam-2672	161	41	+	+	NOUN
ejpam-2672	161	42	c	c	NOUN
ejpam-2672	161	43	u3	u3	PROPN
ejpam-2672	161	44	,	,	PUNCT
ejpam-2672	161	45	f1(x	f1(x	NUM
ejpam-2672	161	46	)	)	PUNCT
ejpam-2672	161	47	=	=	SYM
ejpam-2672	161	48	sin(πx	sin(πx	X
ejpam-2672	161	49	/	/	SYM
ejpam-2672	161	50	a	a	NOUN
ejpam-2672	161	51	)	)	PUNCT
ejpam-2672	161	52	and	and	CCONJ
ejpam-2672	161	53	f2(x	f2(x	NUM
ejpam-2672	161	54	)	)	PUNCT
ejpam-2672	161	55	=	=	SYM
ejpam-2672	161	56	−	−	NOUN
ejpam-2672	161	57	sin(πx	sin(πx	X
ejpam-2672	161	58	/	/	SYM
ejpam-2672	161	59	a	a	NOUN
ejpam-2672	161	60	)	)	PUNCT
ejpam-2672	161	61	{	{	PUNCT
ejpam-2672	161	62	utt(x	utt(x	PROPN
ejpam-2672	161	63	,	,	PUNCT
ejpam-2672	161	64	t	t	PROPN
ejpam-2672	161	65	)	)	PUNCT
ejpam-2672	161	66	=	=	PUNCT
ejpam-2672	162	1	rαxu(x	rαxu(x	PROPN
ejpam-2672	162	2	,	,	PUNCT
ejpam-2672	162	3	t	t	PROPN
ejpam-2672	162	4	)	)	PUNCT
ejpam-2672	162	5	+	+	NUM
ejpam-2672	162	6	u	u	NOUN
ejpam-2672	162	7	+	+	NOUN
ejpam-2672	162	8	c	c	NOUN
ejpam-2672	162	9	u3	u3	NOUN
ejpam-2672	162	10	,	,	PUNCT
ejpam-2672	162	11	−∞	−∞	X
ejpam-2672	162	12	<	<	X
ejpam-2672	162	13	x	x	X
ejpam-2672	162	14	<	<	X
ejpam-2672	162	15	∞	∞	PROPN
ejpam-2672	162	16	,	,	PUNCT
ejpam-2672	162	17	t	t	X
ejpam-2672	162	18	>	>	X
ejpam-2672	162	19	0	0	NUM
ejpam-2672	162	20	,	,	PUNCT
ejpam-2672	162	21	u(x	u(x	NOUN
ejpam-2672	162	22	,	,	PUNCT
ejpam-2672	162	23	0	0	NUM
ejpam-2672	162	24	)	)	PUNCT
ejpam-2672	162	25	=	=	SYM
ejpam-2672	162	26	sin(πx	sin(πx	X
ejpam-2672	162	27	/	/	SYM
ejpam-2672	162	28	a	a	NOUN
ejpam-2672	162	29	)	)	PUNCT
ejpam-2672	162	30	,	,	PUNCT
ejpam-2672	162	31	ut(x	ut(x	NOUN
ejpam-2672	162	32	,	,	PUNCT
ejpam-2672	162	33	0	0	NUM
ejpam-2672	162	34	)	)	PUNCT
ejpam-2672	162	35	=	=	SYM
ejpam-2672	162	36	sin(πx	sin(πx	X
ejpam-2672	162	37	/	/	SYM
ejpam-2672	162	38	a	a	NOUN
ejpam-2672	162	39	)	)	PUNCT
ejpam-2672	162	40	,	,	PUNCT
ejpam-2672	162	41	(	(	PUNCT
ejpam-2672	162	42	49	49	NUM
ejpam-2672	162	43	)	)	PUNCT
ejpam-2672	162	44	where	where	SCONJ
ejpam-2672	162	45	a	a	PRON
ejpam-2672	162	46	is	be	AUX
ejpam-2672	162	47	a	a	DET
ejpam-2672	162	48	constant	constant	ADJ
ejpam-2672	162	49	.	.	PUNCT
ejpam-2672	163	1	the	the	DET
ejpam-2672	163	2	auxiliary	auxiliary	ADJ
ejpam-2672	163	3	linear	linear	ADJ
ejpam-2672	163	4	operator	operator	NOUN
ejpam-2672	163	5	is	be	AUX
ejpam-2672	163	6	chosen	choose	VERB
ejpam-2672	163	7	as	as	ADP
ejpam-2672	163	8	l[φ	l[φ	X
ejpam-2672	163	9	]	]	PUNCT
ejpam-2672	163	10	=	=	SYM
ejpam-2672	163	11	∂2	∂2	NOUN
ejpam-2672	163	12	∂t2	∂t2	NOUN
ejpam-2672	163	13	(	(	PUNCT
ejpam-2672	163	14	φ	φ	NOUN
ejpam-2672	163	15	)	)	PUNCT
ejpam-2672	163	16	,	,	PUNCT
ejpam-2672	163	17	(	(	PUNCT
ejpam-2672	163	18	50	50	NUM
ejpam-2672	163	19	)	)	PUNCT
ejpam-2672	163	20	and	and	CCONJ
ejpam-2672	163	21	the	the	DET
ejpam-2672	163	22	nonlinear	nonlinear	ADJ
ejpam-2672	163	23	operator	operator	NOUN
ejpam-2672	163	24	n	n	NOUN
ejpam-2672	163	25	is	be	AUX
ejpam-2672	163	26	chosen	choose	VERB
ejpam-2672	163	27	as	as	ADP
ejpam-2672	163	28	n	n	PROPN
ejpam-2672	163	29	[	[	X
ejpam-2672	163	30	φ	φ	X
ejpam-2672	163	31	]	]	X
ejpam-2672	163	32	=	=	SYM
ejpam-2672	163	33	φtt	φtt	NOUN
ejpam-2672	163	34	−rαx(φ)−	−rαx(φ)−	PROPN
ejpam-2672	163	35	φ−	φ−	PROPN
ejpam-2672	163	36	c	c	PROPN
ejpam-2672	163	37	φ3	φ3	NOUN
ejpam-2672	163	38	.	.	PUNCT
ejpam-2672	164	1	(	(	PUNCT
ejpam-2672	164	2	51	51	NUM
ejpam-2672	164	3	)	)	PUNCT
ejpam-2672	164	4	then	then	ADV
ejpam-2672	164	5	,	,	PUNCT
ejpam-2672	164	6	m	m	VERB
ejpam-2672	164	7	th	th	X
ejpam-2672	164	8	-	-	PUNCT
ejpam-2672	164	9	order	order	NOUN
ejpam-2672	164	10	deformation	deformation	NOUN
ejpam-2672	164	11	equation	equation	NOUN
ejpam-2672	164	12	for	for	ADP
ejpam-2672	164	13	this	this	DET
ejpam-2672	164	14	problem	problem	NOUN
ejpam-2672	164	15	is	be	AUX
ejpam-2672	164	16	given	give	VERB
ejpam-2672	164	17	by	by	ADP
ejpam-2672	164	18	∂2	∂2	ADJ
ejpam-2672	164	19	∂t2	∂t2	NOUN
ejpam-2672	164	20	[	[	X
ejpam-2672	164	21	um(x	um(x	X
ejpam-2672	164	22	,	,	PUNCT
ejpam-2672	164	23	t)−	t)−	PROPN
ejpam-2672	164	24	χmum−1(x	χmum−1(x	NOUN
ejpam-2672	164	25	,	,	PUNCT
ejpam-2672	164	26	t	t	PROPN
ejpam-2672	164	27	)	)	PUNCT
ejpam-2672	164	28	]	]	PUNCT
ejpam-2672	165	1	=	=	SYM
ejpam-2672	165	2	~h(x	~h(x	NOUN
ejpam-2672	165	3	,	,	PUNCT
ejpam-2672	165	4	t)<m[−→u	t)<m[−→u	NOUN
ejpam-2672	165	5	m−1(x	m−1(x	NOUN
ejpam-2672	165	6	,	,	PUNCT
ejpam-2672	165	7	t	t	PROPN
ejpam-2672	165	8	)	)	PUNCT
ejpam-2672	165	9	]	]	PUNCT
ejpam-2672	165	10	,	,	PUNCT
ejpam-2672	165	11	(	(	PUNCT
ejpam-2672	165	12	52	52	NUM
ejpam-2672	165	13	)	)	PUNCT
ejpam-2672	165	14	a.	a.	NOUN
ejpam-2672	165	15	elsaid	elsaid	PROPN
ejpam-2672	165	16	,	,	PUNCT
ejpam-2672	165	17	s.	s.	PROPN
ejpam-2672	165	18	shamseldeen	shamseldeen	PROPN
ejpam-2672	165	19	,	,	PUNCT
ejpam-2672	165	20	s.	s.	PROPN
ejpam-2672	165	21	madkour	madkour	PROPN
ejpam-2672	165	22	/	/	SYM
ejpam-2672	165	23	eur	eur	PROPN
ejpam-2672	165	24	.	.	PUNCT
ejpam-2672	166	1	j.	j.	PROPN
ejpam-2672	166	2	pure	pure	PROPN
ejpam-2672	166	3	appl	appl	PROPN
ejpam-2672	166	4	.	.	PROPN
ejpam-2672	166	5	math	math	PROPN
ejpam-2672	166	6	,	,	PUNCT
ejpam-2672	166	7	10	10	NUM
ejpam-2672	166	8	(	(	PUNCT
ejpam-2672	166	9	3	3	NUM
ejpam-2672	166	10	)	)	PUNCT
ejpam-2672	166	11	(	(	PUNCT
ejpam-2672	166	12	2017	2017	NUM
ejpam-2672	166	13	)	)	PUNCT
ejpam-2672	166	14	,	,	PUNCT
ejpam-2672	166	15	586	586	NUM
ejpam-2672	166	16	-	-	SYM
ejpam-2672	166	17	601	601	NUM
ejpam-2672	166	18	596	596	NUM
ejpam-2672	166	19	where	where	SCONJ
ejpam-2672	166	20	<	<	X
ejpam-2672	166	21	m[−→u	m[−→u	ADP
ejpam-2672	166	22	m−1(x	m−1(x	NOUN
ejpam-2672	166	23	,	,	PUNCT
ejpam-2672	166	24	t	t	PROPN
ejpam-2672	166	25	)	)	PUNCT
ejpam-2672	166	26	]	]	PUNCT
ejpam-2672	166	27	is	be	AUX
ejpam-2672	166	28	given	give	VERB
ejpam-2672	166	29	by	by	ADP
ejpam-2672	166	30	<	<	X
ejpam-2672	166	31	m[−→u	m[−→u	ADP
ejpam-2672	166	32	m−1(x	m−1(x	NOUN
ejpam-2672	166	33	,	,	PUNCT
ejpam-2672	166	34	t	t	PROPN
ejpam-2672	166	35	)	)	PUNCT
ejpam-2672	166	36	]	]	PUNCT
ejpam-2672	167	1	=	=	SYM
ejpam-2672	167	2	∂2	∂2	NOUN
ejpam-2672	167	3	∂t2	∂t2	NOUN
ejpam-2672	167	4	(	(	PUNCT
ejpam-2672	167	5	um−1)−rαx(um−1)−	um−1)−rαx(um−1)−	PROPN
ejpam-2672	167	6	um−1	um−1	PROPN
ejpam-2672	167	7	−	−	PROPN
ejpam-2672	167	8	c	c	NOUN
ejpam-2672	167	9	m−1∑	m−1∑	PROPN
ejpam-2672	167	10	i=0	i=0	PROPN
ejpam-2672	167	11	i∑	i∑	NUM
ejpam-2672	167	12	j=0	j=0	PRON
ejpam-2672	167	13	um−1−iujui−j	um−1−iujui−j	PROPN
ejpam-2672	167	14	.	.	PUNCT
ejpam-2672	168	1	(	(	PUNCT
ejpam-2672	168	2	53	53	NUM
ejpam-2672	168	3	)	)	PUNCT
ejpam-2672	168	4	we	we	PRON
ejpam-2672	168	5	choose	choose	VERB
ejpam-2672	168	6	h(x	h(x	PROPN
ejpam-2672	168	7	,	,	PUNCT
ejpam-2672	168	8	t	t	PROPN
ejpam-2672	168	9	)	)	PUNCT
ejpam-2672	168	10	=	=	SYM
ejpam-2672	168	11	1	1	NUM
ejpam-2672	168	12	and	and	CCONJ
ejpam-2672	168	13	u0(x	u0(x	NOUN
ejpam-2672	168	14	,	,	PUNCT
ejpam-2672	168	15	t	t	PROPN
ejpam-2672	168	16	)	)	PUNCT
ejpam-2672	168	17	=	=	SYM
ejpam-2672	168	18	f1(x	f1(x	PROPN
ejpam-2672	168	19	)	)	PUNCT
ejpam-2672	169	1	+	+	NUM
ejpam-2672	169	2	t	t	PROPN
ejpam-2672	169	3	f2(x	f2(x	PROPN
ejpam-2672	169	4	)	)	PUNCT
ejpam-2672	169	5	=	=	PUNCT
ejpam-2672	169	6	(	(	PUNCT
ejpam-2672	169	7	1−	1−	NUM
ejpam-2672	169	8	t	t	PROPN
ejpam-2672	169	9	)	)	PUNCT
ejpam-2672	169	10	sin(πx	sin(πx	NOUN
ejpam-2672	169	11	/	/	SYM
ejpam-2672	169	12	a	a	NOUN
ejpam-2672	169	13	)	)	PUNCT
ejpam-2672	169	14	.	.	PUNCT
ejpam-2672	170	1	(	(	PUNCT
ejpam-2672	170	2	54	54	NUM
ejpam-2672	170	3	)	)	PUNCT
ejpam-2672	170	4	by	by	ADP
ejpam-2672	170	5	applying	apply	VERB
ejpam-2672	170	6	the	the	DET
ejpam-2672	170	7	inverse	inverse	ADJ
ejpam-2672	170	8	integral	integral	ADJ
ejpam-2672	170	9	operator	operator	NOUN
ejpam-2672	170	10	to	to	ADP
ejpam-2672	170	11	both	both	DET
ejpam-2672	170	12	sides	side	NOUN
ejpam-2672	170	13	of	of	ADP
ejpam-2672	170	14	equation	equation	NOUN
ejpam-2672	170	15	(	(	PUNCT
ejpam-2672	170	16	52	52	NUM
ejpam-2672	170	17	)	)	PUNCT
ejpam-2672	170	18	,	,	PUNCT
ejpam-2672	170	19	we	we	PRON
ejpam-2672	170	20	obtain	obtain	VERB
ejpam-2672	170	21	u0	u0	ADJ
ejpam-2672	170	22	=	=	PUNCT
ejpam-2672	170	23	(	(	PUNCT
ejpam-2672	170	24	1−	1−	NUM
ejpam-2672	170	25	t	t	PROPN
ejpam-2672	170	26	)	)	PUNCT
ejpam-2672	170	27	sin(πx	sin(πx	NOUN
ejpam-2672	170	28	/	/	SYM
ejpam-2672	170	29	a	a	NOUN
ejpam-2672	170	30	)	)	PUNCT
ejpam-2672	170	31	u1	u1	NOUN
ejpam-2672	170	32	=	=	SYM
ejpam-2672	171	1	−	−	NOUN
ejpam-2672	171	2	ht	ht	INTJ
ejpam-2672	171	3	2	2	NUM
ejpam-2672	171	4	120	120	NUM
ejpam-2672	171	5	(	(	PUNCT
ejpam-2672	171	6	20	20	NUM
ejpam-2672	171	7	(	(	PUNCT
ejpam-2672	171	8	−1	−1	NOUN
ejpam-2672	171	9	+	+	PUNCT
ejpam-2672	171	10	(	(	PUNCT
ejpam-2672	171	11	π	π	PROPN
ejpam-2672	171	12	a	a	X
ejpam-2672	171	13	)	)	PUNCT
ejpam-2672	171	14	α	α	NOUN
ejpam-2672	171	15	)	)	PUNCT
ejpam-2672	171	16	(	(	PUNCT
ejpam-2672	171	17	−3	−3	PROPN
ejpam-2672	171	18	+	+	NUM
ejpam-2672	171	19	t	t	PROPN
ejpam-2672	171	20	)	)	PUNCT
ejpam-2672	171	21	)	)	PUNCT
ejpam-2672	172	1	sin	sin	NOUN
ejpam-2672	172	2	(	(	PUNCT
ejpam-2672	172	3	πx	πx	X
ejpam-2672	172	4	a	a	NOUN
ejpam-2672	172	5	)	)	PUNCT
ejpam-2672	172	6	−	−	NOUN
ejpam-2672	173	1	ht	ht	INTJ
ejpam-2672	173	2	2	2	NUM
ejpam-2672	173	3	120	120	NUM
ejpam-2672	173	4	(	(	PUNCT
ejpam-2672	173	5	−3c2	−3c2	NUM
ejpam-2672	173	6	(	(	PUNCT
ejpam-2672	173	7	−10	−10	X
ejpam-2672	173	8	+	+	CCONJ
ejpam-2672	173	9	10t−	10t−	NUM
ejpam-2672	173	10	5t2	5t2	NUM
ejpam-2672	173	11	+	+	CCONJ
ejpam-2672	173	12	t3	t3	NOUN
ejpam-2672	173	13	)	)	PUNCT
ejpam-2672	174	1	[	[	PUNCT
ejpam-2672	174	2	1−	1−	NUM
ejpam-2672	174	3	cos	cos	X
ejpam-2672	174	4	(	(	PUNCT
ejpam-2672	174	5	2πx	2πx	NOUN
ejpam-2672	174	6	a	a	X
ejpam-2672	174	7	)	)	PUNCT
ejpam-2672	174	8	]	]	PUNCT
ejpam-2672	174	9	)	)	PUNCT
ejpam-2672	174	10	sin	sin	NOUN
ejpam-2672	174	11	(	(	PUNCT
ejpam-2672	174	12	πx	πx	X
ejpam-2672	174	13	a	a	NOUN
ejpam-2672	174	14	)	)	PUNCT
ejpam-2672	174	15	...	...	PUNCT
ejpam-2672	174	16	table	table	NOUN
ejpam-2672	174	17	2	2	NUM
ejpam-2672	174	18	shows	show	VERB
ejpam-2672	174	19	the	the	DET
ejpam-2672	174	20	estimated	estimate	VERB
ejpam-2672	174	21	values	value	NOUN
ejpam-2672	174	22	of	of	ADP
ejpam-2672	174	23	the	the	DET
ejpam-2672	174	24	optimal	optimal	ADJ
ejpam-2672	174	25	convergence	convergence	NOUN
ejpam-2672	174	26	control	control	NOUN
ejpam-2672	174	27	parameter	parameter	NOUN
ejpam-2672	174	28	~	~	PUNCT
ejpam-2672	174	29	and	and	CCONJ
ejpam-2672	174	30	the	the	DET
ejpam-2672	174	31	corresponding	corresponding	ADJ
ejpam-2672	174	32	residual	residual	ADJ
ejpam-2672	174	33	error	error	NOUN
ejpam-2672	174	34	em	em	PRON
ejpam-2672	174	35	for	for	ADP
ejpam-2672	174	36	problem	problem	NOUN
ejpam-2672	174	37	(	(	PUNCT
ejpam-2672	174	38	49	49	NUM
ejpam-2672	174	39	)	)	PUNCT
ejpam-2672	174	40	at	at	ADP
ejpam-2672	174	41	different	different	ADJ
ejpam-2672	174	42	values	value	NOUN
ejpam-2672	174	43	of	of	ADP
ejpam-2672	174	44	the	the	DET
ejpam-2672	174	45	fractional	fractional	ADJ
ejpam-2672	174	46	derivative	derivative	ADJ
ejpam-2672	174	47	α	α	NOUN
ejpam-2672	174	48	in	in	ADP
ejpam-2672	174	49	the	the	DET
ejpam-2672	174	50	space	space	NOUN
ejpam-2672	174	51	domain	domain	NOUN
ejpam-2672	174	52	0	0	NUM
ejpam-2672	174	53	≤	≤	NUM
ejpam-2672	174	54	x	x	SYM
ejpam-2672	174	55	≤	≤	NOUN
ejpam-2672	174	56	2.0	2.0	NUM
ejpam-2672	174	57	and	and	CCONJ
ejpam-2672	174	58	the	the	DET
ejpam-2672	174	59	time	time	NOUN
ejpam-2672	174	60	interval	interval	NOUN
ejpam-2672	174	61	0	0	NUM
ejpam-2672	174	62	≤	≤	NUM
ejpam-2672	174	63	t	t	PROPN
ejpam-2672	174	64	≤	≤	NOUN
ejpam-2672	174	65	2.0	2.0	NUM
ejpam-2672	174	66	.	.	PUNCT
ejpam-2672	174	67	table	table	NOUN
ejpam-2672	174	68	2	2	NUM
ejpam-2672	174	69	:	:	PUNCT
ejpam-2672	174	70	the	the	DET
ejpam-2672	174	71	estimated	estimate	VERB
ejpam-2672	174	72	optimal	optimal	ADJ
ejpam-2672	174	73	convergence	convergence	NOUN
ejpam-2672	174	74	parameter	parameter	NOUN
ejpam-2672	174	75	~	~	PUNCT
ejpam-2672	174	76	and	and	CCONJ
ejpam-2672	174	77	the	the	DET
ejpam-2672	174	78	corresponding	corresponding	ADJ
ejpam-2672	174	79	residual	residual	ADJ
ejpam-2672	174	80	error	error	NOUN
ejpam-2672	174	81	em	em	PRON
ejpam-2672	174	82	for	for	ADP
ejpam-2672	174	83	0	0	NUM
ejpam-2672	174	84	≤	≤	NUM
ejpam-2672	174	85	x	x	SYM
ejpam-2672	174	86	≤	≤	NOUN
ejpam-2672	174	87	2.0	2.0	NUM
ejpam-2672	174	88	and	and	CCONJ
ejpam-2672	174	89	0	0	NUM
ejpam-2672	174	90	≤	≤	NUM
ejpam-2672	174	91	t	t	NOUN
ejpam-2672	174	92	≤	≤	NOUN
ejpam-2672	174	93	2.0	2.0	NUM
ejpam-2672	174	94	at	at	ADP
ejpam-2672	174	95	different	different	ADJ
ejpam-2672	174	96	fractional	fractional	ADJ
ejpam-2672	174	97	derivative	derivative	ADJ
ejpam-2672	174	98	α	α	NOUN
ejpam-2672	174	99	for	for	ADP
ejpam-2672	174	100	example	example	NOUN
ejpam-2672	174	101	(	(	PUNCT
ejpam-2672	174	102	2	2	NUM
ejpam-2672	174	103	)	)	PUNCT
ejpam-2672	174	104	.	.	PUNCT
ejpam-2672	175	1	α	α	X
ejpam-2672	175	2	~	~	PUNCT
ejpam-2672	175	3	em	em	PRON
ejpam-2672	175	4	optimal	optimal	ADJ
ejpam-2672	175	5	parameter	parameter	NOUN
ejpam-2672	175	6	residual	residual	ADJ
ejpam-2672	175	7	error	error	NOUN
ejpam-2672	175	8	1.7	1.7	NUM
ejpam-2672	175	9	−0.620896	−0.620896	NUM
ejpam-2672	176	1	1.66374e	1.66374e	NUM
ejpam-2672	177	1	−	−	NOUN
ejpam-2672	177	2	3	3	NUM
ejpam-2672	177	3	1.8	1.8	NUM
ejpam-2672	177	4	−0.687193	−0.687193	NOUN
ejpam-2672	177	5	3.59934e	3.59934e	NUM
ejpam-2672	177	6	−	−	NOUN
ejpam-2672	177	7	3	3	NUM
ejpam-2672	177	8	1.9	1.9	NUM
ejpam-2672	177	9	−0.740338	−0.740338	NUM
ejpam-2672	178	1	5.55095e	5.55095e	PRON
ejpam-2672	178	2	−	−	NUM
ejpam-2672	178	3	3	3	NUM
ejpam-2672	178	4	2.0	2.0	NUM
ejpam-2672	178	5	−0.736543	−0.736543	NOUN
ejpam-2672	178	6	7.51805e	7.51805e	NOUN
ejpam-2672	178	7	−	−	PROPN
ejpam-2672	178	8	3	3	NUM
ejpam-2672	178	9	α	α	NOUN
ejpam-2672	178	10	=	=	NOUN
ejpam-2672	178	11	1.7	1.7	NUM
ejpam-2672	178	12	α	α	NOUN
ejpam-2672	178	13	=	=	PUNCT
ejpam-2672	178	14	1.8	1.8	NUM
ejpam-2672	178	15	α	α	NOUN
ejpam-2672	178	16	=	=	SYM
ejpam-2672	178	17	1.9	1.9	NUM
ejpam-2672	178	18	α	α	NOUN
ejpam-2672	178	19	=	=	PUNCT
ejpam-2672	178	20	2.0	2.0	NUM
ejpam-2672	178	21	0.5	0.5	NUM
ejpam-2672	178	22	1.0	1.0	NUM
ejpam-2672	178	23	1.5	1.5	NUM
ejpam-2672	178	24	2.0	2.0	NUM
ejpam-2672	178	25	x	x	SYM
ejpam-2672	178	26	0.02	0.02	NUM
ejpam-2672	178	27	0.04	0.04	NUM
ejpam-2672	178	28	0.06	0.06	NUM
ejpam-2672	178	29	0.08	0.08	NUM
ejpam-2672	178	30	0.10	0.10	NUM
ejpam-2672	178	31	0.12	0.12	NUM
ejpam-2672	178	32	uαhx,0.7l	uαhx,0.7l	PROPN
ejpam-2672	178	33	figure	figure	NOUN
ejpam-2672	178	34	4	4	NUM
ejpam-2672	178	35	:	:	PUNCT
ejpam-2672	178	36	the	the	DET
ejpam-2672	178	37	solution	solution	NOUN
ejpam-2672	178	38	of	of	ADP
ejpam-2672	178	39	(	(	PUNCT
ejpam-2672	178	40	49	49	NUM
ejpam-2672	178	41	)	)	PUNCT
ejpam-2672	178	42	at	at	ADP
ejpam-2672	178	43	t	t	NOUN
ejpam-2672	178	44	=	=	SYM
ejpam-2672	178	45	0.5	0.5	NUM
ejpam-2672	178	46	,	,	PUNCT
ejpam-2672	178	47	0	0	NUM
ejpam-2672	178	48	≤	≤	NUM
ejpam-2672	178	49	x	x	SYM
ejpam-2672	178	50	≤	≤	NUM
ejpam-2672	178	51	2	2	NUM
ejpam-2672	178	52	and	and	CCONJ
ejpam-2672	178	53	different	different	ADJ
ejpam-2672	178	54	values	value	NOUN
ejpam-2672	178	55	of	of	ADP
ejpam-2672	178	56	the	the	DET
ejpam-2672	178	57	fractional	fractional	ADJ
ejpam-2672	178	58	order	order	NOUN
ejpam-2672	178	59	α	α	NOUN
ejpam-2672	178	60	=	=	SYM
ejpam-2672	178	61	1.7	1.7	NUM
ejpam-2672	178	62	,	,	PUNCT
ejpam-2672	178	63	1.8	1.8	NUM
ejpam-2672	178	64	,	,	PUNCT
ejpam-2672	178	65	1.9	1.9	NUM
ejpam-2672	178	66	and	and	CCONJ
ejpam-2672	178	67	2.0	2.0	NUM
ejpam-2672	178	68	.	.	PUNCT
ejpam-2672	179	1	a.	a.	PROPN
ejpam-2672	179	2	elsaid	elsaid	PROPN
ejpam-2672	179	3	,	,	PUNCT
ejpam-2672	179	4	s.	s.	PROPN
ejpam-2672	179	5	shamseldeen	shamseldeen	PROPN
ejpam-2672	179	6	,	,	PUNCT
ejpam-2672	179	7	s.	s.	PROPN
ejpam-2672	179	8	madkour	madkour	PROPN
ejpam-2672	179	9	/	/	SYM
ejpam-2672	179	10	eur	eur	PROPN
ejpam-2672	179	11	.	.	PUNCT
ejpam-2672	180	1	j.	j.	PROPN
ejpam-2672	180	2	pure	pure	PROPN
ejpam-2672	180	3	appl	appl	PROPN
ejpam-2672	180	4	.	.	PROPN
ejpam-2672	180	5	math	math	PROPN
ejpam-2672	180	6	,	,	PUNCT
ejpam-2672	180	7	10	10	NUM
ejpam-2672	180	8	(	(	PUNCT
ejpam-2672	180	9	3	3	NUM
ejpam-2672	180	10	)	)	PUNCT
ejpam-2672	180	11	(	(	PUNCT
ejpam-2672	180	12	2017	2017	NUM
ejpam-2672	180	13	)	)	PUNCT
ejpam-2672	180	14	,	,	PUNCT
ejpam-2672	180	15	586	586	NUM
ejpam-2672	180	16	-	-	SYM
ejpam-2672	180	17	601	601	NUM
ejpam-2672	180	18	597	597	NUM
ejpam-2672	180	19	α	α	NOUN
ejpam-2672	180	20	=	=	NOUN
ejpam-2672	180	21	1.7	1.7	NUM
ejpam-2672	180	22	α	α	NOUN
ejpam-2672	180	23	=	=	PUNCT
ejpam-2672	180	24	1.8	1.8	NUM
ejpam-2672	180	25	α	α	NOUN
ejpam-2672	180	26	=	=	SYM
ejpam-2672	180	27	1.9	1.9	NUM
ejpam-2672	180	28	α	α	NOUN
ejpam-2672	180	29	=	=	PUNCT
ejpam-2672	180	30	2.0	2.0	NUM
ejpam-2672	180	31	0.5	0.5	NUM
ejpam-2672	180	32	1.0	1.0	NUM
ejpam-2672	180	33	1.5	1.5	NUM
ejpam-2672	180	34	2.0	2.0	NUM
ejpam-2672	180	35	x	x	SYM
ejpam-2672	180	36	-0.4	-0.4	PROPN
ejpam-2672	180	37	-0.3	-0.3	PROPN
ejpam-2672	180	38	-0.2	-0.2	PROPN
ejpam-2672	180	39	-0.1	-0.1	PROPN
ejpam-2672	180	40	uαhx,1.0l	uαhx,1.0l	NOUN
ejpam-2672	180	41	figure	figure	NOUN
ejpam-2672	180	42	5	5	NUM
ejpam-2672	180	43	:	:	PUNCT
ejpam-2672	180	44	the	the	DET
ejpam-2672	180	45	solution	solution	NOUN
ejpam-2672	180	46	of	of	ADP
ejpam-2672	180	47	(	(	PUNCT
ejpam-2672	180	48	49	49	NUM
ejpam-2672	180	49	)	)	PUNCT
ejpam-2672	180	50	at	at	ADP
ejpam-2672	180	51	t	t	NOUN
ejpam-2672	180	52	=	=	SYM
ejpam-2672	180	53	1.0	1.0	NUM
ejpam-2672	180	54	,	,	PUNCT
ejpam-2672	180	55	0	0	NUM
ejpam-2672	180	56	≤	≤	NUM
ejpam-2672	180	57	x	x	SYM
ejpam-2672	180	58	≤	≤	NUM
ejpam-2672	180	59	2	2	NUM
ejpam-2672	180	60	and	and	CCONJ
ejpam-2672	180	61	different	different	ADJ
ejpam-2672	180	62	values	value	NOUN
ejpam-2672	180	63	of	of	ADP
ejpam-2672	180	64	the	the	DET
ejpam-2672	180	65	fractional	fractional	ADJ
ejpam-2672	180	66	order	order	NOUN
ejpam-2672	180	67	α	α	NOUN
ejpam-2672	180	68	=	=	SYM
ejpam-2672	180	69	1.7	1.7	NUM
ejpam-2672	180	70	,	,	PUNCT
ejpam-2672	180	71	1.8	1.8	NUM
ejpam-2672	180	72	,	,	PUNCT
ejpam-2672	180	73	1.9	1.9	NUM
ejpam-2672	180	74	and	and	CCONJ
ejpam-2672	180	75	2.0	2.0	NUM
ejpam-2672	180	76	.	.	PUNCT
ejpam-2672	181	1	t	t	PROPN
ejpam-2672	181	2	=	=	NUM
ejpam-2672	181	3	0.5	0.5	NUM
ejpam-2672	181	4	t	t	NOUN
ejpam-2672	181	5	=	=	SYM
ejpam-2672	181	6	0.0	0.0	NUM
ejpam-2672	181	7	t	t	NOUN
ejpam-2672	181	8	=	=	SYM
ejpam-2672	181	9	1.0	1.0	NUM
ejpam-2672	181	10	t	t	NOUN
ejpam-2672	181	11	=	=	SYM
ejpam-2672	181	12	1.5	1.5	NUM
ejpam-2672	181	13	0.5	0.5	NUM
ejpam-2672	181	14	1.0	1.0	NUM
ejpam-2672	181	15	1.5	1.5	NUM
ejpam-2672	181	16	2.0	2.0	NUM
ejpam-2672	181	17	x	x	SYM
ejpam-2672	181	18	-1.0	-1.0	PROPN
ejpam-2672	181	19	-0.5	-0.5	NUM
ejpam-2672	181	20	0.5	0.5	NUM
ejpam-2672	181	21	1.0	1.0	NUM
ejpam-2672	181	22	u1.9hx	u1.9hx	NOUN
ejpam-2672	181	23	,	,	PUNCT
ejpam-2672	181	24	tl	tl	PROPN
ejpam-2672	181	25	figure	figure	VERB
ejpam-2672	181	26	6	6	NUM
ejpam-2672	181	27	:	:	PUNCT
ejpam-2672	181	28	the	the	DET
ejpam-2672	181	29	solution	solution	NOUN
ejpam-2672	181	30	of	of	ADP
ejpam-2672	181	31	(	(	PUNCT
ejpam-2672	181	32	49	49	NUM
ejpam-2672	181	33	)	)	PUNCT
ejpam-2672	181	34	at	at	ADP
ejpam-2672	181	35	different	different	ADJ
ejpam-2672	181	36	times	time	NOUN
ejpam-2672	181	37	t	t	NOUN
ejpam-2672	181	38	=	=	SYM
ejpam-2672	181	39	0.0	0.0	NUM
ejpam-2672	181	40	,	,	PUNCT
ejpam-2672	181	41	0.5	0.5	NUM
ejpam-2672	181	42	,	,	PUNCT
ejpam-2672	181	43	1.0	1.0	NUM
ejpam-2672	181	44	,	,	PUNCT
ejpam-2672	181	45	and	and	CCONJ
ejpam-2672	181	46	1.5	1.5	NUM
ejpam-2672	181	47	,	,	PUNCT
ejpam-2672	181	48	0	0	NUM
ejpam-2672	181	49	≤	≤	NUM
ejpam-2672	181	50	x	x	SYM
ejpam-2672	181	51	≤	≤	NUM
ejpam-2672	181	52	2	2	NUM
ejpam-2672	181	53	and	and	CCONJ
ejpam-2672	181	54	the	the	DET
ejpam-2672	181	55	fractional	fractional	ADJ
ejpam-2672	181	56	order	order	NOUN
ejpam-2672	181	57	α	α	NOUN
ejpam-2672	181	58	=	=	SYM
ejpam-2672	181	59	1.9	1.9	NUM
ejpam-2672	181	60	.	.	PUNCT
ejpam-2672	182	1	and	and	CCONJ
ejpam-2672	182	2	the	the	DET
ejpam-2672	182	3	solution	solution	NOUN
ejpam-2672	182	4	is	be	AUX
ejpam-2672	182	5	thus	thus	ADV
ejpam-2672	182	6	obtained	obtain	VERB
ejpam-2672	182	7	as	as	ADP
ejpam-2672	182	8	u	u	NOUN
ejpam-2672	182	9	=	=	X
ejpam-2672	182	10	u0	u0	ADJ
ejpam-2672	182	11	+	+	NUM
ejpam-2672	182	12	u1	u1	NOUN
ejpam-2672	182	13	+	+	CCONJ
ejpam-2672	182	14	u2	u2	NOUN
ejpam-2672	182	15	+	+	CCONJ
ejpam-2672	182	16	u3	u3	NOUN
ejpam-2672	182	17	+	+	CCONJ
ejpam-2672	182	18	....	....	PUNCT
ejpam-2672	182	19	the	the	DET
ejpam-2672	182	20	solution	solution	NOUN
ejpam-2672	182	21	behavior	behavior	NOUN
ejpam-2672	182	22	as	as	SCONJ
ejpam-2672	182	23	the	the	DET
ejpam-2672	182	24	riesz	riesz	PROPN
ejpam-2672	182	25	parameter	parameter	NOUN
ejpam-2672	182	26	α	α	PROPN
ejpam-2672	182	27	changes	change	NOUN
ejpam-2672	182	28	is	be	AUX
ejpam-2672	182	29	shown	show	VERB
ejpam-2672	182	30	in	in	ADP
ejpam-2672	182	31	figures	figure	NOUN
ejpam-2672	182	32	(	(	PUNCT
ejpam-2672	182	33	4	4	NUM
ejpam-2672	182	34	)	)	PUNCT
ejpam-2672	182	35	and	and	CCONJ
ejpam-2672	182	36	(	(	PUNCT
ejpam-2672	182	37	5	5	NUM
ejpam-2672	182	38	)	)	PUNCT
ejpam-2672	182	39	at	at	ADP
ejpam-2672	182	40	a	a	DET
ejpam-2672	182	41	fixed	fix	VERB
ejpam-2672	182	42	time	time	NOUN
ejpam-2672	182	43	t	t	NOUN
ejpam-2672	182	44	=	=	SYM
ejpam-2672	182	45	0.5	0.5	NUM
ejpam-2672	182	46	and	and	CCONJ
ejpam-2672	182	47	t	t	NOUN
ejpam-2672	182	48	=	=	SYM
ejpam-2672	182	49	1.0	1.0	NUM
ejpam-2672	182	50	,	,	PUNCT
ejpam-2672	182	51	respectively	respectively	ADV
ejpam-2672	182	52	.	.	PUNCT
ejpam-2672	183	1	as	as	ADP
ejpam-2672	183	2	α	α	NOUN
ejpam-2672	183	3	increases	increase	NOUN
ejpam-2672	183	4	,	,	PUNCT
ejpam-2672	183	5	the	the	DET
ejpam-2672	183	6	amplitude	amplitude	NOUN
ejpam-2672	183	7	of	of	ADP
ejpam-2672	183	8	the	the	DET
ejpam-2672	183	9	sinusoidal	sinusoidal	ADJ
ejpam-2672	183	10	behavior	behavior	NOUN
ejpam-2672	183	11	in	in	ADP
ejpam-2672	183	12	solution	solution	NOUN
ejpam-2672	183	13	decreases	decrease	VERB
ejpam-2672	183	14	.	.	PUNCT
ejpam-2672	184	1	the	the	DET
ejpam-2672	184	2	series	series	NOUN
ejpam-2672	184	3	displayed	display	VERB
ejpam-2672	184	4	in	in	ADP
ejpam-2672	184	5	plots	plot	NOUN
ejpam-2672	184	6	is	be	AUX
ejpam-2672	184	7	the	the	DET
ejpam-2672	184	8	partial	partial	ADJ
ejpam-2672	184	9	sum	sum	NOUN
ejpam-2672	184	10	of	of	ADP
ejpam-2672	184	11	the	the	DET
ejpam-2672	184	12	first	first	ADJ
ejpam-2672	184	13	four	four	NUM
ejpam-2672	184	14	terms	term	NOUN
ejpam-2672	184	15	;	;	PUNCT
ejpam-2672	184	16	n	n	NOUN
ejpam-2672	184	17	=	=	SYM
ejpam-2672	184	18	3	3	NUM
ejpam-2672	184	19	(	(	PUNCT
ejpam-2672	184	20	summing	sum	VERB
ejpam-2672	184	21	u0	u0	NOUN
ejpam-2672	184	22	to	to	ADP
ejpam-2672	184	23	u3	u3	NOUN
ejpam-2672	184	24	)	)	PUNCT
ejpam-2672	184	25	.	.	PUNCT
ejpam-2672	185	1	figure	figure	NOUN
ejpam-2672	185	2	(	(	PUNCT
ejpam-2672	185	3	6	6	NUM
ejpam-2672	185	4	)	)	PUNCT
ejpam-2672	185	5	shows	show	VERB
ejpam-2672	185	6	the	the	DET
ejpam-2672	185	7	evolution	evolution	NOUN
ejpam-2672	185	8	with	with	ADP
ejpam-2672	185	9	time	time	NOUN
ejpam-2672	185	10	of	of	ADP
ejpam-2672	185	11	the	the	DET
ejpam-2672	185	12	solution	solution	NOUN
ejpam-2672	185	13	at	at	ADP
ejpam-2672	185	14	a	a	DET
ejpam-2672	185	15	fixed	fix	VERB
ejpam-2672	185	16	fractional	fractional	ADJ
ejpam-2672	185	17	order	order	NOUN
ejpam-2672	185	18	α	α	NOUN
ejpam-2672	185	19	=	=	SYM
ejpam-2672	185	20	1.9	1.9	NUM
ejpam-2672	185	21	in	in	ADP
ejpam-2672	185	22	the	the	DET
ejpam-2672	185	23	interval	interval	NOUN
ejpam-2672	185	24	0	0	NUM
ejpam-2672	185	25	≤	≤	NUM
ejpam-2672	185	26	x	x	SYM
ejpam-2672	185	27	≤	≤	NUM
ejpam-2672	185	28	2	2	NUM
ejpam-2672	185	29	.	.	PUNCT
ejpam-2672	185	30	example	example	NOUN
ejpam-2672	185	31	3	3	X
ejpam-2672	185	32	.	.	X
ejpam-2672	186	1	consider	consider	VERB
ejpam-2672	186	2	the	the	DET
ejpam-2672	186	3	problem	problem	NOUN
ejpam-2672	186	4	(	(	PUNCT
ejpam-2672	186	5	1	1	NUM
ejpam-2672	186	6	-	-	SYM
ejpam-2672	186	7	2	2	NUM
ejpam-2672	186	8	)	)	PUNCT
ejpam-2672	186	9	with	with	ADP
ejpam-2672	186	10	p(u	p(u	NOUN
ejpam-2672	186	11	)	)	PUNCT
ejpam-2672	187	1	=	=	PUNCT
ejpam-2672	188	1	−	−	PROPN
ejpam-2672	188	2	sin(u	sin(u	NOUN
ejpam-2672	188	3	)	)	PUNCT
ejpam-2672	188	4	,	,	PUNCT
ejpam-2672	188	5	f1(x	f1(x	NOUN
ejpam-2672	188	6	)	)	PUNCT
ejpam-2672	188	7	=	=	PUNCT
ejpam-2672	188	8	π+	π+	PUNCT
ejpam-2672	188	9	ε	ε	PROPN
ejpam-2672	188	10	cos(µx	cos(µx	PROPN
ejpam-2672	188	11	)	)	PUNCT
ejpam-2672	188	12	and	and	CCONJ
ejpam-2672	188	13	f2(x	f2(x	NUM
ejpam-2672	188	14	)	)	PUNCT
ejpam-2672	188	15	=	=	SYM
ejpam-2672	188	16	0	0	PUNCT
ejpam-2672	188	17	(	(	PUNCT
ejpam-2672	188	18	the	the	DET
ejpam-2672	188	19	space	space	NOUN
ejpam-2672	188	20	-	-	PUNCT
ejpam-2672	188	21	fractional	fractional	ADJ
ejpam-2672	188	22	sine	sine	NOUN
ejpam-2672	188	23	-	-	PUNCT
ejpam-2672	188	24	gordan	gordan	PROPN
ejpam-2672	188	25	equation	equation	PROPN
ejpam-2672	188	26	)	)	PUNCT
ejpam-2672	188	27	,	,	PUNCT
ejpam-2672	188	28	i.e.	i.e.	X
ejpam-2672	188	29	,	,	PUNCT
ejpam-2672	188	30	{	{	PUNCT
ejpam-2672	188	31	utt(x	utt(x	PROPN
ejpam-2672	188	32	,	,	PUNCT
ejpam-2672	188	33	t	t	PROPN
ejpam-2672	188	34	)	)	PUNCT
ejpam-2672	188	35	=	=	SYM
ejpam-2672	189	1	rαxu(x	rαxu(x	NOUN
ejpam-2672	189	2	,	,	PUNCT
ejpam-2672	189	3	t)−	t)−	PROPN
ejpam-2672	189	4	sin(u	sin(u	PROPN
ejpam-2672	189	5	)	)	PUNCT
ejpam-2672	189	6	,	,	PUNCT
ejpam-2672	189	7	−∞	−∞	PUNCT
ejpam-2672	189	8	<	<	X
ejpam-2672	189	9	x	x	X
ejpam-2672	189	10	<	<	X
ejpam-2672	189	11	∞	∞	PROPN
ejpam-2672	189	12	,	,	PUNCT
ejpam-2672	189	13	t	t	X
ejpam-2672	189	14	>	>	X
ejpam-2672	189	15	0	0	NUM
ejpam-2672	189	16	,	,	PUNCT
ejpam-2672	189	17	u(x	u(x	NOUN
ejpam-2672	189	18	,	,	PUNCT
ejpam-2672	189	19	0	0	NUM
ejpam-2672	189	20	)	)	PUNCT
ejpam-2672	189	21	=	=	PUNCT
ejpam-2672	190	1	π	π	PROPN
ejpam-2672	190	2	+	+	CCONJ
ejpam-2672	190	3	ε	ε	PROPN
ejpam-2672	190	4	cos(µx	cos(µx	PROPN
ejpam-2672	190	5	)	)	PUNCT
ejpam-2672	190	6	,	,	PUNCT
ejpam-2672	190	7	ut(x	ut(x	NOUN
ejpam-2672	190	8	,	,	PUNCT
ejpam-2672	190	9	0	0	NUM
ejpam-2672	190	10	)	)	PUNCT
ejpam-2672	190	11	=	=	SYM
ejpam-2672	190	12	0	0	NUM
ejpam-2672	190	13	,	,	PUNCT
ejpam-2672	190	14	(	(	PUNCT
ejpam-2672	190	15	55	55	NUM
ejpam-2672	190	16	)	)	PUNCT
ejpam-2672	190	17	where	where	SCONJ
ejpam-2672	190	18	ε	ε	PROPN
ejpam-2672	190	19	and	and	CCONJ
ejpam-2672	190	20	µ	µ	PROPN
ejpam-2672	190	21	are	be	AUX
ejpam-2672	190	22	real	real	ADJ
ejpam-2672	190	23	constants	constant	NOUN
ejpam-2672	190	24	.	.	PUNCT
ejpam-2672	191	1	here	here	ADV
ejpam-2672	191	2	the	the	DET
ejpam-2672	191	3	auxiliary	auxiliary	ADJ
ejpam-2672	191	4	linear	linear	ADJ
ejpam-2672	191	5	operator	operator	NOUN
ejpam-2672	191	6	is	be	AUX
ejpam-2672	191	7	l[φ	l[φ	X
ejpam-2672	191	8	]	]	PUNCT
ejpam-2672	191	9	=	=	SYM
ejpam-2672	191	10	∂2	∂2	NOUN
ejpam-2672	191	11	∂t2	∂t2	NOUN
ejpam-2672	191	12	(	(	PUNCT
ejpam-2672	191	13	φ	φ	NOUN
ejpam-2672	191	14	)	)	PUNCT
ejpam-2672	191	15	,	,	PUNCT
ejpam-2672	191	16	(	(	PUNCT
ejpam-2672	191	17	56	56	X
ejpam-2672	191	18	)	)	PUNCT
ejpam-2672	191	19	a.	a.	NOUN
ejpam-2672	191	20	elsaid	elsaid	PROPN
ejpam-2672	191	21	,	,	PUNCT
ejpam-2672	191	22	s.	s.	PROPN
ejpam-2672	191	23	shamseldeen	shamseldeen	PROPN
ejpam-2672	191	24	,	,	PUNCT
ejpam-2672	191	25	s.	s.	PROPN
ejpam-2672	191	26	madkour	madkour	PROPN
ejpam-2672	191	27	/	/	SYM
ejpam-2672	191	28	eur	eur	PROPN
ejpam-2672	191	29	.	.	PUNCT
ejpam-2672	192	1	j.	j.	PROPN
ejpam-2672	192	2	pure	pure	PROPN
ejpam-2672	192	3	appl	appl	PROPN
ejpam-2672	192	4	.	.	PROPN
ejpam-2672	192	5	math	math	PROPN
ejpam-2672	192	6	,	,	PUNCT
ejpam-2672	192	7	10	10	NUM
ejpam-2672	192	8	(	(	PUNCT
ejpam-2672	192	9	3	3	NUM
ejpam-2672	192	10	)	)	PUNCT
ejpam-2672	192	11	(	(	PUNCT
ejpam-2672	192	12	2017	2017	NUM
ejpam-2672	192	13	)	)	PUNCT
ejpam-2672	192	14	,	,	PUNCT
ejpam-2672	192	15	586	586	NUM
ejpam-2672	192	16	-	-	SYM
ejpam-2672	192	17	601	601	NUM
ejpam-2672	192	18	598	598	NUM
ejpam-2672	192	19	and	and	CCONJ
ejpam-2672	192	20	the	the	DET
ejpam-2672	192	21	nonlinear	nonlinear	ADJ
ejpam-2672	192	22	operator	operator	NOUN
ejpam-2672	192	23	n	n	NOUN
ejpam-2672	192	24	is	be	AUX
ejpam-2672	192	25	chosen	choose	VERB
ejpam-2672	192	26	as	as	ADP
ejpam-2672	192	27	n	n	PROPN
ejpam-2672	192	28	[	[	X
ejpam-2672	192	29	φ	φ	X
ejpam-2672	192	30	]	]	X
ejpam-2672	192	31	=	=	SYM
ejpam-2672	192	32	φtt	φtt	NOUN
ejpam-2672	192	33	−rαx(φ	−rαx(φ	NOUN
ejpam-2672	192	34	)	)	PUNCT
ejpam-2672	192	35	+	+	NOUN
ejpam-2672	192	36	sin(φ	sin(φ	X
ejpam-2672	192	37	)	)	PUNCT
ejpam-2672	192	38	.	.	PUNCT
ejpam-2672	193	1	(	(	PUNCT
ejpam-2672	193	2	57	57	NUM
ejpam-2672	193	3	)	)	PUNCT
ejpam-2672	193	4	then	then	ADV
ejpam-2672	193	5	,	,	PUNCT
ejpam-2672	193	6	m	m	VERB
ejpam-2672	193	7	th	th	X
ejpam-2672	193	8	-	-	PUNCT
ejpam-2672	193	9	order	order	NOUN
ejpam-2672	193	10	deformation	deformation	NOUN
ejpam-2672	193	11	equation	equation	NOUN
ejpam-2672	193	12	for	for	ADP
ejpam-2672	193	13	this	this	DET
ejpam-2672	193	14	problem	problem	NOUN
ejpam-2672	193	15	is	be	AUX
ejpam-2672	193	16	given	give	VERB
ejpam-2672	193	17	by	by	ADP
ejpam-2672	193	18	∂2	∂2	ADJ
ejpam-2672	193	19	∂t2	∂t2	NOUN
ejpam-2672	193	20	[	[	X
ejpam-2672	193	21	um(x	um(x	X
ejpam-2672	193	22	,	,	PUNCT
ejpam-2672	193	23	t)−	t)−	PROPN
ejpam-2672	193	24	χmum−1(x	χmum−1(x	NOUN
ejpam-2672	193	25	,	,	PUNCT
ejpam-2672	193	26	t	t	PROPN
ejpam-2672	193	27	)	)	PUNCT
ejpam-2672	193	28	]	]	PUNCT
ejpam-2672	194	1	=	=	SYM
ejpam-2672	194	2	~h(x	~h(x	NOUN
ejpam-2672	194	3	,	,	PUNCT
ejpam-2672	194	4	t)<m[−→u	t)<m[−→u	NOUN
ejpam-2672	194	5	m−1(x	m−1(x	NOUN
ejpam-2672	194	6	,	,	PUNCT
ejpam-2672	194	7	t	t	PROPN
ejpam-2672	194	8	)	)	PUNCT
ejpam-2672	194	9	]	]	PUNCT
ejpam-2672	194	10	,	,	PUNCT
ejpam-2672	194	11	(	(	PUNCT
ejpam-2672	194	12	58	58	NUM
ejpam-2672	194	13	)	)	PUNCT
ejpam-2672	194	14	where	where	SCONJ
ejpam-2672	194	15	<	<	X
ejpam-2672	194	16	m[−→u	m[−→u	ADP
ejpam-2672	194	17	m−1(x	m−1(x	NOUN
ejpam-2672	194	18	,	,	PUNCT
ejpam-2672	194	19	t	t	PROPN
ejpam-2672	194	20	)	)	PUNCT
ejpam-2672	194	21	]	]	PUNCT
ejpam-2672	194	22	is	be	AUX
ejpam-2672	194	23	given	give	VERB
ejpam-2672	194	24	by	by	ADP
ejpam-2672	194	25	<	<	X
ejpam-2672	194	26	m[−→u	m[−→u	ADP
ejpam-2672	194	27	m−1(x	m−1(x	NOUN
ejpam-2672	194	28	,	,	PUNCT
ejpam-2672	194	29	t	t	PROPN
ejpam-2672	194	30	)	)	PUNCT
ejpam-2672	194	31	]	]	PUNCT
ejpam-2672	195	1	=	=	SYM
ejpam-2672	195	2	∂2	∂2	NOUN
ejpam-2672	195	3	∂t2	∂t2	NOUN
ejpam-2672	195	4	(	(	PUNCT
ejpam-2672	195	5	um−1)−rαx(um−1	um−1)−rαx(um−1	NOUN
ejpam-2672	195	6	)	)	PUNCT
ejpam-2672	195	7	+	+	CCONJ
ejpam-2672	195	8	m−1∑	m−1∑	PROPN
ejpam-2672	195	9	k=0	k=0	PROPN
ejpam-2672	195	10	ak	ak	PROPN
ejpam-2672	195	11	,	,	PUNCT
ejpam-2672	195	12	(	(	PUNCT
ejpam-2672	195	13	59	59	NUM
ejpam-2672	195	14	)	)	PUNCT
ejpam-2672	195	15	where	where	SCONJ
ejpam-2672	195	16	ak	ak	PROPN
ejpam-2672	195	17	is	be	AUX
ejpam-2672	195	18	the	the	DET
ejpam-2672	195	19	adomian	adomian	NOUN
ejpam-2672	195	20	polynomials	polynomial	NOUN
ejpam-2672	195	21	for	for	ADP
ejpam-2672	195	22	sin(u	sin(u	NOUN
ejpam-2672	195	23	)	)	PUNCT
ejpam-2672	196	1	[	[	X
ejpam-2672	196	2	?	?	X
ejpam-2672	196	3	]	]	X
ejpam-2672	196	4	:	:	PUNCT
ejpam-2672	196	5	a0	a0	PROPN
ejpam-2672	196	6	=	=	SYM
ejpam-2672	196	7	sin(u0	sin(u0	PROPN
ejpam-2672	196	8	)	)	PUNCT
ejpam-2672	196	9	,	,	PUNCT
ejpam-2672	196	10	a1	a1	NOUN
ejpam-2672	196	11	=	=	SYM
ejpam-2672	196	12	u1	u1	PROPN
ejpam-2672	196	13	cos(u0	cos(u0	PROPN
ejpam-2672	196	14	)	)	PUNCT
ejpam-2672	196	15	,	,	PUNCT
ejpam-2672	196	16	a2	a2	PROPN
ejpam-2672	196	17	=	=	SYM
ejpam-2672	196	18	1/2(−u2	1/2(−u2	NOUN
ejpam-2672	196	19	1	1	NUM
ejpam-2672	196	20	sin(u0	sin(u0	NOUN
ejpam-2672	196	21	)	)	PUNCT
ejpam-2672	196	22	+	+	CCONJ
ejpam-2672	196	23	2u2	2u2	NUM
ejpam-2672	196	24	cos(u0	cos(u0	NOUN
ejpam-2672	196	25	)	)	PUNCT
ejpam-2672	196	26	)	)	PUNCT
ejpam-2672	196	27	,	,	PUNCT
ejpam-2672	196	28	....	....	PUNCT
ejpam-2672	197	1	we	we	PRON
ejpam-2672	197	2	choose	choose	VERB
ejpam-2672	197	3	h(x	h(x	PROPN
ejpam-2672	197	4	,	,	PUNCT
ejpam-2672	197	5	t	t	PROPN
ejpam-2672	197	6	)	)	PUNCT
ejpam-2672	197	7	=	=	SYM
ejpam-2672	197	8	1	1	NUM
ejpam-2672	197	9	,	,	PUNCT
ejpam-2672	197	10	and	and	CCONJ
ejpam-2672	197	11	by	by	ADP
ejpam-2672	197	12	applying	apply	VERB
ejpam-2672	197	13	the	the	DET
ejpam-2672	197	14	inverse	inverse	ADJ
ejpam-2672	197	15	integral	integral	ADJ
ejpam-2672	197	16	operator	operator	NOUN
ejpam-2672	197	17	to	to	ADP
ejpam-2672	197	18	both	both	DET
ejpam-2672	197	19	sides	side	NOUN
ejpam-2672	197	20	of	of	ADP
ejpam-2672	197	21	(	(	PUNCT
ejpam-2672	197	22	58	58	NUM
ejpam-2672	197	23	)	)	PUNCT
ejpam-2672	197	24	,	,	PUNCT
ejpam-2672	197	25	one	one	PRON
ejpam-2672	197	26	can	can	AUX
ejpam-2672	197	27	obtain	obtain	VERB
ejpam-2672	197	28	the	the	DET
ejpam-2672	197	29	first	first	ADJ
ejpam-2672	197	30	four	four	NUM
ejpam-2672	197	31	terms	term	NOUN
ejpam-2672	197	32	as	as	ADP
ejpam-2672	197	33	u0	u0	ADJ
ejpam-2672	197	34	=	=	SYM
ejpam-2672	197	35	π	π	PROPN
ejpam-2672	197	36	,	,	PUNCT
ejpam-2672	197	37	u1	u1	NOUN
ejpam-2672	197	38	=	=	SYM
ejpam-2672	197	39	ε	ε	PROPN
ejpam-2672	197	40	cos(µx	cos(µx	PROPN
ejpam-2672	197	41	)	)	PUNCT
ejpam-2672	197	42	,	,	PUNCT
ejpam-2672	197	43	u2	u2	PROPN
ejpam-2672	197	44	=	=	SYM
ejpam-2672	197	45	ε	ε	PROPN
ejpam-2672	197	46	2	2	NUM
ejpam-2672	197	47	(	(	PUNCT
ejpam-2672	197	48	2	2	NUM
ejpam-2672	197	49	+	+	NUM
ejpam-2672	197	50	h	h	NOUN
ejpam-2672	197	51	(	(	PUNCT
ejpam-2672	197	52	2	2	NUM
ejpam-2672	197	53	+	+	NUM
ejpam-2672	197	54	t2	t2	NOUN
ejpam-2672	197	55	(	(	PUNCT
ejpam-2672	197	56	−1	−1	NOUN
ejpam-2672	197	57	+	+	CCONJ
ejpam-2672	197	58	µα	µα	X
ejpam-2672	197	59	)	)	PUNCT
ejpam-2672	197	60	)	)	PUNCT
ejpam-2672	197	61	)	)	PUNCT
ejpam-2672	197	62	cos(µx	cos(µx	NUM
ejpam-2672	197	63	)	)	PUNCT
ejpam-2672	197	64	,	,	PUNCT
ejpam-2672	197	65	u3	u3	NOUN
ejpam-2672	197	66	=	=	SYM
ejpam-2672	197	67	ε	ε	PROPN
ejpam-2672	197	68	24	24	NUM
ejpam-2672	197	69	(	(	PUNCT
ejpam-2672	197	70	24	24	NUM
ejpam-2672	197	71	+	+	CCONJ
ejpam-2672	197	72	24h(2	24h(2	NUM
ejpam-2672	197	73	+	+	CCONJ
ejpam-2672	197	74	t2(−1	t2(−1	NOUN
ejpam-2672	197	75	+	+	CCONJ
ejpam-2672	197	76	µα	µα	X
ejpam-2672	197	77	)	)	PUNCT
ejpam-2672	197	78	)	)	PUNCT
ejpam-2672	198	1	+	+	CCONJ
ejpam-2672	198	2	h2(24	h2(24	PROPN
ejpam-2672	198	3	+	+	CCONJ
ejpam-2672	198	4	24t2(−1	24t2(−1	NUM
ejpam-2672	198	5	+	+	CCONJ
ejpam-2672	198	6	µα	µα	X
ejpam-2672	198	7	)	)	PUNCT
ejpam-2672	198	8	+	+	NUM
ejpam-2672	198	9	t4(−1	t4(−1	X
ejpam-2672	198	10	+	+	CCONJ
ejpam-2672	198	11	µα)2	µα)2	NOUN
ejpam-2672	198	12	)	)	PUNCT
ejpam-2672	198	13	)	)	PUNCT
ejpam-2672	198	14	cos(µx	cos(µx	NUM
ejpam-2672	198	15	)	)	PUNCT
ejpam-2672	198	16	and	and	CCONJ
ejpam-2672	198	17	the	the	DET
ejpam-2672	198	18	solution	solution	NOUN
ejpam-2672	198	19	is	be	AUX
ejpam-2672	198	20	u	u	NOUN
ejpam-2672	198	21	=	=	X
ejpam-2672	198	22	u0	u0	ADJ
ejpam-2672	198	23	+	+	NUM
ejpam-2672	198	24	u1	u1	NOUN
ejpam-2672	198	25	+	+	CCONJ
ejpam-2672	198	26	u2	u2	NOUN
ejpam-2672	198	27	+	+	CCONJ
ejpam-2672	198	28	u3	u3	NOUN
ejpam-2672	198	29	+	+	CCONJ
ejpam-2672	198	30	.....	.....	PUNCT
ejpam-2672	198	31	table	table	NOUN
ejpam-2672	198	32	3	3	NUM
ejpam-2672	198	33	shows	show	VERB
ejpam-2672	198	34	the	the	DET
ejpam-2672	198	35	estimated	estimate	VERB
ejpam-2672	198	36	values	value	NOUN
ejpam-2672	198	37	of	of	ADP
ejpam-2672	198	38	the	the	DET
ejpam-2672	198	39	optimal	optimal	ADJ
ejpam-2672	198	40	convergence	convergence	NOUN
ejpam-2672	198	41	control	control	NOUN
ejpam-2672	198	42	parameter	parameter	NOUN
ejpam-2672	198	43	~	~	PUNCT
ejpam-2672	198	44	and	and	CCONJ
ejpam-2672	198	45	the	the	DET
ejpam-2672	198	46	corresponding	corresponding	ADJ
ejpam-2672	198	47	residual	residual	ADJ
ejpam-2672	198	48	error	error	NOUN
ejpam-2672	198	49	em	em	PRON
ejpam-2672	198	50	for	for	ADP
ejpam-2672	198	51	the	the	DET
ejpam-2672	198	52	problem	problem	NOUN
ejpam-2672	198	53	displayed	display	VERB
ejpam-2672	198	54	in	in	ADP
ejpam-2672	198	55	(	(	PUNCT
ejpam-2672	198	56	55	55	NUM
ejpam-2672	198	57	)	)	PUNCT
ejpam-2672	198	58	at	at	ADP
ejpam-2672	198	59	different	different	ADJ
ejpam-2672	198	60	values	value	NOUN
ejpam-2672	198	61	of	of	ADP
ejpam-2672	198	62	the	the	DET
ejpam-2672	198	63	fractional	fractional	ADJ
ejpam-2672	198	64	derivative	derivative	ADJ
ejpam-2672	198	65	α	α	NOUN
ejpam-2672	198	66	in	in	ADP
ejpam-2672	198	67	the	the	DET
ejpam-2672	198	68	space	space	NOUN
ejpam-2672	198	69	domain	domain	NOUN
ejpam-2672	198	70	0	0	NUM
ejpam-2672	198	71	≤	≤	NUM
ejpam-2672	198	72	x	x	SYM
ejpam-2672	198	73	≤	≤	NOUN
ejpam-2672	198	74	2.0	2.0	NUM
ejpam-2672	198	75	and	and	CCONJ
ejpam-2672	198	76	the	the	DET
ejpam-2672	198	77	time	time	NOUN
ejpam-2672	198	78	interval	interval	NOUN
ejpam-2672	198	79	0	0	NUM
ejpam-2672	198	80	≤	≤	NUM
ejpam-2672	198	81	t	t	PROPN
ejpam-2672	198	82	≤	≤	NOUN
ejpam-2672	198	83	2.0	2.0	NUM
ejpam-2672	198	84	.	.	PUNCT
ejpam-2672	198	85	table	table	NOUN
ejpam-2672	198	86	3	3	NUM
ejpam-2672	198	87	:	:	PUNCT
ejpam-2672	198	88	the	the	DET
ejpam-2672	198	89	estimated	estimate	VERB
ejpam-2672	198	90	optimal	optimal	ADJ
ejpam-2672	198	91	convergence	convergence	NOUN
ejpam-2672	198	92	parameter	parameter	NOUN
ejpam-2672	198	93	~	~	PUNCT
ejpam-2672	198	94	and	and	CCONJ
ejpam-2672	198	95	the	the	DET
ejpam-2672	198	96	corresponding	corresponding	ADJ
ejpam-2672	198	97	residual	residual	ADJ
ejpam-2672	198	98	error	error	NOUN
ejpam-2672	198	99	em	em	PRON
ejpam-2672	198	100	for	for	ADP
ejpam-2672	198	101	0	0	NUM
ejpam-2672	198	102	≤	≤	NUM
ejpam-2672	198	103	x	x	SYM
ejpam-2672	198	104	≤	≤	NOUN
ejpam-2672	198	105	2.0	2.0	NUM
ejpam-2672	198	106	and	and	CCONJ
ejpam-2672	198	107	0	0	NUM
ejpam-2672	198	108	≤	≤	NUM
ejpam-2672	198	109	t	t	NOUN
ejpam-2672	198	110	≤	≤	NOUN
ejpam-2672	198	111	2.0	2.0	NUM
ejpam-2672	198	112	at	at	ADP
ejpam-2672	198	113	different	different	ADJ
ejpam-2672	198	114	fractional	fractional	ADJ
ejpam-2672	198	115	derivative	derivative	ADJ
ejpam-2672	198	116	α	α	NOUN
ejpam-2672	198	117	for	for	ADP
ejpam-2672	198	118	example	example	NOUN
ejpam-2672	198	119	(	(	PUNCT
ejpam-2672	198	120	3	3	NUM
ejpam-2672	198	121	)	)	PUNCT
ejpam-2672	198	122	.	.	PUNCT
ejpam-2672	199	1	α	α	X
ejpam-2672	199	2	~	~	PUNCT
ejpam-2672	199	3	em	em	PRON
ejpam-2672	199	4	optimal	optimal	ADJ
ejpam-2672	199	5	parameter	parameter	NOUN
ejpam-2672	199	6	residual	residual	ADJ
ejpam-2672	199	7	error	error	NOUN
ejpam-2672	199	8	1.7	1.7	NUM
ejpam-2672	199	9	−0.928016	−0.928016	PROPN
ejpam-2672	199	10	1.42983e	1.42983e	NUM
ejpam-2672	199	11	−	−	PROPN
ejpam-2672	199	12	4	4	NUM
ejpam-2672	199	13	1.8	1.8	NUM
ejpam-2672	199	14	−0.926483	−0.926483	PROPN
ejpam-2672	199	15	3.41879e	3.41879e	NUM
ejpam-2672	199	16	−	−	PROPN
ejpam-2672	199	17	4	4	NUM
ejpam-2672	199	18	1.9	1.9	NUM
ejpam-2672	199	19	−0.925981	−0.925981	NUM
ejpam-2672	199	20	6.10878e	6.10878e	ADP
ejpam-2672	199	21	−	−	PROPN
ejpam-2672	199	22	4	4	NUM
ejpam-2672	199	23	2.0	2.0	NUM
ejpam-2672	199	24	−0.923954	−0.923954	NOUN
ejpam-2672	199	25	9.76395e	9.76395e	NOUN
ejpam-2672	199	26	−	−	NOUN
ejpam-2672	199	27	4	4	NUM
ejpam-2672	199	28	the	the	DET
ejpam-2672	199	29	behavior	behavior	NOUN
ejpam-2672	199	30	of	of	ADP
ejpam-2672	199	31	the	the	DET
ejpam-2672	199	32	solution	solution	NOUN
ejpam-2672	199	33	of	of	ADP
ejpam-2672	199	34	the	the	DET
ejpam-2672	199	35	sine	sine	ADJ
ejpam-2672	199	36	-	-	PUNCT
ejpam-2672	199	37	gordan	gordan	PROPN
ejpam-2672	199	38	equation	equation	NOUN
ejpam-2672	199	39	(	(	PUNCT
ejpam-2672	199	40	55	55	NUM
ejpam-2672	199	41	)	)	PUNCT
ejpam-2672	199	42	as	as	SCONJ
ejpam-2672	199	43	the	the	DET
ejpam-2672	199	44	riesz	riesz	PROPN
ejpam-2672	199	45	parameter	parameter	NOUN
ejpam-2672	199	46	α	α	PROPN
ejpam-2672	199	47	changes	change	NOUN
ejpam-2672	199	48	is	be	AUX
ejpam-2672	199	49	shown	show	VERB
ejpam-2672	199	50	in	in	ADP
ejpam-2672	199	51	figures	figure	NOUN
ejpam-2672	199	52	(	(	PUNCT
ejpam-2672	199	53	7	7	NUM
ejpam-2672	199	54	)	)	PUNCT
ejpam-2672	199	55	and	and	CCONJ
ejpam-2672	199	56	(	(	PUNCT
ejpam-2672	199	57	8)	8)	NUM
ejpam-2672	199	58	at	at	ADP
ejpam-2672	199	59	a	a	DET
ejpam-2672	199	60	fixed	fix	VERB
ejpam-2672	199	61	time	time	NOUN
ejpam-2672	199	62	t	t	PROPN
ejpam-2672	199	63	=	=	SYM
ejpam-2672	199	64	1.0	1.0	NUM
ejpam-2672	199	65	and	and	CCONJ
ejpam-2672	199	66	t	t	NOUN
ejpam-2672	199	67	=	=	SYM
ejpam-2672	199	68	1.5	1.5	NUM
ejpam-2672	199	69	,	,	PUNCT
ejpam-2672	199	70	respectively	respectively	ADV
ejpam-2672	199	71	,	,	PUNCT
ejpam-2672	199	72	while	while	SCONJ
ejpam-2672	199	73	the	the	DET
ejpam-2672	199	74	temporal	temporal	ADJ
ejpam-2672	199	75	evolution	evolution	NOUN
ejpam-2672	199	76	of	of	ADP
ejpam-2672	199	77	the	the	DET
ejpam-2672	199	78	solution	solution	NOUN
ejpam-2672	199	79	is	be	AUX
ejpam-2672	199	80	depicted	depict	VERB
ejpam-2672	199	81	in	in	ADP
ejpam-2672	199	82	figure	figure	NOUN
ejpam-2672	199	83	(	(	PUNCT
ejpam-2672	199	84	9	9	NUM
ejpam-2672	199	85	)	)	PUNCT
ejpam-2672	199	86	at	at	ADP
ejpam-2672	199	87	a	a	DET
ejpam-2672	199	88	fixed	fix	VERB
ejpam-2672	199	89	fractional	fractional	ADJ
ejpam-2672	199	90	order	order	NOUN
ejpam-2672	199	91	α	α	NOUN
ejpam-2672	199	92	=	=	SYM
ejpam-2672	199	93	1.9	1.9	NUM
ejpam-2672	199	94	.	.	PUNCT
ejpam-2672	200	1	as	as	ADP
ejpam-2672	200	2	α	α	NOUN
ejpam-2672	200	3	increases	increase	NOUN
ejpam-2672	200	4	,	,	PUNCT
ejpam-2672	200	5	the	the	DET
ejpam-2672	200	6	amplitude	amplitude	NOUN
ejpam-2672	200	7	of	of	ADP
ejpam-2672	200	8	the	the	DET
ejpam-2672	200	9	sinusoidal	sinusoidal	ADJ
ejpam-2672	200	10	behavior	behavior	NOUN
ejpam-2672	200	11	in	in	ADP
ejpam-2672	200	12	solution	solution	NOUN
ejpam-2672	200	13	decreases	decrease	VERB
ejpam-2672	200	14	.	.	PUNCT
ejpam-2672	201	1	the	the	DET
ejpam-2672	201	2	series	series	NOUN
ejpam-2672	201	3	displayed	display	VERB
ejpam-2672	201	4	in	in	ADP
ejpam-2672	201	5	the	the	DET
ejpam-2672	201	6	figures	figure	NOUN
ejpam-2672	201	7	is	be	AUX
ejpam-2672	201	8	the	the	DET
ejpam-2672	201	9	partial	partial	ADJ
ejpam-2672	201	10	sum	sum	NOUN
ejpam-2672	201	11	of	of	ADP
ejpam-2672	201	12	the	the	DET
ejpam-2672	201	13	first	first	ADJ
ejpam-2672	201	14	four	four	NUM
ejpam-2672	201	15	terms	term	NOUN
ejpam-2672	201	16	;	;	PUNCT
ejpam-2672	201	17	n	n	NOUN
ejpam-2672	201	18	=	=	SYM
ejpam-2672	201	19	3	3	NUM
ejpam-2672	201	20	(	(	PUNCT
ejpam-2672	201	21	summing	sum	VERB
ejpam-2672	201	22	u0	u0	NOUN
ejpam-2672	201	23	to	to	ADP
ejpam-2672	201	24	u3	u3	NOUN
ejpam-2672	201	25	)	)	PUNCT
ejpam-2672	201	26	.	.	PUNCT
ejpam-2672	202	1	references	reference	NOUN
ejpam-2672	202	2	599	599	NUM
ejpam-2672	202	3	α	α	NOUN
ejpam-2672	202	4	=	=	NOUN
ejpam-2672	202	5	1.7	1.7	NUM
ejpam-2672	202	6	α	α	NOUN
ejpam-2672	202	7	=	=	PUNCT
ejpam-2672	202	8	1.8	1.8	NUM
ejpam-2672	202	9	α	α	NOUN
ejpam-2672	202	10	=	=	VERB
ejpam-2672	202	11	2.0	2.0	NUM
ejpam-2672	202	12	α	α	NOUN
ejpam-2672	202	13	=	=	SYM
ejpam-2672	202	14	1.9	1.9	NUM
ejpam-2672	202	15	0.5	0.5	NUM
ejpam-2672	202	16	1.0	1.0	NUM
ejpam-2672	202	17	1.5	1.5	NUM
ejpam-2672	202	18	2.0	2.0	NUM
ejpam-2672	202	19	x	x	SYM
ejpam-2672	202	20	3.05	3.05	NUM
ejpam-2672	202	21	3.10	3.10	NUM
ejpam-2672	202	22	3.15	3.15	NUM
ejpam-2672	202	23	3.20	3.20	NUM
ejpam-2672	202	24	3.25	3.25	NUM
ejpam-2672	202	25	3.30	3.30	NUM
ejpam-2672	202	26	uαhx,1.0l	uαhx,1.0l	NOUN
ejpam-2672	202	27	figure	figure	NOUN
ejpam-2672	202	28	7	7	NUM
ejpam-2672	202	29	:	:	PUNCT
ejpam-2672	202	30	the	the	DET
ejpam-2672	202	31	solution	solution	NOUN
ejpam-2672	202	32	of	of	ADP
ejpam-2672	202	33	(	(	PUNCT
ejpam-2672	202	34	55	55	NUM
ejpam-2672	202	35	)	)	PUNCT
ejpam-2672	202	36	at	at	ADP
ejpam-2672	202	37	ε	ε	PROPN
ejpam-2672	202	38	=	=	SYM
ejpam-2672	202	39	0.3	0.3	NUM
ejpam-2672	202	40	,	,	PUNCT
ejpam-2672	202	41	µ	µ	NOUN
ejpam-2672	202	42	=	=	SYM
ejpam-2672	202	43	π/2	π/2	NUM
ejpam-2672	202	44	,	,	PUNCT
ejpam-2672	202	45	t	t	X
ejpam-2672	202	46	=	=	SYM
ejpam-2672	202	47	1.0	1.0	NUM
ejpam-2672	202	48	,	,	PUNCT
ejpam-2672	202	49	0	0	NUM
ejpam-2672	202	50	≤	≤	NUM
ejpam-2672	202	51	x	x	SYM
ejpam-2672	202	52	≤	≤	NUM
ejpam-2672	202	53	0.2	0.2	NUM
ejpam-2672	202	54	and	and	CCONJ
ejpam-2672	202	55	different	different	ADJ
ejpam-2672	202	56	values	value	NOUN
ejpam-2672	202	57	of	of	ADP
ejpam-2672	202	58	the	the	DET
ejpam-2672	202	59	fractional	fractional	ADJ
ejpam-2672	202	60	order	order	NOUN
ejpam-2672	202	61	α	α	NOUN
ejpam-2672	202	62	=	=	SYM
ejpam-2672	202	63	1.7	1.7	NUM
ejpam-2672	202	64	,	,	PUNCT
ejpam-2672	202	65	1.8	1.8	NUM
ejpam-2672	202	66	,	,	PUNCT
ejpam-2672	202	67	1.9	1.9	NUM
ejpam-2672	202	68	and	and	CCONJ
ejpam-2672	202	69	2.0	2.0	NUM
ejpam-2672	202	70	.	.	PUNCT
ejpam-2672	203	1	α	α	X
ejpam-2672	203	2	=	=	PUNCT
ejpam-2672	203	3	2.0	2.0	NUM
ejpam-2672	203	4	α	α	NOUN
ejpam-2672	203	5	=	=	PUNCT
ejpam-2672	203	6	1.9	1.9	NUM
ejpam-2672	203	7	α	α	NOUN
ejpam-2672	203	8	=	=	PUNCT
ejpam-2672	203	9	1.8	1.8	NUM
ejpam-2672	203	10	α	α	NOUN
ejpam-2672	203	11	=	=	SYM
ejpam-2672	203	12	1.7	1.7	NUM
ejpam-2672	203	13	0.5	0.5	NUM
ejpam-2672	203	14	1.0	1.0	NUM
ejpam-2672	203	15	1.5	1.5	NUM
ejpam-2672	203	16	2.0	2.0	NUM
ejpam-2672	203	17	x	x	SYM
ejpam-2672	203	18	3.15	3.15	NUM
ejpam-2672	203	19	3.20	3.20	NUM
ejpam-2672	203	20	uαhx,1.5l	uαhx,1.5l	NOUN
ejpam-2672	203	21	figure	figure	NOUN
ejpam-2672	203	22	8	8	NUM
ejpam-2672	203	23	:	:	PUNCT
ejpam-2672	203	24	the	the	DET
ejpam-2672	203	25	solution	solution	NOUN
ejpam-2672	203	26	of	of	ADP
ejpam-2672	203	27	(	(	PUNCT
ejpam-2672	203	28	55	55	NUM
ejpam-2672	203	29	)	)	PUNCT
ejpam-2672	203	30	at	at	ADP
ejpam-2672	203	31	ε	ε	PROPN
ejpam-2672	203	32	=	=	SYM
ejpam-2672	203	33	0.3	0.3	NUM
ejpam-2672	203	34	,	,	PUNCT
ejpam-2672	203	35	µ	µ	NOUN
ejpam-2672	203	36	=	=	SYM
ejpam-2672	203	37	π/2	π/2	NUM
ejpam-2672	203	38	,	,	PUNCT
ejpam-2672	203	39	t	t	NOUN
ejpam-2672	203	40	=	=	SYM
ejpam-2672	203	41	1.5	1.5	NUM
ejpam-2672	203	42	,	,	PUNCT
ejpam-2672	203	43	0	0	NUM
ejpam-2672	203	44	≤	≤	NUM
ejpam-2672	203	45	x	x	SYM
ejpam-2672	203	46	≤	≤	NUM
ejpam-2672	203	47	0.2	0.2	NUM
ejpam-2672	203	48	and	and	CCONJ
ejpam-2672	203	49	different	different	ADJ
ejpam-2672	203	50	values	value	NOUN
ejpam-2672	203	51	of	of	ADP
ejpam-2672	203	52	the	the	DET
ejpam-2672	203	53	fractional	fractional	ADJ
ejpam-2672	203	54	order	order	NOUN
ejpam-2672	203	55	α	α	NOUN
ejpam-2672	203	56	=	=	SYM
ejpam-2672	203	57	1.7	1.7	NUM
ejpam-2672	203	58	,	,	PUNCT
ejpam-2672	203	59	1.8	1.8	NUM
ejpam-2672	203	60	,	,	PUNCT
ejpam-2672	203	61	1.9	1.9	NUM
ejpam-2672	203	62	and	and	CCONJ
ejpam-2672	203	63	2.0	2.0	NUM
ejpam-2672	203	64	.	.	NOUN
ejpam-2672	204	1	6	6	NUM
ejpam-2672	204	2	.	.	X
ejpam-2672	204	3	conclusion	conclusion	NOUN
ejpam-2672	204	4	we	we	PRON
ejpam-2672	204	5	present	present	VERB
ejpam-2672	204	6	a	a	DET
ejpam-2672	204	7	study	study	NOUN
ejpam-2672	204	8	to	to	ADP
ejpam-2672	204	9	the	the	DET
ejpam-2672	204	10	behavior	behavior	NOUN
ejpam-2672	204	11	of	of	ADP
ejpam-2672	204	12	the	the	DET
ejpam-2672	204	13	solution	solution	NOUN
ejpam-2672	204	14	to	to	ADP
ejpam-2672	204	15	the	the	DET
ejpam-2672	204	16	space	space	NOUN
ejpam-2672	204	17	-	-	PUNCT
ejpam-2672	204	18	fractional	fractional	ADJ
ejpam-2672	204	19	wave	wave	NOUN
ejpam-2672	204	20	equation	equation	NOUN
ejpam-2672	204	21	where	where	SCONJ
ejpam-2672	204	22	the	the	DET
ejpam-2672	204	23	spatial	spatial	ADJ
ejpam-2672	204	24	derivative	derivative	NOUN
ejpam-2672	204	25	is	be	AUX
ejpam-2672	204	26	given	give	VERB
ejpam-2672	204	27	in	in	ADP
ejpam-2672	204	28	riesz	riesz	PROPN
ejpam-2672	204	29	sense	sense	NOUN
ejpam-2672	204	30	.	.	PUNCT
ejpam-2672	205	1	we	we	PRON
ejpam-2672	205	2	proved	prove	VERB
ejpam-2672	205	3	the	the	DET
ejpam-2672	205	4	continuation	continuation	NOUN
ejpam-2672	205	5	of	of	ADP
ejpam-2672	205	6	the	the	DET
ejpam-2672	205	7	solution	solution	NOUN
ejpam-2672	205	8	of	of	ADP
ejpam-2672	205	9	the	the	DET
ejpam-2672	205	10	considered	consider	VERB
ejpam-2672	205	11	fractional	fractional	ADJ
ejpam-2672	205	12	-	-	PUNCT
ejpam-2672	205	13	order	order	NOUN
ejpam-2672	205	14	wave	wave	NOUN
ejpam-2672	205	15	equation	equation	NOUN
ejpam-2672	205	16	to	to	ADP
ejpam-2672	205	17	the	the	DET
ejpam-2672	205	18	solution	solution	NOUN
ejpam-2672	205	19	of	of	ADP
ejpam-2672	205	20	the	the	DET
ejpam-2672	205	21	corresponding	corresponding	ADJ
ejpam-2672	205	22	integer	integer	NOUN
ejpam-2672	205	23	order	order	NOUN
ejpam-2672	205	24	problem	problem	NOUN
ejpam-2672	205	25	.	.	PUNCT
ejpam-2672	206	1	the	the	DET
ejpam-2672	206	2	iterative	iterative	NOUN
ejpam-2672	206	3	series	series	NOUN
ejpam-2672	206	4	solution	solution	NOUN
ejpam-2672	206	5	for	for	ADP
ejpam-2672	206	6	the	the	DET
ejpam-2672	206	7	fractional	fractional	ADJ
ejpam-2672	206	8	equation	equation	NOUN
ejpam-2672	206	9	is	be	AUX
ejpam-2672	206	10	obtained	obtain	VERB
ejpam-2672	206	11	using	use	VERB
ejpam-2672	206	12	the	the	DET
ejpam-2672	206	13	oham	oham	NOUN
ejpam-2672	206	14	.	.	PUNCT
ejpam-2672	207	1	the	the	DET
ejpam-2672	207	2	advantage	advantage	NOUN
ejpam-2672	207	3	of	of	ADP
ejpam-2672	207	4	using	use	VERB
ejpam-2672	207	5	this	this	DET
ejpam-2672	207	6	technique	technique	NOUN
ejpam-2672	207	7	is	be	AUX
ejpam-2672	207	8	the	the	DET
ejpam-2672	207	9	ability	ability	NOUN
ejpam-2672	207	10	to	to	PART
ejpam-2672	207	11	estimate	estimate	VERB
ejpam-2672	207	12	an	an	DET
ejpam-2672	207	13	approximation	approximation	NOUN
ejpam-2672	207	14	to	to	ADP
ejpam-2672	207	15	the	the	DET
ejpam-2672	207	16	residual	residual	ADJ
ejpam-2672	207	17	error	error	NOUN
ejpam-2672	207	18	.	.	PUNCT
ejpam-2672	208	1	the	the	DET
ejpam-2672	208	2	results	result	NOUN
ejpam-2672	208	3	obtained	obtain	VERB
ejpam-2672	208	4	illustrate	illustrate	NOUN
ejpam-2672	208	5	graphically	graphically	ADV
ejpam-2672	208	6	the	the	DET
ejpam-2672	208	7	continuation	continuation	NOUN
ejpam-2672	208	8	of	of	ADP
ejpam-2672	208	9	the	the	DET
ejpam-2672	208	10	solution	solution	NOUN
ejpam-2672	208	11	we	we	PRON
ejpam-2672	208	12	proved	prove	VERB
ejpam-2672	208	13	theoretically	theoretically	ADV
ejpam-2672	208	14	.	.	PUNCT
ejpam-2672	209	1	references	reference	NOUN
ejpam-2672	209	2	[	[	X
ejpam-2672	209	3	1	1	NUM
ejpam-2672	209	4	]	]	X
ejpam-2672	209	5	ronald	ronald	PROPN
ejpam-2672	209	6	l	l	PROPN
ejpam-2672	209	7	bagley	bagley	PROPN
ejpam-2672	209	8	.	.	PUNCT
ejpam-2672	210	1	power	power	NOUN
ejpam-2672	210	2	law	law	NOUN
ejpam-2672	210	3	and	and	CCONJ
ejpam-2672	210	4	fractional	fractional	ADJ
ejpam-2672	210	5	calculus	calculus	NOUN
ejpam-2672	210	6	model	model	NOUN
ejpam-2672	210	7	of	of	ADP
ejpam-2672	210	8	viscoelasticity	viscoelasticity	NOUN
ejpam-2672	210	9	.	.	PUNCT
ejpam-2672	211	1	aiaa	aiaa	PROPN
ejpam-2672	211	2	journal	journal	PROPN
ejpam-2672	211	3	,	,	PUNCT
ejpam-2672	211	4	27(10):1412–1417	27(10):1412–1417	NUM
ejpam-2672	211	5	,	,	PUNCT
ejpam-2672	211	6	1989	1989	NUM
ejpam-2672	211	7	.	.	PUNCT
ejpam-2672	212	1	[	[	X
ejpam-2672	212	2	2	2	NUM
ejpam-2672	212	3	]	]	X
ejpam-2672	212	4	yann	yann	PROPN
ejpam-2672	212	5	bouremel	bouremel	PROPN
ejpam-2672	212	6	.	.	PUNCT
ejpam-2672	213	1	explicit	explicit	ADJ
ejpam-2672	213	2	series	series	NOUN
ejpam-2672	213	3	solution	solution	NOUN
ejpam-2672	213	4	for	for	ADP
ejpam-2672	213	5	the	the	DET
ejpam-2672	213	6	glauert	glauert	ADJ
ejpam-2672	213	7	-	-	PUNCT
ejpam-2672	213	8	jet	jet	NOUN
ejpam-2672	213	9	problem	problem	NOUN
ejpam-2672	213	10	by	by	ADP
ejpam-2672	213	11	means	mean	NOUN
ejpam-2672	213	12	of	of	ADP
ejpam-2672	213	13	the	the	DET
ejpam-2672	213	14	homotopy	homotopy	NOUN
ejpam-2672	213	15	analysis	analysis	NOUN
ejpam-2672	213	16	method	method	NOUN
ejpam-2672	213	17	.	.	PUNCT
ejpam-2672	214	1	communications	communication	NOUN
ejpam-2672	214	2	in	in	ADP
ejpam-2672	214	3	nonlinear	nonlinear	ADJ
ejpam-2672	214	4	science	science	NOUN
ejpam-2672	214	5	and	and	CCONJ
ejpam-2672	214	6	numerical	numerical	PROPN
ejpam-2672	214	7	simulation	simulation	PROPN
ejpam-2672	214	8	,	,	PUNCT
ejpam-2672	214	9	12(5):714–724	12(5):714–724	NUM
ejpam-2672	214	10	,	,	PUNCT
ejpam-2672	214	11	2007	2007	NUM
ejpam-2672	214	12	.	.	PUNCT
ejpam-2672	215	1	[	[	X
ejpam-2672	215	2	3	3	X
ejpam-2672	215	3	]	]	X
ejpam-2672	215	4	jie	jie	PROPN
ejpam-2672	215	5	cang	cang	PROPN
ejpam-2672	215	6	,	,	PUNCT
ejpam-2672	215	7	yue	yue	PROPN
ejpam-2672	215	8	tan	tan	PROPN
ejpam-2672	215	9	,	,	PUNCT
ejpam-2672	215	10	hang	hang	PROPN
ejpam-2672	215	11	xu	xu	PROPN
ejpam-2672	215	12	,	,	PUNCT
ejpam-2672	215	13	and	and	CCONJ
ejpam-2672	215	14	shi	shi	PROPN
ejpam-2672	215	15	-	-	PUNCT
ejpam-2672	215	16	jun	jun	PROPN
ejpam-2672	215	17	liao	liao	PROPN
ejpam-2672	215	18	.	.	PROPN
ejpam-2672	216	1	series	series	PROPN
ejpam-2672	216	2	solutions	solution	NOUN
ejpam-2672	216	3	of	of	ADP
ejpam-2672	216	4	non	non	ADJ
ejpam-2672	216	5	-	-	ADJ
ejpam-2672	216	6	linear	linear	ADJ
ejpam-2672	216	7	riccati	riccati	PROPN
ejpam-2672	216	8	differential	differential	NOUN
ejpam-2672	216	9	equations	equation	NOUN
ejpam-2672	216	10	with	with	ADP
ejpam-2672	216	11	fractional	fractional	ADJ
ejpam-2672	216	12	order	order	NOUN
ejpam-2672	216	13	.	.	PUNCT
ejpam-2672	217	1	chaos	chaos	NOUN
ejpam-2672	217	2	,	,	PUNCT
ejpam-2672	217	3	solitons	soliton	NOUN
ejpam-2672	217	4	&	&	CCONJ
ejpam-2672	217	5	fractals	fractal	NOUN
ejpam-2672	217	6	,	,	PUNCT
ejpam-2672	217	7	40(1):1–9	40(1):1–9	NUM
ejpam-2672	217	8	,	,	PUNCT
ejpam-2672	217	9	2009	2009	NUM
ejpam-2672	217	10	.	.	PUNCT
ejpam-2672	218	1	references	reference	NOUN
ejpam-2672	218	2	600	600	NUM
ejpam-2672	218	3	t	t	NOUN
ejpam-2672	218	4	=	=	SYM
ejpam-2672	218	5	0.7	0.7	NUM
ejpam-2672	218	6	t	t	NOUN
ejpam-2672	218	7	=	=	SYM
ejpam-2672	218	8	1.5	1.5	NUM
ejpam-2672	218	9	t	t	NOUN
ejpam-2672	218	10	=	=	SYM
ejpam-2672	218	11	2.0	2.0	NUM
ejpam-2672	218	12	t	t	NOUN
ejpam-2672	218	13	=	=	SYM
ejpam-2672	218	14	0.0	0.0	NUM
ejpam-2672	218	15	0.5	0.5	NUM
ejpam-2672	218	16	1.0	1.0	NUM
ejpam-2672	218	17	1.5	1.5	NUM
ejpam-2672	218	18	2.0	2.0	NUM
ejpam-2672	218	19	x	x	SYM
ejpam-2672	218	20	3.0	3.0	NUM
ejpam-2672	218	21	3.1	3.1	NUM
ejpam-2672	218	22	3.2	3.2	NUM
ejpam-2672	218	23	3.3	3.3	NUM
ejpam-2672	218	24	3.4	3.4	NUM
ejpam-2672	218	25	u1.9hx	u1.9hx	NOUN
ejpam-2672	218	26	,	,	PUNCT
ejpam-2672	218	27	tl	tl	PROPN
ejpam-2672	218	28	figure	figure	VERB
ejpam-2672	218	29	9	9	NUM
ejpam-2672	218	30	:	:	PUNCT
ejpam-2672	218	31	the	the	DET
ejpam-2672	218	32	solution	solution	NOUN
ejpam-2672	218	33	of	of	ADP
ejpam-2672	218	34	(	(	PUNCT
ejpam-2672	218	35	55	55	NUM
ejpam-2672	218	36	)	)	PUNCT
ejpam-2672	218	37	when	when	SCONJ
ejpam-2672	218	38	ε	ε	PROPN
ejpam-2672	218	39	=	=	SYM
ejpam-2672	218	40	0.3	0.3	NUM
ejpam-2672	218	41	,	,	PUNCT
ejpam-2672	218	42	µ	µ	NOUN
ejpam-2672	218	43	=	=	SYM
ejpam-2672	218	44	π/2,the	π/2,the	DET
ejpam-2672	218	45	fractional	fractional	ADJ
ejpam-2672	218	46	order	order	NOUN
ejpam-2672	218	47	α	α	NOUN
ejpam-2672	218	48	=	=	SYM
ejpam-2672	218	49	1.9	1.9	NUM
ejpam-2672	218	50	and	and	CCONJ
ejpam-2672	218	51	at	at	ADP
ejpam-2672	218	52	different	different	ADJ
ejpam-2672	218	53	times	time	NOUN
ejpam-2672	218	54	t	t	NOUN
ejpam-2672	218	55	=	=	SYM
ejpam-2672	218	56	0.0	0.0	NUM
ejpam-2672	218	57	,	,	PUNCT
ejpam-2672	218	58	0.7	0.7	NUM
ejpam-2672	218	59	,	,	PUNCT
ejpam-2672	218	60	1.5	1.5	NUM
ejpam-2672	218	61	,	,	PUNCT
ejpam-2672	218	62	and	and	CCONJ
ejpam-2672	218	63	2.0	2.0	NUM
ejpam-2672	218	64	,	,	PUNCT
ejpam-2672	218	65	0	0	NUM
ejpam-2672	218	66	≤	≤	NUM
ejpam-2672	218	67	x	x	SYM
ejpam-2672	218	68	≤	≤	NUM
ejpam-2672	218	69	2	2	NUM
ejpam-2672	218	70	.	.	PUNCT
ejpam-2672	219	1	[	[	X
ejpam-2672	219	2	4	4	X
ejpam-2672	219	3	]	]	X
ejpam-2672	219	4	w	w	PROPN
ejpam-2672	219	5	chen	chen	PROPN
ejpam-2672	219	6	and	and	CCONJ
ejpam-2672	219	7	s	s	PROPN
ejpam-2672	219	8	holm	holm	PROPN
ejpam-2672	219	9	.	.	PUNCT
ejpam-2672	219	10	modified	modify	VERB
ejpam-2672	219	11	szabos	szabo	NOUN
ejpam-2672	219	12	wave	wave	VERB
ejpam-2672	219	13	equation	equation	NOUN
ejpam-2672	219	14	models	model	NOUN
ejpam-2672	219	15	for	for	ADP
ejpam-2672	219	16	lossy	lossy	ADJ
ejpam-2672	219	17	media	medium	NOUN
ejpam-2672	219	18	obeying	obey	VERB
ejpam-2672	219	19	frequency	frequency	NOUN
ejpam-2672	219	20	power	power	NOUN
ejpam-2672	219	21	law	law	NOUN
ejpam-2672	219	22	.	.	PUNCT
ejpam-2672	220	1	the	the	DET
ejpam-2672	220	2	journal	journal	NOUN
ejpam-2672	220	3	of	of	ADP
ejpam-2672	220	4	the	the	DET
ejpam-2672	220	5	acoustical	acoustical	ADJ
ejpam-2672	220	6	society	society	NOUN
ejpam-2672	220	7	of	of	ADP
ejpam-2672	220	8	america	america	PROPN
ejpam-2672	220	9	,	,	PUNCT
ejpam-2672	220	10	114(5):2570	114(5):2570	NOUN
ejpam-2672	220	11	–	–	PUNCT
ejpam-2672	220	12	2574	2574	NUM
ejpam-2672	220	13	,	,	PUNCT
ejpam-2672	220	14	2003	2003	NUM
ejpam-2672	220	15	.	.	PUNCT
ejpam-2672	221	1	[	[	X
ejpam-2672	221	2	5	5	NUM
ejpam-2672	221	3	]	]	X
ejpam-2672	221	4	w	w	PROPN
ejpam-2672	221	5	chen	chen	PROPN
ejpam-2672	221	6	and	and	CCONJ
ejpam-2672	221	7	s	s	PROPN
ejpam-2672	221	8	holm	holm	PROPN
ejpam-2672	221	9	.	.	PUNCT
ejpam-2672	222	1	fractional	fractional	ADJ
ejpam-2672	222	2	laplacian	laplacian	ADJ
ejpam-2672	222	3	time	time	NOUN
ejpam-2672	222	4	-	-	PUNCT
ejpam-2672	222	5	space	space	NOUN
ejpam-2672	222	6	models	model	NOUN
ejpam-2672	222	7	for	for	ADP
ejpam-2672	222	8	linear	linear	ADJ
ejpam-2672	222	9	and	and	CCONJ
ejpam-2672	222	10	nonlinear	nonlinear	ADJ
ejpam-2672	222	11	lossy	lossy	ADJ
ejpam-2672	222	12	media	medium	NOUN
ejpam-2672	222	13	exhibiting	exhibit	VERB
ejpam-2672	222	14	arbitrary	arbitrary	ADJ
ejpam-2672	222	15	frequency	frequency	NOUN
ejpam-2672	222	16	power	power	NOUN
ejpam-2672	222	17	-	-	PUNCT
ejpam-2672	222	18	law	law	NOUN
ejpam-2672	222	19	dependency	dependency	NOUN
ejpam-2672	222	20	.	.	PUNCT
ejpam-2672	223	1	the	the	DET
ejpam-2672	223	2	journal	journal	NOUN
ejpam-2672	223	3	of	of	ADP
ejpam-2672	223	4	the	the	DET
ejpam-2672	223	5	acoustical	acoustical	ADJ
ejpam-2672	223	6	society	society	NOUN
ejpam-2672	223	7	of	of	ADP
ejpam-2672	223	8	america	america	PROPN
ejpam-2672	223	9	,	,	PUNCT
ejpam-2672	223	10	115(4):1424–1430	115(4):1424–1430	PROPN
ejpam-2672	223	11	,	,	PUNCT
ejpam-2672	223	12	2004	2004	NUM
ejpam-2672	223	13	.	.	PUNCT
ejpam-2672	224	1	[	[	X
ejpam-2672	224	2	6	6	NUM
ejpam-2672	224	3	]	]	PUNCT
ejpam-2672	224	4	a	a	DET
ejpam-2672	224	5	elsaid	elsaid	NOUN
ejpam-2672	224	6	.	.	PUNCT
ejpam-2672	225	1	homotopy	homotopy	VERB
ejpam-2672	225	2	analysis	analysis	NOUN
ejpam-2672	225	3	method	method	NOUN
ejpam-2672	225	4	for	for	ADP
ejpam-2672	225	5	solving	solve	VERB
ejpam-2672	225	6	a	a	DET
ejpam-2672	225	7	class	class	NOUN
ejpam-2672	225	8	of	of	ADP
ejpam-2672	225	9	fractional	fractional	ADJ
ejpam-2672	225	10	partial	partial	ADJ
ejpam-2672	225	11	differential	differential	NOUN
ejpam-2672	225	12	equations	equation	NOUN
ejpam-2672	225	13	.	.	PUNCT
ejpam-2672	226	1	communications	communication	NOUN
ejpam-2672	226	2	in	in	ADP
ejpam-2672	226	3	nonlinear	nonlinear	ADJ
ejpam-2672	226	4	science	science	NOUN
ejpam-2672	226	5	and	and	CCONJ
ejpam-2672	226	6	numerical	numerical	PROPN
ejpam-2672	226	7	simulation	simulation	PROPN
ejpam-2672	226	8	,	,	PUNCT
ejpam-2672	226	9	16(9):3655–3664	16(9):3655–3664	NUM
ejpam-2672	226	10	,	,	PUNCT
ejpam-2672	226	11	2011	2011	NUM
ejpam-2672	226	12	.	.	PUNCT
ejpam-2672	227	1	[	[	X
ejpam-2672	227	2	7	7	X
ejpam-2672	227	3	]	]	X
ejpam-2672	227	4	ahmed	ahmed	PROPN
ejpam-2672	227	5	elsaid	elsaid	PROPN
ejpam-2672	227	6	.	.	PUNCT
ejpam-2672	228	1	the	the	DET
ejpam-2672	228	2	variational	variational	ADJ
ejpam-2672	228	3	iteration	iteration	NOUN
ejpam-2672	228	4	method	method	NOUN
ejpam-2672	228	5	for	for	ADP
ejpam-2672	228	6	solving	solve	VERB
ejpam-2672	228	7	riesz	riesz	NOUN
ejpam-2672	228	8	fractional	fractional	ADJ
ejpam-2672	228	9	partial	partial	ADJ
ejpam-2672	228	10	differential	differential	NOUN
ejpam-2672	228	11	equations	equation	NOUN
ejpam-2672	228	12	.	.	PUNCT
ejpam-2672	229	1	computers	computer	NOUN
ejpam-2672	229	2	&	&	CCONJ
ejpam-2672	229	3	mathematics	mathematics	PROPN
ejpam-2672	229	4	with	with	ADP
ejpam-2672	229	5	applications	application	NOUN
ejpam-2672	229	6	,	,	PUNCT
ejpam-2672	229	7	60(7):1940–1947	60(7):1940–1947	NUM
ejpam-2672	229	8	,	,	PUNCT
ejpam-2672	229	9	2010	2010	NUM
ejpam-2672	229	10	.	.	PUNCT
ejpam-2672	230	1	[	[	X
ejpam-2672	230	2	8	8	NUM
ejpam-2672	230	3	]	]	X
ejpam-2672	230	4	rudolf	rudolf	NOUN
ejpam-2672	230	5	gorenflo	gorenflo	NOUN
ejpam-2672	230	6	,	,	PUNCT
ejpam-2672	230	7	francesco	francesco	PROPN
ejpam-2672	230	8	mainardi	mainardi	PROPN
ejpam-2672	230	9	,	,	PUNCT
ejpam-2672	230	10	daniele	daniele	PROPN
ejpam-2672	230	11	moretti	moretti	PROPN
ejpam-2672	230	12	,	,	PUNCT
ejpam-2672	230	13	gianni	gianni	PROPN
ejpam-2672	230	14	pagnini	pagnini	PROPN
ejpam-2672	230	15	,	,	PUNCT
ejpam-2672	230	16	and	and	CCONJ
ejpam-2672	230	17	paolo	paolo	PROPN
ejpam-2672	230	18	paradisi	paradisi	ADJ
ejpam-2672	230	19	.	.	PUNCT
ejpam-2672	231	1	discrete	discrete	ADJ
ejpam-2672	231	2	random	random	ADJ
ejpam-2672	231	3	walk	walk	NOUN
ejpam-2672	231	4	models	model	NOUN
ejpam-2672	231	5	for	for	ADP
ejpam-2672	231	6	space	space	NOUN
ejpam-2672	231	7	–	–	PUNCT
ejpam-2672	231	8	time	time	NOUN
ejpam-2672	231	9	fractional	fractional	ADJ
ejpam-2672	231	10	diffusion	diffusion	NOUN
ejpam-2672	231	11	.	.	PUNCT
ejpam-2672	232	1	chemical	chemical	PROPN
ejpam-2672	232	2	physics	physics	PROPN
ejpam-2672	232	3	,	,	PUNCT
ejpam-2672	232	4	284(1):521–541	284(1):521–541	PRON
ejpam-2672	232	5	,	,	PUNCT
ejpam-2672	232	6	2002	2002	NUM
ejpam-2672	232	7	.	.	PUNCT
ejpam-2672	233	1	[	[	X
ejpam-2672	233	2	9	9	NUM
ejpam-2672	233	3	]	]	X
ejpam-2672	233	4	shijun	shijun	PROPN
ejpam-2672	233	5	liao	liao	PROPN
ejpam-2672	233	6	.	.	PROPN
ejpam-2672	234	1	beyond	beyond	ADP
ejpam-2672	234	2	perturbation	perturbation	NOUN
ejpam-2672	234	3	:	:	PUNCT
ejpam-2672	234	4	introduction	introduction	NOUN
ejpam-2672	234	5	to	to	ADP
ejpam-2672	234	6	the	the	DET
ejpam-2672	234	7	homotopy	homotopy	NOUN
ejpam-2672	234	8	analysis	analysis	NOUN
ejpam-2672	234	9	method	method	NOUN
ejpam-2672	234	10	.	.	PUNCT
ejpam-2672	235	1	crc	crc	PROPN
ejpam-2672	235	2	press	press	PROPN
ejpam-2672	235	3	,	,	PUNCT
ejpam-2672	235	4	2003	2003	NUM
ejpam-2672	235	5	.	.	PUNCT
ejpam-2672	236	1	[	[	X
ejpam-2672	236	2	10	10	NUM
ejpam-2672	236	3	]	]	X
ejpam-2672	236	4	shijun	shijun	PROPN
ejpam-2672	236	5	liao	liao	PROPN
ejpam-2672	236	6	.	.	PUNCT
ejpam-2672	237	1	an	an	DET
ejpam-2672	237	2	optimal	optimal	ADJ
ejpam-2672	237	3	homotopy	homotopy	NOUN
ejpam-2672	237	4	-	-	PUNCT
ejpam-2672	237	5	analysis	analysis	NOUN
ejpam-2672	237	6	approach	approach	NOUN
ejpam-2672	237	7	for	for	ADP
ejpam-2672	237	8	strongly	strongly	ADV
ejpam-2672	237	9	nonlinear	nonlinear	ADJ
ejpam-2672	237	10	differential	differential	ADJ
ejpam-2672	237	11	equations	equation	NOUN
ejpam-2672	237	12	.	.	PUNCT
ejpam-2672	238	1	communications	communication	NOUN
ejpam-2672	238	2	in	in	ADP
ejpam-2672	238	3	nonlinear	nonlinear	ADJ
ejpam-2672	238	4	science	science	NOUN
ejpam-2672	238	5	and	and	CCONJ
ejpam-2672	238	6	numerical	numerical	PROPN
ejpam-2672	238	7	simulation	simulation	PROPN
ejpam-2672	238	8	,	,	PUNCT
ejpam-2672	238	9	15(8):2003–2016	15(8):2003–2016	NUM
ejpam-2672	238	10	,	,	PUNCT
ejpam-2672	238	11	2010	2010	NUM
ejpam-2672	238	12	.	.	PUNCT
ejpam-2672	239	1	[	[	X
ejpam-2672	239	2	11	11	NUM
ejpam-2672	239	3	]	]	X
ejpam-2672	239	4	francesco	francesco	PROPN
ejpam-2672	239	5	mainardi	mainardi	PROPN
ejpam-2672	239	6	and	and	CCONJ
ejpam-2672	239	7	giorgio	giorgio	PROPN
ejpam-2672	239	8	spada	spada	PROPN
ejpam-2672	239	9	.	.	PUNCT
ejpam-2672	239	10	creep	creep	PROPN
ejpam-2672	239	11	,	,	PUNCT
ejpam-2672	239	12	relaxation	relaxation	NOUN
ejpam-2672	239	13	and	and	CCONJ
ejpam-2672	239	14	viscosity	viscosity	NOUN
ejpam-2672	239	15	properties	property	NOUN
ejpam-2672	239	16	for	for	ADP
ejpam-2672	239	17	basic	basic	ADJ
ejpam-2672	239	18	fractional	fractional	ADJ
ejpam-2672	239	19	models	model	NOUN
ejpam-2672	239	20	in	in	ADP
ejpam-2672	239	21	rheology	rheology	NOUN
ejpam-2672	239	22	.	.	PUNCT
ejpam-2672	240	1	the	the	DET
ejpam-2672	240	2	european	european	PROPN
ejpam-2672	240	3	physical	physical	PROPN
ejpam-2672	240	4	journal	journal	PROPN
ejpam-2672	240	5	special	special	ADJ
ejpam-2672	240	6	topics	topic	NOUN
ejpam-2672	240	7	,	,	PUNCT
ejpam-2672	240	8	193(1):133–160	193(1):133–160	NUM
ejpam-2672	240	9	,	,	PUNCT
ejpam-2672	240	10	2011	2011	NUM
ejpam-2672	240	11	.	.	PUNCT
ejpam-2672	241	1	[	[	X
ejpam-2672	241	2	12	12	NUM
ejpam-2672	241	3	]	]	PUNCT
ejpam-2672	241	4	mark	mark	PROPN
ejpam-2672	241	5	m	m	PROPN
ejpam-2672	241	6	meerschaert	meerschaert	PROPN
ejpam-2672	241	7	,	,	PUNCT
ejpam-2672	241	8	david	david	PROPN
ejpam-2672	241	9	a	a	DET
ejpam-2672	241	10	benson	benson	PROPN
ejpam-2672	241	11	,	,	PUNCT
ejpam-2672	241	12	hans	hans	PROPN
ejpam-2672	241	13	-	-	PUNCT
ejpam-2672	241	14	peter	peter	PROPN
ejpam-2672	241	15	scheffler	scheffler	NOUN
ejpam-2672	241	16	,	,	PUNCT
ejpam-2672	241	17	and	and	CCONJ
ejpam-2672	241	18	boris	boris	PROPN
ejpam-2672	241	19	baeumer	baeumer	PROPN
ejpam-2672	241	20	.	.	PUNCT
ejpam-2672	242	1	stochastic	stochastic	ADJ
ejpam-2672	242	2	solution	solution	NOUN
ejpam-2672	242	3	of	of	ADP
ejpam-2672	242	4	space	space	NOUN
ejpam-2672	242	5	-	-	PUNCT
ejpam-2672	242	6	time	time	NOUN
ejpam-2672	242	7	fractional	fractional	ADJ
ejpam-2672	242	8	diffusion	diffusion	NOUN
ejpam-2672	242	9	equations	equation	NOUN
ejpam-2672	242	10	.	.	PUNCT
ejpam-2672	243	1	physical	physical	ADJ
ejpam-2672	243	2	review	review	PROPN
ejpam-2672	243	3	e	e	NOUN
ejpam-2672	243	4	,	,	PUNCT
ejpam-2672	243	5	65(4):041103	65(4):041103	NUM
ejpam-2672	243	6	,	,	PUNCT
ejpam-2672	243	7	2002	2002	NUM
ejpam-2672	243	8	.	.	PUNCT
ejpam-2672	244	1	references	reference	NOUN
ejpam-2672	244	2	601	601	NUM
ejpam-2672	245	1	[	[	X
ejpam-2672	245	2	13	13	NUM
ejpam-2672	245	3	]	]	PUNCT
ejpam-2672	245	4	ralf	ralf	PROPN
ejpam-2672	245	5	metzler	metzler	PROPN
ejpam-2672	245	6	and	and	CCONJ
ejpam-2672	245	7	joseph	joseph	PROPN
ejpam-2672	245	8	klafter	klafter	PROPN
ejpam-2672	245	9	.	.	PUNCT
ejpam-2672	246	1	the	the	DET
ejpam-2672	246	2	random	random	ADJ
ejpam-2672	246	3	walk	walk	NOUN
ejpam-2672	246	4	’s	’s	PART
ejpam-2672	246	5	guide	guide	NOUN
ejpam-2672	246	6	to	to	ADP
ejpam-2672	246	7	anomalous	anomalous	ADJ
ejpam-2672	246	8	diffusion	diffusion	NOUN
ejpam-2672	246	9	:	:	PUNCT
ejpam-2672	246	10	a	a	DET
ejpam-2672	246	11	fractional	fractional	ADJ
ejpam-2672	246	12	dynamics	dynamic	NOUN
ejpam-2672	246	13	approach	approach	NOUN
ejpam-2672	246	14	.	.	PUNCT
ejpam-2672	247	1	physics	physics	NOUN
ejpam-2672	247	2	reports	report	NOUN
ejpam-2672	247	3	,	,	PUNCT
ejpam-2672	247	4	339(1):1–77	339(1):1–77	NUM
ejpam-2672	247	5	,	,	PUNCT
ejpam-2672	247	6	2000	2000	NUM
ejpam-2672	247	7	.	.	PUNCT
ejpam-2672	248	1	[	[	X
ejpam-2672	248	2	14	14	NUM
ejpam-2672	248	3	]	]	SYM
ejpam-2672	248	4	wr	wr	PROPN
ejpam-2672	248	5	schneider	schneider	NOUN
ejpam-2672	248	6	and	and	CCONJ
ejpam-2672	248	7	w	w	PROPN
ejpam-2672	248	8	wyss	wyss	NOUN
ejpam-2672	248	9	.	.	PUNCT
ejpam-2672	249	1	fractional	fractional	ADJ
ejpam-2672	249	2	diffusion	diffusion	NOUN
ejpam-2672	249	3	and	and	CCONJ
ejpam-2672	249	4	wave	wave	NOUN
ejpam-2672	249	5	equations	equation	NOUN
ejpam-2672	249	6	.	.	PUNCT
ejpam-2672	250	1	journal	journal	PROPN
ejpam-2672	250	2	of	of	ADP
ejpam-2672	250	3	mathematical	mathematical	ADJ
ejpam-2672	250	4	physics	physics	NOUN
ejpam-2672	250	5	,	,	PUNCT
ejpam-2672	250	6	30(1):134–144	30(1):134–144	NUM
ejpam-2672	250	7	,	,	PUNCT
ejpam-2672	250	8	1989	1989	NUM
ejpam-2672	250	9	.	.	PUNCT
ejpam-2672	251	1	[	[	X
ejpam-2672	251	2	15	15	NUM
ejpam-2672	251	3	]	]	X
ejpam-2672	251	4	hongguang	hongguang	PROPN
ejpam-2672	251	5	sun	sun	PROPN
ejpam-2672	251	6	,	,	PUNCT
ejpam-2672	251	7	wen	wen	PROPN
ejpam-2672	251	8	chen	chen	PROPN
ejpam-2672	251	9	,	,	PUNCT
ejpam-2672	251	10	and	and	CCONJ
ejpam-2672	251	11	yangquan	yangquan	PROPN
ejpam-2672	251	12	chen	chen	PROPN
ejpam-2672	251	13	.	.	PUNCT
ejpam-2672	252	1	variable	variable	ADJ
ejpam-2672	252	2	-	-	PUNCT
ejpam-2672	252	3	order	order	NOUN
ejpam-2672	252	4	fractional	fractional	ADJ
ejpam-2672	252	5	differential	differential	NOUN
ejpam-2672	252	6	operators	operator	NOUN
ejpam-2672	252	7	in	in	ADP
ejpam-2672	252	8	anomalous	anomalous	ADJ
ejpam-2672	252	9	diffusion	diffusion	NOUN
ejpam-2672	252	10	modeling	modeling	NOUN
ejpam-2672	252	11	.	.	PUNCT
ejpam-2672	253	1	physica	physica	NOUN
ejpam-2672	253	2	a	a	DET
ejpam-2672	253	3	:	:	PUNCT
ejpam-2672	253	4	statistical	statistical	ADJ
ejpam-2672	253	5	mechanics	mechanic	NOUN
ejpam-2672	253	6	and	and	CCONJ
ejpam-2672	253	7	its	its	PRON
ejpam-2672	253	8	applications	application	NOUN
ejpam-2672	253	9	,	,	PUNCT
ejpam-2672	253	10	388(21):4586–4592	388(21):4586–4592	NUM
ejpam-2672	253	11	,	,	PUNCT
ejpam-2672	253	12	2009	2009	NUM
ejpam-2672	253	13	.	.	PUNCT
ejpam-2672	254	1	[	[	X
ejpam-2672	254	2	16	16	NUM
ejpam-2672	254	3	]	]	X
ejpam-2672	254	4	hongmei	hongmei	PROPN
ejpam-2672	254	5	zhang	zhang	PROPN
ejpam-2672	254	6	and	and	CCONJ
ejpam-2672	254	7	fawang	fawang	PROPN
ejpam-2672	254	8	liu	liu	PROPN
ejpam-2672	254	9	.	.	PUNCT
ejpam-2672	255	1	the	the	DET
ejpam-2672	255	2	fundamental	fundamental	ADJ
ejpam-2672	255	3	solutions	solution	NOUN
ejpam-2672	255	4	of	of	ADP
ejpam-2672	255	5	the	the	DET
ejpam-2672	255	6	space	space	NOUN
ejpam-2672	255	7	,	,	PUNCT
ejpam-2672	255	8	spacetime	spacetime	NOUN
ejpam-2672	255	9	riesz	riesz	VERB
ejpam-2672	255	10	fractional	fractional	ADJ
ejpam-2672	255	11	partial	partial	ADJ
ejpam-2672	255	12	differential	differential	NOUN
ejpam-2672	255	13	equations	equation	NOUN
ejpam-2672	255	14	with	with	ADP
ejpam-2672	255	15	periodic	periodic	ADJ
ejpam-2672	255	16	conditions	condition	NOUN
ejpam-2672	255	17	.	.	PUNCT
ejpam-2672	256	1	numerical	numerical	PROPN
ejpam-2672	256	2	mathematics	mathematics	PROPN
ejpam-2672	256	3	-	-	PUNCT
ejpam-2672	256	4	english	english	PROPN
ejpam-2672	256	5	series-	series-	PROPN
ejpam-2672	256	6	,	,	PUNCT
ejpam-2672	256	7	16(2):181	16(2):181	NUM
ejpam-2672	256	8	,	,	PUNCT
ejpam-2672	256	9	2007	2007	NUM
ejpam-2672	256	10	.	.	PUNCT