id	sid	tid	token	lemma	pos
ejpam-6316	1	1	european	european	PROPN
ejpam-6316	1	2	journal	journal	PROPN
ejpam-6316	1	3	of	of	ADP
ejpam-6316	1	4	pure	pure	ADJ
ejpam-6316	1	5	and	and	CCONJ
ejpam-6316	1	6	applied	applied	ADJ
ejpam-6316	1	7	mathematics	mathematic	NOUN
ejpam-6316	1	8	2025	2025	NUM
ejpam-6316	1	9	,	,	PUNCT
ejpam-6316	1	10	vol	vol	NOUN
ejpam-6316	1	11	.	.	PROPN
ejpam-6316	1	12	18	18	NUM
ejpam-6316	1	13	,	,	PUNCT
ejpam-6316	1	14	issue	issue	NOUN
ejpam-6316	1	15	3	3	NUM
ejpam-6316	1	16	,	,	PUNCT
ejpam-6316	1	17	article	article	NOUN
ejpam-6316	1	18	number	number	NOUN
ejpam-6316	1	19	6316	6316	NUM
ejpam-6316	1	20	issn	issn	PROPN
ejpam-6316	1	21	1307	1307	NUM
ejpam-6316	1	22	-	-	SYM
ejpam-6316	1	23	5543	5543	NUM
ejpam-6316	1	24	–	–	PUNCT
ejpam-6316	1	25	ejpam.com	ejpam.com	X
ejpam-6316	1	26	published	publish	VERB
ejpam-6316	1	27	by	by	ADP
ejpam-6316	1	28	new	new	PROPN
ejpam-6316	1	29	york	york	PROPN
ejpam-6316	1	30	business	business	PROPN
ejpam-6316	1	31	global	global	ADJ
ejpam-6316	1	32	advanced	advanced	ADJ
ejpam-6316	1	33	mathematical	mathematical	ADJ
ejpam-6316	1	34	approaches	approach	NOUN
ejpam-6316	1	35	for	for	ADP
ejpam-6316	1	36	solving	solve	VERB
ejpam-6316	1	37	fractional	fractional	ADJ
ejpam-6316	1	38	-	-	PUNCT
ejpam-6316	1	39	order	order	NOUN
ejpam-6316	1	40	korteweg	korteweg	NOUN
ejpam-6316	1	41	-	-	PUNCT
ejpam-6316	1	42	de	de	PROPN
ejpam-6316	1	43	vries	vries	PROPN
ejpam-6316	1	44	equations	equations	PROPN
ejpam-6316	1	45	naveed	naveed	PROPN
ejpam-6316	1	46	iqbal1,∗	iqbal1,∗	PROPN
ejpam-6316	1	47	,	,	PUNCT
ejpam-6316	1	48	shah	shah	NOUN
ejpam-6316	1	49	hussain1	hussain1	PROPN
ejpam-6316	1	50	,	,	PUNCT
ejpam-6316	1	51	amjad	amjad	PROPN
ejpam-6316	1	52	e.	e.	PROPN
ejpam-6316	1	53	hamza1	hamza1	PROPN
ejpam-6316	1	54	,	,	PUNCT
ejpam-6316	1	55	yousef	yousef	PROPN
ejpam-6316	1	56	jawarneh1	jawarneh1	PROPN
ejpam-6316	1	57	,	,	PUNCT
ejpam-6316	1	58	fazal	fazal	PROPN
ejpam-6316	1	59	ghani2	ghani2	PROPN
ejpam-6316	1	60	1	1	NUM
ejpam-6316	1	61	department	department	NOUN
ejpam-6316	1	62	of	of	ADP
ejpam-6316	1	63	mathematics	mathematic	NOUN
ejpam-6316	1	64	,	,	PUNCT
ejpam-6316	1	65	college	college	NOUN
ejpam-6316	1	66	of	of	ADP
ejpam-6316	1	67	science	science	NOUN
ejpam-6316	1	68	,	,	PUNCT
ejpam-6316	1	69	university	university	NOUN
ejpam-6316	1	70	of	of	ADP
ejpam-6316	1	71	ha’il	ha’il	PROPN
ejpam-6316	1	72	,	,	PUNCT
ejpam-6316	1	73	ha’il	ha’il	PROPN
ejpam-6316	1	74	2440	2440	NUM
ejpam-6316	1	75	,	,	PUNCT
ejpam-6316	1	76	saudi	saudi	PROPN
ejpam-6316	1	77	arabia	arabia	PROPN
ejpam-6316	1	78	2	2	NUM
ejpam-6316	1	79	department	department	NOUN
ejpam-6316	1	80	of	of	ADP
ejpam-6316	1	81	mathematics	mathematic	NOUN
ejpam-6316	1	82	,	,	PUNCT
ejpam-6316	1	83	abdul	abdul	PROPN
ejpam-6316	1	84	wali	wali	PROPN
ejpam-6316	1	85	khan	khan	PROPN
ejpam-6316	1	86	university	university	PROPN
ejpam-6316	1	87	,	,	PUNCT
ejpam-6316	1	88	mardan	mardan	NOUN
ejpam-6316	1	89	23200	23200	NUM
ejpam-6316	1	90	,	,	PUNCT
ejpam-6316	1	91	pakistan	pakistan	PROPN
ejpam-6316	1	92	abstract	abstract	NOUN
ejpam-6316	1	93	.	.	PUNCT
ejpam-6316	2	1	in	in	ADP
ejpam-6316	2	2	this	this	DET
ejpam-6316	2	3	work	work	NOUN
ejpam-6316	2	4	,	,	PUNCT
ejpam-6316	2	5	we	we	PRON
ejpam-6316	2	6	investigate	investigate	VERB
ejpam-6316	2	7	the	the	DET
ejpam-6316	2	8	use	use	NOUN
ejpam-6316	2	9	of	of	ADP
ejpam-6316	2	10	two	two	NUM
ejpam-6316	2	11	new	new	ADJ
ejpam-6316	2	12	methods	method	NOUN
ejpam-6316	2	13	,	,	PUNCT
ejpam-6316	2	14	residual	residual	ADJ
ejpam-6316	2	15	power	power	NOUN
ejpam-6316	2	16	series	series	PROPN
ejpam-6316	2	17	natural	natural	ADJ
ejpam-6316	2	18	transform	transform	NOUN
ejpam-6316	2	19	method	method	NOUN
ejpam-6316	2	20	(	(	PUNCT
ejpam-6316	2	21	rpsntm	rpsntm	PROPN
ejpam-6316	2	22	)	)	PUNCT
ejpam-6316	2	23	and	and	CCONJ
ejpam-6316	2	24	new	new	ADJ
ejpam-6316	2	25	iteration	iteration	NOUN
ejpam-6316	2	26	natural	natural	ADJ
ejpam-6316	2	27	transform	transform	NOUN
ejpam-6316	2	28	method	method	NOUN
ejpam-6316	2	29	(	(	PUNCT
ejpam-6316	2	30	nintm	nintm	PROPN
ejpam-6316	2	31	)	)	PUNCT
ejpam-6316	2	32	,	,	PUNCT
ejpam-6316	2	33	to	to	PART
ejpam-6316	2	34	tackle	tackle	VERB
ejpam-6316	2	35	the	the	DET
ejpam-6316	2	36	fractional	fractional	ADJ
ejpam-6316	2	37	-	-	PUNCT
ejpam-6316	2	38	order	order	NOUN
ejpam-6316	2	39	korteweg	korteweg	NOUN
ejpam-6316	2	40	-	-	PUNCT
ejpam-6316	2	41	de	de	PROPN
ejpam-6316	2	42	vries	vries	PROPN
ejpam-6316	2	43	(	(	PUNCT
ejpam-6316	2	44	kdv	kdv	NOUN
ejpam-6316	2	45	)	)	PUNCT
ejpam-6316	2	46	equation	equation	NOUN
ejpam-6316	2	47	.	.	PUNCT
ejpam-6316	3	1	many	many	ADJ
ejpam-6316	3	2	wave	wave	NOUN
ejpam-6316	3	3	effects	effect	NOUN
ejpam-6316	3	4	in	in	ADP
ejpam-6316	3	5	fluid	fluid	ADJ
ejpam-6316	3	6	dynamics	dynamic	NOUN
ejpam-6316	3	7	,	,	PUNCT
ejpam-6316	3	8	plasma	plasma	NOUN
ejpam-6316	3	9	physics	physics	NOUN
ejpam-6316	3	10	and	and	CCONJ
ejpam-6316	3	11	traffic	traffic	NOUN
ejpam-6316	3	12	flow	flow	NOUN
ejpam-6316	3	13	are	be	AUX
ejpam-6316	3	14	described	describe	VERB
ejpam-6316	3	15	with	with	ADP
ejpam-6316	3	16	the	the	DET
ejpam-6316	3	17	help	help	NOUN
ejpam-6316	3	18	of	of	ADP
ejpam-6316	3	19	the	the	DET
ejpam-6316	3	20	fractional	fractional	ADJ
ejpam-6316	3	21	-	-	PUNCT
ejpam-6316	3	22	order	order	NOUN
ejpam-6316	3	23	kdv	kdv	NOUN
ejpam-6316	3	24	equation	equation	NOUN
ejpam-6316	3	25	.	.	PUNCT
ejpam-6316	4	1	traditional	traditional	ADJ
ejpam-6316	4	2	techniques	technique	NOUN
ejpam-6316	4	3	used	use	VERB
ejpam-6316	4	4	to	to	PART
ejpam-6316	4	5	solve	solve	VERB
ejpam-6316	4	6	equations	equation	NOUN
ejpam-6316	4	7	generally	generally	ADV
ejpam-6316	4	8	are	be	AUX
ejpam-6316	4	9	not	not	PART
ejpam-6316	4	10	adapted	adapt	VERB
ejpam-6316	4	11	to	to	PART
ejpam-6316	4	12	deal	deal	VERB
ejpam-6316	4	13	with	with	ADP
ejpam-6316	4	14	the	the	DET
ejpam-6316	4	15	complications	complication	NOUN
ejpam-6316	4	16	caused	cause	VERB
ejpam-6316	4	17	by	by	ADP
ejpam-6316	4	18	fractional	fractional	ADJ
ejpam-6316	4	19	derivatives	derivative	NOUN
ejpam-6316	4	20	.	.	PUNCT
ejpam-6316	5	1	the	the	DET
ejpam-6316	5	2	rpsntm	rpsntm	NOUN
ejpam-6316	5	3	is	be	AUX
ejpam-6316	5	4	presented	present	VERB
ejpam-6316	5	5	as	as	ADP
ejpam-6316	5	6	a	a	DET
ejpam-6316	5	7	valuable	valuable	ADJ
ejpam-6316	5	8	method	method	NOUN
ejpam-6316	5	9	to	to	PART
ejpam-6316	5	10	approximate	approximate	VERB
ejpam-6316	5	11	how	how	SCONJ
ejpam-6316	5	12	the	the	DET
ejpam-6316	5	13	solution	solution	NOUN
ejpam-6316	5	14	will	will	AUX
ejpam-6316	5	15	change	change	VERB
ejpam-6316	5	16	with	with	ADP
ejpam-6316	5	17	time	time	NOUN
ejpam-6316	5	18	by	by	ADP
ejpam-6316	5	19	converting	convert	VERB
ejpam-6316	5	20	the	the	DET
ejpam-6316	5	21	problem	problem	NOUN
ejpam-6316	5	22	into	into	ADP
ejpam-6316	5	23	a	a	DET
ejpam-6316	5	24	step	step	NOUN
ejpam-6316	5	25	-	-	PUNCT
ejpam-6316	5	26	by	by	ADP
ejpam-6316	5	27	-	-	PUNCT
ejpam-6316	5	28	step	step	NOUN
ejpam-6316	5	29	series	series	NOUN
ejpam-6316	5	30	.	.	PUNCT
ejpam-6316	6	1	the	the	DET
ejpam-6316	6	2	nintm	nintm	PROPN
ejpam-6316	6	3	is	be	AUX
ejpam-6316	6	4	also	also	ADV
ejpam-6316	6	5	used	use	VERB
ejpam-6316	6	6	to	to	PART
ejpam-6316	6	7	make	make	VERB
ejpam-6316	6	8	the	the	DET
ejpam-6316	6	9	solution	solution	NOUN
ejpam-6316	6	10	more	more	ADV
ejpam-6316	6	11	effective	effective	ADJ
ejpam-6316	6	12	and	and	CCONJ
ejpam-6316	6	13	reliable	reliable	ADJ
ejpam-6316	6	14	gradually	gradually	ADV
ejpam-6316	6	15	.	.	PUNCT
ejpam-6316	7	1	applying	apply	VERB
ejpam-6316	7	2	both	both	DET
ejpam-6316	7	3	approaches	approach	NOUN
ejpam-6316	7	4	offers	offer	VERB
ejpam-6316	7	5	a	a	DET
ejpam-6316	7	6	strong	strong	ADJ
ejpam-6316	7	7	way	way	NOUN
ejpam-6316	7	8	to	to	PART
ejpam-6316	7	9	find	find	VERB
ejpam-6316	7	10	approximate	approximate	ADJ
ejpam-6316	7	11	analytical	analytical	ADJ
ejpam-6316	7	12	answers	answer	NOUN
ejpam-6316	7	13	to	to	ADP
ejpam-6316	7	14	the	the	DET
ejpam-6316	7	15	kdv	kdv	NOUN
ejpam-6316	7	16	fractional	fractional	ADJ
ejpam-6316	7	17	-	-	PUNCT
ejpam-6316	7	18	order	order	NOUN
ejpam-6316	7	19	equation	equation	NOUN
ejpam-6316	7	20	.	.	PUNCT
ejpam-6316	8	1	numerical	numerical	PROPN
ejpam-6316	8	2	data	data	PROPN
ejpam-6316	8	3	is	be	AUX
ejpam-6316	8	4	used	use	VERB
ejpam-6316	8	5	to	to	PART
ejpam-6316	8	6	reveal	reveal	VERB
ejpam-6316	8	7	that	that	SCONJ
ejpam-6316	8	8	the	the	DET
ejpam-6316	8	9	presented	present	VERB
ejpam-6316	8	10	methods	method	NOUN
ejpam-6316	8	11	work	work	VERB
ejpam-6316	8	12	better	well	ADV
ejpam-6316	8	13	and	and	CCONJ
ejpam-6316	8	14	faster	fast	ADV
ejpam-6316	8	15	than	than	ADP
ejpam-6316	8	16	existing	exist	VERB
ejpam-6316	8	17	methods	method	NOUN
ejpam-6316	8	18	in	in	ADP
ejpam-6316	8	19	terms	term	NOUN
ejpam-6316	8	20	of	of	ADP
ejpam-6316	8	21	precision	precision	NOUN
ejpam-6316	8	22	and	and	CCONJ
ejpam-6316	8	23	speed	speed	NOUN
ejpam-6316	8	24	of	of	ADP
ejpam-6316	8	25	convergence	convergence	NOUN
ejpam-6316	8	26	.	.	PUNCT
ejpam-6316	9	1	these	these	DET
ejpam-6316	9	2	results	result	NOUN
ejpam-6316	9	3	create	create	VERB
ejpam-6316	9	4	new	new	ADJ
ejpam-6316	9	5	opportunities	opportunity	NOUN
ejpam-6316	9	6	to	to	PART
ejpam-6316	9	7	apply	apply	VERB
ejpam-6316	9	8	fractional	fractional	ADJ
ejpam-6316	9	9	calculus	calculus	NOUN
ejpam-6316	9	10	in	in	ADP
ejpam-6316	9	11	analyzing	analyze	VERB
ejpam-6316	9	12	nonlinear	nonlinear	ADJ
ejpam-6316	9	13	waves.preparation	waves.preparation	PROPN
ejpam-6316	9	14	.	.	PUNCT
ejpam-6316	10	1	2020	2020	NUM
ejpam-6316	10	2	mathematics	mathematic	NOUN
ejpam-6316	10	3	subject	subject	NOUN
ejpam-6316	10	4	classifications	classification	NOUN
ejpam-6316	10	5	:	:	PUNCT
ejpam-6316	10	6	35a20	35a20	NUM
ejpam-6316	10	7	,	,	PUNCT
ejpam-6316	10	8	35j35	35j35	NUM
ejpam-6316	10	9	,	,	PUNCT
ejpam-6316	10	10	74h10	74h10	NOUN
ejpam-6316	10	11	,	,	PUNCT
ejpam-6316	10	12	74h20	74h20	NUM
ejpam-6316	10	13	,	,	PUNCT
ejpam-6316	10	14	74h25	74h25	NUM
ejpam-6316	10	15	key	key	ADJ
ejpam-6316	10	16	words	word	NOUN
ejpam-6316	10	17	and	and	CCONJ
ejpam-6316	10	18	phrases	phrase	NOUN
ejpam-6316	10	19	:	:	PUNCT
ejpam-6316	10	20	fractional	fractional	ADJ
ejpam-6316	10	21	-	-	PUNCT
ejpam-6316	10	22	order	order	NOUN
ejpam-6316	10	23	kdv	kdv	NOUN
ejpam-6316	10	24	equation	equation	NOUN
ejpam-6316	10	25	,	,	PUNCT
ejpam-6316	10	26	residual	residual	ADJ
ejpam-6316	10	27	power	power	NOUN
ejpam-6316	10	28	series	series	PROPN
ejpam-6316	10	29	natural	natural	ADJ
ejpam-6316	10	30	transform	transform	NOUN
ejpam-6316	10	31	method	method	NOUN
ejpam-6316	10	32	,	,	PUNCT
ejpam-6316	10	33	new	new	ADJ
ejpam-6316	10	34	iteration	iteration	NOUN
ejpam-6316	10	35	natural	natural	ADJ
ejpam-6316	10	36	transform	transform	NOUN
ejpam-6316	10	37	method	method	NOUN
ejpam-6316	10	38	1	1	NUM
ejpam-6316	10	39	.	.	PUNCT
ejpam-6316	10	40	introduction	introduction	NOUN
ejpam-6316	10	41	fractional	fractional	ADJ
ejpam-6316	10	42	partial	partial	ADJ
ejpam-6316	10	43	differential	differential	NOUN
ejpam-6316	10	44	equations	equation	NOUN
ejpam-6316	10	45	(	(	PUNCT
ejpam-6316	10	46	fpdes	fpde	NOUN
ejpam-6316	10	47	)	)	PUNCT
ejpam-6316	10	48	add	add	VERB
ejpam-6316	10	49	non	non	ADJ
ejpam-6316	10	50	-	-	ADJ
ejpam-6316	10	51	integer	integer	ADJ
ejpam-6316	10	52	derivative	derivative	ADJ
ejpam-6316	10	53	terms	term	NOUN
ejpam-6316	10	54	,	,	PUNCT
ejpam-6316	10	55	which	which	PRON
ejpam-6316	10	56	are	be	AUX
ejpam-6316	10	57	commonly	commonly	ADV
ejpam-6316	10	58	referred	refer	VERB
ejpam-6316	10	59	to	to	ADP
ejpam-6316	10	60	as	as	ADP
ejpam-6316	10	61	”	"	PUNCT
ejpam-6316	10	62	fractional	fractional	ADJ
ejpam-6316	10	63	derivatives	derivative	NOUN
ejpam-6316	10	64	,	,	PUNCT
ejpam-6316	10	65	”	"	PUNCT
ejpam-6316	10	66	to	to	ADP
ejpam-6316	10	67	classical	classical	ADJ
ejpam-6316	10	68	partial	partial	ADJ
ejpam-6316	10	69	differential	differential	NOUN
ejpam-6316	10	70	equations	equation	NOUN
ejpam-6316	10	71	.	.	PUNCT
ejpam-6316	11	1	they	they	PRON
ejpam-6316	11	2	give	give	VERB
ejpam-6316	11	3	us	we	PRON
ejpam-6316	11	4	a	a	DET
ejpam-6316	11	5	method	method	NOUN
ejpam-6316	11	6	to	to	PART
ejpam-6316	11	7	describe	describe	VERB
ejpam-6316	11	8	anomalous	anomalous	ADJ
ejpam-6316	11	9	diffusion	diffusion	NOUN
ejpam-6316	11	10	,	,	PUNCT
ejpam-6316	11	11	memory	memory	NOUN
ejpam-6316	11	12	effects	effect	NOUN
ejpam-6316	11	13	or	or	CCONJ
ejpam-6316	11	14	long	long	ADJ
ejpam-6316	11	15	-	-	PUNCT
ejpam-6316	11	16	range	range	NOUN
ejpam-6316	11	17	interactions	interaction	NOUN
ejpam-6316	11	18	,	,	PUNCT
ejpam-6316	11	19	situations	situation	NOUN
ejpam-6316	11	20	where	where	SCONJ
ejpam-6316	11	21	traditional	traditional	ADJ
ejpam-6316	11	22	integer	integer	NOUN
ejpam-6316	11	23	-	-	PUNCT
ejpam-6316	11	24	order	order	NOUN
ejpam-6316	11	25	derivatives	derivative	NOUN
ejpam-6316	11	26	are	be	AUX
ejpam-6316	11	27	not	not	PART
ejpam-6316	11	28	enough	enough	ADJ
ejpam-6316	11	29	.	.	PUNCT
ejpam-6316	12	1	using	use	VERB
ejpam-6316	12	2	fractional	fractional	ADJ
ejpam-6316	12	3	derivatives	derivative	NOUN
ejpam-6316	12	4	,	,	PUNCT
ejpam-6316	12	5	fpdes	fpde	NOUN
ejpam-6316	12	6	can	can	AUX
ejpam-6316	12	7	describe	describe	VERB
ejpam-6316	12	8	systems	system	NOUN
ejpam-6316	12	9	that	that	PRON
ejpam-6316	12	10	do	do	AUX
ejpam-6316	12	11	not	not	PART
ejpam-6316	12	12	remain	remain	VERB
ejpam-6316	12	13	∗corresponding	∗corresponde	VERB
ejpam-6316	12	14	author	author	NOUN
ejpam-6316	12	15	.	.	PUNCT
ejpam-6316	13	1	doi	doi	NOUN
ejpam-6316	13	2	:	:	PUNCT
ejpam-6316	13	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6316	https://doi.org/10.29020/nybg.ejpam.v18i3.6316	ADJ
ejpam-6316	13	4	email	email	NOUN
ejpam-6316	13	5	addresses	address	NOUN
ejpam-6316	13	6	:	:	PUNCT
ejpam-6316	13	7	n.iqbal@uoh.edu.sa	n.iqbal@uoh.edu.sa	NUM
ejpam-6316	13	8	(	(	PUNCT
ejpam-6316	13	9	n.	n.	PROPN
ejpam-6316	13	10	iqbal	iqbal	PROPN
ejpam-6316	13	11	)	)	PUNCT
ejpam-6316	13	12	,	,	PUNCT
ejpam-6316	13	13	s.khan@uoh.edu.sa	s.khan@uoh.edu.sa	PROPN
ejpam-6316	13	14	(	(	PUNCT
ejpam-6316	13	15	s.	s.	PROPN
ejpam-6316	13	16	hussain	hussain	PROPN
ejpam-6316	13	17	)	)	PUNCT
ejpam-6316	13	18	,	,	PUNCT
ejpam-6316	13	19	ae.hamza@uoh.edu.sa	ae.hamza@uoh.edu.sa	PROPN
ejpam-6316	13	20	(	(	PUNCT
ejpam-6316	13	21	a.e.hamza	a.e.hamza	NOUN
ejpam-6316	13	22	)	)	PUNCT
ejpam-6316	13	23	,	,	PUNCT
ejpam-6316	13	24	y.jawarrneh@uoh.edu.sa	y.jawarrneh@uoh.edu.sa	PROPN
ejpam-6316	13	25	(	(	PUNCT
ejpam-6316	13	26	y.	y.	PROPN
ejpam-6316	13	27	jawarneh	jawarneh	PROPN
ejpam-6316	13	28	)	)	PUNCT
ejpam-6316	13	29	,	,	PUNCT
ejpam-6316	13	30	fghanimath@awkum.edu.pk	fghanimath@awkum.edu.pk	PROPN
ejpam-6316	13	31	(	(	PUNCT
ejpam-6316	13	32	f.	f.	PROPN
ejpam-6316	13	33	ghani	ghani	PROPN
ejpam-6316	13	34	)	)	PUNCT
ejpam-6316	13	35	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6316	14	1	1	1	NUM
ejpam-6316	14	2	copyright	copyright	NOUN
ejpam-6316	14	3	:	:	PUNCT
ejpam-6316	14	4	©	©	PROPN
ejpam-6316	14	5	2025	2025	NUM
ejpam-6316	14	6	the	the	DET
ejpam-6316	14	7	author(s	author(s	NOUN
ejpam-6316	14	8	)	)	PUNCT
ejpam-6316	14	9	.	.	PUNCT
ejpam-6316	15	1	(	(	PUNCT
ejpam-6316	15	2	cc	cc	NOUN
ejpam-6316	15	3	by	by	ADP
ejpam-6316	15	4	-	-	PUNCT
ejpam-6316	15	5	nc	nc	PROPN
ejpam-6316	15	6	4.0	4.0	NUM
ejpam-6316	15	7	)	)	PUNCT
ejpam-6316	15	8	n.	n.	PROPN
ejpam-6316	15	9	iqbal	iqbal	PROPN
ejpam-6316	15	10	et	et	PROPN
ejpam-6316	15	11	al	al	PROPN
ejpam-6316	15	12	.	.	PUNCT
ejpam-6316	15	13	/	/	SYM
ejpam-6316	15	14	eur	eur	PROPN
ejpam-6316	15	15	.	.	PUNCT
ejpam-6316	16	1	j.	j.	PROPN
ejpam-6316	16	2	pure	pure	PROPN
ejpam-6316	16	3	appl	appl	PROPN
ejpam-6316	16	4	.	.	PROPN
ejpam-6316	16	5	math	math	PROPN
ejpam-6316	16	6	,	,	PUNCT
ejpam-6316	16	7	18	18	NUM
ejpam-6316	16	8	(	(	PUNCT
ejpam-6316	16	9	3	3	NUM
ejpam-6316	16	10	)	)	PUNCT
ejpam-6316	16	11	(	(	PUNCT
ejpam-6316	16	12	2025	2025	NUM
ejpam-6316	16	13	)	)	PUNCT
ejpam-6316	16	14	,	,	PUNCT
ejpam-6316	16	15	6316	6316	NUM
ejpam-6316	16	16	2	2	NUM
ejpam-6316	16	17	of	of	ADP
ejpam-6316	16	18	21	21	NUM
ejpam-6316	16	19	the	the	DET
ejpam-6316	16	20	same	same	ADJ
ejpam-6316	16	21	everywhere	everywhere	ADV
ejpam-6316	16	22	,	,	PUNCT
ejpam-6316	16	23	which	which	PRON
ejpam-6316	16	24	gives	give	VERB
ejpam-6316	16	25	them	they	PRON
ejpam-6316	16	26	value	value	NOUN
ejpam-6316	16	27	in	in	ADP
ejpam-6316	16	28	physics	physics	NOUN
ejpam-6316	16	29	,	,	PUNCT
ejpam-6316	16	30	finance	finance	NOUN
ejpam-6316	16	31	,	,	PUNCT
ejpam-6316	16	32	biology	biology	NOUN
ejpam-6316	16	33	and	and	CCONJ
ejpam-6316	16	34	engineering	engineering	NOUN
ejpam-6316	16	35	.	.	PUNCT
ejpam-6316	17	1	they	they	PRON
ejpam-6316	17	2	serve	serve	VERB
ejpam-6316	17	3	to	to	PART
ejpam-6316	17	4	bridge	bridge	VERB
ejpam-6316	17	5	the	the	DET
ejpam-6316	17	6	divide	divide	NOUN
ejpam-6316	17	7	between	between	ADP
ejpam-6316	17	8	models	model	NOUN
ejpam-6316	17	9	for	for	ADP
ejpam-6316	17	10	the	the	DET
ejpam-6316	17	11	large	large	ADJ
ejpam-6316	17	12	-	-	PUNCT
ejpam-6316	17	13	scale	scale	NOUN
ejpam-6316	17	14	and	and	CCONJ
ejpam-6316	17	15	small	small	ADJ
ejpam-6316	17	16	-	-	PUNCT
ejpam-6316	17	17	scale	scale	NOUN
ejpam-6316	17	18	world	world	NOUN
ejpam-6316	17	19	,	,	PUNCT
ejpam-6316	17	20	giving	give	VERB
ejpam-6316	17	21	us	we	PRON
ejpam-6316	17	22	a	a	DET
ejpam-6316	17	23	better	well	ADJ
ejpam-6316	17	24	picture	picture	NOUN
ejpam-6316	17	25	of	of	ADP
ejpam-6316	17	26	things	thing	NOUN
ejpam-6316	17	27	that	that	PRON
ejpam-6316	17	28	happen	happen	VERB
ejpam-6316	17	29	across	across	ADP
ejpam-6316	17	30	many	many	ADJ
ejpam-6316	17	31	scales	scale	NOUN
ejpam-6316	17	32	in	in	ADP
ejpam-6316	17	33	nature	nature	NOUN
ejpam-6316	17	34	.	.	PUNCT
ejpam-6316	18	1	fractional	fractional	ADJ
ejpam-6316	18	2	calculus	calculus	NOUN
ejpam-6316	18	3	,	,	PUNCT
ejpam-6316	18	4	which	which	PRON
ejpam-6316	18	5	covers	cover	VERB
ejpam-6316	18	6	differentiation	differentiation	NOUN
ejpam-6316	18	7	and	and	CCONJ
ejpam-6316	18	8	integration	integration	NOUN
ejpam-6316	18	9	beyond	beyond	ADP
ejpam-6316	18	10	whole	whole	ADJ
ejpam-6316	18	11	numbers	number	NOUN
ejpam-6316	18	12	,	,	PUNCT
ejpam-6316	18	13	forms	form	VERB
ejpam-6316	18	14	the	the	DET
ejpam-6316	18	15	mathematical	mathematical	ADJ
ejpam-6316	18	16	base	base	NOUN
ejpam-6316	18	17	of	of	ADP
ejpam-6316	18	18	fpdes	fpde	NOUN
ejpam-6316	18	19	[	[	X
ejpam-6316	18	20	1–3	1–3	NOUN
ejpam-6316	18	21	]	]	X
ejpam-6316	18	22	.	.	PUNCT
ejpam-6316	19	1	if	if	SCONJ
ejpam-6316	19	2	a	a	DET
ejpam-6316	19	3	system	system	NOUN
ejpam-6316	19	4	’s	’s	PART
ejpam-6316	19	5	behavior	behavior	NOUN
ejpam-6316	19	6	is	be	AUX
ejpam-6316	19	7	non	non	ADJ
ejpam-6316	19	8	-	-	ADJ
ejpam-6316	19	9	markovian	markovian	ADJ
ejpam-6316	19	10	,	,	PUNCT
ejpam-6316	19	11	meaning	mean	VERB
ejpam-6316	19	12	past	past	ADJ
ejpam-6316	19	13	events	event	NOUN
ejpam-6316	19	14	affect	affect	VERB
ejpam-6316	19	15	future	future	ADJ
ejpam-6316	19	16	states	state	NOUN
ejpam-6316	19	17	throughout	throughout	ADP
ejpam-6316	19	18	the	the	DET
ejpam-6316	19	19	system	system	NOUN
ejpam-6316	19	20	,	,	PUNCT
ejpam-6316	19	21	these	these	DET
ejpam-6316	19	22	fractional	fractional	ADJ
ejpam-6316	19	23	operators	operator	NOUN
ejpam-6316	19	24	are	be	AUX
ejpam-6316	19	25	beneficial	beneficial	ADJ
ejpam-6316	19	26	.	.	PUNCT
ejpam-6316	20	1	fpdes	fpde	NOUN
ejpam-6316	20	2	are	be	AUX
ejpam-6316	20	3	now	now	ADV
ejpam-6316	20	4	being	be	AUX
ejpam-6316	20	5	used	use	VERB
ejpam-6316	20	6	more	more	ADV
ejpam-6316	20	7	often	often	ADV
ejpam-6316	20	8	to	to	PART
ejpam-6316	20	9	model	model	VERB
ejpam-6316	20	10	systems	system	NOUN
ejpam-6316	20	11	that	that	PRON
ejpam-6316	20	12	recall	recall	VERB
ejpam-6316	20	13	their	their	PRON
ejpam-6316	20	14	past	past	NOUN
ejpam-6316	20	15	,	,	PUNCT
ejpam-6316	20	16	influence	influence	VERB
ejpam-6316	20	17	their	their	PRON
ejpam-6316	20	18	children	child	NOUN
ejpam-6316	20	19	genetically	genetically	ADV
ejpam-6316	20	20	,	,	PUNCT
ejpam-6316	20	21	and	and	CCONJ
ejpam-6316	20	22	have	have	VERB
ejpam-6316	20	23	different	different	ADJ
ejpam-6316	20	24	features	feature	NOUN
ejpam-6316	20	25	in	in	ADP
ejpam-6316	20	26	different	different	ADJ
ejpam-6316	20	27	parts	part	NOUN
ejpam-6316	20	28	of	of	ADP
ejpam-6316	20	29	space	space	NOUN
ejpam-6316	20	30	.	.	PUNCT
ejpam-6316	21	1	although	although	SCONJ
ejpam-6316	21	2	solving	solving	NOUN
ejpam-6316	21	3	fpdes	fpde	NOUN
ejpam-6316	21	4	is	be	AUX
ejpam-6316	21	5	a	a	DET
ejpam-6316	21	6	much	much	ADV
ejpam-6316	21	7	more	more	ADV
ejpam-6316	21	8	challenging	challenging	ADJ
ejpam-6316	21	9	task	task	NOUN
ejpam-6316	21	10	than	than	ADP
ejpam-6316	21	11	classical	classical	ADJ
ejpam-6316	21	12	pdes	pde	NOUN
ejpam-6316	21	13	,	,	PUNCT
ejpam-6316	21	14	valuable	valuable	ADJ
ejpam-6316	21	15	ways	way	NOUN
ejpam-6316	21	16	to	to	PART
ejpam-6316	21	17	solve	solve	VERB
ejpam-6316	21	18	them	they	PRON
ejpam-6316	21	19	,	,	PUNCT
ejpam-6316	21	20	such	such	ADJ
ejpam-6316	21	21	as	as	ADP
ejpam-6316	21	22	finite	finite	ADJ
ejpam-6316	21	23	difference	difference	NOUN
ejpam-6316	21	24	methods	method	NOUN
ejpam-6316	21	25	,	,	PUNCT
ejpam-6316	21	26	spectral	spectral	ADJ
ejpam-6316	21	27	methods	method	NOUN
ejpam-6316	21	28	and	and	CCONJ
ejpam-6316	21	29	variational	variational	ADJ
ejpam-6316	21	30	techniques	technique	NOUN
ejpam-6316	21	31	,	,	PUNCT
ejpam-6316	21	32	have	have	AUX
ejpam-6316	21	33	been	be	AUX
ejpam-6316	21	34	found	find	VERB
ejpam-6316	21	35	[	[	X
ejpam-6316	21	36	4–8	4–8	NOUN
ejpam-6316	21	37	]	]	X
ejpam-6316	21	38	.	.	PUNCT
ejpam-6316	22	1	many	many	ADJ
ejpam-6316	22	2	works	work	VERB
ejpam-6316	22	3	in	in	ADP
ejpam-6316	22	4	the	the	DET
ejpam-6316	22	5	field	field	NOUN
ejpam-6316	22	6	use	use	VERB
ejpam-6316	22	7	the	the	DET
ejpam-6316	22	8	korteweg	korteweg	NOUN
ejpam-6316	22	9	-	-	PUNCT
ejpam-6316	22	10	de	de	NOUN
ejpam-6316	22	11	vries	vries	PROPN
ejpam-6316	22	12	equation	equation	NOUN
ejpam-6316	22	13	,	,	PUNCT
ejpam-6316	22	14	a	a	DET
ejpam-6316	22	15	simple	simple	ADJ
ejpam-6316	22	16	-	-	PUNCT
ejpam-6316	22	17	looking	look	VERB
ejpam-6316	22	18	nonlinear	nonlinear	ADJ
ejpam-6316	22	19	partial	partial	ADJ
ejpam-6316	22	20	differential	differential	NOUN
ejpam-6316	22	21	equation	equation	NOUN
ejpam-6316	22	22	which	which	PRON
ejpam-6316	22	23	is	be	AUX
ejpam-6316	22	24	respected	respect	VERB
ejpam-6316	22	25	for	for	ADP
ejpam-6316	22	26	its	its	PRON
ejpam-6316	22	27	way	way	NOUN
ejpam-6316	22	28	of	of	ADP
ejpam-6316	22	29	balancing	balance	VERB
ejpam-6316	22	30	nonlinearity	nonlinearity	NOUN
ejpam-6316	22	31	and	and	CCONJ
ejpam-6316	22	32	dispersion	dispersion	NOUN
ejpam-6316	22	33	.	.	PUNCT
ejpam-6316	23	1	it	it	PRON
ejpam-6316	23	2	is	be	AUX
ejpam-6316	23	3	important	important	ADJ
ejpam-6316	23	4	because	because	SCONJ
ejpam-6316	23	5	it	it	PRON
ejpam-6316	23	6	can	can	AUX
ejpam-6316	23	7	reproduce	reproduce	VERB
ejpam-6316	23	8	many	many	ADJ
ejpam-6316	23	9	physical	physical	ADJ
ejpam-6316	23	10	processes	process	NOUN
ejpam-6316	23	11	from	from	ADP
ejpam-6316	23	12	shallow	shallow	ADJ
ejpam-6316	23	13	water	water	NOUN
ejpam-6316	23	14	waves	wave	NOUN
ejpam-6316	23	15	to	to	ADP
ejpam-6316	23	16	those	those	PRON
ejpam-6316	23	17	found	find	VERB
ejpam-6316	23	18	in	in	ADP
ejpam-6316	23	19	plasma	plasma	NOUN
ejpam-6316	23	20	physics	physics	NOUN
ejpam-6316	23	21	and	and	CCONJ
ejpam-6316	23	22	nonlinear	nonlinear	ADJ
ejpam-6316	23	23	optics	optic	NOUN
ejpam-6316	23	24	[	[	X
ejpam-6316	23	25	9	9	NUM
ejpam-6316	23	26	]	]	PUNCT
ejpam-6316	23	27	.	.	PUNCT
ejpam-6316	24	1	the	the	DET
ejpam-6316	24	2	idea	idea	NOUN
ejpam-6316	24	3	for	for	ADP
ejpam-6316	24	4	the	the	DET
ejpam-6316	24	5	equation	equation	NOUN
ejpam-6316	24	6	began	begin	VERB
ejpam-6316	24	7	with	with	ADP
ejpam-6316	24	8	the	the	DET
ejpam-6316	24	9	work	work	NOUN
ejpam-6316	24	10	of	of	ADP
ejpam-6316	24	11	diederik	diederik	NOUN
ejpam-6316	24	12	korteweg	korteweg	NOUN
ejpam-6316	24	13	and	and	CCONJ
ejpam-6316	24	14	gustav	gustav	PROPN
ejpam-6316	24	15	de	de	PROPN
ejpam-6316	24	16	vries	vries	PROPN
ejpam-6316	24	17	in	in	ADP
ejpam-6316	24	18	1895	1895	NUM
ejpam-6316	24	19	as	as	SCONJ
ejpam-6316	24	20	they	they	PRON
ejpam-6316	24	21	tried	try	VERB
ejpam-6316	24	22	to	to	PART
ejpam-6316	24	23	characterize	characterize	VERB
ejpam-6316	24	24	the	the	DET
ejpam-6316	24	25	movement	movement	NOUN
ejpam-6316	24	26	of	of	ADP
ejpam-6316	24	27	water	water	NOUN
ejpam-6316	24	28	waves	wave	NOUN
ejpam-6316	24	29	that	that	PRON
ejpam-6316	24	30	are	be	AUX
ejpam-6316	24	31	long	long	ADJ
ejpam-6316	24	32	and	and	CCONJ
ejpam-6316	24	33	only	only	ADV
ejpam-6316	24	34	slightly	slightly	ADV
ejpam-6316	24	35	high	high	ADJ
ejpam-6316	24	36	in	in	ADP
ejpam-6316	24	37	a	a	DET
ejpam-6316	24	38	rectangular	rectangular	ADJ
ejpam-6316	24	39	channel	channel	NOUN
ejpam-6316	24	40	.	.	PUNCT
ejpam-6316	25	1	they	they	PRON
ejpam-6316	25	2	found	find	VERB
ejpam-6316	25	3	a	a	DET
ejpam-6316	25	4	way	way	NOUN
ejpam-6316	25	5	to	to	PART
ejpam-6316	25	6	understand	understand	VERB
ejpam-6316	25	7	what	what	PRON
ejpam-6316	25	8	controls	control	VERB
ejpam-6316	25	9	these	these	DET
ejpam-6316	25	10	waves	wave	NOUN
ejpam-6316	25	11	by	by	ADP
ejpam-6316	25	12	proving	prove	VERB
ejpam-6316	25	13	that	that	SCONJ
ejpam-6316	25	14	nonlinearity	nonlinearity	NOUN
ejpam-6316	25	15	can	can	AUX
ejpam-6316	25	16	neutralize	neutralize	VERB
ejpam-6316	25	17	dispersion	dispersion	NOUN
ejpam-6316	25	18	and	and	CCONJ
ejpam-6316	25	19	cause	cause	VERB
ejpam-6316	25	20	the	the	DET
ejpam-6316	25	21	creation	creation	NOUN
ejpam-6316	25	22	of	of	ADP
ejpam-6316	25	23	solitons	soliton	NOUN
ejpam-6316	25	24	which	which	PRON
ejpam-6316	25	25	remain	remain	VERB
ejpam-6316	25	26	at	at	ADP
ejpam-6316	25	27	a	a	DET
ejpam-6316	25	28	specific	specific	ADJ
ejpam-6316	25	29	place	place	NOUN
ejpam-6316	25	30	.	.	PUNCT
ejpam-6316	26	1	solitons	soliton	NOUN
ejpam-6316	26	2	which	which	PRON
ejpam-6316	26	3	travel	travel	VERB
ejpam-6316	26	4	without	without	ADP
ejpam-6316	26	5	changing	change	VERB
ejpam-6316	26	6	shape	shape	NOUN
ejpam-6316	26	7	and	and	CCONJ
ejpam-6316	26	8	bounce	bounce	VERB
ejpam-6316	26	9	off	off	ADP
ejpam-6316	26	10	other	other	ADJ
ejpam-6316	26	11	solitons	soliton	NOUN
ejpam-6316	26	12	with	with	ADP
ejpam-6316	26	13	no	no	DET
ejpam-6316	26	14	energy	energy	NOUN
ejpam-6316	26	15	loss	loss	NOUN
ejpam-6316	26	16	,	,	PUNCT
ejpam-6316	26	17	break	break	VERB
ejpam-6316	26	18	away	away	ADV
ejpam-6316	26	19	from	from	ADP
ejpam-6316	26	20	how	how	SCONJ
ejpam-6316	26	21	linear	linear	ADJ
ejpam-6316	26	22	waves	wave	NOUN
ejpam-6316	26	23	are	be	AUX
ejpam-6316	26	24	meant	mean	VERB
ejpam-6316	26	25	to	to	PART
ejpam-6316	26	26	operate	operate	VERB
ejpam-6316	26	27	[	[	X
ejpam-6316	26	28	10	10	NUM
ejpam-6316	26	29	]	]	PUNCT
ejpam-6316	26	30	.	.	PUNCT
ejpam-6316	27	1	the	the	DET
ejpam-6316	27	2	kdv	kdv	NOUN
ejpam-6316	27	3	equation	equation	NOUN
ejpam-6316	27	4	looks	look	VERB
ejpam-6316	27	5	easy	easy	ADJ
ejpam-6316	27	6	to	to	PART
ejpam-6316	27	7	understand	understand	VERB
ejpam-6316	27	8	,	,	PUNCT
ejpam-6316	27	9	but	but	CCONJ
ejpam-6316	27	10	it	it	PRON
ejpam-6316	27	11	has	have	VERB
ejpam-6316	27	12	a	a	DET
ejpam-6316	27	13	lot	lot	NOUN
ejpam-6316	27	14	of	of	ADP
ejpam-6316	27	15	interesting	interesting	ADJ
ejpam-6316	27	16	details	detail	NOUN
ejpam-6316	27	17	and	and	CCONJ
ejpam-6316	27	18	answers	answer	NOUN
ejpam-6316	27	19	.	.	PUNCT
ejpam-6316	28	1	integrability	integrability	NOUN
ejpam-6316	28	2	is	be	AUX
ejpam-6316	28	3	an	an	DET
ejpam-6316	28	4	unusual	unusual	ADJ
ejpam-6316	28	5	trait	trait	NOUN
ejpam-6316	28	6	among	among	ADP
ejpam-6316	28	7	nonlinear	nonlinear	ADJ
ejpam-6316	28	8	partial	partial	ADJ
ejpam-6316	28	9	differential	differential	NOUN
ejpam-6316	28	10	equations	equation	NOUN
ejpam-6316	28	11	which	which	PRON
ejpam-6316	28	12	means	mean	VERB
ejpam-6316	28	13	the	the	DET
ejpam-6316	28	14	inverse	inverse	NOUN
ejpam-6316	28	15	scattering	scattering	NOUN
ejpam-6316	28	16	transform	transform	NOUN
ejpam-6316	28	17	can	can	AUX
ejpam-6316	28	18	be	be	AUX
ejpam-6316	28	19	applied	apply	VERB
ejpam-6316	28	20	to	to	PART
ejpam-6316	28	21	precisely	precisely	ADV
ejpam-6316	28	22	solve	solve	VERB
ejpam-6316	28	23	such	such	ADJ
ejpam-6316	28	24	equations	equation	NOUN
ejpam-6316	28	25	.	.	PUNCT
ejpam-6316	29	1	the	the	DET
ejpam-6316	29	2	inverse	inverse	NOUN
ejpam-6316	29	3	scattering	scattering	NOUN
ejpam-6316	29	4	transform	transform	NOUN
ejpam-6316	29	5	,	,	PUNCT
ejpam-6316	29	6	developed	develop	VERB
ejpam-6316	29	7	by	by	ADP
ejpam-6316	29	8	gardner	gardner	NOUN
ejpam-6316	29	9	,	,	PUNCT
ejpam-6316	29	10	greene	greene	PROPN
ejpam-6316	29	11	,	,	PUNCT
ejpam-6316	29	12	kruskal	kruskal	NOUN
ejpam-6316	29	13	and	and	CCONJ
ejpam-6316	29	14	miura	miura	PROPN
ejpam-6316	29	15	in	in	ADP
ejpam-6316	29	16	the	the	DET
ejpam-6316	29	17	1960s	1960	NOUN
ejpam-6316	29	18	,	,	PUNCT
ejpam-6316	29	19	enables	enable	VERB
ejpam-6316	29	20	us	we	PRON
ejpam-6316	29	21	to	to	PART
ejpam-6316	29	22	solve	solve	VERB
ejpam-6316	29	23	the	the	DET
ejpam-6316	29	24	kdv	kdv	NOUN
ejpam-6316	29	25	equation	equation	NOUN
ejpam-6316	29	26	as	as	ADP
ejpam-6316	29	27	a	a	DET
ejpam-6316	29	28	linear	linear	ADJ
ejpam-6316	29	29	problem	problem	NOUN
ejpam-6316	29	30	through	through	ADP
ejpam-6316	29	31	standard	standard	ADJ
ejpam-6316	29	32	approaches	approach	NOUN
ejpam-6316	29	33	.	.	PUNCT
ejpam-6316	30	1	the	the	DET
ejpam-6316	30	2	results	result	NOUN
ejpam-6316	30	3	from	from	ADP
ejpam-6316	30	4	the	the	DET
ejpam-6316	30	5	linear	linear	ADJ
ejpam-6316	30	6	solutions	solution	NOUN
ejpam-6316	30	7	can	can	AUX
ejpam-6316	30	8	be	be	AUX
ejpam-6316	30	9	used	use	VERB
ejpam-6316	30	10	to	to	PART
ejpam-6316	30	11	return	return	VERB
ejpam-6316	30	12	solutions	solution	NOUN
ejpam-6316	30	13	to	to	ADP
ejpam-6316	30	14	the	the	DET
ejpam-6316	30	15	kdv	kdv	NOUN
ejpam-6316	30	16	equation	equation	NOUN
ejpam-6316	30	17	,	,	PUNCT
ejpam-6316	30	18	showing	show	VERB
ejpam-6316	30	19	the	the	DET
ejpam-6316	30	20	soliton	soliton	NOUN
ejpam-6316	30	21	patterns	pattern	NOUN
ejpam-6316	30	22	and	and	CCONJ
ejpam-6316	30	23	their	their	PRON
ejpam-6316	30	24	interactions	interaction	NOUN
ejpam-6316	30	25	with	with	ADP
ejpam-6316	30	26	each	each	DET
ejpam-6316	30	27	other	other	ADJ
ejpam-6316	30	28	.	.	PUNCT
ejpam-6316	31	1	because	because	SCONJ
ejpam-6316	31	2	the	the	DET
ejpam-6316	31	3	kdv	kdv	NOUN
ejpam-6316	31	4	equation	equation	NOUN
ejpam-6316	31	5	is	be	AUX
ejpam-6316	31	6	integrable	integrable	ADJ
ejpam-6316	31	7	,	,	PUNCT
ejpam-6316	31	8	it	it	PRON
ejpam-6316	31	9	has	have	VERB
ejpam-6316	31	10	many	many	ADJ
ejpam-6316	31	11	conserved	conserved	ADJ
ejpam-6316	31	12	quantities	quantity	NOUN
ejpam-6316	31	13	.	.	PUNCT
ejpam-6316	32	1	these	these	DET
ejpam-6316	32	2	quantities	quantity	NOUN
ejpam-6316	32	3	are	be	AUX
ejpam-6316	32	4	very	very	ADV
ejpam-6316	32	5	important	important	ADJ
ejpam-6316	32	6	for	for	ADP
ejpam-6316	32	7	the	the	DET
ejpam-6316	32	8	stability	stability	NOUN
ejpam-6316	32	9	and	and	CCONJ
ejpam-6316	32	10	extended	extended	ADJ
ejpam-6316	32	11	behavior	behavior	NOUN
ejpam-6316	32	12	of	of	ADP
ejpam-6316	32	13	its	its	PRON
ejpam-6316	32	14	solutions	solution	NOUN
ejpam-6316	32	15	[	[	X
ejpam-6316	32	16	11–14	11–14	NUM
ejpam-6316	32	17	]	]	PUNCT
ejpam-6316	32	18	.	.	PUNCT
ejpam-6316	33	1	residual	residual	ADJ
ejpam-6316	33	2	power	power	NOUN
ejpam-6316	33	3	series	series	PROPN
ejpam-6316	33	4	natural	natural	ADJ
ejpam-6316	33	5	transform	transform	NOUN
ejpam-6316	33	6	(	(	PUNCT
ejpam-6316	33	7	rpsnt	rpsnt	NOUN
ejpam-6316	33	8	)	)	PUNCT
ejpam-6316	33	9	is	be	AUX
ejpam-6316	33	10	a	a	DET
ejpam-6316	33	11	method	method	NOUN
ejpam-6316	33	12	that	that	PRON
ejpam-6316	33	13	allows	allow	VERB
ejpam-6316	33	14	for	for	ADP
ejpam-6316	33	15	problemsolving	problemsolving	NOUN
ejpam-6316	33	16	involving	involve	VERB
ejpam-6316	33	17	crucial	crucial	ADJ
ejpam-6316	33	18	nonlinear	nonlinear	ADJ
ejpam-6316	33	19	and	and	CCONJ
ejpam-6316	33	20	fractional	fractional	ADJ
ejpam-6316	33	21	differential	differential	ADJ
ejpam-6316	33	22	equations	equation	NOUN
ejpam-6316	33	23	.	.	PUNCT
ejpam-6316	34	1	using	use	VERB
ejpam-6316	34	2	this	this	DET
ejpam-6316	34	3	technique	technique	NOUN
ejpam-6316	34	4	,	,	PUNCT
ejpam-6316	34	5	solutions	solution	NOUN
ejpam-6316	34	6	to	to	ADP
ejpam-6316	34	7	difficult	difficult	ADJ
ejpam-6316	34	8	differential	differential	ADJ
ejpam-6316	34	9	equations	equation	NOUN
ejpam-6316	34	10	can	can	AUX
ejpam-6316	34	11	be	be	AUX
ejpam-6316	34	12	found	find	VERB
ejpam-6316	34	13	more	more	ADV
ejpam-6316	34	14	easily	easily	ADV
ejpam-6316	34	15	than	than	ADP
ejpam-6316	34	16	with	with	ADP
ejpam-6316	34	17	regular	regular	ADJ
ejpam-6316	34	18	methods	method	NOUN
ejpam-6316	34	19	.	.	PUNCT
ejpam-6316	35	1	the	the	DET
ejpam-6316	35	2	method	method	NOUN
ejpam-6316	35	3	centres	centre	VERB
ejpam-6316	35	4	on	on	ADP
ejpam-6316	35	5	converting	convert	VERB
ejpam-6316	35	6	the	the	DET
ejpam-6316	35	7	original	original	ADJ
ejpam-6316	35	8	problem	problem	NOUN
ejpam-6316	35	9	to	to	ADP
ejpam-6316	35	10	easy	easy	ADJ
ejpam-6316	35	11	-	-	PUNCT
ejpam-6316	35	12	to	to	PART
ejpam-6316	35	13	-	-	PUNCT
ejpam-6316	35	14	manage	manage	VERB
ejpam-6316	35	15	terms	term	NOUN
ejpam-6316	35	16	with	with	ADP
ejpam-6316	35	17	natural	natural	ADJ
ejpam-6316	35	18	transforms	transform	NOUN
ejpam-6316	35	19	and	and	CCONJ
ejpam-6316	35	20	completing	complete	VERB
ejpam-6316	35	21	the	the	DET
ejpam-6316	35	22	solution	solution	NOUN
ejpam-6316	35	23	using	use	VERB
ejpam-6316	35	24	an	an	DET
ejpam-6316	35	25	approximation	approximation	NOUN
ejpam-6316	35	26	with	with	ADP
ejpam-6316	35	27	a	a	DET
ejpam-6316	35	28	series	series	NOUN
ejpam-6316	35	29	.	.	PUNCT
ejpam-6316	36	1	the	the	DET
ejpam-6316	36	2	technique	technique	NOUN
ejpam-6316	36	3	is	be	AUX
ejpam-6316	36	4	well	well	ADV
ejpam-6316	36	5	-	-	PUNCT
ejpam-6316	36	6	suited	suited	ADJ
ejpam-6316	36	7	for	for	ADP
ejpam-6316	36	8	addressing	address	VERB
ejpam-6316	36	9	nonlinear	nonlinear	ADJ
ejpam-6316	36	10	and	and	CCONJ
ejpam-6316	36	11	memory	memory	NOUN
ejpam-6316	36	12	-	-	PUNCT
ejpam-6316	36	13	related	relate	VERB
ejpam-6316	36	14	differential	differential	ADJ
ejpam-6316	36	15	equations	equation	NOUN
ejpam-6316	36	16	,	,	PUNCT
ejpam-6316	36	17	along	along	ADP
ejpam-6316	36	18	with	with	ADP
ejpam-6316	36	19	various	various	ADJ
ejpam-6316	36	20	other	other	ADJ
ejpam-6316	36	21	challenging	challenging	ADJ
ejpam-6316	36	22	behaviors	behavior	NOUN
ejpam-6316	36	23	.	.	PUNCT
ejpam-6316	37	1	physics	physics	NOUN
ejpam-6316	37	2	,	,	PUNCT
ejpam-6316	37	3	engineering	engineering	NOUN
ejpam-6316	37	4	and	and	CCONJ
ejpam-6316	37	5	applied	apply	VERB
ejpam-6316	37	6	mathematics	mathematic	NOUN
ejpam-6316	37	7	use	use	VERB
ejpam-6316	37	8	this	this	DET
ejpam-6316	37	9	method	method	NOUN
ejpam-6316	37	10	extensively	extensively	ADV
ejpam-6316	37	11	,	,	PUNCT
ejpam-6316	37	12	as	as	SCONJ
ejpam-6316	37	13	the	the	DET
ejpam-6316	37	14	equations	equation	NOUN
ejpam-6316	37	15	describing	describe	VERB
ejpam-6316	37	16	those	those	DET
ejpam-6316	37	17	problems	problem	NOUN
ejpam-6316	37	18	often	often	ADV
ejpam-6316	37	19	do	do	AUX
ejpam-6316	37	20	not	not	PART
ejpam-6316	37	21	have	have	VERB
ejpam-6316	37	22	quick	quick	ADJ
ejpam-6316	37	23	,	,	PUNCT
ejpam-6316	37	24	exact	exact	ADJ
ejpam-6316	37	25	solutions	solution	NOUN
ejpam-6316	37	26	.	.	PUNCT
ejpam-6316	38	1	with	with	ADP
ejpam-6316	38	2	the	the	DET
ejpam-6316	38	3	help	help	NOUN
ejpam-6316	38	4	of	of	ADP
ejpam-6316	38	5	power	power	NOUN
ejpam-6316	38	6	series	series	NOUN
ejpam-6316	38	7	,	,	PUNCT
ejpam-6316	38	8	the	the	DET
ejpam-6316	38	9	rpsnt	rpsnt	NOUN
ejpam-6316	38	10	method	method	NOUN
ejpam-6316	38	11	allows	allow	VERB
ejpam-6316	38	12	for	for	ADP
ejpam-6316	38	13	fast	fast	ADJ
ejpam-6316	38	14	and	and	CCONJ
ejpam-6316	38	15	helpful	helpful	ADJ
ejpam-6316	38	16	findings	finding	NOUN
ejpam-6316	38	17	about	about	ADP
ejpam-6316	38	18	the	the	DET
ejpam-6316	38	19	system	system	NOUN
ejpam-6316	38	20	’s	’s	PART
ejpam-6316	38	21	performance	performance	NOUN
ejpam-6316	38	22	.	.	PUNCT
ejpam-6316	39	1	furthermore	furthermore	ADV
ejpam-6316	39	2	,	,	PUNCT
ejpam-6316	39	3	because	because	SCONJ
ejpam-6316	39	4	the	the	DET
ejpam-6316	39	5	technique	technique	NOUN
ejpam-6316	39	6	can	can	AUX
ejpam-6316	39	7	be	be	AUX
ejpam-6316	39	8	integrated	integrate	VERB
ejpam-6316	39	9	with	with	ADP
ejpam-6316	39	10	other	other	ADJ
ejpam-6316	39	11	computation	computation	NOUN
ejpam-6316	39	12	methods	method	NOUN
ejpam-6316	39	13	,	,	PUNCT
ejpam-6316	39	14	it	it	PRON
ejpam-6316	39	15	supports	support	VERB
ejpam-6316	39	16	both	both	PRON
ejpam-6316	39	17	laboratory	laboratory	NOUN
ejpam-6316	39	18	and	and	CCONJ
ejpam-6316	39	19	theoretical	theoretical	ADJ
ejpam-6316	39	20	work	work	NOUN
ejpam-6316	39	21	[	[	X
ejpam-6316	39	22	15–19	15–19	NOUN
ejpam-6316	39	23	]	]	PUNCT
ejpam-6316	39	24	.	.	PUNCT
ejpam-6316	40	1	n.	n.	PROPN
ejpam-6316	40	2	iqbal	iqbal	PROPN
ejpam-6316	40	3	et	et	PROPN
ejpam-6316	40	4	al	al	PROPN
ejpam-6316	40	5	.	.	PUNCT
ejpam-6316	40	6	/	/	SYM
ejpam-6316	40	7	eur	eur	PROPN
ejpam-6316	40	8	.	.	PUNCT
ejpam-6316	41	1	j.	j.	PROPN
ejpam-6316	41	2	pure	pure	PROPN
ejpam-6316	41	3	appl	appl	PROPN
ejpam-6316	41	4	.	.	PROPN
ejpam-6316	41	5	math	math	PROPN
ejpam-6316	41	6	,	,	PUNCT
ejpam-6316	41	7	18	18	NUM
ejpam-6316	41	8	(	(	PUNCT
ejpam-6316	41	9	3	3	NUM
ejpam-6316	41	10	)	)	PUNCT
ejpam-6316	41	11	(	(	PUNCT
ejpam-6316	41	12	2025	2025	NUM
ejpam-6316	41	13	)	)	PUNCT
ejpam-6316	41	14	,	,	PUNCT
ejpam-6316	41	15	6316	6316	NUM
ejpam-6316	41	16	3	3	NUM
ejpam-6316	41	17	of	of	ADP
ejpam-6316	41	18	21	21	NUM
ejpam-6316	41	19	nint	nint	NOUN
ejpam-6316	41	20	is	be	AUX
ejpam-6316	41	21	a	a	DET
ejpam-6316	41	22	modern	modern	ADJ
ejpam-6316	41	23	way	way	NOUN
ejpam-6316	41	24	to	to	PART
ejpam-6316	41	25	solve	solve	VERB
ejpam-6316	41	26	a	a	DET
ejpam-6316	41	27	wide	wide	ADJ
ejpam-6316	41	28	variety	variety	NOUN
ejpam-6316	41	29	of	of	ADP
ejpam-6316	41	30	complex	complex	ADJ
ejpam-6316	41	31	differential	differential	ADJ
ejpam-6316	41	32	equations	equation	NOUN
ejpam-6316	41	33	,	,	PUNCT
ejpam-6316	41	34	most	most	ADV
ejpam-6316	41	35	commonly	commonly	ADV
ejpam-6316	41	36	those	those	PRON
ejpam-6316	41	37	with	with	ADP
ejpam-6316	41	38	nonlinearities	nonlinearitie	NOUN
ejpam-6316	41	39	or	or	CCONJ
ejpam-6316	41	40	fractional	fractional	ADJ
ejpam-6316	41	41	parts	part	NOUN
ejpam-6316	41	42	.	.	PUNCT
ejpam-6316	42	1	the	the	DET
ejpam-6316	42	2	method	method	NOUN
ejpam-6316	42	3	connects	connect	VERB
ejpam-6316	42	4	iterative	iterative	NOUN
ejpam-6316	42	5	techniques	technique	NOUN
ejpam-6316	42	6	with	with	ADP
ejpam-6316	42	7	natural	natural	ADJ
ejpam-6316	42	8	transforms	transform	NOUN
ejpam-6316	42	9	,	,	PUNCT
ejpam-6316	42	10	for	for	ADP
ejpam-6316	42	11	example	example	NOUN
ejpam-6316	42	12	,	,	PUNCT
ejpam-6316	42	13	the	the	DET
ejpam-6316	42	14	laplace	laplace	NOUN
ejpam-6316	42	15	and	and	CCONJ
ejpam-6316	42	16	fourier	fourier	NOUN
ejpam-6316	42	17	transforms	transform	VERB
ejpam-6316	42	18	,	,	PUNCT
ejpam-6316	42	19	so	so	SCONJ
ejpam-6316	42	20	that	that	SCONJ
ejpam-6316	42	21	approximating	approximate	VERB
ejpam-6316	42	22	solutions	solution	NOUN
ejpam-6316	42	23	becomes	become	VERB
ejpam-6316	42	24	both	both	CCONJ
ejpam-6316	42	25	more	more	ADV
ejpam-6316	42	26	accurate	accurate	ADJ
ejpam-6316	42	27	and	and	CCONJ
ejpam-6316	42	28	efficient	efficient	ADJ
ejpam-6316	42	29	.	.	PUNCT
ejpam-6316	43	1	applying	apply	VERB
ejpam-6316	43	2	the	the	DET
ejpam-6316	43	3	natural	natural	ADJ
ejpam-6316	43	4	transform	transform	NOUN
ejpam-6316	43	5	to	to	ADP
ejpam-6316	43	6	the	the	DET
ejpam-6316	43	7	differential	differential	ADJ
ejpam-6316	43	8	equation	equation	NOUN
ejpam-6316	43	9	repeatedly	repeatedly	ADV
ejpam-6316	43	10	and	and	CCONJ
ejpam-6316	43	11	then	then	ADV
ejpam-6316	43	12	updating	update	VERB
ejpam-6316	43	13	the	the	DET
ejpam-6316	43	14	solution	solution	NOUN
ejpam-6316	43	15	each	each	DET
ejpam-6316	43	16	time	time	NOUN
ejpam-6316	43	17	forms	form	VERB
ejpam-6316	43	18	the	the	DET
ejpam-6316	43	19	main	main	ADJ
ejpam-6316	43	20	idea	idea	NOUN
ejpam-6316	43	21	behind	behind	ADP
ejpam-6316	43	22	the	the	DET
ejpam-6316	43	23	nint	nint	NOUN
ejpam-6316	43	24	method	method	NOUN
ejpam-6316	43	25	.	.	PUNCT
ejpam-6316	44	1	with	with	ADP
ejpam-6316	44	2	this	this	DET
ejpam-6316	44	3	approach	approach	NOUN
ejpam-6316	44	4	,	,	PUNCT
ejpam-6316	44	5	the	the	DET
ejpam-6316	44	6	method	method	NOUN
ejpam-6316	44	7	can	can	AUX
ejpam-6316	44	8	address	address	VERB
ejpam-6316	44	9	linear	linear	NOUN
ejpam-6316	44	10	and	and	CCONJ
ejpam-6316	44	11	nonlinear	nonlinear	ADJ
ejpam-6316	44	12	equations	equation	NOUN
ejpam-6316	44	13	,	,	PUNCT
ejpam-6316	44	14	providing	provide	VERB
ejpam-6316	44	15	a	a	DET
ejpam-6316	44	16	useful	useful	ADJ
ejpam-6316	44	17	solution	solution	NOUN
ejpam-6316	44	18	for	for	ADP
ejpam-6316	44	19	equations	equation	NOUN
ejpam-6316	44	20	that	that	PRON
ejpam-6316	44	21	are	be	AUX
ejpam-6316	44	22	difficult	difficult	ADJ
ejpam-6316	44	23	to	to	PART
ejpam-6316	44	24	solve	solve	VERB
ejpam-6316	44	25	in	in	ADP
ejpam-6316	44	26	other	other	ADJ
ejpam-6316	44	27	ways	way	NOUN
ejpam-6316	44	28	.	.	PUNCT
ejpam-6316	45	1	a	a	DET
ejpam-6316	45	2	major	major	ADJ
ejpam-6316	45	3	advantage	advantage	NOUN
ejpam-6316	45	4	of	of	ADP
ejpam-6316	45	5	the	the	DET
ejpam-6316	45	6	nint	nint	NOUN
ejpam-6316	45	7	method	method	NOUN
ejpam-6316	45	8	is	be	AUX
ejpam-6316	45	9	that	that	SCONJ
ejpam-6316	45	10	it	it	PRON
ejpam-6316	45	11	treats	treat	VERB
ejpam-6316	45	12	complicated	complicated	ADJ
ejpam-6316	45	13	and	and	CCONJ
ejpam-6316	45	14	unpredictable	unpredictable	ADJ
ejpam-6316	45	15	equations	equation	NOUN
ejpam-6316	45	16	commonly	commonly	ADV
ejpam-6316	45	17	used	use	VERB
ejpam-6316	45	18	in	in	ADP
ejpam-6316	45	19	physics	physics	NOUN
ejpam-6316	45	20	,	,	PUNCT
ejpam-6316	45	21	engineering	engineering	NOUN
ejpam-6316	45	22	and	and	CCONJ
ejpam-6316	45	23	mathematics	mathematic	NOUN
ejpam-6316	45	24	.	.	PUNCT
ejpam-6316	46	1	by	by	ADP
ejpam-6316	46	2	carrying	carry	VERB
ejpam-6316	46	3	out	out	ADP
ejpam-6316	46	4	the	the	DET
ejpam-6316	46	5	different	different	ADJ
ejpam-6316	46	6	parts	part	NOUN
ejpam-6316	46	7	of	of	ADP
ejpam-6316	46	8	the	the	DET
ejpam-6316	46	9	method	method	NOUN
ejpam-6316	46	10	again	again	ADV
ejpam-6316	46	11	and	and	CCONJ
ejpam-6316	46	12	again	again	ADV
ejpam-6316	46	13	,	,	PUNCT
ejpam-6316	46	14	the	the	DET
ejpam-6316	46	15	solution	solution	NOUN
ejpam-6316	46	16	gets	get	VERB
ejpam-6316	46	17	better	well	ADJ
ejpam-6316	46	18	and	and	CCONJ
ejpam-6316	46	19	finally	finally	ADV
ejpam-6316	46	20	comes	come	VERB
ejpam-6316	46	21	close	close	ADV
ejpam-6316	46	22	to	to	ADP
ejpam-6316	46	23	being	be	AUX
ejpam-6316	46	24	the	the	DET
ejpam-6316	46	25	true	true	ADJ
ejpam-6316	46	26	solution	solution	NOUN
ejpam-6316	46	27	.	.	PUNCT
ejpam-6316	47	1	such	such	DET
ejpam-6316	47	2	a	a	DET
ejpam-6316	47	3	method	method	NOUN
ejpam-6316	47	4	is	be	AUX
ejpam-6316	47	5	most	most	ADV
ejpam-6316	47	6	valuable	valuable	ADJ
ejpam-6316	47	7	when	when	SCONJ
ejpam-6316	47	8	conventional	conventional	ADJ
ejpam-6316	47	9	methods	method	NOUN
ejpam-6316	47	10	have	have	VERB
ejpam-6316	47	11	difficulty	difficulty	NOUN
ejpam-6316	47	12	with	with	ADP
ejpam-6316	47	13	chaotic	chaotic	ADJ
ejpam-6316	47	14	actions	action	NOUN
ejpam-6316	47	15	,	,	PUNCT
ejpam-6316	47	16	complex	complex	ADJ
ejpam-6316	47	17	shapes	shape	NOUN
ejpam-6316	47	18	or	or	CCONJ
ejpam-6316	47	19	unusual	unusual	ADJ
ejpam-6316	47	20	boundaries	boundary	NOUN
ejpam-6316	47	21	.	.	PUNCT
ejpam-6316	48	1	through	through	ADP
ejpam-6316	48	2	the	the	DET
ejpam-6316	48	3	new	new	ADJ
ejpam-6316	48	4	iteration	iteration	NOUN
ejpam-6316	48	5	natural	natural	ADJ
ejpam-6316	48	6	transform	transform	NOUN
ejpam-6316	48	7	technique	technique	NOUN
ejpam-6316	48	8	,	,	PUNCT
ejpam-6316	48	9	numerical	numerical	ADJ
ejpam-6316	48	10	analysis	analysis	NOUN
ejpam-6316	48	11	is	be	AUX
ejpam-6316	48	12	given	give	VERB
ejpam-6316	48	13	a	a	DET
ejpam-6316	48	14	flexible	flexible	ADJ
ejpam-6316	48	15	and	and	CCONJ
ejpam-6316	48	16	effective	effective	ADJ
ejpam-6316	48	17	way	way	NOUN
ejpam-6316	48	18	to	to	PART
ejpam-6316	48	19	deal	deal	VERB
ejpam-6316	48	20	with	with	ADP
ejpam-6316	48	21	different	different	ADJ
ejpam-6316	48	22	kinds	kind	NOUN
ejpam-6316	48	23	of	of	ADP
ejpam-6316	48	24	challenging	challenge	VERB
ejpam-6316	48	25	differential	differential	ADJ
ejpam-6316	48	26	equations	equation	NOUN
ejpam-6316	48	27	[	[	X
ejpam-6316	48	28	20–25	20–25	NUM
ejpam-6316	48	29	]	]	PUNCT
ejpam-6316	48	30	.	.	PUNCT
ejpam-6316	49	1	2	2	X
ejpam-6316	49	2	.	.	X
ejpam-6316	49	3	basic	basic	ADJ
ejpam-6316	49	4	definitions	definition	NOUN
ejpam-6316	49	5	2.1	2.1	NUM
ejpam-6316	49	6	.	.	PUNCT
ejpam-6316	50	1	definition	definition	NOUN
ejpam-6316	50	2	the	the	DET
ejpam-6316	50	3	fractional	fractional	ADJ
ejpam-6316	50	4	rieman	rieman	NOUN
ejpam-6316	50	5	-	-	PUNCT
ejpam-6316	50	6	liouville	liouville	NOUN
ejpam-6316	50	7	integral	integral	ADJ
ejpam-6316	50	8	of	of	ADP
ejpam-6316	50	9	order	order	NOUN
ejpam-6316	50	10	a	a	DET
ejpam-6316	50	11	p	p	X
ejpam-6316	50	12	∈	∈	PROPN
ejpam-6316	50	13	r+	r+	NOUN
ejpam-6316	50	14	of	of	ADP
ejpam-6316	50	15	a	a	DET
ejpam-6316	50	16	function	function	NOUN
ejpam-6316	50	17	h(γ	h(γ	NOUN
ejpam-6316	50	18	)	)	PUNCT
ejpam-6316	50	19	∈	∈	PROPN
ejpam-6316	50	20	l([0	l([0	VERB
ejpam-6316	50	21	,	,	PUNCT
ejpam-6316	50	22	1],r	1],r	NUM
ejpam-6316	50	23	)	)	PUNCT
ejpam-6316	50	24	is	be	AUX
ejpam-6316	50	25	given	give	VERB
ejpam-6316	50	26	as	as	ADP
ejpam-6316	50	27	[	[	X
ejpam-6316	50	28	26–28	26–28	X
ejpam-6316	50	29	]	]	X
ejpam-6316	50	30	ip0h(γ	ip0h(γ	PROPN
ejpam-6316	50	31	)	)	PUNCT
ejpam-6316	50	32	=	=	SYM
ejpam-6316	50	33	1	1	NUM
ejpam-6316	50	34	γ(p	γ(p	NUM
ejpam-6316	50	35	)	)	PUNCT
ejpam-6316	50	36	∫	∫	PROPN
ejpam-6316	51	1	σ	σ	PROPN
ejpam-6316	51	2	0	0	NUM
ejpam-6316	51	3	(	(	PUNCT
ejpam-6316	51	4	σ	σ	NOUN
ejpam-6316	51	5	−	−	PROPN
ejpam-6316	51	6	s)p−1h(s)ds	s)p−1h(s)ds	ADV
ejpam-6316	51	7	,	,	PUNCT
ejpam-6316	51	8	provided	provide	VERB
ejpam-6316	51	9	that	that	SCONJ
ejpam-6316	51	10	the	the	DET
ejpam-6316	51	11	integral	integral	NOUN
ejpam-6316	51	12	on	on	ADP
ejpam-6316	51	13	the	the	DET
ejpam-6316	51	14	right	right	ADJ
ejpam-6316	51	15	side	side	NOUN
ejpam-6316	51	16	converges	converge	NOUN
ejpam-6316	51	17	.	.	PUNCT
ejpam-6316	52	1	2.2	2.2	NUM
ejpam-6316	52	2	.	.	PUNCT
ejpam-6316	53	1	definition	definition	PROPN
ejpam-6316	53	2	caputo	caputo	PROPN
ejpam-6316	53	3	’s	’s	PART
ejpam-6316	53	4	fractional	fractional	ADJ
ejpam-6316	53	5	order	order	NOUN
ejpam-6316	53	6	derivative	derivative	NOUN
ejpam-6316	53	7	of	of	ADP
ejpam-6316	53	8	a	a	DET
ejpam-6316	53	9	function	function	NOUN
ejpam-6316	53	10	h	h	NOUN
ejpam-6316	53	11	∈	∈	PROPN
ejpam-6316	53	12	cn−1	cn−1	VERB
ejpam-6316	53	13	with	with	ADP
ejpam-6316	53	14	n	n	PRON
ejpam-6316	53	15	∈	∈	PROPN
ejpam-6316	53	16	n∪{0	n∪{0	NOUN
ejpam-6316	53	17	}	}	PUNCT
ejpam-6316	53	18	is	be	AUX
ejpam-6316	53	19	expressed	express	VERB
ejpam-6316	53	20	as	as	ADP
ejpam-6316	53	21	[	[	X
ejpam-6316	53	22	27	27	NUM
ejpam-6316	53	23	,	,	PUNCT
ejpam-6316	53	24	28	28	NUM
ejpam-6316	53	25	]	]	X
ejpam-6316	53	26	dp	dp	NOUN
ejpam-6316	53	27	σh(σ	σh(σ	NOUN
ejpam-6316	53	28	)	)	PUNCT
ejpam-6316	54	1	=	=	SYM
ejpam-6316	54	2	{	{	PUNCT
ejpam-6316	54	3	in−pf	in−pf	X
ejpam-6316	54	4	(	(	PUNCT
ejpam-6316	54	5	n	n	CCONJ
ejpam-6316	54	6	)	)	PUNCT
ejpam-6316	54	7	,	,	PUNCT
ejpam-6316	54	8	n−	n−	NOUN
ejpam-6316	54	9	1	1	NUM
ejpam-6316	54	10	<	<	X
ejpam-6316	54	11	p	p	X
ejpam-6316	54	12	≤	≤	NUM
ejpam-6316	54	13	n	n	CCONJ
ejpam-6316	54	14	,	,	PUNCT
ejpam-6316	54	15	n	n	PROPN
ejpam-6316	54	16	∈	∈	PROPN
ejpam-6316	54	17	n	n	CCONJ
ejpam-6316	54	18	,	,	PUNCT
ejpam-6316	54	19	dn	dn	NOUN
ejpam-6316	54	20	dσnh(σ	dσnh(σ	PROPN
ejpam-6316	54	21	)	)	PUNCT
ejpam-6316	54	22	,	,	PUNCT
ejpam-6316	54	23	p	p	NOUN
ejpam-6316	54	24	=	=	SYM
ejpam-6316	54	25	n	n	CCONJ
ejpam-6316	54	26	,	,	PUNCT
ejpam-6316	54	27	n	n	PROPN
ejpam-6316	54	28	∈	∈	PROPN
ejpam-6316	54	29	n.	n.	NOUN
ejpam-6316	54	30	2.3	2.3	NUM
ejpam-6316	54	31	.	.	PUNCT
ejpam-6316	55	1	definition	definition	NOUN
ejpam-6316	55	2	a	a	DET
ejpam-6316	55	3	two	two	NUM
ejpam-6316	55	4	parameter	parameter	NOUN
ejpam-6316	55	5	mittag	mittag	ADJ
ejpam-6316	55	6	-	-	PUNCT
ejpam-6316	55	7	leffler	leffler	NOUN
ejpam-6316	55	8	function	function	NOUN
ejpam-6316	55	9	is	be	AUX
ejpam-6316	55	10	given	give	VERB
ejpam-6316	55	11	by	by	ADP
ejpam-6316	55	12	[	[	X
ejpam-6316	55	13	27	27	NUM
ejpam-6316	55	14	,	,	PUNCT
ejpam-6316	55	15	28	28	NUM
ejpam-6316	55	16	]	]	X
ejpam-6316	55	17	:	:	PUNCT
ejpam-6316	55	18	ep	ep	PROPN
ejpam-6316	55	19	,	,	PUNCT
ejpam-6316	55	20	β(σ	β(σ	PROPN
ejpam-6316	55	21	)	)	PUNCT
ejpam-6316	55	22	=	=	PUNCT
ejpam-6316	56	1	∞∑	∞∑	NUM
ejpam-6316	56	2	k=0	k=0	PUNCT
ejpam-6316	56	3	σk	σk	ADP
ejpam-6316	56	4	γ(kp+	γ(kp+	X
ejpam-6316	56	5	β	β	X
ejpam-6316	56	6	)	)	PUNCT
ejpam-6316	56	7	.	.	PUNCT
ejpam-6316	57	1	for	for	ADP
ejpam-6316	57	2	p	p	NOUN
ejpam-6316	57	3	=	=	PUNCT
ejpam-6316	57	4	β	β	X
ejpam-6316	57	5	=	=	SYM
ejpam-6316	57	6	1	1	NUM
ejpam-6316	57	7	,	,	PUNCT
ejpam-6316	57	8	e1,1(σ	e1,1(σ	PROPN
ejpam-6316	57	9	)	)	PUNCT
ejpam-6316	57	10	=	=	SYM
ejpam-6316	57	11	eσ	eσ	NOUN
ejpam-6316	57	12	and	and	CCONJ
ejpam-6316	57	13	e1,1(−σ	e1,1(−σ	NOUN
ejpam-6316	57	14	)	)	PUNCT
ejpam-6316	58	1	=	=	SYM
ejpam-6316	58	2	e−σ	e−σ	NOUN
ejpam-6316	58	3	.	.	PUNCT
ejpam-6316	59	1	n.	n.	PROPN
ejpam-6316	59	2	iqbal	iqbal	PROPN
ejpam-6316	59	3	et	et	PROPN
ejpam-6316	59	4	al	al	PROPN
ejpam-6316	59	5	.	.	PUNCT
ejpam-6316	59	6	/	/	SYM
ejpam-6316	59	7	eur	eur	PROPN
ejpam-6316	59	8	.	.	PUNCT
ejpam-6316	60	1	j.	j.	PROPN
ejpam-6316	60	2	pure	pure	PROPN
ejpam-6316	60	3	appl	appl	PROPN
ejpam-6316	60	4	.	.	PROPN
ejpam-6316	60	5	math	math	PROPN
ejpam-6316	60	6	,	,	PUNCT
ejpam-6316	60	7	18	18	NUM
ejpam-6316	60	8	(	(	PUNCT
ejpam-6316	60	9	3	3	NUM
ejpam-6316	60	10	)	)	PUNCT
ejpam-6316	60	11	(	(	PUNCT
ejpam-6316	60	12	2025	2025	NUM
ejpam-6316	60	13	)	)	PUNCT
ejpam-6316	60	14	,	,	PUNCT
ejpam-6316	60	15	6316	6316	NUM
ejpam-6316	60	16	4	4	NUM
ejpam-6316	60	17	of	of	ADP
ejpam-6316	60	18	21	21	NUM
ejpam-6316	60	19	2.4	2.4	NUM
ejpam-6316	60	20	.	.	PUNCT
ejpam-6316	61	1	definition	definition	NOUN
ejpam-6316	61	2	the	the	DET
ejpam-6316	61	3	natural	natural	ADJ
ejpam-6316	61	4	transform	transform	NOUN
ejpam-6316	61	5	(	(	PUNCT
ejpam-6316	61	6	nt	not	PART
ejpam-6316	61	7	)	)	PUNCT
ejpam-6316	61	8	of	of	ADP
ejpam-6316	61	9	a	a	DET
ejpam-6316	61	10	function	function	NOUN
ejpam-6316	61	11	v(υ	v(υ	PROPN
ejpam-6316	61	12	,	,	PUNCT
ejpam-6316	61	13	σ	σ	NOUN
ejpam-6316	61	14	)	)	PUNCT
ejpam-6316	61	15	for	for	ADP
ejpam-6316	61	16	σ	σ	PROPN
ejpam-6316	61	17	≥	≥	X
ejpam-6316	61	18	0	0	NUM
ejpam-6316	61	19	is	be	AUX
ejpam-6316	61	20	given	give	VERB
ejpam-6316	61	21	as	as	ADP
ejpam-6316	61	22	[	[	X
ejpam-6316	61	23	27	27	NUM
ejpam-6316	61	24	,	,	PUNCT
ejpam-6316	61	25	28	28	NUM
ejpam-6316	61	26	]	]	PUNCT
ejpam-6316	61	27	n	n	PRON
ejpam-6316	61	28	[	[	X
ejpam-6316	61	29	v(υ	v(υ	PROPN
ejpam-6316	61	30	,	,	PUNCT
ejpam-6316	61	31	σ	σ	NOUN
ejpam-6316	61	32	)	)	PUNCT
ejpam-6316	61	33	]	]	PUNCT
ejpam-6316	62	1	=	=	SYM
ejpam-6316	62	2	r(υ	r(υ	NOUN
ejpam-6316	62	3	,	,	PUNCT
ejpam-6316	62	4	s	s	NOUN
ejpam-6316	62	5	,	,	PUNCT
ejpam-6316	62	6	u	u	NOUN
ejpam-6316	62	7	)	)	PUNCT
ejpam-6316	62	8	=	=	SYM
ejpam-6316	62	9	∫	∫	PROPN
ejpam-6316	62	10	∞	∞	PROPN
ejpam-6316	62	11	0	0	NUM
ejpam-6316	62	12	e−sσv(υ	e−sσv(υ	NUM
ejpam-6316	62	13	,	,	PUNCT
ejpam-6316	62	14	uσ)dσ	uσ)dσ	PROPN
ejpam-6316	62	15	,	,	PUNCT
ejpam-6316	62	16	where	where	SCONJ
ejpam-6316	62	17	u	u	NOUN
ejpam-6316	62	18	and	and	CCONJ
ejpam-6316	62	19	s	s	PROPN
ejpam-6316	62	20	for	for	ADP
ejpam-6316	62	21	the	the	DET
ejpam-6316	62	22	transformation	transformation	NOUN
ejpam-6316	62	23	parameter	parameter	NOUN
ejpam-6316	62	24	and	and	CCONJ
ejpam-6316	62	25	are	be	AUX
ejpam-6316	62	26	assumed	assume	VERB
ejpam-6316	62	27	to	to	PART
ejpam-6316	62	28	be	be	AUX
ejpam-6316	62	29	real	real	ADJ
ejpam-6316	62	30	and	and	CCONJ
ejpam-6316	62	31	positive	positive	ADJ
ejpam-6316	62	32	.	.	PUNCT
ejpam-6316	63	1	3	3	X
ejpam-6316	63	2	.	.	X
ejpam-6316	63	3	the	the	DET
ejpam-6316	63	4	suggested	suggest	VERB
ejpam-6316	63	5	methods	method	NOUN
ejpam-6316	63	6	3.1	3.1	NUM
ejpam-6316	63	7	.	.	PUNCT
ejpam-6316	63	8	residual	residual	ADJ
ejpam-6316	63	9	power	power	NOUN
ejpam-6316	63	10	series	series	PROPN
ejpam-6316	63	11	natural	natural	ADJ
ejpam-6316	63	12	transform	transform	NOUN
ejpam-6316	63	13	method	method	NOUN
ejpam-6316	63	14	consider	consider	VERB
ejpam-6316	63	15	the	the	DET
ejpam-6316	63	16	fractional	fractional	ADJ
ejpam-6316	63	17	pde	pde	NOUN
ejpam-6316	63	18	is	be	AUX
ejpam-6316	63	19	given	give	VERB
ejpam-6316	63	20	as	as	ADP
ejpam-6316	63	21	:	:	PUNCT
ejpam-6316	63	22	dp	dp	NOUN
ejpam-6316	63	23	σψ(υ	σψ(υ	NOUN
ejpam-6316	63	24	,	,	PUNCT
ejpam-6316	63	25	σ	σ	NOUN
ejpam-6316	63	26	)	)	PUNCT
ejpam-6316	63	27	=	=	SYM
ejpam-6316	63	28	nυ[ψ(υ	nυ[ψ(υ	PROPN
ejpam-6316	63	29	,	,	PUNCT
ejpam-6316	63	30	σ	σ	PROPN
ejpam-6316	63	31	)	)	PUNCT
ejpam-6316	63	32	]	]	PUNCT
ejpam-6316	63	33	ψ(υ	ψ(υ	PROPN
ejpam-6316	63	34	,	,	PUNCT
ejpam-6316	63	35	0	0	NUM
ejpam-6316	63	36	)	)	PUNCT
ejpam-6316	64	1	=	=	SYM
ejpam-6316	64	2	f(υ	f(υ	PROPN
ejpam-6316	64	3	)	)	PUNCT
ejpam-6316	64	4	(	(	PUNCT
ejpam-6316	64	5	1	1	X
ejpam-6316	64	6	)	)	PUNCT
ejpam-6316	64	7	where	where	SCONJ
ejpam-6316	64	8	nυ	nυ	ADV
ejpam-6316	64	9	is	be	AUX
ejpam-6316	64	10	a	a	DET
ejpam-6316	64	11	nonlinear	nonlinear	ADJ
ejpam-6316	64	12	function	function	NOUN
ejpam-6316	64	13	depending	depend	VERB
ejpam-6316	64	14	on	on	ADP
ejpam-6316	64	15	υ	υ	NOUN
ejpam-6316	64	16	with	with	ADP
ejpam-6316	64	17	degree	degree	NOUN
ejpam-6316	64	18	r	r	NOUN
ejpam-6316	64	19	,	,	PUNCT
ejpam-6316	64	20	υ	υ	PROPN
ejpam-6316	64	21	∈	∈	PROPN
ejpam-6316	65	1	i	i	PRON
ejpam-6316	65	2	,	,	PUNCT
ejpam-6316	65	3	σ	σ	PROPN
ejpam-6316	65	4	≥	≥	PROPN
ejpam-6316	65	5	0	0	NUM
ejpam-6316	65	6	,	,	PUNCT
ejpam-6316	65	7	ψ(υ	ψ(υ	PROPN
ejpam-6316	65	8	,	,	PUNCT
ejpam-6316	65	9	σ	σ	PROPN
ejpam-6316	65	10	)	)	PUNCT
ejpam-6316	65	11	is	be	AUX
ejpam-6316	65	12	an	an	DET
ejpam-6316	65	13	unknown	unknown	ADJ
ejpam-6316	65	14	term	term	NOUN
ejpam-6316	65	15	and	and	CCONJ
ejpam-6316	65	16	dp	dp	NOUN
ejpam-6316	65	17	σ	σ	NOUN
ejpam-6316	65	18	is	be	AUX
ejpam-6316	65	19	the	the	DET
ejpam-6316	65	20	p	p	PROPN
ejpam-6316	65	21	-	-	PUNCT
ejpam-6316	65	22	th	th	X
ejpam-6316	65	23	fractional	fractional	PROPN
ejpam-6316	65	24	caputo	caputo	PROPN
ejpam-6316	65	25	operator	operator	NOUN
ejpam-6316	65	26	for	for	ADP
ejpam-6316	65	27	p	p	PROPN
ejpam-6316	65	28	∈	∈	PROPN
ejpam-6316	65	29	(	(	PUNCT
ejpam-6316	65	30	0	0	NUM
ejpam-6316	65	31	,	,	PUNCT
ejpam-6316	65	32	1	1	NUM
ejpam-6316	65	33	]	]	PUNCT
ejpam-6316	65	34	.	.	PUNCT
ejpam-6316	66	1	step	step	NOUN
ejpam-6316	66	2	1	1	NUM
ejpam-6316	66	3	:	:	PUNCT
ejpam-6316	66	4	applying	apply	VERB
ejpam-6316	66	5	the	the	DET
ejpam-6316	66	6	nt	nt	NOUN
ejpam-6316	66	7	on	on	ADP
ejpam-6316	66	8	both	both	DET
ejpam-6316	66	9	sides	side	NOUN
ejpam-6316	66	10	of	of	ADP
ejpam-6316	66	11	eq	eq	PROPN
ejpam-6316	66	12	.	.	PUNCT
ejpam-6316	67	1	(	(	PUNCT
ejpam-6316	67	2	1	1	NUM
ejpam-6316	67	3	)	)	PUNCT
ejpam-6316	67	4	,	,	PUNCT
ejpam-6316	67	5	ψ(υ	ψ(υ	PROPN
ejpam-6316	67	6	,	,	PUNCT
ejpam-6316	67	7	s	s	NOUN
ejpam-6316	67	8	)	)	PUNCT
ejpam-6316	67	9	=	=	SYM
ejpam-6316	67	10	f(υ	f(υ	PROPN
ejpam-6316	67	11	)	)	PUNCT
ejpam-6316	67	12	s	s	VERB
ejpam-6316	67	13	−	−	NOUN
ejpam-6316	67	14	up	up	ADP
ejpam-6316	67	15	sp	sp	ADP
ejpam-6316	67	16	n	n	PRON
ejpam-6316	67	17	{	{	PUNCT
ejpam-6316	67	18	nυ[ψ(υ	nυ[ψ(υ	PROPN
ejpam-6316	67	19	,	,	PUNCT
ejpam-6316	67	20	σ	σ	PROPN
ejpam-6316	67	21	)	)	PUNCT
ejpam-6316	67	22	]	]	PUNCT
ejpam-6316	67	23	}	}	PUNCT
ejpam-6316	67	24	,	,	PUNCT
ejpam-6316	67	25	where	where	SCONJ
ejpam-6316	67	26	ψ(υ	ψ(υ	PROPN
ejpam-6316	67	27	,	,	PUNCT
ejpam-6316	67	28	s	s	NOUN
ejpam-6316	67	29	)	)	PUNCT
ejpam-6316	67	30	=	=	SYM
ejpam-6316	68	1	n	n	PROPN
ejpam-6316	69	1	[	[	X
ejpam-6316	69	2	ψ(υ	ψ(υ	NOUN
ejpam-6316	69	3	,	,	PUNCT
ejpam-6316	69	4	σ)](s	σ)](s	PROPN
ejpam-6316	69	5	)	)	PUNCT
ejpam-6316	69	6	,	,	PUNCT
ejpam-6316	69	7	s	s	PART
ejpam-6316	69	8	>	>	X
ejpam-6316	69	9	σ	σ	PROPN
ejpam-6316	69	10	.	.	PUNCT
ejpam-6316	70	1	(	(	PUNCT
ejpam-6316	70	2	2	2	X
ejpam-6316	70	3	)	)	PUNCT
ejpam-6316	70	4	step	step	NOUN
ejpam-6316	70	5	2	2	NUM
ejpam-6316	70	6	:	:	PUNCT
ejpam-6316	70	7	consider	consider	VERB
ejpam-6316	70	8	the	the	DET
ejpam-6316	70	9	following	follow	VERB
ejpam-6316	70	10	fractional	fractional	ADJ
ejpam-6316	70	11	approximate	approximate	ADJ
ejpam-6316	70	12	result	result	NOUN
ejpam-6316	70	13	of	of	ADP
ejpam-6316	70	14	the	the	DET
ejpam-6316	70	15	eq	eq	NOUN
ejpam-6316	70	16	.	.	PUNCT
ejpam-6316	71	1	(	(	PUNCT
ejpam-6316	71	2	2	2	NUM
ejpam-6316	71	3	):	):	PUNCT
ejpam-6316	71	4	ψ(υ	ψ(υ	PROPN
ejpam-6316	71	5	,	,	PUNCT
ejpam-6316	71	6	s	s	NOUN
ejpam-6316	71	7	)	)	PUNCT
ejpam-6316	71	8	=	=	SYM
ejpam-6316	71	9	f(υ	f(υ	PROPN
ejpam-6316	71	10	)	)	PUNCT
ejpam-6316	71	11	s	s	PART
ejpam-6316	72	1	+	+	NOUN
ejpam-6316	72	2	∞∑	∞∑	NUM
ejpam-6316	72	3	n=1	n=1	ADJ
ejpam-6316	72	4	uphn(υ	uphn(υ	PROPN
ejpam-6316	72	5	)	)	PUNCT
ejpam-6316	72	6	snp+1	snp+1	NOUN
ejpam-6316	72	7	,	,	PUNCT
ejpam-6316	72	8	x	x	PUNCT
ejpam-6316	72	9	∈	∈	PROPN
ejpam-6316	73	1	i	i	PRON
ejpam-6316	73	2	,	,	PUNCT
ejpam-6316	73	3	s	s	PART
ejpam-6316	73	4	>	>	X
ejpam-6316	73	5	σ	σ	X
ejpam-6316	73	6	≥	≥	PROPN
ejpam-6316	73	7	0	0	NUM
ejpam-6316	73	8	,	,	PUNCT
ejpam-6316	73	9	(	(	PUNCT
ejpam-6316	73	10	3	3	NUM
ejpam-6316	73	11	)	)	PUNCT
ejpam-6316	73	12	and	and	CCONJ
ejpam-6316	73	13	the	the	DET
ejpam-6316	73	14	k	k	NOUN
ejpam-6316	73	15	-	-	PUNCT
ejpam-6316	73	16	th	th	VERB
ejpam-6316	73	17	natural	natural	ADJ
ejpam-6316	73	18	series	series	NOUN
ejpam-6316	73	19	solutions	solution	NOUN
ejpam-6316	73	20	is	be	AUX
ejpam-6316	73	21	defined	define	VERB
ejpam-6316	73	22	by	by	ADP
ejpam-6316	73	23	:	:	PUNCT
ejpam-6316	73	24	ψk(υ	ψk(υ	NUM
ejpam-6316	73	25	,	,	PUNCT
ejpam-6316	73	26	s	s	X
ejpam-6316	73	27	)	)	PUNCT
ejpam-6316	73	28	=	=	SYM
ejpam-6316	73	29	f(υ	f(υ	PROPN
ejpam-6316	73	30	)	)	PUNCT
ejpam-6316	73	31	s	s	PART
ejpam-6316	73	32	+	+	CCONJ
ejpam-6316	73	33	k∑	k∑	ADJ
ejpam-6316	73	34	n=1	n=1	PROPN
ejpam-6316	73	35	uphn(υ	uphn(υ	PROPN
ejpam-6316	73	36	)	)	PUNCT
ejpam-6316	73	37	snp+1	snp+1	NOUN
ejpam-6316	73	38	,	,	PUNCT
ejpam-6316	73	39	υ	υ	PROPN
ejpam-6316	73	40	∈	∈	PROPN
ejpam-6316	74	1	i	i	PRON
ejpam-6316	74	2	,	,	PUNCT
ejpam-6316	74	3	s	s	PART
ejpam-6316	74	4	>	>	X
ejpam-6316	74	5	σ	σ	X
ejpam-6316	74	6	≥	≥	PROPN
ejpam-6316	74	7	0	0	NUM
ejpam-6316	74	8	.	.	PUNCT
ejpam-6316	75	1	(	(	PUNCT
ejpam-6316	75	2	4	4	X
ejpam-6316	75	3	)	)	PUNCT
ejpam-6316	75	4	step	step	NOUN
ejpam-6316	75	5	3	3	NUM
ejpam-6316	75	6	:	:	PUNCT
ejpam-6316	75	7	the	the	DET
ejpam-6316	75	8	fractional	fractional	ADJ
ejpam-6316	75	9	k	k	NOUN
ejpam-6316	75	10	-	-	PUNCT
ejpam-6316	75	11	th	th	VERB
ejpam-6316	75	12	natural	natural	ADJ
ejpam-6316	75	13	residual	residual	ADJ
ejpam-6316	75	14	function	function	NOUN
ejpam-6316	75	15	(	(	PUNCT
ejpam-6316	75	16	nrf	nrf	NOUN
ejpam-6316	75	17	)	)	PUNCT
ejpam-6316	75	18	of	of	ADP
ejpam-6316	75	19	(	(	PUNCT
ejpam-6316	75	20	2	2	X
ejpam-6316	75	21	)	)	PUNCT
ejpam-6316	75	22	is	be	AUX
ejpam-6316	75	23	given	give	VERB
ejpam-6316	75	24	as	as	ADP
ejpam-6316	75	25	:	:	PUNCT
ejpam-6316	75	26	n	n	CCONJ
ejpam-6316	75	27	(	(	PUNCT
ejpam-6316	75	28	resψk	resψk	PROPN
ejpam-6316	75	29	(	(	PUNCT
ejpam-6316	75	30	υ	υ	PROPN
ejpam-6316	75	31	,	,	PUNCT
ejpam-6316	75	32	s	s	NOUN
ejpam-6316	75	33	)	)	PUNCT
ejpam-6316	75	34	)	)	PUNCT
ejpam-6316	76	1	=	=	SYM
ejpam-6316	76	2	ψk(υ	ψk(υ	PUNCT
ejpam-6316	76	3	,	,	PUNCT
ejpam-6316	76	4	s)−	s)−	PROPN
ejpam-6316	76	5	f(υ	f(υ	PROPN
ejpam-6316	76	6	)	)	PUNCT
ejpam-6316	76	7	s	s	PART
ejpam-6316	77	1	+	+	X
ejpam-6316	77	2	up	up	ADP
ejpam-6316	77	3	sp	sp	ADP
ejpam-6316	77	4	n	n	PRON
ejpam-6316	77	5	{	{	PUNCT
ejpam-6316	77	6	nυ[ψ(υ	nυ[ψ(υ	PROPN
ejpam-6316	77	7	,	,	PUNCT
ejpam-6316	77	8	σ	σ	PROPN
ejpam-6316	77	9	)	)	PUNCT
ejpam-6316	77	10	]	]	PUNCT
ejpam-6316	77	11	}	}	PUNCT
ejpam-6316	77	12	,	,	PUNCT
ejpam-6316	77	13	(	(	PUNCT
ejpam-6316	77	14	5	5	NUM
ejpam-6316	77	15	)	)	PUNCT
ejpam-6316	77	16	and	and	CCONJ
ejpam-6316	77	17	(	(	PUNCT
ejpam-6316	77	18	2	2	X
ejpam-6316	77	19	)	)	PUNCT
ejpam-6316	77	20	nrf	nrf	NOUN
ejpam-6316	77	21	is	be	AUX
ejpam-6316	77	22	given	give	VERB
ejpam-6316	77	23	as	as	ADP
ejpam-6316	77	24	:	:	PUNCT
ejpam-6316	77	25	lim	lim	PROPN
ejpam-6316	77	26	k→∞	k→∞	PROPN
ejpam-6316	77	27	n	n	PROPN
ejpam-6316	77	28	(	(	PUNCT
ejpam-6316	77	29	resψk	resψk	PROPN
ejpam-6316	77	30	(	(	PUNCT
ejpam-6316	77	31	υ	υ	PROPN
ejpam-6316	77	32	,	,	PUNCT
ejpam-6316	77	33	s	s	NOUN
ejpam-6316	77	34	)	)	PUNCT
ejpam-6316	77	35	)	)	PUNCT
ejpam-6316	78	1	=	=	SYM
ejpam-6316	78	2	n	n	X
ejpam-6316	78	3	(	(	PUNCT
ejpam-6316	78	4	resψ(υ	resψ(υ	PROPN
ejpam-6316	78	5	,	,	PUNCT
ejpam-6316	78	6	s	s	NOUN
ejpam-6316	78	7	)	)	PUNCT
ejpam-6316	78	8	)	)	PUNCT
ejpam-6316	79	1	=	=	SYM
ejpam-6316	79	2	ψ(υ	ψ(υ	PROPN
ejpam-6316	79	3	,	,	PUNCT
ejpam-6316	79	4	s)−	s)−	PROPN
ejpam-6316	79	5	f(υ	f(υ	PROPN
ejpam-6316	79	6	)	)	PUNCT
ejpam-6316	79	7	s	s	PART
ejpam-6316	80	1	+	+	X
ejpam-6316	80	2	up	up	ADP
ejpam-6316	80	3	sp	sp	ADP
ejpam-6316	80	4	n	n	PRON
ejpam-6316	80	5	{	{	PUNCT
ejpam-6316	80	6	nυ[ψ(υ	nυ[ψ(υ	PROPN
ejpam-6316	80	7	,	,	PUNCT
ejpam-6316	80	8	σ	σ	PROPN
ejpam-6316	80	9	)	)	PUNCT
ejpam-6316	80	10	]	]	PUNCT
ejpam-6316	80	11	}	}	PUNCT
ejpam-6316	80	12	.	.	PUNCT
ejpam-6316	81	1	(	(	PUNCT
ejpam-6316	81	2	6	6	X
ejpam-6316	81	3	)	)	PUNCT
ejpam-6316	81	4	the	the	DET
ejpam-6316	81	5	nrf	nrf	ADJ
ejpam-6316	81	6	solution	solution	NOUN
ejpam-6316	81	7	:	:	PUNCT
ejpam-6316	82	1	limk→∞n	limk→∞n	NOUN
ejpam-6316	82	2	(	(	PUNCT
ejpam-6316	82	3	resψk	resψk	PROPN
ejpam-6316	82	4	(	(	PUNCT
ejpam-6316	82	5	υ	υ	PROPN
ejpam-6316	82	6	,	,	PUNCT
ejpam-6316	82	7	s	s	NOUN
ejpam-6316	82	8	)	)	PUNCT
ejpam-6316	82	9	)	)	PUNCT
ejpam-6316	82	10	=	=	SYM
ejpam-6316	83	1	n	n	X
ejpam-6316	83	2	(	(	PUNCT
ejpam-6316	83	3	resψ(υ	resψ(υ	PROPN
ejpam-6316	83	4	,	,	PUNCT
ejpam-6316	83	5	s	s	NOUN
ejpam-6316	83	6	)	)	PUNCT
ejpam-6316	83	7	)	)	PUNCT
ejpam-6316	83	8	,	,	PUNCT
ejpam-6316	83	9	for	for	ADP
ejpam-6316	83	10	υ	υ	PRON
ejpam-6316	83	11	∈	∈	PROPN
ejpam-6316	83	12	i	i	PROPN
ejpam-6316	83	13	,	,	PUNCT
ejpam-6316	83	14	s	s	PART
ejpam-6316	83	15	>	>	X
ejpam-6316	83	16	σ	σ	X
ejpam-6316	83	17	≥	≥	PROPN
ejpam-6316	83	18	0	0	NUM
ejpam-6316	83	19	.	.	PUNCT
ejpam-6316	84	1	n	n	PROPN
ejpam-6316	84	2	(	(	PUNCT
ejpam-6316	84	3	resψ(υ	resψ(υ	PROPN
ejpam-6316	84	4	,	,	PUNCT
ejpam-6316	84	5	s	s	NOUN
ejpam-6316	84	6	)	)	PUNCT
ejpam-6316	84	7	)	)	PUNCT
ejpam-6316	84	8	=	=	SYM
ejpam-6316	84	9	0	0	NUM
ejpam-6316	84	10	,	,	PUNCT
ejpam-6316	84	11	for	for	ADP
ejpam-6316	84	12	υ	υ	DET
ejpam-6316	84	13	∈	∈	PROPN
ejpam-6316	85	1	i	i	PROPN
ejpam-6316	85	2	,	,	PUNCT
ejpam-6316	85	3	s	s	PART
ejpam-6316	85	4	>	>	X
ejpam-6316	85	5	σ	σ	X
ejpam-6316	85	6	≥	≥	PROPN
ejpam-6316	85	7	0	0	NUM
ejpam-6316	85	8	.	.	PUNCT
ejpam-6316	86	1	lims→∞	lims→∞	PROPN
ejpam-6316	86	2	skp+1n	skp+1n	VERB
ejpam-6316	86	3	(	(	PUNCT
ejpam-6316	86	4	resψk	resψk	PROPN
ejpam-6316	86	5	(	(	PUNCT
ejpam-6316	86	6	υ	υ	PROPN
ejpam-6316	86	7	,	,	PUNCT
ejpam-6316	86	8	s	s	NOUN
ejpam-6316	86	9	)	)	PUNCT
ejpam-6316	86	10	)	)	PUNCT
ejpam-6316	87	1	=	=	SYM
ejpam-6316	87	2	0	0	NUM
ejpam-6316	87	3	,	,	PUNCT
ejpam-6316	87	4	for	for	ADP
ejpam-6316	87	5	n.	n.	PROPN
ejpam-6316	87	6	iqbal	iqbal	PROPN
ejpam-6316	87	7	et	et	PROPN
ejpam-6316	87	8	al	al	PROPN
ejpam-6316	87	9	.	.	PUNCT
ejpam-6316	87	10	/	/	SYM
ejpam-6316	87	11	eur	eur	PROPN
ejpam-6316	87	12	.	.	PUNCT
ejpam-6316	88	1	j.	j.	PROPN
ejpam-6316	88	2	pure	pure	PROPN
ejpam-6316	88	3	appl	appl	PROPN
ejpam-6316	88	4	.	.	PROPN
ejpam-6316	88	5	math	math	PROPN
ejpam-6316	88	6	,	,	PUNCT
ejpam-6316	88	7	18	18	NUM
ejpam-6316	88	8	(	(	PUNCT
ejpam-6316	88	9	3	3	NUM
ejpam-6316	88	10	)	)	PUNCT
ejpam-6316	88	11	(	(	PUNCT
ejpam-6316	88	12	2025	2025	NUM
ejpam-6316	88	13	)	)	PUNCT
ejpam-6316	88	14	,	,	PUNCT
ejpam-6316	88	15	6316	6316	NUM
ejpam-6316	88	16	5	5	NUM
ejpam-6316	88	17	of	of	ADP
ejpam-6316	88	18	21	21	NUM
ejpam-6316	88	19	υ	υ	NOUN
ejpam-6316	88	20	∈	∈	PROPN
ejpam-6316	89	1	i	i	PRON
ejpam-6316	89	2	,	,	PUNCT
ejpam-6316	89	3	s	s	PART
ejpam-6316	89	4	>	>	X
ejpam-6316	89	5	σ	σ	X
ejpam-6316	89	6	≥	≥	PROPN
ejpam-6316	89	7	0	0	NUM
ejpam-6316	89	8	,	,	PUNCT
ejpam-6316	89	9	and	and	CCONJ
ejpam-6316	89	10	k	k	X
ejpam-6316	89	11	=	=	SYM
ejpam-6316	89	12	1	1	NUM
ejpam-6316	89	13	,	,	PUNCT
ejpam-6316	89	14	2	2	NUM
ejpam-6316	89	15	,	,	PUNCT
ejpam-6316	89	16	3	3	NUM
ejpam-6316	89	17	,	,	PUNCT
ejpam-6316	89	18	.	.	PUNCT
ejpam-6316	89	19	.	.	PUNCT
ejpam-6316	89	20	.	.	PUNCT
ejpam-6316	90	1	step	step	NOUN
ejpam-6316	90	2	4	4	NUM
ejpam-6316	90	3	:	:	PUNCT
ejpam-6316	90	4	now	now	ADV
ejpam-6316	90	5	put	put	VERB
ejpam-6316	90	6	the	the	DET
ejpam-6316	90	7	k	k	NOUN
ejpam-6316	90	8	-	-	PUNCT
ejpam-6316	90	9	th	th	VERB
ejpam-6316	90	10	natural	natural	ADJ
ejpam-6316	90	11	series	series	NOUN
ejpam-6316	90	12	solution	solution	NOUN
ejpam-6316	90	13	(	(	PUNCT
ejpam-6316	90	14	4	4	NUM
ejpam-6316	90	15	)	)	PUNCT
ejpam-6316	90	16	into	into	ADP
ejpam-6316	90	17	the	the	DET
ejpam-6316	90	18	k	k	NOUN
ejpam-6316	90	19	-	-	PUNCT
ejpam-6316	90	20	th	th	VERB
ejpam-6316	90	21	natural	natural	ADJ
ejpam-6316	90	22	fractional	fractional	ADJ
ejpam-6316	90	23	residual	residual	ADJ
ejpam-6316	90	24	function	function	NOUN
ejpam-6316	90	25	of	of	ADP
ejpam-6316	90	26	(	(	PUNCT
ejpam-6316	90	27	5	5	NUM
ejpam-6316	90	28	)	)	PUNCT
ejpam-6316	90	29	.	.	PUNCT
ejpam-6316	91	1	step	step	NOUN
ejpam-6316	91	2	5	5	NUM
ejpam-6316	91	3	:	:	PUNCT
ejpam-6316	91	4	the	the	DET
ejpam-6316	91	5	unknown	unknown	ADJ
ejpam-6316	91	6	coefficients	coefficient	NOUN
ejpam-6316	91	7	hk(υ	hk(υ	NUM
ejpam-6316	91	8	)	)	PUNCT
ejpam-6316	91	9	,	,	PUNCT
ejpam-6316	91	10	for	for	ADP
ejpam-6316	91	11	k	k	PROPN
ejpam-6316	91	12	=	=	SYM
ejpam-6316	91	13	1	1	NUM
ejpam-6316	91	14	,	,	PUNCT
ejpam-6316	91	15	2	2	NUM
ejpam-6316	91	16	,	,	PUNCT
ejpam-6316	91	17	3	3	NUM
ejpam-6316	91	18	,	,	PUNCT
ejpam-6316	91	19	.	.	PUNCT
ejpam-6316	91	20	.	.	PUNCT
ejpam-6316	92	1	.	.	PUNCT
ejpam-6316	93	1	,	,	PUNCT
ejpam-6316	93	2	might	might	AUX
ejpam-6316	93	3	be	be	AUX
ejpam-6316	93	4	obtained	obtain	VERB
ejpam-6316	93	5	by	by	ADP
ejpam-6316	93	6	solving	solve	VERB
ejpam-6316	93	7	the	the	DET
ejpam-6316	93	8	system	system	NOUN
ejpam-6316	93	9	lims→∞	lims→∞	PROPN
ejpam-6316	93	10	ska+1n	ska+1n	VERB
ejpam-6316	93	11	(	(	PUNCT
ejpam-6316	93	12	resψk	resψk	PROPN
ejpam-6316	93	13	(	(	PUNCT
ejpam-6316	93	14	υ	υ	PROPN
ejpam-6316	93	15	,	,	PUNCT
ejpam-6316	93	16	s	s	NOUN
ejpam-6316	93	17	)	)	PUNCT
ejpam-6316	93	18	)	)	PUNCT
ejpam-6316	94	1	=	=	PUNCT
ejpam-6316	94	2	0	0	X
ejpam-6316	94	3	.	.	PUNCT
ejpam-6316	95	1	the	the	DET
ejpam-6316	95	2	achieved	achieve	VERB
ejpam-6316	95	3	coefficient	coefficient	NOUN
ejpam-6316	95	4	applying	apply	VERB
ejpam-6316	95	5	fractional	fractional	ADJ
ejpam-6316	95	6	expansion	expansion	NOUN
ejpam-6316	95	7	series	series	NOUN
ejpam-6316	95	8	(	(	PUNCT
ejpam-6316	95	9	4	4	NUM
ejpam-6316	95	10	)	)	PUNCT
ejpam-6316	95	11	ψk(υ	ψk(υ	PUNCT
ejpam-6316	95	12	,	,	PUNCT
ejpam-6316	95	13	s	s	PART
ejpam-6316	95	14	)	)	PUNCT
ejpam-6316	95	15	.	.	PUNCT
ejpam-6316	96	1	step	step	NOUN
ejpam-6316	96	2	6	6	NUM
ejpam-6316	96	3	:	:	PUNCT
ejpam-6316	96	4	applying	apply	VERB
ejpam-6316	96	5	the	the	DET
ejpam-6316	96	6	inverse	inverse	ADJ
ejpam-6316	96	7	natural	natural	ADJ
ejpam-6316	96	8	transform	transform	NOUN
ejpam-6316	96	9	operator	operator	NOUN
ejpam-6316	96	10	to	to	ADP
ejpam-6316	96	11	both	both	DET
ejpam-6316	96	12	sides	side	NOUN
ejpam-6316	96	13	of	of	ADP
ejpam-6316	96	14	the	the	DET
ejpam-6316	96	15	natural	natural	ADJ
ejpam-6316	96	16	series	series	NOUN
ejpam-6316	96	17	solution	solution	NOUN
ejpam-6316	96	18	to	to	PART
ejpam-6316	96	19	obtain	obtain	VERB
ejpam-6316	96	20	an	an	DET
ejpam-6316	96	21	estimated	estimate	VERB
ejpam-6316	96	22	solution	solution	NOUN
ejpam-6316	96	23	ψk(υ	ψk(υ	PUNCT
ejpam-6316	96	24	,	,	PUNCT
ejpam-6316	96	25	σ	σ	PROPN
ejpam-6316	96	26	)	)	PUNCT
ejpam-6316	96	27	,	,	PUNCT
ejpam-6316	96	28	of	of	ADP
ejpam-6316	96	29	the	the	DET
ejpam-6316	96	30	main	main	ADJ
ejpam-6316	96	31	equation	equation	NOUN
ejpam-6316	96	32	(	(	PUNCT
ejpam-6316	96	33	1	1	NUM
ejpam-6316	96	34	)	)	PUNCT
ejpam-6316	96	35	.	.	PUNCT
ejpam-6316	97	1	3.2	3.2	NUM
ejpam-6316	97	2	.	.	PUNCT
ejpam-6316	97	3	idea	idea	NOUN
ejpam-6316	97	4	of	of	ADP
ejpam-6316	97	5	the	the	DET
ejpam-6316	97	6	natural	natural	ADJ
ejpam-6316	97	7	iterative	iterative	NOUN
ejpam-6316	97	8	transform	transform	NOUN
ejpam-6316	97	9	method	method	NOUN
ejpam-6316	97	10	consider	consider	VERB
ejpam-6316	97	11	the	the	DET
ejpam-6316	97	12	general	general	ADJ
ejpam-6316	97	13	fractional	fractional	ADJ
ejpam-6316	97	14	pde	pde	NOUN
ejpam-6316	97	15	is	be	AUX
ejpam-6316	97	16	given	give	VERB
ejpam-6316	97	17	as	as	ADP
ejpam-6316	97	18	dp	dp	NOUN
ejpam-6316	97	19	σψ(υ	σψ(υ	NOUN
ejpam-6316	97	20	,	,	PUNCT
ejpam-6316	97	21	σ	σ	NOUN
ejpam-6316	98	1	)	)	PUNCT
ejpam-6316	98	2	=	=	SYM
ejpam-6316	98	3	φ	φ	PROPN
ejpam-6316	98	4	(	(	PUNCT
ejpam-6316	98	5	ψ(υ	ψ(υ	PROPN
ejpam-6316	98	6	,	,	PUNCT
ejpam-6316	98	7	σ	σ	PROPN
ejpam-6316	98	8	)	)	PUNCT
ejpam-6316	98	9	,	,	PUNCT
ejpam-6316	98	10	dσ	dσ	PROPN
ejpam-6316	98	11	υψ(υ	υψ(υ	PROPN
ejpam-6316	98	12	,	,	PUNCT
ejpam-6316	98	13	σ	σ	PROPN
ejpam-6316	98	14	)	)	PUNCT
ejpam-6316	98	15	,	,	PUNCT
ejpam-6316	99	1	d	d	X
ejpam-6316	99	2	2σ	2σ	NUM
ejpam-6316	99	3	υ	υ	PROPN
ejpam-6316	99	4	ψ(υ	ψ(υ	PROPN
ejpam-6316	99	5	,	,	PUNCT
ejpam-6316	99	6	σ	σ	PROPN
ejpam-6316	99	7	)	)	PUNCT
ejpam-6316	99	8	,	,	PUNCT
ejpam-6316	100	1	d	d	PROPN
ejpam-6316	100	2	3σ	3σ	NUM
ejpam-6316	100	3	υ	υ	PROPN
ejpam-6316	100	4	ψ(υ	ψ(υ	PROPN
ejpam-6316	100	5	,	,	PUNCT
ejpam-6316	100	6	σ	σ	PROPN
ejpam-6316	100	7	)	)	PUNCT
ejpam-6316	100	8	)	)	PUNCT
ejpam-6316	100	9	,	,	PUNCT
ejpam-6316	100	10	0	0	PUNCT
ejpam-6316	100	11	<	<	X
ejpam-6316	100	12	p	p	X
ejpam-6316	100	13	,	,	PUNCT
ejpam-6316	100	14	σ	σ	PROPN
ejpam-6316	100	15	≤	≤	NOUN
ejpam-6316	100	16	1	1	NUM
ejpam-6316	100	17	,	,	PUNCT
ejpam-6316	100	18	(	(	PUNCT
ejpam-6316	100	19	7	7	X
ejpam-6316	100	20	)	)	PUNCT
ejpam-6316	100	21	initial	initial	ADJ
ejpam-6316	100	22	scenarios	scenario	NOUN
ejpam-6316	100	23	ψ(k)(υ	ψ(k)(υ	NOUN
ejpam-6316	100	24	,	,	PUNCT
ejpam-6316	100	25	0	0	NUM
ejpam-6316	100	26	)	)	PUNCT
ejpam-6316	100	27	=	=	SYM
ejpam-6316	100	28	hk	hk	PROPN
ejpam-6316	100	29	,	,	PUNCT
ejpam-6316	100	30	k	k	PROPN
ejpam-6316	100	31	=	=	SYM
ejpam-6316	100	32	0	0	NUM
ejpam-6316	100	33	,	,	PUNCT
ejpam-6316	100	34	1	1	NUM
ejpam-6316	100	35	,	,	PUNCT
ejpam-6316	100	36	2	2	NUM
ejpam-6316	100	37	,	,	PUNCT
ejpam-6316	100	38	·	·	PUNCT
ejpam-6316	100	39	·	·	PUNCT
ejpam-6316	100	40	·	·	PUNCT
ejpam-6316	100	41	,	,	PUNCT
ejpam-6316	100	42	m−	m−	PROPN
ejpam-6316	100	43	1	1	NUM
ejpam-6316	100	44	,	,	PUNCT
ejpam-6316	100	45	(	(	PUNCT
ejpam-6316	100	46	8)	8)	NUM
ejpam-6316	100	47	applying	apply	VERB
ejpam-6316	100	48	the	the	DET
ejpam-6316	100	49	nt	nt	NOUN
ejpam-6316	100	50	to	to	ADP
ejpam-6316	100	51	eq	eq	PROPN
ejpam-6316	100	52	.	.	PROPN
ejpam-6316	100	53	7	7	NUM
ejpam-6316	100	54	;	;	PUNCT
ejpam-6316	100	55	ψ(υ	ψ(υ	PROPN
ejpam-6316	100	56	,	,	PUNCT
ejpam-6316	100	57	σ	σ	PROPN
ejpam-6316	100	58	)	)	PUNCT
ejpam-6316	100	59	is	be	AUX
ejpam-6316	100	60	defined	define	VERB
ejpam-6316	100	61	as	as	ADP
ejpam-6316	100	62	ψ	ψ	X
ejpam-6316	100	63	.	.	PUNCT
ejpam-6316	101	1	n	n	PRON
ejpam-6316	102	1	[	[	X
ejpam-6316	102	2	ψ(υ	ψ(υ	PROPN
ejpam-6316	102	3	,	,	PUNCT
ejpam-6316	102	4	σ	σ	PROPN
ejpam-6316	102	5	)	)	PUNCT
ejpam-6316	102	6	]	]	PUNCT
ejpam-6316	102	7	=	=	SYM
ejpam-6316	102	8	1	1	NUM
ejpam-6316	102	9	sp	sp	ADP
ejpam-6316	102	10	(	(	PUNCT
ejpam-6316	102	11	m−1∑	m−1∑	PROPN
ejpam-6316	102	12	k=0	k=0	PROPN
ejpam-6316	102	13	ψ(k)(υ	ψ(k)(υ	NOUN
ejpam-6316	102	14	,	,	PUNCT
ejpam-6316	102	15	0	0	NUM
ejpam-6316	102	16	)	)	PUNCT
ejpam-6316	102	17	s2−p+k	s2−p+k	NOUN
ejpam-6316	103	1	+	+	NOUN
ejpam-6316	103	2	n	n	PRON
ejpam-6316	103	3	[	[	PUNCT
ejpam-6316	103	4	φ	φ	X
ejpam-6316	103	5	(	(	PUNCT
ejpam-6316	103	6	ψ(υ	ψ(υ	PROPN
ejpam-6316	103	7	,	,	PUNCT
ejpam-6316	103	8	σ	σ	PROPN
ejpam-6316	103	9	)	)	PUNCT
ejpam-6316	103	10	,	,	PUNCT
ejpam-6316	103	11	dσ	dσ	PROPN
ejpam-6316	103	12	υψ(υ	υψ(υ	PROPN
ejpam-6316	103	13	,	,	PUNCT
ejpam-6316	103	14	σ	σ	PROPN
ejpam-6316	103	15	)	)	PUNCT
ejpam-6316	103	16	,	,	PUNCT
ejpam-6316	104	1	d	d	X
ejpam-6316	104	2	2σ	2σ	NUM
ejpam-6316	104	3	υ	υ	PROPN
ejpam-6316	104	4	ψ(υ	ψ(υ	PROPN
ejpam-6316	104	5	,	,	PUNCT
ejpam-6316	104	6	σ	σ	PROPN
ejpam-6316	104	7	)	)	PUNCT
ejpam-6316	104	8	,	,	PUNCT
ejpam-6316	104	9	d	d	PROPN
ejpam-6316	104	10	3σ	3σ	NUM
ejpam-6316	104	11	υ	υ	PROPN
ejpam-6316	104	12	ψ(υ	ψ(υ	PROPN
ejpam-6316	104	13	,	,	PUNCT
ejpam-6316	104	14	σ	σ	PROPN
ejpam-6316	104	15	)	)	PUNCT
ejpam-6316	104	16	)	)	PUNCT
ejpam-6316	105	1	]	]	PUNCT
ejpam-6316	105	2	)	)	PUNCT
ejpam-6316	105	3	,	,	PUNCT
ejpam-6316	105	4	(	(	PUNCT
ejpam-6316	105	5	9	9	X
ejpam-6316	105	6	)	)	PUNCT
ejpam-6316	105	7	now	now	ADV
ejpam-6316	105	8	we	we	PRON
ejpam-6316	105	9	apply	apply	VERB
ejpam-6316	105	10	inverse	inverse	NOUN
ejpam-6316	105	11	nt	not	PART
ejpam-6316	105	12	is	be	AUX
ejpam-6316	105	13	defined	define	VERB
ejpam-6316	105	14	as	as	ADP
ejpam-6316	105	15	ψ(υ	ψ(υ	PROPN
ejpam-6316	105	16	,	,	PUNCT
ejpam-6316	105	17	σ	σ	NOUN
ejpam-6316	106	1	)	)	PUNCT
ejpam-6316	106	2	=	=	SYM
ejpam-6316	106	3	n−1	n−1	PROPN
ejpam-6316	106	4	[	[	PUNCT
ejpam-6316	106	5	1	1	NUM
ejpam-6316	106	6	sp	sp	ADP
ejpam-6316	106	7	(	(	PUNCT
ejpam-6316	106	8	m−1∑	m−1∑	PROPN
ejpam-6316	106	9	k=0	k=0	PROPN
ejpam-6316	106	10	ψ(k)(υ	ψ(k)(υ	NOUN
ejpam-6316	106	11	,	,	PUNCT
ejpam-6316	106	12	0	0	NUM
ejpam-6316	106	13	)	)	PUNCT
ejpam-6316	106	14	s2−p+k	s2−p+k	NOUN
ejpam-6316	106	15	+	+	NOUN
ejpam-6316	106	16	n	n	PRON
ejpam-6316	106	17	[	[	PUNCT
ejpam-6316	106	18	φ	φ	X
ejpam-6316	106	19	(	(	PUNCT
ejpam-6316	106	20	ψ(υ	ψ(υ	PROPN
ejpam-6316	106	21	,	,	PUNCT
ejpam-6316	106	22	σ	σ	PROPN
ejpam-6316	106	23	)	)	PUNCT
ejpam-6316	106	24	,	,	PUNCT
ejpam-6316	106	25	dσ	dσ	PROPN
ejpam-6316	106	26	υψ(υ	υψ(υ	PROPN
ejpam-6316	106	27	,	,	PUNCT
ejpam-6316	106	28	σ	σ	PROPN
ejpam-6316	106	29	)	)	PUNCT
ejpam-6316	106	30	,	,	PUNCT
ejpam-6316	107	1	d	d	X
ejpam-6316	107	2	2σ	2σ	NUM
ejpam-6316	107	3	υ	υ	PROPN
ejpam-6316	107	4	ψ(υ	ψ(υ	PROPN
ejpam-6316	107	5	,	,	PUNCT
ejpam-6316	107	6	σ	σ	PROPN
ejpam-6316	107	7	)	)	PUNCT
ejpam-6316	107	8	,	,	PUNCT
ejpam-6316	107	9	d	d	PROPN
ejpam-6316	107	10	3σ	3σ	NUM
ejpam-6316	107	11	υ	υ	PROPN
ejpam-6316	107	12	ψ(υ	ψ(υ	PROPN
ejpam-6316	107	13	,	,	PUNCT
ejpam-6316	107	14	σ	σ	PROPN
ejpam-6316	107	15	)	)	PUNCT
ejpam-6316	107	16	)	)	PUNCT
ejpam-6316	108	1	]	]	PUNCT
ejpam-6316	108	2	)	)	PUNCT
ejpam-6316	108	3	]	]	PUNCT
ejpam-6316	108	4	.	.	PUNCT
ejpam-6316	109	1	(	(	PUNCT
ejpam-6316	109	2	10	10	NUM
ejpam-6316	109	3	)	)	PUNCT
ejpam-6316	109	4	the	the	DET
ejpam-6316	109	5	iterative	iterative	NOUN
ejpam-6316	109	6	procedure	procedure	NOUN
ejpam-6316	109	7	is	be	AUX
ejpam-6316	109	8	given	give	VERB
ejpam-6316	109	9	as	as	ADP
ejpam-6316	109	10	ψ(υ	ψ(υ	PROPN
ejpam-6316	109	11	,	,	PUNCT
ejpam-6316	109	12	σ	σ	NOUN
ejpam-6316	109	13	)	)	PUNCT
ejpam-6316	109	14	=	=	PUNCT
ejpam-6316	110	1	∞∑	∞∑	NUM
ejpam-6316	110	2	i=0	i=0	PROPN
ejpam-6316	110	3	ψi	ψi	NOUN
ejpam-6316	110	4	.	.	PUNCT
ejpam-6316	111	1	(	(	PUNCT
ejpam-6316	111	2	11	11	NUM
ejpam-6316	111	3	)	)	PUNCT
ejpam-6316	111	4	since	since	SCONJ
ejpam-6316	111	5	φ	φ	PROPN
ejpam-6316	111	6	(	(	PUNCT
ejpam-6316	111	7	ψ	ψ	PROPN
ejpam-6316	111	8	,	,	PUNCT
ejpam-6316	111	9	dσ	dσ	PROPN
ejpam-6316	111	10	υψ	υψ	PROPN
ejpam-6316	111	11	,	,	PUNCT
ejpam-6316	111	12	d	d	PROPN
ejpam-6316	111	13	2σ	2σ	NUM
ejpam-6316	111	14	υ	υ	X
ejpam-6316	111	15	ψ	ψ	NOUN
ejpam-6316	111	16	,	,	PUNCT
ejpam-6316	111	17	d	d	PROPN
ejpam-6316	111	18	3σ	3σ	NUM
ejpam-6316	111	19	υ	υ	NOUN
ejpam-6316	111	20	ψ	ψ	NOUN
ejpam-6316	111	21	)	)	PUNCT
ejpam-6316	111	22	are	be	AUX
ejpam-6316	111	23	non	non	ADJ
ejpam-6316	111	24	-	-	ADJ
ejpam-6316	111	25	linear	linear	ADJ
ejpam-6316	111	26	and	and	CCONJ
ejpam-6316	111	27	linear	linear	ADJ
ejpam-6316	111	28	functions	function	NOUN
ejpam-6316	111	29	that	that	PRON
ejpam-6316	111	30	can	can	AUX
ejpam-6316	111	31	be	be	AUX
ejpam-6316	111	32	decompose	decompose	VERB
ejpam-6316	111	33	as	as	ADP
ejpam-6316	111	34	:	:	PUNCT
ejpam-6316	111	35	φ	φ	PROPN
ejpam-6316	111	36	(	(	PUNCT
ejpam-6316	111	37	ψ	ψ	PROPN
ejpam-6316	111	38	,	,	PUNCT
ejpam-6316	111	39	dσ	dσ	PROPN
ejpam-6316	111	40	υψ	υψ	PROPN
ejpam-6316	111	41	,	,	PUNCT
ejpam-6316	111	42	d	d	PROPN
ejpam-6316	111	43	2σ	2σ	NUM
ejpam-6316	111	44	υ	υ	X
ejpam-6316	111	45	ψ	ψ	NOUN
ejpam-6316	111	46	,	,	PUNCT
ejpam-6316	111	47	d	d	PROPN
ejpam-6316	111	48	3σ	3σ	NUM
ejpam-6316	111	49	υ	υ	NOUN
ejpam-6316	111	50	ψ	ψ	NOUN
ejpam-6316	111	51	)	)	PUNCT
ejpam-6316	112	1	=	=	SYM
ejpam-6316	112	2	φ	φ	PROPN
ejpam-6316	112	3	(	(	PUNCT
ejpam-6316	112	4	ψ0	ψ0	PROPN
ejpam-6316	112	5	,	,	PUNCT
ejpam-6316	112	6	d	d	PROPN
ejpam-6316	112	7	σ	σ	X
ejpam-6316	112	8	υψ0	υψ0	PROPN
ejpam-6316	112	9	,	,	PUNCT
ejpam-6316	112	10	d	d	PROPN
ejpam-6316	112	11	2σ	2σ	NUM
ejpam-6316	112	12	υ	υ	NOUN
ejpam-6316	112	13	ψ0	ψ0	ADJ
ejpam-6316	112	14	,	,	PUNCT
ejpam-6316	112	15	d	d	PROPN
ejpam-6316	112	16	3σ	3σ	NUM
ejpam-6316	112	17	υ	υ	NOUN
ejpam-6316	112	18	ψ0	ψ0	ADV
ejpam-6316	112	19	)	)	PUNCT
ejpam-6316	113	1	+	+	CCONJ
ejpam-6316	113	2	∞∑	∞∑	NUM
ejpam-6316	113	3	i=0	i=0	PROPN
ejpam-6316	113	4	(	(	PUNCT
ejpam-6316	113	5	φ	φ	X
ejpam-6316	113	6	(	(	PUNCT
ejpam-6316	113	7	i∑	i∑	PROPN
ejpam-6316	113	8	k=0	k=0	PROPN
ejpam-6316	113	9	(	(	PUNCT
ejpam-6316	113	10	ψk	ψk	INTJ
ejpam-6316	113	11	,	,	PUNCT
ejpam-6316	113	12	d	d	PROPN
ejpam-6316	113	13	σ	σ	NUM
ejpam-6316	113	14	υψk	υψk	NOUN
ejpam-6316	113	15	,	,	PUNCT
ejpam-6316	113	16	d	d	PROPN
ejpam-6316	113	17	2σ	2σ	NUM
ejpam-6316	113	18	υ	υ	NOUN
ejpam-6316	113	19	ψk	ψk	VERB
ejpam-6316	113	20	,	,	PUNCT
ejpam-6316	113	21	d	d	PROPN
ejpam-6316	113	22	3σ	3σ	NUM
ejpam-6316	113	23	υ	υ	NOUN
ejpam-6316	113	24	ψk	ψk	NOUN
ejpam-6316	113	25	)	)	PUNCT
ejpam-6316	113	26	)	)	PUNCT
ejpam-6316	114	1	−	−	PROPN
ejpam-6316	114	2	φ	φ	PROPN
ejpam-6316	114	3	(	(	PUNCT
ejpam-6316	114	4	i−1∑	i−1∑	PROPN
ejpam-6316	114	5	k=1	k=1	PROPN
ejpam-6316	115	1	(	(	PUNCT
ejpam-6316	116	1	ψk	ψk	INTJ
ejpam-6316	116	2	,	,	PUNCT
ejpam-6316	116	3	d	d	PROPN
ejpam-6316	116	4	σ	σ	NUM
ejpam-6316	116	5	υψk	υψk	NOUN
ejpam-6316	116	6	,	,	PUNCT
ejpam-6316	117	1	d	d	PROPN
ejpam-6316	117	2	2σ	2σ	NUM
ejpam-6316	117	3	υ	υ	NOUN
ejpam-6316	117	4	ψk	ψk	VERB
ejpam-6316	117	5	,	,	PUNCT
ejpam-6316	117	6	d	d	PROPN
ejpam-6316	117	7	3σ	3σ	NUM
ejpam-6316	117	8	υ	υ	NOUN
ejpam-6316	117	9	ψk	ψk	NOUN
ejpam-6316	117	10	)	)	PUNCT
ejpam-6316	117	11	)	)	PUNCT
ejpam-6316	117	12	)	)	PUNCT
ejpam-6316	117	13	.	.	PUNCT
ejpam-6316	118	1	(	(	PUNCT
ejpam-6316	118	2	12	12	X
ejpam-6316	118	3	)	)	PUNCT
ejpam-6316	118	4	n.	n.	NOUN
ejpam-6316	118	5	iqbal	iqbal	PROPN
ejpam-6316	118	6	et	et	PROPN
ejpam-6316	118	7	al	al	PROPN
ejpam-6316	118	8	.	.	PUNCT
ejpam-6316	118	9	/	/	SYM
ejpam-6316	118	10	eur	eur	PROPN
ejpam-6316	118	11	.	.	PUNCT
ejpam-6316	119	1	j.	j.	PROPN
ejpam-6316	119	2	pure	pure	PROPN
ejpam-6316	119	3	appl	appl	PROPN
ejpam-6316	119	4	.	.	PROPN
ejpam-6316	119	5	math	math	PROPN
ejpam-6316	119	6	,	,	PUNCT
ejpam-6316	119	7	18	18	NUM
ejpam-6316	119	8	(	(	PUNCT
ejpam-6316	119	9	3	3	NUM
ejpam-6316	119	10	)	)	PUNCT
ejpam-6316	119	11	(	(	PUNCT
ejpam-6316	119	12	2025	2025	NUM
ejpam-6316	119	13	)	)	PUNCT
ejpam-6316	119	14	,	,	PUNCT
ejpam-6316	119	15	6316	6316	NUM
ejpam-6316	119	16	6	6	NUM
ejpam-6316	119	17	of	of	ADP
ejpam-6316	119	18	21	21	NUM
ejpam-6316	119	19	eqs	eq	NOUN
ejpam-6316	119	20	.	.	PROPN
ejpam-6316	119	21	12	12	NUM
ejpam-6316	119	22	and	and	CCONJ
ejpam-6316	119	23	11	11	NUM
ejpam-6316	119	24	putting	put	VERB
ejpam-6316	119	25	into	into	ADP
ejpam-6316	119	26	eq	eq	NOUN
ejpam-6316	119	27	.	.	PROPN
ejpam-6316	119	28	10	10	NUM
ejpam-6316	119	29	.	.	PUNCT
ejpam-6316	120	1	∞∑	∞∑	PRON
ejpam-6316	120	2	i=0	i=0	PROPN
ejpam-6316	120	3	ψi(υ	ψi(υ	NUM
ejpam-6316	120	4	,	,	PUNCT
ejpam-6316	120	5	σ	σ	X
ejpam-6316	120	6	)	)	PUNCT
ejpam-6316	120	7	=	=	SYM
ejpam-6316	120	8	n−1	n−1	PROPN
ejpam-6316	120	9	[	[	PUNCT
ejpam-6316	120	10	1	1	NUM
ejpam-6316	120	11	sp	sp	ADP
ejpam-6316	120	12	(	(	PUNCT
ejpam-6316	120	13	m−1∑	m−1∑	PROPN
ejpam-6316	120	14	k=0	k=0	PROPN
ejpam-6316	120	15	ψ(k)(υ	ψ(k)(υ	NOUN
ejpam-6316	120	16	,	,	PUNCT
ejpam-6316	120	17	0	0	NUM
ejpam-6316	120	18	)	)	PUNCT
ejpam-6316	120	19	s2−p+k	s2−p+k	NOUN
ejpam-6316	120	20	+	+	NOUN
ejpam-6316	120	21	n	n	CCONJ
ejpam-6316	120	22	[	[	X
ejpam-6316	120	23	φ(ψ0	φ(ψ0	NOUN
ejpam-6316	120	24	,	,	PUNCT
ejpam-6316	120	25	d	d	PROPN
ejpam-6316	120	26	σ	σ	X
ejpam-6316	120	27	υψ0	υψ0	PROPN
ejpam-6316	120	28	,	,	PUNCT
ejpam-6316	120	29	d	d	PROPN
ejpam-6316	120	30	2σ	2σ	NUM
ejpam-6316	120	31	υ	υ	NOUN
ejpam-6316	120	32	ψ0	ψ0	ADJ
ejpam-6316	120	33	,	,	PUNCT
ejpam-6316	120	34	d	d	PROPN
ejpam-6316	120	35	3σ	3σ	NUM
ejpam-6316	120	36	υ	υ	NOUN
ejpam-6316	120	37	ψ0	ψ0	ADJ
ejpam-6316	120	38	)	)	PUNCT
ejpam-6316	120	39	]	]	PUNCT
ejpam-6316	120	40	)	)	PUNCT
ejpam-6316	120	41	]	]	PUNCT
ejpam-6316	121	1	+	+	PUNCT
ejpam-6316	121	2	n−1	n−1	PROPN
ejpam-6316	121	3	[	[	PUNCT
ejpam-6316	121	4	1	1	NUM
ejpam-6316	121	5	sp	sp	ADP
ejpam-6316	121	6	(	(	PUNCT
ejpam-6316	121	7	n	n	X
ejpam-6316	121	8	[	[	PUNCT
ejpam-6316	121	9	∞∑	∞∑	PROPN
ejpam-6316	121	10	i=0	i=0	PROPN
ejpam-6316	121	11	(	(	PUNCT
ejpam-6316	121	12	φ	φ	PROPN
ejpam-6316	121	13	i∑	i∑	PROPN
ejpam-6316	121	14	k=0	k=0	PROPN
ejpam-6316	121	15	(	(	PUNCT
ejpam-6316	121	16	ψk	ψk	INTJ
ejpam-6316	121	17	,	,	PUNCT
ejpam-6316	121	18	d	d	PROPN
ejpam-6316	121	19	σ	σ	NUM
ejpam-6316	121	20	υψk	υψk	NOUN
ejpam-6316	121	21	,	,	PUNCT
ejpam-6316	121	22	d	d	PROPN
ejpam-6316	121	23	2σ	2σ	NUM
ejpam-6316	121	24	υ	υ	NOUN
ejpam-6316	121	25	ψk	ψk	VERB
ejpam-6316	121	26	,	,	PUNCT
ejpam-6316	121	27	d	d	PROPN
ejpam-6316	121	28	3σ	3σ	NUM
ejpam-6316	121	29	υ	υ	NOUN
ejpam-6316	121	30	ψk	ψk	NOUN
ejpam-6316	121	31	)	)	PUNCT
ejpam-6316	121	32	)	)	PUNCT
ejpam-6316	121	33	]	]	PUNCT
ejpam-6316	121	34	)	)	PUNCT
ejpam-6316	121	35	]	]	PUNCT
ejpam-6316	122	1	−n−1	−n−1	NUM
ejpam-6316	122	2	[	[	PUNCT
ejpam-6316	122	3	1	1	NUM
ejpam-6316	122	4	sp	sp	ADP
ejpam-6316	122	5	(	(	PUNCT
ejpam-6316	122	6	n	n	X
ejpam-6316	122	7	[	[	X
ejpam-6316	122	8	(	(	PUNCT
ejpam-6316	122	9	φ	φ	PROPN
ejpam-6316	122	10	i−1∑	i−1∑	NUM
ejpam-6316	122	11	k=1	k=1	X
ejpam-6316	122	12	(	(	PUNCT
ejpam-6316	122	13	ψk	ψk	INTJ
ejpam-6316	122	14	,	,	PUNCT
ejpam-6316	122	15	d	d	PROPN
ejpam-6316	122	16	σ	σ	NUM
ejpam-6316	122	17	υψk	υψk	NOUN
ejpam-6316	122	18	,	,	PUNCT
ejpam-6316	122	19	d	d	PROPN
ejpam-6316	122	20	2σ	2σ	NUM
ejpam-6316	122	21	υ	υ	NOUN
ejpam-6316	122	22	ψk	ψk	VERB
ejpam-6316	122	23	,	,	PUNCT
ejpam-6316	122	24	d	d	PROPN
ejpam-6316	122	25	3σ	3σ	NUM
ejpam-6316	122	26	υ	υ	NOUN
ejpam-6316	122	27	ψk	ψk	NOUN
ejpam-6316	122	28	)	)	PUNCT
ejpam-6316	122	29	)	)	PUNCT
ejpam-6316	122	30	]	]	PUNCT
ejpam-6316	122	31	)	)	PUNCT
ejpam-6316	122	32	]	]	PUNCT
ejpam-6316	122	33	(	(	PUNCT
ejpam-6316	122	34	13	13	NUM
ejpam-6316	122	35	)	)	PUNCT
ejpam-6316	122	36	ψ0(υ	ψ0(υ	PROPN
ejpam-6316	122	37	,	,	PUNCT
ejpam-6316	122	38	σ	σ	NOUN
ejpam-6316	122	39	)	)	PUNCT
ejpam-6316	122	40	=	=	SYM
ejpam-6316	123	1	n−1	n−1	PROPN
ejpam-6316	123	2	[	[	PUNCT
ejpam-6316	123	3	1	1	NUM
ejpam-6316	123	4	sp	sp	ADP
ejpam-6316	123	5	(	(	PUNCT
ejpam-6316	123	6	m−1∑	m−1∑	PROPN
ejpam-6316	123	7	k=0	k=0	PROPN
ejpam-6316	123	8	ψ(k)(υ	ψ(k)(υ	NOUN
ejpam-6316	123	9	,	,	PUNCT
ejpam-6316	123	10	0	0	NUM
ejpam-6316	123	11	)	)	PUNCT
ejpam-6316	123	12	s2−p+k	s2−p+k	NOUN
ejpam-6316	123	13	)	)	PUNCT
ejpam-6316	123	14	]	]	PUNCT
ejpam-6316	123	15	,	,	PUNCT
ejpam-6316	123	16	ψ1(υ	ψ1(υ	PROPN
ejpam-6316	123	17	,	,	PUNCT
ejpam-6316	123	18	σ	σ	PROPN
ejpam-6316	123	19	)	)	PUNCT
ejpam-6316	123	20	=	=	SYM
ejpam-6316	123	21	n−1	n−1	PROPN
ejpam-6316	123	22	[	[	PUNCT
ejpam-6316	123	23	1	1	NUM
ejpam-6316	123	24	sp	sp	ADP
ejpam-6316	123	25	(	(	PUNCT
ejpam-6316	123	26	n	n	CCONJ
ejpam-6316	123	27	[	[	X
ejpam-6316	123	28	φ(ψ0	φ(ψ0	NOUN
ejpam-6316	123	29	,	,	PUNCT
ejpam-6316	123	30	d	d	PROPN
ejpam-6316	123	31	σ	σ	X
ejpam-6316	123	32	υψ0	υψ0	PROPN
ejpam-6316	123	33	,	,	PUNCT
ejpam-6316	124	1	d	d	PROPN
ejpam-6316	124	2	2σ	2σ	NUM
ejpam-6316	124	3	υ	υ	NOUN
ejpam-6316	124	4	ψ0	ψ0	ADJ
ejpam-6316	124	5	,	,	PUNCT
ejpam-6316	124	6	d	d	PROPN
ejpam-6316	124	7	3σ	3σ	NUM
ejpam-6316	124	8	υ	υ	NOUN
ejpam-6316	124	9	ψ0	ψ0	ADJ
ejpam-6316	124	10	)	)	PUNCT
ejpam-6316	124	11	]	]	PUNCT
ejpam-6316	124	12	)	)	PUNCT
ejpam-6316	124	13	]	]	PUNCT
ejpam-6316	124	14	,	,	PUNCT
ejpam-6316	124	15	...	...	PUNCT
ejpam-6316	125	1	ψm+1(υ	ψm+1(υ	ADV
ejpam-6316	125	2	,	,	PUNCT
ejpam-6316	125	3	σ	σ	NOUN
ejpam-6316	125	4	)	)	PUNCT
ejpam-6316	125	5	=	=	SYM
ejpam-6316	125	6	n−1	n−1	PROPN
ejpam-6316	125	7	[	[	PUNCT
ejpam-6316	125	8	1	1	NUM
ejpam-6316	125	9	sp	sp	ADP
ejpam-6316	125	10	(	(	PUNCT
ejpam-6316	125	11	n	n	X
ejpam-6316	125	12	[	[	PUNCT
ejpam-6316	125	13	∞∑	∞∑	PROPN
ejpam-6316	125	14	i=0	i=0	PROPN
ejpam-6316	125	15	(	(	PUNCT
ejpam-6316	125	16	φ	φ	PROPN
ejpam-6316	125	17	i∑	i∑	PROPN
ejpam-6316	125	18	k=0	k=0	PROPN
ejpam-6316	125	19	(	(	PUNCT
ejpam-6316	125	20	ψk	ψk	INTJ
ejpam-6316	125	21	,	,	PUNCT
ejpam-6316	125	22	d	d	PROPN
ejpam-6316	125	23	σ	σ	NUM
ejpam-6316	125	24	υψk	υψk	NOUN
ejpam-6316	125	25	,	,	PUNCT
ejpam-6316	126	1	d	d	PROPN
ejpam-6316	126	2	2σ	2σ	NUM
ejpam-6316	126	3	υ	υ	NOUN
ejpam-6316	126	4	ψk	ψk	VERB
ejpam-6316	126	5	,	,	PUNCT
ejpam-6316	126	6	d	d	PROPN
ejpam-6316	126	7	3σ	3σ	NUM
ejpam-6316	126	8	υ	υ	NOUN
ejpam-6316	126	9	ψk	ψk	NOUN
ejpam-6316	126	10	)	)	PUNCT
ejpam-6316	126	11	)	)	PUNCT
ejpam-6316	126	12	]	]	PUNCT
ejpam-6316	126	13	)	)	PUNCT
ejpam-6316	126	14	]	]	PUNCT
ejpam-6316	127	1	−n−1	−n−1	NUM
ejpam-6316	127	2	[	[	PUNCT
ejpam-6316	127	3	1	1	NUM
ejpam-6316	127	4	sp	sp	ADP
ejpam-6316	127	5	(	(	PUNCT
ejpam-6316	127	6	n	n	X
ejpam-6316	127	7	[	[	X
ejpam-6316	127	8	(	(	PUNCT
ejpam-6316	127	9	φ	φ	PROPN
ejpam-6316	127	10	i−1∑	i−1∑	NUM
ejpam-6316	127	11	k=1	k=1	X
ejpam-6316	127	12	(	(	PUNCT
ejpam-6316	127	13	ψk	ψk	INTJ
ejpam-6316	127	14	,	,	PUNCT
ejpam-6316	127	15	d	d	PROPN
ejpam-6316	127	16	σ	σ	NUM
ejpam-6316	127	17	υψk	υψk	NOUN
ejpam-6316	127	18	,	,	PUNCT
ejpam-6316	127	19	d	d	PROPN
ejpam-6316	127	20	2σ	2σ	NUM
ejpam-6316	127	21	υ	υ	NOUN
ejpam-6316	127	22	ψk	ψk	VERB
ejpam-6316	127	23	,	,	PUNCT
ejpam-6316	127	24	d	d	PROPN
ejpam-6316	127	25	3σ	3σ	NUM
ejpam-6316	127	26	υ	υ	NOUN
ejpam-6316	127	27	ψk	ψk	NOUN
ejpam-6316	127	28	)	)	PUNCT
ejpam-6316	127	29	)	)	PUNCT
ejpam-6316	127	30	]	]	PUNCT
ejpam-6316	127	31	)	)	PUNCT
ejpam-6316	127	32	]	]	PUNCT
ejpam-6316	127	33	,	,	PUNCT
ejpam-6316	127	34	m	m	VERB
ejpam-6316	127	35	=	=	NOUN
ejpam-6316	127	36	1	1	NUM
ejpam-6316	127	37	,	,	PUNCT
ejpam-6316	127	38	2	2	NUM
ejpam-6316	127	39	,	,	PUNCT
ejpam-6316	127	40	·	·	PUNCT
ejpam-6316	127	41	·	·	PUNCT
ejpam-6316	127	42	·	·	PUNCT
ejpam-6316	127	43	.	.	PUNCT
ejpam-6316	128	1	(	(	PUNCT
ejpam-6316	128	2	14	14	NUM
ejpam-6316	128	3	)	)	PUNCT
ejpam-6316	128	4	the	the	DET
ejpam-6316	128	5	following	follow	VERB
ejpam-6316	128	6	eq	eq	ADP
ejpam-6316	128	7	.	.	PROPN
ejpam-6316	128	8	7	7	NUM
ejpam-6316	128	9	yield	yield	VERB
ejpam-6316	128	10	the	the	DET
ejpam-6316	128	11	semi	semi	ADJ
ejpam-6316	128	12	-	-	ADJ
ejpam-6316	128	13	analytical	analytical	ADJ
ejpam-6316	128	14	result	result	NOUN
ejpam-6316	128	15	for	for	ADP
ejpam-6316	128	16	the	the	DET
ejpam-6316	128	17	i	i	NOUN
ejpam-6316	128	18	-	-	PUNCT
ejpam-6316	128	19	terms	term	NOUN
ejpam-6316	128	20	defined	define	VERB
ejpam-6316	128	21	as	as	ADP
ejpam-6316	128	22	:	:	PUNCT
ejpam-6316	128	23	ψ(υ	ψ(υ	PROPN
ejpam-6316	128	24	,	,	PUNCT
ejpam-6316	128	25	σ	σ	NOUN
ejpam-6316	128	26	)	)	PUNCT
ejpam-6316	128	27	=	=	PUNCT
ejpam-6316	129	1	m−1∑	m−1∑	NUM
ejpam-6316	129	2	i=0	i=0	PROPN
ejpam-6316	129	3	ψi	ψi	NOUN
ejpam-6316	129	4	.	.	PUNCT
ejpam-6316	130	1	(	(	PUNCT
ejpam-6316	130	2	15	15	NUM
ejpam-6316	130	3	)	)	PUNCT
ejpam-6316	130	4	3.3	3.3	NUM
ejpam-6316	130	5	.	.	PUNCT
ejpam-6316	131	1	problem	problem	NOUN
ejpam-6316	131	2	1	1	NUM
ejpam-6316	131	3	3.3.1	3.3.1	NUM
ejpam-6316	131	4	.	.	PUNCT
ejpam-6316	132	1	implementation	implementation	NOUN
ejpam-6316	132	2	of	of	ADP
ejpam-6316	132	3	rpsntm	rpsntm	PROPN
ejpam-6316	132	4	consider	consider	VERB
ejpam-6316	132	5	the	the	DET
ejpam-6316	132	6	following	follow	VERB
ejpam-6316	132	7	fractional	fractional	ADJ
ejpam-6316	132	8	dispersive	dispersive	ADJ
ejpam-6316	132	9	kdv	kdv	NOUN
ejpam-6316	132	10	equation	equation	NOUN
ejpam-6316	132	11	dp	dp	NOUN
ejpam-6316	132	12	σψ	σψ	NOUN
ejpam-6316	133	1	+	+	CCONJ
ejpam-6316	133	2	2	2	NUM
ejpam-6316	133	3	∂ψ	∂ψ	ADJ
ejpam-6316	133	4	∂υ	∂υ	NOUN
ejpam-6316	133	5	+	+	CCONJ
ejpam-6316	133	6	∂3ψ	∂3ψ	NOUN
ejpam-6316	133	7	∂υ3	∂υ3	PROPN
ejpam-6316	133	8	=	=	SYM
ejpam-6316	133	9	0	0	PUNCT
ejpam-6316	133	10	σ	σ	PROPN
ejpam-6316	133	11	>	>	X
ejpam-6316	133	12	0	0	PROPN
ejpam-6316	133	13	,	,	PUNCT
ejpam-6316	133	14	where	where	SCONJ
ejpam-6316	133	15	0	0	X
ejpam-6316	133	16	<	<	X
ejpam-6316	133	17	p	p	X
ejpam-6316	133	18	≤	≤	ADJ
ejpam-6316	133	19	1	1	NUM
ejpam-6316	133	20	(	(	PUNCT
ejpam-6316	133	21	16	16	NUM
ejpam-6316	133	22	)	)	PUNCT
ejpam-6316	133	23	having	have	VERB
ejpam-6316	133	24	ic	ic	PRON
ejpam-6316	133	25	’s	’s	PART
ejpam-6316	133	26	:	:	PUNCT
ejpam-6316	133	27	ψ(υ	ψ(υ	NOUN
ejpam-6316	133	28	,	,	PUNCT
ejpam-6316	133	29	0	0	NUM
ejpam-6316	133	30	)	)	PUNCT
ejpam-6316	133	31	=	=	SYM
ejpam-6316	133	32	sin(υ	sin(υ	NOUN
ejpam-6316	133	33	)	)	PUNCT
ejpam-6316	133	34	(	(	PUNCT
ejpam-6316	133	35	17	17	NUM
ejpam-6316	133	36	)	)	PUNCT
ejpam-6316	133	37	using	use	VERB
ejpam-6316	133	38	eq	eq	X
ejpam-6316	133	39	.	.	PUNCT
ejpam-6316	133	40	(	(	PUNCT
ejpam-6316	133	41	17	17	NUM
ejpam-6316	133	42	)	)	PUNCT
ejpam-6316	133	43	and	and	CCONJ
ejpam-6316	133	44	applying	apply	VERB
ejpam-6316	133	45	nt	not	PART
ejpam-6316	133	46	to	to	ADP
ejpam-6316	133	47	eq	eq	PROPN
ejpam-6316	133	48	.	.	PUNCT
ejpam-6316	134	1	(	(	PUNCT
ejpam-6316	134	2	16	16	NUM
ejpam-6316	134	3	)	)	PUNCT
ejpam-6316	134	4	,	,	PUNCT
ejpam-6316	134	5	we	we	PRON
ejpam-6316	134	6	obtain	obtain	VERB
ejpam-6316	134	7	:	:	PUNCT
ejpam-6316	134	8	ψ(υ	ψ(υ	PROPN
ejpam-6316	134	9	,	,	PUNCT
ejpam-6316	134	10	0)−	0)−	PUNCT
ejpam-6316	135	1	sin(υ	sin(υ	X
ejpam-6316	135	2	)	)	PUNCT
ejpam-6316	135	3	s	s	PART
ejpam-6316	136	1	+	+	X
ejpam-6316	136	2	up	up	ADP
ejpam-6316	136	3	sp	sp	ADP
ejpam-6316	136	4	∂3ψ(υ	∂3ψ(υ	NOUN
ejpam-6316	136	5	,	,	PUNCT
ejpam-6316	136	6	0	0	NUM
ejpam-6316	136	7	)	)	PUNCT
ejpam-6316	137	1	∂υ3	∂υ3	PROPN
ejpam-6316	137	2	+	+	CCONJ
ejpam-6316	137	3	2up	2up	ADJ
ejpam-6316	137	4	sp	sp	ADP
ejpam-6316	137	5	∂ψ(υ	∂ψ(υ	PROPN
ejpam-6316	137	6	,	,	PUNCT
ejpam-6316	137	7	0	0	NUM
ejpam-6316	137	8	)	)	PUNCT
ejpam-6316	138	1	∂υ	∂υ	NOUN
ejpam-6316	139	1	=	=	SYM
ejpam-6316	139	2	0	0	NUM
ejpam-6316	140	1	(	(	PUNCT
ejpam-6316	140	2	18	18	NUM
ejpam-6316	140	3	)	)	PUNCT
ejpam-6316	140	4	n.	n.	NOUN
ejpam-6316	140	5	iqbal	iqbal	PROPN
ejpam-6316	140	6	et	et	PROPN
ejpam-6316	140	7	al	al	PROPN
ejpam-6316	140	8	.	.	PUNCT
ejpam-6316	140	9	/	/	SYM
ejpam-6316	140	10	eur	eur	PROPN
ejpam-6316	140	11	.	.	PUNCT
ejpam-6316	141	1	j.	j.	PROPN
ejpam-6316	141	2	pure	pure	PROPN
ejpam-6316	141	3	appl	appl	PROPN
ejpam-6316	141	4	.	.	PROPN
ejpam-6316	141	5	math	math	PROPN
ejpam-6316	141	6	,	,	PUNCT
ejpam-6316	141	7	18	18	NUM
ejpam-6316	141	8	(	(	PUNCT
ejpam-6316	141	9	3	3	NUM
ejpam-6316	141	10	)	)	PUNCT
ejpam-6316	141	11	(	(	PUNCT
ejpam-6316	141	12	2025	2025	NUM
ejpam-6316	141	13	)	)	PUNCT
ejpam-6316	141	14	,	,	PUNCT
ejpam-6316	141	15	6316	6316	NUM
ejpam-6316	141	16	7	7	NUM
ejpam-6316	141	17	of	of	ADP
ejpam-6316	141	18	21	21	NUM
ejpam-6316	141	19	thus	thus	ADV
ejpam-6316	141	20	,	,	PUNCT
ejpam-6316	141	21	the	the	DET
ejpam-6316	141	22	term	term	NOUN
ejpam-6316	141	23	series	series	NOUN
ejpam-6316	141	24	that	that	PRON
ejpam-6316	141	25	are	be	AUX
ejpam-6316	141	26	kth	kth	NOUN
ejpam-6316	141	27	-	-	PUNCT
ejpam-6316	141	28	truncated	truncate	VERB
ejpam-6316	141	29	are	be	AUX
ejpam-6316	141	30	:	:	PUNCT
ejpam-6316	141	31	ψ(υ	ψ(υ	PROPN
ejpam-6316	141	32	,	,	PUNCT
ejpam-6316	141	33	s	s	NOUN
ejpam-6316	141	34	)	)	PUNCT
ejpam-6316	141	35	=	=	SYM
ejpam-6316	142	1	sin(υ	sin(υ	PROPN
ejpam-6316	142	2	)	)	PUNCT
ejpam-6316	142	3	s	s	PART
ejpam-6316	143	1	+	+	CCONJ
ejpam-6316	143	2	k∑	k∑	NOUN
ejpam-6316	143	3	r=1	r=1	NOUN
ejpam-6316	143	4	urp+1fr(υ	urp+1fr(υ	NOUN
ejpam-6316	143	5	,	,	PUNCT
ejpam-6316	143	6	s	s	NOUN
ejpam-6316	143	7	)	)	PUNCT
ejpam-6316	143	8	srp+1	srp+1	NOUN
ejpam-6316	143	9	,	,	PUNCT
ejpam-6316	143	10	r	r	NOUN
ejpam-6316	143	11	=	=	SYM
ejpam-6316	143	12	1	1	NUM
ejpam-6316	143	13	,	,	PUNCT
ejpam-6316	143	14	2	2	NUM
ejpam-6316	143	15	,	,	PUNCT
ejpam-6316	143	16	3	3	NUM
ejpam-6316	143	17	,	,	PUNCT
ejpam-6316	143	18	·	·	PUNCT
ejpam-6316	143	19	·	·	PUNCT
ejpam-6316	143	20	·	·	PUNCT
ejpam-6316	143	21	.	.	PUNCT
ejpam-6316	144	1	(	(	PUNCT
ejpam-6316	144	2	19	19	NUM
ejpam-6316	144	3	)	)	PUNCT
ejpam-6316	144	4	natural	natural	ADJ
ejpam-6316	144	5	residual	residual	ADJ
ejpam-6316	144	6	functions	function	NOUN
ejpam-6316	144	7	(	(	PUNCT
ejpam-6316	144	8	nrfs	nrf	NOUN
ejpam-6316	144	9	)	)	PUNCT
ejpam-6316	144	10	provided	provide	VERB
ejpam-6316	144	11	as	as	ADP
ejpam-6316	144	12	follows	follow	VERB
ejpam-6316	144	13	:	:	PUNCT
ejpam-6316	144	14	nσres(υ	nσres(υ	NUM
ejpam-6316	144	15	,	,	PUNCT
ejpam-6316	144	16	s	s	PART
ejpam-6316	144	17	)	)	PUNCT
ejpam-6316	144	18	=	=	SYM
ejpam-6316	144	19	ψ(υ	ψ(υ	PROPN
ejpam-6316	144	20	,	,	PUNCT
ejpam-6316	144	21	0)−	0)−	PUNCT
ejpam-6316	145	1	sin(υ	sin(υ	X
ejpam-6316	145	2	)	)	PUNCT
ejpam-6316	145	3	s	s	PART
ejpam-6316	146	1	+	+	X
ejpam-6316	146	2	up	up	ADP
ejpam-6316	146	3	sp	sp	ADP
ejpam-6316	146	4	∂3ψ(υ	∂3ψ(υ	NOUN
ejpam-6316	146	5	,	,	PUNCT
ejpam-6316	146	6	0	0	NUM
ejpam-6316	146	7	)	)	PUNCT
ejpam-6316	147	1	∂υ3	∂υ3	PROPN
ejpam-6316	147	2	+	+	CCONJ
ejpam-6316	147	3	2up	2up	ADJ
ejpam-6316	147	4	sp	sp	ADP
ejpam-6316	147	5	∂ψ(υ	∂ψ(υ	PROPN
ejpam-6316	147	6	,	,	PUNCT
ejpam-6316	147	7	0	0	NUM
ejpam-6316	147	8	)	)	PUNCT
ejpam-6316	148	1	∂υ	∂υ	NOUN
ejpam-6316	148	2	=	=	SYM
ejpam-6316	148	3	0	0	NUM
ejpam-6316	148	4	,	,	PUNCT
ejpam-6316	148	5	(	(	PUNCT
ejpam-6316	148	6	20	20	NUM
ejpam-6316	148	7	)	)	PUNCT
ejpam-6316	148	8	along	along	ADP
ejpam-6316	148	9	with	with	ADP
ejpam-6316	148	10	the	the	DET
ejpam-6316	148	11	kth	kth	NOUN
ejpam-6316	148	12	-	-	PUNCT
ejpam-6316	148	13	nrfs	nrf	NOUN
ejpam-6316	148	14	as	as	ADP
ejpam-6316	148	15	:	:	PUNCT
ejpam-6316	148	16	nσresk(υ	nσresk(υ	PROPN
ejpam-6316	148	17	,	,	PUNCT
ejpam-6316	148	18	s	s	PART
ejpam-6316	148	19	)	)	PUNCT
ejpam-6316	148	20	=	=	PRON
ejpam-6316	148	21	ψk(υ	ψk(υ	X
ejpam-6316	148	22	,	,	PUNCT
ejpam-6316	148	23	0)−	0)−	PUNCT
ejpam-6316	148	24	sin(υ	sin(υ	X
ejpam-6316	148	25	)	)	PUNCT
ejpam-6316	148	26	s	s	PART
ejpam-6316	149	1	+	+	X
ejpam-6316	149	2	up	up	ADP
ejpam-6316	149	3	sp	sp	ADP
ejpam-6316	149	4	∂3ψk(x	∂3ψk(x	PROPN
ejpam-6316	149	5	,	,	PUNCT
ejpam-6316	149	6	0	0	NUM
ejpam-6316	149	7	)	)	PUNCT
ejpam-6316	150	1	∂υ3	∂υ3	PROPN
ejpam-6316	150	2	+	+	CCONJ
ejpam-6316	150	3	2up	2up	ADJ
ejpam-6316	150	4	sp	sp	ADP
ejpam-6316	150	5	∂ψk(υ	∂ψk(υ	PROPN
ejpam-6316	150	6	,	,	PUNCT
ejpam-6316	150	7	0	0	NUM
ejpam-6316	150	8	)	)	PUNCT
ejpam-6316	150	9	∂υ	∂υ	NOUN
ejpam-6316	150	10	=	=	SYM
ejpam-6316	151	1	0	0	X
ejpam-6316	151	2	.	.	PUNCT
ejpam-6316	152	1	(	(	PUNCT
ejpam-6316	152	2	21	21	NUM
ejpam-6316	152	3	)	)	PUNCT
ejpam-6316	152	4	to	to	PART
ejpam-6316	152	5	find	find	VERB
ejpam-6316	152	6	fr(υ	fr(υ	NOUN
ejpam-6316	152	7	,	,	PUNCT
ejpam-6316	152	8	s	s	PART
ejpam-6316	152	9	)	)	PUNCT
ejpam-6316	152	10	now	now	ADV
ejpam-6316	152	11	,	,	PUNCT
ejpam-6316	152	12	r	r	NOUN
ejpam-6316	152	13	=	=	SYM
ejpam-6316	152	14	1	1	NUM
ejpam-6316	152	15	,	,	PUNCT
ejpam-6316	152	16	2	2	NUM
ejpam-6316	152	17	,	,	PUNCT
ejpam-6316	152	18	3	3	NUM
ejpam-6316	152	19	,	,	PUNCT
ejpam-6316	152	20	·	·	PUNCT
ejpam-6316	152	21	·	·	PUNCT
ejpam-6316	152	22	·	·	PUNCT
ejpam-6316	152	23	we	we	PRON
ejpam-6316	152	24	multiply	multiply	VERB
ejpam-6316	152	25	the	the	DET
ejpam-6316	152	26	resulting	result	VERB
ejpam-6316	152	27	equation	equation	NOUN
ejpam-6316	152	28	by	by	ADP
ejpam-6316	152	29	srp+1	srp+1	NOUN
ejpam-6316	152	30	,	,	PUNCT
ejpam-6316	152	31	substitute	substitute	VERB
ejpam-6316	152	32	the	the	DET
ejpam-6316	152	33	rσh	rσh	NOUN
ejpam-6316	152	34	-	-	PUNCT
ejpam-6316	152	35	truncated	truncate	VERB
ejpam-6316	152	36	series	series	NOUN
ejpam-6316	152	37	eq	eq	PROPN
ejpam-6316	152	38	.	.	PUNCT
ejpam-6316	153	1	(	(	PUNCT
ejpam-6316	153	2	19	19	NUM
ejpam-6316	153	3	)	)	PUNCT
ejpam-6316	153	4	into	into	ADP
ejpam-6316	153	5	the	the	DET
ejpam-6316	153	6	rσh	rσh	NOUN
ejpam-6316	153	7	-	-	PUNCT
ejpam-6316	153	8	natural	natural	ADJ
ejpam-6316	153	9	residual	residual	ADJ
ejpam-6316	153	10	function	function	NOUN
ejpam-6316	153	11	eq	eq	ADP
ejpam-6316	153	12	.	.	PUNCT
ejpam-6316	154	1	(	(	PUNCT
ejpam-6316	154	2	21	21	NUM
ejpam-6316	154	3	)	)	PUNCT
ejpam-6316	154	4	,	,	PUNCT
ejpam-6316	154	5	and	and	CCONJ
ejpam-6316	154	6	solve	solve	VERB
ejpam-6316	154	7	the	the	DET
ejpam-6316	154	8	relation	relation	NOUN
ejpam-6316	154	9	lims→∞(srp+1nσresψ	lims→∞(srp+1nσresψ	NOUN
ejpam-6316	154	10	,	,	PUNCT
ejpam-6316	154	11	r(σ	r(σ	PROPN
ejpam-6316	154	12	,	,	PUNCT
ejpam-6316	154	13	s	s	NOUN
ejpam-6316	154	14	)	)	PUNCT
ejpam-6316	154	15	)	)	PUNCT
ejpam-6316	155	1	=	=	SYM
ejpam-6316	155	2	0	0	NUM
ejpam-6316	155	3	recursively	recursively	NOUN
ejpam-6316	155	4	.	.	PUNCT
ejpam-6316	156	1	1	1	NUM
ejpam-6316	156	2	,	,	PUNCT
ejpam-6316	156	3	2	2	NUM
ejpam-6316	156	4	,	,	PUNCT
ejpam-6316	156	5	3	3	NUM
ejpam-6316	156	6	,	,	PUNCT
ejpam-6316	156	7	·	·	PUNCT
ejpam-6316	156	8	·	·	PUNCT
ejpam-6316	156	9	·	·	PUNCT
ejpam-6316	156	10	.	.	PUNCT
ejpam-6316	157	1	here	here	ADV
ejpam-6316	157	2	are	be	AUX
ejpam-6316	157	3	the	the	DET
ejpam-6316	157	4	first	first	ADJ
ejpam-6316	157	5	few	few	ADJ
ejpam-6316	157	6	of	of	ADP
ejpam-6316	157	7	terms	term	NOUN
ejpam-6316	157	8	:	:	PUNCT
ejpam-6316	157	9	f1(υ	f1(υ	NUM
ejpam-6316	157	10	,	,	PUNCT
ejpam-6316	157	11	s	s	PART
ejpam-6316	157	12	)	)	PUNCT
ejpam-6316	157	13	=	=	SYM
ejpam-6316	157	14	−	−	PROPN
ejpam-6316	157	15	cos(υ	cos(υ	NOUN
ejpam-6316	157	16	)	)	PUNCT
ejpam-6316	157	17	,	,	PUNCT
ejpam-6316	157	18	(	(	PUNCT
ejpam-6316	157	19	22	22	NUM
ejpam-6316	157	20	)	)	PUNCT
ejpam-6316	157	21	f2(υ	f2(υ	PROPN
ejpam-6316	157	22	,	,	PUNCT
ejpam-6316	157	23	s	s	NOUN
ejpam-6316	157	24	)	)	PUNCT
ejpam-6316	157	25	=	=	SYM
ejpam-6316	157	26	−	−	PROPN
ejpam-6316	157	27	sin(υ	sin(υ	NUM
ejpam-6316	157	28	)	)	PUNCT
ejpam-6316	157	29	,	,	PUNCT
ejpam-6316	157	30	(	(	PUNCT
ejpam-6316	157	31	23	23	NUM
ejpam-6316	157	32	)	)	PUNCT
ejpam-6316	157	33	f3(υ	f3(υ	PROPN
ejpam-6316	157	34	,	,	PUNCT
ejpam-6316	157	35	s	s	PART
ejpam-6316	157	36	)	)	PUNCT
ejpam-6316	157	37	=	=	SYM
ejpam-6316	157	38	cos(υ	cos(υ	PROPN
ejpam-6316	157	39	)	)	PUNCT
ejpam-6316	157	40	(	(	PUNCT
ejpam-6316	157	41	24	24	NUM
ejpam-6316	157	42	)	)	PUNCT
ejpam-6316	157	43	and	and	CCONJ
ejpam-6316	157	44	so	so	ADV
ejpam-6316	157	45	on	on	ADV
ejpam-6316	157	46	.	.	PUNCT
ejpam-6316	158	1	in	in	ADP
ejpam-6316	158	2	eq	eq	ADP
ejpam-6316	158	3	.	.	PUNCT
ejpam-6316	159	1	(	(	PUNCT
ejpam-6316	159	2	19	19	NUM
ejpam-6316	159	3	)	)	PUNCT
ejpam-6316	159	4	,	,	PUNCT
ejpam-6316	159	5	substitute	substitute	VERB
ejpam-6316	159	6	the	the	DET
ejpam-6316	159	7	values	value	NOUN
ejpam-6316	159	8	of	of	ADP
ejpam-6316	159	9	fr(υ	fr(υ	NOUN
ejpam-6316	159	10	,	,	PUNCT
ejpam-6316	159	11	s	s	PART
ejpam-6316	159	12	)	)	PUNCT
ejpam-6316	159	13	,	,	PUNCT
ejpam-6316	159	14	r	r	NOUN
ejpam-6316	159	15	=	=	SYM
ejpam-6316	159	16	1	1	NUM
ejpam-6316	159	17	,	,	PUNCT
ejpam-6316	159	18	2	2	NUM
ejpam-6316	159	19	,	,	PUNCT
ejpam-6316	159	20	3	3	NUM
ejpam-6316	159	21	,	,	PUNCT
ejpam-6316	159	22	·	·	PUNCT
ejpam-6316	159	23	·	·	PUNCT
ejpam-6316	159	24	·	·	PUNCT
ejpam-6316	159	25	,	,	PUNCT
ejpam-6316	159	26	we	we	PRON
ejpam-6316	159	27	get	get	VERB
ejpam-6316	159	28	:	:	PUNCT
ejpam-6316	159	29	ψ(υ	ψ(υ	NOUN
ejpam-6316	159	30	,	,	PUNCT
ejpam-6316	159	31	s	s	PART
ejpam-6316	159	32	)	)	PUNCT
ejpam-6316	160	1	=	=	SYM
ejpam-6316	160	2	u	u	NOUN
ejpam-6316	160	3	sin(υ	sin(υ	PROPN
ejpam-6316	160	4	)	)	PUNCT
ejpam-6316	160	5	s	s	PART
ejpam-6316	160	6	−	−	PROPN
ejpam-6316	160	7	up	up	ADP
ejpam-6316	160	8	cos(υ	cos(υ	PROPN
ejpam-6316	160	9	)	)	PUNCT
ejpam-6316	160	10	sp+1	sp+1	PROPN
ejpam-6316	160	11	−	−	NOUN
ejpam-6316	161	1	up	up	ADP
ejpam-6316	161	2	sin(υ	sin(υ	PROPN
ejpam-6316	161	3	)	)	PUNCT
ejpam-6316	161	4	s2p+1	s2p+1	NOUN
ejpam-6316	161	5	+	+	CCONJ
ejpam-6316	161	6	up	up	ADP
ejpam-6316	161	7	cos(υ	cos(υ	PROPN
ejpam-6316	161	8	)	)	PUNCT
ejpam-6316	161	9	s3p+1	s3p+1	NOUN
ejpam-6316	161	10	,	,	PUNCT
ejpam-6316	161	11	(	(	PUNCT
ejpam-6316	161	12	25	25	NUM
ejpam-6316	161	13	)	)	PUNCT
ejpam-6316	161	14	using	use	VERB
ejpam-6316	161	15	inverse	inverse	ADJ
ejpam-6316	161	16	natural	natural	ADJ
ejpam-6316	161	17	transform	transform	NOUN
ejpam-6316	161	18	,	,	PUNCT
ejpam-6316	161	19	we	we	PRON
ejpam-6316	161	20	get	get	VERB
ejpam-6316	161	21	ψ(υ	ψ(υ	PROPN
ejpam-6316	161	22	,	,	PUNCT
ejpam-6316	161	23	σ	σ	NOUN
ejpam-6316	161	24	)	)	PUNCT
ejpam-6316	162	1	=	=	PROPN
ejpam-6316	162	2	sin(υ)−	sin(υ)−	NOUN
ejpam-6316	162	3	σp	σp	PROPN
ejpam-6316	162	4	cos(υ	cos(υ	PROPN
ejpam-6316	162	5	)	)	PUNCT
ejpam-6316	162	6	γ(p+	γ(p+	VERB
ejpam-6316	162	7	1	1	X
ejpam-6316	162	8	)	)	PUNCT
ejpam-6316	162	9	−	−	PROPN
ejpam-6316	162	10	σ2p	σ2p	PROPN
ejpam-6316	162	11	sin(υ	sin(υ	PROPN
ejpam-6316	162	12	)	)	PUNCT
ejpam-6316	162	13	γ(2p+	γ(2p+	NOUN
ejpam-6316	162	14	1	1	NUM
ejpam-6316	162	15	)	)	PUNCT
ejpam-6316	162	16	+	+	CCONJ
ejpam-6316	162	17	σ3p	σ3p	PROPN
ejpam-6316	162	18	cos(υ	cos(υ	PROPN
ejpam-6316	162	19	)	)	PUNCT
ejpam-6316	162	20	γ(3p+	γ(3p+	NOUN
ejpam-6316	162	21	1	1	NUM
ejpam-6316	162	22	)	)	PUNCT
ejpam-6316	162	23	+	+	CCONJ
ejpam-6316	162	24	·	·	PUNCT
ejpam-6316	162	25	·	·	PUNCT
ejpam-6316	162	26	·	·	PUNCT
ejpam-6316	162	27	.	.	PUNCT
ejpam-6316	163	1	(	(	PUNCT
ejpam-6316	163	2	26	26	NUM
ejpam-6316	163	3	)	)	PUNCT
ejpam-6316	163	4	n.	n.	NOUN
ejpam-6316	163	5	iqbal	iqbal	PROPN
ejpam-6316	163	6	et	et	PROPN
ejpam-6316	163	7	al	al	PROPN
ejpam-6316	163	8	.	.	PUNCT
ejpam-6316	163	9	/	/	SYM
ejpam-6316	163	10	eur	eur	PROPN
ejpam-6316	163	11	.	.	PUNCT
ejpam-6316	164	1	j.	j.	PROPN
ejpam-6316	164	2	pure	pure	PROPN
ejpam-6316	164	3	appl	appl	PROPN
ejpam-6316	164	4	.	.	PROPN
ejpam-6316	164	5	math	math	PROPN
ejpam-6316	164	6	,	,	PUNCT
ejpam-6316	164	7	18	18	NUM
ejpam-6316	164	8	(	(	PUNCT
ejpam-6316	164	9	3	3	NUM
ejpam-6316	164	10	)	)	PUNCT
ejpam-6316	164	11	(	(	PUNCT
ejpam-6316	164	12	2025	2025	NUM
ejpam-6316	164	13	)	)	PUNCT
ejpam-6316	164	14	,	,	PUNCT
ejpam-6316	164	15	6316	6316	NUM
ejpam-6316	164	16	8	8	NUM
ejpam-6316	164	17	of	of	ADP
ejpam-6316	164	18	21	21	NUM
ejpam-6316	164	19	figure	figure	NOUN
ejpam-6316	164	20	1	1	NUM
ejpam-6316	164	21	:	:	PUNCT
ejpam-6316	164	22	in	in	ADP
ejpam-6316	164	23	figure	figure	NOUN
ejpam-6316	164	24	1	1	NUM
ejpam-6316	164	25	,	,	PUNCT
ejpam-6316	164	26	analysis	analysis	NOUN
ejpam-6316	164	27	of	of	ADP
ejpam-6316	164	28	fractional	fractional	ADJ
ejpam-6316	164	29	order	order	NOUN
ejpam-6316	164	30	p	p	NOUN
ejpam-6316	164	31	for	for	ADP
ejpam-6316	164	32	σ	σ	NOUN
ejpam-6316	164	33	=	=	NOUN
ejpam-6316	164	34	0.05	0.05	NUM
ejpam-6316	164	35	of	of	ADP
ejpam-6316	164	36	ψ(υ	ψ(υ	PROPN
ejpam-6316	164	37	,	,	PUNCT
ejpam-6316	164	38	σ	σ	PROPN
ejpam-6316	164	39	)	)	PUNCT
ejpam-6316	164	40	of	of	ADP
ejpam-6316	164	41	example	example	NOUN
ejpam-6316	164	42	1	1	NUM
ejpam-6316	164	43	using	use	VERB
ejpam-6316	164	44	rpsntm	rpsntm	PROPN
ejpam-6316	164	45	.	.	PUNCT
ejpam-6316	165	1	figure	figure	NOUN
ejpam-6316	165	2	2	2	NUM
ejpam-6316	165	3	:	:	PUNCT
ejpam-6316	165	4	in	in	ADP
ejpam-6316	165	5	figure	figure	NOUN
ejpam-6316	165	6	2	2	NUM
ejpam-6316	165	7	,	,	PUNCT
ejpam-6316	165	8	2d	2d	NUM
ejpam-6316	165	9	analysis	analysis	NOUN
ejpam-6316	165	10	of	of	ADP
ejpam-6316	165	11	rpsntm	rpsntm	NOUN
ejpam-6316	165	12	at	at	ADP
ejpam-6316	165	13	σ	σ	PROPN
ejpam-6316	165	14	=	=	PROPN
ejpam-6316	165	15	0.05	0.05	NUM
ejpam-6316	165	16	.	.	PUNCT
ejpam-6316	166	1	3.3.2	3.3.2	NUM
ejpam-6316	166	2	.	.	PUNCT
ejpam-6316	167	1	implementation	implementation	NOUN
ejpam-6316	167	2	of	of	ADP
ejpam-6316	167	3	nintm	nintm	PROPN
ejpam-6316	167	4	we	we	PRON
ejpam-6316	167	5	derive	derive	VERB
ejpam-6316	167	6	the	the	DET
ejpam-6316	167	7	corresponding	correspond	VERB
ejpam-6316	167	8	form	form	NOUN
ejpam-6316	167	9	given	give	VERB
ejpam-6316	167	10	below	below	ADV
ejpam-6316	167	11	by	by	ADP
ejpam-6316	167	12	applying	apply	VERB
ejpam-6316	167	13	the	the	DET
ejpam-6316	167	14	rl	rl	NOUN
ejpam-6316	167	15	integral	integral	ADJ
ejpam-6316	167	16	on	on	ADP
ejpam-6316	167	17	eq.16	eq.16	PROPN
ejpam-6316	167	18	:	:	PUNCT
ejpam-6316	167	19	ψ(υ	ψ(υ	PROPN
ejpam-6316	167	20	,	,	PUNCT
ejpam-6316	167	21	σ	σ	NOUN
ejpam-6316	167	22	)	)	PUNCT
ejpam-6316	167	23	=	=	SYM
ejpam-6316	167	24	sin(υ)−n	sin(υ)−n	PROPN
ejpam-6316	167	25	p	p	PROPN
ejpam-6316	167	26	σ	σ	PROPN
ejpam-6316	167	27	[	[	PUNCT
ejpam-6316	167	28	−	−	PROPN
ejpam-6316	167	29	2	2	NUM
ejpam-6316	167	30	∂ψ	∂ψ	PROPN
ejpam-6316	167	31	∂υ	∂υ	PROPN
ejpam-6316	167	32	−	−	NOUN
ejpam-6316	167	33	∂3ψ	∂3ψ	NOUN
ejpam-6316	167	34	∂υ3	∂υ3	PROPN
ejpam-6316	167	35	]	]	PUNCT
ejpam-6316	167	36	.	.	PUNCT
ejpam-6316	168	1	(	(	PUNCT
ejpam-6316	168	2	27	27	NUM
ejpam-6316	168	3	)	)	PUNCT
ejpam-6316	168	4	n.	n.	NOUN
ejpam-6316	168	5	iqbal	iqbal	PROPN
ejpam-6316	168	6	et	et	PROPN
ejpam-6316	168	7	al	al	PROPN
ejpam-6316	168	8	.	.	PUNCT
ejpam-6316	168	9	/	/	SYM
ejpam-6316	168	10	eur	eur	PROPN
ejpam-6316	168	11	.	.	PUNCT
ejpam-6316	169	1	j.	j.	PROPN
ejpam-6316	169	2	pure	pure	PROPN
ejpam-6316	169	3	appl	appl	PROPN
ejpam-6316	169	4	.	.	PROPN
ejpam-6316	169	5	math	math	PROPN
ejpam-6316	169	6	,	,	PUNCT
ejpam-6316	169	7	18	18	NUM
ejpam-6316	169	8	(	(	PUNCT
ejpam-6316	169	9	3	3	NUM
ejpam-6316	169	10	)	)	PUNCT
ejpam-6316	169	11	(	(	PUNCT
ejpam-6316	169	12	2025	2025	NUM
ejpam-6316	169	13	)	)	PUNCT
ejpam-6316	169	14	,	,	PUNCT
ejpam-6316	169	15	6316	6316	NUM
ejpam-6316	169	16	9	9	NUM
ejpam-6316	169	17	of	of	ADP
ejpam-6316	169	18	21	21	NUM
ejpam-6316	169	19	we	we	PRON
ejpam-6316	169	20	obtain	obtain	VERB
ejpam-6316	169	21	the	the	DET
ejpam-6316	169	22	following	follow	VERB
ejpam-6316	169	23	several	several	ADJ
ejpam-6316	169	24	terms	term	NOUN
ejpam-6316	169	25	based	base	VERB
ejpam-6316	169	26	on	on	ADP
ejpam-6316	169	27	the	the	DET
ejpam-6316	169	28	nintm	nintm	PROPN
ejpam-6316	169	29	procedure	procedure	NOUN
ejpam-6316	169	30	:	:	PUNCT
ejpam-6316	169	31	ψ0(υ	ψ0(υ	PROPN
ejpam-6316	169	32	,	,	PUNCT
ejpam-6316	169	33	σ	σ	NOUN
ejpam-6316	169	34	)	)	PUNCT
ejpam-6316	169	35	=	=	SYM
ejpam-6316	169	36	sin(υ	sin(υ	NOUN
ejpam-6316	169	37	)	)	PUNCT
ejpam-6316	169	38	,	,	PUNCT
ejpam-6316	169	39	ψ1(υ	ψ1(υ	PROPN
ejpam-6316	169	40	,	,	PUNCT
ejpam-6316	169	41	σ	σ	PROPN
ejpam-6316	169	42	)	)	PUNCT
ejpam-6316	169	43	=	=	SYM
ejpam-6316	169	44	−σ	−σ	NOUN
ejpam-6316	169	45	p	p	PROPN
ejpam-6316	169	46	cos(υ	cos(υ	PROPN
ejpam-6316	169	47	)	)	PUNCT
ejpam-6316	169	48	pγ(p	pγ(p	PROPN
ejpam-6316	169	49	)	)	PUNCT
ejpam-6316	169	50	,	,	PUNCT
ejpam-6316	169	51	ψ2(υ	ψ2(υ	PROPN
ejpam-6316	169	52	,	,	PUNCT
ejpam-6316	169	53	σ	σ	NOUN
ejpam-6316	169	54	)	)	PUNCT
ejpam-6316	169	55	=	=	PRON
ejpam-6316	169	56	−σ	−σ	NOUN
ejpam-6316	169	57	2p	2p	NUM
ejpam-6316	169	58	sin(υ	sin(υ	NOUN
ejpam-6316	169	59	)	)	PUNCT
ejpam-6316	169	60	p2γ(p)2	p2γ(p)2	NOUN
ejpam-6316	169	61	,	,	PUNCT
ejpam-6316	169	62	ψ3(υ	ψ3(υ	PROPN
ejpam-6316	169	63	,	,	PUNCT
ejpam-6316	169	64	σ	σ	NOUN
ejpam-6316	169	65	)	)	PUNCT
ejpam-6316	169	66	=	=	SYM
ejpam-6316	169	67	σ3p	σ3p	PROPN
ejpam-6316	169	68	cos(υ	cos(υ	PROPN
ejpam-6316	169	69	)	)	PUNCT
ejpam-6316	169	70	p3γ(p)3	p3γ(p)3	NUM
ejpam-6316	169	71	.	.	PUNCT
ejpam-6316	170	1	(	(	PUNCT
ejpam-6316	170	2	28	28	NUM
ejpam-6316	170	3	)	)	PUNCT
ejpam-6316	170	4	t3he	t3he	DET
ejpam-6316	170	5	final	final	ADJ
ejpam-6316	170	6	nintm	nintm	PROPN
ejpam-6316	170	7	algorithm	algorithm	NOUN
ejpam-6316	170	8	solution	solution	NOUN
ejpam-6316	170	9	is	be	AUX
ejpam-6316	170	10	as	as	SCONJ
ejpam-6316	170	11	follows	follow	VERB
ejpam-6316	170	12	:	:	PUNCT
ejpam-6316	170	13	ψ(υ	ψ(υ	NOUN
ejpam-6316	170	14	,	,	PUNCT
ejpam-6316	170	15	σ	σ	PROPN
ejpam-6316	170	16	)	)	PUNCT
ejpam-6316	170	17	=	=	PUNCT
ejpam-6316	171	1	ψ0(υ	ψ0(υ	PROPN
ejpam-6316	171	2	,	,	PUNCT
ejpam-6316	171	3	σ	σ	NOUN
ejpam-6316	171	4	)	)	PUNCT
ejpam-6316	171	5	+	+	SYM
ejpam-6316	172	1	ψ1(υ	ψ1(υ	PROPN
ejpam-6316	172	2	,	,	PUNCT
ejpam-6316	172	3	σ	σ	PROPN
ejpam-6316	172	4	)	)	PUNCT
ejpam-6316	172	5	+	+	CCONJ
ejpam-6316	172	6	ψ2(υ	ψ2(υ	PROPN
ejpam-6316	172	7	,	,	PUNCT
ejpam-6316	172	8	σ	σ	NOUN
ejpam-6316	172	9	)	)	PUNCT
ejpam-6316	172	10	+	+	CCONJ
ejpam-6316	172	11	·	·	PUNCT
ejpam-6316	172	12	·	·	PUNCT
ejpam-6316	172	13	·	·	PUNCT
ejpam-6316	172	14	,	,	PUNCT
ejpam-6316	172	15	(	(	PUNCT
ejpam-6316	172	16	29	29	NUM
ejpam-6316	172	17	)	)	PUNCT
ejpam-6316	172	18	ψ(υ	ψ(υ	PROPN
ejpam-6316	172	19	,	,	PUNCT
ejpam-6316	172	20	σ	σ	NOUN
ejpam-6316	172	21	)	)	PUNCT
ejpam-6316	172	22	=	=	PROPN
ejpam-6316	172	23	sin(υ)−	sin(υ)−	NOUN
ejpam-6316	172	24	σp	σp	PROPN
ejpam-6316	172	25	cos(υ	cos(υ	PROPN
ejpam-6316	172	26	)	)	PUNCT
ejpam-6316	172	27	pγ(p	pγ(p	PROPN
ejpam-6316	172	28	)	)	PUNCT
ejpam-6316	172	29	−	−	PROPN
ejpam-6316	172	30	υ2p	υ2p	NOUN
ejpam-6316	172	31	sin(υ	sin(υ	PROPN
ejpam-6316	172	32	)	)	PUNCT
ejpam-6316	172	33	p2γ(p)2	p2γ(p)2	PROPN
ejpam-6316	172	34	+	+	CCONJ
ejpam-6316	172	35	σ3p	σ3p	PROPN
ejpam-6316	172	36	cos(υ	cos(υ	PROPN
ejpam-6316	172	37	)	)	PUNCT
ejpam-6316	172	38	p3γ(p)3	p3γ(p)3	NUM
ejpam-6316	172	39	.	.	PUNCT
ejpam-6316	173	1	(	(	PUNCT
ejpam-6316	173	2	30	30	NUM
ejpam-6316	173	3	)	)	PUNCT
ejpam-6316	173	4	figure	figure	NOUN
ejpam-6316	173	5	3	3	NUM
ejpam-6316	173	6	:	:	PUNCT
ejpam-6316	173	7	in	in	ADP
ejpam-6316	173	8	figure	figure	NOUN
ejpam-6316	173	9	3	3	NUM
ejpam-6316	173	10	,	,	PUNCT
ejpam-6316	173	11	analysis	analysis	NOUN
ejpam-6316	173	12	of	of	ADP
ejpam-6316	173	13	fractional	fractional	ADJ
ejpam-6316	173	14	order	order	NOUN
ejpam-6316	173	15	p	p	NOUN
ejpam-6316	173	16	for	for	ADP
ejpam-6316	173	17	σ	σ	NOUN
ejpam-6316	173	18	=	=	NOUN
ejpam-6316	173	19	0.05	0.05	NUM
ejpam-6316	173	20	of	of	ADP
ejpam-6316	173	21	ψ(υ	ψ(υ	PROPN
ejpam-6316	173	22	,	,	PUNCT
ejpam-6316	173	23	σ	σ	PROPN
ejpam-6316	173	24	)	)	PUNCT
ejpam-6316	173	25	of	of	ADP
ejpam-6316	173	26	example	example	NOUN
ejpam-6316	173	27	1	1	NUM
ejpam-6316	173	28	using	use	VERB
ejpam-6316	173	29	nintm	nintm	PROPN
ejpam-6316	173	30	.	.	PUNCT
ejpam-6316	174	1	n.	n.	PROPN
ejpam-6316	174	2	iqbal	iqbal	PROPN
ejpam-6316	174	3	et	et	PROPN
ejpam-6316	174	4	al	al	PROPN
ejpam-6316	174	5	.	.	PUNCT
ejpam-6316	174	6	/	/	SYM
ejpam-6316	174	7	eur	eur	PROPN
ejpam-6316	174	8	.	.	PUNCT
ejpam-6316	175	1	j.	j.	PROPN
ejpam-6316	175	2	pure	pure	PROPN
ejpam-6316	175	3	appl	appl	PROPN
ejpam-6316	175	4	.	.	PROPN
ejpam-6316	175	5	math	math	PROPN
ejpam-6316	175	6	,	,	PUNCT
ejpam-6316	175	7	18	18	NUM
ejpam-6316	175	8	(	(	PUNCT
ejpam-6316	175	9	3	3	NUM
ejpam-6316	175	10	)	)	PUNCT
ejpam-6316	175	11	(	(	PUNCT
ejpam-6316	175	12	2025	2025	NUM
ejpam-6316	175	13	)	)	PUNCT
ejpam-6316	175	14	,	,	PUNCT
ejpam-6316	175	15	6316	6316	NUM
ejpam-6316	175	16	10	10	NUM
ejpam-6316	175	17	of	of	ADP
ejpam-6316	175	18	21	21	NUM
ejpam-6316	175	19	figure	figure	NOUN
ejpam-6316	175	20	4	4	NUM
ejpam-6316	175	21	:	:	PUNCT
ejpam-6316	175	22	in	in	ADP
ejpam-6316	175	23	figure	figure	NOUN
ejpam-6316	175	24	4	4	NUM
ejpam-6316	175	25	,	,	PUNCT
ejpam-6316	175	26	2d	2d	NUM
ejpam-6316	175	27	analysis	analysis	NOUN
ejpam-6316	175	28	of	of	ADP
ejpam-6316	175	29	nintm	nintm	PROPN
ejpam-6316	175	30	at	at	ADP
ejpam-6316	175	31	σ	σ	PROPN
ejpam-6316	175	32	=	=	PROPN
ejpam-6316	175	33	0.05	0.05	NUM
ejpam-6316	175	34	.	.	PUNCT
ejpam-6316	176	1	3.4	3.4	NUM
ejpam-6316	176	2	.	.	PUNCT
ejpam-6316	176	3	problem	problem	NOUN
ejpam-6316	176	4	2	2	NUM
ejpam-6316	176	5	3.4.1	3.4.1	NUM
ejpam-6316	176	6	.	.	PUNCT
ejpam-6316	177	1	implementation	implementation	NOUN
ejpam-6316	177	2	of	of	ADP
ejpam-6316	177	3	rpsntm	rpsntm	PROPN
ejpam-6316	177	4	consider	consider	VERB
ejpam-6316	177	5	the	the	DET
ejpam-6316	177	6	following	follow	VERB
ejpam-6316	177	7	fractional	fractional	ADJ
ejpam-6316	177	8	dispersive	dispersive	ADJ
ejpam-6316	177	9	kdv	kdv	NOUN
ejpam-6316	177	10	equation	equation	NOUN
ejpam-6316	177	11	dp	dp	NOUN
ejpam-6316	177	12	σψ	σψ	NOUN
ejpam-6316	177	13	+	+	NUM
ejpam-6316	177	14	∂3ψ	∂3ψ	PROPN
ejpam-6316	177	15	∂υ3	∂υ3	PROPN
ejpam-6316	177	16	+	+	CCONJ
ejpam-6316	177	17	∂3ψ	∂3ψ	VERB
ejpam-6316	177	18	∂ρ3	∂ρ3	NOUN
ejpam-6316	177	19	=	=	SYM
ejpam-6316	177	20	0	0	NUM
ejpam-6316	177	21	σ	σ	NOUN
ejpam-6316	177	22	>	>	X
ejpam-6316	177	23	0	0	PROPN
ejpam-6316	177	24	,	,	PUNCT
ejpam-6316	177	25	where	where	SCONJ
ejpam-6316	177	26	0	0	X
ejpam-6316	177	27	<	<	X
ejpam-6316	177	28	p	p	X
ejpam-6316	177	29	≤	≤	ADJ
ejpam-6316	177	30	1	1	NUM
ejpam-6316	177	31	(	(	PUNCT
ejpam-6316	177	32	31	31	NUM
ejpam-6316	177	33	)	)	PUNCT
ejpam-6316	177	34	having	have	VERB
ejpam-6316	177	35	ic	ic	PRON
ejpam-6316	177	36	’s	’	NOUN
ejpam-6316	177	37	are	be	AUX
ejpam-6316	177	38	:	:	PUNCT
ejpam-6316	177	39	ψ(υ	ψ(υ	PROPN
ejpam-6316	177	40	,	,	PUNCT
ejpam-6316	177	41	0	0	NUM
ejpam-6316	177	42	)	)	PUNCT
ejpam-6316	178	1	=	=	SYM
ejpam-6316	178	2	cos(υ	cos(υ	PROPN
ejpam-6316	178	3	+	+	CCONJ
ejpam-6316	178	4	ρ	ρ	PROPN
ejpam-6316	178	5	)	)	PUNCT
ejpam-6316	178	6	(	(	PUNCT
ejpam-6316	178	7	32	32	NUM
ejpam-6316	178	8	)	)	PUNCT
ejpam-6316	178	9	using	use	VERB
ejpam-6316	178	10	eq	eq	X
ejpam-6316	178	11	.	.	PUNCT
ejpam-6316	179	1	(	(	PUNCT
ejpam-6316	179	2	32	32	NUM
ejpam-6316	179	3	)	)	PUNCT
ejpam-6316	179	4	and	and	CCONJ
ejpam-6316	179	5	applying	apply	VERB
ejpam-6316	179	6	nt	not	PART
ejpam-6316	179	7	to	to	ADP
ejpam-6316	179	8	eq	eq	PROPN
ejpam-6316	179	9	.	.	PUNCT
ejpam-6316	180	1	(	(	PUNCT
ejpam-6316	180	2	31	31	NUM
ejpam-6316	180	3	)	)	PUNCT
ejpam-6316	180	4	,	,	PUNCT
ejpam-6316	180	5	we	we	PRON
ejpam-6316	180	6	obtain	obtain	VERB
ejpam-6316	180	7	:	:	PUNCT
ejpam-6316	180	8	ψ(υ	ψ(υ	PROPN
ejpam-6316	180	9	,	,	PUNCT
ejpam-6316	180	10	0)−	0)−	PUNCT
ejpam-6316	181	1	u	u	NOUN
ejpam-6316	181	2	cos(ψ	cos(ψ	PROPN
ejpam-6316	182	1	+	+	CCONJ
ejpam-6316	182	2	ρ	ρ	NOUN
ejpam-6316	182	3	)	)	PUNCT
ejpam-6316	182	4	s	s	PART
ejpam-6316	182	5	−	−	NOUN
ejpam-6316	182	6	up	up	ADP
ejpam-6316	182	7	sp	sp	ADP
ejpam-6316	182	8	∂3ψ	∂3ψ	NOUN
ejpam-6316	182	9	∂υ3	∂υ3	PROPN
ejpam-6316	182	10	+	+	X
ejpam-6316	182	11	up	up	ADP
ejpam-6316	182	12	sp	sp	ADP
ejpam-6316	182	13	∂3ψ	∂3ψ	NOUN
ejpam-6316	183	1	∂ρ3	∂ρ3	NOUN
ejpam-6316	183	2	=	=	SYM
ejpam-6316	183	3	0	0	NUM
ejpam-6316	183	4	(	(	PUNCT
ejpam-6316	183	5	33	33	NUM
ejpam-6316	183	6	)	)	PUNCT
ejpam-6316	183	7	thus	thus	ADV
ejpam-6316	183	8	,	,	PUNCT
ejpam-6316	183	9	the	the	DET
ejpam-6316	183	10	term	term	NOUN
ejpam-6316	183	11	series	series	NOUN
ejpam-6316	183	12	that	that	PRON
ejpam-6316	183	13	are	be	AUX
ejpam-6316	183	14	kth	kth	NOUN
ejpam-6316	183	15	-	-	PUNCT
ejpam-6316	183	16	truncated	truncate	VERB
ejpam-6316	183	17	are	be	AUX
ejpam-6316	183	18	:	:	PUNCT
ejpam-6316	183	19	ψ(υ	ψ(υ	PROPN
ejpam-6316	183	20	,	,	PUNCT
ejpam-6316	183	21	s	s	PART
ejpam-6316	183	22	)	)	PUNCT
ejpam-6316	183	23	=	=	SYM
ejpam-6316	183	24	cos(υ	cos(υ	PROPN
ejpam-6316	183	25	+	+	CCONJ
ejpam-6316	183	26	ρ	ρ	PROPN
ejpam-6316	183	27	)	)	PUNCT
ejpam-6316	183	28	s	s	PART
ejpam-6316	183	29	+	+	CCONJ
ejpam-6316	183	30	k∑	k∑	NOUN
ejpam-6316	183	31	r=1	r=1	NOUN
ejpam-6316	183	32	urp+1fr(υ	urp+1fr(υ	NOUN
ejpam-6316	183	33	,	,	PUNCT
ejpam-6316	183	34	s	s	NOUN
ejpam-6316	183	35	)	)	PUNCT
ejpam-6316	183	36	srp+1	srp+1	NOUN
ejpam-6316	183	37	,	,	PUNCT
ejpam-6316	183	38	r	r	NOUN
ejpam-6316	183	39	=	=	SYM
ejpam-6316	183	40	1	1	NUM
ejpam-6316	183	41	,	,	PUNCT
ejpam-6316	183	42	2	2	NUM
ejpam-6316	183	43	,	,	PUNCT
ejpam-6316	183	44	3	3	NUM
ejpam-6316	183	45	,	,	PUNCT
ejpam-6316	183	46	4	4	NUM
ejpam-6316	183	47	·	·	PUNCT
ejpam-6316	183	48	·	·	PUNCT
ejpam-6316	183	49	·	·	PUNCT
ejpam-6316	183	50	.	.	PUNCT
ejpam-6316	184	1	(	(	PUNCT
ejpam-6316	184	2	34	34	NUM
ejpam-6316	184	3	)	)	PUNCT
ejpam-6316	184	4	natural	natural	ADJ
ejpam-6316	184	5	residual	residual	ADJ
ejpam-6316	184	6	functions	function	NOUN
ejpam-6316	184	7	(	(	PUNCT
ejpam-6316	184	8	nrfs	nrf	NOUN
ejpam-6316	184	9	)	)	PUNCT
ejpam-6316	184	10	provided	provide	VERB
ejpam-6316	184	11	as	as	ADP
ejpam-6316	184	12	follows	follow	VERB
ejpam-6316	184	13	:	:	PUNCT
ejpam-6316	184	14	nσres(υ	nσres(υ	NUM
ejpam-6316	184	15	,	,	PUNCT
ejpam-6316	184	16	s	s	PART
ejpam-6316	184	17	)	)	PUNCT
ejpam-6316	184	18	=	=	SYM
ejpam-6316	184	19	ψ(υ	ψ(υ	PROPN
ejpam-6316	184	20	,	,	PUNCT
ejpam-6316	184	21	0)−	0)−	PUNCT
ejpam-6316	184	22	u	u	PROPN
ejpam-6316	184	23	cos(υ	cos(υ	PROPN
ejpam-6316	184	24	+	+	CCONJ
ejpam-6316	184	25	ρ	ρ	PROPN
ejpam-6316	184	26	)	)	PUNCT
ejpam-6316	184	27	s	s	PART
ejpam-6316	184	28	−	−	NOUN
ejpam-6316	184	29	up	up	ADP
ejpam-6316	184	30	sp	sp	ADP
ejpam-6316	184	31	∂3ψ	∂3ψ	NOUN
ejpam-6316	184	32	∂υ3	∂υ3	PROPN
ejpam-6316	184	33	+	+	X
ejpam-6316	184	34	up	up	ADP
ejpam-6316	184	35	sp	sp	ADP
ejpam-6316	184	36	∂3w	∂3w	NOUN
ejpam-6316	184	37	∂ρ3	∂ρ3	NOUN
ejpam-6316	184	38	=	=	SYM
ejpam-6316	184	39	0	0	NUM
ejpam-6316	184	40	,	,	PUNCT
ejpam-6316	184	41	(	(	PUNCT
ejpam-6316	184	42	35	35	NUM
ejpam-6316	184	43	)	)	PUNCT
ejpam-6316	184	44	along	along	ADP
ejpam-6316	184	45	with	with	ADP
ejpam-6316	184	46	the	the	DET
ejpam-6316	184	47	kth	kth	NOUN
ejpam-6316	184	48	-	-	PUNCT
ejpam-6316	184	49	nrfs	nrf	NOUN
ejpam-6316	184	50	as	as	ADP
ejpam-6316	184	51	:	:	PUNCT
ejpam-6316	184	52	nσresk(υ	nσresk(υ	PROPN
ejpam-6316	184	53	,	,	PUNCT
ejpam-6316	184	54	s	s	PART
ejpam-6316	184	55	)	)	PUNCT
ejpam-6316	184	56	=	=	PRON
ejpam-6316	184	57	ψk(υ	ψk(υ	PUNCT
ejpam-6316	184	58	,	,	PUNCT
ejpam-6316	184	59	0)−	0)−	PUNCT
ejpam-6316	185	1	cos(υ	cos(υ	PROPN
ejpam-6316	185	2	+	+	CCONJ
ejpam-6316	185	3	ρ	ρ	PROPN
ejpam-6316	185	4	)	)	PUNCT
ejpam-6316	185	5	s	s	PART
ejpam-6316	185	6	−	−	NOUN
ejpam-6316	185	7	up	up	ADP
ejpam-6316	185	8	sp	sp	ADP
ejpam-6316	185	9	∂3ψk	∂3ψk	NOUN
ejpam-6316	185	10	∂υ3	∂υ3	PROPN
ejpam-6316	185	11	+	+	CCONJ
ejpam-6316	185	12	up	up	ADP
ejpam-6316	185	13	sp	sp	ADP
ejpam-6316	185	14	∂3ψk	∂3ψk	NOUN
ejpam-6316	185	15	∂ρ3	∂ρ3	NOUN
ejpam-6316	185	16	=	=	SYM
ejpam-6316	185	17	0	0	NUM
ejpam-6316	185	18	.	.	PUNCT
ejpam-6316	186	1	(	(	PUNCT
ejpam-6316	186	2	36	36	NUM
ejpam-6316	186	3	)	)	PUNCT
ejpam-6316	186	4	to	to	PART
ejpam-6316	186	5	find	find	VERB
ejpam-6316	186	6	fr(υ	fr(υ	NOUN
ejpam-6316	186	7	,	,	PUNCT
ejpam-6316	186	8	s	s	PART
ejpam-6316	186	9	)	)	PUNCT
ejpam-6316	186	10	now	now	ADV
ejpam-6316	186	11	,	,	PUNCT
ejpam-6316	186	12	r	r	NOUN
ejpam-6316	186	13	=	=	SYM
ejpam-6316	186	14	1	1	NUM
ejpam-6316	186	15	,	,	PUNCT
ejpam-6316	186	16	2	2	NUM
ejpam-6316	186	17	,	,	PUNCT
ejpam-6316	186	18	3	3	NUM
ejpam-6316	186	19	,	,	PUNCT
ejpam-6316	186	20	·	·	PUNCT
ejpam-6316	186	21	·	·	PUNCT
ejpam-6316	186	22	·	·	PUNCT
ejpam-6316	186	23	we	we	PRON
ejpam-6316	186	24	multiply	multiply	VERB
ejpam-6316	186	25	the	the	DET
ejpam-6316	186	26	resulting	result	VERB
ejpam-6316	186	27	equation	equation	NOUN
ejpam-6316	186	28	by	by	ADP
ejpam-6316	186	29	srp+1	srp+1	NOUN
ejpam-6316	186	30	,	,	PUNCT
ejpam-6316	186	31	substitute	substitute	VERB
ejpam-6316	186	32	the	the	DET
ejpam-6316	186	33	rσh	rσh	NOUN
ejpam-6316	186	34	-	-	PUNCT
ejpam-6316	186	35	truncated	truncate	VERB
ejpam-6316	186	36	series	series	NOUN
ejpam-6316	186	37	eq	eq	PROPN
ejpam-6316	186	38	.	.	PUNCT
ejpam-6316	187	1	(	(	PUNCT
ejpam-6316	187	2	34	34	NUM
ejpam-6316	187	3	)	)	PUNCT
ejpam-6316	187	4	into	into	ADP
ejpam-6316	187	5	the	the	DET
ejpam-6316	187	6	rσh	rσh	NOUN
ejpam-6316	187	7	-	-	PUNCT
ejpam-6316	187	8	natural	natural	ADJ
ejpam-6316	187	9	residual	residual	ADJ
ejpam-6316	187	10	function	function	NOUN
ejpam-6316	187	11	eq	eq	ADP
ejpam-6316	187	12	.	.	PUNCT
ejpam-6316	188	1	(	(	PUNCT
ejpam-6316	188	2	36	36	NUM
ejpam-6316	188	3	)	)	PUNCT
ejpam-6316	188	4	,	,	PUNCT
ejpam-6316	188	5	and	and	CCONJ
ejpam-6316	188	6	solve	solve	VERB
ejpam-6316	188	7	n.	n.	PROPN
ejpam-6316	188	8	iqbal	iqbal	PROPN
ejpam-6316	188	9	et	et	PROPN
ejpam-6316	188	10	al	al	PROPN
ejpam-6316	188	11	.	.	PUNCT
ejpam-6316	188	12	/	/	SYM
ejpam-6316	188	13	eur	eur	PROPN
ejpam-6316	188	14	.	.	PUNCT
ejpam-6316	189	1	j.	j.	PROPN
ejpam-6316	189	2	pure	pure	PROPN
ejpam-6316	189	3	appl	appl	PROPN
ejpam-6316	189	4	.	.	PROPN
ejpam-6316	189	5	math	math	PROPN
ejpam-6316	189	6	,	,	PUNCT
ejpam-6316	189	7	18	18	NUM
ejpam-6316	189	8	(	(	PUNCT
ejpam-6316	189	9	3	3	NUM
ejpam-6316	189	10	)	)	PUNCT
ejpam-6316	189	11	(	(	PUNCT
ejpam-6316	189	12	2025	2025	NUM
ejpam-6316	189	13	)	)	PUNCT
ejpam-6316	189	14	,	,	PUNCT
ejpam-6316	189	15	6316	6316	NUM
ejpam-6316	189	16	11	11	NUM
ejpam-6316	189	17	of	of	ADP
ejpam-6316	189	18	21	21	NUM
ejpam-6316	189	19	the	the	DET
ejpam-6316	189	20	relation	relation	NOUN
ejpam-6316	189	21	lims→∞(srp+1nσresψ	lims→∞(srp+1nσresψ	NOUN
ejpam-6316	189	22	,	,	PUNCT
ejpam-6316	189	23	r(σ	r(σ	PROPN
ejpam-6316	189	24	,	,	PUNCT
ejpam-6316	189	25	s	s	NOUN
ejpam-6316	189	26	)	)	PUNCT
ejpam-6316	189	27	)	)	PUNCT
ejpam-6316	190	1	=	=	SYM
ejpam-6316	190	2	0	0	NUM
ejpam-6316	190	3	recursively	recursively	NOUN
ejpam-6316	190	4	.	.	PUNCT
ejpam-6316	191	1	1	1	NUM
ejpam-6316	191	2	,	,	PUNCT
ejpam-6316	191	3	2	2	NUM
ejpam-6316	191	4	,	,	PUNCT
ejpam-6316	191	5	3	3	NUM
ejpam-6316	191	6	,	,	PUNCT
ejpam-6316	191	7	·	·	PUNCT
ejpam-6316	191	8	·	·	PUNCT
ejpam-6316	191	9	·	·	PUNCT
ejpam-6316	191	10	.	.	PUNCT
ejpam-6316	192	1	here	here	ADV
ejpam-6316	192	2	are	be	AUX
ejpam-6316	192	3	the	the	DET
ejpam-6316	192	4	first	first	ADJ
ejpam-6316	192	5	few	few	ADJ
ejpam-6316	192	6	of	of	ADP
ejpam-6316	192	7	terms	term	NOUN
ejpam-6316	192	8	:	:	PUNCT
ejpam-6316	192	9	f1(υ	f1(υ	NUM
ejpam-6316	192	10	,	,	PUNCT
ejpam-6316	192	11	s	s	PART
ejpam-6316	192	12	)	)	PUNCT
ejpam-6316	192	13	=	=	SYM
ejpam-6316	192	14	−2	−2	NOUN
ejpam-6316	192	15	sin(υ	sin(υ	PROPN
ejpam-6316	192	16	+	+	NUM
ejpam-6316	192	17	ρ	ρ	NOUN
ejpam-6316	192	18	)	)	PUNCT
ejpam-6316	192	19	,	,	PUNCT
ejpam-6316	192	20	(	(	PUNCT
ejpam-6316	192	21	37	37	NUM
ejpam-6316	192	22	)	)	PUNCT
ejpam-6316	192	23	f2(υ	f2(υ	PROPN
ejpam-6316	192	24	,	,	PUNCT
ejpam-6316	192	25	s	s	PART
ejpam-6316	192	26	)	)	PUNCT
ejpam-6316	192	27	=	=	PUNCT
ejpam-6316	193	1	−4	−4	PUNCT
ejpam-6316	194	1	cos(υ	cos(υ	PROPN
ejpam-6316	194	2	+	+	CCONJ
ejpam-6316	194	3	ρ	ρ	NOUN
ejpam-6316	194	4	)	)	PUNCT
ejpam-6316	194	5	,	,	PUNCT
ejpam-6316	194	6	(	(	PUNCT
ejpam-6316	194	7	38	38	NUM
ejpam-6316	194	8	)	)	PUNCT
ejpam-6316	194	9	f3(υ	f3(υ	PROPN
ejpam-6316	194	10	,	,	PUNCT
ejpam-6316	194	11	s	s	PART
ejpam-6316	194	12	)	)	PUNCT
ejpam-6316	194	13	=	=	SYM
ejpam-6316	194	14	8	8	NUM
ejpam-6316	194	15	sin(υ	sin(υ	PROPN
ejpam-6316	194	16	+	+	NUM
ejpam-6316	194	17	ρ	ρ	NOUN
ejpam-6316	194	18	)	)	PUNCT
ejpam-6316	194	19	,	,	PUNCT
ejpam-6316	194	20	(	(	PUNCT
ejpam-6316	194	21	39	39	NUM
ejpam-6316	194	22	)	)	PUNCT
ejpam-6316	194	23	and	and	CCONJ
ejpam-6316	194	24	so	so	ADV
ejpam-6316	194	25	on	on	ADV
ejpam-6316	194	26	.	.	PUNCT
ejpam-6316	195	1	in	in	ADP
ejpam-6316	195	2	eq	eq	ADP
ejpam-6316	195	3	.	.	PUNCT
ejpam-6316	196	1	(	(	PUNCT
ejpam-6316	196	2	34	34	NUM
ejpam-6316	196	3	)	)	PUNCT
ejpam-6316	196	4	,	,	PUNCT
ejpam-6316	196	5	substitute	substitute	VERB
ejpam-6316	196	6	the	the	DET
ejpam-6316	196	7	values	value	NOUN
ejpam-6316	196	8	of	of	ADP
ejpam-6316	196	9	fr(υ	fr(υ	NOUN
ejpam-6316	196	10	,	,	PUNCT
ejpam-6316	196	11	s	s	PART
ejpam-6316	196	12	)	)	PUNCT
ejpam-6316	196	13	,	,	PUNCT
ejpam-6316	196	14	r	r	NOUN
ejpam-6316	196	15	=	=	SYM
ejpam-6316	196	16	1	1	NUM
ejpam-6316	196	17	,	,	PUNCT
ejpam-6316	196	18	2	2	NUM
ejpam-6316	196	19	,	,	PUNCT
ejpam-6316	196	20	3	3	NUM
ejpam-6316	196	21	,	,	PUNCT
ejpam-6316	196	22	·	·	PUNCT
ejpam-6316	196	23	·	·	PUNCT
ejpam-6316	196	24	·	·	PUNCT
ejpam-6316	196	25	,	,	PUNCT
ejpam-6316	196	26	we	we	PRON
ejpam-6316	196	27	get	get	VERB
ejpam-6316	196	28	:	:	PUNCT
ejpam-6316	196	29	ψ(υ	ψ(υ	NOUN
ejpam-6316	196	30	,	,	PUNCT
ejpam-6316	196	31	s	s	PART
ejpam-6316	196	32	)	)	PUNCT
ejpam-6316	196	33	=	=	SYM
ejpam-6316	196	34	u	u	SYM
ejpam-6316	196	35	cos(υ	cos(υ	PROPN
ejpam-6316	196	36	+	+	CCONJ
ejpam-6316	196	37	ρ	ρ	PROPN
ejpam-6316	196	38	)	)	PUNCT
ejpam-6316	196	39	s	s	PART
ejpam-6316	196	40	−	−	PROPN
ejpam-6316	196	41	2up	2up	ADJ
ejpam-6316	196	42	sin(υ	sin(υ	PROPN
ejpam-6316	196	43	+	+	CCONJ
ejpam-6316	196	44	ρ	ρ	NUM
ejpam-6316	196	45	)	)	PUNCT
ejpam-6316	196	46	sp+1	sp+1	NOUN
ejpam-6316	196	47	−	−	PROPN
ejpam-6316	196	48	4up	4up	ADJ
ejpam-6316	196	49	cos(υ	cos(υ	PROPN
ejpam-6316	196	50	+	+	CCONJ
ejpam-6316	196	51	ρ	ρ	PROPN
ejpam-6316	196	52	)	)	PUNCT
ejpam-6316	196	53	s2p+1	s2p+1	NOUN
ejpam-6316	197	1	+	+	NUM
ejpam-6316	197	2	8up	8up	ADJ
ejpam-6316	197	3	sin(υ	sin(υ	PROPN
ejpam-6316	197	4	+	+	CCONJ
ejpam-6316	197	5	ρ	ρ	PROPN
ejpam-6316	197	6	)	)	PUNCT
ejpam-6316	197	7	s3p+1	s3p+1	PROPN
ejpam-6316	197	8	,	,	PUNCT
ejpam-6316	197	9	(	(	PUNCT
ejpam-6316	197	10	40	40	NUM
ejpam-6316	197	11	)	)	PUNCT
ejpam-6316	197	12	with	with	ADP
ejpam-6316	197	13	the	the	DET
ejpam-6316	197	14	inverse	inverse	ADJ
ejpam-6316	197	15	natural	natural	ADJ
ejpam-6316	197	16	transform	transform	NOUN
ejpam-6316	197	17	,	,	PUNCT
ejpam-6316	197	18	we	we	PRON
ejpam-6316	197	19	obtain	obtain	VERB
ejpam-6316	197	20	:	:	PUNCT
ejpam-6316	197	21	ψ(υ	ψ(υ	PROPN
ejpam-6316	197	22	,	,	PUNCT
ejpam-6316	197	23	σ	σ	NOUN
ejpam-6316	197	24	)	)	PUNCT
ejpam-6316	198	1	=	=	SYM
ejpam-6316	198	2	cos(υ	cos(υ	PROPN
ejpam-6316	199	1	+	+	CCONJ
ejpam-6316	199	2	ρ)−	ρ)−	PROPN
ejpam-6316	199	3	2σp	2σp	VERB
ejpam-6316	200	1	sin(υ	sin(υ	NOUN
ejpam-6316	200	2	+	+	CCONJ
ejpam-6316	200	3	ρ	ρ	PROPN
ejpam-6316	200	4	)	)	PUNCT
ejpam-6316	200	5	γ(p+	γ(p+	PROPN
ejpam-6316	200	6	1	1	X
ejpam-6316	200	7	)	)	PUNCT
ejpam-6316	200	8	−	−	PROPN
ejpam-6316	200	9	4σ2p	4σ2p	PROPN
ejpam-6316	200	10	cos(υ	cos(υ	PROPN
ejpam-6316	200	11	+	+	CCONJ
ejpam-6316	200	12	ρ	ρ	PROPN
ejpam-6316	200	13	)	)	PUNCT
ejpam-6316	200	14	γ(2p+	γ(2p+	NOUN
ejpam-6316	200	15	1	1	NUM
ejpam-6316	200	16	)	)	PUNCT
ejpam-6316	201	1	+	+	NUM
ejpam-6316	201	2	8σ3p	8σ3p	NUM
ejpam-6316	201	3	sin(υ	sin(υ	NOUN
ejpam-6316	201	4	+	+	NUM
ejpam-6316	201	5	ρ	ρ	NOUN
ejpam-6316	201	6	)	)	PUNCT
ejpam-6316	201	7	γ(3p+	γ(3p+	NOUN
ejpam-6316	201	8	1	1	NUM
ejpam-6316	201	9	)	)	PUNCT
ejpam-6316	201	10	.	.	PUNCT
ejpam-6316	202	1	(	(	PUNCT
ejpam-6316	202	2	41	41	NUM
ejpam-6316	202	3	)	)	PUNCT
ejpam-6316	202	4	3.4.2	3.4.2	NUM
ejpam-6316	202	5	.	.	PUNCT
ejpam-6316	203	1	implementation	implementation	NOUN
ejpam-6316	203	2	of	of	ADP
ejpam-6316	203	3	nintm	nintm	PROPN
ejpam-6316	203	4	we	we	PRON
ejpam-6316	203	5	derive	derive	VERB
ejpam-6316	203	6	the	the	DET
ejpam-6316	203	7	corresponding	correspond	VERB
ejpam-6316	203	8	form	form	NOUN
ejpam-6316	203	9	given	give	VERB
ejpam-6316	203	10	below	below	ADV
ejpam-6316	203	11	by	by	ADP
ejpam-6316	203	12	applying	apply	VERB
ejpam-6316	203	13	the	the	DET
ejpam-6316	203	14	rl	rl	NOUN
ejpam-6316	203	15	integral	integral	ADJ
ejpam-6316	203	16	on	on	ADP
ejpam-6316	203	17	eq.31	eq.31	NOUN
ejpam-6316	203	18	:	:	PUNCT
ejpam-6316	203	19	ψ(υ	ψ(υ	PROPN
ejpam-6316	203	20	,	,	PUNCT
ejpam-6316	203	21	σ	σ	NOUN
ejpam-6316	203	22	)	)	PUNCT
ejpam-6316	203	23	=	=	SYM
ejpam-6316	203	24	sin(υ)−n	sin(υ)−n	PROPN
ejpam-6316	203	25	p	p	PROPN
ejpam-6316	203	26	σ	σ	PROPN
ejpam-6316	203	27	[	[	PUNCT
ejpam-6316	203	28	−	−	PROPN
ejpam-6316	203	29	2	2	NUM
ejpam-6316	203	30	∂ψ	∂ψ	PROPN
ejpam-6316	203	31	∂υ	∂υ	PROPN
ejpam-6316	203	32	−	−	NOUN
ejpam-6316	203	33	∂3ψ	∂3ψ	NOUN
ejpam-6316	203	34	∂υ3	∂υ3	PROPN
ejpam-6316	203	35	]	]	PUNCT
ejpam-6316	203	36	.	.	PUNCT
ejpam-6316	204	1	(	(	PUNCT
ejpam-6316	204	2	42	42	X
ejpam-6316	204	3	)	)	PUNCT
ejpam-6316	204	4	we	we	PRON
ejpam-6316	204	5	obtain	obtain	VERB
ejpam-6316	204	6	the	the	DET
ejpam-6316	204	7	following	follow	VERB
ejpam-6316	204	8	several	several	ADJ
ejpam-6316	204	9	terms	term	NOUN
ejpam-6316	204	10	based	base	VERB
ejpam-6316	204	11	on	on	ADP
ejpam-6316	204	12	the	the	DET
ejpam-6316	204	13	nintm	nintm	PROPN
ejpam-6316	204	14	procedure	procedure	NOUN
ejpam-6316	204	15	:	:	PUNCT
ejpam-6316	204	16	ψ0(υ	ψ0(υ	PROPN
ejpam-6316	204	17	,	,	PUNCT
ejpam-6316	204	18	σ	σ	NOUN
ejpam-6316	204	19	)	)	PUNCT
ejpam-6316	204	20	=	=	SYM
ejpam-6316	204	21	sin(υ	sin(υ	NOUN
ejpam-6316	204	22	)	)	PUNCT
ejpam-6316	204	23	,	,	PUNCT
ejpam-6316	204	24	ψ1(υ	ψ1(υ	PROPN
ejpam-6316	204	25	,	,	PUNCT
ejpam-6316	204	26	σ	σ	PROPN
ejpam-6316	204	27	)	)	PUNCT
ejpam-6316	204	28	=	=	SYM
ejpam-6316	204	29	−σ	−σ	NOUN
ejpam-6316	204	30	p	p	PROPN
ejpam-6316	204	31	cos(υ	cos(υ	PROPN
ejpam-6316	204	32	)	)	PUNCT
ejpam-6316	204	33	pγ(p	pγ(p	PROPN
ejpam-6316	204	34	)	)	PUNCT
ejpam-6316	204	35	,	,	PUNCT
ejpam-6316	204	36	ψ2(υ	ψ2(υ	PROPN
ejpam-6316	204	37	,	,	PUNCT
ejpam-6316	204	38	σ	σ	NOUN
ejpam-6316	204	39	)	)	PUNCT
ejpam-6316	204	40	=	=	PRON
ejpam-6316	204	41	−σ	−σ	NOUN
ejpam-6316	204	42	2p	2p	NUM
ejpam-6316	204	43	sin(υ	sin(υ	NOUN
ejpam-6316	204	44	)	)	PUNCT
ejpam-6316	204	45	p2γ(p)2	p2γ(p)2	NOUN
ejpam-6316	204	46	,	,	PUNCT
ejpam-6316	204	47	ψ3(υ	ψ3(υ	PROPN
ejpam-6316	204	48	,	,	PUNCT
ejpam-6316	204	49	σ	σ	NOUN
ejpam-6316	204	50	)	)	PUNCT
ejpam-6316	204	51	=	=	SYM
ejpam-6316	204	52	σ3p	σ3p	PROPN
ejpam-6316	204	53	cos(υ	cos(υ	PROPN
ejpam-6316	204	54	)	)	PUNCT
ejpam-6316	204	55	p3γ(p)3	p3γ(p)3	NUM
ejpam-6316	204	56	.	.	PUNCT
ejpam-6316	205	1	(	(	PUNCT
ejpam-6316	205	2	43	43	NUM
ejpam-6316	205	3	)	)	PUNCT
ejpam-6316	205	4	the	the	DET
ejpam-6316	205	5	final	final	ADJ
ejpam-6316	205	6	nintm	nintm	PROPN
ejpam-6316	205	7	algorithm	algorithm	PROPN
ejpam-6316	205	8	solution	solution	NOUN
ejpam-6316	205	9	is	be	AUX
ejpam-6316	205	10	as	as	SCONJ
ejpam-6316	205	11	follows	follow	VERB
ejpam-6316	205	12	:	:	PUNCT
ejpam-6316	205	13	ψ(υ	ψ(υ	NOUN
ejpam-6316	205	14	,	,	PUNCT
ejpam-6316	205	15	σ	σ	PROPN
ejpam-6316	205	16	)	)	PUNCT
ejpam-6316	205	17	=	=	PUNCT
ejpam-6316	206	1	ψ0(υ	ψ0(υ	PROPN
ejpam-6316	206	2	,	,	PUNCT
ejpam-6316	206	3	σ	σ	NOUN
ejpam-6316	206	4	)	)	PUNCT
ejpam-6316	206	5	+	+	SYM
ejpam-6316	207	1	ψ1(υ	ψ1(υ	PROPN
ejpam-6316	207	2	,	,	PUNCT
ejpam-6316	207	3	σ	σ	PROPN
ejpam-6316	207	4	)	)	PUNCT
ejpam-6316	207	5	+	+	CCONJ
ejpam-6316	207	6	ψ2(υ	ψ2(υ	PROPN
ejpam-6316	207	7	,	,	PUNCT
ejpam-6316	207	8	σ	σ	NOUN
ejpam-6316	207	9	)	)	PUNCT
ejpam-6316	207	10	+	+	CCONJ
ejpam-6316	207	11	·	·	PUNCT
ejpam-6316	207	12	·	·	PUNCT
ejpam-6316	207	13	·	·	PUNCT
ejpam-6316	207	14	,	,	PUNCT
ejpam-6316	207	15	(	(	PUNCT
ejpam-6316	207	16	44	44	NUM
ejpam-6316	207	17	)	)	PUNCT
ejpam-6316	207	18	ψ(υ	ψ(υ	PROPN
ejpam-6316	207	19	,	,	PUNCT
ejpam-6316	207	20	σ	σ	NOUN
ejpam-6316	207	21	)	)	PUNCT
ejpam-6316	207	22	=	=	PROPN
ejpam-6316	207	23	sin(υ)−	sin(υ)−	NOUN
ejpam-6316	207	24	σp	σp	PROPN
ejpam-6316	207	25	cos(υ	cos(υ	PROPN
ejpam-6316	207	26	)	)	PUNCT
ejpam-6316	207	27	pγ(p	pγ(p	PROPN
ejpam-6316	207	28	)	)	PUNCT
ejpam-6316	207	29	−	−	PROPN
ejpam-6316	207	30	σ2p	σ2p	PROPN
ejpam-6316	207	31	sin(υ	sin(υ	NOUN
ejpam-6316	207	32	)	)	PUNCT
ejpam-6316	207	33	p2γ(p)2	p2γ(p)2	PROPN
ejpam-6316	207	34	+	+	CCONJ
ejpam-6316	207	35	σ3p	σ3p	PROPN
ejpam-6316	207	36	cos(υ	cos(υ	PROPN
ejpam-6316	207	37	)	)	PUNCT
ejpam-6316	207	38	p3γ(p)3	p3γ(p)3	NUM
ejpam-6316	207	39	.	.	PUNCT
ejpam-6316	208	1	(	(	PUNCT
ejpam-6316	208	2	45	45	NUM
ejpam-6316	208	3	)	)	PUNCT
ejpam-6316	208	4	n.	n.	NOUN
ejpam-6316	208	5	iqbal	iqbal	PROPN
ejpam-6316	208	6	et	et	PROPN
ejpam-6316	208	7	al	al	PROPN
ejpam-6316	208	8	.	.	PUNCT
ejpam-6316	208	9	/	/	SYM
ejpam-6316	208	10	eur	eur	PROPN
ejpam-6316	208	11	.	.	PUNCT
ejpam-6316	209	1	j.	j.	PROPN
ejpam-6316	209	2	pure	pure	PROPN
ejpam-6316	209	3	appl	appl	PROPN
ejpam-6316	209	4	.	.	PROPN
ejpam-6316	209	5	math	math	PROPN
ejpam-6316	209	6	,	,	PUNCT
ejpam-6316	209	7	18	18	NUM
ejpam-6316	209	8	(	(	PUNCT
ejpam-6316	209	9	3	3	NUM
ejpam-6316	209	10	)	)	PUNCT
ejpam-6316	209	11	(	(	PUNCT
ejpam-6316	209	12	2025	2025	NUM
ejpam-6316	209	13	)	)	PUNCT
ejpam-6316	209	14	,	,	PUNCT
ejpam-6316	209	15	6316	6316	NUM
ejpam-6316	209	16	12	12	NUM
ejpam-6316	209	17	of	of	ADP
ejpam-6316	209	18	21	21	NUM
ejpam-6316	209	19	figure	figure	NOUN
ejpam-6316	209	20	5	5	NUM
ejpam-6316	209	21	:	:	PUNCT
ejpam-6316	209	22	in	in	ADP
ejpam-6316	209	23	figure	figure	NOUN
ejpam-6316	209	24	5	5	NUM
ejpam-6316	209	25	,	,	PUNCT
ejpam-6316	209	26	analysis	analysis	NOUN
ejpam-6316	209	27	of	of	ADP
ejpam-6316	209	28	fractional	fractional	ADJ
ejpam-6316	209	29	order	order	NOUN
ejpam-6316	209	30	p	p	NOUN
ejpam-6316	209	31	for	for	ADP
ejpam-6316	209	32	σ	σ	NOUN
ejpam-6316	209	33	=	=	PROPN
ejpam-6316	209	34	0.7	0.7	NUM
ejpam-6316	209	35	of	of	ADP
ejpam-6316	209	36	ψ(υ	ψ(υ	PROPN
ejpam-6316	209	37	,	,	PUNCT
ejpam-6316	209	38	σ	σ	PROPN
ejpam-6316	209	39	)	)	PUNCT
ejpam-6316	209	40	of	of	ADP
ejpam-6316	209	41	example	example	NOUN
ejpam-6316	209	42	2	2	NUM
ejpam-6316	209	43	using	use	VERB
ejpam-6316	209	44	rpsntm	rpsntm	NOUN
ejpam-6316	209	45	.	.	PUNCT
ejpam-6316	210	1	3.5	3.5	NUM
ejpam-6316	210	2	.	.	PUNCT
ejpam-6316	210	3	problem	problem	NOUN
ejpam-6316	210	4	3	3	NUM
ejpam-6316	210	5	3.5.1	3.5.1	NUM
ejpam-6316	210	6	.	.	PUNCT
ejpam-6316	211	1	implementation	implementation	NOUN
ejpam-6316	211	2	of	of	ADP
ejpam-6316	211	3	rpsntm	rpsntm	NOUN
ejpam-6316	211	4	we	we	PRON
ejpam-6316	211	5	consider	consider	VERB
ejpam-6316	211	6	an	an	DET
ejpam-6316	211	7	fkdv	fkdv	NOUN
ejpam-6316	211	8	equation	equation	NOUN
ejpam-6316	211	9	with	with	ADP
ejpam-6316	211	10	initial	initial	ADJ
ejpam-6316	211	11	condition	condition	NOUN
ejpam-6316	211	12	is	be	AUX
ejpam-6316	211	13	given	give	VERB
ejpam-6316	211	14	by	by	ADP
ejpam-6316	211	15	:	:	PUNCT
ejpam-6316	211	16	dp	dp	NOUN
ejpam-6316	211	17	σψ(υ	σψ(υ	NOUN
ejpam-6316	211	18	,	,	PUNCT
ejpam-6316	211	19	σ	σ	PROPN
ejpam-6316	211	20	)	)	PUNCT
ejpam-6316	211	21	+	+	PUNCT
ejpam-6316	211	22	ψ	ψ	X
ejpam-6316	211	23	∂ψ	∂ψ	PROPN
ejpam-6316	211	24	∂υ	∂υ	PROPN
ejpam-6316	211	25	−	−	NOUN
ejpam-6316	211	26	ψ	ψ	NOUN
ejpam-6316	211	27	∂3ψ	∂3ψ	PROPN
ejpam-6316	211	28	∂υ3	∂υ3	PROPN
ejpam-6316	211	29	+	+	CCONJ
ejpam-6316	211	30	∂5ψ	∂5ψ	PROPN
ejpam-6316	211	31	∂υ5	∂υ5	PROPN
ejpam-6316	211	32	=	=	PUNCT
ejpam-6316	211	33	0	0	PROPN
ejpam-6316	211	34	,	,	PUNCT
ejpam-6316	211	35	where	where	SCONJ
ejpam-6316	211	36	σ	σ	PROPN
ejpam-6316	211	37	>	>	X
ejpam-6316	211	38	0	0	PROPN
ejpam-6316	211	39	,	,	PUNCT
ejpam-6316	211	40	ψ	ψ	X
ejpam-6316	211	41	∈	∈	PROPN
ejpam-6316	211	42	<	<	X
ejpam-6316	211	43	,	,	PUNCT
ejpam-6316	211	44	0	0	PUNCT
ejpam-6316	211	45	<	<	X
ejpam-6316	211	46	p	p	X
ejpam-6316	211	47	≤	≤	ADJ
ejpam-6316	211	48	1	1	NUM
ejpam-6316	211	49	(	(	PUNCT
ejpam-6316	211	50	46	46	NUM
ejpam-6316	211	51	)	)	PUNCT
ejpam-6316	211	52	the	the	DET
ejpam-6316	211	53	following	follow	VERB
ejpam-6316	211	54	ics	ic	NOUN
ejpam-6316	211	55	are	be	AUX
ejpam-6316	211	56	applicable	applicable	ADJ
ejpam-6316	211	57	:	:	PUNCT
ejpam-6316	211	58	ψ(υ	ψ(υ	NOUN
ejpam-6316	211	59	,	,	PUNCT
ejpam-6316	211	60	0	0	NUM
ejpam-6316	211	61	)	)	PUNCT
ejpam-6316	211	62	=	=	SYM
ejpam-6316	212	1	eυ	eυ	PROPN
ejpam-6316	212	2	(	(	PUNCT
ejpam-6316	212	3	47	47	NUM
ejpam-6316	212	4	)	)	PUNCT
ejpam-6316	212	5	using	use	VERB
ejpam-6316	212	6	eq	eq	X
ejpam-6316	212	7	.	.	PUNCT
ejpam-6316	213	1	(	(	PUNCT
ejpam-6316	213	2	47	47	NUM
ejpam-6316	213	3	)	)	PUNCT
ejpam-6316	214	1	and	and	CCONJ
ejpam-6316	214	2	applying	apply	VERB
ejpam-6316	214	3	nt	not	PART
ejpam-6316	214	4	to	to	ADP
ejpam-6316	214	5	eq	eq	PROPN
ejpam-6316	214	6	.	.	PUNCT
ejpam-6316	215	1	(	(	PUNCT
ejpam-6316	215	2	46	46	NUM
ejpam-6316	215	3	)	)	PUNCT
ejpam-6316	215	4	,	,	PUNCT
ejpam-6316	215	5	we	we	PRON
ejpam-6316	215	6	obtain	obtain	VERB
ejpam-6316	215	7	:	:	PUNCT
ejpam-6316	215	8	ψ(υ	ψ(υ	NOUN
ejpam-6316	215	9	,	,	PUNCT
ejpam-6316	215	10	s)−	s)−	PROPN
ejpam-6316	215	11	eυ	eυ	ADP
ejpam-6316	215	12	s	s	NOUN
ejpam-6316	215	13	+	+	X
ejpam-6316	215	14	up	up	ADP
ejpam-6316	215	15	sp	sp	ADP
ejpam-6316	215	16	nσ[(n−1	nσ[(n−1	PROPN
ejpam-6316	215	17	σ	σ	PROPN
ejpam-6316	215	18	ψ(υ	ψ(υ	PROPN
ejpam-6316	215	19	,	,	PUNCT
ejpam-6316	215	20	σ	σ	PROPN
ejpam-6316	215	21	)	)	PUNCT
ejpam-6316	215	22	∂(n−1	∂(n−1	PROPN
ejpam-6316	216	1	σ	σ	PROPN
ejpam-6316	216	2	ψ(υ	ψ(υ	PROPN
ejpam-6316	216	3	,	,	PUNCT
ejpam-6316	216	4	σ	σ	PROPN
ejpam-6316	216	5	)	)	PUNCT
ejpam-6316	216	6	∂υ	∂υ	PROPN
ejpam-6316	216	7	]	]	PUNCT
ejpam-6316	216	8	−	−	X
ejpam-6316	216	9	up	up	ADP
ejpam-6316	216	10	sp	sp	ADP
ejpam-6316	216	11	nσ[(n−1	nσ[(n−1	PROPN
ejpam-6316	216	12	σ	σ	PROPN
ejpam-6316	216	13	ψ(υ	ψ(υ	PROPN
ejpam-6316	216	14	,	,	PUNCT
ejpam-6316	216	15	σ	σ	PROPN
ejpam-6316	216	16	)	)	PUNCT
ejpam-6316	216	17	∂3(n−1	∂3(n−1	PROPN
ejpam-6316	216	18	σ	σ	PROPN
ejpam-6316	216	19	ψ(υ	ψ(υ	PROPN
ejpam-6316	216	20	,	,	PUNCT
ejpam-6316	216	21	σ	σ	PROPN
ejpam-6316	216	22	)	)	PUNCT
ejpam-6316	216	23	∂υ3	∂υ3	PROPN
ejpam-6316	216	24	]	]	PUNCT
ejpam-6316	217	1	+	+	CCONJ
ejpam-6316	217	2	up	up	ADP
ejpam-6316	217	3	sp	sp	ADP
ejpam-6316	217	4	[	[	PUNCT
ejpam-6316	217	5	∂5ψ(υ	∂5ψ(υ	PROPN
ejpam-6316	217	6	,	,	PUNCT
ejpam-6316	217	7	σ	σ	PROPN
ejpam-6316	217	8	)	)	PUNCT
ejpam-6316	217	9	∂υ5	∂υ5	ADJ
ejpam-6316	217	10	]	]	PUNCT
ejpam-6316	218	1	=	=	PUNCT
ejpam-6316	218	2	0	0	NUM
ejpam-6316	218	3	,	,	PUNCT
ejpam-6316	218	4	(	(	PUNCT
ejpam-6316	218	5	48	48	NUM
ejpam-6316	218	6	)	)	PUNCT
ejpam-6316	218	7	n.	n.	PROPN
ejpam-6316	218	8	iqbal	iqbal	PROPN
ejpam-6316	218	9	et	et	PROPN
ejpam-6316	218	10	al	al	PROPN
ejpam-6316	218	11	.	.	PUNCT
ejpam-6316	218	12	/	/	SYM
ejpam-6316	218	13	eur	eur	PROPN
ejpam-6316	218	14	.	.	PUNCT
ejpam-6316	219	1	j.	j.	PROPN
ejpam-6316	219	2	pure	pure	PROPN
ejpam-6316	219	3	appl	appl	PROPN
ejpam-6316	219	4	.	.	PROPN
ejpam-6316	219	5	math	math	PROPN
ejpam-6316	219	6	,	,	PUNCT
ejpam-6316	219	7	18	18	NUM
ejpam-6316	219	8	(	(	PUNCT
ejpam-6316	219	9	3	3	NUM
ejpam-6316	219	10	)	)	PUNCT
ejpam-6316	219	11	(	(	PUNCT
ejpam-6316	219	12	2025	2025	NUM
ejpam-6316	219	13	)	)	PUNCT
ejpam-6316	219	14	,	,	PUNCT
ejpam-6316	219	15	6316	6316	NUM
ejpam-6316	219	16	13	13	NUM
ejpam-6316	219	17	of	of	ADP
ejpam-6316	219	18	21	21	NUM
ejpam-6316	219	19	figure	figure	NOUN
ejpam-6316	219	20	6	6	NUM
ejpam-6316	219	21	:	:	PUNCT
ejpam-6316	219	22	in	in	ADP
ejpam-6316	219	23	figure	figure	NOUN
ejpam-6316	219	24	6	6	NUM
ejpam-6316	219	25	,	,	PUNCT
ejpam-6316	219	26	2d	2d	NUM
ejpam-6316	219	27	analysis	analysis	NOUN
ejpam-6316	219	28	of	of	ADP
ejpam-6316	219	29	rpsntm	rpsntm	NOUN
ejpam-6316	219	30	at	at	ADP
ejpam-6316	219	31	σ	σ	PROPN
ejpam-6316	219	32	=	=	PROPN
ejpam-6316	219	33	0.7	0.7	NUM
ejpam-6316	219	34	.	.	PUNCT
ejpam-6316	220	1	thus	thus	ADV
ejpam-6316	220	2	,	,	PUNCT
ejpam-6316	220	3	the	the	DET
ejpam-6316	220	4	term	term	NOUN
ejpam-6316	220	5	series	series	NOUN
ejpam-6316	220	6	that	that	PRON
ejpam-6316	220	7	are	be	AUX
ejpam-6316	220	8	kth	kth	NOUN
ejpam-6316	220	9	-	-	PUNCT
ejpam-6316	220	10	truncated	truncate	VERB
ejpam-6316	220	11	are	be	AUX
ejpam-6316	220	12	:	:	PUNCT
ejpam-6316	220	13	ψ(υ	ψ(υ	PROPN
ejpam-6316	220	14	,	,	PUNCT
ejpam-6316	220	15	s	s	X
ejpam-6316	220	16	)	)	PUNCT
ejpam-6316	220	17	=	=	PUNCT
ejpam-6316	220	18	eυ	eυ	PROPN
ejpam-6316	220	19	s	s	PART
ejpam-6316	220	20	+	+	CCONJ
ejpam-6316	220	21	k∑	k∑	ADJ
ejpam-6316	220	22	r=1	r=1	NOUN
ejpam-6316	220	23	urp+1fr(υ	urp+1fr(υ	NOUN
ejpam-6316	220	24	,	,	PUNCT
ejpam-6316	220	25	s	s	NOUN
ejpam-6316	220	26	)	)	PUNCT
ejpam-6316	220	27	srp+1	srp+1	NOUN
ejpam-6316	220	28	,	,	PUNCT
ejpam-6316	220	29	r	r	NOUN
ejpam-6316	220	30	=	=	SYM
ejpam-6316	220	31	1	1	NUM
ejpam-6316	220	32	,	,	PUNCT
ejpam-6316	220	33	2	2	NUM
ejpam-6316	220	34	,	,	PUNCT
ejpam-6316	220	35	3	3	NUM
ejpam-6316	220	36	,	,	PUNCT
ejpam-6316	220	37	4	4	NUM
ejpam-6316	220	38	·	·	PUNCT
ejpam-6316	220	39	·	·	PUNCT
ejpam-6316	220	40	·	·	PUNCT
ejpam-6316	220	41	.	.	PUNCT
ejpam-6316	221	1	(	(	PUNCT
ejpam-6316	221	2	49	49	NUM
ejpam-6316	221	3	)	)	PUNCT
ejpam-6316	221	4	natural	natural	ADJ
ejpam-6316	221	5	residual	residual	ADJ
ejpam-6316	221	6	functions	function	NOUN
ejpam-6316	221	7	(	(	PUNCT
ejpam-6316	221	8	nrfs	nrf	NOUN
ejpam-6316	221	9	)	)	PUNCT
ejpam-6316	221	10	provided	provide	VERB
ejpam-6316	221	11	as	as	ADP
ejpam-6316	221	12	follows	follow	VERB
ejpam-6316	221	13	:	:	PUNCT
ejpam-6316	221	14	nσres(υ	nσres(υ	NUM
ejpam-6316	221	15	,	,	PUNCT
ejpam-6316	221	16	s	s	PART
ejpam-6316	221	17	)	)	PUNCT
ejpam-6316	221	18	=	=	SYM
ejpam-6316	221	19	ψ(υ	ψ(υ	PROPN
ejpam-6316	221	20	,	,	PUNCT
ejpam-6316	221	21	s)−	s)−	PROPN
ejpam-6316	221	22	eυ	eυ	NOUN
ejpam-6316	221	23	s	s	NOUN
ejpam-6316	221	24	+	+	X
ejpam-6316	221	25	up	up	ADP
ejpam-6316	221	26	sp	sp	ADP
ejpam-6316	221	27	nσ[(n−1	nσ[(n−1	PROPN
ejpam-6316	221	28	σ	σ	PROPN
ejpam-6316	221	29	ψ(υ	ψ(υ	PROPN
ejpam-6316	221	30	,	,	PUNCT
ejpam-6316	221	31	σ	σ	PROPN
ejpam-6316	221	32	)	)	PUNCT
ejpam-6316	221	33	∂(n−1	∂(n−1	PROPN
ejpam-6316	222	1	σ	σ	PROPN
ejpam-6316	222	2	ψ(υ	ψ(υ	PROPN
ejpam-6316	222	3	,	,	PUNCT
ejpam-6316	222	4	σ	σ	PROPN
ejpam-6316	222	5	)	)	PUNCT
ejpam-6316	222	6	∂υ	∂υ	PROPN
ejpam-6316	222	7	]	]	PUNCT
ejpam-6316	223	1	−u	−u	PROPN
ejpam-6316	223	2	p	p	NOUN
ejpam-6316	223	3	sp	sp	ADP
ejpam-6316	223	4	nσ[(n−1	nσ[(n−1	PROPN
ejpam-6316	223	5	σ	σ	PROPN
ejpam-6316	223	6	ψ(υ	ψ(υ	PROPN
ejpam-6316	223	7	,	,	PUNCT
ejpam-6316	223	8	σ	σ	PROPN
ejpam-6316	223	9	)	)	PUNCT
ejpam-6316	223	10	∂3(n−1	∂3(n−1	PROPN
ejpam-6316	223	11	σ	σ	PROPN
ejpam-6316	223	12	ψ(υ	ψ(υ	PROPN
ejpam-6316	223	13	,	,	PUNCT
ejpam-6316	223	14	σ	σ	PROPN
ejpam-6316	223	15	)	)	PUNCT
ejpam-6316	223	16	∂υ3	∂υ3	PROPN
ejpam-6316	223	17	]	]	PUNCT
ejpam-6316	224	1	+	+	CCONJ
ejpam-6316	224	2	up	up	ADP
ejpam-6316	224	3	sp	sp	ADP
ejpam-6316	224	4	[	[	PUNCT
ejpam-6316	224	5	∂5ψ(υ	∂5ψ(υ	PROPN
ejpam-6316	224	6	,	,	PUNCT
ejpam-6316	224	7	σ	σ	PROPN
ejpam-6316	224	8	)	)	PUNCT
ejpam-6316	224	9	∂υ5	∂υ5	ADJ
ejpam-6316	224	10	]	]	PUNCT
ejpam-6316	225	1	=	=	PUNCT
ejpam-6316	225	2	0	0	NUM
ejpam-6316	225	3	,	,	PUNCT
ejpam-6316	225	4	(	(	PUNCT
ejpam-6316	225	5	50	50	NUM
ejpam-6316	225	6	)	)	PUNCT
ejpam-6316	225	7	along	along	ADP
ejpam-6316	225	8	with	with	ADP
ejpam-6316	225	9	the	the	DET
ejpam-6316	225	10	kth	kth	NOUN
ejpam-6316	225	11	-	-	PUNCT
ejpam-6316	225	12	nrfs	nrf	NOUN
ejpam-6316	225	13	as	as	ADP
ejpam-6316	225	14	nσresk(υ	nσresk(υ	PROPN
ejpam-6316	225	15	,	,	PUNCT
ejpam-6316	225	16	s	s	NOUN
ejpam-6316	225	17	)	)	PUNCT
ejpam-6316	225	18	=	=	PRON
ejpam-6316	225	19	ψk(υ	ψk(υ	PUNCT
ejpam-6316	225	20	,	,	PUNCT
ejpam-6316	225	21	s)−	s)−	PROPN
ejpam-6316	225	22	eυ	eυ	NOUN
ejpam-6316	225	23	s	s	NOUN
ejpam-6316	225	24	+	+	X
ejpam-6316	225	25	up	up	ADP
ejpam-6316	225	26	sp	sp	ADP
ejpam-6316	225	27	nσ[(n−1	nσ[(n−1	PROPN
ejpam-6316	225	28	σ	σ	PROPN
ejpam-6316	225	29	ψk(υ	ψk(υ	PROPN
ejpam-6316	225	30	,	,	PUNCT
ejpam-6316	225	31	σ	σ	PROPN
ejpam-6316	225	32	)	)	PUNCT
ejpam-6316	225	33	∂(n−1	∂(n−1	PROPN
ejpam-6316	226	1	σ	σ	PROPN
ejpam-6316	226	2	ψk(υ	ψk(υ	PROPN
ejpam-6316	226	3	,	,	PUNCT
ejpam-6316	226	4	σ	σ	PROPN
ejpam-6316	226	5	)	)	PUNCT
ejpam-6316	226	6	∂υ	∂υ	PROPN
ejpam-6316	226	7	]	]	PUNCT
ejpam-6316	227	1	−u	−u	PROPN
ejpam-6316	227	2	p	p	NOUN
ejpam-6316	227	3	sp	sp	ADP
ejpam-6316	227	4	nσ[(n−1	nσ[(n−1	PROPN
ejpam-6316	227	5	σ	σ	PROPN
ejpam-6316	227	6	ψk(υ	ψk(υ	PROPN
ejpam-6316	227	7	,	,	PUNCT
ejpam-6316	227	8	σ	σ	PROPN
ejpam-6316	227	9	)	)	PUNCT
ejpam-6316	227	10	∂3(n−1	∂3(n−1	PROPN
ejpam-6316	227	11	σ	σ	PROPN
ejpam-6316	227	12	ψk(υ	ψk(υ	PROPN
ejpam-6316	227	13	,	,	PUNCT
ejpam-6316	227	14	σ	σ	PROPN
ejpam-6316	227	15	)	)	PUNCT
ejpam-6316	227	16	∂υ3	∂υ3	PROPN
ejpam-6316	227	17	]	]	PUNCT
ejpam-6316	228	1	+	+	CCONJ
ejpam-6316	228	2	up	up	ADP
ejpam-6316	228	3	sp	sp	ADP
ejpam-6316	228	4	[	[	PUNCT
ejpam-6316	228	5	∂5ψk(υ	∂5ψk(υ	PROPN
ejpam-6316	228	6	,	,	PUNCT
ejpam-6316	228	7	σ	σ	PROPN
ejpam-6316	228	8	)	)	PUNCT
ejpam-6316	228	9	∂υ5	∂υ5	ADJ
ejpam-6316	228	10	]	]	PUNCT
ejpam-6316	229	1	=	=	PUNCT
ejpam-6316	229	2	0	0	NUM
ejpam-6316	229	3	,	,	PUNCT
ejpam-6316	229	4	(	(	PUNCT
ejpam-6316	229	5	51	51	NUM
ejpam-6316	229	6	)	)	PUNCT
ejpam-6316	229	7	to	to	PART
ejpam-6316	229	8	find	find	VERB
ejpam-6316	229	9	fr(υ	fr(υ	NOUN
ejpam-6316	229	10	,	,	PUNCT
ejpam-6316	229	11	s	s	PART
ejpam-6316	229	12	)	)	PUNCT
ejpam-6316	229	13	now	now	ADV
ejpam-6316	229	14	,	,	PUNCT
ejpam-6316	229	15	r	r	NOUN
ejpam-6316	229	16	=	=	SYM
ejpam-6316	229	17	1	1	NUM
ejpam-6316	229	18	,	,	PUNCT
ejpam-6316	229	19	2	2	NUM
ejpam-6316	229	20	,	,	PUNCT
ejpam-6316	229	21	3	3	NUM
ejpam-6316	229	22	,	,	PUNCT
ejpam-6316	229	23	·	·	PUNCT
ejpam-6316	229	24	·	·	PUNCT
ejpam-6316	229	25	·	·	PUNCT
ejpam-6316	229	26	we	we	PRON
ejpam-6316	229	27	multiply	multiply	VERB
ejpam-6316	229	28	the	the	DET
ejpam-6316	229	29	resulting	result	VERB
ejpam-6316	229	30	equation	equation	NOUN
ejpam-6316	229	31	by	by	ADP
ejpam-6316	229	32	srp+1	srp+1	NOUN
ejpam-6316	229	33	,	,	PUNCT
ejpam-6316	229	34	substitute	substitute	VERB
ejpam-6316	229	35	the	the	DET
ejpam-6316	229	36	rσh	rσh	NOUN
ejpam-6316	229	37	-	-	PUNCT
ejpam-6316	229	38	truncated	truncate	VERB
ejpam-6316	229	39	series	series	NOUN
ejpam-6316	229	40	eq	eq	PROPN
ejpam-6316	229	41	.	.	PUNCT
ejpam-6316	230	1	(	(	PUNCT
ejpam-6316	230	2	49	49	NUM
ejpam-6316	230	3	)	)	PUNCT
ejpam-6316	230	4	into	into	ADP
ejpam-6316	230	5	the	the	DET
ejpam-6316	230	6	rσh	rσh	NOUN
ejpam-6316	230	7	-	-	PUNCT
ejpam-6316	230	8	natural	natural	ADJ
ejpam-6316	230	9	residual	residual	ADJ
ejpam-6316	230	10	function	function	NOUN
ejpam-6316	230	11	eq	eq	ADP
ejpam-6316	230	12	.	.	PUNCT
ejpam-6316	231	1	(	(	PUNCT
ejpam-6316	231	2	51	51	NUM
ejpam-6316	231	3	)	)	PUNCT
ejpam-6316	231	4	,	,	PUNCT
ejpam-6316	231	5	and	and	CCONJ
ejpam-6316	231	6	solve	solve	VERB
ejpam-6316	231	7	the	the	DET
ejpam-6316	231	8	relation	relation	NOUN
ejpam-6316	231	9	lims→∞(srp+1nσresψ	lims→∞(srp+1nσresψ	NOUN
ejpam-6316	231	10	,	,	PUNCT
ejpam-6316	231	11	r(σ	r(σ	PROPN
ejpam-6316	231	12	,	,	PUNCT
ejpam-6316	231	13	s	s	NOUN
ejpam-6316	231	14	)	)	PUNCT
ejpam-6316	231	15	)	)	PUNCT
ejpam-6316	232	1	=	=	SYM
ejpam-6316	232	2	0	0	NUM
ejpam-6316	232	3	recursively	recursively	NOUN
ejpam-6316	232	4	.	.	PUNCT
ejpam-6316	233	1	1	1	NUM
ejpam-6316	233	2	,	,	PUNCT
ejpam-6316	233	3	2	2	NUM
ejpam-6316	233	4	,	,	PUNCT
ejpam-6316	233	5	3	3	NUM
ejpam-6316	233	6	,	,	PUNCT
ejpam-6316	233	7	·	·	PUNCT
ejpam-6316	233	8	·	·	PUNCT
ejpam-6316	233	9	·	·	PUNCT
ejpam-6316	233	10	.	.	PUNCT
ejpam-6316	234	1	here	here	ADV
ejpam-6316	234	2	are	be	AUX
ejpam-6316	234	3	the	the	DET
ejpam-6316	234	4	first	first	ADJ
ejpam-6316	234	5	few	few	ADJ
ejpam-6316	234	6	of	of	ADP
ejpam-6316	234	7	terms	term	NOUN
ejpam-6316	234	8	:	:	PUNCT
ejpam-6316	234	9	f1(υ	f1(υ	NUM
ejpam-6316	234	10	,	,	PUNCT
ejpam-6316	234	11	s	s	PART
ejpam-6316	234	12	)	)	PUNCT
ejpam-6316	234	13	=	=	SYM
ejpam-6316	234	14	−eυ	−eυ	PROPN
ejpam-6316	234	15	,	,	PUNCT
ejpam-6316	234	16	(	(	PUNCT
ejpam-6316	234	17	52	52	NUM
ejpam-6316	234	18	)	)	PUNCT
ejpam-6316	234	19	f2(υ	f2(υ	PROPN
ejpam-6316	234	20	,	,	PUNCT
ejpam-6316	234	21	s	s	PART
ejpam-6316	234	22	)	)	PUNCT
ejpam-6316	234	23	=	=	SYM
ejpam-6316	234	24	eυ	eυ	PROPN
ejpam-6316	234	25	,	,	PUNCT
ejpam-6316	234	26	(	(	PUNCT
ejpam-6316	234	27	53	53	NUM
ejpam-6316	234	28	)	)	PUNCT
ejpam-6316	234	29	and	and	CCONJ
ejpam-6316	234	30	so	so	ADV
ejpam-6316	234	31	on	on	ADV
ejpam-6316	234	32	.	.	PUNCT
ejpam-6316	235	1	in	in	ADP
ejpam-6316	235	2	eq	eq	ADP
ejpam-6316	235	3	.	.	PUNCT
ejpam-6316	235	4	(	(	PUNCT
ejpam-6316	235	5	49	49	NUM
ejpam-6316	235	6	)	)	PUNCT
ejpam-6316	235	7	,	,	PUNCT
ejpam-6316	235	8	substitute	substitute	VERB
ejpam-6316	235	9	the	the	DET
ejpam-6316	235	10	values	value	NOUN
ejpam-6316	235	11	of	of	ADP
ejpam-6316	235	12	fr(υ	fr(υ	NOUN
ejpam-6316	235	13	,	,	PUNCT
ejpam-6316	235	14	s	s	PART
ejpam-6316	235	15	)	)	PUNCT
ejpam-6316	235	16	,	,	PUNCT
ejpam-6316	235	17	r	r	NOUN
ejpam-6316	235	18	=	=	SYM
ejpam-6316	235	19	1	1	NUM
ejpam-6316	235	20	,	,	PUNCT
ejpam-6316	235	21	2	2	NUM
ejpam-6316	235	22	,	,	PUNCT
ejpam-6316	235	23	3	3	NUM
ejpam-6316	235	24	,	,	PUNCT
ejpam-6316	235	25	·	·	PUNCT
ejpam-6316	235	26	·	·	PUNCT
ejpam-6316	235	27	·	·	PUNCT
ejpam-6316	235	28	,	,	PUNCT
ejpam-6316	235	29	we	we	PRON
ejpam-6316	235	30	get	get	VERB
ejpam-6316	235	31	:	:	PUNCT
ejpam-6316	235	32	ψ(υ	ψ(υ	NOUN
ejpam-6316	235	33	,	,	PUNCT
ejpam-6316	235	34	s	s	X
ejpam-6316	235	35	)	)	PUNCT
ejpam-6316	235	36	=	=	PUNCT
ejpam-6316	235	37	eυ	eυ	PROPN
ejpam-6316	235	38	s	s	NOUN
ejpam-6316	235	39	−	−	NOUN
ejpam-6316	235	40	upeυ	upeυ	NOUN
ejpam-6316	235	41	sp+1	sp+1	PROPN
ejpam-6316	235	42	+	+	CCONJ
ejpam-6316	235	43	upeυ	upeυ	VERB
ejpam-6316	235	44	s2p+1	s2p+1	PROPN
ejpam-6316	235	45	,	,	PUNCT
ejpam-6316	235	46	(	(	PUNCT
ejpam-6316	235	47	54	54	NUM
ejpam-6316	235	48	)	)	PUNCT
ejpam-6316	235	49	n.	n.	PROPN
ejpam-6316	235	50	iqbal	iqbal	PROPN
ejpam-6316	235	51	et	et	PROPN
ejpam-6316	235	52	al	al	PROPN
ejpam-6316	235	53	.	.	PUNCT
ejpam-6316	235	54	/	/	SYM
ejpam-6316	235	55	eur	eur	PROPN
ejpam-6316	235	56	.	.	PUNCT
ejpam-6316	236	1	j.	j.	PROPN
ejpam-6316	236	2	pure	pure	PROPN
ejpam-6316	236	3	appl	appl	PROPN
ejpam-6316	236	4	.	.	PROPN
ejpam-6316	236	5	math	math	PROPN
ejpam-6316	236	6	,	,	PUNCT
ejpam-6316	236	7	18	18	NUM
ejpam-6316	236	8	(	(	PUNCT
ejpam-6316	236	9	3	3	NUM
ejpam-6316	236	10	)	)	PUNCT
ejpam-6316	236	11	(	(	PUNCT
ejpam-6316	236	12	2025	2025	NUM
ejpam-6316	236	13	)	)	PUNCT
ejpam-6316	236	14	,	,	PUNCT
ejpam-6316	236	15	6316	6316	NUM
ejpam-6316	236	16	14	14	NUM
ejpam-6316	236	17	of	of	ADP
ejpam-6316	236	18	21	21	NUM
ejpam-6316	236	19	figure	figure	NOUN
ejpam-6316	236	20	7	7	NUM
ejpam-6316	236	21	:	:	PUNCT
ejpam-6316	236	22	in	in	ADP
ejpam-6316	236	23	figure	figure	NOUN
ejpam-6316	236	24	7	7	NUM
ejpam-6316	236	25	,	,	PUNCT
ejpam-6316	236	26	analysis	analysis	NOUN
ejpam-6316	236	27	of	of	ADP
ejpam-6316	236	28	various	various	ADJ
ejpam-6316	236	29	order	order	NOUN
ejpam-6316	236	30	p	p	NOUN
ejpam-6316	236	31	for	for	ADP
ejpam-6316	236	32	σ	σ	NOUN
ejpam-6316	236	33	=	=	PROPN
ejpam-6316	236	34	0.7	0.7	NUM
ejpam-6316	236	35	of	of	ADP
ejpam-6316	236	36	ψ(υ	ψ(υ	PROPN
ejpam-6316	236	37	,	,	PUNCT
ejpam-6316	236	38	σ	σ	PROPN
ejpam-6316	236	39	)	)	PUNCT
ejpam-6316	236	40	of	of	ADP
ejpam-6316	236	41	example	example	NOUN
ejpam-6316	236	42	2	2	NUM
ejpam-6316	236	43	using	use	VERB
ejpam-6316	236	44	nintm	nintm	PROPN
ejpam-6316	236	45	.	.	PUNCT
ejpam-6316	237	1	with	with	ADP
ejpam-6316	237	2	the	the	DET
ejpam-6316	237	3	inverse	inverse	ADJ
ejpam-6316	237	4	natural	natural	ADJ
ejpam-6316	237	5	transform	transform	NOUN
ejpam-6316	237	6	,	,	PUNCT
ejpam-6316	237	7	we	we	PRON
ejpam-6316	237	8	obtain	obtain	VERB
ejpam-6316	237	9	ψ(υ	ψ(υ	PROPN
ejpam-6316	237	10	,	,	PUNCT
ejpam-6316	237	11	σ	σ	PROPN
ejpam-6316	237	12	)	)	PUNCT
ejpam-6316	237	13	=	=	SYM
ejpam-6316	237	14	eυ	eυ	PROPN
ejpam-6316	237	15	(	(	PUNCT
ejpam-6316	237	16	1−	1−	NUM
ejpam-6316	237	17	σp	σp	PROPN
ejpam-6316	237	18	γ(p+	γ(p+	PROPN
ejpam-6316	237	19	1	1	NUM
ejpam-6316	237	20	)	)	PUNCT
ejpam-6316	237	21	+	+	NOUN
ejpam-6316	237	22	σ2p	σ2p	PROPN
ejpam-6316	237	23	γ(2p+	γ(2p+	NOUN
ejpam-6316	237	24	1	1	NUM
ejpam-6316	237	25	)	)	PUNCT
ejpam-6316	237	26	)	)	PUNCT
ejpam-6316	238	1	+	+	CCONJ
ejpam-6316	238	2	·	·	PUNCT
ejpam-6316	238	3	·	·	PUNCT
ejpam-6316	238	4	·	·	PUNCT
ejpam-6316	238	5	.	.	PUNCT
ejpam-6316	239	1	(	(	PUNCT
ejpam-6316	239	2	55	55	X
ejpam-6316	239	3	)	)	PUNCT
ejpam-6316	239	4	n.	n.	PROPN
ejpam-6316	239	5	iqbal	iqbal	PROPN
ejpam-6316	239	6	et	et	PROPN
ejpam-6316	239	7	al	al	PROPN
ejpam-6316	239	8	.	.	PUNCT
ejpam-6316	239	9	/	/	SYM
ejpam-6316	239	10	eur	eur	PROPN
ejpam-6316	239	11	.	.	PUNCT
ejpam-6316	240	1	j.	j.	PROPN
ejpam-6316	240	2	pure	pure	PROPN
ejpam-6316	240	3	appl	appl	PROPN
ejpam-6316	240	4	.	.	PROPN
ejpam-6316	240	5	math	math	PROPN
ejpam-6316	240	6	,	,	PUNCT
ejpam-6316	240	7	18	18	NUM
ejpam-6316	240	8	(	(	PUNCT
ejpam-6316	240	9	3	3	NUM
ejpam-6316	240	10	)	)	PUNCT
ejpam-6316	240	11	(	(	PUNCT
ejpam-6316	240	12	2025	2025	NUM
ejpam-6316	240	13	)	)	PUNCT
ejpam-6316	240	14	,	,	PUNCT
ejpam-6316	240	15	6316	6316	NUM
ejpam-6316	240	16	15	15	NUM
ejpam-6316	240	17	of	of	ADP
ejpam-6316	240	18	21	21	NUM
ejpam-6316	240	19	figure	figure	NOUN
ejpam-6316	240	20	8	8	NUM
ejpam-6316	240	21	:	:	PUNCT
ejpam-6316	240	22	in	in	ADP
ejpam-6316	240	23	figure	figure	NOUN
ejpam-6316	240	24	8	8	NUM
ejpam-6316	240	25	,	,	PUNCT
ejpam-6316	240	26	2d	2d	NUM
ejpam-6316	240	27	analysis	analysis	NOUN
ejpam-6316	240	28	of	of	ADP
ejpam-6316	240	29	nintm	nintm	PROPN
ejpam-6316	240	30	at	at	ADP
ejpam-6316	240	31	σ	σ	PROPN
ejpam-6316	240	32	=	=	SYM
ejpam-6316	240	33	0.7	0.7	NUM
ejpam-6316	240	34	.	.	PUNCT
ejpam-6316	240	35	figure	figure	NOUN
ejpam-6316	240	36	9	9	NUM
ejpam-6316	240	37	:	:	PUNCT
ejpam-6316	240	38	in	in	ADP
ejpam-6316	240	39	figure	figure	NOUN
ejpam-6316	240	40	9	9	NUM
ejpam-6316	240	41	,	,	PUNCT
ejpam-6316	240	42	analysis	analysis	NOUN
ejpam-6316	240	43	of	of	ADP
ejpam-6316	240	44	fractional	fractional	ADJ
ejpam-6316	240	45	order	order	NOUN
ejpam-6316	240	46	p	p	NOUN
ejpam-6316	240	47	for	for	ADP
ejpam-6316	240	48	σ	σ	NOUN
ejpam-6316	240	49	=	=	SYM
ejpam-6316	240	50	0.1	0.1	NUM
ejpam-6316	240	51	of	of	ADP
ejpam-6316	240	52	ψ(υ	ψ(υ	PROPN
ejpam-6316	240	53	,	,	PUNCT
ejpam-6316	240	54	σ	σ	PROPN
ejpam-6316	240	55	)	)	PUNCT
ejpam-6316	240	56	of	of	ADP
ejpam-6316	240	57	example	example	NOUN
ejpam-6316	240	58	3	3	NUM
ejpam-6316	240	59	using	use	VERB
ejpam-6316	240	60	rpsntm	rpsntm	NOUN
ejpam-6316	240	61	.	.	PUNCT
ejpam-6316	241	1	n.	n.	PROPN
ejpam-6316	241	2	iqbal	iqbal	PROPN
ejpam-6316	241	3	et	et	PROPN
ejpam-6316	241	4	al	al	PROPN
ejpam-6316	241	5	.	.	PUNCT
ejpam-6316	241	6	/	/	SYM
ejpam-6316	241	7	eur	eur	PROPN
ejpam-6316	241	8	.	.	PUNCT
ejpam-6316	242	1	j.	j.	PROPN
ejpam-6316	242	2	pure	pure	PROPN
ejpam-6316	242	3	appl	appl	PROPN
ejpam-6316	242	4	.	.	PROPN
ejpam-6316	242	5	math	math	PROPN
ejpam-6316	242	6	,	,	PUNCT
ejpam-6316	242	7	18	18	NUM
ejpam-6316	242	8	(	(	PUNCT
ejpam-6316	242	9	3	3	NUM
ejpam-6316	242	10	)	)	PUNCT
ejpam-6316	242	11	(	(	PUNCT
ejpam-6316	242	12	2025	2025	NUM
ejpam-6316	242	13	)	)	PUNCT
ejpam-6316	242	14	,	,	PUNCT
ejpam-6316	242	15	6316	6316	NUM
ejpam-6316	242	16	16	16	NUM
ejpam-6316	242	17	of	of	ADP
ejpam-6316	242	18	21	21	NUM
ejpam-6316	242	19	figure	figure	NOUN
ejpam-6316	242	20	10	10	NUM
ejpam-6316	242	21	:	:	PUNCT
ejpam-6316	242	22	in	in	ADP
ejpam-6316	242	23	figure	figure	NOUN
ejpam-6316	242	24	10	10	NUM
ejpam-6316	242	25	,	,	PUNCT
ejpam-6316	242	26	2d	2d	NUM
ejpam-6316	242	27	analysis	analysis	NOUN
ejpam-6316	242	28	of	of	ADP
ejpam-6316	242	29	fractional	fractional	ADJ
ejpam-6316	242	30	order	order	NOUN
ejpam-6316	242	31	p	p	NOUN
ejpam-6316	242	32	of	of	ADP
ejpam-6316	242	33	ψ(υ	ψ(υ	PROPN
ejpam-6316	242	34	,	,	PUNCT
ejpam-6316	242	35	σ	σ	PROPN
ejpam-6316	242	36	)	)	PUNCT
ejpam-6316	242	37	using	use	VERB
ejpam-6316	242	38	rpsntm	rpsntm	NOUN
ejpam-6316	242	39	for	for	ADP
ejpam-6316	242	40	σ	σ	PROPN
ejpam-6316	242	41	=	=	PROPN
ejpam-6316	242	42	0.1	0.1	NUM
ejpam-6316	242	43	.	.	PUNCT
ejpam-6316	243	1	3.5.2	3.5.2	X
ejpam-6316	243	2	.	.	X
ejpam-6316	243	3	implementation	implementation	NOUN
ejpam-6316	243	4	of	of	ADP
ejpam-6316	243	5	nim	nim	PROPN
ejpam-6316	243	6	we	we	PRON
ejpam-6316	243	7	derive	derive	VERB
ejpam-6316	243	8	the	the	DET
ejpam-6316	243	9	corresponding	correspond	VERB
ejpam-6316	243	10	form	form	NOUN
ejpam-6316	243	11	given	give	VERB
ejpam-6316	243	12	below	below	ADV
ejpam-6316	243	13	by	by	ADP
ejpam-6316	243	14	applying	apply	VERB
ejpam-6316	243	15	the	the	DET
ejpam-6316	243	16	rl	rl	NOUN
ejpam-6316	243	17	integral	integral	ADJ
ejpam-6316	243	18	on	on	ADP
ejpam-6316	243	19	eq.46	eq.46	PROPN
ejpam-6316	243	20	:	:	PUNCT
ejpam-6316	243	21	ψ(υ	ψ(υ	PROPN
ejpam-6316	243	22	,	,	PUNCT
ejpam-6316	243	23	σ	σ	PROPN
ejpam-6316	243	24	)	)	PUNCT
ejpam-6316	243	25	=	=	PUNCT
ejpam-6316	243	26	eυ	eυ	PROPN
ejpam-6316	243	27	−n	−n	ADP
ejpam-6316	243	28	p	p	PROPN
ejpam-6316	243	29	σ	σ	PROPN
ejpam-6316	244	1	[	[	PUNCT
ejpam-6316	244	2	−ψ∂ψ	−ψ∂ψ	PROPN
ejpam-6316	244	3	∂υ	∂υ	PROPN
ejpam-6316	244	4	+	+	NUM
ejpam-6316	244	5	ψ	ψ	NOUN
ejpam-6316	244	6	∂3ψ	∂3ψ	NOUN
ejpam-6316	244	7	∂υ3	∂υ3	PROPN
ejpam-6316	244	8	−	−	PROPN
ejpam-6316	244	9	∂5ψ	∂5ψ	NOUN
ejpam-6316	244	10	∂υ5	∂υ5	PROPN
ejpam-6316	244	11	]	]	PUNCT
ejpam-6316	244	12	.	.	PUNCT
ejpam-6316	245	1	(	(	PUNCT
ejpam-6316	245	2	56	56	X
ejpam-6316	245	3	)	)	PUNCT
ejpam-6316	245	4	we	we	PRON
ejpam-6316	245	5	obtain	obtain	VERB
ejpam-6316	245	6	the	the	DET
ejpam-6316	245	7	following	follow	VERB
ejpam-6316	245	8	several	several	ADJ
ejpam-6316	245	9	terms	term	NOUN
ejpam-6316	245	10	based	base	VERB
ejpam-6316	245	11	on	on	ADP
ejpam-6316	245	12	the	the	DET
ejpam-6316	245	13	nim	nim	PROPN
ejpam-6316	245	14	procedure	procedure	NOUN
ejpam-6316	245	15	:	:	PUNCT
ejpam-6316	245	16	ψ0(υ	ψ0(υ	PROPN
ejpam-6316	245	17	,	,	PUNCT
ejpam-6316	245	18	σ	σ	NOUN
ejpam-6316	245	19	)	)	PUNCT
ejpam-6316	245	20	=	=	SYM
ejpam-6316	246	1	eυ	eυ	PROPN
ejpam-6316	246	2	,	,	PUNCT
ejpam-6316	246	3	ψ1(υ	ψ1(υ	PROPN
ejpam-6316	246	4	,	,	PUNCT
ejpam-6316	246	5	σ	σ	PROPN
ejpam-6316	246	6	)	)	PUNCT
ejpam-6316	246	7	=	=	SYM
ejpam-6316	246	8	−	−	PROPN
ejpam-6316	246	9	eυσp	eυσp	PROPN
ejpam-6316	246	10	pγ(p	pγ(p	PROPN
ejpam-6316	246	11	)	)	PUNCT
ejpam-6316	246	12	,	,	PUNCT
ejpam-6316	246	13	ψ2(υ	ψ2(υ	PROPN
ejpam-6316	246	14	,	,	PUNCT
ejpam-6316	246	15	σ	σ	NOUN
ejpam-6316	246	16	)	)	PUNCT
ejpam-6316	246	17	=	=	SYM
ejpam-6316	247	1	eυσ2p	eυσ2p	PROPN
ejpam-6316	247	2	p2γ(p)2	p2γ(p)2	NOUN
ejpam-6316	247	3	.	.	PUNCT
ejpam-6316	248	1	(	(	PUNCT
ejpam-6316	248	2	57	57	NUM
ejpam-6316	248	3	)	)	PUNCT
ejpam-6316	248	4	the	the	DET
ejpam-6316	248	5	final	final	ADJ
ejpam-6316	248	6	nim	nim	PROPN
ejpam-6316	248	7	algorithm	algorithm	PROPN
ejpam-6316	248	8	solution	solution	NOUN
ejpam-6316	248	9	is	be	AUX
ejpam-6316	248	10	as	as	SCONJ
ejpam-6316	248	11	follows	follow	VERB
ejpam-6316	248	12	:	:	PUNCT
ejpam-6316	248	13	ψ(υ	ψ(υ	NOUN
ejpam-6316	248	14	,	,	PUNCT
ejpam-6316	248	15	σ	σ	PROPN
ejpam-6316	248	16	)	)	PUNCT
ejpam-6316	248	17	=	=	PUNCT
ejpam-6316	249	1	ψ0(υ	ψ0(υ	PROPN
ejpam-6316	249	2	,	,	PUNCT
ejpam-6316	249	3	σ	σ	NOUN
ejpam-6316	249	4	)	)	PUNCT
ejpam-6316	249	5	+	+	SYM
ejpam-6316	250	1	ψ1(υ	ψ1(υ	PROPN
ejpam-6316	250	2	,	,	PUNCT
ejpam-6316	250	3	σ	σ	PROPN
ejpam-6316	250	4	)	)	PUNCT
ejpam-6316	250	5	+	+	CCONJ
ejpam-6316	250	6	ψ2(υ	ψ2(υ	PROPN
ejpam-6316	250	7	,	,	PUNCT
ejpam-6316	250	8	σ	σ	NOUN
ejpam-6316	250	9	)	)	PUNCT
ejpam-6316	250	10	+	+	CCONJ
ejpam-6316	250	11	·	·	PUNCT
ejpam-6316	250	12	·	·	PUNCT
ejpam-6316	250	13	·	·	PUNCT
ejpam-6316	250	14	,	,	PUNCT
ejpam-6316	250	15	(	(	PUNCT
ejpam-6316	250	16	58	58	X
ejpam-6316	250	17	)	)	PUNCT
ejpam-6316	250	18	ψ(υ	ψ(υ	PROPN
ejpam-6316	250	19	,	,	PUNCT
ejpam-6316	250	20	σ	σ	PROPN
ejpam-6316	250	21	)	)	PUNCT
ejpam-6316	250	22	=	=	PUNCT
ejpam-6316	250	23	eυ	eυ	PRON
ejpam-6316	250	24	−	−	NOUN
ejpam-6316	250	25	eυσp	eυσp	PROPN
ejpam-6316	250	26	pγ(p	pγ(p	PROPN
ejpam-6316	250	27	)	)	PUNCT
ejpam-6316	251	1	+	+	CCONJ
ejpam-6316	251	2	eυσ2p	eυσ2p	PRON
ejpam-6316	251	3	p2γ(p)2	p2γ(p)2	NOUN
ejpam-6316	251	4	.	.	PUNCT
ejpam-6316	252	1	(	(	PUNCT
ejpam-6316	252	2	59	59	NUM
ejpam-6316	252	3	)	)	PUNCT
ejpam-6316	252	4	n.	n.	NOUN
ejpam-6316	252	5	iqbal	iqbal	PROPN
ejpam-6316	252	6	et	et	PROPN
ejpam-6316	252	7	al	al	PROPN
ejpam-6316	252	8	.	.	PUNCT
ejpam-6316	252	9	/	/	SYM
ejpam-6316	252	10	eur	eur	PROPN
ejpam-6316	252	11	.	.	PUNCT
ejpam-6316	253	1	j.	j.	PROPN
ejpam-6316	253	2	pure	pure	PROPN
ejpam-6316	253	3	appl	appl	PROPN
ejpam-6316	253	4	.	.	PROPN
ejpam-6316	253	5	math	math	PROPN
ejpam-6316	253	6	,	,	PUNCT
ejpam-6316	253	7	18	18	NUM
ejpam-6316	253	8	(	(	PUNCT
ejpam-6316	253	9	3	3	NUM
ejpam-6316	253	10	)	)	PUNCT
ejpam-6316	253	11	(	(	PUNCT
ejpam-6316	253	12	2025	2025	NUM
ejpam-6316	253	13	)	)	PUNCT
ejpam-6316	253	14	,	,	PUNCT
ejpam-6316	253	15	6316	6316	NUM
ejpam-6316	253	16	17	17	NUM
ejpam-6316	253	17	of	of	ADP
ejpam-6316	253	18	21	21	NUM
ejpam-6316	253	19	figure	figure	NOUN
ejpam-6316	253	20	11	11	NUM
ejpam-6316	253	21	:	:	PUNCT
ejpam-6316	253	22	in	in	ADP
ejpam-6316	253	23	figure	figure	NOUN
ejpam-6316	253	24	11	11	NUM
ejpam-6316	253	25	,	,	PUNCT
ejpam-6316	253	26	analysis	analysis	NOUN
ejpam-6316	253	27	of	of	ADP
ejpam-6316	253	28	fractional	fractional	ADJ
ejpam-6316	253	29	order	order	NOUN
ejpam-6316	253	30	p	p	NOUN
ejpam-6316	253	31	for	for	ADP
ejpam-6316	253	32	σ	σ	NOUN
ejpam-6316	253	33	=	=	SYM
ejpam-6316	253	34	0.1	0.1	NUM
ejpam-6316	253	35	of	of	ADP
ejpam-6316	253	36	ψ(υ	ψ(υ	PROPN
ejpam-6316	253	37	,	,	PUNCT
ejpam-6316	253	38	σ	σ	PROPN
ejpam-6316	253	39	)	)	PUNCT
ejpam-6316	253	40	of	of	ADP
ejpam-6316	253	41	example	example	NOUN
ejpam-6316	253	42	3	3	NUM
ejpam-6316	253	43	using	use	VERB
ejpam-6316	253	44	nim	nim	PROPN
ejpam-6316	253	45	.	.	PROPN
ejpam-6316	253	46	figure	figure	NOUN
ejpam-6316	253	47	12	12	NUM
ejpam-6316	253	48	:	:	PUNCT
ejpam-6316	253	49	in	in	ADP
ejpam-6316	253	50	figure	figure	NOUN
ejpam-6316	253	51	12	12	NUM
ejpam-6316	253	52	,	,	PUNCT
ejpam-6316	253	53	2d	2d	NUM
ejpam-6316	253	54	analysis	analysis	NOUN
ejpam-6316	253	55	of	of	ADP
ejpam-6316	253	56	fractional	fractional	ADJ
ejpam-6316	253	57	order	order	NOUN
ejpam-6316	253	58	p	p	NOUN
ejpam-6316	253	59	of	of	ADP
ejpam-6316	253	60	ψ(υ	ψ(υ	PROPN
ejpam-6316	253	61	,	,	PUNCT
ejpam-6316	253	62	σ	σ	PROPN
ejpam-6316	253	63	)	)	PUNCT
ejpam-6316	253	64	using	use	VERB
ejpam-6316	253	65	nim	nim	PROPN
ejpam-6316	253	66	for	for	ADP
ejpam-6316	253	67	σ	σ	PROPN
ejpam-6316	253	68	=	=	PROPN
ejpam-6316	253	69	0.1	0.1	NUM
ejpam-6316	253	70	the	the	DET
ejpam-6316	253	71	rpsntm	rpsntm	NOUN
ejpam-6316	253	72	and	and	CCONJ
ejpam-6316	253	73	nintm	nintm	PROPN
ejpam-6316	253	74	approaches	approach	VERB
ejpam-6316	253	75	for	for	ADP
ejpam-6316	253	76	fractional	fractional	ADJ
ejpam-6316	253	77	-	-	PUNCT
ejpam-6316	253	78	order	order	NOUN
ejpam-6316	253	79	kdv	kdv	NOUN
ejpam-6316	253	80	equations	equation	NOUN
ejpam-6316	253	81	in	in	ADP
ejpam-6316	253	82	connection	connection	NOUN
ejpam-6316	253	83	with	with	ADP
ejpam-6316	253	84	their	their	PRON
ejpam-6316	253	85	dispersive	dispersive	ADJ
ejpam-6316	253	86	effects	effect	NOUN
ejpam-6316	253	87	in	in	ADP
ejpam-6316	253	88	a	a	DET
ejpam-6316	253	89	plasma	plasma	NOUN
ejpam-6316	253	90	setting	setting	NOUN
ejpam-6316	253	91	.	.	PUNCT
ejpam-6316	254	1	techniques	technique	NOUN
ejpam-6316	254	2	were	be	AUX
ejpam-6316	254	3	reviewed	review	VERB
ejpam-6316	254	4	with	with	ADP
ejpam-6316	254	5	through	through	ADP
ejpam-6316	254	6	graphical	graphical	ADJ
ejpam-6316	254	7	drawings	drawing	NOUN
ejpam-6316	254	8	and	and	CCONJ
ejpam-6316	254	9	numerical	numerical	ADJ
ejpam-6316	254	10	illustrations	illustration	NOUN
ejpam-6316	254	11	,	,	PUNCT
ejpam-6316	254	12	showing	show	VERB
ejpam-6316	254	13	that	that	SCONJ
ejpam-6316	254	14	they	they	PRON
ejpam-6316	254	15	permit	permit	VERB
ejpam-6316	254	16	approximating	approximate	VERB
ejpam-6316	254	17	solutions	solution	NOUN
ejpam-6316	254	18	to	to	ADP
ejpam-6316	254	19	challenging	challenge	VERB
ejpam-6316	254	20	fractional	fractional	ADJ
ejpam-6316	254	21	differential	differential	ADJ
ejpam-6316	254	22	equations	equation	NOUN
ejpam-6316	254	23	.	.	PUNCT
ejpam-6316	255	1	initial	initial	ADJ
ejpam-6316	255	2	solutions	solution	NOUN
ejpam-6316	255	3	were	be	AUX
ejpam-6316	255	4	found	find	VERB
ejpam-6316	255	5	easily	easily	ADV
ejpam-6316	255	6	using	use	VERB
ejpam-6316	255	7	the	the	DET
ejpam-6316	255	8	rpsntm	rpsntm	NOUN
ejpam-6316	255	9	and	and	CCONJ
ejpam-6316	255	10	the	the	DET
ejpam-6316	255	11	nintm	nintm	PROPN
ejpam-6316	255	12	improved	improve	VERB
ejpam-6316	255	13	them	they	PRON
ejpam-6316	255	14	by	by	ADP
ejpam-6316	255	15	making	make	VERB
ejpam-6316	255	16	them	they	PRON
ejpam-6316	255	17	more	more	ADV
ejpam-6316	255	18	n.	n.	PROPN
ejpam-6316	255	19	iqbal	iqbal	PROPN
ejpam-6316	255	20	et	et	PROPN
ejpam-6316	255	21	al	al	PROPN
ejpam-6316	255	22	.	.	PUNCT
ejpam-6316	255	23	/	/	SYM
ejpam-6316	255	24	eur	eur	PROPN
ejpam-6316	255	25	.	.	PUNCT
ejpam-6316	256	1	j.	j.	PROPN
ejpam-6316	256	2	pure	pure	PROPN
ejpam-6316	256	3	appl	appl	PROPN
ejpam-6316	256	4	.	.	PROPN
ejpam-6316	256	5	math	math	PROPN
ejpam-6316	256	6	,	,	PUNCT
ejpam-6316	256	7	18	18	NUM
ejpam-6316	256	8	(	(	PUNCT
ejpam-6316	256	9	3	3	NUM
ejpam-6316	256	10	)	)	PUNCT
ejpam-6316	256	11	(	(	PUNCT
ejpam-6316	256	12	2025	2025	NUM
ejpam-6316	256	13	)	)	PUNCT
ejpam-6316	256	14	,	,	PUNCT
ejpam-6316	256	15	6316	6316	NUM
ejpam-6316	256	16	18	18	NUM
ejpam-6316	256	17	of	of	ADP
ejpam-6316	256	18	21	21	NUM
ejpam-6316	256	19	accurate	accurate	ADJ
ejpam-6316	256	20	and	and	CCONJ
ejpam-6316	256	21	stable	stable	ADJ
ejpam-6316	256	22	.	.	PUNCT
ejpam-6316	257	1	figures	figure	NOUN
ejpam-6316	257	2	1	1	NUM
ejpam-6316	257	3	and	and	CCONJ
ejpam-6316	257	4	3	3	NUM
ejpam-6316	257	5	clearly	clearly	ADV
ejpam-6316	257	6	show	show	VERB
ejpam-6316	257	7	that	that	SCONJ
ejpam-6316	257	8	the	the	DET
ejpam-6316	257	9	fractional	fractional	ADJ
ejpam-6316	257	10	order	order	NOUN
ejpam-6316	257	11	p	p	NOUN
ejpam-6316	257	12	has	have	VERB
ejpam-6316	257	13	an	an	DET
ejpam-6316	257	14	effect	effect	NOUN
ejpam-6316	257	15	on	on	ADP
ejpam-6316	257	16	the	the	DET
ejpam-6316	257	17	solution	solution	NOUN
ejpam-6316	257	18	ψ(υ	ψ(υ	PROPN
ejpam-6316	257	19	,	,	PUNCT
ejpam-6316	257	20	0.05	0.05	NUM
ejpam-6316	257	21	)	)	PUNCT
ejpam-6316	257	22	.	.	PUNCT
ejpam-6316	258	1	as	as	SCONJ
ejpam-6316	258	2	shown	show	VERB
ejpam-6316	258	3	in	in	ADP
ejpam-6316	258	4	figure	figure	NOUN
ejpam-6316	258	5	1	1	NUM
ejpam-6316	258	6	,	,	PUNCT
ejpam-6316	258	7	there	there	PRON
ejpam-6316	258	8	is	be	VERB
ejpam-6316	258	9	an	an	DET
ejpam-6316	258	10	impact	impact	NOUN
ejpam-6316	258	11	on	on	ADP
ejpam-6316	258	12	the	the	DET
ejpam-6316	258	13	solution	solution	NOUN
ejpam-6316	258	14	’s	’s	PART
ejpam-6316	258	15	behavior	behavior	NOUN
ejpam-6316	258	16	as	as	ADP
ejpam-6316	258	17	the	the	DET
ejpam-6316	258	18	order	order	NOUN
ejpam-6316	258	19	p	p	NOUN
ejpam-6316	258	20	changes	change	NOUN
ejpam-6316	258	21	and	and	CCONJ
ejpam-6316	258	22	in	in	ADP
ejpam-6316	258	23	figure	figure	NOUN
ejpam-6316	258	24	3	3	NUM
ejpam-6316	258	25	,	,	PUNCT
ejpam-6316	258	26	using	use	VERB
ejpam-6316	258	27	the	the	DET
ejpam-6316	258	28	nintm	nintm	PROPN
ejpam-6316	258	29	,	,	PUNCT
ejpam-6316	258	30	the	the	DET
ejpam-6316	258	31	same	same	ADJ
ejpam-6316	258	32	analysis	analysis	NOUN
ejpam-6316	258	33	is	be	AUX
ejpam-6316	258	34	seen	see	VERB
ejpam-6316	258	35	with	with	ADP
ejpam-6316	258	36	greatly	greatly	ADV
ejpam-6316	258	37	enhanced	enhance	VERB
ejpam-6316	258	38	accuracy	accuracy	NOUN
ejpam-6316	258	39	.	.	PUNCT
ejpam-6316	259	1	the	the	DET
ejpam-6316	259	2	calculations	calculation	NOUN
ejpam-6316	259	3	show	show	VERB
ejpam-6316	259	4	that	that	SCONJ
ejpam-6316	259	5	systems	system	NOUN
ejpam-6316	259	6	such	such	ADJ
ejpam-6316	259	7	as	as	ADP
ejpam-6316	259	8	the	the	DET
ejpam-6316	259	9	fractional	fractional	ADJ
ejpam-6316	259	10	-	-	PUNCT
ejpam-6316	259	11	order	order	NOUN
ejpam-6316	259	12	kdv	kdv	NOUN
ejpam-6316	259	13	equations	equation	NOUN
ejpam-6316	259	14	generally	generally	ADV
ejpam-6316	259	15	converge	converge	VERB
ejpam-6316	259	16	and	and	CCONJ
ejpam-6316	259	17	deliver	deliver	VERB
ejpam-6316	259	18	more	more	ADV
ejpam-6316	259	19	accurate	accurate	ADJ
ejpam-6316	259	20	answers	answer	NOUN
ejpam-6316	259	21	with	with	ADP
ejpam-6316	259	22	iterative	iterative	ADJ
ejpam-6316	259	23	methods	method	NOUN
ejpam-6316	259	24	such	such	ADJ
ejpam-6316	259	25	as	as	ADP
ejpam-6316	259	26	nintm	nintm	PROPN
ejpam-6316	259	27	.	.	PUNCT
ejpam-6316	260	1	shown	show	VERB
ejpam-6316	260	2	in	in	ADP
ejpam-6316	260	3	figures	figure	NOUN
ejpam-6316	260	4	2	2	NUM
ejpam-6316	260	5	and	and	CCONJ
ejpam-6316	260	6	4	4	NUM
ejpam-6316	260	7	are	be	AUX
ejpam-6316	260	8	top	top	ADJ
ejpam-6316	260	9	views	view	NOUN
ejpam-6316	260	10	of	of	ADP
ejpam-6316	260	11	the	the	DET
ejpam-6316	260	12	solutions	solution	NOUN
ejpam-6316	260	13	found	find	VERB
ejpam-6316	260	14	by	by	ADP
ejpam-6316	260	15	rpsntm	rpsntm	PROPN
ejpam-6316	260	16	and	and	CCONJ
ejpam-6316	260	17	nintm	nintm	PROPN
ejpam-6316	260	18	when	when	SCONJ
ejpam-6316	260	19	σ	σ	PROPN
ejpam-6316	260	20	=	=	NOUN
ejpam-6316	260	21	0.05	0.05	NUM
ejpam-6316	260	22	.	.	PUNCT
ejpam-6316	261	1	they	they	PRON
ejpam-6316	261	2	show	show	VERB
ejpam-6316	261	3	the	the	DET
ejpam-6316	261	4	development	development	NOUN
ejpam-6316	261	5	of	of	ADP
ejpam-6316	261	6	waveforms	waveform	NOUN
ejpam-6316	261	7	in	in	ADP
ejpam-6316	261	8	space	space	NOUN
ejpam-6316	261	9	and	and	CCONJ
ejpam-6316	261	10	time	time	NOUN
ejpam-6316	261	11	throughout	throughout	ADP
ejpam-6316	261	12	the	the	DET
ejpam-6316	261	13	plasma	plasma	NOUN
ejpam-6316	261	14	area	area	NOUN
ejpam-6316	261	15	.	.	PUNCT
ejpam-6316	262	1	although	although	SCONJ
ejpam-6316	262	2	rpsntm	rpsntm	ADJ
ejpam-6316	262	3	estimates	estimate	VERB
ejpam-6316	262	4	how	how	SCONJ
ejpam-6316	262	5	waves	wave	NOUN
ejpam-6316	262	6	behave	behave	VERB
ejpam-6316	262	7	,	,	PUNCT
ejpam-6316	262	8	nintm	nintm	PROPN
ejpam-6316	262	9	refines	refine	VERB
ejpam-6316	262	10	this	this	DET
ejpam-6316	262	11	idea	idea	NOUN
ejpam-6316	262	12	and	and	CCONJ
ejpam-6316	262	13	shows	show	VERB
ejpam-6316	262	14	how	how	SCONJ
ejpam-6316	262	15	waves	wave	NOUN
ejpam-6316	262	16	travel	travel	VERB
ejpam-6316	262	17	more	more	ADV
ejpam-6316	262	18	accurately	accurately	ADV
ejpam-6316	262	19	.	.	PUNCT
ejpam-6316	263	1	the	the	DET
ejpam-6316	263	2	distinct	distinct	ADJ
ejpam-6316	263	3	images	image	NOUN
ejpam-6316	263	4	from	from	ADP
ejpam-6316	263	5	the	the	DET
ejpam-6316	263	6	two	two	NUM
ejpam-6316	263	7	methods	method	NOUN
ejpam-6316	263	8	reveal	reveal	VERB
ejpam-6316	263	9	the	the	DET
ejpam-6316	263	10	superior	superior	ADJ
ejpam-6316	263	11	accuracy	accuracy	NOUN
ejpam-6316	263	12	of	of	ADP
ejpam-6316	263	13	the	the	DET
ejpam-6316	263	14	nintm	nintm	PROPN
ejpam-6316	263	15	which	which	PRON
ejpam-6316	263	16	is	be	AUX
ejpam-6316	263	17	useful	useful	ADJ
ejpam-6316	263	18	for	for	ADP
ejpam-6316	263	19	dealing	deal	VERB
ejpam-6316	263	20	with	with	ADP
ejpam-6316	263	21	wave	wave	NOUN
ejpam-6316	263	22	dynamics	dynamic	NOUN
ejpam-6316	263	23	and	and	CCONJ
ejpam-6316	263	24	fractional	fractional	ADJ
ejpam-6316	263	25	calculus	calculus	NOUN
ejpam-6316	263	26	.	.	PUNCT
ejpam-6316	264	1	figures	figure	NOUN
ejpam-6316	264	2	5	5	NUM
ejpam-6316	264	3	and	and	CCONJ
ejpam-6316	264	4	7	7	NUM
ejpam-6316	264	5	illustrate	illustrate	VERB
ejpam-6316	264	6	the	the	DET
ejpam-6316	264	7	findings	finding	NOUN
ejpam-6316	264	8	of	of	ADP
ejpam-6316	264	9	using	use	VERB
ejpam-6316	264	10	rpsntm	rpsntm	PROPN
ejpam-6316	264	11	and	and	CCONJ
ejpam-6316	264	12	nintm	nintm	PROPN
ejpam-6316	264	13	on	on	ADP
ejpam-6316	264	14	example	example	NOUN
ejpam-6316	264	15	2	2	NUM
ejpam-6316	264	16	when	when	SCONJ
ejpam-6316	264	17	σ	σ	X
ejpam-6316	264	18	=	=	PROPN
ejpam-6316	264	19	0.7	0.7	NUM
ejpam-6316	264	20	and	and	CCONJ
ejpam-6316	264	21	p	p	NOUN
ejpam-6316	264	22	is	be	AUX
ejpam-6316	264	23	changed	change	VERB
ejpam-6316	264	24	.	.	PUNCT
ejpam-6316	265	1	we	we	PRON
ejpam-6316	265	2	can	can	AUX
ejpam-6316	265	3	see	see	VERB
ejpam-6316	265	4	from	from	ADP
ejpam-6316	265	5	these	these	DET
ejpam-6316	265	6	pictures	picture	NOUN
ejpam-6316	265	7	that	that	SCONJ
ejpam-6316	265	8	a	a	DET
ejpam-6316	265	9	larger	large	ADJ
ejpam-6316	265	10	value	value	NOUN
ejpam-6316	265	11	of	of	ADP
ejpam-6316	265	12	σ	σ	NOUN
ejpam-6316	265	13	strongly	strongly	ADV
ejpam-6316	265	14	affects	affect	VERB
ejpam-6316	265	15	both	both	DET
ejpam-6316	265	16	wave	wave	NOUN
ejpam-6316	265	17	spreading	spread	VERB
ejpam-6316	265	18	and	and	CCONJ
ejpam-6316	265	19	dispersion	dispersion	NOUN
ejpam-6316	265	20	.	.	PUNCT
ejpam-6316	266	1	for	for	ADP
ejpam-6316	266	2	increasing	increase	VERB
ejpam-6316	266	3	values	value	NOUN
ejpam-6316	266	4	of	of	ADP
ejpam-6316	266	5	fractional	fractional	ADJ
ejpam-6316	266	6	order	order	NOUN
ejpam-6316	266	7	p	p	NOUN
ejpam-6316	266	8	,	,	PUNCT
ejpam-6316	266	9	larger	large	ADJ
ejpam-6316	266	10	dispersion	dispersion	NOUN
ejpam-6316	266	11	appears	appear	VERB
ejpam-6316	266	12	and	and	CCONJ
ejpam-6316	266	13	the	the	DET
ejpam-6316	266	14	nintm	nintm	PROPN
ejpam-6316	266	15	gives	give	VERB
ejpam-6316	266	16	better	well	ADJ
ejpam-6316	266	17	and	and	CCONJ
ejpam-6316	266	18	more	more	ADV
ejpam-6316	266	19	accurate	accurate	ADJ
ejpam-6316	266	20	results	result	NOUN
ejpam-6316	266	21	than	than	ADP
ejpam-6316	266	22	the	the	DET
ejpam-6316	266	23	rpsntm	rpsntm	NOUN
ejpam-6316	266	24	.	.	PUNCT
ejpam-6316	267	1	it	it	PRON
ejpam-6316	267	2	demonstrates	demonstrate	VERB
ejpam-6316	267	3	that	that	SCONJ
ejpam-6316	267	4	repeating	repeat	VERB
ejpam-6316	267	5	the	the	DET
ejpam-6316	267	6	method	method	NOUN
ejpam-6316	267	7	refines	refine	VERB
ejpam-6316	267	8	the	the	DET
ejpam-6316	267	9	study	study	NOUN
ejpam-6316	267	10	of	of	ADP
ejpam-6316	267	11	plasma	plasma	NOUN
ejpam-6316	267	12	waves	wave	NOUN
ejpam-6316	267	13	and	and	CCONJ
ejpam-6316	267	14	allows	allow	VERB
ejpam-6316	267	15	for	for	ADP
ejpam-6316	267	16	better	well	ADJ
ejpam-6316	267	17	observations	observation	NOUN
ejpam-6316	267	18	of	of	ADP
ejpam-6316	267	19	their	their	PRON
ejpam-6316	267	20	behavior	behavior	NOUN
ejpam-6316	267	21	.	.	PUNCT
ejpam-6316	268	1	figures	figure	NOUN
ejpam-6316	268	2	6	6	NUM
ejpam-6316	268	3	and	and	CCONJ
ejpam-6316	268	4	8	8	NUM
ejpam-6316	268	5	show	show	VERB
ejpam-6316	268	6	the	the	DET
ejpam-6316	268	7	results	result	NOUN
ejpam-6316	268	8	of	of	ADP
ejpam-6316	268	9	the	the	DET
ejpam-6316	268	10	two	two	NUM
ejpam-6316	268	11	-	-	PUNCT
ejpam-6316	268	12	dimensional	dimensional	ADJ
ejpam-6316	268	13	analysis	analysis	NOUN
ejpam-6316	268	14	for	for	ADP
ejpam-6316	268	15	σ	σ	NOUN
ejpam-6316	268	16	=	=	SYM
ejpam-6316	268	17	0.7	0.7	NUM
ejpam-6316	268	18	comparing	compare	VERB
ejpam-6316	268	19	the	the	DET
ejpam-6316	268	20	rpsntm	rpsntm	NOUN
ejpam-6316	268	21	and	and	CCONJ
ejpam-6316	268	22	nintm	nintm	PROPN
ejpam-6316	268	23	findings	findings	PROPN
ejpam-6316	268	24	.	.	PUNCT
ejpam-6316	269	1	nintm	nintm	PROPN
ejpam-6316	269	2	demonstrates	demonstrate	VERB
ejpam-6316	269	3	wave	wave	NOUN
ejpam-6316	269	4	behavior	behavior	NOUN
ejpam-6316	269	5	more	more	ADV
ejpam-6316	269	6	clearly	clearly	ADV
ejpam-6316	269	7	and	and	CCONJ
ejpam-6316	269	8	accurately	accurately	ADV
ejpam-6316	269	9	than	than	ADP
ejpam-6316	269	10	the	the	DET
ejpam-6316	269	11	older	old	ADJ
ejpam-6316	269	12	method	method	NOUN
ejpam-6316	269	13	.	.	PUNCT
ejpam-6316	270	1	the	the	DET
ejpam-6316	270	2	experiments	experiment	NOUN
ejpam-6316	270	3	prove	prove	VERB
ejpam-6316	270	4	that	that	SCONJ
ejpam-6316	270	5	the	the	DET
ejpam-6316	270	6	nintm	nintm	PROPN
ejpam-6316	270	7	performs	perform	VERB
ejpam-6316	270	8	much	much	ADV
ejpam-6316	270	9	better	well	ADV
ejpam-6316	270	10	in	in	ADP
ejpam-6316	270	11	solving	solve	VERB
ejpam-6316	270	12	nonlinear	nonlinear	ADJ
ejpam-6316	270	13	dispersive	dispersive	ADJ
ejpam-6316	270	14	equations	equation	NOUN
ejpam-6316	270	15	.	.	PUNCT
ejpam-6316	271	1	in	in	ADP
ejpam-6316	271	2	example	example	NOUN
ejpam-6316	271	3	3	3	NUM
ejpam-6316	271	4	,	,	PUNCT
ejpam-6316	271	5	figures	figure	NOUN
ejpam-6316	271	6	9	9	NUM
ejpam-6316	271	7	and	and	CCONJ
ejpam-6316	271	8	11	11	NUM
ejpam-6316	271	9	illustrate	illustrate	VERB
ejpam-6316	271	10	once	once	ADV
ejpam-6316	271	11	more	more	ADV
ejpam-6316	271	12	the	the	DET
ejpam-6316	271	13	role	role	NOUN
ejpam-6316	271	14	of	of	ADP
ejpam-6316	271	15	fractional	fractional	ADJ
ejpam-6316	271	16	order	order	NOUN
ejpam-6316	271	17	in	in	ADP
ejpam-6316	271	18	controlling	control	VERB
ejpam-6316	271	19	the	the	DET
ejpam-6316	271	20	dispersive	dispersive	ADJ
ejpam-6316	271	21	properties	property	NOUN
ejpam-6316	271	22	of	of	ADP
ejpam-6316	271	23	the	the	DET
ejpam-6316	271	24	wave	wave	NOUN
ejpam-6316	271	25	.	.	PUNCT
ejpam-6316	272	1	looking	look	VERB
ejpam-6316	272	2	at	at	ADP
ejpam-6316	272	3	the	the	DET
ejpam-6316	272	4	results	result	NOUN
ejpam-6316	272	5	from	from	ADP
ejpam-6316	272	6	rpsntm	rpsntm	NOUN
ejpam-6316	272	7	(	(	PUNCT
ejpam-6316	272	8	figure	figure	NOUN
ejpam-6316	272	9	9	9	NUM
ejpam-6316	272	10	)	)	PUNCT
ejpam-6316	272	11	and	and	CCONJ
ejpam-6316	272	12	nintm	nintm	PROPN
ejpam-6316	272	13	(	(	PUNCT
ejpam-6316	272	14	figure	figure	NOUN
ejpam-6316	272	15	11	11	NUM
ejpam-6316	272	16	)	)	PUNCT
ejpam-6316	272	17	,	,	PUNCT
ejpam-6316	272	18	it	it	PRON
ejpam-6316	272	19	’s	’	VERB
ejpam-6316	272	20	noticeable	noticeable	ADJ
ejpam-6316	272	21	that	that	SCONJ
ejpam-6316	272	22	in	in	ADP
ejpam-6316	272	23	both	both	DET
ejpam-6316	272	24	cases	case	NOUN
ejpam-6316	272	25	,	,	PUNCT
ejpam-6316	272	26	changing	change	VERB
ejpam-6316	272	27	the	the	DET
ejpam-6316	272	28	value	value	NOUN
ejpam-6316	272	29	of	of	ADP
ejpam-6316	272	30	p	p	NOUN
ejpam-6316	272	31	changes	change	VERB
ejpam-6316	272	32	the	the	DET
ejpam-6316	272	33	pattern	pattern	NOUN
ejpam-6316	272	34	of	of	ADP
ejpam-6316	272	35	shapes	shape	NOUN
ejpam-6316	272	36	.	.	PUNCT
ejpam-6316	273	1	the	the	DET
ejpam-6316	273	2	nintm	nintm	PROPN
ejpam-6316	273	3	once	once	ADV
ejpam-6316	273	4	more	more	ADV
ejpam-6316	273	5	gives	give	VERB
ejpam-6316	273	6	a	a	DET
ejpam-6316	273	7	more	more	ADV
ejpam-6316	273	8	accurate	accurate	ADJ
ejpam-6316	273	9	answer	answer	NOUN
ejpam-6316	273	10	.	.	PUNCT
ejpam-6316	274	1	in	in	ADP
ejpam-6316	274	2	a	a	DET
ejpam-6316	274	3	similar	similar	ADJ
ejpam-6316	274	4	manner	manner	NOUN
ejpam-6316	274	5	,	,	PUNCT
ejpam-6316	274	6	figures	figure	VERB
ejpam-6316	274	7	10	10	NUM
ejpam-6316	274	8	and	and	CCONJ
ejpam-6316	274	9	12	12	NUM
ejpam-6316	274	10	show	show	NOUN
ejpam-6316	274	11	that	that	SCONJ
ejpam-6316	274	12	the	the	DET
ejpam-6316	274	13	nintm	nintm	PROPN
ejpam-6316	274	14	more	more	ADV
ejpam-6316	274	15	precisely	precisely	ADV
ejpam-6316	274	16	and	and	CCONJ
ejpam-6316	274	17	clearly	clearly	ADV
ejpam-6316	274	18	represents	represent	VERB
ejpam-6316	274	19	the	the	DET
ejpam-6316	274	20	spreading	spread	VERB
ejpam-6316	274	21	wave	wave	NOUN
ejpam-6316	274	22	at	at	ADP
ejpam-6316	274	23	σ	σ	NOUN
ejpam-6316	274	24	=	=	SYM
ejpam-6316	274	25	0.1	0.1	NUM
ejpam-6316	274	26	than	than	ADP
ejpam-6316	274	27	the	the	DET
ejpam-6316	274	28	rpsntm	rpsntm	NOUN
ejpam-6316	274	29	.	.	PUNCT
ejpam-6316	275	1	in	in	ADP
ejpam-6316	275	2	all	all	PRON
ejpam-6316	275	3	,	,	PUNCT
ejpam-6316	275	4	using	use	VERB
ejpam-6316	275	5	rpsntm	rpsntm	PROPN
ejpam-6316	275	6	and	and	CCONJ
ejpam-6316	275	7	nintm	nintm	PROPN
ejpam-6316	275	8	together	together	ADV
ejpam-6316	275	9	creates	create	VERB
ejpam-6316	275	10	a	a	DET
ejpam-6316	275	11	potent	potent	ADJ
ejpam-6316	275	12	framework	framework	NOUN
ejpam-6316	275	13	for	for	ADP
ejpam-6316	275	14	resolving	resolve	VERB
ejpam-6316	275	15	fractional	fractional	ADJ
ejpam-6316	275	16	-	-	PUNCT
ejpam-6316	275	17	order	order	NOUN
ejpam-6316	275	18	kdv	kdv	NOUN
ejpam-6316	275	19	equations	equation	NOUN
ejpam-6316	275	20	in	in	ADP
ejpam-6316	275	21	connection	connection	NOUN
ejpam-6316	275	22	with	with	ADP
ejpam-6316	275	23	dispersive	dispersive	ADJ
ejpam-6316	275	24	waves	wave	NOUN
ejpam-6316	275	25	in	in	ADP
ejpam-6316	275	26	plasma	plasma	NOUN
ejpam-6316	275	27	conditions	condition	NOUN
ejpam-6316	275	28	.	.	PUNCT
ejpam-6316	276	1	the	the	DET
ejpam-6316	276	2	graphs	graph	NOUN
ejpam-6316	276	3	show	show	VERB
ejpam-6316	276	4	how	how	SCONJ
ejpam-6316	276	5	these	these	DET
ejpam-6316	276	6	methods	method	NOUN
ejpam-6316	276	7	skillfully	skillfully	ADV
ejpam-6316	276	8	handle	handle	VERB
ejpam-6316	276	9	nonlinear	nonlinear	ADJ
ejpam-6316	276	10	dynamics	dynamic	NOUN
ejpam-6316	276	11	and	and	CCONJ
ejpam-6316	276	12	nintm	nintm	PROPN
ejpam-6316	276	13	does	do	VERB
ejpam-6316	276	14	this	this	PRON
ejpam-6316	276	15	more	more	ADV
ejpam-6316	276	16	accurately	accurately	ADV
ejpam-6316	276	17	.	.	PUNCT
ejpam-6316	277	1	these	these	DET
ejpam-6316	277	2	methods	method	NOUN
ejpam-6316	277	3	are	be	AUX
ejpam-6316	277	4	enhanced	enhance	VERB
ejpam-6316	277	5	,	,	PUNCT
ejpam-6316	277	6	according	accord	VERB
ejpam-6316	277	7	to	to	ADP
ejpam-6316	277	8	the	the	DET
ejpam-6316	277	9	visual	visual	ADJ
ejpam-6316	277	10	information	information	NOUN
ejpam-6316	277	11	,	,	PUNCT
ejpam-6316	277	12	by	by	ADP
ejpam-6316	277	13	being	be	AUX
ejpam-6316	277	14	able	able	ADJ
ejpam-6316	277	15	to	to	PART
ejpam-6316	277	16	get	get	VERB
ejpam-6316	277	17	good	good	ADJ
ejpam-6316	277	18	approximations	approximation	NOUN
ejpam-6316	277	19	for	for	ADP
ejpam-6316	277	20	fractional	fractional	ADJ
ejpam-6316	277	21	differential	differential	ADJ
ejpam-6316	277	22	equations	equation	NOUN
ejpam-6316	277	23	,	,	PUNCT
ejpam-6316	277	24	covering	cover	VERB
ejpam-6316	277	25	a	a	DET
ejpam-6316	277	26	large	large	ADJ
ejpam-6316	277	27	number	number	NOUN
ejpam-6316	277	28	of	of	ADP
ejpam-6316	277	29	scientific	scientific	ADJ
ejpam-6316	277	30	and	and	CCONJ
ejpam-6316	277	31	engineering	engineering	NOUN
ejpam-6316	277	32	situations	situation	NOUN
ejpam-6316	277	33	.	.	PUNCT
ejpam-6316	278	1	new	new	ADJ
ejpam-6316	278	2	research	research	NOUN
ejpam-6316	278	3	might	might	AUX
ejpam-6316	278	4	test	test	VERB
ejpam-6316	278	5	these	these	DET
ejpam-6316	278	6	methods	method	NOUN
ejpam-6316	278	7	in	in	ADP
ejpam-6316	278	8	nonlinear	nonlinear	ADJ
ejpam-6316	278	9	fractional	fractional	ADJ
ejpam-6316	278	10	cases	case	NOUN
ejpam-6316	278	11	,	,	PUNCT
ejpam-6316	278	12	helping	help	VERB
ejpam-6316	278	13	these	these	DET
ejpam-6316	278	14	methods	method	NOUN
ejpam-6316	278	15	have	have	VERB
ejpam-6316	278	16	a	a	DET
ejpam-6316	278	17	stronger	strong	ADJ
ejpam-6316	278	18	impact	impact	NOUN
ejpam-6316	278	19	in	in	ADP
ejpam-6316	278	20	mathematical	mathematical	ADJ
ejpam-6316	278	21	physics	physics	NOUN
ejpam-6316	278	22	and	and	CCONJ
ejpam-6316	278	23	computational	computational	ADJ
ejpam-6316	278	24	science	science	NOUN
ejpam-6316	278	25	.	.	PUNCT
ejpam-6316	279	1	4	4	X
ejpam-6316	279	2	.	.	X
ejpam-6316	279	3	conclusion	conclusion	NOUN
ejpam-6316	279	4	in	in	ADP
ejpam-6316	279	5	this	this	DET
ejpam-6316	279	6	study	study	NOUN
ejpam-6316	279	7	,	,	PUNCT
ejpam-6316	279	8	we	we	PRON
ejpam-6316	279	9	have	have	AUX
ejpam-6316	279	10	successfully	successfully	ADV
ejpam-6316	279	11	applied	apply	VERB
ejpam-6316	279	12	the	the	DET
ejpam-6316	279	13	residual	residual	ADJ
ejpam-6316	279	14	power	power	NOUN
ejpam-6316	279	15	series	series	NOUN
ejpam-6316	279	16	natural	natural	ADJ
ejpam-6316	279	17	transform	transform	NOUN
ejpam-6316	279	18	method	method	NOUN
ejpam-6316	279	19	(	(	PUNCT
ejpam-6316	279	20	rpsntm	rpsntm	PROPN
ejpam-6316	279	21	)	)	PUNCT
ejpam-6316	279	22	and	and	CCONJ
ejpam-6316	279	23	the	the	DET
ejpam-6316	279	24	natural	natural	ADJ
ejpam-6316	279	25	new	new	ADJ
ejpam-6316	279	26	iteration	iteration	NOUN
ejpam-6316	279	27	method	method	NOUN
ejpam-6316	279	28	(	(	PUNCT
ejpam-6316	279	29	nintm	nintm	PROPN
ejpam-6316	279	30	)	)	PUNCT
ejpam-6316	279	31	to	to	PART
ejpam-6316	279	32	solve	solve	VERB
ejpam-6316	279	33	fractionalorder	fractionalorder	PROPN
ejpam-6316	279	34	korteweg	korteweg	PROPN
ejpam-6316	279	35	-	-	PUNCT
ejpam-6316	279	36	de	de	PROPN
ejpam-6316	279	37	vries	vries	PROPN
ejpam-6316	279	38	(	(	PUNCT
ejpam-6316	279	39	kdv	kdv	PROPN
ejpam-6316	279	40	)	)	PUNCT
ejpam-6316	279	41	equations	equation	NOUN
ejpam-6316	279	42	,	,	PUNCT
ejpam-6316	279	43	particularly	particularly	ADV
ejpam-6316	279	44	focusing	focus	VERB
ejpam-6316	279	45	on	on	ADP
ejpam-6316	279	46	their	their	PRON
ejpam-6316	279	47	dispersive	dispersive	ADJ
ejpam-6316	279	48	properties	property	NOUN
ejpam-6316	279	49	within	within	ADP
ejpam-6316	279	50	a	a	DET
ejpam-6316	279	51	plasma	plasma	NOUN
ejpam-6316	279	52	environment	environment	NOUN
ejpam-6316	279	53	.	.	PUNCT
ejpam-6316	280	1	these	these	DET
ejpam-6316	280	2	methods	method	NOUN
ejpam-6316	280	3	proved	prove	VERB
ejpam-6316	280	4	to	to	PART
ejpam-6316	280	5	be	be	AUX
ejpam-6316	280	6	effective	effective	ADJ
ejpam-6316	280	7	and	and	CCONJ
ejpam-6316	280	8	reliable	reliable	ADJ
ejpam-6316	280	9	for	for	ADP
ejpam-6316	280	10	deriving	derive	VERB
ejpam-6316	280	11	approximate	approximate	ADJ
ejpam-6316	280	12	analytical	analytical	ADJ
ejpam-6316	280	13	solutions	solution	NOUN
ejpam-6316	280	14	to	to	ADP
ejpam-6316	280	15	complex	complex	ADJ
ejpam-6316	280	16	fractional	fractional	ADJ
ejpam-6316	280	17	differential	differential	ADJ
ejpam-6316	280	18	equations	equation	NOUN
ejpam-6316	280	19	.	.	PUNCT
ejpam-6316	281	1	n.	n.	PROPN
ejpam-6316	281	2	iqbal	iqbal	PROPN
ejpam-6316	281	3	et	et	PROPN
ejpam-6316	281	4	al	al	PROPN
ejpam-6316	281	5	.	.	PUNCT
ejpam-6316	281	6	/	/	SYM
ejpam-6316	281	7	eur	eur	PROPN
ejpam-6316	281	8	.	.	PUNCT
ejpam-6316	282	1	j.	j.	PROPN
ejpam-6316	282	2	pure	pure	PROPN
ejpam-6316	282	3	appl	appl	PROPN
ejpam-6316	282	4	.	.	PROPN
ejpam-6316	282	5	math	math	PROPN
ejpam-6316	282	6	,	,	PUNCT
ejpam-6316	282	7	18	18	NUM
ejpam-6316	282	8	(	(	PUNCT
ejpam-6316	282	9	3	3	NUM
ejpam-6316	282	10	)	)	PUNCT
ejpam-6316	282	11	(	(	PUNCT
ejpam-6316	282	12	2025	2025	NUM
ejpam-6316	282	13	)	)	PUNCT
ejpam-6316	282	14	,	,	PUNCT
ejpam-6316	282	15	6316	6316	NUM
ejpam-6316	282	16	19	19	NUM
ejpam-6316	282	17	of	of	ADP
ejpam-6316	282	18	21	21	NUM
ejpam-6316	282	19	the	the	DET
ejpam-6316	282	20	rpsntm	rpsntm	NOUN
ejpam-6316	282	21	provided	provide	VERB
ejpam-6316	282	22	a	a	DET
ejpam-6316	282	23	straightforward	straightforward	ADJ
ejpam-6316	282	24	approach	approach	NOUN
ejpam-6316	282	25	to	to	ADP
ejpam-6316	282	26	obtaining	obtain	VERB
ejpam-6316	282	27	initial	initial	ADJ
ejpam-6316	282	28	solutions	solution	NOUN
ejpam-6316	282	29	,	,	PUNCT
ejpam-6316	282	30	while	while	SCONJ
ejpam-6316	282	31	the	the	DET
ejpam-6316	282	32	nintm	nintm	PROPN
ejpam-6316	282	33	further	far	ADV
ejpam-6316	282	34	refined	refine	VERB
ejpam-6316	282	35	these	these	DET
ejpam-6316	282	36	solutions	solution	NOUN
ejpam-6316	282	37	,	,	PUNCT
ejpam-6316	282	38	enhancing	enhance	VERB
ejpam-6316	282	39	their	their	PRON
ejpam-6316	282	40	accuracy	accuracy	NOUN
ejpam-6316	282	41	and	and	CCONJ
ejpam-6316	282	42	convergence	convergence	NOUN
ejpam-6316	282	43	.	.	PUNCT
ejpam-6316	283	1	our	our	PRON
ejpam-6316	283	2	analysis	analysis	NOUN
ejpam-6316	283	3	demonstrated	demonstrate	VERB
ejpam-6316	283	4	that	that	SCONJ
ejpam-6316	283	5	these	these	DET
ejpam-6316	283	6	natural	natural	ADJ
ejpam-6316	283	7	-	-	PUNCT
ejpam-6316	283	8	based	base	VERB
ejpam-6316	283	9	methods	method	NOUN
ejpam-6316	283	10	offer	offer	VERB
ejpam-6316	283	11	significant	significant	ADJ
ejpam-6316	283	12	advantages	advantage	NOUN
ejpam-6316	283	13	in	in	ADP
ejpam-6316	283	14	dealing	deal	VERB
ejpam-6316	283	15	with	with	ADP
ejpam-6316	283	16	the	the	DET
ejpam-6316	283	17	nonlinear	nonlinear	ADJ
ejpam-6316	283	18	dynamics	dynamic	NOUN
ejpam-6316	283	19	of	of	ADP
ejpam-6316	283	20	wave	wave	NOUN
ejpam-6316	283	21	propagation	propagation	NOUN
ejpam-6316	283	22	in	in	ADP
ejpam-6316	283	23	plasma	plasma	NOUN
ejpam-6316	283	24	,	,	PUNCT
ejpam-6316	283	25	where	where	SCONJ
ejpam-6316	283	26	traditional	traditional	ADJ
ejpam-6316	283	27	methods	method	NOUN
ejpam-6316	283	28	might	might	AUX
ejpam-6316	283	29	struggle	struggle	VERB
ejpam-6316	283	30	with	with	ADP
ejpam-6316	283	31	the	the	DET
ejpam-6316	283	32	intricacies	intricacy	NOUN
ejpam-6316	283	33	of	of	ADP
ejpam-6316	283	34	fractional	fractional	ADJ
ejpam-6316	283	35	calculus	calculus	NOUN
ejpam-6316	283	36	.	.	PUNCT
ejpam-6316	284	1	the	the	DET
ejpam-6316	284	2	numerical	numerical	ADJ
ejpam-6316	284	3	examples	example	NOUN
ejpam-6316	284	4	and	and	CCONJ
ejpam-6316	284	5	graphical	graphical	ADJ
ejpam-6316	284	6	illustrations	illustration	NOUN
ejpam-6316	284	7	presented	present	VERB
ejpam-6316	284	8	in	in	ADP
ejpam-6316	284	9	this	this	DET
ejpam-6316	284	10	work	work	NOUN
ejpam-6316	284	11	underscore	underscore	VERB
ejpam-6316	284	12	the	the	DET
ejpam-6316	284	13	robustness	robustness	NOUN
ejpam-6316	284	14	of	of	ADP
ejpam-6316	284	15	these	these	DET
ejpam-6316	284	16	methods	method	NOUN
ejpam-6316	284	17	,	,	PUNCT
ejpam-6316	284	18	making	make	VERB
ejpam-6316	284	19	them	they	PRON
ejpam-6316	284	20	valuable	valuable	ADJ
ejpam-6316	284	21	tools	tool	NOUN
ejpam-6316	284	22	for	for	ADP
ejpam-6316	284	23	researchers	researcher	NOUN
ejpam-6316	284	24	and	and	CCONJ
ejpam-6316	284	25	engineers	engineer	NOUN
ejpam-6316	284	26	working	work	VERB
ejpam-6316	284	27	on	on	ADP
ejpam-6316	284	28	nonlinear	nonlinear	ADJ
ejpam-6316	284	29	dispersive	dispersive	ADJ
ejpam-6316	284	30	equations	equation	NOUN
ejpam-6316	284	31	in	in	ADP
ejpam-6316	284	32	various	various	ADJ
ejpam-6316	284	33	scientific	scientific	ADJ
ejpam-6316	284	34	and	and	CCONJ
ejpam-6316	284	35	engineering	engineering	NOUN
ejpam-6316	284	36	applications	application	NOUN
ejpam-6316	284	37	.	.	PUNCT
ejpam-6316	285	1	in	in	ADP
ejpam-6316	285	2	conclusion	conclusion	NOUN
ejpam-6316	285	3	,	,	PUNCT
ejpam-6316	285	4	the	the	DET
ejpam-6316	285	5	combination	combination	NOUN
ejpam-6316	285	6	of	of	ADP
ejpam-6316	285	7	rpsntm	rpsntm	PROPN
ejpam-6316	285	8	and	and	CCONJ
ejpam-6316	285	9	nintm	nintm	PROPN
ejpam-6316	285	10	presents	present	VERB
ejpam-6316	285	11	a	a	DET
ejpam-6316	285	12	powerful	powerful	ADJ
ejpam-6316	285	13	framework	framework	NOUN
ejpam-6316	285	14	for	for	ADP
ejpam-6316	285	15	solving	solve	VERB
ejpam-6316	285	16	fractional	fractional	ADJ
ejpam-6316	285	17	-	-	PUNCT
ejpam-6316	285	18	order	order	NOUN
ejpam-6316	285	19	equations	equation	NOUN
ejpam-6316	285	20	,	,	PUNCT
ejpam-6316	285	21	extending	extend	VERB
ejpam-6316	285	22	their	their	PRON
ejpam-6316	285	23	applicability	applicability	NOUN
ejpam-6316	285	24	to	to	ADP
ejpam-6316	285	25	a	a	DET
ejpam-6316	285	26	broader	broad	ADJ
ejpam-6316	285	27	range	range	NOUN
ejpam-6316	285	28	of	of	ADP
ejpam-6316	285	29	problems	problem	NOUN
ejpam-6316	285	30	in	in	ADP
ejpam-6316	285	31	mathematical	mathematical	ADJ
ejpam-6316	285	32	physics	physics	NOUN
ejpam-6316	285	33	and	and	CCONJ
ejpam-6316	285	34	engineering	engineering	NOUN
ejpam-6316	285	35	,	,	PUNCT
ejpam-6316	285	36	particularly	particularly	ADV
ejpam-6316	285	37	in	in	ADP
ejpam-6316	285	38	the	the	DET
ejpam-6316	285	39	study	study	NOUN
ejpam-6316	285	40	of	of	ADP
ejpam-6316	285	41	plasma	plasma	NOUN
ejpam-6316	285	42	waves	wave	NOUN
ejpam-6316	285	43	and	and	CCONJ
ejpam-6316	285	44	other	other	ADJ
ejpam-6316	285	45	complex	complex	ADJ
ejpam-6316	285	46	systems	system	NOUN
ejpam-6316	285	47	.	.	PUNCT
ejpam-6316	286	1	future	future	ADJ
ejpam-6316	286	2	research	research	NOUN
ejpam-6316	286	3	could	could	AUX
ejpam-6316	286	4	explore	explore	VERB
ejpam-6316	286	5	the	the	DET
ejpam-6316	286	6	extension	extension	NOUN
ejpam-6316	286	7	of	of	ADP
ejpam-6316	286	8	these	these	DET
ejpam-6316	286	9	methods	method	NOUN
ejpam-6316	286	10	to	to	ADP
ejpam-6316	286	11	other	other	ADJ
ejpam-6316	286	12	nonlinear	nonlinear	ADJ
ejpam-6316	286	13	fractional	fractional	ADJ
ejpam-6316	286	14	systems	system	NOUN
ejpam-6316	286	15	,	,	PUNCT
ejpam-6316	286	16	further	far	ADV
ejpam-6316	286	17	expanding	expand	VERB
ejpam-6316	286	18	their	their	PRON
ejpam-6316	286	19	utility	utility	NOUN
ejpam-6316	286	20	and	and	CCONJ
ejpam-6316	286	21	impact	impact	NOUN
ejpam-6316	286	22	in	in	ADP
ejpam-6316	286	23	applied	applied	ADJ
ejpam-6316	286	24	mathematics	mathematic	NOUN
ejpam-6316	286	25	and	and	CCONJ
ejpam-6316	286	26	computational	computational	ADJ
ejpam-6316	286	27	physics	physic	NOUN
ejpam-6316	286	28	.	.	PUNCT
ejpam-6316	287	1	acknowledgements	acknowledgement	NOUN
ejpam-6316	287	2	this	this	DET
ejpam-6316	287	3	research	research	NOUN
ejpam-6316	287	4	has	have	AUX
ejpam-6316	287	5	been	be	AUX
ejpam-6316	287	6	funded	fund	VERB
ejpam-6316	287	7	by	by	ADP
ejpam-6316	287	8	scientific	scientific	ADJ
ejpam-6316	287	9	research	research	NOUN
ejpam-6316	287	10	deanship	deanship	NOUN
ejpam-6316	287	11	at	at	ADP
ejpam-6316	287	12	university	university	NOUN
ejpam-6316	287	13	of	of	ADP
ejpam-6316	287	14	ha’il	ha’il	PROPN
ejpam-6316	287	15	–	–	PUNCT
ejpam-6316	287	16	saudi	saudi	PROPN
ejpam-6316	287	17	arabia	arabia	PROPN
ejpam-6316	287	18	through	through	ADP
ejpam-6316	287	19	project	project	NOUN
ejpam-6316	287	20	number	number	NOUN
ejpam-6316	287	21	rg-23	rg-23	NOUN
ejpam-6316	287	22	059	059	NUM
ejpam-6316	287	23	.	.	PUNCT
ejpam-6316	288	1	references	reference	NOUN
ejpam-6316	288	2	[	[	X
ejpam-6316	288	3	1	1	X
ejpam-6316	288	4	]	]	PUNCT
ejpam-6316	288	5	a	a	DET
ejpam-6316	288	6	akgul	akgul	NOUN
ejpam-6316	288	7	.	.	PUNCT
ejpam-6316	289	1	a	a	DET
ejpam-6316	289	2	novel	novel	ADJ
ejpam-6316	289	3	method	method	NOUN
ejpam-6316	289	4	for	for	ADP
ejpam-6316	289	5	a	a	DET
ejpam-6316	289	6	fractional	fractional	ADJ
ejpam-6316	289	7	derivative	derivative	NOUN
ejpam-6316	289	8	with	with	ADP
ejpam-6316	289	9	non	non	ADJ
ejpam-6316	289	10	-	-	ADJ
ejpam-6316	289	11	local	local	ADJ
ejpam-6316	289	12	and	and	CCONJ
ejpam-6316	289	13	non	non	ADJ
ejpam-6316	289	14	-	-	ADJ
ejpam-6316	289	15	singular	singular	ADJ
ejpam-6316	289	16	kernel	kernel	NOUN
ejpam-6316	289	17	.	.	PUNCT
ejpam-6316	290	1	chaos	chaos	NOUN
ejpam-6316	290	2	,	,	PUNCT
ejpam-6316	290	3	solitons	soliton	NOUN
ejpam-6316	290	4	and	and	CCONJ
ejpam-6316	290	5	fractals	fractal	NOUN
ejpam-6316	290	6	,	,	PUNCT
ejpam-6316	290	7	114:478–482	114:478–482	NUM
ejpam-6316	290	8	,	,	PUNCT
ejpam-6316	290	9	2018	2018	NUM
ejpam-6316	290	10	.	.	PUNCT
ejpam-6316	291	1	[	[	X
ejpam-6316	291	2	2	2	NUM
ejpam-6316	291	3	]	]	PUNCT
ejpam-6316	291	4	e	e	PROPN
ejpam-6316	291	5	k	k	PROPN
ejpam-6316	291	6	akgul	akgul	PROPN
ejpam-6316	291	7	.	.	PUNCT
ejpam-6316	292	1	solutions	solution	NOUN
ejpam-6316	292	2	of	of	ADP
ejpam-6316	292	3	the	the	DET
ejpam-6316	292	4	linear	linear	ADJ
ejpam-6316	292	5	and	and	CCONJ
ejpam-6316	292	6	nonlinear	nonlinear	ADJ
ejpam-6316	292	7	differential	differential	ADJ
ejpam-6316	292	8	equations	equation	NOUN
ejpam-6316	292	9	within	within	ADP
ejpam-6316	292	10	the	the	DET
ejpam-6316	292	11	generalized	generalized	ADJ
ejpam-6316	292	12	fractional	fractional	ADJ
ejpam-6316	292	13	derivatives	derivative	NOUN
ejpam-6316	292	14	.	.	PUNCT
ejpam-6316	293	1	chaos	chaos	NOUN
ejpam-6316	293	2	:	:	PUNCT
ejpam-6316	293	3	an	an	DET
ejpam-6316	293	4	interdisciplinary	interdisciplinary	ADJ
ejpam-6316	293	5	journal	journal	NOUN
ejpam-6316	293	6	of	of	ADP
ejpam-6316	293	7	nonlinear	nonlinear	ADJ
ejpam-6316	293	8	science	science	NOUN
ejpam-6316	293	9	,	,	PUNCT
ejpam-6316	293	10	29(2	29(2	NUM
ejpam-6316	293	11	)	)	PUNCT
ejpam-6316	293	12	,	,	PUNCT
ejpam-6316	293	13	2019	2019	NUM
ejpam-6316	293	14	.	.	PUNCT
ejpam-6316	294	1	[	[	X
ejpam-6316	294	2	3	3	X
ejpam-6316	294	3	]	]	X
ejpam-6316	294	4	a	a	DET
ejpam-6316	294	5	atangana	atangana	PROPN
ejpam-6316	294	6	.	.	PUNCT
ejpam-6316	295	1	fractal	fractal	ADJ
ejpam-6316	295	2	-	-	PUNCT
ejpam-6316	295	3	fractional	fractional	ADJ
ejpam-6316	295	4	differentiation	differentiation	NOUN
ejpam-6316	295	5	and	and	CCONJ
ejpam-6316	295	6	integration	integration	NOUN
ejpam-6316	295	7	:	:	PUNCT
ejpam-6316	295	8	connecting	connect	VERB
ejpam-6316	295	9	fractal	fractal	ADJ
ejpam-6316	295	10	calculus	calculus	NOUN
ejpam-6316	295	11	and	and	CCONJ
ejpam-6316	295	12	fractional	fractional	ADJ
ejpam-6316	295	13	calculus	calculus	NOUN
ejpam-6316	295	14	to	to	PART
ejpam-6316	295	15	predict	predict	VERB
ejpam-6316	295	16	complex	complex	ADJ
ejpam-6316	295	17	system	system	NOUN
ejpam-6316	295	18	.	.	PUNCT
ejpam-6316	296	1	chaos	chaos	NOUN
ejpam-6316	296	2	,	,	PUNCT
ejpam-6316	296	3	solitons	soliton	NOUN
ejpam-6316	296	4	and	and	CCONJ
ejpam-6316	296	5	fractals	fractal	NOUN
ejpam-6316	296	6	,	,	PUNCT
ejpam-6316	296	7	102:396–406	102:396–406	NUM
ejpam-6316	296	8	,	,	PUNCT
ejpam-6316	296	9	2017	2017	NUM
ejpam-6316	296	10	.	.	PUNCT
ejpam-6316	297	1	[	[	X
ejpam-6316	297	2	4	4	NUM
ejpam-6316	297	3	]	]	X
ejpam-6316	297	4	m	m	PROPN
ejpam-6316	297	5	caputo	caputo	PROPN
ejpam-6316	297	6	.	.	PUNCT
ejpam-6316	297	7	linear	linear	PROPN
ejpam-6316	297	8	models	model	NOUN
ejpam-6316	297	9	of	of	ADP
ejpam-6316	297	10	dissipation	dissipation	NOUN
ejpam-6316	297	11	whose	whose	DET
ejpam-6316	297	12	q	q	NOUN
ejpam-6316	297	13	is	be	AUX
ejpam-6316	297	14	almost	almost	ADV
ejpam-6316	297	15	frequency	frequency	VERB
ejpam-6316	297	16	independent	independent	ADJ
ejpam-6316	297	17	-	-	PUNCT
ejpam-6316	297	18	ii	ii	NOUN
ejpam-6316	297	19	.	.	PUNCT
ejpam-6316	298	1	geophysical	geophysical	ADJ
ejpam-6316	298	2	journal	journal	PROPN
ejpam-6316	298	3	international	international	PROPN
ejpam-6316	298	4	,	,	PUNCT
ejpam-6316	298	5	13(5):529–539	13(5):529–539	NUM
ejpam-6316	298	6	,	,	PUNCT
ejpam-6316	298	7	1967	1967	NUM
ejpam-6316	298	8	.	.	PUNCT
ejpam-6316	299	1	[	[	X
ejpam-6316	299	2	5	5	NUM
ejpam-6316	299	3	]	]	X
ejpam-6316	299	4	m	m	VERB
ejpam-6316	299	5	caputo	caputo	PROPN
ejpam-6316	299	6	and	and	CCONJ
ejpam-6316	299	7	m	m	PROPN
ejpam-6316	299	8	fabrizio	fabrizio	PROPN
ejpam-6316	299	9	.	.	PUNCT
ejpam-6316	300	1	a	a	DET
ejpam-6316	300	2	new	new	ADJ
ejpam-6316	300	3	definition	definition	NOUN
ejpam-6316	300	4	of	of	ADP
ejpam-6316	300	5	fractional	fractional	ADJ
ejpam-6316	300	6	derivative	derivative	NOUN
ejpam-6316	300	7	without	without	ADP
ejpam-6316	300	8	singular	singular	ADJ
ejpam-6316	300	9	kernel	kernel	PROPN
ejpam-6316	300	10	.	.	PUNCT
ejpam-6316	301	1	progress	progress	NOUN
ejpam-6316	301	2	in	in	ADP
ejpam-6316	301	3	fractional	fractional	ADJ
ejpam-6316	301	4	differentiation	differentiation	NOUN
ejpam-6316	301	5	and	and	CCONJ
ejpam-6316	301	6	applications	application	NOUN
ejpam-6316	301	7	,	,	PUNCT
ejpam-6316	301	8	1(2):73–85	1(2):73–85	NUM
ejpam-6316	301	9	,	,	PUNCT
ejpam-6316	301	10	2015	2015	NUM
ejpam-6316	301	11	.	.	PUNCT
ejpam-6316	302	1	[	[	X
ejpam-6316	302	2	6	6	NUM
ejpam-6316	302	3	]	]	PUNCT
ejpam-6316	302	4	a	a	DET
ejpam-6316	302	5	a	a	DET
ejpam-6316	302	6	kilbas	kilbas	NOUN
ejpam-6316	302	7	,	,	PUNCT
ejpam-6316	302	8	h	h	PROPN
ejpam-6316	302	9	m	m	PROPN
ejpam-6316	302	10	srivastava	srivastava	PROPN
ejpam-6316	302	11	,	,	PUNCT
ejpam-6316	302	12	and	and	CCONJ
ejpam-6316	302	13	j	j	PROPN
ejpam-6316	302	14	j	j	PROPN
ejpam-6316	302	15	trujillo	trujillo	PROPN
ejpam-6316	302	16	.	.	PUNCT
ejpam-6316	302	17	theory	theory	NOUN
ejpam-6316	302	18	and	and	CCONJ
ejpam-6316	302	19	applications	application	NOUN
ejpam-6316	302	20	of	of	ADP
ejpam-6316	302	21	fractional	fractional	ADJ
ejpam-6316	302	22	differential	differential	ADJ
ejpam-6316	302	23	equations	equation	NOUN
ejpam-6316	302	24	,	,	PUNCT
ejpam-6316	302	25	volume	volume	NOUN
ejpam-6316	302	26	204	204	NUM
ejpam-6316	302	27	.	.	PUNCT
ejpam-6316	303	1	elsevier	elsevier	NOUN
ejpam-6316	303	2	,	,	PUNCT
ejpam-6316	303	3	2006	2006	NUM
ejpam-6316	303	4	.	.	PUNCT
ejpam-6316	304	1	[	[	X
ejpam-6316	304	2	7	7	NUM
ejpam-6316	304	3	]	]	X
ejpam-6316	304	4	m	m	VERB
ejpam-6316	304	5	nadeem	nadeem	ADJ
ejpam-6316	304	6	,	,	PUNCT
ejpam-6316	304	7	q	q	PROPN
ejpam-6316	304	8	t	t	PROPN
ejpam-6316	304	9	ain	ain	PROPN
ejpam-6316	304	10	,	,	PUNCT
ejpam-6316	304	11	n	n	NOUN
ejpam-6316	304	12	almakayeel	almakayeel	NOUN
ejpam-6316	304	13	,	,	PUNCT
ejpam-6316	304	14	y	y	PROPN
ejpam-6316	304	15	shao	shao	PROPN
ejpam-6316	304	16	,	,	PUNCT
ejpam-6316	304	17	s	s	PROPN
ejpam-6316	304	18	wang	wang	PROPN
ejpam-6316	304	19	,	,	PUNCT
ejpam-6316	304	20	and	and	CCONJ
ejpam-6316	304	21	m	m	PROPN
ejpam-6316	304	22	shutaywi	shutaywi	NOUN
ejpam-6316	304	23	.	.	PUNCT
ejpam-6316	305	1	analysis	analysis	NOUN
ejpam-6316	305	2	of	of	ADP
ejpam-6316	305	3	nanobeam	nanobeam	NOUN
ejpam-6316	305	4	-	-	PUNCT
ejpam-6316	305	5	based	base	VERB
ejpam-6316	305	6	microstructure	microstructure	NOUN
ejpam-6316	305	7	in	in	ADP
ejpam-6316	305	8	n	n	CCONJ
ejpam-6316	305	9	/	/	SYM
ejpam-6316	305	10	mems	mem	NOUN
ejpam-6316	305	11	system	system	NOUN
ejpam-6316	305	12	using	use	VERB
ejpam-6316	305	13	van	van	PROPN
ejpam-6316	305	14	der	der	ADJ
ejpam-6316	305	15	waals	waal	NOUN
ejpam-6316	305	16	forces	force	NOUN
ejpam-6316	305	17	.	.	PUNCT
ejpam-6316	306	1	facta	facta	PROPN
ejpam-6316	306	2	universitatis	universitatis	PROPN
ejpam-6316	306	3	,	,	PUNCT
ejpam-6316	306	4	series	series	NOUN
ejpam-6316	306	5	:	:	PUNCT
ejpam-6316	306	6	mechanical	mechanical	ADJ
ejpam-6316	306	7	engineering	engineering	NOUN
ejpam-6316	306	8	,	,	PUNCT
ejpam-6316	306	9	pages	page	NOUN
ejpam-6316	306	10	673–688	673–688	NUM
ejpam-6316	306	11	,	,	PUNCT
ejpam-6316	306	12	2024	2024	NUM
ejpam-6316	306	13	.	.	PUNCT
ejpam-6316	307	1	[	[	X
ejpam-6316	307	2	8	8	NUM
ejpam-6316	307	3	]	]	X
ejpam-6316	307	4	m	m	VERB
ejpam-6316	307	5	nadeem	nadeem	ADJ
ejpam-6316	307	6	,	,	PUNCT
ejpam-6316	307	7	m	m	VERB
ejpam-6316	307	8	sharaf	sharaf	NOUN
ejpam-6316	307	9	,	,	PUNCT
ejpam-6316	307	10	and	and	CCONJ
ejpam-6316	307	11	s	s	VERB
ejpam-6316	307	12	mahamad	mahamad	NOUN
ejpam-6316	307	13	.	.	PUNCT
ejpam-6316	308	1	numerical	numerical	ADJ
ejpam-6316	308	2	investigation	investigation	NOUN
ejpam-6316	308	3	of	of	ADP
ejpam-6316	308	4	two	two	NUM
ejpam-6316	308	5	-	-	PUNCT
ejpam-6316	308	6	dimensional	dimensional	ADJ
ejpam-6316	308	7	fractional	fractional	ADJ
ejpam-6316	308	8	helmholtz	helmholtz	NOUN
ejpam-6316	308	9	equation	equation	NOUN
ejpam-6316	308	10	using	use	VERB
ejpam-6316	308	11	aboodh	aboodh	PROPN
ejpam-6316	308	12	transform	transform	VERB
ejpam-6316	308	13	scheme	scheme	NOUN
ejpam-6316	308	14	.	.	PUNCT
ejpam-6316	309	1	international	international	ADJ
ejpam-6316	309	2	journal	journal	PROPN
ejpam-6316	309	3	of	of	ADP
ejpam-6316	309	4	numerical	numerical	ADJ
ejpam-6316	309	5	methods	method	NOUN
ejpam-6316	309	6	for	for	ADP
ejpam-6316	309	7	heat	heat	NOUN
ejpam-6316	309	8	&	&	CCONJ
ejpam-6316	309	9	fluid	fluid	ADJ
ejpam-6316	309	10	flow	flow	NOUN
ejpam-6316	309	11	,	,	PUNCT
ejpam-6316	309	12	34(12):4520–4534	34(12):4520–4534	NUM
ejpam-6316	309	13	,	,	PUNCT
ejpam-6316	309	14	2024	2024	NUM
ejpam-6316	309	15	.	.	PUNCT
ejpam-6316	310	1	n.	n.	PROPN
ejpam-6316	310	2	iqbal	iqbal	PROPN
ejpam-6316	310	3	et	et	PROPN
ejpam-6316	310	4	al	al	PROPN
ejpam-6316	310	5	.	.	PUNCT
ejpam-6316	310	6	/	/	SYM
ejpam-6316	310	7	eur	eur	PROPN
ejpam-6316	310	8	.	.	PUNCT
ejpam-6316	311	1	j.	j.	PROPN
ejpam-6316	311	2	pure	pure	PROPN
ejpam-6316	311	3	appl	appl	PROPN
ejpam-6316	311	4	.	.	PROPN
ejpam-6316	311	5	math	math	PROPN
ejpam-6316	311	6	,	,	PUNCT
ejpam-6316	311	7	18	18	NUM
ejpam-6316	311	8	(	(	PUNCT
ejpam-6316	311	9	3	3	NUM
ejpam-6316	311	10	)	)	PUNCT
ejpam-6316	311	11	(	(	PUNCT
ejpam-6316	311	12	2025	2025	NUM
ejpam-6316	311	13	)	)	PUNCT
ejpam-6316	311	14	,	,	PUNCT
ejpam-6316	311	15	6316	6316	NUM
ejpam-6316	311	16	20	20	NUM
ejpam-6316	311	17	of	of	ADP
ejpam-6316	311	18	21	21	NUM
ejpam-6316	311	19	[	[	X
ejpam-6316	311	20	9	9	NUM
ejpam-6316	311	21	]	]	SYM
ejpam-6316	311	22	k	k	PROPN
ejpam-6316	311	23	sawada	sawada	PROPN
ejpam-6316	311	24	and	and	CCONJ
ejpam-6316	311	25	t	t	PROPN
ejpam-6316	311	26	kotera	kotera	PROPN
ejpam-6316	311	27	.	.	PUNCT
ejpam-6316	312	1	a	a	DET
ejpam-6316	312	2	method	method	NOUN
ejpam-6316	312	3	for	for	ADP
ejpam-6316	312	4	finding	find	VERB
ejpam-6316	312	5	n	n	CCONJ
ejpam-6316	312	6	-	-	PUNCT
ejpam-6316	312	7	soliton	soliton	NOUN
ejpam-6316	312	8	solutions	solution	NOUN
ejpam-6316	312	9	of	of	ADP
ejpam-6316	312	10	the	the	DET
ejpam-6316	312	11	kdv	kdv	NOUN
ejpam-6316	312	12	equation	equation	NOUN
ejpam-6316	312	13	and	and	CCONJ
ejpam-6316	312	14	kdv	kdv	NOUN
ejpam-6316	312	15	-	-	PUNCT
ejpam-6316	312	16	like	like	ADJ
ejpam-6316	312	17	equation	equation	NOUN
ejpam-6316	312	18	.	.	PUNCT
ejpam-6316	313	1	progress	progress	NOUN
ejpam-6316	313	2	of	of	ADP
ejpam-6316	313	3	theoretical	theoretical	ADJ
ejpam-6316	313	4	physics	physics	NOUN
ejpam-6316	313	5	,	,	PUNCT
ejpam-6316	313	6	51(5):1355–1367	51(5):1355–1367	NUM
ejpam-6316	313	7	,	,	PUNCT
ejpam-6316	313	8	1974	1974	NUM
ejpam-6316	313	9	.	.	PUNCT
ejpam-6316	314	1	[	[	X
ejpam-6316	314	2	10	10	NUM
ejpam-6316	314	3	]	]	X
ejpam-6316	314	4	a	a	DET
ejpam-6316	314	5	m	m	NOUN
ejpam-6316	314	6	wazwaz	wazwaz	NOUN
ejpam-6316	314	7	.	.	PUNCT
ejpam-6316	315	1	the	the	DET
ejpam-6316	315	2	kdv	kdv	NOUN
ejpam-6316	315	3	equation	equation	NOUN
ejpam-6316	315	4	.	.	PUNCT
ejpam-6316	316	1	handbook	handbook	NOUN
ejpam-6316	316	2	of	of	ADP
ejpam-6316	316	3	differential	differential	ADJ
ejpam-6316	316	4	equations	equation	NOUN
ejpam-6316	316	5	:	:	PUNCT
ejpam-6316	316	6	evolutionary	evolutionary	ADJ
ejpam-6316	316	7	equations	equation	NOUN
ejpam-6316	316	8	,	,	PUNCT
ejpam-6316	316	9	4:485–568	4:485–568	NUM
ejpam-6316	316	10	,	,	PUNCT
ejpam-6316	316	11	2008	2008	NUM
ejpam-6316	316	12	.	.	PUNCT
ejpam-6316	317	1	[	[	X
ejpam-6316	317	2	11	11	NUM
ejpam-6316	317	3	]	]	X
ejpam-6316	317	4	h	h	NOUN
ejpam-6316	317	5	yasmin	yasmin	PROPN
ejpam-6316	317	6	and	and	CCONJ
ejpam-6316	317	7	n	n	PROPN
ejpam-6316	317	8	iqbal	iqbal	PROPN
ejpam-6316	317	9	.	.	PUNCT
ejpam-6316	318	1	a	a	DET
ejpam-6316	318	2	comparative	comparative	ADJ
ejpam-6316	318	3	study	study	NOUN
ejpam-6316	318	4	of	of	ADP
ejpam-6316	318	5	the	the	DET
ejpam-6316	318	6	fractional	fractional	ADJ
ejpam-6316	318	7	coupled	couple	VERB
ejpam-6316	318	8	burgers	burger	NOUN
ejpam-6316	318	9	and	and	CCONJ
ejpam-6316	318	10	hirota	hirota	NOUN
ejpam-6316	318	11	-	-	PUNCT
ejpam-6316	318	12	satsuma	satsuma	NOUN
ejpam-6316	318	13	kdv	kdv	NOUN
ejpam-6316	318	14	equations	equation	NOUN
ejpam-6316	318	15	via	via	ADP
ejpam-6316	318	16	analytical	analytical	ADJ
ejpam-6316	318	17	techniques	technique	NOUN
ejpam-6316	318	18	.	.	PUNCT
ejpam-6316	319	1	symmetry	symmetry	NOUN
ejpam-6316	319	2	,	,	PUNCT
ejpam-6316	319	3	14(7):1364	14(7):1364	NUM
ejpam-6316	319	4	,	,	PUNCT
ejpam-6316	319	5	2022	2022	NUM
ejpam-6316	319	6	.	.	PUNCT
ejpam-6316	320	1	[	[	X
ejpam-6316	320	2	12	12	NUM
ejpam-6316	320	3	]	]	X
ejpam-6316	320	4	m	m	NOUN
ejpam-6316	320	5	naeem	naeem	PROPN
ejpam-6316	320	6	,	,	PUNCT
ejpam-6316	320	7	h	h	PROPN
ejpam-6316	320	8	rezazadeh	rezazadeh	PROPN
ejpam-6316	320	9	,	,	PUNCT
ejpam-6316	320	10	a	a	DET
ejpam-6316	320	11	a	a	DET
ejpam-6316	320	12	khammash	khammash	NOUN
ejpam-6316	320	13	,	,	PUNCT
ejpam-6316	320	14	and	and	CCONJ
ejpam-6316	320	15	s	s	VERB
ejpam-6316	320	16	zaland	zaland	NOUN
ejpam-6316	320	17	.	.	PUNCT
ejpam-6316	321	1	analysis	analysis	NOUN
ejpam-6316	321	2	of	of	ADP
ejpam-6316	321	3	the	the	DET
ejpam-6316	321	4	fuzzy	fuzzy	ADJ
ejpam-6316	321	5	fractional	fractional	ADJ
ejpam-6316	321	6	-	-	PUNCT
ejpam-6316	321	7	order	order	NOUN
ejpam-6316	321	8	solitary	solitary	ADJ
ejpam-6316	321	9	wave	wave	NOUN
ejpam-6316	321	10	solutions	solution	NOUN
ejpam-6316	321	11	for	for	ADP
ejpam-6316	321	12	the	the	DET
ejpam-6316	321	13	kdv	kdv	NOUN
ejpam-6316	321	14	equation	equation	NOUN
ejpam-6316	321	15	in	in	ADP
ejpam-6316	321	16	the	the	DET
ejpam-6316	321	17	sense	sense	NOUN
ejpam-6316	321	18	of	of	ADP
ejpam-6316	321	19	caputofabrizio	caputofabrizio	PROPN
ejpam-6316	321	20	derivative	derivative	PROPN
ejpam-6316	321	21	.	.	PUNCT
ejpam-6316	322	1	journal	journal	PROPN
ejpam-6316	322	2	of	of	ADP
ejpam-6316	322	3	mathematics	mathematic	NOUN
ejpam-6316	322	4	,	,	PUNCT
ejpam-6316	322	5	2022(1):3688916	2022(1):3688916	NUM
ejpam-6316	322	6	,	,	PUNCT
ejpam-6316	322	7	2022	2022	NUM
ejpam-6316	322	8	.	.	PUNCT
ejpam-6316	323	1	[	[	X
ejpam-6316	323	2	13	13	NUM
ejpam-6316	323	3	]	]	X
ejpam-6316	323	4	r	r	NOUN
ejpam-6316	323	5	shah	shah	NOUN
ejpam-6316	323	6	,	,	PUNCT
ejpam-6316	323	7	a	a	DET
ejpam-6316	323	8	a	a	DET
ejpam-6316	323	9	hyder	hyder	NOUN
ejpam-6316	323	10	,	,	PUNCT
ejpam-6316	323	11	n	n	PRON
ejpam-6316	323	12	iqbal	iqbal	NOUN
ejpam-6316	323	13	,	,	PUNCT
ejpam-6316	323	14	and	and	CCONJ
ejpam-6316	323	15	t	t	PROPN
ejpam-6316	323	16	botmart	botmart	NOUN
ejpam-6316	323	17	.	.	PUNCT
ejpam-6316	324	1	fractional	fractional	ADJ
ejpam-6316	324	2	view	view	NOUN
ejpam-6316	324	3	evaluation	evaluation	NOUN
ejpam-6316	324	4	system	system	NOUN
ejpam-6316	324	5	of	of	ADP
ejpam-6316	324	6	schrodinger	schrodinger	ADJ
ejpam-6316	324	7	-	-	PUNCT
ejpam-6316	324	8	kdv	kdv	NOUN
ejpam-6316	324	9	equation	equation	NOUN
ejpam-6316	324	10	by	by	ADP
ejpam-6316	324	11	a	a	DET
ejpam-6316	324	12	comparative	comparative	ADJ
ejpam-6316	324	13	analysis	analysis	NOUN
ejpam-6316	324	14	.	.	PUNCT
ejpam-6316	325	1	aims	aim	VERB
ejpam-6316	325	2	math	math	NOUN
ejpam-6316	325	3	,	,	PUNCT
ejpam-6316	325	4	7(11):19846–19864	7(11):19846–19864	NUM
ejpam-6316	325	5	,	,	PUNCT
ejpam-6316	325	6	2022	2022	NUM
ejpam-6316	325	7	.	.	PUNCT
ejpam-6316	326	1	[	[	X
ejpam-6316	326	2	14	14	NUM
ejpam-6316	326	3	]	]	PUNCT
ejpam-6316	326	4	n	n	PROPN
ejpam-6316	326	5	h	h	NOUN
ejpam-6316	326	6	aljahdaly	aljahdaly	PROPN
ejpam-6316	326	7	,	,	PUNCT
ejpam-6316	326	8	r	r	NOUN
ejpam-6316	326	9	shah	shah	NOUN
ejpam-6316	326	10	,	,	PUNCT
ejpam-6316	326	11	r	r	PROPN
ejpam-6316	326	12	p	p	PROPN
ejpam-6316	326	13	agarwal	agarwal	NOUN
ejpam-6316	326	14	,	,	PUNCT
ejpam-6316	326	15	and	and	CCONJ
ejpam-6316	326	16	t	t	PROPN
ejpam-6316	326	17	botmart	botmart	NOUN
ejpam-6316	326	18	.	.	PUNCT
ejpam-6316	327	1	the	the	DET
ejpam-6316	327	2	analysis	analysis	NOUN
ejpam-6316	327	3	of	of	ADP
ejpam-6316	327	4	the	the	DET
ejpam-6316	327	5	fractionalorder	fractionalorder	ADJ
ejpam-6316	327	6	system	system	NOUN
ejpam-6316	327	7	of	of	ADP
ejpam-6316	327	8	third	third	ADJ
ejpam-6316	327	9	-	-	PUNCT
ejpam-6316	327	10	order	order	NOUN
ejpam-6316	327	11	kdv	kdv	NOUN
ejpam-6316	327	12	equation	equation	NOUN
ejpam-6316	327	13	within	within	ADP
ejpam-6316	327	14	different	different	ADJ
ejpam-6316	327	15	operators	operator	NOUN
ejpam-6316	327	16	.	.	PUNCT
ejpam-6316	328	1	alexandria	alexandria	PROPN
ejpam-6316	328	2	engineering	engineering	PROPN
ejpam-6316	328	3	journal	journal	PROPN
ejpam-6316	328	4	,	,	PUNCT
ejpam-6316	328	5	61(12):11825–11834	61(12):11825–11834	PROPN
ejpam-6316	328	6	,	,	PUNCT
ejpam-6316	328	7	2022	2022	NUM
ejpam-6316	328	8	.	.	PUNCT
ejpam-6316	329	1	[	[	X
ejpam-6316	329	2	15	15	NUM
ejpam-6316	329	3	]	]	PUNCT
ejpam-6316	329	4	a	a	DET
ejpam-6316	329	5	kumar	kumar	PROPN
ejpam-6316	329	6	,	,	PUNCT
ejpam-6316	329	7	s	s	PROPN
ejpam-6316	329	8	kumar	kumar	PROPN
ejpam-6316	329	9	,	,	PUNCT
ejpam-6316	329	10	and	and	CCONJ
ejpam-6316	329	11	s	s	VERB
ejpam-6316	329	12	p	p	PROPN
ejpam-6316	329	13	yan	yan	PROPN
ejpam-6316	329	14	.	.	PUNCT
ejpam-6316	330	1	residual	residual	ADJ
ejpam-6316	330	2	power	power	NOUN
ejpam-6316	330	3	series	series	PROPN
ejpam-6316	330	4	method	method	NOUN
ejpam-6316	330	5	for	for	ADP
ejpam-6316	330	6	fractional	fractional	ADJ
ejpam-6316	330	7	diffusion	diffusion	NOUN
ejpam-6316	330	8	equations	equation	NOUN
ejpam-6316	330	9	.	.	PUNCT
ejpam-6316	331	1	fundamenta	fundamenta	PROPN
ejpam-6316	331	2	informaticae	informaticae	PROPN
ejpam-6316	331	3	,	,	PUNCT
ejpam-6316	331	4	151(1	151(1	NUM
ejpam-6316	331	5	-	-	SYM
ejpam-6316	331	6	4):213–230	4):213–230	NUM
ejpam-6316	331	7	,	,	PUNCT
ejpam-6316	331	8	2017	2017	NUM
ejpam-6316	331	9	.	.	PUNCT
ejpam-6316	332	1	[	[	X
ejpam-6316	332	2	16	16	NUM
ejpam-6316	332	3	]	]	X
ejpam-6316	332	4	w	w	PROPN
ejpam-6316	332	5	albalawi	albalawi	PROPN
ejpam-6316	332	6	,	,	PUNCT
ejpam-6316	332	7	k	k	PROPN
ejpam-6316	332	8	nonlaopon	nonlaopon	ADV
ejpam-6316	332	9	,	,	PUNCT
ejpam-6316	332	10	l	l	PROPN
ejpam-6316	332	11	s	s	VERB
ejpam-6316	332	12	el	el	PROPN
ejpam-6316	332	13	-	-	PUNCT
ejpam-6316	332	14	sherif	sherif	PROPN
ejpam-6316	332	15	,	,	PUNCT
ejpam-6316	332	16	and	and	CCONJ
ejpam-6316	332	17	s	s	VERB
ejpam-6316	332	18	a	a	DET
ejpam-6316	332	19	el	el	NOUN
ejpam-6316	332	20	-	-	PUNCT
ejpam-6316	332	21	tantawy	tantawy	NOUN
ejpam-6316	332	22	.	.	PUNCT
ejpam-6316	333	1	laplace	laplace	PROPN
ejpam-6316	333	2	residual	residual	ADJ
ejpam-6316	333	3	power	power	NOUN
ejpam-6316	333	4	series	series	NOUN
ejpam-6316	333	5	method	method	NOUN
ejpam-6316	333	6	for	for	ADP
ejpam-6316	333	7	solving	solve	VERB
ejpam-6316	333	8	three	three	NUM
ejpam-6316	333	9	-	-	PUNCT
ejpam-6316	333	10	dimensional	dimensional	ADJ
ejpam-6316	333	11	fractional	fractional	ADJ
ejpam-6316	333	12	helmholtz	helmholtz	NOUN
ejpam-6316	333	13	equations	equation	NOUN
ejpam-6316	333	14	.	.	PUNCT
ejpam-6316	334	1	symmetry	symmetry	PROPN
ejpam-6316	334	2	,	,	PUNCT
ejpam-6316	334	3	15(1):194	15(1):194	NUM
ejpam-6316	334	4	,	,	PUNCT
ejpam-6316	334	5	2023	2023	NUM
ejpam-6316	334	6	.	.	PUNCT
ejpam-6316	335	1	[	[	X
ejpam-6316	335	2	17	17	NUM
ejpam-6316	335	3	]	]	PUNCT
ejpam-6316	335	4	a	a	DET
ejpam-6316	335	5	shafee	shafee	NOUN
ejpam-6316	335	6	and	and	CCONJ
ejpam-6316	335	7	y	y	PROPN
ejpam-6316	335	8	alkhezi	alkhezi	PROPN
ejpam-6316	335	9	.	.	PUNCT
ejpam-6316	336	1	efficient	efficient	ADJ
ejpam-6316	336	2	solution	solution	NOUN
ejpam-6316	336	3	of	of	ADP
ejpam-6316	336	4	fractional	fractional	ADJ
ejpam-6316	336	5	system	system	NOUN
ejpam-6316	336	6	partial	partial	ADJ
ejpam-6316	336	7	differential	differential	NOUN
ejpam-6316	336	8	equations	equation	NOUN
ejpam-6316	336	9	using	use	VERB
ejpam-6316	336	10	laplace	laplace	NOUN
ejpam-6316	336	11	residual	residual	ADJ
ejpam-6316	336	12	power	power	NOUN
ejpam-6316	336	13	series	series	PROPN
ejpam-6316	336	14	method	method	PROPN
ejpam-6316	336	15	.	.	PUNCT
ejpam-6316	337	1	fractal	fractal	PROPN
ejpam-6316	337	2	and	and	CCONJ
ejpam-6316	337	3	fractional	fractional	ADJ
ejpam-6316	337	4	,	,	PUNCT
ejpam-6316	337	5	7(6):429	7(6):429	NUM
ejpam-6316	337	6	,	,	PUNCT
ejpam-6316	337	7	2023	2023	NUM
ejpam-6316	337	8	.	.	PUNCT
ejpam-6316	338	1	[	[	X
ejpam-6316	338	2	18	18	NUM
ejpam-6316	338	3	]	]	X
ejpam-6316	338	4	m	m	VERB
ejpam-6316	338	5	m	m	VERB
ejpam-6316	338	6	al	al	PROPN
ejpam-6316	338	7	-	-	PUNCT
ejpam-6316	338	8	sawalha	sawalha	NOUN
ejpam-6316	338	9	,	,	PUNCT
ejpam-6316	338	10	o	o	PROPN
ejpam-6316	338	11	y	y	PROPN
ejpam-6316	338	12	ababneh	ababneh	PROPN
ejpam-6316	338	13	,	,	PUNCT
ejpam-6316	338	14	n	n	CCONJ
ejpam-6316	338	15	a	a	DET
ejpam-6316	338	16	shah	shah	NOUN
ejpam-6316	338	17	,	,	PUNCT
ejpam-6316	338	18	and	and	CCONJ
ejpam-6316	338	19	k	k	ADP
ejpam-6316	338	20	nonlaopon	nonlaopon	NOUN
ejpam-6316	338	21	.	.	PUNCT
ejpam-6316	339	1	combination	combination	NOUN
ejpam-6316	339	2	of	of	ADP
ejpam-6316	339	3	laplace	laplace	NOUN
ejpam-6316	339	4	transform	transform	NOUN
ejpam-6316	339	5	and	and	CCONJ
ejpam-6316	339	6	residual	residual	ADJ
ejpam-6316	339	7	power	power	NOUN
ejpam-6316	339	8	series	series	NOUN
ejpam-6316	339	9	techniques	technique	NOUN
ejpam-6316	339	10	of	of	ADP
ejpam-6316	339	11	special	special	ADJ
ejpam-6316	339	12	fractional	fractional	ADJ
ejpam-6316	339	13	-	-	PUNCT
ejpam-6316	339	14	order	order	NOUN
ejpam-6316	339	15	non	non	ADJ
ejpam-6316	339	16	-	-	ADJ
ejpam-6316	339	17	linear	linear	ADJ
ejpam-6316	339	18	partial	partial	ADJ
ejpam-6316	339	19	differential	differential	NOUN
ejpam-6316	339	20	equations	equation	NOUN
ejpam-6316	339	21	.	.	PUNCT
ejpam-6316	340	1	aims	aim	VERB
ejpam-6316	340	2	math	math	NOUN
ejpam-6316	340	3	,	,	PUNCT
ejpam-6316	340	4	8:5266–5280	8:5266–5280	NUM
ejpam-6316	340	5	,	,	PUNCT
ejpam-6316	340	6	2023	2023	NUM
ejpam-6316	340	7	.	.	PUNCT
ejpam-6316	341	1	[	[	X
ejpam-6316	341	2	19	19	NUM
ejpam-6316	341	3	]	]	PUNCT
ejpam-6316	341	4	a	a	DET
ejpam-6316	341	5	qazza	qazza	NOUN
ejpam-6316	341	6	,	,	PUNCT
ejpam-6316	341	7	a	a	DET
ejpam-6316	341	8	burqan	burqan	NOUN
ejpam-6316	341	9	,	,	PUNCT
ejpam-6316	341	10	r	r	NOUN
ejpam-6316	341	11	saadeh	saadeh	NOUN
ejpam-6316	341	12	,	,	PUNCT
ejpam-6316	341	13	and	and	CCONJ
ejpam-6316	341	14	r	r	PROPN
ejpam-6316	341	15	khalil	khalil	PROPN
ejpam-6316	341	16	.	.	PUNCT
ejpam-6316	342	1	applications	application	NOUN
ejpam-6316	342	2	on	on	ADP
ejpam-6316	342	3	double	double	ADJ
ejpam-6316	342	4	ara	ara	NOUN
ejpam-6316	342	5	-	-	PUNCT
ejpam-6316	342	6	sumudu	sumudu	NOUN
ejpam-6316	342	7	transform	transform	NOUN
ejpam-6316	342	8	in	in	ADP
ejpam-6316	342	9	solving	solve	VERB
ejpam-6316	342	10	fractional	fractional	ADJ
ejpam-6316	342	11	partial	partial	ADJ
ejpam-6316	342	12	differential	differential	NOUN
ejpam-6316	342	13	equations	equation	NOUN
ejpam-6316	342	14	.	.	PUNCT
ejpam-6316	343	1	symmetry	symmetry	PROPN
ejpam-6316	343	2	,	,	PUNCT
ejpam-6316	343	3	14(9):1817	14(9):1817	NUM
ejpam-6316	343	4	,	,	PUNCT
ejpam-6316	343	5	2022	2022	NUM
ejpam-6316	343	6	.	.	PUNCT
ejpam-6316	344	1	[	[	X
ejpam-6316	344	2	20	20	NUM
ejpam-6316	344	3	]	]	X
ejpam-6316	344	4	m	m	PROPN
ejpam-6316	344	5	naeem	naeem	PROPN
ejpam-6316	344	6	,	,	PUNCT
ejpam-6316	344	7	a	a	DET
ejpam-6316	344	8	m	m	NOUN
ejpam-6316	344	9	zidan	zidan	ADJ
ejpam-6316	344	10	,	,	PUNCT
ejpam-6316	344	11	k	k	PROPN
ejpam-6316	344	12	nonlaopon	nonlaopon	NOUN
ejpam-6316	344	13	,	,	PUNCT
ejpam-6316	344	14	m	m	VERB
ejpam-6316	344	15	i	i	NOUN
ejpam-6316	344	16	syam	syam	NOUN
ejpam-6316	344	17	,	,	PUNCT
ejpam-6316	344	18	and	and	CCONJ
ejpam-6316	344	19	z	z	PROPN
ejpam-6316	344	20	al	al	PROPN
ejpam-6316	344	21	-	-	PUNCT
ejpam-6316	344	22	zhour	zhour	PROPN
ejpam-6316	344	23	.	.	PUNCT
ejpam-6316	345	1	a	a	DET
ejpam-6316	345	2	new	new	ADJ
ejpam-6316	345	3	analysis	analysis	NOUN
ejpam-6316	345	4	of	of	ADP
ejpam-6316	345	5	fractional	fractional	ADJ
ejpam-6316	345	6	-	-	PUNCT
ejpam-6316	345	7	order	order	NOUN
ejpam-6316	345	8	equal	equal	ADJ
ejpam-6316	345	9	-	-	PUNCT
ejpam-6316	345	10	width	width	NOUN
ejpam-6316	345	11	equations	equation	NOUN
ejpam-6316	345	12	via	via	ADP
ejpam-6316	345	13	novel	novel	ADJ
ejpam-6316	345	14	techniques	technique	NOUN
ejpam-6316	345	15	.	.	PUNCT
ejpam-6316	346	1	symmetry	symmetry	NOUN
ejpam-6316	346	2	,	,	PUNCT
ejpam-6316	346	3	13(5):886	13(5):886	NUM
ejpam-6316	346	4	,	,	PUNCT
ejpam-6316	346	5	2021	2021	NUM
ejpam-6316	346	6	.	.	PUNCT
ejpam-6316	347	1	[	[	X
ejpam-6316	347	2	21	21	NUM
ejpam-6316	347	3	]	]	X
ejpam-6316	347	4	s	s	VERB
ejpam-6316	347	5	noor	noor	PROPN
ejpam-6316	347	6	,	,	PUNCT
ejpam-6316	347	7	a	a	DET
ejpam-6316	347	8	w	w	NOUN
ejpam-6316	347	9	alrowaily	alrowaily	ADV
ejpam-6316	347	10	,	,	PUNCT
ejpam-6316	347	11	m	m	PROPN
ejpam-6316	347	12	alqudah	alqudah	NOUN
ejpam-6316	347	13	,	,	PUNCT
ejpam-6316	347	14	and	and	CCONJ
ejpam-6316	347	15	s	s	VERB
ejpam-6316	347	16	a	a	DET
ejpam-6316	347	17	el	el	NOUN
ejpam-6316	347	18	-	-	PUNCT
ejpam-6316	347	19	tantawy	tantawy	NOUN
ejpam-6316	347	20	.	.	PUNCT
ejpam-6316	348	1	innovative	innovative	ADJ
ejpam-6316	348	2	solutions	solution	NOUN
ejpam-6316	348	3	to	to	ADP
ejpam-6316	348	4	the	the	DET
ejpam-6316	348	5	fractional	fractional	ADJ
ejpam-6316	348	6	diffusion	diffusion	NOUN
ejpam-6316	348	7	equation	equation	NOUN
ejpam-6316	348	8	using	use	VERB
ejpam-6316	348	9	the	the	DET
ejpam-6316	348	10	elzaki	elzaki	NOUN
ejpam-6316	348	11	transform	transform	NOUN
ejpam-6316	348	12	.	.	PUNCT
ejpam-6316	349	1	mathematical	mathematical	ADJ
ejpam-6316	349	2	and	and	CCONJ
ejpam-6316	349	3	computational	computational	ADJ
ejpam-6316	349	4	applications	application	NOUN
ejpam-6316	349	5	,	,	PUNCT
ejpam-6316	349	6	29(5):75	29(5):75	NUM
ejpam-6316	349	7	,	,	PUNCT
ejpam-6316	349	8	2024	2024	NUM
ejpam-6316	349	9	.	.	PUNCT
ejpam-6316	350	1	[	[	X
ejpam-6316	350	2	22	22	NUM
ejpam-6316	350	3	]	]	X
ejpam-6316	350	4	m	m	VERB
ejpam-6316	350	5	m	m	VERB
ejpam-6316	350	6	al	al	PROPN
ejpam-6316	350	7	-	-	PUNCT
ejpam-6316	350	8	sawalha	sawalha	NOUN
ejpam-6316	350	9	,	,	PUNCT
ejpam-6316	350	10	n	n	X
ejpam-6316	350	11	amir	amir	X
ejpam-6316	350	12	,	,	PUNCT
ejpam-6316	350	13	and	and	CCONJ
ejpam-6316	350	14	m	m	PROPN
ejpam-6316	350	15	yar	yar	PROPN
ejpam-6316	350	16	.	.	PUNCT
ejpam-6316	350	17	novel	novel	ADJ
ejpam-6316	350	18	analysis	analysis	NOUN
ejpam-6316	350	19	of	of	ADP
ejpam-6316	350	20	fuzzy	fuzzy	ADJ
ejpam-6316	350	21	fractional	fractional	ADJ
ejpam-6316	350	22	emdenfowler	emdenfowler	NOUN
ejpam-6316	350	23	equations	equation	NOUN
ejpam-6316	350	24	within	within	ADP
ejpam-6316	350	25	new	new	ADJ
ejpam-6316	350	26	iterative	iterative	NOUN
ejpam-6316	350	27	transform	transform	NOUN
ejpam-6316	350	28	method	method	NOUN
ejpam-6316	350	29	.	.	PUNCT
ejpam-6316	351	1	journal	journal	NOUN
ejpam-6316	351	2	of	of	ADP
ejpam-6316	351	3	function	function	NOUN
ejpam-6316	351	4	spaces	space	NOUN
ejpam-6316	351	5	,	,	PUNCT
ejpam-6316	351	6	2022(1):7731135	2022(1):7731135	NOUN
ejpam-6316	351	7	,	,	PUNCT
ejpam-6316	351	8	2022	2022	NUM
ejpam-6316	351	9	.	.	PUNCT
ejpam-6316	352	1	[	[	X
ejpam-6316	352	2	23	23	NUM
ejpam-6316	352	3	]	]	X
ejpam-6316	352	4	m	m	VERB
ejpam-6316	352	5	almheidat	almheidat	NOUN
ejpam-6316	352	6	,	,	PUNCT
ejpam-6316	352	7	h	h	PROPN
ejpam-6316	352	8	yasmin	yasmin	PROPN
ejpam-6316	352	9	,	,	PUNCT
ejpam-6316	352	10	m	m	PROPN
ejpam-6316	352	11	al	al	PROPN
ejpam-6316	352	12	huwayz	huwayz	PROPN
ejpam-6316	352	13	,	,	PUNCT
ejpam-6316	352	14	and	and	CCONJ
ejpam-6316	352	15	s	s	VERB
ejpam-6316	352	16	a	a	DET
ejpam-6316	352	17	el	el	NOUN
ejpam-6316	352	18	-	-	PUNCT
ejpam-6316	352	19	tantawy	tantawy	NOUN
ejpam-6316	352	20	.	.	PUNCT
ejpam-6316	353	1	a	a	DET
ejpam-6316	353	2	novel	novel	ADJ
ejpam-6316	353	3	investigation	investigation	NOUN
ejpam-6316	353	4	into	into	ADP
ejpam-6316	353	5	time	time	NOUN
ejpam-6316	353	6	-	-	PUNCT
ejpam-6316	353	7	fractional	fractional	ADJ
ejpam-6316	353	8	multi	multi	ADJ
ejpam-6316	353	9	-	-	ADJ
ejpam-6316	353	10	dimensional	dimensional	ADJ
ejpam-6316	353	11	navier	navier	NOUN
ejpam-6316	353	12	-	-	PUNCT
ejpam-6316	353	13	stokes	stoke	NOUN
ejpam-6316	353	14	equations	equation	NOUN
ejpam-6316	353	15	within	within	ADP
ejpam-6316	353	16	aboodh	aboodh	ADJ
ejpam-6316	353	17	transform	transform	NOUN
ejpam-6316	353	18	.	.	PUNCT
ejpam-6316	354	1	open	open	ADJ
ejpam-6316	354	2	physics	physics	PROPN
ejpam-6316	354	3	,	,	PUNCT
ejpam-6316	354	4	22(1):20240081	22(1):20240081	NUM
ejpam-6316	354	5	,	,	PUNCT
ejpam-6316	354	6	2024	2024	NUM
ejpam-6316	354	7	.	.	PUNCT
ejpam-6316	355	1	[	[	X
ejpam-6316	355	2	24	24	NUM
ejpam-6316	355	3	]	]	PUNCT
ejpam-6316	355	4	a	a	DET
ejpam-6316	355	5	s	s	NOUN
ejpam-6316	355	6	alshehry	alshehry	NOUN
ejpam-6316	355	7	,	,	PUNCT
ejpam-6316	355	8	n	n	X
ejpam-6316	355	9	amir	amir	X
ejpam-6316	355	10	,	,	PUNCT
ejpam-6316	355	11	n	n	X
ejpam-6316	355	12	iqbal	iqbal	NOUN
ejpam-6316	355	13	,	,	PUNCT
ejpam-6316	355	14	and	and	CCONJ
ejpam-6316	355	15	k	k	X
ejpam-6316	355	16	nonlaopon	nonlaopon	ADV
ejpam-6316	355	17	.	.	PUNCT
ejpam-6316	356	1	on	on	ADP
ejpam-6316	356	2	the	the	DET
ejpam-6316	356	3	solution	solution	NOUN
ejpam-6316	356	4	of	of	ADP
ejpam-6316	356	5	nonlinear	nonlinear	ADJ
ejpam-6316	356	6	fractional	fractional	ADJ
ejpam-6316	356	7	-	-	PUNCT
ejpam-6316	356	8	order	order	NOUN
ejpam-6316	356	9	shock	shock	NOUN
ejpam-6316	356	10	wave	wave	NOUN
ejpam-6316	356	11	equation	equation	NOUN
ejpam-6316	356	12	via	via	ADP
ejpam-6316	356	13	analytical	analytical	ADJ
ejpam-6316	356	14	method	method	NOUN
ejpam-6316	356	15	.	.	PUNCT
ejpam-6316	357	1	aims	aim	VERB
ejpam-6316	357	2	mathematics	mathematic	NOUN
ejpam-6316	357	3	,	,	PUNCT
ejpam-6316	357	4	n.	n.	PROPN
ejpam-6316	357	5	iqbal	iqbal	PROPN
ejpam-6316	357	6	et	et	PROPN
ejpam-6316	357	7	al	al	PROPN
ejpam-6316	357	8	.	.	PUNCT
ejpam-6316	357	9	/	/	SYM
ejpam-6316	357	10	eur	eur	PROPN
ejpam-6316	357	11	.	.	PUNCT
ejpam-6316	358	1	j.	j.	PROPN
ejpam-6316	358	2	pure	pure	PROPN
ejpam-6316	358	3	appl	appl	PROPN
ejpam-6316	358	4	.	.	PROPN
ejpam-6316	358	5	math	math	PROPN
ejpam-6316	358	6	,	,	PUNCT
ejpam-6316	358	7	18	18	NUM
ejpam-6316	358	8	(	(	PUNCT
ejpam-6316	358	9	3	3	NUM
ejpam-6316	358	10	)	)	PUNCT
ejpam-6316	358	11	(	(	PUNCT
ejpam-6316	358	12	2025	2025	NUM
ejpam-6316	358	13	)	)	PUNCT
ejpam-6316	358	14	,	,	PUNCT
ejpam-6316	358	15	6316	6316	NUM
ejpam-6316	358	16	21	21	NUM
ejpam-6316	358	17	of	of	ADP
ejpam-6316	358	18	21	21	NUM
ejpam-6316	358	19	7(10):19325–19343	7(10):19325–19343	NUM
ejpam-6316	358	20	,	,	PUNCT
ejpam-6316	358	21	2022	2022	NUM
ejpam-6316	358	22	.	.	PUNCT
ejpam-6316	359	1	[	[	X
ejpam-6316	359	2	25	25	NUM
ejpam-6316	359	3	]	]	X
ejpam-6316	359	4	m	m	VERB
ejpam-6316	359	5	areshi	areshi	NOUN
ejpam-6316	359	6	,	,	PUNCT
ejpam-6316	359	7	a	a	DET
ejpam-6316	359	8	m	m	NOUN
ejpam-6316	359	9	zidan	zidan	ADJ
ejpam-6316	359	10	,	,	PUNCT
ejpam-6316	359	11	r	r	NOUN
ejpam-6316	359	12	shah	shah	NOUN
ejpam-6316	359	13	,	,	PUNCT
ejpam-6316	359	14	and	and	CCONJ
ejpam-6316	359	15	k	k	X
ejpam-6316	359	16	nonlaopon	nonlaopon	ADV
ejpam-6316	359	17	.	.	PUNCT
ejpam-6316	360	1	a	a	DET
ejpam-6316	360	2	modified	modify	VERB
ejpam-6316	360	3	techniques	technique	NOUN
ejpam-6316	360	4	of	of	ADP
ejpam-6316	360	5	fractionalorder	fractionalorder	ADJ
ejpam-6316	360	6	cauchy	cauchy	PROPN
ejpam-6316	360	7	-	-	PUNCT
ejpam-6316	360	8	reaction	reaction	NOUN
ejpam-6316	360	9	diffusion	diffusion	NOUN
ejpam-6316	360	10	equation	equation	NOUN
ejpam-6316	360	11	via	via	ADP
ejpam-6316	360	12	shehu	shehu	PROPN
ejpam-6316	360	13	transform	transform	NOUN
ejpam-6316	360	14	.	.	PUNCT
ejpam-6316	361	1	journal	journal	PROPN
ejpam-6316	361	2	of	of	ADP
ejpam-6316	361	3	function	function	NOUN
ejpam-6316	361	4	spaces	space	NOUN
ejpam-6316	361	5	,	,	PUNCT
ejpam-6316	361	6	2021(1):5726822	2021(1):5726822	NUM
ejpam-6316	361	7	,	,	PUNCT
ejpam-6316	361	8	2021	2021	NUM
ejpam-6316	361	9	.	.	PUNCT
ejpam-6316	362	1	[	[	X
ejpam-6316	362	2	26	26	NUM
ejpam-6316	362	3	]	]	X
ejpam-6316	362	4	z	z	NOUN
ejpam-6316	362	5	h	h	PROPN
ejpam-6316	362	6	khan	khan	PROPN
ejpam-6316	362	7	and	and	CCONJ
ejpam-6316	362	8	w	w	ADP
ejpam-6316	362	9	a	a	DET
ejpam-6316	362	10	khan	khan	PROPN
ejpam-6316	362	11	.	.	PUNCT
ejpam-6316	363	1	n	n	CCONJ
ejpam-6316	363	2	-	-	PUNCT
ejpam-6316	363	3	transform	transform	NOUN
ejpam-6316	363	4	properties	property	NOUN
ejpam-6316	363	5	and	and	CCONJ
ejpam-6316	363	6	applications	application	NOUN
ejpam-6316	363	7	.	.	PUNCT
ejpam-6316	364	1	nust	nust	PROPN
ejpam-6316	364	2	j	j	PROPN
ejpam-6316	364	3	eng	eng	PROPN
ejpam-6316	364	4	sci	sci	PROPN
ejpam-6316	364	5	,	,	PUNCT
ejpam-6316	364	6	1(1):127–133	1(1):127–133	NUM
ejpam-6316	364	7	,	,	PUNCT
ejpam-6316	364	8	2008	2008	NUM
ejpam-6316	364	9	.	.	PUNCT
ejpam-6316	365	1	[	[	X
ejpam-6316	365	2	27	27	NUM
ejpam-6316	365	3	]	]	X
ejpam-6316	365	4	s	s	PART
ejpam-6316	365	5	kumar	kumar	PROPN
ejpam-6316	365	6	,	,	PUNCT
ejpam-6316	365	7	a	a	DET
ejpam-6316	365	8	yildirim	yildirim	PROPN
ejpam-6316	365	9	,	,	PUNCT
ejpam-6316	365	10	y	y	PROPN
ejpam-6316	365	11	khan	khan	PROPN
ejpam-6316	365	12	,	,	PUNCT
ejpam-6316	365	13	and	and	CCONJ
ejpam-6316	365	14	l	l	PROPN
ejpam-6316	365	15	wei	wei	PROPN
ejpam-6316	365	16	.	.	PUNCT
ejpam-6316	366	1	a	a	DET
ejpam-6316	366	2	fractional	fractional	ADJ
ejpam-6316	366	3	model	model	NOUN
ejpam-6316	366	4	of	of	ADP
ejpam-6316	366	5	the	the	DET
ejpam-6316	366	6	diffusion	diffusion	NOUN
ejpam-6316	366	7	equation	equation	NOUN
ejpam-6316	366	8	and	and	CCONJ
ejpam-6316	366	9	its	its	PRON
ejpam-6316	366	10	analytical	analytical	ADJ
ejpam-6316	366	11	solution	solution	NOUN
ejpam-6316	366	12	using	use	VERB
ejpam-6316	366	13	laplace	laplace	NOUN
ejpam-6316	366	14	transform	transform	NOUN
ejpam-6316	366	15	.	.	PUNCT
ejpam-6316	367	1	sci	sci	PROPN
ejpam-6316	367	2	iran	iran	PROPN
ejpam-6316	367	3	b	b	PROPN
ejpam-6316	367	4	,	,	PUNCT
ejpam-6316	367	5	19(4):1117–1123	19(4):1117–1123	NUM
ejpam-6316	367	6	,	,	PUNCT
ejpam-6316	367	7	2012	2012	NUM
ejpam-6316	367	8	.	.	PUNCT
ejpam-6316	368	1	[	[	X
ejpam-6316	368	2	28	28	NUM
ejpam-6316	368	3	]	]	X
ejpam-6316	368	4	k	k	PROPN
ejpam-6316	368	5	shah	shah	PROPN
ejpam-6316	368	6	,	,	PUNCT
ejpam-6316	368	7	h	h	PROPN
ejpam-6316	368	8	khalil	khalil	PROPN
ejpam-6316	368	9	,	,	PUNCT
ejpam-6316	368	10	and	and	CCONJ
ejpam-6316	368	11	r	r	X
ejpam-6316	368	12	a	a	DET
ejpam-6316	368	13	khan	khan	PROPN
ejpam-6316	368	14	.	.	PUNCT
ejpam-6316	369	1	analytical	analytical	ADJ
ejpam-6316	369	2	solutions	solution	NOUN
ejpam-6316	369	3	of	of	ADP
ejpam-6316	369	4	fractional	fractional	ADJ
ejpam-6316	369	5	order	order	NOUN
ejpam-6316	369	6	diffusion	diffusion	NOUN
ejpam-6316	369	7	equations	equation	NOUN
ejpam-6316	369	8	by	by	ADP
ejpam-6316	369	9	natural	natural	ADJ
ejpam-6316	369	10	transform	transform	NOUN
ejpam-6316	369	11	method	method	NOUN
ejpam-6316	369	12	.	.	PUNCT
ejpam-6316	370	1	iranian	iranian	ADJ
ejpam-6316	370	2	journal	journal	PROPN
ejpam-6316	370	3	of	of	ADP
ejpam-6316	370	4	science	science	NOUN
ejpam-6316	370	5	and	and	CCONJ
ejpam-6316	370	6	technology	technology	NOUN
ejpam-6316	370	7	,	,	PUNCT
ejpam-6316	370	8	transactions	transaction	VERB
ejpam-6316	370	9	a	a	DET
ejpam-6316	370	10	:	:	PUNCT
ejpam-6316	370	11	science	science	NOUN
ejpam-6316	370	12	,	,	PUNCT
ejpam-6316	370	13	42(3):1479–1490	42(3):1479–1490	NUM
ejpam-6316	370	14	,	,	PUNCT
ejpam-6316	370	15	2018	2018	NUM
ejpam-6316	370	16	.	.	PUNCT