id	sid	tid	token	lemma	pos
ejpam-5935	1	1	european	european	PROPN
ejpam-5935	1	2	journal	journal	PROPN
ejpam-5935	1	3	of	of	ADP
ejpam-5935	1	4	pure	pure	ADJ
ejpam-5935	1	5	and	and	CCONJ
ejpam-5935	1	6	applied	applied	ADJ
ejpam-5935	1	7	mathematics	mathematic	NOUN
ejpam-5935	1	8	2025	2025	NUM
ejpam-5935	1	9	,	,	PUNCT
ejpam-5935	1	10	vol	vol	NOUN
ejpam-5935	1	11	.	.	PROPN
ejpam-5935	1	12	18	18	NUM
ejpam-5935	1	13	,	,	PUNCT
ejpam-5935	1	14	issue	issue	NOUN
ejpam-5935	1	15	2	2	NUM
ejpam-5935	1	16	,	,	PUNCT
ejpam-5935	1	17	article	article	NOUN
ejpam-5935	1	18	number	number	NOUN
ejpam-5935	1	19	5935	5935	NUM
ejpam-5935	1	20	issn	issn	VERB
ejpam-5935	1	21	1307	1307	NUM
ejpam-5935	1	22	-	-	SYM
ejpam-5935	1	23	5543	5543	NUM
ejpam-5935	1	24	–	–	PUNCT
ejpam-5935	1	25	ejpam.com	ejpam.com	X
ejpam-5935	1	26	published	publish	VERB
ejpam-5935	1	27	by	by	ADP
ejpam-5935	1	28	new	new	PROPN
ejpam-5935	1	29	york	york	PROPN
ejpam-5935	1	30	business	business	PROPN
ejpam-5935	1	31	global	global	ADJ
ejpam-5935	1	32	existence	existence	NOUN
ejpam-5935	1	33	of	of	ADP
ejpam-5935	1	34	solutions	solution	NOUN
ejpam-5935	1	35	for	for	ADP
ejpam-5935	1	36	fractional	fractional	ADJ
ejpam-5935	1	37	order	order	NOUN
ejpam-5935	1	38	differential	differential	ADJ
ejpam-5935	1	39	equations	equation	NOUN
ejpam-5935	1	40	:	:	PUNCT
ejpam-5935	1	41	extended	extend	VERB
ejpam-5935	1	42	results	result	NOUN
ejpam-5935	1	43	saleh	saleh	PROPN
ejpam-5935	1	44	fahad	fahad	PROPN
ejpam-5935	1	45	aljurbua1,∗	aljurbua1,∗	PROPN
ejpam-5935	1	46	,	,	PUNCT
ejpam-5935	1	47	asamh	asamh	PROPN
ejpam-5935	1	48	alluhayb1	alluhayb1	PROPN
ejpam-5935	1	49	,	,	PUNCT
ejpam-5935	1	50	rawan	rawan	PROPN
ejpam-5935	1	51	alashwan1	alashwan1	PROPN
ejpam-5935	1	52	,	,	PUNCT
ejpam-5935	1	53	dhay	dhay	PROPN
ejpam-5935	1	54	alharbi1	alharbi1	PROPN
ejpam-5935	1	55	,	,	PUNCT
ejpam-5935	1	56	najd	najd	ADV
ejpam-5935	1	57	alharbi1	alharbi1	PROPN
ejpam-5935	1	58	,	,	PUNCT
ejpam-5935	1	59	wejdan	wejdan	PROPN
ejpam-5935	1	60	alrawji1	alrawji1	PROPN
ejpam-5935	1	61	,	,	PUNCT
ejpam-5935	1	62	najla	najla	PROPN
ejpam-5935	1	63	alharbi1	alharbi1	PROPN
ejpam-5935	1	64	,	,	PUNCT
ejpam-5935	1	65	majd	majd	PROPN
ejpam-5935	1	66	saad1	saad1	PROPN
ejpam-5935	1	67	,	,	PUNCT
ejpam-5935	1	68	rawan	rawan	PROPN
ejpam-5935	1	69	almutairi1	almutairi1	PROPN
ejpam-5935	1	70	,	,	PUNCT
ejpam-5935	1	71	reham	reham	NOUN
ejpam-5935	1	72	alharbi1	alharbi1	PROPN
ejpam-5935	1	73	,	,	PUNCT
ejpam-5935	1	74	asrar	asrar	VERB
ejpam-5935	1	75	alrashidi1	alrashidi1	PROPN
ejpam-5935	1	76	,	,	PUNCT
ejpam-5935	1	77	munirah	munirah	PROPN
ejpam-5935	1	78	alrashidi1	alrashidi1	PROPN
ejpam-5935	1	79	,	,	PUNCT
ejpam-5935	1	80	nuha	nuha	NOUN
ejpam-5935	1	81	alfuraih1	alfuraih1	ADJ
ejpam-5935	1	82	1	1	NUM
ejpam-5935	1	83	department	department	NOUN
ejpam-5935	1	84	of	of	ADP
ejpam-5935	1	85	mathematics	mathematic	NOUN
ejpam-5935	1	86	.	.	PUNCT
ejpam-5935	1	87	,	,	PUNCT
ejpam-5935	1	88	college	college	NOUN
ejpam-5935	1	89	of	of	ADP
ejpam-5935	1	90	science	science	NOUN
ejpam-5935	1	91	,	,	PUNCT
ejpam-5935	1	92	qassim	qassim	PROPN
ejpam-5935	1	93	university	university	PROPN
ejpam-5935	1	94	,	,	PUNCT
ejpam-5935	1	95	p.o	p.o	PROPN
ejpam-5935	1	96	.	.	PROPN
ejpam-5935	1	97	box	box	PROPN
ejpam-5935	1	98	6644	6644	NUM
ejpam-5935	1	99	,	,	PUNCT
ejpam-5935	1	100	buraydah	buraydah	NOUN
ejpam-5935	1	101	,	,	PUNCT
ejpam-5935	1	102	51452	51452	NUM
ejpam-5935	1	103	,	,	PUNCT
ejpam-5935	1	104	saudi	saudi	PROPN
ejpam-5935	1	105	arabia	arabia	PROPN
ejpam-5935	1	106	abstract	abstract	NOUN
ejpam-5935	1	107	.	.	PUNCT
ejpam-5935	2	1	this	this	DET
ejpam-5935	2	2	study	study	NOUN
ejpam-5935	2	3	investigates	investigate	VERB
ejpam-5935	2	4	the	the	DET
ejpam-5935	2	5	existence	existence	NOUN
ejpam-5935	2	6	of	of	ADP
ejpam-5935	2	7	solutions	solution	NOUN
ejpam-5935	2	8	for	for	ADP
ejpam-5935	2	9	nonlinear	nonlinear	ADJ
ejpam-5935	2	10	fractional	fractional	ADJ
ejpam-5935	2	11	differential	differential	ADJ
ejpam-5935	2	12	equations	equation	NOUN
ejpam-5935	2	13	of	of	ADP
ejpam-5935	2	14	order	order	NOUN
ejpam-5935	2	15	q	q	X
ejpam-5935	2	16	∈	∈	NOUN
ejpam-5935	2	17	(	(	PUNCT
ejpam-5935	2	18	1	1	NUM
ejpam-5935	2	19	,	,	PUNCT
ejpam-5935	2	20	2	2	NUM
ejpam-5935	2	21	]	]	PUNCT
ejpam-5935	2	22	.	.	PUNCT
ejpam-5935	3	1	we	we	PRON
ejpam-5935	3	2	establish	establish	VERB
ejpam-5935	3	3	new	new	ADJ
ejpam-5935	3	4	existence	existence	NOUN
ejpam-5935	3	5	results	result	NOUN
ejpam-5935	3	6	for	for	ADP
ejpam-5935	3	7	the	the	DET
ejpam-5935	3	8	boundary	boundary	ADJ
ejpam-5935	3	9	conditions	condition	NOUN
ejpam-5935	3	10	ξ(κ	ξ(κ	NUM
ejpam-5935	3	11	)	)	PUNCT
ejpam-5935	4	1	=	=	PUNCT
ejpam-5935	5	1	α	α	X
ejpam-5935	5	2	̸=	̸=	PROPN
ejpam-5935	5	3	0	0	NUM
ejpam-5935	5	4	and	and	CCONJ
ejpam-5935	5	5	ξ(ω	ξ(ω	NOUN
ejpam-5935	5	6	)	)	PUNCT
ejpam-5935	6	1	=	=	PUNCT
ejpam-5935	6	2	β	β	X
ejpam-5935	6	3	̸=	̸=	PROPN
ejpam-5935	6	4	0	0	NUM
ejpam-5935	6	5	by	by	ADP
ejpam-5935	6	6	incorporating	incorporate	VERB
ejpam-5935	6	7	an	an	DET
ejpam-5935	6	8	intermediate	intermediate	ADJ
ejpam-5935	6	9	point	point	NOUN
ejpam-5935	6	10	,	,	PUNCT
ejpam-5935	6	11	extending	extend	VERB
ejpam-5935	6	12	existing	exist	VERB
ejpam-5935	6	13	methodologies	methodology	NOUN
ejpam-5935	6	14	.	.	PUNCT
ejpam-5935	7	1	our	our	PRON
ejpam-5935	7	2	results	result	NOUN
ejpam-5935	7	3	rely	rely	VERB
ejpam-5935	7	4	on	on	ADP
ejpam-5935	7	5	fixed	fix	VERB
ejpam-5935	7	6	point	point	NOUN
ejpam-5935	7	7	theorems	theorem	NOUN
ejpam-5935	7	8	and	and	CCONJ
ejpam-5935	7	9	the	the	DET
ejpam-5935	7	10	contraction	contraction	NOUN
ejpam-5935	7	11	principle	principle	NOUN
ejpam-5935	7	12	,	,	PUNCT
ejpam-5935	7	13	which	which	PRON
ejpam-5935	7	14	provide	provide	VERB
ejpam-5935	7	15	a	a	DET
ejpam-5935	7	16	robust	robust	ADJ
ejpam-5935	7	17	framework	framework	NOUN
ejpam-5935	7	18	for	for	ADP
ejpam-5935	7	19	analyzing	analyze	VERB
ejpam-5935	7	20	these	these	DET
ejpam-5935	7	21	equations	equation	NOUN
ejpam-5935	7	22	.	.	PUNCT
ejpam-5935	8	1	we	we	PRON
ejpam-5935	8	2	also	also	ADV
ejpam-5935	8	3	provide	provide	VERB
ejpam-5935	8	4	several	several	ADJ
ejpam-5935	8	5	illustrative	illustrative	ADJ
ejpam-5935	8	6	examples	example	NOUN
ejpam-5935	8	7	to	to	PART
ejpam-5935	8	8	demonstrate	demonstrate	VERB
ejpam-5935	8	9	our	our	PRON
ejpam-5935	8	10	results	result	NOUN
ejpam-5935	8	11	,	,	PUNCT
ejpam-5935	8	12	showcasing	showcase	VERB
ejpam-5935	8	13	their	their	PRON
ejpam-5935	8	14	relevance	relevance	NOUN
ejpam-5935	8	15	in	in	ADP
ejpam-5935	8	16	theoretical	theoretical	ADJ
ejpam-5935	8	17	and	and	CCONJ
ejpam-5935	8	18	applied	applied	ADJ
ejpam-5935	8	19	contexts	context	NOUN
ejpam-5935	8	20	.	.	PUNCT
ejpam-5935	9	1	2020	2020	NUM
ejpam-5935	9	2	mathematics	mathematic	NOUN
ejpam-5935	9	3	subject	subject	NOUN
ejpam-5935	9	4	classifications	classification	NOUN
ejpam-5935	9	5	:	:	PUNCT
ejpam-5935	9	6	26a33	26a33	NUM
ejpam-5935	9	7	,	,	PUNCT
ejpam-5935	9	8	34a08	34a08	NUM
ejpam-5935	9	9	,	,	PUNCT
ejpam-5935	9	10	33e30	33e30	NUM
ejpam-5935	9	11	,	,	PUNCT
ejpam-5935	9	12	34a35	34a35	NUM
ejpam-5935	9	13	,	,	PUNCT
ejpam-5935	9	14	34a34	34a34	NUM
ejpam-5935	9	15	,	,	PUNCT
ejpam-5935	9	16	34k37	34k37	NUM
ejpam-5935	9	17	key	key	ADJ
ejpam-5935	9	18	words	word	NOUN
ejpam-5935	9	19	and	and	CCONJ
ejpam-5935	9	20	phrases	phrase	NOUN
ejpam-5935	9	21	:	:	PUNCT
ejpam-5935	9	22	fractional	fractional	ADJ
ejpam-5935	9	23	derivatives	derivative	NOUN
ejpam-5935	9	24	,	,	PUNCT
ejpam-5935	9	25	differential	differential	ADJ
ejpam-5935	9	26	equations	equation	NOUN
ejpam-5935	9	27	,	,	PUNCT
ejpam-5935	9	28	fractional	fractional	ADJ
ejpam-5935	9	29	differential	differential	NOUN
ejpam-5935	9	30	equations	equation	NOUN
ejpam-5935	9	31	,	,	PUNCT
ejpam-5935	9	32	antiperiodic	antiperiodic	ADJ
ejpam-5935	9	33	,	,	PUNCT
ejpam-5935	9	34	nonlocal	nonlocal	ADJ
ejpam-5935	9	35	boundary	boundary	ADJ
ejpam-5935	9	36	conditions	condition	NOUN
ejpam-5935	9	37	,	,	PUNCT
ejpam-5935	9	38	existence	existence	NOUN
ejpam-5935	9	39	1	1	NUM
ejpam-5935	9	40	.	.	PUNCT
ejpam-5935	9	41	introduction	introduction	NOUN
ejpam-5935	9	42	in	in	ADP
ejpam-5935	9	43	this	this	DET
ejpam-5935	9	44	research	research	NOUN
ejpam-5935	9	45	article	article	NOUN
ejpam-5935	9	46	,	,	PUNCT
ejpam-5935	9	47	we	we	PRON
ejpam-5935	9	48	study	study	VERB
ejpam-5935	9	49	the	the	DET
ejpam-5935	9	50	existence	existence	NOUN
ejpam-5935	9	51	of	of	ADP
ejpam-5935	9	52	solution	solution	NOUN
ejpam-5935	9	53	for	for	ADP
ejpam-5935	9	54	the	the	DET
ejpam-5935	9	55	following	following	NOUN
ejpam-5935	9	56	:	:	PUNCT
ejpam-5935	9	57	{	{	PUNCT
ejpam-5935	9	58	cdqξ(ρ	cdqξ(ρ	PROPN
ejpam-5935	9	59	)	)	PUNCT
ejpam-5935	9	60	=	=	SYM
ejpam-5935	9	61	ξ(ρ	ξ(ρ	PROPN
ejpam-5935	9	62	,	,	PUNCT
ejpam-5935	9	63	ξ(ρ	ξ(ρ	PROPN
ejpam-5935	9	64	)	)	PUNCT
ejpam-5935	9	65	)	)	PUNCT
ejpam-5935	9	66	,	,	PUNCT
ejpam-5935	9	67	1	1	NUM
ejpam-5935	9	68	<	<	X
ejpam-5935	9	69	q	q	X
ejpam-5935	9	70	≤	≤	NUM
ejpam-5935	9	71	2	2	NUM
ejpam-5935	9	72	,	,	PUNCT
ejpam-5935	9	73	ρ	ρ	PROPN
ejpam-5935	9	74	∈	∈	PROPN
ejpam-5935	10	1	[	[	X
ejpam-5935	10	2	0	0	NUM
ejpam-5935	10	3	,	,	PUNCT
ejpam-5935	10	4	ω	ω	NOUN
ejpam-5935	10	5	]	]	X
ejpam-5935	10	6	ξ(κ	ξ(κ	NUM
ejpam-5935	10	7	)	)	PUNCT
ejpam-5935	10	8	=	=	SYM
ejpam-5935	10	9	α	α	X
ejpam-5935	10	10	,	,	PUNCT
ejpam-5935	10	11	ξ(ω	ξ(ω	NOUN
ejpam-5935	10	12	)	)	PUNCT
ejpam-5935	10	13	=	=	PUNCT
ejpam-5935	10	14	β	β	X
ejpam-5935	10	15	,	,	PUNCT
ejpam-5935	10	16	0	0	NUM
ejpam-5935	10	17	≤	≤	NUM
ejpam-5935	10	18	κ	κ	X
ejpam-5935	10	19	<	<	X
ejpam-5935	10	20	ω	ω	PROPN
ejpam-5935	10	21	,	,	PUNCT
ejpam-5935	10	22	0	0	PUNCT
ejpam-5935	10	23	<	<	X
ejpam-5935	10	24	α	α	X
ejpam-5935	10	25	<	<	X
ejpam-5935	10	26	β	β	X
ejpam-5935	10	27	(	(	PUNCT
ejpam-5935	10	28	1	1	NUM
ejpam-5935	10	29	)	)	PUNCT
ejpam-5935	10	30	where	where	SCONJ
ejpam-5935	10	31	,	,	PUNCT
ejpam-5935	10	32	ξ	ξ	PROPN
ejpam-5935	10	33	∈	∈	PROPN
ejpam-5935	10	34	c([0	c([0	NOUN
ejpam-5935	10	35	,	,	PUNCT
ejpam-5935	10	36	ω],r	ω],r	NUM
ejpam-5935	10	37	)	)	PUNCT
ejpam-5935	10	38	and	and	CCONJ
ejpam-5935	10	39	ξ	ξ	PRON
ejpam-5935	10	40	:	:	PUNCT
ejpam-5935	11	1	[	[	X
ejpam-5935	11	2	0	0	NUM
ejpam-5935	11	3	,	,	PUNCT
ejpam-5935	11	4	ω]×r	ω]×r	NUM
ejpam-5935	11	5	−→	−→	ADJ
ejpam-5935	11	6	r	r	NOUN
ejpam-5935	11	7	,	,	PUNCT
ejpam-5935	11	8	and	and	CCONJ
ejpam-5935	11	9	cdq	cdq	NOUN
ejpam-5935	11	10	represents	represent	VERB
ejpam-5935	11	11	the	the	DET
ejpam-5935	11	12	caputo	caputo	PROPN
ejpam-5935	11	13	fractional	fractional	PROPN
ejpam-5935	11	14	derivative	derivative	NOUN
ejpam-5935	11	15	of	of	ADP
ejpam-5935	11	16	order	order	NOUN
ejpam-5935	11	17	q	q	X
ejpam-5935	11	18	∈	∈	NOUN
ejpam-5935	11	19	(	(	PUNCT
ejpam-5935	11	20	1	1	NUM
ejpam-5935	11	21	,	,	PUNCT
ejpam-5935	11	22	2	2	NUM
ejpam-5935	11	23	]	]	PUNCT
ejpam-5935	11	24	,	,	PUNCT
ejpam-5935	11	25	by	by	ADP
ejpam-5935	11	26	applying	apply	VERB
ejpam-5935	11	27	contraction	contraction	NOUN
ejpam-5935	11	28	principal	principal	NOUN
ejpam-5935	11	29	and	and	CCONJ
ejpam-5935	11	30	fixed	fix	VERB
ejpam-5935	11	31	point	point	NOUN
ejpam-5935	11	32	theorem	theorem	NOUN
ejpam-5935	11	33	of	of	ADP
ejpam-5935	11	34	∗corresponding	∗corresponde	VERB
ejpam-5935	11	35	author	author	NOUN
ejpam-5935	11	36	.	.	PUNCT
ejpam-5935	12	1	doi	doi	NOUN
ejpam-5935	12	2	:	:	PUNCT
ejpam-5935	12	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5935	https://doi.org/10.29020/nybg.ejpam.v18i2.5935	PROPN
ejpam-5935	12	4	email	email	NOUN
ejpam-5935	12	5	addresses	address	NOUN
ejpam-5935	12	6	:	:	PUNCT
ejpam-5935	12	7	s.aljurbua@qu.edu.sa	s.aljurbua@qu.edu.sa	PROPN
ejpam-5935	12	8	(	(	PUNCT
ejpam-5935	12	9	s.	s.	PROPN
ejpam-5935	12	10	aljurbua	aljurbua	PROPN
ejpam-5935	12	11	)	)	PUNCT
ejpam-5935	12	12	,	,	PUNCT
ejpam-5935	12	13	a.alluhayb@qu.edu.sa	a.alluhayb@qu.edu.sa	PROPN
ejpam-5935	12	14	(	(	PUNCT
ejpam-5935	12	15	a.	a.	NOUN
ejpam-5935	12	16	alluhayb	alluhayb	PROPN
ejpam-5935	12	17	)	)	PUNCT
ejpam-5935	12	18	,	,	PUNCT
ejpam-5935	12	19	431215616@qu.edu.sa	431215616@qu.edu.sa	PROPN
ejpam-5935	12	20	(	(	PUNCT
ejpam-5935	12	21	r.	r.	PROPN
ejpam-5935	12	22	alashwan	alashwan	PROPN
ejpam-5935	12	23	)	)	PUNCT
ejpam-5935	12	24	,	,	PUNCT
ejpam-5935	12	25	431202689@qu.edu.sa	431202689@qu.edu.sa	NUM
ejpam-5935	12	26	(	(	PUNCT
ejpam-5935	12	27	d.	d.	PROPN
ejpam-5935	12	28	alharbi	alharbi	PROPN
ejpam-5935	12	29	)	)	PUNCT
ejpam-5935	12	30	,	,	PUNCT
ejpam-5935	12	31	411203093@qu.edu.sa	411203093@qu.edu.sa	NUM
ejpam-5935	12	32	(	(	PUNCT
ejpam-5935	12	33	n.	n.	NOUN
ejpam-5935	12	34	alharbi	alharbi	PROPN
ejpam-5935	12	35	)	)	PUNCT
ejpam-5935	12	36	,	,	PUNCT
ejpam-5935	12	37	421215387@qu.edu.sa	421215387@qu.edu.sa	NUM
ejpam-5935	12	38	(	(	PUNCT
ejpam-5935	12	39	w.	w.	NOUN
ejpam-5935	12	40	alrawji	alrawji	PROPN
ejpam-5935	12	41	)	)	PUNCT
ejpam-5935	12	42	,	,	PUNCT
ejpam-5935	12	43	431215451@qu.edu.sa	431215451@qu.edu.sa	PROPN
ejpam-5935	12	44	(	(	PUNCT
ejpam-5935	12	45	n.	n.	NOUN
ejpam-5935	12	46	alharbi	alharbi	PROPN
ejpam-5935	12	47	)	)	PUNCT
ejpam-5935	12	48	,	,	PUNCT
ejpam-5935	12	49	431202709@qu.edu.sa	431202709@qu.edu.sa	NUM
ejpam-5935	12	50	(	(	PUNCT
ejpam-5935	12	51	m.	m.	NOUN
ejpam-5935	12	52	saad	saad	PROPN
ejpam-5935	12	53	)	)	PUNCT
ejpam-5935	12	54	,	,	PUNCT
ejpam-5935	12	55	422215646@qu.edu.sa	422215646@qu.edu.sa	PROPN
ejpam-5935	12	56	(	(	PUNCT
ejpam-5935	12	57	r.	r.	PROPN
ejpam-5935	12	58	almutairi	almutairi	PROPN
ejpam-5935	12	59	)	)	PUNCT
ejpam-5935	12	60	,	,	PUNCT
ejpam-5935	12	61	391204002@qu.edu.sa	391204002@qu.edu.sa	NUM
ejpam-5935	12	62	(	(	PUNCT
ejpam-5935	12	63	r.	r.	PROPN
ejpam-5935	12	64	alharbi	alharbi	PROPN
ejpam-5935	12	65	)	)	PUNCT
ejpam-5935	12	66	,	,	PUNCT
ejpam-5935	12	67	431202725@qu.edu.sa	431202725@qu.edu.sa	NUM
ejpam-5935	12	68	(	(	PUNCT
ejpam-5935	12	69	a.	a.	NOUN
ejpam-5935	12	70	alrashidi	alrashidi	PROPN
ejpam-5935	12	71	)	)	PUNCT
ejpam-5935	12	72	,	,	PUNCT
ejpam-5935	12	73	392215056@qu.edu.sa	392215056@qu.edu.sa	PROPN
ejpam-5935	12	74	(	(	PUNCT
ejpam-5935	12	75	m.	m.	NOUN
ejpam-5935	12	76	alrashidi	alrashidi	NOUN
ejpam-5935	12	77	)	)	PUNCT
ejpam-5935	12	78	,	,	PUNCT
ejpam-5935	12	79	431203212@qu.edu.sa	431203212@qu.edu.sa	NUM
ejpam-5935	12	80	(	(	PUNCT
ejpam-5935	12	81	n.	n.	PROPN
ejpam-5935	12	82	alfuraih	alfuraih	PROPN
ejpam-5935	12	83	)	)	PUNCT
ejpam-5935	12	84	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5935	13	1	1	1	NUM
ejpam-5935	13	2	copyright	copyright	NOUN
ejpam-5935	13	3	:	:	PUNCT
ejpam-5935	13	4	©	©	PROPN
ejpam-5935	13	5	2025	2025	NUM
ejpam-5935	13	6	the	the	DET
ejpam-5935	13	7	author(s	author(s	NOUN
ejpam-5935	13	8	)	)	PUNCT
ejpam-5935	13	9	.	.	PUNCT
ejpam-5935	14	1	(	(	PUNCT
ejpam-5935	14	2	cc	cc	NOUN
ejpam-5935	14	3	by	by	ADP
ejpam-5935	14	4	-	-	PUNCT
ejpam-5935	14	5	nc	nc	PROPN
ejpam-5935	14	6	4.0	4.0	NUM
ejpam-5935	14	7	)	)	PUNCT
ejpam-5935	14	8	s.	s.	PROPN
ejpam-5935	14	9	f.	f.	PROPN
ejpam-5935	14	10	aljurbua	aljurbua	PROPN
ejpam-5935	14	11	et	et	PROPN
ejpam-5935	14	12	al	al	PROPN
ejpam-5935	14	13	.	.	PUNCT
ejpam-5935	14	14	/	/	SYM
ejpam-5935	14	15	eur	eur	PROPN
ejpam-5935	14	16	.	.	PUNCT
ejpam-5935	15	1	j.	j.	PROPN
ejpam-5935	15	2	pure	pure	PROPN
ejpam-5935	15	3	appl	appl	PROPN
ejpam-5935	15	4	.	.	PROPN
ejpam-5935	15	5	math	math	PROPN
ejpam-5935	15	6	,	,	PUNCT
ejpam-5935	15	7	18	18	NUM
ejpam-5935	15	8	(	(	PUNCT
ejpam-5935	15	9	2	2	NUM
ejpam-5935	15	10	)	)	PUNCT
ejpam-5935	15	11	(	(	PUNCT
ejpam-5935	15	12	2025	2025	NUM
ejpam-5935	15	13	)	)	PUNCT
ejpam-5935	15	14	,	,	PUNCT
ejpam-5935	15	15	5935	5935	NUM
ejpam-5935	15	16	2	2	NUM
ejpam-5935	15	17	of	of	ADP
ejpam-5935	15	18	10	10	NUM
ejpam-5935	15	19	krasnoselskii	krasnoselskii	PROPN
ejpam-5935	15	20	’s	’s	PART
ejpam-5935	15	21	.	.	PUNCT
ejpam-5935	16	1	fractional	fractional	ADJ
ejpam-5935	16	2	differential	differential	ADJ
ejpam-5935	16	3	equations	equation	NOUN
ejpam-5935	16	4	(	(	PUNCT
ejpam-5935	16	5	fdes	fde	NOUN
ejpam-5935	16	6	)	)	PUNCT
ejpam-5935	16	7	extend	extend	VERB
ejpam-5935	16	8	the	the	DET
ejpam-5935	16	9	concepts	concept	NOUN
ejpam-5935	16	10	of	of	ADP
ejpam-5935	16	11	traditional	traditional	ADJ
ejpam-5935	16	12	calculus	calculus	NOUN
ejpam-5935	16	13	,	,	PUNCT
ejpam-5935	16	14	offering	offer	VERB
ejpam-5935	16	15	mathematical	mathematical	ADJ
ejpam-5935	16	16	frameworks	framework	NOUN
ejpam-5935	16	17	to	to	PART
ejpam-5935	16	18	analyze	analyze	VERB
ejpam-5935	16	19	systems	system	NOUN
ejpam-5935	16	20	where	where	SCONJ
ejpam-5935	16	21	memory	memory	NOUN
ejpam-5935	16	22	effects	effect	NOUN
ejpam-5935	16	23	,	,	PUNCT
ejpam-5935	16	24	ongoing	ongoing	ADJ
ejpam-5935	16	25	influences	influence	NOUN
ejpam-5935	16	26	,	,	PUNCT
ejpam-5935	16	27	or	or	CCONJ
ejpam-5935	16	28	irregular	irregular	ADJ
ejpam-5935	16	29	spatial	spatial	ADJ
ejpam-5935	16	30	characteristics	characteristic	NOUN
ejpam-5935	16	31	present	present	ADJ
ejpam-5935	16	32	challenges	challenge	NOUN
ejpam-5935	16	33	for	for	ADP
ejpam-5935	16	34	standard	standard	ADJ
ejpam-5935	16	35	modeling	modeling	NOUN
ejpam-5935	16	36	techniques	technique	NOUN
ejpam-5935	16	37	[	[	X
ejpam-5935	16	38	1	1	NUM
ejpam-5935	16	39	,	,	PUNCT
ejpam-5935	16	40	2	2	NUM
ejpam-5935	16	41	]	]	PUNCT
ejpam-5935	16	42	.	.	PUNCT
ejpam-5935	17	1	the	the	DET
ejpam-5935	17	2	roots	root	NOUN
ejpam-5935	17	3	of	of	ADP
ejpam-5935	17	4	fractional	fractional	ADJ
ejpam-5935	17	5	calculus	calculus	NOUN
ejpam-5935	17	6	are	be	AUX
ejpam-5935	17	7	linked	link	VERB
ejpam-5935	17	8	to	to	ADP
ejpam-5935	17	9	the	the	DET
ejpam-5935	17	10	17th	17th	ADJ
ejpam-5935	17	11	century	century	NOUN
ejpam-5935	17	12	,	,	PUNCT
ejpam-5935	17	13	as	as	SCONJ
ejpam-5935	17	14	mathematicians	mathematician	NOUN
ejpam-5935	17	15	such	such	ADJ
ejpam-5935	17	16	as	as	ADP
ejpam-5935	17	17	leibniz	leibniz	PROPN
ejpam-5935	17	18	explored	explore	VERB
ejpam-5935	17	19	the	the	DET
ejpam-5935	17	20	concept	concept	NOUN
ejpam-5935	17	21	of	of	ADP
ejpam-5935	17	22	derivatives	derivative	NOUN
ejpam-5935	17	23	of	of	ADP
ejpam-5935	17	24	varying	vary	VERB
ejpam-5935	17	25	orders	order	NOUN
ejpam-5935	17	26	.	.	PUNCT
ejpam-5935	18	1	nevertheless	nevertheless	ADV
ejpam-5935	18	2	,	,	PUNCT
ejpam-5935	18	3	in	in	ADP
ejpam-5935	18	4	the	the	DET
ejpam-5935	18	5	19th	19th	ADJ
ejpam-5935	18	6	century	century	NOUN
ejpam-5935	18	7	,	,	PUNCT
ejpam-5935	18	8	foundational	foundational	ADJ
ejpam-5935	18	9	formulations	formulation	NOUN
ejpam-5935	18	10	by	by	ADP
ejpam-5935	18	11	riemann	riemann	PROPN
ejpam-5935	18	12	,	,	PUNCT
ejpam-5935	18	13	liouville	liouville	VERB
ejpam-5935	18	14	,	,	PUNCT
ejpam-5935	18	15	and	and	CCONJ
ejpam-5935	18	16	their	their	PRON
ejpam-5935	18	17	successors	successor	NOUN
ejpam-5935	18	18	established	establish	VERB
ejpam-5935	18	19	the	the	DET
ejpam-5935	18	20	basis	basis	NOUN
ejpam-5935	18	21	for	for	ADP
ejpam-5935	18	22	contemporary	contemporary	ADJ
ejpam-5935	18	23	fractional	fractional	ADJ
ejpam-5935	18	24	calculus	calculus	NOUN
ejpam-5935	19	1	[	[	X
ejpam-5935	19	2	3	3	NUM
ejpam-5935	19	3	]	]	PUNCT
ejpam-5935	19	4	.	.	PUNCT
ejpam-5935	20	1	nowadays	nowadays	ADV
ejpam-5935	20	2	,	,	PUNCT
ejpam-5935	20	3	fdes	fde	NOUN
ejpam-5935	20	4	are	be	AUX
ejpam-5935	20	5	a	a	DET
ejpam-5935	20	6	crucial	crucial	ADJ
ejpam-5935	20	7	link	link	NOUN
ejpam-5935	20	8	between	between	ADP
ejpam-5935	20	9	theoretical	theoretical	ADJ
ejpam-5935	20	10	constructs	construct	NOUN
ejpam-5935	20	11	and	and	CCONJ
ejpam-5935	20	12	practical	practical	ADJ
ejpam-5935	20	13	applications	application	NOUN
ejpam-5935	20	14	[	[	X
ejpam-5935	20	15	3	3	NUM
ejpam-5935	20	16	]	]	PUNCT
ejpam-5935	20	17	.	.	PUNCT
ejpam-5935	21	1	for	for	ADP
ejpam-5935	21	2	instance	instance	NOUN
ejpam-5935	21	3	,	,	PUNCT
ejpam-5935	21	4	engineers	engineer	NOUN
ejpam-5935	21	5	utilize	utilize	VERB
ejpam-5935	21	6	these	these	DET
ejpam-5935	21	7	equations	equation	NOUN
ejpam-5935	21	8	to	to	PART
ejpam-5935	21	9	forecast	forecast	VERB
ejpam-5935	21	10	stress	stress	ADJ
ejpam-5935	21	11	relaxation	relaxation	NOUN
ejpam-5935	21	12	in	in	ADP
ejpam-5935	21	13	viscoelastic	viscoelastic	ADJ
ejpam-5935	21	14	materials	material	NOUN
ejpam-5935	21	15	,	,	PUNCT
ejpam-5935	21	16	which	which	PRON
ejpam-5935	21	17	”	"	PUNCT
ejpam-5935	21	18	remember	remember	VERB
ejpam-5935	21	19	”	"	PUNCT
ejpam-5935	21	20	previous	previous	ADJ
ejpam-5935	21	21	deformations	deformation	NOUN
ejpam-5935	21	22	.	.	PUNCT
ejpam-5935	22	1	geophysicists	geophysicist	NOUN
ejpam-5935	22	2	model	model	VERB
ejpam-5935	22	3	unusual	unusual	ADJ
ejpam-5935	22	4	diffusion	diffusion	NOUN
ejpam-5935	22	5	patterns	pattern	NOUN
ejpam-5935	22	6	in	in	ADP
ejpam-5935	22	7	fractured	fractured	ADJ
ejpam-5935	22	8	geological	geological	ADJ
ejpam-5935	22	9	formations	formation	NOUN
ejpam-5935	22	10	,	,	PUNCT
ejpam-5935	22	11	where	where	SCONJ
ejpam-5935	22	12	particles	particle	NOUN
ejpam-5935	22	13	exhibit	exhibit	VERB
ejpam-5935	22	14	unpredictable	unpredictable	ADJ
ejpam-5935	22	15	movement	movement	NOUN
ejpam-5935	22	16	[	[	X
ejpam-5935	22	17	4	4	NUM
ejpam-5935	22	18	]	]	PUNCT
ejpam-5935	22	19	.	.	PUNCT
ejpam-5935	23	1	in	in	ADP
ejpam-5935	23	2	biology	biology	NOUN
ejpam-5935	23	3	,	,	PUNCT
ejpam-5935	23	4	researchers	researcher	NOUN
ejpam-5935	23	5	apply	apply	VERB
ejpam-5935	23	6	them	they	PRON
ejpam-5935	23	7	to	to	PART
ejpam-5935	23	8	study	study	VERB
ejpam-5935	23	9	cellular	cellular	ADJ
ejpam-5935	23	10	processes	process	NOUN
ejpam-5935	23	11	affected	affect	VERB
ejpam-5935	23	12	by	by	ADP
ejpam-5935	23	13	delayed	delay	VERB
ejpam-5935	23	14	responses	response	NOUN
ejpam-5935	23	15	,	,	PUNCT
ejpam-5935	23	16	while	while	SCONJ
ejpam-5935	23	17	economists	economist	NOUN
ejpam-5935	23	18	investigate	investigate	VERB
ejpam-5935	23	19	their	their	PRON
ejpam-5935	23	20	potential	potential	NOUN
ejpam-5935	23	21	to	to	PART
ejpam-5935	23	22	predict	predict	VERB
ejpam-5935	23	23	market	market	NOUN
ejpam-5935	23	24	fluctuations	fluctuation	NOUN
ejpam-5935	23	25	driven	drive	VERB
ejpam-5935	23	26	by	by	ADP
ejpam-5935	23	27	long	long	ADJ
ejpam-5935	23	28	-	-	PUNCT
ejpam-5935	23	29	term	term	NOUN
ejpam-5935	23	30	patterns	pattern	NOUN
ejpam-5935	23	31	[	[	X
ejpam-5935	23	32	5	5	NUM
ejpam-5935	23	33	,	,	PUNCT
ejpam-5935	23	34	6	6	NUM
ejpam-5935	23	35	]	]	PUNCT
ejpam-5935	23	36	.	.	PUNCT
ejpam-5935	24	1	unlike	unlike	ADP
ejpam-5935	24	2	traditional	traditional	ADJ
ejpam-5935	24	3	integer	integer	NOUN
ejpam-5935	24	4	-	-	PUNCT
ejpam-5935	24	5	order	order	NOUN
ejpam-5935	24	6	models	model	NOUN
ejpam-5935	24	7	,	,	PUNCT
ejpam-5935	24	8	fractional	fractional	ADJ
ejpam-5935	24	9	approaches	approach	NOUN
ejpam-5935	24	10	inherently	inherently	ADV
ejpam-5935	24	11	consider	consider	VERB
ejpam-5935	24	12	historical	historical	ADJ
ejpam-5935	24	13	context	context	NOUN
ejpam-5935	24	14	through	through	ADP
ejpam-5935	24	15	operators	operator	NOUN
ejpam-5935	24	16	such	such	ADJ
ejpam-5935	24	17	as	as	ADP
ejpam-5935	24	18	the	the	DET
ejpam-5935	24	19	caputo	caputo	PROPN
ejpam-5935	24	20	derivative	derivative	NOUN
ejpam-5935	24	21	,	,	PUNCT
ejpam-5935	24	22	compatible	compatible	ADJ
ejpam-5935	24	23	with	with	ADP
ejpam-5935	24	24	physical	physical	ADJ
ejpam-5935	24	25	initial	initial	ADJ
ejpam-5935	24	26	conditions	condition	NOUN
ejpam-5935	24	27	,	,	PUNCT
ejpam-5935	24	28	or	or	CCONJ
ejpam-5935	24	29	the	the	DET
ejpam-5935	24	30	riemann	riemann	PROPN
ejpam-5935	24	31	-	-	PUNCT
ejpam-5935	24	32	liouville	liouville	NOUN
ejpam-5935	24	33	integral	integral	ADJ
ejpam-5935	24	34	,	,	PUNCT
ejpam-5935	24	35	which	which	PRON
ejpam-5935	24	36	emphasizes	emphasize	VERB
ejpam-5935	24	37	past	past	ADJ
ejpam-5935	24	38	states	state	NOUN
ejpam-5935	24	39	in	in	ADP
ejpam-5935	24	40	varied	varied	ADJ
ejpam-5935	24	41	ways	way	NOUN
ejpam-5935	24	42	[	[	X
ejpam-5935	24	43	7	7	NUM
ejpam-5935	24	44	]	]	PUNCT
ejpam-5935	24	45	.	.	PUNCT
ejpam-5935	25	1	the	the	DET
ejpam-5935	25	2	increasing	increase	VERB
ejpam-5935	25	3	integration	integration	NOUN
ejpam-5935	25	4	of	of	ADP
ejpam-5935	25	5	fdes	fde	NOUN
ejpam-5935	25	6	into	into	ADP
ejpam-5935	25	7	research	research	NOUN
ejpam-5935	25	8	highlights	highlight	NOUN
ejpam-5935	25	9	a	a	DET
ejpam-5935	25	10	transformation	transformation	NOUN
ejpam-5935	25	11	in	in	ADP
ejpam-5935	25	12	scientific	scientific	ADJ
ejpam-5935	25	13	understanding	understanding	NOUN
ejpam-5935	25	14	:	:	PUNCT
ejpam-5935	25	15	many	many	ADJ
ejpam-5935	25	16	natural	natural	ADJ
ejpam-5935	25	17	and	and	CCONJ
ejpam-5935	25	18	engineering	engineering	NOUN
ejpam-5935	25	19	systems	system	NOUN
ejpam-5935	25	20	are	be	AUX
ejpam-5935	25	21	complex	complex	ADJ
ejpam-5935	25	22	and	and	CCONJ
ejpam-5935	25	23	influenced	influence	VERB
ejpam-5935	25	24	by	by	ADP
ejpam-5935	25	25	memory	memory	NOUN
ejpam-5935	25	26	.	.	PUNCT
ejpam-5935	26	1	from	from	ADP
ejpam-5935	26	2	climate	climate	NOUN
ejpam-5935	26	3	dynamics	dynamic	NOUN
ejpam-5935	26	4	shaped	shape	VERB
ejpam-5935	26	5	by	by	ADP
ejpam-5935	26	6	years	year	NOUN
ejpam-5935	26	7	of	of	ADP
ejpam-5935	26	8	greenhouse	greenhouse	NOUN
ejpam-5935	26	9	gas	gas	NOUN
ejpam-5935	26	10	emissions	emission	NOUN
ejpam-5935	26	11	to	to	ADP
ejpam-5935	26	12	health	health	NOUN
ejpam-5935	26	13	treatments	treatment	NOUN
ejpam-5935	26	14	based	base	VERB
ejpam-5935	26	15	on	on	ADP
ejpam-5935	26	16	cumulative	cumulative	ADJ
ejpam-5935	26	17	drug	drug	NOUN
ejpam-5935	26	18	effects	effect	NOUN
ejpam-5935	26	19	,	,	PUNCT
ejpam-5935	26	20	fractional	fractional	ADJ
ejpam-5935	26	21	calculus	calculus	NOUN
ejpam-5935	26	22	offers	offer	VERB
ejpam-5935	26	23	valuable	valuable	ADJ
ejpam-5935	26	24	insights	insight	NOUN
ejpam-5935	26	25	into	into	ADP
ejpam-5935	26	26	navigating	navigate	VERB
ejpam-5935	26	27	this	this	DET
ejpam-5935	26	28	complexity	complexity	NOUN
ejpam-5935	26	29	[	[	X
ejpam-5935	26	30	1	1	NUM
ejpam-5935	26	31	]	]	PUNCT
ejpam-5935	26	32	.	.	PUNCT
ejpam-5935	27	1	in	in	ADP
ejpam-5935	27	2	the	the	DET
ejpam-5935	27	3	literature	literature	NOUN
ejpam-5935	27	4	,	,	PUNCT
ejpam-5935	27	5	the	the	DET
ejpam-5935	27	6	stability	stability	NOUN
ejpam-5935	27	7	,	,	PUNCT
ejpam-5935	27	8	existence	existence	NOUN
ejpam-5935	27	9	,	,	PUNCT
ejpam-5935	27	10	and	and	CCONJ
ejpam-5935	27	11	uniqueness	uniqueness	NOUN
ejpam-5935	27	12	of	of	ADP
ejpam-5935	27	13	the	the	DET
ejpam-5935	27	14	solution	solution	NOUN
ejpam-5935	27	15	for	for	ADP
ejpam-5935	27	16	fractional	fractional	ADJ
ejpam-5935	27	17	differential	differential	ADJ
ejpam-5935	27	18	equations	equation	NOUN
ejpam-5935	27	19	have	have	AUX
ejpam-5935	27	20	been	be	AUX
ejpam-5935	27	21	discussed	discuss	VERB
ejpam-5935	27	22	widely	widely	ADV
ejpam-5935	27	23	with	with	ADP
ejpam-5935	27	24	different	different	ADJ
ejpam-5935	27	25	methods	method	NOUN
ejpam-5935	27	26	due	due	ADP
ejpam-5935	27	27	to	to	ADP
ejpam-5935	27	28	the	the	DET
ejpam-5935	27	29	importance	importance	NOUN
ejpam-5935	27	30	of	of	ADP
ejpam-5935	27	31	the	the	DET
ejpam-5935	27	32	equations	equation	NOUN
ejpam-5935	27	33	in	in	ADP
ejpam-5935	27	34	practical	practical	ADJ
ejpam-5935	27	35	applications	application	NOUN
ejpam-5935	27	36	[	[	X
ejpam-5935	27	37	8–12	8–12	NOUN
ejpam-5935	27	38	]	]	X
ejpam-5935	27	39	.	.	PUNCT
ejpam-5935	28	1	in	in	ADP
ejpam-5935	28	2	[	[	X
ejpam-5935	28	3	13	13	NUM
ejpam-5935	28	4	]	]	PUNCT
ejpam-5935	28	5	,	,	PUNCT
ejpam-5935	28	6	zhang	zhang	PROPN
ejpam-5935	28	7	found	find	VERB
ejpam-5935	28	8	the	the	DET
ejpam-5935	28	9	expression	expression	NOUN
ejpam-5935	28	10	of	of	ADP
ejpam-5935	28	11	the	the	DET
ejpam-5935	28	12	solution	solution	NOUN
ejpam-5935	28	13	,	,	PUNCT
ejpam-5935	28	14	under	under	ADP
ejpam-5935	28	15	the	the	DET
ejpam-5935	28	16	boundary	boundary	ADJ
ejpam-5935	28	17	conditions	condition	NOUN
ejpam-5935	28	18	ξ(0	ξ(0	NOUN
ejpam-5935	28	19	)	)	PUNCT
ejpam-5935	29	1	=	=	PUNCT
ejpam-5935	29	2	α	α	X
ejpam-5935	29	3	̸=	̸=	PROPN
ejpam-5935	29	4	0	0	NUM
ejpam-5935	29	5	and	and	CCONJ
ejpam-5935	29	6	ξ(1	ξ(1	PROPN
ejpam-5935	29	7	)	)	PUNCT
ejpam-5935	29	8	=	=	PUNCT
ejpam-5935	30	1	β	β	X
ejpam-5935	30	2	̸=	̸=	PROPN
ejpam-5935	30	3	0	0	NUM
ejpam-5935	30	4	,	,	PUNCT
ejpam-5935	30	5	with	with	ADP
ejpam-5935	30	6	the	the	DET
ejpam-5935	30	7	aid	aid	NOUN
ejpam-5935	30	8	of	of	ADP
ejpam-5935	30	9	laplace	laplace	NOUN
ejpam-5935	30	10	transformation	transformation	NOUN
ejpam-5935	30	11	,	,	PUNCT
ejpam-5935	30	12	by	by	ADP
ejpam-5935	30	13	highlighting	highlight	VERB
ejpam-5935	30	14	the	the	DET
ejpam-5935	30	15	role	role	NOUN
ejpam-5935	30	16	of	of	ADP
ejpam-5935	30	17	schauder	schauder	NOUN
ejpam-5935	30	18	’s	’s	PART
ejpam-5935	30	19	fixed	fix	VERB
ejpam-5935	30	20	-	-	PUNCT
ejpam-5935	30	21	point	point	NOUN
ejpam-5935	30	22	theorem	theorem	ADJ
ejpam-5935	30	23	and	and	CCONJ
ejpam-5935	30	24	mittag	mittag	ADJ
ejpam-5935	30	25	-	-	PUNCT
ejpam-5935	30	26	leffler	leffler	NOUN
ejpam-5935	30	27	functions	function	NOUN
ejpam-5935	30	28	in	in	ADP
ejpam-5935	30	29	solving	solve	VERB
ejpam-5935	30	30	these	these	DET
ejpam-5935	30	31	boundary	boundary	ADJ
ejpam-5935	30	32	value	value	NOUN
ejpam-5935	30	33	problems	problem	NOUN
ejpam-5935	30	34	.	.	PUNCT
ejpam-5935	31	1	bashir	bashir	PROPN
ejpam-5935	31	2	and	and	CCONJ
ejpam-5935	31	3	nieto	nieto	PROPN
ejpam-5935	32	1	[	[	X
ejpam-5935	32	2	13	13	NUM
ejpam-5935	32	3	]	]	PUNCT
ejpam-5935	32	4	gave	give	VERB
ejpam-5935	32	5	some	some	DET
ejpam-5935	32	6	interesting	interesting	ADJ
ejpam-5935	32	7	results	result	NOUN
ejpam-5935	32	8	for	for	ADP
ejpam-5935	32	9	fractional	fractional	ADJ
ejpam-5935	32	10	differential	differential	ADJ
ejpam-5935	32	11	equations	equation	NOUN
ejpam-5935	32	12	with	with	ADP
ejpam-5935	32	13	anti	anti	ADJ
ejpam-5935	32	14	-	-	ADJ
ejpam-5935	32	15	periodic	periodic	ADJ
ejpam-5935	32	16	boundary	boundary	ADJ
ejpam-5935	32	17	conditions	condition	NOUN
ejpam-5935	32	18	,	,	PUNCT
ejpam-5935	32	19	ξ(0	ξ(0	NOUN
ejpam-5935	32	20	)	)	PUNCT
ejpam-5935	32	21	=	=	SYM
ejpam-5935	32	22	−ξ(0	−ξ(0	NUM
ejpam-5935	32	23	)	)	PUNCT
ejpam-5935	32	24	,	,	PUNCT
ejpam-5935	32	25	and	and	CCONJ
ejpam-5935	32	26	ξ′(ω	ξ′(ω	NOUN
ejpam-5935	32	27	)	)	PUNCT
ejpam-5935	32	28	=	=	SYM
ejpam-5935	32	29	−ξ′(ω	−ξ′(ω	PROPN
ejpam-5935	32	30	)	)	PUNCT
ejpam-5935	32	31	,	,	PUNCT
ejpam-5935	32	32	by	by	ADP
ejpam-5935	32	33	using	use	VERB
ejpam-5935	32	34	leray	leray	ADJ
ejpam-5935	32	35	-	-	PUNCT
ejpam-5935	32	36	schauder	schauder	NOUN
ejpam-5935	32	37	degree	degree	NOUN
ejpam-5935	32	38	theory	theory	NOUN
ejpam-5935	32	39	.	.	PUNCT
ejpam-5935	33	1	r.	r.	PROPN
ejpam-5935	33	2	agarwal	agarwal	PROPN
ejpam-5935	33	3	,	,	PUNCT
ejpam-5935	33	4	b.	b.	PROPN
ejpam-5935	33	5	ahmad	ahmad	PROPN
ejpam-5935	33	6	,	,	PUNCT
ejpam-5935	33	7	and	and	CCONJ
ejpam-5935	33	8	j.	j.	PROPN
ejpam-5935	33	9	nieto	nieto	PROPN
ejpam-5935	33	10	in	in	ADP
ejpam-5935	33	11	[	[	X
ejpam-5935	33	12	14	14	NUM
ejpam-5935	33	13	]	]	X
ejpam-5935	33	14	introduce	introduce	NOUN
ejpam-5935	33	15	and	and	CCONJ
ejpam-5935	33	16	solve	solve	VERB
ejpam-5935	33	17	fractional	fractional	ADJ
ejpam-5935	33	18	and	and	CCONJ
ejpam-5935	33	19	sequential	sequential	ADJ
ejpam-5935	33	20	fdes	fde	NOUN
ejpam-5935	33	21	with	with	ADP
ejpam-5935	33	22	parametric	parametric	ADJ
ejpam-5935	33	23	type	type	NOUN
ejpam-5935	33	24	conditions	condition	NOUN
ejpam-5935	33	25	where	where	SCONJ
ejpam-5935	33	26	they	they	PRON
ejpam-5935	33	27	consider	consider	VERB
ejpam-5935	33	28	intermediate	intermediate	ADJ
ejpam-5935	33	29	points	point	NOUN
ejpam-5935	33	30	using	use	VERB
ejpam-5935	33	31	standard	standard	ADJ
ejpam-5935	33	32	fixed	fix	VERB
ejpam-5935	33	33	point	point	NOUN
ejpam-5935	33	34	theorem	theorem	VERB
ejpam-5935	33	35	.	.	PUNCT
ejpam-5935	34	1	in	in	ADP
ejpam-5935	34	2	[	[	X
ejpam-5935	34	3	15	15	NUM
ejpam-5935	34	4	]	]	PUNCT
ejpam-5935	34	5	,	,	PUNCT
ejpam-5935	34	6	extended	extend	VERB
ejpam-5935	34	7	the	the	DET
ejpam-5935	34	8	existence	existence	NOUN
ejpam-5935	34	9	and	and	CCONJ
ejpam-5935	34	10	uniqueness	uniqueness	NOUN
ejpam-5935	34	11	results	result	NOUN
ejpam-5935	34	12	of	of	ADP
ejpam-5935	34	13	[	[	X
ejpam-5935	34	14	16	16	NUM
ejpam-5935	34	15	]	]	PUNCT
ejpam-5935	34	16	with	with	ADP
ejpam-5935	34	17	nonlocal	nonlocal	ADJ
ejpam-5935	34	18	boundary	boundary	ADJ
ejpam-5935	34	19	conditions	condition	NOUN
ejpam-5935	34	20	under	under	ADP
ejpam-5935	34	21	essential	essential	ADJ
ejpam-5935	34	22	conditions	condition	NOUN
ejpam-5935	34	23	using	use	VERB
ejpam-5935	34	24	the	the	DET
ejpam-5935	34	25	fixed	fix	VERB
ejpam-5935	34	26	-	-	PUNCT
ejpam-5935	34	27	point	point	NOUN
ejpam-5935	34	28	theorem	theorem	NOUN
ejpam-5935	34	29	of	of	ADP
ejpam-5935	34	30	krasnoselskii	krasnoselskii	PROPN
ejpam-5935	34	31	and	and	CCONJ
ejpam-5935	34	32	the	the	DET
ejpam-5935	34	33	contraction	contraction	NOUN
ejpam-5935	34	34	principle	principle	NOUN
ejpam-5935	34	35	,	,	PUNCT
ejpam-5935	34	36	the	the	DET
ejpam-5935	34	37	research	research	NOUN
ejpam-5935	34	38	broadens	broaden	VERB
ejpam-5935	34	39	the	the	DET
ejpam-5935	34	40	scope	scope	NOUN
ejpam-5935	34	41	of	of	ADP
ejpam-5935	34	42	these	these	DET
ejpam-5935	34	43	equations	equation	NOUN
ejpam-5935	34	44	,	,	PUNCT
ejpam-5935	34	45	demonstrating	demonstrate	VERB
ejpam-5935	34	46	applications	application	NOUN
ejpam-5935	34	47	to	to	ADP
ejpam-5935	34	48	classical	classical	ADJ
ejpam-5935	34	49	fractional	fractional	ADJ
ejpam-5935	34	50	differential	differential	ADJ
ejpam-5935	34	51	equations	equation	NOUN
ejpam-5935	34	52	.	.	PUNCT
ejpam-5935	35	1	fractional	fractional	ADJ
ejpam-5935	35	2	derivatives	derivative	NOUN
ejpam-5935	35	3	can	can	AUX
ejpam-5935	35	4	be	be	AUX
ejpam-5935	35	5	defined	define	VERB
ejpam-5935	35	6	in	in	ADP
ejpam-5935	35	7	various	various	ADJ
ejpam-5935	35	8	ways	way	NOUN
ejpam-5935	35	9	,	,	PUNCT
ejpam-5935	35	10	with	with	ADP
ejpam-5935	35	11	notable	notable	ADJ
ejpam-5935	35	12	formulations	formulation	NOUN
ejpam-5935	35	13	including	include	VERB
ejpam-5935	35	14	the	the	DET
ejpam-5935	35	15	grünwald	grünwald	NOUN
ejpam-5935	35	16	–	–	PUNCT
ejpam-5935	35	17	letnikov	letnikov	ADJ
ejpam-5935	35	18	,	,	PUNCT
ejpam-5935	35	19	liouville	liouville	NOUN
ejpam-5935	35	20	,	,	PUNCT
ejpam-5935	35	21	hadamard	hadamard	NOUN
ejpam-5935	35	22	,	,	PUNCT
ejpam-5935	35	23	riesz	riesz	NOUN
ejpam-5935	35	24	,	,	PUNCT
ejpam-5935	35	25	and	and	CCONJ
ejpam-5935	35	26	caputo	caputo	PROPN
ejpam-5935	35	27	derivatives	derivative	NOUN
ejpam-5935	35	28	.	.	PUNCT
ejpam-5935	36	1	these	these	DET
ejpam-5935	36	2	definitions	definition	NOUN
ejpam-5935	36	3	have	have	AUX
ejpam-5935	36	4	been	be	AUX
ejpam-5935	36	5	widely	widely	ADV
ejpam-5935	36	6	utilized	utilize	VERB
ejpam-5935	36	7	to	to	PART
ejpam-5935	36	8	explore	explore	VERB
ejpam-5935	36	9	solutions	solution	NOUN
ejpam-5935	36	10	,	,	PUNCT
ejpam-5935	36	11	analyze	analyze	VERB
ejpam-5935	36	12	system	system	NOUN
ejpam-5935	36	13	stability	stability	NOUN
ejpam-5935	36	14	,	,	PUNCT
ejpam-5935	36	15	and	and	CCONJ
ejpam-5935	36	16	define	define	VERB
ejpam-5935	36	17	and	and	CCONJ
ejpam-5935	36	18	characterize	characterize	VERB
ejpam-5935	36	19	various	various	ADJ
ejpam-5935	36	20	functional	functional	ADJ
ejpam-5935	36	21	spaces	space	NOUN
ejpam-5935	36	22	.	.	PUNCT
ejpam-5935	37	1	this	this	DET
ejpam-5935	37	2	study	study	NOUN
ejpam-5935	37	3	specifically	specifically	ADV
ejpam-5935	37	4	focuses	focus	VERB
ejpam-5935	37	5	on	on	ADP
ejpam-5935	37	6	the	the	DET
ejpam-5935	37	7	s.	s.	PROPN
ejpam-5935	37	8	f.	f.	PROPN
ejpam-5935	37	9	aljurbua	aljurbua	PROPN
ejpam-5935	37	10	et	et	PROPN
ejpam-5935	37	11	al	al	PROPN
ejpam-5935	37	12	.	.	PUNCT
ejpam-5935	37	13	/	/	SYM
ejpam-5935	37	14	eur	eur	PROPN
ejpam-5935	37	15	.	.	PUNCT
ejpam-5935	38	1	j.	j.	PROPN
ejpam-5935	38	2	pure	pure	PROPN
ejpam-5935	38	3	appl	appl	PROPN
ejpam-5935	38	4	.	.	PROPN
ejpam-5935	38	5	math	math	PROPN
ejpam-5935	38	6	,	,	PUNCT
ejpam-5935	38	7	18	18	NUM
ejpam-5935	38	8	(	(	PUNCT
ejpam-5935	38	9	2	2	NUM
ejpam-5935	38	10	)	)	PUNCT
ejpam-5935	38	11	(	(	PUNCT
ejpam-5935	38	12	2025	2025	NUM
ejpam-5935	38	13	)	)	PUNCT
ejpam-5935	38	14	,	,	PUNCT
ejpam-5935	38	15	5935	5935	NUM
ejpam-5935	38	16	3	3	NUM
ejpam-5935	38	17	of	of	ADP
ejpam-5935	38	18	10	10	NUM
ejpam-5935	38	19	caputo	caputo	PROPN
ejpam-5935	38	20	fractional	fractional	PROPN
ejpam-5935	38	21	derivative	derivative	NOUN
ejpam-5935	38	22	due	due	ADP
ejpam-5935	38	23	to	to	ADP
ejpam-5935	38	24	its	its	PRON
ejpam-5935	38	25	close	close	ADJ
ejpam-5935	38	26	relationship	relationship	NOUN
ejpam-5935	38	27	with	with	ADP
ejpam-5935	38	28	classical	classical	ADJ
ejpam-5935	38	29	differential	differential	ADJ
ejpam-5935	38	30	equations	equation	NOUN
ejpam-5935	38	31	and	and	CCONJ
ejpam-5935	38	32	its	its	PRON
ejpam-5935	38	33	proven	prove	VERB
ejpam-5935	38	34	effectiveness	effectiveness	NOUN
ejpam-5935	38	35	in	in	ADP
ejpam-5935	38	36	addressing	address	VERB
ejpam-5935	38	37	antiperiodic	antiperiodic	ADJ
ejpam-5935	38	38	boundary	boundary	ADJ
ejpam-5935	38	39	value	value	NOUN
ejpam-5935	38	40	problems	problem	NOUN
ejpam-5935	38	41	.	.	PUNCT
ejpam-5935	39	1	the	the	DET
ejpam-5935	39	2	caputo	caputo	PROPN
ejpam-5935	39	3	fractional	fractional	PROPN
ejpam-5935	39	4	derivative	derivative	PROPN
ejpam-5935	39	5	has	have	AUX
ejpam-5935	39	6	gained	gain	VERB
ejpam-5935	39	7	significant	significant	ADJ
ejpam-5935	39	8	attention	attention	NOUN
ejpam-5935	39	9	because	because	SCONJ
ejpam-5935	39	10	of	of	ADP
ejpam-5935	39	11	its	its	PRON
ejpam-5935	39	12	ability	ability	NOUN
ejpam-5935	39	13	to	to	PART
ejpam-5935	39	14	model	model	VERB
ejpam-5935	39	15	real	real	ADJ
ejpam-5935	39	16	-	-	PUNCT
ejpam-5935	39	17	world	world	NOUN
ejpam-5935	39	18	phenomena	phenomenon	NOUN
ejpam-5935	39	19	involving	involve	VERB
ejpam-5935	39	20	memory	memory	NOUN
ejpam-5935	39	21	and	and	CCONJ
ejpam-5935	39	22	hereditary	hereditary	ADJ
ejpam-5935	39	23	properties	property	NOUN
ejpam-5935	39	24	since	since	SCONJ
ejpam-5935	39	25	it	it	PRON
ejpam-5935	39	26	offers	offer	VERB
ejpam-5935	39	27	a	a	DET
ejpam-5935	39	28	solid	solid	ADJ
ejpam-5935	39	29	framework	framework	NOUN
ejpam-5935	39	30	for	for	ADP
ejpam-5935	39	31	addressing	address	VERB
ejpam-5935	39	32	boundary	boundary	ADJ
ejpam-5935	39	33	value	value	NOUN
ejpam-5935	39	34	problems	problem	NOUN
ejpam-5935	39	35	.	.	PUNCT
ejpam-5935	40	1	this	this	DET
ejpam-5935	40	2	paper	paper	NOUN
ejpam-5935	40	3	extends	extend	VERB
ejpam-5935	40	4	these	these	DET
ejpam-5935	40	5	results	result	NOUN
ejpam-5935	40	6	by	by	ADP
ejpam-5935	40	7	introducing	introduce	VERB
ejpam-5935	40	8	significantly	significantly	ADV
ejpam-5935	40	9	broadening	broaden	VERB
ejpam-5935	40	10	the	the	DET
ejpam-5935	40	11	existing	exist	VERB
ejpam-5935	40	12	solution	solution	NOUN
ejpam-5935	40	13	frameworks	framework	NOUN
ejpam-5935	40	14	.	.	PUNCT
ejpam-5935	41	1	introducing	introduce	VERB
ejpam-5935	41	2	this	this	DET
ejpam-5935	41	3	novel	novel	ADJ
ejpam-5935	41	4	intermediate	intermediate	ADJ
ejpam-5935	41	5	condition	condition	NOUN
ejpam-5935	41	6	facilitates	facilitate	VERB
ejpam-5935	41	7	a	a	DET
ejpam-5935	41	8	more	more	ADV
ejpam-5935	41	9	diverse	diverse	ADJ
ejpam-5935	41	10	array	array	NOUN
ejpam-5935	41	11	of	of	ADP
ejpam-5935	41	12	boundary	boundary	ADJ
ejpam-5935	41	13	behaviors	behavior	NOUN
ejpam-5935	41	14	and	and	CCONJ
ejpam-5935	41	15	significantly	significantly	ADV
ejpam-5935	41	16	enhances	enhance	VERB
ejpam-5935	41	17	the	the	DET
ejpam-5935	41	18	applicability	applicability	NOUN
ejpam-5935	41	19	of	of	ADP
ejpam-5935	41	20	various	various	ADJ
ejpam-5935	41	21	solution	solution	NOUN
ejpam-5935	41	22	methodologies	methodology	NOUN
ejpam-5935	41	23	.	.	PUNCT
ejpam-5935	42	1	unlike	unlike	ADP
ejpam-5935	42	2	prior	prior	ADJ
ejpam-5935	42	3	works	work	NOUN
ejpam-5935	42	4	that	that	PRON
ejpam-5935	42	5	focus	focus	VERB
ejpam-5935	42	6	primarily	primarily	ADV
ejpam-5935	42	7	on	on	ADP
ejpam-5935	42	8	boundary	boundary	ADJ
ejpam-5935	42	9	conditions	condition	NOUN
ejpam-5935	42	10	at	at	ADP
ejpam-5935	42	11	the	the	DET
ejpam-5935	42	12	endpoints	endpoint	NOUN
ejpam-5935	42	13	or	or	CCONJ
ejpam-5935	42	14	involve	involve	VERB
ejpam-5935	42	15	periodicity	periodicity	NOUN
ejpam-5935	42	16	or	or	CCONJ
ejpam-5935	42	17	anti	anti	ADJ
ejpam-5935	42	18	-	-	NOUN
ejpam-5935	42	19	periodicity	periodicity	NOUN
ejpam-5935	42	20	,	,	PUNCT
ejpam-5935	42	21	the	the	DET
ejpam-5935	42	22	inclusion	inclusion	NOUN
ejpam-5935	42	23	of	of	ADP
ejpam-5935	42	24	an	an	DET
ejpam-5935	42	25	intermediate	intermediate	ADJ
ejpam-5935	42	26	condition	condition	NOUN
ejpam-5935	42	27	provides	provide	VERB
ejpam-5935	42	28	a	a	DET
ejpam-5935	42	29	more	more	ADV
ejpam-5935	42	30	flexible	flexible	ADJ
ejpam-5935	42	31	and	and	CCONJ
ejpam-5935	42	32	general	general	ADJ
ejpam-5935	42	33	approach	approach	NOUN
ejpam-5935	42	34	to	to	ADP
ejpam-5935	42	35	solving	solve	VERB
ejpam-5935	42	36	fractional	fractional	ADJ
ejpam-5935	42	37	differential	differential	ADJ
ejpam-5935	42	38	equations	equation	NOUN
ejpam-5935	42	39	.	.	PUNCT
ejpam-5935	43	1	moreover	moreover	ADV
ejpam-5935	43	2	,	,	PUNCT
ejpam-5935	43	3	our	our	PRON
ejpam-5935	43	4	results	result	NOUN
ejpam-5935	43	5	offer	offer	VERB
ejpam-5935	43	6	new	new	ADJ
ejpam-5935	43	7	insight	insight	NOUN
ejpam-5935	43	8	into	into	ADP
ejpam-5935	43	9	the	the	DET
ejpam-5935	43	10	existence	existence	NOUN
ejpam-5935	43	11	and	and	CCONJ
ejpam-5935	43	12	uniqueness	uniqueness	NOUN
ejpam-5935	43	13	of	of	ADP
ejpam-5935	43	14	solutions	solution	NOUN
ejpam-5935	43	15	under	under	ADP
ejpam-5935	43	16	more	more	ADJ
ejpam-5935	43	17	complex	complex	ADJ
ejpam-5935	43	18	boundary	boundary	ADJ
ejpam-5935	43	19	scenarios	scenario	NOUN
ejpam-5935	43	20	,	,	PUNCT
ejpam-5935	43	21	thereby	thereby	ADV
ejpam-5935	43	22	expanding	expand	VERB
ejpam-5935	43	23	the	the	DET
ejpam-5935	43	24	scope	scope	NOUN
ejpam-5935	43	25	of	of	ADP
ejpam-5935	43	26	previous	previous	ADJ
ejpam-5935	43	27	research	research	NOUN
ejpam-5935	43	28	.	.	PUNCT
ejpam-5935	44	1	for	for	ADP
ejpam-5935	44	2	more	more	ADV
ejpam-5935	44	3	interesting	interesting	ADJ
ejpam-5935	44	4	results	result	NOUN
ejpam-5935	44	5	,	,	PUNCT
ejpam-5935	44	6	see	see	VERB
ejpam-5935	44	7	[	[	X
ejpam-5935	44	8	17–20	17–20	NUM
ejpam-5935	44	9	]	]	PUNCT
ejpam-5935	44	10	.	.	PUNCT
ejpam-5935	45	1	the	the	DET
ejpam-5935	45	2	paper	paper	NOUN
ejpam-5935	45	3	is	be	AUX
ejpam-5935	45	4	organized	organize	VERB
ejpam-5935	45	5	as	as	SCONJ
ejpam-5935	45	6	follows	follow	VERB
ejpam-5935	45	7	:	:	PUNCT
ejpam-5935	45	8	section	section	NOUN
ejpam-5935	45	9	2	2	NUM
ejpam-5935	45	10	presents	present	VERB
ejpam-5935	45	11	the	the	DET
ejpam-5935	45	12	material	material	NOUN
ejpam-5935	45	13	and	and	CCONJ
ejpam-5935	45	14	methods	method	NOUN
ejpam-5935	45	15	used	use	VERB
ejpam-5935	45	16	in	in	ADP
ejpam-5935	45	17	the	the	DET
ejpam-5935	45	18	research	research	NOUN
ejpam-5935	45	19	article	article	NOUN
ejpam-5935	45	20	,	,	PUNCT
ejpam-5935	45	21	detailing	detail	VERB
ejpam-5935	45	22	the	the	DET
ejpam-5935	45	23	theoretical	theoretical	ADJ
ejpam-5935	45	24	framework	framework	NOUN
ejpam-5935	45	25	.	.	PUNCT
ejpam-5935	46	1	this	this	PRON
ejpam-5935	46	2	is	be	AUX
ejpam-5935	46	3	followed	follow	VERB
ejpam-5935	46	4	by	by	ADP
ejpam-5935	46	5	the	the	DET
ejpam-5935	46	6	results	result	NOUN
ejpam-5935	46	7	derived	derive	VERB
ejpam-5935	46	8	from	from	ADP
ejpam-5935	46	9	the	the	DET
ejpam-5935	46	10	analysis	analysis	NOUN
ejpam-5935	46	11	,	,	PUNCT
ejpam-5935	46	12	highlighting	highlight	VERB
ejpam-5935	46	13	key	key	ADJ
ejpam-5935	46	14	findings	finding	NOUN
ejpam-5935	46	15	and	and	CCONJ
ejpam-5935	46	16	their	their	PRON
ejpam-5935	46	17	implications	implication	NOUN
ejpam-5935	46	18	.	.	PUNCT
ejpam-5935	47	1	section	section	NOUN
ejpam-5935	47	2	4	4	NUM
ejpam-5935	47	3	provides	provide	VERB
ejpam-5935	47	4	an	an	DET
ejpam-5935	47	5	example	example	NOUN
ejpam-5935	47	6	to	to	PART
ejpam-5935	47	7	illustrate	illustrate	VERB
ejpam-5935	47	8	and	and	CCONJ
ejpam-5935	47	9	validate	validate	VERB
ejpam-5935	47	10	the	the	DET
ejpam-5935	47	11	results	result	NOUN
ejpam-5935	47	12	.	.	PUNCT
ejpam-5935	48	1	finally	finally	ADV
ejpam-5935	48	2	,	,	PUNCT
ejpam-5935	48	3	the	the	DET
ejpam-5935	48	4	last	last	ADJ
ejpam-5935	48	5	section	section	NOUN
ejpam-5935	48	6	presents	present	VERB
ejpam-5935	48	7	the	the	DET
ejpam-5935	48	8	conclusion	conclusion	NOUN
ejpam-5935	48	9	.	.	PUNCT
ejpam-5935	49	1	2	2	X
ejpam-5935	49	2	.	.	X
ejpam-5935	49	3	materials	material	NOUN
ejpam-5935	49	4	and	and	CCONJ
ejpam-5935	49	5	methods	method	NOUN
ejpam-5935	49	6	definition	definition	NOUN
ejpam-5935	49	7	1	1	NUM
ejpam-5935	49	8	.	.	PUNCT
ejpam-5935	50	1	[	[	X
ejpam-5935	50	2	1	1	X
ejpam-5935	50	3	]	]	PUNCT
ejpam-5935	50	4	we	we	PRON
ejpam-5935	50	5	define	define	VERB
ejpam-5935	50	6	the	the	DET
ejpam-5935	50	7	caputo	caputo	PROPN
ejpam-5935	50	8	fractional	fractional	PROPN
ejpam-5935	50	9	derivative	derivative	NOUN
ejpam-5935	50	10	of	of	ADP
ejpam-5935	50	11	order	order	NOUN
ejpam-5935	50	12	q	q	X
ejpam-5935	50	13	>	>	X
ejpam-5935	50	14	0	0	PROPN
ejpam-5935	50	15	,	,	PUNCT
ejpam-5935	50	16	denoted	denote	VERB
ejpam-5935	50	17	cdq	cdq	NOUN
ejpam-5935	50	18	,	,	PUNCT
ejpam-5935	50	19	for	for	ADP
ejpam-5935	50	20	a	a	DET
ejpam-5935	50	21	given	give	VERB
ejpam-5935	50	22	function	function	NOUN
ejpam-5935	50	23	ψ	ψ	X
ejpam-5935	50	24	∈	∈	PROPN
ejpam-5935	50	25	ck([0	ck([0	PROPN
ejpam-5935	50	26	,	,	PUNCT
ejpam-5935	50	27	ω	ω	NOUN
ejpam-5935	50	28	]	]	X
ejpam-5935	50	29	)	)	PUNCT
ejpam-5935	50	30	,	,	PUNCT
ejpam-5935	50	31	is	be	AUX
ejpam-5935	50	32	defined	define	VERB
ejpam-5935	50	33	by	by	ADP
ejpam-5935	50	34	:	:	PUNCT
ejpam-5935	50	35	cdqψ(ρ	cdqψ(ρ	PROPN
ejpam-5935	50	36	)	)	PUNCT
ejpam-5935	50	37	=	=	SYM
ejpam-5935	50	38	1	1	NUM
ejpam-5935	50	39	γ(k	γ(k	NOUN
ejpam-5935	50	40	−	−	PROPN
ejpam-5935	50	41	q	q	NOUN
ejpam-5935	50	42	)	)	PUNCT
ejpam-5935	50	43	∫	∫	PROPN
ejpam-5935	51	1	ρ	ρ	PROPN
ejpam-5935	51	2	0	0	NUM
ejpam-5935	51	3	(	(	PUNCT
ejpam-5935	51	4	ρ−ϖ)k−q−1ψ	ρ−ϖ)k−q−1ψ	NUM
ejpam-5935	51	5	(	(	PUNCT
ejpam-5935	51	6	k)(ϖ)dϖ	k)(ϖ)dϖ	NOUN
ejpam-5935	51	7	,	,	PUNCT
ejpam-5935	51	8	where	where	SCONJ
ejpam-5935	51	9	,	,	PUNCT
ejpam-5935	51	10	k	k	PROPN
ejpam-5935	51	11	=	=	PUNCT
ejpam-5935	52	1	[	[	X
ejpam-5935	52	2	q	q	X
ejpam-5935	52	3	]	]	X
ejpam-5935	52	4	+	+	NOUN
ejpam-5935	52	5	1	1	X
ejpam-5935	52	6	.	.	X
ejpam-5935	52	7	definition	definition	NOUN
ejpam-5935	52	8	2	2	NUM
ejpam-5935	52	9	.	.	PUNCT
ejpam-5935	53	1	[	[	X
ejpam-5935	53	2	1	1	X
ejpam-5935	53	3	]	]	PUNCT
ejpam-5935	53	4	the	the	DET
ejpam-5935	53	5	riemann	riemann	PROPN
ejpam-5935	53	6	-	-	PUNCT
ejpam-5935	53	7	liouville	liouville	VERB
ejpam-5935	53	8	fractional	fractional	ADJ
ejpam-5935	53	9	integral	integral	ADJ
ejpam-5935	53	10	of	of	ADP
ejpam-5935	53	11	order	order	NOUN
ejpam-5935	53	12	q	q	PROPN
ejpam-5935	53	13	>	>	X
ejpam-5935	53	14	0	0	PROPN
ejpam-5935	53	15	,	,	PUNCT
ejpam-5935	53	16	denoted	denote	VERB
ejpam-5935	53	17	iq	iq	NOUN
ejpam-5935	53	18	,	,	PUNCT
ejpam-5935	53	19	for	for	ADP
ejpam-5935	53	20	a	a	DET
ejpam-5935	53	21	defined	define	VERB
ejpam-5935	53	22	function	function	NOUN
ejpam-5935	53	23	ψ	ψ	ADP
ejpam-5935	53	24	∈	∈	PROPN
ejpam-5935	53	25	c([0	c([0	NOUN
ejpam-5935	53	26	,	,	PUNCT
ejpam-5935	53	27	ω	ω	NOUN
ejpam-5935	53	28	]	]	X
ejpam-5935	53	29	)	)	PUNCT
ejpam-5935	53	30	,	,	PUNCT
ejpam-5935	53	31	is	be	AUX
ejpam-5935	53	32	defined	define	VERB
ejpam-5935	53	33	by	by	ADP
ejpam-5935	53	34	:	:	PUNCT
ejpam-5935	53	35	iqψ(ρ	iqψ(ρ	PROPN
ejpam-5935	53	36	)	)	PUNCT
ejpam-5935	53	37	=	=	SYM
ejpam-5935	53	38	1	1	NUM
ejpam-5935	53	39	γ(q	γ(q	PROPN
ejpam-5935	53	40	)	)	PUNCT
ejpam-5935	53	41	∫	∫	PROPN
ejpam-5935	54	1	ρ	ρ	PROPN
ejpam-5935	54	2	0	0	PUNCT
ejpam-5935	55	1	(	(	PUNCT
ejpam-5935	55	2	ρ−ϖ)q−1ψ(ϖ)dϖ.	ρ−ϖ)q−1ψ(ϖ)dϖ.	ADV
ejpam-5935	55	3	lemma	lemma	PROPN
ejpam-5935	55	4	1	1	NUM
ejpam-5935	55	5	.	.	PUNCT
ejpam-5935	56	1	[	[	X
ejpam-5935	56	2	1	1	X
ejpam-5935	56	3	]	]	PUNCT
ejpam-5935	56	4	for	for	ADP
ejpam-5935	56	5	q	q	PROPN
ejpam-5935	56	6	>	>	X
ejpam-5935	56	7	0	0	PROPN
ejpam-5935	56	8	,	,	PUNCT
ejpam-5935	56	9	the	the	DET
ejpam-5935	56	10	general	general	ADJ
ejpam-5935	56	11	solution	solution	NOUN
ejpam-5935	56	12	of	of	ADP
ejpam-5935	56	13	cdqξ(ρ	cdqξ(ρ	PROPN
ejpam-5935	56	14	)	)	PUNCT
ejpam-5935	56	15	=	=	SYM
ejpam-5935	56	16	0	0	NUM
ejpam-5935	56	17	is	be	AUX
ejpam-5935	56	18	given	give	VERB
ejpam-5935	56	19	by	by	ADP
ejpam-5935	56	20	,	,	PUNCT
ejpam-5935	56	21	ξ(ρ	ξ(ρ	PROPN
ejpam-5935	56	22	)	)	PUNCT
ejpam-5935	56	23	=	=	SYM
ejpam-5935	56	24	a0	a0	NOUN
ejpam-5935	56	25	+	+	CCONJ
ejpam-5935	56	26	a1ρ+	a1ρ+	NOUN
ejpam-5935	56	27	a2ρ	a2ρ	ADV
ejpam-5935	56	28	2	2	NUM
ejpam-5935	56	29	+	+	CCONJ
ejpam-5935	56	30	...	...	PUNCT
ejpam-5935	57	1	+	+	CCONJ
ejpam-5935	57	2	ak−1ρ	ak−1ρ	PROPN
ejpam-5935	57	3	k−1	k−1	PROPN
ejpam-5935	57	4	,	,	PUNCT
ejpam-5935	57	5	where	where	SCONJ
ejpam-5935	57	6	,	,	PUNCT
ejpam-5935	57	7	ai	ai	VERB
ejpam-5935	57	8	∈	∈	PROPN
ejpam-5935	57	9	r	r	NOUN
ejpam-5935	57	10	,	,	PUNCT
ejpam-5935	57	11	for	for	ADP
ejpam-5935	57	12	i	i	PROPN
ejpam-5935	57	13	=	=	SYM
ejpam-5935	57	14	1	1	NUM
ejpam-5935	57	15	,	,	PUNCT
ejpam-5935	57	16	2	2	NUM
ejpam-5935	57	17	,	,	PUNCT
ejpam-5935	57	18	and	and	CCONJ
ejpam-5935	57	19	k	k	PROPN
ejpam-5935	57	20	=	=	PUNCT
ejpam-5935	58	1	[	[	X
ejpam-5935	58	2	q	q	X
ejpam-5935	58	3	]	]	X
ejpam-5935	58	4	+	+	NUM
ejpam-5935	58	5	1	1	X
ejpam-5935	58	6	.	.	X
ejpam-5935	58	7	lemma	lemma	PROPN
ejpam-5935	58	8	2	2	NUM
ejpam-5935	58	9	.	.	PUNCT
ejpam-5935	58	10	the	the	DET
ejpam-5935	58	11	unique	unique	ADJ
ejpam-5935	58	12	solution	solution	NOUN
ejpam-5935	58	13	of	of	ADP
ejpam-5935	58	14	the	the	DET
ejpam-5935	58	15	following	follow	VERB
ejpam-5935	58	16	problem	problem	NOUN
ejpam-5935	58	17	{	{	PUNCT
ejpam-5935	58	18	cdqξ(ρ	cdqξ(ρ	PROPN
ejpam-5935	58	19	)	)	PUNCT
ejpam-5935	58	20	=	=	SYM
ejpam-5935	59	1	δ(ρ	δ(ρ	VERB
ejpam-5935	59	2	)	)	PUNCT
ejpam-5935	59	3	,	,	PUNCT
ejpam-5935	59	4	1	1	NUM
ejpam-5935	59	5	<	<	X
ejpam-5935	59	6	q	q	X
ejpam-5935	59	7	≤	≤	NUM
ejpam-5935	59	8	2	2	NUM
ejpam-5935	59	9	,	,	PUNCT
ejpam-5935	59	10	ρ	ρ	PROPN
ejpam-5935	59	11	∈	∈	PROPN
ejpam-5935	60	1	[	[	X
ejpam-5935	60	2	0	0	NUM
ejpam-5935	60	3	,	,	PUNCT
ejpam-5935	60	4	ω	ω	NOUN
ejpam-5935	60	5	]	]	X
ejpam-5935	60	6	ξ(κ	ξ(κ	NUM
ejpam-5935	60	7	)	)	PUNCT
ejpam-5935	60	8	=	=	SYM
ejpam-5935	60	9	α	α	X
ejpam-5935	60	10	,	,	PUNCT
ejpam-5935	60	11	ξ(ω	ξ(ω	NOUN
ejpam-5935	60	12	)	)	PUNCT
ejpam-5935	60	13	=	=	PUNCT
ejpam-5935	60	14	β	β	X
ejpam-5935	60	15	,	,	PUNCT
ejpam-5935	60	16	0	0	NUM
ejpam-5935	60	17	≤	≤	NUM
ejpam-5935	60	18	κ	κ	X
ejpam-5935	60	19	<	<	X
ejpam-5935	60	20	ω	ω	PROPN
ejpam-5935	60	21	,	,	PUNCT
ejpam-5935	60	22	0	0	PUNCT
ejpam-5935	60	23	<	<	X
ejpam-5935	60	24	α	α	X
ejpam-5935	60	25	<	<	X
ejpam-5935	60	26	β	β	X
ejpam-5935	60	27	,	,	PUNCT
ejpam-5935	60	28	(	(	PUNCT
ejpam-5935	60	29	2	2	X
ejpam-5935	60	30	)	)	PUNCT
ejpam-5935	60	31	s.	s.	PROPN
ejpam-5935	60	32	f.	f.	PROPN
ejpam-5935	60	33	aljurbua	aljurbua	PROPN
ejpam-5935	60	34	et	et	PROPN
ejpam-5935	60	35	al	al	PROPN
ejpam-5935	60	36	.	.	PUNCT
ejpam-5935	60	37	/	/	SYM
ejpam-5935	60	38	eur	eur	PROPN
ejpam-5935	60	39	.	.	PUNCT
ejpam-5935	61	1	j.	j.	PROPN
ejpam-5935	61	2	pure	pure	PROPN
ejpam-5935	61	3	appl	appl	PROPN
ejpam-5935	61	4	.	.	PROPN
ejpam-5935	61	5	math	math	PROPN
ejpam-5935	61	6	,	,	PUNCT
ejpam-5935	61	7	18	18	NUM
ejpam-5935	61	8	(	(	PUNCT
ejpam-5935	61	9	2	2	NUM
ejpam-5935	61	10	)	)	PUNCT
ejpam-5935	61	11	(	(	PUNCT
ejpam-5935	61	12	2025	2025	NUM
ejpam-5935	61	13	)	)	PUNCT
ejpam-5935	61	14	,	,	PUNCT
ejpam-5935	61	15	5935	5935	NUM
ejpam-5935	61	16	4	4	NUM
ejpam-5935	61	17	of	of	ADP
ejpam-5935	61	18	10	10	NUM
ejpam-5935	61	19	is	be	AUX
ejpam-5935	61	20	given	give	VERB
ejpam-5935	61	21	by	by	ADP
ejpam-5935	61	22	:	:	PUNCT
ejpam-5935	61	23	ξ(ρ	ξ(ρ	PROPN
ejpam-5935	61	24	)	)	PUNCT
ejpam-5935	61	25	=	=	SYM
ejpam-5935	62	1	αω	αω	NUM
ejpam-5935	62	2	−	−	NOUN
ejpam-5935	63	1	βκ	βκ	INTJ
ejpam-5935	64	1	ω	ω	NUM
ejpam-5935	64	2	−	−	NOUN
ejpam-5935	64	3	κ	κ	NOUN
ejpam-5935	64	4	+	+	X
ejpam-5935	65	1	β	β	X
ejpam-5935	65	2	−	−	PROPN
ejpam-5935	65	3	α	α	PROPN
ejpam-5935	65	4	ω	ω	PROPN
ejpam-5935	66	1	−	−	PROPN
ejpam-5935	67	1	κ	κ	PROPN
ejpam-5935	67	2	ρ+	ρ+	NOUN
ejpam-5935	67	3	1	1	NUM
ejpam-5935	67	4	γ(q	γ(q	NOUN
ejpam-5935	67	5	)	)	PUNCT
ejpam-5935	67	6	∫	∫	PROPN
ejpam-5935	68	1	ρ	ρ	PROPN
ejpam-5935	68	2	0	0	PROPN
ejpam-5935	68	3	(	(	PUNCT
ejpam-5935	68	4	ρ−ϖ)q−1δ(ϖ	ρ−ϖ)q−1δ(ϖ	PROPN
ejpam-5935	68	5	)	)	PUNCT
ejpam-5935	68	6	dϖ	dϖ	ADP
ejpam-5935	68	7	−	−	PROPN
ejpam-5935	68	8	ρ−	ρ−	PROPN
ejpam-5935	68	9	κ	κ	VERB
ejpam-5935	68	10	γ(q)(ω	γ(q)(ω	NUM
ejpam-5935	68	11	−	−	PROPN
ejpam-5935	68	12	κ	κ	NOUN
ejpam-5935	68	13	)	)	PUNCT
ejpam-5935	68	14	[	[	PUNCT
ejpam-5935	68	15	∫	∫	PROPN
ejpam-5935	68	16	ω	ω	NUM
ejpam-5935	68	17	0	0	NUM
ejpam-5935	68	18	(	(	PUNCT
ejpam-5935	68	19	ω	ω	PROPN
ejpam-5935	68	20	−ϖ)q−1δ(ϖ	−ϖ)q−1δ(ϖ	PROPN
ejpam-5935	68	21	)	)	PUNCT
ejpam-5935	68	22	dϖ	dϖ	X
ejpam-5935	68	23	]	]	PUNCT
ejpam-5935	69	1	+	+	CCONJ
ejpam-5935	69	2	ρ−	ρ−	PROPN
ejpam-5935	69	3	ω	ω	NUM
ejpam-5935	69	4	γ(q)(ω	γ(q)(ω	NUM
ejpam-5935	69	5	−	−	PROPN
ejpam-5935	69	6	κ	κ	NOUN
ejpam-5935	69	7	)	)	PUNCT
ejpam-5935	69	8	[	[	PUNCT
ejpam-5935	69	9	∫	∫	PROPN
ejpam-5935	69	10	κ	κ	PROPN
ejpam-5935	69	11	0	0	PROPN
ejpam-5935	69	12	(	(	PUNCT
ejpam-5935	69	13	κ−ϖ)q−1δ(ϖ	κ−ϖ)q−1δ(ϖ	PROPN
ejpam-5935	69	14	)	)	PUNCT
ejpam-5935	69	15	dϖ	dϖ	NOUN
ejpam-5935	69	16	]	]	PUNCT
ejpam-5935	69	17	.	.	PUNCT
ejpam-5935	70	1	(	(	PUNCT
ejpam-5935	70	2	3	3	X
ejpam-5935	70	3	)	)	PUNCT
ejpam-5935	70	4	proof	proof	NOUN
ejpam-5935	70	5	.	.	PUNCT
ejpam-5935	71	1	by	by	ADP
ejpam-5935	71	2	lemma	lemma	PROPN
ejpam-5935	71	3	1	1	NUM
ejpam-5935	71	4	,	,	PUNCT
ejpam-5935	71	5	the	the	DET
ejpam-5935	71	6	solution	solution	NOUN
ejpam-5935	71	7	of	of	ADP
ejpam-5935	71	8	(	(	PUNCT
ejpam-5935	71	9	2	2	NUM
ejpam-5935	71	10	)	)	PUNCT
ejpam-5935	71	11	is	be	AUX
ejpam-5935	71	12	given	give	VERB
ejpam-5935	71	13	by	by	ADP
ejpam-5935	71	14	ξ(ρ	ξ(ρ	NOUN
ejpam-5935	71	15	)	)	PUNCT
ejpam-5935	71	16	=	=	SYM
ejpam-5935	71	17	iqδ(ρ	iqδ(ρ	PROPN
ejpam-5935	71	18	)	)	PUNCT
ejpam-5935	71	19	−	−	PROPN
ejpam-5935	71	20	a0	a0	PROPN
ejpam-5935	71	21	−	−	PROPN
ejpam-5935	71	22	a1ρ	a1ρ	PROPN
ejpam-5935	71	23	where	where	SCONJ
ejpam-5935	71	24	,	,	PUNCT
ejpam-5935	71	25	ai	ai	VERB
ejpam-5935	71	26	∈	∈	PROPN
ejpam-5935	71	27	r	r	NOUN
ejpam-5935	71	28	,	,	PUNCT
ejpam-5935	71	29	for	for	ADP
ejpam-5935	71	30	i	i	PROPN
ejpam-5935	71	31	=	=	SYM
ejpam-5935	71	32	1	1	NUM
ejpam-5935	71	33	,	,	PUNCT
ejpam-5935	71	34	2	2	NUM
ejpam-5935	71	35	.	.	PUNCT
ejpam-5935	71	36	by	by	ADP
ejpam-5935	71	37	applying	apply	VERB
ejpam-5935	71	38	the	the	DET
ejpam-5935	71	39	boundary	boundary	ADJ
ejpam-5935	71	40	conditions	condition	NOUN
ejpam-5935	71	41	we	we	PRON
ejpam-5935	71	42	get	get	VERB
ejpam-5935	71	43	,	,	PUNCT
ejpam-5935	71	44	a0	a0	PROPN
ejpam-5935	71	45	=	=	SYM
ejpam-5935	71	46	βκ−	βκ−	PROPN
ejpam-5935	71	47	αω	αω	NUM
ejpam-5935	71	48	ω	ω	NUM
ejpam-5935	71	49	−	−	PROPN
ejpam-5935	71	50	κ	κ	NOUN
ejpam-5935	71	51	−	−	PROPN
ejpam-5935	71	52	1	1	NUM
ejpam-5935	71	53	γ(q)(ω	γ(q)(ω	NUM
ejpam-5935	71	54	−	−	PROPN
ejpam-5935	71	55	κ	κ	NOUN
ejpam-5935	71	56	)	)	PUNCT
ejpam-5935	71	57	[	[	PUNCT
ejpam-5935	71	58	κ	κ	X
ejpam-5935	71	59	∫	∫	PROPN
ejpam-5935	71	60	ω	ω	PROPN
ejpam-5935	71	61	0	0	NUM
ejpam-5935	71	62	(	(	PUNCT
ejpam-5935	71	63	ω	ω	PROPN
ejpam-5935	71	64	−ϖ)q−1δ(ϖ)dϖ	−ϖ)q−1δ(ϖ)dϖ	NOUN
ejpam-5935	71	65	−	−	PROPN
ejpam-5935	71	66	ω	ω	NUM
ejpam-5935	71	67	∫	∫	PROPN
ejpam-5935	71	68	κ	κ	PROPN
ejpam-5935	71	69	0	0	PROPN
ejpam-5935	71	70	(	(	PUNCT
ejpam-5935	71	71	κ−ϖ)q−1δ(ϖ	κ−ϖ)q−1δ(ϖ	PROPN
ejpam-5935	71	72	)	)	PUNCT
ejpam-5935	71	73	]	]	PUNCT
ejpam-5935	72	1	a1	a1	NOUN
ejpam-5935	72	2	=	=	SYM
ejpam-5935	72	3	α−	α−	ADP
ejpam-5935	72	4	β	β	X
ejpam-5935	72	5	ω	ω	NUM
ejpam-5935	72	6	−	−	PROPN
ejpam-5935	72	7	κ	κ	NOUN
ejpam-5935	73	1	+	+	CCONJ
ejpam-5935	73	2	1	1	NUM
ejpam-5935	73	3	γ(q)(ω	γ(q)(ω	NUM
ejpam-5935	73	4	−	−	PROPN
ejpam-5935	73	5	κ	κ	NOUN
ejpam-5935	73	6	)	)	PUNCT
ejpam-5935	73	7	[	[	PUNCT
ejpam-5935	73	8	∫	∫	PROPN
ejpam-5935	73	9	ω	ω	NUM
ejpam-5935	73	10	0	0	NUM
ejpam-5935	73	11	(	(	PUNCT
ejpam-5935	73	12	ω	ω	PROPN
ejpam-5935	73	13	−ϖ)q−1δ(ϖ)dϖ	−ϖ)q−1δ(ϖ)dϖ	NOUN
ejpam-5935	74	1	−	−	PROPN
ejpam-5935	74	2	∫	∫	PROPN
ejpam-5935	74	3	κ	κ	PROPN
ejpam-5935	74	4	0	0	PUNCT
ejpam-5935	74	5	(	(	PUNCT
ejpam-5935	74	6	κ−ϖ)q−1δ(ϖ)dϖ	κ−ϖ)q−1δ(ϖ)dϖ	NOUN
ejpam-5935	74	7	]	]	PUNCT
ejpam-5935	74	8	by	by	ADP
ejpam-5935	74	9	using	use	VERB
ejpam-5935	74	10	the	the	DET
ejpam-5935	74	11	values	value	NOUN
ejpam-5935	74	12	of	of	ADP
ejpam-5935	74	13	a0	a0	NOUN
ejpam-5935	74	14	,	,	PUNCT
ejpam-5935	74	15	a1	a1	NOUN
ejpam-5935	74	16	we	we	PRON
ejpam-5935	74	17	get	get	VERB
ejpam-5935	74	18	ξ(ρ	ξ(ρ	NOUN
ejpam-5935	74	19	)	)	PUNCT
ejpam-5935	74	20	=	=	SYM
ejpam-5935	75	1	αω	αω	NUM
ejpam-5935	75	2	−	−	NOUN
ejpam-5935	76	1	βκ	βκ	INTJ
ejpam-5935	77	1	ω	ω	NUM
ejpam-5935	77	2	−	−	NOUN
ejpam-5935	77	3	κ	κ	NOUN
ejpam-5935	77	4	+	+	X
ejpam-5935	78	1	β	β	X
ejpam-5935	78	2	−	−	PROPN
ejpam-5935	78	3	α	α	PROPN
ejpam-5935	78	4	ω	ω	PROPN
ejpam-5935	79	1	−	−	PROPN
ejpam-5935	80	1	κ	κ	PROPN
ejpam-5935	80	2	ρ+	ρ+	NOUN
ejpam-5935	80	3	1	1	NUM
ejpam-5935	80	4	γ(q	γ(q	NOUN
ejpam-5935	80	5	)	)	PUNCT
ejpam-5935	80	6	∫	∫	PROPN
ejpam-5935	81	1	ρ	ρ	PROPN
ejpam-5935	81	2	0	0	PROPN
ejpam-5935	81	3	(	(	PUNCT
ejpam-5935	81	4	ρ−ϖ)q−1δ(ϖ	ρ−ϖ)q−1δ(ϖ	PROPN
ejpam-5935	81	5	)	)	PUNCT
ejpam-5935	81	6	dϖ	dϖ	ADP
ejpam-5935	81	7	−	−	PROPN
ejpam-5935	81	8	ρ−	ρ−	PROPN
ejpam-5935	81	9	κ	κ	VERB
ejpam-5935	81	10	γ(q)(ω	γ(q)(ω	NUM
ejpam-5935	81	11	−	−	PROPN
ejpam-5935	81	12	κ	κ	NOUN
ejpam-5935	81	13	)	)	PUNCT
ejpam-5935	81	14	[	[	PUNCT
ejpam-5935	81	15	∫	∫	PROPN
ejpam-5935	81	16	ω	ω	NUM
ejpam-5935	81	17	0	0	NUM
ejpam-5935	81	18	(	(	PUNCT
ejpam-5935	81	19	ω	ω	PROPN
ejpam-5935	81	20	−ϖ)q−1δ(ϖ	−ϖ)q−1δ(ϖ	PROPN
ejpam-5935	81	21	)	)	PUNCT
ejpam-5935	81	22	dϖ	dϖ	X
ejpam-5935	81	23	]	]	PUNCT
ejpam-5935	82	1	+	+	CCONJ
ejpam-5935	82	2	ρ−	ρ−	PROPN
ejpam-5935	82	3	ω	ω	NUM
ejpam-5935	82	4	γ(q)(ω	γ(q)(ω	NUM
ejpam-5935	82	5	−	−	PROPN
ejpam-5935	82	6	κ	κ	NOUN
ejpam-5935	82	7	)	)	PUNCT
ejpam-5935	82	8	[	[	PUNCT
ejpam-5935	82	9	∫	∫	PROPN
ejpam-5935	82	10	κ	κ	PROPN
ejpam-5935	82	11	0	0	PROPN
ejpam-5935	82	12	(	(	PUNCT
ejpam-5935	82	13	κ−ϖ)q−1δ(ϖ	κ−ϖ)q−1δ(ϖ	PROPN
ejpam-5935	82	14	)	)	PUNCT
ejpam-5935	82	15	dϖ	dϖ	X
ejpam-5935	82	16	]	]	PUNCT
ejpam-5935	82	17	,	,	PUNCT
ejpam-5935	82	18	completing	complete	VERB
ejpam-5935	82	19	the	the	DET
ejpam-5935	82	20	proof	proof	NOUN
ejpam-5935	82	21	.	.	PUNCT
ejpam-5935	83	1	remark	remark	NOUN
ejpam-5935	83	2	1	1	NUM
ejpam-5935	83	3	.	.	PUNCT
ejpam-5935	83	4	note	note	VERB
ejpam-5935	83	5	that	that	SCONJ
ejpam-5935	83	6	as	as	SCONJ
ejpam-5935	83	7	κ	κ	PRON
ejpam-5935	83	8	−→	−→	NOUN
ejpam-5935	83	9	0	0	NUM
ejpam-5935	83	10	+	+	NUM
ejpam-5935	83	11	and	and	CCONJ
ejpam-5935	83	12	ω	ω	NUM
ejpam-5935	83	13	=	=	SYM
ejpam-5935	83	14	1	1	NUM
ejpam-5935	83	15	in	in	ADP
ejpam-5935	83	16	3	3	NUM
ejpam-5935	83	17	we	we	PRON
ejpam-5935	83	18	will	will	AUX
ejpam-5935	83	19	get	get	VERB
ejpam-5935	83	20	the	the	DET
ejpam-5935	83	21	integral	integral	ADJ
ejpam-5935	83	22	solution	solution	NOUN
ejpam-5935	83	23	in	in	ADP
ejpam-5935	83	24	[	[	X
ejpam-5935	83	25	13	13	NUM
ejpam-5935	83	26	]	]	PUNCT
ejpam-5935	83	27	.	.	PUNCT
ejpam-5935	84	1	meaning	mean	VERB
ejpam-5935	84	2	that	that	SCONJ
ejpam-5935	84	3	the	the	DET
ejpam-5935	84	4	results	result	NOUN
ejpam-5935	84	5	in	in	ADP
ejpam-5935	84	6	this	this	DET
ejpam-5935	84	7	paper	paper	NOUN
ejpam-5935	84	8	extend	extend	VERB
ejpam-5935	84	9	and	and	CCONJ
ejpam-5935	84	10	generalize	generalize	VERB
ejpam-5935	84	11	the	the	DET
ejpam-5935	84	12	results	result	NOUN
ejpam-5935	84	13	in	in	ADP
ejpam-5935	84	14	[	[	X
ejpam-5935	84	15	13	13	NUM
ejpam-5935	84	16	]	]	PUNCT
ejpam-5935	84	17	.	.	PUNCT
ejpam-5935	85	1	theorem	theorem	NOUN
ejpam-5935	85	2	1	1	NUM
ejpam-5935	85	3	.	.	PUNCT
ejpam-5935	86	1	[	[	X
ejpam-5935	86	2	21	21	NUM
ejpam-5935	86	3	]	]	PUNCT
ejpam-5935	86	4	let	let	VERB
ejpam-5935	86	5	c	c	PRON
ejpam-5935	86	6	be	be	AUX
ejpam-5935	86	7	a	a	DET
ejpam-5935	86	8	complete	complete	ADJ
ejpam-5935	86	9	nonempty	nonempty	ADJ
ejpam-5935	86	10	metric	metric	ADJ
ejpam-5935	86	11	space	space	NOUN
ejpam-5935	86	12	into	into	ADP
ejpam-5935	86	13	itself	itself	PRON
ejpam-5935	86	14	,	,	PUNCT
ejpam-5935	86	15	then	then	ADV
ejpam-5935	86	16	every	every	DET
ejpam-5935	86	17	contraction	contraction	NOUN
ejpam-5935	86	18	mapping	mapping	NOUN
ejpam-5935	86	19	on	on	ADP
ejpam-5935	86	20	c	c	PROPN
ejpam-5935	86	21	has	have	VERB
ejpam-5935	86	22	a	a	DET
ejpam-5935	86	23	unique	unique	ADJ
ejpam-5935	86	24	fixed	fix	VERB
ejpam-5935	86	25	point	point	NOUN
ejpam-5935	86	26	in	in	ADP
ejpam-5935	86	27	c.	c.	PROPN
ejpam-5935	86	28	theorem	theorem	NOUN
ejpam-5935	86	29	2	2	NUM
ejpam-5935	86	30	.	.	PUNCT
ejpam-5935	87	1	[	[	X
ejpam-5935	87	2	21	21	NUM
ejpam-5935	87	3	]	]	X
ejpam-5935	87	4	let	let	AUX
ejpam-5935	87	5	b	b	PRON
ejpam-5935	87	6	be	be	AUX
ejpam-5935	87	7	a	a	DET
ejpam-5935	87	8	banach	banach	NOUN
ejpam-5935	87	9	space	space	NOUN
ejpam-5935	87	10	,	,	PUNCT
ejpam-5935	87	11	and	and	CCONJ
ejpam-5935	87	12	ϕ	ϕ	PROPN
ejpam-5935	87	13	be	be	AUX
ejpam-5935	87	14	convex	convex	NOUN
ejpam-5935	87	15	nonempty	nonempty	ADV
ejpam-5935	87	16	closed	close	VERB
ejpam-5935	87	17	subset	subset	NOUN
ejpam-5935	87	18	of	of	ADP
ejpam-5935	87	19	b	b	NOUN
ejpam-5935	87	20	,	,	PUNCT
ejpam-5935	87	21	suppose	suppose	VERB
ejpam-5935	87	22	that	that	SCONJ
ejpam-5935	87	23	ϑi	ϑi	PRON
ejpam-5935	87	24	:	:	PUNCT
ejpam-5935	87	25	ϕ	ϕ	PROPN
ejpam-5935	87	26	−→	−→	NOUN
ejpam-5935	87	27	b	b	PROPN
ejpam-5935	87	28	for	for	ADP
ejpam-5935	87	29	i	i	PRON
ejpam-5935	87	30	=	=	NOUN
ejpam-5935	87	31	1	1	NUM
ejpam-5935	87	32	,	,	PUNCT
ejpam-5935	87	33	2	2	NUM
ejpam-5935	87	34	and	and	CCONJ
ejpam-5935	87	35	ϑ1ξ1	ϑ1ξ1	PROPN
ejpam-5935	87	36	+	+	CCONJ
ejpam-5935	87	37	ϑ2ξ2	ϑ2ξ2	X
ejpam-5935	87	38	∈	∈	NOUN
ejpam-5935	87	39	ϕ	ϕ	NOUN
ejpam-5935	87	40	for	for	ADP
ejpam-5935	87	41	all	all	DET
ejpam-5935	87	42	ξ1	ξ1	NOUN
ejpam-5935	87	43	,	,	PUNCT
ejpam-5935	87	44	ξ2	ξ2	PROPN
ejpam-5935	87	45	∈	∈	PROPN
ejpam-5935	87	46	ϕ	ϕ	NOUN
ejpam-5935	87	47	,	,	PUNCT
ejpam-5935	87	48	ϑ1	ϑ1	PROPN
ejpam-5935	87	49	is	be	AUX
ejpam-5935	87	50	continuous	continuous	ADJ
ejpam-5935	87	51	and	and	CCONJ
ejpam-5935	87	52	compact	compact	ADJ
ejpam-5935	87	53	,	,	PUNCT
ejpam-5935	87	54	ϑ2	ϑ2	PROPN
ejpam-5935	87	55	is	be	AUX
ejpam-5935	87	56	a	a	DET
ejpam-5935	87	57	contraction	contraction	NOUN
ejpam-5935	87	58	mapping	mapping	NOUN
ejpam-5935	87	59	.	.	PUNCT
ejpam-5935	88	1	then	then	ADV
ejpam-5935	88	2	there	there	PRON
ejpam-5935	88	3	exists	exist	VERB
ejpam-5935	88	4	a	a	DET
ejpam-5935	88	5	ξ	ξ	PROPN
ejpam-5935	88	6	∈	∈	PROPN
ejpam-5935	88	7	ϕ	ϕ	NOUN
ejpam-5935	88	8	such	such	DET
ejpam-5935	88	9	that	that	DET
ejpam-5935	88	10	ϑ1	ϑ1	PROPN
ejpam-5935	88	11	ξ	ξ	PROPN
ejpam-5935	89	1	+	+	CCONJ
ejpam-5935	89	2	ϑ2	ϑ2	PROPN
ejpam-5935	89	3	ξ	ξ	X
ejpam-5935	89	4	=	=	SYM
ejpam-5935	89	5	ξ	ξ	PROPN
ejpam-5935	89	6	.	.	NOUN
ejpam-5935	89	7	3	3	X
ejpam-5935	89	8	.	.	X
ejpam-5935	89	9	results	result	NOUN
ejpam-5935	89	10	let	let	VERB
ejpam-5935	89	11	z	z	NOUN
ejpam-5935	89	12	=	=	SYM
ejpam-5935	89	13	c([0	c([0	NOUN
ejpam-5935	89	14	,	,	PUNCT
ejpam-5935	89	15	ω],r	ω],r	NUM
ejpam-5935	89	16	)	)	PUNCT
ejpam-5935	89	17	denotes	denote	VERB
ejpam-5935	89	18	the	the	DET
ejpam-5935	89	19	banach	banach	NOUN
ejpam-5935	89	20	space	space	NOUN
ejpam-5935	89	21	equipped	equip	VERB
ejpam-5935	89	22	with	with	ADP
ejpam-5935	89	23	the	the	DET
ejpam-5935	89	24	norm	norm	NOUN
ejpam-5935	90	1	||ξ||	||ξ||	VERB
ejpam-5935	90	2	=	=	SYM
ejpam-5935	90	3	sup	sup	NUM
ejpam-5935	90	4	|ξ(ρ)|,∀ρ	|ξ(ρ)|,∀ρ	NOUN
ejpam-5935	90	5	∈	∈	PROPN
ejpam-5935	91	1	[	[	X
ejpam-5935	91	2	0	0	NUM
ejpam-5935	91	3	,	,	PUNCT
ejpam-5935	91	4	ω	ω	NOUN
ejpam-5935	91	5	]	]	PUNCT
ejpam-5935	91	6	.	.	PUNCT
ejpam-5935	92	1	define	define	VERB
ejpam-5935	92	2	the	the	DET
ejpam-5935	92	3	operator	operator	NOUN
ejpam-5935	92	4	l	l	NOUN
ejpam-5935	92	5	:	:	PUNCT
ejpam-5935	93	1	z	z	NOUN
ejpam-5935	93	2	−→	−→	NOUN
ejpam-5935	93	3	z	z	PROPN
ejpam-5935	93	4	as	as	ADP
ejpam-5935	93	5	(	(	PUNCT
ejpam-5935	93	6	lξ)(ρ	lξ)(ρ	PROPN
ejpam-5935	93	7	)	)	PUNCT
ejpam-5935	93	8	=	=	PUNCT
ejpam-5935	94	1	αω	αω	NUM
ejpam-5935	94	2	−	−	NOUN
ejpam-5935	95	1	βκ	βκ	INTJ
ejpam-5935	96	1	ω	ω	NUM
ejpam-5935	96	2	−	−	NOUN
ejpam-5935	96	3	κ	κ	NOUN
ejpam-5935	96	4	+	+	X
ejpam-5935	97	1	β	β	X
ejpam-5935	97	2	−	−	PROPN
ejpam-5935	97	3	α	α	PROPN
ejpam-5935	97	4	ω	ω	PROPN
ejpam-5935	98	1	−	−	PROPN
ejpam-5935	99	1	κ	κ	PROPN
ejpam-5935	99	2	ρ+	ρ+	NOUN
ejpam-5935	99	3	1	1	NUM
ejpam-5935	99	4	γ(q	γ(q	NOUN
ejpam-5935	99	5	)	)	PUNCT
ejpam-5935	99	6	∫	∫	PROPN
ejpam-5935	100	1	ρ	ρ	PROPN
ejpam-5935	100	2	0	0	PROPN
ejpam-5935	100	3	(	(	PUNCT
ejpam-5935	100	4	ρ−ϖ)q−1ξ(ϖ	ρ−ϖ)q−1ξ(ϖ	NOUN
ejpam-5935	100	5	,	,	PUNCT
ejpam-5935	100	6	ξ(ϖ	ξ(ϖ	PROPN
ejpam-5935	100	7	)	)	PUNCT
ejpam-5935	100	8	)	)	PUNCT
ejpam-5935	101	1	dϖ	dϖ	ADP
ejpam-5935	101	2	s.	s.	PROPN
ejpam-5935	101	3	f.	f.	PROPN
ejpam-5935	101	4	aljurbua	aljurbua	PROPN
ejpam-5935	101	5	et	et	PROPN
ejpam-5935	101	6	al	al	PROPN
ejpam-5935	101	7	.	.	PUNCT
ejpam-5935	101	8	/	/	SYM
ejpam-5935	101	9	eur	eur	PROPN
ejpam-5935	101	10	.	.	PUNCT
ejpam-5935	102	1	j.	j.	PROPN
ejpam-5935	102	2	pure	pure	PROPN
ejpam-5935	102	3	appl	appl	PROPN
ejpam-5935	102	4	.	.	PROPN
ejpam-5935	102	5	math	math	PROPN
ejpam-5935	102	6	,	,	PUNCT
ejpam-5935	102	7	18	18	NUM
ejpam-5935	102	8	(	(	PUNCT
ejpam-5935	102	9	2	2	NUM
ejpam-5935	102	10	)	)	PUNCT
ejpam-5935	102	11	(	(	PUNCT
ejpam-5935	102	12	2025	2025	NUM
ejpam-5935	102	13	)	)	PUNCT
ejpam-5935	102	14	,	,	PUNCT
ejpam-5935	102	15	5935	5935	NUM
ejpam-5935	102	16	5	5	NUM
ejpam-5935	102	17	of	of	ADP
ejpam-5935	102	18	10	10	NUM
ejpam-5935	102	19	−	−	NOUN
ejpam-5935	102	20	ρ−	ρ−	NOUN
ejpam-5935	102	21	κ	κ	VERB
ejpam-5935	102	22	γ(q)(ω	γ(q)(ω	NUM
ejpam-5935	102	23	−	−	PROPN
ejpam-5935	102	24	κ	κ	NOUN
ejpam-5935	102	25	)	)	PUNCT
ejpam-5935	102	26	[	[	PUNCT
ejpam-5935	102	27	∫	∫	PROPN
ejpam-5935	102	28	ω	ω	NUM
ejpam-5935	102	29	0	0	NUM
ejpam-5935	102	30	(	(	PUNCT
ejpam-5935	102	31	ω	ω	PROPN
ejpam-5935	102	32	−ϖ)q−1ξ(ϖ	−ϖ)q−1ξ(ϖ	PROPN
ejpam-5935	102	33	,	,	PUNCT
ejpam-5935	102	34	ξ(ϖ	ξ(ϖ	PROPN
ejpam-5935	102	35	)	)	PUNCT
ejpam-5935	102	36	)	)	PUNCT
ejpam-5935	103	1	dϖ	dϖ	ADP
ejpam-5935	103	2	]	]	PUNCT
ejpam-5935	104	1	+	+	CCONJ
ejpam-5935	104	2	ρ−	ρ−	PROPN
ejpam-5935	104	3	ω	ω	NUM
ejpam-5935	104	4	γ(q)(ω	γ(q)(ω	NUM
ejpam-5935	104	5	−	−	PROPN
ejpam-5935	104	6	κ	κ	NOUN
ejpam-5935	104	7	)	)	PUNCT
ejpam-5935	104	8	[	[	PUNCT
ejpam-5935	104	9	∫	∫	PROPN
ejpam-5935	104	10	κ	κ	PROPN
ejpam-5935	104	11	0	0	PROPN
ejpam-5935	104	12	(	(	PUNCT
ejpam-5935	104	13	κ−ϖ)q−1ξ(ϖ	κ−ϖ)q−1ξ(ϖ	PROPN
ejpam-5935	104	14	,	,	PUNCT
ejpam-5935	104	15	ξ(ϖ	ξ(ϖ	PROPN
ejpam-5935	104	16	)	)	PUNCT
ejpam-5935	104	17	)	)	PUNCT
ejpam-5935	104	18	dϖ	dϖ	ADP
ejpam-5935	104	19	]	]	PUNCT
ejpam-5935	104	20	.	.	PUNCT
ejpam-5935	105	1	(	(	PUNCT
ejpam-5935	105	2	4	4	X
ejpam-5935	105	3	)	)	PUNCT
ejpam-5935	105	4	lemma	lemma	AUX
ejpam-5935	105	5	3	3	X
ejpam-5935	105	6	.	.	PUNCT
ejpam-5935	105	7	assume	assume	VERB
ejpam-5935	105	8	ξ	ξ	PROPN
ejpam-5935	105	9	is	be	AUX
ejpam-5935	105	10	continuous	continuous	ADJ
ejpam-5935	105	11	function	function	NOUN
ejpam-5935	105	12	then	then	ADV
ejpam-5935	105	13	l	l	PROPN
ejpam-5935	105	14	is	be	AUX
ejpam-5935	105	15	a	a	DET
ejpam-5935	105	16	completely	completely	ADV
ejpam-5935	105	17	compact	compact	ADJ
ejpam-5935	105	18	operator	operator	NOUN
ejpam-5935	105	19	.	.	PUNCT
ejpam-5935	106	1	proof	proof	NOUN
ejpam-5935	106	2	.	.	PUNCT
ejpam-5935	107	1	define	define	VERB
ejpam-5935	107	2	the	the	DET
ejpam-5935	107	3	operator	operator	NOUN
ejpam-5935	107	4	l	l	NOUN
ejpam-5935	107	5	as	as	ADP
ejpam-5935	107	6	in	in	ADP
ejpam-5935	107	7	(	(	PUNCT
ejpam-5935	107	8	4	4	NUM
ejpam-5935	107	9	):	):	PUNCT
ejpam-5935	107	10	since	since	SCONJ
ejpam-5935	107	11	ξ	ξ	PROPN
ejpam-5935	107	12	is	be	AUX
ejpam-5935	107	13	continuous	continuous	ADJ
ejpam-5935	107	14	and	and	CCONJ
ejpam-5935	107	15	l	l	NOUN
ejpam-5935	107	16	is	be	AUX
ejpam-5935	107	17	continuous	continuous	ADJ
ejpam-5935	107	18	.	.	PUNCT
ejpam-5935	108	1	assume	assume	VERB
ejpam-5935	108	2	m=	m=	NUM
ejpam-5935	108	3	maxρ∈[0,ω	maxρ∈[0,ω	X
ejpam-5935	108	4	]	]	X
ejpam-5935	108	5	|ξ(ρ	|ξ(ρ	PROPN
ejpam-5935	108	6	,	,	PUNCT
ejpam-5935	108	7	ξ(ρ))|	ξ(ρ))|	PROPN
ejpam-5935	108	8	.	.	PUNCT
ejpam-5935	109	1	then	then	ADV
ejpam-5935	109	2	,	,	PUNCT
ejpam-5935	109	3	for	for	ADP
ejpam-5935	109	4	ξ	ξ	PROPN
ejpam-5935	109	5	∈	∈	PROPN
ejpam-5935	109	6	b	b	X
ejpam-5935	109	7	=	=	SYM
ejpam-5935	109	8	{	{	PUNCT
ejpam-5935	109	9	ξ	ξ	PROPN
ejpam-5935	109	10	∈	∈	PROPN
ejpam-5935	109	11	c([0	c([0	NOUN
ejpam-5935	109	12	,	,	PUNCT
ejpam-5935	109	13	ω	ω	NOUN
ejpam-5935	109	14	]	]	PUNCT
ejpam-5935	109	15	)	)	PUNCT
ejpam-5935	109	16	;	;	PUNCT
ejpam-5935	109	17	||ξ||	||ξ||	VERB
ejpam-5935	109	18	<	<	X
ejpam-5935	109	19	m	m	PRON
ejpam-5935	109	20	}	}	PUNCT
ejpam-5935	109	21	we	we	PRON
ejpam-5935	109	22	have	have	VERB
ejpam-5935	109	23	,	,	PUNCT
ejpam-5935	109	24	|(lξ)(ρ)|	|(lξ)(ρ)|	PROPN
ejpam-5935	109	25	≤	≤	PUNCT
ejpam-5935	109	26	∣∣∣∣αω	∣∣∣∣αω	VERB
ejpam-5935	109	27	−	−	PROPN
ejpam-5935	110	1	βκ	βκ	INTJ
ejpam-5935	111	1	ω	ω	NUM
ejpam-5935	111	2	−	−	NOUN
ejpam-5935	111	3	κ	κ	NOUN
ejpam-5935	111	4	+	+	X
ejpam-5935	112	1	β	β	X
ejpam-5935	112	2	−	−	PROPN
ejpam-5935	112	3	α	α	PROPN
ejpam-5935	112	4	ω	ω	PROPN
ejpam-5935	112	5	−	−	PROPN
ejpam-5935	112	6	κ	κ	PROPN
ejpam-5935	112	7	ρ	ρ	PROPN
ejpam-5935	112	8	∣∣∣∣+∣∣∣∣	∣∣∣∣+∣∣∣∣	PROPN
ejpam-5935	112	9	mγ(q	mγ(q	NOUN
ejpam-5935	112	10	)	)	PUNCT
ejpam-5935	112	11	∫	∫	PROPN
ejpam-5935	113	1	ρ	ρ	PROPN
ejpam-5935	113	2	0	0	PUNCT
ejpam-5935	114	1	(	(	PUNCT
ejpam-5935	114	2	ρ−ϖ)q−1	ρ−ϖ)q−1	ADP
ejpam-5935	114	3	dϖ	dϖ	ADP
ejpam-5935	114	4	∣∣∣∣+∣∣∣∣	∣∣∣∣+∣∣∣∣	PROPN
ejpam-5935	114	5	m(ρ−	m(ρ−	PROPN
ejpam-5935	114	6	κ	κ	NOUN
ejpam-5935	114	7	)	)	PUNCT
ejpam-5935	114	8	γ(q)(ω	γ(q)(ω	CCONJ
ejpam-5935	114	9	−	−	PROPN
ejpam-5935	114	10	κ	κ	NOUN
ejpam-5935	114	11	)	)	PUNCT
ejpam-5935	114	12	∫	∫	PROPN
ejpam-5935	115	1	ω	ω	NUM
ejpam-5935	115	2	0	0	NUM
ejpam-5935	116	1	(	(	PUNCT
ejpam-5935	116	2	ω−ϖ)q−1	ω−ϖ)q−1	NUM
ejpam-5935	116	3	dϖ	dϖ	ADP
ejpam-5935	116	4	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5935	116	5	+	+	CCONJ
ejpam-5935	116	6	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5935	116	7	m(ρ−	m(ρ−	PROPN
ejpam-5935	116	8	ω	ω	NOUN
ejpam-5935	116	9	)	)	PUNCT
ejpam-5935	116	10	γ(q)(ω	γ(q)(ω	CCONJ
ejpam-5935	116	11	−	−	PROPN
ejpam-5935	116	12	κ	κ	NOUN
ejpam-5935	116	13	)	)	PUNCT
ejpam-5935	116	14	∫	∫	PROPN
ejpam-5935	116	15	κ	κ	PROPN
ejpam-5935	116	16	0	0	PUNCT
ejpam-5935	116	17	(	(	PUNCT
ejpam-5935	116	18	κ−ϖ)q−1	κ−ϖ)q−1	PRON
ejpam-5935	116	19	dϖ	dϖ	ADP
ejpam-5935	116	20	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5935	116	21	≤	≤	PUNCT
ejpam-5935	116	22	∣∣∣∣αω	∣∣∣∣αω	PROPN
ejpam-5935	116	23	−	−	PROPN
ejpam-5935	116	24	βκ+	βκ+	NOUN
ejpam-5935	116	25	(	(	PUNCT
ejpam-5935	116	26	β	β	X
ejpam-5935	116	27	−	−	NOUN
ejpam-5935	116	28	α)ρ	α)ρ	PROPN
ejpam-5935	117	1	ω	ω	NUM
ejpam-5935	117	2	−	−	NOUN
ejpam-5935	117	3	κ	κ	PROPN
ejpam-5935	117	4	∣∣∣∣+∣∣∣∣	∣∣∣∣+∣∣∣∣	PROPN
ejpam-5935	117	5	mρq	mρq	ADJ
ejpam-5935	117	6	γ(q	γ(q	PROPN
ejpam-5935	117	7	+	+	CCONJ
ejpam-5935	117	8	1	1	NUM
ejpam-5935	117	9	)	)	PUNCT
ejpam-5935	117	10	∣∣∣∣+∣∣∣∣	∣∣∣∣+∣∣∣∣	NOUN
ejpam-5935	117	11	m(ρ−	m(ρ−	PROPN
ejpam-5935	117	12	κ)ωq	κ)ωq	PROPN
ejpam-5935	117	13	γ(q	γ(q	PROPN
ejpam-5935	118	1	+	+	NOUN
ejpam-5935	118	2	1)(ω	1)(ω	NUM
ejpam-5935	118	3	−	−	NOUN
ejpam-5935	118	4	κ	κ	NOUN
ejpam-5935	118	5	)	)	PUNCT
ejpam-5935	118	6	∣∣∣∣+∣∣∣∣	∣∣∣∣+∣∣∣∣	NOUN
ejpam-5935	118	7	m(ρ−	m(ρ−	PROPN
ejpam-5935	118	8	ω)κq	ω)κq	PROPN
ejpam-5935	118	9	γ(q	γ(q	PROPN
ejpam-5935	118	10	+	+	NOUN
ejpam-5935	118	11	1)(ω	1)(ω	NUM
ejpam-5935	118	12	−	−	NOUN
ejpam-5935	118	13	κ	κ	NOUN
ejpam-5935	118	14	)	)	PUNCT
ejpam-5935	118	15	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5935	118	16	≤	≤	NOUN
ejpam-5935	118	17	β+	β+	PUNCT
ejpam-5935	118	18	2mωq	2mωq	PROPN
ejpam-5935	118	19	γ(q	γ(q	NOUN
ejpam-5935	118	20	+	+	CCONJ
ejpam-5935	118	21	1	1	X
ejpam-5935	118	22	)	)	PUNCT
ejpam-5935	118	23	=	=	NOUN
ejpam-5935	118	24	m1	m1	PROPN
ejpam-5935	118	25	therefore	therefore	ADV
ejpam-5935	118	26	,	,	PUNCT
ejpam-5935	118	27	l	l	NOUN
ejpam-5935	118	28	is	be	AUX
ejpam-5935	118	29	bounded	bound	VERB
ejpam-5935	118	30	.	.	PUNCT
ejpam-5935	119	1	now	now	ADV
ejpam-5935	119	2	proving	prove	VERB
ejpam-5935	119	3	equicontinuity	equicontinuity	NOUN
ejpam-5935	119	4	of	of	ADP
ejpam-5935	119	5	l(m	l(m	PROPN
ejpam-5935	119	6	)	)	PUNCT
ejpam-5935	119	7	for	for	ADP
ejpam-5935	119	8	all	all	DET
ejpam-5935	119	9	ξ	ξ	PROPN
ejpam-5935	119	10	∈	∈	PROPN
ejpam-5935	119	11	b	b	PROPN
ejpam-5935	119	12	,	,	PUNCT
ejpam-5935	119	13	∀ϵ	∀ϵ	NOUN
ejpam-5935	119	14	>	>	X
ejpam-5935	119	15	0	0	PROPN
ejpam-5935	119	16	,	,	PUNCT
ejpam-5935	119	17	ρ1	ρ1	NOUN
ejpam-5935	119	18	<	<	X
ejpam-5935	119	19	ρ2	ρ2	NOUN
ejpam-5935	119	20	∈	∈	PROPN
ejpam-5935	120	1	[	[	X
ejpam-5935	120	2	0	0	NUM
ejpam-5935	120	3	,	,	PUNCT
ejpam-5935	120	4	ω	ω	NOUN
ejpam-5935	120	5	]	]	X
ejpam-5935	120	6	,	,	PUNCT
ejpam-5935	120	7	choose	choose	VERB
ejpam-5935	120	8	ρ2−ρ1	ρ2−ρ1	NUM
ejpam-5935	120	9	<	<	X
ejpam-5935	120	10	ν	ν	X
ejpam-5935	120	11	<	<	X
ejpam-5935	120	12	{	{	PUNCT
ejpam-5935	120	13	ϵ(ω−κ	ϵ(ω−κ	PROPN
ejpam-5935	120	14	)	)	PUNCT
ejpam-5935	120	15	3(β−α	3(β−α	NOUN
ejpam-5935	120	16	)	)	PUNCT
ejpam-5935	120	17	,	,	PUNCT
ejpam-5935	120	18	ϵγ(q	ϵγ(q	NOUN
ejpam-5935	120	19	)	)	PUNCT
ejpam-5935	120	20	3m(ωq+κq	3m(ωq+κq	NUM
ejpam-5935	120	21	)	)	PUNCT
ejpam-5935	120	22	,	,	PUNCT
ejpam-5935	120	23	(	(	PUNCT
ejpam-5935	120	24	ϵγ(q+1	ϵγ(q+1	X
ejpam-5935	120	25	)	)	PUNCT
ejpam-5935	120	26	6	6	NUM
ejpam-5935	120	27	m	m	NOUN
ejpam-5935	120	28	)	)	PUNCT
ejpam-5935	121	1	1	1	NUM
ejpam-5935	121	2	q−1	q−1	PROPN
ejpam-5935	121	3	}	}	PUNCT
ejpam-5935	121	4	.	.	PUNCT
ejpam-5935	122	1	then	then	ADV
ejpam-5935	122	2	,	,	PUNCT
ejpam-5935	122	3	we	we	PRON
ejpam-5935	122	4	have	have	VERB
ejpam-5935	122	5	|lξ(ρ2)−	|lξ(ρ2)−	NOUN
ejpam-5935	122	6	lξ(ρ1)|	lξ(ρ1)|	NOUN
ejpam-5935	123	1	=	=	PUNCT
ejpam-5935	124	1	∣∣∣∣β	∣∣∣∣β	PROPN
ejpam-5935	125	1	−	−	PROPN
ejpam-5935	126	1	α	α	PROPN
ejpam-5935	126	2	ω	ω	PROPN
ejpam-5935	126	3	−	−	PROPN
ejpam-5935	126	4	κ	κ	PROPN
ejpam-5935	126	5	(	(	PUNCT
ejpam-5935	126	6	ρ2	ρ2	NOUN
ejpam-5935	126	7	−	−	PROPN
ejpam-5935	126	8	ρ1	ρ1	NOUN
ejpam-5935	126	9	)	)	PUNCT
ejpam-5935	127	1	+	+	CCONJ
ejpam-5935	127	2	iq−1i1ξ(ρ2	iq−1i1ξ(ρ2	ADJ
ejpam-5935	127	3	,	,	PUNCT
ejpam-5935	127	4	ξ(ρ2))−	ξ(ρ2))−	NOUN
ejpam-5935	127	5	iq−1i1ξ(ρ1	iq−1i1ξ(ρ1	ADJ
ejpam-5935	127	6	,	,	PUNCT
ejpam-5935	127	7	ξ(ρ1	ξ(ρ1	NOUN
ejpam-5935	127	8	)	)	PUNCT
ejpam-5935	127	9	)	)	PUNCT
ejpam-5935	128	1	−	−	PROPN
ejpam-5935	128	2	ρ2	ρ2	NOUN
ejpam-5935	128	3	−	−	PROPN
ejpam-5935	128	4	ρ1	ρ1	NOUN
ejpam-5935	128	5	γ(q)(ω	γ(q)(ω	CCONJ
ejpam-5935	128	6	−	−	PROPN
ejpam-5935	128	7	κ	κ	NOUN
ejpam-5935	128	8	)	)	PUNCT
ejpam-5935	128	9	[	[	PUNCT
ejpam-5935	128	10	∫	∫	PROPN
ejpam-5935	128	11	ω	ω	NUM
ejpam-5935	128	12	0	0	NUM
ejpam-5935	128	13	(	(	PUNCT
ejpam-5935	128	14	ω−ϖ)q−1ξ(ϖ	ω−ϖ)q−1ξ(ϖ	PROPN
ejpam-5935	128	15	,	,	PUNCT
ejpam-5935	128	16	ξ(ϖ	ξ(ϖ	PROPN
ejpam-5935	128	17	)	)	PUNCT
ejpam-5935	128	18	)	)	PUNCT
ejpam-5935	129	1	dϖ	dϖ	ADP
ejpam-5935	129	2	]	]	PUNCT
ejpam-5935	130	1	+	+	CCONJ
ejpam-5935	130	2	ρ2	ρ2	NOUN
ejpam-5935	130	3	−	−	PROPN
ejpam-5935	130	4	ρ1	ρ1	NOUN
ejpam-5935	130	5	γ(q)(ω	γ(q)(ω	CCONJ
ejpam-5935	130	6	−	−	PROPN
ejpam-5935	130	7	κ	κ	NOUN
ejpam-5935	130	8	)	)	PUNCT
ejpam-5935	130	9	[	[	PUNCT
ejpam-5935	130	10	∫	∫	PROPN
ejpam-5935	130	11	κ	κ	PROPN
ejpam-5935	130	12	0	0	PROPN
ejpam-5935	130	13	(	(	PUNCT
ejpam-5935	130	14	κ−ϖ)q−1ξ(ϖ	κ−ϖ)q−1ξ(ϖ	PROPN
ejpam-5935	130	15	,	,	PUNCT
ejpam-5935	130	16	ξ(ϖ	ξ(ϖ	PROPN
ejpam-5935	130	17	)	)	PUNCT
ejpam-5935	130	18	)	)	PUNCT
ejpam-5935	130	19	dϖ	dϖ	ADP
ejpam-5935	130	20	]	]	PUNCT
ejpam-5935	130	21	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5935	130	22	≤	≤	PUNCT
ejpam-5935	130	23	∣∣∣∣β	∣∣∣∣β	NOUN
ejpam-5935	131	1	−	−	PROPN
ejpam-5935	132	1	α	α	PROPN
ejpam-5935	132	2	ω	ω	PROPN
ejpam-5935	132	3	−	−	PROPN
ejpam-5935	133	1	κ	κ	PROPN
ejpam-5935	133	2	∣∣∣∣(ρ2	∣∣∣∣(ρ2	NOUN
ejpam-5935	133	3	−	−	NUM
ejpam-5935	133	4	ρ1	ρ1	NOUN
ejpam-5935	133	5	)	)	PUNCT
ejpam-5935	134	1	+	+	NUM
ejpam-5935	134	2	m	m	PROPN
ejpam-5935	134	3	γ(q	γ(q	NOUN
ejpam-5935	134	4	−	−	PROPN
ejpam-5935	134	5	1	1	NUM
ejpam-5935	134	6	)	)	PUNCT
ejpam-5935	134	7	∫	∫	PROPN
ejpam-5935	134	8	ρ1	ρ1	NOUN
ejpam-5935	134	9	0	0	NUM
ejpam-5935	135	1	(	(	PUNCT
ejpam-5935	135	2	(	(	PUNCT
ejpam-5935	135	3	ρ1	ρ1	NOUN
ejpam-5935	135	4	−ϖ)q−2	−ϖ)q−2	NOUN
ejpam-5935	135	5	−	−	PROPN
ejpam-5935	135	6	(	(	PUNCT
ejpam-5935	135	7	ρ2	ρ2	NOUN
ejpam-5935	135	8	−ϖ)q−2)dϖ	−ϖ)q−2)dϖ	NOUN
ejpam-5935	135	9	+	+	CCONJ
ejpam-5935	135	10	m	m	PROPN
ejpam-5935	135	11	γ(q	γ(q	NOUN
ejpam-5935	135	12	−	−	PROPN
ejpam-5935	135	13	1	1	NUM
ejpam-5935	135	14	)	)	PUNCT
ejpam-5935	135	15	∫	∫	PROPN
ejpam-5935	135	16	ρ2	ρ2	PROPN
ejpam-5935	135	17	ρ1	ρ1	NOUN
ejpam-5935	135	18	(	(	PUNCT
ejpam-5935	135	19	ρ2−ϖ)q−2dϖ+	ρ2−ϖ)q−2dϖ+	ADJ
ejpam-5935	135	20	m(ρ2	m(ρ2	NOUN
ejpam-5935	135	21	−	−	PROPN
ejpam-5935	135	22	ρ1	ρ1	NOUN
ejpam-5935	135	23	)	)	PUNCT
ejpam-5935	135	24	γ(q)(ω	γ(q)(ω	CCONJ
ejpam-5935	135	25	−	−	PROPN
ejpam-5935	135	26	κ	κ	NOUN
ejpam-5935	135	27	)	)	PUNCT
ejpam-5935	135	28	[	[	PUNCT
ejpam-5935	135	29	∫	∫	PROPN
ejpam-5935	135	30	ω	ω	NUM
ejpam-5935	135	31	0	0	NUM
ejpam-5935	136	1	(	(	PUNCT
ejpam-5935	136	2	ω−ϖ)q−1	ω−ϖ)q−1	PRON
ejpam-5935	136	3	dϖ	dϖ	X
ejpam-5935	136	4	]	]	PUNCT
ejpam-5935	136	5	+	+	PUNCT
ejpam-5935	136	6	m(ρ2	m(ρ2	NOUN
ejpam-5935	136	7	−	−	PROPN
ejpam-5935	136	8	ρ1	ρ1	NOUN
ejpam-5935	136	9	)	)	PUNCT
ejpam-5935	136	10	γ(q)(ω	γ(q)(ω	CCONJ
ejpam-5935	136	11	−	−	PROPN
ejpam-5935	136	12	κ	κ	NOUN
ejpam-5935	136	13	)	)	PUNCT
ejpam-5935	136	14	[	[	PUNCT
ejpam-5935	136	15	∫	∫	PROPN
ejpam-5935	136	16	κ	κ	X
ejpam-5935	136	17	0	0	PUNCT
ejpam-5935	136	18	(	(	PUNCT
ejpam-5935	136	19	κ−ϖ)q−1	κ−ϖ)q−1	SYM
ejpam-5935	136	20	dϖ	dϖ	ADP
ejpam-5935	136	21	]	]	PUNCT
ejpam-5935	136	22	≤	≤	NUM
ejpam-5935	136	23	β	β	X
ejpam-5935	136	24	−	−	PROPN
ejpam-5935	136	25	α	α	PROPN
ejpam-5935	136	26	ω	ω	PROPN
ejpam-5935	136	27	−	−	PROPN
ejpam-5935	136	28	κ	κ	PROPN
ejpam-5935	136	29	(	(	PUNCT
ejpam-5935	136	30	ρ2	ρ2	NOUN
ejpam-5935	136	31	−	−	PROPN
ejpam-5935	136	32	ρ1	ρ1	NOUN
ejpam-5935	136	33	)	)	PUNCT
ejpam-5935	137	1	+	+	NUM
ejpam-5935	137	2	m	m	NUM
ejpam-5935	137	3	γ(q	γ(q	NOUN
ejpam-5935	137	4	)	)	PUNCT
ejpam-5935	137	5	(	(	PUNCT
ejpam-5935	137	6	ρq−1	ρq−1	NOUN
ejpam-5935	137	7	2	2	NUM
ejpam-5935	137	8	+	+	CCONJ
ejpam-5935	137	9	2(ρ2	2(ρ2	NUM
ejpam-5935	137	10	−	−	NOUN
ejpam-5935	137	11	ρ1	ρ1	NOUN
ejpam-5935	137	12	)	)	PUNCT
ejpam-5935	138	1	q−1	q−1	PROPN
ejpam-5935	139	1	−	−	PROPN
ejpam-5935	139	2	ρq−1	ρq−1	NOUN
ejpam-5935	139	3	2	2	NUM
ejpam-5935	139	4	)	)	PUNCT
ejpam-5935	139	5	+	+	NUM
ejpam-5935	139	6	m(ωq	m(ωq	PROPN
ejpam-5935	139	7	+	+	CCONJ
ejpam-5935	139	8	κq	κq	NOUN
ejpam-5935	139	9	)	)	PUNCT
ejpam-5935	139	10	γ(q	γ(q	PROPN
ejpam-5935	140	1	+	+	CCONJ
ejpam-5935	140	2	1	1	NUM
ejpam-5935	140	3	)	)	PUNCT
ejpam-5935	140	4	(	(	PUNCT
ejpam-5935	140	5	ρ2	ρ2	NOUN
ejpam-5935	140	6	−	−	PROPN
ejpam-5935	140	7	ρ1	ρ1	NOUN
ejpam-5935	140	8	)	)	PUNCT
ejpam-5935	140	9	≤	≤	NOUN
ejpam-5935	141	1	β	β	X
ejpam-5935	141	2	−	−	PROPN
ejpam-5935	141	3	α	α	PROPN
ejpam-5935	141	4	ω	ω	PROPN
ejpam-5935	141	5	−	−	PROPN
ejpam-5935	141	6	κ	κ	NOUN
ejpam-5935	141	7	ν	ν	NOUN
ejpam-5935	141	8	+	+	CCONJ
ejpam-5935	141	9	2	2	NUM
ejpam-5935	141	10	m	m	NOUN
ejpam-5935	141	11	γ(q	γ(q	NOUN
ejpam-5935	141	12	)	)	PUNCT
ejpam-5935	142	1	νq−1	νq−1	NOUN
ejpam-5935	142	2	+	+	NUM
ejpam-5935	142	3	m(ωq	m(ωq	PROPN
ejpam-5935	142	4	+	+	CCONJ
ejpam-5935	142	5	κq	κq	NOUN
ejpam-5935	142	6	)	)	PUNCT
ejpam-5935	142	7	γ(q	γ(q	PROPN
ejpam-5935	143	1	+	+	CCONJ
ejpam-5935	143	2	1	1	X
ejpam-5935	143	3	)	)	PUNCT
ejpam-5935	143	4	ν	ν	X
ejpam-5935	143	5	<	<	X
ejpam-5935	143	6	ϵ	ϵ	X
ejpam-5935	143	7	3	3	NUM
ejpam-5935	143	8	+	+	CCONJ
ejpam-5935	143	9	ϵ	ϵ	SYM
ejpam-5935	143	10	3	3	NUM
ejpam-5935	144	1	+	+	CCONJ
ejpam-5935	144	2	ϵ	ϵ	SYM
ejpam-5935	144	3	3	3	X
ejpam-5935	144	4	=	=	SYM
ejpam-5935	144	5	ϵ.	ϵ.	NOUN
ejpam-5935	144	6	therefore	therefore	ADV
ejpam-5935	144	7	,	,	PUNCT
ejpam-5935	144	8	we	we	PRON
ejpam-5935	144	9	proved	prove	VERB
ejpam-5935	144	10	that	that	SCONJ
ejpam-5935	144	11	l	l	NOUN
ejpam-5935	144	12	is	be	AUX
ejpam-5935	144	13	equicontinuous	equicontinuous	ADJ
ejpam-5935	144	14	.	.	PUNCT
ejpam-5935	145	1	hence	hence	ADV
ejpam-5935	145	2	,	,	PUNCT
ejpam-5935	145	3	the	the	DET
ejpam-5935	145	4	operator	operator	NOUN
ejpam-5935	145	5	l	l	NOUN
ejpam-5935	145	6	is	be	AUX
ejpam-5935	145	7	completely	completely	ADV
ejpam-5935	145	8	continuous	continuous	ADJ
ejpam-5935	145	9	by	by	ADP
ejpam-5935	145	10	arzela	arzela	PROPN
ejpam-5935	145	11	-	-	PUNCT
ejpam-5935	145	12	ascoli	ascoli	PROPN
ejpam-5935	145	13	theorem	theorem	PROPN
ejpam-5935	145	14	[	[	X
ejpam-5935	145	15	22	22	NUM
ejpam-5935	145	16	]	]	PUNCT
ejpam-5935	145	17	.	.	PUNCT
ejpam-5935	146	1	s.	s.	PROPN
ejpam-5935	146	2	f.	f.	PROPN
ejpam-5935	146	3	aljurbua	aljurbua	PROPN
ejpam-5935	146	4	et	et	PROPN
ejpam-5935	146	5	al	al	PROPN
ejpam-5935	146	6	.	.	PUNCT
ejpam-5935	146	7	/	/	SYM
ejpam-5935	146	8	eur	eur	PROPN
ejpam-5935	146	9	.	.	PUNCT
ejpam-5935	147	1	j.	j.	PROPN
ejpam-5935	147	2	pure	pure	PROPN
ejpam-5935	147	3	appl	appl	PROPN
ejpam-5935	147	4	.	.	PROPN
ejpam-5935	147	5	math	math	PROPN
ejpam-5935	147	6	,	,	PUNCT
ejpam-5935	147	7	18	18	NUM
ejpam-5935	147	8	(	(	PUNCT
ejpam-5935	147	9	2	2	NUM
ejpam-5935	147	10	)	)	PUNCT
ejpam-5935	147	11	(	(	PUNCT
ejpam-5935	147	12	2025	2025	NUM
ejpam-5935	147	13	)	)	PUNCT
ejpam-5935	147	14	,	,	PUNCT
ejpam-5935	147	15	5935	5935	NUM
ejpam-5935	147	16	6	6	NUM
ejpam-5935	147	17	of	of	ADP
ejpam-5935	147	18	10	10	NUM
ejpam-5935	147	19	theorem	theorem	NOUN
ejpam-5935	147	20	3	3	X
ejpam-5935	147	21	.	.	PUNCT
ejpam-5935	147	22	suppose	suppose	VERB
ejpam-5935	148	1	ξ	ξ	X
ejpam-5935	148	2	:	:	PUNCT
ejpam-5935	148	3	[	[	X
ejpam-5935	148	4	0	0	NUM
ejpam-5935	148	5	,	,	PUNCT
ejpam-5935	148	6	ω]×	ω]×	ADV
ejpam-5935	148	7	r	r	NOUN
ejpam-5935	148	8	−→	−→	NOUN
ejpam-5935	148	9	r	r	NOUN
ejpam-5935	148	10	is	be	AUX
ejpam-5935	148	11	a	a	DET
ejpam-5935	148	12	continuous	continuous	ADJ
ejpam-5935	148	13	function	function	NOUN
ejpam-5935	148	14	satisfying∣∣ξ(ρ	satisfying∣∣ξ(ρ	PROPN
ejpam-5935	148	15	,	,	PUNCT
ejpam-5935	148	16	ξ1	ξ1	NOUN
ejpam-5935	148	17	)	)	PUNCT
ejpam-5935	148	18	−	−	PROPN
ejpam-5935	148	19	ξ(ρ	ξ(ρ	PROPN
ejpam-5935	148	20	,	,	PUNCT
ejpam-5935	148	21	ξ2	ξ2	NOUN
ejpam-5935	148	22	)	)	PUNCT
ejpam-5935	148	23	∣∣	∣∣	X
ejpam-5935	148	24	≤	≤	NUM
ejpam-5935	148	25	l	l	NOUN
ejpam-5935	148	26	∣∣ξ1	∣∣ξ1	NOUN
ejpam-5935	148	27	−	−	PROPN
ejpam-5935	148	28	ξ2	ξ2	PROPN
ejpam-5935	148	29	∣∣	∣∣	AUX
ejpam-5935	148	30	,	,	PUNCT
ejpam-5935	148	31	for	for	ADP
ejpam-5935	148	32	all	all	DET
ejpam-5935	148	33	ρ	ρ	NOUN
ejpam-5935	148	34	∈	∈	PROPN
ejpam-5935	149	1	[	[	X
ejpam-5935	149	2	0	0	NUM
ejpam-5935	149	3	,	,	PUNCT
ejpam-5935	149	4	ω	ω	NOUN
ejpam-5935	149	5	]	]	X
ejpam-5935	149	6	,	,	PUNCT
ejpam-5935	149	7	l	l	NOUN
ejpam-5935	149	8	>	>	X
ejpam-5935	149	9	0	0	NUM
ejpam-5935	149	10	,	,	PUNCT
ejpam-5935	149	11	and	and	CCONJ
ejpam-5935	149	12	∣∣ξ(ρ	∣∣ξ(ρ	PROPN
ejpam-5935	149	13	,	,	PUNCT
ejpam-5935	149	14	ξ(ρ))∣∣	ξ(ρ))∣∣	PROPN
ejpam-5935	149	15	≤	≤	NOUN
ejpam-5935	149	16	∣∣ψ(ρ)∣∣	∣∣ψ(ρ)∣∣	NOUN
ejpam-5935	149	17	,	,	PUNCT
ejpam-5935	149	18	for	for	ADP
ejpam-5935	149	19	all	all	DET
ejpam-5935	149	20	(	(	PUNCT
ejpam-5935	149	21	ρ	ρ	PROPN
ejpam-5935	149	22	,	,	PUNCT
ejpam-5935	149	23	ξ	ξ	NOUN
ejpam-5935	149	24	)	)	PUNCT
ejpam-5935	149	25	∈	∈	PROPN
ejpam-5935	150	1	[	[	X
ejpam-5935	150	2	0	0	NUM
ejpam-5935	150	3	,	,	PUNCT
ejpam-5935	150	4	ω]×	ω]×	ADV
ejpam-5935	150	5	r	r	NOUN
ejpam-5935	150	6	,	,	PUNCT
ejpam-5935	150	7	and	and	CCONJ
ejpam-5935	150	8	ψ	ψ	X
ejpam-5935	150	9	∈	∈	NOUN
ejpam-5935	150	10	l1([0	l1([0	NOUN
ejpam-5935	150	11	,	,	PUNCT
ejpam-5935	150	12	ω],r+	ω],r+	PROPN
ejpam-5935	150	13	)	)	PUNCT
ejpam-5935	150	14	.	.	PUNCT
ejpam-5935	151	1	then	then	ADV
ejpam-5935	151	2	(	(	PUNCT
ejpam-5935	151	3	1	1	X
ejpam-5935	151	4	)	)	PUNCT
ejpam-5935	151	5	has	have	VERB
ejpam-5935	151	6	at	at	ADV
ejpam-5935	151	7	least	least	ADV
ejpam-5935	151	8	one	one	NUM
ejpam-5935	151	9	solution	solution	NOUN
ejpam-5935	151	10	on	on	ADP
ejpam-5935	151	11	[	[	X
ejpam-5935	151	12	0	0	NUM
ejpam-5935	151	13	,	,	PUNCT
ejpam-5935	151	14	ω	ω	NOUN
ejpam-5935	151	15	]	]	X
ejpam-5935	151	16	if	if	SCONJ
ejpam-5935	151	17	lωq	lωq	PROPN
ejpam-5935	151	18	γ(q+1	γ(q+1	PROPN
ejpam-5935	151	19	)	)	PUNCT
ejpam-5935	151	20	<	<	X
ejpam-5935	152	1	1	1	X
ejpam-5935	152	2	.	.	PUNCT
ejpam-5935	152	3	proof	proof	NOUN
ejpam-5935	152	4	.	.	PUNCT
ejpam-5935	153	1	define	define	VERB
ejpam-5935	153	2	sup(ρ	sup(ρ	PROPN
ejpam-5935	153	3	,	,	PUNCT
ejpam-5935	153	4	ξ)∈[0,ω]×br	ξ)∈[0,ω]×br	PROPN
ejpam-5935	153	5	||ξ(ρ	||ξ(ρ	PROPN
ejpam-5935	153	6	,	,	PUNCT
ejpam-5935	153	7	ξ)||	ξ)||	NOUN
ejpam-5935	153	8	=	=	NOUN
ejpam-5935	153	9	ξmax	ξmax	NOUN
ejpam-5935	153	10	<	<	X
ejpam-5935	153	11	∞	∞	PROPN
ejpam-5935	153	12	,	,	PUNCT
ejpam-5935	153	13	and	and	CCONJ
ejpam-5935	153	14	let	let	VERB
ejpam-5935	153	15	the	the	DET
ejpam-5935	153	16	operators	operator	NOUN
ejpam-5935	153	17	l1	l1	PROPN
ejpam-5935	153	18	and	and	CCONJ
ejpam-5935	153	19	l2	l2	NOUN
ejpam-5935	153	20	defined	define	VERB
ejpam-5935	153	21	as	as	SCONJ
ejpam-5935	153	22	follows	follow	VERB
ejpam-5935	153	23	:	:	PUNCT
ejpam-5935	153	24	(	(	PUNCT
ejpam-5935	153	25	l1ξ)(ρ	l1ξ)(ρ	PROPN
ejpam-5935	153	26	)	)	PUNCT
ejpam-5935	153	27	=	=	SYM
ejpam-5935	153	28	1	1	NUM
ejpam-5935	153	29	γ(q	γ(q	PROPN
ejpam-5935	153	30	)	)	PUNCT
ejpam-5935	153	31	∫	∫	PROPN
ejpam-5935	154	1	ρ	ρ	PROPN
ejpam-5935	154	2	0	0	PROPN
ejpam-5935	154	3	(	(	PUNCT
ejpam-5935	154	4	ρ−ϖ)q−1ξ(ϖ	ρ−ϖ)q−1ξ(ϖ	NOUN
ejpam-5935	154	5	,	,	PUNCT
ejpam-5935	154	6	ξ(ϖ))dϖ	ξ(ϖ))dϖ	NOUN
ejpam-5935	155	1	+	+	CCONJ
ejpam-5935	155	2	αω	αω	NUM
ejpam-5935	155	3	−	−	NOUN
ejpam-5935	156	1	βκ	βκ	INTJ
ejpam-5935	157	1	ω	ω	NUM
ejpam-5935	157	2	−	−	NOUN
ejpam-5935	157	3	κ	κ	NOUN
ejpam-5935	157	4	+	+	X
ejpam-5935	158	1	β	β	X
ejpam-5935	158	2	−	−	PROPN
ejpam-5935	158	3	α	α	PROPN
ejpam-5935	158	4	ω	ω	PROPN
ejpam-5935	158	5	−	−	PROPN
ejpam-5935	158	6	κ	κ	PROPN
ejpam-5935	158	7	ρ	ρ	PROPN
ejpam-5935	158	8	,	,	PUNCT
ejpam-5935	158	9	(	(	PUNCT
ejpam-5935	158	10	l2ξ)(ρ	l2ξ)(ρ	PROPN
ejpam-5935	158	11	)	)	PUNCT
ejpam-5935	158	12	=	=	SYM
ejpam-5935	159	1	−	−	PROPN
ejpam-5935	159	2	ρ−	ρ−	NOUN
ejpam-5935	159	3	κ	κ	VERB
ejpam-5935	159	4	γ(q)(ω	γ(q)(ω	NUM
ejpam-5935	159	5	−	−	PROPN
ejpam-5935	159	6	κ	κ	NOUN
ejpam-5935	159	7	)	)	PUNCT
ejpam-5935	159	8	[	[	PUNCT
ejpam-5935	159	9	∫	∫	PROPN
ejpam-5935	159	10	ω	ω	NUM
ejpam-5935	159	11	0	0	NUM
ejpam-5935	159	12	(	(	PUNCT
ejpam-5935	159	13	ω	ω	PROPN
ejpam-5935	159	14	−ϖ)q−1ξ(ϖ	−ϖ)q−1ξ(ϖ	PROPN
ejpam-5935	159	15	,	,	PUNCT
ejpam-5935	159	16	ξ(ϖ	ξ(ϖ	PROPN
ejpam-5935	159	17	)	)	PUNCT
ejpam-5935	159	18	)	)	PUNCT
ejpam-5935	160	1	dϖ	dϖ	ADP
ejpam-5935	160	2	]	]	PUNCT
ejpam-5935	161	1	+	+	CCONJ
ejpam-5935	161	2	ρ−	ρ−	PROPN
ejpam-5935	161	3	ω	ω	NUM
ejpam-5935	161	4	γ(q)(ω	γ(q)(ω	NUM
ejpam-5935	161	5	−	−	PROPN
ejpam-5935	161	6	κ	κ	NOUN
ejpam-5935	161	7	)	)	PUNCT
ejpam-5935	161	8	[	[	PUNCT
ejpam-5935	161	9	∫	∫	PROPN
ejpam-5935	161	10	κ	κ	PROPN
ejpam-5935	161	11	0	0	PROPN
ejpam-5935	161	12	(	(	PUNCT
ejpam-5935	161	13	κ−ϖ)q−1ξ(ϖ	κ−ϖ)q−1ξ(ϖ	PROPN
ejpam-5935	161	14	,	,	PUNCT
ejpam-5935	161	15	ξ(ϖ	ξ(ϖ	PROPN
ejpam-5935	161	16	)	)	PUNCT
ejpam-5935	161	17	)	)	PUNCT
ejpam-5935	161	18	dϖ	dϖ	ADP
ejpam-5935	161	19	]	]	PUNCT
ejpam-5935	161	20	.	.	PUNCT
ejpam-5935	162	1	also	also	ADV
ejpam-5935	162	2	,	,	PUNCT
ejpam-5935	162	3	define	define	VERB
ejpam-5935	162	4	a	a	DET
ejpam-5935	162	5	ball	ball	NOUN
ejpam-5935	162	6	br	br	NOUN
ejpam-5935	162	7	=	=	PUNCT
ejpam-5935	162	8	{	{	PUNCT
ejpam-5935	162	9	ξ	ξ	X
ejpam-5935	162	10	∈	∈	PROPN
ejpam-5935	162	11	c([0	c([0	NOUN
ejpam-5935	162	12	,	,	PUNCT
ejpam-5935	162	13	ω],r	ω],r	NUM
ejpam-5935	162	14	)	)	PUNCT
ejpam-5935	162	15	:	:	PUNCT
ejpam-5935	162	16	||ξ||	||ξ||	VERB
ejpam-5935	162	17	≤	≤	ADJ
ejpam-5935	162	18	r	r	NOUN
ejpam-5935	162	19	}	}	PUNCT
ejpam-5935	162	20	,	,	PUNCT
ejpam-5935	162	21	such	such	ADJ
ejpam-5935	162	22	that	that	SCONJ
ejpam-5935	162	23	r	r	NOUN
ejpam-5935	162	24	>	>	X
ejpam-5935	162	25	{	{	PUNCT
ejpam-5935	162	26	2β	2β	NOUN
ejpam-5935	162	27	,	,	PUNCT
ejpam-5935	162	28	4||ψ||ω	4||ψ||ω	NUM
ejpam-5935	162	29	q	q	PUNCT
ejpam-5935	162	30	γ(q+1	γ(q+1	PROPN
ejpam-5935	162	31	)	)	PUNCT
ejpam-5935	162	32	}	}	PUNCT
ejpam-5935	162	33	then	then	ADV
ejpam-5935	162	34	for	for	ADP
ejpam-5935	162	35	ξ1	ξ1	NOUN
ejpam-5935	162	36	,	,	PUNCT
ejpam-5935	162	37	ξ2	ξ2	NOUN
ejpam-5935	162	38	∈	∈	PROPN
ejpam-5935	162	39	br,∣∣∣∣l1ξ1	br,∣∣∣∣l1ξ1	PROPN
ejpam-5935	162	40	+	+	CCONJ
ejpam-5935	163	1	l2ξ2	l2ξ2	VERB
ejpam-5935	163	2	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5935	163	3	≤	≤	NOUN
ejpam-5935	163	4	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5935	163	5	1	1	NUM
ejpam-5935	163	6	γ(q	γ(q	PROPN
ejpam-5935	163	7	)	)	PUNCT
ejpam-5935	163	8	∫	∫	PROPN
ejpam-5935	164	1	ρ	ρ	PROPN
ejpam-5935	164	2	0	0	PROPN
ejpam-5935	164	3	(	(	PUNCT
ejpam-5935	164	4	ρ−ϖ)q−1ξ(ϖ	ρ−ϖ)q−1ξ(ϖ	NOUN
ejpam-5935	164	5	,	,	PUNCT
ejpam-5935	164	6	ξ1(ϖ))dϖ	ξ1(ϖ))dϖ	NOUN
ejpam-5935	164	7	+	+	CCONJ
ejpam-5935	164	8	αω	αω	NUM
ejpam-5935	164	9	−	−	NOUN
ejpam-5935	164	10	βκ	βκ	INTJ
ejpam-5935	164	11	ω	ω	NUM
ejpam-5935	164	12	−	−	NOUN
ejpam-5935	164	13	κ	κ	NOUN
ejpam-5935	164	14	+	+	X
ejpam-5935	164	15	β	β	X
ejpam-5935	164	16	−	−	PROPN
ejpam-5935	164	17	α	α	PROPN
ejpam-5935	164	18	ω	ω	PROPN
ejpam-5935	164	19	−	−	PROPN
ejpam-5935	164	20	κ	κ	PROPN
ejpam-5935	164	21	ρ	ρ	PROPN
ejpam-5935	164	22	−	−	PROPN
ejpam-5935	164	23	ρ−	ρ−	PROPN
ejpam-5935	164	24	κ	κ	X
ejpam-5935	164	25	γ(q)(ω	γ(q)(ω	NUM
ejpam-5935	164	26	−	−	PROPN
ejpam-5935	164	27	κ	κ	NOUN
ejpam-5935	164	28	)	)	PUNCT
ejpam-5935	164	29	[	[	PUNCT
ejpam-5935	164	30	∫	∫	PROPN
ejpam-5935	164	31	ω	ω	NUM
ejpam-5935	164	32	0	0	NUM
ejpam-5935	164	33	(	(	PUNCT
ejpam-5935	164	34	ω	ω	PROPN
ejpam-5935	164	35	−ϖ)q−1ξ(ϖ	−ϖ)q−1ξ(ϖ	PROPN
ejpam-5935	164	36	,	,	PUNCT
ejpam-5935	164	37	ξ2(ϖ	ξ2(ϖ	NOUN
ejpam-5935	164	38	)	)	PUNCT
ejpam-5935	164	39	)	)	PUNCT
ejpam-5935	165	1	dϖ	dϖ	ADP
ejpam-5935	165	2	]	]	PUNCT
ejpam-5935	166	1	+	+	CCONJ
ejpam-5935	166	2	ρ−	ρ−	PROPN
ejpam-5935	166	3	ω	ω	NUM
ejpam-5935	166	4	γ(q)(ω	γ(q)(ω	NUM
ejpam-5935	166	5	−	−	PROPN
ejpam-5935	166	6	κ	κ	NOUN
ejpam-5935	166	7	)	)	PUNCT
ejpam-5935	166	8	[	[	PUNCT
ejpam-5935	166	9	∫	∫	PROPN
ejpam-5935	166	10	κ	κ	PROPN
ejpam-5935	166	11	0	0	PROPN
ejpam-5935	166	12	(	(	PUNCT
ejpam-5935	166	13	κ−ϖ)q−1ξ(ϖ	κ−ϖ)q−1ξ(ϖ	PROPN
ejpam-5935	166	14	,	,	PUNCT
ejpam-5935	166	15	ξ2(ϖ	ξ2(ϖ	NOUN
ejpam-5935	166	16	)	)	PUNCT
ejpam-5935	166	17	)	)	PUNCT
ejpam-5935	166	18	dϖ	dϖ	ADP
ejpam-5935	166	19	]	]	PUNCT
ejpam-5935	166	20	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5935	166	21	≤	≤	NOUN
ejpam-5935	166	22	||ψ||	||ψ||	ADJ
ejpam-5935	166	23	γ(q	γ(q	NOUN
ejpam-5935	166	24	)	)	PUNCT
ejpam-5935	166	25	[	[	PUNCT
ejpam-5935	166	26	∫	∫	PROPN
ejpam-5935	166	27	ρ	ρ	PROPN
ejpam-5935	166	28	0	0	NUM
ejpam-5935	166	29	(	(	PUNCT
ejpam-5935	166	30	ρ−ϖ)q−1dϖ+	ρ−ϖ)q−1dϖ+	PROPN
ejpam-5935	166	31	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5935	166	32	ρ−	ρ−	NOUN
ejpam-5935	166	33	κ	κ	PROPN
ejpam-5935	166	34	ω	ω	NUM
ejpam-5935	166	35	−	−	PROPN
ejpam-5935	166	36	κ	κ	PROPN
ejpam-5935	166	37	[	[	PUNCT
ejpam-5935	166	38	∫	∫	PROPN
ejpam-5935	166	39	ω	ω	NUM
ejpam-5935	166	40	0	0	NUM
ejpam-5935	166	41	(	(	PUNCT
ejpam-5935	166	42	ω−ϖ)q−1dϖ	ω−ϖ)q−1dϖ	NUM
ejpam-5935	166	43	]	]	SYM
ejpam-5935	166	44	∣∣∣∣+∣∣∣∣ρ−	∣∣∣∣+∣∣∣∣ρ−	PROPN
ejpam-5935	166	45	ω	ω	NUM
ejpam-5935	166	46	ω	ω	PROPN
ejpam-5935	166	47	−	−	PROPN
ejpam-5935	166	48	κ	κ	PROPN
ejpam-5935	166	49	[	[	PUNCT
ejpam-5935	166	50	∫	∫	PROPN
ejpam-5935	166	51	κ	κ	PROPN
ejpam-5935	166	52	0	0	NUM
ejpam-5935	166	53	(	(	PUNCT
ejpam-5935	166	54	κ−ϖ)q−1dϖ	κ−ϖ)q−1dϖ	X
ejpam-5935	166	55	]	]	PUNCT
ejpam-5935	166	56	∣∣∣∣]+β	∣∣∣∣]+β	VERB
ejpam-5935	166	57	≤	≤	NOUN
ejpam-5935	166	58	||ψ||	||ψ||	NOUN
ejpam-5935	166	59	γ(q	γ(q	PROPN
ejpam-5935	167	1	+	+	CCONJ
ejpam-5935	167	2	1	1	NUM
ejpam-5935	167	3	)	)	PUNCT
ejpam-5935	167	4	[	[	PUNCT
ejpam-5935	167	5	2ωq	2ωq	NOUN
ejpam-5935	167	6	]	]	PUNCT
ejpam-5935	168	1	+	+	CCONJ
ejpam-5935	168	2	β	β	X
ejpam-5935	168	3	<	<	X
ejpam-5935	168	4	r	r	NOUN
ejpam-5935	168	5	2	2	NUM
ejpam-5935	168	6	+	+	CCONJ
ejpam-5935	168	7	r	r	NOUN
ejpam-5935	168	8	2	2	NUM
ejpam-5935	168	9	=	=	SYM
ejpam-5935	168	10	r	r	NOUN
ejpam-5935	168	11	therefore	therefore	ADV
ejpam-5935	168	12	,	,	PUNCT
ejpam-5935	168	13	l1ξ1	l1ξ1	X
ejpam-5935	168	14	+	+	CCONJ
ejpam-5935	168	15	l2ξ2	l2ξ2	X
ejpam-5935	168	16	∈	∈	NOUN
ejpam-5935	168	17	br	br	NOUN
ejpam-5935	168	18	.	.	PUNCT
ejpam-5935	169	1	also	also	ADV
ejpam-5935	169	2	,	,	PUNCT
ejpam-5935	169	3	since	since	SCONJ
ejpam-5935	169	4	ξ	ξ	PROPN
ejpam-5935	169	5	is	be	AUX
ejpam-5935	169	6	continuous	continuous	ADJ
ejpam-5935	169	7	,	,	PUNCT
ejpam-5935	169	8	l1	l1	PROPN
ejpam-5935	169	9	is	be	AUX
ejpam-5935	169	10	also	also	ADV
ejpam-5935	169	11	continuous	continuous	ADJ
ejpam-5935	169	12	and	and	CCONJ
ejpam-5935	169	13	uniformly	uniformly	ADV
ejpam-5935	169	14	bounded	bound	VERB
ejpam-5935	169	15	as	as	ADP
ejpam-5935	169	16	||l1ξ||	||l1ξ||	X
ejpam-5935	169	17	≤	≤	NOUN
ejpam-5935	169	18	ωq	ωq	ADP
ejpam-5935	169	19	||ψ||	||ψ||	PROPN
ejpam-5935	169	20	γ(q+1	γ(q+1	PROPN
ejpam-5935	169	21	)	)	PUNCT
ejpam-5935	170	1	+	+	NUM
ejpam-5935	170	2	β	β	X
ejpam-5935	170	3	.	.	PUNCT
ejpam-5935	171	1	moreover	moreover	ADV
ejpam-5935	171	2	,	,	PUNCT
ejpam-5935	171	3	for	for	ADP
ejpam-5935	171	4	ρ1	ρ1	NOUN
ejpam-5935	171	5	,	,	PUNCT
ejpam-5935	171	6	ρ2	ρ2	PROPN
ejpam-5935	171	7	∈	∈	PROPN
ejpam-5935	171	8	[	[	X
ejpam-5935	171	9	0	0	NUM
ejpam-5935	171	10	,	,	PUNCT
ejpam-5935	171	11	ω],we	ω],we	PRON
ejpam-5935	171	12	see	see	VERB
ejpam-5935	171	13	that∣∣∣∣∣∣∣∣(l1ξ)(ρ1)−	that∣∣∣∣∣∣∣∣(l1ξ)(ρ1)−	NOUN
ejpam-5935	171	14	(	(	PUNCT
ejpam-5935	171	15	l1ξ)(ρ2	l1ξ)(ρ2	NOUN
ejpam-5935	171	16	)	)	PUNCT
ejpam-5935	171	17	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	ADP
ejpam-5935	171	18	≤	≤	ADJ
ejpam-5935	171	19	1	1	NUM
ejpam-5935	171	20	γ(q	γ(q	NOUN
ejpam-5935	171	21	)	)	PUNCT
ejpam-5935	171	22	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	ADP
ejpam-5935	171	23	∫	∫	PROPN
ejpam-5935	171	24	ρ1	ρ1	PROPN
ejpam-5935	171	25	0	0	NUM
ejpam-5935	172	1	[	[	PUNCT
ejpam-5935	172	2	(	(	PUNCT
ejpam-5935	172	3	ρ1	ρ1	NOUN
ejpam-5935	172	4	−ϖ)q−1	−ϖ)q−1	NOUN
ejpam-5935	172	5	−	−	PROPN
ejpam-5935	173	1	(	(	PUNCT
ejpam-5935	173	2	ρ2	ρ2	VERB
ejpam-5935	173	3	−ϖ)q−1	−ϖ)q−1	NOUN
ejpam-5935	173	4	]	]	X
ejpam-5935	174	1	ξ(ϖ	ξ(ϖ	PROPN
ejpam-5935	174	2	,	,	PUNCT
ejpam-5935	174	3	ξ(ϖ))dϖ	ξ(ϖ))dϖ	NOUN
ejpam-5935	174	4	+	+	CCONJ
ejpam-5935	174	5	∫	∫	PROPN
ejpam-5935	174	6	ρ2	ρ2	NOUN
ejpam-5935	174	7	ρ1	ρ1	NOUN
ejpam-5935	174	8	(	(	PUNCT
ejpam-5935	174	9	ρ2	ρ2	NOUN
ejpam-5935	174	10	−ϖ)q−1ξ(ϖ	−ϖ)q−1ξ(ϖ	PROPN
ejpam-5935	174	11	,	,	PUNCT
ejpam-5935	174	12	ξ(ϖ))dϖ	ξ(ϖ))dϖ	NOUN
ejpam-5935	174	13	∣∣∣∣∣∣∣∣+	∣∣∣∣∣∣∣∣+	PROPN
ejpam-5935	174	14	||β	||β	NOUN
ejpam-5935	174	15	−	−	PROPN
ejpam-5935	174	16	α	α	PROPN
ejpam-5935	174	17	ω	ω	PROPN
ejpam-5935	174	18	−	−	PROPN
ejpam-5935	174	19	κ	κ	PROPN
ejpam-5935	174	20	(	(	PUNCT
ejpam-5935	174	21	ρ1	ρ1	NOUN
ejpam-5935	174	22	−	−	PROPN
ejpam-5935	174	23	ρ2)||	ρ2)||	NOUN
ejpam-5935	174	24	≤	≤	NOUN
ejpam-5935	174	25	ξmax	ξmax	VERB
ejpam-5935	174	26	γ(ξ	γ(ξ	PROPN
ejpam-5935	174	27	+	+	CCONJ
ejpam-5935	174	28	1	1	X
ejpam-5935	174	29	)	)	PUNCT
ejpam-5935	174	30	[	[	X
ejpam-5935	174	31	2(ρ2	2(ρ2	NUM
ejpam-5935	174	32	−	−	NOUN
ejpam-5935	174	33	ρ1	ρ1	NOUN
ejpam-5935	174	34	)	)	PUNCT
ejpam-5935	174	35	q	q	PROPN
ejpam-5935	175	1	+	+	NUM
ejpam-5935	175	2	ρq1	ρq1	PROPN
ejpam-5935	175	3	−	−	PROPN
ejpam-5935	175	4	ρq2	ρq2	NOUN
ejpam-5935	175	5	]	]	X
ejpam-5935	175	6	+	+	CCONJ
ejpam-5935	175	7	||β	||β	NOUN
ejpam-5935	175	8	−	−	PROPN
ejpam-5935	175	9	α	α	PROPN
ejpam-5935	175	10	ω	ω	PROPN
ejpam-5935	175	11	−	−	PROPN
ejpam-5935	175	12	κ	κ	PROPN
ejpam-5935	175	13	(	(	PUNCT
ejpam-5935	175	14	ρ1	ρ1	NOUN
ejpam-5935	175	15	−	−	PROPN
ejpam-5935	175	16	ρ2)||	ρ2)||	NOUN
ejpam-5935	175	17	as	as	ADP
ejpam-5935	175	18	ρ2	ρ2	NOUN
ejpam-5935	175	19	−→	−→	NOUN
ejpam-5935	175	20	ρ1	ρ1	NOUN
ejpam-5935	175	21	we	we	PRON
ejpam-5935	175	22	see	see	VERB
ejpam-5935	175	23	that	that	SCONJ
ejpam-5935	175	24	∣∣∣∣∣∣∣∣(l1ξ)(ρ1	∣∣∣∣∣∣∣∣(l1ξ)(ρ1	NOUN
ejpam-5935	175	25	)	)	PUNCT
ejpam-5935	175	26	−	−	PROPN
ejpam-5935	175	27	(	(	PUNCT
ejpam-5935	175	28	l1ξ)(ρ2	l1ξ)(ρ2	NOUN
ejpam-5935	175	29	)	)	PUNCT
ejpam-5935	175	30	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	ADP
ejpam-5935	175	31	−→	−→	NOUN
ejpam-5935	175	32	0	0	NUM
ejpam-5935	175	33	,	,	PUNCT
ejpam-5935	175	34	proving	prove	VERB
ejpam-5935	175	35	that	that	SCONJ
ejpam-5935	175	36	l1	l1	PROPN
ejpam-5935	175	37	is	be	AUX
ejpam-5935	175	38	uniformly	uniformly	ADV
ejpam-5935	175	39	bounded	bound	VERB
ejpam-5935	175	40	and	and	CCONJ
ejpam-5935	175	41	relatively	relatively	ADV
ejpam-5935	175	42	compact	compact	ADJ
ejpam-5935	175	43	on	on	ADP
ejpam-5935	175	44	br	br	PROPN
ejpam-5935	175	45	.	.	PUNCT
ejpam-5935	176	1	therefore	therefore	ADV
ejpam-5935	176	2	,	,	PUNCT
ejpam-5935	176	3	l1	l1	PROPN
ejpam-5935	176	4	is	be	AUX
ejpam-5935	176	5	compact	compact	ADJ
ejpam-5935	176	6	.	.	PUNCT
ejpam-5935	177	1	finally	finally	ADV
ejpam-5935	177	2	,	,	PUNCT
ejpam-5935	177	3	l2	l2	NOUN
ejpam-5935	177	4	is	be	AUX
ejpam-5935	177	5	a	a	DET
ejpam-5935	177	6	contraction	contraction	NOUN
ejpam-5935	177	7	by	by	ADP
ejpam-5935	177	8	assumption	assumption	NOUN
ejpam-5935	177	9	since	since	SCONJ
ejpam-5935	177	10	lωq	lωq	PROPN
ejpam-5935	177	11	γ(q+1	γ(q+1	PROPN
ejpam-5935	177	12	)	)	PUNCT
ejpam-5935	177	13	<	<	X
ejpam-5935	178	1	1	1	X
ejpam-5935	178	2	.	.	PUNCT
ejpam-5935	178	3	therefore	therefore	ADV
ejpam-5935	178	4	,	,	PUNCT
ejpam-5935	178	5	theorem	theorem	ADJ
ejpam-5935	178	6	(	(	PUNCT
ejpam-5935	178	7	2	2	NUM
ejpam-5935	178	8	)	)	PUNCT
ejpam-5935	178	9	guarantee	guarantee	VERB
ejpam-5935	178	10	that	that	SCONJ
ejpam-5935	178	11	(	(	PUNCT
ejpam-5935	178	12	1	1	X
ejpam-5935	178	13	)	)	PUNCT
ejpam-5935	178	14	has	have	VERB
ejpam-5935	178	15	at	at	ADP
ejpam-5935	178	16	least	least	ADJ
ejpam-5935	178	17	on	on	ADP
ejpam-5935	178	18	solution	solution	NOUN
ejpam-5935	178	19	on	on	ADP
ejpam-5935	178	20	[	[	X
ejpam-5935	178	21	0	0	NUM
ejpam-5935	178	22	,	,	PUNCT
ejpam-5935	178	23	ω	ω	NOUN
ejpam-5935	178	24	]	]	X
ejpam-5935	178	25	.	.	PUNCT
ejpam-5935	179	1	s.	s.	PROPN
ejpam-5935	179	2	f.	f.	PROPN
ejpam-5935	179	3	aljurbua	aljurbua	PROPN
ejpam-5935	179	4	et	et	PROPN
ejpam-5935	179	5	al	al	PROPN
ejpam-5935	179	6	.	.	PUNCT
ejpam-5935	179	7	/	/	SYM
ejpam-5935	179	8	eur	eur	PROPN
ejpam-5935	179	9	.	.	PUNCT
ejpam-5935	180	1	j.	j.	PROPN
ejpam-5935	180	2	pure	pure	PROPN
ejpam-5935	180	3	appl	appl	PROPN
ejpam-5935	180	4	.	.	PROPN
ejpam-5935	180	5	math	math	PROPN
ejpam-5935	180	6	,	,	PUNCT
ejpam-5935	180	7	18	18	NUM
ejpam-5935	180	8	(	(	PUNCT
ejpam-5935	180	9	2	2	NUM
ejpam-5935	180	10	)	)	PUNCT
ejpam-5935	180	11	(	(	PUNCT
ejpam-5935	180	12	2025	2025	NUM
ejpam-5935	180	13	)	)	PUNCT
ejpam-5935	180	14	,	,	PUNCT
ejpam-5935	180	15	5935	5935	NUM
ejpam-5935	180	16	7	7	NUM
ejpam-5935	180	17	of	of	ADP
ejpam-5935	180	18	10	10	NUM
ejpam-5935	180	19	theorem	theorem	VERB
ejpam-5935	180	20	4	4	NUM
ejpam-5935	180	21	.	.	X
ejpam-5935	181	1	for	for	ADP
ejpam-5935	181	2	a	a	DET
ejpam-5935	181	3	continuous	continuous	ADJ
ejpam-5935	181	4	function	function	NOUN
ejpam-5935	181	5	ξ	ξ	NOUN
ejpam-5935	181	6	:	:	PUNCT
ejpam-5935	181	7	[	[	X
ejpam-5935	181	8	0	0	NUM
ejpam-5935	181	9	,	,	PUNCT
ejpam-5935	181	10	ω]×r	ω]×r	NUM
ejpam-5935	181	11	−→	−→	ADJ
ejpam-5935	181	12	r	r	NOUN
ejpam-5935	181	13	,	,	PUNCT
ejpam-5935	181	14	assume	assume	VERB
ejpam-5935	181	15	∣∣∣∣ξ(ρ	∣∣∣∣ξ(ρ	PROPN
ejpam-5935	181	16	,	,	PUNCT
ejpam-5935	181	17	ξ1)−ξ(ρ	ξ1)−ξ(ρ	NOUN
ejpam-5935	181	18	,	,	PUNCT
ejpam-5935	181	19	ξ2	ξ2	ADJ
ejpam-5935	181	20	)	)	PUNCT
ejpam-5935	181	21	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5935	181	22	≤	≤	NUM
ejpam-5935	181	23	l	l	NOUN
ejpam-5935	181	24	∣∣∣∣ξ1	∣∣∣∣ξ1	PUNCT
ejpam-5935	182	1	−	−	NOUN
ejpam-5935	182	2	ξ2	ξ2	ADJ
ejpam-5935	182	3	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5935	182	4	holds	hold	VERB
ejpam-5935	182	5	for	for	ADP
ejpam-5935	182	6	all	all	DET
ejpam-5935	182	7	ρ	ρ	NOUN
ejpam-5935	182	8	∈	∈	PROPN
ejpam-5935	183	1	[	[	X
ejpam-5935	183	2	0	0	NUM
ejpam-5935	183	3	,	,	PUNCT
ejpam-5935	183	4	ω	ω	NOUN
ejpam-5935	183	5	]	]	X
ejpam-5935	183	6	,	,	PUNCT
ejpam-5935	183	7	l	l	NOUN
ejpam-5935	183	8	>	>	X
ejpam-5935	183	9	0	0	NUM
ejpam-5935	183	10	,	,	PUNCT
ejpam-5935	183	11	ξ1	ξ1	NOUN
ejpam-5935	183	12	,	,	PUNCT
ejpam-5935	183	13	ξ2	ξ2	ADJ
ejpam-5935	183	14	,	,	PUNCT
ejpam-5935	183	15	and	and	CCONJ
ejpam-5935	183	16	2lωq	2lωq	PROPN
ejpam-5935	183	17	γ(q+1	γ(q+1	ADJ
ejpam-5935	183	18	)	)	PUNCT
ejpam-5935	183	19	<	<	X
ejpam-5935	184	1	1	1	X
ejpam-5935	184	2	.	.	PUNCT
ejpam-5935	184	3	then	then	ADV
ejpam-5935	184	4	(	(	PUNCT
ejpam-5935	184	5	1	1	X
ejpam-5935	184	6	)	)	PUNCT
ejpam-5935	184	7	has	have	VERB
ejpam-5935	184	8	a	a	DET
ejpam-5935	184	9	unique	unique	ADJ
ejpam-5935	184	10	solution	solution	NOUN
ejpam-5935	184	11	on	on	ADP
ejpam-5935	184	12	[	[	X
ejpam-5935	184	13	0	0	NUM
ejpam-5935	184	14	,	,	PUNCT
ejpam-5935	184	15	ω	ω	NOUN
ejpam-5935	184	16	]	]	X
ejpam-5935	184	17	.	.	PUNCT
ejpam-5935	185	1	proof	proof	NOUN
ejpam-5935	185	2	.	.	PUNCT
ejpam-5935	186	1	let	let	VERB
ejpam-5935	186	2	l	l	NOUN
ejpam-5935	186	3	be	be	AUX
ejpam-5935	186	4	an	an	DET
ejpam-5935	186	5	operator	operator	NOUN
ejpam-5935	186	6	defined	define	VERB
ejpam-5935	186	7	as	as	ADP
ejpam-5935	186	8	in	in	ADP
ejpam-5935	186	9	4	4	NUM
ejpam-5935	186	10	(	(	PUNCT
ejpam-5935	186	11	lξ)(ρ	lξ)(ρ	X
ejpam-5935	186	12	)	)	PUNCT
ejpam-5935	187	1	=	=	PUNCT
ejpam-5935	187	2	αω	αω	NUM
ejpam-5935	187	3	−	−	NOUN
ejpam-5935	188	1	βκ	βκ	INTJ
ejpam-5935	189	1	ω	ω	NUM
ejpam-5935	189	2	−	−	NOUN
ejpam-5935	189	3	κ	κ	NOUN
ejpam-5935	189	4	+	+	X
ejpam-5935	190	1	β	β	X
ejpam-5935	190	2	−	−	PROPN
ejpam-5935	190	3	α	α	PROPN
ejpam-5935	190	4	ω	ω	PROPN
ejpam-5935	191	1	−	−	PROPN
ejpam-5935	192	1	κ	κ	PROPN
ejpam-5935	192	2	ρ+	ρ+	NOUN
ejpam-5935	192	3	1	1	NUM
ejpam-5935	192	4	γ(q	γ(q	NOUN
ejpam-5935	192	5	)	)	PUNCT
ejpam-5935	192	6	∫	∫	PROPN
ejpam-5935	193	1	ρ	ρ	PROPN
ejpam-5935	193	2	0	0	PROPN
ejpam-5935	193	3	(	(	PUNCT
ejpam-5935	193	4	ρ−ϖ)q−1ξ(ϖ	ρ−ϖ)q−1ξ(ϖ	NOUN
ejpam-5935	193	5	,	,	PUNCT
ejpam-5935	193	6	ξ(ϖ	ξ(ϖ	PROPN
ejpam-5935	193	7	)	)	PUNCT
ejpam-5935	193	8	)	)	PUNCT
ejpam-5935	194	1	dϖ	dϖ	ADP
ejpam-5935	194	2	−	−	PROPN
ejpam-5935	194	3	ρ−	ρ−	PROPN
ejpam-5935	194	4	κ	κ	VERB
ejpam-5935	194	5	γ(q)(ω	γ(q)(ω	NUM
ejpam-5935	194	6	−	−	PROPN
ejpam-5935	194	7	κ	κ	NOUN
ejpam-5935	194	8	)	)	PUNCT
ejpam-5935	194	9	[	[	PUNCT
ejpam-5935	194	10	∫	∫	PROPN
ejpam-5935	194	11	ω	ω	NUM
ejpam-5935	194	12	0	0	NUM
ejpam-5935	194	13	(	(	PUNCT
ejpam-5935	194	14	ω	ω	PROPN
ejpam-5935	194	15	−ϖ)q−1ξ(ϖ	−ϖ)q−1ξ(ϖ	PROPN
ejpam-5935	194	16	,	,	PUNCT
ejpam-5935	194	17	ξ(ϖ	ξ(ϖ	PROPN
ejpam-5935	194	18	)	)	PUNCT
ejpam-5935	194	19	)	)	PUNCT
ejpam-5935	194	20	dϖ	dϖ	ADP
ejpam-5935	194	21	]	]	PUNCT
ejpam-5935	195	1	+	+	CCONJ
ejpam-5935	195	2	ρ−	ρ−	PROPN
ejpam-5935	195	3	ω	ω	NUM
ejpam-5935	195	4	γ(q)(ω	γ(q)(ω	NUM
ejpam-5935	195	5	−	−	PROPN
ejpam-5935	195	6	κ	κ	NOUN
ejpam-5935	195	7	)	)	PUNCT
ejpam-5935	195	8	[	[	PUNCT
ejpam-5935	195	9	∫	∫	PROPN
ejpam-5935	195	10	κ	κ	PROPN
ejpam-5935	195	11	0	0	PROPN
ejpam-5935	195	12	(	(	PUNCT
ejpam-5935	195	13	κ−ϖ)q−1ξ(ϖ	κ−ϖ)q−1ξ(ϖ	PROPN
ejpam-5935	195	14	,	,	PUNCT
ejpam-5935	195	15	ξ(ϖ	ξ(ϖ	PROPN
ejpam-5935	195	16	)	)	PUNCT
ejpam-5935	195	17	)	)	PUNCT
ejpam-5935	195	18	dϖ	dϖ	ADP
ejpam-5935	195	19	]	]	PUNCT
ejpam-5935	195	20	,	,	PUNCT
ejpam-5935	195	21	and	and	CCONJ
ejpam-5935	195	22	for	for	ADP
ejpam-5935	195	23	each	each	DET
ejpam-5935	195	24	ρ	ρ	PROPN
ejpam-5935	195	25	∈	∈	PROPN
ejpam-5935	196	1	[	[	X
ejpam-5935	196	2	0	0	NUM
ejpam-5935	196	3	,	,	PUNCT
ejpam-5935	196	4	ω	ω	NOUN
ejpam-5935	196	5	]	]	PUNCT
ejpam-5935	196	6	and	and	CCONJ
ejpam-5935	196	7	any	any	DET
ejpam-5935	196	8	ξ1	ξ1	NOUN
ejpam-5935	196	9	,	,	PUNCT
ejpam-5935	196	10	ξ2	ξ2	PROPN
ejpam-5935	196	11	∈	∈	PROPN
ejpam-5935	196	12	c([0	c([0	NOUN
ejpam-5935	196	13	,	,	PUNCT
ejpam-5935	196	14	ω	ω	PROPN
ejpam-5935	196	15	]	]	X
ejpam-5935	196	16	)	)	PUNCT
ejpam-5935	196	17	we	we	PRON
ejpam-5935	196	18	have	have	VERB
ejpam-5935	196	19	∣∣∣∣lξ1	∣∣∣∣lξ1	ADJ
ejpam-5935	196	20	−	−	NOUN
ejpam-5935	196	21	lξ2	lξ2	PROPN
ejpam-5935	196	22	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5935	197	1	=	=	PUNCT
ejpam-5935	197	2	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	ADP
ejpam-5935	197	3	1	1	NUM
ejpam-5935	197	4	γ(q	γ(q	NOUN
ejpam-5935	197	5	)	)	PUNCT
ejpam-5935	197	6	∫	∫	PROPN
ejpam-5935	198	1	ρ	ρ	PROPN
ejpam-5935	198	2	0	0	PUNCT
ejpam-5935	199	1	(	(	PUNCT
ejpam-5935	199	2	ρ−ϖ)q−1	ρ−ϖ)q−1	X
ejpam-5935	199	3	[	[	PUNCT
ejpam-5935	199	4	ξ(ϖ	ξ(ϖ	PROPN
ejpam-5935	199	5	,	,	PUNCT
ejpam-5935	199	6	ξ1(ϖ))−	ξ1(ϖ))−	PROPN
ejpam-5935	199	7	ξ(ϖ	ξ(ϖ	PROPN
ejpam-5935	199	8	,	,	PUNCT
ejpam-5935	199	9	ξ2(ϖ	ξ2(ϖ	PROPN
ejpam-5935	199	10	)	)	PUNCT
ejpam-5935	199	11	)	)	PUNCT
ejpam-5935	199	12	]	]	PUNCT
ejpam-5935	200	1	dϖ	dϖ	ADP
ejpam-5935	200	2	−	−	PROPN
ejpam-5935	200	3	ρ−	ρ−	PROPN
ejpam-5935	200	4	κ	κ	VERB
ejpam-5935	200	5	γ(q)(ω	γ(q)(ω	NUM
ejpam-5935	200	6	−	−	PROPN
ejpam-5935	200	7	κ	κ	NOUN
ejpam-5935	200	8	)	)	PUNCT
ejpam-5935	200	9	[	[	PUNCT
ejpam-5935	200	10	∫	∫	PROPN
ejpam-5935	200	11	ω	ω	NUM
ejpam-5935	200	12	0	0	NUM
ejpam-5935	201	1	(	(	PUNCT
ejpam-5935	201	2	ω	ω	NUM
ejpam-5935	201	3	−ϖ)q−1	−ϖ)q−1	X
ejpam-5935	201	4	[	[	PUNCT
ejpam-5935	201	5	ξ(ϖ	ξ(ϖ	PROPN
ejpam-5935	201	6	,	,	PUNCT
ejpam-5935	201	7	ξ1(ϖ))−	ξ1(ϖ))−	PROPN
ejpam-5935	201	8	ξ(ϖ	ξ(ϖ	PROPN
ejpam-5935	201	9	,	,	PUNCT
ejpam-5935	201	10	ξ2(ϖ	ξ2(ϖ	PROPN
ejpam-5935	201	11	)	)	PUNCT
ejpam-5935	201	12	)	)	PUNCT
ejpam-5935	201	13	]	]	PUNCT
ejpam-5935	202	1	dϖ	dϖ	X
ejpam-5935	202	2	]	]	PUNCT
ejpam-5935	203	1	+	+	CCONJ
ejpam-5935	203	2	ρ−	ρ−	PROPN
ejpam-5935	203	3	ω	ω	NUM
ejpam-5935	203	4	γ(q)(ω	γ(q)(ω	NUM
ejpam-5935	203	5	−	−	PROPN
ejpam-5935	203	6	κ	κ	NOUN
ejpam-5935	203	7	)	)	PUNCT
ejpam-5935	203	8	[	[	PUNCT
ejpam-5935	203	9	∫	∫	PROPN
ejpam-5935	203	10	κ	κ	X
ejpam-5935	203	11	0	0	NUM
ejpam-5935	203	12	(	(	PUNCT
ejpam-5935	203	13	κ−ϖ)q−1	κ−ϖ)q−1	X
ejpam-5935	203	14	[	[	PUNCT
ejpam-5935	203	15	ξ(ϖ	ξ(ϖ	PROPN
ejpam-5935	203	16	,	,	PUNCT
ejpam-5935	203	17	ξ1(ϖ))−	ξ1(ϖ))−	PROPN
ejpam-5935	203	18	ξ(ϖ	ξ(ϖ	PROPN
ejpam-5935	203	19	,	,	PUNCT
ejpam-5935	203	20	ξ2(ϖ	ξ2(ϖ	NUM
ejpam-5935	203	21	)	)	PUNCT
ejpam-5935	203	22	)	)	PUNCT
ejpam-5935	203	23	dϖ	dϖ	ADP
ejpam-5935	203	24	]	]	X
ejpam-5935	203	25	]	]	X
ejpam-5935	203	26	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	ADP
ejpam-5935	203	27	≤	≤	ADJ
ejpam-5935	203	28	l	l	NOUN
ejpam-5935	203	29	γ(q	γ(q	NOUN
ejpam-5935	203	30	)	)	PUNCT
ejpam-5935	203	31	[	[	PUNCT
ejpam-5935	203	32	∫	∫	PROPN
ejpam-5935	203	33	ρ	ρ	PROPN
ejpam-5935	203	34	0	0	NUM
ejpam-5935	203	35	(	(	PUNCT
ejpam-5935	203	36	ρ−ϖ)q−1dϖ+	ρ−ϖ)q−1dϖ+	X
ejpam-5935	204	1	|ρ−	|ρ−	NOUN
ejpam-5935	204	2	κ|	κ|	NOUN
ejpam-5935	204	3	ω	ω	NUM
ejpam-5935	204	4	−	−	PROPN
ejpam-5935	204	5	κ	κ	PROPN
ejpam-5935	204	6	[	[	PUNCT
ejpam-5935	204	7	∫	∫	PROPN
ejpam-5935	204	8	ω	ω	NUM
ejpam-5935	204	9	0	0	NUM
ejpam-5935	204	10	(	(	PUNCT
ejpam-5935	204	11	ω−ϖ)q−1dϖ	ω−ϖ)q−1dϖ	X
ejpam-5935	204	12	]	]	PUNCT
ejpam-5935	204	13	+	+	NUM
ejpam-5935	204	14	|ρ−	|ρ−	NOUN
ejpam-5935	204	15	ω|	ω|	NOUN
ejpam-5935	204	16	ω	ω	NUM
ejpam-5935	204	17	−	−	NOUN
ejpam-5935	204	18	κ	κ	PROPN
ejpam-5935	204	19	∫	∫	PROPN
ejpam-5935	204	20	κ	κ	PROPN
ejpam-5935	204	21	0	0	NUM
ejpam-5935	204	22	(	(	PUNCT
ejpam-5935	204	23	κ−ϖ)q−1dϖ	κ−ϖ)q−1dϖ	X
ejpam-5935	204	24	]	]	X
ejpam-5935	204	25	]	]	X
ejpam-5935	204	26	||ξ1−ξ2||	||ξ1−ξ2||	X
ejpam-5935	204	27	≤	≤	NUM
ejpam-5935	204	28	l	l	NOUN
ejpam-5935	204	29	γ(q	γ(q	PROPN
ejpam-5935	204	30	+	+	CCONJ
ejpam-5935	204	31	1	1	NUM
ejpam-5935	204	32	)	)	PUNCT
ejpam-5935	204	33	[	[	PUNCT
ejpam-5935	204	34	2ωq	2ωq	NOUN
ejpam-5935	204	35	]	]	X
ejpam-5935	204	36	||ξ1	||ξ1	NOUN
ejpam-5935	204	37	−	−	PROPN
ejpam-5935	204	38	ξ2||	ξ2||	PROPN
ejpam-5935	204	39	=	=	SYM
ejpam-5935	204	40	2lωq	2lωq	NUM
ejpam-5935	204	41	γ(q	γ(q	NOUN
ejpam-5935	205	1	+	+	CCONJ
ejpam-5935	205	2	1	1	X
ejpam-5935	205	3	)	)	PUNCT
ejpam-5935	205	4	[	[	PUNCT
ejpam-5935	205	5	||ξ1	||ξ1	NOUN
ejpam-5935	205	6	−	−	PROPN
ejpam-5935	205	7	ξ2||	ξ2||	PROPN
ejpam-5935	205	8	.	.	PUNCT
ejpam-5935	206	1	thus	thus	ADV
ejpam-5935	206	2	,	,	PUNCT
ejpam-5935	206	3	2lωq	2lωq	PROPN
ejpam-5935	206	4	γ(q+1	γ(q+1	PUNCT
ejpam-5935	206	5	)	)	PUNCT
ejpam-5935	206	6	<	<	X
ejpam-5935	206	7	1	1	NUM
ejpam-5935	206	8	,	,	PUNCT
ejpam-5935	206	9	meaning	mean	VERB
ejpam-5935	206	10	that	that	SCONJ
ejpam-5935	206	11	l	l	NOUN
ejpam-5935	206	12	is	be	AUX
ejpam-5935	206	13	a	a	DET
ejpam-5935	206	14	contraction	contraction	NOUN
ejpam-5935	206	15	depending	depend	VERB
ejpam-5935	206	16	on	on	ADP
ejpam-5935	206	17	l	l	NOUN
ejpam-5935	206	18	,	,	PUNCT
ejpam-5935	206	19	q	q	X
ejpam-5935	206	20	,	,	PUNCT
ejpam-5935	206	21	ω	ω	PROPN
ejpam-5935	206	22	,	,	PUNCT
ejpam-5935	206	23	κ	κ	X
ejpam-5935	206	24	.	.	PUNCT
ejpam-5935	206	25	now	now	ADV
ejpam-5935	206	26	setting	set	VERB
ejpam-5935	206	27	supρ∈[0,ω	supρ∈[0,ω	VERB
ejpam-5935	206	28	]	]	X
ejpam-5935	207	1	∣∣ξ(ρ	∣∣ξ(ρ	PROPN
ejpam-5935	207	2	,	,	PUNCT
ejpam-5935	207	3	0)∣∣	0)∣∣	NUM
ejpam-5935	207	4	=	=	SYM
ejpam-5935	207	5	n	n	CCONJ
ejpam-5935	207	6	,	,	PUNCT
ejpam-5935	207	7	and	and	CCONJ
ejpam-5935	207	8	choosing	choose	VERB
ejpam-5935	207	9	br	br	NOUN
ejpam-5935	207	10	=	=	PUNCT
ejpam-5935	207	11	{	{	PUNCT
ejpam-5935	207	12	ξ	ξ	X
ejpam-5935	207	13	∈	∈	PROPN
ejpam-5935	207	14	c([0	c([0	NOUN
ejpam-5935	207	15	,	,	PUNCT
ejpam-5935	207	16	ω],r	ω],r	NUM
ejpam-5935	207	17	)	)	PUNCT
ejpam-5935	207	18	:	:	PUNCT
ejpam-5935	207	19	||ξ||	||ξ||	VERB
ejpam-5935	207	20	≤	≤	ADJ
ejpam-5935	207	21	r	r	AUX
ejpam-5935	207	22	}	}	PUNCT
ejpam-5935	207	23	be	be	AUX
ejpam-5935	207	24	a	a	DET
ejpam-5935	207	25	ball	ball	NOUN
ejpam-5935	207	26	with	with	ADP
ejpam-5935	207	27	a	a	DET
ejpam-5935	207	28	radius	radius	NOUN
ejpam-5935	207	29	r	r	NOUN
ejpam-5935	207	30	≥	≥	NOUN
ejpam-5935	207	31	β+nd	β+nd	PUNCT
ejpam-5935	208	1	1−ld	1−ld	NUM
ejpam-5935	208	2	where	where	SCONJ
ejpam-5935	208	3	d	d	NOUN
ejpam-5935	208	4	=	=	SYM
ejpam-5935	208	5	2ωq	2ωq	NOUN
ejpam-5935	208	6	γ(q+1	γ(q+1	ADJ
ejpam-5935	208	7	)	)	PUNCT
ejpam-5935	209	1	so	so	SCONJ
ejpam-5935	209	2	we	we	PRON
ejpam-5935	209	3	have	have	VERB
ejpam-5935	209	4	||(lξ)(ρ)||	||(lξ)(ρ)||	VERB
ejpam-5935	209	5	≤	≤	NUM
ejpam-5935	209	6	max	max	PROPN
ejpam-5935	209	7	ρ∈[0,ω	ρ∈[0,ω	PUNCT
ejpam-5935	209	8	]	]	X
ejpam-5935	210	1	[	[	X
ejpam-5935	210	2	∣∣∣∣αω	∣∣∣∣αω	PROPN
ejpam-5935	210	3	−	−	PROPN
ejpam-5935	210	4	βκ	βκ	INTJ
ejpam-5935	210	5	ω	ω	NUM
ejpam-5935	211	1	−	−	NOUN
ejpam-5935	211	2	κ	κ	NOUN
ejpam-5935	211	3	+	+	X
ejpam-5935	212	1	β	β	X
ejpam-5935	212	2	−	−	PROPN
ejpam-5935	212	3	α	α	PROPN
ejpam-5935	212	4	ω	ω	PROPN
ejpam-5935	212	5	−	−	PROPN
ejpam-5935	212	6	κ	κ	PROPN
ejpam-5935	212	7	ρ	ρ	PROPN
ejpam-5935	212	8	∣∣∣∣+	∣∣∣∣+	PROPN
ejpam-5935	212	9	1	1	NUM
ejpam-5935	212	10	γ(q	γ(q	PROPN
ejpam-5935	212	11	)	)	PUNCT
ejpam-5935	212	12	∫	∫	PROPN
ejpam-5935	213	1	ρ	ρ	PROPN
ejpam-5935	213	2	0	0	PUNCT
ejpam-5935	214	1	(	(	PUNCT
ejpam-5935	214	2	ρ−ϖ)q−1	ρ−ϖ)q−1	PRON
ejpam-5935	214	3	[	[	X
ejpam-5935	214	4	∣∣∣∣ξ(ϖ	∣∣∣∣ξ(ϖ	PROPN
ejpam-5935	214	5	,	,	PUNCT
ejpam-5935	214	6	ξ(ϖ))−	ξ(ϖ))−	VERB
ejpam-5935	214	7	ξ(ϖ	ξ(ϖ	PROPN
ejpam-5935	214	8	,	,	PUNCT
ejpam-5935	214	9	0	0	NUM
ejpam-5935	214	10	)	)	PUNCT
ejpam-5935	214	11	)	)	PUNCT
ejpam-5935	215	1	∣∣∣∣+	∣∣∣∣+	PROPN
ejpam-5935	215	2	∣∣∣∣ξ(ϖ	∣∣∣∣ξ(ϖ	PROPN
ejpam-5935	215	3	,	,	PUNCT
ejpam-5935	215	4	0))∣∣∣∣	0))∣∣∣∣	NUM
ejpam-5935	215	5	]	]	X
ejpam-5935	215	6	dϖ	dϖ	ADP
ejpam-5935	215	7	+	+	CCONJ
ejpam-5935	215	8	|ρ−	|ρ−	NOUN
ejpam-5935	215	9	κ|	κ|	NOUN
ejpam-5935	215	10	γ(q)(ω	γ(q)(ω	NUM
ejpam-5935	215	11	−	−	PROPN
ejpam-5935	215	12	κ	κ	NOUN
ejpam-5935	215	13	)	)	PUNCT
ejpam-5935	215	14	[	[	PUNCT
ejpam-5935	215	15	∫	∫	PROPN
ejpam-5935	215	16	ω	ω	NUM
ejpam-5935	215	17	0	0	NUM
ejpam-5935	215	18	(	(	PUNCT
ejpam-5935	215	19	ω	ω	NUM
ejpam-5935	215	20	−ϖ)q−1	−ϖ)q−1	X
ejpam-5935	216	1	[	[	X
ejpam-5935	216	2	∣∣∣∣ξ(ϖ	∣∣∣∣ξ(ϖ	PROPN
ejpam-5935	216	3	,	,	PUNCT
ejpam-5935	216	4	ξ(ϖ))−	ξ(ϖ))−	VERB
ejpam-5935	216	5	ξ(ϖ	ξ(ϖ	PROPN
ejpam-5935	216	6	,	,	PUNCT
ejpam-5935	216	7	0	0	NUM
ejpam-5935	216	8	)	)	PUNCT
ejpam-5935	216	9	)	)	PUNCT
ejpam-5935	217	1	∣∣∣∣+	∣∣∣∣+	PROPN
ejpam-5935	217	2	∣∣∣∣ξ(ϖ	∣∣∣∣ξ(ϖ	PROPN
ejpam-5935	217	3	,	,	PUNCT
ejpam-5935	217	4	0))∣∣∣∣	0))∣∣∣∣	NUM
ejpam-5935	217	5	]	]	X
ejpam-5935	217	6	dϖ	dϖ	X
ejpam-5935	217	7	]	]	X
ejpam-5935	217	8	+	+	CCONJ
ejpam-5935	217	9	|ρ−	|ρ−	NOUN
ejpam-5935	217	10	ω|	ω|	NOUN
ejpam-5935	217	11	γ(q)(ω	γ(q)(ω	CCONJ
ejpam-5935	217	12	−	−	PROPN
ejpam-5935	217	13	κ	κ	NOUN
ejpam-5935	217	14	)	)	PUNCT
ejpam-5935	217	15	∫	∫	PROPN
ejpam-5935	217	16	κ	κ	PROPN
ejpam-5935	217	17	0	0	PUNCT
ejpam-5935	217	18	(	(	PUNCT
ejpam-5935	217	19	κ−ϖ)q−1	κ−ϖ)q−1	SYM
ejpam-5935	217	20	[	[	X
ejpam-5935	217	21	∣∣∣∣ξ(ϖ	∣∣∣∣ξ(ϖ	PROPN
ejpam-5935	217	22	,	,	PUNCT
ejpam-5935	217	23	ξ(ϖ))−	ξ(ϖ))−	VERB
ejpam-5935	217	24	ξ(ϖ	ξ(ϖ	PROPN
ejpam-5935	217	25	,	,	PUNCT
ejpam-5935	217	26	0	0	NUM
ejpam-5935	217	27	)	)	PUNCT
ejpam-5935	217	28	)	)	PUNCT
ejpam-5935	217	29	∣∣∣∣+	∣∣∣∣+	PROPN
ejpam-5935	217	30	∣∣∣∣ξ(ϖ	∣∣∣∣ξ(ϖ	PROPN
ejpam-5935	217	31	,	,	PUNCT
ejpam-5935	217	32	0))∣∣∣∣	0))∣∣∣∣	NUM
ejpam-5935	217	33	]	]	X
ejpam-5935	217	34	dϖ	dϖ	X
ejpam-5935	217	35	]	]	PUNCT
ejpam-5935	217	36	≤	≤	NUM
ejpam-5935	217	37	β	β	X
ejpam-5935	217	38	+	+	X
ejpam-5935	217	39	(	(	PUNCT
ejpam-5935	217	40	lr	lr	INTJ
ejpam-5935	217	41	+	+	NOUN
ejpam-5935	217	42	n	n	NOUN
ejpam-5935	217	43	)	)	PUNCT
ejpam-5935	218	1	[	[	PUNCT
ejpam-5935	218	2	2ωq	2ωq	ADJ
ejpam-5935	218	3	γ(q	γ(q	NOUN
ejpam-5935	218	4	+	+	CCONJ
ejpam-5935	218	5	1	1	NUM
ejpam-5935	218	6	)	)	PUNCT
ejpam-5935	218	7	]	]	PUNCT
ejpam-5935	219	1	<	<	X
ejpam-5935	219	2	r	r	NOUN
ejpam-5935	219	3	implying	imply	VERB
ejpam-5935	219	4	that	that	DET
ejpam-5935	219	5	lbr	lbr	NOUN
ejpam-5935	219	6	⊂	⊂	PROPN
ejpam-5935	219	7	br	br	PROPN
ejpam-5935	219	8	.	.	PUNCT
ejpam-5935	220	1	hence	hence	ADV
ejpam-5935	220	2	we	we	PRON
ejpam-5935	220	3	proved	prove	VERB
ejpam-5935	220	4	the	the	DET
ejpam-5935	220	5	uniqueness	uniqueness	NOUN
ejpam-5935	220	6	for	for	ADP
ejpam-5935	220	7	(	(	PUNCT
ejpam-5935	220	8	1	1	NUM
ejpam-5935	220	9	)	)	PUNCT
ejpam-5935	220	10	.	.	PUNCT
ejpam-5935	221	1	s.	s.	PROPN
ejpam-5935	221	2	f.	f.	PROPN
ejpam-5935	221	3	aljurbua	aljurbua	PROPN
ejpam-5935	221	4	et	et	PROPN
ejpam-5935	221	5	al	al	PROPN
ejpam-5935	221	6	.	.	PUNCT
ejpam-5935	221	7	/	/	SYM
ejpam-5935	221	8	eur	eur	PROPN
ejpam-5935	221	9	.	.	PUNCT
ejpam-5935	222	1	j.	j.	PROPN
ejpam-5935	222	2	pure	pure	PROPN
ejpam-5935	222	3	appl	appl	PROPN
ejpam-5935	222	4	.	.	PROPN
ejpam-5935	222	5	math	math	PROPN
ejpam-5935	222	6	,	,	PUNCT
ejpam-5935	222	7	18	18	NUM
ejpam-5935	222	8	(	(	PUNCT
ejpam-5935	222	9	2	2	NUM
ejpam-5935	222	10	)	)	PUNCT
ejpam-5935	222	11	(	(	PUNCT
ejpam-5935	222	12	2025	2025	NUM
ejpam-5935	222	13	)	)	PUNCT
ejpam-5935	222	14	,	,	PUNCT
ejpam-5935	222	15	5935	5935	NUM
ejpam-5935	222	16	8	8	NUM
ejpam-5935	222	17	of	of	ADP
ejpam-5935	222	18	10	10	NUM
ejpam-5935	222	19	remark	remark	NOUN
ejpam-5935	222	20	2	2	NUM
ejpam-5935	222	21	.	.	PUNCT
ejpam-5935	223	1	by	by	ADP
ejpam-5935	223	2	using	use	VERB
ejpam-5935	223	3	κ	κ	NOUN
ejpam-5935	223	4	in	in	ADP
ejpam-5935	223	5	the	the	DET
ejpam-5935	223	6	boundary	boundary	ADJ
ejpam-5935	223	7	condition	condition	NOUN
ejpam-5935	223	8	,	,	PUNCT
ejpam-5935	223	9	we	we	PRON
ejpam-5935	223	10	allow	allow	VERB
ejpam-5935	223	11	the	the	DET
ejpam-5935	223	12	possibility	possibility	NOUN
ejpam-5935	223	13	of	of	ADP
ejpam-5935	223	14	intermediate	intermediate	ADJ
ejpam-5935	223	15	boundary	boundary	ADJ
ejpam-5935	223	16	conditions	condition	NOUN
ejpam-5935	223	17	that	that	PRON
ejpam-5935	223	18	are	be	AUX
ejpam-5935	223	19	more	more	ADV
ejpam-5935	223	20	applicable	applicable	ADJ
ejpam-5935	223	21	in	in	ADP
ejpam-5935	223	22	many	many	ADJ
ejpam-5935	223	23	practical	practical	ADJ
ejpam-5935	223	24	scenarios	scenario	NOUN
ejpam-5935	223	25	.	.	PUNCT
ejpam-5935	224	1	instead	instead	ADV
ejpam-5935	224	2	of	of	ADP
ejpam-5935	224	3	assuming	assume	VERB
ejpam-5935	224	4	that	that	SCONJ
ejpam-5935	224	5	the	the	DET
ejpam-5935	224	6	system	system	NOUN
ejpam-5935	224	7	’s	’s	PART
ejpam-5935	224	8	behavior	behavior	NOUN
ejpam-5935	224	9	at	at	ADP
ejpam-5935	224	10	the	the	DET
ejpam-5935	224	11	endpoints	endpoint	NOUN
ejpam-5935	224	12	dictates	dictate	VERB
ejpam-5935	224	13	the	the	DET
ejpam-5935	224	14	solution	solution	NOUN
ejpam-5935	224	15	,	,	PUNCT
ejpam-5935	224	16	this	this	DET
ejpam-5935	224	17	formulation	formulation	NOUN
ejpam-5935	224	18	allows	allow	VERB
ejpam-5935	224	19	the	the	DET
ejpam-5935	224	20	solution	solution	NOUN
ejpam-5935	224	21	to	to	PART
ejpam-5935	224	22	be	be	AUX
ejpam-5935	224	23	influenced	influence	VERB
ejpam-5935	224	24	by	by	ADP
ejpam-5935	224	25	conditions	condition	NOUN
ejpam-5935	224	26	at	at	ADP
ejpam-5935	224	27	an	an	DET
ejpam-5935	224	28	interior	interior	ADJ
ejpam-5935	224	29	point	point	NOUN
ejpam-5935	224	30	κ	κ	NOUN
ejpam-5935	224	31	.	.	PUNCT
ejpam-5935	225	1	moreover	moreover	ADV
ejpam-5935	225	2	,	,	PUNCT
ejpam-5935	225	3	flexibility	flexibility	NOUN
ejpam-5935	225	4	in	in	ADP
ejpam-5935	225	5	dealing	deal	VERB
ejpam-5935	225	6	with	with	ADP
ejpam-5935	225	7	nonlocal	nonlocal	ADJ
ejpam-5935	225	8	or	or	CCONJ
ejpam-5935	225	9	nonlinear	nonlinear	ADJ
ejpam-5935	225	10	systems	system	NOUN
ejpam-5935	225	11	,	,	PUNCT
ejpam-5935	225	12	where	where	SCONJ
ejpam-5935	225	13	the	the	DET
ejpam-5935	225	14	condition	condition	NOUN
ejpam-5935	225	15	is	be	AUX
ejpam-5935	225	16	at	at	ADP
ejpam-5935	225	17	some	some	DET
ejpam-5935	225	18	intermediate	intermediate	ADJ
ejpam-5935	225	19	point	point	NOUN
ejpam-5935	225	20	(	(	PUNCT
ejpam-5935	225	21	rather	rather	ADV
ejpam-5935	225	22	than	than	ADP
ejpam-5935	225	23	at	at	ADP
ejpam-5935	225	24	the	the	DET
ejpam-5935	225	25	boundaries	boundary	NOUN
ejpam-5935	225	26	)	)	PUNCT
ejpam-5935	225	27	,	,	PUNCT
ejpam-5935	225	28	could	could	AUX
ejpam-5935	225	29	be	be	AUX
ejpam-5935	225	30	crucial	crucial	ADJ
ejpam-5935	225	31	for	for	ADP
ejpam-5935	225	32	the	the	DET
ejpam-5935	225	33	system	system	NOUN
ejpam-5935	225	34	’s	’s	PART
ejpam-5935	225	35	evolution	evolution	NOUN
ejpam-5935	225	36	,	,	PUNCT
ejpam-5935	225	37	providing	provide	VERB
ejpam-5935	225	38	accuracy	accuracy	NOUN
ejpam-5935	225	39	when	when	SCONJ
ejpam-5935	225	40	placing	place	VERB
ejpam-5935	225	41	boundary	boundary	ADJ
ejpam-5935	225	42	conditions	condition	NOUN
ejpam-5935	225	43	where	where	SCONJ
ejpam-5935	225	44	they	they	PRON
ejpam-5935	225	45	are	be	AUX
ejpam-5935	225	46	most	most	ADV
ejpam-5935	225	47	relevant	relevant	ADJ
ejpam-5935	225	48	.	.	PUNCT
ejpam-5935	226	1	4	4	X
ejpam-5935	226	2	.	.	NOUN
ejpam-5935	226	3	example	example	NOUN
ejpam-5935	226	4	fractional	fractional	ADJ
ejpam-5935	226	5	differential	differential	NOUN
ejpam-5935	226	6	equations	equation	NOUN
ejpam-5935	226	7	play	play	VERB
ejpam-5935	226	8	a	a	DET
ejpam-5935	226	9	major	major	ADJ
ejpam-5935	226	10	rule	rule	NOUN
ejpam-5935	226	11	in	in	ADP
ejpam-5935	226	12	many	many	ADJ
ejpam-5935	226	13	models	model	NOUN
ejpam-5935	226	14	such	such	ADJ
ejpam-5935	226	15	as	as	ADP
ejpam-5935	226	16	viscoelastic	viscoelastic	ADJ
ejpam-5935	226	17	material	material	NOUN
ejpam-5935	226	18	models	model	NOUN
ejpam-5935	226	19	where	where	SCONJ
ejpam-5935	226	20	the	the	DET
ejpam-5935	226	21	displacement	displacement	NOUN
ejpam-5935	226	22	ξ(ρ	ξ(ρ	PROPN
ejpam-5935	226	23	)	)	PUNCT
ejpam-5935	226	24	is	be	AUX
ejpam-5935	226	25	influenced	influence	VERB
ejpam-5935	226	26	by	by	ADP
ejpam-5935	226	27	both	both	PRON
ejpam-5935	226	28	local	local	ADJ
ejpam-5935	226	29	elasticity	elasticity	NOUN
ejpam-5935	226	30	and	and	CCONJ
ejpam-5935	226	31	nonlocal	nonlocal	ADJ
ejpam-5935	226	32	effects	effect	NOUN
ejpam-5935	226	33	.	.	PUNCT
ejpam-5935	227	1	moreover	moreover	ADV
ejpam-5935	227	2	,	,	PUNCT
ejpam-5935	227	3	some	some	DET
ejpam-5935	227	4	system	system	NOUN
ejpam-5935	227	5	exhibits	exhibit	VERB
ejpam-5935	227	6	typical	typical	ADJ
ejpam-5935	227	7	viscoelastic	viscoelastic	ADJ
ejpam-5935	227	8	behavior	behavior	NOUN
ejpam-5935	227	9	,	,	PUNCT
ejpam-5935	227	10	where	where	SCONJ
ejpam-5935	227	11	the	the	DET
ejpam-5935	227	12	elastic	elastic	ADJ
ejpam-5935	227	13	term	term	NOUN
ejpam-5935	227	14	dominates	dominate	VERB
ejpam-5935	227	15	at	at	ADP
ejpam-5935	227	16	higher	high	ADJ
ejpam-5935	227	17	frequencies	frequency	NOUN
ejpam-5935	227	18	,	,	PUNCT
ejpam-5935	227	19	and	and	CCONJ
ejpam-5935	227	20	the	the	DET
ejpam-5935	227	21	memory	memory	NOUN
ejpam-5935	227	22	(	(	PUNCT
ejpam-5935	227	23	nonlocal	nonlocal	ADJ
ejpam-5935	227	24	)	)	PUNCT
ejpam-5935	227	25	effects	effect	NOUN
ejpam-5935	227	26	become	become	VERB
ejpam-5935	227	27	more	more	ADV
ejpam-5935	227	28	significant	significant	ADJ
ejpam-5935	227	29	at	at	ADP
ejpam-5935	227	30	lower	low	ADJ
ejpam-5935	227	31	frequencies	frequency	NOUN
ejpam-5935	227	32	or	or	CCONJ
ejpam-5935	227	33	for	for	ADP
ejpam-5935	227	34	longer	long	ADJ
ejpam-5935	227	35	times	time	NOUN
ejpam-5935	227	36	.	.	PUNCT
ejpam-5935	228	1	the	the	DET
ejpam-5935	228	2	next	next	ADJ
ejpam-5935	228	3	examples	example	NOUN
ejpam-5935	228	4	show	show	VERB
ejpam-5935	228	5	how	how	SCONJ
ejpam-5935	228	6	fractional	fractional	ADJ
ejpam-5935	228	7	derivatives	derivative	NOUN
ejpam-5935	228	8	can	can	AUX
ejpam-5935	228	9	be	be	AUX
ejpam-5935	228	10	used	use	VERB
ejpam-5935	228	11	to	to	PART
ejpam-5935	228	12	describe	describe	VERB
ejpam-5935	228	13	systems	system	NOUN
ejpam-5935	228	14	with	with	ADP
ejpam-5935	228	15	memory	memory	NOUN
ejpam-5935	228	16	or	or	CCONJ
ejpam-5935	228	17	delayed	delayed	ADJ
ejpam-5935	228	18	response	response	NOUN
ejpam-5935	228	19	.	.	PUNCT
ejpam-5935	229	1	example	example	NOUN
ejpam-5935	230	1	1	1	NUM
ejpam-5935	230	2	.	.	PUNCT
ejpam-5935	230	3	{	{	PUNCT
ejpam-5935	230	4	cd	cd	NOUN
ejpam-5935	230	5	1	1	NUM
ejpam-5935	230	6	2	2	NUM
ejpam-5935	230	7	ξ(ρ	ξ(ρ	PROPN
ejpam-5935	230	8	)	)	PUNCT
ejpam-5935	230	9	=	=	SYM
ejpam-5935	230	10	γ(q+1	γ(q+1	ADJ
ejpam-5935	230	11	)	)	PUNCT
ejpam-5935	230	12	10	10	NUM
ejpam-5935	230	13	|ξ|	|ξ|	PROPN
ejpam-5935	230	14	1+|ξ|	1+|ξ|	NUM
ejpam-5935	230	15	+	+	CCONJ
ejpam-5935	230	16	ρν	ρν	PROPN
ejpam-5935	230	17	,	,	PUNCT
ejpam-5935	230	18	ρ	ρ	PROPN
ejpam-5935	230	19	∈	∈	PROPN
ejpam-5935	231	1	[	[	X
ejpam-5935	231	2	0	0	NUM
ejpam-5935	231	3	,	,	PUNCT
ejpam-5935	231	4	1	1	NUM
ejpam-5935	231	5	]	]	PUNCT
ejpam-5935	231	6	,	,	PUNCT
ejpam-5935	231	7	ν	ν	X
ejpam-5935	231	8	>	>	X
ejpam-5935	231	9	0	0	NUM
ejpam-5935	231	10	ξ(0	ξ(0	NOUN
ejpam-5935	231	11	)	)	PUNCT
ejpam-5935	231	12	=	=	PUNCT
ejpam-5935	232	1	α	α	X
ejpam-5935	232	2	̸=	̸=	PROPN
ejpam-5935	232	3	0	0	NUM
ejpam-5935	232	4	,	,	PUNCT
ejpam-5935	232	5	ξ(1	ξ(1	PROPN
ejpam-5935	232	6	)	)	PUNCT
ejpam-5935	232	7	=	=	PUNCT
ejpam-5935	233	1	β	β	X
ejpam-5935	233	2	̸=	̸=	PROPN
ejpam-5935	233	3	0	0	NUM
ejpam-5935	233	4	,	,	PUNCT
ejpam-5935	233	5	0	0	NUM
ejpam-5935	233	6	<	<	X
ejpam-5935	233	7	α	α	X
ejpam-5935	233	8	<	<	X
ejpam-5935	233	9	β	β	X
ejpam-5935	233	10	(	(	PUNCT
ejpam-5935	233	11	5	5	NUM
ejpam-5935	233	12	)	)	PUNCT
ejpam-5935	233	13	note	note	NOUN
ejpam-5935	233	14	that	that	SCONJ
ejpam-5935	233	15	,	,	PUNCT
ejpam-5935	233	16	ω	ω	PROPN
ejpam-5935	233	17	=	=	SYM
ejpam-5935	233	18	1	1	NUM
ejpam-5935	233	19	,	,	PUNCT
ejpam-5935	233	20	q	q	NOUN
ejpam-5935	233	21	=	=	NOUN
ejpam-5935	233	22	1	1	NUM
ejpam-5935	233	23	2	2	NUM
ejpam-5935	233	24	,	,	PUNCT
ejpam-5935	233	25	ξ(ρ	ξ(ρ	PROPN
ejpam-5935	233	26	,	,	PUNCT
ejpam-5935	233	27	ξ(ρ	ξ(ρ	PROPN
ejpam-5935	233	28	)	)	PUNCT
ejpam-5935	233	29	)	)	PUNCT
ejpam-5935	233	30	=	=	SYM
ejpam-5935	234	1	γ(q+1	γ(q+1	ADJ
ejpam-5935	234	2	)	)	PUNCT
ejpam-5935	234	3	10	10	NUM
ejpam-5935	234	4	|ξ|	|ξ|	PROPN
ejpam-5935	234	5	1+|ξ|	1+|ξ|	NUM
ejpam-5935	234	6	+	+	CCONJ
ejpam-5935	234	7	ρν	ρν	NOUN
ejpam-5935	234	8	,	,	PUNCT
ejpam-5935	234	9	and	and	CCONJ
ejpam-5935	234	10	∣∣ξ(ρ	∣∣ξ(ρ	PROPN
ejpam-5935	234	11	,	,	PUNCT
ejpam-5935	234	12	ξ1	ξ1	NOUN
ejpam-5935	234	13	)	)	PUNCT
ejpam-5935	234	14	−	−	PROPN
ejpam-5935	234	15	ξ(ρ	ξ(ρ	PROPN
ejpam-5935	234	16	,	,	PUNCT
ejpam-5935	234	17	ξ2	ξ2	NOUN
ejpam-5935	234	18	)	)	PUNCT
ejpam-5935	234	19	∣∣	∣∣	PROPN
ejpam-5935	235	1	≤	≤	ADV
ejpam-5935	235	2	√	√	NUM
ejpam-5935	235	3	π	π	PROPN
ejpam-5935	235	4	20	20	NUM
ejpam-5935	235	5	|ξ1	|ξ1	NOUN
ejpam-5935	235	6	−	−	NUM
ejpam-5935	235	7	ξ2|	ξ2|	NOUN
ejpam-5935	235	8	,	,	PUNCT
ejpam-5935	235	9	where	where	SCONJ
ejpam-5935	235	10	l	l	NOUN
ejpam-5935	235	11	=	=	PUNCT
ejpam-5935	235	12	√	√	PROPN
ejpam-5935	235	13	π	π	PROPN
ejpam-5935	235	14	20	20	NUM
ejpam-5935	235	15	.	.	PUNCT
ejpam-5935	236	1	also	also	ADV
ejpam-5935	236	2	,	,	PUNCT
ejpam-5935	236	3	2lωq	2lωq	PROPN
ejpam-5935	236	4	γ(q+1	γ(q+1	ADJ
ejpam-5935	236	5	)	)	PUNCT
ejpam-5935	236	6	=	=	SYM
ejpam-5935	237	1	1	1	NUM
ejpam-5935	237	2	5	5	NUM
ejpam-5935	237	3	<	<	SYM
ejpam-5935	237	4	1	1	NUM
ejpam-5935	237	5	.	.	PUNCT
ejpam-5935	237	6	therefore	therefore	ADV
ejpam-5935	237	7	,	,	PUNCT
ejpam-5935	237	8	theorem	theorem	ADJ
ejpam-5935	237	9	(	(	PUNCT
ejpam-5935	237	10	4	4	NUM
ejpam-5935	237	11	)	)	PUNCT
ejpam-5935	237	12	guarantee	guarantee	VERB
ejpam-5935	237	13	that	that	SCONJ
ejpam-5935	237	14	(	(	PUNCT
ejpam-5935	237	15	5	5	NUM
ejpam-5935	237	16	)	)	PUNCT
ejpam-5935	237	17	has	have	VERB
ejpam-5935	237	18	a	a	DET
ejpam-5935	237	19	unique	unique	ADJ
ejpam-5935	237	20	solution	solution	NOUN
ejpam-5935	237	21	in	in	ADP
ejpam-5935	237	22	[	[	X
ejpam-5935	237	23	0	0	NUM
ejpam-5935	237	24	,	,	PUNCT
ejpam-5935	237	25	1	1	NUM
ejpam-5935	237	26	]	]	PUNCT
ejpam-5935	237	27	.	.	PUNCT
ejpam-5935	238	1	example	example	NOUN
ejpam-5935	239	1	2	2	NUM
ejpam-5935	239	2	.	.	PUNCT
ejpam-5935	239	3	{	{	PUNCT
ejpam-5935	239	4	cd	cd	NOUN
ejpam-5935	239	5	1	1	NUM
ejpam-5935	239	6	2	2	NUM
ejpam-5935	239	7	ξ(ρ	ξ(ρ	PROPN
ejpam-5935	239	8	)	)	PUNCT
ejpam-5935	239	9	=	=	SYM
ejpam-5935	239	10	cos(ρ	cos(ρ	X
ejpam-5935	239	11	)	)	PUNCT
ejpam-5935	239	12	7	7	NUM
ejpam-5935	239	13	ξ(ρ	ξ(ρ	NOUN
ejpam-5935	239	14	)	)	PUNCT
ejpam-5935	239	15	,	,	PUNCT
ejpam-5935	239	16	ρ	ρ	PROPN
ejpam-5935	239	17	∈	∈	PROPN
ejpam-5935	240	1	[	[	X
ejpam-5935	240	2	0	0	NUM
ejpam-5935	240	3	,	,	PUNCT
ejpam-5935	240	4	1	1	NUM
ejpam-5935	240	5	]	]	PUNCT
ejpam-5935	240	6	,	,	PUNCT
ejpam-5935	240	7	ξ(12	ξ(12	PROPN
ejpam-5935	240	8	)	)	PUNCT
ejpam-5935	240	9	=	=	PUNCT
ejpam-5935	241	1	α	α	X
ejpam-5935	241	2	̸=	̸=	PROPN
ejpam-5935	241	3	0	0	NUM
ejpam-5935	241	4	,	,	PUNCT
ejpam-5935	241	5	ξ(12	ξ(12	NUM
ejpam-5935	241	6	)	)	PUNCT
ejpam-5935	241	7	=	=	PUNCT
ejpam-5935	242	1	β	β	X
ejpam-5935	242	2	̸=	̸=	PROPN
ejpam-5935	242	3	0	0	NUM
ejpam-5935	242	4	,	,	PUNCT
ejpam-5935	242	5	0	0	NUM
ejpam-5935	242	6	<	<	X
ejpam-5935	242	7	α	α	X
ejpam-5935	242	8	<	<	X
ejpam-5935	242	9	β	β	X
ejpam-5935	242	10	,	,	PUNCT
ejpam-5935	242	11	(	(	PUNCT
ejpam-5935	242	12	6	6	X
ejpam-5935	242	13	)	)	PUNCT
ejpam-5935	242	14	note	note	NOUN
ejpam-5935	242	15	that	that	SCONJ
ejpam-5935	242	16	,	,	PUNCT
ejpam-5935	242	17	ω	ω	PROPN
ejpam-5935	242	18	=	=	SYM
ejpam-5935	242	19	1	1	NUM
ejpam-5935	242	20	,	,	PUNCT
ejpam-5935	242	21	q	q	NOUN
ejpam-5935	242	22	=	=	NOUN
ejpam-5935	242	23	1	1	NUM
ejpam-5935	242	24	2	2	NUM
ejpam-5935	242	25	,	,	PUNCT
ejpam-5935	242	26	ξ(ρ	ξ(ρ	PROPN
ejpam-5935	242	27	,	,	PUNCT
ejpam-5935	242	28	ξ(ρ	ξ(ρ	NOUN
ejpam-5935	242	29	)	)	PUNCT
ejpam-5935	242	30	)	)	PUNCT
ejpam-5935	243	1	=	=	SYM
ejpam-5935	243	2	cos(ρ	cos(ρ	X
ejpam-5935	243	3	)	)	PUNCT
ejpam-5935	243	4	7	7	NUM
ejpam-5935	243	5	ξ(ρ	ξ(ρ	NOUN
ejpam-5935	243	6	)	)	PUNCT
ejpam-5935	243	7	,	,	PUNCT
ejpam-5935	243	8	|ξ(ρ	|ξ(ρ	PROPN
ejpam-5935	243	9	,	,	PUNCT
ejpam-5935	243	10	ξ1)−ξ(ρ	ξ1)−ξ(ρ	NOUN
ejpam-5935	243	11	,	,	PUNCT
ejpam-5935	243	12	ξ2	ξ2	NOUN
ejpam-5935	243	13	)	)	PUNCT
ejpam-5935	243	14	∣∣	∣∣	NUM
ejpam-5935	243	15	≤	≤	NUM
ejpam-5935	243	16	1	1	NUM
ejpam-5935	243	17	7	7	NUM
ejpam-5935	243	18	|ξ1−ξ2|	|ξ1−ξ2|	NOUN
ejpam-5935	243	19	,	,	PUNCT
ejpam-5935	243	20	where	where	SCONJ
ejpam-5935	243	21	l	l	NOUN
ejpam-5935	243	22	=	=	NOUN
ejpam-5935	243	23	1	1	NUM
ejpam-5935	243	24	7	7	NUM
ejpam-5935	243	25	,	,	PUNCT
ejpam-5935	243	26	and	and	CCONJ
ejpam-5935	243	27	∣∣ξ(ρ	∣∣ξ(ρ	PROPN
ejpam-5935	243	28	,	,	PUNCT
ejpam-5935	243	29	ξ(ρ))∣∣	ξ(ρ))∣∣	PROPN
ejpam-5935	243	30	≤	≤	ADV
ejpam-5935	243	31	1	1	NUM
ejpam-5935	243	32	7	7	NUM
ejpam-5935	243	33	∣∣ξ(ρ)∣∣.	∣∣ξ(ρ)∣∣.	PROPN
ejpam-5935	243	34	also	also	ADV
ejpam-5935	243	35	,	,	PUNCT
ejpam-5935	243	36	lωq	lωq	PROPN
ejpam-5935	243	37	γ(q+1	γ(q+1	PROPN
ejpam-5935	243	38	)	)	PUNCT
ejpam-5935	243	39	=	=	SYM
ejpam-5935	244	1	2	2	NUM
ejpam-5935	244	2	7	7	NUM
ejpam-5935	244	3	√	√	PROPN
ejpam-5935	244	4	π	π	PROPN
ejpam-5935	244	5	≈	≈	PROPN
ejpam-5935	244	6	0.161228	0.161228	PROPN
ejpam-5935	244	7	<	<	X
ejpam-5935	244	8	1	1	NUM
ejpam-5935	244	9	.	.	PUNCT
ejpam-5935	244	10	therefore	therefore	ADV
ejpam-5935	244	11	,	,	PUNCT
ejpam-5935	244	12	theorem	theorem	ADJ
ejpam-5935	244	13	(	(	PUNCT
ejpam-5935	244	14	3	3	NUM
ejpam-5935	244	15	)	)	PUNCT
ejpam-5935	244	16	guarantee	guarantee	VERB
ejpam-5935	244	17	that	that	SCONJ
ejpam-5935	244	18	(	(	PUNCT
ejpam-5935	244	19	6	6	NUM
ejpam-5935	244	20	)	)	PUNCT
ejpam-5935	244	21	has	have	VERB
ejpam-5935	244	22	at	at	ADV
ejpam-5935	244	23	least	least	ADV
ejpam-5935	244	24	one	one	NUM
ejpam-5935	244	25	solution	solution	NOUN
ejpam-5935	244	26	in	in	ADP
ejpam-5935	244	27	[	[	X
ejpam-5935	244	28	0	0	NUM
ejpam-5935	244	29	,	,	PUNCT
ejpam-5935	244	30	1	1	NUM
ejpam-5935	244	31	]	]	PUNCT
ejpam-5935	244	32	.	.	PUNCT
ejpam-5935	245	1	5	5	X
ejpam-5935	245	2	.	.	X
ejpam-5935	245	3	conclusions	conclusion	NOUN
ejpam-5935	245	4	in	in	ADP
ejpam-5935	245	5	this	this	DET
ejpam-5935	245	6	paper	paper	NOUN
ejpam-5935	245	7	,	,	PUNCT
ejpam-5935	245	8	we	we	PRON
ejpam-5935	245	9	investigate	investigate	VERB
ejpam-5935	245	10	a	a	DET
ejpam-5935	245	11	boundary	boundary	ADJ
ejpam-5935	245	12	value	value	NOUN
ejpam-5935	245	13	problem	problem	NOUN
ejpam-5935	245	14	of	of	ADP
ejpam-5935	245	15	an	an	DET
ejpam-5935	245	16	intermediate	intermediate	ADJ
ejpam-5935	245	17	point	point	NOUN
ejpam-5935	245	18	.	.	PUNCT
ejpam-5935	246	1	it	it	PRON
ejpam-5935	246	2	has	have	AUX
ejpam-5935	246	3	been	be	AUX
ejpam-5935	246	4	shown	show	VERB
ejpam-5935	246	5	that	that	SCONJ
ejpam-5935	246	6	including	include	VERB
ejpam-5935	246	7	additional	additional	ADJ
ejpam-5935	246	8	terms	term	NOUN
ejpam-5935	246	9	in	in	ADP
ejpam-5935	246	10	the	the	DET
ejpam-5935	246	11	integral	integral	ADJ
ejpam-5935	246	12	solutions	solution	NOUN
ejpam-5935	246	13	significantly	significantly	ADV
ejpam-5935	246	14	affects	affect	VERB
ejpam-5935	246	15	the	the	DET
ejpam-5935	246	16	behavior	behavior	NOUN
ejpam-5935	246	17	of	of	ADP
ejpam-5935	246	18	the	the	DET
ejpam-5935	246	19	fractional	fractional	ADJ
ejpam-5935	246	20	-	-	PUNCT
ejpam-5935	246	21	order	order	NOUN
ejpam-5935	246	22	problems	problem	NOUN
ejpam-5935	246	23	under	under	ADP
ejpam-5935	246	24	consideration	consideration	NOUN
ejpam-5935	246	25	.	.	PUNCT
ejpam-5935	247	1	furthermore	furthermore	ADV
ejpam-5935	247	2	,	,	PUNCT
ejpam-5935	247	3	the	the	DET
ejpam-5935	247	4	results	result	NOUN
ejpam-5935	247	5	presented	present	VERB
ejpam-5935	247	6	here	here	ADV
ejpam-5935	247	7	are	be	AUX
ejpam-5935	247	8	adaptable	adaptable	ADJ
ejpam-5935	247	9	,	,	PUNCT
ejpam-5935	247	10	particularly	particularly	ADV
ejpam-5935	247	11	in	in	ADP
ejpam-5935	247	12	scenarios	scenario	NOUN
ejpam-5935	247	13	where	where	SCONJ
ejpam-5935	247	14	there	there	PRON
ejpam-5935	247	15	is	be	VERB
ejpam-5935	247	16	a	a	DET
ejpam-5935	247	17	shift	shift	NOUN
ejpam-5935	247	18	in	in	ADP
ejpam-5935	247	19	the	the	DET
ejpam-5935	247	20	location	location	NOUN
ejpam-5935	247	21	of	of	ADP
ejpam-5935	247	22	the	the	DET
ejpam-5935	247	23	boundary	boundary	ADJ
ejpam-5935	247	24	phenomena	phenomenon	NOUN
ejpam-5935	247	25	near	near	ADP
ejpam-5935	247	26	the	the	DET
ejpam-5935	247	27	left	left	ADJ
ejpam-5935	247	28	endpoint	endpoint	NOUN
ejpam-5935	247	29	of	of	ADP
ejpam-5935	247	30	the	the	DET
ejpam-5935	247	31	interval	interval	NOUN
ejpam-5935	247	32	[	[	X
ejpam-5935	247	33	0	0	NUM
ejpam-5935	247	34	,	,	PUNCT
ejpam-5935	247	35	ω	ω	NOUN
ejpam-5935	247	36	]	]	PUNCT
ejpam-5935	247	37	with	with	ADP
ejpam-5935	247	38	κ	κ	PROPN
ejpam-5935	247	39	<	<	X
ejpam-5935	247	40	ω	ω	PROPN
ejpam-5935	247	41	.	.	PUNCT
ejpam-5935	248	1	notably	notably	ADV
ejpam-5935	248	2	,	,	PUNCT
ejpam-5935	248	3	it	it	PRON
ejpam-5935	248	4	is	be	AUX
ejpam-5935	248	5	demonstrated	demonstrate	VERB
ejpam-5935	248	6	that	that	SCONJ
ejpam-5935	248	7	the	the	DET
ejpam-5935	248	8	classical	classical	ADJ
ejpam-5935	248	9	boundary	boundary	ADJ
ejpam-5935	248	10	conditions	condition	NOUN
ejpam-5935	248	11	in	in	ADP
ejpam-5935	248	12	[	[	X
ejpam-5935	248	13	13	13	NUM
ejpam-5935	248	14	]	]	PUNCT
ejpam-5935	248	15	s.	s.	PROPN
ejpam-5935	248	16	f.	f.	PROPN
ejpam-5935	248	17	aljurbua	aljurbua	PROPN
ejpam-5935	248	18	et	et	PROPN
ejpam-5935	248	19	al	al	PROPN
ejpam-5935	248	20	.	.	PUNCT
ejpam-5935	248	21	/	/	SYM
ejpam-5935	248	22	eur	eur	PROPN
ejpam-5935	248	23	.	.	PUNCT
ejpam-5935	249	1	j.	j.	PROPN
ejpam-5935	249	2	pure	pure	PROPN
ejpam-5935	249	3	appl	appl	PROPN
ejpam-5935	249	4	.	.	PROPN
ejpam-5935	249	5	math	math	PROPN
ejpam-5935	249	6	,	,	PUNCT
ejpam-5935	249	7	18	18	NUM
ejpam-5935	249	8	(	(	PUNCT
ejpam-5935	249	9	2	2	NUM
ejpam-5935	249	10	)	)	PUNCT
ejpam-5935	249	11	(	(	PUNCT
ejpam-5935	249	12	2025	2025	NUM
ejpam-5935	249	13	)	)	PUNCT
ejpam-5935	249	14	,	,	PUNCT
ejpam-5935	249	15	5935	5935	NUM
ejpam-5935	249	16	9	9	NUM
ejpam-5935	249	17	of	of	ADP
ejpam-5935	249	18	10	10	NUM
ejpam-5935	249	19	can	can	AUX
ejpam-5935	249	20	be	be	AUX
ejpam-5935	249	21	derived	derive	VERB
ejpam-5935	249	22	from	from	ADP
ejpam-5935	249	23	our	our	PRON
ejpam-5935	249	24	results	result	NOUN
ejpam-5935	249	25	as	as	ADP
ejpam-5935	249	26	κ	κ	NOUN
ejpam-5935	249	27	approaches	approach	NOUN
ejpam-5935	249	28	0	0	NUM
ejpam-5935	250	1	+	+	X
ejpam-5935	250	2	.	.	PUNCT
ejpam-5935	250	3	additionally	additionally	ADV
ejpam-5935	250	4	,	,	PUNCT
ejpam-5935	250	5	the	the	DET
ejpam-5935	250	6	results	result	NOUN
ejpam-5935	250	7	presented	present	VERB
ejpam-5935	250	8	in	in	ADP
ejpam-5935	250	9	section	section	NOUN
ejpam-5935	250	10	3	3	NUM
ejpam-5935	250	11	,	,	PUNCT
ejpam-5935	250	12	which	which	PRON
ejpam-5935	250	13	focus	focus	VERB
ejpam-5935	250	14	on	on	ADP
ejpam-5935	250	15	fractional	fractional	ADJ
ejpam-5935	250	16	differential	differential	ADJ
ejpam-5935	250	17	equations	equation	NOUN
ejpam-5935	250	18	in	in	ADP
ejpam-5935	250	19	the	the	DET
ejpam-5935	250	20	limit	limit	NOUN
ejpam-5935	250	21	κ	κ	X
ejpam-5935	250	22	→	→	SYM
ejpam-5935	250	23	0	0	NUM
ejpam-5935	250	24	+	+	ADJ
ejpam-5935	250	25	,	,	PUNCT
ejpam-5935	250	26	are	be	AUX
ejpam-5935	250	27	novel	novel	ADJ
ejpam-5935	250	28	contributions	contribution	NOUN
ejpam-5935	250	29	to	to	ADP
ejpam-5935	250	30	the	the	DET
ejpam-5935	250	31	field	field	NOUN
ejpam-5935	250	32	.	.	PUNCT
ejpam-5935	251	1	ultimately	ultimately	ADV
ejpam-5935	251	2	,	,	PUNCT
ejpam-5935	251	3	the	the	DET
ejpam-5935	251	4	nonlocal	nonlocal	ADJ
ejpam-5935	251	5	characteristics	characteristic	NOUN
ejpam-5935	251	6	of	of	ADP
ejpam-5935	251	7	the	the	DET
ejpam-5935	251	8	classical	classical	ADJ
ejpam-5935	251	9	boundary	boundary	ADJ
ejpam-5935	251	10	conditions	condition	NOUN
ejpam-5935	251	11	allow	allow	VERB
ejpam-5935	251	12	the	the	DET
ejpam-5935	251	13	boundary	boundary	ADJ
ejpam-5935	251	14	phenomena	phenomenon	NOUN
ejpam-5935	251	15	to	to	PART
ejpam-5935	251	16	occur	occur	VERB
ejpam-5935	251	17	at	at	ADP
ejpam-5935	251	18	any	any	DET
ejpam-5935	251	19	intermediate	intermediate	ADJ
ejpam-5935	251	20	position	position	NOUN
ejpam-5935	251	21	within	within	ADP
ejpam-5935	251	22	the	the	DET
ejpam-5935	251	23	specified	specified	ADJ
ejpam-5935	251	24	interval	interval	NOUN
ejpam-5935	251	25	.	.	PUNCT
ejpam-5935	252	1	acknowledgements	acknowledgement	NOUN
ejpam-5935	252	2	the	the	DET
ejpam-5935	252	3	researchers	researcher	NOUN
ejpam-5935	252	4	would	would	AUX
ejpam-5935	252	5	like	like	VERB
ejpam-5935	252	6	to	to	PART
ejpam-5935	252	7	thank	thank	VERB
ejpam-5935	252	8	the	the	DET
ejpam-5935	252	9	college	college	NOUN
ejpam-5935	252	10	of	of	ADP
ejpam-5935	252	11	science	science	NOUN
ejpam-5935	252	12	and	and	CCONJ
ejpam-5935	252	13	the	the	DET
ejpam-5935	252	14	department	department	NOUN
ejpam-5935	252	15	of	of	ADP
ejpam-5935	252	16	mathematics	mathematics	PROPN
ejpam-5935	252	17	at	at	ADP
ejpam-5935	252	18	qassim	qassim	PROPN
ejpam-5935	252	19	university	university	PROPN
ejpam-5935	252	20	for	for	ADP
ejpam-5935	252	21	their	their	PRON
ejpam-5935	252	22	support	support	NOUN
ejpam-5935	252	23	in	in	ADP
ejpam-5935	252	24	the	the	DET
ejpam-5935	252	25	creation	creation	NOUN
ejpam-5935	252	26	of	of	ADP
ejpam-5935	252	27	this	this	DET
ejpam-5935	252	28	work	work	NOUN
ejpam-5935	252	29	.	.	PUNCT
ejpam-5935	253	1	author	author	NOUN
ejpam-5935	253	2	contributions	contribution	NOUN
ejpam-5935	253	3	methodology	methodology	NOUN
ejpam-5935	253	4	:	:	PUNCT
ejpam-5935	253	5	s.	s.	PROPN
ejpam-5935	253	6	aljurbua	aljurbua	VERB
ejpam-5935	253	7	first	first	ADJ
ejpam-5935	253	8	draft	draft	NOUN
ejpam-5935	253	9	:	:	PUNCT
ejpam-5935	253	10	a.	a.	PROPN
ejpam-5935	253	11	alluhayb	alluhayb	PROPN
ejpam-5935	253	12	writing	writing	NOUN
ejpam-5935	253	13	–	–	PUNCT
ejpam-5935	253	14	review	review	NOUN
ejpam-5935	253	15	&	&	CCONJ
ejpam-5935	253	16	editing	editing	PROPN
ejpam-5935	253	17	:	:	PUNCT
ejpam-5935	253	18	r.	r.	PROPN
ejpam-5935	253	19	alashwan	alashwan	PROPN
ejpam-5935	253	20	,	,	PUNCT
ejpam-5935	253	21	d.	d.	PROPN
ejpam-5935	253	22	alharbi	alharbi	PROPN
ejpam-5935	253	23	,	,	PUNCT
ejpam-5935	253	24	n.	n.	NOUN
ejpam-5935	253	25	alharbi	alharbi	PROPN
ejpam-5935	253	26	,	,	PUNCT
ejpam-5935	253	27	w.	w.	PROPN
ejpam-5935	253	28	alrawji	alrawji	PROPN
ejpam-5935	253	29	,	,	PUNCT
ejpam-5935	253	30	n.	n.	NOUN
ejpam-5935	253	31	alharbi	alharbi	PROPN
ejpam-5935	253	32	,	,	PUNCT
ejpam-5935	253	33	m.	m.	NOUN
ejpam-5935	253	34	saad	saad	PROPN
ejpam-5935	253	35	,	,	PUNCT
ejpam-5935	253	36	r.	r.	PROPN
ejpam-5935	253	37	almutairi	almutairi	PROPN
ejpam-5935	253	38	,	,	PUNCT
ejpam-5935	253	39	r.	r.	PROPN
ejpam-5935	253	40	alharbi	alharbi	PROPN
ejpam-5935	253	41	,	,	PUNCT
ejpam-5935	253	42	a.	a.	NOUN
ejpam-5935	253	43	alrashidi	alrashidi	NOUN
ejpam-5935	253	44	,	,	PUNCT
ejpam-5935	253	45	m.	m.	NOUN
ejpam-5935	253	46	alrashidi	alrashidi	NOUN
ejpam-5935	253	47	,	,	PUNCT
ejpam-5935	253	48	n.	n.	PROPN
ejpam-5935	253	49	alfuraih	alfuraih	PROPN
ejpam-5935	253	50	supervision	supervision	NOUN
ejpam-5935	253	51	:	:	PUNCT
ejpam-5935	253	52	dr	dr	PROPN
ejpam-5935	253	53	.	.	PROPN
ejpam-5935	253	54	s.	s.	PROPN
ejpam-5935	253	55	aljurbua	aljurbua	PROPN
ejpam-5935	253	56	and	and	CCONJ
ejpam-5935	253	57	dr	dr	PROPN
ejpam-5935	253	58	.	.	PROPN
ejpam-5935	253	59	a.	a.	PROPN
ejpam-5935	253	60	alluhayb	alluhayb	PROPN
ejpam-5935	253	61	references	reference	NOUN
ejpam-5935	253	62	[	[	X
ejpam-5935	253	63	1	1	NUM
ejpam-5935	253	64	]	]	PUNCT
ejpam-5935	253	65	i.	i.	NOUN
ejpam-5935	253	66	podlubny	podlubny	PROPN
ejpam-5935	253	67	.	.	PUNCT
ejpam-5935	254	1	fractional	fractional	ADJ
ejpam-5935	254	2	differential	differential	ADJ
ejpam-5935	254	3	equations	equation	NOUN
ejpam-5935	254	4	,	,	PUNCT
ejpam-5935	254	5	volume	volume	NOUN
ejpam-5935	254	6	198	198	NUM
ejpam-5935	254	7	of	of	ADP
ejpam-5935	254	8	mathematics	mathematic	NOUN
ejpam-5935	254	9	in	in	ADP
ejpam-5935	254	10	science	science	NOUN
ejpam-5935	254	11	and	and	CCONJ
ejpam-5935	254	12	engineering	engineering	NOUN
ejpam-5935	254	13	.	.	PUNCT
ejpam-5935	255	1	elsevier	elsevier	PROPN
ejpam-5935	255	2	,	,	PUNCT
ejpam-5935	255	3	san	san	PROPN
ejpam-5935	255	4	diego	diego	PROPN
ejpam-5935	255	5	,	,	PUNCT
ejpam-5935	255	6	1999	1999	NUM
ejpam-5935	255	7	.	.	PUNCT
ejpam-5935	256	1	[	[	X
ejpam-5935	256	2	2	2	X
ejpam-5935	256	3	]	]	PUNCT
ejpam-5935	256	4	s.	s.	PROPN
ejpam-5935	256	5	abbas	abbas	PROPN
ejpam-5935	256	6	,	,	PUNCT
ejpam-5935	256	7	m.	m.	NOUN
ejpam-5935	256	8	benchohra	benchohra	NOUN
ejpam-5935	256	9	,	,	PUNCT
ejpam-5935	256	10	and	and	CCONJ
ejpam-5935	256	11	g.	g.	PROPN
ejpam-5935	256	12	m.	m.	NOUN
ejpam-5935	256	13	n’guerekata	n’guerekata	PROPN
ejpam-5935	256	14	.	.	PUNCT
ejpam-5935	257	1	topics	topic	NOUN
ejpam-5935	257	2	in	in	ADP
ejpam-5935	257	3	fractional	fractional	ADJ
ejpam-5935	257	4	differential	differential	ADJ
ejpam-5935	257	5	equations	equation	NOUN
ejpam-5935	257	6	.	.	PUNCT
ejpam-5935	258	1	springer	springer	NOUN
ejpam-5935	258	2	,	,	PUNCT
ejpam-5935	258	3	new	new	PROPN
ejpam-5935	258	4	york	york	PROPN
ejpam-5935	258	5	,	,	PUNCT
ejpam-5935	258	6	2012	2012	NUM
ejpam-5935	258	7	.	.	PUNCT
ejpam-5935	259	1	[	[	X
ejpam-5935	259	2	3	3	X
ejpam-5935	259	3	]	]	X
ejpam-5935	259	4	k.	k.	PROPN
ejpam-5935	259	5	oldham	oldham	PROPN
ejpam-5935	259	6	and	and	CCONJ
ejpam-5935	259	7	j.	j.	PROPN
ejpam-5935	259	8	spanier	spanier	PROPN
ejpam-5935	259	9	.	.	PUNCT
ejpam-5935	260	1	the	the	DET
ejpam-5935	260	2	fractional	fractional	ADJ
ejpam-5935	260	3	calculus	calculus	NOUN
ejpam-5935	260	4	:	:	PUNCT
ejpam-5935	260	5	theory	theory	NOUN
ejpam-5935	260	6	and	and	CCONJ
ejpam-5935	260	7	applications	application	NOUN
ejpam-5935	260	8	of	of	ADP
ejpam-5935	260	9	differentiation	differentiation	NOUN
ejpam-5935	260	10	and	and	CCONJ
ejpam-5935	260	11	integration	integration	NOUN
ejpam-5935	260	12	to	to	ADP
ejpam-5935	260	13	arbitrary	arbitrary	ADJ
ejpam-5935	260	14	order	order	NOUN
ejpam-5935	260	15	.	.	PUNCT
ejpam-5935	261	1	elsevier	elsevier	NOUN
ejpam-5935	261	2	,	,	PUNCT
ejpam-5935	261	3	new	new	PROPN
ejpam-5935	261	4	york	york	PROPN
ejpam-5935	261	5	,	,	PUNCT
ejpam-5935	261	6	1974	1974	NUM
ejpam-5935	261	7	.	.	PUNCT
ejpam-5935	262	1	[	[	X
ejpam-5935	262	2	4	4	NUM
ejpam-5935	262	3	]	]	PUNCT
ejpam-5935	262	4	r.	r.	PROPN
ejpam-5935	262	5	metzler	metzler	PROPN
ejpam-5935	262	6	and	and	CCONJ
ejpam-5935	262	7	j.	j.	PROPN
ejpam-5935	262	8	klafter	klafter	PROPN
ejpam-5935	262	9	.	.	PUNCT
ejpam-5935	263	1	the	the	DET
ejpam-5935	263	2	random	random	ADJ
ejpam-5935	263	3	walk	walk	NOUN
ejpam-5935	263	4	’s	’s	PART
ejpam-5935	263	5	guide	guide	NOUN
ejpam-5935	263	6	to	to	ADP
ejpam-5935	263	7	anomalous	anomalous	ADJ
ejpam-5935	263	8	diffusion	diffusion	NOUN
ejpam-5935	263	9	:	:	PUNCT
ejpam-5935	263	10	a	a	DET
ejpam-5935	263	11	fractional	fractional	ADJ
ejpam-5935	263	12	dynamics	dynamic	NOUN
ejpam-5935	263	13	approach	approach	NOUN
ejpam-5935	263	14	.	.	PUNCT
ejpam-5935	264	1	physics	physics	NOUN
ejpam-5935	264	2	reports	report	NOUN
ejpam-5935	264	3	,	,	PUNCT
ejpam-5935	264	4	339(1):1–77	339(1):1–77	NUM
ejpam-5935	264	5	,	,	PUNCT
ejpam-5935	264	6	2000	2000	NUM
ejpam-5935	264	7	.	.	PUNCT
ejpam-5935	265	1	[	[	X
ejpam-5935	265	2	5	5	NUM
ejpam-5935	265	3	]	]	PUNCT
ejpam-5935	265	4	m.	m.	PROPN
ejpam-5935	265	5	richard	richard	PROPN
ejpam-5935	265	6	.	.	PUNCT
ejpam-5935	266	1	fractional	fractional	ADJ
ejpam-5935	266	2	calculus	calculus	NOUN
ejpam-5935	266	3	in	in	ADP
ejpam-5935	266	4	bioengineering	bioengineering	NOUN
ejpam-5935	266	5	.	.	PUNCT
ejpam-5935	267	1	critical	critical	ADJ
ejpam-5935	267	2	reviews	review	NOUN
ejpam-5935	267	3	in	in	ADP
ejpam-5935	267	4	biomedical	biomedical	ADJ
ejpam-5935	267	5	engineering	engineering	NOUN
ejpam-5935	267	6	,	,	PUNCT
ejpam-5935	267	7	32(1):1–92	32(1):1–92	NUM
ejpam-5935	267	8	,	,	PUNCT
ejpam-5935	267	9	2004	2004	NUM
ejpam-5935	267	10	.	.	PUNCT
ejpam-5935	268	1	[	[	X
ejpam-5935	268	2	6	6	NUM
ejpam-5935	268	3	]	]	X
ejpam-5935	268	4	h.	h.	PROPN
ejpam-5935	268	5	ming	ming	PROPN
ejpam-5935	268	6	,	,	PUNCT
ejpam-5935	268	7	j.	j.	PROPN
ejpam-5935	268	8	wang	wang	PROPN
ejpam-5935	268	9	,	,	PUNCT
ejpam-5935	268	10	and	and	CCONJ
ejpam-5935	268	11	m.	m.	NOUN
ejpam-5935	268	12	feckan	feckan	PROPN
ejpam-5935	268	13	.	.	PUNCT
ejpam-5935	269	1	the	the	DET
ejpam-5935	269	2	application	application	NOUN
ejpam-5935	269	3	of	of	ADP
ejpam-5935	269	4	fractional	fractional	ADJ
ejpam-5935	269	5	calculus	calculus	NOUN
ejpam-5935	269	6	in	in	ADP
ejpam-5935	269	7	chinese	chinese	ADJ
ejpam-5935	269	8	economic	economic	ADJ
ejpam-5935	269	9	growth	growth	NOUN
ejpam-5935	269	10	models	model	NOUN
ejpam-5935	269	11	.	.	PUNCT
ejpam-5935	270	1	mathematics	mathematic	NOUN
ejpam-5935	270	2	,	,	PUNCT
ejpam-5935	270	3	7(8):665	7(8):665	NUM
ejpam-5935	270	4	,	,	PUNCT
ejpam-5935	270	5	2019	2019	NUM
ejpam-5935	270	6	.	.	PUNCT
ejpam-5935	271	1	[	[	X
ejpam-5935	271	2	7	7	X
ejpam-5935	271	3	]	]	X
ejpam-5935	271	4	s.	s.	PROPN
ejpam-5935	271	5	samko	samko	PROPN
ejpam-5935	271	6	,	,	PUNCT
ejpam-5935	271	7	a.	a.	NOUN
ejpam-5935	271	8	kilbas	kilbas	PROPN
ejpam-5935	271	9	,	,	PUNCT
ejpam-5935	271	10	and	and	CCONJ
ejpam-5935	271	11	o.	o.	PROPN
ejpam-5935	271	12	marichev	marichev	PROPN
ejpam-5935	271	13	.	.	PUNCT
ejpam-5935	272	1	fractional	fractional	ADJ
ejpam-5935	272	2	integrals	integral	NOUN
ejpam-5935	272	3	and	and	CCONJ
ejpam-5935	272	4	derivatives	derivative	NOUN
ejpam-5935	272	5	:	:	PUNCT
ejpam-5935	272	6	theory	theory	NOUN
ejpam-5935	272	7	and	and	CCONJ
ejpam-5935	272	8	applications	application	NOUN
ejpam-5935	272	9	.	.	PUNCT
ejpam-5935	273	1	gordon	gordon	PROPN
ejpam-5935	273	2	and	and	CCONJ
ejpam-5935	273	3	breach	breach	NOUN
ejpam-5935	273	4	,	,	PUNCT
ejpam-5935	273	5	yverdon	yverdon	PROPN
ejpam-5935	273	6	,	,	PUNCT
ejpam-5935	273	7	1993	1993	NUM
ejpam-5935	273	8	.	.	PUNCT
ejpam-5935	274	1	[	[	X
ejpam-5935	274	2	8	8	NUM
ejpam-5935	274	3	]	]	X
ejpam-5935	274	4	s.	s.	PROPN
ejpam-5935	274	5	aljurbua	aljurbua	PROPN
ejpam-5935	274	6	.	.	PUNCT
ejpam-5935	275	1	generalized	generalized	ADJ
ejpam-5935	275	2	existence	existence	NOUN
ejpam-5935	275	3	results	result	NOUN
ejpam-5935	275	4	for	for	ADP
ejpam-5935	275	5	solutions	solution	NOUN
ejpam-5935	275	6	of	of	ADP
ejpam-5935	275	7	nonlinear	nonlinear	ADJ
ejpam-5935	275	8	fractional	fractional	ADJ
ejpam-5935	275	9	differential	differential	ADJ
ejpam-5935	275	10	equations	equation	NOUN
ejpam-5935	275	11	with	with	ADP
ejpam-5935	275	12	nonlocal	nonlocal	ADJ
ejpam-5935	275	13	boundary	boundary	ADJ
ejpam-5935	275	14	conditions	condition	NOUN
ejpam-5935	275	15	.	.	PUNCT
ejpam-5935	276	1	ain	ain	PROPN
ejpam-5935	276	2	shams	sham	VERB
ejpam-5935	276	3	engineering	engineering	NOUN
ejpam-5935	276	4	journal	journal	NOUN
ejpam-5935	276	5	,	,	PUNCT
ejpam-5935	276	6	15(11):103035	15(11):103035	NUM
ejpam-5935	276	7	,	,	PUNCT
ejpam-5935	276	8	2024	2024	NUM
ejpam-5935	276	9	.	.	PUNCT
ejpam-5935	277	1	[	[	X
ejpam-5935	277	2	9	9	NUM
ejpam-5935	277	3	]	]	X
ejpam-5935	277	4	h.	h.	PROPN
ejpam-5935	277	5	hasanen	hasanen	PROPN
ejpam-5935	277	6	and	and	CCONJ
ejpam-5935	277	7	s.	s.	PROPN
ejpam-5935	277	8	aljurbua	aljurbua	PROPN
ejpam-5935	277	9	.	.	PUNCT
ejpam-5935	278	1	solving	solve	VERB
ejpam-5935	278	2	fractional	fractional	ADJ
ejpam-5935	278	3	random	random	ADJ
ejpam-5935	278	4	differential	differential	NOUN
ejpam-5935	278	5	equations	equation	NOUN
ejpam-5935	278	6	by	by	ADP
ejpam-5935	278	7	using	use	VERB
ejpam-5935	278	8	fixed	fix	VERB
ejpam-5935	278	9	point	point	NOUN
ejpam-5935	278	10	methodologies	methodology	NOUN
ejpam-5935	278	11	under	under	ADP
ejpam-5935	278	12	mild	mild	ADJ
ejpam-5935	278	13	boundary	boundary	ADJ
ejpam-5935	278	14	conditions	condition	NOUN
ejpam-5935	278	15	.	.	PUNCT
ejpam-5935	279	1	fractal	fractal	ADJ
ejpam-5935	279	2	and	and	CCONJ
ejpam-5935	279	3	fractional	fractional	ADJ
ejpam-5935	279	4	,	,	PUNCT
ejpam-5935	279	5	8(7):384	8(7):384	NUM
ejpam-5935	279	6	,	,	PUNCT
ejpam-5935	279	7	2024	2024	NUM
ejpam-5935	279	8	.	.	PUNCT
ejpam-5935	280	1	[	[	X
ejpam-5935	280	2	10	10	NUM
ejpam-5935	280	3	]	]	X
ejpam-5935	280	4	s.	s.	PROPN
ejpam-5935	280	5	aljurbua	aljurbua	PROPN
ejpam-5935	280	6	.	.	PROPN
ejpam-5935	281	1	extended	extended	ADJ
ejpam-5935	281	2	existence	existence	NOUN
ejpam-5935	281	3	results	result	NOUN
ejpam-5935	281	4	of	of	ADP
ejpam-5935	281	5	solutions	solution	NOUN
ejpam-5935	281	6	for	for	ADP
ejpam-5935	281	7	fdes	fde	NOUN
ejpam-5935	281	8	of	of	ADP
ejpam-5935	281	9	order	order	NOUN
ejpam-5935	281	10	1	1	NUM
ejpam-5935	281	11	<	<	X
ejpam-5935	281	12	γ	γ	X
ejpam-5935	281	13	≤	≤	ADJ
ejpam-5935	281	14	2	2	NUM
ejpam-5935	281	15	.	.	PUNCT
ejpam-5935	281	16	aims	aim	VERB
ejpam-5935	281	17	mathematics	mathematic	NOUN
ejpam-5935	281	18	,	,	PUNCT
ejpam-5935	281	19	9(6):13077–13086	9(6):13077–13086	NUM
ejpam-5935	281	20	,	,	PUNCT
ejpam-5935	281	21	2024	2024	NUM
ejpam-5935	281	22	.	.	PUNCT
ejpam-5935	282	1	s.	s.	PROPN
ejpam-5935	282	2	f.	f.	PROPN
ejpam-5935	282	3	aljurbua	aljurbua	PROPN
ejpam-5935	282	4	et	et	PROPN
ejpam-5935	282	5	al	al	PROPN
ejpam-5935	282	6	.	.	PUNCT
ejpam-5935	282	7	/	/	SYM
ejpam-5935	282	8	eur	eur	PROPN
ejpam-5935	282	9	.	.	PUNCT
ejpam-5935	283	1	j.	j.	PROPN
ejpam-5935	283	2	pure	pure	PROPN
ejpam-5935	283	3	appl	appl	PROPN
ejpam-5935	283	4	.	.	PROPN
ejpam-5935	283	5	math	math	PROPN
ejpam-5935	283	6	,	,	PUNCT
ejpam-5935	283	7	18	18	NUM
ejpam-5935	283	8	(	(	PUNCT
ejpam-5935	283	9	2	2	NUM
ejpam-5935	283	10	)	)	PUNCT
ejpam-5935	283	11	(	(	PUNCT
ejpam-5935	283	12	2025	2025	NUM
ejpam-5935	283	13	)	)	PUNCT
ejpam-5935	283	14	,	,	PUNCT
ejpam-5935	283	15	5935	5935	NUM
ejpam-5935	283	16	10	10	NUM
ejpam-5935	283	17	of	of	ADP
ejpam-5935	283	18	10	10	NUM
ejpam-5935	283	19	[	[	SYM
ejpam-5935	283	20	11	11	NUM
ejpam-5935	283	21	]	]	PUNCT
ejpam-5935	283	22	s.	s.	PROPN
ejpam-5935	283	23	aljurbua	aljurbua	PROPN
ejpam-5935	283	24	,	,	PUNCT
ejpam-5935	283	25	h.	h.	PROPN
ejpam-5935	283	26	hammad	hammad	PROPN
ejpam-5935	283	27	,	,	PUNCT
ejpam-5935	283	28	and	and	CCONJ
ejpam-5935	283	29	n.	n.	PROPN
ejpam-5935	283	30	almutairi	almutairi	NOUN
ejpam-5935	283	31	.	.	PUNCT
ejpam-5935	284	1	existence	existence	NOUN
ejpam-5935	284	2	of	of	ADP
ejpam-5935	284	3	solutions	solution	NOUN
ejpam-5935	284	4	to	to	ADP
ejpam-5935	284	5	a	a	DET
ejpam-5935	284	6	new	new	ADJ
ejpam-5935	284	7	class	class	NOUN
ejpam-5935	284	8	of	of	ADP
ejpam-5935	284	9	fractional	fractional	ADJ
ejpam-5935	284	10	differential	differential	ADJ
ejpam-5935	284	11	equations	equation	NOUN
ejpam-5935	284	12	with	with	ADP
ejpam-5935	284	13	antiperiodic	antiperiodic	ADJ
ejpam-5935	284	14	boundary	boundary	ADJ
ejpam-5935	284	15	conditions	condition	NOUN
ejpam-5935	284	16	.	.	PUNCT
ejpam-5935	285	1	european	european	ADJ
ejpam-5935	285	2	journal	journal	PROPN
ejpam-5935	285	3	of	of	ADP
ejpam-5935	285	4	pure	pure	ADJ
ejpam-5935	285	5	and	and	CCONJ
ejpam-5935	285	6	applied	applied	ADJ
ejpam-5935	285	7	mathematics	mathematic	NOUN
ejpam-5935	285	8	,	,	PUNCT
ejpam-5935	285	9	18(1):5671	18(1):5671	NUM
ejpam-5935	285	10	,	,	PUNCT
ejpam-5935	285	11	2025	2025	NUM
ejpam-5935	285	12	.	.	PUNCT
ejpam-5935	286	1	[	[	X
ejpam-5935	286	2	12	12	NUM
ejpam-5935	286	3	]	]	X
ejpam-5935	286	4	u.	u.	PROPN
ejpam-5935	286	5	tshering	tshering	PROPN
ejpam-5935	286	6	,	,	PUNCT
ejpam-5935	286	7	e.	e.	PROPN
ejpam-5935	286	8	thailert	thailert	PROPN
ejpam-5935	286	9	,	,	PUNCT
ejpam-5935	286	10	and	and	CCONJ
ejpam-5935	286	11	s.	s.	PROPN
ejpam-5935	286	12	ntouyas	ntouyas	PROPN
ejpam-5935	286	13	.	.	PUNCT
ejpam-5935	287	1	existence	existence	NOUN
ejpam-5935	287	2	and	and	CCONJ
ejpam-5935	287	3	stability	stability	NOUN
ejpam-5935	287	4	results	result	VERB
ejpam-5935	287	5	for	for	ADP
ejpam-5935	287	6	a	a	DET
ejpam-5935	287	7	coupled	couple	VERB
ejpam-5935	287	8	system	system	NOUN
ejpam-5935	287	9	of	of	ADP
ejpam-5935	287	10	hilfer	hilfer	NOUN
ejpam-5935	287	11	-	-	PUNCT
ejpam-5935	287	12	hadamard	hadamard	NOUN
ejpam-5935	287	13	sequential	sequential	ADJ
ejpam-5935	287	14	fractional	fractional	ADJ
ejpam-5935	287	15	differential	differential	NOUN
ejpam-5935	287	16	equations	equation	NOUN
ejpam-5935	287	17	with	with	ADP
ejpam-5935	287	18	multi	multi	ADJ
ejpam-5935	287	19	-	-	ADJ
ejpam-5935	287	20	point	point	ADJ
ejpam-5935	287	21	fractional	fractional	ADJ
ejpam-5935	287	22	integral	integral	ADJ
ejpam-5935	287	23	boundary	boundary	ADJ
ejpam-5935	287	24	conditions	condition	NOUN
ejpam-5935	287	25	.	.	PUNCT
ejpam-5935	288	1	aims	aim	VERB
ejpam-5935	288	2	mathematics	mathematic	NOUN
ejpam-5935	288	3	,	,	PUNCT
ejpam-5935	288	4	9(10):25849	9(10):25849	NOUN
ejpam-5935	288	5	–	–	PUNCT
ejpam-5935	288	6	25878	25878	NUM
ejpam-5935	288	7	,	,	PUNCT
ejpam-5935	288	8	2024	2024	NUM
ejpam-5935	288	9	.	.	PUNCT
ejpam-5935	289	1	[	[	X
ejpam-5935	289	2	13	13	NUM
ejpam-5935	289	3	]	]	PUNCT
ejpam-5935	289	4	z.	z.	PROPN
ejpam-5935	289	5	shuqin	shuqin	PROPN
ejpam-5935	289	6	.	.	PUNCT
ejpam-5935	290	1	existence	existence	NOUN
ejpam-5935	290	2	of	of	ADP
ejpam-5935	290	3	solution	solution	NOUN
ejpam-5935	290	4	for	for	ADP
ejpam-5935	290	5	a	a	DET
ejpam-5935	290	6	boundary	boundary	ADJ
ejpam-5935	290	7	value	value	NOUN
ejpam-5935	290	8	problem	problem	NOUN
ejpam-5935	290	9	of	of	ADP
ejpam-5935	290	10	fractional	fractional	ADJ
ejpam-5935	290	11	order	order	NOUN
ejpam-5935	290	12	.	.	PUNCT
ejpam-5935	291	1	acta	acta	PROPN
ejpam-5935	291	2	mathematica	mathematica	PROPN
ejpam-5935	291	3	scientia	scientia	PROPN
ejpam-5935	291	4	,	,	PUNCT
ejpam-5935	291	5	26(2):220–228	26(2):220–228	PROPN
ejpam-5935	291	6	,	,	PUNCT
ejpam-5935	291	7	2006	2006	NUM
ejpam-5935	291	8	.	.	PUNCT
ejpam-5935	292	1	[	[	X
ejpam-5935	292	2	14	14	NUM
ejpam-5935	292	3	]	]	X
ejpam-5935	292	4	r.	r.	PROPN
ejpam-5935	292	5	p.	p.	PROPN
ejpam-5935	292	6	agarwal	agarwal	PROPN
ejpam-5935	292	7	,	,	PUNCT
ejpam-5935	292	8	b.	b.	PROPN
ejpam-5935	292	9	ahmad	ahmad	PROPN
ejpam-5935	292	10	,	,	PUNCT
ejpam-5935	292	11	and	and	CCONJ
ejpam-5935	292	12	j.	j.	PROPN
ejpam-5935	292	13	j.	j.	PROPN
ejpam-5935	292	14	nieto	nieto	PROPN
ejpam-5935	292	15	.	.	PUNCT
ejpam-5935	293	1	fractional	fractional	ADJ
ejpam-5935	293	2	differential	differential	ADJ
ejpam-5935	293	3	equations	equation	NOUN
ejpam-5935	293	4	with	with	ADP
ejpam-5935	293	5	nonlocal	nonlocal	ADJ
ejpam-5935	293	6	(	(	PUNCT
ejpam-5935	293	7	parametric	parametric	ADJ
ejpam-5935	293	8	type	type	NOUN
ejpam-5935	293	9	)	)	PUNCT
ejpam-5935	293	10	anti	anti	ADJ
ejpam-5935	293	11	-	-	ADJ
ejpam-5935	293	12	periodic	periodic	ADJ
ejpam-5935	293	13	boundary	boundary	ADJ
ejpam-5935	293	14	conditions	condition	NOUN
ejpam-5935	293	15	.	.	PUNCT
ejpam-5935	294	1	filomat	filomat	NOUN
ejpam-5935	294	2	,	,	PUNCT
ejpam-5935	294	3	31(5):1207	31(5):1207	NUM
ejpam-5935	294	4	–	–	PUNCT
ejpam-5935	294	5	1214	1214	NUM
ejpam-5935	294	6	,	,	PUNCT
ejpam-5935	294	7	2017	2017	NUM
ejpam-5935	294	8	.	.	PUNCT
ejpam-5935	295	1	[	[	X
ejpam-5935	295	2	15	15	NUM
ejpam-5935	295	3	]	]	X
ejpam-5935	295	4	s.	s.	PROPN
ejpam-5935	295	5	aljurbua	aljurbua	PROPN
ejpam-5935	295	6	.	.	PROPN
ejpam-5935	296	1	extended	extended	ADJ
ejpam-5935	296	2	existence	existence	NOUN
ejpam-5935	296	3	results	result	NOUN
ejpam-5935	296	4	for	for	ADP
ejpam-5935	296	5	fdes	fde	NOUN
ejpam-5935	296	6	with	with	ADP
ejpam-5935	296	7	nonlocal	nonlocal	ADJ
ejpam-5935	296	8	conditions	condition	NOUN
ejpam-5935	296	9	.	.	PUNCT
ejpam-5935	297	1	aims	aim	VERB
ejpam-5935	297	2	mathematics	mathematic	NOUN
ejpam-5935	297	3	,	,	PUNCT
ejpam-5935	297	4	9(4):9049–9058	9(4):9049–9058	NUM
ejpam-5935	297	5	,	,	PUNCT
ejpam-5935	297	6	2024	2024	NUM
ejpam-5935	297	7	.	.	PUNCT
ejpam-5935	298	1	[	[	X
ejpam-5935	298	2	16	16	NUM
ejpam-5935	298	3	]	]	X
ejpam-5935	298	4	b.	b.	PROPN
ejpam-5935	298	5	ahmad	ahmad	PROPN
ejpam-5935	298	6	and	and	CCONJ
ejpam-5935	298	7	j.	j.	PROPN
ejpam-5935	298	8	j.	j.	PROPN
ejpam-5935	298	9	nieto	nieto	PROPN
ejpam-5935	298	10	.	.	PUNCT
ejpam-5935	299	1	extended	extend	VERB
ejpam-5935	299	2	existence	existence	NOUN
ejpam-5935	299	3	results	result	NOUN
ejpam-5935	299	4	for	for	ADP
ejpam-5935	299	5	fdes	fde	NOUN
ejpam-5935	299	6	with	with	ADP
ejpam-5935	299	7	nonlocal	nonlocal	ADJ
ejpam-5935	299	8	conditions	condition	NOUN
ejpam-5935	299	9	.	.	PUNCT
ejpam-5935	300	1	topological	topological	ADJ
ejpam-5935	300	2	methods	method	NOUN
ejpam-5935	300	3	in	in	ADP
ejpam-5935	300	4	nonlinear	nonlinear	ADJ
ejpam-5935	300	5	analysis	analysis	NOUN
ejpam-5935	300	6	,	,	PUNCT
ejpam-5935	300	7	35(2):295–304	35(2):295–304	PROPN
ejpam-5935	300	8	,	,	PUNCT
ejpam-5935	300	9	2010	2010	NUM
ejpam-5935	300	10	.	.	PUNCT
ejpam-5935	301	1	[	[	X
ejpam-5935	301	2	17	17	NUM
ejpam-5935	301	3	]	]	PUNCT
ejpam-5935	301	4	m.	m.	NOUN
ejpam-5935	301	5	alaroud	alaroud	PROPN
ejpam-5935	301	6	,	,	PUNCT
ejpam-5935	301	7	h.	h.	PROPN
ejpam-5935	301	8	aljarrah	aljarrah	PROPN
ejpam-5935	301	9	,	,	PUNCT
ejpam-5935	301	10	k.	k.	PROPN
ejpam-5935	301	11	alomari	alomari	PROPN
ejpam-5935	301	12	,	,	PUNCT
ejpam-5935	301	13	a.	a.	NOUN
ejpam-5935	301	14	ishak	ishak	PROPN
ejpam-5935	301	15	,	,	PUNCT
ejpam-5935	301	16	and	and	CCONJ
ejpam-5935	301	17	m.	m.	NOUN
ejpam-5935	301	18	darus	darus	NOUN
ejpam-5935	301	19	.	.	PUNCT
ejpam-5935	302	1	explicit	explicit	ADJ
ejpam-5935	302	2	and	and	CCONJ
ejpam-5935	302	3	approximate	approximate	ADJ
ejpam-5935	302	4	series	series	NOUN
ejpam-5935	302	5	solutions	solution	NOUN
ejpam-5935	302	6	for	for	ADP
ejpam-5935	302	7	nonlinear	nonlinear	ADJ
ejpam-5935	302	8	fractional	fractional	ADJ
ejpam-5935	302	9	wave	wave	NOUN
ejpam-5935	302	10	-	-	PUNCT
ejpam-5935	302	11	like	like	ADJ
ejpam-5935	302	12	differential	differential	ADJ
ejpam-5935	302	13	equations	equation	NOUN
ejpam-5935	302	14	with	with	ADP
ejpam-5935	302	15	variable	variable	ADJ
ejpam-5935	302	16	coefficients	coefficient	NOUN
ejpam-5935	302	17	.	.	PUNCT
ejpam-5935	303	1	partial	partial	ADJ
ejpam-5935	303	2	differential	differential	ADJ
ejpam-5935	303	3	equations	equation	NOUN
ejpam-5935	303	4	in	in	ADP
ejpam-5935	303	5	applied	applied	ADJ
ejpam-5935	303	6	mathematics	mathematic	NOUN
ejpam-5935	303	7	,	,	PUNCT
ejpam-5935	303	8	10:100680	10:100680	NUM
ejpam-5935	303	9	,	,	PUNCT
ejpam-5935	303	10	2024	2024	NUM
ejpam-5935	303	11	.	.	PUNCT
ejpam-5935	304	1	[	[	X
ejpam-5935	304	2	18	18	NUM
ejpam-5935	304	3	]	]	X
ejpam-5935	304	4	h.	h.	PROPN
ejpam-5935	304	5	aljarrah	aljarrah	PROPN
ejpam-5935	304	6	,	,	PUNCT
ejpam-5935	304	7	m.	m.	PROPN
ejpam-5935	304	8	alaroud	alaroud	PROPN
ejpam-5935	304	9	,	,	PUNCT
ejpam-5935	304	10	k.	k.	PROPN
ejpam-5935	304	11	alomari	alomari	PROPN
ejpam-5935	304	12	,	,	PUNCT
ejpam-5935	304	13	a.	a.	NOUN
ejpam-5935	304	14	ishak	ishak	PROPN
ejpam-5935	304	15	,	,	PUNCT
ejpam-5935	304	16	m.	m.	NOUN
ejpam-5935	304	17	darus	darus	NOUN
ejpam-5935	304	18	,	,	PUNCT
ejpam-5935	304	19	and	and	CCONJ
ejpam-5935	304	20	s.	s.	PROPN
ejpam-5935	304	21	momani	momani	PROPN
ejpam-5935	304	22	.	.	PUNCT
ejpam-5935	305	1	exact	exact	ADJ
ejpam-5935	305	2	and	and	CCONJ
ejpam-5935	305	3	approximate	approximate	ADJ
ejpam-5935	305	4	solutions	solution	NOUN
ejpam-5935	305	5	of	of	ADP
ejpam-5935	305	6	heat	heat	NOUN
ejpam-5935	305	7	fractional	fractional	ADJ
ejpam-5935	305	8	differential	differential	NOUN
ejpam-5935	305	9	equation	equation	NOUN
ejpam-5935	305	10	using	use	VERB
ejpam-5935	305	11	laplace	laplace	NOUN
ejpam-5935	305	12	residual	residual	ADJ
ejpam-5935	305	13	power	power	NOUN
ejpam-5935	305	14	series	series	NOUN
ejpam-5935	305	15	method	method	NOUN
ejpam-5935	305	16	.	.	PUNCT
ejpam-5935	306	1	in	in	ADP
ejpam-5935	306	2	2023	2023	NUM
ejpam-5935	306	3	international	international	ADJ
ejpam-5935	306	4	conference	conference	NOUN
ejpam-5935	306	5	on	on	ADP
ejpam-5935	306	6	fractional	fractional	ADJ
ejpam-5935	306	7	differentiation	differentiation	NOUN
ejpam-5935	306	8	and	and	CCONJ
ejpam-5935	306	9	its	its	PRON
ejpam-5935	306	10	applications	application	NOUN
ejpam-5935	306	11	(	(	PUNCT
ejpam-5935	306	12	icfda	icfda	PROPN
ejpam-5935	306	13	)	)	PUNCT
ejpam-5935	306	14	,	,	PUNCT
ejpam-5935	306	15	pages	page	NOUN
ejpam-5935	306	16	1–5	1–5	NUM
ejpam-5935	306	17	,	,	PUNCT
ejpam-5935	306	18	ajman	ajman	PROPN
ejpam-5935	306	19	,	,	PUNCT
ejpam-5935	306	20	united	united	PROPN
ejpam-5935	306	21	arab	arab	PROPN
ejpam-5935	306	22	emirates	emirates	PROPN
ejpam-5935	306	23	,	,	PUNCT
ejpam-5935	306	24	2023	2023	NUM
ejpam-5935	306	25	.	.	PUNCT
ejpam-5935	307	1	ieee	ieee	NOUN
ejpam-5935	307	2	.	.	PUNCT
ejpam-5935	308	1	[	[	X
ejpam-5935	308	2	19	19	NUM
ejpam-5935	308	3	]	]	X
ejpam-5935	308	4	s.	s.	PROPN
ejpam-5935	308	5	khirsariya	khirsariya	PROPN
ejpam-5935	308	6	and	and	CCONJ
ejpam-5935	308	7	s.	s.	PROPN
ejpam-5935	308	8	rao	rao	PROPN
ejpam-5935	308	9	.	.	PUNCT
ejpam-5935	309	1	solution	solution	NOUN
ejpam-5935	309	2	of	of	ADP
ejpam-5935	309	3	fractional	fractional	ADJ
ejpam-5935	309	4	sawada	sawada	NOUN
ejpam-5935	309	5	–	–	PUNCT
ejpam-5935	309	6	kotera	kotera	PROPN
ejpam-5935	309	7	–	–	PUNCT
ejpam-5935	309	8	ito	ito	PROPN
ejpam-5935	309	9	equation	equation	NOUN
ejpam-5935	309	10	using	use	VERB
ejpam-5935	309	11	caputo	caputo	PROPN
ejpam-5935	309	12	and	and	CCONJ
ejpam-5935	309	13	atangana	atangana	PROPN
ejpam-5935	309	14	–	–	PUNCT
ejpam-5935	309	15	baleanu	baleanu	ADJ
ejpam-5935	309	16	derivatives	derivative	NOUN
ejpam-5935	309	17	.	.	PUNCT
ejpam-5935	310	1	mathematical	mathematical	ADJ
ejpam-5935	310	2	methods	method	NOUN
ejpam-5935	310	3	in	in	ADP
ejpam-5935	310	4	the	the	DET
ejpam-5935	310	5	applied	apply	VERB
ejpam-5935	310	6	sciences	science	NOUN
ejpam-5935	310	7	,	,	PUNCT
ejpam-5935	310	8	46(15):16072–16091	46(15):16072–16091	NUM
ejpam-5935	310	9	,	,	PUNCT
ejpam-5935	310	10	2023	2023	NUM
ejpam-5935	310	11	.	.	PUNCT
ejpam-5935	311	1	[	[	X
ejpam-5935	311	2	20	20	NUM
ejpam-5935	311	3	]	]	PUNCT
ejpam-5935	311	4	s.	s.	PROPN
ejpam-5935	311	5	khirsariya	khirsariya	PROPN
ejpam-5935	311	6	,	,	PUNCT
ejpam-5935	311	7	s.	s.	PROPN
ejpam-5935	311	8	rao	rao	PROPN
ejpam-5935	311	9	,	,	PUNCT
ejpam-5935	311	10	and	and	CCONJ
ejpam-5935	311	11	j.	j.	PROPN
ejpam-5935	311	12	chauhan	chauhan	PROPN
ejpam-5935	311	13	.	.	PUNCT
ejpam-5935	312	1	a	a	DET
ejpam-5935	312	2	novel	novel	ADJ
ejpam-5935	312	3	hybrid	hybrid	NOUN
ejpam-5935	312	4	technique	technique	NOUN
ejpam-5935	312	5	to	to	PART
ejpam-5935	312	6	obtain	obtain	VERB
ejpam-5935	312	7	the	the	DET
ejpam-5935	312	8	solution	solution	NOUN
ejpam-5935	312	9	of	of	ADP
ejpam-5935	312	10	generalized	generalized	ADJ
ejpam-5935	312	11	fractional	fractional	ADJ
ejpam-5935	312	12	-	-	PUNCT
ejpam-5935	312	13	order	order	NOUN
ejpam-5935	312	14	differential	differential	ADJ
ejpam-5935	312	15	equations	equation	NOUN
ejpam-5935	312	16	.	.	PUNCT
ejpam-5935	313	1	mathematics	mathematic	NOUN
ejpam-5935	313	2	and	and	CCONJ
ejpam-5935	313	3	computers	computer	NOUN
ejpam-5935	313	4	in	in	ADP
ejpam-5935	313	5	simulation	simulation	NOUN
ejpam-5935	313	6	,	,	PUNCT
ejpam-5935	313	7	205:272–290	205:272–290	NUM
ejpam-5935	313	8	,	,	PUNCT
ejpam-5935	313	9	2023	2023	NUM
ejpam-5935	313	10	.	.	PUNCT
ejpam-5935	314	1	[	[	X
ejpam-5935	314	2	21	21	NUM
ejpam-5935	314	3	]	]	X
ejpam-5935	314	4	d.	d.	PROPN
ejpam-5935	314	5	r.	r.	PROPN
ejpam-5935	314	6	smart	smart	PROPN
ejpam-5935	314	7	.	.	PUNCT
ejpam-5935	315	1	fixed	fix	VERB
ejpam-5935	315	2	point	point	NOUN
ejpam-5935	315	3	theorems	theorem	NOUN
ejpam-5935	315	4	.	.	PROPN
ejpam-5935	316	1	cambridge	cambridge	PROPN
ejpam-5935	316	2	university	university	PROPN
ejpam-5935	316	3	press	press	PROPN
ejpam-5935	316	4	,	,	PUNCT
ejpam-5935	316	5	cambridge	cambridge	PROPN
ejpam-5935	316	6	,	,	PUNCT
ejpam-5935	316	7	1980	1980	NUM
ejpam-5935	316	8	.	.	PUNCT
ejpam-5935	317	1	[	[	X
ejpam-5935	317	2	22	22	NUM
ejpam-5935	317	3	]	]	X
ejpam-5935	317	4	y.	y.	PROPN
ejpam-5935	317	5	zhou	zhou	PROPN
ejpam-5935	317	6	.	.	PUNCT
ejpam-5935	318	1	fractional	fractional	ADJ
ejpam-5935	318	2	evolution	evolution	NOUN
ejpam-5935	318	3	equations	equation	NOUN
ejpam-5935	318	4	and	and	CCONJ
ejpam-5935	318	5	inclusions	inclusion	NOUN
ejpam-5935	318	6	:	:	PUNCT
ejpam-5935	318	7	analysis	analysis	NOUN
ejpam-5935	318	8	and	and	CCONJ
ejpam-5935	318	9	control	control	NOUN
ejpam-5935	318	10	.	.	PUNCT
ejpam-5935	319	1	academic	academic	ADJ
ejpam-5935	319	2	press	press	PROPN
ejpam-5935	319	3	,	,	PUNCT
ejpam-5935	319	4	london	london	PROPN
ejpam-5935	319	5	,	,	PUNCT
ejpam-5935	319	6	2016	2016	NUM
ejpam-5935	319	7	.	.	PUNCT