id	sid	tid	token	lemma	pos
ejpam-5237	1	1	european	european	PROPN
ejpam-5237	1	2	journal	journal	PROPN
ejpam-5237	1	3	of	of	ADP
ejpam-5237	1	4	pure	pure	ADJ
ejpam-5237	1	5	and	and	CCONJ
ejpam-5237	1	6	applied	apply	VERB
ejpam-5237	1	7	mathematics	mathematic	NOUN
ejpam-5237	1	8	vol	vol	NOUN
ejpam-5237	1	9	.	.	PROPN
ejpam-5237	2	1	17	17	NUM
ejpam-5237	2	2	,	,	PUNCT
ejpam-5237	2	3	no	no	INTJ
ejpam-5237	2	4	.	.	NOUN
ejpam-5237	2	5	3	3	NUM
ejpam-5237	2	6	,	,	PUNCT
ejpam-5237	2	7	2024	2024	NUM
ejpam-5237	2	8	,	,	PUNCT
ejpam-5237	2	9	1842	1842	NUM
ejpam-5237	2	10	-	-	SYM
ejpam-5237	2	11	1854	1854	NUM
ejpam-5237	2	12	issn	issn	PROPN
ejpam-5237	2	13	1307	1307	NUM
ejpam-5237	2	14	-	-	SYM
ejpam-5237	2	15	5543	5543	NUM
ejpam-5237	2	16	–	–	PUNCT
ejpam-5237	2	17	ejpam.com	ejpam.com	X
ejpam-5237	2	18	published	publish	VERB
ejpam-5237	2	19	by	by	ADP
ejpam-5237	2	20	new	new	PROPN
ejpam-5237	2	21	york	york	PROPN
ejpam-5237	2	22	business	business	PROPN
ejpam-5237	3	1	global	global	PROPN
ejpam-5237	3	2	a	a	DET
ejpam-5237	3	3	comparative	comparative	ADJ
ejpam-5237	3	4	analysis	analysis	NOUN
ejpam-5237	3	5	of	of	ADP
ejpam-5237	3	6	conformable	conformable	ADJ
ejpam-5237	3	7	,	,	PUNCT
ejpam-5237	3	8	non	non	ADJ
ejpam-5237	3	9	-	-	ADJ
ejpam-5237	3	10	conformable	conformable	ADJ
ejpam-5237	3	11	,	,	PUNCT
ejpam-5237	3	12	riemann	riemann	PROPN
ejpam-5237	3	13	-	-	PUNCT
ejpam-5237	3	14	liouville	liouville	NOUN
ejpam-5237	3	15	,	,	PUNCT
ejpam-5237	3	16	and	and	CCONJ
ejpam-5237	3	17	caputo	caputo	PROPN
ejpam-5237	3	18	fractional	fractional	PROPN
ejpam-5237	3	19	derivatives	derivative	NOUN
ejpam-5237	3	20	a.	a.	NOUN
ejpam-5237	3	21	ait	ait	PROPN
ejpam-5237	3	22	brahim1,∗	brahim1,∗	PROPN
ejpam-5237	3	23	,	,	PUNCT
ejpam-5237	3	24	j.	j.	PROPN
ejpam-5237	3	25	el	el	PROPN
ejpam-5237	3	26	ghordaf1	ghordaf1	PROPN
ejpam-5237	3	27	,	,	PUNCT
ejpam-5237	3	28	a.	a.	PROPN
ejpam-5237	3	29	el	el	PROPN
ejpam-5237	3	30	hajaji2	hajaji2	PROPN
ejpam-5237	3	31	,	,	PUNCT
ejpam-5237	3	32	k.	k.	PROPN
ejpam-5237	3	33	hilal1	hilal1	PROPN
ejpam-5237	3	34	,	,	PUNCT
ejpam-5237	3	35	j.	j.	PROPN
ejpam-5237	3	36	e.nápoles	e.nápoles	PROPN
ejpam-5237	3	37	valdes3	valdes3	PROPN
ejpam-5237	3	38	1	1	NUM
ejpam-5237	3	39	amsc	amsc	NOUN
ejpam-5237	3	40	laboratory	laboratory	NOUN
ejpam-5237	3	41	,	,	PUNCT
ejpam-5237	3	42	university	university	NOUN
ejpam-5237	3	43	of	of	ADP
ejpam-5237	3	44	sciences	science	NOUN
ejpam-5237	3	45	and	and	CCONJ
ejpam-5237	3	46	technology	technology	NOUN
ejpam-5237	3	47	,	,	PUNCT
ejpam-5237	3	48	beni	beni	ADJ
ejpam-5237	3	49	mellal	mellal	PROPN
ejpam-5237	3	50	,	,	PUNCT
ejpam-5237	3	51	morocco	morocco	PROPN
ejpam-5237	3	52	2	2	NUM
ejpam-5237	3	53	oee	oee	NOUN
ejpam-5237	3	54	departement	departement	NOUN
ejpam-5237	3	55	,	,	PUNCT
ejpam-5237	3	56	encgj	encgj	PROPN
ejpam-5237	3	57	,	,	PUNCT
ejpam-5237	3	58	university	university	NOUN
ejpam-5237	3	59	of	of	ADP
ejpam-5237	3	60	chouaib	chouaib	PROPN
ejpam-5237	3	61	doukali	doukali	PROPN
ejpam-5237	3	62	,	,	PUNCT
ejpam-5237	3	63	el	el	PROPN
ejpam-5237	3	64	jadida	jadida	PROPN
ejpam-5237	3	65	,	,	PUNCT
ejpam-5237	3	66	morocco	morocco	PROPN
ejpam-5237	3	67	3	3	NUM
ejpam-5237	3	68	facena	facena	PROPN
ejpam-5237	3	69	laboratory	laboratory	PROPN
ejpam-5237	3	70	universidad	universidad	PROPN
ejpam-5237	3	71	nacional	nacional	PROPN
ejpam-5237	3	72	del	del	PROPN
ejpam-5237	3	73	nordeste	nordeste	PROPN
ejpam-5237	3	74	,	,	PUNCT
ejpam-5237	3	75	(	(	PUNCT
ejpam-5237	3	76	3400	3400	NUM
ejpam-5237	3	77	)	)	PUNCT
ejpam-5237	3	78	corrientes	corriente	NOUN
ejpam-5237	3	79	,	,	PUNCT
ejpam-5237	3	80	argentina	argentina	PROPN
ejpam-5237	3	81	abstract	abstract	PROPN
ejpam-5237	3	82	.	.	PUNCT
ejpam-5237	4	1	this	this	DET
ejpam-5237	4	2	study	study	NOUN
ejpam-5237	4	3	undertakes	undertake	VERB
ejpam-5237	4	4	a	a	DET
ejpam-5237	4	5	comparative	comparative	ADJ
ejpam-5237	4	6	analysis	analysis	NOUN
ejpam-5237	4	7	of	of	ADP
ejpam-5237	4	8	the	the	DET
ejpam-5237	4	9	non	non	ADJ
ejpam-5237	4	10	conformable	conformable	ADJ
ejpam-5237	4	11	and	and	CCONJ
ejpam-5237	4	12	conformable	conformable	ADJ
ejpam-5237	4	13	fractional	fractional	ADJ
ejpam-5237	4	14	derivatives	derivative	NOUN
ejpam-5237	4	15	alongside	alongside	ADP
ejpam-5237	4	16	the	the	DET
ejpam-5237	4	17	riemann	riemann	PROPN
ejpam-5237	4	18	-	-	PUNCT
ejpam-5237	4	19	liouville	liouville	PROPN
ejpam-5237	4	20	and	and	CCONJ
ejpam-5237	4	21	caputo	caputo	PROPN
ejpam-5237	4	22	fractional	fractional	ADJ
ejpam-5237	4	23	derivatives	derivative	NOUN
ejpam-5237	4	24	.	.	PUNCT
ejpam-5237	5	1	it	it	PRON
ejpam-5237	5	2	examines	examine	VERB
ejpam-5237	5	3	their	their	PRON
ejpam-5237	5	4	efficacy	efficacy	NOUN
ejpam-5237	5	5	in	in	ADP
ejpam-5237	5	6	solving	solve	VERB
ejpam-5237	5	7	fractional	fractional	ADJ
ejpam-5237	5	8	ordinary	ordinary	ADJ
ejpam-5237	5	9	differential	differential	ADJ
ejpam-5237	5	10	equations	equation	NOUN
ejpam-5237	5	11	and	and	CCONJ
ejpam-5237	5	12	explores	explore	VERB
ejpam-5237	5	13	their	their	PRON
ejpam-5237	5	14	applications	application	NOUN
ejpam-5237	5	15	in	in	ADP
ejpam-5237	5	16	physics	physics	NOUN
ejpam-5237	5	17	through	through	ADP
ejpam-5237	5	18	numerical	numerical	ADJ
ejpam-5237	5	19	simulations	simulation	NOUN
ejpam-5237	5	20	.	.	PUNCT
ejpam-5237	6	1	the	the	DET
ejpam-5237	6	2	findings	finding	NOUN
ejpam-5237	6	3	suggest	suggest	VERB
ejpam-5237	6	4	that	that	SCONJ
ejpam-5237	6	5	the	the	DET
ejpam-5237	6	6	conformable	conformable	ADJ
ejpam-5237	6	7	fractional	fractional	ADJ
ejpam-5237	6	8	derivative	derivative	ADJ
ejpam-5237	6	9	emerges	emerge	NOUN
ejpam-5237	6	10	as	as	ADP
ejpam-5237	6	11	a	a	DET
ejpam-5237	6	12	promising	promising	ADJ
ejpam-5237	6	13	substitute	substitute	NOUN
ejpam-5237	6	14	for	for	ADP
ejpam-5237	6	15	the	the	DET
ejpam-5237	6	16	non	non	ADJ
ejpam-5237	6	17	conformable	conformable	NOUN
ejpam-5237	6	18	,	,	PUNCT
ejpam-5237	6	19	riemann	riemann	PROPN
ejpam-5237	6	20	-	-	PUNCT
ejpam-5237	6	21	liouville	liouville	PROPN
ejpam-5237	6	22	and	and	CCONJ
ejpam-5237	6	23	caputo	caputo	PROPN
ejpam-5237	6	24	fractional	fractional	ADJ
ejpam-5237	6	25	derivatives	derivative	NOUN
ejpam-5237	6	26	within	within	ADP
ejpam-5237	6	27	the	the	DET
ejpam-5237	6	28	range	range	NOUN
ejpam-5237	6	29	of	of	ADP
ejpam-5237	6	30	order	order	NOUN
ejpam-5237	6	31	α	α	PRON
ejpam-5237	6	32	where	where	SCONJ
ejpam-5237	6	33	1/2	1/2	NUM
ejpam-5237	6	34	<	<	X
ejpam-5237	6	35	α	α	X
ejpam-5237	6	36	<	<	X
ejpam-5237	6	37	1	1	NUM
ejpam-5237	6	38	.	.	SYM
ejpam-5237	6	39	2020	2020	NUM
ejpam-5237	6	40	mathematics	mathematic	NOUN
ejpam-5237	6	41	subject	subject	NOUN
ejpam-5237	6	42	classifications	classification	NOUN
ejpam-5237	6	43	:	:	PUNCT
ejpam-5237	6	44	26a33	26a33	NUM
ejpam-5237	6	45	,	,	PUNCT
ejpam-5237	6	46	34a08	34a08	NUM
ejpam-5237	6	47	,	,	PUNCT
ejpam-5237	6	48	65r20	65r20	NUM
ejpam-5237	6	49	,	,	PUNCT
ejpam-5237	6	50	35r11	35r11	NUM
ejpam-5237	6	51	key	key	ADJ
ejpam-5237	6	52	words	word	NOUN
ejpam-5237	6	53	and	and	CCONJ
ejpam-5237	6	54	phrases	phrase	NOUN
ejpam-5237	6	55	:	:	PUNCT
ejpam-5237	6	56	conformbale	conformbale	ADJ
ejpam-5237	6	57	fractional	fractional	ADJ
ejpam-5237	6	58	derivative	derivative	ADJ
ejpam-5237	6	59	,	,	PUNCT
ejpam-5237	6	60	non	non	ADJ
ejpam-5237	6	61	-	-	ADJ
ejpam-5237	6	62	conformable	conformable	ADJ
ejpam-5237	6	63	fractional	fractional	ADJ
ejpam-5237	6	64	derivative	derivative	NOUN
ejpam-5237	6	65	,	,	PUNCT
ejpam-5237	6	66	riemann	riemann	PROPN
ejpam-5237	6	67	-	-	PUNCT
ejpam-5237	6	68	liouville	liouville	PROPN
ejpam-5237	6	69	,	,	PUNCT
ejpam-5237	6	70	caputo	caputo	PROPN
ejpam-5237	6	71	fractional	fractional	ADJ
ejpam-5237	6	72	derivatives	derivative	NOUN
ejpam-5237	6	73	1	1	NUM
ejpam-5237	6	74	.	.	PUNCT
ejpam-5237	6	75	introduction	introduction	NOUN
ejpam-5237	6	76	the	the	DET
ejpam-5237	6	77	principles	principle	NOUN
ejpam-5237	6	78	of	of	ADP
ejpam-5237	6	79	classical	classical	ADJ
ejpam-5237	6	80	calculus	calculus	NOUN
ejpam-5237	6	81	,	,	PUNCT
ejpam-5237	6	82	which	which	PRON
ejpam-5237	6	83	form	form	VERB
ejpam-5237	6	84	the	the	DET
ejpam-5237	6	85	bedrock	bedrock	NOUN
ejpam-5237	6	86	of	of	ADP
ejpam-5237	6	87	mathematical	mathematical	ADJ
ejpam-5237	6	88	analysis	analysis	NOUN
ejpam-5237	6	89	,	,	PUNCT
ejpam-5237	6	90	have	have	AUX
ejpam-5237	6	91	been	be	AUX
ejpam-5237	6	92	instrumental	instrumental	ADJ
ejpam-5237	6	93	in	in	ADP
ejpam-5237	6	94	understanding	understanding	NOUN
ejpam-5237	6	95	and	and	CCONJ
ejpam-5237	6	96	modeling	model	VERB
ejpam-5237	6	97	various	various	ADJ
ejpam-5237	6	98	phenomena	phenomenon	NOUN
ejpam-5237	6	99	across	across	ADP
ejpam-5237	6	100	science	science	NOUN
ejpam-5237	6	101	and	and	CCONJ
ejpam-5237	6	102	engineering	engineering	NOUN
ejpam-5237	6	103	.	.	PUNCT
ejpam-5237	7	1	however	however	ADV
ejpam-5237	7	2	,	,	PUNCT
ejpam-5237	7	3	there	there	PRON
ejpam-5237	7	4	exist	exist	VERB
ejpam-5237	7	5	numerous	numerous	ADJ
ejpam-5237	7	6	real	real	ADJ
ejpam-5237	7	7	-	-	PUNCT
ejpam-5237	7	8	world	world	NOUN
ejpam-5237	7	9	phenomena	phenomenon	NOUN
ejpam-5237	7	10	that	that	PRON
ejpam-5237	7	11	defy	defy	VERB
ejpam-5237	7	12	straightforward	straightforward	ADJ
ejpam-5237	7	13	modeling	modeling	NOUN
ejpam-5237	7	14	using	use	VERB
ejpam-5237	7	15	classical	classical	ADJ
ejpam-5237	7	16	calculus	calculus	NOUN
ejpam-5237	7	17	due	due	ADP
ejpam-5237	7	18	to	to	ADP
ejpam-5237	7	19	their	their	PRON
ejpam-5237	7	20	non	non	ADJ
ejpam-5237	7	21	-	-	ADJ
ejpam-5237	7	22	local	local	ADJ
ejpam-5237	7	23	behavior	behavior	NOUN
ejpam-5237	7	24	or	or	CCONJ
ejpam-5237	7	25	longterm	longterm	NOUN
ejpam-5237	7	26	memory	memory	NOUN
ejpam-5237	7	27	effects	effect	NOUN
ejpam-5237	7	28	.	.	PUNCT
ejpam-5237	8	1	fractional	fractional	ADJ
ejpam-5237	8	2	calculus	calculus	NOUN
ejpam-5237	8	3	emerges	emerge	VERB
ejpam-5237	8	4	as	as	ADP
ejpam-5237	8	5	a	a	DET
ejpam-5237	8	6	powerful	powerful	ADJ
ejpam-5237	8	7	framework	framework	NOUN
ejpam-5237	8	8	to	to	PART
ejpam-5237	8	9	address	address	VERB
ejpam-5237	8	10	such	such	ADJ
ejpam-5237	8	11	complexities	complexity	NOUN
ejpam-5237	8	12	by	by	ADP
ejpam-5237	8	13	extending	extend	VERB
ejpam-5237	8	14	the	the	DET
ejpam-5237	8	15	traditional	traditional	ADJ
ejpam-5237	8	16	notions	notion	NOUN
ejpam-5237	8	17	of	of	ADP
ejpam-5237	8	18	derivatives	derivative	NOUN
ejpam-5237	8	19	and	and	CCONJ
ejpam-5237	8	20	integrals	integral	NOUN
ejpam-5237	8	21	to	to	ADP
ejpam-5237	8	22	non	non	ADJ
ejpam-5237	8	23	-	-	ADJ
ejpam-5237	8	24	integer	integer	ADJ
ejpam-5237	8	25	orders	order	NOUN
ejpam-5237	8	26	[	[	X
ejpam-5237	8	27	1–3	1–3	NOUN
ejpam-5237	8	28	,	,	PUNCT
ejpam-5237	8	29	5	5	NUM
ejpam-5237	8	30	]	]	PUNCT
ejpam-5237	8	31	.	.	PUNCT
ejpam-5237	9	1	in	in	ADP
ejpam-5237	9	2	recent	recent	ADJ
ejpam-5237	9	3	years	year	NOUN
ejpam-5237	9	4	,	,	PUNCT
ejpam-5237	9	5	fractional	fractional	ADJ
ejpam-5237	9	6	calculus	calculus	NOUN
ejpam-5237	9	7	has	have	AUX
ejpam-5237	9	8	garnered	garner	VERB
ejpam-5237	9	9	significant	significant	ADJ
ejpam-5237	9	10	attention	attention	NOUN
ejpam-5237	9	11	across	across	ADP
ejpam-5237	9	12	a	a	DET
ejpam-5237	9	13	multitude	multitude	NOUN
ejpam-5237	9	14	of	of	ADP
ejpam-5237	9	15	scientific	scientific	ADJ
ejpam-5237	9	16	and	and	CCONJ
ejpam-5237	9	17	engineering	engineering	NOUN
ejpam-5237	9	18	disciplines	discipline	NOUN
ejpam-5237	9	19	.	.	PUNCT
ejpam-5237	10	1	this	this	DET
ejpam-5237	10	2	surge	surge	NOUN
ejpam-5237	10	3	in	in	ADP
ejpam-5237	10	4	interest	interest	NOUN
ejpam-5237	10	5	is	be	AUX
ejpam-5237	10	6	driven	drive	VERB
ejpam-5237	10	7	by	by	ADP
ejpam-5237	10	8	its	its	PRON
ejpam-5237	10	9	remarkable	remarkable	ADJ
ejpam-5237	10	10	capacity	capacity	NOUN
ejpam-5237	10	11	to	to	PART
ejpam-5237	10	12	capture	capture	VERB
ejpam-5237	10	13	and	and	CCONJ
ejpam-5237	10	14	describe	describe	VERB
ejpam-5237	10	15	phenomena	phenomenon	NOUN
ejpam-5237	10	16	that	that	PRON
ejpam-5237	10	17	exhibit	exhibit	VERB
ejpam-5237	10	18	intricate	intricate	ADJ
ejpam-5237	10	19	temporal	temporal	ADJ
ejpam-5237	10	20	dependencies	dependency	NOUN
ejpam-5237	10	21	or	or	CCONJ
ejpam-5237	10	22	spatial	spatial	ADJ
ejpam-5237	10	23	interactions	interaction	NOUN
ejpam-5237	10	24	.	.	PUNCT
ejpam-5237	11	1	whether	whether	SCONJ
ejpam-5237	11	2	it	it	PRON
ejpam-5237	11	3	’s	’	VERB
ejpam-5237	11	4	the	the	DET
ejpam-5237	11	5	diffusion	diffusion	NOUN
ejpam-5237	11	6	of	of	ADP
ejpam-5237	11	7	particles	particle	NOUN
ejpam-5237	11	8	in	in	ADP
ejpam-5237	11	9	porous	porous	ADJ
ejpam-5237	11	10	media	medium	NOUN
ejpam-5237	11	11	,	,	PUNCT
ejpam-5237	11	12	the	the	DET
ejpam-5237	11	13	dynamics	dynamic	NOUN
ejpam-5237	11	14	of	of	ADP
ejpam-5237	11	15	complex	complex	ADJ
ejpam-5237	11	16	networks	network	NOUN
ejpam-5237	11	17	,	,	PUNCT
ejpam-5237	11	18	or	or	CCONJ
ejpam-5237	11	19	the	the	DET
ejpam-5237	11	20	behavior	behavior	NOUN
ejpam-5237	11	21	of	of	ADP
ejpam-5237	11	22	viscoelastic	viscoelastic	NOUN
ejpam-5237	11	23	∗corresponding	∗corresponding	NOUN
ejpam-5237	11	24	author	author	NOUN
ejpam-5237	11	25	.	.	PUNCT
ejpam-5237	12	1	doi	doi	NOUN
ejpam-5237	12	2	:	:	PUNCT
ejpam-5237	12	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5237	https://doi.org/10.29020/nybg.ejpam.v17i3.5237	PRON
ejpam-5237	12	4	email	email	NOUN
ejpam-5237	12	5	addresses	address	NOUN
ejpam-5237	12	6	:	:	PUNCT
ejpam-5237	12	7	abdessamad11117@gmail.com	abdessamad11117@gmail.com	PROPN
ejpam-5237	12	8	(	(	PUNCT
ejpam-5237	12	9	a.	a.	PROPN
ejpam-5237	12	10	ait	ait	PROPN
ejpam-5237	12	11	brahim	brahim	PROPN
ejpam-5237	12	12	)	)	PUNCT
ejpam-5237	12	13	,	,	PUNCT
ejpam-5237	12	14	a	a	DET
ejpam-5237	12	15	elhajaji@yahou.fr	elhajaji@yahou.fr	PROPN
ejpam-5237	12	16	(	(	PUNCT
ejpam-5237	12	17	a.	a.	PROPN
ejpam-5237	12	18	el	el	PROPN
ejpam-5237	12	19	hajaji	hajaji	PROPN
ejpam-5237	12	20	)	)	PUNCT
ejpam-5237	12	21	,	,	PUNCT
ejpam-5237	12	22	hilalkhalid2005@yahou.fr	hilalkhalid2005@yahou.fr	PROPN
ejpam-5237	12	23	(	(	PUNCT
ejpam-5237	12	24	k.	k.	PROPN
ejpam-5237	12	25	hilal	hilal	PROPN
ejpam-5237	12	26	)	)	PUNCT
ejpam-5237	12	27	,	,	PUNCT
ejpam-5237	12	28	elg	elg	PROPN
ejpam-5237	12	29	jalila@yahou.fr	jalila@yahou.fr	PROPN
ejpam-5237	12	30	(	(	PUNCT
ejpam-5237	12	31	j.	j.	PROPN
ejpam-5237	12	32	el	el	PROPN
ejpam-5237	12	33	ghordaf	ghordaf	PROPN
ejpam-5237	12	34	)	)	PUNCT
ejpam-5237	12	35	,	,	PUNCT
ejpam-5237	12	36	jnapoles@exa.unne.edu.ar	jnapoles@exa.unne.edu.ar	X
ejpam-5237	12	37	(	(	PUNCT
ejpam-5237	12	38	j.n	j.n	PROPN
ejpam-5237	12	39	.	.	PROPN
ejpam-5237	12	40	valdes	valdes	PROPN
ejpam-5237	12	41	)	)	PUNCT
ejpam-5237	12	42	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5237	12	43	1842	1842	NUM
ejpam-5237	13	1	©	©	ADP
ejpam-5237	13	2	2024	2024	NUM
ejpam-5237	13	3	ejpam	ejpam	NOUN
ejpam-5237	13	4	all	all	DET
ejpam-5237	13	5	rights	right	NOUN
ejpam-5237	13	6	reserved	reserve	VERB
ejpam-5237	13	7	.	.	PUNCT
ejpam-5237	14	1	a.	a.	PROPN
ejpam-5237	14	2	ait	ait	PROPN
ejpam-5237	14	3	brahim	brahim	PROPN
ejpam-5237	14	4	et	et	PROPN
ejpam-5237	14	5	all	all	DET
ejpam-5237	14	6	/	/	SYM
ejpam-5237	14	7	eur	eur	PROPN
ejpam-5237	14	8	.	.	PUNCT
ejpam-5237	15	1	j.	j.	PROPN
ejpam-5237	15	2	pure	pure	PROPN
ejpam-5237	15	3	appl	appl	PROPN
ejpam-5237	15	4	.	.	PROPN
ejpam-5237	15	5	math	math	PROPN
ejpam-5237	15	6	,	,	PUNCT
ejpam-5237	15	7	17	17	NUM
ejpam-5237	15	8	(	(	PUNCT
ejpam-5237	15	9	3	3	NUM
ejpam-5237	15	10	)	)	PUNCT
ejpam-5237	15	11	(	(	PUNCT
ejpam-5237	15	12	2024	2024	NUM
ejpam-5237	15	13	)	)	PUNCT
ejpam-5237	15	14	,	,	PUNCT
ejpam-5237	15	15	1842	1842	NUM
ejpam-5237	15	16	-	-	SYM
ejpam-5237	15	17	1854	1854	NUM
ejpam-5237	15	18	1843	1843	NUM
ejpam-5237	15	19	materials	material	NOUN
ejpam-5237	15	20	,	,	PUNCT
ejpam-5237	15	21	fractional	fractional	ADJ
ejpam-5237	15	22	calculus	calculus	NOUN
ejpam-5237	15	23	provides	provide	VERB
ejpam-5237	15	24	a	a	DET
ejpam-5237	15	25	versatile	versatile	ADJ
ejpam-5237	15	26	toolkit	toolkit	NOUN
ejpam-5237	15	27	for	for	ADP
ejpam-5237	15	28	modeling	modeling	NOUN
ejpam-5237	15	29	and	and	CCONJ
ejpam-5237	15	30	analyzing	analyze	VERB
ejpam-5237	15	31	these	these	DET
ejpam-5237	15	32	systems	system	NOUN
ejpam-5237	15	33	with	with	ADP
ejpam-5237	15	34	unprecedented	unprecedented	ADJ
ejpam-5237	15	35	accuracy	accuracy	NOUN
ejpam-5237	15	36	and	and	CCONJ
ejpam-5237	15	37	depth	depth	NOUN
ejpam-5237	15	38	.	.	PUNCT
ejpam-5237	16	1	the	the	DET
ejpam-5237	16	2	applications	application	NOUN
ejpam-5237	16	3	of	of	ADP
ejpam-5237	16	4	fractional	fractional	ADJ
ejpam-5237	16	5	calculus	calculus	NOUN
ejpam-5237	16	6	span	span	NOUN
ejpam-5237	16	7	a	a	DET
ejpam-5237	16	8	wide	wide	ADJ
ejpam-5237	16	9	spectrum	spectrum	NOUN
ejpam-5237	16	10	,	,	PUNCT
ejpam-5237	16	11	encompassing	encompass	VERB
ejpam-5237	16	12	fields	field	NOUN
ejpam-5237	16	13	such	such	ADJ
ejpam-5237	16	14	as	as	ADP
ejpam-5237	16	15	physics	physics	NOUN
ejpam-5237	16	16	,	,	PUNCT
ejpam-5237	16	17	biology	biology	NOUN
ejpam-5237	16	18	,	,	PUNCT
ejpam-5237	16	19	finance	finance	NOUN
ejpam-5237	16	20	,	,	PUNCT
ejpam-5237	16	21	signal	signal	NOUN
ejpam-5237	16	22	processing	processing	NOUN
ejpam-5237	16	23	,	,	PUNCT
ejpam-5237	16	24	and	and	CCONJ
ejpam-5237	16	25	control	control	NOUN
ejpam-5237	16	26	theory	theory	NOUN
ejpam-5237	16	27	,	,	PUNCT
ejpam-5237	16	28	among	among	ADP
ejpam-5237	16	29	others	other	NOUN
ejpam-5237	16	30	.	.	PUNCT
ejpam-5237	17	1	from	from	ADP
ejpam-5237	17	2	characterizing	characterize	VERB
ejpam-5237	17	3	anomalous	anomalous	ADJ
ejpam-5237	17	4	diffusion	diffusion	NOUN
ejpam-5237	17	5	processes	process	NOUN
ejpam-5237	17	6	in	in	ADP
ejpam-5237	17	7	biological	biological	ADJ
ejpam-5237	17	8	systems	system	NOUN
ejpam-5237	17	9	to	to	ADP
ejpam-5237	17	10	optimizing	optimize	VERB
ejpam-5237	17	11	the	the	DET
ejpam-5237	17	12	performance	performance	NOUN
ejpam-5237	17	13	of	of	ADP
ejpam-5237	17	14	control	control	NOUN
ejpam-5237	17	15	systems	system	NOUN
ejpam-5237	17	16	with	with	ADP
ejpam-5237	17	17	fractional	fractional	ADJ
ejpam-5237	17	18	-	-	PUNCT
ejpam-5237	17	19	order	order	NOUN
ejpam-5237	17	20	controllers	controller	NOUN
ejpam-5237	17	21	,	,	PUNCT
ejpam-5237	17	22	the	the	DET
ejpam-5237	17	23	influence	influence	NOUN
ejpam-5237	17	24	of	of	ADP
ejpam-5237	17	25	fractional	fractional	ADJ
ejpam-5237	17	26	calculus	calculus	NOUN
ejpam-5237	17	27	permeates	permeate	VERB
ejpam-5237	17	28	numerous	numerous	ADJ
ejpam-5237	17	29	facets	facet	NOUN
ejpam-5237	17	30	of	of	ADP
ejpam-5237	17	31	modern	modern	ADJ
ejpam-5237	17	32	science	science	NOUN
ejpam-5237	17	33	and	and	CCONJ
ejpam-5237	17	34	technology	technology	NOUN
ejpam-5237	17	35	.	.	PUNCT
ejpam-5237	18	1	in	in	ADP
ejpam-5237	18	2	this	this	DET
ejpam-5237	18	3	context	context	NOUN
ejpam-5237	18	4	,	,	PUNCT
ejpam-5237	18	5	the	the	DET
ejpam-5237	18	6	significance	significance	NOUN
ejpam-5237	18	7	of	of	ADP
ejpam-5237	18	8	fractional	fractional	ADJ
ejpam-5237	18	9	calculus	calculus	NOUN
ejpam-5237	18	10	extends	extend	VERB
ejpam-5237	18	11	far	far	ADV
ejpam-5237	18	12	beyond	beyond	ADP
ejpam-5237	18	13	its	its	PRON
ejpam-5237	18	14	theoretical	theoretical	ADJ
ejpam-5237	18	15	foundations	foundation	NOUN
ejpam-5237	18	16	;	;	PUNCT
ejpam-5237	18	17	it	it	PRON
ejpam-5237	18	18	serves	serve	VERB
ejpam-5237	18	19	as	as	ADP
ejpam-5237	18	20	a	a	DET
ejpam-5237	18	21	practical	practical	ADJ
ejpam-5237	18	22	bridge	bridge	NOUN
ejpam-5237	18	23	between	between	ADP
ejpam-5237	18	24	theoretical	theoretical	ADJ
ejpam-5237	18	25	insights	insight	NOUN
ejpam-5237	18	26	and	and	CCONJ
ejpam-5237	18	27	real	real	ADJ
ejpam-5237	18	28	-	-	PUNCT
ejpam-5237	18	29	world	world	NOUN
ejpam-5237	18	30	applications	application	NOUN
ejpam-5237	18	31	.	.	PUNCT
ejpam-5237	19	1	as	as	SCONJ
ejpam-5237	19	2	researchers	researcher	NOUN
ejpam-5237	19	3	continue	continue	VERB
ejpam-5237	19	4	to	to	PART
ejpam-5237	19	5	explore	explore	VERB
ejpam-5237	19	6	and	and	CCONJ
ejpam-5237	19	7	refine	refine	VERB
ejpam-5237	19	8	the	the	DET
ejpam-5237	19	9	methodologies	methodology	NOUN
ejpam-5237	19	10	within	within	ADP
ejpam-5237	19	11	this	this	DET
ejpam-5237	19	12	field	field	NOUN
ejpam-5237	19	13	,	,	PUNCT
ejpam-5237	19	14	the	the	DET
ejpam-5237	19	15	potential	potential	NOUN
ejpam-5237	19	16	for	for	ADP
ejpam-5237	19	17	breakthroughs	breakthrough	NOUN
ejpam-5237	19	18	in	in	ADP
ejpam-5237	19	19	understanding	understand	VERB
ejpam-5237	19	20	complex	complex	ADJ
ejpam-5237	19	21	phenomena	phenomenon	NOUN
ejpam-5237	19	22	and	and	CCONJ
ejpam-5237	19	23	developing	develop	VERB
ejpam-5237	19	24	innovative	innovative	ADJ
ejpam-5237	19	25	solutions	solution	NOUN
ejpam-5237	19	26	grows	grow	VERB
ejpam-5237	19	27	ever	ever	ADV
ejpam-5237	19	28	greater	great	ADJ
ejpam-5237	19	29	.	.	PUNCT
ejpam-5237	20	1	in	in	ADP
ejpam-5237	20	2	this	this	DET
ejpam-5237	20	3	dynamic	dynamic	ADJ
ejpam-5237	20	4	landscape	landscape	NOUN
ejpam-5237	20	5	,	,	PUNCT
ejpam-5237	20	6	the	the	DET
ejpam-5237	20	7	exploration	exploration	NOUN
ejpam-5237	20	8	of	of	ADP
ejpam-5237	20	9	fractional	fractional	ADJ
ejpam-5237	20	10	calculus	calculus	NOUN
ejpam-5237	20	11	promises	promise	NOUN
ejpam-5237	20	12	to	to	PART
ejpam-5237	20	13	yield	yield	VERB
ejpam-5237	20	14	profound	profound	ADJ
ejpam-5237	20	15	insights	insight	NOUN
ejpam-5237	20	16	and	and	CCONJ
ejpam-5237	20	17	transformative	transformative	ADJ
ejpam-5237	20	18	advancements	advancement	NOUN
ejpam-5237	20	19	across	across	ADP
ejpam-5237	20	20	diverse	diverse	ADJ
ejpam-5237	20	21	domains	domain	NOUN
ejpam-5237	20	22	,	,	PUNCT
ejpam-5237	20	23	shaping	shape	VERB
ejpam-5237	20	24	the	the	DET
ejpam-5237	20	25	future	future	NOUN
ejpam-5237	20	26	of	of	ADP
ejpam-5237	20	27	science	science	NOUN
ejpam-5237	20	28	and	and	CCONJ
ejpam-5237	20	29	engineering	engineering	NOUN
ejpam-5237	20	30	in	in	ADP
ejpam-5237	20	31	profound	profound	ADJ
ejpam-5237	20	32	ways	way	NOUN
ejpam-5237	20	33	.	.	PUNCT
ejpam-5237	21	1	during	during	ADP
ejpam-5237	21	2	the	the	DET
ejpam-5237	21	3	late	late	ADJ
ejpam-5237	21	4	1950s	1950	NOUN
ejpam-5237	21	5	and	and	CCONJ
ejpam-5237	21	6	early	early	ADJ
ejpam-5237	21	7	1960s	1960	NOUN
ejpam-5237	21	8	,	,	PUNCT
ejpam-5237	21	9	local	local	ADJ
ejpam-5237	21	10	non	non	ADJ
ejpam-5237	21	11	-	-	ADJ
ejpam-5237	21	12	integer	integer	ADJ
ejpam-5237	21	13	differential	differential	NOUN
ejpam-5237	21	14	operators	operator	NOUN
ejpam-5237	21	15	were	be	AUX
ejpam-5237	21	16	introduced	introduce	VERB
ejpam-5237	21	17	,	,	PUNCT
ejpam-5237	21	18	defined	define	VERB
ejpam-5237	21	19	in	in	ADP
ejpam-5237	21	20	terms	term	NOUN
ejpam-5237	21	21	of	of	ADP
ejpam-5237	21	22	incremental	incremental	ADJ
ejpam-5237	21	23	quotients	quotient	NOUN
ejpam-5237	21	24	.	.	PUNCT
ejpam-5237	22	1	however	however	ADV
ejpam-5237	22	2	,	,	PUNCT
ejpam-5237	22	3	their	their	PRON
ejpam-5237	22	4	utilization	utilization	NOUN
ejpam-5237	22	5	remained	remain	VERB
ejpam-5237	22	6	sporadic	sporadic	ADJ
ejpam-5237	22	7	over	over	ADP
ejpam-5237	22	8	the	the	DET
ejpam-5237	22	9	following	follow	VERB
ejpam-5237	22	10	five	five	NUM
ejpam-5237	22	11	decades	decade	NOUN
ejpam-5237	22	12	,	,	PUNCT
ejpam-5237	22	13	hindering	hinder	VERB
ejpam-5237	22	14	widespread	widespread	ADJ
ejpam-5237	22	15	dissemination	dissemination	NOUN
ejpam-5237	22	16	and	and	CCONJ
ejpam-5237	22	17	understanding	understanding	NOUN
ejpam-5237	22	18	of	of	ADP
ejpam-5237	22	19	their	their	PRON
ejpam-5237	22	20	potential	potential	NOUN
ejpam-5237	22	21	.	.	PUNCT
ejpam-5237	23	1	it	it	PRON
ejpam-5237	23	2	was	be	AUX
ejpam-5237	23	3	n’t	not	PART
ejpam-5237	23	4	until	until	ADP
ejpam-5237	23	5	2014	2014	NUM
ejpam-5237	23	6	that	that	SCONJ
ejpam-5237	23	7	the	the	DET
ejpam-5237	23	8	first	first	ADJ
ejpam-5237	23	9	comprehensive	comprehensive	ADJ
ejpam-5237	23	10	formalization	formalization	NOUN
ejpam-5237	23	11	of	of	ADP
ejpam-5237	23	12	these	these	DET
ejpam-5237	23	13	local	local	ADJ
ejpam-5237	23	14	operators	operator	NOUN
ejpam-5237	23	15	emerged	emerge	VERB
ejpam-5237	23	16	,	,	PUNCT
ejpam-5237	23	17	marking	mark	VERB
ejpam-5237	23	18	a	a	DET
ejpam-5237	23	19	significant	significant	ADJ
ejpam-5237	23	20	milestone	milestone	NOUN
ejpam-5237	23	21	in	in	ADP
ejpam-5237	23	22	the	the	DET
ejpam-5237	23	23	development	development	NOUN
ejpam-5237	23	24	of	of	ADP
ejpam-5237	23	25	non	non	ADJ
ejpam-5237	23	26	-	-	ADJ
ejpam-5237	23	27	integer	integer	ADJ
ejpam-5237	23	28	order	order	NOUN
ejpam-5237	23	29	calculus	calculus	NOUN
ejpam-5237	23	30	.	.	PUNCT
ejpam-5237	24	1	this	this	DET
ejpam-5237	24	2	contribution	contribution	NOUN
ejpam-5237	24	3	addressed	address	VERB
ejpam-5237	24	4	the	the	DET
ejpam-5237	24	5	limitations	limitation	NOUN
ejpam-5237	24	6	of	of	ADP
ejpam-5237	24	7	global	global	ADJ
ejpam-5237	24	8	operators	operator	NOUN
ejpam-5237	24	9	.	.	PUNCT
ejpam-5237	25	1	r.	r.	PROPN
ejpam-5237	25	2	khalil	khalil	PROPN
ejpam-5237	25	3	et	et	PROPN
ejpam-5237	25	4	al	al	PROPN
ejpam-5237	25	5	.	.	PROPN
ejpam-5237	26	1	in	in	ADP
ejpam-5237	26	2	their	their	PRON
ejpam-5237	26	3	article	article	NOUN
ejpam-5237	26	4	”	"	PUNCT
ejpam-5237	26	5	a	a	DET
ejpam-5237	26	6	new	new	ADJ
ejpam-5237	26	7	definition	definition	NOUN
ejpam-5237	26	8	of	of	ADP
ejpam-5237	26	9	the	the	DET
ejpam-5237	26	10	fractional	fractional	ADJ
ejpam-5237	26	11	derivative	derivative	NOUN
ejpam-5237	26	12	”	"	PUNCT
ejpam-5237	26	13	(	(	PUNCT
ejpam-5237	26	14	refer	refer	VERB
ejpam-5237	26	15	to	to	ADP
ejpam-5237	26	16	[	[	X
ejpam-5237	26	17	9	9	NUM
ejpam-5237	26	18	]	]	NUM
ejpam-5237	26	19	)	)	PUNCT
ejpam-5237	26	20	,	,	PUNCT
ejpam-5237	26	21	introduced	introduce	VERB
ejpam-5237	26	22	the	the	DET
ejpam-5237	26	23	concept	concept	NOUN
ejpam-5237	26	24	of	of	ADP
ejpam-5237	26	25	the	the	DET
ejpam-5237	26	26	”	"	PUNCT
ejpam-5237	26	27	conformable	conformable	ADJ
ejpam-5237	26	28	fractional	fractional	ADJ
ejpam-5237	26	29	derivative	derivative	NOUN
ejpam-5237	26	30	”	"	PUNCT
ejpam-5237	26	31	with	with	ADP
ejpam-5237	26	32	the	the	DET
ejpam-5237	26	33	following	follow	VERB
ejpam-5237	26	34	definition	definition	NOUN
ejpam-5237	26	35	:	:	PUNCT
ejpam-5237	26	36	let	let	VERB
ejpam-5237	26	37	α	α	PRON
ejpam-5237	26	38	∈]0	∈]0	ADJ
ejpam-5237	26	39	,	,	PUNCT
ejpam-5237	26	40	1	1	NUM
ejpam-5237	26	41	]	]	PUNCT
ejpam-5237	26	42	and	and	CCONJ
ejpam-5237	26	43	m	m	VERB
ejpam-5237	26	44	:]	:]	NOUN
ejpam-5237	26	45	0,+∞[−→	0,+∞[−→	NOUN
ejpam-5237	26	46	r	r	NOUN
ejpam-5237	26	47	.	.	PUNCT
ejpam-5237	27	1	therefore	therefore	ADV
ejpam-5237	27	2	,	,	PUNCT
ejpam-5237	27	3	the	the	DET
ejpam-5237	27	4	conformable	conformable	ADJ
ejpam-5237	27	5	fractional	fractional	ADJ
ejpam-5237	27	6	derivative	derivative	NOUN
ejpam-5237	27	7	of	of	ADP
ejpam-5237	27	8	order	order	NOUN
ejpam-5237	27	9	α	α	NOUN
ejpam-5237	27	10	at	at	ADP
ejpam-5237	27	11	t0	t0	PROPN
ejpam-5237	27	12	≻	≻	X
ejpam-5237	27	13	0	0	NUM
ejpam-5237	27	14	is	be	AUX
ejpam-5237	27	15	defined	define	VERB
ejpam-5237	27	16	by	by	ADP
ejpam-5237	27	17	m	m	PROPN
ejpam-5237	27	18	(	(	PUNCT
ejpam-5237	27	19	α	α	NOUN
ejpam-5237	27	20	)	)	PUNCT
ejpam-5237	27	21	(	(	PUNCT
ejpam-5237	27	22	t0	t0	NOUN
ejpam-5237	27	23	)	)	PUNCT
ejpam-5237	28	1	=	=	PROPN
ejpam-5237	28	2	lim	lim	PROPN
ejpam-5237	28	3	ε−→0	ε−→0	PROPN
ejpam-5237	28	4	m	m	VERB
ejpam-5237	28	5	(	(	PUNCT
ejpam-5237	28	6	t+	t+	ADP
ejpam-5237	28	7	εt0	εt0	X
ejpam-5237	28	8	1−α	1−α	NUM
ejpam-5237	28	9	)	)	PUNCT
ejpam-5237	28	10	−m	−m	NOUN
ejpam-5237	28	11	(	(	PUNCT
ejpam-5237	28	12	t0	t0	PROPN
ejpam-5237	28	13	)	)	PUNCT
ejpam-5237	28	14	ε	ε	PROPN
ejpam-5237	28	15	,	,	PUNCT
ejpam-5237	28	16	(	(	PUNCT
ejpam-5237	28	17	1	1	X
ejpam-5237	28	18	)	)	PUNCT
ejpam-5237	28	19	if	if	SCONJ
ejpam-5237	28	20	it	it	PRON
ejpam-5237	28	21	exists	exist	VERB
ejpam-5237	28	22	.	.	PUNCT
ejpam-5237	29	1	in	in	ADP
ejpam-5237	29	2	fact	fact	NOUN
ejpam-5237	29	3	,	,	PUNCT
ejpam-5237	29	4	this	this	DET
ejpam-5237	29	5	novel	novel	ADJ
ejpam-5237	29	6	form	form	NOUN
ejpam-5237	29	7	of	of	ADP
ejpam-5237	29	8	derivation	derivation	NOUN
ejpam-5237	29	9	upholds	uphold	VERB
ejpam-5237	29	10	all	all	DET
ejpam-5237	29	11	properties	property	NOUN
ejpam-5237	29	12	of	of	ADP
ejpam-5237	29	13	conventional	conventional	ADJ
ejpam-5237	29	14	derivation	derivation	NOUN
ejpam-5237	29	15	except	except	SCONJ
ejpam-5237	29	16	for	for	ADP
ejpam-5237	29	17	semi	semi	ADJ
ejpam-5237	29	18	-	-	NOUN
ejpam-5237	29	19	groups	group	NOUN
ejpam-5237	29	20	.	.	PUNCT
ejpam-5237	30	1	r.	r.	PROPN
ejpam-5237	30	2	khalil	khalil	PROPN
ejpam-5237	30	3	et	et	PROPN
ejpam-5237	30	4	al	al	PROPN
ejpam-5237	30	5	.	.	PROPN
ejpam-5237	30	6	,	,	PUNCT
ejpam-5237	30	7	along	along	ADP
ejpam-5237	30	8	with	with	ADP
ejpam-5237	30	9	t.	t.	PROPN
ejpam-5237	30	10	abdeljawad	abdeljawad	NOUN
ejpam-5237	30	11	,	,	PUNCT
ejpam-5237	30	12	the	the	DET
ejpam-5237	30	13	”	"	PUNCT
ejpam-5237	30	14	pioneer	pioneer	NOUN
ejpam-5237	30	15	”	"	PUNCT
ejpam-5237	30	16	of	of	ADP
ejpam-5237	30	17	this	this	DET
ejpam-5237	30	18	innovative	innovative	ADJ
ejpam-5237	30	19	concept	concept	NOUN
ejpam-5237	30	20	,	,	PUNCT
ejpam-5237	30	21	laid	lay	VERB
ejpam-5237	30	22	the	the	DET
ejpam-5237	30	23	theoretical	theoretical	ADJ
ejpam-5237	30	24	groundwork	groundwork	NOUN
ejpam-5237	30	25	in	in	ADP
ejpam-5237	30	26	their	their	PRON
ejpam-5237	30	27	article	article	NOUN
ejpam-5237	30	28	”	"	PUNCT
ejpam-5237	30	29	on	on	ADP
ejpam-5237	30	30	conformable	conformable	ADJ
ejpam-5237	30	31	fractional	fractional	ADJ
ejpam-5237	30	32	calculus	calculus	NOUN
ejpam-5237	30	33	”	"	PUNCT
ejpam-5237	31	1	[	[	X
ejpam-5237	31	2	3	3	NUM
ejpam-5237	31	3	]	]	PUNCT
ejpam-5237	31	4	.	.	PUNCT
ejpam-5237	32	1	a.	a.	NOUN
ejpam-5237	32	2	abdelhakim	abdelhakim	PROPN
ejpam-5237	33	1	[	[	X
ejpam-5237	33	2	1	1	NUM
ejpam-5237	33	3	]	]	PUNCT
ejpam-5237	33	4	,	,	PUNCT
ejpam-5237	33	5	in	in	ADP
ejpam-5237	33	6	a	a	DET
ejpam-5237	33	7	2019	2019	NUM
ejpam-5237	33	8	publication	publication	NOUN
ejpam-5237	33	9	,	,	PUNCT
ejpam-5237	33	10	demonstrated	demonstrate	VERB
ejpam-5237	33	11	that	that	SCONJ
ejpam-5237	33	12	the	the	DET
ejpam-5237	33	13	existence	existence	NOUN
ejpam-5237	33	14	of	of	ADP
ejpam-5237	33	15	limits	limit	NOUN
ejpam-5237	33	16	is	be	AUX
ejpam-5237	33	17	tantamount	tantamount	ADJ
ejpam-5237	33	18	to	to	ADP
ejpam-5237	33	19	differentiability	differentiability	NOUN
ejpam-5237	33	20	in	in	ADP
ejpam-5237	33	21	the	the	DET
ejpam-5237	33	22	classical	classical	ADJ
ejpam-5237	33	23	sense	sense	NOUN
ejpam-5237	33	24	,	,	PUNCT
ejpam-5237	33	25	highlighting	highlight	VERB
ejpam-5237	33	26	both	both	CCONJ
ejpam-5237	33	27	the	the	DET
ejpam-5237	33	28	fractional	fractional	ADJ
ejpam-5237	33	29	nature	nature	NOUN
ejpam-5237	33	30	of	of	ADP
ejpam-5237	33	31	this	this	DET
ejpam-5237	33	32	approach	approach	NOUN
ejpam-5237	33	33	and	and	CCONJ
ejpam-5237	33	34	the	the	DET
ejpam-5237	33	35	broader	broad	ADJ
ejpam-5237	33	36	significance	significance	NOUN
ejpam-5237	33	37	of	of	ADP
ejpam-5237	33	38	the	the	DET
ejpam-5237	33	39	theory	theory	NOUN
ejpam-5237	33	40	initiated	initiate	VERB
ejpam-5237	33	41	by	by	ADP
ejpam-5237	33	42	r.	r.	PROPN
ejpam-5237	33	43	khalil	khalil	PROPN
ejpam-5237	33	44	et	et	PROPN
ejpam-5237	33	45	al	al	PROPN
ejpam-5237	33	46	.	.	PROPN
ejpam-5237	33	47	and	and	CCONJ
ejpam-5237	33	48	t.	t.	PROPN
ejpam-5237	33	49	abdeljawad	abdeljawad	NOUN
ejpam-5237	33	50	.	.	PUNCT
ejpam-5237	34	1	this	this	PRON
ejpam-5237	34	2	has	have	AUX
ejpam-5237	34	3	sparked	spark	VERB
ejpam-5237	34	4	ongoing	ongoing	ADJ
ejpam-5237	34	5	debates	debate	NOUN
ejpam-5237	34	6	among	among	ADP
ejpam-5237	34	7	proponents	proponent	NOUN
ejpam-5237	34	8	and	and	CCONJ
ejpam-5237	34	9	critics	critic	NOUN
ejpam-5237	34	10	of	of	ADP
ejpam-5237	34	11	the	the	DET
ejpam-5237	34	12	methodology	methodology	NOUN
ejpam-5237	34	13	.	.	PUNCT
ejpam-5237	35	1	this	this	DET
ejpam-5237	35	2	paper	paper	NOUN
ejpam-5237	35	3	examines	examine	VERB
ejpam-5237	35	4	the	the	DET
ejpam-5237	35	5	research	research	NOUN
ejpam-5237	35	6	by	by	ADP
ejpam-5237	35	7	d.	d.	PROPN
ejpam-5237	35	8	r.	r.	PROPN
ejpam-5237	35	9	anderson	anderson	PROPN
ejpam-5237	35	10	and	and	CCONJ
ejpam-5237	35	11	d.	d.	PROPN
ejpam-5237	35	12	j.	j.	PROPN
ejpam-5237	35	13	ulness	ulness	PROPN
ejpam-5237	35	14	published	publish	VERB
ejpam-5237	35	15	in	in	ADP
ejpam-5237	35	16	2015	2015	NUM
ejpam-5237	35	17	under	under	ADP
ejpam-5237	35	18	the	the	DET
ejpam-5237	35	19	title	title	NOUN
ejpam-5237	35	20	”	"	PUNCT
ejpam-5237	35	21	newly	newly	ADV
ejpam-5237	35	22	defined	define	VERB
ejpam-5237	35	23	conformable	conformable	ADJ
ejpam-5237	35	24	derivatives	derivative	NOUN
ejpam-5237	35	25	”	"	PUNCT
ejpam-5237	35	26	[	[	X
ejpam-5237	35	27	4	4	NUM
ejpam-5237	35	28	]	]	PUNCT
ejpam-5237	35	29	.	.	PUNCT
ejpam-5237	36	1	building	build	VERB
ejpam-5237	36	2	upon	upon	SCONJ
ejpam-5237	36	3	the	the	DET
ejpam-5237	36	4	provided	provide	VERB
ejpam-5237	36	5	definition	definition	NOUN
ejpam-5237	36	6	,	,	PUNCT
ejpam-5237	36	7	we	we	PRON
ejpam-5237	36	8	presume	presume	VERB
ejpam-5237	36	9	ordinary	ordinary	ADJ
ejpam-5237	36	10	differentiability	differentiability	NOUN
ejpam-5237	36	11	.	.	PUNCT
ejpam-5237	37	1	furthermore	furthermore	ADV
ejpam-5237	37	2	,	,	PUNCT
ejpam-5237	37	3	it	it	PRON
ejpam-5237	37	4	reflects	reflect	VERB
ejpam-5237	37	5	the	the	DET
ejpam-5237	37	6	viewpoints	viewpoint	NOUN
ejpam-5237	37	7	of	of	ADP
ejpam-5237	37	8	r.	r.	PROPN
ejpam-5237	37	9	khalil	khalil	PROPN
ejpam-5237	37	10	et	et	PROPN
ejpam-5237	37	11	al	al	PROPN
ejpam-5237	37	12	.	.	PROPN
ejpam-5237	38	1	as	as	SCONJ
ejpam-5237	38	2	referenced	reference	VERB
ejpam-5237	38	3	in	in	ADP
ejpam-5237	38	4	[	[	X
ejpam-5237	38	5	9	9	NUM
ejpam-5237	38	6	]	]	PUNCT
ejpam-5237	38	7	.	.	PUNCT
ejpam-5237	39	1	since	since	SCONJ
ejpam-5237	39	2	differentiability	differentiability	NOUN
ejpam-5237	39	3	aligns	align	VERB
ejpam-5237	39	4	with	with	ADP
ejpam-5237	39	5	the	the	DET
ejpam-5237	39	6	principles	principle	NOUN
ejpam-5237	39	7	outlined	outline	VERB
ejpam-5237	39	8	in	in	ADP
ejpam-5237	39	9	[	[	X
ejpam-5237	39	10	4	4	NUM
ejpam-5237	39	11	]	]	PUNCT
ejpam-5237	39	12	,	,	PUNCT
ejpam-5237	39	13	we	we	PRON
ejpam-5237	39	14	present	present	VERB
ejpam-5237	39	15	the	the	DET
ejpam-5237	39	16	primary	primary	ADJ
ejpam-5237	39	17	computations	computation	NOUN
ejpam-5237	39	18	without	without	ADP
ejpam-5237	39	19	proofs	proof	NOUN
ejpam-5237	39	20	,	,	PUNCT
ejpam-5237	39	21	establish	establish	VERB
ejpam-5237	39	22	the	the	DET
ejpam-5237	39	23	rules	rule	NOUN
ejpam-5237	39	24	specified	specify	VERB
ejpam-5237	39	25	in	in	ADP
ejpam-5237	39	26	[	[	X
ejpam-5237	39	27	4	4	NUM
ejpam-5237	39	28	]	]	PUNCT
ejpam-5237	39	29	,	,	PUNCT
ejpam-5237	39	30	and	and	CCONJ
ejpam-5237	39	31	introduce	introduce	VERB
ejpam-5237	39	32	additional	additional	ADJ
ejpam-5237	39	33	properties	property	NOUN
ejpam-5237	39	34	.	.	PUNCT
ejpam-5237	40	1	in	in	ADP
ejpam-5237	40	2	response	response	NOUN
ejpam-5237	40	3	to	to	ADP
ejpam-5237	40	4	these	these	DET
ejpam-5237	40	5	limitations	limitation	NOUN
ejpam-5237	40	6	,	,	PUNCT
ejpam-5237	40	7	khalil	khalil	PROPN
ejpam-5237	40	8	et	et	PROPN
ejpam-5237	40	9	al	al	PROPN
ejpam-5237	40	10	.	.	PROPN
ejpam-5237	40	11	introduced	introduce	VERB
ejpam-5237	40	12	a	a	DET
ejpam-5237	40	13	new	new	ADJ
ejpam-5237	40	14	definition	definition	NOUN
ejpam-5237	40	15	of	of	ADP
ejpam-5237	40	16	fractional	fractional	ADJ
ejpam-5237	40	17	derivative	derivative	NOUN
ejpam-5237	40	18	that	that	PRON
ejpam-5237	40	19	satisfies	satisfy	VERB
ejpam-5237	40	20	these	these	DET
ejpam-5237	40	21	properties	property	NOUN
ejpam-5237	40	22	,	,	PUNCT
ejpam-5237	40	23	which	which	PRON
ejpam-5237	40	24	are	be	AUX
ejpam-5237	40	25	absent	absent	ADJ
ejpam-5237	40	26	in	in	ADP
ejpam-5237	40	27	riemann	riemann	PROPN
ejpam-5237	40	28	-	-	PUNCT
ejpam-5237	40	29	liouville	liouville	NOUN
ejpam-5237	40	30	and	and	CCONJ
ejpam-5237	40	31	caa	caa	NOUN
ejpam-5237	40	32	.	.	PUNCT
ejpam-5237	41	1	ait	ait	NOUN
ejpam-5237	41	2	brahim	brahim	PROPN
ejpam-5237	41	3	et	et	PROPN
ejpam-5237	41	4	all	all	DET
ejpam-5237	41	5	/	/	SYM
ejpam-5237	41	6	eur	eur	PROPN
ejpam-5237	41	7	.	.	PUNCT
ejpam-5237	42	1	j.	j.	PROPN
ejpam-5237	42	2	pure	pure	PROPN
ejpam-5237	42	3	appl	appl	PROPN
ejpam-5237	42	4	.	.	PROPN
ejpam-5237	42	5	math	math	PROPN
ejpam-5237	42	6	,	,	PUNCT
ejpam-5237	42	7	17	17	NUM
ejpam-5237	42	8	(	(	PUNCT
ejpam-5237	42	9	3	3	NUM
ejpam-5237	42	10	)	)	PUNCT
ejpam-5237	42	11	(	(	PUNCT
ejpam-5237	42	12	2024	2024	NUM
ejpam-5237	42	13	)	)	PUNCT
ejpam-5237	42	14	,	,	PUNCT
ejpam-5237	42	15	1842	1842	NUM
ejpam-5237	42	16	-	-	SYM
ejpam-5237	42	17	1854	1854	NUM
ejpam-5237	42	18	1844	1844	NUM
ejpam-5237	42	19	puto	puto	NOUN
ejpam-5237	42	20	fractional	fractional	ADJ
ejpam-5237	42	21	derivatives	derivative	NOUN
ejpam-5237	42	22	.	.	PUNCT
ejpam-5237	43	1	this	this	DET
ejpam-5237	43	2	new	new	ADJ
ejpam-5237	43	3	derivative	derivative	NOUN
ejpam-5237	43	4	is	be	AUX
ejpam-5237	43	5	known	know	VERB
ejpam-5237	43	6	as	as	ADP
ejpam-5237	43	7	the	the	DET
ejpam-5237	43	8	conformable	conformable	ADJ
ejpam-5237	43	9	fractional	fractional	ADJ
ejpam-5237	43	10	derivative	derivative	NOUN
ejpam-5237	43	11	.	.	PUNCT
ejpam-5237	44	1	abdeljawad	abdeljawad	NOUN
ejpam-5237	44	2	(	(	PUNCT
ejpam-5237	44	3	2015	2015	NUM
ejpam-5237	44	4	)	)	PUNCT
ejpam-5237	44	5	further	far	ADV
ejpam-5237	44	6	refined	refine	VERB
ejpam-5237	44	7	the	the	DET
ejpam-5237	44	8	concept	concept	NOUN
ejpam-5237	44	9	of	of	ADP
ejpam-5237	44	10	the	the	DET
ejpam-5237	44	11	conformable	conformable	ADJ
ejpam-5237	44	12	fractional	fractional	ADJ
ejpam-5237	44	13	derivative	derivative	NOUN
ejpam-5237	44	14	,	,	PUNCT
ejpam-5237	44	15	providing	provide	VERB
ejpam-5237	44	16	a	a	DET
ejpam-5237	44	17	more	more	ADV
ejpam-5237	44	18	comprehensive	comprehensive	ADJ
ejpam-5237	44	19	understanding	understanding	NOUN
ejpam-5237	44	20	of	of	ADP
ejpam-5237	44	21	its	its	PRON
ejpam-5237	44	22	properties	property	NOUN
ejpam-5237	44	23	.	.	PUNCT
ejpam-5237	45	1	notably	notably	ADV
ejpam-5237	45	2	,	,	PUNCT
ejpam-5237	45	3	the	the	DET
ejpam-5237	45	4	conformable	conformable	ADJ
ejpam-5237	45	5	fractional	fractional	ADJ
ejpam-5237	45	6	derivative	derivative	NOUN
ejpam-5237	45	7	is	be	AUX
ejpam-5237	45	8	defined	define	VERB
ejpam-5237	45	9	in	in	ADP
ejpam-5237	45	10	a	a	DET
ejpam-5237	45	11	simpler	simple	ADJ
ejpam-5237	45	12	manner	manner	NOUN
ejpam-5237	45	13	compared	compare	VERB
ejpam-5237	45	14	to	to	ADP
ejpam-5237	45	15	riemannliouville	riemannliouville	PROPN
ejpam-5237	45	16	and	and	CCONJ
ejpam-5237	45	17	caputo	caputo	PROPN
ejpam-5237	45	18	fractional	fractional	ADJ
ejpam-5237	45	19	derivatives	derivative	NOUN
ejpam-5237	45	20	.	.	PUNCT
ejpam-5237	46	1	among	among	ADP
ejpam-5237	46	2	these	these	DET
ejpam-5237	46	3	definitions	definition	NOUN
ejpam-5237	46	4	,	,	PUNCT
ejpam-5237	46	5	two	two	NUM
ejpam-5237	46	6	of	of	ADP
ejpam-5237	46	7	the	the	DET
ejpam-5237	46	8	most	most	ADV
ejpam-5237	46	9	prominent	prominent	ADJ
ejpam-5237	46	10	are	be	AUX
ejpam-5237	46	11	:	:	PUNCT
ejpam-5237	46	12	if	if	SCONJ
ejpam-5237	46	13	n	n	PRON
ejpam-5237	46	14	is	be	AUX
ejpam-5237	46	15	a	a	DET
ejpam-5237	46	16	positive	positive	ADJ
ejpam-5237	46	17	integer	integer	NOUN
ejpam-5237	46	18	and	and	CCONJ
ejpam-5237	46	19	α	α	PRON
ejpam-5237	46	20	∈	∈	PROPN
ejpam-5237	47	1	[	[	X
ejpam-5237	47	2	n−	n−	NOUN
ejpam-5237	47	3	1	1	NUM
ejpam-5237	47	4	,	,	PUNCT
ejpam-5237	47	5	n	n	CCONJ
ejpam-5237	47	6	]	]	X
ejpam-5237	47	7	derivative	derivative	NOUN
ejpam-5237	47	8	of	of	ADP
ejpam-5237	47	9	n	n	PROPN
ejpam-5237	47	10	is	be	AUX
ejpam-5237	47	11	given	give	VERB
ejpam-5237	47	12	by	by	ADP
ejpam-5237	47	13	:	:	PUNCT
ejpam-5237	47	14	•	•	NUM
ejpam-5237	47	15	riemann	riemann	PROPN
ejpam-5237	47	16	-	-	PUNCT
ejpam-5237	47	17	liouville	liouville	NOUN
ejpam-5237	47	18	definition	definition	NOUN
ejpam-5237	47	19	:	:	PUNCT
ejpam-5237	47	20	dα	dα	ADP
ejpam-5237	47	21	a	a	DET
ejpam-5237	47	22	(	(	PUNCT
ejpam-5237	47	23	m)(t	m)(t	PROPN
ejpam-5237	47	24	)	)	PUNCT
ejpam-5237	47	25	=	=	SYM
ejpam-5237	47	26	1	1	NUM
ejpam-5237	47	27	γ(n−	γ(n−	PROPN
ejpam-5237	47	28	α	α	NOUN
ejpam-5237	47	29	)	)	PUNCT
ejpam-5237	47	30	dn	dn	PROPN
ejpam-5237	47	31	dtn	dtn	PROPN
ejpam-5237	47	32	∫	∫	PROPN
ejpam-5237	47	33	t	t	PROPN
ejpam-5237	47	34	a	a	DET
ejpam-5237	47	35	m(u	m(u	PROPN
ejpam-5237	47	36	)	)	PUNCT
ejpam-5237	47	37	(	(	PUNCT
ejpam-5237	47	38	t−	t−	PROPN
ejpam-5237	47	39	u)α−n+1	u)α−n+1	PROPN
ejpam-5237	47	40	du	du	PROPN
ejpam-5237	47	41	.	.	PROPN
ejpam-5237	48	1	(	(	PUNCT
ejpam-5237	48	2	2	2	NUM
ejpam-5237	48	3	)	)	PUNCT
ejpam-5237	48	4	•	•	NOUN
ejpam-5237	48	5	caputo	caputo	PROPN
ejpam-5237	48	6	definition	definition	NOUN
ejpam-5237	48	7	:	:	PUNCT
ejpam-5237	48	8	if	if	SCONJ
ejpam-5237	48	9	n	n	PRON
ejpam-5237	48	10	is	be	AUX
ejpam-5237	48	11	a	a	DET
ejpam-5237	48	12	positive	positive	ADJ
ejpam-5237	48	13	integer	integer	NOUN
ejpam-5237	48	14	and	and	CCONJ
ejpam-5237	48	15	α	α	PRON
ejpam-5237	48	16	∈	∈	PROPN
ejpam-5237	49	1	[	[	X
ejpam-5237	49	2	n−	n−	NOUN
ejpam-5237	49	3	1	1	NUM
ejpam-5237	49	4	,	,	PUNCT
ejpam-5237	49	5	n	n	CCONJ
ejpam-5237	49	6	)	)	PUNCT
ejpam-5237	49	7	,	,	PUNCT
ejpam-5237	49	8	α	α	PROPN
ejpam-5237	49	9	derivative	derivative	NOUN
ejpam-5237	49	10	of	of	ADP
ejpam-5237	49	11	n	n	PROPN
ejpam-5237	49	12	is	be	AUX
ejpam-5237	49	13	given	give	VERB
ejpam-5237	49	14	by	by	ADP
ejpam-5237	49	15	dα	dα	ADP
ejpam-5237	49	16	a	a	DET
ejpam-5237	49	17	(	(	PUNCT
ejpam-5237	49	18	m)(t	m)(t	PROPN
ejpam-5237	49	19	)	)	PUNCT
ejpam-5237	49	20	=	=	SYM
ejpam-5237	49	21	1	1	NUM
ejpam-5237	49	22	γ(n−	γ(n−	PROPN
ejpam-5237	49	23	α	α	NOUN
ejpam-5237	49	24	)	)	PUNCT
ejpam-5237	49	25	∫	∫	PROPN
ejpam-5237	49	26	t	t	PROPN
ejpam-5237	49	27	a	a	DET
ejpam-5237	49	28	m	m	PROPN
ejpam-5237	49	29	(	(	PUNCT
ejpam-5237	49	30	n)(u	n)(u	PROPN
ejpam-5237	49	31	)	)	PUNCT
ejpam-5237	49	32	(	(	PUNCT
ejpam-5237	49	33	t−	t−	PROPN
ejpam-5237	49	34	u)α−n+1	u)α−n+1	PROPN
ejpam-5237	49	35	du	du	PROPN
ejpam-5237	49	36	.	.	PROPN
ejpam-5237	50	1	(	(	PUNCT
ejpam-5237	50	2	3	3	X
ejpam-5237	50	3	)	)	PUNCT
ejpam-5237	50	4	in	in	ADP
ejpam-5237	50	5	their	their	PRON
ejpam-5237	50	6	work	work	NOUN
ejpam-5237	50	7	referenced	reference	VERB
ejpam-5237	50	8	as	as	ADP
ejpam-5237	50	9	[	[	X
ejpam-5237	50	10	9	9	NUM
ejpam-5237	50	11	]	]	PUNCT
ejpam-5237	50	12	,	,	PUNCT
ejpam-5237	50	13	r.	r.	PROPN
ejpam-5237	50	14	khalil	khalil	PROPN
ejpam-5237	50	15	et	et	PROPN
ejpam-5237	50	16	al	al	PROPN
ejpam-5237	50	17	.	.	PROPN
ejpam-5237	50	18	introduced	introduce	VERB
ejpam-5237	50	19	a	a	DET
ejpam-5237	50	20	novel	novel	ADJ
ejpam-5237	50	21	concept	concept	NOUN
ejpam-5237	50	22	termed	term	VERB
ejpam-5237	50	23	the	the	DET
ejpam-5237	50	24	”	"	PUNCT
ejpam-5237	50	25	conformable	conformable	ADJ
ejpam-5237	50	26	fractional	fractional	ADJ
ejpam-5237	50	27	derivative	derivative	NOUN
ejpam-5237	50	28	.	.	PUNCT
ejpam-5237	50	29	”	"	PUNCT
ejpam-5237	51	1	unlike	unlike	ADP
ejpam-5237	51	2	the	the	DET
ejpam-5237	51	3	traditional	traditional	ADJ
ejpam-5237	51	4	riemann	riemann	PROPN
ejpam-5237	51	5	-	-	PUNCT
ejpam-5237	51	6	liouville	liouville	PROPN
ejpam-5237	51	7	and	and	CCONJ
ejpam-5237	51	8	caputo	caputo	PROPN
ejpam-5237	51	9	derivatives	derivative	NOUN
ejpam-5237	51	10	,	,	PUNCT
ejpam-5237	51	11	which	which	PRON
ejpam-5237	51	12	operate	operate	VERB
ejpam-5237	51	13	as	as	ADP
ejpam-5237	51	14	nonlocal	nonlocal	ADJ
ejpam-5237	51	15	operators	operator	NOUN
ejpam-5237	51	16	,	,	PUNCT
ejpam-5237	51	17	the	the	DET
ejpam-5237	51	18	conformable	conformable	ADJ
ejpam-5237	51	19	fractional	fractional	ADJ
ejpam-5237	51	20	derivative	derivative	ADJ
ejpam-5237	51	21	functions	function	NOUN
ejpam-5237	51	22	locally	locally	ADV
ejpam-5237	51	23	,	,	PUNCT
ejpam-5237	51	24	closely	closely	ADV
ejpam-5237	51	25	resembling	resemble	VERB
ejpam-5237	51	26	the	the	DET
ejpam-5237	51	27	conventional	conventional	ADJ
ejpam-5237	51	28	derivative	derivative	NOUN
ejpam-5237	51	29	.	.	PUNCT
ejpam-5237	52	1	furthermore	furthermore	ADV
ejpam-5237	52	2	,	,	PUNCT
ejpam-5237	52	3	a	a	DET
ejpam-5237	52	4	new	new	ADJ
ejpam-5237	52	5	definition	definition	NOUN
ejpam-5237	52	6	of	of	ADP
ejpam-5237	52	7	”	"	PUNCT
ejpam-5237	52	8	non	non	ADJ
ejpam-5237	52	9	-	-	ADJ
ejpam-5237	52	10	conformable	conformable	ADJ
ejpam-5237	52	11	”	"	PUNCT
ejpam-5237	52	12	derivatives	derivative	NOUN
ejpam-5237	52	13	has	have	AUX
ejpam-5237	52	14	been	be	AUX
ejpam-5237	52	15	introduced	introduce	VERB
ejpam-5237	52	16	in	in	ADP
ejpam-5237	52	17	a	a	DET
ejpam-5237	52	18	separate	separate	ADJ
ejpam-5237	52	19	work	work	NOUN
ejpam-5237	52	20	[	[	X
ejpam-5237	52	21	11	11	NUM
ejpam-5237	52	22	]	]	PUNCT
ejpam-5237	52	23	.	.	PUNCT
ejpam-5237	53	1	although	although	SCONJ
ejpam-5237	53	2	these	these	DET
ejpam-5237	53	3	definitions	definition	NOUN
ejpam-5237	53	4	effectively	effectively	ADV
ejpam-5237	53	5	apply	apply	VERB
ejpam-5237	53	6	in	in	ADP
ejpam-5237	53	7	the	the	DET
ejpam-5237	53	8	case	case	NOUN
ejpam-5237	53	9	of	of	ADP
ejpam-5237	53	10	0	0	NUM
ejpam-5237	53	11	<	<	X
ejpam-5237	53	12	α	α	X
ejpam-5237	53	13	<	<	X
ejpam-5237	53	14	1	1	NUM
ejpam-5237	53	15	,	,	PUNCT
ejpam-5237	53	16	there	there	PRON
ejpam-5237	53	17	arises	arise	VERB
ejpam-5237	53	18	a	a	DET
ejpam-5237	53	19	necessity	necessity	NOUN
ejpam-5237	53	20	for	for	ADP
ejpam-5237	53	21	a	a	DET
ejpam-5237	53	22	general	general	ADJ
ejpam-5237	53	23	definition	definition	NOUN
ejpam-5237	53	24	catering	cater	VERB
ejpam-5237	53	25	to	to	PART
ejpam-5237	53	26	conformable	conformable	VERB
ejpam-5237	53	27	derivatives	derivative	NOUN
ejpam-5237	53	28	of	of	ADP
ejpam-5237	53	29	any	any	DET
ejpam-5237	53	30	order	order	NOUN
ejpam-5237	53	31	,	,	PUNCT
ejpam-5237	53	32	integer	integer	NOUN
ejpam-5237	53	33	or	or	CCONJ
ejpam-5237	53	34	otherwise	otherwise	ADV
ejpam-5237	53	35	,	,	PUNCT
ejpam-5237	53	36	thereby	thereby	ADV
ejpam-5237	53	37	extending	extend	VERB
ejpam-5237	53	38	the	the	DET
ejpam-5237	53	39	scope	scope	NOUN
ejpam-5237	53	40	of	of	ADP
ejpam-5237	53	41	conformable	conformable	ADJ
ejpam-5237	53	42	derivatives	derivative	NOUN
ejpam-5237	53	43	to	to	ADP
ejpam-5237	53	44	higher	high	ADJ
ejpam-5237	53	45	orders	order	NOUN
ejpam-5237	53	46	[	[	X
ejpam-5237	53	47	11	11	NUM
ejpam-5237	53	48	]	]	PUNCT
ejpam-5237	53	49	.	.	PUNCT
ejpam-5237	54	1	interested	interested	ADJ
ejpam-5237	54	2	readers	reader	NOUN
ejpam-5237	54	3	can	can	AUX
ejpam-5237	54	4	also	also	ADV
ejpam-5237	54	5	refer	refer	VERB
ejpam-5237	54	6	to	to	ADP
ejpam-5237	54	7	additional	additional	ADJ
ejpam-5237	54	8	sources	source	NOUN
ejpam-5237	54	9	such	such	ADJ
ejpam-5237	54	10	as	as	ADP
ejpam-5237	54	11	[	[	X
ejpam-5237	54	12	7	7	NUM
ejpam-5237	54	13	]	]	PUNCT
ejpam-5237	54	14	,	,	PUNCT
ejpam-5237	54	15	[	[	X
ejpam-5237	54	16	16	16	NUM
ejpam-5237	54	17	]	]	PUNCT
ejpam-5237	54	18	,	,	PUNCT
ejpam-5237	54	19	and	and	CCONJ
ejpam-5237	54	20	[	[	X
ejpam-5237	54	21	17	17	NUM
ejpam-5237	54	22	]	]	PUNCT
ejpam-5237	54	23	for	for	ADP
ejpam-5237	54	24	further	further	ADJ
ejpam-5237	54	25	insights	insight	NOUN
ejpam-5237	54	26	.	.	PUNCT
ejpam-5237	55	1	moreover	moreover	ADV
ejpam-5237	55	2	,	,	PUNCT
ejpam-5237	55	3	the	the	DET
ejpam-5237	55	4	realm	realm	NOUN
ejpam-5237	55	5	of	of	ADP
ejpam-5237	55	6	fractional	fractional	ADJ
ejpam-5237	55	7	and	and	CCONJ
ejpam-5237	55	8	generalized	generalized	ADJ
ejpam-5237	55	9	calculus	calculus	NOUN
ejpam-5237	55	10	has	have	AUX
ejpam-5237	55	11	witnessed	witness	VERB
ejpam-5237	55	12	a	a	DET
ejpam-5237	55	13	surge	surge	NOUN
ejpam-5237	55	14	in	in	ADP
ejpam-5237	55	15	applications	application	NOUN
ejpam-5237	55	16	across	across	ADP
ejpam-5237	55	17	various	various	ADJ
ejpam-5237	55	18	scientific	scientific	ADJ
ejpam-5237	55	19	and	and	CCONJ
ejpam-5237	55	20	technological	technological	ADJ
ejpam-5237	55	21	domains	domain	NOUN
ejpam-5237	55	22	[	[	X
ejpam-5237	55	23	6	6	NUM
ejpam-5237	55	24	,	,	PUNCT
ejpam-5237	55	25	10	10	NUM
ejpam-5237	55	26	,	,	PUNCT
ejpam-5237	55	27	13	13	NUM
ejpam-5237	55	28	]	]	PUNCT
ejpam-5237	55	29	,	,	PUNCT
ejpam-5237	55	30	showcasing	showcase	VERB
ejpam-5237	55	31	advancements	advancement	NOUN
ejpam-5237	55	32	beyond	beyond	ADP
ejpam-5237	55	33	the	the	DET
ejpam-5237	55	34	traditional	traditional	ADJ
ejpam-5237	55	35	integer	integer	NOUN
ejpam-5237	55	36	orders	order	NOUN
ejpam-5237	55	37	.	.	PUNCT
ejpam-5237	56	1	for	for	ADP
ejpam-5237	56	2	a	a	DET
ejpam-5237	56	3	comprehensive	comprehensive	ADJ
ejpam-5237	56	4	understanding	understanding	NOUN
ejpam-5237	56	5	of	of	ADP
ejpam-5237	56	6	historical	historical	ADJ
ejpam-5237	56	7	and	and	CCONJ
ejpam-5237	56	8	technical	technical	ADJ
ejpam-5237	56	9	aspects	aspect	NOUN
ejpam-5237	56	10	,	,	PUNCT
ejpam-5237	56	11	readers	reader	NOUN
ejpam-5237	56	12	are	be	AUX
ejpam-5237	56	13	encouraged	encourage	VERB
ejpam-5237	56	14	to	to	PART
ejpam-5237	56	15	explore	explore	VERB
ejpam-5237	56	16	[	[	X
ejpam-5237	56	17	14	14	NUM
ejpam-5237	56	18	]	]	PUNCT
ejpam-5237	56	19	.	.	PUNCT
ejpam-5237	57	1	this	this	DET
ejpam-5237	57	2	study	study	NOUN
ejpam-5237	57	3	delves	delve	VERB
ejpam-5237	57	4	into	into	ADP
ejpam-5237	57	5	the	the	DET
ejpam-5237	57	6	analysis	analysis	NOUN
ejpam-5237	57	7	and	and	CCONJ
ejpam-5237	57	8	comparison	comparison	NOUN
ejpam-5237	57	9	of	of	ADP
ejpam-5237	57	10	conformable	conformable	NOUN
ejpam-5237	57	11	,	,	PUNCT
ejpam-5237	57	12	riemann	riemann	PROPN
ejpam-5237	57	13	-	-	PUNCT
ejpam-5237	57	14	liouville	liouville	NOUN
ejpam-5237	57	15	,	,	PUNCT
ejpam-5237	57	16	and	and	CCONJ
ejpam-5237	57	17	caputo	caputo	PROPN
ejpam-5237	57	18	fractional	fractional	ADJ
ejpam-5237	57	19	derivatives	derivative	NOUN
ejpam-5237	57	20	with	with	ADP
ejpam-5237	57	21	order	order	NOUN
ejpam-5237	57	22	α	α	NOUN
ejpam-5237	57	23	,	,	PUNCT
ejpam-5237	57	24	where	where	SCONJ
ejpam-5237	57	25	0	0	X
ejpam-5237	57	26	<	<	X
ejpam-5237	57	27	α	α	X
ejpam-5237	57	28	<	<	X
ejpam-5237	57	29	1	1	NUM
ejpam-5237	57	30	.	.	PUNCT
ejpam-5237	57	31	to	to	PART
ejpam-5237	57	32	enable	enable	VERB
ejpam-5237	57	33	a	a	DET
ejpam-5237	57	34	comprehensive	comprehensive	ADJ
ejpam-5237	57	35	comparison	comparison	NOUN
ejpam-5237	57	36	,	,	PUNCT
ejpam-5237	57	37	we	we	PRON
ejpam-5237	57	38	conduct	conduct	VERB
ejpam-5237	57	39	numerical	numerical	ADJ
ejpam-5237	57	40	simulations	simulation	NOUN
ejpam-5237	57	41	to	to	PART
ejpam-5237	57	42	explore	explore	VERB
ejpam-5237	57	43	the	the	DET
ejpam-5237	57	44	solutions	solution	NOUN
ejpam-5237	57	45	of	of	ADP
ejpam-5237	57	46	fractional	fractional	ADJ
ejpam-5237	57	47	ordinary	ordinary	ADJ
ejpam-5237	57	48	differential	differential	ADJ
ejpam-5237	57	49	equations	equation	NOUN
ejpam-5237	57	50	incorporating	incorporate	VERB
ejpam-5237	57	51	these	these	DET
ejpam-5237	57	52	three	three	NUM
ejpam-5237	57	53	types	type	NOUN
ejpam-5237	57	54	of	of	ADP
ejpam-5237	57	55	fractional	fractional	ADJ
ejpam-5237	57	56	derivatives	derivative	NOUN
ejpam-5237	57	57	.	.	PUNCT
ejpam-5237	58	1	2	2	X
ejpam-5237	58	2	.	.	X
ejpam-5237	58	3	main	main	ADJ
ejpam-5237	58	4	results	result	NOUN
ejpam-5237	58	5	of	of	ADP
ejpam-5237	58	6	conformable	conformable	ADJ
ejpam-5237	58	7	derivative	derivative	ADJ
ejpam-5237	58	8	first	first	ADV
ejpam-5237	58	9	,	,	PUNCT
ejpam-5237	58	10	let	let	VERB
ejpam-5237	58	11	’s	’s	PRON
ejpam-5237	58	12	recall	recall	VERB
ejpam-5237	58	13	the	the	DET
ejpam-5237	58	14	definition	definition	NOUN
ejpam-5237	58	15	of	of	ADP
ejpam-5237	58	16	nα	nα	PRON
ejpam-5237	58	17	1	1	NUM
ejpam-5237	58	18	m(t	m(t	NOUN
ejpam-5237	58	19	)	)	PUNCT
ejpam-5237	58	20	,	,	PUNCT
ejpam-5237	58	21	which	which	PRON
ejpam-5237	58	22	represents	represent	VERB
ejpam-5237	58	23	a	a	DET
ejpam-5237	58	24	non	non	ADJ
ejpam-5237	58	25	-	-	ADJ
ejpam-5237	58	26	conformable	conformable	ADJ
ejpam-5237	58	27	fractional	fractional	ADJ
ejpam-5237	58	28	derivative	derivative	NOUN
ejpam-5237	58	29	of	of	ADP
ejpam-5237	58	30	a	a	DET
ejpam-5237	58	31	function	function	NOUN
ejpam-5237	58	32	at	at	ADP
ejpam-5237	58	33	a	a	DET
ejpam-5237	58	34	point	point	NOUN
ejpam-5237	58	35	t	t	NOUN
ejpam-5237	58	36	,	,	PUNCT
ejpam-5237	58	37	as	as	SCONJ
ejpam-5237	58	38	defined	define	VERB
ejpam-5237	58	39	in	in	ADP
ejpam-5237	58	40	[	[	X
ejpam-5237	58	41	13	13	NUM
ejpam-5237	58	42	]	]	PUNCT
ejpam-5237	58	43	.	.	PUNCT
ejpam-5237	59	1	this	this	DET
ejpam-5237	59	2	definition	definition	NOUN
ejpam-5237	59	3	forms	form	VERB
ejpam-5237	59	4	the	the	DET
ejpam-5237	59	5	basis	basis	NOUN
ejpam-5237	59	6	of	of	ADP
ejpam-5237	59	7	our	our	PRON
ejpam-5237	59	8	results	result	NOUN
ejpam-5237	59	9	,	,	PUNCT
ejpam-5237	59	10	which	which	PRON
ejpam-5237	59	11	closely	closely	ADV
ejpam-5237	59	12	resemble	resemble	VERB
ejpam-5237	59	13	those	those	PRON
ejpam-5237	59	14	found	find	VERB
ejpam-5237	59	15	in	in	ADP
ejpam-5237	59	16	classical	classical	ADJ
ejpam-5237	59	17	calculus	calculus	NOUN
ejpam-5237	59	18	.	.	PUNCT
ejpam-5237	60	1	a.	a.	PROPN
ejpam-5237	60	2	ait	ait	PROPN
ejpam-5237	60	3	brahim	brahim	PROPN
ejpam-5237	60	4	et	et	PROPN
ejpam-5237	60	5	all	all	DET
ejpam-5237	60	6	/	/	SYM
ejpam-5237	60	7	eur	eur	PROPN
ejpam-5237	60	8	.	.	PUNCT
ejpam-5237	61	1	j.	j.	PROPN
ejpam-5237	61	2	pure	pure	PROPN
ejpam-5237	61	3	appl	appl	PROPN
ejpam-5237	61	4	.	.	PROPN
ejpam-5237	61	5	math	math	PROPN
ejpam-5237	61	6	,	,	PUNCT
ejpam-5237	61	7	17	17	NUM
ejpam-5237	61	8	(	(	PUNCT
ejpam-5237	61	9	3	3	NUM
ejpam-5237	61	10	)	)	PUNCT
ejpam-5237	61	11	(	(	PUNCT
ejpam-5237	61	12	2024	2024	NUM
ejpam-5237	61	13	)	)	PUNCT
ejpam-5237	61	14	,	,	PUNCT
ejpam-5237	61	15	1842	1842	NUM
ejpam-5237	61	16	-	-	SYM
ejpam-5237	61	17	1854	1854	NUM
ejpam-5237	61	18	1845	1845	NUM
ejpam-5237	61	19	definition	definition	NOUN
ejpam-5237	61	20	1	1	NUM
ejpam-5237	61	21	.	.	PUNCT
ejpam-5237	62	1	(	(	PUNCT
ejpam-5237	62	2	see[13	see[13	PROPN
ejpam-5237	62	3	]	]	PUNCT
ejpam-5237	62	4	)	)	PUNCT
ejpam-5237	62	5	given	give	VERB
ejpam-5237	62	6	a	a	DET
ejpam-5237	62	7	function	function	NOUN
ejpam-5237	62	8	m	m	NOUN
ejpam-5237	62	9	:	:	PUNCT
ejpam-5237	63	1	[	[	X
ejpam-5237	63	2	0,+∞	0,+∞	NUM
ejpam-5237	63	3	)	)	PUNCT
ejpam-5237	63	4	→	→	PUNCT
ejpam-5237	63	5	r.	r.	PROPN
ejpam-5237	63	6	then	then	ADV
ejpam-5237	63	7	the	the	DET
ejpam-5237	63	8	n	n	ADV
ejpam-5237	63	9	-derivative	-derivative	NOUN
ejpam-5237	63	10	of	of	ADP
ejpam-5237	63	11	m	m	PRON
ejpam-5237	63	12	of	of	ADP
ejpam-5237	63	13	order	order	NOUN
ejpam-5237	63	14	α	α	NOUN
ejpam-5237	63	15	is	be	AUX
ejpam-5237	63	16	defined	define	VERB
ejpam-5237	63	17	by	by	ADP
ejpam-5237	63	18	nα	nα	PRON
ejpam-5237	63	19	1	1	NUM
ejpam-5237	63	20	m(t	m(t	NOUN
ejpam-5237	63	21	)	)	PUNCT
ejpam-5237	64	1	=	=	SYM
ejpam-5237	64	2	lim	lim	PROPN
ejpam-5237	64	3	ε→0	ε→0	NOUN
ejpam-5237	64	4	m	m	VERB
ejpam-5237	64	5	(	(	PUNCT
ejpam-5237	64	6	t+	t+	NOUN
ejpam-5237	64	7	εet	εet	PROPN
ejpam-5237	64	8	−α	−α	PROPN
ejpam-5237	64	9	)	)	PUNCT
ejpam-5237	64	10	−m(t	−m(t	PROPN
ejpam-5237	64	11	)	)	PUNCT
ejpam-5237	64	12	ε	ε	PROPN
ejpam-5237	64	13	,	,	PUNCT
ejpam-5237	64	14	(	(	PUNCT
ejpam-5237	64	15	4	4	X
ejpam-5237	64	16	)	)	PUNCT
ejpam-5237	64	17	for	for	ADP
ejpam-5237	64	18	all	all	DET
ejpam-5237	64	19	t	t	PROPN
ejpam-5237	64	20	>	>	X
ejpam-5237	64	21	0	0	PROPN
ejpam-5237	64	22	,	,	PUNCT
ejpam-5237	64	23	α	α	PROPN
ejpam-5237	64	24	∈	∈	PROPN
ejpam-5237	64	25	(	(	PUNCT
ejpam-5237	64	26	0	0	NUM
ejpam-5237	64	27	,	,	PUNCT
ejpam-5237	64	28	1	1	NUM
ejpam-5237	64	29	)	)	PUNCT
ejpam-5237	64	30	.	.	PUNCT
ejpam-5237	65	1	if	if	SCONJ
ejpam-5237	65	2	m	m	PROPN
ejpam-5237	65	3	is	be	AUX
ejpam-5237	65	4	α	α	NOUN
ejpam-5237	65	5	-	-	NOUN
ejpam-5237	65	6	differentiable	differentiable	ADJ
ejpam-5237	65	7	in	in	ADP
ejpam-5237	65	8	some	some	PRON
ejpam-5237	65	9	(	(	PUNCT
ejpam-5237	65	10	0	0	NUM
ejpam-5237	65	11	,	,	PUNCT
ejpam-5237	65	12	a	a	NOUN
ejpam-5237	65	13	)	)	PUNCT
ejpam-5237	65	14	,	,	PUNCT
ejpam-5237	65	15	and	and	CCONJ
ejpam-5237	65	16	limt→0	limt→0	PROPN
ejpam-5237	65	17	+	+	CCONJ
ejpam-5237	65	18	n	n	PROPN
ejpam-5237	65	19	(	(	PUNCT
ejpam-5237	65	20	α	α	NOUN
ejpam-5237	65	21	)	)	PUNCT
ejpam-5237	65	22	1	1	NUM
ejpam-5237	65	23	m(t	m(t	NOUN
ejpam-5237	65	24	)	)	PUNCT
ejpam-5237	65	25	exists	exist	VERB
ejpam-5237	65	26	,	,	PUNCT
ejpam-5237	65	27	then	then	ADV
ejpam-5237	65	28	define	define	VERB
ejpam-5237	65	29	n	n	PROPN
ejpam-5237	65	30	(	(	PUNCT
ejpam-5237	65	31	α	α	NOUN
ejpam-5237	65	32	)	)	PUNCT
ejpam-5237	65	33	1	1	NUM
ejpam-5237	65	34	m(0	m(0	PROPN
ejpam-5237	65	35	)	)	PUNCT
ejpam-5237	65	36	=	=	SYM
ejpam-5237	65	37	lim	lim	PROPN
ejpam-5237	65	38	t→0	t→0	PROPN
ejpam-5237	65	39	+	+	CCONJ
ejpam-5237	65	40	n	n	CCONJ
ejpam-5237	65	41	(	(	PUNCT
ejpam-5237	65	42	α	α	NOUN
ejpam-5237	65	43	)	)	PUNCT
ejpam-5237	65	44	1	1	NUM
ejpam-5237	65	45	m(t	m(t	NOUN
ejpam-5237	65	46	)	)	PUNCT
ejpam-5237	65	47	.	.	PUNCT
ejpam-5237	66	1	(	(	PUNCT
ejpam-5237	66	2	5	5	NUM
ejpam-5237	66	3	)	)	PUNCT
ejpam-5237	66	4	by	by	ADP
ejpam-5237	66	5	following	follow	VERB
ejpam-5237	66	6	an	an	DET
ejpam-5237	66	7	analogous	analogous	ADJ
ejpam-5237	66	8	procedure	procedure	NOUN
ejpam-5237	66	9	to	to	ADP
ejpam-5237	66	10	that	that	PRON
ejpam-5237	66	11	of	of	ADP
ejpam-5237	66	12	ordinary	ordinary	ADJ
ejpam-5237	66	13	calculus	calculus	NOUN
ejpam-5237	66	14	,	,	PUNCT
ejpam-5237	66	15	we	we	PRON
ejpam-5237	66	16	can	can	AUX
ejpam-5237	66	17	establish	establish	VERB
ejpam-5237	66	18	the	the	DET
ejpam-5237	66	19	following	follow	VERB
ejpam-5237	66	20	result	result	NOUN
ejpam-5237	66	21	.	.	PUNCT
ejpam-5237	67	1	definition	definition	NOUN
ejpam-5237	67	2	2	2	NUM
ejpam-5237	67	3	.	.	PUNCT
ejpam-5237	67	4	(	(	PUNCT
ejpam-5237	67	5	see[11	see[11	VERB
ejpam-5237	67	6	]	]	PUNCT
ejpam-5237	67	7	)	)	PUNCT
ejpam-5237	67	8	be	be	AUX
ejpam-5237	67	9	the	the	DET
ejpam-5237	67	10	function	function	NOUN
ejpam-5237	67	11	m	m	VERB
ejpam-5237	67	12	:	:	PUNCT
ejpam-5237	68	1	[	[	X
ejpam-5237	68	2	0,+∞	0,+∞	NUM
ejpam-5237	68	3	)	)	PUNCT
ejpam-5237	68	4	→	→	AUX
ejpam-5237	68	5	r.	r.	VERB
ejpam-5237	68	6	the	the	DET
ejpam-5237	68	7	n	n	NUM
ejpam-5237	68	8	-derivative	-derivative	NOUN
ejpam-5237	68	9	of	of	ADP
ejpam-5237	68	10	function	function	NOUN
ejpam-5237	68	11	m	m	NOUN
ejpam-5237	68	12	of	of	ADP
ejpam-5237	68	13	order	order	NOUN
ejpam-5237	68	14	α	α	NOUN
ejpam-5237	68	15	is	be	AUX
ejpam-5237	68	16	defined	define	VERB
ejpam-5237	68	17	by	by	ADP
ejpam-5237	68	18	nα	nα	PRON
ejpam-5237	68	19	fm(t	fm(t	NUM
ejpam-5237	68	20	)	)	PUNCT
ejpam-5237	69	1	=	=	SYM
ejpam-5237	69	2	lim	lim	PROPN
ejpam-5237	69	3	ε→0	ε→0	NOUN
ejpam-5237	69	4	m(t+	m(t+	PROPN
ejpam-5237	69	5	εf	εf	PROPN
ejpam-5237	69	6	(	(	PUNCT
ejpam-5237	69	7	t	t	PROPN
ejpam-5237	69	8	,	,	PUNCT
ejpam-5237	69	9	α))−m(t	α))−m(t	NOUN
ejpam-5237	69	10	)	)	PUNCT
ejpam-5237	69	11	ε	ε	PROPN
ejpam-5237	69	12	,	,	PUNCT
ejpam-5237	69	13	(	(	PUNCT
ejpam-5237	69	14	6	6	NUM
ejpam-5237	69	15	)	)	PUNCT
ejpam-5237	69	16	for	for	ADP
ejpam-5237	69	17	all	all	DET
ejpam-5237	69	18	t	t	PROPN
ejpam-5237	69	19	>	>	X
ejpam-5237	69	20	0	0	PROPN
ejpam-5237	69	21	,	,	PUNCT
ejpam-5237	69	22	α	α	PROPN
ejpam-5237	69	23	∈	∈	PROPN
ejpam-5237	69	24	(	(	PUNCT
ejpam-5237	69	25	0	0	NUM
ejpam-5237	69	26	,	,	PUNCT
ejpam-5237	69	27	1	1	X
ejpam-5237	69	28	)	)	PUNCT
ejpam-5237	69	29	being	be	AUX
ejpam-5237	69	30	f	f	X
ejpam-5237	69	31	(	(	PUNCT
ejpam-5237	69	32	α	α	PROPN
ejpam-5237	69	33	,	,	PUNCT
ejpam-5237	69	34	t	t	PROPN
ejpam-5237	69	35	)	)	PUNCT
ejpam-5237	69	36	is	be	AUX
ejpam-5237	69	37	some	some	DET
ejpam-5237	69	38	function	function	NOUN
ejpam-5237	69	39	.	.	PUNCT
ejpam-5237	70	1	here	here	ADV
ejpam-5237	70	2	we	we	PRON
ejpam-5237	70	3	will	will	AUX
ejpam-5237	70	4	use	use	VERB
ejpam-5237	70	5	some	some	DET
ejpam-5237	70	6	cases	case	NOUN
ejpam-5237	70	7	of	of	ADP
ejpam-5237	70	8	f	f	PROPN
ejpam-5237	70	9	defined	define	VERB
ejpam-5237	70	10	in	in	ADP
ejpam-5237	70	11	function	function	NOUN
ejpam-5237	70	12	of	of	ADP
ejpam-5237	70	13	ea	ea	PROPN
ejpam-5237	70	14	,	,	PUNCT
ejpam-5237	70	15	b	b	PROPN
ejpam-5237	70	16	(	(	PUNCT
ejpam-5237	70	17	)	)	PUNCT
ejpam-5237	70	18	.	.	PUNCT
ejpam-5237	71	1	theorem	theorem	NOUN
ejpam-5237	71	2	1	1	NUM
ejpam-5237	71	3	.	.	PUNCT
ejpam-5237	71	4	(	(	PUNCT
ejpam-5237	71	5	see[11	see[11	VERB
ejpam-5237	71	6	]	]	PUNCT
ejpam-5237	71	7	)	)	PUNCT
ejpam-5237	72	1	let	let	VERB
ejpam-5237	72	2	m	m	PRON
ejpam-5237	72	3	and	and	CCONJ
ejpam-5237	72	4	g	g	PROPN
ejpam-5237	72	5	be	be	VERB
ejpam-5237	72	6	n	n	ADV
ejpam-5237	72	7	-differentiable	-differentiable	ADJ
ejpam-5237	72	8	at	at	ADP
ejpam-5237	72	9	a	a	DET
ejpam-5237	72	10	point	point	NOUN
ejpam-5237	72	11	t	t	NOUN
ejpam-5237	72	12	>	>	X
ejpam-5237	72	13	0	0	PUNCT
ejpam-5237	73	1	and	and	CCONJ
ejpam-5237	73	2	α	α	PRON
ejpam-5237	73	3	∈	∈	PROPN
ejpam-5237	73	4	(	(	PUNCT
ejpam-5237	73	5	0	0	NUM
ejpam-5237	73	6	,	,	PUNCT
ejpam-5237	73	7	1	1	NUM
ejpam-5237	73	8	]	]	PUNCT
ejpam-5237	73	9	:	:	PUNCT
ejpam-5237	73	10	a	a	X
ejpam-5237	73	11	)	)	PUNCT
ejpam-5237	73	12	nα	nα	ADP
ejpam-5237	73	13	f	f	PROPN
ejpam-5237	73	14	(	(	PUNCT
ejpam-5237	73	15	am	be	AUX
ejpam-5237	73	16	+	+	X
ejpam-5237	73	17	bg)(t	bg)(t	PUNCT
ejpam-5237	73	18	)	)	PUNCT
ejpam-5237	74	1	=	=	PUNCT
ejpam-5237	74	2	anα	anα	PROPN
ejpam-5237	74	3	f	f	PROPN
ejpam-5237	74	4	(	(	PUNCT
ejpam-5237	74	5	m)(t	m)(t	PROPN
ejpam-5237	74	6	)	)	PUNCT
ejpam-5237	74	7	+	+	NUM
ejpam-5237	74	8	bnα	bnα	NOUN
ejpam-5237	74	9	f	f	PROPN
ejpam-5237	74	10	(	(	PUNCT
ejpam-5237	74	11	g)(t	g)(t	ADJ
ejpam-5237	74	12	)	)	PUNCT
ejpam-5237	74	13	.	.	PUNCT
ejpam-5237	75	1	b	b	X
ejpam-5237	75	2	)	)	PUNCT
ejpam-5237	75	3	na	na	ADP
ejpam-5237	75	4	f	f	PROPN
ejpam-5237	75	5	(	(	PUNCT
ejpam-5237	75	6	tp	tp	NOUN
ejpam-5237	75	7	)	)	PUNCT
ejpam-5237	75	8	=	=	SYM
ejpam-5237	75	9	et−αptt−1	et−αptt−1	NOUN
ejpam-5237	75	10	,	,	PUNCT
ejpam-5237	75	11	p	p	PROPN
ejpam-5237	75	12	∈	∈	PROPN
ejpam-5237	75	13	r.	r.	PROPN
ejpam-5237	75	14	c	c	NOUN
ejpam-5237	75	15	)	)	PUNCT
ejpam-5237	75	16	if	if	SCONJ
ejpam-5237	75	17	,	,	PUNCT
ejpam-5237	75	18	in	in	ADP
ejpam-5237	75	19	addition	addition	NOUN
ejpam-5237	75	20	,	,	PUNCT
ejpam-5237	75	21	m	m	VERB
ejpam-5237	75	22	is	be	AUX
ejpam-5237	75	23	differentiable	differentiable	ADJ
ejpam-5237	75	24	then	then	ADV
ejpam-5237	75	25	nf	nf	INTJ
ejpam-5237	75	26	(	(	PUNCT
ejpam-5237	75	27	m	m	NOUN
ejpam-5237	75	28	)	)	PUNCT
ejpam-5237	75	29	=	=	SYM
ejpam-5237	75	30	f	f	PROPN
ejpam-5237	75	31	(	(	PUNCT
ejpam-5237	75	32	t	t	PROPN
ejpam-5237	75	33	,	,	PUNCT
ejpam-5237	75	34	α)m	α)m	X
ejpam-5237	75	35	′(t	′(t	NOUN
ejpam-5237	75	36	)	)	PUNCT
ejpam-5237	75	37	.	.	PUNCT
ejpam-5237	76	1	definition	definition	NOUN
ejpam-5237	76	2	3	3	NUM
ejpam-5237	76	3	.	.	PUNCT
ejpam-5237	77	1	the	the	DET
ejpam-5237	77	2	conformable	conformable	ADJ
ejpam-5237	77	3	fractional	fractional	ADJ
ejpam-5237	77	4	derivative	derivative	NOUN
ejpam-5237	77	5	of	of	ADP
ejpam-5237	77	6	m	m	PRON
ejpam-5237	77	7	in	in	ADP
ejpam-5237	77	8	order	order	NOUN
ejpam-5237	77	9	α	α	NOUN
ejpam-5237	77	10	is	be	AUX
ejpam-5237	77	11	represented	represent	VERB
ejpam-5237	77	12	by	by	ADP
ejpam-5237	77	13	(	(	PUNCT
ejpam-5237	77	14	dαm	dαm	NOUN
ejpam-5237	77	15	)	)	PUNCT
ejpam-5237	77	16	(	(	PUNCT
ejpam-5237	77	17	t	t	NOUN
ejpam-5237	77	18	)	)	PUNCT
ejpam-5237	77	19	=	=	PROPN
ejpam-5237	77	20	lim	lim	PROPN
ejpam-5237	77	21	v→0	v→0	VERB
ejpam-5237	77	22	m	m	VERB
ejpam-5237	77	23	(	(	PUNCT
ejpam-5237	77	24	t+	t+	NOUN
ejpam-5237	77	25	ve(α−1)t	ve(α−1)t	PROPN
ejpam-5237	77	26	)	)	PUNCT
ejpam-5237	77	27	−m(t	−m(t	PROPN
ejpam-5237	77	28	)	)	PUNCT
ejpam-5237	77	29	v	v	NOUN
ejpam-5237	77	30	,	,	PUNCT
ejpam-5237	77	31	(	(	PUNCT
ejpam-5237	77	32	7	7	NUM
ejpam-5237	77	33	)	)	PUNCT
ejpam-5237	77	34	with	with	ADP
ejpam-5237	77	35	,	,	PUNCT
ejpam-5237	77	36	α	α	PROPN
ejpam-5237	77	37	∈	∈	PROPN
ejpam-5237	78	1	[	[	X
ejpam-5237	78	2	0	0	NUM
ejpam-5237	78	3	,	,	PUNCT
ejpam-5237	78	4	1	1	NUM
ejpam-5237	78	5	]	]	PUNCT
ejpam-5237	78	6	and	and	CCONJ
ejpam-5237	78	7	t	t	X
ejpam-5237	78	8	>	>	X
ejpam-5237	78	9	0	0	X
ejpam-5237	78	10	.	.	PUNCT
ejpam-5237	79	1	on	on	ADP
ejpam-5237	79	2	the	the	DET
ejpam-5237	79	3	other	other	ADJ
ejpam-5237	79	4	hand	hand	NOUN
ejpam-5237	79	5	if	if	SCONJ
ejpam-5237	79	6	m	m	NOUN
ejpam-5237	79	7	is	be	AUX
ejpam-5237	79	8	differentiable	differentiable	ADJ
ejpam-5237	79	9	of	of	ADP
ejpam-5237	79	10	order	order	NOUN
ejpam-5237	79	11	α	α	NOUN
ejpam-5237	79	12	in	in	ADP
ejpam-5237	79	13	[	[	X
ejpam-5237	79	14	0	0	NUM
ejpam-5237	79	15	,	,	PUNCT
ejpam-5237	79	16	a	a	PRON
ejpam-5237	79	17	]	]	X
ejpam-5237	79	18	,	,	PUNCT
ejpam-5237	79	19	a	a	PRON
ejpam-5237	79	20	>	>	X
ejpam-5237	79	21	0	0	NUM
ejpam-5237	79	22	,	,	PUNCT
ejpam-5237	79	23	and	and	CCONJ
ejpam-5237	79	24	limt→0	limt→0	PROPN
ejpam-5237	79	25	+	+	CCONJ
ejpam-5237	79	26	(	(	PUNCT
ejpam-5237	79	27	dαm	dαm	NOUN
ejpam-5237	79	28	)	)	PUNCT
ejpam-5237	79	29	(	(	PUNCT
ejpam-5237	79	30	t	t	NOUN
ejpam-5237	79	31	)	)	PUNCT
ejpam-5237	79	32	exists	exist	VERB
ejpam-5237	79	33	,	,	PUNCT
ejpam-5237	79	34	we	we	PRON
ejpam-5237	79	35	gets	get	VERB
ejpam-5237	79	36	dαm(0	dαm(0	ADJ
ejpam-5237	79	37	)	)	PUNCT
ejpam-5237	80	1	=	=	SYM
ejpam-5237	80	2	lim	lim	PROPN
ejpam-5237	80	3	t−→0	t−→0	PROPN
ejpam-5237	80	4	+	+	CCONJ
ejpam-5237	80	5	(	(	PUNCT
ejpam-5237	80	6	dαm)(t	dαm)(t	NOUN
ejpam-5237	80	7	)	)	PUNCT
ejpam-5237	80	8	.	.	PUNCT
ejpam-5237	81	1	(	(	PUNCT
ejpam-5237	81	2	8)	8)	NUM
ejpam-5237	81	3	theorem	theorem	NOUN
ejpam-5237	81	4	2	2	NUM
ejpam-5237	81	5	.	.	PUNCT
ejpam-5237	81	6	(	(	PUNCT
ejpam-5237	81	7	see	see	VERB
ejpam-5237	81	8	[	[	X
ejpam-5237	81	9	8	8	NUM
ejpam-5237	81	10	]	]	SYM
ejpam-5237	81	11	)	)	PUNCT
ejpam-5237	81	12	if	if	SCONJ
ejpam-5237	81	13	m	m	NOUN
ejpam-5237	81	14	differentiable	differentiable	ADJ
ejpam-5237	81	15	of	of	ADP
ejpam-5237	81	16	order	order	NOUN
ejpam-5237	81	17	α	α	NOUN
ejpam-5237	81	18	at	at	ADP
ejpam-5237	81	19	t0	t0	PROPN
ejpam-5237	81	20	>	>	PUNCT
ejpam-5237	81	21	0	0	PUNCT
ejpam-5237	81	22	and	and	CCONJ
ejpam-5237	81	23	m	m	PRON
ejpam-5237	81	24	:	:	PUNCT
ejpam-5237	82	1	[	[	X
ejpam-5237	82	2	0,+∞	0,+∞	NUM
ejpam-5237	82	3	)	)	PUNCT
ejpam-5237	83	1	−→	−→	NOUN
ejpam-5237	83	2	r	r	NOUN
ejpam-5237	83	3	then	then	ADV
ejpam-5237	83	4	m	m	VERB
ejpam-5237	83	5	is	be	AUX
ejpam-5237	83	6	continuous	continuous	ADJ
ejpam-5237	83	7	at	at	ADP
ejpam-5237	83	8	t0	t0	PROPN
ejpam-5237	83	9	.	.	PUNCT
ejpam-5237	84	1	theorem	theorem	VERB
ejpam-5237	84	2	3	3	NUM
ejpam-5237	84	3	.	.	PUNCT
ejpam-5237	84	4	(	(	PUNCT
ejpam-5237	84	5	see[8	see[8	NOUN
ejpam-5237	84	6	]	]	PUNCT
ejpam-5237	84	7	)	)	PUNCT
ejpam-5237	84	8	if	if	SCONJ
ejpam-5237	84	9	m	m	NOUN
ejpam-5237	84	10	be	be	VERB
ejpam-5237	84	11	α	α	NOUN
ejpam-5237	84	12	differentiable	differentiable	ADJ
ejpam-5237	84	13	at	at	ADP
ejpam-5237	84	14	a	a	DET
ejpam-5237	84	15	point	point	NOUN
ejpam-5237	84	16	t	t	NOUN
ejpam-5237	84	17	>	>	X
ejpam-5237	84	18	0	0	X
ejpam-5237	84	19	.	.	PUNCT
ejpam-5237	85	1	we	we	PRON
ejpam-5237	85	2	have	have	VERB
ejpam-5237	85	3	(	(	PUNCT
ejpam-5237	85	4	i	i	NOUN
ejpam-5237	85	5	)	)	PUNCT
ejpam-5237	85	6	dα(am	dα(am	PROPN
ejpam-5237	85	7	+	+	CCONJ
ejpam-5237	85	8	bm	bm	PROPN
ejpam-5237	85	9	)	)	PUNCT
ejpam-5237	85	10	=	=	SYM
ejpam-5237	86	1	a	a	DET
ejpam-5237	86	2	(	(	PUNCT
ejpam-5237	86	3	dαm	dαm	NOUN
ejpam-5237	86	4	)	)	PUNCT
ejpam-5237	87	1	+	+	SYM
ejpam-5237	87	2	b	b	X
ejpam-5237	87	3	(	(	PUNCT
ejpam-5237	87	4	dαm	dαm	NOUN
ejpam-5237	87	5	)	)	PUNCT
ejpam-5237	87	6	,	,	PUNCT
ejpam-5237	87	7	for	for	ADP
ejpam-5237	87	8	all	all	DET
ejpam-5237	87	9	a	a	PRON
ejpam-5237	87	10	,	,	PUNCT
ejpam-5237	87	11	b	b	X
ejpam-5237	87	12	∈	∈	PROPN
ejpam-5237	87	13	r	r	NOUN
ejpam-5237	87	14	(	(	PUNCT
ejpam-5237	87	15	ii	ii	NOUN
ejpam-5237	87	16	)	)	PUNCT
ejpam-5237	87	17	(	(	PUNCT
ejpam-5237	87	18	dα(m	dα(m	NOUN
ejpam-5237	87	19	/	/	SYM
ejpam-5237	87	20	h	h	NOUN
ejpam-5237	87	21	)	)	PUNCT
ejpam-5237	87	22	)	)	PUNCT
ejpam-5237	88	1	=	=	PRON
ejpam-5237	88	2	(	(	PUNCT
ejpam-5237	88	3	m	m	PROPN
ejpam-5237	88	4	(	(	PUNCT
ejpam-5237	88	5	dαh	dαh	PROPN
ejpam-5237	88	6	)	)	PUNCT
ejpam-5237	89	1	+	+	NOUN
ejpam-5237	89	2	h	h	NOUN
ejpam-5237	89	3	(	(	PUNCT
ejpam-5237	89	4	dαm	dαm	NOUN
ejpam-5237	89	5	)	)	PUNCT
ejpam-5237	89	6	)	)	PUNCT
ejpam-5237	89	7	/h2	/h2	PROPN
ejpam-5237	89	8	.	.	PUNCT
ejpam-5237	90	1	(	(	PUNCT
ejpam-5237	90	2	iii	iii	X
ejpam-5237	90	3	)	)	PUNCT
ejpam-5237	90	4	if	if	SCONJ
ejpam-5237	90	5	m	m	NOUN
ejpam-5237	90	6	is	be	AUX
ejpam-5237	90	7	differentiable	differentiable	ADJ
ejpam-5237	90	8	,	,	PUNCT
ejpam-5237	90	9	then	then	ADV
ejpam-5237	90	10	(	(	PUNCT
ejpam-5237	90	11	dαm	dαm	NOUN
ejpam-5237	90	12	)	)	PUNCT
ejpam-5237	90	13	(	(	PUNCT
ejpam-5237	90	14	t	t	NOUN
ejpam-5237	90	15	)	)	PUNCT
ejpam-5237	90	16	=	=	SYM
ejpam-5237	90	17	e(α−1)tm	e(α−1)tm	NUM
ejpam-5237	90	18	′(t	′(t	PROPN
ejpam-5237	90	19	)	)	PUNCT
ejpam-5237	90	20	.	.	PUNCT
ejpam-5237	91	1	a.	a.	PROPN
ejpam-5237	91	2	ait	ait	PROPN
ejpam-5237	91	3	brahim	brahim	PROPN
ejpam-5237	91	4	et	et	PROPN
ejpam-5237	91	5	all	all	DET
ejpam-5237	91	6	/	/	SYM
ejpam-5237	91	7	eur	eur	PROPN
ejpam-5237	91	8	.	.	PUNCT
ejpam-5237	92	1	j.	j.	PROPN
ejpam-5237	92	2	pure	pure	PROPN
ejpam-5237	92	3	appl	appl	PROPN
ejpam-5237	92	4	.	.	PROPN
ejpam-5237	92	5	math	math	PROPN
ejpam-5237	92	6	,	,	PUNCT
ejpam-5237	92	7	17	17	NUM
ejpam-5237	92	8	(	(	PUNCT
ejpam-5237	92	9	3	3	NUM
ejpam-5237	92	10	)	)	PUNCT
ejpam-5237	92	11	(	(	PUNCT
ejpam-5237	92	12	2024	2024	NUM
ejpam-5237	92	13	)	)	PUNCT
ejpam-5237	92	14	,	,	PUNCT
ejpam-5237	92	15	1842	1842	NUM
ejpam-5237	92	16	-	-	SYM
ejpam-5237	92	17	1854	1854	NUM
ejpam-5237	92	18	1846	1846	NUM
ejpam-5237	92	19	3	3	NUM
ejpam-5237	92	20	.	.	PUNCT
ejpam-5237	92	21	fractional	fractional	ADJ
ejpam-5237	92	22	ordinary	ordinary	ADJ
ejpam-5237	92	23	differential	differential	ADJ
ejpam-5237	92	24	equations	equation	NOUN
ejpam-5237	92	25	:	:	PUNCT
ejpam-5237	92	26	3.1	3.1	NUM
ejpam-5237	92	27	.	.	PUNCT
ejpam-5237	92	28	fractional	fractional	ADJ
ejpam-5237	92	29	ordinary	ordinary	ADJ
ejpam-5237	92	30	differential	differential	ADJ
ejpam-5237	92	31	equation	equation	NOUN
ejpam-5237	92	32	with	with	ADP
ejpam-5237	92	33	non	non	ADJ
ejpam-5237	92	34	-	-	ADJ
ejpam-5237	92	35	conformable	conformable	ADJ
ejpam-5237	92	36	fractional	fractional	ADJ
ejpam-5237	92	37	derivative	derivative	NOUN
ejpam-5237	92	38	the	the	DET
ejpam-5237	92	39	initial	initial	ADJ
ejpam-5237	92	40	value	value	NOUN
ejpam-5237	92	41	problem	problem	NOUN
ejpam-5237	92	42	of	of	ADP
ejpam-5237	92	43	fractional	fractional	ADJ
ejpam-5237	92	44	ordinary	ordinary	ADJ
ejpam-5237	92	45	differential	differential	ADJ
ejpam-5237	92	46	equations	equation	NOUN
ejpam-5237	92	47	with	with	ADP
ejpam-5237	92	48	generalized	generalized	ADJ
ejpam-5237	92	49	derivative	derivative	NOUN
ejpam-5237	92	50	,	,	PUNCT
ejpam-5237	92	51	for	for	ADP
ejpam-5237	92	52	0	0	NUM
ejpam-5237	92	53	<	<	X
ejpam-5237	92	54	α	α	X
ejpam-5237	92	55	<	<	X
ejpam-5237	92	56	1	1	NUM
ejpam-5237	92	57	nα	nα	PROPN
ejpam-5237	92	58	f	f	PROPN
ejpam-5237	92	59	y(t	y(t	PROPN
ejpam-5237	92	60	)	)	PUNCT
ejpam-5237	92	61	=	=	SYM
ejpam-5237	93	1	λy(t	λy(t	NOUN
ejpam-5237	93	2	)	)	PUNCT
ejpam-5237	93	3	,	,	PUNCT
ejpam-5237	93	4	(	(	PUNCT
ejpam-5237	93	5	9	9	X
ejpam-5237	93	6	)	)	PUNCT
ejpam-5237	93	7	with	with	ADP
ejpam-5237	93	8	the	the	DET
ejpam-5237	93	9	initial	initial	ADJ
ejpam-5237	93	10	condition	condition	NOUN
ejpam-5237	93	11	y(t0	y(t0	NOUN
ejpam-5237	93	12	)	)	PUNCT
ejpam-5237	94	1	=	=	PUNCT
ejpam-5237	94	2	y0	y0	NOUN
ejpam-5237	94	3	has	have	VERB
ejpam-5237	94	4	the	the	DET
ejpam-5237	94	5	solution	solution	NOUN
ejpam-5237	94	6	y(t	y(t	NUM
ejpam-5237	94	7	)	)	PUNCT
ejpam-5237	95	1	=	=	SYM
ejpam-5237	95	2	y0e	y0e	NOUN
ejpam-5237	95	3	λ(t−t0	λ(t−t0	NOUN
ejpam-5237	95	4	)	)	PUNCT
ejpam-5237	95	5	.	.	PUNCT
ejpam-5237	96	1	(	(	PUNCT
ejpam-5237	96	2	10	10	NUM
ejpam-5237	96	3	)	)	PUNCT
ejpam-5237	96	4	in	in	ADP
ejpam-5237	96	5	general	general	ADJ
ejpam-5237	96	6	form	form	NOUN
ejpam-5237	96	7	,	,	PUNCT
ejpam-5237	96	8	if	if	SCONJ
ejpam-5237	96	9	instead	instead	ADV
ejpam-5237	96	10	of	of	ADP
ejpam-5237	96	11	(	(	PUNCT
ejpam-5237	96	12	9	9	X
ejpam-5237	96	13	)	)	PUNCT
ejpam-5237	96	14	we	we	PRON
ejpam-5237	96	15	have	have	VERB
ejpam-5237	96	16	:	:	PUNCT
ejpam-5237	97	1	nα	nα	VERB
ejpam-5237	97	2	f	f	PROPN
ejpam-5237	97	3	y(t	y(t	PROPN
ejpam-5237	97	4	)	)	PUNCT
ejpam-5237	98	1	=	=	SYM
ejpam-5237	98	2	f(t	f(t	NOUN
ejpam-5237	98	3	)	)	PUNCT
ejpam-5237	98	4	,	,	PUNCT
ejpam-5237	98	5	(	(	PUNCT
ejpam-5237	98	6	11	11	NUM
ejpam-5237	98	7	)	)	PUNCT
ejpam-5237	98	8	with	with	ADP
ejpam-5237	98	9	the	the	DET
ejpam-5237	98	10	initial	initial	ADJ
ejpam-5237	98	11	condition	condition	NOUN
ejpam-5237	98	12	y(t0	y(t0	NOUN
ejpam-5237	98	13	)	)	PUNCT
ejpam-5237	99	1	=	=	SYM
ejpam-5237	99	2	y0	y0	NOUN
ejpam-5237	99	3	,	,	PUNCT
ejpam-5237	99	4	the	the	DET
ejpam-5237	99	5	solution	solution	NOUN
ejpam-5237	99	6	is	be	AUX
ejpam-5237	99	7	y(t	y(t	NOUN
ejpam-5237	99	8	)	)	PUNCT
ejpam-5237	100	1	=	=	SYM
ejpam-5237	100	2	y0e	y0e	NOUN
ejpam-5237	100	3	∫	∫	PROPN
ejpam-5237	100	4	t	t	PROPN
ejpam-5237	100	5	t0	t0	PROPN
ejpam-5237	100	6	f(s)dαf	f(s)dαf	PROPN
ejpam-5237	100	7	s	s	PART
ejpam-5237	100	8	=	=	PUNCT
ejpam-5237	100	9	y0e	y0e	NOUN
ejpam-5237	100	10	nf	nf	NOUN
ejpam-5237	100	11	jα	jα	PROPN
ejpam-5237	100	12	t0	t0	PROPN
ejpam-5237	100	13	f(t	f(t	PROPN
ejpam-5237	100	14	)	)	PUNCT
ejpam-5237	100	15	.	.	PUNCT
ejpam-5237	101	1	(	(	PUNCT
ejpam-5237	101	2	12	12	NUM
ejpam-5237	101	3	)	)	PUNCT
ejpam-5237	101	4	3.2	3.2	NUM
ejpam-5237	101	5	.	.	PUNCT
ejpam-5237	102	1	fractional	fractional	ADJ
ejpam-5237	102	2	ordinary	ordinary	ADJ
ejpam-5237	102	3	differential	differential	ADJ
ejpam-5237	102	4	equation	equation	NOUN
ejpam-5237	102	5	with	with	ADP
ejpam-5237	102	6	riemann	riemann	PROPN
ejpam-5237	102	7	liouville	liouville	PROPN
ejpam-5237	102	8	,	,	PUNCT
ejpam-5237	102	9	caputo	caputo	PROPN
ejpam-5237	102	10	,	,	PUNCT
ejpam-5237	102	11	and	and	CCONJ
ejpam-5237	102	12	conformable	conformable	ADJ
ejpam-5237	102	13	fractional	fractional	ADJ
ejpam-5237	102	14	derivatives	derivative	NOUN
ejpam-5237	102	15	this	this	DET
ejpam-5237	102	16	section	section	NOUN
ejpam-5237	102	17	discusses	discuss	VERB
ejpam-5237	102	18	solutions	solution	NOUN
ejpam-5237	102	19	to	to	PART
ejpam-5237	102	20	fractional	fractional	VERB
ejpam-5237	102	21	ordinary	ordinary	ADJ
ejpam-5237	102	22	differential	differential	ADJ
ejpam-5237	102	23	equations	equation	NOUN
ejpam-5237	102	24	using	use	VERB
ejpam-5237	102	25	riemann	riemann	PROPN
ejpam-5237	102	26	liouville	liouville	PROPN
ejpam-5237	102	27	,	,	PUNCT
ejpam-5237	102	28	caputo	caputo	PROPN
ejpam-5237	102	29	,	,	PUNCT
ejpam-5237	102	30	and	and	CCONJ
ejpam-5237	102	31	conformable	conformable	ADJ
ejpam-5237	102	32	fractional	fractional	ADJ
ejpam-5237	102	33	derivatives	derivative	NOUN
ejpam-5237	102	34	and	and	CCONJ
ejpam-5237	102	35	then	then	ADV
ejpam-5237	102	36	their	their	PRON
ejpam-5237	102	37	numerical	numerical	ADJ
ejpam-5237	102	38	simulations	simulation	NOUN
ejpam-5237	102	39	.	.	PUNCT
ejpam-5237	103	1	for	for	ADP
ejpam-5237	103	2	more	more	ADJ
ejpam-5237	103	3	detail	detail	NOUN
ejpam-5237	103	4	concerning	concern	VERB
ejpam-5237	103	5	these	these	PRON
ejpam-5237	103	6	,	,	PUNCT
ejpam-5237	103	7	one	one	PRON
ejpam-5237	103	8	can	can	AUX
ejpam-5237	103	9	refer	refer	VERB
ejpam-5237	103	10	to	to	ADP
ejpam-5237	103	11	abdeljawad	abdeljawad	NOUN
ejpam-5237	103	12	(	(	PUNCT
ejpam-5237	103	13	2015	2015	NUM
ejpam-5237	103	14	)	)	PUNCT
ejpam-5237	103	15	,	,	PUNCT
ejpam-5237	103	16	khalil	khalil	PROPN
ejpam-5237	103	17	et	et	PROPN
ejpam-5237	103	18	al	al	PROPN
ejpam-5237	103	19	.	.	PROPN
ejpam-5237	104	1	(	(	PUNCT
ejpam-5237	104	2	2014	2014	NUM
ejpam-5237	104	3	)	)	PUNCT
ejpam-5237	104	4	,	,	PUNCT
ejpam-5237	104	5	podlubny	podlubny	NOUN
ejpam-5237	104	6	(	(	PUNCT
ejpam-5237	104	7	1999	1999	NUM
ejpam-5237	104	8	)	)	PUNCT
ejpam-5237	104	9	,	,	PUNCT
ejpam-5237	104	10	and	and	CCONJ
ejpam-5237	104	11	kilbas	kilbas	PROPN
ejpam-5237	104	12	(	(	PUNCT
ejpam-5237	104	13	2006	2006	NUM
ejpam-5237	104	14	)	)	PUNCT
ejpam-5237	104	15	.	.	PUNCT
ejpam-5237	105	1	solutions	solution	VERB
ejpam-5237	105	2	the	the	DET
ejpam-5237	105	3	initial	initial	ADJ
ejpam-5237	105	4	value	value	NOUN
ejpam-5237	105	5	problem	problem	NOUN
ejpam-5237	105	6	of	of	ADP
ejpam-5237	105	7	fractional	fractional	ADJ
ejpam-5237	105	8	ordinary	ordinary	ADJ
ejpam-5237	105	9	differential	differential	ADJ
ejpam-5237	105	10	equations	equation	NOUN
ejpam-5237	105	11	with	with	ADP
ejpam-5237	105	12	riemann	riemann	PROPN
ejpam-5237	105	13	-	-	PUNCT
ejpam-5237	105	14	liouville	liouville	VERB
ejpam-5237	105	15	fractional	fractional	ADJ
ejpam-5237	105	16	derivative	derivative	NOUN
ejpam-5237	105	17	,	,	PUNCT
ejpam-5237	105	18	for	for	ADP
ejpam-5237	105	19	0	0	NUM
ejpam-5237	105	20	<	<	X
ejpam-5237	105	21	α	α	X
ejpam-5237	105	22	<	<	X
ejpam-5237	105	23	1	1	NUM
ejpam-5237	105	24	,	,	PUNCT
ejpam-5237	105	25	rdα	rdα	PROPN
ejpam-5237	105	26	t	t	PROPN
ejpam-5237	105	27	w(t	w(t	PROPN
ejpam-5237	105	28	)	)	PUNCT
ejpam-5237	105	29	=	=	PUNCT
ejpam-5237	106	1	λw(t	λw(t	PUNCT
ejpam-5237	106	2	)	)	PUNCT
ejpam-5237	106	3	,	,	PUNCT
ejpam-5237	106	4	t	t	PROPN
ejpam-5237	106	5	>	>	X
ejpam-5237	106	6	0	0	NUM
ejpam-5237	106	7	,	,	PUNCT
ejpam-5237	106	8	(	(	PUNCT
ejpam-5237	106	9	13	13	NUM
ejpam-5237	106	10	)	)	PUNCT
ejpam-5237	106	11	with	with	ADP
ejpam-5237	106	12	the	the	DET
ejpam-5237	106	13	initial	initial	ADJ
ejpam-5237	106	14	condition	condition	NOUN
ejpam-5237	106	15	i1−α	i1−α	PROPN
ejpam-5237	106	16	t	t	PROPN
ejpam-5237	106	17	w(t	w(t	PROPN
ejpam-5237	106	18	)	)	PUNCT
ejpam-5237	106	19	∣∣	∣∣	NUM
ejpam-5237	106	20	t=0	t=0	PROPN
ejpam-5237	106	21	=	=	SYM
ejpam-5237	106	22	w0	w0	PROPN
ejpam-5237	106	23	,	,	PUNCT
ejpam-5237	106	24	(	(	PUNCT
ejpam-5237	106	25	14	14	NUM
ejpam-5237	106	26	)	)	PUNCT
ejpam-5237	106	27	has	have	VERB
ejpam-5237	106	28	the	the	DET
ejpam-5237	106	29	solution	solution	NOUN
ejpam-5237	106	30	w(t	w(t	PROPN
ejpam-5237	106	31	)	)	PUNCT
ejpam-5237	106	32	=	=	SYM
ejpam-5237	106	33	w0	w0	PROPN
ejpam-5237	106	34	t	t	PROPN
ejpam-5237	106	35	α−1eα	α−1eα	NOUN
ejpam-5237	106	36	,	,	PUNCT
ejpam-5237	106	37	α	α	PROPN
ejpam-5237	106	38	(	(	PUNCT
ejpam-5237	106	39	λt	λt	ADP
ejpam-5237	106	40	α	α	NOUN
ejpam-5237	106	41	)	)	PUNCT
ejpam-5237	106	42	,	,	PUNCT
ejpam-5237	106	43	(	(	PUNCT
ejpam-5237	106	44	15	15	NUM
ejpam-5237	106	45	)	)	PUNCT
ejpam-5237	106	46	where	where	SCONJ
ejpam-5237	106	47	eα	eα	NOUN
ejpam-5237	106	48	,	,	PUNCT
ejpam-5237	106	49	β	β	X
ejpam-5237	106	50	is	be	AUX
ejpam-5237	106	51	the	the	DET
ejpam-5237	106	52	mittag	mittag	ADJ
ejpam-5237	106	53	-	-	PUNCT
ejpam-5237	106	54	leffler	leffler	NOUN
ejpam-5237	106	55	function	function	NOUN
ejpam-5237	106	56	defined	define	VERB
ejpam-5237	106	57	by	by	ADP
ejpam-5237	106	58	eα	eα	NOUN
ejpam-5237	106	59	,	,	PUNCT
ejpam-5237	106	60	β(t	β(t	PROPN
ejpam-5237	106	61	)	)	PUNCT
ejpam-5237	106	62	=	=	PUNCT
ejpam-5237	107	1	∞∑	∞∑	NUM
ejpam-5237	107	2	k=0	k=0	PROPN
ejpam-5237	107	3	tk	tk	PROPN
ejpam-5237	107	4	γ(αk	γ(αk	PROPN
ejpam-5237	107	5	+	+	CCONJ
ejpam-5237	107	6	β	β	NOUN
ejpam-5237	107	7	)	)	PUNCT
ejpam-5237	107	8	,	,	PUNCT
ejpam-5237	107	9	α	α	X
ejpam-5237	107	10	,	,	PUNCT
ejpam-5237	107	11	β	β	X
ejpam-5237	107	12	>	>	X
ejpam-5237	107	13	0	0	NUM
ejpam-5237	107	14	.	.	PUNCT
ejpam-5237	108	1	(	(	PUNCT
ejpam-5237	108	2	16	16	NUM
ejpam-5237	108	3	)	)	PUNCT
ejpam-5237	108	4	a.	a.	NOUN
ejpam-5237	108	5	ait	ait	NOUN
ejpam-5237	108	6	brahim	brahim	PROPN
ejpam-5237	108	7	et	et	PROPN
ejpam-5237	108	8	all	all	DET
ejpam-5237	108	9	/	/	SYM
ejpam-5237	108	10	eur	eur	PROPN
ejpam-5237	108	11	.	.	PUNCT
ejpam-5237	109	1	j.	j.	PROPN
ejpam-5237	109	2	pure	pure	PROPN
ejpam-5237	109	3	appl	appl	PROPN
ejpam-5237	109	4	.	.	PROPN
ejpam-5237	109	5	math	math	PROPN
ejpam-5237	109	6	,	,	PUNCT
ejpam-5237	109	7	17	17	NUM
ejpam-5237	109	8	(	(	PUNCT
ejpam-5237	109	9	3	3	NUM
ejpam-5237	109	10	)	)	PUNCT
ejpam-5237	109	11	(	(	PUNCT
ejpam-5237	109	12	2024	2024	NUM
ejpam-5237	109	13	)	)	PUNCT
ejpam-5237	109	14	,	,	PUNCT
ejpam-5237	109	15	1842	1842	NUM
ejpam-5237	109	16	-	-	SYM
ejpam-5237	109	17	1854	1854	NUM
ejpam-5237	109	18	1847	1847	NUM
ejpam-5237	109	19	figure	figure	NOUN
ejpam-5237	109	20	1	1	NUM
ejpam-5237	109	21	:	:	PUNCT
ejpam-5237	109	22	comparative	comparative	ADJ
ejpam-5237	109	23	solutions	solution	NOUN
ejpam-5237	109	24	for	for	ADP
ejpam-5237	109	25	serval	serval	NOUN
ejpam-5237	109	26	values	value	NOUN
ejpam-5237	109	27	of	of	ADP
ejpam-5237	109	28	α	α	NOUN
ejpam-5237	109	29	,	,	PUNCT
ejpam-5237	109	30	with	with	ADP
ejpam-5237	109	31	riemann	riemann	PROPN
ejpam-5237	109	32	-	-	PUNCT
ejpam-5237	109	33	liouville	liouville	VERB
ejpam-5237	109	34	fractional	fractional	ADJ
ejpam-5237	109	35	derivative	derivative	NOUN
ejpam-5237	109	36	.	.	PUNCT
ejpam-5237	110	1	the	the	DET
ejpam-5237	110	2	initial	initial	ADJ
ejpam-5237	110	3	value	value	NOUN
ejpam-5237	110	4	problem	problem	NOUN
ejpam-5237	110	5	of	of	ADP
ejpam-5237	110	6	fractional	fractional	ADJ
ejpam-5237	110	7	ordinary	ordinary	ADJ
ejpam-5237	110	8	differential	differential	ADJ
ejpam-5237	110	9	equations	equation	NOUN
ejpam-5237	110	10	with	with	ADP
ejpam-5237	110	11	caputo	caputo	PROPN
ejpam-5237	110	12	fractional	fractional	PROPN
ejpam-5237	110	13	derivative	derivative	NOUN
ejpam-5237	110	14	,	,	PUNCT
ejpam-5237	110	15	for	for	ADP
ejpam-5237	110	16	0	0	NUM
ejpam-5237	110	17	<	<	X
ejpam-5237	110	18	α	α	X
ejpam-5237	110	19	<	<	X
ejpam-5237	110	20	1	1	NUM
ejpam-5237	110	21	,	,	PUNCT
ejpam-5237	110	22	cdα	cdα	NOUN
ejpam-5237	110	23	t	t	PROPN
ejpam-5237	110	24	w(t	w(t	PROPN
ejpam-5237	110	25	)	)	PUNCT
ejpam-5237	110	26	=	=	PUNCT
ejpam-5237	111	1	λw(t	λw(t	PUNCT
ejpam-5237	111	2	)	)	PUNCT
ejpam-5237	111	3	,	,	PUNCT
ejpam-5237	111	4	t	t	PROPN
ejpam-5237	111	5	>	>	X
ejpam-5237	111	6	0	0	NUM
ejpam-5237	111	7	,	,	PUNCT
ejpam-5237	111	8	(	(	PUNCT
ejpam-5237	111	9	17	17	NUM
ejpam-5237	111	10	)	)	PUNCT
ejpam-5237	111	11	with	with	ADP
ejpam-5237	111	12	the	the	DET
ejpam-5237	111	13	initial	initial	ADJ
ejpam-5237	111	14	condition	condition	NOUN
ejpam-5237	111	15	w(t)|t=0	w(t)|t=0	PUNCT
ejpam-5237	112	1	=	=	SYM
ejpam-5237	112	2	w0	w0	PROPN
ejpam-5237	112	3	,	,	PUNCT
ejpam-5237	112	4	(	(	PUNCT
ejpam-5237	112	5	18	18	NUM
ejpam-5237	112	6	)	)	PUNCT
ejpam-5237	112	7	has	have	VERB
ejpam-5237	112	8	the	the	DET
ejpam-5237	112	9	solution	solution	NOUN
ejpam-5237	112	10	w(t	w(t	PROPN
ejpam-5237	112	11	)	)	PUNCT
ejpam-5237	113	1	=	=	SYM
ejpam-5237	113	2	w0eα,1	w0eα,1	PROPN
ejpam-5237	113	3	(	(	PUNCT
ejpam-5237	113	4	λt	λt	ADP
ejpam-5237	113	5	α	α	NOUN
ejpam-5237	113	6	)	)	PUNCT
ejpam-5237	113	7	.	.	PUNCT
ejpam-5237	114	1	(	(	PUNCT
ejpam-5237	114	2	19	19	NUM
ejpam-5237	114	3	)	)	PUNCT
ejpam-5237	114	4	figure	figure	NOUN
ejpam-5237	114	5	2	2	NUM
ejpam-5237	114	6	:	:	PUNCT
ejpam-5237	114	7	comparative	comparative	ADJ
ejpam-5237	114	8	solutions	solution	NOUN
ejpam-5237	114	9	for	for	ADP
ejpam-5237	114	10	serval	serval	NOUN
ejpam-5237	114	11	values	value	NOUN
ejpam-5237	114	12	of	of	ADP
ejpam-5237	114	13	α	α	NOUN
ejpam-5237	114	14	,	,	PUNCT
ejpam-5237	114	15	with	with	ADP
ejpam-5237	114	16	caputo	caputo	PROPN
ejpam-5237	114	17	fractional	fractional	PROPN
ejpam-5237	114	18	derivative	derivative	PROPN
ejpam-5237	114	19	.	.	PUNCT
ejpam-5237	115	1	a.	a.	PROPN
ejpam-5237	115	2	ait	ait	PROPN
ejpam-5237	115	3	brahim	brahim	PROPN
ejpam-5237	115	4	et	et	PROPN
ejpam-5237	115	5	all	all	DET
ejpam-5237	115	6	/	/	SYM
ejpam-5237	115	7	eur	eur	PROPN
ejpam-5237	115	8	.	.	PUNCT
ejpam-5237	116	1	j.	j.	PROPN
ejpam-5237	116	2	pure	pure	PROPN
ejpam-5237	116	3	appl	appl	PROPN
ejpam-5237	116	4	.	.	PROPN
ejpam-5237	116	5	math	math	PROPN
ejpam-5237	116	6	,	,	PUNCT
ejpam-5237	116	7	17	17	NUM
ejpam-5237	116	8	(	(	PUNCT
ejpam-5237	116	9	3	3	NUM
ejpam-5237	116	10	)	)	PUNCT
ejpam-5237	116	11	(	(	PUNCT
ejpam-5237	116	12	2024	2024	NUM
ejpam-5237	116	13	)	)	PUNCT
ejpam-5237	116	14	,	,	PUNCT
ejpam-5237	116	15	1842	1842	NUM
ejpam-5237	116	16	-	-	SYM
ejpam-5237	116	17	1854	1854	NUM
ejpam-5237	116	18	1848	1848	NUM
ejpam-5237	116	19	the	the	DET
ejpam-5237	116	20	initial	initial	ADJ
ejpam-5237	116	21	value	value	NOUN
ejpam-5237	116	22	of	of	ADP
ejpam-5237	116	23	fractional	fractional	ADJ
ejpam-5237	116	24	ordinary	ordinary	ADJ
ejpam-5237	116	25	differential	differential	ADJ
ejpam-5237	116	26	equations	equation	NOUN
ejpam-5237	116	27	employing	employ	VERB
ejpam-5237	116	28	the	the	DET
ejpam-5237	116	29	conformable	conformable	ADJ
ejpam-5237	116	30	fractional	fractional	ADJ
ejpam-5237	116	31	derivative	derivative	NOUN
ejpam-5237	116	32	,	,	PUNCT
ejpam-5237	116	33	with	with	ADP
ejpam-5237	116	34	0	0	NUM
ejpam-5237	116	35	<	<	X
ejpam-5237	116	36	α	α	X
ejpam-5237	116	37	<	<	X
ejpam-5237	116	38	1	1	NUM
ejpam-5237	116	39	,	,	PUNCT
ejpam-5237	116	40	tα	tα	PROPN
ejpam-5237	116	41	t	t	PROPN
ejpam-5237	116	42	w(t	w(t	PROPN
ejpam-5237	116	43	)	)	PUNCT
ejpam-5237	116	44	=	=	PUNCT
ejpam-5237	117	1	λw(t	λw(t	PUNCT
ejpam-5237	117	2	)	)	PUNCT
ejpam-5237	117	3	,	,	PUNCT
ejpam-5237	117	4	t	t	PROPN
ejpam-5237	117	5	>	>	X
ejpam-5237	117	6	0	0	NUM
ejpam-5237	117	7	,	,	PUNCT
ejpam-5237	117	8	(	(	PUNCT
ejpam-5237	117	9	20	20	NUM
ejpam-5237	117	10	)	)	PUNCT
ejpam-5237	117	11	with	with	ADP
ejpam-5237	117	12	the	the	DET
ejpam-5237	117	13	initial	initial	ADJ
ejpam-5237	117	14	condition	condition	NOUN
ejpam-5237	117	15	w(t)|t=0	w(t)|t=0	PUNCT
ejpam-5237	118	1	=	=	SYM
ejpam-5237	118	2	w0	w0	PROPN
ejpam-5237	118	3	,	,	PUNCT
ejpam-5237	118	4	(	(	PUNCT
ejpam-5237	118	5	21	21	NUM
ejpam-5237	118	6	)	)	PUNCT
ejpam-5237	118	7	has	have	VERB
ejpam-5237	118	8	the	the	DET
ejpam-5237	118	9	solution	solution	NOUN
ejpam-5237	118	10	w(t	w(t	PROPN
ejpam-5237	118	11	)	)	PUNCT
ejpam-5237	119	1	=	=	PUNCT
ejpam-5237	119	2	w0e	w0e	PROPN
ejpam-5237	119	3	λ	λ	X
ejpam-5237	119	4	tα	tα	PROPN
ejpam-5237	119	5	α	α	X
ejpam-5237	119	6	.	.	PUNCT
ejpam-5237	120	1	(	(	PUNCT
ejpam-5237	120	2	22	22	NUM
ejpam-5237	120	3	)	)	PUNCT
ejpam-5237	120	4	figure	figure	NOUN
ejpam-5237	120	5	3	3	NUM
ejpam-5237	120	6	:	:	PUNCT
ejpam-5237	120	7	comparative	comparative	ADJ
ejpam-5237	120	8	solutions	solution	NOUN
ejpam-5237	120	9	for	for	ADP
ejpam-5237	120	10	serval	serval	NOUN
ejpam-5237	120	11	values	value	NOUN
ejpam-5237	120	12	of	of	ADP
ejpam-5237	120	13	α	α	NOUN
ejpam-5237	120	14	,	,	PUNCT
ejpam-5237	120	15	with	with	ADP
ejpam-5237	120	16	the	the	DET
ejpam-5237	120	17	conformable	conformable	ADJ
ejpam-5237	120	18	fractional	fractional	ADJ
ejpam-5237	120	19	derivative	derivative	NOUN
ejpam-5237	120	20	.	.	PUNCT
ejpam-5237	121	1	this	this	DET
ejpam-5237	121	2	study	study	NOUN
ejpam-5237	121	3	figure	figure	NOUN
ejpam-5237	121	4	1	1	NUM
ejpam-5237	121	5	,	,	PUNCT
ejpam-5237	121	6	figure	figure	NOUN
ejpam-5237	121	7	2	2	NUM
ejpam-5237	121	8	and	and	CCONJ
ejpam-5237	121	9	figure	figure	VERB
ejpam-5237	121	10	3	3	NUM
ejpam-5237	121	11	delves	delf	NOUN
ejpam-5237	121	12	into	into	ADP
ejpam-5237	121	13	the	the	DET
ejpam-5237	121	14	analysis	analysis	NOUN
ejpam-5237	121	15	and	and	CCONJ
ejpam-5237	121	16	comparison	comparison	NOUN
ejpam-5237	121	17	of	of	ADP
ejpam-5237	121	18	conformable	conformable	NOUN
ejpam-5237	121	19	,	,	PUNCT
ejpam-5237	121	20	riemann	riemann	PROPN
ejpam-5237	121	21	-	-	PUNCT
ejpam-5237	121	22	liouville	liouville	NOUN
ejpam-5237	121	23	,	,	PUNCT
ejpam-5237	121	24	and	and	CCONJ
ejpam-5237	121	25	caputo	caputo	PROPN
ejpam-5237	121	26	fractional	fractional	ADJ
ejpam-5237	121	27	derivatives	derivative	NOUN
ejpam-5237	121	28	of	of	ADP
ejpam-5237	121	29	order	order	NOUN
ejpam-5237	121	30	α	α	NOUN
ejpam-5237	121	31	,	,	PUNCT
ejpam-5237	121	32	where	where	SCONJ
ejpam-5237	121	33	0	0	X
ejpam-5237	121	34	<	<	X
ejpam-5237	121	35	α	α	X
ejpam-5237	121	36	<	<	X
ejpam-5237	121	37	1	1	NUM
ejpam-5237	121	38	.	.	PUNCT
ejpam-5237	121	39	to	to	PART
ejpam-5237	121	40	facilitate	facilitate	VERB
ejpam-5237	121	41	a	a	DET
ejpam-5237	121	42	comprehensive	comprehensive	ADJ
ejpam-5237	121	43	comparison	comparison	NOUN
ejpam-5237	121	44	,	,	PUNCT
ejpam-5237	121	45	we	we	PRON
ejpam-5237	121	46	conduct	conduct	VERB
ejpam-5237	121	47	numerical	numerical	ADJ
ejpam-5237	121	48	simulations	simulation	NOUN
ejpam-5237	121	49	to	to	PART
ejpam-5237	121	50	examine	examine	VERB
ejpam-5237	121	51	the	the	DET
ejpam-5237	121	52	solutions	solution	NOUN
ejpam-5237	121	53	of	of	ADP
ejpam-5237	121	54	fractional	fractional	ADJ
ejpam-5237	121	55	ordinary	ordinary	ADJ
ejpam-5237	121	56	differential	differential	ADJ
ejpam-5237	121	57	equations	equation	NOUN
ejpam-5237	121	58	that	that	PRON
ejpam-5237	121	59	incorporate	incorporate	VERB
ejpam-5237	121	60	these	these	DET
ejpam-5237	121	61	three	three	NUM
ejpam-5237	121	62	types	type	NOUN
ejpam-5237	121	63	of	of	ADP
ejpam-5237	121	64	fractional	fractional	ADJ
ejpam-5237	121	65	derivatives	derivative	NOUN
ejpam-5237	121	66	.	.	PUNCT
ejpam-5237	122	1	4	4	X
ejpam-5237	122	2	.	.	X
ejpam-5237	122	3	application	application	NOUN
ejpam-5237	122	4	to	to	ADP
ejpam-5237	122	5	physics	physics	PROPN
ejpam-5237	122	6	4.1	4.1	NUM
ejpam-5237	122	7	.	.	PUNCT
ejpam-5237	123	1	newton	newton	PROPN
ejpam-5237	123	2	’s	’s	PART
ejpam-5237	123	3	cooling	cool	VERB
ejpam-5237	123	4	problem	problem	NOUN
ejpam-5237	123	5	:	:	PUNCT
ejpam-5237	123	6	newton	newton	PROPN
ejpam-5237	123	7	’s	’s	PART
ejpam-5237	123	8	cooling	cool	VERB
ejpam-5237	123	9	problem	problem	NOUN
ejpam-5237	123	10	is	be	AUX
ejpam-5237	123	11	a	a	DET
ejpam-5237	123	12	fundamental	fundamental	ADJ
ejpam-5237	123	13	concept	concept	NOUN
ejpam-5237	123	14	in	in	ADP
ejpam-5237	123	15	physics	physics	NOUN
ejpam-5237	123	16	that	that	PRON
ejpam-5237	123	17	studies	study	VERB
ejpam-5237	123	18	how	how	SCONJ
ejpam-5237	123	19	an	an	DET
ejpam-5237	123	20	object	object	NOUN
ejpam-5237	123	21	loses	lose	VERB
ejpam-5237	123	22	heat	heat	NOUN
ejpam-5237	123	23	when	when	SCONJ
ejpam-5237	123	24	exposed	expose	VERB
ejpam-5237	123	25	to	to	ADP
ejpam-5237	123	26	a	a	DET
ejpam-5237	123	27	colder	cold	ADJ
ejpam-5237	123	28	environment	environment	NOUN
ejpam-5237	123	29	.	.	PUNCT
ejpam-5237	124	1	this	this	DET
ejpam-5237	124	2	phenomenon	phenomenon	NOUN
ejpam-5237	124	3	,	,	PUNCT
ejpam-5237	124	4	named	name	VERB
ejpam-5237	124	5	after	after	ADP
ejpam-5237	124	6	the	the	DET
ejpam-5237	124	7	famous	famous	ADJ
ejpam-5237	124	8	physicist	physicist	NOUN
ejpam-5237	124	9	sir	sir	PROPN
ejpam-5237	124	10	isaac	isaac	PROPN
ejpam-5237	124	11	newton	newton	PROPN
ejpam-5237	124	12	,	,	PUNCT
ejpam-5237	124	13	is	be	AUX
ejpam-5237	124	14	crucial	crucial	ADJ
ejpam-5237	124	15	in	in	ADP
ejpam-5237	124	16	many	many	ADJ
ejpam-5237	124	17	fields	field	NOUN
ejpam-5237	124	18	,	,	PUNCT
ejpam-5237	124	19	from	from	ADP
ejpam-5237	124	20	engineering	engineer	VERB
ejpam-5237	124	21	to	to	ADP
ejpam-5237	124	22	meteorology	meteorology	NOUN
ejpam-5237	124	23	to	to	ADP
ejpam-5237	124	24	biology	biology	NOUN
ejpam-5237	124	25	.	.	PUNCT
ejpam-5237	125	1	we	we	PRON
ejpam-5237	125	2	define	define	VERB
ejpam-5237	125	3	the	the	DET
ejpam-5237	125	4	problem	problem	NOUN
ejpam-5237	125	5	of	of	ADP
ejpam-5237	125	6	newton	newton	PROPN
ejpam-5237	125	7	’s	’s	PART
ejpam-5237	125	8	cooling	cool	VERB
ejpam-5237	125	9	law	law	NOUN
ejpam-5237	125	10	states	state	VERB
ejpam-5237	125	11	that	that	SCONJ
ejpam-5237	125	12	the	the	DET
ejpam-5237	125	13	cooling	cooling	NOUN
ejpam-5237	125	14	by	by	ADP
ejpam-5237	125	15	equation	equation	NOUN
ejpam-5237	125	16	dt	dt	NOUN
ejpam-5237	125	17	dt	dt	X
ejpam-5237	125	18	=	=	PUNCT
ejpam-5237	125	19	−κ	−κ	PROPN
ejpam-5237	125	20	(	(	PUNCT
ejpam-5237	125	21	t	t	PROPN
ejpam-5237	125	22	(	(	PUNCT
ejpam-5237	125	23	t)−	t)−	PROPN
ejpam-5237	125	24	tc	tc	X
ejpam-5237	125	25	)	)	PUNCT
ejpam-5237	125	26	,	,	PUNCT
ejpam-5237	125	27	t	t	PROPN
ejpam-5237	125	28	(	(	PUNCT
ejpam-5237	125	29	0	0	NUM
ejpam-5237	125	30	)	)	PUNCT
ejpam-5237	125	31	=	=	SYM
ejpam-5237	125	32	t0	t0	PROPN
ejpam-5237	125	33	.	.	PUNCT
ejpam-5237	126	1	(	(	PUNCT
ejpam-5237	126	2	23	23	NUM
ejpam-5237	126	3	)	)	PUNCT
ejpam-5237	126	4	a.	a.	NOUN
ejpam-5237	126	5	ait	ait	NOUN
ejpam-5237	126	6	brahim	brahim	PROPN
ejpam-5237	126	7	et	et	PROPN
ejpam-5237	126	8	all	all	DET
ejpam-5237	126	9	/	/	SYM
ejpam-5237	126	10	eur	eur	PROPN
ejpam-5237	126	11	.	.	PUNCT
ejpam-5237	127	1	j.	j.	PROPN
ejpam-5237	127	2	pure	pure	PROPN
ejpam-5237	127	3	appl	appl	PROPN
ejpam-5237	127	4	.	.	PROPN
ejpam-5237	127	5	math	math	PROPN
ejpam-5237	127	6	,	,	PUNCT
ejpam-5237	127	7	17	17	NUM
ejpam-5237	127	8	(	(	PUNCT
ejpam-5237	127	9	3	3	NUM
ejpam-5237	127	10	)	)	PUNCT
ejpam-5237	127	11	(	(	PUNCT
ejpam-5237	127	12	2024	2024	NUM
ejpam-5237	127	13	)	)	PUNCT
ejpam-5237	127	14	,	,	PUNCT
ejpam-5237	127	15	1842	1842	NUM
ejpam-5237	127	16	-	-	SYM
ejpam-5237	127	17	1854	1854	NUM
ejpam-5237	127	18	1849	1849	NUM
ejpam-5237	127	19	in	in	ADP
ejpam-5237	127	20	t	t	PROPN
ejpam-5237	127	21	=	=	SYM
ejpam-5237	127	22	0	0	NUM
ejpam-5237	128	1	we	we	PRON
ejpam-5237	128	2	have	have	VERB
ejpam-5237	128	3	the	the	DET
ejpam-5237	128	4	initial	initial	ADJ
ejpam-5237	128	5	temperature	temperature	NOUN
ejpam-5237	128	6	t0	t0	NOUN
ejpam-5237	128	7	,	,	PUNCT
ejpam-5237	128	8	and	and	CCONJ
ejpam-5237	128	9	we	we	PRON
ejpam-5237	128	10	gets	get	VERB
ejpam-5237	128	11	the	the	DET
ejpam-5237	128	12	solution	solution	NOUN
ejpam-5237	128	13	:	:	PUNCT
ejpam-5237	128	14	t	t	PROPN
ejpam-5237	128	15	(	(	PUNCT
ejpam-5237	128	16	t	t	PROPN
ejpam-5237	128	17	)	)	PUNCT
ejpam-5237	128	18	=	=	SYM
ejpam-5237	129	1	tc	tc	X
ejpam-5237	129	2	+	+	CCONJ
ejpam-5237	129	3	(	(	PUNCT
ejpam-5237	129	4	t0	t0	PROPN
ejpam-5237	129	5	−	−	PROPN
ejpam-5237	129	6	tc	tc	NUM
ejpam-5237	129	7	)	)	PUNCT
ejpam-5237	129	8	e	e	NOUN
ejpam-5237	129	9	−κt	−κt	PROPN
ejpam-5237	129	10	.	.	PUNCT
ejpam-5237	130	1	(	(	PUNCT
ejpam-5237	130	2	24	24	NUM
ejpam-5237	130	3	)	)	PUNCT
ejpam-5237	130	4	first	first	ADV
ejpam-5237	130	5	of	of	ADP
ejpam-5237	130	6	all	all	PRON
ejpam-5237	130	7	,	,	PUNCT
ejpam-5237	130	8	we	we	PRON
ejpam-5237	130	9	must	must	AUX
ejpam-5237	130	10	ensure	ensure	VERB
ejpam-5237	130	11	that	that	SCONJ
ejpam-5237	130	12	in	in	ADP
ejpam-5237	130	13	the	the	DET
ejpam-5237	130	14	pass	pass	NOUN
ejpam-5237	130	15	of	of	ADP
ejpam-5237	130	16	equation	equation	NOUN
ejpam-5237	130	17	(	(	PUNCT
ejpam-5237	130	18	23	23	NUM
ejpam-5237	130	19	)	)	PUNCT
ejpam-5237	130	20	to	to	ADP
ejpam-5237	130	21	its	its	PRON
ejpam-5237	130	22	corresponding	corresponding	ADJ
ejpam-5237	130	23	fractional	fractional	ADJ
ejpam-5237	130	24	equation	equation	NOUN
ejpam-5237	130	25	,	,	PUNCT
ejpam-5237	130	26	the	the	DET
ejpam-5237	130	27	physical	physical	ADJ
ejpam-5237	130	28	parameters	parameter	NOUN
ejpam-5237	130	29	in	in	ADP
ejpam-5237	130	30	it	it	PRON
ejpam-5237	130	31	retain	retain	VERB
ejpam-5237	130	32	their	their	PRON
ejpam-5237	130	33	physical	physical	ADJ
ejpam-5237	130	34	units	unit	NOUN
ejpam-5237	130	35	.	.	PUNCT
ejpam-5237	131	1	following	follow	VERB
ejpam-5237	131	2	[	[	X
ejpam-5237	131	3	12	12	NUM
ejpam-5237	131	4	]	]	PUNCT
ejpam-5237	131	5	,	,	PUNCT
ejpam-5237	131	6	it	it	PRON
ejpam-5237	131	7	is	be	AUX
ejpam-5237	131	8	necessary	necessary	ADJ
ejpam-5237	131	9	to	to	PART
ejpam-5237	131	10	take	take	VERB
ejpam-5237	131	11	into	into	ADP
ejpam-5237	131	12	account	account	NOUN
ejpam-5237	131	13	“	"	PUNCT
ejpam-5237	131	14	the	the	DET
ejpam-5237	131	15	distortion	distortion	NOUN
ejpam-5237	131	16	”	"	PUNCT
ejpam-5237	131	17	suffered	suffer	VERB
ejpam-5237	131	18	by	by	ADP
ejpam-5237	131	19	the	the	DET
ejpam-5237	131	20	derivative	derivative	NOUN
ejpam-5237	131	21	when	when	SCONJ
ejpam-5237	131	22	going	go	VERB
ejpam-5237	131	23	from	from	ADP
ejpam-5237	131	24	the	the	DET
ejpam-5237	131	25	ordinary	ordinary	ADJ
ejpam-5237	131	26	case	case	NOUN
ejpam-5237	131	27	to	to	ADP
ejpam-5237	131	28	the	the	DET
ejpam-5237	131	29	non	non	ADJ
ejpam-5237	131	30	-	-	NOUN
ejpam-5237	131	31	integer	integer	ADJ
ejpam-5237	131	32	.	.	PUNCT
ejpam-5237	132	1	we	we	PRON
ejpam-5237	132	2	can	can	AUX
ejpam-5237	132	3	use	use	VERB
ejpam-5237	132	4	the	the	DET
ejpam-5237	132	5	physical	physical	ADJ
ejpam-5237	132	6	parameter	parameter	NOUN
ejpam-5237	133	1	[	[	X
ejpam-5237	133	2	k	k	X
ejpam-5237	133	3	]	]	X
ejpam-5237	133	4	=	=	X
ejpam-5237	133	5	s−1	s−1	PROPN
ejpam-5237	133	6	to	to	PART
ejpam-5237	133	7	pass	pass	VERB
ejpam-5237	133	8	from	from	ADP
ejpam-5237	133	9	the	the	DET
ejpam-5237	133	10	ordinary	ordinary	ADJ
ejpam-5237	133	11	differential	differential	ADJ
ejpam-5237	133	12	operator	operator	NOUN
ejpam-5237	133	13	to	to	ADP
ejpam-5237	133	14	the	the	DET
ejpam-5237	133	15	fractional	fractional	ADJ
ejpam-5237	133	16	one	one	NUM
ejpam-5237	134	1	[	[	X
ejpam-5237	134	2	11	11	NUM
ejpam-5237	134	3	]	]	PUNCT
ejpam-5237	134	4	,	,	PUNCT
ejpam-5237	134	5	as	as	SCONJ
ejpam-5237	134	6	follows	follow	VERB
ejpam-5237	134	7	d	d	NOUN
ejpam-5237	134	8	dt	dt	X
ejpam-5237	134	9	→	→	SYM
ejpam-5237	134	10	f	f	PROPN
ejpam-5237	134	11	(	(	PUNCT
ejpam-5237	134	12	k−1	k−1	PROPN
ejpam-5237	134	13	,	,	PUNCT
ejpam-5237	134	14	α	α	NOUN
ejpam-5237	134	15	)	)	PUNCT
ejpam-5237	134	16	nα	nα	ADP
ejpam-5237	134	17	f	f	PROPN
ejpam-5237	134	18	.	.	PUNCT
ejpam-5237	135	1	(	(	PUNCT
ejpam-5237	135	2	25	25	NUM
ejpam-5237	135	3	)	)	PUNCT
ejpam-5237	135	4	in	in	ADP
ejpam-5237	135	5	this	this	DET
ejpam-5237	135	6	way	way	NOUN
ejpam-5237	135	7	,	,	PUNCT
ejpam-5237	135	8	the	the	DET
ejpam-5237	135	9	differential	differential	ADJ
ejpam-5237	135	10	operator	operator	NOUN
ejpam-5237	135	11	retains	retain	VERB
ejpam-5237	135	12	its	its	PRON
ejpam-5237	135	13	dimensionality	dimensionality	NOUN
ejpam-5237	135	14	[	[	X
ejpam-5237	135	15	d	d	X
ejpam-5237	135	16	/	/	SYM
ejpam-5237	135	17	dt	dt	X
ejpam-5237	135	18	]	]	X
ejpam-5237	135	19	=	=	SYM
ejpam-5237	135	20	s−1	s−1	PROPN
ejpam-5237	135	21	,	,	PUNCT
ejpam-5237	135	22	and	and	CCONJ
ejpam-5237	135	23	α	α	PRON
ejpam-5237	135	24	is	be	AUX
ejpam-5237	135	25	the	the	DET
ejpam-5237	135	26	order	order	NOUN
ejpam-5237	135	27	of	of	ADP
ejpam-5237	135	28	derivative	derivative	NOUN
ejpam-5237	135	29	.	.	PUNCT
ejpam-5237	136	1	susbstituting	susbstitute	VERB
ejpam-5237	136	2	(	(	PUNCT
ejpam-5237	136	3	25	25	NUM
ejpam-5237	136	4	)	)	PUNCT
ejpam-5237	136	5	in	in	ADP
ejpam-5237	136	6	(	(	PUNCT
ejpam-5237	136	7	23	23	NUM
ejpam-5237	136	8	)	)	PUNCT
ejpam-5237	136	9	,	,	PUNCT
ejpam-5237	136	10	we	we	PRON
ejpam-5237	136	11	obtain	obtain	VERB
ejpam-5237	136	12	the	the	DET
ejpam-5237	136	13	fractional	fractional	ADJ
ejpam-5237	136	14	model	model	NOUN
ejpam-5237	136	15	as	as	ADP
ejpam-5237	136	16	nα	nα	ADP
ejpam-5237	136	17	ft	ft	PROPN
ejpam-5237	136	18	(	(	PUNCT
ejpam-5237	136	19	t	t	PROPN
ejpam-5237	136	20	)	)	PUNCT
ejpam-5237	136	21	+	+	CCONJ
ejpam-5237	137	1	f−1	f−1	PROPN
ejpam-5237	137	2	(	(	PUNCT
ejpam-5237	137	3	k−1	k−1	PROPN
ejpam-5237	137	4	,	,	PUNCT
ejpam-5237	137	5	α	α	NOUN
ejpam-5237	137	6	)	)	PUNCT
ejpam-5237	137	7	κt	κt	PROPN
ejpam-5237	137	8	(	(	PUNCT
ejpam-5237	137	9	t	t	NOUN
ejpam-5237	137	10	)	)	PUNCT
ejpam-5237	137	11	=	=	SYM
ejpam-5237	137	12	f−1	f−1	PROPN
ejpam-5237	137	13	(	(	PUNCT
ejpam-5237	137	14	k−1	k−1	PROPN
ejpam-5237	137	15	,	,	PUNCT
ejpam-5237	137	16	α	α	NOUN
ejpam-5237	137	17	)	)	PUNCT
ejpam-5237	137	18	κϵ(t	κϵ(t	NOUN
ejpam-5237	137	19	)	)	PUNCT
ejpam-5237	137	20	f	f	PROPN
ejpam-5237	137	21	(	(	PUNCT
ejpam-5237	137	22	t	t	PROPN
ejpam-5237	137	23	,	,	PUNCT
ejpam-5237	137	24	α)t	α)t	NOUN
ejpam-5237	137	25	′(t	′(t	NOUN
ejpam-5237	137	26	)	)	PUNCT
ejpam-5237	137	27	+	+	CCONJ
ejpam-5237	137	28	f−1	f−1	PROPN
ejpam-5237	137	29	(	(	PUNCT
ejpam-5237	137	30	k−1	k−1	PROPN
ejpam-5237	137	31	,	,	PUNCT
ejpam-5237	137	32	α	α	NOUN
ejpam-5237	137	33	)	)	PUNCT
ejpam-5237	137	34	κt	κt	PROPN
ejpam-5237	137	35	(	(	PUNCT
ejpam-5237	137	36	t	t	NOUN
ejpam-5237	137	37	)	)	PUNCT
ejpam-5237	137	38	=	=	SYM
ejpam-5237	137	39	f−1	f−1	PROPN
ejpam-5237	137	40	(	(	PUNCT
ejpam-5237	137	41	k−1	k−1	PROPN
ejpam-5237	137	42	,	,	PUNCT
ejpam-5237	137	43	α	α	NOUN
ejpam-5237	137	44	)	)	PUNCT
ejpam-5237	137	45	κϵ(t	κϵ(t	NOUN
ejpam-5237	137	46	)	)	PUNCT
ejpam-5237	137	47	t	t	PROPN
ejpam-5237	137	48	′(t	′(t	PROPN
ejpam-5237	137	49	)	)	PUNCT
ejpam-5237	138	1	+	+	CCONJ
ejpam-5237	138	2	f−1	f−1	PROPN
ejpam-5237	138	3	(	(	PUNCT
ejpam-5237	138	4	k−1	k−1	PROPN
ejpam-5237	138	5	,	,	PUNCT
ejpam-5237	138	6	α	α	PROPN
ejpam-5237	138	7	)	)	PUNCT
ejpam-5237	138	8	f	f	PROPN
ejpam-5237	138	9	(	(	PUNCT
ejpam-5237	138	10	t	t	PROPN
ejpam-5237	138	11	,	,	PUNCT
ejpam-5237	138	12	α	α	NOUN
ejpam-5237	138	13	)	)	PUNCT
ejpam-5237	138	14	κt	κt	PROPN
ejpam-5237	138	15	(	(	PUNCT
ejpam-5237	138	16	t	t	NOUN
ejpam-5237	138	17	)	)	PUNCT
ejpam-5237	139	1	=	=	SYM
ejpam-5237	139	2	f−1	f−1	PROPN
ejpam-5237	139	3	(	(	PUNCT
ejpam-5237	139	4	k−1	k−1	PROPN
ejpam-5237	139	5	,	,	PUNCT
ejpam-5237	139	6	α	α	PROPN
ejpam-5237	139	7	)	)	PUNCT
ejpam-5237	139	8	f	f	PROPN
ejpam-5237	139	9	(	(	PUNCT
ejpam-5237	139	10	t	t	PROPN
ejpam-5237	139	11	,	,	PUNCT
ejpam-5237	139	12	α	α	NOUN
ejpam-5237	139	13	)	)	PUNCT
ejpam-5237	139	14	κϵ(t	κϵ(t	NOUN
ejpam-5237	139	15	)	)	PUNCT
ejpam-5237	139	16	.	.	PUNCT
ejpam-5237	140	1	since	since	SCONJ
ejpam-5237	140	2	p	p	PROPN
ejpam-5237	140	3	(	(	PUNCT
ejpam-5237	140	4	t	t	NOUN
ejpam-5237	140	5	)	)	PUNCT
ejpam-5237	140	6	=	=	SYM
ejpam-5237	140	7	κf−1	κf−1	PROPN
ejpam-5237	140	8	(	(	PUNCT
ejpam-5237	140	9	k−1	k−1	PROPN
ejpam-5237	140	10	,	,	PUNCT
ejpam-5237	140	11	α	α	PROPN
ejpam-5237	140	12	)	)	PUNCT
ejpam-5237	140	13	f	f	PROPN
ejpam-5237	140	14	(	(	PUNCT
ejpam-5237	140	15	t	t	PROPN
ejpam-5237	140	16	,	,	PUNCT
ejpam-5237	140	17	α	α	NOUN
ejpam-5237	140	18	)	)	PUNCT
ejpam-5237	140	19	,	,	PUNCT
ejpam-5237	140	20	then	then	ADV
ejpam-5237	140	21	exp	exp	PROPN
ejpam-5237	140	22	(	(	PUNCT
ejpam-5237	140	23	∫	∫	PROPN
ejpam-5237	140	24	κf−1	κf−1	PROPN
ejpam-5237	140	25	(	(	PUNCT
ejpam-5237	140	26	k−1	k−1	PROPN
ejpam-5237	140	27	,	,	PUNCT
ejpam-5237	140	28	α	α	PROPN
ejpam-5237	140	29	)	)	PUNCT
ejpam-5237	140	30	f	f	PROPN
ejpam-5237	140	31	(	(	PUNCT
ejpam-5237	140	32	t	t	PROPN
ejpam-5237	140	33	,	,	PUNCT
ejpam-5237	140	34	α	α	NOUN
ejpam-5237	140	35	)	)	PUNCT
ejpam-5237	140	36	dt	dt	PUNCT
ejpam-5237	140	37	)	)	PUNCT
ejpam-5237	141	1	=	=	SYM
ejpam-5237	141	2	exp	exp	NOUN
ejpam-5237	141	3	(	(	PUNCT
ejpam-5237	141	4	κf−1	κf−1	PROPN
ejpam-5237	141	5	(	(	PUNCT
ejpam-5237	141	6	k−1	k−1	PROPN
ejpam-5237	141	7	,	,	PUNCT
ejpam-5237	141	8	α	α	PROPN
ejpam-5237	141	9	)	)	PUNCT
ejpam-5237	141	10	∫	∫	PROPN
ejpam-5237	142	1	dt	dt	X
ejpam-5237	142	2	f	f	PROPN
ejpam-5237	142	3	(	(	PUNCT
ejpam-5237	142	4	t	t	PROPN
ejpam-5237	142	5	,	,	PUNCT
ejpam-5237	142	6	α	α	NOUN
ejpam-5237	142	7	)	)	PUNCT
ejpam-5237	142	8	)	)	PUNCT
ejpam-5237	142	9	.	.	PUNCT
ejpam-5237	143	1	d	d	X
ejpam-5237	143	2	dt	dt	X
ejpam-5237	143	3	[	[	PUNCT
ejpam-5237	143	4	exp	exp	NOUN
ejpam-5237	143	5	(	(	PUNCT
ejpam-5237	143	6	κf−1	κf−1	PROPN
ejpam-5237	143	7	(	(	PUNCT
ejpam-5237	143	8	k−1	k−1	PROPN
ejpam-5237	143	9	,	,	PUNCT
ejpam-5237	143	10	α	α	PROPN
ejpam-5237	143	11	)	)	PUNCT
ejpam-5237	143	12	∫	∫	PROPN
ejpam-5237	144	1	dt	dt	X
ejpam-5237	144	2	f	f	PROPN
ejpam-5237	144	3	(	(	PUNCT
ejpam-5237	144	4	t	t	PROPN
ejpam-5237	144	5	,	,	PUNCT
ejpam-5237	144	6	α	α	NOUN
ejpam-5237	144	7	)	)	PUNCT
ejpam-5237	144	8	)	)	PUNCT
ejpam-5237	145	1	t	t	PROPN
ejpam-5237	145	2	(	(	PUNCT
ejpam-5237	145	3	t	t	PROPN
ejpam-5237	145	4	)	)	PUNCT
ejpam-5237	145	5	]	]	PUNCT
ejpam-5237	146	1	=	=	SYM
ejpam-5237	146	2	exp	exp	NOUN
ejpam-5237	146	3	(	(	PUNCT
ejpam-5237	146	4	κf−1	κf−1	PROPN
ejpam-5237	146	5	(	(	PUNCT
ejpam-5237	146	6	k−1	k−1	PROPN
ejpam-5237	146	7	,	,	PUNCT
ejpam-5237	146	8	α	α	PROPN
ejpam-5237	146	9	)	)	PUNCT
ejpam-5237	146	10	∫	∫	PROPN
ejpam-5237	147	1	dt	dt	X
ejpam-5237	147	2	f	f	PROPN
ejpam-5237	147	3	(	(	PUNCT
ejpam-5237	147	4	t	t	PROPN
ejpam-5237	147	5	,	,	PUNCT
ejpam-5237	147	6	α	α	NOUN
ejpam-5237	147	7	)	)	PUNCT
ejpam-5237	147	8	)	)	PUNCT
ejpam-5237	148	1	f−1	f−1	PROPN
ejpam-5237	148	2	(	(	PUNCT
ejpam-5237	148	3	k−1	k−1	PROPN
ejpam-5237	148	4	,	,	PUNCT
ejpam-5237	148	5	α	α	PROPN
ejpam-5237	148	6	)	)	PUNCT
ejpam-5237	148	7	f	f	PROPN
ejpam-5237	148	8	(	(	PUNCT
ejpam-5237	148	9	t	t	PROPN
ejpam-5237	148	10	,	,	PUNCT
ejpam-5237	148	11	α	α	NOUN
ejpam-5237	148	12	)	)	PUNCT
ejpam-5237	148	13	κϵ(t)exp	κϵ(t)exp	NOUN
ejpam-5237	148	14	(	(	PUNCT
ejpam-5237	148	15	κf−1	κf−1	PROPN
ejpam-5237	148	16	(	(	PUNCT
ejpam-5237	148	17	k−1	k−1	PROPN
ejpam-5237	148	18	,	,	PUNCT
ejpam-5237	148	19	α	α	PROPN
ejpam-5237	148	20	)	)	PUNCT
ejpam-5237	148	21	∫	∫	PROPN
ejpam-5237	149	1	dt	dt	X
ejpam-5237	149	2	f	f	PROPN
ejpam-5237	149	3	(	(	PUNCT
ejpam-5237	149	4	t	t	PROPN
ejpam-5237	149	5	,	,	PUNCT
ejpam-5237	149	6	α	α	NOUN
ejpam-5237	149	7	)	)	PUNCT
ejpam-5237	149	8	)	)	PUNCT
ejpam-5237	150	1	t	t	PROPN
ejpam-5237	150	2	(	(	PUNCT
ejpam-5237	150	3	t	t	PROPN
ejpam-5237	150	4	)	)	PUNCT
ejpam-5237	150	5	=	=	SYM
ejpam-5237	151	1	κf−1	κf−1	PROPN
ejpam-5237	151	2	(	(	PUNCT
ejpam-5237	151	3	k−1	k−1	PROPN
ejpam-5237	151	4	,	,	PUNCT
ejpam-5237	151	5	α	α	PROPN
ejpam-5237	151	6	)	)	PUNCT
ejpam-5237	151	7	∫	∫	PROPN
ejpam-5237	151	8	exp	exp	PROPN
ejpam-5237	151	9	(	(	PUNCT
ejpam-5237	151	10	κf−1	κf−1	PROPN
ejpam-5237	151	11	(	(	PUNCT
ejpam-5237	151	12	k−1	k−1	PROPN
ejpam-5237	151	13	,	,	PUNCT
ejpam-5237	151	14	α	α	PROPN
ejpam-5237	151	15	)	)	PUNCT
ejpam-5237	151	16	∫	∫	PROPN
ejpam-5237	152	1	dt	dt	X
ejpam-5237	152	2	f	f	PROPN
ejpam-5237	152	3	(	(	PUNCT
ejpam-5237	152	4	t	t	PROPN
ejpam-5237	152	5	,	,	PUNCT
ejpam-5237	152	6	α	α	NOUN
ejpam-5237	152	7	)	)	PUNCT
ejpam-5237	152	8	)	)	PUNCT
ejpam-5237	153	1	ϵ	ϵ	X
ejpam-5237	153	2	(	(	PUNCT
ejpam-5237	153	3	t	t	PROPN
ejpam-5237	153	4	)	)	PUNCT
ejpam-5237	153	5	f	f	PROPN
ejpam-5237	153	6	(	(	PUNCT
ejpam-5237	153	7	t	t	PROPN
ejpam-5237	153	8	,	,	PUNCT
ejpam-5237	153	9	α	α	NOUN
ejpam-5237	153	10	)	)	PUNCT
ejpam-5237	153	11	dt	dt	PROPN
ejpam-5237	153	12	.	.	PUNCT
ejpam-5237	154	1	therefore	therefore	ADV
ejpam-5237	154	2	,	,	PUNCT
ejpam-5237	154	3	t	t	PROPN
ejpam-5237	154	4	(	(	PUNCT
ejpam-5237	154	5	t	t	PROPN
ejpam-5237	154	6	,	,	PUNCT
ejpam-5237	154	7	α	α	NOUN
ejpam-5237	154	8	)	)	PUNCT
ejpam-5237	154	9	=	=	SYM
ejpam-5237	154	10	exp	exp	NOUN
ejpam-5237	154	11	(	(	PUNCT
ejpam-5237	154	12	−κf−1	−κf−1	X
ejpam-5237	154	13	(	(	PUNCT
ejpam-5237	154	14	k−1	k−1	PROPN
ejpam-5237	154	15	,	,	PUNCT
ejpam-5237	154	16	α	α	PROPN
ejpam-5237	154	17	)	)	PUNCT
ejpam-5237	154	18	∫	∫	PROPN
ejpam-5237	155	1	dt	dt	X
ejpam-5237	155	2	f	f	PROPN
ejpam-5237	155	3	(	(	PUNCT
ejpam-5237	155	4	t	t	PROPN
ejpam-5237	155	5	,	,	PUNCT
ejpam-5237	155	6	α	α	NOUN
ejpam-5237	155	7	)	)	PUNCT
ejpam-5237	155	8	)	)	PUNCT
ejpam-5237	156	1	κf−1	κf−1	PROPN
ejpam-5237	156	2	(	(	PUNCT
ejpam-5237	156	3	k−1	k−1	PROPN
ejpam-5237	156	4	,	,	PUNCT
ejpam-5237	156	5	α	α	PROPN
ejpam-5237	156	6	)	)	PUNCT
ejpam-5237	156	7	∫	∫	PROPN
ejpam-5237	156	8	exp	exp	PROPN
ejpam-5237	156	9	(	(	PUNCT
ejpam-5237	156	10	κf−1	κf−1	PROPN
ejpam-5237	156	11	(	(	PUNCT
ejpam-5237	156	12	k−1	k−1	PROPN
ejpam-5237	156	13	,	,	PUNCT
ejpam-5237	156	14	α	α	PROPN
ejpam-5237	156	15	)	)	PUNCT
ejpam-5237	156	16	∫	∫	PROPN
ejpam-5237	157	1	dt	dt	X
ejpam-5237	157	2	f	f	PROPN
ejpam-5237	157	3	(	(	PUNCT
ejpam-5237	157	4	t	t	PROPN
ejpam-5237	157	5	,	,	PUNCT
ejpam-5237	157	6	α	α	NOUN
ejpam-5237	157	7	)	)	PUNCT
ejpam-5237	157	8	)	)	PUNCT
ejpam-5237	158	1	ϵ	ϵ	X
ejpam-5237	158	2	(	(	PUNCT
ejpam-5237	158	3	t	t	PROPN
ejpam-5237	158	4	)	)	PUNCT
ejpam-5237	158	5	f	f	PROPN
ejpam-5237	158	6	(	(	PUNCT
ejpam-5237	158	7	t	t	PROPN
ejpam-5237	158	8	,	,	PUNCT
ejpam-5237	158	9	α	α	NOUN
ejpam-5237	158	10	)	)	PUNCT
ejpam-5237	158	11	dt	dt	PROPN
ejpam-5237	158	12	.	.	PUNCT
ejpam-5237	159	1	(	(	PUNCT
ejpam-5237	159	2	26	26	NUM
ejpam-5237	159	3	)	)	PUNCT
ejpam-5237	159	4	the	the	DET
ejpam-5237	159	5	representation	representation	NOUN
ejpam-5237	159	6	of	of	ADP
ejpam-5237	159	7	this	this	DET
ejpam-5237	159	8	solution	solution	NOUN
ejpam-5237	159	9	of	of	ADP
ejpam-5237	159	10	the	the	DET
ejpam-5237	159	11	new	new	ADJ
ejpam-5237	159	12	fractional	fractional	ADJ
ejpam-5237	159	13	derivative	derivative	NOUN
ejpam-5237	159	14	for	for	ADP
ejpam-5237	159	15	the	the	DET
ejpam-5237	159	16	values	value	NOUN
ejpam-5237	159	17	of	of	ADP
ejpam-5237	159	18	α	α	NOUN
ejpam-5237	159	19	=	=	SYM
ejpam-5237	159	20	0	0	PROPN
ejpam-5237	159	21	,	,	PUNCT
ejpam-5237	159	22	α	α	NOUN
ejpam-5237	159	23	=	=	NOUN
ejpam-5237	159	24	0.25	0.25	NUM
ejpam-5237	159	25	,	,	PUNCT
ejpam-5237	159	26	α	α	NOUN
ejpam-5237	159	27	=	=	SYM
ejpam-5237	159	28	0.5	0.5	NUM
ejpam-5237	159	29	,	,	PUNCT
ejpam-5237	159	30	and	and	CCONJ
ejpam-5237	159	31	α	α	X
ejpam-5237	159	32	=	=	SYM
ejpam-5237	159	33	0.75	0.75	NUM
ejpam-5237	159	34	is	be	AUX
ejpam-5237	159	35	compared	compare	VERB
ejpam-5237	159	36	with	with	ADP
ejpam-5237	159	37	results	result	NOUN
ejpam-5237	159	38	obtained	obtain	VERB
ejpam-5237	159	39	using	use	VERB
ejpam-5237	159	40	the	the	DET
ejpam-5237	159	41	factor	factor	NOUN
ejpam-5237	159	42	t	t	PROPN
ejpam-5237	159	43	(	(	PUNCT
ejpam-5237	159	44	t	t	PROPN
ejpam-5237	159	45	,	,	PUNCT
ejpam-5237	159	46	α	α	NOUN
ejpam-5237	159	47	)	)	PUNCT
ejpam-5237	159	48	=	=	SYM
ejpam-5237	159	49	e(α−1)t	e(α−1)t	PROPN
ejpam-5237	159	50	directly	directly	ADV
ejpam-5237	159	51	,	,	PUNCT
ejpam-5237	159	52	as	as	ADV
ejpam-5237	159	53	well	well	ADV
ejpam-5237	159	54	as	as	ADP
ejpam-5237	159	55	non	non	ADJ
ejpam-5237	159	56	-	-	ADJ
ejpam-5237	159	57	conformable	conformable	ADJ
ejpam-5237	159	58	fractional	fractional	ADJ
ejpam-5237	159	59	derivatives	derivative	NOUN
ejpam-5237	159	60	using	use	VERB
ejpam-5237	159	61	the	the	DET
ejpam-5237	159	62	factor	factor	NOUN
ejpam-5237	159	63	t	t	PROPN
ejpam-5237	159	64	(	(	PUNCT
ejpam-5237	159	65	t	t	PROPN
ejpam-5237	159	66	,	,	PUNCT
ejpam-5237	159	67	α	α	NOUN
ejpam-5237	159	68	)	)	PUNCT
ejpam-5237	159	69	=	=	SYM
ejpam-5237	160	1	t−α	t−α	PROPN
ejpam-5237	160	2	(	(	PUNCT
ejpam-5237	160	3	see	see	VERB
ejpam-5237	160	4	[	[	X
ejpam-5237	160	5	5	5	NUM
ejpam-5237	160	6	,	,	PUNCT
ejpam-5237	160	7	15	15	NUM
ejpam-5237	160	8	]	]	NUM
ejpam-5237	160	9	)	)	PUNCT
ejpam-5237	160	10	.	.	PUNCT
ejpam-5237	161	1	these	these	DET
ejpam-5237	161	2	comparisons	comparison	NOUN
ejpam-5237	161	3	illustrate	illustrate	VERB
ejpam-5237	161	4	the	the	DET
ejpam-5237	161	5	differences	difference	NOUN
ejpam-5237	161	6	and	and	CCONJ
ejpam-5237	161	7	similarities	similarity	NOUN
ejpam-5237	161	8	a.	a.	NOUN
ejpam-5237	161	9	ait	ait	NOUN
ejpam-5237	161	10	brahim	brahim	PROPN
ejpam-5237	161	11	et	et	PROPN
ejpam-5237	161	12	all	all	DET
ejpam-5237	161	13	/	/	SYM
ejpam-5237	161	14	eur	eur	PROPN
ejpam-5237	161	15	.	.	PUNCT
ejpam-5237	162	1	j.	j.	PROPN
ejpam-5237	162	2	pure	pure	PROPN
ejpam-5237	162	3	appl	appl	PROPN
ejpam-5237	162	4	.	.	PROPN
ejpam-5237	162	5	math	math	PROPN
ejpam-5237	162	6	,	,	PUNCT
ejpam-5237	162	7	17	17	NUM
ejpam-5237	162	8	(	(	PUNCT
ejpam-5237	162	9	3	3	NUM
ejpam-5237	162	10	)	)	PUNCT
ejpam-5237	162	11	(	(	PUNCT
ejpam-5237	162	12	2024	2024	NUM
ejpam-5237	162	13	)	)	PUNCT
ejpam-5237	162	14	,	,	PUNCT
ejpam-5237	162	15	1842	1842	NUM
ejpam-5237	162	16	-	-	SYM
ejpam-5237	162	17	1854	1854	NUM
ejpam-5237	162	18	1850	1850	NUM
ejpam-5237	162	19	in	in	ADP
ejpam-5237	162	20	behavior	behavior	NOUN
ejpam-5237	162	21	between	between	ADP
ejpam-5237	162	22	the	the	DET
ejpam-5237	162	23	new	new	ADJ
ejpam-5237	162	24	fractional	fractional	ADJ
ejpam-5237	162	25	derivative	derivative	ADJ
ejpam-5237	162	26	approach	approach	NOUN
ejpam-5237	162	27	and	and	CCONJ
ejpam-5237	162	28	the	the	DET
ejpam-5237	162	29	established	establish	VERB
ejpam-5237	162	30	methods	method	NOUN
ejpam-5237	162	31	.	.	PUNCT
ejpam-5237	163	1	specifically	specifically	ADV
ejpam-5237	163	2	,	,	PUNCT
ejpam-5237	163	3	the	the	DET
ejpam-5237	163	4	comparison	comparison	NOUN
ejpam-5237	163	5	with	with	ADP
ejpam-5237	163	6	t	t	PROPN
ejpam-5237	163	7	(	(	PUNCT
ejpam-5237	163	8	t	t	PROPN
ejpam-5237	163	9	,	,	PUNCT
ejpam-5237	163	10	α	α	NOUN
ejpam-5237	163	11	)	)	PUNCT
ejpam-5237	163	12	=	=	SYM
ejpam-5237	163	13	e(α−1)t	e(α−1)t	PROPN
ejpam-5237	163	14	showcases	showcase	VERB
ejpam-5237	163	15	how	how	SCONJ
ejpam-5237	163	16	the	the	DET
ejpam-5237	163	17	exponential	exponential	ADJ
ejpam-5237	163	18	factor	factor	NOUN
ejpam-5237	163	19	influences	influence	VERB
ejpam-5237	163	20	the	the	DET
ejpam-5237	163	21	solutions	solution	NOUN
ejpam-5237	163	22	for	for	ADP
ejpam-5237	163	23	various	various	ADJ
ejpam-5237	163	24	values	value	NOUN
ejpam-5237	163	25	of	of	ADP
ejpam-5237	163	26	α	α	PRON
ejpam-5237	163	27	.	.	PUNCT
ejpam-5237	164	1	meanwhile	meanwhile	ADV
ejpam-5237	164	2	,	,	PUNCT
ejpam-5237	164	3	the	the	DET
ejpam-5237	164	4	comparison	comparison	NOUN
ejpam-5237	164	5	with	with	ADP
ejpam-5237	164	6	non	non	ADJ
ejpam-5237	164	7	-	-	ADJ
ejpam-5237	164	8	conformable	conformable	ADJ
ejpam-5237	164	9	fractional	fractional	ADJ
ejpam-5237	164	10	derivatives	derivative	NOUN
ejpam-5237	164	11	,	,	PUNCT
ejpam-5237	164	12	which	which	PRON
ejpam-5237	164	13	utilize	utilize	VERB
ejpam-5237	164	14	the	the	DET
ejpam-5237	164	15	algebraic	algebraic	ADJ
ejpam-5237	164	16	factor	factor	NOUN
ejpam-5237	164	17	t	t	PROPN
ejpam-5237	164	18	(	(	PUNCT
ejpam-5237	164	19	t	t	PROPN
ejpam-5237	164	20	,	,	PUNCT
ejpam-5237	164	21	α	α	NOUN
ejpam-5237	164	22	)	)	PUNCT
ejpam-5237	164	23	=	=	SYM
ejpam-5237	164	24	t−α	t−α	PROPN
ejpam-5237	164	25	,	,	PUNCT
ejpam-5237	164	26	highlights	highlight	VERB
ejpam-5237	164	27	the	the	DET
ejpam-5237	164	28	impact	impact	NOUN
ejpam-5237	164	29	of	of	ADP
ejpam-5237	164	30	a	a	DET
ejpam-5237	164	31	different	different	ADJ
ejpam-5237	164	32	functional	functional	ADJ
ejpam-5237	164	33	form	form	NOUN
ejpam-5237	164	34	on	on	ADP
ejpam-5237	164	35	the	the	DET
ejpam-5237	164	36	solution	solution	NOUN
ejpam-5237	164	37	’s	’s	PART
ejpam-5237	164	38	characteristics	characteristic	NOUN
ejpam-5237	164	39	.	.	PUNCT
ejpam-5237	165	1	these	these	DET
ejpam-5237	165	2	graphical	graphical	ADJ
ejpam-5237	165	3	comparisons	comparison	NOUN
ejpam-5237	165	4	are	be	AUX
ejpam-5237	165	5	essential	essential	ADJ
ejpam-5237	165	6	for	for	ADP
ejpam-5237	165	7	understanding	understand	VERB
ejpam-5237	165	8	the	the	DET
ejpam-5237	165	9	nuances	nuance	NOUN
ejpam-5237	165	10	and	and	CCONJ
ejpam-5237	165	11	potential	potential	ADJ
ejpam-5237	165	12	advantages	advantage	NOUN
ejpam-5237	165	13	of	of	ADP
ejpam-5237	165	14	the	the	DET
ejpam-5237	165	15	new	new	ADJ
ejpam-5237	165	16	fractional	fractional	ADJ
ejpam-5237	165	17	derivative	derivative	ADJ
ejpam-5237	165	18	method	method	NOUN
ejpam-5237	165	19	over	over	ADP
ejpam-5237	165	20	traditional	traditional	ADJ
ejpam-5237	165	21	approaches	approach	NOUN
ejpam-5237	165	22	,	,	PUNCT
ejpam-5237	165	23	providing	provide	VERB
ejpam-5237	165	24	deeper	deep	ADJ
ejpam-5237	165	25	insights	insight	NOUN
ejpam-5237	165	26	into	into	ADP
ejpam-5237	165	27	its	its	PRON
ejpam-5237	165	28	applicability	applicability	NOUN
ejpam-5237	165	29	and	and	CCONJ
ejpam-5237	165	30	performance	performance	NOUN
ejpam-5237	165	31	in	in	ADP
ejpam-5237	165	32	various	various	ADJ
ejpam-5237	165	33	scenarios	scenario	NOUN
ejpam-5237	165	34	.	.	PUNCT
ejpam-5237	166	1	4.2	4.2	NUM
ejpam-5237	166	2	.	.	X
ejpam-5237	167	1	falling	fall	VERB
ejpam-5237	167	2	body	body	NOUN
ejpam-5237	167	3	problem	problem	NOUN
ejpam-5237	167	4	:	:	PUNCT
ejpam-5237	167	5	the	the	DET
ejpam-5237	167	6	problem	problem	NOUN
ejpam-5237	167	7	of	of	ADP
ejpam-5237	167	8	falling	fall	VERB
ejpam-5237	167	9	bodies	body	NOUN
ejpam-5237	167	10	,	,	PUNCT
ejpam-5237	167	11	also	also	ADV
ejpam-5237	167	12	known	know	VERB
ejpam-5237	167	13	as	as	ADP
ejpam-5237	167	14	the	the	DET
ejpam-5237	167	15	free	free	ADJ
ejpam-5237	167	16	fall	fall	NOUN
ejpam-5237	167	17	problem	problem	NOUN
ejpam-5237	167	18	,	,	PUNCT
ejpam-5237	167	19	is	be	AUX
ejpam-5237	167	20	a	a	DET
ejpam-5237	167	21	classic	classic	ADJ
ejpam-5237	167	22	physics	physics	NOUN
ejpam-5237	167	23	scenario	scenario	NOUN
ejpam-5237	167	24	that	that	PRON
ejpam-5237	167	25	examines	examine	VERB
ejpam-5237	167	26	the	the	DET
ejpam-5237	167	27	motion	motion	NOUN
ejpam-5237	167	28	of	of	ADP
ejpam-5237	167	29	objects	object	NOUN
ejpam-5237	167	30	under	under	ADP
ejpam-5237	167	31	the	the	DET
ejpam-5237	167	32	influence	influence	NOUN
ejpam-5237	167	33	of	of	ADP
ejpam-5237	167	34	gravity	gravity	NOUN
ejpam-5237	167	35	alone	alone	ADV
ejpam-5237	167	36	,	,	PUNCT
ejpam-5237	167	37	disregarding	disregard	VERB
ejpam-5237	167	38	other	other	ADJ
ejpam-5237	167	39	forces	force	NOUN
ejpam-5237	167	40	such	such	ADJ
ejpam-5237	167	41	as	as	ADP
ejpam-5237	167	42	air	air	NOUN
ejpam-5237	167	43	resistance	resistance	NOUN
ejpam-5237	167	44	.	.	PUNCT
ejpam-5237	168	1	it	it	PRON
ejpam-5237	168	2	serves	serve	VERB
ejpam-5237	168	3	as	as	ADP
ejpam-5237	168	4	a	a	DET
ejpam-5237	168	5	fundamental	fundamental	ADJ
ejpam-5237	168	6	concept	concept	NOUN
ejpam-5237	168	7	in	in	ADP
ejpam-5237	168	8	physics	physics	NOUN
ejpam-5237	168	9	,	,	PUNCT
ejpam-5237	168	10	providing	provide	VERB
ejpam-5237	168	11	insights	insight	NOUN
ejpam-5237	168	12	into	into	ADP
ejpam-5237	168	13	motion	motion	NOUN
ejpam-5237	168	14	,	,	PUNCT
ejpam-5237	168	15	acceleration	acceleration	NOUN
ejpam-5237	168	16	,	,	PUNCT
ejpam-5237	168	17	and	and	CCONJ
ejpam-5237	168	18	gravitational	gravitational	ADJ
ejpam-5237	168	19	effects	effect	NOUN
ejpam-5237	168	20	.	.	PUNCT
ejpam-5237	169	1	when	when	SCONJ
ejpam-5237	169	2	an	an	DET
ejpam-5237	169	3	object	object	NOUN
ejpam-5237	169	4	is	be	AUX
ejpam-5237	169	5	in	in	ADP
ejpam-5237	169	6	free	free	ADJ
ejpam-5237	169	7	fall	fall	NOUN
ejpam-5237	169	8	,	,	PUNCT
ejpam-5237	169	9	it	it	PRON
ejpam-5237	169	10	experiences	experience	VERB
ejpam-5237	169	11	a	a	DET
ejpam-5237	169	12	constant	constant	ADJ
ejpam-5237	169	13	acceleration	acceleration	NOUN
ejpam-5237	169	14	due	due	ADP
ejpam-5237	169	15	to	to	ADP
ejpam-5237	169	16	gravity	gravity	NOUN
ejpam-5237	169	17	,	,	PUNCT
ejpam-5237	169	18	which	which	PRON
ejpam-5237	169	19	on	on	ADP
ejpam-5237	169	20	the	the	DET
ejpam-5237	169	21	surface	surface	NOUN
ejpam-5237	169	22	of	of	ADP
ejpam-5237	169	23	the	the	DET
ejpam-5237	169	24	earth	earth	NOUN
ejpam-5237	169	25	is	be	AUX
ejpam-5237	169	26	approximately	approximately	ADV
ejpam-5237	169	27	9.8	9.8	NUM
ejpam-5237	169	28	m.s−1	m.s−1	NUM
ejpam-5237	169	29	directed	direct	VERB
ejpam-5237	169	30	towards	towards	ADP
ejpam-5237	169	31	the	the	DET
ejpam-5237	169	32	center	center	NOUN
ejpam-5237	169	33	of	of	ADP
ejpam-5237	169	34	the	the	DET
ejpam-5237	169	35	earth	earth	NOUN
ejpam-5237	169	36	.	.	PUNCT
ejpam-5237	170	1	this	this	DET
ejpam-5237	170	2	acceleration	acceleration	NOUN
ejpam-5237	170	3	is	be	AUX
ejpam-5237	170	4	represented	represent	VERB
ejpam-5237	170	5	by	by	ADP
ejpam-5237	170	6	the	the	DET
ejpam-5237	170	7	symbol	symbol	NOUN
ejpam-5237	170	8	g.	g.	VERB
ejpam-5237	170	9	the	the	DET
ejpam-5237	170	10	motion	motion	NOUN
ejpam-5237	170	11	of	of	ADP
ejpam-5237	170	12	falling	fall	VERB
ejpam-5237	170	13	bodies	body	NOUN
ejpam-5237	170	14	can	can	AUX
ejpam-5237	170	15	be	be	AUX
ejpam-5237	170	16	described	describe	VERB
ejpam-5237	170	17	using	use	VERB
ejpam-5237	170	18	equations	equation	NOUN
ejpam-5237	170	19	derived	derive	VERB
ejpam-5237	170	20	from	from	ADP
ejpam-5237	170	21	newton	newton	PROPN
ejpam-5237	170	22	’s	’s	PART
ejpam-5237	170	23	laws	law	NOUN
ejpam-5237	170	24	of	of	ADP
ejpam-5237	170	25	motion	motion	NOUN
ejpam-5237	170	26	and	and	CCONJ
ejpam-5237	170	27	kinematic	kinematic	ADJ
ejpam-5237	170	28	equations	equation	NOUN
ejpam-5237	170	29	.	.	PUNCT
ejpam-5237	171	1	these	these	DET
ejpam-5237	171	2	equations	equation	NOUN
ejpam-5237	171	3	allow	allow	VERB
ejpam-5237	171	4	us	we	PRON
ejpam-5237	171	5	to	to	PART
ejpam-5237	171	6	predict	predict	VERB
ejpam-5237	171	7	various	various	ADJ
ejpam-5237	171	8	aspects	aspect	NOUN
ejpam-5237	171	9	of	of	ADP
ejpam-5237	171	10	the	the	DET
ejpam-5237	171	11	motion	motion	NOUN
ejpam-5237	171	12	,	,	PUNCT
ejpam-5237	171	13	such	such	ADJ
ejpam-5237	171	14	as	as	ADP
ejpam-5237	171	15	the	the	DET
ejpam-5237	171	16	time	time	NOUN
ejpam-5237	171	17	taken	take	VERB
ejpam-5237	171	18	to	to	PART
ejpam-5237	171	19	fall	fall	VERB
ejpam-5237	171	20	,	,	PUNCT
ejpam-5237	171	21	the	the	DET
ejpam-5237	171	22	velocity	velocity	NOUN
ejpam-5237	171	23	at	at	ADP
ejpam-5237	171	24	any	any	DET
ejpam-5237	171	25	given	give	VERB
ejpam-5237	171	26	time	time	NOUN
ejpam-5237	171	27	,	,	PUNCT
ejpam-5237	171	28	and	and	CCONJ
ejpam-5237	171	29	the	the	DET
ejpam-5237	171	30	distance	distance	NOUN
ejpam-5237	171	31	traveled	travel	VERB
ejpam-5237	171	32	during	during	ADP
ejpam-5237	171	33	the	the	DET
ejpam-5237	171	34	fall	fall	NOUN
ejpam-5237	171	35	.	.	PUNCT
ejpam-5237	172	1	this	this	DET
ejpam-5237	172	2	problem	problem	NOUN
ejpam-5237	172	3	considers	consider	VERB
ejpam-5237	172	4	the	the	DET
ejpam-5237	172	5	fall	fall	NOUN
ejpam-5237	172	6	of	of	ADP
ejpam-5237	172	7	a	a	DET
ejpam-5237	172	8	body	body	NOUN
ejpam-5237	172	9	of	of	ADP
ejpam-5237	172	10	massm	massm	NOUN
ejpam-5237	172	11	,	,	PUNCT
ejpam-5237	172	12	starting	start	VERB
ejpam-5237	172	13	from	from	ADP
ejpam-5237	172	14	rest	rest	NOUN
ejpam-5237	172	15	,	,	PUNCT
ejpam-5237	172	16	under	under	ADP
ejpam-5237	172	17	the	the	DET
ejpam-5237	172	18	action	action	NOUN
ejpam-5237	172	19	of	of	ADP
ejpam-5237	172	20	gravity	gravity	NOUN
ejpam-5237	172	21	.	.	PUNCT
ejpam-5237	173	1	suppose	suppose	VERB
ejpam-5237	173	2	that	that	SCONJ
ejpam-5237	173	3	the	the	DET
ejpam-5237	173	4	chosen	choose	VERB
ejpam-5237	173	5	reference	reference	NOUN
ejpam-5237	173	6	system	system	NOUN
ejpam-5237	173	7	has	have	VERB
ejpam-5237	173	8	as	as	ADP
ejpam-5237	173	9	its	its	PRON
ejpam-5237	173	10	origin	origin	NOUN
ejpam-5237	173	11	the	the	DET
ejpam-5237	173	12	starting	starting	NOUN
ejpam-5237	173	13	point	point	NOUN
ejpam-5237	173	14	(	(	PUNCT
ejpam-5237	173	15	rest	rest	NOUN
ejpam-5237	173	16	of	of	ADP
ejpam-5237	173	17	the	the	DET
ejpam-5237	173	18	body	body	NOUN
ejpam-5237	173	19	)	)	PUNCT
ejpam-5237	173	20	at	at	ADP
ejpam-5237	173	21	a	a	DET
ejpam-5237	173	22	height	height	NOUN
ejpam-5237	173	23	a	a	PRON
ejpam-5237	173	24	from	from	ADP
ejpam-5237	173	25	the	the	DET
ejpam-5237	173	26	floor	floor	NOUN
ejpam-5237	173	27	at	at	ADP
ejpam-5237	173	28	the	the	DET
ejpam-5237	173	29	moment	moment	NOUN
ejpam-5237	173	30	the	the	DET
ejpam-5237	173	31	fall	fall	NOUN
ejpam-5237	173	32	begins	begin	VERB
ejpam-5237	173	33	,	,	PUNCT
ejpam-5237	173	34	that	that	ADV
ejpam-5237	173	35	is	is	ADV
ejpam-5237	173	36	,	,	PUNCT
ejpam-5237	173	37	at	at	ADP
ejpam-5237	173	38	t	t	NOUN
ejpam-5237	173	39	=	=	SYM
ejpam-5237	173	40	0	0	PROPN
ejpam-5237	173	41	.	.	PUNCT
ejpam-5237	174	1	the	the	DET
ejpam-5237	174	2	downward	downward	ADJ
ejpam-5237	174	3	movement	movement	NOUN
ejpam-5237	174	4	will	will	AUX
ejpam-5237	174	5	be	be	AUX
ejpam-5237	174	6	chosen	choose	VERB
ejpam-5237	174	7	as	as	ADP
ejpam-5237	174	8	positive	positive	ADJ
ejpam-5237	174	9	.	.	PUNCT
ejpam-5237	175	1	at	at	ADP
ejpam-5237	175	2	any	any	DET
ejpam-5237	175	3	point	point	NOUN
ejpam-5237	175	4	p	p	NOUN
ejpam-5237	175	5	on	on	ADP
ejpam-5237	175	6	its	its	PRON
ejpam-5237	175	7	trajectory	trajectory	NOUN
ejpam-5237	175	8	,	,	PUNCT
ejpam-5237	175	9	the	the	DET
ejpam-5237	175	10	distance	distance	NOUN
ejpam-5237	175	11	traveled	travel	VERB
ejpam-5237	175	12	will	will	AUX
ejpam-5237	175	13	be	be	AUX
ejpam-5237	175	14	the	the	DET
ejpam-5237	175	15	function	function	NOUN
ejpam-5237	175	16	y	y	PROPN
ejpam-5237	175	17	dependent	dependent	ADJ
ejpam-5237	175	18	on	on	ADP
ejpam-5237	175	19	time	time	NOUN
ejpam-5237	175	20	t	t	PROPN
ejpam-5237	175	21	,	,	PUNCT
ejpam-5237	175	22	consequently	consequently	ADV
ejpam-5237	175	23	,	,	PUNCT
ejpam-5237	175	24	using	use	VERB
ejpam-5237	175	25	ordinary	ordinary	ADJ
ejpam-5237	175	26	derivatives	derivative	NOUN
ejpam-5237	175	27	,	,	PUNCT
ejpam-5237	175	28	the	the	DET
ejpam-5237	175	29	instantaneous	instantaneous	ADJ
ejpam-5237	175	30	velocity	velocity	NOUN
ejpam-5237	175	31	and	and	CCONJ
ejpam-5237	175	32	acceleration	acceleration	NOUN
ejpam-5237	175	33	snapshot	snapshot	NOUN
ejpam-5237	175	34	,	,	PUNCT
ejpam-5237	175	35	respectively	respectively	ADV
ejpam-5237	175	36	,	,	PUNCT
ejpam-5237	175	37	are	be	AUX
ejpam-5237	175	38	given	give	VERB
ejpam-5237	175	39	by	by	ADP
ejpam-5237	175	40	v(t	v(t	ADJ
ejpam-5237	175	41	)	)	PUNCT
ejpam-5237	175	42	=	=	PUNCT
ejpam-5237	175	43	dy(t	dy(t	X
ejpam-5237	175	44	)	)	PUNCT
ejpam-5237	175	45	dt	dt	X
ejpam-5237	175	46	,	,	PUNCT
ejpam-5237	175	47	a	a	PRON
ejpam-5237	175	48	=	=	X
ejpam-5237	175	49	dv(t	dv(t	NOUN
ejpam-5237	175	50	)	)	PUNCT
ejpam-5237	175	51	dt	dt	NOUN
ejpam-5237	176	1	=	=	SYM
ejpam-5237	176	2	d2y(t	d2y(t	PROPN
ejpam-5237	176	3	)	)	PUNCT
ejpam-5237	176	4	dt2	dt2	PROPN
ejpam-5237	176	5	.	.	PUNCT
ejpam-5237	177	1	(	(	PUNCT
ejpam-5237	177	2	27	27	NUM
ejpam-5237	177	3	)	)	PUNCT
ejpam-5237	177	4	according	accord	VERB
ejpam-5237	177	5	to	to	ADP
ejpam-5237	177	6	newton	newton	PROPN
ejpam-5237	177	7	’s	’s	PART
ejpam-5237	177	8	law	law	NOUN
ejpam-5237	177	9	,	,	PUNCT
ejpam-5237	177	10	we	we	PRON
ejpam-5237	177	11	have	have	VERB
ejpam-5237	177	12	f	f	NOUN
ejpam-5237	177	13	=	=	SYM
ejpam-5237	177	14	mg	mg	PROPN
ejpam-5237	177	15	,	,	PUNCT
ejpam-5237	178	1	dv(t)dt	dv(t)dt	NOUN
ejpam-5237	178	2	=	=	PROPN
ejpam-5237	178	3	g.	g.	PROPN
ejpam-5237	178	4	then	then	ADV
ejpam-5237	178	5	this	this	DET
ejpam-5237	178	6	problem	problem	NOUN
ejpam-5237	178	7	is	be	AUX
ejpam-5237	178	8	modeled	model	VERB
ejpam-5237	178	9	by	by	ADP
ejpam-5237	178	10	the	the	DET
ejpam-5237	178	11	following	follow	VERB
ejpam-5237	178	12	differential	differential	ADJ
ejpam-5237	178	13	equation	equation	NOUN
ejpam-5237	178	14	with	with	ADP
ejpam-5237	178	15	initial	initial	ADJ
ejpam-5237	178	16	condition	condition	NOUN
ejpam-5237	178	17	as	as	SCONJ
ejpam-5237	178	18	follows	follow	VERB
ejpam-5237	178	19	dv(t	dv(t	NOUN
ejpam-5237	178	20	)	)	PUNCT
ejpam-5237	178	21	dt	dt	NOUN
ejpam-5237	178	22	=	=	SYM
ejpam-5237	178	23	g	g	PROPN
ejpam-5237	178	24	,	,	PUNCT
ejpam-5237	178	25	v(0	v(0	PROPN
ejpam-5237	178	26	)	)	PUNCT
ejpam-5237	178	27	=	=	SYM
ejpam-5237	178	28	0	0	NUM
ejpam-5237	178	29	,	,	PUNCT
ejpam-5237	178	30	y(0	y(0	PROPN
ejpam-5237	178	31	)	)	PUNCT
ejpam-5237	178	32	=	=	SYM
ejpam-5237	178	33	a.	a.	NOUN
ejpam-5237	178	34	(	(	PUNCT
ejpam-5237	178	35	28	28	NUM
ejpam-5237	178	36	)	)	PUNCT
ejpam-5237	178	37	now	now	ADV
ejpam-5237	178	38	consider	consider	VERB
ejpam-5237	178	39	the	the	DET
ejpam-5237	178	40	problem	problem	NOUN
ejpam-5237	178	41	with	with	ADP
ejpam-5237	178	42	the	the	DET
ejpam-5237	178	43	new	new	ADJ
ejpam-5237	178	44	conformable	conformable	ADJ
ejpam-5237	178	45	fractional	fractional	ADJ
ejpam-5237	178	46	derivative	derivative	NOUN
ejpam-5237	178	47	defined	define	VERB
ejpam-5237	178	48	in	in	ADP
ejpam-5237	178	49	definition	definition	NOUN
ejpam-5237	178	50	1	1	NUM
ejpam-5237	178	51	.	.	PUNCT
ejpam-5237	179	1	dαv(t	dαv(t	X
ejpam-5237	179	2	)	)	PUNCT
ejpam-5237	179	3	=	=	SYM
ejpam-5237	179	4	g	g	PROPN
ejpam-5237	179	5	,	,	PUNCT
ejpam-5237	179	6	v(0	v(0	PROPN
ejpam-5237	179	7	)	)	PUNCT
ejpam-5237	179	8	=	=	SYM
ejpam-5237	179	9	0	0	NUM
ejpam-5237	179	10	,	,	PUNCT
ejpam-5237	179	11	y(0	y(0	PROPN
ejpam-5237	179	12	)	)	PUNCT
ejpam-5237	179	13	=	=	SYM
ejpam-5237	179	14	a.	a.	NOUN
ejpam-5237	179	15	(	(	PUNCT
ejpam-5237	179	16	29	29	NUM
ejpam-5237	179	17	)	)	PUNCT
ejpam-5237	179	18	using	use	VERB
ejpam-5237	179	19	theorem	theorem	NOUN
ejpam-5237	179	20	2.4	2.4	NUM
ejpam-5237	179	21	,	,	PUNCT
ejpam-5237	179	22	part	part	NOUN
ejpam-5237	179	23	6	6	NUM
ejpam-5237	179	24	)	)	PUNCT
ejpam-5237	179	25	we	we	PRON
ejpam-5237	179	26	get	get	VERB
ejpam-5237	179	27	:	:	PUNCT
ejpam-5237	179	28	e(α−1)tv′(t	e(α−1)tv′(t	X
ejpam-5237	179	29	)	)	PUNCT
ejpam-5237	179	30	=	=	SYM
ejpam-5237	179	31	g.	g.	NOUN
ejpam-5237	179	32	(	(	PUNCT
ejpam-5237	179	33	30	30	NUM
ejpam-5237	179	34	)	)	PUNCT
ejpam-5237	179	35	a.	a.	NOUN
ejpam-5237	179	36	ait	ait	NOUN
ejpam-5237	179	37	brahim	brahim	PROPN
ejpam-5237	179	38	et	et	PROPN
ejpam-5237	179	39	all	all	DET
ejpam-5237	179	40	/	/	SYM
ejpam-5237	179	41	eur	eur	PROPN
ejpam-5237	179	42	.	.	PUNCT
ejpam-5237	180	1	j.	j.	PROPN
ejpam-5237	180	2	pure	pure	PROPN
ejpam-5237	180	3	appl	appl	PROPN
ejpam-5237	180	4	.	.	PROPN
ejpam-5237	180	5	math	math	PROPN
ejpam-5237	180	6	,	,	PUNCT
ejpam-5237	180	7	17	17	NUM
ejpam-5237	180	8	(	(	PUNCT
ejpam-5237	180	9	3	3	NUM
ejpam-5237	180	10	)	)	PUNCT
ejpam-5237	180	11	(	(	PUNCT
ejpam-5237	180	12	2024	2024	NUM
ejpam-5237	180	13	)	)	PUNCT
ejpam-5237	180	14	,	,	PUNCT
ejpam-5237	180	15	1842	1842	NUM
ejpam-5237	180	16	-	-	SYM
ejpam-5237	180	17	1854	1854	NUM
ejpam-5237	180	18	1851	1851	NUM
ejpam-5237	180	19	integrating	integrating	NOUN
ejpam-5237	180	20	,	,	PUNCT
ejpam-5237	180	21	we	we	PRON
ejpam-5237	180	22	obtain	obtain	VERB
ejpam-5237	180	23	:	:	PUNCT
ejpam-5237	181	1	v(t	v(t	NUM
ejpam-5237	181	2	)	)	PUNCT
ejpam-5237	181	3	=	=	SYM
ejpam-5237	181	4	g	g	NOUN
ejpam-5237	181	5	(	(	PUNCT
ejpam-5237	181	6	1	1	NUM
ejpam-5237	181	7	1−	1−	NUM
ejpam-5237	181	8	α	α	NOUN
ejpam-5237	181	9	e(1−α)t	e(1−α)t	NOUN
ejpam-5237	181	10	)	)	PUNCT
ejpam-5237	182	1	+	+	CCONJ
ejpam-5237	182	2	c.	c.	NOUN
ejpam-5237	182	3	(	(	PUNCT
ejpam-5237	182	4	31	31	NUM
ejpam-5237	182	5	)	)	PUNCT
ejpam-5237	182	6	using	use	VERB
ejpam-5237	182	7	the	the	DET
ejpam-5237	182	8	initial	initial	ADJ
ejpam-5237	182	9	condition	condition	NOUN
ejpam-5237	182	10	,	,	PUNCT
ejpam-5237	182	11	namely	namely	ADV
ejpam-5237	182	12	v(0	v(0	NOUN
ejpam-5237	182	13	)	)	PUNCT
ejpam-5237	182	14	=	=	SYM
ejpam-5237	182	15	0	0	NUM
ejpam-5237	182	16	,	,	PUNCT
ejpam-5237	182	17	we	we	PRON
ejpam-5237	182	18	find	find	VERB
ejpam-5237	182	19	that	that	SCONJ
ejpam-5237	182	20	the	the	DET
ejpam-5237	182	21	constant	constant	ADJ
ejpam-5237	182	22	is	be	AUX
ejpam-5237	182	23	zero	zero	NUM
ejpam-5237	182	24	.	.	PUNCT
ejpam-5237	183	1	similary	similary	ADJ
ejpam-5237	183	2	,	,	PUNCT
ejpam-5237	183	3	we	we	PRON
ejpam-5237	183	4	obtain	obtain	VERB
ejpam-5237	183	5	:	:	PUNCT
ejpam-5237	183	6	y′(t	y′(t	X
ejpam-5237	183	7	)	)	PUNCT
ejpam-5237	183	8	=	=	SYM
ejpam-5237	183	9	ge(1−α)t	ge(1−α)t	PROPN
ejpam-5237	183	10	(	(	PUNCT
ejpam-5237	183	11	1	1	NUM
ejpam-5237	183	12	1−	1−	NUM
ejpam-5237	183	13	α	α	NOUN
ejpam-5237	183	14	e(1−α)t	e(1−α)t	NOUN
ejpam-5237	183	15	)	)	PUNCT
ejpam-5237	183	16	.	.	PUNCT
ejpam-5237	184	1	(	(	PUNCT
ejpam-5237	184	2	32	32	NUM
ejpam-5237	184	3	)	)	PUNCT
ejpam-5237	184	4	then	then	ADV
ejpam-5237	184	5	,	,	PUNCT
ejpam-5237	184	6	we	we	PRON
ejpam-5237	184	7	have	have	VERB
ejpam-5237	184	8	:	:	PUNCT
ejpam-5237	184	9	y(t	y(t	X
ejpam-5237	184	10	)	)	PUNCT
ejpam-5237	185	1	=	=	SYM
ejpam-5237	185	2	g	g	PROPN
ejpam-5237	185	3	2(1−	2(1−	NUM
ejpam-5237	185	4	α)2	α)2	NOUN
ejpam-5237	185	5	e2(1−α)t	e2(1−α)t	VERB
ejpam-5237	186	1	+	+	PROPN
ejpam-5237	186	2	m.	m.	NOUN
ejpam-5237	186	3	(	(	PUNCT
ejpam-5237	186	4	33	33	NUM
ejpam-5237	186	5	)	)	PUNCT
ejpam-5237	186	6	using	use	VERB
ejpam-5237	186	7	the	the	DET
ejpam-5237	186	8	condition	condition	NOUN
ejpam-5237	186	9	initial	initial	NOUN
ejpam-5237	186	10	,	,	PUNCT
ejpam-5237	186	11	we	we	PRON
ejpam-5237	186	12	find	find	VERB
ejpam-5237	186	13	that	that	PRON
ejpam-5237	186	14	:	:	PUNCT
ejpam-5237	186	15	y(t	y(t	X
ejpam-5237	186	16	)	)	PUNCT
ejpam-5237	187	1	=	=	SYM
ejpam-5237	187	2	g	g	PROPN
ejpam-5237	187	3	2(1−	2(1−	NUM
ejpam-5237	187	4	α)2	α)2	NOUN
ejpam-5237	187	5	e2(1−α)t	e2(1−α)t	VERB
ejpam-5237	188	1	+	+	PROPN
ejpam-5237	188	2	a.	a.	NOUN
ejpam-5237	188	3	(	(	PUNCT
ejpam-5237	188	4	34	34	NUM
ejpam-5237	188	5	)	)	PUNCT
ejpam-5237	188	6	figure	figure	NOUN
ejpam-5237	188	7	4	4	NUM
ejpam-5237	188	8	:	:	PUNCT
ejpam-5237	188	9	comparative	comparative	ADJ
ejpam-5237	188	10	solutions	solution	NOUN
ejpam-5237	188	11	for	for	ADP
ejpam-5237	188	12	serval	serval	NOUN
ejpam-5237	188	13	values	value	NOUN
ejpam-5237	188	14	of	of	ADP
ejpam-5237	188	15	α	α	NOUN
ejpam-5237	188	16	,	,	PUNCT
ejpam-5237	188	17	with	with	ADP
ejpam-5237	188	18	the	the	DET
ejpam-5237	188	19	new	new	ADJ
ejpam-5237	188	20	conformable	conformable	ADJ
ejpam-5237	188	21	fractional	fractional	ADJ
ejpam-5237	188	22	derivative	derivative	NOUN
ejpam-5237	188	23	.	.	PUNCT
ejpam-5237	189	1	in	in	ADP
ejpam-5237	189	2	this	this	DET
ejpam-5237	189	3	example	example	NOUN
ejpam-5237	189	4	,	,	PUNCT
ejpam-5237	189	5	we	we	PRON
ejpam-5237	189	6	present	present	VERB
ejpam-5237	189	7	the	the	DET
ejpam-5237	189	8	solution	solution	NOUN
ejpam-5237	189	9	for	for	ADP
ejpam-5237	189	10	various	various	ADJ
ejpam-5237	189	11	values	value	NOUN
ejpam-5237	189	12	of	of	ADP
ejpam-5237	189	13	α	α	NOUN
ejpam-5237	189	14	:	:	PUNCT
ejpam-5237	189	15	α	α	NOUN
ejpam-5237	189	16	=	=	SYM
ejpam-5237	189	17	0	0	PROPN
ejpam-5237	189	18	,	,	PUNCT
ejpam-5237	189	19	α	α	NOUN
ejpam-5237	189	20	=	=	NOUN
ejpam-5237	189	21	0.25	0.25	NUM
ejpam-5237	189	22	,	,	PUNCT
ejpam-5237	189	23	α	α	NOUN
ejpam-5237	189	24	=	=	SYM
ejpam-5237	189	25	0.5	0.5	NUM
ejpam-5237	189	26	,	,	PUNCT
ejpam-5237	189	27	and	and	CCONJ
ejpam-5237	189	28	α	α	NOUN
ejpam-5237	189	29	=	=	SYM
ejpam-5237	189	30	0.75	0.75	NUM
ejpam-5237	189	31	,	,	PUNCT
ejpam-5237	189	32	utilizing	utilize	VERB
ejpam-5237	189	33	the	the	DET
ejpam-5237	189	34	new	new	ADJ
ejpam-5237	189	35	conformable	conformable	ADJ
ejpam-5237	189	36	fractional	fractional	ADJ
ejpam-5237	189	37	calculus	calculus	NOUN
ejpam-5237	189	38	(	(	PUNCT
ejpam-5237	189	39	see	see	VERB
ejpam-5237	189	40	[	[	X
ejpam-5237	189	41	1	1	NUM
ejpam-5237	189	42	,	,	PUNCT
ejpam-5237	189	43	12	12	NUM
ejpam-5237	189	44	]	]	PUNCT
ejpam-5237	189	45	)	)	PUNCT
ejpam-5237	189	46	.	.	PUNCT
ejpam-5237	190	1	we	we	PRON
ejpam-5237	190	2	then	then	ADV
ejpam-5237	190	3	compare	compare	VERB
ejpam-5237	190	4	these	these	DET
ejpam-5237	190	5	solutions	solution	NOUN
ejpam-5237	190	6	with	with	ADP
ejpam-5237	190	7	those	those	PRON
ejpam-5237	190	8	obtained	obtain	VERB
ejpam-5237	190	9	using	use	VERB
ejpam-5237	190	10	other	other	ADJ
ejpam-5237	190	11	methods	method	NOUN
ejpam-5237	190	12	,	,	PUNCT
ejpam-5237	190	13	such	such	ADJ
ejpam-5237	190	14	as	as	ADP
ejpam-5237	190	15	khalil	khalil	PROPN
ejpam-5237	190	16	’s	’s	PART
ejpam-5237	190	17	conformable	conformable	ADJ
ejpam-5237	190	18	fractional	fractional	ADJ
ejpam-5237	190	19	derivative	derivative	NOUN
ejpam-5237	190	20	(	(	PUNCT
ejpam-5237	190	21	see	see	VERB
ejpam-5237	190	22	[	[	X
ejpam-5237	190	23	13	13	NUM
ejpam-5237	190	24	]	]	NUM
ejpam-5237	190	25	)	)	PUNCT
ejpam-5237	190	26	,	,	PUNCT
ejpam-5237	190	27	as	as	ADV
ejpam-5237	190	28	well	well	ADV
ejpam-5237	190	29	as	as	ADP
ejpam-5237	190	30	ordinary	ordinary	ADJ
ejpam-5237	190	31	derivatives	derivative	NOUN
ejpam-5237	190	32	.	.	PUNCT
ejpam-5237	191	1	this	this	DET
ejpam-5237	191	2	comparison	comparison	NOUN
ejpam-5237	191	3	highlights	highlight	VERB
ejpam-5237	191	4	the	the	DET
ejpam-5237	191	5	differences	difference	NOUN
ejpam-5237	191	6	in	in	ADP
ejpam-5237	191	7	the	the	DET
ejpam-5237	191	8	behavior	behavior	NOUN
ejpam-5237	191	9	of	of	ADP
ejpam-5237	191	10	the	the	DET
ejpam-5237	191	11	solutions	solution	NOUN
ejpam-5237	191	12	across	across	ADP
ejpam-5237	191	13	these	these	DET
ejpam-5237	191	14	methods	method	NOUN
ejpam-5237	191	15	,	,	PUNCT
ejpam-5237	191	16	illustrating	illustrate	VERB
ejpam-5237	191	17	the	the	DET
ejpam-5237	191	18	potential	potential	ADJ
ejpam-5237	191	19	advantages	advantage	NOUN
ejpam-5237	191	20	and	and	CCONJ
ejpam-5237	191	21	limitations	limitation	NOUN
ejpam-5237	191	22	of	of	ADP
ejpam-5237	191	23	the	the	DET
ejpam-5237	191	24	new	new	ADJ
ejpam-5237	191	25	conformable	conformable	ADJ
ejpam-5237	191	26	fractional	fractional	ADJ
ejpam-5237	191	27	calculus	calculus	NOUN
ejpam-5237	191	28	in	in	ADP
ejpam-5237	191	29	contrast	contrast	NOUN
ejpam-5237	191	30	to	to	ADP
ejpam-5237	191	31	more	more	ADV
ejpam-5237	191	32	traditional	traditional	ADJ
ejpam-5237	191	33	approaches	approach	NOUN
ejpam-5237	191	34	.	.	PUNCT
ejpam-5237	192	1	a.	a.	PROPN
ejpam-5237	192	2	ait	ait	PROPN
ejpam-5237	192	3	brahim	brahim	PROPN
ejpam-5237	192	4	et	et	PROPN
ejpam-5237	192	5	all	all	DET
ejpam-5237	192	6	/	/	SYM
ejpam-5237	192	7	eur	eur	PROPN
ejpam-5237	192	8	.	.	PUNCT
ejpam-5237	193	1	j.	j.	PROPN
ejpam-5237	193	2	pure	pure	PROPN
ejpam-5237	193	3	appl	appl	PROPN
ejpam-5237	193	4	.	.	PROPN
ejpam-5237	193	5	math	math	PROPN
ejpam-5237	193	6	,	,	PUNCT
ejpam-5237	193	7	17	17	NUM
ejpam-5237	193	8	(	(	PUNCT
ejpam-5237	193	9	3	3	NUM
ejpam-5237	193	10	)	)	PUNCT
ejpam-5237	193	11	(	(	PUNCT
ejpam-5237	193	12	2024	2024	NUM
ejpam-5237	193	13	)	)	PUNCT
ejpam-5237	193	14	,	,	PUNCT
ejpam-5237	193	15	1842	1842	NUM
ejpam-5237	193	16	-	-	SYM
ejpam-5237	193	17	1854	1854	NUM
ejpam-5237	193	18	1852	1852	NUM
ejpam-5237	193	19	5	5	NUM
ejpam-5237	193	20	.	.	PUNCT
ejpam-5237	194	1	conclusion	conclusion	NOUN
ejpam-5237	194	2	numerical	numerical	ADJ
ejpam-5237	194	3	simulations	simulation	NOUN
ejpam-5237	194	4	conducted	conduct	VERB
ejpam-5237	194	5	on	on	ADP
ejpam-5237	194	6	the	the	DET
ejpam-5237	194	7	solutions	solution	NOUN
ejpam-5237	194	8	to	to	ADP
ejpam-5237	194	9	initial	initial	ADJ
ejpam-5237	194	10	value	value	NOUN
ejpam-5237	194	11	problems	problem	NOUN
ejpam-5237	194	12	of	of	ADP
ejpam-5237	194	13	fractional	fractional	ADJ
ejpam-5237	194	14	ordinary	ordinary	ADJ
ejpam-5237	194	15	differential	differential	ADJ
ejpam-5237	194	16	equations	equation	NOUN
ejpam-5237	194	17	reveal	reveal	VERB
ejpam-5237	194	18	that	that	SCONJ
ejpam-5237	194	19	the	the	DET
ejpam-5237	194	20	graphs	graph	NOUN
ejpam-5237	194	21	of	of	ADP
ejpam-5237	194	22	solutions	solution	NOUN
ejpam-5237	194	23	using	use	VERB
ejpam-5237	194	24	riemann	riemann	PROPN
ejpam-5237	194	25	-	-	PUNCT
ejpam-5237	194	26	liouville	liouville	VERB
ejpam-5237	194	27	and	and	CCONJ
ejpam-5237	194	28	conformable	conformable	ADJ
ejpam-5237	194	29	fractional	fractional	ADJ
ejpam-5237	194	30	derivatives	derivative	NOUN
ejpam-5237	194	31	exhibit	exhibit	VERB
ejpam-5237	194	32	significant	significant	ADJ
ejpam-5237	194	33	proximity	proximity	NOUN
ejpam-5237	194	34	for	for	ADP
ejpam-5237	194	35	0	0	NUM
ejpam-5237	194	36	<	<	X
ejpam-5237	194	37	α	α	X
ejpam-5237	194	38	<	<	X
ejpam-5237	194	39	1	1	NUM
ejpam-5237	194	40	.	.	PUNCT
ejpam-5237	195	1	furthermore	furthermore	ADV
ejpam-5237	195	2	,	,	PUNCT
ejpam-5237	195	3	the	the	DET
ejpam-5237	195	4	solutions	solution	NOUN
ejpam-5237	195	5	’	'	PUNCT
ejpam-5237	195	6	graphs	graph	NOUN
ejpam-5237	195	7	employing	employ	VERB
ejpam-5237	195	8	all	all	DET
ejpam-5237	195	9	three	three	NUM
ejpam-5237	195	10	fractional	fractional	ADJ
ejpam-5237	195	11	derivatives	derivative	NOUN
ejpam-5237	195	12	show	show	VERB
ejpam-5237	195	13	substantial	substantial	ADJ
ejpam-5237	195	14	similarity	similarity	NOUN
ejpam-5237	195	15	for	for	ADP
ejpam-5237	195	16	1/2	1/2	NUM
ejpam-5237	195	17	<	<	X
ejpam-5237	195	18	α	α	X
ejpam-5237	195	19	<	<	X
ejpam-5237	195	20	1	1	NUM
ejpam-5237	195	21	.	.	PUNCT
ejpam-5237	196	1	hence	hence	ADV
ejpam-5237	196	2	,	,	PUNCT
ejpam-5237	196	3	conformable	conformable	ADJ
ejpam-5237	196	4	fractional	fractional	ADJ
ejpam-5237	196	5	derivatives	derivative	NOUN
ejpam-5237	196	6	offer	offer	VERB
ejpam-5237	196	7	a	a	DET
ejpam-5237	196	8	viable	viable	ADJ
ejpam-5237	196	9	alternative	alternative	NOUN
ejpam-5237	196	10	to	to	ADP
ejpam-5237	196	11	riemann	riemann	PROPN
ejpam-5237	196	12	-	-	PUNCT
ejpam-5237	196	13	liouville	liouville	PROPN
ejpam-5237	196	14	and	and	CCONJ
ejpam-5237	196	15	caputo	caputo	PROPN
ejpam-5237	196	16	derivatives	derivative	NOUN
ejpam-5237	196	17	within	within	ADP
ejpam-5237	196	18	the	the	DET
ejpam-5237	196	19	range	range	NOUN
ejpam-5237	196	20	of	of	ADP
ejpam-5237	196	21	1/2	1/2	NUM
ejpam-5237	196	22	<	<	X
ejpam-5237	196	23	α	α	X
ejpam-5237	196	24	<	<	X
ejpam-5237	196	25	1	1	NUM
ejpam-5237	196	26	.	.	PUNCT
ejpam-5237	197	1	the	the	DET
ejpam-5237	197	2	simplicity	simplicity	NOUN
ejpam-5237	197	3	of	of	ADP
ejpam-5237	197	4	the	the	DET
ejpam-5237	197	5	conformable	conformable	ADJ
ejpam-5237	197	6	fractional	fractional	ADJ
ejpam-5237	197	7	derivative	derivative	NOUN
ejpam-5237	197	8	’s	’s	PART
ejpam-5237	197	9	definition	definition	NOUN
ejpam-5237	197	10	stands	stand	VERB
ejpam-5237	197	11	out	out	ADP
ejpam-5237	197	12	as	as	ADP
ejpam-5237	197	13	a	a	DET
ejpam-5237	197	14	notable	notable	ADJ
ejpam-5237	197	15	advantage	advantage	NOUN
ejpam-5237	197	16	over	over	ADP
ejpam-5237	197	17	riemann	riemann	PROPN
ejpam-5237	197	18	-	-	PUNCT
ejpam-5237	197	19	liouville	liouville	PROPN
ejpam-5237	197	20	and	and	CCONJ
ejpam-5237	197	21	caputo	caputo	PROPN
ejpam-5237	197	22	derivatives	derivative	NOUN
ejpam-5237	197	23	.	.	PUNCT
ejpam-5237	198	1	unlike	unlike	ADP
ejpam-5237	198	2	these	these	DET
ejpam-5237	198	3	traditional	traditional	ADJ
ejpam-5237	198	4	fractional	fractional	ADJ
ejpam-5237	198	5	derivatives	derivative	NOUN
ejpam-5237	198	6	,	,	PUNCT
ejpam-5237	198	7	the	the	DET
ejpam-5237	198	8	conformable	conformable	ADJ
ejpam-5237	198	9	fractional	fractional	ADJ
ejpam-5237	198	10	derivative	derivative	NOUN
ejpam-5237	198	11	is	be	AUX
ejpam-5237	198	12	more	more	ADV
ejpam-5237	198	13	intuitive	intuitive	ADJ
ejpam-5237	198	14	and	and	CCONJ
ejpam-5237	198	15	straightforward	straightforward	ADJ
ejpam-5237	198	16	to	to	PART
ejpam-5237	198	17	implement	implement	VERB
ejpam-5237	198	18	,	,	PUNCT
ejpam-5237	198	19	reducing	reduce	VERB
ejpam-5237	198	20	the	the	DET
ejpam-5237	198	21	complexity	complexity	NOUN
ejpam-5237	198	22	often	often	ADV
ejpam-5237	198	23	associated	associate	VERB
ejpam-5237	198	24	with	with	ADP
ejpam-5237	198	25	fractional	fractional	ADJ
ejpam-5237	198	26	calculus	calculus	NOUN
ejpam-5237	198	27	.	.	PUNCT
ejpam-5237	199	1	additionally	additionally	ADV
ejpam-5237	199	2	,	,	PUNCT
ejpam-5237	199	3	the	the	DET
ejpam-5237	199	4	conformable	conformable	ADJ
ejpam-5237	199	5	fractional	fractional	ADJ
ejpam-5237	199	6	derivative	derivative	ADJ
ejpam-5237	199	7	aligns	align	NOUN
ejpam-5237	199	8	with	with	ADP
ejpam-5237	199	9	several	several	ADJ
ejpam-5237	199	10	fundamental	fundamental	ADJ
ejpam-5237	199	11	properties	property	NOUN
ejpam-5237	199	12	of	of	ADP
ejpam-5237	199	13	the	the	DET
ejpam-5237	199	14	usual	usual	ADJ
ejpam-5237	199	15	derivative	derivative	NOUN
ejpam-5237	199	16	,	,	PUNCT
ejpam-5237	199	17	such	such	ADJ
ejpam-5237	199	18	as	as	ADP
ejpam-5237	199	19	the	the	DET
ejpam-5237	199	20	product	product	NOUN
ejpam-5237	199	21	rule	rule	NOUN
ejpam-5237	199	22	,	,	PUNCT
ejpam-5237	199	23	quotient	quotient	NOUN
ejpam-5237	199	24	rule	rule	NOUN
ejpam-5237	199	25	,	,	PUNCT
ejpam-5237	199	26	and	and	CCONJ
ejpam-5237	199	27	chain	chain	NOUN
ejpam-5237	199	28	rule	rule	NOUN
ejpam-5237	199	29	,	,	PUNCT
ejpam-5237	199	30	which	which	PRON
ejpam-5237	199	31	are	be	AUX
ejpam-5237	199	32	not	not	PART
ejpam-5237	199	33	entirely	entirely	ADV
ejpam-5237	199	34	satisfied	satisfied	ADJ
ejpam-5237	199	35	by	by	ADP
ejpam-5237	199	36	riemann	riemann	PROPN
ejpam-5237	199	37	-	-	PUNCT
ejpam-5237	199	38	liouville	liouville	PROPN
ejpam-5237	199	39	and	and	CCONJ
ejpam-5237	199	40	caputo	caputo	PROPN
ejpam-5237	199	41	derivatives	derivative	NOUN
ejpam-5237	199	42	.	.	PUNCT
ejpam-5237	200	1	this	this	DET
ejpam-5237	200	2	compatibility	compatibility	NOUN
ejpam-5237	200	3	with	with	ADP
ejpam-5237	200	4	classical	classical	ADJ
ejpam-5237	200	5	derivative	derivative	ADJ
ejpam-5237	200	6	properties	property	NOUN
ejpam-5237	200	7	further	far	ADV
ejpam-5237	200	8	enhances	enhance	VERB
ejpam-5237	200	9	its	its	PRON
ejpam-5237	200	10	appeal	appeal	NOUN
ejpam-5237	200	11	and	and	CCONJ
ejpam-5237	200	12	broadens	broaden	VERB
ejpam-5237	200	13	its	its	PRON
ejpam-5237	200	14	applicability	applicability	NOUN
ejpam-5237	200	15	in	in	ADP
ejpam-5237	200	16	various	various	ADJ
ejpam-5237	200	17	fields	field	NOUN
ejpam-5237	200	18	.	.	PUNCT
ejpam-5237	201	1	furthermore	furthermore	ADV
ejpam-5237	201	2	,	,	PUNCT
ejpam-5237	201	3	the	the	DET
ejpam-5237	201	4	conformable	conformable	ADJ
ejpam-5237	201	5	fractional	fractional	ADJ
ejpam-5237	201	6	derivative	derivative	NOUN
ejpam-5237	201	7	offers	offer	VERB
ejpam-5237	201	8	a	a	DET
ejpam-5237	201	9	unique	unique	ADJ
ejpam-5237	201	10	flexibility	flexibility	NOUN
ejpam-5237	201	11	by	by	ADP
ejpam-5237	201	12	allowing	allow	VERB
ejpam-5237	201	13	for	for	ADP
ejpam-5237	201	14	the	the	DET
ejpam-5237	201	15	consideration	consideration	NOUN
ejpam-5237	201	16	of	of	ADP
ejpam-5237	201	17	both	both	CCONJ
ejpam-5237	201	18	conformable	conformable	ADJ
ejpam-5237	201	19	and	and	CCONJ
ejpam-5237	201	20	non	non	ADJ
ejpam-5237	201	21	-	-	ADJ
ejpam-5237	201	22	conformable	conformable	ADJ
ejpam-5237	201	23	kernels	kernel	NOUN
ejpam-5237	201	24	,	,	PUNCT
ejpam-5237	201	25	as	as	ADV
ejpam-5237	201	26	well	well	ADV
ejpam-5237	201	27	as	as	ADP
ejpam-5237	201	28	the	the	DET
ejpam-5237	201	29	ability	ability	NOUN
ejpam-5237	201	30	to	to	PART
ejpam-5237	201	31	vary	vary	VERB
ejpam-5237	201	32	the	the	DET
ejpam-5237	201	33	order	order	NOUN
ejpam-5237	201	34	of	of	ADP
ejpam-5237	201	35	α	α	PRON
ejpam-5237	201	36	.	.	PUNCT
ejpam-5237	202	1	this	this	DET
ejpam-5237	202	2	dual	dual	ADJ
ejpam-5237	202	3	capability	capability	NOUN
ejpam-5237	202	4	provides	provide	VERB
ejpam-5237	202	5	a	a	DET
ejpam-5237	202	6	significant	significant	ADJ
ejpam-5237	202	7	advantage	advantage	NOUN
ejpam-5237	202	8	in	in	ADP
ejpam-5237	202	9	modeling	modeling	NOUN
ejpam-5237	202	10	and	and	CCONJ
ejpam-5237	202	11	analysis	analysis	NOUN
ejpam-5237	202	12	,	,	PUNCT
ejpam-5237	202	13	enabling	enable	VERB
ejpam-5237	202	14	researchers	researcher	NOUN
ejpam-5237	202	15	and	and	CCONJ
ejpam-5237	202	16	practitioners	practitioner	NOUN
ejpam-5237	202	17	to	to	PART
ejpam-5237	202	18	tailor	tailor	VERB
ejpam-5237	202	19	their	their	PRON
ejpam-5237	202	20	approach	approach	NOUN
ejpam-5237	202	21	to	to	ADP
ejpam-5237	202	22	the	the	DET
ejpam-5237	202	23	specific	specific	ADJ
ejpam-5237	202	24	characteristics	characteristic	NOUN
ejpam-5237	202	25	of	of	ADP
ejpam-5237	202	26	the	the	DET
ejpam-5237	202	27	problem	problem	NOUN
ejpam-5237	202	28	at	at	ADP
ejpam-5237	202	29	hand	hand	NOUN
ejpam-5237	202	30	.	.	PUNCT
ejpam-5237	203	1	the	the	DET
ejpam-5237	203	2	ability	ability	NOUN
ejpam-5237	203	3	to	to	PART
ejpam-5237	203	4	switch	switch	VERB
ejpam-5237	203	5	between	between	ADP
ejpam-5237	203	6	conformable	conformable	ADJ
ejpam-5237	203	7	and	and	CCONJ
ejpam-5237	203	8	non	non	ADJ
ejpam-5237	203	9	-	-	ADJ
ejpam-5237	203	10	conformable	conformable	ADJ
ejpam-5237	203	11	kernels	kernel	NOUN
ejpam-5237	203	12	and	and	CCONJ
ejpam-5237	203	13	to	to	PART
ejpam-5237	203	14	adjust	adjust	VERB
ejpam-5237	203	15	the	the	DET
ejpam-5237	203	16	fractional	fractional	ADJ
ejpam-5237	203	17	order	order	NOUN
ejpam-5237	203	18	introduces	introduce	VERB
ejpam-5237	203	19	a	a	DET
ejpam-5237	203	20	level	level	NOUN
ejpam-5237	203	21	of	of	ADP
ejpam-5237	203	22	versatility	versatility	NOUN
ejpam-5237	203	23	that	that	PRON
ejpam-5237	203	24	is	be	AUX
ejpam-5237	203	25	not	not	PART
ejpam-5237	203	26	available	available	ADJ
ejpam-5237	203	27	in	in	ADP
ejpam-5237	203	28	traditional	traditional	ADJ
ejpam-5237	203	29	ordinary	ordinary	ADJ
ejpam-5237	203	30	or	or	CCONJ
ejpam-5237	203	31	even	even	ADV
ejpam-5237	203	32	other	other	ADJ
ejpam-5237	203	33	conformable	conformable	ADJ
ejpam-5237	203	34	models	model	NOUN
ejpam-5237	203	35	.	.	PUNCT
ejpam-5237	204	1	this	this	DET
ejpam-5237	204	2	adaptability	adaptability	NOUN
ejpam-5237	204	3	makes	make	VERB
ejpam-5237	204	4	the	the	DET
ejpam-5237	204	5	conformable	conformable	ADJ
ejpam-5237	204	6	fractional	fractional	ADJ
ejpam-5237	204	7	derivative	derivative	NOUN
ejpam-5237	204	8	particularly	particularly	ADV
ejpam-5237	204	9	useful	useful	ADJ
ejpam-5237	204	10	in	in	ADP
ejpam-5237	204	11	applications	application	NOUN
ejpam-5237	204	12	where	where	SCONJ
ejpam-5237	204	13	the	the	DET
ejpam-5237	204	14	behavior	behavior	NOUN
ejpam-5237	204	15	of	of	ADP
ejpam-5237	204	16	the	the	DET
ejpam-5237	204	17	system	system	NOUN
ejpam-5237	204	18	or	or	CCONJ
ejpam-5237	204	19	process	process	NOUN
ejpam-5237	204	20	can	can	AUX
ejpam-5237	204	21	be	be	AUX
ejpam-5237	204	22	better	well	ADV
ejpam-5237	204	23	captured	capture	VERB
ejpam-5237	204	24	through	through	ADP
ejpam-5237	204	25	a	a	DET
ejpam-5237	204	26	variable	variable	ADJ
ejpam-5237	204	27	-	-	PUNCT
ejpam-5237	204	28	order	order	NOUN
ejpam-5237	204	29	derivative	derivative	NOUN
ejpam-5237	204	30	,	,	PUNCT
ejpam-5237	204	31	or	or	CCONJ
ejpam-5237	204	32	where	where	SCONJ
ejpam-5237	204	33	the	the	DET
ejpam-5237	204	34	inclusion	inclusion	NOUN
ejpam-5237	204	35	of	of	ADP
ejpam-5237	204	36	different	different	ADJ
ejpam-5237	204	37	kernel	kernel	NOUN
ejpam-5237	204	38	types	type	NOUN
ejpam-5237	204	39	can	can	AUX
ejpam-5237	204	40	offer	offer	VERB
ejpam-5237	204	41	a	a	DET
ejpam-5237	204	42	more	more	ADV
ejpam-5237	204	43	accurate	accurate	ADJ
ejpam-5237	204	44	representation	representation	NOUN
ejpam-5237	204	45	.	.	PUNCT
ejpam-5237	205	1	consequently	consequently	ADV
ejpam-5237	205	2	,	,	PUNCT
ejpam-5237	205	3	the	the	DET
ejpam-5237	205	4	conformable	conformable	ADJ
ejpam-5237	205	5	fractional	fractional	ADJ
ejpam-5237	205	6	derivative	derivative	NOUN
ejpam-5237	205	7	stands	stand	VERB
ejpam-5237	205	8	out	out	ADP
ejpam-5237	205	9	as	as	ADP
ejpam-5237	205	10	a	a	DET
ejpam-5237	205	11	powerful	powerful	ADJ
ejpam-5237	205	12	tool	tool	NOUN
ejpam-5237	205	13	in	in	ADP
ejpam-5237	205	14	the	the	DET
ejpam-5237	205	15	realm	realm	NOUN
ejpam-5237	205	16	of	of	ADP
ejpam-5237	205	17	fractional	fractional	ADJ
ejpam-5237	205	18	calculus	calculus	NOUN
ejpam-5237	205	19	,	,	PUNCT
ejpam-5237	205	20	providing	provide	VERB
ejpam-5237	205	21	both	both	DET
ejpam-5237	205	22	simplicity	simplicity	NOUN
ejpam-5237	205	23	in	in	ADP
ejpam-5237	205	24	definition	definition	NOUN
ejpam-5237	205	25	and	and	CCONJ
ejpam-5237	205	26	extensive	extensive	ADJ
ejpam-5237	205	27	flexibility	flexibility	NOUN
ejpam-5237	205	28	in	in	ADP
ejpam-5237	205	29	application	application	NOUN
ejpam-5237	205	30	.	.	PUNCT
ejpam-5237	206	1	authors	author	NOUN
ejpam-5237	206	2	’	'	PUNCT
ejpam-5237	206	3	contributions	contribution	NOUN
ejpam-5237	206	4	all	all	DET
ejpam-5237	206	5	authors	author	NOUN
ejpam-5237	206	6	have	have	AUX
ejpam-5237	206	7	read	read	VERB
ejpam-5237	206	8	and	and	CCONJ
ejpam-5237	206	9	approved	approve	VERB
ejpam-5237	206	10	the	the	DET
ejpam-5237	206	11	final	final	ADJ
ejpam-5237	206	12	version	version	NOUN
ejpam-5237	206	13	of	of	ADP
ejpam-5237	206	14	the	the	DET
ejpam-5237	206	15	manuscript	manuscript	NOUN
ejpam-5237	206	16	.	.	PUNCT
ejpam-5237	207	1	the	the	DET
ejpam-5237	207	2	authors	author	NOUN
ejpam-5237	207	3	contributed	contribute	VERB
ejpam-5237	207	4	equally	equally	ADV
ejpam-5237	207	5	to	to	ADP
ejpam-5237	207	6	this	this	DET
ejpam-5237	207	7	work	work	NOUN
ejpam-5237	207	8	.	.	PUNCT
ejpam-5237	208	1	conflicts	conflict	NOUN
ejpam-5237	208	2	of	of	ADP
ejpam-5237	208	3	interest	interest	NOUN
ejpam-5237	208	4	the	the	DET
ejpam-5237	208	5	authors	author	NOUN
ejpam-5237	208	6	declare	declare	VERB
ejpam-5237	208	7	that	that	SCONJ
ejpam-5237	208	8	there	there	PRON
ejpam-5237	208	9	are	be	VERB
ejpam-5237	208	10	no	no	DET
ejpam-5237	208	11	conflicts	conflict	NOUN
ejpam-5237	208	12	of	of	ADP
ejpam-5237	208	13	interest	interest	NOUN
ejpam-5237	208	14	regarding	regard	VERB
ejpam-5237	208	15	the	the	DET
ejpam-5237	208	16	publication	publication	NOUN
ejpam-5237	208	17	of	of	ADP
ejpam-5237	208	18	this	this	DET
ejpam-5237	208	19	paper	paper	NOUN
ejpam-5237	208	20	.	.	PUNCT
ejpam-5237	209	1	references	reference	NOUN
ejpam-5237	209	2	1853	1853	NUM
ejpam-5237	209	3	references	reference	NOUN
ejpam-5237	209	4	[	[	X
ejpam-5237	209	5	1	1	NUM
ejpam-5237	209	6	]	]	PUNCT
ejpam-5237	209	7	a.	a.	NOUN
ejpam-5237	209	8	a.	a.	NOUN
ejpam-5237	209	9	abdelhakim	abdelhakim	PROPN
ejpam-5237	209	10	.	.	PUNCT
ejpam-5237	210	1	the	the	DET
ejpam-5237	210	2	flaw	flaw	NOUN
ejpam-5237	210	3	in	in	ADP
ejpam-5237	210	4	the	the	DET
ejpam-5237	210	5	conformable	conformable	ADJ
ejpam-5237	210	6	calculus	calculus	NOUN
ejpam-5237	210	7	:	:	PUNCT
ejpam-5237	210	8	it	it	PRON
ejpam-5237	210	9	is	be	AUX
ejpam-5237	210	10	conformable	conformable	ADJ
ejpam-5237	210	11	because	because	SCONJ
ejpam-5237	210	12	it	it	PRON
ejpam-5237	210	13	is	be	AUX
ejpam-5237	210	14	not	not	PART
ejpam-5237	210	15	fractional	fractional	ADJ
ejpam-5237	210	16	.	.	PUNCT
ejpam-5237	211	1	fractional	fractional	ADJ
ejpam-5237	211	2	calculus	calculus	NOUN
ejpam-5237	211	3	and	and	CCONJ
ejpam-5237	211	4	applied	apply	VERB
ejpam-5237	211	5	analysis	analysis	NOUN
ejpam-5237	211	6	,	,	PUNCT
ejpam-5237	211	7	22(2):242–254	22(2):242–254	NUM
ejpam-5237	211	8	,	,	PUNCT
ejpam-5237	211	9	2019	2019	NUM
ejpam-5237	211	10	.	.	PUNCT
ejpam-5237	212	1	[	[	X
ejpam-5237	212	2	2	2	X
ejpam-5237	212	3	]	]	PUNCT
ejpam-5237	212	4	t.	t.	NOUN
ejpam-5237	212	5	abdeljawad	abdeljawad	NOUN
ejpam-5237	212	6	.	.	PUNCT
ejpam-5237	213	1	dualities	duality	NOUN
ejpam-5237	213	2	in	in	ADP
ejpam-5237	213	3	fractional	fractional	ADJ
ejpam-5237	213	4	difference	difference	NOUN
ejpam-5237	213	5	calculus	calculus	NOUN
ejpam-5237	213	6	within	within	ADP
ejpam-5237	213	7	riemann	riemann	PROPN
ejpam-5237	213	8	.	.	PUNCT
ejpam-5237	214	1	advances	advance	NOUN
ejpam-5237	214	2	in	in	ADP
ejpam-5237	214	3	difference	difference	NOUN
ejpam-5237	214	4	equations	equation	NOUN
ejpam-5237	214	5	,	,	PUNCT
ejpam-5237	214	6	2013	2013	NUM
ejpam-5237	214	7	.	.	PUNCT
ejpam-5237	215	1	[	[	X
ejpam-5237	215	2	3	3	X
ejpam-5237	215	3	]	]	PUNCT
ejpam-5237	215	4	t.	t.	NOUN
ejpam-5237	215	5	abdeljawad	abdeljawad	NOUN
ejpam-5237	215	6	.	.	PUNCT
ejpam-5237	216	1	on	on	ADP
ejpam-5237	216	2	conformable	conformable	ADJ
ejpam-5237	216	3	fractional	fractional	ADJ
ejpam-5237	216	4	calculus	calculus	NOUN
ejpam-5237	216	5	.	.	PUNCT
ejpam-5237	217	1	journal	journal	PROPN
ejpam-5237	217	2	of	of	ADP
ejpam-5237	217	3	computational	computational	ADJ
ejpam-5237	217	4	and	and	CCONJ
ejpam-5237	217	5	applied	applied	ADJ
ejpam-5237	217	6	mathematics	mathematic	NOUN
ejpam-5237	217	7	,	,	PUNCT
ejpam-5237	217	8	279:57–66	279:57–66	NUM
ejpam-5237	217	9	,	,	PUNCT
ejpam-5237	217	10	2015	2015	NUM
ejpam-5237	217	11	.	.	PUNCT
ejpam-5237	218	1	[	[	X
ejpam-5237	218	2	4	4	NUM
ejpam-5237	218	3	]	]	X
ejpam-5237	218	4	d.r	d.r	PROPN
ejpam-5237	218	5	.	.	PROPN
ejpam-5237	218	6	anderson	anderson	PROPN
ejpam-5237	218	7	and	and	CCONJ
ejpam-5237	218	8	d.j	d.j	PROPN
ejpam-5237	218	9	.	.	PROPN
ejpam-5237	218	10	ulness	ulness	PROPN
ejpam-5237	218	11	.	.	PUNCT
ejpam-5237	219	1	newly	newly	ADV
ejpam-5237	219	2	defined	define	VERB
ejpam-5237	219	3	conformable	conformable	ADJ
ejpam-5237	219	4	derivatives	derivative	NOUN
ejpam-5237	219	5	.	.	PUNCT
ejpam-5237	220	1	advances	advance	NOUN
ejpam-5237	220	2	in	in	ADP
ejpam-5237	220	3	dynamical	dynamical	ADJ
ejpam-5237	220	4	systems	system	NOUN
ejpam-5237	220	5	and	and	CCONJ
ejpam-5237	220	6	applications	application	NOUN
ejpam-5237	220	7	,	,	PUNCT
ejpam-5237	220	8	10(02):109–137	10(02):109–137	NUM
ejpam-5237	220	9	,	,	PUNCT
ejpam-5237	220	10	2015	2015	NUM
ejpam-5237	220	11	.	.	PUNCT
ejpam-5237	221	1	[	[	X
ejpam-5237	221	2	5	5	NUM
ejpam-5237	221	3	]	]	PUNCT
ejpam-5237	221	4	a.	a.	NOUN
ejpam-5237	221	5	ait	ait	PROPN
ejpam-5237	221	6	brahim	brahim	PROPN
ejpam-5237	221	7	,	,	PUNCT
ejpam-5237	221	8	a.	a.	PROPN
ejpam-5237	221	9	el	el	PROPN
ejpam-5237	221	10	hajaji	hajaji	PROPN
ejpam-5237	221	11	,	,	PUNCT
ejpam-5237	221	12	k.	k.	PROPN
ejpam-5237	221	13	hilal	hilal	PROPN
ejpam-5237	221	14	,	,	PUNCT
ejpam-5237	221	15	and	and	CCONJ
ejpam-5237	221	16	j.	j.	PROPN
ejpam-5237	221	17	el	el	PROPN
ejpam-5237	221	18	ghordaf	ghordaf	PROPN
ejpam-5237	221	19	.	.	PUNCT
ejpam-5237	222	1	on	on	ADP
ejpam-5237	222	2	a	a	DET
ejpam-5237	222	3	novel	novel	ADJ
ejpam-5237	222	4	fractional	fractional	ADJ
ejpam-5237	222	5	calculus	calculus	NOUN
ejpam-5237	222	6	and	and	CCONJ
ejpam-5237	222	7	its	its	PRON
ejpam-5237	222	8	applications	application	NOUN
ejpam-5237	222	9	to	to	ADP
ejpam-5237	222	10	well	well	ADV
ejpam-5237	222	11	-	-	PUNCT
ejpam-5237	222	12	known	know	VERB
ejpam-5237	222	13	problems	problem	NOUN
ejpam-5237	222	14	.	.	PUNCT
ejpam-5237	223	1	european	european	ADJ
ejpam-5237	223	2	journal	journal	PROPN
ejpam-5237	223	3	of	of	ADP
ejpam-5237	223	4	pure	pure	ADJ
ejpam-5237	223	5	and	and	CCONJ
ejpam-5237	223	6	applied	applied	ADJ
ejpam-5237	223	7	mathematics	mathematic	NOUN
ejpam-5237	223	8	,	,	PUNCT
ejpam-5237	223	9	april	april	PROPN
ejpam-5237	223	10	2024	2024	NUM
ejpam-5237	223	11	.	.	PUNCT
ejpam-5237	224	1	[	[	X
ejpam-5237	224	2	6	6	NUM
ejpam-5237	224	3	]	]	PUNCT
ejpam-5237	224	4	a.	a.	NOUN
ejpam-5237	224	5	fleitas	fleita	NOUN
ejpam-5237	224	6	,	,	PUNCT
ejpam-5237	224	7	j.	j.	PROPN
ejpam-5237	224	8	a.	a.	PROPN
ejpam-5237	224	9	méndez	méndez	PROPN
ejpam-5237	224	10	,	,	PUNCT
ejpam-5237	224	11	j.	j.	PROPN
ejpam-5237	224	12	e.	e.	PROPN
ejpam-5237	224	13	nápoles	nápoles	PROPN
ejpam-5237	224	14	,	,	PUNCT
ejpam-5237	224	15	and	and	CCONJ
ejpam-5237	224	16	j.	j.	PROPN
ejpam-5237	224	17	m.	m.	PROPN
ejpam-5237	224	18	sigarreta	sigarreta	PROPN
ejpam-5237	224	19	.	.	PUNCT
ejpam-5237	225	1	on	on	ADP
ejpam-5237	225	2	fractional	fractional	ADJ
ejpam-5237	225	3	liénardtype	liénardtype	NOUN
ejpam-5237	225	4	systems	system	NOUN
ejpam-5237	225	5	.	.	PUNCT
ejpam-5237	226	1	revista	revista	PROPN
ejpam-5237	226	2	mexicana	mexicana	PROPN
ejpam-5237	226	3	de	de	PROPN
ejpam-5237	226	4	f́ısica	f́ısica	PROPN
ejpam-5237	226	5	,	,	PUNCT
ejpam-5237	226	6	65:618–625	65:618–625	NOUN
ejpam-5237	226	7	,	,	PUNCT
ejpam-5237	226	8	2019	2019	NUM
ejpam-5237	226	9	.	.	PUNCT
ejpam-5237	227	1	[	[	X
ejpam-5237	227	2	7	7	NUM
ejpam-5237	227	3	]	]	PUNCT
ejpam-5237	227	4	a.	a.	NOUN
ejpam-5237	227	5	fleitas	fleita	NOUN
ejpam-5237	227	6	,	,	PUNCT
ejpam-5237	227	7	j.	j.	PROPN
ejpam-5237	227	8	e.	e.	PROPN
ejpam-5237	227	9	nápoles	nápoles	PROPN
ejpam-5237	227	10	,	,	PUNCT
ejpam-5237	227	11	j.	j.	PROPN
ejpam-5237	227	12	m.	m.	PROPN
ejpam-5237	227	13	rodŕıguez	rodŕıguez	PROPN
ejpam-5237	227	14	,	,	PUNCT
ejpam-5237	227	15	and	and	CCONJ
ejpam-5237	227	16	j.	j.	PROPN
ejpam-5237	227	17	m.	m.	PROPN
ejpam-5237	227	18	sigarreta	sigarreta	PROPN
ejpam-5237	227	19	.	.	PUNCT
ejpam-5237	228	1	note	note	NOUN
ejpam-5237	228	2	on	on	ADP
ejpam-5237	228	3	the	the	DET
ejpam-5237	228	4	generalized	generalized	ADJ
ejpam-5237	228	5	conformable	conformable	ADJ
ejpam-5237	228	6	derivative	derivative	NOUN
ejpam-5237	228	7	.	.	PUNCT
ejpam-5237	229	1	revista	revista	PROPN
ejpam-5237	229	2	de	de	X
ejpam-5237	229	3	la	la	X
ejpam-5237	229	4	uma	uma	PROPN
ejpam-5237	229	5	,	,	PUNCT
ejpam-5237	229	6	62(2):443–457	62(2):443–457	PROPN
ejpam-5237	229	7	,	,	PUNCT
ejpam-5237	229	8	2021	2021	NUM
ejpam-5237	229	9	.	.	PUNCT
ejpam-5237	230	1	[	[	X
ejpam-5237	230	2	8	8	NUM
ejpam-5237	230	3	]	]	X
ejpam-5237	230	4	ahmed	ahmed	PROPN
ejpam-5237	230	5	kajouni	kajouni	PROPN
ejpam-5237	230	6	,	,	PUNCT
ejpam-5237	230	7	ahmed	ahmed	PROPN
ejpam-5237	230	8	chafiki	chafiki	PROPN
ejpam-5237	230	9	,	,	PUNCT
ejpam-5237	230	10	khalid	khalid	PROPN
ejpam-5237	230	11	hilal	hilal	PROPN
ejpam-5237	230	12	,	,	PUNCT
ejpam-5237	230	13	and	and	CCONJ
ejpam-5237	230	14	mohamed	mohamed	PROPN
ejpam-5237	230	15	oukessou	oukessou	PROPN
ejpam-5237	230	16	.	.	PUNCT
ejpam-5237	231	1	a	a	DET
ejpam-5237	231	2	new	new	ADJ
ejpam-5237	231	3	conformable	conformable	ADJ
ejpam-5237	231	4	fractional	fractional	ADJ
ejpam-5237	231	5	derivative	derivative	NOUN
ejpam-5237	231	6	and	and	CCONJ
ejpam-5237	231	7	applications	application	NOUN
ejpam-5237	231	8	.	.	PUNCT
ejpam-5237	232	1	hindawi	hindawi	ADJ
ejpam-5237	232	2	,	,	PUNCT
ejpam-5237	232	3	2022	2022	NUM
ejpam-5237	232	4	.	.	PUNCT
ejpam-5237	233	1	[	[	X
ejpam-5237	233	2	9	9	NUM
ejpam-5237	233	3	]	]	PUNCT
ejpam-5237	233	4	r.	r.	PROPN
ejpam-5237	233	5	khalil	khalil	PROPN
ejpam-5237	233	6	,	,	PUNCT
ejpam-5237	233	7	m.	m.	PROPN
ejpam-5237	233	8	al	al	PROPN
ejpam-5237	233	9	-	-	PUNCT
ejpam-5237	233	10	horani	horani	PROPN
ejpam-5237	233	11	,	,	PUNCT
ejpam-5237	233	12	a.	a.	NOUN
ejpam-5237	233	13	youcef	youcef	PROPN
ejpam-5237	233	14	,	,	PUNCT
ejpam-5237	233	15	and	and	CCONJ
ejpam-5237	233	16	m.	m.	NOUN
ejpam-5237	233	17	sababheh	sababheh	NOUN
ejpam-5237	233	18	.	.	PUNCT
ejpam-5237	234	1	a	a	DET
ejpam-5237	234	2	new	new	ADJ
ejpam-5237	234	3	definition	definition	NOUN
ejpam-5237	234	4	of	of	ADP
ejpam-5237	234	5	fractional	fractional	ADJ
ejpam-5237	234	6	derivative	derivative	NOUN
ejpam-5237	234	7	.	.	PUNCT
ejpam-5237	235	1	journal	journal	PROPN
ejpam-5237	235	2	of	of	ADP
ejpam-5237	235	3	computational	computational	ADJ
ejpam-5237	235	4	and	and	CCONJ
ejpam-5237	235	5	applied	applied	ADJ
ejpam-5237	235	6	mathematics	mathematic	NOUN
ejpam-5237	235	7	,	,	PUNCT
ejpam-5237	235	8	264:65–70	264:65–70	NUM
ejpam-5237	235	9	,	,	PUNCT
ejpam-5237	235	10	2014	2014	NUM
ejpam-5237	235	11	.	.	PUNCT
ejpam-5237	236	1	[	[	X
ejpam-5237	236	2	10	10	NUM
ejpam-5237	236	3	]	]	X
ejpam-5237	236	4	f.	f.	PROPN
ejpam-5237	236	5	mart́ınez	mart́ınez	PROPN
ejpam-5237	236	6	and	and	CCONJ
ejpam-5237	236	7	j.	j.	PROPN
ejpam-5237	236	8	e.	e.	PROPN
ejpam-5237	236	9	nápoles	nápoles	PROPN
ejpam-5237	236	10	valdés	valdés	PROPN
ejpam-5237	236	11	.	.	PUNCT
ejpam-5237	237	1	towards	towards	ADP
ejpam-5237	237	2	a	a	DET
ejpam-5237	237	3	non	non	ADJ
ejpam-5237	237	4	-	-	ADJ
ejpam-5237	237	5	conformable	conformable	ADJ
ejpam-5237	237	6	fractional	fractional	ADJ
ejpam-5237	237	7	calculus	calculus	NOUN
ejpam-5237	237	8	of	of	ADP
ejpam-5237	237	9	n	n	CCONJ
ejpam-5237	237	10	-	-	PUNCT
ejpam-5237	237	11	variables	variable	NOUN
ejpam-5237	237	12	.	.	PUNCT
ejpam-5237	238	1	journal	journal	NOUN
ejpam-5237	238	2	of	of	ADP
ejpam-5237	238	3	mathematics	mathematic	NOUN
ejpam-5237	238	4	and	and	CCONJ
ejpam-5237	238	5	applications	application	NOUN
ejpam-5237	238	6	,	,	PUNCT
ejpam-5237	238	7	(	(	PUNCT
ejpam-5237	238	8	43):87–98	43):87–98	NUM
ejpam-5237	238	9	,	,	PUNCT
ejpam-5237	238	10	2020	2020	NUM
ejpam-5237	238	11	.	.	PUNCT
ejpam-5237	239	1	[	[	X
ejpam-5237	239	2	11	11	NUM
ejpam-5237	239	3	]	]	PUNCT
ejpam-5237	239	4	j.	j.	PROPN
ejpam-5237	239	5	e.	e.	PROPN
ejpam-5237	239	6	nápoles	nápoles	PROPN
ejpam-5237	239	7	,	,	PUNCT
ejpam-5237	239	8	p.	p.	NOUN
ejpam-5237	239	9	m.	m.	NOUN
ejpam-5237	239	10	guzmán	guzmán	PROPN
ejpam-5237	239	11	,	,	PUNCT
ejpam-5237	239	12	l.	l.	PROPN
ejpam-5237	239	13	m.	m.	PROPN
ejpam-5237	239	14	lugo	lugo	PROPN
ejpam-5237	239	15	,	,	PUNCT
ejpam-5237	239	16	and	and	CCONJ
ejpam-5237	239	17	a.	a.	NOUN
ejpam-5237	239	18	kashuri	kashuri	PROPN
ejpam-5237	239	19	.	.	PUNCT
ejpam-5237	240	1	the	the	DET
ejpam-5237	240	2	local	local	ADJ
ejpam-5237	240	3	non	non	ADJ
ejpam-5237	240	4	conformable	conformable	ADJ
ejpam-5237	240	5	derivative	derivative	ADJ
ejpam-5237	240	6	and	and	CCONJ
ejpam-5237	240	7	mittag	mittag	ADJ
ejpam-5237	240	8	leffler	leffl	ADJ
ejpam-5237	240	9	function	function	NOUN
ejpam-5237	240	10	.	.	PUNCT
ejpam-5237	241	1	sigma	sigma	PROPN
ejpam-5237	241	2	journal	journal	PROPN
ejpam-5237	241	3	of	of	ADP
ejpam-5237	241	4	engineering	engineering	NOUN
ejpam-5237	241	5	and	and	CCONJ
ejpam-5237	241	6	natural	natural	ADJ
ejpam-5237	241	7	sciences	science	NOUN
ejpam-5237	241	8	,	,	PUNCT
ejpam-5237	241	9	38(2):1007–1017	38(2):1007–1017	NUM
ejpam-5237	241	10	,	,	PUNCT
ejpam-5237	241	11	2020	2020	NUM
ejpam-5237	241	12	.	.	PUNCT
ejpam-5237	242	1	[	[	X
ejpam-5237	242	2	12	12	NUM
ejpam-5237	242	3	]	]	X
ejpam-5237	242	4	j.j	j.j	PROPN
ejpam-5237	242	5	.	.	PROPN
ejpam-5237	242	6	rosales	rosales	PROPN
ejpam-5237	242	7	,	,	PUNCT
ejpam-5237	242	8	j.f	j.f	PROPN
ejpam-5237	242	9	.	.	PROPN
ejpam-5237	242	10	gómez	gómez	PROPN
ejpam-5237	242	11	,	,	PUNCT
ejpam-5237	242	12	m.	m.	NOUN
ejpam-5237	242	13	gúıa	gúıa	NOUN
ejpam-5237	242	14	,	,	PUNCT
ejpam-5237	242	15	and	and	CCONJ
ejpam-5237	242	16	v.i	v.i	PROPN
ejpam-5237	242	17	.	.	PROPN
ejpam-5237	242	18	tkach	tkach	NOUN
ejpam-5237	242	19	.	.	PUNCT
ejpam-5237	243	1	lfnm	lfnm	PROPN
ejpam-5237	243	2	.	.	PUNCT
ejpam-5237	244	1	in	in	ADP
ejpam-5237	244	2	international	international	ADJ
ejpam-5237	244	3	conference	conference	NOUN
ejpam-5237	244	4	on	on	ADP
ejpam-5237	244	5	laser	laser	NOUN
ejpam-5237	244	6	and	and	CCONJ
ejpam-5237	244	7	fiber	fiber	NOUN
ejpam-5237	244	8	-	-	PUNCT
ejpam-5237	244	9	optical	optical	ADJ
ejpam-5237	244	10	networks	network	NOUN
ejpam-5237	244	11	modelling	modelling	NOUN
ejpam-5237	244	12	,	,	PUNCT
ejpam-5237	244	13	2011	2011	NUM
ejpam-5237	244	14	.	.	PUNCT
ejpam-5237	245	1	[	[	X
ejpam-5237	245	2	13	13	NUM
ejpam-5237	245	3	]	]	PUNCT
ejpam-5237	245	4	j.	j.	PROPN
ejpam-5237	245	5	e.	e.	PROPN
ejpam-5237	245	6	nápoles	nápoles	PROPN
ejpam-5237	245	7	valdés	valdés	PROPN
ejpam-5237	245	8	,	,	PUNCT
ejpam-5237	245	9	p.	p.	NOUN
ejpam-5237	245	10	m.	m.	NOUN
ejpam-5237	245	11	guzmán	guzmán	PROPN
ejpam-5237	245	12	,	,	PUNCT
ejpam-5237	245	13	and	and	CCONJ
ejpam-5237	245	14	l.	l.	PROPN
ejpam-5237	245	15	m.	m.	PROPN
ejpam-5237	245	16	lugo	lugo	PROPN
ejpam-5237	245	17	.	.	PUNCT
ejpam-5237	246	1	some	some	DET
ejpam-5237	246	2	new	new	ADJ
ejpam-5237	246	3	results	result	NOUN
ejpam-5237	246	4	on	on	ADP
ejpam-5237	246	5	nonconformable	nonconformable	ADJ
ejpam-5237	246	6	fractional	fractional	ADJ
ejpam-5237	246	7	calculus	calculus	NOUN
ejpam-5237	246	8	.	.	PUNCT
ejpam-5237	247	1	advances	advance	NOUN
ejpam-5237	247	2	in	in	ADP
ejpam-5237	247	3	dynamical	dynamical	ADJ
ejpam-5237	247	4	systems	system	NOUN
ejpam-5237	247	5	and	and	CCONJ
ejpam-5237	247	6	applications	application	NOUN
ejpam-5237	247	7	,	,	PUNCT
ejpam-5237	247	8	13(2):167–175	13(2):167–175	NUM
ejpam-5237	247	9	,	,	PUNCT
ejpam-5237	247	10	2018	2018	NUM
ejpam-5237	247	11	.	.	PUNCT
ejpam-5237	248	1	[	[	X
ejpam-5237	248	2	14	14	NUM
ejpam-5237	248	3	]	]	X
ejpam-5237	248	4	juan	juan	PROPN
ejpam-5237	248	5	e.	e.	PROPN
ejpam-5237	248	6	nápoles	nápoles	PROPN
ejpam-5237	248	7	valdés	valdés	PROPN
ejpam-5237	248	8	.	.	PUNCT
ejpam-5237	249	1	the	the	DET
ejpam-5237	249	2	non	non	ADJ
ejpam-5237	249	3	-	-	ADJ
ejpam-5237	249	4	integer	integer	ADJ
ejpam-5237	249	5	local	local	ADJ
ejpam-5237	249	6	order	order	NOUN
ejpam-5237	249	7	calculus	calculus	NOUN
ejpam-5237	249	8	.	.	PUNCT
ejpam-5237	250	1	physics	physics	PROPN
ejpam-5237	250	2	astronomy	astronomy	PROPN
ejpam-5237	250	3	international	international	PROPN
ejpam-5237	250	4	journal	journal	PROPN
ejpam-5237	250	5	,	,	PUNCT
ejpam-5237	250	6	7(3):163–168	7(3):163–168	NOUN
ejpam-5237	250	7	,	,	PUNCT
ejpam-5237	250	8	2023	2023	NUM
ejpam-5237	250	9	.	.	PUNCT
ejpam-5237	251	1	[	[	X
ejpam-5237	251	2	15	15	NUM
ejpam-5237	251	3	]	]	X
ejpam-5237	251	4	m.	m.	NOUN
ejpam-5237	251	5	vivas	vivas	PROPN
ejpam-5237	251	6	-	-	NOUN
ejpam-5237	251	7	cortez	cortez	PROPN
ejpam-5237	251	8	,	,	PUNCT
ejpam-5237	251	9	a.	a.	NOUN
ejpam-5237	251	10	fleitas	fleita	NOUN
ejpam-5237	251	11	,	,	PUNCT
ejpam-5237	251	12	p.m.	p.m.	NOUN
ejpam-5237	251	13	guzmán	guzmán	PROPN
ejpam-5237	251	14	,	,	PUNCT
ejpam-5237	251	15	j.e	j.e	PROPN
ejpam-5237	251	16	.	.	PROPN
ejpam-5237	251	17	nápoles	nápoles	PROPN
ejpam-5237	251	18	,	,	PUNCT
ejpam-5237	251	19	and	and	CCONJ
ejpam-5237	251	20	j.j	j.j	PROPN
ejpam-5237	251	21	.	.	PROPN
ejpam-5237	251	22	rosales	rosales	PROPN
ejpam-5237	251	23	.	.	PUNCT
ejpam-5237	252	1	newton	newton	PROPN
ejpam-5237	252	2	’s	’s	PART
ejpam-5237	252	3	law	law	NOUN
ejpam-5237	252	4	of	of	ADP
ejpam-5237	252	5	cooling	cool	VERB
ejpam-5237	252	6	with	with	ADP
ejpam-5237	252	7	generalized	generalized	ADJ
ejpam-5237	252	8	conformable	conformable	ADJ
ejpam-5237	252	9	derivatives	derivative	NOUN
ejpam-5237	252	10	.	.	PUNCT
ejpam-5237	253	1	symmetry	symmetry	NOUN
ejpam-5237	253	2	,	,	PUNCT
ejpam-5237	253	3	13	13	NUM
ejpam-5237	253	4	,	,	PUNCT
ejpam-5237	253	5	2021	2021	NUM
ejpam-5237	253	6	.	.	PUNCT
ejpam-5237	254	1	references	reference	NOUN
ejpam-5237	254	2	1854	1854	NUM
ejpam-5237	255	1	[	[	X
ejpam-5237	255	2	16	16	NUM
ejpam-5237	255	3	]	]	X
ejpam-5237	255	4	miguel	miguel	PROPN
ejpam-5237	255	5	vivas	vivas	PROPN
ejpam-5237	255	6	-	-	PROPN
ejpam-5237	255	7	cortez	cortez	PROPN
ejpam-5237	255	8	,	,	PUNCT
ejpam-5237	255	9	juan	juan	PROPN
ejpam-5237	255	10	e.	e.	PROPN
ejpam-5237	255	11	nápoles	nápoles	PROPN
ejpam-5237	255	12	valdés	valdés	PROPN
ejpam-5237	255	13	,	,	PUNCT
ejpam-5237	255	14	shilpi	shilpi	NOUN
ejpam-5237	255	15	jain	jain	NOUN
ejpam-5237	255	16	,	,	PUNCT
ejpam-5237	255	17	and	and	CCONJ
ejpam-5237	255	18	praveen	praveen	PROPN
ejpam-5237	255	19	agarwal	agarwal	PROPN
ejpam-5237	255	20	.	.	PUNCT
ejpam-5237	256	1	on	on	ADP
ejpam-5237	256	2	a	a	DET
ejpam-5237	256	3	generalized	generalized	ADJ
ejpam-5237	256	4	fractional	fractional	ADJ
ejpam-5237	256	5	integral	integral	ADJ
ejpam-5237	256	6	and	and	CCONJ
ejpam-5237	256	7	related	relate	VERB
ejpam-5237	256	8	methodological	methodological	ADJ
ejpam-5237	256	9	remarks	remark	NOUN
ejpam-5237	256	10	.	.	PUNCT
ejpam-5237	257	1	applied	apply	VERB
ejpam-5237	257	2	mathematics	mathematics	PROPN
ejpam-5237	257	3	&	&	CCONJ
ejpam-5237	257	4	information	information	NOUN
ejpam-5237	257	5	sciences	sciences	PROPN
ejpam-5237	257	6	,	,	PUNCT
ejpam-5237	257	7	17(4):615–623	17(4):615–623	NUM
ejpam-5237	257	8	,	,	PUNCT
ejpam-5237	257	9	2023	2023	NUM
ejpam-5237	257	10	.	.	PUNCT
ejpam-5237	258	1	[	[	X
ejpam-5237	258	2	17	17	NUM
ejpam-5237	258	3	]	]	X
ejpam-5237	258	4	d.	d.	PROPN
ejpam-5237	258	5	zhao	zhao	PROPN
ejpam-5237	258	6	and	and	CCONJ
ejpam-5237	258	7	m.	m.	PROPN
ejpam-5237	258	8	luo	luo	PROPN
ejpam-5237	258	9	.	.	PROPN
ejpam-5237	258	10	general	general	ADJ
ejpam-5237	258	11	conformable	conformable	ADJ
ejpam-5237	258	12	fractional	fractional	ADJ
ejpam-5237	258	13	derivative	derivative	NOUN
ejpam-5237	258	14	and	and	CCONJ
ejpam-5237	258	15	its	its	PRON
ejpam-5237	258	16	physical	physical	ADJ
ejpam-5237	258	17	interpretation	interpretation	NOUN
ejpam-5237	258	18	.	.	PUNCT
ejpam-5237	259	1	calcolo	calcolo	PROPN
ejpam-5237	259	2	,	,	PUNCT
ejpam-5237	259	3	54:903–917	54:903–917	PROPN
ejpam-5237	259	4	,	,	PUNCT
ejpam-5237	259	5	2017	2017	NUM
ejpam-5237	259	6	.	.	PUNCT