id	sid	tid	token	lemma	pos
ejpam-5159	1	1	european	european	PROPN
ejpam-5159	1	2	journal	journal	PROPN
ejpam-5159	1	3	of	of	ADP
ejpam-5159	1	4	pure	pure	ADJ
ejpam-5159	1	5	and	and	CCONJ
ejpam-5159	1	6	applied	apply	VERB
ejpam-5159	1	7	mathematics	mathematic	NOUN
ejpam-5159	1	8	vol	vol	NOUN
ejpam-5159	1	9	.	.	PROPN
ejpam-5159	2	1	17	17	NUM
ejpam-5159	2	2	,	,	PUNCT
ejpam-5159	2	3	no	no	INTJ
ejpam-5159	2	4	.	.	NOUN
ejpam-5159	2	5	2	2	NUM
ejpam-5159	2	6	,	,	PUNCT
ejpam-5159	2	7	2024	2024	NUM
ejpam-5159	2	8	,	,	PUNCT
ejpam-5159	2	9	1155	1155	NUM
ejpam-5159	2	10	-	-	SYM
ejpam-5159	2	11	1167	1167	NUM
ejpam-5159	2	12	issn	issn	PROPN
ejpam-5159	2	13	1307	1307	NUM
ejpam-5159	2	14	-	-	SYM
ejpam-5159	2	15	5543	5543	NUM
ejpam-5159	2	16	–	–	PUNCT
ejpam-5159	2	17	ejpam.com	ejpam.com	X
ejpam-5159	2	18	published	publish	VERB
ejpam-5159	2	19	by	by	ADP
ejpam-5159	2	20	new	new	PROPN
ejpam-5159	2	21	york	york	PROPN
ejpam-5159	2	22	business	business	PROPN
ejpam-5159	2	23	global	global	PROPN
ejpam-5159	2	24	on	on	ADP
ejpam-5159	2	25	a	a	DET
ejpam-5159	2	26	novel	novel	ADJ
ejpam-5159	2	27	fractional	fractional	ADJ
ejpam-5159	2	28	calculus	calculus	NOUN
ejpam-5159	2	29	and	and	CCONJ
ejpam-5159	2	30	its	its	PRON
ejpam-5159	2	31	applications	application	NOUN
ejpam-5159	2	32	to	to	ADP
ejpam-5159	2	33	well	well	ADV
ejpam-5159	2	34	-	-	PUNCT
ejpam-5159	2	35	known	know	VERB
ejpam-5159	2	36	problems	problem	NOUN
ejpam-5159	2	37	a.	a.	PROPN
ejpam-5159	2	38	ait	ait	PROPN
ejpam-5159	2	39	brahim1,∗	brahim1,∗	PROPN
ejpam-5159	2	40	,	,	PUNCT
ejpam-5159	2	41	a.	a.	PROPN
ejpam-5159	2	42	el	el	PROPN
ejpam-5159	2	43	hajaji2	hajaji2	PROPN
ejpam-5159	2	44	,	,	PUNCT
ejpam-5159	2	45	k.	k.	PROPN
ejpam-5159	2	46	hilal	hilal	PROPN
ejpam-5159	2	47	1	1	NUM
ejpam-5159	2	48	,	,	PUNCT
ejpam-5159	2	49	j.	j.	PROPN
ejpam-5159	2	50	el	el	PROPN
ejpam-5159	2	51	ghordaf1	ghordaf1	VERB
ejpam-5159	2	52	1	1	NUM
ejpam-5159	2	53	laboratory	laboratory	NOUN
ejpam-5159	2	54	of	of	ADP
ejpam-5159	2	55	applied	apply	VERB
ejpam-5159	2	56	mathematics	mathematic	NOUN
ejpam-5159	2	57	and	and	CCONJ
ejpam-5159	2	58	scientific	scientific	ADJ
ejpam-5159	2	59	calculus	calculus	NOUN
ejpam-5159	2	60	,	,	PUNCT
ejpam-5159	2	61	university	university	NOUN
ejpam-5159	2	62	of	of	ADP
ejpam-5159	2	63	sciences	science	NOUN
ejpam-5159	2	64	and	and	CCONJ
ejpam-5159	2	65	technology	technology	NOUN
ejpam-5159	2	66	,	,	PUNCT
ejpam-5159	2	67	béni	béni	CCONJ
ejpam-5159	2	68	mellal	mellal	NOUN
ejpam-5159	2	69	,	,	PUNCT
ejpam-5159	2	70	morocco	morocco	PROPN
ejpam-5159	2	71	.	.	PUNCT
ejpam-5159	3	1	2	2	NUM
ejpam-5159	3	2	oee	oee	ADJ
ejpam-5159	3	3	departement	departement	NOUN
ejpam-5159	3	4	,	,	PUNCT
ejpam-5159	3	5	encgj	encgj	PROPN
ejpam-5159	3	6	,	,	PUNCT
ejpam-5159	3	7	university	university	NOUN
ejpam-5159	3	8	of	of	ADP
ejpam-5159	3	9	chouaib	chouaib	PROPN
ejpam-5159	3	10	doukali	doukali	PROPN
ejpam-5159	3	11	,	,	PUNCT
ejpam-5159	3	12	el	el	PROPN
ejpam-5159	3	13	jadida	jadida	PROPN
ejpam-5159	3	14	,	,	PUNCT
ejpam-5159	3	15	morocco	morocco	PROPN
ejpam-5159	3	16	abstract	abstract	PROPN
ejpam-5159	3	17	.	.	PUNCT
ejpam-5159	4	1	the	the	DET
ejpam-5159	4	2	objective	objective	NOUN
ejpam-5159	4	3	of	of	ADP
ejpam-5159	4	4	this	this	DET
ejpam-5159	4	5	study	study	NOUN
ejpam-5159	4	6	is	be	AUX
ejpam-5159	4	7	to	to	PART
ejpam-5159	4	8	introduce	introduce	VERB
ejpam-5159	4	9	three	three	NUM
ejpam-5159	4	10	novel	novel	ADJ
ejpam-5159	4	11	and	and	CCONJ
ejpam-5159	4	12	comprehensive	comprehensive	ADJ
ejpam-5159	4	13	models	model	NOUN
ejpam-5159	4	14	utilizing	utilize	VERB
ejpam-5159	4	15	the	the	DET
ejpam-5159	4	16	concept	concept	NOUN
ejpam-5159	4	17	of	of	ADP
ejpam-5159	4	18	conformable	conformable	ADJ
ejpam-5159	4	19	fractional	fractional	ADJ
ejpam-5159	4	20	calculus	calculus	NOUN
ejpam-5159	4	21	.	.	PUNCT
ejpam-5159	5	1	these	these	DET
ejpam-5159	5	2	models	model	NOUN
ejpam-5159	5	3	encompass	encompass	VERB
ejpam-5159	5	4	the	the	DET
ejpam-5159	5	5	fractional	fractional	ADJ
ejpam-5159	5	6	population	population	NOUN
ejpam-5159	5	7	growth	growth	NOUN
ejpam-5159	5	8	model	model	NOUN
ejpam-5159	5	9	(	(	PUNCT
ejpam-5159	5	10	fpgm	fpgm	NOUN
ejpam-5159	5	11	)	)	PUNCT
ejpam-5159	5	12	,	,	PUNCT
ejpam-5159	5	13	the	the	DET
ejpam-5159	5	14	fractional	fractional	ADJ
ejpam-5159	5	15	body	body	NOUN
ejpam-5159	5	16	cooling	cool	VERB
ejpam-5159	5	17	model	model	NOUN
ejpam-5159	5	18	(	(	PUNCT
ejpam-5159	5	19	fbcm	fbcm	NOUN
ejpam-5159	5	20	)	)	PUNCT
ejpam-5159	5	21	,	,	PUNCT
ejpam-5159	5	22	and	and	CCONJ
ejpam-5159	5	23	the	the	DET
ejpam-5159	5	24	fractional	fractional	ADJ
ejpam-5159	5	25	heat	heat	NOUN
ejpam-5159	5	26	differential	differential	NOUN
ejpam-5159	5	27	equation	equation	NOUN
ejpam-5159	5	28	(	(	PUNCT
ejpam-5159	5	29	fhde	fhde	PROPN
ejpam-5159	5	30	)	)	PUNCT
ejpam-5159	5	31	.	.	PUNCT
ejpam-5159	6	1	firstly	firstly	ADV
ejpam-5159	6	2	,	,	PUNCT
ejpam-5159	6	3	using	use	VERB
ejpam-5159	6	4	new	new	ADJ
ejpam-5159	6	5	results	result	NOUN
ejpam-5159	6	6	,	,	PUNCT
ejpam-5159	6	7	a	a	DET
ejpam-5159	6	8	type	type	NOUN
ejpam-5159	6	9	of	of	ADP
ejpam-5159	6	10	new	new	ADJ
ejpam-5159	6	11	conformable	conformable	ADJ
ejpam-5159	6	12	fractional	fractional	ADJ
ejpam-5159	6	13	derivative	derivative	NOUN
ejpam-5159	6	14	introduced	introduce	VERB
ejpam-5159	6	15	in	in	ADP
ejpam-5159	6	16	[	[	X
ejpam-5159	6	17	5	5	NUM
ejpam-5159	6	18	]	]	NUM
ejpam-5159	6	19	:	:	PUNCT
ejpam-5159	6	20	(	(	PUNCT
ejpam-5159	6	21	dαh	dαh	NOUN
ejpam-5159	6	22	)	)	PUNCT
ejpam-5159	6	23	(	(	PUNCT
ejpam-5159	6	24	y	y	NOUN
ejpam-5159	6	25	)	)	PUNCT
ejpam-5159	6	26	=	=	SYM
ejpam-5159	6	27	limz−→0	limz−→0	SYM
ejpam-5159	6	28	h(y+ze(α−1)y)−h(y	h(y+ze(α−1)y)−h(y	ADJ
ejpam-5159	6	29	)	)	PUNCT
ejpam-5159	6	30	z	z	NOUN
ejpam-5159	6	31	,	,	PUNCT
ejpam-5159	6	32	where	where	SCONJ
ejpam-5159	6	33	α	α	DET
ejpam-5159	6	34	∈	∈	PROPN
ejpam-5159	6	35	(	(	PUNCT
ejpam-5159	6	36	0	0	NUM
ejpam-5159	6	37	,	,	PUNCT
ejpam-5159	6	38	1	1	NUM
ejpam-5159	6	39	]	]	PUNCT
ejpam-5159	6	40	and	and	CCONJ
ejpam-5159	6	41	h	h	NOUN
ejpam-5159	6	42	is	be	AUX
ejpam-5159	6	43	a	a	DET
ejpam-5159	6	44	function	function	NOUN
ejpam-5159	6	45	.	.	PUNCT
ejpam-5159	7	1	we	we	PRON
ejpam-5159	7	2	obtain	obtain	VERB
ejpam-5159	7	3	exact	exact	ADJ
ejpam-5159	7	4	solutions	solution	NOUN
ejpam-5159	7	5	of	of	ADP
ejpam-5159	7	6	the	the	DET
ejpam-5159	7	7	considered	consider	VERB
ejpam-5159	7	8	models	model	NOUN
ejpam-5159	7	9	.	.	PUNCT
ejpam-5159	8	1	the	the	DET
ejpam-5159	8	2	results	result	NOUN
ejpam-5159	8	3	feature	feature	VERB
ejpam-5159	8	4	excellent	excellent	ADJ
ejpam-5159	8	5	agreement	agreement	NOUN
ejpam-5159	8	6	of	of	ADP
ejpam-5159	8	7	exact	exact	ADJ
ejpam-5159	8	8	solutions	solution	NOUN
ejpam-5159	8	9	.	.	PUNCT
ejpam-5159	9	1	finally	finally	ADV
ejpam-5159	9	2	,	,	PUNCT
ejpam-5159	9	3	it	it	PRON
ejpam-5159	9	4	is	be	AUX
ejpam-5159	9	5	shown	show	VERB
ejpam-5159	9	6	that	that	SCONJ
ejpam-5159	9	7	the	the	DET
ejpam-5159	9	8	proposed	propose	VERB
ejpam-5159	9	9	method	method	NOUN
ejpam-5159	9	10	provides	provide	VERB
ejpam-5159	9	11	a	a	DET
ejpam-5159	9	12	more	more	ADV
ejpam-5159	9	13	powerful	powerful	ADJ
ejpam-5159	9	14	mathematical	mathematical	ADJ
ejpam-5159	9	15	tool	tool	NOUN
ejpam-5159	9	16	for	for	ADP
ejpam-5159	9	17	solving	solve	VERB
ejpam-5159	9	18	models	model	NOUN
ejpam-5159	9	19	in	in	ADP
ejpam-5159	9	20	mathematical	mathematical	ADJ
ejpam-5159	9	21	physics	physics	NOUN
ejpam-5159	9	22	.	.	PUNCT
ejpam-5159	10	1	2020	2020	NUM
ejpam-5159	10	2	mathematics	mathematics	PROPN
ejpam-5159	10	3	subject	subject	NOUN
ejpam-5159	10	4	classifications	classification	NOUN
ejpam-5159	10	5	:	:	PUNCT
ejpam-5159	10	6	26a33	26a33	NUM
ejpam-5159	10	7	,	,	PUNCT
ejpam-5159	10	8	34a08	34a08	NUM
ejpam-5159	10	9	,	,	PUNCT
ejpam-5159	10	10	65m70	65m70	NUM
ejpam-5159	10	11	,	,	PUNCT
ejpam-5159	10	12	35r11	35r11	NUM
ejpam-5159	10	13	,	,	PUNCT
ejpam-5159	10	14	92d25	92d25	NUM
ejpam-5159	10	15	key	key	ADJ
ejpam-5159	10	16	words	word	NOUN
ejpam-5159	10	17	and	and	CCONJ
ejpam-5159	10	18	phrases	phrase	NOUN
ejpam-5159	10	19	:	:	PUNCT
ejpam-5159	10	20	new	new	ADJ
ejpam-5159	10	21	conformable	conformable	ADJ
ejpam-5159	10	22	fractional	fractional	ADJ
ejpam-5159	10	23	derivative	derivative	NOUN
ejpam-5159	10	24	,	,	PUNCT
ejpam-5159	10	25	population	population	NOUN
ejpam-5159	10	26	grow	grow	VERB
ejpam-5159	10	27	model	model	NOUN
ejpam-5159	10	28	,	,	PUNCT
ejpam-5159	10	29	body	body	NOUN
ejpam-5159	10	30	coolig	coolig	NOUN
ejpam-5159	10	31	model	model	PROPN
ejpam-5159	10	32	,	,	PUNCT
ejpam-5159	10	33	fractional	fractional	ADJ
ejpam-5159	10	34	heat	heat	NOUN
ejpam-5159	10	35	equation	equation	NOUN
ejpam-5159	10	36	.	.	PUNCT
ejpam-5159	11	1	1	1	X
ejpam-5159	11	2	.	.	X
ejpam-5159	11	3	introduction	introduction	NOUN
ejpam-5159	11	4	historically	historically	ADV
ejpam-5159	11	5	,	,	PUNCT
ejpam-5159	11	6	the	the	DET
ejpam-5159	11	7	origins	origin	NOUN
ejpam-5159	11	8	of	of	ADP
ejpam-5159	11	9	fractional	fractional	ADJ
ejpam-5159	11	10	calculus	calculus	NOUN
ejpam-5159	11	11	began	begin	VERB
ejpam-5159	11	12	with	with	ADP
ejpam-5159	11	13	the	the	DET
ejpam-5159	11	14	correspondence	correspondence	NOUN
ejpam-5159	11	15	between	between	ADP
ejpam-5159	11	16	l’hopital	l’hopital	PROPN
ejpam-5159	11	17	and	and	CCONJ
ejpam-5159	11	18	leibniz	leibniz	NOUN
ejpam-5159	12	1	[	[	X
ejpam-5159	12	2	1	1	NUM
ejpam-5159	12	3	,	,	PUNCT
ejpam-5159	12	4	2	2	NUM
ejpam-5159	12	5	]	]	PUNCT
ejpam-5159	12	6	,	,	PUNCT
ejpam-5159	12	7	where	where	SCONJ
ejpam-5159	12	8	the	the	DET
ejpam-5159	12	9	former	former	ADJ
ejpam-5159	12	10	answered	answer	VERB
ejpam-5159	12	11	the	the	DET
ejpam-5159	12	12	question	question	NOUN
ejpam-5159	12	13	of	of	ADP
ejpam-5159	12	14	whether	whether	SCONJ
ejpam-5159	12	15	the	the	DET
ejpam-5159	12	16	order	order	NOUN
ejpam-5159	12	17	of	of	ADP
ejpam-5159	12	18	derivation	derivation	NOUN
ejpam-5159	12	19	in	in	ADP
ejpam-5159	12	20	an	an	DET
ejpam-5159	12	21	expression	expression	NOUN
ejpam-5159	12	22	could	could	AUX
ejpam-5159	12	23	be	be	AUX
ejpam-5159	12	24	of	of	ADP
ejpam-5159	12	25	a	a	DET
ejpam-5159	12	26	fractional	fractional	ADJ
ejpam-5159	12	27	nature	nature	NOUN
ejpam-5159	12	28	.	.	PUNCT
ejpam-5159	13	1	obviously	obviously	ADV
ejpam-5159	13	2	,	,	PUNCT
ejpam-5159	13	3	this	this	DET
ejpam-5159	13	4	question	question	NOUN
ejpam-5159	13	5	is	be	AUX
ejpam-5159	13	6	self	self	NOUN
ejpam-5159	13	7	-	-	PUNCT
ejpam-5159	13	8	contradictory	contradictory	ADJ
ejpam-5159	13	9	,	,	PUNCT
ejpam-5159	13	10	because	because	SCONJ
ejpam-5159	13	11	the	the	DET
ejpam-5159	13	12	order	order	NOUN
ejpam-5159	13	13	of	of	ADP
ejpam-5159	13	14	derivation	derivation	NOUN
ejpam-5159	13	15	indicates	indicate	VERB
ejpam-5159	13	16	the	the	DET
ejpam-5159	13	17	frequency	frequency	NOUN
ejpam-5159	13	18	with	with	ADP
ejpam-5159	13	19	which	which	PRON
ejpam-5159	13	20	the	the	DET
ejpam-5159	13	21	differential	differential	ADJ
ejpam-5159	13	22	operator	operator	NOUN
ejpam-5159	13	23	is	be	AUX
ejpam-5159	13	24	applied	apply	VERB
ejpam-5159	13	25	,	,	PUNCT
ejpam-5159	13	26	that	that	ADV
ejpam-5159	13	27	is	is	ADV
ejpam-5159	13	28	,	,	PUNCT
ejpam-5159	13	29	it	it	PRON
ejpam-5159	13	30	counts	count	VERB
ejpam-5159	13	31	the	the	DET
ejpam-5159	13	32	number	number	NOUN
ejpam-5159	13	33	of	of	ADP
ejpam-5159	13	34	repetitions	repetition	NOUN
ejpam-5159	13	35	of	of	ADP
ejpam-5159	13	36	the	the	DET
ejpam-5159	13	37	entire	entire	ADJ
ejpam-5159	13	38	differential	differential	ADJ
ejpam-5159	13	39	process	process	NOUN
ejpam-5159	13	40	.	.	PUNCT
ejpam-5159	14	1	this	this	DET
ejpam-5159	14	2	origin	origin	NOUN
ejpam-5159	14	3	was	be	AUX
ejpam-5159	14	4	followed	follow	VERB
ejpam-5159	14	5	by	by	ADP
ejpam-5159	14	6	further	further	ADJ
ejpam-5159	14	7	contributions	contribution	NOUN
ejpam-5159	14	8	by	by	ADP
ejpam-5159	14	9	eminent	eminent	ADJ
ejpam-5159	14	10	mathematicians	mathematician	NOUN
ejpam-5159	14	11	,	,	PUNCT
ejpam-5159	14	12	including	include	VERB
ejpam-5159	14	13	the	the	DET
ejpam-5159	14	14	european	european	PROPN
ejpam-5159	14	15	euler	euler	PROPN
ejpam-5159	14	16	,	,	PUNCT
ejpam-5159	14	17	lacroix	lacroix	NOUN
ejpam-5159	14	18	,	,	PUNCT
ejpam-5159	14	19	laplace	laplace	NOUN
ejpam-5159	14	20	,	,	PUNCT
ejpam-5159	14	21	etc	etc	X
ejpam-5159	14	22	.	.	X
ejpam-5159	14	23	one	one	NUM
ejpam-5159	14	24	of	of	ADP
ejpam-5159	14	25	the	the	DET
ejpam-5159	14	26	most	most	ADV
ejpam-5159	14	27	∗corresponding	∗corresponde	VERB
ejpam-5159	14	28	author	author	NOUN
ejpam-5159	14	29	.	.	PUNCT
ejpam-5159	15	1	doi	doi	NOUN
ejpam-5159	15	2	:	:	PUNCT
ejpam-5159	15	3	https://doi.org/10.29020/nybg.ejpam.v17i2.5159	https://doi.org/10.29020/nybg.ejpam.v17i2.5159	ADJ
ejpam-5159	15	4	email	email	NOUN
ejpam-5159	15	5	addresses	address	NOUN
ejpam-5159	15	6	:	:	PUNCT
ejpam-5159	15	7	abdessamad11117@gmail.com	abdessamad11117@gmail.com	X
ejpam-5159	15	8	(	(	PUNCT
ejpam-5159	15	9	a.	a.	PROPN
ejpam-5159	15	10	ait	ait	PROPN
ejpam-5159	15	11	brahim	brahim	PROPN
ejpam-5159	15	12	)	)	PUNCT
ejpam-5159	15	13	,	,	PUNCT
ejpam-5159	15	14	a	a	DET
ejpam-5159	15	15	elhajaji@yahou.fr	elhajaji@yahou.fr	PROPN
ejpam-5159	15	16	(	(	PUNCT
ejpam-5159	15	17	a.	a.	PROPN
ejpam-5159	15	18	el	el	PROPN
ejpam-5159	15	19	hajaji	hajaji	PROPN
ejpam-5159	15	20	)	)	PUNCT
ejpam-5159	15	21	,	,	PUNCT
ejpam-5159	15	22	hilalkhalid2005@yahou.fr	hilalkhalid2005@yahou.fr	PROPN
ejpam-5159	15	23	(	(	PUNCT
ejpam-5159	15	24	k.	k.	PROPN
ejpam-5159	15	25	hilal	hilal	PROPN
ejpam-5159	15	26	)	)	PUNCT
ejpam-5159	15	27	,	,	PUNCT
ejpam-5159	15	28	elg	elg	PROPN
ejpam-5159	15	29	jalila@yahou.fr	jalila@yahou.fr	PROPN
ejpam-5159	15	30	(	(	PUNCT
ejpam-5159	15	31	j.el	j.el	PROPN
ejpam-5159	15	32	ghordaf	ghordaf	NOUN
ejpam-5159	15	33	)	)	PUNCT
ejpam-5159	15	34	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5159	15	35	1155	1155	NUM
ejpam-5159	16	1	©	©	PROPN
ejpam-5159	16	2	2024	2024	NUM
ejpam-5159	16	3	ejpam	ejpam	NOUN
ejpam-5159	16	4	all	all	DET
ejpam-5159	16	5	rights	right	NOUN
ejpam-5159	16	6	reserved	reserve	VERB
ejpam-5159	16	7	.	.	PUNCT
ejpam-5159	17	1	a.	a.	PROPN
ejpam-5159	17	2	ait	ait	PROPN
ejpam-5159	17	3	brahim	brahim	PROPN
ejpam-5159	17	4	et	et	PROPN
ejpam-5159	17	5	al	al	PROPN
ejpam-5159	17	6	.	.	PUNCT
ejpam-5159	17	7	/	/	SYM
ejpam-5159	17	8	eur	eur	PROPN
ejpam-5159	17	9	.	.	PUNCT
ejpam-5159	18	1	j.	j.	PROPN
ejpam-5159	18	2	pure	pure	PROPN
ejpam-5159	18	3	appl	appl	PROPN
ejpam-5159	18	4	.	.	PROPN
ejpam-5159	18	5	math	math	PROPN
ejpam-5159	18	6	,	,	PUNCT
ejpam-5159	18	7	17	17	NUM
ejpam-5159	18	8	(	(	PUNCT
ejpam-5159	18	9	2	2	NUM
ejpam-5159	18	10	)	)	PUNCT
ejpam-5159	18	11	(	(	PUNCT
ejpam-5159	18	12	2024	2024	NUM
ejpam-5159	18	13	)	)	PUNCT
ejpam-5159	18	14	,	,	PUNCT
ejpam-5159	18	15	1155	1155	NUM
ejpam-5159	18	16	-	-	SYM
ejpam-5159	18	17	1167	1167	NUM
ejpam-5159	18	18	1156	1156	NUM
ejpam-5159	18	19	interesting	interesting	ADJ
ejpam-5159	18	20	,	,	PUNCT
ejpam-5159	18	21	comprehensive	comprehensive	ADJ
ejpam-5159	18	22	,	,	PUNCT
ejpam-5159	18	23	and	and	CCONJ
ejpam-5159	18	24	well	well	ADV
ejpam-5159	18	25	-	-	PUNCT
ejpam-5159	18	26	founded	found	VERB
ejpam-5159	18	27	the	the	DET
ejpam-5159	18	28	work	work	NOUN
ejpam-5159	18	29	is	be	AUX
ejpam-5159	18	30	riemman	riemman	NOUN
ejpam-5159	18	31	-	-	PUNCT
ejpam-5159	18	32	liouville	liouville	NOUN
ejpam-5159	19	1	[	[	X
ejpam-5159	19	2	2	2	NUM
ejpam-5159	19	3	]	]	PUNCT
ejpam-5159	19	4	,	,	PUNCT
ejpam-5159	19	5	the	the	DET
ejpam-5159	19	6	corresponding	corresponding	ADJ
ejpam-5159	19	7	fracture	fracture	PROPN
ejpam-5159	19	8	model	model	NOUN
ejpam-5159	19	9	starts	start	VERB
ejpam-5159	19	10	from	from	ADP
ejpam-5159	19	11	fractional	fractional	ADJ
ejpam-5159	19	12	differential	differential	ADJ
ejpam-5159	19	13	operators	operator	NOUN
ejpam-5159	19	14	with	with	ADP
ejpam-5159	19	15	two	two	NUM
ejpam-5159	19	16	forms	form	NOUN
ejpam-5159	19	17	dα	dα	DET
ejpam-5159	19	18	c+h(z	c+h(z	NOUN
ejpam-5159	19	19	)	)	PUNCT
ejpam-5159	19	20	=	=	SYM
ejpam-5159	19	21	1	1	NUM
ejpam-5159	19	22	γ(m−	γ(m−	PROPN
ejpam-5159	19	23	α	α	NOUN
ejpam-5159	19	24	)	)	PUNCT
ejpam-5159	19	25	dm	dm	PROPN
ejpam-5159	19	26	dtm	dtm	PROPN
ejpam-5159	19	27	∫	∫	PROPN
ejpam-5159	19	28	z	z	PROPN
ejpam-5159	19	29	c	c	PROPN
ejpam-5159	19	30	h(t	h(t	PROPN
ejpam-5159	19	31	)	)	PUNCT
ejpam-5159	20	1	(	(	PUNCT
ejpam-5159	20	2	z	z	NOUN
ejpam-5159	20	3	−	−	NOUN
ejpam-5159	20	4	t)α+1−m	t)α+1−m	NUM
ejpam-5159	20	5	dt	dt	NOUN
ejpam-5159	20	6	,	,	PUNCT
ejpam-5159	20	7	m−	m−	PROPN
ejpam-5159	20	8	1	1	NUM
ejpam-5159	20	9	<	<	X
ejpam-5159	20	10	α	α	X
ejpam-5159	20	11	<	<	X
ejpam-5159	20	12	m	m	PROPN
ejpam-5159	20	13	∈	∈	PROPN
ejpam-5159	20	14	n	n	CCONJ
ejpam-5159	20	15	,	,	PUNCT
ejpam-5159	20	16	(	(	PUNCT
ejpam-5159	20	17	1	1	X
ejpam-5159	20	18	)	)	PUNCT
ejpam-5159	20	19	dα	dα	PRON
ejpam-5159	20	20	d−h(z	d−h(z	PROPN
ejpam-5159	20	21	)	)	PUNCT
ejpam-5159	20	22	=	=	SYM
ejpam-5159	20	23	1	1	NUM
ejpam-5159	20	24	γ(m−	γ(m−	PROPN
ejpam-5159	20	25	α	α	NOUN
ejpam-5159	20	26	)	)	PUNCT
ejpam-5159	20	27	dm	dm	NOUN
ejpam-5159	20	28	dtm	dtm	PROPN
ejpam-5159	20	29	∫	∫	PROPN
ejpam-5159	21	1	d	d	PROPN
ejpam-5159	21	2	z	z	PROPN
ejpam-5159	21	3	h(t	h(t	PROPN
ejpam-5159	21	4	)	)	PUNCT
ejpam-5159	22	1	(	(	PUNCT
ejpam-5159	22	2	z	z	NOUN
ejpam-5159	22	3	−	−	NOUN
ejpam-5159	22	4	t)α+1−m	t)α+1−m	NUM
ejpam-5159	22	5	dt	dt	NOUN
ejpam-5159	22	6	,	,	PUNCT
ejpam-5159	22	7	m−	m−	PROPN
ejpam-5159	22	8	1	1	NUM
ejpam-5159	22	9	<	<	X
ejpam-5159	22	10	α	α	X
ejpam-5159	22	11	<	<	X
ejpam-5159	22	12	m	m	PROPN
ejpam-5159	22	13	∈	∈	PROPN
ejpam-5159	22	14	n.	n.	NOUN
ejpam-5159	22	15	(	(	PUNCT
ejpam-5159	22	16	2	2	NUM
ejpam-5159	22	17	)	)	PUNCT
ejpam-5159	22	18	recently	recently	ADV
ejpam-5159	22	19	,	,	PUNCT
ejpam-5159	22	20	the	the	DET
ejpam-5159	22	21	authors	author	NOUN
ejpam-5159	22	22	of	of	ADP
ejpam-5159	22	23	[	[	X
ejpam-5159	22	24	3	3	NUM
ejpam-5159	22	25	]	]	PUNCT
ejpam-5159	22	26	and	and	CCONJ
ejpam-5159	22	27	[	[	X
ejpam-5159	22	28	4	4	X
ejpam-5159	22	29	]	]	PUNCT
ejpam-5159	22	30	defined	define	VERB
ejpam-5159	22	31	the	the	DET
ejpam-5159	22	32	classical	classical	ADJ
ejpam-5159	22	33	fractional	fractional	ADJ
ejpam-5159	22	34	derivatives	derivative	NOUN
ejpam-5159	22	35	,	,	PUNCT
ejpam-5159	22	36	supposedly	supposedly	ADV
ejpam-5159	22	37	conformable	conformable	ADJ
ejpam-5159	22	38	derivatives	derivative	NOUN
ejpam-5159	22	39	fractional	fractional	ADJ
ejpam-5159	22	40	derivatives	derivative	NOUN
ejpam-5159	22	41	,	,	PUNCT
ejpam-5159	22	42	depending	depend	VERB
ejpam-5159	22	43	only	only	ADV
ejpam-5159	22	44	on	on	ADP
ejpam-5159	22	45	the	the	DET
ejpam-5159	22	46	fundamental	fundamental	ADJ
ejpam-5159	22	47	limit	limit	NOUN
ejpam-5159	22	48	definition	definition	NOUN
ejpam-5159	22	49	derivation	derivation	NOUN
ejpam-5159	22	50	of	of	ADP
ejpam-5159	22	51	khalil	khalil	PROPN
ejpam-5159	22	52	et	et	PROPN
ejpam-5159	22	53	al	al	PROPN
ejpam-5159	22	54	.	.	PUNCT
ejpam-5159	23	1	[	[	X
ejpam-5159	23	2	3	3	X
ejpam-5159	23	3	]	]	PUNCT
ejpam-5159	23	4	presented	present	VERB
ejpam-5159	23	5	a	a	DET
ejpam-5159	23	6	new	new	ADJ
ejpam-5159	23	7	derivation	derivation	NOUN
ejpam-5159	23	8	of	of	ADP
ejpam-5159	23	9	h	h	NOUN
ejpam-5159	23	10	of	of	ADP
ejpam-5159	23	11	order	order	NOUN
ejpam-5159	23	12	α	α	NOUN
ejpam-5159	23	13	,	,	PUNCT
ejpam-5159	23	14	known	know	VERB
ejpam-5159	23	15	as	as	ADP
ejpam-5159	23	16	:	:	PUNCT
ejpam-5159	23	17	tαh(t	tαh(t	NUM
ejpam-5159	23	18	)	)	PUNCT
ejpam-5159	23	19	=	=	SYM
ejpam-5159	23	20	lim	lim	PROPN
ejpam-5159	23	21	ε−→0	ε−→0	PROPN
ejpam-5159	23	22	h	h	PROPN
ejpam-5159	23	23	(	(	PUNCT
ejpam-5159	23	24	t+	t+	NOUN
ejpam-5159	23	25	ϵt1−α	ϵt1−α	X
ejpam-5159	23	26	)	)	PUNCT
ejpam-5159	23	27	−h(t	−h(t	ADJ
ejpam-5159	23	28	)	)	PUNCT
ejpam-5159	23	29	ε	ε	PROPN
ejpam-5159	23	30	,	,	PUNCT
ejpam-5159	23	31	(	(	PUNCT
ejpam-5159	23	32	3	3	X
ejpam-5159	23	33	)	)	PUNCT
ejpam-5159	23	34	at	at	ADP
ejpam-5159	23	35	0	0	NUM
ejpam-5159	23	36	the	the	DET
ejpam-5159	23	37	fractional	fractional	ADJ
ejpam-5159	23	38	derivative	derivative	NOUN
ejpam-5159	23	39	is	be	AUX
ejpam-5159	23	40	defined	define	VERB
ejpam-5159	23	41	as	as	ADP
ejpam-5159	23	42	h(α)(0	h(α)(0	NUM
ejpam-5159	23	43	)	)	PUNCT
ejpam-5159	23	44	=	=	PUNCT
ejpam-5159	24	1	limt−→0	limt−→0	PROPN
ejpam-5159	24	2	+	+	NOUN
ejpam-5159	24	3	tα(h)(t	tα(h)(t	NUM
ejpam-5159	24	4	)	)	PUNCT
ejpam-5159	24	5	.	.	PUNCT
ejpam-5159	25	1	also	also	ADV
ejpam-5159	25	2	,	,	PUNCT
ejpam-5159	25	3	katugampola	katugampola	PROPN
ejpam-5159	26	1	[	[	X
ejpam-5159	26	2	4	4	X
ejpam-5159	26	3	]	]	PUNCT
ejpam-5159	26	4	proposed	propose	VERB
ejpam-5159	26	5	a	a	DET
ejpam-5159	26	6	new	new	ADJ
ejpam-5159	26	7	container	container	NOUN
ejpam-5159	26	8	defined	define	VERB
ejpam-5159	26	9	as	as	ADP
ejpam-5159	26	10	dα(h)(t	dα(h)(t	NUM
ejpam-5159	26	11	)	)	PUNCT
ejpam-5159	27	1	=	=	PROPN
ejpam-5159	27	2	lim	lim	PROPN
ejpam-5159	27	3	ε−→0	ε−→0	PROPN
ejpam-5159	27	4	h	h	PROPN
ejpam-5159	27	5	(	(	PUNCT
ejpam-5159	27	6	teεt	teεt	NOUN
ejpam-5159	27	7	−α	−α	NOUN
ejpam-5159	27	8	)	)	PUNCT
ejpam-5159	27	9	−h(t	−h(t	VERB
ejpam-5159	27	10	)	)	PUNCT
ejpam-5159	27	11	ε	ε	PROPN
ejpam-5159	27	12	,	,	PUNCT
ejpam-5159	27	13	(	(	PUNCT
ejpam-5159	27	14	4	4	NUM
ejpam-5159	27	15	)	)	PUNCT
ejpam-5159	27	16	with	with	ADP
ejpam-5159	27	17	t	t	PROPN
ejpam-5159	27	18	>	>	X
ejpam-5159	27	19	0	0	PUNCT
ejpam-5159	27	20	and	and	CCONJ
ejpam-5159	27	21	α	α	PRON
ejpam-5159	27	22	∈	∈	PROPN
ejpam-5159	28	1	[	[	X
ejpam-5159	28	2	0	0	NUM
ejpam-5159	28	3	,	,	PUNCT
ejpam-5159	28	4	1	1	NUM
ejpam-5159	28	5	]	]	PUNCT
ejpam-5159	28	6	.	.	PUNCT
ejpam-5159	29	1	if	if	SCONJ
ejpam-5159	29	2	h	h	NOUN
ejpam-5159	29	3	is	be	AUX
ejpam-5159	29	4	differentiable	differentiable	ADJ
ejpam-5159	29	5	in	in	ADP
ejpam-5159	29	6	order	order	NOUN
ejpam-5159	29	7	α	α	NOUN
ejpam-5159	29	8	in	in	ADP
ejpam-5159	29	9	some	some	PRON
ejpam-5159	29	10	(	(	PUNCT
ejpam-5159	29	11	[	[	X
ejpam-5159	29	12	0	0	NUM
ejpam-5159	29	13	,	,	PUNCT
ejpam-5159	29	14	a	a	PRON
ejpam-5159	29	15	]	]	X
ejpam-5159	29	16	,	,	PUNCT
ejpam-5159	29	17	a	a	PRON
ejpam-5159	29	18	>	>	X
ejpam-5159	29	19	0	0	NUM
ejpam-5159	29	20	,	,	PUNCT
ejpam-5159	29	21	and	and	CCONJ
ejpam-5159	29	22	limt→0	limt→0	PROPN
ejpam-5159	29	23	+	+	CCONJ
ejpam-5159	29	24	dα(h)(t	dα(h)(t	NUM
ejpam-5159	29	25	)	)	PUNCT
ejpam-5159	29	26	exists	exist	VERB
ejpam-5159	29	27	,	,	PUNCT
ejpam-5159	29	28	then	then	ADV
ejpam-5159	29	29	we	we	PRON
ejpam-5159	29	30	obtain	obtain	VERB
ejpam-5159	29	31	:	:	PUNCT
ejpam-5159	29	32	dα(h)(0	dα(h)(0	NUM
ejpam-5159	29	33	)	)	PUNCT
ejpam-5159	29	34	=	=	PROPN
ejpam-5159	29	35	lim	lim	PROPN
ejpam-5159	29	36	t−→0	t−→0	PROPN
ejpam-5159	29	37	+	+	PROPN
ejpam-5159	29	38	dα(h)(t	dα(h)(t	NUM
ejpam-5159	29	39	)	)	PUNCT
ejpam-5159	29	40	.	.	PUNCT
ejpam-5159	30	1	(	(	PUNCT
ejpam-5159	30	2	5	5	X
ejpam-5159	30	3	)	)	PUNCT
ejpam-5159	30	4	the	the	DET
ejpam-5159	30	5	studies	study	NOUN
ejpam-5159	30	6	cited	cite	VERB
ejpam-5159	30	7	in	in	ADP
ejpam-5159	30	8	references	reference	NOUN
ejpam-5159	30	9	[	[	X
ejpam-5159	30	10	3	3	NUM
ejpam-5159	30	11	,	,	PUNCT
ejpam-5159	30	12	4	4	NUM
ejpam-5159	30	13	,	,	PUNCT
ejpam-5159	30	14	20	20	NUM
ejpam-5159	30	15	]	]	PUNCT
ejpam-5159	30	16	have	have	AUX
ejpam-5159	30	17	significantly	significantly	ADV
ejpam-5159	30	18	contributed	contribute	VERB
ejpam-5159	30	19	to	to	ADP
ejpam-5159	30	20	our	our	PRON
ejpam-5159	30	21	understanding	understanding	NOUN
ejpam-5159	30	22	of	of	ADP
ejpam-5159	30	23	the	the	DET
ejpam-5159	30	24	properties	property	NOUN
ejpam-5159	30	25	of	of	ADP
ejpam-5159	30	26	derivatives	derivative	NOUN
ejpam-5159	30	27	with	with	ADP
ejpam-5159	30	28	respect	respect	NOUN
ejpam-5159	30	29	to	to	ADP
ejpam-5159	30	30	the	the	DET
ejpam-5159	30	31	parameter	parameter	NOUN
ejpam-5159	30	32	α	α	NOUN
ejpam-5159	30	33	.	.	PUNCT
ejpam-5159	31	1	these	these	DET
ejpam-5159	31	2	investigations	investigation	NOUN
ejpam-5159	31	3	have	have	AUX
ejpam-5159	31	4	revealed	reveal	VERB
ejpam-5159	31	5	that	that	SCONJ
ejpam-5159	31	6	the	the	DET
ejpam-5159	31	7	derivatives	derivative	NOUN
ejpam-5159	31	8	of	of	ADP
ejpam-5159	31	9	α	α	NOUN
ejpam-5159	31	10	adhere	adhere	VERB
ejpam-5159	31	11	to	to	ADP
ejpam-5159	31	12	fundamental	fundamental	ADJ
ejpam-5159	31	13	rules	rule	NOUN
ejpam-5159	31	14	such	such	ADJ
ejpam-5159	31	15	as	as	ADP
ejpam-5159	31	16	the	the	DET
ejpam-5159	31	17	quotient	quotient	NOUN
ejpam-5159	31	18	rule	rule	NOUN
ejpam-5159	31	19	and	and	CCONJ
ejpam-5159	31	20	product	product	NOUN
ejpam-5159	31	21	rule	rule	NOUN
ejpam-5159	31	22	,	,	PUNCT
ejpam-5159	31	23	akin	akin	ADJ
ejpam-5159	31	24	to	to	ADP
ejpam-5159	31	25	their	their	PRON
ejpam-5159	31	26	counterparts	counterpart	NOUN
ejpam-5159	31	27	in	in	ADP
ejpam-5159	31	28	traditional	traditional	ADJ
ejpam-5159	31	29	calculus	calculus	NOUN
ejpam-5159	31	30	.	.	PUNCT
ejpam-5159	32	1	notably	notably	ADV
ejpam-5159	32	2	,	,	PUNCT
ejpam-5159	32	3	these	these	DET
ejpam-5159	32	4	findings	finding	NOUN
ejpam-5159	32	5	evoke	evoke	VERB
ejpam-5159	32	6	parallels	parallel	NOUN
ejpam-5159	32	7	with	with	ADP
ejpam-5159	32	8	well	well	ADV
ejpam-5159	32	9	-	-	PUNCT
ejpam-5159	32	10	known	know	VERB
ejpam-5159	32	11	theorems	theorem	NOUN
ejpam-5159	32	12	like	like	ADP
ejpam-5159	32	13	rolle	rolle	PROPN
ejpam-5159	32	14	’s	’s	PART
ejpam-5159	32	15	theorem	theorem	PROPN
ejpam-5159	32	16	and	and	CCONJ
ejpam-5159	32	17	the	the	DET
ejpam-5159	32	18	mean	mean	ADJ
ejpam-5159	32	19	value	value	NOUN
ejpam-5159	32	20	theorem	theorem	VERB
ejpam-5159	32	21	,	,	PUNCT
ejpam-5159	32	22	underscoring	underscore	VERB
ejpam-5159	32	23	the	the	DET
ejpam-5159	32	24	robustness	robustness	NOUN
ejpam-5159	32	25	and	and	CCONJ
ejpam-5159	32	26	applicability	applicability	NOUN
ejpam-5159	32	27	of	of	ADP
ejpam-5159	32	28	the	the	DET
ejpam-5159	32	29	principles	principle	NOUN
ejpam-5159	32	30	of	of	ADP
ejpam-5159	32	31	calculus	calculus	NOUN
ejpam-5159	32	32	in	in	ADP
ejpam-5159	32	33	the	the	DET
ejpam-5159	32	34	context	context	NOUN
ejpam-5159	32	35	of	of	ADP
ejpam-5159	32	36	fractional	fractional	ADJ
ejpam-5159	32	37	calculus	calculus	NOUN
ejpam-5159	32	38	.	.	PUNCT
ejpam-5159	33	1	by	by	ADP
ejpam-5159	33	2	elucidating	elucidate	VERB
ejpam-5159	33	3	these	these	DET
ejpam-5159	33	4	parallels	parallel	NOUN
ejpam-5159	33	5	,	,	PUNCT
ejpam-5159	33	6	these	these	DET
ejpam-5159	33	7	studies	study	NOUN
ejpam-5159	33	8	provide	provide	VERB
ejpam-5159	33	9	valuable	valuable	ADJ
ejpam-5159	33	10	insights	insight	NOUN
ejpam-5159	33	11	into	into	ADP
ejpam-5159	33	12	the	the	DET
ejpam-5159	33	13	behavior	behavior	NOUN
ejpam-5159	33	14	and	and	CCONJ
ejpam-5159	33	15	characteristics	characteristic	NOUN
ejpam-5159	33	16	of	of	ADP
ejpam-5159	33	17	fractional	fractional	ADJ
ejpam-5159	33	18	derivatives	derivative	NOUN
ejpam-5159	33	19	,	,	PUNCT
ejpam-5159	33	20	enriching	enrich	VERB
ejpam-5159	33	21	our	our	PRON
ejpam-5159	33	22	toolkit	toolkit	NOUN
ejpam-5159	33	23	for	for	ADP
ejpam-5159	33	24	analyzing	analyze	VERB
ejpam-5159	33	25	and	and	CCONJ
ejpam-5159	33	26	solving	solve	VERB
ejpam-5159	33	27	complex	complex	ADJ
ejpam-5159	33	28	problems	problem	NOUN
ejpam-5159	33	29	across	across	ADP
ejpam-5159	33	30	various	various	ADJ
ejpam-5159	33	31	scientific	scientific	ADJ
ejpam-5159	33	32	disciplines	discipline	NOUN
ejpam-5159	33	33	.	.	PUNCT
ejpam-5159	34	1	the	the	DET
ejpam-5159	34	2	aim	aim	NOUN
ejpam-5159	34	3	of	of	ADP
ejpam-5159	34	4	this	this	DET
ejpam-5159	34	5	study	study	NOUN
ejpam-5159	34	6	is	be	AUX
ejpam-5159	34	7	to	to	PART
ejpam-5159	34	8	leverage	leverage	VERB
ejpam-5159	34	9	the	the	DET
ejpam-5159	34	10	outcomes	outcome	NOUN
ejpam-5159	34	11	derived	derive	VERB
ejpam-5159	34	12	in	in	ADP
ejpam-5159	34	13	[	[	X
ejpam-5159	34	14	5	5	NUM
ejpam-5159	34	15	]	]	PUNCT
ejpam-5159	34	16	and	and	CCONJ
ejpam-5159	34	17	extend	extend	VERB
ejpam-5159	34	18	their	their	PRON
ejpam-5159	34	19	application	application	NOUN
ejpam-5159	34	20	to	to	ADP
ejpam-5159	34	21	physics	physics	NOUN
ejpam-5159	34	22	,	,	PUNCT
ejpam-5159	34	23	specifically	specifically	ADV
ejpam-5159	34	24	in	in	ADP
ejpam-5159	34	25	heat	heat	NOUN
ejpam-5159	34	26	differential	differential	NOUN
ejpam-5159	34	27	formulas	formula	NOUN
ejpam-5159	34	28	,	,	PUNCT
ejpam-5159	34	29	body	body	NOUN
ejpam-5159	34	30	cooling	cooling	NOUN
ejpam-5159	34	31	,	,	PUNCT
ejpam-5159	34	32	and	and	CCONJ
ejpam-5159	34	33	population	population	NOUN
ejpam-5159	34	34	growth	growth	NOUN
ejpam-5159	34	35	models	model	NOUN
ejpam-5159	34	36	.	.	PUNCT
ejpam-5159	35	1	these	these	DET
ejpam-5159	35	2	applications	application	NOUN
ejpam-5159	35	3	have	have	AUX
ejpam-5159	35	4	previously	previously	ADV
ejpam-5159	35	5	been	be	AUX
ejpam-5159	35	6	explored	explore	VERB
ejpam-5159	35	7	by	by	ADP
ejpam-5159	35	8	khalil	khalil	PROPN
ejpam-5159	35	9	et	et	PROPN
ejpam-5159	35	10	al	al	PROPN
ejpam-5159	35	11	.	.	PUNCT
ejpam-5159	36	1	in	in	ADP
ejpam-5159	36	2	[	[	X
ejpam-5159	36	3	6	6	NUM
ejpam-5159	36	4	]	]	PUNCT
ejpam-5159	36	5	,	,	PUNCT
ejpam-5159	36	6	j.	j.	PROPN
ejpam-5159	36	7	e.	e.	PROPN
ejpam-5159	36	8	napoles	napoles	PROPN
ejpam-5159	36	9	valdes	valde	VERB
ejpam-5159	36	10	et	et	PROPN
ejpam-5159	36	11	al	al	PROPN
ejpam-5159	36	12	.	.	PUNCT
ejpam-5159	37	1	in	in	ADP
ejpam-5159	37	2	[	[	X
ejpam-5159	37	3	19	19	NUM
ejpam-5159	37	4	]	]	PUNCT
ejpam-5159	37	5	,	,	PUNCT
ejpam-5159	37	6	and	and	CCONJ
ejpam-5159	37	7	also	also	ADV
ejpam-5159	37	8	in	in	ADP
ejpam-5159	37	9	various	various	ADJ
ejpam-5159	37	10	references	reference	NOUN
ejpam-5159	37	11	[	[	X
ejpam-5159	37	12	20–23	20–23	NOUN
ejpam-5159	37	13	]	]	X
ejpam-5159	37	14	.	.	PUNCT
ejpam-5159	38	1	our	our	PRON
ejpam-5159	38	2	work	work	NOUN
ejpam-5159	38	3	builds	build	VERB
ejpam-5159	38	4	upon	upon	SCONJ
ejpam-5159	38	5	these	these	DET
ejpam-5159	38	6	previous	previous	ADJ
ejpam-5159	38	7	studies	study	NOUN
ejpam-5159	38	8	by	by	ADP
ejpam-5159	38	9	applying	apply	VERB
ejpam-5159	38	10	simpler	simple	ADJ
ejpam-5159	38	11	models	model	NOUN
ejpam-5159	38	12	using	use	VERB
ejpam-5159	38	13	the	the	DET
ejpam-5159	38	14	novel	novel	ADJ
ejpam-5159	38	15	results	result	NOUN
ejpam-5159	38	16	of	of	ADP
ejpam-5159	38	17	the	the	DET
ejpam-5159	38	18	conformable	conformable	ADJ
ejpam-5159	38	19	fractional	fractional	ADJ
ejpam-5159	38	20	derivative	derivative	NOUN
ejpam-5159	38	21	outlined	outline	VERB
ejpam-5159	38	22	in	in	ADP
ejpam-5159	38	23	[	[	X
ejpam-5159	38	24	5	5	NUM
ejpam-5159	38	25	]	]	PUNCT
ejpam-5159	38	26	.	.	PUNCT
ejpam-5159	39	1	a.	a.	PROPN
ejpam-5159	39	2	ait	ait	PROPN
ejpam-5159	39	3	brahim	brahim	PROPN
ejpam-5159	39	4	et	et	PROPN
ejpam-5159	39	5	al	al	PROPN
ejpam-5159	39	6	.	.	PUNCT
ejpam-5159	39	7	/	/	SYM
ejpam-5159	39	8	eur	eur	PROPN
ejpam-5159	39	9	.	.	PUNCT
ejpam-5159	40	1	j.	j.	PROPN
ejpam-5159	40	2	pure	pure	PROPN
ejpam-5159	40	3	appl	appl	PROPN
ejpam-5159	40	4	.	.	PROPN
ejpam-5159	40	5	math	math	PROPN
ejpam-5159	40	6	,	,	PUNCT
ejpam-5159	40	7	17	17	NUM
ejpam-5159	40	8	(	(	PUNCT
ejpam-5159	40	9	2	2	NUM
ejpam-5159	40	10	)	)	PUNCT
ejpam-5159	40	11	(	(	PUNCT
ejpam-5159	40	12	2024	2024	NUM
ejpam-5159	40	13	)	)	PUNCT
ejpam-5159	40	14	,	,	PUNCT
ejpam-5159	40	15	1155	1155	NUM
ejpam-5159	40	16	-	-	SYM
ejpam-5159	40	17	1167	1167	NUM
ejpam-5159	40	18	1157	1157	NUM
ejpam-5159	40	19	2	2	NUM
ejpam-5159	40	20	.	.	PUNCT
ejpam-5159	41	1	new	new	ADJ
ejpam-5159	41	2	results	result	NOUN
ejpam-5159	41	3	of	of	ADP
ejpam-5159	41	4	fractional	fractional	ADJ
ejpam-5159	41	5	calculus	calculus	NOUN
ejpam-5159	41	6	from	from	ADP
ejpam-5159	41	7	calculus	calculus	NOUN
ejpam-5159	41	8	we	we	PRON
ejpam-5159	41	9	see	see	VERB
ejpam-5159	41	10	that	that	SCONJ
ejpam-5159	41	11	the	the	DET
ejpam-5159	41	12	derivative	derivative	NOUN
ejpam-5159	41	13	of	of	ADP
ejpam-5159	41	14	the	the	DET
ejpam-5159	41	15	function	function	NOUN
ejpam-5159	41	16	h	h	NOUN
ejpam-5159	41	17	at	at	ADP
ejpam-5159	41	18	a	a	DET
ejpam-5159	41	19	given	give	VERB
ejpam-5159	41	20	point	point	NOUN
ejpam-5159	41	21	z	z	NOUN
ejpam-5159	42	1	=	=	SYM
ejpam-5159	42	2	d	d	NOUN
ejpam-5159	42	3	in	in	ADP
ejpam-5159	42	4	its	its	PRON
ejpam-5159	42	5	domain	domain	NOUN
ejpam-5159	42	6	is	be	AUX
ejpam-5159	42	7	defined	define	VERB
ejpam-5159	42	8	by	by	ADP
ejpam-5159	42	9	the	the	DET
ejpam-5159	42	10	following	follow	VERB
ejpam-5159	42	11	restriction	restriction	NOUN
ejpam-5159	42	12	:	:	PUNCT
ejpam-5159	42	13	h	h	NOUN
ejpam-5159	42	14	′(d	′(d	NOUN
ejpam-5159	42	15	)	)	PUNCT
ejpam-5159	43	1	=	=	VERB
ejpam-5159	43	2	lim	lim	PROPN
ejpam-5159	43	3	h→0	h→0	ADP
ejpam-5159	43	4	h(d+	h(d+	PROPN
ejpam-5159	43	5	h)−h(d	h)−h(d	PROPN
ejpam-5159	43	6	)	)	PUNCT
ejpam-5159	43	7	h	h	NOUN
ejpam-5159	43	8	.	.	PUNCT
ejpam-5159	44	1	(	(	PUNCT
ejpam-5159	44	2	6	6	X
ejpam-5159	44	3	)	)	PUNCT
ejpam-5159	44	4	we	we	PRON
ejpam-5159	44	5	define	define	VERB
ejpam-5159	44	6	h	h	NOUN
ejpam-5159	44	7	as	as	ADP
ejpam-5159	44	8	a	a	DET
ejpam-5159	44	9	differentiable	differentiable	ADJ
ejpam-5159	44	10	function	function	NOUN
ejpam-5159	44	11	at	at	ADP
ejpam-5159	44	12	z	z	NOUN
ejpam-5159	44	13	=	=	PUNCT
ejpam-5159	45	1	d	d	NOUN
ejpam-5159	45	2	if	if	SCONJ
ejpam-5159	45	3	its	its	PRON
ejpam-5159	45	4	limit	limit	NOUN
ejpam-5159	45	5	exists	exist	VERB
ejpam-5159	45	6	,	,	PUNCT
ejpam-5159	45	7	denoted	denote	VERB
ejpam-5159	45	8	as	as	ADP
ejpam-5159	45	9	h	h	NOUN
ejpam-5159	45	10	′(d	′(d	NOUN
ejpam-5159	45	11	)	)	PUNCT
ejpam-5159	45	12	,	,	PUNCT
ejpam-5159	45	13	furthermore	furthermore	ADV
ejpam-5159	45	14	,	,	PUNCT
ejpam-5159	45	15	if	if	SCONJ
ejpam-5159	45	16	h	h	NOUN
ejpam-5159	45	17	is	be	AUX
ejpam-5159	45	18	differentiable	differentiable	ADJ
ejpam-5159	45	19	at	at	ADP
ejpam-5159	45	20	this	this	DET
ejpam-5159	45	21	point	point	NOUN
ejpam-5159	45	22	,	,	PUNCT
ejpam-5159	45	23	it	it	PRON
ejpam-5159	45	24	is	be	AUX
ejpam-5159	45	25	also	also	ADV
ejpam-5159	45	26	continuous	continuous	ADJ
ejpam-5159	45	27	at	at	ADP
ejpam-5159	45	28	the	the	DET
ejpam-5159	45	29	same	same	ADJ
ejpam-5159	45	30	point	point	NOUN
ejpam-5159	45	31	.	.	PUNCT
ejpam-5159	46	1	definition	definition	NOUN
ejpam-5159	46	2	1	1	NUM
ejpam-5159	46	3	.	.	PUNCT
ejpam-5159	47	1	the	the	DET
ejpam-5159	47	2	new	new	ADJ
ejpam-5159	47	3	fractional	fractional	ADJ
ejpam-5159	47	4	derivative	derivative	NOUN
ejpam-5159	47	5	of	of	ADP
ejpam-5159	47	6	h	h	NOUN
ejpam-5159	47	7	in	in	ADP
ejpam-5159	47	8	order	order	NOUN
ejpam-5159	47	9	α	α	NOUN
ejpam-5159	47	10	is	be	AUX
ejpam-5159	47	11	represented	represent	VERB
ejpam-5159	47	12	by	by	ADP
ejpam-5159	47	13	(	(	PUNCT
ejpam-5159	47	14	dαh	dαh	PROPN
ejpam-5159	47	15	)	)	PUNCT
ejpam-5159	47	16	(	(	PUNCT
ejpam-5159	47	17	t	t	NOUN
ejpam-5159	47	18	)	)	PUNCT
ejpam-5159	47	19	=	=	PROPN
ejpam-5159	47	20	lim	lim	PROPN
ejpam-5159	47	21	v→0	v→0	PROPN
ejpam-5159	47	22	h	h	PROPN
ejpam-5159	47	23	(	(	PUNCT
ejpam-5159	47	24	t+	t+	NOUN
ejpam-5159	47	25	ve(α−1)t	ve(α−1)t	PROPN
ejpam-5159	47	26	)	)	PUNCT
ejpam-5159	47	27	−h(t	−h(t	PROPN
ejpam-5159	47	28	)	)	PUNCT
ejpam-5159	47	29	v	v	NOUN
ejpam-5159	47	30	,	,	PUNCT
ejpam-5159	47	31	(	(	PUNCT
ejpam-5159	47	32	7	7	NUM
ejpam-5159	47	33	)	)	PUNCT
ejpam-5159	47	34	with	with	ADP
ejpam-5159	47	35	,	,	PUNCT
ejpam-5159	47	36	α	α	PROPN
ejpam-5159	47	37	∈	∈	PROPN
ejpam-5159	48	1	[	[	X
ejpam-5159	48	2	0	0	NUM
ejpam-5159	48	3	,	,	PUNCT
ejpam-5159	48	4	1	1	NUM
ejpam-5159	48	5	]	]	PUNCT
ejpam-5159	48	6	and	and	CCONJ
ejpam-5159	48	7	t	t	X
ejpam-5159	48	8	>	>	X
ejpam-5159	48	9	0	0	X
ejpam-5159	48	10	.	.	PUNCT
ejpam-5159	49	1	on	on	ADP
ejpam-5159	49	2	the	the	DET
ejpam-5159	49	3	other	other	ADJ
ejpam-5159	49	4	hand	hand	NOUN
ejpam-5159	49	5	if	if	SCONJ
ejpam-5159	49	6	h	h	NOUN
ejpam-5159	49	7	is	be	AUX
ejpam-5159	49	8	differentiable	differentiable	ADJ
ejpam-5159	49	9	of	of	ADP
ejpam-5159	49	10	order	order	NOUN
ejpam-5159	49	11	α	α	NOUN
ejpam-5159	49	12	in	in	ADP
ejpam-5159	49	13	[	[	X
ejpam-5159	49	14	0	0	NUM
ejpam-5159	49	15	,	,	PUNCT
ejpam-5159	49	16	a	a	PRON
ejpam-5159	49	17	]	]	X
ejpam-5159	49	18	,	,	PUNCT
ejpam-5159	49	19	a	a	PRON
ejpam-5159	49	20	>	>	X
ejpam-5159	49	21	0	0	NUM
ejpam-5159	49	22	,	,	PUNCT
ejpam-5159	49	23	and	and	CCONJ
ejpam-5159	49	24	limt→0	limt→0	PROPN
ejpam-5159	49	25	+	+	CCONJ
ejpam-5159	49	26	(	(	PUNCT
ejpam-5159	49	27	dαh	dαh	NOUN
ejpam-5159	49	28	)	)	PUNCT
ejpam-5159	49	29	(	(	PUNCT
ejpam-5159	49	30	t	t	NOUN
ejpam-5159	49	31	)	)	PUNCT
ejpam-5159	49	32	exists	exist	VERB
ejpam-5159	49	33	,	,	PUNCT
ejpam-5159	49	34	we	we	PRON
ejpam-5159	49	35	have	have	VERB
ejpam-5159	49	36	:	:	PUNCT
ejpam-5159	49	37	dαh(0	dαh(0	NOUN
ejpam-5159	49	38	)	)	PUNCT
ejpam-5159	50	1	=	=	SYM
ejpam-5159	50	2	lim	lim	PROPN
ejpam-5159	50	3	t−→0	t−→0	PROPN
ejpam-5159	50	4	+	+	CCONJ
ejpam-5159	50	5	(	(	PUNCT
ejpam-5159	50	6	dαh)(t	dαh)(t	ADJ
ejpam-5159	50	7	)	)	PUNCT
ejpam-5159	50	8	.	.	PUNCT
ejpam-5159	51	1	(	(	PUNCT
ejpam-5159	51	2	8)	8)	NUM
ejpam-5159	51	3	theorem	theorem	NOUN
ejpam-5159	51	4	1	1	NUM
ejpam-5159	51	5	.	.	PUNCT
ejpam-5159	51	6	(	(	PUNCT
ejpam-5159	51	7	see[5	see[5	NOUN
ejpam-5159	51	8	]	]	PUNCT
ejpam-5159	51	9	)	)	PUNCT
ejpam-5159	51	10	if	if	SCONJ
ejpam-5159	51	11	h	h	NOUN
ejpam-5159	51	12	is	be	AUX
ejpam-5159	51	13	differentiable	differentiable	ADJ
ejpam-5159	51	14	of	of	ADP
ejpam-5159	51	15	order	order	NOUN
ejpam-5159	51	16	α	α	NOUN
ejpam-5159	51	17	at	at	ADP
ejpam-5159	51	18	t0	t0	PROPN
ejpam-5159	51	19	>	>	PUNCT
ejpam-5159	51	20	0	0	PROPN
ejpam-5159	51	21	,	,	PUNCT
ejpam-5159	51	22	and	and	CCONJ
ejpam-5159	51	23	h	h	NOUN
ejpam-5159	51	24	:	:	PUNCT
ejpam-5159	52	1	[	[	X
ejpam-5159	52	2	0,+∞	0,+∞	NUM
ejpam-5159	52	3	)	)	PUNCT
ejpam-5159	52	4	−→	−→	NOUN
ejpam-5159	52	5	r	r	NOUN
ejpam-5159	52	6	,	,	PUNCT
ejpam-5159	52	7	then	then	ADV
ejpam-5159	52	8	h	h	NOUN
ejpam-5159	52	9	is	be	AUX
ejpam-5159	52	10	continuous	continuous	ADJ
ejpam-5159	52	11	at	at	ADP
ejpam-5159	52	12	t0	t0	PROPN
ejpam-5159	52	13	.	.	PUNCT
ejpam-5159	53	1	theorem	theorem	NOUN
ejpam-5159	53	2	2	2	NUM
ejpam-5159	53	3	.	.	PUNCT
ejpam-5159	53	4	(	(	PUNCT
ejpam-5159	53	5	see[5	see[5	NOUN
ejpam-5159	53	6	]	]	PUNCT
ejpam-5159	53	7	)	)	PUNCT
ejpam-5159	53	8	if	if	SCONJ
ejpam-5159	53	9	h	h	PRON
ejpam-5159	53	10	be	be	VERB
ejpam-5159	53	11	α	α	NOUN
ejpam-5159	53	12	differentiable	differentiable	ADJ
ejpam-5159	53	13	at	at	ADP
ejpam-5159	53	14	a	a	DET
ejpam-5159	53	15	point	point	NOUN
ejpam-5159	53	16	t	t	X
ejpam-5159	53	17	>	>	X
ejpam-5159	53	18	0	0	NUM
ejpam-5159	53	19	,	,	PUNCT
ejpam-5159	53	20	we	we	PRON
ejpam-5159	53	21	have	have	VERB
ejpam-5159	53	22	:	:	PUNCT
ejpam-5159	53	23	1	1	X
ejpam-5159	53	24	)	)	PUNCT
ejpam-5159	53	25	dα(ah	dα(ah	NOUN
ejpam-5159	53	26	+	+	CCONJ
ejpam-5159	53	27	bh	bh	NOUN
ejpam-5159	53	28	)	)	PUNCT
ejpam-5159	53	29	=	=	SYM
ejpam-5159	53	30	a	a	PRON
ejpam-5159	53	31	(	(	PUNCT
ejpam-5159	53	32	dαh	dαh	NOUN
ejpam-5159	53	33	)	)	PUNCT
ejpam-5159	54	1	+	+	SYM
ejpam-5159	54	2	b	b	X
ejpam-5159	54	3	(	(	PUNCT
ejpam-5159	54	4	dαh	dαh	NOUN
ejpam-5159	54	5	)	)	PUNCT
ejpam-5159	54	6	,	,	PUNCT
ejpam-5159	54	7	for	for	ADP
ejpam-5159	54	8	all	all	DET
ejpam-5159	54	9	a	a	PRON
ejpam-5159	54	10	,	,	PUNCT
ejpam-5159	54	11	b	b	X
ejpam-5159	54	12	∈	∈	PROPN
ejpam-5159	54	13	r	r	NOUN
ejpam-5159	54	14	2	2	NUM
ejpam-5159	54	15	)	)	PUNCT
ejpam-5159	54	16	dα	dα	PROPN
ejpam-5159	54	17	(	(	PUNCT
ejpam-5159	54	18	tn	tn	NOUN
ejpam-5159	54	19	)	)	PUNCT
ejpam-5159	54	20	=	=	PUNCT
ejpam-5159	54	21	ne(α−1)ttn−1	ne(α−1)ttn−1	ADJ
ejpam-5159	54	22	for	for	ADP
ejpam-5159	54	23	all	all	PRON
ejpam-5159	54	24	n	n	PRON
ejpam-5159	54	25	∈	∈	NOUN
ejpam-5159	54	26	r	r	NOUN
ejpam-5159	54	27	3	3	NUM
ejpam-5159	54	28	)	)	PUNCT
ejpam-5159	54	29	dα(β	dα(β	NOUN
ejpam-5159	54	30	)	)	PUNCT
ejpam-5159	54	31	=	=	SYM
ejpam-5159	54	32	0	0	NUM
ejpam-5159	54	33	,	,	PUNCT
ejpam-5159	54	34	for	for	ADP
ejpam-5159	54	35	all	all	DET
ejpam-5159	54	36	constant	constant	ADJ
ejpam-5159	54	37	h(t	h(t	PROPN
ejpam-5159	54	38	)	)	PUNCT
ejpam-5159	54	39	=	=	PUNCT
ejpam-5159	54	40	β	β	X
ejpam-5159	54	41	.	.	NOUN
ejpam-5159	54	42	4	4	NUM
ejpam-5159	54	43	)	)	PUNCT
ejpam-5159	54	44	dα(hg	dα(hg	PROPN
ejpam-5159	54	45	)	)	PUNCT
ejpam-5159	55	1	=	=	SYM
ejpam-5159	55	2	h	h	PROPN
ejpam-5159	55	3	(	(	PUNCT
ejpam-5159	55	4	dαg	dαg	PROPN
ejpam-5159	55	5	)	)	PUNCT
ejpam-5159	55	6	+	+	PROPN
ejpam-5159	55	7	g	g	NOUN
ejpam-5159	55	8	(	(	PUNCT
ejpam-5159	55	9	dαh	dαh	PROPN
ejpam-5159	55	10	)	)	PUNCT
ejpam-5159	55	11	.	.	PUNCT
ejpam-5159	56	1	5	5	X
ejpam-5159	56	2	)	)	PUNCT
ejpam-5159	56	3	dα(h	dα(h	NOUN
ejpam-5159	56	4	/	/	SYM
ejpam-5159	56	5	g	g	NOUN
ejpam-5159	56	6	)	)	PUNCT
ejpam-5159	57	1	=	=	SYM
ejpam-5159	57	2	h	h	PROPN
ejpam-5159	57	3	(	(	PUNCT
ejpam-5159	57	4	dαg	dαg	PROPN
ejpam-5159	57	5	)	)	PUNCT
ejpam-5159	57	6	+	+	PROPN
ejpam-5159	57	7	g	g	PROPN
ejpam-5159	57	8	(	(	PUNCT
ejpam-5159	57	9	dαh	dαh	PROPN
ejpam-5159	57	10	)	)	PUNCT
ejpam-5159	57	11	/g2	/g2	PROPN
ejpam-5159	57	12	.	.	PUNCT
ejpam-5159	58	1	6	6	NUM
ejpam-5159	58	2	)	)	PUNCT
ejpam-5159	58	3	if	if	SCONJ
ejpam-5159	58	4	h	h	NOUN
ejpam-5159	58	5	is	be	AUX
ejpam-5159	58	6	differentiable	differentiable	ADJ
ejpam-5159	58	7	,	,	PUNCT
ejpam-5159	58	8	then	then	ADV
ejpam-5159	58	9	(	(	PUNCT
ejpam-5159	58	10	dαh	dαh	PROPN
ejpam-5159	58	11	)	)	PUNCT
ejpam-5159	58	12	(	(	PUNCT
ejpam-5159	58	13	t	t	NOUN
ejpam-5159	58	14	)	)	PUNCT
ejpam-5159	58	15	=	=	PUNCT
ejpam-5159	58	16	e(α−1)th	e(α−1)th	NOUN
ejpam-5159	58	17	′(t	′(t	NOUN
ejpam-5159	58	18	)	)	PUNCT
ejpam-5159	58	19	.	.	PUNCT
ejpam-5159	59	1	theorem	theorem	NOUN
ejpam-5159	59	2	3	3	X
ejpam-5159	59	3	.	.	PUNCT
ejpam-5159	60	1	let	let	VERB
ejpam-5159	60	2	α	α	PRON
ejpam-5159	60	3	∈	∈	PROPN
ejpam-5159	60	4	(	(	PUNCT
ejpam-5159	60	5	0	0	NUM
ejpam-5159	60	6	,	,	PUNCT
ejpam-5159	60	7	1	1	NUM
ejpam-5159	60	8	]	]	PUNCT
ejpam-5159	60	9	,	,	PUNCT
ejpam-5159	60	10	then	then	ADV
ejpam-5159	60	11	:	:	PUNCT
ejpam-5159	60	12	1	1	X
ejpam-5159	60	13	)	)	PUNCT
ejpam-5159	60	14	dα	dα	NOUN
ejpam-5159	60	15	(	(	PUNCT
ejpam-5159	60	16	1	1	NUM
ejpam-5159	60	17	1−αe	1−αe	PROPN
ejpam-5159	60	18	(	(	PUNCT
ejpam-5159	60	19	1−α)t	1−α)t	NUM
ejpam-5159	60	20	)	)	PUNCT
ejpam-5159	60	21	=	=	SYM
ejpam-5159	61	1	1	1	NUM
ejpam-5159	61	2	.	.	NOUN
ejpam-5159	61	3	2	2	NUM
ejpam-5159	61	4	)	)	PUNCT
ejpam-5159	61	5	dα	dα	NOUN
ejpam-5159	61	6	(	(	PUNCT
ejpam-5159	61	7	sin	sin	PROPN
ejpam-5159	61	8	1	1	NUM
ejpam-5159	61	9	1−αe	1−αe	PROPN
ejpam-5159	61	10	(	(	PUNCT
ejpam-5159	61	11	1−α)t	1−α)t	NUM
ejpam-5159	61	12	)	)	PUNCT
ejpam-5159	61	13	=	=	SYM
ejpam-5159	61	14	cos	cos	ADP
ejpam-5159	61	15	1	1	NUM
ejpam-5159	61	16	1−αe	1−αe	PROPN
ejpam-5159	61	17	(	(	PUNCT
ejpam-5159	61	18	1−α)t	1−α)t	NUM
ejpam-5159	61	19	.	.	NOUN
ejpam-5159	61	20	3	3	X
ejpam-5159	61	21	)	)	PUNCT
ejpam-5159	61	22	dα	dα	NOUN
ejpam-5159	61	23	(	(	PUNCT
ejpam-5159	61	24	cos	cos	PROPN
ejpam-5159	61	25	1	1	PROPN
ejpam-5159	61	26	1−αe	1−αe	PROPN
ejpam-5159	61	27	(	(	PUNCT
ejpam-5159	61	28	1−α)t	1−α)t	NUM
ejpam-5159	61	29	)	)	PUNCT
ejpam-5159	61	30	=	=	SYM
ejpam-5159	62	1	−	−	PROPN
ejpam-5159	62	2	sin	sin	NOUN
ejpam-5159	62	3	1	1	NUM
ejpam-5159	62	4	1−αe	1−αe	PROPN
ejpam-5159	62	5	(	(	PUNCT
ejpam-5159	62	6	1−α)t	1−α)t	NUM
ejpam-5159	62	7	.	.	NOUN
ejpam-5159	62	8	4	4	X
ejpam-5159	62	9	)	)	PUNCT
ejpam-5159	62	10	dα	dα	NOUN
ejpam-5159	62	11	(	(	PUNCT
ejpam-5159	62	12	e	e	PROPN
ejpam-5159	62	13	1	1	NUM
ejpam-5159	62	14	1−α	1−α	NUM
ejpam-5159	62	15	e(1−α)t	e(1−α)t	NOUN
ejpam-5159	62	16	)	)	PUNCT
ejpam-5159	63	1	=	=	PUNCT
ejpam-5159	63	2	e	e	X
ejpam-5159	63	3	1	1	NUM
ejpam-5159	63	4	1−α	1−α	NUM
ejpam-5159	63	5	e(1−α)t	e(1−α)t	NOUN
ejpam-5159	63	6	.	.	PUNCT
ejpam-5159	64	1	3	3	X
ejpam-5159	64	2	.	.	X
ejpam-5159	64	3	applications	application	NOUN
ejpam-5159	64	4	to	to	ADP
ejpam-5159	64	5	physics	physics	PROPN
ejpam-5159	64	6	3.1	3.1	NUM
ejpam-5159	64	7	.	.	PUNCT
ejpam-5159	65	1	model	model	NOUN
ejpam-5159	65	2	of	of	ADP
ejpam-5159	65	3	population	population	NOUN
ejpam-5159	65	4	growth	growth	NOUN
ejpam-5159	65	5	population	population	NOUN
ejpam-5159	65	6	growth	growth	NOUN
ejpam-5159	65	7	models	model	NOUN
ejpam-5159	65	8	are	be	AUX
ejpam-5159	65	9	essential	essential	ADJ
ejpam-5159	65	10	tools	tool	NOUN
ejpam-5159	65	11	in	in	ADP
ejpam-5159	65	12	understanding	understand	VERB
ejpam-5159	65	13	the	the	DET
ejpam-5159	65	14	dynamics	dynamic	NOUN
ejpam-5159	65	15	of	of	ADP
ejpam-5159	65	16	populations	population	NOUN
ejpam-5159	65	17	over	over	ADP
ejpam-5159	65	18	time	time	NOUN
ejpam-5159	65	19	.	.	PUNCT
ejpam-5159	66	1	they	they	PRON
ejpam-5159	66	2	are	be	AUX
ejpam-5159	66	3	used	use	VERB
ejpam-5159	66	4	in	in	ADP
ejpam-5159	66	5	various	various	ADJ
ejpam-5159	66	6	fields	field	NOUN
ejpam-5159	66	7	such	such	ADJ
ejpam-5159	66	8	as	as	ADP
ejpam-5159	66	9	biology	biology	NOUN
ejpam-5159	66	10	,	,	PUNCT
ejpam-5159	66	11	ecology	ecology	NOUN
ejpam-5159	66	12	,	,	PUNCT
ejpam-5159	66	13	epidemiology	epidemiology	NOUN
ejpam-5159	66	14	,	,	PUNCT
ejpam-5159	66	15	a.	a.	PROPN
ejpam-5159	66	16	ait	ait	PROPN
ejpam-5159	66	17	brahim	brahim	PROPN
ejpam-5159	66	18	et	et	PROPN
ejpam-5159	66	19	al	al	PROPN
ejpam-5159	66	20	.	.	PUNCT
ejpam-5159	66	21	/	/	SYM
ejpam-5159	66	22	eur	eur	PROPN
ejpam-5159	66	23	.	.	PUNCT
ejpam-5159	67	1	j.	j.	PROPN
ejpam-5159	67	2	pure	pure	PROPN
ejpam-5159	67	3	appl	appl	PROPN
ejpam-5159	67	4	.	.	PROPN
ejpam-5159	67	5	math	math	PROPN
ejpam-5159	67	6	,	,	PUNCT
ejpam-5159	67	7	17	17	NUM
ejpam-5159	67	8	(	(	PUNCT
ejpam-5159	67	9	2	2	NUM
ejpam-5159	67	10	)	)	PUNCT
ejpam-5159	67	11	(	(	PUNCT
ejpam-5159	67	12	2024	2024	NUM
ejpam-5159	67	13	)	)	PUNCT
ejpam-5159	67	14	,	,	PUNCT
ejpam-5159	67	15	1155	1155	NUM
ejpam-5159	67	16	-	-	SYM
ejpam-5159	67	17	1167	1167	NUM
ejpam-5159	67	18	1158	1158	NUM
ejpam-5159	67	19	and	and	CCONJ
ejpam-5159	67	20	sociology	sociology	NOUN
ejpam-5159	67	21	to	to	PART
ejpam-5159	67	22	predict	predict	VERB
ejpam-5159	67	23	and	and	CCONJ
ejpam-5159	67	24	analyze	analyze	VERB
ejpam-5159	67	25	changes	change	NOUN
ejpam-5159	67	26	in	in	ADP
ejpam-5159	67	27	population	population	NOUN
ejpam-5159	67	28	size	size	NOUN
ejpam-5159	67	29	.	.	PUNCT
ejpam-5159	68	1	we	we	PRON
ejpam-5159	68	2	define	define	VERB
ejpam-5159	68	3	the	the	DET
ejpam-5159	68	4	problem	problem	NOUN
ejpam-5159	68	5	of	of	ADP
ejpam-5159	68	6	population	population	NOUN
ejpam-5159	68	7	growth	growth	NOUN
ejpam-5159	68	8	model	model	NOUN
ejpam-5159	68	9	by	by	ADP
ejpam-5159	68	10	dz	dz	ADJ
ejpam-5159	68	11	dt	dt	PROPN
ejpam-5159	68	12	=	=	SYM
ejpam-5159	68	13	kz(t	kz(t	PROPN
ejpam-5159	68	14	)	)	PUNCT
ejpam-5159	68	15	,	,	PUNCT
ejpam-5159	68	16	z(0	z(0	X
ejpam-5159	68	17	)	)	PUNCT
ejpam-5159	68	18	=	=	SYM
ejpam-5159	68	19	n.	n.	NOUN
ejpam-5159	68	20	(	(	PUNCT
ejpam-5159	68	21	9	9	NUM
ejpam-5159	68	22	)	)	PUNCT
ejpam-5159	68	23	here	here	ADV
ejpam-5159	68	24	l	l	NOUN
ejpam-5159	68	25	is	be	AUX
ejpam-5159	68	26	constant	constant	ADJ
ejpam-5159	68	27	,	,	PUNCT
ejpam-5159	68	28	n	n	PRON
ejpam-5159	68	29	is	be	AUX
ejpam-5159	68	30	the	the	DET
ejpam-5159	68	31	initial	initial	ADJ
ejpam-5159	68	32	value	value	NOUN
ejpam-5159	68	33	of	of	ADP
ejpam-5159	68	34	population	population	NOUN
ejpam-5159	68	35	and	and	CCONJ
ejpam-5159	68	36	z	z	NOUN
ejpam-5159	68	37	is	be	AUX
ejpam-5159	68	38	the	the	DET
ejpam-5159	68	39	population	population	NOUN
ejpam-5159	68	40	function	function	NOUN
ejpam-5159	68	41	,	,	PUNCT
ejpam-5159	68	42	and	and	CCONJ
ejpam-5159	68	43	we	we	PRON
ejpam-5159	68	44	can	can	AUX
ejpam-5159	68	45	write	write	VERB
ejpam-5159	68	46	the	the	DET
ejpam-5159	68	47	solution	solution	NOUN
ejpam-5159	68	48	of	of	ADP
ejpam-5159	68	49	this	this	DET
ejpam-5159	68	50	problem	problem	NOUN
ejpam-5159	68	51	z(t	z(t	NOUN
ejpam-5159	68	52	)	)	PUNCT
ejpam-5159	68	53	=	=	SYM
ejpam-5159	68	54	nelt	nelt	PROPN
ejpam-5159	68	55	.	.	PUNCT
ejpam-5159	69	1	(	(	PUNCT
ejpam-5159	69	2	10	10	NUM
ejpam-5159	69	3	)	)	PUNCT
ejpam-5159	69	4	the	the	DET
ejpam-5159	69	5	following	follow	VERB
ejpam-5159	69	6	figure	figure	NOUN
ejpam-5159	69	7	shows	show	VERB
ejpam-5159	69	8	this	this	DET
ejpam-5159	69	9	solution	solution	NOUN
ejpam-5159	69	10	:	:	PUNCT
ejpam-5159	69	11	now	now	ADV
ejpam-5159	69	12	,	,	PUNCT
ejpam-5159	69	13	we	we	PRON
ejpam-5159	69	14	present	present	VERB
ejpam-5159	69	15	this	this	DET
ejpam-5159	69	16	problem	problem	NOUN
ejpam-5159	69	17	in	in	ADP
ejpam-5159	69	18	the	the	DET
ejpam-5159	69	19	form	form	NOUN
ejpam-5159	69	20	of	of	ADP
ejpam-5159	69	21	new	new	ADJ
ejpam-5159	69	22	conformable	conformable	ADJ
ejpam-5159	69	23	fractional	fractional	NOUN
ejpam-5159	69	24	:	:	PUNCT
ejpam-5159	69	25	z(α)(t	z(α)(t	NUM
ejpam-5159	69	26	)	)	PUNCT
ejpam-5159	69	27	=	=	SYM
ejpam-5159	69	28	lz(t	lz(t	NOUN
ejpam-5159	69	29	)	)	PUNCT
ejpam-5159	69	30	,	,	PUNCT
ejpam-5159	69	31	z(0	z(0	X
ejpam-5159	69	32	)	)	PUNCT
ejpam-5159	69	33	=	=	SYM
ejpam-5159	70	1	n.	n.	NOUN
ejpam-5159	70	2	(	(	PUNCT
ejpam-5159	70	3	11	11	NUM
ejpam-5159	70	4	)	)	PUNCT
ejpam-5159	70	5	from	from	ADP
ejpam-5159	70	6	property	property	NOUN
ejpam-5159	70	7	(	(	PUNCT
ejpam-5159	70	8	6	6	NUM
ejpam-5159	70	9	)	)	PUNCT
ejpam-5159	70	10	theorem(2	theorem(2	PROPN
ejpam-5159	70	11	)	)	PUNCT
ejpam-5159	70	12	,	,	PUNCT
ejpam-5159	70	13	we	we	PRON
ejpam-5159	70	14	have	have	VERB
ejpam-5159	70	15	:	:	PUNCT
ejpam-5159	70	16	e(α−1)tz	e(α−1)tz	PROPN
ejpam-5159	70	17	′(t	′(t	PROPN
ejpam-5159	70	18	)	)	PUNCT
ejpam-5159	70	19	=	=	SYM
ejpam-5159	70	20	lz(t	lz(t	PROPN
ejpam-5159	70	21	)	)	PUNCT
ejpam-5159	70	22	.	.	PUNCT
ejpam-5159	71	1	(	(	PUNCT
ejpam-5159	71	2	12	12	NUM
ejpam-5159	71	3	)	)	PUNCT
ejpam-5159	71	4	therefore	therefore	ADV
ejpam-5159	71	5	,	,	PUNCT
ejpam-5159	71	6	we	we	PRON
ejpam-5159	71	7	can	can	AUX
ejpam-5159	71	8	continue	continue	VERB
ejpam-5159	71	9	to	to	PART
ejpam-5159	71	10	use	use	VERB
ejpam-5159	71	11	the	the	DET
ejpam-5159	71	12	following	follow	VERB
ejpam-5159	71	13	expression	expression	NOUN
ejpam-5159	71	14	z	z	PROPN
ejpam-5159	71	15	′(t	′(t	PROPN
ejpam-5159	71	16	)	)	PUNCT
ejpam-5159	71	17	=	=	SYM
ejpam-5159	71	18	ke(α−1)tz(t	ke(α−1)tz(t	PROPN
ejpam-5159	71	19	)	)	PUNCT
ejpam-5159	71	20	or	or	CCONJ
ejpam-5159	71	21	dz(t	dz(t	NOUN
ejpam-5159	71	22	)	)	PUNCT
ejpam-5159	71	23	dt	dt	X
ejpam-5159	71	24	=	=	SYM
ejpam-5159	71	25	le(α−1)tz(t	le(α−1)tz(t	PROPN
ejpam-5159	71	26	)	)	PUNCT
ejpam-5159	71	27	.	.	PUNCT
ejpam-5159	72	1	(	(	PUNCT
ejpam-5159	72	2	13	13	NUM
ejpam-5159	72	3	)	)	PUNCT
ejpam-5159	72	4	by	by	ADP
ejpam-5159	72	5	applying	apply	VERB
ejpam-5159	72	6	the	the	DET
ejpam-5159	72	7	separation	separation	NOUN
ejpam-5159	72	8	of	of	ADP
ejpam-5159	72	9	variables	variable	NOUN
ejpam-5159	72	10	,	,	PUNCT
ejpam-5159	72	11	we	we	PRON
ejpam-5159	72	12	obtain	obtain	VERB
ejpam-5159	72	13	:	:	PUNCT
ejpam-5159	72	14	dz(t	dz(t	X
ejpam-5159	72	15	)	)	PUNCT
ejpam-5159	72	16	y(t	y(t	NUM
ejpam-5159	72	17	)	)	PUNCT
ejpam-5159	73	1	=	=	SYM
ejpam-5159	73	2	le(α−1)tdt	le(α−1)tdt	PROPN
ejpam-5159	73	3	.	.	PUNCT
ejpam-5159	74	1	(	(	PUNCT
ejpam-5159	74	2	14	14	NUM
ejpam-5159	74	3	)	)	PUNCT
ejpam-5159	74	4	a.	a.	NOUN
ejpam-5159	74	5	ait	ait	NOUN
ejpam-5159	74	6	brahim	brahim	PROPN
ejpam-5159	74	7	et	et	PROPN
ejpam-5159	74	8	al	al	PROPN
ejpam-5159	74	9	.	.	PUNCT
ejpam-5159	74	10	/	/	SYM
ejpam-5159	74	11	eur	eur	PROPN
ejpam-5159	74	12	.	.	PUNCT
ejpam-5159	75	1	j.	j.	PROPN
ejpam-5159	75	2	pure	pure	PROPN
ejpam-5159	75	3	appl	appl	PROPN
ejpam-5159	75	4	.	.	PROPN
ejpam-5159	75	5	math	math	PROPN
ejpam-5159	75	6	,	,	PUNCT
ejpam-5159	75	7	17	17	NUM
ejpam-5159	75	8	(	(	PUNCT
ejpam-5159	75	9	2	2	NUM
ejpam-5159	75	10	)	)	PUNCT
ejpam-5159	75	11	(	(	PUNCT
ejpam-5159	75	12	2024	2024	NUM
ejpam-5159	75	13	)	)	PUNCT
ejpam-5159	75	14	,	,	PUNCT
ejpam-5159	75	15	1155	1155	NUM
ejpam-5159	75	16	-	-	SYM
ejpam-5159	75	17	1167	1167	NUM
ejpam-5159	75	18	1159	1159	NUM
ejpam-5159	75	19	now	now	ADV
ejpam-5159	75	20	by	by	ADP
ejpam-5159	75	21	integration	integration	NOUN
ejpam-5159	75	22	we	we	PRON
ejpam-5159	75	23	have	have	VERB
ejpam-5159	75	24	:	:	PUNCT
ejpam-5159	75	25	lnz(t	lnz(t	X
ejpam-5159	75	26	)	)	PUNCT
ejpam-5159	75	27	=	=	SYM
ejpam-5159	76	1	k	k	X
ejpam-5159	76	2	α−	α−	ADP
ejpam-5159	76	3	1	1	NUM
ejpam-5159	76	4	e(α−1)t	e(α−1)t	PROPN
ejpam-5159	77	1	+	+	PROPN
ejpam-5159	77	2	b	b	PROPN
ejpam-5159	77	3	,	,	PUNCT
ejpam-5159	77	4	(	(	PUNCT
ejpam-5159	77	5	15	15	X
ejpam-5159	77	6	)	)	PUNCT
ejpam-5159	77	7	we	we	PRON
ejpam-5159	77	8	obtain	obtain	VERB
ejpam-5159	77	9	:	:	PUNCT
ejpam-5159	77	10	z(t	z(t	X
ejpam-5159	77	11	)	)	PUNCT
ejpam-5159	78	1	=	=	SYM
ejpam-5159	78	2	ebe	ebe	PROPN
ejpam-5159	78	3	l	l	PROPN
ejpam-5159	78	4	α−1	α−1	PROPN
ejpam-5159	79	1	e(α−1)t	e(α−1)t	PROPN
ejpam-5159	79	2	,	,	PUNCT
ejpam-5159	79	3	(	(	PUNCT
ejpam-5159	79	4	16	16	NUM
ejpam-5159	79	5	)	)	PUNCT
ejpam-5159	79	6	and	and	CCONJ
ejpam-5159	79	7	we	we	PRON
ejpam-5159	79	8	use	use	VERB
ejpam-5159	79	9	the	the	DET
ejpam-5159	79	10	initial	initial	ADJ
ejpam-5159	79	11	condition	condition	NOUN
ejpam-5159	79	12	:	:	PUNCT
ejpam-5159	79	13	z(t	z(t	X
ejpam-5159	79	14	)	)	PUNCT
ejpam-5159	79	15	=	=	SYM
ejpam-5159	79	16	ne	ne	PROPN
ejpam-5159	79	17	l	l	PROPN
ejpam-5159	79	18	α−1	α−1	PROPN
ejpam-5159	79	19	e(α−1)t	e(α−1)t	PROPN
ejpam-5159	79	20	.	.	PUNCT
ejpam-5159	80	1	(	(	PUNCT
ejpam-5159	80	2	17	17	NUM
ejpam-5159	80	3	)	)	PUNCT
ejpam-5159	80	4	in	in	ADP
ejpam-5159	80	5	this	this	DET
ejpam-5159	80	6	example	example	NOUN
ejpam-5159	80	7	,	,	PUNCT
ejpam-5159	80	8	we	we	PRON
ejpam-5159	80	9	present	present	VERB
ejpam-5159	80	10	the	the	DET
ejpam-5159	80	11	solution	solution	NOUN
ejpam-5159	80	12	for	for	ADP
ejpam-5159	80	13	different	different	ADJ
ejpam-5159	80	14	values	value	NOUN
ejpam-5159	80	15	of	of	ADP
ejpam-5159	80	16	α	α	NOUN
ejpam-5159	80	17	:	:	PUNCT
ejpam-5159	80	18	α	α	NOUN
ejpam-5159	80	19	=	=	SYM
ejpam-5159	80	20	0	0	PROPN
ejpam-5159	80	21	,	,	PUNCT
ejpam-5159	80	22	α	α	NOUN
ejpam-5159	80	23	=	=	NOUN
ejpam-5159	80	24	0.25	0.25	NUM
ejpam-5159	80	25	,	,	PUNCT
ejpam-5159	80	26	α	α	NOUN
ejpam-5159	80	27	=	=	SYM
ejpam-5159	80	28	0.5	0.5	NUM
ejpam-5159	80	29	,	,	PUNCT
ejpam-5159	80	30	and	and	CCONJ
ejpam-5159	80	31	α	α	X
ejpam-5159	80	32	=	=	NOUN
ejpam-5159	80	33	0.75	0.75	NUM
ejpam-5159	80	34	using	use	VERB
ejpam-5159	80	35	the	the	DET
ejpam-5159	80	36	new	new	ADJ
ejpam-5159	80	37	conformable	conformable	ADJ
ejpam-5159	80	38	fractional	fractional	ADJ
ejpam-5159	80	39	calculus	calculus	NOUN
ejpam-5159	80	40	(	(	PUNCT
ejpam-5159	80	41	see	see	VERB
ejpam-5159	80	42	[	[	X
ejpam-5159	80	43	5	5	NUM
ejpam-5159	80	44	]	]	NUM
ejpam-5159	80	45	)	)	PUNCT
ejpam-5159	80	46	,	,	PUNCT
ejpam-5159	80	47	and	and	CCONJ
ejpam-5159	80	48	we	we	PRON
ejpam-5159	80	49	compare	compare	VERB
ejpam-5159	80	50	it	it	PRON
ejpam-5159	80	51	with	with	ADP
ejpam-5159	80	52	other	other	ADJ
ejpam-5159	80	53	methods	method	NOUN
ejpam-5159	80	54	like	like	ADP
ejpam-5159	80	55	khalil	khalil	PROPN
ejpam-5159	80	56	’s	’s	PART
ejpam-5159	80	57	conformable	conformable	ADJ
ejpam-5159	80	58	fractional	fractional	ADJ
ejpam-5159	80	59	derivative	derivative	NOUN
ejpam-5159	80	60	(	(	PUNCT
ejpam-5159	80	61	see	see	VERB
ejpam-5159	80	62	[	[	X
ejpam-5159	80	63	3	3	NUM
ejpam-5159	80	64	]	]	PUNCT
ejpam-5159	80	65	)	)	PUNCT
ejpam-5159	80	66	and	and	CCONJ
ejpam-5159	80	67	ordinary	ordinary	ADJ
ejpam-5159	80	68	derivatives	derivative	NOUN
ejpam-5159	80	69	.	.	PUNCT
ejpam-5159	81	1	3.2	3.2	NUM
ejpam-5159	81	2	.	.	PUNCT
ejpam-5159	81	3	model	model	NOUN
ejpam-5159	81	4	of	of	ADP
ejpam-5159	81	5	body	body	NOUN
ejpam-5159	81	6	cooling	cool	VERB
ejpam-5159	81	7	as	as	SCONJ
ejpam-5159	81	8	he	he	PRON
ejpam-5159	81	9	shifted	shift	VERB
ejpam-5159	81	10	his	his	PRON
ejpam-5159	81	11	sweater	sweater	NOUN
ejpam-5159	81	12	over	over	ADP
ejpam-5159	81	13	time	time	NOUN
ejpam-5159	81	14	,	,	PUNCT
ejpam-5159	81	15	newton	newton	PROPN
ejpam-5159	81	16	’s	’s	PART
ejpam-5159	81	17	law	law	NOUN
ejpam-5159	81	18	of	of	ADP
ejpam-5159	81	19	cold	cold	ADJ
ejpam-5159	81	20	was	be	AUX
ejpam-5159	81	21	a	a	DET
ejpam-5159	81	22	body	body	NOUN
ejpam-5159	81	23	law	law	NOUN
ejpam-5159	81	24	designed	design	VERB
ejpam-5159	81	25	to	to	ADP
ejpam-5159	81	26	body	body	NOUN
ejpam-5159	81	27	warming	warming	NOUN
ejpam-5159	81	28	is	be	AUX
ejpam-5159	81	29	proportional	proportional	ADJ
ejpam-5159	81	30	to	to	ADP
ejpam-5159	81	31	the	the	DET
ejpam-5159	81	32	temperature	temperature	NOUN
ejpam-5159	81	33	difference	difference	NOUN
ejpam-5159	81	34	between	between	ADP
ejpam-5159	81	35	the	the	DET
ejpam-5159	81	36	body	body	NOUN
ejpam-5159	81	37	and	and	CCONJ
ejpam-5159	81	38	its	its	PRON
ejpam-5159	81	39	a.	a.	NOUN
ejpam-5159	81	40	ait	ait	NOUN
ejpam-5159	81	41	brahim	brahim	PROPN
ejpam-5159	82	1	et	et	PROPN
ejpam-5159	82	2	al	al	PROPN
ejpam-5159	82	3	.	.	PUNCT
ejpam-5159	82	4	/	/	SYM
ejpam-5159	82	5	eur	eur	PROPN
ejpam-5159	82	6	.	.	PUNCT
ejpam-5159	83	1	j.	j.	PROPN
ejpam-5159	83	2	pure	pure	PROPN
ejpam-5159	83	3	appl	appl	PROPN
ejpam-5159	83	4	.	.	PROPN
ejpam-5159	83	5	math	math	PROPN
ejpam-5159	83	6	,	,	PUNCT
ejpam-5159	83	7	17	17	NUM
ejpam-5159	83	8	(	(	PUNCT
ejpam-5159	83	9	2	2	NUM
ejpam-5159	83	10	)	)	PUNCT
ejpam-5159	83	11	(	(	PUNCT
ejpam-5159	83	12	2024	2024	NUM
ejpam-5159	83	13	)	)	PUNCT
ejpam-5159	83	14	,	,	PUNCT
ejpam-5159	83	15	1155	1155	NUM
ejpam-5159	83	16	-	-	SYM
ejpam-5159	83	17	1167	1167	NUM
ejpam-5159	83	18	1160	1160	NUM
ejpam-5159	83	19	surroundings	surrounding	NOUN
ejpam-5159	83	20	.	.	PUNCT
ejpam-5159	84	1	the	the	DET
ejpam-5159	84	2	procedure	procedure	NOUN
ejpam-5159	84	3	is	be	AUX
ejpam-5159	84	4	only	only	ADV
ejpam-5159	84	5	a	a	DET
ejpam-5159	84	6	slight	slight	ADJ
ejpam-5159	84	7	difference	difference	NOUN
ejpam-5159	84	8	,	,	PUNCT
ejpam-5159	84	9	since	since	SCONJ
ejpam-5159	84	10	one	one	PRON
ejpam-5159	84	11	must	must	AUX
ejpam-5159	84	12	take	take	VERB
ejpam-5159	84	13	into	into	ADP
ejpam-5159	84	14	account	account	NOUN
ejpam-5159	84	15	the	the	DET
ejpam-5159	84	16	impossibility	impossibility	NOUN
ejpam-5159	84	17	of	of	ADP
ejpam-5159	84	18	temperature	temperature	NOUN
ejpam-5159	84	19	differences	difference	NOUN
ejpam-5159	84	20	and	and	CCONJ
ejpam-5159	84	21	the	the	DET
ejpam-5159	84	22	way	way	NOUN
ejpam-5159	84	23	the	the	DET
ejpam-5159	84	24	sweater	sweater	NOUN
ejpam-5159	84	25	transfers	transfer	NOUN
ejpam-5159	84	26	in	in	ADP
ejpam-5159	84	27	the	the	DET
ejpam-5159	84	28	same	same	ADJ
ejpam-5159	84	29	way	way	NOUN
ejpam-5159	84	30	.	.	PUNCT
ejpam-5159	85	1	this	this	PRON
ejpam-5159	85	2	is	be	AUX
ejpam-5159	85	3	equivalent	equivalent	ADJ
ejpam-5159	85	4	to	to	ADP
ejpam-5159	85	5	confirming	confirm	VERB
ejpam-5159	85	6	that	that	SCONJ
ejpam-5159	85	7	the	the	DET
ejpam-5159	85	8	heat	heat	NOUN
ejpam-5159	85	9	transfer	transfer	NOUN
ejpam-5159	85	10	coefficient	coefficient	NOUN
ejpam-5159	85	11	between	between	ADP
ejpam-5159	85	12	the	the	DET
ejpam-5159	85	13	heat	heat	NOUN
ejpam-5159	85	14	sink	sink	NOUN
ejpam-5159	85	15	and	and	CCONJ
ejpam-5159	85	16	the	the	DET
ejpam-5159	85	17	temperature	temperature	NOUN
ejpam-5159	85	18	difference	difference	NOUN
ejpam-5159	85	19	is	be	AUX
ejpam-5159	85	20	a	a	DET
ejpam-5159	85	21	constant	constant	ADJ
ejpam-5159	85	22	.	.	PUNCT
ejpam-5159	86	1	we	we	PRON
ejpam-5159	86	2	define	define	VERB
ejpam-5159	86	3	the	the	DET
ejpam-5159	86	4	problem	problem	NOUN
ejpam-5159	86	5	of	of	ADP
ejpam-5159	86	6	newton	newton	PROPN
ejpam-5159	86	7	’s	’s	PART
ejpam-5159	86	8	cooling	cool	VERB
ejpam-5159	86	9	law	law	NOUN
ejpam-5159	86	10	states	state	VERB
ejpam-5159	86	11	that	that	SCONJ
ejpam-5159	86	12	the	the	DET
ejpam-5159	86	13	cooling	cooling	NOUN
ejpam-5159	86	14	by	by	ADP
ejpam-5159	86	15	equation	equation	NOUN
ejpam-5159	86	16	dt	dt	NOUN
ejpam-5159	86	17	dt	dt	X
ejpam-5159	86	18	=	=	PUNCT
ejpam-5159	86	19	−k	−k	PROPN
ejpam-5159	86	20	(	(	PUNCT
ejpam-5159	86	21	t	t	PROPN
ejpam-5159	86	22	(	(	PUNCT
ejpam-5159	86	23	t)−	t)−	PROPN
ejpam-5159	86	24	tc	tc	X
ejpam-5159	86	25	)	)	PUNCT
ejpam-5159	86	26	,	,	PUNCT
ejpam-5159	86	27	t	t	PROPN
ejpam-5159	86	28	(	(	PUNCT
ejpam-5159	86	29	0	0	NUM
ejpam-5159	86	30	)	)	PUNCT
ejpam-5159	86	31	=	=	SYM
ejpam-5159	86	32	t0	t0	PROPN
ejpam-5159	86	33	.	.	PUNCT
ejpam-5159	87	1	(	(	PUNCT
ejpam-5159	87	2	18	18	NUM
ejpam-5159	87	3	)	)	PUNCT
ejpam-5159	87	4	in	in	ADP
ejpam-5159	87	5	t	t	NOUN
ejpam-5159	87	6	=	=	SYM
ejpam-5159	87	7	0	0	NUM
ejpam-5159	87	8	we	we	PRON
ejpam-5159	87	9	have	have	VERB
ejpam-5159	87	10	the	the	DET
ejpam-5159	87	11	initial	initial	ADJ
ejpam-5159	87	12	temperature	temperature	NOUN
ejpam-5159	87	13	t0	t0	NOUN
ejpam-5159	87	14	,	,	PUNCT
ejpam-5159	87	15	and	and	CCONJ
ejpam-5159	87	16	we	we	PRON
ejpam-5159	87	17	obtain	obtain	VERB
ejpam-5159	87	18	the	the	DET
ejpam-5159	87	19	solution	solution	NOUN
ejpam-5159	87	20	:	:	PUNCT
ejpam-5159	87	21	t	t	PROPN
ejpam-5159	87	22	(	(	PUNCT
ejpam-5159	87	23	t	t	PROPN
ejpam-5159	87	24	)	)	PUNCT
ejpam-5159	87	25	=	=	SYM
ejpam-5159	88	1	tc	tc	X
ejpam-5159	88	2	+	+	CCONJ
ejpam-5159	88	3	(	(	PUNCT
ejpam-5159	88	4	t0	t0	PROPN
ejpam-5159	88	5	−	−	PROPN
ejpam-5159	88	6	tc	tc	NUM
ejpam-5159	88	7	)	)	PUNCT
ejpam-5159	88	8	e	e	NOUN
ejpam-5159	88	9	−kt	−kt	PROPN
ejpam-5159	88	10	.	.	PUNCT
ejpam-5159	89	1	(	(	PUNCT
ejpam-5159	89	2	19	19	NUM
ejpam-5159	89	3	)	)	PUNCT
ejpam-5159	89	4	the	the	DET
ejpam-5159	89	5	following	follow	VERB
ejpam-5159	89	6	figure	figure	NOUN
ejpam-5159	89	7	shows	show	VERB
ejpam-5159	89	8	this	this	DET
ejpam-5159	89	9	solution	solution	NOUN
ejpam-5159	89	10	:	:	PUNCT
ejpam-5159	89	11	utilizing	utilize	VERB
ejpam-5159	89	12	property	property	NOUN
ejpam-5159	89	13	(	(	PUNCT
ejpam-5159	89	14	6	6	NUM
ejpam-5159	89	15	)	)	PUNCT
ejpam-5159	89	16	of	of	ADP
ejpam-5159	89	17	theorem	theorem	NOUN
ejpam-5159	89	18	(	(	PUNCT
ejpam-5159	89	19	2	2	NUM
ejpam-5159	89	20	)	)	PUNCT
ejpam-5159	89	21	,	,	PUNCT
ejpam-5159	89	22	we	we	PRON
ejpam-5159	89	23	derive	derive	VERB
ejpam-5159	89	24	the	the	DET
ejpam-5159	89	25	novel	novel	ADJ
ejpam-5159	89	26	conformable	conformable	ADJ
ejpam-5159	89	27	fractional	fractional	ADJ
ejpam-5159	89	28	differential	differential	NOUN
ejpam-5159	89	29	formula	formula	NOUN
ejpam-5159	89	30	for	for	ADP
ejpam-5159	89	31	this	this	DET
ejpam-5159	89	32	particular	particular	ADJ
ejpam-5159	89	33	problem	problem	NOUN
ejpam-5159	89	34	:	:	PUNCT
ejpam-5159	89	35	dαt	dαt	NOUN
ejpam-5159	89	36	(	(	PUNCT
ejpam-5159	89	37	t	t	NOUN
ejpam-5159	89	38	)	)	PUNCT
ejpam-5159	89	39	dtα	dtα	NOUN
ejpam-5159	89	40	=	=	PUNCT
ejpam-5159	89	41	−k	−k	PROPN
ejpam-5159	89	42	(	(	PUNCT
ejpam-5159	89	43	t	t	PROPN
ejpam-5159	89	44	(	(	PUNCT
ejpam-5159	89	45	t)−	t)−	PROPN
ejpam-5159	89	46	tc	tc	X
ejpam-5159	89	47	)	)	PUNCT
ejpam-5159	89	48	,	,	PUNCT
ejpam-5159	89	49	(	(	PUNCT
ejpam-5159	89	50	20	20	NUM
ejpam-5159	89	51	)	)	PUNCT
ejpam-5159	89	52	so	so	ADV
ejpam-5159	89	53	,	,	PUNCT
ejpam-5159	89	54	e(α−1)tt	e(α−1)tt	NOUN
ejpam-5159	89	55	′(t	′(t	PROPN
ejpam-5159	89	56	)	)	PUNCT
ejpam-5159	89	57	=	=	SYM
ejpam-5159	90	1	−k	−k	PROPN
ejpam-5159	90	2	(	(	PUNCT
ejpam-5159	90	3	t	t	PROPN
ejpam-5159	90	4	(	(	PUNCT
ejpam-5159	90	5	t)−	t)−	PROPN
ejpam-5159	90	6	tc	tc	X
ejpam-5159	90	7	)	)	PUNCT
ejpam-5159	90	8	.	.	PUNCT
ejpam-5159	91	1	(	(	PUNCT
ejpam-5159	91	2	21	21	NUM
ejpam-5159	91	3	)	)	PUNCT
ejpam-5159	91	4	then	then	ADV
ejpam-5159	91	5	,	,	PUNCT
ejpam-5159	91	6	we	we	PRON
ejpam-5159	91	7	have	have	VERB
ejpam-5159	91	8	:	:	PUNCT
ejpam-5159	91	9	dt	dt	X
ejpam-5159	91	10	(	(	PUNCT
ejpam-5159	91	11	t	t	NOUN
ejpam-5159	91	12	)	)	PUNCT
ejpam-5159	92	1	dt	dt	NOUN
ejpam-5159	93	1	=	=	PUNCT
ejpam-5159	94	1	−e(1−α)tk	−e(1−α)tk	PROPN
ejpam-5159	94	2	(	(	PUNCT
ejpam-5159	94	3	t	t	PROPN
ejpam-5159	94	4	(	(	PUNCT
ejpam-5159	94	5	t)−	t)−	PROPN
ejpam-5159	94	6	tc	tc	X
ejpam-5159	94	7	)	)	PUNCT
ejpam-5159	94	8	,	,	PUNCT
ejpam-5159	94	9	(	(	PUNCT
ejpam-5159	94	10	22	22	NUM
ejpam-5159	94	11	)	)	PUNCT
ejpam-5159	94	12	a.	a.	NOUN
ejpam-5159	94	13	ait	ait	NOUN
ejpam-5159	94	14	brahim	brahim	PROPN
ejpam-5159	94	15	et	et	PROPN
ejpam-5159	94	16	al	al	PROPN
ejpam-5159	94	17	.	.	PUNCT
ejpam-5159	94	18	/	/	SYM
ejpam-5159	94	19	eur	eur	PROPN
ejpam-5159	94	20	.	.	PUNCT
ejpam-5159	95	1	j.	j.	PROPN
ejpam-5159	95	2	pure	pure	PROPN
ejpam-5159	95	3	appl	appl	PROPN
ejpam-5159	95	4	.	.	PROPN
ejpam-5159	95	5	math	math	PROPN
ejpam-5159	95	6	,	,	PUNCT
ejpam-5159	95	7	17	17	NUM
ejpam-5159	95	8	(	(	PUNCT
ejpam-5159	95	9	2	2	NUM
ejpam-5159	95	10	)	)	PUNCT
ejpam-5159	95	11	(	(	PUNCT
ejpam-5159	95	12	2024	2024	NUM
ejpam-5159	95	13	)	)	PUNCT
ejpam-5159	95	14	,	,	PUNCT
ejpam-5159	95	15	1155	1155	NUM
ejpam-5159	95	16	-	-	SYM
ejpam-5159	95	17	1167	1167	NUM
ejpam-5159	95	18	1161	1161	NUM
ejpam-5159	95	19	and	and	CCONJ
ejpam-5159	95	20	dt	dt	PROPN
ejpam-5159	95	21	(	(	PUNCT
ejpam-5159	95	22	t	t	PROPN
ejpam-5159	95	23	)	)	PUNCT
ejpam-5159	95	24	t	t	PROPN
ejpam-5159	95	25	(	(	PUNCT
ejpam-5159	95	26	t)−	t)−	PROPN
ejpam-5159	95	27	tc	tc	X
ejpam-5159	96	1	=	=	PUNCT
ejpam-5159	96	2	−e(1−α)tk	−e(1−α)tk	PROPN
ejpam-5159	96	3	.	.	PUNCT
ejpam-5159	97	1	(	(	PUNCT
ejpam-5159	97	2	23	23	NUM
ejpam-5159	97	3	)	)	PUNCT
ejpam-5159	97	4	therefore	therefore	ADV
ejpam-5159	97	5	,	,	PUNCT
ejpam-5159	97	6	ln	ln	X
ejpam-5159	97	7	(	(	PUNCT
ejpam-5159	97	8	t	t	PROPN
ejpam-5159	97	9	(	(	PUNCT
ejpam-5159	97	10	t)−	t)−	PROPN
ejpam-5159	97	11	tc	tc	NOUN
ejpam-5159	97	12	)	)	PUNCT
ejpam-5159	97	13	=	=	SYM
ejpam-5159	98	1	−ke(1−α)t	−ke(1−α)t	PROPN
ejpam-5159	98	2	1−	1−	NUM
ejpam-5159	98	3	α	α	NOUN
ejpam-5159	98	4	+	+	X
ejpam-5159	99	1	c	c	X
ejpam-5159	99	2	,	,	PUNCT
ejpam-5159	99	3	(	(	PUNCT
ejpam-5159	99	4	24	24	NUM
ejpam-5159	99	5	)	)	PUNCT
ejpam-5159	99	6	then	then	ADV
ejpam-5159	99	7	,	,	PUNCT
ejpam-5159	99	8	t	t	PROPN
ejpam-5159	99	9	(	(	PUNCT
ejpam-5159	99	10	t	t	PROPN
ejpam-5159	99	11	)	)	PUNCT
ejpam-5159	99	12	=	=	SYM
ejpam-5159	100	1	tc	tc	PROPN
ejpam-5159	100	2	+	+	NUM
ejpam-5159	100	3	ece	ece	PROPN
ejpam-5159	100	4	−ke(1−α)t	−ke(1−α)t	PROPN
ejpam-5159	100	5	1−α	1−α	NUM
ejpam-5159	100	6	,	,	PUNCT
ejpam-5159	100	7	(	(	PUNCT
ejpam-5159	100	8	25	25	NUM
ejpam-5159	100	9	)	)	PUNCT
ejpam-5159	100	10	with	with	ADP
ejpam-5159	100	11	the	the	DET
ejpam-5159	100	12	initial	initial	ADJ
ejpam-5159	100	13	condition	condition	NOUN
ejpam-5159	101	1	,	,	PUNCT
ejpam-5159	101	2	we	we	PRON
ejpam-5159	101	3	have	have	VERB
ejpam-5159	101	4	the	the	DET
ejpam-5159	101	5	final	final	ADJ
ejpam-5159	101	6	solution	solution	NOUN
ejpam-5159	101	7	:	:	PUNCT
ejpam-5159	101	8	t	t	PROPN
ejpam-5159	101	9	(	(	PUNCT
ejpam-5159	101	10	t	t	PROPN
ejpam-5159	101	11	)	)	PUNCT
ejpam-5159	101	12	=	=	SYM
ejpam-5159	102	1	tc	tc	X
ejpam-5159	102	2	+	+	CCONJ
ejpam-5159	102	3	(	(	PUNCT
ejpam-5159	102	4	t0	t0	PROPN
ejpam-5159	102	5	−	−	PROPN
ejpam-5159	102	6	tc	tc	NUM
ejpam-5159	102	7	)	)	PUNCT
ejpam-5159	102	8	e	e	NOUN
ejpam-5159	102	9	−ke(1−α)t	−ke(1−α)t	PROPN
ejpam-5159	102	10	1−α	1−α	NUM
ejpam-5159	102	11	.	.	PUNCT
ejpam-5159	103	1	(	(	PUNCT
ejpam-5159	103	2	26	26	NUM
ejpam-5159	103	3	)	)	PUNCT
ejpam-5159	103	4	the	the	DET
ejpam-5159	103	5	graphical	graphical	ADJ
ejpam-5159	103	6	representation	representation	NOUN
ejpam-5159	103	7	of	of	ADP
ejpam-5159	103	8	this	this	DET
ejpam-5159	103	9	solution	solution	NOUN
ejpam-5159	103	10	of	of	ADP
ejpam-5159	103	11	the	the	DET
ejpam-5159	103	12	new	new	ADJ
ejpam-5159	103	13	fractional	fractional	ADJ
ejpam-5159	103	14	derivative	derivative	NOUN
ejpam-5159	103	15	for	for	ADP
ejpam-5159	103	16	the	the	DET
ejpam-5159	103	17	values	value	NOUN
ejpam-5159	103	18	of	of	ADP
ejpam-5159	103	19	α	α	NOUN
ejpam-5159	103	20	=	=	SYM
ejpam-5159	103	21	0	0	PROPN
ejpam-5159	103	22	,	,	PUNCT
ejpam-5159	103	23	α	α	NOUN
ejpam-5159	103	24	=	=	NOUN
ejpam-5159	103	25	0.25	0.25	NUM
ejpam-5159	103	26	,	,	PUNCT
ejpam-5159	103	27	α	α	NOUN
ejpam-5159	103	28	=	=	SYM
ejpam-5159	103	29	0.5	0.5	NUM
ejpam-5159	103	30	,	,	PUNCT
ejpam-5159	103	31	and	and	CCONJ
ejpam-5159	103	32	α	α	X
ejpam-5159	103	33	=	=	SYM
ejpam-5159	103	34	0.75	0.75	NUM
ejpam-5159	103	35	is	be	AUX
ejpam-5159	103	36	compared	compare	VERB
ejpam-5159	103	37	with	with	ADP
ejpam-5159	103	38	results	result	NOUN
ejpam-5159	103	39	obtained	obtain	VERB
ejpam-5159	103	40	using	use	VERB
ejpam-5159	103	41	the	the	DET
ejpam-5159	103	42	factor	factor	NOUN
ejpam-5159	103	43	t	t	PROPN
ejpam-5159	103	44	(	(	PUNCT
ejpam-5159	103	45	t	t	PROPN
ejpam-5159	103	46	,	,	PUNCT
ejpam-5159	103	47	α	α	NOUN
ejpam-5159	103	48	)	)	PUNCT
ejpam-5159	103	49	=	=	SYM
ejpam-5159	103	50	e(α−1)t	e(α−1)t	PROPN
ejpam-5159	103	51	directly	directly	ADV
ejpam-5159	103	52	,	,	PUNCT
ejpam-5159	103	53	as	as	ADV
ejpam-5159	103	54	well	well	ADV
ejpam-5159	103	55	as	as	ADP
ejpam-5159	103	56	non	non	ADJ
ejpam-5159	103	57	-	-	ADJ
ejpam-5159	103	58	conformable	conformable	ADJ
ejpam-5159	103	59	fractional	fractional	ADJ
ejpam-5159	103	60	derivatives	derivative	NOUN
ejpam-5159	103	61	using	use	VERB
ejpam-5159	103	62	the	the	DET
ejpam-5159	103	63	factor	factor	NOUN
ejpam-5159	103	64	t	t	PROPN
ejpam-5159	103	65	(	(	PUNCT
ejpam-5159	103	66	t	t	PROPN
ejpam-5159	103	67	,	,	PUNCT
ejpam-5159	103	68	α	α	NOUN
ejpam-5159	103	69	)	)	PUNCT
ejpam-5159	103	70	=	=	SYM
ejpam-5159	104	1	t−α	t−α	PROPN
ejpam-5159	104	2	(	(	PUNCT
ejpam-5159	104	3	see	see	VERB
ejpam-5159	104	4	[	[	X
ejpam-5159	104	5	19	19	NUM
ejpam-5159	104	6	]	]	NUM
ejpam-5159	104	7	)	)	PUNCT
ejpam-5159	104	8	.	.	PUNCT
ejpam-5159	105	1	a.	a.	PROPN
ejpam-5159	105	2	ait	ait	PROPN
ejpam-5159	105	3	brahim	brahim	PROPN
ejpam-5159	105	4	et	et	PROPN
ejpam-5159	105	5	al	al	PROPN
ejpam-5159	105	6	.	.	PUNCT
ejpam-5159	105	7	/	/	SYM
ejpam-5159	105	8	eur	eur	PROPN
ejpam-5159	105	9	.	.	PUNCT
ejpam-5159	106	1	j.	j.	PROPN
ejpam-5159	106	2	pure	pure	PROPN
ejpam-5159	106	3	appl	appl	PROPN
ejpam-5159	106	4	.	.	PROPN
ejpam-5159	106	5	math	math	PROPN
ejpam-5159	106	6	,	,	PUNCT
ejpam-5159	106	7	17	17	NUM
ejpam-5159	106	8	(	(	PUNCT
ejpam-5159	106	9	2	2	NUM
ejpam-5159	106	10	)	)	PUNCT
ejpam-5159	106	11	(	(	PUNCT
ejpam-5159	106	12	2024	2024	NUM
ejpam-5159	106	13	)	)	PUNCT
ejpam-5159	106	14	,	,	PUNCT
ejpam-5159	106	15	1155	1155	NUM
ejpam-5159	106	16	-	-	SYM
ejpam-5159	106	17	1167	1167	NUM
ejpam-5159	106	18	1162	1162	NUM
ejpam-5159	106	19	3.3	3.3	NUM
ejpam-5159	106	20	.	.	PUNCT
ejpam-5159	107	1	fractional	fractional	ADJ
ejpam-5159	107	2	heat	heat	NOUN
ejpam-5159	107	3	equation	equation	NOUN
ejpam-5159	107	4	the	the	DET
ejpam-5159	107	5	heat	heat	NOUN
ejpam-5159	107	6	equation	equation	NOUN
ejpam-5159	107	7	is	be	AUX
ejpam-5159	107	8	a	a	DET
ejpam-5159	107	9	fundamental	fundamental	ADJ
ejpam-5159	107	10	concept	concept	NOUN
ejpam-5159	107	11	in	in	ADP
ejpam-5159	107	12	physics	physics	NOUN
ejpam-5159	107	13	and	and	CCONJ
ejpam-5159	107	14	thermal	thermal	ADJ
ejpam-5159	107	15	engineering	engineering	NOUN
ejpam-5159	107	16	.	.	PUNCT
ejpam-5159	108	1	it	it	PRON
ejpam-5159	108	2	describes	describe	VERB
ejpam-5159	108	3	how	how	SCONJ
ejpam-5159	108	4	the	the	DET
ejpam-5159	108	5	temperature	temperature	NOUN
ejpam-5159	108	6	in	in	ADP
ejpam-5159	108	7	a	a	DET
ejpam-5159	108	8	material	material	NOUN
ejpam-5159	108	9	varies	vary	VERB
ejpam-5159	108	10	over	over	ADP
ejpam-5159	108	11	time	time	NOUN
ejpam-5159	108	12	depending	depend	VERB
ejpam-5159	108	13	on	on	ADP
ejpam-5159	108	14	the	the	DET
ejpam-5159	108	15	heat	heat	NOUN
ejpam-5159	108	16	applied	apply	VERB
ejpam-5159	108	17	to	to	ADP
ejpam-5159	108	18	it	it	PRON
ejpam-5159	108	19	and	and	CCONJ
ejpam-5159	108	20	its	its	PRON
ejpam-5159	108	21	thermal	thermal	ADJ
ejpam-5159	108	22	properties	property	NOUN
ejpam-5159	108	23	.	.	PUNCT
ejpam-5159	109	1	this	this	DET
ejpam-5159	109	2	equation	equation	NOUN
ejpam-5159	109	3	is	be	AUX
ejpam-5159	109	4	widely	widely	ADV
ejpam-5159	109	5	used	use	VERB
ejpam-5159	109	6	in	in	ADP
ejpam-5159	109	7	many	many	ADJ
ejpam-5159	109	8	fields	field	NOUN
ejpam-5159	109	9	such	such	ADJ
ejpam-5159	109	10	as	as	ADP
ejpam-5159	109	11	thermodynamics	thermodynamic	NOUN
ejpam-5159	109	12	,	,	PUNCT
ejpam-5159	109	13	geophysics	geophysic	NOUN
ejpam-5159	109	14	,	,	PUNCT
ejpam-5159	109	15	meteorology	meteorology	NOUN
ejpam-5159	109	16	,	,	PUNCT
ejpam-5159	109	17	materials	material	NOUN
ejpam-5159	109	18	engineering	engineering	NOUN
ejpam-5159	109	19	,	,	PUNCT
ejpam-5159	109	20	and	and	CCONJ
ejpam-5159	109	21	many	many	ADJ
ejpam-5159	109	22	others	other	NOUN
ejpam-5159	109	23	.	.	PUNCT
ejpam-5159	110	1	solving	solve	VERB
ejpam-5159	110	2	the	the	DET
ejpam-5159	110	3	heat	heat	NOUN
ejpam-5159	110	4	equation	equation	NOUN
ejpam-5159	110	5	makes	make	VERB
ejpam-5159	110	6	it	it	PRON
ejpam-5159	110	7	possible	possible	ADJ
ejpam-5159	110	8	to	to	PART
ejpam-5159	110	9	predict	predict	VERB
ejpam-5159	110	10	the	the	DET
ejpam-5159	110	11	temporal	temporal	ADJ
ejpam-5159	110	12	evolution	evolution	NOUN
ejpam-5159	110	13	of	of	ADP
ejpam-5159	110	14	the	the	DET
ejpam-5159	110	15	temperature	temperature	NOUN
ejpam-5159	110	16	in	in	ADP
ejpam-5159	110	17	a	a	DET
ejpam-5159	110	18	given	give	VERB
ejpam-5159	110	19	material	material	NOUN
ejpam-5159	110	20	.	.	PUNCT
ejpam-5159	111	1	solutions	solution	NOUN
ejpam-5159	111	2	can	can	AUX
ejpam-5159	111	3	be	be	AUX
ejpam-5159	111	4	obtained	obtain	VERB
ejpam-5159	111	5	analytically	analytically	ADV
ejpam-5159	111	6	in	in	ADP
ejpam-5159	111	7	some	some	DET
ejpam-5159	111	8	simple	simple	ADJ
ejpam-5159	111	9	cases	case	NOUN
ejpam-5159	111	10	,	,	PUNCT
ejpam-5159	111	11	but	but	CCONJ
ejpam-5159	111	12	in	in	ADP
ejpam-5159	111	13	most	most	ADJ
ejpam-5159	111	14	cases	case	NOUN
ejpam-5159	111	15	numerical	numerical	ADJ
ejpam-5159	111	16	methods	method	NOUN
ejpam-5159	111	17	are	be	AUX
ejpam-5159	111	18	required	require	VERB
ejpam-5159	111	19	to	to	PART
ejpam-5159	111	20	obtain	obtain	VERB
ejpam-5159	111	21	accurate	accurate	ADJ
ejpam-5159	111	22	solutions	solution	NOUN
ejpam-5159	111	23	.	.	PUNCT
ejpam-5159	112	1	techniques	technique	NOUN
ejpam-5159	112	2	such	such	ADJ
ejpam-5159	112	3	as	as	ADP
ejpam-5159	112	4	the	the	DET
ejpam-5159	112	5	finite	finite	ADJ
ejpam-5159	112	6	difference	difference	NOUN
ejpam-5159	112	7	method	method	NOUN
ejpam-5159	112	8	,	,	PUNCT
ejpam-5159	112	9	finite	finite	ADJ
ejpam-5159	112	10	element	element	NOUN
ejpam-5159	112	11	method	method	NOUN
ejpam-5159	112	12	or	or	CCONJ
ejpam-5159	112	13	finite	finite	ADJ
ejpam-5159	112	14	volume	volume	NOUN
ejpam-5159	112	15	method	method	NOUN
ejpam-5159	112	16	are	be	AUX
ejpam-5159	112	17	commonly	commonly	ADV
ejpam-5159	112	18	used	use	VERB
ejpam-5159	112	19	for	for	ADP
ejpam-5159	112	20	this	this	DET
ejpam-5159	112	21	purpose	purpose	NOUN
ejpam-5159	112	22	.	.	PUNCT
ejpam-5159	113	1	the	the	DET
ejpam-5159	113	2	heat	heat	NOUN
ejpam-5159	113	3	equation	equation	NOUN
ejpam-5159	113	4	has	have	VERB
ejpam-5159	113	5	many	many	ADJ
ejpam-5159	113	6	practical	practical	ADJ
ejpam-5159	113	7	applications	application	NOUN
ejpam-5159	113	8	.	.	PUNCT
ejpam-5159	114	1	for	for	ADP
ejpam-5159	114	2	example	example	NOUN
ejpam-5159	114	3	:	:	PUNCT
ejpam-5159	114	4	•	•	NUM
ejpam-5159	114	5	modeling	model	VERB
ejpam-5159	114	6	heat	heat	NOUN
ejpam-5159	114	7	transfers	transfer	NOUN
ejpam-5159	114	8	in	in	ADP
ejpam-5159	114	9	buildings	building	NOUN
ejpam-5159	114	10	to	to	PART
ejpam-5159	114	11	improve	improve	VERB
ejpam-5159	114	12	energy	energy	NOUN
ejpam-5159	114	13	efficiency	efficiency	NOUN
ejpam-5159	114	14	.	.	PUNCT
ejpam-5159	115	1	prediction	prediction	NOUN
ejpam-5159	115	2	of	of	ADP
ejpam-5159	115	3	temperature	temperature	NOUN
ejpam-5159	115	4	distribution	distribution	NOUN
ejpam-5159	115	5	in	in	ADP
ejpam-5159	115	6	materials	material	NOUN
ejpam-5159	115	7	during	during	ADP
ejpam-5159	115	8	manufacturing	manufacturing	NOUN
ejpam-5159	115	9	processes	process	NOUN
ejpam-5159	115	10	.	.	PUNCT
ejpam-5159	116	1	•	•	NUM
ejpam-5159	116	2	study	study	NOUN
ejpam-5159	116	3	of	of	ADP
ejpam-5159	116	4	heat	heat	NOUN
ejpam-5159	116	5	propagation	propagation	NOUN
ejpam-5159	116	6	in	in	ADP
ejpam-5159	116	7	soils	soil	NOUN
ejpam-5159	116	8	for	for	ADP
ejpam-5159	116	9	geothermal	geothermal	ADJ
ejpam-5159	116	10	energy	energy	NOUN
ejpam-5159	116	11	.	.	PUNCT
ejpam-5159	117	1	understanding	understanding	NOUN
ejpam-5159	117	2	of	of	ADP
ejpam-5159	117	3	weather	weather	NOUN
ejpam-5159	117	4	phenomena	phenomenon	NOUN
ejpam-5159	117	5	such	such	ADJ
ejpam-5159	117	6	as	as	ADP
ejpam-5159	117	7	cloud	cloud	ADJ
ejpam-5159	117	8	formation	formation	NOUN
ejpam-5159	117	9	and	and	CCONJ
ejpam-5159	117	10	ocean	ocean	NOUN
ejpam-5159	117	11	currents	current	NOUN
ejpam-5159	117	12	.	.	PUNCT
ejpam-5159	118	1	the	the	DET
ejpam-5159	118	2	heat	heat	NOUN
ejpam-5159	118	3	equation	equation	NOUN
ejpam-5159	118	4	is	be	AUX
ejpam-5159	118	5	an	an	DET
ejpam-5159	118	6	essential	essential	ADJ
ejpam-5159	118	7	tool	tool	NOUN
ejpam-5159	118	8	for	for	ADP
ejpam-5159	118	9	understanding	understanding	NOUN
ejpam-5159	118	10	and	and	CCONJ
ejpam-5159	118	11	predicting	predict	VERB
ejpam-5159	118	12	thermal	thermal	ADJ
ejpam-5159	118	13	phenomena	phenomenon	NOUN
ejpam-5159	118	14	in	in	ADP
ejpam-5159	118	15	a	a	DET
ejpam-5159	118	16	wide	wide	ADJ
ejpam-5159	118	17	variety	variety	NOUN
ejpam-5159	118	18	of	of	ADP
ejpam-5159	118	19	scientific	scientific	ADJ
ejpam-5159	118	20	fields	field	NOUN
ejpam-5159	118	21	and	and	CCONJ
ejpam-5159	118	22	technological	technological	ADJ
ejpam-5159	118	23	applications	application	NOUN
ejpam-5159	118	24	.	.	PUNCT
ejpam-5159	119	1	its	its	PRON
ejpam-5159	119	2	simple	simple	ADJ
ejpam-5159	119	3	but	but	CCONJ
ejpam-5159	119	4	powerful	powerful	ADJ
ejpam-5159	119	5	mathematical	mathematical	ADJ
ejpam-5159	119	6	formulation	formulation	NOUN
ejpam-5159	119	7	makes	make	VERB
ejpam-5159	119	8	it	it	PRON
ejpam-5159	119	9	a	a	DET
ejpam-5159	119	10	pillar	pillar	NOUN
ejpam-5159	119	11	of	of	ADP
ejpam-5159	119	12	thermal	thermal	ADJ
ejpam-5159	119	13	modeling	modeling	NOUN
ejpam-5159	119	14	and	and	CCONJ
ejpam-5159	119	15	contributes	contribute	VERB
ejpam-5159	119	16	to	to	ADP
ejpam-5159	119	17	many	many	ADJ
ejpam-5159	119	18	advances	advance	NOUN
ejpam-5159	119	19	in	in	ADP
ejpam-5159	119	20	science	science	NOUN
ejpam-5159	119	21	and	and	CCONJ
ejpam-5159	119	22	engineering	engineering	NOUN
ejpam-5159	119	23	.	.	PUNCT
ejpam-5159	120	1	then	then	ADV
ejpam-5159	120	2	form	form	NOUN
ejpam-5159	120	3	of	of	ADP
ejpam-5159	120	4	fractional	fractional	ADJ
ejpam-5159	120	5	heat	heat	NOUN
ejpam-5159	120	6	equation	equation	NOUN
ejpam-5159	120	7	represented	represent	VERB
ejpam-5159	120	8	by	by	ADP
ejpam-5159	120	9	:	:	PUNCT
ejpam-5159	120	10	∂α	∂α	PROPN
ejpam-5159	120	11	∂tα	∂tα	PROPN
ejpam-5159	120	12	∂αz(x	∂αz(x	PROPN
ejpam-5159	120	13	,	,	PUNCT
ejpam-5159	120	14	t	t	PROPN
ejpam-5159	120	15	)	)	PUNCT
ejpam-5159	120	16	∂tα	∂tα	PROPN
ejpam-5159	120	17	=	=	SYM
ejpam-5159	120	18	∂2z(x	∂2z(x	NUM
ejpam-5159	120	19	,	,	PUNCT
ejpam-5159	120	20	t	t	PROPN
ejpam-5159	120	21	)	)	PUNCT
ejpam-5159	120	22	∂x2	∂x2	NOUN
ejpam-5159	120	23	,	,	PUNCT
ejpam-5159	120	24	(	(	PUNCT
ejpam-5159	120	25	27	27	NUM
ejpam-5159	120	26	)	)	PUNCT
ejpam-5159	120	27	z(0	z(0	PROPN
ejpam-5159	120	28	,	,	PUNCT
ejpam-5159	120	29	t	t	PROPN
ejpam-5159	120	30	)	)	PUNCT
ejpam-5159	120	31	=	=	SYM
ejpam-5159	120	32	0	0	NUM
ejpam-5159	120	33	,	,	PUNCT
ejpam-5159	120	34	t	t	X
ejpam-5159	120	35	>	>	X
ejpam-5159	120	36	0	0	NUM
ejpam-5159	120	37	,	,	PUNCT
ejpam-5159	120	38	(	(	PUNCT
ejpam-5159	120	39	28	28	NUM
ejpam-5159	120	40	)	)	PUNCT
ejpam-5159	120	41	z(1	z(1	PROPN
ejpam-5159	120	42	,	,	PUNCT
ejpam-5159	120	43	t	t	PROPN
ejpam-5159	120	44	)	)	PUNCT
ejpam-5159	120	45	=	=	SYM
ejpam-5159	120	46	0	0	NUM
ejpam-5159	120	47	,	,	PUNCT
ejpam-5159	120	48	t	t	X
ejpam-5159	120	49	>	>	X
ejpam-5159	120	50	0	0	NUM
ejpam-5159	120	51	,	,	PUNCT
ejpam-5159	120	52	(	(	PUNCT
ejpam-5159	120	53	29	29	NUM
ejpam-5159	120	54	)	)	PUNCT
ejpam-5159	120	55	∂z(x	∂z(x	PROPN
ejpam-5159	120	56	,	,	PUNCT
ejpam-5159	120	57	0	0	NUM
ejpam-5159	120	58	)	)	PUNCT
ejpam-5159	120	59	∂t	∂t	PROPN
ejpam-5159	120	60	=	=	SYM
ejpam-5159	120	61	0	0	PROPN
ejpam-5159	120	62	,	,	PUNCT
ejpam-5159	120	63	(	(	PUNCT
ejpam-5159	120	64	30	30	NUM
ejpam-5159	120	65	)	)	PUNCT
ejpam-5159	120	66	z(x	z(x	NUM
ejpam-5159	120	67	,	,	PUNCT
ejpam-5159	120	68	0	0	NUM
ejpam-5159	120	69	)	)	PUNCT
ejpam-5159	120	70	=	=	SYM
ejpam-5159	120	71	f	f	X
ejpam-5159	120	72	(	(	PUNCT
ejpam-5159	120	73	x	x	NOUN
ejpam-5159	120	74	)	)	PUNCT
ejpam-5159	120	75	,	,	PUNCT
ejpam-5159	120	76	0	0	PUNCT
ejpam-5159	120	77	<	<	X
ejpam-5159	120	78	x	x	X
ejpam-5159	120	79	<	<	X
ejpam-5159	120	80	1	1	NUM
ejpam-5159	120	81	.	.	PUNCT
ejpam-5159	120	82	(	(	PUNCT
ejpam-5159	120	83	31	31	NUM
ejpam-5159	120	84	)	)	PUNCT
ejpam-5159	120	85	consider	consider	VERB
ejpam-5159	120	86	the	the	DET
ejpam-5159	120	87	conformable	conformable	ADJ
ejpam-5159	120	88	fractional	fractional	ADJ
ejpam-5159	120	89	linear	linear	ADJ
ejpam-5159	120	90	differential	differential	NOUN
ejpam-5159	120	91	equations	equation	NOUN
ejpam-5159	120	92	with	with	ADP
ejpam-5159	120	93	constant	constant	ADJ
ejpam-5159	120	94	coefficients	coefficient	NOUN
ejpam-5159	120	95	using	use	VERB
ejpam-5159	120	96	the	the	DET
ejpam-5159	120	97	findings	finding	NOUN
ejpam-5159	120	98	presented	present	VERB
ejpam-5159	120	99	in	in	ADP
ejpam-5159	120	100	[	[	X
ejpam-5159	120	101	20	20	NUM
ejpam-5159	120	102	,	,	PUNCT
ejpam-5159	120	103	23	23	NUM
ejpam-5159	120	104	]	]	PUNCT
ejpam-5159	120	105	:	:	PUNCT
ejpam-5159	120	106	dα	dα	PROPN
ejpam-5159	120	107	dyα	dyα	PROPN
ejpam-5159	120	108	dαz	dαz	PROPN
ejpam-5159	120	109	dyα	dyα	PROPN
ejpam-5159	120	110	±	±	PROPN
ejpam-5159	120	111	µ2z	µ2z	PROPN
ejpam-5159	120	112	=	=	SYM
ejpam-5159	120	113	0	0	PROPN
ejpam-5159	120	114	.	.	PUNCT
ejpam-5159	121	1	(	(	PUNCT
ejpam-5159	121	2	32	32	NUM
ejpam-5159	121	3	)	)	PUNCT
ejpam-5159	121	4	we	we	PRON
ejpam-5159	121	5	use	use	VERB
ejpam-5159	121	6	the	the	DET
ejpam-5159	121	7	equation	equation	NOUN
ejpam-5159	121	8	r2	r2	PROPN
ejpam-5159	121	9	±	±	PROPN
ejpam-5159	121	10	µ2	µ2	PROPN
ejpam-5159	121	11	=	=	PROPN
ejpam-5159	121	12	0	0	NUM
ejpam-5159	121	13	,	,	PUNCT
ejpam-5159	121	14	and	and	CCONJ
ejpam-5159	121	15	associate	associate	VERB
ejpam-5159	121	16	to	to	ADP
ejpam-5159	121	17	this	this	DET
ejpam-5159	121	18	equation	equation	NOUN
ejpam-5159	121	19	,	,	PUNCT
ejpam-5159	121	20	then	then	ADV
ejpam-5159	121	21	we	we	PRON
ejpam-5159	121	22	have	have	VERB
ejpam-5159	121	23	r	r	NOUN
ejpam-5159	121	24	=	=	SYM
ejpam-5159	121	25	±ν	±ν	PROPN
ejpam-5159	121	26	,	,	PUNCT
ejpam-5159	121	27	or	or	CCONJ
ejpam-5159	121	28	r	r	NOUN
ejpam-5159	121	29	=	=	PUNCT
ejpam-5159	121	30	±µi	±µi	NOUN
ejpam-5159	121	31	.	.	PUNCT
ejpam-5159	122	1	furthermore	furthermore	ADV
ejpam-5159	122	2	,	,	PUNCT
ejpam-5159	122	3	according	accord	VERB
ejpam-5159	122	4	to	to	ADP
ejpam-5159	122	5	theorem	theorem	NOUN
ejpam-5159	122	6	(	(	PUNCT
ejpam-5159	122	7	3	3	NUM
ejpam-5159	122	8	)	)	PUNCT
ejpam-5159	122	9	,	,	PUNCT
ejpam-5159	122	10	we	we	PRON
ejpam-5159	122	11	establish	establish	VERB
ejpam-5159	122	12	that	that	SCONJ
ejpam-5159	122	13	z	z	NOUN
ejpam-5159	122	14	=	=	PUNCT
ejpam-5159	122	15	e∓	e∓	PROPN
ejpam-5159	122	16	µ	µ	X
ejpam-5159	122	17	1−α	1−α	NUM
ejpam-5159	122	18	e(1−α)t	e(1−α)t	NOUN
ejpam-5159	122	19	,	,	PUNCT
ejpam-5159	122	20	(	(	PUNCT
ejpam-5159	122	21	33	33	NUM
ejpam-5159	122	22	)	)	PUNCT
ejpam-5159	122	23	constitute	constitute	VERB
ejpam-5159	122	24	two	two	NUM
ejpam-5159	122	25	distinct	distinct	ADJ
ejpam-5159	122	26	solutions	solution	NOUN
ejpam-5159	122	27	of	of	ADP
ejpam-5159	122	28	the	the	DET
ejpam-5159	122	29	equation	equation	NOUN
ejpam-5159	122	30	.	.	PUNCT
ejpam-5159	123	1	also	also	ADV
ejpam-5159	123	2	,	,	PUNCT
ejpam-5159	123	3	in	in	ADP
ejpam-5159	123	4	the	the	DET
ejpam-5159	123	5	second	second	ADJ
ejpam-5159	123	6	case	case	NOUN
ejpam-5159	123	7	we	we	PRON
ejpam-5159	123	8	obtain	obtain	VERB
ejpam-5159	123	9	by	by	ADP
ejpam-5159	123	10	properties	property	NOUN
ejpam-5159	123	11	(	(	PUNCT
ejpam-5159	123	12	2	2	NUM
ejpam-5159	123	13	)	)	PUNCT
ejpam-5159	123	14	and	and	CCONJ
ejpam-5159	123	15	(	(	PUNCT
ejpam-5159	123	16	3	3	X
ejpam-5159	123	17	)	)	PUNCT
ejpam-5159	123	18	above	above	ADV
ejpam-5159	123	19	(	(	PUNCT
ejpam-5159	123	20	see	see	VERB
ejpam-5159	123	21	theorem(3	theorem(3	NOUN
ejpam-5159	123	22	)	)	PUNCT
ejpam-5159	123	23	)	)	PUNCT
ejpam-5159	123	24	,	,	PUNCT
ejpam-5159	123	25	that	that	SCONJ
ejpam-5159	123	26	z1	z1	NOUN
ejpam-5159	123	27	=	=	SYM
ejpam-5159	123	28	sin	sin	NOUN
ejpam-5159	123	29	(	(	PUNCT
ejpam-5159	123	30	µ	µ	X
ejpam-5159	123	31	1−	1−	NUM
ejpam-5159	123	32	α	α	NOUN
ejpam-5159	123	33	e(1−α)t	e(1−α)t	NOUN
ejpam-5159	123	34	)	)	PUNCT
ejpam-5159	123	35	and	and	CCONJ
ejpam-5159	123	36	z2	z2	PROPN
ejpam-5159	123	37	=	=	SYM
ejpam-5159	123	38	cos	cos	PROPN
ejpam-5159	123	39	(	(	PUNCT
ejpam-5159	123	40	µ	µ	PROPN
ejpam-5159	123	41	1−	1−	NUM
ejpam-5159	123	42	α	α	NOUN
ejpam-5159	123	43	e(1−α)t	e(1−α)t	NOUN
ejpam-5159	123	44	)	)	PUNCT
ejpam-5159	123	45	.	.	PUNCT
ejpam-5159	124	1	(	(	PUNCT
ejpam-5159	124	2	34	34	NUM
ejpam-5159	124	3	)	)	PUNCT
ejpam-5159	124	4	a.	a.	NOUN
ejpam-5159	124	5	ait	ait	NOUN
ejpam-5159	124	6	brahim	brahim	PROPN
ejpam-5159	124	7	et	et	PROPN
ejpam-5159	124	8	al	al	PROPN
ejpam-5159	124	9	.	.	PUNCT
ejpam-5159	124	10	/	/	SYM
ejpam-5159	124	11	eur	eur	PROPN
ejpam-5159	124	12	.	.	PUNCT
ejpam-5159	125	1	j.	j.	PROPN
ejpam-5159	125	2	pure	pure	PROPN
ejpam-5159	125	3	appl	appl	PROPN
ejpam-5159	125	4	.	.	PROPN
ejpam-5159	125	5	math	math	PROPN
ejpam-5159	125	6	,	,	PUNCT
ejpam-5159	125	7	17	17	NUM
ejpam-5159	125	8	(	(	PUNCT
ejpam-5159	125	9	2	2	NUM
ejpam-5159	125	10	)	)	PUNCT
ejpam-5159	125	11	(	(	PUNCT
ejpam-5159	125	12	2024	2024	NUM
ejpam-5159	125	13	)	)	PUNCT
ejpam-5159	125	14	,	,	PUNCT
ejpam-5159	125	15	1155	1155	NUM
ejpam-5159	125	16	-	-	SYM
ejpam-5159	125	17	1167	1167	NUM
ejpam-5159	125	18	1163	1163	NUM
ejpam-5159	125	19	a.	a.	NOUN
ejpam-5159	125	20	ait	ait	NOUN
ejpam-5159	125	21	brahim	brahim	PROPN
ejpam-5159	125	22	et	et	PROPN
ejpam-5159	125	23	al	al	PROPN
ejpam-5159	125	24	.	.	PUNCT
ejpam-5159	125	25	/	/	SYM
ejpam-5159	125	26	eur	eur	PROPN
ejpam-5159	125	27	.	.	PUNCT
ejpam-5159	126	1	j.	j.	PROPN
ejpam-5159	126	2	pure	pure	PROPN
ejpam-5159	126	3	appl	appl	PROPN
ejpam-5159	126	4	.	.	PROPN
ejpam-5159	126	5	math	math	PROPN
ejpam-5159	126	6	,	,	PUNCT
ejpam-5159	126	7	17	17	NUM
ejpam-5159	126	8	(	(	PUNCT
ejpam-5159	126	9	2	2	NUM
ejpam-5159	126	10	)	)	PUNCT
ejpam-5159	126	11	(	(	PUNCT
ejpam-5159	126	12	2024	2024	NUM
ejpam-5159	126	13	)	)	PUNCT
ejpam-5159	126	14	,	,	PUNCT
ejpam-5159	126	15	1155	1155	NUM
ejpam-5159	126	16	-	-	SYM
ejpam-5159	126	17	1167	1167	NUM
ejpam-5159	126	18	1164	1164	NUM
ejpam-5159	126	19	let	let	VERB
ejpam-5159	126	20	z1	z1	PROPN
ejpam-5159	126	21	=	=	SYM
ejpam-5159	126	22	sin	sin	NOUN
ejpam-5159	126	23	(	(	PUNCT
ejpam-5159	126	24	µ	µ	PROPN
ejpam-5159	126	25	1−αe	1−αe	PROPN
ejpam-5159	126	26	(	(	PUNCT
ejpam-5159	126	27	1−α)t	1−α)t	NUM
ejpam-5159	126	28	)	)	PUNCT
ejpam-5159	126	29	and	and	CCONJ
ejpam-5159	126	30	z2	z2	PROPN
ejpam-5159	126	31	=	=	SYM
ejpam-5159	126	32	cos	cos	PROPN
ejpam-5159	126	33	(	(	PUNCT
ejpam-5159	126	34	µ	µ	PROPN
ejpam-5159	126	35	1−αe	1−αe	PROPN
ejpam-5159	126	36	(	(	PUNCT
ejpam-5159	126	37	1−α)t	1−α)t	NUM
ejpam-5159	126	38	)	)	PUNCT
ejpam-5159	126	39	are	be	AUX
ejpam-5159	126	40	two	two	NUM
ejpam-5159	126	41	independent	independent	ADJ
ejpam-5159	126	42	solutions	solution	NOUN
ejpam-5159	126	43	,	,	PUNCT
ejpam-5159	126	44	we	we	PRON
ejpam-5159	126	45	use	use	VERB
ejpam-5159	126	46	the	the	DET
ejpam-5159	126	47	new	new	ADJ
ejpam-5159	126	48	fractional	fractional	NOUN
ejpam-5159	127	1	[	[	X
ejpam-5159	127	2	5	5	NUM
ejpam-5159	127	3	]	]	PUNCT
ejpam-5159	127	4	,	,	PUNCT
ejpam-5159	127	5	for	for	ADP
ejpam-5159	127	6	different	different	ADJ
ejpam-5159	127	7	value	value	NOUN
ejpam-5159	127	8	of	of	ADP
ejpam-5159	127	9	α	α	NOUN
ejpam-5159	127	10	:	:	PUNCT
ejpam-5159	127	11	α	α	X
ejpam-5159	127	12	=	=	SYM
ejpam-5159	127	13	0	0	PROPN
ejpam-5159	127	14	,	,	PUNCT
ejpam-5159	127	15	α	α	NOUN
ejpam-5159	127	16	=	=	NOUN
ejpam-5159	127	17	0.25	0.25	NUM
ejpam-5159	127	18	,	,	PUNCT
ejpam-5159	127	19	α	α	NOUN
ejpam-5159	127	20	=	=	SYM
ejpam-5159	127	21	0.5	0.5	NUM
ejpam-5159	127	22	,	,	PUNCT
ejpam-5159	127	23	and	and	CCONJ
ejpam-5159	127	24	α	α	NOUN
ejpam-5159	127	25	=	=	NOUN
ejpam-5159	127	26	0.75	0.75	NUM
ejpam-5159	127	27	,	,	PUNCT
ejpam-5159	127	28	and	and	CCONJ
ejpam-5159	127	29	we	we	PRON
ejpam-5159	127	30	compare	compare	VERB
ejpam-5159	127	31	with	with	ADP
ejpam-5159	127	32	ordinary	ordinary	ADJ
ejpam-5159	127	33	derivative	derivative	ADJ
ejpam-5159	127	34	and	and	CCONJ
ejpam-5159	127	35	khalil	khalil	PROPN
ejpam-5159	127	36	conformable	conformable	ADJ
ejpam-5159	127	37	fractional	fractional	NOUN
ejpam-5159	128	1	[	[	X
ejpam-5159	128	2	3	3	NUM
ejpam-5159	128	3	]	]	PUNCT
ejpam-5159	128	4	.	.	PUNCT
ejpam-5159	129	1	also	also	ADV
ejpam-5159	129	2	,	,	PUNCT
ejpam-5159	129	3	we	we	PRON
ejpam-5159	129	4	have	have	VERB
ejpam-5159	129	5	the	the	DET
ejpam-5159	129	6	form	form	NOUN
ejpam-5159	129	7	of	of	ADP
ejpam-5159	129	8	new	new	ADJ
ejpam-5159	129	9	fractional	fractional	ADJ
ejpam-5159	129	10	differential	differential	ADJ
ejpam-5159	129	11	formula	formula	NOUN
ejpam-5159	129	12	of	of	ADP
ejpam-5159	129	13	order	order	NOUN
ejpam-5159	129	14	2α	2α	NOUN
ejpam-5159	129	15	with	with	ADP
ejpam-5159	129	16	constant	constant	ADJ
ejpam-5159	129	17	coefficients	coefficient	NOUN
ejpam-5159	129	18	represented	represent	VERB
ejpam-5159	129	19	by	by	ADP
ejpam-5159	129	20	dα	dα	DET
ejpam-5159	129	21	dxα	dxα	ADJ
ejpam-5159	129	22	dαz	dαz	X
ejpam-5159	129	23	dxα	dxα	NOUN
ejpam-5159	129	24	+	+	CCONJ
ejpam-5159	129	25	a	a	DET
ejpam-5159	129	26	dαz	dαz	X
ejpam-5159	129	27	dxα	dxα	ADJ
ejpam-5159	129	28	+	+	CCONJ
ejpam-5159	129	29	bz	bz	PROPN
ejpam-5159	129	30	=	=	SYM
ejpam-5159	129	31	h(x	h(x	PROPN
ejpam-5159	129	32	)	)	PUNCT
ejpam-5159	129	33	.	.	PUNCT
ejpam-5159	130	1	(	(	PUNCT
ejpam-5159	130	2	35	35	NUM
ejpam-5159	130	3	)	)	PUNCT
ejpam-5159	130	4	can	can	AUX
ejpam-5159	130	5	be	be	AUX
ejpam-5159	130	6	write	write	VERB
ejpam-5159	130	7	dα	dα	NOUN
ejpam-5159	130	8	for	for	ADP
ejpam-5159	130	9	dα	dα	X
ejpam-5159	130	10	dxα	dxα	NOUN
ejpam-5159	130	11	,	,	PUNCT
ejpam-5159	130	12	then	then	ADV
ejpam-5159	130	13	we	we	PRON
ejpam-5159	130	14	have	have	VERB
ejpam-5159	130	15	:	:	PUNCT
ejpam-5159	130	16	dα	dα	PRON
ejpam-5159	130	17	(	(	PUNCT
ejpam-5159	130	18	dαz	dαz	PROPN
ejpam-5159	130	19	)	)	PUNCT
ejpam-5159	131	1	+	+	CCONJ
ejpam-5159	131	2	adαz	adαz	ADJ
ejpam-5159	131	3	+	+	CCONJ
ejpam-5159	131	4	bz	bz	PROPN
ejpam-5159	131	5	=	=	SYM
ejpam-5159	131	6	h(x	h(x	PROPN
ejpam-5159	131	7	)	)	PUNCT
ejpam-5159	131	8	.	.	PUNCT
ejpam-5159	132	1	(	(	PUNCT
ejpam-5159	132	2	36	36	NUM
ejpam-5159	132	3	)	)	PUNCT
ejpam-5159	132	4	to	to	PART
ejpam-5159	132	5	obtain	obtain	VERB
ejpam-5159	132	6	the	the	DET
ejpam-5159	132	7	solution	solution	NOUN
ejpam-5159	132	8	,	,	PUNCT
ejpam-5159	132	9	we	we	PRON
ejpam-5159	132	10	consider	consider	VERB
ejpam-5159	132	11	the	the	DET
ejpam-5159	132	12	equation	equation	NOUN
ejpam-5159	132	13	r2+ar+	r2+ar+	PUNCT
ejpam-5159	132	14	b	b	NOUN
ejpam-5159	132	15	=	=	SYM
ejpam-5159	132	16	0	0	NOUN
ejpam-5159	132	17	.	.	PUNCT
ejpam-5159	132	18	utilizing	utilize	VERB
ejpam-5159	132	19	the	the	DET
ejpam-5159	132	20	properties	property	NOUN
ejpam-5159	132	21	of	of	ADP
ejpam-5159	132	22	the	the	DET
ejpam-5159	132	23	new	new	ADJ
ejpam-5159	132	24	conformable	conformable	ADJ
ejpam-5159	132	25	fractional	fractional	ADJ
ejpam-5159	132	26	derivative	derivative	NOUN
ejpam-5159	132	27	as	as	SCONJ
ejpam-5159	132	28	outlined	outline	VERB
ejpam-5159	132	29	in	in	ADP
ejpam-5159	132	30	[	[	X
ejpam-5159	132	31	5	5	NUM
ejpam-5159	132	32	]	]	PUNCT
ejpam-5159	132	33	,	,	PUNCT
ejpam-5159	132	34	along	along	ADP
ejpam-5159	132	35	with	with	ADP
ejpam-5159	132	36	properties	property	NOUN
ejpam-5159	132	37	(	(	PUNCT
ejpam-5159	132	38	2	2	NUM
ejpam-5159	132	39	)	)	PUNCT
ejpam-5159	132	40	,	,	PUNCT
ejpam-5159	132	41	(	(	PUNCT
ejpam-5159	132	42	3	3	NUM
ejpam-5159	132	43	)	)	PUNCT
ejpam-5159	132	44	,	,	PUNCT
ejpam-5159	132	45	and	and	CCONJ
ejpam-5159	132	46	(	(	PUNCT
ejpam-5159	132	47	4	4	NUM
ejpam-5159	132	48	)	)	PUNCT
ejpam-5159	132	49	(	(	PUNCT
ejpam-5159	132	50	refer	refer	VERB
ejpam-5159	132	51	to	to	ADP
ejpam-5159	132	52	theorem	theorem	NOUN
ejpam-5159	132	53	(	(	PUNCT
ejpam-5159	132	54	3	3	NUM
ejpam-5159	132	55	)	)	PUNCT
ejpam-5159	132	56	)	)	PUNCT
ejpam-5159	132	57	,	,	PUNCT
ejpam-5159	132	58	we	we	PRON
ejpam-5159	132	59	arrive	arrive	VERB
ejpam-5159	132	60	at	at	ADP
ejpam-5159	132	61	a	a	DET
ejpam-5159	132	62	theory	theory	NOUN
ejpam-5159	132	63	akin	akin	ADJ
ejpam-5159	132	64	to	to	ADP
ejpam-5159	132	65	that	that	PRON
ejpam-5159	132	66	of	of	ADP
ejpam-5159	132	67	conventional	conventional	ADJ
ejpam-5159	132	68	linear	linear	ADJ
ejpam-5159	132	69	differential	differential	NOUN
ejpam-5159	132	70	equations	equation	NOUN
ejpam-5159	132	71	.	.	PUNCT
ejpam-5159	133	1	now	now	ADV
ejpam-5159	133	2	,	,	PUNCT
ejpam-5159	133	3	let	let	VERB
ejpam-5159	133	4	’s	’s	PRON
ejpam-5159	133	5	delve	delve	VERB
ejpam-5159	133	6	into	into	ADP
ejpam-5159	133	7	the	the	DET
ejpam-5159	133	8	discussion	discussion	NOUN
ejpam-5159	133	9	of	of	ADP
ejpam-5159	133	10	our	our	PRON
ejpam-5159	133	11	heat	heat	NOUN
ejpam-5159	133	12	equation	equation	NOUN
ejpam-5159	133	13	(	(	PUNCT
ejpam-5159	133	14	27	27	NUM
ejpam-5159	133	15	)	)	PUNCT
ejpam-5159	133	16	.	.	PUNCT
ejpam-5159	134	1	we	we	PRON
ejpam-5159	134	2	will	will	AUX
ejpam-5159	134	3	employ	employ	VERB
ejpam-5159	134	4	the	the	DET
ejpam-5159	134	5	method	method	NOUN
ejpam-5159	134	6	of	of	ADP
ejpam-5159	134	7	separation	separation	NOUN
ejpam-5159	134	8	of	of	ADP
ejpam-5159	134	9	variables	variable	NOUN
ejpam-5159	134	10	.	.	PUNCT
ejpam-5159	135	1	assume	assume	VERB
ejpam-5159	135	2	z(x	z(x	NUM
ejpam-5159	135	3	,	,	PUNCT
ejpam-5159	135	4	t	t	PROPN
ejpam-5159	135	5	)	)	PUNCT
ejpam-5159	135	6	=	=	SYM
ejpam-5159	135	7	m(x)r(t	m(x)r(t	NOUN
ejpam-5159	135	8	)	)	PUNCT
ejpam-5159	135	9	.	.	PUNCT
ejpam-5159	136	1	substituting	substitute	VERB
ejpam-5159	136	2	this	this	PRON
ejpam-5159	136	3	into	into	ADP
ejpam-5159	136	4	the	the	DET
ejpam-5159	136	5	differential	differential	ADJ
ejpam-5159	136	6	equation	equation	NOUN
ejpam-5159	136	7	yields	yield	NOUN
ejpam-5159	136	8	:	:	PUNCT
ejpam-5159	136	9	dα	dα	PROPN
ejpam-5159	136	10	dtα	dtα	NOUN
ejpam-5159	136	11	dαr(t	dαr(t	PROPN
ejpam-5159	136	12	)	)	PUNCT
ejpam-5159	136	13	dtα	dtα	NOUN
ejpam-5159	136	14	m(x	m(x	PROPN
ejpam-5159	136	15	)	)	PUNCT
ejpam-5159	136	16	=	=	SYM
ejpam-5159	136	17	r(t	r(t	NOUN
ejpam-5159	136	18	)	)	PUNCT
ejpam-5159	136	19	d2m(x	d2m(x	PROPN
ejpam-5159	136	20	)	)	PUNCT
ejpam-5159	136	21	dx2	dx2	PROPN
ejpam-5159	136	22	,	,	PUNCT
ejpam-5159	136	23	(	(	PUNCT
ejpam-5159	136	24	37	37	NUM
ejpam-5159	136	25	)	)	PUNCT
ejpam-5159	136	26	then	then	ADV
ejpam-5159	136	27	,	,	PUNCT
ejpam-5159	136	28	we	we	PRON
ejpam-5159	136	29	obtain	obtain	VERB
ejpam-5159	136	30	:	:	PUNCT
ejpam-5159	136	31	dα	dα	PROPN
ejpam-5159	136	32	dtα	dtα	NOUN
ejpam-5159	136	33	dαr(t	dαr(t	PROPN
ejpam-5159	136	34	)	)	PUNCT
ejpam-5159	136	35	dtα	dtα	NOUN
ejpam-5159	136	36	/r(t	/r(t	PUNCT
ejpam-5159	136	37	)	)	PUNCT
ejpam-5159	137	1	=	=	SYM
ejpam-5159	137	2	d2m(x	d2m(x	PROPN
ejpam-5159	137	3	)	)	PUNCT
ejpam-5159	137	4	dx2	dx2	NOUN
ejpam-5159	137	5	/p	/p	PUNCT
ejpam-5159	137	6	=	=	SYM
ejpam-5159	137	7	β	β	X
ejpam-5159	137	8	,	,	PUNCT
ejpam-5159	137	9	(	(	PUNCT
ejpam-5159	137	10	38	38	NUM
ejpam-5159	137	11	)	)	PUNCT
ejpam-5159	137	12	for	for	ADP
ejpam-5159	137	13	some	some	DET
ejpam-5159	137	14	constant	constant	ADJ
ejpam-5159	137	15	.	.	PUNCT
ejpam-5159	138	1	then	then	ADV
ejpam-5159	138	2	:	:	PUNCT
ejpam-5159	138	3	dα	dα	PROPN
ejpam-5159	138	4	dtα	dtα	NOUN
ejpam-5159	138	5	dαr(t	dαr(t	PROPN
ejpam-5159	138	6	)	)	PUNCT
ejpam-5159	138	7	dtα	dtα	NOUN
ejpam-5159	138	8	−	−	NOUN
ejpam-5159	139	1	βr	βr	NOUN
ejpam-5159	139	2	=	=	SYM
ejpam-5159	139	3	0	0	NUM
ejpam-5159	139	4	,	,	PUNCT
ejpam-5159	139	5	and	and	CCONJ
ejpam-5159	139	6	d2m(x	d2m(x	PROPN
ejpam-5159	139	7	)	)	PUNCT
ejpam-5159	139	8	dx2	dx2	PROPN
ejpam-5159	140	1	−	−	PROPN
ejpam-5159	140	2	βm	βm	VERB
ejpam-5159	140	3	=	=	SYM
ejpam-5159	140	4	0	0	PROPN
ejpam-5159	140	5	.	.	PUNCT
ejpam-5159	141	1	(	(	PUNCT
ejpam-5159	141	2	39	39	NUM
ejpam-5159	141	3	)	)	PUNCT
ejpam-5159	141	4	we	we	PRON
ejpam-5159	141	5	consider	consider	VERB
ejpam-5159	141	6	the	the	DET
ejpam-5159	141	7	formula	formula	NOUN
ejpam-5159	141	8	:	:	PUNCT
ejpam-5159	141	9	d2m(x	d2m(x	NOUN
ejpam-5159	141	10	)	)	PUNCT
ejpam-5159	141	11	dx2	dx2	PROPN
ejpam-5159	141	12	−	−	PROPN
ejpam-5159	141	13	βm	βm	VERB
ejpam-5159	141	14	=	=	SYM
ejpam-5159	141	15	0	0	PROPN
ejpam-5159	141	16	.	.	PUNCT
ejpam-5159	142	1	(	(	PUNCT
ejpam-5159	142	2	40	40	NUM
ejpam-5159	142	3	)	)	PUNCT
ejpam-5159	142	4	as	as	SCONJ
ejpam-5159	142	5	is	be	AUX
ejpam-5159	142	6	well	well	ADV
ejpam-5159	142	7	known	know	VERB
ejpam-5159	142	8	,	,	PUNCT
ejpam-5159	142	9	there	there	PRON
ejpam-5159	142	10	are	be	VERB
ejpam-5159	142	11	three	three	NUM
ejpam-5159	142	12	cases	case	NOUN
ejpam-5159	142	13	for	for	ADP
ejpam-5159	142	14	the	the	DET
ejpam-5159	142	15	values	value	NOUN
ejpam-5159	142	16	of	of	ADP
ejpam-5159	142	17	β	β	PRON
ejpam-5159	142	18	to	to	PART
ejpam-5159	142	19	be	be	AUX
ejpam-5159	142	20	considered	consider	VERB
ejpam-5159	142	21	.	.	PUNCT
ejpam-5159	143	1	β	β	X
ejpam-5159	143	2	=	=	PUNCT
ejpam-5159	143	3	0	0	PROPN
ejpam-5159	143	4	,	,	PUNCT
ejpam-5159	143	5	β	β	X
ejpam-5159	143	6	=	=	SYM
ejpam-5159	143	7	−ν2	−ν2	PROPN
ejpam-5159	143	8	and	and	CCONJ
ejpam-5159	143	9	β	β	NOUN
ejpam-5159	143	10	=	=	NOUN
ejpam-5159	143	11	ν2	ν2	PROPN
ejpam-5159	143	12	.	.	PUNCT
ejpam-5159	144	1	conditions	condition	NOUN
ejpam-5159	144	2	(	(	PUNCT
ejpam-5159	144	3	28	28	NUM
ejpam-5159	144	4	)	)	PUNCT
ejpam-5159	144	5	and	and	CCONJ
ejpam-5159	144	6	(	(	PUNCT
ejpam-5159	144	7	29	29	NUM
ejpam-5159	144	8	)	)	PUNCT
ejpam-5159	144	9	forces	force	NOUN
ejpam-5159	144	10	ν	ν	NOUN
ejpam-5159	144	11	=	=	PUNCT
ejpam-5159	144	12	nπ	nπ	NOUN
ejpam-5159	144	13	and	and	CCONJ
ejpam-5159	144	14	mn(x	mn(x	NUM
ejpam-5159	144	15	)	)	PUNCT
ejpam-5159	144	16	=	=	SYM
ejpam-5159	144	17	cn	cn	PROPN
ejpam-5159	144	18	sin(nπx	sin(nπx	PROPN
ejpam-5159	144	19	)	)	PUNCT
ejpam-5159	144	20	.	.	PUNCT
ejpam-5159	145	1	(	(	PUNCT
ejpam-5159	145	2	41	41	NUM
ejpam-5159	145	3	)	)	PUNCT
ejpam-5159	145	4	through	through	ADP
ejpam-5159	145	5	equations	equation	NOUN
ejpam-5159	145	6	(	(	PUNCT
ejpam-5159	145	7	32	32	NUM
ejpam-5159	145	8	)	)	PUNCT
ejpam-5159	145	9	and	and	CCONJ
ejpam-5159	145	10	(	(	PUNCT
ejpam-5159	145	11	34	34	NUM
ejpam-5159	145	12	)	)	PUNCT
ejpam-5159	145	13	,	,	PUNCT
ejpam-5159	145	14	we	we	PRON
ejpam-5159	145	15	obtain	obtain	VERB
ejpam-5159	145	16	:	:	PUNCT
ejpam-5159	145	17	r(t	r(t	NOUN
ejpam-5159	145	18	)	)	PUNCT
ejpam-5159	146	1	=	=	SYM
ejpam-5159	146	2	b1	b1	PROPN
ejpam-5159	146	3	cos	cos	PROPN
ejpam-5159	146	4	(	(	PUNCT
ejpam-5159	146	5	nπ	nπ	NOUN
ejpam-5159	146	6	1−	1−	NUM
ejpam-5159	146	7	α	α	PROPN
ejpam-5159	146	8	e(1−α)t	e(1−α)t	NOUN
ejpam-5159	146	9	)	)	PUNCT
ejpam-5159	147	1	+	+	NUM
ejpam-5159	147	2	b2	b2	NOUN
ejpam-5159	147	3	sin	sin	NOUN
ejpam-5159	147	4	(	(	PUNCT
ejpam-5159	147	5	nπ	nπ	NOUN
ejpam-5159	147	6	1−	1−	NUM
ejpam-5159	147	7	α	α	PROPN
ejpam-5159	147	8	e(1−α)t	e(1−α)t	NOUN
ejpam-5159	147	9	)	)	PUNCT
ejpam-5159	147	10	.	.	PUNCT
ejpam-5159	148	1	(	(	PUNCT
ejpam-5159	148	2	42	42	NUM
ejpam-5159	148	3	)	)	PUNCT
ejpam-5159	148	4	and	and	CCONJ
ejpam-5159	148	5	the	the	DET
ejpam-5159	148	6	condition	condition	NOUN
ejpam-5159	148	7	(	(	PUNCT
ejpam-5159	148	8	30	30	NUM
ejpam-5159	148	9	)	)	PUNCT
ejpam-5159	148	10	now	now	ADV
ejpam-5159	148	11	gives	give	VERB
ejpam-5159	148	12	b2	b2	NOUN
ejpam-5159	148	13	=	=	SYM
ejpam-5159	148	14	0	0	NUM
ejpam-5159	148	15	,	,	PUNCT
ejpam-5159	148	16	and	and	CCONJ
ejpam-5159	148	17	r(t	r(t	NOUN
ejpam-5159	148	18	)	)	PUNCT
ejpam-5159	149	1	=	=	SYM
ejpam-5159	149	2	b1	b1	PROPN
ejpam-5159	149	3	cos	cos	PROPN
ejpam-5159	149	4	(	(	PUNCT
ejpam-5159	149	5	nπ	nπ	ADP
ejpam-5159	149	6	1−αe	1−αe	PROPN
ejpam-5159	149	7	(	(	PUNCT
ejpam-5159	149	8	1−α)t	1−α)t	NUM
ejpam-5159	149	9	)	)	PUNCT
ejpam-5159	149	10	,	,	PUNCT
ejpam-5159	149	11	then	then	ADV
ejpam-5159	149	12	,	,	PUNCT
ejpam-5159	149	13	using	use	VERB
ejpam-5159	149	14	equation	equation	NOUN
ejpam-5159	149	15	(	(	PUNCT
ejpam-5159	149	16	41	41	NUM
ejpam-5159	149	17	)	)	PUNCT
ejpam-5159	149	18	,	,	PUNCT
ejpam-5159	149	19	we	we	PRON
ejpam-5159	149	20	obtain	obtain	VERB
ejpam-5159	149	21	:	:	PUNCT
ejpam-5159	149	22	z(x	z(x	NUM
ejpam-5159	149	23	,	,	PUNCT
ejpam-5159	149	24	t	t	PROPN
ejpam-5159	149	25	)	)	PUNCT
ejpam-5159	149	26	=	=	NOUN
ejpam-5159	150	1	∞∑	∞∑	NUM
ejpam-5159	150	2	n=1	n=1	ADP
ejpam-5159	150	3	an	an	DET
ejpam-5159	150	4	sin(nπx	sin(nπx	NOUN
ejpam-5159	150	5	)	)	PUNCT
ejpam-5159	151	1	cos	cos	PROPN
ejpam-5159	151	2	(	(	PUNCT
ejpam-5159	151	3	nπ	nπ	NOUN
ejpam-5159	151	4	1−	1−	NUM
ejpam-5159	151	5	α	α	PROPN
ejpam-5159	151	6	e(1−α)t	e(1−α)t	NOUN
ejpam-5159	151	7	)	)	PUNCT
ejpam-5159	151	8	,	,	PUNCT
ejpam-5159	151	9	(	(	PUNCT
ejpam-5159	151	10	43	43	X
ejpam-5159	151	11	)	)	PUNCT
ejpam-5159	151	12	references	reference	NOUN
ejpam-5159	151	13	1165	1165	NUM
ejpam-5159	151	14	using	use	VERB
ejpam-5159	151	15	condition	condition	NOUN
ejpam-5159	151	16	(	(	PUNCT
ejpam-5159	151	17	31	31	NUM
ejpam-5159	151	18	)	)	PUNCT
ejpam-5159	151	19	we	we	PRON
ejpam-5159	151	20	find	find	VERB
ejpam-5159	151	21	that	that	SCONJ
ejpam-5159	151	22	an	an	PRON
ejpam-5159	151	23	is	be	AUX
ejpam-5159	151	24	the	the	DET
ejpam-5159	151	25	nth	nth	ADJ
ejpam-5159	151	26	fourier	fourier	NOUN
ejpam-5159	151	27	coefficient	coefficient	NOUN
ejpam-5159	151	28	of	of	ADP
ejpam-5159	151	29	the	the	DET
ejpam-5159	151	30	function	function	NOUN
ejpam-5159	151	31	h(x	h(x	PROPN
ejpam-5159	151	32	)	)	PUNCT
ejpam-5159	151	33	.	.	PUNCT
ejpam-5159	152	1	finally	finally	ADV
ejpam-5159	152	2	,	,	PUNCT
ejpam-5159	152	3	we	we	PRON
ejpam-5159	152	4	can	can	AUX
ejpam-5159	152	5	consider	consider	VERB
ejpam-5159	152	6	the	the	DET
ejpam-5159	152	7	following	follow	VERB
ejpam-5159	152	8	form	form	NOUN
ejpam-5159	152	9	of	of	ADP
ejpam-5159	152	10	the	the	DET
ejpam-5159	152	11	new	new	ADJ
ejpam-5159	152	12	fractional	fractional	ADJ
ejpam-5159	152	13	heat	heat	NOUN
ejpam-5159	152	14	differential	differential	NOUN
ejpam-5159	152	15	equation	equation	NOUN
ejpam-5159	152	16	:	:	PUNCT
ejpam-5159	152	17	∂α	∂α	PROPN
ejpam-5159	152	18	∂xα	∂xα	PROPN
ejpam-5159	152	19	∂αz(x	∂αz(x	PROPN
ejpam-5159	152	20	,	,	PUNCT
ejpam-5159	152	21	t	t	PROPN
ejpam-5159	152	22	)	)	PUNCT
ejpam-5159	152	23	∂xα	∂xα	PROPN
ejpam-5159	152	24	=	=	SYM
ejpam-5159	152	25	∂z	∂z	PROPN
ejpam-5159	152	26	∂t	∂t	PROPN
ejpam-5159	152	27	,	,	PUNCT
ejpam-5159	152	28	(	(	PUNCT
ejpam-5159	152	29	44	44	NUM
ejpam-5159	152	30	)	)	PUNCT
ejpam-5159	152	31	with	with	ADP
ejpam-5159	152	32	conditions	condition	NOUN
ejpam-5159	152	33	:	:	PUNCT
ejpam-5159	152	34	z(x	z(x	NUM
ejpam-5159	152	35	,	,	PUNCT
ejpam-5159	152	36	0	0	NUM
ejpam-5159	152	37	)	)	PUNCT
ejpam-5159	152	38	=	=	SYM
ejpam-5159	152	39	h(x	h(x	PROPN
ejpam-5159	152	40	)	)	PUNCT
ejpam-5159	152	41	,	,	PUNCT
ejpam-5159	152	42	0	0	PUNCT
ejpam-5159	152	43	<	<	X
ejpam-5159	152	44	x	x	X
ejpam-5159	152	45	<	<	X
ejpam-5159	152	46	1	1	NUM
ejpam-5159	152	47	,	,	PUNCT
ejpam-5159	152	48	z(0	z(0	AUX
ejpam-5159	152	49	,	,	PUNCT
ejpam-5159	152	50	t	t	PROPN
ejpam-5159	152	51	)	)	PUNCT
ejpam-5159	152	52	=	=	SYM
ejpam-5159	152	53	0	0	NUM
ejpam-5159	152	54	,	,	PUNCT
ejpam-5159	152	55	t	t	X
ejpam-5159	152	56	>	>	X
ejpam-5159	152	57	0	0	PROPN
ejpam-5159	152	58	,	,	PUNCT
ejpam-5159	152	59	z(1	z(1	PROPN
ejpam-5159	152	60	,	,	PUNCT
ejpam-5159	152	61	t	t	PROPN
ejpam-5159	152	62	)	)	PUNCT
ejpam-5159	152	63	=	=	SYM
ejpam-5159	153	1	0	0	NUM
ejpam-5159	153	2	,	,	PUNCT
ejpam-5159	153	3	t	t	X
ejpam-5159	153	4	>	>	X
ejpam-5159	153	5	0	0	X
ejpam-5159	153	6	.	.	PUNCT
ejpam-5159	154	1	in	in	ADP
ejpam-5159	154	2	this	this	DET
ejpam-5159	154	3	context	context	NOUN
ejpam-5159	154	4	,	,	PUNCT
ejpam-5159	154	5	equation	equation	NOUN
ejpam-5159	154	6	(	(	PUNCT
ejpam-5159	154	7	27	27	NUM
ejpam-5159	154	8	)	)	PUNCT
ejpam-5159	154	9	can	can	AUX
ejpam-5159	154	10	be	be	AUX
ejpam-5159	154	11	effectively	effectively	ADV
ejpam-5159	154	12	applied	apply	VERB
ejpam-5159	154	13	,	,	PUNCT
ejpam-5159	154	14	enabling	enable	VERB
ejpam-5159	154	15	the	the	DET
ejpam-5159	154	16	solution	solution	NOUN
ejpam-5159	154	17	of	of	ADP
ejpam-5159	154	18	problem	problem	NOUN
ejpam-5159	154	19	(	(	PUNCT
ejpam-5159	154	20	44	44	NUM
ejpam-5159	154	21	)	)	PUNCT
ejpam-5159	154	22	with	with	ADP
ejpam-5159	154	23	the	the	DET
ejpam-5159	154	24	provided	provide	VERB
ejpam-5159	154	25	boundary	boundary	ADJ
ejpam-5159	154	26	conditions	condition	NOUN
ejpam-5159	154	27	in	in	ADP
ejpam-5159	154	28	a	a	DET
ejpam-5159	154	29	manner	manner	NOUN
ejpam-5159	154	30	akin	akin	ADJ
ejpam-5159	154	31	to	to	ADP
ejpam-5159	154	32	solving	solve	VERB
ejpam-5159	154	33	the	the	DET
ejpam-5159	154	34	ordinary	ordinary	ADJ
ejpam-5159	154	35	heat	heat	NOUN
ejpam-5159	154	36	equation	equation	NOUN
ejpam-5159	154	37	.	.	PUNCT
ejpam-5159	155	1	this	this	DET
ejpam-5159	155	2	approach	approach	NOUN
ejpam-5159	155	3	considers	consider	VERB
ejpam-5159	155	4	properties	property	NOUN
ejpam-5159	155	5	(	(	PUNCT
ejpam-5159	155	6	2	2	NUM
ejpam-5159	155	7	)	)	PUNCT
ejpam-5159	155	8	,	,	PUNCT
ejpam-5159	155	9	(	(	PUNCT
ejpam-5159	155	10	3	3	NUM
ejpam-5159	155	11	)	)	PUNCT
ejpam-5159	155	12	,	,	PUNCT
ejpam-5159	155	13	and	and	CCONJ
ejpam-5159	155	14	(	(	PUNCT
ejpam-5159	155	15	4	4	NUM
ejpam-5159	155	16	)	)	PUNCT
ejpam-5159	155	17	(	(	PUNCT
ejpam-5159	155	18	refer	refer	VERB
ejpam-5159	155	19	to	to	ADP
ejpam-5159	155	20	theorem	theorem	NOUN
ejpam-5159	155	21	(	(	PUNCT
ejpam-5159	155	22	3	3	NUM
ejpam-5159	155	23	)	)	PUNCT
ejpam-5159	155	24	)	)	PUNCT
ejpam-5159	155	25	.	.	PUNCT
ejpam-5159	156	1	remark	remark	PROPN
ejpam-5159	156	2	1	1	NUM
ejpam-5159	156	3	.	.	PUNCT
ejpam-5159	157	1	one	one	PRON
ejpam-5159	157	2	should	should	AUX
ejpam-5159	157	3	note	note	VERB
ejpam-5159	157	4	that	that	SCONJ
ejpam-5159	157	5	if	if	SCONJ
ejpam-5159	157	6	we	we	PRON
ejpam-5159	157	7	set	set	VERB
ejpam-5159	157	8	α	α	NOUN
ejpam-5159	157	9	=	=	SYM
ejpam-5159	157	10	1	1	NUM
ejpam-5159	157	11	,	,	PUNCT
ejpam-5159	157	12	problem	problem	NOUN
ejpam-5159	157	13	(	(	PUNCT
ejpam-5159	157	14	44	44	NUM
ejpam-5159	157	15	)	)	PUNCT
ejpam-5159	157	16	will	will	AUX
ejpam-5159	157	17	become	become	VERB
ejpam-5159	157	18	the	the	DET
ejpam-5159	157	19	original	original	ADJ
ejpam-5159	157	20	problem	problem	NOUN
ejpam-5159	157	21	treated	treat	VERB
ejpam-5159	157	22	by	by	ADP
ejpam-5159	157	23	the	the	DET
ejpam-5159	157	24	fractional	fractional	ADJ
ejpam-5159	157	25	black	black	ADJ
ejpam-5159	157	26	-	-	PUNCT
ejpam-5159	157	27	scholes	schole	NOUN
ejpam-5159	157	28	equation	equation	NOUN
ejpam-5159	157	29	(	(	PUNCT
ejpam-5159	157	30	see	see	VERB
ejpam-5159	157	31	[	[	X
ejpam-5159	157	32	8	8	NUM
ejpam-5159	157	33	]	]	NUM
ejpam-5159	157	34	)	)	PUNCT
ejpam-5159	157	35	,	,	PUNCT
ejpam-5159	157	36	a	a	DET
ejpam-5159	157	37	significant	significant	ADJ
ejpam-5159	157	38	equation	equation	NOUN
ejpam-5159	157	39	in	in	ADP
ejpam-5159	157	40	financial	financial	ADJ
ejpam-5159	157	41	mathematics	mathematic	NOUN
ejpam-5159	157	42	.	.	PUNCT
ejpam-5159	158	1	utilizing	utilize	VERB
ejpam-5159	158	2	this	this	DET
ejpam-5159	158	3	solution	solution	NOUN
ejpam-5159	158	4	of	of	ADP
ejpam-5159	158	5	the	the	DET
ejpam-5159	158	6	heat	heat	NOUN
ejpam-5159	158	7	equation	equation	NOUN
ejpam-5159	158	8	,	,	PUNCT
ejpam-5159	158	9	we	we	PRON
ejpam-5159	158	10	deduce	deduce	VERB
ejpam-5159	158	11	the	the	DET
ejpam-5159	158	12	solution	solution	NOUN
ejpam-5159	158	13	of	of	ADP
ejpam-5159	158	14	the	the	DET
ejpam-5159	158	15	black	black	ADJ
ejpam-5159	158	16	-	-	PUNCT
ejpam-5159	158	17	scholes	schole	NOUN
ejpam-5159	158	18	model	model	NOUN
ejpam-5159	158	19	.	.	PUNCT
ejpam-5159	159	1	4	4	X
ejpam-5159	159	2	.	.	X
ejpam-5159	159	3	conclusion	conclusion	NOUN
ejpam-5159	159	4	in	in	ADP
ejpam-5159	159	5	conclusion	conclusion	NOUN
ejpam-5159	159	6	,	,	PUNCT
ejpam-5159	159	7	this	this	DET
ejpam-5159	159	8	informative	informative	ADJ
ejpam-5159	159	9	article	article	NOUN
ejpam-5159	159	10	has	have	AUX
ejpam-5159	159	11	shed	shed	VERB
ejpam-5159	159	12	light	light	NOUN
ejpam-5159	159	13	on	on	ADP
ejpam-5159	159	14	the	the	DET
ejpam-5159	159	15	novel	novel	ADJ
ejpam-5159	159	16	concept	concept	NOUN
ejpam-5159	159	17	of	of	ADP
ejpam-5159	159	18	conformable	conformable	ADJ
ejpam-5159	159	19	derivatives	derivative	NOUN
ejpam-5159	159	20	and	and	CCONJ
ejpam-5159	159	21	their	their	PRON
ejpam-5159	159	22	definitions	definition	NOUN
ejpam-5159	159	23	,	,	PUNCT
ejpam-5159	159	24	unveiling	unveil	VERB
ejpam-5159	159	25	a	a	DET
ejpam-5159	159	26	rich	rich	ADJ
ejpam-5159	159	27	landscape	landscape	NOUN
ejpam-5159	159	28	of	of	ADP
ejpam-5159	159	29	possibilities	possibility	NOUN
ejpam-5159	159	30	in	in	ADP
ejpam-5159	159	31	mathematical	mathematical	ADJ
ejpam-5159	159	32	analysis	analysis	NOUN
ejpam-5159	159	33	and	and	CCONJ
ejpam-5159	159	34	applications	application	NOUN
ejpam-5159	159	35	across	across	ADP
ejpam-5159	159	36	various	various	ADJ
ejpam-5159	159	37	scientific	scientific	ADJ
ejpam-5159	159	38	domains	domain	NOUN
ejpam-5159	159	39	.	.	PUNCT
ejpam-5159	160	1	by	by	ADP
ejpam-5159	160	2	delving	delve	VERB
ejpam-5159	160	3	into	into	ADP
ejpam-5159	160	4	the	the	DET
ejpam-5159	160	5	fundamental	fundamental	ADJ
ejpam-5159	160	6	properties	property	NOUN
ejpam-5159	160	7	of	of	ADP
ejpam-5159	160	8	adaptive	adaptive	ADJ
ejpam-5159	160	9	differential	differential	ADJ
ejpam-5159	160	10	operators	operator	NOUN
ejpam-5159	160	11	,	,	PUNCT
ejpam-5159	160	12	we	we	PRON
ejpam-5159	160	13	’ve	’ve	AUX
ejpam-5159	160	14	unlocked	unlock	VERB
ejpam-5159	160	15	new	new	ADJ
ejpam-5159	160	16	avenues	avenue	NOUN
ejpam-5159	160	17	for	for	ADP
ejpam-5159	160	18	understanding	understand	VERB
ejpam-5159	160	19	complex	complex	ADJ
ejpam-5159	160	20	phenomena	phenomenon	NOUN
ejpam-5159	160	21	in	in	ADP
ejpam-5159	160	22	physics	physics	NOUN
ejpam-5159	160	23	and	and	CCONJ
ejpam-5159	160	24	beyond	beyond	ADP
ejpam-5159	160	25	.	.	PUNCT
ejpam-5159	161	1	the	the	DET
ejpam-5159	161	2	inclusion	inclusion	NOUN
ejpam-5159	161	3	of	of	ADP
ejpam-5159	161	4	graphical	graphical	ADJ
ejpam-5159	161	5	representations	representation	NOUN
ejpam-5159	161	6	has	have	AUX
ejpam-5159	161	7	not	not	PART
ejpam-5159	161	8	only	only	ADV
ejpam-5159	161	9	enhanced	enhance	VERB
ejpam-5159	161	10	our	our	PRON
ejpam-5159	161	11	comprehension	comprehension	NOUN
ejpam-5159	161	12	of	of	ADP
ejpam-5159	161	13	the	the	DET
ejpam-5159	161	14	proposed	propose	VERB
ejpam-5159	161	15	fractional	fractional	ADJ
ejpam-5159	161	16	differential	differential	ADJ
ejpam-5159	161	17	equations	equation	NOUN
ejpam-5159	161	18	but	but	CCONJ
ejpam-5159	161	19	has	have	AUX
ejpam-5159	161	20	also	also	ADV
ejpam-5159	161	21	demonstrated	demonstrate	VERB
ejpam-5159	161	22	their	their	PRON
ejpam-5159	161	23	remarkable	remarkable	ADJ
ejpam-5159	161	24	resemblance	resemblance	NOUN
ejpam-5159	161	25	to	to	ADP
ejpam-5159	161	26	solutions	solution	NOUN
ejpam-5159	161	27	obtained	obtain	VERB
ejpam-5159	161	28	using	use	VERB
ejpam-5159	161	29	traditional	traditional	ADJ
ejpam-5159	161	30	derivatives	derivative	NOUN
ejpam-5159	161	31	,	,	PUNCT
ejpam-5159	161	32	underscoring	underscore	VERB
ejpam-5159	161	33	the	the	DET
ejpam-5159	161	34	efficacy	efficacy	NOUN
ejpam-5159	161	35	of	of	ADP
ejpam-5159	161	36	these	these	DET
ejpam-5159	161	37	novel	novel	ADJ
ejpam-5159	161	38	mathematical	mathematical	ADJ
ejpam-5159	161	39	tools	tool	NOUN
ejpam-5159	161	40	.	.	PUNCT
ejpam-5159	162	1	looking	look	VERB
ejpam-5159	162	2	ahead	ahead	ADV
ejpam-5159	162	3	,	,	PUNCT
ejpam-5159	162	4	the	the	DET
ejpam-5159	162	5	insights	insight	NOUN
ejpam-5159	162	6	gleaned	glean	VERB
ejpam-5159	162	7	from	from	ADP
ejpam-5159	162	8	our	our	PRON
ejpam-5159	162	9	exploration	exploration	NOUN
ejpam-5159	162	10	,	,	PUNCT
ejpam-5159	162	11	particularly	particularly	ADV
ejpam-5159	162	12	in	in	ADP
ejpam-5159	162	13	the	the	DET
ejpam-5159	162	14	realm	realm	NOUN
ejpam-5159	162	15	of	of	ADP
ejpam-5159	162	16	the	the	DET
ejpam-5159	162	17	fractional	fractional	ADJ
ejpam-5159	162	18	heat	heat	NOUN
ejpam-5159	162	19	equation	equation	NOUN
ejpam-5159	162	20	,	,	PUNCT
ejpam-5159	162	21	hold	hold	VERB
ejpam-5159	162	22	promise	promise	NOUN
ejpam-5159	162	23	for	for	ADP
ejpam-5159	162	24	addressing	address	VERB
ejpam-5159	162	25	significant	significant	ADJ
ejpam-5159	162	26	challenges	challenge	NOUN
ejpam-5159	162	27	in	in	ADP
ejpam-5159	162	28	financial	financial	ADJ
ejpam-5159	162	29	modeling	modeling	NOUN
ejpam-5159	162	30	.	.	PUNCT
ejpam-5159	163	1	leveraging	leverage	VERB
ejpam-5159	163	2	these	these	DET
ejpam-5159	163	3	outcomes	outcome	NOUN
ejpam-5159	163	4	to	to	PART
ejpam-5159	163	5	tackle	tackle	VERB
ejpam-5159	163	6	the	the	DET
ejpam-5159	163	7	fractional	fractional	ADJ
ejpam-5159	163	8	black	black	ADJ
ejpam-5159	163	9	-	-	PUNCT
ejpam-5159	163	10	scholes	schole	NOUN
ejpam-5159	163	11	model	model	NOUN
ejpam-5159	163	12	represents	represent	VERB
ejpam-5159	163	13	a	a	DET
ejpam-5159	163	14	natural	natural	ADJ
ejpam-5159	163	15	progression	progression	NOUN
ejpam-5159	163	16	,	,	PUNCT
ejpam-5159	163	17	offering	offer	VERB
ejpam-5159	163	18	potential	potential	ADJ
ejpam-5159	163	19	breakthroughs	breakthrough	NOUN
ejpam-5159	163	20	in	in	ADP
ejpam-5159	163	21	pricing	price	VERB
ejpam-5159	163	22	exotic	exotic	ADJ
ejpam-5159	163	23	options	option	NOUN
ejpam-5159	163	24	and	and	CCONJ
ejpam-5159	163	25	managing	manage	VERB
ejpam-5159	163	26	risk	risk	NOUN
ejpam-5159	163	27	in	in	ADP
ejpam-5159	163	28	modern	modern	ADJ
ejpam-5159	163	29	financial	financial	ADJ
ejpam-5159	163	30	markets	market	NOUN
ejpam-5159	163	31	.	.	PUNCT
ejpam-5159	164	1	as	as	SCONJ
ejpam-5159	164	2	we	we	PRON
ejpam-5159	164	3	continue	continue	VERB
ejpam-5159	164	4	to	to	PART
ejpam-5159	164	5	push	push	VERB
ejpam-5159	164	6	the	the	DET
ejpam-5159	164	7	boundaries	boundary	NOUN
ejpam-5159	164	8	of	of	ADP
ejpam-5159	164	9	mathematical	mathematical	ADJ
ejpam-5159	164	10	innovation	innovation	NOUN
ejpam-5159	164	11	and	and	CCONJ
ejpam-5159	164	12	its	its	PRON
ejpam-5159	164	13	applications	application	NOUN
ejpam-5159	164	14	,	,	PUNCT
ejpam-5159	164	15	the	the	DET
ejpam-5159	164	16	journey	journey	NOUN
ejpam-5159	164	17	of	of	ADP
ejpam-5159	164	18	discovery	discovery	NOUN
ejpam-5159	164	19	sparked	spark	VERB
ejpam-5159	164	20	by	by	ADP
ejpam-5159	164	21	conformable	conformable	ADJ
ejpam-5159	164	22	derivatives	derivative	NOUN
ejpam-5159	164	23	promises	promise	NOUN
ejpam-5159	164	24	to	to	PART
ejpam-5159	164	25	be	be	AUX
ejpam-5159	164	26	both	both	PRON
ejpam-5159	164	27	exciting	exciting	ADJ
ejpam-5159	164	28	and	and	CCONJ
ejpam-5159	164	29	fruitful	fruitful	ADJ
ejpam-5159	164	30	,	,	PUNCT
ejpam-5159	164	31	paving	pave	VERB
ejpam-5159	164	32	the	the	DET
ejpam-5159	164	33	way	way	NOUN
ejpam-5159	164	34	for	for	ADP
ejpam-5159	164	35	deeper	deep	ADJ
ejpam-5159	164	36	insights	insight	NOUN
ejpam-5159	164	37	into	into	ADP
ejpam-5159	164	38	the	the	DET
ejpam-5159	164	39	intricacies	intricacy	NOUN
ejpam-5159	164	40	of	of	ADP
ejpam-5159	164	41	natural	natural	ADJ
ejpam-5159	164	42	phenomena	phenomenon	NOUN
ejpam-5159	164	43	and	and	CCONJ
ejpam-5159	164	44	the	the	DET
ejpam-5159	164	45	complexities	complexity	NOUN
ejpam-5159	164	46	of	of	ADP
ejpam-5159	164	47	financial	financial	ADJ
ejpam-5159	164	48	systems	system	NOUN
ejpam-5159	164	49	.	.	PUNCT
ejpam-5159	165	1	references	reference	NOUN
ejpam-5159	165	2	[	[	X
ejpam-5159	165	3	1	1	NUM
ejpam-5159	165	4	]	]	PUNCT
ejpam-5159	165	5	leibniz	leibniz	PROPN
ejpam-5159	165	6	gw	gw	PROPN
ejpam-5159	165	7	.	.	PROPN
ejpam-5159	165	8	letter	letter	PROPN
ejpam-5159	165	9	from	from	ADP
ejpam-5159	165	10	hannover	hannover	PROPN
ejpam-5159	165	11	to	to	ADP
ejpam-5159	165	12	g.	g.	PROPN
ejpam-5159	165	13	f.	f.	PROPN
ejpam-5159	165	14	a.	a.	PROPN
ejpam-5159	165	15	l’hopital	l’hopital	PROPN
ejpam-5159	165	16	.	.	PUNCT
ejpam-5159	166	1	olms	olms	PROPN
ejpam-5159	166	2	verlag	verlag	PROPN
ejpam-5159	166	3	1849	1849	NUM
ejpam-5159	166	4	,	,	PUNCT
ejpam-5159	166	5	2(1):301302	2(1):301302	NUM
ejpam-5159	166	6	.	.	PUNCT
ejpam-5159	166	7	references	reference	NOUN
ejpam-5159	166	8	1166	1166	NUM
ejpam-5159	167	1	[	[	X
ejpam-5159	167	2	2	2	NUM
ejpam-5159	167	3	]	]	PUNCT
ejpam-5159	167	4	riemann	riemann	PROPN
ejpam-5159	167	5	b.	b.	PROPN
ejpam-5159	167	6	versuch	versuch	PROPN
ejpam-5159	167	7	einer	einer	PROPN
ejpam-5159	167	8	allgemeinen	allgemeinen	PROPN
ejpam-5159	167	9	auffassung	auffassung	PROPN
ejpam-5159	167	10	der	der	ADJ
ejpam-5159	167	11	integration	integration	NOUN
ejpam-5159	167	12	und	und	VERB
ejpam-5159	167	13	differentiation	differentiation	NOUN
ejpam-5159	167	14	,	,	PUNCT
ejpam-5159	167	15	1847	1847	NUM
ejpam-5159	167	16	.	.	PUNCT
ejpam-5159	168	1	[	[	X
ejpam-5159	168	2	3	3	NUM
ejpam-5159	168	3	]	]	SYM
ejpam-5159	168	4	villac´ıs	villac´ıs	PROPN
ejpam-5159	168	5	j	j	PROPN
ejpam-5159	168	6	,	,	PUNCT
ejpam-5159	168	7	vivas	vivas	PROPN
ejpam-5159	168	8	-	-	PROPN
ejpam-5159	168	9	cortez	cortez	PROPN
ejpam-5159	168	10	m.	m.	NOUN
ejpam-5159	168	11	khalil	khalil	PROPN
ejpam-5159	168	12	conformable	conformable	PROPN
ejpam-5159	168	13	fractional	fractional	ADJ
ejpam-5159	168	14	derivative	derivative	NOUN
ejpam-5159	168	15	and	and	CCONJ
ejpam-5159	168	16	its	its	PRON
ejpam-5159	168	17	applications	application	NOUN
ejpam-5159	168	18	to	to	ADP
ejpam-5159	168	19	population	population	NOUN
ejpam-5159	168	20	growth	growth	NOUN
ejpam-5159	168	21	and	and	CCONJ
ejpam-5159	168	22	body	body	NOUN
ejpam-5159	168	23	cooling	cool	VERB
ejpam-5159	168	24	models	model	NOUN
ejpam-5159	168	25	.	.	PUNCT
ejpam-5159	169	1	selecciones	seleccione	NOUN
ejpam-5159	169	2	matem´aticas	matem´aticas	X
ejpam-5159	169	3	.	.	PUNCT
ejpam-5159	170	1	2022;9(1):44–52	2022;9(1):44–52	NUM
ejpam-5159	170	2	.	.	PUNCT
ejpam-5159	171	1	http://dx.doi.org/10.17268/sel	http://dx.doi.org/10.17268/sel	X
ejpam-5159	171	2	.	.	PUNCT
ejpam-5159	172	1	mat.2022.01.04	mat.2022.01.04	PROPN
ejpam-5159	172	2	.	.	PUNCT
ejpam-5159	173	1	[	[	X
ejpam-5159	173	2	4	4	X
ejpam-5159	173	3	]	]	X
ejpam-5159	173	4	u.	u.	PROPN
ejpam-5159	173	5	n.	n.	PROPN
ejpam-5159	173	6	katugampola	katugampola	PROPN
ejpam-5159	173	7	,	,	PUNCT
ejpam-5159	173	8	“	"	PUNCT
ejpam-5159	173	9	a	a	DET
ejpam-5159	173	10	new	new	ADJ
ejpam-5159	173	11	fractional	fractional	ADJ
ejpam-5159	173	12	derivative	derivative	NOUN
ejpam-5159	173	13	with	with	ADP
ejpam-5159	173	14	classical	classical	ADJ
ejpam-5159	173	15	properties	property	NOUN
ejpam-5159	173	16	,	,	PUNCT
ejpam-5159	173	17	”	"	PUNCT
ejpam-5159	173	18	e	e	NOUN
ejpam-5159	173	19	-	-	NOUN
ejpam-5159	173	20	print	print	NOUN
ejpam-5159	173	21	arxiv:1410.6535	arxiv:1410.6535	NOUN
ejpam-5159	173	22	.	.	PUNCT
ejpam-5159	174	1	[	[	X
ejpam-5159	174	2	5	5	NUM
ejpam-5159	174	3	]	]	PUNCT
ejpam-5159	174	4	ahmed	ahmed	PROPN
ejpam-5159	174	5	kajouni	kajouni	PROPN
ejpam-5159	174	6	,	,	PUNCT
ejpam-5159	174	7	ahmed	ahmed	PROPN
ejpam-5159	174	8	chafiki	chafiki	PROPN
ejpam-5159	174	9	,	,	PUNCT
ejpam-5159	174	10	khalid	khalid	PROPN
ejpam-5159	174	11	hilal	hilal	PROPN
ejpam-5159	174	12	,	,	PUNCT
ejpam-5159	174	13	and	and	CCONJ
ejpam-5159	174	14	mohamed	mohame	VERB
ejpam-5159	174	15	oukessoua	oukessoua	ADJ
ejpam-5159	174	16	new	new	ADJ
ejpam-5159	174	17	conformable	conformable	ADJ
ejpam-5159	174	18	fractional	fractional	ADJ
ejpam-5159	174	19	derivative	derivative	NOUN
ejpam-5159	174	20	and	and	CCONJ
ejpam-5159	174	21	applications	application	NOUN
ejpam-5159	174	22	2021.https://doi.org/10.1155/2021/6245435	2021.https://doi.org/10.1155/2021/6245435	NUM
ejpam-5159	174	23	[	[	X
ejpam-5159	174	24	6	6	NUM
ejpam-5159	174	25	]	]	X
ejpam-5159	174	26	soumia	soumia	ADJ
ejpam-5159	174	27	tayebi	tayebi	NOUN
ejpam-5159	174	28	,	,	PUNCT
ejpam-5159	174	29	shaher	shaher	ADJ
ejpam-5159	174	30	momani	momani	NOUN
ejpam-5159	174	31	,	,	PUNCT
ejpam-5159	174	32	omar	omar	PROPN
ejpam-5159	174	33	abu	abu	PROPN
ejpam-5159	174	34	arqub	arqub	PROPN
ejpam-5159	174	35	,	,	PUNCT
ejpam-5159	174	36	the	the	DET
ejpam-5159	174	37	cubic	cubic	ADJ
ejpam-5159	174	38	b	b	PROPN
ejpam-5159	174	39	-	-	PUNCT
ejpam-5159	174	40	spline	spline	NOUN
ejpam-5159	174	41	interpolation	interpolation	NOUN
ejpam-5159	174	42	method	method	NOUN
ejpam-5159	174	43	for	for	ADP
ejpam-5159	174	44	numerical	numerical	ADJ
ejpam-5159	174	45	point	point	NOUN
ejpam-5159	174	46	solutions	solution	NOUN
ejpam-5159	174	47	of	of	ADP
ejpam-5159	174	48	conformable	conformable	ADJ
ejpam-5159	174	49	boundary	boundary	ADJ
ejpam-5159	174	50	value	value	NOUN
ejpam-5159	174	51	problems	problem	NOUN
ejpam-5159	174	52	,	,	PUNCT
ejpam-5159	174	53	alexandria	alexandria	PROPN
ejpam-5159	174	54	engineering	engineering	PROPN
ejpam-5159	174	55	journal	journal	PROPN
ejpam-5159	174	56	,	,	PUNCT
ejpam-5159	174	57	https://doi.org/10.1016/j.aej.2021.06.057	https://doi.org/10.1016/j.aej.2021.06.057	INTJ
ejpam-5159	174	58	.	.	PUNCT
ejpam-5159	175	1	[	[	X
ejpam-5159	175	2	7	7	X
ejpam-5159	175	3	]	]	X
ejpam-5159	175	4	khalil	khalil	PROPN
ejpam-5159	175	5	r	r	PROPN
ejpam-5159	175	6	,	,	PUNCT
ejpam-5159	175	7	al	al	PROPN
ejpam-5159	175	8	-	-	PUNCT
ejpam-5159	175	9	horani	horani	PROPN
ejpam-5159	175	10	m	m	PROPN
ejpam-5159	175	11	,	,	PUNCT
ejpam-5159	175	12	yousef	yousef	PROPN
ejpam-5159	175	13	a	a	X
ejpam-5159	175	14	,	,	PUNCT
ejpam-5159	175	15	sababheh	sababheh	ADJ
ejpam-5159	175	16	m.	m.	NOUN
ejpam-5159	175	17	a	a	DET
ejpam-5159	175	18	new	new	ADJ
ejpam-5159	175	19	definition	definition	NOUN
ejpam-5159	175	20	of	of	ADP
ejpam-5159	175	21	fractional	fractional	ADJ
ejpam-5159	175	22	derivative	derivative	NOUN
ejpam-5159	175	23	.	.	PUNCT
ejpam-5159	176	1	journal	journal	PROPN
ejpam-5159	176	2	of	of	ADP
ejpam-5159	176	3	computational	computational	ADJ
ejpam-5159	176	4	and	and	CCONJ
ejpam-5159	176	5	applied	applied	ADJ
ejpam-5159	176	6	mathematics	mathematic	NOUN
ejpam-5159	176	7	2014	2014	NUM
ejpam-5159	176	8	;	;	PUNCT
ejpam-5159	176	9	264:65	264:65	NUM
ejpam-5159	176	10	-	-	SYM
ejpam-5159	176	11	70	70	NUM
ejpam-5159	176	12	.	.	PUNCT
ejpam-5159	177	1	[	[	X
ejpam-5159	177	2	8	8	NUM
ejpam-5159	177	3	]	]	X
ejpam-5159	177	4	s.m	s.m	PROPN
ejpam-5159	177	5	.	.	PROPN
ejpam-5159	177	6	nuugulu	nuugulu	PROPN
ejpam-5159	177	7	,	,	PUNCT
ejpam-5159	177	8	f.	f.	PROPN
ejpam-5159	177	9	gideon	gideon	PROPN
ejpam-5159	177	10	and	and	CCONJ
ejpam-5159	177	11	k.c	k.c	PROPN
ejpam-5159	177	12	.	.	PROPN
ejpam-5159	177	13	patidar	patidar	PROPN
ejpam-5159	177	14	,	,	PUNCT
ejpam-5159	177	15	a	a	DET
ejpam-5159	177	16	robust	robust	ADJ
ejpam-5159	177	17	numerical	numerical	ADJ
ejpam-5159	177	18	solution	solution	NOUN
ejpam-5159	177	19	to	to	ADP
ejpam-5159	177	20	a	a	DET
ejpam-5159	177	21	timefractional	timefractional	ADJ
ejpam-5159	177	22	black	black	ADJ
ejpam-5159	177	23	–	–	PUNCT
ejpam-5159	177	24	scholes	schole	NOUN
ejpam-5159	177	25	equation	equation	NOUN
ejpam-5159	177	26	https://doi.org/10.1186/s13662-021-03259-2	https://doi.org/10.1186/s13662-021-03259-2	NOUN
ejpam-5159	178	1	[	[	X
ejpam-5159	178	2	9	9	NUM
ejpam-5159	178	3	]	]	X
ejpam-5159	178	4	p.	p.	NOUN
ejpam-5159	178	5	m.	m.	NOUN
ejpam-5159	178	6	guzmán	guzmán	PROPN
ejpam-5159	178	7	,	,	PUNCT
ejpam-5159	178	8	g.	g.	PROPN
ejpam-5159	178	9	langton	langton	PROPN
ejpam-5159	178	10	,	,	PUNCT
ejpam-5159	178	11	l.	l.	PROPN
ejpam-5159	178	12	m.	m.	PROPN
ejpam-5159	178	13	lugo	lugo	PROPN
ejpam-5159	178	14	motta	motta	PROPN
ejpam-5159	178	15	,	,	PUNCT
ejpam-5159	178	16	j.	j.	PROPN
ejpam-5159	178	17	medina	medina	PROPN
ejpam-5159	178	18	,	,	PUNCT
ejpam-5159	178	19	j.	j.	PROPN
ejpam-5159	178	20	e.	e.	PROPN
ejpam-5159	178	21	nápoles	nápoles	PROPN
ejpam-5159	178	22	,	,	PUNCT
ejpam-5159	178	23	a	a	DET
ejpam-5159	178	24	new	new	ADJ
ejpam-5159	178	25	definition	definition	NOUN
ejpam-5159	178	26	of	of	ADP
ejpam-5159	178	27	a	a	DET
ejpam-5159	178	28	fractional	fractional	ADJ
ejpam-5159	178	29	derivative	derivative	NOUN
ejpam-5159	178	30	of	of	ADP
ejpam-5159	178	31	local	local	ADJ
ejpam-5159	178	32	type	type	NOUN
ejpam-5159	178	33	.	.	PUNCT
ejpam-5159	179	1	j.	j.	PROPN
ejpam-5159	179	2	math	math	PROPN
ejpam-5159	179	3	.	.	PUNCT
ejpam-5159	180	1	anal	anal	ADJ
ejpam-5159	180	2	.	.	PUNCT
ejpam-5159	181	1	2018	2018	NUM
ejpam-5159	181	2	,	,	PUNCT
ejpam-5159	181	3	9	9	NUM
ejpam-5159	181	4	,	,	PUNCT
ejpam-5159	181	5	88–96	88–96	NUM
ejpam-5159	181	6	.	.	PUNCT
ejpam-5159	182	1	[	[	X
ejpam-5159	182	2	10	10	NUM
ejpam-5159	182	3	]	]	X
ejpam-5159	182	4	j.	j.	PROPN
ejpam-5159	182	5	e.	e.	PROPN
ejpam-5159	182	6	nápoles	nápoles	PROPN
ejpam-5159	182	7	,	,	PUNCT
ejpam-5159	182	8	p.	p.	NOUN
ejpam-5159	182	9	m.	m.	NOUN
ejpam-5159	182	10	guzmán	guzmán	PROPN
ejpam-5159	182	11	,	,	PUNCT
ejpam-5159	182	12	l.	l.	PROPN
ejpam-5159	182	13	m.	m.	PROPN
ejpam-5159	182	14	lugo	lugo	PROPN
ejpam-5159	182	15	,	,	PUNCT
ejpam-5159	182	16	a.	a.	NOUN
ejpam-5159	182	17	kashuri	kashuri	PROPN
ejpam-5159	182	18	,	,	PUNCT
ejpam-5159	182	19	the	the	DET
ejpam-5159	182	20	local	local	ADJ
ejpam-5159	182	21	non	non	ADJ
ejpam-5159	182	22	conformable	conformable	ADJ
ejpam-5159	182	23	derivative	derivative	ADJ
ejpam-5159	182	24	and	and	CCONJ
ejpam-5159	182	25	mittag	mittag	ADJ
ejpam-5159	182	26	leffler	leffl	ADJ
ejpam-5159	182	27	function	function	NOUN
ejpam-5159	182	28	,	,	PUNCT
ejpam-5159	182	29	sigma	sigma	PROPN
ejpam-5159	182	30	j	j	PROPN
ejpam-5159	182	31	eng	eng	PROPN
ejpam-5159	182	32	&	&	CCONJ
ejpam-5159	182	33	nat	nat	PROPN
ejpam-5159	182	34	sci	sci	PROPN
ejpam-5159	182	35	38	38	NUM
ejpam-5159	182	36	(	(	PUNCT
ejpam-5159	182	37	2	2	NUM
ejpam-5159	182	38	)	)	PUNCT
ejpam-5159	182	39	,	,	PUNCT
ejpam-5159	182	40	2020	2020	NUM
ejpam-5159	182	41	,	,	PUNCT
ejpam-5159	182	42	1007	1007	NUM
ejpam-5159	182	43	-	-	SYM
ejpam-5159	182	44	1017	1017	NUM
ejpam-5159	182	45	[	[	X
ejpam-5159	182	46	11	11	NUM
ejpam-5159	182	47	]	]	PUNCT
ejpam-5159	182	48	a.	a.	NOUN
ejpam-5159	182	49	fleitas	fleitas	PROPN
ejpam-5159	182	50	,	,	PUNCT
ejpam-5159	182	51	j.	j.	PROPN
ejpam-5159	182	52	e.	e.	PROPN
ejpam-5159	182	53	nápoles	nápoles	PROPN
ejpam-5159	182	54	,	,	PUNCT
ejpam-5159	182	55	j.	j.	PROPN
ejpam-5159	182	56	m.	m.	PROPN
ejpam-5159	182	57	rodŕıguez	rodŕıguez	PROPN
ejpam-5159	182	58	,	,	PUNCT
ejpam-5159	182	59	j.	j.	PROPN
ejpam-5159	182	60	m.	m.	PROPN
ejpam-5159	182	61	sigarreta	sigarreta	PROPN
ejpam-5159	182	62	,	,	PUNCT
ejpam-5159	182	63	note	note	VERB
ejpam-5159	182	64	on	on	ADP
ejpam-5159	182	65	the	the	DET
ejpam-5159	182	66	generalized	generalized	ADJ
ejpam-5159	182	67	conformable	conformable	ADJ
ejpam-5159	182	68	derivative	derivative	ADJ
ejpam-5159	182	69	,	,	PUNCT
ejpam-5159	182	70	revista	revista	X
ejpam-5159	182	71	de	de	X
ejpam-5159	182	72	la	la	PROPN
ejpam-5159	182	73	uma	uma	PROPN
ejpam-5159	182	74	,	,	PUNCT
ejpam-5159	182	75	volume	volume	NOUN
ejpam-5159	182	76	62	62	NUM
ejpam-5159	182	77	,	,	PUNCT
ejpam-5159	182	78	no	no	INTJ
ejpam-5159	182	79	.	.	NOUN
ejpam-5159	182	80	2	2	NUM
ejpam-5159	182	81	(	(	PUNCT
ejpam-5159	182	82	2021	2021	NUM
ejpam-5159	182	83	)	)	PUNCT
ejpam-5159	182	84	,	,	PUNCT
ejpam-5159	182	85	443	443	NUM
ejpam-5159	182	86	-	-	SYM
ejpam-5159	182	87	457	457	NUM
ejpam-5159	182	88	https://doi.org/10.33044/revuma.1930	https://doi.org/10.33044/revuma.1930	NOUN
ejpam-5159	183	1	[	[	X
ejpam-5159	183	2	12	12	NUM
ejpam-5159	183	3	]	]	X
ejpam-5159	183	4	miguel	miguel	PROPN
ejpam-5159	183	5	vivas	vivas	PROPN
ejpam-5159	183	6	-	-	PROPN
ejpam-5159	183	7	cortez	cortez	PROPN
ejpam-5159	183	8	,	,	PUNCT
ejpam-5159	183	9	juan	juan	PROPN
ejpam-5159	183	10	e.	e.	PROPN
ejpam-5159	183	11	nápoles	nápoles	PROPN
ejpam-5159	183	12	valdés	valdés	PROPN
ejpam-5159	183	13	,	,	PUNCT
ejpam-5159	183	14	shilpi	shilpi	NOUN
ejpam-5159	183	15	jain	jain	PROPN
ejpam-5159	183	16	,	,	PUNCT
ejpam-5159	183	17	praveen	praveen	PROPN
ejpam-5159	183	18	agarwal	agarwal	PROPN
ejpam-5159	183	19	,	,	PUNCT
ejpam-5159	183	20	on	on	ADP
ejpam-5159	183	21	a	a	DET
ejpam-5159	183	22	generalized	generalized	ADJ
ejpam-5159	183	23	fractional	fractional	ADJ
ejpam-5159	183	24	integral	integral	ADJ
ejpam-5159	183	25	and	and	CCONJ
ejpam-5159	183	26	related	related	ADJ
ejpam-5159	183	27	methodological	methodological	ADJ
ejpam-5159	183	28	remarks	remark	NOUN
ejpam-5159	183	29	,	,	PUNCT
ejpam-5159	183	30	applied	apply	VERB
ejpam-5159	183	31	mathematics	mathematics	PROPN
ejpam-5159	183	32	&	&	CCONJ
ejpam-5159	183	33	information	information	PROPN
ejpam-5159	183	34	sciences	sciences	PROPN
ejpam-5159	183	35	(	(	PUNCT
ejpam-5159	183	36	17)4	17)4	NUM
ejpam-5159	183	37	(	(	PUNCT
ejpam-5159	183	38	jul	jul	PROPN
ejpam-5159	183	39	.	.	PROPN
ejpam-5159	183	40	2023	2023	NUM
ejpam-5159	183	41	)	)	PUNCT
ejpam-5159	183	42	,	,	PUNCT
ejpam-5159	183	43	615	615	NUM
ejpam-5159	183	44	-	-	SYM
ejpam-5159	183	45	623	623	NUM
ejpam-5159	183	46	doi:10.18576	doi:10.18576	NOUN
ejpam-5159	183	47	/	/	SYM
ejpam-5159	183	48	amis/170409	amis/170409	PROPN
ejpam-5159	184	1	[	[	X
ejpam-5159	184	2	13	13	NUM
ejpam-5159	184	3	]	]	PUNCT
ejpam-5159	184	4	d.	d.	PROPN
ejpam-5159	184	5	zhao	zhao	PROPN
ejpam-5159	184	6	,	,	PUNCT
ejpam-5159	184	7	m.	m.	NOUN
ejpam-5159	184	8	luo	luo	PROPN
ejpam-5159	184	9	,	,	PUNCT
ejpam-5159	184	10	general	general	ADJ
ejpam-5159	184	11	conformable	conformable	ADJ
ejpam-5159	184	12	fractional	fractional	ADJ
ejpam-5159	184	13	derivative	derivative	NOUN
ejpam-5159	184	14	and	and	CCONJ
ejpam-5159	184	15	its	its	PRON
ejpam-5159	184	16	physical	physical	ADJ
ejpam-5159	184	17	interpretation	interpretation	NOUN
ejpam-5159	184	18	.	.	PUNCT
ejpam-5159	185	1	calcolo	calcolo	PROPN
ejpam-5159	185	2	2017	2017	NUM
ejpam-5159	185	3	,	,	PUNCT
ejpam-5159	185	4	54	54	NUM
ejpam-5159	185	5	,	,	PUNCT
ejpam-5159	185	6	903–917	903–917	NUM
ejpam-5159	185	7	.	.	PUNCT
ejpam-5159	186	1	[	[	X
ejpam-5159	186	2	14	14	NUM
ejpam-5159	186	3	]	]	PUNCT
ejpam-5159	186	4	a.	a.	NOUN
ejpam-5159	186	5	fleitas	fleitas	PROPN
ejpam-5159	186	6	,	,	PUNCT
ejpam-5159	186	7	j.	j.	PROPN
ejpam-5159	186	8	a.	a.	PROPN
ejpam-5159	186	9	méndez	méndez	PROPN
ejpam-5159	186	10	,	,	PUNCT
ejpam-5159	186	11	j.	j.	PROPN
ejpam-5159	186	12	e.	e.	PROPN
ejpam-5159	186	13	nápoles	nápoles	PROPN
ejpam-5159	186	14	,	,	PUNCT
ejpam-5159	186	15	j.	j.	PROPN
ejpam-5159	186	16	m.	m.	PROPN
ejpam-5159	186	17	sigarreta	sigarreta	PROPN
ejpam-5159	186	18	,	,	PUNCT
ejpam-5159	186	19	on	on	ADP
ejpam-5159	186	20	fractional	fractional	ADJ
ejpam-5159	186	21	liénard	liénard	NOUN
ejpam-5159	186	22	-	-	PUNCT
ejpam-5159	186	23	type	type	NOUN
ejpam-5159	186	24	systems	system	NOUN
ejpam-5159	186	25	,	,	PUNCT
ejpam-5159	186	26	rev	rev	PROPN
ejpam-5159	186	27	.	.	PROPN
ejpam-5159	186	28	mex	mex	PROPN
ejpam-5159	186	29	.	.	PUNCT
ejpam-5159	187	1	f́ısica	f́ısica	PRON
ejpam-5159	187	2	2019	2019	NUM
ejpam-5159	187	3	,	,	PUNCT
ejpam-5159	187	4	65	65	NUM
ejpam-5159	187	5	,	,	PUNCT
ejpam-5159	187	6	618–625	618–625	NUM
ejpam-5159	187	7	.	.	PUNCT
ejpam-5159	188	1	[	[	X
ejpam-5159	188	2	15	15	NUM
ejpam-5159	188	3	]	]	X
ejpam-5159	188	4	f.	f.	PROPN
ejpam-5159	188	5	mart́ınez	mart́ınez	PROPN
ejpam-5159	188	6	,	,	PUNCT
ejpam-5159	188	7	j.	j.	PROPN
ejpam-5159	188	8	e.	e.	PROPN
ejpam-5159	188	9	nápoles	nápoles	PROPN
ejpam-5159	188	10	valdés	valdés	PROPN
ejpam-5159	188	11	,	,	PUNCT
ejpam-5159	188	12	towards	towards	ADP
ejpam-5159	188	13	a	a	DET
ejpam-5159	188	14	non	non	ADJ
ejpam-5159	188	15	-	-	ADJ
ejpam-5159	188	16	conformable	conformable	ADJ
ejpam-5159	188	17	fractional	fractional	ADJ
ejpam-5159	188	18	calculus	calculus	NOUN
ejpam-5159	188	19	of	of	ADP
ejpam-5159	188	20	n	n	CCONJ
ejpam-5159	188	21	-	-	PUNCT
ejpam-5159	188	22	variables	variable	NOUN
ejpam-5159	188	23	,	,	PUNCT
ejpam-5159	188	24	journal	journal	NOUN
ejpam-5159	188	25	of	of	ADP
ejpam-5159	188	26	mathematics	mathematic	NOUN
ejpam-5159	188	27	and	and	CCONJ
ejpam-5159	188	28	applications	application	NOUN
ejpam-5159	188	29	,	,	PUNCT
ejpam-5159	188	30	jma	jma	PROPN
ejpam-5159	188	31	no	no	PRON
ejpam-5159	188	32	43	43	NUM
ejpam-5159	188	33	,	,	PUNCT
ejpam-5159	188	34	87	87	NUM
ejpam-5159	188	35	-	-	SYM
ejpam-5159	188	36	98	98	NUM
ejpam-5159	188	37	(	(	PUNCT
ejpam-5159	188	38	2020	2020	NUM
ejpam-5159	188	39	)	)	PUNCT
ejpam-5159	188	40	references	reference	NOUN
ejpam-5159	188	41	1167	1167	NUM
ejpam-5159	189	1	[	[	X
ejpam-5159	189	2	16	16	NUM
ejpam-5159	189	3	]	]	PUNCT
ejpam-5159	189	4	j.	j.	PROPN
ejpam-5159	189	5	e.	e.	PROPN
ejpam-5159	189	6	nápoles	nápoles	PROPN
ejpam-5159	189	7	valdés	valdés	PROPN
ejpam-5159	189	8	,	,	PUNCT
ejpam-5159	189	9	p.	p.	NOUN
ejpam-5159	189	10	m.	m.	NOUN
ejpam-5159	189	11	guzmán	guzmán	PROPN
ejpam-5159	189	12	,	,	PUNCT
ejpam-5159	189	13	l.	l.	PROPN
ejpam-5159	189	14	m.	m.	PROPN
ejpam-5159	189	15	lugo	lugo	PROPN
ejpam-5159	189	16	,	,	PUNCT
ejpam-5159	189	17	some	some	DET
ejpam-5159	189	18	new	new	ADJ
ejpam-5159	189	19	results	result	NOUN
ejpam-5159	189	20	on	on	ADP
ejpam-5159	189	21	nonconformable	nonconformable	ADJ
ejpam-5159	189	22	fractional	fractional	ADJ
ejpam-5159	189	23	calculus	calculus	NOUN
ejpam-5159	189	24	,	,	PUNCT
ejpam-5159	189	25	advances	advance	NOUN
ejpam-5159	189	26	in	in	ADP
ejpam-5159	189	27	dynamical	dynamical	ADJ
ejpam-5159	189	28	systems	system	NOUN
ejpam-5159	189	29	and	and	CCONJ
ejpam-5159	189	30	applications	application	NOUN
ejpam-5159	189	31	,	,	PUNCT
ejpam-5159	189	32	volume	volume	NOUN
ejpam-5159	189	33	13	13	NUM
ejpam-5159	189	34	,	,	PUNCT
ejpam-5159	189	35	number	number	NOUN
ejpam-5159	189	36	2	2	NUM
ejpam-5159	189	37	,	,	PUNCT
ejpam-5159	189	38	2018	2018	NUM
ejpam-5159	189	39	,	,	PUNCT
ejpam-5159	189	40	167–175	167–175	NUM
ejpam-5159	189	41	.	.	PUNCT
ejpam-5159	190	1	[	[	X
ejpam-5159	190	2	17	17	NUM
ejpam-5159	190	3	]	]	X
ejpam-5159	190	4	juan	juan	PROPN
ejpam-5159	190	5	e.	e.	PROPN
ejpam-5159	190	6	nápoles	nápoles	PROPN
ejpam-5159	190	7	valdes	valde	NOUN
ejpam-5159	190	8	,	,	PUNCT
ejpam-5159	190	9	the	the	DET
ejpam-5159	190	10	non	non	ADJ
ejpam-5159	190	11	-	-	ADJ
ejpam-5159	190	12	integer	integer	ADJ
ejpam-5159	190	13	local	local	ADJ
ejpam-5159	190	14	order	order	NOUN
ejpam-5159	190	15	calculus	calculus	NOUN
ejpam-5159	190	16	,	,	PUNCT
ejpam-5159	190	17	phys	phy	NOUN
ejpam-5159	190	18	astron	astron	ADJ
ejpam-5159	190	19	int	int	NOUN
ejpam-5159	190	20	j.	j.	PROPN
ejpam-5159	190	21	2023	2023	NUM
ejpam-5159	190	22	;	;	PUNCT
ejpam-5159	190	23	7(3):163	7(3):163	NUM
ejpam-5159	190	24	-	-	SYM
ejpam-5159	190	25	168	168	NUM
ejpam-5159	190	26	.	.	PUNCT
ejpam-5159	191	1	doi	doi	NOUN
ejpam-5159	191	2	:	:	PUNCT
ejpam-5159	191	3	10.15406	10.15406	NUM
ejpam-5159	191	4	/	/	SYM
ejpam-5159	191	5	paij.2023.07.00304	paij.2023.07.00304	NOUN
ejpam-5159	191	6	.	.	PUNCT
ejpam-5159	192	1	[	[	X
ejpam-5159	192	2	18	18	NUM
ejpam-5159	192	3	]	]	PUNCT
ejpam-5159	192	4	f.	f.	PROPN
ejpam-5159	192	5	mart́ınez	mart́ınez	PROPN
ejpam-5159	192	6	,	,	PUNCT
ejpam-5159	192	7	f.	f.	PROPN
ejpam-5159	192	8	,	,	PUNCT
ejpam-5159	192	9	p.	p.	PROPN
ejpam-5159	192	10	o.	o.	PROPN
ejpam-5159	192	11	mohammed	mohammed	PROPN
ejpam-5159	192	12	,	,	PUNCT
ejpam-5159	192	13	j.	j.	PROPN
ejpam-5159	192	14	e.	e.	PROPN
ejpam-5159	192	15	nápoles	nápoles	PROPN
ejpam-5159	192	16	valdés	valdés	PROPN
ejpam-5159	192	17	,	,	PUNCT
ejpam-5159	192	18	non	non	X
ejpam-5159	192	19	conformable	conformable	ADJ
ejpam-5159	192	20	fractional	fractional	ADJ
ejpam-5159	192	21	laplace	laplace	NOUN
ejpam-5159	192	22	transform	transform	NOUN
ejpam-5159	192	23	.	.	PUNCT
ejpam-5159	193	1	kragujevac	kragujevac	PROPN
ejpam-5159	193	2	j.	j.	PROPN
ejpam-5159	193	3	of	of	ADP
ejpam-5159	193	4	math	math	NOUN
ejpam-5159	193	5	.	.	PUNCT
ejpam-5159	194	1	2022	2022	NUM
ejpam-5159	194	2	,	,	PUNCT
ejpam-5159	194	3	46(3	46(3	NOUN
ejpam-5159	194	4	)	)	PUNCT
ejpam-5159	195	1	,	,	PUNCT
ejpam-5159	195	2	pages	page	VERB
ejpam-5159	195	3	341	341	NUM
ejpam-5159	195	4	-	-	SYM
ejpam-5159	195	5	354	354	NUM
ejpam-5159	195	6	.	.	PUNCT
ejpam-5159	196	1	[	[	X
ejpam-5159	196	2	19	19	NUM
ejpam-5159	196	3	]	]	X
ejpam-5159	196	4	vivas	vivas	PROPN
ejpam-5159	196	5	-	-	NOUN
ejpam-5159	196	6	cortez	cortez	PROPN
ejpam-5159	196	7	,	,	PUNCT
ejpam-5159	196	8	m.	m.	NOUN
ejpam-5159	196	9	;	;	PUNCT
ejpam-5159	196	10	fleitas	fleita	NOUN
ejpam-5159	196	11	,	,	PUNCT
ejpam-5159	196	12	a.	a.	NOUN
ejpam-5159	196	13	;	;	PUNCT
ejpam-5159	196	14	guzmán	guzmán	PROPN
ejpam-5159	196	15	,	,	PUNCT
ejpam-5159	196	16	p.m.	p.m.	NOUN
ejpam-5159	196	17	;	;	PUNCT
ejpam-5159	196	18	nápoles	nápoles	PROPN
ejpam-5159	196	19	,	,	PUNCT
ejpam-5159	196	20	j.e	j.e	PROPN
ejpam-5159	196	21	.	.	PROPN
ejpam-5159	196	22	;	;	PUNCT
ejpam-5159	196	23	rosales	rosale	NOUN
ejpam-5159	196	24	,	,	PUNCT
ejpam-5159	196	25	j.j	j.j	PROPN
ejpam-5159	196	26	.	.	PROPN
ejpam-5159	196	27	newton	newton	PROPN
ejpam-5159	196	28	’s	’s	PART
ejpam-5159	196	29	law	law	NOUN
ejpam-5159	196	30	of	of	ADP
ejpam-5159	196	31	cooling	cool	VERB
ejpam-5159	196	32	with	with	ADP
ejpam-5159	196	33	generalized	generalized	ADJ
ejpam-5159	196	34	conformable	conformable	ADJ
ejpam-5159	196	35	derivatives	derivative	NOUN
ejpam-5159	196	36	.	.	PUNCT
ejpam-5159	197	1	symmetry	symmetry	NOUN
ejpam-5159	197	2	2021	2021	NUM
ejpam-5159	197	3	,	,	PUNCT
ejpam-5159	197	4	13	13	NUM
ejpam-5159	197	5	,	,	PUNCT
ejpam-5159	197	6	1093	1093	NUM
ejpam-5159	197	7	.	.	PUNCT
ejpam-5159	198	1	https://doi.org/10.3390/sym13061093	https://doi.org/10.3390/sym13061093	PROPN
ejpam-5159	198	2	.	.	PUNCT
ejpam-5159	199	1	[	[	X
ejpam-5159	199	2	20	20	NUM
ejpam-5159	199	3	]	]	PUNCT
ejpam-5159	199	4	m.	m.	NOUN
ejpam-5159	199	5	abu	abu	PROPN
ejpam-5159	199	6	hammad	hammad	PROPN
ejpam-5159	199	7	,	,	PUNCT
ejpam-5159	199	8	r.	r.	PROPN
ejpam-5159	199	9	khalil	khalil	PROPN
ejpam-5159	199	10	,	,	PUNCT
ejpam-5159	199	11	conformable	conformable	ADJ
ejpam-5159	199	12	fractional	fractional	ADJ
ejpam-5159	199	13	heat	heat	NOUN
ejpam-5159	199	14	differential	differential	NOUN
ejpam-5159	199	15	equation	equation	NOUN
ejpam-5159	199	16	,	,	PUNCT
ejpam-5159	199	17	international	international	ADJ
ejpam-5159	199	18	journal	journal	NOUN
ejpam-5159	199	19	of	of	ADP
ejpam-5159	199	20	pure	pure	ADJ
ejpam-5159	199	21	and	and	CCONJ
ejpam-5159	199	22	applied	applied	ADJ
ejpam-5159	199	23	mathematics	mathematic	NOUN
ejpam-5159	199	24	,	,	PUNCT
ejpam-5159	199	25	http://dx.doi.org/10.12732/ijpam.v94i2.8	http://dx.doi.org/10.12732/ijpam.v94i2.8	PROPN
ejpam-5159	199	26	.	.	PUNCT
ejpam-5159	200	1	[	[	X
ejpam-5159	200	2	21	21	NUM
ejpam-5159	200	3	]	]	X
ejpam-5159	200	4	fareeha	fareeha	PROPN
ejpam-5159	200	5	sami	sami	PROPN
ejpam-5159	200	6	khan	khan	PROPN
ejpam-5159	200	7	,	,	PUNCT
ejpam-5159	200	8	m.	m.	PROPN
ejpam-5159	200	9	khalid	khalid	PROPN
ejpam-5159	200	10	,	,	PUNCT
ejpam-5159	200	11	areej	areej	PROPN
ejpam-5159	200	12	a.	a.	PROPN
ejpam-5159	200	13	al	al	PROPN
ejpam-5159	200	14	-	-	PROPN
ejpam-5159	200	15	moneef	moneef	PROPN
ejpam-5159	200	16	,	,	PUNCT
ejpam-5159	200	17	ali	ali	PROPN
ejpam-5159	200	18	hasan	hasan	PROPN
ejpam-5159	200	19	ali	ali	PROPN
ejpam-5159	200	20	,	,	PUNCT
ejpam-5159	200	21	and	and	CCONJ
ejpam-5159	200	22	omar	omar	PROPN
ejpam-5159	200	23	bazighifan	bazighifan	PROPN
ejpam-5159	200	24	,	,	PUNCT
ejpam-5159	200	25	freelance	freelance	NOUN
ejpam-5159	200	26	model	model	NOUN
ejpam-5159	200	27	with	with	ADP
ejpam-5159	200	28	atangana	atangana	PROPN
ejpam-5159	200	29	–	–	PUNCT
ejpam-5159	200	30	baleanu	baleanu	PROPN
ejpam-5159	200	31	caputo	caputo	PROPN
ejpam-5159	200	32	fractional	fractional	PROPN
ejpam-5159	200	33	derivative	derivative	PROPN
ejpam-5159	200	34	,	,	PUNCT
ejpam-5159	200	35	symmetry	symmetry	NOUN
ejpam-5159	200	36	in	in	ADP
ejpam-5159	200	37	nonlinear	nonlinear	ADJ
ejpam-5159	200	38	and	and	CCONJ
ejpam-5159	200	39	convex	convex	ADJ
ejpam-5159	200	40	analysis	analysis	NOUN
ejpam-5159	200	41	,	,	PUNCT
ejpam-5159	200	42	https://doi.org/10.3390/sym14112424	https://doi.org/10.3390/sym14112424	NUM
ejpam-5159	200	43	.	.	PUNCT
ejpam-5159	201	1	[	[	X
ejpam-5159	201	2	22	22	NUM
ejpam-5159	201	3	]	]	X
ejpam-5159	201	4	robert	robert	PROPN
ejpam-5159	201	5	reynolds	reynolds	PROPN
ejpam-5159	201	6	,	,	PUNCT
ejpam-5159	201	7	allan	allan	PROPN
ejpam-5159	201	8	stauffer	stauffer	PROPN
ejpam-5159	201	9	,	,	PUNCT
ejpam-5159	201	10	extended	extend	VERB
ejpam-5159	201	11	apelblat	apelblat	NOUN
ejpam-5159	201	12	integrals	integral	NOUN
ejpam-5159	201	13	for	for	ADP
ejpam-5159	201	14	fractional	fractional	ADJ
ejpam-5159	201	15	calculus	calculus	NOUN
ejpam-5159	201	16	,	,	PUNCT
ejpam-5159	201	17	european	european	ADJ
ejpam-5159	201	18	journal	journal	PROPN
ejpam-5159	201	19	of	of	ADP
ejpam-5159	201	20	pure	pure	ADJ
ejpam-5159	201	21	and	and	CCONJ
ejpam-5159	201	22	applied	applied	ADJ
ejpam-5159	201	23	mathematics	mathematic	NOUN
ejpam-5159	201	24	,	,	PUNCT
ejpam-5159	201	25	https://doi.org/10.29020/nybg.ejpam.v15i1.4181	https://doi.org/10.29020/nybg.ejpam.v15i1.4181	PRON
ejpam-5159	201	26	.	.	PUNCT
ejpam-5159	202	1	[	[	X
ejpam-5159	202	2	23	23	NUM
ejpam-5159	202	3	]	]	X
ejpam-5159	202	4	iman	iman	PROPN
ejpam-5159	202	5	aldarawi1	aldarawi1	NOUN
ejpam-5159	202	6	,	,	PUNCT
ejpam-5159	202	7	,	,	PUNCT
ejpam-5159	202	8	banan	banan	PROPN
ejpam-5159	202	9	maayah	maayah	PROPN
ejpam-5159	202	10	,	,	PUNCT
ejpam-5159	202	11	eman	eman	PROPN
ejpam-5159	202	12	aldabbas	aldabbas	PROPN
ejpam-5159	202	13	,	,	PUNCT
ejpam-5159	202	14	eman	eman	PROPN
ejpam-5159	202	15	abuteen	abuteen	PROPN
ejpam-5159	202	16	,	,	PUNCT
ejpam-5159	202	17	numerical	numerical	ADJ
ejpam-5159	202	18	solutions	solution	NOUN
ejpam-5159	202	19	of	of	ADP
ejpam-5159	202	20	some	some	DET
ejpam-5159	202	21	classes	class	NOUN
ejpam-5159	202	22	of	of	ADP
ejpam-5159	202	23	partial	partial	ADJ
ejpam-5159	202	24	differential	differential	ADJ
ejpam-5159	202	25	equations	equation	NOUN
ejpam-5159	202	26	of	of	ADP
ejpam-5159	202	27	fractional	fractional	ADJ
ejpam-5159	202	28	order	order	NOUN
ejpam-5159	202	29	,	,	PUNCT
ejpam-5159	202	30	european	european	ADJ
ejpam-5159	202	31	journal	journal	PROPN
ejpam-5159	202	32	of	of	ADP
ejpam-5159	202	33	pure	pure	ADJ
ejpam-5159	202	34	and	and	CCONJ
ejpam-5159	202	35	applied	applied	ADJ
ejpam-5159	202	36	mathematics	mathematic	NOUN
ejpam-5159	202	37	,	,	PUNCT
ejpam-5159	202	38	https://doi.org/10.29020/nybg.ejpam.v16i4.4928	https://doi.org/10.29020/nybg.ejpam.v16i4.4928	PROPN
ejpam-5159	202	39	.	.	PUNCT