id	sid	tid	token	lemma	pos
ejpam-4012	1	1	european	european	PROPN
ejpam-4012	1	2	journal	journal	PROPN
ejpam-4012	1	3	of	of	ADP
ejpam-4012	1	4	pure	pure	ADJ
ejpam-4012	1	5	and	and	CCONJ
ejpam-4012	1	6	applied	apply	VERB
ejpam-4012	1	7	mathematics	mathematic	NOUN
ejpam-4012	1	8	vol	vol	NOUN
ejpam-4012	1	9	.	.	PUNCT
ejpam-4012	2	1	14	14	NUM
ejpam-4012	2	2	,	,	PUNCT
ejpam-4012	2	3	no	no	INTJ
ejpam-4012	2	4	.	.	NOUN
ejpam-4012	2	5	3	3	NUM
ejpam-4012	2	6	,	,	PUNCT
ejpam-4012	2	7	2021	2021	NUM
ejpam-4012	2	8	,	,	PUNCT
ejpam-4012	2	9	942	942	NUM
ejpam-4012	2	10	-	-	SYM
ejpam-4012	2	11	948	948	NUM
ejpam-4012	2	12	issn	issn	PROPN
ejpam-4012	2	13	1307	1307	NUM
ejpam-4012	2	14	-	-	SYM
ejpam-4012	2	15	5543	5543	NUM
ejpam-4012	2	16	–	–	PUNCT
ejpam-4012	2	17	ejpam.com	ejpam.com	X
ejpam-4012	2	18	published	publish	VERB
ejpam-4012	2	19	by	by	ADP
ejpam-4012	2	20	new	new	PROPN
ejpam-4012	2	21	york	york	PROPN
ejpam-4012	2	22	business	business	PROPN
ejpam-4012	2	23	global	global	ADJ
ejpam-4012	2	24	tensor	tensor	NOUN
ejpam-4012	2	25	product	product	NOUN
ejpam-4012	2	26	and	and	CCONJ
ejpam-4012	2	27	certain	certain	ADJ
ejpam-4012	2	28	solutions	solution	NOUN
ejpam-4012	2	29	of	of	ADP
ejpam-4012	2	30	fractional	fractional	ADJ
ejpam-4012	2	31	wave	wave	NOUN
ejpam-4012	2	32	type	type	NOUN
ejpam-4012	2	33	equation	equation	NOUN
ejpam-4012	2	34	ibtissem	ibtissem	PROPN
ejpam-4012	2	35	benkemache1	benkemache1	PROPN
ejpam-4012	2	36	,	,	PUNCT
ejpam-4012	2	37	mohammed	mohammed	PROPN
ejpam-4012	2	38	al	al	PROPN
ejpam-4012	2	39	horani1	horani1	PROPN
ejpam-4012	2	40	,	,	PUNCT
ejpam-4012	2	41	roshdi	roshdi	ADJ
ejpam-4012	2	42	khalil1,∗	khalil1,∗	NOUN
ejpam-4012	2	43	1	1	NUM
ejpam-4012	2	44	department	department	NOUN
ejpam-4012	2	45	of	of	ADP
ejpam-4012	2	46	mathematics	mathematic	NOUN
ejpam-4012	2	47	,	,	PUNCT
ejpam-4012	2	48	school	school	NOUN
ejpam-4012	2	49	of	of	ADP
ejpam-4012	2	50	science	science	NOUN
ejpam-4012	2	51	,	,	PUNCT
ejpam-4012	2	52	the	the	DET
ejpam-4012	2	53	university	university	PROPN
ejpam-4012	2	54	of	of	ADP
ejpam-4012	2	55	jordan	jordan	PROPN
ejpam-4012	2	56	,	,	PUNCT
ejpam-4012	2	57	amman	amman	PROPN
ejpam-4012	2	58	,	,	PUNCT
ejpam-4012	2	59	jordan	jordan	PROPN
ejpam-4012	2	60	abstract	abstract	PROPN
ejpam-4012	2	61	.	.	PUNCT
ejpam-4012	3	1	in	in	ADP
ejpam-4012	3	2	this	this	DET
ejpam-4012	3	3	paper	paper	NOUN
ejpam-4012	3	4	we	we	PRON
ejpam-4012	3	5	find	find	VERB
ejpam-4012	3	6	certain	certain	ADJ
ejpam-4012	3	7	solutions	solution	NOUN
ejpam-4012	3	8	of	of	ADP
ejpam-4012	3	9	some	some	DET
ejpam-4012	3	10	fractional	fractional	ADJ
ejpam-4012	3	11	partial	partial	ADJ
ejpam-4012	3	12	differential	differential	NOUN
ejpam-4012	3	13	equations	equation	NOUN
ejpam-4012	3	14	.	.	PUNCT
ejpam-4012	4	1	tensor	tensor	NOUN
ejpam-4012	4	2	product	product	NOUN
ejpam-4012	4	3	of	of	ADP
ejpam-4012	4	4	banach	banach	NOUN
ejpam-4012	4	5	spaces	space	NOUN
ejpam-4012	4	6	is	be	AUX
ejpam-4012	4	7	used	use	VERB
ejpam-4012	4	8	to	to	PART
ejpam-4012	4	9	find	find	VERB
ejpam-4012	4	10	some	some	DET
ejpam-4012	4	11	solutions	solution	NOUN
ejpam-4012	4	12	where	where	SCONJ
ejpam-4012	4	13	separation	separation	NOUN
ejpam-4012	4	14	of	of	ADP
ejpam-4012	4	15	variables	variable	NOUN
ejpam-4012	4	16	does	do	AUX
ejpam-4012	4	17	not	not	PART
ejpam-4012	4	18	work	work	VERB
ejpam-4012	4	19	.	.	PUNCT
ejpam-4012	5	1	we	we	PRON
ejpam-4012	5	2	solve	solve	VERB
ejpam-4012	5	3	the	the	DET
ejpam-4012	5	4	fractional	fractional	ADJ
ejpam-4012	5	5	wave	wave	NOUN
ejpam-4012	5	6	type	type	NOUN
ejpam-4012	5	7	equation	equation	NOUN
ejpam-4012	5	8	using	use	VERB
ejpam-4012	5	9	fractional	fractional	ADJ
ejpam-4012	5	10	fourier	fourier	NOUN
ejpam-4012	5	11	series	series	NOUN
ejpam-4012	5	12	2020	2020	NUM
ejpam-4012	5	13	mathematics	mathematics	PROPN
ejpam-4012	5	14	subject	subject	NOUN
ejpam-4012	5	15	classifications	classification	NOUN
ejpam-4012	5	16	:	:	PUNCT
ejpam-4012	5	17	26a33	26a33	NUM
ejpam-4012	5	18	key	key	ADJ
ejpam-4012	5	19	words	word	NOUN
ejpam-4012	5	20	and	and	CCONJ
ejpam-4012	5	21	phrases	phrase	NOUN
ejpam-4012	5	22	:	:	PUNCT
ejpam-4012	5	23	conformable	conformable	ADJ
ejpam-4012	5	24	derivative	derivative	ADJ
ejpam-4012	5	25	,	,	PUNCT
ejpam-4012	5	26	fractional	fractional	ADJ
ejpam-4012	5	27	fourier	fourier	NOUN
ejpam-4012	5	28	series	series	NOUN
ejpam-4012	5	29	,	,	PUNCT
ejpam-4012	5	30	fractional	fractional	ADJ
ejpam-4012	5	31	wave	wave	NOUN
ejpam-4012	5	32	type	type	NOUN
ejpam-4012	5	33	equation	equation	NOUN
ejpam-4012	5	34	.	.	PUNCT
ejpam-4012	6	1	1	1	X
ejpam-4012	6	2	.	.	X
ejpam-4012	6	3	introduction	introduction	NOUN
ejpam-4012	6	4	in	in	ADP
ejpam-4012	6	5	[	[	X
ejpam-4012	6	6	7	7	NUM
ejpam-4012	6	7	]	]	PUNCT
ejpam-4012	6	8	,	,	PUNCT
ejpam-4012	6	9	a	a	DET
ejpam-4012	6	10	definition	definition	NOUN
ejpam-4012	6	11	of	of	ADP
ejpam-4012	6	12	the	the	DET
ejpam-4012	6	13	so	so	ADV
ejpam-4012	6	14	-	-	PUNCT
ejpam-4012	6	15	called	call	VERB
ejpam-4012	6	16	α−conformable	α−conformable	ADJ
ejpam-4012	6	17	fractional	fractional	ADJ
ejpam-4012	6	18	derivative	derivative	NOUN
ejpam-4012	6	19	was	be	AUX
ejpam-4012	6	20	introduced	introduce	VERB
ejpam-4012	6	21	:	:	PUNCT
ejpam-4012	6	22	let	let	VERB
ejpam-4012	6	23	α	α	X
ejpam-4012	6	24	∈	∈	PROPN
ejpam-4012	6	25	(	(	PUNCT
ejpam-4012	6	26	0	0	NUM
ejpam-4012	6	27	,	,	PUNCT
ejpam-4012	6	28	1	1	NUM
ejpam-4012	6	29	)	)	PUNCT
ejpam-4012	6	30	,	,	PUNCT
ejpam-4012	6	31	and	and	CCONJ
ejpam-4012	6	32	f	f	X
ejpam-4012	6	33	:	:	PUNCT
ejpam-4012	6	34	e	e	X
ejpam-4012	6	35	⊆	⊆	NUM
ejpam-4012	6	36	(	(	PUNCT
ejpam-4012	6	37	0,∞)→	0,∞)→	PROPN
ejpam-4012	6	38	r.	r.	PROPN
ejpam-4012	6	39	for	for	ADP
ejpam-4012	6	40	x	x	PROPN
ejpam-4012	6	41	∈	∈	PROPN
ejpam-4012	6	42	e	e	NOUN
ejpam-4012	6	43	,	,	PUNCT
ejpam-4012	6	44	let	let	VERB
ejpam-4012	6	45	:	:	PUNCT
ejpam-4012	6	46	dαf(x	dαf(x	PROPN
ejpam-4012	6	47	)	)	PUNCT
ejpam-4012	6	48	=	=	PROPN
ejpam-4012	6	49	lim	lim	PROPN
ejpam-4012	6	50	ε→0	ε→0	NOUN
ejpam-4012	6	51	f(x+	f(x+	AUX
ejpam-4012	6	52	εx1−α)−	εx1−α)−	VERB
ejpam-4012	6	53	f(x	f(x	PROPN
ejpam-4012	6	54	)	)	PUNCT
ejpam-4012	6	55	ε	ε	PROPN
ejpam-4012	6	56	.	.	PUNCT
ejpam-4012	7	1	if	if	SCONJ
ejpam-4012	7	2	the	the	DET
ejpam-4012	7	3	limit	limit	NOUN
ejpam-4012	7	4	exists	exist	VERB
ejpam-4012	7	5	,	,	PUNCT
ejpam-4012	7	6	then	then	ADV
ejpam-4012	7	7	it	it	PRON
ejpam-4012	7	8	is	be	AUX
ejpam-4012	7	9	called	call	VERB
ejpam-4012	7	10	the	the	DET
ejpam-4012	7	11	α−conformable	α−conformable	ADJ
ejpam-4012	7	12	fractional	fractional	ADJ
ejpam-4012	7	13	derivative	derivative	NOUN
ejpam-4012	7	14	of	of	ADP
ejpam-4012	7	15	f	f	PROPN
ejpam-4012	7	16	at	at	ADP
ejpam-4012	7	17	x.	x.	PROPN
ejpam-4012	7	18	if	if	SCONJ
ejpam-4012	7	19	f	f	PROPN
ejpam-4012	7	20	is	be	AUX
ejpam-4012	7	21	α−differentiable	α−differentiable	ADJ
ejpam-4012	7	22	on	on	ADP
ejpam-4012	7	23	(	(	PUNCT
ejpam-4012	7	24	0	0	NUM
ejpam-4012	7	25	,	,	PUNCT
ejpam-4012	7	26	r	r	NOUN
ejpam-4012	7	27	)	)	PUNCT
ejpam-4012	7	28	for	for	ADP
ejpam-4012	7	29	some	some	DET
ejpam-4012	7	30	r	r	NOUN
ejpam-4012	7	31	>	>	X
ejpam-4012	7	32	0	0	NUM
ejpam-4012	7	33	,	,	PUNCT
ejpam-4012	7	34	and	and	CCONJ
ejpam-4012	7	35	lim	lim	PROPN
ejpam-4012	7	36	x→0	x→0	PROPN
ejpam-4012	7	37	+	+	NUM
ejpam-4012	7	38	dαf(x	dαf(x	PROPN
ejpam-4012	7	39	)	)	PUNCT
ejpam-4012	7	40	exists	exist	VERB
ejpam-4012	7	41	then	then	ADV
ejpam-4012	7	42	we	we	PRON
ejpam-4012	7	43	define	define	VERB
ejpam-4012	7	44	dαf(0	dαf(0	NOUN
ejpam-4012	7	45	)	)	PUNCT
ejpam-4012	8	1	=	=	SYM
ejpam-4012	8	2	lim	lim	PROPN
ejpam-4012	8	3	x→0	x→0	PROPN
ejpam-4012	8	4	dαf(x	dαf(x	PROPN
ejpam-4012	8	5	)	)	PUNCT
ejpam-4012	8	6	.	.	PUNCT
ejpam-4012	9	1	for	for	ADP
ejpam-4012	9	2	α	α	DET
ejpam-4012	9	3	∈	∈	PROPN
ejpam-4012	9	4	(	(	PUNCT
ejpam-4012	9	5	0	0	NUM
ejpam-4012	9	6	,	,	PUNCT
ejpam-4012	9	7	1	1	NUM
ejpam-4012	9	8	]	]	PUNCT
ejpam-4012	9	9	and	and	CCONJ
ejpam-4012	9	10	f	f	X
ejpam-4012	9	11	,	,	PUNCT
ejpam-4012	9	12	g	g	PROPN
ejpam-4012	9	13	are	be	AUX
ejpam-4012	9	14	α−differentiable	α−differentiable	ADJ
ejpam-4012	9	15	at	at	ADP
ejpam-4012	9	16	a	a	DET
ejpam-4012	9	17	point	point	NOUN
ejpam-4012	9	18	t	t	NOUN
ejpam-4012	9	19	,	,	PUNCT
ejpam-4012	9	20	one	one	PRON
ejpam-4012	9	21	can	can	AUX
ejpam-4012	9	22	easily	easily	ADV
ejpam-4012	9	23	see	see	VERB
ejpam-4012	9	24	that	that	SCONJ
ejpam-4012	9	25	the	the	DET
ejpam-4012	9	26	conformable	conformable	ADJ
ejpam-4012	9	27	derivative	derivative	ADJ
ejpam-4012	9	28	satisfies	satisfie	NOUN
ejpam-4012	9	29	:	:	PUNCT
ejpam-4012	9	30	1	1	X
ejpam-4012	9	31	.	.	X
ejpam-4012	9	32	dα(af	dα(af	PROPN
ejpam-4012	9	33	+	+	CCONJ
ejpam-4012	9	34	bg	bg	PROPN
ejpam-4012	9	35	)	)	PUNCT
ejpam-4012	9	36	=	=	SYM
ejpam-4012	9	37	adα(f	adα(f	PROPN
ejpam-4012	9	38	)	)	PUNCT
ejpam-4012	10	1	+	+	CCONJ
ejpam-4012	10	2	bdα(g	bdα(g	PROPN
ejpam-4012	10	3	)	)	PUNCT
ejpam-4012	10	4	,	,	PUNCT
ejpam-4012	10	5	for	for	ADP
ejpam-4012	10	6	all	all	DET
ejpam-4012	10	7	a	a	PRON
ejpam-4012	10	8	,	,	PUNCT
ejpam-4012	10	9	b	b	PROPN
ejpam-4012	10	10	∈	∈	PROPN
ejpam-4012	10	11	r.	r.	PROPN
ejpam-4012	10	12	2	2	NUM
ejpam-4012	10	13	.	.	PUNCT
ejpam-4012	10	14	dα(λ	dα(λ	X
ejpam-4012	10	15	)	)	PUNCT
ejpam-4012	11	1	=	=	SYM
ejpam-4012	11	2	0	0	NUM
ejpam-4012	11	3	,	,	PUNCT
ejpam-4012	11	4	for	for	ADP
ejpam-4012	11	5	all	all	DET
ejpam-4012	11	6	constant	constant	ADJ
ejpam-4012	11	7	functions	function	NOUN
ejpam-4012	11	8	f(t	f(t	NOUN
ejpam-4012	11	9	)	)	PUNCT
ejpam-4012	12	1	=	=	SYM
ejpam-4012	12	2	λ	λ	X
ejpam-4012	12	3	.	.	NOUN
ejpam-4012	12	4	3	3	NUM
ejpam-4012	12	5	.	.	PUNCT
ejpam-4012	12	6	dα(fg	dα(fg	NOUN
ejpam-4012	12	7	)	)	PUNCT
ejpam-4012	12	8	=	=	PUNCT
ejpam-4012	12	9	fdα(g	fdα(g	PROPN
ejpam-4012	12	10	)	)	PUNCT
ejpam-4012	12	11	+	+	NUM
ejpam-4012	12	12	gdα(f	gdα(f	NOUN
ejpam-4012	12	13	)	)	PUNCT
ejpam-4012	12	14	.	.	PUNCT
ejpam-4012	13	1	∗corresponding	∗corresponde	VERB
ejpam-4012	13	2	author	author	NOUN
ejpam-4012	13	3	.	.	PUNCT
ejpam-4012	14	1	doi	doi	NOUN
ejpam-4012	14	2	:	:	PUNCT
ejpam-4012	14	3	https://doi.org/10.29020/nybg.ejpam.v14i3.4012	https://doi.org/10.29020/nybg.ejpam.v14i3.4012	PRON
ejpam-4012	14	4	email	email	NOUN
ejpam-4012	14	5	addresses	address	VERB
ejpam-4012	14	6	:	:	PUNCT
ejpam-4012	14	7	ibtissem19932017@gmail.com	ibtissem19932017@gmail.com	X
ejpam-4012	15	1	(	(	PUNCT
ejpam-4012	15	2	i.	i.	PROPN
ejpam-4012	15	3	benkemache	benkemache	PROPN
ejpam-4012	15	4	)	)	PUNCT
ejpam-4012	15	5	,	,	PUNCT
ejpam-4012	16	1	horani@ju.edu.jo	horani@ju.edu.jo	NOUN
ejpam-4012	16	2	(	(	PUNCT
ejpam-4012	16	3	m.	m.	NOUN
ejpam-4012	16	4	al	al	PROPN
ejpam-4012	16	5	horani	horani	PROPN
ejpam-4012	16	6	)	)	PUNCT
ejpam-4012	16	7	,	,	PUNCT
ejpam-4012	16	8	roshdi@ju.edu.jo	roshdi@ju.edu.jo	PROPN
ejpam-4012	16	9	(	(	PUNCT
ejpam-4012	16	10	r.	r.	PROPN
ejpam-4012	16	11	khalil	khalil	PROPN
ejpam-4012	16	12	)	)	PUNCT
ejpam-4012	16	13	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4012	17	1	942	942	NUM
ejpam-4012	17	2	©	©	PROPN
ejpam-4012	17	3	2021	2021	NUM
ejpam-4012	17	4	ejpam	ejpam	VERB
ejpam-4012	17	5	all	all	DET
ejpam-4012	17	6	rights	right	NOUN
ejpam-4012	17	7	reserved	reserve	VERB
ejpam-4012	17	8	.	.	PUNCT
ejpam-4012	18	1	i.	i.	PROPN
ejpam-4012	18	2	benkemache	benkemache	PROPN
ejpam-4012	18	3	,	,	PUNCT
ejpam-4012	18	4	m.	m.	NOUN
ejpam-4012	18	5	al	al	PROPN
ejpam-4012	18	6	horani	horani	PROPN
ejpam-4012	18	7	,	,	PUNCT
ejpam-4012	18	8	r.	r.	PROPN
ejpam-4012	18	9	khalil	khalil	PROPN
ejpam-4012	18	10	/	/	SYM
ejpam-4012	18	11	eur	eur	PROPN
ejpam-4012	18	12	.	.	PUNCT
ejpam-4012	19	1	j.	j.	PROPN
ejpam-4012	19	2	pure	pure	PROPN
ejpam-4012	19	3	appl	appl	PROPN
ejpam-4012	19	4	.	.	PROPN
ejpam-4012	19	5	math	math	PROPN
ejpam-4012	19	6	,	,	PUNCT
ejpam-4012	19	7	14	14	NUM
ejpam-4012	19	8	(	(	PUNCT
ejpam-4012	19	9	3	3	NUM
ejpam-4012	19	10	)	)	PUNCT
ejpam-4012	19	11	(	(	PUNCT
ejpam-4012	19	12	2021	2021	NUM
ejpam-4012	19	13	)	)	PUNCT
ejpam-4012	19	14	,	,	PUNCT
ejpam-4012	19	15	942	942	NUM
ejpam-4012	19	16	-	-	SYM
ejpam-4012	19	17	948	948	NUM
ejpam-4012	19	18	943	943	NUM
ejpam-4012	19	19	4	4	NUM
ejpam-4012	19	20	.	.	PUNCT
ejpam-4012	19	21	dα(fg	dα(fg	NOUN
ejpam-4012	19	22	)	)	PUNCT
ejpam-4012	19	23	=	=	PUNCT
ejpam-4012	19	24	gdα(f)−fdα(g	gdα(f)−fdα(g	PROPN
ejpam-4012	19	25	)	)	PUNCT
ejpam-4012	19	26	g2	g2	PROPN
ejpam-4012	19	27	,	,	PUNCT
ejpam-4012	19	28	g(t	g(t	PROPN
ejpam-4012	19	29	)	)	PUNCT
ejpam-4012	19	30	6=	6=	ADP
ejpam-4012	19	31	0	0	X
ejpam-4012	19	32	.	.	PUNCT
ejpam-4012	20	1	we	we	PRON
ejpam-4012	20	2	list	list	VERB
ejpam-4012	20	3	here	here	ADV
ejpam-4012	20	4	the	the	DET
ejpam-4012	20	5	fractional	fractional	ADJ
ejpam-4012	20	6	derivatives	derivative	NOUN
ejpam-4012	20	7	of	of	ADP
ejpam-4012	20	8	certain	certain	ADJ
ejpam-4012	20	9	functions	function	NOUN
ejpam-4012	20	10	,	,	PUNCT
ejpam-4012	20	11	(	(	PUNCT
ejpam-4012	20	12	i	i	NOUN
ejpam-4012	20	13	)	)	PUNCT
ejpam-4012	20	14	dα(tp	dα(tp	PROPN
ejpam-4012	20	15	)	)	PUNCT
ejpam-4012	20	16	=	=	SYM
ejpam-4012	21	1	p	p	PROPN
ejpam-4012	21	2	tp−α	tp−α	PROPN
ejpam-4012	21	3	.	.	PUNCT
ejpam-4012	22	1	(	(	PUNCT
ejpam-4012	22	2	ii	ii	NOUN
ejpam-4012	22	3	)	)	PUNCT
ejpam-4012	22	4	dα(sin	dα(sin	NOUN
ejpam-4012	22	5	1	1	NUM
ejpam-4012	22	6	α	α	NOUN
ejpam-4012	22	7	t	t	NOUN
ejpam-4012	22	8	α	α	NOUN
ejpam-4012	22	9	)	)	PUNCT
ejpam-4012	23	1	=	=	SYM
ejpam-4012	23	2	cos	cos	ADP
ejpam-4012	23	3	1	1	NUM
ejpam-4012	23	4	α	α	NOUN
ejpam-4012	23	5	t	t	NOUN
ejpam-4012	23	6	α	α	PRON
ejpam-4012	23	7	.	.	PUNCT
ejpam-4012	24	1	(	(	PUNCT
ejpam-4012	24	2	iii	iii	X
ejpam-4012	24	3	)	)	PUNCT
ejpam-4012	24	4	dα(cos	dα(cos	ADV
ejpam-4012	24	5	1	1	NUM
ejpam-4012	24	6	α	α	NOUN
ejpam-4012	24	7	t	t	NOUN
ejpam-4012	24	8	α	α	NOUN
ejpam-4012	24	9	)	)	PUNCT
ejpam-4012	24	10	=	=	SYM
ejpam-4012	25	1	−	−	PROPN
ejpam-4012	25	2	sin	sin	NOUN
ejpam-4012	25	3	1	1	NUM
ejpam-4012	25	4	α	α	NOUN
ejpam-4012	25	5	t	t	NOUN
ejpam-4012	25	6	α	α	PRON
ejpam-4012	25	7	.	.	PUNCT
ejpam-4012	26	1	(	(	PUNCT
ejpam-4012	26	2	iv	iv	X
ejpam-4012	26	3	)	)	PUNCT
ejpam-4012	26	4	dα(e	dα(e	VERB
ejpam-4012	26	5	1	1	NUM
ejpam-4012	26	6	α	α	NOUN
ejpam-4012	26	7	tα	tα	PROPN
ejpam-4012	26	8	)	)	PUNCT
ejpam-4012	26	9	=	=	PUNCT
ejpam-4012	27	1	e	e	X
ejpam-4012	27	2	1	1	NUM
ejpam-4012	27	3	α	α	NOUN
ejpam-4012	27	4	tα	tα	PROPN
ejpam-4012	27	5	.	.	PUNCT
ejpam-4012	28	1	on	on	ADP
ejpam-4012	28	2	letting	let	VERB
ejpam-4012	28	3	α	α	NOUN
ejpam-4012	28	4	=	=	NOUN
ejpam-4012	28	5	1	1	NUM
ejpam-4012	28	6	in	in	ADP
ejpam-4012	28	7	these	these	DET
ejpam-4012	28	8	derivatives	derivative	NOUN
ejpam-4012	28	9	,	,	PUNCT
ejpam-4012	28	10	we	we	PRON
ejpam-4012	28	11	get	get	VERB
ejpam-4012	28	12	the	the	DET
ejpam-4012	28	13	corresponding	corresponding	ADJ
ejpam-4012	28	14	classical	classical	ADJ
ejpam-4012	28	15	rules	rule	NOUN
ejpam-4012	28	16	for	for	ADP
ejpam-4012	28	17	ordinary	ordinary	ADJ
ejpam-4012	28	18	derivatives	derivative	NOUN
ejpam-4012	28	19	.	.	PUNCT
ejpam-4012	29	1	further	far	ADV
ejpam-4012	29	2	,	,	PUNCT
ejpam-4012	29	3	one	one	PRON
ejpam-4012	29	4	should	should	AUX
ejpam-4012	29	5	notice	notice	VERB
ejpam-4012	29	6	that	that	SCONJ
ejpam-4012	29	7	a	a	DET
ejpam-4012	29	8	function	function	NOUN
ejpam-4012	29	9	could	could	AUX
ejpam-4012	29	10	be	be	AUX
ejpam-4012	29	11	α−conformable	α−conformable	ADJ
ejpam-4012	29	12	differentiable	differentiable	ADJ
ejpam-4012	29	13	at	at	ADP
ejpam-4012	29	14	a	a	DET
ejpam-4012	29	15	point	point	NOUN
ejpam-4012	29	16	but	but	CCONJ
ejpam-4012	29	17	not	not	PART
ejpam-4012	29	18	differentiable	differentiable	ADJ
ejpam-4012	29	19	,	,	PUNCT
ejpam-4012	29	20	for	for	ADP
ejpam-4012	29	21	example	example	NOUN
ejpam-4012	29	22	,	,	PUNCT
ejpam-4012	29	23	take	take	VERB
ejpam-4012	29	24	f(t	f(t	NOUN
ejpam-4012	29	25	)	)	PUNCT
ejpam-4012	30	1	=	=	SYM
ejpam-4012	31	1	2	2	NUM
ejpam-4012	31	2	√	√	NUM
ejpam-4012	31	3	t	t	PROPN
ejpam-4012	31	4	,	,	PUNCT
ejpam-4012	31	5	then	then	ADV
ejpam-4012	31	6	d	d	PROPN
ejpam-4012	31	7	1	1	NUM
ejpam-4012	31	8	2	2	NUM
ejpam-4012	31	9	(	(	PUNCT
ejpam-4012	31	10	f)(0	f)(0	NUM
ejpam-4012	31	11	)	)	PUNCT
ejpam-4012	31	12	=	=	SYM
ejpam-4012	32	1	1	1	X
ejpam-4012	32	2	.	.	PUNCT
ejpam-4012	33	1	this	this	PRON
ejpam-4012	33	2	is	be	AUX
ejpam-4012	33	3	not	not	PART
ejpam-4012	33	4	the	the	DET
ejpam-4012	33	5	case	case	NOUN
ejpam-4012	33	6	for	for	ADP
ejpam-4012	33	7	the	the	DET
ejpam-4012	33	8	known	know	VERB
ejpam-4012	33	9	classical	classical	ADJ
ejpam-4012	33	10	fractional	fractional	ADJ
ejpam-4012	33	11	derivatives	derivative	NOUN
ejpam-4012	33	12	,	,	PUNCT
ejpam-4012	33	13	since	since	SCONJ
ejpam-4012	33	14	d1(f)(0	d1(f)(0	NUM
ejpam-4012	33	15	)	)	PUNCT
ejpam-4012	33	16	does	do	AUX
ejpam-4012	33	17	not	not	PART
ejpam-4012	33	18	exist	exist	VERB
ejpam-4012	33	19	.	.	PUNCT
ejpam-4012	34	1	for	for	ADP
ejpam-4012	34	2	more	more	ADJ
ejpam-4012	34	3	on	on	ADP
ejpam-4012	34	4	fractional	fractional	ADJ
ejpam-4012	34	5	calculus	calculus	NOUN
ejpam-4012	34	6	and	and	CCONJ
ejpam-4012	34	7	its	its	PRON
ejpam-4012	34	8	applications	application	NOUN
ejpam-4012	34	9	we	we	PRON
ejpam-4012	34	10	refer	refer	VERB
ejpam-4012	34	11	to	to	ADP
ejpam-4012	34	12	[	[	X
ejpam-4012	34	13	7]-[6	7]-[6	X
ejpam-4012	34	14	]	]	PUNCT
ejpam-4012	34	15	.	.	PUNCT
ejpam-4012	35	1	many	many	ADJ
ejpam-4012	35	2	differential	differential	ADJ
ejpam-4012	35	3	equations	equation	NOUN
ejpam-4012	35	4	can	can	AUX
ejpam-4012	35	5	be	be	AUX
ejpam-4012	35	6	transformed	transform	VERB
ejpam-4012	35	7	to	to	ADP
ejpam-4012	35	8	fractional	fractional	ADJ
ejpam-4012	35	9	form	form	NOUN
ejpam-4012	35	10	and	and	CCONJ
ejpam-4012	35	11	can	can	AUX
ejpam-4012	35	12	have	have	VERB
ejpam-4012	35	13	many	many	ADJ
ejpam-4012	35	14	applications	application	NOUN
ejpam-4012	35	15	in	in	ADP
ejpam-4012	35	16	many	many	ADJ
ejpam-4012	35	17	branches	branch	NOUN
ejpam-4012	35	18	of	of	ADP
ejpam-4012	35	19	science	science	NOUN
ejpam-4012	35	20	.	.	PUNCT
ejpam-4012	36	1	the	the	DET
ejpam-4012	36	2	main	main	ADJ
ejpam-4012	36	3	technique	technique	NOUN
ejpam-4012	36	4	to	to	PART
ejpam-4012	36	5	solve	solve	VERB
ejpam-4012	36	6	partial	partial	ADJ
ejpam-4012	36	7	differential	differential	NOUN
ejpam-4012	36	8	equations	equation	NOUN
ejpam-4012	36	9	is	be	AUX
ejpam-4012	36	10	using	use	VERB
ejpam-4012	36	11	fourier	fourier	NOUN
ejpam-4012	36	12	series	series	NOUN
ejpam-4012	36	13	.	.	PUNCT
ejpam-4012	37	1	so	so	ADV
ejpam-4012	37	2	,	,	PUNCT
ejpam-4012	37	3	fractional	fractional	ADJ
ejpam-4012	37	4	fourier	fourier	NOUN
ejpam-4012	37	5	series	series	NOUN
ejpam-4012	37	6	was	be	AUX
ejpam-4012	37	7	introduced	introduce	VERB
ejpam-4012	37	8	in	in	ADP
ejpam-4012	37	9	[	[	X
ejpam-4012	37	10	3	3	NUM
ejpam-4012	37	11	]	]	PUNCT
ejpam-4012	37	12	.	.	PUNCT
ejpam-4012	38	1	such	such	DET
ejpam-4012	38	2	a	a	DET
ejpam-4012	38	3	concept	concept	NOUN
ejpam-4012	38	4	proved	prove	VERB
ejpam-4012	38	5	to	to	PART
ejpam-4012	38	6	be	be	AUX
ejpam-4012	38	7	very	very	ADV
ejpam-4012	38	8	fruitful	fruitful	ADJ
ejpam-4012	38	9	in	in	ADP
ejpam-4012	38	10	solving	solve	VERB
ejpam-4012	38	11	fractional	fractional	ADJ
ejpam-4012	38	12	partial	partial	ADJ
ejpam-4012	38	13	differential	differential	NOUN
ejpam-4012	38	14	equations	equation	NOUN
ejpam-4012	38	15	.	.	PUNCT
ejpam-4012	39	1	in	in	ADP
ejpam-4012	39	2	this	this	DET
ejpam-4012	39	3	paper	paper	NOUN
ejpam-4012	39	4	we	we	PRON
ejpam-4012	39	5	will	will	AUX
ejpam-4012	39	6	use	use	VERB
ejpam-4012	39	7	fractional	fractional	ADJ
ejpam-4012	39	8	fourier	fourier	NOUN
ejpam-4012	39	9	series	series	NOUN
ejpam-4012	39	10	to	to	PART
ejpam-4012	39	11	solve	solve	VERB
ejpam-4012	39	12	a	a	DET
ejpam-4012	39	13	fractional	fractional	ADJ
ejpam-4012	39	14	wave	wave	NOUN
ejpam-4012	39	15	type	type	NOUN
ejpam-4012	39	16	equation	equation	NOUN
ejpam-4012	39	17	.	.	PUNCT
ejpam-4012	40	1	in	in	ADP
ejpam-4012	40	2	section	section	NOUN
ejpam-4012	40	3	2	2	NUM
ejpam-4012	40	4	we	we	PRON
ejpam-4012	40	5	introduce	introduce	VERB
ejpam-4012	40	6	the	the	DET
ejpam-4012	40	7	atomic	atomic	ADJ
ejpam-4012	40	8	solution	solution	NOUN
ejpam-4012	40	9	.	.	PUNCT
ejpam-4012	41	1	the	the	DET
ejpam-4012	41	2	complete	complete	ADJ
ejpam-4012	41	3	solution	solution	NOUN
ejpam-4012	41	4	is	be	AUX
ejpam-4012	41	5	given	give	VERB
ejpam-4012	41	6	in	in	ADP
ejpam-4012	41	7	section	section	NOUN
ejpam-4012	41	8	3	3	NUM
ejpam-4012	41	9	.	.	NOUN
ejpam-4012	41	10	2	2	NUM
ejpam-4012	41	11	.	.	X
ejpam-4012	41	12	atomic	atomic	ADJ
ejpam-4012	41	13	solution	solution	NOUN
ejpam-4012	41	14	let	let	VERB
ejpam-4012	41	15	x	x	PRON
ejpam-4012	41	16	and	and	CCONJ
ejpam-4012	41	17	y	y	PROPN
ejpam-4012	41	18	be	be	AUX
ejpam-4012	41	19	two	two	NUM
ejpam-4012	41	20	banach	banach	NOUN
ejpam-4012	41	21	spaces	space	NOUN
ejpam-4012	41	22	and	and	CCONJ
ejpam-4012	41	23	x∗	x∗	PROPN
ejpam-4012	41	24	be	be	VERB
ejpam-4012	41	25	the	the	DET
ejpam-4012	41	26	dual	dual	ADJ
ejpam-4012	41	27	of	of	ADP
ejpam-4012	41	28	x.	x.	NOUN
ejpam-4012	41	29	assume	assume	VERB
ejpam-4012	41	30	x	x	X
ejpam-4012	41	31	∈	∈	PROPN
ejpam-4012	41	32	x	x	X
ejpam-4012	41	33	and	and	CCONJ
ejpam-4012	41	34	y	y	PROPN
ejpam-4012	41	35	∈	∈	PROPN
ejpam-4012	41	36	y.	y.	NOUN
ejpam-4012	41	37	the	the	DET
ejpam-4012	41	38	operator	operator	NOUN
ejpam-4012	41	39	t	t	NOUN
ejpam-4012	41	40	:	:	PUNCT
ejpam-4012	41	41	x∗	x∗	PROPN
ejpam-4012	41	42	→	→	SYM
ejpam-4012	41	43	y	y	PROPN
ejpam-4012	41	44	,	,	PUNCT
ejpam-4012	41	45	defined	define	VERB
ejpam-4012	41	46	by	by	ADP
ejpam-4012	41	47	t	t	PROPN
ejpam-4012	41	48	(	(	PUNCT
ejpam-4012	41	49	x∗	x∗	PROPN
ejpam-4012	41	50	)	)	PUNCT
ejpam-4012	42	1	=	=	PUNCT
ejpam-4012	42	2	x∗(x)y	x∗(x)y	PROPN
ejpam-4012	42	3	is	be	AUX
ejpam-4012	42	4	a	a	DET
ejpam-4012	42	5	bounded	bounded	ADJ
ejpam-4012	42	6	one	one	NUM
ejpam-4012	42	7	rank	rank	NOUN
ejpam-4012	42	8	linear	linear	NOUN
ejpam-4012	42	9	operator	operator	NOUN
ejpam-4012	42	10	.	.	PUNCT
ejpam-4012	43	1	we	we	PRON
ejpam-4012	43	2	write	write	VERB
ejpam-4012	43	3	x⊗y	x⊗y	PROPN
ejpam-4012	43	4	for	for	ADP
ejpam-4012	43	5	t.	t.	NOUN
ejpam-4012	43	6	such	such	ADJ
ejpam-4012	43	7	operators	operator	NOUN
ejpam-4012	43	8	are	be	AUX
ejpam-4012	43	9	called	call	VERB
ejpam-4012	43	10	atoms	atom	NOUN
ejpam-4012	43	11	.	.	PUNCT
ejpam-4012	44	1	atoms	atom	NOUN
ejpam-4012	44	2	are	be	AUX
ejpam-4012	44	3	among	among	ADP
ejpam-4012	44	4	the	the	DET
ejpam-4012	44	5	main	main	ADJ
ejpam-4012	44	6	ingredient	ingredient	NOUN
ejpam-4012	44	7	in	in	ADP
ejpam-4012	44	8	the	the	DET
ejpam-4012	44	9	theory	theory	NOUN
ejpam-4012	44	10	of	of	ADP
ejpam-4012	44	11	tensor	tensor	NOUN
ejpam-4012	44	12	products	product	NOUN
ejpam-4012	44	13	.	.	PUNCT
ejpam-4012	45	1	atoms	atom	NOUN
ejpam-4012	45	2	are	be	AUX
ejpam-4012	45	3	used	use	VERB
ejpam-4012	45	4	in	in	ADP
ejpam-4012	45	5	theory	theory	NOUN
ejpam-4012	45	6	of	of	ADP
ejpam-4012	45	7	best	good	ADJ
ejpam-4012	45	8	approximation	approximation	NOUN
ejpam-4012	45	9	in	in	ADP
ejpam-4012	45	10	banach	banach	NOUN
ejpam-4012	45	11	spaces	space	NOUN
ejpam-4012	45	12	,	,	PUNCT
ejpam-4012	45	13	see	see	VERB
ejpam-4012	45	14	[	[	X
ejpam-4012	45	15	2	2	NUM
ejpam-4012	45	16	]	]	PUNCT
ejpam-4012	45	17	.	.	PUNCT
ejpam-4012	46	1	one	one	NUM
ejpam-4012	46	2	of	of	ADP
ejpam-4012	46	3	the	the	DET
ejpam-4012	46	4	known	know	VERB
ejpam-4012	46	5	results	result	NOUN
ejpam-4012	46	6	,	,	PUNCT
ejpam-4012	46	7	see	see	VERB
ejpam-4012	46	8	[	[	X
ejpam-4012	46	9	4	4	NUM
ejpam-4012	46	10	]	]	PUNCT
ejpam-4012	46	11	,	,	PUNCT
ejpam-4012	46	12	that	that	SCONJ
ejpam-4012	46	13	we	we	PRON
ejpam-4012	46	14	need	need	VERB
ejpam-4012	46	15	in	in	ADP
ejpam-4012	46	16	our	our	PRON
ejpam-4012	46	17	paper	paper	NOUN
ejpam-4012	46	18	is	be	AUX
ejpam-4012	46	19	that	that	SCONJ
ejpam-4012	46	20	:	:	PUNCT
ejpam-4012	46	21	if	if	SCONJ
ejpam-4012	46	22	the	the	DET
ejpam-4012	46	23	sum	sum	NOUN
ejpam-4012	46	24	of	of	ADP
ejpam-4012	46	25	two	two	NUM
ejpam-4012	46	26	atoms	atom	NOUN
ejpam-4012	46	27	is	be	AUX
ejpam-4012	46	28	an	an	DET
ejpam-4012	46	29	atom	atom	NOUN
ejpam-4012	46	30	,	,	PUNCT
ejpam-4012	46	31	then	then	ADV
ejpam-4012	46	32	either	either	CCONJ
ejpam-4012	46	33	the	the	DET
ejpam-4012	46	34	first	first	ADJ
ejpam-4012	46	35	components	component	NOUN
ejpam-4012	46	36	are	be	AUX
ejpam-4012	46	37	dependent	dependent	ADJ
ejpam-4012	46	38	or	or	CCONJ
ejpam-4012	46	39	the	the	DET
ejpam-4012	46	40	second	second	ADJ
ejpam-4012	46	41	ones	one	NOUN
ejpam-4012	46	42	are	be	AUX
ejpam-4012	46	43	dependent	dependent	ADJ
ejpam-4012	46	44	.	.	PUNCT
ejpam-4012	47	1	for	for	ADP
ejpam-4012	47	2	more	more	ADJ
ejpam-4012	47	3	on	on	ADP
ejpam-4012	47	4	tensor	tensor	NOUN
ejpam-4012	47	5	products	product	NOUN
ejpam-4012	47	6	of	of	ADP
ejpam-4012	47	7	banach	banach	NOUN
ejpam-4012	47	8	spaces	space	NOUN
ejpam-4012	47	9	,	,	PUNCT
ejpam-4012	47	10	we	we	PRON
ejpam-4012	47	11	refer	refer	VERB
ejpam-4012	47	12	to	to	ADP
ejpam-4012	47	13	[	[	X
ejpam-4012	47	14	4	4	NUM
ejpam-4012	47	15	]	]	PUNCT
ejpam-4012	47	16	.	.	PUNCT
ejpam-4012	48	1	let	let	VERB
ejpam-4012	48	2	us	we	PRON
ejpam-4012	48	3	write	write	VERB
ejpam-4012	48	4	dα	dα	NOUN
ejpam-4012	48	5	xu	xu	PROPN
ejpam-4012	48	6	to	to	PART
ejpam-4012	48	7	mean	mean	VERB
ejpam-4012	48	8	the	the	DET
ejpam-4012	48	9	partial	partial	ADJ
ejpam-4012	48	10	α−derivative	α−derivative	NOUN
ejpam-4012	48	11	of	of	ADP
ejpam-4012	48	12	u	u	NOUN
ejpam-4012	48	13	with	with	ADP
ejpam-4012	48	14	respect	respect	NOUN
ejpam-4012	48	15	to	to	ADP
ejpam-4012	48	16	x.	x.	NOUN
ejpam-4012	48	17	further	far	ADV
ejpam-4012	48	18	we	we	PRON
ejpam-4012	48	19	write	write	VERB
ejpam-4012	48	20	d2α	d2α	NOUN
ejpam-4012	48	21	x	x	ADP
ejpam-4012	48	22	u	u	NOUN
ejpam-4012	48	23	to	to	PART
ejpam-4012	48	24	mean	mean	VERB
ejpam-4012	48	25	dα	dα	VERB
ejpam-4012	49	1	xd	xd	INTJ
ejpam-4012	49	2	α	α	PROPN
ejpam-4012	49	3	xu	xu	PROPN
ejpam-4012	49	4	.	.	PUNCT
ejpam-4012	50	1	similarly	similarly	ADV
ejpam-4012	50	2	for	for	ADP
ejpam-4012	50	3	derivatives	derivative	NOUN
ejpam-4012	50	4	with	with	ADP
ejpam-4012	50	5	respect	respect	NOUN
ejpam-4012	50	6	to	to	ADP
ejpam-4012	50	7	y.	y.	NOUN
ejpam-4012	50	8	if	if	SCONJ
ejpam-4012	50	9	f	f	PROPN
ejpam-4012	50	10	is	be	AUX
ejpam-4012	50	11	a	a	DET
ejpam-4012	50	12	function	function	NOUN
ejpam-4012	50	13	of	of	ADP
ejpam-4012	50	14	one	one	NUM
ejpam-4012	50	15	variable	variable	NOUN
ejpam-4012	50	16	,	,	PUNCT
ejpam-4012	50	17	say	say	VERB
ejpam-4012	50	18	x	x	SYM
ejpam-4012	50	19	,	,	PUNCT
ejpam-4012	50	20	we	we	PRON
ejpam-4012	50	21	write	write	VERB
ejpam-4012	50	22	fα	fα	ADP
ejpam-4012	50	23	,	,	PUNCT
ejpam-4012	50	24	f2α	f2α	PRON
ejpam-4012	50	25	to	to	PART
ejpam-4012	50	26	denote	denote	VERB
ejpam-4012	50	27	dα	dα	PROPN
ejpam-4012	50	28	xf	xf	PROPN
ejpam-4012	50	29	and	and	CCONJ
ejpam-4012	50	30	d2α	d2α	NOUN
ejpam-4012	50	31	x	x	X
ejpam-4012	50	32	f	f	PROPN
ejpam-4012	50	33	respectively	respectively	ADV
ejpam-4012	50	34	.	.	PUNCT
ejpam-4012	51	1	i.	i.	PROPN
ejpam-4012	51	2	benkemache	benkemache	PROPN
ejpam-4012	51	3	,	,	PUNCT
ejpam-4012	51	4	m.	m.	NOUN
ejpam-4012	51	5	al	al	PROPN
ejpam-4012	51	6	horani	horani	PROPN
ejpam-4012	51	7	,	,	PUNCT
ejpam-4012	51	8	r.	r.	PROPN
ejpam-4012	51	9	khalil	khalil	PROPN
ejpam-4012	51	10	/	/	SYM
ejpam-4012	51	11	eur	eur	PROPN
ejpam-4012	51	12	.	.	PUNCT
ejpam-4012	52	1	j.	j.	PROPN
ejpam-4012	52	2	pure	pure	PROPN
ejpam-4012	52	3	appl	appl	PROPN
ejpam-4012	52	4	.	.	PROPN
ejpam-4012	52	5	math	math	PROPN
ejpam-4012	52	6	,	,	PUNCT
ejpam-4012	52	7	14	14	NUM
ejpam-4012	52	8	(	(	PUNCT
ejpam-4012	52	9	3	3	NUM
ejpam-4012	52	10	)	)	PUNCT
ejpam-4012	52	11	(	(	PUNCT
ejpam-4012	52	12	2021	2021	NUM
ejpam-4012	52	13	)	)	PUNCT
ejpam-4012	52	14	,	,	PUNCT
ejpam-4012	52	15	942	942	NUM
ejpam-4012	52	16	-	-	SYM
ejpam-4012	52	17	948	948	NUM
ejpam-4012	52	18	944	944	NUM
ejpam-4012	52	19	our	our	PRON
ejpam-4012	52	20	main	main	ADJ
ejpam-4012	52	21	object	object	NOUN
ejpam-4012	52	22	in	in	ADP
ejpam-4012	52	23	this	this	DET
ejpam-4012	52	24	section	section	NOUN
ejpam-4012	52	25	is	be	AUX
ejpam-4012	52	26	to	to	PART
ejpam-4012	52	27	find	find	VERB
ejpam-4012	52	28	an	an	DET
ejpam-4012	52	29	atomic	atomic	ADJ
ejpam-4012	52	30	solution	solution	NOUN
ejpam-4012	52	31	of	of	ADP
ejpam-4012	52	32	the	the	DET
ejpam-4012	52	33	equation	equation	NOUN
ejpam-4012	52	34	d2α	d2α	NOUN
ejpam-4012	52	35	x	x	X
ejpam-4012	52	36	d2β	d2β	VERB
ejpam-4012	52	37	y	y	NOUN
ejpam-4012	52	38	u+dα	u+dα	NOUN
ejpam-4012	52	39	xd	xd	ADP
ejpam-4012	52	40	β	β	X
ejpam-4012	52	41	yu	yu	PROPN
ejpam-4012	52	42	=	=	PROPN
ejpam-4012	52	43	2u	2u	PROPN
ejpam-4012	52	44	,	,	PUNCT
ejpam-4012	52	45	(	(	PUNCT
ejpam-4012	52	46	1	1	X
ejpam-4012	52	47	)	)	PUNCT
ejpam-4012	52	48	where	where	SCONJ
ejpam-4012	52	49	by	by	ADP
ejpam-4012	52	50	an	an	DET
ejpam-4012	52	51	atomic	atomic	ADJ
ejpam-4012	52	52	solution	solution	NOUN
ejpam-4012	52	53	we	we	PRON
ejpam-4012	52	54	mean	mean	VERB
ejpam-4012	52	55	a	a	DET
ejpam-4012	52	56	solution	solution	NOUN
ejpam-4012	52	57	of	of	ADP
ejpam-4012	52	58	the	the	DET
ejpam-4012	52	59	form	form	NOUN
ejpam-4012	52	60	u(x	u(x	NOUN
ejpam-4012	52	61	,	,	PUNCT
ejpam-4012	52	62	y	y	NOUN
ejpam-4012	52	63	)	)	PUNCT
ejpam-4012	52	64	=	=	SYM
ejpam-4012	53	1	p	p	X
ejpam-4012	53	2	(	(	PUNCT
ejpam-4012	53	3	x)q(y	x)q(y	PROPN
ejpam-4012	53	4	)	)	PUNCT
ejpam-4012	53	5	.	.	PUNCT
ejpam-4012	54	1	remark	remark	PROPN
ejpam-4012	54	2	1	1	NUM
ejpam-4012	54	3	.	.	PUNCT
ejpam-4012	55	1	one	one	PRON
ejpam-4012	55	2	should	should	AUX
ejpam-4012	55	3	remark	remark	VERB
ejpam-4012	55	4	that	that	SCONJ
ejpam-4012	55	5	not	not	PART
ejpam-4012	55	6	every	every	DET
ejpam-4012	55	7	linear	linear	ADJ
ejpam-4012	55	8	partial	partial	ADJ
ejpam-4012	55	9	differential	differential	NOUN
ejpam-4012	55	10	equation	equation	NOUN
ejpam-4012	55	11	(	(	PUNCT
ejpam-4012	55	12	fractional	fractional	ADJ
ejpam-4012	55	13	or	or	CCONJ
ejpam-4012	55	14	not	not	PART
ejpam-4012	55	15	)	)	PUNCT
ejpam-4012	55	16	can	can	AUX
ejpam-4012	55	17	be	be	AUX
ejpam-4012	55	18	solved	solve	VERB
ejpam-4012	55	19	using	use	VERB
ejpam-4012	55	20	separation	separation	NOUN
ejpam-4012	55	21	of	of	ADP
ejpam-4012	55	22	variables	variable	NOUN
ejpam-4012	55	23	.	.	PUNCT
ejpam-4012	56	1	in	in	ADP
ejpam-4012	56	2	such	such	DET
ejpam-4012	56	3	a	a	DET
ejpam-4012	56	4	case	case	NOUN
ejpam-4012	56	5	,	,	PUNCT
ejpam-4012	56	6	the	the	DET
ejpam-4012	56	7	concept	concept	NOUN
ejpam-4012	56	8	of	of	ADP
ejpam-4012	56	9	atomic	atomic	ADJ
ejpam-4012	56	10	solution	solution	NOUN
ejpam-4012	56	11	is	be	AUX
ejpam-4012	56	12	inevitable	inevitable	ADJ
ejpam-4012	56	13	.	.	PUNCT
ejpam-4012	57	1	in	in	ADP
ejpam-4012	57	2	equation	equation	NOUN
ejpam-4012	57	3	(	(	PUNCT
ejpam-4012	57	4	1	1	NUM
ejpam-4012	57	5	)	)	PUNCT
ejpam-4012	57	6	,	,	PUNCT
ejpam-4012	57	7	the	the	DET
ejpam-4012	57	8	method	method	NOUN
ejpam-4012	57	9	of	of	ADP
ejpam-4012	57	10	separation	separation	NOUN
ejpam-4012	57	11	of	of	ADP
ejpam-4012	57	12	variables	variable	NOUN
ejpam-4012	57	13	is	be	AUX
ejpam-4012	57	14	not	not	PART
ejpam-4012	57	15	possible	possible	ADJ
ejpam-4012	57	16	though	though	SCONJ
ejpam-4012	57	17	the	the	DET
ejpam-4012	57	18	equation	equation	NOUN
ejpam-4012	57	19	is	be	AUX
ejpam-4012	57	20	linear	linear	ADJ
ejpam-4012	57	21	.	.	PUNCT
ejpam-4012	58	1	hence	hence	ADV
ejpam-4012	58	2	we	we	PRON
ejpam-4012	58	3	try	try	VERB
ejpam-4012	58	4	to	to	PART
ejpam-4012	58	5	find	find	VERB
ejpam-4012	58	6	an	an	DET
ejpam-4012	58	7	atomic	atomic	ADJ
ejpam-4012	58	8	solution	solution	NOUN
ejpam-4012	58	9	of	of	ADP
ejpam-4012	58	10	this	this	DET
ejpam-4012	58	11	equation	equation	NOUN
ejpam-4012	58	12	.	.	PUNCT
ejpam-4012	59	1	in	in	ADP
ejpam-4012	59	2	other	other	ADJ
ejpam-4012	59	3	words	word	NOUN
ejpam-4012	59	4	,	,	PUNCT
ejpam-4012	59	5	we	we	PRON
ejpam-4012	59	6	look	look	VERB
ejpam-4012	59	7	for	for	ADP
ejpam-4012	59	8	a	a	DET
ejpam-4012	59	9	solution	solution	NOUN
ejpam-4012	59	10	of	of	ADP
ejpam-4012	59	11	the	the	DET
ejpam-4012	59	12	form	form	NOUN
ejpam-4012	59	13	u(x	u(x	NOUN
ejpam-4012	59	14	,	,	PUNCT
ejpam-4012	59	15	y	y	NOUN
ejpam-4012	59	16	)	)	PUNCT
ejpam-4012	60	1	=	=	SYM
ejpam-4012	60	2	p	p	X
ejpam-4012	60	3	(	(	PUNCT
ejpam-4012	60	4	x)q(y	x)q(y	PROPN
ejpam-4012	60	5	)	)	PUNCT
ejpam-4012	60	6	.	.	PUNCT
ejpam-4012	61	1	procedure	procedure	NOUN
ejpam-4012	61	2	let	let	VERB
ejpam-4012	61	3	u(x	u(x	NOUN
ejpam-4012	61	4	,	,	PUNCT
ejpam-4012	61	5	y	y	NOUN
ejpam-4012	61	6	)	)	PUNCT
ejpam-4012	61	7	=	=	SYM
ejpam-4012	62	1	p	p	X
ejpam-4012	62	2	(	(	PUNCT
ejpam-4012	62	3	x)q(y	x)q(y	PROPN
ejpam-4012	62	4	)	)	PUNCT
ejpam-4012	62	5	.	.	PUNCT
ejpam-4012	63	1	substitute	substitute	NOUN
ejpam-4012	63	2	in	in	ADP
ejpam-4012	63	3	equation	equation	NOUN
ejpam-4012	63	4	(	(	PUNCT
ejpam-4012	63	5	1	1	NUM
ejpam-4012	63	6	)	)	PUNCT
ejpam-4012	63	7	to	to	PART
ejpam-4012	63	8	get	get	VERB
ejpam-4012	63	9	:	:	PUNCT
ejpam-4012	63	10	p	p	NOUN
ejpam-4012	63	11	2α(x)q2β(y	2α(x)q2β(y	NUM
ejpam-4012	63	12	)	)	PUNCT
ejpam-4012	63	13	+	+	NUM
ejpam-4012	63	14	pα(x)qβ(y	pα(x)qβ(y	NOUN
ejpam-4012	63	15	)	)	PUNCT
ejpam-4012	63	16	=	=	SYM
ejpam-4012	63	17	2p	2p	NOUN
ejpam-4012	63	18	(	(	PUNCT
ejpam-4012	63	19	x)q(y	x)q(y	NOUN
ejpam-4012	63	20	)	)	PUNCT
ejpam-4012	63	21	.	.	PUNCT
ejpam-4012	64	1	this	this	PRON
ejpam-4012	64	2	can	can	AUX
ejpam-4012	64	3	written	write	VERB
ejpam-4012	64	4	in	in	ADP
ejpam-4012	64	5	tensor	tensor	NOUN
ejpam-4012	64	6	product	product	NOUN
ejpam-4012	64	7	form	form	NOUN
ejpam-4012	64	8	as	as	ADP
ejpam-4012	64	9	:	:	PUNCT
ejpam-4012	64	10	p	p	X
ejpam-4012	64	11	2α	2α	NOUN
ejpam-4012	64	12	⊗q2β	⊗q2β	NUM
ejpam-4012	64	13	+	+	CCONJ
ejpam-4012	64	14	pα	pα	INTJ
ejpam-4012	64	15	⊗qβ	⊗qβ	NOUN
ejpam-4012	64	16	=	=	SYM
ejpam-4012	65	1	p	p	X
ejpam-4012	65	2	⊗	⊗	NUM
ejpam-4012	65	3	2q	2q	NUM
ejpam-4012	65	4	.	.	PUNCT
ejpam-4012	66	1	(	(	PUNCT
ejpam-4012	66	2	2	2	X
ejpam-4012	66	3	)	)	PUNCT
ejpam-4012	66	4	let	let	VERB
ejpam-4012	66	5	us	we	PRON
ejpam-4012	66	6	consider	consider	VERB
ejpam-4012	66	7	the	the	DET
ejpam-4012	66	8	following	follow	VERB
ejpam-4012	66	9	conditions	condition	NOUN
ejpam-4012	66	10	:	:	PUNCT
ejpam-4012	66	11	p	p	X
ejpam-4012	66	12	(	(	PUNCT
ejpam-4012	66	13	0	0	NUM
ejpam-4012	66	14	)	)	PUNCT
ejpam-4012	66	15	=	=	SYM
ejpam-4012	66	16	0	0	NUM
ejpam-4012	66	17	,	,	PUNCT
ejpam-4012	66	18	pα(0	pα(0	NOUN
ejpam-4012	66	19	)	)	PUNCT
ejpam-4012	66	20	=	=	NOUN
ejpam-4012	67	1	1	1	X
ejpam-4012	67	2	.	.	X
ejpam-4012	67	3	in	in	ADP
ejpam-4012	67	4	equation	equation	NOUN
ejpam-4012	67	5	(	(	PUNCT
ejpam-4012	67	6	2	2	NUM
ejpam-4012	67	7	)	)	PUNCT
ejpam-4012	67	8	,	,	PUNCT
ejpam-4012	67	9	we	we	PRON
ejpam-4012	67	10	have	have	VERB
ejpam-4012	67	11	the	the	DET
ejpam-4012	67	12	situation	situation	NOUN
ejpam-4012	67	13	:	:	PUNCT
ejpam-4012	67	14	the	the	DET
ejpam-4012	67	15	sum	sum	NOUN
ejpam-4012	67	16	of	of	ADP
ejpam-4012	67	17	two	two	NUM
ejpam-4012	67	18	atoms	atom	NOUN
ejpam-4012	67	19	is	be	AUX
ejpam-4012	67	20	an	an	DET
ejpam-4012	67	21	atom	atom	NOUN
ejpam-4012	67	22	.	.	PUNCT
ejpam-4012	68	1	hence	hence	ADV
ejpam-4012	68	2	we	we	PRON
ejpam-4012	68	3	have	have	VERB
ejpam-4012	68	4	two	two	NUM
ejpam-4012	68	5	cases	case	NOUN
ejpam-4012	68	6	:	:	PUNCT
ejpam-4012	68	7	case(i	case(i	NOUN
ejpam-4012	68	8	):	):	PUNCT
ejpam-4012	68	9	p	p	NOUN
ejpam-4012	68	10	2α	2α	NOUN
ejpam-4012	68	11	=	=	SYM
ejpam-4012	68	12	pα	pα	NOUN
ejpam-4012	68	13	.	.	PUNCT
ejpam-4012	69	1	using	use	VERB
ejpam-4012	69	2	the	the	DET
ejpam-4012	69	3	result	result	NOUN
ejpam-4012	69	4	in	in	ADP
ejpam-4012	69	5	[	[	X
ejpam-4012	69	6	5	5	NUM
ejpam-4012	69	7	]	]	PUNCT
ejpam-4012	69	8	,	,	PUNCT
ejpam-4012	69	9	we	we	PRON
ejpam-4012	69	10	get	get	VERB
ejpam-4012	69	11	p	p	NOUN
ejpam-4012	69	12	(	(	PUNCT
ejpam-4012	69	13	x	x	NOUN
ejpam-4012	69	14	)	)	PUNCT
ejpam-4012	70	1	=	=	SYM
ejpam-4012	70	2	e	e	X
ejpam-4012	70	3	xα	xα	PROPN
ejpam-4012	70	4	α	α	PROPN
ejpam-4012	70	5	.	.	PUNCT
ejpam-4012	71	1	(	(	PUNCT
ejpam-4012	71	2	3	3	X
ejpam-4012	71	3	)	)	PUNCT
ejpam-4012	71	4	now	now	ADV
ejpam-4012	71	5	,	,	PUNCT
ejpam-4012	71	6	we	we	PRON
ejpam-4012	71	7	substitute	substitute	VERB
ejpam-4012	71	8	in	in	ADP
ejpam-4012	71	9	(	(	PUNCT
ejpam-4012	71	10	2	2	NUM
ejpam-4012	71	11	)	)	PUNCT
ejpam-4012	71	12	to	to	PART
ejpam-4012	71	13	get	get	VERB
ejpam-4012	71	14	ex	ex	PRON
ejpam-4012	71	15	⊗	⊗	PROPN
ejpam-4012	72	1	[	[	X
ejpam-4012	72	2	q2β	q2β	X
ejpam-4012	72	3	+	+	NOUN
ejpam-4012	72	4	qβ	qβ	X
ejpam-4012	72	5	]	]	X
ejpam-4012	72	6	=	=	PUNCT
ejpam-4012	72	7	ex	ex	PRON
ejpam-4012	72	8	⊗q	⊗q	NOUN
ejpam-4012	72	9	.	.	PUNCT
ejpam-4012	73	1	hence	hence	ADV
ejpam-4012	73	2	,	,	PUNCT
ejpam-4012	73	3	q2β	q2β	X
ejpam-4012	73	4	+	+	ADJ
ejpam-4012	73	5	qβ	qβ	X
ejpam-4012	73	6	=	=	ADJ
ejpam-4012	73	7	2q	2q	NOUN
ejpam-4012	73	8	.	.	PUNCT
ejpam-4012	74	1	again	again	ADV
ejpam-4012	74	2	,	,	PUNCT
ejpam-4012	74	3	using	use	VERB
ejpam-4012	74	4	the	the	DET
ejpam-4012	74	5	result	result	NOUN
ejpam-4012	74	6	in	in	ADP
ejpam-4012	74	7	[	[	X
ejpam-4012	74	8	5	5	NUM
ejpam-4012	74	9	]	]	PUNCT
ejpam-4012	74	10	,	,	PUNCT
ejpam-4012	74	11	q(y	q(y	X
ejpam-4012	74	12	)	)	PUNCT
ejpam-4012	74	13	=	=	SYM
ejpam-4012	74	14	c1e	c1e	NOUN
ejpam-4012	74	15	−2	−2	X
ejpam-4012	74	16	y	y	NOUN
ejpam-4012	74	17	β	β	X
ejpam-4012	74	18	β	β	X
ejpam-4012	74	19	+	+	CCONJ
ejpam-4012	74	20	c2e	c2e	PROPN
ejpam-4012	74	21	yβ	yβ	NOUN
ejpam-4012	74	22	β	β	X
ejpam-4012	74	23	using	use	VERB
ejpam-4012	74	24	the	the	DET
ejpam-4012	74	25	conditions	condition	NOUN
ejpam-4012	74	26	q(0	q(0	NOUN
ejpam-4012	74	27	)	)	PUNCT
ejpam-4012	74	28	=	=	SYM
ejpam-4012	74	29	qβ(0	qβ(0	NOUN
ejpam-4012	74	30	)	)	PUNCT
ejpam-4012	74	31	=	=	SYM
ejpam-4012	74	32	1	1	NUM
ejpam-4012	74	33	,	,	PUNCT
ejpam-4012	74	34	we	we	PRON
ejpam-4012	74	35	get	get	VERB
ejpam-4012	74	36	q(y	q(y	NOUN
ejpam-4012	74	37	)	)	PUNCT
ejpam-4012	75	1	=	=	PUNCT
ejpam-4012	75	2	−1	−1	NOUN
ejpam-4012	75	3	3	3	NUM
ejpam-4012	75	4	e	e	NOUN
ejpam-4012	75	5	−2	−2	NOUN
ejpam-4012	75	6	y	y	PROPN
ejpam-4012	75	7	β	β	X
ejpam-4012	75	8	β	β	X
ejpam-4012	75	9	+	+	NOUN
ejpam-4012	75	10	1	1	NUM
ejpam-4012	75	11	3	3	NUM
ejpam-4012	75	12	e	e	NOUN
ejpam-4012	75	13	yβ	yβ	NOUN
ejpam-4012	75	14	β	β	X
ejpam-4012	75	15	.	.	PUNCT
ejpam-4012	76	1	(	(	PUNCT
ejpam-4012	76	2	4	4	NUM
ejpam-4012	76	3	)	)	PUNCT
ejpam-4012	76	4	from	from	ADP
ejpam-4012	76	5	(	(	PUNCT
ejpam-4012	76	6	3	3	NUM
ejpam-4012	76	7	)	)	PUNCT
ejpam-4012	76	8	and	and	CCONJ
ejpam-4012	76	9	(	(	PUNCT
ejpam-4012	76	10	4	4	NUM
ejpam-4012	76	11	)	)	PUNCT
ejpam-4012	76	12	,	,	PUNCT
ejpam-4012	76	13	we	we	PRON
ejpam-4012	76	14	obtain	obtain	VERB
ejpam-4012	76	15	the	the	DET
ejpam-4012	76	16	atomic	atomic	ADJ
ejpam-4012	76	17	solution	solution	NOUN
ejpam-4012	76	18	of	of	ADP
ejpam-4012	76	19	(	(	PUNCT
ejpam-4012	76	20	1	1	NUM
ejpam-4012	76	21	)	)	PUNCT
ejpam-4012	76	22	as	as	ADP
ejpam-4012	76	23	:	:	PUNCT
ejpam-4012	76	24	u(x	u(x	PROPN
ejpam-4012	76	25	,	,	PUNCT
ejpam-4012	76	26	y	y	NOUN
ejpam-4012	76	27	)	)	PUNCT
ejpam-4012	77	1	=	=	SYM
ejpam-4012	77	2	e	e	X
ejpam-4012	77	3	xα	xα	PROPN
ejpam-4012	77	4	α	α	PROPN
ejpam-4012	77	5	(	(	PUNCT
ejpam-4012	77	6	−1	−1	NOUN
ejpam-4012	77	7	3	3	NUM
ejpam-4012	77	8	e	e	NOUN
ejpam-4012	77	9	−2	−2	NOUN
ejpam-4012	77	10	y	y	PROPN
ejpam-4012	77	11	β	β	X
ejpam-4012	77	12	β	β	X
ejpam-4012	77	13	+	+	NOUN
ejpam-4012	77	14	1	1	NUM
ejpam-4012	77	15	3	3	NUM
ejpam-4012	77	16	e	e	NOUN
ejpam-4012	77	17	yβ	yβ	NOUN
ejpam-4012	77	18	β	β	PROPN
ejpam-4012	77	19	)	)	PUNCT
ejpam-4012	77	20	.	.	PUNCT
ejpam-4012	78	1	(	(	PUNCT
ejpam-4012	78	2	5	5	X
ejpam-4012	78	3	)	)	PUNCT
ejpam-4012	78	4	i.	i.	PROPN
ejpam-4012	78	5	benkemache	benkemache	PROPN
ejpam-4012	78	6	,	,	PUNCT
ejpam-4012	78	7	m.	m.	NOUN
ejpam-4012	78	8	al	al	PROPN
ejpam-4012	78	9	horani	horani	PROPN
ejpam-4012	78	10	,	,	PUNCT
ejpam-4012	78	11	r.	r.	PROPN
ejpam-4012	78	12	khalil	khalil	PROPN
ejpam-4012	78	13	/	/	SYM
ejpam-4012	78	14	eur	eur	PROPN
ejpam-4012	78	15	.	.	PUNCT
ejpam-4012	79	1	j.	j.	PROPN
ejpam-4012	79	2	pure	pure	PROPN
ejpam-4012	79	3	appl	appl	PROPN
ejpam-4012	79	4	.	.	PROPN
ejpam-4012	79	5	math	math	PROPN
ejpam-4012	79	6	,	,	PUNCT
ejpam-4012	79	7	14	14	NUM
ejpam-4012	79	8	(	(	PUNCT
ejpam-4012	79	9	3	3	NUM
ejpam-4012	79	10	)	)	PUNCT
ejpam-4012	79	11	(	(	PUNCT
ejpam-4012	79	12	2021	2021	NUM
ejpam-4012	79	13	)	)	PUNCT
ejpam-4012	79	14	,	,	PUNCT
ejpam-4012	79	15	942	942	NUM
ejpam-4012	79	16	-	-	SYM
ejpam-4012	79	17	948	948	NUM
ejpam-4012	79	18	945	945	NUM
ejpam-4012	79	19	one	one	NUM
ejpam-4012	79	20	can	can	AUX
ejpam-4012	79	21	easily	easily	ADV
ejpam-4012	79	22	check	check	VERB
ejpam-4012	79	23	that	that	SCONJ
ejpam-4012	79	24	the	the	DET
ejpam-4012	79	25	atom	atom	NOUN
ejpam-4012	79	26	u	u	NOUN
ejpam-4012	79	27	in	in	ADP
ejpam-4012	79	28	(	(	PUNCT
ejpam-4012	79	29	5	5	NUM
ejpam-4012	79	30	)	)	PUNCT
ejpam-4012	79	31	satisfies	satisfie	NOUN
ejpam-4012	79	32	(	(	PUNCT
ejpam-4012	79	33	1	1	NUM
ejpam-4012	79	34	)	)	PUNCT
ejpam-4012	79	35	.	.	PUNCT
ejpam-4012	80	1	case	case	NOUN
ejpam-4012	80	2	(	(	PUNCT
ejpam-4012	80	3	ii	ii	NUM
ejpam-4012	80	4	):	):	PUNCT
ejpam-4012	80	5	q2β	q2β	PROPN
ejpam-4012	80	6	=	=	SYM
ejpam-4012	80	7	qβ	qβ	PROPN
ejpam-4012	80	8	.	.	PUNCT
ejpam-4012	81	1	following	follow	VERB
ejpam-4012	81	2	the	the	DET
ejpam-4012	81	3	same	same	ADJ
ejpam-4012	81	4	steps	step	NOUN
ejpam-4012	81	5	as	as	ADP
ejpam-4012	81	6	in	in	ADP
ejpam-4012	81	7	case	case	NOUN
ejpam-4012	81	8	(	(	PUNCT
ejpam-4012	81	9	i	i	NOUN
ejpam-4012	81	10	)	)	PUNCT
ejpam-4012	81	11	,	,	PUNCT
ejpam-4012	81	12	we	we	PRON
ejpam-4012	81	13	find	find	VERB
ejpam-4012	81	14	the	the	DET
ejpam-4012	81	15	atomic	atomic	ADJ
ejpam-4012	81	16	solution	solution	NOUN
ejpam-4012	81	17	in	in	ADP
ejpam-4012	81	18	the	the	DET
ejpam-4012	81	19	form	form	NOUN
ejpam-4012	81	20	u(x	u(x	NOUN
ejpam-4012	81	21	,	,	PUNCT
ejpam-4012	81	22	y	y	NOUN
ejpam-4012	81	23	)	)	PUNCT
ejpam-4012	81	24	=	=	PRON
ejpam-4012	81	25	(	(	PUNCT
ejpam-4012	81	26	−1	−1	NOUN
ejpam-4012	81	27	3	3	X
ejpam-4012	82	1	e−2	e−2	INTJ
ejpam-4012	82	2	xα	xα	ADP
ejpam-4012	82	3	α	α	PRON
ejpam-4012	83	1	+	+	NOUN
ejpam-4012	83	2	1	1	NUM
ejpam-4012	83	3	3	3	NUM
ejpam-4012	83	4	e	e	NOUN
ejpam-4012	83	5	xα	xα	X
ejpam-4012	83	6	α	α	NOUN
ejpam-4012	83	7	)	)	PUNCT
ejpam-4012	83	8	e	e	X
ejpam-4012	83	9	yβ	yβ	PROPN
ejpam-4012	83	10	β	β	PROPN
ejpam-4012	83	11	3	3	NUM
ejpam-4012	83	12	.	.	PUNCT
ejpam-4012	83	13	complete	complete	ADJ
ejpam-4012	83	14	solution	solution	NOUN
ejpam-4012	83	15	consider	consider	VERB
ejpam-4012	83	16	the	the	DET
ejpam-4012	83	17	fractional	fractional	ADJ
ejpam-4012	83	18	partial	partial	ADJ
ejpam-4012	83	19	differential	differential	NOUN
ejpam-4012	83	20	equation	equation	NOUN
ejpam-4012	83	21	d2β	d2β	VERB
ejpam-4012	83	22	x	x	SYM
ejpam-4012	83	23	u−	u−	PROPN
ejpam-4012	83	24	c2d2α	c2d2α	X
ejpam-4012	83	25	y	y	NOUN
ejpam-4012	83	26	u	u	NOUN
ejpam-4012	83	27	=	=	NOUN
ejpam-4012	83	28	dα	dα	PROPN
ejpam-4012	83	29	y	y	PROPN
ejpam-4012	83	30	u	u	PROPN
ejpam-4012	83	31	(	(	PUNCT
ejpam-4012	83	32	6	6	NUM
ejpam-4012	83	33	)	)	PUNCT
ejpam-4012	83	34	with	with	ADP
ejpam-4012	83	35	conditions	condition	NOUN
ejpam-4012	83	36	u(x	u(x	NOUN
ejpam-4012	83	37	,	,	PUNCT
ejpam-4012	83	38	0	0	NUM
ejpam-4012	83	39	)	)	PUNCT
ejpam-4012	83	40	=	=	SYM
ejpam-4012	83	41	f(x	f(x	PROPN
ejpam-4012	83	42	)	)	PUNCT
ejpam-4012	83	43	,	,	PUNCT
ejpam-4012	83	44	u(x	u(x	PROPN
ejpam-4012	83	45	,	,	PUNCT
ejpam-4012	83	46	1	1	NUM
ejpam-4012	83	47	)	)	PUNCT
ejpam-4012	83	48	=	=	SYM
ejpam-4012	83	49	0	0	NUM
ejpam-4012	83	50	,	,	PUNCT
ejpam-4012	83	51	u(l	u(l	PROPN
ejpam-4012	83	52	,	,	PUNCT
ejpam-4012	83	53	y	y	NOUN
ejpam-4012	83	54	)	)	PUNCT
ejpam-4012	83	55	=	=	SYM
ejpam-4012	83	56	0	0	NUM
ejpam-4012	83	57	,	,	PUNCT
ejpam-4012	83	58	u(0	u(0	PROPN
ejpam-4012	83	59	,	,	PUNCT
ejpam-4012	83	60	y	y	PROPN
ejpam-4012	83	61	)	)	PUNCT
ejpam-4012	83	62	=	=	SYM
ejpam-4012	83	63	0	0	NUM
ejpam-4012	83	64	,	,	PUNCT
ejpam-4012	83	65	0	0	NUM
ejpam-4012	83	66	<	<	X
ejpam-4012	83	67	α	α	X
ejpam-4012	83	68	,	,	PUNCT
ejpam-4012	83	69	β	β	X
ejpam-4012	83	70	<	<	X
ejpam-4012	83	71	1	1	NUM
ejpam-4012	83	72	.	.	PUNCT
ejpam-4012	84	1	here	here	ADV
ejpam-4012	84	2	c	c	PROPN
ejpam-4012	84	3	is	be	AUX
ejpam-4012	84	4	a	a	DET
ejpam-4012	84	5	given	give	VERB
ejpam-4012	84	6	constant	constant	NOUN
ejpam-4012	84	7	.	.	PUNCT
ejpam-4012	85	1	this	this	PRON
ejpam-4012	85	2	is	be	AUX
ejpam-4012	85	3	called	call	VERB
ejpam-4012	85	4	fractional	fractional	ADJ
ejpam-4012	85	5	wave	wave	NOUN
ejpam-4012	85	6	type	type	NOUN
ejpam-4012	85	7	equation	equation	NOUN
ejpam-4012	85	8	.	.	PUNCT
ejpam-4012	86	1	we	we	PRON
ejpam-4012	86	2	will	will	AUX
ejpam-4012	86	3	use	use	VERB
ejpam-4012	86	4	fractional	fractional	ADJ
ejpam-4012	86	5	fourier	fourier	NOUN
ejpam-4012	86	6	series	series	NOUN
ejpam-4012	86	7	and	and	CCONJ
ejpam-4012	86	8	separation	separation	NOUN
ejpam-4012	86	9	of	of	ADP
ejpam-4012	86	10	variables	variable	NOUN
ejpam-4012	86	11	to	to	PART
ejpam-4012	86	12	solve	solve	VERB
ejpam-4012	86	13	equation	equation	NOUN
ejpam-4012	86	14	(	(	PUNCT
ejpam-4012	86	15	6	6	NUM
ejpam-4012	86	16	)	)	PUNCT
ejpam-4012	86	17	.	.	PUNCT
ejpam-4012	87	1	remark	remark	NOUN
ejpam-4012	87	2	2	2	NUM
ejpam-4012	87	3	.	.	PUNCT
ejpam-4012	88	1	one	one	PRON
ejpam-4012	88	2	may	may	AUX
ejpam-4012	88	3	attempt	attempt	VERB
ejpam-4012	88	4	to	to	PART
ejpam-4012	88	5	use	use	VERB
ejpam-4012	88	6	change	change	NOUN
ejpam-4012	88	7	of	of	ADP
ejpam-4012	88	8	variables	variable	NOUN
ejpam-4012	88	9	to	to	PART
ejpam-4012	88	10	transform	transform	VERB
ejpam-4012	88	11	it	it	PRON
ejpam-4012	88	12	to	to	ADP
ejpam-4012	88	13	an	an	DET
ejpam-4012	88	14	ordinary	ordinary	ADJ
ejpam-4012	88	15	partial	partial	ADJ
ejpam-4012	88	16	differential	differential	NOUN
ejpam-4012	88	17	equation	equation	NOUN
ejpam-4012	88	18	.	.	PUNCT
ejpam-4012	89	1	this	this	PRON
ejpam-4012	89	2	is	be	AUX
ejpam-4012	89	3	possible	possible	ADJ
ejpam-4012	89	4	if	if	SCONJ
ejpam-4012	89	5	in	in	ADP
ejpam-4012	89	6	equation	equation	NOUN
ejpam-4012	89	7	(	(	PUNCT
ejpam-4012	89	8	1	1	NUM
ejpam-4012	89	9	)	)	PUNCT
ejpam-4012	89	10	and	and	CCONJ
ejpam-4012	89	11	(	(	PUNCT
ejpam-4012	89	12	6	6	NUM
ejpam-4012	89	13	)	)	PUNCT
ejpam-4012	89	14	,	,	PUNCT
ejpam-4012	89	15	the	the	DET
ejpam-4012	89	16	function	function	NOUN
ejpam-4012	89	17	u	u	NOUN
ejpam-4012	89	18	is	be	AUX
ejpam-4012	89	19	u	u	NOUN
ejpam-4012	89	20	=	=	PROPN
ejpam-4012	89	21	u(x	u(x	PROPN
ejpam-4012	89	22	α	α	PROPN
ejpam-4012	89	23	α	α	NOUN
ejpam-4012	89	24	,	,	PUNCT
ejpam-4012	89	25	yα	yα	VERB
ejpam-4012	89	26	α	α	NOUN
ejpam-4012	89	27	)	)	PUNCT
ejpam-4012	89	28	.	.	PUNCT
ejpam-4012	90	1	but	but	CCONJ
ejpam-4012	90	2	the	the	DET
ejpam-4012	90	3	function	function	NOUN
ejpam-4012	90	4	u	u	NOUN
ejpam-4012	90	5	in	in	ADP
ejpam-4012	90	6	equations	equation	NOUN
ejpam-4012	90	7	in	in	ADP
ejpam-4012	90	8	(	(	PUNCT
ejpam-4012	90	9	1	1	NUM
ejpam-4012	90	10	)	)	PUNCT
ejpam-4012	90	11	and	and	CCONJ
ejpam-4012	90	12	(	(	PUNCT
ejpam-4012	90	13	6	6	NUM
ejpam-4012	90	14	)	)	PUNCT
ejpam-4012	90	15	is	be	AUX
ejpam-4012	90	16	u	u	NOUN
ejpam-4012	90	17	=	=	SYM
ejpam-4012	90	18	u(x	u(x	PROPN
ejpam-4012	90	19	,	,	PUNCT
ejpam-4012	90	20	y	y	NOUN
ejpam-4012	90	21	)	)	PUNCT
ejpam-4012	90	22	.	.	PUNCT
ejpam-4012	91	1	so	so	ADV
ejpam-4012	91	2	any	any	DET
ejpam-4012	91	3	change	change	NOUN
ejpam-4012	91	4	of	of	ADP
ejpam-4012	91	5	variables	variable	NOUN
ejpam-4012	91	6	will	will	AUX
ejpam-4012	91	7	not	not	PART
ejpam-4012	91	8	simplify	simplify	VERB
ejpam-4012	91	9	the	the	DET
ejpam-4012	91	10	problem	problem	NOUN
ejpam-4012	91	11	.	.	PUNCT
ejpam-4012	92	1	further	far	ADV
ejpam-4012	92	2	,	,	PUNCT
ejpam-4012	92	3	the	the	DET
ejpam-4012	92	4	partial	partial	ADJ
ejpam-4012	92	5	derivatives	derivative	NOUN
ejpam-4012	92	6	of	of	ADP
ejpam-4012	92	7	u	u	NOUN
ejpam-4012	92	8	:	:	PUNCT
ejpam-4012	92	9	ux	ux	PROPN
ejpam-4012	92	10	and	and	CCONJ
ejpam-4012	92	11	uy	uy	PROPN
ejpam-4012	92	12	need	need	VERB
ejpam-4012	92	13	not	not	PART
ejpam-4012	92	14	to	to	PART
ejpam-4012	92	15	be	be	AUX
ejpam-4012	92	16	exist	exist	VERB
ejpam-4012	92	17	even	even	ADV
ejpam-4012	92	18	if	if	SCONJ
ejpam-4012	92	19	dα	dα	PRON
ejpam-4012	93	1	xu	xu	INTJ
ejpam-4012	93	2	and	and	CCONJ
ejpam-4012	93	3	dα	dα	PROPN
ejpam-4012	93	4	y	y	PROPN
ejpam-4012	93	5	u	u	NOUN
ejpam-4012	93	6	exist	exist	VERB
ejpam-4012	93	7	,	,	PUNCT
ejpam-4012	93	8	see	see	VERB
ejpam-4012	93	9	[	[	X
ejpam-4012	93	10	7	7	NUM
ejpam-4012	93	11	]	]	PUNCT
ejpam-4012	93	12	.	.	PUNCT
ejpam-4012	94	1	let	let	VERB
ejpam-4012	94	2	u(x	u(x	NOUN
ejpam-4012	94	3	,	,	PUNCT
ejpam-4012	94	4	y	y	NOUN
ejpam-4012	94	5	)	)	PUNCT
ejpam-4012	95	1	=	=	SYM
ejpam-4012	96	1	p	p	X
ejpam-4012	96	2	(	(	PUNCT
ejpam-4012	96	3	x)q(y	x)q(y	PROPN
ejpam-4012	96	4	)	)	PUNCT
ejpam-4012	96	5	.	.	PUNCT
ejpam-4012	97	1	substitute	substitute	NOUN
ejpam-4012	97	2	in	in	ADP
ejpam-4012	97	3	the	the	DET
ejpam-4012	97	4	equation	equation	NOUN
ejpam-4012	97	5	(	(	PUNCT
ejpam-4012	97	6	6	6	NUM
ejpam-4012	97	7	)	)	PUNCT
ejpam-4012	97	8	to	to	PART
ejpam-4012	97	9	get	get	VERB
ejpam-4012	97	10	p	p	PROPN
ejpam-4012	97	11	2β(x)q(y)−	2β(x)q(y)−	NUM
ejpam-4012	97	12	c2p	c2p	NOUN
ejpam-4012	97	13	(	(	PUNCT
ejpam-4012	97	14	x)q2α(y	x)q2α(y	X
ejpam-4012	97	15	)	)	PUNCT
ejpam-4012	98	1	=	=	SYM
ejpam-4012	98	2	p	p	X
ejpam-4012	98	3	(	(	PUNCT
ejpam-4012	98	4	x)qα(y	x)qα(y	PROPN
ejpam-4012	98	5	)	)	PUNCT
ejpam-4012	98	6	.	.	PUNCT
ejpam-4012	99	1	simplifying	simplify	VERB
ejpam-4012	99	2	to	to	PART
ejpam-4012	99	3	get	get	VERB
ejpam-4012	99	4	p	p	PROPN
ejpam-4012	99	5	2β(x)q(y)−	2β(x)q(y)−	NUM
ejpam-4012	99	6	c2p	c2p	NOUN
ejpam-4012	99	7	(	(	PUNCT
ejpam-4012	99	8	x)q2α(y)−	x)q2α(y)−	PROPN
ejpam-4012	99	9	p	p	X
ejpam-4012	99	10	(	(	PUNCT
ejpam-4012	99	11	x)qα(y	x)qα(y	PROPN
ejpam-4012	99	12	)	)	PUNCT
ejpam-4012	99	13	=	=	SYM
ejpam-4012	99	14	0	0	NUM
ejpam-4012	99	15	,	,	PUNCT
ejpam-4012	99	16	p	p	NOUN
ejpam-4012	99	17	2β(x)q(y)−	2β(x)q(y)−	NOUN
ejpam-4012	99	18	p	p	X
ejpam-4012	99	19	(	(	PUNCT
ejpam-4012	99	20	x	x	NOUN
ejpam-4012	99	21	)	)	PUNCT
ejpam-4012	99	22	(	(	PUNCT
ejpam-4012	99	23	c2q2α(y	c2q2α(y	PROPN
ejpam-4012	99	24	)	)	PUNCT
ejpam-4012	99	25	+	+	NOUN
ejpam-4012	99	26	qα(y	qα(y	NOUN
ejpam-4012	99	27	)	)	PUNCT
ejpam-4012	99	28	)	)	PUNCT
ejpam-4012	100	1	=	=	SYM
ejpam-4012	100	2	0	0	NUM
ejpam-4012	100	3	,	,	PUNCT
ejpam-4012	100	4	p	p	NOUN
ejpam-4012	100	5	2β(x)q(y	2β(x)q(y	ADJ
ejpam-4012	100	6	)	)	PUNCT
ejpam-4012	100	7	=	=	SYM
ejpam-4012	101	1	p	p	X
ejpam-4012	101	2	(	(	PUNCT
ejpam-4012	101	3	x	x	NOUN
ejpam-4012	101	4	)	)	PUNCT
ejpam-4012	101	5	(	(	PUNCT
ejpam-4012	101	6	c2q2α(y	c2q2α(y	PROPN
ejpam-4012	101	7	)	)	PUNCT
ejpam-4012	101	8	+	+	NOUN
ejpam-4012	101	9	qα(y	qα(y	NOUN
ejpam-4012	101	10	)	)	PUNCT
ejpam-4012	101	11	)	)	PUNCT
ejpam-4012	101	12	.	.	PUNCT
ejpam-4012	102	1	from	from	ADP
ejpam-4012	102	2	which	which	PRON
ejpam-4012	102	3	we	we	PRON
ejpam-4012	102	4	obtain	obtain	VERB
ejpam-4012	102	5	p	p	ADJ
ejpam-4012	102	6	2β(x	2β(x	NOUN
ejpam-4012	102	7	)	)	PUNCT
ejpam-4012	103	1	p	p	NOUN
ejpam-4012	103	2	(	(	PUNCT
ejpam-4012	103	3	x	x	NOUN
ejpam-4012	103	4	)	)	PUNCT
ejpam-4012	103	5	=	=	SYM
ejpam-4012	103	6	c2q2α(y	c2q2α(y	PROPN
ejpam-4012	103	7	)	)	PUNCT
ejpam-4012	103	8	+	+	NOUN
ejpam-4012	103	9	qα(y	qα(y	NOUN
ejpam-4012	103	10	)	)	PUNCT
ejpam-4012	103	11	q(y	q(y	X
ejpam-4012	103	12	)	)	PUNCT
ejpam-4012	103	13	=	=	SYM
ejpam-4012	103	14	λ	λ	NOUN
ejpam-4012	103	15	.	.	PUNCT
ejpam-4012	104	1	since	since	SCONJ
ejpam-4012	104	2	x	x	PROPN
ejpam-4012	104	3	and	and	CCONJ
ejpam-4012	104	4	y	y	PROPN
ejpam-4012	104	5	are	be	AUX
ejpam-4012	104	6	independent	independent	ADJ
ejpam-4012	104	7	variables	variable	NOUN
ejpam-4012	104	8	,	,	PUNCT
ejpam-4012	104	9	then	then	ADV
ejpam-4012	104	10	we	we	PRON
ejpam-4012	104	11	get	get	VERB
ejpam-4012	104	12	p	p	ADJ
ejpam-4012	104	13	2β(x	2β(x	NOUN
ejpam-4012	104	14	)	)	PUNCT
ejpam-4012	105	1	p	p	NOUN
ejpam-4012	105	2	(	(	PUNCT
ejpam-4012	105	3	x	x	NOUN
ejpam-4012	105	4	)	)	PUNCT
ejpam-4012	105	5	=	=	SYM
ejpam-4012	105	6	λ	λ	PROPN
ejpam-4012	105	7	i.	i.	PROPN
ejpam-4012	105	8	benkemache	benkemache	PROPN
ejpam-4012	105	9	,	,	PUNCT
ejpam-4012	105	10	m.	m.	NOUN
ejpam-4012	105	11	al	al	PROPN
ejpam-4012	105	12	horani	horani	PROPN
ejpam-4012	105	13	,	,	PUNCT
ejpam-4012	105	14	r.	r.	PROPN
ejpam-4012	105	15	khalil	khalil	PROPN
ejpam-4012	105	16	/	/	SYM
ejpam-4012	105	17	eur	eur	PROPN
ejpam-4012	105	18	.	.	PUNCT
ejpam-4012	106	1	j.	j.	PROPN
ejpam-4012	106	2	pure	pure	PROPN
ejpam-4012	106	3	appl	appl	PROPN
ejpam-4012	106	4	.	.	PROPN
ejpam-4012	106	5	math	math	PROPN
ejpam-4012	106	6	,	,	PUNCT
ejpam-4012	106	7	14	14	NUM
ejpam-4012	106	8	(	(	PUNCT
ejpam-4012	106	9	3	3	NUM
ejpam-4012	106	10	)	)	PUNCT
ejpam-4012	106	11	(	(	PUNCT
ejpam-4012	106	12	2021	2021	NUM
ejpam-4012	106	13	)	)	PUNCT
ejpam-4012	106	14	,	,	PUNCT
ejpam-4012	106	15	942	942	NUM
ejpam-4012	106	16	-	-	SYM
ejpam-4012	106	17	948	948	NUM
ejpam-4012	106	18	946	946	NUM
ejpam-4012	106	19	and	and	CCONJ
ejpam-4012	106	20	c2q2α(y	c2q2α(y	PROPN
ejpam-4012	106	21	)	)	PUNCT
ejpam-4012	107	1	+	+	NOUN
ejpam-4012	107	2	qα(y	qα(y	NOUN
ejpam-4012	107	3	)	)	PUNCT
ejpam-4012	107	4	q(y	q(y	X
ejpam-4012	107	5	)	)	PUNCT
ejpam-4012	108	1	=	=	SYM
ejpam-4012	108	2	λ	λ	NOUN
ejpam-4012	108	3	.	.	PUNCT
ejpam-4012	109	1	simplifying	simplify	VERB
ejpam-4012	109	2	to	to	PART
ejpam-4012	109	3	get	get	VERB
ejpam-4012	109	4	p	p	PROPN
ejpam-4012	109	5	2β(x)−	2β(x)−	NUM
ejpam-4012	109	6	λp	λp	PRON
ejpam-4012	109	7	(	(	PUNCT
ejpam-4012	109	8	x	x	X
ejpam-4012	109	9	)	)	PUNCT
ejpam-4012	109	10	=	=	SYM
ejpam-4012	109	11	0	0	PUNCT
ejpam-4012	109	12	(	(	PUNCT
ejpam-4012	109	13	7	7	NUM
ejpam-4012	109	14	)	)	PUNCT
ejpam-4012	109	15	and	and	CCONJ
ejpam-4012	109	16	c2q2α(y	c2q2α(y	PROPN
ejpam-4012	109	17	)	)	PUNCT
ejpam-4012	110	1	+	+	NOUN
ejpam-4012	110	2	qα(y)−	qα(y)−	PROPN
ejpam-4012	110	3	λq(y	λq(y	PUNCT
ejpam-4012	110	4	)	)	PUNCT
ejpam-4012	110	5	=	=	SYM
ejpam-4012	110	6	0	0	X
ejpam-4012	110	7	.	.	PUNCT
ejpam-4012	111	1	(	(	PUNCT
ejpam-4012	111	2	8)	8)	NUM
ejpam-4012	111	3	let	let	VERB
ejpam-4012	111	4	us	we	PRON
ejpam-4012	111	5	first	first	ADJ
ejpam-4012	111	6	deal	deal	VERB
ejpam-4012	111	7	with	with	ADP
ejpam-4012	111	8	equation	equation	NOUN
ejpam-4012	111	9	(	(	PUNCT
ejpam-4012	111	10	7	7	NUM
ejpam-4012	111	11	)	)	PUNCT
ejpam-4012	111	12	.	.	PUNCT
ejpam-4012	112	1	there	there	PRON
ejpam-4012	112	2	are	be	VERB
ejpam-4012	112	3	three	three	NUM
ejpam-4012	112	4	possibilities	possibility	NOUN
ejpam-4012	112	5	for	for	ADP
ejpam-4012	112	6	λ	λ	NOUN
ejpam-4012	112	7	:	:	PUNCT
ejpam-4012	112	8	case	case	NOUN
ejpam-4012	112	9	1	1	NUM
ejpam-4012	112	10	:	:	PUNCT
ejpam-4012	112	11	λ	λ	X
ejpam-4012	112	12	=	=	SYM
ejpam-4012	112	13	0	0	NUM
ejpam-4012	112	14	then	then	ADV
ejpam-4012	112	15	equation	equation	NOUN
ejpam-4012	112	16	(	(	PUNCT
ejpam-4012	112	17	7	7	X
ejpam-4012	112	18	)	)	PUNCT
ejpam-4012	112	19	becomes	become	VERB
ejpam-4012	112	20	p	p	NOUN
ejpam-4012	112	21	2β(x	2β(x	NOUN
ejpam-4012	112	22	)	)	PUNCT
ejpam-4012	112	23	=	=	SYM
ejpam-4012	113	1	0	0	X
ejpam-4012	113	2	.	.	PUNCT
ejpam-4012	114	1	using	use	VERB
ejpam-4012	114	2	the	the	DET
ejpam-4012	114	3	result	result	NOUN
ejpam-4012	114	4	in	in	ADP
ejpam-4012	114	5	[	[	X
ejpam-4012	114	6	1	1	NUM
ejpam-4012	114	7	]	]	PUNCT
ejpam-4012	114	8	,	,	PUNCT
ejpam-4012	114	9	we	we	PRON
ejpam-4012	114	10	see	see	VERB
ejpam-4012	114	11	that	that	SCONJ
ejpam-4012	114	12	p	p	X
ejpam-4012	114	13	(	(	PUNCT
ejpam-4012	114	14	x	x	NOUN
ejpam-4012	114	15	)	)	PUNCT
ejpam-4012	114	16	=	=	SYM
ejpam-4012	114	17	c1	c1	PROPN
ejpam-4012	114	18	xβ	xβ	PROPN
ejpam-4012	114	19	β	β	PROPN
ejpam-4012	114	20	+	+	X
ejpam-4012	114	21	c2	c2	PROPN
ejpam-4012	114	22	.	.	PUNCT
ejpam-4012	115	1	by	by	ADP
ejpam-4012	115	2	using	use	VERB
ejpam-4012	115	3	the	the	DET
ejpam-4012	115	4	condition	condition	NOUN
ejpam-4012	115	5	u(0	u(0	PROPN
ejpam-4012	115	6	,	,	PUNCT
ejpam-4012	115	7	y	y	PROPN
ejpam-4012	115	8	)	)	PUNCT
ejpam-4012	115	9	=	=	SYM
ejpam-4012	115	10	0	0	NUM
ejpam-4012	115	11	,	,	PUNCT
ejpam-4012	115	12	we	we	PRON
ejpam-4012	115	13	get	get	VERB
ejpam-4012	115	14	c2	c2	PROPN
ejpam-4012	115	15	=	=	SYM
ejpam-4012	115	16	0	0	PROPN
ejpam-4012	115	17	.	.	PUNCT
ejpam-4012	116	1	another	another	DET
ejpam-4012	116	2	use	use	NOUN
ejpam-4012	116	3	of	of	ADP
ejpam-4012	116	4	condition	condition	NOUN
ejpam-4012	116	5	u(l	u(l	ADJ
ejpam-4012	116	6	,	,	PUNCT
ejpam-4012	116	7	y	y	NOUN
ejpam-4012	116	8	)	)	PUNCT
ejpam-4012	117	1	=	=	SYM
ejpam-4012	117	2	0	0	NUM
ejpam-4012	118	1	we	we	PRON
ejpam-4012	118	2	get	get	VERB
ejpam-4012	118	3	c1	c1	NOUN
ejpam-4012	118	4	=	=	PUNCT
ejpam-4012	119	1	0	0	X
ejpam-4012	119	2	.	.	PUNCT
ejpam-4012	120	1	so	so	ADV
ejpam-4012	120	2	,	,	PUNCT
ejpam-4012	120	3	p	p	X
ejpam-4012	120	4	(	(	PUNCT
ejpam-4012	120	5	x	x	NOUN
ejpam-4012	120	6	)	)	PUNCT
ejpam-4012	120	7	=	=	SYM
ejpam-4012	120	8	0	0	X
ejpam-4012	120	9	.	.	PUNCT
ejpam-4012	121	1	thus	thus	ADV
ejpam-4012	121	2	λ	λ	X
ejpam-4012	121	3	=	=	SYM
ejpam-4012	121	4	0	0	NUM
ejpam-4012	121	5	gives	give	VERB
ejpam-4012	121	6	the	the	DET
ejpam-4012	121	7	trivial	trivial	ADJ
ejpam-4012	121	8	solution	solution	NOUN
ejpam-4012	121	9	.	.	PUNCT
ejpam-4012	122	1	case	case	NOUN
ejpam-4012	122	2	2	2	NUM
ejpam-4012	122	3	:	:	PUNCT
ejpam-4012	122	4	λ	λ	X
ejpam-4012	122	5	=	=	SYM
ejpam-4012	123	1	µ2	µ2	PROPN
ejpam-4012	123	2	>	>	X
ejpam-4012	123	3	0	0	PUNCT
ejpam-4012	124	1	then	then	ADV
ejpam-4012	124	2	equation	equation	NOUN
ejpam-4012	124	3	(	(	PUNCT
ejpam-4012	124	4	7	7	X
ejpam-4012	124	5	)	)	PUNCT
ejpam-4012	124	6	becomes	become	VERB
ejpam-4012	124	7	p	p	NOUN
ejpam-4012	124	8	2β(x	2β(x	NOUN
ejpam-4012	124	9	)	)	PUNCT
ejpam-4012	124	10	=	=	PUNCT
ejpam-4012	124	11	µ2p	µ2p	X
ejpam-4012	124	12	(	(	PUNCT
ejpam-4012	124	13	x	x	X
ejpam-4012	124	14	)	)	PUNCT
ejpam-4012	124	15	.	.	PUNCT
ejpam-4012	125	1	using	use	VERB
ejpam-4012	125	2	the	the	DET
ejpam-4012	125	3	result	result	NOUN
ejpam-4012	125	4	in	in	ADP
ejpam-4012	125	5	[	[	X
ejpam-4012	125	6	5	5	NUM
ejpam-4012	125	7	]	]	PUNCT
ejpam-4012	125	8	,	,	PUNCT
ejpam-4012	125	9	we	we	PRON
ejpam-4012	125	10	see	see	VERB
ejpam-4012	125	11	that	that	SCONJ
ejpam-4012	125	12	p	p	X
ejpam-4012	125	13	(	(	PUNCT
ejpam-4012	125	14	x	x	NOUN
ejpam-4012	125	15	)	)	PUNCT
ejpam-4012	125	16	=	=	SYM
ejpam-4012	125	17	c1e	c1e	NOUN
ejpam-4012	125	18	µx	µx	VERB
ejpam-4012	125	19	β	β	X
ejpam-4012	125	20	β	β	X
ejpam-4012	125	21	+	+	CCONJ
ejpam-4012	125	22	c2e	c2e	ADJ
ejpam-4012	125	23	−µx	−µx	ADV
ejpam-4012	125	24	β	β	X
ejpam-4012	125	25	β	β	X
ejpam-4012	125	26	.	.	PUNCT
ejpam-4012	126	1	using	use	VERB
ejpam-4012	126	2	the	the	DET
ejpam-4012	126	3	condition	condition	NOUN
ejpam-4012	126	4	u(0	u(0	PROPN
ejpam-4012	126	5	,	,	PUNCT
ejpam-4012	126	6	y	y	PROPN
ejpam-4012	126	7	)	)	PUNCT
ejpam-4012	126	8	=	=	SYM
ejpam-4012	126	9	0	0	NUM
ejpam-4012	126	10	,	,	PUNCT
ejpam-4012	126	11	we	we	PRON
ejpam-4012	126	12	get	get	VERB
ejpam-4012	126	13	c1	c1	NOUN
ejpam-4012	126	14	=	=	PROPN
ejpam-4012	126	15	−c2	−c2	PROPN
ejpam-4012	126	16	.	.	PUNCT
ejpam-4012	127	1	so	so	ADV
ejpam-4012	127	2	,	,	PUNCT
ejpam-4012	127	3	p	p	X
ejpam-4012	127	4	(	(	PUNCT
ejpam-4012	127	5	x	x	NOUN
ejpam-4012	127	6	)	)	PUNCT
ejpam-4012	127	7	=	=	SYM
ejpam-4012	128	1	2c1	2c1	NUM
ejpam-4012	128	2	sinh(µx	sinh(µx	ADJ
ejpam-4012	128	3	β	β	X
ejpam-4012	128	4	β	β	NOUN
ejpam-4012	128	5	)	)	PUNCT
ejpam-4012	128	6	.	.	PUNCT
ejpam-4012	129	1	another	another	DET
ejpam-4012	129	2	use	use	NOUN
ejpam-4012	129	3	of	of	ADP
ejpam-4012	129	4	condition	condition	NOUN
ejpam-4012	129	5	u(l	u(l	ADJ
ejpam-4012	129	6	,	,	PUNCT
ejpam-4012	129	7	y	y	NOUN
ejpam-4012	129	8	)	)	PUNCT
ejpam-4012	130	1	=	=	SYM
ejpam-4012	130	2	0	0	NUM
ejpam-4012	131	1	we	we	PRON
ejpam-4012	131	2	get	get	VERB
ejpam-4012	131	3	2c1	2c1	NUM
ejpam-4012	131	4	sinh(µl	sinh(µl	NOUN
ejpam-4012	131	5	β	β	X
ejpam-4012	131	6	β	β	X
ejpam-4012	131	7	)	)	PUNCT
ejpam-4012	132	1	=	=	PUNCT
ejpam-4012	132	2	0	0	X
ejpam-4012	132	3	.	.	PUNCT
ejpam-4012	133	1	hence	hence	ADV
ejpam-4012	133	2	,	,	PUNCT
ejpam-4012	133	3	c1	c1	PROPN
ejpam-4012	133	4	6=	6=	ADP
ejpam-4012	133	5	0	0	NUM
ejpam-4012	133	6	and	and	CCONJ
ejpam-4012	133	7	so	so	ADV
ejpam-4012	133	8	µ	µ	ADV
ejpam-4012	133	9	=	=	SYM
ejpam-4012	133	10	0	0	NUM
ejpam-4012	133	11	.	.	PUNCT
ejpam-4012	134	1	thus	thus	ADV
ejpam-4012	134	2	,	,	PUNCT
ejpam-4012	134	3	p	p	X
ejpam-4012	134	4	(	(	PUNCT
ejpam-4012	134	5	x	x	NOUN
ejpam-4012	134	6	)	)	PUNCT
ejpam-4012	134	7	=	=	SYM
ejpam-4012	134	8	0	0	X
ejpam-4012	134	9	.	.	PUNCT
ejpam-4012	134	10	therefore	therefore	ADV
ejpam-4012	134	11	λ	λ	X
ejpam-4012	134	12	>	>	X
ejpam-4012	134	13	0	0	PUNCT
ejpam-4012	134	14	gives	give	VERB
ejpam-4012	134	15	the	the	DET
ejpam-4012	134	16	trivial	trivial	ADJ
ejpam-4012	134	17	solution	solution	NOUN
ejpam-4012	134	18	.	.	PUNCT
ejpam-4012	135	1	case	case	NOUN
ejpam-4012	135	2	3	3	NUM
ejpam-4012	135	3	:	:	PUNCT
ejpam-4012	136	1	λ	λ	X
ejpam-4012	136	2	=	=	PUNCT
ejpam-4012	136	3	−µ2	−µ2	PROPN
ejpam-4012	136	4	<	<	X
ejpam-4012	136	5	0	0	PUNCT
ejpam-4012	136	6	then	then	ADV
ejpam-4012	136	7	equation	equation	NOUN
ejpam-4012	136	8	(	(	PUNCT
ejpam-4012	136	9	7	7	X
ejpam-4012	136	10	)	)	PUNCT
ejpam-4012	136	11	becomes	become	VERB
ejpam-4012	136	12	p	p	NOUN
ejpam-4012	136	13	2β(x	2β(x	NOUN
ejpam-4012	136	14	)	)	PUNCT
ejpam-4012	137	1	+	+	CCONJ
ejpam-4012	137	2	µ2p	µ2p	SYM
ejpam-4012	137	3	(	(	PUNCT
ejpam-4012	137	4	x	x	X
ejpam-4012	137	5	)	)	PUNCT
ejpam-4012	137	6	=	=	SYM
ejpam-4012	137	7	0	0	PUNCT
ejpam-4012	137	8	.	.	PUNCT
ejpam-4012	138	1	using	use	VERB
ejpam-4012	138	2	results	result	NOUN
ejpam-4012	138	3	in	in	ADP
ejpam-4012	138	4	[	[	X
ejpam-4012	138	5	5	5	NUM
ejpam-4012	138	6	]	]	PUNCT
ejpam-4012	138	7	,	,	PUNCT
ejpam-4012	138	8	we	we	PRON
ejpam-4012	138	9	get	get	VERB
ejpam-4012	138	10	p	p	NOUN
ejpam-4012	138	11	(	(	PUNCT
ejpam-4012	138	12	x	x	NOUN
ejpam-4012	138	13	)	)	PUNCT
ejpam-4012	138	14	=	=	SYM
ejpam-4012	138	15	c1	c1	PROPN
ejpam-4012	138	16	cos(µ	cos(µ	PROPN
ejpam-4012	138	17	xβ	xβ	PROPN
ejpam-4012	138	18	β	β	PROPN
ejpam-4012	138	19	)	)	PUNCT
ejpam-4012	139	1	+	+	CCONJ
ejpam-4012	139	2	c2	c2	PROPN
ejpam-4012	139	3	sin(µ	sin(µ	PROPN
ejpam-4012	139	4	xβ	xβ	PROPN
ejpam-4012	139	5	β	β	NOUN
ejpam-4012	139	6	)	)	PUNCT
ejpam-4012	139	7	.	.	PUNCT
ejpam-4012	140	1	applying	apply	VERB
ejpam-4012	140	2	the	the	DET
ejpam-4012	140	3	condition	condition	NOUN
ejpam-4012	140	4	u(0	u(0	PROPN
ejpam-4012	140	5	,	,	PUNCT
ejpam-4012	140	6	y	y	PROPN
ejpam-4012	140	7	)	)	PUNCT
ejpam-4012	141	1	=	=	SYM
ejpam-4012	141	2	0	0	NUM
ejpam-4012	142	1	we	we	PRON
ejpam-4012	142	2	get	get	VERB
ejpam-4012	142	3	c1	c1	NOUN
ejpam-4012	142	4	=	=	PUNCT
ejpam-4012	143	1	0	0	X
ejpam-4012	143	2	.	.	PUNCT
ejpam-4012	144	1	so	so	ADV
ejpam-4012	144	2	,	,	PUNCT
ejpam-4012	144	3	p	p	X
ejpam-4012	144	4	(	(	PUNCT
ejpam-4012	144	5	x	x	NOUN
ejpam-4012	144	6	)	)	PUNCT
ejpam-4012	144	7	=	=	SYM
ejpam-4012	144	8	c2	c2	PROPN
ejpam-4012	144	9	sin(µx	sin(µx	VERB
ejpam-4012	144	10	β	β	X
ejpam-4012	144	11	β	β	NOUN
ejpam-4012	144	12	)	)	PUNCT
ejpam-4012	144	13	.	.	PUNCT
ejpam-4012	145	1	another	another	DET
ejpam-4012	145	2	use	use	NOUN
ejpam-4012	145	3	of	of	ADP
ejpam-4012	145	4	condition	condition	NOUN
ejpam-4012	145	5	u(l	u(l	ADJ
ejpam-4012	145	6	,	,	PUNCT
ejpam-4012	145	7	y	y	NOUN
ejpam-4012	145	8	)	)	PUNCT
ejpam-4012	145	9	=	=	SYM
ejpam-4012	145	10	0	0	PROPN
ejpam-4012	145	11	gives	give	VERB
ejpam-4012	145	12	c2	c2	PROPN
ejpam-4012	145	13	sin(µl	sin(µl	NOUN
ejpam-4012	145	14	β	β	X
ejpam-4012	145	15	β	β	X
ejpam-4012	145	16	)	)	PUNCT
ejpam-4012	146	1	=	=	PUNCT
ejpam-4012	146	2	0	0	X
ejpam-4012	146	3	.	.	PUNCT
ejpam-4012	147	1	then	then	ADV
ejpam-4012	147	2	c2	c2	PROPN
ejpam-4012	147	3	6=	6=	PRON
ejpam-4012	147	4	0	0	NUM
ejpam-4012	148	1	and	and	CCONJ
ejpam-4012	148	2	so	so	ADV
ejpam-4012	148	3	sin(µl	sin(µl	PROPN
ejpam-4012	148	4	β	β	X
ejpam-4012	148	5	β	β	X
ejpam-4012	148	6	)	)	PUNCT
ejpam-4012	149	1	=	=	PUNCT
ejpam-4012	149	2	0	0	X
ejpam-4012	149	3	.	.	PUNCT
ejpam-4012	150	1	hence	hence	ADV
ejpam-4012	150	2	,	,	PUNCT
ejpam-4012	150	3	µ	µ	X
ejpam-4012	150	4	=	=	X
ejpam-4012	150	5	nπ	nπ	NOUN
ejpam-4012	150	6	β	β	PROPN
ejpam-4012	150	7	lβ	lβ	PROPN
ejpam-4012	150	8	.	.	PUNCT
ejpam-4012	151	1	(	(	PUNCT
ejpam-4012	151	2	9	9	NUM
ejpam-4012	151	3	)	)	PUNCT
ejpam-4012	151	4	so	so	ADV
ejpam-4012	151	5	,	,	PUNCT
ejpam-4012	151	6	p	p	X
ejpam-4012	151	7	(	(	PUNCT
ejpam-4012	151	8	x	x	NOUN
ejpam-4012	151	9	)	)	PUNCT
ejpam-4012	151	10	=	=	SYM
ejpam-4012	151	11	cn	cn	X
ejpam-4012	151	12	sin(nπ	sin(nπ	PROPN
ejpam-4012	151	13	xβ	xβ	NOUN
ejpam-4012	151	14	lβ	lβ	ADP
ejpam-4012	151	15	)	)	PUNCT
ejpam-4012	151	16	,	,	PUNCT
ejpam-4012	151	17	n	n	NOUN
ejpam-4012	151	18	=	=	SYM
ejpam-4012	151	19	1	1	NUM
ejpam-4012	151	20	,	,	PUNCT
ejpam-4012	151	21	2	2	NUM
ejpam-4012	151	22	,	,	PUNCT
ejpam-4012	151	23	...	...	PUNCT
ejpam-4012	151	24	.	.	PUNCT
ejpam-4012	152	1	(	(	PUNCT
ejpam-4012	152	2	10	10	NUM
ejpam-4012	152	3	)	)	PUNCT
ejpam-4012	152	4	i.	i.	PROPN
ejpam-4012	152	5	benkemache	benkemache	PROPN
ejpam-4012	152	6	,	,	PUNCT
ejpam-4012	152	7	m.	m.	NOUN
ejpam-4012	152	8	al	al	PROPN
ejpam-4012	152	9	horani	horani	PROPN
ejpam-4012	152	10	,	,	PUNCT
ejpam-4012	152	11	r.	r.	PROPN
ejpam-4012	152	12	khalil	khalil	PROPN
ejpam-4012	152	13	/	/	SYM
ejpam-4012	152	14	eur	eur	PROPN
ejpam-4012	152	15	.	.	PUNCT
ejpam-4012	153	1	j.	j.	PROPN
ejpam-4012	153	2	pure	pure	PROPN
ejpam-4012	153	3	appl	appl	PROPN
ejpam-4012	153	4	.	.	PROPN
ejpam-4012	153	5	math	math	PROPN
ejpam-4012	153	6	,	,	PUNCT
ejpam-4012	153	7	14	14	NUM
ejpam-4012	153	8	(	(	PUNCT
ejpam-4012	153	9	3	3	NUM
ejpam-4012	153	10	)	)	PUNCT
ejpam-4012	153	11	(	(	PUNCT
ejpam-4012	153	12	2021	2021	NUM
ejpam-4012	153	13	)	)	PUNCT
ejpam-4012	153	14	,	,	PUNCT
ejpam-4012	153	15	942	942	NUM
ejpam-4012	153	16	-	-	SYM
ejpam-4012	153	17	948	948	NUM
ejpam-4012	153	18	947	947	NUM
ejpam-4012	153	19	now	now	ADV
ejpam-4012	153	20	,	,	PUNCT
ejpam-4012	153	21	we	we	PRON
ejpam-4012	153	22	go	go	VERB
ejpam-4012	153	23	back	back	ADV
ejpam-4012	153	24	to	to	ADP
ejpam-4012	153	25	equation	equation	NOUN
ejpam-4012	153	26	(	(	PUNCT
ejpam-4012	153	27	8)	8)	NUM
ejpam-4012	153	28	.	.	PUNCT
ejpam-4012	154	1	substituting	substitute	VERB
ejpam-4012	154	2	the	the	DET
ejpam-4012	154	3	value	value	NOUN
ejpam-4012	154	4	of	of	ADP
ejpam-4012	154	5	µ	µ	PRON
ejpam-4012	154	6	that	that	PRON
ejpam-4012	154	7	we	we	PRON
ejpam-4012	154	8	got	get	VERB
ejpam-4012	154	9	in	in	ADP
ejpam-4012	154	10	(	(	PUNCT
ejpam-4012	154	11	9	9	NUM
ejpam-4012	154	12	)	)	PUNCT
ejpam-4012	154	13	,	,	PUNCT
ejpam-4012	154	14	equation	equation	NOUN
ejpam-4012	154	15	(	(	PUNCT
ejpam-4012	154	16	8)	8)	NUM
ejpam-4012	154	17	becomes	become	VERB
ejpam-4012	154	18	c2q2α(y	c2q2α(y	PROPN
ejpam-4012	154	19	)	)	PUNCT
ejpam-4012	154	20	+	+	NOUN
ejpam-4012	154	21	qα(y	qα(y	NOUN
ejpam-4012	154	22	)	)	PUNCT
ejpam-4012	155	1	+	+	SYM
ejpam-4012	155	2	µ2q(y	µ2q(y	ADJ
ejpam-4012	155	3	)	)	PUNCT
ejpam-4012	155	4	=	=	SYM
ejpam-4012	156	1	0	0	NUM
ejpam-4012	156	2	.	.	PUNCT
ejpam-4012	157	1	another	another	DET
ejpam-4012	157	2	use	use	NOUN
ejpam-4012	157	3	of	of	ADP
ejpam-4012	157	4	the	the	DET
ejpam-4012	157	5	result	result	NOUN
ejpam-4012	157	6	in	in	ADP
ejpam-4012	157	7	[	[	X
ejpam-4012	157	8	5	5	NUM
ejpam-4012	157	9	]	]	PUNCT
ejpam-4012	157	10	,	,	PUNCT
ejpam-4012	157	11	we	we	PRON
ejpam-4012	157	12	get	get	VERB
ejpam-4012	157	13	two	two	NUM
ejpam-4012	157	14	cases	case	NOUN
ejpam-4012	157	15	under	under	ADP
ejpam-4012	157	16	consideration	consideration	NOUN
ejpam-4012	157	17	:	:	PUNCT
ejpam-4012	157	18	case	case	NOUN
ejpam-4012	157	19	i	i	PRON
ejpam-4012	157	20	:	:	PUNCT
ejpam-4012	157	21	1−	1−	NUM
ejpam-4012	157	22	4µ2c2	4µ2c2	NUM
ejpam-4012	157	23	>	>	X
ejpam-4012	157	24	0	0	X
ejpam-4012	157	25	.	.	PUNCT
ejpam-4012	158	1	µ2	µ2	VERB
ejpam-4012	158	2	<	<	X
ejpam-4012	158	3	1	1	NUM
ejpam-4012	158	4	,	,	PUNCT
ejpam-4012	158	5	|	|	ADV
ejpam-4012	158	6	µ	µ	X
ejpam-4012	158	7	|	|	NOUN
ejpam-4012	158	8	<	<	X
ejpam-4012	158	9	1	1	NUM
ejpam-4012	158	10	,	,	PUNCT
ejpam-4012	158	11	1−	1−	NUM
ejpam-4012	158	12	4µ2c2	4µ2c2	NUM
ejpam-4012	158	13	=	=	SYM
ejpam-4012	158	14	(	(	PUNCT
ejpam-4012	158	15	√	√	NUM
ejpam-4012	158	16	1−	1−	NUM
ejpam-4012	158	17	4µ2c2)2	4µ2c2)2	NUM
ejpam-4012	158	18	.	.	PUNCT
ejpam-4012	159	1	then	then	ADV
ejpam-4012	159	2	we	we	PRON
ejpam-4012	159	3	get	get	VERB
ejpam-4012	159	4	,	,	PUNCT
ejpam-4012	159	5	r	r	NOUN
ejpam-4012	159	6	=	=	PUNCT
ejpam-4012	159	7	−1±	−1±	NOUN
ejpam-4012	159	8	√	√	NUM
ejpam-4012	159	9	1−	1−	NUM
ejpam-4012	159	10	4µ2c2	4µ2c2	NUM
ejpam-4012	159	11	2c2	2c2	NUM
ejpam-4012	159	12	.	.	PUNCT
ejpam-4012	160	1	so	so	ADV
ejpam-4012	160	2	q(y	q(y	X
ejpam-4012	160	3	)	)	PUNCT
ejpam-4012	160	4	=	=	PUNCT
ejpam-4012	160	5	c1e	c1e	NOUN
ejpam-4012	160	6	−1	−1	NOUN
ejpam-4012	160	7	+	+	NOUN
ejpam-4012	160	8	√	√	PROPN
ejpam-4012	160	9	1−4µ2c2	1−4µ2c2	NUM
ejpam-4012	160	10	2c2	2c2	NUM
ejpam-4012	160	11	yα	yα	VERB
ejpam-4012	160	12	α	α	PROPN
ejpam-4012	160	13	+	+	CCONJ
ejpam-4012	161	1	c2e	c2e	PROPN
ejpam-4012	161	2	−1−	−1−	PROPN
ejpam-4012	161	3	√	√	NUM
ejpam-4012	162	1	1−4µ2c2	1−4µ2c2	NUM
ejpam-4012	163	1	2c2	2c2	NUM
ejpam-4012	163	2	yα	yα	VERB
ejpam-4012	163	3	α	α	X
ejpam-4012	163	4	.	.	PUNCT
ejpam-4012	164	1	using	use	VERB
ejpam-4012	164	2	condition	condition	NOUN
ejpam-4012	164	3	u(x	u(x	NOUN
ejpam-4012	164	4	,	,	PUNCT
ejpam-4012	164	5	0	0	NUM
ejpam-4012	164	6	)	)	PUNCT
ejpam-4012	164	7	=	=	SYM
ejpam-4012	164	8	0	0	NUM
ejpam-4012	164	9	,	,	PUNCT
ejpam-4012	164	10	we	we	PRON
ejpam-4012	164	11	get	get	VERB
ejpam-4012	164	12	c1	c1	NOUN
ejpam-4012	164	13	=	=	PROPN
ejpam-4012	164	14	−c2	−c2	PROPN
ejpam-4012	164	15	.	.	PUNCT
ejpam-4012	165	1	so	so	ADV
ejpam-4012	165	2	,	,	PUNCT
ejpam-4012	165	3	q(y	q(y	PROPN
ejpam-4012	165	4	)	)	PUNCT
ejpam-4012	165	5	=	=	SYM
ejpam-4012	165	6	2c1	2c1	NUM
ejpam-4012	165	7	sinh	sinh	NOUN
ejpam-4012	165	8	(	(	PUNCT
ejpam-4012	165	9	−1	−1	NOUN
ejpam-4012	165	10	+	+	CCONJ
ejpam-4012	165	11	√	√	INTJ
ejpam-4012	165	12	1−	1−	NUM
ejpam-4012	165	13	4µ2c2	4µ2c2	NUM
ejpam-4012	166	1	2c2	2c2	NUM
ejpam-4012	166	2	yα	yα	VERB
ejpam-4012	166	3	α	α	NOUN
ejpam-4012	166	4	)	)	PUNCT
ejpam-4012	166	5	.	.	PUNCT
ejpam-4012	167	1	(	(	PUNCT
ejpam-4012	167	2	11	11	NUM
ejpam-4012	167	3	)	)	PUNCT
ejpam-4012	167	4	thus	thus	ADV
ejpam-4012	167	5	,	,	PUNCT
ejpam-4012	167	6	combining	combine	VERB
ejpam-4012	167	7	(	(	PUNCT
ejpam-4012	167	8	10	10	NUM
ejpam-4012	167	9	)	)	PUNCT
ejpam-4012	167	10	and	and	CCONJ
ejpam-4012	167	11	(	(	PUNCT
ejpam-4012	167	12	11	11	X
ejpam-4012	167	13	)	)	PUNCT
ejpam-4012	167	14	we	we	PRON
ejpam-4012	167	15	get	get	VERB
ejpam-4012	167	16	:	:	PUNCT
ejpam-4012	167	17	u(x	u(x	NOUN
ejpam-4012	167	18	,	,	PUNCT
ejpam-4012	167	19	y	y	NOUN
ejpam-4012	167	20	)	)	PUNCT
ejpam-4012	167	21	=	=	NOUN
ejpam-4012	168	1	∞∑	∞∑	NUM
ejpam-4012	168	2	n=1	n=1	ADP
ejpam-4012	168	3	bn	bn	NOUN
ejpam-4012	168	4	sin	sin	NOUN
ejpam-4012	168	5	(	(	PUNCT
ejpam-4012	168	6	nπ	nπ	NOUN
ejpam-4012	168	7	xβ	xβ	PROPN
ejpam-4012	168	8	lβ	lβ	PROPN
ejpam-4012	168	9	)	)	PUNCT
ejpam-4012	168	10	sinh	sinh	PROPN
ejpam-4012	168	11	−1	−1	PROPN
ejpam-4012	169	1	+	+	CCONJ
ejpam-4012	169	2	√	√	PROPN
ejpam-4012	169	3	1−	1−	NUM
ejpam-4012	169	4	4(nβπ	4(nβπ	NOUN
ejpam-4012	169	5	lβ	lβ	PROPN
ejpam-4012	169	6	)	)	PUNCT
ejpam-4012	169	7	2c2	2c2	NUM
ejpam-4012	170	1	2c2	2c2	NUM
ejpam-4012	170	2	yα	yα	VERB
ejpam-4012	170	3	α	α	DET
ejpam-4012	170	4			PROPN
ejpam-4012	170	5	.	.	PUNCT
ejpam-4012	171	1	by	by	ADP
ejpam-4012	171	2	using	use	VERB
ejpam-4012	171	3	dβ	dβ	ADP
ejpam-4012	171	4	y	y	PROPN
ejpam-4012	171	5	(	(	PUNCT
ejpam-4012	171	6	x	x	NOUN
ejpam-4012	171	7	,	,	PUNCT
ejpam-4012	171	8	0	0	NUM
ejpam-4012	171	9	)	)	PUNCT
ejpam-4012	171	10	=	=	SYM
ejpam-4012	171	11	f(x	f(x	PROPN
ejpam-4012	171	12	)	)	PUNCT
ejpam-4012	171	13	we	we	PRON
ejpam-4012	171	14	get	get	VERB
ejpam-4012	171	15	f(x	f(x	NOUN
ejpam-4012	171	16	)	)	PUNCT
ejpam-4012	172	1	=	=	PUNCT
ejpam-4012	173	1	∞∑	∞∑	NUM
ejpam-4012	173	2	n=1	n=1	PROPN
ejpam-4012	173	3	bn	bn	NOUN
ejpam-4012	173	4	−1	−1	PROPN
ejpam-4012	173	5	+	+	CCONJ
ejpam-4012	173	6	√	√	PROPN
ejpam-4012	173	7	1−	1−	NUM
ejpam-4012	173	8	4(nβπ	4(nβπ	NOUN
ejpam-4012	173	9	lβ	lβ	PROPN
ejpam-4012	173	10	)	)	PUNCT
ejpam-4012	173	11	2c2	2c2	NUM
ejpam-4012	173	12	2c2	2c2	NUM
ejpam-4012	174	1			PROPN
ejpam-4012	174	2	sin	sin	NOUN
ejpam-4012	174	3	(	(	PUNCT
ejpam-4012	174	4	nπ	nπ	NOUN
ejpam-4012	174	5	xβ	xβ	PROPN
ejpam-4012	174	6	lβ	lβ	PROPN
ejpam-4012	174	7	)	)	PUNCT
ejpam-4012	174	8	.	.	PUNCT
ejpam-4012	175	1	so	so	ADV
ejpam-4012	175	2	bn	bn	NOUN
ejpam-4012	175	3	=	=	NOUN
ejpam-4012	175	4	2β	2β	NOUN
ejpam-4012	175	5	p	p	NOUN
ejpam-4012	175	6	β	β	X
ejpam-4012	175	7	(	(	PUNCT
ejpam-4012	175	8	−1	−1	NOUN
ejpam-4012	175	9	+	+	ADP
ejpam-4012	175	10	√	√	NOUN
ejpam-4012	175	11	1−4(nβπ	1−4(nβπ	NOUN
ejpam-4012	175	12	lβ	lβ	PROPN
ejpam-4012	175	13	)	)	PUNCT
ejpam-4012	175	14	2c2	2c2	NUM
ejpam-4012	175	15	2c2	2c2	NUM
ejpam-4012	175	16	)	)	PUNCT
ejpam-4012	176	1	∫	∫	PROPN
ejpam-4012	176	2	p	p	NOUN
ejpam-4012	176	3	0	0	NUM
ejpam-4012	176	4	f(x	f(x	PROPN
ejpam-4012	176	5	)	)	PUNCT
ejpam-4012	176	6	sin	sin	NOUN
ejpam-4012	176	7	(	(	PUNCT
ejpam-4012	176	8	nπ	nπ	NOUN
ejpam-4012	176	9	xβ	xβ	PROPN
ejpam-4012	176	10	lβ	lβ	PRON
ejpam-4012	176	11	)	)	PUNCT
ejpam-4012	176	12	dx	dx	PROPN
ejpam-4012	176	13	x1−β	x1−β	PROPN
ejpam-4012	176	14	.	.	PUNCT
ejpam-4012	177	1	case	case	NOUN
ejpam-4012	177	2	ii	ii	PROPN
ejpam-4012	177	3	:	:	PUNCT
ejpam-4012	177	4	1−	1−	NUM
ejpam-4012	177	5	4µ2c2	4µ2c2	NUM
ejpam-4012	177	6	<	<	X
ejpam-4012	177	7	0	0	X
ejpam-4012	177	8	.	.	PUNCT
ejpam-4012	178	1	µ2	µ2	VERB
ejpam-4012	178	2	>	>	X
ejpam-4012	178	3	1	1	NUM
ejpam-4012	178	4	,	,	PUNCT
ejpam-4012	178	5	|	|	ADV
ejpam-4012	178	6	µ	µ	X
ejpam-4012	178	7	|	|	NOUN
ejpam-4012	178	8	>	>	X
ejpam-4012	178	9	1	1	NUM
ejpam-4012	178	10	,	,	PUNCT
ejpam-4012	178	11	1−	1−	NUM
ejpam-4012	178	12	4µ2c2	4µ2c2	NUM
ejpam-4012	179	1	=	=	PUNCT
ejpam-4012	179	2	−(4µ2c2	−(4µ2c2	PROPN
ejpam-4012	179	3	−	−	NOUN
ejpam-4012	179	4	1	1	NUM
ejpam-4012	179	5	)	)	PUNCT
ejpam-4012	179	6	=	=	NOUN
ejpam-4012	179	7	(	(	PUNCT
ejpam-4012	179	8	√	√	NUM
ejpam-4012	179	9	4µ2c2	4µ2c2	NUM
ejpam-4012	179	10	−	−	NUM
ejpam-4012	179	11	1	1	NUM
ejpam-4012	179	12	2	2	NUM
ejpam-4012	179	13	)	)	PUNCT
ejpam-4012	179	14	.	.	PUNCT
ejpam-4012	180	1	then	then	ADV
ejpam-4012	180	2	we	we	PRON
ejpam-4012	180	3	get	get	VERB
ejpam-4012	180	4	,	,	PUNCT
ejpam-4012	180	5	r	r	NOUN
ejpam-4012	180	6	=	=	PUNCT
ejpam-4012	180	7	−1±	−1±	PROPN
ejpam-4012	181	1	i	i	PRON
ejpam-4012	181	2	√	√	VERB
ejpam-4012	181	3	4µ2c2	4µ2c2	NUM
ejpam-4012	182	1	−	−	NUM
ejpam-4012	182	2	1	1	NUM
ejpam-4012	182	3	2c2	2c2	NUM
ejpam-4012	182	4	.	.	PUNCT
ejpam-4012	183	1	so	so	ADV
ejpam-4012	183	2	q(y	q(y	X
ejpam-4012	183	3	)	)	PUNCT
ejpam-4012	183	4	=	=	PROPN
ejpam-4012	183	5	c1	c1	PROPN
ejpam-4012	183	6	cos	cos	PROPN
ejpam-4012	183	7	(	(	PUNCT
ejpam-4012	183	8	−1	−1	NOUN
ejpam-4012	183	9	+	+	CCONJ
ejpam-4012	183	10	√	√	NUM
ejpam-4012	183	11	4µ2c2	4µ2c2	NUM
ejpam-4012	183	12	−	−	NUM
ejpam-4012	184	1	1	1	NUM
ejpam-4012	185	1	2c2	2c2	NUM
ejpam-4012	185	2	yα	yα	VERB
ejpam-4012	185	3	α	α	NOUN
ejpam-4012	185	4	)	)	PUNCT
ejpam-4012	186	1	+	+	CCONJ
ejpam-4012	186	2	c2	c2	PROPN
ejpam-4012	186	3	sin	sin	NOUN
ejpam-4012	186	4	(	(	PUNCT
ejpam-4012	186	5	−1	−1	NOUN
ejpam-4012	186	6	+	+	CCONJ
ejpam-4012	186	7	√	√	NUM
ejpam-4012	186	8	4µ2c2	4µ2c2	NUM
ejpam-4012	186	9	−	−	NUM
ejpam-4012	186	10	1	1	NUM
ejpam-4012	187	1	2c2	2c2	NUM
ejpam-4012	187	2	yα	yα	VERB
ejpam-4012	187	3	α	α	NOUN
ejpam-4012	187	4	)	)	PUNCT
ejpam-4012	187	5	references	reference	NOUN
ejpam-4012	187	6	948	948	NUM
ejpam-4012	187	7	by	by	ADP
ejpam-4012	187	8	using	use	VERB
ejpam-4012	187	9	condition	condition	NOUN
ejpam-4012	187	10	u(x	u(x	NOUN
ejpam-4012	187	11	,	,	PUNCT
ejpam-4012	187	12	0	0	NUM
ejpam-4012	187	13	)	)	PUNCT
ejpam-4012	187	14	=	=	SYM
ejpam-4012	187	15	0	0	NUM
ejpam-4012	188	1	we	we	PRON
ejpam-4012	188	2	get	get	VERB
ejpam-4012	188	3	c1	c1	NOUN
ejpam-4012	188	4	=	=	PUNCT
ejpam-4012	189	1	0	0	X
ejpam-4012	189	2	.	.	PUNCT
ejpam-4012	190	1	then	then	ADV
ejpam-4012	190	2	,	,	PUNCT
ejpam-4012	190	3	q(y	q(y	PROPN
ejpam-4012	190	4	)	)	PUNCT
ejpam-4012	190	5	=	=	SYM
ejpam-4012	190	6	c2	c2	PROPN
ejpam-4012	190	7	sin	sin	NOUN
ejpam-4012	190	8	(	(	PUNCT
ejpam-4012	190	9	−1	−1	NOUN
ejpam-4012	190	10	+	+	CCONJ
ejpam-4012	190	11	√	√	NUM
ejpam-4012	190	12	4µ2c2	4µ2c2	NUM
ejpam-4012	190	13	−	−	NUM
ejpam-4012	191	1	1	1	NUM
ejpam-4012	191	2	2c2	2c2	NUM
ejpam-4012	191	3	yα	yα	VERB
ejpam-4012	191	4	α	α	NOUN
ejpam-4012	191	5	)	)	PUNCT
ejpam-4012	191	6	.	.	PUNCT
ejpam-4012	192	1	(	(	PUNCT
ejpam-4012	192	2	12	12	NUM
ejpam-4012	192	3	)	)	PUNCT
ejpam-4012	192	4	thus	thus	ADV
ejpam-4012	192	5	,	,	PUNCT
ejpam-4012	192	6	(	(	PUNCT
ejpam-4012	192	7	10	10	NUM
ejpam-4012	192	8	)	)	PUNCT
ejpam-4012	192	9	and	and	CCONJ
ejpam-4012	192	10	(	(	PUNCT
ejpam-4012	192	11	12	12	NUM
ejpam-4012	192	12	)	)	PUNCT
ejpam-4012	192	13	gives	give	VERB
ejpam-4012	192	14	u(x	u(x	NOUN
ejpam-4012	192	15	,	,	PUNCT
ejpam-4012	192	16	y	y	NOUN
ejpam-4012	192	17	)	)	PUNCT
ejpam-4012	193	1	=	=	NOUN
ejpam-4012	194	1	∞∑	∞∑	NUM
ejpam-4012	194	2	n=1	n=1	ADP
ejpam-4012	194	3	bn	bn	NOUN
ejpam-4012	194	4	sin	sin	NOUN
ejpam-4012	194	5	(	(	PUNCT
ejpam-4012	194	6	nπ	nπ	NOUN
ejpam-4012	194	7	xβ	xβ	PROPN
ejpam-4012	194	8	lβ	lβ	PRON
ejpam-4012	194	9	)	)	PUNCT
ejpam-4012	194	10	sin	sin	NOUN
ejpam-4012	194	11	(	(	PUNCT
ejpam-4012	194	12	−1	−1	NOUN
ejpam-4012	194	13	+	+	CCONJ
ejpam-4012	194	14	√	√	NUM
ejpam-4012	194	15	4µ2c2	4µ2c2	NUM
ejpam-4012	194	16	−	−	NUM
ejpam-4012	194	17	1	1	NUM
ejpam-4012	194	18	2c2	2c2	NUM
ejpam-4012	194	19	yα	yα	VERB
ejpam-4012	194	20	α	α	NOUN
ejpam-4012	194	21	)	)	PUNCT
ejpam-4012	194	22	.	.	PUNCT
ejpam-4012	195	1	(	(	PUNCT
ejpam-4012	195	2	13	13	NUM
ejpam-4012	195	3	)	)	PUNCT
ejpam-4012	195	4	by	by	ADP
ejpam-4012	195	5	using	use	VERB
ejpam-4012	195	6	condition	condition	NOUN
ejpam-4012	195	7	uy(x	uy(x	ADP
ejpam-4012	195	8	,	,	PUNCT
ejpam-4012	195	9	0	0	NUM
ejpam-4012	195	10	)	)	PUNCT
ejpam-4012	195	11	=	=	SYM
ejpam-4012	195	12	f(x	f(x	PROPN
ejpam-4012	195	13	)	)	PUNCT
ejpam-4012	195	14	we	we	PRON
ejpam-4012	195	15	deduce	deduce	VERB
ejpam-4012	195	16	that	that	SCONJ
ejpam-4012	195	17	f(x	f(x	NOUN
ejpam-4012	195	18	)	)	PUNCT
ejpam-4012	196	1	=	=	PUNCT
ejpam-4012	197	1	∞∑	∞∑	NUM
ejpam-4012	197	2	n=1	n=1	PROPN
ejpam-4012	197	3	bn	bn	NOUN
ejpam-4012	197	4	−1	−1	PROPN
ejpam-4012	198	1	+	+	CCONJ
ejpam-4012	198	2	√	√	INTJ
ejpam-4012	198	3	4(nβπ	4(nβπ	NOUN
ejpam-4012	198	4	lβ	lβ	PROPN
ejpam-4012	198	5	)	)	PUNCT
ejpam-4012	198	6	2c2	2c2	NUM
ejpam-4012	199	1	−	−	NOUN
ejpam-4012	199	2	1	1	NUM
ejpam-4012	199	3	2c2	2c2	NUM
ejpam-4012	199	4			PROPN
ejpam-4012	199	5	sin	sin	NOUN
ejpam-4012	199	6	(	(	PUNCT
ejpam-4012	199	7	nπ	nπ	NOUN
ejpam-4012	199	8	xβ	xβ	PROPN
ejpam-4012	199	9	lβ	lβ	PROPN
ejpam-4012	199	10	)	)	PUNCT
ejpam-4012	199	11	.	.	PUNCT
ejpam-4012	200	1	hence	hence	ADV
ejpam-4012	200	2	,	,	PUNCT
ejpam-4012	200	3	using	use	VERB
ejpam-4012	200	4	[	[	X
ejpam-4012	200	5	3	3	NUM
ejpam-4012	200	6	]	]	PUNCT
ejpam-4012	200	7	,	,	PUNCT
ejpam-4012	200	8	we	we	PRON
ejpam-4012	200	9	find	find	VERB
ejpam-4012	200	10	bn	bn	NOUN
ejpam-4012	200	11	=	=	NOUN
ejpam-4012	200	12	2β	2β	NOUN
ejpam-4012	200	13	p	p	NOUN
ejpam-4012	200	14	β	β	X
ejpam-4012	200	15	(	(	PUNCT
ejpam-4012	200	16	−1	−1	NOUN
ejpam-4012	200	17	+	+	CCONJ
ejpam-4012	200	18	√	√	VERB
ejpam-4012	200	19	4(nβπ	4(nβπ	NOUN
ejpam-4012	200	20	lβ	lβ	PROPN
ejpam-4012	200	21	)	)	PUNCT
ejpam-4012	201	1	2c2−1	2c2−1	NUM
ejpam-4012	201	2	2c2	2c2	NUM
ejpam-4012	201	3	)	)	PUNCT
ejpam-4012	202	1	∫	∫	PROPN
ejpam-4012	203	1	p	p	NOUN
ejpam-4012	203	2	0	0	NUM
ejpam-4012	204	1	f(x)sin(nπ	f(x)sin(nπ	NUM
ejpam-4012	204	2	xβ	xβ	PROPN
ejpam-4012	205	1	lβ	lβ	PRON
ejpam-4012	205	2	)	)	PUNCT
ejpam-4012	205	3	dx	dx	PROPN
ejpam-4012	205	4	x1−β	x1−β	PROPN
ejpam-4012	205	5	where	where	SCONJ
ejpam-4012	205	6	p	p	NOUN
ejpam-4012	205	7	is	be	AUX
ejpam-4012	205	8	a	a	DET
ejpam-4012	205	9	period	period	NOUN
ejpam-4012	205	10	of	of	ADP
ejpam-4012	205	11	the	the	DET
ejpam-4012	205	12	function	function	NOUN
ejpam-4012	205	13	f	f	PROPN
ejpam-4012	205	14	which	which	PRON
ejpam-4012	205	15	equals	equal	VERB
ejpam-4012	205	16	to	to	PART
ejpam-4012	205	17	(	(	PUNCT
ejpam-4012	205	18	2βπ	2βπ	NOUN
ejpam-4012	205	19	)	)	PUNCT
ejpam-4012	205	20	1	1	NUM
ejpam-4012	205	21	β	β	NOUN
ejpam-4012	205	22	.	.	PUNCT
ejpam-4012	206	1	so	so	ADV
ejpam-4012	206	2	we	we	PRON
ejpam-4012	206	3	got	get	VERB
ejpam-4012	206	4	the	the	DET
ejpam-4012	206	5	complete	complete	ADJ
ejpam-4012	206	6	solution	solution	NOUN
ejpam-4012	206	7	of	of	ADP
ejpam-4012	206	8	the	the	DET
ejpam-4012	206	9	differential	differential	ADJ
ejpam-4012	206	10	equations	equation	NOUN
ejpam-4012	206	11	(	(	PUNCT
ejpam-4012	206	12	6	6	NUM
ejpam-4012	206	13	)	)	PUNCT
ejpam-4012	206	14	.	.	PUNCT
ejpam-4012	207	1	references	reference	NOUN
ejpam-4012	207	2	[	[	X
ejpam-4012	207	3	1	1	X
ejpam-4012	207	4	]	]	PUNCT
ejpam-4012	207	5	t.	t.	NOUN
ejpam-4012	207	6	abdeljawad	abdeljawad	NOUN
ejpam-4012	207	7	.	.	PUNCT
ejpam-4012	208	1	on	on	ADP
ejpam-4012	208	2	conformable	conformable	ADJ
ejpam-4012	208	3	fractional	fractional	ADJ
ejpam-4012	208	4	calculus	calculus	NOUN
ejpam-4012	208	5	.	.	PUNCT
ejpam-4012	209	1	journal	journal	PROPN
ejpam-4012	209	2	of	of	ADP
ejpam-4012	209	3	computational	computational	ADJ
ejpam-4012	209	4	and	and	CCONJ
ejpam-4012	209	5	applied	applied	ADJ
ejpam-4012	209	6	mathematics	mathematic	NOUN
ejpam-4012	209	7	,	,	PUNCT
ejpam-4012	209	8	259:57–66	259:57–66	NUM
ejpam-4012	209	9	,	,	PUNCT
ejpam-4012	209	10	2015	2015	NUM
ejpam-4012	209	11	.	.	PUNCT
ejpam-4012	210	1	[	[	X
ejpam-4012	210	2	2	2	X
ejpam-4012	210	3	]	]	PUNCT
ejpam-4012	210	4	w.	w.	PROPN
ejpam-4012	210	5	deeb	deeb	PROPN
ejpam-4012	210	6	and	and	CCONJ
ejpam-4012	210	7	r.	r.	PROPN
ejpam-4012	210	8	khalil	khalil	PROPN
ejpam-4012	210	9	.	.	PUNCT
ejpam-4012	211	1	best	good	ADJ
ejpam-4012	211	2	approximation	approximation	NOUN
ejpam-4012	211	3	in	in	ADP
ejpam-4012	211	4	l(x	l(x	PROPN
ejpam-4012	211	5	;	;	PUNCT
ejpam-4012	211	6	y	y	PROPN
ejpam-4012	211	7	)	)	PUNCT
ejpam-4012	211	8	.	.	PUNCT
ejpam-4012	212	1	mathematical	mathematical	ADJ
ejpam-4012	212	2	proceedings	proceeding	NOUN
ejpam-4012	212	3	of	of	ADP
ejpam-4012	212	4	the	the	DET
ejpam-4012	212	5	cambridge	cambridge	PROPN
ejpam-4012	212	6	philosophical	philosophical	ADJ
ejpam-4012	212	7	society	society	NOUN
ejpam-4012	212	8	,	,	PUNCT
ejpam-4012	212	9	104:527–531	104:527–531	NUM
ejpam-4012	212	10	,	,	PUNCT
ejpam-4012	212	11	1988	1988	NUM
ejpam-4012	212	12	.	.	PUNCT
ejpam-4012	213	1	[	[	X
ejpam-4012	213	2	3	3	X
ejpam-4012	213	3	]	]	PUNCT
ejpam-4012	213	4	m.	m.	NOUN
ejpam-4012	213	5	abu	abu	PROPN
ejpam-4012	213	6	hammad	hammad	PROPN
ejpam-4012	213	7	and	and	CCONJ
ejpam-4012	213	8	r.	r.	PROPN
ejpam-4012	213	9	khalil	khalil	PROPN
ejpam-4012	213	10	.	.	PUNCT
ejpam-4012	214	1	fractional	fractional	ADJ
ejpam-4012	214	2	fourier	fourier	PROPN
ejpam-4012	214	3	series	series	NOUN
ejpam-4012	214	4	with	with	ADP
ejpam-4012	214	5	applications	application	NOUN
ejpam-4012	214	6	.	.	PUNCT
ejpam-4012	215	1	american	american	ADJ
ejpam-4012	215	2	journal	journal	PROPN
ejpam-4012	215	3	of	of	ADP
ejpam-4012	215	4	computational	computational	ADJ
ejpam-4012	215	5	and	and	CCONJ
ejpam-4012	215	6	applied	applied	ADJ
ejpam-4012	215	7	mathematics	mathematic	NOUN
ejpam-4012	215	8	,	,	PUNCT
ejpam-4012	215	9	4(6):187–191	4(6):187–191	NUM
ejpam-4012	215	10	,	,	PUNCT
ejpam-4012	215	11	2014	2014	NUM
ejpam-4012	215	12	.	.	PUNCT
ejpam-4012	216	1	[	[	X
ejpam-4012	216	2	4	4	X
ejpam-4012	216	3	]	]	PUNCT
ejpam-4012	216	4	r.	r.	PROPN
ejpam-4012	216	5	khalil	khalil	PROPN
ejpam-4012	216	6	.	.	PUNCT
ejpam-4012	217	1	isometries	isometry	NOUN
ejpam-4012	217	2	of	of	ADP
ejpam-4012	217	3	lp	lp	NOUN
ejpam-4012	217	4	∗	∗	NOUN
ejpam-4012	217	5	∧	∧	PROPN
ejpam-4012	217	6	⊗lp	⊗lp	PROPN
ejpam-4012	217	7	.	.	PUNCT
ejpam-4012	218	1	tam	tam	PROPN
ejpam-4012	218	2	.	.	PUNCT
ejpam-4012	219	1	j.	j.	PROPN
ejpam-4012	219	2	math	math	PROPN
ejpam-4012	219	3	.	.	PROPN
ejpam-4012	219	4	,	,	PUNCT
ejpam-4012	219	5	16:77–85	16:77–85	NUM
ejpam-4012	219	6	,	,	PUNCT
ejpam-4012	219	7	1985	1985	NUM
ejpam-4012	219	8	.	.	PUNCT
ejpam-4012	220	1	[	[	X
ejpam-4012	220	2	5	5	NUM
ejpam-4012	220	3	]	]	PUNCT
ejpam-4012	220	4	r.	r.	PROPN
ejpam-4012	220	5	khalil	khalil	PROPN
ejpam-4012	220	6	m.	m.	PROPN
ejpam-4012	220	7	al	al	PROPN
ejpam-4012	220	8	-	-	PUNCT
ejpam-4012	220	9	horani	horani	PROPN
ejpam-4012	220	10	and	and	CCONJ
ejpam-4012	220	11	i.	i.	PROPN
ejpam-4012	220	12	aldarawi	aldarawi	PROPN
ejpam-4012	220	13	.	.	PUNCT
ejpam-4012	221	1	fractional	fractional	PROPN
ejpam-4012	221	2	cauchy	cauchy	PROPN
ejpam-4012	221	3	euler	euler	PROPN
ejpam-4012	221	4	differential	differential	PROPN
ejpam-4012	221	5	equation	equation	NOUN
ejpam-4012	221	6	.	.	PUNCT
ejpam-4012	222	1	j.	j.	PROPN
ejpam-4012	222	2	computational	computational	ADJ
ejpam-4012	222	3	analysis	analysis	NOUN
ejpam-4012	222	4	and	and	CCONJ
ejpam-4012	222	5	applications	application	NOUN
ejpam-4012	222	6	,	,	PUNCT
ejpam-4012	222	7	28(2):226–233	28(2):226–233	NUM
ejpam-4012	222	8	,	,	PUNCT
ejpam-4012	222	9	2019	2019	NUM
ejpam-4012	222	10	.	.	PUNCT
ejpam-4012	223	1	[	[	X
ejpam-4012	223	2	6	6	NUM
ejpam-4012	223	3	]	]	PUNCT
ejpam-4012	223	4	m.	m.	NOUN
ejpam-4012	223	5	mhailan	mhailan	PROPN
ejpam-4012	223	6	,	,	PUNCT
ejpam-4012	223	7	m.	m.	NOUN
ejpam-4012	223	8	abuhammad	abuhammad	PROPN
ejpam-4012	223	9	,	,	PUNCT
ejpam-4012	223	10	m.	m.	NOUN
ejpam-4012	223	11	alhorani	alhorani	PROPN
ejpam-4012	223	12	,	,	PUNCT
ejpam-4012	223	13	and	and	CCONJ
ejpam-4012	223	14	r.	r.	PROPN
ejpam-4012	223	15	khalil	khalil	PROPN
ejpam-4012	223	16	.	.	PUNCT
ejpam-4012	224	1	fractional	fractional	ADJ
ejpam-4012	224	2	vector	vector	NOUN
ejpam-4012	224	3	analysis	analysis	NOUN
ejpam-4012	224	4	.	.	PUNCT
ejpam-4012	225	1	journal	journal	PROPN
ejpam-4012	225	2	of	of	ADP
ejpam-4012	225	3	mathematical	mathematical	ADJ
ejpam-4012	225	4	and	and	CCONJ
ejpam-4012	225	5	computational	computational	ADJ
ejpam-4012	225	6	science	science	NOUN
ejpam-4012	225	7	.	.	PUNCT
ejpam-4012	225	8	,	,	PUNCT
ejpam-4012	225	9	610:2320	610:2320	NOUN
ejpam-4012	225	10	–	–	PUNCT
ejpam-4012	225	11	2326	2326	NUM
ejpam-4012	225	12	,	,	PUNCT
ejpam-4012	225	13	2020	2020	NUM
ejpam-4012	225	14	.	.	PUNCT
ejpam-4012	226	1	[	[	X
ejpam-4012	226	2	7	7	NUM
ejpam-4012	226	3	]	]	PUNCT
ejpam-4012	226	4	a.	a.	NOUN
ejpam-4012	226	5	yousef	yousef	PROPN
ejpam-4012	226	6	r.	r.	PROPN
ejpam-4012	226	7	khalil	khalil	PROPN
ejpam-4012	226	8	,	,	PUNCT
ejpam-4012	226	9	m.	m.	PROPN
ejpam-4012	226	10	al	al	PROPN
ejpam-4012	226	11	horani	horani	PROPN
ejpam-4012	226	12	and	and	CCONJ
ejpam-4012	226	13	m.	m.	NOUN
ejpam-4012	226	14	sababheh	sababheh	NOUN
ejpam-4012	226	15	.	.	PUNCT
ejpam-4012	227	1	a	a	DET
ejpam-4012	227	2	new	new	ADJ
ejpam-4012	227	3	definition	definition	NOUN
ejpam-4012	227	4	of	of	ADP
ejpam-4012	227	5	fractional	fractional	ADJ
ejpam-4012	227	6	derivative	derivative	NOUN
ejpam-4012	227	7	.	.	PUNCT
ejpam-4012	228	1	journal	journal	PROPN
ejpam-4012	228	2	of	of	ADP
ejpam-4012	228	3	computational	computational	ADJ
ejpam-4012	228	4	allied	allied	ADJ
ejpam-4012	228	5	mathematics	mathematic	NOUN
ejpam-4012	228	6	,	,	PUNCT
ejpam-4012	228	7	264:65–70	264:65–70	NUM
ejpam-4012	228	8	,	,	PUNCT
ejpam-4012	228	9	2014	2014	NUM
ejpam-4012	228	10	.	.	PUNCT