id	sid	tid	token	lemma	pos
ejpam-6378	1	1	european	european	PROPN
ejpam-6378	1	2	journal	journal	PROPN
ejpam-6378	1	3	of	of	ADP
ejpam-6378	1	4	pure	pure	ADJ
ejpam-6378	1	5	and	and	CCONJ
ejpam-6378	1	6	applied	applied	ADJ
ejpam-6378	1	7	mathematics	mathematic	NOUN
ejpam-6378	1	8	2025	2025	NUM
ejpam-6378	1	9	,	,	PUNCT
ejpam-6378	1	10	vol	vol	NOUN
ejpam-6378	1	11	.	.	PROPN
ejpam-6378	1	12	18	18	NUM
ejpam-6378	1	13	,	,	PUNCT
ejpam-6378	1	14	issue	issue	NOUN
ejpam-6378	1	15	4	4	NUM
ejpam-6378	1	16	,	,	PUNCT
ejpam-6378	1	17	article	article	NOUN
ejpam-6378	1	18	number	number	NOUN
ejpam-6378	1	19	6378	6378	NUM
ejpam-6378	1	20	issn	issn	VERB
ejpam-6378	1	21	1307	1307	NUM
ejpam-6378	1	22	-	-	SYM
ejpam-6378	1	23	5543	5543	NUM
ejpam-6378	1	24	–	–	PUNCT
ejpam-6378	1	25	ejpam.com	ejpam.com	X
ejpam-6378	1	26	published	publish	VERB
ejpam-6378	1	27	by	by	ADP
ejpam-6378	1	28	new	new	PROPN
ejpam-6378	1	29	york	york	PROPN
ejpam-6378	1	30	business	business	PROPN
ejpam-6378	1	31	global	global	ADJ
ejpam-6378	1	32	analytical	analytical	ADJ
ejpam-6378	1	33	investigation	investigation	NOUN
ejpam-6378	1	34	for	for	ADP
ejpam-6378	1	35	some	some	DET
ejpam-6378	1	36	problems	problem	NOUN
ejpam-6378	1	37	under	under	ADP
ejpam-6378	1	38	different	different	ADJ
ejpam-6378	1	39	fractional	fractional	ADJ
ejpam-6378	1	40	differential	differential	NOUN
ejpam-6378	1	41	and	and	CCONJ
ejpam-6378	1	42	integral	integral	ADJ
ejpam-6378	1	43	operators	operator	NOUN
ejpam-6378	1	44	muhammad	muhammad	PROPN
ejpam-6378	1	45	sohail1,2,∗	sohail1,2,∗	PROPN
ejpam-6378	1	46	,	,	PUNCT
ejpam-6378	1	47	eiman1	eiman1	PROPN
ejpam-6378	1	48	,	,	PUNCT
ejpam-6378	1	49	hassan	hassan	PROPN
ejpam-6378	1	50	khan2,3	khan2,3	PROPN
ejpam-6378	1	51	,	,	PUNCT
ejpam-6378	1	52	muhammad	muhammad	PROPN
ejpam-6378	1	53	sarwar1,4	sarwar1,4	PROPN
ejpam-6378	1	54	,	,	PUNCT
ejpam-6378	1	55	kamal	kamal	PROPN
ejpam-6378	1	56	shah1,4	shah1,4	PROPN
ejpam-6378	1	57	,	,	PUNCT
ejpam-6378	1	58	thabet	thabet	ADJ
ejpam-6378	1	59	abdeljawad4	abdeljawad4	NOUN
ejpam-6378	1	60	1	1	NUM
ejpam-6378	1	61	department	department	NOUN
ejpam-6378	1	62	of	of	ADP
ejpam-6378	1	63	mathematics	mathematic	NOUN
ejpam-6378	1	64	,	,	PUNCT
ejpam-6378	1	65	university	university	NOUN
ejpam-6378	1	66	of	of	ADP
ejpam-6378	1	67	malakand	malakand	PROPN
ejpam-6378	1	68	,	,	PUNCT
ejpam-6378	1	69	chakdara	chakdara	NOUN
ejpam-6378	1	70	dir	dir	NOUN
ejpam-6378	1	71	(	(	PUNCT
ejpam-6378	1	72	l	l	NOUN
ejpam-6378	1	73	)	)	PUNCT
ejpam-6378	1	74	18000	18000	NUM
ejpam-6378	1	75	,	,	PUNCT
ejpam-6378	1	76	kpk	kpk	PROPN
ejpam-6378	1	77	,	,	PUNCT
ejpam-6378	1	78	pakistan	pakistan	PROPN
ejpam-6378	1	79	2	2	NUM
ejpam-6378	1	80	department	department	NOUN
ejpam-6378	1	81	of	of	ADP
ejpam-6378	1	82	mathematics	mathematic	NOUN
ejpam-6378	1	83	,	,	PUNCT
ejpam-6378	1	84	abdul	abdul	PROPN
ejpam-6378	1	85	wali	wali	PROPN
ejpam-6378	1	86	khan	khan	PROPN
ejpam-6378	1	87	university	university	PROPN
ejpam-6378	1	88	mardan	mardan	PROPN
ejpam-6378	1	89	23200	23200	NUM
ejpam-6378	1	90	,	,	PUNCT
ejpam-6378	1	91	pakistan	pakistan	PROPN
ejpam-6378	1	92	3	3	NUM
ejpam-6378	1	93	department	department	NOUN
ejpam-6378	1	94	of	of	ADP
ejpam-6378	1	95	mathematics	mathematic	NOUN
ejpam-6378	1	96	,	,	PUNCT
ejpam-6378	1	97	near	near	ADP
ejpam-6378	1	98	east	east	PROPN
ejpam-6378	1	99	university	university	PROPN
ejpam-6378	1	100	trnc	trnc	NOUN
ejpam-6378	1	101	,	,	PUNCT
ejpam-6378	1	102	10	10	NUM
ejpam-6378	1	103	,	,	PUNCT
ejpam-6378	1	104	mersin	mersin	PROPN
ejpam-6378	1	105	,	,	PUNCT
ejpam-6378	1	106	turkey	turkey	PROPN
ejpam-6378	1	107	4	4	NUM
ejpam-6378	1	108	department	department	NOUN
ejpam-6378	1	109	of	of	ADP
ejpam-6378	1	110	mathematics	mathematic	NOUN
ejpam-6378	1	111	and	and	CCONJ
ejpam-6378	1	112	sciences	science	NOUN
ejpam-6378	1	113	,	,	PUNCT
ejpam-6378	1	114	prince	prince	PROPN
ejpam-6378	1	115	sultan	sultan	PROPN
ejpam-6378	1	116	university	university	PROPN
ejpam-6378	1	117	,	,	PUNCT
ejpam-6378	1	118	66833	66833	NUM
ejpam-6378	1	119	,	,	PUNCT
ejpam-6378	1	120	11586	11586	NUM
ejpam-6378	1	121	riyadh	riyadh	NOUN
ejpam-6378	1	122	,	,	PUNCT
ejpam-6378	1	123	saudi	saudi	PROPN
ejpam-6378	1	124	arabia	arabia	PROPN
ejpam-6378	1	125	abstract	abstract	NOUN
ejpam-6378	1	126	.	.	PUNCT
ejpam-6378	2	1	this	this	DET
ejpam-6378	2	2	article	article	NOUN
ejpam-6378	2	3	presents	present	VERB
ejpam-6378	2	4	the	the	DET
ejpam-6378	2	5	three	three	NUM
ejpam-6378	2	6	well	well	ADV
ejpam-6378	2	7	-	-	PUNCT
ejpam-6378	2	8	known	know	VERB
ejpam-6378	2	9	fractional	fractional	ADJ
ejpam-6378	2	10	order	order	NOUN
ejpam-6378	2	11	differential	differential	NOUN
ejpam-6378	2	12	operators	operator	NOUN
ejpam-6378	2	13	including	include	VERB
ejpam-6378	2	14	the	the	DET
ejpam-6378	2	15	caputo	caputo	PROPN
ejpam-6378	2	16	,	,	PUNCT
ejpam-6378	2	17	caputo	caputo	PROPN
ejpam-6378	2	18	-	-	PUNCT
ejpam-6378	2	19	fabrizio	fabrizio	PROPN
ejpam-6378	2	20	,	,	PUNCT
ejpam-6378	2	21	and	and	CCONJ
ejpam-6378	2	22	atangana	atangana	PROPN
ejpam-6378	2	23	-	-	PUNCT
ejpam-6378	2	24	baleanu	baleanu	PROPN
ejpam-6378	2	25	to	to	PART
ejpam-6378	2	26	describe	describe	VERB
ejpam-6378	2	27	the	the	DET
ejpam-6378	2	28	solutions	solution	NOUN
ejpam-6378	2	29	of	of	ADP
ejpam-6378	2	30	a	a	DET
ejpam-6378	2	31	class	class	NOUN
ejpam-6378	2	32	of	of	ADP
ejpam-6378	2	33	non	non	ADJ
ejpam-6378	2	34	-	-	ADJ
ejpam-6378	2	35	linear	linear	ADJ
ejpam-6378	2	36	fractional	fractional	ADJ
ejpam-6378	2	37	partial	partial	ADJ
ejpam-6378	2	38	differential	differential	NOUN
ejpam-6378	2	39	equation	equation	NOUN
ejpam-6378	2	40	(	(	PUNCT
ejpam-6378	2	41	fpde	fpde	NOUN
ejpam-6378	2	42	)	)	PUNCT
ejpam-6378	2	43	.	.	PUNCT
ejpam-6378	3	1	a	a	DET
ejpam-6378	3	2	method	method	NOUN
ejpam-6378	3	3	called	call	VERB
ejpam-6378	3	4	the	the	DET
ejpam-6378	3	5	adomian	adomian	NOUN
ejpam-6378	3	6	decomposition	decomposition	NOUN
ejpam-6378	3	7	method	method	NOUN
ejpam-6378	3	8	(	(	PUNCT
ejpam-6378	3	9	adm	adm	PROPN
ejpam-6378	3	10	)	)	PUNCT
ejpam-6378	3	11	is	be	AUX
ejpam-6378	3	12	used	use	VERB
ejpam-6378	3	13	to	to	PART
ejpam-6378	3	14	find	find	VERB
ejpam-6378	3	15	series	series	NOUN
ejpam-6378	3	16	solutions	solution	NOUN
ejpam-6378	3	17	in	in	ADP
ejpam-6378	3	18	a	a	DET
ejpam-6378	3	19	semi	semi	ADJ
ejpam-6378	3	20	-	-	ADJ
ejpam-6378	3	21	analytical	analytical	ADJ
ejpam-6378	3	22	way	way	NOUN
ejpam-6378	3	23	,	,	PUNCT
ejpam-6378	3	24	using	use	VERB
ejpam-6378	3	25	different	different	ADJ
ejpam-6378	3	26	transforms	transform	NOUN
ejpam-6378	3	27	like	like	ADP
ejpam-6378	3	28	laplace	laplace	NOUN
ejpam-6378	3	29	,	,	PUNCT
ejpam-6378	3	30	elzaki	elzaki	NOUN
ejpam-6378	3	31	,	,	PUNCT
ejpam-6378	3	32	sumudu	sumudu	NOUN
ejpam-6378	3	33	,	,	PUNCT
ejpam-6378	3	34	aboodh	aboodh	NOUN
ejpam-6378	3	35	,	,	PUNCT
ejpam-6378	3	36	mohand	mohand	NOUN
ejpam-6378	3	37	,	,	PUNCT
ejpam-6378	3	38	yang	yang	PROPN
ejpam-6378	3	39	,	,	PUNCT
ejpam-6378	3	40	natural	natural	ADJ
ejpam-6378	3	41	,	,	PUNCT
ejpam-6378	3	42	and	and	CCONJ
ejpam-6378	3	43	shehu	shehu	NOUN
ejpam-6378	3	44	.	.	PUNCT
ejpam-6378	4	1	the	the	DET
ejpam-6378	4	2	solutions	solution	NOUN
ejpam-6378	4	3	obtained	obtain	VERB
ejpam-6378	4	4	by	by	ADP
ejpam-6378	4	5	the	the	DET
ejpam-6378	4	6	proposed	propose	VERB
ejpam-6378	4	7	method	method	NOUN
ejpam-6378	4	8	have	have	VERB
ejpam-6378	4	9	precision	precision	NOUN
ejpam-6378	4	10	and	and	CCONJ
ejpam-6378	4	11	a	a	DET
ejpam-6378	4	12	high	high	ADJ
ejpam-6378	4	13	rate	rate	NOUN
ejpam-6378	4	14	of	of	ADP
ejpam-6378	4	15	convergence	convergence	NOUN
ejpam-6378	4	16	.	.	PUNCT
ejpam-6378	5	1	we	we	PRON
ejpam-6378	5	2	then	then	ADV
ejpam-6378	5	3	verify	verify	VERB
ejpam-6378	5	4	the	the	DET
ejpam-6378	5	5	derived	derive	VERB
ejpam-6378	5	6	solutions	solution	NOUN
ejpam-6378	5	7	numerically	numerically	ADV
ejpam-6378	5	8	and	and	CCONJ
ejpam-6378	5	9	graphically	graphically	ADV
ejpam-6378	5	10	for	for	ADP
ejpam-6378	5	11	both	both	CCONJ
ejpam-6378	5	12	fractional	fractional	ADJ
ejpam-6378	5	13	and	and	CCONJ
ejpam-6378	5	14	integer	integer	NOUN
ejpam-6378	5	15	orders	order	NOUN
ejpam-6378	5	16	.	.	PUNCT
ejpam-6378	6	1	furthermore	furthermore	ADV
ejpam-6378	6	2	,	,	PUNCT
ejpam-6378	6	3	the	the	DET
ejpam-6378	6	4	solutions	solution	NOUN
ejpam-6378	6	5	under	under	ADP
ejpam-6378	6	6	these	these	DET
ejpam-6378	6	7	transformations	transformation	NOUN
ejpam-6378	6	8	are	be	AUX
ejpam-6378	6	9	the	the	DET
ejpam-6378	6	10	same	same	ADJ
ejpam-6378	6	11	.	.	PUNCT
ejpam-6378	7	1	the	the	DET
ejpam-6378	7	2	proposed	propose	VERB
ejpam-6378	7	3	simulations	simulation	NOUN
ejpam-6378	7	4	show	show	VERB
ejpam-6378	7	5	that	that	SCONJ
ejpam-6378	7	6	as	as	ADP
ejpam-6378	7	7	the	the	DET
ejpam-6378	7	8	number	number	NOUN
ejpam-6378	7	9	of	of	ADP
ejpam-6378	7	10	iterations	iteration	NOUN
ejpam-6378	7	11	increases	increase	NOUN
ejpam-6378	7	12	,	,	PUNCT
ejpam-6378	7	13	the	the	DET
ejpam-6378	7	14	corresponding	corresponding	ADJ
ejpam-6378	7	15	absolute	absolute	ADJ
ejpam-6378	7	16	error	error	NOUN
ejpam-6378	7	17	reduces	reduce	VERB
ejpam-6378	7	18	.	.	PUNCT
ejpam-6378	8	1	moreover	moreover	ADV
ejpam-6378	8	2	,	,	PUNCT
ejpam-6378	8	3	fractional	fractional	ADJ
ejpam-6378	8	4	order	order	NOUN
ejpam-6378	8	5	solutions	solution	NOUN
ejpam-6378	8	6	are	be	AUX
ejpam-6378	8	7	converging	converge	VERB
ejpam-6378	8	8	to	to	ADP
ejpam-6378	8	9	integer	integer	NOUN
ejpam-6378	8	10	order	order	NOUN
ejpam-6378	8	11	solutions	solution	NOUN
ejpam-6378	8	12	.	.	PUNCT
ejpam-6378	9	1	2020	2020	NUM
ejpam-6378	9	2	mathematics	mathematic	NOUN
ejpam-6378	9	3	subject	subject	NOUN
ejpam-6378	9	4	classifications	classification	NOUN
ejpam-6378	9	5	:	:	PUNCT
ejpam-6378	9	6	26a33	26a33	NUM
ejpam-6378	9	7	,	,	PUNCT
ejpam-6378	9	8	34a08	34a08	DET
ejpam-6378	9	9	key	key	ADJ
ejpam-6378	9	10	words	word	NOUN
ejpam-6378	9	11	and	and	CCONJ
ejpam-6378	9	12	phrases	phrase	NOUN
ejpam-6378	9	13	:	:	PUNCT
ejpam-6378	9	14	adomian	adomian	NOUN
ejpam-6378	9	15	decomposition	decomposition	NOUN
ejpam-6378	9	16	method	method	NOUN
ejpam-6378	9	17	,	,	PUNCT
ejpam-6378	9	18	integral	integral	ADJ
ejpam-6378	9	19	transforms	transform	NOUN
ejpam-6378	9	20	,	,	PUNCT
ejpam-6378	9	21	caputo	caputo	PROPN
ejpam-6378	9	22	derivative	derivative	ADJ
ejpam-6378	9	23	operator	operator	NOUN
ejpam-6378	9	24	,	,	PUNCT
ejpam-6378	9	25	caputo	caputo	PROPN
ejpam-6378	9	26	-	-	PUNCT
ejpam-6378	9	27	fabrizio	fabrizio	PROPN
ejpam-6378	9	28	derivative	derivative	ADJ
ejpam-6378	9	29	operator	operator	NOUN
ejpam-6378	9	30	,	,	PUNCT
ejpam-6378	9	31	atangana	atangana	PROPN
ejpam-6378	9	32	-	-	PUNCT
ejpam-6378	9	33	baleanu	baleanu	ADJ
ejpam-6378	9	34	derivative	derivative	ADJ
ejpam-6378	9	35	operator	operator	NOUN
ejpam-6378	9	36	1	1	NUM
ejpam-6378	9	37	.	.	PUNCT
ejpam-6378	10	1	introduction	introduction	NOUN
ejpam-6378	10	2	in	in	ADP
ejpam-6378	10	3	the	the	DET
ejpam-6378	10	4	past	past	ADJ
ejpam-6378	10	5	few	few	ADJ
ejpam-6378	10	6	decades	decade	NOUN
ejpam-6378	10	7	,	,	PUNCT
ejpam-6378	10	8	mathematicians	mathematician	NOUN
ejpam-6378	10	9	have	have	AUX
ejpam-6378	10	10	established	establish	VERB
ejpam-6378	10	11	many	many	ADJ
ejpam-6378	10	12	mathematical	mathematical	ADJ
ejpam-6378	10	13	models	model	NOUN
ejpam-6378	10	14	utilizing	utilize	VERB
ejpam-6378	10	15	the	the	DET
ejpam-6378	10	16	idea	idea	NOUN
ejpam-6378	10	17	of	of	ADP
ejpam-6378	10	18	fractional	fractional	ADJ
ejpam-6378	10	19	order	order	NOUN
ejpam-6378	10	20	derivatives	derivative	NOUN
ejpam-6378	10	21	.	.	PUNCT
ejpam-6378	11	1	these	these	DET
ejpam-6378	11	2	fractional	fractional	ADJ
ejpam-6378	11	3	-	-	PUNCT
ejpam-6378	11	4	order	order	NOUN
ejpam-6378	11	5	mathematical	mathematical	ADJ
ejpam-6378	11	6	models	model	NOUN
ejpam-6378	11	7	provided	provide	VERB
ejpam-6378	11	8	an	an	DET
ejpam-6378	11	9	extremely	extremely	ADV
ejpam-6378	11	10	accurate	accurate	ADJ
ejpam-6378	11	11	match	match	NOUN
ejpam-6378	11	12	to	to	ADP
ejpam-6378	11	13	the	the	DET
ejpam-6378	11	14	data	datum	NOUN
ejpam-6378	11	15	from	from	ADP
ejpam-6378	11	16	experiments	experiment	NOUN
ejpam-6378	11	17	of	of	ADP
ejpam-6378	11	18	the	the	DET
ejpam-6378	11	19	associated	associate	VERB
ejpam-6378	11	20	problems	problem	NOUN
ejpam-6378	11	21	as	as	SCONJ
ejpam-6378	11	22	opposed	oppose	VERB
ejpam-6378	11	23	to	to	ADP
ejpam-6378	11	24	traditional	traditional	ADJ
ejpam-6378	11	25	models	model	NOUN
ejpam-6378	11	26	.	.	PUNCT
ejpam-6378	12	1	the	the	DET
ejpam-6378	12	2	scientists	scientist	NOUN
ejpam-6378	12	3	and	and	CCONJ
ejpam-6378	12	4	scholars	scholar	NOUN
ejpam-6378	12	5	have	have	AUX
ejpam-6378	12	6	initiated	initiate	VERB
ejpam-6378	12	7	unique	unique	ADJ
ejpam-6378	12	8	mathematical	mathematical	ADJ
ejpam-6378	12	9	models	model	NOUN
ejpam-6378	12	10	employing	employ	VERB
ejpam-6378	12	11	fractional	fractional	ADJ
ejpam-6378	12	12	differential	differential	ADJ
ejpam-6378	12	13	/	/	SYM
ejpam-6378	12	14	integral	integral	ADJ
ejpam-6378	12	15	equations	equation	NOUN
ejpam-6378	12	16	.	.	PUNCT
ejpam-6378	13	1	due	due	ADP
ejpam-6378	13	2	to	to	ADP
ejpam-6378	13	3	∗corresponding	∗corresponde	VERB
ejpam-6378	13	4	author	author	NOUN
ejpam-6378	13	5	.	.	PUNCT
ejpam-6378	14	1	doi	doi	NOUN
ejpam-6378	14	2	:	:	PUNCT
ejpam-6378	14	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6378	https://doi.org/10.29020/nybg.ejpam.v18i4.6378	PRON
ejpam-6378	14	4	email	email	NOUN
ejpam-6378	14	5	addresses	address	NOUN
ejpam-6378	14	6	:	:	PUNCT
ejpam-6378	14	7	muhammad.sohail@awkum.edu.pk	muhammad.sohail@awkum.edu.pk	PROPN
ejpam-6378	14	8	(	(	PUNCT
ejpam-6378	14	9	m.	m.	NOUN
ejpam-6378	14	10	sohail	sohail	PROPN
ejpam-6378	14	11	,	,	PUNCT
ejpam-6378	14	12	eiman	eiman	NOUN
ejpam-6378	14	13	)	)	PUNCT
ejpam-6378	14	14	,	,	PUNCT
ejpam-6378	14	15	hassanmath@awkum.edu.pk	hassanmath@awkum.edu.pk	NOUN
ejpam-6378	14	16	(	(	PUNCT
ejpam-6378	14	17	h.	h.	PROPN
ejpam-6378	14	18	khan	khan	PROPN
ejpam-6378	14	19	)	)	PUNCT
ejpam-6378	14	20	,	,	PUNCT
ejpam-6378	14	21	ehuzaifa@gmail.com	ehuzaifa@gmail.com	X
ejpam-6378	14	22	(	(	PUNCT
ejpam-6378	14	23	eiman	eiman	NOUN
ejpam-6378	14	24	)	)	PUNCT
ejpam-6378	14	25	,	,	PUNCT
ejpam-6378	14	26	sarwarswati@gmail.com	sarwarswati@gmail.com	X
ejpam-6378	14	27	(	(	PUNCT
ejpam-6378	14	28	m.	m.	NOUN
ejpam-6378	14	29	sarwar	sarwar	PROPN
ejpam-6378	14	30	)	)	PUNCT
ejpam-6378	14	31	,	,	PUNCT
ejpam-6378	14	32	kshah@psu.edu.sa	kshah@psu.edu.sa	PROPN
ejpam-6378	14	33	(	(	PUNCT
ejpam-6378	14	34	k.	k.	NOUN
ejpam-6378	14	35	shah	shah	PROPN
ejpam-6378	14	36	)	)	PUNCT
ejpam-6378	14	37	,	,	PUNCT
ejpam-6378	14	38	tabdeljawad@psu.edu.sa	tabdeljawad@psu.edu.sa	PROPN
ejpam-6378	14	39	(	(	PUNCT
ejpam-6378	14	40	t.	t.	NOUN
ejpam-6378	14	41	abdeljawad	abdeljawad	PROPN
ejpam-6378	14	42	)	)	PUNCT
ejpam-6378	14	43	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6378	14	44	1	1	NUM
ejpam-6378	14	45	copyright	copyright	NOUN
ejpam-6378	14	46	:	:	PUNCT
ejpam-6378	15	1	©	©	PROPN
ejpam-6378	15	2	2025	2025	NUM
ejpam-6378	15	3	the	the	DET
ejpam-6378	15	4	author(s	author(s	NOUN
ejpam-6378	15	5	)	)	PUNCT
ejpam-6378	15	6	.	.	PUNCT
ejpam-6378	16	1	(	(	PUNCT
ejpam-6378	16	2	cc	cc	NOUN
ejpam-6378	16	3	by	by	ADP
ejpam-6378	16	4	-	-	PUNCT
ejpam-6378	16	5	nc	nc	PROPN
ejpam-6378	16	6	4.0	4.0	NUM
ejpam-6378	16	7	)	)	PUNCT
ejpam-6378	16	8	m.	m.	NOUN
ejpam-6378	16	9	sohail	sohail	PROPN
ejpam-6378	16	10	et	et	PROPN
ejpam-6378	16	11	al	al	PROPN
ejpam-6378	16	12	.	.	PUNCT
ejpam-6378	16	13	/	/	SYM
ejpam-6378	16	14	eur	eur	PROPN
ejpam-6378	16	15	.	.	PUNCT
ejpam-6378	17	1	j.	j.	PROPN
ejpam-6378	17	2	pure	pure	PROPN
ejpam-6378	17	3	appl	appl	PROPN
ejpam-6378	17	4	.	.	PROPN
ejpam-6378	17	5	math	math	PROPN
ejpam-6378	17	6	,	,	PUNCT
ejpam-6378	17	7	18	18	NUM
ejpam-6378	17	8	(	(	PUNCT
ejpam-6378	17	9	4	4	NUM
ejpam-6378	17	10	)	)	PUNCT
ejpam-6378	17	11	(	(	PUNCT
ejpam-6378	17	12	2025	2025	NUM
ejpam-6378	17	13	)	)	PUNCT
ejpam-6378	17	14	,	,	PUNCT
ejpam-6378	17	15	6378	6378	NUM
ejpam-6378	17	16	2	2	NUM
ejpam-6378	17	17	of	of	ADP
ejpam-6378	17	18	20	20	NUM
ejpam-6378	17	19	the	the	DET
ejpam-6378	17	20	numerous	numerous	ADJ
ejpam-6378	17	21	uses	use	NOUN
ejpam-6378	17	22	of	of	ADP
ejpam-6378	17	23	fractional	fractional	ADJ
ejpam-6378	17	24	differential	differential	ADJ
ejpam-6378	17	25	equations	equation	NOUN
ejpam-6378	17	26	(	(	PUNCT
ejpam-6378	17	27	fdes	fde	NOUN
ejpam-6378	17	28	)	)	PUNCT
ejpam-6378	17	29	in	in	ADP
ejpam-6378	17	30	the	the	DET
ejpam-6378	17	31	fields	field	NOUN
ejpam-6378	17	32	of	of	ADP
ejpam-6378	17	33	science	science	NOUN
ejpam-6378	17	34	and	and	CCONJ
ejpam-6378	17	35	engineering	engineering	NOUN
ejpam-6378	17	36	,	,	PUNCT
ejpam-6378	17	37	mathematicians	mathematician	NOUN
ejpam-6378	17	38	are	be	AUX
ejpam-6378	17	39	increasingly	increasingly	ADV
ejpam-6378	17	40	focusing	focus	VERB
ejpam-6378	17	41	on	on	ADP
ejpam-6378	17	42	this	this	DET
ejpam-6378	17	43	area	area	NOUN
ejpam-6378	17	44	of	of	ADP
ejpam-6378	17	45	study	study	NOUN
ejpam-6378	17	46	.	.	PUNCT
ejpam-6378	18	1	fractional	fractional	ADJ
ejpam-6378	18	2	calculus	calculus	NOUN
ejpam-6378	18	3	is	be	AUX
ejpam-6378	18	4	widely	widely	ADV
ejpam-6378	18	5	used	use	VERB
ejpam-6378	18	6	in	in	ADP
ejpam-6378	18	7	mathematical	mathematical	ADJ
ejpam-6378	18	8	biology	biology	NOUN
ejpam-6378	18	9	[	[	X
ejpam-6378	18	10	1	1	NUM
ejpam-6378	18	11	,	,	PUNCT
ejpam-6378	18	12	2	2	NUM
ejpam-6378	18	13	]	]	PUNCT
ejpam-6378	18	14	,	,	PUNCT
ejpam-6378	18	15	quantum	quantum	ADJ
ejpam-6378	18	16	field	field	NOUN
ejpam-6378	18	17	theory	theory	NOUN
ejpam-6378	18	18	[	[	X
ejpam-6378	18	19	3	3	NUM
ejpam-6378	18	20	]	]	PUNCT
ejpam-6378	18	21	,	,	PUNCT
ejpam-6378	18	22	fluid	fluid	ADJ
ejpam-6378	18	23	mechanics	mechanic	NOUN
ejpam-6378	18	24	[	[	X
ejpam-6378	18	25	4	4	NUM
ejpam-6378	18	26	]	]	PUNCT
ejpam-6378	18	27	,	,	PUNCT
ejpam-6378	18	28	and	and	CCONJ
ejpam-6378	18	29	plasma	plasma	NOUN
ejpam-6378	18	30	physics	physics	NOUN
ejpam-6378	19	1	[	[	X
ejpam-6378	19	2	5	5	NUM
ejpam-6378	19	3	]	]	PUNCT
ejpam-6378	19	4	.	.	PUNCT
ejpam-6378	20	1	in	in	ADP
ejpam-6378	20	2	control	control	PROPN
ejpam-6378	20	3	engineering	engineering	NOUN
ejpam-6378	20	4	,	,	PUNCT
ejpam-6378	20	5	it	it	PRON
ejpam-6378	20	6	is	be	AUX
ejpam-6378	20	7	essential	essential	ADJ
ejpam-6378	20	8	for	for	ADP
ejpam-6378	20	9	fractional	fractional	ADJ
ejpam-6378	20	10	order	order	NOUN
ejpam-6378	20	11	systems	system	NOUN
ejpam-6378	20	12	[	[	X
ejpam-6378	20	13	6	6	NUM
ejpam-6378	20	14	]	]	PUNCT
ejpam-6378	20	15	and	and	CCONJ
ejpam-6378	20	16	pid	pid	NOUN
ejpam-6378	20	17	controllers	controller	NOUN
ejpam-6378	20	18	[	[	X
ejpam-6378	20	19	7	7	NUM
ejpam-6378	20	20	]	]	PUNCT
ejpam-6378	20	21	.	.	PUNCT
ejpam-6378	21	1	applications	application	NOUN
ejpam-6378	21	2	also	also	ADV
ejpam-6378	21	3	encompass	encompass	VERB
ejpam-6378	21	4	neural	neural	ADJ
ejpam-6378	21	5	networks	network	NOUN
ejpam-6378	21	6	[	[	X
ejpam-6378	21	7	8	8	NUM
ejpam-6378	21	8	]	]	PUNCT
ejpam-6378	21	9	,	,	PUNCT
ejpam-6378	21	10	optical	optical	ADJ
ejpam-6378	21	11	communications	communication	NOUN
ejpam-6378	21	12	[	[	X
ejpam-6378	21	13	9	9	NUM
ejpam-6378	21	14	]	]	PUNCT
ejpam-6378	21	15	,	,	PUNCT
ejpam-6378	21	16	and	and	CCONJ
ejpam-6378	21	17	electrochemical	electrochemical	ADJ
ejpam-6378	21	18	processes	process	NOUN
ejpam-6378	21	19	[	[	X
ejpam-6378	21	20	10	10	NUM
ejpam-6378	21	21	]	]	PUNCT
ejpam-6378	21	22	.	.	PUNCT
ejpam-6378	22	1	moreover	moreover	ADV
ejpam-6378	22	2	,	,	PUNCT
ejpam-6378	22	3	fractional	fractional	ADJ
ejpam-6378	22	4	calculus	calculus	NOUN
ejpam-6378	22	5	is	be	AUX
ejpam-6378	22	6	employed	employ	VERB
ejpam-6378	22	7	in	in	ADP
ejpam-6378	22	8	the	the	DET
ejpam-6378	22	9	modeling	modeling	NOUN
ejpam-6378	22	10	of	of	ADP
ejpam-6378	22	11	time	time	NOUN
ejpam-6378	22	12	-	-	PUNCT
ejpam-6378	22	13	space	space	NOUN
ejpam-6378	22	14	fractional	fractional	ADJ
ejpam-6378	22	15	diffusion	diffusion	NOUN
ejpam-6378	22	16	equations	equation	NOUN
ejpam-6378	23	1	[	[	X
ejpam-6378	23	2	11	11	NUM
ejpam-6378	23	3	]	]	PUNCT
ejpam-6378	23	4	,	,	PUNCT
ejpam-6378	23	5	groundwater	groundwater	NOUN
ejpam-6378	23	6	contamination	contamination	NOUN
ejpam-6378	23	7	[	[	X
ejpam-6378	23	8	12	12	NUM
ejpam-6378	23	9	]	]	PUNCT
ejpam-6378	23	10	,	,	PUNCT
ejpam-6378	23	11	heat	heat	NOUN
ejpam-6378	23	12	conduction	conduction	NOUN
ejpam-6378	23	13	in	in	ADP
ejpam-6378	23	14	materials	material	NOUN
ejpam-6378	23	15	[	[	X
ejpam-6378	23	16	13	13	NUM
ejpam-6378	23	17	]	]	PUNCT
ejpam-6378	23	18	,	,	PUNCT
ejpam-6378	23	19	and	and	CCONJ
ejpam-6378	23	20	acoustic	acoustic	ADJ
ejpam-6378	23	21	wave	wave	NOUN
ejpam-6378	23	22	propagation	propagation	NOUN
ejpam-6378	23	23	[	[	X
ejpam-6378	23	24	14	14	NUM
ejpam-6378	23	25	]	]	PUNCT
ejpam-6378	23	26	.	.	PUNCT
ejpam-6378	24	1	emerging	emerge	VERB
ejpam-6378	24	2	applications	application	NOUN
ejpam-6378	24	3	encompass	encompass	VERB
ejpam-6378	24	4	fractional	fractional	ADJ
ejpam-6378	24	5	dynamical	dynamical	ADJ
ejpam-6378	24	6	systems	system	NOUN
ejpam-6378	24	7	in	in	ADP
ejpam-6378	24	8	economics	economic	NOUN
ejpam-6378	24	9	[	[	X
ejpam-6378	24	10	15	15	NUM
ejpam-6378	24	11	]	]	PUNCT
ejpam-6378	24	12	,	,	PUNCT
ejpam-6378	24	13	fractional	fractional	ADJ
ejpam-6378	24	14	modeling	modeling	NOUN
ejpam-6378	24	15	in	in	ADP
ejpam-6378	24	16	image	image	NOUN
ejpam-6378	24	17	processing	processing	NOUN
ejpam-6378	24	18	[	[	X
ejpam-6378	24	19	16	16	NUM
ejpam-6378	24	20	]	]	PUNCT
ejpam-6378	24	21	,	,	PUNCT
ejpam-6378	24	22	and	and	CCONJ
ejpam-6378	24	23	machine	machine	NOUN
ejpam-6378	24	24	learning	learn	VERB
ejpam-6378	24	25	algorithms	algorithm	NOUN
ejpam-6378	24	26	[	[	X
ejpam-6378	24	27	17	17	NUM
ejpam-6378	24	28	]	]	PUNCT
ejpam-6378	24	29	.	.	PUNCT
ejpam-6378	25	1	nonlinear	nonlinear	ADJ
ejpam-6378	25	2	partial	partial	ADJ
ejpam-6378	25	3	differential	differential	NOUN
ejpam-6378	25	4	equations	equation	NOUN
ejpam-6378	25	5	(	(	PUNCT
ejpam-6378	25	6	pdes	pde	NOUN
ejpam-6378	25	7	)	)	PUNCT
ejpam-6378	25	8	can	can	AUX
ejpam-6378	25	9	be	be	AUX
ejpam-6378	25	10	tricky	tricky	ADJ
ejpam-6378	25	11	to	to	PART
ejpam-6378	25	12	solve	solve	VERB
ejpam-6378	25	13	precisely	precisely	ADV
ejpam-6378	25	14	.	.	PUNCT
ejpam-6378	26	1	consequently	consequently	ADV
ejpam-6378	26	2	,	,	PUNCT
ejpam-6378	26	3	in	in	ADP
ejpam-6378	26	4	recent	recent	ADJ
ejpam-6378	26	5	decades	decade	NOUN
ejpam-6378	26	6	,	,	PUNCT
ejpam-6378	26	7	mathematicians	mathematician	NOUN
ejpam-6378	26	8	and	and	CCONJ
ejpam-6378	26	9	scholars	scholar	NOUN
ejpam-6378	26	10	have	have	AUX
ejpam-6378	26	11	investigated	investigate	VERB
ejpam-6378	26	12	and	and	CCONJ
ejpam-6378	26	13	introduced	introduce	VERB
ejpam-6378	26	14	several	several	ADJ
ejpam-6378	26	15	numerical	numerical	ADJ
ejpam-6378	26	16	methods	method	NOUN
ejpam-6378	26	17	and	and	CCONJ
ejpam-6378	26	18	methodologies	methodology	NOUN
ejpam-6378	26	19	for	for	ADP
ejpam-6378	26	20	addressing	address	VERB
ejpam-6378	26	21	nonlinear	nonlinear	ADJ
ejpam-6378	26	22	pdes	pde	NOUN
ejpam-6378	26	23	.	.	PUNCT
ejpam-6378	27	1	given	give	VERB
ejpam-6378	27	2	the	the	DET
ejpam-6378	27	3	absence	absence	NOUN
ejpam-6378	27	4	of	of	ADP
ejpam-6378	27	5	universal	universal	ADJ
ejpam-6378	27	6	methods	method	NOUN
ejpam-6378	27	7	applicable	applicable	ADJ
ejpam-6378	27	8	to	to	ADP
ejpam-6378	27	9	all	all	DET
ejpam-6378	27	10	equation	equation	NOUN
ejpam-6378	27	11	types	type	NOUN
ejpam-6378	27	12	and	and	CCONJ
ejpam-6378	27	13	the	the	DET
ejpam-6378	27	14	necessity	necessity	NOUN
ejpam-6378	27	15	to	to	PART
ejpam-6378	27	16	treat	treat	VERB
ejpam-6378	27	17	each	each	DET
ejpam-6378	27	18	equation	equation	NOUN
ejpam-6378	27	19	as	as	ADP
ejpam-6378	27	20	an	an	DET
ejpam-6378	27	21	individual	individual	ADJ
ejpam-6378	27	22	problem	problem	NOUN
ejpam-6378	27	23	,	,	PUNCT
ejpam-6378	27	24	solving	solve	VERB
ejpam-6378	27	25	nonlinear	nonlinear	ADJ
ejpam-6378	27	26	pdes	pde	NOUN
ejpam-6378	27	27	presents	present	VERB
ejpam-6378	27	28	significant	significant	ADJ
ejpam-6378	27	29	challenges	challenge	NOUN
ejpam-6378	27	30	.	.	PUNCT
ejpam-6378	28	1	we	we	PRON
ejpam-6378	28	2	can	can	AUX
ejpam-6378	28	3	assess	assess	VERB
ejpam-6378	28	4	and	and	CCONJ
ejpam-6378	28	5	understand	understand	VERB
ejpam-6378	28	6	the	the	DET
ejpam-6378	28	7	numerical	numerical	ADJ
ejpam-6378	28	8	methods	method	NOUN
ejpam-6378	28	9	and	and	CCONJ
ejpam-6378	28	10	the	the	DET
ejpam-6378	28	11	physical	physical	ADJ
ejpam-6378	28	12	phenomena	phenomenon	NOUN
ejpam-6378	28	13	clarified	clarify	VERB
ejpam-6378	28	14	through	through	ADP
ejpam-6378	28	15	analytical	analytical	ADJ
ejpam-6378	28	16	solutions	solution	NOUN
ejpam-6378	28	17	to	to	ADP
ejpam-6378	28	18	fpdes	fpde	NOUN
ejpam-6378	28	19	.	.	PUNCT
ejpam-6378	29	1	numerical	numerical	ADJ
ejpam-6378	29	2	and	and	CCONJ
ejpam-6378	29	3	novel	novel	ADJ
ejpam-6378	29	4	analytical	analytical	ADJ
ejpam-6378	29	5	methodologies	methodology	NOUN
ejpam-6378	29	6	that	that	PRON
ejpam-6378	29	7	exist	exist	VERB
ejpam-6378	29	8	for	for	ADP
ejpam-6378	29	9	solving	solve	VERB
ejpam-6378	29	10	fpdes	fpde	NOUN
ejpam-6378	29	11	are	be	AUX
ejpam-6378	29	12	numerical	numerical	ADJ
ejpam-6378	29	13	methods	method	NOUN
ejpam-6378	29	14	include	include	VERB
ejpam-6378	29	15	the	the	DET
ejpam-6378	29	16	grünwaldletnikov	grünwaldletnikov	PROPN
ejpam-6378	29	17	method	method	NOUN
ejpam-6378	29	18	[	[	X
ejpam-6378	29	19	18	18	NUM
ejpam-6378	29	20	]	]	PUNCT
ejpam-6378	29	21	,	,	PUNCT
ejpam-6378	29	22	finite	finite	ADJ
ejpam-6378	29	23	difference	difference	NOUN
ejpam-6378	29	24	methods	method	NOUN
ejpam-6378	29	25	[	[	X
ejpam-6378	29	26	19	19	NUM
ejpam-6378	29	27	]	]	PUNCT
ejpam-6378	29	28	,	,	PUNCT
ejpam-6378	29	29	fractional	fractional	PROPN
ejpam-6378	29	30	adams	adams	PROPN
ejpam-6378	29	31	-	-	PUNCT
ejpam-6378	29	32	bashforth	bashforth	NOUN
ejpam-6378	29	33	and	and	CCONJ
ejpam-6378	29	34	adams	adams	PROPN
ejpam-6378	29	35	-	-	PUNCT
ejpam-6378	29	36	moulton	moulton	PROPN
ejpam-6378	29	37	methods	method	NOUN
ejpam-6378	29	38	[	[	X
ejpam-6378	29	39	20	20	NUM
ejpam-6378	29	40	]	]	PUNCT
ejpam-6378	29	41	,	,	PUNCT
ejpam-6378	29	42	spectral	spectral	ADJ
ejpam-6378	29	43	methods	method	NOUN
ejpam-6378	29	44	[	[	X
ejpam-6378	29	45	21	21	NUM
ejpam-6378	29	46	]	]	PUNCT
ejpam-6378	29	47	,	,	PUNCT
ejpam-6378	29	48	fractional	fractional	ADJ
ejpam-6378	29	49	order	order	NOUN
ejpam-6378	29	50	runge	runge	NOUN
ejpam-6378	29	51	-	-	PUNCT
ejpam-6378	29	52	kutta	kutta	NOUN
ejpam-6378	29	53	methods	method	NOUN
ejpam-6378	29	54	[	[	X
ejpam-6378	29	55	22	22	NUM
ejpam-6378	29	56	]	]	PUNCT
ejpam-6378	29	57	,	,	PUNCT
ejpam-6378	29	58	wavelet	wavelet	NOUN
ejpam-6378	29	59	methods	method	NOUN
ejpam-6378	29	60	[	[	X
ejpam-6378	29	61	23	23	NUM
ejpam-6378	29	62	]	]	PUNCT
ejpam-6378	29	63	,	,	PUNCT
ejpam-6378	29	64	and	and	CCONJ
ejpam-6378	29	65	fractional	fractional	ADJ
ejpam-6378	29	66	discrete	discrete	ADJ
ejpam-6378	29	67	fourier	fourier	NOUN
ejpam-6378	29	68	transform	transform	NOUN
ejpam-6378	29	69	[	[	X
ejpam-6378	29	70	24	24	NUM
ejpam-6378	29	71	]	]	PUNCT
ejpam-6378	29	72	.	.	PUNCT
ejpam-6378	30	1	analytical	analytical	ADJ
ejpam-6378	30	2	methods	method	NOUN
ejpam-6378	30	3	include	include	VERB
ejpam-6378	30	4	the	the	DET
ejpam-6378	30	5	laplace	laplace	NOUN
ejpam-6378	30	6	transform	transform	NOUN
ejpam-6378	30	7	[	[	X
ejpam-6378	30	8	25	25	NUM
ejpam-6378	30	9	]	]	PUNCT
ejpam-6378	30	10	,	,	PUNCT
ejpam-6378	30	11	series	series	NOUN
ejpam-6378	30	12	solutions	solution	NOUN
ejpam-6378	30	13	[	[	X
ejpam-6378	30	14	26	26	NUM
ejpam-6378	30	15	]	]	PUNCT
ejpam-6378	30	16	,	,	PUNCT
ejpam-6378	30	17	fourier	fourier	PROPN
ejpam-6378	30	18	series	series	NOUN
ejpam-6378	30	19	technique	technique	NOUN
ejpam-6378	30	20	[	[	X
ejpam-6378	30	21	27	27	NUM
ejpam-6378	30	22	]	]	PUNCT
ejpam-6378	30	23	,	,	PUNCT
ejpam-6378	30	24	the	the	DET
ejpam-6378	30	25	homotopy	homotopy	NOUN
ejpam-6378	30	26	perturbation	perturbation	NOUN
ejpam-6378	30	27	method	method	NOUN
ejpam-6378	30	28	[	[	X
ejpam-6378	30	29	28	28	NUM
ejpam-6378	30	30	]	]	PUNCT
ejpam-6378	30	31	,	,	PUNCT
ejpam-6378	30	32	variational	variational	ADJ
ejpam-6378	30	33	methods	method	NOUN
ejpam-6378	30	34	[	[	X
ejpam-6378	30	35	29	29	NUM
ejpam-6378	30	36	]	]	PUNCT
ejpam-6378	30	37	,	,	PUNCT
ejpam-6378	30	38	and	and	CCONJ
ejpam-6378	30	39	the	the	DET
ejpam-6378	30	40	method	method	NOUN
ejpam-6378	30	41	of	of	ADP
ejpam-6378	30	42	successive	successive	ADJ
ejpam-6378	30	43	approximations	approximation	NOUN
ejpam-6378	30	44	[	[	X
ejpam-6378	30	45	30	30	NUM
ejpam-6378	30	46	]	]	PUNCT
ejpam-6378	30	47	.	.	PUNCT
ejpam-6378	31	1	besides	besides	SCONJ
ejpam-6378	31	2	these	these	PRON
ejpam-6378	31	3	,	,	PUNCT
ejpam-6378	31	4	other	other	ADJ
ejpam-6378	31	5	methods	method	NOUN
ejpam-6378	31	6	are	be	AUX
ejpam-6378	31	7	[	[	X
ejpam-6378	31	8	31–35	31–35	NUM
ejpam-6378	31	9	]	]	X
ejpam-6378	31	10	.	.	PUNCT
ejpam-6378	32	1	the	the	DET
ejpam-6378	32	2	primary	primary	ADJ
ejpam-6378	32	3	objective	objective	NOUN
ejpam-6378	32	4	is	be	AUX
ejpam-6378	32	5	to	to	PART
ejpam-6378	32	6	illustrate	illustrate	VERB
ejpam-6378	32	7	the	the	DET
ejpam-6378	32	8	solutions	solution	NOUN
ejpam-6378	32	9	of	of	ADP
ejpam-6378	32	10	non	non	ADJ
ejpam-6378	32	11	-	-	ADJ
ejpam-6378	32	12	linear	linear	ADJ
ejpam-6378	32	13	fpdes	fpde	NOUN
ejpam-6378	32	14	with	with	ADP
ejpam-6378	32	15	initial	initial	ADJ
ejpam-6378	32	16	conditions	condition	NOUN
ejpam-6378	32	17	(	(	PUNCT
ejpam-6378	32	18	ics	ics	NOUN
ejpam-6378	32	19	)	)	PUNCT
ejpam-6378	32	20	by	by	ADP
ejpam-6378	32	21	employing	employ	VERB
ejpam-6378	32	22	the	the	DET
ejpam-6378	32	23	caputo	caputo	PROPN
ejpam-6378	32	24	fractional	fractional	PROPN
ejpam-6378	32	25	derivative	derivative	PROPN
ejpam-6378	32	26	(	(	PUNCT
ejpam-6378	32	27	cfd	cfd	NOUN
ejpam-6378	32	28	)	)	PUNCT
ejpam-6378	32	29	operator	operator	NOUN
ejpam-6378	32	30	,	,	PUNCT
ejpam-6378	32	31	the	the	DET
ejpam-6378	32	32	caputo	caputo	PROPN
ejpam-6378	32	33	-	-	PUNCT
ejpam-6378	32	34	fabrizio	fabrizio	PROPN
ejpam-6378	32	35	fractional	fractional	NOUN
ejpam-6378	32	36	(	(	PUNCT
ejpam-6378	32	37	cffd	cffd	NOUN
ejpam-6378	32	38	)	)	PUNCT
ejpam-6378	32	39	operator	operator	NOUN
ejpam-6378	32	40	,	,	PUNCT
ejpam-6378	32	41	and	and	CCONJ
ejpam-6378	32	42	the	the	DET
ejpam-6378	32	43	atangana	atangana	PROPN
ejpam-6378	32	44	-	-	PUNCT
ejpam-6378	32	45	baleanu	baleanu	ADJ
ejpam-6378	32	46	fractional	fractional	ADJ
ejpam-6378	32	47	(	(	PUNCT
ejpam-6378	32	48	abfd	abfd	PROPN
ejpam-6378	32	49	)	)	PUNCT
ejpam-6378	32	50	operator	operator	NOUN
ejpam-6378	32	51	in	in	ADP
ejpam-6378	32	52	a	a	DET
ejpam-6378	32	53	mathematical	mathematical	ADJ
ejpam-6378	32	54	model	model	NOUN
ejpam-6378	32	55	.	.	PUNCT
ejpam-6378	33	1	fractional	fractional	ADJ
ejpam-6378	33	2	derivatives	derivative	NOUN
ejpam-6378	33	3	of	of	ADP
ejpam-6378	33	4	the	the	DET
ejpam-6378	33	5	proposed	propose	VERB
ejpam-6378	33	6	operators	operator	NOUN
ejpam-6378	33	7	will	will	AUX
ejpam-6378	33	8	be	be	AUX
ejpam-6378	33	9	utilized	utilize	VERB
ejpam-6378	33	10	to	to	PART
ejpam-6378	33	11	illustrate	illustrate	VERB
ejpam-6378	33	12	the	the	DET
ejpam-6378	33	13	positive	positive	ADJ
ejpam-6378	33	14	effects	effect	NOUN
ejpam-6378	33	15	of	of	ADP
ejpam-6378	33	16	employing	employ	VERB
ejpam-6378	33	17	these	these	DET
ejpam-6378	33	18	operators	operator	NOUN
ejpam-6378	33	19	to	to	PART
ejpam-6378	33	20	solve	solve	VERB
ejpam-6378	33	21	a	a	DET
ejpam-6378	33	22	mathematical	mathematical	ADJ
ejpam-6378	33	23	problem	problem	NOUN
ejpam-6378	33	24	.	.	PUNCT
ejpam-6378	34	1	outcomes	outcome	NOUN
ejpam-6378	34	2	from	from	ADP
ejpam-6378	34	3	these	these	DET
ejpam-6378	34	4	operators	operator	NOUN
ejpam-6378	34	5	are	be	AUX
ejpam-6378	34	6	analyzed	analyze	VERB
ejpam-6378	34	7	to	to	PART
ejpam-6378	34	8	demonstrate	demonstrate	VERB
ejpam-6378	34	9	their	their	PRON
ejpam-6378	34	10	efficacy	efficacy	NOUN
ejpam-6378	34	11	and	and	CCONJ
ejpam-6378	34	12	precision	precision	NOUN
ejpam-6378	34	13	.	.	PUNCT
ejpam-6378	35	1	in	in	ADP
ejpam-6378	35	2	1966	1966	NUM
ejpam-6378	35	3	,	,	PUNCT
ejpam-6378	35	4	caputo	caputo	PROPN
ejpam-6378	35	5	[	[	X
ejpam-6378	35	6	36	36	NUM
ejpam-6378	35	7	]	]	PUNCT
ejpam-6378	35	8	proposed	propose	VERB
ejpam-6378	35	9	the	the	DET
ejpam-6378	35	10	caputo	caputo	PROPN
ejpam-6378	35	11	derivative	derivative	NOUN
ejpam-6378	35	12	,	,	PUNCT
ejpam-6378	35	13	that	that	PRON
ejpam-6378	35	14	includes	include	VERB
ejpam-6378	35	15	a	a	DET
ejpam-6378	35	16	singular	singular	ADJ
ejpam-6378	35	17	kernel	kernel	NOUN
ejpam-6378	35	18	(	(	PUNCT
ejpam-6378	35	19	power	power	NOUN
ejpam-6378	35	20	law	law	NOUN
ejpam-6378	35	21	kernel	kernel	PROPN
ejpam-6378	35	22	)	)	PUNCT
ejpam-6378	35	23	.	.	PUNCT
ejpam-6378	36	1	in	in	ADP
ejpam-6378	36	2	2015	2015	NUM
ejpam-6378	36	3	,	,	PUNCT
ejpam-6378	36	4	caputo	caputo	PROPN
ejpam-6378	36	5	and	and	CCONJ
ejpam-6378	36	6	fabrizio	fabrizio	PROPN
ejpam-6378	36	7	[	[	X
ejpam-6378	36	8	37	37	NUM
ejpam-6378	36	9	]	]	PUNCT
ejpam-6378	36	10	introduced	introduce	VERB
ejpam-6378	36	11	the	the	DET
ejpam-6378	36	12	caputo	caputo	PROPN
ejpam-6378	36	13	-	-	PUNCT
ejpam-6378	36	14	fabrizio	fabrizio	PROPN
ejpam-6378	36	15	fractional	fractional	PROPN
ejpam-6378	36	16	derivative	derivative	NOUN
ejpam-6378	36	17	,	,	PUNCT
ejpam-6378	36	18	characterized	characterize	VERB
ejpam-6378	36	19	by	by	ADP
ejpam-6378	36	20	a	a	DET
ejpam-6378	36	21	non	non	ADJ
ejpam-6378	36	22	-	-	ADJ
ejpam-6378	36	23	singular	singular	ADJ
ejpam-6378	36	24	kernel	kernel	NOUN
ejpam-6378	36	25	featuring	feature	VERB
ejpam-6378	36	26	an	an	DET
ejpam-6378	36	27	exponential	exponential	ADJ
ejpam-6378	36	28	function	function	NOUN
ejpam-6378	36	29	.	.	PUNCT
ejpam-6378	37	1	in	in	ADP
ejpam-6378	37	2	2016	2016	NUM
ejpam-6378	37	3	,	,	PUNCT
ejpam-6378	37	4	atangana	atangana	PROPN
ejpam-6378	37	5	and	and	CCONJ
ejpam-6378	37	6	baleanu	baleanu	X
ejpam-6378	37	7	[	[	X
ejpam-6378	37	8	38	38	NUM
ejpam-6378	37	9	]	]	PUNCT
ejpam-6378	37	10	presented	present	VERB
ejpam-6378	37	11	the	the	DET
ejpam-6378	37	12	derivative	derivative	NOUN
ejpam-6378	37	13	with	with	ADP
ejpam-6378	37	14	a	a	DET
ejpam-6378	37	15	non	non	ADJ
ejpam-6378	37	16	-	-	ADJ
ejpam-6378	37	17	singular	singular	ADJ
ejpam-6378	37	18	kernel	kernel	NOUN
ejpam-6378	37	19	utilizing	utilize	VERB
ejpam-6378	37	20	the	the	DET
ejpam-6378	37	21	mittag	mittag	ADJ
ejpam-6378	37	22	-	-	PUNCT
ejpam-6378	37	23	leffler	leffler	NOUN
ejpam-6378	37	24	function	function	NOUN
ejpam-6378	37	25	.	.	PUNCT
ejpam-6378	38	1	the	the	DET
ejpam-6378	38	2	adm	adm	PROPN
ejpam-6378	38	3	,	,	PUNCT
ejpam-6378	38	4	developed	develop	VERB
ejpam-6378	38	5	by	by	ADP
ejpam-6378	38	6	george	george	PROPN
ejpam-6378	38	7	adomian	adomian	NOUN
ejpam-6378	38	8	between	between	ADP
ejpam-6378	38	9	the	the	DET
ejpam-6378	38	10	1970s	1970	NOUN
ejpam-6378	38	11	and	and	CCONJ
ejpam-6378	38	12	1990s	1990s	NUM
ejpam-6378	38	13	,	,	PUNCT
ejpam-6378	38	14	is	be	AUX
ejpam-6378	38	15	a	a	DET
ejpam-6378	38	16	semianalytical	semianalytical	ADJ
ejpam-6378	38	17	technique	technique	NOUN
ejpam-6378	38	18	that	that	PRON
ejpam-6378	38	19	decomposes	decompose	VERB
ejpam-6378	38	20	the	the	DET
ejpam-6378	38	21	unknown	unknown	ADJ
ejpam-6378	38	22	term	term	NOUN
ejpam-6378	38	23	of	of	ADP
ejpam-6378	38	24	equations	equation	NOUN
ejpam-6378	38	25	both	both	CCONJ
ejpam-6378	38	26	linear	linear	ADJ
ejpam-6378	38	27	and	and	CCONJ
ejpam-6378	38	28	nonlinear	nonlinear	ADJ
ejpam-6378	38	29	differential	differential	ADJ
ejpam-6378	38	30	and	and	CCONJ
ejpam-6378	38	31	integral	integral	ADJ
ejpam-6378	38	32	equations	equation	NOUN
ejpam-6378	38	33	into	into	ADP
ejpam-6378	38	34	components	component	NOUN
ejpam-6378	38	35	of	of	ADP
ejpam-6378	38	36	varying	vary	VERB
ejpam-6378	38	37	degrees	degree	NOUN
ejpam-6378	38	38	.	.	PUNCT
ejpam-6378	39	1	these	these	DET
ejpam-6378	39	2	components	component	NOUN
ejpam-6378	39	3	are	be	AUX
ejpam-6378	39	4	subsequently	subsequently	ADV
ejpam-6378	39	5	summed	sum	VERB
ejpam-6378	39	6	,	,	PUNCT
ejpam-6378	39	7	and	and	CCONJ
ejpam-6378	39	8	the	the	DET
ejpam-6378	39	9	method	method	NOUN
ejpam-6378	39	10	seeks	seek	VERB
ejpam-6378	39	11	to	to	PART
ejpam-6378	39	12	determine	determine	VERB
ejpam-6378	39	13	the	the	DET
ejpam-6378	39	14	solutions	solution	NOUN
ejpam-6378	39	15	for	for	ADP
ejpam-6378	39	16	each	each	DET
ejpam-6378	39	17	order	order	NOUN
ejpam-6378	39	18	,	,	PUNCT
ejpam-6378	39	19	which	which	PRON
ejpam-6378	39	20	constitutes	constitute	VERB
ejpam-6378	39	21	the	the	DET
ejpam-6378	39	22	fundamental	fundamental	ADJ
ejpam-6378	39	23	principle	principle	NOUN
ejpam-6378	39	24	of	of	ADP
ejpam-6378	39	25	adm	adm	PROPN
ejpam-6378	39	26	.	.	PUNCT
ejpam-6378	40	1	the	the	DET
ejpam-6378	40	2	method	method	NOUN
ejpam-6378	40	3	’s	’s	PART
ejpam-6378	40	4	essential	essential	ADJ
ejpam-6378	40	5	element	element	NOUN
ejpam-6378	40	6	is	be	AUX
ejpam-6378	40	7	the	the	DET
ejpam-6378	40	8	utilization	utilization	NOUN
ejpam-6378	40	9	of	of	ADP
ejpam-6378	40	10	”	"	PUNCT
ejpam-6378	40	11	adomian	adomian	NOUN
ejpam-6378	40	12	polynomials	polynomial	NOUN
ejpam-6378	40	13	”	"	PUNCT
ejpam-6378	40	14	which	which	PRON
ejpam-6378	40	15	facilitate	facilitate	VERB
ejpam-6378	40	16	the	the	DET
ejpam-6378	40	17	convergence	convergence	NOUN
ejpam-6378	40	18	of	of	ADP
ejpam-6378	40	19	solutions	solution	NOUN
ejpam-6378	40	20	for	for	ADP
ejpam-6378	40	21	the	the	DET
ejpam-6378	40	22	nonlinear	nonlinear	ADJ
ejpam-6378	40	23	portion	portion	NOUN
ejpam-6378	40	24	of	of	ADP
ejpam-6378	40	25	the	the	DET
ejpam-6378	40	26	equation	equation	NOUN
ejpam-6378	40	27	by	by	ADP
ejpam-6378	40	28	simple	simple	ADJ
ejpam-6378	40	29	linearization	linearization	NOUN
ejpam-6378	40	30	of	of	ADP
ejpam-6378	40	31	the	the	DET
ejpam-6378	40	32	problem	problem	NOUN
ejpam-6378	40	33	.	.	PUNCT
ejpam-6378	41	1	this	this	DET
ejpam-6378	41	2	study	study	NOUN
ejpam-6378	41	3	integrates	integrate	VERB
ejpam-6378	41	4	adm	adm	PROPN
ejpam-6378	41	5	with	with	ADP
ejpam-6378	41	6	various	various	ADJ
ejpam-6378	41	7	transforms	transform	NOUN
ejpam-6378	41	8	and	and	CCONJ
ejpam-6378	41	9	subsequently	subsequently	ADV
ejpam-6378	41	10	analyzes	analyze	VERB
ejpam-6378	41	11	the	the	DET
ejpam-6378	41	12	results	result	NOUN
ejpam-6378	41	13	m.	m.	PROPN
ejpam-6378	41	14	sohail	sohail	PROPN
ejpam-6378	41	15	et	et	PROPN
ejpam-6378	41	16	al	al	PROPN
ejpam-6378	41	17	.	.	PUNCT
ejpam-6378	41	18	/	/	SYM
ejpam-6378	41	19	eur	eur	PROPN
ejpam-6378	41	20	.	.	PUNCT
ejpam-6378	42	1	j.	j.	PROPN
ejpam-6378	42	2	pure	pure	PROPN
ejpam-6378	42	3	appl	appl	PROPN
ejpam-6378	42	4	.	.	PROPN
ejpam-6378	42	5	math	math	PROPN
ejpam-6378	42	6	,	,	PUNCT
ejpam-6378	42	7	18	18	NUM
ejpam-6378	42	8	(	(	PUNCT
ejpam-6378	42	9	4	4	NUM
ejpam-6378	42	10	)	)	PUNCT
ejpam-6378	42	11	(	(	PUNCT
ejpam-6378	42	12	2025	2025	NUM
ejpam-6378	42	13	)	)	PUNCT
ejpam-6378	42	14	,	,	PUNCT
ejpam-6378	42	15	6378	6378	NUM
ejpam-6378	42	16	3	3	NUM
ejpam-6378	42	17	of	of	ADP
ejpam-6378	42	18	20	20	NUM
ejpam-6378	42	19	using	use	VERB
ejpam-6378	42	20	tables	table	NOUN
ejpam-6378	42	21	and	and	CCONJ
ejpam-6378	42	22	graphs	graph	NOUN
ejpam-6378	42	23	.	.	PUNCT
ejpam-6378	43	1	analytical	analytical	ADJ
ejpam-6378	43	2	methods	method	NOUN
ejpam-6378	43	3	have	have	VERB
ejpam-6378	43	4	a	a	DET
ejpam-6378	43	5	significant	significant	ADJ
ejpam-6378	43	6	role	role	NOUN
ejpam-6378	43	7	in	in	ADP
ejpam-6378	43	8	fractional	fractional	ADJ
ejpam-6378	43	9	calculus	calculus	NOUN
ejpam-6378	43	10	because	because	SCONJ
ejpam-6378	43	11	solutions	solution	NOUN
ejpam-6378	43	12	obtained	obtain	VERB
ejpam-6378	43	13	by	by	ADP
ejpam-6378	43	14	analytical	analytical	ADJ
ejpam-6378	43	15	methods	method	NOUN
ejpam-6378	43	16	are	be	AUX
ejpam-6378	43	17	exact	exact	ADJ
ejpam-6378	43	18	and	and	CCONJ
ejpam-6378	43	19	closed	closed	ADJ
ejpam-6378	43	20	-	-	PUNCT
ejpam-6378	43	21	form	form	NOUN
ejpam-6378	43	22	.	.	PUNCT
ejpam-6378	44	1	this	this	PRON
ejpam-6378	44	2	ensures	ensure	VERB
ejpam-6378	44	3	the	the	DET
ejpam-6378	44	4	accuracy	accuracy	NOUN
ejpam-6378	44	5	of	of	ADP
ejpam-6378	44	6	the	the	DET
ejpam-6378	44	7	resulting	result	VERB
ejpam-6378	44	8	quantitative	quantitative	ADJ
ejpam-6378	44	9	predictions	prediction	NOUN
ejpam-6378	44	10	.	.	PUNCT
ejpam-6378	45	1	on	on	ADP
ejpam-6378	45	2	the	the	DET
ejpam-6378	45	3	other	other	ADJ
ejpam-6378	45	4	side	side	NOUN
ejpam-6378	45	5	,	,	PUNCT
ejpam-6378	45	6	the	the	DET
ejpam-6378	45	7	numerical	numerical	ADJ
ejpam-6378	45	8	methods	method	NOUN
ejpam-6378	45	9	generate	generate	VERB
ejpam-6378	45	10	errors	error	NOUN
ejpam-6378	45	11	that	that	PRON
ejpam-6378	45	12	may	may	AUX
ejpam-6378	45	13	lead	lead	VERB
ejpam-6378	45	14	to	to	ADP
ejpam-6378	45	15	results	result	NOUN
ejpam-6378	45	16	significantly	significantly	ADV
ejpam-6378	45	17	diverging	diverge	VERB
ejpam-6378	45	18	from	from	ADP
ejpam-6378	45	19	the	the	DET
ejpam-6378	45	20	exact	exact	ADJ
ejpam-6378	45	21	solutions	solution	NOUN
ejpam-6378	45	22	.	.	PUNCT
ejpam-6378	46	1	adm	adm	PROPN
ejpam-6378	46	2	is	be	AUX
ejpam-6378	46	3	a	a	DET
ejpam-6378	46	4	semi	semi	ADJ
ejpam-6378	46	5	-	-	ADJ
ejpam-6378	46	6	analytical	analytical	ADJ
ejpam-6378	46	7	method	method	NOUN
ejpam-6378	46	8	that	that	PRON
ejpam-6378	46	9	has	have	VERB
ejpam-6378	46	10	precision	precision	NOUN
ejpam-6378	46	11	and	and	CCONJ
ejpam-6378	46	12	a	a	DET
ejpam-6378	46	13	high	high	ADJ
ejpam-6378	46	14	rate	rate	NOUN
ejpam-6378	46	15	of	of	ADP
ejpam-6378	46	16	convergence	convergence	NOUN
ejpam-6378	46	17	to	to	ADP
ejpam-6378	46	18	closed	closed	ADJ
ejpam-6378	46	19	-	-	PUNCT
ejpam-6378	46	20	form	form	NOUN
ejpam-6378	46	21	solutions	solution	NOUN
ejpam-6378	46	22	.	.	PUNCT
ejpam-6378	47	1	the	the	DET
ejpam-6378	47	2	laplace	laplace	NOUN
ejpam-6378	47	3	[	[	X
ejpam-6378	47	4	39	39	NUM
ejpam-6378	47	5	]	]	PUNCT
ejpam-6378	47	6	,	,	PUNCT
ejpam-6378	47	7	elzaki	elzaki	VERB
ejpam-6378	47	8	[	[	X
ejpam-6378	47	9	40	40	NUM
ejpam-6378	47	10	]	]	PUNCT
ejpam-6378	47	11	,	,	PUNCT
ejpam-6378	47	12	aboodh	aboodh	VERB
ejpam-6378	48	1	[	[	X
ejpam-6378	48	2	41	41	NUM
ejpam-6378	48	3	]	]	PUNCT
ejpam-6378	48	4	,	,	PUNCT
ejpam-6378	48	5	sumudu[42],yang[43	sumudu[42],yang[43	PROPN
ejpam-6378	48	6	]	]	PUNCT
ejpam-6378	48	7	,	,	PUNCT
ejpam-6378	48	8	mohand	mohand	NOUN
ejpam-6378	48	9	[	[	X
ejpam-6378	48	10	44	44	NUM
ejpam-6378	48	11	]	]	PUNCT
ejpam-6378	48	12	,	,	PUNCT
ejpam-6378	48	13	natural	natural	ADJ
ejpam-6378	48	14	[	[	X
ejpam-6378	48	15	45	45	NUM
ejpam-6378	48	16	]	]	PUNCT
ejpam-6378	48	17	,	,	PUNCT
ejpam-6378	48	18	and	and	CCONJ
ejpam-6378	48	19	shehu	shehu	X
ejpam-6378	48	20	[	[	X
ejpam-6378	48	21	46	46	NUM
ejpam-6378	48	22	]	]	PUNCT
ejpam-6378	48	23	transforms	transform	VERB
ejpam-6378	48	24	are	be	AUX
ejpam-6378	48	25	integral	integral	ADJ
ejpam-6378	48	26	transforms	transform	NOUN
ejpam-6378	48	27	employed	employ	VERB
ejpam-6378	48	28	to	to	PART
ejpam-6378	48	29	solve	solve	VERB
ejpam-6378	48	30	fpdes	fpde	NOUN
ejpam-6378	48	31	across	across	ADP
ejpam-6378	48	32	different	different	ADJ
ejpam-6378	48	33	fields	field	NOUN
ejpam-6378	48	34	,	,	PUNCT
ejpam-6378	48	35	including	include	VERB
ejpam-6378	48	36	engineering	engineering	NOUN
ejpam-6378	48	37	and	and	CCONJ
ejpam-6378	48	38	mathematics	mathematic	NOUN
ejpam-6378	48	39	.	.	PUNCT
ejpam-6378	49	1	these	these	PRON
ejpam-6378	49	2	transforms	transform	VERB
ejpam-6378	49	3	,	,	PUNCT
ejpam-6378	49	4	essential	essential	ADJ
ejpam-6378	49	5	instruments	instrument	NOUN
ejpam-6378	49	6	,	,	PUNCT
ejpam-6378	49	7	convert	convert	VERB
ejpam-6378	49	8	time	time	NOUN
ejpam-6378	49	9	-	-	PUNCT
ejpam-6378	49	10	domain	domain	NOUN
ejpam-6378	49	11	functions	function	NOUN
ejpam-6378	49	12	into	into	ADP
ejpam-6378	49	13	the	the	DET
ejpam-6378	49	14	complex	complex	ADJ
ejpam-6378	49	15	frequency	frequency	NOUN
ejpam-6378	49	16	domain	domain	NOUN
ejpam-6378	49	17	.	.	PUNCT
ejpam-6378	50	1	there	there	PRON
ejpam-6378	50	2	are	be	VERB
ejpam-6378	50	3	some	some	DET
ejpam-6378	50	4	basic	basic	ADJ
ejpam-6378	50	5	definitions	definition	NOUN
ejpam-6378	50	6	along	along	ADP
ejpam-6378	50	7	with	with	ADP
ejpam-6378	50	8	some	some	DET
ejpam-6378	50	9	mathematical	mathematical	ADJ
ejpam-6378	50	10	calculations	calculation	NOUN
ejpam-6378	50	11	for	for	ADP
ejpam-6378	50	12	different	different	ADJ
ejpam-6378	50	13	transformations	transformation	NOUN
ejpam-6378	50	14	and	and	CCONJ
ejpam-6378	50	15	derivative	derivative	ADJ
ejpam-6378	50	16	operators	operator	NOUN
ejpam-6378	50	17	in	in	ADP
ejpam-6378	50	18	section	section	NOUN
ejpam-6378	50	19	(	(	PUNCT
ejpam-6378	50	20	2	2	NUM
ejpam-6378	50	21	)	)	PUNCT
ejpam-6378	50	22	.	.	PUNCT
ejpam-6378	51	1	a	a	DET
ejpam-6378	51	2	simple	simple	ADJ
ejpam-6378	51	3	,	,	PUNCT
ejpam-6378	51	4	straightforward	straightforward	ADJ
ejpam-6378	51	5	,	,	PUNCT
ejpam-6378	51	6	and	and	CCONJ
ejpam-6378	51	7	general	general	ADJ
ejpam-6378	51	8	methodology	methodology	NOUN
ejpam-6378	51	9	in	in	ADP
ejpam-6378	51	10	section	section	NOUN
ejpam-6378	51	11	(	(	PUNCT
ejpam-6378	51	12	3	3	NUM
ejpam-6378	51	13	)	)	PUNCT
ejpam-6378	51	14	.	.	PUNCT
ejpam-6378	52	1	in	in	ADP
ejpam-6378	52	2	section	section	NOUN
ejpam-6378	52	3	(	(	PUNCT
ejpam-6378	52	4	4	4	NUM
ejpam-6378	52	5	)	)	PUNCT
ejpam-6378	52	6	,	,	PUNCT
ejpam-6378	52	7	we	we	PRON
ejpam-6378	52	8	solve	solve	VERB
ejpam-6378	52	9	a	a	DET
ejpam-6378	52	10	non	non	ADJ
ejpam-6378	52	11	-	-	ADJ
ejpam-6378	52	12	linear	linear	ADJ
ejpam-6378	52	13	fpde	fpde	NOUN
ejpam-6378	52	14	under	under	ADP
ejpam-6378	52	15	different	different	ADJ
ejpam-6378	52	16	derivative	derivative	ADJ
ejpam-6378	52	17	operators	operator	NOUN
ejpam-6378	52	18	and	and	CCONJ
ejpam-6378	52	19	transformations	transformation	NOUN
ejpam-6378	52	20	.	.	PUNCT
ejpam-6378	53	1	2	2	X
ejpam-6378	53	2	.	.	X
ejpam-6378	53	3	preliminaries	preliminary	NOUN
ejpam-6378	53	4	definition	definition	NOUN
ejpam-6378	53	5	1	1	NUM
ejpam-6378	53	6	.	.	PUNCT
ejpam-6378	54	1	the	the	DET
ejpam-6378	54	2	laplace	laplace	NOUN
ejpam-6378	54	3	transform	transform	NOUN
ejpam-6378	54	4	[	[	X
ejpam-6378	54	5	39	39	NUM
ejpam-6378	54	6	]	]	PUNCT
ejpam-6378	54	7	of	of	ADP
ejpam-6378	54	8	g(τ	g(τ	PROPN
ejpam-6378	54	9	)	)	PUNCT
ejpam-6378	54	10	is	be	AUX
ejpam-6378	54	11	a	a	DET
ejpam-6378	54	12	function	function	NOUN
ejpam-6378	54	13	g(s	g(s	NOUN
ejpam-6378	54	14	)	)	PUNCT
ejpam-6378	54	15	of	of	ADP
ejpam-6378	54	16	another	another	DET
ejpam-6378	54	17	variable	variable	NOUN
ejpam-6378	54	18	s	s	VERB
ejpam-6378	54	19	defined	define	VERB
ejpam-6378	54	20	by	by	ADP
ejpam-6378	54	21	g(s	g(	NOUN
ejpam-6378	54	22	)	)	PUNCT
ejpam-6378	54	23	=	=	SYM
ejpam-6378	54	24	l[g(τ	l[g(τ	NOUN
ejpam-6378	54	25	)	)	PUNCT
ejpam-6378	54	26	]	]	PUNCT
ejpam-6378	55	1	=	=	PUNCT
ejpam-6378	55	2	∫	∫	PROPN
ejpam-6378	55	3	∞	∞	PROPN
ejpam-6378	55	4	0	0	NUM
ejpam-6378	55	5	e−s	e−s	PROPN
ejpam-6378	55	6	τg(τ)dτ	τg(τ)dτ	PROPN
ejpam-6378	55	7	,	,	PUNCT
ejpam-6378	55	8	where	where	SCONJ
ejpam-6378	55	9	τ	τ	PROPN
ejpam-6378	55	10	≥	≥	NOUN
ejpam-6378	55	11	0	0	NUM
ejpam-6378	55	12	.	.	PUNCT
ejpam-6378	56	1	(	(	PUNCT
ejpam-6378	56	2	1	1	X
ejpam-6378	56	3	)	)	PUNCT
ejpam-6378	56	4	where	where	SCONJ
ejpam-6378	56	5	g(τ	g(τ	PROPN
ejpam-6378	56	6	)	)	PUNCT
ejpam-6378	56	7	be	be	VERB
ejpam-6378	56	8	a	a	DET
ejpam-6378	56	9	continuous	continuous	ADJ
ejpam-6378	56	10	or	or	CCONJ
ejpam-6378	56	11	sectionally	sectionally	ADV
ejpam-6378	56	12	continuous	continuous	ADJ
ejpam-6378	56	13	function	function	NOUN
ejpam-6378	56	14	of	of	ADP
ejpam-6378	56	15	τ	τ	PROPN
ejpam-6378	56	16	.	.	PUNCT
ejpam-6378	57	1	definition	definition	NOUN
ejpam-6378	57	2	2	2	NUM
ejpam-6378	57	3	.	.	PUNCT
ejpam-6378	58	1	the	the	DET
ejpam-6378	58	2	elzaki	elzaki	NOUN
ejpam-6378	58	3	transform	transform	VERB
ejpam-6378	58	4	[	[	X
ejpam-6378	58	5	40	40	NUM
ejpam-6378	58	6	]	]	PUNCT
ejpam-6378	58	7	of	of	ADP
ejpam-6378	58	8	g(τ	g(τ	PROPN
ejpam-6378	58	9	)	)	PUNCT
ejpam-6378	58	10	is	be	AUX
ejpam-6378	58	11	defined	define	VERB
ejpam-6378	58	12	by	by	ADP
ejpam-6378	58	13	g(s	g(	NOUN
ejpam-6378	58	14	)	)	PUNCT
ejpam-6378	58	15	=	=	SYM
ejpam-6378	58	16	e[g(τ	e[g(τ	NOUN
ejpam-6378	58	17	)	)	PUNCT
ejpam-6378	58	18	]	]	PUNCT
ejpam-6378	59	1	=	=	SYM
ejpam-6378	59	2	s	s	PART
ejpam-6378	59	3	∫	∫	PROPN
ejpam-6378	59	4	∞	∞	NOUN
ejpam-6378	59	5	0	0	NUM
ejpam-6378	60	1	e−	e−	PROPN
ejpam-6378	60	2	τ	τ	PROPN
ejpam-6378	60	3	s	s	PART
ejpam-6378	60	4	g(τ)dτ	g(τ)dτ	PROPN
ejpam-6378	60	5	,	,	PUNCT
ejpam-6378	60	6	τ	τ	X
ejpam-6378	60	7	≥	≥	NOUN
ejpam-6378	60	8	0	0	NUM
ejpam-6378	60	9	.	.	PUNCT
ejpam-6378	61	1	(	(	PUNCT
ejpam-6378	61	2	2	2	X
ejpam-6378	61	3	)	)	PUNCT
ejpam-6378	61	4	definition	definition	NOUN
ejpam-6378	61	5	3	3	NUM
ejpam-6378	61	6	.	.	PUNCT
ejpam-6378	62	1	the	the	DET
ejpam-6378	62	2	aboodh	aboodh	PROPN
ejpam-6378	62	3	transform	transform	NOUN
ejpam-6378	62	4	[	[	X
ejpam-6378	62	5	41	41	NUM
ejpam-6378	62	6	]	]	PUNCT
ejpam-6378	62	7	of	of	ADP
ejpam-6378	62	8	g(τ	g(τ	PROPN
ejpam-6378	62	9	)	)	PUNCT
ejpam-6378	62	10	is	be	AUX
ejpam-6378	62	11	defined	define	VERB
ejpam-6378	62	12	by	by	ADP
ejpam-6378	62	13	g(s	g(	NOUN
ejpam-6378	62	14	)	)	PUNCT
ejpam-6378	62	15	=	=	PUNCT
ejpam-6378	62	16	a[g(τ	a[g(τ	NUM
ejpam-6378	62	17	)	)	PUNCT
ejpam-6378	62	18	]	]	PUNCT
ejpam-6378	63	1	=	=	PUNCT
ejpam-6378	63	2	1	1	NUM
ejpam-6378	63	3	s	s	NOUN
ejpam-6378	63	4	∫	∫	PROPN
ejpam-6378	63	5	∞	∞	PROPN
ejpam-6378	63	6	0	0	PROPN
ejpam-6378	63	7	e−s	e−s	PROPN
ejpam-6378	63	8	τg(τ)dτ	τg(τ)dτ	PROPN
ejpam-6378	63	9	,	,	PUNCT
ejpam-6378	63	10	τ	τ	PROPN
ejpam-6378	63	11	≥	≥	NOUN
ejpam-6378	63	12	0	0	NUM
ejpam-6378	63	13	.	.	PUNCT
ejpam-6378	64	1	(	(	PUNCT
ejpam-6378	64	2	3	3	X
ejpam-6378	64	3	)	)	PUNCT
ejpam-6378	64	4	definition	definition	NOUN
ejpam-6378	64	5	4	4	NUM
ejpam-6378	64	6	.	.	PUNCT
ejpam-6378	65	1	the	the	DET
ejpam-6378	65	2	sumudu	sumudu	NOUN
ejpam-6378	65	3	transform	transform	VERB
ejpam-6378	65	4	[	[	X
ejpam-6378	65	5	42	42	NUM
ejpam-6378	65	6	]	]	PUNCT
ejpam-6378	65	7	of	of	ADP
ejpam-6378	65	8	g(τ	g(τ	PROPN
ejpam-6378	65	9	)	)	PUNCT
ejpam-6378	65	10	is	be	AUX
ejpam-6378	65	11	defined	define	VERB
ejpam-6378	65	12	by	by	ADP
ejpam-6378	65	13	g(s	g(	NOUN
ejpam-6378	65	14	)	)	PUNCT
ejpam-6378	65	15	=	=	SYM
ejpam-6378	65	16	s[g(τ	s[g(τ	PROPN
ejpam-6378	65	17	)	)	PUNCT
ejpam-6378	65	18	]	]	PUNCT
ejpam-6378	66	1	=	=	PUNCT
ejpam-6378	66	2	1	1	NUM
ejpam-6378	66	3	s	s	NOUN
ejpam-6378	66	4	∫	∫	PROPN
ejpam-6378	66	5	∞	∞	NOUN
ejpam-6378	66	6	0	0	NUM
ejpam-6378	67	1	e−	e−	PROPN
ejpam-6378	67	2	τ	τ	PROPN
ejpam-6378	67	3	s	s	PART
ejpam-6378	67	4	g(τ)dτ	g(τ)dτ	PROPN
ejpam-6378	67	5	,	,	PUNCT
ejpam-6378	67	6	τ	τ	X
ejpam-6378	67	7	≥	≥	NOUN
ejpam-6378	67	8	0	0	NUM
ejpam-6378	67	9	.	.	PUNCT
ejpam-6378	68	1	(	(	PUNCT
ejpam-6378	68	2	4	4	X
ejpam-6378	68	3	)	)	PUNCT
ejpam-6378	68	4	definition	definition	NOUN
ejpam-6378	68	5	5	5	NUM
ejpam-6378	68	6	.	.	PUNCT
ejpam-6378	69	1	the	the	DET
ejpam-6378	69	2	yang	yang	PROPN
ejpam-6378	69	3	transform	transform	NOUN
ejpam-6378	69	4	[	[	X
ejpam-6378	69	5	43	43	NUM
ejpam-6378	69	6	]	]	PUNCT
ejpam-6378	69	7	of	of	ADP
ejpam-6378	69	8	g(τ	g(τ	PROPN
ejpam-6378	69	9	)	)	PUNCT
ejpam-6378	69	10	is	be	AUX
ejpam-6378	69	11	defined	define	VERB
ejpam-6378	69	12	by	by	ADP
ejpam-6378	69	13	g(s	g(	NOUN
ejpam-6378	69	14	)	)	PUNCT
ejpam-6378	69	15	=	=	SYM
ejpam-6378	69	16	y[g(τ	y[g(τ	NOUN
ejpam-6378	69	17	)	)	PUNCT
ejpam-6378	69	18	]	]	PUNCT
ejpam-6378	70	1	=	=	PUNCT
ejpam-6378	70	2	∫	∫	PROPN
ejpam-6378	70	3	∞	∞	NOUN
ejpam-6378	70	4	0	0	NUM
ejpam-6378	71	1	e−	e−	PROPN
ejpam-6378	71	2	τ	τ	PROPN
ejpam-6378	71	3	s	s	PART
ejpam-6378	71	4	g(τ)dτ	g(τ)dτ	PROPN
ejpam-6378	71	5	,	,	PUNCT
ejpam-6378	71	6	τ	τ	X
ejpam-6378	71	7	≥	≥	NOUN
ejpam-6378	71	8	0	0	NUM
ejpam-6378	71	9	.	.	PUNCT
ejpam-6378	72	1	(	(	PUNCT
ejpam-6378	72	2	5	5	X
ejpam-6378	72	3	)	)	PUNCT
ejpam-6378	72	4	definition	definition	NOUN
ejpam-6378	72	5	6	6	NUM
ejpam-6378	72	6	.	.	PUNCT
ejpam-6378	73	1	the	the	DET
ejpam-6378	73	2	mohand	mohand	NOUN
ejpam-6378	73	3	transform	transform	VERB
ejpam-6378	73	4	[	[	X
ejpam-6378	73	5	44	44	NUM
ejpam-6378	73	6	]	]	PUNCT
ejpam-6378	73	7	of	of	ADP
ejpam-6378	73	8	g(τ	g(τ	PROPN
ejpam-6378	73	9	)	)	PUNCT
ejpam-6378	73	10	is	be	AUX
ejpam-6378	73	11	defined	define	VERB
ejpam-6378	73	12	by	by	ADP
ejpam-6378	73	13	g(s	g(	NOUN
ejpam-6378	73	14	)	)	PUNCT
ejpam-6378	73	15	=	=	SYM
ejpam-6378	73	16	m[g(τ	m[g(τ	NOUN
ejpam-6378	73	17	)	)	PUNCT
ejpam-6378	73	18	]	]	PUNCT
ejpam-6378	74	1	=	=	PUNCT
ejpam-6378	74	2	s2	s2	PROPN
ejpam-6378	74	3	∫	∫	PROPN
ejpam-6378	74	4	∞	∞	PROPN
ejpam-6378	74	5	0	0	NUM
ejpam-6378	75	1	e−sτg(τ)dτ	e−sτg(τ)dτ	PROPN
ejpam-6378	75	2	,	,	PUNCT
ejpam-6378	75	3	τ	τ	X
ejpam-6378	75	4	≥	≥	NOUN
ejpam-6378	75	5	0	0	NUM
ejpam-6378	75	6	.	.	PUNCT
ejpam-6378	76	1	(	(	PUNCT
ejpam-6378	76	2	6	6	NUM
ejpam-6378	76	3	)	)	PUNCT
ejpam-6378	76	4	m.	m.	NOUN
ejpam-6378	76	5	sohail	sohail	PROPN
ejpam-6378	76	6	et	et	PROPN
ejpam-6378	76	7	al	al	PROPN
ejpam-6378	76	8	.	.	PUNCT
ejpam-6378	76	9	/	/	SYM
ejpam-6378	76	10	eur	eur	PROPN
ejpam-6378	76	11	.	.	PUNCT
ejpam-6378	77	1	j.	j.	PROPN
ejpam-6378	77	2	pure	pure	PROPN
ejpam-6378	77	3	appl	appl	PROPN
ejpam-6378	77	4	.	.	PROPN
ejpam-6378	77	5	math	math	PROPN
ejpam-6378	77	6	,	,	PUNCT
ejpam-6378	77	7	18	18	NUM
ejpam-6378	77	8	(	(	PUNCT
ejpam-6378	77	9	4	4	NUM
ejpam-6378	77	10	)	)	PUNCT
ejpam-6378	77	11	(	(	PUNCT
ejpam-6378	77	12	2025	2025	NUM
ejpam-6378	77	13	)	)	PUNCT
ejpam-6378	77	14	,	,	PUNCT
ejpam-6378	77	15	6378	6378	NUM
ejpam-6378	77	16	4	4	NUM
ejpam-6378	77	17	of	of	ADP
ejpam-6378	77	18	20	20	NUM
ejpam-6378	77	19	definition	definition	NOUN
ejpam-6378	77	20	7	7	NUM
ejpam-6378	77	21	.	.	PUNCT
ejpam-6378	78	1	the	the	DET
ejpam-6378	78	2	natural	natural	ADJ
ejpam-6378	78	3	transform	transform	NOUN
ejpam-6378	78	4	[	[	X
ejpam-6378	78	5	45	45	NUM
ejpam-6378	78	6	]	]	PUNCT
ejpam-6378	78	7	of	of	ADP
ejpam-6378	78	8	g(τ	g(τ	PROPN
ejpam-6378	78	9	)	)	PUNCT
ejpam-6378	78	10	is	be	AUX
ejpam-6378	78	11	defined	define	VERB
ejpam-6378	78	12	by	by	ADP
ejpam-6378	78	13	f	f	PROPN
ejpam-6378	78	14	(	(	PUNCT
ejpam-6378	78	15	s	s	PROPN
ejpam-6378	78	16	,	,	PUNCT
ejpam-6378	78	17	θ	θ	NOUN
ejpam-6378	78	18	)	)	PUNCT
ejpam-6378	78	19	=	=	SYM
ejpam-6378	78	20	n	n	NUM
ejpam-6378	78	21	[	[	X
ejpam-6378	78	22	g(τ	g(τ	PROPN
ejpam-6378	78	23	)	)	PUNCT
ejpam-6378	78	24	]	]	PUNCT
ejpam-6378	79	1	=	=	SYM
ejpam-6378	79	2	1	1	NUM
ejpam-6378	79	3	θ	θ	NOUN
ejpam-6378	79	4	∫	∫	PROPN
ejpam-6378	79	5	∞	∞	NOUN
ejpam-6378	79	6	0	0	NUM
ejpam-6378	80	1	e−	e−	NOUN
ejpam-6378	80	2	sτ	sτ	ADP
ejpam-6378	80	3	θ	θ	PROPN
ejpam-6378	80	4	g(τ)dτ	g(τ)dτ	PROPN
ejpam-6378	80	5	,	,	PUNCT
ejpam-6378	80	6	τ	τ	X
ejpam-6378	80	7	≥	≥	NOUN
ejpam-6378	80	8	0	0	NUM
ejpam-6378	80	9	.	.	PUNCT
ejpam-6378	81	1	(	(	PUNCT
ejpam-6378	81	2	7	7	X
ejpam-6378	81	3	)	)	PUNCT
ejpam-6378	81	4	definition	definition	NOUN
ejpam-6378	81	5	8	8	NUM
ejpam-6378	81	6	.	.	PUNCT
ejpam-6378	82	1	the	the	DET
ejpam-6378	82	2	shehu	shehu	PROPN
ejpam-6378	82	3	transform	transform	VERB
ejpam-6378	82	4	[	[	X
ejpam-6378	82	5	46	46	NUM
ejpam-6378	82	6	]	]	PUNCT
ejpam-6378	82	7	of	of	ADP
ejpam-6378	82	8	g(τ	g(τ	PROPN
ejpam-6378	82	9	)	)	PUNCT
ejpam-6378	82	10	is	be	AUX
ejpam-6378	82	11	defined	define	VERB
ejpam-6378	82	12	by	by	ADP
ejpam-6378	82	13	f	f	PROPN
ejpam-6378	82	14	(	(	PUNCT
ejpam-6378	82	15	s	s	PROPN
ejpam-6378	82	16	,	,	PUNCT
ejpam-6378	82	17	θ	θ	NOUN
ejpam-6378	82	18	)	)	PUNCT
ejpam-6378	82	19	=	=	SYM
ejpam-6378	82	20	s[g(τ	s[g(τ	PROPN
ejpam-6378	82	21	)	)	PUNCT
ejpam-6378	82	22	]	]	PUNCT
ejpam-6378	83	1	=	=	PUNCT
ejpam-6378	83	2	∫	∫	PROPN
ejpam-6378	84	1	∞	∞	NOUN
ejpam-6378	84	2	0	0	NUM
ejpam-6378	85	1	e−	e−	NOUN
ejpam-6378	85	2	sτ	sτ	ADP
ejpam-6378	85	3	θ	θ	PROPN
ejpam-6378	85	4	g(τ)dτ	g(τ)dτ	PROPN
ejpam-6378	85	5	,	,	PUNCT
ejpam-6378	85	6	τ	τ	X
ejpam-6378	85	7	≥	≥	NOUN
ejpam-6378	85	8	0	0	NUM
ejpam-6378	85	9	.	.	PUNCT
ejpam-6378	86	1	(	(	PUNCT
ejpam-6378	86	2	8)	8)	NUM
ejpam-6378	86	3	definition	definition	NOUN
ejpam-6378	86	4	9	9	NUM
ejpam-6378	86	5	.	.	PUNCT
ejpam-6378	87	1	the	the	DET
ejpam-6378	87	2	kernel	kernel	NOUN
ejpam-6378	87	3	of	of	ADP
ejpam-6378	87	4	the	the	DET
ejpam-6378	87	5	integral	integral	ADJ
ejpam-6378	87	6	equation	equation	NOUN
ejpam-6378	87	7	w(θ	w(θ	ADJ
ejpam-6378	87	8	)	)	PUNCT
ejpam-6378	87	9	=	=	SYM
ejpam-6378	87	10	∫	∫	PROPN
ejpam-6378	87	11	q(θ	q(θ	PROPN
ejpam-6378	87	12	)	)	PUNCT
ejpam-6378	87	13	p(θ	p(θ	PROPN
ejpam-6378	87	14	)	)	PUNCT
ejpam-6378	87	15	κ(χ	κ(χ	PROPN
ejpam-6378	87	16	,	,	PUNCT
ejpam-6378	87	17	θ)w(θ)dθ	θ)w(θ)dθ	NOUN
ejpam-6378	87	18	.	.	PUNCT
ejpam-6378	88	1	(	(	PUNCT
ejpam-6378	88	2	9	9	X
ejpam-6378	88	3	)	)	PUNCT
ejpam-6378	88	4	is	be	AUX
ejpam-6378	88	5	κ(χ	κ(χ	PROPN
ejpam-6378	88	6	,	,	PUNCT
ejpam-6378	88	7	θ	θ	NOUN
ejpam-6378	88	8	)	)	PUNCT
ejpam-6378	88	9	.	.	PUNCT
ejpam-6378	89	1	if	if	SCONJ
ejpam-6378	89	2	the	the	DET
ejpam-6378	89	3	kernel	kernel	NOUN
ejpam-6378	89	4	is	be	AUX
ejpam-6378	89	5	singular	singular	ADJ
ejpam-6378	89	6	,	,	PUNCT
ejpam-6378	89	7	then	then	ADV
ejpam-6378	89	8	equation	equation	NOUN
ejpam-6378	89	9	(	(	PUNCT
ejpam-6378	89	10	9	9	NUM
ejpam-6378	89	11	)	)	PUNCT
ejpam-6378	89	12	becomes	become	VERB
ejpam-6378	89	13	a	a	DET
ejpam-6378	89	14	singular	singular	ADJ
ejpam-6378	89	15	integral	integral	ADJ
ejpam-6378	89	16	equation	equation	NOUN
ejpam-6378	89	17	.	.	PUNCT
ejpam-6378	90	1	the	the	DET
ejpam-6378	90	2	kernel	kernel	NOUN
ejpam-6378	90	3	is	be	AUX
ejpam-6378	90	4	singular	singular	ADJ
ejpam-6378	90	5	if	if	SCONJ
ejpam-6378	90	6	one	one	NUM
ejpam-6378	90	7	or	or	CCONJ
ejpam-6378	90	8	both	both	DET
ejpam-6378	90	9	limits	limit	NOUN
ejpam-6378	90	10	of	of	ADP
ejpam-6378	90	11	integration	integration	NOUN
ejpam-6378	90	12	become	become	VERB
ejpam-6378	90	13	infinite	infinite	ADJ
ejpam-6378	90	14	,	,	PUNCT
ejpam-6378	90	15	or	or	CCONJ
ejpam-6378	90	16	if	if	SCONJ
ejpam-6378	90	17	it	it	PRON
ejpam-6378	90	18	becomes	become	VERB
ejpam-6378	90	19	infinite	infinite	ADJ
ejpam-6378	90	20	at	at	ADP
ejpam-6378	90	21	one	one	NUM
ejpam-6378	90	22	point	point	NOUN
ejpam-6378	90	23	or	or	CCONJ
ejpam-6378	90	24	more	more	ADJ
ejpam-6378	90	25	points	point	NOUN
ejpam-6378	90	26	in	in	ADP
ejpam-6378	90	27	the	the	DET
ejpam-6378	90	28	interval	interval	NOUN
ejpam-6378	90	29	of	of	ADP
ejpam-6378	90	30	integration	integration	NOUN
ejpam-6378	90	31	,	,	PUNCT
ejpam-6378	90	32	mathematically	mathematically	ADV
ejpam-6378	90	33	κ(χ	κ(χ	PROPN
ejpam-6378	90	34	,	,	PUNCT
ejpam-6378	90	35	θ	θ	NOUN
ejpam-6378	90	36	)	)	PUNCT
ejpam-6378	90	37	→	→	SYM
ejpam-6378	90	38	∞	∞	PROPN
ejpam-6378	90	39	with	with	ADP
ejpam-6378	90	40	θ	θ	PROPN
ejpam-6378	90	41	→	→	SYM
ejpam-6378	90	42	χ	χ	X
ejpam-6378	90	43	.	.	PUNCT
ejpam-6378	91	1	definition	definition	NOUN
ejpam-6378	91	2	10	10	NUM
ejpam-6378	91	3	.	.	PUNCT
ejpam-6378	92	1	consider	consider	VERB
ejpam-6378	92	2	,	,	PUNCT
ejpam-6378	92	3	g1	g1	PROPN
ejpam-6378	92	4	and	and	CCONJ
ejpam-6378	92	5	g2	g2	PROPN
ejpam-6378	92	6	are	be	AUX
ejpam-6378	92	7	two	two	NUM
ejpam-6378	92	8	piecewise	piecewise	NOUN
ejpam-6378	92	9	continuous	continuous	ADJ
ejpam-6378	92	10	functions	function	NOUN
ejpam-6378	92	11	of	of	ADP
ejpam-6378	92	12	exponential	exponential	ADJ
ejpam-6378	92	13	order	order	NOUN
ejpam-6378	92	14	on	on	ADP
ejpam-6378	92	15	the	the	DET
ejpam-6378	92	16	interval	interval	NOUN
ejpam-6378	92	17	[	[	X
ejpam-6378	92	18	0,∞	0,∞	NOUN
ejpam-6378	92	19	)	)	PUNCT
ejpam-6378	92	20	,	,	PUNCT
ejpam-6378	92	21	then	then	ADV
ejpam-6378	92	22	the	the	DET
ejpam-6378	92	23	convolution	convolution	NOUN
ejpam-6378	92	24	is	be	AUX
ejpam-6378	92	25	defined	define	VERB
ejpam-6378	92	26	on	on	ADP
ejpam-6378	92	27	g1	g1	PROPN
ejpam-6378	92	28	and	and	CCONJ
ejpam-6378	92	29	g2	g2	PROPN
ejpam-6378	92	30	as	as	SCONJ
ejpam-6378	92	31	g1	g1	PROPN
ejpam-6378	92	32	∗	∗	NOUN
ejpam-6378	92	33	g2	g2	PROPN
ejpam-6378	93	1	=	=	SYM
ejpam-6378	93	2	∫	∫	PROPN
ejpam-6378	93	3	τ	τ	PROPN
ejpam-6378	93	4	0	0	NUM
ejpam-6378	94	1	g1(τ	g1(τ	NOUN
ejpam-6378	94	2	−	−	NOUN
ejpam-6378	94	3	τ)g2(τ)dτ	τ)g2(τ)dτ	NOUN
ejpam-6378	95	1	=	=	SYM
ejpam-6378	95	2	∫	∫	PROPN
ejpam-6378	95	3	τ	τ	PROPN
ejpam-6378	95	4	0	0	PROPN
ejpam-6378	95	5	g2(τ)g1(τ	g2(τ)g1(τ	PROPN
ejpam-6378	95	6	−	−	PROPN
ejpam-6378	96	1	τ)dτ	τ)dτ	PROPN
ejpam-6378	96	2	=	=	SYM
ejpam-6378	96	3	g2	g2	PROPN
ejpam-6378	96	4	∗	∗	NOUN
ejpam-6378	96	5	g1	g1	PROPN
ejpam-6378	96	6	,	,	PUNCT
ejpam-6378	96	7	(	(	PUNCT
ejpam-6378	96	8	10	10	NUM
ejpam-6378	96	9	)	)	PUNCT
ejpam-6378	96	10	showing	showing	NOUN
ejpam-6378	96	11	,	,	PUNCT
ejpam-6378	96	12	g1	g1	PROPN
ejpam-6378	96	13	∗	∗	PROPN
ejpam-6378	96	14	g2	g2	PROPN
ejpam-6378	96	15	=	=	PROPN
ejpam-6378	96	16	g2	g2	PROPN
ejpam-6378	96	17	∗	∗	NOUN
ejpam-6378	96	18	g1	g1	PROPN
ejpam-6378	96	19	.	.	PUNCT
ejpam-6378	97	1	further	far	ADV
ejpam-6378	97	2	,	,	PUNCT
ejpam-6378	97	3	let	let	VERB
ejpam-6378	97	4	take	take	VERB
ejpam-6378	97	5	lt	lt	PRON
ejpam-6378	97	6	l(g1	l(g1	ADJ
ejpam-6378	97	7	∗	∗	NOUN
ejpam-6378	97	8	g2	g2	PROPN
ejpam-6378	97	9	)	)	PUNCT
ejpam-6378	98	1	=	=	PUNCT
ejpam-6378	98	2	l	l	PUNCT
ejpam-6378	99	1	[	[	X
ejpam-6378	99	2	∫	∫	X
ejpam-6378	99	3	τ	τ	X
ejpam-6378	99	4	0	0	NUM
ejpam-6378	100	1	g1(τ	g1(τ	NOUN
ejpam-6378	100	2	−	−	NOUN
ejpam-6378	100	3	τ)g2(τ)dτ	τ)g2(τ)dτ	NOUN
ejpam-6378	100	4	]	]	X
ejpam-6378	100	5	=	=	PUNCT
ejpam-6378	100	6	l[g1(τ)]l[g2(τ	l[g1(τ)]l[g2(τ	NOUN
ejpam-6378	100	7	)	)	PUNCT
ejpam-6378	100	8	]	]	PUNCT
ejpam-6378	100	9	=	=	PUNCT
ejpam-6378	100	10	g1(s)g2(s	g1(s)g2(s	NOUN
ejpam-6378	100	11	)	)	PUNCT
ejpam-6378	100	12	.	.	PUNCT
ejpam-6378	101	1	(	(	PUNCT
ejpam-6378	101	2	11	11	NUM
ejpam-6378	101	3	)	)	PUNCT
ejpam-6378	101	4	similarly	similarly	ADV
ejpam-6378	101	5	,	,	PUNCT
ejpam-6378	101	6	convolution	convolution	NOUN
ejpam-6378	101	7	under	under	ADP
ejpam-6378	101	8	different	different	ADJ
ejpam-6378	101	9	transformations	transformation	NOUN
ejpam-6378	101	10	;	;	PUNCT
ejpam-6378	101	11	given	give	VERB
ejpam-6378	101	12	in	in	ADP
ejpam-6378	101	13	the	the	DET
ejpam-6378	101	14	equation	equation	NOUN
ejpam-6378	101	15	(	(	PUNCT
ejpam-6378	101	16	12).	12).	NUM
ejpam-6378	101	17	l[g1	l[g1	NOUN
ejpam-6378	101	18	∗	∗	NOUN
ejpam-6378	101	19	g2	g2	PROPN
ejpam-6378	101	20	]	]	X
ejpam-6378	101	21	=	=	PUNCT
ejpam-6378	101	22	l[g1(τ)]l[g2(τ	l[g1(τ)]l[g2(τ	NOUN
ejpam-6378	101	23	)	)	PUNCT
ejpam-6378	101	24	]	]	PUNCT
ejpam-6378	102	1	=	=	PUNCT
ejpam-6378	102	2	g1(s)g2(s	g1(s)g2(s	NOUN
ejpam-6378	102	3	)	)	PUNCT
ejpam-6378	102	4	.	.	PUNCT
ejpam-6378	103	1	e[g1	e[g1	VERB
ejpam-6378	103	2	∗	∗	PROPN
ejpam-6378	103	3	g2	g2	PROPN
ejpam-6378	103	4	]	]	X
ejpam-6378	103	5	=	=	SYM
ejpam-6378	103	6	e[g1(τ)]e[g2(τ	e[g1(τ)]e[g2(τ	PROPN
ejpam-6378	103	7	)	)	PUNCT
ejpam-6378	103	8	]	]	PUNCT
ejpam-6378	104	1	s	s	NOUN
ejpam-6378	104	2	=	=	NOUN
ejpam-6378	104	3	g1(s)g2(s	g1(s)g2(s	NOUN
ejpam-6378	104	4	)	)	PUNCT
ejpam-6378	104	5	s	s	PART
ejpam-6378	104	6	.	.	PUNCT
ejpam-6378	105	1	a[g1	a[g1	PROPN
ejpam-6378	105	2	∗	∗	NOUN
ejpam-6378	105	3	g2	g2	PROPN
ejpam-6378	105	4	]	]	X
ejpam-6378	105	5	=	=	SYM
ejpam-6378	105	6	sa[g1(τ)]a[g2(τ	sa[g1(τ)]a[g2(τ	PROPN
ejpam-6378	105	7	)	)	PUNCT
ejpam-6378	105	8	]	]	PUNCT
ejpam-6378	105	9	=	=	SYM
ejpam-6378	105	10	sg1(s)g2(s	sg1(s)g2(s	NOUN
ejpam-6378	105	11	)	)	PUNCT
ejpam-6378	105	12	.	.	PUNCT
ejpam-6378	106	1	s[g1	s[g1	VERB
ejpam-6378	106	2	∗	∗	PROPN
ejpam-6378	106	3	g2	g2	PROPN
ejpam-6378	106	4	]	]	PUNCT
ejpam-6378	107	1	=	=	PUNCT
ejpam-6378	107	2	ss[g1(τ)]s[g2(τ	ss[g1(τ)]s[g2(τ	PROPN
ejpam-6378	107	3	)	)	PUNCT
ejpam-6378	107	4	]	]	PUNCT
ejpam-6378	107	5	=	=	SYM
ejpam-6378	107	6	sg1(s)g2(s	sg1(s)g2(s	NOUN
ejpam-6378	107	7	)	)	PUNCT
ejpam-6378	107	8	.	.	PUNCT
ejpam-6378	108	1	y[g1	y[g1	PROPN
ejpam-6378	108	2	∗	∗	PROPN
ejpam-6378	108	3	g2	g2	PROPN
ejpam-6378	108	4	]	]	X
ejpam-6378	108	5	=	=	SYM
ejpam-6378	108	6	y[g1(τ)]y[g2(τ	y[g1(τ)]y[g2(τ	NOUN
ejpam-6378	108	7	)	)	PUNCT
ejpam-6378	108	8	]	]	PUNCT
ejpam-6378	109	1	=	=	PUNCT
ejpam-6378	109	2	g1(s)g2(s	g1(s)g2(s	NOUN
ejpam-6378	109	3	)	)	PUNCT
ejpam-6378	109	4	.	.	PUNCT
ejpam-6378	110	1	m[g1	m[g1	VERB
ejpam-6378	110	2	∗	∗	PROPN
ejpam-6378	110	3	g2	g2	PROPN
ejpam-6378	110	4	]	]	PUNCT
ejpam-6378	110	5	=	=	SYM
ejpam-6378	110	6	m[g1(τ)]m[g2(τ	m[g1(τ)]m[g2(τ	NOUN
ejpam-6378	110	7	)	)	PUNCT
ejpam-6378	110	8	]	]	PUNCT
ejpam-6378	110	9	s2	s2	NOUN
ejpam-6378	110	10	=	=	SYM
ejpam-6378	110	11	g1(s)g2(s	g1(s)g2(s	NOUN
ejpam-6378	110	12	)	)	PUNCT
ejpam-6378	110	13	s2	s2	NOUN
ejpam-6378	110	14	.	.	PUNCT
ejpam-6378	111	1	n	n	CCONJ
ejpam-6378	112	1	[	[	X
ejpam-6378	112	2	g1	g1	PROPN
ejpam-6378	112	3	∗	∗	PROPN
ejpam-6378	112	4	g2	g2	PROPN
ejpam-6378	112	5	]	]	PUNCT
ejpam-6378	113	1	=	=	PUNCT
ejpam-6378	113	2	θn	θn	X
ejpam-6378	114	1	[	[	X
ejpam-6378	114	2	g1(τ)]n	g1(τ)]n	PROPN
ejpam-6378	114	3	[	[	X
ejpam-6378	114	4	g2(τ	g2(τ	X
ejpam-6378	114	5	)	)	PUNCT
ejpam-6378	114	6	]	]	PUNCT
ejpam-6378	115	1	=	=	PUNCT
ejpam-6378	115	2	θ	θ	NOUN
ejpam-6378	115	3	g1(s)g2(s	g1(s)g2(s	NOUN
ejpam-6378	115	4	)	)	PUNCT
ejpam-6378	115	5	.	.	PUNCT
ejpam-6378	116	1	s[g1	s[g1	VERB
ejpam-6378	116	2	∗	∗	PROPN
ejpam-6378	116	3	g2	g2	PROPN
ejpam-6378	116	4	]	]	PUNCT
ejpam-6378	117	1	=	=	SYM
ejpam-6378	117	2	s[g1(τ)]s[g2(τ	s[g1(τ)]s[g2(τ	PROPN
ejpam-6378	117	3	)	)	PUNCT
ejpam-6378	117	4	]	]	PUNCT
ejpam-6378	117	5	=	=	PUNCT
ejpam-6378	117	6	g1(s)g2(s	g1(s)g2(s	NOUN
ejpam-6378	117	7	)	)	PUNCT
ejpam-6378	117	8	.	.	PUNCT
ejpam-6378	118	1	(	(	PUNCT
ejpam-6378	118	2	12	12	NUM
ejpam-6378	118	3	)	)	PUNCT
ejpam-6378	118	4	m.	m.	NOUN
ejpam-6378	118	5	sohail	sohail	PROPN
ejpam-6378	118	6	et	et	PROPN
ejpam-6378	118	7	al	al	PROPN
ejpam-6378	118	8	.	.	PUNCT
ejpam-6378	118	9	/	/	SYM
ejpam-6378	118	10	eur	eur	PROPN
ejpam-6378	118	11	.	.	PUNCT
ejpam-6378	119	1	j.	j.	PROPN
ejpam-6378	119	2	pure	pure	PROPN
ejpam-6378	119	3	appl	appl	PROPN
ejpam-6378	119	4	.	.	PROPN
ejpam-6378	119	5	math	math	PROPN
ejpam-6378	119	6	,	,	PUNCT
ejpam-6378	119	7	18	18	NUM
ejpam-6378	119	8	(	(	PUNCT
ejpam-6378	119	9	4	4	NUM
ejpam-6378	119	10	)	)	PUNCT
ejpam-6378	119	11	(	(	PUNCT
ejpam-6378	119	12	2025	2025	NUM
ejpam-6378	119	13	)	)	PUNCT
ejpam-6378	119	14	,	,	PUNCT
ejpam-6378	119	15	6378	6378	NUM
ejpam-6378	119	16	5	5	NUM
ejpam-6378	119	17	of	of	ADP
ejpam-6378	119	18	20	20	NUM
ejpam-6378	119	19	now	now	ADV
ejpam-6378	119	20	,	,	PUNCT
ejpam-6378	119	21	first	first	ADJ
ejpam-6378	119	22	order	order	NOUN
ejpam-6378	119	23	derivative	derivative	NOUN
ejpam-6378	119	24	under	under	ADP
ejpam-6378	119	25	different	different	ADJ
ejpam-6378	119	26	transform	transform	NOUN
ejpam-6378	119	27	are	are	NOUN
ejpam-6378	119	28	l[g′(τ	l[g′(τ	ADV
ejpam-6378	119	29	)	)	PUNCT
ejpam-6378	119	30	]	]	PUNCT
ejpam-6378	120	1	=	=	PUNCT
ejpam-6378	120	2	sg(s)−	sg(s)−	PROPN
ejpam-6378	120	3	g(0	g(0	PROPN
ejpam-6378	120	4	)	)	PUNCT
ejpam-6378	120	5	.	.	PUNCT
ejpam-6378	121	1	e[g′(τ	e[g′(τ	PROPN
ejpam-6378	121	2	)	)	PUNCT
ejpam-6378	121	3	]	]	PUNCT
ejpam-6378	121	4	=	=	SYM
ejpam-6378	121	5	g(s	g(s	PROPN
ejpam-6378	121	6	)	)	PUNCT
ejpam-6378	121	7	s	s	PART
ejpam-6378	121	8	−	−	PROPN
ejpam-6378	121	9	s	s	NOUN
ejpam-6378	121	10	g(0	g(0	PROPN
ejpam-6378	121	11	)	)	PUNCT
ejpam-6378	121	12	.	.	PUNCT
ejpam-6378	122	1	a[g′(τ	a[g′(τ	ADV
ejpam-6378	122	2	)	)	PUNCT
ejpam-6378	122	3	]	]	PUNCT
ejpam-6378	123	1	=	=	SYM
ejpam-6378	123	2	sg(s)−	sg(s)−	PROPN
ejpam-6378	123	3	g(0	g(0	PROPN
ejpam-6378	123	4	)	)	PUNCT
ejpam-6378	123	5	s	s	PROPN
ejpam-6378	123	6	.	.	PUNCT
ejpam-6378	124	1	s[g′(τ	s[g′(τ	ADP
ejpam-6378	124	2	)	)	PUNCT
ejpam-6378	124	3	]	]	PUNCT
ejpam-6378	125	1	=	=	SYM
ejpam-6378	125	2	g(s	g(s	PROPN
ejpam-6378	125	3	)	)	PUNCT
ejpam-6378	125	4	s	s	PART
ejpam-6378	125	5	−	−	PROPN
ejpam-6378	125	6	g(0	g(0	PROPN
ejpam-6378	125	7	)	)	PUNCT
ejpam-6378	125	8	s	s	PART
ejpam-6378	125	9	.	.	PUNCT
ejpam-6378	126	1	y[g′(τ	y[g′(τ	PROPN
ejpam-6378	126	2	)	)	PUNCT
ejpam-6378	126	3	]	]	PUNCT
ejpam-6378	127	1	=	=	SYM
ejpam-6378	127	2	g(s	g(s	PROPN
ejpam-6378	127	3	)	)	PUNCT
ejpam-6378	127	4	s	s	PART
ejpam-6378	127	5	−	−	PROPN
ejpam-6378	127	6	g(0	g(0	NOUN
ejpam-6378	127	7	)	)	PUNCT
ejpam-6378	127	8	.	.	PUNCT
ejpam-6378	128	1	m[g′(τ	m[g′(τ	NUM
ejpam-6378	128	2	)	)	PUNCT
ejpam-6378	128	3	]	]	PUNCT
ejpam-6378	129	1	=	=	SYM
ejpam-6378	129	2	sg(s)−	sg(s)−	PROPN
ejpam-6378	129	3	s2	s2	PROPN
ejpam-6378	129	4	g(0	g(0	PROPN
ejpam-6378	129	5	)	)	PUNCT
ejpam-6378	129	6	.	.	PUNCT
ejpam-6378	130	1	n	n	PRON
ejpam-6378	131	1	[	[	X
ejpam-6378	132	1	g′(τ	g′(τ	NOUN
ejpam-6378	132	2	)	)	PUNCT
ejpam-6378	132	3	]	]	PUNCT
ejpam-6378	133	1	=	=	SYM
ejpam-6378	133	2	sg(s	sg(s	PROPN
ejpam-6378	133	3	,	,	PUNCT
ejpam-6378	133	4	θ	θ	NOUN
ejpam-6378	133	5	)	)	PUNCT
ejpam-6378	133	6	θ	θ	PROPN
ejpam-6378	133	7	−	−	PROPN
ejpam-6378	133	8	g(0	g(0	PROPN
ejpam-6378	133	9	)	)	PUNCT
ejpam-6378	133	10	θ	θ	PROPN
ejpam-6378	133	11	.	.	PUNCT
ejpam-6378	134	1	s[g′(τ	s[g′(τ	ADJ
ejpam-6378	134	2	)	)	PUNCT
ejpam-6378	134	3	]	]	PUNCT
ejpam-6378	135	1	=	=	SYM
ejpam-6378	135	2	sg(s	sg(s	PROPN
ejpam-6378	135	3	,	,	PUNCT
ejpam-6378	135	4	θ	θ	NOUN
ejpam-6378	135	5	)	)	PUNCT
ejpam-6378	135	6	θ	θ	PROPN
ejpam-6378	135	7	−	−	PROPN
ejpam-6378	135	8	g(0	g(0	PROPN
ejpam-6378	135	9	)	)	PUNCT
ejpam-6378	135	10	.	.	PUNCT
ejpam-6378	136	1	(	(	PUNCT
ejpam-6378	136	2	13	13	NUM
ejpam-6378	136	3	)	)	PUNCT
ejpam-6378	136	4	definition	definition	NOUN
ejpam-6378	136	5	11	11	NUM
ejpam-6378	136	6	.	.	PUNCT
ejpam-6378	137	1	the	the	DET
ejpam-6378	137	2	cfd	cfd	NOUN
ejpam-6378	137	3	[	[	X
ejpam-6378	137	4	36	36	NUM
ejpam-6378	137	5	]	]	PUNCT
ejpam-6378	137	6	is	be	AUX
ejpam-6378	137	7	defined	define	VERB
ejpam-6378	137	8	as	as	ADP
ejpam-6378	137	9	cdα	cdα	NOUN
ejpam-6378	137	10	θ	θ	NOUN
ejpam-6378	137	11	χ(θ	χ(θ	PROPN
ejpam-6378	137	12	)	)	PUNCT
ejpam-6378	137	13	=	=	SYM
ejpam-6378	137	14	1	1	NUM
ejpam-6378	137	15	γ(1−	γ(1−	NOUN
ejpam-6378	137	16	α	α	NUM
ejpam-6378	137	17	)	)	PUNCT
ejpam-6378	137	18	∫	∫	PROPN
ejpam-6378	137	19	θ	θ	PROPN
ejpam-6378	137	20	0	0	PUNCT
ejpam-6378	138	1	(	(	PUNCT
ejpam-6378	138	2	θ	θ	PROPN
ejpam-6378	138	3	−	−	PROPN
ejpam-6378	138	4	τ)−α	τ)−α	SYM
ejpam-6378	138	5	∂	∂	NOUN
ejpam-6378	138	6	∂τ	∂τ	PROPN
ejpam-6378	138	7	χ(τ	χ(τ	NOUN
ejpam-6378	138	8	)	)	PUNCT
ejpam-6378	138	9	dτ	dτ	NOUN
ejpam-6378	138	10	.	.	PROPN
ejpam-6378	139	1	(	(	PUNCT
ejpam-6378	139	2	14	14	NUM
ejpam-6378	139	3	)	)	PUNCT
ejpam-6378	139	4	taking	take	VERB
ejpam-6378	139	5	lt	lt	NOUN
ejpam-6378	139	6	,	,	PUNCT
ejpam-6378	139	7	implies	imply	VERB
ejpam-6378	139	8	l[cdα	l[cdα	PROPN
ejpam-6378	139	9	θ	θ	NOUN
ejpam-6378	139	10	χ(θ	χ(θ	NOUN
ejpam-6378	139	11	)	)	PUNCT
ejpam-6378	139	12	]	]	PUNCT
ejpam-6378	140	1	=	=	PUNCT
ejpam-6378	140	2	l	l	X
ejpam-6378	140	3	[	[	PUNCT
ejpam-6378	140	4	1	1	NUM
ejpam-6378	140	5	γ	γ	X
ejpam-6378	140	6	(	(	PUNCT
ejpam-6378	140	7	1−	1−	NUM
ejpam-6378	140	8	α	α	NOUN
ejpam-6378	140	9	)	)	PUNCT
ejpam-6378	140	10	(	(	PUNCT
ejpam-6378	140	11	θ−α	θ−α	NOUN
ejpam-6378	140	12	∗	∗	NOUN
ejpam-6378	140	13	∂	∂	NOUN
ejpam-6378	140	14	∂θ	∂θ	NOUN
ejpam-6378	140	15	χ	χ	X
ejpam-6378	140	16	(	(	PUNCT
ejpam-6378	140	17	θ	θ	NOUN
ejpam-6378	140	18	)	)	PUNCT
ejpam-6378	140	19	)	)	PUNCT
ejpam-6378	140	20	]	]	PUNCT
ejpam-6378	140	21	=	=	SYM
ejpam-6378	140	22	1	1	NUM
ejpam-6378	140	23	γ	γ	X
ejpam-6378	140	24	(	(	PUNCT
ejpam-6378	140	25	1−	1−	NUM
ejpam-6378	140	26	α	α	NOUN
ejpam-6378	140	27	)	)	PUNCT
ejpam-6378	140	28	(	(	PUNCT
ejpam-6378	140	29	l[θ−α]l	l[θ−α]l	ADJ
ejpam-6378	140	30	[	[	PUNCT
ejpam-6378	140	31	∂	∂	NOUN
ejpam-6378	140	32	∂θ	∂θ	PROPN
ejpam-6378	140	33	χ	χ	X
ejpam-6378	140	34	(	(	PUNCT
ejpam-6378	140	35	θ	θ	NOUN
ejpam-6378	140	36	)	)	PUNCT
ejpam-6378	140	37	]	]	PUNCT
ejpam-6378	140	38	)	)	PUNCT
ejpam-6378	140	39	=	=	SYM
ejpam-6378	140	40	1	1	NUM
ejpam-6378	140	41	γ	γ	X
ejpam-6378	140	42	(	(	PUNCT
ejpam-6378	140	43	1−	1−	NUM
ejpam-6378	140	44	α	α	NOUN
ejpam-6378	140	45	)	)	PUNCT
ejpam-6378	140	46	(	(	PUNCT
ejpam-6378	140	47	γ	γ	X
ejpam-6378	140	48	(	(	PUNCT
ejpam-6378	140	49	1−	1−	NUM
ejpam-6378	140	50	α	α	NOUN
ejpam-6378	140	51	)	)	PUNCT
ejpam-6378	140	52	s1−α	s1−α	PROPN
ejpam-6378	140	53	(	(	PUNCT
ejpam-6378	140	54	sx(s)−	sx(s)−	PROPN
ejpam-6378	140	55	χ(0	χ(0	PROPN
ejpam-6378	140	56	)	)	PUNCT
ejpam-6378	140	57	)	)	PUNCT
ejpam-6378	140	58	)	)	PUNCT
ejpam-6378	141	1	=	=	PUNCT
ejpam-6378	141	2	sα−1	sα−1	NOUN
ejpam-6378	141	3	(	(	PUNCT
ejpam-6378	141	4	sx(s)−	sx(s)−	PROPN
ejpam-6378	141	5	χ(0	χ(0	PROPN
ejpam-6378	141	6	)	)	PUNCT
ejpam-6378	141	7	)	)	PUNCT
ejpam-6378	142	1	=	=	PROPN
ejpam-6378	142	2	sαx(s)−	sαx(s)−	PROPN
ejpam-6378	142	3	sα−1χ(0	sα−1χ(0	PROPN
ejpam-6378	142	4	)	)	PUNCT
ejpam-6378	142	5	.	.	PUNCT
ejpam-6378	143	1	(	(	PUNCT
ejpam-6378	143	2	15	15	NUM
ejpam-6378	143	3	)	)	PUNCT
ejpam-6378	143	4	implies	imply	VERB
ejpam-6378	143	5	l	l	NOUN
ejpam-6378	143	6	[	[	PUNCT
ejpam-6378	143	7	cdα	cdα	NOUN
ejpam-6378	143	8	θ	θ	NOUN
ejpam-6378	143	9	χ(θ	χ(θ	PROPN
ejpam-6378	143	10	)	)	PUNCT
ejpam-6378	143	11	]	]	PUNCT
ejpam-6378	144	1	=	=	PUNCT
ejpam-6378	144	2	sαx(s)−	sαx(s)−	PROPN
ejpam-6378	144	3	sα−1χ(0	sα−1χ(0	PROPN
ejpam-6378	144	4	)	)	PUNCT
ejpam-6378	144	5	,	,	PUNCT
ejpam-6378	144	6	where	where	SCONJ
ejpam-6378	144	7	0	0	X
ejpam-6378	144	8	<	<	X
ejpam-6378	144	9	α	α	X
ejpam-6378	144	10	≤	≤	NUM
ejpam-6378	144	11	1	1	NUM
ejpam-6378	144	12	.	.	PUNCT
ejpam-6378	145	1	(	(	PUNCT
ejpam-6378	145	2	16	16	NUM
ejpam-6378	145	3	)	)	PUNCT
ejpam-6378	145	4	similarly	similarly	ADV
ejpam-6378	145	5	,	,	PUNCT
ejpam-6378	145	6	under	under	ADP
ejpam-6378	145	7	different	different	ADJ
ejpam-6378	145	8	transformations	transformation	NOUN
ejpam-6378	145	9	are	be	AUX
ejpam-6378	145	10	given	give	VERB
ejpam-6378	145	11	in	in	ADP
ejpam-6378	145	12	the	the	DET
ejpam-6378	145	13	equation	equation	NOUN
ejpam-6378	145	14	(	(	PUNCT
ejpam-6378	145	15	17).	17).	NUM
ejpam-6378	145	16	l	l	NOUN
ejpam-6378	145	17	[	[	PUNCT
ejpam-6378	145	18	cdα	cdα	NOUN
ejpam-6378	145	19	θ	θ	NOUN
ejpam-6378	145	20	χ(θ	χ(θ	PROPN
ejpam-6378	145	21	)	)	PUNCT
ejpam-6378	145	22	]	]	PUNCT
ejpam-6378	146	1	=	=	PUNCT
ejpam-6378	146	2	sαx(s)−	sαx(s)−	PROPN
ejpam-6378	146	3	sα−1χ(0	sα−1χ(0	PROPN
ejpam-6378	146	4	)	)	PUNCT
ejpam-6378	146	5	.	.	PUNCT
ejpam-6378	147	1	e	e	X
ejpam-6378	147	2	[	[	PUNCT
ejpam-6378	147	3	cdα	cdα	NOUN
ejpam-6378	147	4	θ	θ	NOUN
ejpam-6378	147	5	χ(θ	χ(θ	PROPN
ejpam-6378	147	6	)	)	PUNCT
ejpam-6378	147	7	]	]	PUNCT
ejpam-6378	147	8	=	=	PUNCT
ejpam-6378	147	9	s−αx(s)−	s−αx(s)−	VERB
ejpam-6378	147	10	s2−αχ(0	s2−αχ(0	NUM
ejpam-6378	147	11	)	)	PUNCT
ejpam-6378	147	12	.	.	PUNCT
ejpam-6378	148	1	a	a	DET
ejpam-6378	148	2	[	[	PUNCT
ejpam-6378	148	3	cdα	cdα	NOUN
ejpam-6378	148	4	θ	θ	NOUN
ejpam-6378	148	5	χ(θ	χ(θ	PROPN
ejpam-6378	148	6	)	)	PUNCT
ejpam-6378	148	7	]	]	PUNCT
ejpam-6378	149	1	=	=	PUNCT
ejpam-6378	149	2	sαx(s)−	sαx(s)−	PROPN
ejpam-6378	149	3	sα−2χ(0	sα−2χ(0	PROPN
ejpam-6378	149	4	)	)	PUNCT
ejpam-6378	149	5	.	.	PUNCT
ejpam-6378	150	1	s	s	X
ejpam-6378	150	2	[	[	PUNCT
ejpam-6378	150	3	cdα	cdα	NOUN
ejpam-6378	150	4	θ	θ	NOUN
ejpam-6378	150	5	χ(θ	χ(θ	PROPN
ejpam-6378	150	6	)	)	PUNCT
ejpam-6378	150	7	]	]	PUNCT
ejpam-6378	151	1	=	=	VERB
ejpam-6378	151	2	s−αx(s)−	s−αx(s)−	VERB
ejpam-6378	151	3	s−αχ(0	s−αχ(0	PROPN
ejpam-6378	151	4	)	)	PUNCT
ejpam-6378	151	5	.	.	PUNCT
ejpam-6378	152	1	x	x	PUNCT
ejpam-6378	152	2	[	[	PUNCT
ejpam-6378	152	3	cdα	cdα	NOUN
ejpam-6378	152	4	θ	θ	NOUN
ejpam-6378	152	5	χ(θ	χ(θ	PROPN
ejpam-6378	152	6	)	)	PUNCT
ejpam-6378	152	7	]	]	PUNCT
ejpam-6378	153	1	=	=	PUNCT
ejpam-6378	153	2	s−αx(s)−	s−αx(s)−	VERB
ejpam-6378	153	3	s1−αχ(0	s1−αχ(0	ADJ
ejpam-6378	153	4	)	)	PUNCT
ejpam-6378	153	5	.	.	PUNCT
ejpam-6378	154	1	m	m	PROPN
ejpam-6378	154	2	[	[	X
ejpam-6378	154	3	cdα	cdα	NOUN
ejpam-6378	154	4	θ	θ	PROPN
ejpam-6378	154	5	χ(θ	χ(θ	PROPN
ejpam-6378	154	6	)	)	PUNCT
ejpam-6378	154	7	]	]	PUNCT
ejpam-6378	155	1	=	=	PUNCT
ejpam-6378	155	2	sαx(s)−	sαx(s)−	PROPN
ejpam-6378	155	3	sα+1χ(0	sα+1χ(0	PROPN
ejpam-6378	155	4	)	)	PUNCT
ejpam-6378	155	5	.	.	PUNCT
ejpam-6378	156	1	n	n	CCONJ
ejpam-6378	156	2	[	[	PUNCT
ejpam-6378	156	3	cdα	cdα	NOUN
ejpam-6378	156	4	θ	θ	PROPN
ejpam-6378	156	5	χ(θ	χ(θ	PROPN
ejpam-6378	156	6	)	)	PUNCT
ejpam-6378	156	7	]	]	PUNCT
ejpam-6378	157	1	=	=	PUNCT
ejpam-6378	157	2	(	(	PUNCT
ejpam-6378	157	3	s	s	AUX
ejpam-6378	157	4	ς	ς	PROPN
ejpam-6378	157	5	)	)	PUNCT
ejpam-6378	157	6	α	α	PROPN
ejpam-6378	157	7	x(s	x(s	PROPN
ejpam-6378	157	8	,	,	PUNCT
ejpam-6378	157	9	ς)−	ς)−	PROPN
ejpam-6378	157	10	(	(	PUNCT
ejpam-6378	157	11	s	s	PROPN
ejpam-6378	157	12	ς	ς	PROPN
ejpam-6378	157	13	)	)	PUNCT
ejpam-6378	157	14	α	α	PROPN
ejpam-6378	157	15	1	1	NUM
ejpam-6378	157	16	s	s	NOUN
ejpam-6378	157	17	χ(0	χ(0	NOUN
ejpam-6378	157	18	)	)	PUNCT
ejpam-6378	157	19	.	.	PUNCT
ejpam-6378	158	1	s	s	X
ejpam-6378	158	2	[	[	PUNCT
ejpam-6378	158	3	cdα	cdα	NOUN
ejpam-6378	158	4	θ	θ	NOUN
ejpam-6378	158	5	χ(θ	χ(θ	PROPN
ejpam-6378	158	6	)	)	PUNCT
ejpam-6378	158	7	]	]	PUNCT
ejpam-6378	159	1	=	=	PUNCT
ejpam-6378	159	2	(	(	PUNCT
ejpam-6378	159	3	s	s	PROPN
ejpam-6378	159	4	ς	ς	PROPN
ejpam-6378	159	5	)	)	PUNCT
ejpam-6378	159	6	α	α	PROPN
ejpam-6378	159	7	x(s	x(s	PROPN
ejpam-6378	159	8	,	,	PUNCT
ejpam-6378	159	9	ς)−	ς)−	PROPN
ejpam-6378	159	10	(	(	PUNCT
ejpam-6378	159	11	s	s	PROPN
ejpam-6378	159	12	ς	ς	PROPN
ejpam-6378	159	13	)	)	PUNCT
ejpam-6378	159	14	α−1	α−1	PROPN
ejpam-6378	159	15	χ(0	χ(0	PROPN
ejpam-6378	159	16	)	)	PUNCT
ejpam-6378	159	17	.	.	PUNCT
ejpam-6378	160	1	(	(	PUNCT
ejpam-6378	160	2	17	17	NUM
ejpam-6378	160	3	)	)	PUNCT
ejpam-6378	160	4	m.	m.	NOUN
ejpam-6378	160	5	sohail	sohail	PROPN
ejpam-6378	160	6	et	et	PROPN
ejpam-6378	160	7	al	al	PROPN
ejpam-6378	160	8	.	.	PUNCT
ejpam-6378	160	9	/	/	SYM
ejpam-6378	160	10	eur	eur	PROPN
ejpam-6378	160	11	.	.	PUNCT
ejpam-6378	161	1	j.	j.	PROPN
ejpam-6378	161	2	pure	pure	PROPN
ejpam-6378	161	3	appl	appl	PROPN
ejpam-6378	161	4	.	.	PROPN
ejpam-6378	161	5	math	math	PROPN
ejpam-6378	161	6	,	,	PUNCT
ejpam-6378	161	7	18	18	NUM
ejpam-6378	161	8	(	(	PUNCT
ejpam-6378	161	9	4	4	NUM
ejpam-6378	161	10	)	)	PUNCT
ejpam-6378	161	11	(	(	PUNCT
ejpam-6378	161	12	2025	2025	NUM
ejpam-6378	161	13	)	)	PUNCT
ejpam-6378	161	14	,	,	PUNCT
ejpam-6378	161	15	6378	6378	NUM
ejpam-6378	161	16	6	6	NUM
ejpam-6378	161	17	of	of	ADP
ejpam-6378	161	18	20	20	NUM
ejpam-6378	161	19	definition	definition	NOUN
ejpam-6378	161	20	12	12	NUM
ejpam-6378	161	21	.	.	PUNCT
ejpam-6378	162	1	the	the	DET
ejpam-6378	162	2	cffd	cffd	NOUN
ejpam-6378	163	1	[	[	X
ejpam-6378	163	2	37	37	NUM
ejpam-6378	163	3	]	]	PUNCT
ejpam-6378	163	4	is	be	AUX
ejpam-6378	163	5	defined	define	VERB
ejpam-6378	163	6	as	as	ADP
ejpam-6378	163	7	:	:	PUNCT
ejpam-6378	163	8	cfdα	cfdα	NOUN
ejpam-6378	163	9	θ	θ	NOUN
ejpam-6378	163	10	χ(θ	χ(θ	NOUN
ejpam-6378	163	11	)	)	PUNCT
ejpam-6378	163	12	=	=	SYM
ejpam-6378	163	13	n(α	n(α	PROPN
ejpam-6378	163	14	)	)	PUNCT
ejpam-6378	163	15	1−	1−	NUM
ejpam-6378	164	1	α	α	NUM
ejpam-6378	164	2	∫	∫	PROPN
ejpam-6378	164	3	θ	θ	NOUN
ejpam-6378	164	4	0	0	NUM
ejpam-6378	165	1	e−	e−	PROPN
ejpam-6378	165	2	α	α	PROPN
ejpam-6378	165	3	1−α	1−α	NUM
ejpam-6378	165	4	(	(	PUNCT
ejpam-6378	165	5	θ−τ	θ−τ	NUM
ejpam-6378	165	6	)	)	PUNCT
ejpam-6378	165	7	∂	∂	NOUN
ejpam-6378	165	8	∂τ	∂τ	PROPN
ejpam-6378	165	9	χ(τ	χ(τ	NOUN
ejpam-6378	165	10	)	)	PUNCT
ejpam-6378	165	11	dτ	dτ	NOUN
ejpam-6378	165	12	,	,	PUNCT
ejpam-6378	165	13	(	(	PUNCT
ejpam-6378	165	14	18	18	NUM
ejpam-6378	165	15	)	)	PUNCT
ejpam-6378	165	16	where	where	SCONJ
ejpam-6378	165	17	n(0	n(0	NOUN
ejpam-6378	165	18	)	)	PUNCT
ejpam-6378	165	19	=	=	SYM
ejpam-6378	165	20	n(1	n(1	NOUN
ejpam-6378	165	21	)	)	PUNCT
ejpam-6378	165	22	=	=	SYM
ejpam-6378	166	1	1	1	X
ejpam-6378	166	2	.	.	PUNCT
ejpam-6378	166	3	taking	take	VERB
ejpam-6378	166	4	lt	lt	PRON
ejpam-6378	166	5	l[cfdα	l[cfdα	NOUN
ejpam-6378	166	6	θ	θ	NOUN
ejpam-6378	166	7	χ(θ	χ(θ	NOUN
ejpam-6378	166	8	)	)	PUNCT
ejpam-6378	166	9	]	]	PUNCT
ejpam-6378	167	1	=	=	X
ejpam-6378	167	2	l	l	X
ejpam-6378	167	3	[	[	PUNCT
ejpam-6378	167	4	n(α	n(α	PROPN
ejpam-6378	167	5	)	)	PUNCT
ejpam-6378	167	6	1−	1−	NUM
ejpam-6378	167	7	α	α	NOUN
ejpam-6378	167	8	(	(	PUNCT
ejpam-6378	167	9	e−	e−	PROPN
ejpam-6378	167	10	α	α	PROPN
ejpam-6378	167	11	1−α	1−α	NUM
ejpam-6378	167	12	θ	θ	PROPN
ejpam-6378	167	13	∗	∗	NOUN
ejpam-6378	167	14	∂	∂	NOUN
ejpam-6378	168	1	∂θ	∂θ	NOUN
ejpam-6378	168	2	χ	χ	X
ejpam-6378	168	3	(	(	PUNCT
ejpam-6378	168	4	θ	θ	NOUN
ejpam-6378	168	5	)	)	PUNCT
ejpam-6378	168	6	)	)	PUNCT
ejpam-6378	168	7	]	]	PUNCT
ejpam-6378	169	1	=	=	PUNCT
ejpam-6378	169	2	n(α	n(α	PROPN
ejpam-6378	169	3	)	)	PUNCT
ejpam-6378	169	4	1−	1−	NUM
ejpam-6378	169	5	α	α	INTJ
ejpam-6378	169	6	(	(	PUNCT
ejpam-6378	169	7	l	l	X
ejpam-6378	169	8	[	[	PUNCT
ejpam-6378	169	9	e−	e−	PROPN
ejpam-6378	169	10	α	α	PROPN
ejpam-6378	169	11	1−α	1−α	NUM
ejpam-6378	169	12	θ	θ	X
ejpam-6378	169	13	]	]	PUNCT
ejpam-6378	169	14	l	l	X
ejpam-6378	169	15	[	[	PUNCT
ejpam-6378	169	16	∂	∂	NOUN
ejpam-6378	169	17	∂θ	∂θ	PROPN
ejpam-6378	169	18	χ	χ	X
ejpam-6378	169	19	(	(	PUNCT
ejpam-6378	169	20	θ	θ	NOUN
ejpam-6378	169	21	)	)	PUNCT
ejpam-6378	169	22	]	]	PUNCT
ejpam-6378	169	23	)	)	PUNCT
ejpam-6378	169	24	=	=	SYM
ejpam-6378	169	25	n(α	n(α	PROPN
ejpam-6378	169	26	)	)	PUNCT
ejpam-6378	169	27	1−	1−	NUM
ejpam-6378	170	1	α	α	PRON
ejpam-6378	170	2	1	1	NUM
ejpam-6378	170	3	s−	s−	PROPN
ejpam-6378	170	4	(	(	PUNCT
ejpam-6378	170	5	−	−	PROPN
ejpam-6378	170	6	α	α	PROPN
ejpam-6378	170	7	1−α	1−α	NUM
ejpam-6378	170	8	)	)	PUNCT
ejpam-6378	170	9	(	(	PUNCT
ejpam-6378	170	10	sx(s)−	sx(s)−	PROPN
ejpam-6378	170	11	χ(0	χ(0	PROPN
ejpam-6378	170	12	)	)	PUNCT
ejpam-6378	170	13	)	)	PUNCT
ejpam-6378	171	1	=	=	SYM
ejpam-6378	171	2	n(α	n(α	PROPN
ejpam-6378	171	3	)	)	PUNCT
ejpam-6378	171	4	(	(	PUNCT
ejpam-6378	171	5	1−	1−	NUM
ejpam-6378	171	6	α)(s+	α)(s+	VERB
ejpam-6378	171	7	α	α	NOUN
ejpam-6378	171	8	1−α	1−α	NUM
ejpam-6378	171	9	)	)	PUNCT
ejpam-6378	171	10	(	(	PUNCT
ejpam-6378	171	11	sx(s)−	sx(s)−	PROPN
ejpam-6378	171	12	χ(0	χ(0	PROPN
ejpam-6378	171	13	)	)	PUNCT
ejpam-6378	171	14	)	)	PUNCT
ejpam-6378	171	15	,	,	PUNCT
ejpam-6378	171	16	(	(	PUNCT
ejpam-6378	171	17	19	19	NUM
ejpam-6378	171	18	)	)	PUNCT
ejpam-6378	171	19	implies	imply	VERB
ejpam-6378	171	20	l	l	NOUN
ejpam-6378	171	21	[	[	PUNCT
ejpam-6378	171	22	cfdα	cfdα	NOUN
ejpam-6378	171	23	θ	θ	NOUN
ejpam-6378	171	24	χ(θ	χ(θ	NOUN
ejpam-6378	171	25	)	)	PUNCT
ejpam-6378	171	26	]	]	PUNCT
ejpam-6378	172	1	=	=	PUNCT
ejpam-6378	172	2	n(α	n(α	PROPN
ejpam-6378	172	3	)	)	PUNCT
ejpam-6378	172	4	(	(	PUNCT
ejpam-6378	172	5	1−	1−	NUM
ejpam-6378	172	6	α)s+	α)s+	NUM
ejpam-6378	172	7	α	α	NOUN
ejpam-6378	172	8	(	(	PUNCT
ejpam-6378	172	9	sx(s)−	sx(s)−	PROPN
ejpam-6378	172	10	χ(0	χ(0	PROPN
ejpam-6378	172	11	)	)	PUNCT
ejpam-6378	172	12	)	)	PUNCT
ejpam-6378	172	13	.	.	PUNCT
ejpam-6378	173	1	(	(	PUNCT
ejpam-6378	173	2	20	20	NUM
ejpam-6378	173	3	)	)	PUNCT
ejpam-6378	173	4	similarly	similarly	ADV
ejpam-6378	173	5	,	,	PUNCT
ejpam-6378	173	6	under	under	ADP
ejpam-6378	173	7	different	different	ADJ
ejpam-6378	173	8	transformations	transformation	NOUN
ejpam-6378	173	9	in	in	ADP
ejpam-6378	173	10	equation	equation	NOUN
ejpam-6378	173	11	(	(	PUNCT
ejpam-6378	173	12	21)	21)	NUM
ejpam-6378	173	13	l	l	NOUN
ejpam-6378	173	14	[	[	PUNCT
ejpam-6378	173	15	cfdα	cfdα	NOUN
ejpam-6378	173	16	θ	θ	NOUN
ejpam-6378	173	17	χ(θ	χ(θ	NOUN
ejpam-6378	173	18	)	)	PUNCT
ejpam-6378	173	19	]	]	PUNCT
ejpam-6378	173	20	=	=	PUNCT
ejpam-6378	173	21	n(α	n(α	PROPN
ejpam-6378	173	22	)	)	PUNCT
ejpam-6378	173	23	s(1−α)+α(sx	s(1−α)+α(sx	NOUN
ejpam-6378	173	24	(	(	PUNCT
ejpam-6378	173	25	s)−	s)−	PROPN
ejpam-6378	173	26	χ	χ	X
ejpam-6378	173	27	(	(	PUNCT
ejpam-6378	173	28	0	0	NUM
ejpam-6378	173	29	)	)	PUNCT
ejpam-6378	173	30	)	)	PUNCT
ejpam-6378	173	31	.	.	PUNCT
ejpam-6378	174	1	e	e	X
ejpam-6378	174	2	[	[	PUNCT
ejpam-6378	174	3	cfdα	cfdα	NOUN
ejpam-6378	174	4	θ	θ	NOUN
ejpam-6378	174	5	χ(θ	χ(θ	NOUN
ejpam-6378	174	6	)	)	PUNCT
ejpam-6378	174	7	]	]	PUNCT
ejpam-6378	174	8	=	=	PUNCT
ejpam-6378	174	9	n(α	n(α	PROPN
ejpam-6378	174	10	)	)	PUNCT
ejpam-6378	175	1	1+α(s−1	1+α(s−1	NUM
ejpam-6378	175	2	)	)	PUNCT
ejpam-6378	175	3	(	(	PUNCT
ejpam-6378	175	4	x	x	X
ejpam-6378	175	5	(	(	PUNCT
ejpam-6378	175	6	s)−	s)−	PROPN
ejpam-6378	175	7	s2	s2	PROPN
ejpam-6378	175	8	χ	χ	X
ejpam-6378	175	9	(	(	PUNCT
ejpam-6378	175	10	0	0	NUM
ejpam-6378	175	11	)	)	PUNCT
ejpam-6378	175	12	)	)	PUNCT
ejpam-6378	175	13	.	.	PUNCT
ejpam-6378	176	1	a	a	DET
ejpam-6378	176	2	[	[	PUNCT
ejpam-6378	176	3	cfdα	cfdα	NOUN
ejpam-6378	176	4	θ	θ	NOUN
ejpam-6378	176	5	χ(θ	χ(θ	NOUN
ejpam-6378	176	6	)	)	PUNCT
ejpam-6378	176	7	]	]	PUNCT
ejpam-6378	177	1	=	=	PUNCT
ejpam-6378	177	2	n(α	n(α	PROPN
ejpam-6378	177	3	)	)	PUNCT
ejpam-6378	177	4	s2(1−α)+αs	s2(1−α)+αs	VERB
ejpam-6378	177	5	(	(	PUNCT
ejpam-6378	177	6	s2x	s2x	PROPN
ejpam-6378	177	7	(	(	PUNCT
ejpam-6378	177	8	s)−	s)−	PROPN
ejpam-6378	177	9	χ	χ	X
ejpam-6378	177	10	(	(	PUNCT
ejpam-6378	177	11	0	0	NUM
ejpam-6378	177	12	)	)	PUNCT
ejpam-6378	177	13	)	)	PUNCT
ejpam-6378	177	14	.	.	PUNCT
ejpam-6378	178	1	s	s	X
ejpam-6378	178	2	[	[	PUNCT
ejpam-6378	178	3	cfdα	cfdα	NOUN
ejpam-6378	178	4	θ	θ	NOUN
ejpam-6378	178	5	χ(θ	χ(θ	NOUN
ejpam-6378	178	6	)	)	PUNCT
ejpam-6378	178	7	]	]	PUNCT
ejpam-6378	179	1	=	=	PUNCT
ejpam-6378	179	2	n(α	n(α	PROPN
ejpam-6378	179	3	)	)	PUNCT
ejpam-6378	180	1	1+α(s−1	1+α(s−1	NUM
ejpam-6378	180	2	)	)	PUNCT
ejpam-6378	180	3	(	(	PUNCT
ejpam-6378	180	4	x	x	X
ejpam-6378	180	5	(	(	PUNCT
ejpam-6378	180	6	s)−	s)−	PROPN
ejpam-6378	180	7	χ	χ	X
ejpam-6378	180	8	(	(	PUNCT
ejpam-6378	180	9	0	0	NUM
ejpam-6378	180	10	)	)	PUNCT
ejpam-6378	180	11	)	)	PUNCT
ejpam-6378	180	12	.	.	PUNCT
ejpam-6378	181	1	x	x	PUNCT
ejpam-6378	181	2	[	[	PUNCT
ejpam-6378	181	3	cfdα	cfdα	NOUN
ejpam-6378	181	4	θ	θ	NOUN
ejpam-6378	181	5	χ(θ	χ(θ	NOUN
ejpam-6378	181	6	)	)	PUNCT
ejpam-6378	181	7	]	]	PUNCT
ejpam-6378	181	8	=	=	PUNCT
ejpam-6378	181	9	n(α	n(α	PROPN
ejpam-6378	181	10	)	)	PUNCT
ejpam-6378	181	11	1+α(s−1)(x	1+α(s−1)(x	NUM
ejpam-6378	181	12	(	(	PUNCT
ejpam-6378	181	13	s)−	s)−	PROPN
ejpam-6378	181	14	s	s	PART
ejpam-6378	181	15	χ	χ	X
ejpam-6378	181	16	(	(	PUNCT
ejpam-6378	181	17	0	0	NUM
ejpam-6378	181	18	)	)	PUNCT
ejpam-6378	181	19	)	)	PUNCT
ejpam-6378	181	20	.	.	PUNCT
ejpam-6378	182	1	m	m	PUNCT
ejpam-6378	183	1	[	[	PUNCT
ejpam-6378	183	2	cfdα	cfdα	NOUN
ejpam-6378	183	3	θ	θ	NOUN
ejpam-6378	183	4	χ(θ	χ(θ	NOUN
ejpam-6378	183	5	)	)	PUNCT
ejpam-6378	183	6	]	]	PUNCT
ejpam-6378	184	1	=	=	PUNCT
ejpam-6378	184	2	n(α	n(α	PROPN
ejpam-6378	184	3	)	)	PUNCT
ejpam-6378	184	4	s(1−α)+α(sx	s(1−α)+α(sx	NOUN
ejpam-6378	184	5	(	(	PUNCT
ejpam-6378	184	6	s)−	s)−	PROPN
ejpam-6378	184	7	s2	s2	PROPN
ejpam-6378	184	8	χ	χ	X
ejpam-6378	184	9	(	(	PUNCT
ejpam-6378	184	10	0	0	NUM
ejpam-6378	184	11	)	)	PUNCT
ejpam-6378	184	12	)	)	PUNCT
ejpam-6378	184	13	.	.	PUNCT
ejpam-6378	185	1	n	n	CCONJ
ejpam-6378	185	2	[	[	PUNCT
ejpam-6378	185	3	cfdα	cfdα	NOUN
ejpam-6378	185	4	θ	θ	NOUN
ejpam-6378	185	5	χ(θ	χ(θ	NOUN
ejpam-6378	185	6	)	)	PUNCT
ejpam-6378	185	7	]	]	PUNCT
ejpam-6378	186	1	=	=	PUNCT
ejpam-6378	186	2	n(α	n(α	PROPN
ejpam-6378	186	3	)	)	PUNCT
ejpam-6378	186	4	s	s	PART
ejpam-6378	186	5	ς	ς	PROPN
ejpam-6378	186	6	(	(	PUNCT
ejpam-6378	186	7	1−α)+α	1−α)+α	NUM
ejpam-6378	186	8	(	(	PUNCT
ejpam-6378	186	9	s	s	VERB
ejpam-6378	186	10	ςx	ςx	INTJ
ejpam-6378	186	11	(	(	PUNCT
ejpam-6378	186	12	s	s	PROPN
ejpam-6378	186	13	,	,	PUNCT
ejpam-6378	186	14	ς)−	ς)−	PROPN
ejpam-6378	186	15	χ(0	χ(0	PROPN
ejpam-6378	186	16	)	)	PUNCT
ejpam-6378	186	17	ς	ς	PROPN
ejpam-6378	186	18	)	)	PUNCT
ejpam-6378	186	19	.	.	PUNCT
ejpam-6378	187	1	s	s	X
ejpam-6378	187	2	[	[	PUNCT
ejpam-6378	187	3	cfdα	cfdα	NOUN
ejpam-6378	187	4	θ	θ	NOUN
ejpam-6378	187	5	χ(θ	χ(θ	NOUN
ejpam-6378	187	6	)	)	PUNCT
ejpam-6378	187	7	]	]	PUNCT
ejpam-6378	188	1	=	=	PUNCT
ejpam-6378	188	2	n(α	n(α	PROPN
ejpam-6378	188	3	)	)	PUNCT
ejpam-6378	188	4	s	s	PART
ejpam-6378	188	5	ς	ς	PROPN
ejpam-6378	188	6	(	(	PUNCT
ejpam-6378	188	7	1−α)+α	1−α)+α	NUM
ejpam-6378	188	8	(	(	PUNCT
ejpam-6378	188	9	s	s	VERB
ejpam-6378	188	10	ςx	ςx	INTJ
ejpam-6378	188	11	(	(	PUNCT
ejpam-6378	188	12	s	s	X
ejpam-6378	188	13	,	,	PUNCT
ejpam-6378	188	14	ς)−	ς)−	PROPN
ejpam-6378	188	15	χ	χ	X
ejpam-6378	188	16	(	(	PUNCT
ejpam-6378	188	17	0	0	NUM
ejpam-6378	188	18	)	)	PUNCT
ejpam-6378	188	19	)	)	PUNCT
ejpam-6378	188	20	.	.	PUNCT
ejpam-6378	189	1	(	(	PUNCT
ejpam-6378	189	2	21	21	NUM
ejpam-6378	189	3	)	)	PUNCT
ejpam-6378	189	4	definition	definition	NOUN
ejpam-6378	189	5	13	13	NUM
ejpam-6378	189	6	.	.	PUNCT
ejpam-6378	190	1	the	the	DET
ejpam-6378	190	2	abfd	abfd	PROPN
ejpam-6378	191	1	[	[	X
ejpam-6378	191	2	38	38	NUM
ejpam-6378	191	3	]	]	PUNCT
ejpam-6378	191	4	defined	define	VERB
ejpam-6378	191	5	as	as	ADP
ejpam-6378	191	6	:	:	PUNCT
ejpam-6378	191	7	abdα	abdα	NOUN
ejpam-6378	191	8	θ	θ	NOUN
ejpam-6378	191	9	χ(θ	χ(θ	PROPN
ejpam-6378	191	10	)	)	PUNCT
ejpam-6378	191	11	=	=	PUNCT
ejpam-6378	191	12	ab(α	ab(α	NUM
ejpam-6378	191	13	)	)	PUNCT
ejpam-6378	191	14	1−	1−	NUM
ejpam-6378	192	1	α	α	NUM
ejpam-6378	192	2	∫	∫	NOUN
ejpam-6378	192	3	θ	θ	NOUN
ejpam-6378	192	4	0	0	PUNCT
ejpam-6378	193	1	eα	eα	NOUN
ejpam-6378	193	2	(	(	PUNCT
ejpam-6378	193	3	−	−	PROPN
ejpam-6378	193	4	α	α	NOUN
ejpam-6378	193	5	1−	1−	NUM
ejpam-6378	193	6	α	α	NOUN
ejpam-6378	193	7	(	(	PUNCT
ejpam-6378	193	8	θ	θ	NOUN
ejpam-6378	193	9	−	−	NOUN
ejpam-6378	193	10	τ)α	τ)α	PUNCT
ejpam-6378	193	11	)	)	PUNCT
ejpam-6378	193	12	∂	∂	NUM
ejpam-6378	193	13	∂τ	∂τ	PROPN
ejpam-6378	193	14	χ(τ	χ(τ	NOUN
ejpam-6378	193	15	)	)	PUNCT
ejpam-6378	193	16	dτ	dτ	NOUN
ejpam-6378	193	17	,	,	PUNCT
ejpam-6378	193	18	(	(	PUNCT
ejpam-6378	193	19	22	22	NUM
ejpam-6378	193	20	)	)	PUNCT
ejpam-6378	193	21	where	where	SCONJ
ejpam-6378	193	22	ab(0	ab(0	NOUN
ejpam-6378	193	23	)	)	PUNCT
ejpam-6378	193	24	=	=	SYM
ejpam-6378	193	25	ab(1	ab(1	PROPN
ejpam-6378	193	26	)	)	PUNCT
ejpam-6378	193	27	=	=	SYM
ejpam-6378	193	28	1	1	NUM
ejpam-6378	193	29	and	and	CCONJ
ejpam-6378	193	30	eα	eα	PROPN
ejpam-6378	193	31	(	(	PUNCT
ejpam-6378	193	32	·	·	PUNCT
ejpam-6378	193	33	)	)	PUNCT
ejpam-6378	193	34	denoted	denote	VERB
ejpam-6378	193	35	the	the	DET
ejpam-6378	193	36	mittag	mittag	ADJ
ejpam-6378	193	37	-	-	PUNCT
ejpam-6378	193	38	leffler	leffler	NOUN
ejpam-6378	193	39	function	function	NOUN
ejpam-6378	193	40	[	[	X
ejpam-6378	193	41	47	47	NUM
ejpam-6378	193	42	]	]	PUNCT
ejpam-6378	193	43	i.e.	i.e.	X
ejpam-6378	193	44	eα(θ	eα(θ	NOUN
ejpam-6378	193	45	)	)	PUNCT
ejpam-6378	193	46	=	=	SYM
ejpam-6378	193	47	eα,1(θ	eα,1(θ	PROPN
ejpam-6378	193	48	)	)	PUNCT
ejpam-6378	193	49	=	=	PUNCT
ejpam-6378	194	1	∞∑	∞∑	PROPN
ejpam-6378	194	2	i=0	i=0	PROPN
ejpam-6378	194	3	θi	θi	NUM
ejpam-6378	194	4	γ(iα+	γ(iα+	NOUN
ejpam-6378	194	5	β	β	NOUN
ejpam-6378	194	6	)	)	PUNCT
ejpam-6378	194	7	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-6378	195	1	β=1	β=1	PUNCT
ejpam-6378	195	2	α	α	X
ejpam-6378	195	3	>	>	X
ejpam-6378	195	4	0	0	PROPN
ejpam-6378	195	5	.	.	PUNCT
ejpam-6378	196	1	(	(	PUNCT
ejpam-6378	196	2	23	23	NUM
ejpam-6378	196	3	)	)	PUNCT
ejpam-6378	196	4	m.	m.	NOUN
ejpam-6378	196	5	sohail	sohail	PROPN
ejpam-6378	196	6	et	et	PROPN
ejpam-6378	196	7	al	al	PROPN
ejpam-6378	196	8	.	.	PUNCT
ejpam-6378	196	9	/	/	SYM
ejpam-6378	196	10	eur	eur	PROPN
ejpam-6378	196	11	.	.	PUNCT
ejpam-6378	197	1	j.	j.	PROPN
ejpam-6378	197	2	pure	pure	PROPN
ejpam-6378	197	3	appl	appl	PROPN
ejpam-6378	197	4	.	.	PROPN
ejpam-6378	197	5	math	math	PROPN
ejpam-6378	197	6	,	,	PUNCT
ejpam-6378	197	7	18	18	NUM
ejpam-6378	197	8	(	(	PUNCT
ejpam-6378	197	9	4	4	NUM
ejpam-6378	197	10	)	)	PUNCT
ejpam-6378	197	11	(	(	PUNCT
ejpam-6378	197	12	2025	2025	NUM
ejpam-6378	197	13	)	)	PUNCT
ejpam-6378	197	14	,	,	PUNCT
ejpam-6378	197	15	6378	6378	NUM
ejpam-6378	197	16	7	7	NUM
ejpam-6378	197	17	of	of	ADP
ejpam-6378	197	18	20	20	NUM
ejpam-6378	197	19	taking	take	VERB
ejpam-6378	197	20	lt	lt	PRON
ejpam-6378	197	21	l[abdα	l[abdα	NOUN
ejpam-6378	197	22	θ	θ	NOUN
ejpam-6378	197	23	χ(θ	χ(θ	NOUN
ejpam-6378	197	24	)	)	PUNCT
ejpam-6378	197	25	]	]	PUNCT
ejpam-6378	198	1	=	=	X
ejpam-6378	198	2	l	l	X
ejpam-6378	198	3	[	[	PUNCT
ejpam-6378	198	4	ab(α	ab(α	NUM
ejpam-6378	198	5	)	)	PUNCT
ejpam-6378	198	6	1−	1−	NUM
ejpam-6378	198	7	α	α	NOUN
ejpam-6378	198	8	(	(	PUNCT
ejpam-6378	198	9	eα	eα	PROPN
ejpam-6378	198	10	(	(	PUNCT
ejpam-6378	198	11	−	−	PROPN
ejpam-6378	198	12	α	α	NOUN
ejpam-6378	198	13	1−	1−	NUM
ejpam-6378	198	14	α	α	NOUN
ejpam-6378	198	15	θα	θα	NOUN
ejpam-6378	198	16	)	)	PUNCT
ejpam-6378	198	17	∗	∗	NOUN
ejpam-6378	198	18	∂	∂	NUM
ejpam-6378	199	1	∂θ	∂θ	NOUN
ejpam-6378	199	2	χ	χ	X
ejpam-6378	199	3	(	(	PUNCT
ejpam-6378	199	4	θ	θ	NOUN
ejpam-6378	199	5	)	)	PUNCT
ejpam-6378	199	6	)	)	PUNCT
ejpam-6378	199	7	]	]	PUNCT
ejpam-6378	200	1	=	=	SYM
ejpam-6378	200	2	ab(α	ab(α	X
ejpam-6378	200	3	)	)	PUNCT
ejpam-6378	200	4	1−	1−	NUM
ejpam-6378	200	5	α	α	NOUN
ejpam-6378	200	6	(	(	PUNCT
ejpam-6378	200	7	l	l	X
ejpam-6378	200	8	[	[	PUNCT
ejpam-6378	200	9	eα	eα	X
ejpam-6378	200	10	(	(	PUNCT
ejpam-6378	200	11	−	−	PROPN
ejpam-6378	200	12	α	α	NOUN
ejpam-6378	200	13	1−	1−	NUM
ejpam-6378	200	14	α	α	NOUN
ejpam-6378	200	15	θα	θα	NOUN
ejpam-6378	200	16	)	)	PUNCT
ejpam-6378	200	17	]	]	PUNCT
ejpam-6378	200	18	l	l	NOUN
ejpam-6378	200	19	[	[	PUNCT
ejpam-6378	200	20	∂	∂	NOUN
ejpam-6378	200	21	∂θ	∂θ	PROPN
ejpam-6378	200	22	χ	χ	X
ejpam-6378	200	23	(	(	PUNCT
ejpam-6378	200	24	θ	θ	NOUN
ejpam-6378	200	25	)	)	PUNCT
ejpam-6378	200	26	]	]	PUNCT
ejpam-6378	200	27	)	)	PUNCT
ejpam-6378	200	28	=	=	SYM
ejpam-6378	200	29	ab(α	ab(α	NUM
ejpam-6378	200	30	)	)	PUNCT
ejpam-6378	200	31	1−	1−	NUM
ejpam-6378	201	1	α	α	X
ejpam-6378	201	2			PROPN
ejpam-6378	201	3	sα−1	sα−1	NOUN
ejpam-6378	201	4	sα	sα	ADV
ejpam-6378	201	5	−	−	PROPN
ejpam-6378	202	1	(	(	PUNCT
ejpam-6378	202	2	−	−	PROPN
ejpam-6378	202	3	α	α	PROPN
ejpam-6378	202	4	1−α	1−α	NUM
ejpam-6378	202	5	)	)	PUNCT
ejpam-6378	202	6	(	(	PUNCT
ejpam-6378	202	7	sx(s)−	sx(s)−	PROPN
ejpam-6378	202	8	χ(0	χ(0	PROPN
ejpam-6378	202	9	)	)	PUNCT
ejpam-6378	202	10	)	)	PUNCT
ejpam-6378	203	1			PROPN
ejpam-6378	203	2	=	=	SYM
ejpam-6378	203	3	sα−1ab(α	sα−1ab(α	PROPN
ejpam-6378	203	4	)	)	PUNCT
ejpam-6378	203	5	sα(1−	sα(1−	PROPN
ejpam-6378	203	6	α	α	NOUN
ejpam-6378	203	7	)	)	PUNCT
ejpam-6378	204	1	+	+	CCONJ
ejpam-6378	204	2	α	α	PROPN
ejpam-6378	204	3	(	(	PUNCT
ejpam-6378	204	4	sx(s)−	sx(s)−	PROPN
ejpam-6378	204	5	χ(0	χ(0	PROPN
ejpam-6378	204	6	)	)	PUNCT
ejpam-6378	204	7	)	)	PUNCT
ejpam-6378	204	8	,	,	PUNCT
ejpam-6378	204	9	(	(	PUNCT
ejpam-6378	204	10	24	24	NUM
ejpam-6378	204	11	)	)	PUNCT
ejpam-6378	204	12	implies	imply	VERB
ejpam-6378	204	13	l[abdα	l[abdα	PROPN
ejpam-6378	204	14	θ	θ	NOUN
ejpam-6378	204	15	χ(θ	χ(θ	PROPN
ejpam-6378	204	16	)	)	PUNCT
ejpam-6378	204	17	]	]	PUNCT
ejpam-6378	205	1	=	=	SYM
ejpam-6378	205	2	sα−1ab(α	sα−1ab(α	X
ejpam-6378	205	3	)	)	PUNCT
ejpam-6378	205	4	sα(1−	sα(1−	PROPN
ejpam-6378	205	5	α	α	NOUN
ejpam-6378	205	6	)	)	PUNCT
ejpam-6378	205	7	+	+	CCONJ
ejpam-6378	205	8	α	α	PROPN
ejpam-6378	205	9	(	(	PUNCT
ejpam-6378	205	10	sx(s)−	sx(s)−	PROPN
ejpam-6378	205	11	χ(0	χ(0	PROPN
ejpam-6378	205	12	)	)	PUNCT
ejpam-6378	205	13	)	)	PUNCT
ejpam-6378	205	14	.	.	PUNCT
ejpam-6378	206	1	(	(	PUNCT
ejpam-6378	206	2	25	25	NUM
ejpam-6378	206	3	)	)	PUNCT
ejpam-6378	206	4	similarly	similarly	ADV
ejpam-6378	206	5	,	,	PUNCT
ejpam-6378	206	6	the	the	DET
ejpam-6378	206	7	equation	equation	NOUN
ejpam-6378	206	8	(	(	PUNCT
ejpam-6378	206	9	26	26	NUM
ejpam-6378	206	10	)	)	PUNCT
ejpam-6378	206	11	for	for	ADP
ejpam-6378	206	12	different	different	ADJ
ejpam-6378	206	13	transformations.	transformations.	PROPN
ejpam-6378	206	14	l[abdα	l[abdα	NOUN
ejpam-6378	206	15	θ	θ	X
ejpam-6378	206	16	χ(θ	χ(θ	PROPN
ejpam-6378	206	17	)	)	PUNCT
ejpam-6378	206	18	]	]	PUNCT
ejpam-6378	207	1	=	=	SYM
ejpam-6378	207	2	sα−1ab(α	sα−1ab(α	PROPN
ejpam-6378	207	3	)	)	PUNCT
ejpam-6378	207	4	(	(	PUNCT
ejpam-6378	207	5	1−α	1−α	NUM
ejpam-6378	207	6	)	)	PUNCT
ejpam-6378	207	7	(	(	PUNCT
ejpam-6378	207	8	α	α	PROPN
ejpam-6378	207	9	1−α	1−α	NUM
ejpam-6378	208	1	+	+	ADJ
ejpam-6378	208	2	sα	sα	X
ejpam-6378	208	3	)	)	PUNCT
ejpam-6378	208	4	(	(	PUNCT
ejpam-6378	208	5	sx	sx	PROPN
ejpam-6378	208	6	(	(	PUNCT
ejpam-6378	208	7	s)−	s)−	PROPN
ejpam-6378	208	8	χ	χ	X
ejpam-6378	208	9	(	(	PUNCT
ejpam-6378	208	10	0	0	NUM
ejpam-6378	208	11	)	)	PUNCT
ejpam-6378	208	12	)	)	PUNCT
ejpam-6378	208	13	.	.	PUNCT
ejpam-6378	209	1	e[abdα	e[abdα	NUM
ejpam-6378	209	2	θ	θ	NOUN
ejpam-6378	209	3	χ(θ	χ(θ	NOUN
ejpam-6378	209	4	)	)	PUNCT
ejpam-6378	209	5	]	]	PUNCT
ejpam-6378	210	1	=	=	PUNCT
ejpam-6378	210	2	s	s	X
ejpam-6378	210	3	ab(α	ab(α	NUM
ejpam-6378	210	4	)	)	PUNCT
ejpam-6378	210	5	(	(	PUNCT
ejpam-6378	210	6	1−α	1−α	NUM
ejpam-6378	210	7	)	)	PUNCT
ejpam-6378	210	8	(	(	PUNCT
ejpam-6378	210	9	α	α	PROPN
ejpam-6378	210	10	1−α	1−α	NUM
ejpam-6378	210	11	sα+1	sα+1	NOUN
ejpam-6378	210	12	)	)	PUNCT
ejpam-6378	210	13	(	(	PUNCT
ejpam-6378	210	14	x(s	x(s	PROPN
ejpam-6378	210	15	)	)	PUNCT
ejpam-6378	210	16	s	s	VERB
ejpam-6378	210	17	−	−	PROPN
ejpam-6378	210	18	s	s	PART
ejpam-6378	210	19	χ	χ	X
ejpam-6378	210	20	(	(	PUNCT
ejpam-6378	210	21	0	0	NUM
ejpam-6378	210	22	)	)	PUNCT
ejpam-6378	210	23	)	)	PUNCT
ejpam-6378	210	24	.	.	PUNCT
ejpam-6378	211	1	a[abdα	a[abdα	PROPN
ejpam-6378	212	1	θ	θ	PROPN
ejpam-6378	212	2	χ(θ	χ(θ	PROPN
ejpam-6378	212	3	)	)	PUNCT
ejpam-6378	212	4	]	]	PUNCT
ejpam-6378	213	1	=	=	SYM
ejpam-6378	213	2	sα−1ab(α	sα−1ab(α	PROPN
ejpam-6378	213	3	)	)	PUNCT
ejpam-6378	213	4	(	(	PUNCT
ejpam-6378	213	5	1−α	1−α	NUM
ejpam-6378	213	6	)	)	PUNCT
ejpam-6378	213	7	(	(	PUNCT
ejpam-6378	213	8	α	α	PROPN
ejpam-6378	213	9	1−α	1−α	NUM
ejpam-6378	214	1	+	+	ADJ
ejpam-6378	214	2	sα	sα	X
ejpam-6378	214	3	)	)	PUNCT
ejpam-6378	214	4	(	(	PUNCT
ejpam-6378	214	5	sx	sx	PROPN
ejpam-6378	214	6	(	(	PUNCT
ejpam-6378	214	7	s)−	s)−	PROPN
ejpam-6378	214	8	χ(0	χ(0	PROPN
ejpam-6378	214	9	)	)	PUNCT
ejpam-6378	214	10	s	s	PART
ejpam-6378	214	11	)	)	PUNCT
ejpam-6378	214	12	.	.	PUNCT
ejpam-6378	215	1	s[abdα	s[abdα	NUM
ejpam-6378	215	2	θ	θ	NOUN
ejpam-6378	215	3	χ(θ	χ(θ	NOUN
ejpam-6378	215	4	)	)	PUNCT
ejpam-6378	215	5	]	]	PUNCT
ejpam-6378	216	1	=	=	PUNCT
ejpam-6378	216	2	s	s	X
ejpam-6378	216	3	ab(α	ab(α	NUM
ejpam-6378	216	4	)	)	PUNCT
ejpam-6378	216	5	(	(	PUNCT
ejpam-6378	216	6	1−α	1−α	NUM
ejpam-6378	216	7	)	)	PUNCT
ejpam-6378	216	8	(	(	PUNCT
ejpam-6378	216	9	α	α	PROPN
ejpam-6378	216	10	1−α	1−α	NUM
ejpam-6378	216	11	sα+1	sα+1	NOUN
ejpam-6378	216	12	)	)	PUNCT
ejpam-6378	216	13	(	(	PUNCT
ejpam-6378	216	14	x(s	x(s	PROPN
ejpam-6378	216	15	)	)	PUNCT
ejpam-6378	216	16	s	s	PART
ejpam-6378	216	17	−	−	PROPN
ejpam-6378	216	18	χ(0	χ(0	PROPN
ejpam-6378	216	19	)	)	PUNCT
ejpam-6378	216	20	s	s	PART
ejpam-6378	216	21	)	)	PUNCT
ejpam-6378	216	22	.	.	PUNCT
ejpam-6378	217	1	x	x	PUNCT
ejpam-6378	218	1	[	[	X
ejpam-6378	218	2	abdα	abdα	NOUN
ejpam-6378	218	3	θ	θ	NOUN
ejpam-6378	218	4	χ(θ	χ(θ	NOUN
ejpam-6378	218	5	)	)	PUNCT
ejpam-6378	218	6	]	]	PUNCT
ejpam-6378	219	1	=	=	PUNCT
ejpam-6378	219	2	s	s	X
ejpam-6378	219	3	ab(α	ab(α	NUM
ejpam-6378	219	4	)	)	PUNCT
ejpam-6378	219	5	(	(	PUNCT
ejpam-6378	219	6	1−α	1−α	NUM
ejpam-6378	219	7	)	)	PUNCT
ejpam-6378	219	8	(	(	PUNCT
ejpam-6378	219	9	α	α	PROPN
ejpam-6378	219	10	1−α	1−α	NUM
ejpam-6378	219	11	sα+1	sα+1	NOUN
ejpam-6378	219	12	)	)	PUNCT
ejpam-6378	219	13	(	(	PUNCT
ejpam-6378	219	14	x(s	x(s	PROPN
ejpam-6378	219	15	)	)	PUNCT
ejpam-6378	219	16	s	s	VERB
ejpam-6378	220	1	−	−	PROPN
ejpam-6378	220	2	χ	χ	X
ejpam-6378	220	3	(	(	PUNCT
ejpam-6378	220	4	0	0	NUM
ejpam-6378	220	5	)	)	PUNCT
ejpam-6378	220	6	)	)	PUNCT
ejpam-6378	220	7	.	.	PUNCT
ejpam-6378	221	1	m[abdα	m[abdα	VERB
ejpam-6378	222	1	θ	θ	NOUN
ejpam-6378	222	2	χ(θ	χ(θ	PROPN
ejpam-6378	222	3	)	)	PUNCT
ejpam-6378	222	4	]	]	PUNCT
ejpam-6378	223	1	=	=	SYM
ejpam-6378	223	2	sα−1ab(α	sα−1ab(α	PROPN
ejpam-6378	223	3	)	)	PUNCT
ejpam-6378	223	4	(	(	PUNCT
ejpam-6378	223	5	1−α	1−α	NUM
ejpam-6378	223	6	)	)	PUNCT
ejpam-6378	223	7	(	(	PUNCT
ejpam-6378	223	8	α	α	PROPN
ejpam-6378	223	9	1−α	1−α	NUM
ejpam-6378	224	1	+	+	ADJ
ejpam-6378	224	2	sα	sα	X
ejpam-6378	224	3	)	)	PUNCT
ejpam-6378	224	4	(	(	PUNCT
ejpam-6378	224	5	sx	sx	PROPN
ejpam-6378	224	6	(	(	PUNCT
ejpam-6378	224	7	s)−	s)−	PROPN
ejpam-6378	224	8	s2χ	s2χ	PROPN
ejpam-6378	224	9	(	(	PUNCT
ejpam-6378	224	10	0	0	NUM
ejpam-6378	224	11	)	)	PUNCT
ejpam-6378	224	12	)	)	PUNCT
ejpam-6378	224	13	.	.	PUNCT
ejpam-6378	225	1	n	n	CCONJ
ejpam-6378	226	1	[	[	X
ejpam-6378	226	2	abdα	abdα	NOUN
ejpam-6378	226	3	θ	θ	NOUN
ejpam-6378	226	4	χ(θ	χ(θ	NOUN
ejpam-6378	226	5	)	)	PUNCT
ejpam-6378	226	6	]	]	PUNCT
ejpam-6378	227	1	=	=	SYM
ejpam-6378	227	2	ςsα−1ab(α	ςsα−1ab(α	X
ejpam-6378	227	3	)	)	PUNCT
ejpam-6378	227	4	(	(	PUNCT
ejpam-6378	227	5	1−α	1−α	NUM
ejpam-6378	227	6	)	)	PUNCT
ejpam-6378	227	7	(	(	PUNCT
ejpam-6378	227	8	α	α	PROPN
ejpam-6378	227	9	1−α	1−α	NUM
ejpam-6378	227	10	ςα+sα	ςα+sα	NOUN
ejpam-6378	227	11	)	)	PUNCT
ejpam-6378	227	12	(	(	PUNCT
ejpam-6378	227	13	s	s	VERB
ejpam-6378	227	14	ςx	ςx	INTJ
ejpam-6378	227	15	(	(	PUNCT
ejpam-6378	227	16	s)−	s)−	PROPN
ejpam-6378	227	17	χ(0	χ(0	PROPN
ejpam-6378	227	18	)	)	PUNCT
ejpam-6378	227	19	ς	ς	PROPN
ejpam-6378	227	20	)	)	PUNCT
ejpam-6378	227	21	.	.	PUNCT
ejpam-6378	228	1	s[abdα	s[abdα	NUM
ejpam-6378	228	2	θ	θ	NOUN
ejpam-6378	228	3	χ(θ	χ(θ	NOUN
ejpam-6378	228	4	)	)	PUNCT
ejpam-6378	228	5	]	]	PUNCT
ejpam-6378	229	1	=	=	SYM
ejpam-6378	229	2	ςsα−1ab(α	ςsα−1ab(α	X
ejpam-6378	229	3	)	)	PUNCT
ejpam-6378	229	4	(	(	PUNCT
ejpam-6378	229	5	1−α	1−α	NUM
ejpam-6378	229	6	)	)	PUNCT
ejpam-6378	229	7	(	(	PUNCT
ejpam-6378	229	8	α	α	PROPN
ejpam-6378	229	9	1−α	1−α	NUM
ejpam-6378	229	10	ςα+sα	ςα+sα	NOUN
ejpam-6378	229	11	)	)	PUNCT
ejpam-6378	229	12	(	(	PUNCT
ejpam-6378	229	13	s	s	VERB
ejpam-6378	229	14	ςx	ςx	INTJ
ejpam-6378	229	15	(	(	PUNCT
ejpam-6378	229	16	s)−	s)−	PROPN
ejpam-6378	229	17	χ	χ	X
ejpam-6378	229	18	(	(	PUNCT
ejpam-6378	229	19	0	0	NUM
ejpam-6378	229	20	)	)	PUNCT
ejpam-6378	229	21	)	)	PUNCT
ejpam-6378	229	22	.	.	PUNCT
ejpam-6378	230	1	(	(	PUNCT
ejpam-6378	230	2	26	26	NUM
ejpam-6378	230	3	)	)	PUNCT
ejpam-6378	230	4	at	at	ADP
ejpam-6378	230	5	last	last	ADV
ejpam-6378	230	6	,	,	PUNCT
ejpam-6378	230	7	we	we	PRON
ejpam-6378	230	8	have	have	AUX
ejpam-6378	230	9	calculated	calculate	VERB
ejpam-6378	230	10	the	the	DET
ejpam-6378	230	11	transformations	transformation	NOUN
ejpam-6378	230	12	of	of	ADP
ejpam-6378	230	13	some	some	DET
ejpam-6378	230	14	basic	basic	ADJ
ejpam-6378	230	15	functions	function	NOUN
ejpam-6378	230	16	,	,	PUNCT
ejpam-6378	230	17	which	which	PRON
ejpam-6378	230	18	are	be	AUX
ejpam-6378	230	19	given	give	VERB
ejpam-6378	230	20	in	in	ADP
ejpam-6378	230	21	the	the	DET
ejpam-6378	230	22	table	table	NOUN
ejpam-6378	230	23	(	(	PUNCT
ejpam-6378	230	24	1	1	NUM
ejpam-6378	230	25	)	)	PUNCT
ejpam-6378	230	26	.	.	PUNCT
ejpam-6378	231	1	m.	m.	PROPN
ejpam-6378	231	2	sohail	sohail	PROPN
ejpam-6378	231	3	et	et	PROPN
ejpam-6378	231	4	al	al	PROPN
ejpam-6378	231	5	.	.	PUNCT
ejpam-6378	231	6	/	/	SYM
ejpam-6378	231	7	eur	eur	PROPN
ejpam-6378	231	8	.	.	PUNCT
ejpam-6378	232	1	j.	j.	PROPN
ejpam-6378	232	2	pure	pure	PROPN
ejpam-6378	232	3	appl	appl	PROPN
ejpam-6378	232	4	.	.	PROPN
ejpam-6378	232	5	math	math	PROPN
ejpam-6378	232	6	,	,	PUNCT
ejpam-6378	232	7	18	18	NUM
ejpam-6378	232	8	(	(	PUNCT
ejpam-6378	232	9	4	4	NUM
ejpam-6378	232	10	)	)	PUNCT
ejpam-6378	232	11	(	(	PUNCT
ejpam-6378	232	12	2025	2025	NUM
ejpam-6378	232	13	)	)	PUNCT
ejpam-6378	232	14	,	,	PUNCT
ejpam-6378	232	15	6378	6378	NUM
ejpam-6378	232	16	8	8	NUM
ejpam-6378	232	17	of	of	ADP
ejpam-6378	232	18	20	20	NUM
ejpam-6378	232	19	table	table	NOUN
ejpam-6378	232	20	1	1	NUM
ejpam-6378	232	21	:	:	PUNCT
ejpam-6378	232	22	basic	basic	ADJ
ejpam-6378	232	23	functions	function	NOUN
ejpam-6378	232	24	under	under	ADP
ejpam-6378	232	25	different	different	ADJ
ejpam-6378	232	26	transformations	transformation	NOUN
ejpam-6378	232	27	.	.	PUNCT
ejpam-6378	233	1	functions	function	NOUN
ejpam-6378	233	2	laplace	laplace	PROPN
ejpam-6378	233	3	elzaki	elzaki	PROPN
ejpam-6378	233	4	aboodh	aboodh	PROPN
ejpam-6378	233	5	sumudu	sumudu	NOUN
ejpam-6378	233	6	1	1	NUM
ejpam-6378	233	7	1	1	NUM
ejpam-6378	233	8	s	s	NOUN
ejpam-6378	233	9	s2	s2	NOUN
ejpam-6378	233	10	1	1	NUM
ejpam-6378	233	11	s2	s2	PROPN
ejpam-6378	233	12	1	1	NUM
ejpam-6378	233	13	µ	µ	PROPN
ejpam-6378	233	14	µ	µ	X
ejpam-6378	233	15	s	s	PART
ejpam-6378	233	16	s2µ	s2µ	PROPN
ejpam-6378	233	17	µ	µ	X
ejpam-6378	233	18	s2	s2	NOUN
ejpam-6378	233	19	µ	µ	PRON
ejpam-6378	233	20	θ	θ	PROPN
ejpam-6378	233	21	1	1	NUM
ejpam-6378	233	22	s2	s2	NOUN
ejpam-6378	233	23	s3	s3	NOUN
ejpam-6378	233	24	1	1	NUM
ejpam-6378	233	25	s3	s3	PROPN
ejpam-6378	233	26	s	s	PROPN
ejpam-6378	233	27	θ2	θ2	PROPN
ejpam-6378	233	28	2	2	NUM
ejpam-6378	233	29	s3	s3	PROPN
ejpam-6378	233	30	2	2	NUM
ejpam-6378	233	31	s4	s4	PROPN
ejpam-6378	233	32	2	2	NUM
ejpam-6378	233	33	s4	s4	PROPN
ejpam-6378	233	34	2	2	NUM
ejpam-6378	233	35	s2	s2	NOUN
ejpam-6378	233	36	θn	θn	PROPN
ejpam-6378	233	37	γ(n+1	γ(n+1	PROPN
ejpam-6378	233	38	)	)	PUNCT
ejpam-6378	233	39	sn+1	sn+1	PROPN
ejpam-6378	233	40	s2+nγ	s2+nγ	PROPN
ejpam-6378	233	41	(	(	PUNCT
ejpam-6378	233	42	n+	n+	NOUN
ejpam-6378	233	43	1	1	NUM
ejpam-6378	233	44	)	)	PUNCT
ejpam-6378	233	45	γ(n+1	γ(n+1	PUNCT
ejpam-6378	233	46	)	)	PUNCT
ejpam-6378	233	47	sn+2	sn+2	PROPN
ejpam-6378	233	48	γ	γ	X
ejpam-6378	233	49	(	(	PUNCT
ejpam-6378	233	50	n+	n+	NUM
ejpam-6378	233	51	1	1	X
ejpam-6378	233	52	)	)	PUNCT
ejpam-6378	233	53	sn	sn	PROPN
ejpam-6378	233	54	sin	sin	NOUN
ejpam-6378	233	55	(	(	PUNCT
ejpam-6378	233	56	µ	µ	X
ejpam-6378	233	57	θ	θ	NOUN
ejpam-6378	233	58	)	)	PUNCT
ejpam-6378	233	59	µ	µ	PROPN
ejpam-6378	233	60	µ2+s2	µ2+s2	PROPN
ejpam-6378	233	61	s3µ	s3µ	PROPN
ejpam-6378	233	62	µ2s2	µ2s2	NOUN
ejpam-6378	233	63	+	+	PROPN
ejpam-6378	233	64	1	1	NUM
ejpam-6378	233	65	µ	µ	X
ejpam-6378	233	66	(	(	PUNCT
ejpam-6378	233	67	µ2+s2)s	µ2+s2)s	PROPN
ejpam-6378	233	68	µ	µ	X
ejpam-6378	233	69	s	s	X
ejpam-6378	233	70	µ2s2	µ2s2	NOUN
ejpam-6378	233	71	+	+	NOUN
ejpam-6378	233	72	1	1	NUM
ejpam-6378	233	73	cos	cos	X
ejpam-6378	233	74	(	(	PUNCT
ejpam-6378	233	75	µ	µ	X
ejpam-6378	233	76	θ	θ	NOUN
ejpam-6378	233	77	)	)	PUNCT
ejpam-6378	233	78	s	s	PART
ejpam-6378	233	79	µ2+s2	µ2+s2	PROPN
ejpam-6378	233	80	s2	s2	NOUN
ejpam-6378	233	81	µ2s2	µ2s2	NOUN
ejpam-6378	233	82	+	+	NOUN
ejpam-6378	233	83	1	1	NUM
ejpam-6378	233	84	1	1	NUM
ejpam-6378	233	85	µ2+s2	µ2+s2	PROPN
ejpam-6378	233	86	1	1	NUM
ejpam-6378	233	87	µ2s2	µ2s2	NOUN
ejpam-6378	233	88	+	+	NOUN
ejpam-6378	233	89	1	1	NUM
ejpam-6378	233	90	sinh	sinh	NOUN
ejpam-6378	233	91	(	(	PUNCT
ejpam-6378	233	92	µ	µ	X
ejpam-6378	233	93	θ	θ	NOUN
ejpam-6378	233	94	)	)	PUNCT
ejpam-6378	233	95	µ	µ	PRON
ejpam-6378	233	96	−µ2+s2	−µ2+s2	NOUN
ejpam-6378	233	97	−	−	PROPN
ejpam-6378	233	98	s3µ	s3µ	NOUN
ejpam-6378	233	99	µ2s2−1	µ2s2−1	ADP
ejpam-6378	233	100	µ	µ	X
ejpam-6378	233	101	−µ2s+s3	−µ2s+s3	NOUN
ejpam-6378	233	102	−	−	PROPN
ejpam-6378	233	103	µ	µ	NOUN
ejpam-6378	233	104	s	s	X
ejpam-6378	233	105	µ2s2−1	µ2s2−1	DET
ejpam-6378	233	106	cosh	cosh	NOUN
ejpam-6378	233	107	(	(	PUNCT
ejpam-6378	233	108	µ	µ	X
ejpam-6378	233	109	θ	θ	NOUN
ejpam-6378	233	110	)	)	PUNCT
ejpam-6378	233	111	s	s	PART
ejpam-6378	233	112	−µ2+s2	−µ2+s2	ADJ
ejpam-6378	233	113	−	−	PROPN
ejpam-6378	233	114	s2	s2	NOUN
ejpam-6378	233	115	µ2s2−1	µ2s2−1	ADP
ejpam-6378	233	116	1	1	NUM
ejpam-6378	233	117	s2−µ2	s2−µ2	NUM
ejpam-6378	233	118	1	1	NUM
ejpam-6378	233	119	1−µ2s2	1−µ2s2	NOUN
ejpam-6378	233	120	eµ	eµ	NOUN
ejpam-6378	233	121	θ	θ	NOUN
ejpam-6378	233	122	1	1	NUM
ejpam-6378	233	123	s−µ	s−µ	NOUN
ejpam-6378	233	124	s2	s2	NOUN
ejpam-6378	233	125	1−µ	1−µ	NUM
ejpam-6378	233	126	s	s	PART
ejpam-6378	233	127	1	1	NUM
ejpam-6378	233	128	(	(	PUNCT
ejpam-6378	233	129	s−µ)s	s−µ)s	NOUN
ejpam-6378	233	130	1	1	NUM
ejpam-6378	233	131	1−µ	1−µ	NOUN
ejpam-6378	233	132	s	s	NOUN
ejpam-6378	233	133	epθ−eqθ	epθ−eqθ	NOUN
ejpam-6378	233	134	p−q	p−q	NOUN
ejpam-6378	233	135	1	1	NUM
ejpam-6378	233	136	(	(	PUNCT
ejpam-6378	233	137	s−p)(s−q	s−p)(s−q	PROPN
ejpam-6378	233	138	)	)	PUNCT
ejpam-6378	233	139	s2	s2	NOUN
ejpam-6378	233	140	(	(	PUNCT
ejpam-6378	233	141	p−	p−	NOUN
ejpam-6378	233	142	1	1	NUM
ejpam-6378	233	143	s	s	NOUN
ejpam-6378	233	144	)	)	PUNCT
ejpam-6378	233	145	(	(	PUNCT
ejpam-6378	233	146	q−	q−	PROPN
ejpam-6378	233	147	1	1	NUM
ejpam-6378	233	148	s	s	PART
ejpam-6378	233	149	)	)	PUNCT
ejpam-6378	233	150	1	1	NUM
ejpam-6378	233	151	s	s	PART
ejpam-6378	233	152	(	(	PUNCT
ejpam-6378	233	153	p−s)(q−s	p−s)(q−s	NOUN
ejpam-6378	233	154	)	)	PUNCT
ejpam-6378	233	155	1	1	NUM
ejpam-6378	233	156	(	(	PUNCT
ejpam-6378	233	157	p−	p−	NOUN
ejpam-6378	233	158	1	1	NUM
ejpam-6378	233	159	s	s	NOUN
ejpam-6378	233	160	)	)	PUNCT
ejpam-6378	233	161	(	(	PUNCT
ejpam-6378	233	162	q−	q−	PROPN
ejpam-6378	233	163	1	1	NUM
ejpam-6378	233	164	s	s	PART
ejpam-6378	233	165	)	)	PUNCT
ejpam-6378	233	166	eα	eα	PROPN
ejpam-6378	233	167	(	(	PUNCT
ejpam-6378	233	168	−µ	−µ	NOUN
ejpam-6378	233	169	θα	θα	NOUN
ejpam-6378	233	170	)	)	PUNCT
ejpam-6378	233	171	sα	sα	ADP
ejpam-6378	233	172	s(µ+sα	s(µ+sα	PROPN
ejpam-6378	233	173	)	)	PUNCT
ejpam-6378	233	174	s2	s2	NOUN
ejpam-6378	233	175	µ	µ	PRON
ejpam-6378	233	176	sα+1	sα+1	NOUN
ejpam-6378	233	177	sα	sα	ADV
ejpam-6378	233	178	s2(µ+sα	s2(µ+sα	NOUN
ejpam-6378	233	179	)	)	PUNCT
ejpam-6378	233	180	1	1	NUM
ejpam-6378	233	181	(	(	PUNCT
ejpam-6378	233	182	µ	µ	X
ejpam-6378	233	183	sα+1	sα+1	NOUN
ejpam-6378	233	184	)	)	PUNCT
ejpam-6378	233	185	1−	1−	NUM
ejpam-6378	233	186	eα	eα	NOUN
ejpam-6378	233	187	(	(	PUNCT
ejpam-6378	233	188	−µ	−µ	NOUN
ejpam-6378	233	189	θα	θα	NOUN
ejpam-6378	233	190	)	)	PUNCT
ejpam-6378	233	191	µ	µ	PRON
ejpam-6378	233	192	s(µ+sα	s(µ+sα	NUM
ejpam-6378	233	193	)	)	PUNCT
ejpam-6378	233	194	sα+2µ	sα+2µ	NOUN
ejpam-6378	233	195	w	w	PROPN
ejpam-6378	233	196	sα+1	sα+1	NOUN
ejpam-6378	233	197	µ	µ	X
ejpam-6378	233	198	s2(µ+sα	s2(µ+sα	NOUN
ejpam-6378	233	199	)	)	PUNCT
ejpam-6378	233	200	µ	µ	X
ejpam-6378	233	201	sα	sα	PROPN
ejpam-6378	233	202	w	w	PROPN
ejpam-6378	233	203	sα+1	sα+1	NOUN
ejpam-6378	233	204	functions	function	NOUN
ejpam-6378	233	205	yang	yang	PROPN
ejpam-6378	233	206	mohand	mohand	PROPN
ejpam-6378	233	207	natural	natural	ADJ
ejpam-6378	233	208	shehu	shehu	NOUN
ejpam-6378	233	209	1	1	NUM
ejpam-6378	233	210	s	s	NOUN
ejpam-6378	233	211	s	s	NOUN
ejpam-6378	233	212	1	1	NUM
ejpam-6378	233	213	s	s	NOUN
ejpam-6378	233	214	ς	ς	PROPN
ejpam-6378	233	215	s	s	PROPN
ejpam-6378	233	216	µ	µ	X
ejpam-6378	233	217	µ	µ	X
ejpam-6378	233	218	s	s	X
ejpam-6378	233	219	µ	µ	X
ejpam-6378	233	220	s	s	X
ejpam-6378	233	221	µ	µ	X
ejpam-6378	233	222	s	s	X
ejpam-6378	233	223	µ	µ	PRON
ejpam-6378	233	224	ς	ς	PROPN
ejpam-6378	233	225	s	s	PROPN
ejpam-6378	233	226	θ	θ	PROPN
ejpam-6378	233	227	s2	s2	NOUN
ejpam-6378	233	228	1	1	NUM
ejpam-6378	233	229	ς	ς	PROPN
ejpam-6378	233	230	s2	s2	NOUN
ejpam-6378	233	231	ς2	ς2	PROPN
ejpam-6378	233	232	s2	s2	NOUN
ejpam-6378	233	233	θ2	θ2	ADV
ejpam-6378	233	234	2	2	NUM
ejpam-6378	233	235	s3	s3	PROPN
ejpam-6378	233	236	2	2	NUM
ejpam-6378	233	237	s	s	PART
ejpam-6378	233	238	2	2	NUM
ejpam-6378	233	239	ς2	ς2	PROPN
ejpam-6378	233	240	s3	s3	NOUN
ejpam-6378	233	241	2	2	NUM
ejpam-6378	233	242	ς3	ς3	NOUN
ejpam-6378	233	243	s3	s3	PROPN
ejpam-6378	233	244	θn	θn	ADP
ejpam-6378	233	245	γ	γ	X
ejpam-6378	233	246	(	(	PUNCT
ejpam-6378	233	247	n+	n+	NOUN
ejpam-6378	233	248	1	1	NUM
ejpam-6378	233	249	)	)	PUNCT
ejpam-6378	233	250	sn+1	sn+1	NOUN
ejpam-6378	233	251	γ(n+1	γ(n+1	PROPN
ejpam-6378	233	252	)	)	PUNCT
ejpam-6378	234	1	sn−1	sn−1	PROPN
ejpam-6378	234	2	γ(n+1)ςn	γ(n+1)ςn	PROPN
ejpam-6378	234	3	sn+1	sn+1	VERB
ejpam-6378	234	4	γ(n+1)ςn+1	γ(n+1)ςn+1	PROPN
ejpam-6378	234	5	sn+1	sn+1	X
ejpam-6378	234	6	sin	sin	NOUN
ejpam-6378	234	7	(	(	PUNCT
ejpam-6378	234	8	µ	µ	X
ejpam-6378	234	9	θ	θ	NOUN
ejpam-6378	234	10	)	)	PUNCT
ejpam-6378	234	11	s2µ	s2µ	NOUN
ejpam-6378	234	12	µ2s2	µ2s2	PROPN
ejpam-6378	234	13	+	+	NOUN
ejpam-6378	234	14	1	1	NUM
ejpam-6378	234	15	s2µ	s2µ	PROPN
ejpam-6378	234	16	µ2+s2	µ2+s2	PROPN
ejpam-6378	234	17	µ	µ	NUM
ejpam-6378	234	18	ς	ς	NOUN
ejpam-6378	234	19	µ2ς2+s2	µ2ς2+s2	NOUN
ejpam-6378	234	20	µ	µ	PRON
ejpam-6378	234	21	ς2	ς2	PROPN
ejpam-6378	234	22	µ2ς2+s2	µ2ς2+s2	NOUN
ejpam-6378	234	23	cos	cos	ADP
ejpam-6378	234	24	(	(	PUNCT
ejpam-6378	234	25	µ	µ	X
ejpam-6378	234	26	θ	θ	NOUN
ejpam-6378	234	27	)	)	PUNCT
ejpam-6378	234	28	s	s	PART
ejpam-6378	235	1	µ2s2	µ2s2	PROPN
ejpam-6378	235	2	+	+	PROPN
ejpam-6378	235	3	1	1	NUM
ejpam-6378	235	4	s3	s3	PROPN
ejpam-6378	235	5	µ2+s2	µ2+s2	PROPN
ejpam-6378	235	6	s	s	PART
ejpam-6378	235	7	µ2ς2+s2	µ2ς2+s2	NOUN
ejpam-6378	235	8	s	s	NOUN
ejpam-6378	235	9	ς	ς	PROPN
ejpam-6378	235	10	µ2ς2+s2	µ2ς2+s2	NOUN
ejpam-6378	235	11	sinh	sinh	NOUN
ejpam-6378	235	12	(	(	PUNCT
ejpam-6378	235	13	µ	µ	X
ejpam-6378	235	14	θ	θ	NOUN
ejpam-6378	235	15	)	)	PUNCT
ejpam-6378	235	16	−	−	NOUN
ejpam-6378	236	1	s2µ	s2µ	NOUN
ejpam-6378	236	2	µ2s2−1	µ2s2−1	ADP
ejpam-6378	236	3	s2µ	s2µ	PROPN
ejpam-6378	236	4	−µ2+s2	−µ2+s2	PART
ejpam-6378	236	5	µ	µ	PROPN
ejpam-6378	236	6	ς	ς	PROPN
ejpam-6378	236	7	−µ2ς2+s2	−µ2ς2+s2	NOUN
ejpam-6378	236	8	µ	µ	PROPN
ejpam-6378	236	9	ς2	ς2	PROPN
ejpam-6378	236	10	−µ2ς2+s2	−µ2ς2+s2	VERB
ejpam-6378	236	11	cosh	cosh	NOUN
ejpam-6378	236	12	(	(	PUNCT
ejpam-6378	236	13	µ	µ	X
ejpam-6378	236	14	θ	θ	NOUN
ejpam-6378	236	15	)	)	PUNCT
ejpam-6378	237	1	−	−	PROPN
ejpam-6378	237	2	s	s	PART
ejpam-6378	237	3	µ2s2−1	µ2s2−1	PROPN
ejpam-6378	237	4	s3	s3	PROPN
ejpam-6378	237	5	−µ2+s2	−µ2+s2	NOUN
ejpam-6378	237	6	s	s	VERB
ejpam-6378	237	7	−µ2ς2+s2	−µ2ς2+s2	NOUN
ejpam-6378	237	8	s	s	PROPN
ejpam-6378	237	9	ς	ς	PROPN
ejpam-6378	237	10	−µ2ς2+s2	−µ2ς2+s2	NOUN
ejpam-6378	237	11	eµ	eµ	NOUN
ejpam-6378	237	12	θ	θ	PROPN
ejpam-6378	237	13	s2	s2	NOUN
ejpam-6378	237	14	s−µ	s−µ	NOUN
ejpam-6378	237	15	−	−	PROPN
ejpam-6378	237	16	s3	s3	PROPN
ejpam-6378	237	17	µ	µ	ADV
ejpam-6378	237	18	s−1	s−1	PROPN
ejpam-6378	237	19	1	1	NUM
ejpam-6378	237	20	s−µ	s−µ	NOUN
ejpam-6378	237	21	ς	ς	PROPN
ejpam-6378	237	22	ς	ς	PROPN
ejpam-6378	237	23	−µ	−µ	NOUN
ejpam-6378	237	24	ς+s	ς+s	NUM
ejpam-6378	237	25	epθ−eqθ	epθ−eqθ	NOUN
ejpam-6378	237	26	p−q	p−q	NOUN
ejpam-6378	237	27	s	s	PART
ejpam-6378	237	28	(	(	PUNCT
ejpam-6378	237	29	p−	p−	PROPN
ejpam-6378	237	30	1	1	NUM
ejpam-6378	237	31	s	s	NOUN
ejpam-6378	237	32	)	)	PUNCT
ejpam-6378	237	33	(	(	PUNCT
ejpam-6378	237	34	q−	q−	PROPN
ejpam-6378	237	35	1	1	NUM
ejpam-6378	237	36	s	s	PART
ejpam-6378	237	37	)	)	PUNCT
ejpam-6378	237	38	s2	s2	NOUN
ejpam-6378	237	39	(	(	PUNCT
ejpam-6378	237	40	p−s)(q−s	p−s)(q−s	PROPN
ejpam-6378	237	41	)	)	PUNCT
ejpam-6378	237	42	1	1	NUM
ejpam-6378	237	43	(	(	PUNCT
ejpam-6378	237	44	p−	p−	NOUN
ejpam-6378	237	45	s	s	NOUN
ejpam-6378	237	46	ς	ς	PROPN
ejpam-6378	237	47	)	)	PUNCT
ejpam-6378	237	48	(	(	PUNCT
ejpam-6378	237	49	q−	q−	PROPN
ejpam-6378	237	50	s	s	PROPN
ejpam-6378	237	51	ς	ς	PROPN
ejpam-6378	237	52	)	)	PUNCT
ejpam-6378	237	53	ς	ς	PROPN
ejpam-6378	237	54	(	(	PUNCT
ejpam-6378	237	55	p−	p−	NOUN
ejpam-6378	237	56	s	s	NOUN
ejpam-6378	237	57	ς	ς	PROPN
ejpam-6378	237	58	)	)	PUNCT
ejpam-6378	237	59	(	(	PUNCT
ejpam-6378	237	60	q−	q−	PROPN
ejpam-6378	237	61	s	s	PROPN
ejpam-6378	237	62	ς	ς	PROPN
ejpam-6378	237	63	)	)	PUNCT
ejpam-6378	237	64	eα	eα	PROPN
ejpam-6378	237	65	(	(	PUNCT
ejpam-6378	237	66	−µ	−µ	NOUN
ejpam-6378	237	67	θα	θα	NOUN
ejpam-6378	237	68	)	)	PUNCT
ejpam-6378	237	69	s	s	PART
ejpam-6378	237	70	µ	µ	PRON
ejpam-6378	237	71	sα+1	sα+1	NOUN
ejpam-6378	237	72	sα+1	sα+1	NOUN
ejpam-6378	237	73	µ+sα	µ+sα	PRON
ejpam-6378	237	74	sα	sα	ADP
ejpam-6378	237	75	s(µ	s(µ	PROPN
ejpam-6378	237	76	ςα+sα	ςα+sα	NOUN
ejpam-6378	237	77	)	)	PUNCT
ejpam-6378	237	78	sας	sας	NOUN
ejpam-6378	237	79	s(µ	s(µ	PROPN
ejpam-6378	237	80	ςα+sα	ςα+sα	NOUN
ejpam-6378	237	81	)	)	PUNCT
ejpam-6378	237	82	1−	1−	NUM
ejpam-6378	237	83	eα	eα	NOUN
ejpam-6378	237	84	(	(	PUNCT
ejpam-6378	237	85	−µ	−µ	NOUN
ejpam-6378	237	86	θα	θα	NOUN
ejpam-6378	237	87	)	)	PUNCT
ejpam-6378	237	88	µ	µ	PRON
ejpam-6378	237	89	sα+1	sα+1	NOUN
ejpam-6378	237	90	µ	µ	PROPN
ejpam-6378	237	91	sα+1	sα+1	NOUN
ejpam-6378	237	92	sµ	sµ	ADP
ejpam-6378	237	93	µ+sα	µ+sα	DET
ejpam-6378	237	94	µ	µ	X
ejpam-6378	237	95	ςα	ςα	ADP
ejpam-6378	237	96	s(µ	s(µ	PROPN
ejpam-6378	237	97	ςα+sα	ςα+sα	NOUN
ejpam-6378	237	98	)	)	PUNCT
ejpam-6378	237	99	µ	µ	X
ejpam-6378	237	100	ςα+1	ςα+1	NOUN
ejpam-6378	237	101	s(µ	s(µ	PROPN
ejpam-6378	237	102	ςα+sα	ςα+sα	NOUN
ejpam-6378	237	103	)	)	PUNCT
ejpam-6378	237	104	the	the	DET
ejpam-6378	237	105	table	table	NOUN
ejpam-6378	237	106	1	1	NUM
ejpam-6378	237	107	demonstrates	demonstrate	VERB
ejpam-6378	237	108	some	some	DET
ejpam-6378	237	109	convolutions	convolution	NOUN
ejpam-6378	237	110	results	result	NOUN
ejpam-6378	237	111	against	against	ADP
ejpam-6378	237	112	different	different	ADJ
ejpam-6378	237	113	fractional	fractional	ADJ
ejpam-6378	237	114	order	order	NOUN
ejpam-6378	237	115	operators	operator	NOUN
ejpam-6378	237	116	.	.	PUNCT
ejpam-6378	238	1	m.	m.	PROPN
ejpam-6378	238	2	sohail	sohail	PROPN
ejpam-6378	238	3	et	et	PROPN
ejpam-6378	238	4	al	al	PROPN
ejpam-6378	238	5	.	.	PUNCT
ejpam-6378	238	6	/	/	SYM
ejpam-6378	238	7	eur	eur	PROPN
ejpam-6378	238	8	.	.	PUNCT
ejpam-6378	239	1	j.	j.	PROPN
ejpam-6378	239	2	pure	pure	PROPN
ejpam-6378	239	3	appl	appl	PROPN
ejpam-6378	239	4	.	.	PROPN
ejpam-6378	239	5	math	math	PROPN
ejpam-6378	239	6	,	,	PUNCT
ejpam-6378	239	7	18	18	NUM
ejpam-6378	239	8	(	(	PUNCT
ejpam-6378	239	9	4	4	NUM
ejpam-6378	239	10	)	)	PUNCT
ejpam-6378	239	11	(	(	PUNCT
ejpam-6378	239	12	2025	2025	NUM
ejpam-6378	239	13	)	)	PUNCT
ejpam-6378	239	14	,	,	PUNCT
ejpam-6378	239	15	6378	6378	NUM
ejpam-6378	239	16	9	9	NUM
ejpam-6378	239	17	of	of	ADP
ejpam-6378	239	18	20	20	NUM
ejpam-6378	239	19	3	3	NUM
ejpam-6378	239	20	.	.	PUNCT
ejpam-6378	239	21	suggested	suggest	VERB
ejpam-6378	239	22	adm	adm	PROPN
ejpam-6378	239	23	method	method	NOUN
ejpam-6378	239	24	by	by	ADP
ejpam-6378	239	25	using	use	VERB
ejpam-6378	239	26	different	different	ADJ
ejpam-6378	239	27	fractional	fractional	ADJ
ejpam-6378	239	28	differential	differential	NOUN
ejpam-6378	239	29	operators	operator	NOUN
ejpam-6378	239	30	let	let	VERB
ejpam-6378	239	31	us	we	PRON
ejpam-6378	239	32	have	have	VERB
ejpam-6378	239	33	a	a	DET
ejpam-6378	239	34	general	general	ADJ
ejpam-6378	239	35	nonlinear	nonlinear	ADJ
ejpam-6378	239	36	fpde	fpde	NOUN
ejpam-6378	239	37	in	in	ADP
ejpam-6378	239	38	the	the	DET
ejpam-6378	239	39	form	form	NOUN
ejpam-6378	239	40	of	of	ADP
ejpam-6378	239	41	cdα	cdα	NOUN
ejpam-6378	240	1	θ	θ	PROPN
ejpam-6378	240	2	ν	ν	X
ejpam-6378	240	3	(	(	PUNCT
ejpam-6378	240	4	κ	κ	NOUN
ejpam-6378	240	5	,	,	PUNCT
ejpam-6378	240	6	θ	θ	NOUN
ejpam-6378	240	7	)	)	PUNCT
ejpam-6378	240	8	+	+	NUM
ejpam-6378	240	9	fν(κ	fν(κ	ADP
ejpam-6378	240	10	,	,	PUNCT
ejpam-6378	240	11	θ	θ	NOUN
ejpam-6378	240	12	)	)	PUNCT
ejpam-6378	240	13	+	+	NOUN
ejpam-6378	240	14	nν(κ	nν(κ	NUM
ejpam-6378	240	15	,	,	PUNCT
ejpam-6378	240	16	θ	θ	NOUN
ejpam-6378	240	17	)	)	PUNCT
ejpam-6378	240	18	=	=	SYM
ejpam-6378	240	19	f(κ	f(κ	PROPN
ejpam-6378	240	20	,	,	PUNCT
ejpam-6378	240	21	θ	θ	PROPN
ejpam-6378	240	22	)	)	PUNCT
ejpam-6378	240	23	,	,	PUNCT
ejpam-6378	240	24	u(κ	u(κ	PROPN
ejpam-6378	240	25	,	,	PUNCT
ejpam-6378	240	26	0	0	NUM
ejpam-6378	240	27	)	)	PUNCT
ejpam-6378	240	28	=	=	SYM
ejpam-6378	240	29	f(κ	f(κ	PROPN
ejpam-6378	240	30	)	)	PUNCT
ejpam-6378	240	31	.	.	PUNCT
ejpam-6378	241	1	(	(	PUNCT
ejpam-6378	241	2	27	27	NUM
ejpam-6378	241	3	)	)	PUNCT
ejpam-6378	241	4	where	where	SCONJ
ejpam-6378	241	5	fν(κ	fν(κ	ADP
ejpam-6378	241	6	,	,	PUNCT
ejpam-6378	241	7	θ	θ	NOUN
ejpam-6378	241	8	)	)	PUNCT
ejpam-6378	241	9	and	and	CCONJ
ejpam-6378	241	10	nν(κ	nν(κ	NUM
ejpam-6378	241	11	,	,	PUNCT
ejpam-6378	241	12	θ	θ	NOUN
ejpam-6378	241	13	)	)	PUNCT
ejpam-6378	241	14	are	be	AUX
ejpam-6378	241	15	linear	linear	ADJ
ejpam-6378	241	16	and	and	CCONJ
ejpam-6378	241	17	nonlinear	nonlinear	ADJ
ejpam-6378	241	18	parts	part	NOUN
ejpam-6378	241	19	,	,	PUNCT
ejpam-6378	241	20	respectively	respectively	ADV
ejpam-6378	241	21	.	.	PUNCT
ejpam-6378	242	1	taking	take	VERB
ejpam-6378	242	2	lt	lt	PRON
ejpam-6378	242	3	(	(	PUNCT
ejpam-6378	242	4	27	27	NUM
ejpam-6378	242	5	)	)	PUNCT
ejpam-6378	242	6	implies	imply	VERB
ejpam-6378	242	7	l	l	NOUN
ejpam-6378	242	8	[	[	PUNCT
ejpam-6378	242	9	cdα	cdα	NOUN
ejpam-6378	242	10	θ	θ	PROPN
ejpam-6378	242	11	ν	ν	X
ejpam-6378	242	12	(	(	PUNCT
ejpam-6378	242	13	κ	κ	NOUN
ejpam-6378	242	14	,	,	PUNCT
ejpam-6378	242	15	θ	θ	NOUN
ejpam-6378	242	16	)	)	PUNCT
ejpam-6378	242	17	]	]	PUNCT
ejpam-6378	243	1	=	=	PUNCT
ejpam-6378	243	2	−l	−l	PROPN
ejpam-6378	243	3	[	[	PUNCT
ejpam-6378	243	4	fν(κ	fν(κ	PROPN
ejpam-6378	243	5	,	,	PUNCT
ejpam-6378	243	6	θ	θ	NOUN
ejpam-6378	243	7	)	)	PUNCT
ejpam-6378	243	8	+	+	NOUN
ejpam-6378	243	9	nν(κ	nν(κ	NOUN
ejpam-6378	243	10	,	,	PUNCT
ejpam-6378	243	11	θ)−	θ)−	PROPN
ejpam-6378	243	12	f(κ	f(κ	PROPN
ejpam-6378	243	13	,	,	PUNCT
ejpam-6378	243	14	θ	θ	PROPN
ejpam-6378	243	15	)	)	PUNCT
ejpam-6378	243	16	]	]	PUNCT
ejpam-6378	243	17	.	.	PUNCT
ejpam-6378	244	1	(	(	PUNCT
ejpam-6378	244	2	28	28	NUM
ejpam-6378	244	3	)	)	PUNCT
ejpam-6378	244	4	by	by	ADP
ejpam-6378	244	5	using	use	VERB
ejpam-6378	244	6	equation	equation	NOUN
ejpam-6378	244	7	(	(	PUNCT
ejpam-6378	244	8	16	16	NUM
ejpam-6378	244	9	)	)	PUNCT
ejpam-6378	244	10	,	,	PUNCT
ejpam-6378	244	11	implies	imply	VERB
ejpam-6378	244	12	u(κ	u(κ	PROPN
ejpam-6378	244	13	,	,	PUNCT
ejpam-6378	244	14	s	s	NOUN
ejpam-6378	244	15	)	)	PUNCT
ejpam-6378	244	16	=	=	SYM
ejpam-6378	244	17	ν(κ	ν(κ	NOUN
ejpam-6378	244	18	,	,	PUNCT
ejpam-6378	244	19	0	0	NUM
ejpam-6378	244	20	)	)	PUNCT
ejpam-6378	244	21	s	s	VERB
ejpam-6378	244	22	−	−	PROPN
ejpam-6378	244	23	1	1	NUM
ejpam-6378	244	24	sα	sα	NOUN
ejpam-6378	244	25	l	l	NOUN
ejpam-6378	244	26	[	[	PUNCT
ejpam-6378	244	27	fν(κ	fν(κ	PROPN
ejpam-6378	244	28	,	,	PUNCT
ejpam-6378	244	29	θ	θ	NOUN
ejpam-6378	244	30	)	)	PUNCT
ejpam-6378	244	31	+	+	NOUN
ejpam-6378	244	32	nν(κ	nν(κ	NOUN
ejpam-6378	244	33	,	,	PUNCT
ejpam-6378	244	34	θ)−	θ)−	PROPN
ejpam-6378	244	35	f(κ	f(κ	PROPN
ejpam-6378	244	36	,	,	PUNCT
ejpam-6378	244	37	θ	θ	PROPN
ejpam-6378	244	38	)	)	PUNCT
ejpam-6378	244	39	]	]	PUNCT
ejpam-6378	244	40	.	.	PUNCT
ejpam-6378	245	1	now	now	ADV
ejpam-6378	245	2	,	,	PUNCT
ejpam-6378	245	3	taking	take	VERB
ejpam-6378	245	4	the	the	DET
ejpam-6378	245	5	inverse	inverse	NOUN
ejpam-6378	245	6	lt	lt	PRON
ejpam-6378	245	7	l−1[u(κ	l−1[u(κ	PROPN
ejpam-6378	245	8	,	,	PUNCT
ejpam-6378	245	9	s	s	NOUN
ejpam-6378	245	10	)	)	PUNCT
ejpam-6378	245	11	]	]	PUNCT
ejpam-6378	246	1	=	=	SYM
ejpam-6378	246	2	ν(κ	ν(κ	X
ejpam-6378	246	3	,	,	PUNCT
ejpam-6378	246	4	θ	θ	NOUN
ejpam-6378	246	5	)	)	PUNCT
ejpam-6378	246	6	=	=	SYM
ejpam-6378	246	7	l−1	l−1	PROPN
ejpam-6378	246	8	[	[	PUNCT
ejpam-6378	246	9	ν(κ	ν(κ	NOUN
ejpam-6378	246	10	,	,	PUNCT
ejpam-6378	246	11	0	0	NUM
ejpam-6378	246	12	)	)	PUNCT
ejpam-6378	246	13	s	s	VERB
ejpam-6378	246	14	−	−	PROPN
ejpam-6378	246	15	1	1	NUM
ejpam-6378	246	16	sα	sα	NOUN
ejpam-6378	246	17	l	l	NOUN
ejpam-6378	246	18	[	[	PUNCT
ejpam-6378	246	19	fν(κ	fν(κ	PROPN
ejpam-6378	246	20	,	,	PUNCT
ejpam-6378	246	21	θ	θ	NOUN
ejpam-6378	246	22	)	)	PUNCT
ejpam-6378	246	23	+	+	NOUN
ejpam-6378	246	24	nν(κ	nν(κ	NOUN
ejpam-6378	246	25	,	,	PUNCT
ejpam-6378	246	26	θ)−	θ)−	PROPN
ejpam-6378	246	27	f(κ	f(κ	PROPN
ejpam-6378	246	28	,	,	PUNCT
ejpam-6378	246	29	θ	θ	PROPN
ejpam-6378	246	30	)	)	PUNCT
ejpam-6378	246	31	]	]	PUNCT
ejpam-6378	246	32	]	]	PUNCT
ejpam-6378	246	33	.	.	PUNCT
ejpam-6378	247	1	(	(	PUNCT
ejpam-6378	247	2	29	29	NUM
ejpam-6378	247	3	)	)	PUNCT
ejpam-6378	247	4	nν(κ	nν(κ	NUM
ejpam-6378	247	5	,	,	PUNCT
ejpam-6378	247	6	θ	θ	NOUN
ejpam-6378	247	7	)	)	PUNCT
ejpam-6378	247	8	will	will	AUX
ejpam-6378	247	9	be	be	AUX
ejpam-6378	247	10	decomposed	decompose	VERB
ejpam-6378	247	11	by	by	ADP
ejpam-6378	247	12	adomian	adomian	NOUN
ejpam-6378	247	13	polynomial	polynomial	NOUN
ejpam-6378	247	14	,	,	PUNCT
ejpam-6378	247	15	defined	define	VERB
ejpam-6378	247	16	as	as	ADP
ejpam-6378	247	17	nν(κ	nν(κ	NUM
ejpam-6378	247	18	,	,	PUNCT
ejpam-6378	247	19	θ	θ	NOUN
ejpam-6378	247	20	)	)	PUNCT
ejpam-6378	247	21	=	=	SYM
ejpam-6378	248	1	∞∑	∞∑	PRON
ejpam-6378	248	2	n=0	n=0	NUM
ejpam-6378	248	3	pn	pn	NOUN
ejpam-6378	248	4	,	,	PUNCT
ejpam-6378	248	5	where	where	SCONJ
ejpam-6378	248	6	pn	pn	PROPN
ejpam-6378	248	7	=	=	SYM
ejpam-6378	248	8	1	1	NUM
ejpam-6378	248	9	n	n	NOUN
ejpam-6378	248	10	!	!	PUNCT
ejpam-6378	249	1	∂n	∂n	PROPN
ejpam-6378	249	2	∂γn	∂γn	PROPN
ejpam-6378	249	3	(	(	PUNCT
ejpam-6378	249	4	n	n	CCONJ
ejpam-6378	249	5	(	(	PUNCT
ejpam-6378	249	6	∞∑	∞∑	NUM
ejpam-6378	249	7	i=0	i=0	PROPN
ejpam-6378	249	8	γi	γi	ADJ
ejpam-6378	249	9	νi	νi	NOUN
ejpam-6378	249	10	)	)	PUNCT
ejpam-6378	249	11	)	)	PUNCT
ejpam-6378	250	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6378	250	2	γ=0	γ=0	PUNCT
ejpam-6378	251	1	n	n	NOUN
ejpam-6378	251	2	=	=	SYM
ejpam-6378	251	3	0	0	NUM
ejpam-6378	251	4	,	,	PUNCT
ejpam-6378	251	5	1	1	NUM
ejpam-6378	251	6	,	,	PUNCT
ejpam-6378	251	7	2	2	NUM
ejpam-6378	251	8	,	,	PUNCT
ejpam-6378	251	9	3	3	NUM
ejpam-6378	251	10	,	,	PUNCT
ejpam-6378	251	11	.	.	PUNCT
ejpam-6378	251	12	.	.	PUNCT
ejpam-6378	251	13	.	.	PUNCT
ejpam-6378	251	14	.	.	PUNCT
ejpam-6378	252	1	thus	thus	ADV
ejpam-6378	252	2	,	,	PUNCT
ejpam-6378	252	3	ladm	ladm	ADP
ejpam-6378	252	4	decompose	decompose	NOUN
ejpam-6378	252	5	equation	equation	NOUN
ejpam-6378	252	6	(	(	PUNCT
ejpam-6378	252	7	29	29	NUM
ejpam-6378	252	8	)	)	PUNCT
ejpam-6378	252	9	as	as	ADP
ejpam-6378	252	10	νk+1(κ	νk+1(κ	PROPN
ejpam-6378	252	11	,	,	PUNCT
ejpam-6378	252	12	θ	θ	NOUN
ejpam-6378	252	13	)	)	PUNCT
ejpam-6378	252	14	=	=	SYM
ejpam-6378	252	15	l−1	l−1	PROPN
ejpam-6378	252	16	[	[	PUNCT
ejpam-6378	252	17	−	−	PROPN
ejpam-6378	252	18	1	1	NUM
ejpam-6378	252	19	sα	sα	NOUN
ejpam-6378	252	20	l	l	NOUN
ejpam-6378	252	21	[	[	PUNCT
ejpam-6378	252	22	fνk(κ	fνk(κ	X
ejpam-6378	252	23	,	,	PUNCT
ejpam-6378	252	24	θ	θ	NOUN
ejpam-6378	252	25	)	)	PUNCT
ejpam-6378	253	1	+	+	NUM
ejpam-6378	253	2	pk	pk	NOUN
ejpam-6378	253	3	]	]	X
ejpam-6378	253	4	]	]	PUNCT
ejpam-6378	253	5	,	,	PUNCT
ejpam-6378	253	6	k	k	X
ejpam-6378	253	7	≥	≥	PROPN
ejpam-6378	253	8	0	0	NUM
ejpam-6378	253	9	.	.	PUNCT
ejpam-6378	254	1	(	(	PUNCT
ejpam-6378	254	2	30	30	NUM
ejpam-6378	254	3	)	)	PUNCT
ejpam-6378	254	4	where	where	SCONJ
ejpam-6378	254	5	ν0(κ	ν0(κ	ADV
ejpam-6378	254	6	,	,	PUNCT
ejpam-6378	254	7	θ	θ	NOUN
ejpam-6378	254	8	)	)	PUNCT
ejpam-6378	254	9	=	=	SYM
ejpam-6378	254	10	l−1	l−1	PROPN
ejpam-6378	254	11	[	[	PUNCT
ejpam-6378	254	12	ν(κ	ν(κ	NOUN
ejpam-6378	254	13	,	,	PUNCT
ejpam-6378	254	14	0	0	NUM
ejpam-6378	254	15	)	)	PUNCT
ejpam-6378	254	16	s	s	PART
ejpam-6378	255	1	+	+	ADJ
ejpam-6378	255	2	1	1	NUM
ejpam-6378	255	3	sα	sα	ADJ
ejpam-6378	255	4	l	l	NOUN
ejpam-6378	255	5	[	[	PUNCT
ejpam-6378	255	6	f(κ	f(κ	PROPN
ejpam-6378	255	7	,	,	PUNCT
ejpam-6378	255	8	θ	θ	PROPN
ejpam-6378	255	9	)	)	PUNCT
ejpam-6378	255	10	]	]	PUNCT
ejpam-6378	255	11	]	]	PUNCT
ejpam-6378	255	12	.	.	PUNCT
ejpam-6378	256	1	(	(	PUNCT
ejpam-6378	256	2	31	31	NUM
ejpam-6378	256	3	)	)	PUNCT
ejpam-6378	256	4	m.	m.	NOUN
ejpam-6378	256	5	sohail	sohail	PROPN
ejpam-6378	256	6	et	et	PROPN
ejpam-6378	256	7	al	al	PROPN
ejpam-6378	256	8	.	.	PUNCT
ejpam-6378	256	9	/	/	SYM
ejpam-6378	256	10	eur	eur	PROPN
ejpam-6378	256	11	.	.	PUNCT
ejpam-6378	257	1	j.	j.	PROPN
ejpam-6378	257	2	pure	pure	PROPN
ejpam-6378	257	3	appl	appl	PROPN
ejpam-6378	257	4	.	.	PROPN
ejpam-6378	257	5	math	math	PROPN
ejpam-6378	257	6	,	,	PUNCT
ejpam-6378	257	7	18	18	NUM
ejpam-6378	257	8	(	(	PUNCT
ejpam-6378	257	9	4	4	NUM
ejpam-6378	257	10	)	)	PUNCT
ejpam-6378	257	11	(	(	PUNCT
ejpam-6378	257	12	2025	2025	NUM
ejpam-6378	257	13	)	)	PUNCT
ejpam-6378	257	14	,	,	PUNCT
ejpam-6378	257	15	6378	6378	NUM
ejpam-6378	257	16	10	10	NUM
ejpam-6378	257	17	of	of	ADP
ejpam-6378	257	18	20	20	NUM
ejpam-6378	257	19	similarly	similarly	ADV
ejpam-6378	257	20	,	,	PUNCT
ejpam-6378	257	21	adm	adm	PROPN
ejpam-6378	257	22	iterative	iterative	NOUN
ejpam-6378	257	23	terms	term	NOUN
ejpam-6378	257	24	under	under	ADP
ejpam-6378	257	25	different	different	ADJ
ejpam-6378	257	26	transformations	transformation	NOUN
ejpam-6378	257	27	for	for	ADP
ejpam-6378	257	28	cfd	cfd	NOUN
ejpam-6378	257	29	in	in	ADP
ejpam-6378	257	30	equation	equation	NOUN
ejpam-6378	257	31	(	(	PUNCT
ejpam-6378	257	32	32).	32).	NUM
ejpam-6378	257	33	νk+1(κ	νk+1(κ	PROPN
ejpam-6378	257	34	,	,	PUNCT
ejpam-6378	257	35	θ	θ	NOUN
ejpam-6378	257	36	)	)	PUNCT
ejpam-6378	257	37	=	=	SYM
ejpam-6378	257	38	l−1	l−1	PROPN
ejpam-6378	257	39	[	[	PUNCT
ejpam-6378	257	40	−	−	PROPN
ejpam-6378	257	41	1	1	NUM
ejpam-6378	257	42	sα	sα	NOUN
ejpam-6378	257	43	l	l	NOUN
ejpam-6378	257	44	[	[	PUNCT
ejpam-6378	257	45	fνk(κ	fνk(κ	X
ejpam-6378	257	46	,	,	PUNCT
ejpam-6378	257	47	θ	θ	NOUN
ejpam-6378	257	48	)	)	PUNCT
ejpam-6378	258	1	+	+	NUM
ejpam-6378	258	2	pk	pk	NOUN
ejpam-6378	258	3	]	]	X
ejpam-6378	258	4	]	]	PUNCT
ejpam-6378	258	5	.	.	PUNCT
ejpam-6378	259	1	νk+1(κ	νk+1(κ	PROPN
ejpam-6378	259	2	,	,	PUNCT
ejpam-6378	259	3	θ	θ	NOUN
ejpam-6378	259	4	)	)	PUNCT
ejpam-6378	259	5	=	=	SYM
ejpam-6378	259	6	a−1	a−1	PROPN
ejpam-6378	259	7	[	[	PUNCT
ejpam-6378	259	8	−	−	PROPN
ejpam-6378	259	9	1	1	NUM
ejpam-6378	259	10	sα	sα	ADV
ejpam-6378	259	11	a	a	DET
ejpam-6378	259	12	[	[	PUNCT
ejpam-6378	259	13	fνk(κ	fνk(κ	PROPN
ejpam-6378	259	14	,	,	PUNCT
ejpam-6378	259	15	θ	θ	NOUN
ejpam-6378	259	16	)	)	PUNCT
ejpam-6378	259	17	+	+	NUM
ejpam-6378	259	18	pk	pk	NOUN
ejpam-6378	259	19	]	]	X
ejpam-6378	259	20	]	]	PUNCT
ejpam-6378	259	21	.	.	PUNCT
ejpam-6378	260	1	νk+1(κ	νk+1(κ	PROPN
ejpam-6378	260	2	,	,	PUNCT
ejpam-6378	260	3	θ	θ	NOUN
ejpam-6378	260	4	)	)	PUNCT
ejpam-6378	260	5	=	=	SYM
ejpam-6378	261	1	m−1	m−1	PROPN
ejpam-6378	261	2	[	[	PUNCT
ejpam-6378	261	3	−	−	PROPN
ejpam-6378	261	4	1	1	NUM
ejpam-6378	261	5	sα	sα	NOUN
ejpam-6378	261	6	m	m	PRON
ejpam-6378	261	7	[	[	PUNCT
ejpam-6378	261	8	fνk(κ	fνk(κ	PROPN
ejpam-6378	261	9	,	,	PUNCT
ejpam-6378	261	10	θ	θ	NOUN
ejpam-6378	261	11	)	)	PUNCT
ejpam-6378	261	12	+	+	NUM
ejpam-6378	261	13	pk	pk	NOUN
ejpam-6378	261	14	]	]	X
ejpam-6378	261	15	]	]	PUNCT
ejpam-6378	261	16	.	.	PUNCT
ejpam-6378	262	1	νk+1(κ	νk+1(κ	PROPN
ejpam-6378	262	2	,	,	PUNCT
ejpam-6378	262	3	θ	θ	NOUN
ejpam-6378	262	4	)	)	PUNCT
ejpam-6378	262	5	=	=	SYM
ejpam-6378	262	6	y−1	y−1	PROPN
ejpam-6378	262	7	[	[	PUNCT
ejpam-6378	262	8	−sα	−sα	X
ejpam-6378	262	9	y	y	PROPN
ejpam-6378	262	10	[	[	PUNCT
ejpam-6378	262	11	fνk(κ	fνk(κ	PROPN
ejpam-6378	262	12	,	,	PUNCT
ejpam-6378	262	13	θ	θ	NOUN
ejpam-6378	262	14	)	)	PUNCT
ejpam-6378	262	15	+	+	NUM
ejpam-6378	262	16	pk	pk	NOUN
ejpam-6378	262	17	]	]	X
ejpam-6378	262	18	]	]	PUNCT
ejpam-6378	262	19	.	.	PUNCT
ejpam-6378	263	1	νk+1(κ	νk+1(κ	PROPN
ejpam-6378	263	2	,	,	PUNCT
ejpam-6378	263	3	θ	θ	NOUN
ejpam-6378	263	4	)	)	PUNCT
ejpam-6378	263	5	=	=	SYM
ejpam-6378	263	6	e−1	e−1	PROPN
ejpam-6378	263	7	[	[	PUNCT
ejpam-6378	263	8	−sα	−sα	X
ejpam-6378	263	9	e	e	X
ejpam-6378	263	10	[	[	PUNCT
ejpam-6378	263	11	fνk(κ	fνk(κ	PROPN
ejpam-6378	263	12	,	,	PUNCT
ejpam-6378	263	13	θ	θ	NOUN
ejpam-6378	263	14	)	)	PUNCT
ejpam-6378	263	15	+	+	NUM
ejpam-6378	263	16	pk	pk	NOUN
ejpam-6378	263	17	]	]	X
ejpam-6378	263	18	]	]	PUNCT
ejpam-6378	263	19	.	.	PUNCT
ejpam-6378	264	1	νk+1(κ	νk+1(κ	PROPN
ejpam-6378	264	2	,	,	PUNCT
ejpam-6378	264	3	θ	θ	NOUN
ejpam-6378	264	4	)	)	PUNCT
ejpam-6378	264	5	=	=	SYM
ejpam-6378	264	6	s−1	s−1	PROPN
ejpam-6378	264	7	[	[	PUNCT
ejpam-6378	264	8	−sα	−sα	X
ejpam-6378	264	9	s	s	X
ejpam-6378	264	10	[	[	PUNCT
ejpam-6378	264	11	fνk(κ	fνk(κ	PROPN
ejpam-6378	264	12	,	,	PUNCT
ejpam-6378	264	13	θ	θ	NOUN
ejpam-6378	264	14	)	)	PUNCT
ejpam-6378	264	15	+	+	NUM
ejpam-6378	264	16	pk	pk	NOUN
ejpam-6378	264	17	]	]	X
ejpam-6378	264	18	]	]	PUNCT
ejpam-6378	264	19	.	.	PUNCT
ejpam-6378	265	1	νk+1(κ	νk+1(κ	PROPN
ejpam-6378	265	2	,	,	PUNCT
ejpam-6378	265	3	θ	θ	NOUN
ejpam-6378	265	4	)	)	PUNCT
ejpam-6378	265	5	=	=	SYM
ejpam-6378	265	6	s−1	s−1	PROPN
ejpam-6378	265	7	[	[	PUNCT
ejpam-6378	265	8	−	−	PROPN
ejpam-6378	265	9	ςα	ςα	INTJ
ejpam-6378	265	10	sα	sα	NOUN
ejpam-6378	265	11	s	s	X
ejpam-6378	265	12	[	[	PUNCT
ejpam-6378	265	13	fνk(κ	fνk(κ	PROPN
ejpam-6378	265	14	,	,	PUNCT
ejpam-6378	265	15	θ	θ	NOUN
ejpam-6378	265	16	)	)	PUNCT
ejpam-6378	265	17	+	+	NUM
ejpam-6378	265	18	pk	pk	NOUN
ejpam-6378	265	19	]	]	X
ejpam-6378	265	20	]	]	PUNCT
ejpam-6378	265	21	.	.	PUNCT
ejpam-6378	266	1	νk+1(κ	νk+1(κ	PROPN
ejpam-6378	266	2	,	,	PUNCT
ejpam-6378	266	3	θ	θ	NOUN
ejpam-6378	266	4	)	)	PUNCT
ejpam-6378	266	5	=	=	SYM
ejpam-6378	266	6	n−1	n−1	PROPN
ejpam-6378	266	7	[	[	PUNCT
ejpam-6378	266	8	−	−	PROPN
ejpam-6378	266	9	ςα	ςα	INTJ
ejpam-6378	266	10	sα	sα	VERB
ejpam-6378	266	11	n	n	PROPN
ejpam-6378	266	12	[	[	PUNCT
ejpam-6378	266	13	fνk(κ	fνk(κ	PROPN
ejpam-6378	266	14	,	,	PUNCT
ejpam-6378	266	15	θ	θ	NOUN
ejpam-6378	266	16	)	)	PUNCT
ejpam-6378	266	17	+	+	NUM
ejpam-6378	266	18	pk	pk	NOUN
ejpam-6378	266	19	]	]	X
ejpam-6378	266	20	]	]	PUNCT
ejpam-6378	266	21	.	.	PUNCT
ejpam-6378	267	1	(	(	PUNCT
ejpam-6378	267	2	32	32	NUM
ejpam-6378	267	3	)	)	PUNCT
ejpam-6378	267	4	similarly	similarly	ADV
ejpam-6378	267	5	,	,	PUNCT
ejpam-6378	267	6	using	use	VERB
ejpam-6378	267	7	cffd	cffd	NOUN
ejpam-6378	267	8	,	,	PUNCT
ejpam-6378	267	9	iterative	iterative	ADJ
ejpam-6378	267	10	terms	term	NOUN
ejpam-6378	267	11	for	for	ADP
ejpam-6378	267	12	adm	adm	PROPN
ejpam-6378	267	13	under	under	ADP
ejpam-6378	267	14	different	different	ADJ
ejpam-6378	267	15	transformations	transformation	NOUN
ejpam-6378	267	16	,	,	PUNCT
ejpam-6378	267	17	are	be	AUX
ejpam-6378	267	18	given	give	VERB
ejpam-6378	267	19	in	in	ADP
ejpam-6378	267	20	equation	equation	NOUN
ejpam-6378	267	21	(	(	PUNCT
ejpam-6378	267	22	35	35	NUM
ejpam-6378	267	23	)	)	PUNCT
ejpam-6378	267	24	νk+1(κ	νk+1(κ	PROPN
ejpam-6378	267	25	,	,	PUNCT
ejpam-6378	267	26	θ	θ	NOUN
ejpam-6378	267	27	)	)	PUNCT
ejpam-6378	268	1	=	=	SYM
ejpam-6378	268	2	l−1	l−1	PROPN
ejpam-6378	268	3	[	[	PUNCT
ejpam-6378	268	4	−	−	PROPN
ejpam-6378	268	5	1−	1−	NUM
ejpam-6378	268	6	α	α	PROPN
ejpam-6378	268	7	n(α)s	n(α)s	NOUN
ejpam-6378	268	8	(	(	PUNCT
ejpam-6378	268	9	s+	s+	ADV
ejpam-6378	268	10	α	α	PROPN
ejpam-6378	268	11	1−	1−	NUM
ejpam-6378	268	12	α	α	NOUN
ejpam-6378	268	13	)	)	PUNCT
ejpam-6378	268	14	l	l	NOUN
ejpam-6378	268	15	[	[	PUNCT
ejpam-6378	268	16	fνk(κ	fνk(κ	X
ejpam-6378	268	17	,	,	PUNCT
ejpam-6378	268	18	θ	θ	NOUN
ejpam-6378	268	19	)	)	PUNCT
ejpam-6378	268	20	+	+	NUM
ejpam-6378	268	21	pk	pk	NOUN
ejpam-6378	268	22	]	]	X
ejpam-6378	268	23	]	]	PUNCT
ejpam-6378	268	24	,	,	PUNCT
ejpam-6378	268	25	k	k	X
ejpam-6378	268	26	≥	≥	PROPN
ejpam-6378	268	27	0	0	NUM
ejpam-6378	268	28	,	,	PUNCT
ejpam-6378	268	29	(	(	PUNCT
ejpam-6378	268	30	33	33	NUM
ejpam-6378	268	31	)	)	PUNCT
ejpam-6378	268	32	and	and	CCONJ
ejpam-6378	268	33	νk+1(κ	νk+1(κ	PROPN
ejpam-6378	268	34	,	,	PUNCT
ejpam-6378	268	35	θ	θ	NOUN
ejpam-6378	268	36	)	)	PUNCT
ejpam-6378	268	37	=	=	SYM
ejpam-6378	268	38	l−1	l−1	PROPN
ejpam-6378	268	39	[	[	PUNCT
ejpam-6378	268	40	−sα(1−	−sα(1−	VERB
ejpam-6378	268	41	α	α	NUM
ejpam-6378	268	42	)	)	PUNCT
ejpam-6378	268	43	+	+	CCONJ
ejpam-6378	268	44	α	α	NUM
ejpam-6378	268	45	ab(α)sα	ab(α)sα	ADP
ejpam-6378	268	46	l	l	NOUN
ejpam-6378	268	47	[	[	PUNCT
ejpam-6378	268	48	fνk(κ	fνk(κ	PROPN
ejpam-6378	268	49	,	,	PUNCT
ejpam-6378	268	50	θ	θ	NOUN
ejpam-6378	268	51	)	)	PUNCT
ejpam-6378	268	52	+	+	NUM
ejpam-6378	268	53	pk	pk	NOUN
ejpam-6378	268	54	]	]	X
ejpam-6378	268	55	]	]	PUNCT
ejpam-6378	268	56	,	,	PUNCT
ejpam-6378	268	57	k	k	X
ejpam-6378	268	58	≥	≥	PROPN
ejpam-6378	268	59	0	0	NUM
ejpam-6378	268	60	.	.	PUNCT
ejpam-6378	269	1	(	(	PUNCT
ejpam-6378	269	2	34	34	NUM
ejpam-6378	269	3	)	)	PUNCT
ejpam-6378	269	4			PROPN
ejpam-6378	269	5	νk+1(κ	νk+1(κ	PROPN
ejpam-6378	269	6	,	,	PUNCT
ejpam-6378	269	7	θ	θ	NOUN
ejpam-6378	269	8	)	)	PUNCT
ejpam-6378	269	9	=	=	SYM
ejpam-6378	269	10	l−1	l−1	PROPN
ejpam-6378	269	11	[	[	PUNCT
ejpam-6378	269	12	−	−	PROPN
ejpam-6378	269	13	1−α	1−α	NUM
ejpam-6378	269	14	n(α)s(s+	n(α)s(s+	CCONJ
ejpam-6378	269	15	α	α	PROPN
ejpam-6378	269	16	1−α)l	1−α)l	PROPN
ejpam-6378	269	17	[	[	PUNCT
ejpam-6378	269	18	fνk(κ	fνk(κ	PROPN
ejpam-6378	269	19	,	,	PUNCT
ejpam-6378	269	20	θ	θ	NOUN
ejpam-6378	269	21	)	)	PUNCT
ejpam-6378	269	22	+	+	NUM
ejpam-6378	269	23	pk	pk	NOUN
ejpam-6378	269	24	]	]	X
ejpam-6378	269	25	]	]	PUNCT
ejpam-6378	269	26	.	.	PUNCT
ejpam-6378	270	1	νk+1(κ	νk+1(κ	PROPN
ejpam-6378	270	2	,	,	PUNCT
ejpam-6378	270	3	θ	θ	NOUN
ejpam-6378	270	4	)	)	PUNCT
ejpam-6378	270	5	=	=	SYM
ejpam-6378	270	6	a−1	a−1	PROPN
ejpam-6378	270	7	[	[	PUNCT
ejpam-6378	270	8	−	−	PROPN
ejpam-6378	270	9	1−α	1−α	NUM
ejpam-6378	270	10	n(α)s(s+	n(α)s(s+	NUM
ejpam-6378	270	11	α	α	PROPN
ejpam-6378	270	12	1−α)a	1−α)a	NUM
ejpam-6378	270	13	[	[	PUNCT
ejpam-6378	270	14	fνk(κ	fνk(κ	PROPN
ejpam-6378	270	15	,	,	PUNCT
ejpam-6378	270	16	θ	θ	NOUN
ejpam-6378	270	17	)	)	PUNCT
ejpam-6378	270	18	+	+	NUM
ejpam-6378	270	19	pk	pk	NOUN
ejpam-6378	270	20	]	]	X
ejpam-6378	270	21	]	]	PUNCT
ejpam-6378	270	22	.	.	PUNCT
ejpam-6378	271	1	νk+1(κ	νk+1(κ	PROPN
ejpam-6378	271	2	,	,	PUNCT
ejpam-6378	271	3	θ	θ	NOUN
ejpam-6378	271	4	)	)	PUNCT
ejpam-6378	271	5	=	=	SYM
ejpam-6378	272	1	m−1	m−1	PROPN
ejpam-6378	272	2	[	[	PUNCT
ejpam-6378	272	3	−	−	PROPN
ejpam-6378	272	4	1−α	1−α	NUM
ejpam-6378	272	5	n(α)s(s+	n(α)s(s+	CCONJ
ejpam-6378	272	6	α	α	PROPN
ejpam-6378	272	7	1−α)m	1−α)m	NUM
ejpam-6378	272	8	[	[	PUNCT
ejpam-6378	272	9	fνk(κ	fνk(κ	PROPN
ejpam-6378	272	10	,	,	PUNCT
ejpam-6378	272	11	θ	θ	NOUN
ejpam-6378	272	12	)	)	PUNCT
ejpam-6378	272	13	+	+	NUM
ejpam-6378	272	14	pk	pk	NOUN
ejpam-6378	272	15	]	]	X
ejpam-6378	272	16	]	]	PUNCT
ejpam-6378	272	17	.	.	PUNCT
ejpam-6378	273	1	νk+1(κ	νk+1(κ	PROPN
ejpam-6378	273	2	,	,	PUNCT
ejpam-6378	273	3	θ	θ	NOUN
ejpam-6378	273	4	)	)	PUNCT
ejpam-6378	273	5	=	=	SYM
ejpam-6378	273	6	y−1	y−1	PROPN
ejpam-6378	273	7	[	[	PUNCT
ejpam-6378	273	8	−1+α(s−1	−1+α(s−1	NOUN
ejpam-6378	273	9	)	)	PUNCT
ejpam-6378	273	10	n(α	n(α	PROPN
ejpam-6378	273	11	)	)	PUNCT
ejpam-6378	274	1	y	y	PROPN
ejpam-6378	274	2	[	[	PUNCT
ejpam-6378	274	3	fνk(κ	fνk(κ	PROPN
ejpam-6378	274	4	,	,	PUNCT
ejpam-6378	274	5	θ	θ	NOUN
ejpam-6378	274	6	)	)	PUNCT
ejpam-6378	274	7	+	+	NUM
ejpam-6378	274	8	pk	pk	NOUN
ejpam-6378	274	9	]	]	X
ejpam-6378	274	10	]	]	PUNCT
ejpam-6378	274	11	.	.	PUNCT
ejpam-6378	275	1	νk+1(κ	νk+1(κ	PROPN
ejpam-6378	275	2	,	,	PUNCT
ejpam-6378	275	3	θ	θ	NOUN
ejpam-6378	275	4	)	)	PUNCT
ejpam-6378	275	5	=	=	SYM
ejpam-6378	275	6	e−1	e−1	PROPN
ejpam-6378	275	7	[	[	PUNCT
ejpam-6378	275	8	−1+α(s−1	−1+α(s−1	NOUN
ejpam-6378	275	9	)	)	PUNCT
ejpam-6378	275	10	n(α	n(α	PROPN
ejpam-6378	275	11	)	)	PUNCT
ejpam-6378	276	1	e	e	X
ejpam-6378	276	2	[	[	PUNCT
ejpam-6378	276	3	fνk(κ	fνk(κ	PROPN
ejpam-6378	276	4	,	,	PUNCT
ejpam-6378	276	5	θ	θ	NOUN
ejpam-6378	276	6	)	)	PUNCT
ejpam-6378	276	7	+	+	NUM
ejpam-6378	276	8	pk	pk	NOUN
ejpam-6378	276	9	]	]	X
ejpam-6378	276	10	]	]	PUNCT
ejpam-6378	276	11	.	.	PUNCT
ejpam-6378	277	1	νk+1(κ	νk+1(κ	PROPN
ejpam-6378	277	2	,	,	PUNCT
ejpam-6378	277	3	θ	θ	NOUN
ejpam-6378	277	4	)	)	PUNCT
ejpam-6378	277	5	=	=	SYM
ejpam-6378	277	6	s−1	s−1	PROPN
ejpam-6378	277	7	[	[	PUNCT
ejpam-6378	277	8	−1+α(s−1	−1+α(s−1	NOUN
ejpam-6378	277	9	)	)	PUNCT
ejpam-6378	277	10	n(α	n(α	PROPN
ejpam-6378	277	11	)	)	PUNCT
ejpam-6378	277	12	s	s	PART
ejpam-6378	277	13	[	[	PUNCT
ejpam-6378	277	14	fνk(κ	fνk(κ	PROPN
ejpam-6378	277	15	,	,	PUNCT
ejpam-6378	277	16	θ	θ	NOUN
ejpam-6378	277	17	)	)	PUNCT
ejpam-6378	278	1	+	+	NUM
ejpam-6378	278	2	pk	pk	NOUN
ejpam-6378	278	3	]	]	X
ejpam-6378	278	4	]	]	PUNCT
ejpam-6378	278	5	.	.	PUNCT
ejpam-6378	279	1	νk+1(κ	νk+1(κ	PROPN
ejpam-6378	279	2	,	,	PUNCT
ejpam-6378	279	3	θ	θ	NOUN
ejpam-6378	279	4	)	)	PUNCT
ejpam-6378	279	5	=	=	SYM
ejpam-6378	279	6	s−1	s−1	PROPN
ejpam-6378	279	7	[	[	PUNCT
ejpam-6378	279	8	−	−	PROPN
ejpam-6378	279	9	(	(	PUNCT
ejpam-6378	279	10	1−α)ς	1−α)ς	NUM
ejpam-6378	279	11	sn(α	sn(α	NUM
ejpam-6378	279	12	)	)	PUNCT
ejpam-6378	279	13	(	(	PUNCT
ejpam-6378	279	14	s	s	X
ejpam-6378	279	15	ς	ς	PROPN
ejpam-6378	279	16	+	+	PROPN
ejpam-6378	279	17	α	α	PROPN
ejpam-6378	279	18	1−α)s	1−α)s	NUM
ejpam-6378	279	19	[	[	PUNCT
ejpam-6378	279	20	fνk(κ	fνk(κ	PROPN
ejpam-6378	279	21	,	,	PUNCT
ejpam-6378	279	22	θ	θ	NOUN
ejpam-6378	279	23	)	)	PUNCT
ejpam-6378	279	24	+	+	NUM
ejpam-6378	279	25	pk	pk	NOUN
ejpam-6378	279	26	]	]	X
ejpam-6378	279	27	]	]	PUNCT
ejpam-6378	279	28	.	.	PUNCT
ejpam-6378	280	1	νk+1(κ	νk+1(κ	PROPN
ejpam-6378	280	2	,	,	PUNCT
ejpam-6378	280	3	θ	θ	NOUN
ejpam-6378	280	4	)	)	PUNCT
ejpam-6378	280	5	=	=	SYM
ejpam-6378	280	6	n−1	n−1	PROPN
ejpam-6378	280	7	[	[	PUNCT
ejpam-6378	280	8	−	−	PROPN
ejpam-6378	280	9	(	(	PUNCT
ejpam-6378	280	10	1−α)ς	1−α)ς	NUM
ejpam-6378	280	11	sn(α	sn(α	NUM
ejpam-6378	280	12	)	)	PUNCT
ejpam-6378	280	13	(	(	PUNCT
ejpam-6378	280	14	s	s	X
ejpam-6378	280	15	ς	ς	PROPN
ejpam-6378	280	16	+	+	NOUN
ejpam-6378	280	17	α	α	PROPN
ejpam-6378	280	18	1−α)n	1−α)n	X
ejpam-6378	280	19	[	[	PUNCT
ejpam-6378	280	20	fνk(κ	fνk(κ	PROPN
ejpam-6378	280	21	,	,	PUNCT
ejpam-6378	280	22	θ	θ	NOUN
ejpam-6378	280	23	)	)	PUNCT
ejpam-6378	280	24	+	+	NUM
ejpam-6378	280	25	pk	pk	NOUN
ejpam-6378	280	26	]	]	X
ejpam-6378	280	27	]	]	PUNCT
ejpam-6378	280	28	.	.	PUNCT
ejpam-6378	281	1	(	(	PUNCT
ejpam-6378	281	2	35	35	NUM
ejpam-6378	281	3	)	)	PUNCT
ejpam-6378	281	4	m.	m.	NOUN
ejpam-6378	281	5	sohail	sohail	PROPN
ejpam-6378	281	6	et	et	PROPN
ejpam-6378	281	7	al	al	PROPN
ejpam-6378	281	8	.	.	PUNCT
ejpam-6378	281	9	/	/	SYM
ejpam-6378	281	10	eur	eur	PROPN
ejpam-6378	281	11	.	.	PUNCT
ejpam-6378	282	1	j.	j.	PROPN
ejpam-6378	282	2	pure	pure	PROPN
ejpam-6378	282	3	appl	appl	PROPN
ejpam-6378	282	4	.	.	PROPN
ejpam-6378	282	5	math	math	PROPN
ejpam-6378	282	6	,	,	PUNCT
ejpam-6378	282	7	18	18	NUM
ejpam-6378	282	8	(	(	PUNCT
ejpam-6378	282	9	4	4	NUM
ejpam-6378	282	10	)	)	PUNCT
ejpam-6378	282	11	(	(	PUNCT
ejpam-6378	282	12	2025	2025	NUM
ejpam-6378	282	13	)	)	PUNCT
ejpam-6378	282	14	,	,	PUNCT
ejpam-6378	282	15	6378	6378	NUM
ejpam-6378	282	16	11	11	NUM
ejpam-6378	282	17	of	of	ADP
ejpam-6378	282	18	20	20	NUM
ejpam-6378	282	19	similarly	similarly	ADV
ejpam-6378	282	20	,	,	PUNCT
ejpam-6378	282	21	using	use	VERB
ejpam-6378	282	22	abfd	abfd	PROPN
ejpam-6378	282	23	,	,	PUNCT
ejpam-6378	282	24	iterative	iterative	ADJ
ejpam-6378	282	25	terms	term	NOUN
ejpam-6378	282	26	for	for	ADP
ejpam-6378	282	27	adm	adm	PROPN
ejpam-6378	282	28	under	under	ADP
ejpam-6378	282	29	different	different	ADJ
ejpam-6378	282	30	transformations	transformation	NOUN
ejpam-6378	282	31	,	,	PUNCT
ejpam-6378	282	32	are	be	AUX
ejpam-6378	282	33	given	give	VERB
ejpam-6378	282	34	in	in	ADP
ejpam-6378	282	35	equations	equation	NOUN
ejpam-6378	282	36	(	(	PUNCT
ejpam-6378	282	37	36)	36)	NUM
ejpam-6378	282	38	νk+1(κ	νk+1(κ	PROPN
ejpam-6378	282	39	,	,	PUNCT
ejpam-6378	282	40	θ	θ	NOUN
ejpam-6378	282	41	)	)	PUNCT
ejpam-6378	282	42	=	=	SYM
ejpam-6378	282	43	l−1	l−1	PROPN
ejpam-6378	282	44	[	[	PUNCT
ejpam-6378	282	45	−	−	NOUN
ejpam-6378	282	46	sα(1−α)+α	sα(1−α)+α	X
ejpam-6378	282	47	ab(α)sα	ab(α)sα	ADV
ejpam-6378	282	48	l	l	NOUN
ejpam-6378	282	49	[	[	PUNCT
ejpam-6378	282	50	fνk(κ	fνk(κ	PROPN
ejpam-6378	282	51	,	,	PUNCT
ejpam-6378	282	52	θ	θ	NOUN
ejpam-6378	282	53	)	)	PUNCT
ejpam-6378	282	54	+	+	NUM
ejpam-6378	282	55	pk	pk	NOUN
ejpam-6378	282	56	]	]	X
ejpam-6378	282	57	]	]	PUNCT
ejpam-6378	282	58	.	.	PUNCT
ejpam-6378	283	1	νk+1(κ	νk+1(κ	PROPN
ejpam-6378	283	2	,	,	PUNCT
ejpam-6378	283	3	θ	θ	NOUN
ejpam-6378	283	4	)	)	PUNCT
ejpam-6378	283	5	=	=	SYM
ejpam-6378	283	6	a−1	a−1	PROPN
ejpam-6378	283	7	[	[	PUNCT
ejpam-6378	283	8	−	−	NOUN
ejpam-6378	283	9	sα(1−α)+α	sα(1−α)+α	X
ejpam-6378	283	10	ab(α)sα	ab(α)sα	CCONJ
ejpam-6378	283	11	a	a	DET
ejpam-6378	283	12	[	[	PUNCT
ejpam-6378	283	13	fνk(κ	fνk(κ	PROPN
ejpam-6378	283	14	,	,	PUNCT
ejpam-6378	283	15	θ	θ	NOUN
ejpam-6378	283	16	)	)	PUNCT
ejpam-6378	283	17	+	+	NUM
ejpam-6378	283	18	pk	pk	NOUN
ejpam-6378	283	19	]	]	X
ejpam-6378	283	20	]	]	PUNCT
ejpam-6378	283	21	.	.	PUNCT
ejpam-6378	284	1	νk+1(κ	νk+1(κ	PROPN
ejpam-6378	284	2	,	,	PUNCT
ejpam-6378	284	3	θ	θ	NOUN
ejpam-6378	284	4	)	)	PUNCT
ejpam-6378	284	5	=	=	SYM
ejpam-6378	285	1	m−1	m−1	PROPN
ejpam-6378	285	2	[	[	PUNCT
ejpam-6378	285	3	−	−	NOUN
ejpam-6378	285	4	sα(1−α)+α	sα(1−α)+α	X
ejpam-6378	285	5	ab(α)sα	ab(α)sα	ADV
ejpam-6378	285	6	m	m	PROPN
ejpam-6378	285	7	[	[	PUNCT
ejpam-6378	285	8	fνk(κ	fνk(κ	PROPN
ejpam-6378	285	9	,	,	PUNCT
ejpam-6378	285	10	θ	θ	NOUN
ejpam-6378	285	11	)	)	PUNCT
ejpam-6378	285	12	+	+	NUM
ejpam-6378	285	13	pk	pk	NOUN
ejpam-6378	285	14	]	]	X
ejpam-6378	285	15	]	]	PUNCT
ejpam-6378	285	16	.	.	PUNCT
ejpam-6378	286	1	νk+1(κ	νk+1(κ	PROPN
ejpam-6378	286	2	,	,	PUNCT
ejpam-6378	286	3	θ	θ	NOUN
ejpam-6378	286	4	)	)	PUNCT
ejpam-6378	286	5	=	=	SYM
ejpam-6378	286	6	y−1	y−1	PROPN
ejpam-6378	286	7	[	[	PUNCT
ejpam-6378	286	8	−α(sα−1)+1	−α(sα−1)+1	NUM
ejpam-6378	286	9	ab(α	ab(α	NUM
ejpam-6378	286	10	)	)	PUNCT
ejpam-6378	286	11	y	y	PROPN
ejpam-6378	286	12	[	[	PUNCT
ejpam-6378	286	13	fνk(κ	fνk(κ	PROPN
ejpam-6378	286	14	,	,	PUNCT
ejpam-6378	286	15	θ	θ	NOUN
ejpam-6378	286	16	)	)	PUNCT
ejpam-6378	286	17	+	+	NUM
ejpam-6378	286	18	pk	pk	NOUN
ejpam-6378	286	19	]	]	X
ejpam-6378	286	20	]	]	PUNCT
ejpam-6378	286	21	.	.	PUNCT
ejpam-6378	287	1	νk+1(κ	νk+1(κ	PROPN
ejpam-6378	287	2	,	,	PUNCT
ejpam-6378	287	3	θ	θ	NOUN
ejpam-6378	287	4	)	)	PUNCT
ejpam-6378	287	5	=	=	SYM
ejpam-6378	287	6	e−1	e−1	PROPN
ejpam-6378	287	7	[	[	PUNCT
ejpam-6378	287	8	−α(sα−1)+1	−α(sα−1)+1	NUM
ejpam-6378	287	9	ab(α	ab(α	NUM
ejpam-6378	287	10	)	)	PUNCT
ejpam-6378	287	11	e	e	X
ejpam-6378	287	12	[	[	PUNCT
ejpam-6378	287	13	fνk(κ	fνk(κ	PROPN
ejpam-6378	287	14	,	,	PUNCT
ejpam-6378	287	15	θ	θ	NOUN
ejpam-6378	287	16	)	)	PUNCT
ejpam-6378	287	17	+	+	NUM
ejpam-6378	287	18	pk	pk	NOUN
ejpam-6378	287	19	]	]	X
ejpam-6378	287	20	]	]	PUNCT
ejpam-6378	287	21	.	.	PUNCT
ejpam-6378	288	1	νk+1(κ	νk+1(κ	PROPN
ejpam-6378	288	2	,	,	PUNCT
ejpam-6378	288	3	θ	θ	NOUN
ejpam-6378	288	4	)	)	PUNCT
ejpam-6378	288	5	=	=	SYM
ejpam-6378	288	6	s−1	s−1	PROPN
ejpam-6378	288	7	[	[	PUNCT
ejpam-6378	288	8	−α(sα−1)+1	−α(sα−1)+1	NUM
ejpam-6378	288	9	ab(α	ab(α	NUM
ejpam-6378	288	10	)	)	PUNCT
ejpam-6378	288	11	s	s	PART
ejpam-6378	288	12	[	[	PUNCT
ejpam-6378	288	13	fνk(κ	fνk(κ	PROPN
ejpam-6378	288	14	,	,	PUNCT
ejpam-6378	288	15	θ	θ	NOUN
ejpam-6378	288	16	)	)	PUNCT
ejpam-6378	288	17	+	+	NUM
ejpam-6378	288	18	pk	pk	NOUN
ejpam-6378	288	19	]	]	X
ejpam-6378	288	20	]	]	PUNCT
ejpam-6378	288	21	.	.	PUNCT
ejpam-6378	289	1	νk+1(κ	νk+1(κ	PROPN
ejpam-6378	289	2	,	,	PUNCT
ejpam-6378	289	3	θ	θ	NOUN
ejpam-6378	289	4	)	)	PUNCT
ejpam-6378	289	5	=	=	SYM
ejpam-6378	289	6	s−1	s−1	PROPN
ejpam-6378	289	7	[	[	PUNCT
ejpam-6378	289	8	−	−	PROPN
ejpam-6378	289	9	sα(1−α)+	sα(1−α)+	NOUN
ejpam-6378	289	10	α	α	NOUN
ejpam-6378	289	11	ςα	ςα	NOUN
ejpam-6378	289	12	ab(α)sα	ab(α)sα	ADP
ejpam-6378	289	13	s	s	X
ejpam-6378	289	14	[	[	PUNCT
ejpam-6378	289	15	fνk(κ	fνk(κ	PROPN
ejpam-6378	289	16	,	,	PUNCT
ejpam-6378	289	17	θ	θ	NOUN
ejpam-6378	289	18	)	)	PUNCT
ejpam-6378	289	19	+	+	NUM
ejpam-6378	289	20	pk	pk	NOUN
ejpam-6378	289	21	]	]	X
ejpam-6378	289	22	]	]	PUNCT
ejpam-6378	289	23	.	.	PUNCT
ejpam-6378	290	1	νk+1(κ	νk+1(κ	PROPN
ejpam-6378	290	2	,	,	PUNCT
ejpam-6378	290	3	θ	θ	NOUN
ejpam-6378	290	4	)	)	PUNCT
ejpam-6378	290	5	=	=	SYM
ejpam-6378	290	6	n−1	n−1	PROPN
ejpam-6378	290	7	[	[	PUNCT
ejpam-6378	290	8	−	−	PROPN
ejpam-6378	290	9	sα(1−α)+	sα(1−α)+	NOUN
ejpam-6378	290	10	α	α	NOUN
ejpam-6378	290	11	ςα	ςα	NOUN
ejpam-6378	290	12	ab(α)sα	ab(α)sα	ADP
ejpam-6378	290	13	n	n	CCONJ
ejpam-6378	290	14	[	[	PUNCT
ejpam-6378	290	15	fνk(κ	fνk(κ	PROPN
ejpam-6378	290	16	,	,	PUNCT
ejpam-6378	290	17	θ	θ	NOUN
ejpam-6378	290	18	)	)	PUNCT
ejpam-6378	290	19	+	+	NUM
ejpam-6378	290	20	pk	pk	NOUN
ejpam-6378	290	21	]	]	X
ejpam-6378	290	22	]	]	PUNCT
ejpam-6378	290	23	.	.	PUNCT
ejpam-6378	291	1	(	(	PUNCT
ejpam-6378	291	2	36	36	NUM
ejpam-6378	291	3	)	)	PUNCT
ejpam-6378	291	4	if	if	SCONJ
ejpam-6378	291	5	f(κ	f(κ	PROPN
ejpam-6378	291	6	,	,	PUNCT
ejpam-6378	291	7	θ	θ	NOUN
ejpam-6378	291	8	)	)	PUNCT
ejpam-6378	291	9	=	=	SYM
ejpam-6378	291	10	0	0	NUM
ejpam-6378	291	11	then	then	ADV
ejpam-6378	291	12	ν0(κ	ν0(κ	NUM
ejpam-6378	291	13	,	,	PUNCT
ejpam-6378	291	14	θ	θ	NOUN
ejpam-6378	291	15	)	)	PUNCT
ejpam-6378	291	16	is	be	AUX
ejpam-6378	291	17	calculated	calculate	VERB
ejpam-6378	291	18	as	as	ADP
ejpam-6378	291	19	ν0(κ	ν0(κ	PROPN
ejpam-6378	291	20	,	,	PUNCT
ejpam-6378	291	21	θ	θ	NOUN
ejpam-6378	291	22	)	)	PUNCT
ejpam-6378	291	23	=	=	SYM
ejpam-6378	291	24	l−1	l−1	PROPN
ejpam-6378	291	25	[	[	PUNCT
ejpam-6378	291	26	ν(κ	ν(κ	NOUN
ejpam-6378	291	27	,	,	PUNCT
ejpam-6378	291	28	0	0	NUM
ejpam-6378	291	29	)	)	PUNCT
ejpam-6378	291	30	s	s	PART
ejpam-6378	291	31	]	]	PUNCT
ejpam-6378	291	32	.	.	PUNCT
ejpam-6378	292	1	(	(	PUNCT
ejpam-6378	292	2	37	37	NUM
ejpam-6378	292	3	)	)	PUNCT
ejpam-6378	292	4	similarly	similarly	ADV
ejpam-6378	292	5	,	,	PUNCT
ejpam-6378	292	6	equation	equation	NOUN
ejpam-6378	292	7	(	(	PUNCT
ejpam-6378	292	8	38	38	NUM
ejpam-6378	292	9	)	)	PUNCT
ejpam-6378	292	10	,	,	PUNCT
ejpam-6378	292	11	for	for	ADP
ejpam-6378	292	12	ν0(κ	ν0(κ	ADV
ejpam-6378	292	13	,	,	PUNCT
ejpam-6378	292	14	θ	θ	NOUN
ejpam-6378	292	15	)	)	PUNCT
ejpam-6378	292	16	under	under	ADP
ejpam-6378	292	17	different	different	ADJ
ejpam-6378	292	18	transforms.	transforms.	PROPN
ejpam-6378	292	19	ν0(κ	ν0(κ	PROPN
ejpam-6378	292	20	,	,	PUNCT
ejpam-6378	292	21	θ	θ	NOUN
ejpam-6378	292	22	)	)	PUNCT
ejpam-6378	292	23	=	=	SYM
ejpam-6378	293	1	l−1	l−1	PROPN
ejpam-6378	293	2	[	[	PUNCT
ejpam-6378	293	3	ν(κ,0	ν(κ,0	PROPN
ejpam-6378	293	4	)	)	PUNCT
ejpam-6378	293	5	s	s	PART
ejpam-6378	293	6	]	]	PUNCT
ejpam-6378	293	7	.	.	PUNCT
ejpam-6378	294	1	ν0(κ	ν0(κ	ADV
ejpam-6378	294	2	,	,	PUNCT
ejpam-6378	294	3	θ	θ	NOUN
ejpam-6378	294	4	)	)	PUNCT
ejpam-6378	295	1	=	=	SYM
ejpam-6378	295	2	e−1	e−1	PROPN
ejpam-6378	295	3	[	[	PUNCT
ejpam-6378	295	4	s2ν(κ	s2ν(κ	PROPN
ejpam-6378	295	5	,	,	PUNCT
ejpam-6378	295	6	0	0	NUM
ejpam-6378	295	7	)	)	PUNCT
ejpam-6378	295	8	]	]	PUNCT
ejpam-6378	295	9	.	.	PUNCT
ejpam-6378	296	1	ν0(κ	ν0(κ	ADV
ejpam-6378	296	2	,	,	PUNCT
ejpam-6378	296	3	θ	θ	NOUN
ejpam-6378	296	4	)	)	PUNCT
ejpam-6378	296	5	=	=	SYM
ejpam-6378	296	6	a−1	a−1	PROPN
ejpam-6378	296	7	[	[	PUNCT
ejpam-6378	296	8	ν(κ,0	ν(κ,0	PROPN
ejpam-6378	296	9	)	)	PUNCT
ejpam-6378	296	10	s2	s2	NOUN
ejpam-6378	296	11	]	]	PUNCT
ejpam-6378	296	12	.	.	PUNCT
ejpam-6378	297	1	ν0(κ	ν0(κ	ADV
ejpam-6378	297	2	,	,	PUNCT
ejpam-6378	297	3	θ	θ	NOUN
ejpam-6378	297	4	)	)	PUNCT
ejpam-6378	298	1	=	=	SYM
ejpam-6378	298	2	s−1	s−1	PROPN
ejpam-6378	298	3	[	[	PUNCT
ejpam-6378	298	4	ν(κ	ν(κ	NOUN
ejpam-6378	298	5	,	,	PUNCT
ejpam-6378	298	6	0	0	NUM
ejpam-6378	298	7	)	)	PUNCT
ejpam-6378	298	8	]	]	PUNCT
ejpam-6378	298	9	.	.	PUNCT
ejpam-6378	299	1	ν0(κ	ν0(κ	ADV
ejpam-6378	299	2	,	,	PUNCT
ejpam-6378	299	3	θ	θ	NOUN
ejpam-6378	299	4	)	)	PUNCT
ejpam-6378	299	5	=	=	SYM
ejpam-6378	299	6	y−1	y−1	PROPN
ejpam-6378	299	7	[	[	PUNCT
ejpam-6378	299	8	s	s	NOUN
ejpam-6378	299	9	ν(κ	ν(κ	NOUN
ejpam-6378	299	10	,	,	PUNCT
ejpam-6378	299	11	0	0	NUM
ejpam-6378	299	12	)	)	PUNCT
ejpam-6378	299	13	]	]	PUNCT
ejpam-6378	299	14	.	.	PUNCT
ejpam-6378	300	1	ν0(κ	ν0(κ	ADV
ejpam-6378	300	2	,	,	PUNCT
ejpam-6378	300	3	θ	θ	NOUN
ejpam-6378	300	4	)	)	PUNCT
ejpam-6378	301	1	=	=	SYM
ejpam-6378	301	2	m−1	m−1	PROPN
ejpam-6378	301	3	[	[	PUNCT
ejpam-6378	301	4	s	s	NOUN
ejpam-6378	301	5	ν(κ	ν(κ	NOUN
ejpam-6378	301	6	,	,	PUNCT
ejpam-6378	301	7	0	0	NUM
ejpam-6378	301	8	)	)	PUNCT
ejpam-6378	301	9	]	]	PUNCT
ejpam-6378	301	10	.	.	PUNCT
ejpam-6378	302	1	ν0(κ	ν0(κ	ADV
ejpam-6378	302	2	,	,	PUNCT
ejpam-6378	302	3	θ	θ	NOUN
ejpam-6378	302	4	)	)	PUNCT
ejpam-6378	303	1	=	=	SYM
ejpam-6378	303	2	n−1	n−1	PROPN
ejpam-6378	303	3	[	[	PUNCT
ejpam-6378	303	4	ν(κ,0	ν(κ,0	PROPN
ejpam-6378	303	5	)	)	PUNCT
ejpam-6378	303	6	s	s	PART
ejpam-6378	303	7	]	]	PUNCT
ejpam-6378	303	8	.	.	PUNCT
ejpam-6378	304	1	ν0(κ	ν0(κ	ADV
ejpam-6378	304	2	,	,	PUNCT
ejpam-6378	304	3	θ	θ	NOUN
ejpam-6378	304	4	)	)	PUNCT
ejpam-6378	305	1	=	=	SYM
ejpam-6378	305	2	s−1	s−1	PROPN
ejpam-6378	305	3	[	[	PUNCT
ejpam-6378	305	4	ν(κ	ν(κ	NOUN
ejpam-6378	305	5	,	,	PUNCT
ejpam-6378	305	6	0	0	NUM
ejpam-6378	305	7	)	)	PUNCT
ejpam-6378	305	8	ς	ς	PROPN
ejpam-6378	305	9	s	s	X
ejpam-6378	305	10	]	]	PUNCT
ejpam-6378	305	11	.	.	PUNCT
ejpam-6378	306	1	(	(	PUNCT
ejpam-6378	306	2	38	38	NUM
ejpam-6378	306	3	)	)	PUNCT
ejpam-6378	306	4	the	the	DET
ejpam-6378	306	5	term	term	NOUN
ejpam-6378	306	6	-	-	PUNCT
ejpam-6378	306	7	wise	wise	ADJ
ejpam-6378	306	8	iterative	iterative	NOUN
ejpam-6378	306	9	solution	solution	NOUN
ejpam-6378	306	10	of	of	ADP
ejpam-6378	306	11	adm	adm	PROPN
ejpam-6378	306	12	with	with	ADP
ejpam-6378	306	13	different	different	ADJ
ejpam-6378	306	14	transforms	transform	NOUN
ejpam-6378	306	15	for	for	ADP
ejpam-6378	306	16	the	the	DET
ejpam-6378	306	17	equations	equation	NOUN
ejpam-6378	306	18	(	(	PUNCT
ejpam-6378	306	19	32	32	NUM
ejpam-6378	306	20	,	,	PUNCT
ejpam-6378	306	21	35	35	NUM
ejpam-6378	306	22	,	,	PUNCT
ejpam-6378	306	23	and	and	CCONJ
ejpam-6378	306	24	36	36	NUM
ejpam-6378	306	25	)	)	PUNCT
ejpam-6378	306	26	are	be	AUX
ejpam-6378	306	27	represented	represent	VERB
ejpam-6378	306	28	as	as	ADP
ejpam-6378	306	29	ν(κ	ν(κ	NOUN
ejpam-6378	306	30	,	,	PUNCT
ejpam-6378	306	31	θ	θ	NOUN
ejpam-6378	306	32	)	)	PUNCT
ejpam-6378	306	33	=	=	PUNCT
ejpam-6378	307	1	∞∑	∞∑	PRON
ejpam-6378	307	2	n=0	n=0	NUM
ejpam-6378	307	3	νn(κ	νn(κ	NOUN
ejpam-6378	307	4	,	,	PUNCT
ejpam-6378	307	5	θ	θ	NOUN
ejpam-6378	307	6	)	)	PUNCT
ejpam-6378	307	7	.	.	PUNCT
ejpam-6378	308	1	(	(	PUNCT
ejpam-6378	308	2	39	39	NUM
ejpam-6378	308	3	)	)	PUNCT
ejpam-6378	308	4	m.	m.	NOUN
ejpam-6378	308	5	sohail	sohail	PROPN
ejpam-6378	308	6	et	et	PROPN
ejpam-6378	308	7	al	al	PROPN
ejpam-6378	308	8	.	.	PUNCT
ejpam-6378	308	9	/	/	SYM
ejpam-6378	308	10	eur	eur	PROPN
ejpam-6378	308	11	.	.	PUNCT
ejpam-6378	309	1	j.	j.	PROPN
ejpam-6378	309	2	pure	pure	PROPN
ejpam-6378	309	3	appl	appl	PROPN
ejpam-6378	309	4	.	.	PROPN
ejpam-6378	309	5	math	math	PROPN
ejpam-6378	309	6	,	,	PUNCT
ejpam-6378	309	7	18	18	NUM
ejpam-6378	309	8	(	(	PUNCT
ejpam-6378	309	9	4	4	NUM
ejpam-6378	309	10	)	)	PUNCT
ejpam-6378	309	11	(	(	PUNCT
ejpam-6378	309	12	2025	2025	NUM
ejpam-6378	309	13	)	)	PUNCT
ejpam-6378	309	14	,	,	PUNCT
ejpam-6378	309	15	6378	6378	NUM
ejpam-6378	309	16	12	12	NUM
ejpam-6378	309	17	of	of	ADP
ejpam-6378	309	18	20	20	NUM
ejpam-6378	309	19	4	4	NUM
ejpam-6378	309	20	.	.	PUNCT
ejpam-6378	309	21	problem	problem	NOUN
ejpam-6378	309	22	solution	solution	NOUN
ejpam-6378	309	23	dα	dα	VERB
ejpam-6378	309	24	τ	τ	PROPN
ejpam-6378	309	25	µ(χ	µ(χ	PROPN
ejpam-6378	309	26	,	,	PUNCT
ejpam-6378	309	27	τ)−	τ)−	PROPN
ejpam-6378	309	28	d2µ	d2µ	X
ejpam-6378	309	29	dχ2	dχ2	NOUN
ejpam-6378	309	30	+	+	NOUN
ejpam-6378	309	31	dµ	dµ	PROPN
ejpam-6378	309	32	dχ	dχ	NOUN
ejpam-6378	309	33	−	−	PROPN
ejpam-6378	310	1	µ−	µ−	PROPN
ejpam-6378	310	2	µ	µ	X
ejpam-6378	310	3	(	(	PUNCT
ejpam-6378	310	4	d2µ	d2µ	NOUN
ejpam-6378	310	5	dχ2	dχ2	NOUN
ejpam-6378	310	6	)	)	PUNCT
ejpam-6378	311	1	+	+	CCONJ
ejpam-6378	311	2	µ2	µ2	PROPN
ejpam-6378	311	3	=	=	SYM
ejpam-6378	311	4	0	0	NUM
ejpam-6378	311	5	;	;	PUNCT
ejpam-6378	311	6	µ(χ	µ(χ	PROPN
ejpam-6378	311	7	,	,	PUNCT
ejpam-6378	311	8	0	0	NUM
ejpam-6378	311	9	)	)	PUNCT
ejpam-6378	311	10	=	=	SYM
ejpam-6378	311	11	eχ	eχ	PROPN
ejpam-6378	311	12	.	.	PUNCT
ejpam-6378	312	1	(	(	PUNCT
ejpam-6378	312	2	40	40	NUM
ejpam-6378	312	3	)	)	PUNCT
ejpam-6378	312	4	having	have	VERB
ejpam-6378	312	5	an	an	DET
ejpam-6378	312	6	exact	exact	ADJ
ejpam-6378	312	7	solution	solution	NOUN
ejpam-6378	312	8	µ(χ	µ(χ	PROPN
ejpam-6378	312	9	,	,	PUNCT
ejpam-6378	312	10	τ	τ	X
ejpam-6378	312	11	)	)	PUNCT
ejpam-6378	312	12	=	=	VERB
ejpam-6378	312	13	eχ+τ	eχ+τ	NOUN
ejpam-6378	312	14	.	.	PUNCT
ejpam-6378	313	1	(	(	PUNCT
ejpam-6378	313	2	41	41	NUM
ejpam-6378	313	3	)	)	PUNCT
ejpam-6378	313	4	4.1	4.1	NUM
ejpam-6378	313	5	.	.	PUNCT
ejpam-6378	314	1	solving	solve	VERB
ejpam-6378	314	2	under	under	ADP
ejpam-6378	314	3	caputo	caputo	PROPN
ejpam-6378	314	4	fractional	fractional	PROPN
ejpam-6378	314	5	differential	differential	NOUN
ejpam-6378	314	6	operator	operator	NOUN
ejpam-6378	314	7	µ0(χ	µ0(χ	NUM
ejpam-6378	314	8	,	,	PUNCT
ejpam-6378	314	9	τ	τ	X
ejpam-6378	314	10	)	)	PUNCT
ejpam-6378	314	11	=	=	NOUN
ejpam-6378	314	12	eχ	eχ	NOUN
ejpam-6378	314	13	.	.	PUNCT
ejpam-6378	315	1	(	(	PUNCT
ejpam-6378	315	2	42	42	X
ejpam-6378	315	3	)	)	PUNCT
ejpam-6378	315	4	µ1(χ	µ1(χ	PROPN
ejpam-6378	315	5	,	,	PUNCT
ejpam-6378	315	6	τ	τ	X
ejpam-6378	315	7	)	)	PUNCT
ejpam-6378	315	8	=	=	NOUN
ejpam-6378	315	9	eχτα	eχτα	NOUN
ejpam-6378	316	1	γ(1	γ(1	PROPN
ejpam-6378	316	2	+	+	CCONJ
ejpam-6378	316	3	α	α	NOUN
ejpam-6378	316	4	)	)	PUNCT
ejpam-6378	316	5	.	.	PUNCT
ejpam-6378	317	1	(	(	PUNCT
ejpam-6378	317	2	43	43	NUM
ejpam-6378	317	3	)	)	PUNCT
ejpam-6378	317	4	µ2(χ	µ2(χ	PROPN
ejpam-6378	317	5	,	,	PUNCT
ejpam-6378	317	6	τ	τ	X
ejpam-6378	317	7	)	)	PUNCT
ejpam-6378	317	8	=	=	SYM
ejpam-6378	317	9	eχ	eχ	PROPN
ejpam-6378	317	10	(	(	PUNCT
ejpam-6378	317	11	τα)2	τα)2	PROPN
ejpam-6378	317	12	γ(1	γ(1	NOUN
ejpam-6378	317	13	+	+	NUM
ejpam-6378	317	14	2α	2α	NOUN
ejpam-6378	317	15	)	)	PUNCT
ejpam-6378	317	16	.	.	PUNCT
ejpam-6378	318	1	(	(	PUNCT
ejpam-6378	318	2	44	44	NUM
ejpam-6378	318	3	)	)	PUNCT
ejpam-6378	318	4	µ3(χ	µ3(χ	PROPN
ejpam-6378	318	5	,	,	PUNCT
ejpam-6378	318	6	τ	τ	X
ejpam-6378	318	7	)	)	PUNCT
ejpam-6378	318	8	=	=	SYM
ejpam-6378	318	9	eχ	eχ	PROPN
ejpam-6378	318	10	(	(	PUNCT
ejpam-6378	318	11	τα)3	τα)3	X
ejpam-6378	318	12	γ(1	γ(1	PROPN
ejpam-6378	318	13	+	+	NUM
ejpam-6378	318	14	3α	3α	NOUN
ejpam-6378	318	15	)	)	PUNCT
ejpam-6378	318	16	.	.	PUNCT
ejpam-6378	319	1	(	(	PUNCT
ejpam-6378	319	2	45	45	NUM
ejpam-6378	319	3	)	)	PUNCT
ejpam-6378	319	4	µ4(χ	µ4(χ	NUM
ejpam-6378	319	5	,	,	PUNCT
ejpam-6378	319	6	τ	τ	X
ejpam-6378	319	7	)	)	PUNCT
ejpam-6378	320	1	=	=	SYM
ejpam-6378	320	2	eχ	eχ	PROPN
ejpam-6378	320	3	(	(	PUNCT
ejpam-6378	320	4	τα)4	τα)4	NOUN
ejpam-6378	320	5	γ(1	γ(1	PROPN
ejpam-6378	320	6	+	+	NUM
ejpam-6378	320	7	4α	4α	NOUN
ejpam-6378	320	8	)	)	PUNCT
ejpam-6378	320	9	.	.	PUNCT
ejpam-6378	321	1	(	(	PUNCT
ejpam-6378	321	2	46	46	NUM
ejpam-6378	321	3	)	)	PUNCT
ejpam-6378	321	4	µ(χ	µ(χ	PROPN
ejpam-6378	321	5	,	,	PUNCT
ejpam-6378	321	6	τ	τ	X
ejpam-6378	321	7	)	)	PUNCT
ejpam-6378	321	8	=	=	NOUN
ejpam-6378	321	9	eχ	eχ	NOUN
ejpam-6378	321	10	+	+	NUM
ejpam-6378	321	11	eχτα	eχτα	NOUN
ejpam-6378	321	12	γ(1	γ(1	NOUN
ejpam-6378	321	13	+	+	CCONJ
ejpam-6378	321	14	α	α	X
ejpam-6378	321	15	)	)	PUNCT
ejpam-6378	321	16	+	+	NUM
ejpam-6378	321	17	eχ	eχ	ADP
ejpam-6378	321	18	(	(	PUNCT
ejpam-6378	321	19	τα)2	τα)2	PROPN
ejpam-6378	321	20	γ(1	γ(1	NOUN
ejpam-6378	321	21	+	+	NUM
ejpam-6378	321	22	2α	2α	NOUN
ejpam-6378	321	23	)	)	PUNCT
ejpam-6378	322	1	+	+	SYM
ejpam-6378	322	2	eχ	eχ	ADP
ejpam-6378	322	3	(	(	PUNCT
ejpam-6378	322	4	τα)3	τα)3	X
ejpam-6378	322	5	γ(1	γ(1	PROPN
ejpam-6378	322	6	+	+	NUM
ejpam-6378	322	7	3α	3α	NOUN
ejpam-6378	322	8	)	)	PUNCT
ejpam-6378	323	1	+	+	NUM
ejpam-6378	323	2	eχ	eχ	ADP
ejpam-6378	323	3	(	(	PUNCT
ejpam-6378	323	4	τα)4	τα)4	NOUN
ejpam-6378	323	5	γ(1	γ(1	PROPN
ejpam-6378	323	6	+	+	NUM
ejpam-6378	323	7	4α	4α	NOUN
ejpam-6378	323	8	)	)	PUNCT
ejpam-6378	324	1	+	+	CCONJ
ejpam-6378	324	2	·	·	PUNCT
ejpam-6378	324	3	·	·	PUNCT
ejpam-6378	324	4	·	·	PUNCT
ejpam-6378	324	5	.	.	PUNCT
ejpam-6378	325	1	(	(	PUNCT
ejpam-6378	325	2	47	47	NUM
ejpam-6378	325	3	)	)	PUNCT
ejpam-6378	325	4	taking	take	VERB
ejpam-6378	325	5	α	α	NOUN
ejpam-6378	325	6	=	=	SYM
ejpam-6378	325	7	1	1	NUM
ejpam-6378	325	8	,	,	PUNCT
ejpam-6378	325	9	implies	imply	VERB
ejpam-6378	325	10	µ(χ	µ(χ	PROPN
ejpam-6378	325	11	,	,	PUNCT
ejpam-6378	325	12	τ	τ	X
ejpam-6378	325	13	)	)	PUNCT
ejpam-6378	326	1	=	=	NOUN
ejpam-6378	326	2	eχ	eχ	NOUN
ejpam-6378	326	3	+	+	NOUN
ejpam-6378	326	4	eχτ	eχτ	VERB
ejpam-6378	326	5	+	+	NUM
ejpam-6378	326	6	eχτ2	eχτ2	PROPN
ejpam-6378	326	7	2	2	NUM
ejpam-6378	326	8	+	+	NUM
ejpam-6378	326	9	eχτ3	eχτ3	NOUN
ejpam-6378	326	10	6	6	NUM
ejpam-6378	326	11	+	+	CCONJ
ejpam-6378	326	12	eχτ4	eχτ4	NOUN
ejpam-6378	326	13	24	24	NUM
ejpam-6378	326	14	+	+	CCONJ
ejpam-6378	326	15	eχτ5	eχτ5	VERB
ejpam-6378	326	16	120	120	NUM
ejpam-6378	327	1	+	+	CCONJ
ejpam-6378	327	2	·	·	PUNCT
ejpam-6378	327	3	·	·	PUNCT
ejpam-6378	327	4	·	·	PUNCT
ejpam-6378	327	5	.	.	PUNCT
ejpam-6378	328	1	(	(	PUNCT
ejpam-6378	328	2	48	48	NUM
ejpam-6378	328	3	)	)	PUNCT
ejpam-6378	328	4	clearly	clearly	ADV
ejpam-6378	328	5	equation	equation	NOUN
ejpam-6378	328	6	(	(	PUNCT
ejpam-6378	328	7	48	48	NUM
ejpam-6378	328	8	)	)	PUNCT
ejpam-6378	328	9	is	be	AUX
ejpam-6378	328	10	converging	converge	VERB
ejpam-6378	328	11	to	to	ADP
ejpam-6378	328	12	the	the	DET
ejpam-6378	328	13	exact	exact	ADJ
ejpam-6378	328	14	solution	solution	NOUN
ejpam-6378	328	15	.	.	PUNCT
ejpam-6378	329	1	4.2	4.2	NUM
ejpam-6378	329	2	.	.	PUNCT
ejpam-6378	330	1	solving	solve	VERB
ejpam-6378	330	2	under	under	ADP
ejpam-6378	330	3	cf	cf	NOUN
ejpam-6378	330	4	fractional	fractional	ADJ
ejpam-6378	330	5	differential	differential	NOUN
ejpam-6378	330	6	operator	operator	NOUN
ejpam-6378	330	7	µ0(χ	µ0(χ	NUM
ejpam-6378	330	8	,	,	PUNCT
ejpam-6378	330	9	τ	τ	X
ejpam-6378	330	10	)	)	PUNCT
ejpam-6378	330	11	=	=	NOUN
ejpam-6378	330	12	eχ	eχ	NOUN
ejpam-6378	330	13	.	.	PUNCT
ejpam-6378	331	1	(	(	PUNCT
ejpam-6378	331	2	49	49	NUM
ejpam-6378	331	3	)	)	PUNCT
ejpam-6378	331	4	µ1(χ	µ1(χ	PROPN
ejpam-6378	331	5	,	,	PUNCT
ejpam-6378	331	6	τ	τ	X
ejpam-6378	331	7	)	)	PUNCT
ejpam-6378	331	8	=	=	SYM
ejpam-6378	331	9	eχ	eχ	PROPN
ejpam-6378	331	10	(	(	PUNCT
ejpam-6378	331	11	α	α	NOUN
ejpam-6378	331	12	(	(	PUNCT
ejpam-6378	331	13	−1	−1	NOUN
ejpam-6378	331	14	+	+	CCONJ
ejpam-6378	331	15	τ	τ	X
ejpam-6378	331	16	)	)	PUNCT
ejpam-6378	332	1	+	+	NUM
ejpam-6378	332	2	1	1	X
ejpam-6378	332	3	)	)	PUNCT
ejpam-6378	332	4	m(α	m(α	PROPN
ejpam-6378	332	5	)	)	PUNCT
ejpam-6378	332	6	.	.	PUNCT
ejpam-6378	333	1	(	(	PUNCT
ejpam-6378	333	2	50	50	NUM
ejpam-6378	333	3	)	)	PUNCT
ejpam-6378	333	4	µ2(χ	µ2(χ	PROPN
ejpam-6378	333	5	,	,	PUNCT
ejpam-6378	333	6	τ	τ	X
ejpam-6378	333	7	)	)	PUNCT
ejpam-6378	333	8	=	=	PUNCT
ejpam-6378	333	9	(	(	PUNCT
ejpam-6378	333	10	2	2	NUM
ejpam-6378	334	1	+	+	CCONJ
ejpam-6378	334	2	α2	α2	ADJ
ejpam-6378	334	3	(	(	PUNCT
ejpam-6378	334	4	τ2	τ2	NOUN
ejpam-6378	334	5	−	−	NOUN
ejpam-6378	334	6	4τ	4τ	NOUN
ejpam-6378	334	7	+	+	CCONJ
ejpam-6378	334	8	2	2	NUM
ejpam-6378	334	9	)	)	PUNCT
ejpam-6378	334	10	+	+	CCONJ
ejpam-6378	334	11	(	(	PUNCT
ejpam-6378	334	12	4τ	4τ	NUM
ejpam-6378	334	13	−	−	PROPN
ejpam-6378	334	14	4)α	4)α	NUM
ejpam-6378	334	15	)	)	PUNCT
ejpam-6378	334	16	eχ	eχ	ADP
ejpam-6378	334	17	2m(α)2	2m(α)2	NUM
ejpam-6378	334	18	.	.	PUNCT
ejpam-6378	335	1	(	(	PUNCT
ejpam-6378	335	2	51	51	NUM
ejpam-6378	335	3	)	)	PUNCT
ejpam-6378	335	4	m.	m.	NOUN
ejpam-6378	335	5	sohail	sohail	PROPN
ejpam-6378	335	6	et	et	PROPN
ejpam-6378	335	7	al	al	PROPN
ejpam-6378	335	8	.	.	PUNCT
ejpam-6378	335	9	/	/	SYM
ejpam-6378	335	10	eur	eur	PROPN
ejpam-6378	335	11	.	.	PUNCT
ejpam-6378	336	1	j.	j.	PROPN
ejpam-6378	336	2	pure	pure	PROPN
ejpam-6378	336	3	appl	appl	PROPN
ejpam-6378	336	4	.	.	PROPN
ejpam-6378	336	5	math	math	PROPN
ejpam-6378	336	6	,	,	PUNCT
ejpam-6378	336	7	18	18	NUM
ejpam-6378	336	8	(	(	PUNCT
ejpam-6378	336	9	4	4	NUM
ejpam-6378	336	10	)	)	PUNCT
ejpam-6378	336	11	(	(	PUNCT
ejpam-6378	336	12	2025	2025	NUM
ejpam-6378	336	13	)	)	PUNCT
ejpam-6378	336	14	,	,	PUNCT
ejpam-6378	336	15	6378	6378	NUM
ejpam-6378	336	16	13	13	NUM
ejpam-6378	336	17	of	of	ADP
ejpam-6378	336	18	20	20	NUM
ejpam-6378	336	19	µ3(χ	µ3(χ	PROPN
ejpam-6378	336	20	,	,	PUNCT
ejpam-6378	336	21	τ	τ	X
ejpam-6378	336	22	)	)	PUNCT
ejpam-6378	336	23	=	=	SYM
ejpam-6378	336	24	eχ	eχ	PROPN
ejpam-6378	336	25	6m(α)3	6m(α)3	NUM
ejpam-6378	336	26	(	(	PUNCT
ejpam-6378	336	27	α3	α3	PROPN
ejpam-6378	336	28	(	(	PUNCT
ejpam-6378	336	29	τ3	τ3	NOUN
ejpam-6378	336	30	−	−	PROPN
ejpam-6378	336	31	9τ2	9τ2	NUM
ejpam-6378	336	32	+	+	CCONJ
ejpam-6378	336	33	18τ	18τ	NUM
ejpam-6378	336	34	−	−	PROPN
ejpam-6378	336	35	6	6	NUM
ejpam-6378	336	36	)	)	PUNCT
ejpam-6378	336	37	+	+	CCONJ
ejpam-6378	336	38	9α2	9α2	NUM
ejpam-6378	336	39	(	(	PUNCT
ejpam-6378	336	40	τ2	τ2	NOUN
ejpam-6378	336	41	−	−	NOUN
ejpam-6378	336	42	4τ	4τ	NOUN
ejpam-6378	336	43	+	+	CCONJ
ejpam-6378	336	44	2	2	NUM
ejpam-6378	336	45	)	)	PUNCT
ejpam-6378	336	46	+	+	NUM
ejpam-6378	336	47	18α	18α	NUM
ejpam-6378	336	48	(	(	PUNCT
ejpam-6378	336	49	−1	−1	NOUN
ejpam-6378	336	50	+	+	CCONJ
ejpam-6378	336	51	τ	τ	X
ejpam-6378	336	52	)	)	PUNCT
ejpam-6378	337	1	+	+	CCONJ
ejpam-6378	337	2	6	6	NUM
ejpam-6378	337	3	)	)	PUNCT
ejpam-6378	337	4	.	.	PUNCT
ejpam-6378	338	1	(	(	PUNCT
ejpam-6378	338	2	52	52	NUM
ejpam-6378	338	3	)	)	PUNCT
ejpam-6378	338	4	µ4(χ	µ4(χ	NUM
ejpam-6378	338	5	,	,	PUNCT
ejpam-6378	338	6	τ	τ	X
ejpam-6378	338	7	)	)	PUNCT
ejpam-6378	339	1	=	=	SYM
ejpam-6378	339	2	eχ	eχ	ADP
ejpam-6378	339	3	24m(α)4	24m(α)4	PROPN
ejpam-6378	339	4	(	(	PUNCT
ejpam-6378	339	5	α4	α4	PROPN
ejpam-6378	339	6	(	(	PUNCT
ejpam-6378	339	7	τ4	τ4	NOUN
ejpam-6378	339	8	−	−	PROPN
ejpam-6378	339	9	16τ3	16τ3	NUM
ejpam-6378	339	10	+	+	NUM
ejpam-6378	339	11	72τ2	72τ2	NUM
ejpam-6378	339	12	−	−	NOUN
ejpam-6378	339	13	96τ	96τ	NUM
ejpam-6378	339	14	+	+	CCONJ
ejpam-6378	339	15	24	24	NUM
ejpam-6378	339	16	)	)	PUNCT
ejpam-6378	340	1	+	+	CCONJ
ejpam-6378	340	2	16α3	16α3	NUM
ejpam-6378	340	3	(	(	PUNCT
ejpam-6378	340	4	τ3	τ3	NOUN
ejpam-6378	340	5	−	−	PROPN
ejpam-6378	340	6	9τ2	9τ2	NUM
ejpam-6378	340	7	+	+	CCONJ
ejpam-6378	340	8	18τ	18τ	NUM
ejpam-6378	340	9	−	−	PROPN
ejpam-6378	340	10	6	6	NUM
ejpam-6378	340	11	)	)	PUNCT
ejpam-6378	340	12	+	+	CCONJ
ejpam-6378	341	1	72α2	72α2	NUM
ejpam-6378	341	2	(	(	PUNCT
ejpam-6378	341	3	τ2	τ2	NOUN
ejpam-6378	341	4	−	−	NOUN
ejpam-6378	341	5	4τ	4τ	NOUN
ejpam-6378	341	6	+	+	CCONJ
ejpam-6378	341	7	2	2	NUM
ejpam-6378	341	8	)	)	PUNCT
ejpam-6378	342	1	+	+	NUM
ejpam-6378	342	2	96α	96α	NOUN
ejpam-6378	342	3	(	(	PUNCT
ejpam-6378	342	4	−1	−1	NOUN
ejpam-6378	342	5	+	+	CCONJ
ejpam-6378	342	6	τ	τ	X
ejpam-6378	342	7	)	)	PUNCT
ejpam-6378	342	8	+	+	NUM
ejpam-6378	342	9	24	24	NUM
ejpam-6378	342	10	)	)	PUNCT
ejpam-6378	342	11	.	.	PUNCT
ejpam-6378	343	1	(	(	PUNCT
ejpam-6378	343	2	53	53	NUM
ejpam-6378	343	3	)	)	PUNCT
ejpam-6378	343	4	µ(χ	µ(χ	PROPN
ejpam-6378	343	5	,	,	PUNCT
ejpam-6378	343	6	τ	τ	X
ejpam-6378	343	7	)	)	PUNCT
ejpam-6378	344	1	=	=	NOUN
ejpam-6378	344	2	eχ	eχ	PROPN
ejpam-6378	344	3	+	+	NOUN
ejpam-6378	344	4	eχ	eχ	PROPN
ejpam-6378	344	5	(	(	PUNCT
ejpam-6378	344	6	α	α	NOUN
ejpam-6378	344	7	(	(	PUNCT
ejpam-6378	344	8	−1	−1	NOUN
ejpam-6378	344	9	+	+	CCONJ
ejpam-6378	344	10	τ	τ	X
ejpam-6378	344	11	)	)	PUNCT
ejpam-6378	344	12	+	+	NUM
ejpam-6378	344	13	1	1	X
ejpam-6378	344	14	)	)	PUNCT
ejpam-6378	344	15	m(α	m(α	PROPN
ejpam-6378	344	16	)	)	PUNCT
ejpam-6378	345	1	+	+	CCONJ
ejpam-6378	345	2	(	(	PUNCT
ejpam-6378	345	3	2	2	NUM
ejpam-6378	345	4	+	+	CCONJ
ejpam-6378	345	5	α2	α2	ADJ
ejpam-6378	345	6	(	(	PUNCT
ejpam-6378	345	7	τ2	τ2	NOUN
ejpam-6378	345	8	−	−	NOUN
ejpam-6378	345	9	4τ	4τ	NOUN
ejpam-6378	345	10	+	+	CCONJ
ejpam-6378	345	11	2	2	NUM
ejpam-6378	345	12	)	)	PUNCT
ejpam-6378	345	13	+	+	CCONJ
ejpam-6378	345	14	(	(	PUNCT
ejpam-6378	345	15	4τ	4τ	NUM
ejpam-6378	345	16	−	−	PROPN
ejpam-6378	345	17	4)α	4)α	NUM
ejpam-6378	345	18	)	)	PUNCT
ejpam-6378	345	19	eχ	eχ	ADP
ejpam-6378	345	20	2m(α)2	2m(α)2	NUM
ejpam-6378	345	21	+	+	CCONJ
ejpam-6378	345	22	·	·	PUNCT
ejpam-6378	345	23	·	·	PUNCT
ejpam-6378	345	24	·	·	PUNCT
ejpam-6378	345	25	.	.	PUNCT
ejpam-6378	346	1	(	(	PUNCT
ejpam-6378	346	2	54	54	NUM
ejpam-6378	346	3	)	)	PUNCT
ejpam-6378	346	4	by	by	ADP
ejpam-6378	346	5	putting	put	VERB
ejpam-6378	346	6	α	α	NOUN
ejpam-6378	346	7	=	=	SYM
ejpam-6378	346	8	1	1	NUM
ejpam-6378	346	9	equation(54	equation(54	NOUN
ejpam-6378	346	10	)	)	PUNCT
ejpam-6378	346	11	implies	imply	VERB
ejpam-6378	346	12	µ(χ	µ(χ	PROPN
ejpam-6378	346	13	,	,	PUNCT
ejpam-6378	346	14	τ	τ	X
ejpam-6378	346	15	)	)	PUNCT
ejpam-6378	347	1	=	=	NOUN
ejpam-6378	347	2	eχ	eχ	NOUN
ejpam-6378	347	3	+	+	NOUN
ejpam-6378	347	4	eχτ	eχτ	VERB
ejpam-6378	347	5	+	+	SYM
ejpam-6378	347	6	τ2eχ	τ2eχ	SYM
ejpam-6378	347	7	2	2	NUM
ejpam-6378	348	1	+	+	CCONJ
ejpam-6378	348	2	eχτ3	eχτ3	NOUN
ejpam-6378	348	3	6	6	NUM
ejpam-6378	348	4	+	+	CCONJ
ejpam-6378	348	5	eχτ4	eχτ4	NOUN
ejpam-6378	348	6	24	24	NUM
ejpam-6378	348	7	+	+	CCONJ
ejpam-6378	348	8	eχτ5	eχτ5	VERB
ejpam-6378	348	9	120	120	NUM
ejpam-6378	348	10	+	+	CCONJ
ejpam-6378	348	11	·	·	PUNCT
ejpam-6378	348	12	·	·	PUNCT
ejpam-6378	348	13	·	·	PUNCT
ejpam-6378	348	14	.	.	PUNCT
ejpam-6378	349	1	(	(	PUNCT
ejpam-6378	349	2	55	55	NUM
ejpam-6378	349	3	)	)	PUNCT
ejpam-6378	349	4	clearly	clearly	ADV
ejpam-6378	349	5	equation	equation	NOUN
ejpam-6378	349	6	(	(	PUNCT
ejpam-6378	349	7	55	55	NUM
ejpam-6378	349	8	)	)	PUNCT
ejpam-6378	349	9	is	be	AUX
ejpam-6378	349	10	converging	converge	VERB
ejpam-6378	349	11	to	to	ADP
ejpam-6378	349	12	the	the	DET
ejpam-6378	349	13	exact	exact	ADJ
ejpam-6378	349	14	solution	solution	NOUN
ejpam-6378	349	15	.	.	PUNCT
ejpam-6378	350	1	4.3	4.3	NUM
ejpam-6378	350	2	.	.	PUNCT
ejpam-6378	351	1	solving	solve	VERB
ejpam-6378	351	2	under	under	ADP
ejpam-6378	351	3	abc	abc	PROPN
ejpam-6378	351	4	fractional	fractional	ADJ
ejpam-6378	351	5	differential	differential	NOUN
ejpam-6378	351	6	operator	operator	NOUN
ejpam-6378	351	7	µ0(χ	µ0(χ	NUM
ejpam-6378	351	8	,	,	PUNCT
ejpam-6378	351	9	τ	τ	X
ejpam-6378	351	10	)	)	PUNCT
ejpam-6378	351	11	=	=	NOUN
ejpam-6378	351	12	eχ	eχ	NOUN
ejpam-6378	351	13	.	.	PUNCT
ejpam-6378	352	1	(	(	PUNCT
ejpam-6378	352	2	56	56	X
ejpam-6378	352	3	)	)	PUNCT
ejpam-6378	352	4	µ1(χ	µ1(χ	PROPN
ejpam-6378	352	5	,	,	PUNCT
ejpam-6378	352	6	τ	τ	X
ejpam-6378	352	7	)	)	PUNCT
ejpam-6378	353	1	=	=	NOUN
ejpam-6378	353	2	−	−	PROPN
ejpam-6378	353	3	eχ	eχ	PROPN
ejpam-6378	353	4	(	(	PUNCT
ejpam-6378	353	5	−1	−1	NOUN
ejpam-6378	353	6	+	+	CCONJ
ejpam-6378	353	7	α−	α−	ADP
ejpam-6378	353	8	α	α	NOUN
ejpam-6378	353	9	τα	τα	NOUN
ejpam-6378	353	10	γ(1+α	γ(1+α	PROPN
ejpam-6378	353	11	)	)	PUNCT
ejpam-6378	353	12	)	)	PUNCT
ejpam-6378	353	13	ab(α	ab(α	NUM
ejpam-6378	353	14	)	)	PUNCT
ejpam-6378	353	15	.	.	PUNCT
ejpam-6378	354	1	(	(	PUNCT
ejpam-6378	354	2	57	57	NUM
ejpam-6378	354	3	)	)	PUNCT
ejpam-6378	354	4	µ2(χ	µ2(χ	PROPN
ejpam-6378	354	5	,	,	PUNCT
ejpam-6378	354	6	τ	τ	X
ejpam-6378	354	7	)	)	PUNCT
ejpam-6378	355	1	=	=	NOUN
ejpam-6378	355	2	−	−	PROPN
ejpam-6378	355	3	eχ	eχ	ADP
ejpam-6378	355	4	(	(	PUNCT
ejpam-6378	355	5	−	−	PROPN
ejpam-6378	355	6	α2τ2α	α2τ2α	NUM
ejpam-6378	356	1	γ(1	γ(1	X
ejpam-6378	356	2	+	+	NOUN
ejpam-6378	356	3	2α	2α	NOUN
ejpam-6378	356	4	)	)	PUNCT
ejpam-6378	356	5	+	+	NUM
ejpam-6378	356	6	2ταα(−1+α	2ταα(−1+α	NUM
ejpam-6378	356	7	)	)	PUNCT
ejpam-6378	356	8	γ(1+α	γ(1+α	PROPN
ejpam-6378	356	9	)	)	PUNCT
ejpam-6378	357	1	−	−	ADP
ejpam-6378	357	2	1	1	NUM
ejpam-6378	358	1	+	+	NUM
ejpam-6378	358	2	2α−	2α−	NUM
ejpam-6378	358	3	α2	α2	ADJ
ejpam-6378	358	4	)	)	PUNCT
ejpam-6378	358	5	ab(α)2	ab(α)2	PROPN
ejpam-6378	358	6	.	.	PUNCT
ejpam-6378	359	1	(	(	PUNCT
ejpam-6378	359	2	58	58	X
ejpam-6378	359	3	)	)	PUNCT
ejpam-6378	359	4	µ3(χ	µ3(χ	PROPN
ejpam-6378	359	5	,	,	PUNCT
ejpam-6378	359	6	τ	τ	X
ejpam-6378	359	7	)	)	PUNCT
ejpam-6378	360	1	=	=	NOUN
ejpam-6378	360	2	−	−	PROPN
ejpam-6378	360	3	eχ	eχ	ADP
ejpam-6378	360	4	(	(	PUNCT
ejpam-6378	360	5	−	−	PROPN
ejpam-6378	360	6	α3τ3α	α3τ3α	SYM
ejpam-6378	360	7	γ(1	γ(1	PROPN
ejpam-6378	360	8	+	+	NOUN
ejpam-6378	360	9	3α	3α	NOUN
ejpam-6378	360	10	)	)	PUNCT
ejpam-6378	360	11	−	−	PROPN
ejpam-6378	360	12	3ταα(−1+α)2	3ταα(−1+α)2	NUM
ejpam-6378	360	13	γ(1+α	γ(1+α	NUM
ejpam-6378	360	14	)	)	PUNCT
ejpam-6378	361	1	+	+	CCONJ
ejpam-6378	361	2	3τ2αα2(−1+α	3τ2αα2(−1+α	NUM
ejpam-6378	361	3	)	)	PUNCT
ejpam-6378	362	1	γ(1	γ(1	PROPN
ejpam-6378	362	2	+	+	NOUN
ejpam-6378	362	3	2α	2α	NOUN
ejpam-6378	362	4	)	)	PUNCT
ejpam-6378	363	1	−	−	PROPN
ejpam-6378	363	2	1−	1−	NUM
ejpam-6378	363	3	3α2	3α2	NUM
ejpam-6378	364	1	+	+	CCONJ
ejpam-6378	364	2	3α+	3α+	NUM
ejpam-6378	364	3	α3	α3	NOUN
ejpam-6378	364	4	)	)	PUNCT
ejpam-6378	364	5	ab(α)3	ab(α)3	PROPN
ejpam-6378	364	6	.	.	PUNCT
ejpam-6378	365	1	(	(	PUNCT
ejpam-6378	365	2	59	59	NUM
ejpam-6378	365	3	)	)	PUNCT
ejpam-6378	365	4	µ4(χ	µ4(χ	NUM
ejpam-6378	365	5	,	,	PUNCT
ejpam-6378	365	6	τ	τ	X
ejpam-6378	365	7	)	)	PUNCT
ejpam-6378	366	1	=	=	NOUN
ejpam-6378	366	2	−	−	PROPN
ejpam-6378	366	3	eχ	eχ	PROPN
ejpam-6378	366	4	(	(	PUNCT
ejpam-6378	366	5	−1	−1	NOUN
ejpam-6378	367	1	+	+	CCONJ
ejpam-6378	367	2	4α3	4α3	NUM
ejpam-6378	367	3	−	−	NOUN
ejpam-6378	367	4	α4	α4	NOUN
ejpam-6378	367	5	−	−	NOUN
ejpam-6378	367	6	α4τ4α	α4τ4α	PUNCT
ejpam-6378	368	1	γ(1	γ(1	ADP
ejpam-6378	368	2	+	+	NOUN
ejpam-6378	368	3	4α	4α	NOUN
ejpam-6378	368	4	)	)	PUNCT
ejpam-6378	369	1	+	+	CCONJ
ejpam-6378	370	1	4α−	4α−	NUM
ejpam-6378	370	2	6α2	6α2	NUM
ejpam-6378	371	1	+	+	CCONJ
ejpam-6378	371	2	4ταα(−1+α)3	4ταα(−1+α)3	NUM
ejpam-6378	371	3	γ(1+α	γ(1+α	NUM
ejpam-6378	371	4	)	)	PUNCT
ejpam-6378	371	5	−	−	PROPN
ejpam-6378	372	1	6τ2αα2(−1+α)2	6τ2αα2(−1+α)2	NUM
ejpam-6378	372	2	γ(1	γ(1	NOUN
ejpam-6378	372	3	+	+	NOUN
ejpam-6378	372	4	2α	2α	NOUN
ejpam-6378	372	5	)	)	PUNCT
ejpam-6378	373	1	+	+	X
ejpam-6378	373	2	4τ3αα3(−1+α	4τ3αα3(−1+α	X
ejpam-6378	373	3	)	)	PUNCT
ejpam-6378	374	1	γ(1	γ(1	PROPN
ejpam-6378	374	2	+	+	NOUN
ejpam-6378	374	3	3α	3α	NOUN
ejpam-6378	374	4	)	)	PUNCT
ejpam-6378	374	5	)	)	PUNCT
ejpam-6378	375	1	ab(α)4	ab(α)4	NOUN
ejpam-6378	375	2	.	.	PUNCT
ejpam-6378	376	1	(	(	PUNCT
ejpam-6378	376	2	60	60	NUM
ejpam-6378	376	3	)	)	PUNCT
ejpam-6378	376	4	µ(χ	µ(χ	PROPN
ejpam-6378	376	5	,	,	PUNCT
ejpam-6378	376	6	τ	τ	X
ejpam-6378	376	7	)	)	PUNCT
ejpam-6378	377	1	=	=	NOUN
ejpam-6378	377	2	eχ	eχ	ADP
ejpam-6378	377	3	−	−	PROPN
ejpam-6378	377	4	eχ	eχ	PROPN
ejpam-6378	377	5	(	(	PUNCT
ejpam-6378	377	6	−1	−1	NOUN
ejpam-6378	377	7	+	+	CCONJ
ejpam-6378	377	8	α−	α−	ADP
ejpam-6378	377	9	α	α	NOUN
ejpam-6378	377	10	τα	τα	NOUN
ejpam-6378	377	11	γ(1+α	γ(1+α	PROPN
ejpam-6378	377	12	)	)	PUNCT
ejpam-6378	377	13	)	)	PUNCT
ejpam-6378	377	14	ab(α	ab(α	NUM
ejpam-6378	377	15	)	)	PUNCT
ejpam-6378	377	16	−	−	PROPN
ejpam-6378	377	17	eχ	eχ	PROPN
ejpam-6378	377	18	(	(	PUNCT
ejpam-6378	377	19	−1	−1	NOUN
ejpam-6378	377	20	+	+	PUNCT
ejpam-6378	377	21	2α−	2α−	NUM
ejpam-6378	377	22	α2	α2	ADJ
ejpam-6378	377	23	−	−	NOUN
ejpam-6378	377	24	α2τ2α	α2τ2α	PUNCT
ejpam-6378	378	1	γ(1	γ(1	X
ejpam-6378	378	2	+	+	NOUN
ejpam-6378	378	3	2α	2α	NOUN
ejpam-6378	378	4	)	)	PUNCT
ejpam-6378	378	5	+	+	NUM
ejpam-6378	378	6	2ταα(−1+α	2ταα(−1+α	NUM
ejpam-6378	378	7	)	)	PUNCT
ejpam-6378	378	8	γ(1+α	γ(1+α	PROPN
ejpam-6378	378	9	)	)	PUNCT
ejpam-6378	378	10	)	)	PUNCT
ejpam-6378	379	1	ab(α)2	ab(α)2	PROPN
ejpam-6378	380	1	+	+	NUM
ejpam-6378	380	2	·	·	PUNCT
ejpam-6378	380	3	·	·	PUNCT
ejpam-6378	380	4	·	·	PUNCT
ejpam-6378	380	5	.	.	PUNCT
ejpam-6378	381	1	(	(	PUNCT
ejpam-6378	381	2	61	61	NUM
ejpam-6378	381	3	)	)	PUNCT
ejpam-6378	381	4	m.	m.	NOUN
ejpam-6378	381	5	sohail	sohail	PROPN
ejpam-6378	381	6	et	et	PROPN
ejpam-6378	381	7	al	al	PROPN
ejpam-6378	381	8	.	.	PUNCT
ejpam-6378	381	9	/	/	SYM
ejpam-6378	381	10	eur	eur	PROPN
ejpam-6378	381	11	.	.	PUNCT
ejpam-6378	382	1	j.	j.	PROPN
ejpam-6378	382	2	pure	pure	PROPN
ejpam-6378	382	3	appl	appl	PROPN
ejpam-6378	382	4	.	.	PROPN
ejpam-6378	382	5	math	math	PROPN
ejpam-6378	382	6	,	,	PUNCT
ejpam-6378	382	7	18	18	NUM
ejpam-6378	382	8	(	(	PUNCT
ejpam-6378	382	9	4	4	NUM
ejpam-6378	382	10	)	)	PUNCT
ejpam-6378	382	11	(	(	PUNCT
ejpam-6378	382	12	2025	2025	NUM
ejpam-6378	382	13	)	)	PUNCT
ejpam-6378	382	14	,	,	PUNCT
ejpam-6378	382	15	6378	6378	NUM
ejpam-6378	382	16	14	14	NUM
ejpam-6378	382	17	of	of	ADP
ejpam-6378	382	18	20	20	NUM
ejpam-6378	382	19	by	by	ADP
ejpam-6378	382	20	putting	put	VERB
ejpam-6378	382	21	α	α	NOUN
ejpam-6378	382	22	=	=	SYM
ejpam-6378	382	23	1	1	NUM
ejpam-6378	382	24	equation(61	equation(61	ADV
ejpam-6378	382	25	)	)	PUNCT
ejpam-6378	382	26	implies	imply	VERB
ejpam-6378	382	27	µ(χ	µ(χ	PROPN
ejpam-6378	382	28	,	,	PUNCT
ejpam-6378	382	29	τ	τ	X
ejpam-6378	382	30	)	)	PUNCT
ejpam-6378	382	31	=	=	NOUN
ejpam-6378	382	32	eχ	eχ	NOUN
ejpam-6378	382	33	+	+	NOUN
ejpam-6378	382	34	eχτ	eχτ	VERB
ejpam-6378	382	35	+	+	NUM
ejpam-6378	382	36	eχτ2	eχτ2	PROPN
ejpam-6378	382	37	2	2	NUM
ejpam-6378	382	38	+	+	NUM
ejpam-6378	382	39	eχτ3	eχτ3	NOUN
ejpam-6378	382	40	6	6	NUM
ejpam-6378	382	41	+	+	CCONJ
ejpam-6378	382	42	eχτ4	eχτ4	NOUN
ejpam-6378	382	43	24	24	NUM
ejpam-6378	382	44	+	+	CCONJ
ejpam-6378	382	45	eχτ5	eχτ5	VERB
ejpam-6378	382	46	120	120	NUM
ejpam-6378	382	47	+	+	CCONJ
ejpam-6378	382	48	·	·	PUNCT
ejpam-6378	382	49	·	·	PUNCT
ejpam-6378	382	50	·	·	PUNCT
ejpam-6378	382	51	.	.	PUNCT
ejpam-6378	383	1	(	(	PUNCT
ejpam-6378	383	2	62	62	NUM
ejpam-6378	383	3	)	)	PUNCT
ejpam-6378	383	4	clearly	clearly	ADV
ejpam-6378	383	5	equation	equation	NOUN
ejpam-6378	383	6	(	(	PUNCT
ejpam-6378	383	7	62	62	NUM
ejpam-6378	383	8	)	)	PUNCT
ejpam-6378	383	9	is	be	AUX
ejpam-6378	383	10	converging	converge	VERB
ejpam-6378	383	11	to	to	ADP
ejpam-6378	383	12	the	the	DET
ejpam-6378	383	13	exact	exact	ADJ
ejpam-6378	383	14	solution	solution	NOUN
ejpam-6378	383	15	.	.	PUNCT
ejpam-6378	384	1	here	here	ADV
ejpam-6378	384	2	,	,	PUNCT
ejpam-6378	384	3	in	in	ADP
ejpam-6378	384	4	figure	figure	NOUN
ejpam-6378	384	5	1	1	NUM
ejpam-6378	384	6	,	,	PUNCT
ejpam-6378	384	7	we	we	PRON
ejpam-6378	384	8	present	present	VERB
ejpam-6378	384	9	2d	2d	NUM
ejpam-6378	384	10	graphs	graph	NOUN
ejpam-6378	384	11	of	of	ADP
ejpam-6378	384	12	our	our	PRON
ejpam-6378	384	13	solution	solution	NOUN
ejpam-6378	384	14	.	.	PUNCT
ejpam-6378	385	1	figure	figure	NOUN
ejpam-6378	385	2	1	1	NUM
ejpam-6378	385	3	:	:	PUNCT
ejpam-6378	385	4	2d	2d	NUM
ejpam-6378	385	5	graphs	graph	NOUN
ejpam-6378	385	6	of	of	ADP
ejpam-6378	385	7	solutions	solution	NOUN
ejpam-6378	385	8	at	at	ADP
ejpam-6378	385	9	different	different	ADJ
ejpam-6378	385	10	fractional	fractional	ADJ
ejpam-6378	385	11	orders	order	NOUN
ejpam-6378	385	12	.	.	PUNCT
ejpam-6378	386	1	the	the	DET
ejpam-6378	386	2	error	error	NOUN
ejpam-6378	386	3	minimization	minimization	NOUN
ejpam-6378	386	4	procedure	procedure	NOUN
ejpam-6378	386	5	has	have	AUX
ejpam-6378	386	6	presented	present	VERB
ejpam-6378	386	7	in	in	ADP
ejpam-6378	386	8	figure	figure	NOUN
ejpam-6378	386	9	2	2	NUM
ejpam-6378	386	10	.	.	PUNCT
ejpam-6378	386	11	figure	figure	NOUN
ejpam-6378	386	12	2	2	NUM
ejpam-6378	386	13	:	:	PUNCT
ejpam-6378	386	14	the	the	DET
ejpam-6378	386	15	error	error	NOUN
ejpam-6378	386	16	is	be	AUX
ejpam-6378	386	17	minimized	minimize	VERB
ejpam-6378	386	18	as	as	ADP
ejpam-6378	386	19	the	the	DET
ejpam-6378	386	20	number	number	NOUN
ejpam-6378	386	21	of	of	ADP
ejpam-6378	386	22	solution	solution	NOUN
ejpam-6378	386	23	terms	term	NOUN
ejpam-6378	386	24	increases	increase	NOUN
ejpam-6378	386	25	.	.	PUNCT
ejpam-6378	387	1	we	we	PRON
ejpam-6378	387	2	have	have	AUX
ejpam-6378	387	3	presented	present	VERB
ejpam-6378	387	4	graphical	graphical	ADJ
ejpam-6378	387	5	illustrations	illustration	NOUN
ejpam-6378	387	6	of	of	ADP
ejpam-6378	387	7	solutions	solution	NOUN
ejpam-6378	387	8	for	for	ADP
ejpam-6378	387	9	various	various	ADJ
ejpam-6378	387	10	operators	operator	NOUN
ejpam-6378	387	11	in	in	ADP
ejpam-6378	387	12	figure	figure	NOUN
ejpam-6378	387	13	3	3	NUM
ejpam-6378	387	14	.	.	PUNCT
ejpam-6378	387	15	m.	m.	PROPN
ejpam-6378	387	16	sohail	sohail	PROPN
ejpam-6378	387	17	et	et	PROPN
ejpam-6378	387	18	al	al	PROPN
ejpam-6378	387	19	.	.	PUNCT
ejpam-6378	387	20	/	/	SYM
ejpam-6378	387	21	eur	eur	PROPN
ejpam-6378	387	22	.	.	PUNCT
ejpam-6378	388	1	j.	j.	PROPN
ejpam-6378	388	2	pure	pure	PROPN
ejpam-6378	388	3	appl	appl	PROPN
ejpam-6378	388	4	.	.	PROPN
ejpam-6378	388	5	math	math	PROPN
ejpam-6378	388	6	,	,	PUNCT
ejpam-6378	388	7	18	18	NUM
ejpam-6378	388	8	(	(	PUNCT
ejpam-6378	388	9	4	4	NUM
ejpam-6378	388	10	)	)	PUNCT
ejpam-6378	388	11	(	(	PUNCT
ejpam-6378	388	12	2025	2025	NUM
ejpam-6378	388	13	)	)	PUNCT
ejpam-6378	388	14	,	,	PUNCT
ejpam-6378	388	15	6378	6378	NUM
ejpam-6378	388	16	15	15	NUM
ejpam-6378	388	17	of	of	ADP
ejpam-6378	388	18	20	20	NUM
ejpam-6378	388	19	(	(	PUNCT
ejpam-6378	388	20	a	a	NOUN
ejpam-6378	388	21	)	)	PUNCT
ejpam-6378	388	22	(	(	PUNCT
ejpam-6378	388	23	b	b	X
ejpam-6378	388	24	)	)	PUNCT
ejpam-6378	388	25	(	(	PUNCT
ejpam-6378	388	26	c	c	X
ejpam-6378	388	27	)	)	PUNCT
ejpam-6378	388	28	figure	figure	NOUN
ejpam-6378	388	29	3	3	NUM
ejpam-6378	388	30	:	:	PUNCT
ejpam-6378	388	31	solution	solution	NOUN
ejpam-6378	388	32	graphs	graph	NOUN
ejpam-6378	388	33	under	under	ADP
ejpam-6378	388	34	different	different	ADJ
ejpam-6378	388	35	differential	differential	ADJ
ejpam-6378	388	36	operators	operator	NOUN
ejpam-6378	388	37	:	:	PUNCT
ejpam-6378	388	38	(	(	PUNCT
ejpam-6378	388	39	a	a	X
ejpam-6378	388	40	):	):	PUNCT
ejpam-6378	388	41	cfd	cfd	NOUN
ejpam-6378	388	42	(	(	PUNCT
ejpam-6378	388	43	b	b	NOUN
ejpam-6378	388	44	):	):	PUNCT
ejpam-6378	388	45	cffd	cffd	NOUN
ejpam-6378	388	46	(	(	PUNCT
ejpam-6378	388	47	c	c	NOUN
ejpam-6378	388	48	):	):	PUNCT
ejpam-6378	388	49	abfd	abfd	PROPN
ejpam-6378	388	50	.	.	PUNCT
ejpam-6378	389	1	m.	m.	PROPN
ejpam-6378	389	2	sohail	sohail	PROPN
ejpam-6378	389	3	et	et	PROPN
ejpam-6378	389	4	al	al	PROPN
ejpam-6378	389	5	.	.	PUNCT
ejpam-6378	389	6	/	/	SYM
ejpam-6378	389	7	eur	eur	PROPN
ejpam-6378	389	8	.	.	PUNCT
ejpam-6378	390	1	j.	j.	PROPN
ejpam-6378	390	2	pure	pure	PROPN
ejpam-6378	390	3	appl	appl	PROPN
ejpam-6378	390	4	.	.	PROPN
ejpam-6378	390	5	math	math	PROPN
ejpam-6378	390	6	,	,	PUNCT
ejpam-6378	390	7	18	18	NUM
ejpam-6378	390	8	(	(	PUNCT
ejpam-6378	390	9	4	4	NUM
ejpam-6378	390	10	)	)	PUNCT
ejpam-6378	390	11	(	(	PUNCT
ejpam-6378	390	12	2025	2025	NUM
ejpam-6378	390	13	)	)	PUNCT
ejpam-6378	390	14	,	,	PUNCT
ejpam-6378	390	15	6378	6378	NUM
ejpam-6378	390	16	16	16	NUM
ejpam-6378	390	17	of	of	ADP
ejpam-6378	390	18	20	20	NUM
ejpam-6378	390	19	fractional	fractional	ADJ
ejpam-6378	390	20	order	order	NOUN
ejpam-6378	390	21	τ	τ	PROPN
ejpam-6378	390	22	cfd	cfd	NOUN
ejpam-6378	390	23	operator	operator	NOUN
ejpam-6378	390	24	cffd	cffd	NOUN
ejpam-6378	390	25	operator	operator	NOUN
ejpam-6378	390	26	abfd	abfd	NOUN
ejpam-6378	390	27	operator	operator	VERB
ejpam-6378	390	28	0.10	0.10	NUM
ejpam-6378	390	29	3.004166021	3.004166021	NUM
ejpam-6378	390	30	3.004166021	3.004166021	NUM
ejpam-6378	390	31	3.004166021	3.004166021	NUM
ejpam-6378	390	32	0.20	0.20	NUM
ejpam-6378	390	33	3.320116674	3.320116674	NUM
ejpam-6378	390	34	3.320116674	3.320116674	NUM
ejpam-6378	390	35	3.320116674	3.320116674	NUM
ejpam-6378	390	36	1.00	1.00	NUM
ejpam-6378	390	37	0.30	0.30	NUM
ejpam-6378	390	38	3.669293792	3.669293792	NUM
ejpam-6378	390	39	3.669293792	3.669293792	NUM
ejpam-6378	390	40	3.669293792	3.669293792	NUM
ejpam-6378	390	41	0.40	0.40	NUM
ejpam-6378	390	42	4.055183573	4.055183573	NUM
ejpam-6378	390	43	4.055183573	4.055183573	NUM
ejpam-6378	390	44	4.055183573	4.055183573	NUM
ejpam-6378	390	45	0.50	0.50	NUM
ejpam-6378	390	46	4.481625588	4.481625588	NUM
ejpam-6378	390	47	4.481625588	4.481625588	NUM
ejpam-6378	390	48	4.481625588	4.481625588	NUM
ejpam-6378	390	49	0.10	0.10	NUM
ejpam-6378	390	50	3.049062427	3.049062427	NUM
ejpam-6378	390	51	3.162276707	3.162276707	NUM
ejpam-6378	390	52	3.209534249	3.209534249	NUM
ejpam-6378	390	53	0.20	0.20	NUM
ejpam-6378	390	54	3.395391468	3.395391468	NUM
ejpam-6378	390	55	3.494836859	3.494836859	NUM
ejpam-6378	390	56	3.574059501	3.574059501	NUM
ejpam-6378	390	57	0.95	0.95	NUM
ejpam-6378	390	58	0.30	0.30	NUM
ejpam-6378	390	59	3.772474744	3.772474744	NUM
ejpam-6378	390	60	3.862326090	3.862326090	NUM
ejpam-6378	390	61	3.970883434	3.970883434	NUM
ejpam-6378	390	62	0.40	0.40	NUM
ejpam-6378	390	63	4.185951335	4.185951335	NUM
ejpam-6378	390	64	4.268359634	4.268359634	NUM
ejpam-6378	390	65	4.405859090	4.405859090	NUM
ejpam-6378	390	66	0.50	0.50	NUM
ejpam-6378	390	67	4.640664007	4.640664007	NUM
ejpam-6378	390	68	4.716892562	4.716892562	NUM
ejpam-6378	391	1	4.883957994	4.883957994	NUM
ejpam-6378	391	2	0.10	0.10	NUM
ejpam-6378	391	3	3.101148306	3.101148306	NUM
ejpam-6378	391	4	3.337913899	3.337913899	NUM
ejpam-6378	391	5	3.445629081	3.445629081	NUM
ejpam-6378	391	6	0.20	0.20	NUM
ejpam-6378	391	7	3.480848024	3.480848024	NUM
ejpam-6378	391	8	3.688814956	3.688814956	NUM
ejpam-6378	391	9	3.867192329	3.867192329	NUM
ejpam-6378	391	10	0.90	0.90	NUM
ejpam-6378	391	11	0.30	0.30	NUM
ejpam-6378	391	12	3.888474328	3.888474328	NUM
ejpam-6378	391	13	4.076407078	4.076407078	NUM
ejpam-6378	391	14	4.319300743	4.319300743	NUM
ejpam-6378	391	15	0.40	0.40	NUM
ejpam-6378	391	16	4.332160489	4.332160489	NUM
ejpam-6378	391	17	4.504383671	4.504383671	NUM
ejpam-6378	391	18	4.810635889	4.810635889	NUM
ejpam-6378	391	19	0.50	0.50	NUM
ejpam-6378	391	20	4.817860678	4.817860678	NUM
ejpam-6378	391	21	4.976753819	4.976753819	NUM
ejpam-6378	391	22	5.347337632	5.347337632	NUM
ejpam-6378	391	23	0.10	0.10	NUM
ejpam-6378	391	24	3.161737693	3.161737693	NUM
ejpam-6378	391	25	3.534026565	3.534026565	NUM
ejpam-6378	391	26	3.719068724	3.719068724	NUM
ejpam-6378	391	27	0.20	0.20	NUM
ejpam-6378	391	28	3.578250433	3.578250433	NUM
ejpam-6378	391	29	3.905096972	3.905096972	NUM
ejpam-6378	391	30	4.207468721	4.207468721	NUM
ejpam-6378	391	31	0.85	0.85	NUM
ejpam-6378	391	32	0.30	0.30	NUM
ejpam-6378	391	33	4.019492351	4.019492351	NUM
ejpam-6378	391	34	4.314587569	4.314587569	NUM
ejpam-6378	391	35	4.723204464	4.723204464	NUM
ejpam-6378	391	36	0.40	0.40	NUM
ejpam-6378	391	37	4.496450273	4.496450273	NUM
ejpam-6378	391	38	4.766204929	4.766204929	NUM
ejpam-6378	391	39	5.278274854	5.278274854	NUM
ejpam-6378	391	40	0.50	0.50	NUM
ejpam-6378	391	41	5.016292557	5.016292557	NUM
ejpam-6378	391	42	5.263940139	5.263940139	NUM
ejpam-6378	391	43	5.879974675	5.879974675	NUM
ejpam-6378	391	44	0.10	0.10	NUM
ejpam-6378	391	45	3.232462725	3.232462725	NUM
ejpam-6378	391	46	3.754097180	3.754097180	NUM
ejpam-6378	391	47	4.037868933	4.037868933	NUM
ejpam-6378	391	48	0.20	0.20	NUM
ejpam-6378	391	49	3.689797588	3.689797588	NUM
ejpam-6378	391	50	4.147155788	4.147155788	NUM
ejpam-6378	391	51	4.603938816	4.603938816	NUM
ejpam-6378	391	52	0.80	0.80	NUM
ejpam-6378	391	53	0.30	0.30	NUM
ejpam-6378	391	54	4.168268841	4.168268841	NUM
ejpam-6378	391	55	4.580217667	4.580217667	NUM
ejpam-6378	391	56	5.191702098	5.191702098	NUM
ejpam-6378	391	57	0.40	0.40	NUM
ejpam-6378	391	58	4.682091666	4.682091666	NUM
ejpam-6378	391	59	5.056930340	5.056930340	NUM
ejpam-6378	391	60	5.817070731	5.817070731	NUM
ejpam-6378	391	61	0.50	0.50	NUM
ejpam-6378	391	62	5.239738787	5.239738787	NUM
ejpam-6378	391	63	5.581190749	5.581190749	NUM
ejpam-6378	391	64	6.488496318	6.488496318	NUM
ejpam-6378	391	65	0.10	0.10	NUM
ejpam-6378	391	66	3.315379658	3.315379658	NUM
ejpam-6378	391	67	4.002197630	4.002197630	NUM
ejpam-6378	391	68	4.411458682	4.411458682	NUM
ejpam-6378	391	69	0.20	0.20	NUM
ejpam-6378	391	70	3.818266181	3.818266181	NUM
ejpam-6378	391	71	4.418910210	4.418910210	NUM
ejpam-6378	391	72	5.066371531	5.066371531	NUM
ejpam-6378	391	73	0.75	0.75	NUM
ejpam-6378	391	74	0.30	0.30	NUM
ejpam-6378	391	75	4.338252697	4.338252697	NUM
ejpam-6378	391	76	4.876937276	4.876937276	NUM
ejpam-6378	391	77	5.733580680	5.733580680	NUM
ejpam-6378	391	78	0.40	0.40	NUM
ejpam-6378	391	79	4.893167590	4.893167590	NUM
ejpam-6378	391	80	5.379793868	5.379793868	NUM
ejpam-6378	391	81	6.433753129	6.433753129	NUM
ejpam-6378	391	82	0.50	0.50	NUM
ejpam-6378	391	83	5.492854752	5.492854752	NUM
ejpam-6378	391	84	5.931207911	5.931207911	NUM
ejpam-6378	391	85	7.176619194	7.176619194	NUM
ejpam-6378	391	86	table	table	NOUN
ejpam-6378	391	87	2	2	NUM
ejpam-6378	391	88	:	:	PUNCT
ejpam-6378	391	89	approximate	approximate	ADJ
ejpam-6378	391	90	solutions	solution	NOUN
ejpam-6378	391	91	under	under	ADP
ejpam-6378	391	92	different	different	ADJ
ejpam-6378	391	93	differential	differential	NOUN
ejpam-6378	391	94	operators	operator	NOUN
ejpam-6378	391	95	at	at	ADP
ejpam-6378	391	96	χ	χ	NOUN
ejpam-6378	391	97	=	=	SYM
ejpam-6378	391	98	1	1	X
ejpam-6378	391	99	.	.	PUNCT
ejpam-6378	391	100	in	in	ADP
ejpam-6378	391	101	table	table	NOUN
ejpam-6378	391	102	2	2	NUM
ejpam-6378	391	103	,	,	PUNCT
ejpam-6378	391	104	we	we	PRON
ejpam-6378	391	105	have	have	AUX
ejpam-6378	391	106	displayed	display	VERB
ejpam-6378	391	107	the	the	DET
ejpam-6378	391	108	approximate	approximate	ADJ
ejpam-6378	391	109	solutions	solution	NOUN
ejpam-6378	391	110	corresponding	correspond	VERB
ejpam-6378	391	111	to	to	ADP
ejpam-6378	391	112	various	various	ADJ
ejpam-6378	391	113	differential	differential	ADJ
ejpam-6378	391	114	operators	operator	NOUN
ejpam-6378	391	115	of	of	ADP
ejpam-6378	391	116	fractional	fractional	ADJ
ejpam-6378	391	117	orders	order	NOUN
ejpam-6378	391	118	.	.	PUNCT
ejpam-6378	392	1	5	5	X
ejpam-6378	392	2	.	.	X
ejpam-6378	392	3	conclusions	conclusion	NOUN
ejpam-6378	392	4	this	this	DET
ejpam-6378	392	5	study	study	NOUN
ejpam-6378	392	6	conducts	conduct	VERB
ejpam-6378	392	7	an	an	DET
ejpam-6378	392	8	analytic	analytic	ADJ
ejpam-6378	392	9	investigation	investigation	NOUN
ejpam-6378	392	10	of	of	ADP
ejpam-6378	392	11	a	a	DET
ejpam-6378	392	12	non	non	ADJ
ejpam-6378	392	13	-	-	ADJ
ejpam-6378	392	14	linear	linear	ADJ
ejpam-6378	392	15	fpde	fpde	NOUN
ejpam-6378	392	16	utilizing	utilize	VERB
ejpam-6378	392	17	various	various	ADJ
ejpam-6378	392	18	derivative	derivative	ADJ
ejpam-6378	392	19	operators	operator	NOUN
ejpam-6378	392	20	and	and	CCONJ
ejpam-6378	392	21	transformations	transformation	NOUN
ejpam-6378	392	22	.	.	PUNCT
ejpam-6378	393	1	a	a	DET
ejpam-6378	393	2	clearly	clearly	ADV
ejpam-6378	393	3	stated	state	VERB
ejpam-6378	393	4	general	general	ADJ
ejpam-6378	393	5	methodology	methodology	NOUN
ejpam-6378	393	6	is	be	AUX
ejpam-6378	393	7	developed	develop	VERB
ejpam-6378	393	8	for	for	ADP
ejpam-6378	393	9	fractional	fractional	ADJ
ejpam-6378	393	10	operators	operator	NOUN
ejpam-6378	393	11	under	under	ADP
ejpam-6378	393	12	transformations	transformation	NOUN
ejpam-6378	393	13	in	in	ADP
ejpam-6378	393	14	the	the	DET
ejpam-6378	393	15	context	context	NOUN
ejpam-6378	393	16	of	of	ADP
ejpam-6378	393	17	solving	solve	VERB
ejpam-6378	393	18	fpdes	fpde	NOUN
ejpam-6378	393	19	.	.	PUNCT
ejpam-6378	394	1	the	the	DET
ejpam-6378	394	2	study	study	NOUN
ejpam-6378	394	3	concludes	conclude	VERB
ejpam-6378	394	4	that	that	SCONJ
ejpam-6378	394	5	the	the	DET
ejpam-6378	394	6	adm	adm	PROPN
ejpam-6378	394	7	,	,	PUNCT
ejpam-6378	394	8	when	when	SCONJ
ejpam-6378	394	9	applied	apply	VERB
ejpam-6378	394	10	with	with	ADP
ejpam-6378	394	11	various	various	ADJ
ejpam-6378	394	12	transforms	transform	NOUN
ejpam-6378	394	13	,	,	PUNCT
ejpam-6378	394	14	is	be	AUX
ejpam-6378	394	15	an	an	DET
ejpam-6378	394	16	effective	effective	ADJ
ejpam-6378	394	17	m.	m.	NOUN
ejpam-6378	394	18	sohail	sohail	PROPN
ejpam-6378	394	19	et	et	PROPN
ejpam-6378	394	20	al	al	PROPN
ejpam-6378	394	21	.	.	PUNCT
ejpam-6378	394	22	/	/	SYM
ejpam-6378	394	23	eur	eur	PROPN
ejpam-6378	394	24	.	.	PUNCT
ejpam-6378	395	1	j.	j.	PROPN
ejpam-6378	395	2	pure	pure	PROPN
ejpam-6378	395	3	appl	appl	PROPN
ejpam-6378	395	4	.	.	PROPN
ejpam-6378	395	5	math	math	PROPN
ejpam-6378	395	6	,	,	PUNCT
ejpam-6378	395	7	18	18	NUM
ejpam-6378	395	8	(	(	PUNCT
ejpam-6378	395	9	4	4	NUM
ejpam-6378	395	10	)	)	PUNCT
ejpam-6378	395	11	(	(	PUNCT
ejpam-6378	395	12	2025	2025	NUM
ejpam-6378	395	13	)	)	PUNCT
ejpam-6378	395	14	,	,	PUNCT
ejpam-6378	395	15	6378	6378	NUM
ejpam-6378	395	16	17	17	NUM
ejpam-6378	395	17	of	of	ADP
ejpam-6378	395	18	20	20	NUM
ejpam-6378	395	19	tool	tool	NOUN
ejpam-6378	395	20	for	for	ADP
ejpam-6378	395	21	solving	solve	VERB
ejpam-6378	395	22	both	both	CCONJ
ejpam-6378	395	23	linear	linear	ADJ
ejpam-6378	395	24	and	and	CCONJ
ejpam-6378	395	25	non	non	ADJ
ejpam-6378	395	26	-	-	ADJ
ejpam-6378	395	27	linear	linear	ADJ
ejpam-6378	395	28	fpdes	fpde	NOUN
ejpam-6378	395	29	,	,	PUNCT
ejpam-6378	395	30	demonstrating	demonstrate	VERB
ejpam-6378	395	31	high	high	ADJ
ejpam-6378	395	32	accuracy	accuracy	NOUN
ejpam-6378	395	33	and	and	CCONJ
ejpam-6378	395	34	reduced	reduce	VERB
ejpam-6378	395	35	labor	labor	NOUN
ejpam-6378	395	36	effort	effort	NOUN
ejpam-6378	395	37	.	.	PUNCT
ejpam-6378	396	1	furthermore	furthermore	ADV
ejpam-6378	396	2	,	,	PUNCT
ejpam-6378	396	3	the	the	DET
ejpam-6378	396	4	data	datum	NOUN
ejpam-6378	396	5	presented	present	VERB
ejpam-6378	396	6	in	in	ADP
ejpam-6378	396	7	the	the	DET
ejpam-6378	396	8	tables	table	NOUN
ejpam-6378	396	9	and	and	CCONJ
ejpam-6378	396	10	plots	plot	NOUN
ejpam-6378	396	11	indicate	indicate	VERB
ejpam-6378	396	12	that	that	SCONJ
ejpam-6378	396	13	the	the	DET
ejpam-6378	396	14	solutions	solution	NOUN
ejpam-6378	396	15	to	to	ADP
ejpam-6378	396	16	the	the	DET
ejpam-6378	396	17	fpdes	fpde	NOUN
ejpam-6378	396	18	using	use	VERB
ejpam-6378	396	19	the	the	DET
ejpam-6378	396	20	caputo	caputo	PROPN
ejpam-6378	396	21	,	,	PUNCT
ejpam-6378	396	22	caputo	caputo	PROPN
ejpam-6378	396	23	-	-	PUNCT
ejpam-6378	396	24	fabrizio	fabrizio	PROPN
ejpam-6378	396	25	,	,	PUNCT
ejpam-6378	396	26	and	and	CCONJ
ejpam-6378	396	27	atangana	atangana	PROPN
ejpam-6378	396	28	-	-	PUNCT
ejpam-6378	396	29	baleanu	baleanu	ADJ
ejpam-6378	396	30	fractional	fractional	ADJ
ejpam-6378	396	31	derivatives	derivative	NOUN
ejpam-6378	396	32	at	at	ADP
ejpam-6378	396	33	an	an	DET
ejpam-6378	396	34	integer	integer	NOUN
ejpam-6378	396	35	level	level	NOUN
ejpam-6378	396	36	are	be	AUX
ejpam-6378	396	37	equivalent	equivalent	ADJ
ejpam-6378	396	38	and	and	CCONJ
ejpam-6378	396	39	converge	converge	VERB
ejpam-6378	396	40	to	to	ADP
ejpam-6378	396	41	the	the	DET
ejpam-6378	396	42	exact	exact	ADJ
ejpam-6378	396	43	solution	solution	NOUN
ejpam-6378	396	44	.	.	PUNCT
ejpam-6378	397	1	furthermore	furthermore	ADV
ejpam-6378	397	2	,	,	PUNCT
ejpam-6378	397	3	plots	plot	NOUN
ejpam-6378	397	4	indicate	indicate	VERB
ejpam-6378	397	5	that	that	SCONJ
ejpam-6378	397	6	absolute	absolute	ADJ
ejpam-6378	397	7	errors	error	NOUN
ejpam-6378	397	8	diminish	diminish	VERB
ejpam-6378	397	9	as	as	ADP
ejpam-6378	397	10	the	the	DET
ejpam-6378	397	11	iterations	iteration	NOUN
ejpam-6378	397	12	of	of	ADP
ejpam-6378	397	13	adm	adm	PROPN
ejpam-6378	397	14	with	with	ADP
ejpam-6378	397	15	various	various	ADJ
ejpam-6378	397	16	transformations	transformation	NOUN
ejpam-6378	397	17	increase	increase	NOUN
ejpam-6378	397	18	.	.	PUNCT
ejpam-6378	398	1	2d	2d	PROPN
ejpam-6378	398	2	&	&	CCONJ
ejpam-6378	398	3	3d	3d	NOUN
ejpam-6378	398	4	-	-	PUNCT
ejpam-6378	398	5	plots	plot	NOUN
ejpam-6378	398	6	show	show	VERB
ejpam-6378	398	7	that	that	SCONJ
ejpam-6378	398	8	fractional	fractional	ADJ
ejpam-6378	398	9	order	order	NOUN
ejpam-6378	398	10	solutions	solution	NOUN
ejpam-6378	398	11	under	under	ADP
ejpam-6378	398	12	different	different	ADJ
ejpam-6378	398	13	operators	operator	NOUN
ejpam-6378	398	14	are	be	AUX
ejpam-6378	398	15	converging	converge	VERB
ejpam-6378	398	16	to	to	ADP
ejpam-6378	398	17	integer	integer	NOUN
ejpam-6378	398	18	order	order	NOUN
ejpam-6378	398	19	.	.	PUNCT
ejpam-6378	399	1	the	the	DET
ejpam-6378	399	2	adm	adm	PROPN
ejpam-6378	399	3	series	series	PROPN
ejpam-6378	399	4	solutions	solution	NOUN
ejpam-6378	399	5	are	be	AUX
ejpam-6378	399	6	the	the	DET
ejpam-6378	399	7	same	same	ADJ
ejpam-6378	399	8	under	under	ADP
ejpam-6378	399	9	different	different	ADJ
ejpam-6378	399	10	transforms	transform	NOUN
ejpam-6378	399	11	.	.	PUNCT
ejpam-6378	400	1	our	our	PRON
ejpam-6378	400	2	research	research	NOUN
ejpam-6378	400	3	indicates	indicate	VERB
ejpam-6378	400	4	that	that	SCONJ
ejpam-6378	400	5	adm	adm	PROPN
ejpam-6378	400	6	with	with	ADP
ejpam-6378	400	7	various	various	ADJ
ejpam-6378	400	8	transformations	transformation	NOUN
ejpam-6378	400	9	offers	offer	VERB
ejpam-6378	400	10	a	a	DET
ejpam-6378	400	11	straightforward	straightforward	ADJ
ejpam-6378	400	12	and	and	CCONJ
ejpam-6378	400	13	precise	precise	ADJ
ejpam-6378	400	14	solution	solution	NOUN
ejpam-6378	400	15	to	to	ADP
ejpam-6378	400	16	fpdes	fpde	NOUN
ejpam-6378	400	17	involving	involve	VERB
ejpam-6378	400	18	different	different	ADJ
ejpam-6378	400	19	operators	operator	NOUN
ejpam-6378	400	20	.	.	PUNCT
ejpam-6378	401	1	acknowledgements	acknowledgement	NOUN
ejpam-6378	401	2	authors	author	NOUN
ejpam-6378	401	3	are	be	AUX
ejpam-6378	401	4	thankful	thankful	ADJ
ejpam-6378	401	5	to	to	ADP
ejpam-6378	401	6	prince	prince	PROPN
ejpam-6378	401	7	sultan	sultan	PROPN
ejpam-6378	401	8	university	university	PROPN
ejpam-6378	401	9	for	for	ADP
ejpam-6378	401	10	apc	apc	PROPN
ejpam-6378	401	11	and	and	CCONJ
ejpam-6378	401	12	support	support	VERB
ejpam-6378	401	13	through	through	ADP
ejpam-6378	401	14	tas	ta	NOUN
ejpam-6378	401	15	research	research	NOUN
ejpam-6378	401	16	lab	lab	NOUN
ejpam-6378	401	17	.	.	PUNCT
ejpam-6378	402	1	references	reference	NOUN
ejpam-6378	402	2	[	[	X
ejpam-6378	402	3	1	1	NUM
ejpam-6378	402	4	]	]	PUNCT
ejpam-6378	402	5	richard	richard	PROPN
ejpam-6378	402	6	l	l	PROPN
ejpam-6378	402	7	magin	magin	NOUN
ejpam-6378	402	8	.	.	PUNCT
ejpam-6378	403	1	fractional	fractional	ADJ
ejpam-6378	403	2	calculus	calculus	NOUN
ejpam-6378	403	3	models	model	NOUN
ejpam-6378	403	4	of	of	ADP
ejpam-6378	403	5	complex	complex	ADJ
ejpam-6378	403	6	dynamics	dynamic	NOUN
ejpam-6378	403	7	in	in	ADP
ejpam-6378	403	8	biological	biological	ADJ
ejpam-6378	403	9	tissues	tissue	NOUN
ejpam-6378	403	10	.	.	PUNCT
ejpam-6378	404	1	computers	computer	NOUN
ejpam-6378	404	2	&	&	CCONJ
ejpam-6378	404	3	mathematics	mathematics	PROPN
ejpam-6378	404	4	with	with	ADP
ejpam-6378	404	5	applications	application	NOUN
ejpam-6378	404	6	,	,	PUNCT
ejpam-6378	404	7	59(5):1586–1593	59(5):1586–1593	NUM
ejpam-6378	404	8	,	,	PUNCT
ejpam-6378	404	9	2010	2010	NUM
ejpam-6378	404	10	.	.	PUNCT
ejpam-6378	405	1	[	[	X
ejpam-6378	405	2	2	2	NUM
ejpam-6378	405	3	]	]	PUNCT
ejpam-6378	405	4	hasib	hasib	PROPN
ejpam-6378	405	5	khan	khan	PROPN
ejpam-6378	405	6	,	,	PUNCT
ejpam-6378	405	7	jehad	jehad	PROPN
ejpam-6378	405	8	alzabut	alzabut	PROPN
ejpam-6378	405	9	,	,	PUNCT
ejpam-6378	405	10	anwar	anwar	PROPN
ejpam-6378	405	11	shah	shah	PROPN
ejpam-6378	405	12	,	,	PUNCT
ejpam-6378	405	13	zai	zai	NOUN
ejpam-6378	405	14	-	-	PUNCT
ejpam-6378	405	15	yin	yin	NOUN
ejpam-6378	405	16	he	he	PRON
ejpam-6378	405	17	,	,	PUNCT
ejpam-6378	405	18	sina	sina	PROPN
ejpam-6378	405	19	etemad	etemad	PROPN
ejpam-6378	405	20	,	,	PUNCT
ejpam-6378	405	21	shahram	shahram	PROPN
ejpam-6378	405	22	rezapour	rezapour	PROPN
ejpam-6378	405	23	,	,	PUNCT
ejpam-6378	405	24	and	and	CCONJ
ejpam-6378	405	25	akbar	akbar	PROPN
ejpam-6378	405	26	zada	zada	PROPN
ejpam-6378	405	27	.	.	PUNCT
ejpam-6378	406	1	on	on	ADP
ejpam-6378	406	2	fractal	fractal	ADJ
ejpam-6378	406	3	-	-	PUNCT
ejpam-6378	406	4	fractional	fractional	ADJ
ejpam-6378	406	5	waterborne	waterborne	ADJ
ejpam-6378	406	6	disease	disease	NOUN
ejpam-6378	406	7	model	model	NOUN
ejpam-6378	406	8	:	:	PUNCT
ejpam-6378	406	9	a	a	DET
ejpam-6378	406	10	study	study	NOUN
ejpam-6378	406	11	on	on	ADP
ejpam-6378	406	12	theoretical	theoretical	ADJ
ejpam-6378	406	13	and	and	CCONJ
ejpam-6378	406	14	numerical	numerical	ADJ
ejpam-6378	406	15	aspects	aspect	NOUN
ejpam-6378	406	16	of	of	ADP
ejpam-6378	406	17	solutions	solution	NOUN
ejpam-6378	406	18	via	via	ADP
ejpam-6378	406	19	simulations	simulation	NOUN
ejpam-6378	406	20	.	.	PUNCT
ejpam-6378	407	1	fractals	fractal	NOUN
ejpam-6378	407	2	,	,	PUNCT
ejpam-6378	407	3	31(04):2340055	31(04):2340055	NUM
ejpam-6378	407	4	,	,	PUNCT
ejpam-6378	407	5	2023	2023	NUM
ejpam-6378	407	6	.	.	PUNCT
ejpam-6378	408	1	[	[	X
ejpam-6378	408	2	3	3	X
ejpam-6378	408	3	]	]	X
ejpam-6378	408	4	vasily	vasily	NOUN
ejpam-6378	408	5	e	e	NOUN
ejpam-6378	408	6	tarasov	tarasov	NOUN
ejpam-6378	408	7	.	.	PUNCT
ejpam-6378	409	1	fractional	fractional	ADJ
ejpam-6378	409	2	quantum	quantum	ADJ
ejpam-6378	409	3	field	field	NOUN
ejpam-6378	409	4	theory	theory	NOUN
ejpam-6378	409	5	:	:	PUNCT
ejpam-6378	409	6	from	from	ADP
ejpam-6378	409	7	lattice	lattice	NOUN
ejpam-6378	409	8	to	to	ADP
ejpam-6378	409	9	continuum	continuum	PROPN
ejpam-6378	409	10	.	.	PUNCT
ejpam-6378	410	1	advances	advance	NOUN
ejpam-6378	410	2	in	in	ADP
ejpam-6378	410	3	high	high	ADJ
ejpam-6378	410	4	energy	energy	NOUN
ejpam-6378	410	5	physics	physics	NOUN
ejpam-6378	410	6	,	,	PUNCT
ejpam-6378	410	7	2014(1):957863	2014(1):957863	NUM
ejpam-6378	410	8	,	,	PUNCT
ejpam-6378	410	9	2014	2014	NUM
ejpam-6378	410	10	.	.	PUNCT
ejpam-6378	411	1	[	[	X
ejpam-6378	411	2	4	4	NUM
ejpam-6378	411	3	]	]	X
ejpam-6378	411	4	vladimir	vladimir	NOUN
ejpam-6378	411	5	v	v	X
ejpam-6378	411	6	kulish	kulish	PROPN
ejpam-6378	411	7	and	and	CCONJ
ejpam-6378	411	8	josé	josé	ADJ
ejpam-6378	411	9	l	l	PROPN
ejpam-6378	411	10	lage	lage	PROPN
ejpam-6378	411	11	.	.	PUNCT
ejpam-6378	412	1	application	application	NOUN
ejpam-6378	412	2	of	of	ADP
ejpam-6378	412	3	fractional	fractional	ADJ
ejpam-6378	412	4	calculus	calculus	NOUN
ejpam-6378	412	5	to	to	ADP
ejpam-6378	412	6	fluid	fluid	ADJ
ejpam-6378	412	7	mechanics	mechanic	NOUN
ejpam-6378	412	8	.	.	PUNCT
ejpam-6378	413	1	j.	j.	PROPN
ejpam-6378	413	2	fluids	fluids	PROPN
ejpam-6378	413	3	eng	eng	PROPN
ejpam-6378	413	4	.	.	PROPN
ejpam-6378	413	5	,	,	PUNCT
ejpam-6378	413	6	124(3):803–806	124(3):803–806	PROPN
ejpam-6378	413	7	,	,	PUNCT
ejpam-6378	413	8	2002	2002	NUM
ejpam-6378	413	9	.	.	PUNCT
ejpam-6378	414	1	[	[	X
ejpam-6378	414	2	5	5	NUM
ejpam-6378	414	3	]	]	PUNCT
ejpam-6378	414	4	mohamed	mohamed	PROPN
ejpam-6378	414	5	aly	aly	PROPN
ejpam-6378	414	6	abdou	abdou	PROPN
ejpam-6378	414	7	.	.	PUNCT
ejpam-6378	415	1	an	an	DET
ejpam-6378	415	2	analytical	analytical	ADJ
ejpam-6378	415	3	method	method	NOUN
ejpam-6378	415	4	for	for	ADP
ejpam-6378	415	5	space	space	NOUN
ejpam-6378	415	6	–	–	PUNCT
ejpam-6378	415	7	time	time	NOUN
ejpam-6378	415	8	fractional	fractional	ADJ
ejpam-6378	415	9	nonlinear	nonlinear	ADJ
ejpam-6378	415	10	differential	differential	ADJ
ejpam-6378	415	11	equations	equation	NOUN
ejpam-6378	415	12	arising	arise	VERB
ejpam-6378	415	13	in	in	ADP
ejpam-6378	415	14	plasma	plasma	NOUN
ejpam-6378	415	15	physics	physic	NOUN
ejpam-6378	415	16	.	.	PUNCT
ejpam-6378	416	1	journal	journal	PROPN
ejpam-6378	416	2	of	of	ADP
ejpam-6378	416	3	ocean	ocean	PROPN
ejpam-6378	416	4	engineering	engineering	NOUN
ejpam-6378	416	5	and	and	CCONJ
ejpam-6378	416	6	science	science	NOUN
ejpam-6378	416	7	,	,	PUNCT
ejpam-6378	416	8	2(4):288–292	2(4):288–292	NUM
ejpam-6378	416	9	,	,	PUNCT
ejpam-6378	416	10	2017	2017	NUM
ejpam-6378	416	11	.	.	PUNCT
ejpam-6378	417	1	[	[	X
ejpam-6378	417	2	6	6	NUM
ejpam-6378	417	3	]	]	X
ejpam-6378	417	4	ivo	ivo	PROPN
ejpam-6378	417	5	petráš.	petráš.	PROPN
ejpam-6378	417	6	chapter	chapter	NOUN
ejpam-6378	417	7	three	three	NUM
ejpam-6378	417	8	fractional	fractional	ADJ
ejpam-6378	417	9	-	-	PUNCT
ejpam-6378	417	10	order	order	NOUN
ejpam-6378	417	11	control	control	NOUN
ejpam-6378	417	12	:	:	PUNCT
ejpam-6378	417	13	new	new	ADJ
ejpam-6378	417	14	control	control	NOUN
ejpam-6378	417	15	techniques	technique	NOUN
ejpam-6378	417	16	.	.	PUNCT
ejpam-6378	418	1	in	in	ADP
ejpam-6378	418	2	ahmed	ahmed	PROPN
ejpam-6378	418	3	g.	g.	PROPN
ejpam-6378	418	4	radwan	radwan	PROPN
ejpam-6378	418	5	,	,	PUNCT
ejpam-6378	418	6	farooq	farooq	PROPN
ejpam-6378	418	7	ahmad	ahmad	PROPN
ejpam-6378	418	8	khanday	khanday	PROPN
ejpam-6378	418	9	,	,	PUNCT
ejpam-6378	418	10	and	and	CCONJ
ejpam-6378	418	11	lobna	lobna	PROPN
ejpam-6378	418	12	a.	a.	NOUN
ejpam-6378	418	13	said	say	VERB
ejpam-6378	418	14	,	,	PUNCT
ejpam-6378	418	15	editors	editor	NOUN
ejpam-6378	418	16	,	,	PUNCT
ejpam-6378	418	17	fractional	fractional	ADJ
ejpam-6378	418	18	order	order	NOUN
ejpam-6378	418	19	systems	system	NOUN
ejpam-6378	418	20	,	,	PUNCT
ejpam-6378	418	21	volume	volume	NOUN
ejpam-6378	418	22	1	1	NUM
ejpam-6378	418	23	of	of	ADP
ejpam-6378	418	24	emerging	emerge	VERB
ejpam-6378	418	25	methodologies	methodology	NOUN
ejpam-6378	418	26	and	and	CCONJ
ejpam-6378	418	27	applications	application	NOUN
ejpam-6378	418	28	in	in	ADP
ejpam-6378	418	29	modelling	modelling	NOUN
ejpam-6378	418	30	,	,	PUNCT
ejpam-6378	418	31	pages	page	NOUN
ejpam-6378	418	32	71–106	71–106	NUM
ejpam-6378	418	33	.	.	PUNCT
ejpam-6378	419	1	academic	academic	ADJ
ejpam-6378	419	2	press	press	NOUN
ejpam-6378	419	3	,	,	PUNCT
ejpam-6378	419	4	2022	2022	NUM
ejpam-6378	419	5	.	.	PUNCT
ejpam-6378	420	1	[	[	X
ejpam-6378	420	2	7	7	NUM
ejpam-6378	420	3	]	]	X
ejpam-6378	420	4	pritesh	pritesh	ADJ
ejpam-6378	420	5	shah	shah	NOUN
ejpam-6378	420	6	and	and	CCONJ
ejpam-6378	420	7	sudhir	sudhir	PROPN
ejpam-6378	420	8	agashe	agashe	PROPN
ejpam-6378	420	9	.	.	PUNCT
ejpam-6378	421	1	review	review	NOUN
ejpam-6378	421	2	of	of	ADP
ejpam-6378	421	3	fractional	fractional	ADJ
ejpam-6378	421	4	pid	pid	NOUN
ejpam-6378	421	5	controller	controller	NOUN
ejpam-6378	421	6	.	.	PUNCT
ejpam-6378	422	1	mechatronics	mechatronic	NOUN
ejpam-6378	422	2	,	,	PUNCT
ejpam-6378	422	3	38:29–41	38:29–41	NUM
ejpam-6378	422	4	,	,	PUNCT
ejpam-6378	422	5	2016	2016	NUM
ejpam-6378	422	6	.	.	PUNCT
ejpam-6378	423	1	[	[	X
ejpam-6378	423	2	8	8	NUM
ejpam-6378	423	3	]	]	X
ejpam-6378	423	4	manisha	manisha	PROPN
ejpam-6378	423	5	joshi	joshi	PROPN
ejpam-6378	423	6	,	,	PUNCT
ejpam-6378	423	7	savita	savita	PROPN
ejpam-6378	423	8	bhosale	bhosale	PROPN
ejpam-6378	423	9	,	,	PUNCT
ejpam-6378	423	10	and	and	CCONJ
ejpam-6378	423	11	vishwesh	vishwesh	VERB
ejpam-6378	423	12	a	a	DET
ejpam-6378	423	13	vyawahare	vyawahare	NOUN
ejpam-6378	423	14	.	.	PUNCT
ejpam-6378	424	1	a	a	DET
ejpam-6378	424	2	survey	survey	NOUN
ejpam-6378	424	3	of	of	ADP
ejpam-6378	424	4	fractional	fractional	ADJ
ejpam-6378	424	5	calculus	calculus	NOUN
ejpam-6378	424	6	applications	application	NOUN
ejpam-6378	424	7	in	in	ADP
ejpam-6378	424	8	artificial	artificial	ADJ
ejpam-6378	424	9	neural	neural	ADJ
ejpam-6378	424	10	networks	network	NOUN
ejpam-6378	424	11	.	.	PUNCT
ejpam-6378	425	1	artificial	artificial	ADJ
ejpam-6378	425	2	intelligence	intelligence	NOUN
ejpam-6378	425	3	review	review	NOUN
ejpam-6378	425	4	,	,	PUNCT
ejpam-6378	425	5	56(11):13897–13950	56(11):13897–13950	NUM
ejpam-6378	425	6	,	,	PUNCT
ejpam-6378	425	7	2023	2023	NUM
ejpam-6378	425	8	.	.	PUNCT
ejpam-6378	426	1	[	[	X
ejpam-6378	426	2	9	9	NUM
ejpam-6378	426	3	]	]	SYM
ejpam-6378	426	4	j	j	PROPN
ejpam-6378	426	5	tenreiro	tenreiro	PROPN
ejpam-6378	426	6	machado	machado	PROPN
ejpam-6378	426	7	,	,	PUNCT
ejpam-6378	426	8	virginia	virginia	PROPN
ejpam-6378	426	9	kiryakova	kiryakova	PROPN
ejpam-6378	426	10	,	,	PUNCT
ejpam-6378	426	11	and	and	CCONJ
ejpam-6378	426	12	francesco	francesco	PROPN
ejpam-6378	426	13	mainardi	mainardi	PROPN
ejpam-6378	426	14	.	.	PUNCT
ejpam-6378	427	1	recent	recent	ADJ
ejpam-6378	427	2	history	history	NOUN
ejpam-6378	427	3	of	of	ADP
ejpam-6378	427	4	fractional	fractional	ADJ
ejpam-6378	427	5	calculus	calculus	NOUN
ejpam-6378	427	6	.	.	PUNCT
ejpam-6378	428	1	communications	communication	NOUN
ejpam-6378	428	2	in	in	ADP
ejpam-6378	428	3	nonlinear	nonlinear	ADJ
ejpam-6378	428	4	science	science	NOUN
ejpam-6378	428	5	and	and	CCONJ
ejpam-6378	428	6	numerical	numerical	PROPN
ejpam-6378	428	7	simulation	simulation	PROPN
ejpam-6378	428	8	,	,	PUNCT
ejpam-6378	428	9	16(3):1140–1153	16(3):1140–1153	NUM
ejpam-6378	428	10	,	,	PUNCT
ejpam-6378	428	11	2011	2011	NUM
ejpam-6378	428	12	.	.	PUNCT
ejpam-6378	429	1	m.	m.	PROPN
ejpam-6378	429	2	sohail	sohail	PROPN
ejpam-6378	429	3	et	et	PROPN
ejpam-6378	429	4	al	al	PROPN
ejpam-6378	429	5	.	.	PUNCT
ejpam-6378	429	6	/	/	SYM
ejpam-6378	429	7	eur	eur	PROPN
ejpam-6378	429	8	.	.	PUNCT
ejpam-6378	430	1	j.	j.	PROPN
ejpam-6378	430	2	pure	pure	PROPN
ejpam-6378	430	3	appl	appl	PROPN
ejpam-6378	430	4	.	.	PROPN
ejpam-6378	430	5	math	math	PROPN
ejpam-6378	430	6	,	,	PUNCT
ejpam-6378	430	7	18	18	NUM
ejpam-6378	430	8	(	(	PUNCT
ejpam-6378	430	9	4	4	NUM
ejpam-6378	430	10	)	)	PUNCT
ejpam-6378	430	11	(	(	PUNCT
ejpam-6378	430	12	2025	2025	NUM
ejpam-6378	430	13	)	)	PUNCT
ejpam-6378	430	14	,	,	PUNCT
ejpam-6378	430	15	6378	6378	NUM
ejpam-6378	430	16	18	18	NUM
ejpam-6378	430	17	of	of	ADP
ejpam-6378	430	18	20	20	NUM
ejpam-6378	430	19	[	[	SYM
ejpam-6378	430	20	10	10	NUM
ejpam-6378	430	21	]	]	X
ejpam-6378	430	22	bm	bm	PROPN
ejpam-6378	430	23	vinagre	vinagre	PROPN
ejpam-6378	430	24	and	and	CCONJ
ejpam-6378	430	25	v	v	ADP
ejpam-6378	430	26	feliu	feliu	NOUN
ejpam-6378	430	27	.	.	PUNCT
ejpam-6378	431	1	modeling	modeling	NOUN
ejpam-6378	431	2	and	and	CCONJ
ejpam-6378	431	3	control	control	NOUN
ejpam-6378	431	4	of	of	ADP
ejpam-6378	431	5	dynamic	dynamic	ADJ
ejpam-6378	431	6	system	system	NOUN
ejpam-6378	431	7	using	use	VERB
ejpam-6378	431	8	fractional	fractional	ADJ
ejpam-6378	431	9	calculus	calculus	NOUN
ejpam-6378	431	10	:	:	PUNCT
ejpam-6378	431	11	application	application	NOUN
ejpam-6378	431	12	to	to	ADP
ejpam-6378	431	13	electrochemical	electrochemical	ADJ
ejpam-6378	431	14	processes	process	NOUN
ejpam-6378	431	15	and	and	CCONJ
ejpam-6378	431	16	flexible	flexible	ADJ
ejpam-6378	431	17	structures	structure	NOUN
ejpam-6378	431	18	.	.	PUNCT
ejpam-6378	432	1	in	in	ADP
ejpam-6378	432	2	proc	proc	NOUN
ejpam-6378	432	3	.	.	PUNCT
ejpam-6378	433	1	41st	41st	ADJ
ejpam-6378	433	2	ieee	ieee	PROPN
ejpam-6378	433	3	conf	conf	NOUN
ejpam-6378	433	4	.	.	PUNCT
ejpam-6378	434	1	decision	decision	NOUN
ejpam-6378	434	2	and	and	CCONJ
ejpam-6378	434	3	control	control	NOUN
ejpam-6378	434	4	,	,	PUNCT
ejpam-6378	434	5	volume	volume	NOUN
ejpam-6378	434	6	1	1	NUM
ejpam-6378	434	7	,	,	PUNCT
ejpam-6378	434	8	pages	page	NOUN
ejpam-6378	434	9	214–239	214–239	NUM
ejpam-6378	434	10	,	,	PUNCT
ejpam-6378	434	11	2002	2002	NUM
ejpam-6378	434	12	.	.	PUNCT
ejpam-6378	435	1	[	[	X
ejpam-6378	435	2	11	11	NUM
ejpam-6378	435	3	]	]	X
ejpam-6378	435	4	qianqian	qianqian	PROPN
ejpam-6378	435	5	yang	yang	PROPN
ejpam-6378	435	6	,	,	PUNCT
ejpam-6378	435	7	ian	ian	PROPN
ejpam-6378	435	8	turner	turner	PROPN
ejpam-6378	435	9	,	,	PUNCT
ejpam-6378	435	10	fawang	fawang	PROPN
ejpam-6378	435	11	liu	liu	PROPN
ejpam-6378	435	12	,	,	PUNCT
ejpam-6378	435	13	and	and	CCONJ
ejpam-6378	435	14	milos	milo	NOUN
ejpam-6378	435	15	ilić.	ilić.	PROPN
ejpam-6378	435	16	novel	novel	ADJ
ejpam-6378	435	17	numerical	numerical	ADJ
ejpam-6378	435	18	methods	method	NOUN
ejpam-6378	435	19	for	for	ADP
ejpam-6378	435	20	solving	solve	VERB
ejpam-6378	435	21	the	the	DET
ejpam-6378	435	22	time	time	NOUN
ejpam-6378	435	23	-	-	PUNCT
ejpam-6378	435	24	space	space	NOUN
ejpam-6378	435	25	fractional	fractional	ADJ
ejpam-6378	435	26	diffusion	diffusion	NOUN
ejpam-6378	435	27	equation	equation	NOUN
ejpam-6378	435	28	in	in	ADP
ejpam-6378	435	29	two	two	NUM
ejpam-6378	435	30	dimensions	dimension	NOUN
ejpam-6378	435	31	.	.	PUNCT
ejpam-6378	436	1	siam	siam	PROPN
ejpam-6378	436	2	journal	journal	PROPN
ejpam-6378	436	3	on	on	ADP
ejpam-6378	436	4	scientific	scientific	ADJ
ejpam-6378	436	5	computing	computing	NOUN
ejpam-6378	436	6	,	,	PUNCT
ejpam-6378	436	7	33(3):1159–1180	33(3):1159–1180	NUM
ejpam-6378	436	8	,	,	PUNCT
ejpam-6378	436	9	2011	2011	NUM
ejpam-6378	436	10	.	.	PUNCT
ejpam-6378	437	1	[	[	X
ejpam-6378	437	2	12	12	NUM
ejpam-6378	437	3	]	]	X
ejpam-6378	437	4	imtiaz	imtiaz	PROPN
ejpam-6378	437	5	ahmad	ahmad	PROPN
ejpam-6378	437	6	,	,	PUNCT
ejpam-6378	437	7	ihteram	ihteram	PROPN
ejpam-6378	437	8	ali	ali	PROPN
ejpam-6378	437	9	,	,	PUNCT
ejpam-6378	437	10	rashid	rashid	PROPN
ejpam-6378	437	11	jan	jan	PROPN
ejpam-6378	437	12	,	,	PUNCT
ejpam-6378	437	13	sahar	sahar	PROPN
ejpam-6378	437	14	ahmed	ahmed	PROPN
ejpam-6378	437	15	idris	idris	PROPN
ejpam-6378	437	16	,	,	PUNCT
ejpam-6378	437	17	and	and	CCONJ
ejpam-6378	437	18	mohamed	mohamed	PROPN
ejpam-6378	437	19	mousa	mousa	PROPN
ejpam-6378	437	20	.	.	PUNCT
ejpam-6378	438	1	solutions	solution	NOUN
ejpam-6378	438	2	of	of	ADP
ejpam-6378	438	3	a	a	DET
ejpam-6378	438	4	three	three	NUM
ejpam-6378	438	5	-	-	PUNCT
ejpam-6378	438	6	dimensional	dimensional	ADJ
ejpam-6378	438	7	multi	multi	ADJ
ejpam-6378	438	8	-	-	ADJ
ejpam-6378	438	9	term	term	ADJ
ejpam-6378	438	10	fractional	fractional	ADJ
ejpam-6378	438	11	anomalous	anomalous	ADJ
ejpam-6378	438	12	solute	solute	NOUN
ejpam-6378	438	13	transport	transport	NOUN
ejpam-6378	438	14	model	model	NOUN
ejpam-6378	438	15	for	for	ADP
ejpam-6378	438	16	contamination	contamination	NOUN
ejpam-6378	438	17	in	in	ADP
ejpam-6378	438	18	groundwater	groundwater	NOUN
ejpam-6378	438	19	.	.	PUNCT
ejpam-6378	439	1	plos	plos	PROPN
ejpam-6378	439	2	one	one	NUM
ejpam-6378	439	3	,	,	PUNCT
ejpam-6378	439	4	18(12):e0294348	18(12):e0294348	PROPN
ejpam-6378	439	5	,	,	PUNCT
ejpam-6378	439	6	2023	2023	NUM
ejpam-6378	439	7	.	.	PUNCT
ejpam-6378	440	1	[	[	X
ejpam-6378	440	2	13	13	NUM
ejpam-6378	440	3	]	]	PUNCT
ejpam-6378	440	4	dominik	dominik	PROPN
ejpam-6378	440	5	sierociuk	sierociuk	PROPN
ejpam-6378	440	6	,	,	PUNCT
ejpam-6378	440	7	andrzej	andrzej	PROPN
ejpam-6378	440	8	dzieliński	dzieliński	PROPN
ejpam-6378	440	9	,	,	PUNCT
ejpam-6378	440	10	grzegorz	grzegorz	NOUN
ejpam-6378	440	11	sarwas	sarwas	PROPN
ejpam-6378	440	12	,	,	PUNCT
ejpam-6378	440	13	ivo	ivo	PROPN
ejpam-6378	440	14	petras	petras	PROPN
ejpam-6378	440	15	,	,	PUNCT
ejpam-6378	440	16	igor	igor	NOUN
ejpam-6378	440	17	podlubny	podlubny	NOUN
ejpam-6378	440	18	,	,	PUNCT
ejpam-6378	440	19	and	and	CCONJ
ejpam-6378	440	20	tomas	toma	NOUN
ejpam-6378	440	21	skovranek	skovranek	VERB
ejpam-6378	440	22	.	.	PUNCT
ejpam-6378	441	1	modelling	model	VERB
ejpam-6378	441	2	heat	heat	NOUN
ejpam-6378	441	3	transfer	transfer	NOUN
ejpam-6378	441	4	in	in	ADP
ejpam-6378	441	5	heterogeneous	heterogeneous	ADJ
ejpam-6378	441	6	media	medium	NOUN
ejpam-6378	441	7	using	use	VERB
ejpam-6378	441	8	fractional	fractional	ADJ
ejpam-6378	441	9	calculus	calculus	NOUN
ejpam-6378	441	10	.	.	PUNCT
ejpam-6378	442	1	philosophical	philosophical	ADJ
ejpam-6378	442	2	transactions	transaction	NOUN
ejpam-6378	442	3	of	of	ADP
ejpam-6378	442	4	the	the	DET
ejpam-6378	442	5	royal	royal	ADJ
ejpam-6378	442	6	society	society	NOUN
ejpam-6378	442	7	a	a	DET
ejpam-6378	442	8	:	:	PUNCT
ejpam-6378	442	9	mathematical	mathematical	ADJ
ejpam-6378	442	10	,	,	PUNCT
ejpam-6378	442	11	physical	physical	ADJ
ejpam-6378	442	12	and	and	CCONJ
ejpam-6378	442	13	engineering	engineering	NOUN
ejpam-6378	442	14	sciences	science	NOUN
ejpam-6378	442	15	,	,	PUNCT
ejpam-6378	442	16	371(1990):20120146	371(1990):20120146	NUM
ejpam-6378	442	17	,	,	PUNCT
ejpam-6378	442	18	2013	2013	NUM
ejpam-6378	442	19	.	.	PUNCT
ejpam-6378	443	1	[	[	X
ejpam-6378	443	2	14	14	NUM
ejpam-6378	443	3	]	]	X
ejpam-6378	443	4	wei	wei	PROPN
ejpam-6378	443	5	cai	cai	PROPN
ejpam-6378	443	6	,	,	PUNCT
ejpam-6378	443	7	wen	wen	PROPN
ejpam-6378	443	8	chen	chen	PROPN
ejpam-6378	443	9	,	,	PUNCT
ejpam-6378	443	10	jun	jun	PROPN
ejpam-6378	443	11	fang	fang	X
ejpam-6378	443	12	,	,	PUNCT
ejpam-6378	443	13	and	and	CCONJ
ejpam-6378	443	14	sverre	sverre	PROPN
ejpam-6378	443	15	holm	holm	PROPN
ejpam-6378	443	16	.	.	PUNCT
ejpam-6378	444	1	a	a	DET
ejpam-6378	444	2	survey	survey	NOUN
ejpam-6378	444	3	on	on	ADP
ejpam-6378	444	4	fractional	fractional	ADJ
ejpam-6378	444	5	derivative	derivative	ADJ
ejpam-6378	444	6	modeling	modeling	NOUN
ejpam-6378	444	7	of	of	ADP
ejpam-6378	444	8	power	power	NOUN
ejpam-6378	444	9	-	-	PUNCT
ejpam-6378	444	10	law	law	NOUN
ejpam-6378	444	11	frequency	frequency	NOUN
ejpam-6378	444	12	-	-	PUNCT
ejpam-6378	444	13	dependent	dependent	ADJ
ejpam-6378	444	14	viscous	viscous	ADJ
ejpam-6378	444	15	dissipative	dissipative	NOUN
ejpam-6378	444	16	and	and	CCONJ
ejpam-6378	444	17	scattering	scatter	VERB
ejpam-6378	444	18	attenuation	attenuation	NOUN
ejpam-6378	444	19	in	in	ADP
ejpam-6378	444	20	acoustic	acoustic	ADJ
ejpam-6378	444	21	wave	wave	NOUN
ejpam-6378	444	22	propagation	propagation	NOUN
ejpam-6378	444	23	.	.	PUNCT
ejpam-6378	445	1	applied	apply	VERB
ejpam-6378	445	2	mechanics	mechanic	NOUN
ejpam-6378	445	3	reviews	review	NOUN
ejpam-6378	445	4	,	,	PUNCT
ejpam-6378	445	5	70(3):030802	70(3):030802	NUM
ejpam-6378	445	6	,	,	PUNCT
ejpam-6378	445	7	2018	2018	NUM
ejpam-6378	445	8	.	.	PUNCT
ejpam-6378	446	1	[	[	X
ejpam-6378	446	2	15	15	NUM
ejpam-6378	446	3	]	]	X
ejpam-6378	446	4	piotr	piotr	PROPN
ejpam-6378	446	5	kulczycki	kulczycki	PROPN
ejpam-6378	446	6	,	,	PUNCT
ejpam-6378	446	7	józef	józef	PROPN
ejpam-6378	446	8	korbicz	korbicz	PROPN
ejpam-6378	446	9	,	,	PUNCT
ejpam-6378	446	10	and	and	CCONJ
ejpam-6378	446	11	janusz	janusz	PROPN
ejpam-6378	446	12	kacprzyk	kacprzyk	PROPN
ejpam-6378	446	13	.	.	PUNCT
ejpam-6378	447	1	fractional	fractional	ADJ
ejpam-6378	447	2	dynamical	dynamical	ADJ
ejpam-6378	447	3	systems	system	NOUN
ejpam-6378	447	4	:	:	PUNCT
ejpam-6378	447	5	methods	method	NOUN
ejpam-6378	447	6	,	,	PUNCT
ejpam-6378	447	7	algorithms	algorithm	NOUN
ejpam-6378	447	8	and	and	CCONJ
ejpam-6378	447	9	applications	application	NOUN
ejpam-6378	447	10	,	,	PUNCT
ejpam-6378	447	11	volume	volume	NOUN
ejpam-6378	447	12	402	402	NUM
ejpam-6378	447	13	.	.	PUNCT
ejpam-6378	447	14	springer	springer	NOUN
ejpam-6378	447	15	,	,	PUNCT
ejpam-6378	447	16	2022	2022	NUM
ejpam-6378	447	17	.	.	PUNCT
ejpam-6378	448	1	[	[	X
ejpam-6378	448	2	16	16	NUM
ejpam-6378	448	3	]	]	X
ejpam-6378	448	4	piotr	piotr	PROPN
ejpam-6378	448	5	ostalczyk	ostalczyk	PROPN
ejpam-6378	448	6	.	.	PUNCT
ejpam-6378	449	1	discrete	discrete	ADJ
ejpam-6378	449	2	fractional	fractional	ADJ
ejpam-6378	449	3	calculus	calculus	NOUN
ejpam-6378	449	4	:	:	PUNCT
ejpam-6378	449	5	applications	application	NOUN
ejpam-6378	449	6	in	in	ADP
ejpam-6378	449	7	control	control	NOUN
ejpam-6378	449	8	and	and	CCONJ
ejpam-6378	449	9	image	image	NOUN
ejpam-6378	449	10	processing	processing	NOUN
ejpam-6378	449	11	,	,	PUNCT
ejpam-6378	449	12	volume	volume	NOUN
ejpam-6378	449	13	4	4	NUM
ejpam-6378	449	14	.	.	PUNCT
ejpam-6378	450	1	world	world	NOUN
ejpam-6378	450	2	scientific	scientific	ADJ
ejpam-6378	450	3	,	,	PUNCT
ejpam-6378	450	4	2015	2015	NUM
ejpam-6378	450	5	.	.	PUNCT
ejpam-6378	451	1	[	[	X
ejpam-6378	451	2	17	17	NUM
ejpam-6378	451	3	]	]	X
ejpam-6378	451	4	sebastian	sebastian	PROPN
ejpam-6378	451	5	raubitzek	raubitzek	PROPN
ejpam-6378	451	6	,	,	PUNCT
ejpam-6378	451	7	kevin	kevin	PROPN
ejpam-6378	451	8	mallinger	mallinger	NOUN
ejpam-6378	451	9	,	,	PUNCT
ejpam-6378	451	10	and	and	CCONJ
ejpam-6378	451	11	thomas	thomas	PROPN
ejpam-6378	451	12	neubauer	neubauer	PROPN
ejpam-6378	451	13	.	.	PUNCT
ejpam-6378	452	1	combining	combine	VERB
ejpam-6378	452	2	fractional	fractional	ADJ
ejpam-6378	452	3	derivatives	derivative	NOUN
ejpam-6378	452	4	and	and	CCONJ
ejpam-6378	452	5	machine	machine	NOUN
ejpam-6378	452	6	learning	learning	NOUN
ejpam-6378	452	7	:	:	PUNCT
ejpam-6378	452	8	a	a	DET
ejpam-6378	452	9	review	review	NOUN
ejpam-6378	452	10	.	.	PUNCT
ejpam-6378	453	1	entropy	entropy	PROPN
ejpam-6378	453	2	,	,	PUNCT
ejpam-6378	453	3	25(1):35	25(1):35	NUM
ejpam-6378	453	4	,	,	PUNCT
ejpam-6378	453	5	2022	2022	NUM
ejpam-6378	453	6	.	.	PUNCT
ejpam-6378	454	1	[	[	X
ejpam-6378	454	2	18	18	NUM
ejpam-6378	454	3	]	]	PUNCT
ejpam-6378	454	4	igor	igor	NOUN
ejpam-6378	454	5	podlubny	podlubny	PROPN
ejpam-6378	454	6	.	.	PUNCT
ejpam-6378	455	1	fractional	fractional	ADJ
ejpam-6378	455	2	differential	differential	ADJ
ejpam-6378	455	3	equations	equation	NOUN
ejpam-6378	455	4	:	:	PUNCT
ejpam-6378	455	5	an	an	DET
ejpam-6378	455	6	introduction	introduction	NOUN
ejpam-6378	455	7	to	to	ADP
ejpam-6378	455	8	fractional	fractional	ADJ
ejpam-6378	455	9	derivatives	derivative	NOUN
ejpam-6378	455	10	,	,	PUNCT
ejpam-6378	455	11	fractional	fractional	ADJ
ejpam-6378	455	12	differential	differential	ADJ
ejpam-6378	455	13	equations	equation	NOUN
ejpam-6378	455	14	,	,	PUNCT
ejpam-6378	455	15	to	to	ADP
ejpam-6378	455	16	methods	method	NOUN
ejpam-6378	455	17	of	of	ADP
ejpam-6378	455	18	their	their	PRON
ejpam-6378	455	19	solution	solution	NOUN
ejpam-6378	455	20	and	and	CCONJ
ejpam-6378	455	21	some	some	PRON
ejpam-6378	455	22	of	of	ADP
ejpam-6378	455	23	their	their	PRON
ejpam-6378	455	24	applications	application	NOUN
ejpam-6378	455	25	,	,	PUNCT
ejpam-6378	455	26	volume	volume	NOUN
ejpam-6378	455	27	198	198	NUM
ejpam-6378	455	28	.	.	PUNCT
ejpam-6378	456	1	elsevier	elsevier	NOUN
ejpam-6378	456	2	,	,	PUNCT
ejpam-6378	456	3	1998	1998	NUM
ejpam-6378	456	4	.	.	PUNCT
ejpam-6378	457	1	[	[	X
ejpam-6378	457	2	19	19	NUM
ejpam-6378	457	3	]	]	X
ejpam-6378	457	4	changpin	changpin	NOUN
ejpam-6378	457	5	li	li	PROPN
ejpam-6378	457	6	and	and	CCONJ
ejpam-6378	457	7	fanhai	fanhai	PROPN
ejpam-6378	457	8	zeng	zeng	PROPN
ejpam-6378	457	9	.	.	PUNCT
ejpam-6378	458	1	finite	finite	PROPN
ejpam-6378	458	2	difference	difference	NOUN
ejpam-6378	458	3	methods	method	NOUN
ejpam-6378	458	4	for	for	ADP
ejpam-6378	458	5	fractional	fractional	ADJ
ejpam-6378	458	6	differential	differential	ADJ
ejpam-6378	458	7	equations	equation	NOUN
ejpam-6378	458	8	.	.	PUNCT
ejpam-6378	459	1	international	international	ADJ
ejpam-6378	459	2	journal	journal	NOUN
ejpam-6378	459	3	of	of	ADP
ejpam-6378	459	4	bifurcation	bifurcation	NOUN
ejpam-6378	459	5	and	and	CCONJ
ejpam-6378	459	6	chaos	chaos	NOUN
ejpam-6378	459	7	,	,	PUNCT
ejpam-6378	459	8	22(04):1230014	22(04):1230014	NUM
ejpam-6378	459	9	,	,	PUNCT
ejpam-6378	459	10	2012	2012	NUM
ejpam-6378	459	11	.	.	PUNCT
ejpam-6378	460	1	[	[	X
ejpam-6378	460	2	20	20	NUM
ejpam-6378	460	3	]	]	X
ejpam-6378	460	4	haci	haci	PROPN
ejpam-6378	460	5	mehmet	mehmet	PROPN
ejpam-6378	460	6	baskonus	baskonus	PROPN
ejpam-6378	460	7	and	and	CCONJ
ejpam-6378	460	8	hasan	hasan	PROPN
ejpam-6378	460	9	bulut	bulut	PROPN
ejpam-6378	460	10	.	.	PUNCT
ejpam-6378	461	1	on	on	ADP
ejpam-6378	461	2	the	the	DET
ejpam-6378	461	3	numerical	numerical	ADJ
ejpam-6378	461	4	solutions	solution	NOUN
ejpam-6378	461	5	of	of	ADP
ejpam-6378	461	6	some	some	DET
ejpam-6378	461	7	fractional	fractional	ADJ
ejpam-6378	461	8	ordinary	ordinary	ADJ
ejpam-6378	461	9	differential	differential	ADJ
ejpam-6378	461	10	equations	equation	NOUN
ejpam-6378	461	11	by	by	ADP
ejpam-6378	461	12	fractional	fractional	PROPN
ejpam-6378	461	13	adams	adams	PROPN
ejpam-6378	461	14	-	-	PUNCT
ejpam-6378	461	15	bashforth	bashforth	PROPN
ejpam-6378	461	16	-	-	PUNCT
ejpam-6378	461	17	moulton	moulton	PROPN
ejpam-6378	461	18	method	method	NOUN
ejpam-6378	461	19	.	.	PUNCT
ejpam-6378	462	1	open	open	ADJ
ejpam-6378	462	2	mathematics	mathematic	NOUN
ejpam-6378	462	3	,	,	PUNCT
ejpam-6378	462	4	13(1):000010151520150052	13(1):000010151520150052	NUM
ejpam-6378	462	5	,	,	PUNCT
ejpam-6378	462	6	2015	2015	NUM
ejpam-6378	462	7	.	.	PUNCT
ejpam-6378	463	1	[	[	X
ejpam-6378	463	2	21	21	NUM
ejpam-6378	463	3	]	]	X
ejpam-6378	463	4	xianjuan	xianjuan	PROPN
ejpam-6378	463	5	li	li	PROPN
ejpam-6378	463	6	and	and	CCONJ
ejpam-6378	463	7	chuanju	chuanju	PROPN
ejpam-6378	463	8	xu	xu	PROPN
ejpam-6378	463	9	.	.	PUNCT
ejpam-6378	464	1	a	a	DET
ejpam-6378	464	2	space	space	NOUN
ejpam-6378	464	3	-	-	PUNCT
ejpam-6378	464	4	time	time	NOUN
ejpam-6378	464	5	spectral	spectral	ADJ
ejpam-6378	464	6	method	method	NOUN
ejpam-6378	464	7	for	for	ADP
ejpam-6378	464	8	the	the	DET
ejpam-6378	464	9	time	time	NOUN
ejpam-6378	464	10	fractional	fractional	ADJ
ejpam-6378	464	11	diffusion	diffusion	NOUN
ejpam-6378	464	12	equation	equation	NOUN
ejpam-6378	464	13	.	.	PUNCT
ejpam-6378	465	1	siam	siam	PROPN
ejpam-6378	465	2	journal	journal	PROPN
ejpam-6378	465	3	on	on	ADP
ejpam-6378	465	4	numerical	numerical	ADJ
ejpam-6378	465	5	analysis	analysis	NOUN
ejpam-6378	465	6	,	,	PUNCT
ejpam-6378	465	7	47(3):2108–2131	47(3):2108–2131	NUM
ejpam-6378	465	8	,	,	PUNCT
ejpam-6378	465	9	2009	2009	NUM
ejpam-6378	465	10	.	.	PUNCT
ejpam-6378	466	1	[	[	X
ejpam-6378	466	2	22	22	NUM
ejpam-6378	466	3	]	]	PUNCT
ejpam-6378	466	4	farideh	farideh	NOUN
ejpam-6378	466	5	ghoreishi	ghoreishi	NOUN
ejpam-6378	466	6	,	,	PUNCT
ejpam-6378	466	7	rezvan	rezvan	ADJ
ejpam-6378	466	8	ghaffari	ghaffari	NOUN
ejpam-6378	466	9	,	,	PUNCT
ejpam-6378	466	10	and	and	CCONJ
ejpam-6378	466	11	nasser	nasser	PROPN
ejpam-6378	466	12	saad	saad	PROPN
ejpam-6378	466	13	.	.	PUNCT
ejpam-6378	467	1	fractional	fractional	ADJ
ejpam-6378	467	2	order	order	NOUN
ejpam-6378	467	3	runge	runge	NOUN
ejpam-6378	467	4	–	–	PUNCT
ejpam-6378	467	5	kutta	kutta	NOUN
ejpam-6378	467	6	methods	method	NOUN
ejpam-6378	467	7	.	.	PUNCT
ejpam-6378	468	1	fractal	fractal	PROPN
ejpam-6378	468	2	and	and	CCONJ
ejpam-6378	468	3	fractional	fractional	ADJ
ejpam-6378	468	4	,	,	PUNCT
ejpam-6378	468	5	7(3):245	7(3):245	NUM
ejpam-6378	468	6	,	,	PUNCT
ejpam-6378	468	7	2023	2023	NUM
ejpam-6378	468	8	.	.	PUNCT
ejpam-6378	469	1	[	[	X
ejpam-6378	469	2	23	23	NUM
ejpam-6378	469	3	]	]	X
ejpam-6378	469	4	ak	ak	PROPN
ejpam-6378	469	5	gupta	gupta	PROPN
ejpam-6378	469	6	and	and	CCONJ
ejpam-6378	469	7	s	s	PROPN
ejpam-6378	469	8	saha	saha	PROPN
ejpam-6378	469	9	ray	ray	PROPN
ejpam-6378	469	10	.	.	PUNCT
ejpam-6378	470	1	wavelet	wavelet	NOUN
ejpam-6378	470	2	methods	method	NOUN
ejpam-6378	470	3	for	for	ADP
ejpam-6378	470	4	solving	solve	VERB
ejpam-6378	470	5	fractional	fractional	ADJ
ejpam-6378	470	6	order	order	NOUN
ejpam-6378	470	7	differential	differential	NOUN
ejpam-6378	470	8	equations	equation	NOUN
ejpam-6378	470	9	.	.	PUNCT
ejpam-6378	471	1	mathematical	mathematical	ADJ
ejpam-6378	471	2	problems	problem	NOUN
ejpam-6378	471	3	in	in	ADP
ejpam-6378	471	4	engineering	engineering	NOUN
ejpam-6378	471	5	,	,	PUNCT
ejpam-6378	471	6	2014(1):140453	2014(1):140453	NUM
ejpam-6378	471	7	,	,	PUNCT
ejpam-6378	471	8	2014	2014	NUM
ejpam-6378	471	9	.	.	PUNCT
ejpam-6378	472	1	[	[	X
ejpam-6378	472	2	24	24	NUM
ejpam-6378	472	3	]	]	PUNCT
ejpam-6378	472	4	cagatay	cagatay	NOUN
ejpam-6378	472	5	candan	candan	PROPN
ejpam-6378	472	6	,	,	PUNCT
ejpam-6378	472	7	m	m	PROPN
ejpam-6378	472	8	alper	alper	PROPN
ejpam-6378	472	9	kutay	kutay	PROPN
ejpam-6378	472	10	,	,	PUNCT
ejpam-6378	472	11	and	and	CCONJ
ejpam-6378	472	12	haldun	haldun	PROPN
ejpam-6378	472	13	m	m	PROPN
ejpam-6378	472	14	ozaktas	ozakta	NOUN
ejpam-6378	472	15	.	.	PUNCT
ejpam-6378	473	1	the	the	DET
ejpam-6378	473	2	discrete	discrete	ADJ
ejpam-6378	473	3	fractional	fractional	ADJ
ejpam-6378	473	4	fourier	fourier	NOUN
ejpam-6378	473	5	transform	transform	NOUN
ejpam-6378	473	6	.	.	PUNCT
ejpam-6378	474	1	ieee	ieee	NOUN
ejpam-6378	474	2	transactions	transaction	NOUN
ejpam-6378	474	3	on	on	ADP
ejpam-6378	474	4	signal	signal	ADJ
ejpam-6378	474	5	processing	processing	NOUN
ejpam-6378	474	6	,	,	PUNCT
ejpam-6378	474	7	48(5):1329–1337	48(5):1329–1337	NOUN
ejpam-6378	474	8	,	,	PUNCT
ejpam-6378	474	9	2000	2000	NUM
ejpam-6378	474	10	.	.	PUNCT
ejpam-6378	475	1	[	[	X
ejpam-6378	475	2	25	25	NUM
ejpam-6378	475	3	]	]	X
ejpam-6378	475	4	anatolĭı	anatolĭı	PROPN
ejpam-6378	475	5	kilbas	kilbas	PROPN
ejpam-6378	475	6	.	.	PROPN
ejpam-6378	476	1	theory	theory	NOUN
ejpam-6378	476	2	and	and	CCONJ
ejpam-6378	476	3	applications	application	NOUN
ejpam-6378	476	4	of	of	ADP
ejpam-6378	476	5	fractional	fractional	ADJ
ejpam-6378	476	6	differential	differential	ADJ
ejpam-6378	476	7	equations	equation	NOUN
ejpam-6378	476	8	.	.	PUNCT
ejpam-6378	477	1	[	[	X
ejpam-6378	477	2	26	26	NUM
ejpam-6378	477	3	]	]	PUNCT
ejpam-6378	477	4	zeyad	zeyad	PROPN
ejpam-6378	477	5	al	al	PROPN
ejpam-6378	477	6	-	-	PUNCT
ejpam-6378	477	7	zhour	zhour	PROPN
ejpam-6378	477	8	,	,	PUNCT
ejpam-6378	477	9	nouf	nouf	PROPN
ejpam-6378	477	10	al	al	PROPN
ejpam-6378	477	11	-	-	PUNCT
ejpam-6378	477	12	mutairi	mutairi	PROPN
ejpam-6378	477	13	,	,	PUNCT
ejpam-6378	477	14	fatimah	fatimah	PROPN
ejpam-6378	477	15	alrawajeh	alrawajeh	PROPN
ejpam-6378	477	16	,	,	PUNCT
ejpam-6378	477	17	and	and	CCONJ
ejpam-6378	477	18	raed	raed	PROPN
ejpam-6378	477	19	alkhasawneh	alkhasawneh	PROPN
ejpam-6378	477	20	.	.	PUNCT
ejpam-6378	478	1	series	series	PROPN
ejpam-6378	478	2	solutions	solution	NOUN
ejpam-6378	478	3	for	for	ADP
ejpam-6378	478	4	the	the	DET
ejpam-6378	478	5	laguerre	laguerre	NOUN
ejpam-6378	478	6	and	and	CCONJ
ejpam-6378	478	7	lane	lane	NOUN
ejpam-6378	478	8	-	-	PUNCT
ejpam-6378	478	9	emden	emden	ADJ
ejpam-6378	478	10	fractional	fractional	ADJ
ejpam-6378	478	11	differential	differential	ADJ
ejpam-6378	478	12	equations	equation	NOUN
ejpam-6378	478	13	in	in	ADP
ejpam-6378	478	14	the	the	DET
ejpam-6378	478	15	sense	sense	NOUN
ejpam-6378	478	16	of	of	ADP
ejpam-6378	478	17	conformable	conformable	ADJ
ejpam-6378	478	18	fractional	fractional	ADJ
ejpam-6378	478	19	derivative	derivative	NOUN
ejpam-6378	478	20	.	.	PUNCT
ejpam-6378	479	1	alexandria	alexandria	PROPN
ejpam-6378	479	2	engineering	engineering	PROPN
ejpam-6378	479	3	journal	journal	PROPN
ejpam-6378	479	4	,	,	PUNCT
ejpam-6378	479	5	58(4):1413	58(4):1413	PROPN
ejpam-6378	479	6	–	–	PUNCT
ejpam-6378	479	7	m.	m.	NOUN
ejpam-6378	479	8	sohail	sohail	PROPN
ejpam-6378	479	9	et	et	PROPN
ejpam-6378	479	10	al	al	PROPN
ejpam-6378	479	11	.	.	PUNCT
ejpam-6378	479	12	/	/	SYM
ejpam-6378	479	13	eur	eur	PROPN
ejpam-6378	479	14	.	.	PUNCT
ejpam-6378	480	1	j.	j.	PROPN
ejpam-6378	480	2	pure	pure	PROPN
ejpam-6378	480	3	appl	appl	PROPN
ejpam-6378	480	4	.	.	PROPN
ejpam-6378	480	5	math	math	PROPN
ejpam-6378	480	6	,	,	PUNCT
ejpam-6378	480	7	18	18	NUM
ejpam-6378	480	8	(	(	PUNCT
ejpam-6378	480	9	4	4	NUM
ejpam-6378	480	10	)	)	PUNCT
ejpam-6378	480	11	(	(	PUNCT
ejpam-6378	480	12	2025	2025	NUM
ejpam-6378	480	13	)	)	PUNCT
ejpam-6378	480	14	,	,	PUNCT
ejpam-6378	480	15	6378	6378	NUM
ejpam-6378	480	16	19	19	NUM
ejpam-6378	480	17	of	of	ADP
ejpam-6378	480	18	20	20	NUM
ejpam-6378	480	19	1420	1420	NUM
ejpam-6378	480	20	,	,	PUNCT
ejpam-6378	480	21	2019	2019	NUM
ejpam-6378	480	22	.	.	PUNCT
ejpam-6378	481	1	[	[	X
ejpam-6378	481	2	27	27	NUM
ejpam-6378	481	3	]	]	X
ejpam-6378	481	4	mizan	mizan	PROPN
ejpam-6378	481	5	rahman	rahman	PROPN
ejpam-6378	481	6	.	.	PUNCT
ejpam-6378	482	1	applications	application	NOUN
ejpam-6378	482	2	of	of	ADP
ejpam-6378	482	3	fourier	fourier	NOUN
ejpam-6378	482	4	transforms	transform	VERB
ejpam-6378	482	5	to	to	ADP
ejpam-6378	482	6	generalized	generalized	ADJ
ejpam-6378	482	7	functions	function	NOUN
ejpam-6378	482	8	.	.	PUNCT
ejpam-6378	483	1	wit	wit	ADJ
ejpam-6378	483	2	press	press	PROPN
ejpam-6378	483	3	,	,	PUNCT
ejpam-6378	483	4	2011	2011	NUM
ejpam-6378	483	5	.	.	PUNCT
ejpam-6378	484	1	[	[	X
ejpam-6378	484	2	28	28	NUM
ejpam-6378	484	3	]	]	X
ejpam-6378	484	4	ji	ji	PROPN
ejpam-6378	484	5	-	-	PROPN
ejpam-6378	484	6	huan	huan	PROPN
ejpam-6378	484	7	he	he	PROPN
ejpam-6378	484	8	.	.	PUNCT
ejpam-6378	485	1	homotopy	homotopy	VERB
ejpam-6378	485	2	perturbation	perturbation	NOUN
ejpam-6378	485	3	method	method	NOUN
ejpam-6378	485	4	:	:	PUNCT
ejpam-6378	485	5	a	a	DET
ejpam-6378	485	6	new	new	ADJ
ejpam-6378	485	7	nonlinear	nonlinear	ADJ
ejpam-6378	485	8	analytical	analytical	ADJ
ejpam-6378	485	9	technique	technique	NOUN
ejpam-6378	485	10	.	.	PUNCT
ejpam-6378	486	1	applied	apply	VERB
ejpam-6378	486	2	mathematics	mathematic	NOUN
ejpam-6378	486	3	and	and	CCONJ
ejpam-6378	486	4	computation	computation	NOUN
ejpam-6378	486	5	,	,	PUNCT
ejpam-6378	486	6	135(1):73–79	135(1):73–79	NUM
ejpam-6378	486	7	,	,	PUNCT
ejpam-6378	486	8	2003	2003	NUM
ejpam-6378	486	9	.	.	PUNCT
ejpam-6378	487	1	[	[	X
ejpam-6378	487	2	29	29	NUM
ejpam-6378	487	3	]	]	X
ejpam-6378	487	4	guo	guo	PROPN
ejpam-6378	487	5	-	-	PUNCT
ejpam-6378	487	6	cheng	cheng	PROPN
ejpam-6378	487	7	wu	wu	PROPN
ejpam-6378	487	8	.	.	PUNCT
ejpam-6378	488	1	a	a	DET
ejpam-6378	488	2	fractional	fractional	ADJ
ejpam-6378	488	3	variational	variational	ADJ
ejpam-6378	488	4	iteration	iteration	NOUN
ejpam-6378	488	5	method	method	NOUN
ejpam-6378	488	6	for	for	ADP
ejpam-6378	488	7	solving	solve	VERB
ejpam-6378	488	8	fractional	fractional	ADJ
ejpam-6378	488	9	nonlinear	nonlinear	ADJ
ejpam-6378	488	10	differential	differential	ADJ
ejpam-6378	488	11	equations	equation	NOUN
ejpam-6378	488	12	.	.	PUNCT
ejpam-6378	489	1	computers	computer	NOUN
ejpam-6378	489	2	&	&	CCONJ
ejpam-6378	489	3	mathematics	mathematics	PROPN
ejpam-6378	489	4	with	with	ADP
ejpam-6378	489	5	applications	application	NOUN
ejpam-6378	489	6	,	,	PUNCT
ejpam-6378	489	7	61(8):2186	61(8):2186	NUM
ejpam-6378	489	8	–	–	PUNCT
ejpam-6378	489	9	2190	2190	NUM
ejpam-6378	489	10	,	,	PUNCT
ejpam-6378	489	11	2011	2011	NUM
ejpam-6378	489	12	.	.	PUNCT
ejpam-6378	490	1	[	[	X
ejpam-6378	490	2	30	30	NUM
ejpam-6378	490	3	]	]	X
ejpam-6378	490	4	khosro	khosro	PROPN
ejpam-6378	490	5	sayevand	sayevand	PROPN
ejpam-6378	490	6	and	and	CCONJ
ejpam-6378	490	7	kazem	kazem	PROPN
ejpam-6378	490	8	pichaghchi	pichaghchi	NOUN
ejpam-6378	490	9	.	.	PUNCT
ejpam-6378	491	1	successive	successive	ADJ
ejpam-6378	491	2	approximation	approximation	NOUN
ejpam-6378	491	3	:	:	PUNCT
ejpam-6378	491	4	a	a	DET
ejpam-6378	491	5	survey	survey	NOUN
ejpam-6378	491	6	on	on	ADP
ejpam-6378	491	7	stable	stable	ADJ
ejpam-6378	491	8	manifold	manifold	NOUN
ejpam-6378	491	9	of	of	ADP
ejpam-6378	491	10	fractional	fractional	ADJ
ejpam-6378	491	11	differential	differential	NOUN
ejpam-6378	491	12	systems	system	NOUN
ejpam-6378	491	13	.	.	PUNCT
ejpam-6378	492	1	fractional	fractional	ADJ
ejpam-6378	492	2	calculus	calculus	NOUN
ejpam-6378	492	3	and	and	CCONJ
ejpam-6378	492	4	applied	apply	VERB
ejpam-6378	492	5	analysis	analysis	NOUN
ejpam-6378	492	6	,	,	PUNCT
ejpam-6378	492	7	18:621–641	18:621–641	NUM
ejpam-6378	492	8	,	,	PUNCT
ejpam-6378	492	9	2015	2015	NUM
ejpam-6378	492	10	.	.	PUNCT
ejpam-6378	493	1	[	[	X
ejpam-6378	493	2	31	31	NUM
ejpam-6378	493	3	]	]	X
ejpam-6378	493	4	hasib	hasib	PROPN
ejpam-6378	493	5	khan	khan	PROPN
ejpam-6378	493	6	,	,	PUNCT
ejpam-6378	493	7	saim	saim	PROPN
ejpam-6378	493	8	ahmed	ahmed	PROPN
ejpam-6378	493	9	,	,	PUNCT
ejpam-6378	493	10	jehad	jehad	PROPN
ejpam-6378	493	11	alzabut	alzabut	PROPN
ejpam-6378	493	12	,	,	PUNCT
ejpam-6378	493	13	ahmad	ahmad	PROPN
ejpam-6378	493	14	taher	taher	PROPN
ejpam-6378	493	15	azar	azar	PROPN
ejpam-6378	493	16	,	,	PUNCT
ejpam-6378	493	17	and	and	CCONJ
ejpam-6378	493	18	jf	jf	PROPN
ejpam-6378	493	19	gómezaguilar	gómezaguilar	PROPN
ejpam-6378	493	20	.	.	PROPN
ejpam-6378	494	1	nonlinear	nonlinear	ADJ
ejpam-6378	494	2	variable	variable	ADJ
ejpam-6378	494	3	order	order	NOUN
ejpam-6378	494	4	system	system	NOUN
ejpam-6378	494	5	of	of	ADP
ejpam-6378	494	6	multi	multi	ADJ
ejpam-6378	494	7	-	-	ADJ
ejpam-6378	494	8	point	point	ADJ
ejpam-6378	494	9	boundary	boundary	ADJ
ejpam-6378	494	10	conditions	condition	NOUN
ejpam-6378	494	11	with	with	ADP
ejpam-6378	494	12	adaptive	adaptive	ADJ
ejpam-6378	494	13	finite	finite	ADJ
ejpam-6378	494	14	-	-	PUNCT
ejpam-6378	494	15	time	time	NOUN
ejpam-6378	494	16	fractional	fractional	ADJ
ejpam-6378	494	17	-	-	PUNCT
ejpam-6378	494	18	order	order	NOUN
ejpam-6378	494	19	sliding	slide	VERB
ejpam-6378	494	20	mode	mode	NOUN
ejpam-6378	494	21	control	control	NOUN
ejpam-6378	494	22	.	.	PUNCT
ejpam-6378	495	1	international	international	ADJ
ejpam-6378	495	2	journal	journal	PROPN
ejpam-6378	495	3	of	of	ADP
ejpam-6378	495	4	dynamics	dynamic	NOUN
ejpam-6378	495	5	and	and	CCONJ
ejpam-6378	495	6	control	control	NOUN
ejpam-6378	495	7	,	,	PUNCT
ejpam-6378	495	8	12(7):2597–2613	12(7):2597–2613	NUM
ejpam-6378	495	9	,	,	PUNCT
ejpam-6378	495	10	2024	2024	NUM
ejpam-6378	495	11	.	.	PUNCT
ejpam-6378	496	1	[	[	X
ejpam-6378	496	2	32	32	NUM
ejpam-6378	496	3	]	]	SYM
ejpam-6378	496	4	hasib	hasib	PROPN
ejpam-6378	496	5	khan	khan	PROPN
ejpam-6378	496	6	,	,	PUNCT
ejpam-6378	496	7	jehad	jehad	PROPN
ejpam-6378	496	8	alzabut	alzabut	PROPN
ejpam-6378	496	9	,	,	PUNCT
ejpam-6378	496	10	jf	jf	PROPN
ejpam-6378	496	11	gómez	gómez	NOUN
ejpam-6378	496	12	-	-	PUNCT
ejpam-6378	496	13	aguilar	aguilar	ADJ
ejpam-6378	496	14	,	,	PUNCT
ejpam-6378	496	15	and	and	CCONJ
ejpam-6378	496	16	abdulwasea	abdulwasea	NOUN
ejpam-6378	496	17	alkhazan	alkhazan	NOUN
ejpam-6378	496	18	.	.	PUNCT
ejpam-6378	497	1	essential	essential	ADJ
ejpam-6378	497	2	criteria	criterion	NOUN
ejpam-6378	497	3	for	for	ADP
ejpam-6378	497	4	existence	existence	NOUN
ejpam-6378	497	5	of	of	ADP
ejpam-6378	497	6	solution	solution	NOUN
ejpam-6378	497	7	of	of	ADP
ejpam-6378	497	8	a	a	DET
ejpam-6378	497	9	modified	modify	VERB
ejpam-6378	497	10	-	-	PUNCT
ejpam-6378	497	11	abc	abc	NOUN
ejpam-6378	497	12	fractional	fractional	ADJ
ejpam-6378	497	13	order	order	NOUN
ejpam-6378	497	14	smoking	smoking	NOUN
ejpam-6378	497	15	model	model	NOUN
ejpam-6378	497	16	.	.	PUNCT
ejpam-6378	498	1	ain	ain	PROPN
ejpam-6378	498	2	shams	sham	NOUN
ejpam-6378	498	3	engineering	engineering	NOUN
ejpam-6378	498	4	journal	journal	NOUN
ejpam-6378	498	5	,	,	PUNCT
ejpam-6378	498	6	15(5):102646	15(5):102646	NUM
ejpam-6378	498	7	,	,	PUNCT
ejpam-6378	498	8	2024	2024	NUM
ejpam-6378	498	9	.	.	PUNCT
ejpam-6378	499	1	[	[	X
ejpam-6378	499	2	33	33	NUM
ejpam-6378	499	3	]	]	X
ejpam-6378	499	4	saim	saim	PROPN
ejpam-6378	499	5	ahmed	ahmed	PROPN
ejpam-6378	499	6	,	,	PUNCT
ejpam-6378	499	7	ahmad	ahmad	PROPN
ejpam-6378	499	8	taher	taher	PROPN
ejpam-6378	499	9	azar	azar	PROPN
ejpam-6378	499	10	,	,	PUNCT
ejpam-6378	499	11	mahmoud	mahmoud	PROPN
ejpam-6378	499	12	abdel	abdel	PROPN
ejpam-6378	499	13	-	-	PUNCT
ejpam-6378	499	14	aty	aty	PROPN
ejpam-6378	499	15	,	,	PUNCT
ejpam-6378	499	16	hasib	hasib	PROPN
ejpam-6378	499	17	khan	khan	PROPN
ejpam-6378	499	18	,	,	PUNCT
ejpam-6378	499	19	and	and	CCONJ
ejpam-6378	499	20	jehad	jehad	PROPN
ejpam-6378	499	21	alzabut	alzabut	PROPN
ejpam-6378	499	22	.	.	PUNCT
ejpam-6378	500	1	a	a	DET
ejpam-6378	500	2	nonlinear	nonlinear	ADJ
ejpam-6378	500	3	system	system	NOUN
ejpam-6378	500	4	of	of	ADP
ejpam-6378	500	5	hybrid	hybrid	ADJ
ejpam-6378	500	6	fractional	fractional	ADJ
ejpam-6378	500	7	differential	differential	ADJ
ejpam-6378	500	8	equations	equation	NOUN
ejpam-6378	500	9	with	with	ADP
ejpam-6378	500	10	application	application	NOUN
ejpam-6378	500	11	to	to	ADP
ejpam-6378	500	12	fixed	fix	VERB
ejpam-6378	500	13	time	time	NOUN
ejpam-6378	500	14	sliding	slide	VERB
ejpam-6378	500	15	mode	mode	NOUN
ejpam-6378	500	16	control	control	NOUN
ejpam-6378	500	17	for	for	ADP
ejpam-6378	500	18	leukemia	leukemia	NOUN
ejpam-6378	500	19	therapy	therapy	NOUN
ejpam-6378	500	20	.	.	PUNCT
ejpam-6378	501	1	ain	ain	PROPN
ejpam-6378	501	2	shams	sham	VERB
ejpam-6378	501	3	engineering	engineering	NOUN
ejpam-6378	501	4	journal	journal	NOUN
ejpam-6378	501	5	,	,	PUNCT
ejpam-6378	501	6	15(4):102566	15(4):102566	NUM
ejpam-6378	501	7	,	,	PUNCT
ejpam-6378	501	8	2024	2024	NUM
ejpam-6378	501	9	.	.	PUNCT
ejpam-6378	502	1	[	[	X
ejpam-6378	502	2	34	34	NUM
ejpam-6378	502	3	]	]	X
ejpam-6378	502	4	wafa	wafa	PROPN
ejpam-6378	502	5	f	f	PROPN
ejpam-6378	502	6	alfwzan	alfwzan	PROPN
ejpam-6378	502	7	,	,	PUNCT
ejpam-6378	502	8	hasib	hasib	PROPN
ejpam-6378	502	9	khan	khan	PROPN
ejpam-6378	502	10	,	,	PUNCT
ejpam-6378	502	11	and	and	CCONJ
ejpam-6378	502	12	jehad	jehad	PROPN
ejpam-6378	502	13	alzabut	alzabut	PROPN
ejpam-6378	502	14	.	.	PUNCT
ejpam-6378	503	1	stability	stability	NOUN
ejpam-6378	503	2	analysis	analysis	NOUN
ejpam-6378	503	3	for	for	ADP
ejpam-6378	503	4	a	a	DET
ejpam-6378	503	5	fractional	fractional	ADJ
ejpam-6378	503	6	coupled	couple	VERB
ejpam-6378	503	7	hybrid	hybrid	ADJ
ejpam-6378	503	8	pantograph	pantograph	NOUN
ejpam-6378	503	9	system	system	NOUN
ejpam-6378	503	10	with	with	ADP
ejpam-6378	503	11	p	p	NOUN
ejpam-6378	503	12	-	-	PUNCT
ejpam-6378	503	13	laplacian	laplacian	ADJ
ejpam-6378	503	14	operator	operator	NOUN
ejpam-6378	503	15	.	.	PUNCT
ejpam-6378	504	1	results	result	NOUN
ejpam-6378	504	2	in	in	ADP
ejpam-6378	504	3	control	control	NOUN
ejpam-6378	504	4	and	and	CCONJ
ejpam-6378	504	5	optimization	optimization	NOUN
ejpam-6378	504	6	,	,	PUNCT
ejpam-6378	504	7	14:100333	14:100333	NUM
ejpam-6378	504	8	,	,	PUNCT
ejpam-6378	504	9	2024	2024	NUM
ejpam-6378	504	10	.	.	PUNCT
ejpam-6378	505	1	[	[	X
ejpam-6378	505	2	35	35	NUM
ejpam-6378	505	3	]	]	X
ejpam-6378	505	4	muhammad	muhammad	PROPN
ejpam-6378	505	5	sohail	sohail	PROPN
ejpam-6378	505	6	,	,	PUNCT
ejpam-6378	505	7	hassan	hassan	PROPN
ejpam-6378	505	8	khan	khan	PROPN
ejpam-6378	505	9	,	,	PUNCT
ejpam-6378	505	10	fairouz	fairouz	ADJ
ejpam-6378	505	11	tchier	tchier	NOUN
ejpam-6378	505	12	,	,	PUNCT
ejpam-6378	505	13	samaruddin	samaruddin	ADJ
ejpam-6378	505	14	jebran	jebran	NOUN
ejpam-6378	505	15	,	,	PUNCT
ejpam-6378	505	16	and	and	CCONJ
ejpam-6378	505	17	muhammad	muhammad	PROPN
ejpam-6378	505	18	nadeem	nadeem	PROPN
ejpam-6378	505	19	.	.	PUNCT
ejpam-6378	506	1	the	the	DET
ejpam-6378	506	2	analytical	analytical	ADJ
ejpam-6378	506	3	analysis	analysis	NOUN
ejpam-6378	506	4	of	of	ADP
ejpam-6378	506	5	fractional	fractional	ADJ
ejpam-6378	506	6	differential	differential	NOUN
ejpam-6378	506	7	system	system	NOUN
ejpam-6378	506	8	via	via	ADP
ejpam-6378	506	9	different	different	ADJ
ejpam-6378	506	10	operators	operator	NOUN
ejpam-6378	506	11	and	and	CCONJ
ejpam-6378	506	12	normalization	normalization	NOUN
ejpam-6378	506	13	functions	function	NOUN
ejpam-6378	506	14	.	.	PUNCT
ejpam-6378	507	1	partial	partial	ADJ
ejpam-6378	507	2	differential	differential	ADJ
ejpam-6378	507	3	equations	equation	NOUN
ejpam-6378	507	4	in	in	ADP
ejpam-6378	507	5	applied	applied	ADJ
ejpam-6378	507	6	mathematics	mathematic	NOUN
ejpam-6378	507	7	,	,	PUNCT
ejpam-6378	507	8	10:100687	10:100687	NUM
ejpam-6378	507	9	,	,	PUNCT
ejpam-6378	507	10	2024	2024	NUM
ejpam-6378	507	11	.	.	PUNCT
ejpam-6378	508	1	[	[	X
ejpam-6378	508	2	36	36	NUM
ejpam-6378	508	3	]	]	X
ejpam-6378	508	4	michele	michele	PROPN
ejpam-6378	508	5	caputo	caputo	PROPN
ejpam-6378	508	6	.	.	PROPN
ejpam-6378	509	1	linear	linear	PROPN
ejpam-6378	509	2	models	model	NOUN
ejpam-6378	509	3	of	of	ADP
ejpam-6378	509	4	dissipation	dissipation	NOUN
ejpam-6378	509	5	whose	whose	DET
ejpam-6378	509	6	q	q	NOUN
ejpam-6378	509	7	is	be	AUX
ejpam-6378	509	8	almost	almost	ADV
ejpam-6378	509	9	frequency	frequency	ADJ
ejpam-6378	509	10	independent	independent	ADJ
ejpam-6378	509	11	.	.	PUNCT
ejpam-6378	510	1	annals	annal	NOUN
ejpam-6378	510	2	of	of	ADP
ejpam-6378	510	3	geophysics	geophysic	NOUN
ejpam-6378	510	4	,	,	PUNCT
ejpam-6378	510	5	19(4):383–393	19(4):383–393	PROPN
ejpam-6378	510	6	,	,	PUNCT
ejpam-6378	510	7	1966	1966	NUM
ejpam-6378	510	8	.	.	PUNCT
ejpam-6378	511	1	[	[	X
ejpam-6378	511	2	37	37	NUM
ejpam-6378	511	3	]	]	PUNCT
ejpam-6378	511	4	michele	michele	PROPN
ejpam-6378	511	5	caputo	caputo	PROPN
ejpam-6378	511	6	and	and	CCONJ
ejpam-6378	511	7	mauro	mauro	PROPN
ejpam-6378	511	8	fabrizio	fabrizio	PROPN
ejpam-6378	511	9	.	.	PUNCT
ejpam-6378	512	1	a	a	DET
ejpam-6378	512	2	new	new	ADJ
ejpam-6378	512	3	definition	definition	NOUN
ejpam-6378	512	4	of	of	ADP
ejpam-6378	512	5	fractional	fractional	ADJ
ejpam-6378	512	6	derivative	derivative	NOUN
ejpam-6378	512	7	without	without	ADP
ejpam-6378	512	8	singular	singular	ADJ
ejpam-6378	512	9	kernel	kernel	PROPN
ejpam-6378	512	10	.	.	PUNCT
ejpam-6378	513	1	progress	progress	NOUN
ejpam-6378	513	2	in	in	ADP
ejpam-6378	513	3	fractional	fractional	ADJ
ejpam-6378	513	4	differentiation	differentiation	NOUN
ejpam-6378	513	5	&	&	CCONJ
ejpam-6378	513	6	applications	application	NOUN
ejpam-6378	513	7	,	,	PUNCT
ejpam-6378	513	8	1(2):73–85	1(2):73–85	NUM
ejpam-6378	513	9	,	,	PUNCT
ejpam-6378	513	10	2015	2015	NUM
ejpam-6378	513	11	.	.	PUNCT
ejpam-6378	514	1	[	[	X
ejpam-6378	514	2	38	38	NUM
ejpam-6378	514	3	]	]	PUNCT
ejpam-6378	514	4	abdon	abdon	PROPN
ejpam-6378	514	5	atangana	atangana	PROPN
ejpam-6378	514	6	and	and	CCONJ
ejpam-6378	514	7	dumitru	dumitru	PROPN
ejpam-6378	514	8	baleanu	baleanu	NOUN
ejpam-6378	514	9	.	.	PUNCT
ejpam-6378	515	1	new	new	ADJ
ejpam-6378	515	2	fractional	fractional	ADJ
ejpam-6378	515	3	derivatives	derivative	NOUN
ejpam-6378	515	4	with	with	ADP
ejpam-6378	515	5	nonlocal	nonlocal	ADJ
ejpam-6378	515	6	and	and	CCONJ
ejpam-6378	515	7	non	non	ADJ
ejpam-6378	515	8	-	-	ADJ
ejpam-6378	515	9	singular	singular	ADJ
ejpam-6378	515	10	kernel	kernel	NOUN
ejpam-6378	515	11	:	:	PUNCT
ejpam-6378	515	12	theory	theory	NOUN
ejpam-6378	515	13	and	and	CCONJ
ejpam-6378	515	14	application	application	NOUN
ejpam-6378	515	15	to	to	PART
ejpam-6378	515	16	heat	heat	NOUN
ejpam-6378	515	17	transfer	transfer	NOUN
ejpam-6378	515	18	model	model	NOUN
ejpam-6378	515	19	.	.	PUNCT
ejpam-6378	516	1	arxiv	arxiv	PROPN
ejpam-6378	516	2	preprint	preprint	VERB
ejpam-6378	516	3	arxiv:1602.03408	arxiv:1602.03408	PROPN
ejpam-6378	516	4	,	,	PUNCT
ejpam-6378	516	5	2016	2016	NUM
ejpam-6378	516	6	.	.	PUNCT
ejpam-6378	517	1	[	[	X
ejpam-6378	517	2	39	39	NUM
ejpam-6378	517	3	]	]	PUNCT
ejpam-6378	517	4	david	david	PROPN
ejpam-6378	517	5	vernon	vernon	PROPN
ejpam-6378	517	6	widder	widder	PROPN
ejpam-6378	517	7	.	.	PUNCT
ejpam-6378	518	1	laplace	laplace	PROPN
ejpam-6378	518	2	transform	transform	PROPN
ejpam-6378	518	3	.	.	PUNCT
ejpam-6378	519	1	princeton	princeton	PROPN
ejpam-6378	519	2	university	university	PROPN
ejpam-6378	519	3	press	press	PROPN
ejpam-6378	519	4	,	,	PUNCT
ejpam-6378	519	5	princeton	princeton	PROPN
ejpam-6378	519	6	,	,	PUNCT
ejpam-6378	519	7	1941	1941	NUM
ejpam-6378	519	8	.	.	PUNCT
ejpam-6378	520	1	[	[	X
ejpam-6378	520	2	40	40	NUM
ejpam-6378	520	3	]	]	PUNCT
ejpam-6378	520	4	tarig	tarig	PROPN
ejpam-6378	520	5	m	m	NOUN
ejpam-6378	520	6	elzaki	elzaki	ADJ
ejpam-6378	520	7	.	.	PUNCT
ejpam-6378	521	1	the	the	DET
ejpam-6378	521	2	new	new	ADJ
ejpam-6378	521	3	integral	integral	ADJ
ejpam-6378	521	4	transform	transform	NOUN
ejpam-6378	521	5	elzaki	elzaki	NOUN
ejpam-6378	521	6	transform	transform	NOUN
ejpam-6378	521	7	.	.	PUNCT
ejpam-6378	522	1	global	global	ADJ
ejpam-6378	522	2	journal	journal	PROPN
ejpam-6378	522	3	of	of	ADP
ejpam-6378	522	4	pure	pure	ADJ
ejpam-6378	522	5	and	and	CCONJ
ejpam-6378	522	6	applied	applied	ADJ
ejpam-6378	522	7	mathematics	mathematic	NOUN
ejpam-6378	522	8	,	,	PUNCT
ejpam-6378	522	9	7(1):57–64	7(1):57–64	NUM
ejpam-6378	522	10	,	,	PUNCT
ejpam-6378	522	11	2011	2011	NUM
ejpam-6378	522	12	.	.	PUNCT
ejpam-6378	523	1	[	[	X
ejpam-6378	523	2	41	41	NUM
ejpam-6378	523	3	]	]	X
ejpam-6378	523	4	khalid	khalid	PROPN
ejpam-6378	523	5	suliman	suliman	PROPN
ejpam-6378	523	6	aboodh	aboodh	PROPN
ejpam-6378	523	7	.	.	PUNCT
ejpam-6378	524	1	the	the	DET
ejpam-6378	524	2	new	new	ADJ
ejpam-6378	524	3	integral	integral	ADJ
ejpam-6378	524	4	transform’aboodh	transform’aboodh	ADJ
ejpam-6378	524	5	transform	transform	NOUN
ejpam-6378	524	6	.	.	PUNCT
ejpam-6378	525	1	global	global	ADJ
ejpam-6378	525	2	journal	journal	PROPN
ejpam-6378	525	3	of	of	ADP
ejpam-6378	525	4	pure	pure	ADJ
ejpam-6378	525	5	and	and	CCONJ
ejpam-6378	525	6	applied	applied	ADJ
ejpam-6378	525	7	mathematics	mathematic	NOUN
ejpam-6378	525	8	,	,	PUNCT
ejpam-6378	525	9	9(1):35–43	9(1):35–43	NUM
ejpam-6378	525	10	,	,	PUNCT
ejpam-6378	525	11	2013	2013	NUM
ejpam-6378	525	12	.	.	PUNCT
ejpam-6378	526	1	m.	m.	PROPN
ejpam-6378	526	2	sohail	sohail	PROPN
ejpam-6378	526	3	et	et	PROPN
ejpam-6378	526	4	al	al	PROPN
ejpam-6378	526	5	.	.	PUNCT
ejpam-6378	526	6	/	/	SYM
ejpam-6378	526	7	eur	eur	PROPN
ejpam-6378	526	8	.	.	PUNCT
ejpam-6378	527	1	j.	j.	PROPN
ejpam-6378	527	2	pure	pure	PROPN
ejpam-6378	527	3	appl	appl	PROPN
ejpam-6378	527	4	.	.	PROPN
ejpam-6378	527	5	math	math	PROPN
ejpam-6378	527	6	,	,	PUNCT
ejpam-6378	527	7	18	18	NUM
ejpam-6378	527	8	(	(	PUNCT
ejpam-6378	527	9	4	4	NUM
ejpam-6378	527	10	)	)	PUNCT
ejpam-6378	527	11	(	(	PUNCT
ejpam-6378	527	12	2025	2025	NUM
ejpam-6378	527	13	)	)	PUNCT
ejpam-6378	527	14	,	,	PUNCT
ejpam-6378	527	15	6378	6378	NUM
ejpam-6378	527	16	20	20	NUM
ejpam-6378	527	17	of	of	ADP
ejpam-6378	527	18	20	20	NUM
ejpam-6378	527	19	[	[	SYM
ejpam-6378	527	20	42	42	NUM
ejpam-6378	527	21	]	]	X
ejpam-6378	527	22	fethi	fethi	PROPN
ejpam-6378	527	23	bin	bin	PROPN
ejpam-6378	527	24	muhammed	muhamme	VERB
ejpam-6378	527	25	belgacem	belgacem	PROPN
ejpam-6378	527	26	and	and	CCONJ
ejpam-6378	527	27	ahmed	ahmed	PROPN
ejpam-6378	527	28	abdullatif	abdullatif	PROPN
ejpam-6378	527	29	karaballi	karaballi	PROPN
ejpam-6378	527	30	.	.	PUNCT
ejpam-6378	528	1	sumudu	sumudu	NOUN
ejpam-6378	528	2	transform	transform	VERB
ejpam-6378	528	3	fundamental	fundamental	ADJ
ejpam-6378	528	4	properties	property	NOUN
ejpam-6378	528	5	investigations	investigation	NOUN
ejpam-6378	528	6	and	and	CCONJ
ejpam-6378	528	7	applications	application	NOUN
ejpam-6378	528	8	.	.	PUNCT
ejpam-6378	529	1	international	international	ADJ
ejpam-6378	529	2	journal	journal	NOUN
ejpam-6378	529	3	of	of	ADP
ejpam-6378	529	4	stochastic	stochastic	ADJ
ejpam-6378	529	5	analysis	analysis	NOUN
ejpam-6378	529	6	,	,	PUNCT
ejpam-6378	529	7	2006(1):091083	2006(1):091083	NOUN
ejpam-6378	529	8	,	,	PUNCT
ejpam-6378	529	9	2006	2006	NUM
ejpam-6378	529	10	.	.	PUNCT
ejpam-6378	530	1	[	[	X
ejpam-6378	530	2	43	43	NUM
ejpam-6378	530	3	]	]	X
ejpam-6378	530	4	yu	yu	PROPN
ejpam-6378	530	5	-	-	PROPN
ejpam-6378	530	6	zhu	zhu	PROPN
ejpam-6378	530	7	zhang	zhang	PROPN
ejpam-6378	530	8	,	,	PUNCT
ejpam-6378	530	9	ai	ai	PROPN
ejpam-6378	530	10	-	-	PUNCT
ejpam-6378	530	11	min	min	NOUN
ejpam-6378	530	12	yang	yang	PROPN
ejpam-6378	530	13	,	,	PUNCT
ejpam-6378	530	14	and	and	CCONJ
ejpam-6378	530	15	yue	yue	PROPN
ejpam-6378	530	16	long	long	ADV
ejpam-6378	530	17	.	.	PUNCT
ejpam-6378	531	1	initial	initial	ADJ
ejpam-6378	531	2	boundary	boundary	ADJ
ejpam-6378	531	3	value	value	NOUN
ejpam-6378	531	4	problem	problem	NOUN
ejpam-6378	531	5	for	for	ADP
ejpam-6378	531	6	fractal	fractal	ADJ
ejpam-6378	531	7	heat	heat	NOUN
ejpam-6378	531	8	equation	equation	NOUN
ejpam-6378	531	9	in	in	ADP
ejpam-6378	531	10	the	the	DET
ejpam-6378	531	11	semi	semi	ADJ
ejpam-6378	531	12	-	-	ADJ
ejpam-6378	531	13	infinite	infinite	ADJ
ejpam-6378	531	14	region	region	NOUN
ejpam-6378	531	15	by	by	ADP
ejpam-6378	531	16	yang	yang	PROPN
ejpam-6378	531	17	-	-	PUNCT
ejpam-6378	531	18	laplace	laplace	PROPN
ejpam-6378	531	19	transform	transform	NOUN
ejpam-6378	531	20	.	.	PUNCT
ejpam-6378	532	1	thermal	thermal	ADJ
ejpam-6378	532	2	science	science	NOUN
ejpam-6378	532	3	,	,	PUNCT
ejpam-6378	532	4	18(2):677–681	18(2):677–681	PROPN
ejpam-6378	532	5	,	,	PUNCT
ejpam-6378	532	6	2014	2014	NUM
ejpam-6378	532	7	.	.	PUNCT
ejpam-6378	533	1	[	[	X
ejpam-6378	533	2	44	44	NUM
ejpam-6378	533	3	]	]	PUNCT
ejpam-6378	533	4	sudhanshu	sudhanshu	NOUN
ejpam-6378	533	5	aggarwal	aggarwal	NOUN
ejpam-6378	533	6	and	and	CCONJ
ejpam-6378	533	7	renu	renu	PROPN
ejpam-6378	533	8	chaudhary	chaudhary	PROPN
ejpam-6378	533	9	.	.	PUNCT
ejpam-6378	534	1	a	a	DET
ejpam-6378	534	2	comparative	comparative	ADJ
ejpam-6378	534	3	study	study	NOUN
ejpam-6378	534	4	of	of	ADP
ejpam-6378	534	5	mohand	mohand	NOUN
ejpam-6378	534	6	and	and	CCONJ
ejpam-6378	534	7	laplace	laplace	NOUN
ejpam-6378	534	8	transforms	transform	VERB
ejpam-6378	534	9	.	.	PUNCT
ejpam-6378	535	1	journal	journal	NOUN
ejpam-6378	535	2	of	of	ADP
ejpam-6378	535	3	emerging	emerge	VERB
ejpam-6378	535	4	technologies	technology	NOUN
ejpam-6378	535	5	and	and	CCONJ
ejpam-6378	535	6	innovative	innovative	ADJ
ejpam-6378	535	7	research	research	NOUN
ejpam-6378	535	8	,	,	PUNCT
ejpam-6378	535	9	6(2):230–240	6(2):230–240	NUM
ejpam-6378	535	10	,	,	PUNCT
ejpam-6378	535	11	2019	2019	NUM
ejpam-6378	535	12	.	.	PUNCT
ejpam-6378	536	1	[	[	X
ejpam-6378	536	2	45	45	NUM
ejpam-6378	536	3	]	]	X
ejpam-6378	536	4	fethi	fethi	PROPN
ejpam-6378	536	5	bin	bin	NOUN
ejpam-6378	536	6	muhammed	muhamme	VERB
ejpam-6378	536	7	belgacem	belgacem	NOUN
ejpam-6378	536	8	and	and	CCONJ
ejpam-6378	536	9	r	r	PROPN
ejpam-6378	536	10	silambarasan	silambarasan	NOUN
ejpam-6378	536	11	.	.	PUNCT
ejpam-6378	537	1	theory	theory	NOUN
ejpam-6378	537	2	of	of	ADP
ejpam-6378	537	3	natural	natural	ADJ
ejpam-6378	537	4	transform	transform	NOUN
ejpam-6378	537	5	.	.	PUNCT
ejpam-6378	538	1	math	math	NOUN
ejpam-6378	538	2	.	.	PUNCT
ejpam-6378	539	1	engg	engg	PROPN
ejpam-6378	539	2	.	.	PUNCT
ejpam-6378	540	1	sci	sci	PROPN
ejpam-6378	540	2	.	.	PUNCT
ejpam-6378	540	3	aeros	aero	NOUN
ejpam-6378	540	4	,	,	PUNCT
ejpam-6378	540	5	3:99–124	3:99–124	NUM
ejpam-6378	540	6	,	,	PUNCT
ejpam-6378	540	7	2012	2012	NUM
ejpam-6378	540	8	.	.	PUNCT
ejpam-6378	541	1	[	[	X
ejpam-6378	541	2	46	46	NUM
ejpam-6378	541	3	]	]	PUNCT
ejpam-6378	541	4	shehu	shehu	NOUN
ejpam-6378	541	5	maitama	maitama	PROPN
ejpam-6378	541	6	and	and	CCONJ
ejpam-6378	541	7	weidong	weidong	PROPN
ejpam-6378	541	8	zhao	zhao	PROPN
ejpam-6378	541	9	.	.	PUNCT
ejpam-6378	542	1	new	new	ADJ
ejpam-6378	542	2	integral	integral	ADJ
ejpam-6378	542	3	transform	transform	NOUN
ejpam-6378	542	4	:	:	PUNCT
ejpam-6378	542	5	shehu	shehu	PROPN
ejpam-6378	542	6	transform	transform	VERB
ejpam-6378	542	7	a	a	DET
ejpam-6378	542	8	generalization	generalization	NOUN
ejpam-6378	542	9	of	of	ADP
ejpam-6378	542	10	sumudu	sumudu	NOUN
ejpam-6378	542	11	and	and	CCONJ
ejpam-6378	542	12	laplace	laplace	NOUN
ejpam-6378	542	13	transform	transform	NOUN
ejpam-6378	542	14	for	for	ADP
ejpam-6378	542	15	solving	solve	VERB
ejpam-6378	542	16	differential	differential	ADJ
ejpam-6378	542	17	equations	equation	NOUN
ejpam-6378	542	18	.	.	PUNCT
ejpam-6378	543	1	arxiv	arxiv	PROPN
ejpam-6378	543	2	preprint	preprint	NOUN
ejpam-6378	543	3	arxiv:1904.11370	arxiv:1904.11370	NOUN
ejpam-6378	543	4	,	,	PUNCT
ejpam-6378	543	5	2019	2019	NUM
ejpam-6378	543	6	.	.	PUNCT
ejpam-6378	544	1	[	[	X
ejpam-6378	544	2	47	47	NUM
ejpam-6378	544	3	]	]	X
ejpam-6378	544	4	richard	richard	PROPN
ejpam-6378	544	5	magin	magin	PROPN
ejpam-6378	544	6	.	.	PUNCT
ejpam-6378	545	1	fractional	fractional	ADJ
ejpam-6378	545	2	calculus	calculus	NOUN
ejpam-6378	545	3	in	in	ADP
ejpam-6378	545	4	bioengineering	bioengineering	NOUN
ejpam-6378	545	5	,	,	PUNCT
ejpam-6378	545	6	part	part	NOUN
ejpam-6378	545	7	1	1	NUM
ejpam-6378	545	8	.	.	PUNCT
ejpam-6378	546	1	critical	critical	ADJ
ejpam-6378	546	2	reviews	review	NOUN
ejpam-6378	546	3	in	in	ADP
ejpam-6378	546	4	biomedical	biomedical	ADJ
ejpam-6378	546	5	engineering	engineering	NOUN
ejpam-6378	546	6	,	,	PUNCT
ejpam-6378	546	7	32(1	32(1	NUM
ejpam-6378	546	8	)	)	PUNCT
ejpam-6378	546	9	,	,	PUNCT
ejpam-6378	546	10	2004	2004	NUM
ejpam-6378	546	11	.	.	PUNCT