id	sid	tid	token	lemma	pos
ejpam-5884	1	1	european	european	PROPN
ejpam-5884	1	2	journal	journal	PROPN
ejpam-5884	1	3	of	of	ADP
ejpam-5884	1	4	pure	pure	ADJ
ejpam-5884	1	5	and	and	CCONJ
ejpam-5884	1	6	applied	applied	ADJ
ejpam-5884	1	7	mathematics	mathematic	NOUN
ejpam-5884	1	8	2025	2025	NUM
ejpam-5884	1	9	,	,	PUNCT
ejpam-5884	1	10	vol	vol	NOUN
ejpam-5884	1	11	.	.	PROPN
ejpam-5884	1	12	18	18	NUM
ejpam-5884	1	13	,	,	PUNCT
ejpam-5884	1	14	issue	issue	NOUN
ejpam-5884	1	15	2	2	NUM
ejpam-5884	1	16	,	,	PUNCT
ejpam-5884	1	17	article	article	NOUN
ejpam-5884	1	18	number	number	NOUN
ejpam-5884	1	19	5884	5884	NUM
ejpam-5884	1	20	issn	issn	PROPN
ejpam-5884	1	21	1307	1307	NUM
ejpam-5884	1	22	-	-	SYM
ejpam-5884	1	23	5543	5543	NUM
ejpam-5884	1	24	–	–	PUNCT
ejpam-5884	1	25	ejpam.com	ejpam.com	X
ejpam-5884	1	26	published	publish	VERB
ejpam-5884	1	27	by	by	ADP
ejpam-5884	1	28	new	new	PROPN
ejpam-5884	1	29	york	york	PROPN
ejpam-5884	1	30	business	business	PROPN
ejpam-5884	1	31	global	global	PROPN
ejpam-5884	1	32	an	an	DET
ejpam-5884	1	33	iterative	iterative	NOUN
ejpam-5884	1	34	fractional	fractional	ADJ
ejpam-5884	1	35	operational	operational	ADJ
ejpam-5884	1	36	matrix	matrix	NOUN
ejpam-5884	1	37	method	method	NOUN
ejpam-5884	1	38	for	for	ADP
ejpam-5884	1	39	solving	solve	VERB
ejpam-5884	1	40	fractional	fractional	ADJ
ejpam-5884	1	41	undamped	undampe	VERB
ejpam-5884	1	42	duffing	duffing	NOUN
ejpam-5884	1	43	equation	equation	NOUN
ejpam-5884	1	44	with	with	ADP
ejpam-5884	1	45	high	high	ADJ
ejpam-5884	1	46	nonlinearity	nonlinearity	NOUN
ejpam-5884	1	47	muhammed	muhamme	VERB
ejpam-5884	1	48	i.	i.	PROPN
ejpam-5884	1	49	syam1,∗	syam1,∗	PROPN
ejpam-5884	1	50	,	,	PUNCT
ejpam-5884	1	51	mwaffag	mwaffag	NOUN
ejpam-5884	1	52	sharadga2	sharadga2	NOUN
ejpam-5884	1	53	,	,	PUNCT
ejpam-5884	1	54	ishak	ishak	PROPN
ejpam-5884	1	55	hashim2	hashim2	PROPN
ejpam-5884	1	56	,	,	PUNCT
ejpam-5884	1	57	mohd	mohd	PROPN
ejpam-5884	1	58	almie	almie	PROPN
ejpam-5884	1	59	alias2	alias2	PROPN
ejpam-5884	1	60	,	,	PUNCT
ejpam-5884	1	61	mohammed	mohammed	PROPN
ejpam-5884	1	62	abuomar1	abuomar1	PROPN
ejpam-5884	1	63	,	,	PUNCT
ejpam-5884	1	64	shaher	shaher	ADJ
ejpam-5884	1	65	momani3	momani3	PROPN
ejpam-5884	1	66	1	1	NUM
ejpam-5884	1	67	department	department	PROPN
ejpam-5884	1	68	of	of	ADP
ejpam-5884	1	69	mathematical	mathematical	ADJ
ejpam-5884	1	70	sciences	sciences	PROPN
ejpam-5884	1	71	,	,	PUNCT
ejpam-5884	1	72	united	united	PROPN
ejpam-5884	1	73	arab	arab	PROPN
ejpam-5884	1	74	emirates	emirates	PROPN
ejpam-5884	1	75	university	university	PROPN
ejpam-5884	1	76	,	,	PUNCT
ejpam-5884	1	77	al	al	PROPN
ejpam-5884	1	78	-	-	PUNCT
ejpam-5884	1	79	ain	ain	PROPN
ejpam-5884	1	80	,	,	PUNCT
ejpam-5884	1	81	united	united	PROPN
ejpam-5884	1	82	arab	arab	PROPN
ejpam-5884	1	83	emirates	emirates	PROPN
ejpam-5884	1	84	2	2	NUM
ejpam-5884	1	85	department	department	NOUN
ejpam-5884	1	86	of	of	ADP
ejpam-5884	1	87	mathematical	mathematical	ADJ
ejpam-5884	1	88	sciences	science	NOUN
ejpam-5884	1	89	,	,	PUNCT
ejpam-5884	1	90	faculty	faculty	NOUN
ejpam-5884	1	91	of	of	ADP
ejpam-5884	1	92	science	science	PROPN
ejpam-5884	1	93	&	&	CCONJ
ejpam-5884	1	94	technology	technology	PROPN
ejpam-5884	1	95	,	,	PUNCT
ejpam-5884	1	96	universiti	universiti	PROPN
ejpam-5884	1	97	kebangsaan	kebangsaan	PROPN
ejpam-5884	1	98	malaysia	malaysia	PROPN
ejpam-5884	1	99	,	,	PUNCT
ejpam-5884	1	100	malaysia	malaysia	PROPN
ejpam-5884	1	101	3	3	NUM
ejpam-5884	1	102	department	department	NOUN
ejpam-5884	1	103	of	of	ADP
ejpam-5884	1	104	mathematics	mathematic	NOUN
ejpam-5884	1	105	,	,	PUNCT
ejpam-5884	1	106	faculty	faculty	NOUN
ejpam-5884	1	107	of	of	ADP
ejpam-5884	1	108	science	science	NOUN
ejpam-5884	1	109	,	,	PUNCT
ejpam-5884	1	110	the	the	DET
ejpam-5884	1	111	university	university	PROPN
ejpam-5884	1	112	of	of	ADP
ejpam-5884	1	113	jordan	jordan	PROPN
ejpam-5884	1	114	,	,	PUNCT
ejpam-5884	1	115	amman	amman	PROPN
ejpam-5884	1	116	,	,	PUNCT
ejpam-5884	1	117	11942	11942	NUM
ejpam-5884	1	118	,	,	PUNCT
ejpam-5884	1	119	jordan	jordan	PROPN
ejpam-5884	1	120	abstract	abstract	PROPN
ejpam-5884	1	121	.	.	PUNCT
ejpam-5884	2	1	this	this	DET
ejpam-5884	2	2	study	study	NOUN
ejpam-5884	2	3	presents	present	VERB
ejpam-5884	2	4	a	a	DET
ejpam-5884	2	5	novel	novel	ADJ
ejpam-5884	2	6	iterative	iterative	NOUN
ejpam-5884	2	7	fractional	fractional	ADJ
ejpam-5884	2	8	operational	operational	ADJ
ejpam-5884	2	9	matrix	matrix	NOUN
ejpam-5884	2	10	method	method	NOUN
ejpam-5884	2	11	for	for	ADP
ejpam-5884	2	12	solving	solve	VERB
ejpam-5884	2	13	the	the	DET
ejpam-5884	2	14	highly	highly	ADV
ejpam-5884	2	15	nonlinear	nonlinear	ADJ
ejpam-5884	2	16	fractional	fractional	ADJ
ejpam-5884	2	17	undamped	undampe	VERB
ejpam-5884	2	18	duffing	duffing	NOUN
ejpam-5884	2	19	equation	equation	NOUN
ejpam-5884	2	20	.	.	PUNCT
ejpam-5884	3	1	the	the	DET
ejpam-5884	3	2	proposed	propose	VERB
ejpam-5884	3	3	method	method	NOUN
ejpam-5884	3	4	efficiently	efficiently	ADV
ejpam-5884	3	5	approximates	approximate	VERB
ejpam-5884	3	6	the	the	DET
ejpam-5884	3	7	solution	solution	NOUN
ejpam-5884	3	8	by	by	ADP
ejpam-5884	3	9	transforming	transform	VERB
ejpam-5884	3	10	the	the	DET
ejpam-5884	3	11	original	original	ADJ
ejpam-5884	3	12	fractional	fractional	ADJ
ejpam-5884	3	13	differential	differential	ADJ
ejpam-5884	3	14	equation	equation	NOUN
ejpam-5884	3	15	into	into	ADP
ejpam-5884	3	16	a	a	DET
ejpam-5884	3	17	system	system	NOUN
ejpam-5884	3	18	of	of	ADP
ejpam-5884	3	19	algebraic	algebraic	ADJ
ejpam-5884	3	20	equations	equation	NOUN
ejpam-5884	3	21	using	use	VERB
ejpam-5884	3	22	modified	modify	VERB
ejpam-5884	3	23	operational	operational	ADJ
ejpam-5884	3	24	matrices	matrix	NOUN
ejpam-5884	3	25	.	.	PUNCT
ejpam-5884	4	1	the	the	DET
ejpam-5884	4	2	accuracy	accuracy	NOUN
ejpam-5884	4	3	and	and	CCONJ
ejpam-5884	4	4	effectiveness	effectiveness	NOUN
ejpam-5884	4	5	of	of	ADP
ejpam-5884	4	6	this	this	DET
ejpam-5884	4	7	approach	approach	NOUN
ejpam-5884	4	8	are	be	AUX
ejpam-5884	4	9	validated	validate	VERB
ejpam-5884	4	10	through	through	ADP
ejpam-5884	4	11	comparisons	comparison	NOUN
ejpam-5884	4	12	with	with	ADP
ejpam-5884	4	13	established	establish	VERB
ejpam-5884	4	14	numerical	numerical	ADJ
ejpam-5884	4	15	methods	method	NOUN
ejpam-5884	4	16	and	and	CCONJ
ejpam-5884	4	17	alternative	alternative	ADJ
ejpam-5884	4	18	analytical	analytical	ADJ
ejpam-5884	4	19	techniques	technique	NOUN
ejpam-5884	4	20	from	from	ADP
ejpam-5884	4	21	the	the	DET
ejpam-5884	4	22	literature	literature	NOUN
ejpam-5884	4	23	.	.	PUNCT
ejpam-5884	5	1	the	the	DET
ejpam-5884	5	2	results	result	NOUN
ejpam-5884	5	3	demonstrate	demonstrate	VERB
ejpam-5884	5	4	that	that	SCONJ
ejpam-5884	5	5	the	the	DET
ejpam-5884	5	6	proposed	propose	VERB
ejpam-5884	5	7	method	method	NOUN
ejpam-5884	5	8	provides	provide	VERB
ejpam-5884	5	9	a	a	DET
ejpam-5884	5	10	highly	highly	ADV
ejpam-5884	5	11	accurate	accurate	ADJ
ejpam-5884	5	12	approximation	approximation	NOUN
ejpam-5884	5	13	with	with	ADP
ejpam-5884	5	14	rapid	rapid	ADJ
ejpam-5884	5	15	convergence	convergence	NOUN
ejpam-5884	5	16	.	.	PUNCT
ejpam-5884	6	1	furthermore	furthermore	ADV
ejpam-5884	6	2	,	,	PUNCT
ejpam-5884	6	3	a	a	DET
ejpam-5884	6	4	rigorous	rigorous	ADJ
ejpam-5884	6	5	convergence	convergence	NOUN
ejpam-5884	6	6	analysis	analysis	NOUN
ejpam-5884	6	7	is	be	AUX
ejpam-5884	6	8	conducted	conduct	VERB
ejpam-5884	6	9	to	to	PART
ejpam-5884	6	10	establish	establish	VERB
ejpam-5884	6	11	the	the	DET
ejpam-5884	6	12	existence	existence	NOUN
ejpam-5884	6	13	and	and	CCONJ
ejpam-5884	6	14	uniqueness	uniqueness	NOUN
ejpam-5884	6	15	of	of	ADP
ejpam-5884	6	16	the	the	DET
ejpam-5884	6	17	solution	solution	NOUN
ejpam-5884	6	18	.	.	PUNCT
ejpam-5884	7	1	notably	notably	ADV
ejpam-5884	7	2	,	,	PUNCT
ejpam-5884	7	3	the	the	DET
ejpam-5884	7	4	study	study	NOUN
ejpam-5884	7	5	explores	explore	VERB
ejpam-5884	7	6	the	the	DET
ejpam-5884	7	7	impact	impact	NOUN
ejpam-5884	7	8	of	of	ADP
ejpam-5884	7	9	varying	vary	VERB
ejpam-5884	7	10	the	the	DET
ejpam-5884	7	11	fractional	fractional	ADJ
ejpam-5884	7	12	order	order	NOUN
ejpam-5884	7	13	revealing	reveal	VERB
ejpam-5884	7	14	its	its	PRON
ejpam-5884	7	15	significant	significant	ADJ
ejpam-5884	7	16	influence	influence	NOUN
ejpam-5884	7	17	on	on	ADP
ejpam-5884	7	18	the	the	DET
ejpam-5884	7	19	system	system	NOUN
ejpam-5884	7	20	’s	’s	PART
ejpam-5884	7	21	dynamic	dynamic	ADJ
ejpam-5884	7	22	behavior	behavior	NOUN
ejpam-5884	7	23	.	.	PUNCT
ejpam-5884	8	1	as	as	SCONJ
ejpam-5884	8	2	the	the	DET
ejpam-5884	8	3	fractional	fractional	ADJ
ejpam-5884	8	4	order	order	NOUN
ejpam-5884	8	5	approaches	approach	VERB
ejpam-5884	8	6	unity	unity	NOUN
ejpam-5884	8	7	,	,	PUNCT
ejpam-5884	8	8	the	the	DET
ejpam-5884	8	9	fractional	fractional	ADJ
ejpam-5884	8	10	model	model	NOUN
ejpam-5884	8	11	converges	converge	NOUN
ejpam-5884	8	12	to	to	ADP
ejpam-5884	8	13	its	its	PRON
ejpam-5884	8	14	classical	classical	ADJ
ejpam-5884	8	15	counterpart	counterpart	NOUN
ejpam-5884	8	16	,	,	PUNCT
ejpam-5884	8	17	highlighting	highlight	VERB
ejpam-5884	8	18	the	the	DET
ejpam-5884	8	19	role	role	NOUN
ejpam-5884	8	20	of	of	ADP
ejpam-5884	8	21	fractional	fractional	ADJ
ejpam-5884	8	22	derivatives	derivative	NOUN
ejpam-5884	8	23	in	in	ADP
ejpam-5884	8	24	capturing	capture	VERB
ejpam-5884	8	25	memory	memory	NOUN
ejpam-5884	8	26	effects	effect	NOUN
ejpam-5884	8	27	and	and	CCONJ
ejpam-5884	8	28	hereditary	hereditary	ADJ
ejpam-5884	8	29	properties	property	NOUN
ejpam-5884	8	30	in	in	ADP
ejpam-5884	8	31	physical	physical	ADJ
ejpam-5884	8	32	systems	system	NOUN
ejpam-5884	8	33	.	.	PUNCT
ejpam-5884	9	1	2020	2020	NUM
ejpam-5884	9	2	mathematics	mathematic	NOUN
ejpam-5884	9	3	subject	subject	NOUN
ejpam-5884	9	4	classifications	classification	NOUN
ejpam-5884	9	5	:	:	PUNCT
ejpam-5884	9	6	65l03	65l03	NUM
ejpam-5884	9	7	,	,	PUNCT
ejpam-5884	9	8	34a08	34a08	DET
ejpam-5884	9	9	key	key	ADJ
ejpam-5884	9	10	words	word	NOUN
ejpam-5884	9	11	and	and	CCONJ
ejpam-5884	9	12	phrases	phrase	NOUN
ejpam-5884	9	13	:	:	PUNCT
ejpam-5884	9	14	modified	modify	VERB
ejpam-5884	9	15	operational	operational	ADJ
ejpam-5884	9	16	matrices	matrix	NOUN
ejpam-5884	9	17	,	,	PUNCT
ejpam-5884	9	18	undamped	undampe	VERB
ejpam-5884	9	19	duffing	duffing	NOUN
ejpam-5884	9	20	equation	equation	NOUN
ejpam-5884	9	21	,	,	PUNCT
ejpam-5884	9	22	high	high	ADJ
ejpam-5884	9	23	nonlinearity	nonlinearity	NOUN
ejpam-5884	9	24	∗corresponding	∗corresponde	VERB
ejpam-5884	9	25	author	author	NOUN
ejpam-5884	9	26	.	.	PUNCT
ejpam-5884	10	1	doi	doi	NOUN
ejpam-5884	10	2	:	:	PUNCT
ejpam-5884	10	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5884	https://doi.org/10.29020/nybg.ejpam.v18i2.5884	ADJ
ejpam-5884	10	4	email	email	NOUN
ejpam-5884	10	5	addresses	address	NOUN
ejpam-5884	10	6	:	:	PUNCT
ejpam-5884	10	7	m.syam@uaeu.ac.ae	m.syam@uaeu.ac.ae	NUM
ejpam-5884	10	8	(	(	PUNCT
ejpam-5884	10	9	m.	m.	NOUN
ejpam-5884	10	10	syam	syam	NOUN
ejpam-5884	10	11	)	)	PUNCT
ejpam-5884	10	12	,	,	PUNCT
ejpam-5884	10	13	p101953@siswa.ukm.edu.my	p101953@siswa.ukm.edu.my	NOUN
ejpam-5884	10	14	(	(	PUNCT
ejpam-5884	10	15	m.	m.	NOUN
ejpam-5884	10	16	sharadga	sharadga	NOUN
ejpam-5884	10	17	)	)	PUNCT
ejpam-5884	10	18	,	,	PUNCT
ejpam-5884	10	19	ishak	ishak	PROPN
ejpam-5884	10	20	h@ukm.my	h@ukm.my	PROPN
ejpam-5884	10	21	(	(	PUNCT
ejpam-5884	10	22	i.	i.	PROPN
ejpam-5884	10	23	hashim	hashim	PROPN
ejpam-5884	10	24	)	)	PUNCT
ejpam-5884	10	25	,	,	PUNCT
ejpam-5884	10	26	almie.alias@monash.edu	almie.alias@monash.edu	PROPN
ejpam-5884	10	27	(	(	PUNCT
ejpam-5884	10	28	m.	m.	NOUN
ejpam-5884	10	29	alias	alias	PROPN
ejpam-5884	10	30	)	)	PUNCT
ejpam-5884	10	31	,	,	PUNCT
ejpam-5884	10	32	mohammed	mohammed	PROPN
ejpam-5884	10	33	m@uaeu.ac.ae	m@uaeu.ac.ae	PROPN
ejpam-5884	10	34	(	(	PUNCT
ejpam-5884	10	35	m.	m.	PROPN
ejpam-5884	10	36	abuomar	abuomar	PROPN
ejpam-5884	10	37	)	)	PUNCT
ejpam-5884	10	38	,	,	PUNCT
ejpam-5884	10	39	shahermm@yahoo.com	shahermm@yahoo.com	X
ejpam-5884	10	40	(	(	PUNCT
ejpam-5884	10	41	s.	s.	PROPN
ejpam-5884	10	42	momani	momani	PROPN
ejpam-5884	10	43	)	)	PUNCT
ejpam-5884	10	44	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5884	11	1	1	1	NUM
ejpam-5884	11	2	copyright	copyright	NOUN
ejpam-5884	11	3	:	:	PUNCT
ejpam-5884	11	4	©	©	PROPN
ejpam-5884	11	5	2025	2025	NUM
ejpam-5884	11	6	the	the	DET
ejpam-5884	11	7	author(s	author(s	NOUN
ejpam-5884	11	8	)	)	PUNCT
ejpam-5884	11	9	.	.	PUNCT
ejpam-5884	12	1	(	(	PUNCT
ejpam-5884	12	2	cc	cc	NOUN
ejpam-5884	12	3	by	by	ADP
ejpam-5884	12	4	-	-	PUNCT
ejpam-5884	12	5	nc	nc	PROPN
ejpam-5884	12	6	4.0	4.0	NUM
ejpam-5884	12	7	)	)	PUNCT
ejpam-5884	12	8	m.	m.	NOUN
ejpam-5884	12	9	i.	i.	PROPN
ejpam-5884	12	10	syam	syam	PROPN
ejpam-5884	12	11	et	et	PROPN
ejpam-5884	12	12	al	al	PROPN
ejpam-5884	12	13	.	.	PUNCT
ejpam-5884	12	14	/	/	SYM
ejpam-5884	12	15	eur	eur	PROPN
ejpam-5884	12	16	.	.	PUNCT
ejpam-5884	13	1	j.	j.	PROPN
ejpam-5884	13	2	pure	pure	PROPN
ejpam-5884	13	3	appl	appl	PROPN
ejpam-5884	13	4	.	.	PROPN
ejpam-5884	13	5	math	math	PROPN
ejpam-5884	13	6	,	,	PUNCT
ejpam-5884	13	7	18	18	NUM
ejpam-5884	13	8	(	(	PUNCT
ejpam-5884	13	9	2	2	NUM
ejpam-5884	13	10	)	)	PUNCT
ejpam-5884	13	11	(	(	PUNCT
ejpam-5884	13	12	2025	2025	NUM
ejpam-5884	13	13	)	)	PUNCT
ejpam-5884	13	14	,	,	PUNCT
ejpam-5884	13	15	5884	5884	NUM
ejpam-5884	13	16	2	2	NUM
ejpam-5884	13	17	of	of	ADP
ejpam-5884	13	18	18	18	NUM
ejpam-5884	13	19	1	1	NUM
ejpam-5884	13	20	.	.	PUNCT
ejpam-5884	13	21	introduction	introduction	NOUN
ejpam-5884	13	22	the	the	DET
ejpam-5884	13	23	domain	domain	NOUN
ejpam-5884	13	24	of	of	ADP
ejpam-5884	13	25	fractional	fractional	ADJ
ejpam-5884	13	26	calculus	calculus	NOUN
ejpam-5884	13	27	broadens	broaden	VERB
ejpam-5884	13	28	the	the	DET
ejpam-5884	13	29	conventional	conventional	ADJ
ejpam-5884	13	30	concepts	concept	NOUN
ejpam-5884	13	31	of	of	ADP
ejpam-5884	13	32	differentiation	differentiation	NOUN
ejpam-5884	13	33	and	and	CCONJ
ejpam-5884	13	34	integration	integration	NOUN
ejpam-5884	13	35	to	to	PART
ejpam-5884	13	36	encompass	encompass	VERB
ejpam-5884	13	37	non	non	ADJ
ejpam-5884	13	38	-	-	ADJ
ejpam-5884	13	39	integer	integer	ADJ
ejpam-5884	13	40	orders	order	NOUN
ejpam-5884	13	41	,	,	PUNCT
ejpam-5884	13	42	thereby	thereby	ADV
ejpam-5884	13	43	offering	offer	VERB
ejpam-5884	13	44	a	a	DET
ejpam-5884	13	45	more	more	ADV
ejpam-5884	13	46	comprehensive	comprehensive	ADJ
ejpam-5884	13	47	mathematical	mathematical	ADJ
ejpam-5884	13	48	framework	framework	NOUN
ejpam-5884	13	49	for	for	ADP
ejpam-5884	13	50	these	these	DET
ejpam-5884	13	51	operations	operation	NOUN
ejpam-5884	13	52	.	.	PUNCT
ejpam-5884	14	1	the	the	DET
ejpam-5884	14	2	origins	origin	NOUN
ejpam-5884	14	3	of	of	ADP
ejpam-5884	14	4	fractional	fractional	ADJ
ejpam-5884	14	5	differentiation	differentiation	NOUN
ejpam-5884	14	6	and	and	CCONJ
ejpam-5884	14	7	integration	integration	NOUN
ejpam-5884	14	8	date	date	NOUN
ejpam-5884	14	9	back	back	ADV
ejpam-5884	14	10	to	to	ADP
ejpam-5884	14	11	1695	1695	NUM
ejpam-5884	14	12	,	,	PUNCT
ejpam-5884	14	13	when	when	SCONJ
ejpam-5884	14	14	leibniz	leibniz	PROPN
ejpam-5884	14	15	and	and	CCONJ
ejpam-5884	14	16	euler	euler	PROPN
ejpam-5884	14	17	first	first	ADV
ejpam-5884	14	18	introduced	introduce	VERB
ejpam-5884	14	19	these	these	DET
ejpam-5884	14	20	concepts	concept	NOUN
ejpam-5884	14	21	[	[	X
ejpam-5884	14	22	1	1	NUM
ejpam-5884	14	23	]	]	PUNCT
ejpam-5884	14	24	.	.	PUNCT
ejpam-5884	15	1	a	a	DET
ejpam-5884	15	2	distinguishing	distinguish	VERB
ejpam-5884	15	3	characteristic	characteristic	NOUN
ejpam-5884	15	4	of	of	ADP
ejpam-5884	15	5	fractional	fractional	ADJ
ejpam-5884	15	6	operators	operator	NOUN
ejpam-5884	15	7	is	be	AUX
ejpam-5884	15	8	their	their	PRON
ejpam-5884	15	9	non	non	ADJ
ejpam-5884	15	10	-	-	ADJ
ejpam-5884	15	11	local	local	ADJ
ejpam-5884	15	12	behavior	behavior	NOUN
ejpam-5884	15	13	,	,	PUNCT
ejpam-5884	15	14	which	which	PRON
ejpam-5884	15	15	provides	provide	VERB
ejpam-5884	15	16	valuable	valuable	ADJ
ejpam-5884	15	17	insights	insight	NOUN
ejpam-5884	15	18	into	into	ADP
ejpam-5884	15	19	the	the	DET
ejpam-5884	15	20	historical	historical	ADJ
ejpam-5884	15	21	and	and	CCONJ
ejpam-5884	15	22	dynamic	dynamic	ADJ
ejpam-5884	15	23	significance	significance	NOUN
ejpam-5884	15	24	of	of	ADP
ejpam-5884	15	25	fractional	fractional	ADJ
ejpam-5884	15	26	models	model	NOUN
ejpam-5884	15	27	.	.	PUNCT
ejpam-5884	16	1	in	in	ADP
ejpam-5884	16	2	recent	recent	ADJ
ejpam-5884	16	3	years	year	NOUN
ejpam-5884	16	4	,	,	PUNCT
ejpam-5884	16	5	fractional	fractional	ADJ
ejpam-5884	16	6	differential	differential	ADJ
ejpam-5884	16	7	equations	equation	NOUN
ejpam-5884	16	8	have	have	AUX
ejpam-5884	16	9	found	find	VERB
ejpam-5884	16	10	widespread	widespread	ADJ
ejpam-5884	16	11	applications	application	NOUN
ejpam-5884	16	12	in	in	ADP
ejpam-5884	16	13	modeling	model	VERB
ejpam-5884	16	14	diverse	diverse	ADJ
ejpam-5884	16	15	real	real	ADJ
ejpam-5884	16	16	-	-	PUNCT
ejpam-5884	16	17	world	world	NOUN
ejpam-5884	16	18	phenomena	phenomenon	NOUN
ejpam-5884	16	19	.	.	PUNCT
ejpam-5884	17	1	for	for	ADP
ejpam-5884	17	2	instance	instance	NOUN
ejpam-5884	17	3	,	,	PUNCT
ejpam-5884	17	4	it	it	PRON
ejpam-5884	17	5	is	be	AUX
ejpam-5884	17	6	examined	examine	VERB
ejpam-5884	17	7	their	their	PRON
ejpam-5884	17	8	utility	utility	NOUN
ejpam-5884	17	9	in	in	ADP
ejpam-5884	17	10	analyzing	analyze	VERB
ejpam-5884	17	11	and	and	CCONJ
ejpam-5884	17	12	designing	design	VERB
ejpam-5884	17	13	control	control	NOUN
ejpam-5884	17	14	systems	system	NOUN
ejpam-5884	17	15	,	,	PUNCT
ejpam-5884	17	16	see	see	VERB
ejpam-5884	17	17	[	[	X
ejpam-5884	17	18	2	2	NUM
ejpam-5884	17	19	]	]	PUNCT
ejpam-5884	17	20	.	.	PUNCT
ejpam-5884	18	1	magin	magin	PROPN
ejpam-5884	19	1	[	[	X
ejpam-5884	19	2	3	3	NUM
ejpam-5884	19	3	]	]	PUNCT
ejpam-5884	19	4	identified	identify	VERB
ejpam-5884	19	5	three	three	NUM
ejpam-5884	19	6	bioengineering	bioengineering	NOUN
ejpam-5884	19	7	domains	domain	NOUN
ejpam-5884	19	8	where	where	SCONJ
ejpam-5884	19	9	fractional	fractional	ADJ
ejpam-5884	19	10	calculus	calculus	NOUN
ejpam-5884	19	11	principles	principle	NOUN
ejpam-5884	19	12	have	have	AUX
ejpam-5884	19	13	been	be	AUX
ejpam-5884	19	14	instrumental	instrumental	ADJ
ejpam-5884	19	15	in	in	ADP
ejpam-5884	19	16	developing	develop	VERB
ejpam-5884	19	17	innovative	innovative	ADJ
ejpam-5884	19	18	mathematical	mathematical	ADJ
ejpam-5884	19	19	models	model	NOUN
ejpam-5884	19	20	.	.	PUNCT
ejpam-5884	20	1	similarly	similarly	ADV
ejpam-5884	20	2	,	,	PUNCT
ejpam-5884	20	3	matlob	matlob	PROPN
ejpam-5884	20	4	and	and	CCONJ
ejpam-5884	20	5	jamali	jamali	PROPN
ejpam-5884	21	1	[	[	X
ejpam-5884	21	2	4	4	NUM
ejpam-5884	21	3	]	]	PUNCT
ejpam-5884	21	4	employed	employ	VERB
ejpam-5884	21	5	fractional	fractional	ADJ
ejpam-5884	21	6	differential	differential	ADJ
ejpam-5884	21	7	equations	equation	NOUN
ejpam-5884	21	8	to	to	PART
ejpam-5884	21	9	study	study	VERB
ejpam-5884	21	10	the	the	DET
ejpam-5884	21	11	dynamics	dynamic	NOUN
ejpam-5884	21	12	of	of	ADP
ejpam-5884	21	13	viscoelastic	viscoelastic	NOUN
ejpam-5884	21	14	systems	system	NOUN
ejpam-5884	21	15	.	.	PUNCT
ejpam-5884	22	1	in	in	ADP
ejpam-5884	22	2	image	image	NOUN
ejpam-5884	22	3	processing	processing	NOUN
ejpam-5884	22	4	,	,	PUNCT
ejpam-5884	22	5	fractional	fractional	ADJ
ejpam-5884	22	6	orders	order	NOUN
ejpam-5884	22	7	have	have	AUX
ejpam-5884	22	8	been	be	AUX
ejpam-5884	22	9	utilized	utilize	VERB
ejpam-5884	22	10	to	to	PART
ejpam-5884	22	11	improve	improve	VERB
ejpam-5884	22	12	denoising	denoising	NOUN
ejpam-5884	22	13	techniques	technique	NOUN
ejpam-5884	22	14	[	[	X
ejpam-5884	22	15	5	5	NUM
ejpam-5884	22	16	]	]	PUNCT
ejpam-5884	22	17	,	,	PUNCT
ejpam-5884	22	18	while	while	SCONJ
ejpam-5884	22	19	other	other	ADJ
ejpam-5884	22	20	notable	notable	ADJ
ejpam-5884	22	21	applications	application	NOUN
ejpam-5884	22	22	include	include	VERB
ejpam-5884	22	23	finance	finance	NOUN
ejpam-5884	22	24	[	[	X
ejpam-5884	22	25	6	6	NUM
ejpam-5884	22	26	]	]	PUNCT
ejpam-5884	22	27	,	,	PUNCT
ejpam-5884	22	28	solid	solid	ADJ
ejpam-5884	22	29	mechanics	mechanic	NOUN
ejpam-5884	22	30	[	[	X
ejpam-5884	22	31	7	7	NUM
ejpam-5884	22	32	]	]	PUNCT
ejpam-5884	22	33	,	,	PUNCT
ejpam-5884	22	34	and	and	CCONJ
ejpam-5884	22	35	mathematical	mathematical	ADJ
ejpam-5884	22	36	biology	biology	NOUN
ejpam-5884	22	37	[	[	X
ejpam-5884	22	38	8–12	8–12	X
ejpam-5884	22	39	]	]	X
ejpam-5884	22	40	.	.	PUNCT
ejpam-5884	23	1	a	a	DET
ejpam-5884	23	2	significant	significant	ADJ
ejpam-5884	23	3	recent	recent	ADJ
ejpam-5884	23	4	development	development	NOUN
ejpam-5884	23	5	in	in	ADP
ejpam-5884	23	6	fractional	fractional	ADJ
ejpam-5884	23	7	calculus	calculus	NOUN
ejpam-5884	23	8	is	be	AUX
ejpam-5884	23	9	the	the	DET
ejpam-5884	23	10	atangana	atangana	PROPN
ejpam-5884	23	11	-	-	PUNCT
ejpam-5884	23	12	baleanu	baleanu	ADJ
ejpam-5884	23	13	fractional	fractional	ADJ
ejpam-5884	23	14	derivative	derivative	NOUN
ejpam-5884	24	1	[	[	X
ejpam-5884	24	2	8	8	NUM
ejpam-5884	24	3	]	]	PUNCT
ejpam-5884	24	4	.	.	PUNCT
ejpam-5884	25	1	proposed	propose	VERB
ejpam-5884	25	2	by	by	ADP
ejpam-5884	25	3	abdon	abdon	PROPN
ejpam-5884	25	4	atangana	atangana	PROPN
ejpam-5884	25	5	and	and	CCONJ
ejpam-5884	25	6	dumitru	dumitru	PROPN
ejpam-5884	25	7	baleanu	baleanu	NOUN
ejpam-5884	25	8	in	in	ADP
ejpam-5884	25	9	2016	2016	NUM
ejpam-5884	25	10	,	,	PUNCT
ejpam-5884	25	11	this	this	DET
ejpam-5884	25	12	derivative	derivative	NOUN
ejpam-5884	25	13	incorporates	incorporate	VERB
ejpam-5884	25	14	non	non	ADJ
ejpam-5884	25	15	-	-	ADJ
ejpam-5884	25	16	singular	singular	ADJ
ejpam-5884	25	17	kernels	kernel	NOUN
ejpam-5884	25	18	and	and	CCONJ
ejpam-5884	25	19	the	the	DET
ejpam-5884	25	20	mittag	mittag	ADJ
ejpam-5884	25	21	-	-	PUNCT
ejpam-5884	25	22	leffler	leffler	NOUN
ejpam-5884	25	23	function	function	NOUN
ejpam-5884	25	24	.	.	PUNCT
ejpam-5884	26	1	the	the	DET
ejpam-5884	26	2	application	application	NOUN
ejpam-5884	26	3	of	of	ADP
ejpam-5884	26	4	fractional	fractional	ADJ
ejpam-5884	26	5	differentiation	differentiation	NOUN
ejpam-5884	26	6	in	in	ADP
ejpam-5884	26	7	[	[	X
ejpam-5884	26	8	8	8	NUM
ejpam-5884	26	9	]	]	PUNCT
ejpam-5884	26	10	led	lead	VERB
ejpam-5884	26	11	to	to	ADP
ejpam-5884	26	12	the	the	DET
ejpam-5884	26	13	formulation	formulation	NOUN
ejpam-5884	26	14	of	of	ADP
ejpam-5884	26	15	a	a	DET
ejpam-5884	26	16	mathematical	mathematical	ADJ
ejpam-5884	26	17	model	model	NOUN
ejpam-5884	26	18	for	for	ADP
ejpam-5884	26	19	heat	heat	NOUN
ejpam-5884	26	20	conduction	conduction	NOUN
ejpam-5884	26	21	in	in	ADP
ejpam-5884	26	22	materials	material	NOUN
ejpam-5884	26	23	.	.	PUNCT
ejpam-5884	27	1	this	this	DET
ejpam-5884	27	2	methodology	methodology	NOUN
ejpam-5884	27	3	has	have	AUX
ejpam-5884	27	4	proven	prove	VERB
ejpam-5884	27	5	effective	effective	ADJ
ejpam-5884	27	6	in	in	ADP
ejpam-5884	27	7	addressing	address	VERB
ejpam-5884	27	8	a	a	DET
ejpam-5884	27	9	wide	wide	ADJ
ejpam-5884	27	10	range	range	NOUN
ejpam-5884	27	11	of	of	ADP
ejpam-5884	27	12	real	real	ADJ
ejpam-5884	27	13	-	-	PUNCT
ejpam-5884	27	14	world	world	NOUN
ejpam-5884	27	15	problems	problem	NOUN
ejpam-5884	27	16	,	,	PUNCT
ejpam-5884	27	17	as	as	SCONJ
ejpam-5884	27	18	evidenced	evidence	VERB
ejpam-5884	27	19	in	in	ADP
ejpam-5884	27	20	[	[	X
ejpam-5884	27	21	13–23	13–23	NUM
ejpam-5884	27	22	]	]	PUNCT
ejpam-5884	27	23	.	.	PUNCT
ejpam-5884	28	1	in	in	ADP
ejpam-5884	28	2	1918	1918	NUM
ejpam-5884	28	3	,	,	PUNCT
ejpam-5884	28	4	george	george	PROPN
ejpam-5884	28	5	duffing	duffing	PROPN
ejpam-5884	28	6	introduced	introduce	VERB
ejpam-5884	28	7	the	the	DET
ejpam-5884	28	8	duffing	duffing	NOUN
ejpam-5884	28	9	equation	equation	NOUN
ejpam-5884	28	10	in	in	ADP
ejpam-5884	28	11	his	his	PRON
ejpam-5884	28	12	publication	publication	NOUN
ejpam-5884	28	13	[	[	X
ejpam-5884	28	14	24	24	NUM
ejpam-5884	28	15	]	]	PUNCT
ejpam-5884	28	16	.	.	PUNCT
ejpam-5884	29	1	within	within	ADP
ejpam-5884	29	2	his	his	PRON
ejpam-5884	29	3	work	work	NOUN
ejpam-5884	29	4	,	,	PUNCT
ejpam-5884	29	5	duffing	duffe	VERB
ejpam-5884	29	6	proposed	propose	VERB
ejpam-5884	29	7	a	a	DET
ejpam-5884	29	8	simplified	simplified	ADJ
ejpam-5884	29	9	mathematical	mathematical	ADJ
ejpam-5884	29	10	model	model	NOUN
ejpam-5884	29	11	x′′(t	x′′(t	NOUN
ejpam-5884	29	12	)	)	PUNCT
ejpam-5884	30	1	+	+	CCONJ
ejpam-5884	30	2	a2x(t)−	a2x(t)−	PROPN
ejpam-5884	30	3	βx2(t)−	βx2(t)−	PROPN
ejpam-5884	30	4	γx3(t	γx3(t	PROPN
ejpam-5884	30	5	)	)	PUNCT
ejpam-5884	31	1	=	=	SYM
ejpam-5884	31	2	k	k	X
ejpam-5884	31	3	sin(ωt	sin(ωt	PROPN
ejpam-5884	31	4	)	)	PUNCT
ejpam-5884	31	5	,	,	PUNCT
ejpam-5884	31	6	(	(	PUNCT
ejpam-5884	31	7	1	1	X
ejpam-5884	31	8	)	)	PUNCT
ejpam-5884	31	9	where	where	SCONJ
ejpam-5884	31	10	he	he	PRON
ejpam-5884	31	11	calculated	calculate	VERB
ejpam-5884	31	12	the	the	DET
ejpam-5884	31	13	first	first	ADJ
ejpam-5884	31	14	term	term	NOUN
ejpam-5884	31	15	,	,	PUNCT
ejpam-5884	31	16	h	h	NOUN
ejpam-5884	31	17	sin(ωt	sin(ωt	NOUN
ejpam-5884	31	18	)	)	PUNCT
ejpam-5884	31	19	,	,	PUNCT
ejpam-5884	31	20	of	of	ADP
ejpam-5884	31	21	the	the	DET
ejpam-5884	31	22	periodic	periodic	ADJ
ejpam-5884	31	23	solution	solution	NOUN
ejpam-5884	31	24	.	.	PUNCT
ejpam-5884	32	1	duffing	duffing	NOUN
ejpam-5884	32	2	also	also	ADV
ejpam-5884	32	3	proposed	propose	VERB
ejpam-5884	32	4	simplified	simplified	ADJ
ejpam-5884	32	5	forms	form	NOUN
ejpam-5884	32	6	of	of	ADP
ejpam-5884	32	7	this	this	DET
ejpam-5884	32	8	equation	equation	NOUN
ejpam-5884	32	9	to	to	PART
ejpam-5884	32	10	describe	describe	VERB
ejpam-5884	32	11	the	the	DET
ejpam-5884	32	12	motion	motion	NOUN
ejpam-5884	32	13	of	of	ADP
ejpam-5884	32	14	pendulums	pendulum	NOUN
ejpam-5884	32	15	.	.	PUNCT
ejpam-5884	33	1	for	for	ADP
ejpam-5884	33	2	a	a	DET
ejpam-5884	33	3	symmetric	symmetric	ADJ
ejpam-5884	33	4	pendulum	pendulum	NOUN
ejpam-5884	33	5	,	,	PUNCT
ejpam-5884	33	6	the	the	DET
ejpam-5884	33	7	equation	equation	NOUN
ejpam-5884	33	8	takes	take	VERB
ejpam-5884	33	9	the	the	DET
ejpam-5884	33	10	form	form	NOUN
ejpam-5884	33	11	x′′(t	x′′(t	NOUN
ejpam-5884	33	12	)	)	PUNCT
ejpam-5884	34	1	+	+	CCONJ
ejpam-5884	34	2	αx(t)−	αx(t)−	PROPN
ejpam-5884	34	3	γx3(t	γx3(t	PROPN
ejpam-5884	34	4	)	)	PUNCT
ejpam-5884	34	5	=	=	SYM
ejpam-5884	34	6	0	0	NUM
ejpam-5884	34	7	,	,	PUNCT
ejpam-5884	34	8	(	(	PUNCT
ejpam-5884	34	9	2	2	X
ejpam-5884	34	10	)	)	PUNCT
ejpam-5884	34	11	while	while	SCONJ
ejpam-5884	34	12	for	for	ADP
ejpam-5884	34	13	an	an	DET
ejpam-5884	34	14	asymmetric	asymmetric	ADJ
ejpam-5884	34	15	pendulum	pendulum	NOUN
ejpam-5884	34	16	,	,	PUNCT
ejpam-5884	34	17	it	it	PRON
ejpam-5884	34	18	becomes	become	VERB
ejpam-5884	34	19	:	:	PUNCT
ejpam-5884	34	20	x′′(t	x′′(t	NUM
ejpam-5884	34	21	)	)	PUNCT
ejpam-5884	35	1	+	+	CCONJ
ejpam-5884	35	2	αx(t)−	αx(t)−	PROPN
ejpam-5884	35	3	γx2(t	γx2(t	NOUN
ejpam-5884	35	4	)	)	PUNCT
ejpam-5884	35	5	=	=	SYM
ejpam-5884	36	1	0	0	X
ejpam-5884	36	2	.	.	PUNCT
ejpam-5884	37	1	(	(	PUNCT
ejpam-5884	37	2	3	3	X
ejpam-5884	37	3	)	)	PUNCT
ejpam-5884	37	4	since	since	SCONJ
ejpam-5884	37	5	its	its	PRON
ejpam-5884	37	6	introduction	introduction	NOUN
ejpam-5884	37	7	,	,	PUNCT
ejpam-5884	37	8	differential	differential	ADJ
ejpam-5884	37	9	equations	equation	NOUN
ejpam-5884	37	10	with	with	ADP
ejpam-5884	37	11	polynomial	polynomial	ADJ
ejpam-5884	37	12	nonlinearities	nonlinearitie	NOUN
ejpam-5884	37	13	have	have	AUX
ejpam-5884	37	14	been	be	AUX
ejpam-5884	37	15	referred	refer	VERB
ejpam-5884	37	16	to	to	ADP
ejpam-5884	37	17	as	as	ADP
ejpam-5884	37	18	duffing	duffe	VERB
ejpam-5884	37	19	’s	’s	PART
ejpam-5884	37	20	equations	equation	NOUN
ejpam-5884	38	1	[	[	X
ejpam-5884	38	2	25	25	NUM
ejpam-5884	38	3	]	]	PUNCT
ejpam-5884	38	4	.	.	PUNCT
ejpam-5884	39	1	ganji	ganji	PROPN
ejpam-5884	39	2	et	et	PROPN
ejpam-5884	39	3	al	al	PROPN
ejpam-5884	39	4	.	.	PUNCT
ejpam-5884	40	1	[	[	X
ejpam-5884	40	2	26	26	NUM
ejpam-5884	40	3	]	]	PUNCT
ejpam-5884	40	4	formulated	formulate	VERB
ejpam-5884	40	5	a	a	DET
ejpam-5884	40	6	nonlinear	nonlinear	ADJ
ejpam-5884	40	7	differential	differential	ADJ
ejpam-5884	40	8	equation	equation	NOUN
ejpam-5884	40	9	for	for	ADP
ejpam-5884	40	10	the	the	DET
ejpam-5884	40	11	cubic	cubic	ADJ
ejpam-5884	40	12	free	free	ADJ
ejpam-5884	40	13	undamped	undampe	VERB
ejpam-5884	40	14	duffing	duffing	NOUN
ejpam-5884	40	15	oscillator	oscillator	NOUN
ejpam-5884	40	16	x′′(t	x′′(t	NOUN
ejpam-5884	40	17	)	)	PUNCT
ejpam-5884	41	1	+	+	CCONJ
ejpam-5884	41	2	αx(t	αx(t	NOUN
ejpam-5884	41	3	)	)	PUNCT
ejpam-5884	41	4	+	+	NUM
ejpam-5884	41	5	βx3(t	βx3(t	NOUN
ejpam-5884	41	6	)	)	PUNCT
ejpam-5884	41	7	=	=	SYM
ejpam-5884	41	8	0	0	NUM
ejpam-5884	41	9	,	,	PUNCT
ejpam-5884	41	10	(	(	PUNCT
ejpam-5884	41	11	4	4	X
ejpam-5884	41	12	)	)	PUNCT
ejpam-5884	41	13	subject	subject	NOUN
ejpam-5884	41	14	to	to	ADP
ejpam-5884	41	15	the	the	DET
ejpam-5884	41	16	initial	initial	ADJ
ejpam-5884	41	17	conditions	condition	NOUN
ejpam-5884	41	18	:	:	PUNCT
ejpam-5884	41	19	x(0	x(0	PROPN
ejpam-5884	41	20	)	)	PUNCT
ejpam-5884	42	1	=	=	SYM
ejpam-5884	43	1	a	a	X
ejpam-5884	43	2	,	,	PUNCT
ejpam-5884	43	3	x′(0	x′(0	X
ejpam-5884	43	4	)	)	PUNCT
ejpam-5884	43	5	=	=	SYM
ejpam-5884	44	1	0	0	X
ejpam-5884	44	2	.	.	PUNCT
ejpam-5884	45	1	(	(	PUNCT
ejpam-5884	45	2	5	5	X
ejpam-5884	45	3	)	)	PUNCT
ejpam-5884	45	4	m.	m.	NOUN
ejpam-5884	45	5	i.	i.	PROPN
ejpam-5884	45	6	syam	syam	PROPN
ejpam-5884	45	7	et	et	PROPN
ejpam-5884	45	8	al	al	PROPN
ejpam-5884	45	9	.	.	PUNCT
ejpam-5884	45	10	/	/	SYM
ejpam-5884	45	11	eur	eur	PROPN
ejpam-5884	45	12	.	.	PUNCT
ejpam-5884	46	1	j.	j.	PROPN
ejpam-5884	46	2	pure	pure	PROPN
ejpam-5884	46	3	appl	appl	PROPN
ejpam-5884	46	4	.	.	PROPN
ejpam-5884	46	5	math	math	PROPN
ejpam-5884	46	6	,	,	PUNCT
ejpam-5884	46	7	18	18	NUM
ejpam-5884	46	8	(	(	PUNCT
ejpam-5884	46	9	2	2	NUM
ejpam-5884	46	10	)	)	PUNCT
ejpam-5884	46	11	(	(	PUNCT
ejpam-5884	46	12	2025	2025	NUM
ejpam-5884	46	13	)	)	PUNCT
ejpam-5884	46	14	,	,	PUNCT
ejpam-5884	46	15	5884	5884	NUM
ejpam-5884	46	16	3	3	NUM
ejpam-5884	46	17	of	of	ADP
ejpam-5884	46	18	18	18	NUM
ejpam-5884	46	19	various	various	ADJ
ejpam-5884	46	20	researchers	researcher	NOUN
ejpam-5884	46	21	have	have	AUX
ejpam-5884	46	22	addressed	address	VERB
ejpam-5884	46	23	this	this	DET
ejpam-5884	46	24	problem	problem	NOUN
ejpam-5884	46	25	numerically	numerically	ADV
ejpam-5884	46	26	.	.	PUNCT
ejpam-5884	47	1	for	for	ADP
ejpam-5884	47	2	instance	instance	NOUN
ejpam-5884	47	3	,	,	PUNCT
ejpam-5884	47	4	he	he	PRON
ejpam-5884	47	5	[	[	X
ejpam-5884	47	6	27	27	NUM
ejpam-5884	47	7	]	]	PUNCT
ejpam-5884	47	8	applied	apply	VERB
ejpam-5884	47	9	the	the	DET
ejpam-5884	47	10	homotopy	homotopy	NOUN
ejpam-5884	47	11	perturbation	perturbation	NOUN
ejpam-5884	47	12	method	method	NOUN
ejpam-5884	47	13	to	to	PART
ejpam-5884	47	14	solve	solve	VERB
ejpam-5884	47	15	the	the	DET
ejpam-5884	47	16	duffing	duffing	NOUN
ejpam-5884	47	17	equation	equation	NOUN
ejpam-5884	47	18	,	,	PUNCT
ejpam-5884	47	19	while	while	SCONJ
ejpam-5884	47	20	beléndez	beléndez	PROPN
ejpam-5884	47	21	et	et	PROPN
ejpam-5884	47	22	al	al	PROPN
ejpam-5884	47	23	.	.	PUNCT
ejpam-5884	48	1	[	[	X
ejpam-5884	48	2	28	28	NUM
ejpam-5884	48	3	]	]	PUNCT
ejpam-5884	48	4	employed	employ	VERB
ejpam-5884	48	5	a	a	DET
ejpam-5884	48	6	modified	modify	VERB
ejpam-5884	48	7	version	version	NOUN
ejpam-5884	48	8	of	of	ADP
ejpam-5884	48	9	the	the	DET
ejpam-5884	48	10	homotopy	homotopy	NOUN
ejpam-5884	48	11	perturbation	perturbation	NOUN
ejpam-5884	48	12	method	method	NOUN
ejpam-5884	48	13	.	.	PUNCT
ejpam-5884	49	1	additionally	additionally	ADV
ejpam-5884	49	2	,	,	PUNCT
ejpam-5884	49	3	ramos	ramos	PROPN
ejpam-5884	49	4	,	,	PUNCT
ejpam-5884	49	5	syam	syam	NOUN
ejpam-5884	49	6	,	,	PUNCT
ejpam-5884	49	7	and	and	CCONJ
ejpam-5884	49	8	wazwaz	wazwaz	NOUN
ejpam-5884	49	9	utilized	utilize	VERB
ejpam-5884	49	10	the	the	DET
ejpam-5884	49	11	variational	variational	ADJ
ejpam-5884	49	12	iteration	iteration	NOUN
ejpam-5884	49	13	method	method	NOUN
ejpam-5884	49	14	[	[	X
ejpam-5884	49	15	29–34	29–34	NOUN
ejpam-5884	49	16	]	]	PUNCT
ejpam-5884	49	17	,	,	PUNCT
ejpam-5884	49	18	and	and	CCONJ
ejpam-5884	49	19	ghosh	ghosh	PROPN
ejpam-5884	49	20	et	et	PROPN
ejpam-5884	49	21	al	al	PROPN
ejpam-5884	49	22	.	.	PUNCT
ejpam-5884	50	1	[	[	X
ejpam-5884	50	2	35	35	NUM
ejpam-5884	50	3	]	]	PUNCT
ejpam-5884	50	4	used	use	VERB
ejpam-5884	50	5	the	the	DET
ejpam-5884	50	6	adomian	adomian	NOUN
ejpam-5884	50	7	decomposition	decomposition	NOUN
ejpam-5884	50	8	method	method	NOUN
ejpam-5884	50	9	.	.	PUNCT
ejpam-5884	51	1	other	other	ADJ
ejpam-5884	51	2	techniques	technique	NOUN
ejpam-5884	51	3	include	include	VERB
ejpam-5884	51	4	the	the	DET
ejpam-5884	51	5	artificial	artificial	ADJ
ejpam-5884	51	6	parameter	parameter	NOUN
ejpam-5884	51	7	decomposition	decomposition	NOUN
ejpam-5884	51	8	method	method	NOUN
ejpam-5884	51	9	by	by	ADP
ejpam-5884	51	10	ramos	ramos	PROPN
ejpam-5884	51	11	[	[	X
ejpam-5884	51	12	36	36	NUM
ejpam-5884	51	13	]	]	PUNCT
ejpam-5884	51	14	and	and	CCONJ
ejpam-5884	51	15	he	he	PRON
ejpam-5884	51	16	’s	’	VERB
ejpam-5884	51	17	parameter	parameter	NOUN
ejpam-5884	51	18	expanding	expand	VERB
ejpam-5884	51	19	method	method	NOUN
ejpam-5884	51	20	by	by	ADP
ejpam-5884	51	21	syam	syam	NOUN
ejpam-5884	52	1	[	[	X
ejpam-5884	52	2	37	37	NUM
ejpam-5884	52	3	]	]	PUNCT
ejpam-5884	52	4	.	.	PUNCT
ejpam-5884	53	1	several	several	ADJ
ejpam-5884	53	2	analytical	analytical	ADJ
ejpam-5884	53	3	methods	method	NOUN
ejpam-5884	53	4	have	have	AUX
ejpam-5884	53	5	been	be	AUX
ejpam-5884	53	6	developed	develop	VERB
ejpam-5884	53	7	for	for	ADP
ejpam-5884	53	8	solving	solve	VERB
ejpam-5884	53	9	duffing	duffing	NOUN
ejpam-5884	53	10	equations	equation	NOUN
ejpam-5884	53	11	.	.	PUNCT
ejpam-5884	54	1	for	for	ADP
ejpam-5884	54	2	weak	weak	ADJ
ejpam-5884	54	3	nonlinearity	nonlinearity	NOUN
ejpam-5884	54	4	,	,	PUNCT
ejpam-5884	54	5	approaches	approach	VERB
ejpam-5884	54	6	such	such	ADJ
ejpam-5884	54	7	as	as	ADP
ejpam-5884	54	8	the	the	DET
ejpam-5884	54	9	method	method	NOUN
ejpam-5884	54	10	of	of	ADP
ejpam-5884	54	11	multiple	multiple	ADJ
ejpam-5884	54	12	scales	scale	NOUN
ejpam-5884	54	13	[	[	X
ejpam-5884	54	14	38	38	NUM
ejpam-5884	54	15	]	]	PUNCT
ejpam-5884	54	16	,	,	PUNCT
ejpam-5884	54	17	the	the	DET
ejpam-5884	54	18	krylov	krylov	NOUN
ejpam-5884	54	19	-	-	PUNCT
ejpam-5884	54	20	bogolubov	bogolubov	PROPN
ejpam-5884	54	21	method	method	NOUN
ejpam-5884	54	22	[	[	X
ejpam-5884	54	23	14	14	NUM
ejpam-5884	54	24	]	]	X
ejpam-5884	54	25	,	,	PUNCT
ejpam-5884	54	26	straightforward	straightforward	ADJ
ejpam-5884	54	27	expansions	expansion	NOUN
ejpam-5884	54	28	[	[	X
ejpam-5884	54	29	39	39	NUM
ejpam-5884	54	30	]	]	PUNCT
ejpam-5884	54	31	,	,	PUNCT
ejpam-5884	54	32	and	and	CCONJ
ejpam-5884	54	33	the	the	DET
ejpam-5884	54	34	lindstedtpoincaré	lindstedtpoincaré	ADJ
ejpam-5884	54	35	method	method	NOUN
ejpam-5884	54	36	[	[	X
ejpam-5884	54	37	39	39	NUM
ejpam-5884	54	38	]	]	PUNCT
ejpam-5884	54	39	have	have	AUX
ejpam-5884	54	40	been	be	AUX
ejpam-5884	54	41	employed	employ	VERB
ejpam-5884	54	42	.	.	PUNCT
ejpam-5884	55	1	strong	strong	ADJ
ejpam-5884	55	2	cubic	cubic	ADJ
ejpam-5884	55	3	nonlinearity	nonlinearity	NOUN
ejpam-5884	55	4	has	have	AUX
ejpam-5884	55	5	also	also	ADV
ejpam-5884	55	6	been	be	AUX
ejpam-5884	55	7	studied	study	VERB
ejpam-5884	55	8	,	,	PUNCT
ejpam-5884	55	9	as	as	SCONJ
ejpam-5884	55	10	discussed	discuss	VERB
ejpam-5884	55	11	in	in	ADP
ejpam-5884	55	12	[	[	X
ejpam-5884	55	13	40	40	NUM
ejpam-5884	55	14	,	,	PUNCT
ejpam-5884	55	15	41	41	NUM
ejpam-5884	55	16	]	]	PUNCT
ejpam-5884	55	17	.	.	PUNCT
ejpam-5884	56	1	in	in	ADP
ejpam-5884	56	2	this	this	DET
ejpam-5884	56	3	paper	paper	NOUN
ejpam-5884	56	4	,	,	PUNCT
ejpam-5884	56	5	we	we	PRON
ejpam-5884	56	6	extend	extend	VERB
ejpam-5884	56	7	the	the	DET
ejpam-5884	56	8	problem	problem	NOUN
ejpam-5884	56	9	defined	define	VERB
ejpam-5884	56	10	in	in	ADP
ejpam-5884	56	11	equations	equation	NOUN
ejpam-5884	56	12	(	(	PUNCT
ejpam-5884	56	13	4)-(5	4)-(5	NUM
ejpam-5884	56	14	)	)	PUNCT
ejpam-5884	56	15	to	to	ADP
ejpam-5884	56	16	the	the	DET
ejpam-5884	56	17	fractional	fractional	ADJ
ejpam-5884	56	18	domain	domain	NOUN
ejpam-5884	56	19	.	.	PUNCT
ejpam-5884	57	1	the	the	DET
ejpam-5884	57	2	generalized	generalized	ADJ
ejpam-5884	57	3	form	form	NOUN
ejpam-5884	57	4	is	be	AUX
ejpam-5884	57	5	given	give	VERB
ejpam-5884	57	6	by	by	ADP
ejpam-5884	57	7	d2αx(t	d2αx(t	NOUN
ejpam-5884	57	8	)	)	PUNCT
ejpam-5884	57	9	+	+	CCONJ
ejpam-5884	57	10	βx(t	βx(t	NUM
ejpam-5884	57	11	)	)	PUNCT
ejpam-5884	58	1	+	+	CCONJ
ejpam-5884	58	2	γx3(t	γx3(t	X
ejpam-5884	58	3	)	)	PUNCT
ejpam-5884	58	4	=	=	SYM
ejpam-5884	58	5	0	0	NUM
ejpam-5884	58	6	,	,	PUNCT
ejpam-5884	58	7	1	1	NUM
ejpam-5884	58	8	2	2	NUM
ejpam-5884	58	9	<	<	X
ejpam-5884	58	10	α	α	PROPN
ejpam-5884	58	11	≤	≤	NUM
ejpam-5884	58	12	1	1	NUM
ejpam-5884	58	13	,	,	PUNCT
ejpam-5884	58	14	0	0	NUM
ejpam-5884	58	15	<	<	X
ejpam-5884	58	16	t	t	X
ejpam-5884	58	17	<	<	X
ejpam-5884	58	18	t	t	PROPN
ejpam-5884	58	19	,	,	PUNCT
ejpam-5884	58	20	(	(	PUNCT
ejpam-5884	58	21	6	6	NUM
ejpam-5884	58	22	)	)	PUNCT
ejpam-5884	58	23	subject	subject	NOUN
ejpam-5884	58	24	to	to	ADP
ejpam-5884	58	25	the	the	DET
ejpam-5884	58	26	initial	initial	ADJ
ejpam-5884	58	27	conditions	condition	NOUN
ejpam-5884	58	28	x(0	x(0	PRON
ejpam-5884	58	29	)	)	PUNCT
ejpam-5884	58	30	=	=	SYM
ejpam-5884	59	1	a	a	PRON
ejpam-5884	59	2	,	,	PUNCT
ejpam-5884	59	3	dαx(0	dαx(0	NOUN
ejpam-5884	59	4	)	)	PUNCT
ejpam-5884	60	1	=	=	PUNCT
ejpam-5884	60	2	0	0	X
ejpam-5884	60	3	.	.	PUNCT
ejpam-5884	61	1	(	(	PUNCT
ejpam-5884	61	2	7	7	X
ejpam-5884	61	3	)	)	PUNCT
ejpam-5884	61	4	here	here	ADV
ejpam-5884	61	5	,	,	PUNCT
ejpam-5884	61	6	the	the	DET
ejpam-5884	61	7	derivative	derivative	ADJ
ejpam-5884	61	8	dα	dα	NOUN
ejpam-5884	61	9	is	be	AUX
ejpam-5884	61	10	interpreted	interpret	VERB
ejpam-5884	61	11	in	in	ADP
ejpam-5884	61	12	the	the	DET
ejpam-5884	61	13	caputo	caputo	PROPN
ejpam-5884	61	14	sense	sense	NOUN
ejpam-5884	61	15	.	.	PUNCT
ejpam-5884	62	1	the	the	DET
ejpam-5884	62	2	operational	operational	ADJ
ejpam-5884	62	3	matrix	matrix	NOUN
ejpam-5884	62	4	method	method	NOUN
ejpam-5884	62	5	(	(	PUNCT
ejpam-5884	62	6	omm	omm	NOUN
ejpam-5884	62	7	)	)	PUNCT
ejpam-5884	62	8	is	be	AUX
ejpam-5884	62	9	a	a	DET
ejpam-5884	62	10	robust	robust	ADJ
ejpam-5884	62	11	numerical	numerical	ADJ
ejpam-5884	62	12	approach	approach	NOUN
ejpam-5884	62	13	widely	widely	ADV
ejpam-5884	62	14	employed	employ	VERB
ejpam-5884	62	15	for	for	ADP
ejpam-5884	62	16	solving	solve	VERB
ejpam-5884	62	17	differential	differential	ADJ
ejpam-5884	62	18	equations	equation	NOUN
ejpam-5884	62	19	,	,	PUNCT
ejpam-5884	62	20	particularly	particularly	ADV
ejpam-5884	62	21	those	those	PRON
ejpam-5884	62	22	arising	arise	VERB
ejpam-5884	62	23	in	in	ADP
ejpam-5884	62	24	engineering	engineering	NOUN
ejpam-5884	62	25	and	and	CCONJ
ejpam-5884	62	26	applied	apply	VERB
ejpam-5884	62	27	mathematics	mathematic	NOUN
ejpam-5884	62	28	[	[	X
ejpam-5884	62	29	42–49	42–49	NUM
ejpam-5884	62	30	]	]	PUNCT
ejpam-5884	62	31	.	.	PUNCT
ejpam-5884	63	1	by	by	ADP
ejpam-5884	63	2	converting	convert	VERB
ejpam-5884	63	3	differential	differential	ADJ
ejpam-5884	63	4	operators	operator	NOUN
ejpam-5884	63	5	into	into	ADP
ejpam-5884	63	6	operational	operational	ADJ
ejpam-5884	63	7	matrices	matrix	NOUN
ejpam-5884	63	8	,	,	PUNCT
ejpam-5884	63	9	omm	omm	PROPN
ejpam-5884	63	10	effectively	effectively	ADV
ejpam-5884	63	11	transforms	transform	VERB
ejpam-5884	63	12	differential	differential	ADJ
ejpam-5884	63	13	equations	equation	NOUN
ejpam-5884	63	14	into	into	ADP
ejpam-5884	63	15	algebraic	algebraic	ADJ
ejpam-5884	63	16	matrix	matrix	NOUN
ejpam-5884	63	17	equations	equation	NOUN
ejpam-5884	63	18	[	[	X
ejpam-5884	63	19	43	43	NUM
ejpam-5884	63	20	,	,	PUNCT
ejpam-5884	63	21	44	44	NUM
ejpam-5884	63	22	]	]	PUNCT
ejpam-5884	63	23	.	.	PUNCT
ejpam-5884	64	1	this	this	DET
ejpam-5884	64	2	transformation	transformation	NOUN
ejpam-5884	64	3	eliminates	eliminate	VERB
ejpam-5884	64	4	the	the	DET
ejpam-5884	64	5	necessity	necessity	NOUN
ejpam-5884	64	6	for	for	ADP
ejpam-5884	64	7	explicit	explicit	ADJ
ejpam-5884	64	8	analytical	analytical	ADJ
ejpam-5884	64	9	integration	integration	NOUN
ejpam-5884	64	10	or	or	CCONJ
ejpam-5884	64	11	symbolic	symbolic	ADJ
ejpam-5884	64	12	computation	computation	NOUN
ejpam-5884	64	13	,	,	PUNCT
ejpam-5884	64	14	streamlining	streamline	VERB
ejpam-5884	64	15	the	the	DET
ejpam-5884	64	16	process	process	NOUN
ejpam-5884	64	17	of	of	ADP
ejpam-5884	64	18	finding	find	VERB
ejpam-5884	64	19	solutions	solution	NOUN
ejpam-5884	64	20	.	.	PUNCT
ejpam-5884	65	1	omm	omm	NOUN
ejpam-5884	65	2	is	be	AUX
ejpam-5884	65	3	particularly	particularly	ADV
ejpam-5884	65	4	advantageous	advantageous	ADJ
ejpam-5884	65	5	in	in	ADP
ejpam-5884	65	6	scenarios	scenario	NOUN
ejpam-5884	65	7	where	where	SCONJ
ejpam-5884	65	8	the	the	DET
ejpam-5884	65	9	solutions	solution	NOUN
ejpam-5884	65	10	can	can	AUX
ejpam-5884	65	11	be	be	AUX
ejpam-5884	65	12	approximated	approximate	VERB
ejpam-5884	65	13	using	use	VERB
ejpam-5884	65	14	polynomials	polynomial	NOUN
ejpam-5884	65	15	or	or	CCONJ
ejpam-5884	65	16	linear	linear	ADJ
ejpam-5884	65	17	combinations	combination	NOUN
ejpam-5884	65	18	of	of	ADP
ejpam-5884	65	19	polynomial	polynomial	ADJ
ejpam-5884	65	20	functions	function	NOUN
ejpam-5884	65	21	.	.	PUNCT
ejpam-5884	66	1	it	it	PRON
ejpam-5884	66	2	has	have	AUX
ejpam-5884	66	3	found	find	VERB
ejpam-5884	66	4	extensive	extensive	ADJ
ejpam-5884	66	5	applications	application	NOUN
ejpam-5884	66	6	in	in	ADP
ejpam-5884	66	7	fields	field	NOUN
ejpam-5884	66	8	such	such	ADJ
ejpam-5884	66	9	as	as	ADP
ejpam-5884	66	10	control	control	NOUN
ejpam-5884	66	11	system	system	NOUN
ejpam-5884	66	12	analysis	analysis	NOUN
ejpam-5884	66	13	,	,	PUNCT
ejpam-5884	66	14	structural	structural	ADJ
ejpam-5884	66	15	dynamics	dynamic	NOUN
ejpam-5884	66	16	,	,	PUNCT
ejpam-5884	66	17	heat	heat	NOUN
ejpam-5884	66	18	transfer	transfer	NOUN
ejpam-5884	66	19	,	,	PUNCT
ejpam-5884	66	20	and	and	CCONJ
ejpam-5884	66	21	fluid	fluid	ADJ
ejpam-5884	66	22	mechanics	mechanic	NOUN
ejpam-5884	66	23	.	.	PUNCT
ejpam-5884	67	1	the	the	DET
ejpam-5884	67	2	method	method	NOUN
ejpam-5884	67	3	’s	’s	PART
ejpam-5884	67	4	versatility	versatility	NOUN
ejpam-5884	67	5	and	and	CCONJ
ejpam-5884	67	6	computational	computational	ADJ
ejpam-5884	67	7	efficiency	efficiency	NOUN
ejpam-5884	67	8	have	have	AUX
ejpam-5884	67	9	made	make	VERB
ejpam-5884	67	10	it	it	PRON
ejpam-5884	67	11	an	an	DET
ejpam-5884	67	12	essential	essential	ADJ
ejpam-5884	67	13	tool	tool	NOUN
ejpam-5884	67	14	in	in	ADP
ejpam-5884	67	15	addressing	address	VERB
ejpam-5884	67	16	a	a	DET
ejpam-5884	67	17	diverse	diverse	ADJ
ejpam-5884	67	18	array	array	NOUN
ejpam-5884	67	19	of	of	ADP
ejpam-5884	67	20	problems	problem	NOUN
ejpam-5884	67	21	across	across	ADP
ejpam-5884	67	22	scientific	scientific	ADJ
ejpam-5884	67	23	and	and	CCONJ
ejpam-5884	67	24	engineering	engineering	NOUN
ejpam-5884	67	25	disciplines	discipline	NOUN
ejpam-5884	67	26	.	.	PUNCT
ejpam-5884	68	1	the	the	DET
ejpam-5884	68	2	effectiveness	effectiveness	NOUN
ejpam-5884	68	3	of	of	ADP
ejpam-5884	68	4	the	the	DET
ejpam-5884	68	5	operational	operational	ADJ
ejpam-5884	68	6	matrix	matrix	NOUN
ejpam-5884	68	7	method	method	NOUN
ejpam-5884	68	8	lies	lie	VERB
ejpam-5884	68	9	in	in	ADP
ejpam-5884	68	10	its	its	PRON
ejpam-5884	68	11	ability	ability	NOUN
ejpam-5884	68	12	to	to	PART
ejpam-5884	68	13	accurately	accurately	ADV
ejpam-5884	68	14	approximate	approximate	VERB
ejpam-5884	68	15	solutions	solution	NOUN
ejpam-5884	68	16	by	by	ADP
ejpam-5884	68	17	converting	convert	VERB
ejpam-5884	68	18	differential	differential	ADJ
ejpam-5884	68	19	or	or	CCONJ
ejpam-5884	68	20	integral	integral	ADJ
ejpam-5884	68	21	equations	equation	NOUN
ejpam-5884	68	22	into	into	ADP
ejpam-5884	68	23	a	a	DET
ejpam-5884	68	24	system	system	NOUN
ejpam-5884	68	25	of	of	ADP
ejpam-5884	68	26	algebraic	algebraic	ADJ
ejpam-5884	68	27	equations	equation	NOUN
ejpam-5884	68	28	.	.	PUNCT
ejpam-5884	69	1	this	this	PRON
ejpam-5884	69	2	is	be	AUX
ejpam-5884	69	3	achieved	achieve	VERB
ejpam-5884	69	4	through	through	ADP
ejpam-5884	69	5	the	the	DET
ejpam-5884	69	6	use	use	NOUN
ejpam-5884	69	7	of	of	ADP
ejpam-5884	69	8	operational	operational	ADJ
ejpam-5884	69	9	matrices	matrix	NOUN
ejpam-5884	69	10	,	,	PUNCT
ejpam-5884	69	11	which	which	PRON
ejpam-5884	69	12	efficiently	efficiently	ADV
ejpam-5884	69	13	handle	handle	VERB
ejpam-5884	69	14	the	the	DET
ejpam-5884	69	15	underlying	underlying	ADJ
ejpam-5884	69	16	mathematical	mathematical	ADJ
ejpam-5884	69	17	operations	operation	NOUN
ejpam-5884	69	18	.	.	PUNCT
ejpam-5884	70	1	the	the	DET
ejpam-5884	70	2	method	method	NOUN
ejpam-5884	70	3	is	be	AUX
ejpam-5884	70	4	especially	especially	ADV
ejpam-5884	70	5	well	well	ADV
ejpam-5884	70	6	-	-	PUNCT
ejpam-5884	70	7	suited	suit	VERB
ejpam-5884	70	8	for	for	ADP
ejpam-5884	70	9	problems	problem	NOUN
ejpam-5884	70	10	where	where	SCONJ
ejpam-5884	70	11	solutions	solution	NOUN
ejpam-5884	70	12	can	can	AUX
ejpam-5884	70	13	either	either	CCONJ
ejpam-5884	70	14	be	be	AUX
ejpam-5884	70	15	directly	directly	ADV
ejpam-5884	70	16	expressed	express	VERB
ejpam-5884	70	17	in	in	ADP
ejpam-5884	70	18	terms	term	NOUN
ejpam-5884	70	19	of	of	ADP
ejpam-5884	70	20	polynomial	polynomial	ADJ
ejpam-5884	70	21	functions	function	NOUN
ejpam-5884	70	22	or	or	CCONJ
ejpam-5884	70	23	approximated	approximate	VERB
ejpam-5884	70	24	as	as	ADP
ejpam-5884	70	25	linear	linear	ADJ
ejpam-5884	70	26	combinations	combination	NOUN
ejpam-5884	70	27	of	of	ADP
ejpam-5884	70	28	such	such	ADJ
ejpam-5884	70	29	functions	function	NOUN
ejpam-5884	70	30	.	.	PUNCT
ejpam-5884	71	1	the	the	DET
ejpam-5884	71	2	omm	omm	PROPN
ejpam-5884	71	3	approach	approach	NOUN
ejpam-5884	71	4	simplifies	simplify	VERB
ejpam-5884	71	5	the	the	DET
ejpam-5884	71	6	computational	computational	ADJ
ejpam-5884	71	7	process	process	NOUN
ejpam-5884	71	8	,	,	PUNCT
ejpam-5884	71	9	reduces	reduce	VERB
ejpam-5884	71	10	computational	computational	ADJ
ejpam-5884	71	11	overhead	overhead	NOUN
ejpam-5884	71	12	,	,	PUNCT
ejpam-5884	71	13	and	and	CCONJ
ejpam-5884	71	14	enhances	enhance	VERB
ejpam-5884	71	15	the	the	DET
ejpam-5884	71	16	accuracy	accuracy	NOUN
ejpam-5884	71	17	of	of	ADP
ejpam-5884	71	18	the	the	DET
ejpam-5884	71	19	results	result	NOUN
ejpam-5884	71	20	.	.	PUNCT
ejpam-5884	72	1	these	these	DET
ejpam-5884	72	2	advantages	advantage	NOUN
ejpam-5884	72	3	have	have	AUX
ejpam-5884	72	4	made	make	VERB
ejpam-5884	72	5	it	it	PRON
ejpam-5884	72	6	a	a	DET
ejpam-5884	72	7	preferred	preferred	ADJ
ejpam-5884	72	8	technique	technique	NOUN
ejpam-5884	72	9	in	in	ADP
ejpam-5884	72	10	numerous	numerous	ADJ
ejpam-5884	72	11	scientific	scientific	ADJ
ejpam-5884	72	12	and	and	CCONJ
ejpam-5884	72	13	engineering	engineering	NOUN
ejpam-5884	72	14	domains	domain	NOUN
ejpam-5884	72	15	.	.	PUNCT
ejpam-5884	73	1	applications	application	NOUN
ejpam-5884	73	2	of	of	ADP
ejpam-5884	73	3	omm	omm	NOUN
ejpam-5884	73	4	include	include	VERB
ejpam-5884	73	5	,	,	PUNCT
ejpam-5884	73	6	but	but	CCONJ
ejpam-5884	73	7	are	be	AUX
ejpam-5884	73	8	not	not	PART
ejpam-5884	73	9	limited	limit	VERB
ejpam-5884	73	10	to	to	ADP
ejpam-5884	73	11	,	,	PUNCT
ejpam-5884	73	12	control	control	NOUN
ejpam-5884	73	13	system	system	NOUN
ejpam-5884	73	14	design	design	NOUN
ejpam-5884	73	15	,	,	PUNCT
ejpam-5884	73	16	modeling	modeling	NOUN
ejpam-5884	73	17	of	of	ADP
ejpam-5884	73	18	structural	structural	ADJ
ejpam-5884	73	19	dynamics	dynamic	NOUN
ejpam-5884	73	20	,	,	PUNCT
ejpam-5884	73	21	heat	heat	NOUN
ejpam-5884	73	22	conduction	conduction	NOUN
ejpam-5884	73	23	problems	problem	NOUN
ejpam-5884	73	24	,	,	PUNCT
ejpam-5884	73	25	and	and	CCONJ
ejpam-5884	73	26	fluid	fluid	ADJ
ejpam-5884	73	27	flow	flow	NOUN
ejpam-5884	73	28	analysis	analysis	NOUN
ejpam-5884	73	29	.	.	PUNCT
ejpam-5884	74	1	the	the	DET
ejpam-5884	74	2	extensive	extensive	ADJ
ejpam-5884	74	3	use	use	NOUN
ejpam-5884	74	4	of	of	ADP
ejpam-5884	74	5	omm	omm	NOUN
ejpam-5884	74	6	in	in	ADP
ejpam-5884	74	7	these	these	DET
ejpam-5884	74	8	areas	area	NOUN
ejpam-5884	74	9	highlights	highlight	VERB
ejpam-5884	74	10	its	its	PRON
ejpam-5884	74	11	adaptability	adaptability	NOUN
ejpam-5884	74	12	and	and	CCONJ
ejpam-5884	74	13	robustness	robustness	NOUN
ejpam-5884	74	14	in	in	ADP
ejpam-5884	74	15	solving	solve	VERB
ejpam-5884	74	16	a	a	DET
ejpam-5884	74	17	broad	broad	ADJ
ejpam-5884	74	18	spectrum	spectrum	NOUN
ejpam-5884	74	19	of	of	ADP
ejpam-5884	74	20	mathematical	mathematical	ADJ
ejpam-5884	74	21	and	and	CCONJ
ejpam-5884	74	22	physical	physical	ADJ
ejpam-5884	74	23	problems	problem	NOUN
ejpam-5884	74	24	.	.	PUNCT
ejpam-5884	75	1	the	the	DET
ejpam-5884	75	2	m.	m.	NOUN
ejpam-5884	75	3	i.	i.	PROPN
ejpam-5884	75	4	syam	syam	PROPN
ejpam-5884	75	5	et	et	PROPN
ejpam-5884	75	6	al	al	PROPN
ejpam-5884	75	7	.	.	PUNCT
ejpam-5884	75	8	/	/	SYM
ejpam-5884	75	9	eur	eur	PROPN
ejpam-5884	75	10	.	.	PUNCT
ejpam-5884	76	1	j.	j.	PROPN
ejpam-5884	76	2	pure	pure	PROPN
ejpam-5884	76	3	appl	appl	PROPN
ejpam-5884	76	4	.	.	PROPN
ejpam-5884	76	5	math	math	PROPN
ejpam-5884	76	6	,	,	PUNCT
ejpam-5884	76	7	18	18	NUM
ejpam-5884	76	8	(	(	PUNCT
ejpam-5884	76	9	2	2	NUM
ejpam-5884	76	10	)	)	PUNCT
ejpam-5884	76	11	(	(	PUNCT
ejpam-5884	76	12	2025	2025	NUM
ejpam-5884	76	13	)	)	PUNCT
ejpam-5884	76	14	,	,	PUNCT
ejpam-5884	76	15	5884	5884	NUM
ejpam-5884	76	16	4	4	NUM
ejpam-5884	76	17	of	of	ADP
ejpam-5884	76	18	18	18	NUM
ejpam-5884	76	19	operational	operational	ADJ
ejpam-5884	76	20	matrix	matrix	NOUN
ejpam-5884	76	21	method	method	NOUN
ejpam-5884	76	22	stands	stand	VERB
ejpam-5884	76	23	out	out	ADP
ejpam-5884	76	24	as	as	ADP
ejpam-5884	76	25	a	a	DET
ejpam-5884	76	26	highly	highly	ADV
ejpam-5884	76	27	efficient	efficient	ADJ
ejpam-5884	76	28	numerical	numerical	ADJ
ejpam-5884	76	29	technique	technique	NOUN
ejpam-5884	76	30	for	for	ADP
ejpam-5884	76	31	solving	solve	VERB
ejpam-5884	76	32	both	both	CCONJ
ejpam-5884	76	33	linear	linear	ADJ
ejpam-5884	76	34	and	and	CCONJ
ejpam-5884	76	35	nonlinear	nonlinear	ADJ
ejpam-5884	76	36	differential	differential	ADJ
ejpam-5884	76	37	equations	equation	NOUN
ejpam-5884	76	38	,	,	PUNCT
ejpam-5884	76	39	particularly	particularly	ADV
ejpam-5884	76	40	those	those	PRON
ejpam-5884	76	41	involving	involve	VERB
ejpam-5884	76	42	polynomial	polynomial	ADJ
ejpam-5884	76	43	forms	form	NOUN
ejpam-5884	76	44	,	,	PUNCT
ejpam-5884	76	45	[	[	X
ejpam-5884	76	46	45	45	NUM
ejpam-5884	76	47	,	,	PUNCT
ejpam-5884	76	48	50–56	50–56	NUM
ejpam-5884	76	49	]	]	PUNCT
ejpam-5884	76	50	.	.	PUNCT
ejpam-5884	77	1	its	its	PRON
ejpam-5884	77	2	ability	ability	NOUN
ejpam-5884	77	3	to	to	PART
ejpam-5884	77	4	transform	transform	VERB
ejpam-5884	77	5	complex	complex	ADJ
ejpam-5884	77	6	mathematical	mathematical	ADJ
ejpam-5884	77	7	problems	problem	NOUN
ejpam-5884	77	8	into	into	ADP
ejpam-5884	77	9	simpler	simple	ADJ
ejpam-5884	77	10	algebraic	algebraic	ADJ
ejpam-5884	77	11	systems	system	NOUN
ejpam-5884	77	12	has	have	AUX
ejpam-5884	77	13	solidified	solidify	VERB
ejpam-5884	77	14	its	its	PRON
ejpam-5884	77	15	position	position	NOUN
ejpam-5884	77	16	as	as	ADP
ejpam-5884	77	17	a	a	DET
ejpam-5884	77	18	valuable	valuable	ADJ
ejpam-5884	77	19	tool	tool	NOUN
ejpam-5884	77	20	in	in	ADP
ejpam-5884	77	21	applied	applied	ADJ
ejpam-5884	77	22	mathematics	mathematic	NOUN
ejpam-5884	77	23	and	and	CCONJ
ejpam-5884	77	24	engineering	engineering	NOUN
ejpam-5884	77	25	.	.	PUNCT
ejpam-5884	78	1	the	the	DET
ejpam-5884	78	2	references	reference	NOUN
ejpam-5884	78	3	[	[	X
ejpam-5884	78	4	50–53	50–53	X
ejpam-5884	78	5	]	]	PUNCT
ejpam-5884	78	6	provide	provide	VERB
ejpam-5884	78	7	further	further	ADJ
ejpam-5884	78	8	insights	insight	NOUN
ejpam-5884	78	9	into	into	ADP
ejpam-5884	78	10	the	the	DET
ejpam-5884	78	11	diverse	diverse	ADJ
ejpam-5884	78	12	applications	application	NOUN
ejpam-5884	78	13	of	of	ADP
ejpam-5884	78	14	omm	omm	PROPN
ejpam-5884	78	15	,	,	PUNCT
ejpam-5884	78	16	showcasing	showcase	VERB
ejpam-5884	78	17	its	its	PRON
ejpam-5884	78	18	reliability	reliability	NOUN
ejpam-5884	78	19	and	and	CCONJ
ejpam-5884	78	20	effectiveness	effectiveness	NOUN
ejpam-5884	78	21	in	in	ADP
ejpam-5884	78	22	tackling	tackle	VERB
ejpam-5884	78	23	real	real	ADJ
ejpam-5884	78	24	-	-	PUNCT
ejpam-5884	78	25	world	world	NOUN
ejpam-5884	78	26	challenges	challenge	NOUN
ejpam-5884	78	27	.	.	PUNCT
ejpam-5884	79	1	the	the	DET
ejpam-5884	79	2	organization	organization	NOUN
ejpam-5884	79	3	of	of	ADP
ejpam-5884	79	4	this	this	DET
ejpam-5884	79	5	paper	paper	NOUN
ejpam-5884	79	6	is	be	AUX
ejpam-5884	79	7	as	as	SCONJ
ejpam-5884	79	8	follows	follow	VERB
ejpam-5884	79	9	.	.	PUNCT
ejpam-5884	80	1	section	section	NOUN
ejpam-5884	80	2	2	2	NUM
ejpam-5884	80	3	outlines	outline	VERB
ejpam-5884	80	4	essential	essential	ADJ
ejpam-5884	80	5	definitions	definition	NOUN
ejpam-5884	80	6	and	and	CCONJ
ejpam-5884	80	7	lemmas	lemma	NOUN
ejpam-5884	80	8	that	that	PRON
ejpam-5884	80	9	serve	serve	VERB
ejpam-5884	80	10	as	as	ADP
ejpam-5884	80	11	the	the	DET
ejpam-5884	80	12	foundation	foundation	NOUN
ejpam-5884	80	13	for	for	ADP
ejpam-5884	80	14	the	the	DET
ejpam-5884	80	15	subsequent	subsequent	ADJ
ejpam-5884	80	16	analysis	analysis	NOUN
ejpam-5884	80	17	.	.	PUNCT
ejpam-5884	81	1	in	in	ADP
ejpam-5884	81	2	section	section	NOUN
ejpam-5884	81	3	3	3	NUM
ejpam-5884	81	4	,	,	PUNCT
ejpam-5884	81	5	we	we	PRON
ejpam-5884	81	6	present	present	VERB
ejpam-5884	81	7	the	the	DET
ejpam-5884	81	8	modified	modified	ADJ
ejpam-5884	81	9	iterative	iterative	NOUN
ejpam-5884	81	10	formulation	formulation	NOUN
ejpam-5884	81	11	of	of	ADP
ejpam-5884	81	12	the	the	DET
ejpam-5884	81	13	operational	operational	ADJ
ejpam-5884	81	14	matrix	matrix	NOUN
ejpam-5884	81	15	method	method	NOUN
ejpam-5884	81	16	(	(	PUNCT
ejpam-5884	81	17	omm	omm	PROPN
ejpam-5884	81	18	)	)	PUNCT
ejpam-5884	81	19	,	,	PUNCT
ejpam-5884	81	20	detailing	detail	VERB
ejpam-5884	81	21	its	its	PRON
ejpam-5884	81	22	theoretical	theoretical	ADJ
ejpam-5884	81	23	framework	framework	NOUN
ejpam-5884	81	24	and	and	CCONJ
ejpam-5884	81	25	implementation	implementation	NOUN
ejpam-5884	81	26	.	.	PUNCT
ejpam-5884	82	1	section	section	NOUN
ejpam-5884	82	2	4	4	NUM
ejpam-5884	82	3	is	be	AUX
ejpam-5884	82	4	devoted	devote	VERB
ejpam-5884	82	5	to	to	ADP
ejpam-5884	82	6	establishing	establish	VERB
ejpam-5884	82	7	key	key	ADJ
ejpam-5884	82	8	theoretical	theoretical	ADJ
ejpam-5884	82	9	findings	finding	NOUN
ejpam-5884	82	10	,	,	PUNCT
ejpam-5884	82	11	including	include	VERB
ejpam-5884	82	12	proofs	proof	NOUN
ejpam-5884	82	13	for	for	ADP
ejpam-5884	82	14	the	the	DET
ejpam-5884	82	15	existence	existence	NOUN
ejpam-5884	82	16	and	and	CCONJ
ejpam-5884	82	17	uniqueness	uniqueness	NOUN
ejpam-5884	82	18	of	of	ADP
ejpam-5884	82	19	solutions	solution	NOUN
ejpam-5884	82	20	,	,	PUNCT
ejpam-5884	82	21	error	error	NOUN
ejpam-5884	82	22	estimation	estimation	NOUN
ejpam-5884	82	23	,	,	PUNCT
ejpam-5884	82	24	and	and	CCONJ
ejpam-5884	82	25	a	a	DET
ejpam-5884	82	26	comprehensive	comprehensive	ADJ
ejpam-5884	82	27	convergence	convergence	NOUN
ejpam-5884	82	28	analysis	analysis	NOUN
ejpam-5884	82	29	.	.	PUNCT
ejpam-5884	83	1	in	in	ADP
ejpam-5884	83	2	section	section	NOUN
ejpam-5884	83	3	5	5	NUM
ejpam-5884	83	4	,	,	PUNCT
ejpam-5884	83	5	we	we	PRON
ejpam-5884	83	6	illustrate	illustrate	VERB
ejpam-5884	83	7	the	the	DET
ejpam-5884	83	8	practical	practical	ADJ
ejpam-5884	83	9	applicability	applicability	NOUN
ejpam-5884	83	10	of	of	ADP
ejpam-5884	83	11	the	the	DET
ejpam-5884	83	12	proposed	propose	VERB
ejpam-5884	83	13	method	method	NOUN
ejpam-5884	83	14	through	through	ADP
ejpam-5884	83	15	three	three	NUM
ejpam-5884	83	16	numerical	numerical	ADJ
ejpam-5884	83	17	examples	example	NOUN
ejpam-5884	83	18	,	,	PUNCT
ejpam-5884	83	19	demonstrating	demonstrate	VERB
ejpam-5884	83	20	its	its	PRON
ejpam-5884	83	21	convergence	convergence	NOUN
ejpam-5884	83	22	to	to	ADP
ejpam-5884	83	23	the	the	DET
ejpam-5884	83	24	unique	unique	ADJ
ejpam-5884	83	25	solution	solution	NOUN
ejpam-5884	83	26	of	of	ADP
ejpam-5884	83	27	problem	problem	NOUN
ejpam-5884	83	28	(	(	PUNCT
ejpam-5884	83	29	6)-(7	6)-(7	NOUN
ejpam-5884	83	30	)	)	PUNCT
ejpam-5884	83	31	.	.	PUNCT
ejpam-5884	84	1	the	the	DET
ejpam-5884	84	2	paper	paper	NOUN
ejpam-5884	84	3	concludes	conclude	VERB
ejpam-5884	84	4	with	with	ADP
ejpam-5884	84	5	section	section	NOUN
ejpam-5884	84	6	6	6	NUM
ejpam-5884	84	7	,	,	PUNCT
ejpam-5884	84	8	where	where	SCONJ
ejpam-5884	84	9	we	we	PRON
ejpam-5884	84	10	provide	provide	VERB
ejpam-5884	84	11	a	a	DET
ejpam-5884	84	12	summary	summary	NOUN
ejpam-5884	84	13	of	of	ADP
ejpam-5884	84	14	our	our	PRON
ejpam-5884	84	15	findings	finding	NOUN
ejpam-5884	84	16	and	and	CCONJ
ejpam-5884	84	17	offer	offer	VERB
ejpam-5884	84	18	remarks	remark	NOUN
ejpam-5884	84	19	on	on	ADP
ejpam-5884	84	20	potential	potential	ADJ
ejpam-5884	84	21	future	future	ADJ
ejpam-5884	84	22	research	research	NOUN
ejpam-5884	84	23	directions	direction	NOUN
ejpam-5884	84	24	.	.	PUNCT
ejpam-5884	85	1	2	2	X
ejpam-5884	85	2	.	.	X
ejpam-5884	85	3	preliminarily	preliminarily	ADV
ejpam-5884	85	4	this	this	DET
ejpam-5884	85	5	section	section	NOUN
ejpam-5884	85	6	presents	present	VERB
ejpam-5884	85	7	several	several	ADJ
ejpam-5884	85	8	essential	essential	ADJ
ejpam-5884	85	9	definitions	definition	NOUN
ejpam-5884	85	10	and	and	CCONJ
ejpam-5884	85	11	results	result	NOUN
ejpam-5884	85	12	that	that	PRON
ejpam-5884	85	13	are	be	AUX
ejpam-5884	85	14	integral	integral	ADJ
ejpam-5884	85	15	to	to	ADP
ejpam-5884	85	16	the	the	DET
ejpam-5884	85	17	analysis	analysis	NOUN
ejpam-5884	85	18	within	within	ADP
ejpam-5884	85	19	this	this	DET
ejpam-5884	85	20	paper	paper	NOUN
ejpam-5884	85	21	.	.	PUNCT
ejpam-5884	86	1	definition	definition	NOUN
ejpam-5884	86	2	1	1	NUM
ejpam-5884	86	3	.	.	PUNCT
ejpam-5884	87	1	[	[	X
ejpam-5884	87	2	1	1	X
ejpam-5884	87	3	]	]	PUNCT
ejpam-5884	87	4	for	for	ADP
ejpam-5884	87	5	α	α	PRON
ejpam-5884	87	6	∈	∈	PROPN
ejpam-5884	87	7	(	(	PUNCT
ejpam-5884	87	8	0	0	NUM
ejpam-5884	87	9	,	,	PUNCT
ejpam-5884	87	10	1	1	NUM
ejpam-5884	87	11	)	)	PUNCT
ejpam-5884	87	12	and	and	CCONJ
ejpam-5884	87	13	t	t	X
ejpam-5884	87	14	>	>	X
ejpam-5884	87	15	0	0	PROPN
ejpam-5884	87	16	,	,	PUNCT
ejpam-5884	87	17	the	the	DET
ejpam-5884	87	18	caputo	caputo	PROPN
ejpam-5884	87	19	derivative	derivative	PROPN
ejpam-5884	87	20	(	(	PUNCT
ejpam-5884	87	21	cd	cd	PROPN
ejpam-5884	87	22	)	)	PUNCT
ejpam-5884	87	23	of	of	ADP
ejpam-5884	87	24	the	the	DET
ejpam-5884	87	25	function	function	NOUN
ejpam-5884	87	26	x(t	x(t	PROPN
ejpam-5884	87	27	)	)	PUNCT
ejpam-5884	87	28	is	be	AUX
ejpam-5884	87	29	defined	define	VERB
ejpam-5884	87	30	as	as	ADP
ejpam-5884	87	31	dαx(t	dαx(t	PROPN
ejpam-5884	87	32	)	)	PUNCT
ejpam-5884	87	33	=	=	SYM
ejpam-5884	88	1	1	1	NUM
ejpam-5884	88	2	γ(1−	γ(1−	NOUN
ejpam-5884	88	3	α	α	NUM
ejpam-5884	88	4	)	)	PUNCT
ejpam-5884	88	5	∫	∫	PROPN
ejpam-5884	88	6	t	t	PROPN
ejpam-5884	88	7	0	0	NUM
ejpam-5884	88	8	(	(	PUNCT
ejpam-5884	88	9	t−	t−	PROPN
ejpam-5884	88	10	s)−αx′(s	s)−αx′(s	PROPN
ejpam-5884	88	11	)	)	PUNCT
ejpam-5884	88	12	ds	ds	PROPN
ejpam-5884	88	13	,	,	PUNCT
ejpam-5884	88	14	(	(	PUNCT
ejpam-5884	88	15	8)	8)	NUM
ejpam-5884	88	16	while	while	SCONJ
ejpam-5884	88	17	the	the	DET
ejpam-5884	88	18	fractional	fractional	ADJ
ejpam-5884	88	19	integral	integral	ADJ
ejpam-5884	88	20	(	(	PUNCT
ejpam-5884	88	21	fi	fi	NOUN
ejpam-5884	88	22	)	)	PUNCT
ejpam-5884	88	23	operator	operator	NOUN
ejpam-5884	88	24	is	be	AUX
ejpam-5884	88	25	expressed	express	VERB
ejpam-5884	88	26	as	as	ADP
ejpam-5884	88	27	:	:	PUNCT
ejpam-5884	88	28	iαx(t	iαx(t	PROPN
ejpam-5884	88	29	)	)	PUNCT
ejpam-5884	88	30	=	=	SYM
ejpam-5884	88	31	1	1	NUM
ejpam-5884	88	32	γ(α	γ(α	NOUN
ejpam-5884	88	33	)	)	PUNCT
ejpam-5884	88	34	∫	∫	PROPN
ejpam-5884	89	1	t	t	PROPN
ejpam-5884	89	2	0	0	NUM
ejpam-5884	89	3	(	(	PUNCT
ejpam-5884	89	4	t−	t−	PROPN
ejpam-5884	89	5	s)α−1x(s	s)α−1x(s	PROPN
ejpam-5884	89	6	)	)	PUNCT
ejpam-5884	89	7	ds	ds	PROPN
ejpam-5884	89	8	.	.	PUNCT
ejpam-5884	89	9	(	(	PUNCT
ejpam-5884	89	10	9	9	X
ejpam-5884	89	11	)	)	PUNCT
ejpam-5884	89	12	the	the	DET
ejpam-5884	89	13	subsequent	subsequent	ADJ
ejpam-5884	89	14	lemma	lemma	PROPN
ejpam-5884	89	15	outlines	outline	VERB
ejpam-5884	89	16	key	key	ADJ
ejpam-5884	89	17	properties	property	NOUN
ejpam-5884	89	18	of	of	ADP
ejpam-5884	89	19	the	the	DET
ejpam-5884	89	20	caputo	caputo	PROPN
ejpam-5884	89	21	derivative	derivative	PROPN
ejpam-5884	89	22	and	and	CCONJ
ejpam-5884	89	23	the	the	DET
ejpam-5884	89	24	fractional	fractional	ADJ
ejpam-5884	89	25	integral	integral	NOUN
ejpam-5884	89	26	.	.	PUNCT
ejpam-5884	90	1	lemma	lemma	PROPN
ejpam-5884	90	2	1	1	NUM
ejpam-5884	90	3	.	.	PUNCT
ejpam-5884	91	1	[	[	X
ejpam-5884	91	2	1	1	X
ejpam-5884	91	3	]	]	PUNCT
ejpam-5884	91	4	for	for	ADP
ejpam-5884	91	5	α	α	PRON
ejpam-5884	91	6	∈	∈	PROPN
ejpam-5884	91	7	(	(	PUNCT
ejpam-5884	91	8	0	0	NUM
ejpam-5884	91	9	,	,	PUNCT
ejpam-5884	91	10	1	1	NUM
ejpam-5884	91	11	)	)	PUNCT
ejpam-5884	91	12	and	and	CCONJ
ejpam-5884	91	13	x(t	x(t	PROPN
ejpam-5884	91	14	)	)	PUNCT
ejpam-5884	91	15	∈	∈	PROPN
ejpam-5884	91	16	c[0	c[0	PROPN
ejpam-5884	91	17	,	,	PUNCT
ejpam-5884	91	18	t	t	X
ejpam-5884	91	19	]	]	PUNCT
ejpam-5884	91	20	,	,	PUNCT
ejpam-5884	91	21	the	the	DET
ejpam-5884	91	22	following	follow	VERB
ejpam-5884	91	23	relations	relation	NOUN
ejpam-5884	91	24	hold	hold	VERB
ejpam-5884	91	25	:	:	PUNCT
ejpam-5884	91	26	iαdαx(t	iαdαx(t	VERB
ejpam-5884	91	27	)	)	PUNCT
ejpam-5884	91	28	=	=	SYM
ejpam-5884	92	1	x(t)−	x(t)−	PROPN
ejpam-5884	92	2	x(0	x(0	PROPN
ejpam-5884	92	3	)	)	PUNCT
ejpam-5884	92	4	,	,	PUNCT
ejpam-5884	92	5	(	(	PUNCT
ejpam-5884	92	6	10	10	X
ejpam-5884	92	7	)	)	PUNCT
ejpam-5884	92	8	dαiαx(t	dαiαx(t	NOUN
ejpam-5884	92	9	)	)	PUNCT
ejpam-5884	92	10	=	=	SYM
ejpam-5884	92	11	x(t	x(t	PROPN
ejpam-5884	92	12	)	)	PUNCT
ejpam-5884	92	13	.	.	PUNCT
ejpam-5884	93	1	(	(	PUNCT
ejpam-5884	93	2	11	11	NUM
ejpam-5884	93	3	)	)	PUNCT
ejpam-5884	93	4	in	in	ADP
ejpam-5884	93	5	this	this	DET
ejpam-5884	93	6	paper	paper	NOUN
ejpam-5884	93	7	,	,	PUNCT
ejpam-5884	93	8	we	we	PRON
ejpam-5884	93	9	utilize	utilize	VERB
ejpam-5884	93	10	the	the	DET
ejpam-5884	93	11	concept	concept	NOUN
ejpam-5884	93	12	of	of	ADP
ejpam-5884	93	13	the	the	DET
ejpam-5884	93	14	sequential	sequential	ADJ
ejpam-5884	93	15	caputo	caputo	PROPN
ejpam-5884	93	16	derivative	derivative	NOUN
ejpam-5884	93	17	,	,	PUNCT
ejpam-5884	93	18	defined	define	VERB
ejpam-5884	93	19	as	as	ADP
ejpam-5884	93	20	follows	follow	VERB
ejpam-5884	93	21	.	.	PUNCT
ejpam-5884	94	1	definition	definition	NOUN
ejpam-5884	94	2	2	2	NUM
ejpam-5884	94	3	.	.	PUNCT
ejpam-5884	95	1	[	[	X
ejpam-5884	95	2	43	43	NUM
ejpam-5884	95	3	]	]	PUNCT
ejpam-5884	95	4	let	let	VERB
ejpam-5884	95	5	α	α	PRON
ejpam-5884	95	6	∈	∈	PROPN
ejpam-5884	95	7	(	(	PUNCT
ejpam-5884	95	8	0	0	NUM
ejpam-5884	95	9	,	,	PUNCT
ejpam-5884	95	10	1	1	NUM
ejpam-5884	95	11	)	)	PUNCT
ejpam-5884	95	12	,	,	PUNCT
ejpam-5884	95	13	and	and	CCONJ
ejpam-5884	95	14	for	for	ADP
ejpam-5884	95	15	a	a	DET
ejpam-5884	95	16	given	give	VERB
ejpam-5884	95	17	function	function	NOUN
ejpam-5884	95	18	x(t	x(t	PROPN
ejpam-5884	95	19	)	)	PUNCT
ejpam-5884	95	20	,	,	PUNCT
ejpam-5884	95	21	the	the	DET
ejpam-5884	95	22	sequential	sequential	ADJ
ejpam-5884	95	23	caputo	caputo	PROPN
ejpam-5884	95	24	derivative	derivative	NOUN
ejpam-5884	95	25	of	of	ADP
ejpam-5884	95	26	order	order	NOUN
ejpam-5884	95	27	α	α	NOUN
ejpam-5884	95	28	is	be	AUX
ejpam-5884	95	29	defined	define	VERB
ejpam-5884	95	30	recursively	recursively	ADV
ejpam-5884	95	31	as	as	ADP
ejpam-5884	95	32	cdlαx(t	cdlαx(t	NOUN
ejpam-5884	95	33	)	)	PUNCT
ejpam-5884	96	1	=	=	SYM
ejpam-5884	96	2	cdα	cdα	NOUN
ejpam-5884	96	3	(	(	PUNCT
ejpam-5884	96	4	cd(l−1)αx(s	cd(l−1)αx(s	PROPN
ejpam-5884	96	5	)	)	PUNCT
ejpam-5884	96	6	)	)	PUNCT
ejpam-5884	96	7	,	,	PUNCT
ejpam-5884	96	8	l	l	PROPN
ejpam-5884	96	9	∈	∈	PROPN
ejpam-5884	96	10	n	n	CCONJ
ejpam-5884	96	11	,	,	PUNCT
ejpam-5884	96	12	(	(	PUNCT
ejpam-5884	96	13	12	12	NUM
ejpam-5884	96	14	)	)	PUNCT
ejpam-5884	96	15	m.	m.	NOUN
ejpam-5884	96	16	i.	i.	PROPN
ejpam-5884	96	17	syam	syam	PROPN
ejpam-5884	96	18	et	et	PROPN
ejpam-5884	96	19	al	al	PROPN
ejpam-5884	96	20	.	.	PUNCT
ejpam-5884	96	21	/	/	SYM
ejpam-5884	96	22	eur	eur	PROPN
ejpam-5884	96	23	.	.	PUNCT
ejpam-5884	97	1	j.	j.	PROPN
ejpam-5884	97	2	pure	pure	PROPN
ejpam-5884	97	3	appl	appl	PROPN
ejpam-5884	97	4	.	.	PROPN
ejpam-5884	97	5	math	math	PROPN
ejpam-5884	97	6	,	,	PUNCT
ejpam-5884	97	7	18	18	NUM
ejpam-5884	97	8	(	(	PUNCT
ejpam-5884	97	9	2	2	NUM
ejpam-5884	97	10	)	)	PUNCT
ejpam-5884	97	11	(	(	PUNCT
ejpam-5884	97	12	2025	2025	NUM
ejpam-5884	97	13	)	)	PUNCT
ejpam-5884	97	14	,	,	PUNCT
ejpam-5884	97	15	5884	5884	NUM
ejpam-5884	97	16	5	5	NUM
ejpam-5884	97	17	of	of	ADP
ejpam-5884	97	18	18	18	NUM
ejpam-5884	97	19	where	where	SCONJ
ejpam-5884	97	20	scdlαx(t	scdlαx(t	NOUN
ejpam-5884	97	21	)	)	PUNCT
ejpam-5884	97	22	denotes	denote	VERB
ejpam-5884	97	23	the	the	DET
ejpam-5884	97	24	sequential	sequential	PROPN
ejpam-5884	97	25	caputo	caputo	PROPN
ejpam-5884	97	26	derivative	derivative	NOUN
ejpam-5884	97	27	of	of	ADP
ejpam-5884	97	28	order	order	NOUN
ejpam-5884	97	29	α	α	X
ejpam-5884	97	30	.	.	PUNCT
ejpam-5884	98	1	for	for	ADP
ejpam-5884	98	2	ease	ease	NOUN
ejpam-5884	98	3	of	of	ADP
ejpam-5884	98	4	notation	notation	NOUN
ejpam-5884	98	5	,	,	PUNCT
ejpam-5884	98	6	we	we	PRON
ejpam-5884	98	7	will	will	AUX
ejpam-5884	98	8	refer	refer	VERB
ejpam-5884	98	9	to	to	ADP
ejpam-5884	98	10	it	it	PRON
ejpam-5884	98	11	simply	simply	ADV
ejpam-5884	98	12	as	as	ADP
ejpam-5884	98	13	dlαx(t	dlαx(t	NOUN
ejpam-5884	98	14	)	)	PUNCT
ejpam-5884	98	15	when	when	SCONJ
ejpam-5884	98	16	discussing	discuss	VERB
ejpam-5884	98	17	the	the	DET
ejpam-5884	98	18	sequential	sequential	ADJ
ejpam-5884	98	19	derivative	derivative	NOUN
ejpam-5884	98	20	.	.	PUNCT
ejpam-5884	99	1	next	next	ADV
ejpam-5884	99	2	,	,	PUNCT
ejpam-5884	99	3	we	we	PRON
ejpam-5884	99	4	introduce	introduce	VERB
ejpam-5884	99	5	the	the	DET
ejpam-5884	99	6	operational	operational	ADJ
ejpam-5884	99	7	matrix	matrix	NOUN
ejpam-5884	99	8	method	method	NOUN
ejpam-5884	99	9	(	(	PUNCT
ejpam-5884	99	10	omm	omm	PROPN
ejpam-5884	99	11	)	)	PUNCT
ejpam-5884	99	12	with	with	ADP
ejpam-5884	99	13	the	the	DET
ejpam-5884	99	14	following	follow	VERB
ejpam-5884	99	15	definition	definition	NOUN
ejpam-5884	99	16	.	.	PUNCT
ejpam-5884	100	1	definition	definition	NOUN
ejpam-5884	100	2	3	3	NUM
ejpam-5884	100	3	.	.	PUNCT
ejpam-5884	101	1	[	[	X
ejpam-5884	101	2	42	42	NUM
ejpam-5884	101	3	,	,	PUNCT
ejpam-5884	101	4	49	49	NUM
ejpam-5884	101	5	]	]	PUNCT
ejpam-5884	101	6	let	let	VERB
ejpam-5884	101	7	ts	ts	X
ejpam-5884	101	8	=	=	PUNCT
ejpam-5884	101	9	s∆	s∆	PROPN
ejpam-5884	101	10	for	for	ADP
ejpam-5884	101	11	s	s	PROPN
ejpam-5884	101	12	∈	∈	PROPN
ejpam-5884	101	13	{	{	PUNCT
ejpam-5884	101	14	0	0	NUM
ejpam-5884	101	15	,	,	PUNCT
ejpam-5884	101	16	1	1	NUM
ejpam-5884	101	17	,	,	PUNCT
ejpam-5884	101	18	2	2	NUM
ejpam-5884	101	19	,	,	PUNCT
ejpam-5884	101	20	.	.	PUNCT
ejpam-5884	101	21	.	.	PUNCT
ejpam-5884	101	22	.	.	PUNCT
ejpam-5884	102	1	,	,	PUNCT
ejpam-5884	102	2	m−1	m−1	PROPN
ejpam-5884	102	3	}	}	PUNCT
ejpam-5884	102	4	and	and	CCONJ
ejpam-5884	102	5	∆	∆	PROPN
ejpam-5884	103	1	=	=	SYM
ejpam-5884	103	2	t	t	PROPN
ejpam-5884	103	3	m	m	PROPN
ejpam-5884	103	4	,	,	PUNCT
ejpam-5884	103	5	where	where	SCONJ
ejpam-5884	103	6	m	m	PROPN
ejpam-5884	103	7	∈	∈	PROPN
ejpam-5884	103	8	n.	n.	NOUN
ejpam-5884	103	9	the	the	DET
ejpam-5884	103	10	s	s	NOUN
ejpam-5884	103	11	-	-	PUNCT
ejpam-5884	103	12	block	block	ADJ
ejpam-5884	103	13	pulse	pulse	NOUN
ejpam-5884	103	14	function	function	NOUN
ejpam-5884	103	15	(	(	PUNCT
ejpam-5884	103	16	bpf	bpf	NOUN
ejpam-5884	103	17	)	)	PUNCT
ejpam-5884	103	18	is	be	AUX
ejpam-5884	103	19	defined	define	VERB
ejpam-5884	103	20	as	as	ADP
ejpam-5884	103	21	:	:	PUNCT
ejpam-5884	103	22	µs(t	µs(t	NUM
ejpam-5884	103	23	)	)	PUNCT
ejpam-5884	104	1	=	=	PRON
ejpam-5884	104	2	{	{	PUNCT
ejpam-5884	104	3	1	1	NUM
ejpam-5884	104	4	,	,	PUNCT
ejpam-5884	104	5	ts	ts	ADP
ejpam-5884	104	6	≤	≤	PROPN
ejpam-5884	104	7	t	t	NOUN
ejpam-5884	104	8	<	<	X
ejpam-5884	104	9	ts+1	ts+1	PROPN
ejpam-5884	104	10	,	,	PUNCT
ejpam-5884	104	11	0	0	NUM
ejpam-5884	104	12	,	,	PUNCT
ejpam-5884	104	13	otherwise	otherwise	ADV
ejpam-5884	104	14	,	,	PUNCT
ejpam-5884	104	15	0	0	NUM
ejpam-5884	104	16	≤	≤	NOUN
ejpam-5884	104	17	s	s	PART
ejpam-5884	104	18	<	<	X
ejpam-5884	104	19	m.	m.	NOUN
ejpam-5884	104	20	the	the	DET
ejpam-5884	104	21	product	product	NOUN
ejpam-5884	104	22	and	and	CCONJ
ejpam-5884	104	23	orthogonality	orthogonality	NOUN
ejpam-5884	104	24	properties	property	NOUN
ejpam-5884	104	25	of	of	ADP
ejpam-5884	104	26	bpfs	bpf	NOUN
ejpam-5884	104	27	follow	follow	VERB
ejpam-5884	104	28	directly	directly	ADV
ejpam-5884	104	29	from	from	ADP
ejpam-5884	104	30	the	the	DET
ejpam-5884	104	31	above	above	ADJ
ejpam-5884	104	32	definition	definition	NOUN
ejpam-5884	104	33	,	,	PUNCT
ejpam-5884	104	34	as	as	SCONJ
ejpam-5884	104	35	given	give	VERB
ejpam-5884	104	36	in	in	ADP
ejpam-5884	104	37	the	the	DET
ejpam-5884	104	38	next	next	ADJ
ejpam-5884	104	39	theorem	theorem	PROPN
ejpam-5884	104	40	.	.	PUNCT
ejpam-5884	104	41	theorem	theorem	NOUN
ejpam-5884	104	42	1	1	NUM
ejpam-5884	104	43	.	.	PUNCT
ejpam-5884	105	1	[	[	X
ejpam-5884	105	2	43–45	43–45	X
ejpam-5884	105	3	]	]	X
ejpam-5884	105	4	let	let	VERB
ejpam-5884	105	5	{	{	PUNCT
ejpam-5884	105	6	t0	t0	X
ejpam-5884	105	7	=	=	SYM
ejpam-5884	105	8	0	0	NUM
ejpam-5884	105	9	,	,	PUNCT
ejpam-5884	105	10	t1	t1	NOUN
ejpam-5884	105	11	,	,	PUNCT
ejpam-5884	105	12	.	.	PUNCT
ejpam-5884	105	13	.	.	PUNCT
ejpam-5884	105	14	.	.	PUNCT
ejpam-5884	106	1	,	,	PUNCT
ejpam-5884	106	2	tm	tm	PROPN
ejpam-5884	106	3	=	=	PROPN
ejpam-5884	106	4	t	t	PROPN
ejpam-5884	106	5	}	}	PUNCT
ejpam-5884	106	6	be	be	AUX
ejpam-5884	106	7	a	a	DET
ejpam-5884	106	8	uniform	uniform	ADJ
ejpam-5884	106	9	partition	partition	NOUN
ejpam-5884	106	10	of	of	ADP
ejpam-5884	106	11	[	[	X
ejpam-5884	106	12	0	0	NUM
ejpam-5884	106	13	,	,	PUNCT
ejpam-5884	106	14	t	t	X
ejpam-5884	106	15	]	]	PUNCT
ejpam-5884	106	16	,	,	PUNCT
ejpam-5884	106	17	and	and	CCONJ
ejpam-5884	106	18	let	let	VERB
ejpam-5884	106	19	{	{	PUNCT
ejpam-5884	106	20	µ0(t	µ0(t	NOUN
ejpam-5884	106	21	)	)	PUNCT
ejpam-5884	106	22	,	,	PUNCT
ejpam-5884	106	23	µ1(t	µ1(t	PROPN
ejpam-5884	106	24	)	)	PUNCT
ejpam-5884	106	25	,	,	PUNCT
ejpam-5884	106	26	.	.	PUNCT
ejpam-5884	106	27	.	.	PUNCT
ejpam-5884	107	1	.	.	PUNCT
ejpam-5884	108	1	,	,	PUNCT
ejpam-5884	108	2	µm−1(t	µm−1(t	NUM
ejpam-5884	108	3	)	)	PUNCT
ejpam-5884	108	4	}	}	PUNCT
ejpam-5884	108	5	be	be	AUX
ejpam-5884	108	6	the	the	DET
ejpam-5884	108	7	corresponding	corresponding	ADJ
ejpam-5884	108	8	bpfs	bpf	NOUN
ejpam-5884	108	9	.	.	PUNCT
ejpam-5884	109	1	then	then	ADV
ejpam-5884	109	2	,	,	PUNCT
ejpam-5884	109	3	for	for	ADP
ejpam-5884	109	4	any	any	DET
ejpam-5884	109	5	0	0	NUM
ejpam-5884	109	6	≤	≤	NOUN
ejpam-5884	109	7	i	i	PRON
ejpam-5884	109	8	,	,	PUNCT
ejpam-5884	109	9	j	j	PROPN
ejpam-5884	109	10	≤	≤	PROPN
ejpam-5884	109	11	m	m	VERB
ejpam-5884	109	12	−	−	PROPN
ejpam-5884	109	13	1	1	NUM
ejpam-5884	109	14	,	,	PUNCT
ejpam-5884	109	15	the	the	DET
ejpam-5884	109	16	following	follow	VERB
ejpam-5884	109	17	relations	relation	NOUN
ejpam-5884	109	18	hold	hold	VERB
ejpam-5884	109	19	:	:	PUNCT
ejpam-5884	109	20	µi(t)µj(t	µi(t)µj(t	X
ejpam-5884	109	21	)	)	PUNCT
ejpam-5884	109	22	=	=	SYM
ejpam-5884	109	23	{	{	PUNCT
ejpam-5884	109	24	µi(t	µi(t	ADV
ejpam-5884	109	25	)	)	PUNCT
ejpam-5884	109	26	,	,	PUNCT
ejpam-5884	109	27	if	if	SCONJ
ejpam-5884	109	28	i	i	PRON
ejpam-5884	109	29	=	=	SYM
ejpam-5884	109	30	j	j	PROPN
ejpam-5884	109	31	,	,	PUNCT
ejpam-5884	109	32	0	0	NUM
ejpam-5884	109	33	,	,	PUNCT
ejpam-5884	109	34	otherwise	otherwise	ADV
ejpam-5884	109	35	.	.	PUNCT
ejpam-5884	110	1	(	(	PUNCT
ejpam-5884	110	2	13	13	NUM
ejpam-5884	110	3	)	)	PUNCT
ejpam-5884	110	4	and	and	CCONJ
ejpam-5884	110	5	∫	∫	PROPN
ejpam-5884	110	6	t	t	PROPN
ejpam-5884	110	7	0	0	NUM
ejpam-5884	110	8	µi(t)µj(t	µi(t)µj(t	X
ejpam-5884	110	9	)	)	PUNCT
ejpam-5884	110	10	dt	dt	PUNCT
ejpam-5884	111	1	=	=	PUNCT
ejpam-5884	111	2	{	{	PUNCT
ejpam-5884	111	3	∆	∆	PROPN
ejpam-5884	111	4	,	,	PUNCT
ejpam-5884	111	5	if	if	SCONJ
ejpam-5884	111	6	i	i	PRON
ejpam-5884	111	7	=	=	SYM
ejpam-5884	111	8	j	j	PROPN
ejpam-5884	111	9	,	,	PUNCT
ejpam-5884	111	10	0	0	NUM
ejpam-5884	111	11	,	,	PUNCT
ejpam-5884	111	12	otherwise	otherwise	ADV
ejpam-5884	111	13	.	.	PUNCT
ejpam-5884	112	1	(	(	PUNCT
ejpam-5884	112	2	14	14	NUM
ejpam-5884	112	3	)	)	PUNCT
ejpam-5884	112	4	we	we	PRON
ejpam-5884	112	5	conclude	conclude	VERB
ejpam-5884	112	6	this	this	DET
ejpam-5884	112	7	section	section	NOUN
ejpam-5884	112	8	by	by	ADP
ejpam-5884	112	9	stating	state	VERB
ejpam-5884	112	10	the	the	DET
ejpam-5884	112	11	completeness	completeness	NOUN
ejpam-5884	112	12	property	property	NOUN
ejpam-5884	112	13	in	in	ADP
ejpam-5884	112	14	the	the	DET
ejpam-5884	112	15	following	follow	VERB
ejpam-5884	112	16	lemma	lemma	PROPN
ejpam-5884	112	17	.	.	PUNCT
ejpam-5884	113	1	lemma	lemma	PROPN
ejpam-5884	113	2	2	2	NUM
ejpam-5884	113	3	.	.	PUNCT
ejpam-5884	114	1	[	[	X
ejpam-5884	114	2	45–47	45–47	X
ejpam-5884	114	3	]	]	X
ejpam-5884	114	4	if	if	SCONJ
ejpam-5884	114	5	x	x	PROPN
ejpam-5884	114	6	∈	∈	PROPN
ejpam-5884	114	7	l2[0	l2[0	PROPN
ejpam-5884	114	8	,	,	PUNCT
ejpam-5884	114	9	t	t	PROPN
ejpam-5884	114	10	)	)	PUNCT
ejpam-5884	114	11	,	,	PUNCT
ejpam-5884	114	12	then	then	ADV
ejpam-5884	114	13	we	we	PRON
ejpam-5884	114	14	have	have	VERB
ejpam-5884	114	15	the	the	DET
ejpam-5884	114	16	expansion	expansion	NOUN
ejpam-5884	114	17	:	:	PUNCT
ejpam-5884	114	18	x(t	x(t	PROPN
ejpam-5884	114	19	)	)	PUNCT
ejpam-5884	114	20	=	=	PUNCT
ejpam-5884	115	1	∞∑	∞∑	NUM
ejpam-5884	115	2	s=0	s=0	PROPN
ejpam-5884	115	3	xsµs(t	xsµs(t	NUM
ejpam-5884	115	4	)	)	PUNCT
ejpam-5884	115	5	,	,	PUNCT
ejpam-5884	115	6	(	(	PUNCT
ejpam-5884	115	7	15	15	NUM
ejpam-5884	115	8	)	)	PUNCT
ejpam-5884	115	9	where	where	SCONJ
ejpam-5884	115	10	xs	xs	PROPN
ejpam-5884	115	11	=	=	SYM
ejpam-5884	115	12	1	1	NUM
ejpam-5884	115	13	∆	∆	X
ejpam-5884	115	14	∫	∫	NOUN
ejpam-5884	115	15	(	(	PUNCT
ejpam-5884	115	16	s+1)∆	s+1)∆	NOUN
ejpam-5884	115	17	s∆	s∆	PROPN
ejpam-5884	115	18	x(r	x(r	PROPN
ejpam-5884	115	19	)	)	PUNCT
ejpam-5884	115	20	dr	dr	PROPN
ejpam-5884	115	21	.	.	PROPN
ejpam-5884	115	22	(	(	PUNCT
ejpam-5884	115	23	16	16	NUM
ejpam-5884	115	24	)	)	PUNCT
ejpam-5884	115	25	for	for	ADP
ejpam-5884	115	26	numerical	numerical	ADJ
ejpam-5884	115	27	purposes	purpose	NOUN
ejpam-5884	115	28	,	,	PUNCT
ejpam-5884	115	29	we	we	PRON
ejpam-5884	115	30	approximate	approximate	VERB
ejpam-5884	115	31	x(t	x(t	PROPN
ejpam-5884	115	32	)	)	PUNCT
ejpam-5884	115	33	by	by	ADP
ejpam-5884	115	34	:	:	PUNCT
ejpam-5884	115	35	x(t	x(t	PROPN
ejpam-5884	115	36	)	)	PUNCT
ejpam-5884	116	1	≈	≈	PROPN
ejpam-5884	116	2	m−1∑	m−1∑	PROPN
ejpam-5884	116	3	s=0	s=0	PROPN
ejpam-5884	116	4	xsµs(t	xsµs(t	PROPN
ejpam-5884	116	5	)	)	PUNCT
ejpam-5884	116	6	,	,	PUNCT
ejpam-5884	116	7	m	m	VERB
ejpam-5884	116	8	≫	≫	PROPN
ejpam-5884	116	9	1	1	NUM
ejpam-5884	116	10	.	.	PUNCT
ejpam-5884	117	1	(	(	PUNCT
ejpam-5884	117	2	17	17	NUM
ejpam-5884	117	3	)	)	PUNCT
ejpam-5884	117	4	m.	m.	NOUN
ejpam-5884	117	5	i.	i.	PROPN
ejpam-5884	117	6	syam	syam	PROPN
ejpam-5884	117	7	et	et	PROPN
ejpam-5884	117	8	al	al	PROPN
ejpam-5884	117	9	.	.	PUNCT
ejpam-5884	117	10	/	/	SYM
ejpam-5884	117	11	eur	eur	PROPN
ejpam-5884	117	12	.	.	PUNCT
ejpam-5884	118	1	j.	j.	PROPN
ejpam-5884	118	2	pure	pure	PROPN
ejpam-5884	118	3	appl	appl	PROPN
ejpam-5884	118	4	.	.	PROPN
ejpam-5884	118	5	math	math	PROPN
ejpam-5884	118	6	,	,	PUNCT
ejpam-5884	118	7	18	18	NUM
ejpam-5884	118	8	(	(	PUNCT
ejpam-5884	118	9	2	2	NUM
ejpam-5884	118	10	)	)	PUNCT
ejpam-5884	118	11	(	(	PUNCT
ejpam-5884	118	12	2025	2025	NUM
ejpam-5884	118	13	)	)	PUNCT
ejpam-5884	118	14	,	,	PUNCT
ejpam-5884	118	15	5884	5884	NUM
ejpam-5884	118	16	6	6	NUM
ejpam-5884	118	17	of	of	ADP
ejpam-5884	118	18	18	18	NUM
ejpam-5884	118	19	3	3	NUM
ejpam-5884	118	20	.	.	NOUN
ejpam-5884	119	1	iterative	iterative	ADJ
ejpam-5884	119	2	operational	operational	ADJ
ejpam-5884	119	3	matrix	matrix	NOUN
ejpam-5884	119	4	method	method	NOUN
ejpam-5884	119	5	syam	syam	NOUN
ejpam-5884	119	6	et	et	PROPN
ejpam-5884	119	7	al	al	PROPN
ejpam-5884	119	8	.	.	PUNCT
ejpam-5884	120	1	[	[	X
ejpam-5884	120	2	42–44	42–44	NUM
ejpam-5884	120	3	,	,	PUNCT
ejpam-5884	120	4	46–49	46–49	PROPN
ejpam-5884	120	5	]	]	PUNCT
ejpam-5884	120	6	,	,	PUNCT
ejpam-5884	120	7	introduced	introduce	VERB
ejpam-5884	120	8	an	an	DET
ejpam-5884	120	9	inefficient	inefficient	ADJ
ejpam-5884	120	10	iterative	iterative	NOUN
ejpam-5884	120	11	method	method	NOUN
ejpam-5884	120	12	which	which	PRON
ejpam-5884	120	13	reduce	reduce	VERB
ejpam-5884	120	14	the	the	DET
ejpam-5884	120	15	computational	computational	ADJ
ejpam-5884	120	16	time	time	NOUN
ejpam-5884	120	17	and	and	CCONJ
ejpam-5884	120	18	cost	cost	NOUN
ejpam-5884	120	19	,	,	PUNCT
ejpam-5884	120	20	and	and	CCONJ
ejpam-5884	120	21	increase	increase	VERB
ejpam-5884	120	22	the	the	DET
ejpam-5884	120	23	effecinet	effecinet	NOUN
ejpam-5884	120	24	of	of	ADP
ejpam-5884	120	25	the	the	DET
ejpam-5884	120	26	omm	omm	PROPN
ejpam-5884	120	27	.	.	PUNCT
ejpam-5884	121	1	in	in	ADP
ejpam-5884	121	2	this	this	DET
ejpam-5884	121	3	section	section	NOUN
ejpam-5884	121	4	,	,	PUNCT
ejpam-5884	121	5	we	we	PRON
ejpam-5884	121	6	will	will	AUX
ejpam-5884	121	7	follow	follow	VERB
ejpam-5884	121	8	this	this	DET
ejpam-5884	121	9	approach	approach	NOUN
ejpam-5884	121	10	to	to	PART
ejpam-5884	121	11	solve	solve	VERB
ejpam-5884	121	12	our	our	PRON
ejpam-5884	121	13	problem	problem	NOUN
ejpam-5884	121	14	(	(	PUNCT
ejpam-5884	121	15	6)-(7	6)-(7	NOUN
ejpam-5884	121	16	)	)	PUNCT
ejpam-5884	121	17	.	.	PUNCT
ejpam-5884	122	1	first	first	ADV
ejpam-5884	122	2	,	,	PUNCT
ejpam-5884	122	3	by	by	ADP
ejpam-5884	122	4	applying	apply	VERB
ejpam-5884	122	5	the	the	DET
ejpam-5884	122	6	fractional	fractional	ADJ
ejpam-5884	122	7	integral	integral	ADJ
ejpam-5884	122	8	operator	operator	NOUN
ejpam-5884	122	9	(	(	PUNCT
ejpam-5884	122	10	9	9	NUM
ejpam-5884	122	11	)	)	PUNCT
ejpam-5884	122	12	to	to	ADP
ejpam-5884	122	13	both	both	DET
ejpam-5884	122	14	sides	side	NOUN
ejpam-5884	122	15	of	of	ADP
ejpam-5884	122	16	(	(	PUNCT
ejpam-5884	122	17	6	6	NUM
ejpam-5884	122	18	)	)	PUNCT
ejpam-5884	122	19	,	,	PUNCT
ejpam-5884	122	20	we	we	PRON
ejpam-5884	122	21	obtain	obtain	VERB
ejpam-5884	122	22	the	the	DET
ejpam-5884	122	23	following	follow	VERB
ejpam-5884	122	24	equation	equation	NOUN
ejpam-5884	122	25	:	:	PUNCT
ejpam-5884	122	26	dαx(t)−dαx(0	dαx(t)−dαx(0	NUM
ejpam-5884	122	27	)	)	PUNCT
ejpam-5884	122	28	+	+	CCONJ
ejpam-5884	122	29	β	β	X
ejpam-5884	122	30	γ(α	γ(α	PROPN
ejpam-5884	122	31	)	)	PUNCT
ejpam-5884	122	32	∫	∫	PROPN
ejpam-5884	123	1	t	t	PROPN
ejpam-5884	123	2	0	0	NUM
ejpam-5884	124	1	x(s)(t−	x(s)(t−	NUM
ejpam-5884	124	2	s)α−1ds+	s)α−1ds+	PROPN
ejpam-5884	125	1	γ	γ	PROPN
ejpam-5884	125	2	γ(α	γ(α	PROPN
ejpam-5884	125	3	)	)	PUNCT
ejpam-5884	126	1	∫	∫	PROPN
ejpam-5884	126	2	t	t	PROPN
ejpam-5884	126	3	0	0	NUM
ejpam-5884	127	1	x3(s)(t−	x3(s)(t−	PROPN
ejpam-5884	127	2	s)α−1ds	s)α−1ds	NOUN
ejpam-5884	127	3	=	=	NOUN
ejpam-5884	127	4	0	0	X
ejpam-5884	127	5	.	.	PUNCT
ejpam-5884	128	1	since	since	SCONJ
ejpam-5884	128	2	dαx(0	dαx(0	NOUN
ejpam-5884	128	3	)	)	PUNCT
ejpam-5884	128	4	=	=	SYM
ejpam-5884	128	5	0	0	NUM
ejpam-5884	128	6	,	,	PUNCT
ejpam-5884	128	7	this	this	DET
ejpam-5884	128	8	simplifies	simplifie	NOUN
ejpam-5884	128	9	to	to	PART
ejpam-5884	128	10	:	:	PUNCT
ejpam-5884	128	11	dαx(t	dαx(t	PROPN
ejpam-5884	128	12	)	)	PUNCT
ejpam-5884	128	13	=	=	PUNCT
ejpam-5884	128	14	−	−	PROPN
ejpam-5884	128	15	β	β	X
ejpam-5884	128	16	γ(α	γ(α	PROPN
ejpam-5884	128	17	)	)	PUNCT
ejpam-5884	128	18	∫	∫	PROPN
ejpam-5884	128	19	t	t	PROPN
ejpam-5884	128	20	0	0	NUM
ejpam-5884	128	21	x(s)(t−	x(s)(t−	PROPN
ejpam-5884	128	22	s)α−1ds−	s)α−1ds−	VERB
ejpam-5884	128	23	γ	γ	PROPN
ejpam-5884	128	24	γ(α	γ(α	PROPN
ejpam-5884	128	25	)	)	PUNCT
ejpam-5884	129	1	∫	∫	PROPN
ejpam-5884	129	2	t	t	PROPN
ejpam-5884	129	3	0	0	NUM
ejpam-5884	130	1	x3(s)(t−	x3(s)(t−	PROPN
ejpam-5884	130	2	s)α−1ds	s)α−1ds	NOUN
ejpam-5884	130	3	.	.	PUNCT
ejpam-5884	131	1	(	(	PUNCT
ejpam-5884	131	2	18	18	NUM
ejpam-5884	131	3	)	)	PUNCT
ejpam-5884	131	4	next	next	ADV
ejpam-5884	131	5	,	,	PUNCT
ejpam-5884	131	6	applying	apply	VERB
ejpam-5884	131	7	the	the	DET
ejpam-5884	131	8	fractional	fractional	ADJ
ejpam-5884	131	9	integral	integral	ADJ
ejpam-5884	131	10	operator	operator	NOUN
ejpam-5884	131	11	(	(	PUNCT
ejpam-5884	131	12	9	9	NUM
ejpam-5884	131	13	)	)	PUNCT
ejpam-5884	131	14	again	again	ADV
ejpam-5884	131	15	to	to	ADP
ejpam-5884	131	16	both	both	DET
ejpam-5884	131	17	sides	side	NOUN
ejpam-5884	131	18	of	of	ADP
ejpam-5884	131	19	equation	equation	NOUN
ejpam-5884	131	20	(	(	PUNCT
ejpam-5884	131	21	18	18	NUM
ejpam-5884	131	22	)	)	PUNCT
ejpam-5884	131	23	,	,	PUNCT
ejpam-5884	131	24	we	we	PRON
ejpam-5884	131	25	obtain	obtain	VERB
ejpam-5884	131	26	x(t)−	x(t)−	PROPN
ejpam-5884	131	27	x(0	x(0	PROPN
ejpam-5884	131	28	)	)	PUNCT
ejpam-5884	132	1	=	=	PUNCT
ejpam-5884	133	1	−	−	PROPN
ejpam-5884	133	2	β	β	X
ejpam-5884	133	3	γ2(α	γ2(α	PROPN
ejpam-5884	133	4	)	)	PUNCT
ejpam-5884	133	5	∫	∫	PROPN
ejpam-5884	133	6	t	t	PROPN
ejpam-5884	133	7	0	0	NUM
ejpam-5884	133	8	∫	∫	PROPN
ejpam-5884	133	9	s	s	PART
ejpam-5884	133	10	0	0	NUM
ejpam-5884	133	11	x(w)(t−	x(w)(t−	ADP
ejpam-5884	134	1	s)α−1(s−	s)α−1(s−	PROPN
ejpam-5884	134	2	w)α−1dwds	w)α−1dwds	PROPN
ejpam-5884	135	1	−	−	PROPN
ejpam-5884	135	2	γ	γ	PROPN
ejpam-5884	135	3	γ2(α	γ2(α	PROPN
ejpam-5884	135	4	)	)	PUNCT
ejpam-5884	135	5	∫	∫	PROPN
ejpam-5884	135	6	t	t	PROPN
ejpam-5884	135	7	0	0	NUM
ejpam-5884	135	8	∫	∫	PROPN
ejpam-5884	135	9	s	s	PART
ejpam-5884	135	10	0	0	NUM
ejpam-5884	136	1	x3(w)(t−	x3(w)(t−	PROPN
ejpam-5884	136	2	s)α−1(s−	s)α−1(s−	PROPN
ejpam-5884	136	3	w)α−1dw	w)α−1dw	PROPN
ejpam-5884	136	4	ds	ds	PROPN
ejpam-5884	136	5	.	.	PROPN
ejpam-5884	136	6	since	since	SCONJ
ejpam-5884	136	7	x(0	x(0	PROPN
ejpam-5884	136	8	)	)	PUNCT
ejpam-5884	137	1	=	=	SYM
ejpam-5884	138	1	a	a	X
ejpam-5884	138	2	,	,	PUNCT
ejpam-5884	138	3	we	we	PRON
ejpam-5884	138	4	can	can	AUX
ejpam-5884	138	5	rewrite	rewrite	VERB
ejpam-5884	138	6	this	this	PRON
ejpam-5884	138	7	as	as	ADP
ejpam-5884	138	8	:	:	PUNCT
ejpam-5884	138	9	x(t	x(t	PROPN
ejpam-5884	138	10	)	)	PUNCT
ejpam-5884	138	11	=	=	SYM
ejpam-5884	139	1	a−	a−	PROPN
ejpam-5884	139	2	β	β	X
ejpam-5884	139	3	γ2(α	γ2(α	PROPN
ejpam-5884	139	4	)	)	PUNCT
ejpam-5884	139	5	∫	∫	PROPN
ejpam-5884	139	6	t	t	PROPN
ejpam-5884	139	7	0	0	NUM
ejpam-5884	139	8	∫	∫	PROPN
ejpam-5884	139	9	s	s	PART
ejpam-5884	139	10	0	0	NUM
ejpam-5884	139	11	x(w)(t−	x(w)(t−	ADP
ejpam-5884	139	12	s)α−1(s−	s)α−1(s−	PROPN
ejpam-5884	139	13	w)α−1dw	w)α−1dw	PROPN
ejpam-5884	139	14	ds	ds	ADJ
ejpam-5884	139	15	−	−	PROPN
ejpam-5884	139	16	γ	γ	X
ejpam-5884	139	17	γ2(α	γ2(α	PROPN
ejpam-5884	139	18	)	)	PUNCT
ejpam-5884	139	19	∫	∫	PROPN
ejpam-5884	139	20	t	t	PROPN
ejpam-5884	139	21	0	0	NUM
ejpam-5884	139	22	∫	∫	PROPN
ejpam-5884	139	23	s	s	PART
ejpam-5884	139	24	0	0	NUM
ejpam-5884	140	1	x3(w)(t−	x3(w)(t−	PROPN
ejpam-5884	140	2	s)α−1(s−	s)α−1(s−	PROPN
ejpam-5884	140	3	w)α−1dwds	w)α−1dwds	PROPN
ejpam-5884	140	4	.	.	PUNCT
ejpam-5884	141	1	(	(	PUNCT
ejpam-5884	141	2	19	19	NUM
ejpam-5884	141	3	)	)	PUNCT
ejpam-5884	141	4	let	let	VERB
ejpam-5884	141	5	{	{	PUNCT
ejpam-5884	141	6	t0	t0	NOUN
ejpam-5884	141	7	=	=	SYM
ejpam-5884	141	8	0	0	NUM
ejpam-5884	141	9	,	,	PUNCT
ejpam-5884	141	10	t1	t1	NOUN
ejpam-5884	141	11	,	,	PUNCT
ejpam-5884	141	12	.	.	PUNCT
ejpam-5884	141	13	.	.	PUNCT
ejpam-5884	142	1	.	.	PUNCT
ejpam-5884	143	1	,	,	PUNCT
ejpam-5884	143	2	tm	tm	PROPN
ejpam-5884	143	3	=	=	PROPN
ejpam-5884	143	4	t	t	PROPN
ejpam-5884	143	5	}	}	PUNCT
ejpam-5884	143	6	represent	represent	VERB
ejpam-5884	143	7	a	a	DET
ejpam-5884	143	8	uniform	uniform	ADJ
ejpam-5884	143	9	partition	partition	NOUN
ejpam-5884	143	10	of	of	ADP
ejpam-5884	143	11	[	[	X
ejpam-5884	143	12	0	0	NUM
ejpam-5884	143	13	,	,	PUNCT
ejpam-5884	143	14	t	t	X
ejpam-5884	143	15	]	]	PUNCT
ejpam-5884	143	16	,	,	PUNCT
ejpam-5884	143	17	and	and	CCONJ
ejpam-5884	143	18	let	let	VERB
ejpam-5884	143	19	{	{	PUNCT
ejpam-5884	143	20	µ0(t	µ0(t	NOUN
ejpam-5884	143	21	)	)	PUNCT
ejpam-5884	143	22	,	,	PUNCT
ejpam-5884	143	23	µ1(t	µ1(t	PROPN
ejpam-5884	143	24	)	)	PUNCT
ejpam-5884	143	25	,	,	PUNCT
ejpam-5884	143	26	.	.	PUNCT
ejpam-5884	143	27	.	.	PUNCT
ejpam-5884	144	1	.	.	PUNCT
ejpam-5884	145	1	,	,	PUNCT
ejpam-5884	145	2	µm−1(t	µm−1(t	NUM
ejpam-5884	145	3	)	)	PUNCT
ejpam-5884	145	4	}	}	PUNCT
ejpam-5884	145	5	be	be	AUX
ejpam-5884	145	6	the	the	DET
ejpam-5884	145	7	corresponding	corresponding	ADJ
ejpam-5884	145	8	block	block	NOUN
ejpam-5884	145	9	pulse	pulse	NOUN
ejpam-5884	145	10	functions	function	NOUN
ejpam-5884	145	11	(	(	PUNCT
ejpam-5884	145	12	bpfs	bpfs	PROPN
ejpam-5884	145	13	)	)	PUNCT
ejpam-5884	145	14	.	.	PUNCT
ejpam-5884	146	1	we	we	PRON
ejpam-5884	146	2	approximate	approximate	VERB
ejpam-5884	146	3	x(t	x(t	PROPN
ejpam-5884	146	4	)	)	PUNCT
ejpam-5884	146	5	using	use	VERB
ejpam-5884	146	6	these	these	DET
ejpam-5884	146	7	bpfs	bpf	NOUN
ejpam-5884	146	8	as	as	SCONJ
ejpam-5884	146	9	follows	follow	VERB
ejpam-5884	146	10	x(t	x(t	PROPN
ejpam-5884	146	11	)	)	PUNCT
ejpam-5884	147	1	=	=	PUNCT
ejpam-5884	147	2	m−1∑	m−1∑	NUM
ejpam-5884	147	3	i=0	i=0	PROPN
ejpam-5884	147	4	xiµi(t	xiµi(t	NOUN
ejpam-5884	147	5	)	)	PUNCT
ejpam-5884	147	6	.	.	PUNCT
ejpam-5884	148	1	(	(	PUNCT
ejpam-5884	148	2	20	20	NUM
ejpam-5884	148	3	)	)	PUNCT
ejpam-5884	148	4	by	by	ADP
ejpam-5884	148	5	applying	apply	VERB
ejpam-5884	148	6	the	the	DET
ejpam-5884	148	7	collocation	collocation	NOUN
ejpam-5884	148	8	method	method	NOUN
ejpam-5884	148	9	to	to	ADP
ejpam-5884	148	10	equation	equation	NOUN
ejpam-5884	148	11	(	(	PUNCT
ejpam-5884	148	12	20	20	NUM
ejpam-5884	148	13	)	)	PUNCT
ejpam-5884	148	14	with	with	ADP
ejpam-5884	148	15	collocation	collocation	NOUN
ejpam-5884	148	16	points	point	NOUN
ejpam-5884	148	17	at	at	ADP
ejpam-5884	148	18	tj	tj	NOUN
ejpam-5884	148	19	,	,	PUNCT
ejpam-5884	148	20	where	where	SCONJ
ejpam-5884	148	21	1	1	NUM
ejpam-5884	148	22	≤	≤	NUM
ejpam-5884	148	23	j	j	NOUN
ejpam-5884	148	24	<	<	X
ejpam-5884	148	25	m	m	X
ejpam-5884	148	26	,	,	PUNCT
ejpam-5884	148	27	we	we	PRON
ejpam-5884	148	28	get	get	VERB
ejpam-5884	148	29	x(tj	x(tj	NUM
ejpam-5884	148	30	)	)	PUNCT
ejpam-5884	148	31	=	=	PUNCT
ejpam-5884	148	32	m−1∑	m−1∑	NUM
ejpam-5884	148	33	i=0	i=0	PROPN
ejpam-5884	148	34	xiµi(tj	xiµi(tj	PROPN
ejpam-5884	148	35	)	)	PUNCT
ejpam-5884	148	36	=	=	SYM
ejpam-5884	148	37	xj	xj	PROPN
ejpam-5884	148	38	,	,	PUNCT
ejpam-5884	148	39	0	0	NUM
ejpam-5884	148	40	≤	≤	NUM
ejpam-5884	148	41	j	j	PROPN
ejpam-5884	148	42	≤	≤	NUM
ejpam-5884	148	43	m	m	VERB
ejpam-5884	148	44	−	−	PROPN
ejpam-5884	148	45	1	1	NUM
ejpam-5884	148	46	,	,	PUNCT
ejpam-5884	148	47	(	(	PUNCT
ejpam-5884	148	48	21	21	NUM
ejpam-5884	148	49	)	)	PUNCT
ejpam-5884	148	50	which	which	PRON
ejpam-5884	148	51	leads	lead	VERB
ejpam-5884	148	52	to	to	ADP
ejpam-5884	148	53	the	the	DET
ejpam-5884	148	54	following	follow	VERB
ejpam-5884	148	55	equation	equation	NOUN
ejpam-5884	148	56	:	:	PUNCT
ejpam-5884	148	57	xj	xj	PROPN
ejpam-5884	148	58	=	=	SYM
ejpam-5884	148	59	a−	a−	PROPN
ejpam-5884	148	60	β	β	X
ejpam-5884	148	61	γ2(α	γ2(α	PROPN
ejpam-5884	148	62	)	)	PUNCT
ejpam-5884	148	63	∫	∫	PROPN
ejpam-5884	149	1	tj	tj	PROPN
ejpam-5884	149	2	0	0	NUM
ejpam-5884	149	3	∫	∫	PROPN
ejpam-5884	149	4	s	s	PART
ejpam-5884	149	5	0	0	NUM
ejpam-5884	149	6	(	(	PUNCT
ejpam-5884	149	7	m−1∑	m−1∑	PROPN
ejpam-5884	149	8	i=0	i=0	PROPN
ejpam-5884	149	9	xiµi(w	xiµi(w	PROPN
ejpam-5884	149	10	)	)	PUNCT
ejpam-5884	149	11	)	)	PUNCT
ejpam-5884	150	1	(	(	PUNCT
ejpam-5884	150	2	tj	tj	X
ejpam-5884	150	3	−	−	PROPN
ejpam-5884	150	4	s)α−1(s−	s)α−1(s−	PROPN
ejpam-5884	150	5	w)α−1dw	w)α−1dw	PROPN
ejpam-5884	150	6	ds	ds	PROPN
ejpam-5884	150	7	m.	m.	NOUN
ejpam-5884	150	8	i.	i.	PROPN
ejpam-5884	150	9	syam	syam	PROPN
ejpam-5884	150	10	et	et	PROPN
ejpam-5884	150	11	al	al	PROPN
ejpam-5884	150	12	.	.	PUNCT
ejpam-5884	150	13	/	/	SYM
ejpam-5884	150	14	eur	eur	PROPN
ejpam-5884	150	15	.	.	PUNCT
ejpam-5884	151	1	j.	j.	PROPN
ejpam-5884	151	2	pure	pure	PROPN
ejpam-5884	151	3	appl	appl	PROPN
ejpam-5884	151	4	.	.	PROPN
ejpam-5884	151	5	math	math	PROPN
ejpam-5884	151	6	,	,	PUNCT
ejpam-5884	151	7	18	18	NUM
ejpam-5884	151	8	(	(	PUNCT
ejpam-5884	151	9	2	2	NUM
ejpam-5884	151	10	)	)	PUNCT
ejpam-5884	151	11	(	(	PUNCT
ejpam-5884	151	12	2025	2025	NUM
ejpam-5884	151	13	)	)	PUNCT
ejpam-5884	151	14	,	,	PUNCT
ejpam-5884	151	15	5884	5884	NUM
ejpam-5884	151	16	7	7	NUM
ejpam-5884	151	17	of	of	ADP
ejpam-5884	151	18	18	18	NUM
ejpam-5884	151	19	−	−	PROPN
ejpam-5884	151	20	γ	γ	X
ejpam-5884	151	21	γ2(α	γ2(α	PROPN
ejpam-5884	151	22	)	)	PUNCT
ejpam-5884	151	23	∫	∫	PROPN
ejpam-5884	152	1	tj	tj	PROPN
ejpam-5884	152	2	0	0	NUM
ejpam-5884	152	3	∫	∫	PROPN
ejpam-5884	152	4	s	s	PART
ejpam-5884	152	5	0	0	NUM
ejpam-5884	152	6	(	(	PUNCT
ejpam-5884	152	7	m−1∑	m−1∑	PROPN
ejpam-5884	152	8	i=0	i=0	PROPN
ejpam-5884	152	9	xiµi(w	xiµi(w	PROPN
ejpam-5884	152	10	)	)	PUNCT
ejpam-5884	152	11	)	)	PUNCT
ejpam-5884	152	12	3	3	NUM
ejpam-5884	152	13	(	(	PUNCT
ejpam-5884	152	14	tj	tj	NOUN
ejpam-5884	152	15	−	−	PROPN
ejpam-5884	152	16	s)α−1(s−	s)α−1(s−	PROPN
ejpam-5884	152	17	w)α−1dw	w)α−1dw	PROPN
ejpam-5884	152	18	ds	ds	PROPN
ejpam-5884	152	19	.	.	PUNCT
ejpam-5884	153	1	(	(	PUNCT
ejpam-5884	153	2	22	22	NUM
ejpam-5884	153	3	)	)	PUNCT
ejpam-5884	153	4	this	this	DET
ejpam-5884	153	5	equation	equation	NOUN
ejpam-5884	153	6	can	can	AUX
ejpam-5884	153	7	be	be	AUX
ejpam-5884	153	8	solved	solve	VERB
ejpam-5884	153	9	due	due	ADP
ejpam-5884	153	10	to	to	ADP
ejpam-5884	153	11	the	the	DET
ejpam-5884	153	12	fact	fact	NOUN
ejpam-5884	153	13	that	that	SCONJ
ejpam-5884	153	14	µi(tj	µi(tj	NOUN
ejpam-5884	153	15	)	)	PUNCT
ejpam-5884	153	16	=	=	PRON
ejpam-5884	153	17	{	{	PUNCT
ejpam-5884	154	1	1	1	NUM
ejpam-5884	154	2	,	,	PUNCT
ejpam-5884	154	3	if	if	SCONJ
ejpam-5884	154	4	i	i	PRON
ejpam-5884	154	5	=	=	SYM
ejpam-5884	154	6	j	j	PROPN
ejpam-5884	154	7	0	0	NUM
ejpam-5884	154	8	,	,	PUNCT
ejpam-5884	154	9	if	if	SCONJ
ejpam-5884	154	10	i	i	PRON
ejpam-5884	154	11	̸=	̸=	PROPN
ejpam-5884	154	12	j	j	PROPN
ejpam-5884	154	13	.	.	PUNCT
ejpam-5884	155	1	by	by	ADP
ejpam-5884	155	2	utilizing	utilize	VERB
ejpam-5884	155	3	the	the	DET
ejpam-5884	155	4	properties	property	NOUN
ejpam-5884	155	5	of	of	ADP
ejpam-5884	155	6	the	the	DET
ejpam-5884	155	7	riemann	riemann	PROPN
ejpam-5884	155	8	integral	integral	PROPN
ejpam-5884	155	9	,	,	PUNCT
ejpam-5884	155	10	equation	equation	NOUN
ejpam-5884	155	11	(	(	PUNCT
ejpam-5884	155	12	22	22	NUM
ejpam-5884	155	13	)	)	PUNCT
ejpam-5884	155	14	simplifies	simplifie	NOUN
ejpam-5884	155	15	to	to	ADP
ejpam-5884	155	16	xj	xj	NOUN
ejpam-5884	155	17	=	=	SYM
ejpam-5884	155	18	a−	a−	PROPN
ejpam-5884	155	19	β	β	X
ejpam-5884	155	20	γ2(α	γ2(α	PROPN
ejpam-5884	155	21	)	)	PUNCT
ejpam-5884	155	22	j−1∑	j−1∑	PROPN
ejpam-5884	155	23	k=0	k=0	PROPN
ejpam-5884	155	24	∫	∫	PROPN
ejpam-5884	156	1	tk+1	tk+1	NUM
ejpam-5884	156	2	tk	tk	PROPN
ejpam-5884	156	3	∫	∫	PROPN
ejpam-5884	156	4	s	s	PART
ejpam-5884	156	5	0	0	NUM
ejpam-5884	156	6	(	(	PUNCT
ejpam-5884	156	7	m−1∑	m−1∑	PROPN
ejpam-5884	156	8	i=0	i=0	PROPN
ejpam-5884	156	9	xiµi(w	xiµi(w	PROPN
ejpam-5884	156	10	)	)	PUNCT
ejpam-5884	156	11	)	)	PUNCT
ejpam-5884	157	1	(	(	PUNCT
ejpam-5884	157	2	tj	tj	X
ejpam-5884	157	3	−	−	PROPN
ejpam-5884	157	4	s)α−1(s−	s)α−1(s−	PROPN
ejpam-5884	157	5	w)α−1dw	w)α−1dw	PROPN
ejpam-5884	157	6	ds	ds	ADJ
ejpam-5884	157	7	−	−	PROPN
ejpam-5884	157	8	γ	γ	X
ejpam-5884	157	9	γ2(α	γ2(α	PROPN
ejpam-5884	157	10	)	)	PUNCT
ejpam-5884	157	11	j−1∑	j−1∑	PROPN
ejpam-5884	157	12	k=0	k=0	PROPN
ejpam-5884	157	13	∫	∫	PROPN
ejpam-5884	158	1	tk+1	tk+1	NUM
ejpam-5884	158	2	tk	tk	PROPN
ejpam-5884	158	3	∫	∫	PROPN
ejpam-5884	158	4	s	s	PART
ejpam-5884	158	5	0	0	NUM
ejpam-5884	158	6	(	(	PUNCT
ejpam-5884	158	7	m−1∑	m−1∑	PROPN
ejpam-5884	158	8	i=0	i=0	PROPN
ejpam-5884	158	9	xiµi(w	xiµi(w	PROPN
ejpam-5884	158	10	)	)	PUNCT
ejpam-5884	158	11	)	)	PUNCT
ejpam-5884	158	12	3	3	NUM
ejpam-5884	158	13	(	(	PUNCT
ejpam-5884	158	14	tj	tj	NOUN
ejpam-5884	158	15	−	−	PROPN
ejpam-5884	158	16	s)α−1(s−	s)α−1(s−	PROPN
ejpam-5884	158	17	w)α−1dw	w)α−1dw	PROPN
ejpam-5884	158	18	ds	ds	PROPN
ejpam-5884	158	19	.	.	PUNCT
ejpam-5884	159	1	(	(	PUNCT
ejpam-5884	159	2	23	23	NUM
ejpam-5884	159	3	)	)	PUNCT
ejpam-5884	159	4	for	for	ADP
ejpam-5884	159	5	any	any	DET
ejpam-5884	159	6	1	1	NUM
ejpam-5884	159	7	≤	≤	NUM
ejpam-5884	159	8	k	k	PROPN
ejpam-5884	159	9	,	,	PUNCT
ejpam-5884	159	10	j	j	X
ejpam-5884	159	11	<	<	X
ejpam-5884	159	12	m	m	X
ejpam-5884	159	13	,	,	PUNCT
ejpam-5884	159	14	we	we	PRON
ejpam-5884	159	15	know	know	VERB
ejpam-5884	159	16	that	that	PRON
ejpam-5884	159	17	µj(t	µj(t	PUNCT
ejpam-5884	159	18	)	)	PUNCT
ejpam-5884	160	1	=	=	PRON
ejpam-5884	160	2	{	{	PUNCT
ejpam-5884	160	3	1	1	NUM
ejpam-5884	160	4	,	,	PUNCT
ejpam-5884	160	5	if	if	SCONJ
ejpam-5884	160	6	j	j	PROPN
ejpam-5884	160	7	=	=	SYM
ejpam-5884	160	8	k	k	PROPN
ejpam-5884	160	9	0	0	PUNCT
ejpam-5884	160	10	,	,	PUNCT
ejpam-5884	160	11	if	if	SCONJ
ejpam-5884	160	12	j	j	PROPN
ejpam-5884	160	13	̸=	̸=	PROPN
ejpam-5884	160	14	k	k	PROPN
ejpam-5884	160	15	,	,	PUNCT
ejpam-5884	160	16	t	t	PROPN
ejpam-5884	160	17	∈	∈	PROPN
ejpam-5884	161	1	[	[	X
ejpam-5884	161	2	tk	tk	X
ejpam-5884	161	3	,	,	PUNCT
ejpam-5884	161	4	tk+1	tk+1	NUM
ejpam-5884	161	5	)	)	PUNCT
ejpam-5884	161	6	.	.	PUNCT
ejpam-5884	162	1	this	this	PRON
ejpam-5884	162	2	leads	lead	VERB
ejpam-5884	162	3	to	to	ADP
ejpam-5884	162	4	the	the	DET
ejpam-5884	162	5	following	follow	VERB
ejpam-5884	162	6	simplifications∫	simplifications∫	ADV
ejpam-5884	162	7	tk+1	tk+1	NUM
ejpam-5884	162	8	tk	tk	PROPN
ejpam-5884	162	9	∫	∫	PROPN
ejpam-5884	162	10	s	s	PART
ejpam-5884	162	11	0	0	NUM
ejpam-5884	162	12	(	(	PUNCT
ejpam-5884	162	13	m−1∑	m−1∑	PROPN
ejpam-5884	162	14	i=0	i=0	PROPN
ejpam-5884	162	15	xiµi(w	xiµi(w	PROPN
ejpam-5884	162	16	)	)	PUNCT
ejpam-5884	162	17	)	)	PUNCT
ejpam-5884	163	1	(	(	PUNCT
ejpam-5884	163	2	tj	tj	X
ejpam-5884	163	3	−	−	PROPN
ejpam-5884	163	4	s)α−1(s−	s)α−1(s−	PROPN
ejpam-5884	163	5	w)α−1dw	w)α−1dw	PROPN
ejpam-5884	163	6	ds	ds	PROPN
ejpam-5884	163	7	=	=	SYM
ejpam-5884	163	8	∫	∫	PROPN
ejpam-5884	163	9	tk+1	tk+1	NUM
ejpam-5884	164	1	tk	tk	PROPN
ejpam-5884	164	2	∫	∫	PROPN
ejpam-5884	164	3	s	s	PART
ejpam-5884	164	4	0	0	NUM
ejpam-5884	164	5	xk(tj	xk(tj	PROPN
ejpam-5884	165	1	−	−	PROPN
ejpam-5884	165	2	s)α−1(s−	s)α−1(s−	PROPN
ejpam-5884	165	3	w)α−1dw	w)α−1dw	PROPN
ejpam-5884	165	4	ds	ds	PROPN
ejpam-5884	165	5	,	,	PUNCT
ejpam-5884	165	6	∫	∫	PROPN
ejpam-5884	165	7	tk+1	tk+1	NUM
ejpam-5884	166	1	tk	tk	PROPN
ejpam-5884	166	2	∫	∫	PROPN
ejpam-5884	166	3	s	s	PART
ejpam-5884	166	4	0	0	NUM
ejpam-5884	166	5	(	(	PUNCT
ejpam-5884	166	6	m−1∑	m−1∑	PROPN
ejpam-5884	166	7	i=0	i=0	PROPN
ejpam-5884	166	8	xiµi(w	xiµi(w	PROPN
ejpam-5884	166	9	)	)	PUNCT
ejpam-5884	166	10	)	)	PUNCT
ejpam-5884	166	11	3	3	NUM
ejpam-5884	166	12	(	(	PUNCT
ejpam-5884	166	13	tj	tj	NOUN
ejpam-5884	166	14	−	−	PROPN
ejpam-5884	166	15	s)α−1(s−	s)α−1(s−	PROPN
ejpam-5884	166	16	w)α−1dw	w)α−1dw	PROPN
ejpam-5884	166	17	ds	ds	PROPN
ejpam-5884	166	18	=	=	SYM
ejpam-5884	166	19	∫	∫	PROPN
ejpam-5884	167	1	tk+1	tk+1	NUM
ejpam-5884	167	2	tk	tk	PROPN
ejpam-5884	167	3	∫	∫	PROPN
ejpam-5884	167	4	s	s	PART
ejpam-5884	167	5	0	0	NUM
ejpam-5884	167	6	x3k(tj	x3k(tj	PROPN
ejpam-5884	167	7	−	−	PROPN
ejpam-5884	167	8	s)α−1(s−	s)α−1(s−	PROPN
ejpam-5884	167	9	w)α−1dw	w)α−1dw	PROPN
ejpam-5884	167	10	ds	ds	PROPN
ejpam-5884	167	11	.	.	PUNCT
ejpam-5884	168	1	thus	thus	ADV
ejpam-5884	168	2	,	,	PUNCT
ejpam-5884	168	3	we	we	PRON
ejpam-5884	168	4	can	can	AUX
ejpam-5884	168	5	express	express	VERB
ejpam-5884	168	6	the	the	DET
ejpam-5884	168	7	equation	equation	NOUN
ejpam-5884	168	8	for	for	ADP
ejpam-5884	168	9	xj	xj	PROPN
ejpam-5884	168	10	as	as	ADP
ejpam-5884	168	11	xj	xj	PROPN
ejpam-5884	168	12	=	=	SYM
ejpam-5884	168	13	a−	a−	PROPN
ejpam-5884	168	14	β	β	X
ejpam-5884	168	15	γ2(α	γ2(α	PROPN
ejpam-5884	168	16	)	)	PUNCT
ejpam-5884	168	17	j−1∑	j−1∑	NOUN
ejpam-5884	168	18	k=0	k=0	PROPN
ejpam-5884	168	19	ηjkxk	ηjkxk	VERB
ejpam-5884	168	20	−	−	PROPN
ejpam-5884	168	21	γ	γ	PROPN
ejpam-5884	168	22	γ2(α	γ2(α	PROPN
ejpam-5884	168	23	)	)	PUNCT
ejpam-5884	168	24	j−1∑	j−1∑	NOUN
ejpam-5884	168	25	k=0	k=0	PROPN
ejpam-5884	168	26	ηjkx	ηjkx	VERB
ejpam-5884	168	27	3	3	NUM
ejpam-5884	168	28	k	k	NOUN
ejpam-5884	168	29	,	,	PUNCT
ejpam-5884	168	30	(	(	PUNCT
ejpam-5884	168	31	24	24	NUM
ejpam-5884	168	32	)	)	PUNCT
ejpam-5884	168	33	where	where	SCONJ
ejpam-5884	168	34	the	the	DET
ejpam-5884	168	35	coefficients	coefficient	NOUN
ejpam-5884	168	36	ηjk	ηjk	NOUN
ejpam-5884	168	37	are	be	AUX
ejpam-5884	168	38	defined	define	VERB
ejpam-5884	168	39	as	as	ADP
ejpam-5884	168	40	ηjk	ηjk	NOUN
ejpam-5884	168	41	=	=	SYM
ejpam-5884	169	1	∫	∫	PROPN
ejpam-5884	169	2	tk+1	tk+1	NUM
ejpam-5884	170	1	tk	tk	PROPN
ejpam-5884	170	2	∫	∫	PROPN
ejpam-5884	170	3	s	s	PART
ejpam-5884	170	4	0	0	NUM
ejpam-5884	170	5	(	(	PUNCT
ejpam-5884	170	6	tj	tj	NOUN
ejpam-5884	170	7	−	−	PROPN
ejpam-5884	170	8	s)α−1(s−	s)α−1(s−	PROPN
ejpam-5884	170	9	w)α−1dw	w)α−1dw	PROPN
ejpam-5884	170	10	ds	ds	PROPN
ejpam-5884	170	11	.	.	PUNCT
ejpam-5884	170	12	(	(	PUNCT
ejpam-5884	170	13	25	25	NUM
ejpam-5884	170	14	)	)	PUNCT
ejpam-5884	170	15	m.	m.	NOUN
ejpam-5884	170	16	i.	i.	PROPN
ejpam-5884	170	17	syam	syam	PROPN
ejpam-5884	170	18	et	et	PROPN
ejpam-5884	170	19	al	al	PROPN
ejpam-5884	170	20	.	.	PUNCT
ejpam-5884	170	21	/	/	SYM
ejpam-5884	170	22	eur	eur	PROPN
ejpam-5884	170	23	.	.	PUNCT
ejpam-5884	171	1	j.	j.	PROPN
ejpam-5884	171	2	pure	pure	PROPN
ejpam-5884	171	3	appl	appl	PROPN
ejpam-5884	171	4	.	.	PROPN
ejpam-5884	171	5	math	math	PROPN
ejpam-5884	171	6	,	,	PUNCT
ejpam-5884	171	7	18	18	NUM
ejpam-5884	171	8	(	(	PUNCT
ejpam-5884	171	9	2	2	NUM
ejpam-5884	171	10	)	)	PUNCT
ejpam-5884	171	11	(	(	PUNCT
ejpam-5884	171	12	2025	2025	NUM
ejpam-5884	171	13	)	)	PUNCT
ejpam-5884	171	14	,	,	PUNCT
ejpam-5884	171	15	5884	5884	NUM
ejpam-5884	171	16	8	8	NUM
ejpam-5884	171	17	of	of	ADP
ejpam-5884	171	18	18	18	NUM
ejpam-5884	171	19	4	4	NUM
ejpam-5884	171	20	.	.	PUNCT
ejpam-5884	171	21	error	error	NOUN
ejpam-5884	171	22	analysis	analysis	NOUN
ejpam-5884	171	23	let	let	VERB
ejpam-5884	171	24	x	x	SYM
ejpam-5884	171	25	∈	∈	PROPN
ejpam-5884	171	26	l2([0	l2([0	PROPN
ejpam-5884	171	27	,	,	PUNCT
ejpam-5884	171	28	t	t	NOUN
ejpam-5884	171	29	)	)	PUNCT
ejpam-5884	171	30	)	)	PUNCT
ejpam-5884	171	31	be	be	AUX
ejpam-5884	171	32	a	a	DET
ejpam-5884	171	33	function	function	NOUN
ejpam-5884	171	34	,	,	PUNCT
ejpam-5884	171	35	and	and	CCONJ
ejpam-5884	171	36	its	its	PRON
ejpam-5884	171	37	norm	norm	NOUN
ejpam-5884	171	38	is	be	AUX
ejpam-5884	171	39	defined	define	VERB
ejpam-5884	171	40	by	by	ADP
ejpam-5884	171	41	the	the	DET
ejpam-5884	171	42	following	follow	VERB
ejpam-5884	171	43	formula	formula	NOUN
ejpam-5884	171	44	:	:	PUNCT
ejpam-5884	171	45	||x||	||x||	ADP
ejpam-5884	171	46	=	=	PUNCT
ejpam-5884	171	47	√∫	√∫	PROPN
ejpam-5884	171	48	t	t	NOUN
ejpam-5884	171	49	0	0	PUNCT
ejpam-5884	171	50	|x(t)|2	|x(t)|2	SYM
ejpam-5884	171	51	dt	dt	PROPN
ejpam-5884	171	52	.	.	PUNCT
ejpam-5884	172	1	(	(	PUNCT
ejpam-5884	172	2	26	26	NUM
ejpam-5884	172	3	)	)	PUNCT
ejpam-5884	172	4	according	accord	VERB
ejpam-5884	172	5	to	to	ADP
ejpam-5884	172	6	lemma	lemma	PROPN
ejpam-5884	172	7	(	(	PUNCT
ejpam-5884	172	8	2	2	NUM
ejpam-5884	172	9	)	)	PUNCT
ejpam-5884	172	10	,	,	PUNCT
ejpam-5884	172	11	the	the	DET
ejpam-5884	172	12	function	function	NOUN
ejpam-5884	172	13	x(t	x(t	PROPN
ejpam-5884	172	14	)	)	PUNCT
ejpam-5884	172	15	can	can	AUX
ejpam-5884	172	16	be	be	AUX
ejpam-5884	172	17	approximated	approximate	VERB
ejpam-5884	172	18	as	as	ADP
ejpam-5884	172	19	xm	xm	PROPN
ejpam-5884	172	20	(	(	PUNCT
ejpam-5884	172	21	t	t	PROPN
ejpam-5884	172	22	)	)	PUNCT
ejpam-5884	172	23	=	=	PUNCT
ejpam-5884	173	1	m−1∑	m−1∑	PROPN
ejpam-5884	173	2	i=0	i=0	PROPN
ejpam-5884	173	3	xiµi(t	xiµi(t	NOUN
ejpam-5884	173	4	)	)	PUNCT
ejpam-5884	173	5	.	.	PUNCT
ejpam-5884	174	1	(	(	PUNCT
ejpam-5884	174	2	27	27	NUM
ejpam-5884	174	3	)	)	PUNCT
ejpam-5884	174	4	the	the	DET
ejpam-5884	174	5	aim	aim	NOUN
ejpam-5884	174	6	of	of	ADP
ejpam-5884	174	7	theorem	theorem	NOUN
ejpam-5884	174	8	(	(	PUNCT
ejpam-5884	174	9	2	2	NUM
ejpam-5884	174	10	)	)	PUNCT
ejpam-5884	174	11	is	be	AUX
ejpam-5884	174	12	to	to	PART
ejpam-5884	174	13	demonstrate	demonstrate	VERB
ejpam-5884	174	14	that	that	SCONJ
ejpam-5884	174	15	the	the	DET
ejpam-5884	174	16	mean	mean	ADJ
ejpam-5884	174	17	square	square	ADJ
ejpam-5884	174	18	error	error	NOUN
ejpam-5884	174	19	is	be	AUX
ejpam-5884	174	20	minimized	minimize	VERB
ejpam-5884	174	21	when	when	SCONJ
ejpam-5884	174	22	the	the	DET
ejpam-5884	174	23	coefficients	coefficient	NOUN
ejpam-5884	174	24	xi	xi	X
ejpam-5884	174	25	are	be	AUX
ejpam-5884	174	26	chosen	choose	VERB
ejpam-5884	174	27	according	accord	VERB
ejpam-5884	174	28	to	to	ADP
ejpam-5884	174	29	equation	equation	NOUN
ejpam-5884	174	30	(	(	PUNCT
ejpam-5884	174	31	16	16	NUM
ejpam-5884	174	32	)	)	PUNCT
ejpam-5884	174	33	.	.	PUNCT
ejpam-5884	175	1	theorem	theorem	NOUN
ejpam-5884	175	2	2	2	NUM
ejpam-5884	175	3	.	.	PUNCT
ejpam-5884	176	1	let	let	VERB
ejpam-5884	176	2	x	x	X
ejpam-5884	176	3	∈	∈	PROPN
ejpam-5884	176	4	l2([0	l2([0	PROPN
ejpam-5884	176	5	,	,	PUNCT
ejpam-5884	176	6	t	t	NOUN
ejpam-5884	176	7	)	)	PUNCT
ejpam-5884	176	8	)	)	PUNCT
ejpam-5884	176	9	and	and	CCONJ
ejpam-5884	176	10	define	define	VERB
ejpam-5884	176	11	xm	xm	PROPN
ejpam-5884	176	12	(	(	PUNCT
ejpam-5884	176	13	t	t	PROPN
ejpam-5884	176	14	)	)	PUNCT
ejpam-5884	176	15	as	as	SCONJ
ejpam-5884	176	16	given	give	VERB
ejpam-5884	176	17	in	in	ADP
ejpam-5884	176	18	equation	equation	NOUN
ejpam-5884	176	19	(	(	PUNCT
ejpam-5884	176	20	27	27	NUM
ejpam-5884	176	21	)	)	PUNCT
ejpam-5884	176	22	.	.	PUNCT
ejpam-5884	177	1	then	then	ADV
ejpam-5884	177	2	,	,	PUNCT
ejpam-5884	177	3	the	the	DET
ejpam-5884	177	4	mean	mean	ADJ
ejpam-5884	177	5	square	square	ADJ
ejpam-5884	177	6	error	error	NOUN
ejpam-5884	177	7	term	term	NOUN
ejpam-5884	177	8	a(x0	a(x0	NOUN
ejpam-5884	177	9	,	,	PUNCT
ejpam-5884	177	10	x1	x1	PROPN
ejpam-5884	177	11	,	,	PUNCT
ejpam-5884	177	12	.	.	PUNCT
ejpam-5884	177	13	.	.	PUNCT
ejpam-5884	177	14	.	.	PUNCT
ejpam-5884	178	1	,	,	PUNCT
ejpam-5884	178	2	xm−1	xm−1	PROPN
ejpam-5884	178	3	)	)	PUNCT
ejpam-5884	179	1	=	=	PUNCT
ejpam-5884	180	1	∫	∫	PROPN
ejpam-5884	180	2	t	t	PROPN
ejpam-5884	180	3	0	0	NUM
ejpam-5884	181	1	(	(	PUNCT
ejpam-5884	181	2	x(t)−	x(t)−	PROPN
ejpam-5884	181	3	xm	xm	PROPN
ejpam-5884	181	4	(	(	PUNCT
ejpam-5884	181	5	t))2	t))2	PROPN
ejpam-5884	181	6	dt	dt	VERB
ejpam-5884	181	7	is	be	AUX
ejpam-5884	181	8	minimized	minimize	VERB
ejpam-5884	181	9	when	when	SCONJ
ejpam-5884	181	10	xi	xi	PROPN
ejpam-5884	181	11	is	be	AUX
ejpam-5884	181	12	computed	compute	VERB
ejpam-5884	181	13	according	accord	VERB
ejpam-5884	181	14	to	to	ADP
ejpam-5884	181	15	equation	equation	NOUN
ejpam-5884	181	16	(	(	PUNCT
ejpam-5884	181	17	16	16	NUM
ejpam-5884	181	18	)	)	PUNCT
ejpam-5884	181	19	for	for	ADP
ejpam-5884	181	20	all	all	DET
ejpam-5884	181	21	i	i	PRON
ejpam-5884	181	22	=	=	NOUN
ejpam-5884	181	23	0	0	NUM
ejpam-5884	181	24	,	,	PUNCT
ejpam-5884	181	25	1	1	NUM
ejpam-5884	181	26	,	,	PUNCT
ejpam-5884	181	27	.	.	PUNCT
ejpam-5884	181	28	.	.	PUNCT
ejpam-5884	182	1	.	.	PUNCT
ejpam-5884	183	1	,	,	PUNCT
ejpam-5884	183	2	m	m	VERB
ejpam-5884	183	3	−	−	NOUN
ejpam-5884	184	1	1	1	NUM
ejpam-5884	184	2	.	.	PUNCT
ejpam-5884	185	1	proof	proof	NOUN
ejpam-5884	185	2	.	.	PUNCT
ejpam-5884	186	1	for	for	ADP
ejpam-5884	186	2	0	0	NUM
ejpam-5884	186	3	≤	≤	NUM
ejpam-5884	187	1	i	i	PRON
ejpam-5884	187	2	≤	≤	NUM
ejpam-5884	187	3	m	m	VERB
ejpam-5884	187	4	−	−	PROPN
ejpam-5884	187	5	1	1	NUM
ejpam-5884	187	6	,	,	PUNCT
ejpam-5884	187	7	by	by	ADP
ejpam-5884	187	8	applying	apply	VERB
ejpam-5884	187	9	theorem	theorem	NOUN
ejpam-5884	187	10	(	(	PUNCT
ejpam-5884	187	11	1	1	NUM
ejpam-5884	187	12	)	)	PUNCT
ejpam-5884	187	13	,	,	PUNCT
ejpam-5884	187	14	we	we	PRON
ejpam-5884	187	15	compute	compute	VERB
ejpam-5884	187	16	∂a	∂a	NOUN
ejpam-5884	187	17	∂xi	∂xi	NOUN
ejpam-5884	187	18	=	=	SYM
ejpam-5884	187	19	2	2	NUM
ejpam-5884	187	20	∫	∫	NOUN
ejpam-5884	187	21	t	t	PROPN
ejpam-5884	187	22	0	0	NUM
ejpam-5884	188	1	(	(	PUNCT
ejpam-5884	188	2	x(t)−	x(t)−	PROPN
ejpam-5884	188	3	xm	xm	PROPN
ejpam-5884	188	4	(	(	PUNCT
ejpam-5884	188	5	t))µi(t	t))µi(t	ADP
ejpam-5884	188	6	)	)	PUNCT
ejpam-5884	188	7	dt	dt	NOUN
ejpam-5884	189	1	=	=	SYM
ejpam-5884	189	2	2	2	NUM
ejpam-5884	189	3	(	(	PUNCT
ejpam-5884	189	4	∫	∫	PROPN
ejpam-5884	189	5	t	t	PROPN
ejpam-5884	189	6	0	0	NUM
ejpam-5884	189	7	x(t)µi(t	x(t)µi(t	NOUN
ejpam-5884	189	8	)	)	PUNCT
ejpam-5884	189	9	dt−∆xi	dt−∆xi	X
ejpam-5884	189	10	)	)	PUNCT
ejpam-5884	189	11	=	=	SYM
ejpam-5884	189	12	0	0	X
ejpam-5884	189	13	.	.	PUNCT
ejpam-5884	190	1	therefore	therefore	ADV
ejpam-5884	190	2	,	,	PUNCT
ejpam-5884	190	3	we	we	PRON
ejpam-5884	190	4	obtain	obtain	VERB
ejpam-5884	190	5	xi	xi	ADP
ejpam-5884	190	6	=	=	SYM
ejpam-5884	190	7	1	1	NUM
ejpam-5884	190	8	∆	∆	PROPN
ejpam-5884	190	9	∫	∫	PROPN
ejpam-5884	190	10	t	t	PROPN
ejpam-5884	190	11	0	0	NUM
ejpam-5884	190	12	x(t)µi(t	x(t)µi(t	NOUN
ejpam-5884	190	13	)	)	PUNCT
ejpam-5884	191	1	dt	dt	X
ejpam-5884	191	2	.	.	PUNCT
ejpam-5884	192	1	additionally	additionally	ADV
ejpam-5884	192	2	,	,	PUNCT
ejpam-5884	192	3	theorem	theorem	ADJ
ejpam-5884	192	4	(	(	PUNCT
ejpam-5884	192	5	1	1	NUM
ejpam-5884	192	6	)	)	PUNCT
ejpam-5884	192	7	provides	provide	VERB
ejpam-5884	192	8	the	the	DET
ejpam-5884	192	9	second	second	ADJ
ejpam-5884	192	10	-	-	PUNCT
ejpam-5884	192	11	order	order	NOUN
ejpam-5884	192	12	derivatives	derivative	NOUN
ejpam-5884	192	13	as	as	ADP
ejpam-5884	192	14	:	:	PUNCT
ejpam-5884	192	15	∂2a	∂2a	NOUN
ejpam-5884	192	16	∂xi∂xj	∂xi∂xj	NOUN
ejpam-5884	192	17	=	=	PUNCT
ejpam-5884	192	18	{	{	PUNCT
ejpam-5884	192	19	2∆	2∆	NUM
ejpam-5884	192	20	,	,	PUNCT
ejpam-5884	192	21	if	if	SCONJ
ejpam-5884	192	22	i	i	PRON
ejpam-5884	192	23	=	=	SYM
ejpam-5884	192	24	j	j	PROPN
ejpam-5884	192	25	,	,	PUNCT
ejpam-5884	192	26	0	0	NUM
ejpam-5884	192	27	,	,	PUNCT
ejpam-5884	192	28	if	if	SCONJ
ejpam-5884	192	29	i	i	PRON
ejpam-5884	192	30	̸=	̸=	PROPN
ejpam-5884	192	31	j.	j.	PROPN
ejpam-5884	192	32	0	0	PUNCT
ejpam-5884	192	33	≤	≤	PROPN
ejpam-5884	193	1	i	i	PROPN
ejpam-5884	193	2	,	,	PUNCT
ejpam-5884	193	3	j	j	PROPN
ejpam-5884	193	4	≤	≤	PROPN
ejpam-5884	193	5	m	m	VERB
ejpam-5884	193	6	−	−	PROPN
ejpam-5884	193	7	1	1	NUM
ejpam-5884	193	8	.	.	PUNCT
ejpam-5884	194	1	for	for	ADP
ejpam-5884	194	2	any	any	DET
ejpam-5884	194	3	0	0	NUM
ejpam-5884	194	4	≤	≤	NUM
ejpam-5884	195	1	i	i	PRON
ejpam-5884	195	2	≤	≤	NUM
ejpam-5884	195	3	m	m	VERB
ejpam-5884	195	4	−	−	PROPN
ejpam-5884	195	5	1	1	NUM
ejpam-5884	195	6	,	,	PUNCT
ejpam-5884	195	7	we	we	PRON
ejpam-5884	195	8	compute	compute	VERB
ejpam-5884	195	9	the	the	DET
ejpam-5884	195	10	determinant	determinant	NOUN
ejpam-5884	195	11	of	of	ADP
ejpam-5884	195	12	the	the	DET
ejpam-5884	195	13	hessian	hessian	ADJ
ejpam-5884	195	14	matrix:∣∣∣∣∣∣∣∣∣∣∣	matrix:∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5884	195	15	∂2a	∂2a	PROPN
ejpam-5884	195	16	∂x2	∂x2	NOUN
ejpam-5884	195	17	0	0	NUM
ejpam-5884	195	18	∂2a	∂2a	NOUN
ejpam-5884	195	19	∂x0∂x1	∂x0∂x1	NOUN
ejpam-5884	195	20	.	.	PUNCT
ejpam-5884	195	21	.	.	PUNCT
ejpam-5884	195	22	.	.	PUNCT
ejpam-5884	196	1	∂2a	∂2a	PROPN
ejpam-5884	196	2	∂x0∂xi	∂x0∂xi	X
ejpam-5884	196	3	∂2a	∂2a	PROPN
ejpam-5884	196	4	∂x1∂x0	∂x1∂x0	PROPN
ejpam-5884	196	5	∂2a	∂2a	PROPN
ejpam-5884	196	6	∂x2	∂x2	PROPN
ejpam-5884	196	7	1	1	NUM
ejpam-5884	196	8	.	.	PUNCT
ejpam-5884	196	9	.	.	PUNCT
ejpam-5884	196	10	.	.	PUNCT
ejpam-5884	197	1	∂2a	∂2a	NOUN
ejpam-5884	197	2	∂x1∂xi	∂x1∂xi	PROPN
ejpam-5884	197	3	...	...	PUNCT
ejpam-5884	197	4	...	...	PUNCT
ejpam-5884	197	5	.	.	PUNCT
ejpam-5884	197	6	.	.	PUNCT
ejpam-5884	197	7	.	.	PUNCT
ejpam-5884	198	1	...	...	PUNCT
ejpam-5884	199	1	∂2a	∂2a	NOUN
ejpam-5884	199	2	∂xi∂x0	∂xi∂x0	PROPN
ejpam-5884	199	3	∂2a	∂2a	NOUN
ejpam-5884	199	4	∂xi∂x1	∂xi∂x1	VERB
ejpam-5884	199	5	.	.	PUNCT
ejpam-5884	199	6	.	.	PUNCT
ejpam-5884	199	7	.	.	PUNCT
ejpam-5884	200	1	∂2a	∂2a	PROPN
ejpam-5884	200	2	∂x2	∂x2	NOUN
ejpam-5884	200	3	i	i	PRON
ejpam-5884	200	4	∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣	NOUN
ejpam-5884	200	5	=	=	SYM
ejpam-5884	200	6	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5884	200	7	2∆	2∆	NUM
ejpam-5884	200	8	0	0	NUM
ejpam-5884	200	9	.	.	PUNCT
ejpam-5884	200	10	.	.	PUNCT
ejpam-5884	200	11	.	.	PUNCT
ejpam-5884	201	1	0	0	NUM
ejpam-5884	202	1	0	0	NUM
ejpam-5884	202	2	2∆	2∆	NUM
ejpam-5884	202	3	.	.	PUNCT
ejpam-5884	202	4	.	.	PUNCT
ejpam-5884	203	1	.	.	PUNCT
ejpam-5884	204	1	0	0	NUM
ejpam-5884	204	2	...	...	PUNCT
ejpam-5884	204	3	...	...	PUNCT
ejpam-5884	204	4	.	.	PUNCT
ejpam-5884	204	5	.	.	PUNCT
ejpam-5884	204	6	.	.	PUNCT
ejpam-5884	205	1	...	...	PUNCT
ejpam-5884	206	1	0	0	NUM
ejpam-5884	206	2	0	0	NUM
ejpam-5884	206	3	.	.	PUNCT
ejpam-5884	206	4	.	.	PUNCT
ejpam-5884	206	5	.	.	PUNCT
ejpam-5884	207	1	2∆	2∆	NUM
ejpam-5884	207	2	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	SYM
ejpam-5884	207	3	=	=	SYM
ejpam-5884	207	4	(	(	PUNCT
ejpam-5884	207	5	2∆)i+1	2∆)i+1	X
ejpam-5884	207	6	>	>	X
ejpam-5884	207	7	0	0	X
ejpam-5884	207	8	.	.	PUNCT
ejpam-5884	208	1	thus	thus	ADV
ejpam-5884	208	2	,	,	PUNCT
ejpam-5884	208	3	the	the	DET
ejpam-5884	208	4	error	error	NOUN
ejpam-5884	208	5	a	a	NOUN
ejpam-5884	208	6	is	be	AUX
ejpam-5884	208	7	minimized	minimize	VERB
ejpam-5884	208	8	when	when	SCONJ
ejpam-5884	208	9	xi	xi	PROPN
ejpam-5884	208	10	is	be	AUX
ejpam-5884	208	11	computed	compute	VERB
ejpam-5884	208	12	according	accord	VERB
ejpam-5884	208	13	to	to	ADP
ejpam-5884	208	14	equation	equation	NOUN
ejpam-5884	208	15	(	(	PUNCT
ejpam-5884	208	16	16	16	NUM
ejpam-5884	208	17	)	)	PUNCT
ejpam-5884	208	18	for	for	ADP
ejpam-5884	208	19	all	all	DET
ejpam-5884	208	20	i	i	PRON
ejpam-5884	208	21	=	=	NOUN
ejpam-5884	208	22	0	0	NUM
ejpam-5884	208	23	,	,	PUNCT
ejpam-5884	208	24	1	1	NUM
ejpam-5884	208	25	,	,	PUNCT
ejpam-5884	208	26	.	.	PUNCT
ejpam-5884	208	27	.	.	PUNCT
ejpam-5884	208	28	.	.	PUNCT
ejpam-5884	209	1	,	,	PUNCT
ejpam-5884	209	2	m	m	VERB
ejpam-5884	209	3	−	−	NOUN
ejpam-5884	210	1	1	1	NUM
ejpam-5884	210	2	.	.	PUNCT
ejpam-5884	211	1	next	next	ADV
ejpam-5884	211	2	,	,	PUNCT
ejpam-5884	211	3	we	we	PRON
ejpam-5884	211	4	aim	aim	VERB
ejpam-5884	211	5	to	to	PART
ejpam-5884	211	6	establish	establish	VERB
ejpam-5884	211	7	the	the	DET
ejpam-5884	211	8	order	order	NOUN
ejpam-5884	211	9	of	of	ADP
ejpam-5884	211	10	the	the	DET
ejpam-5884	211	11	mean	mean	ADJ
ejpam-5884	211	12	square	square	ADJ
ejpam-5884	211	13	error	error	NOUN
ejpam-5884	211	14	in	in	ADP
ejpam-5884	211	15	approximating	approximate	VERB
ejpam-5884	211	16	x(t	x(t	PROPN
ejpam-5884	211	17	)	)	PUNCT
ejpam-5884	211	18	over	over	ADP
ejpam-5884	211	19	the	the	DET
ejpam-5884	211	20	interval	interval	NOUN
ejpam-5884	211	21	[	[	X
ejpam-5884	211	22	0	0	NUM
ejpam-5884	211	23	,	,	PUNCT
ejpam-5884	211	24	t	t	NOUN
ejpam-5884	211	25	)	)	PUNCT
ejpam-5884	211	26	.	.	PUNCT
ejpam-5884	212	1	m.	m.	PROPN
ejpam-5884	212	2	i.	i.	PROPN
ejpam-5884	212	3	syam	syam	PROPN
ejpam-5884	212	4	et	et	PROPN
ejpam-5884	212	5	al	al	PROPN
ejpam-5884	212	6	.	.	PUNCT
ejpam-5884	212	7	/	/	SYM
ejpam-5884	212	8	eur	eur	PROPN
ejpam-5884	212	9	.	.	PUNCT
ejpam-5884	213	1	j.	j.	PROPN
ejpam-5884	213	2	pure	pure	PROPN
ejpam-5884	213	3	appl	appl	PROPN
ejpam-5884	213	4	.	.	PROPN
ejpam-5884	213	5	math	math	PROPN
ejpam-5884	213	6	,	,	PUNCT
ejpam-5884	213	7	18	18	NUM
ejpam-5884	213	8	(	(	PUNCT
ejpam-5884	213	9	2	2	NUM
ejpam-5884	213	10	)	)	PUNCT
ejpam-5884	213	11	(	(	PUNCT
ejpam-5884	213	12	2025	2025	NUM
ejpam-5884	213	13	)	)	PUNCT
ejpam-5884	213	14	,	,	PUNCT
ejpam-5884	213	15	5884	5884	NUM
ejpam-5884	213	16	9	9	NUM
ejpam-5884	213	17	of	of	ADP
ejpam-5884	213	18	18	18	NUM
ejpam-5884	213	19	theorem	theorem	NOUN
ejpam-5884	213	20	3	3	X
ejpam-5884	213	21	.	.	PUNCT
ejpam-5884	214	1	let	let	AUX
ejpam-5884	214	2	x(t	x(t	PROPN
ejpam-5884	214	3	)	)	PUNCT
ejpam-5884	214	4	be	be	VERB
ejpam-5884	214	5	a	a	DET
ejpam-5884	214	6	differentiable	differentiable	ADJ
ejpam-5884	214	7	function	function	NOUN
ejpam-5884	214	8	on	on	ADP
ejpam-5884	214	9	[	[	X
ejpam-5884	214	10	0	0	NUM
ejpam-5884	214	11	,	,	PUNCT
ejpam-5884	214	12	t	t	NOUN
ejpam-5884	214	13	)	)	PUNCT
ejpam-5884	214	14	such	such	ADJ
ejpam-5884	214	15	that	that	SCONJ
ejpam-5884	214	16	|x′(t)|	|x′(t)|	NUM
ejpam-5884	214	17	≤	≤	ADJ
ejpam-5884	214	18	f	f	X
ejpam-5884	214	19	(	(	PUNCT
ejpam-5884	214	20	28	28	NUM
ejpam-5884	214	21	)	)	PUNCT
ejpam-5884	214	22	for	for	ADP
ejpam-5884	214	23	all	all	DET
ejpam-5884	214	24	t	t	NOUN
ejpam-5884	214	25	∈	∈	PROPN
ejpam-5884	215	1	[	[	X
ejpam-5884	215	2	0	0	NUM
ejpam-5884	215	3	,	,	PUNCT
ejpam-5884	215	4	t	t	NOUN
ejpam-5884	215	5	)	)	PUNCT
ejpam-5884	215	6	,	,	PUNCT
ejpam-5884	215	7	where	where	SCONJ
ejpam-5884	215	8	f	f	PROPN
ejpam-5884	215	9	is	be	AUX
ejpam-5884	215	10	a	a	DET
ejpam-5884	215	11	positive	positive	ADJ
ejpam-5884	215	12	constant	constant	NOUN
ejpam-5884	215	13	.	.	PUNCT
ejpam-5884	216	1	then	then	ADV
ejpam-5884	216	2	,	,	PUNCT
ejpam-5884	216	3	||a||2	||a||2	NOUN
ejpam-5884	216	4	≤	≤	PUNCT
ejpam-5884	217	1	c∆2	c∆2	PROPN
ejpam-5884	217	2	(	(	PUNCT
ejpam-5884	217	3	29	29	NUM
ejpam-5884	217	4	)	)	PUNCT
ejpam-5884	217	5	where	where	SCONJ
ejpam-5884	217	6	a(x	a(x	NOUN
ejpam-5884	217	7	)	)	PUNCT
ejpam-5884	217	8	=	=	SYM
ejpam-5884	217	9	x(t)−	x(t)−	PROPN
ejpam-5884	217	10	xm	xm	PROPN
ejpam-5884	217	11	(	(	PUNCT
ejpam-5884	217	12	t	t	PROPN
ejpam-5884	217	13	)	)	PUNCT
ejpam-5884	217	14	,	,	PUNCT
ejpam-5884	217	15	t	t	PROPN
ejpam-5884	217	16	∈	∈	PROPN
ejpam-5884	218	1	[	[	X
ejpam-5884	218	2	0	0	NUM
ejpam-5884	218	3	,	,	PUNCT
ejpam-5884	218	4	t	t	NOUN
ejpam-5884	218	5	)	)	PUNCT
ejpam-5884	218	6	,	,	PUNCT
ejpam-5884	218	7	and	and	CCONJ
ejpam-5884	218	8	c	c	NOUN
ejpam-5884	218	9	is	be	AUX
ejpam-5884	218	10	a	a	DET
ejpam-5884	218	11	positive	positive	ADJ
ejpam-5884	218	12	constant	constant	NOUN
ejpam-5884	218	13	,	,	PUNCT
ejpam-5884	218	14	with	with	ADP
ejpam-5884	218	15	∆	∆	PROPN
ejpam-5884	218	16	=	=	SYM
ejpam-5884	218	17	t	t	PROPN
ejpam-5884	218	18	m	m	NOUN
ejpam-5884	218	19	.	.	PUNCT
ejpam-5884	219	1	proof	proof	NOUN
ejpam-5884	219	2	.	.	PUNCT
ejpam-5884	220	1	let	let	VERB
ejpam-5884	220	2	ti	ti	NOUN
ejpam-5884	220	3	=	=	SYM
ejpam-5884	220	4	i∆	i∆	ADJ
ejpam-5884	220	5	and	and	CCONJ
ejpam-5884	220	6	ai	ai	VERB
ejpam-5884	220	7	=	=	PUNCT
ejpam-5884	221	1	[	[	X
ejpam-5884	221	2	ti	ti	X
ejpam-5884	221	3	,	,	PUNCT
ejpam-5884	221	4	ti+1	ti+1	NOUN
ejpam-5884	221	5	)	)	PUNCT
ejpam-5884	221	6	,	,	PUNCT
ejpam-5884	222	1	where	where	SCONJ
ejpam-5884	222	2	∆	∆	PROPN
ejpam-5884	222	3	=	=	SYM
ejpam-5884	222	4	t	t	PROPN
ejpam-5884	222	5	m	m	PROPN
ejpam-5884	222	6	and	and	CCONJ
ejpam-5884	222	7	i	i	PRON
ejpam-5884	222	8	=	=	NOUN
ejpam-5884	222	9	0	0	NUM
ejpam-5884	222	10	,	,	PUNCT
ejpam-5884	222	11	1	1	NUM
ejpam-5884	222	12	,	,	PUNCT
ejpam-5884	222	13	.	.	PUNCT
ejpam-5884	222	14	.	.	PUNCT
ejpam-5884	222	15	.	.	PUNCT
ejpam-5884	223	1	,	,	PUNCT
ejpam-5884	223	2	m	m	VERB
ejpam-5884	223	3	−	−	NOUN
ejpam-5884	223	4	1	1	NUM
ejpam-5884	223	5	.	.	PUNCT
ejpam-5884	223	6	by	by	ADP
ejpam-5884	223	7	applying	apply	VERB
ejpam-5884	223	8	the	the	DET
ejpam-5884	223	9	mean	mean	ADJ
ejpam-5884	223	10	value	value	NOUN
ejpam-5884	223	11	theorem	theorem	NOUN
ejpam-5884	223	12	for	for	ADP
ejpam-5884	223	13	integrals	integral	NOUN
ejpam-5884	223	14	and	and	CCONJ
ejpam-5884	223	15	equation	equation	NOUN
ejpam-5884	223	16	(	(	PUNCT
ejpam-5884	223	17	16	16	NUM
ejpam-5884	223	18	)	)	PUNCT
ejpam-5884	223	19	,	,	PUNCT
ejpam-5884	223	20	we	we	PRON
ejpam-5884	223	21	obtain	obtain	VERB
ejpam-5884	223	22	xm	xm	PROPN
ejpam-5884	223	23	(	(	PUNCT
ejpam-5884	223	24	t	t	PROPN
ejpam-5884	223	25	)	)	PUNCT
ejpam-5884	224	1	=	=	SYM
ejpam-5884	224	2	xi	xi	PROPN
ejpam-5884	224	3	,	,	PUNCT
ejpam-5884	224	4	t	t	PROPN
ejpam-5884	224	5	∈	∈	PROPN
ejpam-5884	225	1	[	[	X
ejpam-5884	225	2	ti	ti	NOUN
ejpam-5884	225	3	,	,	PUNCT
ejpam-5884	225	4	ti+1	ti+1	NOUN
ejpam-5884	225	5	)	)	PUNCT
ejpam-5884	225	6	,	,	PUNCT
ejpam-5884	225	7	=	=	SYM
ejpam-5884	225	8	1	1	NUM
ejpam-5884	225	9	∆	∆	X
ejpam-5884	225	10	∫	∫	NOUN
ejpam-5884	225	11	ti+1	ti+1	NOUN
ejpam-5884	225	12	ti	ti	NOUN
ejpam-5884	225	13	x(t	x(t	PROPN
ejpam-5884	225	14	)	)	PUNCT
ejpam-5884	225	15	dt	dt	PROPN
ejpam-5884	225	16	,	,	PUNCT
ejpam-5884	225	17	=	=	SYM
ejpam-5884	225	18	x(νi	x(νi	PROPN
ejpam-5884	225	19	)	)	PUNCT
ejpam-5884	225	20	,	,	PUNCT
ejpam-5884	225	21	νi	νi	PRON
ejpam-5884	225	22	∈	∈	PROPN
ejpam-5884	225	23	[	[	X
ejpam-5884	225	24	ti	ti	NOUN
ejpam-5884	225	25	,	,	PUNCT
ejpam-5884	225	26	ti+1	ti+1	NOUN
ejpam-5884	225	27	)	)	PUNCT
ejpam-5884	225	28	,	,	PUNCT
ejpam-5884	225	29	i	i	PRON
ejpam-5884	225	30	=	=	NOUN
ejpam-5884	225	31	0	0	NUM
ejpam-5884	225	32	,	,	PUNCT
ejpam-5884	225	33	1	1	NUM
ejpam-5884	225	34	,	,	PUNCT
ejpam-5884	225	35	.	.	PUNCT
ejpam-5884	225	36	.	.	PUNCT
ejpam-5884	225	37	.	.	PUNCT
ejpam-5884	226	1	,	,	PUNCT
ejpam-5884	226	2	m	m	VERB
ejpam-5884	226	3	−	−	NOUN
ejpam-5884	226	4	1	1	NUM
ejpam-5884	226	5	.	.	PUNCT
ejpam-5884	227	1	using	use	VERB
ejpam-5884	227	2	the	the	DET
ejpam-5884	227	3	mean	mean	ADJ
ejpam-5884	227	4	value	value	NOUN
ejpam-5884	227	5	theorem	theorem	NOUN
ejpam-5884	227	6	for	for	ADP
ejpam-5884	227	7	integrals	integral	NOUN
ejpam-5884	227	8	,	,	PUNCT
ejpam-5884	227	9	we	we	PRON
ejpam-5884	227	10	have	have	VERB
ejpam-5884	227	11	:	:	PUNCT
ejpam-5884	227	12	||a||2	||a||2	NOUN
ejpam-5884	227	13	=	=	SYM
ejpam-5884	228	1	∫	∫	PROPN
ejpam-5884	229	1	t	t	PROPN
ejpam-5884	229	2	0	0	NUM
ejpam-5884	230	1	(	(	PUNCT
ejpam-5884	230	2	x(t)−	x(t)−	PROPN
ejpam-5884	230	3	xm	xm	PROPN
ejpam-5884	230	4	(	(	PUNCT
ejpam-5884	230	5	t))2	t))2	PROPN
ejpam-5884	230	6	dx	dx	PROPN
ejpam-5884	230	7	=	=	PUNCT
ejpam-5884	230	8	m−1∑	m−1∑	PROPN
ejpam-5884	230	9	i=0	i=0	PROPN
ejpam-5884	230	10	∫	∫	PROPN
ejpam-5884	230	11	ti+1	ti+1	ADV
ejpam-5884	230	12	ti	ti	PROPN
ejpam-5884	230	13	(	(	PUNCT
ejpam-5884	230	14	x(t)−	x(t)−	PROPN
ejpam-5884	230	15	xm	xm	PROPN
ejpam-5884	230	16	(	(	PUNCT
ejpam-5884	230	17	t))2	t))2	PROPN
ejpam-5884	230	18	dx	dx	PROPN
ejpam-5884	230	19	=	=	PUNCT
ejpam-5884	230	20	∆	∆	PROPN
ejpam-5884	230	21	m−1∑	m−1∑	NUM
ejpam-5884	230	22	i=0	i=0	PROPN
ejpam-5884	230	23	(	(	PUNCT
ejpam-5884	230	24	x(ωi)−	x(ωi)−	X
ejpam-5884	230	25	x(νi	x(νi	PROPN
ejpam-5884	230	26	)	)	PUNCT
ejpam-5884	230	27	)	)	PUNCT
ejpam-5884	230	28	2	2	NUM
ejpam-5884	230	29	where	where	SCONJ
ejpam-5884	230	30	ωi	ωi	X
ejpam-5884	230	31	,	,	PUNCT
ejpam-5884	230	32	νi	νi	PRON
ejpam-5884	230	33	∈	∈	PROPN
ejpam-5884	230	34	[	[	X
ejpam-5884	230	35	ti	ti	NOUN
ejpam-5884	230	36	,	,	PUNCT
ejpam-5884	230	37	ti+1	ti+1	NOUN
ejpam-5884	230	38	)	)	PUNCT
ejpam-5884	230	39	.	.	PUNCT
ejpam-5884	231	1	by	by	ADP
ejpam-5884	231	2	the	the	DET
ejpam-5884	231	3	mean	mean	ADJ
ejpam-5884	231	4	value	value	NOUN
ejpam-5884	231	5	theorem	theorem	NOUN
ejpam-5884	231	6	and	and	CCONJ
ejpam-5884	231	7	equation	equation	NOUN
ejpam-5884	231	8	(	(	PUNCT
ejpam-5884	231	9	28	28	NUM
ejpam-5884	231	10	)	)	PUNCT
ejpam-5884	231	11	,	,	PUNCT
ejpam-5884	231	12	we	we	PRON
ejpam-5884	231	13	get	get	VERB
ejpam-5884	231	14	:	:	PUNCT
ejpam-5884	231	15	||a||2	||a||2	NOUN
ejpam-5884	231	16	≤	≤	NUM
ejpam-5884	231	17	∆f2	∆f2	NOUN
ejpam-5884	231	18	m−1∑	m−1∑	X
ejpam-5884	231	19	i=0	i=0	PROPN
ejpam-5884	231	20	(	(	PUNCT
ejpam-5884	231	21	ωi	ωi	NUM
ejpam-5884	231	22	−	−	NUM
ejpam-5884	231	23	νi	νi	NOUN
ejpam-5884	231	24	)	)	PUNCT
ejpam-5884	231	25	2	2	NUM
ejpam-5884	231	26	≤	≤	NOUN
ejpam-5884	231	27	∆f2	∆f2	NOUN
ejpam-5884	231	28	m−1∑	m−1∑	X
ejpam-5884	231	29	i=0	i=0	PROPN
ejpam-5884	231	30	∆2	∆2	X
ejpam-5884	231	31	=	=	SYM
ejpam-5884	231	32	mf2∆3	mf2∆3	NOUN
ejpam-5884	231	33	=	=	SYM
ejpam-5884	231	34	(	(	PUNCT
ejpam-5884	231	35	tf2)∆2	tf2)∆2	NOUN
ejpam-5884	231	36	=	=	PUNCT
ejpam-5884	231	37	c∆2	c∆2	PROPN
ejpam-5884	231	38	.	.	PUNCT
ejpam-5884	232	1	thus	thus	ADV
ejpam-5884	232	2	,	,	PUNCT
ejpam-5884	232	3	c	c	PROPN
ejpam-5884	232	4	=	=	SYM
ejpam-5884	232	5	f2	f2	PROPN
ejpam-5884	232	6	t	t	PROPN
ejpam-5884	232	7	.	.	PUNCT
ejpam-5884	233	1	the	the	DET
ejpam-5884	233	2	above	above	ADJ
ejpam-5884	233	3	result	result	NOUN
ejpam-5884	233	4	confirms	confirm	VERB
ejpam-5884	233	5	that	that	SCONJ
ejpam-5884	233	6	the	the	DET
ejpam-5884	233	7	mean	mean	ADJ
ejpam-5884	233	8	square	square	ADJ
ejpam-5884	233	9	error	error	NOUN
ejpam-5884	233	10	in	in	ADP
ejpam-5884	233	11	the	the	DET
ejpam-5884	233	12	approximation	approximation	NOUN
ejpam-5884	233	13	is	be	AUX
ejpam-5884	233	14	of	of	ADP
ejpam-5884	233	15	order	order	NOUN
ejpam-5884	233	16	∆2	∆2	PROPN
ejpam-5884	233	17	.	.	PUNCT
ejpam-5884	233	18	m.	m.	PROPN
ejpam-5884	233	19	i.	i.	PROPN
ejpam-5884	233	20	syam	syam	PROPN
ejpam-5884	233	21	et	et	PROPN
ejpam-5884	233	22	al	al	PROPN
ejpam-5884	233	23	.	.	PUNCT
ejpam-5884	233	24	/	/	SYM
ejpam-5884	233	25	eur	eur	PROPN
ejpam-5884	233	26	.	.	PUNCT
ejpam-5884	234	1	j.	j.	PROPN
ejpam-5884	234	2	pure	pure	PROPN
ejpam-5884	234	3	appl	appl	PROPN
ejpam-5884	234	4	.	.	PROPN
ejpam-5884	234	5	math	math	PROPN
ejpam-5884	234	6	,	,	PUNCT
ejpam-5884	234	7	18	18	NUM
ejpam-5884	234	8	(	(	PUNCT
ejpam-5884	234	9	2	2	NUM
ejpam-5884	234	10	)	)	PUNCT
ejpam-5884	234	11	(	(	PUNCT
ejpam-5884	234	12	2025	2025	NUM
ejpam-5884	234	13	)	)	PUNCT
ejpam-5884	234	14	,	,	PUNCT
ejpam-5884	234	15	5884	5884	NUM
ejpam-5884	234	16	10	10	NUM
ejpam-5884	234	17	of	of	ADP
ejpam-5884	234	18	18	18	NUM
ejpam-5884	234	19	t	t	NOUN
ejpam-5884	234	20	hpm	hpm	NOUN
ejpam-5884	234	21	mhpm	mhpm	PROPN
ejpam-5884	234	22	shpm	shpm	PROPN
ejpam-5884	234	23	present	present	PROPN
ejpam-5884	234	24	mathematica	mathematica	PROPN
ejpam-5884	234	25	0.5	0.5	NUM
ejpam-5884	235	1	0.762476	0.762476	NUM
ejpam-5884	235	2	0.768902	0.768902	NUM
ejpam-5884	235	3	0.768766	0.768766	NUM
ejpam-5884	235	4	0.768802	0.768802	NUM
ejpam-5884	235	5	0.768802	0.768802	NUM
ejpam-5884	235	6	1.0	1.0	NUM
ejpam-5884	235	7	0.176929	0.176929	NUM
ejpam-5884	235	8	0.233741	0.233741	NUM
ejpam-5884	235	9	0.233680	0.233680	NUM
ejpam-5884	235	10	0.233692	0.233692	NUM
ejpam-5884	235	11	0.233692	0.233692	NUM
ejpam-5884	235	12	2.0	2.0	NUM
ejpam-5884	235	13	−1.055110	−1.055110	NOUN
ejpam-5884	235	14	−0.891260	−0.891260	NUM
ejpam-5884	235	15	−0.859323	−0.859323	ADP
ejpam-5884	235	16	−0.859349	−0.859349	X
ejpam-5884	235	17	−0.859349	−0.859349	NOUN
ejpam-5884	235	18	3.5	3.5	NUM
ejpam-5884	235	19	−0.461650	−0.461650	NOUN
ejpam-5884	235	20	−0.079433	−0.079433	NOUN
ejpam-5884	235	21	−0.093034	−0.093034	X
ejpam-5884	235	22	−0.093013	−0.093013	X
ejpam-5884	235	23	−0.093013	−0.093013	X
ejpam-5884	235	24	5.0	5.0	NUM
ejpam-5884	235	25	2.049041	2.049041	NUM
ejpam-5884	235	26	0.996472	0.996472	NUM
ejpam-5884	235	27	0.947107	0.947107	NUM
ejpam-5884	235	28	0.947130	0.947130	NUM
ejpam-5884	235	29	0.947130	0.947130	NUM
ejpam-5884	235	30	table	table	NOUN
ejpam-5884	235	31	1	1	NUM
ejpam-5884	235	32	:	:	PUNCT
ejpam-5884	235	33	comparison	comparison	NOUN
ejpam-5884	235	34	of	of	ADP
ejpam-5884	235	35	approximate	approximate	ADJ
ejpam-5884	235	36	solutions	solution	NOUN
ejpam-5884	235	37	for	for	ADP
ejpam-5884	235	38	a	a	DET
ejpam-5884	235	39	=	=	SYM
ejpam-5884	235	40	1	1	NUM
ejpam-5884	235	41	,	,	PUNCT
ejpam-5884	235	42	α	α	NOUN
ejpam-5884	235	43	=	=	SYM
ejpam-5884	235	44	1	1	NUM
ejpam-5884	235	45	,	,	PUNCT
ejpam-5884	235	46	β	β	X
ejpam-5884	235	47	=	=	SYM
ejpam-5884	235	48	1	1	NUM
ejpam-5884	235	49	,	,	PUNCT
ejpam-5884	235	50	and	and	CCONJ
ejpam-5884	235	51	γ	γ	X
ejpam-5884	235	52	=	=	SYM
ejpam-5884	235	53	1	1	NUM
ejpam-5884	235	54	.	.	X
ejpam-5884	235	55	t	t	PROPN
ejpam-5884	235	56	hpm	hpm	PROPN
ejpam-5884	235	57	mhpm	mhpm	PROPN
ejpam-5884	235	58	shpm	shpm	PROPN
ejpam-5884	235	59	present	present	PROPN
ejpam-5884	235	60	mathematica	mathematica	PROPN
ejpam-5884	235	61	1	1	NUM
ejpam-5884	236	1	0.056288	0.056288	NUM
ejpam-5884	236	2	0.080176	0.080176	NUM
ejpam-5884	236	3	0.080519	0.080519	NUM
ejpam-5884	236	4	0.080527	0.080527	NUM
ejpam-5884	236	5	0.080527	0.080527	NUM
ejpam-5884	236	6	2	2	NUM
ejpam-5884	236	7	−0.808192	−0.808192	PRON
ejpam-5884	236	8	−0.739174	−0.739174	PROPN
ejpam-5884	236	9	−0.729000	−0.729000	NUM
ejpam-5884	236	10	−0.729018	−0.729018	NOUN
ejpam-5884	236	11	−0.729018	−0.729018	NOUN
ejpam-5884	236	12	3	3	NUM
ejpam-5884	236	13	−0.339208	−0.339208	NUM
ejpam-5884	236	14	−0.239413	−0.239413	X
ejpam-5884	236	15	−0.238620	−0.238620	X
ejpam-5884	237	1	−0.238626	−0.238626	X
ejpam-5884	237	2	−0.238626	−0.238626	PROPN
ejpam-5884	237	3	4	4	NUM
ejpam-5884	237	4	0.891267	0.891267	NUM
ejpam-5884	237	5	0.706827	0.706827	NUM
ejpam-5884	237	6	0.667953	0.667953	NUM
ejpam-5884	238	1	0.668022	0.668022	NUM
ejpam-5884	238	2	0.668022	0.668022	NUM
ejpam-5884	238	3	5	5	NUM
ejpam-5884	238	4	0.893003	0.893003	NUM
ejpam-5884	238	5	0.395315	0.395315	NUM
ejpam-5884	238	6	0.387550	0.387550	NUM
ejpam-5884	238	7	0.387551	0.387551	NUM
ejpam-5884	238	8	0.387551	0.387551	NUM
ejpam-5884	238	9	table	table	NOUN
ejpam-5884	238	10	2	2	NUM
ejpam-5884	238	11	:	:	PUNCT
ejpam-5884	238	12	comparison	comparison	NOUN
ejpam-5884	238	13	of	of	ADP
ejpam-5884	238	14	approximate	approximate	ADJ
ejpam-5884	238	15	solutions	solution	NOUN
ejpam-5884	238	16	for	for	ADP
ejpam-5884	238	17	a	a	DET
ejpam-5884	238	18	=	=	SYM
ejpam-5884	238	19	0.75	0.75	NUM
ejpam-5884	238	20	,	,	PUNCT
ejpam-5884	238	21	α	α	NOUN
ejpam-5884	238	22	=	=	SYM
ejpam-5884	238	23	1	1	NUM
ejpam-5884	238	24	,	,	PUNCT
ejpam-5884	238	25	β	β	X
ejpam-5884	238	26	=	=	SYM
ejpam-5884	238	27	1.5	1.5	NUM
ejpam-5884	238	28	,	,	PUNCT
ejpam-5884	238	29	and	and	CCONJ
ejpam-5884	238	30	γ	γ	X
ejpam-5884	238	31	=	=	SYM
ejpam-5884	238	32	1.5	1.5	NUM
ejpam-5884	238	33	.	.	PUNCT
ejpam-5884	239	1	5	5	NUM
ejpam-5884	239	2	.	.	X
ejpam-5884	239	3	numerical	numerical	ADJ
ejpam-5884	239	4	results	result	NOUN
ejpam-5884	239	5	we	we	PRON
ejpam-5884	239	6	first	first	ADV
ejpam-5884	239	7	analyze	analyze	VERB
ejpam-5884	239	8	problem	problem	NOUN
ejpam-5884	239	9	(	(	PUNCT
ejpam-5884	239	10	6)-(7	6)-(7	NOUN
ejpam-5884	239	11	)	)	PUNCT
ejpam-5884	239	12	for	for	ADP
ejpam-5884	239	13	the	the	DET
ejpam-5884	239	14	case	case	NOUN
ejpam-5884	239	15	where	where	SCONJ
ejpam-5884	239	16	α	α	NOUN
ejpam-5884	239	17	=	=	NOUN
ejpam-5884	239	18	1	1	X
ejpam-5884	239	19	.	.	PUNCT
ejpam-5884	240	1	since	since	SCONJ
ejpam-5884	240	2	the	the	DET
ejpam-5884	240	3	exact	exact	ADJ
ejpam-5884	240	4	solution	solution	NOUN
ejpam-5884	240	5	for	for	ADP
ejpam-5884	240	6	this	this	DET
ejpam-5884	240	7	problem	problem	NOUN
ejpam-5884	240	8	is	be	AUX
ejpam-5884	240	9	unavailable	unavailable	ADJ
ejpam-5884	240	10	,	,	PUNCT
ejpam-5884	240	11	numerical	numerical	ADJ
ejpam-5884	240	12	solutions	solution	NOUN
ejpam-5884	240	13	were	be	AUX
ejpam-5884	240	14	computed	compute	VERB
ejpam-5884	240	15	using	use	VERB
ejpam-5884	240	16	the	the	DET
ejpam-5884	240	17	built	build	VERB
ejpam-5884	240	18	-	-	PUNCT
ejpam-5884	240	19	in	in	ADP
ejpam-5884	240	20	wolfram	wolfram	PROPN
ejpam-5884	240	21	mathematica	mathematica	PROPN
ejpam-5884	240	22	routine	routine	PROPN
ejpam-5884	240	23	,	,	PUNCT
ejpam-5884	240	24	employing	employ	VERB
ejpam-5884	240	25	the	the	DET
ejpam-5884	240	26	fully	fully	ADV
ejpam-5884	240	27	explicit	explicit	ADJ
ejpam-5884	240	28	runge	runge	NOUN
ejpam-5884	240	29	-	-	PUNCT
ejpam-5884	240	30	kutta	kutta	NOUN
ejpam-5884	240	31	method	method	NOUN
ejpam-5884	240	32	.	.	PUNCT
ejpam-5884	241	1	these	these	DET
ejpam-5884	241	2	solutions	solution	NOUN
ejpam-5884	241	3	serve	serve	VERB
ejpam-5884	241	4	as	as	ADP
ejpam-5884	241	5	the	the	DET
ejpam-5884	241	6	standard	standard	ADJ
ejpam-5884	241	7	reference	reference	NOUN
ejpam-5884	241	8	for	for	ADP
ejpam-5884	241	9	comparison	comparison	NOUN
ejpam-5884	241	10	.	.	PUNCT
ejpam-5884	242	1	in	in	ADP
ejpam-5884	242	2	tables	table	NOUN
ejpam-5884	242	3	1	1	NUM
ejpam-5884	242	4	and	and	CCONJ
ejpam-5884	242	5	2	2	NUM
ejpam-5884	242	6	,	,	PUNCT
ejpam-5884	242	7	we	we	PRON
ejpam-5884	242	8	present	present	VERB
ejpam-5884	242	9	a	a	DET
ejpam-5884	242	10	comparison	comparison	NOUN
ejpam-5884	242	11	of	of	ADP
ejpam-5884	242	12	our	our	PRON
ejpam-5884	242	13	results	result	NOUN
ejpam-5884	242	14	with	with	ADP
ejpam-5884	242	15	those	those	PRON
ejpam-5884	242	16	obtained	obtain	VERB
ejpam-5884	242	17	using	use	VERB
ejpam-5884	242	18	hpm	hpm	NOUN
ejpam-5884	242	19	[	[	X
ejpam-5884	242	20	54	54	NUM
ejpam-5884	242	21	]	]	PUNCT
ejpam-5884	242	22	,	,	PUNCT
ejpam-5884	242	23	mhpm	mhpm	NOUN
ejpam-5884	242	24	[	[	X
ejpam-5884	242	25	26	26	NUM
ejpam-5884	242	26	]	]	PUNCT
ejpam-5884	242	27	,	,	PUNCT
ejpam-5884	242	28	and	and	CCONJ
ejpam-5884	242	29	shpm	shpm	VERB
ejpam-5884	242	30	[	[	X
ejpam-5884	242	31	54	54	NUM
ejpam-5884	242	32	]	]	PUNCT
ejpam-5884	242	33	,	,	PUNCT
ejpam-5884	242	34	alongside	alongside	ADP
ejpam-5884	242	35	the	the	DET
ejpam-5884	242	36	numerical	numerical	ADJ
ejpam-5884	242	37	solution	solution	NOUN
ejpam-5884	242	38	.	.	PUNCT
ejpam-5884	243	1	table	table	NOUN
ejpam-5884	243	2	1	1	NUM
ejpam-5884	243	3	corresponds	correspond	NOUN
ejpam-5884	243	4	to	to	ADP
ejpam-5884	243	5	the	the	DET
ejpam-5884	243	6	parameters	parameter	NOUN
ejpam-5884	243	7	a	a	DET
ejpam-5884	243	8	=	=	SYM
ejpam-5884	243	9	1	1	NUM
ejpam-5884	243	10	,	,	PUNCT
ejpam-5884	243	11	α	α	NOUN
ejpam-5884	243	12	=	=	SYM
ejpam-5884	243	13	1	1	NUM
ejpam-5884	243	14	,	,	PUNCT
ejpam-5884	243	15	β	β	X
ejpam-5884	243	16	=	=	SYM
ejpam-5884	243	17	1	1	NUM
ejpam-5884	243	18	,	,	PUNCT
ejpam-5884	243	19	and	and	CCONJ
ejpam-5884	243	20	γ	γ	X
ejpam-5884	243	21	=	=	SYM
ejpam-5884	243	22	1	1	NUM
ejpam-5884	243	23	,	,	PUNCT
ejpam-5884	243	24	while	while	SCONJ
ejpam-5884	243	25	table	table	NOUN
ejpam-5884	243	26	2	2	NUM
ejpam-5884	243	27	pertains	pertain	NOUN
ejpam-5884	243	28	to	to	ADP
ejpam-5884	243	29	a	a	DET
ejpam-5884	243	30	=	=	SYM
ejpam-5884	243	31	0.75	0.75	NUM
ejpam-5884	243	32	,	,	PUNCT
ejpam-5884	243	33	α	α	NOUN
ejpam-5884	243	34	=	=	SYM
ejpam-5884	243	35	1	1	NUM
ejpam-5884	243	36	,	,	PUNCT
ejpam-5884	243	37	β	β	X
ejpam-5884	243	38	=	=	SYM
ejpam-5884	243	39	1.5	1.5	NUM
ejpam-5884	243	40	,	,	PUNCT
ejpam-5884	243	41	and	and	CCONJ
ejpam-5884	243	42	γ	γ	X
ejpam-5884	243	43	=	=	SYM
ejpam-5884	243	44	1.5	1.5	NUM
ejpam-5884	243	45	.	.	PUNCT
ejpam-5884	244	1	figures	figure	VERB
ejpam-5884	244	2	1–5	1–5	PRON
ejpam-5884	244	3	illustrate	illustrate	VERB
ejpam-5884	244	4	the	the	DET
ejpam-5884	244	5	comparisons	comparison	NOUN
ejpam-5884	244	6	between	between	ADP
ejpam-5884	244	7	the	the	DET
ejpam-5884	244	8	current	current	ADJ
ejpam-5884	244	9	method	method	NOUN
ejpam-5884	244	10	and	and	CCONJ
ejpam-5884	244	11	numerical	numerical	ADJ
ejpam-5884	244	12	solutions	solution	NOUN
ejpam-5884	244	13	under	under	ADP
ejpam-5884	244	14	varying	vary	VERB
ejpam-5884	244	15	parameters	parameter	NOUN
ejpam-5884	244	16	.	.	PUNCT
ejpam-5884	245	1	specifically	specifically	ADV
ejpam-5884	245	2	,	,	PUNCT
ejpam-5884	245	3	figure	figure	VERB
ejpam-5884	245	4	1	1	NUM
ejpam-5884	245	5	evaluates	evaluate	VERB
ejpam-5884	245	6	a	a	DET
ejpam-5884	245	7	=	=	SYM
ejpam-5884	245	8	1	1	NUM
ejpam-5884	245	9	,	,	PUNCT
ejpam-5884	245	10	α	α	NOUN
ejpam-5884	245	11	=	=	SYM
ejpam-5884	245	12	1	1	NUM
ejpam-5884	245	13	,	,	PUNCT
ejpam-5884	245	14	β	β	X
ejpam-5884	245	15	=	=	SYM
ejpam-5884	245	16	0.5	0.5	NUM
ejpam-5884	245	17	,	,	PUNCT
ejpam-5884	245	18	and	and	CCONJ
ejpam-5884	245	19	γ	γ	X
ejpam-5884	245	20	=	=	SYM
ejpam-5884	245	21	2	2	NUM
ejpam-5884	245	22	;	;	PUNCT
ejpam-5884	245	23	figure	figure	NOUN
ejpam-5884	245	24	2	2	NUM
ejpam-5884	245	25	examines	examine	VERB
ejpam-5884	245	26	a	a	DET
ejpam-5884	245	27	=	=	SYM
ejpam-5884	245	28	1.5	1.5	NUM
ejpam-5884	245	29	,	,	PUNCT
ejpam-5884	245	30	α	α	NOUN
ejpam-5884	245	31	=	=	SYM
ejpam-5884	245	32	1	1	NUM
ejpam-5884	245	33	,	,	PUNCT
ejpam-5884	245	34	β	β	X
ejpam-5884	245	35	=	=	SYM
ejpam-5884	245	36	1	1	NUM
ejpam-5884	245	37	,	,	PUNCT
ejpam-5884	245	38	and	and	CCONJ
ejpam-5884	245	39	γ	γ	X
ejpam-5884	245	40	=	=	SYM
ejpam-5884	245	41	0.5	0.5	NUM
ejpam-5884	245	42	;	;	PUNCT
ejpam-5884	245	43	figure	figure	NOUN
ejpam-5884	245	44	3	3	NUM
ejpam-5884	245	45	considers	consider	VERB
ejpam-5884	245	46	a	a	DET
ejpam-5884	245	47	=	=	SYM
ejpam-5884	245	48	1.5	1.5	NUM
ejpam-5884	245	49	,	,	PUNCT
ejpam-5884	245	50	α	α	NOUN
ejpam-5884	245	51	=	=	SYM
ejpam-5884	245	52	1	1	NUM
ejpam-5884	245	53	,	,	PUNCT
ejpam-5884	245	54	β	β	X
ejpam-5884	245	55	=	=	SYM
ejpam-5884	245	56	0.5	0.5	NUM
ejpam-5884	245	57	,	,	PUNCT
ejpam-5884	245	58	and	and	CCONJ
ejpam-5884	245	59	γ	γ	X
ejpam-5884	245	60	=	=	SYM
ejpam-5884	245	61	1.5	1.5	NUM
ejpam-5884	245	62	;	;	PUNCT
ejpam-5884	245	63	figure	figure	VERB
ejpam-5884	245	64	4	4	NUM
ejpam-5884	245	65	studies	study	NOUN
ejpam-5884	245	66	a	a	PRON
ejpam-5884	245	67	=	=	SYM
ejpam-5884	245	68	2	2	NUM
ejpam-5884	245	69	,	,	PUNCT
ejpam-5884	245	70	α	α	NOUN
ejpam-5884	245	71	=	=	SYM
ejpam-5884	245	72	1	1	NUM
ejpam-5884	245	73	,	,	PUNCT
ejpam-5884	245	74	β	β	X
ejpam-5884	245	75	=	=	SYM
ejpam-5884	245	76	1.5	1.5	NUM
ejpam-5884	245	77	,	,	PUNCT
ejpam-5884	245	78	and	and	CCONJ
ejpam-5884	245	79	γ	γ	X
ejpam-5884	245	80	=	=	SYM
ejpam-5884	245	81	1	1	NUM
ejpam-5884	245	82	;	;	PUNCT
ejpam-5884	245	83	and	and	CCONJ
ejpam-5884	245	84	figure	figure	VERB
ejpam-5884	245	85	5	5	NUM
ejpam-5884	245	86	assesses	assesse	NOUN
ejpam-5884	245	87	a	a	DET
ejpam-5884	245	88	=	=	SYM
ejpam-5884	245	89	1.5	1.5	NUM
ejpam-5884	245	90	,	,	PUNCT
ejpam-5884	245	91	α	α	NOUN
ejpam-5884	245	92	=	=	SYM
ejpam-5884	245	93	1	1	NUM
ejpam-5884	245	94	,	,	PUNCT
ejpam-5884	245	95	β	β	X
ejpam-5884	245	96	=	=	SYM
ejpam-5884	245	97	1.5	1.5	NUM
ejpam-5884	245	98	,	,	PUNCT
ejpam-5884	245	99	and	and	CCONJ
ejpam-5884	245	100	γ	γ	X
ejpam-5884	245	101	=	=	SYM
ejpam-5884	245	102	1.5	1.5	NUM
ejpam-5884	245	103	.	.	PUNCT
ejpam-5884	246	1	finally	finally	ADV
ejpam-5884	246	2	,	,	PUNCT
ejpam-5884	246	3	the	the	DET
ejpam-5884	246	4	behavior	behavior	NOUN
ejpam-5884	246	5	of	of	ADP
ejpam-5884	246	6	problem	problem	NOUN
ejpam-5884	246	7	(	(	PUNCT
ejpam-5884	246	8	6)-(7	6)-(7	NOUN
ejpam-5884	246	9	)	)	PUNCT
ejpam-5884	246	10	is	be	AUX
ejpam-5884	246	11	investigated	investigate	VERB
ejpam-5884	246	12	for	for	ADP
ejpam-5884	246	13	a	a	DET
ejpam-5884	246	14	=	=	SYM
ejpam-5884	246	15	1	1	NUM
ejpam-5884	246	16	,	,	PUNCT
ejpam-5884	246	17	β	β	X
ejpam-5884	246	18	=	=	SYM
ejpam-5884	246	19	0.5	0.5	NUM
ejpam-5884	246	20	,	,	PUNCT
ejpam-5884	246	21	and	and	CCONJ
ejpam-5884	246	22	γ	γ	X
ejpam-5884	246	23	=	=	SYM
ejpam-5884	246	24	2	2	NUM
ejpam-5884	246	25	with	with	ADP
ejpam-5884	246	26	varying	vary	VERB
ejpam-5884	246	27	values	value	NOUN
ejpam-5884	246	28	of	of	ADP
ejpam-5884	246	29	α	α	PROPN
ejpam-5884	246	30	(	(	PUNCT
ejpam-5884	246	31	α	α	NOUN
ejpam-5884	246	32	=	=	NOUN
ejpam-5884	246	33	0.75	0.75	NUM
ejpam-5884	246	34	,	,	PUNCT
ejpam-5884	246	35	0.85	0.85	NUM
ejpam-5884	246	36	,	,	PUNCT
ejpam-5884	246	37	0.9	0.9	NUM
ejpam-5884	246	38	,	,	PUNCT
ejpam-5884	246	39	0.95	0.95	NUM
ejpam-5884	246	40	,	,	PUNCT
ejpam-5884	246	41	0.995	0.995	NUM
ejpam-5884	246	42	,	,	PUNCT
ejpam-5884	246	43	1	1	NUM
ejpam-5884	246	44	)	)	PUNCT
ejpam-5884	246	45	.	.	PUNCT
ejpam-5884	247	1	results	result	NOUN
ejpam-5884	247	2	are	be	AUX
ejpam-5884	247	3	depicted	depict	VERB
ejpam-5884	247	4	in	in	ADP
ejpam-5884	247	5	figures	figure	NOUN
ejpam-5884	247	6	6	6	NUM
ejpam-5884	247	7	and	and	CCONJ
ejpam-5884	247	8	7	7	NUM
ejpam-5884	247	9	.	.	PUNCT
ejpam-5884	247	10	similarly	similarly	ADV
ejpam-5884	247	11	,	,	PUNCT
ejpam-5884	247	12	for	for	ADP
ejpam-5884	247	13	a	a	DET
ejpam-5884	247	14	=	=	SYM
ejpam-5884	247	15	1.5	1.5	NUM
ejpam-5884	247	16	,	,	PUNCT
ejpam-5884	247	17	β	β	X
ejpam-5884	247	18	=	=	SYM
ejpam-5884	247	19	1.5	1.5	NUM
ejpam-5884	247	20	,	,	PUNCT
ejpam-5884	247	21	and	and	CCONJ
ejpam-5884	247	22	γ	γ	X
ejpam-5884	247	23	=	=	SYM
ejpam-5884	247	24	1.5	1.5	NUM
ejpam-5884	247	25	,	,	PUNCT
ejpam-5884	247	26	outcomes	outcome	NOUN
ejpam-5884	247	27	for	for	ADP
ejpam-5884	247	28	α	α	NOUN
ejpam-5884	247	29	=	=	SYM
ejpam-5884	247	30	0.75	0.75	NUM
ejpam-5884	247	31	,	,	PUNCT
ejpam-5884	247	32	0.85	0.85	NUM
ejpam-5884	247	33	,	,	PUNCT
ejpam-5884	247	34	0.9	0.9	NUM
ejpam-5884	247	35	,	,	PUNCT
ejpam-5884	247	36	0.95	0.95	NUM
ejpam-5884	247	37	,	,	PUNCT
ejpam-5884	247	38	0.995	0.995	NUM
ejpam-5884	247	39	,	,	PUNCT
ejpam-5884	247	40	1	1	NUM
ejpam-5884	247	41	are	be	AUX
ejpam-5884	247	42	illustrated	illustrate	VERB
ejpam-5884	247	43	in	in	ADP
ejpam-5884	247	44	figures	figure	NOUN
ejpam-5884	247	45	8	8	NUM
ejpam-5884	247	46	and	and	CCONJ
ejpam-5884	247	47	9	9	NUM
ejpam-5884	247	48	.	.	PUNCT
ejpam-5884	248	1	as	as	SCONJ
ejpam-5884	248	2	α	α	PROPN
ejpam-5884	248	3	approaches	approach	VERB
ejpam-5884	248	4	1	1	NUM
ejpam-5884	248	5	,	,	PUNCT
ejpam-5884	248	6	the	the	DET
ejpam-5884	248	7	results	result	NOUN
ejpam-5884	248	8	converge	converge	VERB
ejpam-5884	248	9	toward	toward	ADP
ejpam-5884	248	10	the	the	DET
ejpam-5884	248	11	solution	solution	NOUN
ejpam-5884	248	12	of	of	ADP
ejpam-5884	248	13	the	the	DET
ejpam-5884	248	14	classical	classical	ADJ
ejpam-5884	248	15	second	second	ADJ
ejpam-5884	248	16	-	-	PUNCT
ejpam-5884	248	17	order	order	NOUN
ejpam-5884	248	18	differential	differential	ADJ
ejpam-5884	248	19	equation	equation	NOUN
ejpam-5884	248	20	.	.	PUNCT
ejpam-5884	249	1	m.	m.	NOUN
ejpam-5884	249	2	i.	i.	PROPN
ejpam-5884	249	3	syam	syam	PROPN
ejpam-5884	249	4	et	et	PROPN
ejpam-5884	249	5	al	al	PROPN
ejpam-5884	249	6	.	.	PUNCT
ejpam-5884	249	7	/	/	SYM
ejpam-5884	249	8	eur	eur	PROPN
ejpam-5884	249	9	.	.	PUNCT
ejpam-5884	250	1	j.	j.	PROPN
ejpam-5884	250	2	pure	pure	PROPN
ejpam-5884	250	3	appl	appl	PROPN
ejpam-5884	250	4	.	.	PROPN
ejpam-5884	250	5	math	math	PROPN
ejpam-5884	250	6	,	,	PUNCT
ejpam-5884	250	7	18	18	NUM
ejpam-5884	250	8	(	(	PUNCT
ejpam-5884	250	9	2	2	NUM
ejpam-5884	250	10	)	)	PUNCT
ejpam-5884	250	11	(	(	PUNCT
ejpam-5884	250	12	2025	2025	NUM
ejpam-5884	250	13	)	)	PUNCT
ejpam-5884	250	14	,	,	PUNCT
ejpam-5884	250	15	5884	5884	NUM
ejpam-5884	250	16	11	11	NUM
ejpam-5884	250	17	of	of	ADP
ejpam-5884	250	18	18	18	NUM
ejpam-5884	250	19	0	0	NUM
ejpam-5884	250	20	1	1	NUM
ejpam-5884	250	21	2	2	NUM
ejpam-5884	250	22	3	3	NUM
ejpam-5884	250	23	4	4	NUM
ejpam-5884	250	24	5	5	NUM
ejpam-5884	250	25	-1.0	-1.0	PROPN
ejpam-5884	250	26	-0.5	-0.5	X
ejpam-5884	250	27	0.0	0.0	NUM
ejpam-5884	250	28	0.5	0.5	NUM
ejpam-5884	250	29	1.0	1.0	NUM
ejpam-5884	250	30	t	t	NOUN
ejpam-5884	250	31	f	f	PROPN
ejpam-5884	250	32	ht	ht	PROPN
ejpam-5884	250	33	l	l	PROPN
ejpam-5884	250	34	figure	figure	NOUN
ejpam-5884	250	35	1	1	NUM
ejpam-5884	250	36	:	:	PUNCT
ejpam-5884	250	37	a	a	PRON
ejpam-5884	250	38	=	=	SYM
ejpam-5884	250	39	1	1	NUM
ejpam-5884	250	40	,	,	PUNCT
ejpam-5884	250	41	α	α	NOUN
ejpam-5884	250	42	=	=	SYM
ejpam-5884	250	43	1	1	NUM
ejpam-5884	250	44	,	,	PUNCT
ejpam-5884	250	45	β	β	X
ejpam-5884	250	46	=	=	SYM
ejpam-5884	250	47	0.5	0.5	NUM
ejpam-5884	250	48	,	,	PUNCT
ejpam-5884	250	49	and	and	CCONJ
ejpam-5884	250	50	γ	γ	X
ejpam-5884	250	51	=	=	SYM
ejpam-5884	250	52	2	2	NUM
ejpam-5884	250	53	.	.	NOUN
ejpam-5884	250	54	numerical	numerical	PROPN
ejpam-5884	250	55	(	(	PUNCT
ejpam-5884	250	56	solid	solid	ADJ
ejpam-5884	250	57	)	)	PUNCT
ejpam-5884	250	58	vs.	vs.	ADP
ejpam-5884	250	59	present	present	ADJ
ejpam-5884	250	60	method	method	NOUN
ejpam-5884	250	61	(	(	PUNCT
ejpam-5884	250	62	dashed	dash	VERB
ejpam-5884	250	63	)	)	PUNCT
ejpam-5884	250	64	.	.	PUNCT
ejpam-5884	251	1	0	0	NUM
ejpam-5884	251	2	1	1	NUM
ejpam-5884	251	3	2	2	NUM
ejpam-5884	251	4	3	3	NUM
ejpam-5884	251	5	4	4	NUM
ejpam-5884	251	6	5	5	NUM
ejpam-5884	251	7	-1.0	-1.0	PROPN
ejpam-5884	251	8	-0.5	-0.5	X
ejpam-5884	251	9	0.0	0.0	NUM
ejpam-5884	251	10	0.5	0.5	NUM
ejpam-5884	251	11	1.0	1.0	NUM
ejpam-5884	251	12	t	t	NOUN
ejpam-5884	251	13	f	f	PROPN
ejpam-5884	251	14	ht	ht	PROPN
ejpam-5884	251	15	l	l	PROPN
ejpam-5884	251	16	figure	figure	NOUN
ejpam-5884	251	17	2	2	NUM
ejpam-5884	251	18	:	:	PUNCT
ejpam-5884	251	19	a	a	DET
ejpam-5884	251	20	=	=	SYM
ejpam-5884	251	21	1.5	1.5	NUM
ejpam-5884	251	22	,	,	PUNCT
ejpam-5884	251	23	α	α	NOUN
ejpam-5884	251	24	=	=	SYM
ejpam-5884	251	25	1	1	NUM
ejpam-5884	251	26	,	,	PUNCT
ejpam-5884	251	27	β	β	X
ejpam-5884	251	28	=	=	SYM
ejpam-5884	251	29	1	1	NUM
ejpam-5884	251	30	,	,	PUNCT
ejpam-5884	251	31	and	and	CCONJ
ejpam-5884	251	32	γ	γ	X
ejpam-5884	251	33	=	=	SYM
ejpam-5884	251	34	0.5	0.5	NUM
ejpam-5884	251	35	.	.	PUNCT
ejpam-5884	252	1	numerical	numerical	PROPN
ejpam-5884	252	2	(	(	PUNCT
ejpam-5884	252	3	solid	solid	ADJ
ejpam-5884	252	4	)	)	PUNCT
ejpam-5884	252	5	vs.	vs.	ADP
ejpam-5884	252	6	present	present	ADJ
ejpam-5884	252	7	method	method	NOUN
ejpam-5884	252	8	(	(	PUNCT
ejpam-5884	252	9	dashed	dash	VERB
ejpam-5884	252	10	)	)	PUNCT
ejpam-5884	252	11	.	.	PUNCT
ejpam-5884	253	1	0	0	NUM
ejpam-5884	253	2	2	2	NUM
ejpam-5884	253	3	4	4	NUM
ejpam-5884	253	4	6	6	NUM
ejpam-5884	253	5	8	8	NUM
ejpam-5884	253	6	10	10	NUM
ejpam-5884	253	7	-1.5	-1.5	PUNCT
ejpam-5884	253	8	-1.0	-1.0	PROPN
ejpam-5884	253	9	-0.5	-0.5	PROPN
ejpam-5884	253	10	0.0	0.0	NUM
ejpam-5884	253	11	0.5	0.5	NUM
ejpam-5884	253	12	1.0	1.0	NUM
ejpam-5884	253	13	1.5	1.5	NUM
ejpam-5884	253	14	t	t	NOUN
ejpam-5884	253	15	f	f	PROPN
ejpam-5884	253	16	ht	ht	PROPN
ejpam-5884	253	17	l	l	PROPN
ejpam-5884	253	18	figure	figure	NOUN
ejpam-5884	253	19	3	3	NUM
ejpam-5884	253	20	:	:	PUNCT
ejpam-5884	253	21	a	a	DET
ejpam-5884	253	22	=	=	SYM
ejpam-5884	253	23	1.5	1.5	NUM
ejpam-5884	253	24	,	,	PUNCT
ejpam-5884	253	25	α	α	NOUN
ejpam-5884	253	26	=	=	SYM
ejpam-5884	253	27	1	1	NUM
ejpam-5884	253	28	,	,	PUNCT
ejpam-5884	253	29	β	β	X
ejpam-5884	253	30	=	=	SYM
ejpam-5884	253	31	0.5	0.5	NUM
ejpam-5884	253	32	,	,	PUNCT
ejpam-5884	253	33	and	and	CCONJ
ejpam-5884	253	34	γ	γ	X
ejpam-5884	253	35	=	=	SYM
ejpam-5884	253	36	1.5	1.5	NUM
ejpam-5884	253	37	.	.	PUNCT
ejpam-5884	254	1	numerical	numerical	PROPN
ejpam-5884	254	2	(	(	PUNCT
ejpam-5884	254	3	solid	solid	ADJ
ejpam-5884	254	4	)	)	PUNCT
ejpam-5884	254	5	vs.	vs.	ADP
ejpam-5884	254	6	present	present	ADJ
ejpam-5884	254	7	method	method	NOUN
ejpam-5884	254	8	(	(	PUNCT
ejpam-5884	254	9	dashed	dash	VERB
ejpam-5884	254	10	)	)	PUNCT
ejpam-5884	254	11	.	.	PUNCT
ejpam-5884	255	1	m.	m.	PROPN
ejpam-5884	255	2	i.	i.	PROPN
ejpam-5884	255	3	syam	syam	PROPN
ejpam-5884	255	4	et	et	PROPN
ejpam-5884	255	5	al	al	PROPN
ejpam-5884	255	6	.	.	PUNCT
ejpam-5884	255	7	/	/	SYM
ejpam-5884	255	8	eur	eur	PROPN
ejpam-5884	255	9	.	.	PUNCT
ejpam-5884	256	1	j.	j.	PROPN
ejpam-5884	256	2	pure	pure	PROPN
ejpam-5884	256	3	appl	appl	PROPN
ejpam-5884	256	4	.	.	PROPN
ejpam-5884	256	5	math	math	PROPN
ejpam-5884	256	6	,	,	PUNCT
ejpam-5884	256	7	18	18	NUM
ejpam-5884	256	8	(	(	PUNCT
ejpam-5884	256	9	2	2	NUM
ejpam-5884	256	10	)	)	PUNCT
ejpam-5884	256	11	(	(	PUNCT
ejpam-5884	256	12	2025	2025	NUM
ejpam-5884	256	13	)	)	PUNCT
ejpam-5884	256	14	,	,	PUNCT
ejpam-5884	256	15	5884	5884	NUM
ejpam-5884	256	16	12	12	NUM
ejpam-5884	256	17	of	of	ADP
ejpam-5884	256	18	18	18	NUM
ejpam-5884	256	19	2	2	NUM
ejpam-5884	256	20	4	4	NUM
ejpam-5884	256	21	6	6	NUM
ejpam-5884	256	22	8	8	NUM
ejpam-5884	256	23	10	10	NUM
ejpam-5884	256	24	-2	-2	NOUN
ejpam-5884	256	25	-1	-1	NOUN
ejpam-5884	256	26	1	1	NUM
ejpam-5884	256	27	2	2	NUM
ejpam-5884	256	28	figure	figure	NOUN
ejpam-5884	256	29	4	4	NUM
ejpam-5884	256	30	:	:	PUNCT
ejpam-5884	256	31	a	a	DET
ejpam-5884	256	32	=	=	SYM
ejpam-5884	256	33	2	2	NUM
ejpam-5884	256	34	,	,	PUNCT
ejpam-5884	256	35	α	α	NOUN
ejpam-5884	256	36	=	=	SYM
ejpam-5884	256	37	1	1	NUM
ejpam-5884	256	38	,	,	PUNCT
ejpam-5884	256	39	β	β	X
ejpam-5884	256	40	=	=	SYM
ejpam-5884	256	41	1.5	1.5	NUM
ejpam-5884	256	42	,	,	PUNCT
ejpam-5884	256	43	and	and	CCONJ
ejpam-5884	256	44	γ	γ	X
ejpam-5884	256	45	=	=	SYM
ejpam-5884	256	46	1	1	X
ejpam-5884	256	47	.	.	X
ejpam-5884	256	48	numerical	numerical	PROPN
ejpam-5884	256	49	(	(	PUNCT
ejpam-5884	256	50	solid	solid	ADJ
ejpam-5884	256	51	)	)	PUNCT
ejpam-5884	256	52	vs.	vs.	ADP
ejpam-5884	256	53	present	present	ADJ
ejpam-5884	256	54	method	method	NOUN
ejpam-5884	256	55	(	(	PUNCT
ejpam-5884	256	56	dashed	dash	VERB
ejpam-5884	256	57	)	)	PUNCT
ejpam-5884	256	58	.	.	PUNCT
ejpam-5884	257	1	2	2	NUM
ejpam-5884	257	2	4	4	NUM
ejpam-5884	257	3	6	6	NUM
ejpam-5884	257	4	8	8	NUM
ejpam-5884	257	5	10	10	NUM
ejpam-5884	257	6	-1.5	-1.5	PUNCT
ejpam-5884	257	7	-1.0	-1.0	PROPN
ejpam-5884	257	8	-0.5	-0.5	NUM
ejpam-5884	257	9	0.5	0.5	NUM
ejpam-5884	257	10	1.0	1.0	NUM
ejpam-5884	257	11	1.5	1.5	NUM
ejpam-5884	257	12	figure	figure	NOUN
ejpam-5884	257	13	5	5	NUM
ejpam-5884	257	14	:	:	PUNCT
ejpam-5884	257	15	a	a	DET
ejpam-5884	257	16	=	=	SYM
ejpam-5884	257	17	1.5	1.5	NUM
ejpam-5884	257	18	,	,	PUNCT
ejpam-5884	257	19	α	α	NOUN
ejpam-5884	257	20	=	=	SYM
ejpam-5884	257	21	1	1	NUM
ejpam-5884	257	22	,	,	PUNCT
ejpam-5884	257	23	β	β	X
ejpam-5884	257	24	=	=	SYM
ejpam-5884	257	25	1.5	1.5	NUM
ejpam-5884	257	26	,	,	PUNCT
ejpam-5884	257	27	and	and	CCONJ
ejpam-5884	257	28	γ	γ	X
ejpam-5884	257	29	=	=	SYM
ejpam-5884	257	30	1.5	1.5	NUM
ejpam-5884	257	31	.	.	PUNCT
ejpam-5884	258	1	numerical	numerical	PROPN
ejpam-5884	258	2	(	(	PUNCT
ejpam-5884	258	3	solid	solid	ADJ
ejpam-5884	258	4	)	)	PUNCT
ejpam-5884	258	5	vs.	vs.	ADP
ejpam-5884	258	6	present	present	ADJ
ejpam-5884	258	7	method	method	NOUN
ejpam-5884	258	8	(	(	PUNCT
ejpam-5884	258	9	dashed	dash	VERB
ejpam-5884	258	10	)	)	PUNCT
ejpam-5884	258	11	.	.	PUNCT
ejpam-5884	259	1	1	1	NUM
ejpam-5884	259	2	2	2	NUM
ejpam-5884	259	3	3	3	NUM
ejpam-5884	259	4	4	4	NUM
ejpam-5884	259	5	5	5	NUM
ejpam-5884	259	6	-1.0	-1.0	PROPN
ejpam-5884	259	7	-0.5	-0.5	NUM
ejpam-5884	259	8	0.5	0.5	NUM
ejpam-5884	259	9	1.0	1.0	NUM
ejpam-5884	259	10	α=0.75	α=0.75	ADJ
ejpam-5884	259	11	1	1	NUM
ejpam-5884	259	12	2	2	NUM
ejpam-5884	259	13	3	3	NUM
ejpam-5884	259	14	4	4	NUM
ejpam-5884	259	15	5	5	NUM
ejpam-5884	259	16	-1.0	-1.0	PROPN
ejpam-5884	259	17	-0.5	-0.5	NUM
ejpam-5884	259	18	0.5	0.5	NUM
ejpam-5884	259	19	1.0	1.0	NUM
ejpam-5884	259	20	α=0.85	α=0.85	NOUN
ejpam-5884	259	21	1	1	NUM
ejpam-5884	259	22	2	2	NUM
ejpam-5884	259	23	3	3	NUM
ejpam-5884	259	24	4	4	NUM
ejpam-5884	259	25	5	5	NUM
ejpam-5884	259	26	-1.0	-1.0	PROPN
ejpam-5884	259	27	-0.5	-0.5	X
ejpam-5884	259	28	0.5	0.5	NUM
ejpam-5884	259	29	1.0	1.0	NUM
ejpam-5884	259	30	α=0.9	α=0.9	NOUN
ejpam-5884	259	31	1	1	NUM
ejpam-5884	259	32	2	2	NUM
ejpam-5884	259	33	3	3	NUM
ejpam-5884	259	34	4	4	NUM
ejpam-5884	259	35	5	5	NUM
ejpam-5884	259	36	-1.0	-1.0	PROPN
ejpam-5884	259	37	-0.5	-0.5	NUM
ejpam-5884	259	38	0.5	0.5	NUM
ejpam-5884	259	39	1.0	1.0	NUM
ejpam-5884	259	40	α=0.95	α=0.95	NOUN
ejpam-5884	259	41	1	1	NUM
ejpam-5884	259	42	2	2	NUM
ejpam-5884	259	43	3	3	NUM
ejpam-5884	259	44	4	4	NUM
ejpam-5884	259	45	5	5	NUM
ejpam-5884	259	46	-1.0	-1.0	PROPN
ejpam-5884	259	47	-0.5	-0.5	X
ejpam-5884	259	48	0.5	0.5	NUM
ejpam-5884	259	49	1.0	1.0	NUM
ejpam-5884	259	50	α=995	α=995	NUM
ejpam-5884	259	51	1	1	NUM
ejpam-5884	259	52	2	2	NUM
ejpam-5884	259	53	3	3	NUM
ejpam-5884	259	54	4	4	NUM
ejpam-5884	259	55	5	5	NUM
ejpam-5884	259	56	-1.0	-1.0	PROPN
ejpam-5884	259	57	-0.5	-0.5	NUM
ejpam-5884	259	58	0.5	0.5	NUM
ejpam-5884	259	59	1.0	1.0	NUM
ejpam-5884	259	60	α=1	α=1	NOUN
ejpam-5884	259	61	figure	figure	NOUN
ejpam-5884	259	62	6	6	NUM
ejpam-5884	259	63	:	:	PUNCT
ejpam-5884	259	64	a	a	DET
ejpam-5884	259	65	=	=	SYM
ejpam-5884	259	66	1	1	NUM
ejpam-5884	259	67	,	,	PUNCT
ejpam-5884	259	68	β	β	X
ejpam-5884	259	69	=	=	SYM
ejpam-5884	259	70	0.5	0.5	NUM
ejpam-5884	259	71	,	,	PUNCT
ejpam-5884	259	72	and	and	CCONJ
ejpam-5884	259	73	γ	γ	X
ejpam-5884	259	74	=	=	SYM
ejpam-5884	259	75	2	2	NUM
ejpam-5884	259	76	for	for	ADP
ejpam-5884	259	77	α	α	NOUN
ejpam-5884	259	78	=	=	SYM
ejpam-5884	259	79	0.75	0.75	NUM
ejpam-5884	259	80	,	,	PUNCT
ejpam-5884	259	81	0.85	0.85	NUM
ejpam-5884	259	82	,	,	PUNCT
ejpam-5884	259	83	0.9	0.9	NUM
ejpam-5884	259	84	,	,	PUNCT
ejpam-5884	259	85	0.95	0.95	NUM
ejpam-5884	259	86	,	,	PUNCT
ejpam-5884	259	87	0.995	0.995	NUM
ejpam-5884	259	88	,	,	PUNCT
ejpam-5884	259	89	1	1	NUM
ejpam-5884	259	90	.	.	PUNCT
ejpam-5884	259	91	m.	m.	NOUN
ejpam-5884	259	92	i.	i.	PROPN
ejpam-5884	259	93	syam	syam	PROPN
ejpam-5884	259	94	et	et	PROPN
ejpam-5884	259	95	al	al	PROPN
ejpam-5884	259	96	.	.	PUNCT
ejpam-5884	259	97	/	/	SYM
ejpam-5884	259	98	eur	eur	PROPN
ejpam-5884	259	99	.	.	PUNCT
ejpam-5884	260	1	j.	j.	PROPN
ejpam-5884	260	2	pure	pure	PROPN
ejpam-5884	260	3	appl	appl	PROPN
ejpam-5884	260	4	.	.	PROPN
ejpam-5884	260	5	math	math	PROPN
ejpam-5884	260	6	,	,	PUNCT
ejpam-5884	260	7	18	18	NUM
ejpam-5884	260	8	(	(	PUNCT
ejpam-5884	260	9	2	2	NUM
ejpam-5884	260	10	)	)	PUNCT
ejpam-5884	260	11	(	(	PUNCT
ejpam-5884	260	12	2025	2025	NUM
ejpam-5884	260	13	)	)	PUNCT
ejpam-5884	260	14	,	,	PUNCT
ejpam-5884	260	15	5884	5884	NUM
ejpam-5884	260	16	13	13	NUM
ejpam-5884	260	17	of	of	ADP
ejpam-5884	260	18	18	18	NUM
ejpam-5884	260	19	1	1	NUM
ejpam-5884	260	20	2	2	NUM
ejpam-5884	260	21	3	3	NUM
ejpam-5884	260	22	4	4	NUM
ejpam-5884	260	23	5	5	NUM
ejpam-5884	260	24	-1.0	-1.0	PROPN
ejpam-5884	260	25	-0.5	-0.5	NUM
ejpam-5884	260	26	0.5	0.5	NUM
ejpam-5884	260	27	1.0	1.0	NUM
ejpam-5884	260	28	figure	figure	NOUN
ejpam-5884	260	29	7	7	NUM
ejpam-5884	260	30	:	:	PUNCT
ejpam-5884	260	31	results	result	NOUN
ejpam-5884	260	32	for	for	ADP
ejpam-5884	260	33	a	a	DET
ejpam-5884	260	34	=	=	SYM
ejpam-5884	260	35	1	1	NUM
ejpam-5884	260	36	,	,	PUNCT
ejpam-5884	260	37	β	β	X
ejpam-5884	260	38	=	=	SYM
ejpam-5884	260	39	0.5	0.5	NUM
ejpam-5884	260	40	,	,	PUNCT
ejpam-5884	260	41	γ	γ	NOUN
ejpam-5884	260	42	=	=	SYM
ejpam-5884	260	43	2	2	NUM
ejpam-5884	260	44	,	,	PUNCT
ejpam-5884	260	45	α	α	NOUN
ejpam-5884	260	46	=	=	SYM
ejpam-5884	260	47	0.995	0.995	NUM
ejpam-5884	260	48	,	,	PUNCT
ejpam-5884	260	49	1	1	NUM
ejpam-5884	260	50	.	.	SYM
ejpam-5884	260	51	1	1	NUM
ejpam-5884	260	52	2	2	NUM
ejpam-5884	260	53	3	3	NUM
ejpam-5884	260	54	4	4	NUM
ejpam-5884	260	55	5	5	NUM
ejpam-5884	260	56	-1.5	-1.5	PUNCT
ejpam-5884	260	57	-1.0	-1.0	PROPN
ejpam-5884	260	58	-0.5	-0.5	NUM
ejpam-5884	260	59	0.5	0.5	NUM
ejpam-5884	260	60	1.0	1.0	NUM
ejpam-5884	260	61	1.5	1.5	NUM
ejpam-5884	260	62	α=0.75	α=0.75	ADJ
ejpam-5884	260	63	1	1	NUM
ejpam-5884	260	64	2	2	NUM
ejpam-5884	260	65	3	3	NUM
ejpam-5884	260	66	4	4	NUM
ejpam-5884	260	67	5	5	NUM
ejpam-5884	260	68	-1.5	-1.5	PUNCT
ejpam-5884	260	69	-1.0	-1.0	PROPN
ejpam-5884	260	70	-0.5	-0.5	X
ejpam-5884	260	71	0.5	0.5	NUM
ejpam-5884	260	72	1.0	1.0	NUM
ejpam-5884	260	73	1.5	1.5	NUM
ejpam-5884	260	74	α=0.85	α=0.85	NOUN
ejpam-5884	260	75	1	1	NUM
ejpam-5884	260	76	2	2	NUM
ejpam-5884	260	77	3	3	NUM
ejpam-5884	260	78	4	4	NUM
ejpam-5884	260	79	5	5	NUM
ejpam-5884	260	80	-1.5	-1.5	PUNCT
ejpam-5884	260	81	-1.0	-1.0	PROPN
ejpam-5884	260	82	-0.5	-0.5	X
ejpam-5884	260	83	0.5	0.5	NUM
ejpam-5884	260	84	1.0	1.0	NUM
ejpam-5884	260	85	1.5	1.5	NUM
ejpam-5884	260	86	α=0.9	α=0.9	NOUN
ejpam-5884	260	87	1	1	NUM
ejpam-5884	260	88	2	2	NUM
ejpam-5884	260	89	3	3	NUM
ejpam-5884	260	90	4	4	NUM
ejpam-5884	260	91	5	5	NUM
ejpam-5884	260	92	-1.5	-1.5	PUNCT
ejpam-5884	260	93	-1.0	-1.0	PROPN
ejpam-5884	260	94	-0.5	-0.5	X
ejpam-5884	260	95	0.5	0.5	NUM
ejpam-5884	260	96	1.0	1.0	NUM
ejpam-5884	260	97	1.5	1.5	NUM
ejpam-5884	260	98	α=0.95	α=0.95	NOUN
ejpam-5884	260	99	1	1	NUM
ejpam-5884	260	100	2	2	NUM
ejpam-5884	260	101	3	3	NUM
ejpam-5884	260	102	4	4	NUM
ejpam-5884	260	103	5	5	NUM
ejpam-5884	260	104	-1.5	-1.5	PUNCT
ejpam-5884	260	105	-1.0	-1.0	PROPN
ejpam-5884	260	106	-0.5	-0.5	NUM
ejpam-5884	260	107	0.5	0.5	NUM
ejpam-5884	260	108	1.0	1.0	NUM
ejpam-5884	260	109	1.5	1.5	NUM
ejpam-5884	260	110	α=995	α=995	NOUN
ejpam-5884	260	111	1	1	NUM
ejpam-5884	260	112	2	2	NUM
ejpam-5884	260	113	3	3	NUM
ejpam-5884	260	114	4	4	NUM
ejpam-5884	260	115	5	5	NUM
ejpam-5884	260	116	-1.5	-1.5	PUNCT
ejpam-5884	260	117	-1.0	-1.0	PROPN
ejpam-5884	260	118	-0.5	-0.5	X
ejpam-5884	260	119	0.5	0.5	NUM
ejpam-5884	260	120	1.0	1.0	NUM
ejpam-5884	260	121	1.5	1.5	NUM
ejpam-5884	260	122	α=1	α=1	NOUN
ejpam-5884	260	123	figure	figure	NOUN
ejpam-5884	260	124	8	8	NUM
ejpam-5884	260	125	:	:	PUNCT
ejpam-5884	260	126	results	result	VERB
ejpam-5884	260	127	for	for	ADP
ejpam-5884	260	128	a	a	DET
ejpam-5884	260	129	=	=	SYM
ejpam-5884	260	130	1.5	1.5	NUM
ejpam-5884	260	131	,	,	PUNCT
ejpam-5884	260	132	β	β	X
ejpam-5884	260	133	=	=	SYM
ejpam-5884	260	134	1.5	1.5	NUM
ejpam-5884	260	135	,	,	PUNCT
ejpam-5884	260	136	γ	γ	X
ejpam-5884	260	137	=	=	SYM
ejpam-5884	260	138	1.5	1.5	NUM
ejpam-5884	260	139	,	,	PUNCT
ejpam-5884	260	140	α	α	NOUN
ejpam-5884	260	141	=	=	SYM
ejpam-5884	260	142	0.75	0.75	NUM
ejpam-5884	260	143	,	,	PUNCT
ejpam-5884	260	144	0.85	0.85	NUM
ejpam-5884	260	145	,	,	PUNCT
ejpam-5884	260	146	0.9	0.9	NUM
ejpam-5884	260	147	,	,	PUNCT
ejpam-5884	260	148	0.95	0.95	NUM
ejpam-5884	260	149	,	,	PUNCT
ejpam-5884	260	150	0.995	0.995	NUM
ejpam-5884	260	151	,	,	PUNCT
ejpam-5884	260	152	1	1	NUM
ejpam-5884	260	153	.	.	PUNCT
ejpam-5884	260	154	m.	m.	NOUN
ejpam-5884	260	155	i.	i.	PROPN
ejpam-5884	260	156	syam	syam	PROPN
ejpam-5884	260	157	et	et	PROPN
ejpam-5884	260	158	al	al	PROPN
ejpam-5884	260	159	.	.	PUNCT
ejpam-5884	260	160	/	/	SYM
ejpam-5884	260	161	eur	eur	PROPN
ejpam-5884	260	162	.	.	PUNCT
ejpam-5884	261	1	j.	j.	PROPN
ejpam-5884	261	2	pure	pure	PROPN
ejpam-5884	261	3	appl	appl	PROPN
ejpam-5884	261	4	.	.	PROPN
ejpam-5884	261	5	math	math	PROPN
ejpam-5884	261	6	,	,	PUNCT
ejpam-5884	261	7	18	18	NUM
ejpam-5884	261	8	(	(	PUNCT
ejpam-5884	261	9	2	2	NUM
ejpam-5884	261	10	)	)	PUNCT
ejpam-5884	261	11	(	(	PUNCT
ejpam-5884	261	12	2025	2025	NUM
ejpam-5884	261	13	)	)	PUNCT
ejpam-5884	261	14	,	,	PUNCT
ejpam-5884	261	15	5884	5884	NUM
ejpam-5884	261	16	14	14	NUM
ejpam-5884	261	17	of	of	ADP
ejpam-5884	261	18	18	18	NUM
ejpam-5884	261	19	1	1	NUM
ejpam-5884	261	20	2	2	NUM
ejpam-5884	261	21	3	3	NUM
ejpam-5884	261	22	4	4	NUM
ejpam-5884	261	23	5	5	NUM
ejpam-5884	261	24	-1.5	-1.5	PUNCT
ejpam-5884	261	25	-1.0	-1.0	PROPN
ejpam-5884	261	26	-0.5	-0.5	NUM
ejpam-5884	261	27	0.5	0.5	NUM
ejpam-5884	261	28	1.0	1.0	NUM
ejpam-5884	261	29	1.5	1.5	NUM
ejpam-5884	261	30	figure	figure	NOUN
ejpam-5884	261	31	9	9	NUM
ejpam-5884	261	32	:	:	PUNCT
ejpam-5884	261	33	results	result	NOUN
ejpam-5884	261	34	for	for	ADP
ejpam-5884	261	35	a	a	DET
ejpam-5884	261	36	=	=	SYM
ejpam-5884	261	37	1.5	1.5	NUM
ejpam-5884	261	38	,	,	PUNCT
ejpam-5884	261	39	β	β	X
ejpam-5884	261	40	=	=	SYM
ejpam-5884	261	41	1.5	1.5	NUM
ejpam-5884	261	42	,	,	PUNCT
ejpam-5884	261	43	γ	γ	X
ejpam-5884	261	44	=	=	SYM
ejpam-5884	261	45	1.5	1.5	NUM
ejpam-5884	261	46	,	,	PUNCT
ejpam-5884	261	47	α	α	NOUN
ejpam-5884	261	48	=	=	SYM
ejpam-5884	261	49	0.995	0.995	NUM
ejpam-5884	261	50	,	,	PUNCT
ejpam-5884	261	51	1	1	NUM
ejpam-5884	261	52	.	.	NOUN
ejpam-5884	261	53	6	6	NUM
ejpam-5884	261	54	.	.	X
ejpam-5884	261	55	conclusion	conclusion	NOUN
ejpam-5884	261	56	in	in	ADP
ejpam-5884	261	57	this	this	DET
ejpam-5884	261	58	work	work	NOUN
ejpam-5884	261	59	,	,	PUNCT
ejpam-5884	261	60	we	we	PRON
ejpam-5884	261	61	developed	develop	VERB
ejpam-5884	261	62	and	and	CCONJ
ejpam-5884	261	63	analyzed	analyze	VERB
ejpam-5884	261	64	an	an	DET
ejpam-5884	261	65	iterative	iterative	NOUN
ejpam-5884	261	66	fractional	fractional	ADJ
ejpam-5884	261	67	operational	operational	ADJ
ejpam-5884	261	68	matrix	matrix	NOUN
ejpam-5884	261	69	method	method	NOUN
ejpam-5884	261	70	,	,	PUNCT
ejpam-5884	261	71	based	base	VERB
ejpam-5884	261	72	on	on	ADP
ejpam-5884	261	73	the	the	DET
ejpam-5884	261	74	method	method	NOUN
ejpam-5884	261	75	described	describe	VERB
ejpam-5884	261	76	in	in	ADP
ejpam-5884	261	77	[	[	X
ejpam-5884	261	78	13	13	NUM
ejpam-5884	261	79	]	]	PUNCT
ejpam-5884	261	80	,	,	PUNCT
ejpam-5884	261	81	for	for	ADP
ejpam-5884	261	82	solving	solve	VERB
ejpam-5884	261	83	the	the	DET
ejpam-5884	261	84	nonlinear	nonlinear	ADJ
ejpam-5884	261	85	fractional	fractional	ADJ
ejpam-5884	261	86	undamped	undampe	VERB
ejpam-5884	261	87	duffing	duffing	NOUN
ejpam-5884	261	88	equation	equation	NOUN
ejpam-5884	261	89	.	.	PUNCT
ejpam-5884	262	1	the	the	DET
ejpam-5884	262	2	proposed	propose	VERB
ejpam-5884	262	3	method	method	NOUN
ejpam-5884	262	4	efficiently	efficiently	ADV
ejpam-5884	262	5	reduces	reduce	VERB
ejpam-5884	262	6	computational	computational	ADJ
ejpam-5884	262	7	complexity	complexity	NOUN
ejpam-5884	262	8	while	while	SCONJ
ejpam-5884	262	9	maintaining	maintain	VERB
ejpam-5884	262	10	high	high	ADJ
ejpam-5884	262	11	accuracy	accuracy	NOUN
ejpam-5884	262	12	,	,	PUNCT
ejpam-5884	262	13	as	as	SCONJ
ejpam-5884	262	14	demonstrated	demonstrate	VERB
ejpam-5884	262	15	through	through	ADP
ejpam-5884	262	16	comparisons	comparison	NOUN
ejpam-5884	262	17	with	with	ADP
ejpam-5884	262	18	existing	exist	VERB
ejpam-5884	262	19	analytical	analytical	ADJ
ejpam-5884	262	20	and	and	CCONJ
ejpam-5884	262	21	numerical	numerical	ADJ
ejpam-5884	262	22	techniques	technique	NOUN
ejpam-5884	262	23	.	.	PUNCT
ejpam-5884	263	1	the	the	DET
ejpam-5884	263	2	results	result	NOUN
ejpam-5884	263	3	confirm	confirm	VERB
ejpam-5884	263	4	that	that	SCONJ
ejpam-5884	263	5	the	the	DET
ejpam-5884	263	6	method	method	NOUN
ejpam-5884	263	7	provides	provide	VERB
ejpam-5884	263	8	an	an	DET
ejpam-5884	263	9	excellent	excellent	ADJ
ejpam-5884	263	10	approximation	approximation	NOUN
ejpam-5884	263	11	,	,	PUNCT
ejpam-5884	263	12	outperforming	outperform	VERB
ejpam-5884	263	13	classical	classical	ADJ
ejpam-5884	263	14	perturbation	perturbation	NOUN
ejpam-5884	263	15	-	-	PUNCT
ejpam-5884	263	16	based	base	VERB
ejpam-5884	263	17	approaches	approach	NOUN
ejpam-5884	263	18	such	such	ADJ
ejpam-5884	263	19	as	as	ADP
ejpam-5884	263	20	the	the	DET
ejpam-5884	263	21	homotopy	homotopy	NOUN
ejpam-5884	263	22	perturbation	perturbation	NOUN
ejpam-5884	263	23	method	method	NOUN
ejpam-5884	263	24	(	(	PUNCT
ejpam-5884	263	25	hpm	hpm	NOUN
ejpam-5884	263	26	)	)	PUNCT
ejpam-5884	263	27	,	,	PUNCT
ejpam-5884	263	28	modified	modify	VERB
ejpam-5884	263	29	hpm	hpm	NOUN
ejpam-5884	263	30	(	(	PUNCT
ejpam-5884	263	31	mhpm	mhpm	NOUN
ejpam-5884	263	32	)	)	PUNCT
ejpam-5884	263	33	,	,	PUNCT
ejpam-5884	263	34	and	and	CCONJ
ejpam-5884	263	35	simplified	simplified	ADJ
ejpam-5884	263	36	hpm	hpm	NOUN
ejpam-5884	263	37	(	(	PUNCT
ejpam-5884	263	38	shpm	shpm	NOUN
ejpam-5884	263	39	)	)	PUNCT
ejpam-5884	263	40	.	.	PUNCT
ejpam-5884	264	1	a	a	DET
ejpam-5884	264	2	key	key	ADJ
ejpam-5884	264	3	contribution	contribution	NOUN
ejpam-5884	264	4	of	of	ADP
ejpam-5884	264	5	this	this	DET
ejpam-5884	264	6	study	study	NOUN
ejpam-5884	264	7	is	be	AUX
ejpam-5884	264	8	the	the	DET
ejpam-5884	264	9	investigation	investigation	NOUN
ejpam-5884	264	10	of	of	ADP
ejpam-5884	264	11	the	the	DET
ejpam-5884	264	12	effect	effect	NOUN
ejpam-5884	264	13	of	of	ADP
ejpam-5884	264	14	varying	vary	VERB
ejpam-5884	264	15	the	the	DET
ejpam-5884	264	16	fractional	fractional	ADJ
ejpam-5884	264	17	order	order	NOUN
ejpam-5884	264	18	α	α	NOUN
ejpam-5884	264	19	beyond	beyond	ADP
ejpam-5884	264	20	the	the	DET
ejpam-5884	264	21	provided	provide	VERB
ejpam-5884	264	22	range	range	NOUN
ejpam-5884	264	23	.	.	PUNCT
ejpam-5884	265	1	our	our	PRON
ejpam-5884	265	2	findings	finding	NOUN
ejpam-5884	265	3	reveal	reveal	VERB
ejpam-5884	265	4	that	that	SCONJ
ejpam-5884	265	5	decreasing	decrease	VERB
ejpam-5884	265	6	α	α	NOUN
ejpam-5884	265	7	leads	lead	VERB
ejpam-5884	265	8	to	to	ADP
ejpam-5884	265	9	a	a	DET
ejpam-5884	265	10	significant	significant	ADJ
ejpam-5884	265	11	deviation	deviation	NOUN
ejpam-5884	265	12	from	from	ADP
ejpam-5884	265	13	the	the	DET
ejpam-5884	265	14	classical	classical	ADJ
ejpam-5884	265	15	duffing	duffing	NOUN
ejpam-5884	265	16	oscillator	oscillator	NOUN
ejpam-5884	265	17	,	,	PUNCT
ejpam-5884	265	18	introducing	introduce	VERB
ejpam-5884	265	19	memory	memory	NOUN
ejpam-5884	265	20	-	-	PUNCT
ejpam-5884	265	21	dependent	dependent	ADJ
ejpam-5884	265	22	effects	effect	NOUN
ejpam-5884	265	23	and	and	CCONJ
ejpam-5884	265	24	altering	alter	VERB
ejpam-5884	265	25	the	the	DET
ejpam-5884	265	26	system	system	NOUN
ejpam-5884	265	27	’s	’s	PART
ejpam-5884	265	28	response	response	NOUN
ejpam-5884	265	29	dynamics	dynamic	NOUN
ejpam-5884	265	30	.	.	PUNCT
ejpam-5884	266	1	as	as	SCONJ
ejpam-5884	266	2	α	α	PROPN
ejpam-5884	266	3	approaches	approach	VERB
ejpam-5884	266	4	unity	unity	NOUN
ejpam-5884	266	5	,	,	PUNCT
ejpam-5884	266	6	the	the	DET
ejpam-5884	266	7	system	system	NOUN
ejpam-5884	266	8	gradually	gradually	ADV
ejpam-5884	266	9	transitions	transition	VERB
ejpam-5884	266	10	to	to	ADP
ejpam-5884	266	11	the	the	DET
ejpam-5884	266	12	standard	standard	ADJ
ejpam-5884	266	13	integer	integer	NOUN
ejpam-5884	266	14	-	-	PUNCT
ejpam-5884	266	15	order	order	NOUN
ejpam-5884	266	16	duffing	duffing	NOUN
ejpam-5884	266	17	equation	equation	NOUN
ejpam-5884	266	18	,	,	PUNCT
ejpam-5884	266	19	confirming	confirm	VERB
ejpam-5884	266	20	the	the	DET
ejpam-5884	266	21	robustness	robustness	NOUN
ejpam-5884	266	22	of	of	ADP
ejpam-5884	266	23	fractional	fractional	ADJ
ejpam-5884	266	24	modeling	modeling	NOUN
ejpam-5884	266	25	in	in	ADP
ejpam-5884	266	26	capturing	capture	VERB
ejpam-5884	266	27	real	real	ADJ
ejpam-5884	266	28	-	-	PUNCT
ejpam-5884	266	29	world	world	NOUN
ejpam-5884	266	30	physical	physical	ADJ
ejpam-5884	266	31	behaviors	behavior	NOUN
ejpam-5884	266	32	.	.	PUNCT
ejpam-5884	267	1	this	this	DET
ejpam-5884	267	2	insight	insight	NOUN
ejpam-5884	267	3	is	be	AUX
ejpam-5884	267	4	crucial	crucial	ADJ
ejpam-5884	267	5	for	for	ADP
ejpam-5884	267	6	applications	application	NOUN
ejpam-5884	267	7	in	in	ADP
ejpam-5884	267	8	nonlinear	nonlinear	ADJ
ejpam-5884	267	9	dynamics	dynamic	NOUN
ejpam-5884	267	10	,	,	PUNCT
ejpam-5884	267	11	where	where	SCONJ
ejpam-5884	267	12	fractional	fractional	ADJ
ejpam-5884	267	13	-	-	PUNCT
ejpam-5884	267	14	order	order	NOUN
ejpam-5884	267	15	models	model	NOUN
ejpam-5884	267	16	provide	provide	VERB
ejpam-5884	267	17	a	a	DET
ejpam-5884	267	18	more	more	ADV
ejpam-5884	267	19	generalized	generalized	ADJ
ejpam-5884	267	20	framework	framework	NOUN
ejpam-5884	267	21	for	for	ADP
ejpam-5884	267	22	analyzing	analyze	VERB
ejpam-5884	267	23	oscillatory	oscillatory	ADJ
ejpam-5884	267	24	systems	system	NOUN
ejpam-5884	267	25	with	with	ADP
ejpam-5884	267	26	memory	memory	NOUN
ejpam-5884	267	27	effects	effect	NOUN
ejpam-5884	267	28	.	.	PUNCT
ejpam-5884	268	1	future	future	ADJ
ejpam-5884	268	2	research	research	NOUN
ejpam-5884	268	3	directions	direction	NOUN
ejpam-5884	268	4	include	include	VERB
ejpam-5884	268	5	extending	extend	VERB
ejpam-5884	268	6	the	the	DET
ejpam-5884	268	7	method	method	NOUN
ejpam-5884	268	8	to	to	ADP
ejpam-5884	268	9	more	more	ADV
ejpam-5884	268	10	complex	complex	ADJ
ejpam-5884	268	11	nonlinear	nonlinear	ADJ
ejpam-5884	268	12	oscillatory	oscillatory	ADJ
ejpam-5884	268	13	systems	system	NOUN
ejpam-5884	268	14	,	,	PUNCT
ejpam-5884	268	15	exploring	explore	VERB
ejpam-5884	268	16	higher	higher	ADV
ejpam-5884	268	17	-	-	PUNCT
ejpam-5884	268	18	dimensional	dimensional	ADJ
ejpam-5884	268	19	fractional	fractional	ADJ
ejpam-5884	268	20	models	model	NOUN
ejpam-5884	268	21	,	,	PUNCT
ejpam-5884	268	22	and	and	CCONJ
ejpam-5884	268	23	investigating	investigate	VERB
ejpam-5884	268	24	real	real	ADJ
ejpam-5884	268	25	-	-	PUNCT
ejpam-5884	268	26	world	world	NOUN
ejpam-5884	268	27	applications	application	NOUN
ejpam-5884	268	28	such	such	ADJ
ejpam-5884	268	29	as	as	ADP
ejpam-5884	268	30	mechanical	mechanical	ADJ
ejpam-5884	268	31	vibrations	vibration	NOUN
ejpam-5884	268	32	and	and	CCONJ
ejpam-5884	268	33	bioengineering	bioengineering	NOUN
ejpam-5884	268	34	systems	system	NOUN
ejpam-5884	268	35	.	.	PUNCT
ejpam-5884	269	1	additionally	additionally	ADV
ejpam-5884	269	2	,	,	PUNCT
ejpam-5884	269	3	further	further	ADJ
ejpam-5884	269	4	refinement	refinement	NOUN
ejpam-5884	269	5	of	of	ADP
ejpam-5884	269	6	the	the	DET
ejpam-5884	269	7	numerical	numerical	ADJ
ejpam-5884	269	8	scheme	scheme	NOUN
ejpam-5884	269	9	may	may	AUX
ejpam-5884	269	10	improve	improve	VERB
ejpam-5884	269	11	computational	computational	ADJ
ejpam-5884	269	12	efficiency	efficiency	NOUN
ejpam-5884	269	13	for	for	ADP
ejpam-5884	269	14	large	large	ADJ
ejpam-5884	269	15	-	-	PUNCT
ejpam-5884	269	16	scale	scale	NOUN
ejpam-5884	269	17	problems	problem	NOUN
ejpam-5884	269	18	.	.	PUNCT
ejpam-5884	270	1	author	author	NOUN
ejpam-5884	270	2	contributions	contribution	NOUN
ejpam-5884	270	3	:	:	PUNCT
ejpam-5884	270	4	all	all	DET
ejpam-5884	270	5	authors	author	NOUN
ejpam-5884	270	6	have	have	VERB
ejpam-5884	270	7	the	the	DET
ejpam-5884	270	8	same	same	ADJ
ejpam-5884	270	9	contribution	contribution	NOUN
ejpam-5884	270	10	.	.	PUNCT
ejpam-5884	271	1	data	datum	NOUN
ejpam-5884	271	2	availability	availability	NOUN
ejpam-5884	271	3	statement	statement	NOUN
ejpam-5884	271	4	:	:	PUNCT
ejpam-5884	271	5	not	not	PART
ejpam-5884	271	6	applicable	applicable	ADJ
ejpam-5884	271	7	.	.	PUNCT
ejpam-5884	272	1	m.	m.	NOUN
ejpam-5884	272	2	i.	i.	PROPN
ejpam-5884	272	3	syam	syam	PROPN
ejpam-5884	272	4	et	et	PROPN
ejpam-5884	272	5	al	al	PROPN
ejpam-5884	272	6	.	.	PUNCT
ejpam-5884	272	7	/	/	SYM
ejpam-5884	272	8	eur	eur	PROPN
ejpam-5884	272	9	.	.	PUNCT
ejpam-5884	273	1	j.	j.	PROPN
ejpam-5884	273	2	pure	pure	PROPN
ejpam-5884	273	3	appl	appl	PROPN
ejpam-5884	273	4	.	.	PROPN
ejpam-5884	273	5	math	math	PROPN
ejpam-5884	273	6	,	,	PUNCT
ejpam-5884	273	7	18	18	NUM
ejpam-5884	273	8	(	(	PUNCT
ejpam-5884	273	9	2	2	NUM
ejpam-5884	273	10	)	)	PUNCT
ejpam-5884	273	11	(	(	PUNCT
ejpam-5884	273	12	2025	2025	NUM
ejpam-5884	273	13	)	)	PUNCT
ejpam-5884	273	14	,	,	PUNCT
ejpam-5884	273	15	5884	5884	NUM
ejpam-5884	273	16	15	15	NUM
ejpam-5884	273	17	of	of	ADP
ejpam-5884	273	18	18	18	NUM
ejpam-5884	273	19	conflicts	conflict	NOUN
ejpam-5884	273	20	of	of	ADP
ejpam-5884	273	21	interest	interest	NOUN
ejpam-5884	273	22	:	:	PUNCT
ejpam-5884	273	23	the	the	DET
ejpam-5884	273	24	authors	author	NOUN
ejpam-5884	273	25	declare	declare	VERB
ejpam-5884	273	26	no	no	DET
ejpam-5884	273	27	conflict	conflict	NOUN
ejpam-5884	273	28	of	of	ADP
ejpam-5884	273	29	interest	interest	NOUN
ejpam-5884	273	30	.	.	PUNCT
ejpam-5884	274	1	references	reference	NOUN
ejpam-5884	274	2	[	[	X
ejpam-5884	274	3	1	1	NUM
ejpam-5884	274	4	]	]	PUNCT
ejpam-5884	274	5	keith	keith	PROPN
ejpam-5884	274	6	oldham	oldham	PROPN
ejpam-5884	274	7	and	and	CCONJ
ejpam-5884	274	8	jerome	jerome	PROPN
ejpam-5884	274	9	spanier	spanier	NOUN
ejpam-5884	274	10	.	.	PUNCT
ejpam-5884	275	1	the	the	DET
ejpam-5884	275	2	fractional	fractional	ADJ
ejpam-5884	275	3	calculus	calculus	NOUN
ejpam-5884	275	4	theory	theory	NOUN
ejpam-5884	275	5	and	and	CCONJ
ejpam-5884	275	6	applications	application	NOUN
ejpam-5884	275	7	of	of	ADP
ejpam-5884	275	8	differentiation	differentiation	NOUN
ejpam-5884	275	9	and	and	CCONJ
ejpam-5884	275	10	integration	integration	NOUN
ejpam-5884	275	11	to	to	ADP
ejpam-5884	275	12	arbitrary	arbitrary	ADJ
ejpam-5884	275	13	order	order	NOUN
ejpam-5884	275	14	.	.	PUNCT
ejpam-5884	276	1	elsevier	elsevier	NOUN
ejpam-5884	276	2	,	,	PUNCT
ejpam-5884	276	3	1974	1974	NUM
ejpam-5884	276	4	.	.	PUNCT
ejpam-5884	277	1	[	[	X
ejpam-5884	277	2	2	2	NUM
ejpam-5884	277	3	]	]	X
ejpam-5884	277	4	radek	radek	PROPN
ejpam-5884	277	5	matuš.	matuš.	PROPN
ejpam-5884	277	6	application	application	NOUN
ejpam-5884	277	7	of	of	ADP
ejpam-5884	277	8	fractional	fractional	ADJ
ejpam-5884	277	9	order	order	NOUN
ejpam-5884	277	10	calculus	calculus	NOUN
ejpam-5884	277	11	to	to	PART
ejpam-5884	277	12	control	control	VERB
ejpam-5884	277	13	theory	theory	NOUN
ejpam-5884	277	14	.	.	PUNCT
ejpam-5884	278	1	international	international	ADJ
ejpam-5884	278	2	journal	journal	PROPN
ejpam-5884	278	3	of	of	ADP
ejpam-5884	278	4	mathematical	mathematical	ADJ
ejpam-5884	278	5	models	model	NOUN
ejpam-5884	278	6	and	and	CCONJ
ejpam-5884	278	7	methods	method	NOUN
ejpam-5884	278	8	in	in	ADP
ejpam-5884	278	9	applied	applied	ADJ
ejpam-5884	278	10	sciences	science	NOUN
ejpam-5884	278	11	,	,	PUNCT
ejpam-5884	278	12	5(7):1162–1169	5(7):1162–1169	NUM
ejpam-5884	278	13	,	,	PUNCT
ejpam-5884	278	14	2011	2011	NUM
ejpam-5884	278	15	.	.	PUNCT
ejpam-5884	279	1	[	[	X
ejpam-5884	279	2	3	3	X
ejpam-5884	279	3	]	]	X
ejpam-5884	279	4	r.	r.	PROPN
ejpam-5884	279	5	l.	l.	PROPN
ejpam-5884	279	6	magin	magin	PROPN
ejpam-5884	279	7	.	.	PUNCT
ejpam-5884	280	1	fractional	fractional	ADJ
ejpam-5884	280	2	calculus	calculus	NOUN
ejpam-5884	280	3	models	model	NOUN
ejpam-5884	280	4	of	of	ADP
ejpam-5884	280	5	complex	complex	ADJ
ejpam-5884	280	6	dynamics	dynamic	NOUN
ejpam-5884	280	7	in	in	ADP
ejpam-5884	280	8	biological	biological	ADJ
ejpam-5884	280	9	tissues	tissue	NOUN
ejpam-5884	280	10	.	.	PUNCT
ejpam-5884	281	1	comput	comput	NOUN
ejpam-5884	281	2	.	.	PUNCT
ejpam-5884	282	1	math	math	NOUN
ejpam-5884	282	2	.	.	PUNCT
ejpam-5884	283	1	appl	appl	PROPN
ejpam-5884	283	2	.	.	PROPN
ejpam-5884	283	3	,	,	PUNCT
ejpam-5884	284	1	59(5):1586–1593	59(5):1586–1593	NUM
ejpam-5884	284	2	,	,	PUNCT
ejpam-5884	284	3	2010	2010	NUM
ejpam-5884	284	4	.	.	PUNCT
ejpam-5884	285	1	[	[	X
ejpam-5884	285	2	4	4	X
ejpam-5884	285	3	]	]	PUNCT
ejpam-5884	285	4	m.	m.	NOUN
ejpam-5884	285	5	a.	a.	NOUN
ejpam-5884	285	6	matlob	matlob	PROPN
ejpam-5884	285	7	and	and	CCONJ
ejpam-5884	285	8	y.	y.	PROPN
ejpam-5884	285	9	jamali	jamali	PROPN
ejpam-5884	285	10	.	.	PUNCT
ejpam-5884	286	1	the	the	DET
ejpam-5884	286	2	concepts	concept	NOUN
ejpam-5884	286	3	and	and	CCONJ
ejpam-5884	286	4	applications	application	NOUN
ejpam-5884	286	5	of	of	ADP
ejpam-5884	286	6	fractional	fractional	ADJ
ejpam-5884	286	7	order	order	NOUN
ejpam-5884	286	8	differential	differential	ADJ
ejpam-5884	286	9	calculus	calculus	NOUN
ejpam-5884	286	10	in	in	ADP
ejpam-5884	286	11	modeling	modeling	NOUN
ejpam-5884	286	12	of	of	ADP
ejpam-5884	286	13	viscoelastic	viscoelastic	ADJ
ejpam-5884	286	14	systems	system	NOUN
ejpam-5884	286	15	:	:	PUNCT
ejpam-5884	286	16	a	a	DET
ejpam-5884	286	17	primer	primer	NOUN
ejpam-5884	286	18	.	.	PUNCT
ejpam-5884	287	1	crit	crit	PROPN
ejpam-5884	287	2	.	.	PUNCT
ejpam-5884	288	1	rev	rev	PROPN
ejpam-5884	288	2	.	.	PROPN
ejpam-5884	288	3	biomed	biome	VERB
ejpam-5884	288	4	.	.	PUNCT
ejpam-5884	289	1	eng	eng	PROPN
ejpam-5884	289	2	.	.	PROPN
ejpam-5884	289	3	,	,	PUNCT
ejpam-5884	289	4	47(4	47(4	X
ejpam-5884	289	5	)	)	PUNCT
ejpam-5884	289	6	,	,	PUNCT
ejpam-5884	289	7	2019	2019	NUM
ejpam-5884	289	8	.	.	PUNCT
ejpam-5884	290	1	[	[	X
ejpam-5884	290	2	5	5	X
ejpam-5884	290	3	]	]	PUNCT
ejpam-5884	290	4	j.	j.	PROPN
ejpam-5884	290	5	yu	yu	PROPN
ejpam-5884	290	6	,	,	PUNCT
ejpam-5884	290	7	l.	l.	PROPN
ejpam-5884	290	8	tan	tan	PROPN
ejpam-5884	290	9	,	,	PUNCT
ejpam-5884	290	10	s.	s.	PROPN
ejpam-5884	290	11	zhou	zhou	PROPN
ejpam-5884	290	12	,	,	PUNCT
ejpam-5884	290	13	l.	l.	PROPN
ejpam-5884	290	14	wang	wang	PROPN
ejpam-5884	290	15	,	,	PUNCT
ejpam-5884	290	16	and	and	CCONJ
ejpam-5884	290	17	m.	m.	NOUN
ejpam-5884	290	18	a.	a.	NOUN
ejpam-5884	290	19	siddique	siddique	PROPN
ejpam-5884	290	20	.	.	PUNCT
ejpam-5884	291	1	image	image	NOUN
ejpam-5884	291	2	denoising	denoise	VERB
ejpam-5884	291	3	algorithm	algorithm	NOUN
ejpam-5884	291	4	based	base	VERB
ejpam-5884	291	5	on	on	ADP
ejpam-5884	291	6	entropy	entropy	NOUN
ejpam-5884	291	7	and	and	CCONJ
ejpam-5884	291	8	adaptive	adaptive	ADJ
ejpam-5884	291	9	fractional	fractional	ADJ
ejpam-5884	291	10	order	order	NOUN
ejpam-5884	291	11	calculus	calculus	NOUN
ejpam-5884	291	12	operator	operator	NOUN
ejpam-5884	291	13	.	.	PUNCT
ejpam-5884	292	1	ieee	ieee	NOUN
ejpam-5884	292	2	access	access	NOUN
ejpam-5884	292	3	,	,	PUNCT
ejpam-5884	292	4	5:12275–12285	5:12275–12285	NUM
ejpam-5884	292	5	,	,	PUNCT
ejpam-5884	292	6	2017	2017	NUM
ejpam-5884	292	7	.	.	PUNCT
ejpam-5884	293	1	[	[	X
ejpam-5884	293	2	6	6	NUM
ejpam-5884	293	3	]	]	PUNCT
ejpam-5884	293	4	k.	k.	PROPN
ejpam-5884	293	5	b.	b.	PROPN
ejpam-5884	293	6	kachhia	kachhia	PROPN
ejpam-5884	293	7	.	.	PUNCT
ejpam-5884	294	1	chaos	chaos	NOUN
ejpam-5884	294	2	in	in	ADP
ejpam-5884	294	3	fractional	fractional	ADJ
ejpam-5884	294	4	order	order	NOUN
ejpam-5884	294	5	financial	financial	ADJ
ejpam-5884	294	6	model	model	NOUN
ejpam-5884	294	7	with	with	ADP
ejpam-5884	294	8	fractal	fractal	ADJ
ejpam-5884	294	9	–	–	PUNCT
ejpam-5884	294	10	fractional	fractional	ADJ
ejpam-5884	294	11	derivatives	derivative	NOUN
ejpam-5884	294	12	.	.	PUNCT
ejpam-5884	295	1	partial	partial	ADJ
ejpam-5884	295	2	differ	differ	VERB
ejpam-5884	295	3	.	.	PUNCT
ejpam-5884	296	1	equ	equ	PROPN
ejpam-5884	296	2	.	.	PUNCT
ejpam-5884	296	3	appl	appl	PROPN
ejpam-5884	296	4	.	.	PROPN
ejpam-5884	296	5	math	math	PROPN
ejpam-5884	296	6	.	.	PUNCT
ejpam-5884	296	7	,	,	PUNCT
ejpam-5884	297	1	7:100502	7:100502	NUM
ejpam-5884	297	2	,	,	PUNCT
ejpam-5884	297	3	2023	2023	NUM
ejpam-5884	297	4	.	.	PUNCT
ejpam-5884	298	1	[	[	X
ejpam-5884	298	2	7	7	X
ejpam-5884	298	3	]	]	X
ejpam-5884	298	4	y.	y.	PROPN
ejpam-5884	298	5	a.	a.	PROPN
ejpam-5884	298	6	rossikhin	rossikhin	PROPN
ejpam-5884	298	7	and	and	CCONJ
ejpam-5884	298	8	m.	m.	NOUN
ejpam-5884	298	9	v.	v.	ADP
ejpam-5884	298	10	shitikova	shitikova	PROPN
ejpam-5884	298	11	.	.	PUNCT
ejpam-5884	299	1	applications	application	NOUN
ejpam-5884	299	2	of	of	ADP
ejpam-5884	299	3	fractional	fractional	ADJ
ejpam-5884	299	4	calculus	calculus	NOUN
ejpam-5884	299	5	to	to	ADP
ejpam-5884	299	6	dynamic	dynamic	ADJ
ejpam-5884	299	7	problems	problem	NOUN
ejpam-5884	299	8	of	of	ADP
ejpam-5884	299	9	linear	linear	PROPN
ejpam-5884	299	10	and	and	CCONJ
ejpam-5884	299	11	nonlinear	nonlinear	ADJ
ejpam-5884	299	12	hereditary	hereditary	ADJ
ejpam-5884	299	13	mechanics	mechanic	NOUN
ejpam-5884	299	14	of	of	ADP
ejpam-5884	299	15	solids	solid	NOUN
ejpam-5884	299	16	,	,	PUNCT
ejpam-5884	299	17	1997	1997	NUM
ejpam-5884	299	18	.	.	PUNCT
ejpam-5884	300	1	[	[	X
ejpam-5884	300	2	8	8	NUM
ejpam-5884	300	3	]	]	PUNCT
ejpam-5884	300	4	a.	a.	NOUN
ejpam-5884	300	5	atangana	atangana	PROPN
ejpam-5884	300	6	and	and	CCONJ
ejpam-5884	300	7	d.	d.	PROPN
ejpam-5884	300	8	baleanu	baleanu	PROPN
ejpam-5884	300	9	.	.	PUNCT
ejpam-5884	301	1	new	new	ADJ
ejpam-5884	301	2	fractional	fractional	ADJ
ejpam-5884	301	3	derivatives	derivative	NOUN
ejpam-5884	301	4	with	with	ADP
ejpam-5884	301	5	nonlocal	nonlocal	ADJ
ejpam-5884	301	6	and	and	CCONJ
ejpam-5884	301	7	nonsingular	nonsingular	ADJ
ejpam-5884	301	8	kernel	kernel	PROPN
ejpam-5884	301	9	:	:	PUNCT
ejpam-5884	301	10	theory	theory	NOUN
ejpam-5884	301	11	and	and	CCONJ
ejpam-5884	301	12	application	application	NOUN
ejpam-5884	301	13	to	to	PART
ejpam-5884	301	14	heat	heat	NOUN
ejpam-5884	301	15	transfer	transfer	NOUN
ejpam-5884	301	16	model	model	NOUN
ejpam-5884	301	17	.	.	PUNCT
ejpam-5884	302	1	arxiv	arxiv	PROPN
ejpam-5884	302	2	preprint	preprint	PROPN
ejpam-5884	302	3	,	,	PUNCT
ejpam-5884	302	4	2016	2016	NUM
ejpam-5884	302	5	.	.	PUNCT
ejpam-5884	303	1	[	[	X
ejpam-5884	303	2	9	9	NUM
ejpam-5884	303	3	]	]	X
ejpam-5884	303	4	b.	b.	PROPN
ejpam-5884	303	5	ghanbari	ghanbari	PROPN
ejpam-5884	303	6	,	,	PUNCT
ejpam-5884	303	7	h.	h.	PROPN
ejpam-5884	303	8	günerhan	günerhan	PROPN
ejpam-5884	303	9	,	,	PUNCT
ejpam-5884	303	10	and	and	CCONJ
ejpam-5884	303	11	h.	h.	PROPN
ejpam-5884	303	12	m.	m.	PROPN
ejpam-5884	303	13	srivastava	srivastava	PROPN
ejpam-5884	303	14	.	.	PUNCT
ejpam-5884	304	1	an	an	DET
ejpam-5884	304	2	application	application	NOUN
ejpam-5884	304	3	of	of	ADP
ejpam-5884	304	4	the	the	DET
ejpam-5884	304	5	atanganabaleanu	atanganabaleanu	NOUN
ejpam-5884	304	6	fractional	fractional	ADJ
ejpam-5884	304	7	derivative	derivative	NOUN
ejpam-5884	304	8	in	in	ADP
ejpam-5884	304	9	mathematical	mathematical	ADJ
ejpam-5884	304	10	biology	biology	NOUN
ejpam-5884	304	11	:	:	PUNCT
ejpam-5884	304	12	a	a	DET
ejpam-5884	304	13	three	three	NUM
ejpam-5884	304	14	-	-	PUNCT
ejpam-5884	304	15	species	species	NOUN
ejpam-5884	304	16	predator	predator	NOUN
ejpam-5884	304	17	-	-	PUNCT
ejpam-5884	304	18	prey	prey	NOUN
ejpam-5884	304	19	model	model	NOUN
ejpam-5884	304	20	.	.	PUNCT
ejpam-5884	305	1	chaos	chaos	NOUN
ejpam-5884	305	2	solitons	soliton	NOUN
ejpam-5884	305	3	fractals	fractal	NOUN
ejpam-5884	305	4	,	,	PUNCT
ejpam-5884	305	5	138:109910	138:109910	NUM
ejpam-5884	305	6	,	,	PUNCT
ejpam-5884	305	7	2020	2020	NUM
ejpam-5884	305	8	.	.	PUNCT
ejpam-5884	306	1	[	[	X
ejpam-5884	306	2	10	10	NUM
ejpam-5884	306	3	]	]	PUNCT
ejpam-5884	306	4	j.	j.	PROPN
ejpam-5884	306	5	f.	f.	PROPN
ejpam-5884	306	6	gómez	gómez	PROPN
ejpam-5884	306	7	-	-	PUNCT
ejpam-5884	306	8	aguilar	aguilar	PROPN
ejpam-5884	306	9	,	,	PUNCT
ejpam-5884	306	10	r.	r.	PROPN
ejpam-5884	306	11	f.	f.	PROPN
ejpam-5884	306	12	escobar	escobar	PROPN
ejpam-5884	306	13	-	-	PUNCT
ejpam-5884	306	14	jiménez	jiménez	PROPN
ejpam-5884	306	15	,	,	PUNCT
ejpam-5884	306	16	m.	m.	NOUN
ejpam-5884	306	17	g.	g.	PROPN
ejpam-5884	306	18	lópez	lópez	ADV
ejpam-5884	306	19	-	-	PUNCT
ejpam-5884	306	20	lópez	lópez	ADV
ejpam-5884	306	21	,	,	PUNCT
ejpam-5884	306	22	and	and	CCONJ
ejpam-5884	306	23	v.	v.	ADP
ejpam-5884	306	24	m.	m.	NOUN
ejpam-5884	306	25	alvarado	alvarado	PROPN
ejpam-5884	306	26	-	-	PUNCT
ejpam-5884	306	27	mart́ınez	mart́ınez	PROPN
ejpam-5884	306	28	.	.	PUNCT
ejpam-5884	306	29	atangana	atangana	PROPN
ejpam-5884	306	30	-	-	PUNCT
ejpam-5884	306	31	baleanu	baleanu	ADJ
ejpam-5884	306	32	fractional	fractional	ADJ
ejpam-5884	306	33	derivative	derivative	NOUN
ejpam-5884	306	34	applied	apply	VERB
ejpam-5884	306	35	to	to	ADP
ejpam-5884	306	36	electromagnetic	electromagnetic	ADJ
ejpam-5884	306	37	waves	wave	NOUN
ejpam-5884	306	38	in	in	ADP
ejpam-5884	306	39	dielectric	dielectric	ADJ
ejpam-5884	306	40	media	medium	NOUN
ejpam-5884	306	41	.	.	PUNCT
ejpam-5884	307	1	j.	j.	PROPN
ejpam-5884	307	2	electromagn	electromagn	PROPN
ejpam-5884	307	3	.	.	PUNCT
ejpam-5884	308	1	waves	wave	NOUN
ejpam-5884	308	2	appl	appl	PROPN
ejpam-5884	308	3	.	.	PROPN
ejpam-5884	308	4	,	,	PUNCT
ejpam-5884	308	5	30(15):1937–1952	30(15):1937–1952	NUM
ejpam-5884	308	6	,	,	PUNCT
ejpam-5884	308	7	2016	2016	NUM
ejpam-5884	308	8	.	.	PUNCT
ejpam-5884	309	1	[	[	X
ejpam-5884	309	2	11	11	NUM
ejpam-5884	309	3	]	]	PUNCT
ejpam-5884	309	4	e.	e.	PROPN
ejpam-5884	309	5	f.	f.	PROPN
ejpam-5884	309	6	d.	d.	PROPN
ejpam-5884	309	7	goufo	goufo	PROPN
ejpam-5884	309	8	,	,	PUNCT
ejpam-5884	309	9	m.	m.	NOUN
ejpam-5884	309	10	mbehou	mbehou	PROPN
ejpam-5884	309	11	,	,	PUNCT
ejpam-5884	309	12	and	and	CCONJ
ejpam-5884	309	13	m.	m.	NOUN
ejpam-5884	309	14	m.	m.	PROPN
ejpam-5884	309	15	k.	k.	PROPN
ejpam-5884	309	16	pene	pene	PROPN
ejpam-5884	309	17	.	.	PUNCT
ejpam-5884	310	1	a	a	DET
ejpam-5884	310	2	peculiar	peculiar	ADJ
ejpam-5884	310	3	application	application	NOUN
ejpam-5884	310	4	of	of	ADP
ejpam-5884	310	5	atangana	atangana	PROPN
ejpam-5884	310	6	–	–	PUNCT
ejpam-5884	310	7	baleanu	baleanu	ADJ
ejpam-5884	310	8	fractional	fractional	ADJ
ejpam-5884	310	9	derivative	derivative	NOUN
ejpam-5884	310	10	in	in	ADP
ejpam-5884	310	11	neuroscience	neuroscience	NOUN
ejpam-5884	310	12	:	:	PUNCT
ejpam-5884	310	13	chaotic	chaotic	ADJ
ejpam-5884	310	14	burst	burst	ADJ
ejpam-5884	310	15	dynamics	dynamic	NOUN
ejpam-5884	310	16	.	.	PUNCT
ejpam-5884	311	1	chaos	chaos	NOUN
ejpam-5884	311	2	solitons	soliton	NOUN
ejpam-5884	311	3	fractals	fractal	NOUN
ejpam-5884	311	4	,	,	PUNCT
ejpam-5884	311	5	115:170–176	115:170–176	NUM
ejpam-5884	311	6	,	,	PUNCT
ejpam-5884	311	7	2018	2018	NUM
ejpam-5884	311	8	.	.	PUNCT
ejpam-5884	312	1	[	[	X
ejpam-5884	312	2	12	12	NUM
ejpam-5884	312	3	]	]	PUNCT
ejpam-5884	312	4	b.	b.	PROPN
ejpam-5884	312	5	ghanbari	ghanbari	PROPN
ejpam-5884	312	6	and	and	CCONJ
ejpam-5884	312	7	a.	a.	PROPN
ejpam-5884	312	8	atangana	atangana	PROPN
ejpam-5884	312	9	.	.	PUNCT
ejpam-5884	313	1	a	a	DET
ejpam-5884	313	2	new	new	ADJ
ejpam-5884	313	3	application	application	NOUN
ejpam-5884	313	4	of	of	ADP
ejpam-5884	313	5	fractional	fractional	ADJ
ejpam-5884	313	6	atangana	atangana	PROPN
ejpam-5884	313	7	–	–	PUNCT
ejpam-5884	313	8	baleanu	baleanu	ADJ
ejpam-5884	313	9	derivatives	derivative	NOUN
ejpam-5884	313	10	:	:	PUNCT
ejpam-5884	313	11	designing	design	VERB
ejpam-5884	313	12	abc	abc	PROPN
ejpam-5884	313	13	-	-	PUNCT
ejpam-5884	313	14	fractional	fractional	ADJ
ejpam-5884	313	15	masks	mask	NOUN
ejpam-5884	313	16	in	in	ADP
ejpam-5884	313	17	image	image	NOUN
ejpam-5884	313	18	processing	processing	NOUN
ejpam-5884	313	19	.	.	PUNCT
ejpam-5884	314	1	physica	physica	PROPN
ejpam-5884	314	2	a	a	DET
ejpam-5884	314	3	:	:	PUNCT
ejpam-5884	314	4	stat	stat	PROPN
ejpam-5884	314	5	.	.	PUNCT
ejpam-5884	315	1	mech	mech	PROPN
ejpam-5884	315	2	.	.	PUNCT
ejpam-5884	316	1	appl	appl	PROPN
ejpam-5884	316	2	.	.	PROPN
ejpam-5884	316	3	,	,	PUNCT
ejpam-5884	316	4	542:123516	542:123516	NUM
ejpam-5884	316	5	,	,	PUNCT
ejpam-5884	316	6	2020	2020	NUM
ejpam-5884	316	7	.	.	PUNCT
ejpam-5884	317	1	[	[	X
ejpam-5884	317	2	13	13	NUM
ejpam-5884	317	3	]	]	PUNCT
ejpam-5884	317	4	s.	s.	PROPN
ejpam-5884	317	5	m.	m.	PROPN
ejpam-5884	317	6	syam	syam	PROPN
ejpam-5884	317	7	,	,	PUNCT
ejpam-5884	317	8	z.	z.	PROPN
ejpam-5884	317	9	siri	siri	PROPN
ejpam-5884	317	10	,	,	PUNCT
ejpam-5884	317	11	s.	s.	PROPN
ejpam-5884	317	12	h.	h.	PROPN
ejpam-5884	317	13	altoum	altoum	PROPN
ejpam-5884	317	14	,	,	PUNCT
ejpam-5884	317	15	and	and	CCONJ
ejpam-5884	317	16	r.	r.	PROPN
ejpam-5884	317	17	md	md	PROPN
ejpam-5884	317	18	.	.	PUNCT
ejpam-5884	318	1	kasmani	kasmani	PROPN
ejpam-5884	318	2	.	.	PUNCT
ejpam-5884	319	1	analytical	analytical	ADJ
ejpam-5884	319	2	and	and	CCONJ
ejpam-5884	319	3	numerical	numerical	ADJ
ejpam-5884	319	4	methods	method	NOUN
ejpam-5884	319	5	for	for	ADP
ejpam-5884	319	6	solving	solve	VERB
ejpam-5884	319	7	second	second	ADJ
ejpam-5884	319	8	-	-	PUNCT
ejpam-5884	319	9	order	order	NOUN
ejpam-5884	319	10	two	two	NUM
ejpam-5884	319	11	-	-	PUNCT
ejpam-5884	319	12	dimensional	dimensional	ADJ
ejpam-5884	319	13	symmetric	symmetric	ADJ
ejpam-5884	319	14	sequential	sequential	ADJ
ejpam-5884	319	15	fractional	fractional	ADJ
ejpam-5884	319	16	integro	integro	ADJ
ejpam-5884	319	17	-	-	PUNCT
ejpam-5884	319	18	differential	differential	NOUN
ejpam-5884	319	19	equations	equation	NOUN
ejpam-5884	319	20	.	.	PUNCT
ejpam-5884	320	1	symmetry	symmetry	NOUN
ejpam-5884	320	2	,	,	PUNCT
ejpam-5884	320	3	15(6):1263	15(6):1263	NUM
ejpam-5884	320	4	,	,	PUNCT
ejpam-5884	320	5	2023	2023	NUM
ejpam-5884	320	6	.	.	PUNCT
ejpam-5884	321	1	[	[	X
ejpam-5884	321	2	14	14	NUM
ejpam-5884	321	3	]	]	X
ejpam-5884	321	4	n.	n.	PROPN
ejpam-5884	321	5	n.	n.	PROPN
ejpam-5884	321	6	moiseev	moiseev	PROPN
ejpam-5884	321	7	.	.	PUNCT
ejpam-5884	322	1	asimptoticheskie	asimptoticheskie	PROPN
ejpam-5884	322	2	metodi	metodi	PROPN
ejpam-5884	322	3	nelinejnoj	nelinejnoj	PROPN
ejpam-5884	322	4	mehaniki	mehaniki	PROPN
ejpam-5884	322	5	.	.	PUNCT
ejpam-5884	323	1	nauka	nauka	PROPN
ejpam-5884	323	2	,	,	PUNCT
ejpam-5884	323	3	moscow	moscow	PROPN
ejpam-5884	323	4	,	,	PUNCT
ejpam-5884	323	5	1981	1981	NUM
ejpam-5884	323	6	.	.	PUNCT
ejpam-5884	324	1	m.	m.	NOUN
ejpam-5884	324	2	i.	i.	PROPN
ejpam-5884	324	3	syam	syam	PROPN
ejpam-5884	324	4	et	et	PROPN
ejpam-5884	324	5	al	al	PROPN
ejpam-5884	324	6	.	.	PUNCT
ejpam-5884	324	7	/	/	SYM
ejpam-5884	324	8	eur	eur	PROPN
ejpam-5884	324	9	.	.	PUNCT
ejpam-5884	325	1	j.	j.	PROPN
ejpam-5884	325	2	pure	pure	PROPN
ejpam-5884	325	3	appl	appl	PROPN
ejpam-5884	325	4	.	.	PROPN
ejpam-5884	325	5	math	math	PROPN
ejpam-5884	325	6	,	,	PUNCT
ejpam-5884	325	7	18	18	NUM
ejpam-5884	325	8	(	(	PUNCT
ejpam-5884	325	9	2	2	NUM
ejpam-5884	325	10	)	)	PUNCT
ejpam-5884	325	11	(	(	PUNCT
ejpam-5884	325	12	2025	2025	NUM
ejpam-5884	325	13	)	)	PUNCT
ejpam-5884	325	14	,	,	PUNCT
ejpam-5884	325	15	5884	5884	NUM
ejpam-5884	325	16	16	16	NUM
ejpam-5884	325	17	of	of	ADP
ejpam-5884	325	18	18	18	NUM
ejpam-5884	325	19	[	[	SYM
ejpam-5884	325	20	15	15	NUM
ejpam-5884	325	21	]	]	PUNCT
ejpam-5884	325	22	m.	m.	NOUN
ejpam-5884	325	23	al	al	PROPN
ejpam-5884	325	24	-	-	PUNCT
ejpam-5884	325	25	refai	refai	PROPN
ejpam-5884	325	26	and	and	CCONJ
ejpam-5884	325	27	d.	d.	PROPN
ejpam-5884	325	28	baleanu	baleanu	PROPN
ejpam-5884	325	29	.	.	PUNCT
ejpam-5884	326	1	on	on	ADP
ejpam-5884	326	2	an	an	DET
ejpam-5884	326	3	extension	extension	NOUN
ejpam-5884	326	4	of	of	ADP
ejpam-5884	326	5	the	the	DET
ejpam-5884	326	6	operator	operator	NOUN
ejpam-5884	326	7	with	with	ADP
ejpam-5884	326	8	mittag	mittag	ADJ
ejpam-5884	326	9	-	-	PUNCT
ejpam-5884	326	10	leffler	leffler	NOUN
ejpam-5884	326	11	kernel	kernel	NOUN
ejpam-5884	326	12	.	.	PUNCT
ejpam-5884	326	13	fractals	fractal	NOUN
ejpam-5884	326	14	,	,	PUNCT
ejpam-5884	326	15	30(05):2240129	30(05):2240129	NUM
ejpam-5884	326	16	,	,	PUNCT
ejpam-5884	326	17	2022	2022	NUM
ejpam-5884	326	18	.	.	PUNCT
ejpam-5884	327	1	[	[	X
ejpam-5884	327	2	16	16	NUM
ejpam-5884	327	3	]	]	X
ejpam-5884	327	4	mahmmoud	mahmmoud	PROPN
ejpam-5884	327	5	m.	m.	NOUN
ejpam-5884	327	6	syam	syam	PROPN
ejpam-5884	327	7	,	,	PUNCT
ejpam-5884	327	8	farah	farah	PROPN
ejpam-5884	327	9	morsi	morsi	PROPN
ejpam-5884	327	10	,	,	PUNCT
ejpam-5884	327	11	ayaha	ayaha	NOUN
ejpam-5884	327	12	abu	abu	PROPN
ejpam-5884	327	13	eida	eida	PROPN
ejpam-5884	327	14	,	,	PUNCT
ejpam-5884	327	15	and	and	CCONJ
ejpam-5884	327	16	muhammed	muhammed	PROPN
ejpam-5884	327	17	i.	i.	PROPN
ejpam-5884	327	18	syam	syam	PROPN
ejpam-5884	327	19	.	.	PUNCT
ejpam-5884	328	1	investigating	investigate	VERB
ejpam-5884	328	2	convective	convective	ADJ
ejpam-5884	328	3	darcy	darcy	NOUN
ejpam-5884	328	4	–	–	PUNCT
ejpam-5884	328	5	forchheimer	forchheimer	ADJ
ejpam-5884	328	6	flow	flow	NOUN
ejpam-5884	328	7	in	in	ADP
ejpam-5884	328	8	maxwell	maxwell	PROPN
ejpam-5884	328	9	nanofluids	nanofluid	VERB
ejpam-5884	328	10	through	through	ADP
ejpam-5884	328	11	a	a	DET
ejpam-5884	328	12	computational	computational	ADJ
ejpam-5884	328	13	study	study	NOUN
ejpam-5884	328	14	.	.	PUNCT
ejpam-5884	329	1	partial	partial	ADJ
ejpam-5884	329	2	differential	differential	ADJ
ejpam-5884	329	3	equations	equation	NOUN
ejpam-5884	329	4	in	in	ADP
ejpam-5884	329	5	applied	applied	ADJ
ejpam-5884	329	6	mathematics	mathematic	NOUN
ejpam-5884	329	7	,	,	PUNCT
ejpam-5884	329	8	11:100863	11:100863	NUM
ejpam-5884	329	9	,	,	PUNCT
ejpam-5884	329	10	2024	2024	NUM
ejpam-5884	329	11	.	.	PUNCT
ejpam-5884	330	1	[	[	X
ejpam-5884	330	2	17	17	NUM
ejpam-5884	330	3	]	]	PUNCT
ejpam-5884	330	4	m.	m.	NOUN
ejpam-5884	330	5	m.	m.	NOUN
ejpam-5884	330	6	syam	syam	PROPN
ejpam-5884	330	7	,	,	PUNCT
ejpam-5884	330	8	s.	s.	PROPN
ejpam-5884	330	9	cabrera	cabrera	PROPN
ejpam-5884	330	10	-	-	PUNCT
ejpam-5884	330	11	calderon	calderon	PROPN
ejpam-5884	330	12	,	,	PUNCT
ejpam-5884	330	13	k.	k.	PROPN
ejpam-5884	330	14	a.	a.	PROPN
ejpam-5884	330	15	vijayan	vijayan	PROPN
ejpam-5884	330	16	,	,	PUNCT
ejpam-5884	330	17	v.	v.	PROPN
ejpam-5884	330	18	balaji	balaji	PROPN
ejpam-5884	330	19	,	,	PUNCT
ejpam-5884	330	20	p.	p.	PROPN
ejpam-5884	330	21	e.	e.	PROPN
ejpam-5884	330	22	phelan	phelan	PROPN
ejpam-5884	330	23	,	,	PUNCT
ejpam-5884	330	24	and	and	CCONJ
ejpam-5884	330	25	j.	j.	PROPN
ejpam-5884	330	26	r.	r.	PROPN
ejpam-5884	330	27	villalobos	villalobos	PROPN
ejpam-5884	330	28	.	.	PUNCT
ejpam-5884	330	29	mini	mini	ADJ
ejpam-5884	330	30	containers	container	NOUN
ejpam-5884	330	31	to	to	PART
ejpam-5884	330	32	improve	improve	VERB
ejpam-5884	330	33	the	the	DET
ejpam-5884	330	34	cold	cold	ADJ
ejpam-5884	330	35	chain	chain	NOUN
ejpam-5884	330	36	energy	energy	NOUN
ejpam-5884	330	37	efficiency	efficiency	NOUN
ejpam-5884	330	38	and	and	CCONJ
ejpam-5884	330	39	carbon	carbon	NOUN
ejpam-5884	330	40	footprint	footprint	NOUN
ejpam-5884	330	41	.	.	PUNCT
ejpam-5884	331	1	climate	climate	NOUN
ejpam-5884	331	2	,	,	PUNCT
ejpam-5884	331	3	10:76	10:76	NUM
ejpam-5884	331	4	,	,	PUNCT
ejpam-5884	331	5	2022	2022	NUM
ejpam-5884	331	6	.	.	PUNCT
ejpam-5884	332	1	[	[	X
ejpam-5884	332	2	18	18	NUM
ejpam-5884	332	3	]	]	PUNCT
ejpam-5884	332	4	a.	a.	NOUN
ejpam-5884	332	5	h.	h.	PROPN
ejpam-5884	332	6	nayfeh	nayfeh	PROPN
ejpam-5884	332	7	and	and	CCONJ
ejpam-5884	332	8	d.	d.	PROPN
ejpam-5884	332	9	t.	t.	PROPN
ejpam-5884	332	10	mook	mook	PROPN
ejpam-5884	332	11	.	.	PUNCT
ejpam-5884	333	1	nonlinear	nonlinear	ADJ
ejpam-5884	333	2	oscillations	oscillation	NOUN
ejpam-5884	333	3	.	.	PUNCT
ejpam-5884	334	1	wiley	wiley	PROPN
ejpam-5884	334	2	,	,	PUNCT
ejpam-5884	334	3	new	new	PROPN
ejpam-5884	334	4	york	york	PROPN
ejpam-5884	334	5	,	,	PUNCT
ejpam-5884	334	6	1979	1979	NUM
ejpam-5884	334	7	.	.	PUNCT
ejpam-5884	335	1	[	[	X
ejpam-5884	335	2	19	19	NUM
ejpam-5884	335	3	]	]	PUNCT
ejpam-5884	335	4	m.	m.	NOUN
ejpam-5884	335	5	i.	i.	PROPN
ejpam-5884	335	6	syam	syam	PROPN
ejpam-5884	335	7	,	,	PUNCT
ejpam-5884	335	8	m.	m.	NOUN
ejpam-5884	335	9	n.	n.	PROPN
ejpam-5884	335	10	y.	y.	PROPN
ejpam-5884	335	11	anwar	anwar	PROPN
ejpam-5884	335	12	,	,	PUNCT
ejpam-5884	335	13	a.	a.	PROPN
ejpam-5884	335	14	yildirim	yildirim	PROPN
ejpam-5884	335	15	,	,	PUNCT
ejpam-5884	335	16	and	and	CCONJ
ejpam-5884	335	17	et	et	PROPN
ejpam-5884	335	18	al	al	PROPN
ejpam-5884	335	19	.	.	PUNCT
ejpam-5884	336	1	the	the	DET
ejpam-5884	336	2	modified	modify	VERB
ejpam-5884	336	3	fractional	fractional	ADJ
ejpam-5884	336	4	power	power	NOUN
ejpam-5884	336	5	series	series	NOUN
ejpam-5884	336	6	method	method	NOUN
ejpam-5884	336	7	for	for	ADP
ejpam-5884	336	8	solving	solve	VERB
ejpam-5884	336	9	fractional	fractional	ADJ
ejpam-5884	336	10	non	non	ADJ
ejpam-5884	336	11	-	-	ADJ
ejpam-5884	336	12	isothermal	isothermal	ADJ
ejpam-5884	336	13	reaction	reaction	NOUN
ejpam-5884	336	14	–	–	PUNCT
ejpam-5884	336	15	diffusion	diffusion	NOUN
ejpam-5884	336	16	model	model	NOUN
ejpam-5884	336	17	equations	equation	NOUN
ejpam-5884	336	18	in	in	ADP
ejpam-5884	336	19	a	a	DET
ejpam-5884	336	20	spherical	spherical	ADJ
ejpam-5884	336	21	catalyst	catalyst	NOUN
ejpam-5884	336	22	.	.	PUNCT
ejpam-5884	337	1	int	int	NOUN
ejpam-5884	337	2	.	.	PUNCT
ejpam-5884	338	1	j.	j.	PROPN
ejpam-5884	338	2	appl	appl	PROPN
ejpam-5884	338	3	.	.	PUNCT
ejpam-5884	339	1	comput	comput	PROPN
ejpam-5884	339	2	.	.	PUNCT
ejpam-5884	340	1	math	math	NOUN
ejpam-5884	340	2	.	.	PUNCT
ejpam-5884	340	3	,	,	PUNCT
ejpam-5884	340	4	5:38	5:38	NUM
ejpam-5884	340	5	,	,	PUNCT
ejpam-5884	340	6	2019	2019	NUM
ejpam-5884	340	7	.	.	PUNCT
ejpam-5884	341	1	[	[	X
ejpam-5884	341	2	20	20	NUM
ejpam-5884	341	3	]	]	PUNCT
ejpam-5884	341	4	s.	s.	PROPN
ejpam-5884	341	5	al	al	PROPN
ejpam-5884	341	6	omari	omari	PROPN
ejpam-5884	341	7	,	,	PUNCT
ejpam-5884	341	8	a.	a.	PROPN
ejpam-5884	341	9	m.	m.	PROPN
ejpam-5884	341	10	ghazal	ghazal	PROPN
ejpam-5884	341	11	,	,	PUNCT
ejpam-5884	341	12	m.	m.	NOUN
ejpam-5884	341	13	syam	syam	PROPN
ejpam-5884	341	14	,	,	PUNCT
ejpam-5884	341	15	r.	r.	PROPN
ejpam-5884	341	16	al	al	PROPN
ejpam-5884	341	17	najjar	najjar	PROPN
ejpam-5884	341	18	,	,	PUNCT
ejpam-5884	341	19	and	and	CCONJ
ejpam-5884	341	20	m.	m.	PROPN
ejpam-5884	341	21	y.	y.	PROPN
ejpam-5884	341	22	selim	selim	PROPN
ejpam-5884	341	23	.	.	PUNCT
ejpam-5884	342	1	an	an	DET
ejpam-5884	342	2	investigation	investigation	NOUN
ejpam-5884	342	3	on	on	ADP
ejpam-5884	342	4	the	the	DET
ejpam-5884	342	5	thermal	thermal	ADJ
ejpam-5884	342	6	degradation	degradation	NOUN
ejpam-5884	342	7	performance	performance	NOUN
ejpam-5884	342	8	of	of	ADP
ejpam-5884	342	9	crude	crude	ADJ
ejpam-5884	342	10	glycerol	glycerol	NOUN
ejpam-5884	342	11	and	and	CCONJ
ejpam-5884	342	12	date	date	NOUN
ejpam-5884	342	13	seeds	seed	NOUN
ejpam-5884	342	14	blends	blend	NOUN
ejpam-5884	342	15	using	use	VERB
ejpam-5884	342	16	thermogravimetric	thermogravimetric	ADJ
ejpam-5884	342	17	analysis	analysis	NOUN
ejpam-5884	342	18	(	(	PUNCT
ejpam-5884	342	19	tga	tga	NOUN
ejpam-5884	342	20	)	)	PUNCT
ejpam-5884	342	21	.	.	PUNCT
ejpam-5884	343	1	in	in	ADP
ejpam-5884	343	2	5th	5th	ADJ
ejpam-5884	343	3	int	int	NOUN
ejpam-5884	343	4	.	.	PUNCT
ejpam-5884	344	1	conf	conf	NOUN
ejpam-5884	344	2	.	.	PUNCT
ejpam-5884	345	1	renewable	renewable	ADJ
ejpam-5884	345	2	energy	energy	NOUN
ejpam-5884	345	3	:	:	PUNCT
ejpam-5884	345	4	generation	generation	NOUN
ejpam-5884	345	5	and	and	CCONJ
ejpam-5884	345	6	appl	appl	NOUN
ejpam-5884	345	7	.	.	PUNCT
ejpam-5884	346	1	(	(	PUNCT
ejpam-5884	346	2	icrega	icrega	PROPN
ejpam-5884	346	3	2018	2018	NUM
ejpam-5884	346	4	)	)	PUNCT
ejpam-5884	346	5	,	,	PUNCT
ejpam-5884	346	6	pages	page	NOUN
ejpam-5884	346	7	102–106	102–106	NUM
ejpam-5884	346	8	,	,	PUNCT
ejpam-5884	346	9	2018	2018	NUM
ejpam-5884	346	10	.	.	PUNCT
ejpam-5884	347	1	[	[	X
ejpam-5884	347	2	21	21	NUM
ejpam-5884	347	3	]	]	PUNCT
ejpam-5884	347	4	m.	m.	NOUN
ejpam-5884	347	5	i.	i.	PROPN
ejpam-5884	347	6	syam	syam	PROPN
ejpam-5884	347	7	,	,	PUNCT
ejpam-5884	347	8	m.	m.	NOUN
ejpam-5884	347	9	a.	a.	PROPN
ejpam-5884	347	10	raja	raja	PROPN
ejpam-5884	347	11	,	,	PUNCT
ejpam-5884	347	12	m.	m.	NOUN
ejpam-5884	347	13	m.	m.	NOUN
ejpam-5884	347	14	syam	syam	PROPN
ejpam-5884	347	15	,	,	PUNCT
ejpam-5884	347	16	and	and	CCONJ
ejpam-5884	347	17	et	et	PROPN
ejpam-5884	347	18	al	al	PROPN
ejpam-5884	347	19	.	.	PUNCT
ejpam-5884	348	1	an	an	DET
ejpam-5884	348	2	accurate	accurate	ADJ
ejpam-5884	348	3	method	method	NOUN
ejpam-5884	348	4	for	for	ADP
ejpam-5884	348	5	solving	solve	VERB
ejpam-5884	348	6	the	the	DET
ejpam-5884	348	7	undamped	undampe	VERB
ejpam-5884	348	8	duffing	duffing	NOUN
ejpam-5884	348	9	equation	equation	NOUN
ejpam-5884	348	10	with	with	ADP
ejpam-5884	348	11	cubic	cubic	ADJ
ejpam-5884	348	12	nonlinearity	nonlinearity	NOUN
ejpam-5884	348	13	.	.	PUNCT
ejpam-5884	349	1	int	int	NOUN
ejpam-5884	349	2	.	.	PUNCT
ejpam-5884	350	1	j.	j.	PROPN
ejpam-5884	350	2	appl	appl	PROPN
ejpam-5884	350	3	.	.	PUNCT
ejpam-5884	351	1	comput	comput	PROPN
ejpam-5884	351	2	.	.	PUNCT
ejpam-5884	352	1	math	math	NOUN
ejpam-5884	352	2	.	.	PUNCT
ejpam-5884	352	3	,	,	PUNCT
ejpam-5884	352	4	4:69	4:69	NUM
ejpam-5884	352	5	,	,	PUNCT
ejpam-5884	352	6	2018	2018	NUM
ejpam-5884	352	7	.	.	PUNCT
ejpam-5884	353	1	[	[	X
ejpam-5884	353	2	22	22	NUM
ejpam-5884	353	3	]	]	PUNCT
ejpam-5884	353	4	a.-h	a.-h	PROPN
ejpam-5884	353	5	.	.	PUNCT
ejpam-5884	354	1	i.	i.	PROPN
ejpam-5884	354	2	mourad	mourad	PROPN
ejpam-5884	354	3	,	,	PUNCT
ejpam-5884	354	4	a.	a.	PROPN
ejpam-5884	354	5	m.	m.	PROPN
ejpam-5884	354	6	ghazal	ghazal	PROPN
ejpam-5884	354	7	,	,	PUNCT
ejpam-5884	354	8	m.	m.	NOUN
ejpam-5884	354	9	m.	m.	NOUN
ejpam-5884	354	10	syam	syam	PROPN
ejpam-5884	354	11	,	,	PUNCT
ejpam-5884	354	12	o.	o.	PROPN
ejpam-5884	354	13	d.	d.	PROPN
ejpam-5884	354	14	al	al	PROPN
ejpam-5884	354	15	qadi	qadi	PROPN
ejpam-5884	354	16	,	,	PUNCT
ejpam-5884	354	17	and	and	CCONJ
ejpam-5884	354	18	h.	h.	PROPN
ejpam-5884	354	19	al	al	PROPN
ejpam-5884	354	20	jassmi	jassmi	PROPN
ejpam-5884	354	21	.	.	PUNCT
ejpam-5884	355	1	utilization	utilization	NOUN
ejpam-5884	355	2	of	of	ADP
ejpam-5884	355	3	additive	additive	ADJ
ejpam-5884	355	4	manufacturing	manufacturing	NOUN
ejpam-5884	355	5	in	in	ADP
ejpam-5884	355	6	evaluating	evaluate	VERB
ejpam-5884	355	7	the	the	DET
ejpam-5884	355	8	performance	performance	NOUN
ejpam-5884	355	9	of	of	ADP
ejpam-5884	355	10	internally	internally	ADV
ejpam-5884	355	11	defected	defect	VERB
ejpam-5884	355	12	materials	material	NOUN
ejpam-5884	355	13	.	.	PUNCT
ejpam-5884	356	1	iop	iop	PROPN
ejpam-5884	356	2	conf	conf	PROPN
ejpam-5884	356	3	.	.	PUNCT
ejpam-5884	357	1	ser	ser	PROPN
ejpam-5884	357	2	.	.	PUNCT
ejpam-5884	357	3	:	:	PUNCT
ejpam-5884	358	1	mater	mater	NOUN
ejpam-5884	358	2	.	.	PUNCT
ejpam-5884	359	1	sci	sci	PROPN
ejpam-5884	359	2	.	.	PUNCT
ejpam-5884	360	1	eng	eng	PROPN
ejpam-5884	360	2	.	.	PROPN
ejpam-5884	360	3	,	,	PUNCT
ejpam-5884	360	4	362:012026	362:012026	NUM
ejpam-5884	360	5	,	,	PUNCT
ejpam-5884	360	6	2018	2018	NUM
ejpam-5884	360	7	.	.	PUNCT
ejpam-5884	361	1	[	[	X
ejpam-5884	361	2	23	23	NUM
ejpam-5884	361	3	]	]	PUNCT
ejpam-5884	361	4	m.	m.	NOUN
ejpam-5884	361	5	al	al	PROPN
ejpam-5884	361	6	-	-	PUNCT
ejpam-5884	361	7	refai	refai	PROPN
ejpam-5884	361	8	,	,	PUNCT
ejpam-5884	361	9	m.	m.	NOUN
ejpam-5884	361	10	syam	syam	NOUN
ejpam-5884	361	11	,	,	PUNCT
ejpam-5884	361	12	and	and	CCONJ
ejpam-5884	361	13	d.	d.	PROPN
ejpam-5884	361	14	baleanu	baleanu	PROPN
ejpam-5884	361	15	.	.	PUNCT
ejpam-5884	362	1	analytical	analytical	ADJ
ejpam-5884	362	2	treatment	treatment	NOUN
ejpam-5884	362	3	to	to	ADP
ejpam-5884	362	4	systems	system	NOUN
ejpam-5884	362	5	of	of	ADP
ejpam-5884	362	6	fractional	fractional	ADJ
ejpam-5884	362	7	differential	differential	ADJ
ejpam-5884	362	8	equations	equation	NOUN
ejpam-5884	362	9	with	with	ADP
ejpam-5884	362	10	modified	modified	ADJ
ejpam-5884	362	11	atangana	atangana	PROPN
ejpam-5884	362	12	-	-	PUNCT
ejpam-5884	362	13	baleanu	baleanu	PROPN
ejpam-5884	362	14	derivative	derivative	NOUN
ejpam-5884	362	15	.	.	PUNCT
ejpam-5884	363	1	fractals	fractal	NOUN
ejpam-5884	363	2	,	,	PUNCT
ejpam-5884	363	3	31:2340156	31:2340156	NOUN
ejpam-5884	363	4	,	,	PUNCT
ejpam-5884	363	5	2023	2023	NUM
ejpam-5884	363	6	.	.	PUNCT
ejpam-5884	364	1	[	[	X
ejpam-5884	364	2	24	24	NUM
ejpam-5884	364	3	]	]	X
ejpam-5884	364	4	g.	g.	PROPN
ejpam-5884	364	5	duffing	duffing	PROPN
ejpam-5884	364	6	.	.	PUNCT
ejpam-5884	365	1	erzwungene	erzwungene	PROPN
ejpam-5884	366	1	schwingungen	schwingungen	PROPN
ejpam-5884	366	2	bei	bei	NOUN
ejpam-5884	366	3	veränderlicher	veränderlicher	ADP
ejpam-5884	366	4	eigenfrequenz	eigenfrequenz	PROPN
ejpam-5884	366	5	und	und	VERB
ejpam-5884	366	6	ihre	ihre	NOUN
ejpam-5884	366	7	technische	technische	PROPN
ejpam-5884	366	8	bedeutung	bedeutung	PROPN
ejpam-5884	366	9	.	.	PUNCT
ejpam-5884	367	1	druck	druck	PROPN
ejpam-5884	367	2	und	und	PROPN
ejpam-5884	367	3	verlag	verlag	PROPN
ejpam-5884	367	4	von	von	PROPN
ejpam-5884	367	5	fridr	fridr	PROPN
ejpam-5884	367	6	.	.	PUNCT
ejpam-5884	368	1	vieweg	vieweg	PROPN
ejpam-5884	368	2	&	&	CCONJ
ejpam-5884	368	3	sohn	sohn	PROPN
ejpam-5884	368	4	,	,	PUNCT
ejpam-5884	368	5	braunschweig	braunschweig	NOUN
ejpam-5884	368	6	,	,	PUNCT
ejpam-5884	368	7	1918	1918	NUM
ejpam-5884	368	8	.	.	PUNCT
ejpam-5884	369	1	[	[	X
ejpam-5884	369	2	25	25	NUM
ejpam-5884	369	3	]	]	PUNCT
ejpam-5884	369	4	r.	r.	PROPN
ejpam-5884	369	5	h.	h.	PROPN
ejpam-5884	369	6	abraham	abraham	PROPN
ejpam-5884	369	7	and	and	CCONJ
ejpam-5884	369	8	c.	c.	PROPN
ejpam-5884	369	9	d.	d.	PROPN
ejpam-5884	369	10	shaw	shaw	PROPN
ejpam-5884	369	11	.	.	PUNCT
ejpam-5884	369	12	dynamics	dynamic	NOUN
ejpam-5884	369	13	–	–	PUNCT
ejpam-5884	369	14	the	the	DET
ejpam-5884	369	15	geometry	geometry	NOUN
ejpam-5884	369	16	of	of	ADP
ejpam-5884	369	17	behavior	behavior	NOUN
ejpam-5884	369	18	,	,	PUNCT
ejpam-5884	369	19	part	part	NOUN
ejpam-5884	369	20	i.	i.	PROPN
ejpam-5884	369	21	aerial	aerial	PROPN
ejpam-5884	369	22	press	press	NOUN
ejpam-5884	369	23	,	,	PUNCT
ejpam-5884	369	24	santa	santa	PROPN
ejpam-5884	369	25	cruz	cruz	PROPN
ejpam-5884	369	26	,	,	PUNCT
ejpam-5884	369	27	2000	2000	NUM
ejpam-5884	369	28	.	.	PUNCT
ejpam-5884	370	1	[	[	X
ejpam-5884	370	2	26	26	NUM
ejpam-5884	370	3	]	]	X
ejpam-5884	370	4	d.	d.	PROPN
ejpam-5884	370	5	d.	d.	PROPN
ejpam-5884	370	6	ganji	ganji	PROPN
ejpam-5884	370	7	,	,	PUNCT
ejpam-5884	370	8	a.	a.	PROPN
ejpam-5884	370	9	r.	r.	PROPN
ejpam-5884	370	10	sahouli	sahouli	PROPN
ejpam-5884	370	11	,	,	PUNCT
ejpam-5884	370	12	and	and	CCONJ
ejpam-5884	370	13	m.	m.	PROPN
ejpam-5884	370	14	famouri	famouri	PROPN
ejpam-5884	370	15	.	.	PUNCT
ejpam-5884	371	1	a	a	DET
ejpam-5884	371	2	new	new	ADJ
ejpam-5884	371	3	modification	modification	NOUN
ejpam-5884	371	4	of	of	ADP
ejpam-5884	371	5	he	he	PRON
ejpam-5884	371	6	’s	’s	NOUN
ejpam-5884	371	7	homotopy	homotopy	NOUN
ejpam-5884	371	8	perturbation	perturbation	NOUN
ejpam-5884	371	9	method	method	NOUN
ejpam-5884	371	10	for	for	ADP
ejpam-5884	371	11	rapid	rapid	ADJ
ejpam-5884	371	12	convergence	convergence	NOUN
ejpam-5884	371	13	of	of	ADP
ejpam-5884	371	14	nonlinear	nonlinear	ADJ
ejpam-5884	371	15	undamped	undampe	VERB
ejpam-5884	371	16	oscillators	oscillator	NOUN
ejpam-5884	371	17	.	.	PUNCT
ejpam-5884	372	1	j.	j.	PROPN
ejpam-5884	372	2	appl	appl	PROPN
ejpam-5884	372	3	.	.	PROPN
ejpam-5884	372	4	math	math	PROPN
ejpam-5884	372	5	.	.	PUNCT
ejpam-5884	373	1	comput	comput	NOUN
ejpam-5884	373	2	.	.	PUNCT
ejpam-5884	374	1	,	,	PUNCT
ejpam-5884	374	2	30:181–192	30:181–192	PROPN
ejpam-5884	374	3	,	,	PUNCT
ejpam-5884	374	4	2009	2009	NUM
ejpam-5884	374	5	.	.	PUNCT
ejpam-5884	375	1	[	[	X
ejpam-5884	375	2	27	27	NUM
ejpam-5884	375	3	]	]	PUNCT
ejpam-5884	375	4	j.	j.	PROPN
ejpam-5884	375	5	h.	h.	PROPN
ejpam-5884	375	6	he	he	PRON
ejpam-5884	375	7	.	.	PUNCT
ejpam-5884	376	1	homotopy	homotopy	VERB
ejpam-5884	376	2	perturbation	perturbation	NOUN
ejpam-5884	376	3	method	method	NOUN
ejpam-5884	376	4	:	:	PUNCT
ejpam-5884	376	5	a	a	DET
ejpam-5884	376	6	new	new	ADJ
ejpam-5884	376	7	nonlinear	nonlinear	ADJ
ejpam-5884	376	8	analytical	analytical	ADJ
ejpam-5884	376	9	technique	technique	NOUN
ejpam-5884	376	10	.	.	PUNCT
ejpam-5884	377	1	appl	appl	PROPN
ejpam-5884	377	2	.	.	PROPN
ejpam-5884	377	3	math	math	PROPN
ejpam-5884	377	4	.	.	PUNCT
ejpam-5884	378	1	comput	comput	NOUN
ejpam-5884	378	2	.	.	PUNCT
ejpam-5884	378	3	,	,	PUNCT
ejpam-5884	378	4	135:73–79	135:73–79	NUM
ejpam-5884	378	5	,	,	PUNCT
ejpam-5884	378	6	2003	2003	NUM
ejpam-5884	378	7	.	.	PUNCT
ejpam-5884	379	1	[	[	X
ejpam-5884	379	2	28	28	NUM
ejpam-5884	379	3	]	]	X
ejpam-5884	379	4	muhammad	muhammad	PROPN
ejpam-5884	379	5	asif	asif	PROPN
ejpam-5884	379	6	zahoor	zahoor	PROPN
ejpam-5884	379	7	raja	raja	PROPN
ejpam-5884	379	8	,	,	PUNCT
ejpam-5884	379	9	saleem	saleem	PROPN
ejpam-5884	379	10	abbas	abbas	PROPN
ejpam-5884	379	11	,	,	PUNCT
ejpam-5884	379	12	muhammed	muhamme	VERB
ejpam-5884	379	13	ibrahem	ibrahem	PROPN
ejpam-5884	379	14	syam	syam	NOUN
ejpam-5884	379	15	,	,	PUNCT
ejpam-5884	379	16	and	and	CCONJ
ejpam-5884	379	17	abdul	abdul	PROPN
ejpam-5884	379	18	majid	majid	PROPN
ejpam-5884	379	19	wazwaz	wazwaz	PROPN
ejpam-5884	379	20	.	.	PUNCT
ejpam-5884	380	1	design	design	NOUN
ejpam-5884	380	2	of	of	ADP
ejpam-5884	380	3	neuro	neuro	NOUN
ejpam-5884	380	4	-	-	PUNCT
ejpam-5884	380	5	evolutionary	evolutionary	ADJ
ejpam-5884	380	6	model	model	NOUN
ejpam-5884	380	7	for	for	ADP
ejpam-5884	380	8	solving	solve	VERB
ejpam-5884	380	9	nonlinear	nonlinear	NOUN
ejpam-5884	380	10	singularly	singularly	ADV
ejpam-5884	380	11	perturbed	perturb	VERB
ejpam-5884	380	12	boundary	boundary	ADJ
ejpam-5884	380	13	value	value	NOUN
ejpam-5884	380	14	problems	problem	NOUN
ejpam-5884	380	15	.	.	PUNCT
ejpam-5884	381	1	applied	apply	VERB
ejpam-5884	381	2	soft	soft	ADJ
ejpam-5884	381	3	computing	computing	NOUN
ejpam-5884	381	4	,	,	PUNCT
ejpam-5884	381	5	62:373–394	62:373–394	PROPN
ejpam-5884	381	6	,	,	PUNCT
ejpam-5884	381	7	2018	2018	NUM
ejpam-5884	381	8	.	.	PUNCT
ejpam-5884	382	1	[	[	X
ejpam-5884	382	2	29	29	NUM
ejpam-5884	382	3	]	]	PUNCT
ejpam-5884	382	4	j.	j.	PROPN
ejpam-5884	382	5	i.	i.	PROPN
ejpam-5884	382	6	ramos	ramos	PROPN
ejpam-5884	382	7	.	.	PUNCT
ejpam-5884	383	1	on	on	ADP
ejpam-5884	383	2	the	the	DET
ejpam-5884	383	3	variational	variational	ADJ
ejpam-5884	383	4	iteration	iteration	NOUN
ejpam-5884	383	5	method	method	NOUN
ejpam-5884	383	6	and	and	CCONJ
ejpam-5884	383	7	other	other	ADJ
ejpam-5884	383	8	iterative	iterative	NOUN
ejpam-5884	383	9	techniques	technique	NOUN
ejpam-5884	383	10	for	for	ADP
ejpam-5884	383	11	nonlinear	nonlinear	ADJ
ejpam-5884	383	12	differential	differential	ADJ
ejpam-5884	383	13	equations	equation	NOUN
ejpam-5884	383	14	.	.	PUNCT
ejpam-5884	384	1	appl	appl	PROPN
ejpam-5884	384	2	.	.	PROPN
ejpam-5884	384	3	math	math	PROPN
ejpam-5884	384	4	.	.	PUNCT
ejpam-5884	385	1	comput	comput	NOUN
ejpam-5884	385	2	.	.	PUNCT
ejpam-5884	385	3	,	,	PUNCT
ejpam-5884	385	4	199:39–69	199:39–69	NUM
ejpam-5884	385	5	,	,	PUNCT
ejpam-5884	385	6	2008	2008	NUM
ejpam-5884	385	7	.	.	PUNCT
ejpam-5884	386	1	[	[	X
ejpam-5884	386	2	30	30	NUM
ejpam-5884	386	3	]	]	X
ejpam-5884	386	4	m.	m.	NOUN
ejpam-5884	386	5	i.	i.	PROPN
ejpam-5884	386	6	syam	syam	PROPN
ejpam-5884	386	7	and	and	CCONJ
ejpam-5884	386	8	h.	h.	PROPN
ejpam-5884	386	9	i.	i.	PROPN
ejpam-5884	386	10	siyyam	siyyam	PROPN
ejpam-5884	386	11	.	.	PUNCT
ejpam-5884	387	1	numerical	numerical	ADJ
ejpam-5884	387	2	differentiation	differentiation	NOUN
ejpam-5884	387	3	of	of	ADP
ejpam-5884	387	4	implicitly	implicitly	ADV
ejpam-5884	387	5	defined	define	VERB
ejpam-5884	387	6	curves	curve	NOUN
ejpam-5884	387	7	.	.	PUNCT
ejpam-5884	388	1	m.	m.	NOUN
ejpam-5884	388	2	i.	i.	PROPN
ejpam-5884	388	3	syam	syam	PROPN
ejpam-5884	388	4	et	et	PROPN
ejpam-5884	388	5	al	al	PROPN
ejpam-5884	388	6	.	.	PUNCT
ejpam-5884	388	7	/	/	SYM
ejpam-5884	388	8	eur	eur	PROPN
ejpam-5884	388	9	.	.	PUNCT
ejpam-5884	389	1	j.	j.	PROPN
ejpam-5884	389	2	pure	pure	PROPN
ejpam-5884	389	3	appl	appl	PROPN
ejpam-5884	389	4	.	.	PROPN
ejpam-5884	389	5	math	math	PROPN
ejpam-5884	389	6	,	,	PUNCT
ejpam-5884	389	7	18	18	NUM
ejpam-5884	389	8	(	(	PUNCT
ejpam-5884	389	9	2	2	NUM
ejpam-5884	389	10	)	)	PUNCT
ejpam-5884	389	11	(	(	PUNCT
ejpam-5884	389	12	2025	2025	NUM
ejpam-5884	389	13	)	)	PUNCT
ejpam-5884	389	14	,	,	PUNCT
ejpam-5884	389	15	5884	5884	NUM
ejpam-5884	389	16	17	17	NUM
ejpam-5884	389	17	of	of	ADP
ejpam-5884	389	18	18	18	NUM
ejpam-5884	389	19	j.	j.	PROPN
ejpam-5884	389	20	comput	comput	PROPN
ejpam-5884	389	21	.	.	PUNCT
ejpam-5884	390	1	appl	appl	PROPN
ejpam-5884	390	2	.	.	PROPN
ejpam-5884	390	3	math	math	PROPN
ejpam-5884	390	4	.	.	PUNCT
ejpam-5884	390	5	,	,	PUNCT
ejpam-5884	390	6	108(1	108(1	NUM
ejpam-5884	390	7	-	-	SYM
ejpam-5884	390	8	2):131–144	2):131–144	NUM
ejpam-5884	390	9	,	,	PUNCT
ejpam-5884	390	10	1999	1999	NUM
ejpam-5884	390	11	.	.	PUNCT
ejpam-5884	391	1	[	[	X
ejpam-5884	391	2	31	31	NUM
ejpam-5884	391	3	]	]	PUNCT
ejpam-5884	391	4	m.	m.	NOUN
ejpam-5884	391	5	syam	syam	NOUN
ejpam-5884	391	6	.	.	PUNCT
ejpam-5884	392	1	the	the	DET
ejpam-5884	392	2	modified	modify	VERB
ejpam-5884	392	3	broyden	broyden	ADJ
ejpam-5884	392	4	-	-	PUNCT
ejpam-5884	392	5	variational	variational	ADJ
ejpam-5884	392	6	method	method	NOUN
ejpam-5884	392	7	for	for	ADP
ejpam-5884	392	8	solving	solve	VERB
ejpam-5884	392	9	nonlinear	nonlinear	ADJ
ejpam-5884	392	10	elliptic	elliptic	ADJ
ejpam-5884	392	11	differential	differential	ADJ
ejpam-5884	392	12	equations	equation	NOUN
ejpam-5884	392	13	.	.	PUNCT
ejpam-5884	393	1	chaos	chaos	NOUN
ejpam-5884	393	2	,	,	PUNCT
ejpam-5884	393	3	solitons	soliton	NOUN
ejpam-5884	393	4	&	&	CCONJ
ejpam-5884	393	5	fractals	fractal	NOUN
ejpam-5884	393	6	,	,	PUNCT
ejpam-5884	393	7	32(2):392–404	32(2):392–404	PROPN
ejpam-5884	393	8	,	,	PUNCT
ejpam-5884	393	9	2007	2007	NUM
ejpam-5884	393	10	.	.	PUNCT
ejpam-5884	394	1	[	[	X
ejpam-5884	394	2	32	32	NUM
ejpam-5884	394	3	]	]	PUNCT
ejpam-5884	394	4	bothayna	bothayna	PROPN
ejpam-5884	394	5	s.h	s.h	PROPN
ejpam-5884	394	6	.	.	PROPN
ejpam-5884	394	7	kashkaria	kashkaria	PROPN
ejpam-5884	394	8	and	and	CCONJ
ejpam-5884	394	9	muhammed	muhammed	PROPN
ejpam-5884	394	10	i.	i.	PROPN
ejpam-5884	394	11	syam	syam	PROPN
ejpam-5884	394	12	.	.	PUNCT
ejpam-5884	395	1	evolutionary	evolutionary	ADJ
ejpam-5884	395	2	computational	computational	ADJ
ejpam-5884	395	3	intelligence	intelligence	NOUN
ejpam-5884	395	4	in	in	ADP
ejpam-5884	395	5	solving	solve	VERB
ejpam-5884	395	6	a	a	DET
ejpam-5884	395	7	class	class	NOUN
ejpam-5884	395	8	of	of	ADP
ejpam-5884	395	9	nonlinear	nonlinear	PROPN
ejpam-5884	395	10	volterra	volterra	PROPN
ejpam-5884	395	11	–	–	PUNCT
ejpam-5884	395	12	fredholm	fredholm	NOUN
ejpam-5884	395	13	integro	integro	ADJ
ejpam-5884	395	14	-	-	PUNCT
ejpam-5884	395	15	differential	differential	NOUN
ejpam-5884	395	16	equations	equation	NOUN
ejpam-5884	395	17	.	.	PUNCT
ejpam-5884	396	1	journal	journal	NOUN
ejpam-5884	396	2	of	of	ADP
ejpam-5884	396	3	computational	computational	ADJ
ejpam-5884	396	4	and	and	CCONJ
ejpam-5884	396	5	applied	applied	ADJ
ejpam-5884	396	6	mathematics	mathematic	NOUN
ejpam-5884	396	7	,	,	PUNCT
ejpam-5884	396	8	311:314–323	311:314–323	NUM
ejpam-5884	396	9	,	,	PUNCT
ejpam-5884	396	10	2017	2017	NUM
ejpam-5884	396	11	.	.	PUNCT
ejpam-5884	397	1	[	[	X
ejpam-5884	397	2	33	33	NUM
ejpam-5884	397	3	]	]	PUNCT
ejpam-5884	397	4	m.	m.	PROPN
ejpam-5884	397	5	f.	f.	PROPN
ejpam-5884	397	6	el	el	PROPN
ejpam-5884	397	7	-	-	PUNCT
ejpam-5884	397	8	sayed	say	VERB
ejpam-5884	397	9	and	and	CCONJ
ejpam-5884	397	10	m.	m.	NOUN
ejpam-5884	397	11	i.	i.	PROPN
ejpam-5884	397	12	syam	syam	PROPN
ejpam-5884	397	13	.	.	PUNCT
ejpam-5884	398	1	electrohydrodynamic	electrohydrodynamic	ADJ
ejpam-5884	398	2	instability	instability	NOUN
ejpam-5884	398	3	of	of	ADP
ejpam-5884	398	4	a	a	DET
ejpam-5884	398	5	dielectric	dielectric	ADJ
ejpam-5884	398	6	compressible	compressible	ADJ
ejpam-5884	398	7	liquid	liquid	ADJ
ejpam-5884	398	8	sheet	sheet	NOUN
ejpam-5884	398	9	streaming	streaming	NOUN
ejpam-5884	398	10	into	into	ADP
ejpam-5884	398	11	an	an	DET
ejpam-5884	398	12	ambient	ambient	ADJ
ejpam-5884	398	13	stationary	stationary	ADJ
ejpam-5884	398	14	compressible	compressible	ADJ
ejpam-5884	398	15	gas	gas	NOUN
ejpam-5884	398	16	.	.	PUNCT
ejpam-5884	399	1	archive	archive	NOUN
ejpam-5884	399	2	of	of	ADP
ejpam-5884	399	3	applied	apply	VERB
ejpam-5884	399	4	mechanics	mechanic	NOUN
ejpam-5884	399	5	,	,	PUNCT
ejpam-5884	399	6	77:613–626	77:613–626	PROPN
ejpam-5884	399	7	,	,	PUNCT
ejpam-5884	399	8	2007	2007	NUM
ejpam-5884	399	9	.	.	PUNCT
ejpam-5884	400	1	[	[	X
ejpam-5884	400	2	34	34	NUM
ejpam-5884	400	3	]	]	X
ejpam-5884	400	4	h.	h.	PROPN
ejpam-5884	400	5	m.	m.	PROPN
ejpam-5884	400	6	jaradat	jaradat	PROPN
ejpam-5884	400	7	,	,	PUNCT
ejpam-5884	400	8	m.	m.	NOUN
ejpam-5884	400	9	alquran	alquran	PROPN
ejpam-5884	400	10	,	,	PUNCT
ejpam-5884	400	11	and	and	CCONJ
ejpam-5884	400	12	m.	m.	PROPN
ejpam-5884	400	13	i.	i.	PROPN
ejpam-5884	400	14	syam	syam	PROPN
ejpam-5884	400	15	.	.	PUNCT
ejpam-5884	401	1	a	a	DET
ejpam-5884	401	2	reliable	reliable	ADJ
ejpam-5884	401	3	study	study	NOUN
ejpam-5884	401	4	of	of	ADP
ejpam-5884	401	5	new	new	ADJ
ejpam-5884	401	6	nonlinear	nonlinear	ADJ
ejpam-5884	401	7	equation	equation	NOUN
ejpam-5884	401	8	:	:	PUNCT
ejpam-5884	401	9	two	two	NUM
ejpam-5884	401	10	-	-	PUNCT
ejpam-5884	401	11	mode	mode	NOUN
ejpam-5884	401	12	kuramoto	kuramoto	NOUN
ejpam-5884	401	13	–	–	PUNCT
ejpam-5884	401	14	sivashinsky	sivashinsky	NOUN
ejpam-5884	401	15	.	.	PUNCT
ejpam-5884	402	1	international	international	ADJ
ejpam-5884	402	2	journal	journal	PROPN
ejpam-5884	402	3	of	of	ADP
ejpam-5884	402	4	applied	applied	ADJ
ejpam-5884	402	5	and	and	CCONJ
ejpam-5884	402	6	computational	computational	ADJ
ejpam-5884	402	7	mathematics	mathematic	NOUN
ejpam-5884	402	8	,	,	PUNCT
ejpam-5884	402	9	4:64	4:64	NUM
ejpam-5884	402	10	,	,	PUNCT
ejpam-5884	402	11	2018	2018	NUM
ejpam-5884	402	12	.	.	PUNCT
ejpam-5884	403	1	[	[	X
ejpam-5884	403	2	35	35	NUM
ejpam-5884	403	3	]	]	X
ejpam-5884	403	4	s.	s.	PROPN
ejpam-5884	403	5	bourazza	bourazza	PROPN
ejpam-5884	403	6	,	,	PUNCT
ejpam-5884	403	7	sami	sami	PROPN
ejpam-5884	403	8	h.	h.	PROPN
ejpam-5884	403	9	altoum	altoum	PROPN
ejpam-5884	403	10	,	,	PUNCT
ejpam-5884	403	11	and	and	CCONJ
ejpam-5884	403	12	et	et	PROPN
ejpam-5884	403	13	al	al	PROPN
ejpam-5884	403	14	.	.	PROPN
ejpam-5884	404	1	discharging	discharge	VERB
ejpam-5884	404	2	process	process	NOUN
ejpam-5884	404	3	within	within	ADP
ejpam-5884	404	4	a	a	DET
ejpam-5884	404	5	storage	storage	NOUN
ejpam-5884	404	6	container	container	NOUN
ejpam-5884	404	7	considering	consider	VERB
ejpam-5884	404	8	numerical	numerical	ADJ
ejpam-5884	404	9	method	method	NOUN
ejpam-5884	404	10	.	.	PUNCT
ejpam-5884	405	1	journal	journal	PROPN
ejpam-5884	405	2	of	of	ADP
ejpam-5884	405	3	energy	energy	NOUN
ejpam-5884	405	4	storage	storage	NOUN
ejpam-5884	405	5	,	,	PUNCT
ejpam-5884	405	6	66:107490	66:107490	NUM
ejpam-5884	405	7	,	,	PUNCT
ejpam-5884	405	8	2023	2023	NUM
ejpam-5884	405	9	.	.	PUNCT
ejpam-5884	406	1	[	[	X
ejpam-5884	406	2	36	36	NUM
ejpam-5884	406	3	]	]	X
ejpam-5884	406	4	sami	sami	PROPN
ejpam-5884	406	5	h.	h.	PROPN
ejpam-5884	406	6	altoum	altoum	PROPN
ejpam-5884	406	7	and	and	CCONJ
ejpam-5884	406	8	et	et	PROPN
ejpam-5884	406	9	al	al	PROPN
ejpam-5884	406	10	.	.	PROPN
ejpam-5884	406	11	efficacy	efficacy	PROPN
ejpam-5884	406	12	of	of	ADP
ejpam-5884	406	13	magnetic	magnetic	ADJ
ejpam-5884	406	14	force	force	NOUN
ejpam-5884	406	15	on	on	ADP
ejpam-5884	406	16	nanofluid	nanofluid	ADJ
ejpam-5884	406	17	laminar	laminar	ADJ
ejpam-5884	406	18	transportation	transportation	NOUN
ejpam-5884	406	19	and	and	CCONJ
ejpam-5884	406	20	convective	convective	ADJ
ejpam-5884	406	21	flow	flow	NOUN
ejpam-5884	406	22	.	.	PUNCT
ejpam-5884	407	1	journal	journal	PROPN
ejpam-5884	407	2	of	of	ADP
ejpam-5884	407	3	magnetism	magnetism	NOUN
ejpam-5884	407	4	and	and	CCONJ
ejpam-5884	407	5	magnetic	magnetic	ADJ
ejpam-5884	407	6	materials	material	NOUN
ejpam-5884	407	7	,	,	PUNCT
ejpam-5884	407	8	581:170964	581:170964	NUM
ejpam-5884	407	9	,	,	PUNCT
ejpam-5884	407	10	2023	2023	NUM
ejpam-5884	407	11	.	.	PUNCT
ejpam-5884	408	1	[	[	X
ejpam-5884	408	2	37	37	NUM
ejpam-5884	408	3	]	]	SYM
ejpam-5884	408	4	mahmmoud	mahmmoud	PROPN
ejpam-5884	408	5	m.	m.	NOUN
ejpam-5884	408	6	syam	syam	PROPN
ejpam-5884	408	7	,	,	PUNCT
ejpam-5884	408	8	mohammad	mohammad	PROPN
ejpam-5884	408	9	alkhedher	alkhedher	PROPN
ejpam-5884	408	10	,	,	PUNCT
ejpam-5884	408	11	and	and	CCONJ
ejpam-5884	408	12	muhammed	muhammed	PROPN
ejpam-5884	408	13	i.	i.	PROPN
ejpam-5884	408	14	syam	syam	PROPN
ejpam-5884	408	15	.	.	PUNCT
ejpam-5884	409	1	thermal	thermal	ADJ
ejpam-5884	409	2	and	and	CCONJ
ejpam-5884	409	3	hydrodynamic	hydrodynamic	ADJ
ejpam-5884	409	4	analysis	analysis	NOUN
ejpam-5884	409	5	of	of	ADP
ejpam-5884	409	6	mhd	mhd	PROPN
ejpam-5884	409	7	nanofluid	nanofluid	PROPN
ejpam-5884	409	8	flow	flow	NOUN
ejpam-5884	409	9	over	over	ADP
ejpam-5884	409	10	a	a	DET
ejpam-5884	409	11	permeable	permeable	ADJ
ejpam-5884	409	12	stretching	stretch	VERB
ejpam-5884	409	13	surface	surface	NOUN
ejpam-5884	409	14	in	in	ADP
ejpam-5884	409	15	porous	porous	ADJ
ejpam-5884	409	16	media	medium	NOUN
ejpam-5884	409	17	:	:	PUNCT
ejpam-5884	409	18	comparative	comparative	ADJ
ejpam-5884	409	19	study	study	NOUN
ejpam-5884	409	20	of	of	ADP
ejpam-5884	409	21	fe3o4	fe3o4	PROPN
ejpam-5884	409	22	,	,	PUNCT
ejpam-5884	409	23	cu	cu	PROPN
ejpam-5884	409	24	,	,	PUNCT
ejpam-5884	409	25	and	and	CCONJ
ejpam-5884	409	26	ag	ag	PROPN
ejpam-5884	409	27	nanofluids	nanofluid	NOUN
ejpam-5884	409	28	.	.	PUNCT
ejpam-5884	410	1	international	international	ADJ
ejpam-5884	410	2	journal	journal	PROPN
ejpam-5884	410	3	of	of	ADP
ejpam-5884	410	4	thermofluids	thermofluid	NOUN
ejpam-5884	410	5	,	,	PUNCT
ejpam-5884	410	6	26:101055	26:101055	NUM
ejpam-5884	410	7	,	,	PUNCT
ejpam-5884	410	8	2025	2025	NUM
ejpam-5884	410	9	.	.	PUNCT
ejpam-5884	411	1	[	[	X
ejpam-5884	411	2	38	38	NUM
ejpam-5884	411	3	]	]	PUNCT
ejpam-5884	411	4	mahmmoud	mahmmoud	NOUN
ejpam-5884	411	5	m.	m.	NOUN
ejpam-5884	411	6	syam	syam	NOUN
ejpam-5884	411	7	and	and	CCONJ
ejpam-5884	411	8	muhammed	muhammed	PROPN
ejpam-5884	411	9	i.	i.	PROPN
ejpam-5884	411	10	syam	syam	PROPN
ejpam-5884	411	11	.	.	PUNCT
ejpam-5884	412	1	impacts	impact	NOUN
ejpam-5884	412	2	of	of	ADP
ejpam-5884	412	3	energy	energy	NOUN
ejpam-5884	412	4	transmission	transmission	NOUN
ejpam-5884	412	5	properties	property	NOUN
ejpam-5884	412	6	on	on	ADP
ejpam-5884	412	7	non	non	ADJ
ejpam-5884	412	8	-	-	ADJ
ejpam-5884	412	9	newtonian	newtonian	ADJ
ejpam-5884	412	10	fluid	fluid	ADJ
ejpam-5884	412	11	flow	flow	NOUN
ejpam-5884	412	12	in	in	ADP
ejpam-5884	412	13	stratified	stratified	ADJ
ejpam-5884	412	14	and	and	CCONJ
ejpam-5884	412	15	non	non	ADJ
ejpam-5884	412	16	-	-	ADJ
ejpam-5884	412	17	stratified	stratified	ADJ
ejpam-5884	412	18	conditions	condition	NOUN
ejpam-5884	412	19	.	.	PUNCT
ejpam-5884	413	1	international	international	ADJ
ejpam-5884	413	2	journal	journal	PROPN
ejpam-5884	413	3	of	of	ADP
ejpam-5884	413	4	thermofluids	thermofluid	NOUN
ejpam-5884	413	5	,	,	PUNCT
ejpam-5884	413	6	23:100824	23:100824	NUM
ejpam-5884	413	7	,	,	PUNCT
ejpam-5884	413	8	2024	2024	NUM
ejpam-5884	413	9	.	.	PUNCT
ejpam-5884	414	1	[	[	X
ejpam-5884	414	2	39	39	NUM
ejpam-5884	414	3	]	]	PUNCT
ejpam-5884	414	4	r.	r.	PROPN
ejpam-5884	414	5	e.	e.	PROPN
ejpam-5884	414	6	mickens	mickens	PROPN
ejpam-5884	414	7	.	.	PUNCT
ejpam-5884	415	1	nonlinear	nonlinear	ADJ
ejpam-5884	415	2	oscillations	oscillation	NOUN
ejpam-5884	415	3	.	.	PUNCT
ejpam-5884	416	1	cambridge	cambridge	PROPN
ejpam-5884	416	2	university	university	PROPN
ejpam-5884	416	3	press	press	PROPN
ejpam-5884	416	4	,	,	PUNCT
ejpam-5884	416	5	new	new	PROPN
ejpam-5884	416	6	york	york	PROPN
ejpam-5884	416	7	,	,	PUNCT
ejpam-5884	416	8	1981	1981	NUM
ejpam-5884	416	9	.	.	PUNCT
ejpam-5884	417	1	[	[	X
ejpam-5884	417	2	40	40	NUM
ejpam-5884	417	3	]	]	PUNCT
ejpam-5884	417	4	basem	basem	PROPN
ejpam-5884	417	5	s.	s.	PROPN
ejpam-5884	417	6	attili	attili	PROPN
ejpam-5884	417	7	,	,	PUNCT
ejpam-5884	417	8	khalid	khalid	PROPN
ejpam-5884	417	9	furati	furati	PROPN
ejpam-5884	417	10	,	,	PUNCT
ejpam-5884	417	11	and	and	CCONJ
ejpam-5884	417	12	muhammed	muhammed	PROPN
ejpam-5884	417	13	i.	i.	PROPN
ejpam-5884	417	14	syam	syam	PROPN
ejpam-5884	417	15	.	.	PUNCT
ejpam-5884	418	1	an	an	DET
ejpam-5884	418	2	efficient	efficient	ADJ
ejpam-5884	418	3	implicit	implicit	ADJ
ejpam-5884	418	4	runge	runge	NOUN
ejpam-5884	418	5	–	–	PUNCT
ejpam-5884	418	6	kutta	kutta	NOUN
ejpam-5884	418	7	method	method	NOUN
ejpam-5884	418	8	for	for	ADP
ejpam-5884	418	9	second	second	ADJ
ejpam-5884	418	10	order	order	NOUN
ejpam-5884	418	11	systems	system	NOUN
ejpam-5884	418	12	.	.	PUNCT
ejpam-5884	419	1	applied	apply	VERB
ejpam-5884	419	2	mathematics	mathematic	NOUN
ejpam-5884	419	3	and	and	CCONJ
ejpam-5884	419	4	computation	computation	NOUN
ejpam-5884	419	5	,	,	PUNCT
ejpam-5884	419	6	178(2):229–238	178(2):229–238	NUM
ejpam-5884	419	7	,	,	PUNCT
ejpam-5884	419	8	2006	2006	NUM
ejpam-5884	419	9	.	.	PUNCT
ejpam-5884	420	1	[	[	X
ejpam-5884	420	2	41	41	NUM
ejpam-5884	420	3	]	]	X
ejpam-5884	420	4	l.	l.	PROPN
ejpam-5884	420	5	cveticanin	cveticanin	PROPN
ejpam-5884	420	6	.	.	PUNCT
ejpam-5884	421	1	analytic	analytic	ADJ
ejpam-5884	421	2	approach	approach	NOUN
ejpam-5884	421	3	for	for	ADP
ejpam-5884	421	4	the	the	DET
ejpam-5884	421	5	solution	solution	NOUN
ejpam-5884	421	6	of	of	ADP
ejpam-5884	421	7	the	the	DET
ejpam-5884	421	8	complex	complex	ADV
ejpam-5884	421	9	-	-	PUNCT
ejpam-5884	421	10	valued	value	VERB
ejpam-5884	421	11	strong	strong	ADJ
ejpam-5884	421	12	nonlinear	nonlinear	ADJ
ejpam-5884	421	13	differential	differential	ADJ
ejpam-5884	421	14	equation	equation	NOUN
ejpam-5884	421	15	of	of	ADP
ejpam-5884	421	16	duffing	duffing	NOUN
ejpam-5884	421	17	type	type	NOUN
ejpam-5884	421	18	.	.	PUNCT
ejpam-5884	422	1	physica	physica	PROPN
ejpam-5884	422	2	a	a	DET
ejpam-5884	422	3	,	,	PUNCT
ejpam-5884	422	4	297:348–360	297:348–360	NUM
ejpam-5884	422	5	,	,	PUNCT
ejpam-5884	422	6	2001	2001	NUM
ejpam-5884	422	7	.	.	PUNCT
ejpam-5884	423	1	[	[	X
ejpam-5884	423	2	42	42	NUM
ejpam-5884	423	3	]	]	PUNCT
ejpam-5884	423	4	s.	s.	PROPN
ejpam-5884	423	5	m.	m.	PROPN
ejpam-5884	423	6	syam	syam	PROPN
ejpam-5884	423	7	,	,	PUNCT
ejpam-5884	423	8	z.	z.	PROPN
ejpam-5884	423	9	siri	siri	PROPN
ejpam-5884	423	10	,	,	PUNCT
ejpam-5884	423	11	s.	s.	PROPN
ejpam-5884	423	12	h.	h.	PROPN
ejpam-5884	423	13	altoum	altoum	PROPN
ejpam-5884	423	14	,	,	PUNCT
ejpam-5884	423	15	m.	m.	NOUN
ejpam-5884	423	16	a.	a.	PROPN
ejpam-5884	423	17	aigo	aigo	PROPN
ejpam-5884	423	18	,	,	PUNCT
ejpam-5884	423	19	and	and	CCONJ
ejpam-5884	423	20	r.	r.	PROPN
ejpam-5884	423	21	md	md	PROPN
ejpam-5884	423	22	.	.	PUNCT
ejpam-5884	424	1	kasmani	kasmani	PROPN
ejpam-5884	424	2	.	.	PUNCT
ejpam-5884	425	1	a	a	DET
ejpam-5884	425	2	new	new	ADJ
ejpam-5884	425	3	method	method	NOUN
ejpam-5884	425	4	for	for	ADP
ejpam-5884	425	5	solving	solve	VERB
ejpam-5884	425	6	physical	physical	ADJ
ejpam-5884	425	7	problems	problem	NOUN
ejpam-5884	425	8	with	with	ADP
ejpam-5884	425	9	nonlinear	nonlinear	ADJ
ejpam-5884	425	10	phoneme	phoneme	NOUN
ejpam-5884	425	11	within	within	ADP
ejpam-5884	425	12	fractional	fractional	ADJ
ejpam-5884	425	13	derivatives	derivative	NOUN
ejpam-5884	425	14	with	with	ADP
ejpam-5884	425	15	singular	singular	ADJ
ejpam-5884	425	16	kernel	kernel	PROPN
ejpam-5884	425	17	.	.	PUNCT
ejpam-5884	426	1	j.	j.	PROPN
ejpam-5884	426	2	comput	comput	PROPN
ejpam-5884	426	3	.	.	PUNCT
ejpam-5884	427	1	nonlinear	nonlinear	PROPN
ejpam-5884	427	2	dyn	dyn	PROPN
ejpam-5884	427	3	.	.	PUNCT
ejpam-5884	427	4	,	,	PUNCT
ejpam-5884	427	5	19	19	NUM
ejpam-5884	427	6	,	,	PUNCT
ejpam-5884	427	7	2024	2024	NUM
ejpam-5884	427	8	.	.	PUNCT
ejpam-5884	428	1	[	[	X
ejpam-5884	428	2	43	43	NUM
ejpam-5884	428	3	]	]	X
ejpam-5884	428	4	s.	s.	PROPN
ejpam-5884	428	5	m.	m.	PROPN
ejpam-5884	428	6	syam	syam	PROPN
ejpam-5884	428	7	,	,	PUNCT
ejpam-5884	428	8	z.	z.	PROPN
ejpam-5884	428	9	siri	siri	PROPN
ejpam-5884	428	10	,	,	PUNCT
ejpam-5884	428	11	s.	s.	PROPN
ejpam-5884	428	12	h.	h.	PROPN
ejpam-5884	428	13	altoum	altoum	PROPN
ejpam-5884	428	14	,	,	PUNCT
ejpam-5884	428	15	and	and	CCONJ
ejpam-5884	428	16	r.	r.	PROPN
ejpam-5884	428	17	md	md	PROPN
ejpam-5884	428	18	.	.	PUNCT
ejpam-5884	429	1	kasmani	kasmani	PROPN
ejpam-5884	429	2	.	.	PUNCT
ejpam-5884	430	1	an	an	DET
ejpam-5884	430	2	efficient	efficient	ADJ
ejpam-5884	430	3	numerical	numerical	ADJ
ejpam-5884	430	4	approach	approach	NOUN
ejpam-5884	430	5	for	for	ADP
ejpam-5884	430	6	solving	solve	VERB
ejpam-5884	430	7	systems	system	NOUN
ejpam-5884	430	8	of	of	ADP
ejpam-5884	430	9	fractional	fractional	ADJ
ejpam-5884	430	10	problems	problem	NOUN
ejpam-5884	430	11	and	and	CCONJ
ejpam-5884	430	12	their	their	PRON
ejpam-5884	430	13	applications	application	NOUN
ejpam-5884	430	14	in	in	ADP
ejpam-5884	430	15	science	science	NOUN
ejpam-5884	430	16	.	.	PUNCT
ejpam-5884	431	1	mathematics	mathematic	NOUN
ejpam-5884	431	2	,	,	PUNCT
ejpam-5884	431	3	11	11	NUM
ejpam-5884	431	4	,	,	PUNCT
ejpam-5884	431	5	2023	2023	NUM
ejpam-5884	431	6	.	.	PUNCT
ejpam-5884	432	1	[	[	X
ejpam-5884	432	2	44	44	NUM
ejpam-5884	432	3	]	]	PUNCT
ejpam-5884	432	4	s.	s.	PROPN
ejpam-5884	432	5	m.	m.	PROPN
ejpam-5884	432	6	syam	syam	PROPN
ejpam-5884	432	7	,	,	PUNCT
ejpam-5884	432	8	z.	z.	PROPN
ejpam-5884	432	9	siri	siri	PROPN
ejpam-5884	432	10	,	,	PUNCT
ejpam-5884	432	11	r.	r.	PROPN
ejpam-5884	432	12	m.	m.	PROPN
ejpam-5884	432	13	kasmani	kasmani	PROPN
ejpam-5884	432	14	,	,	PUNCT
ejpam-5884	432	15	and	and	CCONJ
ejpam-5884	432	16	k.	k.	PROPN
ejpam-5884	432	17	yildirim	yildirim	PROPN
ejpam-5884	432	18	.	.	PUNCT
ejpam-5884	433	1	a	a	DET
ejpam-5884	433	2	new	new	ADJ
ejpam-5884	433	3	method	method	NOUN
ejpam-5884	433	4	for	for	ADP
ejpam-5884	433	5	solving	solve	VERB
ejpam-5884	433	6	sequential	sequential	ADJ
ejpam-5884	433	7	fractional	fractional	ADJ
ejpam-5884	433	8	wave	wave	NOUN
ejpam-5884	433	9	equations	equation	NOUN
ejpam-5884	433	10	.	.	PUNCT
ejpam-5884	434	1	j.	j.	PROPN
ejpam-5884	434	2	math	math	PROPN
ejpam-5884	434	3	.	.	PUNCT
ejpam-5884	434	4	,	,	PUNCT
ejpam-5884	434	5	2023	2023	NUM
ejpam-5884	434	6	.	.	PUNCT
ejpam-5884	435	1	[	[	X
ejpam-5884	435	2	45	45	NUM
ejpam-5884	435	3	]	]	PUNCT
ejpam-5884	435	4	m.	m.	NOUN
ejpam-5884	435	5	i.	i.	PROPN
ejpam-5884	435	6	syam	syam	PROPN
ejpam-5884	435	7	,	,	PUNCT
ejpam-5884	435	8	m.	m.	NOUN
ejpam-5884	435	9	sharadga	sharadga	NOUN
ejpam-5884	435	10	,	,	PUNCT
ejpam-5884	435	11	and	and	CCONJ
ejpam-5884	435	12	i.	i.	PROPN
ejpam-5884	435	13	hashim	hashim	PROPN
ejpam-5884	435	14	.	.	PUNCT
ejpam-5884	436	1	a	a	DET
ejpam-5884	436	2	numerical	numerical	ADJ
ejpam-5884	436	3	method	method	NOUN
ejpam-5884	436	4	for	for	ADP
ejpam-5884	436	5	solving	solve	VERB
ejpam-5884	436	6	fractional	fractional	ADJ
ejpam-5884	436	7	delay	delay	NOUN
ejpam-5884	436	8	differential	differential	ADJ
ejpam-5884	436	9	equations	equation	NOUN
ejpam-5884	436	10	based	base	VERB
ejpam-5884	436	11	on	on	ADP
ejpam-5884	436	12	the	the	DET
ejpam-5884	436	13	operational	operational	ADJ
ejpam-5884	436	14	matrix	matrix	NOUN
ejpam-5884	436	15	method	method	NOUN
ejpam-5884	436	16	.	.	PUNCT
ejpam-5884	437	1	chaos	chaos	NOUN
ejpam-5884	437	2	,	,	PUNCT
ejpam-5884	437	3	solitons	soliton	NOUN
ejpam-5884	437	4	&	&	CCONJ
ejpam-5884	437	5	fractals	fractal	NOUN
ejpam-5884	437	6	,	,	PUNCT
ejpam-5884	437	7	147:110977	147:110977	NUM
ejpam-5884	437	8	,	,	PUNCT
ejpam-5884	437	9	2021	2021	NUM
ejpam-5884	437	10	.	.	PUNCT
ejpam-5884	438	1	[	[	X
ejpam-5884	438	2	46	46	NUM
ejpam-5884	438	3	]	]	PUNCT
ejpam-5884	438	4	s.	s.	PROPN
ejpam-5884	438	5	m.	m.	PROPN
ejpam-5884	438	6	syam	syam	PROPN
ejpam-5884	438	7	,	,	PUNCT
ejpam-5884	438	8	z.	z.	PROPN
ejpam-5884	438	9	siri	siri	PROPN
ejpam-5884	438	10	,	,	PUNCT
ejpam-5884	438	11	and	and	CCONJ
ejpam-5884	438	12	r.	r.	PROPN
ejpam-5884	438	13	m.	m.	PROPN
ejpam-5884	438	14	kasmani	kasmani	PROPN
ejpam-5884	438	15	.	.	PUNCT
ejpam-5884	439	1	operational	operational	ADJ
ejpam-5884	439	2	matrix	matrix	NOUN
ejpam-5884	439	3	method	method	NOUN
ejpam-5884	439	4	for	for	ADP
ejpam-5884	439	5	solving	solve	VERB
ejpam-5884	439	6	fractional	fractional	ADJ
ejpam-5884	439	7	system	system	NOUN
ejpam-5884	439	8	of	of	ADP
ejpam-5884	439	9	riccati	riccati	PROPN
ejpam-5884	439	10	equations	equation	NOUN
ejpam-5884	439	11	.	.	PUNCT
ejpam-5884	440	1	in	in	ADP
ejpam-5884	440	2	2023	2023	NUM
ejpam-5884	440	3	international	international	ADJ
ejpam-5884	440	4	conference	conference	NOUN
ejpam-5884	440	5	on	on	ADP
ejpam-5884	440	6	fracm	fracm	PROPN
ejpam-5884	440	7	.	.	PUNCT
ejpam-5884	440	8	i.	i.	PROPN
ejpam-5884	440	9	syam	syam	PROPN
ejpam-5884	440	10	et	et	PROPN
ejpam-5884	440	11	al	al	PROPN
ejpam-5884	440	12	.	.	PUNCT
ejpam-5884	440	13	/	/	SYM
ejpam-5884	440	14	eur	eur	PROPN
ejpam-5884	440	15	.	.	PUNCT
ejpam-5884	441	1	j.	j.	PROPN
ejpam-5884	441	2	pure	pure	PROPN
ejpam-5884	441	3	appl	appl	PROPN
ejpam-5884	441	4	.	.	PROPN
ejpam-5884	441	5	math	math	PROPN
ejpam-5884	441	6	,	,	PUNCT
ejpam-5884	441	7	18	18	NUM
ejpam-5884	441	8	(	(	PUNCT
ejpam-5884	441	9	2	2	NUM
ejpam-5884	441	10	)	)	PUNCT
ejpam-5884	441	11	(	(	PUNCT
ejpam-5884	441	12	2025	2025	NUM
ejpam-5884	441	13	)	)	PUNCT
ejpam-5884	441	14	,	,	PUNCT
ejpam-5884	441	15	5884	5884	NUM
ejpam-5884	441	16	18	18	NUM
ejpam-5884	441	17	of	of	ADP
ejpam-5884	441	18	18	18	NUM
ejpam-5884	441	19	tional	tional	ADJ
ejpam-5884	441	20	differentiation	differentiation	NOUN
ejpam-5884	441	21	and	and	CCONJ
ejpam-5884	441	22	its	its	PRON
ejpam-5884	441	23	applications	application	NOUN
ejpam-5884	441	24	(	(	PUNCT
ejpam-5884	441	25	icfda	icfda	PROPN
ejpam-5884	441	26	)	)	PUNCT
ejpam-5884	441	27	,	,	PUNCT
ejpam-5884	441	28	pages	page	NOUN
ejpam-5884	441	29	1–6	1–6	NUM
ejpam-5884	441	30	,	,	PUNCT
ejpam-5884	441	31	ajman	ajman	PROPN
ejpam-5884	441	32	,	,	PUNCT
ejpam-5884	441	33	united	united	PROPN
ejpam-5884	441	34	arab	arab	PROPN
ejpam-5884	441	35	emirates	emirates	PROPN
ejpam-5884	441	36	,	,	PUNCT
ejpam-5884	441	37	2023	2023	NUM
ejpam-5884	441	38	.	.	PUNCT
ejpam-5884	442	1	[	[	X
ejpam-5884	442	2	47	47	NUM
ejpam-5884	442	3	]	]	PUNCT
ejpam-5884	442	4	s.	s.	PROPN
ejpam-5884	442	5	m.	m.	PROPN
ejpam-5884	442	6	syam	syam	PROPN
ejpam-5884	442	7	,	,	PUNCT
ejpam-5884	442	8	z.	z.	PROPN
ejpam-5884	442	9	siri	siri	PROPN
ejpam-5884	442	10	,	,	PUNCT
ejpam-5884	442	11	s.	s.	PROPN
ejpam-5884	442	12	h.	h.	PROPN
ejpam-5884	442	13	altoum	altoum	PROPN
ejpam-5884	442	14	,	,	PUNCT
ejpam-5884	442	15	m.	m.	NOUN
ejpam-5884	442	16	a.	a.	PROPN
ejpam-5884	442	17	aigo	aigo	PROPN
ejpam-5884	442	18	,	,	PUNCT
ejpam-5884	442	19	and	and	CCONJ
ejpam-5884	442	20	r.	r.	PROPN
ejpam-5884	442	21	m.	m.	PROPN
ejpam-5884	442	22	kasmani	kasmani	PROPN
ejpam-5884	442	23	.	.	PUNCT
ejpam-5884	443	1	a	a	DET
ejpam-5884	443	2	novel	novel	ADJ
ejpam-5884	443	3	study	study	NOUN
ejpam-5884	443	4	for	for	ADP
ejpam-5884	443	5	solving	solve	VERB
ejpam-5884	443	6	systems	system	NOUN
ejpam-5884	443	7	of	of	ADP
ejpam-5884	443	8	nonlinear	nonlinear	ADJ
ejpam-5884	443	9	fractional	fractional	ADJ
ejpam-5884	443	10	integral	integral	ADJ
ejpam-5884	443	11	equations	equation	NOUN
ejpam-5884	443	12	.	.	PUNCT
ejpam-5884	444	1	appl	appl	PROPN
ejpam-5884	444	2	.	.	PROPN
ejpam-5884	444	3	math	math	PROPN
ejpam-5884	444	4	.	.	PUNCT
ejpam-5884	445	1	sci	sci	PROPN
ejpam-5884	445	2	.	.	PUNCT
ejpam-5884	446	1	eng	eng	PROPN
ejpam-5884	446	2	.	.	PROPN
ejpam-5884	446	3	,	,	PUNCT
ejpam-5884	446	4	31(1	31(1	NUM
ejpam-5884	446	5	)	)	PUNCT
ejpam-5884	446	6	,	,	PUNCT
ejpam-5884	446	7	2023	2023	NUM
ejpam-5884	446	8	.	.	PUNCT
ejpam-5884	447	1	[	[	X
ejpam-5884	447	2	48	48	NUM
ejpam-5884	447	3	]	]	PUNCT
ejpam-5884	447	4	m.	m.	NOUN
ejpam-5884	447	5	i.	i.	PROPN
ejpam-5884	447	6	syam	syam	PROPN
ejpam-5884	447	7	,	,	PUNCT
ejpam-5884	447	8	h.	h.	PROPN
ejpam-5884	447	9	alahbabi	alahbabi	PROPN
ejpam-5884	447	10	,	,	PUNCT
ejpam-5884	447	11	r.	r.	PROPN
ejpam-5884	447	12	alomari	alomari	PROPN
ejpam-5884	447	13	,	,	PUNCT
ejpam-5884	447	14	s.	s.	PROPN
ejpam-5884	447	15	m.	m.	PROPN
ejpam-5884	447	16	syam	syam	PROPN
ejpam-5884	447	17	,	,	PUNCT
ejpam-5884	447	18	s.	s.	PROPN
ejpam-5884	447	19	m.	m.	PROPN
ejpam-5884	447	20	hussein	hussein	PROPN
ejpam-5884	447	21	,	,	PUNCT
ejpam-5884	447	22	s.	s.	PROPN
ejpam-5884	447	23	rabih	rabih	PROPN
ejpam-5884	447	24	,	,	PUNCT
ejpam-5884	447	25	and	and	CCONJ
ejpam-5884	447	26	n.	n.	PROPN
ejpam-5884	447	27	al	al	PROPN
ejpam-5884	447	28	saafeen	saafeen	PROPN
ejpam-5884	447	29	.	.	PUNCT
ejpam-5884	448	1	a	a	DET
ejpam-5884	448	2	numerical	numerical	ADJ
ejpam-5884	448	3	study	study	NOUN
ejpam-5884	448	4	for	for	ADP
ejpam-5884	448	5	fractional	fractional	ADJ
ejpam-5884	448	6	problems	problem	NOUN
ejpam-5884	448	7	with	with	ADP
ejpam-5884	448	8	nonlinear	nonlinear	ADJ
ejpam-5884	448	9	phenomena	phenomenon	NOUN
ejpam-5884	448	10	in	in	ADP
ejpam-5884	448	11	physics	physics	PROPN
ejpam-5884	448	12	.	.	PUNCT
ejpam-5884	449	1	progress	progress	NOUN
ejpam-5884	449	2	in	in	ADP
ejpam-5884	449	3	fractional	fractional	ADJ
ejpam-5884	449	4	differentiation	differentiation	NOUN
ejpam-5884	449	5	and	and	CCONJ
ejpam-5884	449	6	applications	application	NOUN
ejpam-5884	449	7	,	,	PUNCT
ejpam-5884	449	8	10(3):451–461	10(3):451–461	NUM
ejpam-5884	449	9	,	,	PUNCT
ejpam-5884	449	10	2024	2024	NUM
ejpam-5884	449	11	.	.	PUNCT
ejpam-5884	450	1	[	[	X
ejpam-5884	450	2	49	49	NUM
ejpam-5884	450	3	]	]	PUNCT
ejpam-5884	450	4	l.	l.	PROPN
ejpam-5884	450	5	abdelhaq	abdelhaq	PROPN
ejpam-5884	450	6	,	,	PUNCT
ejpam-5884	450	7	s.	s.	PROPN
ejpam-5884	450	8	m.	m.	PROPN
ejpam-5884	450	9	syam	syam	PROPN
ejpam-5884	450	10	,	,	PUNCT
ejpam-5884	450	11	and	and	CCONJ
ejpam-5884	450	12	m.	m.	PROPN
ejpam-5884	450	13	i.	i.	PROPN
ejpam-5884	450	14	syam	syam	PROPN
ejpam-5884	450	15	.	.	PUNCT
ejpam-5884	451	1	an	an	DET
ejpam-5884	451	2	efficient	efficient	ADJ
ejpam-5884	451	3	numerical	numerical	ADJ
ejpam-5884	451	4	method	method	NOUN
ejpam-5884	451	5	for	for	ADP
ejpam-5884	451	6	twodimensional	twodimensional	ADJ
ejpam-5884	451	7	fractional	fractional	ADJ
ejpam-5884	451	8	integro	integro	ADJ
ejpam-5884	451	9	-	-	PUNCT
ejpam-5884	451	10	differential	differential	NOUN
ejpam-5884	451	11	equations	equation	NOUN
ejpam-5884	451	12	with	with	ADP
ejpam-5884	451	13	modified	modified	ADJ
ejpam-5884	451	14	atangana	atangana	PROPN
ejpam-5884	451	15	–	–	PUNCT
ejpam-5884	451	16	baleanu	baleanu	ADJ
ejpam-5884	451	17	fractional	fractional	ADJ
ejpam-5884	451	18	derivative	derivative	NOUN
ejpam-5884	451	19	using	use	VERB
ejpam-5884	451	20	operational	operational	ADJ
ejpam-5884	451	21	matrix	matrix	NOUN
ejpam-5884	451	22	approach	approach	NOUN
ejpam-5884	451	23	.	.	PUNCT
ejpam-5884	452	1	partial	partial	ADJ
ejpam-5884	452	2	differ	differ	VERB
ejpam-5884	452	3	.	.	PUNCT
ejpam-5884	453	1	equ	equ	PROPN
ejpam-5884	453	2	.	.	PUNCT
ejpam-5884	453	3	appl	appl	PROPN
ejpam-5884	453	4	.	.	PROPN
ejpam-5884	453	5	math	math	PROPN
ejpam-5884	453	6	.	.	PUNCT
ejpam-5884	453	7	,	,	PUNCT
ejpam-5884	453	8	11	11	NUM
ejpam-5884	453	9	,	,	PUNCT
ejpam-5884	453	10	2024	2024	NUM
ejpam-5884	453	11	.	.	PUNCT
ejpam-5884	454	1	[	[	X
ejpam-5884	454	2	50	50	NUM
ejpam-5884	454	3	]	]	PUNCT
ejpam-5884	454	4	m.	m.	NOUN
ejpam-5884	454	5	i.	i.	PROPN
ejpam-5884	454	6	syam	syam	PROPN
ejpam-5884	454	7	and	and	CCONJ
ejpam-5884	454	8	m.	m.	PROPN
ejpam-5884	454	9	al	al	PROPN
ejpam-5884	454	10	-	-	PUNCT
ejpam-5884	454	11	refai	refai	PROPN
ejpam-5884	454	12	.	.	PUNCT
ejpam-5884	455	1	fractional	fractional	ADJ
ejpam-5884	455	2	differential	differential	ADJ
ejpam-5884	455	3	equations	equation	NOUN
ejpam-5884	455	4	with	with	ADP
ejpam-5884	455	5	atangana	atangana	PROPN
ejpam-5884	455	6	–	–	PUNCT
ejpam-5884	455	7	baleanu	baleanu	ADJ
ejpam-5884	455	8	fractional	fractional	ADJ
ejpam-5884	455	9	derivative	derivative	NOUN
ejpam-5884	455	10	:	:	PUNCT
ejpam-5884	455	11	analysis	analysis	NOUN
ejpam-5884	455	12	and	and	CCONJ
ejpam-5884	455	13	applications	application	NOUN
ejpam-5884	455	14	.	.	PUNCT
ejpam-5884	456	1	chaos	chaos	NOUN
ejpam-5884	456	2	solitons	soliton	NOUN
ejpam-5884	456	3	fractals	fractal	NOUN
ejpam-5884	456	4	x	x	NOUN
ejpam-5884	456	5	,	,	PUNCT
ejpam-5884	456	6	2	2	NUM
ejpam-5884	456	7	,	,	PUNCT
ejpam-5884	456	8	2019	2019	NUM
ejpam-5884	456	9	.	.	PUNCT
ejpam-5884	457	1	[	[	X
ejpam-5884	457	2	51	51	NUM
ejpam-5884	457	3	]	]	PUNCT
ejpam-5884	457	4	m.	m.	NOUN
ejpam-5884	457	5	m.	m.	NOUN
ejpam-5884	457	6	syam	syam	PROPN
ejpam-5884	457	7	and	and	CCONJ
ejpam-5884	457	8	m.	m.	PROPN
ejpam-5884	457	9	i.	i.	PROPN
ejpam-5884	457	10	syam	syam	PROPN
ejpam-5884	457	11	.	.	PUNCT
ejpam-5884	458	1	computational	computational	ADJ
ejpam-5884	458	2	study	study	NOUN
ejpam-5884	458	3	of	of	ADP
ejpam-5884	458	4	magnetohydrodynamic	magnetohydrodynamic	ADJ
ejpam-5884	458	5	squeeze	squeeze	NOUN
ejpam-5884	458	6	flow	flow	NOUN
ejpam-5884	458	7	between	between	ADP
ejpam-5884	458	8	infinite	infinite	ADJ
ejpam-5884	458	9	parallel	parallel	ADJ
ejpam-5884	458	10	disks	disk	NOUN
ejpam-5884	458	11	.	.	PUNCT
ejpam-5884	459	1	int	int	NOUN
ejpam-5884	459	2	.	.	PUNCT
ejpam-5884	460	1	j.	j.	PROPN
ejpam-5884	460	2	thermofluids	thermofluids	PROPN
ejpam-5884	460	3	,	,	PUNCT
ejpam-5884	460	4	24	24	NUM
ejpam-5884	460	5	,	,	PUNCT
ejpam-5884	460	6	2024	2024	NUM
ejpam-5884	460	7	.	.	PUNCT
ejpam-5884	461	1	[	[	X
ejpam-5884	461	2	52	52	NUM
ejpam-5884	461	3	]	]	X
ejpam-5884	461	4	a.k	a.k	PROPN
ejpam-5884	461	5	.	.	PROPN
ejpam-5884	461	6	alomari	alomari	PROPN
ejpam-5884	461	7	,	,	PUNCT
ejpam-5884	461	8	muhammed	muhammed	PROPN
ejpam-5884	461	9	i.	i.	PROPN
ejpam-5884	461	10	syam	syam	PROPN
ejpam-5884	461	11	,	,	PUNCT
ejpam-5884	461	12	n.r	n.r	PROPN
ejpam-5884	461	13	.	.	PROPN
ejpam-5884	461	14	anakira	anakira	PROPN
ejpam-5884	461	15	,	,	PUNCT
ejpam-5884	461	16	and	and	CCONJ
ejpam-5884	461	17	a.f	a.f	PROPN
ejpam-5884	461	18	.	.	PROPN
ejpam-5884	461	19	jameel	jameel	PROPN
ejpam-5884	461	20	.	.	PUNCT
ejpam-5884	462	1	homotopy	homotopy	PROPN
ejpam-5884	462	2	sumudu	sumudu	NOUN
ejpam-5884	462	3	transform	transform	NOUN
ejpam-5884	462	4	method	method	NOUN
ejpam-5884	462	5	for	for	ADP
ejpam-5884	462	6	solving	solve	VERB
ejpam-5884	462	7	applications	application	NOUN
ejpam-5884	462	8	in	in	ADP
ejpam-5884	462	9	physics	physics	NOUN
ejpam-5884	462	10	.	.	PUNCT
ejpam-5884	463	1	results	result	NOUN
ejpam-5884	463	2	in	in	ADP
ejpam-5884	463	3	physics	physics	NOUN
ejpam-5884	463	4	,	,	PUNCT
ejpam-5884	463	5	18:103265	18:103265	NUM
ejpam-5884	463	6	,	,	PUNCT
ejpam-5884	463	7	2020	2020	NUM
ejpam-5884	463	8	.	.	PUNCT
ejpam-5884	464	1	[	[	X
ejpam-5884	464	2	53	53	NUM
ejpam-5884	464	3	]	]	PUNCT
ejpam-5884	464	4	m.	m.	NOUN
ejpam-5884	464	5	m.	m.	NOUN
ejpam-5884	464	6	syam	syam	PROPN
ejpam-5884	464	7	and	and	CCONJ
ejpam-5884	464	8	m.	m.	PROPN
ejpam-5884	464	9	i.	i.	PROPN
ejpam-5884	464	10	syam	syam	PROPN
ejpam-5884	464	11	.	.	PUNCT
ejpam-5884	465	1	investigation	investigation	NOUN
ejpam-5884	465	2	of	of	ADP
ejpam-5884	465	3	slip	slip	NOUN
ejpam-5884	465	4	flow	flow	NOUN
ejpam-5884	465	5	dynamics	dynamic	NOUN
ejpam-5884	465	6	involving	involve	VERB
ejpam-5884	465	7	al2o3	al2o3	PROPN
ejpam-5884	465	8	and	and	CCONJ
ejpam-5884	465	9	fe3o4	fe3o4	PROPN
ejpam-5884	465	10	nanoparticles	nanoparticle	NOUN
ejpam-5884	465	11	within	within	ADP
ejpam-5884	465	12	a	a	DET
ejpam-5884	465	13	horizontal	horizontal	ADJ
ejpam-5884	465	14	channel	channel	NOUN
ejpam-5884	465	15	embedded	embed	VERB
ejpam-5884	465	16	with	with	ADP
ejpam-5884	465	17	porous	porous	ADJ
ejpam-5884	465	18	media	medium	NOUN
ejpam-5884	465	19	.	.	PUNCT
ejpam-5884	466	1	int	int	NOUN
ejpam-5884	466	2	.	.	PUNCT
ejpam-5884	467	1	j.	j.	PROPN
ejpam-5884	467	2	thermofluids	thermofluids	PROPN
ejpam-5884	467	3	,	,	PUNCT
ejpam-5884	467	4	24	24	NUM
ejpam-5884	467	5	,	,	PUNCT
ejpam-5884	467	6	2024	2024	NUM
ejpam-5884	467	7	.	.	PUNCT
ejpam-5884	468	1	[	[	X
ejpam-5884	468	2	54	54	NUM
ejpam-5884	468	3	]	]	X
ejpam-5884	468	4	precious	precious	ADJ
ejpam-5884	468	5	sibanda	sibanda	NOUN
ejpam-5884	468	6	and	and	CCONJ
ejpam-5884	468	7	a.	a.	NOUN
ejpam-5884	468	8	khidir	khidir	PROPN
ejpam-5884	468	9	.	.	PUNCT
ejpam-5884	469	1	a	a	DET
ejpam-5884	469	2	new	new	ADJ
ejpam-5884	469	3	modification	modification	NOUN
ejpam-5884	469	4	of	of	ADP
ejpam-5884	469	5	the	the	DET
ejpam-5884	469	6	hpm	hpm	NOUN
ejpam-5884	469	7	for	for	ADP
ejpam-5884	469	8	the	the	DET
ejpam-5884	469	9	duffing	duffing	NOUN
ejpam-5884	469	10	equation	equation	NOUN
ejpam-5884	469	11	with	with	ADP
ejpam-5884	469	12	cubic	cubic	ADJ
ejpam-5884	469	13	nonlinearity	nonlinearity	NOUN
ejpam-5884	469	14	.	.	PUNCT
ejpam-5884	470	1	in	in	ADP
ejpam-5884	470	2	recent	recent	ADJ
ejpam-5884	470	3	researches	research	NOUN
ejpam-5884	470	4	in	in	ADP
ejpam-5884	470	5	applied	applied	ADJ
ejpam-5884	470	6	and	and	CCONJ
ejpam-5884	470	7	computational	computational	ADJ
ejpam-5884	470	8	mathematics	mathematic	NOUN
ejpam-5884	470	9	,	,	PUNCT
ejpam-5884	470	10	pages	page	NOUN
ejpam-5884	470	11	139–145	139–145	NUM
ejpam-5884	470	12	,	,	PUNCT
ejpam-5884	470	13	2011	2011	NUM
ejpam-5884	470	14	.	.	PUNCT
ejpam-5884	471	1	[	[	X
ejpam-5884	471	2	55	55	NUM
ejpam-5884	471	3	]	]	PUNCT
ejpam-5884	471	4	a.	a.	NOUN
ejpam-5884	471	5	verma	verma	PROPN
ejpam-5884	471	6	,	,	PUNCT
ejpam-5884	471	7	w.	w.	PROPN
ejpam-5884	471	8	sumelka	sumelka	PROPN
ejpam-5884	471	9	,	,	PUNCT
ejpam-5884	471	10	and	and	CCONJ
ejpam-5884	471	11	p.	p.	PROPN
ejpam-5884	471	12	k.	k.	PROPN
ejpam-5884	471	13	yadav	yadav	PROPN
ejpam-5884	471	14	.	.	PUNCT
ejpam-5884	472	1	the	the	DET
ejpam-5884	472	2	numerical	numerical	ADJ
ejpam-5884	472	3	solution	solution	NOUN
ejpam-5884	472	4	of	of	ADP
ejpam-5884	472	5	nonlinear	nonlinear	ADJ
ejpam-5884	472	6	fractional	fractional	ADJ
ejpam-5884	472	7	lienard	lienard	NOUN
ejpam-5884	472	8	and	and	CCONJ
ejpam-5884	472	9	duffing	duffe	VERB
ejpam-5884	472	10	equations	equation	NOUN
ejpam-5884	472	11	using	use	VERB
ejpam-5884	472	12	orthogonal	orthogonal	ADJ
ejpam-5884	472	13	perceptron	perceptron	PROPN
ejpam-5884	472	14	.	.	PUNCT
ejpam-5884	473	1	symmetry	symmetry	PROPN
ejpam-5884	473	2	,	,	PUNCT
ejpam-5884	473	3	15:1753	15:1753	NUM
ejpam-5884	473	4	,	,	PUNCT
ejpam-5884	473	5	2023	2023	NUM
ejpam-5884	473	6	.	.	PUNCT
ejpam-5884	474	1	[	[	X
ejpam-5884	474	2	56	56	NUM
ejpam-5884	474	3	]	]	X
ejpam-5884	474	4	h.	h.	PROPN
ejpam-5884	474	5	singh	singh	PROPN
ejpam-5884	474	6	and	and	CCONJ
ejpam-5884	474	7	h.	h.	PROPN
ejpam-5884	474	8	m.	m.	PROPN
ejpam-5884	474	9	srivastava	srivastava	PROPN
ejpam-5884	474	10	.	.	PUNCT
ejpam-5884	475	1	numerical	numerical	PROPN
ejpam-5884	475	2	investigation	investigation	NOUN
ejpam-5884	475	3	of	of	ADP
ejpam-5884	475	4	the	the	DET
ejpam-5884	475	5	fractional	fractional	ADJ
ejpam-5884	475	6	-	-	PUNCT
ejpam-5884	475	7	order	order	NOUN
ejpam-5884	475	8	liénard	liénard	NOUN
ejpam-5884	475	9	and	and	CCONJ
ejpam-5884	475	10	duffing	duffe	VERB
ejpam-5884	475	11	equations	equation	NOUN
ejpam-5884	475	12	arising	arise	VERB
ejpam-5884	475	13	in	in	ADP
ejpam-5884	475	14	oscillating	oscillate	VERB
ejpam-5884	475	15	circuit	circuit	NOUN
ejpam-5884	475	16	theory	theory	NOUN
ejpam-5884	475	17	.	.	PUNCT
ejpam-5884	476	1	frontiers	frontier	NOUN
ejpam-5884	476	2	in	in	ADP
ejpam-5884	476	3	physics	physics	PROPN
ejpam-5884	476	4	,	,	PUNCT
ejpam-5884	476	5	8:120	8:120	NUM
ejpam-5884	476	6	,	,	PUNCT
ejpam-5884	476	7	2020	2020	NUM
ejpam-5884	476	8	.	.	PUNCT