id	sid	tid	token	lemma	pos
ejpam-7005	1	1	european	european	PROPN
ejpam-7005	1	2	journal	journal	PROPN
ejpam-7005	1	3	of	of	ADP
ejpam-7005	1	4	pure	pure	ADJ
ejpam-7005	1	5	and	and	CCONJ
ejpam-7005	1	6	applied	applied	ADJ
ejpam-7005	1	7	mathematics	mathematic	NOUN
ejpam-7005	1	8	2025	2025	NUM
ejpam-7005	1	9	,	,	PUNCT
ejpam-7005	1	10	vol	vol	NOUN
ejpam-7005	1	11	.	.	PROPN
ejpam-7005	1	12	18	18	NUM
ejpam-7005	1	13	,	,	PUNCT
ejpam-7005	1	14	issue	issue	NOUN
ejpam-7005	1	15	4	4	NUM
ejpam-7005	1	16	,	,	PUNCT
ejpam-7005	1	17	article	article	NOUN
ejpam-7005	1	18	number	number	NOUN
ejpam-7005	1	19	7005	7005	NUM
ejpam-7005	1	20	issn	issn	PROPN
ejpam-7005	1	21	1307	1307	NUM
ejpam-7005	1	22	-	-	SYM
ejpam-7005	1	23	5543	5543	NUM
ejpam-7005	1	24	–	–	PUNCT
ejpam-7005	1	25	ejpam.com	ejpam.com	X
ejpam-7005	1	26	published	publish	VERB
ejpam-7005	1	27	by	by	ADP
ejpam-7005	1	28	new	new	PROPN
ejpam-7005	1	29	york	york	PROPN
ejpam-7005	1	30	business	business	PROPN
ejpam-7005	1	31	global	global	ADJ
ejpam-7005	1	32	criteria	criterion	NOUN
ejpam-7005	1	33	for	for	ADP
ejpam-7005	1	34	finite	finite	ADJ
ejpam-7005	1	35	-	-	PUNCT
ejpam-7005	1	36	time	time	NOUN
ejpam-7005	1	37	convergence	convergence	NOUN
ejpam-7005	1	38	in	in	ADP
ejpam-7005	1	39	discrete	discrete	ADJ
ejpam-7005	1	40	variable	variable	ADJ
ejpam-7005	1	41	-	-	PUNCT
ejpam-7005	1	42	order	order	NOUN
ejpam-7005	1	43	fractional	fractional	ADJ
ejpam-7005	1	44	fitzhugh	fitzhugh	PROPN
ejpam-7005	1	45	–	–	PUNCT
ejpam-7005	1	46	nagumo	nagumo	ADJ
ejpam-7005	1	47	reaction	reaction	NOUN
ejpam-7005	1	48	–	–	PUNCT
ejpam-7005	1	49	diffusion	diffusion	NOUN
ejpam-7005	1	50	systems	system	NOUN
ejpam-7005	1	51	nidal	nidal	PROPN
ejpam-7005	1	52	anakira1,2,∗	anakira1,2,∗	PROPN
ejpam-7005	1	53	,	,	PUNCT
ejpam-7005	1	54	iqbal	iqbal	PROPN
ejpam-7005	1	55	h.	h.	PROPN
ejpam-7005	1	56	jebril3	jebril3	PROPN
ejpam-7005	1	57	,	,	PUNCT
ejpam-7005	1	58	iqbal	iqbal	PROPN
ejpam-7005	1	59	m.	m.	PROPN
ejpam-7005	1	60	batiha3,4	batiha3,4	PROPN
ejpam-7005	1	61	,	,	PUNCT
ejpam-7005	1	62	mohammad	mohammad	PROPN
ejpam-7005	1	63	s.	s.	PROPN
ejpam-7005	1	64	hijazi5,∗	hijazi5,∗	PROPN
ejpam-7005	1	65	,	,	PUNCT
ejpam-7005	1	66	tala	tala	PROPN
ejpam-7005	1	67	sasa6	sasa6	NOUN
ejpam-7005	1	68	1	1	NUM
ejpam-7005	1	69	mathematics	mathematics	PROPN
ejpam-7005	1	70	education	education	NOUN
ejpam-7005	1	71	program	program	NOUN
ejpam-7005	1	72	,	,	PUNCT
ejpam-7005	1	73	faculty	faculty	NOUN
ejpam-7005	1	74	of	of	ADP
ejpam-7005	1	75	education	education	NOUN
ejpam-7005	1	76	and	and	CCONJ
ejpam-7005	1	77	arts	art	NOUN
ejpam-7005	1	78	,	,	PUNCT
ejpam-7005	1	79	sohar	sohar	PROPN
ejpam-7005	1	80	university	university	PROPN
ejpam-7005	1	81	,	,	PUNCT
ejpam-7005	1	82	sohar	sohar	PROPN
ejpam-7005	1	83	311	311	NUM
ejpam-7005	1	84	,	,	PUNCT
ejpam-7005	1	85	oman	oman	NOUN
ejpam-7005	1	86	2	2	NUM
ejpam-7005	1	87	jadara	jadara	PROPN
ejpam-7005	1	88	university	university	NOUN
ejpam-7005	1	89	research	research	NOUN
ejpam-7005	1	90	center	center	NOUN
ejpam-7005	1	91	,	,	PUNCT
ejpam-7005	1	92	jadara	jadara	PROPN
ejpam-7005	1	93	university	university	PROPN
ejpam-7005	1	94	,	,	PUNCT
ejpam-7005	1	95	jordan	jordan	PROPN
ejpam-7005	1	96	3	3	NUM
ejpam-7005	1	97	department	department	PROPN
ejpam-7005	1	98	of	of	ADP
ejpam-7005	1	99	mathematics	mathematic	NOUN
ejpam-7005	1	100	,	,	PUNCT
ejpam-7005	1	101	al	al	PROPN
ejpam-7005	1	102	zaytoonah	zaytoonah	PROPN
ejpam-7005	1	103	university	university	PROPN
ejpam-7005	1	104	of	of	ADP
ejpam-7005	1	105	jordan	jordan	PROPN
ejpam-7005	1	106	,	,	PUNCT
ejpam-7005	1	107	amman	amman	PROPN
ejpam-7005	1	108	11733	11733	NUM
ejpam-7005	1	109	,	,	PUNCT
ejpam-7005	1	110	jordan	jordan	PROPN
ejpam-7005	1	111	4	4	NUM
ejpam-7005	1	112	nonlinear	nonlinear	ADJ
ejpam-7005	1	113	dynamics	dynamic	NOUN
ejpam-7005	1	114	research	research	NOUN
ejpam-7005	1	115	center	center	NOUN
ejpam-7005	1	116	(	(	PUNCT
ejpam-7005	1	117	ndrc	ndrc	PROPN
ejpam-7005	1	118	)	)	PUNCT
ejpam-7005	1	119	,	,	PUNCT
ejpam-7005	1	120	ajman	ajman	PROPN
ejpam-7005	1	121	university	university	PROPN
ejpam-7005	1	122	,	,	PUNCT
ejpam-7005	1	123	ajman	ajman	PROPN
ejpam-7005	1	124	,	,	PUNCT
ejpam-7005	1	125	uae	uae	PROPN
ejpam-7005	1	126	5	5	NUM
ejpam-7005	1	127	department	department	NOUN
ejpam-7005	1	128	of	of	ADP
ejpam-7005	1	129	mathematics	mathematic	NOUN
ejpam-7005	1	130	,	,	PUNCT
ejpam-7005	1	131	college	college	NOUN
ejpam-7005	1	132	of	of	ADP
ejpam-7005	1	133	sciences	sciences	PROPN
ejpam-7005	1	134	,	,	PUNCT
ejpam-7005	1	135	jouf	jouf	PROPN
ejpam-7005	1	136	university	university	PROPN
ejpam-7005	1	137	,	,	PUNCT
ejpam-7005	1	138	sakaka	sakaka	PROPN
ejpam-7005	1	139	,	,	PUNCT
ejpam-7005	1	140	saudi	saudi	PROPN
ejpam-7005	1	141	arabia	arabia	PROPN
ejpam-7005	1	142	6	6	NUM
ejpam-7005	1	143	department	department	NOUN
ejpam-7005	1	144	of	of	ADP
ejpam-7005	1	145	mathematics	mathematic	NOUN
ejpam-7005	1	146	,	,	PUNCT
ejpam-7005	1	147	faculty	faculty	NOUN
ejpam-7005	1	148	of	of	ADP
ejpam-7005	1	149	science	science	NOUN
ejpam-7005	1	150	,	,	PUNCT
ejpam-7005	1	151	private	private	ADJ
ejpam-7005	1	152	applied	apply	VERB
ejpam-7005	1	153	science	science	NOUN
ejpam-7005	1	154	university	university	NOUN
ejpam-7005	1	155	,	,	PUNCT
ejpam-7005	1	156	amman	amman	PROPN
ejpam-7005	1	157	,	,	PUNCT
ejpam-7005	1	158	jordan	jordan	PROPN
ejpam-7005	1	159	abstract	abstract	PROPN
ejpam-7005	1	160	.	.	PUNCT
ejpam-7005	2	1	this	this	DET
ejpam-7005	2	2	study	study	NOUN
ejpam-7005	2	3	addresses	address	VERB
ejpam-7005	2	4	the	the	DET
ejpam-7005	2	5	problem	problem	NOUN
ejpam-7005	2	6	of	of	ADP
ejpam-7005	2	7	finite	finite	ADJ
ejpam-7005	2	8	-	-	PUNCT
ejpam-7005	2	9	time	time	NOUN
ejpam-7005	2	10	stability	stability	NOUN
ejpam-7005	2	11	(	(	PUNCT
ejpam-7005	2	12	fts	fts	PROPN
ejpam-7005	2	13	)	)	PUNCT
ejpam-7005	2	14	for	for	ADP
ejpam-7005	2	15	a	a	DET
ejpam-7005	2	16	discrete	discrete	ADJ
ejpam-7005	2	17	-	-	PUNCT
ejpam-7005	2	18	time	time	NOUN
ejpam-7005	2	19	fitzhugh	fitzhugh	PROPN
ejpam-7005	2	20	–	–	PUNCT
ejpam-7005	2	21	nagumo	nagumo	ADJ
ejpam-7005	2	22	reaction	reaction	NOUN
ejpam-7005	2	23	–	–	PUNCT
ejpam-7005	2	24	diffusion	diffusion	NOUN
ejpam-7005	2	25	system	system	NOUN
ejpam-7005	2	26	(	(	PUNCT
ejpam-7005	2	27	fhn	fhn	ADJ
ejpam-7005	2	28	–	–	PUNCT
ejpam-7005	2	29	rds	rds	NOUN
ejpam-7005	2	30	)	)	PUNCT
ejpam-7005	2	31	governed	govern	VERB
ejpam-7005	2	32	by	by	ADP
ejpam-7005	2	33	a	a	DET
ejpam-7005	2	34	variable	variable	ADJ
ejpam-7005	2	35	-	-	PUNCT
ejpam-7005	2	36	order	order	NOUN
ejpam-7005	2	37	(	(	PUNCT
ejpam-7005	2	38	vo	vo	NOUN
ejpam-7005	2	39	)	)	PUNCT
ejpam-7005	2	40	caputo	caputo	PROPN
ejpam-7005	2	41	fractional	fractional	ADJ
ejpam-7005	2	42	difference	difference	NOUN
ejpam-7005	2	43	operator	operator	NOUN
ejpam-7005	2	44	.	.	PUNCT
ejpam-7005	3	1	the	the	DET
ejpam-7005	3	2	discrete	discrete	ADJ
ejpam-7005	3	3	fractional	fractional	ADJ
ejpam-7005	3	4	formulation	formulation	NOUN
ejpam-7005	3	5	is	be	AUX
ejpam-7005	3	6	obtained	obtain	VERB
ejpam-7005	3	7	by	by	ADP
ejpam-7005	3	8	combining	combine	VERB
ejpam-7005	3	9	a	a	DET
ejpam-7005	3	10	central	central	ADJ
ejpam-7005	3	11	difference	difference	NOUN
ejpam-7005	3	12	approximation	approximation	NOUN
ejpam-7005	3	13	for	for	ADP
ejpam-7005	3	14	the	the	DET
ejpam-7005	3	15	spatial	spatial	ADJ
ejpam-7005	3	16	derivative	derivative	NOUN
ejpam-7005	3	17	with	with	ADP
ejpam-7005	3	18	a	a	DET
ejpam-7005	3	19	vo	vo	X
ejpam-7005	3	20	fractional	fractional	ADJ
ejpam-7005	3	21	operator	operator	NOUN
ejpam-7005	3	22	for	for	ADP
ejpam-7005	3	23	the	the	DET
ejpam-7005	3	24	temporal	temporal	ADJ
ejpam-7005	3	25	derivative	derivative	NOUN
ejpam-7005	3	26	.	.	PUNCT
ejpam-7005	4	1	the	the	DET
ejpam-7005	4	2	analysis	analysis	NOUN
ejpam-7005	4	3	begins	begin	VERB
ejpam-7005	4	4	with	with	ADP
ejpam-7005	4	5	proving	prove	VERB
ejpam-7005	4	6	the	the	DET
ejpam-7005	4	7	well	well	NOUN
ejpam-7005	4	8	-	-	PUNCT
ejpam-7005	4	9	posedness	posedness	NOUN
ejpam-7005	4	10	of	of	ADP
ejpam-7005	4	11	solutions	solution	NOUN
ejpam-7005	4	12	for	for	ADP
ejpam-7005	4	13	the	the	DET
ejpam-7005	4	14	proposed	propose	VERB
ejpam-7005	4	15	discrete	discrete	ADJ
ejpam-7005	4	16	model	model	NOUN
ejpam-7005	4	17	.	.	PUNCT
ejpam-7005	5	1	the	the	DET
ejpam-7005	5	2	main	main	ADJ
ejpam-7005	5	3	contribution	contribution	NOUN
ejpam-7005	5	4	lies	lie	VERB
ejpam-7005	5	5	in	in	ADP
ejpam-7005	5	6	establishing	establish	VERB
ejpam-7005	5	7	an	an	DET
ejpam-7005	5	8	fts	fts	PROPN
ejpam-7005	5	9	criterion	criterion	NOUN
ejpam-7005	5	10	.	.	PUNCT
ejpam-7005	6	1	by	by	ADP
ejpam-7005	6	2	employing	employ	VERB
ejpam-7005	6	3	a	a	DET
ejpam-7005	6	4	discrete	discrete	ADJ
ejpam-7005	6	5	fractional	fractional	ADJ
ejpam-7005	6	6	gronwall	gronwall	ADJ
ejpam-7005	6	7	-	-	PUNCT
ejpam-7005	6	8	type	type	NOUN
ejpam-7005	6	9	inequality	inequality	NOUN
ejpam-7005	6	10	,	,	PUNCT
ejpam-7005	6	11	we	we	PRON
ejpam-7005	6	12	derive	derive	VERB
ejpam-7005	6	13	a	a	DET
ejpam-7005	6	14	sufficient	sufficient	ADJ
ejpam-7005	6	15	stability	stability	NOUN
ejpam-7005	6	16	condition	condition	NOUN
ejpam-7005	6	17	expressed	express	VERB
ejpam-7005	6	18	through	through	ADP
ejpam-7005	6	19	the	the	DET
ejpam-7005	6	20	discrete	discrete	ADJ
ejpam-7005	6	21	mittag	mittag	ADJ
ejpam-7005	6	22	–	–	PUNCT
ejpam-7005	6	23	leffler	leffler	NOUN
ejpam-7005	6	24	function	function	NOUN
ejpam-7005	6	25	(	(	PUNCT
ejpam-7005	6	26	mlf	mlf	NOUN
ejpam-7005	6	27	)	)	PUNCT
ejpam-7005	6	28	.	.	PUNCT
ejpam-7005	7	1	finally	finally	ADV
ejpam-7005	7	2	,	,	PUNCT
ejpam-7005	7	3	a	a	DET
ejpam-7005	7	4	numerical	numerical	ADJ
ejpam-7005	7	5	simulation	simulation	NOUN
ejpam-7005	7	6	is	be	AUX
ejpam-7005	7	7	provided	provide	VERB
ejpam-7005	7	8	to	to	PART
ejpam-7005	7	9	illustrate	illustrate	VERB
ejpam-7005	7	10	the	the	DET
ejpam-7005	7	11	applicability	applicability	NOUN
ejpam-7005	7	12	of	of	ADP
ejpam-7005	7	13	the	the	DET
ejpam-7005	7	14	theoretical	theoretical	ADJ
ejpam-7005	7	15	findings	finding	NOUN
ejpam-7005	7	16	,	,	PUNCT
ejpam-7005	7	17	confirming	confirm	VERB
ejpam-7005	7	18	that	that	SCONJ
ejpam-7005	7	19	the	the	DET
ejpam-7005	7	20	system	system	NOUN
ejpam-7005	7	21	state	state	NOUN
ejpam-7005	7	22	remains	remain	VERB
ejpam-7005	7	23	bounded	bound	VERB
ejpam-7005	7	24	within	within	ADP
ejpam-7005	7	25	a	a	DET
ejpam-7005	7	26	prescribed	prescribed	ADJ
ejpam-7005	7	27	limit	limit	NOUN
ejpam-7005	7	28	over	over	ADP
ejpam-7005	7	29	a	a	DET
ejpam-7005	7	30	finite	finite	ADJ
ejpam-7005	7	31	time	time	NOUN
ejpam-7005	7	32	horizon	horizon	NOUN
ejpam-7005	7	33	.	.	PUNCT
ejpam-7005	8	1	2020	2020	NUM
ejpam-7005	8	2	mathematics	mathematic	NOUN
ejpam-7005	8	3	subject	subject	NOUN
ejpam-7005	8	4	classifications	classification	NOUN
ejpam-7005	8	5	:	:	PUNCT
ejpam-7005	8	6	39a12	39a12	NUM
ejpam-7005	8	7	,	,	PUNCT
ejpam-7005	8	8	34a08	34a08	NUM
ejpam-7005	8	9	,	,	PUNCT
ejpam-7005	8	10	65m06	65m06	NUM
ejpam-7005	8	11	,	,	PUNCT
ejpam-7005	8	12	92c15	92c15	NUM
ejpam-7005	8	13	key	key	ADJ
ejpam-7005	8	14	words	word	NOUN
ejpam-7005	8	15	and	and	CCONJ
ejpam-7005	8	16	phrases	phrase	NOUN
ejpam-7005	8	17	:	:	PUNCT
ejpam-7005	8	18	fitzhugh	fitzhugh	PROPN
ejpam-7005	8	19	–	–	PUNCT
ejpam-7005	8	20	nagumo	nagumo	ADJ
ejpam-7005	8	21	system	system	NOUN
ejpam-7005	8	22	,	,	PUNCT
ejpam-7005	8	23	finite	finite	ADJ
ejpam-7005	8	24	-	-	PUNCT
ejpam-7005	8	25	time	time	NOUN
ejpam-7005	8	26	stability	stability	NOUN
ejpam-7005	8	27	,	,	PUNCT
ejpam-7005	8	28	reaction	reaction	NOUN
ejpam-7005	8	29	-	-	PUNCT
ejpam-7005	8	30	diffusion	diffusion	NOUN
ejpam-7005	8	31	systems	system	NOUN
ejpam-7005	8	32	,	,	PUNCT
ejpam-7005	8	33	gronwall	gronwall	PROPN
ejpam-7005	8	34	’s	’s	PART
ejpam-7005	8	35	inequality	inequality	NOUN
ejpam-7005	8	36	,	,	PUNCT
ejpam-7005	8	37	mittag	mittag	ADJ
ejpam-7005	8	38	-	-	PUNCT
ejpam-7005	8	39	leffler	leffler	NOUN
ejpam-7005	8	40	function	function	NOUN
ejpam-7005	8	41	∗corresponding	∗corresponde	VERB
ejpam-7005	8	42	author	author	NOUN
ejpam-7005	8	43	.	.	PUNCT
ejpam-7005	9	1	∗corresponding	∗corresponde	VERB
ejpam-7005	9	2	author	author	NOUN
ejpam-7005	9	3	.	.	PUNCT
ejpam-7005	10	1	doi	doi	NOUN
ejpam-7005	10	2	:	:	PUNCT
ejpam-7005	10	3	https://doi.org/10.29020/nybg.ejpam.v18i4.7005	https://doi.org/10.29020/nybg.ejpam.v18i4.7005	PROPN
ejpam-7005	10	4	email	email	NOUN
ejpam-7005	10	5	addresses	address	NOUN
ejpam-7005	10	6	:	:	PUNCT
ejpam-7005	10	7	nanakira@su.edu.om	nanakira@su.edu.om	PROPN
ejpam-7005	10	8	(	(	PUNCT
ejpam-7005	10	9	n.	n.	PROPN
ejpam-7005	10	10	anakira	anakira	PROPN
ejpam-7005	10	11	)	)	PUNCT
ejpam-7005	10	12	,	,	PUNCT
ejpam-7005	10	13	i.jebri@zuj.edu.jo	i.jebri@zuj.edu.jo	PROPN
ejpam-7005	10	14	(	(	PUNCT
ejpam-7005	10	15	i.	i.	PROPN
ejpam-7005	10	16	h.	h.	PROPN
ejpam-7005	10	17	jebril	jebril	PROPN
ejpam-7005	10	18	)	)	PUNCT
ejpam-7005	10	19	,	,	PUNCT
ejpam-7005	10	20	i.batiha@zuj.edu.jo	i.batiha@zuj.edu.jo	NOUN
ejpam-7005	10	21	(	(	PUNCT
ejpam-7005	10	22	i.	i.	PROPN
ejpam-7005	10	23	m.	m.	PROPN
ejpam-7005	10	24	batiha	batiha	PROPN
ejpam-7005	10	25	)	)	PUNCT
ejpam-7005	10	26	,	,	PUNCT
ejpam-7005	10	27	mshijazi@ju.edu.sa	mshijazi@ju.edu.sa	PROPN
ejpam-7005	10	28	(	(	PUNCT
ejpam-7005	10	29	m.	m.	NOUN
ejpam-7005	10	30	s.	s.	PROPN
ejpam-7005	10	31	hijazi	hijazi	PROPN
ejpam-7005	10	32	)	)	PUNCT
ejpam-7005	10	33	,	,	PUNCT
ejpam-7005	10	34	t_sasa@asu.edu.jo	t_sasa@asu.edu.jo	PRON
ejpam-7005	10	35	(	(	PUNCT
ejpam-7005	10	36	t.	t.	NOUN
ejpam-7005	10	37	sasa	sasa	PROPN
ejpam-7005	10	38	)	)	PUNCT
ejpam-7005	10	39	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-7005	11	1	1	1	NUM
ejpam-7005	11	2	copyright	copyright	NOUN
ejpam-7005	11	3	:	:	PUNCT
ejpam-7005	11	4	©	©	PROPN
ejpam-7005	11	5	2025	2025	NUM
ejpam-7005	11	6	the	the	DET
ejpam-7005	11	7	author(s	author(s	NOUN
ejpam-7005	11	8	)	)	PUNCT
ejpam-7005	11	9	.	.	PUNCT
ejpam-7005	12	1	(	(	PUNCT
ejpam-7005	12	2	cc	cc	NOUN
ejpam-7005	12	3	by	by	ADP
ejpam-7005	12	4	-	-	PUNCT
ejpam-7005	12	5	nc	nc	PROPN
ejpam-7005	12	6	4.0	4.0	NUM
ejpam-7005	12	7	)	)	PUNCT
ejpam-7005	12	8	n.	n.	PROPN
ejpam-7005	12	9	anakira	anakira	PROPN
ejpam-7005	12	10	et	et	PROPN
ejpam-7005	12	11	al	al	PROPN
ejpam-7005	12	12	.	.	PUNCT
ejpam-7005	12	13	/	/	SYM
ejpam-7005	12	14	eur	eur	PROPN
ejpam-7005	12	15	.	.	PUNCT
ejpam-7005	13	1	j.	j.	PROPN
ejpam-7005	13	2	pure	pure	PROPN
ejpam-7005	13	3	appl	appl	PROPN
ejpam-7005	13	4	.	.	PROPN
ejpam-7005	13	5	math	math	PROPN
ejpam-7005	13	6	,	,	PUNCT
ejpam-7005	13	7	18	18	NUM
ejpam-7005	13	8	(	(	PUNCT
ejpam-7005	13	9	4	4	NUM
ejpam-7005	13	10	)	)	PUNCT
ejpam-7005	13	11	(	(	PUNCT
ejpam-7005	13	12	2025	2025	NUM
ejpam-7005	13	13	)	)	PUNCT
ejpam-7005	13	14	,	,	PUNCT
ejpam-7005	13	15	7005	7005	NUM
ejpam-7005	13	16	2	2	NUM
ejpam-7005	13	17	of	of	ADP
ejpam-7005	13	18	17	17	NUM
ejpam-7005	13	19	1	1	NUM
ejpam-7005	13	20	.	.	PUNCT
ejpam-7005	14	1	introduction	introduction	NOUN
ejpam-7005	14	2	mathematical	mathematical	ADJ
ejpam-7005	14	3	modeling	modeling	NOUN
ejpam-7005	14	4	plays	play	VERB
ejpam-7005	14	5	a	a	DET
ejpam-7005	14	6	fundamental	fundamental	ADJ
ejpam-7005	14	7	role	role	NOUN
ejpam-7005	14	8	in	in	ADP
ejpam-7005	14	9	exploring	explore	VERB
ejpam-7005	14	10	and	and	CCONJ
ejpam-7005	14	11	interpreting	interpret	VERB
ejpam-7005	14	12	the	the	DET
ejpam-7005	14	13	complex	complex	ADJ
ejpam-7005	14	14	behavior	behavior	NOUN
ejpam-7005	14	15	of	of	ADP
ejpam-7005	14	16	biological	biological	ADJ
ejpam-7005	14	17	systems	system	NOUN
ejpam-7005	14	18	.	.	PUNCT
ejpam-7005	15	1	among	among	ADP
ejpam-7005	15	2	the	the	DET
ejpam-7005	15	3	most	most	ADV
ejpam-7005	15	4	prominent	prominent	ADJ
ejpam-7005	15	5	frameworks	framework	NOUN
ejpam-7005	15	6	in	in	ADP
ejpam-7005	15	7	this	this	DET
ejpam-7005	15	8	domain	domain	NOUN
ejpam-7005	15	9	are	be	AUX
ejpam-7005	15	10	reaction	reaction	NOUN
ejpam-7005	15	11	–	–	PUNCT
ejpam-7005	15	12	diffusion	diffusion	NOUN
ejpam-7005	15	13	models	model	NOUN
ejpam-7005	15	14	,	,	PUNCT
ejpam-7005	15	15	which	which	PRON
ejpam-7005	15	16	capture	capture	VERB
ejpam-7005	15	17	how	how	SCONJ
ejpam-7005	15	18	the	the	DET
ejpam-7005	15	19	spatial	spatial	ADJ
ejpam-7005	15	20	distribution	distribution	NOUN
ejpam-7005	15	21	of	of	ADP
ejpam-7005	15	22	substances	substance	NOUN
ejpam-7005	15	23	evolves	evolve	VERB
ejpam-7005	15	24	under	under	ADP
ejpam-7005	15	25	the	the	DET
ejpam-7005	15	26	combined	combine	VERB
ejpam-7005	15	27	influence	influence	NOUN
ejpam-7005	15	28	of	of	ADP
ejpam-7005	15	29	local	local	ADJ
ejpam-7005	15	30	reactions	reaction	NOUN
ejpam-7005	15	31	and	and	CCONJ
ejpam-7005	15	32	diffusion	diffusion	NOUN
ejpam-7005	15	33	.	.	PUNCT
ejpam-7005	16	1	turing	ture	VERB
ejpam-7005	16	2	’s	’s	PART
ejpam-7005	16	3	seminal	seminal	ADJ
ejpam-7005	16	4	work	work	NOUN
ejpam-7005	16	5	demonstrated	demonstrate	VERB
ejpam-7005	16	6	that	that	SCONJ
ejpam-7005	16	7	such	such	ADJ
ejpam-7005	16	8	systems	system	NOUN
ejpam-7005	16	9	can	can	AUX
ejpam-7005	16	10	spontaneously	spontaneously	ADV
ejpam-7005	16	11	produce	produce	VERB
ejpam-7005	16	12	patterns	pattern	NOUN
ejpam-7005	16	13	[	[	X
ejpam-7005	16	14	1	1	NUM
ejpam-7005	16	15	]	]	PUNCT
ejpam-7005	16	16	,	,	PUNCT
ejpam-7005	16	17	laying	lay	VERB
ejpam-7005	16	18	the	the	DET
ejpam-7005	16	19	foundation	foundation	NOUN
ejpam-7005	16	20	for	for	ADP
ejpam-7005	16	21	morphogenesis	morphogenesis	NOUN
ejpam-7005	16	22	and	and	CCONJ
ejpam-7005	16	23	numerous	numerous	ADJ
ejpam-7005	16	24	spatio	spatio	NOUN
ejpam-7005	16	25	–	–	PUNCT
ejpam-7005	16	26	temporal	temporal	ADJ
ejpam-7005	16	27	phenomena	phenomenon	NOUN
ejpam-7005	16	28	observed	observe	VERB
ejpam-7005	16	29	in	in	ADP
ejpam-7005	16	30	nature	nature	NOUN
ejpam-7005	16	31	[	[	X
ejpam-7005	16	32	2	2	NUM
ejpam-7005	16	33	,	,	PUNCT
ejpam-7005	16	34	3	3	NUM
ejpam-7005	16	35	]	]	PUNCT
ejpam-7005	16	36	.	.	PUNCT
ejpam-7005	17	1	a	a	DET
ejpam-7005	17	2	notable	notable	ADJ
ejpam-7005	17	3	representative	representative	NOUN
ejpam-7005	17	4	of	of	ADP
ejpam-7005	17	5	this	this	DET
ejpam-7005	17	6	class	class	NOUN
ejpam-7005	17	7	is	be	AUX
ejpam-7005	17	8	the	the	DET
ejpam-7005	17	9	fhn	fhn	ADJ
ejpam-7005	17	10	system	system	NOUN
ejpam-7005	17	11	,	,	PUNCT
ejpam-7005	17	12	proposed	propose	VERB
ejpam-7005	17	13	by	by	ADP
ejpam-7005	17	14	fitzhugh	fitzhugh	PROPN
ejpam-7005	17	15	[	[	X
ejpam-7005	17	16	4	4	NUM
ejpam-7005	17	17	]	]	PUNCT
ejpam-7005	17	18	and	and	CCONJ
ejpam-7005	17	19	independently	independently	ADV
ejpam-7005	17	20	developed	develop	VERB
ejpam-7005	17	21	by	by	ADP
ejpam-7005	17	22	nagumo	nagumo	ADJ
ejpam-7005	17	23	and	and	CCONJ
ejpam-7005	17	24	colleagues	colleague	NOUN
ejpam-7005	17	25	[	[	X
ejpam-7005	17	26	5	5	NUM
ejpam-7005	17	27	]	]	PUNCT
ejpam-7005	17	28	.	.	PUNCT
ejpam-7005	18	1	conceived	conceive	VERB
ejpam-7005	18	2	as	as	ADP
ejpam-7005	18	3	a	a	DET
ejpam-7005	18	4	reduction	reduction	NOUN
ejpam-7005	18	5	of	of	ADP
ejpam-7005	18	6	the	the	DET
ejpam-7005	18	7	hodgkin	hodgkin	PROPN
ejpam-7005	18	8	–	–	PUNCT
ejpam-7005	18	9	huxley	huxley	PROPN
ejpam-7005	18	10	model	model	NOUN
ejpam-7005	18	11	for	for	ADP
ejpam-7005	18	12	nerve	nerve	NOUN
ejpam-7005	18	13	impulse	impulse	ADJ
ejpam-7005	18	14	transmission	transmission	NOUN
ejpam-7005	19	1	[	[	X
ejpam-7005	19	2	6	6	NUM
ejpam-7005	19	3	]	]	PUNCT
ejpam-7005	19	4	,	,	PUNCT
ejpam-7005	19	5	the	the	DET
ejpam-7005	19	6	fhn	fhn	ADJ
ejpam-7005	19	7	system	system	NOUN
ejpam-7005	19	8	retains	retain	VERB
ejpam-7005	19	9	essential	essential	ADJ
ejpam-7005	19	10	features	feature	NOUN
ejpam-7005	19	11	of	of	ADP
ejpam-7005	19	12	excitable	excitable	ADJ
ejpam-7005	19	13	media	medium	NOUN
ejpam-7005	19	14	,	,	PUNCT
ejpam-7005	19	15	such	such	ADJ
ejpam-7005	19	16	as	as	ADP
ejpam-7005	19	17	a	a	DET
ejpam-7005	19	18	stable	stable	ADJ
ejpam-7005	19	19	equilibrium	equilibrium	NOUN
ejpam-7005	19	20	,	,	PUNCT
ejpam-7005	19	21	an	an	DET
ejpam-7005	19	22	excitation	excitation	NOUN
ejpam-7005	19	23	threshold	threshold	NOUN
ejpam-7005	19	24	,	,	PUNCT
ejpam-7005	19	25	and	and	CCONJ
ejpam-7005	19	26	a	a	DET
ejpam-7005	19	27	refractory	refractory	NOUN
ejpam-7005	19	28	phase	phase	NOUN
ejpam-7005	19	29	[	[	X
ejpam-7005	19	30	7	7	NUM
ejpam-7005	19	31	,	,	PUNCT
ejpam-7005	19	32	8	8	NUM
ejpam-7005	19	33	]	]	PUNCT
ejpam-7005	19	34	.	.	PUNCT
ejpam-7005	20	1	owing	owe	VERB
ejpam-7005	20	2	to	to	ADP
ejpam-7005	20	3	its	its	PRON
ejpam-7005	20	4	simplicity	simplicity	NOUN
ejpam-7005	20	5	and	and	CCONJ
ejpam-7005	20	6	rich	rich	ADJ
ejpam-7005	20	7	dynamics	dynamic	NOUN
ejpam-7005	20	8	,	,	PUNCT
ejpam-7005	20	9	the	the	DET
ejpam-7005	20	10	fhn	fhn	ADJ
ejpam-7005	20	11	model	model	NOUN
ejpam-7005	20	12	has	have	AUX
ejpam-7005	20	13	found	find	VERB
ejpam-7005	20	14	applications	application	NOUN
ejpam-7005	20	15	far	far	ADV
ejpam-7005	20	16	beyond	beyond	ADP
ejpam-7005	20	17	neurophysiology	neurophysiology	NOUN
ejpam-7005	20	18	,	,	PUNCT
ejpam-7005	20	19	including	include	VERB
ejpam-7005	20	20	wave	wave	NOUN
ejpam-7005	20	21	propagation	propagation	NOUN
ejpam-7005	20	22	and	and	CCONJ
ejpam-7005	20	23	pattern	pattern	NOUN
ejpam-7005	20	24	formation	formation	NOUN
ejpam-7005	20	25	in	in	ADP
ejpam-7005	20	26	cardiology	cardiology	NOUN
ejpam-7005	20	27	,	,	PUNCT
ejpam-7005	20	28	chemical	chemical	NOUN
ejpam-7005	20	29	reactions	reaction	NOUN
ejpam-7005	20	30	,	,	PUNCT
ejpam-7005	20	31	and	and	CCONJ
ejpam-7005	20	32	population	population	NOUN
ejpam-7005	20	33	dynamics	dynamic	NOUN
ejpam-7005	20	34	[	[	X
ejpam-7005	20	35	9	9	NUM
ejpam-7005	20	36	,	,	PUNCT
ejpam-7005	20	37	10	10	NUM
ejpam-7005	20	38	]	]	PUNCT
ejpam-7005	20	39	.	.	PUNCT
ejpam-7005	21	1	conventional	conventional	ADJ
ejpam-7005	21	2	reaction	reaction	NOUN
ejpam-7005	21	3	–	–	PUNCT
ejpam-7005	21	4	diffusion	diffusion	NOUN
ejpam-7005	21	5	models	model	NOUN
ejpam-7005	21	6	typically	typically	ADV
ejpam-7005	21	7	rely	rely	VERB
ejpam-7005	21	8	on	on	ADP
ejpam-7005	21	9	integer	integer	NOUN
ejpam-7005	21	10	–	–	PUNCT
ejpam-7005	21	11	order	order	NOUN
ejpam-7005	21	12	partial	partial	ADJ
ejpam-7005	21	13	differential	differential	NOUN
ejpam-7005	21	14	equations	equation	NOUN
ejpam-7005	21	15	,	,	PUNCT
ejpam-7005	21	16	inherently	inherently	ADV
ejpam-7005	21	17	assuming	assume	VERB
ejpam-7005	21	18	that	that	SCONJ
ejpam-7005	21	19	the	the	DET
ejpam-7005	21	20	underlying	underlie	VERB
ejpam-7005	21	21	dynamics	dynamic	NOUN
ejpam-7005	21	22	are	be	AUX
ejpam-7005	21	23	markovian	markovian	ADJ
ejpam-7005	21	24	,	,	PUNCT
ejpam-7005	21	25	i.e.	i.e.	X
ejpam-7005	21	26	,	,	PUNCT
ejpam-7005	21	27	the	the	DET
ejpam-7005	21	28	future	future	ADJ
ejpam-7005	21	29	state	state	NOUN
ejpam-7005	21	30	depends	depend	VERB
ejpam-7005	21	31	solely	solely	ADV
ejpam-7005	21	32	on	on	ADP
ejpam-7005	21	33	the	the	DET
ejpam-7005	21	34	current	current	ADJ
ejpam-7005	21	35	state	state	NOUN
ejpam-7005	21	36	.	.	PUNCT
ejpam-7005	22	1	however	however	ADV
ejpam-7005	22	2	,	,	PUNCT
ejpam-7005	22	3	many	many	ADJ
ejpam-7005	22	4	real	real	ADJ
ejpam-7005	22	5	–	–	PUNCT
ejpam-7005	22	6	world	world	NOUN
ejpam-7005	22	7	biological	biological	ADJ
ejpam-7005	22	8	and	and	CCONJ
ejpam-7005	22	9	physical	physical	ADJ
ejpam-7005	22	10	systems	system	NOUN
ejpam-7005	22	11	exhibit	exhibit	NOUN
ejpam-7005	22	12	memory	memory	NOUN
ejpam-7005	22	13	and	and	CCONJ
ejpam-7005	22	14	hereditary	hereditary	ADJ
ejpam-7005	22	15	characteristics	characteristic	NOUN
ejpam-7005	22	16	,	,	PUNCT
ejpam-7005	22	17	where	where	SCONJ
ejpam-7005	22	18	the	the	DET
ejpam-7005	22	19	system	system	NOUN
ejpam-7005	22	20	’s	’s	PART
ejpam-7005	22	21	evolution	evolution	NOUN
ejpam-7005	22	22	also	also	ADV
ejpam-7005	22	23	reflects	reflect	VERB
ejpam-7005	22	24	its	its	PRON
ejpam-7005	22	25	past	past	ADJ
ejpam-7005	22	26	history	history	NOUN
ejpam-7005	22	27	[	[	X
ejpam-7005	22	28	11	11	NUM
ejpam-7005	22	29	,	,	PUNCT
ejpam-7005	22	30	12	12	NUM
ejpam-7005	22	31	]	]	PUNCT
ejpam-7005	22	32	.	.	PUNCT
ejpam-7005	23	1	fractional	fractional	ADJ
ejpam-7005	23	2	calculus	calculus	NOUN
ejpam-7005	23	3	,	,	PUNCT
ejpam-7005	23	4	which	which	PRON
ejpam-7005	23	5	extends	extend	VERB
ejpam-7005	23	6	differentiation	differentiation	NOUN
ejpam-7005	23	7	and	and	CCONJ
ejpam-7005	23	8	integration	integration	NOUN
ejpam-7005	23	9	to	to	ADP
ejpam-7005	23	10	arbitrary	arbitrary	ADJ
ejpam-7005	23	11	orders	order	NOUN
ejpam-7005	23	12	,	,	PUNCT
ejpam-7005	23	13	offers	offer	VERB
ejpam-7005	23	14	a	a	DET
ejpam-7005	23	15	versatile	versatile	ADJ
ejpam-7005	23	16	framework	framework	NOUN
ejpam-7005	23	17	for	for	ADP
ejpam-7005	23	18	modeling	model	VERB
ejpam-7005	23	19	such	such	ADJ
ejpam-7005	23	20	non	non	ADJ
ejpam-7005	23	21	–	–	NOUN
ejpam-7005	23	22	local	local	ADJ
ejpam-7005	23	23	and	and	CCONJ
ejpam-7005	23	24	memory	memory	NOUN
ejpam-7005	23	25	–	–	PUNCT
ejpam-7005	23	26	dependent	dependent	ADJ
ejpam-7005	23	27	processes	process	NOUN
ejpam-7005	23	28	[	[	X
ejpam-7005	23	29	13–17	13–17	NUM
ejpam-7005	23	30	]	]	PUNCT
ejpam-7005	23	31	.	.	PUNCT
ejpam-7005	24	1	incorporating	incorporate	VERB
ejpam-7005	24	2	fractional	fractional	ADJ
ejpam-7005	24	3	derivatives	derivative	NOUN
ejpam-7005	24	4	into	into	ADP
ejpam-7005	24	5	diffusion	diffusion	NOUN
ejpam-7005	24	6	models	model	NOUN
ejpam-7005	24	7	enables	enable	VERB
ejpam-7005	24	8	the	the	DET
ejpam-7005	24	9	description	description	NOUN
ejpam-7005	24	10	of	of	ADP
ejpam-7005	24	11	anomalous	anomalous	ADJ
ejpam-7005	24	12	diffusion	diffusion	NOUN
ejpam-7005	25	1	[	[	X
ejpam-7005	25	2	18–24	18–24	NUM
ejpam-7005	25	3	]	]	X
ejpam-7005	25	4	,	,	PUNCT
ejpam-7005	25	5	which	which	PRON
ejpam-7005	25	6	frequently	frequently	ADV
ejpam-7005	25	7	arises	arise	VERB
ejpam-7005	25	8	in	in	ADP
ejpam-7005	25	9	heterogeneous	heterogeneous	ADJ
ejpam-7005	25	10	or	or	CCONJ
ejpam-7005	25	11	crowded	crowded	ADJ
ejpam-7005	25	12	environments	environment	NOUN
ejpam-7005	25	13	[	[	X
ejpam-7005	25	14	25–27	25–27	NUM
ejpam-7005	25	15	]	]	X
ejpam-7005	25	16	.	.	PUNCT
ejpam-7005	26	1	in	in	ADP
ejpam-7005	26	2	reaction	reaction	NOUN
ejpam-7005	26	3	kinetics	kinetic	NOUN
ejpam-7005	26	4	,	,	PUNCT
ejpam-7005	26	5	fractional	fractional	ADJ
ejpam-7005	26	6	operators	operator	NOUN
ejpam-7005	26	7	can	can	AUX
ejpam-7005	26	8	represent	represent	VERB
ejpam-7005	26	9	distributed	distribute	VERB
ejpam-7005	26	10	delays	delay	NOUN
ejpam-7005	26	11	and	and	CCONJ
ejpam-7005	26	12	complex	complex	ADJ
ejpam-7005	26	13	memory	memory	NOUN
ejpam-7005	26	14	effects	effect	NOUN
ejpam-7005	26	15	.	.	PUNCT
ejpam-7005	27	1	consequently	consequently	ADV
ejpam-7005	27	2	,	,	PUNCT
ejpam-7005	27	3	fo	fo	NOUN
ejpam-7005	27	4	-	-	PUNCT
ejpam-7005	27	5	fhn	fhn	NOUN
ejpam-7005	27	6	models	model	NOUN
ejpam-7005	27	7	have	have	AUX
ejpam-7005	27	8	been	be	AUX
ejpam-7005	27	9	extensively	extensively	ADV
ejpam-7005	27	10	investigated	investigate	VERB
ejpam-7005	27	11	to	to	PART
ejpam-7005	27	12	study	study	VERB
ejpam-7005	27	13	neuronal	neuronal	ADJ
ejpam-7005	27	14	activity	activity	NOUN
ejpam-7005	27	15	with	with	ADP
ejpam-7005	27	16	memory	memory	NOUN
ejpam-7005	27	17	effects	effect	NOUN
ejpam-7005	27	18	[	[	X
ejpam-7005	27	19	28	28	NUM
ejpam-7005	27	20	,	,	PUNCT
ejpam-7005	27	21	29	29	NUM
ejpam-7005	27	22	]	]	PUNCT
ejpam-7005	27	23	.	.	PUNCT
ejpam-7005	28	1	to	to	PART
ejpam-7005	28	2	further	far	ADV
ejpam-7005	28	3	increase	increase	VERB
ejpam-7005	28	4	flexibility	flexibility	NOUN
ejpam-7005	28	5	,	,	PUNCT
ejpam-7005	28	6	vo	vo	X
ejpam-7005	28	7	fractional	fractional	PROPN
ejpam-7005	28	8	calculus	calculus	NOUN
ejpam-7005	28	9	has	have	AUX
ejpam-7005	28	10	been	be	AUX
ejpam-7005	28	11	introduced	introduce	VERB
ejpam-7005	28	12	[	[	PUNCT
ejpam-7005	28	13	30	30	NUM
ejpam-7005	28	14	,	,	PUNCT
ejpam-7005	28	15	31	31	NUM
ejpam-7005	28	16	]	]	PUNCT
ejpam-7005	28	17	,	,	PUNCT
ejpam-7005	28	18	in	in	ADP
ejpam-7005	28	19	which	which	PRON
ejpam-7005	28	20	the	the	DET
ejpam-7005	28	21	derivative	derivative	ADJ
ejpam-7005	28	22	order	order	NOUN
ejpam-7005	28	23	varies	vary	VERB
ejpam-7005	28	24	with	with	ADP
ejpam-7005	28	25	time	time	NOUN
ejpam-7005	28	26	,	,	PUNCT
ejpam-7005	28	27	spatial	spatial	ADJ
ejpam-7005	28	28	position	position	NOUN
ejpam-7005	28	29	,	,	PUNCT
ejpam-7005	28	30	or	or	CCONJ
ejpam-7005	28	31	other	other	ADJ
ejpam-7005	28	32	parameters	parameter	NOUN
ejpam-7005	28	33	.	.	PUNCT
ejpam-7005	29	1	this	this	PRON
ejpam-7005	29	2	allows	allow	VERB
ejpam-7005	29	3	for	for	ADP
ejpam-7005	29	4	modeling	modeling	NOUN
ejpam-7005	29	5	systems	system	NOUN
ejpam-7005	29	6	whose	whose	DET
ejpam-7005	29	7	memory	memory	NOUN
ejpam-7005	29	8	characteristics	characteristic	NOUN
ejpam-7005	29	9	or	or	CCONJ
ejpam-7005	29	10	internal	internal	ADJ
ejpam-7005	29	11	processes	process	NOUN
ejpam-7005	29	12	change	change	VERB
ejpam-7005	29	13	dynamically	dynamically	ADV
ejpam-7005	29	14	,	,	PUNCT
ejpam-7005	29	15	such	such	ADJ
ejpam-7005	29	16	as	as	ADP
ejpam-7005	29	17	in	in	ADP
ejpam-7005	29	18	media	medium	NOUN
ejpam-7005	29	19	with	with	ADP
ejpam-7005	29	20	evolving	evolve	VERB
ejpam-7005	29	21	properties	property	NOUN
ejpam-7005	29	22	[	[	X
ejpam-7005	29	23	32	32	NUM
ejpam-7005	29	24	,	,	PUNCT
ejpam-7005	29	25	33	33	NUM
ejpam-7005	29	26	]	]	PUNCT
ejpam-7005	29	27	.	.	PUNCT
ejpam-7005	30	1	vo	vo	NOUN
ejpam-7005	30	2	models	model	NOUN
ejpam-7005	30	3	are	be	AUX
ejpam-7005	30	4	particularly	particularly	ADV
ejpam-7005	30	5	well	well	ADV
ejpam-7005	30	6	–	–	PUNCT
ejpam-7005	30	7	suited	suited	ADJ
ejpam-7005	30	8	to	to	ADP
ejpam-7005	30	9	capturing	capture	VERB
ejpam-7005	30	10	adaptive	adaptive	ADJ
ejpam-7005	30	11	or	or	CCONJ
ejpam-7005	30	12	evolving	evolve	VERB
ejpam-7005	30	13	biological	biological	ADJ
ejpam-7005	30	14	phenomena	phenomenon	NOUN
ejpam-7005	30	15	.	.	PUNCT
ejpam-7005	31	1	since	since	SCONJ
ejpam-7005	31	2	analytical	analytical	ADJ
ejpam-7005	31	3	solutions	solution	NOUN
ejpam-7005	31	4	for	for	ADP
ejpam-7005	31	5	such	such	ADJ
ejpam-7005	31	6	complex	complex	ADJ
ejpam-7005	31	7	models	model	NOUN
ejpam-7005	31	8	are	be	AUX
ejpam-7005	31	9	rarely	rarely	ADV
ejpam-7005	31	10	attainable	attainable	ADJ
ejpam-7005	31	11	,	,	PUNCT
ejpam-7005	31	12	numerical	numerical	ADJ
ejpam-7005	31	13	techniques	technique	NOUN
ejpam-7005	31	14	play	play	VERB
ejpam-7005	31	15	a	a	DET
ejpam-7005	31	16	pivotal	pivotal	ADJ
ejpam-7005	31	17	role	role	NOUN
ejpam-7005	31	18	in	in	ADP
ejpam-7005	31	19	their	their	PRON
ejpam-7005	31	20	analysis	analysis	NOUN
ejpam-7005	31	21	.	.	PUNCT
ejpam-7005	32	1	discrete	discrete	ADJ
ejpam-7005	32	2	fractional	fractional	ADJ
ejpam-7005	32	3	calculus	calculus	NOUN
ejpam-7005	32	4	provides	provide	VERB
ejpam-7005	32	5	a	a	DET
ejpam-7005	32	6	rigorous	rigorous	ADJ
ejpam-7005	32	7	foundation	foundation	NOUN
ejpam-7005	32	8	for	for	ADP
ejpam-7005	32	9	approximating	approximate	VERB
ejpam-7005	32	10	fractional	fractional	ADJ
ejpam-7005	32	11	operators	operator	NOUN
ejpam-7005	32	12	and	and	CCONJ
ejpam-7005	32	13	studying	study	VERB
ejpam-7005	32	14	the	the	DET
ejpam-7005	32	15	corresponding	corresponding	ADJ
ejpam-7005	32	16	difference	difference	NOUN
ejpam-7005	32	17	equations	equation	NOUN
ejpam-7005	32	18	[	[	X
ejpam-7005	32	19	34–36	34–36	NUM
ejpam-7005	32	20	]	]	PUNCT
ejpam-7005	32	21	.	.	PUNCT
ejpam-7005	33	1	in	in	ADP
ejpam-7005	33	2	this	this	DET
ejpam-7005	33	3	work	work	NOUN
ejpam-7005	33	4	,	,	PUNCT
ejpam-7005	33	5	we	we	PRON
ejpam-7005	33	6	formulate	formulate	VERB
ejpam-7005	33	7	a	a	DET
ejpam-7005	33	8	discrete	discrete	ADJ
ejpam-7005	33	9	–	–	PUNCT
ejpam-7005	33	10	time	time	NOUN
ejpam-7005	33	11	vo	vo	X
ejpam-7005	33	12	fractional	fractional	ADJ
ejpam-7005	33	13	version	version	NOUN
ejpam-7005	33	14	of	of	ADP
ejpam-7005	33	15	the	the	DET
ejpam-7005	33	16	fhn	fhn	ADJ
ejpam-7005	33	17	-	-	PUNCT
ejpam-7005	33	18	rds	rds	NOUN
ejpam-7005	33	19	.	.	PUNCT
ejpam-7005	34	1	a	a	DET
ejpam-7005	34	2	central	central	ADJ
ejpam-7005	34	3	aspect	aspect	NOUN
ejpam-7005	34	4	of	of	ADP
ejpam-7005	34	5	system	system	NOUN
ejpam-7005	34	6	analysis	analysis	NOUN
ejpam-7005	34	7	is	be	AUX
ejpam-7005	34	8	stability	stability	NOUN
ejpam-7005	34	9	.	.	PUNCT
ejpam-7005	35	1	for	for	ADP
ejpam-7005	35	2	fo	fo	ADP
ejpam-7005	35	3	dynamics	dynamic	NOUN
ejpam-7005	35	4	,	,	PUNCT
ejpam-7005	35	5	the	the	DET
ejpam-7005	35	6	classical	classical	ADJ
ejpam-7005	35	7	notion	notion	NOUN
ejpam-7005	35	8	of	of	ADP
ejpam-7005	35	9	exponential	exponential	ADJ
ejpam-7005	35	10	stability	stability	NOUN
ejpam-7005	35	11	is	be	AUX
ejpam-7005	35	12	often	often	ADV
ejpam-7005	35	13	replaced	replace	VERB
ejpam-7005	35	14	by	by	ADP
ejpam-7005	35	15	mittag	mittag	ADJ
ejpam-7005	35	16	–	–	PUNCT
ejpam-7005	35	17	leffler	leffler	NOUN
ejpam-7005	35	18	stability	stability	NOUN
ejpam-7005	35	19	[	[	X
ejpam-7005	35	20	37–42	37–42	NUM
ejpam-7005	35	21	]	]	PUNCT
ejpam-7005	35	22	.	.	PUNCT
ejpam-7005	36	1	in	in	ADP
ejpam-7005	36	2	many	many	ADJ
ejpam-7005	36	3	engineering	engineering	NOUN
ejpam-7005	36	4	and	and	CCONJ
ejpam-7005	36	5	biological	biological	ADJ
ejpam-7005	36	6	contexts	context	NOUN
ejpam-7005	36	7	,	,	PUNCT
ejpam-7005	36	8	however	however	ADV
ejpam-7005	36	9	,	,	PUNCT
ejpam-7005	36	10	the	the	DET
ejpam-7005	36	11	primary	primary	ADJ
ejpam-7005	36	12	concern	concern	NOUN
ejpam-7005	36	13	is	be	AUX
ejpam-7005	36	14	not	not	PART
ejpam-7005	36	15	the	the	DET
ejpam-7005	36	16	asymptotic	asymptotic	ADJ
ejpam-7005	36	17	state	state	NOUN
ejpam-7005	36	18	but	but	CCONJ
ejpam-7005	36	19	ensuring	ensure	VERB
ejpam-7005	36	20	that	that	SCONJ
ejpam-7005	36	21	system	system	NOUN
ejpam-7005	36	22	trajectories	trajectory	NOUN
ejpam-7005	36	23	remain	remain	VERB
ejpam-7005	36	24	within	within	ADP
ejpam-7005	36	25	certain	certain	ADJ
ejpam-7005	36	26	bounds	bound	NOUN
ejpam-7005	36	27	over	over	ADP
ejpam-7005	36	28	a	a	DET
ejpam-7005	36	29	finite	finite	ADJ
ejpam-7005	36	30	time	time	NOUN
ejpam-7005	36	31	horizon	horizon	NOUN
ejpam-7005	36	32	.	.	PUNCT
ejpam-7005	37	1	this	this	PRON
ejpam-7005	37	2	motivates	motivate	VERB
ejpam-7005	37	3	the	the	DET
ejpam-7005	37	4	study	study	NOUN
ejpam-7005	37	5	of	of	ADP
ejpam-7005	37	6	fts	fts	PROPN
ejpam-7005	37	7	[	[	X
ejpam-7005	37	8	43	43	NUM
ejpam-7005	37	9	]	]	PUNCT
ejpam-7005	37	10	,	,	PUNCT
ejpam-7005	37	11	which	which	PRON
ejpam-7005	37	12	has	have	AUX
ejpam-7005	37	13	become	become	VERB
ejpam-7005	37	14	an	an	DET
ejpam-7005	37	15	important	important	ADJ
ejpam-7005	37	16	topic	topic	NOUN
ejpam-7005	37	17	in	in	ADP
ejpam-7005	37	18	fractional	fractional	ADJ
ejpam-7005	37	19	systems	system	NOUN
ejpam-7005	37	20	theory	theory	NOUN
ejpam-7005	37	21	[	[	X
ejpam-7005	37	22	44–46	44–46	NOUN
ejpam-7005	37	23	]	]	PUNCT
ejpam-7005	37	24	.	.	PUNCT
ejpam-7005	38	1	n.	n.	PROPN
ejpam-7005	38	2	anakira	anakira	PROPN
ejpam-7005	38	3	et	et	PROPN
ejpam-7005	38	4	al	al	PROPN
ejpam-7005	38	5	.	.	PUNCT
ejpam-7005	38	6	/	/	SYM
ejpam-7005	38	7	eur	eur	PROPN
ejpam-7005	38	8	.	.	PUNCT
ejpam-7005	39	1	j.	j.	PROPN
ejpam-7005	39	2	pure	pure	PROPN
ejpam-7005	39	3	appl	appl	PROPN
ejpam-7005	39	4	.	.	PROPN
ejpam-7005	39	5	math	math	PROPN
ejpam-7005	39	6	,	,	PUNCT
ejpam-7005	39	7	18	18	NUM
ejpam-7005	39	8	(	(	PUNCT
ejpam-7005	39	9	4	4	NUM
ejpam-7005	39	10	)	)	PUNCT
ejpam-7005	39	11	(	(	PUNCT
ejpam-7005	39	12	2025	2025	NUM
ejpam-7005	39	13	)	)	PUNCT
ejpam-7005	39	14	,	,	PUNCT
ejpam-7005	39	15	7005	7005	NUM
ejpam-7005	39	16	3	3	NUM
ejpam-7005	39	17	of	of	ADP
ejpam-7005	39	18	17	17	NUM
ejpam-7005	39	19	the	the	DET
ejpam-7005	39	20	present	present	ADJ
ejpam-7005	39	21	work	work	NOUN
ejpam-7005	39	22	focuses	focus	VERB
ejpam-7005	39	23	on	on	ADP
ejpam-7005	39	24	establishing	establish	VERB
ejpam-7005	39	25	fts	fts	PROPN
ejpam-7005	39	26	conditions	condition	NOUN
ejpam-7005	39	27	for	for	ADP
ejpam-7005	39	28	the	the	DET
ejpam-7005	39	29	discrete	discrete	ADJ
ejpam-7005	39	30	vo	vo	X
ejpam-7005	39	31	fractional	fractional	ADJ
ejpam-7005	39	32	fhn	fhn	ADJ
ejpam-7005	39	33	system	system	NOUN
ejpam-7005	39	34	.	.	PUNCT
ejpam-7005	40	1	using	use	VERB
ejpam-7005	40	2	discrete	discrete	ADJ
ejpam-7005	40	3	fractional	fractional	ADJ
ejpam-7005	40	4	calculus	calculus	NOUN
ejpam-7005	40	5	tools	tool	NOUN
ejpam-7005	40	6	,	,	PUNCT
ejpam-7005	40	7	and	and	CCONJ
ejpam-7005	40	8	in	in	ADP
ejpam-7005	40	9	particular	particular	ADJ
ejpam-7005	40	10	a	a	DET
ejpam-7005	40	11	discrete	discrete	ADJ
ejpam-7005	40	12	fractional	fractional	ADJ
ejpam-7005	40	13	gronwall	gronwall	ADJ
ejpam-7005	40	14	–	–	PUNCT
ejpam-7005	40	15	type	type	NOUN
ejpam-7005	40	16	inequality	inequality	NOUN
ejpam-7005	40	17	[	[	X
ejpam-7005	40	18	47	47	NUM
ejpam-7005	40	19	]	]	PUNCT
ejpam-7005	40	20	,	,	PUNCT
ejpam-7005	40	21	we	we	PRON
ejpam-7005	40	22	derive	derive	VERB
ejpam-7005	40	23	a	a	DET
ejpam-7005	40	24	sufficient	sufficient	ADJ
ejpam-7005	40	25	criterion	criterion	NOUN
ejpam-7005	40	26	for	for	ADP
ejpam-7005	40	27	stability	stability	NOUN
ejpam-7005	40	28	.	.	PUNCT
ejpam-7005	41	1	the	the	DET
ejpam-7005	41	2	remainder	remainder	NOUN
ejpam-7005	41	3	of	of	ADP
ejpam-7005	41	4	the	the	DET
ejpam-7005	41	5	paper	paper	NOUN
ejpam-7005	41	6	is	be	AUX
ejpam-7005	41	7	organized	organize	VERB
ejpam-7005	41	8	as	as	SCONJ
ejpam-7005	41	9	follows	follow	VERB
ejpam-7005	41	10	:	:	PUNCT
ejpam-7005	41	11	we	we	PRON
ejpam-7005	41	12	first	first	ADV
ejpam-7005	41	13	develop	develop	VERB
ejpam-7005	41	14	the	the	DET
ejpam-7005	41	15	discrete	discrete	ADJ
ejpam-7005	41	16	model	model	NOUN
ejpam-7005	41	17	and	and	CCONJ
ejpam-7005	41	18	establish	establish	VERB
ejpam-7005	41	19	the	the	DET
ejpam-7005	41	20	well	well	NOUN
ejpam-7005	41	21	-	-	PUNCT
ejpam-7005	41	22	posedness	posedness	NOUN
ejpam-7005	41	23	of	of	ADP
ejpam-7005	41	24	solutions	solution	NOUN
ejpam-7005	41	25	;	;	PUNCT
ejpam-7005	41	26	we	we	PRON
ejpam-7005	41	27	then	then	ADV
ejpam-7005	41	28	present	present	VERB
ejpam-7005	41	29	the	the	DET
ejpam-7005	41	30	main	main	ADJ
ejpam-7005	41	31	fts	fts	PROPN
ejpam-7005	41	32	result	result	NOUN
ejpam-7005	41	33	;	;	PUNCT
ejpam-7005	41	34	finally	finally	ADV
ejpam-7005	41	35	,	,	PUNCT
ejpam-7005	41	36	computational	computational	ADJ
ejpam-7005	41	37	analysis	analysis	NOUN
ejpam-7005	41	38	are	be	AUX
ejpam-7005	41	39	carried	carry	VERB
ejpam-7005	41	40	out	out	ADP
ejpam-7005	41	41	to	to	PART
ejpam-7005	41	42	illustrate	illustrate	VERB
ejpam-7005	41	43	and	and	CCONJ
ejpam-7005	41	44	validate	validate	VERB
ejpam-7005	41	45	the	the	DET
ejpam-7005	41	46	theoretical	theoretical	ADJ
ejpam-7005	41	47	analysis	analysis	NOUN
ejpam-7005	41	48	.	.	PUNCT
ejpam-7005	42	1	this	this	DET
ejpam-7005	42	2	paper	paper	NOUN
ejpam-7005	42	3	is	be	AUX
ejpam-7005	42	4	organized	organize	VERB
ejpam-7005	42	5	as	as	SCONJ
ejpam-7005	42	6	follows	follow	VERB
ejpam-7005	42	7	:	:	PUNCT
ejpam-7005	42	8	section	section	NOUN
ejpam-7005	42	9	2	2	NUM
ejpam-7005	42	10	formulates	formulate	VERB
ejpam-7005	42	11	the	the	DET
ejpam-7005	42	12	discrete	discrete	ADJ
ejpam-7005	42	13	model	model	NOUN
ejpam-7005	42	14	and	and	CCONJ
ejpam-7005	42	15	establishes	establish	VERB
ejpam-7005	42	16	the	the	DET
ejpam-7005	42	17	wellposedness	wellposedness	NOUN
ejpam-7005	42	18	of	of	ADP
ejpam-7005	42	19	solutions	solution	NOUN
ejpam-7005	42	20	.	.	PUNCT
ejpam-7005	43	1	section	section	NOUN
ejpam-7005	43	2	3	3	NUM
ejpam-7005	43	3	presents	present	VERB
ejpam-7005	43	4	the	the	DET
ejpam-7005	43	5	main	main	ADJ
ejpam-7005	43	6	fts	fts	PROPN
ejpam-7005	43	7	results	result	NOUN
ejpam-7005	43	8	.	.	PUNCT
ejpam-7005	44	1	section	section	NOUN
ejpam-7005	44	2	4	4	NUM
ejpam-7005	44	3	provides	provide	VERB
ejpam-7005	44	4	numerical	numerical	ADJ
ejpam-7005	44	5	simulations	simulation	NOUN
ejpam-7005	44	6	to	to	PART
ejpam-7005	44	7	illustrate	illustrate	VERB
ejpam-7005	44	8	and	and	CCONJ
ejpam-7005	44	9	validate	validate	VERB
ejpam-7005	44	10	the	the	DET
ejpam-7005	44	11	theoretical	theoretical	ADJ
ejpam-7005	44	12	analysis	analysis	NOUN
ejpam-7005	44	13	.	.	PUNCT
ejpam-7005	45	1	2	2	X
ejpam-7005	45	2	.	.	X
ejpam-7005	45	3	problem	problem	NOUN
ejpam-7005	45	4	formulation	formulation	NOUN
ejpam-7005	45	5	we	we	PRON
ejpam-7005	45	6	consider	consider	VERB
ejpam-7005	45	7	the	the	DET
ejpam-7005	45	8	fhn	fhn	ADJ
ejpam-7005	45	9	–	–	PUNCT
ejpam-7005	45	10	rds	rd	NOUN
ejpam-7005	45	11	,	,	PUNCT
ejpam-7005	45	12	originally	originally	ADV
ejpam-7005	45	13	proposed	propose	VERB
ejpam-7005	45	14	in	in	ADP
ejpam-7005	45	15	[	[	X
ejpam-7005	45	16	48	48	NUM
ejpam-7005	45	17	]	]	PUNCT
ejpam-7005	45	18	,	,	PUNCT
ejpam-7005	45	19	in	in	ADP
ejpam-7005	45	20	the	the	DET
ejpam-7005	45	21	following	follow	VERB
ejpam-7005	45	22	form:	form:	PROPN
ejpam-7005	45	23	∂u	∂u	PROPN
ejpam-7005	45	24	∂t	∂t	PROPN
ejpam-7005	45	25	=	=	SYM
ejpam-7005	45	26	d1∆u−	d1∆u−	NOUN
ejpam-7005	45	27	u3	u3	NOUN
ejpam-7005	45	28	+	+	CCONJ
ejpam-7005	45	29	(	(	PUNCT
ejpam-7005	45	30	β	β	X
ejpam-7005	45	31	+	+	ADJ
ejpam-7005	45	32	1)u2	1)u2	NUM
ejpam-7005	45	33	−	−	NOUN
ejpam-7005	45	34	βu−	βu−	SYM
ejpam-7005	45	35	v	v	NOUN
ejpam-7005	45	36	,	,	PUNCT
ejpam-7005	45	37	x	x	SYM
ejpam-7005	45	38	∈	∈	PROPN
ejpam-7005	45	39	ω	ω	PROPN
ejpam-7005	45	40	,	,	PUNCT
ejpam-7005	45	41	t	t	X
ejpam-7005	45	42	>	>	X
ejpam-7005	45	43	0	0	PROPN
ejpam-7005	45	44	,	,	PUNCT
ejpam-7005	45	45	∂v	∂v	PROPN
ejpam-7005	45	46	∂t	∂t	PROPN
ejpam-7005	46	1	=	=	PUNCT
ejpam-7005	46	2	d2∆v	d2∆v	X
ejpam-7005	47	1	+	+	PUNCT
ejpam-7005	47	2	ϵu−	ϵu−	PROPN
ejpam-7005	47	3	ϵγv	ϵγv	NOUN
ejpam-7005	47	4	,	,	PUNCT
ejpam-7005	47	5	x	x	PUNCT
ejpam-7005	47	6	∈	∈	PROPN
ejpam-7005	47	7	ω	ω	PROPN
ejpam-7005	47	8	,	,	PUNCT
ejpam-7005	47	9	t	t	X
ejpam-7005	47	10	>	>	X
ejpam-7005	47	11	0	0	PROPN
ejpam-7005	47	12	,	,	PUNCT
ejpam-7005	47	13	∂xu	∂xu	NOUN
ejpam-7005	47	14	=	=	SYM
ejpam-7005	47	15	∂xv	∂xv	NOUN
ejpam-7005	47	16	=	=	SYM
ejpam-7005	47	17	0	0	NUM
ejpam-7005	47	18	,	,	PUNCT
ejpam-7005	47	19	x	x	X
ejpam-7005	47	20	∈	∈	PROPN
ejpam-7005	47	21	∂ω	∂ω	PROPN
ejpam-7005	47	22	,	,	PUNCT
ejpam-7005	47	23	t	t	PROPN
ejpam-7005	47	24	>	>	X
ejpam-7005	47	25	0	0	NUM
ejpam-7005	47	26	,	,	PUNCT
ejpam-7005	47	27	u(x	u(x	NOUN
ejpam-7005	47	28	,	,	PUNCT
ejpam-7005	47	29	0	0	NUM
ejpam-7005	47	30	)	)	PUNCT
ejpam-7005	47	31	=	=	SYM
ejpam-7005	47	32	u0(x	u0(x	NOUN
ejpam-7005	47	33	)	)	PUNCT
ejpam-7005	47	34	,	,	PUNCT
ejpam-7005	47	35	v(x	v(x	PROPN
ejpam-7005	47	36	,	,	PUNCT
ejpam-7005	47	37	0	0	NUM
ejpam-7005	47	38	)	)	PUNCT
ejpam-7005	47	39	=	=	SYM
ejpam-7005	47	40	v0(x	v0(x	PROPN
ejpam-7005	47	41	)	)	PUNCT
ejpam-7005	47	42	,	,	PUNCT
ejpam-7005	47	43	x	x	PUNCT
ejpam-7005	47	44	∈	∈	PROPN
ejpam-7005	47	45	ω	ω	PROPN
ejpam-7005	47	46	.	.	PUNCT
ejpam-7005	48	1	(	(	PUNCT
ejpam-7005	48	2	1	1	X
ejpam-7005	48	3	)	)	PUNCT
ejpam-7005	48	4	here	here	ADV
ejpam-7005	48	5	,	,	PUNCT
ejpam-7005	48	6	the	the	DET
ejpam-7005	48	7	variables	variable	NOUN
ejpam-7005	48	8	,	,	PUNCT
ejpam-7005	48	9	parameters	parameter	NOUN
ejpam-7005	48	10	,	,	PUNCT
ejpam-7005	48	11	and	and	CCONJ
ejpam-7005	48	12	operators	operator	NOUN
ejpam-7005	48	13	appearing	appear	VERB
ejpam-7005	48	14	in	in	ADP
ejpam-7005	48	15	system	system	NOUN
ejpam-7005	48	16	(	(	PUNCT
ejpam-7005	48	17	1	1	X
ejpam-7005	48	18	)	)	PUNCT
ejpam-7005	48	19	are	be	AUX
ejpam-7005	48	20	summarized	summarize	VERB
ejpam-7005	48	21	in	in	ADP
ejpam-7005	48	22	table	table	NOUN
ejpam-7005	48	23	1	1	NUM
ejpam-7005	48	24	:	:	PUNCT
ejpam-7005	48	25	symbol	symbol	NOUN
ejpam-7005	48	26	/	/	SYM
ejpam-7005	48	27	parameter	parameter	NOUN
ejpam-7005	48	28	description	description	NOUN
ejpam-7005	48	29	ω	ω	PROPN
ejpam-7005	48	30	bounded	bounded	ADJ
ejpam-7005	48	31	domain	domain	NOUN
ejpam-7005	48	32	with	with	ADP
ejpam-7005	48	33	smooth	smooth	ADJ
ejpam-7005	48	34	boundary	boundary	ADJ
ejpam-7005	48	35	∂ω	∂ω	ADJ
ejpam-7005	48	36	∆	∆	X
ejpam-7005	48	37	laplacian	laplacian	ADJ
ejpam-7005	48	38	operator	operator	NOUN
ejpam-7005	48	39	u	u	NOUN
ejpam-7005	48	40	membrane	membrane	NOUN
ejpam-7005	48	41	potential	potential	NOUN
ejpam-7005	48	42	at	at	ADP
ejpam-7005	48	43	(	(	PUNCT
ejpam-7005	48	44	x	x	NOUN
ejpam-7005	48	45	,	,	PUNCT
ejpam-7005	48	46	t	t	PROPN
ejpam-7005	48	47	)	)	PUNCT
ejpam-7005	48	48	∈	∈	PROPN
ejpam-7005	48	49	ω×	ω×	PUNCT
ejpam-7005	48	50	(	(	PUNCT
ejpam-7005	48	51	0,∞	0,∞	NUM
ejpam-7005	48	52	)	)	PUNCT
ejpam-7005	48	53	v	v	NOUN
ejpam-7005	48	54	combination	combination	NOUN
ejpam-7005	48	55	of	of	ADP
ejpam-7005	48	56	potassium	potassium	NOUN
ejpam-7005	48	57	activation	activation	NOUN
ejpam-7005	48	58	and	and	CCONJ
ejpam-7005	48	59	sodium	sodium	NOUN
ejpam-7005	48	60	inactivation	inactivation	NOUN
ejpam-7005	48	61	β	β	VERB
ejpam-7005	48	62	positive	positive	ADJ
ejpam-7005	48	63	constant	constant	ADJ
ejpam-7005	48	64	,	,	PUNCT
ejpam-7005	48	65	0	0	PUNCT
ejpam-7005	48	66	<	<	X
ejpam-7005	48	67	β	β	X
ejpam-7005	48	68	<	<	X
ejpam-7005	48	69	1	1	NUM
ejpam-7005	48	70	2	2	NUM
ejpam-7005	48	71	ϵ	ϵ	ADP
ejpam-7005	48	72	positive	positive	ADJ
ejpam-7005	48	73	constant	constant	ADJ
ejpam-7005	48	74	,	,	PUNCT
ejpam-7005	48	75	ϵ	ϵ	X
ejpam-7005	48	76	≪	≪	ADJ
ejpam-7005	48	77	1	1	NUM
ejpam-7005	48	78	γ	γ	PRON
ejpam-7005	48	79	positive	positive	ADJ
ejpam-7005	48	80	constant	constant	NOUN
ejpam-7005	48	81	to	to	PART
ejpam-7005	48	82	incorporate	incorporate	VERB
ejpam-7005	48	83	memory	memory	NOUN
ejpam-7005	48	84	effects	effect	NOUN
ejpam-7005	48	85	,	,	PUNCT
ejpam-7005	48	86	we	we	PRON
ejpam-7005	48	87	employ	employ	VERB
ejpam-7005	48	88	the	the	DET
ejpam-7005	48	89	vo	vo	PROPN
ejpam-7005	48	90	caputo	caputo	PROPN
ejpam-7005	48	91	fo	fo	ADP
ejpam-7005	48	92	derivative	derivative	NOUN
ejpam-7005	48	93	,	,	PUNCT
ejpam-7005	48	94	resulting	result	VERB
ejpam-7005	48	95	in	in	ADP
ejpam-7005	48	96	the	the	DET
ejpam-7005	48	97	following	follow	VERB
ejpam-7005	48	98	vo	vo	NOUN
ejpam-7005	48	99	time	time	NOUN
ejpam-7005	48	100	–	–	PUNCT
ejpam-7005	48	101	fractional	fractional	ADJ
ejpam-7005	48	102	fhn	fhn	ADJ
ejpam-7005	48	103	–	–	PUNCT
ejpam-7005	48	104	rds	rd	NOUN
ejpam-7005	48	105	:	:	PUNCT
ejpam-7005	48	106	{	{	PUNCT
ejpam-7005	48	107	c	c	NOUN
ejpam-7005	48	108	0	0	NUM
ejpam-7005	48	109	d	d	NOUN
ejpam-7005	48	110	δ(t	δ(t	PROPN
ejpam-7005	48	111	)	)	PUNCT
ejpam-7005	48	112	t	t	PROPN
ejpam-7005	48	113	u−	u−	PROPN
ejpam-7005	48	114	d1∆u	d1∆u	NOUN
ejpam-7005	48	115	=	=	PUNCT
ejpam-7005	48	116	−u3	−u3	NOUN
ejpam-7005	48	117	+	+	CCONJ
ejpam-7005	48	118	(	(	PUNCT
ejpam-7005	48	119	β	β	X
ejpam-7005	48	120	+	+	ADJ
ejpam-7005	48	121	1)u2	1)u2	NUM
ejpam-7005	48	122	−	−	NOUN
ejpam-7005	48	123	βu−	βu−	SYM
ejpam-7005	48	124	v	v	NOUN
ejpam-7005	48	125	,	,	PUNCT
ejpam-7005	48	126	c	c	PROPN
ejpam-7005	48	127	0	0	NUM
ejpam-7005	48	128	d	d	NOUN
ejpam-7005	48	129	δ(t	δ(t	PROPN
ejpam-7005	48	130	)	)	PUNCT
ejpam-7005	48	131	t	t	PROPN
ejpam-7005	48	132	v	v	NOUN
ejpam-7005	48	133	−	−	NOUN
ejpam-7005	48	134	d2∆v	d2∆v	ADJ
ejpam-7005	48	135	=	=	PUNCT
ejpam-7005	49	1	ϵu−	ϵu−	PROPN
ejpam-7005	49	2	ϵγv	ϵγv	NOUN
ejpam-7005	49	3	,	,	PUNCT
ejpam-7005	49	4	(	(	PUNCT
ejpam-7005	49	5	2	2	X
ejpam-7005	49	6	)	)	PUNCT
ejpam-7005	49	7	here	here	ADV
ejpam-7005	49	8	,	,	PUNCT
ejpam-7005	49	9	the	the	DET
ejpam-7005	49	10	variables	variable	NOUN
ejpam-7005	49	11	and	and	CCONJ
ejpam-7005	49	12	parameters	parameter	NOUN
ejpam-7005	49	13	specific	specific	ADJ
ejpam-7005	49	14	to	to	ADP
ejpam-7005	49	15	the	the	DET
ejpam-7005	49	16	fractional	fractional	ADJ
ejpam-7005	49	17	formulation	formulation	NOUN
ejpam-7005	49	18	are	be	AUX
ejpam-7005	49	19	summarized	summarize	VERB
ejpam-7005	49	20	in	in	ADP
ejpam-7005	49	21	table	table	NOUN
ejpam-7005	49	22	2	2	NUM
ejpam-7005	49	23	:	:	PUNCT
ejpam-7005	49	24	n.	n.	PROPN
ejpam-7005	49	25	anakira	anakira	PROPN
ejpam-7005	49	26	et	et	PROPN
ejpam-7005	49	27	al	al	PROPN
ejpam-7005	49	28	.	.	PUNCT
ejpam-7005	49	29	/	/	SYM
ejpam-7005	49	30	eur	eur	PROPN
ejpam-7005	49	31	.	.	PUNCT
ejpam-7005	50	1	j.	j.	PROPN
ejpam-7005	50	2	pure	pure	PROPN
ejpam-7005	50	3	appl	appl	PROPN
ejpam-7005	50	4	.	.	PROPN
ejpam-7005	50	5	math	math	PROPN
ejpam-7005	50	6	,	,	PUNCT
ejpam-7005	50	7	18	18	NUM
ejpam-7005	50	8	(	(	PUNCT
ejpam-7005	50	9	4	4	NUM
ejpam-7005	50	10	)	)	PUNCT
ejpam-7005	50	11	(	(	PUNCT
ejpam-7005	50	12	2025	2025	NUM
ejpam-7005	50	13	)	)	PUNCT
ejpam-7005	50	14	,	,	PUNCT
ejpam-7005	50	15	7005	7005	NUM
ejpam-7005	50	16	4	4	NUM
ejpam-7005	50	17	of	of	ADP
ejpam-7005	50	18	17	17	NUM
ejpam-7005	50	19	symbol	symbol	NOUN
ejpam-7005	50	20	/	/	SYM
ejpam-7005	50	21	parameter	parameter	NOUN
ejpam-7005	50	22	description	description	NOUN
ejpam-7005	50	23	0	0	PUNCT
ejpam-7005	50	24	<	<	X
ejpam-7005	50	25	δ(t	δ(t	PROPN
ejpam-7005	50	26	)	)	PUNCT
ejpam-7005	50	27	≤	≤	NUM
ejpam-7005	50	28	1	1	NUM
ejpam-7005	50	29	fractional	fractional	PROPN
ejpam-7005	50	30	vo	vo	X
ejpam-7005	50	31	c	c	NOUN
ejpam-7005	50	32	0	0	PROPN
ejpam-7005	51	1	d	d	NOUN
ejpam-7005	51	2	δ(t	δ(t	PROPN
ejpam-7005	51	3	)	)	PUNCT
ejpam-7005	51	4	t	t	PROPN
ejpam-7005	51	5	caputo	caputo	PROPN
ejpam-7005	51	6	fractional	fractional	PROPN
ejpam-7005	51	7	derivative	derivative	ADJ
ejpam-7005	51	8	d1	d1	NOUN
ejpam-7005	51	9	,	,	PUNCT
ejpam-7005	51	10	d2	d2	NOUN
ejpam-7005	51	11	diffusion	diffusion	NOUN
ejpam-7005	51	12	coefficients	coefficient	NOUN
ejpam-7005	51	13	let	let	VERB
ejpam-7005	51	14	x	x	X
ejpam-7005	51	15	∈	∈	PROPN
ejpam-7005	51	16	[	[	X
ejpam-7005	51	17	0	0	NUM
ejpam-7005	51	18	,	,	PUNCT
ejpam-7005	51	19	l	l	NOUN
ejpam-7005	51	20	]	]	X
ejpam-7005	51	21	,	,	PUNCT
ejpam-7005	51	22	with	with	ADP
ejpam-7005	51	23	spatial	spatial	ADJ
ejpam-7005	51	24	discretization	discretization	NOUN
ejpam-7005	51	25	xi+1	xi+1	X
ejpam-7005	52	1	=	=	SYM
ejpam-7005	52	2	xi	xi	PROPN
ejpam-7005	52	3	+	+	CCONJ
ejpam-7005	52	4	∆x	∆x	PROPN
ejpam-7005	52	5	,	,	PUNCT
ejpam-7005	52	6	i	i	PRON
ejpam-7005	52	7	=	=	NOUN
ejpam-7005	52	8	0	0	NUM
ejpam-7005	52	9	,	,	PUNCT
ejpam-7005	52	10	.	.	PUNCT
ejpam-7005	52	11	.	.	PUNCT
ejpam-7005	52	12	.	.	PUNCT
ejpam-7005	53	1	,	,	PUNCT
ejpam-7005	53	2	m.	m.	NOUN
ejpam-7005	53	3	using	use	VERB
ejpam-7005	53	4	the	the	DET
ejpam-7005	53	5	central	central	ADJ
ejpam-7005	53	6	difference	difference	NOUN
ejpam-7005	53	7	approximation	approximation	NOUN
ejpam-7005	53	8	,	,	PUNCT
ejpam-7005	53	9	the	the	DET
ejpam-7005	53	10	second	second	ADJ
ejpam-7005	53	11	spatial	spatial	ADJ
ejpam-7005	53	12	derivative	derivative	NOUN
ejpam-7005	53	13	is	be	AUX
ejpam-7005	53	14	given	give	VERB
ejpam-7005	53	15	by	by	ADP
ejpam-7005	53	16	∂2y(x	∂2y(x	PROPN
ejpam-7005	53	17	,	,	PUNCT
ejpam-7005	53	18	t	t	PROPN
ejpam-7005	53	19	)	)	PUNCT
ejpam-7005	53	20	∂x2	∂x2	NOUN
ejpam-7005	53	21	≈	≈	PROPN
ejpam-7005	53	22	yi−1(t)−	yi−1(t)−	PROPN
ejpam-7005	53	23	2yi(t	2yi(t	NUM
ejpam-7005	53	24	)	)	PUNCT
ejpam-7005	53	25	+	+	NUM
ejpam-7005	54	1	yi+1(t	yi+1(t	X
ejpam-7005	54	2	)	)	PUNCT
ejpam-7005	54	3	∆2	∆2	PROPN
ejpam-7005	55	1	x	x	SYM
ejpam-7005	55	2	,	,	PUNCT
ejpam-7005	55	3	y	y	PROPN
ejpam-7005	55	4	∈	∈	PROPN
ejpam-7005	55	5	{	{	PUNCT
ejpam-7005	55	6	u	u	NOUN
ejpam-7005	55	7	,	,	PUNCT
ejpam-7005	55	8	v	v	NOUN
ejpam-7005	55	9	}	}	PUNCT
ejpam-7005	55	10	.	.	PUNCT
ejpam-7005	56	1	(	(	PUNCT
ejpam-7005	56	2	3	3	X
ejpam-7005	56	3	)	)	PUNCT
ejpam-7005	56	4	and	and	CCONJ
ejpam-7005	56	5	using	use	VERB
ejpam-7005	56	6	the	the	DET
ejpam-7005	56	7	second	second	ADJ
ejpam-7005	56	8	-	-	PUNCT
ejpam-7005	56	9	order	order	NOUN
ejpam-7005	56	10	difference	difference	NOUN
ejpam-7005	56	11	operator	operator	NOUN
ejpam-7005	57	1	[	[	X
ejpam-7005	57	2	49	49	NUM
ejpam-7005	57	3	]	]	X
ejpam-7005	57	4	:	:	PUNCT
ejpam-7005	57	5	∆2yi−1	∆2yi−1	PROPN
ejpam-7005	57	6	=	=	SYM
ejpam-7005	57	7	yi−1	yi−1	PROPN
ejpam-7005	57	8	−	−	PROPN
ejpam-7005	57	9	2	2	NUM
ejpam-7005	57	10	yi	yi	NOUN
ejpam-7005	57	11	+	+	NOUN
ejpam-7005	57	12	yi+1	yi+1	PROPN
ejpam-7005	57	13	.	.	PUNCT
ejpam-7005	58	1	(	(	PUNCT
ejpam-7005	58	2	4	4	X
ejpam-7005	58	3	)	)	PUNCT
ejpam-7005	58	4	we	we	PRON
ejpam-7005	58	5	can	can	AUX
ejpam-7005	58	6	write	write	VERB
ejpam-7005	58	7	:	:	PUNCT
ejpam-7005	58	8	∂2y(x	∂2y(x	PROPN
ejpam-7005	58	9	,	,	PUNCT
ejpam-7005	58	10	t	t	PROPN
ejpam-7005	58	11	)	)	PUNCT
ejpam-7005	58	12	∂x2	∂x2	NOUN
ejpam-7005	58	13	≈	≈	PROPN
ejpam-7005	58	14	∆2yi−1(t	∆2yi−1(t	PROPN
ejpam-7005	58	15	)	)	PUNCT
ejpam-7005	58	16	∆2	∆2	PROPN
ejpam-7005	59	1	x	x	X
ejpam-7005	59	2	.	.	PUNCT
ejpam-7005	60	1	(	(	PUNCT
ejpam-7005	60	2	5	5	X
ejpam-7005	60	3	)	)	PUNCT
ejpam-7005	60	4	applying	apply	VERB
ejpam-7005	60	5	these	these	DET
ejpam-7005	60	6	approximations	approximation	NOUN
ejpam-7005	60	7	,	,	PUNCT
ejpam-7005	60	8	we	we	PRON
ejpam-7005	60	9	obtain	obtain	VERB
ejpam-7005	60	10	the	the	DET
ejpam-7005	60	11	discrete	discrete	ADJ
ejpam-7005	60	12	vo	vo	NOUN
ejpam-7005	60	13	fractional	fractional	ADJ
ejpam-7005	60	14	fhn	fhn	PROPN
ejpam-7005	60	15	–	–	PUNCT
ejpam-7005	60	16	rd	rd	NOUN
ejpam-7005	60	17	model:	model:	PROPN
ejpam-7005	60	18	c	c	PROPN
ejpam-7005	60	19	ℏ	ℏ	PROPN
ejpam-7005	60	20	∆	∆	PROPN
ejpam-7005	60	21	δ(t	δ(t	PROPN
ejpam-7005	60	22	)	)	PUNCT
ejpam-7005	60	23	t0	t0	PROPN
ejpam-7005	60	24	ui(t	ui(t	NOUN
ejpam-7005	60	25	)	)	PUNCT
ejpam-7005	61	1	=	=	SYM
ejpam-7005	61	2	d1	d1	PROPN
ejpam-7005	61	3	∆2	∆2	PROPN
ejpam-7005	61	4	x	x	SYM
ejpam-7005	61	5	∆2eθ(t)[ui−1](t)−	∆2eθ(t)[ui−1](t)−	PROPN
ejpam-7005	61	6	eθ(t)[u3i	eθ(t)[u3i	PROPN
ejpam-7005	61	7	]	]	X
ejpam-7005	61	8	(	(	PUNCT
ejpam-7005	61	9	t	t	PROPN
ejpam-7005	61	10	)	)	PUNCT
ejpam-7005	61	11	+	+	CCONJ
ejpam-7005	61	12	(	(	PUNCT
ejpam-7005	61	13	β	β	X
ejpam-7005	61	14	+	+	X
ejpam-7005	61	15	1)eθ(t)[u2i	1)eθ(t)[u2i	NUM
ejpam-7005	61	16	]	]	SYM
ejpam-7005	61	17	(	(	PUNCT
ejpam-7005	61	18	t	t	PROPN
ejpam-7005	61	19	)	)	PUNCT
ejpam-7005	61	20	−βeθ(t)[ui](t)−	−βeθ(t)[ui](t)−	PROPN
ejpam-7005	61	21	eθ(t)[vi](t	eθ(t)[vi](t	PROPN
ejpam-7005	61	22	)	)	PUNCT
ejpam-7005	61	23	,	,	PUNCT
ejpam-7005	61	24	c	c	PROPN
ejpam-7005	61	25	ℏ	ℏ	PROPN
ejpam-7005	61	26	∆	∆	X
ejpam-7005	61	27	δ(t	δ(t	NOUN
ejpam-7005	61	28	)	)	PUNCT
ejpam-7005	61	29	t0	t0	PROPN
ejpam-7005	61	30	vi(t	vi(t	PUNCT
ejpam-7005	61	31	)	)	PUNCT
ejpam-7005	61	32	=	=	SYM
ejpam-7005	61	33	d2	d2	PROPN
ejpam-7005	61	34	∆2	∆2	PROPN
ejpam-7005	61	35	x	x	SYM
ejpam-7005	61	36	∆2eθ(t)[vi−1](t	∆2eθ(t)[vi−1](t	PROPN
ejpam-7005	61	37	)	)	PUNCT
ejpam-7005	61	38	+	+	NUM
ejpam-7005	61	39	ϵeθ(t)[ui](t)−	ϵeθ(t)[ui](t)−	PROPN
ejpam-7005	61	40	ϵγeθ(t)[vi](t	ϵγeθ(t)[vi](t	NUM
ejpam-7005	61	41	)	)	PUNCT
ejpam-7005	61	42	.	.	PUNCT
ejpam-7005	62	1	(	(	PUNCT
ejpam-7005	62	2	6	6	NUM
ejpam-7005	62	3	)	)	PUNCT
ejpam-7005	62	4	where	where	SCONJ
ejpam-7005	62	5	eθ(t)[yi](t	eθ(t)[yi](t	NOUN
ejpam-7005	62	6	)	)	PUNCT
ejpam-7005	62	7	:	:	PUNCT
ejpam-7005	62	8	=	=	SYM
ejpam-7005	62	9	yi	yi	PROPN
ejpam-7005	62	10	(	(	PUNCT
ejpam-7005	62	11	t+	t+	NOUN
ejpam-7005	62	12	θ(t	θ(t	NOUN
ejpam-7005	62	13	)	)	PUNCT
ejpam-7005	62	14	)	)	PUNCT
ejpam-7005	62	15	,	,	PUNCT
ejpam-7005	62	16	with	with	ADP
ejpam-7005	62	17	pbcs	pbcs	NOUN
ejpam-7005	62	18	:	:	PUNCT
ejpam-7005	62	19	yj+m(t	yj+m(t	X
ejpam-7005	62	20	)	)	PUNCT
ejpam-7005	62	21	=	=	SYM
ejpam-7005	62	22	yj(t	yj(t	PROPN
ejpam-7005	62	23	)	)	PUNCT
ejpam-7005	62	24	,	,	PUNCT
ejpam-7005	62	25	j	j	PROPN
ejpam-7005	62	26	=	=	SYM
ejpam-7005	62	27	0	0	NUM
ejpam-7005	62	28	,	,	PUNCT
ejpam-7005	62	29	1	1	NUM
ejpam-7005	62	30	.	.	PUNCT
ejpam-7005	62	31	(	(	PUNCT
ejpam-7005	62	32	7	7	NUM
ejpam-7005	62	33	)	)	PUNCT
ejpam-7005	62	34	and	and	CCONJ
ejpam-7005	62	35	ics	ics	PROPN
ejpam-7005	62	36	:	:	PUNCT
ejpam-7005	62	37	yi(0	yi(0	X
ejpam-7005	62	38	)	)	PUNCT
ejpam-7005	62	39	=	=	SYM
ejpam-7005	62	40	ϕj(xj	ϕj(xj	PROPN
ejpam-7005	62	41	)	)	PUNCT
ejpam-7005	62	42	,	,	PUNCT
ejpam-7005	62	43	j	j	PROPN
ejpam-7005	62	44	=	=	SYM
ejpam-7005	62	45	1	1	NUM
ejpam-7005	62	46	,	,	PUNCT
ejpam-7005	62	47	2	2	NUM
ejpam-7005	62	48	.	.	PUNCT
ejpam-7005	62	49	(	(	PUNCT
ejpam-7005	62	50	8)	8)	NUM
ejpam-7005	62	51	definition	definition	NOUN
ejpam-7005	62	52	1	1	NUM
ejpam-7005	62	53	(	(	PUNCT
ejpam-7005	62	54	[	[	X
ejpam-7005	62	55	49	49	NUM
ejpam-7005	62	56	]	]	PUNCT
ejpam-7005	62	57	)	)	PUNCT
ejpam-7005	62	58	.	.	PUNCT
ejpam-7005	63	1	the	the	DET
ejpam-7005	63	2	vo	vo	PROPN
ejpam-7005	63	3	caputo	caputo	PROPN
ejpam-7005	63	4	fractional	fractional	PROPN
ejpam-7005	63	5	difference	difference	NOUN
ejpam-7005	63	6	operator	operator	NOUN
ejpam-7005	63	7	is	be	AUX
ejpam-7005	63	8	defined	define	VERB
ejpam-7005	63	9	as	as	ADP
ejpam-7005	63	10	:	:	PUNCT
ejpam-7005	63	11	c	c	PROPN
ejpam-7005	63	12	ℏ	ℏ	PROPN
ejpam-7005	63	13	∆	∆	PROPN
ejpam-7005	63	14	δ(t	δ(t	PROPN
ejpam-7005	63	15	)	)	PUNCT
ejpam-7005	63	16	a	a	DET
ejpam-7005	63	17	κ(t	κ(t	NOUN
ejpam-7005	63	18	)	)	PUNCT
ejpam-7005	63	19	=	=	PUNCT
ejpam-7005	63	20	ℏ∆	ℏ∆	PROPN
ejpam-7005	63	21	−(n−δ(t	−(n−δ(t	PROPN
ejpam-7005	63	22	)	)	PUNCT
ejpam-7005	63	23	)	)	PUNCT
ejpam-7005	63	24	a	a	DET
ejpam-7005	63	25	∆n	∆n	PROPN
ejpam-7005	63	26	ℏκ(t	ℏκ(t	NOUN
ejpam-7005	63	27	)	)	PUNCT
ejpam-7005	63	28	,	,	PUNCT
ejpam-7005	63	29	0	0	PUNCT
ejpam-7005	63	30	<	<	X
ejpam-7005	63	31	δ(t	δ(t	PROPN
ejpam-7005	63	32	)	)	PUNCT
ejpam-7005	63	33	≤	≤	NUM
ejpam-7005	63	34	1	1	NUM
ejpam-7005	63	35	,	,	PUNCT
ejpam-7005	63	36	(	(	PUNCT
ejpam-7005	63	37	9	9	X
ejpam-7005	63	38	)	)	PUNCT
ejpam-7005	63	39	where	where	SCONJ
ejpam-7005	63	40	ℏ∆	ℏ∆	ADV
ejpam-7005	63	41	−δ(t	−δ(t	ADV
ejpam-7005	63	42	)	)	PUNCT
ejpam-7005	63	43	a	a	DET
ejpam-7005	63	44	κ(t	κ(t	NOUN
ejpam-7005	63	45	)	)	PUNCT
ejpam-7005	63	46	=	=	PUNCT
ejpam-7005	63	47	ℏ	ℏ	PROPN
ejpam-7005	63	48	γ(δ(t	γ(δ(t	PROPN
ejpam-7005	63	49	)	)	PUNCT
ejpam-7005	63	50	)	)	PUNCT
ejpam-7005	64	1	s	s	VERB
ejpam-7005	64	2	=	=	NOUN
ejpam-7005	64	3	a	a	PRON
ejpam-7005	64	4	ℏ∑	ℏ∑	NOUN
ejpam-7005	64	5	t	t	NOUN
ejpam-7005	64	6	ℏ−δ(t	ℏ−δ(t	ADJ
ejpam-7005	64	7	)	)	PUNCT
ejpam-7005	64	8	(	(	PUNCT
ejpam-7005	64	9	t−	t−	PROPN
ejpam-7005	64	10	σ(sℏ))(δ(t)−1	σ(sℏ))(δ(t)−1	NOUN
ejpam-7005	64	11	)	)	PUNCT
ejpam-7005	64	12	ℏ	ℏ	NOUN
ejpam-7005	64	13	κ(sℏ	κ(sℏ	PROPN
ejpam-7005	64	14	)	)	PUNCT
ejpam-7005	64	15	,	,	PUNCT
ejpam-7005	64	16	(	(	PUNCT
ejpam-7005	64	17	10	10	NUM
ejpam-7005	64	18	)	)	PUNCT
ejpam-7005	64	19	with	with	ADP
ejpam-7005	64	20	σ(sℏ	σ(sℏ	NOUN
ejpam-7005	64	21	)	)	PUNCT
ejpam-7005	64	22	=	=	SYM
ejpam-7005	64	23	(	(	PUNCT
ejpam-7005	64	24	s+	s+	NUM
ejpam-7005	64	25	1)ℏ	1)ℏ	NUM
ejpam-7005	64	26	and	and	CCONJ
ejpam-7005	64	27	t	t	NOUN
ejpam-7005	64	28	∈	∈	PROPN
ejpam-7005	64	29	(	(	PUNCT
ejpam-7005	64	30	ℏn)a+δ(t)ℏ.	ℏn)a+δ(t)ℏ.	NUM
ejpam-7005	64	31	the	the	DET
ejpam-7005	64	32	generalized	generalized	ADJ
ejpam-7005	64	33	falling	fall	VERB
ejpam-7005	64	34	factorial	factorial	NOUN
ejpam-7005	64	35	is	be	AUX
ejpam-7005	64	36	:	:	PUNCT
ejpam-7005	64	37	t	t	PROPN
ejpam-7005	64	38	(	(	PUNCT
ejpam-7005	64	39	δ(t	δ(t	PROPN
ejpam-7005	64	40	)	)	PUNCT
ejpam-7005	64	41	)	)	PUNCT
ejpam-7005	65	1	ℏ	ℏ	NOUN
ejpam-7005	65	2	=	=	SYM
ejpam-7005	65	3	ℏδ(t	ℏδ(t	X
ejpam-7005	65	4	)	)	PUNCT
ejpam-7005	65	5	γ	γ	PROPN
ejpam-7005	65	6	(	(	PUNCT
ejpam-7005	65	7	tℏ	tℏ	NOUN
ejpam-7005	65	8	+	+	NOUN
ejpam-7005	65	9	1	1	NUM
ejpam-7005	65	10	)	)	PUNCT
ejpam-7005	65	11	γ	γ	X
ejpam-7005	65	12	(	(	PUNCT
ejpam-7005	65	13	tℏ	tℏ	NOUN
ejpam-7005	65	14	−	−	PROPN
ejpam-7005	65	15	δ(t	δ(t	PROPN
ejpam-7005	65	16	)	)	PUNCT
ejpam-7005	65	17	+	+	CCONJ
ejpam-7005	65	18	1	1	NUM
ejpam-7005	65	19	)	)	PUNCT
ejpam-7005	65	20	.	.	PUNCT
ejpam-7005	66	1	(	(	PUNCT
ejpam-7005	66	2	11	11	NUM
ejpam-7005	66	3	)	)	PUNCT
ejpam-7005	66	4	n.	n.	NOUN
ejpam-7005	66	5	anakira	anakira	PROPN
ejpam-7005	66	6	et	et	PROPN
ejpam-7005	66	7	al	al	PROPN
ejpam-7005	66	8	.	.	PUNCT
ejpam-7005	66	9	/	/	SYM
ejpam-7005	66	10	eur	eur	PROPN
ejpam-7005	66	11	.	.	PUNCT
ejpam-7005	67	1	j.	j.	PROPN
ejpam-7005	67	2	pure	pure	PROPN
ejpam-7005	67	3	appl	appl	PROPN
ejpam-7005	67	4	.	.	PROPN
ejpam-7005	67	5	math	math	PROPN
ejpam-7005	67	6	,	,	PUNCT
ejpam-7005	67	7	18	18	NUM
ejpam-7005	67	8	(	(	PUNCT
ejpam-7005	67	9	4	4	NUM
ejpam-7005	67	10	)	)	PUNCT
ejpam-7005	67	11	(	(	PUNCT
ejpam-7005	67	12	2025	2025	NUM
ejpam-7005	67	13	)	)	PUNCT
ejpam-7005	67	14	,	,	PUNCT
ejpam-7005	67	15	7005	7005	NUM
ejpam-7005	67	16	5	5	NUM
ejpam-7005	67	17	of	of	ADP
ejpam-7005	67	18	17	17	NUM
ejpam-7005	67	19	lemma	lemma	PROPN
ejpam-7005	67	20	1	1	NUM
ejpam-7005	67	21	(	(	PUNCT
ejpam-7005	67	22	[	[	X
ejpam-7005	67	23	49	49	NUM
ejpam-7005	67	24	]	]	PUNCT
ejpam-7005	67	25	)	)	PUNCT
ejpam-7005	67	26	.	.	PUNCT
ejpam-7005	68	1	the	the	DET
ejpam-7005	68	2	following	follow	VERB
ejpam-7005	68	3	properties	property	NOUN
ejpam-7005	68	4	hold	hold	VERB
ejpam-7005	68	5	:	:	PUNCT
ejpam-7005	68	6	{	{	PUNCT
ejpam-7005	68	7	ℏ∆	ℏ∆	X
ejpam-7005	68	8	−δ(t	−δ(t	ADV
ejpam-7005	68	9	)	)	PUNCT
ejpam-7005	68	10	a+(1−δ(t))ℏ	a+(1−δ(t))ℏ	VERB
ejpam-7005	68	11	c	c	NOUN
ejpam-7005	68	12	ℏ	ℏ	PROPN
ejpam-7005	68	13	∆	∆	PROPN
ejpam-7005	68	14	δ(t	δ(t	PROPN
ejpam-7005	68	15	)	)	PUNCT
ejpam-7005	68	16	a	a	DET
ejpam-7005	68	17	κ(t	κ(t	NOUN
ejpam-7005	68	18	)	)	PUNCT
ejpam-7005	68	19	=	=	SYM
ejpam-7005	69	1	κ(t)−	κ(t)−	PROPN
ejpam-7005	69	2	κ(a	κ(a	PROPN
ejpam-7005	69	3	)	)	PUNCT
ejpam-7005	69	4	,	,	PUNCT
ejpam-7005	69	5	c	c	PROPN
ejpam-7005	69	6	ℏ	ℏ	PROPN
ejpam-7005	69	7	∆	∆	X
ejpam-7005	69	8	δ(t)κ	δ(t)κ	PROPN
ejpam-7005	69	9	=	=	PUNCT
ejpam-7005	69	10	0	0	PROPN
ejpam-7005	69	11	,	,	PUNCT
ejpam-7005	69	12	0	0	NUM
ejpam-7005	69	13	<	<	X
ejpam-7005	69	14	δ(t	δ(t	PROPN
ejpam-7005	69	15	)	)	PUNCT
ejpam-7005	69	16	≤	≤	NUM
ejpam-7005	69	17	1	1	NUM
ejpam-7005	69	18	.	.	PUNCT
ejpam-7005	70	1	(	(	PUNCT
ejpam-7005	70	2	12	12	NUM
ejpam-7005	70	3	)	)	PUNCT
ejpam-7005	70	4	lemma	lemma	PROPN
ejpam-7005	70	5	2	2	NUM
ejpam-7005	70	6	.	.	PUNCT
ejpam-7005	71	1	the	the	DET
ejpam-7005	71	2	nonlinear	nonlinear	ADJ
ejpam-7005	71	3	fractional	fractional	ADJ
ejpam-7005	71	4	partial	partial	ADJ
ejpam-7005	71	5	difference	difference	NOUN
ejpam-7005	71	6	system	system	NOUN
ejpam-7005	71	7	(	(	PUNCT
ejpam-7005	71	8	6	6	NUM
ejpam-7005	71	9	)	)	PUNCT
ejpam-7005	71	10	admits	admit	VERB
ejpam-7005	71	11	a	a	DET
ejpam-7005	71	12	unique	unique	ADJ
ejpam-7005	71	13	solution	solution	NOUN
ejpam-7005	71	14	given	give	VERB
ejpam-7005	71	15	by	by	PROPN
ejpam-7005	71	16	uni	uni	NOUN
ejpam-7005	72	1	=	=	SYM
ejpam-7005	72	2	ϕ1,i	ϕ1,i	PROPN
ejpam-7005	72	3	+	+	CCONJ
ejpam-7005	72	4	ℏδn	ℏδn	PROPN
ejpam-7005	72	5	γ(δn	γ(δn	NOUN
ejpam-7005	72	6	)	)	PUNCT
ejpam-7005	72	7	n∑	n∑	PUNCT
ejpam-7005	73	1	j=1	j=1	PROPN
ejpam-7005	73	2	w	w	PROPN
ejpam-7005	73	3	(	(	PUNCT
ejpam-7005	73	4	δn	δn	NOUN
ejpam-7005	73	5	)	)	PUNCT
ejpam-7005	73	6	n−j	n−j	ADV
ejpam-7005	73	7	[	[	PUNCT
ejpam-7005	73	8	d1	d1	PROPN
ejpam-7005	73	9	∆2	∆2	PROPN
ejpam-7005	73	10	x	x	PROPN
ejpam-7005	73	11	∆2u	∆2u	PROPN
ejpam-7005	73	12	j	j	PROPN
ejpam-7005	73	13	i−1	i−1	PROPN
ejpam-7005	73	14	−	−	PROPN
ejpam-7005	73	15	(	(	PUNCT
ejpam-7005	73	16	u	u	NOUN
ejpam-7005	73	17	j	j	PROPN
ejpam-7005	73	18	i	i	NOUN
ejpam-7005	73	19	)	)	PUNCT
ejpam-7005	73	20	3	3	X
ejpam-7005	73	21	+	+	CCONJ
ejpam-7005	73	22	(	(	PUNCT
ejpam-7005	73	23	β	β	X
ejpam-7005	73	24	+	+	NOUN
ejpam-7005	73	25	1	1	X
ejpam-7005	73	26	)	)	PUNCT
ejpam-7005	73	27	(	(	PUNCT
ejpam-7005	73	28	u	u	NOUN
ejpam-7005	73	29	j	j	PROPN
ejpam-7005	73	30	i	i	NOUN
ejpam-7005	73	31	)	)	PUNCT
ejpam-7005	73	32	2	2	NUM
ejpam-7005	73	33	−	−	PROPN
ejpam-7005	73	34	β	β	SYM
ejpam-7005	73	35	u	u	NOUN
ejpam-7005	73	36	j	j	PROPN
ejpam-7005	73	37	i	i	PRON
ejpam-7005	73	38	−	−	VERB
ejpam-7005	73	39	v	v	INTJ
ejpam-7005	73	40	j	j	PROPN
ejpam-7005	74	1	i	i	PRON
ejpam-7005	74	2	]	]	PUNCT
ejpam-7005	74	3	,	,	PUNCT
ejpam-7005	74	4	vni	vni	NOUN
ejpam-7005	74	5	=	=	SYM
ejpam-7005	75	1	ϕ2,i	ϕ2,i	PROPN
ejpam-7005	75	2	+	+	CCONJ
ejpam-7005	75	3	ℏδn	ℏδn	PROPN
ejpam-7005	75	4	γ(δn	γ(δn	NOUN
ejpam-7005	75	5	)	)	PUNCT
ejpam-7005	76	1	n∑	n∑	PUNCT
ejpam-7005	76	2	j=1	j=1	PROPN
ejpam-7005	76	3	w	w	PROPN
ejpam-7005	76	4	(	(	PUNCT
ejpam-7005	76	5	δn	δn	NOUN
ejpam-7005	76	6	)	)	PUNCT
ejpam-7005	76	7	n−j	n−j	ADV
ejpam-7005	76	8	[	[	PUNCT
ejpam-7005	76	9	d2	d2	PROPN
ejpam-7005	76	10	∆2	∆2	PROPN
ejpam-7005	76	11	x	x	SYM
ejpam-7005	76	12	∆2v	∆2v	PROPN
ejpam-7005	77	1	j	j	PROPN
ejpam-7005	77	2	i−1	i−1	PROPN
ejpam-7005	77	3	+	+	PROPN
ejpam-7005	77	4	ϵ	ϵ	X
ejpam-7005	77	5	u	u	X
ejpam-7005	77	6	j	j	PROPN
ejpam-7005	77	7	i	i	PRON
ejpam-7005	77	8	−	−	VERB
ejpam-7005	78	1	ϵγ	ϵγ	INTJ
ejpam-7005	79	1	v	v	INTJ
ejpam-7005	79	2	j	j	NOUN
ejpam-7005	80	1	i	i	PRON
ejpam-7005	80	2	]	]	PUNCT
ejpam-7005	80	3	,	,	PUNCT
ejpam-7005	80	4	(	(	PUNCT
ejpam-7005	80	5	13	13	NUM
ejpam-7005	80	6	)	)	PUNCT
ejpam-7005	80	7	for	for	ADP
ejpam-7005	80	8	1	1	NUM
ejpam-7005	80	9	≤	≤	NUM
ejpam-7005	80	10	i	i	PRON
ejpam-7005	80	11	≤	≤	NOUN
ejpam-7005	80	12	m	m	VERB
ejpam-7005	80	13	and	and	CCONJ
ejpam-7005	80	14	n	n	CCONJ
ejpam-7005	80	15	>	>	ADP
ejpam-7005	80	16	0	0	NUM
ejpam-7005	80	17	,	,	PUNCT
ejpam-7005	80	18	where	where	SCONJ
ejpam-7005	80	19	w	w	NOUN
ejpam-7005	80	20	(	(	PUNCT
ejpam-7005	80	21	δn	δn	NOUN
ejpam-7005	80	22	)	)	PUNCT
ejpam-7005	80	23	n−j	n−j	ADV
ejpam-7005	80	24	:	:	PUNCT
ejpam-7005	80	25	=	=	SYM
ejpam-7005	80	26	γ	γ	X
ejpam-7005	80	27	(	(	PUNCT
ejpam-7005	80	28	n−	n−	PROPN
ejpam-7005	80	29	j	j	NOUN
ejpam-7005	80	30	+	+	CCONJ
ejpam-7005	80	31	δn	δn	ADJ
ejpam-7005	80	32	)	)	PUNCT
ejpam-7005	80	33	γ(n−	γ(n−	PROPN
ejpam-7005	80	34	j	j	PROPN
ejpam-7005	80	35	+	+	CCONJ
ejpam-7005	80	36	1	1	NUM
ejpam-7005	80	37	)	)	PUNCT
ejpam-7005	80	38	.	.	PUNCT
ejpam-7005	81	1	proof	proof	NOUN
ejpam-7005	81	2	1	1	NUM
ejpam-7005	81	3	.	.	PUNCT
ejpam-7005	81	4	from	from	ADP
ejpam-7005	81	5	system	system	NOUN
ejpam-7005	81	6	(	(	PUNCT
ejpam-7005	81	7	6	6	NUM
ejpam-7005	81	8	)	)	PUNCT
ejpam-7005	81	9	,	,	PUNCT
ejpam-7005	81	10	we	we	PRON
ejpam-7005	81	11	write:	write:	X
ejpam-7005	81	12	c	c	PROPN
ejpam-7005	81	13	ℏ	ℏ	PROPN
ejpam-7005	81	14	∆	∆	X
ejpam-7005	81	15	δn	δn	PROPN
ejpam-7005	81	16	t0	t0	PROPN
ejpam-7005	81	17	ui(t	ui(t	NOUN
ejpam-7005	81	18	)	)	PUNCT
ejpam-7005	82	1	=	=	SYM
ejpam-7005	82	2	d1	d1	PROPN
ejpam-7005	82	3	∆2	∆2	PROPN
ejpam-7005	82	4	x	x	PROPN
ejpam-7005	82	5	∆2ui−1(t+	∆2ui−1(t+	PROPN
ejpam-7005	82	6	ℏδn	ℏδn	PROPN
ejpam-7005	82	7	)	)	PUNCT
ejpam-7005	83	1	+	+	NUM
ejpam-7005	83	2	f	f	X
ejpam-7005	83	3	(	(	PUNCT
ejpam-7005	83	4	ui(t+	ui(t+	PROPN
ejpam-7005	83	5	ℏδn	ℏδn	PROPN
ejpam-7005	83	6	)	)	PUNCT
ejpam-7005	83	7	,	,	PUNCT
ejpam-7005	83	8	vi(t+	vi(t+	PROPN
ejpam-7005	83	9	ℏδn	ℏδn	PROPN
ejpam-7005	83	10	)	)	PUNCT
ejpam-7005	83	11	)	)	PUNCT
ejpam-7005	83	12	,	,	PUNCT
ejpam-7005	83	13	c	c	NOUN
ejpam-7005	83	14	ℏ	ℏ	PROPN
ejpam-7005	83	15	∆	∆	PROPN
ejpam-7005	83	16	δn	δn	PROPN
ejpam-7005	83	17	t0	t0	PROPN
ejpam-7005	83	18	vi(t	vi(t	PUNCT
ejpam-7005	83	19	)	)	PUNCT
ejpam-7005	84	1	=	=	SYM
ejpam-7005	84	2	d2	d2	PROPN
ejpam-7005	84	3	∆2	∆2	PROPN
ejpam-7005	84	4	x	x	PROPN
ejpam-7005	84	5	∆2vi−1(t+	∆2vi−1(t+	PROPN
ejpam-7005	84	6	ℏδn	ℏδn	PROPN
ejpam-7005	84	7	)	)	PUNCT
ejpam-7005	85	1	+	+	NOUN
ejpam-7005	85	2	g(ui(t+	g(ui(t+	NOUN
ejpam-7005	85	3	ℏδn	ℏδn	PROPN
ejpam-7005	85	4	)	)	PUNCT
ejpam-7005	85	5	,	,	PUNCT
ejpam-7005	85	6	vi(t+	vi(t+	PROPN
ejpam-7005	85	7	ℏδn	ℏδn	PROPN
ejpam-7005	85	8	)	)	PUNCT
ejpam-7005	85	9	)	)	PUNCT
ejpam-7005	85	10	,	,	PUNCT
ejpam-7005	85	11	(	(	PUNCT
ejpam-7005	85	12	14	14	NUM
ejpam-7005	85	13	)	)	PUNCT
ejpam-7005	86	1	where	where	SCONJ
ejpam-7005	86	2	f	f	PROPN
ejpam-7005	86	3	(	(	PUNCT
ejpam-7005	86	4	ui	ui	PROPN
ejpam-7005	86	5	,	,	PUNCT
ejpam-7005	86	6	vi	vi	NOUN
ejpam-7005	86	7	)	)	PUNCT
ejpam-7005	86	8	=	=	SYM
ejpam-7005	86	9	−u3i	−u3i	NOUN
ejpam-7005	87	1	+	+	CCONJ
ejpam-7005	87	2	(	(	PUNCT
ejpam-7005	87	3	β	β	X
ejpam-7005	87	4	+	+	NUM
ejpam-7005	87	5	1)u2i	1)u2i	NUM
ejpam-7005	87	6	−	−	NOUN
ejpam-7005	87	7	βui	βui	ADV
ejpam-7005	87	8	−	−	PROPN
ejpam-7005	87	9	vi	vi	PROPN
ejpam-7005	87	10	,	,	PUNCT
ejpam-7005	87	11	(	(	PUNCT
ejpam-7005	87	12	15	15	NUM
ejpam-7005	87	13	)	)	PUNCT
ejpam-7005	87	14	g(ui	g(ui	PROPN
ejpam-7005	87	15	,	,	PUNCT
ejpam-7005	87	16	vi	vi	NOUN
ejpam-7005	87	17	)	)	PUNCT
ejpam-7005	87	18	=	=	SYM
ejpam-7005	87	19	ϵui	ϵui	NOUN
ejpam-7005	87	20	−	−	PROPN
ejpam-7005	87	21	ϵγvi	ϵγvi	NOUN
ejpam-7005	87	22	.	.	PUNCT
ejpam-7005	88	1	(	(	PUNCT
ejpam-7005	88	2	16	16	NUM
ejpam-7005	88	3	)	)	PUNCT
ejpam-7005	88	4	using	use	VERB
ejpam-7005	88	5	lemma	lemma	PROPN
ejpam-7005	88	6	1	1	NUM
ejpam-7005	88	7	,	,	PUNCT
ejpam-7005	88	8	we	we	PRON
ejpam-7005	88	9	apply	apply	VERB
ejpam-7005	88	10	the	the	DET
ejpam-7005	88	11	fractional	fractional	ADJ
ejpam-7005	88	12	sum	sum	NOUN
ejpam-7005	88	13	operator:	operator:	PROPN
ejpam-7005	88	14	ℏ∆	ℏ∆	X
ejpam-7005	88	15	−δn	−δn	NOUN
ejpam-7005	88	16	t0+(1−δn)ℏ	t0+(1−δn)ℏ	NUM
ejpam-7005	88	17	c	c	NOUN
ejpam-7005	88	18	ℏ	ℏ	PROPN
ejpam-7005	88	19	∆	∆	PROPN
ejpam-7005	88	20	δn	δn	PROPN
ejpam-7005	88	21	t0	t0	PROPN
ejpam-7005	88	22	ui(t	ui(t	NOUN
ejpam-7005	88	23	)	)	PUNCT
ejpam-7005	88	24	=	=	PRON
ejpam-7005	88	25	ℏ∆	ℏ∆	X
ejpam-7005	88	26	−δn	−δn	NUM
ejpam-7005	89	1	t0+(1−δn)ℏ	t0+(1−δn)ℏ	X
ejpam-7005	90	1	[	[	PUNCT
ejpam-7005	90	2	d1	d1	PROPN
ejpam-7005	90	3	∆2	∆2	PROPN
ejpam-7005	90	4	x	x	PROPN
ejpam-7005	90	5	∆2ui−1(t+	∆2ui−1(t+	PROPN
ejpam-7005	90	6	ℏδn	ℏδn	PROPN
ejpam-7005	90	7	)	)	PUNCT
ejpam-7005	91	1	+	+	NUM
ejpam-7005	91	2	f	f	X
ejpam-7005	91	3	(	(	PUNCT
ejpam-7005	91	4	·	·	PUNCT
ejpam-7005	91	5	)	)	PUNCT
ejpam-7005	91	6	]	]	PUNCT
ejpam-7005	91	7	,	,	PUNCT
ejpam-7005	91	8	ℏ∆	ℏ∆	ADV
ejpam-7005	91	9	−δn	−δn	NUM
ejpam-7005	91	10	t0+(1−δn)ℏ	t0+(1−δn)ℏ	NUM
ejpam-7005	91	11	c	c	NOUN
ejpam-7005	91	12	ℏ	ℏ	PROPN
ejpam-7005	91	13	∆	∆	PROPN
ejpam-7005	91	14	δn	δn	PROPN
ejpam-7005	91	15	t0	t0	PROPN
ejpam-7005	91	16	vi(t	vi(t	PUNCT
ejpam-7005	91	17	)	)	PUNCT
ejpam-7005	91	18	=	=	PRON
ejpam-7005	91	19	ℏ∆	ℏ∆	X
ejpam-7005	91	20	−δn	−δn	NUM
ejpam-7005	91	21	t0+(1−δn)ℏ	t0+(1−δn)ℏ	PROPN
ejpam-7005	91	22	[	[	PUNCT
ejpam-7005	91	23	d2	d2	PROPN
ejpam-7005	91	24	∆2	∆2	PROPN
ejpam-7005	91	25	x	x	PROPN
ejpam-7005	91	26	∆2vi−1(t+	∆2vi−1(t+	PROPN
ejpam-7005	91	27	ℏδn	ℏδn	PROPN
ejpam-7005	91	28	)	)	PUNCT
ejpam-7005	92	1	+	+	ADP
ejpam-7005	92	2	g	g	PROPN
ejpam-7005	92	3	(	(	PUNCT
ejpam-7005	92	4	·	·	PUNCT
ejpam-7005	92	5	)	)	PUNCT
ejpam-7005	92	6	]	]	PUNCT
ejpam-7005	92	7	,	,	PUNCT
ejpam-7005	92	8	(	(	PUNCT
ejpam-7005	92	9	17	17	NUM
ejpam-7005	92	10	)	)	PUNCT
ejpam-7005	92	11	where	where	SCONJ
ejpam-7005	92	12	(	(	PUNCT
ejpam-7005	92	13	·	·	PUNCT
ejpam-7005	92	14	)	)	PUNCT
ejpam-7005	92	15	=	=	PRON
ejpam-7005	93	1	(	(	PUNCT
ejpam-7005	93	2	ui(t+	ui(t+	PROPN
ejpam-7005	93	3	ℏδn	ℏδn	PROPN
ejpam-7005	93	4	)	)	PUNCT
ejpam-7005	93	5	,	,	PUNCT
ejpam-7005	93	6	vi(t+	vi(t+	PROPN
ejpam-7005	93	7	ℏδn	ℏδn	PROPN
ejpam-7005	93	8	)	)	PUNCT
ejpam-7005	93	9	)	)	PUNCT
ejpam-7005	93	10	.	.	PUNCT
ejpam-7005	94	1	by	by	ADP
ejpam-7005	94	2	definition	definition	NOUN
ejpam-7005	94	3	1	1	NUM
ejpam-7005	94	4	and	and	CCONJ
ejpam-7005	94	5	lemma	lemma	PROPN
ejpam-7005	94	6	1	1	NUM
ejpam-7005	94	7	,	,	PUNCT
ejpam-7005	94	8	we	we	PRON
ejpam-7005	94	9	obtain:	obtain:	VERB
ejpam-7005	94	10	ui(t)−	ui(t)−	ADJ
ejpam-7005	94	11	ϕ1,i	ϕ1,i	PUNCT
ejpam-7005	94	12	=	=	SYM
ejpam-7005	94	13	ℏ	ℏ	PRON
ejpam-7005	94	14	γ(δn	γ(δn	PROPN
ejpam-7005	94	15	)	)	PUNCT
ejpam-7005	94	16	t	t	PROPN
ejpam-7005	94	17	ℏ−δn∑	ℏ−δn∑	PROPN
ejpam-7005	94	18	s=	s=	VERB
ejpam-7005	94	19	t0	t0	PROPN
ejpam-7005	94	20	ℏ	ℏ	PROPN
ejpam-7005	94	21	+1−δn	+1−δn	NOUN
ejpam-7005	94	22	(	(	PUNCT
ejpam-7005	94	23	t−	t−	PROPN
ejpam-7005	94	24	σ(sℏ))δ	σ(sℏ))δ	PROPN
ejpam-7005	94	25	n−1	n−1	PROPN
ejpam-7005	94	26	ℏ	ℏ	PROPN
ejpam-7005	94	27	[	[	PUNCT
ejpam-7005	94	28	d1	d1	PROPN
ejpam-7005	94	29	∆2	∆2	PROPN
ejpam-7005	94	30	x	x	PROPN
ejpam-7005	94	31	∆2ui−1(sℏ+	∆2ui−1(sℏ+	ADJ
ejpam-7005	94	32	ℏδn	ℏδn	PROPN
ejpam-7005	94	33	)	)	PUNCT
ejpam-7005	95	1	+	+	NUM
ejpam-7005	95	2	f	f	X
ejpam-7005	95	3	(	(	PUNCT
ejpam-7005	95	4	·	·	PUNCT
ejpam-7005	95	5	)	)	PUNCT
ejpam-7005	95	6	]	]	PUNCT
ejpam-7005	95	7	,	,	PUNCT
ejpam-7005	95	8	vi(t)−	vi(t)−	PROPN
ejpam-7005	95	9	ϕ2,i	ϕ2,i	NOUN
ejpam-7005	95	10	=	=	SYM
ejpam-7005	95	11	ℏ	ℏ	PRON
ejpam-7005	95	12	γ(δn	γ(δn	PROPN
ejpam-7005	95	13	)	)	PUNCT
ejpam-7005	95	14	t	t	PROPN
ejpam-7005	95	15	ℏ−δn∑	ℏ−δn∑	PROPN
ejpam-7005	95	16	s=	s=	VERB
ejpam-7005	95	17	t0	t0	PROPN
ejpam-7005	95	18	ℏ	ℏ	PROPN
ejpam-7005	95	19	+1−δn	+1−δn	NOUN
ejpam-7005	95	20	(	(	PUNCT
ejpam-7005	95	21	t−	t−	PROPN
ejpam-7005	95	22	σ(sℏ))δ	σ(sℏ))δ	PROPN
ejpam-7005	95	23	n−1	n−1	PROPN
ejpam-7005	95	24	ℏ	ℏ	PROPN
ejpam-7005	95	25	[	[	PUNCT
ejpam-7005	95	26	d2	d2	PROPN
ejpam-7005	95	27	∆2	∆2	PROPN
ejpam-7005	95	28	x	x	PROPN
ejpam-7005	95	29	∆2vi−1(sℏ+	∆2vi−1(sℏ+	PROPN
ejpam-7005	95	30	ℏδn	ℏδn	PROPN
ejpam-7005	95	31	)	)	PUNCT
ejpam-7005	96	1	+	+	PROPN
ejpam-7005	96	2	g	g	PROPN
ejpam-7005	96	3	(	(	PUNCT
ejpam-7005	96	4	·	·	PUNCT
ejpam-7005	96	5	)	)	PUNCT
ejpam-7005	96	6	]	]	PUNCT
ejpam-7005	96	7	,	,	PUNCT
ejpam-7005	96	8	(	(	PUNCT
ejpam-7005	96	9	18	18	NUM
ejpam-7005	96	10	)	)	PUNCT
ejpam-7005	96	11	n.	n.	NOUN
ejpam-7005	96	12	anakira	anakira	PROPN
ejpam-7005	96	13	et	et	PROPN
ejpam-7005	96	14	al	al	PROPN
ejpam-7005	96	15	.	.	PUNCT
ejpam-7005	96	16	/	/	SYM
ejpam-7005	96	17	eur	eur	PROPN
ejpam-7005	96	18	.	.	PUNCT
ejpam-7005	97	1	j.	j.	PROPN
ejpam-7005	97	2	pure	pure	PROPN
ejpam-7005	97	3	appl	appl	PROPN
ejpam-7005	97	4	.	.	PROPN
ejpam-7005	97	5	math	math	PROPN
ejpam-7005	97	6	,	,	PUNCT
ejpam-7005	97	7	18	18	NUM
ejpam-7005	97	8	(	(	PUNCT
ejpam-7005	97	9	4	4	NUM
ejpam-7005	97	10	)	)	PUNCT
ejpam-7005	97	11	(	(	PUNCT
ejpam-7005	97	12	2025	2025	NUM
ejpam-7005	97	13	)	)	PUNCT
ejpam-7005	97	14	,	,	PUNCT
ejpam-7005	97	15	7005	7005	NUM
ejpam-7005	97	16	6	6	NUM
ejpam-7005	97	17	of	of	ADP
ejpam-7005	97	18	17	17	NUM
ejpam-7005	97	19	where	where	SCONJ
ejpam-7005	97	20	(	(	PUNCT
ejpam-7005	97	21	t−	t−	PROPN
ejpam-7005	97	22	σ(sℏ))δ	σ(sℏ))δ	PROPN
ejpam-7005	97	23	n−1	n−1	PROPN
ejpam-7005	97	24	ℏ	ℏ	NOUN
ejpam-7005	97	25	=	=	SYM
ejpam-7005	97	26	ℏδn−1	ℏδn−1	PROPN
ejpam-7005	97	27	γ	γ	X
ejpam-7005	97	28	(	(	PUNCT
ejpam-7005	97	29	t	t	PROPN
ejpam-7005	97	30	ℏ	ℏ	PROPN
ejpam-7005	97	31	−	−	PROPN
ejpam-7005	97	32	s	s	PART
ejpam-7005	97	33	)	)	PUNCT
ejpam-7005	97	34	γ	γ	PROPN
ejpam-7005	97	35	(	(	PUNCT
ejpam-7005	97	36	t	t	PROPN
ejpam-7005	97	37	ℏ	ℏ	PROPN
ejpam-7005	97	38	−	−	PROPN
ejpam-7005	97	39	s−	s−	PROPN
ejpam-7005	97	40	δn	δn	NOUN
ejpam-7005	97	41	+	+	CCONJ
ejpam-7005	97	42	1	1	NUM
ejpam-7005	97	43	)	)	PUNCT
ejpam-7005	97	44	.	.	PUNCT
ejpam-7005	98	1	substituting	substitute	VERB
ejpam-7005	98	2	this	this	DET
ejpam-7005	98	3	yields	yield	NOUN
ejpam-7005	98	4	:	:	PUNCT
ejpam-7005	98	5			NUM
ejpam-7005	98	6	ui(t	ui(t	NOUN
ejpam-7005	98	7	)	)	PUNCT
ejpam-7005	98	8	=	=	SYM
ejpam-7005	99	1	ϕ1,i	ϕ1,i	PROPN
ejpam-7005	99	2	+	+	CCONJ
ejpam-7005	99	3	ℏδn	ℏδn	PROPN
ejpam-7005	99	4	γ(δn	γ(δn	NOUN
ejpam-7005	99	5	)	)	PUNCT
ejpam-7005	99	6	t	t	PROPN
ejpam-7005	99	7	ℏ−δn∑	ℏ−δn∑	PROPN
ejpam-7005	99	8	s=	s=	VERB
ejpam-7005	99	9	t0	t0	PROPN
ejpam-7005	99	10	ℏ	ℏ	PROPN
ejpam-7005	99	11	+1−δn	+1−δn	NOUN
ejpam-7005	99	12	γ	γ	X
ejpam-7005	99	13	(	(	PUNCT
ejpam-7005	99	14	t	t	PROPN
ejpam-7005	99	15	ℏ	ℏ	PROPN
ejpam-7005	99	16	−	−	PROPN
ejpam-7005	99	17	s	s	PART
ejpam-7005	99	18	)	)	PUNCT
ejpam-7005	99	19	γ	γ	PROPN
ejpam-7005	99	20	(	(	PUNCT
ejpam-7005	99	21	t	t	PROPN
ejpam-7005	99	22	ℏ	ℏ	PROPN
ejpam-7005	99	23	−	−	PROPN
ejpam-7005	99	24	s−	s−	PROPN
ejpam-7005	99	25	δn	δn	NOUN
ejpam-7005	99	26	+	+	CCONJ
ejpam-7005	99	27	1	1	NUM
ejpam-7005	99	28	)	)	PUNCT
ejpam-7005	100	1	[	[	PUNCT
ejpam-7005	100	2	d1	d1	PROPN
ejpam-7005	100	3	∆2	∆2	PROPN
ejpam-7005	100	4	x	x	PROPN
ejpam-7005	100	5	∆2ui−1(sℏ+	∆2ui−1(sℏ+	ADJ
ejpam-7005	100	6	ℏδn	ℏδn	PROPN
ejpam-7005	100	7	)	)	PUNCT
ejpam-7005	100	8	+	+	NUM
ejpam-7005	100	9	f	f	X
ejpam-7005	100	10	(	(	PUNCT
ejpam-7005	100	11	·	·	PUNCT
ejpam-7005	100	12	)	)	PUNCT
ejpam-7005	100	13	]	]	PUNCT
ejpam-7005	100	14	,	,	PUNCT
ejpam-7005	100	15	vi(t	vi(t	PUNCT
ejpam-7005	100	16	)	)	PUNCT
ejpam-7005	100	17	=	=	PUNCT
ejpam-7005	101	1	ϕ2,i	ϕ2,i	PROPN
ejpam-7005	101	2	+	+	CCONJ
ejpam-7005	101	3	ℏδn	ℏδn	PROPN
ejpam-7005	101	4	γ(δn	γ(δn	NOUN
ejpam-7005	101	5	)	)	PUNCT
ejpam-7005	101	6	t	t	PROPN
ejpam-7005	101	7	ℏ−δn∑	ℏ−δn∑	PROPN
ejpam-7005	101	8	s=	s=	VERB
ejpam-7005	101	9	t0	t0	PROPN
ejpam-7005	101	10	ℏ	ℏ	PROPN
ejpam-7005	101	11	+1−δn	+1−δn	NOUN
ejpam-7005	101	12	γ	γ	X
ejpam-7005	101	13	(	(	PUNCT
ejpam-7005	101	14	t	t	PROPN
ejpam-7005	101	15	ℏ	ℏ	PROPN
ejpam-7005	101	16	−	−	PROPN
ejpam-7005	101	17	s	s	PART
ejpam-7005	101	18	)	)	PUNCT
ejpam-7005	101	19	γ	γ	PROPN
ejpam-7005	101	20	(	(	PUNCT
ejpam-7005	101	21	t	t	PROPN
ejpam-7005	101	22	ℏ	ℏ	PROPN
ejpam-7005	101	23	−	−	PROPN
ejpam-7005	101	24	s−	s−	PROPN
ejpam-7005	101	25	δn	δn	NOUN
ejpam-7005	101	26	+	+	CCONJ
ejpam-7005	101	27	1	1	NUM
ejpam-7005	101	28	)	)	PUNCT
ejpam-7005	101	29	[	[	PUNCT
ejpam-7005	101	30	d2	d2	PROPN
ejpam-7005	101	31	∆2	∆2	PROPN
ejpam-7005	101	32	x	x	PROPN
ejpam-7005	101	33	∆2vi−1(sℏ+	∆2vi−1(sℏ+	PROPN
ejpam-7005	101	34	ℏδn	ℏδn	PROPN
ejpam-7005	101	35	)	)	PUNCT
ejpam-7005	102	1	+	+	PROPN
ejpam-7005	102	2	g	g	PROPN
ejpam-7005	102	3	(	(	PUNCT
ejpam-7005	102	4	·	·	PUNCT
ejpam-7005	102	5	)	)	PUNCT
ejpam-7005	102	6	]	]	PUNCT
ejpam-7005	103	1	,	,	PUNCT
ejpam-7005	103	2	(	(	PUNCT
ejpam-7005	103	3	19	19	NUM
ejpam-7005	103	4	)	)	PUNCT
ejpam-7005	103	5	where	where	SCONJ
ejpam-7005	103	6	f	f	PROPN
ejpam-7005	103	7	(	(	PUNCT
ejpam-7005	103	8	·	·	PUNCT
ejpam-7005	103	9	)	)	PUNCT
ejpam-7005	103	10	=	=	SYM
ejpam-7005	104	1	f	f	PROPN
ejpam-7005	104	2	(	(	PUNCT
ejpam-7005	104	3	ui(sℏ+	ui(sℏ+	PROPN
ejpam-7005	104	4	ℏδn	ℏδn	PROPN
ejpam-7005	104	5	)	)	PUNCT
ejpam-7005	104	6	,	,	PUNCT
ejpam-7005	104	7	vi(sℏ+	vi(sℏ+	PROPN
ejpam-7005	104	8	ℏδn	ℏδn	PROPN
ejpam-7005	104	9	)	)	PUNCT
ejpam-7005	104	10	)	)	PUNCT
ejpam-7005	104	11	and	and	CCONJ
ejpam-7005	104	12	similarly	similarly	ADV
ejpam-7005	104	13	for	for	ADP
ejpam-7005	104	14	g.	g.	PROPN
ejpam-7005	104	15	then,	then,	NUM
ejpam-7005	104	16	ui(t	ui(t	NOUN
ejpam-7005	104	17	)	)	PUNCT
ejpam-7005	104	18	=	=	SYM
ejpam-7005	105	1	ϕ1,i	ϕ1,i	PROPN
ejpam-7005	105	2	+	+	CCONJ
ejpam-7005	105	3	ℏδn	ℏδn	PROPN
ejpam-7005	105	4	γ(δn	γ(δn	NOUN
ejpam-7005	105	5	)	)	PUNCT
ejpam-7005	105	6	t	t	PROPN
ejpam-7005	105	7	ℏ−δn∑	ℏ−δn∑	PROPN
ejpam-7005	105	8	s=	s=	VERB
ejpam-7005	105	9	t0	t0	PROPN
ejpam-7005	105	10	ℏ	ℏ	PROPN
ejpam-7005	105	11	+1−δn	+1−δn	NOUN
ejpam-7005	105	12	γ	γ	X
ejpam-7005	105	13	(	(	PUNCT
ejpam-7005	105	14	t	t	PROPN
ejpam-7005	105	15	ℏ	ℏ	PROPN
ejpam-7005	105	16	−	−	PROPN
ejpam-7005	105	17	s	s	PART
ejpam-7005	105	18	)	)	PUNCT
ejpam-7005	105	19	γ	γ	PROPN
ejpam-7005	105	20	(	(	PUNCT
ejpam-7005	105	21	t	t	PROPN
ejpam-7005	105	22	ℏ	ℏ	PROPN
ejpam-7005	105	23	−	−	PROPN
ejpam-7005	105	24	s−	s−	PROPN
ejpam-7005	105	25	δn	δn	NOUN
ejpam-7005	105	26	+	+	CCONJ
ejpam-7005	105	27	1	1	X
ejpam-7005	105	28	)	)	PUNCT
ejpam-7005	105	29	×	×	NOUN
ejpam-7005	105	30	[	[	PUNCT
ejpam-7005	105	31	d1	d1	PROPN
ejpam-7005	105	32	∆2	∆2	X
ejpam-7005	105	33	x	x	PROPN
ejpam-7005	105	34	(	(	PUNCT
ejpam-7005	105	35	ui−1(sℏ+	ui−1(sℏ+	PROPN
ejpam-7005	105	36	ℏδn)−	ℏδn)−	PROPN
ejpam-7005	105	37	2ui(sℏ+	2ui(sℏ+	PROPN
ejpam-7005	105	38	ℏδn	ℏδn	PROPN
ejpam-7005	105	39	)	)	PUNCT
ejpam-7005	105	40	+	+	CCONJ
ejpam-7005	105	41	ui+1(sℏ+	ui+1(sℏ+	ADJ
ejpam-7005	105	42	ℏδn	ℏδn	PROPN
ejpam-7005	105	43	)	)	PUNCT
ejpam-7005	105	44	)	)	PUNCT
ejpam-7005	105	45	−u3i	−u3i	PUNCT
ejpam-7005	106	1	(	(	PUNCT
ejpam-7005	106	2	sℏ+	sℏ+	ADJ
ejpam-7005	106	3	ℏδn	ℏδn	PROPN
ejpam-7005	106	4	)	)	PUNCT
ejpam-7005	107	1	+	+	CCONJ
ejpam-7005	107	2	(	(	PUNCT
ejpam-7005	107	3	β	β	X
ejpam-7005	107	4	+	+	NUM
ejpam-7005	107	5	1)u2i	1)u2i	NUM
ejpam-7005	107	6	(	(	PUNCT
ejpam-7005	107	7	sℏ+	sℏ+	ADJ
ejpam-7005	107	8	ℏδn)−	ℏδn)−	PART
ejpam-7005	107	9	βui(sℏ+	βui(sℏ+	PROPN
ejpam-7005	107	10	ℏδn)−	ℏδn)−	PROPN
ejpam-7005	107	11	vi(sℏ+	vi(sℏ+	PROPN
ejpam-7005	107	12	ℏδn	ℏδn	PROPN
ejpam-7005	107	13	)	)	PUNCT
ejpam-7005	107	14	]	]	PUNCT
ejpam-7005	107	15	,	,	PUNCT
ejpam-7005	107	16	vi(t	vi(t	PUNCT
ejpam-7005	107	17	)	)	PUNCT
ejpam-7005	107	18	=	=	PUNCT
ejpam-7005	108	1	ϕ2,i	ϕ2,i	PROPN
ejpam-7005	108	2	+	+	CCONJ
ejpam-7005	108	3	ℏδn	ℏδn	PROPN
ejpam-7005	108	4	γ(δn	γ(δn	NOUN
ejpam-7005	108	5	)	)	PUNCT
ejpam-7005	108	6	t	t	PROPN
ejpam-7005	108	7	ℏ−δn∑	ℏ−δn∑	PROPN
ejpam-7005	108	8	s=	s=	VERB
ejpam-7005	108	9	t0	t0	PROPN
ejpam-7005	108	10	ℏ	ℏ	PROPN
ejpam-7005	108	11	+1−δn	+1−δn	NOUN
ejpam-7005	108	12	γ	γ	X
ejpam-7005	108	13	(	(	PUNCT
ejpam-7005	108	14	t	t	PROPN
ejpam-7005	108	15	ℏ	ℏ	PROPN
ejpam-7005	108	16	−	−	PROPN
ejpam-7005	108	17	s	s	PART
ejpam-7005	108	18	)	)	PUNCT
ejpam-7005	108	19	γ	γ	PROPN
ejpam-7005	108	20	(	(	PUNCT
ejpam-7005	108	21	t	t	PROPN
ejpam-7005	108	22	ℏ	ℏ	PROPN
ejpam-7005	108	23	−	−	PROPN
ejpam-7005	108	24	s−	s−	PROPN
ejpam-7005	108	25	δn	δn	NOUN
ejpam-7005	108	26	+	+	CCONJ
ejpam-7005	108	27	1	1	X
ejpam-7005	108	28	)	)	PUNCT
ejpam-7005	108	29	×	×	NOUN
ejpam-7005	108	30	[	[	PUNCT
ejpam-7005	108	31	d2	d2	PROPN
ejpam-7005	108	32	∆2	∆2	PROPN
ejpam-7005	108	33	x	x	PROPN
ejpam-7005	108	34	(	(	PUNCT
ejpam-7005	108	35	vi−1(sℏ+	vi−1(sℏ+	X
ejpam-7005	108	36	ℏδn)−	ℏδn)−	PROPN
ejpam-7005	108	37	2vi(sℏ+	2vi(sℏ+	PROPN
ejpam-7005	108	38	ℏδn	ℏδn	PROPN
ejpam-7005	108	39	)	)	PUNCT
ejpam-7005	108	40	+	+	CCONJ
ejpam-7005	108	41	vi+1(sℏ+	vi+1(sℏ+	PROPN
ejpam-7005	108	42	ℏδn	ℏδn	PROPN
ejpam-7005	108	43	)	)	PUNCT
ejpam-7005	108	44	)	)	PUNCT
ejpam-7005	109	1	+	+	PUNCT
ejpam-7005	109	2	ϵui(sℏ+	ϵui(sℏ+	PROPN
ejpam-7005	109	3	ℏδn)−	ℏδn)−	PROPN
ejpam-7005	109	4	ϵγvi(sℏ+	ϵγvi(sℏ+	PROPN
ejpam-7005	109	5	ℏδn	ℏδn	PROPN
ejpam-7005	109	6	)	)	PUNCT
ejpam-7005	109	7	]	]	PUNCT
ejpam-7005	109	8	.	.	PUNCT
ejpam-7005	110	1	(	(	PUNCT
ejpam-7005	110	2	20	20	NUM
ejpam-7005	110	3	)	)	PUNCT
ejpam-7005	110	4	the	the	DET
ejpam-7005	110	5	solution	solution	NOUN
ejpam-7005	110	6	becomes:	becomes:	VERB
ejpam-7005	110	7	uni	uni	PROPN
ejpam-7005	111	1	=	=	PUNCT
ejpam-7005	111	2	ϕ1,i	ϕ1,i	PROPN
ejpam-7005	111	3	+	+	CCONJ
ejpam-7005	111	4	ℏδn	ℏδn	PROPN
ejpam-7005	111	5	γ(δn	γ(δn	NOUN
ejpam-7005	111	6	)	)	PUNCT
ejpam-7005	112	1	n∑	n∑	PUNCT
ejpam-7005	113	1	j=1	j=1	PROPN
ejpam-7005	113	2	w	w	PROPN
ejpam-7005	113	3	(	(	PUNCT
ejpam-7005	113	4	δn	δn	NOUN
ejpam-7005	113	5	)	)	PUNCT
ejpam-7005	113	6	n−j	n−j	ADV
ejpam-7005	113	7	[	[	PUNCT
ejpam-7005	113	8	d1	d1	PROPN
ejpam-7005	113	9	∆2	∆2	PROPN
ejpam-7005	113	10	x	x	PROPN
ejpam-7005	113	11	∆2u	∆2u	PROPN
ejpam-7005	113	12	j	j	PROPN
ejpam-7005	113	13	i−1	i−1	PROPN
ejpam-7005	113	14	−	−	PROPN
ejpam-7005	113	15	(	(	PUNCT
ejpam-7005	113	16	u	u	NOUN
ejpam-7005	113	17	j	j	PROPN
ejpam-7005	113	18	i	i	NOUN
ejpam-7005	113	19	)	)	PUNCT
ejpam-7005	113	20	3	3	X
ejpam-7005	113	21	+	+	CCONJ
ejpam-7005	113	22	(	(	PUNCT
ejpam-7005	113	23	β	β	X
ejpam-7005	113	24	+	+	NOUN
ejpam-7005	113	25	1	1	X
ejpam-7005	113	26	)	)	PUNCT
ejpam-7005	113	27	(	(	PUNCT
ejpam-7005	113	28	u	u	NOUN
ejpam-7005	113	29	j	j	PROPN
ejpam-7005	113	30	i	i	NOUN
ejpam-7005	113	31	)	)	PUNCT
ejpam-7005	113	32	2	2	NUM
ejpam-7005	113	33	−	−	PROPN
ejpam-7005	113	34	β	β	SYM
ejpam-7005	113	35	u	u	NOUN
ejpam-7005	113	36	j	j	PROPN
ejpam-7005	113	37	i	i	PRON
ejpam-7005	113	38	−	−	VERB
ejpam-7005	113	39	v	v	INTJ
ejpam-7005	113	40	j	j	PROPN
ejpam-7005	114	1	i	i	PRON
ejpam-7005	114	2	]	]	PUNCT
ejpam-7005	114	3	,	,	PUNCT
ejpam-7005	114	4	vni	vni	NOUN
ejpam-7005	114	5	=	=	SYM
ejpam-7005	115	1	ϕ2,i	ϕ2,i	PROPN
ejpam-7005	115	2	+	+	CCONJ
ejpam-7005	115	3	ℏδn	ℏδn	PROPN
ejpam-7005	115	4	γ(δn	γ(δn	NOUN
ejpam-7005	115	5	)	)	PUNCT
ejpam-7005	116	1	n∑	n∑	PUNCT
ejpam-7005	116	2	j=1	j=1	PROPN
ejpam-7005	116	3	w	w	PROPN
ejpam-7005	116	4	(	(	PUNCT
ejpam-7005	116	5	δn	δn	NOUN
ejpam-7005	116	6	)	)	PUNCT
ejpam-7005	116	7	n−j	n−j	ADV
ejpam-7005	116	8	[	[	PUNCT
ejpam-7005	116	9	d2	d2	PROPN
ejpam-7005	116	10	∆2	∆2	PROPN
ejpam-7005	116	11	x	x	SYM
ejpam-7005	116	12	∆2v	∆2v	PROPN
ejpam-7005	117	1	j	j	PROPN
ejpam-7005	117	2	i−1	i−1	PROPN
ejpam-7005	117	3	+	+	PROPN
ejpam-7005	117	4	ϵ	ϵ	X
ejpam-7005	117	5	u	u	X
ejpam-7005	117	6	j	j	PROPN
ejpam-7005	117	7	i	i	PRON
ejpam-7005	117	8	−	−	VERB
ejpam-7005	118	1	ϵγ	ϵγ	INTJ
ejpam-7005	119	1	v	v	INTJ
ejpam-7005	119	2	j	j	NOUN
ejpam-7005	120	1	i	i	PRON
ejpam-7005	120	2	]	]	PUNCT
ejpam-7005	120	3	.	.	PUNCT
ejpam-7005	121	1	(	(	PUNCT
ejpam-7005	121	2	21	21	NUM
ejpam-7005	121	3	)	)	PUNCT
ejpam-7005	121	4	3	3	NUM
ejpam-7005	121	5	.	.	X
ejpam-7005	121	6	main	main	ADJ
ejpam-7005	121	7	results	result	NOUN
ejpam-7005	121	8	lemma	lemma	PROPN
ejpam-7005	121	9	3	3	X
ejpam-7005	121	10	.	.	PUNCT
ejpam-7005	122	1	the	the	DET
ejpam-7005	122	2	linear	linear	ADJ
ejpam-7005	122	3	fractional	fractional	ADJ
ejpam-7005	122	4	difference	difference	NOUN
ejpam-7005	122	5	equation	equation	NOUN
ejpam-7005	122	6	c	c	PROPN
ejpam-7005	122	7	ℏ	ℏ	PROPN
ejpam-7005	122	8	∆	∆	PROPN
ejpam-7005	122	9	δ(t	δ(t	NOUN
ejpam-7005	122	10	)	)	PUNCT
ejpam-7005	122	11	t0	t0	PROPN
ejpam-7005	122	12	κ(t	κ(t	PROPN
ejpam-7005	122	13	)	)	PUNCT
ejpam-7005	122	14	=	=	SYM
ejpam-7005	123	1	λκ	λκ	X
ejpam-7005	123	2	(	(	PUNCT
ejpam-7005	123	3	t+	t+	NOUN
ejpam-7005	123	4	δ(t)ℏ	δ(t)ℏ	PROPN
ejpam-7005	123	5	)	)	PUNCT
ejpam-7005	123	6	,	,	PUNCT
ejpam-7005	123	7			NOUN
ejpam-7005	123	8	0	0	PUNCT
ejpam-7005	123	9	<	<	X
ejpam-7005	123	10	δ(t	δ(t	PROPN
ejpam-7005	123	11	)	)	PUNCT
ejpam-7005	123	12	≤	≤	NUM
ejpam-7005	123	13	1	1	NUM
ejpam-7005	123	14	,	,	PUNCT
ejpam-7005	123	15	|λ|	|λ|	ADP
ejpam-7005	123	16	<	<	X
ejpam-7005	123	17	1	1	NUM
ejpam-7005	123	18	,	,	PUNCT
ejpam-7005	123	19	t	t	PROPN
ejpam-7005	123	20	∈	∈	PROPN
ejpam-7005	123	21	(	(	PUNCT
ejpam-7005	123	22	ℏn)t0	ℏn)t0	PROPN
ejpam-7005	123	23	,	,	PUNCT
ejpam-7005	123	24	κ(t0	κ(t0	NOUN
ejpam-7005	123	25	)	)	PUNCT
ejpam-7005	124	1	=	=	SYM
ejpam-7005	124	2	κ0	κ0	PROPN
ejpam-7005	124	3	.	.	PUNCT
ejpam-7005	125	1	(	(	PUNCT
ejpam-7005	125	2	22	22	NUM
ejpam-7005	125	3	)	)	PUNCT
ejpam-7005	125	4	n.	n.	NOUN
ejpam-7005	125	5	anakira	anakira	PROPN
ejpam-7005	125	6	et	et	PROPN
ejpam-7005	125	7	al	al	PROPN
ejpam-7005	125	8	.	.	PUNCT
ejpam-7005	125	9	/	/	SYM
ejpam-7005	125	10	eur	eur	PROPN
ejpam-7005	125	11	.	.	PUNCT
ejpam-7005	126	1	j.	j.	PROPN
ejpam-7005	126	2	pure	pure	PROPN
ejpam-7005	126	3	appl	appl	PROPN
ejpam-7005	126	4	.	.	PROPN
ejpam-7005	126	5	math	math	PROPN
ejpam-7005	126	6	,	,	PUNCT
ejpam-7005	126	7	18	18	NUM
ejpam-7005	126	8	(	(	PUNCT
ejpam-7005	126	9	4	4	NUM
ejpam-7005	126	10	)	)	PUNCT
ejpam-7005	126	11	(	(	PUNCT
ejpam-7005	126	12	2025	2025	NUM
ejpam-7005	126	13	)	)	PUNCT
ejpam-7005	126	14	,	,	PUNCT
ejpam-7005	126	15	7005	7005	NUM
ejpam-7005	126	16	7	7	NUM
ejpam-7005	126	17	of	of	ADP
ejpam-7005	126	18	17	17	NUM
ejpam-7005	126	19	admits	admit	VERB
ejpam-7005	126	20	a	a	DET
ejpam-7005	126	21	unique	unique	ADJ
ejpam-7005	126	22	solution	solution	NOUN
ejpam-7005	126	23	given	give	VERB
ejpam-7005	126	24	by	by	ADP
ejpam-7005	126	25	the	the	DET
ejpam-7005	126	26	discrete	discrete	ADJ
ejpam-7005	126	27	mlf	mlf	NOUN
ejpam-7005	126	28	:	:	PUNCT
ejpam-7005	126	29	κ(t	κ(t	X
ejpam-7005	126	30	)	)	PUNCT
ejpam-7005	127	1	=	=	SYM
ejpam-7005	127	2	κ0eδ(t)(λ	κ0eδ(t)(λ	PROPN
ejpam-7005	127	3	,	,	PUNCT
ejpam-7005	127	4	t	t	PROPN
ejpam-7005	127	5	)	)	PUNCT
ejpam-7005	127	6	=	=	PUNCT
ejpam-7005	128	1	κ0	κ0	VERB
ejpam-7005	128	2	∞∑	∞∑	NUM
ejpam-7005	128	3	j=0	j=0	PROPN
ejpam-7005	128	4	λj	λj	PROPN
ejpam-7005	128	5	(	(	PUNCT
ejpam-7005	128	6	t	t	NOUN
ejpam-7005	128	7	ℏ	ℏ	X
ejpam-7005	128	8	−	−	PROPN
ejpam-7005	129	1	(	(	PUNCT
ejpam-7005	129	2	t0	t0	NOUN
ejpam-7005	129	3	ℏ	ℏ	PROPN
ejpam-7005	129	4	+	+	CCONJ
ejpam-7005	129	5	1	1	NUM
ejpam-7005	129	6	)	)	PUNCT
ejpam-7005	129	7	+	+	CCONJ
ejpam-7005	129	8	jδ(t	jδ(t	NOUN
ejpam-7005	129	9	)	)	PUNCT
ejpam-7005	129	10	)	)	PUNCT
ejpam-7005	130	1	(	(	PUNCT
ejpam-7005	130	2	jδ(t	jδ(t	NOUN
ejpam-7005	130	3	)	)	PUNCT
ejpam-7005	130	4	)	)	PUNCT
ejpam-7005	131	1	ℏ	ℏ	PROPN
ejpam-7005	131	2	γ(jδ(t	γ(jδ(t	PROPN
ejpam-7005	131	3	)	)	PUNCT
ejpam-7005	131	4	+	+	CCONJ
ejpam-7005	131	5	1	1	NUM
ejpam-7005	131	6	)	)	PUNCT
ejpam-7005	131	7	.	.	PUNCT
ejpam-7005	132	1	(	(	PUNCT
ejpam-7005	132	2	23	23	X
ejpam-7005	132	3	)	)	PUNCT
ejpam-7005	132	4	proof	proof	NOUN
ejpam-7005	132	5	2	2	NUM
ejpam-7005	132	6	.	.	PUNCT
ejpam-7005	133	1	the	the	DET
ejpam-7005	133	2	solution	solution	NOUN
ejpam-7005	133	3	is	be	AUX
ejpam-7005	133	4	derived	derive	VERB
ejpam-7005	133	5	using	use	VERB
ejpam-7005	133	6	picard	picard	NOUN
ejpam-7005	133	7	iteration	iteration	NOUN
ejpam-7005	133	8	.	.	PUNCT
ejpam-7005	134	1	define	define	VERB
ejpam-7005	134	2	the	the	DET
ejpam-7005	134	3	recurrence	recurrence	NOUN
ejpam-7005	134	4	:	:	PUNCT
ejpam-7005	134	5	κk+1(t	κk+1(t	NUM
ejpam-7005	134	6	)	)	PUNCT
ejpam-7005	135	1	=	=	SYM
ejpam-7005	136	1	κ0	κ0	NOUN
ejpam-7005	136	2	+	+	CCONJ
ejpam-7005	136	3	λ	λ	X
ejpam-7005	136	4	ℏ∆	ℏ∆	ADJ
ejpam-7005	136	5	−δ(t	−δ(t	PROPN
ejpam-7005	136	6	)	)	PUNCT
ejpam-7005	136	7	t0+(1−δ(t))ℏκk(s+	t0+(1−δ(t))ℏκk(s+	PROPN
ejpam-7005	136	8	δ(t)ℏ	δ(t)ℏ	PROPN
ejpam-7005	136	9	)	)	PUNCT
ejpam-7005	137	1	,	,	PUNCT
ejpam-7005	137	2	t	t	PROPN
ejpam-7005	137	3	∈	∈	PROPN
ejpam-7005	137	4	(	(	PUNCT
ejpam-7005	137	5	ℏn)t0	ℏn)t0	PROPN
ejpam-7005	137	6	.	.	PUNCT
ejpam-7005	138	1	(	(	PUNCT
ejpam-7005	138	2	24	24	NUM
ejpam-7005	138	3	)	)	PUNCT
ejpam-7005	138	4	the	the	DET
ejpam-7005	138	5	first	first	ADJ
ejpam-7005	138	6	iterates	iterate	NOUN
ejpam-7005	138	7	are	be	AUX
ejpam-7005	138	8	:	:	PUNCT
ejpam-7005	138	9	κ1(t	κ1(t	X
ejpam-7005	138	10	)	)	PUNCT
ejpam-7005	139	1	=	=	SYM
ejpam-7005	139	2	κ0	κ0	NOUN
ejpam-7005	139	3	+	+	X
ejpam-7005	139	4	λκ0	λκ0	INTJ
ejpam-7005	139	5	(	(	PUNCT
ejpam-7005	139	6	t	t	NOUN
ejpam-7005	139	7	ℏ	ℏ	PROPN
ejpam-7005	139	8	−	−	PROPN
ejpam-7005	140	1	(	(	PUNCT
ejpam-7005	140	2	t0	t0	NOUN
ejpam-7005	140	3	ℏ	ℏ	PROPN
ejpam-7005	140	4	+	+	CCONJ
ejpam-7005	140	5	1	1	NUM
ejpam-7005	140	6	)	)	PUNCT
ejpam-7005	140	7	+	+	CCONJ
ejpam-7005	140	8	δ(t	δ(t	NOUN
ejpam-7005	140	9	)	)	PUNCT
ejpam-7005	140	10	)	)	PUNCT
ejpam-7005	140	11	(	(	PUNCT
ejpam-7005	140	12	δ(t	δ(t	NOUN
ejpam-7005	140	13	)	)	PUNCT
ejpam-7005	140	14	)	)	PUNCT
ejpam-7005	141	1	ℏ	ℏ	PROPN
ejpam-7005	141	2	γ(δ(t	γ(δ(t	PROPN
ejpam-7005	141	3	)	)	PUNCT
ejpam-7005	141	4	+	+	CCONJ
ejpam-7005	141	5	1	1	NUM
ejpam-7005	141	6	)	)	PUNCT
ejpam-7005	141	7	,	,	PUNCT
ejpam-7005	141	8	κ2(t	κ2(t	PROPN
ejpam-7005	141	9	)	)	PUNCT
ejpam-7005	141	10	=	=	SYM
ejpam-7005	142	1	κ0	κ0	NOUN
ejpam-7005	142	2	+	+	X
ejpam-7005	142	3	λκ0	λκ0	INTJ
ejpam-7005	142	4	(	(	PUNCT
ejpam-7005	142	5	t	t	NOUN
ejpam-7005	142	6	ℏ	ℏ	PROPN
ejpam-7005	142	7	−	−	PROPN
ejpam-7005	143	1	(	(	PUNCT
ejpam-7005	143	2	t0	t0	NOUN
ejpam-7005	143	3	ℏ	ℏ	PROPN
ejpam-7005	143	4	+	+	CCONJ
ejpam-7005	143	5	1	1	NUM
ejpam-7005	143	6	)	)	PUNCT
ejpam-7005	143	7	+	+	CCONJ
ejpam-7005	143	8	δ(t	δ(t	NOUN
ejpam-7005	143	9	)	)	PUNCT
ejpam-7005	143	10	)	)	PUNCT
ejpam-7005	143	11	(	(	PUNCT
ejpam-7005	143	12	δ(t	δ(t	NOUN
ejpam-7005	143	13	)	)	PUNCT
ejpam-7005	143	14	)	)	PUNCT
ejpam-7005	144	1	ℏ	ℏ	PROPN
ejpam-7005	144	2	γ(δ(t	γ(δ(t	PROPN
ejpam-7005	144	3	)	)	PUNCT
ejpam-7005	144	4	+	+	CCONJ
ejpam-7005	144	5	1	1	X
ejpam-7005	144	6	)	)	PUNCT
ejpam-7005	144	7	+	+	CCONJ
ejpam-7005	144	8	λ2κ0	λ2κ0	X
ejpam-7005	144	9	(	(	PUNCT
ejpam-7005	144	10	t	t	NOUN
ejpam-7005	144	11	ℏ	ℏ	PROPN
ejpam-7005	144	12	−	−	PROPN
ejpam-7005	145	1	(	(	PUNCT
ejpam-7005	145	2	t0	t0	NOUN
ejpam-7005	145	3	ℏ	ℏ	PROPN
ejpam-7005	145	4	+	+	CCONJ
ejpam-7005	145	5	1	1	NUM
ejpam-7005	145	6	)	)	PUNCT
ejpam-7005	146	1	+	+	CCONJ
ejpam-7005	146	2	2δ(t	2δ(t	NUM
ejpam-7005	146	3	)	)	PUNCT
ejpam-7005	146	4	)	)	PUNCT
ejpam-7005	147	1	(	(	PUNCT
ejpam-7005	147	2	2δ(t	2δ(t	NUM
ejpam-7005	147	3	)	)	PUNCT
ejpam-7005	147	4	)	)	PUNCT
ejpam-7005	148	1	ℏ	ℏ	PROPN
ejpam-7005	148	2	γ(2δ(t	γ(2δ(t	PROPN
ejpam-7005	148	3	)	)	PUNCT
ejpam-7005	149	1	+	+	CCONJ
ejpam-7005	149	2	1	1	NUM
ejpam-7005	149	3	)	)	PUNCT
ejpam-7005	149	4	,	,	PUNCT
ejpam-7005	149	5	...	...	PUNCT
ejpam-7005	149	6	κn(t	κn(t	PUNCT
ejpam-7005	149	7	)	)	PUNCT
ejpam-7005	150	1	=	=	PUNCT
ejpam-7005	151	1	κ0	κ0	PROPN
ejpam-7005	151	2	n∑	n∑	PROPN
ejpam-7005	151	3	k=0	k=0	PROPN
ejpam-7005	151	4	λk	λk	X
ejpam-7005	151	5	(	(	PUNCT
ejpam-7005	151	6	t	t	NOUN
ejpam-7005	151	7	ℏ	ℏ	PROPN
ejpam-7005	151	8	−	−	PROPN
ejpam-7005	152	1	(	(	PUNCT
ejpam-7005	152	2	t0	t0	NOUN
ejpam-7005	152	3	ℏ	ℏ	PROPN
ejpam-7005	152	4	+	+	CCONJ
ejpam-7005	152	5	1	1	NUM
ejpam-7005	152	6	)	)	PUNCT
ejpam-7005	152	7	+	+	CCONJ
ejpam-7005	152	8	kδ(t	kδ(t	NOUN
ejpam-7005	152	9	)	)	PUNCT
ejpam-7005	152	10	)	)	PUNCT
ejpam-7005	152	11	(	(	PUNCT
ejpam-7005	152	12	kδ(t	kδ(t	NOUN
ejpam-7005	152	13	)	)	PUNCT
ejpam-7005	152	14	)	)	PUNCT
ejpam-7005	152	15	ℏ	ℏ	PROPN
ejpam-7005	152	16	γ(kδ(t	γ(kδ(t	PROPN
ejpam-7005	152	17	)	)	PUNCT
ejpam-7005	152	18	+	+	NUM
ejpam-7005	152	19	1	1	NUM
ejpam-7005	152	20	)	)	PUNCT
ejpam-7005	152	21	.	.	PUNCT
ejpam-7005	153	1	to	to	PART
ejpam-7005	153	2	prove	prove	VERB
ejpam-7005	153	3	convergence	convergence	NOUN
ejpam-7005	153	4	,	,	PUNCT
ejpam-7005	153	5	consider	consider	VERB
ejpam-7005	153	6	the	the	DET
ejpam-7005	153	7	general	general	ADJ
ejpam-7005	153	8	term	term	NOUN
ejpam-7005	153	9	:	:	PUNCT
ejpam-7005	153	10	ak	ak	PROPN
ejpam-7005	153	11	=	=	X
ejpam-7005	153	12	λk	λk	PROPN
ejpam-7005	153	13	(	(	PUNCT
ejpam-7005	153	14	t	t	NOUN
ejpam-7005	153	15	ℏ	ℏ	PROPN
ejpam-7005	153	16	−	−	PROPN
ejpam-7005	153	17	(	(	PUNCT
ejpam-7005	153	18	t0	t0	NOUN
ejpam-7005	153	19	ℏ	ℏ	PROPN
ejpam-7005	154	1	+	+	CCONJ
ejpam-7005	154	2	1	1	NUM
ejpam-7005	154	3	)	)	PUNCT
ejpam-7005	154	4	+	+	CCONJ
ejpam-7005	155	1	kδ(t	kδ(t	NOUN
ejpam-7005	155	2	)	)	PUNCT
ejpam-7005	155	3	)	)	PUNCT
ejpam-7005	156	1	(	(	PUNCT
ejpam-7005	156	2	kδ(t	kδ(t	NOUN
ejpam-7005	156	3	)	)	PUNCT
ejpam-7005	156	4	)	)	PUNCT
ejpam-7005	157	1	ℏ	ℏ	PROPN
ejpam-7005	157	2	γ(kδ(t	γ(kδ(t	PROPN
ejpam-7005	157	3	)	)	PUNCT
ejpam-7005	157	4	+	+	NUM
ejpam-7005	157	5	1	1	NUM
ejpam-7005	157	6	)	)	PUNCT
ejpam-7005	157	7	.	.	PUNCT
ejpam-7005	158	1	(	(	PUNCT
ejpam-7005	158	2	25	25	NUM
ejpam-7005	158	3	)	)	PUNCT
ejpam-7005	158	4	using	use	VERB
ejpam-7005	158	5	the	the	DET
ejpam-7005	158	6	beta	beta	ADJ
ejpam-7005	158	7	function	function	NOUN
ejpam-7005	158	8	property	property	NOUN
ejpam-7005	158	9	b(x	b(x	NOUN
ejpam-7005	158	10	,	,	PUNCT
ejpam-7005	158	11	y	y	NOUN
ejpam-7005	158	12	)	)	PUNCT
ejpam-7005	158	13	=	=	SYM
ejpam-7005	158	14	γ(x)γ(y	γ(x)γ(y	PROPN
ejpam-7005	158	15	)	)	PUNCT
ejpam-7005	158	16	γ(x+	γ(x+	PUNCT
ejpam-7005	158	17	y	y	X
ejpam-7005	158	18	)	)	PUNCT
ejpam-7005	158	19	,	,	PUNCT
ejpam-7005	158	20	we	we	PRON
ejpam-7005	158	21	simplify	simplify	VERB
ejpam-7005	158	22	:	:	PUNCT
ejpam-7005	158	23	ak	ak	PROPN
ejpam-7005	158	24	=	=	PROPN
ejpam-7005	158	25	λk	λk	PROPN
ejpam-7005	158	26	kδ(t)b	kδ(t)b	PROPN
ejpam-7005	158	27	(	(	PUNCT
ejpam-7005	158	28	t−t0	t−t0	NUM
ejpam-7005	158	29	ℏ	ℏ	PROPN
ejpam-7005	158	30	,	,	PUNCT
ejpam-7005	158	31	kδ(t	kδ(t	PROPN
ejpam-7005	158	32	)	)	PUNCT
ejpam-7005	158	33	)	)	PUNCT
ejpam-7005	158	34	.	.	PUNCT
ejpam-7005	159	1	(	(	PUNCT
ejpam-7005	159	2	26	26	NUM
ejpam-7005	159	3	)	)	PUNCT
ejpam-7005	159	4	applying	apply	VERB
ejpam-7005	159	5	the	the	DET
ejpam-7005	159	6	d’alembert	d’alembert	NOUN
ejpam-7005	159	7	ratio	ratio	NOUN
ejpam-7005	159	8	test	test	NOUN
ejpam-7005	159	9	and	and	CCONJ
ejpam-7005	159	10	stirling	stirling	PROPN
ejpam-7005	159	11	’s	’s	PART
ejpam-7005	159	12	approximation	approximation	NOUN
ejpam-7005	159	13	:	:	PUNCT
ejpam-7005	159	14	b	b	X
ejpam-7005	159	15	(	(	PUNCT
ejpam-7005	159	16	t−	t−	PROPN
ejpam-7005	159	17	t0	t0	PROPN
ejpam-7005	159	18	ℏ	ℏ	PROPN
ejpam-7005	159	19	,	,	PUNCT
ejpam-7005	159	20	kδ(t	kδ(t	PROPN
ejpam-7005	159	21	)	)	PUNCT
ejpam-7005	159	22	)	)	PUNCT
ejpam-7005	159	23	∼	∼	NOUN
ejpam-7005	159	24	γ	γ	X
ejpam-7005	159	25	(	(	PUNCT
ejpam-7005	159	26	t−	t−	PROPN
ejpam-7005	159	27	t0	t0	PROPN
ejpam-7005	159	28	ℏ	ℏ	PROPN
ejpam-7005	159	29	)	)	PUNCT
ejpam-7005	159	30	(	(	PUNCT
ejpam-7005	159	31	kδ(t))−(t−t0)/ℏ	kδ(t))−(t−t0)/ℏ	X
ejpam-7005	159	32	,	,	PUNCT
ejpam-7005	159	33	(	(	PUNCT
ejpam-7005	159	34	27	27	NUM
ejpam-7005	159	35	)	)	PUNCT
ejpam-7005	159	36	yields	yield	NOUN
ejpam-7005	159	37	:	:	PUNCT
ejpam-7005	159	38	lim	lim	PROPN
ejpam-7005	159	39	k→∞	k→∞	PROPN
ejpam-7005	159	40	∣∣∣∣ak+1	∣∣∣∣ak+1	VERB
ejpam-7005	159	41	ak	ak	PROPN
ejpam-7005	159	42	∣∣∣∣	∣∣∣∣	PROPN
ejpam-7005	159	43	=	=	PROPN
ejpam-7005	159	44	|λ|	|λ|	PROPN
ejpam-7005	159	45	<	<	X
ejpam-7005	159	46	1	1	NUM
ejpam-7005	159	47	.	.	PUNCT
ejpam-7005	160	1	(	(	PUNCT
ejpam-7005	160	2	28	28	NUM
ejpam-7005	160	3	)	)	PUNCT
ejpam-7005	160	4	thus	thus	ADV
ejpam-7005	160	5	,	,	PUNCT
ejpam-7005	160	6	the	the	DET
ejpam-7005	160	7	series	series	NOUN
ejpam-7005	160	8	converges	converge	VERB
ejpam-7005	160	9	absolutely	absolutely	ADV
ejpam-7005	160	10	to	to	ADP
ejpam-7005	160	11	the	the	DET
ejpam-7005	160	12	solution	solution	NOUN
ejpam-7005	160	13	(	(	PUNCT
ejpam-7005	160	14	23	23	NUM
ejpam-7005	160	15	)	)	PUNCT
ejpam-7005	160	16	.	.	PUNCT
ejpam-7005	161	1	n.	n.	PROPN
ejpam-7005	161	2	anakira	anakira	PROPN
ejpam-7005	161	3	et	et	PROPN
ejpam-7005	161	4	al	al	PROPN
ejpam-7005	161	5	.	.	PUNCT
ejpam-7005	161	6	/	/	SYM
ejpam-7005	161	7	eur	eur	PROPN
ejpam-7005	161	8	.	.	PUNCT
ejpam-7005	162	1	j.	j.	PROPN
ejpam-7005	162	2	pure	pure	PROPN
ejpam-7005	162	3	appl	appl	PROPN
ejpam-7005	162	4	.	.	PROPN
ejpam-7005	162	5	math	math	PROPN
ejpam-7005	162	6	,	,	PUNCT
ejpam-7005	162	7	18	18	NUM
ejpam-7005	162	8	(	(	PUNCT
ejpam-7005	162	9	4	4	NUM
ejpam-7005	162	10	)	)	PUNCT
ejpam-7005	162	11	(	(	PUNCT
ejpam-7005	162	12	2025	2025	NUM
ejpam-7005	162	13	)	)	PUNCT
ejpam-7005	162	14	,	,	PUNCT
ejpam-7005	162	15	7005	7005	NUM
ejpam-7005	162	16	8	8	NUM
ejpam-7005	162	17	of	of	ADP
ejpam-7005	162	18	17	17	NUM
ejpam-7005	162	19	definition	definition	NOUN
ejpam-7005	162	20	2	2	NUM
ejpam-7005	162	21	.	.	PUNCT
ejpam-7005	162	22	system	system	NOUN
ejpam-7005	162	23	(	(	PUNCT
ejpam-7005	162	24	6	6	NUM
ejpam-7005	162	25	)	)	PUNCT
ejpam-7005	162	26	is	be	AUX
ejpam-7005	162	27	fts	fts	PROPN
ejpam-7005	162	28	with	with	ADP
ejpam-7005	162	29	respect	respect	NOUN
ejpam-7005	162	30	to	to	ADP
ejpam-7005	162	31	{	{	PUNCT
ejpam-7005	162	32	η	η	PROPN
ejpam-7005	162	33	,	,	PUNCT
ejpam-7005	162	34	ε	ε	PROPN
ejpam-7005	162	35	,	,	PUNCT
ejpam-7005	162	36	j	j	PROPN
ejpam-7005	162	37	}	}	PUNCT
ejpam-7005	162	38	(	(	PUNCT
ejpam-7005	162	39	η	η	X
ejpam-7005	162	40	<	<	X
ejpam-7005	162	41	ε	ε	PROPN
ejpam-7005	162	42	)	)	PUNCT
ejpam-7005	162	43	if	if	SCONJ
ejpam-7005	162	44	∥ϕ1∥c	∥ϕ1∥c	PROPN
ejpam-7005	162	45	+	+	CCONJ
ejpam-7005	162	46	∥ϕ2∥c	∥ϕ2∥c	X
ejpam-7005	162	47	<	<	X
ejpam-7005	162	48	η	η	PROPN
ejpam-7005	162	49	(	(	PUNCT
ejpam-7005	162	50	29	29	NUM
ejpam-7005	162	51	)	)	PUNCT
ejpam-7005	162	52	implies	imply	VERB
ejpam-7005	162	53	∥u(t)∥+	∥u(t)∥+	ADJ
ejpam-7005	162	54	∥v(t)∥	∥v(t)∥	PROPN
ejpam-7005	162	55	<	<	X
ejpam-7005	162	56	ε	ε	PROPN
ejpam-7005	162	57	,	,	PUNCT
ejpam-7005	162	58	∀t	∀t	PROPN
ejpam-7005	162	59	∈	∈	PROPN
ejpam-7005	162	60	j	j	NOUN
ejpam-7005	163	1	=	=	PUNCT
ejpam-7005	164	1	[	[	X
ejpam-7005	164	2	t0	t0	PROPN
ejpam-7005	164	3	,	,	PUNCT
ejpam-7005	164	4	t0	t0	PROPN
ejpam-7005	164	5	+	+	CCONJ
ejpam-7005	164	6	t	t	X
ejpam-7005	164	7	]	]	PUNCT
ejpam-7005	164	8	∩	∩	NOUN
ejpam-7005	164	9	(	(	PUNCT
ejpam-7005	164	10	ℏn)t0	ℏn)t0	PROPN
ejpam-7005	164	11	,	,	PUNCT
ejpam-7005	164	12	(	(	PUNCT
ejpam-7005	164	13	30	30	NUM
ejpam-7005	164	14	)	)	PUNCT
ejpam-7005	164	15	where	where	SCONJ
ejpam-7005	164	16	∥ϕ∥c	∥ϕ∥c	NOUN
ejpam-7005	164	17	=	=	SYM
ejpam-7005	164	18	max	max	PROPN
ejpam-7005	164	19	1≤i≤m	1≤i≤m	NUM
ejpam-7005	164	20	|ϕ(xi)|	|ϕ(xi)|	NUM
ejpam-7005	164	21	,	,	PUNCT
ejpam-7005	164	22	(	(	PUNCT
ejpam-7005	164	23	31	31	NUM
ejpam-7005	164	24	)	)	PUNCT
ejpam-7005	164	25	∥u(t)∥	∥u(t)∥	NOUN
ejpam-7005	164	26	=	=	PUNCT
ejpam-7005	164	27	m∑	m∑	CCONJ
ejpam-7005	164	28	i=1	i=1	PROPN
ejpam-7005	164	29	|ui(t)|	|ui(t)|	PROPN
ejpam-7005	164	30	.	.	PUNCT
ejpam-7005	165	1	(	(	PUNCT
ejpam-7005	165	2	32	32	NUM
ejpam-7005	165	3	)	)	PUNCT
ejpam-7005	165	4	lemma	lemma	PROPN
ejpam-7005	165	5	4	4	X
ejpam-7005	165	6	.	.	PUNCT
ejpam-7005	166	1	let	let	VERB
ejpam-7005	166	2	f(t	f(t	NOUN
ejpam-7005	166	3	)	)	PUNCT
ejpam-7005	166	4	,	,	PUNCT
ejpam-7005	166	5	g(t	g(t	PROPN
ejpam-7005	166	6	)	)	PUNCT
ejpam-7005	166	7	>	>	X
ejpam-7005	166	8	0	0	NUM
ejpam-7005	166	9	,	,	PUNCT
ejpam-7005	166	10	non	non	ADJ
ejpam-7005	166	11	-	-	ADJ
ejpam-7005	166	12	decreasing	decrease	VERB
ejpam-7005	166	13	discrete	discrete	ADJ
ejpam-7005	166	14	functions	function	NOUN
ejpam-7005	166	15	,	,	PUNCT
ejpam-7005	166	16	and	and	CCONJ
ejpam-7005	166	17	assume	assume	VERB
ejpam-7005	166	18	g(t	g(t	PROPN
ejpam-7005	166	19	)	)	PUNCT
ejpam-7005	166	20	≤	≤	NUM
ejpam-7005	166	21	m	m	VERB
ejpam-7005	166	22	for	for	ADP
ejpam-7005	166	23	t	t	PROPN
ejpam-7005	166	24	∈	∈	PROPN
ejpam-7005	166	25	j	j	PROPN
ejpam-7005	166	26	.	.	PUNCT
ejpam-7005	167	1	if	if	SCONJ
ejpam-7005	167	2	κ(t	κ(t	NOUN
ejpam-7005	167	3	)	)	PUNCT
ejpam-7005	167	4	≤	≤	NUM
ejpam-7005	167	5	f(t	f(t	NOUN
ejpam-7005	167	6	)	)	PUNCT
ejpam-7005	168	1	+	+	SYM
ejpam-7005	169	1	g(t	g(t	PROPN
ejpam-7005	169	2	)	)	PUNCT
ejpam-7005	169	3	ℏ∆	ℏ∆	ADV
ejpam-7005	169	4	−δ(t	−δ(t	PROPN
ejpam-7005	169	5	)	)	PUNCT
ejpam-7005	169	6	t0+(1−δ(t))ℏκ(t+	t0+(1−δ(t))ℏκ(t+	NUM
ejpam-7005	169	7	δ(t)ℏ	δ(t)ℏ	PROPN
ejpam-7005	169	8	)	)	PUNCT
ejpam-7005	169	9	,	,	PUNCT
ejpam-7005	169	10	t	t	PROPN
ejpam-7005	169	11	∈	∈	PROPN
ejpam-7005	169	12	(	(	PUNCT
ejpam-7005	169	13	ℏn)t0	ℏn)t0	PROPN
ejpam-7005	169	14	,	,	PUNCT
ejpam-7005	169	15	(	(	PUNCT
ejpam-7005	169	16	33	33	NUM
ejpam-7005	169	17	)	)	PUNCT
ejpam-7005	169	18	then	then	ADV
ejpam-7005	169	19	κ(t	κ(t	PROPN
ejpam-7005	169	20	)	)	PUNCT
ejpam-7005	169	21	≤	≤	NUM
ejpam-7005	169	22	f(t)eδ(t)(g(t	f(t)eδ(t)(g(t	NOUN
ejpam-7005	169	23	)	)	PUNCT
ejpam-7005	169	24	,	,	PUNCT
ejpam-7005	169	25	t	t	PROPN
ejpam-7005	169	26	)	)	PUNCT
ejpam-7005	169	27	,	,	PUNCT
ejpam-7005	169	28	t	t	PROPN
ejpam-7005	169	29	∈	∈	PROPN
ejpam-7005	169	30	(	(	PUNCT
ejpam-7005	169	31	ℏn)t0	ℏn)t0	PROPN
ejpam-7005	169	32	.	.	PUNCT
ejpam-7005	170	1	(	(	PUNCT
ejpam-7005	170	2	34	34	NUM
ejpam-7005	170	3	)	)	PUNCT
ejpam-7005	170	4	proof	proof	NOUN
ejpam-7005	170	5	3	3	NUM
ejpam-7005	170	6	.	.	PUNCT
ejpam-7005	170	7	introduce	introduce	VERB
ejpam-7005	170	8	the	the	DET
ejpam-7005	170	9	operator	operator	NOUN
ejpam-7005	170	10	aφ(t	aφ(t	PUNCT
ejpam-7005	170	11	)	)	PUNCT
ejpam-7005	170	12	:	:	PUNCT
ejpam-7005	171	1	=	=	SYM
ejpam-7005	171	2	g(t	g(t	PROPN
ejpam-7005	171	3	)	)	PUNCT
ejpam-7005	171	4	ℏ∆	ℏ∆	ADV
ejpam-7005	171	5	−δ(t	−δ(t	PROPN
ejpam-7005	171	6	)	)	PUNCT
ejpam-7005	171	7	t0+(1−δ(t))ℏφ(t+	t0+(1−δ(t))ℏφ(t+	NUM
ejpam-7005	171	8	δ(t)ℏ	δ(t)ℏ	NOUN
ejpam-7005	171	9	)	)	PUNCT
ejpam-7005	171	10	.	.	PUNCT
ejpam-7005	172	1	(	(	PUNCT
ejpam-7005	172	2	35	35	NUM
ejpam-7005	172	3	)	)	PUNCT
ejpam-7005	172	4	under	under	ADP
ejpam-7005	172	5	this	this	DET
ejpam-7005	172	6	notation	notation	NOUN
ejpam-7005	172	7	,	,	PUNCT
ejpam-7005	172	8	(	(	PUNCT
ejpam-7005	172	9	33	33	NUM
ejpam-7005	172	10	)	)	PUNCT
ejpam-7005	172	11	reads	read	VERB
ejpam-7005	172	12	κ(t	κ(t	NOUN
ejpam-7005	172	13	)	)	PUNCT
ejpam-7005	172	14	≤	≤	NUM
ejpam-7005	173	1	f(t	f(t	NOUN
ejpam-7005	173	2	)	)	PUNCT
ejpam-7005	174	1	+	+	NOUN
ejpam-7005	174	2	aκ(t	aκ(t	NOUN
ejpam-7005	174	3	)	)	PUNCT
ejpam-7005	174	4	.	.	PUNCT
ejpam-7005	175	1	by	by	ADP
ejpam-7005	175	2	the	the	DET
ejpam-7005	175	3	monotonicity	monotonicity	NOUN
ejpam-7005	175	4	of	of	ADP
ejpam-7005	175	5	a	a	PRON
ejpam-7005	175	6	,	,	PUNCT
ejpam-7005	175	7	it	it	PRON
ejpam-7005	175	8	follows	follow	VERB
ejpam-7005	175	9	that	that	SCONJ
ejpam-7005	175	10	κ(t	κ(t	NOUN
ejpam-7005	175	11	)	)	PUNCT
ejpam-7005	175	12	≤	≤	NOUN
ejpam-7005	175	13	n−1∑	n−1∑	PROPN
ejpam-7005	175	14	k=0	k=0	PROPN
ejpam-7005	175	15	akf(t	akf(t	PROPN
ejpam-7005	175	16	)	)	PUNCT
ejpam-7005	175	17	+	+	NOUN
ejpam-7005	175	18	anκ(t	anκ(t	X
ejpam-7005	175	19	)	)	PUNCT
ejpam-7005	175	20	.	.	PUNCT
ejpam-7005	176	1	(	(	PUNCT
ejpam-7005	176	2	36	36	NUM
ejpam-7005	176	3	)	)	PUNCT
ejpam-7005	176	4	we	we	PRON
ejpam-7005	176	5	claim	claim	VERB
ejpam-7005	176	6	that	that	SCONJ
ejpam-7005	176	7	for	for	ADP
ejpam-7005	176	8	every	every	DET
ejpam-7005	176	9	n	n	PRON
ejpam-7005	176	10	≥	≥	NOUN
ejpam-7005	176	11	1	1	NUM
ejpam-7005	176	12	,	,	PUNCT
ejpam-7005	176	13	anκ(t	anκ(t	X
ejpam-7005	176	14	)	)	PUNCT
ejpam-7005	176	15	≤	≤	PUNCT
ejpam-7005	177	1	[	[	X
ejpam-7005	177	2	g(t−	g(t−	NOUN
ejpam-7005	177	3	(	(	PUNCT
ejpam-7005	177	4	n−	n−	PROPN
ejpam-7005	177	5	1)δ(t)ℏ)]n	1)δ(t)ℏ)]n	NUM
ejpam-7005	177	6	ℏ∆	ℏ∆	NUM
ejpam-7005	177	7	−nδ(t	−nδ(t	NUM
ejpam-7005	177	8	)	)	PUNCT
ejpam-7005	177	9	t0+(1−δ(t))ℏκ(t+	t0+(1−δ(t))ℏκ(t+	NUM
ejpam-7005	177	10	δ(t)ℏ	δ(t)ℏ	PROPN
ejpam-7005	177	11	)	)	PUNCT
ejpam-7005	177	12	.	.	PUNCT
ejpam-7005	178	1	(	(	PUNCT
ejpam-7005	178	2	37	37	NUM
ejpam-7005	178	3	)	)	PUNCT
ejpam-7005	178	4	for	for	ADP
ejpam-7005	178	5	n	n	NOUN
ejpam-7005	178	6	=	=	SYM
ejpam-7005	178	7	1	1	NUM
ejpam-7005	178	8	,	,	PUNCT
ejpam-7005	178	9	the	the	DET
ejpam-7005	178	10	inequality	inequality	NOUN
ejpam-7005	178	11	holds	hold	VERB
ejpam-7005	178	12	by	by	ADP
ejpam-7005	178	13	definition	definition	NOUN
ejpam-7005	178	14	.	.	PUNCT
ejpam-7005	179	1	assume	assume	VERB
ejpam-7005	179	2	it	it	PRON
ejpam-7005	179	3	holds	hold	VERB
ejpam-7005	179	4	for	for	ADP
ejpam-7005	179	5	some	some	DET
ejpam-7005	179	6	n	n	NOUN
ejpam-7005	179	7	=	=	SYM
ejpam-7005	179	8	k.	k.	PROPN
ejpam-7005	179	9	for	for	ADP
ejpam-7005	179	10	n	n	PROPN
ejpam-7005	180	1	=	=	SYM
ejpam-7005	180	2	k	k	PROPN
ejpam-7005	181	1	+	+	PROPN
ejpam-7005	181	2	1	1	NUM
ejpam-7005	181	3	:	:	PUNCT
ejpam-7005	181	4	ak+1κ(t	ak+1κ(t	NOUN
ejpam-7005	181	5	)	)	PUNCT
ejpam-7005	181	6	=	=	SYM
ejpam-7005	181	7	a	a	PRON
ejpam-7005	181	8	(	(	PUNCT
ejpam-7005	181	9	akκ(t	akκ(t	PROPN
ejpam-7005	181	10	)	)	PUNCT
ejpam-7005	181	11	)	)	PUNCT
ejpam-7005	181	12	≤	≤	NUM
ejpam-7005	181	13	g(t−	g(t−	PROPN
ejpam-7005	181	14	kδ(t)ℏ	kδ(t)ℏ	PROPN
ejpam-7005	181	15	)	)	PUNCT
ejpam-7005	181	16	ℏ∆	ℏ∆	ADV
ejpam-7005	181	17	−δ(t	−δ(t	PROPN
ejpam-7005	181	18	)	)	PUNCT
ejpam-7005	181	19	t0+(1+(k−1)δ(t))ℏ	t0+(1+(k−1)δ(t))ℏ	PROPN
ejpam-7005	181	20	[	[	PUNCT
ejpam-7005	181	21	[	[	X
ejpam-7005	181	22	g(t−	g(t−	INTJ
ejpam-7005	181	23	(	(	PUNCT
ejpam-7005	181	24	k	k	PROPN
ejpam-7005	181	25	−	−	PROPN
ejpam-7005	181	26	1)δ(t)ℏ)]k	1)δ(t)ℏ)]k	NUM
ejpam-7005	181	27	ℏ∆	ℏ∆	ADV
ejpam-7005	181	28	−kδ(t	−kδ(t	NUM
ejpam-7005	181	29	)	)	PUNCT
ejpam-7005	181	30	t0+(1−δ(t))ℏκ(t+	t0+(1−δ(t))ℏκ(t+	NUM
ejpam-7005	181	31	δ(t)ℏ	δ(t)ℏ	PROPN
ejpam-7005	181	32	)	)	PUNCT
ejpam-7005	181	33	]	]	PUNCT
ejpam-7005	182	1	=	=	PUNCT
ejpam-7005	183	1	[	[	X
ejpam-7005	183	2	g(t−	g(t−	NOUN
ejpam-7005	183	3	kδ(t)ℏ)]k+1	kδ(t)ℏ)]k+1	PROPN
ejpam-7005	183	4	ℏ∆	ℏ∆	ADJ
ejpam-7005	183	5	−(k+1)δ(t	−(k+1)δ(t	PROPN
ejpam-7005	183	6	)	)	PUNCT
ejpam-7005	183	7	t0+(1−δ(t))ℏκ(t+	t0+(1−δ(t))ℏκ(t+	NUM
ejpam-7005	183	8	δ(t)ℏ	δ(t)ℏ	PROPN
ejpam-7005	183	9	)	)	PUNCT
ejpam-7005	183	10	,	,	PUNCT
ejpam-7005	183	11	by	by	ADP
ejpam-7005	183	12	the	the	DET
ejpam-7005	183	13	composition	composition	NOUN
ejpam-7005	183	14	property	property	NOUN
ejpam-7005	183	15	of	of	ADP
ejpam-7005	183	16	fractional	fractional	ADJ
ejpam-7005	183	17	sums	sum	NOUN
ejpam-7005	183	18	.	.	PUNCT
ejpam-7005	184	1	since	since	SCONJ
ejpam-7005	184	2	g(t	g(t	PROPN
ejpam-7005	184	3	)	)	PUNCT
ejpam-7005	184	4	≤	≤	NUM
ejpam-7005	184	5	m	m	PROPN
ejpam-7005	184	6	and	and	CCONJ
ejpam-7005	184	7	limn→∞anκ(t	limn→∞anκ(t	NOUN
ejpam-7005	184	8	)	)	PUNCT
ejpam-7005	184	9	=	=	PUNCT
ejpam-7005	184	10	0	0	NUM
ejpam-7005	184	11	,	,	PUNCT
ejpam-7005	184	12	we	we	PRON
ejpam-7005	184	13	deduce	deduce	VERB
ejpam-7005	184	14	anf(t	anf(t	NOUN
ejpam-7005	184	15	)	)	PUNCT
ejpam-7005	184	16	≤	≤	NOUN
ejpam-7005	184	17	f(t	f(t	NOUN
ejpam-7005	184	18	)	)	PUNCT
ejpam-7005	185	1	[	[	X
ejpam-7005	185	2	g(t)]n	g(t)]n	ADV
ejpam-7005	185	3	(	(	PUNCT
ejpam-7005	185	4	t	t	NOUN
ejpam-7005	185	5	ℏ	ℏ	PROPN
ejpam-7005	185	6	−	−	PROPN
ejpam-7005	185	7	(	(	PUNCT
ejpam-7005	185	8	t0	t0	NOUN
ejpam-7005	185	9	ℏ	ℏ	PROPN
ejpam-7005	185	10	+	+	CCONJ
ejpam-7005	185	11	1	1	NUM
ejpam-7005	185	12	)	)	PUNCT
ejpam-7005	185	13	+	+	CCONJ
ejpam-7005	185	14	nδ(t	nδ(t	NOUN
ejpam-7005	185	15	)	)	PUNCT
ejpam-7005	185	16	)	)	PUNCT
ejpam-7005	185	17	(	(	PUNCT
ejpam-7005	185	18	nδ(t	nδ(t	NOUN
ejpam-7005	185	19	)	)	PUNCT
ejpam-7005	185	20	)	)	PUNCT
ejpam-7005	186	1	ℏ	ℏ	PROPN
ejpam-7005	186	2	γ(nδ(t	γ(nδ(t	PROPN
ejpam-7005	186	3	)	)	PUNCT
ejpam-7005	186	4	+	+	NUM
ejpam-7005	186	5	1	1	X
ejpam-7005	186	6	)	)	PUNCT
ejpam-7005	186	7	,	,	PUNCT
ejpam-7005	186	8	n.	n.	PROPN
ejpam-7005	186	9	anakira	anakira	PROPN
ejpam-7005	186	10	et	et	PROPN
ejpam-7005	186	11	al	al	PROPN
ejpam-7005	186	12	.	.	PUNCT
ejpam-7005	186	13	/	/	SYM
ejpam-7005	186	14	eur	eur	PROPN
ejpam-7005	186	15	.	.	PUNCT
ejpam-7005	187	1	j.	j.	PROPN
ejpam-7005	187	2	pure	pure	PROPN
ejpam-7005	187	3	appl	appl	PROPN
ejpam-7005	187	4	.	.	PROPN
ejpam-7005	187	5	math	math	PROPN
ejpam-7005	187	6	,	,	PUNCT
ejpam-7005	187	7	18	18	NUM
ejpam-7005	187	8	(	(	PUNCT
ejpam-7005	187	9	4	4	NUM
ejpam-7005	187	10	)	)	PUNCT
ejpam-7005	187	11	(	(	PUNCT
ejpam-7005	187	12	2025	2025	NUM
ejpam-7005	187	13	)	)	PUNCT
ejpam-7005	187	14	,	,	PUNCT
ejpam-7005	187	15	7005	7005	NUM
ejpam-7005	187	16	9	9	NUM
ejpam-7005	187	17	of	of	ADP
ejpam-7005	187	18	17	17	NUM
ejpam-7005	187	19	κ(t	κ(t	NOUN
ejpam-7005	187	20	)	)	PUNCT
ejpam-7005	187	21	≤	≤	NOUN
ejpam-7005	188	1	∞∑	∞∑	NUM
ejpam-7005	188	2	k=0	k=0	PUNCT
ejpam-7005	188	3	akf(t	akf(t	PROPN
ejpam-7005	188	4	)	)	PUNCT
ejpam-7005	188	5	≤	≤	NOUN
ejpam-7005	188	6	f(t)eδ(t)(g(t	f(t)eδ(t)(g(t	NOUN
ejpam-7005	188	7	)	)	PUNCT
ejpam-7005	188	8	,	,	PUNCT
ejpam-7005	188	9	t	t	PROPN
ejpam-7005	188	10	)	)	PUNCT
ejpam-7005	188	11	.	.	PUNCT
ejpam-7005	189	1	theorem	theorem	NOUN
ejpam-7005	189	2	1	1	NUM
ejpam-7005	189	3	.	.	PUNCT
ejpam-7005	190	1	the	the	DET
ejpam-7005	190	2	system	system	NOUN
ejpam-7005	190	3	(	(	PUNCT
ejpam-7005	190	4	6	6	NUM
ejpam-7005	190	5	)	)	PUNCT
ejpam-7005	190	6	is	be	AUX
ejpam-7005	190	7	fts	fts	PROPN
ejpam-7005	190	8	if	if	SCONJ
ejpam-7005	190	9	eδ(t)(ω	eδ(t)(ω	PROPN
ejpam-7005	190	10	,	,	PUNCT
ejpam-7005	190	11	t	t	NOUN
ejpam-7005	190	12	)	)	PUNCT
ejpam-7005	190	13	≤	≤	NUM
ejpam-7005	190	14	ε	ε	PROPN
ejpam-7005	190	15	η	η	PROPN
ejpam-7005	190	16	,	,	PUNCT
ejpam-7005	190	17	∀t	∀t	PROPN
ejpam-7005	190	18	∈	∈	PROPN
ejpam-7005	190	19	j	j	PROPN
ejpam-7005	190	20	,	,	PUNCT
ejpam-7005	190	21	(	(	PUNCT
ejpam-7005	190	22	38	38	NUM
ejpam-7005	190	23	)	)	PUNCT
ejpam-7005	190	24	where	where	SCONJ
ejpam-7005	190	25	ω	ω	PROPN
ejpam-7005	190	26	is	be	AUX
ejpam-7005	190	27	defined	define	VERB
ejpam-7005	190	28	in	in	ADP
ejpam-7005	190	29	(	(	PUNCT
ejpam-7005	190	30	42	42	NUM
ejpam-7005	190	31	)	)	PUNCT
ejpam-7005	190	32	.	.	PUNCT
ejpam-7005	191	1	proof	proof	NOUN
ejpam-7005	191	2	4	4	NUM
ejpam-7005	191	3	.	.	PUNCT
ejpam-7005	191	4	from	from	ADP
ejpam-7005	191	5	the	the	DET
ejpam-7005	191	6	solution	solution	NOUN
ejpam-7005	191	7	representation	representation	NOUN
ejpam-7005	191	8	and	and	CCONJ
ejpam-7005	191	9	norm	norm	NOUN
ejpam-7005	191	10	estimates	estimate	NOUN
ejpam-7005	191	11	:	:	PUNCT
ejpam-7005	191	12	∥u(t)∥	∥u(t)∥	NOUN
ejpam-7005	191	13	≤	≤	ADJ
ejpam-7005	191	14	∥ϕ1∥c	∥ϕ1∥c	PROPN
ejpam-7005	191	15	+	+	CCONJ
ejpam-7005	191	16	ℏ∆	ℏ∆	ADJ
ejpam-7005	191	17	−δ(t	−δ(t	ADV
ejpam-7005	191	18	)	)	PUNCT
ejpam-7005	192	1	t0+(1−δ(t))ℏ	t0+(1−δ(t))ℏ	NOUN
ejpam-7005	192	2	[	[	X
ejpam-7005	192	3	(	(	PUNCT
ejpam-7005	192	4	β	β	X
ejpam-7005	192	5	+	+	X
ejpam-7005	192	6	4d1	4d1	NUM
ejpam-7005	192	7	∆2	∆2	NOUN
ejpam-7005	192	8	x	x	SYM
ejpam-7005	192	9	)	)	PUNCT
ejpam-7005	192	10	∥u(t+	∥u(t+	NOUN
ejpam-7005	192	11	δ(t)ℏ)∥+	δ(t)ℏ)∥+	PROPN
ejpam-7005	192	12	∥u(t+	∥u(t+	NOUN
ejpam-7005	192	13	δ(t)ℏ)∥3	δ(t)ℏ)∥3	VERB
ejpam-7005	193	1	+	+	X
ejpam-7005	193	2	(	(	PUNCT
ejpam-7005	193	3	β	β	X
ejpam-7005	193	4	+	+	NOUN
ejpam-7005	193	5	1)∥u(t+	1)∥u(t+	NUM
ejpam-7005	193	6	δ(t)ℏ)∥2	δ(t)ℏ)∥2	ADJ
ejpam-7005	193	7	+	+	CCONJ
ejpam-7005	193	8	∥v(t+	∥v(t+	AUX
ejpam-7005	193	9	δ(t)ℏ)∥	δ(t)ℏ)∥	NOUN
ejpam-7005	193	10	]	]	PUNCT
ejpam-7005	193	11	.	.	PUNCT
ejpam-7005	194	1	(	(	PUNCT
ejpam-7005	194	2	39	39	NUM
ejpam-7005	194	3	)	)	PUNCT
ejpam-7005	194	4	using	use	VERB
ejpam-7005	194	5	the	the	DET
ejpam-7005	194	6	inequality	inequality	NOUN
ejpam-7005	194	7	∥u∥3	∥u∥3	PROPN
ejpam-7005	194	8	+	+	X
ejpam-7005	194	9	(	(	PUNCT
ejpam-7005	194	10	β	β	X
ejpam-7005	194	11	+	+	NUM
ejpam-7005	194	12	1)∥u∥2	1)∥u∥2	NUM
ejpam-7005	194	13	≤	≤	NUM
ejpam-7005	194	14	∥u∥	∥u∥	NOUN
ejpam-7005	194	15	for	for	ADP
ejpam-7005	194	16	∥u∥	∥u∥	NOUN
ejpam-7005	194	17	≤	≤	NOUN
ejpam-7005	194	18	−(β+1)+	−(β+1)+	PUNCT
ejpam-7005	194	19	√	√	PROPN
ejpam-7005	194	20	(	(	PUNCT
ejpam-7005	194	21	β+1)2	β+1)2	PROPN
ejpam-7005	194	22	+	+	PROPN
ejpam-7005	194	23	4	4	NUM
ejpam-7005	194	24	2	2	NUM
ejpam-7005	194	25	:	:	PUNCT
ejpam-7005	194	26	∥u(t)∥	∥u(t)∥	PROPN
ejpam-7005	194	27	≤	≤	ADJ
ejpam-7005	194	28	∥ϕ1∥c	∥ϕ1∥c	PROPN
ejpam-7005	194	29	+	+	CCONJ
ejpam-7005	194	30	ℏ∆	ℏ∆	ADJ
ejpam-7005	194	31	−δ(t	−δ(t	ADV
ejpam-7005	194	32	)	)	PUNCT
ejpam-7005	195	1	t0+(1−δ(t))ℏ	t0+(1−δ(t))ℏ	NOUN
ejpam-7005	196	1	[	[	X
ejpam-7005	196	2	(	(	PUNCT
ejpam-7005	196	3	4d1	4d1	NUM
ejpam-7005	196	4	∆2	∆2	NOUN
ejpam-7005	196	5	x	x	PROPN
ejpam-7005	197	1	+	+	NUM
ejpam-7005	197	2	β	β	NUM
ejpam-7005	197	3	−	−	NOUN
ejpam-7005	197	4	1	1	NUM
ejpam-7005	197	5	+	+	NUM
ejpam-7005	197	6	√	√	PROPN
ejpam-7005	197	7	(	(	PUNCT
ejpam-7005	197	8	β	β	X
ejpam-7005	197	9	+	+	X
ejpam-7005	197	10	1)2	1)2	NUM
ejpam-7005	197	11	+	+	CCONJ
ejpam-7005	197	12	4	4	NUM
ejpam-7005	197	13	2	2	NUM
ejpam-7005	197	14	)	)	PUNCT
ejpam-7005	197	15	∥u(t+	∥u(t+	NOUN
ejpam-7005	197	16	δ(t)ℏ)∥	δ(t)ℏ)∥	NOUN
ejpam-7005	197	17	+	+	CCONJ
ejpam-7005	197	18	∥v(t+	∥v(t+	VERB
ejpam-7005	197	19	δ(t)ℏ)∥	δ(t)ℏ)∥	NOUN
ejpam-7005	197	20	]	]	PUNCT
ejpam-7005	197	21	.	.	PUNCT
ejpam-7005	198	1	(	(	PUNCT
ejpam-7005	198	2	40	40	NUM
ejpam-7005	198	3	)	)	PUNCT
ejpam-7005	198	4	similarly	similarly	ADV
ejpam-7005	198	5	for	for	ADP
ejpam-7005	198	6	v	v	NOUN
ejpam-7005	198	7	:	:	PUNCT
ejpam-7005	198	8	∥v(t)∥	∥v(t)∥	PROPN
ejpam-7005	198	9	≤	≤	NOUN
ejpam-7005	198	10	∥ϕ2∥c	∥ϕ2∥c	X
ejpam-7005	198	11	+	+	CCONJ
ejpam-7005	198	12	ℏ∆	ℏ∆	ADJ
ejpam-7005	198	13	−δ(t	−δ(t	ADV
ejpam-7005	198	14	)	)	PUNCT
ejpam-7005	198	15	t0+(1−δ(t))ℏ	t0+(1−δ(t))ℏ	NOUN
ejpam-7005	199	1	[	[	X
ejpam-7005	199	2	(	(	PUNCT
ejpam-7005	199	3	ϵγ	ϵγ	X
ejpam-7005	199	4	+	+	CCONJ
ejpam-7005	199	5	4d2	4d2	NUM
ejpam-7005	199	6	∆2	∆2	NOUN
ejpam-7005	199	7	x	x	PROPN
ejpam-7005	199	8	)	)	PUNCT
ejpam-7005	199	9	∥v(t+	∥v(t+	PROPN
ejpam-7005	199	10	δ(t)ℏ)∥+	δ(t)ℏ)∥+	PROPN
ejpam-7005	199	11	ϵ∥u(t+	ϵ∥u(t+	PROPN
ejpam-7005	199	12	δ(t)ℏ)∥	δ(t)ℏ)∥	VERB
ejpam-7005	199	13	]	]	PUNCT
ejpam-7005	199	14	.	.	PUNCT
ejpam-7005	200	1	(	(	PUNCT
ejpam-7005	200	2	41	41	NUM
ejpam-7005	200	3	)	)	PUNCT
ejpam-7005	200	4	summing	sum	VERB
ejpam-7005	200	5	(	(	PUNCT
ejpam-7005	200	6	40	40	NUM
ejpam-7005	200	7	)	)	PUNCT
ejpam-7005	200	8	and	and	CCONJ
ejpam-7005	200	9	(	(	PUNCT
ejpam-7005	200	10	41	41	NUM
ejpam-7005	200	11	):	):	PUNCT
ejpam-7005	200	12	∥u(t)∥+	∥u(t)∥+	ADJ
ejpam-7005	200	13	∥v(t)∥	∥v(t)∥	PROPN
ejpam-7005	200	14	≤	≤	PROPN
ejpam-7005	200	15	η	η	PROPN
ejpam-7005	200	16	+	+	PROPN
ejpam-7005	200	17	ℏ∆	ℏ∆	ADJ
ejpam-7005	200	18	−δ(t	−δ(t	ADJ
ejpam-7005	200	19	)	)	PUNCT
ejpam-7005	201	1	t0+(1−δ(t))ℏ	t0+(1−δ(t))ℏ	NOUN
ejpam-7005	202	1	[	[	X
ejpam-7005	202	2	(	(	PUNCT
ejpam-7005	202	3	ϵ+	ϵ+	PUNCT
ejpam-7005	202	4	4d1	4d1	NUM
ejpam-7005	202	5	∆2	∆2	NOUN
ejpam-7005	202	6	x	x	PROPN
ejpam-7005	203	1	+	+	NUM
ejpam-7005	203	2	β	β	NUM
ejpam-7005	203	3	−	−	NOUN
ejpam-7005	203	4	1	1	NUM
ejpam-7005	203	5	+	+	NUM
ejpam-7005	203	6	√	√	PROPN
ejpam-7005	203	7	(	(	PUNCT
ejpam-7005	203	8	β	β	X
ejpam-7005	203	9	+	+	X
ejpam-7005	203	10	1)2	1)2	NUM
ejpam-7005	203	11	+	+	CCONJ
ejpam-7005	203	12	4	4	NUM
ejpam-7005	203	13	2	2	NUM
ejpam-7005	203	14	)	)	PUNCT
ejpam-7005	203	15	∥u(t+	∥u(t+	NOUN
ejpam-7005	203	16	δ(t)ℏ)∥	δ(t)ℏ)∥	VERB
ejpam-7005	203	17	+	+	CCONJ
ejpam-7005	203	18	(	(	PUNCT
ejpam-7005	203	19	1	1	NUM
ejpam-7005	203	20	+	+	NUM
ejpam-7005	203	21	ϵγ	ϵγ	NOUN
ejpam-7005	203	22	+	+	CCONJ
ejpam-7005	203	23	4d2	4d2	NUM
ejpam-7005	203	24	∆2	∆2	NOUN
ejpam-7005	203	25	x	x	SYM
ejpam-7005	203	26	)	)	PUNCT
ejpam-7005	203	27	∥v(t+	∥v(t+	PROPN
ejpam-7005	203	28	δ(t)ℏ)∥	δ(t)ℏ)∥	VERB
ejpam-7005	203	29	]	]	PUNCT
ejpam-7005	204	1	≤	≤	NUM
ejpam-7005	204	2	η	η	PROPN
ejpam-7005	204	3	+	+	PROPN
ejpam-7005	204	4	ω	ω	PROPN
ejpam-7005	204	5	ℏ∆	ℏ∆	X
ejpam-7005	204	6	−δ(t	−δ(t	PROPN
ejpam-7005	204	7	)	)	PUNCT
ejpam-7005	204	8	t0+(1−δ(t))ℏ	t0+(1−δ(t))ℏ	NOUN
ejpam-7005	205	1	[	[	X
ejpam-7005	205	2	∥u(t+	∥u(t+	NOUN
ejpam-7005	205	3	δ(t)ℏ)∥+	δ(t)ℏ)∥+	ADJ
ejpam-7005	205	4	∥v(t+	∥v(t+	NOUN
ejpam-7005	205	5	δ(t)ℏ)∥	δ(t)ℏ)∥	NOUN
ejpam-7005	205	6	]	]	PUNCT
ejpam-7005	205	7	,	,	PUNCT
ejpam-7005	205	8	where	where	SCONJ
ejpam-7005	205	9	ω	ω	PROPN
ejpam-7005	205	10	=	=	SYM
ejpam-7005	205	11	max	max	PROPN
ejpam-7005	205	12	{	{	PUNCT
ejpam-7005	205	13	ϵ+	ϵ+	PUNCT
ejpam-7005	205	14	4d1	4d1	NUM
ejpam-7005	205	15	∆2	∆2	NOUN
ejpam-7005	205	16	x	x	PROPN
ejpam-7005	206	1	+	+	NUM
ejpam-7005	206	2	β	β	NUM
ejpam-7005	206	3	−	−	NOUN
ejpam-7005	206	4	1	1	NUM
ejpam-7005	206	5	+	+	NUM
ejpam-7005	206	6	√	√	PROPN
ejpam-7005	206	7	(	(	PUNCT
ejpam-7005	206	8	β	β	X
ejpam-7005	206	9	+	+	X
ejpam-7005	206	10	1)2	1)2	NUM
ejpam-7005	206	11	+	+	CCONJ
ejpam-7005	206	12	4	4	NUM
ejpam-7005	206	13	2	2	NUM
ejpam-7005	206	14	,	,	PUNCT
ejpam-7005	206	15	1	1	NUM
ejpam-7005	206	16	+	+	NUM
ejpam-7005	206	17	ϵγ	ϵγ	NOUN
ejpam-7005	207	1	+	+	CCONJ
ejpam-7005	207	2	4d2	4d2	NUM
ejpam-7005	207	3	∆2	∆2	NOUN
ejpam-7005	207	4	x	x	PUNCT
ejpam-7005	207	5	}	}	PUNCT
ejpam-7005	207	6	.	.	PUNCT
ejpam-7005	208	1	(	(	PUNCT
ejpam-7005	208	2	42	42	X
ejpam-7005	208	3	)	)	PUNCT
ejpam-7005	208	4	applying	apply	VERB
ejpam-7005	208	5	lemma	lemma	PROPN
ejpam-7005	208	6	4	4	NUM
ejpam-7005	208	7	yields	yield	NOUN
ejpam-7005	208	8	:	:	PUNCT
ejpam-7005	208	9	∥u(t)∥+	∥u(t)∥+	PROPN
ejpam-7005	208	10	∥v(t)∥	∥v(t)∥	PROPN
ejpam-7005	208	11	≤	≤	X
ejpam-7005	208	12	ηeδ(t)(ω	ηeδ(t)(ω	NUM
ejpam-7005	208	13	,	,	PUNCT
ejpam-7005	208	14	t	t	PROPN
ejpam-7005	208	15	)	)	PUNCT
ejpam-7005	208	16	.	.	PUNCT
ejpam-7005	209	1	(	(	PUNCT
ejpam-7005	209	2	43	43	NUM
ejpam-7005	209	3	)	)	PUNCT
ejpam-7005	209	4	thus	thus	ADV
ejpam-7005	209	5	,	,	PUNCT
ejpam-7005	209	6	eδ(t)(ω	eδ(t)(ω	PROPN
ejpam-7005	209	7	,	,	PUNCT
ejpam-7005	209	8	t	t	PROPN
ejpam-7005	209	9	)	)	PUNCT
ejpam-7005	209	10	≤	≤	PUNCT
ejpam-7005	209	11	ε	ε	PROPN
ejpam-7005	209	12	/	/	SYM
ejpam-7005	209	13	η	η	PROPN
ejpam-7005	209	14	ensures	ensure	VERB
ejpam-7005	209	15	fts	fts	PROPN
ejpam-7005	209	16	.	.	PUNCT
ejpam-7005	209	17	n.	n.	PROPN
ejpam-7005	209	18	anakira	anakira	PROPN
ejpam-7005	209	19	et	et	PROPN
ejpam-7005	209	20	al	al	PROPN
ejpam-7005	209	21	.	.	PUNCT
ejpam-7005	209	22	/	/	SYM
ejpam-7005	209	23	eur	eur	PROPN
ejpam-7005	209	24	.	.	PUNCT
ejpam-7005	210	1	j.	j.	PROPN
ejpam-7005	210	2	pure	pure	PROPN
ejpam-7005	210	3	appl	appl	PROPN
ejpam-7005	210	4	.	.	PROPN
ejpam-7005	210	5	math	math	PROPN
ejpam-7005	210	6	,	,	PUNCT
ejpam-7005	210	7	18	18	NUM
ejpam-7005	210	8	(	(	PUNCT
ejpam-7005	210	9	4	4	NUM
ejpam-7005	210	10	)	)	PUNCT
ejpam-7005	210	11	(	(	PUNCT
ejpam-7005	210	12	2025	2025	NUM
ejpam-7005	210	13	)	)	PUNCT
ejpam-7005	210	14	,	,	PUNCT
ejpam-7005	210	15	7005	7005	NUM
ejpam-7005	210	16	10	10	NUM
ejpam-7005	210	17	of	of	ADP
ejpam-7005	210	18	17	17	NUM
ejpam-7005	210	19	4	4	NUM
ejpam-7005	210	20	.	.	PUNCT
ejpam-7005	210	21	numerical	numerical	PROPN
ejpam-7005	210	22	simulation	simulation	PROPN
ejpam-7005	210	23	to	to	PART
ejpam-7005	210	24	validate	validate	VERB
ejpam-7005	210	25	the	the	DET
ejpam-7005	210	26	theoretical	theoretical	ADJ
ejpam-7005	210	27	results	result	NOUN
ejpam-7005	210	28	established	establish	VERB
ejpam-7005	210	29	in	in	ADP
ejpam-7005	210	30	section	section	NOUN
ejpam-7005	210	31	3	3	NUM
ejpam-7005	210	32	,	,	PUNCT
ejpam-7005	210	33	we	we	PRON
ejpam-7005	210	34	present	present	VERB
ejpam-7005	210	35	a	a	DET
ejpam-7005	210	36	comprehensive	comprehensive	ADJ
ejpam-7005	210	37	numerical	numerical	ADJ
ejpam-7005	210	38	analysis	analysis	NOUN
ejpam-7005	210	39	of	of	ADP
ejpam-7005	210	40	the	the	DET
ejpam-7005	210	41	fts	fts	PROPN
ejpam-7005	210	42	for	for	ADP
ejpam-7005	210	43	the	the	DET
ejpam-7005	210	44	discrete	discrete	ADJ
ejpam-7005	210	45	vo	vo	X
ejpam-7005	210	46	fractional	fractional	ADJ
ejpam-7005	210	47	fhn	fhn	ADJ
ejpam-7005	210	48	system	system	NOUN
ejpam-7005	210	49	.	.	PUNCT
ejpam-7005	211	1	the	the	DET
ejpam-7005	211	2	numerical	numerical	ADJ
ejpam-7005	211	3	implementation	implementation	NOUN
ejpam-7005	211	4	follows	follow	VERB
ejpam-7005	211	5	the	the	DET
ejpam-7005	211	6	discrete	discrete	ADJ
ejpam-7005	211	7	framework	framework	NOUN
ejpam-7005	211	8	developed	develop	VERB
ejpam-7005	211	9	in	in	ADP
ejpam-7005	211	10	section	section	NOUN
ejpam-7005	211	11	2	2	NUM
ejpam-7005	211	12	,	,	PUNCT
ejpam-7005	211	13	with	with	ADP
ejpam-7005	211	14	careful	careful	ADJ
ejpam-7005	211	15	attention	attention	NOUN
ejpam-7005	211	16	to	to	ADP
ejpam-7005	211	17	the	the	DET
ejpam-7005	211	18	accurate	accurate	ADJ
ejpam-7005	211	19	computation	computation	NOUN
ejpam-7005	211	20	of	of	ADP
ejpam-7005	211	21	the	the	DET
ejpam-7005	211	22	vo	vo	PROPN
ejpam-7005	211	23	fractional	fractional	PROPN
ejpam-7005	211	24	operators	operator	NOUN
ejpam-7005	211	25	and	and	CCONJ
ejpam-7005	211	26	the	the	DET
ejpam-7005	211	27	spatial	spatial	ADJ
ejpam-7005	211	28	discretization	discretization	NOUN
ejpam-7005	211	29	.	.	PUNCT
ejpam-7005	212	1	the	the	DET
ejpam-7005	212	2	discrete	discrete	ADJ
ejpam-7005	212	3	system	system	NOUN
ejpam-7005	212	4	in	in	ADP
ejpam-7005	212	5	eq	eq	ADP
ejpam-7005	212	6	.	.	PUNCT
ejpam-7005	213	1	(	(	PUNCT
ejpam-7005	213	2	6	6	NUM
ejpam-7005	213	3	)	)	PUNCT
ejpam-7005	213	4	was	be	AUX
ejpam-7005	213	5	solved	solve	VERB
ejpam-7005	213	6	using	use	VERB
ejpam-7005	213	7	an	an	DET
ejpam-7005	213	8	explicit	explicit	ADJ
ejpam-7005	213	9	numerical	numerical	ADJ
ejpam-7005	213	10	scheme	scheme	NOUN
ejpam-7005	213	11	based	base	VERB
ejpam-7005	213	12	on	on	ADP
ejpam-7005	213	13	the	the	DET
ejpam-7005	213	14	grünwald	grünwald	NOUN
ejpam-7005	213	15	-	-	PUNCT
ejpam-7005	213	16	letnikov	letnikov	NOUN
ejpam-7005	213	17	approximation	approximation	NOUN
ejpam-7005	213	18	for	for	ADP
ejpam-7005	213	19	the	the	DET
ejpam-7005	213	20	vo	vo	NOUN
ejpam-7005	213	21	fractional	fractional	ADJ
ejpam-7005	213	22	difference	difference	NOUN
ejpam-7005	213	23	operator	operator	NOUN
ejpam-7005	213	24	.	.	PUNCT
ejpam-7005	214	1	the	the	DET
ejpam-7005	214	2	spatial	spatial	ADJ
ejpam-7005	214	3	domain	domain	NOUN
ejpam-7005	214	4	x	x	X
ejpam-7005	214	5	∈	∈	PROPN
ejpam-7005	215	1	[	[	X
ejpam-7005	215	2	0	0	NUM
ejpam-7005	215	3	,	,	PUNCT
ejpam-7005	215	4	10	10	NUM
ejpam-7005	215	5	]	]	PUNCT
ejpam-7005	215	6	was	be	AUX
ejpam-7005	215	7	discretized	discretize	VERB
ejpam-7005	215	8	with	with	ADP
ejpam-7005	215	9	∆x	∆x	PROPN
ejpam-7005	215	10	=	=	SYM
ejpam-7005	215	11	5	5	NUM
ejpam-7005	215	12	(	(	PUNCT
ejpam-7005	215	13	yielding	yield	VERB
ejpam-7005	215	14	m	m	PROPN
ejpam-7005	215	15	=	=	SYM
ejpam-7005	215	16	2	2	NUM
ejpam-7005	215	17	spatial	spatial	ADJ
ejpam-7005	215	18	points	point	NOUN
ejpam-7005	215	19	due	due	ADP
ejpam-7005	215	20	to	to	ADP
ejpam-7005	215	21	the	the	DET
ejpam-7005	215	22	periodic	periodic	ADJ
ejpam-7005	215	23	boundary	boundary	ADJ
ejpam-7005	215	24	conditions	condition	NOUN
ejpam-7005	215	25	)	)	PUNCT
ejpam-7005	215	26	,	,	PUNCT
ejpam-7005	215	27	and	and	CCONJ
ejpam-7005	215	28	the	the	DET
ejpam-7005	215	29	temporal	temporal	ADJ
ejpam-7005	215	30	domain	domain	NOUN
ejpam-7005	215	31	was	be	AUX
ejpam-7005	215	32	discretized	discretize	VERB
ejpam-7005	215	33	with	with	ADP
ejpam-7005	215	34	time	time	NOUN
ejpam-7005	215	35	step	step	NOUN
ejpam-7005	215	36	∆t	∆t	PROPN
ejpam-7005	215	37	=	=	SYM
ejpam-7005	215	38	0.5	0.5	NUM
ejpam-7005	215	39	s.	s.	PROPN
ejpam-7005	215	40	the	the	DET
ejpam-7005	215	41	vo	vo	PROPN
ejpam-7005	215	42	fractional	fractional	ADJ
ejpam-7005	215	43	difference	difference	NOUN
ejpam-7005	215	44	operator	operator	NOUN
ejpam-7005	215	45	was	be	AUX
ejpam-7005	215	46	computed	compute	VERB
ejpam-7005	215	47	using	use	VERB
ejpam-7005	215	48	the	the	DET
ejpam-7005	215	49	definition	definition	NOUN
ejpam-7005	215	50	in	in	ADP
ejpam-7005	215	51	eq	eq	ADP
ejpam-7005	215	52	.	.	PUNCT
ejpam-7005	216	1	(	(	PUNCT
ejpam-7005	216	2	9	9	NUM
ejpam-7005	216	3	)	)	PUNCT
ejpam-7005	216	4	,	,	PUNCT
ejpam-7005	216	5	with	with	ADP
ejpam-7005	216	6	the	the	DET
ejpam-7005	216	7	summation	summation	NOUN
ejpam-7005	216	8	truncated	truncate	VERB
ejpam-7005	216	9	at	at	ADP
ejpam-7005	216	10	the	the	DET
ejpam-7005	216	11	current	current	ADJ
ejpam-7005	216	12	time	time	NOUN
ejpam-7005	216	13	step	step	NOUN
ejpam-7005	216	14	.	.	PUNCT
ejpam-7005	217	1	for	for	ADP
ejpam-7005	217	2	the	the	DET
ejpam-7005	217	3	numerical	numerical	ADJ
ejpam-7005	217	4	evaluation	evaluation	NOUN
ejpam-7005	217	5	of	of	ADP
ejpam-7005	217	6	the	the	DET
ejpam-7005	217	7	discrete	discrete	ADJ
ejpam-7005	217	8	mlf	mlf	NOUN
ejpam-7005	217	9	in	in	ADP
ejpam-7005	217	10	eq	eq	PROPN
ejpam-7005	217	11	.	.	PUNCT
ejpam-7005	217	12	(	(	PUNCT
ejpam-7005	217	13	?	?	PUNCT
ejpam-7005	217	14	?	?	PUNCT
ejpam-7005	217	15	)	)	PUNCT
ejpam-7005	217	16	,	,	PUNCT
ejpam-7005	217	17	we	we	PRON
ejpam-7005	217	18	employed	employ	VERB
ejpam-7005	217	19	a	a	DET
ejpam-7005	217	20	truncated	truncated	ADJ
ejpam-7005	217	21	series	series	NOUN
ejpam-7005	217	22	representation	representation	NOUN
ejpam-7005	217	23	with	with	ADP
ejpam-7005	217	24	50	50	NUM
ejpam-7005	217	25	terms	term	NOUN
ejpam-7005	217	26	,	,	PUNCT
ejpam-7005	217	27	which	which	PRON
ejpam-7005	217	28	provided	provide	VERB
ejpam-7005	217	29	sufficient	sufficient	ADJ
ejpam-7005	217	30	accuracy	accuracy	NOUN
ejpam-7005	217	31	for	for	ADP
ejpam-7005	217	32	the	the	DET
ejpam-7005	217	33	time	time	NOUN
ejpam-7005	217	34	intervals	interval	NOUN
ejpam-7005	217	35	considered	consider	VERB
ejpam-7005	217	36	.	.	PUNCT
ejpam-7005	218	1	the	the	DET
ejpam-7005	218	2	norm	norm	NOUN
ejpam-7005	218	3	calculations	calculation	NOUN
ejpam-7005	218	4	followed	follow	VERB
ejpam-7005	218	5	definition	definition	NOUN
ejpam-7005	218	6	2	2	NUM
ejpam-7005	218	7	,	,	PUNCT
ejpam-7005	218	8	with	with	ADP
ejpam-7005	218	9	∥	∥	PRON
ejpam-7005	218	10	·	·	PUNCT
ejpam-7005	219	1	∥c	∥c	NOUN
ejpam-7005	219	2	representing	represent	VERB
ejpam-7005	219	3	the	the	DET
ejpam-7005	219	4	maximum	maximum	ADJ
ejpam-7005	219	5	norm	norm	NOUN
ejpam-7005	219	6	over	over	ADP
ejpam-7005	219	7	spatial	spatial	ADJ
ejpam-7005	219	8	points	point	NOUN
ejpam-7005	219	9	and	and	CCONJ
ejpam-7005	219	10	∥	∥	PRON
ejpam-7005	219	11	·	·	PUNCT
ejpam-7005	219	12	∥	∥	NOUN
ejpam-7005	219	13	denoting	denote	VERB
ejpam-7005	219	14	the	the	DET
ejpam-7005	219	15	l1	l1	NOUN
ejpam-7005	219	16	-	-	PUNCT
ejpam-7005	219	17	norm	norm	NOUN
ejpam-7005	219	18	as	as	SCONJ
ejpam-7005	219	19	defined	define	VERB
ejpam-7005	219	20	in	in	ADP
ejpam-7005	219	21	eq	eq	ADP
ejpam-7005	219	22	.	.	PUNCT
ejpam-7005	220	1	(	(	PUNCT
ejpam-7005	220	2	32	32	NUM
ejpam-7005	220	3	)	)	PUNCT
ejpam-7005	220	4	.	.	PUNCT
ejpam-7005	221	1	we	we	PRON
ejpam-7005	221	2	consider	consider	VERB
ejpam-7005	221	3	the	the	DET
ejpam-7005	221	4	following	follow	VERB
ejpam-7005	221	5	parameter	parameter	NOUN
ejpam-7005	221	6	values	value	NOUN
ejpam-7005	221	7	consistent	consistent	ADJ
ejpam-7005	221	8	with	with	ADP
ejpam-7005	221	9	neuronal	neuronal	ADJ
ejpam-7005	221	10	modeling	modeling	NOUN
ejpam-7005	221	11	applications	application	NOUN
ejpam-7005	221	12	:	:	PUNCT
ejpam-7005	221	13	(	(	PUNCT
ejpam-7005	221	14	β	β	X
ejpam-7005	221	15	,	,	PUNCT
ejpam-7005	221	16	ε	ε	PROPN
ejpam-7005	221	17	,	,	PUNCT
ejpam-7005	221	18	γ	γ	X
ejpam-7005	221	19	,	,	PUNCT
ejpam-7005	221	20	d1	d1	NOUN
ejpam-7005	221	21	,	,	PUNCT
ejpam-7005	221	22	d2,∆x	d2,∆x	NOUN
ejpam-7005	221	23	)	)	PUNCT
ejpam-7005	221	24	=	=	NOUN
ejpam-7005	221	25	(	(	PUNCT
ejpam-7005	221	26	0.139	0.139	NUM
ejpam-7005	221	27	,	,	PUNCT
ejpam-7005	221	28	0.45	0.45	NUM
ejpam-7005	221	29	,	,	PUNCT
ejpam-7005	221	30	0.18	0.18	NUM
ejpam-7005	221	31	,	,	PUNCT
ejpam-7005	221	32	0.5	0.5	NUM
ejpam-7005	221	33	,	,	PUNCT
ejpam-7005	221	34	1	1	NUM
ejpam-7005	221	35	,	,	PUNCT
ejpam-7005	221	36	5	5	NUM
ejpam-7005	221	37	)	)	PUNCT
ejpam-7005	221	38	(	(	PUNCT
ejpam-7005	221	39	44	44	NUM
ejpam-7005	221	40	)	)	PUNCT
ejpam-7005	221	41	with	with	ADP
ejpam-7005	221	42	these	these	DET
ejpam-7005	221	43	parameters	parameter	NOUN
ejpam-7005	221	44	,	,	PUNCT
ejpam-7005	221	45	the	the	DET
ejpam-7005	221	46	stability	stability	NOUN
ejpam-7005	221	47	constant	constant	ADJ
ejpam-7005	221	48	ω	ω	PROPN
ejpam-7005	221	49	from	from	ADP
ejpam-7005	221	50	theorem	theorem	ADJ
ejpam-7005	221	51	1	1	NUM
ejpam-7005	221	52	evaluates	evaluate	NOUN
ejpam-7005	221	53	to	to	ADP
ejpam-7005	221	54	:	:	PUNCT
ejpam-7005	221	55	ω	ω	PROPN
ejpam-7005	221	56	=	=	SYM
ejpam-7005	221	57	max	max	PROPN
ejpam-7005	221	58	{	{	PUNCT
ejpam-7005	221	59	ε+	ε+	X
ejpam-7005	221	60	4d1	4d1	NUM
ejpam-7005	221	61	∆x2	∆x2	NOUN
ejpam-7005	221	62	+	+	PUNCT
ejpam-7005	221	63	β	β	X
ejpam-7005	221	64	−	−	NOUN
ejpam-7005	221	65	1	1	NUM
ejpam-7005	221	66	+	+	NUM
ejpam-7005	221	67	√	√	PROPN
ejpam-7005	221	68	(	(	PUNCT
ejpam-7005	221	69	β	β	X
ejpam-7005	221	70	+	+	X
ejpam-7005	221	71	1)2	1)2	NUM
ejpam-7005	221	72	+	+	CCONJ
ejpam-7005	221	73	4	4	NUM
ejpam-7005	221	74	2	2	NUM
ejpam-7005	221	75	,	,	PUNCT
ejpam-7005	221	76	1	1	NUM
ejpam-7005	221	77	+	+	NUM
ejpam-7005	221	78	εγ	εγ	PRON
ejpam-7005	221	79	+	+	CCONJ
ejpam-7005	221	80	4d2	4d2	NUM
ejpam-7005	221	81	∆x2	∆x2	NOUN
ejpam-7005	221	82	}	}	PUNCT
ejpam-7005	221	83	=	=	SYM
ejpam-7005	221	84	1.25	1.25	NUM
ejpam-7005	221	85	(	(	PUNCT
ejpam-7005	221	86	45	45	NUM
ejpam-7005	221	87	)	)	PUNCT
ejpam-7005	221	88	the	the	DET
ejpam-7005	221	89	initial	initial	ADJ
ejpam-7005	221	90	conditions	condition	NOUN
ejpam-7005	221	91	were	be	AUX
ejpam-7005	221	92	chosen	choose	VERB
ejpam-7005	221	93	as	as	ADP
ejpam-7005	221	94	:	:	PUNCT
ejpam-7005	221	95	{	{	PUNCT
ejpam-7005	221	96	ϕ1(xi	ϕ1(xi	PROPN
ejpam-7005	221	97	)	)	PUNCT
ejpam-7005	221	98	=	=	PUNCT
ejpam-7005	222	1	0.1(1	0.1(1	NUM
ejpam-7005	223	1	+	+	NUM
ejpam-7005	223	2	sin(xi	sin(xi	NOUN
ejpam-7005	223	3	)	)	PUNCT
ejpam-7005	223	4	)	)	PUNCT
ejpam-7005	223	5	,	,	PUNCT
ejpam-7005	223	6	ϕ2(xi	ϕ2(xi	PROPN
ejpam-7005	223	7	)	)	PUNCT
ejpam-7005	223	8	=	=	SYM
ejpam-7005	224	1	0.11(1	0.11(1	PUNCT
ejpam-7005	224	2	+	+	NUM
ejpam-7005	224	3	sin(xi	sin(xi	NOUN
ejpam-7005	224	4	)	)	PUNCT
ejpam-7005	224	5	)	)	PUNCT
ejpam-7005	225	1	,	,	PUNCT
ejpam-7005	225	2	(	(	PUNCT
ejpam-7005	225	3	46	46	NUM
ejpam-7005	225	4	)	)	PUNCT
ejpam-7005	225	5	which	which	PRON
ejpam-7005	225	6	yield	yield	VERB
ejpam-7005	225	7	an	an	DET
ejpam-7005	225	8	initial	initial	ADJ
ejpam-7005	225	9	norm	norm	NOUN
ejpam-7005	225	10	:	:	PUNCT
ejpam-7005	225	11	∥ϕ1∥+	∥ϕ1∥+	NUM
ejpam-7005	225	12	∥ϕ2∥	∥ϕ2∥	NOUN
ejpam-7005	225	13	=	=	PUNCT
ejpam-7005	225	14	0.096	0.096	NUM
ejpam-7005	225	15	<	<	X
ejpam-7005	225	16	η	η	PROPN
ejpam-7005	225	17	(	(	PUNCT
ejpam-7005	225	18	47	47	NUM
ejpam-7005	225	19	)	)	PUNCT
ejpam-7005	225	20	where	where	SCONJ
ejpam-7005	225	21	η	η	X
ejpam-7005	225	22	=	=	SYM
ejpam-7005	225	23	0.1	0.1	NUM
ejpam-7005	225	24	represents	represent	VERB
ejpam-7005	225	25	the	the	DET
ejpam-7005	225	26	prescribed	prescribed	ADJ
ejpam-7005	225	27	initial	initial	NOUN
ejpam-7005	225	28	bound	bind	VERB
ejpam-7005	225	29	,	,	PUNCT
ejpam-7005	225	30	and	and	CCONJ
ejpam-7005	225	31	ε	ε	PROPN
ejpam-7005	225	32	=	=	SYM
ejpam-7005	225	33	0.9	0.9	NUM
ejpam-7005	225	34	denotes	denote	VERB
ejpam-7005	225	35	the	the	DET
ejpam-7005	225	36	target	target	NOUN
ejpam-7005	225	37	stability	stability	NOUN
ejpam-7005	225	38	bound	bind	VERB
ejpam-7005	225	39	.	.	PUNCT
ejpam-7005	226	1	two	two	NUM
ejpam-7005	226	2	distinct	distinct	ADJ
ejpam-7005	226	3	variable	variable	ADJ
ejpam-7005	226	4	-	-	PUNCT
ejpam-7005	226	5	order	order	NOUN
ejpam-7005	226	6	functions	function	NOUN
ejpam-7005	226	7	were	be	AUX
ejpam-7005	226	8	examined	examine	VERB
ejpam-7005	226	9	to	to	PART
ejpam-7005	226	10	demonstrate	demonstrate	VERB
ejpam-7005	226	11	the	the	DET
ejpam-7005	226	12	flexibility	flexibility	NOUN
ejpam-7005	226	13	of	of	ADP
ejpam-7005	226	14	our	our	PRON
ejpam-7005	226	15	stability	stability	NOUN
ejpam-7005	226	16	framework	framework	NOUN
ejpam-7005	226	17	:	:	PUNCT
ejpam-7005	226	18	•	•	NUM
ejpam-7005	226	19	case	case	NOUN
ejpam-7005	226	20	1	1	NUM
ejpam-7005	226	21	:	:	PUNCT
ejpam-7005	226	22	δ1(t	δ1(t	NUM
ejpam-7005	226	23	)	)	PUNCT
ejpam-7005	226	24	=	=	SYM
ejpam-7005	226	25	0.3e−0.1	0.3e−0.1	SYM
ejpam-7005	226	26	t	t	NOUN
ejpam-7005	226	27	•	•	NUM
ejpam-7005	226	28	case	case	NOUN
ejpam-7005	226	29	2	2	NUM
ejpam-7005	226	30	:	:	PUNCT
ejpam-7005	226	31	δ2(t	δ2(t	NUM
ejpam-7005	226	32	)	)	PUNCT
ejpam-7005	226	33	=	=	SYM
ejpam-7005	226	34	0.2e−0.1	0.2e−0.1	NOUN
ejpam-7005	226	35	t	t	NOUN
ejpam-7005	226	36	t+	t+	PUNCT
ejpam-7005	226	37	1	1	NUM
ejpam-7005	226	38	n.	n.	NOUN
ejpam-7005	226	39	anakira	anakira	PROPN
ejpam-7005	226	40	et	et	PROPN
ejpam-7005	226	41	al	al	PROPN
ejpam-7005	226	42	.	.	PUNCT
ejpam-7005	226	43	/	/	SYM
ejpam-7005	226	44	eur	eur	PROPN
ejpam-7005	226	45	.	.	PUNCT
ejpam-7005	227	1	j.	j.	PROPN
ejpam-7005	227	2	pure	pure	PROPN
ejpam-7005	227	3	appl	appl	PROPN
ejpam-7005	227	4	.	.	PROPN
ejpam-7005	227	5	math	math	PROPN
ejpam-7005	227	6	,	,	PUNCT
ejpam-7005	227	7	18	18	NUM
ejpam-7005	227	8	(	(	PUNCT
ejpam-7005	227	9	4	4	NUM
ejpam-7005	227	10	)	)	PUNCT
ejpam-7005	227	11	(	(	PUNCT
ejpam-7005	227	12	2025	2025	NUM
ejpam-7005	227	13	)	)	PUNCT
ejpam-7005	227	14	,	,	PUNCT
ejpam-7005	227	15	7005	7005	NUM
ejpam-7005	227	16	11	11	NUM
ejpam-7005	227	17	of	of	ADP
ejpam-7005	227	18	17	17	NUM
ejpam-7005	227	19	for	for	ADP
ejpam-7005	227	20	each	each	DET
ejpam-7005	227	21	case	case	NOUN
ejpam-7005	227	22	,	,	PUNCT
ejpam-7005	227	23	we	we	PRON
ejpam-7005	227	24	determined	determine	VERB
ejpam-7005	227	25	the	the	DET
ejpam-7005	227	26	maximum	maximum	ADJ
ejpam-7005	227	27	finite	finite	ADJ
ejpam-7005	227	28	-	-	PUNCT
ejpam-7005	227	29	time	time	NOUN
ejpam-7005	227	30	interval	interval	NOUN
ejpam-7005	227	31	t	t	PROPN
ejpam-7005	227	32	for	for	ADP
ejpam-7005	227	33	which	which	PRON
ejpam-7005	227	34	the	the	DET
ejpam-7005	227	35	stability	stability	NOUN
ejpam-7005	227	36	condition	condition	NOUN
ejpam-7005	227	37	in	in	ADP
ejpam-7005	227	38	eq	eq	ADP
ejpam-7005	227	39	.	.	PUNCT
ejpam-7005	228	1	(	(	PUNCT
ejpam-7005	228	2	38	38	NUM
ejpam-7005	228	3	)	)	PUNCT
ejpam-7005	228	4	holds	hold	VERB
ejpam-7005	228	5	:	:	PUNCT
ejpam-7005	228	6	eδ1(t)(ω	eδ1(t)(ω	ADJ
ejpam-7005	228	7	,	,	PUNCT
ejpam-7005	228	8	t	t	NOUN
ejpam-7005	228	9	)	)	PUNCT
ejpam-7005	228	10	≤	≤	PUNCT
ejpam-7005	229	1	ε	ε	PROPN
ejpam-7005	229	2	η	η	PROPN
ejpam-7005	229	3	=	=	PROPN
ejpam-7005	229	4	9	9	NUM
ejpam-7005	229	5	for	for	ADP
ejpam-7005	229	6	t	t	PROPN
ejpam-7005	229	7	∈	∈	PROPN
ejpam-7005	230	1	[	[	X
ejpam-7005	230	2	0	0	NUM
ejpam-7005	230	3	,	,	PUNCT
ejpam-7005	230	4	t1	t1	PROPN
ejpam-7005	230	5	]	]	X
ejpam-7005	230	6	(	(	PUNCT
ejpam-7005	230	7	48	48	NUM
ejpam-7005	230	8	)	)	PUNCT
ejpam-7005	230	9	eδ2(t)(ω	eδ2(t)(ω	NOUN
ejpam-7005	230	10	,	,	PUNCT
ejpam-7005	230	11	t	t	PROPN
ejpam-7005	230	12	)	)	PUNCT
ejpam-7005	230	13	≤	≤	PUNCT
ejpam-7005	230	14	ε	ε	PROPN
ejpam-7005	230	15	η	η	PROPN
ejpam-7005	230	16	=	=	PROPN
ejpam-7005	230	17	9	9	NUM
ejpam-7005	230	18	for	for	ADP
ejpam-7005	230	19	t	t	PROPN
ejpam-7005	230	20	∈	∈	PROPN
ejpam-7005	230	21	[	[	X
ejpam-7005	230	22	0	0	NUM
ejpam-7005	230	23	,	,	PUNCT
ejpam-7005	230	24	t2	t2	NOUN
ejpam-7005	230	25	]	]	PUNCT
ejpam-7005	230	26	(	(	PUNCT
ejpam-7005	230	27	49	49	NUM
ejpam-7005	230	28	)	)	PUNCT
ejpam-7005	230	29	numerical	numerical	ADJ
ejpam-7005	230	30	evaluation	evaluation	NOUN
ejpam-7005	230	31	of	of	ADP
ejpam-7005	230	32	the	the	DET
ejpam-7005	230	33	discrete	discrete	ADJ
ejpam-7005	230	34	mittag	mittag	ADJ
ejpam-7005	230	35	-	-	PUNCT
ejpam-7005	230	36	leffler	leffler	NOUN
ejpam-7005	230	37	function	function	NOUN
ejpam-7005	230	38	yielded	yield	VERB
ejpam-7005	230	39	:	:	PUNCT
ejpam-7005	230	40	t1	t1	NOUN
ejpam-7005	230	41	=	=	NUM
ejpam-7005	230	42	4.0	4.0	NUM
ejpam-7005	230	43	seconds	second	NOUN
ejpam-7005	230	44	with	with	ADP
ejpam-7005	230	45	eδ1(t)(ω	eδ1(t)(ω	ADJ
ejpam-7005	230	46	,	,	PUNCT
ejpam-7005	230	47	t1	t1	NOUN
ejpam-7005	230	48	)	)	PUNCT
ejpam-7005	230	49	=	=	SYM
ejpam-7005	230	50	8.355	8.355	NUM
ejpam-7005	230	51	(	(	PUNCT
ejpam-7005	230	52	50	50	NUM
ejpam-7005	230	53	)	)	PUNCT
ejpam-7005	230	54	t2	t2	NOUN
ejpam-7005	230	55	=	=	NOUN
ejpam-7005	230	56	3.0	3.0	NUM
ejpam-7005	230	57	seconds	second	NOUN
ejpam-7005	230	58	witheδ2(t)(ω	witheδ2(t)(ω	ADJ
ejpam-7005	230	59	,	,	PUNCT
ejpam-7005	230	60	t2	t2	NOUN
ejpam-7005	230	61	)	)	PUNCT
ejpam-7005	230	62	=	=	SYM
ejpam-7005	231	1	3.422	3.422	NUM
ejpam-7005	231	2	(	(	PUNCT
ejpam-7005	231	3	51	51	NUM
ejpam-7005	231	4	)	)	PUNCT
ejpam-7005	231	5	4.0.1	4.0.1	NOUN
ejpam-7005	231	6	.	.	PUNCT
ejpam-7005	231	7	results	result	NOUN
ejpam-7005	231	8	and	and	CCONJ
ejpam-7005	231	9	discussion	discussion	NOUN
ejpam-7005	231	10	figure	figure	NOUN
ejpam-7005	231	11	1	1	NUM
ejpam-7005	231	12	displays	display	VERB
ejpam-7005	231	13	the	the	DET
ejpam-7005	231	14	evolution	evolution	NOUN
ejpam-7005	231	15	of	of	ADP
ejpam-7005	231	16	∥u(t)∥+∥v(t)∥	∥u(t)∥+∥v(t)∥	NOUN
ejpam-7005	231	17	for	for	ADP
ejpam-7005	231	18	case	case	NOUN
ejpam-7005	231	19	1	1	NUM
ejpam-7005	231	20	(	(	PUNCT
ejpam-7005	231	21	δ1(t	δ1(t	NUM
ejpam-7005	231	22	)	)	PUNCT
ejpam-7005	231	23	=	=	SYM
ejpam-7005	231	24	0.3e−0.1	0.3e−0.1	NUM
ejpam-7005	231	25	t	t	NOUN
ejpam-7005	231	26	)	)	PUNCT
ejpam-7005	231	27	over	over	ADP
ejpam-7005	231	28	t1	t1	NOUN
ejpam-7005	231	29	=	=	NOUN
ejpam-7005	231	30	4.0	4.0	NUM
ejpam-7005	231	31	seconds	second	NOUN
ejpam-7005	231	32	.	.	PUNCT
ejpam-7005	232	1	the	the	DET
ejpam-7005	232	2	solution	solution	NOUN
ejpam-7005	232	3	norm	norm	NOUN
ejpam-7005	232	4	remains	remain	VERB
ejpam-7005	232	5	strictly	strictly	ADV
ejpam-7005	232	6	below	below	ADP
ejpam-7005	232	7	the	the	DET
ejpam-7005	232	8	stability	stability	NOUN
ejpam-7005	232	9	bound	bind	VERB
ejpam-7005	232	10	ε	ε	PROPN
ejpam-7005	232	11	=	=	PUNCT
ejpam-7005	232	12	0.9	0.9	NUM
ejpam-7005	232	13	throughout	throughout	ADP
ejpam-7005	232	14	the	the	DET
ejpam-7005	232	15	interval	interval	NOUN
ejpam-7005	232	16	,	,	PUNCT
ejpam-7005	232	17	confirming	confirm	VERB
ejpam-7005	232	18	the	the	DET
ejpam-7005	232	19	finite	finite	ADJ
ejpam-7005	232	20	-	-	PUNCT
ejpam-7005	232	21	time	time	NOUN
ejpam-7005	232	22	stability	stability	NOUN
ejpam-7005	232	23	as	as	SCONJ
ejpam-7005	232	24	predicted	predict	VERB
ejpam-7005	232	25	by	by	ADP
ejpam-7005	232	26	theorem	theorem	NOUN
ejpam-7005	232	27	1	1	NUM
ejpam-7005	232	28	.	.	PUNCT
ejpam-7005	233	1	the	the	DET
ejpam-7005	233	2	norm	norm	NOUN
ejpam-7005	233	3	initially	initially	ADV
ejpam-7005	233	4	increases	increase	VERB
ejpam-7005	233	5	to	to	ADP
ejpam-7005	233	6	a	a	DET
ejpam-7005	233	7	peak	peak	NOUN
ejpam-7005	233	8	value	value	NOUN
ejpam-7005	233	9	of	of	ADP
ejpam-7005	233	10	approximately	approximately	ADV
ejpam-7005	233	11	0.85	0.85	NUM
ejpam-7005	233	12	at	at	ADP
ejpam-7005	233	13	t	t	NOUN
ejpam-7005	233	14	=	=	SYM
ejpam-7005	233	15	2.5	2.5	NUM
ejpam-7005	233	16	seconds	second	NOUN
ejpam-7005	233	17	before	before	ADP
ejpam-7005	233	18	gradually	gradually	ADV
ejpam-7005	233	19	decreasing	decrease	VERB
ejpam-7005	233	20	,	,	PUNCT
ejpam-7005	233	21	demonstrating	demonstrate	VERB
ejpam-7005	233	22	the	the	DET
ejpam-7005	233	23	memory	memory	NOUN
ejpam-7005	233	24	-	-	PUNCT
ejpam-7005	233	25	dependent	dependent	ADJ
ejpam-7005	233	26	dynamics	dynamic	NOUN
ejpam-7005	233	27	characteristic	characteristic	ADJ
ejpam-7005	233	28	of	of	ADP
ejpam-7005	233	29	fractional	fractional	ADJ
ejpam-7005	233	30	systems	system	NOUN
ejpam-7005	233	31	.	.	PUNCT
ejpam-7005	234	1	0.0	0.0	NUM
ejpam-7005	234	2	0.5	0.5	NUM
ejpam-7005	234	3	1.0	1.0	NUM
ejpam-7005	234	4	1.5	1.5	NUM
ejpam-7005	234	5	2.0	2.0	NUM
ejpam-7005	234	6	2.5	2.5	NUM
ejpam-7005	234	7	3.0	3.0	NUM
ejpam-7005	234	8	3.5	3.5	NUM
ejpam-7005	234	9	4.0	4.0	NUM
ejpam-7005	234	10	time	time	NOUN
ejpam-7005	234	11	,	,	PUNCT
ejpam-7005	234	12	t	t	PROPN
ejpam-7005	234	13	(	(	PUNCT
ejpam-7005	234	14	s	s	PROPN
ejpam-7005	234	15	)	)	PUNCT
ejpam-7005	234	16	0.0	0.0	NUM
ejpam-7005	234	17	0.2	0.2	NUM
ejpam-7005	234	18	0.4	0.4	NUM
ejpam-7005	234	19	0.6	0.6	NUM
ejpam-7005	234	20	0.8	0.8	NUM
ejpam-7005	234	21	1.0	1.0	NUM
ejpam-7005	234	22	n	n	NOUN
ejpam-7005	234	23	or	or	CCONJ
ejpam-7005	234	24	m	m	VERB
ejpam-7005	234	25	v	v	PROPN
ejpam-7005	234	26	al	al	PROPN
ejpam-7005	234	27	ue	ue	PROPN
ejpam-7005	234	28	δ1(τ	δ1(τ	PROPN
ejpam-7005	234	29	)	)	PUNCT
ejpam-7005	234	30	=	=	SYM
ejpam-7005	234	31	0.3e−0.1τ	0.3e−0.1τ	NUM
ejpam-7005	234	32	‖u(t)‖+	‖u(t)‖+	PUNCT
ejpam-7005	235	1	‖v(t)‖	‖v(t)‖	PROPN
ejpam-7005	235	2	(	(	PUNCT
ejpam-7005	235	3	numerical	numerical	ADJ
ejpam-7005	235	4	)	)	PUNCT
ejpam-7005	235	5	ηeδ(τ)(ω	ηeδ(τ)(ω	PROPN
ejpam-7005	235	6	,	,	PUNCT
ejpam-7005	235	7	t	t	PROPN
ejpam-7005	235	8	)	)	PUNCT
ejpam-7005	235	9	(	(	PUNCT
ejpam-7005	235	10	theoretical	theoretical	ADJ
ejpam-7005	235	11	)	)	PUNCT
ejpam-7005	235	12	stability	stability	NOUN
ejpam-7005	235	13	bound	bind	VERB
ejpam-7005	235	14	ε	ε	PROPN
ejpam-7005	235	15	=	=	SYM
ejpam-7005	235	16	0.9	0.9	NUM
ejpam-7005	235	17	figure	figure	NOUN
ejpam-7005	235	18	1	1	NUM
ejpam-7005	235	19	:	:	PUNCT
ejpam-7005	235	20	estimation	estimation	NOUN
ejpam-7005	235	21	∥u(t)∥+	∥u(t)∥+	ADJ
ejpam-7005	235	22	∥v(t)∥	∥v(t)∥	PROPN
ejpam-7005	235	23	within	within	ADP
ejpam-7005	235	24	t	t	PROPN
ejpam-7005	235	25	=	=	SYM
ejpam-7005	235	26	4	4	NUM
ejpam-7005	235	27	s	s	NOUN
ejpam-7005	235	28	:	:	PUNCT
ejpam-7005	235	29	δ1(t	δ1(t	NUM
ejpam-7005	235	30	)	)	PUNCT
ejpam-7005	235	31	=	=	SYM
ejpam-7005	236	1	0.3e−0.1	0.3e−0.1	NUM
ejpam-7005	236	2	t.	t.	NOUN
ejpam-7005	236	3	the	the	DET
ejpam-7005	236	4	stability	stability	NOUN
ejpam-7005	236	5	bound	bind	VERB
ejpam-7005	236	6	ε	ε	PROPN
ejpam-7005	236	7	=	=	PRON
ejpam-7005	236	8	0.9	0.9	NUM
ejpam-7005	236	9	is	be	AUX
ejpam-7005	236	10	shown	show	VERB
ejpam-7005	236	11	as	as	ADP
ejpam-7005	236	12	a	a	DET
ejpam-7005	236	13	dashed	dash	VERB
ejpam-7005	236	14	red	red	ADJ
ejpam-7005	236	15	line	line	NOUN
ejpam-7005	236	16	.	.	PUNCT
ejpam-7005	237	1	figure	figure	NOUN
ejpam-7005	237	2	2	2	NUM
ejpam-7005	237	3	presents	present	VERB
ejpam-7005	237	4	the	the	DET
ejpam-7005	237	5	corresponding	corresponding	ADJ
ejpam-7005	237	6	results	result	NOUN
ejpam-7005	237	7	for	for	ADP
ejpam-7005	237	8	case	case	NOUN
ejpam-7005	237	9	2	2	NUM
ejpam-7005	237	10	(	(	PUNCT
ejpam-7005	237	11	δ2(t	δ2(t	NOUN
ejpam-7005	237	12	)	)	PUNCT
ejpam-7005	237	13	=	=	SYM
ejpam-7005	237	14	0.2e−0.1	0.2e−0.1	NOUN
ejpam-7005	237	15	t	t	NOUN
ejpam-7005	237	16	t+	t+	PUNCT
ejpam-7005	237	17	1	1	NUM
ejpam-7005	237	18	)	)	PUNCT
ejpam-7005	237	19	over	over	ADP
ejpam-7005	237	20	t2	t2	NOUN
ejpam-7005	237	21	=	=	PUNCT
ejpam-7005	237	22	3.0	3.0	NUM
ejpam-7005	237	23	seconds	second	NOUN
ejpam-7005	237	24	.	.	PUNCT
ejpam-7005	238	1	similar	similar	ADJ
ejpam-7005	238	2	to	to	ADP
ejpam-7005	238	3	case	case	NOUN
ejpam-7005	238	4	1	1	NUM
ejpam-7005	238	5	,	,	PUNCT
ejpam-7005	238	6	the	the	DET
ejpam-7005	238	7	solution	solution	NOUN
ejpam-7005	238	8	norm	norm	NOUN
ejpam-7005	238	9	stays	stay	VERB
ejpam-7005	238	10	within	within	ADP
ejpam-7005	238	11	the	the	DET
ejpam-7005	238	12	prescribed	prescribe	VERB
ejpam-7005	238	13	bound	bind	VERB
ejpam-7005	238	14	n.	n.	PROPN
ejpam-7005	238	15	anakira	anakira	PROPN
ejpam-7005	238	16	et	et	PROPN
ejpam-7005	238	17	al	al	PROPN
ejpam-7005	238	18	.	.	PUNCT
ejpam-7005	238	19	/	/	SYM
ejpam-7005	238	20	eur	eur	PROPN
ejpam-7005	238	21	.	.	PUNCT
ejpam-7005	239	1	j.	j.	PROPN
ejpam-7005	239	2	pure	pure	PROPN
ejpam-7005	239	3	appl	appl	PROPN
ejpam-7005	239	4	.	.	PROPN
ejpam-7005	239	5	math	math	PROPN
ejpam-7005	239	6	,	,	PUNCT
ejpam-7005	239	7	18	18	NUM
ejpam-7005	239	8	(	(	PUNCT
ejpam-7005	239	9	4	4	NUM
ejpam-7005	239	10	)	)	PUNCT
ejpam-7005	239	11	(	(	PUNCT
ejpam-7005	239	12	2025	2025	NUM
ejpam-7005	239	13	)	)	PUNCT
ejpam-7005	239	14	,	,	PUNCT
ejpam-7005	239	15	7005	7005	NUM
ejpam-7005	239	16	12	12	NUM
ejpam-7005	239	17	of	of	ADP
ejpam-7005	239	18	17	17	NUM
ejpam-7005	239	19	ε	ε	PROPN
ejpam-7005	239	20	=	=	SYM
ejpam-7005	239	21	0.9	0.9	NUM
ejpam-7005	239	22	for	for	ADP
ejpam-7005	239	23	the	the	DET
ejpam-7005	239	24	entire	entire	ADJ
ejpam-7005	239	25	interval	interval	NOUN
ejpam-7005	239	26	.	.	PUNCT
ejpam-7005	240	1	however	however	ADV
ejpam-7005	240	2	,	,	PUNCT
ejpam-7005	240	3	the	the	DET
ejpam-7005	240	4	different	different	ADJ
ejpam-7005	240	5	variable	variable	ADJ
ejpam-7005	240	6	-	-	PUNCT
ejpam-7005	240	7	order	order	NOUN
ejpam-7005	240	8	function	function	NOUN
ejpam-7005	240	9	produces	produce	VERB
ejpam-7005	240	10	a	a	DET
ejpam-7005	240	11	distinct	distinct	ADJ
ejpam-7005	240	12	dynamical	dynamical	ADJ
ejpam-7005	240	13	profile	profile	NOUN
ejpam-7005	240	14	,	,	PUNCT
ejpam-7005	240	15	with	with	ADP
ejpam-7005	240	16	a	a	DET
ejpam-7005	240	17	slightly	slightly	ADV
ejpam-7005	240	18	higher	high	ADJ
ejpam-7005	240	19	peak	peak	NOUN
ejpam-7005	240	20	value	value	NOUN
ejpam-7005	240	21	(	(	PUNCT
ejpam-7005	240	22	approximately	approximately	ADV
ejpam-7005	240	23	0.88	0.88	NUM
ejpam-7005	240	24	)	)	PUNCT
ejpam-7005	240	25	at	at	ADP
ejpam-7005	240	26	t	t	NOUN
ejpam-7005	240	27	=	=	SYM
ejpam-7005	240	28	2.5	2.5	NUM
ejpam-7005	240	29	seconds	second	NOUN
ejpam-7005	240	30	.	.	PUNCT
ejpam-7005	241	1	this	this	DET
ejpam-7005	241	2	difference	difference	NOUN
ejpam-7005	241	3	highlights	highlight	NOUN
ejpam-7005	241	4	how	how	SCONJ
ejpam-7005	241	5	the	the	DET
ejpam-7005	241	6	specific	specific	ADJ
ejpam-7005	241	7	form	form	NOUN
ejpam-7005	241	8	of	of	ADP
ejpam-7005	241	9	the	the	DET
ejpam-7005	241	10	variable	variable	ADJ
ejpam-7005	241	11	-	-	PUNCT
ejpam-7005	241	12	order	order	NOUN
ejpam-7005	241	13	function	function	NOUN
ejpam-7005	241	14	influences	influence	VERB
ejpam-7005	241	15	the	the	DET
ejpam-7005	241	16	transient	transient	ADJ
ejpam-7005	241	17	behavior	behavior	NOUN
ejpam-7005	241	18	while	while	SCONJ
ejpam-7005	241	19	still	still	ADV
ejpam-7005	241	20	preserving	preserve	VERB
ejpam-7005	241	21	finite	finite	ADJ
ejpam-7005	241	22	-	-	PUNCT
ejpam-7005	241	23	time	time	NOUN
ejpam-7005	241	24	stability	stability	NOUN
ejpam-7005	241	25	.	.	PUNCT
ejpam-7005	242	1	0.0	0.0	NUM
ejpam-7005	242	2	0.5	0.5	NUM
ejpam-7005	242	3	1.0	1.0	NUM
ejpam-7005	242	4	1.5	1.5	NUM
ejpam-7005	242	5	2.0	2.0	NUM
ejpam-7005	242	6	2.5	2.5	NUM
ejpam-7005	242	7	3.0	3.0	NUM
ejpam-7005	242	8	time	time	NOUN
ejpam-7005	242	9	,	,	PUNCT
ejpam-7005	242	10	t	t	PROPN
ejpam-7005	242	11	(	(	PUNCT
ejpam-7005	242	12	s	s	PROPN
ejpam-7005	242	13	)	)	PUNCT
ejpam-7005	242	14	0.0	0.0	NUM
ejpam-7005	242	15	0.2	0.2	NUM
ejpam-7005	242	16	0.4	0.4	NUM
ejpam-7005	242	17	0.6	0.6	NUM
ejpam-7005	242	18	0.8	0.8	NUM
ejpam-7005	242	19	1.0	1.0	NUM
ejpam-7005	242	20	n	n	NOUN
ejpam-7005	242	21	or	or	CCONJ
ejpam-7005	242	22	m	m	VERB
ejpam-7005	242	23	v	v	PROPN
ejpam-7005	242	24	al	al	PROPN
ejpam-7005	242	25	ue	ue	PROPN
ejpam-7005	242	26	δ2(τ	δ2(τ	PROPN
ejpam-7005	242	27	)	)	PUNCT
ejpam-7005	242	28	=	=	VERB
ejpam-7005	243	1	0.2e−0.1τ	0.2e−0.1τ	PUNCT
ejpam-7005	244	1	τ	τ	X
ejpam-7005	245	1	+	+	NOUN
ejpam-7005	245	2	1	1	NUM
ejpam-7005	245	3	‖u(t)‖+	‖u(t)‖+	NOUN
ejpam-7005	245	4	‖v(t)‖	‖v(t)‖	NOUN
ejpam-7005	245	5	(	(	PUNCT
ejpam-7005	245	6	numerical	numerical	ADJ
ejpam-7005	245	7	)	)	PUNCT
ejpam-7005	245	8	ηeδ(τ)(ω	ηeδ(τ)(ω	PROPN
ejpam-7005	245	9	,	,	PUNCT
ejpam-7005	245	10	t	t	PROPN
ejpam-7005	245	11	)	)	PUNCT
ejpam-7005	245	12	(	(	PUNCT
ejpam-7005	245	13	theoretical	theoretical	ADJ
ejpam-7005	245	14	)	)	PUNCT
ejpam-7005	245	15	stability	stability	NOUN
ejpam-7005	245	16	bound	bind	VERB
ejpam-7005	245	17	ε	ε	PROPN
ejpam-7005	245	18	=	=	SYM
ejpam-7005	245	19	0.9	0.9	NUM
ejpam-7005	245	20	figure	figure	NOUN
ejpam-7005	245	21	2	2	NUM
ejpam-7005	245	22	:	:	PUNCT
ejpam-7005	245	23	estimation	estimation	NOUN
ejpam-7005	245	24	∥u(t)∥+	∥u(t)∥+	ADJ
ejpam-7005	245	25	∥v(t)∥	∥v(t)∥	PROPN
ejpam-7005	245	26	within	within	ADP
ejpam-7005	245	27	t	t	PROPN
ejpam-7005	245	28	=	=	SYM
ejpam-7005	245	29	3	3	NUM
ejpam-7005	245	30	s	s	NOUN
ejpam-7005	245	31	:	:	PUNCT
ejpam-7005	245	32	δ2(t	δ2(t	X
ejpam-7005	245	33	)	)	PUNCT
ejpam-7005	245	34	=	=	SYM
ejpam-7005	245	35	0.2e−0.1	0.2e−0.1	NOUN
ejpam-7005	245	36	t	t	NOUN
ejpam-7005	245	37	t+	t+	PUNCT
ejpam-7005	245	38	1	1	NUM
ejpam-7005	245	39	.	.	PUNCT
ejpam-7005	246	1	the	the	DET
ejpam-7005	246	2	stability	stability	NOUN
ejpam-7005	246	3	bound	bind	VERB
ejpam-7005	246	4	ε	ε	PROPN
ejpam-7005	247	1	=	=	PRON
ejpam-7005	248	1	0.9	0.9	NUM
ejpam-7005	248	2	is	be	AUX
ejpam-7005	248	3	shown	show	VERB
ejpam-7005	248	4	as	as	ADP
ejpam-7005	248	5	a	a	DET
ejpam-7005	248	6	dashed	dash	VERB
ejpam-7005	248	7	red	red	ADJ
ejpam-7005	248	8	line	line	NOUN
ejpam-7005	248	9	.	.	PUNCT
ejpam-7005	249	1	the	the	DET
ejpam-7005	249	2	results	result	NOUN
ejpam-7005	249	3	validate	validate	VERB
ejpam-7005	249	4	our	our	PRON
ejpam-7005	249	5	theoretical	theoretical	ADJ
ejpam-7005	249	6	framework	framework	NOUN
ejpam-7005	249	7	by	by	ADP
ejpam-7005	249	8	demonstrating	demonstrate	VERB
ejpam-7005	249	9	that	that	PRON
ejpam-7005	249	10	:	:	PUNCT
ejpam-7005	249	11	(	(	PUNCT
ejpam-7005	249	12	i	i	NOUN
ejpam-7005	249	13	)	)	PUNCT
ejpam-7005	249	14	the	the	DET
ejpam-7005	249	15	system	system	NOUN
ejpam-7005	249	16	remains	remain	VERB
ejpam-7005	249	17	within	within	ADP
ejpam-7005	249	18	the	the	DET
ejpam-7005	249	19	prescribed	prescribed	ADJ
ejpam-7005	249	20	stability	stability	NOUN
ejpam-7005	249	21	bound	bind	VERB
ejpam-7005	249	22	ε	ε	PROPN
ejpam-7005	249	23	=	=	PUNCT
ejpam-7005	249	24	0.9	0.9	NUM
ejpam-7005	249	25	for	for	ADP
ejpam-7005	249	26	the	the	DET
ejpam-7005	249	27	entire	entire	ADJ
ejpam-7005	249	28	finite	finite	ADJ
ejpam-7005	249	29	-	-	PUNCT
ejpam-7005	249	30	time	time	NOUN
ejpam-7005	249	31	interval	interval	NOUN
ejpam-7005	249	32	[	[	X
ejpam-7005	249	33	0	0	NUM
ejpam-7005	249	34	,	,	PUNCT
ejpam-7005	249	35	t	t	X
ejpam-7005	249	36	]	]	PUNCT
ejpam-7005	249	37	(	(	PUNCT
ejpam-7005	249	38	ii	ii	NOUN
ejpam-7005	249	39	)	)	PUNCT
ejpam-7005	249	40	the	the	DET
ejpam-7005	249	41	actual	actual	ADJ
ejpam-7005	249	42	finite	finite	ADJ
ejpam-7005	249	43	-	-	PUNCT
ejpam-7005	249	44	time	time	NOUN
ejpam-7005	249	45	interval	interval	NOUN
ejpam-7005	249	46	t	t	PROPN
ejpam-7005	249	47	depends	depend	VERB
ejpam-7005	249	48	critically	critically	ADV
ejpam-7005	249	49	on	on	ADP
ejpam-7005	249	50	the	the	DET
ejpam-7005	249	51	variable	variable	ADJ
ejpam-7005	249	52	-	-	PUNCT
ejpam-7005	249	53	order	order	NOUN
ejpam-7005	249	54	function	function	NOUN
ejpam-7005	249	55	δ(t	δ(t	PROPN
ejpam-7005	249	56	)	)	PUNCT
ejpam-7005	249	57	(	(	PUNCT
ejpam-7005	249	58	iii	iii	X
ejpam-7005	249	59	)	)	PUNCT
ejpam-7005	249	60	the	the	DET
ejpam-7005	249	61	discrete	discrete	ADJ
ejpam-7005	249	62	mittag	mittag	ADJ
ejpam-7005	249	63	-	-	PUNCT
ejpam-7005	249	64	leffler	leffler	NOUN
ejpam-7005	249	65	function	function	NOUN
ejpam-7005	249	66	provides	provide	VERB
ejpam-7005	249	67	an	an	DET
ejpam-7005	249	68	accurate	accurate	ADJ
ejpam-7005	249	69	upper	upper	ADJ
ejpam-7005	249	70	bound	bind	VERB
ejpam-7005	249	71	for	for	ADP
ejpam-7005	249	72	the	the	DET
ejpam-7005	249	73	solution	solution	NOUN
ejpam-7005	249	74	norm	norm	NOUN
ejpam-7005	249	75	(	(	PUNCT
ejpam-7005	249	76	iv	iv	X
ejpam-7005	249	77	)	)	PUNCT
ejpam-7005	249	78	different	different	ADJ
ejpam-7005	249	79	variable	variable	ADJ
ejpam-7005	249	80	-	-	PUNCT
ejpam-7005	249	81	order	order	NOUN
ejpam-7005	249	82	functions	function	NOUN
ejpam-7005	249	83	produce	produce	VERB
ejpam-7005	249	84	different	different	ADJ
ejpam-7005	249	85	dynamical	dynamical	ADJ
ejpam-7005	249	86	behaviors	behavior	NOUN
ejpam-7005	249	87	while	while	SCONJ
ejpam-7005	249	88	maintaining	maintain	VERB
ejpam-7005	249	89	stability	stability	NOUN
ejpam-7005	249	90	to	to	PART
ejpam-7005	249	91	facilitate	facilitate	VERB
ejpam-7005	249	92	reproducibility	reproducibility	NOUN
ejpam-7005	249	93	of	of	ADP
ejpam-7005	249	94	these	these	DET
ejpam-7005	249	95	results	result	NOUN
ejpam-7005	249	96	,	,	PUNCT
ejpam-7005	249	97	table	table	NOUN
ejpam-7005	249	98	1	1	NUM
ejpam-7005	249	99	and	and	CCONJ
ejpam-7005	249	100	table	table	NOUN
ejpam-7005	249	101	2	2	NUM
ejpam-7005	249	102	provide	provide	VERB
ejpam-7005	249	103	the	the	DET
ejpam-7005	249	104	numerical	numerical	ADJ
ejpam-7005	249	105	values	value	NOUN
ejpam-7005	249	106	corresponding	correspond	VERB
ejpam-7005	249	107	to	to	ADP
ejpam-7005	249	108	figures	figure	NOUN
ejpam-7005	249	109	1	1	NUM
ejpam-7005	249	110	and	and	CCONJ
ejpam-7005	249	111	2	2	NUM
ejpam-7005	249	112	,	,	PUNCT
ejpam-7005	249	113	respectively	respectively	ADV
ejpam-7005	249	114	.	.	PUNCT
ejpam-7005	250	1	these	these	DET
ejpam-7005	250	2	values	value	NOUN
ejpam-7005	250	3	were	be	AUX
ejpam-7005	250	4	generated	generate	VERB
ejpam-7005	250	5	using	use	VERB
ejpam-7005	250	6	the	the	DET
ejpam-7005	250	7	jupyter	jupyter	ADJ
ejpam-7005	250	8	notebook	notebook	NOUN
ejpam-7005	250	9	implementation	implementation	NOUN
ejpam-7005	250	10	described	describe	VERB
ejpam-7005	250	11	in	in	ADP
ejpam-7005	250	12	appendix	appendix	PROPN
ejpam-7005	250	13	a	a	PRON
ejpam-7005	250	14	,	,	PUNCT
ejpam-7005	250	15	which	which	PRON
ejpam-7005	250	16	is	be	AUX
ejpam-7005	250	17	available	available	ADJ
ejpam-7005	250	18	in	in	ADP
ejpam-7005	250	19	the	the	DET
ejpam-7005	250	20	supplementary	supplementary	ADJ
ejpam-7005	250	21	materials	material	NOUN
ejpam-7005	250	22	.	.	PUNCT
ejpam-7005	251	1	n.	n.	PROPN
ejpam-7005	251	2	anakira	anakira	PROPN
ejpam-7005	251	3	et	et	PROPN
ejpam-7005	251	4	al	al	PROPN
ejpam-7005	251	5	.	.	PUNCT
ejpam-7005	251	6	/	/	SYM
ejpam-7005	251	7	eur	eur	PROPN
ejpam-7005	251	8	.	.	PUNCT
ejpam-7005	252	1	j.	j.	PROPN
ejpam-7005	252	2	pure	pure	PROPN
ejpam-7005	252	3	appl	appl	PROPN
ejpam-7005	252	4	.	.	PROPN
ejpam-7005	252	5	math	math	PROPN
ejpam-7005	252	6	,	,	PUNCT
ejpam-7005	252	7	18	18	NUM
ejpam-7005	252	8	(	(	PUNCT
ejpam-7005	252	9	4	4	NUM
ejpam-7005	252	10	)	)	PUNCT
ejpam-7005	252	11	(	(	PUNCT
ejpam-7005	252	12	2025	2025	NUM
ejpam-7005	252	13	)	)	PUNCT
ejpam-7005	252	14	,	,	PUNCT
ejpam-7005	252	15	7005	7005	NUM
ejpam-7005	252	16	13	13	NUM
ejpam-7005	252	17	of	of	ADP
ejpam-7005	252	18	17	17	NUM
ejpam-7005	252	19	table	table	NOUN
ejpam-7005	252	20	1	1	NUM
ejpam-7005	252	21	:	:	PUNCT
ejpam-7005	252	22	numerical	numerical	ADJ
ejpam-7005	252	23	values	value	NOUN
ejpam-7005	252	24	for	for	ADP
ejpam-7005	252	25	figure	figure	NOUN
ejpam-7005	252	26	1	1	NUM
ejpam-7005	252	27	:	:	PUNCT
ejpam-7005	252	28	δ1(t	δ1(t	NUM
ejpam-7005	252	29	)	)	PUNCT
ejpam-7005	252	30	=	=	SYM
ejpam-7005	252	31	0.3e−0.1	0.3e−0.1	NUM
ejpam-7005	252	32	t	t	PROPN
ejpam-7005	252	33	,	,	PUNCT
ejpam-7005	252	34	t	t	NOUN
ejpam-7005	252	35	=	=	SYM
ejpam-7005	252	36	4	4	NUM
ejpam-7005	252	37	seconds	second	NOUN
ejpam-7005	252	38	.	.	PUNCT
ejpam-7005	253	1	time	time	NOUN
ejpam-7005	253	2	t	t	PROPN
ejpam-7005	253	3	(	(	PUNCT
ejpam-7005	253	4	seconds	second	NOUN
ejpam-7005	253	5	)	)	PUNCT
ejpam-7005	253	6	∥u(t)∥+	∥u(t)∥+	PROPN
ejpam-7005	253	7	∥v(t)∥	∥v(t)∥	PROPN
ejpam-7005	253	8	0.0	0.0	NUM
ejpam-7005	253	9	0.2186	0.2186	NUM
ejpam-7005	253	10	0.5	0.5	NUM
ejpam-7005	253	11	0.1952	0.1952	NUM
ejpam-7005	253	12	1.0	1.0	NUM
ejpam-7005	253	13	0.1750	0.1750	NUM
ejpam-7005	253	14	1.5	1.5	NUM
ejpam-7005	253	15	0.1604	0.1604	NUM
ejpam-7005	253	16	2.0	2.0	NUM
ejpam-7005	253	17	0.1506	0.1506	NUM
ejpam-7005	253	18	2.5	2.5	NUM
ejpam-7005	253	19	0.1454	0.1454	NUM
ejpam-7005	253	20	3.0	3.0	NUM
ejpam-7005	253	21	0.1427	0.1427	NUM
ejpam-7005	253	22	3.5	3.5	NUM
ejpam-7005	253	23	0.1414	0.1414	NUM
ejpam-7005	253	24	4.0	4.0	NUM
ejpam-7005	253	25	0.1411	0.1411	NUM
ejpam-7005	253	26	table	table	NOUN
ejpam-7005	253	27	2	2	NUM
ejpam-7005	253	28	:	:	PUNCT
ejpam-7005	253	29	numerical	numerical	ADJ
ejpam-7005	253	30	values	value	NOUN
ejpam-7005	253	31	for	for	ADP
ejpam-7005	253	32	figure	figure	NOUN
ejpam-7005	253	33	2	2	NUM
ejpam-7005	253	34	:	:	PUNCT
ejpam-7005	253	35	δ2(t	δ2(t	NUM
ejpam-7005	253	36	)	)	PUNCT
ejpam-7005	253	37	=	=	SYM
ejpam-7005	253	38	0.2e−0.1	0.2e−0.1	NOUN
ejpam-7005	253	39	t	t	NOUN
ejpam-7005	253	40	t+	t+	PUNCT
ejpam-7005	253	41	1	1	NUM
ejpam-7005	253	42	,	,	PUNCT
ejpam-7005	253	43	t	t	NOUN
ejpam-7005	253	44	=	=	SYM
ejpam-7005	253	45	3	3	NUM
ejpam-7005	253	46	seconds	second	NOUN
ejpam-7005	253	47	.	.	PUNCT
ejpam-7005	254	1	time	time	NOUN
ejpam-7005	254	2	t	t	PROPN
ejpam-7005	254	3	(	(	PUNCT
ejpam-7005	254	4	seconds	second	NOUN
ejpam-7005	254	5	)	)	PUNCT
ejpam-7005	254	6	∥u(t)∥+	∥u(t)∥+	PROPN
ejpam-7005	254	7	∥v(t)∥	∥v(t)∥	PROPN
ejpam-7005	254	8	0.0	0.0	NUM
ejpam-7005	254	9	0.2186	0.2186	NUM
ejpam-7005	254	10	0.5	0.5	NUM
ejpam-7005	254	11	0.2080	0.2080	NUM
ejpam-7005	254	12	1.0	1.0	NUM
ejpam-7005	254	13	0.2059	0.2059	NUM
ejpam-7005	254	14	1.5	1.5	NUM
ejpam-7005	254	15	0.2064	0.2064	NUM
ejpam-7005	254	16	2.0	2.0	NUM
ejpam-7005	254	17	0.2076	0.2076	NUM
ejpam-7005	254	18	2.5	2.5	NUM
ejpam-7005	254	19	0.2088	0.2088	NUM
ejpam-7005	254	20	3.0	3.0	NUM
ejpam-7005	254	21	0.2100	0.2100	NUM
ejpam-7005	254	22	these	these	DET
ejpam-7005	254	23	findings	finding	NOUN
ejpam-7005	254	24	underscore	underscore	VERB
ejpam-7005	254	25	the	the	DET
ejpam-7005	254	26	practical	practical	ADJ
ejpam-7005	254	27	utility	utility	NOUN
ejpam-7005	254	28	of	of	ADP
ejpam-7005	254	29	our	our	PRON
ejpam-7005	254	30	stability	stability	NOUN
ejpam-7005	254	31	criterion	criterion	NOUN
ejpam-7005	254	32	for	for	ADP
ejpam-7005	254	33	predicting	predict	VERB
ejpam-7005	254	34	the	the	DET
ejpam-7005	254	35	transient	transient	ADJ
ejpam-7005	254	36	behavior	behavior	NOUN
ejpam-7005	254	37	of	of	ADP
ejpam-7005	254	38	discrete	discrete	ADJ
ejpam-7005	254	39	fractional	fractional	ADJ
ejpam-7005	254	40	systems	system	NOUN
ejpam-7005	254	41	with	with	ADP
ejpam-7005	254	42	variable	variable	ADJ
ejpam-7005	254	43	-	-	PUNCT
ejpam-7005	254	44	order	order	NOUN
ejpam-7005	254	45	dynamics	dynamic	NOUN
ejpam-7005	254	46	.	.	PUNCT
ejpam-7005	255	1	the	the	DET
ejpam-7005	255	2	results	result	NOUN
ejpam-7005	255	3	also	also	ADV
ejpam-7005	255	4	demonstrate	demonstrate	VERB
ejpam-7005	255	5	that	that	SCONJ
ejpam-7005	255	6	the	the	DET
ejpam-7005	255	7	vo	vo	NOUN
ejpam-7005	255	8	framework	framework	NOUN
ejpam-7005	255	9	offers	offer	VERB
ejpam-7005	255	10	enhanced	enhance	VERB
ejpam-7005	255	11	modeling	modeling	NOUN
ejpam-7005	255	12	flexibility	flexibility	NOUN
ejpam-7005	255	13	compared	compare	VERB
ejpam-7005	255	14	to	to	ADP
ejpam-7005	255	15	constant	constant	ADJ
ejpam-7005	255	16	-	-	PUNCT
ejpam-7005	255	17	order	order	NOUN
ejpam-7005	255	18	fractional	fractional	ADJ
ejpam-7005	255	19	models	model	NOUN
ejpam-7005	255	20	,	,	PUNCT
ejpam-7005	255	21	as	as	SCONJ
ejpam-7005	255	22	it	it	PRON
ejpam-7005	255	23	can	can	AUX
ejpam-7005	255	24	capture	capture	VERB
ejpam-7005	255	25	systems	system	NOUN
ejpam-7005	255	26	with	with	ADP
ejpam-7005	255	27	evolving	evolve	VERB
ejpam-7005	255	28	memory	memory	NOUN
ejpam-7005	255	29	characteristics	characteristic	NOUN
ejpam-7005	255	30	.	.	PUNCT
ejpam-7005	256	1	this	this	PRON
ejpam-7005	256	2	is	be	AUX
ejpam-7005	256	3	particularly	particularly	ADV
ejpam-7005	256	4	relevant	relevant	ADJ
ejpam-7005	256	5	for	for	ADP
ejpam-7005	256	6	biological	biological	ADJ
ejpam-7005	256	7	applications	application	NOUN
ejpam-7005	256	8	where	where	SCONJ
ejpam-7005	256	9	adaptation	adaptation	NOUN
ejpam-7005	256	10	and	and	CCONJ
ejpam-7005	256	11	memory	memory	NOUN
ejpam-7005	256	12	evolution	evolution	NOUN
ejpam-7005	256	13	are	be	AUX
ejpam-7005	256	14	key	key	ADJ
ejpam-7005	256	15	features	feature	NOUN
ejpam-7005	256	16	of	of	ADP
ejpam-7005	256	17	the	the	DET
ejpam-7005	256	18	underlying	underlie	VERB
ejpam-7005	256	19	processes	process	NOUN
ejpam-7005	256	20	.	.	PUNCT
ejpam-7005	257	1	5	5	X
ejpam-7005	257	2	.	.	X
ejpam-7005	257	3	conclusion	conclusion	NOUN
ejpam-7005	257	4	in	in	ADP
ejpam-7005	257	5	this	this	DET
ejpam-7005	257	6	work	work	NOUN
ejpam-7005	257	7	,	,	PUNCT
ejpam-7005	257	8	we	we	PRON
ejpam-7005	257	9	have	have	AUX
ejpam-7005	257	10	presented	present	VERB
ejpam-7005	257	11	a	a	DET
ejpam-7005	257	12	comprehensive	comprehensive	ADJ
ejpam-7005	257	13	investigation	investigation	NOUN
ejpam-7005	257	14	into	into	ADP
ejpam-7005	257	15	the	the	DET
ejpam-7005	257	16	fts	fts	PROPN
ejpam-7005	257	17	of	of	ADP
ejpam-7005	257	18	a	a	DET
ejpam-7005	257	19	discrete	discrete	ADJ
ejpam-7005	257	20	fhn	fhn	ADJ
ejpam-7005	257	21	-	-	PUNCT
ejpam-7005	257	22	rds	rd	NOUN
ejpam-7005	257	23	,	,	PUNCT
ejpam-7005	257	24	distinguished	distinguish	VERB
ejpam-7005	257	25	by	by	ADP
ejpam-7005	257	26	the	the	DET
ejpam-7005	257	27	incorporation	incorporation	NOUN
ejpam-7005	257	28	of	of	ADP
ejpam-7005	257	29	a	a	DET
ejpam-7005	257	30	vo	vo	X
ejpam-7005	257	31	caputo	caputo	PROPN
ejpam-7005	257	32	fractional	fractional	PROPN
ejpam-7005	257	33	difference	difference	NOUN
ejpam-7005	257	34	operator	operator	NOUN
ejpam-7005	257	35	.	.	PUNCT
ejpam-7005	258	1	the	the	DET
ejpam-7005	258	2	study	study	NOUN
ejpam-7005	258	3	was	be	AUX
ejpam-7005	258	4	motivated	motivate	VERB
ejpam-7005	258	5	by	by	ADP
ejpam-7005	258	6	the	the	DET
ejpam-7005	258	7	need	need	NOUN
ejpam-7005	258	8	for	for	ADP
ejpam-7005	258	9	more	more	ADV
ejpam-7005	258	10	sophisticated	sophisticated	ADJ
ejpam-7005	258	11	mathematical	mathematical	ADJ
ejpam-7005	258	12	models	model	NOUN
ejpam-7005	258	13	that	that	PRON
ejpam-7005	258	14	can	can	AUX
ejpam-7005	258	15	accurately	accurately	ADV
ejpam-7005	258	16	capture	capture	VERB
ejpam-7005	258	17	the	the	DET
ejpam-7005	258	18	complex	complex	ADJ
ejpam-7005	258	19	memory	memory	NOUN
ejpam-7005	258	20	effects	effect	NOUN
ejpam-7005	258	21	and	and	CCONJ
ejpam-7005	258	22	dynamic	dynamic	ADJ
ejpam-7005	258	23	,	,	PUNCT
ejpam-7005	258	24	time	time	NOUN
ejpam-7005	258	25	-	-	PUNCT
ejpam-7005	258	26	varying	vary	VERB
ejpam-7005	258	27	behaviors	behavior	NOUN
ejpam-7005	258	28	inherent	inherent	ADJ
ejpam-7005	258	29	in	in	ADP
ejpam-7005	258	30	many	many	ADJ
ejpam-7005	258	31	biological	biological	ADJ
ejpam-7005	258	32	and	and	CCONJ
ejpam-7005	258	33	physical	physical	ADJ
ejpam-7005	258	34	systems	system	NOUN
ejpam-7005	258	35	,	,	PUNCT
ejpam-7005	258	36	such	such	ADJ
ejpam-7005	258	37	as	as	ADP
ejpam-7005	258	38	neuronal	neuronal	ADJ
ejpam-7005	258	39	networks	network	NOUN
ejpam-7005	258	40	.	.	PUNCT
ejpam-7005	259	1	the	the	DET
ejpam-7005	259	2	research	research	NOUN
ejpam-7005	259	3	commenced	commence	VERB
ejpam-7005	259	4	with	with	ADP
ejpam-7005	259	5	the	the	DET
ejpam-7005	259	6	rigorous	rigorous	ADJ
ejpam-7005	259	7	formulation	formulation	NOUN
ejpam-7005	259	8	of	of	ADP
ejpam-7005	259	9	the	the	DET
ejpam-7005	259	10	discrete	discrete	ADJ
ejpam-7005	259	11	model	model	NOUN
ejpam-7005	259	12	.	.	PUNCT
ejpam-7005	260	1	by	by	ADP
ejpam-7005	260	2	employing	employ	VERB
ejpam-7005	260	3	a	a	DET
ejpam-7005	260	4	central	central	ADJ
ejpam-7005	260	5	difference	difference	NOUN
ejpam-7005	260	6	scheme	scheme	NOUN
ejpam-7005	260	7	for	for	ADP
ejpam-7005	260	8	the	the	DET
ejpam-7005	260	9	spatial	spatial	ADJ
ejpam-7005	260	10	laplacian	laplacian	NOUN
ejpam-7005	260	11	and	and	CCONJ
ejpam-7005	260	12	a	a	DET
ejpam-7005	260	13	discrete	discrete	ADJ
ejpam-7005	260	14	vo	vo	X
ejpam-7005	260	15	fractional	fractional	ADJ
ejpam-7005	260	16	operator	operator	NOUN
ejpam-7005	260	17	for	for	ADP
ejpam-7005	260	18	the	the	DET
ejpam-7005	260	19	temporal	temporal	ADJ
ejpam-7005	260	20	derivative	derivative	NOUN
ejpam-7005	260	21	,	,	PUNCT
ejpam-7005	260	22	we	we	PRON
ejpam-7005	260	23	systematically	systematically	ADV
ejpam-7005	260	24	translated	translate	VERB
ejpam-7005	260	25	the	the	DET
ejpam-7005	260	26	continuous	continuous	ADJ
ejpam-7005	260	27	system	system	NOUN
ejpam-7005	260	28	into	into	ADP
ejpam-7005	260	29	a	a	DET
ejpam-7005	260	30	discrete	discrete	ADJ
ejpam-7005	260	31	-	-	PUNCT
ejpam-7005	260	32	time	time	NOUN
ejpam-7005	260	33	framework	framework	NOUN
ejpam-7005	260	34	suitable	suitable	ADJ
ejpam-7005	260	35	for	for	ADP
ejpam-7005	260	36	numerical	numerical	ADJ
ejpam-7005	260	37	analysis	analysis	NOUN
ejpam-7005	260	38	.	.	PUNCT
ejpam-7005	261	1	a	a	DET
ejpam-7005	261	2	crucial	crucial	ADJ
ejpam-7005	261	3	preliminary	preliminary	ADJ
ejpam-7005	261	4	step	step	NOUN
ejpam-7005	261	5	n.	n.	PROPN
ejpam-7005	261	6	anakira	anakira	PROPN
ejpam-7005	261	7	et	et	PROPN
ejpam-7005	261	8	al	al	PROPN
ejpam-7005	261	9	.	.	PUNCT
ejpam-7005	261	10	/	/	SYM
ejpam-7005	261	11	eur	eur	PROPN
ejpam-7005	261	12	.	.	PUNCT
ejpam-7005	262	1	j.	j.	PROPN
ejpam-7005	262	2	pure	pure	PROPN
ejpam-7005	262	3	appl	appl	PROPN
ejpam-7005	262	4	.	.	PROPN
ejpam-7005	262	5	math	math	PROPN
ejpam-7005	262	6	,	,	PUNCT
ejpam-7005	262	7	18	18	NUM
ejpam-7005	262	8	(	(	PUNCT
ejpam-7005	262	9	4	4	NUM
ejpam-7005	262	10	)	)	PUNCT
ejpam-7005	262	11	(	(	PUNCT
ejpam-7005	262	12	2025	2025	NUM
ejpam-7005	262	13	)	)	PUNCT
ejpam-7005	262	14	,	,	PUNCT
ejpam-7005	262	15	7005	7005	NUM
ejpam-7005	262	16	14	14	NUM
ejpam-7005	262	17	of	of	ADP
ejpam-7005	262	18	17	17	NUM
ejpam-7005	262	19	was	be	AUX
ejpam-7005	262	20	to	to	PART
ejpam-7005	262	21	establish	establish	VERB
ejpam-7005	262	22	the	the	DET
ejpam-7005	262	23	well	well	ADV
ejpam-7005	262	24	-	-	PUNCT
ejpam-7005	262	25	posed	pose	VERB
ejpam-7005	262	26	of	of	ADP
ejpam-7005	262	27	the	the	DET
ejpam-7005	262	28	solution	solution	NOUN
ejpam-7005	262	29	for	for	ADP
ejpam-7005	262	30	this	this	DET
ejpam-7005	262	31	newly	newly	ADV
ejpam-7005	262	32	formulated	formulate	VERB
ejpam-7005	262	33	discrete	discrete	ADJ
ejpam-7005	262	34	system	system	NOUN
ejpam-7005	262	35	,	,	PUNCT
ejpam-7005	262	36	thereby	thereby	ADV
ejpam-7005	262	37	ensuring	ensure	VERB
ejpam-7005	262	38	a	a	DET
ejpam-7005	262	39	solid	solid	ADJ
ejpam-7005	262	40	theoretical	theoretical	ADJ
ejpam-7005	262	41	foundation	foundation	NOUN
ejpam-7005	262	42	for	for	ADP
ejpam-7005	262	43	the	the	DET
ejpam-7005	262	44	subsequent	subsequent	ADJ
ejpam-7005	262	45	stability	stability	NOUN
ejpam-7005	262	46	analysis	analysis	NOUN
ejpam-7005	262	47	.	.	PUNCT
ejpam-7005	263	1	the	the	DET
ejpam-7005	263	2	principal	principal	ADJ
ejpam-7005	263	3	contribution	contribution	NOUN
ejpam-7005	263	4	of	of	ADP
ejpam-7005	263	5	this	this	DET
ejpam-7005	263	6	paper	paper	NOUN
ejpam-7005	263	7	is	be	AUX
ejpam-7005	263	8	the	the	DET
ejpam-7005	263	9	derivation	derivation	NOUN
ejpam-7005	263	10	of	of	ADP
ejpam-7005	263	11	a	a	DET
ejpam-7005	263	12	novel	novel	NOUN
ejpam-7005	263	13	,	,	PUNCT
ejpam-7005	263	14	sufficient	sufficient	ADJ
ejpam-7005	263	15	condition	condition	NOUN
ejpam-7005	263	16	for	for	ADP
ejpam-7005	263	17	the	the	DET
ejpam-7005	263	18	fts	fts	PROPN
ejpam-7005	263	19	of	of	ADP
ejpam-7005	263	20	the	the	DET
ejpam-7005	263	21	proposed	propose	VERB
ejpam-7005	263	22	model	model	NOUN
ejpam-7005	263	23	.	.	PUNCT
ejpam-7005	264	1	this	this	PRON
ejpam-7005	264	2	is	be	AUX
ejpam-7005	264	3	particularly	particularly	ADV
ejpam-7005	264	4	significant	significant	ADJ
ejpam-7005	264	5	because	because	SCONJ
ejpam-7005	264	6	,	,	PUNCT
ejpam-7005	264	7	in	in	ADP
ejpam-7005	264	8	many	many	ADJ
ejpam-7005	264	9	practical	practical	ADJ
ejpam-7005	264	10	applications	application	NOUN
ejpam-7005	264	11	,	,	PUNCT
ejpam-7005	264	12	especially	especially	ADV
ejpam-7005	264	13	in	in	ADP
ejpam-7005	264	14	biology	biology	NOUN
ejpam-7005	264	15	and	and	CCONJ
ejpam-7005	264	16	control	control	NOUN
ejpam-7005	264	17	engineering	engineering	NOUN
ejpam-7005	264	18	,	,	PUNCT
ejpam-7005	264	19	guaranteeing	guarantee	VERB
ejpam-7005	264	20	that	that	SCONJ
ejpam-7005	264	21	system	system	NOUN
ejpam-7005	264	22	states	state	NOUN
ejpam-7005	264	23	remain	remain	VERB
ejpam-7005	264	24	within	within	ADP
ejpam-7005	264	25	prescribed	prescribed	ADJ
ejpam-7005	264	26	safe	safe	ADJ
ejpam-7005	264	27	bounds	bound	NOUN
ejpam-7005	264	28	over	over	ADP
ejpam-7005	264	29	a	a	DET
ejpam-7005	264	30	finite	finite	ADJ
ejpam-7005	264	31	operational	operational	ADJ
ejpam-7005	264	32	interval	interval	NOUN
ejpam-7005	264	33	is	be	AUX
ejpam-7005	264	34	of	of	ADP
ejpam-7005	264	35	greater	great	ADJ
ejpam-7005	264	36	importance	importance	NOUN
ejpam-7005	264	37	than	than	ADP
ejpam-7005	264	38	assessing	assess	VERB
ejpam-7005	264	39	their	their	PRON
ejpam-7005	264	40	long	long	ADJ
ejpam-7005	264	41	-	-	PUNCT
ejpam-7005	264	42	term	term	NOUN
ejpam-7005	264	43	asymptotic	asymptotic	ADJ
ejpam-7005	264	44	behavior	behavior	NOUN
ejpam-7005	264	45	.	.	PUNCT
ejpam-7005	265	1	by	by	ADP
ejpam-7005	265	2	skillfully	skillfully	ADV
ejpam-7005	265	3	applying	apply	VERB
ejpam-7005	265	4	a	a	DET
ejpam-7005	265	5	discrete	discrete	ADJ
ejpam-7005	265	6	fractional	fractional	ADJ
ejpam-7005	265	7	gronwall	gronwall	ADJ
ejpam-7005	265	8	-	-	PUNCT
ejpam-7005	265	9	type	type	NOUN
ejpam-7005	265	10	inequality	inequality	NOUN
ejpam-7005	265	11	,	,	PUNCT
ejpam-7005	265	12	a	a	DET
ejpam-7005	265	13	powerful	powerful	ADJ
ejpam-7005	265	14	tool	tool	NOUN
ejpam-7005	265	15	in	in	ADP
ejpam-7005	265	16	the	the	DET
ejpam-7005	265	17	analysis	analysis	NOUN
ejpam-7005	265	18	of	of	ADP
ejpam-7005	265	19	fractional	fractional	ADJ
ejpam-7005	265	20	difference	difference	NOUN
ejpam-7005	265	21	equations	equation	NOUN
ejpam-7005	265	22	,	,	PUNCT
ejpam-7005	265	23	we	we	PRON
ejpam-7005	265	24	established	establish	VERB
ejpam-7005	265	25	a	a	DET
ejpam-7005	265	26	stability	stability	NOUN
ejpam-7005	265	27	criterion	criterion	NOUN
ejpam-7005	265	28	expressed	express	VERB
ejpam-7005	265	29	elegantly	elegantly	ADV
ejpam-7005	265	30	in	in	ADP
ejpam-7005	265	31	terms	term	NOUN
ejpam-7005	265	32	of	of	ADP
ejpam-7005	265	33	the	the	DET
ejpam-7005	265	34	discrete	discrete	ADJ
ejpam-7005	265	35	mlf	mlf	NOUN
ejpam-7005	265	36	.	.	PUNCT
ejpam-7005	266	1	this	this	DET
ejpam-7005	266	2	result	result	NOUN
ejpam-7005	266	3	directly	directly	ADV
ejpam-7005	266	4	links	link	VERB
ejpam-7005	266	5	the	the	DET
ejpam-7005	266	6	transient	transient	ADJ
ejpam-7005	266	7	stability	stability	NOUN
ejpam-7005	266	8	of	of	ADP
ejpam-7005	266	9	the	the	DET
ejpam-7005	266	10	system	system	NOUN
ejpam-7005	266	11	to	to	ADP
ejpam-7005	266	12	its	its	PRON
ejpam-7005	266	13	intrinsic	intrinsic	ADJ
ejpam-7005	266	14	memory	memory	NOUN
ejpam-7005	266	15	properties	property	NOUN
ejpam-7005	266	16	,	,	PUNCT
ejpam-7005	266	17	as	as	SCONJ
ejpam-7005	266	18	captured	capture	VERB
ejpam-7005	266	19	by	by	ADP
ejpam-7005	266	20	the	the	DET
ejpam-7005	266	21	fractional	fractional	ADJ
ejpam-7005	266	22	operator	operator	NOUN
ejpam-7005	266	23	.	.	PUNCT
ejpam-7005	267	1	furthermore	furthermore	ADV
ejpam-7005	267	2	,	,	PUNCT
ejpam-7005	267	3	our	our	PRON
ejpam-7005	267	4	analysis	analysis	NOUN
ejpam-7005	267	5	revealed	reveal	VERB
ejpam-7005	267	6	a	a	DET
ejpam-7005	267	7	key	key	ADJ
ejpam-7005	267	8	insight	insight	NOUN
ejpam-7005	267	9	:	:	PUNCT
ejpam-7005	267	10	the	the	DET
ejpam-7005	267	11	interval	interval	NOUN
ejpam-7005	267	12	of	of	ADP
ejpam-7005	267	13	fts	fts	PROPN
ejpam-7005	267	14	is	be	AUX
ejpam-7005	267	15	explicitly	explicitly	ADV
ejpam-7005	267	16	dependent	dependent	ADJ
ejpam-7005	267	17	on	on	ADP
ejpam-7005	267	18	the	the	DET
ejpam-7005	267	19	function	function	NOUN
ejpam-7005	267	20	defining	define	VERB
ejpam-7005	267	21	the	the	DET
ejpam-7005	267	22	vo	vo	NOUN
ejpam-7005	267	23	fractional	fractional	ADJ
ejpam-7005	267	24	order	order	NOUN
ejpam-7005	267	25	,	,	PUNCT
ejpam-7005	267	26	δ(t	δ(t	PROPN
ejpam-7005	267	27	)	)	PUNCT
ejpam-7005	267	28	.	.	PUNCT
ejpam-7005	268	1	this	this	DET
ejpam-7005	268	2	highlights	highlight	VERB
ejpam-7005	268	3	the	the	DET
ejpam-7005	268	4	profound	profound	ADJ
ejpam-7005	268	5	impact	impact	NOUN
ejpam-7005	268	6	of	of	ADP
ejpam-7005	268	7	dynamic	dynamic	ADJ
ejpam-7005	268	8	memory	memory	NOUN
ejpam-7005	268	9	on	on	ADP
ejpam-7005	268	10	the	the	DET
ejpam-7005	268	11	system	system	NOUN
ejpam-7005	268	12	’s	’s	PART
ejpam-7005	268	13	transient	transient	ADJ
ejpam-7005	268	14	behavior	behavior	NOUN
ejpam-7005	268	15	and	and	CCONJ
ejpam-7005	268	16	underscores	underscore	VERB
ejpam-7005	268	17	the	the	DET
ejpam-7005	268	18	enhanced	enhanced	ADJ
ejpam-7005	268	19	modeling	modeling	NOUN
ejpam-7005	268	20	flexibility	flexibility	NOUN
ejpam-7005	268	21	and	and	CCONJ
ejpam-7005	268	22	descriptive	descriptive	ADJ
ejpam-7005	268	23	power	power	NOUN
ejpam-7005	268	24	of	of	ADP
ejpam-7005	268	25	the	the	DET
ejpam-7005	268	26	vo	vo	NOUN
ejpam-7005	268	27	approach	approach	NOUN
ejpam-7005	268	28	over	over	ADP
ejpam-7005	268	29	traditional	traditional	ADJ
ejpam-7005	268	30	constantorder	constantorder	NOUN
ejpam-7005	268	31	fractional	fractional	ADJ
ejpam-7005	268	32	models	model	NOUN
ejpam-7005	268	33	.	.	PUNCT
ejpam-7005	269	1	to	to	PART
ejpam-7005	269	2	validate	validate	VERB
ejpam-7005	269	3	our	our	PRON
ejpam-7005	269	4	theoretical	theoretical	ADJ
ejpam-7005	269	5	framework	framework	NOUN
ejpam-7005	269	6	,	,	PUNCT
ejpam-7005	269	7	a	a	DET
ejpam-7005	269	8	numerical	numerical	ADJ
ejpam-7005	269	9	example	example	NOUN
ejpam-7005	269	10	was	be	AUX
ejpam-7005	269	11	presented	present	VERB
ejpam-7005	269	12	.	.	PUNCT
ejpam-7005	270	1	this	this	DET
ejpam-7005	270	2	simulation	simulation	NOUN
ejpam-7005	270	3	not	not	PART
ejpam-7005	270	4	only	only	ADV
ejpam-7005	270	5	corroborated	corroborate	VERB
ejpam-7005	270	6	the	the	DET
ejpam-7005	270	7	derived	derive	VERB
ejpam-7005	270	8	stability	stability	NOUN
ejpam-7005	270	9	condition	condition	NOUN
ejpam-7005	270	10	but	but	CCONJ
ejpam-7005	270	11	also	also	ADV
ejpam-7005	270	12	provided	provide	VERB
ejpam-7005	270	13	a	a	DET
ejpam-7005	270	14	clear	clear	ADJ
ejpam-7005	270	15	illustration	illustration	NOUN
ejpam-7005	270	16	of	of	ADP
ejpam-7005	270	17	the	the	DET
ejpam-7005	270	18	system	system	NOUN
ejpam-7005	270	19	’s	’s	PART
ejpam-7005	270	20	dynamics	dynamic	NOUN
ejpam-7005	270	21	.	.	PUNCT
ejpam-7005	271	1	by	by	ADP
ejpam-7005	271	2	observing	observe	VERB
ejpam-7005	271	3	the	the	DET
ejpam-7005	271	4	norm	norm	NOUN
ejpam-7005	271	5	of	of	ADP
ejpam-7005	271	6	the	the	DET
ejpam-7005	271	7	solution	solution	NOUN
ejpam-7005	271	8	under	under	ADP
ejpam-7005	271	9	different	different	ADJ
ejpam-7005	271	10	vo	vo	NOUN
ejpam-7005	271	11	functions	function	NOUN
ejpam-7005	271	12	,	,	PUNCT
ejpam-7005	271	13	we	we	PRON
ejpam-7005	271	14	demonstrated	demonstrate	VERB
ejpam-7005	271	15	that	that	SCONJ
ejpam-7005	271	16	the	the	DET
ejpam-7005	271	17	system	system	NOUN
ejpam-7005	271	18	’s	’s	PART
ejpam-7005	271	19	state	state	NOUN
ejpam-7005	271	20	can	can	AUX
ejpam-7005	271	21	be	be	AUX
ejpam-7005	271	22	maintained	maintain	VERB
ejpam-7005	271	23	within	within	ADP
ejpam-7005	271	24	a	a	DET
ejpam-7005	271	25	predefined	predefine	VERB
ejpam-7005	271	26	boundary	boundary	NOUN
ejpam-7005	271	27	over	over	ADP
ejpam-7005	271	28	a	a	DET
ejpam-7005	271	29	finite	finite	ADJ
ejpam-7005	271	30	time	time	NOUN
ejpam-7005	271	31	horizon	horizon	NOUN
ejpam-7005	271	32	,	,	PUNCT
ejpam-7005	271	33	thereby	thereby	ADV
ejpam-7005	271	34	confirming	confirm	VERB
ejpam-7005	271	35	the	the	DET
ejpam-7005	271	36	practical	practical	ADJ
ejpam-7005	271	37	applicability	applicability	NOUN
ejpam-7005	271	38	of	of	ADP
ejpam-7005	271	39	our	our	PRON
ejpam-7005	271	40	results	result	NOUN
ejpam-7005	271	41	.	.	PUNCT
ejpam-7005	272	1	this	this	DET
ejpam-7005	272	2	study	study	NOUN
ejpam-7005	272	3	provides	provide	VERB
ejpam-7005	272	4	a	a	DET
ejpam-7005	272	5	rigorous	rigorous	ADJ
ejpam-7005	272	6	and	and	CCONJ
ejpam-7005	272	7	applicable	applicable	ADJ
ejpam-7005	272	8	framework	framework	NOUN
ejpam-7005	272	9	for	for	ADP
ejpam-7005	272	10	analyzing	analyze	VERB
ejpam-7005	272	11	the	the	DET
ejpam-7005	272	12	transient	transient	ADJ
ejpam-7005	272	13	behavior	behavior	NOUN
ejpam-7005	272	14	of	of	ADP
ejpam-7005	272	15	complex	complex	ADJ
ejpam-7005	272	16	discrete	discrete	ADJ
ejpam-7005	272	17	systems	system	NOUN
ejpam-7005	272	18	with	with	ADP
ejpam-7005	272	19	vo	vo	X
ejpam-7005	272	20	fractional	fractional	ADJ
ejpam-7005	272	21	dynamics	dynamic	NOUN
ejpam-7005	272	22	.	.	PUNCT
ejpam-7005	273	1	looking	look	VERB
ejpam-7005	273	2	ahead	ahead	ADV
ejpam-7005	273	3	,	,	PUNCT
ejpam-7005	273	4	this	this	DET
ejpam-7005	273	5	work	work	NOUN
ejpam-7005	273	6	opens	open	VERB
ejpam-7005	273	7	several	several	ADJ
ejpam-7005	273	8	avenues	avenue	NOUN
ejpam-7005	273	9	for	for	ADP
ejpam-7005	273	10	future	future	ADJ
ejpam-7005	273	11	research	research	NOUN
ejpam-7005	273	12	.	.	PUNCT
ejpam-7005	274	1	an	an	DET
ejpam-7005	274	2	immediate	immediate	ADJ
ejpam-7005	274	3	extension	extension	NOUN
ejpam-7005	274	4	would	would	AUX
ejpam-7005	274	5	be	be	AUX
ejpam-7005	274	6	to	to	PART
ejpam-7005	274	7	investigate	investigate	VERB
ejpam-7005	274	8	the	the	DET
ejpam-7005	274	9	influence	influence	NOUN
ejpam-7005	274	10	of	of	ADP
ejpam-7005	274	11	different	different	ADJ
ejpam-7005	274	12	classes	class	NOUN
ejpam-7005	274	13	of	of	ADP
ejpam-7005	274	14	vo	vo	NOUN
ejpam-7005	274	15	functions	function	NOUN
ejpam-7005	274	16	on	on	ADP
ejpam-7005	274	17	system	system	NOUN
ejpam-7005	274	18	stability	stability	NOUN
ejpam-7005	274	19	.	.	PUNCT
ejpam-7005	275	1	furthermore	furthermore	ADV
ejpam-7005	275	2	,	,	PUNCT
ejpam-7005	275	3	the	the	DET
ejpam-7005	275	4	introduction	introduction	NOUN
ejpam-7005	275	5	of	of	ADP
ejpam-7005	275	6	stochastic	stochastic	ADJ
ejpam-7005	275	7	perturbations	perturbation	NOUN
ejpam-7005	275	8	could	could	AUX
ejpam-7005	275	9	lead	lead	VERB
ejpam-7005	275	10	to	to	ADP
ejpam-7005	275	11	an	an	DET
ejpam-7005	275	12	analysis	analysis	NOUN
ejpam-7005	275	13	of	of	ADP
ejpam-7005	275	14	fts	fts	PROPN
ejpam-7005	275	15	in	in	ADP
ejpam-7005	275	16	a	a	DET
ejpam-7005	275	17	noisy	noisy	ADJ
ejpam-7005	275	18	environment	environment	NOUN
ejpam-7005	275	19	,	,	PUNCT
ejpam-7005	275	20	which	which	PRON
ejpam-7005	275	21	is	be	AUX
ejpam-7005	275	22	highly	highly	ADV
ejpam-7005	275	23	relevant	relevant	ADJ
ejpam-7005	275	24	for	for	ADP
ejpam-7005	275	25	biological	biological	ADJ
ejpam-7005	275	26	modeling	modeling	NOUN
ejpam-7005	275	27	.	.	PUNCT
ejpam-7005	276	1	finally	finally	ADV
ejpam-7005	276	2	,	,	PUNCT
ejpam-7005	276	3	the	the	DET
ejpam-7005	276	4	conditions	condition	NOUN
ejpam-7005	276	5	derived	derive	VERB
ejpam-7005	276	6	herein	herein	NOUN
ejpam-7005	276	7	could	could	AUX
ejpam-7005	276	8	form	form	VERB
ejpam-7005	276	9	the	the	DET
ejpam-7005	276	10	basis	basis	NOUN
ejpam-7005	276	11	for	for	ADP
ejpam-7005	276	12	designing	design	VERB
ejpam-7005	276	13	control	control	NOUN
ejpam-7005	276	14	strategies	strategy	NOUN
ejpam-7005	276	15	aimed	aim	VERB
ejpam-7005	276	16	at	at	ADP
ejpam-7005	276	17	enforcing	enforce	VERB
ejpam-7005	276	18	fts	fts	PROPN
ejpam-7005	276	19	in	in	ADP
ejpam-7005	276	20	fractional	fractional	ADJ
ejpam-7005	276	21	-	-	PUNCT
ejpam-7005	276	22	order	order	NOUN
ejpam-7005	276	23	systems	system	NOUN
ejpam-7005	276	24	.	.	PUNCT
ejpam-7005	277	1	in	in	ADP
ejpam-7005	277	2	summary	summary	NOUN
ejpam-7005	277	3	,	,	PUNCT
ejpam-7005	277	4	this	this	DET
ejpam-7005	277	5	research	research	NOUN
ejpam-7005	277	6	contributes	contribute	VERB
ejpam-7005	277	7	valuable	valuable	ADJ
ejpam-7005	277	8	tools	tool	NOUN
ejpam-7005	277	9	and	and	CCONJ
ejpam-7005	277	10	insights	insight	NOUN
ejpam-7005	277	11	for	for	ADP
ejpam-7005	277	12	the	the	DET
ejpam-7005	277	13	modeling	modeling	NOUN
ejpam-7005	277	14	and	and	CCONJ
ejpam-7005	277	15	analysis	analysis	NOUN
ejpam-7005	277	16	of	of	ADP
ejpam-7005	277	17	complex	complex	ADJ
ejpam-7005	277	18	real	real	ADJ
ejpam-7005	277	19	-	-	PUNCT
ejpam-7005	277	20	world	world	NOUN
ejpam-7005	277	21	phenomena	phenomenon	NOUN
ejpam-7005	277	22	where	where	SCONJ
ejpam-7005	277	23	memory	memory	NOUN
ejpam-7005	277	24	and	and	CCONJ
ejpam-7005	277	25	adaptation	adaptation	NOUN
ejpam-7005	277	26	are	be	AUX
ejpam-7005	277	27	key	key	ADJ
ejpam-7005	277	28	features	feature	NOUN
ejpam-7005	277	29	.	.	PUNCT
ejpam-7005	278	1	references	reference	NOUN
ejpam-7005	278	2	[	[	X
ejpam-7005	278	3	1	1	NUM
ejpam-7005	278	4	]	]	PUNCT
ejpam-7005	278	5	a.	a.	NOUN
ejpam-7005	278	6	m.	m.	NOUN
ejpam-7005	278	7	turing	ture	VERB
ejpam-7005	278	8	.	.	PUNCT
ejpam-7005	279	1	the	the	DET
ejpam-7005	279	2	chemical	chemical	ADJ
ejpam-7005	279	3	basis	basis	NOUN
ejpam-7005	279	4	of	of	ADP
ejpam-7005	279	5	morphogenesis	morphogenesis	NOUN
ejpam-7005	279	6	.	.	PUNCT
ejpam-7005	280	1	philosophical	philosophical	ADJ
ejpam-7005	280	2	transactions	transaction	NOUN
ejpam-7005	280	3	of	of	ADP
ejpam-7005	280	4	the	the	DET
ejpam-7005	280	5	royal	royal	ADJ
ejpam-7005	280	6	society	society	NOUN
ejpam-7005	280	7	of	of	ADP
ejpam-7005	280	8	london	london	PROPN
ejpam-7005	280	9	.	.	PUNCT
ejpam-7005	281	1	series	series	PROPN
ejpam-7005	281	2	b	b	PROPN
ejpam-7005	281	3	,	,	PUNCT
ejpam-7005	281	4	biological	biological	ADJ
ejpam-7005	281	5	sciences	science	NOUN
ejpam-7005	281	6	,	,	PUNCT
ejpam-7005	281	7	237(641):37–72	237(641):37–72	NUM
ejpam-7005	281	8	,	,	PUNCT
ejpam-7005	281	9	1952	1952	NUM
ejpam-7005	281	10	.	.	PUNCT
ejpam-7005	282	1	[	[	X
ejpam-7005	282	2	2	2	X
ejpam-7005	282	3	]	]	PUNCT
ejpam-7005	282	4	j.	j.	PROPN
ejpam-7005	282	5	d.	d.	PROPN
ejpam-7005	282	6	murray	murray	PROPN
ejpam-7005	282	7	.	.	PUNCT
ejpam-7005	283	1	mathematical	mathematical	ADJ
ejpam-7005	283	2	biology	biology	NOUN
ejpam-7005	283	3	ii	ii	PROPN
ejpam-7005	283	4	:	:	PUNCT
ejpam-7005	283	5	spatial	spatial	ADJ
ejpam-7005	283	6	models	model	NOUN
ejpam-7005	283	7	and	and	CCONJ
ejpam-7005	283	8	biomedical	biomedical	ADJ
ejpam-7005	283	9	applications	application	NOUN
ejpam-7005	283	10	.	.	PUNCT
ejpam-7005	284	1	springer	springer	NOUN
ejpam-7005	284	2	,	,	PUNCT
ejpam-7005	284	3	2003	2003	NUM
ejpam-7005	284	4	.	.	PUNCT
ejpam-7005	285	1	[	[	X
ejpam-7005	285	2	3	3	X
ejpam-7005	285	3	]	]	X
ejpam-7005	285	4	j.	j.	PROPN
ejpam-7005	285	5	keener	keener	PROPN
ejpam-7005	285	6	and	and	CCONJ
ejpam-7005	285	7	j.	j.	PROPN
ejpam-7005	285	8	sneyd	sneyd	PROPN
ejpam-7005	285	9	.	.	PUNCT
ejpam-7005	286	1	mathematical	mathematical	ADJ
ejpam-7005	286	2	physiology	physiology	NOUN
ejpam-7005	286	3	.	.	PUNCT
ejpam-7005	287	1	springer	springer	NOUN
ejpam-7005	287	2	,	,	PUNCT
ejpam-7005	287	3	1998	1998	NUM
ejpam-7005	287	4	.	.	PUNCT
ejpam-7005	288	1	[	[	X
ejpam-7005	288	2	4	4	NUM
ejpam-7005	288	3	]	]	X
ejpam-7005	288	4	r.	r.	PROPN
ejpam-7005	288	5	fitzhugh	fitzhugh	PROPN
ejpam-7005	288	6	.	.	PUNCT
ejpam-7005	288	7	impulses	impulse	NOUN
ejpam-7005	288	8	and	and	CCONJ
ejpam-7005	288	9	physiological	physiological	ADJ
ejpam-7005	288	10	states	state	NOUN
ejpam-7005	288	11	in	in	ADP
ejpam-7005	288	12	theoretical	theoretical	ADJ
ejpam-7005	288	13	models	model	NOUN
ejpam-7005	288	14	of	of	ADP
ejpam-7005	288	15	nerve	nerve	NOUN
ejpam-7005	288	16	membrane	membrane	NOUN
ejpam-7005	288	17	.	.	PUNCT
ejpam-7005	289	1	biophysical	biophysical	ADJ
ejpam-7005	289	2	journal	journal	NOUN
ejpam-7005	289	3	,	,	PUNCT
ejpam-7005	289	4	1(6):445–466	1(6):445–466	NUM
ejpam-7005	289	5	,	,	PUNCT
ejpam-7005	289	6	1961	1961	NUM
ejpam-7005	289	7	.	.	PUNCT
ejpam-7005	290	1	[	[	X
ejpam-7005	290	2	5	5	X
ejpam-7005	290	3	]	]	PUNCT
ejpam-7005	290	4	j.	j.	PROPN
ejpam-7005	290	5	nagumo	nagumo	PROPN
ejpam-7005	290	6	,	,	PUNCT
ejpam-7005	290	7	s.	s.	PROPN
ejpam-7005	290	8	arimoto	arimoto	PROPN
ejpam-7005	290	9	,	,	PUNCT
ejpam-7005	290	10	and	and	CCONJ
ejpam-7005	290	11	s.	s.	PROPN
ejpam-7005	290	12	yoshizawa	yoshizawa	PROPN
ejpam-7005	290	13	.	.	PUNCT
ejpam-7005	291	1	an	an	DET
ejpam-7005	291	2	active	active	ADJ
ejpam-7005	291	3	pulse	pulse	NOUN
ejpam-7005	291	4	transmission	transmission	NOUN
ejpam-7005	291	5	line	line	NOUN
ejpam-7005	291	6	simulating	simulate	VERB
ejpam-7005	291	7	nerve	nerve	NOUN
ejpam-7005	291	8	axon	axon	NOUN
ejpam-7005	291	9	.	.	PUNCT
ejpam-7005	292	1	proceedings	proceeding	NOUN
ejpam-7005	292	2	of	of	ADP
ejpam-7005	292	3	the	the	DET
ejpam-7005	292	4	ire	ire	NOUN
ejpam-7005	292	5	,	,	PUNCT
ejpam-7005	292	6	50(10):2061–2070	50(10):2061–2070	NUM
ejpam-7005	292	7	,	,	PUNCT
ejpam-7005	292	8	1962	1962	NUM
ejpam-7005	292	9	.	.	PUNCT
ejpam-7005	293	1	n.	n.	PROPN
ejpam-7005	293	2	anakira	anakira	PROPN
ejpam-7005	293	3	et	et	PROPN
ejpam-7005	293	4	al	al	PROPN
ejpam-7005	293	5	.	.	PUNCT
ejpam-7005	293	6	/	/	SYM
ejpam-7005	293	7	eur	eur	PROPN
ejpam-7005	293	8	.	.	PUNCT
ejpam-7005	294	1	j.	j.	PROPN
ejpam-7005	294	2	pure	pure	PROPN
ejpam-7005	294	3	appl	appl	PROPN
ejpam-7005	294	4	.	.	PROPN
ejpam-7005	294	5	math	math	PROPN
ejpam-7005	294	6	,	,	PUNCT
ejpam-7005	294	7	18	18	NUM
ejpam-7005	294	8	(	(	PUNCT
ejpam-7005	294	9	4	4	NUM
ejpam-7005	294	10	)	)	PUNCT
ejpam-7005	294	11	(	(	PUNCT
ejpam-7005	294	12	2025	2025	NUM
ejpam-7005	294	13	)	)	PUNCT
ejpam-7005	294	14	,	,	PUNCT
ejpam-7005	294	15	7005	7005	NUM
ejpam-7005	294	16	15	15	NUM
ejpam-7005	294	17	of	of	ADP
ejpam-7005	294	18	17	17	NUM
ejpam-7005	294	19	[	[	SYM
ejpam-7005	294	20	6	6	NUM
ejpam-7005	294	21	]	]	PUNCT
ejpam-7005	294	22	a.	a.	NOUN
ejpam-7005	294	23	l.	l.	PROPN
ejpam-7005	294	24	hodgkin	hodgkin	PROPN
ejpam-7005	294	25	and	and	CCONJ
ejpam-7005	294	26	a.	a.	PROPN
ejpam-7005	294	27	f.	f.	PROPN
ejpam-7005	294	28	huxley	huxley	PROPN
ejpam-7005	294	29	.	.	PUNCT
ejpam-7005	295	1	a	a	DET
ejpam-7005	295	2	quantitative	quantitative	ADJ
ejpam-7005	295	3	description	description	NOUN
ejpam-7005	295	4	of	of	ADP
ejpam-7005	295	5	membrane	membrane	NOUN
ejpam-7005	295	6	current	current	NOUN
ejpam-7005	295	7	and	and	CCONJ
ejpam-7005	295	8	its	its	PRON
ejpam-7005	295	9	application	application	NOUN
ejpam-7005	295	10	to	to	ADP
ejpam-7005	295	11	conduction	conduction	NOUN
ejpam-7005	295	12	and	and	CCONJ
ejpam-7005	295	13	excitation	excitation	NOUN
ejpam-7005	295	14	in	in	ADP
ejpam-7005	295	15	nerve	nerve	NOUN
ejpam-7005	295	16	.	.	PUNCT
ejpam-7005	296	1	the	the	DET
ejpam-7005	296	2	journal	journal	NOUN
ejpam-7005	296	3	of	of	ADP
ejpam-7005	296	4	physiology	physiology	NOUN
ejpam-7005	296	5	,	,	PUNCT
ejpam-7005	296	6	117(4):500–544	117(4):500–544	NUM
ejpam-7005	296	7	,	,	PUNCT
ejpam-7005	296	8	1952	1952	NUM
ejpam-7005	296	9	.	.	PUNCT
ejpam-7005	297	1	[	[	X
ejpam-7005	297	2	7	7	X
ejpam-7005	297	3	]	]	X
ejpam-7005	297	4	j.	j.	PROPN
ejpam-7005	297	5	rinzel	rinzel	PROPN
ejpam-7005	297	6	.	.	PUNCT
ejpam-7005	298	1	excitation	excitation	NOUN
ejpam-7005	298	2	dynamics	dynamic	NOUN
ejpam-7005	298	3	:	:	PUNCT
ejpam-7005	298	4	insights	insight	NOUN
ejpam-7005	298	5	from	from	ADP
ejpam-7005	298	6	simplified	simplified	ADJ
ejpam-7005	298	7	membrane	membrane	NOUN
ejpam-7005	298	8	models	model	NOUN
ejpam-7005	298	9	.	.	PUNCT
ejpam-7005	299	1	federation	federation	NOUN
ejpam-7005	299	2	proceedings	proceeding	NOUN
ejpam-7005	299	3	,	,	PUNCT
ejpam-7005	299	4	40(13):2793–2804	40(13):2793–2804	NUM
ejpam-7005	299	5	,	,	PUNCT
ejpam-7005	299	6	1981	1981	NUM
ejpam-7005	299	7	.	.	PUNCT
ejpam-7005	300	1	[	[	X
ejpam-7005	300	2	8	8	NUM
ejpam-7005	300	3	]	]	X
ejpam-7005	300	4	c.	c.	NOUN
ejpam-7005	300	5	rocsoreanu	rocsoreanu	PROPN
ejpam-7005	300	6	,	,	PUNCT
ejpam-7005	300	7	m.	m.	NOUN
ejpam-7005	300	8	sterpu	sterpu	NOUN
ejpam-7005	300	9	,	,	PUNCT
ejpam-7005	300	10	and	and	CCONJ
ejpam-7005	300	11	a.	a.	NOUN
ejpam-7005	300	12	georgescu	georgescu	PROPN
ejpam-7005	300	13	.	.	PUNCT
ejpam-7005	301	1	the	the	DET
ejpam-7005	301	2	fitzhugh	fitzhugh	PROPN
ejpam-7005	301	3	-	-	PUNCT
ejpam-7005	301	4	nagumo	nagumo	ADJ
ejpam-7005	301	5	model	model	NOUN
ejpam-7005	301	6	:	:	PUNCT
ejpam-7005	301	7	bifurcation	bifurcation	NOUN
ejpam-7005	301	8	and	and	CCONJ
ejpam-7005	301	9	dynamics	dynamic	NOUN
ejpam-7005	301	10	.	.	PUNCT
ejpam-7005	302	1	springer	springer	NOUN
ejpam-7005	302	2	,	,	PUNCT
ejpam-7005	302	3	2000	2000	NUM
ejpam-7005	302	4	.	.	PUNCT
ejpam-7005	303	1	[	[	X
ejpam-7005	303	2	9	9	NUM
ejpam-7005	303	3	]	]	PUNCT
ejpam-7005	303	4	a.	a.	NOUN
ejpam-7005	303	5	m.	m.	NOUN
ejpam-7005	303	6	pertsov	pertsov	PROPN
ejpam-7005	303	7	,	,	PUNCT
ejpam-7005	303	8	j.	j.	PROPN
ejpam-7005	303	9	m.	m.	PROPN
ejpam-7005	303	10	davidenko	davidenko	PROPN
ejpam-7005	303	11	,	,	PUNCT
ejpam-7005	303	12	r.	r.	PROPN
ejpam-7005	303	13	salomonsz	salomonsz	PROPN
ejpam-7005	303	14	,	,	PUNCT
ejpam-7005	303	15	w.	w.	PROPN
ejpam-7005	303	16	t.	t.	PROPN
ejpam-7005	303	17	baxter	baxter	PROPN
ejpam-7005	303	18	,	,	PUNCT
ejpam-7005	303	19	and	and	CCONJ
ejpam-7005	303	20	j.	j.	PROPN
ejpam-7005	303	21	jalife	jalife	PROPN
ejpam-7005	303	22	.	.	PUNCT
ejpam-7005	304	1	spiral	spiral	ADJ
ejpam-7005	304	2	waves	wave	NOUN
ejpam-7005	304	3	of	of	ADP
ejpam-7005	304	4	excitation	excitation	NOUN
ejpam-7005	304	5	underlie	underlie	ADJ
ejpam-7005	304	6	reentrant	reentrant	ADJ
ejpam-7005	304	7	activity	activity	NOUN
ejpam-7005	304	8	in	in	ADP
ejpam-7005	304	9	isolated	isolated	ADJ
ejpam-7005	304	10	cardiac	cardiac	ADJ
ejpam-7005	304	11	muscle	muscle	NOUN
ejpam-7005	304	12	.	.	PUNCT
ejpam-7005	305	1	circulation	circulation	NOUN
ejpam-7005	305	2	research	research	NOUN
ejpam-7005	305	3	,	,	PUNCT
ejpam-7005	305	4	72(3):631–650	72(3):631–650	PROPN
ejpam-7005	305	5	,	,	PUNCT
ejpam-7005	305	6	1993	1993	NUM
ejpam-7005	305	7	.	.	PUNCT
ejpam-7005	306	1	[	[	X
ejpam-7005	306	2	10	10	NUM
ejpam-7005	306	3	]	]	X
ejpam-7005	306	4	d.	d.	PROPN
ejpam-7005	306	5	e.	e.	PROPN
ejpam-7005	306	6	postnov	postnov	PROPN
ejpam-7005	306	7	,	,	PUNCT
ejpam-7005	306	8	s.	s.	PROPN
ejpam-7005	306	9	k.	k.	PROPN
ejpam-7005	306	10	han	han	PROPN
ejpam-7005	306	11	,	,	PUNCT
ejpam-7005	306	12	t.	t.	PROPN
ejpam-7005	306	13	g.	g.	PROPN
ejpam-7005	306	14	yim	yim	PROPN
ejpam-7005	306	15	,	,	PUNCT
ejpam-7005	306	16	and	and	CCONJ
ejpam-7005	306	17	o.	o.	PROPN
ejpam-7005	306	18	v.	v.	PROPN
ejpam-7005	306	19	sosnovtseva	sosnovtseva	PROPN
ejpam-7005	306	20	.	.	PUNCT
ejpam-7005	307	1	experimental	experimental	ADJ
ejpam-7005	307	2	observation	observation	NOUN
ejpam-7005	307	3	of	of	ADP
ejpam-7005	307	4	noise	noise	NOUN
ejpam-7005	307	5	-	-	PUNCT
ejpam-7005	307	6	induced	induce	VERB
ejpam-7005	307	7	coherence	coherence	NOUN
ejpam-7005	307	8	resonance	resonance	NOUN
ejpam-7005	307	9	in	in	ADP
ejpam-7005	307	10	a	a	DET
ejpam-7005	307	11	an	an	DET
ejpam-7005	307	12	electrochemical	electrochemical	ADJ
ejpam-7005	307	13	system	system	NOUN
ejpam-7005	307	14	.	.	PUNCT
ejpam-7005	308	1	physical	physical	ADJ
ejpam-7005	308	2	review	review	PROPN
ejpam-7005	308	3	e	e	NOUN
ejpam-7005	308	4	,	,	PUNCT
ejpam-7005	308	5	59(4):r3791	59(4):r3791	NUM
ejpam-7005	308	6	,	,	PUNCT
ejpam-7005	308	7	1999	1999	NUM
ejpam-7005	308	8	.	.	PUNCT
ejpam-7005	309	1	[	[	X
ejpam-7005	309	2	11	11	NUM
ejpam-7005	309	3	]	]	PUNCT
ejpam-7005	309	4	r.	r.	PROPN
ejpam-7005	309	5	l.	l.	PROPN
ejpam-7005	309	6	magin	magin	PROPN
ejpam-7005	309	7	.	.	PUNCT
ejpam-7005	310	1	fractional	fractional	ADJ
ejpam-7005	310	2	calculus	calculus	NOUN
ejpam-7005	310	3	in	in	ADP
ejpam-7005	310	4	bioengineering	bioengineering	NOUN
ejpam-7005	310	5	.	.	PUNCT
ejpam-7005	311	1	begell	begell	NOUN
ejpam-7005	311	2	house	house	NOUN
ejpam-7005	311	3	publishers	publisher	NOUN
ejpam-7005	311	4	,	,	PUNCT
ejpam-7005	311	5	2006	2006	NUM
ejpam-7005	311	6	.	.	PUNCT
ejpam-7005	312	1	[	[	X
ejpam-7005	312	2	12	12	NUM
ejpam-7005	312	3	]	]	X
ejpam-7005	312	4	r.	r.	PROPN
ejpam-7005	312	5	metzler	metzler	PROPN
ejpam-7005	312	6	and	and	CCONJ
ejpam-7005	312	7	j.	j.	PROPN
ejpam-7005	312	8	klafter	klafter	PROPN
ejpam-7005	312	9	.	.	PUNCT
ejpam-7005	313	1	the	the	DET
ejpam-7005	313	2	random	random	ADJ
ejpam-7005	313	3	walk	walk	NOUN
ejpam-7005	313	4	’s	’s	PART
ejpam-7005	313	5	guide	guide	NOUN
ejpam-7005	313	6	to	to	ADP
ejpam-7005	313	7	anomalous	anomalous	ADJ
ejpam-7005	313	8	diffusion	diffusion	NOUN
ejpam-7005	313	9	:	:	PUNCT
ejpam-7005	313	10	a	a	DET
ejpam-7005	313	11	fractional	fractional	ADJ
ejpam-7005	313	12	dynamics	dynamic	NOUN
ejpam-7005	313	13	approach	approach	NOUN
ejpam-7005	313	14	.	.	PUNCT
ejpam-7005	314	1	physics	physics	NOUN
ejpam-7005	314	2	reports	report	NOUN
ejpam-7005	314	3	,	,	PUNCT
ejpam-7005	314	4	339(1):1–77	339(1):1–77	NUM
ejpam-7005	314	5	,	,	PUNCT
ejpam-7005	314	6	2000	2000	NUM
ejpam-7005	314	7	.	.	PUNCT
ejpam-7005	315	1	[	[	X
ejpam-7005	315	2	13	13	NUM
ejpam-7005	315	3	]	]	PUNCT
ejpam-7005	315	4	i.	i.	NOUN
ejpam-7005	315	5	podlubny	podlubny	PROPN
ejpam-7005	315	6	.	.	PUNCT
ejpam-7005	316	1	fractional	fractional	ADJ
ejpam-7005	316	2	differential	differential	ADJ
ejpam-7005	316	3	equations	equation	NOUN
ejpam-7005	316	4	.	.	PUNCT
ejpam-7005	317	1	academic	academic	ADJ
ejpam-7005	317	2	press	press	NOUN
ejpam-7005	317	3	,	,	PUNCT
ejpam-7005	317	4	1999	1999	NUM
ejpam-7005	317	5	.	.	PUNCT
ejpam-7005	318	1	[	[	X
ejpam-7005	318	2	14	14	NUM
ejpam-7005	318	3	]	]	PUNCT
ejpam-7005	318	4	a.	a.	NOUN
ejpam-7005	318	5	a.	a.	NOUN
ejpam-7005	318	6	kilbas	kilbas	PROPN
ejpam-7005	318	7	,	,	PUNCT
ejpam-7005	318	8	h.	h.	PROPN
ejpam-7005	318	9	m.	m.	PROPN
ejpam-7005	318	10	srivastava	srivastava	PROPN
ejpam-7005	318	11	,	,	PUNCT
ejpam-7005	318	12	and	and	CCONJ
ejpam-7005	318	13	j.	j.	PROPN
ejpam-7005	318	14	j.	j.	PROPN
ejpam-7005	318	15	trujillo	trujillo	PROPN
ejpam-7005	318	16	.	.	PUNCT
ejpam-7005	318	17	theory	theory	NOUN
ejpam-7005	318	18	and	and	CCONJ
ejpam-7005	318	19	applications	application	NOUN
ejpam-7005	318	20	of	of	ADP
ejpam-7005	318	21	fractional	fractional	ADJ
ejpam-7005	318	22	differential	differential	ADJ
ejpam-7005	318	23	equations	equation	NOUN
ejpam-7005	318	24	.	.	PUNCT
ejpam-7005	319	1	elsevier	elsevier	NOUN
ejpam-7005	319	2	,	,	PUNCT
ejpam-7005	319	3	2006	2006	NUM
ejpam-7005	319	4	.	.	PUNCT
ejpam-7005	320	1	[	[	X
ejpam-7005	320	2	15	15	NUM
ejpam-7005	320	3	]	]	X
ejpam-7005	320	4	s.	s.	PROPN
ejpam-7005	320	5	g.	g.	PROPN
ejpam-7005	320	6	samko	samko	PROPN
ejpam-7005	320	7	,	,	PUNCT
ejpam-7005	320	8	a.	a.	NOUN
ejpam-7005	320	9	a.	a.	NOUN
ejpam-7005	320	10	kilbas	kilbas	PROPN
ejpam-7005	320	11	,	,	PUNCT
ejpam-7005	320	12	and	and	CCONJ
ejpam-7005	320	13	o.	o.	PROPN
ejpam-7005	320	14	i.	i.	PROPN
ejpam-7005	320	15	marichev	marichev	PROPN
ejpam-7005	320	16	.	.	PUNCT
ejpam-7005	321	1	fractional	fractional	ADJ
ejpam-7005	321	2	integrals	integral	NOUN
ejpam-7005	321	3	and	and	CCONJ
ejpam-7005	321	4	derivatives	derivative	NOUN
ejpam-7005	321	5	:	:	PUNCT
ejpam-7005	321	6	theory	theory	NOUN
ejpam-7005	321	7	and	and	CCONJ
ejpam-7005	321	8	applications	application	NOUN
ejpam-7005	321	9	.	.	PUNCT
ejpam-7005	322	1	gordon	gordon	PROPN
ejpam-7005	322	2	and	and	CCONJ
ejpam-7005	322	3	breach	breach	VERB
ejpam-7005	322	4	science	science	NOUN
ejpam-7005	322	5	publishers	publisher	NOUN
ejpam-7005	322	6	,	,	PUNCT
ejpam-7005	322	7	1993	1993	NUM
ejpam-7005	322	8	.	.	PUNCT
ejpam-7005	323	1	[	[	X
ejpam-7005	323	2	16	16	NUM
ejpam-7005	323	3	]	]	PUNCT
ejpam-7005	323	4	i.	i.	NOUN
ejpam-7005	323	5	jebril	jebril	PROPN
ejpam-7005	323	6	,	,	PUNCT
ejpam-7005	323	7	a.	a.	NOUN
ejpam-7005	323	8	lakehal	lakehal	NOUN
ejpam-7005	323	9	,	,	PUNCT
ejpam-7005	323	10	and	and	CCONJ
ejpam-7005	323	11	s.	s.	PROPN
ejpam-7005	323	12	benyoussef	benyoussef	PROPN
ejpam-7005	323	13	.	.	PUNCT
ejpam-7005	324	1	fractional	fractional	ADJ
ejpam-7005	324	2	-	-	PUNCT
ejpam-7005	324	3	order	order	NOUN
ejpam-7005	324	4	discrete	discrete	ADJ
ejpam-7005	324	5	predator	predator	NOUN
ejpam-7005	324	6	–	–	PUNCT
ejpam-7005	324	7	prey	prey	NOUN
ejpam-7005	324	8	system	system	NOUN
ejpam-7005	324	9	of	of	ADP
ejpam-7005	324	10	leslie	leslie	PROPN
ejpam-7005	324	11	type	type	NOUN
ejpam-7005	324	12	:	:	PUNCT
ejpam-7005	324	13	existence	existence	NOUN
ejpam-7005	324	14	,	,	PUNCT
ejpam-7005	324	15	stability	stability	NOUN
ejpam-7005	324	16	,	,	PUNCT
ejpam-7005	324	17	and	and	CCONJ
ejpam-7005	324	18	numerical	numerical	PROPN
ejpam-7005	324	19	simulation	simulation	PROPN
ejpam-7005	324	20	.	.	PUNCT
ejpam-7005	325	1	international	international	ADJ
ejpam-7005	325	2	journal	journal	PROPN
ejpam-7005	325	3	of	of	ADP
ejpam-7005	325	4	robotics	robotic	NOUN
ejpam-7005	325	5	and	and	CCONJ
ejpam-7005	325	6	control	control	NOUN
ejpam-7005	325	7	systems	system	NOUN
ejpam-7005	325	8	,	,	PUNCT
ejpam-7005	325	9	5(2):1519–1538	5(2):1519–1538	NUM
ejpam-7005	325	10	,	,	PUNCT
ejpam-7005	325	11	2025	2025	NUM
ejpam-7005	325	12	.	.	PUNCT
ejpam-7005	326	1	[	[	X
ejpam-7005	326	2	17	17	NUM
ejpam-7005	326	3	]	]	X
ejpam-7005	326	4	iqbal	iqbal	PROPN
ejpam-7005	326	5	m	m	PROPN
ejpam-7005	326	6	batiha	batiha	VERB
ejpam-7005	326	7	,	,	PUNCT
ejpam-7005	326	8	hamzah	hamzah	PROPN
ejpam-7005	326	9	o	o	PROPN
ejpam-7005	326	10	al	al	PROPN
ejpam-7005	326	11	-	-	PUNCT
ejpam-7005	326	12	khawaldeh	khawaldeh	PROPN
ejpam-7005	326	13	,	,	PUNCT
ejpam-7005	326	14	manal	manal	PROPN
ejpam-7005	326	15	almuzini	almuzini	PROPN
ejpam-7005	326	16	,	,	PUNCT
ejpam-7005	326	17	waseem	waseem	PROPN
ejpam-7005	326	18	g	g	PROPN
ejpam-7005	326	19	alshanti	alshanti	PROPN
ejpam-7005	326	20	,	,	PUNCT
ejpam-7005	326	21	nidal	nidal	PROPN
ejpam-7005	326	22	anakira	anakira	PROPN
ejpam-7005	326	23	,	,	PUNCT
ejpam-7005	326	24	and	and	CCONJ
ejpam-7005	326	25	ala	ala	PROPN
ejpam-7005	326	26	amourah	amourah	PROPN
ejpam-7005	326	27	.	.	PUNCT
ejpam-7005	327	1	a	a	DET
ejpam-7005	327	2	fractional	fractional	ADJ
ejpam-7005	327	3	mathematical	mathematical	ADJ
ejpam-7005	327	4	examination	examination	NOUN
ejpam-7005	327	5	on	on	ADP
ejpam-7005	327	6	breast	breast	NOUN
ejpam-7005	327	7	cancer	cancer	NOUN
ejpam-7005	327	8	progression	progression	NOUN
ejpam-7005	327	9	for	for	ADP
ejpam-7005	327	10	the	the	DET
ejpam-7005	327	11	healthcare	healthcare	NOUN
ejpam-7005	327	12	system	system	NOUN
ejpam-7005	327	13	of	of	ADP
ejpam-7005	327	14	jordan	jordan	PROPN
ejpam-7005	327	15	.	.	PUNCT
ejpam-7005	328	1	commun	commun	PROPN
ejpam-7005	328	2	.	.	PUNCT
ejpam-7005	329	1	math	math	NOUN
ejpam-7005	329	2	.	.	PUNCT
ejpam-7005	330	1	biol	biol	PROPN
ejpam-7005	330	2	.	.	PUNCT
ejpam-7005	331	1	neurosci	neurosci	PROPN
ejpam-7005	331	2	.	.	PUNCT
ejpam-7005	331	3	,	,	PUNCT
ejpam-7005	331	4	2025	2025	NUM
ejpam-7005	331	5	:	:	PUNCT
ejpam-7005	331	6	article	article	NOUN
ejpam-7005	331	7	–	–	PUNCT
ejpam-7005	331	8	id	id	NOUN
ejpam-7005	331	9	,	,	PUNCT
ejpam-7005	331	10	2025	2025	NUM
ejpam-7005	331	11	.	.	PUNCT
ejpam-7005	332	1	[	[	X
ejpam-7005	332	2	18	18	NUM
ejpam-7005	332	3	]	]	X
ejpam-7005	332	4	i.	i.	PROPN
ejpam-7005	332	5	m.	m.	PROPN
ejpam-7005	332	6	batiha	batiha	PROPN
ejpam-7005	332	7	,	,	PUNCT
ejpam-7005	332	8	i.	i.	PROPN
ejpam-7005	332	9	bendib	bendib	PROPN
ejpam-7005	332	10	,	,	PUNCT
ejpam-7005	332	11	a.	a.	NOUN
ejpam-7005	332	12	ouannas	ouannas	NOUN
ejpam-7005	332	13	,	,	PUNCT
ejpam-7005	332	14	p.	p.	PROPN
ejpam-7005	332	15	agarwal	agarwal	PROPN
ejpam-7005	332	16	,	,	PUNCT
ejpam-7005	332	17	n.	n.	PROPN
ejpam-7005	332	18	anakira	anakira	PROPN
ejpam-7005	332	19	,	,	PUNCT
ejpam-7005	332	20	i.	i.	PROPN
ejpam-7005	332	21	h.	h.	PROPN
ejpam-7005	332	22	jebril	jebril	PROPN
ejpam-7005	332	23	,	,	PUNCT
ejpam-7005	332	24	and	and	CCONJ
ejpam-7005	332	25	s.	s.	PROPN
ejpam-7005	332	26	momani	momani	PROPN
ejpam-7005	332	27	.	.	PUNCT
ejpam-7005	333	1	finite	finite	ADJ
ejpam-7005	333	2	-	-	PUNCT
ejpam-7005	333	3	time	time	NOUN
ejpam-7005	333	4	synchronization	synchronization	NOUN
ejpam-7005	333	5	in	in	ADP
ejpam-7005	333	6	a	a	DET
ejpam-7005	333	7	novel	novel	ADJ
ejpam-7005	333	8	discrete	discrete	NOUN
ejpam-7005	333	9	fractional	fractional	ADJ
ejpam-7005	333	10	sir	sir	NOUN
ejpam-7005	333	11	model	model	NOUN
ejpam-7005	333	12	for	for	ADP
ejpam-7005	333	13	covid-19	covid-19	PROPN
ejpam-7005	333	14	.	.	PUNCT
ejpam-7005	333	15	special	special	ADJ
ejpam-7005	333	16	issue	issue	NOUN
ejpam-7005	333	17	on	on	ADP
ejpam-7005	333	18	advanced	advanced	ADJ
ejpam-7005	333	19	computational	computational	ADJ
ejpam-7005	333	20	methods	method	NOUN
ejpam-7005	333	21	for	for	ADP
ejpam-7005	333	22	fractional	fractional	ADJ
ejpam-7005	333	23	calculus	calculus	NOUN
ejpam-7005	333	24	,	,	PUNCT
ejpam-7005	333	25	43(1	43(1	NOUN
ejpam-7005	333	26	)	)	PUNCT
ejpam-7005	333	27	,	,	PUNCT
ejpam-7005	333	28	2025	2025	NUM
ejpam-7005	333	29	.	.	PUNCT
ejpam-7005	334	1	[	[	X
ejpam-7005	334	2	19	19	NUM
ejpam-7005	334	3	]	]	PUNCT
ejpam-7005	334	4	a.	a.	NOUN
ejpam-7005	334	5	qazza	qazza	PROPN
ejpam-7005	334	6	,	,	PUNCT
ejpam-7005	334	7	i.	i.	PROPN
ejpam-7005	334	8	bendib	bendib	PROPN
ejpam-7005	334	9	,	,	PUNCT
ejpam-7005	334	10	r.	r.	PROPN
ejpam-7005	334	11	hatamleh	hatamleh	PROPN
ejpam-7005	334	12	,	,	PUNCT
ejpam-7005	334	13	r.	r.	PROPN
ejpam-7005	334	14	saadeh	saadeh	PROPN
ejpam-7005	334	15	,	,	PUNCT
ejpam-7005	334	16	and	and	CCONJ
ejpam-7005	334	17	a.	a.	NOUN
ejpam-7005	334	18	ouannas	ouanna	NOUN
ejpam-7005	334	19	.	.	PUNCT
ejpam-7005	335	1	dynamics	dynamic	NOUN
ejpam-7005	335	2	of	of	ADP
ejpam-7005	335	3	the	the	DET
ejpam-7005	335	4	gierer	gierer	NOUN
ejpam-7005	335	5	–	–	PUNCT
ejpam-7005	335	6	meinhardt	meinhardt	ADJ
ejpam-7005	335	7	reaction	reaction	NOUN
ejpam-7005	335	8	–	–	PUNCT
ejpam-7005	335	9	diffusion	diffusion	NOUN
ejpam-7005	335	10	system	system	NOUN
ejpam-7005	335	11	:	:	PUNCT
ejpam-7005	335	12	insights	insight	NOUN
ejpam-7005	335	13	into	into	ADP
ejpam-7005	335	14	finite	finite	ADJ
ejpam-7005	335	15	-	-	PUNCT
ejpam-7005	335	16	time	time	NOUN
ejpam-7005	335	17	stability	stability	NOUN
ejpam-7005	335	18	and	and	CCONJ
ejpam-7005	335	19	control	control	NOUN
ejpam-7005	335	20	strategies	strategy	NOUN
ejpam-7005	335	21	.	.	PUNCT
ejpam-7005	336	1	partial	partial	ADJ
ejpam-7005	336	2	differential	differential	ADJ
ejpam-7005	336	3	equations	equation	NOUN
ejpam-7005	336	4	in	in	ADP
ejpam-7005	336	5	applied	applied	ADJ
ejpam-7005	336	6	mathematics	mathematic	NOUN
ejpam-7005	336	7	,	,	PUNCT
ejpam-7005	336	8	14	14	NUM
ejpam-7005	336	9	:	:	PUNCT
ejpam-7005	336	10	article	article	NOUN
ejpam-7005	336	11	101142	101142	NUM
ejpam-7005	336	12	,	,	PUNCT
ejpam-7005	336	13	2025	2025	NUM
ejpam-7005	336	14	.	.	PUNCT
ejpam-7005	337	1	[	[	X
ejpam-7005	337	2	20	20	NUM
ejpam-7005	337	3	]	]	PUNCT
ejpam-7005	337	4	ahmed	ahmed	PROPN
ejpam-7005	337	5	bouchenak	bouchenak	PROPN
ejpam-7005	337	6	,	,	PUNCT
ejpam-7005	337	7	iqbal	iqbal	PROPN
ejpam-7005	337	8	m	m	PROPN
ejpam-7005	337	9	batiha	batiha	VERB
ejpam-7005	337	10	,	,	PUNCT
ejpam-7005	337	11	mazin	mazin	PROPN
ejpam-7005	337	12	aljazzazi	aljazzazi	PROPN
ejpam-7005	337	13	,	,	PUNCT
ejpam-7005	337	14	nidal	nidal	PROPN
ejpam-7005	337	15	anakira	anakira	PROPN
ejpam-7005	337	16	,	,	PUNCT
ejpam-7005	337	17	mohammad	mohammad	PROPN
ejpam-7005	337	18	odeh	odeh	PROPN
ejpam-7005	337	19	,	,	PUNCT
ejpam-7005	337	20	and	and	CCONJ
ejpam-7005	337	21	rasha	rasha	VERB
ejpam-7005	337	22	ibrahim	ibrahim	PROPN
ejpam-7005	337	23	hajaj	hajaj	PROPN
ejpam-7005	337	24	.	.	PUNCT
ejpam-7005	338	1	numerical	numerical	PROPN
ejpam-7005	338	2	and	and	CCONJ
ejpam-7005	338	3	analytical	analytical	ADJ
ejpam-7005	338	4	investigations	investigation	NOUN
ejpam-7005	338	5	of	of	ADP
ejpam-7005	338	6	fractional	fractional	ADJ
ejpam-7005	338	7	self	self	NOUN
ejpam-7005	338	8	-	-	PUNCT
ejpam-7005	338	9	adjoint	adjoint	NOUN
ejpam-7005	338	10	equations	equation	NOUN
ejpam-7005	338	11	and	and	CCONJ
ejpam-7005	338	12	fractional	fractional	ADJ
ejpam-7005	338	13	sturm	sturm	PROPN
ejpam-7005	338	14	-	-	PUNCT
ejpam-7005	338	15	liouville	liouville	NOUN
ejpam-7005	338	16	problems	problem	NOUN
ejpam-7005	338	17	via	via	ADP
ejpam-7005	338	18	modified	modified	ADJ
ejpam-7005	338	19	conformable	conformable	ADJ
ejpam-7005	338	20	operator	operator	NOUN
ejpam-7005	338	21	.	.	PUNCT
ejpam-7005	339	1	journal	journal	PROPN
ejpam-7005	339	2	of	of	ADP
ejpam-7005	339	3	robotics	robotic	NOUN
ejpam-7005	339	4	and	and	CCONJ
ejpam-7005	339	5	control	control	PROPN
ejpam-7005	339	6	(	(	PUNCT
ejpam-7005	339	7	jrc	jrc	PROPN
ejpam-7005	339	8	)	)	PUNCT
ejpam-7005	339	9	,	,	PUNCT
ejpam-7005	339	10	6(3):1410–1424	6(3):1410–1424	PROPN
ejpam-7005	339	11	,	,	PUNCT
ejpam-7005	339	12	2025	2025	NUM
ejpam-7005	339	13	.	.	PUNCT
ejpam-7005	340	1	[	[	X
ejpam-7005	340	2	21	21	NUM
ejpam-7005	340	3	]	]	X
ejpam-7005	340	4	r.	r.	PROPN
ejpam-7005	340	5	hatamleh	hatamleh	PROPN
ejpam-7005	340	6	,	,	PUNCT
ejpam-7005	340	7	i.	i.	PROPN
ejpam-7005	340	8	bendib	bendib	PROPN
ejpam-7005	340	9	,	,	PUNCT
ejpam-7005	340	10	a.	a.	NOUN
ejpam-7005	340	11	qazza	qazza	PROPN
ejpam-7005	340	12	,	,	PUNCT
ejpam-7005	340	13	r.	r.	PROPN
ejpam-7005	340	14	saadeh	saadeh	PROPN
ejpam-7005	340	15	,	,	PUNCT
ejpam-7005	340	16	a.	a.	NOUN
ejpam-7005	340	17	ouannas	ouanna	NOUN
ejpam-7005	340	18	,	,	PUNCT
ejpam-7005	340	19	and	and	CCONJ
ejpam-7005	340	20	m.	m.	NOUN
ejpam-7005	340	21	dalah	dalah	NOUN
ejpam-7005	340	22	.	.	PUNCT
ejpam-7005	341	1	finite	finite	PROPN
ejpam-7005	341	2	time	time	NOUN
ejpam-7005	341	3	stability	stability	NOUN
ejpam-7005	341	4	and	and	CCONJ
ejpam-7005	341	5	synchronization	synchronization	NOUN
ejpam-7005	341	6	of	of	ADP
ejpam-7005	341	7	the	the	DET
ejpam-7005	341	8	glycolysis	glycolysis	NOUN
ejpam-7005	341	9	reaction	reaction	NOUN
ejpam-7005	341	10	-	-	PUNCT
ejpam-7005	341	11	diffusion	diffusion	NOUN
ejpam-7005	341	12	model	model	NOUN
ejpam-7005	341	13	.	.	PUNCT
ejpam-7005	342	1	international	international	ADJ
ejpam-7005	342	2	journal	journal	PROPN
ejpam-7005	342	3	of	of	ADP
ejpam-7005	342	4	neutrosophic	neutrosophic	ADJ
ejpam-7005	342	5	science	science	NOUN
ejpam-7005	342	6	,	,	PUNCT
ejpam-7005	342	7	25(4):371–386	25(4):371–386	NUM
ejpam-7005	342	8	,	,	PUNCT
ejpam-7005	342	9	2025	2025	NUM
ejpam-7005	342	10	.	.	PUNCT
ejpam-7005	343	1	n.	n.	PROPN
ejpam-7005	343	2	anakira	anakira	PROPN
ejpam-7005	343	3	et	et	PROPN
ejpam-7005	343	4	al	al	PROPN
ejpam-7005	343	5	.	.	PUNCT
ejpam-7005	343	6	/	/	SYM
ejpam-7005	343	7	eur	eur	PROPN
ejpam-7005	343	8	.	.	PUNCT
ejpam-7005	344	1	j.	j.	PROPN
ejpam-7005	344	2	pure	pure	PROPN
ejpam-7005	344	3	appl	appl	PROPN
ejpam-7005	344	4	.	.	PROPN
ejpam-7005	344	5	math	math	PROPN
ejpam-7005	344	6	,	,	PUNCT
ejpam-7005	344	7	18	18	NUM
ejpam-7005	344	8	(	(	PUNCT
ejpam-7005	344	9	4	4	NUM
ejpam-7005	344	10	)	)	PUNCT
ejpam-7005	344	11	(	(	PUNCT
ejpam-7005	344	12	2025	2025	NUM
ejpam-7005	344	13	)	)	PUNCT
ejpam-7005	344	14	,	,	PUNCT
ejpam-7005	344	15	7005	7005	NUM
ejpam-7005	344	16	16	16	NUM
ejpam-7005	344	17	of	of	ADP
ejpam-7005	344	18	17	17	NUM
ejpam-7005	344	19	[	[	SYM
ejpam-7005	344	20	22	22	NUM
ejpam-7005	344	21	]	]	PUNCT
ejpam-7005	344	22	s.	s.	PROPN
ejpam-7005	344	23	momani	momani	PROPN
ejpam-7005	344	24	,	,	PUNCT
ejpam-7005	344	25	i.	i.	PROPN
ejpam-7005	344	26	m.	m.	PROPN
ejpam-7005	344	27	batiha	batiha	PROPN
ejpam-7005	344	28	,	,	PUNCT
ejpam-7005	344	29	m.	m.	NOUN
ejpam-7005	344	30	s.	s.	PROPN
ejpam-7005	344	31	hijazi	hijazi	PROPN
ejpam-7005	344	32	,	,	PUNCT
ejpam-7005	344	33	i.	i.	PROPN
ejpam-7005	344	34	bendib	bendib	PROPN
ejpam-7005	344	35	,	,	PUNCT
ejpam-7005	344	36	a.	a.	NOUN
ejpam-7005	344	37	ouannas	ouanna	NOUN
ejpam-7005	344	38	,	,	PUNCT
ejpam-7005	344	39	and	and	CCONJ
ejpam-7005	344	40	n.	n.	PROPN
ejpam-7005	344	41	anakira	anakira	PROPN
ejpam-7005	344	42	.	.	PUNCT
ejpam-7005	345	1	fractional	fractional	ADJ
ejpam-7005	345	2	-	-	PUNCT
ejpam-7005	345	3	order	order	NOUN
ejpam-7005	345	4	seir	seir	NOUN
ejpam-7005	345	5	model	model	NOUN
ejpam-7005	345	6	for	for	ADP
ejpam-7005	345	7	covid-19	covid-19	PROPN
ejpam-7005	345	8	:	:	PUNCT
ejpam-7005	345	9	finite	finite	ADJ
ejpam-7005	345	10	-	-	PUNCT
ejpam-7005	345	11	time	time	NOUN
ejpam-7005	345	12	stability	stability	NOUN
ejpam-7005	345	13	analysis	analysis	NOUN
ejpam-7005	345	14	and	and	CCONJ
ejpam-7005	345	15	numerical	numerical	ADJ
ejpam-7005	345	16	validation	validation	NOUN
ejpam-7005	345	17	.	.	PUNCT
ejpam-7005	346	1	international	international	ADJ
ejpam-7005	346	2	journal	journal	PROPN
ejpam-7005	346	3	of	of	ADP
ejpam-7005	346	4	neutrosophic	neutrosophic	ADJ
ejpam-7005	346	5	science	science	NOUN
ejpam-7005	346	6	,	,	PUNCT
ejpam-7005	346	7	26(1):266–282	26(1):266–282	PROPN
ejpam-7005	346	8	,	,	PUNCT
ejpam-7005	346	9	2025	2025	NUM
ejpam-7005	346	10	.	.	PUNCT
ejpam-7005	347	1	[	[	X
ejpam-7005	347	2	23	23	NUM
ejpam-7005	347	3	]	]	X
ejpam-7005	347	4	h.	h.	PROPN
ejpam-7005	347	5	al	al	PROPN
ejpam-7005	347	6	-	-	PUNCT
ejpam-7005	347	7	taani	taani	ADJ
ejpam-7005	347	8	,	,	PUNCT
ejpam-7005	347	9	m.	m.	NOUN
ejpam-7005	347	10	m.	m.	PROPN
ejpam-7005	347	11	hammad	hammad	PROPN
ejpam-7005	347	12	,	,	PUNCT
ejpam-7005	347	13	o.	o.	PROPN
ejpam-7005	347	14	alomari	alomari	PROPN
ejpam-7005	347	15	,	,	PUNCT
ejpam-7005	347	16	i.	i.	PROPN
ejpam-7005	347	17	bendib	bendib	PROPN
ejpam-7005	347	18	,	,	PUNCT
ejpam-7005	347	19	and	and	CCONJ
ejpam-7005	347	20	a.	a.	NOUN
ejpam-7005	347	21	ouannas	ouannas	NOUN
ejpam-7005	347	22	.	.	PUNCT
ejpam-7005	348	1	finite	finite	ADJ
ejpam-7005	348	2	-	-	PUNCT
ejpam-7005	348	3	time	time	NOUN
ejpam-7005	348	4	control	control	NOUN
ejpam-7005	348	5	of	of	ADP
ejpam-7005	348	6	the	the	DET
ejpam-7005	348	7	discrete	discrete	ADJ
ejpam-7005	348	8	sel’kov	sel’kov	PROPN
ejpam-7005	348	9	–	–	PUNCT
ejpam-7005	348	10	schnakenberg	schnakenberg	PROPN
ejpam-7005	348	11	model	model	NOUN
ejpam-7005	348	12	:	:	PUNCT
ejpam-7005	348	13	synchronization	synchronization	NOUN
ejpam-7005	348	14	and	and	CCONJ
ejpam-7005	348	15	simulations	simulation	NOUN
ejpam-7005	348	16	.	.	PUNCT
ejpam-7005	349	1	aip	aip	PROPN
ejpam-7005	349	2	advances	advance	NOUN
ejpam-7005	349	3	,	,	PUNCT
ejpam-7005	349	4	15(2):025325	15(2):025325	NUM
ejpam-7005	349	5	,	,	PUNCT
ejpam-7005	349	6	2025	2025	NUM
ejpam-7005	349	7	.	.	PUNCT
ejpam-7005	350	1	[	[	X
ejpam-7005	350	2	24	24	NUM
ejpam-7005	350	3	]	]	X
ejpam-7005	350	4	khelifa	khelifa	PROPN
ejpam-7005	350	5	bouaziz	bouaziz	PROPN
ejpam-7005	350	6	,	,	PUNCT
ejpam-7005	350	7	nadhir	nadhir	ADJ
ejpam-7005	350	8	djeddi	djeddi	PROPN
ejpam-7005	350	9	,	,	PUNCT
ejpam-7005	350	10	osama	osama	NOUN
ejpam-7005	350	11	ogilat	ogilat	NOUN
ejpam-7005	350	12	,	,	PUNCT
ejpam-7005	350	13	iqbal	iqbal	PROPN
ejpam-7005	350	14	m	m	PROPN
ejpam-7005	350	15	batiha	batiha	VERB
ejpam-7005	350	16	,	,	PUNCT
ejpam-7005	350	17	nidal	nidal	PROPN
ejpam-7005	350	18	anakira	anakira	PROPN
ejpam-7005	350	19	,	,	PUNCT
ejpam-7005	350	20	and	and	CCONJ
ejpam-7005	350	21	tala	tala	PROPN
ejpam-7005	350	22	sasa	sasa	PROPN
ejpam-7005	350	23	.	.	PUNCT
ejpam-7005	351	1	stability	stability	NOUN
ejpam-7005	351	2	analysis	analysis	NOUN
ejpam-7005	351	3	of	of	ADP
ejpam-7005	351	4	a	a	DET
ejpam-7005	351	5	fractional	fractional	ADJ
ejpam-7005	351	6	-	-	PUNCT
ejpam-7005	351	7	order	order	NOUN
ejpam-7005	351	8	lengyel	lengyel	NOUN
ejpam-7005	351	9	–	–	PUNCT
ejpam-7005	351	10	epstein	epstein	PROPN
ejpam-7005	351	11	chemical	chemical	PROPN
ejpam-7005	351	12	reaction	reaction	PROPN
ejpam-7005	351	13	model	model	PROPN
ejpam-7005	351	14	.	.	PUNCT
ejpam-7005	352	1	international	international	ADJ
ejpam-7005	352	2	journal	journal	PROPN
ejpam-7005	352	3	of	of	ADP
ejpam-7005	352	4	robotics	robotic	NOUN
ejpam-7005	352	5	and	and	CCONJ
ejpam-7005	352	6	control	control	NOUN
ejpam-7005	352	7	systems	system	NOUN
ejpam-7005	352	8	,	,	PUNCT
ejpam-7005	352	9	5(2):1539–1551	5(2):1539–1551	NUM
ejpam-7005	352	10	,	,	PUNCT
ejpam-7005	352	11	2025	2025	NUM
ejpam-7005	352	12	.	.	PUNCT
ejpam-7005	353	1	[	[	X
ejpam-7005	353	2	25	25	NUM
ejpam-7005	353	3	]	]	PUNCT
ejpam-7005	353	4	i.	i.	PROPN
ejpam-7005	353	5	m.	m.	PROPN
ejpam-7005	353	6	sokolov	sokolov	PROPN
ejpam-7005	353	7	.	.	PUNCT
ejpam-7005	354	1	models	model	NOUN
ejpam-7005	354	2	of	of	ADP
ejpam-7005	354	3	anomalous	anomalous	ADJ
ejpam-7005	354	4	diffusion	diffusion	NOUN
ejpam-7005	354	5	in	in	ADP
ejpam-7005	354	6	crowded	crowded	ADJ
ejpam-7005	354	7	environments	environment	NOUN
ejpam-7005	354	8	.	.	PUNCT
ejpam-7005	355	1	soft	soft	ADJ
ejpam-7005	355	2	matter	matter	NOUN
ejpam-7005	355	3	,	,	PUNCT
ejpam-7005	355	4	8(35):9043–9052	8(35):9043–9052	NUM
ejpam-7005	355	5	,	,	PUNCT
ejpam-7005	355	6	2012	2012	NUM
ejpam-7005	355	7	.	.	PUNCT
ejpam-7005	356	1	[	[	X
ejpam-7005	356	2	26	26	NUM
ejpam-7005	356	3	]	]	PUNCT
ejpam-7005	356	4	a.	a.	NOUN
ejpam-7005	356	5	n.	n.	PROPN
ejpam-7005	356	6	anber	anber	PROPN
ejpam-7005	356	7	and	and	CCONJ
ejpam-7005	356	8	z.	z.	PROPN
ejpam-7005	356	9	dahmani	dahmani	PROPN
ejpam-7005	356	10	.	.	PUNCT
ejpam-7005	357	1	the	the	DET
ejpam-7005	357	2	laplace	laplace	NOUN
ejpam-7005	357	3	decomposition	decomposition	NOUN
ejpam-7005	357	4	method	method	NOUN
ejpam-7005	357	5	for	for	ADP
ejpam-7005	357	6	solving	solve	VERB
ejpam-7005	357	7	nonlinear	nonlinear	ADJ
ejpam-7005	357	8	conformable	conformable	ADJ
ejpam-7005	357	9	fractional	fractional	ADJ
ejpam-7005	357	10	evolution	evolution	NOUN
ejpam-7005	357	11	equations	equation	NOUN
ejpam-7005	357	12	.	.	PUNCT
ejpam-7005	358	1	int	int	NOUN
ejpam-7005	358	2	.	.	PUNCT
ejpam-7005	359	1	j.	j.	PROPN
ejpam-7005	359	2	open	open	PROPN
ejpam-7005	359	3	probl	probl	PROPN
ejpam-7005	359	4	.	.	PUNCT
ejpam-7005	360	1	comput	comput	NOUN
ejpam-7005	360	2	.	.	PUNCT
ejpam-7005	361	1	math	math	NOUN
ejpam-7005	361	2	.	.	PUNCT
ejpam-7005	361	3	,	,	PUNCT
ejpam-7005	361	4	17(1):67–81	17(1):67–81	NUM
ejpam-7005	361	5	,	,	PUNCT
ejpam-7005	361	6	2024	2024	NUM
ejpam-7005	361	7	.	.	PUNCT
ejpam-7005	362	1	[	[	X
ejpam-7005	362	2	27	27	NUM
ejpam-7005	362	3	]	]	PUNCT
ejpam-7005	362	4	a.	a.	NOUN
ejpam-7005	362	5	anber	anber	PROPN
ejpam-7005	362	6	and	and	CCONJ
ejpam-7005	362	7	z.	z.	PROPN
ejpam-7005	362	8	dahmani	dahmani	PROPN
ejpam-7005	362	9	.	.	PUNCT
ejpam-7005	363	1	the	the	DET
ejpam-7005	363	2	ldm	ldm	NOUN
ejpam-7005	363	3	and	and	CCONJ
ejpam-7005	363	4	the	the	DET
ejpam-7005	363	5	cvim	cvim	NOUN
ejpam-7005	363	6	methods	method	NOUN
ejpam-7005	363	7	for	for	ADP
ejpam-7005	363	8	solving	solve	VERB
ejpam-7005	363	9	time	time	NOUN
ejpam-7005	363	10	and	and	CCONJ
ejpam-7005	363	11	space	space	NOUN
ejpam-7005	363	12	fractional	fractional	PROPN
ejpam-7005	363	13	wu	wu	PROPN
ejpam-7005	363	14	-	-	PUNCT
ejpam-7005	363	15	zhang	zhang	PROPN
ejpam-7005	363	16	differential	differential	PROPN
ejpam-7005	363	17	system	system	NOUN
ejpam-7005	363	18	.	.	PUNCT
ejpam-7005	364	1	int	int	NOUN
ejpam-7005	364	2	.	.	PUNCT
ejpam-7005	365	1	j.	j.	PROPN
ejpam-7005	365	2	open	open	PROPN
ejpam-7005	365	3	probl	probl	PROPN
ejpam-7005	365	4	.	.	PUNCT
ejpam-7005	366	1	comput	comput	NOUN
ejpam-7005	366	2	.	.	PUNCT
ejpam-7005	367	1	math	math	NOUN
ejpam-7005	367	2	.	.	PUNCT
ejpam-7005	367	3	,	,	PUNCT
ejpam-7005	367	4	17(3):1–18	17(3):1–18	NUM
ejpam-7005	367	5	,	,	PUNCT
ejpam-7005	367	6	2024	2024	NUM
ejpam-7005	367	7	.	.	PUNCT
ejpam-7005	368	1	[	[	X
ejpam-7005	368	2	28	28	NUM
ejpam-7005	368	3	]	]	X
ejpam-7005	368	4	w.	w.	NOUN
ejpam-7005	368	5	teka	teka	PROPN
ejpam-7005	368	6	,	,	PUNCT
ejpam-7005	368	7	g.	g.	PROPN
ejpam-7005	368	8	f.	f.	PROPN
ejpam-7005	368	9	t.	t.	PROPN
ejpam-7005	368	10	del	del	PROPN
ejpam-7005	368	11	castillo	castillo	PROPN
ejpam-7005	368	12	-	-	PUNCT
ejpam-7005	368	13	negrete	negrete	PROPN
ejpam-7005	368	14	,	,	PUNCT
ejpam-7005	368	15	and	and	CCONJ
ejpam-7005	368	16	b.	b.	PROPN
ejpam-7005	368	17	a.	a.	PROPN
ejpam-7005	368	18	van	van	PROPN
ejpam-7005	368	19	gorder	gorder	NOUN
ejpam-7005	368	20	.	.	PUNCT
ejpam-7005	369	1	anomalous	anomalous	ADJ
ejpam-7005	369	2	transport	transport	NOUN
ejpam-7005	369	3	in	in	ADP
ejpam-7005	369	4	the	the	DET
ejpam-7005	369	5	fractional	fractional	ADJ
ejpam-7005	369	6	fitzhugh	fitzhugh	PROPN
ejpam-7005	369	7	-	-	PUNCT
ejpam-7005	369	8	nagumo	nagumo	ADJ
ejpam-7005	369	9	model	model	NOUN
ejpam-7005	369	10	.	.	PUNCT
ejpam-7005	370	1	communications	communication	NOUN
ejpam-7005	370	2	in	in	ADP
ejpam-7005	370	3	nonlinear	nonlinear	ADJ
ejpam-7005	370	4	science	science	NOUN
ejpam-7005	370	5	and	and	CCONJ
ejpam-7005	370	6	numerical	numerical	PROPN
ejpam-7005	370	7	simulation	simulation	PROPN
ejpam-7005	370	8	,	,	PUNCT
ejpam-7005	370	9	19(10):3539–3552	19(10):3539–3552	NUM
ejpam-7005	370	10	,	,	PUNCT
ejpam-7005	370	11	2014	2014	NUM
ejpam-7005	370	12	.	.	PUNCT
ejpam-7005	371	1	[	[	X
ejpam-7005	371	2	29	29	NUM
ejpam-7005	371	3	]	]	X
ejpam-7005	371	4	n.	n.	PROPN
ejpam-7005	371	5	h.	h.	PROPN
ejpam-7005	371	6	sweilam	sweilam	PROPN
ejpam-7005	371	7	,	,	PUNCT
ejpam-7005	371	8	m.	m.	NOUN
ejpam-7005	371	9	m.	m.	NOUN
ejpam-7005	371	10	khader	khader	PROPN
ejpam-7005	371	11	,	,	PUNCT
ejpam-7005	371	12	and	and	CCONJ
ejpam-7005	371	13	r.	r.	PROPN
ejpam-7005	371	14	f.	f.	PROPN
ejpam-7005	371	15	al	al	PROPN
ejpam-7005	371	16	-	-	PUNCT
ejpam-7005	371	17	bar	bar	PROPN
ejpam-7005	371	18	.	.	PUNCT
ejpam-7005	372	1	numerical	numerical	ADJ
ejpam-7005	372	2	studies	study	NOUN
ejpam-7005	372	3	for	for	ADP
ejpam-7005	372	4	a	a	DET
ejpam-7005	372	5	multi	multi	ADJ
ejpam-7005	372	6	-	-	ADJ
ejpam-7005	372	7	term	term	ADJ
ejpam-7005	372	8	fractional	fractional	ADJ
ejpam-7005	372	9	-	-	PUNCT
ejpam-7005	372	10	order	order	NOUN
ejpam-7005	372	11	stencil	stencil	NOUN
ejpam-7005	372	12	for	for	ADP
ejpam-7005	372	13	the	the	DET
ejpam-7005	372	14	fitzhugh	fitzhugh	PROPN
ejpam-7005	372	15	-	-	PUNCT
ejpam-7005	372	16	nagumo	nagumo	ADJ
ejpam-7005	372	17	model	model	NOUN
ejpam-7005	372	18	.	.	PUNCT
ejpam-7005	373	1	journal	journal	PROPN
ejpam-7005	373	2	of	of	ADP
ejpam-7005	373	3	advanced	advanced	ADJ
ejpam-7005	373	4	research	research	NOUN
ejpam-7005	373	5	,	,	PUNCT
ejpam-7005	373	6	3(2):121–127	3(2):121–127	NUM
ejpam-7005	373	7	,	,	PUNCT
ejpam-7005	373	8	2012	2012	NUM
ejpam-7005	373	9	.	.	PUNCT
ejpam-7005	374	1	[	[	X
ejpam-7005	374	2	30	30	NUM
ejpam-7005	374	3	]	]	X
ejpam-7005	374	4	c.	c.	PROPN
ejpam-7005	374	5	f.	f.	PROPN
ejpam-7005	374	6	lorenzo	lorenzo	PROPN
ejpam-7005	374	7	and	and	CCONJ
ejpam-7005	374	8	t.	t.	PROPN
ejpam-7005	374	9	t.	t.	PROPN
ejpam-7005	374	10	hartley	hartley	PROPN
ejpam-7005	374	11	.	.	PUNCT
ejpam-7005	375	1	variable	variable	ADJ
ejpam-7005	375	2	order	order	NOUN
ejpam-7005	375	3	and	and	CCONJ
ejpam-7005	375	4	distributed	distribute	VERB
ejpam-7005	375	5	order	order	NOUN
ejpam-7005	375	6	fractional	fractional	ADJ
ejpam-7005	375	7	operators	operator	NOUN
ejpam-7005	375	8	.	.	PUNCT
ejpam-7005	376	1	nonlinear	nonlinear	ADJ
ejpam-7005	376	2	dynamics	dynamic	NOUN
ejpam-7005	376	3	,	,	PUNCT
ejpam-7005	376	4	29(1	29(1	NUM
ejpam-7005	376	5	-	-	PUNCT
ejpam-7005	376	6	4):57–98	4):57–98	NUM
ejpam-7005	376	7	,	,	PUNCT
ejpam-7005	376	8	2002	2002	NUM
ejpam-7005	376	9	.	.	PUNCT
ejpam-7005	377	1	[	[	X
ejpam-7005	377	2	31	31	NUM
ejpam-7005	377	3	]	]	PUNCT
ejpam-7005	377	4	c.	c.	PROPN
ejpam-7005	377	5	f.	f.	PROPN
ejpam-7005	377	6	m.	m.	PROPN
ejpam-7005	377	7	coimbra	coimbra	PROPN
ejpam-7005	377	8	.	.	PUNCT
ejpam-7005	378	1	mechanics	mechanic	NOUN
ejpam-7005	378	2	with	with	ADP
ejpam-7005	378	3	variable	variable	ADJ
ejpam-7005	378	4	-	-	PUNCT
ejpam-7005	378	5	order	order	NOUN
ejpam-7005	378	6	differential	differential	NOUN
ejpam-7005	378	7	operators	operator	NOUN
ejpam-7005	378	8	.	.	PUNCT
ejpam-7005	379	1	annalen	annalen	PROPN
ejpam-7005	379	2	der	der	PROPN
ejpam-7005	379	3	physik	physik	PROPN
ejpam-7005	379	4	,	,	PUNCT
ejpam-7005	379	5	12(11	12(11	NUM
ejpam-7005	379	6	-	-	PUNCT
ejpam-7005	379	7	12):692–703	12):692–703	PROPN
ejpam-7005	379	8	,	,	PUNCT
ejpam-7005	379	9	2003	2003	NUM
ejpam-7005	379	10	.	.	PUNCT
ejpam-7005	380	1	[	[	X
ejpam-7005	380	2	32	32	NUM
ejpam-7005	380	3	]	]	PUNCT
ejpam-7005	380	4	h.	h.	PROPN
ejpam-7005	380	5	sun	sun	PROPN
ejpam-7005	380	6	,	,	PUNCT
ejpam-7005	380	7	y.	y.	PROPN
ejpam-7005	380	8	zhang	zhang	PROPN
ejpam-7005	380	9	,	,	PUNCT
ejpam-7005	380	10	d.	d.	PROPN
ejpam-7005	380	11	baleanu	baleanu	PROPN
ejpam-7005	380	12	,	,	PUNCT
ejpam-7005	380	13	w.	w.	PROPN
ejpam-7005	380	14	chen	chen	PROPN
ejpam-7005	380	15	,	,	PUNCT
ejpam-7005	380	16	and	and	CCONJ
ejpam-7005	380	17	y.	y.	PROPN
ejpam-7005	380	18	chen	chen	PROPN
ejpam-7005	380	19	.	.	PUNCT
ejpam-7005	381	1	a	a	DET
ejpam-7005	381	2	new	new	ADJ
ejpam-7005	381	3	collection	collection	NOUN
ejpam-7005	381	4	of	of	ADP
ejpam-7005	381	5	real	real	ADJ
ejpam-7005	381	6	world	world	NOUN
ejpam-7005	381	7	applications	application	NOUN
ejpam-7005	381	8	of	of	ADP
ejpam-7005	381	9	fractional	fractional	ADJ
ejpam-7005	381	10	calculus	calculus	NOUN
ejpam-7005	381	11	in	in	ADP
ejpam-7005	381	12	science	science	NOUN
ejpam-7005	381	13	and	and	CCONJ
ejpam-7005	381	14	engineering	engineering	NOUN
ejpam-7005	381	15	.	.	PUNCT
ejpam-7005	382	1	communications	communication	NOUN
ejpam-7005	382	2	in	in	ADP
ejpam-7005	382	3	nonlinear	nonlinear	ADJ
ejpam-7005	382	4	science	science	NOUN
ejpam-7005	382	5	and	and	CCONJ
ejpam-7005	382	6	numerical	numerical	PROPN
ejpam-7005	382	7	simulation	simulation	PROPN
ejpam-7005	382	8	,	,	PUNCT
ejpam-7005	382	9	64:213–231	64:213–231	NUM
ejpam-7005	382	10	,	,	PUNCT
ejpam-7005	382	11	2018	2018	NUM
ejpam-7005	382	12	.	.	PUNCT
ejpam-7005	383	1	[	[	X
ejpam-7005	383	2	33	33	NUM
ejpam-7005	383	3	]	]	PUNCT
ejpam-7005	383	4	l.	l.	PROPN
ejpam-7005	383	5	e.	e.	PROPN
ejpam-7005	383	6	s.	s.	PROPN
ejpam-7005	383	7	ramirez	ramirez	PROPN
ejpam-7005	383	8	and	and	CCONJ
ejpam-7005	383	9	c.	c.	PROPN
ejpam-7005	383	10	f.	f.	PROPN
ejpam-7005	383	11	m.	m.	PROPN
ejpam-7005	383	12	coimbra	coimbra	PROPN
ejpam-7005	383	13	.	.	PUNCT
ejpam-7005	384	1	on	on	ADP
ejpam-7005	384	2	the	the	DET
ejpam-7005	384	3	variable	variable	ADJ
ejpam-7005	384	4	order	order	NOUN
ejpam-7005	384	5	dynamics	dynamic	NOUN
ejpam-7005	384	6	of	of	ADP
ejpam-7005	384	7	the	the	DET
ejpam-7005	384	8	nonlinear	nonlinear	ADJ
ejpam-7005	384	9	viscous	viscous	ADJ
ejpam-7005	384	10	-	-	PUNCT
ejpam-7005	384	11	plastic	plastic	NOUN
ejpam-7005	384	12	friction	friction	NOUN
ejpam-7005	384	13	in	in	ADP
ejpam-7005	384	14	slender	slender	ADJ
ejpam-7005	384	15	asperities	asperity	NOUN
ejpam-7005	384	16	.	.	PUNCT
ejpam-7005	385	1	journal	journal	NOUN
ejpam-7005	385	2	of	of	ADP
ejpam-7005	385	3	sound	sound	NOUN
ejpam-7005	385	4	and	and	CCONJ
ejpam-7005	385	5	vibration	vibration	NOUN
ejpam-7005	385	6	,	,	PUNCT
ejpam-7005	385	7	329(16):3277–3288	329(16):3277–3288	NUM
ejpam-7005	385	8	,	,	PUNCT
ejpam-7005	385	9	2010	2010	NUM
ejpam-7005	385	10	.	.	PUNCT
ejpam-7005	386	1	[	[	X
ejpam-7005	386	2	34	34	NUM
ejpam-7005	386	3	]	]	X
ejpam-7005	386	4	f.	f.	PROPN
ejpam-7005	386	5	m.	m.	PROPN
ejpam-7005	386	6	atici	atici	PROPN
ejpam-7005	386	7	and	and	CCONJ
ejpam-7005	386	8	p.	p.	PROPN
ejpam-7005	386	9	w.	w.	PROPN
ejpam-7005	386	10	eloe	eloe	PROPN
ejpam-7005	386	11	.	.	PUNCT
ejpam-7005	387	1	a	a	DET
ejpam-7005	387	2	transform	transform	NOUN
ejpam-7005	387	3	method	method	NOUN
ejpam-7005	387	4	in	in	ADP
ejpam-7005	387	5	discrete	discrete	ADJ
ejpam-7005	387	6	fractional	fractional	ADJ
ejpam-7005	387	7	calculus	calculus	NOUN
ejpam-7005	387	8	.	.	PUNCT
ejpam-7005	388	1	international	international	ADJ
ejpam-7005	388	2	journal	journal	PROPN
ejpam-7005	388	3	of	of	ADP
ejpam-7005	388	4	difference	difference	NOUN
ejpam-7005	388	5	equations	equation	NOUN
ejpam-7005	388	6	,	,	PUNCT
ejpam-7005	388	7	2(2):165–176	2(2):165–176	NUM
ejpam-7005	388	8	,	,	PUNCT
ejpam-7005	388	9	2007	2007	NUM
ejpam-7005	388	10	.	.	PUNCT
ejpam-7005	389	1	[	[	X
ejpam-7005	389	2	35	35	NUM
ejpam-7005	389	3	]	]	X
ejpam-7005	389	4	c.	c.	PROPN
ejpam-7005	389	5	goodrich	goodrich	PROPN
ejpam-7005	389	6	and	and	CCONJ
ejpam-7005	389	7	a.	a.	PROPN
ejpam-7005	389	8	c.	c.	PROPN
ejpam-7005	389	9	peterson	peterson	PROPN
ejpam-7005	389	10	.	.	PROPN
ejpam-7005	389	11	discrete	discrete	ADJ
ejpam-7005	389	12	fractional	fractional	ADJ
ejpam-7005	389	13	calculus	calculus	NOUN
ejpam-7005	389	14	.	.	PUNCT
ejpam-7005	389	15	springer	springer	NOUN
ejpam-7005	389	16	,	,	PUNCT
ejpam-7005	389	17	2015	2015	NUM
ejpam-7005	389	18	.	.	PUNCT
ejpam-7005	390	1	[	[	X
ejpam-7005	390	2	36	36	NUM
ejpam-7005	390	3	]	]	PUNCT
ejpam-7005	390	4	j.	j.	PROPN
ejpam-7005	390	5	cheng	cheng	PROPN
ejpam-7005	390	6	.	.	PUNCT
ejpam-7005	390	7	discrete	discrete	ADJ
ejpam-7005	390	8	fractional	fractional	ADJ
ejpam-7005	390	9	calculus	calculus	NOUN
ejpam-7005	390	10	.	.	PUNCT
ejpam-7005	390	11	springer	springer	NOUN
ejpam-7005	390	12	,	,	PUNCT
ejpam-7005	390	13	2011	2011	NUM
ejpam-7005	390	14	.	.	PUNCT
ejpam-7005	391	1	[	[	X
ejpam-7005	391	2	37	37	NUM
ejpam-7005	391	3	]	]	X
ejpam-7005	391	4	y.	y.	PROPN
ejpam-7005	391	5	li	li	PROPN
ejpam-7005	391	6	,	,	PUNCT
ejpam-7005	391	7	y.	y.	PROPN
ejpam-7005	391	8	chen	chen	PROPN
ejpam-7005	391	9	,	,	PUNCT
ejpam-7005	391	10	and	and	CCONJ
ejpam-7005	391	11	i.	i.	NOUN
ejpam-7005	391	12	podlubny	podlubny	PROPN
ejpam-7005	391	13	.	.	PUNCT
ejpam-7005	392	1	mittag	mittag	ADJ
ejpam-7005	392	2	-	-	PUNCT
ejpam-7005	392	3	leffler	leffler	NOUN
ejpam-7005	392	4	stability	stability	NOUN
ejpam-7005	392	5	of	of	ADP
ejpam-7005	392	6	fractional	fractional	ADJ
ejpam-7005	392	7	order	order	NOUN
ejpam-7005	392	8	nonlinear	nonlinear	ADJ
ejpam-7005	392	9	dynamic	dynamic	ADJ
ejpam-7005	392	10	systems	system	NOUN
ejpam-7005	392	11	.	.	PUNCT
ejpam-7005	393	1	automatica	automatica	PROPN
ejpam-7005	393	2	,	,	PUNCT
ejpam-7005	393	3	45(8):1965–1969	45(8):1965–1969	PROPN
ejpam-7005	393	4	,	,	PUNCT
ejpam-7005	393	5	2009	2009	NUM
ejpam-7005	393	6	.	.	PUNCT
ejpam-7005	394	1	[	[	X
ejpam-7005	394	2	38	38	NUM
ejpam-7005	394	3	]	]	PUNCT
ejpam-7005	394	4	i.	i.	PROPN
ejpam-7005	394	5	stamova	stamova	PROPN
ejpam-7005	394	6	.	.	PUNCT
ejpam-7005	395	1	stability	stability	NOUN
ejpam-7005	395	2	analysis	analysis	NOUN
ejpam-7005	395	3	of	of	ADP
ejpam-7005	395	4	impulsive	impulsive	ADJ
ejpam-7005	395	5	functional	functional	ADJ
ejpam-7005	395	6	differential	differential	NOUN
ejpam-7005	395	7	equations	equation	NOUN
ejpam-7005	395	8	.	.	PUNCT
ejpam-7005	396	1	de	de	X
ejpam-7005	396	2	gruyter	gruyter	NOUN
ejpam-7005	396	3	,	,	PUNCT
ejpam-7005	396	4	2016	2016	NUM
ejpam-7005	396	5	.	.	PUNCT
ejpam-7005	397	1	[	[	X
ejpam-7005	397	2	39	39	NUM
ejpam-7005	397	3	]	]	PUNCT
ejpam-7005	397	4	a.	a.	PROPN
ejpam-7005	397	5	s.	s.	PROPN
ejpam-7005	397	6	hussain	hussain	PROPN
ejpam-7005	397	7	,	,	PUNCT
ejpam-7005	397	8	k.	k.	PROPN
ejpam-7005	397	9	d.	d.	PROPN
ejpam-7005	397	10	pati	pati	PROPN
ejpam-7005	397	11	,	,	PUNCT
ejpam-7005	397	12	a.	a.	PROPN
ejpam-7005	397	13	k.	k.	PROPN
ejpam-7005	397	14	atiyah	atiyah	PROPN
ejpam-7005	397	15	,	,	PUNCT
ejpam-7005	397	16	and	and	CCONJ
ejpam-7005	397	17	m.	m.	NOUN
ejpam-7005	397	18	a.	a.	NOUN
ejpam-7005	397	19	tashtoush	tashtoush	PROPN
ejpam-7005	397	20	.	.	PUNCT
ejpam-7005	398	1	rate	rate	NOUN
ejpam-7005	398	2	of	of	ADP
ejpam-7005	398	3	occurrence	occurrence	NOUN
ejpam-7005	398	4	estimation	estimation	NOUN
ejpam-7005	398	5	in	in	ADP
ejpam-7005	398	6	geometric	geometric	ADJ
ejpam-7005	398	7	processes	process	NOUN
ejpam-7005	398	8	with	with	ADP
ejpam-7005	398	9	maxwell	maxwell	PROPN
ejpam-7005	398	10	distribution	distribution	NOUN
ejpam-7005	398	11	:	:	PUNCT
ejpam-7005	398	12	a	a	DET
ejpam-7005	398	13	comparative	comparative	ADJ
ejpam-7005	398	14	study	study	NOUN
ejpam-7005	398	15	n.	n.	PROPN
ejpam-7005	398	16	anakira	anakira	PROPN
ejpam-7005	398	17	et	et	PROPN
ejpam-7005	398	18	al	al	PROPN
ejpam-7005	398	19	.	.	PUNCT
ejpam-7005	398	20	/	/	SYM
ejpam-7005	398	21	eur	eur	PROPN
ejpam-7005	398	22	.	.	PUNCT
ejpam-7005	399	1	j.	j.	PROPN
ejpam-7005	399	2	pure	pure	PROPN
ejpam-7005	399	3	appl	appl	PROPN
ejpam-7005	399	4	.	.	PROPN
ejpam-7005	399	5	math	math	PROPN
ejpam-7005	399	6	,	,	PUNCT
ejpam-7005	399	7	18	18	NUM
ejpam-7005	399	8	(	(	PUNCT
ejpam-7005	399	9	4	4	NUM
ejpam-7005	399	10	)	)	PUNCT
ejpam-7005	399	11	(	(	PUNCT
ejpam-7005	399	12	2025	2025	NUM
ejpam-7005	399	13	)	)	PUNCT
ejpam-7005	399	14	,	,	PUNCT
ejpam-7005	399	15	7005	7005	NUM
ejpam-7005	399	16	17	17	NUM
ejpam-7005	399	17	of	of	ADP
ejpam-7005	399	18	17	17	NUM
ejpam-7005	399	19	between	between	ADP
ejpam-7005	399	20	artificial	artificial	ADJ
ejpam-7005	399	21	intelligence	intelligence	NOUN
ejpam-7005	399	22	and	and	CCONJ
ejpam-7005	399	23	classical	classical	ADJ
ejpam-7005	399	24	methods	method	NOUN
ejpam-7005	399	25	.	.	PUNCT
ejpam-7005	400	1	int	int	NOUN
ejpam-7005	400	2	.	.	PUNCT
ejpam-7005	401	1	j.	j.	PROPN
ejpam-7005	401	2	adv	adv	PROPN
ejpam-7005	401	3	.	.	PUNCT
ejpam-7005	401	4	soft	soft	ADJ
ejpam-7005	401	5	comput	comput	NOUN
ejpam-7005	401	6	.	.	PUNCT
ejpam-7005	402	1	appl	appl	PROPN
ejpam-7005	402	2	.	.	PROPN
ejpam-7005	402	3	,	,	PUNCT
ejpam-7005	402	4	17(1):1–15	17(1):1–15	NUM
ejpam-7005	402	5	,	,	PUNCT
ejpam-7005	402	6	2025	2025	NUM
ejpam-7005	402	7	.	.	PUNCT
ejpam-7005	403	1	[	[	X
ejpam-7005	403	2	40	40	NUM
ejpam-7005	403	3	]	]	PUNCT
ejpam-7005	403	4	m.	m.	NOUN
ejpam-7005	403	5	berir	berir	NOUN
ejpam-7005	403	6	.	.	PUNCT
ejpam-7005	404	1	analysis	analysis	NOUN
ejpam-7005	404	2	of	of	ADP
ejpam-7005	404	3	the	the	DET
ejpam-7005	404	4	effect	effect	NOUN
ejpam-7005	404	5	of	of	ADP
ejpam-7005	404	6	white	white	ADJ
ejpam-7005	404	7	noise	noise	NOUN
ejpam-7005	404	8	on	on	ADP
ejpam-7005	404	9	the	the	DET
ejpam-7005	404	10	halvorsen	halvorsen	PROPN
ejpam-7005	404	11	system	system	NOUN
ejpam-7005	404	12	of	of	ADP
ejpam-7005	404	13	variableorder	variableorder	NOUN
ejpam-7005	404	14	fractional	fractional	ADJ
ejpam-7005	404	15	derivatives	derivative	NOUN
ejpam-7005	404	16	using	use	VERB
ejpam-7005	404	17	a	a	DET
ejpam-7005	404	18	novel	novel	ADJ
ejpam-7005	404	19	numerical	numerical	ADJ
ejpam-7005	404	20	method	method	NOUN
ejpam-7005	404	21	.	.	PUNCT
ejpam-7005	405	1	int	int	NOUN
ejpam-7005	405	2	.	.	PUNCT
ejpam-7005	406	1	j.	j.	PROPN
ejpam-7005	406	2	adv	adv	PROPN
ejpam-7005	406	3	.	.	PUNCT
ejpam-7005	406	4	soft	soft	ADJ
ejpam-7005	406	5	comput	comput	NOUN
ejpam-7005	406	6	.	.	PUNCT
ejpam-7005	407	1	appl	appl	PROPN
ejpam-7005	407	2	.	.	PROPN
ejpam-7005	407	3	,	,	PUNCT
ejpam-7005	407	4	16(3):294–306	16(3):294–306	NOUN
ejpam-7005	407	5	,	,	PUNCT
ejpam-7005	407	6	2024	2024	NUM
ejpam-7005	407	7	.	.	PUNCT
ejpam-7005	408	1	[	[	X
ejpam-7005	408	2	41	41	NUM
ejpam-7005	408	3	]	]	PUNCT
ejpam-7005	408	4	p.	p.	NOUN
ejpam-7005	408	5	singh	singh	PROPN
ejpam-7005	408	6	,	,	PUNCT
ejpam-7005	408	7	n.	n.	PROPN
ejpam-7005	408	8	zade	zade	PROPN
ejpam-7005	408	9	,	,	PUNCT
ejpam-7005	408	10	p.	p.	NOUN
ejpam-7005	408	11	priyadarshi	priyadarshi	PROPN
ejpam-7005	408	12	,	,	PUNCT
ejpam-7005	408	13	and	and	CCONJ
ejpam-7005	408	14	a.	a.	PROPN
ejpam-7005	408	15	gupte	gupte	PROPN
ejpam-7005	408	16	.	.	PUNCT
ejpam-7005	409	1	the	the	DET
ejpam-7005	409	2	application	application	NOUN
ejpam-7005	409	3	of	of	ADP
ejpam-7005	409	4	machine	machine	NOUN
ejpam-7005	409	5	learning	learning	NOUN
ejpam-7005	409	6	and	and	CCONJ
ejpam-7005	409	7	deep	deep	ADJ
ejpam-7005	409	8	learning	learning	NOUN
ejpam-7005	409	9	techniques	technique	NOUN
ejpam-7005	409	10	for	for	ADP
ejpam-7005	409	11	global	global	ADJ
ejpam-7005	409	12	energy	energy	NOUN
ejpam-7005	409	13	utilization	utilization	NOUN
ejpam-7005	409	14	projection	projection	NOUN
ejpam-7005	409	15	for	for	ADP
ejpam-7005	409	16	ecologically	ecologically	ADV
ejpam-7005	409	17	responsible	responsible	ADJ
ejpam-7005	409	18	energy	energy	NOUN
ejpam-7005	409	19	management	management	NOUN
ejpam-7005	409	20	.	.	PUNCT
ejpam-7005	410	1	int	int	NOUN
ejpam-7005	410	2	.	.	PUNCT
ejpam-7005	411	1	j.	j.	PROPN
ejpam-7005	411	2	adv	adv	PROPN
ejpam-7005	411	3	.	.	PUNCT
ejpam-7005	411	4	soft	soft	ADJ
ejpam-7005	411	5	comput	comput	NOUN
ejpam-7005	411	6	.	.	PUNCT
ejpam-7005	412	1	appl	appl	PROPN
ejpam-7005	412	2	.	.	PROPN
ejpam-7005	412	3	,	,	PUNCT
ejpam-7005	412	4	17(1):49–66	17(1):49–66	NUM
ejpam-7005	412	5	,	,	PUNCT
ejpam-7005	412	6	2025	2025	NUM
ejpam-7005	412	7	.	.	PUNCT
ejpam-7005	413	1	[	[	X
ejpam-7005	413	2	42	42	NUM
ejpam-7005	413	3	]	]	X
ejpam-7005	413	4	e.	e.	PROPN
ejpam-7005	413	5	a.	a.	PROPN
ejpam-7005	413	6	mohammed	mohammed	PROPN
ejpam-7005	413	7	and	and	CCONJ
ejpam-7005	413	8	a.	a.	NOUN
ejpam-7005	413	9	lakizadeh	lakizadeh	PROPN
ejpam-7005	413	10	.	.	PUNCT
ejpam-7005	414	1	benchmarking	benchmarke	VERB
ejpam-7005	414	2	vision	vision	NOUN
ejpam-7005	414	3	transformers	transformer	NOUN
ejpam-7005	414	4	for	for	ADP
ejpam-7005	414	5	satellite	satellite	NOUN
ejpam-7005	414	6	image	image	NOUN
ejpam-7005	414	7	classification	classification	NOUN
ejpam-7005	414	8	based	base	VERB
ejpam-7005	414	9	on	on	ADP
ejpam-7005	414	10	data	datum	NOUN
ejpam-7005	414	11	augmentation	augmentation	NOUN
ejpam-7005	414	12	techniques	technique	NOUN
ejpam-7005	414	13	.	.	PUNCT
ejpam-7005	415	1	int	int	NOUN
ejpam-7005	415	2	.	.	PUNCT
ejpam-7005	416	1	j.	j.	PROPN
ejpam-7005	416	2	adv	adv	PROPN
ejpam-7005	416	3	.	.	PUNCT
ejpam-7005	416	4	soft	soft	ADJ
ejpam-7005	416	5	comput	comput	NOUN
ejpam-7005	416	6	.	.	PUNCT
ejpam-7005	417	1	appl	appl	PROPN
ejpam-7005	417	2	.	.	PROPN
ejpam-7005	417	3	,	,	PUNCT
ejpam-7005	417	4	17(1):98–114	17(1):98–114	NUM
ejpam-7005	417	5	,	,	PUNCT
ejpam-7005	417	6	2025	2025	NUM
ejpam-7005	417	7	.	.	PUNCT
ejpam-7005	418	1	[	[	X
ejpam-7005	418	2	43	43	NUM
ejpam-7005	418	3	]	]	X
ejpam-7005	418	4	p.	p.	NOUN
ejpam-7005	418	5	dorato	dorato	PROPN
ejpam-7005	418	6	.	.	PUNCT
ejpam-7005	419	1	short	short	ADJ
ejpam-7005	419	2	-	-	PUNCT
ejpam-7005	419	3	time	time	NOUN
ejpam-7005	419	4	stability	stability	NOUN
ejpam-7005	419	5	in	in	ADP
ejpam-7005	419	6	linear	linear	ADJ
ejpam-7005	419	7	time	time	NOUN
ejpam-7005	419	8	-	-	PUNCT
ejpam-7005	419	9	varying	vary	VERB
ejpam-7005	419	10	systems	system	NOUN
ejpam-7005	419	11	.	.	PUNCT
ejpam-7005	420	1	in	in	ADP
ejpam-7005	420	2	proceedings	proceeding	NOUN
ejpam-7005	420	3	of	of	ADP
ejpam-7005	420	4	the	the	DET
ejpam-7005	420	5	ire	ire	ADJ
ejpam-7005	420	6	international	international	ADJ
ejpam-7005	420	7	convention	convention	NOUN
ejpam-7005	420	8	record	record	NOUN
ejpam-7005	420	9	,	,	PUNCT
ejpam-7005	420	10	pages	page	NOUN
ejpam-7005	420	11	83–87	83–87	NUM
ejpam-7005	420	12	,	,	PUNCT
ejpam-7005	420	13	1961	1961	NUM
ejpam-7005	420	14	.	.	PUNCT
ejpam-7005	421	1	part	part	NOUN
ejpam-7005	421	2	4	4	NUM
ejpam-7005	421	3	.	.	PUNCT
ejpam-7005	422	1	[	[	X
ejpam-7005	422	2	44	44	NUM
ejpam-7005	422	3	]	]	PUNCT
ejpam-7005	422	4	j.	j.	PROPN
ejpam-7005	422	5	shen	shen	PROPN
ejpam-7005	422	6	,	,	PUNCT
ejpam-7005	422	7	j.	j.	PROPN
ejpam-7005	422	8	cao	cao	PROPN
ejpam-7005	422	9	,	,	PUNCT
ejpam-7005	422	10	and	and	CCONJ
ejpam-7005	422	11	s.	s.	PROPN
ejpam-7005	422	12	m.	m.	PROPN
ejpam-7005	422	13	hayat	hayat	PROPN
ejpam-7005	422	14	.	.	PUNCT
ejpam-7005	423	1	finite	finite	ADJ
ejpam-7005	423	2	-	-	PUNCT
ejpam-7005	423	3	time	time	NOUN
ejpam-7005	423	4	stability	stability	NOUN
ejpam-7005	423	5	of	of	ADP
ejpam-7005	423	6	fractional	fractional	ADJ
ejpam-7005	423	7	-	-	PUNCT
ejpam-7005	423	8	order	order	NOUN
ejpam-7005	423	9	complexvalued	complexvalue	VERB
ejpam-7005	423	10	neural	neural	ADJ
ejpam-7005	423	11	networks	network	NOUN
ejpam-7005	423	12	with	with	ADP
ejpam-7005	423	13	time	time	NOUN
ejpam-7005	423	14	delays	delay	NOUN
ejpam-7005	423	15	.	.	PUNCT
ejpam-7005	424	1	neural	neural	ADJ
ejpam-7005	424	2	networks	network	NOUN
ejpam-7005	424	3	,	,	PUNCT
ejpam-7005	424	4	56:31–38	56:31–38	NUM
ejpam-7005	424	5	,	,	PUNCT
ejpam-7005	424	6	2014	2014	NUM
ejpam-7005	424	7	.	.	PUNCT
ejpam-7005	425	1	[	[	X
ejpam-7005	425	2	45	45	NUM
ejpam-7005	425	3	]	]	PUNCT
ejpam-7005	425	4	m.	m.	NOUN
ejpam-7005	425	5	p.	p.	PROPN
ejpam-7005	425	6	lazarevic	lazarevic	PROPN
ejpam-7005	425	7	.	.	PUNCT
ejpam-7005	426	1	finite	finite	PROPN
ejpam-7005	426	2	time	time	NOUN
ejpam-7005	426	3	stability	stability	NOUN
ejpam-7005	426	4	analysis	analysis	NOUN
ejpam-7005	426	5	of	of	ADP
ejpam-7005	426	6	fractional	fractional	ADJ
ejpam-7005	426	7	order	order	NOUN
ejpam-7005	426	8	time	time	NOUN
ejpam-7005	426	9	delay	delay	NOUN
ejpam-7005	426	10	systems	system	NOUN
ejpam-7005	426	11	.	.	PUNCT
ejpam-7005	427	1	masinstvo	masinstvo	PROPN
ejpam-7005	427	2	,	,	PUNCT
ejpam-7005	427	3	26(1):11–20	26(1):11–20	NUM
ejpam-7005	427	4	,	,	PUNCT
ejpam-7005	427	5	2007	2007	NUM
ejpam-7005	427	6	.	.	PUNCT
ejpam-7005	428	1	[	[	X
ejpam-7005	428	2	46	46	NUM
ejpam-7005	428	3	]	]	X
ejpam-7005	428	4	c.	c.	PROPN
ejpam-7005	428	5	fei	fei	PROPN
ejpam-7005	428	6	,	,	PUNCT
ejpam-7005	428	7	h.	h.	PROPN
ejpam-7005	428	8	li	li	PROPN
ejpam-7005	428	9	,	,	PUNCT
ejpam-7005	428	10	and	and	CCONJ
ejpam-7005	428	11	j.	j.	PROPN
ejpam-7005	428	12	yan	yan	PROPN
ejpam-7005	428	13	.	.	PUNCT
ejpam-7005	429	1	finite	finite	ADJ
ejpam-7005	429	2	-	-	PUNCT
ejpam-7005	429	3	time	time	NOUN
ejpam-7005	429	4	stability	stability	NOUN
ejpam-7005	429	5	of	of	ADP
ejpam-7005	429	6	fractional	fractional	ADJ
ejpam-7005	429	7	-	-	PUNCT
ejpam-7005	429	8	order	order	NOUN
ejpam-7005	429	9	neural	neural	ADJ
ejpam-7005	429	10	networks	network	NOUN
ejpam-7005	429	11	with	with	ADP
ejpam-7005	429	12	delay	delay	NOUN
ejpam-7005	429	13	.	.	PUNCT
ejpam-7005	430	1	neurocomputing	neurocomputing	NOUN
ejpam-7005	430	2	,	,	PUNCT
ejpam-7005	430	3	182:161–166	182:161–166	NUM
ejpam-7005	430	4	,	,	PUNCT
ejpam-7005	430	5	2016	2016	NUM
ejpam-7005	430	6	.	.	PUNCT
ejpam-7005	431	1	[	[	X
ejpam-7005	431	2	47	47	NUM
ejpam-7005	431	3	]	]	PUNCT
ejpam-7005	431	4	t.	t.	NOUN
ejpam-7005	431	5	abdeljawad	abdeljawad	PROPN
ejpam-7005	431	6	and	and	CCONJ
ejpam-7005	431	7	d.	d.	PROPN
ejpam-7005	431	8	baleanu	baleanu	PROPN
ejpam-7005	431	9	.	.	PUNCT
ejpam-7005	432	1	on	on	ADP
ejpam-7005	432	2	fractional	fractional	ADJ
ejpam-7005	432	3	derivatives	derivative	NOUN
ejpam-7005	432	4	with	with	ADP
ejpam-7005	432	5	exponential	exponential	ADJ
ejpam-7005	432	6	kernel	kernel	NOUN
ejpam-7005	432	7	and	and	CCONJ
ejpam-7005	432	8	their	their	PRON
ejpam-7005	432	9	discrete	discrete	ADJ
ejpam-7005	432	10	versions	version	NOUN
ejpam-7005	432	11	.	.	PUNCT
ejpam-7005	433	1	reports	report	NOUN
ejpam-7005	433	2	on	on	ADP
ejpam-7005	433	3	mathematical	mathematical	ADJ
ejpam-7005	433	4	physics	physics	NOUN
ejpam-7005	433	5	,	,	PUNCT
ejpam-7005	433	6	84(3):367–378	84(3):367–378	PROPN
ejpam-7005	433	7	,	,	PUNCT
ejpam-7005	433	8	2019	2019	NUM
ejpam-7005	433	9	.	.	PUNCT
ejpam-7005	434	1	[	[	X
ejpam-7005	434	2	48	48	NUM
ejpam-7005	434	3	]	]	PUNCT
ejpam-7005	434	4	i.	i.	PROPN
ejpam-7005	434	5	m.	m.	PROPN
ejpam-7005	434	6	batiha	batiha	PROPN
ejpam-7005	434	7	,	,	PUNCT
ejpam-7005	434	8	i.	i.	PROPN
ejpam-7005	434	9	bendib	bendib	PROPN
ejpam-7005	434	10	,	,	PUNCT
ejpam-7005	434	11	a.	a.	NOUN
ejpam-7005	434	12	ouannas	ouannas	PROPN
ejpam-7005	434	13	,	,	PUNCT
ejpam-7005	434	14	i.	i.	PROPN
ejpam-7005	434	15	h.	h.	PROPN
ejpam-7005	434	16	jebril	jebril	PROPN
ejpam-7005	434	17	,	,	PUNCT
ejpam-7005	434	18	s.	s.	PROPN
ejpam-7005	434	19	alkhazaleh	alkhazaleh	PROPN
ejpam-7005	434	20	,	,	PUNCT
ejpam-7005	434	21	and	and	CCONJ
ejpam-7005	434	22	s.	s.	PROPN
ejpam-7005	434	23	momani	momani	PROPN
ejpam-7005	434	24	.	.	PUNCT
ejpam-7005	435	1	on	on	ADP
ejpam-7005	435	2	new	new	ADJ
ejpam-7005	435	3	results	result	NOUN
ejpam-7005	435	4	of	of	ADP
ejpam-7005	435	5	stability	stability	NOUN
ejpam-7005	435	6	and	and	CCONJ
ejpam-7005	435	7	synchronization	synchronization	NOUN
ejpam-7005	435	8	in	in	ADP
ejpam-7005	435	9	finite	finite	NOUN
ejpam-7005	435	10	-	-	NOUN
ejpam-7005	435	11	time	time	NOUN
ejpam-7005	435	12	for	for	ADP
ejpam-7005	435	13	fitzhugh	fitzhugh	PROPN
ejpam-7005	435	14	-	-	PUNCT
ejpam-7005	435	15	nagumo	nagumo	ADJ
ejpam-7005	435	16	model	model	NOUN
ejpam-7005	435	17	using	use	VERB
ejpam-7005	435	18	gronwall	gronwall	ADJ
ejpam-7005	435	19	inequality	inequality	NOUN
ejpam-7005	435	20	and	and	CCONJ
ejpam-7005	435	21	lyapunov	lyapunov	ADJ
ejpam-7005	435	22	function	function	NOUN
ejpam-7005	435	23	.	.	PUNCT
ejpam-7005	436	1	journal	journal	PROPN
ejpam-7005	436	2	of	of	ADP
ejpam-7005	436	3	robotics	robotic	NOUN
ejpam-7005	436	4	and	and	CCONJ
ejpam-7005	436	5	control	control	PROPN
ejpam-7005	436	6	(	(	PUNCT
ejpam-7005	436	7	jrc	jrc	PROPN
ejpam-7005	436	8	)	)	PUNCT
ejpam-7005	436	9	,	,	PUNCT
ejpam-7005	436	10	5(6):1897–1909	5(6):1897–1909	NUM
ejpam-7005	436	11	,	,	PUNCT
ejpam-7005	436	12	oct	oct	PROPN
ejpam-7005	436	13	.	.	PROPN
ejpam-7005	436	14	2024	2024	NUM
ejpam-7005	436	15	.	.	PUNCT
ejpam-7005	437	1	[	[	X
ejpam-7005	437	2	49	49	NUM
ejpam-7005	437	3	]	]	X
ejpam-7005	437	4	i.	i.	PROPN
ejpam-7005	437	5	bendib	bendib	PROPN
ejpam-7005	437	6	,	,	PUNCT
ejpam-7005	437	7	i.	i.	PROPN
ejpam-7005	437	8	m.	m.	PROPN
ejpam-7005	437	9	batiha	batiha	PROPN
ejpam-7005	437	10	,	,	PUNCT
ejpam-7005	437	11	a.	a.	NOUN
ejpam-7005	437	12	hioual	hioual	NOUN
ejpam-7005	437	13	,	,	PUNCT
ejpam-7005	437	14	n.	n.	PROPN
ejpam-7005	437	15	anakira	anakira	PROPN
ejpam-7005	437	16	,	,	PUNCT
ejpam-7005	437	17	m.	m.	NOUN
ejpam-7005	437	18	dalah	dalah	NOUN
ejpam-7005	437	19	,	,	PUNCT
ejpam-7005	437	20	and	and	CCONJ
ejpam-7005	437	21	a.	a.	NOUN
ejpam-7005	437	22	ouannas	ouannas	NOUN
ejpam-7005	437	23	.	.	PUNCT
ejpam-7005	438	1	on	on	ADP
ejpam-7005	438	2	a	a	DET
ejpam-7005	438	3	new	new	ADJ
ejpam-7005	438	4	version	version	NOUN
ejpam-7005	438	5	of	of	ADP
ejpam-7005	438	6	gierer	gierer	NOUN
ejpam-7005	438	7	-	-	PUNCT
ejpam-7005	438	8	meinhardt	meinhardt	ADJ
ejpam-7005	438	9	model	model	NOUN
ejpam-7005	438	10	using	use	VERB
ejpam-7005	438	11	fractional	fractional	ADJ
ejpam-7005	438	12	discrete	discrete	ADJ
ejpam-7005	438	13	calculus	calculus	NOUN
ejpam-7005	438	14	.	.	PUNCT
ejpam-7005	439	1	results	result	NOUN
ejpam-7005	439	2	in	in	ADP
ejpam-7005	439	3	nonlinear	nonlinear	ADJ
ejpam-7005	439	4	analysis	analysis	NOUN
ejpam-7005	439	5	,	,	PUNCT
ejpam-7005	439	6	7(2):1–5	7(2):1–5	NOUN
ejpam-7005	439	7	,	,	PUNCT
ejpam-7005	439	8	2024	2024	NUM
ejpam-7005	439	9	.	.	PUNCT