id	sid	tid	token	lemma	pos
ejpam-5537	1	1	european	european	PROPN
ejpam-5537	1	2	journal	journal	PROPN
ejpam-5537	1	3	of	of	ADP
ejpam-5537	1	4	pure	pure	ADJ
ejpam-5537	1	5	and	and	CCONJ
ejpam-5537	1	6	applied	apply	VERB
ejpam-5537	1	7	mathematics	mathematic	NOUN
ejpam-5537	1	8	vol	vol	NOUN
ejpam-5537	1	9	.	.	PROPN
ejpam-5537	2	1	17	17	NUM
ejpam-5537	2	2	,	,	PUNCT
ejpam-5537	2	3	no	no	INTJ
ejpam-5537	2	4	.	.	NOUN
ejpam-5537	2	5	4	4	NUM
ejpam-5537	2	6	,	,	PUNCT
ejpam-5537	2	7	2024	2024	NUM
ejpam-5537	2	8	,	,	PUNCT
ejpam-5537	2	9	4003	4003	NUM
ejpam-5537	2	10	-	-	SYM
ejpam-5537	2	11	4013	4013	NUM
ejpam-5537	2	12	issn	issn	PROPN
ejpam-5537	2	13	1307	1307	NUM
ejpam-5537	2	14	-	-	SYM
ejpam-5537	2	15	5543	5543	NUM
ejpam-5537	2	16	–	–	PUNCT
ejpam-5537	2	17	ejpam.com	ejpam.com	X
ejpam-5537	2	18	published	publish	VERB
ejpam-5537	2	19	by	by	ADP
ejpam-5537	2	20	new	new	PROPN
ejpam-5537	2	21	york	york	PROPN
ejpam-5537	2	22	business	business	PROPN
ejpam-5537	2	23	global	global	ADJ
ejpam-5537	2	24	solution	solution	NOUN
ejpam-5537	2	25	of	of	ADP
ejpam-5537	2	26	well	well	ADV
ejpam-5537	2	27	-	-	PUNCT
ejpam-5537	2	28	known	know	VERB
ejpam-5537	2	29	physical	physical	ADJ
ejpam-5537	2	30	problems	problem	NOUN
ejpam-5537	2	31	with	with	ADP
ejpam-5537	2	32	fractional	fractional	ADJ
ejpam-5537	2	33	conformable	conformable	ADJ
ejpam-5537	2	34	derivative	derivative	ADJ
ejpam-5537	2	35	eman	eman	NOUN
ejpam-5537	2	36	abuteen1,∗	abuteen1,∗	NOUN
ejpam-5537	2	37	,	,	PUNCT
ejpam-5537	2	38	abdessamad	abdessamad	NOUN
ejpam-5537	2	39	ait	ait	PROPN
ejpam-5537	2	40	brahim2	brahim2	PROPN
ejpam-5537	2	41	,	,	PUNCT
ejpam-5537	2	42	abdelmajid	abdelmajid	PROPN
ejpam-5537	2	43	el	el	PROPN
ejpam-5537	2	44	hajaji3	hajaji3	PROPN
ejpam-5537	2	45	,	,	PUNCT
ejpam-5537	2	46	khalid	khalid	PROPN
ejpam-5537	2	47	hilal2	hilal2	PROPN
ejpam-5537	2	48	,	,	PUNCT
ejpam-5537	2	49	ayoub	ayoub	PROPN
ejpam-5537	2	50	charhabil4	charhabil4	VERB
ejpam-5537	2	51	1	1	NUM
ejpam-5537	2	52	department	department	NOUN
ejpam-5537	2	53	of	of	ADP
ejpam-5537	2	54	basic	basic	ADJ
ejpam-5537	2	55	scientific	scientific	ADJ
ejpam-5537	2	56	sciences	science	NOUN
ejpam-5537	2	57	,	,	PUNCT
ejpam-5537	2	58	faculty	faculty	NOUN
ejpam-5537	2	59	of	of	ADP
ejpam-5537	2	60	engineering	engineering	NOUN
ejpam-5537	2	61	technology	technology	NOUN
ejpam-5537	2	62	,	,	PUNCT
ejpam-5537	2	63	al	al	PROPN
ejpam-5537	2	64	-	-	PUNCT
ejpam-5537	2	65	balqa	balqa	NOUN
ejpam-5537	2	66	applied	apply	VERB
ejpam-5537	2	67	university	university	NOUN
ejpam-5537	2	68	,	,	PUNCT
ejpam-5537	2	69	jordan	jordan	PROPN
ejpam-5537	2	70	2	2	NUM
ejpam-5537	2	71	amsc	amsc	NOUN
ejpam-5537	2	72	laboratory	laboratory	NOUN
ejpam-5537	2	73	,	,	PUNCT
ejpam-5537	2	74	university	university	NOUN
ejpam-5537	2	75	of	of	ADP
ejpam-5537	2	76	sciences	science	NOUN
ejpam-5537	2	77	and	and	CCONJ
ejpam-5537	2	78	technology	technology	NOUN
ejpam-5537	2	79	,	,	PUNCT
ejpam-5537	2	80	beni	beni	ADJ
ejpam-5537	2	81	mellal	mellal	PROPN
ejpam-5537	2	82	,	,	PUNCT
ejpam-5537	2	83	morocco	morocco	PROPN
ejpam-5537	2	84	3	3	NUM
ejpam-5537	2	85	oee	oee	NOUN
ejpam-5537	2	86	departement	departement	NOUN
ejpam-5537	2	87	,	,	PUNCT
ejpam-5537	2	88	encgj	encgj	PROPN
ejpam-5537	2	89	,	,	PUNCT
ejpam-5537	2	90	university	university	NOUN
ejpam-5537	2	91	of	of	ADP
ejpam-5537	2	92	chouaib	chouaib	PROPN
ejpam-5537	2	93	doukali	doukali	PROPN
ejpam-5537	2	94	,	,	PUNCT
ejpam-5537	2	95	el	el	PROPN
ejpam-5537	2	96	jadida	jadida	PROPN
ejpam-5537	2	97	,	,	PUNCT
ejpam-5537	2	98	morocco	morocco	PROPN
ejpam-5537	2	99	4	4	NUM
ejpam-5537	2	100	laga	laga	NOUN
ejpam-5537	2	101	laboratory	laboratory	NOUN
ejpam-5537	2	102	,	,	PUNCT
ejpam-5537	2	103	university	university	NOUN
ejpam-5537	2	104	sorbonne	sorbonne	PROPN
ejpam-5537	2	105	,	,	PUNCT
ejpam-5537	2	106	paris	paris	PROPN
ejpam-5537	2	107	nord	nord	PROPN
ejpam-5537	2	108	,	,	PUNCT
ejpam-5537	2	109	france	france	PROPN
ejpam-5537	2	110	abstract	abstract	NOUN
ejpam-5537	2	111	.	.	PUNCT
ejpam-5537	3	1	this	this	DET
ejpam-5537	3	2	paper	paper	NOUN
ejpam-5537	3	3	presents	present	VERB
ejpam-5537	3	4	a	a	DET
ejpam-5537	3	5	new	new	ADJ
ejpam-5537	3	6	definition	definition	NOUN
ejpam-5537	3	7	of	of	ADP
ejpam-5537	3	8	fractional	fractional	ADJ
ejpam-5537	3	9	derivatives	derivative	NOUN
ejpam-5537	3	10	and	and	CCONJ
ejpam-5537	3	11	integrals	integral	NOUN
ejpam-5537	3	12	through	through	ADP
ejpam-5537	3	13	the	the	DET
ejpam-5537	3	14	conformable	conformable	ADJ
ejpam-5537	3	15	derivative	derivative	ADJ
ejpam-5537	3	16	approach	approach	NOUN
ejpam-5537	3	17	.	.	PUNCT
ejpam-5537	4	1	this	this	DET
ejpam-5537	4	2	innovative	innovative	ADJ
ejpam-5537	4	3	framework	framework	NOUN
ejpam-5537	4	4	offers	offer	VERB
ejpam-5537	4	5	a	a	DET
ejpam-5537	4	6	closer	close	ADJ
ejpam-5537	4	7	alignment	alignment	NOUN
ejpam-5537	4	8	with	with	ADP
ejpam-5537	4	9	classical	classical	ADJ
ejpam-5537	4	10	derivative	derivative	ADJ
ejpam-5537	4	11	concepts	concept	NOUN
ejpam-5537	4	12	while	while	SCONJ
ejpam-5537	4	13	providing	provide	VERB
ejpam-5537	4	14	a	a	DET
ejpam-5537	4	15	more	more	ADV
ejpam-5537	4	16	practical	practical	ADJ
ejpam-5537	4	17	and	and	CCONJ
ejpam-5537	4	18	intuitive	intuitive	ADJ
ejpam-5537	4	19	basis	basis	NOUN
ejpam-5537	4	20	for	for	ADP
ejpam-5537	4	21	fractional	fractional	ADJ
ejpam-5537	4	22	calculus	calculus	NOUN
ejpam-5537	4	23	.	.	PUNCT
ejpam-5537	5	1	the	the	DET
ejpam-5537	5	2	new	new	ADJ
ejpam-5537	5	3	definition	definition	NOUN
ejpam-5537	5	4	is	be	AUX
ejpam-5537	5	5	applicable	applicable	ADJ
ejpam-5537	5	6	in	in	ADP
ejpam-5537	5	7	two	two	NUM
ejpam-5537	5	8	primary	primary	ADJ
ejpam-5537	5	9	ranges	range	NOUN
ejpam-5537	5	10	:	:	PUNCT
ejpam-5537	5	11	0	0	NUM
ejpam-5537	5	12	≤	≤	NUM
ejpam-5537	5	13	α	α	X
ejpam-5537	5	14	<	<	X
ejpam-5537	5	15	1	1	NUM
ejpam-5537	5	16	and	and	CCONJ
ejpam-5537	5	17	n	n	CCONJ
ejpam-5537	5	18	−	−	PROPN
ejpam-5537	5	19	1	1	NUM
ejpam-5537	5	20	≤	≤	NUM
ejpam-5537	5	21	α	α	X
ejpam-5537	5	22	<	<	X
ejpam-5537	5	23	n	n	CCONJ
ejpam-5537	5	24	,	,	PUNCT
ejpam-5537	5	25	where	where	SCONJ
ejpam-5537	5	26	n	n	PRON
ejpam-5537	5	27	is	be	AUX
ejpam-5537	5	28	a	a	DET
ejpam-5537	5	29	positive	positive	ADJ
ejpam-5537	5	30	integer	integer	NOUN
ejpam-5537	5	31	.	.	PUNCT
ejpam-5537	6	1	it	it	PRON
ejpam-5537	6	2	is	be	AUX
ejpam-5537	6	3	shown	show	VERB
ejpam-5537	6	4	that	that	SCONJ
ejpam-5537	6	5	when	when	SCONJ
ejpam-5537	6	6	α	α	PROPN
ejpam-5537	6	7	=	=	SYM
ejpam-5537	6	8	1	1	NUM
ejpam-5537	6	9	,	,	PUNCT
ejpam-5537	6	10	this	this	DET
ejpam-5537	6	11	definition	definition	NOUN
ejpam-5537	6	12	corresponds	correspond	VERB
ejpam-5537	6	13	precisely	precisely	ADV
ejpam-5537	6	14	to	to	ADP
ejpam-5537	6	15	the	the	DET
ejpam-5537	6	16	classical	classical	ADJ
ejpam-5537	6	17	first	first	ADJ
ejpam-5537	6	18	-	-	PUNCT
ejpam-5537	6	19	order	order	NOUN
ejpam-5537	6	20	derivative	derivative	NOUN
ejpam-5537	6	21	.	.	PUNCT
ejpam-5537	7	1	key	key	ADJ
ejpam-5537	7	2	benefits	benefit	NOUN
ejpam-5537	7	3	of	of	ADP
ejpam-5537	7	4	this	this	DET
ejpam-5537	7	5	approach	approach	NOUN
ejpam-5537	7	6	include	include	VERB
ejpam-5537	7	7	its	its	PRON
ejpam-5537	7	8	improved	improved	ADJ
ejpam-5537	7	9	consistency	consistency	NOUN
ejpam-5537	7	10	with	with	ADP
ejpam-5537	7	11	traditional	traditional	ADJ
ejpam-5537	7	12	calculus	calculus	NOUN
ejpam-5537	7	13	and	and	CCONJ
ejpam-5537	7	14	greater	great	ADJ
ejpam-5537	7	15	computational	computational	ADJ
ejpam-5537	7	16	ease	ease	NOUN
ejpam-5537	7	17	,	,	PUNCT
ejpam-5537	7	18	making	make	VERB
ejpam-5537	7	19	it	it	PRON
ejpam-5537	7	20	a	a	DET
ejpam-5537	7	21	useful	useful	ADJ
ejpam-5537	7	22	tool	tool	NOUN
ejpam-5537	7	23	for	for	ADP
ejpam-5537	7	24	both	both	CCONJ
ejpam-5537	7	25	theoretical	theoretical	ADJ
ejpam-5537	7	26	research	research	NOUN
ejpam-5537	7	27	and	and	CCONJ
ejpam-5537	7	28	practical	practical	ADJ
ejpam-5537	7	29	applications	application	NOUN
ejpam-5537	7	30	.	.	PUNCT
ejpam-5537	8	1	by	by	ADP
ejpam-5537	8	2	integrating	integrate	VERB
ejpam-5537	8	3	fractional	fractional	ADJ
ejpam-5537	8	4	calculus	calculus	NOUN
ejpam-5537	8	5	with	with	ADP
ejpam-5537	8	6	conventional	conventional	ADJ
ejpam-5537	8	7	derivative	derivative	ADJ
ejpam-5537	8	8	ideas	idea	NOUN
ejpam-5537	8	9	,	,	PUNCT
ejpam-5537	8	10	this	this	DET
ejpam-5537	8	11	definition	definition	NOUN
ejpam-5537	8	12	simplifies	simplify	VERB
ejpam-5537	8	13	the	the	DET
ejpam-5537	8	14	analysis	analysis	NOUN
ejpam-5537	8	15	and	and	CCONJ
ejpam-5537	8	16	interpretation	interpretation	NOUN
ejpam-5537	8	17	of	of	ADP
ejpam-5537	8	18	fractional	fractional	ADJ
ejpam-5537	8	19	differential	differential	ADJ
ejpam-5537	8	20	equations	equation	NOUN
ejpam-5537	8	21	and	and	CCONJ
ejpam-5537	8	22	their	their	PRON
ejpam-5537	8	23	solutions	solution	NOUN
ejpam-5537	8	24	.	.	PUNCT
ejpam-5537	9	1	additionally	additionally	ADV
ejpam-5537	9	2	,	,	PUNCT
ejpam-5537	9	3	we	we	PRON
ejpam-5537	9	4	examine	examine	VERB
ejpam-5537	9	5	the	the	DET
ejpam-5537	9	6	definition	definition	NOUN
ejpam-5537	9	7	’s	’s	PART
ejpam-5537	9	8	effects	effect	NOUN
ejpam-5537	9	9	on	on	ADP
ejpam-5537	9	10	stability	stability	NOUN
ejpam-5537	9	11	and	and	CCONJ
ejpam-5537	9	12	convergence	convergence	NOUN
ejpam-5537	9	13	in	in	ADP
ejpam-5537	9	14	numerical	numerical	ADJ
ejpam-5537	9	15	methods	method	NOUN
ejpam-5537	9	16	and	and	CCONJ
ejpam-5537	9	17	provide	provide	VERB
ejpam-5537	9	18	examples	example	NOUN
ejpam-5537	9	19	demonstrating	demonstrate	VERB
ejpam-5537	9	20	its	its	PRON
ejpam-5537	9	21	effectiveness	effectiveness	NOUN
ejpam-5537	9	22	and	and	CCONJ
ejpam-5537	9	23	applicability	applicability	NOUN
ejpam-5537	9	24	.	.	PUNCT
ejpam-5537	10	1	2020	2020	NUM
ejpam-5537	10	2	mathematics	mathematic	NOUN
ejpam-5537	10	3	subject	subject	NOUN
ejpam-5537	10	4	classifications	classification	NOUN
ejpam-5537	10	5	:	:	PUNCT
ejpam-5537	10	6	26a33	26a33	NUM
ejpam-5537	10	7	,	,	PUNCT
ejpam-5537	10	8	34a08	34a08	NUM
ejpam-5537	10	9	,	,	PUNCT
ejpam-5537	10	10	65l05	65l05	NUM
ejpam-5537	10	11	,	,	PUNCT
ejpam-5537	10	12	45d05	45d05	NUM
ejpam-5537	10	13	key	key	ADJ
ejpam-5537	10	14	words	word	NOUN
ejpam-5537	10	15	and	and	CCONJ
ejpam-5537	10	16	phrases	phrase	NOUN
ejpam-5537	10	17	:	:	PUNCT
ejpam-5537	10	18	fractional	fractional	ADJ
ejpam-5537	10	19	differential	differential	ADJ
ejpam-5537	10	20	equations	equation	NOUN
ejpam-5537	10	21	,	,	PUNCT
ejpam-5537	10	22	conformable	conformable	ADJ
ejpam-5537	10	23	derivative	derivative	ADJ
ejpam-5537	10	24	,	,	PUNCT
ejpam-5537	10	25	falling	fall	VERB
ejpam-5537	10	26	body	body	NOUN
ejpam-5537	10	27	,	,	PUNCT
ejpam-5537	10	28	atomic	atomic	ADJ
ejpam-5537	10	29	solution	solution	NOUN
ejpam-5537	10	30	1	1	NUM
ejpam-5537	10	31	.	.	PUNCT
ejpam-5537	11	1	introduction	introduction	NOUN
ejpam-5537	11	2	fractional	fractional	ADJ
ejpam-5537	11	3	calculus	calculus	NOUN
ejpam-5537	11	4	generalizes	generalize	VERB
ejpam-5537	11	5	the	the	DET
ejpam-5537	11	6	ideas	idea	NOUN
ejpam-5537	11	7	of	of	ADP
ejpam-5537	11	8	differentiation	differentiation	NOUN
ejpam-5537	11	9	and	and	CCONJ
ejpam-5537	11	10	integration	integration	NOUN
ejpam-5537	11	11	to	to	ADP
ejpam-5537	11	12	non	non	ADJ
ejpam-5537	11	13	-	-	ADJ
ejpam-5537	11	14	integer	integer	ADJ
ejpam-5537	11	15	(	(	PUNCT
ejpam-5537	11	16	fractional	fractional	ADJ
ejpam-5537	11	17	)	)	PUNCT
ejpam-5537	11	18	orders	order	NOUN
ejpam-5537	11	19	.	.	PUNCT
ejpam-5537	12	1	this	this	DET
ejpam-5537	12	2	mathematical	mathematical	ADJ
ejpam-5537	12	3	field	field	NOUN
ejpam-5537	12	4	has	have	VERB
ejpam-5537	12	5	its	its	PRON
ejpam-5537	12	6	roots	root	NOUN
ejpam-5537	12	7	in	in	ADP
ejpam-5537	12	8	the	the	DET
ejpam-5537	12	9	late	late	ADJ
ejpam-5537	12	10	17th	17th	ADJ
ejpam-5537	12	11	century	century	NOUN
ejpam-5537	12	12	,	,	PUNCT
ejpam-5537	12	13	with	with	ADP
ejpam-5537	12	14	an	an	DET
ejpam-5537	12	15	early	early	ADJ
ejpam-5537	12	16	reference	reference	NOUN
ejpam-5537	12	17	found	find	VERB
ejpam-5537	12	18	in	in	ADP
ejpam-5537	12	19	a	a	DET
ejpam-5537	12	20	letter	letter	NOUN
ejpam-5537	12	21	dated	date	VERB
ejpam-5537	12	22	september	september	PROPN
ejpam-5537	12	23	30	30	NUM
ejpam-5537	12	24	,	,	PUNCT
ejpam-5537	12	25	1695	1695	NUM
ejpam-5537	12	26	,	,	PUNCT
ejpam-5537	12	27	between	between	ADP
ejpam-5537	12	28	leibniz	leibniz	PROPN
ejpam-5537	12	29	and	and	CCONJ
ejpam-5537	12	30	l’hôpital	l’hôpital	PROPN
ejpam-5537	12	31	,	,	PUNCT
ejpam-5537	12	32	where	where	SCONJ
ejpam-5537	12	33	l’hôpital	l’hôpital	ADJ
ejpam-5537	12	34	questioned	question	VERB
ejpam-5537	12	35	the	the	DET
ejpam-5537	12	36	meaning	meaning	NOUN
ejpam-5537	12	37	of	of	ADP
ejpam-5537	12	38	dn	dn	PROPN
ejpam-5537	12	39	dzn	dzn	PROPN
ejpam-5537	12	40	f(x	f(x	PROPN
ejpam-5537	12	41	)	)	PUNCT
ejpam-5537	12	42	when	when	SCONJ
ejpam-5537	12	43	n	n	X
ejpam-5537	12	44	=	=	SYM
ejpam-5537	12	45	1	1	NUM
ejpam-5537	12	46	2	2	NUM
ejpam-5537	12	47	.	.	PUNCT
ejpam-5537	13	1	over	over	ADP
ejpam-5537	13	2	time	time	NOUN
ejpam-5537	13	3	,	,	PUNCT
ejpam-5537	13	4	extensive	extensive	ADJ
ejpam-5537	13	5	research	research	NOUN
ejpam-5537	13	6	has	have	AUX
ejpam-5537	13	7	been	be	AUX
ejpam-5537	13	8	devoted	devote	VERB
ejpam-5537	13	9	to	to	ADP
ejpam-5537	13	10	fractional	fractional	ADJ
ejpam-5537	13	11	integrals	integral	NOUN
ejpam-5537	13	12	and	and	CCONJ
ejpam-5537	13	13	derivatives	derivative	NOUN
ejpam-5537	13	14	.	.	PUNCT
ejpam-5537	14	1	although	although	SCONJ
ejpam-5537	14	2	fractional	fractional	ADJ
ejpam-5537	14	3	∗corresponding	∗corresponde	VERB
ejpam-5537	14	4	author	author	NOUN
ejpam-5537	14	5	.	.	PUNCT
ejpam-5537	15	1	doi	doi	NOUN
ejpam-5537	15	2	:	:	PUNCT
ejpam-5537	15	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5537	https://doi.org/10.29020/nybg.ejpam.v17i4.5537	VERB
ejpam-5537	15	4	email	email	NOUN
ejpam-5537	15	5	addresses	address	NOUN
ejpam-5537	15	6	:	:	PUNCT
ejpam-5537	15	7	dr.eman.abuteen@bau.edu.jo	dr.eman.abuteen@bau.edu.jo	NUM
ejpam-5537	15	8	(	(	PUNCT
ejpam-5537	15	9	e.	e.	PROPN
ejpam-5537	15	10	abuteen	abuteen	PROPN
ejpam-5537	15	11	)	)	PUNCT
ejpam-5537	15	12	,	,	PUNCT
ejpam-5537	15	13	abdessamad191212@gmail.com	abdessamad191212@gmail.com	X
ejpam-5537	15	14	(	(	PUNCT
ejpam-5537	15	15	a.	a.	NOUN
ejpam-5537	15	16	a.	a.	PROPN
ejpam-5537	15	17	brahim	brahim	PROPN
ejpam-5537	15	18	)	)	PUNCT
ejpam-5537	15	19	,	,	PUNCT
ejpam-5537	15	20	a	a	DET
ejpam-5537	15	21	elhajaji@yahoo.fr	elhajaji@yahoo.fr	PROPN
ejpam-5537	15	22	(	(	PUNCT
ejpam-5537	15	23	a.	a.	PROPN
ejpam-5537	15	24	el	el	PROPN
ejpam-5537	15	25	hajaji	hajaji	PROPN
ejpam-5537	15	26	)	)	PUNCT
ejpam-5537	15	27	,	,	PUNCT
ejpam-5537	15	28	hilalkhalid2005@yahoo.fr	hilalkhalid2005@yahoo.fr	PROPN
ejpam-5537	15	29	(	(	PUNCT
ejpam-5537	15	30	k.	k.	PROPN
ejpam-5537	15	31	hilal	hilal	PROPN
ejpam-5537	15	32	)	)	PUNCT
ejpam-5537	15	33	,	,	PUNCT
ejpam-5537	15	34	ayoub.charhabil@gmail.com	ayoub.charhabil@gmail.com	X
ejpam-5537	15	35	(	(	PUNCT
ejpam-5537	15	36	a.	a.	NOUN
ejpam-5537	15	37	charhabil	charhabil	PROPN
ejpam-5537	15	38	)	)	PUNCT
ejpam-5537	15	39	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5537	15	40	4003	4003	NUM
ejpam-5537	16	1	copyright	copyright	NOUN
ejpam-5537	16	2	:	:	PUNCT
ejpam-5537	16	3	©	©	PROPN
ejpam-5537	16	4	2024	2024	NUM
ejpam-5537	16	5	the	the	DET
ejpam-5537	16	6	author(s	author(s	NOUN
ejpam-5537	16	7	)	)	PUNCT
ejpam-5537	16	8	.	.	PUNCT
ejpam-5537	17	1	(	(	PUNCT
ejpam-5537	17	2	cc	cc	NOUN
ejpam-5537	17	3	by	by	ADP
ejpam-5537	17	4	-	-	PUNCT
ejpam-5537	17	5	nc	nc	PROPN
ejpam-5537	17	6	4.0	4.0	NUM
ejpam-5537	17	7	)	)	PUNCT
ejpam-5537	17	8	e.	e.	PROPN
ejpam-5537	17	9	abuteen	abuteen	PROPN
ejpam-5537	17	10	et	et	VERB
ejpam-5537	17	11	all	all	DET
ejpam-5537	17	12	/	/	SYM
ejpam-5537	17	13	eur	eur	NOUN
ejpam-5537	17	14	.	.	PUNCT
ejpam-5537	18	1	j.	j.	PROPN
ejpam-5537	18	2	pure	pure	PROPN
ejpam-5537	18	3	appl	appl	PROPN
ejpam-5537	18	4	.	.	PROPN
ejpam-5537	18	5	math	math	PROPN
ejpam-5537	18	6	,	,	PUNCT
ejpam-5537	18	7	17	17	NUM
ejpam-5537	18	8	(	(	PUNCT
ejpam-5537	18	9	4	4	NUM
ejpam-5537	18	10	)	)	PUNCT
ejpam-5537	18	11	(	(	PUNCT
ejpam-5537	18	12	2024	2024	NUM
ejpam-5537	18	13	)	)	PUNCT
ejpam-5537	18	14	,	,	PUNCT
ejpam-5537	18	15	4003	4003	NUM
ejpam-5537	18	16	-	-	SYM
ejpam-5537	18	17	4013	4013	NUM
ejpam-5537	18	18	4004	4004	NUM
ejpam-5537	18	19	calculus	calculus	NOUN
ejpam-5537	18	20	extends	extend	VERB
ejpam-5537	18	21	classical	classical	ADJ
ejpam-5537	18	22	calculus	calculus	NOUN
ejpam-5537	18	23	principles	principle	NOUN
ejpam-5537	18	24	,	,	PUNCT
ejpam-5537	18	25	its	its	PRON
ejpam-5537	18	26	use	use	NOUN
ejpam-5537	18	27	in	in	ADP
ejpam-5537	18	28	physics	physics	NOUN
ejpam-5537	18	29	has	have	AUX
ejpam-5537	18	30	been	be	AUX
ejpam-5537	18	31	relatively	relatively	ADV
ejpam-5537	18	32	limited	limit	VERB
ejpam-5537	18	33	historically	historically	ADV
ejpam-5537	18	34	[	[	X
ejpam-5537	18	35	2–6	2–6	NOUN
ejpam-5537	18	36	,	,	PUNCT
ejpam-5537	18	37	8–11	8–11	NOUN
ejpam-5537	18	38	]	]	PUNCT
ejpam-5537	18	39	.	.	PUNCT
ejpam-5537	19	1	this	this	DET
ejpam-5537	19	2	limitation	limitation	NOUN
ejpam-5537	19	3	may	may	AUX
ejpam-5537	19	4	be	be	AUX
ejpam-5537	19	5	partly	partly	ADV
ejpam-5537	19	6	due	due	ADJ
ejpam-5537	19	7	to	to	ADP
ejpam-5537	19	8	the	the	DET
ejpam-5537	19	9	difficulty	difficulty	NOUN
ejpam-5537	19	10	in	in	ADP
ejpam-5537	19	11	accessing	access	VERB
ejpam-5537	19	12	foundational	foundational	ADJ
ejpam-5537	19	13	concepts	concept	NOUN
ejpam-5537	19	14	in	in	ADP
ejpam-5537	19	15	earlier	early	ADJ
ejpam-5537	19	16	mathematical	mathematical	ADJ
ejpam-5537	19	17	literature	literature	NOUN
ejpam-5537	19	18	.	.	PUNCT
ejpam-5537	20	1	however	however	ADV
ejpam-5537	20	2	,	,	PUNCT
ejpam-5537	20	3	the	the	DET
ejpam-5537	20	4	applications	application	NOUN
ejpam-5537	20	5	of	of	ADP
ejpam-5537	20	6	fractional	fractional	ADJ
ejpam-5537	20	7	differential	differential	ADJ
ejpam-5537	20	8	equations	equation	NOUN
ejpam-5537	20	9	has	have	AUX
ejpam-5537	20	10	gained	gain	VERB
ejpam-5537	20	11	importance	importance	NOUN
ejpam-5537	20	12	for	for	ADP
ejpam-5537	20	13	accurately	accurately	ADV
ejpam-5537	20	14	modeling	model	VERB
ejpam-5537	20	15	a	a	DET
ejpam-5537	20	16	variety	variety	NOUN
ejpam-5537	20	17	of	of	ADP
ejpam-5537	20	18	systems	system	NOUN
ejpam-5537	20	19	in	in	ADP
ejpam-5537	20	20	science	science	NOUN
ejpam-5537	20	21	and	and	CCONJ
ejpam-5537	20	22	engineering	engineering	NOUN
ejpam-5537	20	23	,	,	PUNCT
ejpam-5537	20	24	such	such	ADJ
ejpam-5537	20	25	as	as	ADP
ejpam-5537	20	26	,	,	PUNCT
ejpam-5537	20	27	control	control	NOUN
ejpam-5537	20	28	theory	theory	NOUN
ejpam-5537	20	29	,	,	PUNCT
ejpam-5537	20	30	viscoelasticity	viscoelasticity	NOUN
ejpam-5537	20	31	,	,	PUNCT
ejpam-5537	20	32	diffusion	diffusion	NOUN
ejpam-5537	20	33	processes	process	NOUN
ejpam-5537	20	34	,	,	PUNCT
ejpam-5537	20	35	heat	heat	NOUN
ejpam-5537	20	36	conduction	conduction	NOUN
ejpam-5537	20	37	,	,	PUNCT
ejpam-5537	20	38	electrochemistry	electrochemistry	NOUN
ejpam-5537	20	39	,	,	PUNCT
ejpam-5537	20	40	mechanics	mechanic	NOUN
ejpam-5537	20	41	,	,	PUNCT
ejpam-5537	20	42	electricity	electricity	NOUN
ejpam-5537	20	43	,	,	PUNCT
ejpam-5537	20	44	fractals	fractal	NOUN
ejpam-5537	20	45	,	,	PUNCT
ejpam-5537	20	46	and	and	CCONJ
ejpam-5537	20	47	chaos	chaos	NOUN
ejpam-5537	20	48	theory	theory	NOUN
ejpam-5537	20	49	.	.	PUNCT
ejpam-5537	21	1	lyapunov	lyapunov	PROPN
ejpam-5537	21	2	’s	’s	PART
ejpam-5537	21	3	second	second	ADJ
ejpam-5537	21	4	or	or	CCONJ
ejpam-5537	21	5	direct	direct	ADJ
ejpam-5537	21	6	method	method	NOUN
ejpam-5537	21	7	is	be	AUX
ejpam-5537	21	8	renowned	renowne	VERB
ejpam-5537	21	9	for	for	ADP
ejpam-5537	21	10	assessing	assess	VERB
ejpam-5537	21	11	the	the	DET
ejpam-5537	21	12	stability	stability	NOUN
ejpam-5537	21	13	of	of	ADP
ejpam-5537	21	14	differential	differential	ADJ
ejpam-5537	21	15	equations	equation	NOUN
ejpam-5537	21	16	without	without	ADP
ejpam-5537	21	17	requiring	require	VERB
ejpam-5537	21	18	explicit	explicit	ADJ
ejpam-5537	21	19	solutions	solution	NOUN
ejpam-5537	21	20	.	.	PUNCT
ejpam-5537	22	1	this	this	DET
ejpam-5537	22	2	method	method	NOUN
ejpam-5537	22	3	utilizes	utilize	VERB
ejpam-5537	22	4	a	a	DET
ejpam-5537	22	5	lyapunov	lyapunov	ADJ
ejpam-5537	22	6	function	function	NOUN
ejpam-5537	22	7	to	to	PART
ejpam-5537	22	8	examine	examine	VERB
ejpam-5537	22	9	the	the	DET
ejpam-5537	22	10	asymptotic	asymptotic	ADJ
ejpam-5537	22	11	behavior	behavior	NOUN
ejpam-5537	22	12	of	of	ADP
ejpam-5537	22	13	solutions	solution	NOUN
ejpam-5537	22	14	,	,	PUNCT
ejpam-5537	22	15	which	which	PRON
ejpam-5537	22	16	is	be	AUX
ejpam-5537	22	17	especially	especially	ADV
ejpam-5537	22	18	useful	useful	ADJ
ejpam-5537	22	19	for	for	ADP
ejpam-5537	22	20	nonlinear	nonlinear	ADJ
ejpam-5537	22	21	systems	system	NOUN
ejpam-5537	22	22	.	.	PUNCT
ejpam-5537	23	1	its	its	PRON
ejpam-5537	23	2	applications	application	NOUN
ejpam-5537	23	3	to	to	ADP
ejpam-5537	23	4	non	non	ADJ
ejpam-5537	23	5	-	-	ADJ
ejpam-5537	23	6	integer	integer	ADJ
ejpam-5537	23	7	order	order	NOUN
ejpam-5537	23	8	systems	system	NOUN
ejpam-5537	23	9	is	be	AUX
ejpam-5537	23	10	significant	significant	ADJ
ejpam-5537	23	11	,	,	PUNCT
ejpam-5537	23	12	as	as	SCONJ
ejpam-5537	23	13	it	it	PRON
ejpam-5537	23	14	extends	extend	VERB
ejpam-5537	23	15	the	the	DET
ejpam-5537	23	16	use	use	NOUN
ejpam-5537	23	17	of	of	ADP
ejpam-5537	23	18	the	the	DET
ejpam-5537	23	19	lyapunov	lyapunov	ADJ
ejpam-5537	23	20	function	function	NOUN
ejpam-5537	23	21	to	to	ADP
ejpam-5537	23	22	systems	system	NOUN
ejpam-5537	23	23	involving	involve	VERB
ejpam-5537	23	24	fractional	fractional	ADJ
ejpam-5537	23	25	derivatives	derivative	NOUN
ejpam-5537	23	26	.	.	PUNCT
ejpam-5537	24	1	in	in	ADP
ejpam-5537	24	2	this	this	DET
ejpam-5537	24	3	article	article	NOUN
ejpam-5537	24	4	,	,	PUNCT
ejpam-5537	24	5	we	we	PRON
ejpam-5537	24	6	explore	explore	VERB
ejpam-5537	24	7	the	the	DET
ejpam-5537	24	8	application	application	NOUN
ejpam-5537	24	9	of	of	ADP
ejpam-5537	24	10	fractional	fractional	ADJ
ejpam-5537	24	11	-	-	PUNCT
ejpam-5537	24	12	like	like	ADJ
ejpam-5537	24	13	derivatives	derivative	NOUN
ejpam-5537	24	14	of	of	ADP
ejpam-5537	24	15	the	the	DET
ejpam-5537	24	16	lyapunov	lyapunov	ADJ
ejpam-5537	24	17	function	function	NOUN
ejpam-5537	24	18	for	for	ADP
ejpam-5537	24	19	analyzing	analyze	VERB
ejpam-5537	24	20	stability	stability	NOUN
ejpam-5537	24	21	in	in	ADP
ejpam-5537	24	22	perturbed	perturb	VERB
ejpam-5537	24	23	motion	motion	NOUN
ejpam-5537	24	24	equations	equation	NOUN
ejpam-5537	24	25	,	,	PUNCT
ejpam-5537	24	26	presenting	present	VERB
ejpam-5537	24	27	several	several	ADJ
ejpam-5537	24	28	theorems	theorem	NOUN
ejpam-5537	24	29	that	that	PRON
ejpam-5537	24	30	parallel	parallel	VERB
ejpam-5537	24	31	those	those	PRON
ejpam-5537	24	32	of	of	ADP
ejpam-5537	24	33	the	the	DET
ejpam-5537	24	34	direct	direct	ADJ
ejpam-5537	24	35	lyapunov	lyapunov	NOUN
ejpam-5537	24	36	method	method	NOUN
ejpam-5537	24	37	for	for	ADP
ejpam-5537	24	38	specific	specific	ADJ
ejpam-5537	24	39	motion	motion	NOUN
ejpam-5537	24	40	equations	equation	NOUN
ejpam-5537	24	41	.	.	PUNCT
ejpam-5537	25	1	several	several	ADJ
ejpam-5537	25	2	operators	operator	NOUN
ejpam-5537	25	3	of	of	ADP
ejpam-5537	25	4	fractional	fractional	ADJ
ejpam-5537	25	5	derivatives	derivative	NOUN
ejpam-5537	25	6	are	be	AUX
ejpam-5537	25	7	defined	define	VERB
ejpam-5537	25	8	as	as	SCONJ
ejpam-5537	25	9	follows	follow	VERB
ejpam-5537	25	10	:	:	PUNCT
ejpam-5537	25	11	1	1	X
ejpam-5537	25	12	.	.	X
ejpam-5537	25	13	riemann	riemann	PROPN
ejpam-5537	25	14	-	-	PUNCT
ejpam-5537	25	15	liouville	liouville	VERB
ejpam-5537	25	16	fractional	fractional	ADJ
ejpam-5537	25	17	derivative	derivative	NOUN
ejpam-5537	25	18	of	of	ADP
ejpam-5537	25	19	order	order	NOUN
ejpam-5537	25	20	α	α	X
ejpam-5537	25	21	∈	∈	PROPN
ejpam-5537	26	1	[	[	X
ejpam-5537	26	2	n−	n−	NOUN
ejpam-5537	26	3	1	1	NUM
ejpam-5537	26	4	,	,	PUNCT
ejpam-5537	26	5	n	n	CCONJ
ejpam-5537	26	6	):	):	PUNCT
ejpam-5537	26	7	rldα	rldα	VERB
ejpam-5537	26	8	a	a	DET
ejpam-5537	26	9	f(t	f(t	NOUN
ejpam-5537	26	10	)	)	PUNCT
ejpam-5537	26	11	=	=	SYM
ejpam-5537	26	12	1	1	NUM
ejpam-5537	26	13	γ(n−	γ(n−	PROPN
ejpam-5537	26	14	α	α	NOUN
ejpam-5537	26	15	)	)	PUNCT
ejpam-5537	26	16	dn	dn	PROPN
ejpam-5537	26	17	dtn	dtn	PROPN
ejpam-5537	26	18	∫	∫	PROPN
ejpam-5537	26	19	t	t	PROPN
ejpam-5537	26	20	a	a	DET
ejpam-5537	26	21	f(x	f(x	PROPN
ejpam-5537	26	22	)	)	PUNCT
ejpam-5537	26	23	(	(	PUNCT
ejpam-5537	26	24	t−	t−	PROPN
ejpam-5537	26	25	x)α−n+1	x)α−n+1	PROPN
ejpam-5537	26	26	dx	dx	PROPN
ejpam-5537	26	27	,	,	PUNCT
ejpam-5537	26	28	2	2	NUM
ejpam-5537	26	29	.	.	PUNCT
ejpam-5537	27	1	caputo	caputo	PROPN
ejpam-5537	27	2	fractional	fractional	PROPN
ejpam-5537	27	3	derivative	derivative	NOUN
ejpam-5537	27	4	of	of	ADP
ejpam-5537	27	5	order	order	NOUN
ejpam-5537	27	6	α	α	X
ejpam-5537	27	7	∈	∈	PROPN
ejpam-5537	28	1	[	[	X
ejpam-5537	28	2	n−	n−	NOUN
ejpam-5537	28	3	1	1	NUM
ejpam-5537	28	4	,	,	PUNCT
ejpam-5537	28	5	n	n	CCONJ
ejpam-5537	28	6	):	):	PUNCT
ejpam-5537	28	7	cdα	cdα	NOUN
ejpam-5537	28	8	a	a	DET
ejpam-5537	28	9	(	(	PUNCT
ejpam-5537	28	10	f)(t	f)(t	PROPN
ejpam-5537	28	11	)	)	PUNCT
ejpam-5537	28	12	=	=	SYM
ejpam-5537	28	13	1	1	NUM
ejpam-5537	28	14	γ(n−	γ(n−	PROPN
ejpam-5537	28	15	α	α	NOUN
ejpam-5537	28	16	)	)	PUNCT
ejpam-5537	28	17	∫	∫	PROPN
ejpam-5537	28	18	t	t	PROPN
ejpam-5537	28	19	a	a	DET
ejpam-5537	28	20	f	f	PROPN
ejpam-5537	28	21	(	(	PUNCT
ejpam-5537	28	22	n)(x	n)(x	PROPN
ejpam-5537	28	23	)	)	PUNCT
ejpam-5537	28	24	(	(	PUNCT
ejpam-5537	28	25	t−	t−	PROPN
ejpam-5537	28	26	x)α−n+1	x)α−n+1	PROPN
ejpam-5537	28	27	dx	dx	PROPN
ejpam-5537	28	28	.	.	PROPN
ejpam-5537	28	29	3	3	X
ejpam-5537	28	30	.	.	X
ejpam-5537	28	31	caputo	caputo	PROPN
ejpam-5537	28	32	-	-	PUNCT
ejpam-5537	28	33	fabrizio	fabrizio	PROPN
ejpam-5537	28	34	fractional	fractional	ADJ
ejpam-5537	28	35	derivative	derivative	NOUN
ejpam-5537	28	36	of	of	ADP
ejpam-5537	28	37	order	order	NOUN
ejpam-5537	28	38	α	α	X
ejpam-5537	28	39	∈	∈	PROPN
ejpam-5537	28	40	(	(	PUNCT
ejpam-5537	28	41	0	0	NUM
ejpam-5537	28	42	,	,	PUNCT
ejpam-5537	28	43	1	1	NUM
ejpam-5537	28	44	):	):	PUNCT
ejpam-5537	28	45	cfdα	cfdα	ADV
ejpam-5537	28	46	a	a	DET
ejpam-5537	28	47	(	(	PUNCT
ejpam-5537	28	48	f)(t	f)(t	PROPN
ejpam-5537	28	49	)	)	PUNCT
ejpam-5537	28	50	=	=	SYM
ejpam-5537	28	51	m(α	m(α	PROPN
ejpam-5537	28	52	)	)	PUNCT
ejpam-5537	28	53	(	(	PUNCT
ejpam-5537	28	54	1−	1−	NUM
ejpam-5537	28	55	α	α	NOUN
ejpam-5537	28	56	)	)	PUNCT
ejpam-5537	28	57	∫	∫	PROPN
ejpam-5537	29	1	t	t	PROPN
ejpam-5537	29	2	a	a	DET
ejpam-5537	29	3	f	f	PROPN
ejpam-5537	29	4	′(x	′(x	NOUN
ejpam-5537	29	5	)	)	PUNCT
ejpam-5537	29	6	exp	exp	NOUN
ejpam-5537	29	7	[	[	PUNCT
ejpam-5537	29	8	−(t−	−(t−	NOUN
ejpam-5537	29	9	x)α	x)α	X
ejpam-5537	30	1	1−	1−	NUM
ejpam-5537	30	2	α	α	NOUN
ejpam-5537	30	3	]	]	PUNCT
ejpam-5537	30	4	dx	dx	PROPN
ejpam-5537	30	5	,	,	PUNCT
ejpam-5537	30	6	where	where	SCONJ
ejpam-5537	30	7	m(α	m(α	PROPN
ejpam-5537	30	8	)	)	PUNCT
ejpam-5537	30	9	is	be	AUX
ejpam-5537	30	10	a	a	DET
ejpam-5537	30	11	normalized	normalize	VERB
ejpam-5537	30	12	function	function	NOUN
ejpam-5537	30	13	such	such	ADJ
ejpam-5537	30	14	that	that	DET
ejpam-5537	30	15	m(0	m(0	NOUN
ejpam-5537	30	16	)	)	PUNCT
ejpam-5537	30	17	=	=	SYM
ejpam-5537	30	18	m(1	m(1	NOUN
ejpam-5537	30	19	)	)	PUNCT
ejpam-5537	30	20	=	=	SYM
ejpam-5537	30	21	1	1	NUM
ejpam-5537	30	22	.	.	NOUN
ejpam-5537	30	23	4	4	NUM
ejpam-5537	30	24	.	.	PUNCT
ejpam-5537	30	25	atangana	atangana	PROPN
ejpam-5537	30	26	-	-	PUNCT
ejpam-5537	30	27	baleanu	baleanu	ADJ
ejpam-5537	30	28	fractional	fractional	ADJ
ejpam-5537	30	29	derivative	derivative	NOUN
ejpam-5537	30	30	*	*	NOUN
ejpam-5537	30	31	*	*	PUNCT
ejpam-5537	30	32	of	of	ADP
ejpam-5537	30	33	order	order	NOUN
ejpam-5537	30	34	α	α	X
ejpam-5537	30	35	∈	∈	PROPN
ejpam-5537	30	36	(	(	PUNCT
ejpam-5537	30	37	0	0	NUM
ejpam-5537	30	38	,	,	PUNCT
ejpam-5537	30	39	1	1	NUM
ejpam-5537	30	40	)	)	PUNCT
ejpam-5537	30	41	in	in	ADP
ejpam-5537	30	42	the	the	DET
ejpam-5537	30	43	caputo	caputo	PROPN
ejpam-5537	30	44	sense	sense	NOUN
ejpam-5537	30	45	:	:	PUNCT
ejpam-5537	30	46	abcdα	abcdα	VERB
ejpam-5537	30	47	a	a	PRON
ejpam-5537	30	48	(	(	PUNCT
ejpam-5537	30	49	f)(t	f)(t	PROPN
ejpam-5537	30	50	)	)	PUNCT
ejpam-5537	30	51	=	=	SYM
ejpam-5537	30	52	m(α	m(α	PROPN
ejpam-5537	30	53	)	)	PUNCT
ejpam-5537	30	54	(	(	PUNCT
ejpam-5537	30	55	1−	1−	NUM
ejpam-5537	30	56	α	α	NOUN
ejpam-5537	30	57	)	)	PUNCT
ejpam-5537	30	58	∫	∫	PROPN
ejpam-5537	31	1	t	t	PROPN
ejpam-5537	31	2	a	a	DET
ejpam-5537	31	3	f	f	PROPN
ejpam-5537	31	4	′(x)eα	′(x)eα	PROPN
ejpam-5537	31	5	[	[	PUNCT
ejpam-5537	31	6	−(t−	−(t−	NOUN
ejpam-5537	31	7	x)α	x)α	X
ejpam-5537	32	1	1−	1−	NUM
ejpam-5537	32	2	α	α	NOUN
ejpam-5537	32	3	]	]	PUNCT
ejpam-5537	32	4	dx	dx	PROPN
ejpam-5537	32	5	,	,	PUNCT
ejpam-5537	32	6	where	where	SCONJ
ejpam-5537	32	7	m(α	m(α	PROPN
ejpam-5537	32	8	)	)	PUNCT
ejpam-5537	32	9	retains	retain	VERB
ejpam-5537	32	10	properties	property	NOUN
ejpam-5537	32	11	similar	similar	ADJ
ejpam-5537	32	12	to	to	ADP
ejpam-5537	32	13	those	those	PRON
ejpam-5537	32	14	in	in	ADP
ejpam-5537	32	15	the	the	DET
ejpam-5537	32	16	caputo	caputo	PROPN
ejpam-5537	32	17	-	-	PUNCT
ejpam-5537	32	18	fabrizio	fabrizio	PROPN
ejpam-5537	32	19	derivative	derivative	NOUN
ejpam-5537	32	20	.	.	PUNCT
ejpam-5537	33	1	many	many	ADJ
ejpam-5537	33	2	of	of	ADP
ejpam-5537	33	3	these	these	DET
ejpam-5537	33	4	definitions	definition	NOUN
ejpam-5537	33	5	deviate	deviate	VERB
ejpam-5537	33	6	from	from	ADP
ejpam-5537	33	7	the	the	DET
ejpam-5537	33	8	fundamental	fundamental	ADJ
ejpam-5537	33	9	characteristics	characteristic	NOUN
ejpam-5537	33	10	of	of	ADP
ejpam-5537	33	11	the	the	DET
ejpam-5537	33	12	ordinary	ordinary	ADJ
ejpam-5537	33	13	derivative	derivative	NOUN
ejpam-5537	33	14	,	,	PUNCT
ejpam-5537	33	15	except	except	SCONJ
ejpam-5537	33	16	for	for	ADP
ejpam-5537	33	17	linearity	linearity	NOUN
ejpam-5537	33	18	.	.	PUNCT
ejpam-5537	34	1	a	a	DET
ejpam-5537	34	2	recent	recent	ADJ
ejpam-5537	34	3	study	study	NOUN
ejpam-5537	34	4	[	[	X
ejpam-5537	34	5	13	13	NUM
ejpam-5537	34	6	]	]	PUNCT
ejpam-5537	34	7	introduced	introduce	VERB
ejpam-5537	34	8	a	a	DET
ejpam-5537	34	9	novel	novel	ADJ
ejpam-5537	34	10	fractional	fractional	ADJ
ejpam-5537	34	11	derivative	derivative	NOUN
ejpam-5537	34	12	that	that	PRON
ejpam-5537	34	13	aligns	align	VERB
ejpam-5537	34	14	with	with	ADP
ejpam-5537	34	15	the	the	DET
ejpam-5537	34	16	basic	basic	ADJ
ejpam-5537	34	17	principles	principle	NOUN
ejpam-5537	34	18	of	of	ADP
ejpam-5537	34	19	the	the	DET
ejpam-5537	34	20	ordinary	ordinary	ADJ
ejpam-5537	34	21	derivative	derivative	NOUN
ejpam-5537	34	22	.	.	PUNCT
ejpam-5537	35	1	this	this	DET
ejpam-5537	35	2	paper	paper	NOUN
ejpam-5537	35	3	applies	apply	VERB
ejpam-5537	35	4	this	this	DET
ejpam-5537	35	5	new	new	ADJ
ejpam-5537	35	6	definition	definition	NOUN
ejpam-5537	35	7	,	,	PUNCT
ejpam-5537	35	8	along	along	ADP
ejpam-5537	35	9	with	with	ADP
ejpam-5537	35	10	the	the	DET
ejpam-5537	35	11	mittag	mittag	ADJ
ejpam-5537	35	12	-	-	PUNCT
ejpam-5537	35	13	leffler	leffler	NOUN
ejpam-5537	35	14	function	function	NOUN
ejpam-5537	35	15	,	,	PUNCT
ejpam-5537	35	16	to	to	PART
ejpam-5537	35	17	propose	propose	VERB
ejpam-5537	35	18	a	a	DET
ejpam-5537	35	19	new	new	ADJ
ejpam-5537	35	20	fractional	fractional	ADJ
ejpam-5537	35	21	derivative	derivative	NOUN
ejpam-5537	35	22	,	,	PUNCT
ejpam-5537	35	23	examine	examine	VERB
ejpam-5537	35	24	its	its	PRON
ejpam-5537	35	25	properties	property	NOUN
ejpam-5537	35	26	,	,	PUNCT
ejpam-5537	35	27	and	and	CCONJ
ejpam-5537	35	28	demonstrate	demonstrate	VERB
ejpam-5537	35	29	its	its	PRON
ejpam-5537	35	30	effectiveness	effectiveness	NOUN
ejpam-5537	35	31	through	through	ADP
ejpam-5537	35	32	various	various	ADJ
ejpam-5537	35	33	examples	example	NOUN
ejpam-5537	35	34	.	.	PUNCT
ejpam-5537	36	1	e.	e.	PROPN
ejpam-5537	36	2	abuteen	abuteen	PROPN
ejpam-5537	36	3	et	et	PROPN
ejpam-5537	36	4	all	all	DET
ejpam-5537	36	5	/	/	SYM
ejpam-5537	36	6	eur	eur	NOUN
ejpam-5537	36	7	.	.	PUNCT
ejpam-5537	37	1	j.	j.	PROPN
ejpam-5537	37	2	pure	pure	PROPN
ejpam-5537	37	3	appl	appl	PROPN
ejpam-5537	37	4	.	.	PROPN
ejpam-5537	37	5	math	math	PROPN
ejpam-5537	37	6	,	,	PUNCT
ejpam-5537	37	7	17	17	NUM
ejpam-5537	37	8	(	(	PUNCT
ejpam-5537	37	9	4	4	NUM
ejpam-5537	37	10	)	)	PUNCT
ejpam-5537	37	11	(	(	PUNCT
ejpam-5537	37	12	2024	2024	NUM
ejpam-5537	37	13	)	)	PUNCT
ejpam-5537	37	14	,	,	PUNCT
ejpam-5537	37	15	4003	4003	NUM
ejpam-5537	37	16	-	-	SYM
ejpam-5537	37	17	4013	4013	NUM
ejpam-5537	37	18	4005	4005	NUM
ejpam-5537	37	19	2	2	NUM
ejpam-5537	37	20	.	.	PUNCT
ejpam-5537	38	1	definition	definition	NOUN
ejpam-5537	38	2	of	of	ADP
ejpam-5537	38	3	new	new	ADJ
ejpam-5537	38	4	fractional	fractional	ADJ
ejpam-5537	38	5	derivative	derivative	NOUN
ejpam-5537	38	6	in	in	ADP
ejpam-5537	38	7	this	this	DET
ejpam-5537	38	8	section	section	NOUN
ejpam-5537	38	9	,	,	PUNCT
ejpam-5537	38	10	we	we	PRON
ejpam-5537	38	11	begin	begin	VERB
ejpam-5537	38	12	by	by	ADP
ejpam-5537	38	13	introducing	introduce	VERB
ejpam-5537	38	14	the	the	DET
ejpam-5537	38	15	mittag	mittag	ADJ
ejpam-5537	38	16	-	-	PUNCT
ejpam-5537	38	17	leffler	leffler	NOUN
ejpam-5537	38	18	function	function	NOUN
ejpam-5537	38	19	,	,	PUNCT
ejpam-5537	38	20	which	which	PRON
ejpam-5537	38	21	plays	play	VERB
ejpam-5537	38	22	a	a	DET
ejpam-5537	38	23	significant	significant	ADJ
ejpam-5537	38	24	role	role	NOUN
ejpam-5537	38	25	in	in	ADP
ejpam-5537	38	26	various	various	ADJ
ejpam-5537	38	27	physical	physical	ADJ
ejpam-5537	38	28	processes	process	NOUN
ejpam-5537	38	29	and	and	CCONJ
ejpam-5537	38	30	often	often	ADV
ejpam-5537	38	31	emerges	emerge	VERB
ejpam-5537	38	32	in	in	ADP
ejpam-5537	38	33	the	the	DET
ejpam-5537	38	34	solutions	solution	NOUN
ejpam-5537	38	35	to	to	ADP
ejpam-5537	38	36	fractional	fractional	ADJ
ejpam-5537	38	37	differential	differential	ADJ
ejpam-5537	38	38	equations	equation	NOUN
ejpam-5537	38	39	.	.	PUNCT
ejpam-5537	39	1	definition	definition	NOUN
ejpam-5537	39	2	1	1	NUM
ejpam-5537	39	3	.	.	PUNCT
ejpam-5537	40	1	the	the	DET
ejpam-5537	40	2	mittag	mittag	ADJ
ejpam-5537	40	3	-	-	PUNCT
ejpam-5537	40	4	leffler	leffler	NOUN
ejpam-5537	40	5	function	function	NOUN
ejpam-5537	40	6	eα	eα	NOUN
ejpam-5537	40	7	is	be	AUX
ejpam-5537	40	8	defined	define	VERB
ejpam-5537	40	9	as	as	ADP
ejpam-5537	40	10	:	:	PUNCT
ejpam-5537	40	11	eα(z	eα(z	NUM
ejpam-5537	40	12	)	)	PUNCT
ejpam-5537	40	13	=	=	PUNCT
ejpam-5537	41	1	∞∑	∞∑	NUM
ejpam-5537	41	2	n=0	n=0	PROPN
ejpam-5537	41	3	zn	zn	NOUN
ejpam-5537	41	4	γ(αn+	γ(αn+	ADP
ejpam-5537	41	5	1	1	NUM
ejpam-5537	41	6	)	)	PUNCT
ejpam-5537	41	7	,	,	PUNCT
ejpam-5537	41	8	(	(	PUNCT
ejpam-5537	41	9	1	1	X
ejpam-5537	41	10	)	)	PUNCT
ejpam-5537	41	11	where	where	SCONJ
ejpam-5537	41	12	α	α	NOUN
ejpam-5537	41	13	is	be	AUX
ejpam-5537	41	14	a	a	DET
ejpam-5537	41	15	positive	positive	ADJ
ejpam-5537	41	16	parameter	parameter	NOUN
ejpam-5537	41	17	and	and	CCONJ
ejpam-5537	41	18	γ	γ	X
ejpam-5537	41	19	(	(	PUNCT
ejpam-5537	41	20	.	.	PUNCT
ejpam-5537	41	21	)	)	PUNCT
ejpam-5537	41	22	is	be	AUX
ejpam-5537	41	23	the	the	DET
ejpam-5537	41	24	gamma	gamma	PROPN
ejpam-5537	41	25	function	function	NOUN
ejpam-5537	41	26	.	.	PUNCT
ejpam-5537	42	1	the	the	DET
ejpam-5537	42	2	following	follow	VERB
ejpam-5537	42	3	new	new	ADJ
ejpam-5537	42	4	fractional	fractional	ADJ
ejpam-5537	42	5	derivative	derivative	NOUN
ejpam-5537	42	6	is	be	AUX
ejpam-5537	42	7	formulated	formulate	VERB
ejpam-5537	42	8	using	use	VERB
ejpam-5537	42	9	the	the	DET
ejpam-5537	42	10	first	first	ADJ
ejpam-5537	42	11	two	two	NUM
ejpam-5537	42	12	terms	term	NOUN
ejpam-5537	42	13	of	of	ADP
ejpam-5537	42	14	the	the	DET
ejpam-5537	42	15	series	series	NOUN
ejpam-5537	42	16	expansion	expansion	NOUN
ejpam-5537	42	17	of	of	ADP
ejpam-5537	42	18	the	the	DET
ejpam-5537	42	19	mittag	mittag	ADJ
ejpam-5537	42	20	-	-	PUNCT
ejpam-5537	42	21	leffler	leffler	NOUN
ejpam-5537	42	22	function	function	NOUN
ejpam-5537	42	23	:	:	PUNCT
ejpam-5537	42	24	eα	eα	PROPN
ejpam-5537	42	25	(	(	PUNCT
ejpam-5537	42	26	εt−α	εt−α	ADV
ejpam-5537	42	27	)	)	PUNCT
ejpam-5537	42	28	=	=	SYM
ejpam-5537	43	1	1	1	NUM
ejpam-5537	44	1	+	+	CCONJ
ejpam-5537	44	2	εt−α	εt−α	PROPN
ejpam-5537	44	3	γ(α+	γ(α+	DET
ejpam-5537	44	4	1	1	NUM
ejpam-5537	44	5	)	)	PUNCT
ejpam-5537	45	1	+	+	NOUN
ejpam-5537	45	2	o	o	X
ejpam-5537	45	3	(	(	PUNCT
ejpam-5537	45	4	t−2α	t−2α	PROPN
ejpam-5537	45	5	)	)	PUNCT
ejpam-5537	45	6	.	.	PUNCT
ejpam-5537	46	1	(	(	PUNCT
ejpam-5537	46	2	2	2	X
ejpam-5537	46	3	)	)	PUNCT
ejpam-5537	46	4	this	this	DET
ejpam-5537	46	5	approximation	approximation	NOUN
ejpam-5537	46	6	allows	allow	VERB
ejpam-5537	46	7	us	we	PRON
ejpam-5537	46	8	to	to	PART
ejpam-5537	46	9	define	define	VERB
ejpam-5537	46	10	a	a	DET
ejpam-5537	46	11	new	new	ADJ
ejpam-5537	46	12	fractional	fractional	ADJ
ejpam-5537	46	13	derivative	derivative	NOUN
ejpam-5537	46	14	that	that	PRON
ejpam-5537	46	15	incorporates	incorporate	VERB
ejpam-5537	46	16	the	the	DET
ejpam-5537	46	17	mittag	mittag	ADJ
ejpam-5537	46	18	-	-	PUNCT
ejpam-5537	46	19	leffler	leffler	NOUN
ejpam-5537	46	20	function	function	NOUN
ejpam-5537	46	21	’s	’s	PART
ejpam-5537	46	22	properties	property	NOUN
ejpam-5537	46	23	,	,	PUNCT
ejpam-5537	46	24	providing	provide	VERB
ejpam-5537	46	25	a	a	DET
ejpam-5537	46	26	refined	refined	ADJ
ejpam-5537	46	27	approach	approach	NOUN
ejpam-5537	46	28	to	to	ADP
ejpam-5537	46	29	modeling	model	VERB
ejpam-5537	46	30	fractional	fractional	ADJ
ejpam-5537	46	31	dynamics	dynamic	NOUN
ejpam-5537	46	32	.	.	PUNCT
ejpam-5537	47	1	the	the	DET
ejpam-5537	47	2	term	term	NOUN
ejpam-5537	47	3	o	o	NOUN
ejpam-5537	47	4	(	(	PUNCT
ejpam-5537	47	5	t−2α	t−2α	NOUN
ejpam-5537	47	6	)	)	PUNCT
ejpam-5537	47	7	represents	represent	VERB
ejpam-5537	47	8	higher	high	ADJ
ejpam-5537	47	9	-	-	PUNCT
ejpam-5537	47	10	order	order	NOUN
ejpam-5537	47	11	terms	term	NOUN
ejpam-5537	47	12	that	that	PRON
ejpam-5537	47	13	are	be	AUX
ejpam-5537	47	14	generally	generally	ADV
ejpam-5537	47	15	small	small	ADJ
ejpam-5537	47	16	compared	compare	VERB
ejpam-5537	47	17	to	to	ADP
ejpam-5537	47	18	the	the	DET
ejpam-5537	47	19	first	first	ADJ
ejpam-5537	47	20	two	two	NUM
ejpam-5537	47	21	terms	term	NOUN
ejpam-5537	47	22	,	,	PUNCT
ejpam-5537	47	23	thus	thus	ADV
ejpam-5537	47	24	simplifying	simplify	VERB
ejpam-5537	47	25	the	the	DET
ejpam-5537	47	26	expression	expression	NOUN
ejpam-5537	47	27	while	while	SCONJ
ejpam-5537	47	28	capturing	capture	VERB
ejpam-5537	47	29	the	the	DET
ejpam-5537	47	30	essential	essential	ADJ
ejpam-5537	47	31	behavior	behavior	NOUN
ejpam-5537	47	32	of	of	ADP
ejpam-5537	47	33	the	the	DET
ejpam-5537	47	34	mittag	mittag	ADJ
ejpam-5537	47	35	-	-	PUNCT
ejpam-5537	47	36	leffler	leffler	NOUN
ejpam-5537	47	37	function	function	NOUN
ejpam-5537	47	38	in	in	ADP
ejpam-5537	47	39	this	this	DET
ejpam-5537	47	40	context	context	NOUN
ejpam-5537	47	41	.	.	PUNCT
ejpam-5537	48	1	definition	definition	NOUN
ejpam-5537	48	2	2	2	NUM
ejpam-5537	48	3	.	.	PUNCT
ejpam-5537	48	4	consider	consider	VERB
ejpam-5537	48	5	a	a	DET
ejpam-5537	48	6	function	function	NOUN
ejpam-5537	48	7	f	f	NOUN
ejpam-5537	48	8	:	:	PUNCT
ejpam-5537	49	1	[	[	X
ejpam-5537	49	2	0,∞	0,∞	NOUN
ejpam-5537	49	3	)	)	PUNCT
ejpam-5537	49	4	→	→	PUNCT
ejpam-5537	49	5	r.	r.	VERB
ejpam-5537	49	6	the	the	DET
ejpam-5537	49	7	new	new	ADJ
ejpam-5537	49	8	fractional	fractional	ADJ
ejpam-5537	49	9	derivative	derivative	NOUN
ejpam-5537	49	10	of	of	ADP
ejpam-5537	49	11	order	order	NOUN
ejpam-5537	49	12	α	α	NOUN
ejpam-5537	49	13	,	,	PUNCT
ejpam-5537	49	14	defined	define	VERB
ejpam-5537	49	15	in	in	ADP
ejpam-5537	49	16	the	the	DET
ejpam-5537	49	17	sense	sense	NOUN
ejpam-5537	49	18	of	of	ADP
ejpam-5537	49	19	the	the	DET
ejpam-5537	49	20	conformable	conformable	ADJ
ejpam-5537	49	21	fractional	fractional	ADJ
ejpam-5537	49	22	derivative	derivative	NOUN
ejpam-5537	49	23	,	,	PUNCT
ejpam-5537	49	24	is	be	AUX
ejpam-5537	49	25	given	give	VERB
ejpam-5537	49	26	by	by	ADP
ejpam-5537	49	27	:	:	PUNCT
ejpam-5537	49	28	dα(f)(t	dα(f)(t	ADJ
ejpam-5537	49	29	)	)	PUNCT
ejpam-5537	50	1	=	=	SYM
ejpam-5537	50	2	lim	lim	PROPN
ejpam-5537	50	3	ε→0	ε→0	X
ejpam-5537	50	4	f	f	PROPN
ejpam-5537	50	5	(	(	PUNCT
ejpam-5537	50	6	teα	teα	INTJ
ejpam-5537	50	7	(	(	PUNCT
ejpam-5537	50	8	εt	εt	PRON
ejpam-5537	50	9	−α))−	−α))−	VERB
ejpam-5537	50	10	f(t	f(t	NOUN
ejpam-5537	50	11	)	)	PUNCT
ejpam-5537	50	12	ε	ε	PROPN
ejpam-5537	50	13	,	,	PUNCT
ejpam-5537	50	14	(	(	PUNCT
ejpam-5537	50	15	3	3	X
ejpam-5537	50	16	)	)	PUNCT
ejpam-5537	50	17	where	where	SCONJ
ejpam-5537	50	18	t	t	PROPN
ejpam-5537	50	19	>	>	X
ejpam-5537	50	20	0	0	PUNCT
ejpam-5537	51	1	and	and	CCONJ
ejpam-5537	51	2	α	α	PRON
ejpam-5537	51	3	∈	∈	PROPN
ejpam-5537	51	4	(	(	PUNCT
ejpam-5537	51	5	0	0	NUM
ejpam-5537	51	6	,	,	PUNCT
ejpam-5537	51	7	1	1	NUM
ejpam-5537	51	8	)	)	PUNCT
ejpam-5537	51	9	.	.	PUNCT
ejpam-5537	52	1	in	in	ADP
ejpam-5537	52	2	this	this	DET
ejpam-5537	52	3	context	context	NOUN
ejpam-5537	52	4	,	,	PUNCT
ejpam-5537	52	5	we	we	PRON
ejpam-5537	52	6	say	say	VERB
ejpam-5537	52	7	that	that	SCONJ
ejpam-5537	52	8	the	the	DET
ejpam-5537	52	9	function	function	NOUN
ejpam-5537	52	10	f	f	PROPN
ejpam-5537	52	11	is	be	AUX
ejpam-5537	52	12	αdifferentiable	αdifferentiable	ADJ
ejpam-5537	52	13	.	.	PUNCT
ejpam-5537	53	1	if	if	SCONJ
ejpam-5537	53	2	f	f	PROPN
ejpam-5537	53	3	is	be	AUX
ejpam-5537	53	4	α	α	NOUN
ejpam-5537	53	5	-	-	NOUN
ejpam-5537	53	6	differentiable	differentiable	ADJ
ejpam-5537	53	7	on	on	ADP
ejpam-5537	53	8	the	the	DET
ejpam-5537	53	9	interval	interval	NOUN
ejpam-5537	53	10	(	(	PUNCT
ejpam-5537	53	11	0	0	NUM
ejpam-5537	53	12	,	,	PUNCT
ejpam-5537	53	13	t	t	PROPN
ejpam-5537	53	14	)	)	PUNCT
ejpam-5537	53	15	,	,	PUNCT
ejpam-5537	53	16	and	and	CCONJ
ejpam-5537	53	17	if	if	SCONJ
ejpam-5537	53	18	the	the	DET
ejpam-5537	53	19	limit	limit	NOUN
ejpam-5537	53	20	lim	lim	NOUN
ejpam-5537	53	21	t→0	t→0	AUX
ejpam-5537	53	22	+	+	CCONJ
ejpam-5537	53	23	f	f	X
ejpam-5537	53	24	(	(	PUNCT
ejpam-5537	53	25	α)(t	α)(t	PROPN
ejpam-5537	53	26	)	)	PUNCT
ejpam-5537	53	27	(	(	PUNCT
ejpam-5537	53	28	4	4	X
ejpam-5537	53	29	)	)	PUNCT
ejpam-5537	53	30	exists	exist	VERB
ejpam-5537	53	31	,	,	PUNCT
ejpam-5537	53	32	then	then	ADV
ejpam-5537	53	33	we	we	PRON
ejpam-5537	53	34	define	define	VERB
ejpam-5537	53	35	the	the	DET
ejpam-5537	53	36	fractional	fractional	ADJ
ejpam-5537	53	37	derivative	derivative	NOUN
ejpam-5537	53	38	at	at	ADP
ejpam-5537	53	39	zero	zero	NUM
ejpam-5537	53	40	as	as	ADP
ejpam-5537	53	41	:	:	PUNCT
ejpam-5537	53	42	f	f	X
ejpam-5537	53	43	(	(	PUNCT
ejpam-5537	53	44	α)(0	α)(0	NUM
ejpam-5537	53	45	)	)	PUNCT
ejpam-5537	53	46	=	=	SYM
ejpam-5537	53	47	lim	lim	PROPN
ejpam-5537	53	48	t→0	t→0	PROPN
ejpam-5537	53	49	+	+	PROPN
ejpam-5537	53	50	f	f	X
ejpam-5537	53	51	(	(	PUNCT
ejpam-5537	53	52	α)(t	α)(t	PROPN
ejpam-5537	53	53	)	)	PUNCT
ejpam-5537	53	54	.	.	PUNCT
ejpam-5537	54	1	(	(	PUNCT
ejpam-5537	54	2	5	5	X
ejpam-5537	54	3	)	)	PUNCT
ejpam-5537	54	4	theorem	theorem	NOUN
ejpam-5537	54	5	1	1	NUM
ejpam-5537	54	6	.	.	PUNCT
ejpam-5537	55	1	[	[	X
ejpam-5537	55	2	6	6	NUM
ejpam-5537	55	3	]	]	PUNCT
ejpam-5537	55	4	let	let	VERB
ejpam-5537	55	5	f	f	PROPN
ejpam-5537	55	6	and	and	CCONJ
ejpam-5537	55	7	g	g	PROPN
ejpam-5537	55	8	be	be	AUX
ejpam-5537	55	9	α	α	DET
ejpam-5537	55	10	-	-	ADJ
ejpam-5537	55	11	differentiable	differentiable	ADJ
ejpam-5537	55	12	functions	function	NOUN
ejpam-5537	55	13	at	at	ADP
ejpam-5537	55	14	a	a	DET
ejpam-5537	55	15	point	point	NOUN
ejpam-5537	55	16	t	t	NOUN
ejpam-5537	55	17	>	>	X
ejpam-5537	55	18	0	0	NUM
ejpam-5537	55	19	,	,	PUNCT
ejpam-5537	55	20	with	with	ADP
ejpam-5537	55	21	0	0	NUM
ejpam-5537	55	22	<	<	X
ejpam-5537	55	23	α	α	PROPN
ejpam-5537	55	24	≤	≤	ADJ
ejpam-5537	55	25	1	1	NUM
ejpam-5537	55	26	.	.	PUNCT
ejpam-5537	56	1	then	then	ADV
ejpam-5537	56	2	the	the	DET
ejpam-5537	56	3	following	follow	VERB
ejpam-5537	56	4	properties	property	NOUN
ejpam-5537	56	5	hold	hold	VERB
ejpam-5537	56	6	:	:	PUNCT
ejpam-5537	56	7	1	1	X
ejpam-5537	56	8	.	.	X
ejpam-5537	56	9	linearity	linearity	NOUN
ejpam-5537	56	10	:	:	PUNCT
ejpam-5537	57	1	dα(af	dα(af	PROPN
ejpam-5537	57	2	+	+	CCONJ
ejpam-5537	57	3	bg	bg	PROPN
ejpam-5537	57	4	)	)	PUNCT
ejpam-5537	57	5	=	=	SYM
ejpam-5537	57	6	adα(f	adα(f	PROPN
ejpam-5537	57	7	)	)	PUNCT
ejpam-5537	58	1	+	+	CCONJ
ejpam-5537	58	2	bdα(g	bdα(g	NOUN
ejpam-5537	58	3	)	)	PUNCT
ejpam-5537	58	4	for	for	ADP
ejpam-5537	58	5	all	all	DET
ejpam-5537	58	6	a	a	DET
ejpam-5537	58	7	,	,	PUNCT
ejpam-5537	58	8	b	b	PROPN
ejpam-5537	58	9	∈	∈	PROPN
ejpam-5537	58	10	r.	r.	PROPN
ejpam-5537	58	11	2	2	NUM
ejpam-5537	58	12	.	.	PUNCT
ejpam-5537	58	13	power	power	NOUN
ejpam-5537	58	14	function	function	NOUN
ejpam-5537	58	15	:	:	PUNCT
ejpam-5537	58	16	dα	dα	X
ejpam-5537	58	17	(	(	PUNCT
ejpam-5537	58	18	tp	tp	NOUN
ejpam-5537	58	19	)	)	PUNCT
ejpam-5537	58	20	=	=	PUNCT
ejpam-5537	58	21	pp−α	pp−α	ADJ
ejpam-5537	58	22	γ(α+1	γ(α+1	NOUN
ejpam-5537	58	23	)	)	PUNCT
ejpam-5537	58	24	for	for	ADP
ejpam-5537	58	25	all	all	DET
ejpam-5537	58	26	p	p	PROPN
ejpam-5537	58	27	∈	∈	PROPN
ejpam-5537	58	28	r.	r.	PROPN
ejpam-5537	58	29	3	3	NUM
ejpam-5537	58	30	.	.	PUNCT
ejpam-5537	58	31	constant	constant	ADJ
ejpam-5537	58	32	function	function	NOUN
ejpam-5537	58	33	:	:	PUNCT
ejpam-5537	58	34	dα(c	dα(c	X
ejpam-5537	58	35	)	)	PUNCT
ejpam-5537	58	36	=	=	SYM
ejpam-5537	58	37	0	0	NUM
ejpam-5537	58	38	for	for	ADP
ejpam-5537	58	39	any	any	DET
ejpam-5537	58	40	constant	constant	ADJ
ejpam-5537	58	41	function	function	NOUN
ejpam-5537	58	42	f(t	f(t	NOUN
ejpam-5537	58	43	)	)	PUNCT
ejpam-5537	58	44	=	=	SYM
ejpam-5537	58	45	c.	c.	NOUN
ejpam-5537	58	46	4	4	NUM
ejpam-5537	58	47	.	.	PUNCT
ejpam-5537	58	48	product	product	NOUN
ejpam-5537	58	49	rule	rule	NOUN
ejpam-5537	58	50	:	:	PUNCT
ejpam-5537	58	51	dα(fg	dα(fg	NOUN
ejpam-5537	58	52	)	)	PUNCT
ejpam-5537	58	53	=	=	PUNCT
ejpam-5537	58	54	fdα(g	fdα(g	PROPN
ejpam-5537	58	55	)	)	PUNCT
ejpam-5537	58	56	+	+	NUM
ejpam-5537	58	57	gdα(f	gdα(f	NOUN
ejpam-5537	58	58	)	)	PUNCT
ejpam-5537	58	59	.	.	PUNCT
ejpam-5537	59	1	5	5	X
ejpam-5537	59	2	.	.	X
ejpam-5537	59	3	quotient	quotient	NOUN
ejpam-5537	59	4	rule	rule	NOUN
ejpam-5537	59	5	:	:	PUNCT
ejpam-5537	59	6	dα	dα	INTJ
ejpam-5537	59	7	(	(	PUNCT
ejpam-5537	59	8	f	f	PROPN
ejpam-5537	59	9	g	g	PROPN
ejpam-5537	59	10	)	)	PUNCT
ejpam-5537	59	11	=	=	PUNCT
ejpam-5537	59	12	gdα(f)−fdα(g	gdα(f)−fdα(g	PROPN
ejpam-5537	59	13	)	)	PUNCT
ejpam-5537	59	14	g2	g2	PROPN
ejpam-5537	59	15	.	.	PUNCT
ejpam-5537	60	1	e.	e.	PROPN
ejpam-5537	60	2	abuteen	abuteen	PROPN
ejpam-5537	60	3	et	et	PROPN
ejpam-5537	60	4	all	all	DET
ejpam-5537	60	5	/	/	SYM
ejpam-5537	60	6	eur	eur	NOUN
ejpam-5537	60	7	.	.	PUNCT
ejpam-5537	61	1	j.	j.	PROPN
ejpam-5537	61	2	pure	pure	PROPN
ejpam-5537	61	3	appl	appl	PROPN
ejpam-5537	61	4	.	.	PROPN
ejpam-5537	61	5	math	math	PROPN
ejpam-5537	61	6	,	,	PUNCT
ejpam-5537	61	7	17	17	NUM
ejpam-5537	61	8	(	(	PUNCT
ejpam-5537	61	9	4	4	NUM
ejpam-5537	61	10	)	)	PUNCT
ejpam-5537	61	11	(	(	PUNCT
ejpam-5537	61	12	2024	2024	NUM
ejpam-5537	61	13	)	)	PUNCT
ejpam-5537	61	14	,	,	PUNCT
ejpam-5537	61	15	4003	4003	NUM
ejpam-5537	61	16	-	-	SYM
ejpam-5537	61	17	4013	4013	NUM
ejpam-5537	61	18	4006	4006	NUM
ejpam-5537	61	19	lemma	lemma	PROPN
ejpam-5537	61	20	1	1	NUM
ejpam-5537	61	21	.	.	PUNCT
ejpam-5537	62	1	[	[	X
ejpam-5537	62	2	6	6	NUM
ejpam-5537	62	3	]	]	PUNCT
ejpam-5537	62	4	let	let	VERB
ejpam-5537	62	5	f	f	PRON
ejpam-5537	62	6	be	be	AUX
ejpam-5537	62	7	both	both	PRON
ejpam-5537	62	8	α	α	NOUN
ejpam-5537	62	9	-	-	ADJ
ejpam-5537	62	10	differentiable	differentiable	ADJ
ejpam-5537	62	11	and	and	CCONJ
ejpam-5537	62	12	differentiable	differentiable	VERB
ejpam-5537	62	13	at	at	ADP
ejpam-5537	62	14	a	a	DET
ejpam-5537	62	15	point	point	NOUN
ejpam-5537	62	16	t	t	X
ejpam-5537	62	17	>	>	X
ejpam-5537	62	18	0	0	NUM
ejpam-5537	62	19	,	,	PUNCT
ejpam-5537	62	20	with	with	ADP
ejpam-5537	62	21	0	0	NUM
ejpam-5537	62	22	<	<	X
ejpam-5537	62	23	α	α	PROPN
ejpam-5537	62	24	≤	≤	ADJ
ejpam-5537	62	25	1	1	NUM
ejpam-5537	62	26	.	.	PUNCT
ejpam-5537	63	1	then	then	ADV
ejpam-5537	63	2	the	the	DET
ejpam-5537	63	3	α	α	NOUN
ejpam-5537	63	4	-	-	PUNCT
ejpam-5537	63	5	fractional	fractional	ADJ
ejpam-5537	63	6	derivative	derivative	NOUN
ejpam-5537	63	7	of	of	ADP
ejpam-5537	63	8	f	f	PROPN
ejpam-5537	63	9	is	be	AUX
ejpam-5537	63	10	given	give	VERB
ejpam-5537	63	11	by	by	ADP
ejpam-5537	63	12	:	:	PUNCT
ejpam-5537	63	13	dα(f)(t	dα(f)(t	ADJ
ejpam-5537	63	14	)	)	PUNCT
ejpam-5537	63	15	=	=	SYM
ejpam-5537	64	1	t1−α	t1−α	NOUN
ejpam-5537	64	2	γ(α+	γ(α+	DET
ejpam-5537	64	3	1	1	NUM
ejpam-5537	64	4	)	)	PUNCT
ejpam-5537	64	5	f	f	PROPN
ejpam-5537	64	6	′(t	′(t	PROPN
ejpam-5537	64	7	)	)	PUNCT
ejpam-5537	64	8	,	,	PUNCT
ejpam-5537	64	9	(	(	PUNCT
ejpam-5537	64	10	6	6	NUM
ejpam-5537	64	11	)	)	PUNCT
ejpam-5537	64	12	where	where	SCONJ
ejpam-5537	64	13	f	f	PROPN
ejpam-5537	64	14	′(t	′(t	PROPN
ejpam-5537	64	15	)	)	PUNCT
ejpam-5537	64	16	denotes	denote	VERB
ejpam-5537	64	17	the	the	DET
ejpam-5537	64	18	standard	standard	ADJ
ejpam-5537	64	19	derivative	derivative	NOUN
ejpam-5537	64	20	of	of	ADP
ejpam-5537	64	21	f	f	PROPN
ejpam-5537	64	22	with	with	ADP
ejpam-5537	64	23	respect	respect	NOUN
ejpam-5537	64	24	to	to	ADP
ejpam-5537	64	25	t	t	PROPN
ejpam-5537	64	26	,	,	PUNCT
ejpam-5537	64	27	and	and	CCONJ
ejpam-5537	64	28	γ(α+	γ(α+	DET
ejpam-5537	64	29	1	1	NUM
ejpam-5537	64	30	)	)	PUNCT
ejpam-5537	64	31	is	be	AUX
ejpam-5537	64	32	the	the	DET
ejpam-5537	64	33	gamma	gamma	NOUN
ejpam-5537	64	34	function	function	NOUN
ejpam-5537	64	35	evaluated	evaluate	VERB
ejpam-5537	64	36	at	at	ADP
ejpam-5537	64	37	α+	α+	DET
ejpam-5537	64	38	1	1	NUM
ejpam-5537	64	39	.	.	X
ejpam-5537	64	40	2.0.1	2.0.1	NUM
ejpam-5537	64	41	.	.	PUNCT
ejpam-5537	65	1	new	new	ADJ
ejpam-5537	65	2	fractional	fractional	ADJ
ejpam-5537	65	3	integral	integral	ADJ
ejpam-5537	65	4	if	if	SCONJ
ejpam-5537	65	5	a	a	DET
ejpam-5537	65	6	function	function	NOUN
ejpam-5537	65	7	f	f	PROPN
ejpam-5537	65	8	is	be	AUX
ejpam-5537	65	9	α	α	NOUN
ejpam-5537	65	10	-	-	NOUN
ejpam-5537	65	11	differentiable	differentiable	ADJ
ejpam-5537	65	12	in	in	ADP
ejpam-5537	65	13	the	the	DET
ejpam-5537	65	14	interval	interval	NOUN
ejpam-5537	65	15	(	(	PUNCT
ejpam-5537	65	16	a	a	DET
ejpam-5537	65	17	,	,	PUNCT
ejpam-5537	65	18	b	b	NOUN
ejpam-5537	65	19	)	)	PUNCT
ejpam-5537	65	20	,	,	PUNCT
ejpam-5537	65	21	we	we	PRON
ejpam-5537	65	22	define	define	VERB
ejpam-5537	65	23	the	the	DET
ejpam-5537	65	24	α	α	NOUN
ejpam-5537	65	25	-	-	PUNCT
ejpam-5537	65	26	fractional	fractional	ADJ
ejpam-5537	65	27	integral	integral	NOUN
ejpam-5537	65	28	of	of	ADP
ejpam-5537	65	29	f	f	PROPN
ejpam-5537	65	30	for	for	ADP
ejpam-5537	65	31	a	a	DET
ejpam-5537	65	32	≥	≥	NOUN
ejpam-5537	65	33	0	0	NUM
ejpam-5537	65	34	and	and	CCONJ
ejpam-5537	65	35	a	a	DET
ejpam-5537	65	36	<	<	X
ejpam-5537	65	37	t	t	X
ejpam-5537	65	38	<	<	X
ejpam-5537	65	39	b	b	PROPN
ejpam-5537	65	40	as	as	SCONJ
ejpam-5537	65	41	follows	follow	VERB
ejpam-5537	65	42	:	:	PUNCT
ejpam-5537	65	43	definition	definition	NOUN
ejpam-5537	65	44	3	3	NUM
ejpam-5537	65	45	.	.	PUNCT
ejpam-5537	66	1	the	the	DET
ejpam-5537	66	2	new	new	ADJ
ejpam-5537	66	3	α	α	X
ejpam-5537	66	4	-	-	PUNCT
ejpam-5537	66	5	fractional	fractional	ADJ
ejpam-5537	66	6	integral	integral	NOUN
ejpam-5537	66	7	of	of	ADP
ejpam-5537	66	8	a	a	DET
ejpam-5537	66	9	function	function	NOUN
ejpam-5537	66	10	f	f	NOUN
ejpam-5537	66	11	that	that	PRON
ejpam-5537	66	12	is	be	AUX
ejpam-5537	66	13	α	α	PRON
ejpam-5537	66	14	-	-	NOUN
ejpam-5537	66	15	differentiable	differentiable	ADJ
ejpam-5537	66	16	is	be	AUX
ejpam-5537	66	17	given	give	VERB
ejpam-5537	66	18	by	by	ADP
ejpam-5537	66	19	:	:	PUNCT
ejpam-5537	66	20	iαa	iαa	ADJ
ejpam-5537	66	21	(	(	PUNCT
ejpam-5537	66	22	f)(t	f)(t	PROPN
ejpam-5537	66	23	)	)	PUNCT
ejpam-5537	66	24	=	=	SYM
ejpam-5537	67	1	∫	∫	PROPN
ejpam-5537	67	2	t	t	PROPN
ejpam-5537	67	3	a	a	PRON
ejpam-5537	67	4	γ(α+	γ(α+	ADJ
ejpam-5537	67	5	1	1	NUM
ejpam-5537	67	6	)	)	PUNCT
ejpam-5537	67	7	x1−α	x1−α	PROPN
ejpam-5537	67	8	f(x	f(x	PROPN
ejpam-5537	67	9	)	)	PUNCT
ejpam-5537	67	10	dx	dx	PROPN
ejpam-5537	67	11	,	,	PUNCT
ejpam-5537	67	12	(	(	PUNCT
ejpam-5537	67	13	7	7	X
ejpam-5537	67	14	)	)	PUNCT
ejpam-5537	67	15	where	where	SCONJ
ejpam-5537	67	16	α	α	PRON
ejpam-5537	67	17	∈	∈	PROPN
ejpam-5537	67	18	(	(	PUNCT
ejpam-5537	67	19	0	0	NUM
ejpam-5537	67	20	,	,	PUNCT
ejpam-5537	67	21	1	1	NUM
ejpam-5537	67	22	)	)	PUNCT
ejpam-5537	67	23	.	.	PUNCT
ejpam-5537	68	1	one	one	NUM
ejpam-5537	68	2	of	of	ADP
ejpam-5537	68	3	the	the	DET
ejpam-5537	68	4	key	key	ADJ
ejpam-5537	68	5	results	result	NOUN
ejpam-5537	68	6	of	of	ADP
ejpam-5537	68	7	this	this	DET
ejpam-5537	68	8	definition	definition	NOUN
ejpam-5537	68	9	is	be	AUX
ejpam-5537	68	10	stated	state	VERB
ejpam-5537	68	11	in	in	ADP
ejpam-5537	68	12	the	the	DET
ejpam-5537	68	13	following	following	NOUN
ejpam-5537	68	14	theorem	theorem	NOUN
ejpam-5537	68	15	:	:	PUNCT
ejpam-5537	68	16	theorem	theorem	NOUN
ejpam-5537	68	17	2	2	NUM
ejpam-5537	68	18	.	.	PUNCT
ejpam-5537	69	1	if	if	SCONJ
ejpam-5537	69	2	f	f	PROPN
ejpam-5537	69	3	is	be	AUX
ejpam-5537	69	4	continuous	continuous	ADJ
ejpam-5537	69	5	on	on	ADP
ejpam-5537	69	6	the	the	DET
ejpam-5537	69	7	domain	domain	NOUN
ejpam-5537	69	8	of	of	ADP
ejpam-5537	69	9	iα	iα	NOUN
ejpam-5537	69	10	for	for	ADP
ejpam-5537	69	11	t	t	PROPN
ejpam-5537	69	12	≥	≥	NOUN
ejpam-5537	69	13	a	a	PRON
ejpam-5537	69	14	,	,	PUNCT
ejpam-5537	69	15	then	then	ADV
ejpam-5537	69	16	:	:	PUNCT
ejpam-5537	69	17	dα	dα	PRON
ejpam-5537	69	18	(	(	PUNCT
ejpam-5537	69	19	iα(f	iα(f	NOUN
ejpam-5537	69	20	)	)	PUNCT
ejpam-5537	69	21	)	)	PUNCT
ejpam-5537	70	1	(	(	PUNCT
ejpam-5537	70	2	t	t	NOUN
ejpam-5537	70	3	)	)	PUNCT
ejpam-5537	70	4	=	=	SYM
ejpam-5537	70	5	f(t	f(t	NOUN
ejpam-5537	70	6	)	)	PUNCT
ejpam-5537	70	7	.	.	PUNCT
ejpam-5537	71	1	(	(	PUNCT
ejpam-5537	71	2	8)	8)	NUM
ejpam-5537	71	3	proof	proof	NOUN
ejpam-5537	71	4	:	:	PUNCT
ejpam-5537	71	5	see	see	VERB
ejpam-5537	71	6	[	[	X
ejpam-5537	71	7	1	1	NUM
ejpam-5537	71	8	]	]	PUNCT
ejpam-5537	71	9	.	.	PUNCT
ejpam-5537	72	1	theorem	theorem	NOUN
ejpam-5537	72	2	3	3	NUM
ejpam-5537	72	3	.	.	PUNCT
ejpam-5537	73	1	[	[	X
ejpam-5537	73	2	6	6	NUM
ejpam-5537	73	3	]	]	PUNCT
ejpam-5537	73	4	let	let	VERB
ejpam-5537	73	5	α	α	PRON
ejpam-5537	73	6	∈	∈	PROPN
ejpam-5537	73	7	(	(	PUNCT
ejpam-5537	73	8	0	0	NUM
ejpam-5537	73	9	,	,	PUNCT
ejpam-5537	73	10	1	1	NUM
ejpam-5537	73	11	]	]	PUNCT
ejpam-5537	73	12	,	,	PUNCT
ejpam-5537	73	13	then	then	ADV
ejpam-5537	73	14	:	:	PUNCT
ejpam-5537	73	15	1	1	X
ejpam-5537	73	16	)	)	PUNCT
ejpam-5537	73	17	dα	dα	PROPN
ejpam-5537	73	18	(	(	PUNCT
ejpam-5537	73	19	γ(1+α	γ(1+α	PROPN
ejpam-5537	73	20	)	)	PUNCT
ejpam-5537	73	21	α	α	PROPN
ejpam-5537	73	22	tα	tα	PROPN
ejpam-5537	73	23	)	)	PUNCT
ejpam-5537	73	24	=	=	PUNCT
ejpam-5537	74	1	1	1	NUM
ejpam-5537	74	2	.	.	NOUN
ejpam-5537	74	3	2	2	NUM
ejpam-5537	74	4	)	)	PUNCT
ejpam-5537	74	5	dα	dα	NOUN
ejpam-5537	74	6	(	(	PUNCT
ejpam-5537	74	7	sin	sin	NOUN
ejpam-5537	74	8	1	1	NUM
ejpam-5537	74	9	α	α	NOUN
ejpam-5537	74	10	t	t	NOUN
ejpam-5537	74	11	α	α	NOUN
ejpam-5537	74	12	)	)	PUNCT
ejpam-5537	75	1	=	=	SYM
ejpam-5537	75	2	cos(γ(1+α	cos(γ(1+α	PROPN
ejpam-5537	75	3	)	)	PUNCT
ejpam-5537	75	4	α	α	PROPN
ejpam-5537	75	5	tα	tα	PROPN
ejpam-5537	75	6	)	)	PUNCT
ejpam-5537	75	7	.	.	PUNCT
ejpam-5537	76	1	3	3	X
ejpam-5537	76	2	)	)	PUNCT
ejpam-5537	76	3	dα	dα	NOUN
ejpam-5537	76	4	(	(	PUNCT
ejpam-5537	76	5	cos	cos	PROPN
ejpam-5537	76	6	1	1	NUM
ejpam-5537	76	7	α	α	NOUN
ejpam-5537	76	8	t	t	NOUN
ejpam-5537	76	9	α	α	NOUN
ejpam-5537	76	10	)	)	PUNCT
ejpam-5537	77	1	=	=	SYM
ejpam-5537	77	2	−	−	PROPN
ejpam-5537	77	3	sin(γ(1+α	sin(γ(1+α	PROPN
ejpam-5537	77	4	)	)	PUNCT
ejpam-5537	77	5	α	α	PROPN
ejpam-5537	77	6	tα	tα	PROPN
ejpam-5537	77	7	)	)	PUNCT
ejpam-5537	77	8	.	.	PUNCT
ejpam-5537	78	1	4	4	X
ejpam-5537	78	2	)	)	PUNCT
ejpam-5537	78	3	dα	dα	NOUN
ejpam-5537	78	4	(	(	PUNCT
ejpam-5537	78	5	e	e	NOUN
ejpam-5537	78	6	1	1	NUM
ejpam-5537	78	7	α	α	NOUN
ejpam-5537	78	8	tα	tα	PROPN
ejpam-5537	78	9	)	)	PUNCT
ejpam-5537	79	1	=	=	PUNCT
ejpam-5537	79	2	e	e	X
ejpam-5537	79	3	γ(1+α	γ(1+α	PROPN
ejpam-5537	79	4	)	)	PUNCT
ejpam-5537	79	5	α	α	PROPN
ejpam-5537	79	6	tα	tα	PROPN
ejpam-5537	79	7	.	.	PUNCT
ejpam-5537	80	1	3	3	X
ejpam-5537	80	2	.	.	X
ejpam-5537	80	3	applications	application	NOUN
ejpam-5537	80	4	3.1	3.1	NUM
ejpam-5537	80	5	.	.	PUNCT
ejpam-5537	80	6	falling	fall	VERB
ejpam-5537	80	7	body	body	NOUN
ejpam-5537	80	8	problem	problem	NOUN
ejpam-5537	80	9	:	:	PUNCT
ejpam-5537	80	10	the	the	DET
ejpam-5537	80	11	problem	problem	NOUN
ejpam-5537	80	12	of	of	ADP
ejpam-5537	80	13	free	free	ADJ
ejpam-5537	80	14	fall	fall	NOUN
ejpam-5537	80	15	examines	examine	NOUN
ejpam-5537	80	16	how	how	SCONJ
ejpam-5537	80	17	objects	object	NOUN
ejpam-5537	80	18	move	move	VERB
ejpam-5537	80	19	under	under	ADP
ejpam-5537	80	20	the	the	DET
ejpam-5537	80	21	sole	sole	ADJ
ejpam-5537	80	22	influence	influence	NOUN
ejpam-5537	80	23	of	of	ADP
ejpam-5537	80	24	gravity	gravity	NOUN
ejpam-5537	80	25	,	,	PUNCT
ejpam-5537	80	26	excluding	exclude	VERB
ejpam-5537	80	27	forces	force	NOUN
ejpam-5537	80	28	like	like	ADP
ejpam-5537	80	29	air	air	NOUN
ejpam-5537	80	30	resistance	resistance	NOUN
ejpam-5537	80	31	.	.	PUNCT
ejpam-5537	81	1	this	this	DET
ejpam-5537	81	2	scenario	scenario	NOUN
ejpam-5537	81	3	offers	offer	VERB
ejpam-5537	81	4	valuable	valuable	ADJ
ejpam-5537	81	5	insights	insight	NOUN
ejpam-5537	81	6	into	into	ADP
ejpam-5537	81	7	motion	motion	NOUN
ejpam-5537	81	8	,	,	PUNCT
ejpam-5537	81	9	acceleration	acceleration	NOUN
ejpam-5537	81	10	,	,	PUNCT
ejpam-5537	81	11	and	and	CCONJ
ejpam-5537	81	12	gravity	gravity	NOUN
ejpam-5537	81	13	effects	effect	NOUN
ejpam-5537	81	14	.	.	PUNCT
ejpam-5537	82	1	during	during	ADP
ejpam-5537	82	2	free	free	ADJ
ejpam-5537	82	3	fall	fall	NOUN
ejpam-5537	82	4	,	,	PUNCT
ejpam-5537	82	5	an	an	DET
ejpam-5537	82	6	object	object	NOUN
ejpam-5537	82	7	experiences	experience	VERB
ejpam-5537	82	8	constant	constant	ADJ
ejpam-5537	82	9	acceleration	acceleration	NOUN
ejpam-5537	82	10	due	due	ADP
ejpam-5537	82	11	to	to	ADP
ejpam-5537	82	12	gravity	gravity	NOUN
ejpam-5537	82	13	,	,	PUNCT
ejpam-5537	82	14	which	which	PRON
ejpam-5537	82	15	is	be	AUX
ejpam-5537	82	16	approximately	approximately	ADV
ejpam-5537	82	17	9.8m	9.8m	PROPN
ejpam-5537	82	18	/	/	SYM
ejpam-5537	82	19	s2	s2	PROPN
ejpam-5537	82	20	,	,	PUNCT
ejpam-5537	82	21	directed	direct	VERB
ejpam-5537	82	22	toward	toward	ADP
ejpam-5537	82	23	the	the	DET
ejpam-5537	82	24	center	center	NOUN
ejpam-5537	82	25	of	of	ADP
ejpam-5537	82	26	the	the	DET
ejpam-5537	82	27	earth	earth	NOUN
ejpam-5537	82	28	.	.	PUNCT
ejpam-5537	83	1	the	the	DET
ejpam-5537	83	2	behavior	behavior	NOUN
ejpam-5537	83	3	of	of	ADP
ejpam-5537	83	4	a	a	DET
ejpam-5537	83	5	falling	fall	VERB
ejpam-5537	83	6	object	object	NOUN
ejpam-5537	83	7	can	can	AUX
ejpam-5537	83	8	be	be	AUX
ejpam-5537	83	9	studied	study	VERB
ejpam-5537	83	10	using	use	VERB
ejpam-5537	83	11	newton	newton	PROPN
ejpam-5537	83	12	’s	’s	PART
ejpam-5537	83	13	laws	law	NOUN
ejpam-5537	83	14	of	of	ADP
ejpam-5537	83	15	motion	motion	NOUN
ejpam-5537	83	16	and	and	CCONJ
ejpam-5537	83	17	kinematic	kinematic	ADJ
ejpam-5537	83	18	equations	equation	NOUN
ejpam-5537	83	19	,	,	PUNCT
ejpam-5537	83	20	which	which	PRON
ejpam-5537	83	21	allow	allow	VERB
ejpam-5537	83	22	us	we	PRON
ejpam-5537	83	23	to	to	PART
ejpam-5537	83	24	calculate	calculate	VERB
ejpam-5537	83	25	various	various	ADJ
ejpam-5537	83	26	aspects	aspect	NOUN
ejpam-5537	83	27	such	such	ADJ
ejpam-5537	83	28	as	as	ADP
ejpam-5537	83	29	the	the	DET
ejpam-5537	83	30	fall	fall	NOUN
ejpam-5537	83	31	duration	duration	NOUN
ejpam-5537	83	32	,	,	PUNCT
ejpam-5537	83	33	e.	e.	PROPN
ejpam-5537	83	34	abuteen	abuteen	PROPN
ejpam-5537	83	35	et	et	PROPN
ejpam-5537	83	36	all	all	DET
ejpam-5537	83	37	/	/	SYM
ejpam-5537	83	38	eur	eur	NOUN
ejpam-5537	83	39	.	.	PUNCT
ejpam-5537	84	1	j.	j.	PROPN
ejpam-5537	84	2	pure	pure	PROPN
ejpam-5537	84	3	appl	appl	PROPN
ejpam-5537	84	4	.	.	PROPN
ejpam-5537	84	5	math	math	PROPN
ejpam-5537	84	6	,	,	PUNCT
ejpam-5537	84	7	17	17	NUM
ejpam-5537	84	8	(	(	PUNCT
ejpam-5537	84	9	4	4	NUM
ejpam-5537	84	10	)	)	PUNCT
ejpam-5537	84	11	(	(	PUNCT
ejpam-5537	84	12	2024	2024	NUM
ejpam-5537	84	13	)	)	PUNCT
ejpam-5537	84	14	,	,	PUNCT
ejpam-5537	84	15	4003	4003	NUM
ejpam-5537	84	16	-	-	SYM
ejpam-5537	84	17	4013	4013	NUM
ejpam-5537	84	18	4007	4007	NUM
ejpam-5537	84	19	velocity	velocity	NOUN
ejpam-5537	84	20	at	at	ADP
ejpam-5537	84	21	specific	specific	ADJ
ejpam-5537	84	22	times	time	NOUN
ejpam-5537	84	23	,	,	PUNCT
ejpam-5537	84	24	and	and	CCONJ
ejpam-5537	84	25	the	the	DET
ejpam-5537	84	26	distance	distance	NOUN
ejpam-5537	84	27	traveled	travel	VERB
ejpam-5537	84	28	.	.	PUNCT
ejpam-5537	85	1	consider	consider	VERB
ejpam-5537	85	2	an	an	DET
ejpam-5537	85	3	object	object	NOUN
ejpam-5537	85	4	of	of	ADP
ejpam-5537	85	5	mass	mass	NOUN
ejpam-5537	85	6	m	m	PROPN
ejpam-5537	85	7	that	that	PRON
ejpam-5537	85	8	begins	begin	VERB
ejpam-5537	85	9	falling	fall	VERB
ejpam-5537	85	10	from	from	ADP
ejpam-5537	85	11	rest	rest	NOUN
ejpam-5537	85	12	at	at	ADP
ejpam-5537	85	13	a	a	DET
ejpam-5537	85	14	height	height	NOUN
ejpam-5537	85	15	a	a	PRON
ejpam-5537	85	16	above	above	ADP
ejpam-5537	85	17	the	the	DET
ejpam-5537	85	18	ground	ground	NOUN
ejpam-5537	85	19	,	,	PUNCT
ejpam-5537	85	20	with	with	ADP
ejpam-5537	85	21	the	the	DET
ejpam-5537	85	22	fall	fall	NOUN
ejpam-5537	85	23	starting	start	VERB
ejpam-5537	85	24	at	at	ADP
ejpam-5537	85	25	t	t	PROPN
ejpam-5537	85	26	=	=	SYM
ejpam-5537	85	27	0	0	X
ejpam-5537	85	28	.	.	PUNCT
ejpam-5537	86	1	we	we	PRON
ejpam-5537	86	2	take	take	VERB
ejpam-5537	86	3	downward	downward	ADJ
ejpam-5537	86	4	motion	motion	NOUN
ejpam-5537	86	5	as	as	ADP
ejpam-5537	86	6	positive	positive	ADJ
ejpam-5537	86	7	.	.	PUNCT
ejpam-5537	87	1	at	at	ADP
ejpam-5537	87	2	any	any	DET
ejpam-5537	87	3	point	point	NOUN
ejpam-5537	87	4	p	p	NOUN
ejpam-5537	87	5	along	along	ADP
ejpam-5537	87	6	the	the	DET
ejpam-5537	87	7	path	path	NOUN
ejpam-5537	87	8	,	,	PUNCT
ejpam-5537	87	9	the	the	DET
ejpam-5537	87	10	distance	distance	NOUN
ejpam-5537	87	11	fallen	fall	VERB
ejpam-5537	87	12	z	z	NOUN
ejpam-5537	87	13	depends	depend	VERB
ejpam-5537	87	14	on	on	ADP
ejpam-5537	87	15	time	time	NOUN
ejpam-5537	87	16	t.	t.	NOUN
ejpam-5537	87	17	the	the	DET
ejpam-5537	87	18	instantaneous	instantaneous	ADJ
ejpam-5537	87	19	velocity	velocity	NOUN
ejpam-5537	87	20	w(t	w(t	PROPN
ejpam-5537	87	21	)	)	PUNCT
ejpam-5537	87	22	and	and	CCONJ
ejpam-5537	87	23	acceleration	acceleration	NOUN
ejpam-5537	87	24	a	a	PRON
ejpam-5537	87	25	are	be	AUX
ejpam-5537	87	26	derived	derive	VERB
ejpam-5537	87	27	from	from	ADP
ejpam-5537	87	28	the	the	DET
ejpam-5537	87	29	distance	distance	NOUN
ejpam-5537	87	30	function	function	NOUN
ejpam-5537	87	31	z(t	z(t	NOUN
ejpam-5537	87	32	)	)	PUNCT
ejpam-5537	87	33	using	use	VERB
ejpam-5537	87	34	the	the	DET
ejpam-5537	87	35	following	follow	VERB
ejpam-5537	87	36	derivatives	derivative	NOUN
ejpam-5537	87	37	:	:	PUNCT
ejpam-5537	87	38	w(t	w(t	X
ejpam-5537	87	39	)	)	PUNCT
ejpam-5537	88	1	=	=	SYM
ejpam-5537	88	2	dz(t	dz(t	NOUN
ejpam-5537	88	3	)	)	PUNCT
ejpam-5537	88	4	dt	dt	X
ejpam-5537	88	5	,	,	PUNCT
ejpam-5537	88	6	a	a	DET
ejpam-5537	88	7	=	=	NOUN
ejpam-5537	88	8	dw(t	dw(t	NOUN
ejpam-5537	88	9	)	)	PUNCT
ejpam-5537	88	10	dt	dt	X
ejpam-5537	89	1	=	=	SYM
ejpam-5537	89	2	d2z(t	d2z(t	PROPN
ejpam-5537	89	3	)	)	PUNCT
ejpam-5537	89	4	dt2	dt2	PROPN
ejpam-5537	89	5	.	.	PUNCT
ejpam-5537	90	1	(	(	PUNCT
ejpam-5537	90	2	9	9	NUM
ejpam-5537	90	3	)	)	PUNCT
ejpam-5537	90	4	according	accord	VERB
ejpam-5537	90	5	to	to	ADP
ejpam-5537	90	6	newton	newton	PROPN
ejpam-5537	90	7	’s	’s	PART
ejpam-5537	90	8	law	law	NOUN
ejpam-5537	90	9	,	,	PUNCT
ejpam-5537	90	10	the	the	DET
ejpam-5537	90	11	force	force	NOUN
ejpam-5537	90	12	f	f	PROPN
ejpam-5537	90	13	acting	act	VERB
ejpam-5537	90	14	on	on	ADP
ejpam-5537	90	15	an	an	DET
ejpam-5537	90	16	object	object	NOUN
ejpam-5537	90	17	in	in	ADP
ejpam-5537	90	18	free	free	ADJ
ejpam-5537	90	19	fall	fall	NOUN
ejpam-5537	90	20	is	be	AUX
ejpam-5537	90	21	given	give	VERB
ejpam-5537	90	22	by	by	ADP
ejpam-5537	90	23	f	f	PROPN
ejpam-5537	90	24	=	=	SYM
ejpam-5537	90	25	mg	mg	PROPN
ejpam-5537	90	26	,	,	PUNCT
ejpam-5537	90	27	and	and	CCONJ
ejpam-5537	90	28	the	the	DET
ejpam-5537	90	29	acceleration	acceleration	NOUN
ejpam-5537	90	30	dw(t	dw(t	PUNCT
ejpam-5537	90	31	)	)	PUNCT
ejpam-5537	90	32	dt	dt	PUNCT
ejpam-5537	90	33	is	be	AUX
ejpam-5537	90	34	equal	equal	ADJ
ejpam-5537	90	35	to	to	PART
ejpam-5537	90	36	g.	g.	VERB
ejpam-5537	90	37	this	this	DET
ejpam-5537	90	38	scenario	scenario	NOUN
ejpam-5537	90	39	is	be	AUX
ejpam-5537	90	40	represented	represent	VERB
ejpam-5537	90	41	with	with	ADP
ejpam-5537	90	42	the	the	DET
ejpam-5537	90	43	following	follow	VERB
ejpam-5537	90	44	differential	differential	ADJ
ejpam-5537	90	45	equation	equation	NOUN
ejpam-5537	90	46	and	and	CCONJ
ejpam-5537	90	47	the	the	DET
ejpam-5537	90	48	initial	initial	ADJ
ejpam-5537	90	49	conditions	condition	NOUN
ejpam-5537	90	50	:	:	PUNCT
ejpam-5537	90	51	dw(t	dw(t	X
ejpam-5537	90	52	)	)	PUNCT
ejpam-5537	90	53	dt	dt	NOUN
ejpam-5537	91	1	=	=	SYM
ejpam-5537	91	2	g	g	PROPN
ejpam-5537	91	3	,	,	PUNCT
ejpam-5537	91	4	w(0	w(0	PROPN
ejpam-5537	91	5	)	)	PUNCT
ejpam-5537	91	6	=	=	SYM
ejpam-5537	91	7	0	0	NUM
ejpam-5537	91	8	,	,	PUNCT
ejpam-5537	91	9	z(0	z(0	CCONJ
ejpam-5537	91	10	)	)	PUNCT
ejpam-5537	91	11	=	=	SYM
ejpam-5537	91	12	a.	a.	NOUN
ejpam-5537	91	13	(	(	PUNCT
ejpam-5537	91	14	10	10	NUM
ejpam-5537	91	15	)	)	PUNCT
ejpam-5537	91	16	now	now	ADV
ejpam-5537	91	17	,	,	PUNCT
ejpam-5537	91	18	consider	consider	VERB
ejpam-5537	91	19	the	the	DET
ejpam-5537	91	20	fractional	fractional	ADJ
ejpam-5537	91	21	differential	differential	ADJ
ejpam-5537	91	22	equation	equation	NOUN
ejpam-5537	91	23	using	use	VERB
ejpam-5537	91	24	the	the	DET
ejpam-5537	91	25	new	new	ADJ
ejpam-5537	91	26	conformable	conformable	ADJ
ejpam-5537	91	27	derivative	derivative	NOUN
ejpam-5537	91	28	:	:	PUNCT
ejpam-5537	91	29	dαw(t	dαw(t	NOUN
ejpam-5537	91	30	)	)	PUNCT
ejpam-5537	91	31	=	=	SYM
ejpam-5537	91	32	g	g	PROPN
ejpam-5537	91	33	,	,	PUNCT
ejpam-5537	91	34	w(0	w(0	PROPN
ejpam-5537	91	35	)	)	PUNCT
ejpam-5537	91	36	=	=	SYM
ejpam-5537	91	37	0	0	NUM
ejpam-5537	91	38	,	,	PUNCT
ejpam-5537	91	39	z(0	z(0	CCONJ
ejpam-5537	91	40	)	)	PUNCT
ejpam-5537	91	41	=	=	SYM
ejpam-5537	91	42	a.	a.	NOUN
ejpam-5537	91	43	(	(	PUNCT
ejpam-5537	91	44	11	11	NUM
ejpam-5537	91	45	)	)	PUNCT
ejpam-5537	91	46	applying	apply	VERB
ejpam-5537	91	47	equation	equation	NOUN
ejpam-5537	91	48	(	(	PUNCT
ejpam-5537	91	49	6	6	NUM
ejpam-5537	91	50	)	)	PUNCT
ejpam-5537	91	51	yields	yield	NOUN
ejpam-5537	91	52	:	:	PUNCT
ejpam-5537	91	53	t1−α	t1−α	PROPN
ejpam-5537	91	54	γ(1	γ(1	PROPN
ejpam-5537	91	55	+	+	CCONJ
ejpam-5537	91	56	α	α	NOUN
ejpam-5537	91	57	)	)	PUNCT
ejpam-5537	91	58	w′(t	w′(t	NOUN
ejpam-5537	91	59	)	)	PUNCT
ejpam-5537	92	1	=	=	SYM
ejpam-5537	92	2	g.	g.	NOUN
ejpam-5537	92	3	(	(	PUNCT
ejpam-5537	92	4	12	12	NUM
ejpam-5537	92	5	)	)	PUNCT
ejpam-5537	92	6	integrating	integrate	VERB
ejpam-5537	92	7	this	this	DET
ejpam-5537	92	8	equation	equation	NOUN
ejpam-5537	92	9	results	result	VERB
ejpam-5537	92	10	in	in	ADP
ejpam-5537	92	11	:	:	PUNCT
ejpam-5537	92	12	w(t	w(t	X
ejpam-5537	92	13	)	)	PUNCT
ejpam-5537	93	1	=	=	SYM
ejpam-5537	93	2	g	g	PROPN
ejpam-5537	93	3	(	(	PUNCT
ejpam-5537	93	4	γ(1	γ(1	PROPN
ejpam-5537	93	5	+	+	CCONJ
ejpam-5537	93	6	α	α	X
ejpam-5537	93	7	)	)	PUNCT
ejpam-5537	93	8	α	α	PROPN
ejpam-5537	93	9	tα	tα	PROPN
ejpam-5537	93	10	)	)	PUNCT
ejpam-5537	94	1	+	+	CCONJ
ejpam-5537	94	2	c.	c.	NOUN
ejpam-5537	94	3	(	(	PUNCT
ejpam-5537	94	4	13	13	NUM
ejpam-5537	94	5	)	)	PUNCT
ejpam-5537	94	6	using	use	VERB
ejpam-5537	94	7	the	the	DET
ejpam-5537	94	8	initial	initial	ADJ
ejpam-5537	94	9	condition	condition	NOUN
ejpam-5537	94	10	w(0	w(0	PROPN
ejpam-5537	94	11	)	)	PUNCT
ejpam-5537	94	12	=	=	SYM
ejpam-5537	94	13	0	0	NUM
ejpam-5537	94	14	,	,	PUNCT
ejpam-5537	94	15	we	we	PRON
ejpam-5537	94	16	get	get	VERB
ejpam-5537	94	17	c	c	NOUN
ejpam-5537	94	18	is	be	AUX
ejpam-5537	94	19	zero	zero	NUM
ejpam-5537	94	20	.	.	PUNCT
ejpam-5537	95	1	similarly	similarly	ADV
ejpam-5537	95	2	,	,	PUNCT
ejpam-5537	95	3	we	we	PRON
ejpam-5537	95	4	have	have	VERB
ejpam-5537	95	5	:	:	PUNCT
ejpam-5537	95	6	z′(t	z′(t	NUM
ejpam-5537	95	7	)	)	PUNCT
ejpam-5537	96	1	=	=	SYM
ejpam-5537	96	2	g	g	PROPN
ejpam-5537	96	3	γ(1	γ(1	PROPN
ejpam-5537	96	4	+	+	CCONJ
ejpam-5537	96	5	α	α	X
ejpam-5537	96	6	)	)	PUNCT
ejpam-5537	96	7	α	α	PROPN
ejpam-5537	96	8	tα	tα	PROPN
ejpam-5537	96	9	.	.	PUNCT
ejpam-5537	97	1	(	(	PUNCT
ejpam-5537	97	2	14	14	NUM
ejpam-5537	97	3	)	)	PUNCT
ejpam-5537	97	4	thus	thus	ADV
ejpam-5537	97	5	,	,	PUNCT
ejpam-5537	97	6	the	the	DET
ejpam-5537	97	7	function	function	NOUN
ejpam-5537	97	8	z(t	z(t	NOUN
ejpam-5537	97	9	)	)	PUNCT
ejpam-5537	97	10	is	be	AUX
ejpam-5537	97	11	:	:	PUNCT
ejpam-5537	97	12	z(t	z(t	X
ejpam-5537	97	13	)	)	PUNCT
ejpam-5537	97	14	=	=	SYM
ejpam-5537	98	1	g	g	PROPN
ejpam-5537	98	2	α(α+	α(α+	NUM
ejpam-5537	98	3	1	1	NUM
ejpam-5537	98	4	)	)	PUNCT
ejpam-5537	98	5	γ(α+	γ(α+	PRON
ejpam-5537	99	1	1)t(α+1)t	1)t(α+1)t	NOUN
ejpam-5537	99	2	+	+	NOUN
ejpam-5537	99	3	m.	m.	NOUN
ejpam-5537	99	4	(	(	PUNCT
ejpam-5537	99	5	15	15	NUM
ejpam-5537	99	6	)	)	PUNCT
ejpam-5537	99	7	using	use	VERB
ejpam-5537	99	8	the	the	DET
ejpam-5537	99	9	initial	initial	ADJ
ejpam-5537	99	10	condition	condition	NOUN
ejpam-5537	99	11	z(0	z(0	NOUN
ejpam-5537	99	12	)	)	PUNCT
ejpam-5537	99	13	=	=	SYM
ejpam-5537	100	1	a	a	X
ejpam-5537	100	2	,	,	PUNCT
ejpam-5537	100	3	we	we	PRON
ejpam-5537	100	4	determine	determine	VERB
ejpam-5537	100	5	that	that	SCONJ
ejpam-5537	100	6	:	:	PUNCT
ejpam-5537	100	7	z(t	z(t	NOUN
ejpam-5537	100	8	)	)	PUNCT
ejpam-5537	100	9	=	=	SYM
ejpam-5537	101	1	g	g	PROPN
ejpam-5537	101	2	α(α+	α(α+	NUM
ejpam-5537	101	3	1	1	NUM
ejpam-5537	101	4	)	)	PUNCT
ejpam-5537	101	5	γ(α+	γ(α+	PRON
ejpam-5537	101	6	1)t(α+1)t	1)t(α+1)t	NOUN
ejpam-5537	102	1	+	+	NOUN
ejpam-5537	102	2	a.	a.	NOUN
ejpam-5537	102	3	(	(	PUNCT
ejpam-5537	102	4	16	16	NUM
ejpam-5537	102	5	)	)	PUNCT
ejpam-5537	102	6	e.	e.	PROPN
ejpam-5537	102	7	abuteen	abuteen	PROPN
ejpam-5537	102	8	et	et	PROPN
ejpam-5537	102	9	all	all	DET
ejpam-5537	102	10	/	/	SYM
ejpam-5537	102	11	eur	eur	NOUN
ejpam-5537	102	12	.	.	PUNCT
ejpam-5537	103	1	j.	j.	PROPN
ejpam-5537	103	2	pure	pure	PROPN
ejpam-5537	103	3	appl	appl	PROPN
ejpam-5537	103	4	.	.	PROPN
ejpam-5537	103	5	math	math	PROPN
ejpam-5537	103	6	,	,	PUNCT
ejpam-5537	103	7	17	17	NUM
ejpam-5537	103	8	(	(	PUNCT
ejpam-5537	103	9	4	4	NUM
ejpam-5537	103	10	)	)	PUNCT
ejpam-5537	103	11	(	(	PUNCT
ejpam-5537	103	12	2024	2024	NUM
ejpam-5537	103	13	)	)	PUNCT
ejpam-5537	103	14	,	,	PUNCT
ejpam-5537	103	15	4003	4003	NUM
ejpam-5537	103	16	-	-	SYM
ejpam-5537	103	17	4013	4013	NUM
ejpam-5537	103	18	4008	4008	NUM
ejpam-5537	103	19	figure	figure	NOUN
ejpam-5537	103	20	1	1	NUM
ejpam-5537	103	21	:	:	PUNCT
ejpam-5537	103	22	comparative	comparative	ADJ
ejpam-5537	103	23	figures	figure	NOUN
ejpam-5537	103	24	using	use	VERB
ejpam-5537	103	25	different	different	ADJ
ejpam-5537	103	26	values	value	NOUN
ejpam-5537	103	27	of	of	ADP
ejpam-5537	103	28	α	α	NOUN
ejpam-5537	103	29	.	.	PUNCT
ejpam-5537	104	1	this	this	DET
ejpam-5537	104	2	example	example	NOUN
ejpam-5537	104	3	investigates	investigate	VERB
ejpam-5537	104	4	the	the	DET
ejpam-5537	104	5	solutions	solution	NOUN
ejpam-5537	104	6	when	when	SCONJ
ejpam-5537	104	7	α	α	PROPN
ejpam-5537	104	8	has	have	VERB
ejpam-5537	104	9	the	the	DET
ejpam-5537	104	10	following	follow	VERB
ejpam-5537	104	11	values	value	NOUN
ejpam-5537	104	12	:	:	PUNCT
ejpam-5537	104	13	α	α	X
ejpam-5537	104	14	=	=	NOUN
ejpam-5537	104	15	0.2	0.2	NUM
ejpam-5537	104	16	,	,	PUNCT
ejpam-5537	104	17	α	α	NOUN
ejpam-5537	104	18	=	=	SYM
ejpam-5537	104	19	0.5	0.5	NUM
ejpam-5537	104	20	,	,	PUNCT
ejpam-5537	104	21	α	α	NOUN
ejpam-5537	104	22	=	=	SYM
ejpam-5537	104	23	0.6	0.6	NUM
ejpam-5537	104	24	and	and	CCONJ
ejpam-5537	104	25	α	α	NOUN
ejpam-5537	104	26	=	=	SYM
ejpam-5537	104	27	0.9	0.9	NUM
ejpam-5537	104	28	,	,	PUNCT
ejpam-5537	104	29	employing	employ	VERB
ejpam-5537	104	30	the	the	DET
ejpam-5537	104	31	recently	recently	ADV
ejpam-5537	104	32	introduced	introduce	VERB
ejpam-5537	104	33	conformable	conformable	ADJ
ejpam-5537	104	34	fractional	fractional	ADJ
ejpam-5537	104	35	calculus	calculus	NOUN
ejpam-5537	104	36	(	(	PUNCT
ejpam-5537	104	37	as	as	SCONJ
ejpam-5537	104	38	detailed	detailed	ADJ
ejpam-5537	104	39	in	in	ADP
ejpam-5537	104	40	[	[	X
ejpam-5537	104	41	3	3	NUM
ejpam-5537	104	42	,	,	PUNCT
ejpam-5537	104	43	4	4	NUM
ejpam-5537	104	44	]	]	NUM
ejpam-5537	104	45	)	)	PUNCT
ejpam-5537	104	46	.	.	PUNCT
ejpam-5537	105	1	a	a	DET
ejpam-5537	105	2	comparison	comparison	NOUN
ejpam-5537	105	3	of	of	ADP
ejpam-5537	105	4	our	our	PRON
ejpam-5537	105	5	results	result	NOUN
ejpam-5537	105	6	with	with	ADP
ejpam-5537	105	7	those	those	PRON
ejpam-5537	105	8	obtained	obtain	VERB
ejpam-5537	105	9	using	use	VERB
ejpam-5537	105	10	other	other	ADJ
ejpam-5537	105	11	techniques	technique	NOUN
ejpam-5537	105	12	illustrates	illustrate	VERB
ejpam-5537	105	13	how	how	SCONJ
ejpam-5537	105	14	the	the	DET
ejpam-5537	105	15	solutions	solution	NOUN
ejpam-5537	105	16	’	'	PUNCT
ejpam-5537	105	17	behavior	behavior	NOUN
ejpam-5537	105	18	changes	change	VERB
ejpam-5537	105	19	across	across	ADP
ejpam-5537	105	20	these	these	DET
ejpam-5537	105	21	methods	method	NOUN
ejpam-5537	105	22	,	,	PUNCT
ejpam-5537	105	23	shedding	shed	VERB
ejpam-5537	105	24	light	light	NOUN
ejpam-5537	105	25	on	on	ADP
ejpam-5537	105	26	the	the	DET
ejpam-5537	105	27	strengths	strength	NOUN
ejpam-5537	105	28	and	and	CCONJ
ejpam-5537	105	29	weaknesses	weakness	NOUN
ejpam-5537	105	30	of	of	ADP
ejpam-5537	105	31	the	the	DET
ejpam-5537	105	32	new	new	ADJ
ejpam-5537	105	33	conformable	conformable	ADJ
ejpam-5537	105	34	fractional	fractional	ADJ
ejpam-5537	105	35	calculus	calculus	NOUN
ejpam-5537	105	36	in	in	ADP
ejpam-5537	105	37	comparison	comparison	NOUN
ejpam-5537	105	38	to	to	ADP
ejpam-5537	105	39	more	more	ADJ
ejpam-5537	105	40	conventional	conventional	ADJ
ejpam-5537	105	41	approaches	approach	NOUN
ejpam-5537	105	42	.	.	PUNCT
ejpam-5537	106	1	3.2	3.2	NUM
ejpam-5537	106	2	.	.	PUNCT
ejpam-5537	106	3	atomic	atomic	ADJ
ejpam-5537	106	4	solution	solution	NOUN
ejpam-5537	106	5	the	the	DET
ejpam-5537	106	6	idea	idea	NOUN
ejpam-5537	106	7	of	of	ADP
ejpam-5537	106	8	atomic	atomic	ADJ
ejpam-5537	106	9	solutions	solution	NOUN
ejpam-5537	106	10	emerges	emerge	VERB
ejpam-5537	106	11	as	as	ADP
ejpam-5537	106	12	a	a	DET
ejpam-5537	106	13	solution	solution	NOUN
ejpam-5537	106	14	for	for	ADP
ejpam-5537	106	15	linear	linear	ADJ
ejpam-5537	106	16	partial	partial	ADJ
ejpam-5537	106	17	differential	differential	NOUN
ejpam-5537	106	18	equations	equation	NOUN
ejpam-5537	106	19	,	,	PUNCT
ejpam-5537	106	20	both	both	CCONJ
ejpam-5537	106	21	fractional	fractional	ADJ
ejpam-5537	106	22	and	and	CCONJ
ejpam-5537	106	23	non	non	ADJ
ejpam-5537	106	24	-	-	ADJ
ejpam-5537	106	25	fractional	fractional	ADJ
ejpam-5537	106	26	,	,	PUNCT
ejpam-5537	106	27	that	that	PRON
ejpam-5537	106	28	can	can	AUX
ejpam-5537	106	29	not	not	PART
ejpam-5537	106	30	be	be	AUX
ejpam-5537	106	31	resolved	resolve	VERB
ejpam-5537	106	32	using	use	VERB
ejpam-5537	106	33	the	the	DET
ejpam-5537	106	34	separation	separation	NOUN
ejpam-5537	106	35	of	of	ADP
ejpam-5537	106	36	variables	variable	NOUN
ejpam-5537	106	37	.	.	PUNCT
ejpam-5537	107	1	let	let	AUX
ejpam-5537	107	2	e	e	NOUN
ejpam-5537	107	3	and	and	CCONJ
ejpam-5537	107	4	f	f	PROPN
ejpam-5537	107	5	be	be	AUX
ejpam-5537	107	6	two	two	NUM
ejpam-5537	107	7	banach	banach	NOUN
ejpam-5537	107	8	spaces	space	NOUN
ejpam-5537	107	9	,	,	PUNCT
ejpam-5537	107	10	and	and	CCONJ
ejpam-5537	107	11	let	let	VERB
ejpam-5537	107	12	e∗	e∗	PROPN
ejpam-5537	107	13	denote	denote	VERB
ejpam-5537	107	14	the	the	DET
ejpam-5537	107	15	dual	dual	ADJ
ejpam-5537	107	16	space	space	NOUN
ejpam-5537	107	17	of	of	ADP
ejpam-5537	107	18	e.	e.	PROPN
ejpam-5537	107	19	for	for	ADP
ejpam-5537	107	20	x	x	PROPN
ejpam-5537	107	21	∈	∈	PROPN
ejpam-5537	107	22	e	e	PROPN
ejpam-5537	107	23	and	and	CCONJ
ejpam-5537	107	24	y	y	PROPN
ejpam-5537	107	25	∈	∈	PROPN
ejpam-5537	107	26	f	f	PROPN
ejpam-5537	107	27	,	,	PUNCT
ejpam-5537	107	28	consider	consider	VERB
ejpam-5537	107	29	the	the	DET
ejpam-5537	107	30	operator	operator	NOUN
ejpam-5537	107	31	h	h	NOUN
ejpam-5537	107	32	:	:	PUNCT
ejpam-5537	107	33	e∗	e∗	PROPN
ejpam-5537	107	34	→	→	SYM
ejpam-5537	107	35	f	f	PROPN
ejpam-5537	107	36	defined	define	VERB
ejpam-5537	107	37	by	by	ADP
ejpam-5537	107	38	h(x∗	h(x∗	X
ejpam-5537	107	39	)	)	PUNCT
ejpam-5537	107	40	=	=	SYM
ejpam-5537	107	41	x∗(x)y	x∗(x)y	PROPN
ejpam-5537	107	42	.	.	PUNCT
ejpam-5537	108	1	this	this	DET
ejpam-5537	108	2	operator	operator	NOUN
ejpam-5537	108	3	h	h	NOUN
ejpam-5537	108	4	is	be	AUX
ejpam-5537	108	5	a	a	DET
ejpam-5537	108	6	bounded	bounded	ADJ
ejpam-5537	108	7	linear	linear	ADJ
ejpam-5537	108	8	operator	operator	NOUN
ejpam-5537	108	9	of	of	ADP
ejpam-5537	108	10	rank	rank	PROPN
ejpam-5537	108	11	one	one	NUM
ejpam-5537	108	12	,	,	PUNCT
ejpam-5537	108	13	which	which	PRON
ejpam-5537	108	14	we	we	PRON
ejpam-5537	108	15	denote	denote	VERB
ejpam-5537	108	16	as	as	SCONJ
ejpam-5537	108	17	x⊗	x⊗	PROPN
ejpam-5537	108	18	y.	y.	PROPN
ejpam-5537	108	19	operators	operators	PROPN
ejpam-5537	108	20	of	of	ADP
ejpam-5537	108	21	this	this	DET
ejpam-5537	108	22	form	form	NOUN
ejpam-5537	108	23	are	be	AUX
ejpam-5537	108	24	known	know	VERB
ejpam-5537	108	25	as	as	ADP
ejpam-5537	108	26	atoms	atom	NOUN
ejpam-5537	108	27	.	.	PUNCT
ejpam-5537	109	1	atoms	atom	NOUN
ejpam-5537	109	2	are	be	AUX
ejpam-5537	109	3	fundamental	fundamental	ADJ
ejpam-5537	109	4	in	in	ADP
ejpam-5537	109	5	the	the	DET
ejpam-5537	109	6	theory	theory	NOUN
ejpam-5537	109	7	of	of	ADP
ejpam-5537	109	8	tensor	tensor	NOUN
ejpam-5537	109	9	products	product	NOUN
ejpam-5537	109	10	and	and	CCONJ
ejpam-5537	109	11	play	play	VERB
ejpam-5537	109	12	a	a	DET
ejpam-5537	109	13	key	key	ADJ
ejpam-5537	109	14	role	role	NOUN
ejpam-5537	109	15	in	in	ADP
ejpam-5537	109	16	the	the	DET
ejpam-5537	109	17	best	good	ADJ
ejpam-5537	109	18	approximation	approximation	NOUN
ejpam-5537	109	19	theory	theory	NOUN
ejpam-5537	109	20	in	in	ADP
ejpam-5537	109	21	banach	banach	NOUN
ejpam-5537	109	22	spaces	space	NOUN
ejpam-5537	109	23	[	[	X
ejpam-5537	109	24	7	7	NUM
ejpam-5537	109	25	]	]	PUNCT
ejpam-5537	109	26	.	.	PUNCT
ejpam-5537	110	1	an	an	DET
ejpam-5537	110	2	important	important	ADJ
ejpam-5537	110	3	result	result	NOUN
ejpam-5537	110	4	utilized	utilize	VERB
ejpam-5537	110	5	in	in	ADP
ejpam-5537	110	6	our	our	PRON
ejpam-5537	110	7	paper	paper	NOUN
ejpam-5537	110	8	[	[	X
ejpam-5537	110	9	12	12	NUM
ejpam-5537	110	10	]	]	PUNCT
ejpam-5537	110	11	states	state	VERB
ejpam-5537	110	12	that	that	SCONJ
ejpam-5537	110	13	adding	add	VERB
ejpam-5537	110	14	two	two	NUM
ejpam-5537	110	15	atoms	atom	NOUN
ejpam-5537	110	16	gives	give	VERB
ejpam-5537	110	17	an	an	DET
ejpam-5537	110	18	atom	atom	NOUN
ejpam-5537	110	19	,	,	PUNCT
ejpam-5537	110	20	then	then	ADV
ejpam-5537	110	21	either	either	CCONJ
ejpam-5537	110	22	their	their	PRON
ejpam-5537	110	23	first	first	ADJ
ejpam-5537	110	24	components	component	NOUN
ejpam-5537	110	25	or	or	CCONJ
ejpam-5537	110	26	their	their	PRON
ejpam-5537	110	27	second	second	ADJ
ejpam-5537	110	28	components	component	NOUN
ejpam-5537	110	29	are	be	AUX
ejpam-5537	110	30	dependent	dependent	ADJ
ejpam-5537	110	31	.	.	PUNCT
ejpam-5537	111	1	for	for	ADP
ejpam-5537	111	2	further	further	ADJ
ejpam-5537	111	3	details	detail	NOUN
ejpam-5537	111	4	on	on	ADP
ejpam-5537	111	5	tensor	tensor	NOUN
ejpam-5537	111	6	products	product	NOUN
ejpam-5537	111	7	in	in	ADP
ejpam-5537	111	8	banach	banach	NOUN
ejpam-5537	111	9	spaces	space	NOUN
ejpam-5537	111	10	,	,	PUNCT
ejpam-5537	111	11	see	see	VERB
ejpam-5537	111	12	[	[	X
ejpam-5537	111	13	12	12	NUM
ejpam-5537	111	14	]	]	PUNCT
ejpam-5537	111	15	.	.	PUNCT
ejpam-5537	112	1	the	the	DET
ejpam-5537	112	2	partial	partial	ADJ
ejpam-5537	112	3	α	α	NOUN
ejpam-5537	112	4	-	-	NOUN
ejpam-5537	112	5	derivative	derivative	NOUN
ejpam-5537	112	6	of	of	ADP
ejpam-5537	112	7	v	v	NOUN
ejpam-5537	112	8	with	with	ADP
ejpam-5537	112	9	respect	respect	NOUN
ejpam-5537	112	10	to	to	ADP
ejpam-5537	112	11	x	x	PROPN
ejpam-5537	112	12	is	be	AUX
ejpam-5537	112	13	denoted	denote	VERB
ejpam-5537	112	14	as	as	ADP
ejpam-5537	112	15	dα	dα	DET
ejpam-5537	112	16	xv	xv	PROPN
ejpam-5537	112	17	,	,	PUNCT
ejpam-5537	112	18	and	and	CCONJ
ejpam-5537	112	19	similarly	similarly	ADV
ejpam-5537	112	20	,	,	PUNCT
ejpam-5537	112	21	d2α	d2α	NOUN
ejpam-5537	112	22	x	x	SYM
ejpam-5537	112	23	v	v	NOUN
ejpam-5537	112	24	represents	represent	VERB
ejpam-5537	112	25	dα	dα	ADP
ejpam-5537	112	26	xvd	xvd	PROPN
ejpam-5537	112	27	α	α	PROPN
ejpam-5537	112	28	xv	xv	PROPN
ejpam-5537	112	29	.	.	PUNCT
ejpam-5537	113	1	the	the	DET
ejpam-5537	113	2	same	same	ADJ
ejpam-5537	113	3	notation	notation	NOUN
ejpam-5537	113	4	applies	apply	VERB
ejpam-5537	113	5	to	to	ADP
ejpam-5537	113	6	derivatives	derivative	NOUN
ejpam-5537	113	7	with	with	ADP
ejpam-5537	113	8	respect	respect	NOUN
ejpam-5537	113	9	to	to	ADP
ejpam-5537	113	10	y.	y.	NOUN
ejpam-5537	113	11	in	in	ADP
ejpam-5537	113	12	equation	equation	NOUN
ejpam-5537	113	13	(	(	PUNCT
ejpam-5537	113	14	17	17	NUM
ejpam-5537	113	15	)	)	PUNCT
ejpam-5537	113	16	,	,	PUNCT
ejpam-5537	113	17	although	although	SCONJ
ejpam-5537	113	18	the	the	DET
ejpam-5537	113	19	equation	equation	NOUN
ejpam-5537	113	20	is	be	AUX
ejpam-5537	113	21	linear	linear	ADJ
ejpam-5537	113	22	,	,	PUNCT
ejpam-5537	113	23	separating	separate	VERB
ejpam-5537	113	24	variables	variable	NOUN
ejpam-5537	113	25	is	be	AUX
ejpam-5537	113	26	not	not	PART
ejpam-5537	113	27	feasible	feasible	ADJ
ejpam-5537	113	28	.	.	PUNCT
ejpam-5537	114	1	therefore	therefore	ADV
ejpam-5537	114	2	,	,	PUNCT
ejpam-5537	114	3	we	we	PRON
ejpam-5537	114	4	seek	seek	VERB
ejpam-5537	114	5	an	an	DET
ejpam-5537	114	6	atomic	atomic	ADJ
ejpam-5537	114	7	solution	solution	NOUN
ejpam-5537	114	8	,	,	PUNCT
ejpam-5537	114	9	which	which	PRON
ejpam-5537	114	10	is	be	AUX
ejpam-5537	114	11	defined	define	VERB
ejpam-5537	114	12	as	as	ADP
ejpam-5537	114	13	a	a	DET
ejpam-5537	114	14	solution	solution	NOUN
ejpam-5537	114	15	of	of	ADP
ejpam-5537	114	16	the	the	DET
ejpam-5537	114	17	form	form	NOUN
ejpam-5537	114	18	v(x	v(x	PROPN
ejpam-5537	114	19	,	,	PUNCT
ejpam-5537	114	20	t	t	PROPN
ejpam-5537	114	21	)	)	PUNCT
ejpam-5537	114	22	=	=	SYM
ejpam-5537	115	1	e.	e.	PROPN
ejpam-5537	115	2	abuteen	abuteen	PROPN
ejpam-5537	115	3	et	et	VERB
ejpam-5537	115	4	all	all	DET
ejpam-5537	115	5	/	/	SYM
ejpam-5537	115	6	eur	eur	NOUN
ejpam-5537	115	7	.	.	PUNCT
ejpam-5537	116	1	j.	j.	PROPN
ejpam-5537	116	2	pure	pure	PROPN
ejpam-5537	116	3	appl	appl	PROPN
ejpam-5537	116	4	.	.	PROPN
ejpam-5537	116	5	math	math	PROPN
ejpam-5537	116	6	,	,	PUNCT
ejpam-5537	116	7	17	17	NUM
ejpam-5537	116	8	(	(	PUNCT
ejpam-5537	116	9	4	4	NUM
ejpam-5537	116	10	)	)	PUNCT
ejpam-5537	116	11	(	(	PUNCT
ejpam-5537	116	12	2024	2024	NUM
ejpam-5537	116	13	)	)	PUNCT
ejpam-5537	116	14	,	,	PUNCT
ejpam-5537	116	15	4003	4003	NUM
ejpam-5537	116	16	-	-	SYM
ejpam-5537	116	17	4013	4013	NUM
ejpam-5537	116	18	4009	4009	NUM
ejpam-5537	116	19	w(x)h(t	w(x)h(t	NOUN
ejpam-5537	116	20	)	)	PUNCT
ejpam-5537	116	21	.	.	PUNCT
ejpam-5537	117	1	we	we	PRON
ejpam-5537	117	2	aim	aim	VERB
ejpam-5537	117	3	to	to	PART
ejpam-5537	117	4	solve	solve	VERB
ejpam-5537	117	5	the	the	DET
ejpam-5537	117	6	equation	equation	NOUN
ejpam-5537	117	7	:	:	PUNCT
ejpam-5537	117	8	dα	dα	PROPN
ejpam-5537	117	9	t	t	PROPN
ejpam-5537	117	10	v	v	NOUN
ejpam-5537	118	1	+	+	PROPN
ejpam-5537	118	2	dβ	dβ	ADV
ejpam-5537	118	3	xd	xd	ADP
ejpam-5537	118	4	β	β	X
ejpam-5537	118	5	xv	xv	NOUN
ejpam-5537	119	1	=	=	PUNCT
ejpam-5537	119	2	d2x	d2x	PROPN
ejpam-5537	119	3	t	t	PROPN
ejpam-5537	119	4	dβ	dβ	ADP
ejpam-5537	119	5	xv	xv	PROPN
ejpam-5537	119	6	,	,	PUNCT
ejpam-5537	119	7	0	0	PUNCT
ejpam-5537	119	8	<	<	X
ejpam-5537	119	9	α	α	X
ejpam-5537	119	10	,	,	PUNCT
ejpam-5537	119	11	β	β	X
ejpam-5537	119	12	<	<	X
ejpam-5537	119	13	1	1	NUM
ejpam-5537	119	14	,	,	PUNCT
ejpam-5537	119	15	(	(	PUNCT
ejpam-5537	119	16	17	17	NUM
ejpam-5537	119	17	)	)	PUNCT
ejpam-5537	119	18	with	with	ADP
ejpam-5537	119	19	initial	initial	ADJ
ejpam-5537	119	20	conditions	condition	NOUN
ejpam-5537	119	21	v(0	v(0	PROPN
ejpam-5537	119	22	,	,	PUNCT
ejpam-5537	119	23	0	0	NUM
ejpam-5537	119	24	)	)	PUNCT
ejpam-5537	119	25	=	=	SYM
ejpam-5537	119	26	0	0	NUM
ejpam-5537	120	1	and	and	CCONJ
ejpam-5537	120	2	dα	dα	PROPN
ejpam-5537	120	3	t	t	PROPN
ejpam-5537	120	4	d	d	PROPN
ejpam-5537	120	5	β	β	X
ejpam-5537	120	6	x(0	x(0	PROPN
ejpam-5537	120	7	,	,	PUNCT
ejpam-5537	120	8	0	0	NUM
ejpam-5537	120	9	)	)	PUNCT
ejpam-5537	120	10	=	=	SYM
ejpam-5537	120	11	1	1	X
ejpam-5537	120	12	.	.	X
ejpam-5537	120	13	procedure	procedure	NOUN
ejpam-5537	120	14	:	:	PUNCT
ejpam-5537	120	15	assume	assume	VERB
ejpam-5537	120	16	v(x	v(x	PROPN
ejpam-5537	120	17	,	,	PUNCT
ejpam-5537	120	18	t	t	PROPN
ejpam-5537	120	19	)	)	PUNCT
ejpam-5537	120	20	=	=	NOUN
ejpam-5537	120	21	w(x)h(t	w(x)h(t	NOUN
ejpam-5537	120	22	)	)	PUNCT
ejpam-5537	120	23	.	.	PUNCT
ejpam-5537	121	1	by	by	ADP
ejpam-5537	121	2	substituting	substitute	VERB
ejpam-5537	121	3	this	this	PRON
ejpam-5537	121	4	into	into	ADP
ejpam-5537	121	5	equation	equation	NOUN
ejpam-5537	121	6	(	(	PUNCT
ejpam-5537	121	7	17	17	NUM
ejpam-5537	121	8	)	)	PUNCT
ejpam-5537	121	9	,	,	PUNCT
ejpam-5537	121	10	we	we	PRON
ejpam-5537	121	11	get	get	VERB
ejpam-5537	121	12	:	:	PUNCT
ejpam-5537	121	13	w(x)hα(t	w(x)hα(t	X
ejpam-5537	121	14	)	)	PUNCT
ejpam-5537	121	15	+	+	CCONJ
ejpam-5537	121	16	w2β(x)h(t	w2β(x)h(t	ADJ
ejpam-5537	121	17	)	)	PUNCT
ejpam-5537	121	18	=	=	SYM
ejpam-5537	121	19	w(x)h2αx(t	w(x)h2αx(t	NOUN
ejpam-5537	121	20	)	)	PUNCT
ejpam-5537	121	21	.	.	PUNCT
ejpam-5537	122	1	(	(	PUNCT
ejpam-5537	122	2	18	18	NUM
ejpam-5537	122	3	)	)	PUNCT
ejpam-5537	122	4	this	this	DET
ejpam-5537	122	5	expression	expression	NOUN
ejpam-5537	122	6	can	can	AUX
ejpam-5537	122	7	be	be	AUX
ejpam-5537	122	8	represented	represent	VERB
ejpam-5537	122	9	in	in	ADP
ejpam-5537	122	10	tensor	tensor	NOUN
ejpam-5537	122	11	product	product	NOUN
ejpam-5537	122	12	form	form	NOUN
ejpam-5537	122	13	as	as	ADP
ejpam-5537	122	14	:	:	PUNCT
ejpam-5537	122	15	w	w	NOUN
ejpam-5537	122	16	⊗hα	⊗hα	NUM
ejpam-5537	122	17	+	+	CCONJ
ejpam-5537	122	18	w2β	w2β	NOUN
ejpam-5537	122	19	⊗h	⊗h	VERB
ejpam-5537	122	20	=	=	SYM
ejpam-5537	122	21	w	w	PROPN
ejpam-5537	122	22	⊗h2α	⊗h2α	PROPN
ejpam-5537	122	23	.	.	PUNCT
ejpam-5537	123	1	(	(	PUNCT
ejpam-5537	123	2	19	19	NUM
ejpam-5537	123	3	)	)	PUNCT
ejpam-5537	123	4	considering	consider	VERB
ejpam-5537	123	5	the	the	DET
ejpam-5537	123	6	initial	initial	ADJ
ejpam-5537	123	7	conditions	condition	NOUN
ejpam-5537	123	8	:	:	PUNCT
ejpam-5537	123	9	h(0	h(0	PROPN
ejpam-5537	123	10	)	)	PUNCT
ejpam-5537	123	11	=	=	SYM
ejpam-5537	123	12	1	1	NUM
ejpam-5537	123	13	,	,	PUNCT
ejpam-5537	123	14	hα(0	hα(0	NOUN
ejpam-5537	123	15	)	)	PUNCT
ejpam-5537	123	16	=	=	SYM
ejpam-5537	123	17	1	1	NUM
ejpam-5537	123	18	,	,	PUNCT
ejpam-5537	123	19	w(0	w(0	PROPN
ejpam-5537	123	20	)	)	PUNCT
ejpam-5537	123	21	=	=	SYM
ejpam-5537	123	22	0	0	NUM
ejpam-5537	123	23	,	,	PUNCT
ejpam-5537	123	24	and	and	CCONJ
ejpam-5537	123	25	wβ(0	wβ(0	NOUN
ejpam-5537	123	26	)	)	PUNCT
ejpam-5537	123	27	=	=	SYM
ejpam-5537	123	28	1	1	X
ejpam-5537	123	29	.	.	X
ejpam-5537	123	30	in	in	ADP
ejpam-5537	123	31	equation	equation	NOUN
ejpam-5537	123	32	(	(	PUNCT
ejpam-5537	123	33	17	17	NUM
ejpam-5537	123	34	)	)	PUNCT
ejpam-5537	123	35	,	,	PUNCT
ejpam-5537	123	36	the	the	DET
ejpam-5537	123	37	sum	sum	NOUN
ejpam-5537	123	38	of	of	ADP
ejpam-5537	123	39	two	two	NUM
ejpam-5537	123	40	atomic	atomic	ADJ
ejpam-5537	123	41	solutions	solution	NOUN
ejpam-5537	123	42	yields	yield	VERB
ejpam-5537	123	43	another	another	DET
ejpam-5537	123	44	atomic	atomic	ADJ
ejpam-5537	123	45	solution	solution	NOUN
ejpam-5537	123	46	,	,	PUNCT
ejpam-5537	123	47	leading	lead	VERB
ejpam-5537	123	48	to	to	ADP
ejpam-5537	123	49	two	two	NUM
ejpam-5537	123	50	cases	case	NOUN
ejpam-5537	123	51	:	:	PUNCT
ejpam-5537	123	52	case	case	NOUN
ejpam-5537	123	53	(	(	PUNCT
ejpam-5537	123	54	i	i	NOUN
ejpam-5537	123	55	):	):	PUNCT
ejpam-5537	123	56	h(t	h(t	PROPN
ejpam-5537	123	57	)	)	PUNCT
ejpam-5537	123	58	=	=	SYM
ejpam-5537	124	1	hα(t	hα(t	X
ejpam-5537	124	2	)	)	PUNCT
ejpam-5537	124	3	=	=	SYM
ejpam-5537	124	4	h2αx(t	h2αx(t	PROPN
ejpam-5537	124	5	)	)	PUNCT
ejpam-5537	124	6	.	.	PUNCT
ejpam-5537	125	1	using	use	VERB
ejpam-5537	125	2	results	result	NOUN
ejpam-5537	125	3	from	from	ADP
ejpam-5537	125	4	[	[	X
ejpam-5537	125	5	1	1	NUM
ejpam-5537	125	6	]	]	PUNCT
ejpam-5537	125	7	,	,	PUNCT
ejpam-5537	125	8	we	we	PRON
ejpam-5537	125	9	find	find	VERB
ejpam-5537	125	10	:	:	PUNCT
ejpam-5537	125	11	h(t	h(t	X
ejpam-5537	125	12	)	)	PUNCT
ejpam-5537	125	13	=	=	PUNCT
ejpam-5537	125	14	e	e	X
ejpam-5537	125	15	γ(1+α)tα	γ(1+α)tα	NUM
ejpam-5537	125	16	α	α	NOUN
ejpam-5537	125	17	.	.	PUNCT
ejpam-5537	126	1	(	(	PUNCT
ejpam-5537	126	2	20	20	NUM
ejpam-5537	126	3	)	)	PUNCT
ejpam-5537	126	4	substituting	substitute	VERB
ejpam-5537	126	5	this	this	PRON
ejpam-5537	126	6	into	into	ADP
ejpam-5537	126	7	equation	equation	NOUN
ejpam-5537	126	8	(	(	PUNCT
ejpam-5537	126	9	19	19	NUM
ejpam-5537	126	10	)	)	PUNCT
ejpam-5537	126	11	gives	give	VERB
ejpam-5537	126	12	:	:	PUNCT
ejpam-5537	126	13	e	e	PROPN
ejpam-5537	126	14	γ(1+α)tα	γ(1+α)tα	NUM
ejpam-5537	126	15	α	α	NOUN
ejpam-5537	126	16	⊗	⊗	PROPN
ejpam-5537	126	17	(	(	PUNCT
ejpam-5537	126	18	w	w	PROPN
ejpam-5537	126	19	+	+	CCONJ
ejpam-5537	126	20	w2β	w2β	NOUN
ejpam-5537	126	21	)	)	PUNCT
ejpam-5537	127	1	=	=	PUNCT
ejpam-5537	127	2	e	e	X
ejpam-5537	127	3	γ(1+α)tα	γ(1+α)tα	NOUN
ejpam-5537	127	4	α	α	NOUN
ejpam-5537	127	5	⊗	⊗	NOUN
ejpam-5537	127	6	wβ	wβ	PROPN
ejpam-5537	127	7	.	.	PUNCT
ejpam-5537	128	1	(	(	PUNCT
ejpam-5537	128	2	21	21	NUM
ejpam-5537	128	3	)	)	PUNCT
ejpam-5537	128	4	thus	thus	ADV
ejpam-5537	128	5	,	,	PUNCT
ejpam-5537	128	6	we	we	PRON
ejpam-5537	128	7	obtain	obtain	VERB
ejpam-5537	128	8	:	:	PUNCT
ejpam-5537	128	9	w2β	w2β	NOUN
ejpam-5537	128	10	−	−	NOUN
ejpam-5537	129	1	wβ	wβ	ADP
ejpam-5537	129	2	+	+	CCONJ
ejpam-5537	129	3	w	w	NOUN
ejpam-5537	129	4	=	=	SYM
ejpam-5537	129	5	0	0	NUM
ejpam-5537	129	6	.	.	PUNCT
ejpam-5537	130	1	(	(	PUNCT
ejpam-5537	130	2	22	22	X
ejpam-5537	130	3	)	)	PUNCT
ejpam-5537	130	4	applying	apply	VERB
ejpam-5537	130	5	results	result	NOUN
ejpam-5537	130	6	from	from	ADP
ejpam-5537	130	7	[	[	X
ejpam-5537	130	8	6	6	NUM
ejpam-5537	130	9	]	]	PUNCT
ejpam-5537	130	10	,	,	PUNCT
ejpam-5537	130	11	we	we	PRON
ejpam-5537	130	12	find	find	VERB
ejpam-5537	130	13	:	:	PUNCT
ejpam-5537	130	14	w(x	w(x	X
ejpam-5537	130	15	)	)	PUNCT
ejpam-5537	130	16	=	=	PUNCT
ejpam-5537	130	17	c1e	c1e	NOUN
ejpam-5537	130	18	1	1	NUM
ejpam-5537	130	19	2	2	NUM
ejpam-5537	130	20	γ(1+β)x	γ(1+β)x	NOUN
ejpam-5537	130	21	β	β	NOUN
ejpam-5537	130	22	β	β	NOUN
ejpam-5537	130	23	√	√	NUM
ejpam-5537	130	24	3	3	NUM
ejpam-5537	130	25	2	2	NUM
ejpam-5537	130	26	γ(1	γ(1	PROPN
ejpam-5537	130	27	+	+	CCONJ
ejpam-5537	130	28	β)xβ	β)xβ	PROPN
ejpam-5537	130	29	β	β	NOUN
ejpam-5537	130	30	+	+	CCONJ
ejpam-5537	130	31	c2e	c2e	NOUN
ejpam-5537	130	32	1	1	NUM
ejpam-5537	130	33	2	2	NUM
ejpam-5537	130	34	γ(1+β)x	γ(1+β)x	NOUN
ejpam-5537	130	35	β	β	X
ejpam-5537	130	36	β	β	X
ejpam-5537	130	37	sin	sin	NOUN
ejpam-5537	130	38	(	(	PUNCT
ejpam-5537	130	39	sin	sin	NOUN
ejpam-5537	130	40	(	(	PUNCT
ejpam-5537	130	41	√	√	NUM
ejpam-5537	130	42	3	3	NUM
ejpam-5537	130	43	2	2	NUM
ejpam-5537	130	44	γ(1	γ(1	PROPN
ejpam-5537	130	45	+	+	CCONJ
ejpam-5537	130	46	β)xβ	β)xβ	PROPN
ejpam-5537	130	47	β	β	NOUN
ejpam-5537	130	48	)	)	PUNCT
ejpam-5537	130	49	)	)	PUNCT
ejpam-5537	130	50	.	.	PUNCT
ejpam-5537	131	1	(	(	PUNCT
ejpam-5537	131	2	23	23	NUM
ejpam-5537	131	3	)	)	PUNCT
ejpam-5537	131	4	using	use	VERB
ejpam-5537	131	5	the	the	DET
ejpam-5537	131	6	initial	initial	ADJ
ejpam-5537	131	7	conditions	condition	NOUN
ejpam-5537	131	8	w(0	w(0	PROPN
ejpam-5537	131	9	)	)	PUNCT
ejpam-5537	131	10	=	=	SYM
ejpam-5537	131	11	0	0	NUM
ejpam-5537	131	12	and	and	CCONJ
ejpam-5537	131	13	wβ(0	wβ(0	NOUN
ejpam-5537	131	14	)	)	PUNCT
ejpam-5537	131	15	=	=	SYM
ejpam-5537	131	16	1	1	NUM
ejpam-5537	131	17	,	,	PUNCT
ejpam-5537	131	18	we	we	PRON
ejpam-5537	131	19	obtain	obtain	VERB
ejpam-5537	131	20	:	:	PUNCT
ejpam-5537	131	21	w(x	w(x	NUM
ejpam-5537	131	22	)	)	PUNCT
ejpam-5537	131	23	=	=	SYM
ejpam-5537	132	1	2√	2√	NUM
ejpam-5537	132	2	3	3	NUM
ejpam-5537	132	3	e	e	NOUN
ejpam-5537	132	4	1	1	NUM
ejpam-5537	132	5	2	2	NUM
ejpam-5537	132	6	γ(1+β)x	γ(1+β)x	NOUN
ejpam-5537	132	7	β	β	X
ejpam-5537	132	8	β	β	X
ejpam-5537	132	9	sin	sin	NOUN
ejpam-5537	132	10	(	(	PUNCT
ejpam-5537	132	11	sin	sin	NOUN
ejpam-5537	132	12	(	(	PUNCT
ejpam-5537	132	13	√	√	NUM
ejpam-5537	132	14	3	3	NUM
ejpam-5537	132	15	2	2	NUM
ejpam-5537	132	16	γ(1	γ(1	PROPN
ejpam-5537	132	17	+	+	CCONJ
ejpam-5537	132	18	β)xβ	β)xβ	PROPN
ejpam-5537	132	19	β	β	NOUN
ejpam-5537	132	20	)	)	PUNCT
ejpam-5537	132	21	)	)	PUNCT
ejpam-5537	132	22	.	.	PUNCT
ejpam-5537	133	1	(	(	PUNCT
ejpam-5537	133	2	24	24	NUM
ejpam-5537	133	3	)	)	PUNCT
ejpam-5537	133	4	combining	combine	VERB
ejpam-5537	133	5	this	this	PRON
ejpam-5537	133	6	with	with	ADP
ejpam-5537	133	7	equation	equation	NOUN
ejpam-5537	133	8	(	(	PUNCT
ejpam-5537	133	9	20	20	NUM
ejpam-5537	133	10	)	)	PUNCT
ejpam-5537	133	11	,	,	PUNCT
ejpam-5537	133	12	the	the	DET
ejpam-5537	133	13	atomic	atomic	ADJ
ejpam-5537	133	14	solution	solution	NOUN
ejpam-5537	133	15	for	for	ADP
ejpam-5537	133	16	equation	equation	NOUN
ejpam-5537	133	17	(	(	PUNCT
ejpam-5537	133	18	24	24	NUM
ejpam-5537	133	19	)	)	PUNCT
ejpam-5537	133	20	is	be	AUX
ejpam-5537	133	21	:	:	PUNCT
ejpam-5537	133	22	v(x	v(x	PROPN
ejpam-5537	133	23	,	,	PUNCT
ejpam-5537	133	24	t	t	PROPN
ejpam-5537	133	25	)	)	PUNCT
ejpam-5537	133	26	=	=	PUNCT
ejpam-5537	134	1	(	(	PUNCT
ejpam-5537	134	2	2√	2√	NUM
ejpam-5537	134	3	3	3	NUM
ejpam-5537	134	4	e	e	NOUN
ejpam-5537	134	5	1	1	NUM
ejpam-5537	134	6	2	2	NUM
ejpam-5537	134	7	γ(1+β)x	γ(1+β)x	NOUN
ejpam-5537	134	8	β	β	X
ejpam-5537	134	9	β	β	X
ejpam-5537	134	10	sin	sin	NOUN
ejpam-5537	134	11	(	(	PUNCT
ejpam-5537	134	12	sin	sin	NOUN
ejpam-5537	134	13	(	(	PUNCT
ejpam-5537	134	14	√	√	NUM
ejpam-5537	134	15	3	3	NUM
ejpam-5537	134	16	2	2	NUM
ejpam-5537	135	1	γ(1	γ(1	NOUN
ejpam-5537	135	2	+	+	NUM
ejpam-5537	135	3	β	β	NOUN
ejpam-5537	135	4	)	)	PUNCT
ejpam-5537	135	5	xβ	xβ	ADV
ejpam-5537	135	6	β	β	NOUN
ejpam-5537	135	7	)	)	PUNCT
ejpam-5537	135	8	)	)	PUNCT
ejpam-5537	135	9	)	)	PUNCT
ejpam-5537	135	10	eγ(1+α	eγ(1+α	PROPN
ejpam-5537	135	11	)	)	PUNCT
ejpam-5537	135	12	t	t	PROPN
ejpam-5537	135	13	α	α	PROPN
ejpam-5537	135	14	α	α	NOUN
ejpam-5537	135	15	.	.	PUNCT
ejpam-5537	136	1	(	(	PUNCT
ejpam-5537	136	2	25	25	NUM
ejpam-5537	136	3	)	)	PUNCT
ejpam-5537	136	4	case	case	NOUN
ejpam-5537	136	5	(	(	PUNCT
ejpam-5537	136	6	ii	ii	NOUN
ejpam-5537	136	7	):	):	PUNCT
ejpam-5537	136	8	when	when	SCONJ
ejpam-5537	136	9	w(x	w(x	NOUN
ejpam-5537	136	10	)	)	PUNCT
ejpam-5537	136	11	=	=	SYM
ejpam-5537	136	12	wβ(x	wβ(x	NOUN
ejpam-5537	136	13	)	)	PUNCT
ejpam-5537	136	14	=	=	SYM
ejpam-5537	136	15	w2β(x	w2β(x	NOUN
ejpam-5537	136	16	)	)	PUNCT
ejpam-5537	136	17	,	,	PUNCT
ejpam-5537	136	18	equation	equation	NOUN
ejpam-5537	136	19	(	(	PUNCT
ejpam-5537	136	20	19	19	NUM
ejpam-5537	136	21	)	)	PUNCT
ejpam-5537	136	22	has	have	VERB
ejpam-5537	136	23	no	no	DET
ejpam-5537	136	24	solution	solution	NOUN
ejpam-5537	136	25	,	,	PUNCT
ejpam-5537	136	26	indicating	indicate	VERB
ejpam-5537	136	27	that	that	SCONJ
ejpam-5537	136	28	no	no	DET
ejpam-5537	136	29	atomic	atomic	ADJ
ejpam-5537	136	30	solution	solution	NOUN
ejpam-5537	136	31	exists	exist	VERB
ejpam-5537	136	32	in	in	ADP
ejpam-5537	136	33	this	this	DET
ejpam-5537	136	34	case	case	NOUN
ejpam-5537	136	35	.	.	PUNCT
ejpam-5537	137	1	e.	e.	PROPN
ejpam-5537	137	2	abuteen	abuteen	PROPN
ejpam-5537	137	3	et	et	PROPN
ejpam-5537	137	4	all	all	DET
ejpam-5537	137	5	/	/	SYM
ejpam-5537	137	6	eur	eur	NOUN
ejpam-5537	137	7	.	.	PUNCT
ejpam-5537	138	1	j.	j.	PROPN
ejpam-5537	138	2	pure	pure	PROPN
ejpam-5537	138	3	appl	appl	PROPN
ejpam-5537	138	4	.	.	PROPN
ejpam-5537	138	5	math	math	PROPN
ejpam-5537	138	6	,	,	PUNCT
ejpam-5537	138	7	17	17	NUM
ejpam-5537	138	8	(	(	PUNCT
ejpam-5537	138	9	4	4	NUM
ejpam-5537	138	10	)	)	PUNCT
ejpam-5537	138	11	(	(	PUNCT
ejpam-5537	138	12	2024	2024	NUM
ejpam-5537	138	13	)	)	PUNCT
ejpam-5537	138	14	,	,	PUNCT
ejpam-5537	138	15	4003	4003	NUM
ejpam-5537	138	16	-	-	SYM
ejpam-5537	138	17	4013	4013	NUM
ejpam-5537	138	18	4010	4010	NUM
ejpam-5537	138	19	figure	figure	NOUN
ejpam-5537	138	20	2	2	NUM
ejpam-5537	138	21	:	:	PUNCT
ejpam-5537	138	22	the	the	DET
ejpam-5537	138	23	exact	exact	ADJ
ejpam-5537	138	24	and	and	CCONJ
ejpam-5537	138	25	approximate	approximate	ADJ
ejpam-5537	138	26	solution	solution	NOUN
ejpam-5537	138	27	of	of	ADP
ejpam-5537	138	28	v(x	v(x	PROPN
ejpam-5537	138	29	,	,	PUNCT
ejpam-5537	138	30	t	t	PROPN
ejpam-5537	138	31	)	)	PUNCT
ejpam-5537	138	32	for	for	ADP
ejpam-5537	138	33	equation	equation	NOUN
ejpam-5537	138	34	(	(	PUNCT
ejpam-5537	138	35	25	25	NUM
ejpam-5537	138	36	)	)	PUNCT
ejpam-5537	138	37	,	,	PUNCT
ejpam-5537	138	38	at	at	ADP
ejpam-5537	138	39	varying	vary	VERB
ejpam-5537	138	40	values	value	NOUN
ejpam-5537	138	41	of	of	ADP
ejpam-5537	138	42	α	α	NOUN
ejpam-5537	138	43	and	and	CCONJ
ejpam-5537	138	44	β	β	X
ejpam-5537	138	45	.	.	PUNCT
ejpam-5537	139	1	e.	e.	PROPN
ejpam-5537	139	2	abuteen	abuteen	PROPN
ejpam-5537	139	3	et	et	PROPN
ejpam-5537	139	4	all	all	DET
ejpam-5537	139	5	/	/	SYM
ejpam-5537	139	6	eur	eur	NOUN
ejpam-5537	139	7	.	.	PUNCT
ejpam-5537	140	1	j.	j.	PROPN
ejpam-5537	140	2	pure	pure	PROPN
ejpam-5537	140	3	appl	appl	PROPN
ejpam-5537	140	4	.	.	PROPN
ejpam-5537	140	5	math	math	PROPN
ejpam-5537	140	6	,	,	PUNCT
ejpam-5537	140	7	17	17	NUM
ejpam-5537	140	8	(	(	PUNCT
ejpam-5537	140	9	4	4	NUM
ejpam-5537	140	10	)	)	PUNCT
ejpam-5537	140	11	(	(	PUNCT
ejpam-5537	140	12	2024	2024	NUM
ejpam-5537	140	13	)	)	PUNCT
ejpam-5537	140	14	,	,	PUNCT
ejpam-5537	140	15	4003	4003	NUM
ejpam-5537	140	16	-	-	SYM
ejpam-5537	140	17	4013	4013	NUM
ejpam-5537	140	18	4011	4011	NUM
ejpam-5537	140	19	figure	figure	NOUN
ejpam-5537	140	20	3	3	NUM
ejpam-5537	140	21	:	:	PUNCT
ejpam-5537	140	22	the	the	DET
ejpam-5537	140	23	exact	exact	ADJ
ejpam-5537	140	24	and	and	CCONJ
ejpam-5537	140	25	approximate	approximate	ADJ
ejpam-5537	140	26	solution	solution	NOUN
ejpam-5537	140	27	of	of	ADP
ejpam-5537	140	28	v(x	v(x	PROPN
ejpam-5537	140	29	,	,	PUNCT
ejpam-5537	140	30	t	t	PROPN
ejpam-5537	140	31	)	)	PUNCT
ejpam-5537	140	32	for	for	ADP
ejpam-5537	140	33	equation	equation	NOUN
ejpam-5537	140	34	(	(	PUNCT
ejpam-5537	140	35	25	25	NUM
ejpam-5537	140	36	)	)	PUNCT
ejpam-5537	140	37	,	,	PUNCT
ejpam-5537	140	38	at	at	ADP
ejpam-5537	140	39	varying	vary	VERB
ejpam-5537	140	40	values	value	NOUN
ejpam-5537	140	41	of	of	ADP
ejpam-5537	140	42	α	α	NOUN
ejpam-5537	140	43	and	and	CCONJ
ejpam-5537	140	44	β	β	NOUN
ejpam-5537	140	45	.	.	PUNCT
ejpam-5537	140	46	references	reference	NOUN
ejpam-5537	140	47	4012	4012	NUM
ejpam-5537	140	48	figure	figure	NOUN
ejpam-5537	140	49	4	4	NUM
ejpam-5537	140	50	:	:	PUNCT
ejpam-5537	140	51	the	the	DET
ejpam-5537	140	52	exact	exact	ADJ
ejpam-5537	140	53	and	and	CCONJ
ejpam-5537	140	54	approximate	approximate	ADJ
ejpam-5537	140	55	solution	solution	NOUN
ejpam-5537	140	56	of	of	ADP
ejpam-5537	140	57	v(x	v(x	PROPN
ejpam-5537	140	58	,	,	PUNCT
ejpam-5537	140	59	t	t	PROPN
ejpam-5537	140	60	)	)	PUNCT
ejpam-5537	140	61	for	for	ADP
ejpam-5537	140	62	equation	equation	NOUN
ejpam-5537	140	63	(	(	PUNCT
ejpam-5537	140	64	25	25	NUM
ejpam-5537	140	65	)	)	PUNCT
ejpam-5537	140	66	,	,	PUNCT
ejpam-5537	140	67	at	at	ADP
ejpam-5537	140	68	varying	vary	VERB
ejpam-5537	140	69	values	value	NOUN
ejpam-5537	140	70	of	of	ADP
ejpam-5537	140	71	α	α	NOUN
ejpam-5537	140	72	and	and	CCONJ
ejpam-5537	140	73	β	β	NOUN
ejpam-5537	140	74	.	.	NOUN
ejpam-5537	141	1	4	4	X
ejpam-5537	141	2	.	.	X
ejpam-5537	141	3	conclusion	conclusion	NOUN
ejpam-5537	141	4	this	this	DET
ejpam-5537	141	5	method	method	NOUN
ejpam-5537	141	6	presents	present	VERB
ejpam-5537	141	7	numerous	numerous	ADJ
ejpam-5537	141	8	benefits	benefit	NOUN
ejpam-5537	141	9	,	,	PUNCT
ejpam-5537	141	10	notably	notably	ADV
ejpam-5537	141	11	its	its	PRON
ejpam-5537	141	12	alignment	alignment	NOUN
ejpam-5537	141	13	with	with	ADP
ejpam-5537	141	14	classical	classical	ADJ
ejpam-5537	141	15	calculus	calculus	NOUN
ejpam-5537	141	16	principles	principle	NOUN
ejpam-5537	141	17	and	and	CCONJ
ejpam-5537	141	18	its	its	PRON
ejpam-5537	141	19	ease	ease	NOUN
ejpam-5537	141	20	of	of	ADP
ejpam-5537	141	21	computation	computation	NOUN
ejpam-5537	141	22	.	.	PUNCT
ejpam-5537	142	1	these	these	DET
ejpam-5537	142	2	features	feature	NOUN
ejpam-5537	142	3	significantly	significantly	ADV
ejpam-5537	142	4	improve	improve	VERB
ejpam-5537	142	5	its	its	PRON
ejpam-5537	142	6	usefulness	usefulness	NOUN
ejpam-5537	142	7	for	for	ADP
ejpam-5537	142	8	both	both	PRON
ejpam-5537	142	9	theoretical	theoretical	ADJ
ejpam-5537	142	10	studies	study	NOUN
ejpam-5537	142	11	and	and	CCONJ
ejpam-5537	142	12	practical	practical	ADJ
ejpam-5537	142	13	applications	application	NOUN
ejpam-5537	142	14	.	.	PUNCT
ejpam-5537	143	1	by	by	ADP
ejpam-5537	143	2	integrating	integrate	VERB
ejpam-5537	143	3	fractional	fractional	ADJ
ejpam-5537	143	4	calculus	calculus	NOUN
ejpam-5537	143	5	concepts	concept	NOUN
ejpam-5537	143	6	with	with	ADP
ejpam-5537	143	7	traditional	traditional	ADJ
ejpam-5537	143	8	derivatives	derivative	NOUN
ejpam-5537	143	9	,	,	PUNCT
ejpam-5537	143	10	our	our	PRON
ejpam-5537	143	11	definition	definition	NOUN
ejpam-5537	143	12	simplifies	simplify	VERB
ejpam-5537	143	13	the	the	DET
ejpam-5537	143	14	analysis	analysis	NOUN
ejpam-5537	143	15	and	and	CCONJ
ejpam-5537	143	16	interpretation	interpretation	NOUN
ejpam-5537	143	17	of	of	ADP
ejpam-5537	143	18	fractional	fractional	ADJ
ejpam-5537	143	19	differential	differential	ADJ
ejpam-5537	143	20	equations	equation	NOUN
ejpam-5537	143	21	and	and	CCONJ
ejpam-5537	143	22	their	their	PRON
ejpam-5537	143	23	solutions	solution	NOUN
ejpam-5537	143	24	.	.	PUNCT
ejpam-5537	144	1	this	this	DET
ejpam-5537	144	2	fusion	fusion	NOUN
ejpam-5537	144	3	not	not	PART
ejpam-5537	144	4	only	only	ADV
ejpam-5537	144	5	clarifies	clarify	VERB
ejpam-5537	144	6	these	these	DET
ejpam-5537	144	7	complex	complex	ADJ
ejpam-5537	144	8	equations	equation	NOUN
ejpam-5537	144	9	but	but	CCONJ
ejpam-5537	144	10	also	also	ADV
ejpam-5537	144	11	facilitates	facilitate	VERB
ejpam-5537	144	12	more	more	ADV
ejpam-5537	144	13	intuitive	intuitive	ADJ
ejpam-5537	144	14	and	and	CCONJ
ejpam-5537	144	15	effective	effective	ADJ
ejpam-5537	144	16	problem	problem	NOUN
ejpam-5537	144	17	-	-	PUNCT
ejpam-5537	144	18	solving	solving	NOUN
ejpam-5537	144	19	.	.	PUNCT
ejpam-5537	145	1	furthermore	furthermore	ADV
ejpam-5537	145	2	,	,	PUNCT
ejpam-5537	145	3	we	we	PRON
ejpam-5537	145	4	explore	explore	VERB
ejpam-5537	145	5	the	the	DET
ejpam-5537	145	6	broader	broad	ADJ
ejpam-5537	145	7	implications	implication	NOUN
ejpam-5537	145	8	of	of	ADP
ejpam-5537	145	9	this	this	DET
ejpam-5537	145	10	definition	definition	NOUN
ejpam-5537	145	11	across	across	ADP
ejpam-5537	145	12	various	various	ADJ
ejpam-5537	145	13	fields	field	NOUN
ejpam-5537	145	14	.	.	PUNCT
ejpam-5537	146	1	this	this	PRON
ejpam-5537	146	2	includes	include	VERB
ejpam-5537	146	3	assessing	assess	VERB
ejpam-5537	146	4	its	its	PRON
ejpam-5537	146	5	impact	impact	NOUN
ejpam-5537	146	6	on	on	ADP
ejpam-5537	146	7	the	the	DET
ejpam-5537	146	8	stability	stability	NOUN
ejpam-5537	146	9	and	and	CCONJ
ejpam-5537	146	10	convergence	convergence	NOUN
ejpam-5537	146	11	of	of	ADP
ejpam-5537	146	12	numerical	numerical	ADJ
ejpam-5537	146	13	methods	method	NOUN
ejpam-5537	146	14	,	,	PUNCT
ejpam-5537	146	15	which	which	PRON
ejpam-5537	146	16	are	be	AUX
ejpam-5537	146	17	essential	essential	ADJ
ejpam-5537	146	18	for	for	ADP
ejpam-5537	146	19	achieving	achieve	VERB
ejpam-5537	146	20	accurate	accurate	ADJ
ejpam-5537	146	21	and	and	CCONJ
ejpam-5537	146	22	dependable	dependable	ADJ
ejpam-5537	146	23	results	result	NOUN
ejpam-5537	146	24	in	in	ADP
ejpam-5537	146	25	computational	computational	ADJ
ejpam-5537	146	26	tasks	task	NOUN
ejpam-5537	146	27	.	.	PUNCT
ejpam-5537	147	1	through	through	ADP
ejpam-5537	147	2	specific	specific	ADJ
ejpam-5537	147	3	examples	example	NOUN
ejpam-5537	147	4	,	,	PUNCT
ejpam-5537	147	5	we	we	PRON
ejpam-5537	147	6	demonstrate	demonstrate	VERB
ejpam-5537	147	7	how	how	SCONJ
ejpam-5537	147	8	our	our	PRON
ejpam-5537	147	9	approach	approach	NOUN
ejpam-5537	147	10	can	can	AUX
ejpam-5537	147	11	be	be	AUX
ejpam-5537	147	12	applied	apply	VERB
ejpam-5537	147	13	effectively	effectively	ADV
ejpam-5537	147	14	in	in	ADP
ejpam-5537	147	15	different	different	ADJ
ejpam-5537	147	16	scenarios	scenario	NOUN
ejpam-5537	147	17	,	,	PUNCT
ejpam-5537	147	18	showcasing	showcase	VERB
ejpam-5537	147	19	its	its	PRON
ejpam-5537	147	20	practical	practical	ADJ
ejpam-5537	147	21	benefits	benefit	NOUN
ejpam-5537	147	22	and	and	CCONJ
ejpam-5537	147	23	flexibility	flexibility	NOUN
ejpam-5537	147	24	.	.	PUNCT
ejpam-5537	148	1	by	by	ADP
ejpam-5537	148	2	emphasizing	emphasize	VERB
ejpam-5537	148	3	these	these	DET
ejpam-5537	148	4	applications	application	NOUN
ejpam-5537	148	5	,	,	PUNCT
ejpam-5537	148	6	we	we	PRON
ejpam-5537	148	7	highlight	highlight	VERB
ejpam-5537	148	8	the	the	DET
ejpam-5537	148	9	definition	definition	NOUN
ejpam-5537	148	10	’s	’s	PART
ejpam-5537	148	11	potential	potential	NOUN
ejpam-5537	148	12	to	to	PART
ejpam-5537	148	13	advance	advance	VERB
ejpam-5537	148	14	both	both	DET
ejpam-5537	148	15	theoretical	theoretical	ADJ
ejpam-5537	148	16	research	research	NOUN
ejpam-5537	148	17	and	and	CCONJ
ejpam-5537	148	18	practical	practical	ADJ
ejpam-5537	148	19	problem	problem	NOUN
ejpam-5537	148	20	-	-	PUNCT
ejpam-5537	148	21	solving	solving	NOUN
ejpam-5537	148	22	in	in	ADP
ejpam-5537	148	23	fractional	fractional	ADJ
ejpam-5537	148	24	calculus	calculus	NOUN
ejpam-5537	148	25	.	.	PUNCT
ejpam-5537	149	1	references	reference	NOUN
ejpam-5537	149	2	[	[	X
ejpam-5537	149	3	1	1	X
ejpam-5537	149	4	]	]	PUNCT
ejpam-5537	149	5	t.	t.	NOUN
ejpam-5537	149	6	abdeljawad	abdeljawad	PROPN
ejpam-5537	149	7	and	and	CCONJ
ejpam-5537	149	8	d.	d.	PROPN
ejpam-5537	149	9	baleanu	baleanu	PROPN
ejpam-5537	149	10	.	.	PUNCT
ejpam-5537	150	1	integration	integration	NOUN
ejpam-5537	150	2	by	by	ADP
ejpam-5537	150	3	parts	part	NOUN
ejpam-5537	150	4	and	and	CCONJ
ejpam-5537	150	5	its	its	PRON
ejpam-5537	150	6	applications	application	NOUN
ejpam-5537	150	7	of	of	ADP
ejpam-5537	150	8	a	a	DET
ejpam-5537	150	9	new	new	ADJ
ejpam-5537	150	10	nonlocal	nonlocal	ADJ
ejpam-5537	150	11	fractional	fractional	ADJ
ejpam-5537	150	12	derivative	derivative	NOUN
ejpam-5537	150	13	with	with	ADP
ejpam-5537	150	14	mittag	mittag	ADJ
ejpam-5537	150	15	-	-	PUNCT
ejpam-5537	150	16	leffler	leffler	NOUN
ejpam-5537	150	17	nonsingular	nonsingular	ADJ
ejpam-5537	150	18	kernel	kernel	PROPN
ejpam-5537	150	19	.	.	PUNCT
ejpam-5537	151	1	journal	journal	PROPN
ejpam-5537	151	2	of	of	ADP
ejpam-5537	151	3	nonlinear	nonlinear	PROPN
ejpam-5537	151	4	sciences	sciences	PROPN
ejpam-5537	151	5	and	and	CCONJ
ejpam-5537	151	6	applications	application	NOUN
ejpam-5537	151	7	(	(	PUNCT
ejpam-5537	151	8	jnsa	jnsa	PROPN
ejpam-5537	151	9	)	)	PUNCT
ejpam-5537	151	10	,	,	PUNCT
ejpam-5537	151	11	10(3	10(3	NUM
ejpam-5537	151	12	)	)	PUNCT
ejpam-5537	151	13	,	,	PUNCT
ejpam-5537	151	14	2017	2017	NUM
ejpam-5537	151	15	.	.	PUNCT
ejpam-5537	152	1	[	[	X
ejpam-5537	152	2	2	2	X
ejpam-5537	152	3	]	]	X
ejpam-5537	152	4	d.	d.	PROPN
ejpam-5537	152	5	baleanu	baleanu	PROPN
ejpam-5537	152	6	and	and	CCONJ
ejpam-5537	152	7	h.	h.	PROPN
ejpam-5537	152	8	k.	k.	PROPN
ejpam-5537	152	9	jassim	jassim	PROPN
ejpam-5537	152	10	.	.	PUNCT
ejpam-5537	153	1	a	a	DET
ejpam-5537	153	2	modification	modification	NOUN
ejpam-5537	153	3	fractional	fractional	ADJ
ejpam-5537	153	4	homotopy	homotopy	NOUN
ejpam-5537	153	5	perturbation	perturbation	NOUN
ejpam-5537	153	6	method	method	NOUN
ejpam-5537	153	7	for	for	ADP
ejpam-5537	153	8	solving	solve	VERB
ejpam-5537	153	9	helmholtz	helmholtz	NOUN
ejpam-5537	153	10	and	and	CCONJ
ejpam-5537	153	11	coupled	couple	VERB
ejpam-5537	153	12	helmholtz	helmholtz	NOUN
ejpam-5537	153	13	equations	equation	NOUN
ejpam-5537	153	14	on	on	ADP
ejpam-5537	153	15	cantor	cantor	NOUN
ejpam-5537	153	16	sets	set	NOUN
ejpam-5537	153	17	.	.	PUNCT
ejpam-5537	154	1	fractal	fractal	ADJ
ejpam-5537	154	2	and	and	CCONJ
ejpam-5537	154	3	fractional	fractional	ADJ
ejpam-5537	154	4	,	,	PUNCT
ejpam-5537	154	5	3(30):1–8	3(30):1–8	NOUN
ejpam-5537	154	6	,	,	PUNCT
ejpam-5537	154	7	2019	2019	NUM
ejpam-5537	154	8	.	.	PUNCT
ejpam-5537	155	1	[	[	X
ejpam-5537	155	2	3	3	NUM
ejpam-5537	155	3	]	]	PUNCT
ejpam-5537	155	4	a.	a.	NOUN
ejpam-5537	155	5	ait	ait	PROPN
ejpam-5537	155	6	brahim	brahim	PROPN
ejpam-5537	155	7	,	,	PUNCT
ejpam-5537	155	8	j.	j.	PROPN
ejpam-5537	155	9	el	el	PROPN
ejpam-5537	155	10	ghordaf	ghordaf	PROPN
ejpam-5537	155	11	,	,	PUNCT
ejpam-5537	155	12	a.	a.	PROPN
ejpam-5537	155	13	el	el	PROPN
ejpam-5537	155	14	hajaji	hajaji	PROPN
ejpam-5537	155	15	,	,	PUNCT
ejpam-5537	155	16	k.	k.	PROPN
ejpam-5537	155	17	hilal	hilal	PROPN
ejpam-5537	155	18	,	,	PUNCT
ejpam-5537	155	19	and	and	CCONJ
ejpam-5537	155	20	j.	j.	PROPN
ejpam-5537	155	21	e.	e.	PROPN
ejpam-5537	155	22	nápoles	nápoles	PROPN
ejpam-5537	155	23	valdes	valde	NOUN
ejpam-5537	155	24	.	.	PUNCT
ejpam-5537	156	1	a	a	DET
ejpam-5537	156	2	comparative	comparative	ADJ
ejpam-5537	156	3	analysis	analysis	NOUN
ejpam-5537	156	4	of	of	ADP
ejpam-5537	156	5	conformable	conformable	ADJ
ejpam-5537	156	6	,	,	PUNCT
ejpam-5537	156	7	non	non	ADJ
ejpam-5537	156	8	-	-	ADJ
ejpam-5537	156	9	conformable	conformable	ADJ
ejpam-5537	156	10	,	,	PUNCT
ejpam-5537	156	11	riemann	riemann	PROPN
ejpam-5537	156	12	-	-	PUNCT
ejpam-5537	156	13	liouville	liouville	NOUN
ejpam-5537	156	14	,	,	PUNCT
ejpam-5537	156	15	and	and	CCONJ
ejpam-5537	156	16	references	reference	NOUN
ejpam-5537	156	17	4013	4013	NUM
ejpam-5537	156	18	caputo	caputo	PROPN
ejpam-5537	156	19	fractional	fractional	ADJ
ejpam-5537	156	20	derivatives	derivative	NOUN
ejpam-5537	156	21	.	.	PUNCT
ejpam-5537	157	1	european	european	ADJ
ejpam-5537	157	2	journal	journal	PROPN
ejpam-5537	157	3	of	of	ADP
ejpam-5537	157	4	pure	pure	ADJ
ejpam-5537	157	5	and	and	CCONJ
ejpam-5537	157	6	applied	applied	ADJ
ejpam-5537	157	7	mathematics	mathematic	NOUN
ejpam-5537	157	8	,	,	PUNCT
ejpam-5537	157	9	july	july	PROPN
ejpam-5537	157	10	2024	2024	NUM
ejpam-5537	157	11	.	.	PUNCT
ejpam-5537	158	1	[	[	X
ejpam-5537	158	2	4	4	NUM
ejpam-5537	158	3	]	]	PUNCT
ejpam-5537	158	4	a.	a.	NOUN
ejpam-5537	158	5	ait	ait	PROPN
ejpam-5537	158	6	brahim	brahim	PROPN
ejpam-5537	158	7	,	,	PUNCT
ejpam-5537	158	8	a.	a.	PROPN
ejpam-5537	158	9	el	el	PROPN
ejpam-5537	158	10	hajaji	hajaji	PROPN
ejpam-5537	158	11	,	,	PUNCT
ejpam-5537	158	12	k.	k.	PROPN
ejpam-5537	158	13	hilal	hilal	PROPN
ejpam-5537	158	14	,	,	PUNCT
ejpam-5537	158	15	and	and	CCONJ
ejpam-5537	158	16	j.	j.	PROPN
ejpam-5537	158	17	el	el	PROPN
ejpam-5537	158	18	ghordaf	ghordaf	PROPN
ejpam-5537	158	19	.	.	PUNCT
ejpam-5537	159	1	on	on	ADP
ejpam-5537	159	2	a	a	DET
ejpam-5537	159	3	novel	novel	ADJ
ejpam-5537	159	4	fractional	fractional	ADJ
ejpam-5537	159	5	calculus	calculus	NOUN
ejpam-5537	159	6	and	and	CCONJ
ejpam-5537	159	7	its	its	PRON
ejpam-5537	159	8	applications	application	NOUN
ejpam-5537	159	9	to	to	ADP
ejpam-5537	159	10	well	well	ADV
ejpam-5537	159	11	-	-	PUNCT
ejpam-5537	159	12	known	know	VERB
ejpam-5537	159	13	problems	problem	NOUN
ejpam-5537	159	14	.	.	PUNCT
ejpam-5537	160	1	european	european	ADJ
ejpam-5537	160	2	journal	journal	PROPN
ejpam-5537	160	3	of	of	ADP
ejpam-5537	160	4	pure	pure	ADJ
ejpam-5537	160	5	and	and	CCONJ
ejpam-5537	160	6	applied	applied	ADJ
ejpam-5537	160	7	mathematics	mathematic	NOUN
ejpam-5537	160	8	,	,	PUNCT
ejpam-5537	160	9	april	april	PROPN
ejpam-5537	160	10	2024	2024	NUM
ejpam-5537	160	11	.	.	PUNCT
ejpam-5537	161	1	[	[	X
ejpam-5537	161	2	5	5	X
ejpam-5537	161	3	]	]	PUNCT
ejpam-5537	161	4	p.	p.	NOUN
ejpam-5537	161	5	cui	cui	NOUN
ejpam-5537	161	6	and	and	CCONJ
ejpam-5537	161	7	h.	h.	PROPN
ejpam-5537	161	8	k.	k.	PROPN
ejpam-5537	161	9	jassim	jassim	PROPN
ejpam-5537	161	10	.	.	PUNCT
ejpam-5537	162	1	local	local	ADJ
ejpam-5537	162	2	fractional	fractional	ADJ
ejpam-5537	162	3	sumudu	sumudu	NOUN
ejpam-5537	162	4	decomposition	decomposition	NOUN
ejpam-5537	162	5	method	method	NOUN
ejpam-5537	162	6	to	to	PART
ejpam-5537	162	7	solve	solve	VERB
ejpam-5537	162	8	fractal	fractal	ADJ
ejpam-5537	162	9	pdes	pde	NOUN
ejpam-5537	162	10	arising	arise	VERB
ejpam-5537	162	11	in	in	ADP
ejpam-5537	162	12	mathematical	mathematical	ADJ
ejpam-5537	162	13	physics	physic	NOUN
ejpam-5537	162	14	.	.	PUNCT
ejpam-5537	163	1	fractals	fractal	NOUN
ejpam-5537	163	2	,	,	PUNCT
ejpam-5537	163	3	32(4):1–6	32(4):1–6	NUM
ejpam-5537	163	4	,	,	PUNCT
ejpam-5537	163	5	2024	2024	NUM
ejpam-5537	163	6	.	.	PUNCT
ejpam-5537	164	1	[	[	X
ejpam-5537	164	2	6	6	NUM
ejpam-5537	164	3	]	]	PUNCT
ejpam-5537	164	4	reza	reza	PROPN
ejpam-5537	164	5	danaei	danaei	PROPN
ejpam-5537	164	6	.	.	PUNCT
ejpam-5537	165	1	new	new	ADJ
ejpam-5537	165	2	definition	definition	NOUN
ejpam-5537	165	3	of	of	ADP
ejpam-5537	165	4	fractional	fractional	ADJ
ejpam-5537	165	5	derivative	derivative	NOUN
ejpam-5537	165	6	included	include	VERB
ejpam-5537	165	7	mittag	mittag	ADJ
ejpam-5537	165	8	-	-	PUNCT
ejpam-5537	165	9	leffler	leffler	NOUN
ejpam-5537	165	10	function	function	NOUN
ejpam-5537	165	11	of	of	ADP
ejpam-5537	165	12	conformable	conformable	ADJ
ejpam-5537	165	13	type	type	NOUN
ejpam-5537	165	14	.	.	PUNCT
ejpam-5537	166	1	journal	journal	PROPN
ejpam-5537	166	2	mathematics	mathematic	NOUN
ejpam-5537	166	3	and	and	CCONJ
ejpam-5537	166	4	computational	computational	ADJ
ejpam-5537	166	5	sciences	science	NOUN
ejpam-5537	166	6	,	,	PUNCT
ejpam-5537	166	7	2024	2024	NUM
ejpam-5537	166	8	.	.	PUNCT
ejpam-5537	167	1	[	[	X
ejpam-5537	167	2	7	7	X
ejpam-5537	167	3	]	]	X
ejpam-5537	167	4	w.	w.	PROPN
ejpam-5537	167	5	deeb	deeb	PROPN
ejpam-5537	167	6	and	and	CCONJ
ejpam-5537	167	7	r.	r.	PROPN
ejpam-5537	167	8	khalil	khalil	PROPN
ejpam-5537	167	9	.	.	PUNCT
ejpam-5537	168	1	best	good	ADJ
ejpam-5537	168	2	approximation	approximation	NOUN
ejpam-5537	168	3	in	in	ADP
ejpam-5537	168	4	l(x	l(x	PROPN
ejpam-5537	168	5	,	,	PUNCT
ejpam-5537	168	6	y	y	PROPN
ejpam-5537	168	7	)	)	PUNCT
ejpam-5537	168	8	.	.	PUNCT
ejpam-5537	169	1	mathematical	mathematical	ADJ
ejpam-5537	169	2	proceedings	proceeding	NOUN
ejpam-5537	169	3	of	of	ADP
ejpam-5537	169	4	the	the	DET
ejpam-5537	169	5	cambridge	cambridge	PROPN
ejpam-5537	169	6	philosophical	philosophical	ADJ
ejpam-5537	169	7	society	society	NOUN
ejpam-5537	169	8	,	,	PUNCT
ejpam-5537	169	9	104(3):527–531	104(3):527–531	NUM
ejpam-5537	169	10	,	,	PUNCT
ejpam-5537	169	11	1988	1988	NUM
ejpam-5537	169	12	.	.	PUNCT
ejpam-5537	170	1	[	[	X
ejpam-5537	170	2	8	8	X
ejpam-5537	170	3	]	]	X
ejpam-5537	170	4	h.	h.	PROPN
ejpam-5537	170	5	jafari	jafari	PROPN
ejpam-5537	170	6	,	,	PUNCT
ejpam-5537	170	7	h.	h.	PROPN
ejpam-5537	170	8	k.	k.	PROPN
ejpam-5537	170	9	jassim	jassim	PROPN
ejpam-5537	170	10	,	,	PUNCT
ejpam-5537	170	11	a.	a.	NOUN
ejpam-5537	170	12	ansari	ansari	PROPN
ejpam-5537	170	13	,	,	PUNCT
ejpam-5537	170	14	and	and	CCONJ
ejpam-5537	170	15	v.	v.	ADP
ejpam-5537	170	16	t.	t.	NOUN
ejpam-5537	170	17	nguyen	nguyen	PROPN
ejpam-5537	170	18	.	.	PUNCT
ejpam-5537	171	1	laplace	laplace	NOUN
ejpam-5537	171	2	decomposition	decomposition	NOUN
ejpam-5537	171	3	method	method	NOUN
ejpam-5537	171	4	for	for	ADP
ejpam-5537	171	5	solving	solve	VERB
ejpam-5537	171	6	the	the	DET
ejpam-5537	171	7	two	two	NUM
ejpam-5537	171	8	-	-	PUNCT
ejpam-5537	171	9	dimensional	dimensional	ADJ
ejpam-5537	171	10	diffusion	diffusion	NOUN
ejpam-5537	171	11	problem	problem	NOUN
ejpam-5537	171	12	in	in	ADP
ejpam-5537	171	13	fractal	fractal	ADJ
ejpam-5537	171	14	heat	heat	NOUN
ejpam-5537	171	15	transfer	transfer	NOUN
ejpam-5537	171	16	.	.	PUNCT
ejpam-5537	172	1	fractals	fractal	NOUN
ejpam-5537	172	2	,	,	PUNCT
ejpam-5537	172	3	32(4):1–6	32(4):1–6	NUM
ejpam-5537	172	4	,	,	PUNCT
ejpam-5537	172	5	2024	2024	NUM
ejpam-5537	172	6	.	.	PUNCT
ejpam-5537	173	1	[	[	X
ejpam-5537	173	2	9	9	NUM
ejpam-5537	173	3	]	]	X
ejpam-5537	173	4	h.	h.	PROPN
ejpam-5537	173	5	jafari	jafari	PROPN
ejpam-5537	173	6	,	,	PUNCT
ejpam-5537	173	7	h.	h.	PROPN
ejpam-5537	173	8	k.	k.	PROPN
ejpam-5537	173	9	jassim	jassim	PROPN
ejpam-5537	173	10	,	,	PUNCT
ejpam-5537	173	11	a.	a.	NOUN
ejpam-5537	173	12	ansari	ansari	PROPN
ejpam-5537	173	13	,	,	PUNCT
ejpam-5537	173	14	and	and	CCONJ
ejpam-5537	173	15	v.	v.	ADP
ejpam-5537	173	16	t.	t.	NOUN
ejpam-5537	173	17	nguyen	nguyen	PROPN
ejpam-5537	173	18	.	.	PUNCT
ejpam-5537	174	1	local	local	ADJ
ejpam-5537	174	2	fractional	fractional	ADJ
ejpam-5537	174	3	variational	variational	ADJ
ejpam-5537	174	4	iteration	iteration	NOUN
ejpam-5537	174	5	transform	transform	NOUN
ejpam-5537	174	6	method	method	NOUN
ejpam-5537	174	7	:	:	PUNCT
ejpam-5537	174	8	a	a	DET
ejpam-5537	174	9	tool	tool	NOUN
ejpam-5537	174	10	for	for	ADP
ejpam-5537	174	11	solving	solve	VERB
ejpam-5537	174	12	local	local	ADJ
ejpam-5537	174	13	fractional	fractional	ADJ
ejpam-5537	174	14	partial	partial	ADJ
ejpam-5537	174	15	differential	differential	NOUN
ejpam-5537	174	16	equations	equation	NOUN
ejpam-5537	174	17	.	.	PUNCT
ejpam-5537	175	1	fractals	fractal	NOUN
ejpam-5537	175	2	,	,	PUNCT
ejpam-5537	175	3	32(4):1–8	32(4):1–8	NUM
ejpam-5537	175	4	,	,	PUNCT
ejpam-5537	175	5	2024	2024	NUM
ejpam-5537	175	6	.	.	PUNCT
ejpam-5537	176	1	[	[	X
ejpam-5537	176	2	10	10	NUM
ejpam-5537	176	3	]	]	X
ejpam-5537	176	4	h.	h.	PROPN
ejpam-5537	176	5	jafari	jafari	PROPN
ejpam-5537	176	6	,	,	PUNCT
ejpam-5537	176	7	h.	h.	PROPN
ejpam-5537	176	8	k.	k.	PROPN
ejpam-5537	176	9	jassim	jassim	PROPN
ejpam-5537	176	10	,	,	PUNCT
ejpam-5537	176	11	and	and	CCONJ
ejpam-5537	176	12	d.	d.	PROPN
ejpam-5537	176	13	baleanu	baleanu	PROPN
ejpam-5537	176	14	.	.	PUNCT
ejpam-5537	177	1	on	on	ADP
ejpam-5537	177	2	the	the	DET
ejpam-5537	177	3	existence	existence	NOUN
ejpam-5537	177	4	and	and	CCONJ
ejpam-5537	177	5	uniqueness	uniqueness	NOUN
ejpam-5537	177	6	of	of	ADP
ejpam-5537	177	7	solutions	solution	NOUN
ejpam-5537	177	8	for	for	ADP
ejpam-5537	177	9	local	local	ADJ
ejpam-5537	177	10	differential	differential	ADJ
ejpam-5537	177	11	equations	equation	NOUN
ejpam-5537	177	12	.	.	PUNCT
ejpam-5537	178	1	entropy	entropy	PROPN
ejpam-5537	178	2	,	,	PUNCT
ejpam-5537	178	3	18:1–9	18:1–9	NUM
ejpam-5537	178	4	,	,	PUNCT
ejpam-5537	178	5	2016	2016	NUM
ejpam-5537	178	6	.	.	PUNCT
ejpam-5537	179	1	[	[	X
ejpam-5537	179	2	11	11	NUM
ejpam-5537	179	3	]	]	X
ejpam-5537	179	4	h.	h.	PROPN
ejpam-5537	179	5	jafari	jafari	PROPN
ejpam-5537	179	6	,	,	PUNCT
ejpam-5537	179	7	m.	m.	PROPN
ejpam-5537	179	8	y.	y.	PROPN
ejpam-5537	179	9	zayir	zayir	PROPN
ejpam-5537	179	10	,	,	PUNCT
ejpam-5537	179	11	and	and	CCONJ
ejpam-5537	179	12	h.	h.	PROPN
ejpam-5537	179	13	k.	k.	PROPN
ejpam-5537	179	14	jassim	jassim	PROPN
ejpam-5537	179	15	.	.	PUNCT
ejpam-5537	180	1	analysis	analysis	NOUN
ejpam-5537	180	2	of	of	ADP
ejpam-5537	180	3	fractional	fractional	ADJ
ejpam-5537	180	4	navier	navier	NOUN
ejpam-5537	180	5	-	-	PUNCT
ejpam-5537	180	6	stokes	stoke	NOUN
ejpam-5537	180	7	equations	equation	NOUN
ejpam-5537	180	8	.	.	PUNCT
ejpam-5537	181	1	heat	heat	NOUN
ejpam-5537	181	2	transfer	transfer	NOUN
ejpam-5537	181	3	,	,	PUNCT
ejpam-5537	181	4	52(3):2859–2877	52(3):2859–2877	PROPN
ejpam-5537	181	5	,	,	PUNCT
ejpam-5537	181	6	2023	2023	NUM
ejpam-5537	181	7	.	.	PUNCT
ejpam-5537	182	1	[	[	X
ejpam-5537	182	2	12	12	NUM
ejpam-5537	182	3	]	]	PUNCT
ejpam-5537	182	4	roshdi	roshdi	NOUN
ejpam-5537	182	5	khalil	khalil	PROPN
ejpam-5537	182	6	.	.	PUNCT
ejpam-5537	183	1	isometries	isometry	NOUN
ejpam-5537	183	2	of	of	ADP
ejpam-5537	183	3	lp	lp	ADJ
ejpam-5537	183	4	⊗lp	⊗lp	PROPN
ejpam-5537	183	5	.	.	PUNCT
ejpam-5537	184	1	tamkangjournalofmathematics	tamkangjournalofmathematic	NOUN
ejpam-5537	184	2	,	,	PUNCT
ejpam-5537	184	3	16	16	NUM
ejpam-5537	184	4	:	:	SYM
ejpam-5537	184	5	77	77	NUM
ejpam-5537	184	6	−	−	NOUN
ejpam-5537	184	7	−85	−85	NOUN
ejpam-5537	184	8	,	,	PUNCT
ejpam-5537	184	9	1985	1985	NUM
ejpam-5537	184	10	.	.	PUNCT
ejpam-5537	185	1	[	[	X
ejpam-5537	185	2	13	13	NUM
ejpam-5537	185	3	]	]	PUNCT
ejpam-5537	185	4	k.	k.	PROPN
ejpam-5537	185	5	m.	m.	PROPN
ejpam-5537	185	6	owolabi	owolabi	NOUN
ejpam-5537	185	7	and	and	CCONJ
ejpam-5537	185	8	a.	a.	NOUN
ejpam-5537	185	9	atangana	atangana	PROPN
ejpam-5537	185	10	.	.	PUNCT
ejpam-5537	186	1	numerical	numerical	ADJ
ejpam-5537	186	2	methods	method	NOUN
ejpam-5537	186	3	for	for	ADP
ejpam-5537	186	4	fractional	fractional	ADJ
ejpam-5537	186	5	differentiation	differentiation	NOUN
ejpam-5537	186	6	,	,	PUNCT
ejpam-5537	186	7	volume	volume	NOUN
ejpam-5537	186	8	54	54	NUM
ejpam-5537	186	9	.	.	PUNCT
ejpam-5537	187	1	springer	springer	PROPN
ejpam-5537	187	2	singapore	singapore	PROPN
ejpam-5537	187	3	,	,	PUNCT
ejpam-5537	187	4	2019	2019	NUM
ejpam-5537	187	5	.	.	PUNCT