id	sid	tid	token	lemma	pos
ejpam-4928	1	1	european	european	PROPN
ejpam-4928	1	2	journal	journal	PROPN
ejpam-4928	1	3	of	of	ADP
ejpam-4928	1	4	pure	pure	ADJ
ejpam-4928	1	5	and	and	CCONJ
ejpam-4928	1	6	applied	apply	VERB
ejpam-4928	1	7	mathematics	mathematic	NOUN
ejpam-4928	1	8	vol	vol	NOUN
ejpam-4928	1	9	.	.	PUNCT
ejpam-4928	2	1	16	16	NUM
ejpam-4928	2	2	,	,	PUNCT
ejpam-4928	2	3	no	no	INTJ
ejpam-4928	2	4	.	.	NOUN
ejpam-4928	2	5	4	4	NUM
ejpam-4928	2	6	,	,	PUNCT
ejpam-4928	2	7	2023	2023	NUM
ejpam-4928	2	8	,	,	PUNCT
ejpam-4928	2	9	2132	2132	NUM
ejpam-4928	2	10	-	-	SYM
ejpam-4928	2	11	2144	2144	NUM
ejpam-4928	2	12	issn	issn	PROPN
ejpam-4928	2	13	1307	1307	NUM
ejpam-4928	2	14	-	-	SYM
ejpam-4928	2	15	5543	5543	NUM
ejpam-4928	2	16	–	–	PUNCT
ejpam-4928	3	1	ejpam.com	ejpam.com	X
ejpam-4928	3	2	published	publish	VERB
ejpam-4928	3	3	by	by	ADP
ejpam-4928	3	4	new	new	PROPN
ejpam-4928	3	5	york	york	PROPN
ejpam-4928	3	6	business	business	PROPN
ejpam-4928	3	7	global	global	PROPN
ejpam-4928	3	8	numerical	numerical	ADJ
ejpam-4928	3	9	solutions	solution	NOUN
ejpam-4928	3	10	of	of	ADP
ejpam-4928	3	11	some	some	DET
ejpam-4928	3	12	classes	class	NOUN
ejpam-4928	3	13	of	of	ADP
ejpam-4928	3	14	partial	partial	ADJ
ejpam-4928	3	15	differential	differential	ADJ
ejpam-4928	3	16	equations	equation	NOUN
ejpam-4928	3	17	of	of	ADP
ejpam-4928	3	18	fractional	fractional	ADJ
ejpam-4928	3	19	order	order	NOUN
ejpam-4928	3	20	iman	iman	NOUN
ejpam-4928	3	21	aldarawi1,∗	aldarawi1,∗	PROPN
ejpam-4928	3	22	,	,	PUNCT
ejpam-4928	3	23	banan	banan	NOUN
ejpam-4928	3	24	maayah1	maayah1	PROPN
ejpam-4928	3	25	,	,	PUNCT
ejpam-4928	3	26	eman	eman	PROPN
ejpam-4928	3	27	aldabbas1	aldabbas1	PROPN
ejpam-4928	3	28	,	,	PUNCT
ejpam-4928	3	29	eman	eman	PROPN
ejpam-4928	3	30	abuteen2	abuteen2	PROPN
ejpam-4928	3	31	1	1	NUM
ejpam-4928	3	32	department	department	NOUN
ejpam-4928	3	33	of	of	ADP
ejpam-4928	3	34	mathematics	mathematic	NOUN
ejpam-4928	3	35	,	,	PUNCT
ejpam-4928	3	36	the	the	DET
ejpam-4928	3	37	university	university	PROPN
ejpam-4928	3	38	of	of	ADP
ejpam-4928	3	39	jordan	jordan	PROPN
ejpam-4928	3	40	,	,	PUNCT
ejpam-4928	3	41	amman	amman	PROPN
ejpam-4928	3	42	11942	11942	NUM
ejpam-4928	3	43	,	,	PUNCT
ejpam-4928	3	44	jordan	jordan	PROPN
ejpam-4928	3	45	2	2	NUM
ejpam-4928	3	46	department	department	NOUN
ejpam-4928	3	47	of	of	ADP
ejpam-4928	3	48	basic	basic	ADJ
ejpam-4928	3	49	scientific	scientific	ADJ
ejpam-4928	3	50	sciences	science	NOUN
ejpam-4928	3	51	,	,	PUNCT
ejpam-4928	3	52	faculty	faculty	NOUN
ejpam-4928	3	53	of	of	ADP
ejpam-4928	3	54	engineering	engineering	NOUN
ejpam-4928	3	55	technology	technology	NOUN
ejpam-4928	3	56	,	,	PUNCT
ejpam-4928	3	57	al	al	PROPN
ejpam-4928	3	58	-	-	PUNCT
ejpam-4928	3	59	balqa	balqa	NOUN
ejpam-4928	3	60	applied	apply	VERB
ejpam-4928	3	61	university	university	NOUN
ejpam-4928	3	62	,	,	PUNCT
ejpam-4928	3	63	al	al	PROPN
ejpam-4928	3	64	-	-	PUNCT
ejpam-4928	3	65	salt	salt	NOUN
ejpam-4928	3	66	19117	19117	NUM
ejpam-4928	3	67	,	,	PUNCT
ejpam-4928	3	68	jordan	jordan	PROPN
ejpam-4928	3	69	abstract	abstract	PROPN
ejpam-4928	3	70	.	.	PUNCT
ejpam-4928	4	1	this	this	DET
ejpam-4928	4	2	paper	paper	NOUN
ejpam-4928	4	3	explores	explore	VERB
ejpam-4928	4	4	the	the	DET
ejpam-4928	4	5	solutions	solution	NOUN
ejpam-4928	4	6	of	of	ADP
ejpam-4928	4	7	certain	certain	ADJ
ejpam-4928	4	8	fractional	fractional	ADJ
ejpam-4928	4	9	partial	partial	ADJ
ejpam-4928	4	10	differential	differential	NOUN
ejpam-4928	4	11	equations	equation	NOUN
ejpam-4928	4	12	using	use	VERB
ejpam-4928	4	13	two	two	NUM
ejpam-4928	4	14	methods	method	NOUN
ejpam-4928	4	15	;	;	PUNCT
ejpam-4928	4	16	the	the	DET
ejpam-4928	4	17	first	first	ADJ
ejpam-4928	4	18	method	method	NOUN
ejpam-4928	4	19	involves	involve	VERB
ejpam-4928	4	20	separation	separation	NOUN
ejpam-4928	4	21	of	of	ADP
ejpam-4928	4	22	variables	variable	NOUN
ejpam-4928	4	23	,	,	PUNCT
ejpam-4928	4	24	which	which	PRON
ejpam-4928	4	25	is	be	AUX
ejpam-4928	4	26	a	a	DET
ejpam-4928	4	27	common	common	ADJ
ejpam-4928	4	28	technique	technique	NOUN
ejpam-4928	4	29	for	for	ADP
ejpam-4928	4	30	solving	solve	VERB
ejpam-4928	4	31	partial	partial	ADJ
ejpam-4928	4	32	differential	differential	ADJ
ejpam-4928	4	33	equations	equation	NOUN
ejpam-4928	4	34	.	.	PUNCT
ejpam-4928	5	1	however	however	ADV
ejpam-4928	5	2	,	,	PUNCT
ejpam-4928	5	3	since	since	SCONJ
ejpam-4928	5	4	many	many	ADJ
ejpam-4928	5	5	equations	equation	NOUN
ejpam-4928	5	6	can	can	AUX
ejpam-4928	5	7	not	not	PART
ejpam-4928	5	8	be	be	AUX
ejpam-4928	5	9	separated	separate	VERB
ejpam-4928	5	10	in	in	ADP
ejpam-4928	5	11	this	this	DET
ejpam-4928	5	12	way	way	NOUN
ejpam-4928	5	13	,	,	PUNCT
ejpam-4928	5	14	the	the	DET
ejpam-4928	5	15	tensor	tensor	NOUN
ejpam-4928	5	16	product	product	NOUN
ejpam-4928	5	17	of	of	ADP
ejpam-4928	5	18	banach	banach	NOUN
ejpam-4928	5	19	spaces	space	NOUN
ejpam-4928	5	20	method	method	NOUN
ejpam-4928	5	21	is	be	AUX
ejpam-4928	5	22	applied	apply	VERB
ejpam-4928	5	23	to	to	PART
ejpam-4928	5	24	find	find	VERB
ejpam-4928	5	25	the	the	DET
ejpam-4928	5	26	atomic	atomic	ADJ
ejpam-4928	5	27	solutions	solution	NOUN
ejpam-4928	5	28	.	.	PUNCT
ejpam-4928	6	1	to	to	PART
ejpam-4928	6	2	solve	solve	VERB
ejpam-4928	6	3	the	the	DET
ejpam-4928	6	4	resulting	result	VERB
ejpam-4928	6	5	ordinary	ordinary	ADJ
ejpam-4928	6	6	differential	differential	ADJ
ejpam-4928	6	7	equations	equation	NOUN
ejpam-4928	6	8	,	,	PUNCT
ejpam-4928	6	9	the	the	DET
ejpam-4928	6	10	reproducing	reproduce	VERB
ejpam-4928	6	11	kernel	kernel	PROPN
ejpam-4928	6	12	hilbert	hilbert	PROPN
ejpam-4928	6	13	space	space	NOUN
ejpam-4928	6	14	method	method	NOUN
ejpam-4928	6	15	is	be	AUX
ejpam-4928	6	16	used	use	VERB
ejpam-4928	6	17	to	to	PART
ejpam-4928	6	18	find	find	VERB
ejpam-4928	6	19	numerical	numerical	ADJ
ejpam-4928	6	20	solutions	solution	NOUN
ejpam-4928	6	21	,	,	PUNCT
ejpam-4928	6	22	which	which	PRON
ejpam-4928	6	23	are	be	AUX
ejpam-4928	6	24	then	then	ADV
ejpam-4928	6	25	used	use	VERB
ejpam-4928	6	26	to	to	PART
ejpam-4928	6	27	find	find	VERB
ejpam-4928	6	28	the	the	DET
ejpam-4928	6	29	numerical	numerical	ADJ
ejpam-4928	6	30	solution	solution	NOUN
ejpam-4928	6	31	of	of	ADP
ejpam-4928	6	32	the	the	DET
ejpam-4928	6	33	partial	partial	ADJ
ejpam-4928	6	34	differential	differential	NOUN
ejpam-4928	6	35	equation	equation	NOUN
ejpam-4928	6	36	.	.	PUNCT
ejpam-4928	7	1	the	the	DET
ejpam-4928	7	2	residual	residual	ADJ
ejpam-4928	7	3	errors	error	NOUN
ejpam-4928	7	4	indicate	indicate	VERB
ejpam-4928	7	5	that	that	SCONJ
ejpam-4928	7	6	this	this	DET
ejpam-4928	7	7	method	method	NOUN
ejpam-4928	7	8	is	be	AUX
ejpam-4928	7	9	effective	effective	ADJ
ejpam-4928	7	10	and	and	CCONJ
ejpam-4928	7	11	powerful	powerful	ADJ
ejpam-4928	7	12	.	.	PUNCT
ejpam-4928	8	1	in	in	ADP
ejpam-4928	8	2	summary	summary	NOUN
ejpam-4928	8	3	,	,	PUNCT
ejpam-4928	8	4	this	this	DET
ejpam-4928	8	5	paper	paper	NOUN
ejpam-4928	8	6	presents	present	VERB
ejpam-4928	8	7	a	a	DET
ejpam-4928	8	8	study	study	NOUN
ejpam-4928	8	9	on	on	ADP
ejpam-4928	8	10	the	the	DET
ejpam-4928	8	11	solutions	solution	NOUN
ejpam-4928	8	12	of	of	ADP
ejpam-4928	8	13	certain	certain	ADJ
ejpam-4928	8	14	fractional	fractional	ADJ
ejpam-4928	8	15	partial	partial	ADJ
ejpam-4928	8	16	differential	differential	NOUN
ejpam-4928	8	17	equations	equation	NOUN
ejpam-4928	8	18	using	use	VERB
ejpam-4928	8	19	two	two	NUM
ejpam-4928	8	20	methods	method	NOUN
ejpam-4928	8	21	and	and	CCONJ
ejpam-4928	8	22	demonstrates	demonstrate	VERB
ejpam-4928	8	23	the	the	DET
ejpam-4928	8	24	effectiveness	effectiveness	NOUN
ejpam-4928	8	25	of	of	ADP
ejpam-4928	8	26	these	these	DET
ejpam-4928	8	27	methods	method	NOUN
ejpam-4928	8	28	in	in	ADP
ejpam-4928	8	29	finding	find	VERB
ejpam-4928	8	30	numerical	numerical	ADJ
ejpam-4928	8	31	solutions	solution	NOUN
ejpam-4928	8	32	.	.	PUNCT
ejpam-4928	9	1	2020	2020	NUM
ejpam-4928	9	2	mathematics	mathematic	NOUN
ejpam-4928	9	3	subject	subject	NOUN
ejpam-4928	9	4	classifications	classification	NOUN
ejpam-4928	9	5	:	:	PUNCT
ejpam-4928	9	6	26a33	26a33	NUM
ejpam-4928	9	7	key	key	ADJ
ejpam-4928	9	8	words	word	NOUN
ejpam-4928	9	9	and	and	CCONJ
ejpam-4928	9	10	phrases	phrase	NOUN
ejpam-4928	9	11	:	:	PUNCT
ejpam-4928	9	12	separation	separation	NOUN
ejpam-4928	9	13	of	of	ADP
ejpam-4928	9	14	variables	variable	NOUN
ejpam-4928	9	15	,	,	PUNCT
ejpam-4928	9	16	tensor	tensor	NOUN
ejpam-4928	9	17	product	product	NOUN
ejpam-4928	9	18	of	of	ADP
ejpam-4928	9	19	banach	banach	NOUN
ejpam-4928	9	20	spaces	space	NOUN
ejpam-4928	9	21	,	,	PUNCT
ejpam-4928	9	22	atomic	atomic	ADJ
ejpam-4928	9	23	solution	solution	NOUN
ejpam-4928	9	24	,	,	PUNCT
ejpam-4928	9	25	conformable	conformable	ADJ
ejpam-4928	9	26	derivatives	derivative	NOUN
ejpam-4928	9	27	1	1	NUM
ejpam-4928	9	28	.	.	PUNCT
ejpam-4928	9	29	introduction	introduction	NOUN
ejpam-4928	9	30	the	the	DET
ejpam-4928	9	31	concept	concept	NOUN
ejpam-4928	9	32	of	of	ADP
ejpam-4928	9	33	fractional	fractional	ADJ
ejpam-4928	9	34	calculus	calculus	NOUN
ejpam-4928	9	35	,	,	PUNCT
ejpam-4928	9	36	which	which	PRON
ejpam-4928	9	37	extends	extend	VERB
ejpam-4928	9	38	on	on	ADP
ejpam-4928	9	39	classical	classical	ADJ
ejpam-4928	9	40	calculus	calculus	NOUN
ejpam-4928	9	41	by	by	ADP
ejpam-4928	9	42	including	include	VERB
ejpam-4928	9	43	derivatives	derivative	NOUN
ejpam-4928	9	44	and	and	CCONJ
ejpam-4928	9	45	integrals	integral	NOUN
ejpam-4928	9	46	of	of	ADP
ejpam-4928	9	47	non	non	ADJ
ejpam-4928	9	48	-	-	ADJ
ejpam-4928	9	49	integer	integer	ADJ
ejpam-4928	9	50	order	order	NOUN
ejpam-4928	9	51	,	,	PUNCT
ejpam-4928	9	52	are	be	AUX
ejpam-4928	9	53	developed	develop	VERB
ejpam-4928	9	54	by	by	ADP
ejpam-4928	9	55	several	several	ADJ
ejpam-4928	9	56	researchers	researcher	NOUN
ejpam-4928	9	57	such	such	ADJ
ejpam-4928	9	58	as	as	ADP
ejpam-4928	9	59	;	;	PUNCT
ejpam-4928	9	60	riemann	riemann	PROPN
ejpam-4928	9	61	-	-	PUNCT
ejpam-4928	9	62	liouville	liouville	VERB
ejpam-4928	9	63	derivative	derivative	NOUN
ejpam-4928	9	64	[	[	X
ejpam-4928	9	65	15	15	NUM
ejpam-4928	9	66	]	]	PUNCT
ejpam-4928	9	67	,	,	PUNCT
ejpam-4928	9	68	caputo	caputo	PROPN
ejpam-4928	9	69	derivative	derivative	NOUN
ejpam-4928	10	1	[	[	X
ejpam-4928	10	2	13	13	NUM
ejpam-4928	10	3	]	]	PUNCT
ejpam-4928	10	4	,	,	PUNCT
ejpam-4928	10	5	caputo	caputo	PROPN
ejpam-4928	10	6	fabrizo	fabrizo	PROPN
ejpam-4928	10	7	derivative	derivative	ADJ
ejpam-4928	11	1	[	[	X
ejpam-4928	11	2	14	14	NUM
ejpam-4928	11	3	]	]	X
ejpam-4928	11	4	,	,	PUNCT
ejpam-4928	11	5	atangana	atangana	PROPN
ejpam-4928	11	6	-	-	PUNCT
ejpam-4928	11	7	baleanu	baleanu	PROPN
ejpam-4928	11	8	derivative	derivative	NOUN
ejpam-4928	12	1	[	[	X
ejpam-4928	12	2	6	6	NUM
ejpam-4928	12	3	]	]	PUNCT
ejpam-4928	12	4	and	and	CCONJ
ejpam-4928	12	5	recently	recently	ADV
ejpam-4928	12	6	conformable	conformable	ADJ
ejpam-4928	12	7	fractional	fractional	ADJ
ejpam-4928	12	8	derivative	derivative	NOUN
ejpam-4928	12	9	by	by	ADP
ejpam-4928	12	10	[	[	X
ejpam-4928	12	11	22	22	NUM
ejpam-4928	12	12	]	]	PUNCT
ejpam-4928	12	13	.	.	PUNCT
ejpam-4928	13	1	the	the	DET
ejpam-4928	13	2	conformable	conformable	ADJ
ejpam-4928	13	3	fractional	fractional	ADJ
ejpam-4928	13	4	derivative	derivative	NOUN
ejpam-4928	13	5	has	have	AUX
ejpam-4928	13	6	been	be	AUX
ejpam-4928	13	7	shown	show	VERB
ejpam-4928	13	8	to	to	PART
ejpam-4928	13	9	have	have	VERB
ejpam-4928	13	10	some	some	DET
ejpam-4928	13	11	advantages	advantage	NOUN
ejpam-4928	13	12	over	over	ADP
ejpam-4928	13	13	these	these	DET
ejpam-4928	13	14	other	other	ADJ
ejpam-4928	13	15	types	type	NOUN
ejpam-4928	13	16	of	of	ADP
ejpam-4928	13	17	fractional	fractional	ADJ
ejpam-4928	13	18	derivatives	derivative	NOUN
ejpam-4928	13	19	,	,	PUNCT
ejpam-4928	13	20	including	include	VERB
ejpam-4928	13	21	better	well	ADJ
ejpam-4928	13	22	preservation	preservation	NOUN
ejpam-4928	13	23	of	of	ADP
ejpam-4928	13	24	certain	certain	ADJ
ejpam-4928	13	25	mathematical	mathematical	ADJ
ejpam-4928	13	26	properties	property	NOUN
ejpam-4928	13	27	such	such	ADJ
ejpam-4928	13	28	as	as	ADP
ejpam-4928	13	29	the	the	DET
ejpam-4928	13	30	chain	chain	NOUN
ejpam-4928	13	31	rule	rule	NOUN
ejpam-4928	13	32	and	and	CCONJ
ejpam-4928	13	33	the	the	DET
ejpam-4928	13	34	product	product	NOUN
ejpam-4928	13	35	rule	rule	NOUN
ejpam-4928	13	36	[	[	X
ejpam-4928	13	37	19	19	NUM
ejpam-4928	13	38	]	]	PUNCT
ejpam-4928	13	39	.	.	PUNCT
ejpam-4928	14	1	partial	partial	ADJ
ejpam-4928	14	2	differential	differential	ADJ
ejpam-4928	14	3	equations	equation	NOUN
ejpam-4928	14	4	with	with	ADP
ejpam-4928	14	5	fractional	fractional	ADJ
ejpam-4928	14	6	order	order	NOUN
ejpam-4928	14	7	have	have	VERB
ejpam-4928	14	8	a	a	DET
ejpam-4928	14	9	wide	wide	ADJ
ejpam-4928	14	10	range	range	NOUN
ejpam-4928	14	11	of	of	ADP
ejpam-4928	14	12	applications	application	NOUN
ejpam-4928	14	13	in	in	ADP
ejpam-4928	14	14	various	various	ADJ
ejpam-4928	14	15	fields	field	NOUN
ejpam-4928	14	16	such	such	ADJ
ejpam-4928	14	17	as	as	ADP
ejpam-4928	14	18	;	;	PUNCT
ejpam-4928	14	19	fluid	fluid	ADJ
ejpam-4928	14	20	dynamics	dynamic	NOUN
ejpam-4928	14	21	in	in	ADP
ejpam-4928	14	22	porous	porous	ADJ
ejpam-4928	14	23	media	medium	NOUN
ejpam-4928	14	24	[	[	X
ejpam-4928	14	25	10	10	NUM
ejpam-4928	14	26	]	]	PUNCT
ejpam-4928	14	27	,	,	PUNCT
ejpam-4928	14	28	electromagnetic	electromagnetic	ADJ
ejpam-4928	14	29	theory	theory	NOUN
ejpam-4928	14	30	[	[	X
ejpam-4928	14	31	8	8	NUM
ejpam-4928	14	32	]	]	PUNCT
ejpam-4928	14	33	,	,	PUNCT
ejpam-4928	14	34	quantum	quantum	ADJ
ejpam-4928	14	35	mechanics	mechanic	NOUN
ejpam-4928	14	36	[	[	X
ejpam-4928	14	37	24	24	NUM
ejpam-4928	14	38	]	]	PUNCT
ejpam-4928	14	39	,	,	PUNCT
ejpam-4928	14	40	finance	finance	NOUN
ejpam-4928	14	41	[	[	X
ejpam-4928	14	42	17	17	NUM
ejpam-4928	14	43	]	]	PUNCT
ejpam-4928	14	44	,	,	PUNCT
ejpam-4928	14	45	heat	heat	NOUN
ejpam-4928	14	46	transfer	transfer	NOUN
ejpam-4928	14	47	[	[	X
ejpam-4928	14	48	26	26	NUM
ejpam-4928	14	49	]	]	PUNCT
ejpam-4928	14	50	,	,	PUNCT
ejpam-4928	14	51	biology	biology	NOUN
ejpam-4928	14	52	and	and	CCONJ
ejpam-4928	14	53	medicine	medicine	NOUN
ejpam-4928	14	54	[	[	X
ejpam-4928	14	55	25	25	NUM
ejpam-4928	14	56	]	]	PUNCT
ejpam-4928	14	57	and	and	CCONJ
ejpam-4928	14	58	∗corresponding	∗corresponde	VERB
ejpam-4928	14	59	author	author	NOUN
ejpam-4928	14	60	.	.	PUNCT
ejpam-4928	15	1	doi	doi	NOUN
ejpam-4928	15	2	:	:	PUNCT
ejpam-4928	15	3	https://doi.org/10.29020/nybg.ejpam.v16i4.4928	https://doi.org/10.29020/nybg.ejpam.v16i4.4928	NOUN
ejpam-4928	15	4	email	email	NOUN
ejpam-4928	15	5	addresses	address	VERB
ejpam-4928	15	6	:	:	PUNCT
ejpam-4928	15	7	i.aldarawi@ju.edu.jo	i.aldarawi@ju.edu.jo	PROPN
ejpam-4928	15	8	(	(	PUNCT
ejpam-4928	15	9	iman	iman	NOUN
ejpam-4928	15	10	aldarawi	aldarawi	VERB
ejpam-4928	15	11	)	)	PUNCT
ejpam-4928	15	12	,	,	PUNCT
ejpam-4928	15	13	b.maayah@ju.edu.jo	b.maayah@ju.edu.jo	ADJ
ejpam-4928	15	14	(	(	PUNCT
ejpam-4928	15	15	banan	banan	NOUN
ejpam-4928	15	16	maayah	maayah	PROPN
ejpam-4928	15	17	)	)	PUNCT
ejpam-4928	15	18	,	,	PUNCT
ejpam-4928	15	19	e	e	X
ejpam-4928	15	20	aldabbas@ju.edu.jo	aldabbas@ju.edu.jo	NOUN
ejpam-4928	15	21	(	(	PUNCT
ejpam-4928	15	22	eman	eman	NOUN
ejpam-4928	15	23	aldabbas	aldabbas	PROPN
ejpam-4928	15	24	)	)	PUNCT
ejpam-4928	15	25	,	,	PUNCT
ejpam-4928	15	26	dr.eman.abuteen@bau.edu.jo	dr.eman.abuteen@bau.edu.jo	PROPN
ejpam-4928	15	27	(	(	PUNCT
ejpam-4928	15	28	eman	eman	NOUN
ejpam-4928	15	29	abuteen	abuteen	ADJ
ejpam-4928	15	30	)	)	PUNCT
ejpam-4928	15	31	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4928	15	32	2132	2132	NUM
ejpam-4928	16	1	©	©	PROPN
ejpam-4928	16	2	2023	2023	NUM
ejpam-4928	16	3	ejpam	ejpam	NOUN
ejpam-4928	16	4	all	all	DET
ejpam-4928	16	5	rights	right	NOUN
ejpam-4928	16	6	reserved	reserve	VERB
ejpam-4928	16	7	.	.	PUNCT
ejpam-4928	17	1	i.	i.	PROPN
ejpam-4928	17	2	aldarawi	aldarawi	VERB
ejpam-4928	17	3	et	et	PROPN
ejpam-4928	17	4	al	al	PROPN
ejpam-4928	17	5	.	.	PUNCT
ejpam-4928	17	6	/	/	SYM
ejpam-4928	17	7	eur	eur	PROPN
ejpam-4928	17	8	.	.	PUNCT
ejpam-4928	18	1	j.	j.	PROPN
ejpam-4928	18	2	pure	pure	PROPN
ejpam-4928	18	3	appl	appl	PROPN
ejpam-4928	18	4	.	.	PROPN
ejpam-4928	18	5	math	math	PROPN
ejpam-4928	18	6	,	,	PUNCT
ejpam-4928	18	7	16	16	NUM
ejpam-4928	18	8	(	(	PUNCT
ejpam-4928	18	9	4	4	NUM
ejpam-4928	18	10	)	)	PUNCT
ejpam-4928	18	11	(	(	PUNCT
ejpam-4928	18	12	2023	2023	NUM
ejpam-4928	18	13	)	)	PUNCT
ejpam-4928	18	14	,	,	PUNCT
ejpam-4928	18	15	2132	2132	NUM
ejpam-4928	18	16	-	-	SYM
ejpam-4928	18	17	2144	2144	NUM
ejpam-4928	18	18	2133	2133	NUM
ejpam-4928	18	19	others	other	NOUN
ejpam-4928	18	20	.	.	PUNCT
ejpam-4928	19	1	some	some	DET
ejpam-4928	19	2	studies	study	NOUN
ejpam-4928	19	3	obtained	obtain	VERB
ejpam-4928	19	4	solutions	solution	NOUN
ejpam-4928	19	5	to	to	ADP
ejpam-4928	19	6	several	several	ADJ
ejpam-4928	19	7	fractional	fractional	ADJ
ejpam-4928	19	8	partial	partial	ADJ
ejpam-4928	19	9	differential	differential	NOUN
ejpam-4928	19	10	equations	equation	NOUN
ejpam-4928	19	11	,	,	PUNCT
ejpam-4928	19	12	for	for	ADP
ejpam-4928	19	13	instance	instance	NOUN
ejpam-4928	19	14	,	,	PUNCT
ejpam-4928	19	15	the	the	DET
ejpam-4928	19	16	fractional	fractional	ADJ
ejpam-4928	19	17	wave	wave	NOUN
ejpam-4928	19	18	-	-	PUNCT
ejpam-4928	19	19	type	type	NOUN
ejpam-4928	19	20	equations	equation	NOUN
ejpam-4928	19	21	are	be	AUX
ejpam-4928	19	22	solved	solve	VERB
ejpam-4928	19	23	by	by	ADP
ejpam-4928	19	24	fourier	fourier	ADJ
ejpam-4928	19	25	series	series	NOUN
ejpam-4928	19	26	by	by	ADP
ejpam-4928	19	27	[	[	X
ejpam-4928	19	28	9	9	NUM
ejpam-4928	19	29	]	]	PUNCT
ejpam-4928	19	30	,	,	PUNCT
ejpam-4928	19	31	[	[	X
ejpam-4928	19	32	7	7	X
ejpam-4928	19	33	]	]	PUNCT
ejpam-4928	19	34	used	use	VERB
ejpam-4928	19	35	the	the	DET
ejpam-4928	19	36	sumudu	sumudu	NOUN
ejpam-4928	19	37	decomposition	decomposition	NOUN
ejpam-4928	19	38	method	method	NOUN
ejpam-4928	19	39	(	(	PUNCT
ejpam-4928	19	40	sdm	sdm	PROPN
ejpam-4928	19	41	)	)	PUNCT
ejpam-4928	19	42	to	to	PART
ejpam-4928	19	43	find	find	VERB
ejpam-4928	19	44	approximate	approximate	ADJ
ejpam-4928	19	45	solutions	solution	NOUN
ejpam-4928	19	46	of	of	ADP
ejpam-4928	19	47	two	two	NUM
ejpam-4928	19	48	-	-	PUNCT
ejpam-4928	19	49	dimensional	dimensional	ADJ
ejpam-4928	19	50	fractional	fractional	ADJ
ejpam-4928	19	51	partial	partial	ADJ
ejpam-4928	19	52	differential	differential	NOUN
ejpam-4928	19	53	equations	equation	NOUN
ejpam-4928	19	54	,	,	PUNCT
ejpam-4928	19	55	[	[	X
ejpam-4928	19	56	18	18	NUM
ejpam-4928	19	57	]	]	PUNCT
ejpam-4928	19	58	used	use	VERB
ejpam-4928	19	59	a	a	DET
ejpam-4928	19	60	relatively	relatively	ADV
ejpam-4928	19	61	new	new	ADJ
ejpam-4928	19	62	method	method	NOUN
ejpam-4928	19	63	for	for	ADP
ejpam-4928	19	64	resolving	resolve	VERB
ejpam-4928	19	65	partial	partial	ADJ
ejpam-4928	19	66	differential	differential	ADJ
ejpam-4928	19	67	equations	equation	NOUN
ejpam-4928	19	68	(	(	PUNCT
ejpam-4928	19	69	pdes	pde	NOUN
ejpam-4928	19	70	)	)	PUNCT
ejpam-4928	19	71	with	with	ADP
ejpam-4928	19	72	fractional	fractional	ADJ
ejpam-4928	19	73	derivatives	derivative	NOUN
ejpam-4928	19	74	is	be	AUX
ejpam-4928	19	75	the	the	DET
ejpam-4928	19	76	tensor	tensor	NOUN
ejpam-4928	19	77	product	product	NOUN
ejpam-4928	19	78	of	of	ADP
ejpam-4928	19	79	banach	banach	NOUN
ejpam-4928	19	80	spaces	space	NOUN
ejpam-4928	19	81	(	(	PUNCT
ejpam-4928	19	82	tpbs	tpb	NOUN
ejpam-4928	19	83	)	)	PUNCT
ejpam-4928	19	84	,	,	PUNCT
ejpam-4928	19	85	which	which	PRON
ejpam-4928	19	86	is	be	AUX
ejpam-4928	19	87	used	use	VERB
ejpam-4928	19	88	in	in	ADP
ejpam-4928	19	89	this	this	DET
ejpam-4928	19	90	research	research	NOUN
ejpam-4928	19	91	.	.	PUNCT
ejpam-4928	20	1	tensor	tensor	NOUN
ejpam-4928	20	2	products	product	NOUN
ejpam-4928	20	3	of	of	ADP
ejpam-4928	20	4	banach	banach	NOUN
ejpam-4928	20	5	spaces	space	NOUN
ejpam-4928	20	6	,	,	PUNCT
ejpam-4928	20	7	which	which	PRON
ejpam-4928	20	8	are	be	AUX
ejpam-4928	20	9	mathematical	mathematical	ADJ
ejpam-4928	20	10	structures	structure	NOUN
ejpam-4928	20	11	that	that	PRON
ejpam-4928	20	12	generalize	generalize	VERB
ejpam-4928	20	13	vector	vector	NOUN
ejpam-4928	20	14	spaces	space	NOUN
ejpam-4928	20	15	and	and	CCONJ
ejpam-4928	20	16	include	include	VERB
ejpam-4928	20	17	norms	norm	NOUN
ejpam-4928	20	18	and	and	CCONJ
ejpam-4928	20	19	metrics	metric	NOUN
ejpam-4928	20	20	,	,	PUNCT
ejpam-4928	20	21	form	form	VERB
ejpam-4928	20	22	the	the	DET
ejpam-4928	20	23	foundation	foundation	NOUN
ejpam-4928	20	24	of	of	ADP
ejpam-4928	20	25	this	this	DET
ejpam-4928	20	26	approach	approach	NOUN
ejpam-4928	20	27	.	.	PUNCT
ejpam-4928	21	1	one	one	NUM
ejpam-4928	21	2	of	of	ADP
ejpam-4928	21	3	the	the	DET
ejpam-4928	21	4	main	main	ADJ
ejpam-4928	21	5	challenges	challenge	NOUN
ejpam-4928	21	6	of	of	ADP
ejpam-4928	21	7	the	the	DET
ejpam-4928	21	8	tpbs	tpb	NOUN
ejpam-4928	21	9	method	method	NOUN
ejpam-4928	21	10	is	be	AUX
ejpam-4928	21	11	the	the	DET
ejpam-4928	21	12	construction	construction	NOUN
ejpam-4928	21	13	of	of	ADP
ejpam-4928	21	14	a	a	DET
ejpam-4928	21	15	suitable	suitable	ADJ
ejpam-4928	21	16	tensor	tensor	NOUN
ejpam-4928	21	17	product	product	NOUN
ejpam-4928	21	18	basis	basis	NOUN
ejpam-4928	21	19	,	,	PUNCT
ejpam-4928	21	20	which	which	PRON
ejpam-4928	21	21	requires	require	VERB
ejpam-4928	21	22	a	a	DET
ejpam-4928	21	23	careful	careful	ADJ
ejpam-4928	21	24	choice	choice	NOUN
ejpam-4928	21	25	of	of	ADP
ejpam-4928	21	26	banach	banach	NOUN
ejpam-4928	21	27	spaces	space	NOUN
ejpam-4928	21	28	and	and	CCONJ
ejpam-4928	21	29	fractional	fractional	ADJ
ejpam-4928	21	30	derivative	derivative	ADJ
ejpam-4928	21	31	operators	operator	NOUN
ejpam-4928	21	32	,	,	PUNCT
ejpam-4928	21	33	another	another	DET
ejpam-4928	21	34	challenge	challenge	NOUN
ejpam-4928	21	35	is	be	AUX
ejpam-4928	21	36	the	the	DET
ejpam-4928	21	37	accurate	accurate	ADJ
ejpam-4928	21	38	approximation	approximation	NOUN
ejpam-4928	21	39	of	of	ADP
ejpam-4928	21	40	the	the	DET
ejpam-4928	21	41	fractional	fractional	ADJ
ejpam-4928	21	42	derivative	derivative	ADJ
ejpam-4928	21	43	operator	operator	NOUN
ejpam-4928	21	44	,	,	PUNCT
ejpam-4928	21	45	which	which	PRON
ejpam-4928	21	46	can	can	AUX
ejpam-4928	21	47	be	be	AUX
ejpam-4928	21	48	numerically	numerically	ADV
ejpam-4928	21	49	unstable	unstable	ADJ
ejpam-4928	21	50	and	and	CCONJ
ejpam-4928	21	51	require	require	VERB
ejpam-4928	21	52	specialized	specialized	ADJ
ejpam-4928	21	53	numerical	numerical	ADJ
ejpam-4928	21	54	techniques	technique	NOUN
ejpam-4928	21	55	.	.	PUNCT
ejpam-4928	22	1	moreover	moreover	ADV
ejpam-4928	22	2	,	,	PUNCT
ejpam-4928	22	3	the	the	DET
ejpam-4928	22	4	reproducing	reproduce	VERB
ejpam-4928	22	5	kernel	kernel	PROPN
ejpam-4928	22	6	hilbert	hilbert	PROPN
ejpam-4928	22	7	space	space	NOUN
ejpam-4928	22	8	method	method	NOUN
ejpam-4928	22	9	is	be	AUX
ejpam-4928	22	10	used	use	VERB
ejpam-4928	22	11	[	[	PUNCT
ejpam-4928	22	12	11	11	NUM
ejpam-4928	22	13	]	]	PUNCT
ejpam-4928	22	14	to	to	PART
ejpam-4928	22	15	find	find	VERB
ejpam-4928	22	16	the	the	DET
ejpam-4928	22	17	numerical	numerical	ADJ
ejpam-4928	22	18	solution	solution	NOUN
ejpam-4928	22	19	for	for	ADP
ejpam-4928	22	20	a	a	DET
ejpam-4928	22	21	certain	certain	ADJ
ejpam-4928	22	22	equation	equation	NOUN
ejpam-4928	22	23	to	to	PART
ejpam-4928	22	24	get	get	VERB
ejpam-4928	22	25	a	a	DET
ejpam-4928	22	26	complete	complete	ADJ
ejpam-4928	22	27	atomic	atomic	ADJ
ejpam-4928	22	28	solution	solution	NOUN
ejpam-4928	22	29	of	of	ADP
ejpam-4928	22	30	a	a	DET
ejpam-4928	22	31	fractional	fractional	ADJ
ejpam-4928	22	32	equation	equation	NOUN
ejpam-4928	22	33	.	.	PUNCT
ejpam-4928	23	1	this	this	DET
ejpam-4928	23	2	paper	paper	NOUN
ejpam-4928	23	3	is	be	AUX
ejpam-4928	23	4	organized	organize	VERB
ejpam-4928	23	5	as	as	SCONJ
ejpam-4928	23	6	follows	follow	VERB
ejpam-4928	23	7	:	:	PUNCT
ejpam-4928	23	8	section	section	NOUN
ejpam-4928	23	9	2	2	NUM
ejpam-4928	23	10	provides	provide	VERB
ejpam-4928	23	11	some	some	DET
ejpam-4928	23	12	basic	basic	ADJ
ejpam-4928	23	13	definitions	definition	NOUN
ejpam-4928	23	14	of	of	ADP
ejpam-4928	23	15	conformable	conformable	ADJ
ejpam-4928	23	16	derivative	derivative	NOUN
ejpam-4928	23	17	,	,	PUNCT
ejpam-4928	23	18	while	while	SCONJ
ejpam-4928	23	19	the	the	DET
ejpam-4928	23	20	fractional	fractional	ADJ
ejpam-4928	23	21	fourier	fourier	NOUN
ejpam-4928	23	22	series	series	NOUN
ejpam-4928	23	23	solution	solution	NOUN
ejpam-4928	23	24	for	for	ADP
ejpam-4928	23	25	the	the	DET
ejpam-4928	23	26	fractional	fractional	ADJ
ejpam-4928	23	27	heat	heat	NOUN
ejpam-4928	23	28	type	type	NOUN
ejpam-4928	23	29	equation	equation	NOUN
ejpam-4928	23	30	is	be	AUX
ejpam-4928	23	31	discussed	discuss	VERB
ejpam-4928	23	32	in	in	ADP
ejpam-4928	23	33	section	section	NOUN
ejpam-4928	23	34	3	3	NUM
ejpam-4928	23	35	.	.	PUNCT
ejpam-4928	24	1	in	in	ADP
ejpam-4928	24	2	section	section	NOUN
ejpam-4928	24	3	4	4	NUM
ejpam-4928	24	4	the	the	DET
ejpam-4928	24	5	atomic	atomic	ADJ
ejpam-4928	24	6	banach	banach	NOUN
ejpam-4928	24	7	space	space	NOUN
ejpam-4928	24	8	method	method	NOUN
ejpam-4928	24	9	is	be	AUX
ejpam-4928	24	10	used	use	VERB
ejpam-4928	24	11	to	to	PART
ejpam-4928	24	12	solve	solve	VERB
ejpam-4928	24	13	two	two	NUM
ejpam-4928	24	14	examples	example	NOUN
ejpam-4928	24	15	of	of	ADP
ejpam-4928	24	16	linear	linear	ADJ
ejpam-4928	24	17	fractional	fractional	ADJ
ejpam-4928	24	18	pdes	pde	NOUN
ejpam-4928	24	19	.	.	PUNCT
ejpam-4928	25	1	finally	finally	ADV
ejpam-4928	25	2	,	,	PUNCT
ejpam-4928	25	3	a	a	DET
ejpam-4928	25	4	conclusion	conclusion	NOUN
ejpam-4928	25	5	is	be	AUX
ejpam-4928	25	6	given	give	VERB
ejpam-4928	25	7	.	.	PUNCT
ejpam-4928	26	1	2	2	X
ejpam-4928	26	2	.	.	NUM
ejpam-4928	26	3	preliminaries	preliminary	NOUN
ejpam-4928	26	4	in	in	ADP
ejpam-4928	26	5	[	[	X
ejpam-4928	26	6	22	22	NUM
ejpam-4928	26	7	]	]	PUNCT
ejpam-4928	26	8	,	,	PUNCT
ejpam-4928	26	9	a	a	DET
ejpam-4928	26	10	definition	definition	NOUN
ejpam-4928	26	11	of	of	ADP
ejpam-4928	26	12	the	the	DET
ejpam-4928	26	13	so	so	ADV
ejpam-4928	26	14	-	-	PUNCT
ejpam-4928	26	15	called	call	VERB
ejpam-4928	26	16	α	α	NOUN
ejpam-4928	26	17	-	-	PUNCT
ejpam-4928	26	18	conformable	conformable	ADJ
ejpam-4928	26	19	fractional	fractional	ADJ
ejpam-4928	26	20	derivative	derivative	NOUN
ejpam-4928	26	21	was	be	AUX
ejpam-4928	26	22	introduced	introduce	VERB
ejpam-4928	26	23	as	as	SCONJ
ejpam-4928	26	24	follows	follow	VERB
ejpam-4928	26	25	:	:	PUNCT
ejpam-4928	26	26	let	let	VERB
ejpam-4928	26	27	α	α	X
ejpam-4928	26	28	∈	∈	PROPN
ejpam-4928	26	29	(	(	PUNCT
ejpam-4928	26	30	0	0	NUM
ejpam-4928	26	31	,	,	PUNCT
ejpam-4928	26	32	1	1	NUM
ejpam-4928	26	33	)	)	PUNCT
ejpam-4928	26	34	,	,	PUNCT
ejpam-4928	26	35	and	and	CCONJ
ejpam-4928	26	36	f	f	X
ejpam-4928	26	37	:	:	PUNCT
ejpam-4928	26	38	e	e	X
ejpam-4928	26	39	⊂	⊂	PROPN
ejpam-4928	26	40	(	(	PUNCT
ejpam-4928	26	41	0,∞	0,∞	NUM
ejpam-4928	26	42	)	)	PUNCT
ejpam-4928	26	43	→	→	PUNCT
ejpam-4928	27	1	r.for	r.for	ADP
ejpam-4928	27	2	x	x	SYM
ejpam-4928	27	3	∈	∈	PROPN
ejpam-4928	27	4	e	e	NOUN
ejpam-4928	27	5	,	,	PUNCT
ejpam-4928	27	6	then	then	ADV
ejpam-4928	27	7	:	:	PUNCT
ejpam-4928	27	8	dα(f)(x	dα(f)(x	NUM
ejpam-4928	27	9	)	)	PUNCT
ejpam-4928	28	1	=	=	SYM
ejpam-4928	28	2	lim	lim	PROPN
ejpam-4928	28	3	ϵ→0	ϵ→0	PROPN
ejpam-4928	28	4	x+	x+	PROPN
ejpam-4928	29	1	ϵx1−α	ϵx1−α	NOUN
ejpam-4928	29	2	−	−	PROPN
ejpam-4928	29	3	f(x	f(x	PROPN
ejpam-4928	29	4	)	)	PUNCT
ejpam-4928	29	5	ϵ	ϵ	X
ejpam-4928	29	6	(	(	PUNCT
ejpam-4928	29	7	1	1	NUM
ejpam-4928	29	8	)	)	PUNCT
ejpam-4928	29	9	if	if	SCONJ
ejpam-4928	29	10	the	the	DET
ejpam-4928	29	11	limit	limit	NOUN
ejpam-4928	29	12	exists	exist	VERB
ejpam-4928	29	13	,	,	PUNCT
ejpam-4928	29	14	then	then	ADV
ejpam-4928	29	15	it	it	PRON
ejpam-4928	29	16	is	be	AUX
ejpam-4928	29	17	called	call	VERB
ejpam-4928	29	18	α	α	DET
ejpam-4928	29	19	-	-	ADJ
ejpam-4928	29	20	conformable	conformable	ADJ
ejpam-4928	29	21	fractional	fractional	ADJ
ejpam-4928	29	22	derivatives	derivative	NOUN
ejpam-4928	29	23	of	of	ADP
ejpam-4928	29	24	f	f	PROPN
ejpam-4928	29	25	at	at	ADP
ejpam-4928	29	26	x.	x.	PROPN
ejpam-4928	29	27	if	if	SCONJ
ejpam-4928	29	28	f	f	PROPN
ejpam-4928	29	29	is	be	AUX
ejpam-4928	29	30	α	α	NOUN
ejpam-4928	29	31	-	-	NOUN
ejpam-4928	29	32	differentiable	differentiable	ADJ
ejpam-4928	29	33	on	on	ADP
ejpam-4928	29	34	(	(	PUNCT
ejpam-4928	29	35	0	0	NUM
ejpam-4928	29	36	,	,	PUNCT
ejpam-4928	29	37	r	r	NOUN
ejpam-4928	29	38	)	)	PUNCT
ejpam-4928	29	39	for	for	ADP
ejpam-4928	29	40	some	some	DET
ejpam-4928	29	41	r	r	NOUN
ejpam-4928	29	42	>	>	X
ejpam-4928	29	43	0	0	NUM
ejpam-4928	29	44	,	,	PUNCT
ejpam-4928	29	45	and	and	CCONJ
ejpam-4928	29	46	lim	lim	PROPN
ejpam-4928	29	47	x→0	x→0	PROPN
ejpam-4928	29	48	+	+	PROPN
ejpam-4928	29	49	dα(f)(x	dα(f)(x	NUM
ejpam-4928	29	50	)	)	PUNCT
ejpam-4928	29	51	exists	exist	VERB
ejpam-4928	29	52	,	,	PUNCT
ejpam-4928	29	53	then	then	ADV
ejpam-4928	29	54	dα(f)(0	dα(f)(0	PROPN
ejpam-4928	29	55	)	)	PUNCT
ejpam-4928	30	1	=	=	PROPN
ejpam-4928	30	2	lim	lim	PROPN
ejpam-4928	30	3	x→0	x→0	PROPN
ejpam-4928	30	4	+	+	PROPN
ejpam-4928	30	5	dα(f)(x	dα(f)(x	NUM
ejpam-4928	30	6	)	)	PUNCT
ejpam-4928	30	7	.	.	PUNCT
ejpam-4928	31	1	for	for	ADP
ejpam-4928	31	2	α	α	PRON
ejpam-4928	31	3	∈	∈	PROPN
ejpam-4928	31	4	(	(	PUNCT
ejpam-4928	31	5	0	0	NUM
ejpam-4928	31	6	,	,	PUNCT
ejpam-4928	31	7	1	1	NUM
ejpam-4928	31	8	]	]	PUNCT
ejpam-4928	31	9	,	,	PUNCT
ejpam-4928	31	10	and	and	CCONJ
ejpam-4928	31	11	f	f	X
ejpam-4928	31	12	,	,	PUNCT
ejpam-4928	31	13	g	g	PROPN
ejpam-4928	31	14	are	be	AUX
ejpam-4928	31	15	differentiable	differentiable	ADJ
ejpam-4928	31	16	are	be	AUX
ejpam-4928	31	17	α	α	X
ejpam-4928	31	18	-	-	NOUN
ejpam-4928	31	19	differentiable	differentiable	ADJ
ejpam-4928	31	20	at	at	ADP
ejpam-4928	31	21	some	some	DET
ejpam-4928	31	22	point	point	NOUN
ejpam-4928	31	23	t	t	PROPN
ejpam-4928	31	24	,	,	PUNCT
ejpam-4928	31	25	one	one	PRON
ejpam-4928	31	26	can	can	AUX
ejpam-4928	31	27	easily	easily	ADV
ejpam-4928	31	28	see	see	VERB
ejpam-4928	31	29	that	that	SCONJ
ejpam-4928	31	30	the	the	DET
ejpam-4928	31	31	conformable	conformable	ADJ
ejpam-4928	31	32	derivative	derivative	ADJ
ejpam-4928	31	33	satisfies	satisfie	NOUN
ejpam-4928	31	34	:	:	PUNCT
ejpam-4928	31	35	1	1	X
ejpam-4928	31	36	.	.	X
ejpam-4928	31	37	dα(af	dα(af	PROPN
ejpam-4928	31	38	+	+	CCONJ
ejpam-4928	31	39	bg	bg	PROPN
ejpam-4928	31	40	)	)	PUNCT
ejpam-4928	31	41	=	=	SYM
ejpam-4928	31	42	adα(f	adα(f	PROPN
ejpam-4928	31	43	)	)	PUNCT
ejpam-4928	32	1	+	+	CCONJ
ejpam-4928	32	2	bdα(g	bdα(g	PROPN
ejpam-4928	32	3	)	)	PUNCT
ejpam-4928	32	4	,	,	PUNCT
ejpam-4928	32	5	for	for	ADP
ejpam-4928	32	6	all	all	DET
ejpam-4928	32	7	a	a	PRON
ejpam-4928	32	8	,	,	PUNCT
ejpam-4928	32	9	b	b	PROPN
ejpam-4928	32	10	∈	∈	PROPN
ejpam-4928	32	11	r.	r.	PROPN
ejpam-4928	32	12	2	2	NUM
ejpam-4928	32	13	.	.	PUNCT
ejpam-4928	32	14	dα(λ	dα(λ	X
ejpam-4928	32	15	)	)	PUNCT
ejpam-4928	33	1	=	=	SYM
ejpam-4928	33	2	0	0	NUM
ejpam-4928	33	3	,	,	PUNCT
ejpam-4928	33	4	for	for	ADP
ejpam-4928	33	5	all	all	DET
ejpam-4928	33	6	constant	constant	ADJ
ejpam-4928	33	7	functions	function	NOUN
ejpam-4928	33	8	f(t	f(t	NOUN
ejpam-4928	33	9	)	)	PUNCT
ejpam-4928	34	1	=	=	SYM
ejpam-4928	34	2	λ	λ	X
ejpam-4928	34	3	.	.	NOUN
ejpam-4928	34	4	3	3	NUM
ejpam-4928	34	5	.	.	PUNCT
ejpam-4928	34	6	dα(fg	dα(fg	NOUN
ejpam-4928	34	7	)	)	PUNCT
ejpam-4928	34	8	=	=	PUNCT
ejpam-4928	34	9	fdα(g	fdα(g	PROPN
ejpam-4928	34	10	)	)	PUNCT
ejpam-4928	34	11	+	+	NUM
ejpam-4928	34	12	gdα(f	gdα(f	NOUN
ejpam-4928	34	13	)	)	PUNCT
ejpam-4928	34	14	.	.	PUNCT
ejpam-4928	35	1	4	4	X
ejpam-4928	35	2	.	.	X
ejpam-4928	35	3	dα(fg	dα(fg	NOUN
ejpam-4928	35	4	)	)	PUNCT
ejpam-4928	36	1	=	=	PUNCT
ejpam-4928	36	2	gdα(f)−	gdα(f)−	PROPN
ejpam-4928	36	3	fdα(g	fdα(g	PROPN
ejpam-4928	36	4	)	)	PUNCT
ejpam-4928	36	5	g2	g2	PROPN
ejpam-4928	36	6	,	,	PUNCT
ejpam-4928	36	7	g(t	g(t	PROPN
ejpam-4928	36	8	)	)	PUNCT
ejpam-4928	36	9	̸=	̸=	PROPN
ejpam-4928	36	10	0	0	NUM
ejpam-4928	36	11	.	.	PUNCT
ejpam-4928	37	1	we	we	PRON
ejpam-4928	37	2	list	list	VERB
ejpam-4928	37	3	here	here	ADV
ejpam-4928	37	4	the	the	DET
ejpam-4928	37	5	fractional	fractional	ADJ
ejpam-4928	37	6	derivatives	derivative	NOUN
ejpam-4928	37	7	of	of	ADP
ejpam-4928	37	8	certain	certain	ADJ
ejpam-4928	37	9	functions	function	NOUN
ejpam-4928	37	10	,	,	PUNCT
ejpam-4928	37	11	i.	i.	PROPN
ejpam-4928	37	12	aldarawi	aldarawi	VERB
ejpam-4928	38	1	et	et	PROPN
ejpam-4928	38	2	al	al	PROPN
ejpam-4928	38	3	.	.	PUNCT
ejpam-4928	38	4	/	/	SYM
ejpam-4928	38	5	eur	eur	PROPN
ejpam-4928	38	6	.	.	PUNCT
ejpam-4928	39	1	j.	j.	PROPN
ejpam-4928	39	2	pure	pure	PROPN
ejpam-4928	39	3	appl	appl	PROPN
ejpam-4928	39	4	.	.	PROPN
ejpam-4928	39	5	math	math	PROPN
ejpam-4928	39	6	,	,	PUNCT
ejpam-4928	39	7	16	16	NUM
ejpam-4928	39	8	(	(	PUNCT
ejpam-4928	39	9	4	4	NUM
ejpam-4928	39	10	)	)	PUNCT
ejpam-4928	39	11	(	(	PUNCT
ejpam-4928	39	12	2023	2023	NUM
ejpam-4928	39	13	)	)	PUNCT
ejpam-4928	39	14	,	,	PUNCT
ejpam-4928	39	15	2132	2132	NUM
ejpam-4928	39	16	-	-	SYM
ejpam-4928	39	17	2144	2144	NUM
ejpam-4928	39	18	2134	2134	NUM
ejpam-4928	39	19	1	1	NUM
ejpam-4928	39	20	.	.	PUNCT
ejpam-4928	40	1	dα(tp	dα(tp	ADJ
ejpam-4928	40	2	)	)	PUNCT
ejpam-4928	40	3	=	=	SYM
ejpam-4928	40	4	ptp−α	ptp−α	X
ejpam-4928	40	5	.	.	NOUN
ejpam-4928	41	1	2	2	X
ejpam-4928	41	2	.	.	X
ejpam-4928	41	3	dα	dα	PROPN
ejpam-4928	41	4	(	(	PUNCT
ejpam-4928	41	5	sin	sin	NOUN
ejpam-4928	41	6	(	(	PUNCT
ejpam-4928	41	7	1α	1α	NUM
ejpam-4928	41	8	t	t	PROPN
ejpam-4928	41	9	α	α	NUM
ejpam-4928	41	10	)	)	PUNCT
ejpam-4928	41	11	)	)	PUNCT
ejpam-4928	42	1	=	=	PUNCT
ejpam-4928	42	2	cos	cos	PROPN
ejpam-4928	42	3	(	(	PUNCT
ejpam-4928	42	4	1α	1α	NUM
ejpam-4928	42	5	t	t	PROPN
ejpam-4928	42	6	α	α	PROPN
ejpam-4928	42	7	)	)	PUNCT
ejpam-4928	42	8	.	.	PUNCT
ejpam-4928	43	1	3	3	X
ejpam-4928	43	2	.	.	X
ejpam-4928	43	3	dα	dα	PROPN
ejpam-4928	43	4	(	(	PUNCT
ejpam-4928	43	5	cos	cos	PROPN
ejpam-4928	43	6	(	(	PUNCT
ejpam-4928	43	7	1α	1α	NUM
ejpam-4928	43	8	t	t	PROPN
ejpam-4928	43	9	α	α	NUM
ejpam-4928	43	10	)	)	PUNCT
ejpam-4928	43	11	)	)	PUNCT
ejpam-4928	43	12	=	=	SYM
ejpam-4928	43	13	−	−	PROPN
ejpam-4928	43	14	sin	sin	NOUN
ejpam-4928	43	15	(	(	PUNCT
ejpam-4928	43	16	1α	1α	NUM
ejpam-4928	43	17	t	t	PROPN
ejpam-4928	43	18	α	α	PROPN
ejpam-4928	43	19	)	)	PUNCT
ejpam-4928	43	20	.	.	PUNCT
ejpam-4928	44	1	4	4	X
ejpam-4928	44	2	.	.	X
ejpam-4928	44	3	dα	dα	PROPN
ejpam-4928	44	4	(	(	PUNCT
ejpam-4928	44	5	e	e	NOUN
ejpam-4928	44	6	1	1	NUM
ejpam-4928	44	7	α	α	NOUN
ejpam-4928	44	8	tα	tα	PROPN
ejpam-4928	44	9	)	)	PUNCT
ejpam-4928	45	1	=	=	PUNCT
ejpam-4928	45	2	e	e	X
ejpam-4928	45	3	1	1	NUM
ejpam-4928	45	4	α	α	NOUN
ejpam-4928	45	5	tα	tα	PROPN
ejpam-4928	45	6	.	.	PUNCT
ejpam-4928	46	1	for	for	ADP
ejpam-4928	46	2	the	the	DET
ejpam-4928	46	3	geometric	geometric	ADJ
ejpam-4928	46	4	meaning	meaning	NOUN
ejpam-4928	46	5	of	of	ADP
ejpam-4928	46	6	α	α	NOUN
ejpam-4928	46	7	-	-	PUNCT
ejpam-4928	46	8	conformable	conformable	ADJ
ejpam-4928	46	9	fractional	fractional	ADJ
ejpam-4928	46	10	derivative	derivative	NOUN
ejpam-4928	46	11	we	we	PRON
ejpam-4928	46	12	refer	refer	VERB
ejpam-4928	46	13	the	the	DET
ejpam-4928	46	14	reader	reader	NOUN
ejpam-4928	46	15	to	to	ADP
ejpam-4928	46	16	[	[	X
ejpam-4928	46	17	21	21	NUM
ejpam-4928	46	18	]	]	PUNCT
ejpam-4928	46	19	.	.	PUNCT
ejpam-4928	47	1	on	on	ADP
ejpam-4928	47	2	putting	put	VERB
ejpam-4928	47	3	α	α	NOUN
ejpam-4928	47	4	=	=	SYM
ejpam-4928	47	5	1	1	NUM
ejpam-4928	47	6	in	in	ADP
ejpam-4928	47	7	these	these	DET
ejpam-4928	47	8	derivatives	derivative	NOUN
ejpam-4928	47	9	,	,	PUNCT
ejpam-4928	47	10	we	we	PRON
ejpam-4928	47	11	get	get	VERB
ejpam-4928	47	12	the	the	DET
ejpam-4928	47	13	corresponding	corresponding	ADJ
ejpam-4928	47	14	classical	classical	ADJ
ejpam-4928	47	15	rules	rule	NOUN
ejpam-4928	47	16	for	for	ADP
ejpam-4928	47	17	ordinary	ordinary	ADJ
ejpam-4928	47	18	derivatives	derivative	NOUN
ejpam-4928	47	19	.	.	PUNCT
ejpam-4928	48	1	for	for	ADP
ejpam-4928	48	2	more	more	ADJ
ejpam-4928	48	3	on	on	ADP
ejpam-4928	48	4	fractional	fractional	ADJ
ejpam-4928	48	5	calculus	calculus	NOUN
ejpam-4928	48	6	and	and	CCONJ
ejpam-4928	48	7	its	its	PRON
ejpam-4928	48	8	applications	application	NOUN
ejpam-4928	48	9	,	,	PUNCT
ejpam-4928	48	10	we	we	PRON
ejpam-4928	48	11	refer	refer	VERB
ejpam-4928	48	12	to	to	ADP
ejpam-4928	48	13	(	(	PUNCT
ejpam-4928	48	14	[	[	X
ejpam-4928	48	15	1	1	NUM
ejpam-4928	48	16	]	]	PUNCT
ejpam-4928	48	17	,	,	PUNCT
ejpam-4928	48	18	[	[	X
ejpam-4928	48	19	2	2	NUM
ejpam-4928	48	20	]	]	PUNCT
ejpam-4928	48	21	,	,	PUNCT
ejpam-4928	48	22	[	[	X
ejpam-4928	48	23	3	3	NUM
ejpam-4928	48	24	]	]	PUNCT
ejpam-4928	48	25	,	,	PUNCT
ejpam-4928	48	26	[	[	X
ejpam-4928	48	27	5	5	NUM
ejpam-4928	48	28	]	]	PUNCT
ejpam-4928	48	29	,	,	PUNCT
ejpam-4928	48	30	[	[	X
ejpam-4928	48	31	4	4	NUM
ejpam-4928	48	32	]	]	PUNCT
ejpam-4928	48	33	,	,	PUNCT
ejpam-4928	48	34	and	and	CCONJ
ejpam-4928	48	35	[	[	X
ejpam-4928	48	36	23	23	NUM
ejpam-4928	48	37	]	]	PUNCT
ejpam-4928	48	38	)	)	PUNCT
ejpam-4928	48	39	.	.	PUNCT
ejpam-4928	49	1	3	3	X
ejpam-4928	49	2	.	.	X
ejpam-4928	49	3	separation	separation	NOUN
ejpam-4928	49	4	of	of	ADP
ejpam-4928	49	5	variables	variable	NOUN
ejpam-4928	49	6	consider	consider	VERB
ejpam-4928	49	7	the	the	DET
ejpam-4928	49	8	following	follow	VERB
ejpam-4928	49	9	heat	heat	NOUN
ejpam-4928	49	10	fractional	fractional	ADJ
ejpam-4928	49	11	differential	differential	NOUN
ejpam-4928	49	12	equation	equation	NOUN
ejpam-4928	49	13	:	:	PUNCT
ejpam-4928	49	14	dα	dα	PROPN
ejpam-4928	49	15	t	t	PROPN
ejpam-4928	49	16	u−	u−	PROPN
ejpam-4928	49	17	kd2β	kd2β	PROPN
ejpam-4928	49	18	x	x	SYM
ejpam-4928	49	19	u	u	NOUN
ejpam-4928	49	20	=	=	PROPN
ejpam-4928	49	21	dβ	dβ	PROPN
ejpam-4928	49	22	xu	xu	PROPN
ejpam-4928	49	23	,	,	PUNCT
ejpam-4928	49	24	(	(	PUNCT
ejpam-4928	49	25	0	0	PUNCT
ejpam-4928	49	26	<	<	X
ejpam-4928	49	27	α	α	NOUN
ejpam-4928	49	28	,	,	PUNCT
ejpam-4928	49	29	β	β	X
ejpam-4928	49	30	<	<	X
ejpam-4928	49	31	1	1	NUM
ejpam-4928	49	32	)	)	PUNCT
ejpam-4928	49	33	(	(	PUNCT
ejpam-4928	49	34	2	2	X
ejpam-4928	49	35	)	)	PUNCT
ejpam-4928	49	36	which	which	PRON
ejpam-4928	49	37	gives	give	VERB
ejpam-4928	49	38	the	the	DET
ejpam-4928	49	39	temperature	temperature	NOUN
ejpam-4928	49	40	u(x	u(x	NOUN
ejpam-4928	49	41	,	,	PUNCT
ejpam-4928	49	42	t	t	PROPN
ejpam-4928	49	43	)	)	PUNCT
ejpam-4928	49	44	in	in	ADP
ejpam-4928	49	45	a	a	DET
ejpam-4928	49	46	body	body	NOUN
ejpam-4928	49	47	of	of	ADP
ejpam-4928	49	48	homogeneous	homogeneous	ADJ
ejpam-4928	49	49	material	material	NOUN
ejpam-4928	49	50	,	,	PUNCT
ejpam-4928	49	51	k	k	PROPN
ejpam-4928	49	52	is	be	AUX
ejpam-4928	49	53	the	the	DET
ejpam-4928	49	54	thermal	thermal	ADJ
ejpam-4928	49	55	diffusivity	diffusivity	NOUN
ejpam-4928	49	56	.	.	PUNCT
ejpam-4928	50	1	as	as	ADP
ejpam-4928	50	2	an	an	DET
ejpam-4928	50	3	important	important	ADJ
ejpam-4928	50	4	application	application	NOUN
ejpam-4928	50	5	,	,	PUNCT
ejpam-4928	50	6	let	let	VERB
ejpam-4928	50	7	us	we	PRON
ejpam-4928	50	8	first	first	ADV
ejpam-4928	50	9	consider	consider	VERB
ejpam-4928	50	10	the	the	DET
ejpam-4928	50	11	temperature	temperature	NOUN
ejpam-4928	50	12	in	in	ADP
ejpam-4928	50	13	a	a	DET
ejpam-4928	50	14	long	long	ADJ
ejpam-4928	50	15	thin	thin	ADJ
ejpam-4928	50	16	bar	bar	NOUN
ejpam-4928	50	17	or	or	CCONJ
ejpam-4928	50	18	wire	wire	NOUN
ejpam-4928	50	19	of	of	ADP
ejpam-4928	50	20	constant	constant	ADJ
ejpam-4928	50	21	cross	cross	NOUN
ejpam-4928	50	22	-	-	NOUN
ejpam-4928	50	23	section	section	ADJ
ejpam-4928	50	24	and	and	CCONJ
ejpam-4928	50	25	homogeneous	homogeneous	ADJ
ejpam-4928	50	26	material	material	NOUN
ejpam-4928	50	27	,	,	PUNCT
ejpam-4928	50	28	which	which	PRON
ejpam-4928	50	29	is	be	AUX
ejpam-4928	50	30	oriented	orient	VERB
ejpam-4928	50	31	along	along	ADP
ejpam-4928	50	32	the	the	DET
ejpam-4928	50	33	x	x	NOUN
ejpam-4928	50	34	-	-	NOUN
ejpam-4928	50	35	axis	axis	ADJ
ejpam-4928	50	36	(	(	PUNCT
ejpam-4928	50	37	figure	figure	NOUN
ejpam-4928	50	38	1	1	NUM
ejpam-4928	50	39	)	)	PUNCT
ejpam-4928	50	40	and	and	CCONJ
ejpam-4928	50	41	is	be	AUX
ejpam-4928	50	42	perfectly	perfectly	ADV
ejpam-4928	50	43	insulated	insulate	VERB
ejpam-4928	50	44	laterally	laterally	ADV
ejpam-4928	50	45	,	,	PUNCT
ejpam-4928	50	46	so	so	SCONJ
ejpam-4928	50	47	that	that	SCONJ
ejpam-4928	50	48	the	the	DET
ejpam-4928	50	49	heat	heat	NOUN
ejpam-4928	50	50	flows	flow	VERB
ejpam-4928	50	51	in	in	ADP
ejpam-4928	50	52	the	the	DET
ejpam-4928	50	53	x	x	NOUN
ejpam-4928	50	54	-	-	NOUN
ejpam-4928	50	55	direction	direction	NOUN
ejpam-4928	50	56	only	only	ADV
ejpam-4928	50	57	.	.	PUNCT
ejpam-4928	51	1	then	then	ADV
ejpam-4928	51	2	u	u	NOUN
ejpam-4928	51	3	depends	depend	VERB
ejpam-4928	51	4	only	only	ADV
ejpam-4928	51	5	on	on	ADP
ejpam-4928	51	6	x	x	PUNCT
ejpam-4928	51	7	and	and	CCONJ
ejpam-4928	51	8	time	time	NOUN
ejpam-4928	51	9	t.	t.	PROPN
ejpam-4928	51	10	we	we	PRON
ejpam-4928	51	11	shall	shall	AUX
ejpam-4928	51	12	solve	solve	VERB
ejpam-4928	51	13	equation	equation	NOUN
ejpam-4928	51	14	(	(	PUNCT
ejpam-4928	51	15	2	2	NUM
ejpam-4928	51	16	)	)	PUNCT
ejpam-4928	51	17	for	for	ADP
ejpam-4928	51	18	some	some	DET
ejpam-4928	51	19	important	important	ADJ
ejpam-4928	51	20	types	type	NOUN
ejpam-4928	51	21	of	of	ADP
ejpam-4928	51	22	boundaries	boundary	NOUN
ejpam-4928	51	23	and	and	CCONJ
ejpam-4928	51	24	initial	initial	ADJ
ejpam-4928	51	25	conditions	condition	NOUN
ejpam-4928	51	26	.	.	PUNCT
ejpam-4928	52	1	we	we	PRON
ejpam-4928	52	2	begin	begin	VERB
ejpam-4928	52	3	with	with	ADP
ejpam-4928	52	4	the	the	DET
ejpam-4928	52	5	case	case	NOUN
ejpam-4928	52	6	in	in	ADP
ejpam-4928	52	7	which	which	PRON
ejpam-4928	52	8	the	the	DET
ejpam-4928	52	9	ends	end	NOUN
ejpam-4928	52	10	x	x	PUNCT
ejpam-4928	52	11	=	=	SYM
ejpam-4928	52	12	0	0	NUM
ejpam-4928	52	13	and	and	CCONJ
ejpam-4928	52	14	x	x	X
ejpam-4928	52	15	=	=	SYM
ejpam-4928	52	16	l	l	NOUN
ejpam-4928	52	17	of	of	ADP
ejpam-4928	52	18	the	the	DET
ejpam-4928	52	19	bar	bar	NOUN
ejpam-4928	52	20	are	be	AUX
ejpam-4928	52	21	kept	keep	VERB
ejpam-4928	52	22	at	at	ADP
ejpam-4928	52	23	temperature	temperature	NOUN
ejpam-4928	52	24	zero	zero	NUM
ejpam-4928	52	25	,	,	PUNCT
ejpam-4928	52	26	so	so	SCONJ
ejpam-4928	52	27	that	that	SCONJ
ejpam-4928	52	28	we	we	PRON
ejpam-4928	52	29	have	have	VERB
ejpam-4928	52	30	the	the	DET
ejpam-4928	52	31	boundary	boundary	ADJ
ejpam-4928	52	32	conditions	condition	NOUN
ejpam-4928	52	33	:	:	PUNCT
ejpam-4928	53	1	u(0	u(0	PROPN
ejpam-4928	53	2	,	,	PUNCT
ejpam-4928	53	3	t	t	PROPN
ejpam-4928	53	4	)	)	PUNCT
ejpam-4928	53	5	=	=	SYM
ejpam-4928	53	6	0	0	NUM
ejpam-4928	53	7	and	and	CCONJ
ejpam-4928	53	8	u(l	u(l	PROPN
ejpam-4928	53	9	,	,	PUNCT
ejpam-4928	53	10	t	t	PROPN
ejpam-4928	53	11	)	)	PUNCT
ejpam-4928	53	12	=	=	SYM
ejpam-4928	53	13	0	0	NUM
ejpam-4928	53	14	for	for	ADP
ejpam-4928	53	15	all	all	DET
ejpam-4928	53	16	t	t	PROPN
ejpam-4928	53	17	,	,	PUNCT
ejpam-4928	53	18	and	and	CCONJ
ejpam-4928	53	19	the	the	DET
ejpam-4928	53	20	initial	initial	ADJ
ejpam-4928	53	21	temperature	temperature	NOUN
ejpam-4928	53	22	in	in	ADP
ejpam-4928	53	23	the	the	DET
ejpam-4928	53	24	bar	bar	NOUN
ejpam-4928	53	25	at	at	ADP
ejpam-4928	53	26	time	time	NOUN
ejpam-4928	53	27	t	t	PROPN
ejpam-4928	53	28	=	=	SYM
ejpam-4928	53	29	0	0	NUM
ejpam-4928	53	30	is	be	AUX
ejpam-4928	53	31	f(x	f(x	PROPN
ejpam-4928	53	32	)	)	PUNCT
ejpam-4928	53	33	,	,	PUNCT
ejpam-4928	53	34	so	so	SCONJ
ejpam-4928	53	35	that	that	SCONJ
ejpam-4928	53	36	we	we	PRON
ejpam-4928	53	37	have	have	VERB
ejpam-4928	53	38	the	the	DET
ejpam-4928	53	39	initial	initial	ADJ
ejpam-4928	53	40	condition	condition	NOUN
ejpam-4928	53	41	u(x	u(x	NOUN
ejpam-4928	53	42	,	,	PUNCT
ejpam-4928	53	43	0	0	NUM
ejpam-4928	53	44	)	)	PUNCT
ejpam-4928	53	45	=	=	SYM
ejpam-4928	53	46	f(x	f(x	PROPN
ejpam-4928	53	47	)	)	PUNCT
ejpam-4928	53	48	,	,	PUNCT
ejpam-4928	53	49	where	where	SCONJ
ejpam-4928	53	50	f(x	f(x	PROPN
ejpam-4928	53	51	)	)	PUNCT
ejpam-4928	53	52	is	be	AUX
ejpam-4928	53	53	given	give	VERB
ejpam-4928	53	54	.	.	PUNCT
ejpam-4928	54	1	figure	figure	NOUN
ejpam-4928	54	2	1	1	NUM
ejpam-4928	54	3	:	:	PUNCT
ejpam-4928	54	4	bar	bar	NOUN
ejpam-4928	54	5	under	under	ADP
ejpam-4928	54	6	consideration	consideration	NOUN
ejpam-4928	54	7	.	.	PUNCT
ejpam-4928	55	1	3.1	3.1	NUM
ejpam-4928	55	2	.	.	PUNCT
ejpam-4928	55	3	solution	solution	NOUN
ejpam-4928	55	4	of	of	ADP
ejpam-4928	55	5	the	the	DET
ejpam-4928	55	6	heat	heat	NOUN
ejpam-4928	55	7	equation	equation	NOUN
ejpam-4928	55	8	(	(	PUNCT
ejpam-4928	55	9	2	2	X
ejpam-4928	55	10	)	)	PUNCT
ejpam-4928	55	11	let	let	VERB
ejpam-4928	55	12	u(x	u(x	NOUN
ejpam-4928	55	13	,	,	PUNCT
ejpam-4928	55	14	t	t	PROPN
ejpam-4928	55	15	)	)	PUNCT
ejpam-4928	55	16	=	=	SYM
ejpam-4928	55	17	x(x)t	x(x)t	PROPN
ejpam-4928	55	18	(	(	PUNCT
ejpam-4928	55	19	t	t	PROPN
ejpam-4928	55	20	)	)	PUNCT
ejpam-4928	55	21	substitute	substitute	NOUN
ejpam-4928	55	22	in	in	ADP
ejpam-4928	55	23	equation	equation	NOUN
ejpam-4928	55	24	(	(	PUNCT
ejpam-4928	55	25	2	2	NUM
ejpam-4928	55	26	)	)	PUNCT
ejpam-4928	55	27	to	to	PART
ejpam-4928	55	28	get	get	VERB
ejpam-4928	55	29	x(x)tα(t)−	x(x)tα(t)−	PUNCT
ejpam-4928	56	1	kx2β(x)t	kx2β(x)t	PROPN
ejpam-4928	56	2	(	(	PUNCT
ejpam-4928	56	3	t	t	NOUN
ejpam-4928	56	4	)	)	PUNCT
ejpam-4928	56	5	=	=	PUNCT
ejpam-4928	57	1	xβ(x)t	xβ(x)t	PROPN
ejpam-4928	57	2	(	(	PUNCT
ejpam-4928	57	3	t	t	PROPN
ejpam-4928	57	4	)	)	PUNCT
ejpam-4928	57	5	i.	i.	PROPN
ejpam-4928	57	6	aldarawi	aldarawi	VERB
ejpam-4928	57	7	et	et	PROPN
ejpam-4928	57	8	al	al	PROPN
ejpam-4928	57	9	.	.	PUNCT
ejpam-4928	57	10	/	/	SYM
ejpam-4928	57	11	eur	eur	PROPN
ejpam-4928	57	12	.	.	PUNCT
ejpam-4928	58	1	j.	j.	PROPN
ejpam-4928	58	2	pure	pure	PROPN
ejpam-4928	58	3	appl	appl	PROPN
ejpam-4928	58	4	.	.	PROPN
ejpam-4928	58	5	math	math	PROPN
ejpam-4928	58	6	,	,	PUNCT
ejpam-4928	58	7	16	16	NUM
ejpam-4928	58	8	(	(	PUNCT
ejpam-4928	58	9	4	4	NUM
ejpam-4928	58	10	)	)	PUNCT
ejpam-4928	58	11	(	(	PUNCT
ejpam-4928	58	12	2023	2023	NUM
ejpam-4928	58	13	)	)	PUNCT
ejpam-4928	58	14	,	,	PUNCT
ejpam-4928	58	15	2132	2132	NUM
ejpam-4928	58	16	-	-	SYM
ejpam-4928	58	17	2144	2144	NUM
ejpam-4928	58	18	2135	2135	NUM
ejpam-4928	58	19	simplify	simplify	NOUN
ejpam-4928	58	20	,	,	PUNCT
ejpam-4928	58	21	then	then	ADV
ejpam-4928	58	22	we	we	PRON
ejpam-4928	58	23	have	have	VERB
ejpam-4928	58	24	x(x)tα(t	x(x)tα(t	X
ejpam-4928	58	25	)	)	PUNCT
ejpam-4928	58	26	=	=	SYM
ejpam-4928	58	27	(	(	PUNCT
ejpam-4928	58	28	kx2β(x	kx2β(x	NOUN
ejpam-4928	58	29	)	)	PUNCT
ejpam-4928	59	1	+	+	ADJ
ejpam-4928	59	2	xβ(x	xβ(x	NOUN
ejpam-4928	59	3	)	)	PUNCT
ejpam-4928	59	4	)	)	PUNCT
ejpam-4928	60	1	t	t	PROPN
ejpam-4928	60	2	(	(	PUNCT
ejpam-4928	60	3	t	t	PROPN
ejpam-4928	60	4	)	)	PUNCT
ejpam-4928	60	5	from	from	ADP
ejpam-4928	60	6	which	which	PRON
ejpam-4928	60	7	we	we	PRON
ejpam-4928	60	8	obtain	obtain	VERB
ejpam-4928	60	9	kx2β(x	kx2β(x	NOUN
ejpam-4928	60	10	)	)	PUNCT
ejpam-4928	61	1	+	+	ADJ
ejpam-4928	61	2	xβ(x	xβ(x	NOUN
ejpam-4928	61	3	)	)	PUNCT
ejpam-4928	61	4	x(x	x(x	PROPN
ejpam-4928	61	5	)	)	PUNCT
ejpam-4928	61	6	=	=	SYM
ejpam-4928	62	1	tα(t	tα(t	X
ejpam-4928	62	2	)	)	PUNCT
ejpam-4928	62	3	t	t	NOUN
ejpam-4928	62	4	(	(	PUNCT
ejpam-4928	62	5	t	t	PROPN
ejpam-4928	62	6	)	)	PUNCT
ejpam-4928	63	1	=	=	SYM
ejpam-4928	63	2	λ	λ	NOUN
ejpam-4928	63	3	since	since	SCONJ
ejpam-4928	63	4	x	x	PROPN
ejpam-4928	63	5	and	and	CCONJ
ejpam-4928	63	6	t	t	PROPN
ejpam-4928	63	7	are	be	AUX
ejpam-4928	63	8	independent	independent	ADJ
ejpam-4928	63	9	variables	variable	NOUN
ejpam-4928	63	10	,	,	PUNCT
ejpam-4928	63	11	then	then	ADV
ejpam-4928	63	12	kx2β(x	kx2β(x	NOUN
ejpam-4928	63	13	)	)	PUNCT
ejpam-4928	64	1	+	+	ADJ
ejpam-4928	64	2	xβ(x	xβ(x	NOUN
ejpam-4928	64	3	)	)	PUNCT
ejpam-4928	64	4	x(x	x(x	PROPN
ejpam-4928	64	5	)	)	PUNCT
ejpam-4928	64	6	=	=	SYM
ejpam-4928	64	7	λ	λ	NOUN
ejpam-4928	64	8	and	and	CCONJ
ejpam-4928	64	9	tα(t	tα(t	NOUN
ejpam-4928	64	10	)	)	PUNCT
ejpam-4928	64	11	t	t	PROPN
ejpam-4928	64	12	(	(	PUNCT
ejpam-4928	64	13	t	t	PROPN
ejpam-4928	64	14	)	)	PUNCT
ejpam-4928	65	1	=	=	PUNCT
ejpam-4928	66	1	λ	λ	NOUN
ejpam-4928	66	2	now	now	ADV
ejpam-4928	66	3	,	,	PUNCT
ejpam-4928	66	4	we	we	PRON
ejpam-4928	66	5	have	have	VERB
ejpam-4928	66	6	the	the	DET
ejpam-4928	66	7	following	follow	VERB
ejpam-4928	66	8	fractional	fractional	ADJ
ejpam-4928	66	9	ordinary	ordinary	ADJ
ejpam-4928	66	10	differential	differential	ADJ
ejpam-4928	66	11	equations	equation	NOUN
ejpam-4928	66	12	kx2β(x	kx2β(x	NOUN
ejpam-4928	66	13	)	)	PUNCT
ejpam-4928	67	1	+	+	ADJ
ejpam-4928	67	2	xβ(x)−	xβ(x)−	PROPN
ejpam-4928	67	3	λx(x	λx(x	PUNCT
ejpam-4928	67	4	)	)	PUNCT
ejpam-4928	68	1	=	=	SYM
ejpam-4928	68	2	0	0	PUNCT
ejpam-4928	68	3	(	(	PUNCT
ejpam-4928	68	4	3	3	X
ejpam-4928	68	5	)	)	PUNCT
ejpam-4928	68	6	tα(t)−	tα(t)−	PROPN
ejpam-4928	68	7	λt	λt	ADP
ejpam-4928	68	8	(	(	PUNCT
ejpam-4928	68	9	t	t	PROPN
ejpam-4928	68	10	)	)	PUNCT
ejpam-4928	68	11	=	=	SYM
ejpam-4928	68	12	0	0	PUNCT
ejpam-4928	68	13	(	(	PUNCT
ejpam-4928	68	14	4	4	NUM
ejpam-4928	68	15	)	)	PUNCT
ejpam-4928	68	16	first	first	ADV
ejpam-4928	68	17	,	,	PUNCT
ejpam-4928	68	18	we	we	PRON
ejpam-4928	68	19	deal	deal	VERB
ejpam-4928	68	20	with	with	ADP
ejpam-4928	68	21	equation	equation	NOUN
ejpam-4928	68	22	(	(	PUNCT
ejpam-4928	68	23	3	3	NUM
ejpam-4928	68	24	)	)	PUNCT
ejpam-4928	68	25	.	.	PUNCT
ejpam-4928	69	1	let	let	VERB
ejpam-4928	69	2	the	the	DET
ejpam-4928	69	3	characteristic	characteristic	ADJ
ejpam-4928	69	4	equation	equation	NOUN
ejpam-4928	69	5	ρ	ρ	NOUN
ejpam-4928	69	6	=	=	PROPN
ejpam-4928	69	7	−1±	−1±	PROPN
ejpam-4928	69	8	√	√	NUM
ejpam-4928	69	9	1	1	NUM
ejpam-4928	69	10	+	+	NUM
ejpam-4928	69	11	4kλ	4kλ	ADJ
ejpam-4928	69	12	2k	2k	NOUN
ejpam-4928	69	13	,	,	PUNCT
ejpam-4928	69	14	then	then	ADV
ejpam-4928	69	15	,	,	PUNCT
ejpam-4928	69	16	using	use	VERB
ejpam-4928	69	17	the	the	DET
ejpam-4928	69	18	results	result	NOUN
ejpam-4928	69	19	in	in	ADP
ejpam-4928	69	20	[	[	X
ejpam-4928	69	21	1	1	X
ejpam-4928	69	22	]	]	PUNCT
ejpam-4928	69	23	there	there	PRON
ejpam-4928	69	24	are	be	VERB
ejpam-4928	69	25	three	three	NUM
ejpam-4928	69	26	cases	case	NOUN
ejpam-4928	69	27	:	:	PUNCT
ejpam-4928	69	28	case(i	case(i	NOUN
ejpam-4928	69	29	):	):	PUNCT
ejpam-4928	69	30	1	1	NUM
ejpam-4928	70	1	+	+	NUM
ejpam-4928	70	2	4kλ	4kλ	ADJ
ejpam-4928	70	3	=	=	SYM
ejpam-4928	70	4	0	0	X
ejpam-4928	70	5	.	.	PUNCT
ejpam-4928	71	1	so	so	ADV
ejpam-4928	71	2	ρ	ρ	PROPN
ejpam-4928	71	3	=	=	SYM
ejpam-4928	71	4	−1	−1	NOUN
ejpam-4928	71	5	2k	2k	NOUN
ejpam-4928	71	6	,	,	PUNCT
ejpam-4928	71	7	then	then	ADV
ejpam-4928	71	8	x(x	x(x	NOUN
ejpam-4928	71	9	)	)	PUNCT
ejpam-4928	72	1	=	=	SYM
ejpam-4928	72	2	c1e	c1e	NOUN
ejpam-4928	72	3	−xβ	−xβ	X
ejpam-4928	72	4	2kβ	2kβ	NOUN
ejpam-4928	73	1	+	+	CCONJ
ejpam-4928	73	2	c2	c2	PROPN
ejpam-4928	73	3	xbeta	xbeta	PROPN
ejpam-4928	73	4	β	β	PROPN
ejpam-4928	73	5	e	e	PROPN
ejpam-4928	73	6	−xβ	−xβ	NUM
ejpam-4928	73	7	2kβ	2kβ	NOUN
ejpam-4928	73	8	.	.	PUNCT
ejpam-4928	74	1	the	the	DET
ejpam-4928	74	2	conditions	condition	NOUN
ejpam-4928	74	3	u(0	u(0	PROPN
ejpam-4928	74	4	,	,	PUNCT
ejpam-4928	74	5	t	t	PROPN
ejpam-4928	74	6	)	)	PUNCT
ejpam-4928	74	7	=	=	SYM
ejpam-4928	75	1	u(l	u(l	PROPN
ejpam-4928	75	2	,	,	PUNCT
ejpam-4928	75	3	t	t	PROPN
ejpam-4928	75	4	)	)	PUNCT
ejpam-4928	75	5	=	=	SYM
ejpam-4928	75	6	0	0	PUNCT
ejpam-4928	75	7	imply	imply	VERB
ejpam-4928	75	8	that	that	DET
ejpam-4928	75	9	c1	c1	NOUN
ejpam-4928	75	10	=	=	PROPN
ejpam-4928	75	11	c2	c2	PROPN
ejpam-4928	75	12	=	=	SYM
ejpam-4928	75	13	0	0	PROPN
ejpam-4928	75	14	.	.	PUNCT
ejpam-4928	76	1	thus	thus	ADV
ejpam-4928	76	2	,	,	PUNCT
ejpam-4928	76	3	x(x	x(x	PROPN
ejpam-4928	76	4	)	)	PUNCT
ejpam-4928	76	5	=	=	SYM
ejpam-4928	76	6	0	0	NUM
ejpam-4928	76	7	,	,	PUNCT
ejpam-4928	76	8	the	the	DET
ejpam-4928	76	9	trivial	trivial	ADJ
ejpam-4928	76	10	solution	solution	NOUN
ejpam-4928	76	11	.	.	PUNCT
ejpam-4928	77	1	case(ii	case(ii	ADJ
ejpam-4928	77	2	):	):	PUNCT
ejpam-4928	77	3	1	1	NUM
ejpam-4928	77	4	+	+	NUM
ejpam-4928	77	5	4kλ	4kλ	NOUN
ejpam-4928	77	6	=	=	PUNCT
ejpam-4928	77	7	µ2	µ2	PROPN
ejpam-4928	77	8	>	>	X
ejpam-4928	77	9	0	0	PROPN
ejpam-4928	77	10	.	.	PUNCT
ejpam-4928	78	1	then	then	ADV
ejpam-4928	78	2	ρ	ρ	PROPN
ejpam-4928	78	3	=	=	PROPN
ejpam-4928	78	4	−1±	−1±	PROPN
ejpam-4928	78	5	µ	µ	PRON
ejpam-4928	78	6	2k	2k	NOUN
ejpam-4928	78	7	,	,	PUNCT
ejpam-4928	78	8	and	and	CCONJ
ejpam-4928	78	9	hence	hence	ADV
ejpam-4928	78	10	x(x	x(x	PROPN
ejpam-4928	78	11	)	)	PUNCT
ejpam-4928	79	1	=	=	PUNCT
ejpam-4928	79	2	c1e	c1e	X
ejpam-4928	79	3	−1+µ	−1+µ	PROPN
ejpam-4928	79	4	2k	2k	NOUN
ejpam-4928	79	5	−xβ	−xβ	NUM
ejpam-4928	79	6	2kβ	2kβ	NOUN
ejpam-4928	80	1	+	+	PUNCT
ejpam-4928	80	2	c2e	c2e	ADJ
ejpam-4928	80	3	−1−µ	−1−µ	NOUN
ejpam-4928	80	4	2k	2k	NUM
ejpam-4928	80	5	−xβ	−xβ	NUM
ejpam-4928	80	6	2kβ	2kβ	NOUN
ejpam-4928	80	7	.	.	PUNCT
ejpam-4928	81	1	using	use	VERB
ejpam-4928	81	2	the	the	DET
ejpam-4928	81	3	condition	condition	NOUN
ejpam-4928	81	4	u(0	u(0	PROPN
ejpam-4928	81	5	,	,	PUNCT
ejpam-4928	81	6	t	t	PROPN
ejpam-4928	81	7	)	)	PUNCT
ejpam-4928	81	8	=	=	SYM
ejpam-4928	82	1	0	0	NUM
ejpam-4928	82	2	,	,	PUNCT
ejpam-4928	82	3	we	we	PRON
ejpam-4928	82	4	getc2	getc2	NOUN
ejpam-4928	82	5	=	=	SYM
ejpam-4928	82	6	−c1	−c1	PROPN
ejpam-4928	82	7	.	.	PUNCT
ejpam-4928	83	1	so	so	ADV
ejpam-4928	83	2	,	,	PUNCT
ejpam-4928	83	3	x(x	x(x	PROPN
ejpam-4928	83	4	)	)	PUNCT
ejpam-4928	83	5	=	=	PROPN
ejpam-4928	83	6	c1	c1	PROPN
ejpam-4928	83	7	(	(	PUNCT
ejpam-4928	83	8	e	e	PROPN
ejpam-4928	83	9	−1+µ	−1+µ	PROPN
ejpam-4928	83	10	2k	2k	NUM
ejpam-4928	83	11	−xβ	−xβ	NUM
ejpam-4928	83	12	2kβ	2kβ	ADJ
ejpam-4928	83	13	−	−	PROPN
ejpam-4928	84	1	e	e	NOUN
ejpam-4928	84	2	−1−µ	−1−µ	NOUN
ejpam-4928	84	3	2k	2k	NUM
ejpam-4928	84	4	−xβ	−xβ	NUM
ejpam-4928	84	5	2kβ	2kβ	NOUN
ejpam-4928	84	6	)	)	PUNCT
ejpam-4928	84	7	and	and	CCONJ
ejpam-4928	84	8	using	use	VERB
ejpam-4928	84	9	the	the	DET
ejpam-4928	84	10	condition	condition	NOUN
ejpam-4928	84	11	u(l	u(l	VERB
ejpam-4928	84	12	,	,	PUNCT
ejpam-4928	84	13	t	t	PROPN
ejpam-4928	84	14	)	)	PUNCT
ejpam-4928	84	15	=	=	SYM
ejpam-4928	85	1	0	0	NUM
ejpam-4928	85	2	,	,	PUNCT
ejpam-4928	85	3	we	we	PRON
ejpam-4928	85	4	get	get	VERB
ejpam-4928	85	5	c1	c1	PROPN
ejpam-4928	85	6	=	=	PUNCT
ejpam-4928	85	7	0	0	NUM
ejpam-4928	85	8	,	,	PUNCT
ejpam-4928	85	9	thus	thus	ADV
ejpam-4928	85	10	x(x	x(x	NOUN
ejpam-4928	85	11	)	)	PUNCT
ejpam-4928	86	1	=	=	SYM
ejpam-4928	86	2	0	0	NUM
ejpam-4928	86	3	,	,	PUNCT
ejpam-4928	86	4	therefore	therefore	ADV
ejpam-4928	86	5	1	1	NUM
ejpam-4928	86	6	+	+	NUM
ejpam-4928	86	7	4kλ	4kλ	NOUN
ejpam-4928	86	8	=	=	PUNCT
ejpam-4928	86	9	µ2	µ2	PROPN
ejpam-4928	86	10	>	>	X
ejpam-4928	86	11	0	0	PUNCT
ejpam-4928	86	12	also	also	ADV
ejpam-4928	86	13	gives	give	VERB
ejpam-4928	86	14	the	the	DET
ejpam-4928	86	15	trivial	trivial	ADJ
ejpam-4928	86	16	solution	solution	NOUN
ejpam-4928	86	17	.	.	PUNCT
ejpam-4928	87	1	case(iii	case(iii	PROPN
ejpam-4928	87	2	):	):	PUNCT
ejpam-4928	87	3	1	1	NUM
ejpam-4928	87	4	+	+	NUM
ejpam-4928	87	5	4kλ	4kλ	NOUN
ejpam-4928	87	6	=	=	PUNCT
ejpam-4928	87	7	−µ2	−µ2	NOUN
ejpam-4928	87	8	<	<	X
ejpam-4928	87	9	0	0	X
ejpam-4928	87	10	.	.	PUNCT
ejpam-4928	88	1	then	then	ADV
ejpam-4928	88	2	ρ	ρ	PROPN
ejpam-4928	88	3	=	=	PROPN
ejpam-4928	88	4	−1±	−1±	PROPN
ejpam-4928	88	5	µ	µ	X
ejpam-4928	88	6	i	i	NOUN
ejpam-4928	88	7	2k	2k	NUM
ejpam-4928	88	8	,	,	PUNCT
ejpam-4928	88	9	and	and	CCONJ
ejpam-4928	88	10	hencex(x	hencex(x	PROPN
ejpam-4928	88	11	)	)	PUNCT
ejpam-4928	89	1	=	=	PROPN
ejpam-4928	89	2	c1e	c1e	PROPN
ejpam-4928	89	3	−xβ	−xβ	PROPN
ejpam-4928	89	4	2kβ	2kβ	NOUN
ejpam-4928	89	5	cos	cos	PROPN
ejpam-4928	89	6	(	(	PUNCT
ejpam-4928	89	7	cos	cos	PROPN
ejpam-4928	89	8	(	(	PUNCT
ejpam-4928	89	9	µxβ	µxβ	PROPN
ejpam-4928	89	10	2k	2k	NUM
ejpam-4928	89	11	β	β	X
ejpam-4928	89	12	)	)	PUNCT
ejpam-4928	89	13	)	)	PUNCT
ejpam-4928	90	1	+	+	ADJ
ejpam-4928	90	2	c2e	c2e	ADJ
ejpam-4928	90	3	−xβ	−xβ	PROPN
ejpam-4928	90	4	2kβ	2kβ	ADJ
ejpam-4928	90	5	sin	sin	NOUN
ejpam-4928	90	6	(	(	PUNCT
ejpam-4928	90	7	sin	sin	NOUN
ejpam-4928	90	8	(	(	PUNCT
ejpam-4928	90	9	µxβ	µxβ	PROPN
ejpam-4928	90	10	2k	2k	NUM
ejpam-4928	90	11	β	β	X
ejpam-4928	90	12	)	)	PUNCT
ejpam-4928	90	13	)	)	PUNCT
ejpam-4928	90	14	.	.	PUNCT
ejpam-4928	91	1	by	by	ADP
ejpam-4928	91	2	using	use	VERB
ejpam-4928	91	3	the	the	DET
ejpam-4928	91	4	condition	condition	NOUN
ejpam-4928	91	5	u(0	u(0	PROPN
ejpam-4928	91	6	,	,	PUNCT
ejpam-4928	91	7	t	t	PROPN
ejpam-4928	91	8	)	)	PUNCT
ejpam-4928	91	9	=	=	SYM
ejpam-4928	91	10	0	0	NUM
ejpam-4928	91	11	,	,	PUNCT
ejpam-4928	91	12	we	we	PRON
ejpam-4928	91	13	get	get	VERB
ejpam-4928	91	14	c1	c1	NOUN
ejpam-4928	91	15	=	=	PUNCT
ejpam-4928	92	1	0	0	X
ejpam-4928	92	2	.	.	PUNCT
ejpam-4928	93	1	so	so	ADV
ejpam-4928	93	2	,	,	PUNCT
ejpam-4928	93	3	x(x	x(x	PROPN
ejpam-4928	93	4	)	)	PUNCT
ejpam-4928	94	1	=	=	SYM
ejpam-4928	94	2	c2e	c2e	NOUN
ejpam-4928	94	3	−xβ	−xβ	PROPN
ejpam-4928	94	4	2kβ	2kβ	ADJ
ejpam-4928	94	5	sin	sin	NOUN
ejpam-4928	94	6	(	(	PUNCT
ejpam-4928	94	7	µxβ	µxβ	PROPN
ejpam-4928	94	8	2k	2k	NUM
ejpam-4928	94	9	β	β	X
ejpam-4928	94	10	)	)	PUNCT
ejpam-4928	94	11	.	.	PUNCT
ejpam-4928	95	1	but	but	CCONJ
ejpam-4928	95	2	i.	i.	PROPN
ejpam-4928	95	3	aldarawi	aldarawi	VERB
ejpam-4928	95	4	et	et	PROPN
ejpam-4928	95	5	al	al	PROPN
ejpam-4928	95	6	.	.	PUNCT
ejpam-4928	95	7	/	/	SYM
ejpam-4928	95	8	eur	eur	PROPN
ejpam-4928	95	9	.	.	PUNCT
ejpam-4928	96	1	j.	j.	PROPN
ejpam-4928	96	2	pure	pure	PROPN
ejpam-4928	96	3	appl	appl	PROPN
ejpam-4928	96	4	.	.	PROPN
ejpam-4928	96	5	math	math	PROPN
ejpam-4928	96	6	,	,	PUNCT
ejpam-4928	96	7	16	16	NUM
ejpam-4928	96	8	(	(	PUNCT
ejpam-4928	96	9	4	4	NUM
ejpam-4928	96	10	)	)	PUNCT
ejpam-4928	96	11	(	(	PUNCT
ejpam-4928	96	12	2023	2023	NUM
ejpam-4928	96	13	)	)	PUNCT
ejpam-4928	96	14	,	,	PUNCT
ejpam-4928	96	15	2132	2132	NUM
ejpam-4928	96	16	-	-	SYM
ejpam-4928	96	17	2144	2144	NUM
ejpam-4928	96	18	2136	2136	NUM
ejpam-4928	96	19	the	the	DET
ejpam-4928	96	20	condition	condition	NOUN
ejpam-4928	96	21	u(l	u(l	PROPN
ejpam-4928	96	22	,	,	PUNCT
ejpam-4928	96	23	t	t	PROPN
ejpam-4928	96	24	)	)	PUNCT
ejpam-4928	96	25	=	=	SYM
ejpam-4928	96	26	0	0	NUM
ejpam-4928	96	27	implies	imply	VERB
ejpam-4928	96	28	that	that	SCONJ
ejpam-4928	96	29	x(x	x(x	PROPN
ejpam-4928	96	30	)	)	PUNCT
ejpam-4928	97	1	=	=	SYM
ejpam-4928	97	2	c2e	c2e	NOUN
ejpam-4928	97	3	−xβ	−xβ	PROPN
ejpam-4928	97	4	2kβ	2kβ	ADJ
ejpam-4928	97	5	sin	sin	NOUN
ejpam-4928	97	6	(	(	PUNCT
ejpam-4928	97	7	µxβ	µxβ	PROPN
ejpam-4928	97	8	2k	2k	NUM
ejpam-4928	97	9	β	β	X
ejpam-4928	97	10	)	)	PUNCT
ejpam-4928	98	1	=	=	PUNCT
ejpam-4928	98	2	0	0	X
ejpam-4928	98	3	.	.	PUNCT
ejpam-4928	99	1	since	since	SCONJ
ejpam-4928	99	2	c2	c2	PROPN
ejpam-4928	99	3	̸=	̸=	PROPN
ejpam-4928	99	4	0	0	NUM
ejpam-4928	99	5	,	,	PUNCT
ejpam-4928	99	6	then	then	ADV
ejpam-4928	99	7	sin	sin	VERB
ejpam-4928	99	8	(	(	PUNCT
ejpam-4928	99	9	µxβ	µxβ	PROPN
ejpam-4928	99	10	2k	2k	NUM
ejpam-4928	99	11	β	β	X
ejpam-4928	99	12	)	)	PUNCT
ejpam-4928	100	1	=	=	PUNCT
ejpam-4928	100	2	0	0	NUM
ejpam-4928	100	3	,	,	PUNCT
ejpam-4928	100	4	and	and	CCONJ
ejpam-4928	100	5	then	then	ADV
ejpam-4928	100	6	we	we	PRON
ejpam-4928	100	7	have	have	VERB
ejpam-4928	100	8	µ	µ	X
ejpam-4928	100	9	=	=	SYM
ejpam-4928	100	10	2knπ	2knπ	PROPN
ejpam-4928	100	11	β	β	X
ejpam-4928	100	12	lβ	lβ	X
ejpam-4928	100	13	(	(	PUNCT
ejpam-4928	100	14	5	5	NUM
ejpam-4928	100	15	)	)	PUNCT
ejpam-4928	100	16	and	and	CCONJ
ejpam-4928	100	17	x(x	x(x	PROPN
ejpam-4928	100	18	)	)	PUNCT
ejpam-4928	101	1	=	=	SYM
ejpam-4928	101	2	c2e	c2e	NOUN
ejpam-4928	101	3	−xβ	−xβ	PROPN
ejpam-4928	101	4	2kβ	2kβ	ADJ
ejpam-4928	101	5	sin	sin	NOUN
ejpam-4928	101	6	(	(	PUNCT
ejpam-4928	101	7	sin	sin	NOUN
ejpam-4928	101	8	(	(	PUNCT
ejpam-4928	101	9	nπxβ	nπxβ	NOUN
ejpam-4928	101	10	lβ	lβ	PROPN
ejpam-4928	101	11	)	)	PUNCT
ejpam-4928	101	12	)	)	PUNCT
ejpam-4928	101	13	(	(	PUNCT
ejpam-4928	101	14	6	6	X
ejpam-4928	101	15	)	)	PUNCT
ejpam-4928	101	16	now	now	ADV
ejpam-4928	101	17	,	,	PUNCT
ejpam-4928	101	18	to	to	PART
ejpam-4928	101	19	solve	solve	VERB
ejpam-4928	101	20	equation	equation	NOUN
ejpam-4928	101	21	(	(	PUNCT
ejpam-4928	101	22	4	4	NUM
ejpam-4928	101	23	)	)	PUNCT
ejpam-4928	101	24	,	,	PUNCT
ejpam-4928	101	25	we	we	PRON
ejpam-4928	101	26	will	will	AUX
ejpam-4928	101	27	rewrite	rewrite	VERB
ejpam-4928	101	28	as	as	SCONJ
ejpam-4928	101	29	follows	follow	VERB
ejpam-4928	101	30	:	:	PUNCT
ejpam-4928	101	31	t1−αt	t1−αt	PRON
ejpam-4928	101	32	(	(	PUNCT
ejpam-4928	101	33	t)−	t)−	PROPN
ejpam-4928	101	34	λt	λt	X
ejpam-4928	101	35	(	(	PUNCT
ejpam-4928	101	36	t	t	NOUN
ejpam-4928	101	37	)	)	PUNCT
ejpam-4928	101	38	=	=	SYM
ejpam-4928	102	1	0	0	NUM
ejpam-4928	102	2	,	,	PUNCT
ejpam-4928	102	3	which	which	PRON
ejpam-4928	102	4	is	be	AUX
ejpam-4928	102	5	a	a	DET
ejpam-4928	102	6	separable	separable	ADJ
ejpam-4928	102	7	differential	differential	ADJ
ejpam-4928	102	8	equation	equation	NOUN
ejpam-4928	102	9	,	,	PUNCT
ejpam-4928	102	10	so	so	SCONJ
ejpam-4928	102	11	t	t	PROPN
ejpam-4928	102	12	(	(	PUNCT
ejpam-4928	102	13	t	t	PROPN
ejpam-4928	102	14	)	)	PUNCT
ejpam-4928	102	15	=	=	NOUN
ejpam-4928	102	16	ane	ane	NOUN
ejpam-4928	102	17	(	(	PUNCT
ejpam-4928	102	18	−(2knπ	−(2knπ	NUM
ejpam-4928	102	19	β	β	PROPN
ejpam-4928	102	20	lβ	lβ	NOUN
ejpam-4928	102	21	)	)	PUNCT
ejpam-4928	102	22	−	−	PROPN
ejpam-4928	102	23	1	1	NUM
ejpam-4928	102	24	4k	4k	NUM
ejpam-4928	102	25	tα	tα	PROPN
ejpam-4928	102	26	α	α	NOUN
ejpam-4928	102	27	)	)	PUNCT
ejpam-4928	102	28	(	(	PUNCT
ejpam-4928	102	29	7	7	X
ejpam-4928	102	30	)	)	PUNCT
ejpam-4928	102	31	combining	combine	VERB
ejpam-4928	102	32	equations	equation	NOUN
ejpam-4928	102	33	(	(	PUNCT
ejpam-4928	102	34	6	6	NUM
ejpam-4928	102	35	)	)	PUNCT
ejpam-4928	102	36	and	and	CCONJ
ejpam-4928	102	37	(	(	PUNCT
ejpam-4928	102	38	7	7	NUM
ejpam-4928	102	39	)	)	PUNCT
ejpam-4928	102	40	,	,	PUNCT
ejpam-4928	102	41	we	we	PRON
ejpam-4928	102	42	get	get	VERB
ejpam-4928	102	43	u(x	u(x	NOUN
ejpam-4928	102	44	,	,	PUNCT
ejpam-4928	102	45	t	t	NOUN
ejpam-4928	102	46	)	)	PUNCT
ejpam-4928	102	47	=	=	PUNCT
ejpam-4928	103	1	∞∑	∞∑	NUM
ejpam-4928	103	2	n=1	n=1	PROPN
ejpam-4928	103	3	bn	bn	PART
ejpam-4928	103	4	e	e	NOUN
ejpam-4928	103	5	(	(	PUNCT
ejpam-4928	103	6	−(2knπ	−(2knπ	NUM
ejpam-4928	103	7	β	β	PROPN
ejpam-4928	103	8	lβ	lβ	NOUN
ejpam-4928	103	9	)	)	PUNCT
ejpam-4928	103	10	−	−	PROPN
ejpam-4928	103	11	1	1	NUM
ejpam-4928	103	12	4k	4k	NUM
ejpam-4928	103	13	tα	tα	PROPN
ejpam-4928	103	14	α	α	NOUN
ejpam-4928	103	15	)	)	PUNCT
ejpam-4928	103	16	e	e	PROPN
ejpam-4928	103	17	−xβ	−xβ	NUM
ejpam-4928	103	18	2kβ	2kβ	ADJ
ejpam-4928	103	19	sin	sin	NOUN
ejpam-4928	103	20	(	(	PUNCT
ejpam-4928	103	21	sin	sin	NOUN
ejpam-4928	103	22	(	(	PUNCT
ejpam-4928	103	23	nπxβ	nπxβ	NOUN
ejpam-4928	103	24	lβ	lβ	PROPN
ejpam-4928	103	25	)	)	PUNCT
ejpam-4928	103	26	)	)	PUNCT
ejpam-4928	103	27	(	(	PUNCT
ejpam-4928	103	28	8)	8)	NUM
ejpam-4928	103	29	by	by	ADP
ejpam-4928	103	30	using	use	VERB
ejpam-4928	103	31	u(x	u(x	NOUN
ejpam-4928	103	32	,	,	PUNCT
ejpam-4928	103	33	0	0	NUM
ejpam-4928	103	34	)	)	PUNCT
ejpam-4928	103	35	=	=	SYM
ejpam-4928	103	36	f(x	f(x	PROPN
ejpam-4928	103	37	)	)	PUNCT
ejpam-4928	103	38	,	,	PUNCT
ejpam-4928	103	39	we	we	PRON
ejpam-4928	103	40	get	get	VERB
ejpam-4928	103	41	f(x	f(x	NOUN
ejpam-4928	103	42	)	)	PUNCT
ejpam-4928	104	1	=	=	PUNCT
ejpam-4928	105	1	∞∑	∞∑	NUM
ejpam-4928	105	2	n=1	n=1	PROPN
ejpam-4928	105	3	bn	bn	ADP
ejpam-4928	105	4	e	e	PROPN
ejpam-4928	105	5	−xβ	−xβ	PROPN
ejpam-4928	105	6	2kβ	2kβ	ADJ
ejpam-4928	105	7	sin	sin	NOUN
ejpam-4928	105	8	(	(	PUNCT
ejpam-4928	105	9	sin	sin	NOUN
ejpam-4928	105	10	(	(	PUNCT
ejpam-4928	105	11	nπxβ	nπxβ	NOUN
ejpam-4928	105	12	lβ	lβ	PROPN
ejpam-4928	105	13	)	)	PUNCT
ejpam-4928	105	14	)	)	PUNCT
ejpam-4928	105	15	.	.	PUNCT
ejpam-4928	106	1	so	so	ADV
ejpam-4928	106	2	,	,	PUNCT
ejpam-4928	106	3	e	e	PROPN
ejpam-4928	106	4	−xβ	−xβ	NUM
ejpam-4928	106	5	2kβ	2kβ	ADJ
ejpam-4928	106	6	f(x	f(x	PROPN
ejpam-4928	106	7	)	)	PUNCT
ejpam-4928	107	1	=	=	X
ejpam-4928	108	1	∞∑	∞∑	NUM
ejpam-4928	108	2	n=1	n=1	ADP
ejpam-4928	108	3	bn	bn	NOUN
ejpam-4928	108	4	sin	sin	NOUN
ejpam-4928	108	5	(	(	PUNCT
ejpam-4928	108	6	sin	sin	NOUN
ejpam-4928	108	7	(	(	PUNCT
ejpam-4928	108	8	nπxβ	nπxβ	NOUN
ejpam-4928	108	9	lβ	lβ	PROPN
ejpam-4928	108	10	)	)	PUNCT
ejpam-4928	108	11	)	)	PUNCT
ejpam-4928	108	12	(	(	PUNCT
ejpam-4928	108	13	9	9	X
ejpam-4928	108	14	)	)	PUNCT
ejpam-4928	108	15	hence	hence	ADV
ejpam-4928	108	16	,	,	PUNCT
ejpam-4928	108	17	(	(	PUNCT
ejpam-4928	108	18	9	9	X
ejpam-4928	108	19	)	)	PUNCT
ejpam-4928	108	20	is	be	AUX
ejpam-4928	108	21	the	the	DET
ejpam-4928	108	22	β	β	NOUN
ejpam-4928	108	23	-	-	ADJ
ejpam-4928	108	24	fourier	fourier	ADJ
ejpam-4928	108	25	series	series	NOUN
ejpam-4928	108	26	[	[	X
ejpam-4928	108	27	12	12	NUM
ejpam-4928	108	28	]	]	PUNCT
ejpam-4928	108	29	and	and	CCONJ
ejpam-4928	108	30	then	then	ADV
ejpam-4928	108	31	,	,	PUNCT
ejpam-4928	108	32	we	we	PRON
ejpam-4928	108	33	can	can	AUX
ejpam-4928	108	34	get	get	VERB
ejpam-4928	108	35	the	the	DET
ejpam-4928	108	36	sine	sine	ADJ
ejpam-4928	108	37	β	β	NOUN
ejpam-4928	108	38	-	-	ADJ
ejpam-4928	108	39	fourier	fourier	NOUN
ejpam-4928	108	40	coefficients	coefficient	NOUN
ejpam-4928	108	41	as	as	ADP
ejpam-4928	108	42	bn	bn	NOUN
ejpam-4928	108	43	=	=	NOUN
ejpam-4928	108	44	2β	2β	NUM
ejpam-4928	109	1	lβ	lβ	INTJ
ejpam-4928	109	2	∫	∫	PROPN
ejpam-4928	109	3	l	l	NOUN
ejpam-4928	109	4	0	0	NUM
ejpam-4928	109	5	f(x	f(x	PROPN
ejpam-4928	109	6	)	)	PUNCT
ejpam-4928	110	1	e	e	NOUN
ejpam-4928	110	2	1	1	NUM
ejpam-4928	110	3	2k	2k	NUM
ejpam-4928	110	4	xβ	xβ	NOUN
ejpam-4928	110	5	2kβ	2kβ	ADJ
ejpam-4928	110	6	1	1	NUM
ejpam-4928	110	7	x1−β	x1−β	PROPN
ejpam-4928	110	8	sin	sin	NOUN
ejpam-4928	110	9	(	(	PUNCT
ejpam-4928	110	10	sin	sin	NOUN
ejpam-4928	110	11	(	(	PUNCT
ejpam-4928	110	12	nπxβ	nπxβ	NOUN
ejpam-4928	110	13	lβ	lβ	PROPN
ejpam-4928	110	14	)	)	PUNCT
ejpam-4928	110	15	)	)	PUNCT
ejpam-4928	110	16	(	(	PUNCT
ejpam-4928	110	17	10	10	NUM
ejpam-4928	110	18	)	)	PUNCT
ejpam-4928	110	19	which	which	PRON
ejpam-4928	110	20	completes	complete	VERB
ejpam-4928	110	21	the	the	DET
ejpam-4928	110	22	solution	solution	NOUN
ejpam-4928	110	23	of	of	ADP
ejpam-4928	110	24	the	the	DET
ejpam-4928	110	25	differential	differential	ADJ
ejpam-4928	110	26	equation	equation	NOUN
ejpam-4928	110	27	(	(	PUNCT
ejpam-4928	110	28	2	2	NUM
ejpam-4928	110	29	)	)	PUNCT
ejpam-4928	110	30	.	.	PUNCT
ejpam-4928	111	1	3.2	3.2	NUM
ejpam-4928	111	2	.	.	PUNCT
ejpam-4928	111	3	applications	application	NOUN
ejpam-4928	111	4	example	example	NOUN
ejpam-4928	111	5	1	1	X
ejpam-4928	111	6	.	.	PUNCT
ejpam-4928	112	1	find	find	VERB
ejpam-4928	112	2	the	the	DET
ejpam-4928	112	3	temperature	temperature	NOUN
ejpam-4928	112	4	u(x	u(x	NOUN
ejpam-4928	112	5	,	,	PUNCT
ejpam-4928	112	6	t	t	PROPN
ejpam-4928	112	7	)	)	PUNCT
ejpam-4928	112	8	in	in	ADP
ejpam-4928	112	9	a	a	DET
ejpam-4928	112	10	laterally	laterally	ADV
ejpam-4928	112	11	insulated	insulate	VERB
ejpam-4928	112	12	copper	copper	NOUN
ejpam-4928	112	13	bar	bar	NOUN
ejpam-4928	112	14	80	80	NUM
ejpam-4928	112	15	cm	cm	NOUN
ejpam-4928	112	16	long	long	ADV
ejpam-4928	112	17	if	if	SCONJ
ejpam-4928	112	18	the	the	DET
ejpam-4928	112	19	initial	initial	ADJ
ejpam-4928	112	20	temperature	temperature	NOUN
ejpam-4928	112	21	is	be	AUX
ejpam-4928	112	22	100	100	NUM
ejpam-4928	112	23	sin(sin(πx80	sin(sin(πx80	NOUN
ejpam-4928	112	24	)	)	PUNCT
ejpam-4928	112	25	)	)	PUNCT
ejpam-4928	113	1	◦	◦	NOUN
ejpam-4928	113	2	c	c	NOUN
ejpam-4928	113	3	and	and	CCONJ
ejpam-4928	113	4	the	the	DET
ejpam-4928	113	5	ends	end	NOUN
ejpam-4928	113	6	are	be	AUX
ejpam-4928	113	7	kept	keep	VERB
ejpam-4928	113	8	at	at	ADP
ejpam-4928	113	9	0	0	NUM
ejpam-4928	113	10	◦	◦	NOUN
ejpam-4928	113	11	c.	c.	NOUN
ejpam-4928	113	12	consider	consider	VERB
ejpam-4928	113	13	k	k	NOUN
ejpam-4928	113	14	=	=	NOUN
ejpam-4928	113	15	1.158	1.158	NUM
ejpam-4928	113	16	cm	cm	NOUN
ejpam-4928	113	17	m2	m2	PROPN
ejpam-4928	113	18	,	,	PUNCT
ejpam-4928	113	19	α	α	NOUN
ejpam-4928	113	20	=	=	SYM
ejpam-4928	113	21	0.5	0.5	NUM
ejpam-4928	113	22	and	and	CCONJ
ejpam-4928	113	23	β	β	X
ejpam-4928	113	24	=	=	NOUN
ejpam-4928	113	25	0.2	0.2	NUM
ejpam-4928	113	26	.	.	PUNCT
ejpam-4928	114	1	i.	i.	PROPN
ejpam-4928	114	2	aldarawi	aldarawi	VERB
ejpam-4928	114	3	et	et	PROPN
ejpam-4928	114	4	al	al	PROPN
ejpam-4928	114	5	.	.	PUNCT
ejpam-4928	114	6	/	/	SYM
ejpam-4928	114	7	eur	eur	PROPN
ejpam-4928	114	8	.	.	PUNCT
ejpam-4928	115	1	j.	j.	PROPN
ejpam-4928	115	2	pure	pure	PROPN
ejpam-4928	115	3	appl	appl	PROPN
ejpam-4928	115	4	.	.	PROPN
ejpam-4928	115	5	math	math	PROPN
ejpam-4928	115	6	,	,	PUNCT
ejpam-4928	115	7	16	16	NUM
ejpam-4928	115	8	(	(	PUNCT
ejpam-4928	115	9	4	4	NUM
ejpam-4928	115	10	)	)	PUNCT
ejpam-4928	115	11	(	(	PUNCT
ejpam-4928	115	12	2023	2023	NUM
ejpam-4928	115	13	)	)	PUNCT
ejpam-4928	115	14	,	,	PUNCT
ejpam-4928	115	15	2132	2132	NUM
ejpam-4928	115	16	-	-	SYM
ejpam-4928	115	17	2144	2144	NUM
ejpam-4928	115	18	2137	2137	NUM
ejpam-4928	115	19	solution	solution	NOUN
ejpam-4928	115	20	.	.	PUNCT
ejpam-4928	116	1	the	the	DET
ejpam-4928	116	2	partial	partial	ADJ
ejpam-4928	116	3	differential	differential	NOUN
ejpam-4928	116	4	equation	equation	NOUN
ejpam-4928	116	5	is	be	AUX
ejpam-4928	116	6	given	give	VERB
ejpam-4928	116	7	by	by	ADP
ejpam-4928	116	8	d0.5	d0.5	PROPN
ejpam-4928	116	9	t	t	PROPN
ejpam-4928	116	10	u−	u−	PROPN
ejpam-4928	116	11	1.158	1.158	NUM
ejpam-4928	116	12	d2(0.2)x	d2(0.2)x	PROPN
ejpam-4928	116	13	u	u	NOUN
ejpam-4928	116	14	=	=	PROPN
ejpam-4928	116	15	d0.2	d0.2	PROPN
ejpam-4928	116	16	x	x	SYM
ejpam-4928	116	17	u	u	PROPN
ejpam-4928	116	18	(	(	PUNCT
ejpam-4928	116	19	11	11	NUM
ejpam-4928	116	20	)	)	PUNCT
ejpam-4928	116	21	with	with	ADP
ejpam-4928	116	22	the	the	DET
ejpam-4928	116	23	boundary	boundary	ADJ
ejpam-4928	116	24	conditions	condition	NOUN
ejpam-4928	116	25	u(0	u(0	PROPN
ejpam-4928	116	26	,	,	PUNCT
ejpam-4928	116	27	t	t	PROPN
ejpam-4928	116	28	)	)	PUNCT
ejpam-4928	116	29	=	=	SYM
ejpam-4928	116	30	u(80	u(80	PROPN
ejpam-4928	116	31	,	,	PUNCT
ejpam-4928	116	32	t	t	PROPN
ejpam-4928	116	33	)	)	PUNCT
ejpam-4928	116	34	=	=	SYM
ejpam-4928	116	35	0	0	NUM
ejpam-4928	116	36	and	and	CCONJ
ejpam-4928	116	37	initial	initial	ADJ
ejpam-4928	116	38	condition	condition	NOUN
ejpam-4928	116	39	u(x	u(x	NOUN
ejpam-4928	116	40	,	,	PUNCT
ejpam-4928	116	41	0	0	NUM
ejpam-4928	116	42	)	)	PUNCT
ejpam-4928	116	43	=	=	NOUN
ejpam-4928	116	44	100	100	NUM
ejpam-4928	116	45	sin(sin(πx80	sin(sin(πx80	NOUN
ejpam-4928	116	46	)	)	PUNCT
ejpam-4928	116	47	.	.	PUNCT
ejpam-4928	117	1	therefore	therefore	ADV
ejpam-4928	117	2	,	,	PUNCT
ejpam-4928	117	3	from	from	ADP
ejpam-4928	117	4	equation	equation	NOUN
ejpam-4928	117	5	(	(	PUNCT
ejpam-4928	117	6	8)	8)	NUM
ejpam-4928	117	7	the	the	DET
ejpam-4928	117	8	solution	solution	NOUN
ejpam-4928	117	9	is	be	AUX
ejpam-4928	117	10	given	give	VERB
ejpam-4928	117	11	by	by	ADP
ejpam-4928	117	12	u(x	u(x	NOUN
ejpam-4928	117	13	,	,	PUNCT
ejpam-4928	117	14	t	t	NOUN
ejpam-4928	117	15	)	)	PUNCT
ejpam-4928	117	16	=	=	PUNCT
ejpam-4928	118	1	∞∑	∞∑	NUM
ejpam-4928	118	2	n=1	n=1	PROPN
ejpam-4928	118	3	bn	bn	NOUN
ejpam-4928	118	4	e	e	NOUN
ejpam-4928	118	5	−	−	PROPN
ejpam-4928	118	6	(	(	PUNCT
ejpam-4928	118	7	0.4632nπ	0.4632nπ	NOUN
ejpam-4928	118	8	5√80	5√80	NUM
ejpam-4928	118	9	)	)	PUNCT
ejpam-4928	118	10	2	2	NUM
ejpam-4928	118	11	−	−	NOUN
ejpam-4928	118	12	1	1	NUM
ejpam-4928	118	13	2.316t0.5	2.316t0.5	NUM
ejpam-4928	118	14	t0.5	t0.5	DET
ejpam-4928	118	15	e	e	NOUN
ejpam-4928	118	16	−x0.2	−x0.2	ADP
ejpam-4928	118	17	0.4632	0.4632	NUM
ejpam-4928	118	18	sin(sin	sin(sin	NOUN
ejpam-4928	118	19	(	(	PUNCT
ejpam-4928	118	20	nπx0.2	nπx0.2	NOUN
ejpam-4928	118	21	80	80	NUM
ejpam-4928	118	22	)	)	PUNCT
ejpam-4928	118	23	)	)	PUNCT
ejpam-4928	118	24	sin(sin	sin(sin	NOUN
ejpam-4928	118	25	(	(	PUNCT
ejpam-4928	118	26	nπx0.2	nπx0.2	NOUN
ejpam-4928	118	27	80	80	NUM
ejpam-4928	118	28	)	)	PUNCT
ejpam-4928	118	29	)	)	PUNCT
ejpam-4928	118	30	,	,	PUNCT
ejpam-4928	118	31	where	where	SCONJ
ejpam-4928	118	32	,	,	PUNCT
ejpam-4928	118	33	bn	bn	NOUN
ejpam-4928	118	34	=	=	NOUN
ejpam-4928	118	35	0.4	0.4	NUM
ejpam-4928	118	36	5	5	NUM
ejpam-4928	118	37	√	√	NUM
ejpam-4928	118	38	80	80	NUM
ejpam-4928	118	39	∫	∫	NOUN
ejpam-4928	118	40	80	80	NUM
ejpam-4928	118	41	0	0	NUM
ejpam-4928	118	42	100	100	NUM
ejpam-4928	118	43	sin(sin	sin(sin	NOUN
ejpam-4928	118	44	(	(	PUNCT
ejpam-4928	118	45	πx	πx	X
ejpam-4928	118	46	80	80	NUM
ejpam-4928	118	47	)	)	PUNCT
ejpam-4928	118	48	)	)	PUNCT
ejpam-4928	119	1	e	e	X
ejpam-4928	119	2	−x0.2	−x0.2	PROPN
ejpam-4928	119	3	0.4632	0.4632	NUM
ejpam-4928	119	4	dx	dx	PROPN
ejpam-4928	119	5	x0.8	x0.8	X
ejpam-4928	119	6	.	.	PUNCT
ejpam-4928	120	1	to	to	PART
ejpam-4928	120	2	verify	verify	VERB
ejpam-4928	120	3	our	our	PRON
ejpam-4928	120	4	method	method	NOUN
ejpam-4928	120	5	,	,	PUNCT
ejpam-4928	120	6	we	we	PRON
ejpam-4928	120	7	take	take	VERB
ejpam-4928	120	8	finite	finite	ADJ
ejpam-4928	120	9	sum	sum	NOUN
ejpam-4928	120	10	of	of	ADP
ejpam-4928	120	11	u(x	u(x	NOUN
ejpam-4928	120	12	,	,	PUNCT
ejpam-4928	120	13	t	t	PROPN
ejpam-4928	120	14	)	)	PUNCT
ejpam-4928	120	15	,	,	PUNCT
ejpam-4928	120	16	and	and	CCONJ
ejpam-4928	120	17	then	then	ADV
ejpam-4928	120	18	the	the	DET
ejpam-4928	120	19	approximate	approximate	ADJ
ejpam-4928	120	20	solution	solution	NOUN
ejpam-4928	120	21	is	be	AUX
ejpam-4928	120	22	given	give	VERB
ejpam-4928	120	23	by	by	ADP
ejpam-4928	120	24	uk(x	uk(x	ADP
ejpam-4928	120	25	,	,	PUNCT
ejpam-4928	120	26	t	t	PROPN
ejpam-4928	120	27	)	)	PUNCT
ejpam-4928	121	1	=	=	SYM
ejpam-4928	121	2	k∑	k∑	VERB
ejpam-4928	121	3	n=1	n=1	PROPN
ejpam-4928	121	4	bn	bn	PROPN
ejpam-4928	121	5	e	e	PROPN
ejpam-4928	121	6	−	−	PROPN
ejpam-4928	121	7	(	(	PUNCT
ejpam-4928	121	8	0.4632nπ	0.4632nπ	NOUN
ejpam-4928	121	9	5√80	5√80	NUM
ejpam-4928	121	10	)	)	PUNCT
ejpam-4928	121	11	2	2	NUM
ejpam-4928	121	12	−	−	NOUN
ejpam-4928	121	13	1	1	NUM
ejpam-4928	121	14	2.316t0.5	2.316t0.5	NUM
ejpam-4928	121	15	t0.5	t0.5	DET
ejpam-4928	121	16	e	e	NOUN
ejpam-4928	121	17	−x0.2	−x0.2	ADP
ejpam-4928	121	18	0.4632	0.4632	NUM
ejpam-4928	121	19	sin(sin	sin(sin	NOUN
ejpam-4928	121	20	(	(	PUNCT
ejpam-4928	121	21	nπx0.2	nπx0.2	NOUN
ejpam-4928	121	22	80	80	NUM
ejpam-4928	121	23	)	)	PUNCT
ejpam-4928	121	24	)	)	PUNCT
ejpam-4928	121	25	sin(sin	sin(sin	NOUN
ejpam-4928	121	26	(	(	PUNCT
ejpam-4928	121	27	nπx0.2	nπx0.2	NOUN
ejpam-4928	121	28	80	80	NUM
ejpam-4928	121	29	)	)	PUNCT
ejpam-4928	121	30	)	)	PUNCT
ejpam-4928	121	31	.	.	PUNCT
ejpam-4928	122	1	figure	figure	NOUN
ejpam-4928	122	2	2a	2a	NUM
ejpam-4928	122	3	plot	plot	VERB
ejpam-4928	122	4	the	the	DET
ejpam-4928	122	5	temperature	temperature	NOUN
ejpam-4928	122	6	u100(x	u100(x	NOUN
ejpam-4928	122	7	,	,	PUNCT
ejpam-4928	122	8	t	t	PROPN
ejpam-4928	122	9	)	)	PUNCT
ejpam-4928	122	10	in	in	ADP
ejpam-4928	122	11	a	a	DET
ejpam-4928	122	12	laterally	laterally	ADV
ejpam-4928	122	13	insulated	insulated	ADJ
ejpam-4928	122	14	copper	copper	NOUN
ejpam-4928	122	15	equation	equation	NOUN
ejpam-4928	122	16	(	(	PUNCT
ejpam-4928	122	17	11	11	NUM
ejpam-4928	122	18	)	)	PUNCT
ejpam-4928	122	19	.	.	PUNCT
ejpam-4928	123	1	in	in	ADP
ejpam-4928	123	2	figure	figure	NOUN
ejpam-4928	123	3	2b	2b	NUM
ejpam-4928	123	4	we	we	PRON
ejpam-4928	123	5	plot	plot	VERB
ejpam-4928	123	6	u100(x	u100(x	PROPN
ejpam-4928	123	7	,	,	PUNCT
ejpam-4928	123	8	t	t	PROPN
ejpam-4928	123	9	)	)	PUNCT
ejpam-4928	123	10	versus	versus	ADP
ejpam-4928	123	11	x	x	PUNCT
ejpam-4928	123	12	at	at	ADP
ejpam-4928	123	13	different	different	ADJ
ejpam-4928	123	14	values	value	NOUN
ejpam-4928	123	15	of	of	ADP
ejpam-4928	123	16	t	t	PROPN
ejpam-4928	123	17	,	,	PUNCT
ejpam-4928	123	18	t	t	PROPN
ejpam-4928	123	19	∈	∈	PROPN
ejpam-4928	123	20	{	{	PUNCT
ejpam-4928	123	21	0.1	0.1	NUM
ejpam-4928	123	22	,	,	PUNCT
ejpam-4928	123	23	0.3	0.3	NUM
ejpam-4928	123	24	,	,	PUNCT
ejpam-4928	123	25	0.7	0.7	NUM
ejpam-4928	123	26	,	,	PUNCT
ejpam-4928	123	27	1	1	NUM
ejpam-4928	123	28	,	,	PUNCT
ejpam-4928	123	29	1.5	1.5	NUM
ejpam-4928	123	30	,	,	PUNCT
ejpam-4928	123	31	2	2	NUM
ejpam-4928	123	32	}	}	PUNCT
ejpam-4928	123	33	,	,	PUNCT
ejpam-4928	123	34	where	where	SCONJ
ejpam-4928	123	35	each	each	DET
ejpam-4928	123	36	curve	curve	NOUN
ejpam-4928	123	37	represents	represent	VERB
ejpam-4928	123	38	a	a	DET
ejpam-4928	123	39	constant	constant	ADJ
ejpam-4928	123	40	time	time	NOUN
ejpam-4928	123	41	distance	distance	NOUN
ejpam-4928	123	42	function	function	NOUN
ejpam-4928	123	43	.	.	PUNCT
ejpam-4928	124	1	in	in	ADP
ejpam-4928	124	2	figure	figure	NOUN
ejpam-4928	124	3	2c	2c	NOUN
ejpam-4928	124	4	we	we	PRON
ejpam-4928	124	5	plot	plot	VERB
ejpam-4928	124	6	u100(x	u100(x	PROPN
ejpam-4928	124	7	,	,	PUNCT
ejpam-4928	124	8	t	t	PROPN
ejpam-4928	124	9	)	)	PUNCT
ejpam-4928	124	10	versus	versus	ADP
ejpam-4928	124	11	t	t	PROPN
ejpam-4928	124	12	at	at	ADP
ejpam-4928	124	13	different	different	ADJ
ejpam-4928	124	14	values	value	NOUN
ejpam-4928	124	15	of	of	ADP
ejpam-4928	124	16	x	x	X
ejpam-4928	124	17	,	,	PUNCT
ejpam-4928	124	18	x	x	SYM
ejpam-4928	124	19	∈	∈	NOUN
ejpam-4928	124	20	{	{	PUNCT
ejpam-4928	124	21	0.1	0.1	NUM
ejpam-4928	124	22	,	,	PUNCT
ejpam-4928	124	23	0.3	0.3	NUM
ejpam-4928	124	24	,	,	PUNCT
ejpam-4928	124	25	0.7	0.7	NUM
ejpam-4928	124	26	,	,	PUNCT
ejpam-4928	124	27	1	1	NUM
ejpam-4928	124	28	,	,	PUNCT
ejpam-4928	124	29	1.5	1.5	NUM
ejpam-4928	124	30	,	,	PUNCT
ejpam-4928	124	31	2	2	NUM
ejpam-4928	124	32	}	}	PUNCT
ejpam-4928	124	33	where	where	SCONJ
ejpam-4928	124	34	each	each	DET
ejpam-4928	124	35	curve	curve	NOUN
ejpam-4928	124	36	represents	represent	VERB
ejpam-4928	124	37	a	a	DET
ejpam-4928	124	38	constant	constant	ADJ
ejpam-4928	124	39	time	time	NOUN
ejpam-4928	124	40	function	function	NOUN
ejpam-4928	124	41	of	of	ADP
ejpam-4928	124	42	time	time	NOUN
ejpam-4928	124	43	.	.	PUNCT
ejpam-4928	125	1	in	in	ADP
ejpam-4928	125	2	figure	figure	NOUN
ejpam-4928	125	3	2d	2d	NOUN
ejpam-4928	125	4	the	the	DET
ejpam-4928	125	5	residual	residual	ADJ
ejpam-4928	125	6	error	error	NOUN
ejpam-4928	125	7	rese(x	rese(x	NOUN
ejpam-4928	125	8	,	,	PUNCT
ejpam-4928	125	9	t	t	PROPN
ejpam-4928	125	10	)	)	PUNCT
ejpam-4928	125	11	=	=	PUNCT
ejpam-4928	125	12	∣∣∣d0.5	∣∣∣d0.5	NOUN
ejpam-4928	125	13	t	t	NOUN
ejpam-4928	125	14	u−	u−	NOUN
ejpam-4928	125	15	1.158	1.158	NUM
ejpam-4928	125	16	d	d	NOUN
ejpam-4928	125	17	2(0.2	2(0.2	NUM
ejpam-4928	125	18	)	)	PUNCT
ejpam-4928	125	19	x	x	NOUN
ejpam-4928	126	1	u−d0.2	u−d0.2	NOUN
ejpam-4928	126	2	x	x	PUNCT
ejpam-4928	126	3	u	u	NOUN
ejpam-4928	126	4	∣∣∣	∣∣∣	ADJ
ejpam-4928	126	5	are	be	AUX
ejpam-4928	126	6	plotted	plot	VERB
ejpam-4928	126	7	to	to	PART
ejpam-4928	126	8	improve	improve	VERB
ejpam-4928	126	9	the	the	DET
ejpam-4928	126	10	solution	solution	NOUN
ejpam-4928	126	11	of	of	ADP
ejpam-4928	126	12	the	the	DET
ejpam-4928	126	13	pde	pde	NOUN
ejpam-4928	126	14	(	(	PUNCT
ejpam-4928	126	15	11	11	NUM
ejpam-4928	126	16	)	)	PUNCT
ejpam-4928	126	17	.	.	PUNCT
ejpam-4928	127	1	i.	i.	PROPN
ejpam-4928	127	2	aldarawi	aldarawi	VERB
ejpam-4928	127	3	et	et	PROPN
ejpam-4928	127	4	al	al	PROPN
ejpam-4928	127	5	.	.	PUNCT
ejpam-4928	127	6	/	/	SYM
ejpam-4928	127	7	eur	eur	PROPN
ejpam-4928	127	8	.	.	PUNCT
ejpam-4928	128	1	j.	j.	PROPN
ejpam-4928	128	2	pure	pure	PROPN
ejpam-4928	128	3	appl	appl	PROPN
ejpam-4928	128	4	.	.	PROPN
ejpam-4928	128	5	math	math	PROPN
ejpam-4928	128	6	,	,	PUNCT
ejpam-4928	128	7	16	16	NUM
ejpam-4928	128	8	(	(	PUNCT
ejpam-4928	128	9	4	4	NUM
ejpam-4928	128	10	)	)	PUNCT
ejpam-4928	128	11	(	(	PUNCT
ejpam-4928	128	12	2023	2023	NUM
ejpam-4928	128	13	)	)	PUNCT
ejpam-4928	128	14	,	,	PUNCT
ejpam-4928	128	15	2132	2132	NUM
ejpam-4928	128	16	-	-	SYM
ejpam-4928	128	17	2144	2144	NUM
ejpam-4928	128	18	2138	2138	NUM
ejpam-4928	128	19	(	(	PUNCT
ejpam-4928	128	20	a	a	NOUN
ejpam-4928	128	21	)	)	PUNCT
ejpam-4928	128	22	(	(	PUNCT
ejpam-4928	128	23	b	b	X
ejpam-4928	128	24	)	)	PUNCT
ejpam-4928	128	25	(	(	PUNCT
ejpam-4928	128	26	c	c	X
ejpam-4928	128	27	)	)	PUNCT
ejpam-4928	128	28	(	(	PUNCT
ejpam-4928	128	29	d	d	X
ejpam-4928	128	30	)	)	PUNCT
ejpam-4928	128	31	figure	figure	NOUN
ejpam-4928	128	32	2	2	NUM
ejpam-4928	128	33	:	:	PUNCT
ejpam-4928	128	34	graphs	graph	NOUN
ejpam-4928	128	35	for	for	ADP
ejpam-4928	128	36	equation	equation	NOUN
ejpam-4928	128	37	(	(	PUNCT
ejpam-4928	128	38	11	11	NUM
ejpam-4928	128	39	)	)	PUNCT
ejpam-4928	128	40	.	.	PUNCT
ejpam-4928	129	1	(	(	PUNCT
ejpam-4928	129	2	a	a	X
ejpam-4928	129	3	)	)	PUNCT
ejpam-4928	129	4	the	the	DET
ejpam-4928	129	5	temperature	temperature	NOUN
ejpam-4928	129	6	function	function	NOUN
ejpam-4928	129	7	u(x	u(x	NOUN
ejpam-4928	129	8	,	,	PUNCT
ejpam-4928	129	9	t	t	PROPN
ejpam-4928	129	10	)	)	PUNCT
ejpam-4928	129	11	.	.	PUNCT
ejpam-4928	130	1	(	(	PUNCT
ejpam-4928	130	2	b	b	X
ejpam-4928	130	3	)	)	PUNCT
ejpam-4928	130	4	the	the	DET
ejpam-4928	130	5	temperature	temperature	NOUN
ejpam-4928	130	6	function	function	NOUN
ejpam-4928	130	7	u(x	u(x	NOUN
ejpam-4928	130	8	,	,	PUNCT
ejpam-4928	130	9	t	t	PROPN
ejpam-4928	130	10	)	)	PUNCT
ejpam-4928	130	11	with	with	ADP
ejpam-4928	130	12	fixed	fix	VERB
ejpam-4928	130	13	t	t	PROPN
ejpam-4928	130	14	∈	∈	PROPN
ejpam-4928	130	15	{	{	PUNCT
ejpam-4928	130	16	0.1	0.1	NUM
ejpam-4928	130	17	,	,	PUNCT
ejpam-4928	130	18	0.3	0.3	NUM
ejpam-4928	130	19	,	,	PUNCT
ejpam-4928	130	20	0.7	0.7	NUM
ejpam-4928	130	21	,	,	PUNCT
ejpam-4928	130	22	1	1	NUM
ejpam-4928	130	23	,	,	PUNCT
ejpam-4928	130	24	1.5	1.5	NUM
ejpam-4928	130	25	,	,	PUNCT
ejpam-4928	130	26	2	2	NUM
ejpam-4928	130	27	}	}	PUNCT
ejpam-4928	130	28	.	.	PUNCT
ejpam-4928	131	1	(	(	PUNCT
ejpam-4928	131	2	c	c	X
ejpam-4928	131	3	)	)	PUNCT
ejpam-4928	131	4	he	he	PRON
ejpam-4928	131	5	temperature	temperature	NOUN
ejpam-4928	131	6	function	function	NOUN
ejpam-4928	131	7	u(x	u(x	NOUN
ejpam-4928	131	8	,	,	PUNCT
ejpam-4928	131	9	t	t	PROPN
ejpam-4928	131	10	)	)	PUNCT
ejpam-4928	131	11	with	with	ADP
ejpam-4928	131	12	fixed	fix	VERB
ejpam-4928	131	13	x	x	SYM
ejpam-4928	131	14	∈	∈	PROPN
ejpam-4928	131	15	{	{	PUNCT
ejpam-4928	131	16	0.1	0.1	NUM
ejpam-4928	131	17	,	,	PUNCT
ejpam-4928	131	18	0.3	0.3	NUM
ejpam-4928	131	19	,	,	PUNCT
ejpam-4928	131	20	0.7	0.7	NUM
ejpam-4928	131	21	,	,	PUNCT
ejpam-4928	131	22	1	1	NUM
ejpam-4928	131	23	,	,	PUNCT
ejpam-4928	131	24	1.5	1.5	NUM
ejpam-4928	131	25	,	,	PUNCT
ejpam-4928	131	26	2	2	NUM
ejpam-4928	131	27	}	}	PUNCT
ejpam-4928	131	28	.	.	PUNCT
ejpam-4928	132	1	(	(	PUNCT
ejpam-4928	132	2	d	d	X
ejpam-4928	132	3	)	)	PUNCT
ejpam-4928	132	4	the	the	DET
ejpam-4928	132	5	residual	residual	ADJ
ejpam-4928	132	6	error	error	NOUN
ejpam-4928	132	7	.	.	PUNCT
ejpam-4928	133	1	4	4	X
ejpam-4928	133	2	.	.	X
ejpam-4928	133	3	atomic	atomic	ADJ
ejpam-4928	133	4	solution	solution	NOUN
ejpam-4928	133	5	since	since	SCONJ
ejpam-4928	133	6	not	not	PART
ejpam-4928	133	7	every	every	DET
ejpam-4928	133	8	linear	linear	ADJ
ejpam-4928	133	9	partial	partial	ADJ
ejpam-4928	133	10	differential	differential	NOUN
ejpam-4928	133	11	(	(	PUNCT
ejpam-4928	133	12	fractional	fractional	ADJ
ejpam-4928	133	13	or	or	CCONJ
ejpam-4928	133	14	not	not	PART
ejpam-4928	133	15	)	)	PUNCT
ejpam-4928	133	16	can	can	AUX
ejpam-4928	133	17	be	be	AUX
ejpam-4928	133	18	solved	solve	VERB
ejpam-4928	133	19	using	use	VERB
ejpam-4928	133	20	the	the	DET
ejpam-4928	133	21	separation	separation	NOUN
ejpam-4928	133	22	of	of	ADP
ejpam-4928	133	23	variables	variable	NOUN
ejpam-4928	133	24	,	,	PUNCT
ejpam-4928	133	25	the	the	DET
ejpam-4928	133	26	concept	concept	NOUN
ejpam-4928	133	27	of	of	ADP
ejpam-4928	133	28	the	the	DET
ejpam-4928	133	29	atomic	atomic	ADJ
ejpam-4928	133	30	solution	solution	NOUN
ejpam-4928	133	31	is	be	AUX
ejpam-4928	133	32	established	establish	VERB
ejpam-4928	133	33	.	.	PUNCT
ejpam-4928	134	1	let	let	VERB
ejpam-4928	134	2	x	x	PRON
ejpam-4928	134	3	and	and	CCONJ
ejpam-4928	134	4	y	y	PROPN
ejpam-4928	134	5	be	be	AUX
ejpam-4928	134	6	two	two	NUM
ejpam-4928	134	7	banach	banach	NOUN
ejpam-4928	134	8	spaces	space	NOUN
ejpam-4928	134	9	and	and	CCONJ
ejpam-4928	134	10	x∗	x∗	PROPN
ejpam-4928	134	11	be	be	VERB
ejpam-4928	134	12	the	the	DET
ejpam-4928	134	13	dual	dual	ADJ
ejpam-4928	134	14	of	of	ADP
ejpam-4928	134	15	x.	x.	NOUN
ejpam-4928	134	16	assume	assume	VERB
ejpam-4928	134	17	x	x	X
ejpam-4928	134	18	∈	∈	PROPN
ejpam-4928	134	19	x	x	X
ejpam-4928	134	20	and	and	CCONJ
ejpam-4928	134	21	y	y	PROPN
ejpam-4928	134	22	∈	∈	PROPN
ejpam-4928	134	23	y	y	PROPN
ejpam-4928	134	24	.	.	PUNCT
ejpam-4928	135	1	the	the	DET
ejpam-4928	135	2	operator	operator	NOUN
ejpam-4928	135	3	t	t	NOUN
ejpam-4928	135	4	:	:	PUNCT
ejpam-4928	135	5	x∗	x∗	PROPN
ejpam-4928	135	6	→	→	SYM
ejpam-4928	135	7	y	y	PROPN
ejpam-4928	135	8	which	which	PRON
ejpam-4928	135	9	is	be	AUX
ejpam-4928	135	10	defined	define	VERB
ejpam-4928	135	11	by	by	ADP
ejpam-4928	135	12	t	t	PROPN
ejpam-4928	135	13	(	(	PUNCT
ejpam-4928	135	14	x∗	x∗	PROPN
ejpam-4928	135	15	)	)	PUNCT
ejpam-4928	135	16	=	=	PUNCT
ejpam-4928	136	1	x∗(x)y	x∗(x)y	PROPN
ejpam-4928	136	2	is	be	AUX
ejpam-4928	136	3	a	a	DET
ejpam-4928	136	4	bounded	bounded	ADJ
ejpam-4928	136	5	one	one	NUM
ejpam-4928	136	6	-	-	PUNCT
ejpam-4928	136	7	rank	rank	NOUN
ejpam-4928	136	8	linear	linear	NOUN
ejpam-4928	136	9	operator	operator	NOUN
ejpam-4928	136	10	.	.	PUNCT
ejpam-4928	137	1	we	we	PRON
ejpam-4928	137	2	write	write	VERB
ejpam-4928	137	3	x⊗y	x⊗y	PROPN
ejpam-4928	137	4	for	for	ADP
ejpam-4928	137	5	t	t	PROPN
ejpam-4928	137	6	.	.	PUNCT
ejpam-4928	138	1	such	such	ADJ
ejpam-4928	138	2	operators	operator	NOUN
ejpam-4928	138	3	are	be	AUX
ejpam-4928	138	4	called	call	VERB
ejpam-4928	138	5	atoms	atom	NOUN
ejpam-4928	138	6	.	.	PUNCT
ejpam-4928	139	1	atoms	atom	NOUN
ejpam-4928	139	2	are	be	AUX
ejpam-4928	139	3	among	among	ADP
ejpam-4928	139	4	the	the	DET
ejpam-4928	139	5	main	main	ADJ
ejpam-4928	139	6	ingredient	ingredient	NOUN
ejpam-4928	139	7	in	in	ADP
ejpam-4928	139	8	the	the	DET
ejpam-4928	139	9	theory	theory	NOUN
ejpam-4928	139	10	of	of	ADP
ejpam-4928	139	11	tensor	tensor	NOUN
ejpam-4928	139	12	products	product	NOUN
ejpam-4928	139	13	.	.	PUNCT
ejpam-4928	140	1	atoms	atom	NOUN
ejpam-4928	140	2	are	be	AUX
ejpam-4928	140	3	used	use	VERB
ejpam-4928	140	4	in	in	ADP
ejpam-4928	140	5	the	the	DET
ejpam-4928	140	6	theory	theory	NOUN
ejpam-4928	140	7	of	of	ADP
ejpam-4928	140	8	best	good	ADJ
ejpam-4928	140	9	approximation	approximation	NOUN
ejpam-4928	140	10	in	in	ADP
ejpam-4928	140	11	banach	banach	NOUN
ejpam-4928	140	12	spaces	space	NOUN
ejpam-4928	140	13	[	[	X
ejpam-4928	140	14	16	16	NUM
ejpam-4928	140	15	]	]	PUNCT
ejpam-4928	140	16	.	.	PUNCT
ejpam-4928	141	1	one	one	NUM
ejpam-4928	141	2	of	of	ADP
ejpam-4928	141	3	the	the	DET
ejpam-4928	141	4	known	know	VERB
ejpam-4928	141	5	results	result	NOUN
ejpam-4928	141	6	[	[	X
ejpam-4928	141	7	20	20	NUM
ejpam-4928	141	8	]	]	PUNCT
ejpam-4928	141	9	that	that	SCONJ
ejpam-4928	141	10	we	we	PRON
ejpam-4928	141	11	need	need	VERB
ejpam-4928	141	12	in	in	ADP
ejpam-4928	141	13	our	our	PRON
ejpam-4928	141	14	paper	paper	NOUN
ejpam-4928	141	15	is	be	AUX
ejpam-4928	141	16	that	that	SCONJ
ejpam-4928	141	17	:	:	PUNCT
ejpam-4928	141	18	if	if	SCONJ
ejpam-4928	141	19	the	the	DET
ejpam-4928	141	20	sum	sum	NOUN
ejpam-4928	141	21	of	of	ADP
ejpam-4928	141	22	two	two	NUM
ejpam-4928	141	23	atoms	atom	NOUN
ejpam-4928	141	24	is	be	AUX
ejpam-4928	141	25	an	an	DET
ejpam-4928	141	26	atom	atom	NOUN
ejpam-4928	141	27	,	,	PUNCT
ejpam-4928	141	28	then	then	ADV
ejpam-4928	141	29	either	either	CCONJ
ejpam-4928	141	30	the	the	DET
ejpam-4928	141	31	first	first	ADJ
ejpam-4928	141	32	components	component	NOUN
ejpam-4928	141	33	are	be	AUX
ejpam-4928	141	34	dependent	dependent	ADJ
ejpam-4928	141	35	,	,	PUNCT
ejpam-4928	141	36	or	or	CCONJ
ejpam-4928	141	37	the	the	DET
ejpam-4928	141	38	second	second	ADJ
ejpam-4928	141	39	ones	one	NOUN
ejpam-4928	141	40	are	be	AUX
ejpam-4928	141	41	dependent	dependent	ADJ
ejpam-4928	141	42	.	.	PUNCT
ejpam-4928	142	1	for	for	ADP
ejpam-4928	142	2	more	more	ADJ
ejpam-4928	142	3	tensor	tensor	NOUN
ejpam-4928	142	4	products	product	NOUN
ejpam-4928	142	5	of	of	ADP
ejpam-4928	142	6	banach	banach	NOUN
ejpam-4928	142	7	spaces	space	NOUN
ejpam-4928	142	8	,	,	PUNCT
ejpam-4928	142	9	we	we	PRON
ejpam-4928	142	10	refer	refer	VERB
ejpam-4928	142	11	to	to	ADP
ejpam-4928	142	12	[	[	X
ejpam-4928	142	13	20	20	NUM
ejpam-4928	142	14	]	]	PUNCT
ejpam-4928	142	15	.	.	PUNCT
ejpam-4928	143	1	let	let	VERB
ejpam-4928	143	2	us	we	PRON
ejpam-4928	143	3	write	write	VERB
ejpam-4928	143	4	dα	dα	NOUN
ejpam-4928	143	5	xu	xu	PROPN
ejpam-4928	143	6	to	to	PART
ejpam-4928	143	7	mean	mean	VERB
ejpam-4928	143	8	the	the	DET
ejpam-4928	143	9	partial	partial	ADJ
ejpam-4928	143	10	α	α	NOUN
ejpam-4928	143	11	-	-	NOUN
ejpam-4928	143	12	derivative	derivative	NOUN
ejpam-4928	143	13	of	of	ADP
ejpam-4928	143	14	u	u	NOUN
ejpam-4928	143	15	with	with	ADP
ejpam-4928	143	16	respect	respect	NOUN
ejpam-4928	143	17	to	to	ADP
ejpam-4928	143	18	x.	x.	PROPN
ejpam-4928	143	19	further	far	ADV
ejpam-4928	143	20	,	,	PUNCT
ejpam-4928	143	21	we	we	PRON
ejpam-4928	143	22	write	write	VERB
ejpam-4928	143	23	d2α	d2α	NOUN
ejpam-4928	143	24	x	x	ADP
ejpam-4928	143	25	u	u	NOUN
ejpam-4928	143	26	to	to	PART
ejpam-4928	143	27	mean	mean	VERB
ejpam-4928	143	28	dα	dα	ADP
ejpam-4928	143	29	xud	xud	PROPN
ejpam-4928	143	30	α	α	PROPN
ejpam-4928	143	31	xu	xu	PROPN
ejpam-4928	143	32	.	.	PUNCT
ejpam-4928	144	1	similarly	similarly	ADV
ejpam-4928	144	2	for	for	ADP
ejpam-4928	144	3	derivatives	derivative	NOUN
ejpam-4928	144	4	with	with	ADP
ejpam-4928	144	5	respect	respect	NOUN
ejpam-4928	144	6	to	to	ADP
ejpam-4928	144	7	y.	y.	PROPN
ejpam-4928	144	8	i.	i.	PROPN
ejpam-4928	144	9	aldarawi	aldarawi	PROPN
ejpam-4928	144	10	et	et	PROPN
ejpam-4928	144	11	al	al	PROPN
ejpam-4928	144	12	.	.	PUNCT
ejpam-4928	144	13	/	/	SYM
ejpam-4928	144	14	eur	eur	PROPN
ejpam-4928	144	15	.	.	PUNCT
ejpam-4928	145	1	j.	j.	PROPN
ejpam-4928	145	2	pure	pure	PROPN
ejpam-4928	145	3	appl	appl	PROPN
ejpam-4928	145	4	.	.	PROPN
ejpam-4928	145	5	math	math	PROPN
ejpam-4928	145	6	,	,	PUNCT
ejpam-4928	145	7	16	16	NUM
ejpam-4928	145	8	(	(	PUNCT
ejpam-4928	145	9	4	4	NUM
ejpam-4928	145	10	)	)	PUNCT
ejpam-4928	145	11	(	(	PUNCT
ejpam-4928	145	12	2023	2023	NUM
ejpam-4928	145	13	)	)	PUNCT
ejpam-4928	145	14	,	,	PUNCT
ejpam-4928	145	15	2132	2132	NUM
ejpam-4928	145	16	-	-	SYM
ejpam-4928	145	17	2144	2144	NUM
ejpam-4928	145	18	2139	2139	NUM
ejpam-4928	145	19	4.1	4.1	NUM
ejpam-4928	145	20	.	.	PUNCT
ejpam-4928	146	1	application	application	NOUN
ejpam-4928	146	2	1	1	NUM
ejpam-4928	146	3	in	in	ADP
ejpam-4928	146	4	equation	equation	NOUN
ejpam-4928	146	5	(	(	PUNCT
ejpam-4928	146	6	12	12	NUM
ejpam-4928	146	7	)	)	PUNCT
ejpam-4928	146	8	,	,	PUNCT
ejpam-4928	146	9	the	the	DET
ejpam-4928	146	10	method	method	NOUN
ejpam-4928	146	11	of	of	ADP
ejpam-4928	146	12	separation	separation	NOUN
ejpam-4928	146	13	of	of	ADP
ejpam-4928	146	14	variables	variable	NOUN
ejpam-4928	146	15	is	be	AUX
ejpam-4928	146	16	not	not	PART
ejpam-4928	146	17	possible	possible	ADJ
ejpam-4928	146	18	though	though	SCONJ
ejpam-4928	146	19	the	the	DET
ejpam-4928	146	20	equation	equation	NOUN
ejpam-4928	146	21	is	be	AUX
ejpam-4928	146	22	linear	linear	ADJ
ejpam-4928	146	23	.	.	PUNCT
ejpam-4928	147	1	hence	hence	ADV
ejpam-4928	147	2	,	,	PUNCT
ejpam-4928	147	3	we	we	PRON
ejpam-4928	147	4	try	try	VERB
ejpam-4928	147	5	to	to	PART
ejpam-4928	147	6	find	find	VERB
ejpam-4928	147	7	an	an	DET
ejpam-4928	147	8	atomic	atomic	ADJ
ejpam-4928	147	9	solution	solution	NOUN
ejpam-4928	147	10	to	to	ADP
ejpam-4928	147	11	this	this	DET
ejpam-4928	147	12	equation	equation	NOUN
ejpam-4928	147	13	dα	dα	VERB
ejpam-4928	147	14	t	t	PROPN
ejpam-4928	147	15	u+dβ	u+dβ	PROPN
ejpam-4928	147	16	x	x	X
ejpam-4928	147	17	d	d	X
ejpam-4928	147	18	β	β	X
ejpam-4928	147	19	xu	xu	PROPN
ejpam-4928	148	1	=	=	PUNCT
ejpam-4928	149	1	d2α	d2α	NOUN
ejpam-4928	149	2	t	t	PROPN
ejpam-4928	149	3	dβ	dβ	PROPN
ejpam-4928	149	4	xu	xu	PROPN
ejpam-4928	149	5	,	,	PUNCT
ejpam-4928	149	6	0	0	PUNCT
ejpam-4928	149	7	<	<	X
ejpam-4928	149	8	α	α	X
ejpam-4928	149	9	,	,	PUNCT
ejpam-4928	149	10	β	β	X
ejpam-4928	149	11	<	<	X
ejpam-4928	149	12	1	1	NUM
ejpam-4928	149	13	(	(	PUNCT
ejpam-4928	149	14	12	12	NUM
ejpam-4928	149	15	)	)	PUNCT
ejpam-4928	149	16	u(0	u(0	NOUN
ejpam-4928	149	17	,	,	PUNCT
ejpam-4928	149	18	0	0	NUM
ejpam-4928	149	19	=	=	SYM
ejpam-4928	149	20	0	0	NUM
ejpam-4928	149	21	)	)	PUNCT
ejpam-4928	149	22	and	and	CCONJ
ejpam-4928	149	23	dα	dα	PRON
ejpam-4928	149	24	t	t	PROPN
ejpam-4928	149	25	dβ	dβ	ADP
ejpam-4928	149	26	x(0	x(0	PROPN
ejpam-4928	149	27	,	,	PUNCT
ejpam-4928	149	28	0	0	NUM
ejpam-4928	149	29	)	)	PUNCT
ejpam-4928	149	30	=	=	SYM
ejpam-4928	149	31	1	1	NUM
ejpam-4928	149	32	,	,	PUNCT
ejpam-4928	149	33	where	where	SCONJ
ejpam-4928	149	34	by	by	ADP
ejpam-4928	149	35	an	an	DET
ejpam-4928	149	36	atomic	atomic	ADJ
ejpam-4928	149	37	solution	solution	NOUN
ejpam-4928	149	38	we	we	PRON
ejpam-4928	149	39	mean	mean	VERB
ejpam-4928	149	40	a	a	DET
ejpam-4928	149	41	solution	solution	NOUN
ejpam-4928	149	42	of	of	ADP
ejpam-4928	149	43	the	the	DET
ejpam-4928	149	44	form	form	NOUN
ejpam-4928	149	45	u(x	u(x	NOUN
ejpam-4928	149	46	,	,	PUNCT
ejpam-4928	149	47	t	t	NOUN
ejpam-4928	149	48	)	)	PUNCT
ejpam-4928	149	49	=	=	SYM
ejpam-4928	150	1	x(x)t	x(x)t	PROPN
ejpam-4928	150	2	(	(	PUNCT
ejpam-4928	150	3	t	t	PROPN
ejpam-4928	150	4	)	)	PUNCT
ejpam-4928	150	5	.	.	PUNCT
ejpam-4928	150	6	procedure	procedure	NOUN
ejpam-4928	150	7	let	let	VERB
ejpam-4928	150	8	u(x	u(x	NOUN
ejpam-4928	150	9	,	,	PUNCT
ejpam-4928	150	10	t	t	PROPN
ejpam-4928	150	11	)	)	PUNCT
ejpam-4928	150	12	=	=	SYM
ejpam-4928	150	13	x(x)t	x(x)t	PROPN
ejpam-4928	150	14	(	(	PUNCT
ejpam-4928	150	15	t	t	PROPN
ejpam-4928	150	16	)	)	PUNCT
ejpam-4928	150	17	.	.	PUNCT
ejpam-4928	151	1	substitute	substitute	NOUN
ejpam-4928	151	2	in	in	ADP
ejpam-4928	151	3	equation	equation	NOUN
ejpam-4928	151	4	(	(	PUNCT
ejpam-4928	151	5	12	12	NUM
ejpam-4928	151	6	)	)	PUNCT
ejpam-4928	151	7	to	to	PART
ejpam-4928	151	8	get	get	VERB
ejpam-4928	151	9	x(x)tα(t	x(x)tα(t	NOUN
ejpam-4928	151	10	)	)	PUNCT
ejpam-4928	152	1	+	+	PROPN
ejpam-4928	152	2	x2β(x)t	x2β(x)t	PROPN
ejpam-4928	152	3	(	(	PUNCT
ejpam-4928	152	4	t	t	PROPN
ejpam-4928	152	5	)	)	PUNCT
ejpam-4928	152	6	=	=	SYM
ejpam-4928	152	7	x(x)t	x(x)t	PROPN
ejpam-4928	152	8	2α(t	2α(t	NUM
ejpam-4928	152	9	)	)	PUNCT
ejpam-4928	152	10	.	.	PUNCT
ejpam-4928	153	1	this	this	PRON
ejpam-4928	153	2	can	can	AUX
ejpam-4928	153	3	be	be	AUX
ejpam-4928	153	4	written	write	VERB
ejpam-4928	153	5	in	in	ADP
ejpam-4928	153	6	tensor	tensor	NOUN
ejpam-4928	153	7	product	product	NOUN
ejpam-4928	153	8	form	form	NOUN
ejpam-4928	153	9	as	as	ADP
ejpam-4928	153	10	:	:	PUNCT
ejpam-4928	153	11	x	x	PROPN
ejpam-4928	153	12	⊗	⊗	PROPN
ejpam-4928	153	13	tα	tα	PROPN
ejpam-4928	153	14	+	+	PROPN
ejpam-4928	153	15	x2β	x2β	PROPN
ejpam-4928	153	16	⊗	⊗	PROPN
ejpam-4928	153	17	t	t	PROPN
ejpam-4928	153	18	=	=	PUNCT
ejpam-4928	153	19	xβ	xβ	PROPN
ejpam-4928	153	20	⊗	⊗	PROPN
ejpam-4928	153	21	t	t	PROPN
ejpam-4928	153	22	2α	2α	NOUN
ejpam-4928	153	23	(	(	PUNCT
ejpam-4928	153	24	13	13	NUM
ejpam-4928	153	25	)	)	PUNCT
ejpam-4928	153	26	let	let	VERB
ejpam-4928	153	27	us	we	PRON
ejpam-4928	153	28	consider	consider	VERB
ejpam-4928	153	29	the	the	DET
ejpam-4928	153	30	following	follow	VERB
ejpam-4928	153	31	conditions	condition	NOUN
ejpam-4928	153	32	:	:	PUNCT
ejpam-4928	153	33	t	t	PROPN
ejpam-4928	153	34	(	(	PUNCT
ejpam-4928	153	35	0	0	NUM
ejpam-4928	153	36	)	)	PUNCT
ejpam-4928	153	37	=	=	SYM
ejpam-4928	153	38	1	1	NUM
ejpam-4928	153	39	,	,	PUNCT
ejpam-4928	153	40	tα(0	tα(0	NOUN
ejpam-4928	153	41	)	)	PUNCT
ejpam-4928	153	42	=	=	SYM
ejpam-4928	153	43	1	1	NUM
ejpam-4928	153	44	,	,	PUNCT
ejpam-4928	153	45	x(0	x(0	PROPN
ejpam-4928	153	46	)	)	PUNCT
ejpam-4928	153	47	=	=	SYM
ejpam-4928	153	48	0	0	NUM
ejpam-4928	153	49	and	and	CCONJ
ejpam-4928	153	50	xβ(0	xβ(0	NUM
ejpam-4928	153	51	)	)	PUNCT
ejpam-4928	153	52	=	=	SYM
ejpam-4928	154	1	1	1	X
ejpam-4928	154	2	.	.	X
ejpam-4928	154	3	in	in	ADP
ejpam-4928	154	4	equation	equation	NOUN
ejpam-4928	154	5	(	(	PUNCT
ejpam-4928	154	6	12	12	NUM
ejpam-4928	154	7	)	)	PUNCT
ejpam-4928	154	8	,	,	PUNCT
ejpam-4928	154	9	we	we	PRON
ejpam-4928	154	10	have	have	VERB
ejpam-4928	154	11	the	the	DET
ejpam-4928	154	12	situation	situation	NOUN
ejpam-4928	154	13	:	:	PUNCT
ejpam-4928	154	14	the	the	DET
ejpam-4928	154	15	sum	sum	NOUN
ejpam-4928	154	16	of	of	ADP
ejpam-4928	154	17	two	two	NUM
ejpam-4928	154	18	atoms	atom	NOUN
ejpam-4928	154	19	is	be	AUX
ejpam-4928	154	20	an	an	DET
ejpam-4928	154	21	atom	atom	NOUN
ejpam-4928	154	22	.	.	PUNCT
ejpam-4928	155	1	hence	hence	ADV
ejpam-4928	155	2	,	,	PUNCT
ejpam-4928	155	3	we	we	PRON
ejpam-4928	155	4	have	have	VERB
ejpam-4928	155	5	two	two	NUM
ejpam-4928	155	6	cases	case	NOUN
ejpam-4928	155	7	:	:	PUNCT
ejpam-4928	155	8	case	case	NOUN
ejpam-4928	155	9	(	(	PUNCT
ejpam-4928	155	10	i	i	PROPN
ejpam-4928	155	11	):	):	PUNCT
ejpam-4928	155	12	t	t	PROPN
ejpam-4928	155	13	(	(	PUNCT
ejpam-4928	155	14	t	t	PROPN
ejpam-4928	155	15	)	)	PUNCT
ejpam-4928	155	16	=	=	SYM
ejpam-4928	155	17	tα(t	tα(t	X
ejpam-4928	155	18	)	)	PUNCT
ejpam-4928	155	19	=	=	SYM
ejpam-4928	155	20	t	t	NOUN
ejpam-4928	155	21	2α(t	2α(t	NUM
ejpam-4928	155	22	)	)	PUNCT
ejpam-4928	155	23	.	.	PUNCT
ejpam-4928	156	1	using	use	VERB
ejpam-4928	156	2	the	the	DET
ejpam-4928	156	3	result	result	NOUN
ejpam-4928	156	4	in	in	ADP
ejpam-4928	156	5	[	[	X
ejpam-4928	156	6	1	1	NUM
ejpam-4928	156	7	]	]	PUNCT
ejpam-4928	156	8	,	,	PUNCT
ejpam-4928	156	9	we	we	PRON
ejpam-4928	156	10	get	get	VERB
ejpam-4928	156	11	t	t	PROPN
ejpam-4928	156	12	(	(	PUNCT
ejpam-4928	156	13	t	t	PROPN
ejpam-4928	156	14	)	)	PUNCT
ejpam-4928	156	15	=	=	PUNCT
ejpam-4928	156	16	e	e	X
ejpam-4928	156	17	tα	tα	PROPN
ejpam-4928	156	18	α	α	PROPN
ejpam-4928	156	19	(	(	PUNCT
ejpam-4928	156	20	14	14	NUM
ejpam-4928	156	21	)	)	PUNCT
ejpam-4928	156	22	now	now	ADV
ejpam-4928	156	23	we	we	PRON
ejpam-4928	156	24	substitute	substitute	VERB
ejpam-4928	156	25	in	in	ADP
ejpam-4928	156	26	(	(	PUNCT
ejpam-4928	156	27	13	13	NUM
ejpam-4928	156	28	)	)	PUNCT
ejpam-4928	156	29	to	to	PART
ejpam-4928	156	30	get	get	VERB
ejpam-4928	156	31	e	e	PROPN
ejpam-4928	156	32	tα	tα	PROPN
ejpam-4928	156	33	α	α	PROPN
ejpam-4928	156	34	⊗	⊗	PROPN
ejpam-4928	156	35	(	(	PUNCT
ejpam-4928	156	36	x	x	PUNCT
ejpam-4928	156	37	+	+	NOUN
ejpam-4928	156	38	x2β	x2β	NOUN
ejpam-4928	156	39	)	)	PUNCT
ejpam-4928	157	1	=	=	PUNCT
ejpam-4928	157	2	e	e	X
ejpam-4928	157	3	tα	tα	PROPN
ejpam-4928	157	4	α	α	NOUN
ejpam-4928	157	5	⊗xβ	⊗xβ	NUM
ejpam-4928	157	6	.	.	PUNCT
ejpam-4928	158	1	hence	hence	ADV
ejpam-4928	158	2	,	,	PUNCT
ejpam-4928	158	3	x2β	x2β	PROPN
ejpam-4928	158	4	−xβ	−xβ	PROPN
ejpam-4928	159	1	+	+	NOUN
ejpam-4928	159	2	x	x	X
ejpam-4928	159	3	=	=	SYM
ejpam-4928	159	4	0	0	X
ejpam-4928	159	5	.	.	PUNCT
ejpam-4928	159	6	again	again	ADV
ejpam-4928	159	7	,	,	PUNCT
ejpam-4928	159	8	using	use	VERB
ejpam-4928	159	9	the	the	DET
ejpam-4928	159	10	result	result	NOUN
ejpam-4928	159	11	in	in	ADP
ejpam-4928	159	12	(	(	PUNCT
ejpam-4928	159	13	al	al	PROPN
ejpam-4928	159	14	horani	horani	PROPN
ejpam-4928	159	15	et	et	PROPN
ejpam-4928	159	16	al	al	PROPN
ejpam-4928	159	17	.	.	PROPN
ejpam-4928	159	18	,	,	PUNCT
ejpam-4928	159	19	2020	2020	NUM
ejpam-4928	159	20	)	)	PUNCT
ejpam-4928	159	21	,	,	PUNCT
ejpam-4928	159	22	we	we	PRON
ejpam-4928	159	23	get	get	VERB
ejpam-4928	159	24	x(x	x(x	NOUN
ejpam-4928	159	25	)	)	PUNCT
ejpam-4928	160	1	=	=	SYM
ejpam-4928	160	2	c1e	c1e	NOUN
ejpam-4928	160	3	1	1	NUM
ejpam-4928	160	4	2	2	NUM
ejpam-4928	160	5	xβ	xβ	NOUN
ejpam-4928	160	6	β	β	NOUN
ejpam-4928	160	7	√	√	ADV
ejpam-4928	160	8	3	3	NUM
ejpam-4928	160	9	2	2	NUM
ejpam-4928	160	10	xβ	xβ	NOUN
ejpam-4928	160	11	β	β	NOUN
ejpam-4928	160	12	+	+	CCONJ
ejpam-4928	160	13	c2e	c2e	NOUN
ejpam-4928	160	14	1	1	NUM
ejpam-4928	160	15	2	2	NUM
ejpam-4928	160	16	xβ	xβ	PROPN
ejpam-4928	160	17	β	β	X
ejpam-4928	160	18	sin(sin	sin(sin	PROPN
ejpam-4928	160	19	(	(	PUNCT
ejpam-4928	160	20	√	√	NUM
ejpam-4928	160	21	3	3	NUM
ejpam-4928	160	22	2	2	NUM
ejpam-4928	160	23	xβ	xβ	NOUN
ejpam-4928	160	24	β	β	NOUN
ejpam-4928	160	25	)	)	PUNCT
ejpam-4928	160	26	)	)	PUNCT
ejpam-4928	160	27	.	.	PUNCT
ejpam-4928	161	1	using	use	VERB
ejpam-4928	161	2	the	the	DET
ejpam-4928	161	3	conditions	condition	NOUN
ejpam-4928	161	4	x(0	x(0	PRON
ejpam-4928	161	5	)	)	PUNCT
ejpam-4928	161	6	=	=	SYM
ejpam-4928	161	7	0	0	NUM
ejpam-4928	161	8	and	and	CCONJ
ejpam-4928	161	9	xβ(0	xβ(0	NUM
ejpam-4928	161	10	)	)	PUNCT
ejpam-4928	161	11	=	=	SYM
ejpam-4928	161	12	1	1	NUM
ejpam-4928	161	13	,	,	PUNCT
ejpam-4928	161	14	we	we	PRON
ejpam-4928	161	15	get	get	VERB
ejpam-4928	161	16	x(x	x(x	NOUN
ejpam-4928	161	17	)	)	PUNCT
ejpam-4928	162	1	=	=	SYM
ejpam-4928	162	2	2√	2√	NUM
ejpam-4928	162	3	3	3	NUM
ejpam-4928	162	4	e	e	NOUN
ejpam-4928	162	5	1	1	NUM
ejpam-4928	162	6	2	2	NUM
ejpam-4928	162	7	xβ	xβ	PROPN
ejpam-4928	162	8	β	β	X
ejpam-4928	162	9	sin(sin	sin(sin	PROPN
ejpam-4928	162	10	(	(	PUNCT
ejpam-4928	162	11	√	√	NUM
ejpam-4928	162	12	3	3	NUM
ejpam-4928	162	13	2	2	NUM
ejpam-4928	162	14	xβ	xβ	NOUN
ejpam-4928	162	15	β	β	NOUN
ejpam-4928	162	16	)	)	PUNCT
ejpam-4928	162	17	)	)	PUNCT
ejpam-4928	162	18	.	.	PUNCT
ejpam-4928	163	1	(	(	PUNCT
ejpam-4928	163	2	15	15	NUM
ejpam-4928	163	3	)	)	PUNCT
ejpam-4928	163	4	from	from	ADP
ejpam-4928	163	5	(	(	PUNCT
ejpam-4928	163	6	14	14	NUM
ejpam-4928	163	7	)	)	PUNCT
ejpam-4928	163	8	and	and	CCONJ
ejpam-4928	163	9	(	(	PUNCT
ejpam-4928	163	10	15	15	NUM
ejpam-4928	163	11	)	)	PUNCT
ejpam-4928	163	12	,	,	PUNCT
ejpam-4928	163	13	we	we	PRON
ejpam-4928	163	14	obtain	obtain	VERB
ejpam-4928	163	15	the	the	DET
ejpam-4928	163	16	atomic	atomic	ADJ
ejpam-4928	163	17	solution	solution	NOUN
ejpam-4928	163	18	of	of	ADP
ejpam-4928	163	19	(	(	PUNCT
ejpam-4928	163	20	12	12	NUM
ejpam-4928	163	21	)	)	PUNCT
ejpam-4928	163	22	as	as	ADP
ejpam-4928	163	23	:	:	PUNCT
ejpam-4928	163	24	u(x	u(x	PROPN
ejpam-4928	163	25	,	,	PUNCT
ejpam-4928	163	26	t	t	PROPN
ejpam-4928	163	27	)	)	PUNCT
ejpam-4928	163	28	=	=	PUNCT
ejpam-4928	164	1	(	(	PUNCT
ejpam-4928	164	2	2√	2√	NUM
ejpam-4928	164	3	3	3	NUM
ejpam-4928	164	4	e	e	NOUN
ejpam-4928	164	5	1	1	NUM
ejpam-4928	164	6	2	2	NUM
ejpam-4928	164	7	xβ	xβ	PROPN
ejpam-4928	164	8	β	β	X
ejpam-4928	164	9	sin(sin	sin(sin	PROPN
ejpam-4928	164	10	(	(	PUNCT
ejpam-4928	164	11	√	√	NUM
ejpam-4928	164	12	3	3	NUM
ejpam-4928	164	13	2	2	NUM
ejpam-4928	164	14	xβ	xβ	NOUN
ejpam-4928	164	15	β	β	NOUN
ejpam-4928	164	16	)	)	PUNCT
ejpam-4928	164	17	)	)	PUNCT
ejpam-4928	164	18	)	)	PUNCT
ejpam-4928	165	1	e	e	X
ejpam-4928	165	2	tα	tα	PROPN
ejpam-4928	165	3	α	α	INTJ
ejpam-4928	165	4	.	.	PUNCT
ejpam-4928	166	1	(	(	PUNCT
ejpam-4928	166	2	16	16	NUM
ejpam-4928	166	3	)	)	PUNCT
ejpam-4928	166	4	in	in	ADP
ejpam-4928	166	5	figure	figure	NOUN
ejpam-4928	166	6	3	3	NUM
ejpam-4928	166	7	,	,	PUNCT
ejpam-4928	166	8	we	we	PRON
ejpam-4928	166	9	plot	plot	VERB
ejpam-4928	166	10	u(x	u(x	NOUN
ejpam-4928	166	11	,	,	PUNCT
ejpam-4928	166	12	t	t	PROPN
ejpam-4928	166	13	)	)	PUNCT
ejpam-4928	166	14	the	the	DET
ejpam-4928	166	15	solution	solution	NOUN
ejpam-4928	166	16	of	of	ADP
ejpam-4928	166	17	equation	equation	NOUN
ejpam-4928	166	18	(	(	PUNCT
ejpam-4928	166	19	12	12	NUM
ejpam-4928	166	20	)	)	PUNCT
ejpam-4928	166	21	at	at	ADP
ejpam-4928	166	22	different	different	ADJ
ejpam-4928	166	23	values	value	NOUN
ejpam-4928	166	24	of	of	ADP
ejpam-4928	166	25	α	α	NOUN
ejpam-4928	166	26	and	and	CCONJ
ejpam-4928	166	27	β	β	X
ejpam-4928	166	28	where	where	SCONJ
ejpam-4928	166	29	the	the	DET
ejpam-4928	166	30	yellow	yellow	ADJ
ejpam-4928	166	31	surface	surface	NOUN
ejpam-4928	166	32	at	at	ADP
ejpam-4928	166	33	α	α	NOUN
ejpam-4928	166	34	=	=	SYM
ejpam-4928	166	35	1	1	NUM
ejpam-4928	166	36	,	,	PUNCT
ejpam-4928	166	37	β	β	X
ejpam-4928	166	38	=	=	SYM
ejpam-4928	166	39	1	1	NUM
ejpam-4928	166	40	,	,	PUNCT
ejpam-4928	166	41	the	the	DET
ejpam-4928	166	42	blue	blue	ADJ
ejpam-4928	166	43	surface	surface	NOUN
ejpam-4928	166	44	at	at	ADP
ejpam-4928	166	45	α	α	NOUN
ejpam-4928	166	46	=	=	SYM
ejpam-4928	166	47	0.9	0.9	NUM
ejpam-4928	166	48	,	,	PUNCT
ejpam-4928	166	49	β	β	X
ejpam-4928	166	50	=	=	SYM
ejpam-4928	166	51	0.9	0.9	NUM
ejpam-4928	166	52	,	,	PUNCT
ejpam-4928	166	53	the	the	DET
ejpam-4928	166	54	green	green	ADJ
ejpam-4928	166	55	surface	surface	NOUN
ejpam-4928	166	56	at	at	ADP
ejpam-4928	166	57	α	α	NOUN
ejpam-4928	166	58	=	=	SYM
ejpam-4928	166	59	1	1	NUM
ejpam-4928	166	60	,	,	PUNCT
ejpam-4928	166	61	β	β	X
ejpam-4928	166	62	=	=	SYM
ejpam-4928	166	63	0.5	0.5	NUM
ejpam-4928	166	64	,	,	PUNCT
ejpam-4928	166	65	the	the	DET
ejpam-4928	166	66	red	red	ADJ
ejpam-4928	166	67	surface	surface	NOUN
ejpam-4928	166	68	at	at	ADP
ejpam-4928	166	69	α	α	NOUN
ejpam-4928	166	70	=	=	SYM
ejpam-4928	166	71	0.5	0.5	NUM
ejpam-4928	166	72	,	,	PUNCT
ejpam-4928	166	73	β	β	X
ejpam-4928	166	74	=	=	SYM
ejpam-4928	166	75	1	1	NUM
ejpam-4928	166	76	and	and	CCONJ
ejpam-4928	166	77	the	the	DET
ejpam-4928	166	78	purple	purple	ADJ
ejpam-4928	166	79	surface	surface	NOUN
ejpam-4928	166	80	at	at	ADP
ejpam-4928	166	81	α	α	NOUN
ejpam-4928	166	82	=	=	SYM
ejpam-4928	166	83	0.6	0.6	NUM
ejpam-4928	166	84	,	,	PUNCT
ejpam-4928	166	85	β	β	X
ejpam-4928	166	86	=	=	NOUN
ejpam-4928	166	87	0.6	0.6	NUM
ejpam-4928	166	88	.	.	PUNCT
ejpam-4928	167	1	(	(	PUNCT
ejpam-4928	167	2	0	0	NUM
ejpam-4928	167	3	≤	≤	NOUN
ejpam-4928	167	4	t	t	NOUN
ejpam-4928	167	5	≤	≤	NUM
ejpam-4928	167	6	1	1	NUM
ejpam-4928	167	7	)	)	PUNCT
ejpam-4928	167	8	,	,	PUNCT
ejpam-4928	167	9	(	(	PUNCT
ejpam-4928	167	10	0	0	NUM
ejpam-4928	167	11	≤	≤	NUM
ejpam-4928	167	12	x	x	SYM
ejpam-4928	167	13	≤	≤	NUM
ejpam-4928	167	14	1	1	NUM
ejpam-4928	167	15	)	)	PUNCT
ejpam-4928	167	16	.	.	PUNCT
ejpam-4928	168	1	case(ii	case(ii	ADJ
ejpam-4928	168	2	):	):	PUNCT
ejpam-4928	168	3	x(x	x(x	PROPN
ejpam-4928	168	4	)	)	PUNCT
ejpam-4928	168	5	=	=	PUNCT
ejpam-4928	168	6	xβ(x	xβ(x	X
ejpam-4928	168	7	)	)	PUNCT
ejpam-4928	168	8	=	=	SYM
ejpam-4928	168	9	x2β(x	x2β(x	NOUN
ejpam-4928	168	10	)	)	PUNCT
ejpam-4928	168	11	.	.	PUNCT
ejpam-4928	169	1	in	in	ADP
ejpam-4928	169	2	this	this	DET
ejpam-4928	169	3	case	case	NOUN
ejpam-4928	169	4	,	,	PUNCT
ejpam-4928	169	5	equation	equation	NOUN
ejpam-4928	169	6	(	(	PUNCT
ejpam-4928	169	7	13	13	NUM
ejpam-4928	169	8	)	)	PUNCT
ejpam-4928	169	9	has	have	VERB
ejpam-4928	169	10	no	no	DET
ejpam-4928	169	11	solution	solution	NOUN
ejpam-4928	169	12	.	.	PUNCT
ejpam-4928	170	1	so	so	ADV
ejpam-4928	170	2	,	,	PUNCT
ejpam-4928	170	3	there	there	PRON
ejpam-4928	170	4	is	be	VERB
ejpam-4928	170	5	no	no	DET
ejpam-4928	170	6	atomic	atomic	ADJ
ejpam-4928	170	7	solution	solution	NOUN
ejpam-4928	170	8	.	.	PUNCT
ejpam-4928	171	1	i.	i.	PROPN
ejpam-4928	171	2	aldarawi	aldarawi	VERB
ejpam-4928	171	3	et	et	PROPN
ejpam-4928	171	4	al	al	PROPN
ejpam-4928	171	5	.	.	PUNCT
ejpam-4928	171	6	/	/	SYM
ejpam-4928	171	7	eur	eur	PROPN
ejpam-4928	171	8	.	.	PUNCT
ejpam-4928	172	1	j.	j.	PROPN
ejpam-4928	172	2	pure	pure	PROPN
ejpam-4928	172	3	appl	appl	PROPN
ejpam-4928	172	4	.	.	PROPN
ejpam-4928	172	5	math	math	PROPN
ejpam-4928	172	6	,	,	PUNCT
ejpam-4928	172	7	16	16	NUM
ejpam-4928	172	8	(	(	PUNCT
ejpam-4928	172	9	4	4	NUM
ejpam-4928	172	10	)	)	PUNCT
ejpam-4928	172	11	(	(	PUNCT
ejpam-4928	172	12	2023	2023	NUM
ejpam-4928	172	13	)	)	PUNCT
ejpam-4928	172	14	,	,	PUNCT
ejpam-4928	172	15	2132	2132	NUM
ejpam-4928	172	16	-	-	SYM
ejpam-4928	172	17	2144	2144	NUM
ejpam-4928	172	18	2140	2140	NUM
ejpam-4928	172	19	figure	figure	NOUN
ejpam-4928	172	20	3	3	NUM
ejpam-4928	172	21	:	:	PUNCT
ejpam-4928	172	22	the	the	DET
ejpam-4928	172	23	solution	solution	NOUN
ejpam-4928	172	24	u(x	u(x	VERB
ejpam-4928	172	25	,	,	PUNCT
ejpam-4928	172	26	t	t	PROPN
ejpam-4928	172	27	)	)	PUNCT
ejpam-4928	172	28	of	of	ADP
ejpam-4928	172	29	equation	equation	NOUN
ejpam-4928	172	30	(	(	PUNCT
ejpam-4928	172	31	12	12	NUM
ejpam-4928	172	32	)	)	PUNCT
ejpam-4928	172	33	.	.	PUNCT
ejpam-4928	173	1	4.2	4.2	NUM
ejpam-4928	173	2	.	.	PUNCT
ejpam-4928	173	3	application	application	NOUN
ejpam-4928	173	4	2	2	NUM
ejpam-4928	173	5	the	the	DET
ejpam-4928	173	6	solution	solution	NOUN
ejpam-4928	173	7	of	of	ADP
ejpam-4928	173	8	d	d	PROPN
ejpam-4928	173	9	3	3	NUM
ejpam-4928	173	10	2	2	NUM
ejpam-4928	173	11	x	x	SYM
ejpam-4928	173	12	u+	u+	NUM
ejpam-4928	173	13	√	√	NOUN
ejpam-4928	173	14	xd	xd	NUM
ejpam-4928	173	15	3	3	NUM
ejpam-4928	173	16	2	2	NUM
ejpam-4928	173	17	y	y	PROPN
ejpam-4928	173	18	u	u	NOUN
ejpam-4928	173	19	=	=	PROPN
ejpam-4928	174	1	d	d	PROPN
ejpam-4928	174	2	1	1	NUM
ejpam-4928	174	3	2	2	NUM
ejpam-4928	174	4	x	x	SYM
ejpam-4928	174	5	ud	ud	INTJ
ejpam-4928	174	6	1	1	NUM
ejpam-4928	174	7	2	2	NUM
ejpam-4928	174	8	y	y	PROPN
ejpam-4928	174	9	u	u	PROPN
ejpam-4928	174	10	(	(	PUNCT
ejpam-4928	174	11	17	17	NUM
ejpam-4928	174	12	)	)	PUNCT
ejpam-4928	174	13	u(0	u(0	NOUN
ejpam-4928	174	14	,	,	PUNCT
ejpam-4928	174	15	0	0	NUM
ejpam-4928	174	16	)	)	PUNCT
ejpam-4928	174	17	=	=	SYM
ejpam-4928	174	18	1	1	NUM
ejpam-4928	174	19	,	,	PUNCT
ejpam-4928	174	20	∂u	∂u	PROPN
ejpam-4928	174	21	∂x	∂x	PROPN
ejpam-4928	174	22	(	(	PUNCT
ejpam-4928	174	23	0	0	NUM
ejpam-4928	174	24	,	,	PUNCT
ejpam-4928	174	25	0	0	NUM
ejpam-4928	174	26	)	)	PUNCT
ejpam-4928	174	27	=	=	SYM
ejpam-4928	174	28	1	1	NUM
ejpam-4928	174	29	and	and	CCONJ
ejpam-4928	174	30	∂u	∂u	PROPN
ejpam-4928	174	31	∂y	∂y	SYM
ejpam-4928	174	32	(	(	PUNCT
ejpam-4928	174	33	0	0	NUM
ejpam-4928	174	34	,	,	PUNCT
ejpam-4928	174	35	0	0	NUM
ejpam-4928	174	36	)	)	PUNCT
ejpam-4928	174	37	=	=	SYM
ejpam-4928	175	1	1	1	NUM
ejpam-4928	175	2	,	,	PUNCT
ejpam-4928	175	3	where	where	SCONJ
ejpam-4928	175	4	by	by	ADP
ejpam-4928	175	5	an	an	DET
ejpam-4928	175	6	atomic	atomic	ADJ
ejpam-4928	175	7	solution	solution	NOUN
ejpam-4928	175	8	we	we	PRON
ejpam-4928	175	9	mean	mean	VERB
ejpam-4928	175	10	a	a	DET
ejpam-4928	175	11	solution	solution	NOUN
ejpam-4928	175	12	of	of	ADP
ejpam-4928	175	13	the	the	DET
ejpam-4928	175	14	form	form	NOUN
ejpam-4928	175	15	u(x	u(x	NOUN
ejpam-4928	175	16	,	,	PUNCT
ejpam-4928	175	17	y	y	NOUN
ejpam-4928	175	18	)	)	PUNCT
ejpam-4928	176	1	=	=	SYM
ejpam-4928	176	2	p	p	X
ejpam-4928	176	3	(	(	PUNCT
ejpam-4928	176	4	x)q(y	x)q(y	PROPN
ejpam-4928	176	5	)	)	PUNCT
ejpam-4928	176	6	.	.	PUNCT
ejpam-4928	177	1	procedure	procedure	NOUN
ejpam-4928	177	2	let	let	VERB
ejpam-4928	177	3	u(x	u(x	NOUN
ejpam-4928	177	4	,	,	PUNCT
ejpam-4928	177	5	t	t	PROPN
ejpam-4928	177	6	)	)	PUNCT
ejpam-4928	177	7	=	=	SYM
ejpam-4928	177	8	x(x)t	x(x)t	PROPN
ejpam-4928	177	9	(	(	PUNCT
ejpam-4928	177	10	t	t	PROPN
ejpam-4928	177	11	)	)	PUNCT
ejpam-4928	177	12	.	.	PUNCT
ejpam-4928	178	1	substitute	substitute	NOUN
ejpam-4928	178	2	in	in	ADP
ejpam-4928	178	3	equation	equation	NOUN
ejpam-4928	178	4	(	(	PUNCT
ejpam-4928	178	5	17	17	NUM
ejpam-4928	178	6	)	)	PUNCT
ejpam-4928	178	7	to	to	PART
ejpam-4928	178	8	get	get	VERB
ejpam-4928	178	9	p	p	NOUN
ejpam-4928	178	10	3	3	NUM
ejpam-4928	178	11	2	2	NUM
ejpam-4928	178	12	(	(	PUNCT
ejpam-4928	178	13	x)q(y	x)q(y	NOUN
ejpam-4928	178	14	)	)	PUNCT
ejpam-4928	179	1	+	+	CCONJ
ejpam-4928	179	2	√	√	ADJ
ejpam-4928	179	3	xp	xp	INTJ
ejpam-4928	179	4	(	(	PUNCT
ejpam-4928	179	5	x)q	x)q	PROPN
ejpam-4928	179	6	3	3	NUM
ejpam-4928	179	7	2	2	NUM
ejpam-4928	179	8	(	(	PUNCT
ejpam-4928	179	9	y	y	NOUN
ejpam-4928	179	10	)	)	PUNCT
ejpam-4928	179	11	=	=	PUNCT
ejpam-4928	180	1	p	p	NOUN
ejpam-4928	180	2	1	1	NUM
ejpam-4928	180	3	2	2	NUM
ejpam-4928	180	4	(	(	PUNCT
ejpam-4928	180	5	x)q	x)q	PROPN
ejpam-4928	180	6	1	1	NUM
ejpam-4928	180	7	2	2	NUM
ejpam-4928	180	8	(	(	PUNCT
ejpam-4928	180	9	y	y	NOUN
ejpam-4928	180	10	)	)	PUNCT
ejpam-4928	180	11	.	.	PUNCT
ejpam-4928	181	1	this	this	PRON
ejpam-4928	181	2	can	can	AUX
ejpam-4928	181	3	be	be	AUX
ejpam-4928	181	4	written	write	VERB
ejpam-4928	181	5	in	in	ADP
ejpam-4928	181	6	tensor	tensor	NOUN
ejpam-4928	181	7	product	product	NOUN
ejpam-4928	181	8	form	form	NOUN
ejpam-4928	181	9	as	as	ADP
ejpam-4928	181	10	:	:	PUNCT
ejpam-4928	181	11	p	p	NOUN
ejpam-4928	181	12	3	3	NUM
ejpam-4928	181	13	2	2	NUM
ejpam-4928	181	14	⊗q+	⊗q+	PROPN
ejpam-4928	181	15	√	√	PROPN
ejpam-4928	181	16	xp	xp	NOUN
ejpam-4928	181	17	⊗q	⊗q	PROPN
ejpam-4928	181	18	3	3	NUM
ejpam-4928	181	19	2	2	NUM
ejpam-4928	181	20	=	=	SYM
ejpam-4928	181	21	p	p	NOUN
ejpam-4928	181	22	1	1	NUM
ejpam-4928	181	23	2	2	NUM
ejpam-4928	181	24	⊗q	⊗q	NOUN
ejpam-4928	181	25	1	1	NUM
ejpam-4928	181	26	2	2	NUM
ejpam-4928	181	27	(	(	PUNCT
ejpam-4928	181	28	18	18	NUM
ejpam-4928	181	29	)	)	PUNCT
ejpam-4928	181	30	let	let	VERB
ejpam-4928	181	31	us	we	PRON
ejpam-4928	181	32	use	use	VERB
ejpam-4928	181	33	the	the	DET
ejpam-4928	181	34	following	following	ADJ
ejpam-4928	181	35	conditions	condition	NOUN
ejpam-4928	181	36	:	:	PUNCT
ejpam-4928	181	37	p	p	X
ejpam-4928	181	38	(	(	PUNCT
ejpam-4928	181	39	0	0	NUM
ejpam-4928	181	40	)	)	PUNCT
ejpam-4928	181	41	=	=	SYM
ejpam-4928	181	42	1	1	NUM
ejpam-4928	181	43	,	,	PUNCT
ejpam-4928	181	44	p	p	NOUN
ejpam-4928	181	45	′(0	′(0	PROPN
ejpam-4928	181	46	)	)	PUNCT
ejpam-4928	181	47	=	=	SYM
ejpam-4928	182	1	1	1	NUM
ejpam-4928	182	2	,	,	PUNCT
ejpam-4928	182	3	q(0	q(0	PROPN
ejpam-4928	182	4	)	)	PUNCT
ejpam-4928	182	5	=	=	SYM
ejpam-4928	182	6	0	0	NUM
ejpam-4928	182	7	and	and	CCONJ
ejpam-4928	182	8	q′(0	q′(0	NOUN
ejpam-4928	182	9	)	)	PUNCT
ejpam-4928	182	10	=	=	SYM
ejpam-4928	183	1	1	1	X
ejpam-4928	183	2	.	.	PUNCT
ejpam-4928	184	1	hence	hence	ADV
ejpam-4928	184	2	,	,	PUNCT
ejpam-4928	184	3	we	we	PRON
ejpam-4928	184	4	have	have	VERB
ejpam-4928	184	5	two	two	NUM
ejpam-4928	184	6	cases	case	NOUN
ejpam-4928	184	7	from	from	ADP
ejpam-4928	184	8	equation	equation	NOUN
ejpam-4928	184	9	(	(	PUNCT
ejpam-4928	184	10	18	18	NUM
ejpam-4928	184	11	):	):	PUNCT
ejpam-4928	184	12	case	case	NOUN
ejpam-4928	184	13	(	(	PUNCT
ejpam-4928	184	14	i	i	NOUN
ejpam-4928	184	15	):	):	PUNCT
ejpam-4928	184	16	p	p	PROPN
ejpam-4928	184	17	3	3	NUM
ejpam-4928	184	18	2	2	NUM
ejpam-4928	184	19	(	(	PUNCT
ejpam-4928	184	20	x	x	NOUN
ejpam-4928	184	21	)	)	PUNCT
ejpam-4928	184	22	=	=	SYM
ejpam-4928	185	1	√	√	NUM
ejpam-4928	185	2	xp	xp	INTJ
ejpam-4928	186	1	(	(	PUNCT
ejpam-4928	186	2	x	x	X
ejpam-4928	186	3	)	)	PUNCT
ejpam-4928	186	4	=	=	SYM
ejpam-4928	187	1	p	p	NOUN
ejpam-4928	187	2	1	1	NUM
ejpam-4928	187	3	2	2	NUM
ejpam-4928	187	4	(	(	PUNCT
ejpam-4928	187	5	x	x	NOUN
ejpam-4928	187	6	)	)	PUNCT
ejpam-4928	187	7	.	.	PUNCT
ejpam-4928	188	1	then	then	ADV
ejpam-4928	188	2	we	we	PRON
ejpam-4928	188	3	get	get	VERB
ejpam-4928	188	4	√	√	ADP
ejpam-4928	188	5	xp	xp	ADV
ejpam-4928	188	6	′′	′′	PROPN
ejpam-4928	188	7	=	=	PUNCT
ejpam-4928	189	1	√	√	NUM
ejpam-4928	189	2	xp	xp	INTJ
ejpam-4928	189	3	(	(	PUNCT
ejpam-4928	189	4	x	x	X
ejpam-4928	189	5	)	)	PUNCT
ejpam-4928	189	6	=	=	SYM
ejpam-4928	190	1	p	p	NOUN
ejpam-4928	190	2	1	1	NUM
ejpam-4928	190	3	2	2	NUM
ejpam-4928	190	4	(	(	PUNCT
ejpam-4928	190	5	x	x	NOUN
ejpam-4928	190	6	)	)	PUNCT
ejpam-4928	190	7	.	.	PUNCT
ejpam-4928	191	1	using	use	VERB
ejpam-4928	191	2	the	the	DET
ejpam-4928	191	3	result	result	NOUN
ejpam-4928	191	4	in	in	ADP
ejpam-4928	191	5	[	[	X
ejpam-4928	191	6	1	1	NUM
ejpam-4928	191	7	]	]	PUNCT
ejpam-4928	191	8	,	,	PUNCT
ejpam-4928	191	9	we	we	PRON
ejpam-4928	191	10	get	get	VERB
ejpam-4928	191	11	p	p	NOUN
ejpam-4928	191	12	(	(	PUNCT
ejpam-4928	191	13	x	x	NOUN
ejpam-4928	191	14	)	)	PUNCT
ejpam-4928	191	15	=	=	SYM
ejpam-4928	192	1	ex	ex	X
ejpam-4928	192	2	.	.	PUNCT
ejpam-4928	192	3	(	(	PUNCT
ejpam-4928	192	4	19	19	NUM
ejpam-4928	192	5	)	)	PUNCT
ejpam-4928	192	6	now	now	ADV
ejpam-4928	192	7	we	we	PRON
ejpam-4928	192	8	substitute	substitute	VERB
ejpam-4928	192	9	in	in	ADP
ejpam-4928	192	10	(	(	PUNCT
ejpam-4928	192	11	18	18	NUM
ejpam-4928	192	12	)	)	PUNCT
ejpam-4928	192	13	to	to	PART
ejpam-4928	192	14	get	get	VERB
ejpam-4928	192	15	:	:	PUNCT
ejpam-4928	192	16	√	√	PROPN
ejpam-4928	192	17	xex	xex	PROPN
ejpam-4928	192	18	⊗	⊗	PROPN
ejpam-4928	192	19	(	(	PUNCT
ejpam-4928	192	20	q+q	q+q	NUM
ejpam-4928	192	21	3	3	NUM
ejpam-4928	192	22	2	2	NUM
ejpam-4928	192	23	)	)	PUNCT
ejpam-4928	192	24	=	=	PUNCT
ejpam-4928	193	1	p	p	NOUN
ejpam-4928	193	2	1	1	NUM
ejpam-4928	193	3	2	2	NUM
ejpam-4928	193	4	⊗q	⊗q	NOUN
ejpam-4928	193	5	1	1	NUM
ejpam-4928	193	6	2	2	NUM
ejpam-4928	193	7	.	.	PUNCT
ejpam-4928	194	1	hence	hence	ADV
ejpam-4928	194	2	,	,	PUNCT
ejpam-4928	194	3	q+q	q+q	PROPN
ejpam-4928	194	4	3	3	NUM
ejpam-4928	194	5	2	2	NUM
ejpam-4928	194	6	−q	−q	NOUN
ejpam-4928	194	7	1	1	NUM
ejpam-4928	194	8	2	2	NUM
ejpam-4928	194	9	=	=	SYM
ejpam-4928	194	10	0	0	NUM
ejpam-4928	194	11	.	.	PUNCT
ejpam-4928	194	12	again	again	ADV
ejpam-4928	194	13	,	,	PUNCT
ejpam-4928	194	14	using	use	VERB
ejpam-4928	194	15	the	the	DET
ejpam-4928	194	16	result	result	NOUN
ejpam-4928	194	17	in	in	ADP
ejpam-4928	194	18	[	[	X
ejpam-4928	194	19	1	1	X
ejpam-4928	194	20	]	]	PUNCT
ejpam-4928	194	21	we	we	PRON
ejpam-4928	194	22	have	have	VERB
ejpam-4928	194	23	√	√	NUM
ejpam-4928	194	24	yq′′(y)−√	yq′′(y)−√	NUM
ejpam-4928	194	25	yq′(y	yq′(y	PROPN
ejpam-4928	194	26	)	)	PUNCT
ejpam-4928	195	1	+	+	NOUN
ejpam-4928	195	2	q(y	q(y	X
ejpam-4928	195	3	)	)	PUNCT
ejpam-4928	195	4	=	=	SYM
ejpam-4928	195	5	0	0	NUM
ejpam-4928	195	6	(	(	PUNCT
ejpam-4928	195	7	20	20	NUM
ejpam-4928	195	8	)	)	PUNCT
ejpam-4928	195	9	i.	i.	PROPN
ejpam-4928	195	10	aldarawi	aldarawi	VERB
ejpam-4928	195	11	et	et	PROPN
ejpam-4928	195	12	al	al	PROPN
ejpam-4928	195	13	.	.	PUNCT
ejpam-4928	195	14	/	/	SYM
ejpam-4928	195	15	eur	eur	PROPN
ejpam-4928	195	16	.	.	PUNCT
ejpam-4928	196	1	j.	j.	PROPN
ejpam-4928	196	2	pure	pure	PROPN
ejpam-4928	196	3	appl	appl	PROPN
ejpam-4928	196	4	.	.	PROPN
ejpam-4928	196	5	math	math	PROPN
ejpam-4928	196	6	,	,	PUNCT
ejpam-4928	196	7	16	16	NUM
ejpam-4928	196	8	(	(	PUNCT
ejpam-4928	196	9	4	4	NUM
ejpam-4928	196	10	)	)	PUNCT
ejpam-4928	196	11	(	(	PUNCT
ejpam-4928	196	12	2023	2023	NUM
ejpam-4928	196	13	)	)	PUNCT
ejpam-4928	196	14	,	,	PUNCT
ejpam-4928	196	15	2132	2132	NUM
ejpam-4928	196	16	-	-	SYM
ejpam-4928	196	17	2144	2144	NUM
ejpam-4928	196	18	2141	2141	NUM
ejpam-4928	196	19	this	this	DET
ejpam-4928	196	20	equation	equation	NOUN
ejpam-4928	196	21	can	can	AUX
ejpam-4928	196	22	be	be	AUX
ejpam-4928	196	23	solved	solve	VERB
ejpam-4928	196	24	numerically	numerically	ADV
ejpam-4928	196	25	by	by	ADP
ejpam-4928	196	26	using	use	VERB
ejpam-4928	196	27	the	the	DET
ejpam-4928	196	28	reproducing	reproduce	VERB
ejpam-4928	196	29	kernel	kernel	PROPN
ejpam-4928	196	30	hilbert	hilbert	PROPN
ejpam-4928	196	31	space	space	NOUN
ejpam-4928	196	32	method	method	NOUN
ejpam-4928	196	33	[	[	X
ejpam-4928	196	34	11	11	NUM
ejpam-4928	196	35	]	]	PUNCT
ejpam-4928	196	36	,	,	PUNCT
ejpam-4928	196	37	where	where	SCONJ
ejpam-4928	196	38	the	the	DET
ejpam-4928	196	39	conditions	condition	NOUN
ejpam-4928	196	40	q0=1	q0=1	PROPN
ejpam-4928	196	41	and	and	CCONJ
ejpam-4928	196	42	q’(0)=1	q’(0)=1	NOUN
ejpam-4928	196	43	,	,	PUNCT
ejpam-4928	196	44	are	be	AUX
ejpam-4928	196	45	used	use	VERB
ejpam-4928	196	46	.	.	PUNCT
ejpam-4928	197	1	from	from	ADP
ejpam-4928	197	2	(	(	PUNCT
ejpam-4928	197	3	19	19	NUM
ejpam-4928	197	4	)	)	PUNCT
ejpam-4928	197	5	and	and	CCONJ
ejpam-4928	197	6	the	the	DET
ejpam-4928	197	7	numerical	numerical	ADJ
ejpam-4928	197	8	solution	solution	NOUN
ejpam-4928	197	9	of	of	ADP
ejpam-4928	197	10	(	(	PUNCT
ejpam-4928	197	11	20	20	NUM
ejpam-4928	197	12	)	)	PUNCT
ejpam-4928	197	13	,	,	PUNCT
ejpam-4928	197	14	we	we	PRON
ejpam-4928	197	15	obtain	obtain	VERB
ejpam-4928	197	16	the	the	DET
ejpam-4928	197	17	atomic	atomic	ADJ
ejpam-4928	197	18	solution	solution	NOUN
ejpam-4928	197	19	of	of	ADP
ejpam-4928	197	20	(	(	PUNCT
ejpam-4928	197	21	17	17	NUM
ejpam-4928	197	22	)	)	PUNCT
ejpam-4928	197	23	.	.	PUNCT
ejpam-4928	198	1	in	in	ADP
ejpam-4928	198	2	figure	figure	NOUN
ejpam-4928	198	3	4(a	4(a	NUM
ejpam-4928	198	4	)	)	PUNCT
ejpam-4928	198	5	we	we	PRON
ejpam-4928	198	6	plot	plot	VERB
ejpam-4928	198	7	the	the	DET
ejpam-4928	198	8	solution	solution	NOUN
ejpam-4928	198	9	u(x	u(x	NOUN
ejpam-4928	198	10	,	,	PUNCT
ejpam-4928	198	11	y	y	NOUN
ejpam-4928	198	12	)	)	PUNCT
ejpam-4928	198	13	of	of	ADP
ejpam-4928	198	14	equation	equation	NOUN
ejpam-4928	198	15	(	(	PUNCT
ejpam-4928	198	16	17	17	NUM
ejpam-4928	198	17	)	)	PUNCT
ejpam-4928	198	18	where	where	SCONJ
ejpam-4928	198	19	0	0	NUM
ejpam-4928	198	20	≤	≤	NUM
ejpam-4928	198	21	x	x	SYM
ejpam-4928	198	22	≤	≤	NUM
ejpam-4928	198	23	1	1	NUM
ejpam-4928	198	24	and	and	CCONJ
ejpam-4928	198	25	0	0	NUM
ejpam-4928	198	26	≤	≤	NUM
ejpam-4928	198	27	y	y	NOUN
ejpam-4928	198	28	≤	≤	NUM
ejpam-4928	198	29	1	1	NUM
ejpam-4928	198	30	.	.	PUNCT
ejpam-4928	199	1	in	in	ADP
ejpam-4928	199	2	figure	figure	NOUN
ejpam-4928	199	3	4(b	4(b	NUM
ejpam-4928	199	4	)	)	PUNCT
ejpam-4928	199	5	we	we	PRON
ejpam-4928	199	6	plot	plot	VERB
ejpam-4928	199	7	u(x	u(x	NOUN
ejpam-4928	199	8	,	,	PUNCT
ejpam-4928	199	9	y	y	NOUN
ejpam-4928	199	10	)	)	PUNCT
ejpam-4928	199	11	versus	versus	ADP
ejpam-4928	199	12	x	x	X
ejpam-4928	199	13	at	at	ADP
ejpam-4928	199	14	different	different	ADJ
ejpam-4928	199	15	values	value	NOUN
ejpam-4928	199	16	of	of	ADP
ejpam-4928	199	17	y	y	PROPN
ejpam-4928	199	18	,	,	PUNCT
ejpam-4928	199	19	y	y	PROPN
ejpam-4928	199	20	∈	∈	PROPN
ejpam-4928	199	21	{	{	PUNCT
ejpam-4928	199	22	0	0	NUM
ejpam-4928	199	23	,	,	PUNCT
ejpam-4928	199	24	0.1	0.1	NUM
ejpam-4928	199	25	,	,	PUNCT
ejpam-4928	199	26	0.7	0.7	NUM
ejpam-4928	199	27	,	,	PUNCT
ejpam-4928	199	28	1	1	NUM
ejpam-4928	199	29	}	}	PUNCT
ejpam-4928	199	30	,	,	PUNCT
ejpam-4928	199	31	where	where	SCONJ
ejpam-4928	199	32	each	each	DET
ejpam-4928	199	33	curve	curve	NOUN
ejpam-4928	199	34	represents	represent	VERB
ejpam-4928	199	35	a	a	DET
ejpam-4928	199	36	constant	constant	ADJ
ejpam-4928	199	37	time	time	NOUN
ejpam-4928	199	38	exponential	exponential	ADJ
ejpam-4928	199	39	function	function	NOUN
ejpam-4928	199	40	.	.	PUNCT
ejpam-4928	200	1	in	in	ADP
ejpam-4928	200	2	figure	figure	NOUN
ejpam-4928	200	3	4(c	4(c	NUM
ejpam-4928	200	4	)	)	PUNCT
ejpam-4928	200	5	we	we	PRON
ejpam-4928	200	6	plot	plot	VERB
ejpam-4928	200	7	u(x	u(x	NOUN
ejpam-4928	200	8	,	,	PUNCT
ejpam-4928	200	9	y	y	NOUN
ejpam-4928	200	10	)	)	PUNCT
ejpam-4928	200	11	versus	versus	ADP
ejpam-4928	200	12	y	y	PROPN
ejpam-4928	200	13	at	at	ADP
ejpam-4928	200	14	different	different	ADJ
ejpam-4928	200	15	values	value	NOUN
ejpam-4928	200	16	of	of	ADP
ejpam-4928	200	17	x	x	X
ejpam-4928	200	18	,	,	PUNCT
ejpam-4928	200	19	x	x	SYM
ejpam-4928	200	20	∈	∈	NOUN
ejpam-4928	200	21	{	{	PUNCT
ejpam-4928	200	22	0	0	NUM
ejpam-4928	200	23	,	,	PUNCT
ejpam-4928	200	24	0.3	0.3	NUM
ejpam-4928	200	25	,	,	PUNCT
ejpam-4928	200	26	0.5	0.5	NUM
ejpam-4928	200	27	,	,	PUNCT
ejpam-4928	200	28	1	1	NUM
ejpam-4928	200	29	}	}	PUNCT
ejpam-4928	200	30	,	,	PUNCT
ejpam-4928	200	31	where	where	SCONJ
ejpam-4928	200	32	each	each	DET
ejpam-4928	200	33	curve	curve	NOUN
ejpam-4928	200	34	represents	represent	VERB
ejpam-4928	200	35	a	a	DET
ejpam-4928	200	36	constant	constant	ADJ
ejpam-4928	200	37	time	time	NOUN
ejpam-4928	200	38	q(y	q(y	PROPN
ejpam-4928	200	39	)	)	PUNCT
ejpam-4928	200	40	.	.	PUNCT
ejpam-4928	201	1	in	in	ADP
ejpam-4928	201	2	figure	figure	NOUN
ejpam-4928	201	3	4(d	4(d	NUM
ejpam-4928	201	4	)	)	PUNCT
ejpam-4928	201	5	we	we	PRON
ejpam-4928	201	6	plot	plot	VERB
ejpam-4928	201	7	the	the	DET
ejpam-4928	201	8	residual	residual	ADJ
ejpam-4928	201	9	error	error	NOUN
ejpam-4928	201	10	for	for	ADP
ejpam-4928	201	11	equation	equation	NOUN
ejpam-4928	201	12	(	(	PUNCT
ejpam-4928	201	13	17	17	NUM
ejpam-4928	201	14	)	)	PUNCT
ejpam-4928	201	15	.	.	PUNCT
ejpam-4928	202	1	rese(x	rese(x	PROPN
ejpam-4928	202	2	,	,	PUNCT
ejpam-4928	202	3	y	y	NOUN
ejpam-4928	202	4	)	)	PUNCT
ejpam-4928	202	5	=	=	PRON
ejpam-4928	202	6	∣∣∣d	∣∣∣d	VERB
ejpam-4928	202	7	3	3	NUM
ejpam-4928	202	8	2	2	NUM
ejpam-4928	202	9	x	x	SYM
ejpam-4928	202	10	u+	u+	NUM
ejpam-4928	202	11	√	√	NOUN
ejpam-4928	203	1	xd	xd	NUM
ejpam-4928	203	2	3	3	NUM
ejpam-4928	203	3	2	2	NUM
ejpam-4928	203	4	y	y	PROPN
ejpam-4928	203	5	u+−d	u+−d	PROPN
ejpam-4928	203	6	1	1	NUM
ejpam-4928	203	7	2	2	NUM
ejpam-4928	203	8	x	x	SYM
ejpam-4928	203	9	ud	ud	INTJ
ejpam-4928	203	10	1	1	NUM
ejpam-4928	203	11	2	2	NUM
ejpam-4928	203	12	y	y	PROPN
ejpam-4928	203	13	u	u	PROPN
ejpam-4928	203	14	∣∣∣	∣∣∣	NOUN
ejpam-4928	203	15	which	which	PRON
ejpam-4928	203	16	proves	prove	VERB
ejpam-4928	203	17	that	that	SCONJ
ejpam-4928	203	18	the	the	DET
ejpam-4928	203	19	obtained	obtain	VERB
ejpam-4928	203	20	result	result	NOUN
ejpam-4928	203	21	is	be	AUX
ejpam-4928	203	22	very	very	ADV
ejpam-4928	203	23	efficient	efficient	ADJ
ejpam-4928	203	24	.	.	PUNCT
ejpam-4928	204	1	(	(	PUNCT
ejpam-4928	204	2	a	a	X
ejpam-4928	204	3	)	)	PUNCT
ejpam-4928	204	4	(	(	PUNCT
ejpam-4928	204	5	b	b	X
ejpam-4928	204	6	)	)	PUNCT
ejpam-4928	204	7	(	(	PUNCT
ejpam-4928	204	8	c	c	X
ejpam-4928	204	9	)	)	PUNCT
ejpam-4928	204	10	(	(	PUNCT
ejpam-4928	204	11	d	d	X
ejpam-4928	204	12	)	)	PUNCT
ejpam-4928	204	13	figure	figure	NOUN
ejpam-4928	204	14	4	4	NUM
ejpam-4928	204	15	:	:	PUNCT
ejpam-4928	204	16	graphs	graph	NOUN
ejpam-4928	204	17	for	for	ADP
ejpam-4928	204	18	equation	equation	NOUN
ejpam-4928	204	19	(	(	PUNCT
ejpam-4928	204	20	17	17	NUM
ejpam-4928	204	21	)	)	PUNCT
ejpam-4928	204	22	.	.	PUNCT
ejpam-4928	205	1	(	(	PUNCT
ejpam-4928	205	2	a	a	X
ejpam-4928	205	3	)	)	PUNCT
ejpam-4928	205	4	the	the	DET
ejpam-4928	205	5	solution	solution	NOUN
ejpam-4928	205	6	u(x	u(x	VERB
ejpam-4928	205	7	,	,	PUNCT
ejpam-4928	205	8	y	y	NOUN
ejpam-4928	205	9	)	)	PUNCT
ejpam-4928	205	10	.	.	PUNCT
ejpam-4928	206	1	(	(	PUNCT
ejpam-4928	206	2	b	b	X
ejpam-4928	206	3	)	)	PUNCT
ejpam-4928	206	4	the	the	DET
ejpam-4928	206	5	solution	solution	NOUN
ejpam-4928	206	6	u(x	u(x	VERB
ejpam-4928	206	7	,	,	PUNCT
ejpam-4928	206	8	y	y	NOUN
ejpam-4928	206	9	)	)	PUNCT
ejpam-4928	206	10	when	when	SCONJ
ejpam-4928	206	11	y	y	PROPN
ejpam-4928	206	12	∈	∈	PROPN
ejpam-4928	206	13	{	{	PUNCT
ejpam-4928	206	14	0	0	NUM
ejpam-4928	206	15	,	,	PUNCT
ejpam-4928	206	16	0.1	0.1	NUM
ejpam-4928	206	17	,	,	PUNCT
ejpam-4928	206	18	0.7	0.7	NUM
ejpam-4928	206	19	,	,	PUNCT
ejpam-4928	206	20	1	1	NUM
ejpam-4928	206	21	}	}	PUNCT
ejpam-4928	206	22	.	.	PUNCT
ejpam-4928	207	1	(	(	PUNCT
ejpam-4928	207	2	c	c	X
ejpam-4928	207	3	)	)	PUNCT
ejpam-4928	207	4	the	the	DET
ejpam-4928	207	5	solution	solution	NOUN
ejpam-4928	207	6	u(x	u(x	VERB
ejpam-4928	207	7	,	,	PUNCT
ejpam-4928	207	8	y	y	NOUN
ejpam-4928	207	9	)	)	PUNCT
ejpam-4928	207	10	when	when	SCONJ
ejpam-4928	207	11	x	x	SYM
ejpam-4928	207	12	∈	∈	PROPN
ejpam-4928	207	13	{	{	PUNCT
ejpam-4928	207	14	0	0	NUM
ejpam-4928	207	15	,	,	PUNCT
ejpam-4928	207	16	0.3	0.3	NUM
ejpam-4928	207	17	,	,	PUNCT
ejpam-4928	207	18	0.5	0.5	NUM
ejpam-4928	207	19	,	,	PUNCT
ejpam-4928	207	20	1	1	NUM
ejpam-4928	207	21	}	}	PUNCT
ejpam-4928	207	22	.	.	PUNCT
ejpam-4928	208	1	(	(	PUNCT
ejpam-4928	208	2	d	d	X
ejpam-4928	208	3	)	)	PUNCT
ejpam-4928	208	4	the	the	DET
ejpam-4928	208	5	residual	residual	ADJ
ejpam-4928	208	6	error	error	NOUN
ejpam-4928	208	7	.	.	PUNCT
ejpam-4928	209	1	case(ii	case(ii	ADJ
ejpam-4928	209	2	):	):	PUNCT
ejpam-4928	209	3	q(y	q(y	PROPN
ejpam-4928	209	4	)	)	PUNCT
ejpam-4928	209	5	=	=	PUNCT
ejpam-4928	209	6	q	q	NOUN
ejpam-4928	209	7	3	3	NUM
ejpam-4928	209	8	2	2	NUM
ejpam-4928	209	9	(	(	PUNCT
ejpam-4928	209	10	y	y	NOUN
ejpam-4928	209	11	)	)	PUNCT
ejpam-4928	209	12	=	=	PUNCT
ejpam-4928	210	1	q	q	NOUN
ejpam-4928	210	2	1	1	NUM
ejpam-4928	210	3	2	2	NUM
ejpam-4928	210	4	(	(	PUNCT
ejpam-4928	210	5	y	y	PROPN
ejpam-4928	210	6	)	)	PUNCT
ejpam-4928	210	7	.	.	PUNCT
ejpam-4928	211	1	has	have	VERB
ejpam-4928	211	2	no	no	DET
ejpam-4928	211	3	solution	solution	NOUN
ejpam-4928	211	4	.	.	PUNCT
ejpam-4928	212	1	so	so	ADV
ejpam-4928	212	2	,	,	PUNCT
ejpam-4928	212	3	there	there	PRON
ejpam-4928	212	4	is	be	VERB
ejpam-4928	212	5	no	no	DET
ejpam-4928	212	6	atomic	atomic	ADJ
ejpam-4928	212	7	solution	solution	NOUN
ejpam-4928	212	8	.	.	PUNCT
ejpam-4928	213	1	references	reference	NOUN
ejpam-4928	213	2	2142	2142	NUM
ejpam-4928	213	3	5	5	NUM
ejpam-4928	213	4	.	.	PUNCT
ejpam-4928	213	5	conclusion	conclusion	VERB
ejpam-4928	213	6	the	the	DET
ejpam-4928	213	7	main	main	ADJ
ejpam-4928	213	8	goal	goal	NOUN
ejpam-4928	213	9	of	of	ADP
ejpam-4928	213	10	this	this	DET
ejpam-4928	213	11	study	study	NOUN
ejpam-4928	213	12	is	be	AUX
ejpam-4928	213	13	to	to	PART
ejpam-4928	213	14	find	find	VERB
ejpam-4928	213	15	solutions	solution	NOUN
ejpam-4928	213	16	for	for	ADP
ejpam-4928	213	17	linear	linear	ADJ
ejpam-4928	213	18	partial	partial	ADJ
ejpam-4928	213	19	differential	differential	ADJ
ejpam-4928	213	20	equations	equation	NOUN
ejpam-4928	213	21	that	that	PRON
ejpam-4928	213	22	involve	involve	VERB
ejpam-4928	213	23	fractional	fractional	ADJ
ejpam-4928	213	24	conformable	conformable	ADJ
ejpam-4928	213	25	derivatives	derivative	NOUN
ejpam-4928	213	26	.	.	PUNCT
ejpam-4928	214	1	to	to	PART
ejpam-4928	214	2	achieve	achieve	VERB
ejpam-4928	214	3	this	this	PRON
ejpam-4928	214	4	,	,	PUNCT
ejpam-4928	214	5	we	we	PRON
ejpam-4928	214	6	have	have	AUX
ejpam-4928	214	7	used	use	VERB
ejpam-4928	214	8	two	two	NUM
ejpam-4928	214	9	methods	method	NOUN
ejpam-4928	214	10	:	:	PUNCT
ejpam-4928	214	11	separation	separation	NOUN
ejpam-4928	214	12	of	of	ADP
ejpam-4928	214	13	variables	variable	NOUN
ejpam-4928	214	14	and	and	CCONJ
ejpam-4928	214	15	tensor	tensor	NOUN
ejpam-4928	214	16	product	product	NOUN
ejpam-4928	214	17	method	method	NOUN
ejpam-4928	214	18	.	.	PUNCT
ejpam-4928	215	1	these	these	DET
ejpam-4928	215	2	methods	method	NOUN
ejpam-4928	215	3	allow	allow	VERB
ejpam-4928	215	4	us	we	PRON
ejpam-4928	215	5	to	to	PART
ejpam-4928	215	6	obtain	obtain	VERB
ejpam-4928	215	7	both	both	CCONJ
ejpam-4928	215	8	exact	exact	ADJ
ejpam-4928	215	9	and	and	CCONJ
ejpam-4928	215	10	numerical	numerical	ADJ
ejpam-4928	215	11	solutions	solution	NOUN
ejpam-4928	215	12	.	.	PUNCT
ejpam-4928	216	1	our	our	PRON
ejpam-4928	216	2	results	result	NOUN
ejpam-4928	216	3	show	show	VERB
ejpam-4928	216	4	that	that	SCONJ
ejpam-4928	216	5	these	these	DET
ejpam-4928	216	6	procedures	procedure	NOUN
ejpam-4928	216	7	are	be	AUX
ejpam-4928	216	8	efficient	efficient	ADJ
ejpam-4928	216	9	,	,	PUNCT
ejpam-4928	216	10	reliable	reliable	ADJ
ejpam-4928	216	11	and	and	CCONJ
ejpam-4928	216	12	sufficient	sufficient	ADJ
ejpam-4928	216	13	.	.	PUNCT
ejpam-4928	217	1	in	in	ADP
ejpam-4928	217	2	other	other	ADJ
ejpam-4928	217	3	words	word	NOUN
ejpam-4928	217	4	,	,	PUNCT
ejpam-4928	217	5	we	we	PRON
ejpam-4928	217	6	have	have	AUX
ejpam-4928	217	7	found	find	VERB
ejpam-4928	217	8	that	that	SCONJ
ejpam-4928	217	9	the	the	DET
ejpam-4928	217	10	solutions	solution	NOUN
ejpam-4928	217	11	we	we	PRON
ejpam-4928	217	12	obtained	obtain	VERB
ejpam-4928	217	13	using	use	VERB
ejpam-4928	217	14	these	these	DET
ejpam-4928	217	15	methods	method	NOUN
ejpam-4928	217	16	are	be	AUX
ejpam-4928	217	17	accurate	accurate	ADJ
ejpam-4928	217	18	and	and	CCONJ
ejpam-4928	217	19	can	can	AUX
ejpam-4928	217	20	be	be	AUX
ejpam-4928	217	21	trusted	trust	VERB
ejpam-4928	217	22	.	.	PUNCT
ejpam-4928	218	1	this	this	PRON
ejpam-4928	218	2	is	be	AUX
ejpam-4928	218	3	important	important	ADJ
ejpam-4928	218	4	because	because	SCONJ
ejpam-4928	218	5	it	it	PRON
ejpam-4928	218	6	means	mean	VERB
ejpam-4928	218	7	that	that	SCONJ
ejpam-4928	218	8	these	these	DET
ejpam-4928	218	9	methods	method	NOUN
ejpam-4928	218	10	can	can	AUX
ejpam-4928	218	11	be	be	AUX
ejpam-4928	218	12	used	use	VERB
ejpam-4928	218	13	to	to	PART
ejpam-4928	218	14	solve	solve	VERB
ejpam-4928	218	15	similar	similar	ADJ
ejpam-4928	218	16	problems	problem	NOUN
ejpam-4928	218	17	in	in	ADP
ejpam-4928	218	18	the	the	DET
ejpam-4928	218	19	future	future	NOUN
ejpam-4928	218	20	.	.	PUNCT
ejpam-4928	219	1	overall	overall	ADV
ejpam-4928	219	2	,	,	PUNCT
ejpam-4928	219	3	our	our	PRON
ejpam-4928	219	4	study	study	NOUN
ejpam-4928	219	5	provides	provide	VERB
ejpam-4928	219	6	a	a	DET
ejpam-4928	219	7	valuable	valuable	ADJ
ejpam-4928	219	8	contribution	contribution	NOUN
ejpam-4928	219	9	to	to	ADP
ejpam-4928	219	10	the	the	DET
ejpam-4928	219	11	field	field	NOUN
ejpam-4928	219	12	of	of	ADP
ejpam-4928	219	13	partial	partial	ADJ
ejpam-4928	219	14	differential	differential	NOUN
ejpam-4928	219	15	equations	equation	NOUN
ejpam-4928	219	16	,	,	PUNCT
ejpam-4928	219	17	demonstrating	demonstrate	VERB
ejpam-4928	219	18	the	the	DET
ejpam-4928	219	19	effectiveness	effectiveness	NOUN
ejpam-4928	219	20	of	of	ADP
ejpam-4928	219	21	the	the	DET
ejpam-4928	219	22	separation	separation	NOUN
ejpam-4928	219	23	of	of	ADP
ejpam-4928	219	24	variables	variable	NOUN
ejpam-4928	219	25	and	and	CCONJ
ejpam-4928	219	26	tensor	tensor	NOUN
ejpam-4928	219	27	product	product	NOUN
ejpam-4928	219	28	method	method	NOUN
ejpam-4928	219	29	for	for	ADP
ejpam-4928	219	30	solving	solve	VERB
ejpam-4928	219	31	these	these	DET
ejpam-4928	219	32	types	type	NOUN
ejpam-4928	219	33	of	of	ADP
ejpam-4928	219	34	equations	equation	NOUN
ejpam-4928	219	35	.	.	PUNCT
ejpam-4928	220	1	references	reference	NOUN
ejpam-4928	220	2	[	[	X
ejpam-4928	220	3	1	1	NUM
ejpam-4928	220	4	]	]	X
ejpam-4928	220	5	m	m	VERB
ejpam-4928	220	6	al	al	PROPN
ejpam-4928	220	7	-	-	PUNCT
ejpam-4928	220	8	horani	horani	PROPN
ejpam-4928	220	9	,	,	PUNCT
ejpam-4928	220	10	r	r	NOUN
ejpam-4928	220	11	khalil	khalil	PROPN
ejpam-4928	220	12	,	,	PUNCT
ejpam-4928	220	13	and	and	CCONJ
ejpam-4928	220	14	i	i	PRON
ejpam-4928	220	15	aldarawi	aldarawi	VERB
ejpam-4928	220	16	.	.	PUNCT
ejpam-4928	221	1	fractional	fractional	PROPN
ejpam-4928	221	2	cauchy	cauchy	PROPN
ejpam-4928	221	3	euler	euler	PROPN
ejpam-4928	221	4	di¤	di¤	PROPN
ejpam-4928	221	5	erential	erential	ADJ
ejpam-4928	221	6	equation	equation	NOUN
ejpam-4928	221	7	.	.	PUNCT
ejpam-4928	222	1	journal	journal	NOUN
ejpam-4928	222	2	of	of	ADP
ejpam-4928	222	3	computational	computational	ADJ
ejpam-4928	222	4	analysis	analysis	NOUN
ejpam-4928	222	5	and	and	CCONJ
ejpam-4928	222	6	applications	application	NOUN
ejpam-4928	222	7	,	,	PUNCT
ejpam-4928	222	8	28(2	28(2	NUM
ejpam-4928	222	9	)	)	PUNCT
ejpam-4928	222	10	,	,	PUNCT
ejpam-4928	222	11	2020	2020	NUM
ejpam-4928	222	12	.	.	PUNCT
ejpam-4928	223	1	[	[	X
ejpam-4928	223	2	2	2	X
ejpam-4928	223	3	]	]	PUNCT
ejpam-4928	223	4	i	i	PRON
ejpam-4928	223	5	aldarawi	aldarawi	VERB
ejpam-4928	223	6	.	.	PUNCT
ejpam-4928	224	1	conformable	conformable	ADJ
ejpam-4928	224	2	fractional	fractional	ADJ
ejpam-4928	224	3	hyper	hyper	ADJ
ejpam-4928	224	4	geometric	geometric	ADJ
ejpam-4928	224	5	equation	equation	NOUN
ejpam-4928	224	6	.	.	PUNCT
ejpam-4928	225	1	j.	j.	PROPN
ejpam-4928	225	2	semigroup	semigroup	PROPN
ejpam-4928	225	3	theory	theory	NOUN
ejpam-4928	225	4	applications	application	NOUN
ejpam-4928	225	5	,	,	PUNCT
ejpam-4928	225	6	2018	2018	NUM
ejpam-4928	225	7	:	:	PUNCT
ejpam-4928	225	8	article	article	NOUN
ejpam-4928	225	9	–	–	PUNCT
ejpam-4928	225	10	id	id	NOUN
ejpam-4928	225	11	,	,	PUNCT
ejpam-4928	225	12	2018	2018	NUM
ejpam-4928	225	13	.	.	PUNCT
ejpam-4928	226	1	[	[	X
ejpam-4928	226	2	3	3	X
ejpam-4928	226	3	]	]	X
ejpam-4928	226	4	iman	iman	NOUN
ejpam-4928	226	5	aldarawi	aldarawi	VERB
ejpam-4928	226	6	.	.	PUNCT
ejpam-4928	227	1	the	the	DET
ejpam-4928	227	2	atomic	atomic	ADJ
ejpam-4928	227	3	solution	solution	NOUN
ejpam-4928	227	4	for	for	ADP
ejpam-4928	227	5	fractional	fractional	ADJ
ejpam-4928	227	6	wave	wave	NOUN
ejpam-4928	227	7	type	type	NOUN
ejpam-4928	227	8	equation	equation	NOUN
ejpam-4928	227	9	.	.	PUNCT
ejpam-4928	228	1	journal	journal	NOUN
ejpam-4928	228	2	of	of	ADP
ejpam-4928	228	3	computational	computational	ADJ
ejpam-4928	228	4	analysis	analysis	NOUN
ejpam-4928	228	5	and	and	CCONJ
ejpam-4928	228	6	applications	application	NOUN
ejpam-4928	228	7	,	,	PUNCT
ejpam-4928	228	8	page	page	NOUN
ejpam-4928	228	9	40	40	NUM
ejpam-4928	228	10	,	,	PUNCT
ejpam-4928	228	11	2022	2022	NUM
ejpam-4928	228	12	.	.	PUNCT
ejpam-4928	229	1	[	[	X
ejpam-4928	229	2	4	4	NUM
ejpam-4928	229	3	]	]	X
ejpam-4928	229	4	asma	asma	PROPN
ejpam-4928	229	5	alhabees	alhabees	PROPN
ejpam-4928	229	6	.	.	PUNCT
ejpam-4928	230	1	exact	exact	ADJ
ejpam-4928	230	2	solutions	solution	NOUN
ejpam-4928	230	3	of	of	ADP
ejpam-4928	230	4	conformable	conformable	ADJ
ejpam-4928	230	5	fractional	fractional	ADJ
ejpam-4928	230	6	harry	harry	PROPN
ejpam-4928	230	7	dym	dym	PROPN
ejpam-4928	230	8	equation	equation	PROPN
ejpam-4928	230	9	.	.	PUNCT
ejpam-4928	231	1	journal	journal	PROPN
ejpam-4928	231	2	of	of	ADP
ejpam-4928	231	3	computational	computational	ADJ
ejpam-4928	231	4	analysis	analysis	NOUN
ejpam-4928	231	5	and	and	CCONJ
ejpam-4928	231	6	applications	application	NOUN
ejpam-4928	231	7	,	,	PUNCT
ejpam-4928	231	8	29(4	29(4	NOUN
ejpam-4928	231	9	)	)	PUNCT
ejpam-4928	231	10	,	,	PUNCT
ejpam-4928	231	11	2021	2021	NUM
ejpam-4928	231	12	.	.	PUNCT
ejpam-4928	232	1	[	[	X
ejpam-4928	232	2	5	5	NUM
ejpam-4928	232	3	]	]	X
ejpam-4928	232	4	asma	asma	PROPN
ejpam-4928	232	5	alhabees	alhabees	PROPN
ejpam-4928	232	6	and	and	CCONJ
ejpam-4928	232	7	iman	iman	PROPN
ejpam-4928	232	8	aldarawi	aldarawi	VERB
ejpam-4928	232	9	.	.	PUNCT
ejpam-4928	233	1	integrating	integrate	VERB
ejpam-4928	233	2	factors	factor	NOUN
ejpam-4928	233	3	for	for	ADP
ejpam-4928	233	4	non	non	ADJ
ejpam-4928	233	5	-	-	ADJ
ejpam-4928	233	6	exact	exact	ADJ
ejpam-4928	233	7	conformable	conformable	ADJ
ejpam-4928	233	8	differential	differential	NOUN
ejpam-4928	233	9	equation	equation	NOUN
ejpam-4928	233	10	.	.	PUNCT
ejpam-4928	234	1	journal	journal	PROPN
ejpam-4928	234	2	of	of	ADP
ejpam-4928	234	3	mathematical	mathematical	ADJ
ejpam-4928	234	4	and	and	CCONJ
ejpam-4928	234	5	computational	computational	ADJ
ejpam-4928	234	6	science	science	NOUN
ejpam-4928	234	7	,	,	PUNCT
ejpam-4928	234	8	10(4):964–979	10(4):964–979	NUM
ejpam-4928	234	9	,	,	PUNCT
ejpam-4928	234	10	2020	2020	NUM
ejpam-4928	234	11	.	.	PUNCT
ejpam-4928	235	1	[	[	X
ejpam-4928	235	2	6	6	NUM
ejpam-4928	235	3	]	]	PUNCT
ejpam-4928	235	4	abdon	abdon	NOUN
ejpam-4928	235	5	atangana	atangana	PROPN
ejpam-4928	235	6	and	and	CCONJ
ejpam-4928	235	7	dumitru	dumitru	PROPN
ejpam-4928	235	8	baleanu	baleanu	NOUN
ejpam-4928	235	9	.	.	PUNCT
ejpam-4928	236	1	new	new	ADJ
ejpam-4928	236	2	fractional	fractional	ADJ
ejpam-4928	236	3	derivatives	derivative	NOUN
ejpam-4928	236	4	with	with	ADP
ejpam-4928	236	5	nonlocal	nonlocal	ADJ
ejpam-4928	236	6	and	and	CCONJ
ejpam-4928	236	7	non	non	ADJ
ejpam-4928	236	8	-	-	ADJ
ejpam-4928	236	9	singular	singular	ADJ
ejpam-4928	236	10	kernel	kernel	NOUN
ejpam-4928	236	11	:	:	PUNCT
ejpam-4928	236	12	theory	theory	NOUN
ejpam-4928	236	13	and	and	CCONJ
ejpam-4928	236	14	application	application	NOUN
ejpam-4928	236	15	to	to	PART
ejpam-4928	236	16	heat	heat	NOUN
ejpam-4928	236	17	transfer	transfer	NOUN
ejpam-4928	236	18	model	model	NOUN
ejpam-4928	236	19	.	.	PUNCT
ejpam-4928	237	1	arxiv	arxiv	PROPN
ejpam-4928	237	2	preprint	preprint	VERB
ejpam-4928	237	3	arxiv:1602.03408	arxiv:1602.03408	PROPN
ejpam-4928	237	4	,	,	PUNCT
ejpam-4928	237	5	2016	2016	NUM
ejpam-4928	237	6	.	.	PUNCT
ejpam-4928	238	1	[	[	X
ejpam-4928	238	2	7	7	X
ejpam-4928	238	3	]	]	X
ejpam-4928	238	4	dumitru	dumitru	PROPN
ejpam-4928	238	5	baleanu	baleanu	NOUN
ejpam-4928	238	6	and	and	CCONJ
ejpam-4928	238	7	hassan	hassan	PROPN
ejpam-4928	238	8	kamil	kamil	PROPN
ejpam-4928	238	9	jassim	jassim	PROPN
ejpam-4928	238	10	.	.	PUNCT
ejpam-4928	239	1	exact	exact	ADJ
ejpam-4928	239	2	solution	solution	NOUN
ejpam-4928	239	3	of	of	ADP
ejpam-4928	239	4	two	two	NUM
ejpam-4928	239	5	-	-	PUNCT
ejpam-4928	239	6	dimensional	dimensional	ADJ
ejpam-4928	239	7	fractional	fractional	ADJ
ejpam-4928	239	8	partial	partial	ADJ
ejpam-4928	239	9	differential	differential	NOUN
ejpam-4928	239	10	equations	equation	NOUN
ejpam-4928	239	11	.	.	PUNCT
ejpam-4928	240	1	fractal	fractal	ADJ
ejpam-4928	240	2	and	and	CCONJ
ejpam-4928	240	3	fractional	fractional	ADJ
ejpam-4928	240	4	,	,	PUNCT
ejpam-4928	240	5	4(2):21	4(2):21	NOUN
ejpam-4928	240	6	,	,	PUNCT
ejpam-4928	240	7	2020	2020	NUM
ejpam-4928	240	8	.	.	PUNCT
ejpam-4928	241	1	[	[	X
ejpam-4928	241	2	8	8	NUM
ejpam-4928	241	3	]	]	X
ejpam-4928	241	4	e	e	X
ejpam-4928	241	5	baskin	baskin	NOUN
ejpam-4928	241	6	and	and	CCONJ
ejpam-4928	241	7	a	a	DET
ejpam-4928	241	8	iomin	iomin	NOUN
ejpam-4928	241	9	.	.	PUNCT
ejpam-4928	242	1	fractional	fractional	ADJ
ejpam-4928	242	2	electrostatic	electrostatic	ADJ
ejpam-4928	242	3	equations	equation	NOUN
ejpam-4928	242	4	in	in	ADP
ejpam-4928	242	5	fractal	fractal	ADJ
ejpam-4928	242	6	composite	composite	ADJ
ejpam-4928	242	7	structures	structure	NOUN
ejpam-4928	242	8	.	.	PUNCT
ejpam-4928	243	1	computers	computer	NOUN
ejpam-4928	243	2	and	and	CCONJ
ejpam-4928	243	3	mathematics	mathematic	NOUN
ejpam-4928	243	4	with	with	ADP
ejpam-4928	243	5	applications	application	NOUN
ejpam-4928	243	6	,	,	PUNCT
ejpam-4928	243	7	64(10):3302–3309	64(10):3302–3309	NUM
ejpam-4928	243	8	,	,	PUNCT
ejpam-4928	243	9	2012	2012	NUM
ejpam-4928	243	10	.	.	PUNCT
ejpam-4928	244	1	[	[	X
ejpam-4928	244	2	9	9	NUM
ejpam-4928	244	3	]	]	X
ejpam-4928	244	4	ibtisam	ibtisam	PROPN
ejpam-4928	244	5	benkemache	benkemache	PROPN
ejpam-4928	244	6	,	,	PUNCT
ejpam-4928	244	7	mohammad	mohammad	PROPN
ejpam-4928	244	8	al	al	PROPN
ejpam-4928	244	9	-	-	PUNCT
ejpam-4928	244	10	horani	horani	PROPN
ejpam-4928	244	11	,	,	PUNCT
ejpam-4928	244	12	and	and	CCONJ
ejpam-4928	244	13	roshdi	roshdi	PROPN
ejpam-4928	244	14	rashid	rashid	PROPN
ejpam-4928	244	15	khalil	khalil	PROPN
ejpam-4928	244	16	.	.	PUNCT
ejpam-4928	245	1	tensor	tensor	NOUN
ejpam-4928	245	2	product	product	NOUN
ejpam-4928	245	3	and	and	CCONJ
ejpam-4928	245	4	certain	certain	ADJ
ejpam-4928	245	5	solutions	solution	NOUN
ejpam-4928	245	6	of	of	ADP
ejpam-4928	245	7	fractional	fractional	ADJ
ejpam-4928	245	8	wave	wave	NOUN
ejpam-4928	245	9	type	type	NOUN
ejpam-4928	245	10	equation	equation	NOUN
ejpam-4928	245	11	.	.	PUNCT
ejpam-4928	246	1	european	european	ADJ
ejpam-4928	246	2	journal	journal	PROPN
ejpam-4928	246	3	of	of	ADP
ejpam-4928	246	4	pure	pure	ADJ
ejpam-4928	246	5	and	and	CCONJ
ejpam-4928	246	6	applied	applied	ADJ
ejpam-4928	246	7	mathematics	mathematic	NOUN
ejpam-4928	246	8	,	,	PUNCT
ejpam-4928	246	9	14(3):942–948	14(3):942–948	NUM
ejpam-4928	246	10	,	,	PUNCT
ejpam-4928	246	11	2021	2021	NUM
ejpam-4928	246	12	.	.	PUNCT
ejpam-4928	247	1	[	[	X
ejpam-4928	247	2	10	10	NUM
ejpam-4928	247	3	]	]	X
ejpam-4928	247	4	david	david	PROPN
ejpam-4928	247	5	a	a	PROPN
ejpam-4928	247	6	benson	benson	PROPN
ejpam-4928	247	7	,	,	PUNCT
ejpam-4928	247	8	stephen	stephen	PROPN
ejpam-4928	247	9	w	w	PROPN
ejpam-4928	247	10	wheatcraft	wheatcraft	NOUN
ejpam-4928	247	11	,	,	PUNCT
ejpam-4928	247	12	and	and	CCONJ
ejpam-4928	247	13	mark	mark	PROPN
ejpam-4928	247	14	m	m	PROPN
ejpam-4928	247	15	meerschaert	meerschaert	NOUN
ejpam-4928	247	16	.	.	PUNCT
ejpam-4928	248	1	the	the	DET
ejpam-4928	248	2	fractionalorder	fractionalorder	ADJ
ejpam-4928	248	3	governing	govern	VERB
ejpam-4928	248	4	equation	equation	NOUN
ejpam-4928	248	5	of	of	ADP
ejpam-4928	248	6	lévy	lévy	X
ejpam-4928	248	7	motion	motion	NOUN
ejpam-4928	248	8	.	.	PUNCT
ejpam-4928	249	1	water	water	NOUN
ejpam-4928	249	2	resources	resource	NOUN
ejpam-4928	249	3	research	research	NOUN
ejpam-4928	249	4	,	,	PUNCT
ejpam-4928	249	5	36(6):1413–1423	36(6):1413–1423	NUM
ejpam-4928	249	6	,	,	PUNCT
ejpam-4928	249	7	2000	2000	NUM
ejpam-4928	249	8	.	.	PUNCT
ejpam-4928	250	1	references	reference	NOUN
ejpam-4928	250	2	2143	2143	PROPN
ejpam-4928	251	1	[	[	X
ejpam-4928	251	2	11	11	NUM
ejpam-4928	251	3	]	]	PUNCT
ejpam-4928	251	4	nadjwa	nadjwa	NOUN
ejpam-4928	251	5	berredjem	berredjem	PROPN
ejpam-4928	251	6	,	,	PUNCT
ejpam-4928	251	7	banan	banan	NOUN
ejpam-4928	251	8	maayah	maayah	PROPN
ejpam-4928	251	9	,	,	PUNCT
ejpam-4928	251	10	and	and	CCONJ
ejpam-4928	251	11	omar	omar	PROPN
ejpam-4928	251	12	abu	abu	PROPN
ejpam-4928	251	13	arqub	arqub	PROPN
ejpam-4928	251	14	.	.	PUNCT
ejpam-4928	252	1	a	a	DET
ejpam-4928	252	2	numerical	numerical	ADJ
ejpam-4928	252	3	method	method	NOUN
ejpam-4928	252	4	for	for	ADP
ejpam-4928	252	5	solving	solve	VERB
ejpam-4928	252	6	conformable	conformable	ADJ
ejpam-4928	252	7	fractional	fractional	ADJ
ejpam-4928	252	8	integrodifferential	integrodifferential	ADJ
ejpam-4928	252	9	systems	system	NOUN
ejpam-4928	252	10	of	of	ADP
ejpam-4928	252	11	second	second	ADJ
ejpam-4928	252	12	-	-	PUNCT
ejpam-4928	252	13	order	order	NOUN
ejpam-4928	252	14	,	,	PUNCT
ejpam-4928	252	15	twopoints	twopoint	VERB
ejpam-4928	252	16	periodic	periodic	ADJ
ejpam-4928	252	17	boundary	boundary	ADJ
ejpam-4928	252	18	conditions	condition	NOUN
ejpam-4928	252	19	.	.	PUNCT
ejpam-4928	253	1	alexandria	alexandria	PROPN
ejpam-4928	253	2	engineering	engineering	PROPN
ejpam-4928	253	3	journal	journal	PROPN
ejpam-4928	253	4	,	,	PUNCT
ejpam-4928	253	5	61(7):5699	61(7):5699	NUM
ejpam-4928	253	6	–	–	PUNCT
ejpam-4928	253	7	5711	5711	NUM
ejpam-4928	253	8	,	,	PUNCT
ejpam-4928	253	9	2022	2022	NUM
ejpam-4928	253	10	.	.	PUNCT
ejpam-4928	254	1	[	[	X
ejpam-4928	254	2	12	12	NUM
ejpam-4928	254	3	]	]	X
ejpam-4928	254	4	ahmed	ahmed	PROPN
ejpam-4928	254	5	bouchenak	bouchenak	PROPN
ejpam-4928	254	6	,	,	PUNCT
ejpam-4928	254	7	r	r	PROPN
ejpam-4928	254	8	khalil	khalil	PROPN
ejpam-4928	254	9	,	,	PUNCT
ejpam-4928	254	10	and	and	CCONJ
ejpam-4928	254	11	m	m	PROPN
ejpam-4928	254	12	alhorani	alhorani	ADJ
ejpam-4928	254	13	.	.	PUNCT
ejpam-4928	255	1	fractional	fractional	ADJ
ejpam-4928	255	2	fourier	fourier	PROPN
ejpam-4928	255	3	series	series	NOUN
ejpam-4928	255	4	with	with	ADP
ejpam-4928	255	5	separation	separation	NOUN
ejpam-4928	255	6	of	of	ADP
ejpam-4928	255	7	variables	variable	NOUN
ejpam-4928	255	8	technique	technique	NOUN
ejpam-4928	255	9	and	and	CCONJ
ejpam-4928	255	10	its	its	PRON
ejpam-4928	255	11	application	application	NOUN
ejpam-4928	255	12	on	on	ADP
ejpam-4928	255	13	fractional	fractional	ADJ
ejpam-4928	255	14	differential	differential	ADJ
ejpam-4928	255	15	equations	equation	NOUN
ejpam-4928	255	16	.	.	PUNCT
ejpam-4928	256	1	wseas	wseas	VERB
ejpam-4928	256	2	transactions	transaction	NOUN
ejpam-4928	256	3	on	on	ADP
ejpam-4928	256	4	mathematics	mathematic	NOUN
ejpam-4928	256	5	,	,	PUNCT
ejpam-4928	256	6	20:461–469	20:461–469	NUM
ejpam-4928	256	7	,	,	PUNCT
ejpam-4928	256	8	2021	2021	NUM
ejpam-4928	256	9	.	.	PUNCT
ejpam-4928	257	1	[	[	X
ejpam-4928	257	2	13	13	NUM
ejpam-4928	257	3	]	]	PUNCT
ejpam-4928	257	4	michele	michele	PROPN
ejpam-4928	257	5	caputo	caputo	PROPN
ejpam-4928	257	6	.	.	PROPN
ejpam-4928	258	1	linear	linear	PROPN
ejpam-4928	258	2	models	model	NOUN
ejpam-4928	258	3	of	of	ADP
ejpam-4928	258	4	dissipation	dissipation	NOUN
ejpam-4928	258	5	whose	whose	DET
ejpam-4928	258	6	q	q	NOUN
ejpam-4928	258	7	is	be	AUX
ejpam-4928	258	8	almost	almost	ADV
ejpam-4928	258	9	frequency	frequency	ADJ
ejpam-4928	258	10	independent	independent	ADJ
ejpam-4928	258	11	—	—	PUNCT
ejpam-4928	258	12	ii	ii	NOUN
ejpam-4928	258	13	.	.	PUNCT
ejpam-4928	258	14	geophysical	geophysical	ADJ
ejpam-4928	258	15	journal	journal	PROPN
ejpam-4928	258	16	international	international	PROPN
ejpam-4928	258	17	,	,	PUNCT
ejpam-4928	258	18	13(5):529–539	13(5):529–539	NUM
ejpam-4928	258	19	,	,	PUNCT
ejpam-4928	258	20	1967	1967	NUM
ejpam-4928	258	21	.	.	PUNCT
ejpam-4928	259	1	[	[	X
ejpam-4928	259	2	14	14	NUM
ejpam-4928	259	3	]	]	X
ejpam-4928	259	4	michele	michele	PROPN
ejpam-4928	259	5	caputo	caputo	PROPN
ejpam-4928	259	6	and	and	CCONJ
ejpam-4928	259	7	mauro	mauro	PROPN
ejpam-4928	259	8	fabrizio	fabrizio	PROPN
ejpam-4928	259	9	.	.	PUNCT
ejpam-4928	260	1	a	a	DET
ejpam-4928	260	2	new	new	ADJ
ejpam-4928	260	3	definition	definition	NOUN
ejpam-4928	260	4	of	of	ADP
ejpam-4928	260	5	fractional	fractional	ADJ
ejpam-4928	260	6	derivative	derivative	NOUN
ejpam-4928	260	7	without	without	ADP
ejpam-4928	260	8	singular	singular	ADJ
ejpam-4928	260	9	kernel	kernel	PROPN
ejpam-4928	260	10	.	.	PUNCT
ejpam-4928	261	1	progress	progress	NOUN
ejpam-4928	261	2	in	in	ADP
ejpam-4928	261	3	fractional	fractional	ADJ
ejpam-4928	261	4	differentiation	differentiation	NOUN
ejpam-4928	261	5	and	and	CCONJ
ejpam-4928	261	6	applications	application	NOUN
ejpam-4928	261	7	,	,	PUNCT
ejpam-4928	261	8	1(2):73–85	1(2):73–85	NUM
ejpam-4928	261	9	,	,	PUNCT
ejpam-4928	261	10	2015	2015	NUM
ejpam-4928	261	11	.	.	PUNCT
ejpam-4928	262	1	[	[	X
ejpam-4928	262	2	15	15	NUM
ejpam-4928	262	3	]	]	X
ejpam-4928	262	4	alberto	alberto	PROPN
ejpam-4928	262	5	carpinteri	carpinteri	PROPN
ejpam-4928	262	6	and	and	CCONJ
ejpam-4928	262	7	francesco	francesco	PROPN
ejpam-4928	262	8	mainardi	mainardi	PROPN
ejpam-4928	262	9	.	.	PUNCT
ejpam-4928	263	1	fractals	fractal	NOUN
ejpam-4928	263	2	and	and	CCONJ
ejpam-4928	263	3	fractional	fractional	ADJ
ejpam-4928	263	4	calculus	calculus	NOUN
ejpam-4928	263	5	in	in	ADP
ejpam-4928	263	6	continuum	continuum	ADJ
ejpam-4928	263	7	mechanics	mechanic	NOUN
ejpam-4928	263	8	,	,	PUNCT
ejpam-4928	263	9	volume	volume	NOUN
ejpam-4928	263	10	378	378	NUM
ejpam-4928	263	11	.	.	PUNCT
ejpam-4928	263	12	springer	springer	NOUN
ejpam-4928	263	13	,	,	PUNCT
ejpam-4928	263	14	2014	2014	NUM
ejpam-4928	263	15	.	.	PUNCT
ejpam-4928	264	1	[	[	X
ejpam-4928	264	2	16	16	NUM
ejpam-4928	264	3	]	]	X
ejpam-4928	264	4	w.	w.	PROPN
ejpam-4928	264	5	deeb	deeb	PROPN
ejpam-4928	264	6	and	and	CCONJ
ejpam-4928	264	7	r.	r.	PROPN
ejpam-4928	264	8	khalil	khalil	PROPN
ejpam-4928	264	9	.	.	PUNCT
ejpam-4928	265	1	best	good	ADJ
ejpam-4928	265	2	approximation	approximation	NOUN
ejpam-4928	265	3	in	in	ADP
ejpam-4928	265	4	l(x	l(x	PROPN
ejpam-4928	265	5	,	,	PUNCT
ejpam-4928	265	6	y	y	PROPN
ejpam-4928	265	7	)	)	PUNCT
ejpam-4928	265	8	.	.	PUNCT
ejpam-4928	266	1	mathematical	mathematical	ADJ
ejpam-4928	266	2	proceedings	proceeding	NOUN
ejpam-4928	266	3	of	of	ADP
ejpam-4928	266	4	the	the	DET
ejpam-4928	266	5	cambridge	cambridge	PROPN
ejpam-4928	266	6	philosophical	philosophical	ADJ
ejpam-4928	266	7	society	society	NOUN
ejpam-4928	266	8	,	,	PUNCT
ejpam-4928	266	9	104(3):527–531	104(3):527–531	NUM
ejpam-4928	266	10	,	,	PUNCT
ejpam-4928	266	11	1988	1988	NUM
ejpam-4928	266	12	.	.	PUNCT
ejpam-4928	267	1	[	[	X
ejpam-4928	267	2	17	17	NUM
ejpam-4928	267	3	]	]	X
ejpam-4928	267	4	hasan	hasan	PROPN
ejpam-4928	267	5	fallahgoul	fallahgoul	PROPN
ejpam-4928	267	6	,	,	PUNCT
ejpam-4928	267	7	sergio	sergio	PROPN
ejpam-4928	267	8	focardi	focardi	PROPN
ejpam-4928	267	9	,	,	PUNCT
ejpam-4928	267	10	and	and	CCONJ
ejpam-4928	267	11	frank	frank	PROPN
ejpam-4928	267	12	fabozzi	fabozzi	PROPN
ejpam-4928	267	13	.	.	PUNCT
ejpam-4928	268	1	fractional	fractional	ADJ
ejpam-4928	268	2	calculus	calculus	NOUN
ejpam-4928	268	3	and	and	CCONJ
ejpam-4928	268	4	fractional	fractional	ADJ
ejpam-4928	268	5	processes	process	NOUN
ejpam-4928	268	6	with	with	ADP
ejpam-4928	268	7	applications	application	NOUN
ejpam-4928	268	8	to	to	ADP
ejpam-4928	268	9	financial	financial	ADJ
ejpam-4928	268	10	economics	economic	NOUN
ejpam-4928	268	11	:	:	PUNCT
ejpam-4928	268	12	theory	theory	NOUN
ejpam-4928	268	13	and	and	CCONJ
ejpam-4928	268	14	application	application	NOUN
ejpam-4928	268	15	.	.	PUNCT
ejpam-4928	269	1	academic	academic	ADJ
ejpam-4928	269	2	press	press	NOUN
ejpam-4928	269	3	,	,	PUNCT
ejpam-4928	269	4	2016	2016	NUM
ejpam-4928	269	5	.	.	PUNCT
ejpam-4928	270	1	[	[	X
ejpam-4928	270	2	18	18	NUM
ejpam-4928	270	3	]	]	X
ejpam-4928	270	4	i	i	PRON
ejpam-4928	270	5	kadri	kadri	PROPN
ejpam-4928	270	6	,	,	PUNCT
ejpam-4928	270	7	m	m	VERB
ejpam-4928	270	8	horani	horani	ADJ
ejpam-4928	270	9	,	,	PUNCT
ejpam-4928	270	10	and	and	CCONJ
ejpam-4928	270	11	r	r	PROPN
ejpam-4928	270	12	khalil	khalil	PROPN
ejpam-4928	270	13	.	.	PUNCT
ejpam-4928	271	1	tensor	tensor	NOUN
ejpam-4928	271	2	product	product	NOUN
ejpam-4928	271	3	technique	technique	NOUN
ejpam-4928	271	4	and	and	CCONJ
ejpam-4928	271	5	fractional	fractional	ADJ
ejpam-4928	271	6	differential	differential	ADJ
ejpam-4928	271	7	equations	equation	NOUN
ejpam-4928	271	8	.	.	PUNCT
ejpam-4928	272	1	journal	journal	PROPN
ejpam-4928	272	2	of	of	ADP
ejpam-4928	272	3	semigroup	semigroup	PROPN
ejpam-4928	272	4	theory	theory	NOUN
ejpam-4928	272	5	and	and	CCONJ
ejpam-4928	272	6	applications	application	NOUN
ejpam-4928	272	7	,	,	PUNCT
ejpam-4928	272	8	2020	2020	NUM
ejpam-4928	272	9	:	:	PUNCT
ejpam-4928	272	10	article	article	NOUN
ejpam-4928	272	11	–	–	PUNCT
ejpam-4928	272	12	id	id	NOUN
ejpam-4928	272	13	,	,	PUNCT
ejpam-4928	272	14	2020	2020	NUM
ejpam-4928	272	15	.	.	PUNCT
ejpam-4928	273	1	[	[	X
ejpam-4928	273	2	19	19	NUM
ejpam-4928	273	3	]	]	X
ejpam-4928	273	4	ahmed	ahmed	PROPN
ejpam-4928	273	5	murshed	murshed	PROPN
ejpam-4928	273	6	kareem	kareem	PROPN
ejpam-4928	273	7	.	.	PUNCT
ejpam-4928	274	1	conformable	conformable	ADJ
ejpam-4928	274	2	fractional	fractional	ADJ
ejpam-4928	274	3	derivatives	derivative	NOUN
ejpam-4928	274	4	and	and	CCONJ
ejpam-4928	274	5	it	it	PRON
ejpam-4928	274	6	is	be	AUX
ejpam-4928	274	7	applications	application	NOUN
ejpam-4928	274	8	for	for	ADP
ejpam-4928	274	9	solving	solve	VERB
ejpam-4928	274	10	fractional	fractional	ADJ
ejpam-4928	274	11	differential	differential	ADJ
ejpam-4928	274	12	equations	equation	NOUN
ejpam-4928	274	13	.	.	PUNCT
ejpam-4928	275	1	journal	journal	PROPN
ejpam-4928	275	2	of	of	ADP
ejpam-4928	275	3	mathemtaics	mathemtaic	NOUN
ejpam-4928	275	4	,	,	PUNCT
ejpam-4928	275	5	13:81–87	13:81–87	NUM
ejpam-4928	275	6	,	,	PUNCT
ejpam-4928	275	7	2017	2017	NUM
ejpam-4928	275	8	.	.	PUNCT
ejpam-4928	276	1	[	[	X
ejpam-4928	276	2	20	20	NUM
ejpam-4928	276	3	]	]	PUNCT
ejpam-4928	276	4	roshdi	roshdi	NOUN
ejpam-4928	276	5	khalil	khalil	PROPN
ejpam-4928	276	6	.	.	PUNCT
ejpam-4928	277	1	isometries	isometry	NOUN
ejpam-4928	277	2	of	of	ADP
ejpam-4928	277	3	lp	lp	NOUN
ejpam-4928	277	4	∗	∗	NOUN
ejpam-4928	277	5	lp	lp	NOUN
ejpam-4928	277	6	.	.	PUNCT
ejpam-4928	278	1	tam	tam	PROPN
ejpam-4928	278	2	.	.	PUNCT
ejpam-4928	279	1	j.	j.	PROPN
ejpam-4928	279	2	math	math	PROPN
ejpam-4928	279	3	.	.	PROPN
ejpam-4928	279	4	,	,	PUNCT
ejpam-4928	279	5	16:77–85	16:77–85	NUM
ejpam-4928	279	6	,	,	PUNCT
ejpam-4928	279	7	1985	1985	NUM
ejpam-4928	279	8	.	.	PUNCT
ejpam-4928	280	1	[	[	X
ejpam-4928	280	2	21	21	NUM
ejpam-4928	280	3	]	]	X
ejpam-4928	280	4	roshdi	roshdi	NOUN
ejpam-4928	280	5	khalil	khalil	PROPN
ejpam-4928	280	6	,	,	PUNCT
ejpam-4928	280	7	mohammed	mohammed	PROPN
ejpam-4928	280	8	al	al	PROPN
ejpam-4928	280	9	horani	horani	PROPN
ejpam-4928	280	10	,	,	PUNCT
ejpam-4928	280	11	and	and	CCONJ
ejpam-4928	280	12	m	m	PROPN
ejpam-4928	280	13	abu	abu	PROPN
ejpam-4928	280	14	hammad	hammad	PROPN
ejpam-4928	280	15	.	.	PUNCT
ejpam-4928	281	1	geometric	geometric	ADJ
ejpam-4928	281	2	meaning	meaning	NOUN
ejpam-4928	281	3	of	of	ADP
ejpam-4928	281	4	conformable	conformable	ADJ
ejpam-4928	281	5	derivative	derivative	NOUN
ejpam-4928	281	6	via	via	ADP
ejpam-4928	281	7	fractional	fractional	ADJ
ejpam-4928	281	8	cords	cord	NOUN
ejpam-4928	281	9	.	.	PUNCT
ejpam-4928	282	1	journal	journal	PROPN
ejpam-4928	282	2	of	of	ADP
ejpam-4928	282	3	mathematical	mathematical	ADJ
ejpam-4928	282	4	and	and	CCONJ
ejpam-4928	282	5	computational	computational	ADJ
ejpam-4928	282	6	science	science	NOUN
ejpam-4928	282	7	,	,	PUNCT
ejpam-4928	282	8	19:241–245	19:241–245	PROPN
ejpam-4928	282	9	,	,	PUNCT
ejpam-4928	282	10	2019	2019	NUM
ejpam-4928	282	11	.	.	PUNCT
ejpam-4928	283	1	[	[	X
ejpam-4928	283	2	22	22	NUM
ejpam-4928	283	3	]	]	PUNCT
ejpam-4928	283	4	roshdi	roshdi	NOUN
ejpam-4928	283	5	khalil	khalil	PROPN
ejpam-4928	283	6	,	,	PUNCT
ejpam-4928	283	7	mohammed	mohammed	PROPN
ejpam-4928	283	8	al	al	PROPN
ejpam-4928	283	9	horani	horani	PROPN
ejpam-4928	283	10	,	,	PUNCT
ejpam-4928	283	11	abdelrahman	abdelrahman	NOUN
ejpam-4928	283	12	yousef	yousef	PROPN
ejpam-4928	283	13	,	,	PUNCT
ejpam-4928	283	14	and	and	CCONJ
ejpam-4928	283	15	mohammad	mohammad	PROPN
ejpam-4928	283	16	sababheh	sababheh	PROPN
ejpam-4928	283	17	.	.	PUNCT
ejpam-4928	284	1	a	a	DET
ejpam-4928	284	2	new	new	ADJ
ejpam-4928	284	3	definition	definition	NOUN
ejpam-4928	284	4	of	of	ADP
ejpam-4928	284	5	fractional	fractional	ADJ
ejpam-4928	284	6	derivative	derivative	NOUN
ejpam-4928	284	7	.	.	PUNCT
ejpam-4928	285	1	journal	journal	PROPN
ejpam-4928	285	2	of	of	ADP
ejpam-4928	285	3	computational	computational	ADJ
ejpam-4928	285	4	and	and	CCONJ
ejpam-4928	285	5	applied	applied	ADJ
ejpam-4928	285	6	mathematics	mathematic	NOUN
ejpam-4928	285	7	,	,	PUNCT
ejpam-4928	285	8	264:65–70	264:65–70	NUM
ejpam-4928	285	9	,	,	PUNCT
ejpam-4928	285	10	2014	2014	NUM
ejpam-4928	285	11	.	.	PUNCT
ejpam-4928	286	1	[	[	X
ejpam-4928	286	2	23	23	NUM
ejpam-4928	286	3	]	]	X
ejpam-4928	286	4	m	m	NOUN
ejpam-4928	286	5	mhailan	mhailan	NOUN
ejpam-4928	286	6	,	,	PUNCT
ejpam-4928	286	7	m	m	VERB
ejpam-4928	286	8	abu	abu	PROPN
ejpam-4928	286	9	hammad	hammad	PROPN
ejpam-4928	286	10	,	,	PUNCT
ejpam-4928	286	11	m	m	PROPN
ejpam-4928	286	12	al	al	PROPN
ejpam-4928	286	13	horani	horani	PROPN
ejpam-4928	286	14	,	,	PUNCT
ejpam-4928	286	15	and	and	CCONJ
ejpam-4928	286	16	r	r	PROPN
ejpam-4928	286	17	khalil	khalil	PROPN
ejpam-4928	286	18	.	.	PUNCT
ejpam-4928	287	1	on	on	ADP
ejpam-4928	287	2	fractional	fractional	ADJ
ejpam-4928	287	3	vector	vector	NOUN
ejpam-4928	287	4	analysis	analysis	NOUN
ejpam-4928	287	5	.	.	PUNCT
ejpam-4928	288	1	journal	journal	PROPN
ejpam-4928	288	2	of	of	ADP
ejpam-4928	288	3	mathematical	mathematical	ADJ
ejpam-4928	288	4	and	and	CCONJ
ejpam-4928	288	5	computational	computational	ADJ
ejpam-4928	288	6	science	science	NOUN
ejpam-4928	288	7	,	,	PUNCT
ejpam-4928	288	8	10(6):2320–2326	10(6):2320–2326	NUM
ejpam-4928	288	9	,	,	PUNCT
ejpam-4928	288	10	2020	2020	NUM
ejpam-4928	288	11	.	.	PUNCT
ejpam-4928	289	1	[	[	X
ejpam-4928	289	2	24	24	NUM
ejpam-4928	289	3	]	]	X
ejpam-4928	289	4	victor	victor	PROPN
ejpam-4928	289	5	namias	namias	PROPN
ejpam-4928	289	6	.	.	PUNCT
ejpam-4928	290	1	the	the	DET
ejpam-4928	290	2	fractional	fractional	ADJ
ejpam-4928	290	3	order	order	NOUN
ejpam-4928	290	4	fourier	fourier	NOUN
ejpam-4928	290	5	transform	transform	NOUN
ejpam-4928	290	6	and	and	CCONJ
ejpam-4928	290	7	its	its	PRON
ejpam-4928	290	8	application	application	NOUN
ejpam-4928	290	9	to	to	ADP
ejpam-4928	290	10	quantum	quantum	ADJ
ejpam-4928	290	11	mechanics	mechanic	NOUN
ejpam-4928	290	12	.	.	PUNCT
ejpam-4928	291	1	i	i	PRON
ejpam-4928	291	2	m	m	VERB
ejpam-4928	291	3	a	a	DET
ejpam-4928	291	4	journal	journal	NOUN
ejpam-4928	291	5	of	of	ADP
ejpam-4928	291	6	applied	apply	VERB
ejpam-4928	291	7	mathematics	mathematic	NOUN
ejpam-4928	291	8	,	,	PUNCT
ejpam-4928	291	9	25(3):241–265	25(3):241–265	NOUN
ejpam-4928	291	10	,	,	PUNCT
ejpam-4928	291	11	1980	1980	NUM
ejpam-4928	291	12	.	.	PUNCT
ejpam-4928	292	1	references	reference	NOUN
ejpam-4928	292	2	2144	2144	NUM
ejpam-4928	292	3	[	[	X
ejpam-4928	292	4	25	25	NUM
ejpam-4928	292	5	]	]	X
ejpam-4928	292	6	ayesha	ayesha	PROPN
ejpam-4928	292	7	sohail	sohail	PROPN
ejpam-4928	292	8	,	,	PUNCT
ejpam-4928	292	9	o	o	PROPN
ejpam-4928	292	10	anwar	anwar	PROPN
ejpam-4928	292	11	bég	bég	PROPN
ejpam-4928	292	12	,	,	PUNCT
ejpam-4928	292	13	zhiwu	zhiwu	PROPN
ejpam-4928	292	14	li	li	PROPN
ejpam-4928	292	15	,	,	PUNCT
ejpam-4928	292	16	and	and	CCONJ
ejpam-4928	292	17	sebahattin	sebahattin	NOUN
ejpam-4928	292	18	celik	celik	PROPN
ejpam-4928	292	19	.	.	PUNCT
ejpam-4928	293	1	physics	physics	PROPN
ejpam-4928	293	2	of	of	ADP
ejpam-4928	293	3	fractional	fractional	ADJ
ejpam-4928	293	4	imaging	imaging	NOUN
ejpam-4928	293	5	in	in	ADP
ejpam-4928	293	6	biomedicine	biomedicine	NOUN
ejpam-4928	293	7	.	.	PUNCT
ejpam-4928	294	1	progress	progress	NOUN
ejpam-4928	294	2	in	in	ADP
ejpam-4928	294	3	biophysics	biophysic	NOUN
ejpam-4928	294	4	and	and	CCONJ
ejpam-4928	294	5	molecular	molecular	ADJ
ejpam-4928	294	6	biology	biology	NOUN
ejpam-4928	294	7	,	,	PUNCT
ejpam-4928	294	8	140:13–20	140:13–20	NUM
ejpam-4928	294	9	,	,	PUNCT
ejpam-4928	294	10	2018	2018	NUM
ejpam-4928	294	11	.	.	PUNCT
ejpam-4928	295	1	[	[	X
ejpam-4928	295	2	26	26	NUM
ejpam-4928	295	3	]	]	PUNCT
ejpam-4928	295	4	anna	anna	PROPN
ejpam-4928	295	5	suzuki	suzuki	PROPN
ejpam-4928	295	6	,	,	PUNCT
ejpam-4928	295	7	sergei	sergei	PROPN
ejpam-4928	295	8	a	a	DET
ejpam-4928	295	9	fomin	fomin	NOUN
ejpam-4928	295	10	,	,	PUNCT
ejpam-4928	295	11	vladimir	vladimir	VERB
ejpam-4928	295	12	a	a	DET
ejpam-4928	295	13	chugunov	chugunov	NOUN
ejpam-4928	295	14	,	,	PUNCT
ejpam-4928	295	15	yuichi	yuichi	PROPN
ejpam-4928	295	16	niibori	niibori	PROPN
ejpam-4928	295	17	,	,	PUNCT
ejpam-4928	295	18	and	and	CCONJ
ejpam-4928	295	19	toshiyuki	toshiyuki	PROPN
ejpam-4928	295	20	hashida	hashida	PROPN
ejpam-4928	295	21	.	.	PUNCT
ejpam-4928	296	1	fractional	fractional	ADJ
ejpam-4928	296	2	diffusion	diffusion	NOUN
ejpam-4928	296	3	modeling	modeling	NOUN
ejpam-4928	296	4	of	of	ADP
ejpam-4928	296	5	heat	heat	NOUN
ejpam-4928	296	6	transfer	transfer	NOUN
ejpam-4928	296	7	in	in	ADP
ejpam-4928	296	8	porous	porous	ADJ
ejpam-4928	296	9	and	and	CCONJ
ejpam-4928	296	10	fractured	fractured	ADJ
ejpam-4928	296	11	media	medium	NOUN
ejpam-4928	296	12	.	.	PUNCT
ejpam-4928	297	1	international	international	ADJ
ejpam-4928	297	2	journal	journal	PROPN
ejpam-4928	297	3	of	of	ADP
ejpam-4928	297	4	heat	heat	NOUN
ejpam-4928	297	5	and	and	CCONJ
ejpam-4928	297	6	mass	mass	NOUN
ejpam-4928	297	7	transfer	transfer	NOUN
ejpam-4928	297	8	,	,	PUNCT
ejpam-4928	297	9	103:611–618	103:611–618	NUM
ejpam-4928	297	10	,	,	PUNCT
ejpam-4928	297	11	2016	2016	NUM
ejpam-4928	297	12	.	.	PUNCT