id	sid	tid	token	lemma	pos
ejde-745	1	1	electronic	electronic	ADJ
ejde-745	1	2	journal	journal	NOUN
ejde-745	1	3	of	of	ADP
ejde-745	1	4	differential	differential	ADJ
ejde-745	1	5	equations	equation	NOUN
ejde-745	1	6	,	,	PUNCT
ejde-745	1	7	vol	vol	NOUN
ejde-745	1	8	.	.	NOUN
ejde-745	1	9	2024	2024	NUM
ejde-745	1	10	(	(	PUNCT
ejde-745	1	11	2024	2024	NUM
ejde-745	1	12	)	)	PUNCT
ejde-745	1	13	,	,	PUNCT
ejde-745	1	14	no	no	INTJ
ejde-745	1	15	.	.	NOUN
ejde-745	1	16	36	36	NUM
ejde-745	1	17	,	,	PUNCT
ejde-745	1	18	pp	pp	ADJ
ejde-745	1	19	.	.	PUNCT
ejde-745	2	1	1–9	1–9	NOUN
ejde-745	2	2	.	.	PUNCT
ejde-745	2	3	issn	issn	PROPN
ejde-745	2	4	:	:	PUNCT
ejde-745	2	5	1072	1072	NUM
ejde-745	2	6	-	-	SYM
ejde-745	2	7	6691	6691	NUM
ejde-745	2	8	.	.	PUNCT
ejde-745	3	1	url	url	PROPN
ejde-745	3	2	:	:	PUNCT
ejde-745	3	3	https://ejde.math.txstate.edu	https://ejde.math.txstate.edu	PROPN
ejde-745	3	4	,	,	PUNCT
ejde-745	3	5	https://ejde.math.unt.edu	https://ejde.math.unt.edu	PROPN
ejde-745	3	6	doi	doi	PROPN
ejde-745	3	7	:	:	PUNCT
ejde-745	3	8	10.58997	10.58997	NUM
ejde-745	3	9	/	/	SYM
ejde-745	3	10	ejde.2024.36	ejde.2024.36	NOUN
ejde-745	3	11	existence	existence	NOUN
ejde-745	3	12	of	of	ADP
ejde-745	3	13	pseudosolutions	pseudosolution	NOUN
ejde-745	3	14	for	for	ADP
ejde-745	3	15	dynamic	dynamic	ADJ
ejde-745	3	16	fractional	fractional	ADJ
ejde-745	3	17	differential	differential	NOUN
ejde-745	3	18	equations	equation	NOUN
ejde-745	3	19	aneta	aneta	PROPN
ejde-745	3	20	sikorska	sikorska	PROPN
ejde-745	3	21	-	-	PUNCT
ejde-745	3	22	nowak	nowak	PROPN
ejde-745	3	23	abstract	abstract	NOUN
ejde-745	3	24	.	.	PUNCT
ejde-745	4	1	in	in	ADP
ejde-745	4	2	this	this	DET
ejde-745	4	3	article	article	NOUN
ejde-745	4	4	,	,	PUNCT
ejde-745	4	5	we	we	PRON
ejde-745	4	6	consider	consider	VERB
ejde-745	4	7	the	the	DET
ejde-745	4	8	existence	existence	NOUN
ejde-745	4	9	of	of	ADP
ejde-745	4	10	pseudosolutions	pseudosolution	NOUN
ejde-745	4	11	for	for	ADP
ejde-745	4	12	boundary	boundary	ADJ
ejde-745	4	13	value	value	NOUN
ejde-745	4	14	problem	problem	NOUN
ejde-745	4	15	for	for	ADP
ejde-745	4	16	fractional	fractional	ADJ
ejde-745	4	17	differential	differential	ADJ
ejde-745	4	18	equations	equation	NOUN
ejde-745	4	19	of	of	ADP
ejde-745	4	20	the	the	DET
ejde-745	4	21	form	form	NOUN
ejde-745	4	22	c	c	PROPN
ejde-745	4	23	t	t	NOUN
ejde-745	4	24	∆αx(t	∆αx(t	PROPN
ejde-745	4	25	)	)	PUNCT
ejde-745	4	26	=	=	PUNCT
ejde-745	5	1	f(t	f(t	NOUN
ejde-745	5	2	,	,	PUNCT
ejde-745	5	3	x(t	x(t	PROPN
ejde-745	5	4	)	)	PUNCT
ejde-745	5	5	)	)	PUNCT
ejde-745	5	6	,	,	PUNCT
ejde-745	5	7	for	for	ADP
ejde-745	5	8	t	t	PROPN
ejde-745	5	9	∈	∈	PROPN
ejde-745	5	10	ia	ia	PROPN
ejde-745	6	1	=	=	PUNCT
ejde-745	7	1	[	[	X
ejde-745	7	2	0	0	NUM
ejde-745	7	3	,	,	PUNCT
ejde-745	7	4	a	a	PRON
ejde-745	7	5	]	]	PUNCT
ejde-745	7	6	∩	∩	PROPN
ejde-745	7	7	t	t	PROPN
ejde-745	7	8	,	,	PUNCT
ejde-745	7	9	x(0	x(0	PROPN
ejde-745	7	10	)	)	PUNCT
ejde-745	7	11	=	=	PUNCT
ejde-745	7	12	x0	x0	PROPN
ejde-745	7	13	,	,	PUNCT
ejde-745	7	14	x0	x0	PROPN
ejde-745	7	15	∈	∈	PROPN
ejde-745	8	1	e	e	NOUN
ejde-745	8	2	,	,	PUNCT
ejde-745	8	3	where	where	SCONJ
ejde-745	8	4	c	c	PROPN
ejde-745	8	5	t	t	NOUN
ejde-745	8	6	∆αx(t	∆αx(t	PROPN
ejde-745	8	7	)	)	PUNCT
ejde-745	8	8	,	,	PUNCT
ejde-745	8	9	α	α	PROPN
ejde-745	8	10	∈	∈	PROPN
ejde-745	8	11	(	(	PUNCT
ejde-745	8	12	0	0	NUM
ejde-745	8	13	,	,	PUNCT
ejde-745	8	14	1	1	NUM
ejde-745	8	15	]	]	PUNCT
ejde-745	8	16	denotes	denote	VERB
ejde-745	8	17	the	the	DET
ejde-745	8	18	caputo	caputo	PROPN
ejde-745	8	19	fractional	fractional	PROPN
ejde-745	8	20	derivative	derivative	PROPN
ejde-745	8	21	,	,	PUNCT
ejde-745	8	22	t	t	PROPN
ejde-745	8	23	denotes	denote	VERB
ejde-745	8	24	a	a	DET
ejde-745	8	25	time	time	NOUN
ejde-745	8	26	scale	scale	NOUN
ejde-745	8	27	,	,	PUNCT
ejde-745	8	28	and	and	CCONJ
ejde-745	8	29	the	the	DET
ejde-745	8	30	function	function	NOUN
ejde-745	8	31	f	f	PROPN
ejde-745	8	32	is	be	AUX
ejde-745	8	33	weakly	weakly	ADV
ejde-745	8	34	-	-	PUNCT
ejde-745	8	35	weakly	weakly	ADV
ejde-745	8	36	sequentially	sequentially	ADV
ejde-745	8	37	continuous	continuous	ADJ
ejde-745	8	38	with	with	ADP
ejde-745	8	39	values	value	NOUN
ejde-745	8	40	in	in	ADP
ejde-745	8	41	a	a	DET
ejde-745	8	42	banach	banach	NOUN
ejde-745	8	43	space	space	NOUN
ejde-745	8	44	e	e	NOUN
ejde-745	8	45	and	and	CCONJ
ejde-745	8	46	satisfies	satisfy	VERB
ejde-745	8	47	some	some	DET
ejde-745	8	48	boundary	boundary	ADJ
ejde-745	8	49	conditions	condition	NOUN
ejde-745	8	50	and	and	CCONJ
ejde-745	8	51	conditions	condition	NOUN
ejde-745	8	52	expressed	express	VERB
ejde-745	8	53	in	in	ADP
ejde-745	8	54	terms	term	NOUN
ejde-745	8	55	of	of	ADP
ejde-745	8	56	measures	measure	NOUN
ejde-745	8	57	of	of	ADP
ejde-745	8	58	weak	weak	ADJ
ejde-745	8	59	non	non	ADJ
ejde-745	8	60	-	-	NOUN
ejde-745	8	61	compactness	compactness	NOUN
ejde-745	8	62	.	.	PUNCT
ejde-745	9	1	1	1	X
ejde-745	9	2	.	.	X
ejde-745	9	3	introduction	introduction	NOUN
ejde-745	9	4	the	the	DET
ejde-745	9	5	research	research	NOUN
ejde-745	9	6	on	on	ADP
ejde-745	9	7	fractional	fractional	ADJ
ejde-745	9	8	calculus	calculus	NOUN
ejde-745	9	9	and	and	CCONJ
ejde-745	9	10	fractional	fractional	ADJ
ejde-745	9	11	differential	differential	ADJ
ejde-745	9	12	equations	equation	NOUN
ejde-745	9	13	in	in	ADP
ejde-745	9	14	banach	banach	NOUN
ejde-745	9	15	spaces	space	NOUN
ejde-745	9	16	,	,	PUNCT
ejde-745	9	17	with	with	ADP
ejde-745	9	18	a	a	DET
ejde-745	9	19	special	special	ADJ
ejde-745	9	20	focus	focus	NOUN
ejde-745	9	21	on	on	ADP
ejde-745	9	22	weak	weak	ADJ
ejde-745	9	23	topology	topology	NOUN
ejde-745	9	24	initiated	initiate	VERB
ejde-745	9	25	in	in	ADP
ejde-745	9	26	2005	2005	NUM
ejde-745	9	27	by	by	ADP
ejde-745	9	28	salem	salem	NOUN
ejde-745	9	29	and	and	CCONJ
ejde-745	9	30	his	his	PRON
ejde-745	9	31	team	team	NOUN
ejde-745	9	32	(	(	PUNCT
ejde-745	9	33	see	see	VERB
ejde-745	9	34	[	[	X
ejde-745	9	35	23	23	NUM
ejde-745	9	36	]	]	PUNCT
ejde-745	9	37	for	for	ADP
ejde-745	9	38	riemann	riemann	PROPN
ejde-745	9	39	-	-	PUNCT
ejde-745	9	40	liouville	liouville	NOUN
ejde-745	9	41	type	type	NOUN
ejde-745	9	42	fractional	fractional	ADJ
ejde-745	9	43	calculus	calculus	NOUN
ejde-745	9	44	and	and	CCONJ
ejde-745	9	45	[	[	X
ejde-745	9	46	22	22	NUM
ejde-745	9	47	]	]	PUNCT
ejde-745	9	48	for	for	ADP
ejde-745	9	49	hadamard	hadamard	ADJ
ejde-745	9	50	type	type	NOUN
ejde-745	9	51	)	)	PUNCT
ejde-745	9	52	,	,	PUNCT
ejde-745	9	53	marked	mark	VERB
ejde-745	9	54	the	the	DET
ejde-745	9	55	beginning	beginning	NOUN
ejde-745	9	56	of	of	ADP
ejde-745	9	57	a	a	DET
ejde-745	9	58	new	new	ADJ
ejde-745	9	59	era	era	NOUN
ejde-745	9	60	in	in	ADP
ejde-745	9	61	this	this	DET
ejde-745	9	62	field	field	NOUN
ejde-745	9	63	of	of	ADP
ejde-745	9	64	mathematics	mathematic	NOUN
ejde-745	9	65	.	.	PUNCT
ejde-745	10	1	the	the	DET
ejde-745	10	2	publication	publication	NOUN
ejde-745	10	3	of	of	ADP
ejde-745	10	4	articles	article	NOUN
ejde-745	10	5	[	[	X
ejde-745	10	6	22	22	NUM
ejde-745	10	7	,	,	PUNCT
ejde-745	10	8	23	23	NUM
ejde-745	10	9	]	]	PUNCT
ejde-745	10	10	triggered	trigger	VERB
ejde-745	10	11	significant	significant	ADJ
ejde-745	10	12	interest	interest	NOUN
ejde-745	10	13	,	,	PUNCT
ejde-745	10	14	as	as	SCONJ
ejde-745	10	15	evidenced	evidence	VERB
ejde-745	10	16	by	by	ADP
ejde-745	10	17	numerous	numerous	ADJ
ejde-745	10	18	citations	citation	NOUN
ejde-745	10	19	such	such	ADJ
ejde-745	10	20	as	as	ADP
ejde-745	10	21	[	[	X
ejde-745	10	22	1	1	NUM
ejde-745	10	23	,	,	PUNCT
ejde-745	10	24	4	4	NUM
ejde-745	10	25	,	,	PUNCT
ejde-745	10	26	6	6	NUM
ejde-745	10	27	,	,	PUNCT
ejde-745	10	28	10	10	NUM
ejde-745	10	29	,	,	PUNCT
ejde-745	10	30	11	11	NUM
ejde-745	10	31	,	,	PUNCT
ejde-745	10	32	16	16	NUM
ejde-745	10	33	,	,	PUNCT
ejde-745	10	34	17	17	NUM
ejde-745	10	35	,	,	PUNCT
ejde-745	10	36	19	19	NUM
ejde-745	10	37	,	,	PUNCT
ejde-745	10	38	21	21	NUM
ejde-745	10	39	,	,	PUNCT
ejde-745	10	40	24	24	NUM
ejde-745	10	41	,	,	PUNCT
ejde-745	10	42	25	25	NUM
ejde-745	10	43	,	,	PUNCT
ejde-745	10	44	26	26	NUM
ejde-745	10	45	]	]	PUNCT
ejde-745	10	46	,	,	PUNCT
ejde-745	10	47	leading	lead	VERB
ejde-745	10	48	to	to	ADP
ejde-745	10	49	the	the	DET
ejde-745	10	50	development	development	NOUN
ejde-745	10	51	of	of	ADP
ejde-745	10	52	a	a	DET
ejde-745	10	53	series	series	NOUN
ejde-745	10	54	of	of	ADP
ejde-745	10	55	studies	study	NOUN
ejde-745	10	56	on	on	ADP
ejde-745	10	57	initial	initial	ADJ
ejde-745	10	58	and	and	CCONJ
ejde-745	10	59	boundary	boundary	ADJ
ejde-745	10	60	value	value	NOUN
ejde-745	10	61	problems	problem	NOUN
ejde-745	10	62	for	for	ADP
ejde-745	10	63	various	various	ADJ
ejde-745	10	64	types	type	NOUN
ejde-745	10	65	of	of	ADP
ejde-745	10	66	fractional	fractional	ADJ
ejde-745	10	67	differential	differential	ADJ
ejde-745	10	68	equations	equation	NOUN
ejde-745	10	69	.	.	PUNCT
ejde-745	11	1	the	the	DET
ejde-745	11	2	introduction	introduction	NOUN
ejde-745	11	3	of	of	ADP
ejde-745	11	4	fractional	fractional	ADJ
ejde-745	11	5	derivatives	derivative	NOUN
ejde-745	11	6	on	on	ADP
ejde-745	11	7	time	time	NOUN
ejde-745	11	8	scales	scale	NOUN
ejde-745	11	9	,	,	PUNCT
ejde-745	11	10	allowing	allow	VERB
ejde-745	11	11	for	for	ADP
ejde-745	11	12	the	the	DET
ejde-745	11	13	simultaneous	simultaneous	ADJ
ejde-745	11	14	modeling	modeling	NOUN
ejde-745	11	15	of	of	ADP
ejde-745	11	16	discrete	discrete	ADJ
ejde-745	11	17	and	and	CCONJ
ejde-745	11	18	continuous	continuous	ADJ
ejde-745	11	19	phenomena	phenomenon	NOUN
ejde-745	11	20	,	,	PUNCT
ejde-745	11	21	provided	provide	VERB
ejde-745	11	22	additional	additional	ADJ
ejde-745	11	23	flexibility	flexibility	NOUN
ejde-745	11	24	in	in	ADP
ejde-745	11	25	modeling	model	VERB
ejde-745	11	26	phenomena	phenomenon	NOUN
ejde-745	11	27	that	that	PRON
ejde-745	11	28	do	do	AUX
ejde-745	11	29	not	not	PART
ejde-745	11	30	change	change	VERB
ejde-745	11	31	in	in	ADP
ejde-745	11	32	a	a	DET
ejde-745	11	33	linear	linear	ADJ
ejde-745	11	34	manner	manner	NOUN
ejde-745	11	35	or	or	CCONJ
ejde-745	11	36	at	at	ADP
ejde-745	11	37	a	a	DET
ejde-745	11	38	constant	constant	ADJ
ejde-745	11	39	rate	rate	NOUN
ejde-745	11	40	.	.	PUNCT
ejde-745	12	1	these	these	DET
ejde-745	12	2	mathematical	mathematical	ADJ
ejde-745	12	3	tools	tool	NOUN
ejde-745	12	4	have	have	AUX
ejde-745	12	5	found	find	VERB
ejde-745	12	6	applications	application	NOUN
ejde-745	12	7	in	in	ADP
ejde-745	12	8	many	many	ADJ
ejde-745	12	9	fields	field	NOUN
ejde-745	12	10	,	,	PUNCT
ejde-745	12	11	from	from	ADP
ejde-745	12	12	physics	physics	NOUN
ejde-745	12	13	and	and	CCONJ
ejde-745	12	14	engineering	engineering	NOUN
ejde-745	12	15	to	to	PART
ejde-745	12	16	control	control	VERB
ejde-745	12	17	theory	theory	NOUN
ejde-745	12	18	and	and	CCONJ
ejde-745	12	19	quantum	quantum	NOUN
ejde-745	12	20	mechanics	mechanic	NOUN
ejde-745	12	21	,	,	PUNCT
ejde-745	12	22	opening	open	VERB
ejde-745	12	23	up	up	ADP
ejde-745	12	24	new	new	ADJ
ejde-745	12	25	possibilities	possibility	NOUN
ejde-745	12	26	in	in	ADP
ejde-745	12	27	financial	financial	ADJ
ejde-745	12	28	market	market	NOUN
ejde-745	12	29	modeling	modeling	NOUN
ejde-745	12	30	and	and	CCONJ
ejde-745	12	31	population	population	NOUN
ejde-745	12	32	dynamics	dynamic	NOUN
ejde-745	12	33	.	.	PUNCT
ejde-745	13	1	in	in	ADP
ejde-745	13	2	1967	1967	NUM
ejde-745	13	3	,	,	PUNCT
ejde-745	13	4	the	the	DET
ejde-745	13	5	italian	italian	ADJ
ejde-745	13	6	mathematician	mathematician	NOUN
ejde-745	13	7	caputo	caputo	PROPN
ejde-745	13	8	introduced	introduce	VERB
ejde-745	13	9	the	the	DET
ejde-745	13	10	differential	differential	ADJ
ejde-745	13	11	operator	operator	NOUN
ejde-745	13	12	known	know	VERB
ejde-745	13	13	as	as	ADP
ejde-745	13	14	the	the	DET
ejde-745	13	15	caputo	caputo	PROPN
ejde-745	13	16	operator	operator	NOUN
ejde-745	13	17	,	,	PUNCT
ejde-745	13	18	allowing	allow	VERB
ejde-745	13	19	for	for	ADP
ejde-745	13	20	a	a	DET
ejde-745	13	21	deeper	deep	ADJ
ejde-745	13	22	understanding	understanding	NOUN
ejde-745	13	23	of	of	ADP
ejde-745	13	24	and	and	CCONJ
ejde-745	13	25	solutions	solution	NOUN
ejde-745	13	26	to	to	ADP
ejde-745	13	27	problems	problem	NOUN
ejde-745	13	28	related	relate	VERB
ejde-745	13	29	to	to	ADP
ejde-745	13	30	viscoelasticity	viscoelasticity	NOUN
ejde-745	13	31	using	use	VERB
ejde-745	13	32	fractional	fractional	ADJ
ejde-745	13	33	derivatives	derivative	NOUN
ejde-745	13	34	.	.	PUNCT
ejde-745	14	1	the	the	DET
ejde-745	14	2	relationship	relationship	NOUN
ejde-745	14	3	between	between	ADP
ejde-745	14	4	the	the	DET
ejde-745	14	5	caputo	caputo	PROPN
ejde-745	14	6	fractional	fractional	PROPN
ejde-745	14	7	derivative	derivative	PROPN
ejde-745	14	8	and	and	CCONJ
ejde-745	14	9	other	other	ADJ
ejde-745	14	10	fractional	fractional	ADJ
ejde-745	14	11	derivatives	derivative	NOUN
ejde-745	14	12	,	,	PUNCT
ejde-745	14	13	such	such	ADJ
ejde-745	14	14	as	as	ADP
ejde-745	14	15	riemann	riemann	PROPN
ejde-745	14	16	-	-	PUNCT
ejde-745	14	17	liouville	liouville	NOUN
ejde-745	14	18	or	or	CCONJ
ejde-745	14	19	atangana	atangana	PROPN
ejde-745	14	20	-	-	PUNCT
ejde-745	14	21	baleanu	baleanu	PROPN
ejde-745	14	22	,	,	PUNCT
ejde-745	14	23	highlighted	highlight	VERB
ejde-745	14	24	the	the	DET
ejde-745	14	25	significance	significance	NOUN
ejde-745	14	26	of	of	ADP
ejde-745	14	27	generalized	generalized	ADJ
ejde-745	14	28	mittag	mittag	ADJ
ejde-745	14	29	-	-	PUNCT
ejde-745	14	30	leffler	leffler	NOUN
ejde-745	14	31	functions	function	NOUN
ejde-745	14	32	in	in	ADP
ejde-745	14	33	mathematical	mathematical	ADJ
ejde-745	14	34	modeling	modeling	NOUN
ejde-745	14	35	.	.	PUNCT
ejde-745	15	1	by	by	ADP
ejde-745	15	2	utilizing	utilize	VERB
ejde-745	15	3	specific	specific	ADJ
ejde-745	15	4	mathematical	mathematical	ADJ
ejde-745	15	5	models	model	NOUN
ejde-745	15	6	,	,	PUNCT
ejde-745	15	7	it	it	PRON
ejde-745	15	8	became	become	VERB
ejde-745	15	9	possible	possible	ADJ
ejde-745	15	10	to	to	ADP
ejde-745	15	11	2020	2020	NUM
ejde-745	15	12	mathematics	mathematic	NOUN
ejde-745	15	13	subject	subject	ADJ
ejde-745	15	14	classification	classification	NOUN
ejde-745	15	15	.	.	PUNCT
ejde-745	16	1	34k40	34k40	NUM
ejde-745	16	2	,	,	PUNCT
ejde-745	16	3	34k42	34k42	NUM
ejde-745	16	4	,	,	PUNCT
ejde-745	16	5	34a08	34a08	NUM
ejde-745	16	6	,	,	PUNCT
ejde-745	16	7	34g20	34g20	NUM
ejde-745	16	8	.	.	PUNCT
ejde-745	17	1	key	key	ADJ
ejde-745	17	2	words	word	NOUN
ejde-745	17	3	and	and	CCONJ
ejde-745	17	4	phrases	phrase	NOUN
ejde-745	17	5	.	.	PUNCT
ejde-745	18	1	fractional	fractional	ADJ
ejde-745	18	2	differential	differential	ADJ
ejde-745	18	3	equations	equation	NOUN
ejde-745	18	4	;	;	PUNCT
ejde-745	18	5	fixed	fix	VERB
ejde-745	18	6	point	point	NOUN
ejde-745	18	7	;	;	PUNCT
ejde-745	18	8	time	time	NOUN
ejde-745	18	9	scales	scale	NOUN
ejde-745	18	10	;	;	PUNCT
ejde-745	18	11	caputo	caputo	PROPN
ejde-745	18	12	fractional	fractional	PROPN
ejde-745	18	13	derivative	derivative	PROPN
ejde-745	18	14	;	;	PUNCT
ejde-745	18	15	delta	delta	NOUN
ejde-745	18	16	hkp	hkp	PROPN
ejde-745	18	17	integral	integral	ADJ
ejde-745	18	18	.	.	PUNCT
ejde-745	19	1	©	©	PROPN
ejde-745	19	2	2024	2024	NUM
ejde-745	19	3	.	.	PUNCT
ejde-745	20	1	this	this	DET
ejde-745	20	2	work	work	NOUN
ejde-745	20	3	is	be	AUX
ejde-745	20	4	licensed	license	VERB
ejde-745	20	5	under	under	ADP
ejde-745	20	6	a	a	DET
ejde-745	20	7	cc	cc	NOUN
ejde-745	20	8	by	by	ADP
ejde-745	20	9	4.0	4.0	NUM
ejde-745	20	10	license	license	NOUN
ejde-745	20	11	.	.	PUNCT
ejde-745	21	1	submitted	submit	VERB
ejde-745	21	2	may	may	PROPN
ejde-745	21	3	20	20	NUM
ejde-745	21	4	,	,	PUNCT
ejde-745	21	5	2024	2024	NUM
ejde-745	21	6	.	.	PUNCT
ejde-745	22	1	published	publish	VERB
ejde-745	22	2	june	june	PROPN
ejde-745	22	3	20	20	NUM
ejde-745	22	4	,	,	PUNCT
ejde-745	22	5	2024	2024	NUM
ejde-745	22	6	.	.	PUNCT
ejde-745	22	7	1	1	NUM
ejde-745	22	8	2	2	NUM
ejde-745	22	9	a.	a.	NOUN
ejde-745	22	10	sikorska	sikorska	ADJ
ejde-745	22	11	-	-	PUNCT
ejde-745	22	12	nowak	nowak	PROPN
ejde-745	22	13	ejde-2024/36	ejde-2024/36	NOUN
ejde-745	22	14	enhance	enhance	VERB
ejde-745	22	15	outcomes	outcome	NOUN
ejde-745	22	16	and	and	CCONJ
ejde-745	22	17	solve	solve	VERB
ejde-745	22	18	problems	problem	NOUN
ejde-745	22	19	previously	previously	ADV
ejde-745	22	20	considered	consider	VERB
ejde-745	22	21	difficult	difficult	ADJ
ejde-745	22	22	or	or	CCONJ
ejde-745	22	23	impossible	impossible	ADJ
ejde-745	22	24	to	to	PART
ejde-745	22	25	address	address	VERB
ejde-745	22	26	,	,	PUNCT
ejde-745	22	27	opening	open	VERB
ejde-745	22	28	new	new	ADJ
ejde-745	22	29	horizons	horizon	NOUN
ejde-745	22	30	in	in	ADP
ejde-745	22	31	the	the	DET
ejde-745	22	32	theoretical	theoretical	ADJ
ejde-745	22	33	and	and	CCONJ
ejde-745	22	34	applied	applied	ADJ
ejde-745	22	35	aspects	aspect	NOUN
ejde-745	22	36	of	of	ADP
ejde-745	22	37	fractional	fractional	ADJ
ejde-745	22	38	calculus	calculus	NOUN
ejde-745	22	39	.	.	PUNCT
ejde-745	23	1	in	in	ADP
ejde-745	23	2	this	this	DET
ejde-745	23	3	paper	paper	NOUN
ejde-745	23	4	,	,	PUNCT
ejde-745	23	5	we	we	PRON
ejde-745	23	6	consider	consider	VERB
ejde-745	23	7	the	the	DET
ejde-745	23	8	existence	existence	NOUN
ejde-745	23	9	of	of	ADP
ejde-745	23	10	a	a	DET
ejde-745	23	11	pseudosolution	pseudosolution	NOUN
ejde-745	23	12	for	for	ADP
ejde-745	23	13	the	the	DET
ejde-745	23	14	boundary	boundary	ADJ
ejde-745	23	15	value	value	NOUN
ejde-745	23	16	problem	problem	NOUN
ejde-745	23	17	for	for	ADP
ejde-745	23	18	fractional	fractional	ADJ
ejde-745	23	19	differential	differential	ADJ
ejde-745	23	20	equations	equation	NOUN
ejde-745	23	21	of	of	ADP
ejde-745	23	22	the	the	DET
ejde-745	23	23	form	form	NOUN
ejde-745	23	24	c	c	PROPN
ejde-745	23	25	t∆	t∆	PROPN
ejde-745	23	26	αx(t	αx(t	NOUN
ejde-745	23	27	)	)	PUNCT
ejde-745	23	28	=	=	PUNCT
ejde-745	23	29	f(t	f(t	NOUN
ejde-745	23	30	,	,	PUNCT
ejde-745	23	31	x(t	x(t	PROPN
ejde-745	23	32	)	)	PUNCT
ejde-745	23	33	)	)	PUNCT
ejde-745	23	34	,	,	PUNCT
ejde-745	23	35	for	for	ADP
ejde-745	23	36	t	t	PROPN
ejde-745	23	37	∈	∈	PROPN
ejde-745	23	38	ia	ia	PROPN
ejde-745	23	39	=	=	PUNCT
ejde-745	24	1	[	[	X
ejde-745	24	2	0	0	NUM
ejde-745	24	3	,	,	PUNCT
ejde-745	24	4	a	a	PRON
ejde-745	24	5	]	]	PUNCT
ejde-745	24	6	∩	∩	PROPN
ejde-745	24	7	t	t	PROPN
ejde-745	24	8	,	,	PUNCT
ejde-745	24	9	x(0	x(0	PROPN
ejde-745	24	10	)	)	PUNCT
ejde-745	24	11	=	=	PUNCT
ejde-745	24	12	x0	x0	PROPN
ejde-745	24	13	,	,	PUNCT
ejde-745	24	14	x0	x0	PROPN
ejde-745	24	15	∈	∈	PROPN
ejde-745	24	16	e	e	NOUN
ejde-745	24	17	,	,	PUNCT
ejde-745	24	18	(	(	PUNCT
ejde-745	24	19	1.1	1.1	NUM
ejde-745	24	20	)	)	PUNCT
ejde-745	24	21	where	where	SCONJ
ejde-745	24	22	c	c	PROPN
ejde-745	24	23	t∆	t∆	PROPN
ejde-745	24	24	αx(t	αx(t	NOUN
ejde-745	24	25	)	)	PUNCT
ejde-745	24	26	,	,	PUNCT
ejde-745	24	27	α	α	PROPN
ejde-745	24	28	∈	∈	PROPN
ejde-745	24	29	(	(	PUNCT
ejde-745	24	30	0	0	NUM
ejde-745	24	31	,	,	PUNCT
ejde-745	24	32	1	1	NUM
ejde-745	24	33	]	]	PUNCT
ejde-745	24	34	is	be	AUX
ejde-745	24	35	the	the	DET
ejde-745	24	36	caputo	caputo	PROPN
ejde-745	24	37	fractional	fractional	PROPN
ejde-745	24	38	derivative	derivative	PROPN
ejde-745	24	39	,	,	PUNCT
ejde-745	24	40	t	t	PROPN
ejde-745	24	41	denotes	denote	VERB
ejde-745	24	42	a	a	DET
ejde-745	24	43	time	time	NOUN
ejde-745	24	44	scale	scale	NOUN
ejde-745	24	45	.	.	PUNCT
ejde-745	25	1	we	we	PRON
ejde-745	25	2	assume	assume	VERB
ejde-745	25	3	that	that	SCONJ
ejde-745	25	4	the	the	DET
ejde-745	25	5	function	function	NOUN
ejde-745	25	6	f	f	PROPN
ejde-745	25	7	is	be	AUX
ejde-745	25	8	weakly	weakly	ADV
ejde-745	25	9	-	-	PUNCT
ejde-745	25	10	weakly	weakly	ADV
ejde-745	25	11	sequentially	sequentially	ADV
ejde-745	25	12	continuous	continuous	ADJ
ejde-745	25	13	with	with	ADP
ejde-745	25	14	values	value	NOUN
ejde-745	25	15	in	in	ADP
ejde-745	25	16	a	a	DET
ejde-745	25	17	banach	banach	NOUN
ejde-745	25	18	space	space	NOUN
ejde-745	25	19	and	and	CCONJ
ejde-745	25	20	satisfies	satisfy	VERB
ejde-745	25	21	some	some	DET
ejde-745	25	22	regularity	regularity	NOUN
ejde-745	25	23	conditions	condition	NOUN
ejde-745	25	24	expressed	express	VERB
ejde-745	25	25	in	in	ADP
ejde-745	25	26	terms	term	NOUN
ejde-745	25	27	of	of	ADP
ejde-745	25	28	the	the	DET
ejde-745	25	29	de	de	X
ejde-745	25	30	blasi	blasi	PROPN
ejde-745	25	31	measure	measure	NOUN
ejde-745	25	32	of	of	ADP
ejde-745	25	33	weak	weak	ADJ
ejde-745	25	34	noncompactness	noncompactness	NOUN
ejde-745	25	35	.	.	PUNCT
ejde-745	26	1	we	we	PRON
ejde-745	26	2	introduce	introduce	VERB
ejde-745	26	3	a	a	DET
ejde-745	26	4	weakly	weakly	ADJ
ejde-745	26	5	sequentially	sequentially	ADV
ejde-745	26	6	continuous	continuous	ADJ
ejde-745	26	7	operator	operator	NOUN
ejde-745	26	8	associated	associate	VERB
ejde-745	26	9	with	with	ADP
ejde-745	26	10	an	an	DET
ejde-745	26	11	integral	integral	ADJ
ejde-745	26	12	equation	equation	NOUN
ejde-745	26	13	that	that	PRON
ejde-745	26	14	is	be	AUX
ejde-745	26	15	equivalent	equivalent	ADJ
ejde-745	26	16	to	to	ADP
ejde-745	26	17	the	the	DET
ejde-745	26	18	initial	initial	ADJ
ejde-745	26	19	problem	problem	NOUN
ejde-745	26	20	.	.	PUNCT
ejde-745	27	1	there	there	PRON
ejde-745	27	2	exist	exist	VERB
ejde-745	27	3	many	many	ADJ
ejde-745	27	4	important	important	ADJ
ejde-745	27	5	examples	example	NOUN
ejde-745	27	6	of	of	ADP
ejde-745	27	7	mappings	mapping	NOUN
ejde-745	27	8	that	that	PRON
ejde-745	27	9	are	be	AUX
ejde-745	27	10	weakly	weakly	ADV
ejde-745	27	11	sequentially	sequentially	ADV
ejde-745	27	12	continuous	continuous	ADJ
ejde-745	27	13	but	but	CCONJ
ejde-745	27	14	not	not	PART
ejde-745	27	15	weakly	weakly	ADV
ejde-745	27	16	continuous	continuous	ADJ
ejde-745	27	17	.	.	PUNCT
ejde-745	28	1	the	the	DET
ejde-745	28	2	relations	relation	NOUN
ejde-745	28	3	between	between	ADP
ejde-745	28	4	weakly	weakly	ADV
ejde-745	28	5	sequentially	sequentially	ADV
ejde-745	28	6	continuous	continuous	ADJ
ejde-745	28	7	and	and	CCONJ
ejde-745	28	8	weakly	weakly	ADJ
ejde-745	28	9	continuous	continuous	ADJ
ejde-745	28	10	mappings	mapping	NOUN
ejde-745	28	11	are	be	AUX
ejde-745	28	12	studied	study	VERB
ejde-745	28	13	by	by	ADP
ejde-745	28	14	ball	ball	NOUN
ejde-745	28	15	[	[	X
ejde-745	28	16	5	5	NUM
ejde-745	28	17	]	]	PUNCT
ejde-745	28	18	.	.	PUNCT
ejde-745	29	1	adopting	adopt	VERB
ejde-745	29	2	the	the	DET
ejde-745	29	3	fixed	fix	VERB
ejde-745	29	4	point	point	NOUN
ejde-745	29	5	theorem	theorem	VERB
ejde-745	29	6	for	for	ADP
ejde-745	29	7	weakly	weakly	ADJ
ejde-745	29	8	sequentially	sequentially	ADV
ejde-745	29	9	continuous	continuous	ADJ
ejde-745	29	10	mappings	mapping	NOUN
ejde-745	29	11	given	give	VERB
ejde-745	29	12	by	by	ADP
ejde-745	29	13	kubiaczyk	kubiaczyk	NOUN
ejde-745	29	14	[	[	X
ejde-745	29	15	14	14	NUM
ejde-745	29	16	]	]	PUNCT
ejde-745	29	17	,	,	PUNCT
ejde-745	29	18	and	and	CCONJ
ejde-745	29	19	the	the	DET
ejde-745	29	20	properties	property	NOUN
ejde-745	29	21	of	of	ADP
ejde-745	29	22	measures	measure	NOUN
ejde-745	29	23	of	of	ADP
ejde-745	29	24	weak	weak	ADJ
ejde-745	29	25	noncompactness	noncompactness	NOUN
ejde-745	29	26	,	,	PUNCT
ejde-745	29	27	we	we	PRON
ejde-745	29	28	are	be	AUX
ejde-745	29	29	able	able	ADJ
ejde-745	29	30	to	to	PART
ejde-745	29	31	study	study	VERB
ejde-745	29	32	the	the	DET
ejde-745	29	33	existence	existence	NOUN
ejde-745	29	34	results	result	VERB
ejde-745	29	35	for	for	ADP
ejde-745	29	36	the	the	DET
ejde-745	29	37	problem	problem	NOUN
ejde-745	29	38	.	.	PUNCT
ejde-745	30	1	2	2	X
ejde-745	30	2	.	.	X
ejde-745	30	3	preliminaries	preliminary	NOUN
ejde-745	30	4	let	let	VERB
ejde-745	30	5	(	(	PUNCT
ejde-745	30	6	e	e	NOUN
ejde-745	30	7	,	,	PUNCT
ejde-745	30	8	∥	∥	X
ejde-745	30	9	·	·	PUNCT
ejde-745	30	10	∥	∥	X
ejde-745	30	11	)	)	PUNCT
ejde-745	30	12	be	be	AUX
ejde-745	30	13	a	a	DET
ejde-745	30	14	banach	banach	NOUN
ejde-745	30	15	space	space	NOUN
ejde-745	30	16	and	and	CCONJ
ejde-745	30	17	let	let	VERB
ejde-745	30	18	e∗	e∗	PROPN
ejde-745	30	19	be	be	AUX
ejde-745	30	20	the	the	DET
ejde-745	30	21	dual	dual	ADJ
ejde-745	30	22	space	space	NOUN
ejde-745	30	23	.	.	PUNCT
ejde-745	31	1	denote	denote	VERB
ejde-745	31	2	by	by	ADP
ejde-745	31	3	(	(	PUNCT
ejde-745	31	4	c(ia	c(ia	PROPN
ejde-745	31	5	,	,	PUNCT
ejde-745	31	6	e	e	NOUN
ejde-745	31	7	)	)	PUNCT
ejde-745	31	8	,	,	PUNCT
ejde-745	31	9	ω	ω	X
ejde-745	31	10	)	)	PUNCT
ejde-745	31	11	the	the	DET
ejde-745	31	12	space	space	NOUN
ejde-745	31	13	of	of	ADP
ejde-745	31	14	all	all	DET
ejde-745	31	15	continuous	continuous	ADJ
ejde-745	31	16	functions	function	NOUN
ejde-745	31	17	from	from	ADP
ejde-745	31	18	ia	ia	PROPN
ejde-745	31	19	to	to	AUX
ejde-745	31	20	e	e	PRON
ejde-745	31	21	endowed	endow	VERB
ejde-745	31	22	with	with	ADP
ejde-745	31	23	the	the	DET
ejde-745	31	24	topology	topology	NOUN
ejde-745	31	25	σ(c(ia	σ(c(ia	PROPN
ejde-745	31	26	,	,	PUNCT
ejde-745	31	27	e	e	NOUN
ejde-745	31	28	)	)	PUNCT
ejde-745	31	29	,	,	PUNCT
ejde-745	31	30	c(ia	c(ia	PROPN
ejde-745	31	31	,	,	PUNCT
ejde-745	31	32	e)∗	e)∗	PROPN
ejde-745	31	33	)	)	PUNCT
ejde-745	31	34	,	,	PUNCT
ejde-745	31	35	and	and	CCONJ
ejde-745	31	36	by	by	ADP
ejde-745	31	37	crd(ia	crd(ia	NOUN
ejde-745	31	38	,	,	PUNCT
ejde-745	31	39	e	e	NOUN
ejde-745	31	40	)	)	PUNCT
ejde-745	31	41	denote	denote	VERB
ejde-745	31	42	the	the	DET
ejde-745	31	43	space	space	NOUN
ejde-745	31	44	of	of	ADP
ejde-745	31	45	all	all	DET
ejde-745	31	46	rdcontinuous	rdcontinuous	ADJ
ejde-745	31	47	functions	function	NOUN
ejde-745	31	48	from	from	ADP
ejde-745	31	49	the	the	DET
ejde-745	31	50	time	time	NOUN
ejde-745	31	51	scale	scale	NOUN
ejde-745	31	52	interval	interval	NOUN
ejde-745	31	53	ia	ia	PROPN
ejde-745	31	54	to	to	PART
ejde-745	31	55	e.	e.	PROPN
ejde-745	31	56	by	by	ADP
ejde-745	31	57	µ∆	µ∆	NOUN
ejde-745	31	58	we	we	PRON
ejde-745	31	59	denote	denote	VERB
ejde-745	31	60	the	the	DET
ejde-745	31	61	lebesgue	lebesgue	ADJ
ejde-745	31	62	measure	measure	NOUN
ejde-745	31	63	on	on	ADP
ejde-745	31	64	time	time	NOUN
ejde-745	31	65	scale	scale	NOUN
ejde-745	31	66	t	t	PROPN
ejde-745	31	67	.	.	PUNCT
ejde-745	32	1	for	for	ADP
ejde-745	32	2	a	a	DET
ejde-745	32	3	precise	precise	ADJ
ejde-745	32	4	definition	definition	NOUN
ejde-745	32	5	and	and	CCONJ
ejde-745	32	6	basic	basic	ADJ
ejde-745	32	7	properties	property	NOUN
ejde-745	32	8	of	of	ADP
ejde-745	32	9	this	this	DET
ejde-745	32	10	measure	measure	NOUN
ejde-745	32	11	we	we	PRON
ejde-745	32	12	refer	refer	VERB
ejde-745	32	13	the	the	DET
ejde-745	32	14	reader	reader	NOUN
ejde-745	32	15	to	to	ADP
ejde-745	32	16	[	[	X
ejde-745	32	17	8	8	NUM
ejde-745	32	18	]	]	PUNCT
ejde-745	32	19	.	.	PUNCT
ejde-745	33	1	we	we	PRON
ejde-745	33	2	now	now	ADV
ejde-745	33	3	gather	gather	VERB
ejde-745	33	4	some	some	DET
ejde-745	33	5	well	well	ADV
ejde-745	33	6	-	-	PUNCT
ejde-745	33	7	known	know	VERB
ejde-745	33	8	definitions	definition	NOUN
ejde-745	33	9	and	and	CCONJ
ejde-745	33	10	results	result	NOUN
ejde-745	33	11	from	from	ADP
ejde-745	33	12	the	the	DET
ejde-745	33	13	literature	literature	NOUN
ejde-745	33	14	,	,	PUNCT
ejde-745	33	15	which	which	PRON
ejde-745	33	16	we	we	PRON
ejde-745	33	17	will	will	AUX
ejde-745	33	18	use	use	VERB
ejde-745	33	19	throughout	throughout	ADP
ejde-745	33	20	this	this	DET
ejde-745	33	21	article	article	NOUN
ejde-745	33	22	.	.	PUNCT
ejde-745	34	1	i.	i.	PROPN
ejde-745	34	2	to	to	PART
ejde-745	34	3	enable	enable	VERB
ejde-745	34	4	the	the	DET
ejde-745	34	5	reader	reader	NOUN
ejde-745	34	6	to	to	PART
ejde-745	34	7	understand	understand	VERB
ejde-745	34	8	the	the	DET
ejde-745	34	9	so	so	ADV
ejde-745	34	10	-	-	PUNCT
ejde-745	34	11	called	call	VERB
ejde-745	34	12	dynamic	dynamic	ADJ
ejde-745	34	13	equations	equation	NOUN
ejde-745	34	14	and	and	CCONJ
ejde-745	34	15	to	to	PART
ejde-745	34	16	follow	follow	VERB
ejde-745	34	17	this	this	DET
ejde-745	34	18	paper	paper	NOUN
ejde-745	34	19	easily	easily	ADV
ejde-745	34	20	,	,	PUNCT
ejde-745	34	21	we	we	PRON
ejde-745	34	22	present	present	VERB
ejde-745	34	23	some	some	DET
ejde-745	34	24	preliminary	preliminary	ADJ
ejde-745	34	25	definitions	definition	NOUN
ejde-745	34	26	and	and	CCONJ
ejde-745	34	27	notations	notation	NOUN
ejde-745	34	28	of	of	ADP
ejde-745	34	29	time	time	NOUN
ejde-745	34	30	scales	scale	NOUN
ejde-745	34	31	which	which	PRON
ejde-745	34	32	are	be	AUX
ejde-745	34	33	very	very	ADV
ejde-745	34	34	common	common	ADJ
ejde-745	34	35	in	in	ADP
ejde-745	34	36	the	the	DET
ejde-745	34	37	literature	literature	NOUN
ejde-745	34	38	(	(	PUNCT
ejde-745	34	39	see	see	VERB
ejde-745	34	40	[	[	X
ejde-745	34	41	2	2	NUM
ejde-745	34	42	,	,	PUNCT
ejde-745	34	43	3	3	NUM
ejde-745	34	44	,	,	PUNCT
ejde-745	34	45	7	7	NUM
ejde-745	34	46	,	,	PUNCT
ejde-745	34	47	12	12	NUM
ejde-745	34	48	,	,	PUNCT
ejde-745	34	49	13	13	NUM
ejde-745	34	50	]	]	PUNCT
ejde-745	34	51	and	and	CCONJ
ejde-745	34	52	references	reference	NOUN
ejde-745	34	53	therein	therein	ADV
ejde-745	34	54	)	)	PUNCT
ejde-745	34	55	.	.	PUNCT
ejde-745	35	1	a	a	DET
ejde-745	35	2	time	time	NOUN
ejde-745	35	3	scale	scale	NOUN
ejde-745	35	4	t	t	PROPN
ejde-745	35	5	is	be	AUX
ejde-745	35	6	a	a	DET
ejde-745	35	7	nonempty	nonempty	ADV
ejde-745	35	8	closed	close	VERB
ejde-745	35	9	subset	subset	NOUN
ejde-745	35	10	of	of	ADP
ejde-745	35	11	real	real	ADJ
ejde-745	35	12	numbers	number	NOUN
ejde-745	35	13	r	r	VERB
ejde-745	35	14	,	,	PUNCT
ejde-745	35	15	with	with	SCONJ
ejde-745	35	16	the	the	DET
ejde-745	35	17	subspace	subspace	NOUN
ejde-745	35	18	topology	topology	NOUN
ejde-745	35	19	inherited	inherit	VERB
ejde-745	35	20	from	from	ADP
ejde-745	35	21	the	the	DET
ejde-745	35	22	standard	standard	ADJ
ejde-745	35	23	topology	topology	NOUN
ejde-745	35	24	of	of	ADP
ejde-745	35	25	r.	r.	PROPN
ejde-745	35	26	by	by	ADP
ejde-745	35	27	an	an	DET
ejde-745	35	28	interval	interval	NOUN
ejde-745	35	29	we	we	PRON
ejde-745	35	30	mean	mean	VERB
ejde-745	35	31	the	the	DET
ejde-745	35	32	time	time	NOUN
ejde-745	35	33	scale	scale	NOUN
ejde-745	35	34	interval	interval	NOUN
ejde-745	35	35	ia	ia	NOUN
ejde-745	36	1	=	=	PUNCT
ejde-745	37	1	[	[	X
ejde-745	37	2	0	0	NUM
ejde-745	37	3	,	,	PUNCT
ejde-745	37	4	a	a	DET
ejde-745	37	5	]	]	PUNCT
ejde-745	37	6	∩	∩	ADJ
ejde-745	37	7	t	t	NOUN
ejde-745	37	8	=	=	SYM
ejde-745	37	9	{	{	PUNCT
ejde-745	37	10	t	t	PROPN
ejde-745	37	11	∈	∈	PROPN
ejde-745	37	12	t	t	PROPN
ejde-745	37	13	:	:	PUNCT
ejde-745	37	14	0	0	NUM
ejde-745	37	15	≤	≤	NUM
ejde-745	37	16	t	t	X
ejde-745	37	17	≤	≤	NOUN
ejde-745	37	18	a	a	PRON
ejde-745	37	19	}	}	PUNCT
ejde-745	37	20	=	=	PUNCT
ejde-745	38	1	[	[	X
ejde-745	38	2	0	0	NUM
ejde-745	38	3	,	,	PUNCT
ejde-745	38	4	a]t	a]t	NOUN
ejde-745	38	5	.	.	PUNCT
ejde-745	39	1	definition	definition	NOUN
ejde-745	39	2	2.1	2.1	NUM
ejde-745	39	3	.	.	PUNCT
ejde-745	40	1	the	the	DET
ejde-745	40	2	forward	forward	ADJ
ejde-745	40	3	jump	jump	NOUN
ejde-745	40	4	operator	operator	NOUN
ejde-745	40	5	σ	σ	NOUN
ejde-745	40	6	:	:	PUNCT
ejde-745	40	7	t	t	PROPN
ejde-745	40	8	→	→	SYM
ejde-745	40	9	t	t	PROPN
ejde-745	40	10	and	and	CCONJ
ejde-745	40	11	the	the	DET
ejde-745	40	12	backward	backward	ADJ
ejde-745	40	13	jump	jump	NOUN
ejde-745	40	14	operator	operator	NOUN
ejde-745	40	15	ρ	ρ	NOUN
ejde-745	40	16	:	:	PUNCT
ejde-745	40	17	t	t	PROPN
ejde-745	40	18	→	→	SYM
ejde-745	40	19	t	t	PROPN
ejde-745	40	20	as	as	ADP
ejde-745	40	21	σ(t	σ(t	PROPN
ejde-745	40	22	)	)	PUNCT
ejde-745	40	23	=	=	PUNCT
ejde-745	40	24	inf{s	inf{s	PROPN
ejde-745	40	25	∈	∈	PROPN
ejde-745	40	26	t	t	NOUN
ejde-745	40	27	:	:	PUNCT
ejde-745	40	28	s	s	X
ejde-745	40	29	>	>	X
ejde-745	40	30	t	t	PROPN
ejde-745	40	31	}	}	PUNCT
ejde-745	40	32	and	and	CCONJ
ejde-745	40	33	ρ(t	ρ(t	NUM
ejde-745	40	34	)	)	PUNCT
ejde-745	40	35	=	=	PUNCT
ejde-745	40	36	sup{s	sup{s	PROPN
ejde-745	40	37	∈	∈	PROPN
ejde-745	40	38	t	t	NOUN
ejde-745	40	39	:	:	PUNCT
ejde-745	40	40	s	s	X
ejde-745	40	41	<	<	X
ejde-745	40	42	t	t	PROPN
ejde-745	40	43	}	}	PUNCT
ejde-745	40	44	,	,	PUNCT
ejde-745	40	45	respectively	respectively	ADV
ejde-745	40	46	.	.	PUNCT
ejde-745	41	1	we	we	PRON
ejde-745	41	2	put	put	VERB
ejde-745	41	3	inf	inf	NOUN
ejde-745	41	4	∅	∅	NOUN
ejde-745	41	5	=	=	SYM
ejde-745	41	6	inf	inf	PROPN
ejde-745	41	7	t	t	PROPN
ejde-745	41	8	(	(	PUNCT
ejde-745	41	9	i.e.	i.e.	X
ejde-745	41	10	ρ(m	ρ(m	NUM
ejde-745	41	11	)	)	PUNCT
ejde-745	41	12	=	=	PUNCT
ejde-745	42	1	m	m	VERB
ejde-745	42	2	if	if	SCONJ
ejde-745	42	3	t	t	PROPN
ejde-745	42	4	has	have	VERB
ejde-745	42	5	a	a	DET
ejde-745	42	6	minimum	minimum	NOUN
ejde-745	42	7	m	m	NOUN
ejde-745	42	8	)	)	PUNCT
ejde-745	42	9	.	.	PUNCT
ejde-745	43	1	the	the	DET
ejde-745	43	2	jump	jump	NOUN
ejde-745	43	3	operators	operator	NOUN
ejde-745	43	4	σ	σ	PROPN
ejde-745	43	5	and	and	CCONJ
ejde-745	43	6	ρ	ρ	PROPN
ejde-745	43	7	allow	allow	VERB
ejde-745	43	8	the	the	DET
ejde-745	43	9	classification	classification	NOUN
ejde-745	43	10	of	of	ADP
ejde-745	43	11	points	point	NOUN
ejde-745	43	12	in	in	ADP
ejde-745	43	13	time	time	NOUN
ejde-745	43	14	scale	scale	NOUN
ejde-745	43	15	in	in	ADP
ejde-745	43	16	the	the	DET
ejde-745	43	17	following	following	ADJ
ejde-745	43	18	way	way	NOUN
ejde-745	43	19	:	:	PUNCT
ejde-745	43	20	t	t	PROPN
ejde-745	43	21	is	be	AUX
ejde-745	43	22	called	call	VERB
ejde-745	43	23	right	right	ADV
ejde-745	43	24	dense	dense	ADJ
ejde-745	43	25	,	,	PUNCT
ejde-745	43	26	right	right	ADJ
ejde-745	43	27	scattered	scatter	VERB
ejde-745	43	28	,	,	PUNCT
ejde-745	43	29	left	leave	VERB
ejde-745	43	30	dense	dense	ADJ
ejde-745	43	31	,	,	PUNCT
ejde-745	43	32	left	leave	VERB
ejde-745	43	33	scattered	scatter	VERB
ejde-745	43	34	,	,	PUNCT
ejde-745	43	35	dense	dense	ADJ
ejde-745	43	36	and	and	CCONJ
ejde-745	43	37	isolated	isolated	ADJ
ejde-745	43	38	if	if	SCONJ
ejde-745	43	39	σ(t	σ(t	NOUN
ejde-745	43	40	)	)	PUNCT
ejde-745	43	41	=	=	SYM
ejde-745	43	42	t	t	PROPN
ejde-745	43	43	,	,	PUNCT
ejde-745	43	44	σ(t	σ(t	PROPN
ejde-745	43	45	)	)	PUNCT
ejde-745	43	46	>	>	X
ejde-745	43	47	t	t	PROPN
ejde-745	43	48	,	,	PUNCT
ejde-745	43	49	ρ(t	ρ(t	NUM
ejde-745	43	50	)	)	PUNCT
ejde-745	43	51	=	=	SYM
ejde-745	43	52	t	t	PROPN
ejde-745	43	53	,	,	PUNCT
ejde-745	43	54	ρ(t	ρ(t	NUM
ejde-745	43	55	)	)	PUNCT
ejde-745	43	56	<	<	X
ejde-745	43	57	t	t	PROPN
ejde-745	43	58	,	,	PUNCT
ejde-745	43	59	ρ(t	ρ(t	NUM
ejde-745	43	60	)	)	PUNCT
ejde-745	43	61	=	=	SYM
ejde-745	43	62	t	t	NOUN
ejde-745	43	63	=	=	PUNCT
ejde-745	43	64	σ(t	σ(t	PROPN
ejde-745	43	65	)	)	PUNCT
ejde-745	43	66	respectively	respectively	ADV
ejde-745	43	67	.	.	PUNCT
ejde-745	44	1	definition	definition	NOUN
ejde-745	44	2	2.2	2.2	NUM
ejde-745	44	3	.	.	PUNCT
ejde-745	45	1	we	we	PRON
ejde-745	45	2	say	say	VERB
ejde-745	45	3	that	that	PRON
ejde-745	45	4	is	be	AUX
ejde-745	45	5	right	right	ADJ
ejde-745	45	6	-	-	PUNCT
ejde-745	45	7	dense	dense	ADJ
ejde-745	45	8	continuous	continuous	ADJ
ejde-745	45	9	(	(	PUNCT
ejde-745	45	10	rd	rd	NOUN
ejde-745	45	11	-	-	ADJ
ejde-745	45	12	continuous	continuous	ADJ
ejde-745	45	13	)	)	PUNCT
ejde-745	45	14	if	if	SCONJ
ejde-745	45	15	k	k	PROPN
ejde-745	45	16	is	be	AUX
ejde-745	45	17	continuous	continuous	ADJ
ejde-745	45	18	at	at	ADP
ejde-745	45	19	every	every	DET
ejde-745	45	20	right	right	ADJ
ejde-745	45	21	-	-	PUNCT
ejde-745	45	22	dense	dense	ADJ
ejde-745	45	23	point	point	NOUN
ejde-745	45	24	t	t	PROPN
ejde-745	45	25	∈	∈	PROPN
ejde-745	45	26	t	t	PROPN
ejde-745	45	27	and	and	CCONJ
ejde-745	45	28	lims→t−	lims→t−	PROPN
ejde-745	45	29	k(s	k(s	PROPN
ejde-745	45	30	)	)	PUNCT
ejde-745	45	31	exists	exist	VERB
ejde-745	45	32	and	and	CCONJ
ejde-745	45	33	is	be	AUX
ejde-745	45	34	finite	finite	ADJ
ejde-745	45	35	at	at	ADP
ejde-745	45	36	every	every	DET
ejde-745	45	37	left	left	ADJ
ejde-745	45	38	-	-	PUNCT
ejde-745	45	39	dense	dense	ADJ
ejde-745	45	40	point	point	NOUN
ejde-745	45	41	t	t	PROPN
ejde-745	45	42	∈	∈	PROPN
ejde-745	45	43	t	t	PROPN
ejde-745	45	44	.	.	PUNCT
ejde-745	46	1	ejde-2024/36	ejde-2024/36	NOUN
ejde-745	46	2	existence	existence	NOUN
ejde-745	46	3	of	of	ADP
ejde-745	46	4	pseudosolutions	pseudosolution	NOUN
ejde-745	46	5	3	3	NUM
ejde-745	46	6	definition	definition	NOUN
ejde-745	46	7	2.3	2.3	NUM
ejde-745	46	8	.	.	PUNCT
ejde-745	47	1	fix	fix	VERB
ejde-745	47	2	t	t	PROPN
ejde-745	47	3	∈	∈	PROPN
ejde-745	47	4	t	t	PROPN
ejde-745	47	5	.	.	PUNCT
ejde-745	48	1	let	let	VERB
ejde-745	48	2	f	f	NOUN
ejde-745	48	3	:	:	PUNCT
ejde-745	48	4	ia	ia	PROPN
ejde-745	48	5	→	→	PROPN
ejde-745	48	6	e.	e.	PROPN
ejde-745	48	7	then	then	ADV
ejde-745	48	8	we	we	PRON
ejde-745	48	9	define	define	VERB
ejde-745	48	10	∆-derivative	∆-derivative	NOUN
ejde-745	48	11	of	of	ADP
ejde-745	48	12	f	f	PROPN
ejde-745	48	13	by	by	ADP
ejde-745	48	14	f∆(t	f∆(t	NOUN
ejde-745	48	15	)	)	PUNCT
ejde-745	49	1	=	=	VERB
ejde-745	50	1	lim	lim	PROPN
ejde-745	50	2	s→t	s→t	NUM
ejde-745	50	3	f(σ(t))−	f(σ(t))−	PROPN
ejde-745	50	4	f(s	f(	NOUN
ejde-745	50	5	)	)	PUNCT
ejde-745	51	1	σ(t)−	σ(t)−	PROPN
ejde-745	51	2	s	s	PROPN
ejde-745	51	3	.	.	PUNCT
ejde-745	52	1	the	the	DET
ejde-745	52	2	function	function	NOUN
ejde-745	52	3	f	f	PROPN
ejde-745	52	4	is	be	AUX
ejde-745	52	5	called	call	VERB
ejde-745	52	6	∆-differentiable	∆-differentiable	ADJ
ejde-745	52	7	on	on	ADP
ejde-745	52	8	t	t	PROPN
ejde-745	52	9	,	,	PUNCT
ejde-745	52	10	if	if	SCONJ
ejde-745	52	11	for	for	ADP
ejde-745	52	12	each	each	DET
ejde-745	52	13	t	t	PROPN
ejde-745	52	14	∈	∈	PROPN
ejde-745	52	15	t	t	NOUN
ejde-745	52	16	there	there	PRON
ejde-745	52	17	exists	exist	VERB
ejde-745	52	18	f∆(t	f∆(t	NOUN
ejde-745	52	19	)	)	PUNCT
ejde-745	52	20	.	.	PUNCT
ejde-745	53	1	note	note	VERB
ejde-745	53	2	that	that	SCONJ
ejde-745	53	3	(	(	PUNCT
ejde-745	53	4	1	1	X
ejde-745	53	5	)	)	PUNCT
ejde-745	53	6	f∆	f∆	NOUN
ejde-745	54	1	=	=	PUNCT
ejde-745	55	1	f	f	X
ejde-745	55	2	′	′	NOUN
ejde-745	55	3	is	be	AUX
ejde-745	55	4	the	the	DET
ejde-745	55	5	usual	usual	ADJ
ejde-745	55	6	derivative	derivative	NOUN
ejde-745	55	7	if	if	SCONJ
ejde-745	55	8	t	t	NOUN
ejde-745	55	9	=	=	SYM
ejde-745	55	10	r	r	NOUN
ejde-745	55	11	,	,	PUNCT
ejde-745	55	12	(	(	PUNCT
ejde-745	55	13	2	2	NUM
ejde-745	55	14	)	)	PUNCT
ejde-745	55	15	f∆	f∆	NOUN
ejde-745	55	16	=	=	SYM
ejde-745	55	17	∆f	∆f	PROPN
ejde-745	55	18	,	,	PUNCT
ejde-745	55	19	is	be	AUX
ejde-745	55	20	the	the	DET
ejde-745	55	21	usual	usual	ADJ
ejde-745	55	22	forward	forward	ADJ
ejde-745	55	23	difference	difference	NOUN
ejde-745	55	24	operator	operator	NOUN
ejde-745	55	25	if	if	SCONJ
ejde-745	55	26	t	t	PROPN
ejde-745	55	27	=	=	SYM
ejde-745	55	28	z	z	PROPN
ejde-745	55	29	,	,	PUNCT
ejde-745	55	30	(	(	PUNCT
ejde-745	55	31	3	3	X
ejde-745	55	32	)	)	PUNCT
ejde-745	55	33	f∆	f∆	NOUN
ejde-745	55	34	=	=	PUNCT
ejde-745	55	35	dqf	dqf	NOUN
ejde-745	55	36	is	be	AUX
ejde-745	55	37	the	the	DET
ejde-745	55	38	q	q	NOUN
ejde-745	55	39	-	-	NOUN
ejde-745	55	40	derivative	derivative	ADJ
ejde-745	55	41	if	if	SCONJ
ejde-745	55	42	t	t	NOUN
ejde-745	55	43	=	=	SYM
ejde-745	55	44	qn0	qn0	PROPN
ejde-745	55	45	=	=	X
ejde-745	55	46	{	{	PUNCT
ejde-745	55	47	qt	qt	NOUN
ejde-745	55	48	:	:	PUNCT
ejde-745	55	49	t	t	PROPN
ejde-745	55	50	∈	∈	PROPN
ejde-745	55	51	n0	n0	PROPN
ejde-745	55	52	,	,	PUNCT
ejde-745	55	53	q	q	X
ejde-745	55	54	>	>	X
ejde-745	55	55	1	1	NUM
ejde-745	55	56	}	}	PUNCT
ejde-745	55	57	.	.	PUNCT
ejde-745	56	1	hence	hence	ADV
ejde-745	56	2	,	,	PUNCT
ejde-745	56	3	the	the	DET
ejde-745	56	4	time	time	NOUN
ejde-745	56	5	scale	scale	NOUN
ejde-745	56	6	allows	allow	VERB
ejde-745	56	7	us	we	PRON
ejde-745	56	8	to	to	PART
ejde-745	56	9	consider	consider	VERB
ejde-745	56	10	the	the	DET
ejde-745	56	11	unification	unification	NOUN
ejde-745	56	12	of	of	ADP
ejde-745	56	13	differential	differential	ADJ
ejde-745	56	14	,	,	PUNCT
ejde-745	56	15	difference	difference	NOUN
ejde-745	56	16	and	and	CCONJ
ejde-745	56	17	q	q	ADJ
ejde-745	56	18	-	-	PUNCT
ejde-745	56	19	difference	difference	NOUN
ejde-745	56	20	equations	equation	NOUN
ejde-745	56	21	as	as	ADP
ejde-745	56	22	particular	particular	ADJ
ejde-745	56	23	cases	case	NOUN
ejde-745	56	24	.	.	PUNCT
ejde-745	57	1	however	however	ADV
ejde-745	57	2	,	,	PUNCT
ejde-745	57	3	our	our	PRON
ejde-745	57	4	results	result	NOUN
ejde-745	57	5	also	also	ADV
ejde-745	57	6	hold	hold	VERB
ejde-745	57	7	for	for	ADP
ejde-745	57	8	more	more	ADV
ejde-745	57	9	exotic	exotic	ADJ
ejde-745	57	10	time	time	NOUN
ejde-745	57	11	scales	scale	NOUN
ejde-745	57	12	,	,	PUNCT
ejde-745	57	13	which	which	PRON
ejde-745	57	14	appear	appear	VERB
ejde-745	57	15	in	in	ADP
ejde-745	57	16	fields	field	NOUN
ejde-745	57	17	such	such	ADJ
ejde-745	57	18	as	as	ADP
ejde-745	57	19	mathematical	mathematical	ADJ
ejde-745	57	20	biology	biology	NOUN
ejde-745	57	21	or	or	CCONJ
ejde-745	57	22	economics	economic	NOUN
ejde-745	57	23	(	(	PUNCT
ejde-745	57	24	see	see	VERB
ejde-745	57	25	[	[	X
ejde-745	57	26	7	7	NUM
ejde-745	57	27	]	]	PUNCT
ejde-745	57	28	,	,	PUNCT
ejde-745	57	29	for	for	ADP
ejde-745	57	30	instance	instance	NOUN
ejde-745	57	31	)	)	PUNCT
ejde-745	57	32	.	.	PUNCT
ejde-745	58	1	ii	ii	PROPN
ejde-745	58	2	.	.	PUNCT
ejde-745	59	1	as	as	ADP
ejde-745	59	2	in	in	ADP
ejde-745	59	3	classical	classical	ADJ
ejde-745	59	4	case	case	NOUN
ejde-745	59	5	,	,	PUNCT
ejde-745	59	6	we	we	PRON
ejde-745	59	7	need	need	VERB
ejde-745	59	8	to	to	PART
ejde-745	59	9	introduce	introduce	VERB
ejde-745	59	10	vector	vector	NOUN
ejde-745	59	11	valued	value	VERB
ejde-745	59	12	henstock	henstock	PROPN
ejde-745	59	13	-	-	PUNCT
ejde-745	59	14	kurzweil	kurzweil	PROPN
ejde-745	59	15	∆-integrals	∆-integral	NOUN
ejde-745	59	16	.	.	PUNCT
ejde-745	60	1	definitions	definition	NOUN
ejde-745	60	2	and	and	CCONJ
ejde-745	60	3	basic	basic	ADJ
ejde-745	60	4	properties	property	NOUN
ejde-745	60	5	of	of	ADP
ejde-745	60	6	non	non	ADJ
ejde-745	60	7	absolute	absolute	ADJ
ejde-745	60	8	integrals	integral	NOUN
ejde-745	60	9	were	be	AUX
ejde-745	60	10	presented	present	VERB
ejde-745	60	11	in	in	ADP
ejde-745	60	12	[	[	X
ejde-745	60	13	9	9	NUM
ejde-745	60	14	]	]	PUNCT
ejde-745	60	15	.	.	PUNCT
ejde-745	61	1	we	we	PRON
ejde-745	61	2	will	will	AUX
ejde-745	61	3	use	use	VERB
ejde-745	61	4	the	the	DET
ejde-745	61	5	notation	notation	NOUN
ejde-745	61	6	η(t	η(t	NOUN
ejde-745	61	7	)	)	PUNCT
ejde-745	61	8	:	:	PUNCT
ejde-745	61	9	=	=	SYM
ejde-745	61	10	σ(t	σ(t	NOUN
ejde-745	61	11	)	)	PUNCT
ejde-745	61	12	−	−	PROPN
ejde-745	61	13	t(t	t(t	NOUN
ejde-745	61	14	)	)	PUNCT
ejde-745	61	15	where	where	SCONJ
ejde-745	61	16	η	η	PROPN
ejde-745	61	17	is	be	AUX
ejde-745	61	18	called	call	VERB
ejde-745	61	19	the	the	DET
ejde-745	61	20	graininess	graininess	NOUN
ejde-745	61	21	function	function	NOUN
ejde-745	61	22	and	and	CCONJ
ejde-745	61	23	v(t	v(t	NOUN
ejde-745	61	24	)	)	PUNCT
ejde-745	61	25	:	:	PUNCT
ejde-745	62	1	=	=	SYM
ejde-745	62	2	t−	t−	PROPN
ejde-745	62	3	ρ(t	ρ(t	NUM
ejde-745	62	4	)	)	PUNCT
ejde-745	62	5	,	,	PUNCT
ejde-745	62	6	where	where	SCONJ
ejde-745	62	7	v	v	NOUN
ejde-745	62	8	is	be	AUX
ejde-745	62	9	called	call	VERB
ejde-745	62	10	the	the	DET
ejde-745	62	11	left	left	ADJ
ejde-745	62	12	graininess	graininess	NOUN
ejde-745	62	13	function	function	NOUN
ejde-745	62	14	.	.	PUNCT
ejde-745	63	1	we	we	PRON
ejde-745	63	2	say	say	VERB
ejde-745	63	3	that	that	SCONJ
ejde-745	63	4	δ	δ	PROPN
ejde-745	63	5	=	=	PRON
ejde-745	63	6	(	(	PUNCT
ejde-745	63	7	δl	δl	PROPN
ejde-745	63	8	,	,	PUNCT
ejde-745	63	9	δr	δr	PROPN
ejde-745	63	10	)	)	PUNCT
ejde-745	63	11	is	be	AUX
ejde-745	63	12	a	a	DET
ejde-745	63	13	∆-gauge	∆-gauge	NOUN
ejde-745	63	14	for	for	ADP
ejde-745	63	15	time	time	NOUN
ejde-745	63	16	scale	scale	NOUN
ejde-745	63	17	interval	interval	NOUN
ejde-745	63	18	[	[	X
ejde-745	63	19	a	a	X
ejde-745	63	20	,	,	PUNCT
ejde-745	63	21	b	b	NOUN
ejde-745	63	22	]	]	PUNCT
ejde-745	63	23	provided	provide	VERB
ejde-745	63	24	δl(t	δl(t	NOUN
ejde-745	63	25	)	)	PUNCT
ejde-745	63	26	>	>	X
ejde-745	63	27	0	0	PUNCT
ejde-745	64	1	on	on	ADP
ejde-745	64	2	(	(	PUNCT
ejde-745	64	3	a	a	DET
ejde-745	64	4	,	,	PUNCT
ejde-745	64	5	b	b	NOUN
ejde-745	64	6	]	]	X
ejde-745	64	7	,	,	PUNCT
ejde-745	64	8	δr(t	δr(t	X
ejde-745	64	9	)	)	PUNCT
ejde-745	64	10	>	>	X
ejde-745	64	11	0	0	PUNCT
ejde-745	65	1	on	on	ADP
ejde-745	65	2	[	[	X
ejde-745	65	3	a	a	DET
ejde-745	65	4	,	,	PUNCT
ejde-745	65	5	b	b	NOUN
ejde-745	65	6	)	)	PUNCT
ejde-745	65	7	,	,	PUNCT
ejde-745	65	8	δl(t	δl(t	X
ejde-745	65	9	)	)	PUNCT
ejde-745	65	10	≥	≥	NOUN
ejde-745	65	11	0	0	NUM
ejde-745	65	12	,	,	PUNCT
ejde-745	65	13	δr(t	δr(t	NOUN
ejde-745	65	14	)	)	PUNCT
ejde-745	65	15	≥	≥	NOUN
ejde-745	65	16	0	0	NUM
ejde-745	65	17	and	and	CCONJ
ejde-745	65	18	δr(t	δr(t	NOUN
ejde-745	65	19	)	)	PUNCT
ejde-745	65	20	≥	≥	NOUN
ejde-745	65	21	η(t	η(t	NOUN
ejde-745	65	22	)	)	PUNCT
ejde-745	65	23	for	for	ADP
ejde-745	65	24	all	all	DET
ejde-745	65	25	t	t	NOUN
ejde-745	65	26	∈	∈	PROPN
ejde-745	65	27	[	[	X
ejde-745	65	28	a	a	DET
ejde-745	65	29	,	,	PUNCT
ejde-745	65	30	b	b	NOUN
ejde-745	65	31	)	)	PUNCT
ejde-745	65	32	.	.	PUNCT
ejde-745	66	1	we	we	PRON
ejde-745	66	2	say	say	VERB
ejde-745	66	3	that	that	SCONJ
ejde-745	66	4	a	a	DET
ejde-745	66	5	partition	partition	NOUN
ejde-745	66	6	d	d	NOUN
ejde-745	66	7	for	for	ADP
ejde-745	66	8	a	a	DET
ejde-745	66	9	time	time	NOUN
ejde-745	66	10	scale	scale	NOUN
ejde-745	66	11	interval	interval	NOUN
ejde-745	66	12	[	[	X
ejde-745	66	13	a	a	X
ejde-745	66	14	,	,	PUNCT
ejde-745	66	15	b	b	NOUN
ejde-745	66	16	]	]	PUNCT
ejde-745	66	17	given	give	VERB
ejde-745	66	18	by	by	ADP
ejde-745	66	19	d	d	PROPN
ejde-745	66	20	=	=	PUNCT
ejde-745	66	21	{	{	PUNCT
ejde-745	66	22	a	a	DET
ejde-745	66	23	=	=	SYM
ejde-745	66	24	t0	t0	PROPN
ejde-745	66	25	≤	≤	NOUN
ejde-745	66	26	ξ1	ξ1	PROPN
ejde-745	66	27	≤	≤	NUM
ejde-745	66	28	t1	t1	PROPN
ejde-745	66	29	≤	≤	PUNCT
ejde-745	66	30	·	·	PUNCT
ejde-745	66	31	·	·	PUNCT
ejde-745	66	32	·	·	PUNCT
ejde-745	66	33	≤	≤	NUM
ejde-745	67	1	tn−1	tn−1	ADJ
ejde-745	67	2	≤	≤	PUNCT
ejde-745	67	3	ξn	ξn	PROPN
ejde-745	67	4	≤	≤	NUM
ejde-745	67	5	tn	tn	NOUN
ejde-745	67	6	=	=	SYM
ejde-745	67	7	b	b	X
ejde-745	67	8	}	}	PUNCT
ejde-745	67	9	with	with	ADP
ejde-745	67	10	ti	ti	PROPN
ejde-745	67	11	>	>	X
ejde-745	67	12	ti−1	ti−1	NOUN
ejde-745	67	13	,	,	PUNCT
ejde-745	67	14	for	for	ADP
ejde-745	67	15	1	1	NUM
ejde-745	67	16	≤	≤	NUM
ejde-745	67	17	i	i	PRON
ejde-745	67	18	≤	≤	ADJ
ejde-745	67	19	n	n	CCONJ
ejde-745	67	20	and	and	CCONJ
ejde-745	67	21	ti	ti	NOUN
ejde-745	67	22	,	,	PUNCT
ejde-745	67	23	ξi	ξi	PROPN
ejde-745	67	24	∈	∈	PROPN
ejde-745	67	25	t	t	PROPN
ejde-745	67	26	is	be	AUX
ejde-745	67	27	δ	δ	NOUN
ejde-745	67	28	-	-	PUNCT
ejde-745	67	29	fine	fine	ADJ
ejde-745	67	30	if	if	SCONJ
ejde-745	67	31	ξi	ξi	NUM
ejde-745	67	32	−	−	PROPN
ejde-745	67	33	δl(ξi	δl(ξi	PROPN
ejde-745	67	34	)	)	PUNCT
ejde-745	67	35	≤	≤	NUM
ejde-745	67	36	ti−1	ti−1	NOUN
ejde-745	67	37	<	<	X
ejde-745	67	38	ti	ti	NOUN
ejde-745	67	39	≤	≤	NUM
ejde-745	67	40	ξi	ξi	NOUN
ejde-745	67	41	+	+	CCONJ
ejde-745	67	42	δr(ξi	δr(ξi	ADJ
ejde-745	67	43	)	)	PUNCT
ejde-745	67	44	,	,	PUNCT
ejde-745	67	45	for	for	ADP
ejde-745	67	46	1	1	NUM
ejde-745	67	47	≤	≤	NUM
ejde-745	68	1	i	i	PRON
ejde-745	68	2	≤	≤	ADJ
ejde-745	68	3	n.	n.	NOUN
ejde-745	68	4	definition	definition	NOUN
ejde-745	68	5	2.4	2.4	NUM
ejde-745	68	6	.	.	PUNCT
ejde-745	69	1	a	a	DET
ejde-745	69	2	function	function	NOUN
ejde-745	69	3	f	f	NOUN
ejde-745	69	4	:	:	PUNCT
ejde-745	70	1	[	[	X
ejde-745	70	2	a	a	X
ejde-745	70	3	,	,	PUNCT
ejde-745	70	4	b	b	NOUN
ejde-745	70	5	]	]	X
ejde-745	70	6	→	→	PUNCT
ejde-745	70	7	e	e	X
ejde-745	70	8	is	be	AUX
ejde-745	70	9	the	the	DET
ejde-745	70	10	henstock	henstock	NOUN
ejde-745	70	11	-	-	PUNCT
ejde-745	70	12	kurzweil	kurzweil	NOUN
ejde-745	70	13	∆-integrable	∆-integrable	ADJ
ejde-745	70	14	on	on	ADP
ejde-745	70	15	[	[	X
ejde-745	70	16	a	a	X
ejde-745	70	17	,	,	PUNCT
ejde-745	70	18	b	b	NOUN
ejde-745	70	19	]	]	X
ejde-745	70	20	(	(	PUNCT
ejde-745	70	21	hk	hk	PROPN
ejde-745	70	22	∆-integrable	∆-integrable	ADJ
ejde-745	70	23	in	in	ADP
ejde-745	70	24	short	short	ADJ
ejde-745	70	25	)	)	PUNCT
ejde-745	70	26	if	if	SCONJ
ejde-745	70	27	there	there	PRON
ejde-745	70	28	exists	exist	VERB
ejde-745	70	29	a	a	DET
ejde-745	70	30	function	function	NOUN
ejde-745	70	31	f	f	NOUN
ejde-745	70	32	:	:	PUNCT
ejde-745	71	1	[	[	X
ejde-745	71	2	a	a	X
ejde-745	71	3	,	,	PUNCT
ejde-745	71	4	b	b	NOUN
ejde-745	71	5	]	]	X
ejde-745	71	6	→	→	SYM
ejde-745	71	7	e	e	NOUN
ejde-745	71	8	,	,	PUNCT
ejde-745	71	9	defined	define	VERB
ejde-745	71	10	on	on	ADP
ejde-745	71	11	the	the	DET
ejde-745	71	12	subintervals	subinterval	NOUN
ejde-745	71	13	of	of	ADP
ejde-745	71	14	[	[	X
ejde-745	71	15	a	a	X
ejde-745	71	16	,	,	PUNCT
ejde-745	71	17	b	b	NOUN
ejde-745	71	18	]	]	X
ejde-745	71	19	,	,	PUNCT
ejde-745	71	20	satisfying	satisfy	VERB
ejde-745	71	21	the	the	DET
ejde-745	71	22	following	follow	VERB
ejde-745	71	23	property	property	NOUN
ejde-745	71	24	:	:	PUNCT
ejde-745	71	25	given	give	VERB
ejde-745	71	26	ϵ	ϵ	ADP
ejde-745	71	27	>	>	X
ejde-745	71	28	0	0	PUNCT
ejde-745	72	1	there	there	PRON
ejde-745	72	2	exists	exist	VERB
ejde-745	72	3	a	a	DET
ejde-745	72	4	positive	positive	ADJ
ejde-745	72	5	function	function	NOUN
ejde-745	72	6	δ	δ	PROPN
ejde-745	72	7	on	on	ADP
ejde-745	72	8	[	[	X
ejde-745	72	9	a	a	DET
ejde-745	72	10	,	,	PUNCT
ejde-745	72	11	b	b	NOUN
ejde-745	72	12	]	]	X
ejde-745	72	13	such	such	ADJ
ejde-745	72	14	that	that	SCONJ
ejde-745	72	15	d	d	NOUN
ejde-745	72	16	=	=	PRON
ejde-745	72	17	{	{	PUNCT
ejde-745	72	18	[	[	X
ejde-745	72	19	u	u	NOUN
ejde-745	72	20	,	,	PUNCT
ejde-745	72	21	v	v	ADP
ejde-745	72	22	]	]	X
ejde-745	72	23	,	,	PUNCT
ejde-745	72	24	ξ	ξ	X
ejde-745	72	25	}	}	PUNCT
ejde-745	72	26	is	be	AUX
ejde-745	72	27	δ	δ	PROPN
ejde-745	72	28	-	-	PUNCT
ejde-745	72	29	fine	fine	ADJ
ejde-745	72	30	division	division	NOUN
ejde-745	72	31	of	of	ADP
ejde-745	72	32	a	a	DET
ejde-745	72	33	[	[	X
ejde-745	72	34	a	a	X
ejde-745	72	35	,	,	PUNCT
ejde-745	72	36	b	b	NOUN
ejde-745	72	37	]	]	X
ejde-745	72	38	,	,	PUNCT
ejde-745	72	39	we	we	PRON
ejde-745	72	40	have	have	VERB
ejde-745	72	41	∥	∥	X
ejde-745	72	42	∑	∑	PUNCT
ejde-745	72	43	d	d	PROPN
ejde-745	72	44	f(ξ)(v	f(ξ)(v	PUNCT
ejde-745	72	45	−	−	PROPN
ejde-745	72	46	u)−	u)−	PROPN
ejde-745	72	47	(	(	PUNCT
ejde-745	72	48	f	f	PROPN
ejde-745	72	49	(	(	PUNCT
ejde-745	72	50	v)−	v)−	PROPN
ejde-745	72	51	f	f	X
ejde-745	72	52	(	(	PUNCT
ejde-745	72	53	u))∥	u))∥	ADV
ejde-745	72	54	<	<	X
ejde-745	72	55	ϵ	ϵ	X
ejde-745	72	56	definition	definition	NOUN
ejde-745	72	57	2.5	2.5	NUM
ejde-745	72	58	.	.	PUNCT
ejde-745	73	1	a	a	DET
ejde-745	73	2	function	function	NOUN
ejde-745	73	3	f	f	NOUN
ejde-745	73	4	:	:	PUNCT
ejde-745	73	5	ia	ia	PROPN
ejde-745	73	6	→	→	SYM
ejde-745	73	7	e	e	PROPN
ejde-745	73	8	is	be	AUX
ejde-745	73	9	henstock	henstock	NOUN
ejde-745	73	10	-	-	PUNCT
ejde-745	73	11	kurzweil	kurzweil	NOUN
ejde-745	73	12	-	-	PUNCT
ejde-745	73	13	pettis	pettis	PROPN
ejde-745	73	14	∆-integrable	∆-integrable	ADJ
ejde-745	73	15	(	(	PUNCT
ejde-745	73	16	hkp	hkp	PROPN
ejde-745	73	17	∆-integrable	∆-integrable	ADJ
ejde-745	73	18	for	for	ADP
ejde-745	73	19	short	short	ADJ
ejde-745	73	20	)	)	PUNCT
ejde-745	73	21	if	if	SCONJ
ejde-745	73	22	(	(	PUNCT
ejde-745	73	23	1	1	X
ejde-745	73	24	)	)	PUNCT
ejde-745	73	25	for	for	ADP
ejde-745	73	26	all	all	DET
ejde-745	73	27	x∗	x∗	PROPN
ejde-745	73	28	∈	∈	PROPN
ejde-745	73	29	e∗	e∗	PROPN
ejde-745	73	30	,	,	PUNCT
ejde-745	73	31	x∗f	x∗f	NUM
ejde-745	73	32	is	be	AUX
ejde-745	73	33	henstock	henstock	NOUN
ejde-745	73	34	-	-	PUNCT
ejde-745	73	35	kurzweil	kurzweil	NOUN
ejde-745	73	36	∆-integrable	∆-integrable	ADJ
ejde-745	73	37	on	on	ADP
ejde-745	73	38	ia	ia	PROPN
ejde-745	73	39	,	,	PUNCT
ejde-745	73	40	(	(	PUNCT
ejde-745	73	41	2	2	X
ejde-745	73	42	)	)	PUNCT
ejde-745	73	43	forall	forall	NOUN
ejde-745	73	44	t	t	PROPN
ejde-745	73	45	∈	∈	PROPN
ejde-745	73	46	ia	ia	PROPN
ejde-745	73	47	and	and	CCONJ
ejde-745	73	48	all	all	DET
ejde-745	73	49	x∗	x∗	PROPN
ejde-745	73	50	∈	∈	PROPN
ejde-745	73	51	e∗	e∗	PROPN
ejde-745	73	52	,	,	PUNCT
ejde-745	73	53	x∗g(t	x∗g(t	PROPN
ejde-745	73	54	)	)	PUNCT
ejde-745	74	1	=	=	PUNCT
ejde-745	74	2	(	(	PUNCT
ejde-745	74	3	delta	delta	NOUN
ejde-745	74	4	-	-	PUNCT
ejde-745	74	5	hk	hk	PROPN
ejde-745	74	6	)	)	PUNCT
ejde-745	74	7	∫	∫	PROPN
ejde-745	75	1	t	t	PROPN
ejde-745	75	2	0	0	NUM
ejde-745	75	3	x∗f(s)∆s	x∗f(s)∆s	PROPN
ejde-745	75	4	.	.	PUNCT
ejde-745	76	1	the	the	DET
ejde-745	76	2	function	function	NOUN
ejde-745	76	3	g	g	PROPN
ejde-745	76	4	will	will	AUX
ejde-745	76	5	be	be	AUX
ejde-745	76	6	called	call	VERB
ejde-745	76	7	a	a	DET
ejde-745	76	8	primitive	primitive	NOUN
ejde-745	76	9	of	of	ADP
ejde-745	76	10	f	f	PROPN
ejde-745	76	11	and	and	CCONJ
ejde-745	76	12	by	by	ADP
ejde-745	76	13	g(t	g(t	PROPN
ejde-745	76	14	)	)	PUNCT
ejde-745	77	1	=	=	PUNCT
ejde-745	77	2	(	(	PUNCT
ejde-745	77	3	delta	delta	NOUN
ejde-745	77	4	-	-	PUNCT
ejde-745	77	5	hk	hk	PROPN
ejde-745	77	6	)	)	PUNCT
ejde-745	77	7	)	)	PUNCT
ejde-745	78	1	∫	∫	PROPN
ejde-745	78	2	t	t	PROPN
ejde-745	78	3	0	0	NUM
ejde-745	78	4	f(s)∆s	f(s)∆s	PROPN
ejde-745	78	5	we	we	PRON
ejde-745	78	6	will	will	AUX
ejde-745	78	7	denote	denote	VERB
ejde-745	78	8	the	the	DET
ejde-745	78	9	henstock	henstock	NOUN
ejde-745	78	10	-	-	PUNCT
ejde-745	78	11	kurzweil	kurzweil	NOUN
ejde-745	78	12	-	-	PUNCT
ejde-745	78	13	pettis	pettis	PROPN
ejde-745	78	14	∆-integral	∆-integral	NOUN
ejde-745	78	15	of	of	ADP
ejde-745	78	16	fon	fon	PROPN
ejde-745	78	17	the	the	DET
ejde-745	78	18	interval	interval	NOUN
ejde-745	78	19	ia	ia	PROPN
ejde-745	78	20	.	.	PUNCT
ejde-745	79	1	in	in	ADP
ejde-745	79	2	[	[	X
ejde-745	79	3	9	9	NUM
ejde-745	79	4	]	]	PUNCT
ejde-745	79	5	the	the	DET
ejde-745	79	6	author	author	NOUN
ejde-745	79	7	give	give	VERB
ejde-745	79	8	examples	example	NOUN
ejde-745	79	9	of	of	ADP
ejde-745	79	10	henstock	henstock	NOUN
ejde-745	79	11	-	-	PUNCT
ejde-745	79	12	kurzweil	kurzweil	NOUN
ejde-745	79	13	-	-	PUNCT
ejde-745	79	14	pettis	pettis	PROPN
ejde-745	79	15	∆-integrable	∆-integrable	ADJ
ejde-745	79	16	functions	function	NOUN
ejde-745	79	17	which	which	PRON
ejde-745	79	18	are	be	AUX
ejde-745	79	19	not	not	PART
ejde-745	79	20	integrable	integrable	ADJ
ejde-745	79	21	in	in	ADP
ejde-745	79	22	the	the	DET
ejde-745	79	23	sense	sense	NOUN
ejde-745	79	24	of	of	ADP
ejde-745	79	25	pettis	pettis	NOUN
ejde-745	79	26	and	and	CCONJ
ejde-745	79	27	henstock	henstock	NOUN
ejde-745	79	28	-	-	PUNCT
ejde-745	79	29	kurzweil	kurzweil	NOUN
ejde-745	79	30	on	on	ADP
ejde-745	79	31	time	time	NOUN
ejde-745	79	32	scales	scale	NOUN
ejde-745	79	33	.	.	PUNCT
ejde-745	80	1	theorem	theorem	VERB
ejde-745	80	2	2.6	2.6	NUM
ejde-745	80	3	.	.	PUNCT
ejde-745	81	1	suppose	suppose	VERB
ejde-745	81	2	that	that	SCONJ
ejde-745	81	3	f	f	X
ejde-745	81	4	,	,	PUNCT
ejde-745	81	5	fn	fn	INTJ
ejde-745	81	6	:	:	PUNCT
ejde-745	81	7	[	[	X
ejde-745	81	8	a	a	X
ejde-745	81	9	,	,	PUNCT
ejde-745	81	10	b	b	NOUN
ejde-745	81	11	]	]	X
ejde-745	81	12	→	→	SYM
ejde-745	81	13	e	e	X
ejde-745	81	14	,	,	PUNCT
ejde-745	81	15	n	n	NOUN
ejde-745	81	16	=	=	SYM
ejde-745	81	17	1	1	NUM
ejde-745	81	18	,	,	PUNCT
ejde-745	81	19	2	2	NUM
ejde-745	81	20	,	,	PUNCT
ejde-745	81	21	.	.	PUNCT
ejde-745	81	22	.	.	PUNCT
ejde-745	81	23	.	.	PUNCT
ejde-745	82	1	are	be	AUX
ejde-745	82	2	hkp∆-integrable	hkp∆-integrable	ADJ
ejde-745	82	3	functions	function	NOUN
ejde-745	82	4	.	.	PUNCT
ejde-745	83	1	let	let	VERB
ejde-745	83	2	fn	fn	PRON
ejde-745	83	3	be	be	AUX
ejde-745	83	4	a	a	DET
ejde-745	83	5	primitive	primitive	NOUN
ejde-745	83	6	of	of	ADP
ejde-745	83	7	fn	fn	NOUN
ejde-745	83	8	.	.	PUNCT
ejde-745	84	1	if	if	SCONJ
ejde-745	84	2	one	one	PRON
ejde-745	84	3	assumes	assume	VERB
ejde-745	84	4	that	that	SCONJ
ejde-745	84	5	:	:	PUNCT
ejde-745	84	6	(	(	PUNCT
ejde-745	84	7	1	1	X
ejde-745	84	8	)	)	PUNCT
ejde-745	84	9	for	for	ADP
ejde-745	84	10	all	all	DET
ejde-745	84	11	x∗	x∗	PROPN
ejde-745	84	12	∈	∈	PROPN
ejde-745	84	13	e∗	e∗	PROPN
ejde-745	84	14	,	,	PUNCT
ejde-745	84	15	x∗fn(x	x∗fn(x	PROPN
ejde-745	84	16	)	)	PUNCT
ejde-745	84	17	→	→	SYM
ejde-745	84	18	x∗f(x	x∗f(x	PROPN
ejde-745	84	19	)	)	PUNCT
ejde-745	84	20	µ∆	µ∆	NOUN
ejde-745	84	21	almost	almost	ADV
ejde-745	84	22	everywhere	everywhere	ADV
ejde-745	84	23	on	on	ADP
ejde-745	84	24	ia	ia	PROPN
ejde-745	84	25	,	,	PUNCT
ejde-745	84	26	(	(	PUNCT
ejde-745	84	27	2	2	X
ejde-745	84	28	)	)	PUNCT
ejde-745	84	29	for	for	ADP
ejde-745	84	30	all	all	DET
ejde-745	84	31	x∗	x∗	PROPN
ejde-745	84	32	∈	∈	PROPN
ejde-745	84	33	e∗	e∗	NOUN
ejde-745	84	34	the	the	DET
ejde-745	84	35	family	family	NOUN
ejde-745	84	36	g	g	PROPN
ejde-745	84	37	=	=	PUNCT
ejde-745	84	38	{	{	PUNCT
ejde-745	84	39	x∗fn	x∗fn	NOUN
ejde-745	84	40	:	:	PUNCT
ejde-745	84	41	n	n	NOUN
ejde-745	84	42	=	=	SYM
ejde-745	84	43	1	1	NUM
ejde-745	84	44	,	,	PUNCT
ejde-745	84	45	2	2	NUM
ejde-745	84	46	,	,	PUNCT
ejde-745	84	47	.	.	PUNCT
ejde-745	84	48	.	.	PUNCT
ejde-745	84	49	.	.	PUNCT
ejde-745	85	1	}	}	PUNCT
ejde-745	85	2	is	be	AUX
ejde-745	85	3	uniformly	uniformly	ADV
ejde-745	85	4	acg∗	acg∗	NOUN
ejde-745	85	5	on	on	ADP
ejde-745	85	6	ia	ia	PROPN
ejde-745	85	7	(	(	PUNCT
ejde-745	85	8	i.e.	i.e.	X
ejde-745	85	9	,	,	PUNCT
ejde-745	85	10	weakly	weakly	ADJ
ejde-745	85	11	uniformly	uniformly	ADJ
ejde-745	85	12	acg∗	acg∗	NOUN
ejde-745	85	13	on	on	ADP
ejde-745	85	14	ia	ia	PROPN
ejde-745	85	15	)	)	PUNCT
ejde-745	85	16	,	,	PUNCT
ejde-745	85	17	(	(	PUNCT
ejde-745	85	18	3	3	X
ejde-745	85	19	)	)	PUNCT
ejde-745	85	20	for	for	ADP
ejde-745	85	21	each	each	DET
ejde-745	85	22	x∗	x∗	PROPN
ejde-745	85	23	∈	∈	PROPN
ejde-745	85	24	e∗	e∗	PROPN
ejde-745	85	25	the	the	DET
ejde-745	85	26	set	set	NOUN
ejde-745	85	27	g	g	NOUN
ejde-745	85	28	is	be	AUX
ejde-745	85	29	equicontinuous	equicontinuous	ADJ
ejde-745	85	30	on	on	ADP
ejde-745	85	31	ia	ia	PROPN
ejde-745	85	32	4	4	NUM
ejde-745	85	33	a.	a.	NOUN
ejde-745	85	34	sikorska	sikorska	PROPN
ejde-745	85	35	-	-	PUNCT
ejde-745	85	36	nowak	nowak	PROPN
ejde-745	85	37	ejde-2024/36	ejde-2024/36	NOUN
ejde-745	85	38	then	then	ADV
ejde-745	85	39	f	f	PROPN
ejde-745	85	40	is	be	AUX
ejde-745	85	41	∆-hkp	∆-hkp	NOUN
ejde-745	85	42	integrable	integrable	ADJ
ejde-745	85	43	on	on	ADP
ejde-745	85	44	ia	ia	PROPN
ejde-745	85	45	and	and	CCONJ
ejde-745	85	46	∫	∫	PROPN
ejde-745	85	47	t	t	PROPN
ejde-745	85	48	0	0	NUM
ejde-745	85	49	fn(s)∆s	fn(s)∆s	NOUN
ejde-745	85	50	tends	tend	VERB
ejde-745	85	51	weakly	weakly	ADJ
ejde-745	85	52	in	in	ADP
ejde-745	85	53	e	e	NOUN
ejde-745	85	54	to	to	ADP
ejde-745	85	55	∫	∫	PROPN
ejde-745	85	56	t	t	PROPN
ejde-745	85	57	0	0	NUM
ejde-745	85	58	f(s)∆s	f(s)∆s	NOUN
ejde-745	85	59	for	for	ADP
ejde-745	85	60	each	each	DET
ejde-745	85	61	t	t	PROPN
ejde-745	85	62	∈	∈	PROPN
ejde-745	85	63	ia	ia	PROPN
ejde-745	85	64	.	.	PROPN
ejde-745	85	65	theorem	theorem	VERB
ejde-745	85	66	2.7	2.7	NUM
ejde-745	85	67	(	(	PUNCT
ejde-745	85	68	(	(	PUNCT
ejde-745	85	69	mean	mean	VERB
ejde-745	85	70	value	value	NOUN
ejde-745	85	71	theorem	theorem	NOUN
ejde-745	85	72	)	)	PUNCT
ejde-745	85	73	.	.	PUNCT
ejde-745	86	1	for	for	ADP
ejde-745	86	2	each	each	DET
ejde-745	86	3	∆-subinterval	∆-subinterval	NOUN
ejde-745	86	4	[	[	X
ejde-745	86	5	c	c	X
ejde-745	86	6	,	,	PUNCT
ejde-745	86	7	d	d	X
ejde-745	86	8	]	]	X
ejde-745	86	9	⊂	⊂	X
ejde-745	87	1	[	[	X
ejde-745	87	2	a	a	X
ejde-745	87	3	,	,	PUNCT
ejde-745	87	4	b	b	NOUN
ejde-745	87	5	]	]	X
ejde-745	87	6	,	,	PUNCT
ejde-745	87	7	if	if	SCONJ
ejde-745	87	8	the	the	DET
ejde-745	87	9	integral	integral	ADJ
ejde-745	87	10	(	(	PUNCT
ejde-745	87	11	∆-hkp	∆-hkp	NOUN
ejde-745	87	12	)	)	PUNCT
ejde-745	87	13	∫	∫	PROPN
ejde-745	88	1	d	d	PROPN
ejde-745	88	2	c	c	PROPN
ejde-745	88	3	y(s)∆s	y(s)∆s	PROPN
ejde-745	88	4	exists	exist	VERB
ejde-745	88	5	,	,	PUNCT
ejde-745	88	6	then	then	ADV
ejde-745	88	7	we	we	PRON
ejde-745	88	8	have	have	VERB
ejde-745	88	9	(	(	PUNCT
ejde-745	88	10	∆-hkp	∆-hkp	NOUN
ejde-745	88	11	)	)	PUNCT
ejde-745	88	12	∫	∫	PROPN
ejde-745	89	1	d	d	PROPN
ejde-745	89	2	c	c	PROPN
ejde-745	89	3	y(s)∆s	y(s)∆s	PROPN
ejde-745	89	4	∈	∈	PROPN
ejde-745	89	5	µ∆([c	µ∆([c	PROPN
ejde-745	89	6	,	,	PUNCT
ejde-745	89	7	d	d	NOUN
ejde-745	89	8	]	]	X
ejde-745	89	9	)	)	PUNCT
ejde-745	90	1	·	·	PUNCT
ejde-745	90	2	convy([c	convy([c	PROPN
ejde-745	90	3	,	,	PUNCT
ejde-745	90	4	d	d	X
ejde-745	90	5	]	]	X
ejde-745	90	6	)	)	PUNCT
ejde-745	90	7	,	,	PUNCT
ejde-745	90	8	where	where	SCONJ
ejde-745	90	9	convy([c	convy([c	NOUN
ejde-745	90	10	,	,	PUNCT
ejde-745	90	11	d	d	NOUN
ejde-745	90	12	]	]	X
ejde-745	90	13	)	)	PUNCT
ejde-745	90	14	denotes	denote	VERB
ejde-745	90	15	the	the	DET
ejde-745	90	16	close	close	ADJ
ejde-745	90	17	convex	convex	NOUN
ejde-745	90	18	hull	hull	NOUN
ejde-745	90	19	of	of	ADP
ejde-745	90	20	the	the	DET
ejde-745	90	21	set	set	NOUN
ejde-745	90	22	y([c	y([c	PROPN
ejde-745	90	23	,	,	PUNCT
ejde-745	90	24	d	d	NOUN
ejde-745	90	25	]	]	X
ejde-745	90	26	)	)	PUNCT
ejde-745	90	27	.	.	PUNCT
ejde-745	91	1	for	for	ADP
ejde-745	91	2	completeness	completeness	NOUN
ejde-745	91	3	we	we	PRON
ejde-745	91	4	introduce	introduce	VERB
ejde-745	91	5	the	the	DET
ejde-745	91	6	definitions	definition	NOUN
ejde-745	91	7	of	of	ADP
ejde-745	91	8	the	the	DET
ejde-745	91	9	caputo	caputo	PROPN
ejde-745	91	10	derivative	derivative	NOUN
ejde-745	91	11	of	of	ADP
ejde-745	91	12	fractional	fractional	ADJ
ejde-745	91	13	order	order	NOUN
ejde-745	91	14	.	.	PUNCT
ejde-745	92	1	definition	definition	NOUN
ejde-745	92	2	2.8	2.8	NUM
ejde-745	92	3	.	.	PUNCT
ejde-745	92	4	suppose	suppose	VERB
ejde-745	92	5	that	that	SCONJ
ejde-745	92	6	t	t	PROPN
ejde-745	92	7	is	be	AUX
ejde-745	92	8	a	a	DET
ejde-745	92	9	time	time	NOUN
ejde-745	92	10	scale	scale	NOUN
ejde-745	92	11	.	.	PUNCT
ejde-745	93	1	the	the	DET
ejde-745	93	2	caputo	caputo	PROPN
ejde-745	93	3	fractional	fractional	PROPN
ejde-745	93	4	derivative	derivative	NOUN
ejde-745	93	5	of	of	ADP
ejde-745	93	6	g	g	PROPN
ejde-745	93	7	is	be	AUX
ejde-745	93	8	defined	define	VERB
ejde-745	93	9	by	by	ADP
ejde-745	93	10	c	c	PROPN
ejde-745	93	11	t∆	t∆	PROPN
ejde-745	93	12	αg(t	αg(t	PUNCT
ejde-745	93	13	)	)	PUNCT
ejde-745	93	14	=	=	SYM
ejde-745	93	15	1	1	NUM
ejde-745	93	16	γ(n−	γ(n−	PROPN
ejde-745	93	17	α	α	NOUN
ejde-745	94	1	)	)	PUNCT
ejde-745	94	2	∫	∫	PROPN
ejde-745	94	3	t	t	PROPN
ejde-745	94	4	0	0	NUM
ejde-745	95	1	(	(	PUNCT
ejde-745	95	2	t−	t−	PROPN
ejde-745	95	3	s)n−α−1g∆	s)n−α−1g∆	ADV
ejde-745	95	4	n	n	CCONJ
ejde-745	95	5	(	(	PUNCT
ejde-745	95	6	s)∆s	s)∆s	PROPN
ejde-745	95	7	,	,	PUNCT
ejde-745	95	8	t	t	PROPN
ejde-745	95	9	∈	∈	PROPN
ejde-745	95	10	ia	ia	PROPN
ejde-745	95	11	,	,	PUNCT
ejde-745	95	12	where	where	SCONJ
ejde-745	95	13	n	n	ADV
ejde-745	95	14	=	=	PUNCT
ejde-745	96	1	[	[	X
ejde-745	96	2	α	α	X
ejde-745	96	3	]	]	X
ejde-745	96	4	+	+	CCONJ
ejde-745	96	5	1	1	NUM
ejde-745	96	6	and	and	CCONJ
ejde-745	96	7	[	[	X
ejde-745	96	8	α	α	X
ejde-745	96	9	]	]	X
ejde-745	96	10	denote	denote	VERB
ejde-745	96	11	the	the	DET
ejde-745	96	12	integer	integer	NOUN
ejde-745	96	13	part	part	NOUN
ejde-745	96	14	of	of	ADP
ejde-745	96	15	α	α	NOUN
ejde-745	96	16	and	and	CCONJ
ejde-745	96	17	integral	integral	ADJ
ejde-745	96	18	is	be	AUX
ejde-745	96	19	taken	take	VERB
ejde-745	96	20	in	in	ADP
ejde-745	96	21	the	the	DET
ejde-745	96	22	sense	sense	NOUN
ejde-745	96	23	of	of	ADP
ejde-745	96	24	delta	delta	NOUN
ejde-745	96	25	-	-	PUNCT
ejde-745	96	26	hkp	hkp	PROPN
ejde-745	96	27	,	,	PUNCT
ejde-745	96	28	γ	γ	X
ejde-745	96	29	is	be	AUX
ejde-745	96	30	the	the	DET
ejde-745	96	31	gamma	gamma	PROPN
ejde-745	96	32	function	function	NOUN
ejde-745	96	33	.	.	PUNCT
ejde-745	97	1	definition	definition	NOUN
ejde-745	97	2	2.9	2.9	NUM
ejde-745	97	3	.	.	PUNCT
ejde-745	97	4	suppose	suppose	VERB
ejde-745	97	5	that	that	SCONJ
ejde-745	97	6	t	t	PROPN
ejde-745	97	7	is	be	AUX
ejde-745	97	8	a	a	DET
ejde-745	97	9	time	time	NOUN
ejde-745	97	10	scale	scale	NOUN
ejde-745	97	11	,	,	PUNCT
ejde-745	97	12	g	g	NOUN
ejde-745	97	13	:	:	PUNCT
ejde-745	97	14	i	i	PROPN
ejde-745	97	15	→	→	PUNCT
ejde-745	97	16	e	e	NOUN
ejde-745	97	17	is	be	AUX
ejde-745	97	18	∆-hkp	∆-hkp	NOUN
ejde-745	97	19	integrable	integrable	ADJ
ejde-745	97	20	function	function	NOUN
ejde-745	97	21	.	.	PUNCT
ejde-745	98	1	the	the	DET
ejde-745	98	2	fractional	fractional	ADJ
ejde-745	98	3	∆-hkp	∆-hkp	NOUN
ejde-745	98	4	integral	integral	ADJ
ejde-745	98	5	of	of	ADP
ejde-745	98	6	the	the	DET
ejde-745	98	7	order	order	NOUN
ejde-745	98	8	α	α	X
ejde-745	98	9	∈	∈	PROPN
ejde-745	98	10	r+	r+	NOUN
ejde-745	98	11	of	of	ADP
ejde-745	98	12	g	g	PROPN
ejde-745	98	13	is	be	AUX
ejde-745	98	14	defined	define	VERB
ejde-745	98	15	by	by	ADP
ejde-745	98	16	iαg(t	iαg(t	PROPN
ejde-745	98	17	)	)	PUNCT
ejde-745	98	18	=	=	SYM
ejde-745	99	1	∫	∫	PROPN
ejde-745	99	2	t	t	PROPN
ejde-745	99	3	a	a	X
ejde-745	99	4	(	(	PUNCT
ejde-745	99	5	t−	t−	PROPN
ejde-745	99	6	s)α−1	s)α−1	PROPN
ejde-745	99	7	γ(α	γ(α	NOUN
ejde-745	99	8	)	)	PUNCT
ejde-745	99	9	g(s)∆s	g(s)∆s	NOUN
ejde-745	99	10	,	,	PUNCT
ejde-745	99	11	where	where	SCONJ
ejde-745	99	12	integral	integral	ADJ
ejde-745	99	13	is	be	AUX
ejde-745	99	14	taken	take	VERB
ejde-745	99	15	in	in	ADP
ejde-745	99	16	the	the	DET
ejde-745	99	17	sense	sense	NOUN
ejde-745	99	18	of	of	ADP
ejde-745	99	19	∆-hkp	∆-hkp	NOUN
ejde-745	99	20	and	and	CCONJ
ejde-745	99	21	γ	γ	X
ejde-745	99	22	is	be	AUX
ejde-745	99	23	the	the	DET
ejde-745	99	24	gamma	gamma	PROPN
ejde-745	99	25	function	function	NOUN
ejde-745	99	26	.	.	PUNCT
ejde-745	100	1	iii	iii	X
ejde-745	100	2	.	.	PUNCT
ejde-745	101	1	our	our	PRON
ejde-745	101	2	fundamental	fundamental	ADJ
ejde-745	101	3	tools	tool	NOUN
ejde-745	101	4	is	be	AUX
ejde-745	101	5	the	the	DET
ejde-745	101	6	deblasi	deblasi	NOUN
ejde-745	101	7	measure	measure	NOUN
ejde-745	101	8	of	of	ADP
ejde-745	101	9	weak	weak	ADJ
ejde-745	101	10	noncompactness	noncompactness	ADJ
ejde-745	101	11	β(a	β(a	NOUN
ejde-745	101	12	)	)	PUNCT
ejde-745	101	13	.	.	PUNCT
ejde-745	102	1	the	the	DET
ejde-745	102	2	deblasi	deblasi	NOUN
ejde-745	102	3	measure	measure	NOUN
ejde-745	102	4	of	of	ADP
ejde-745	102	5	weak	weak	ADJ
ejde-745	102	6	noncompactness	noncompactness	ADJ
ejde-745	102	7	β(a	β(a	NOUN
ejde-745	102	8	)	)	PUNCT
ejde-745	102	9	is	be	AUX
ejde-745	102	10	defined	define	VERB
ejde-745	102	11	by	by	ADP
ejde-745	102	12	β(a	β(a	PROPN
ejde-745	102	13	)	)	PUNCT
ejde-745	102	14	=	=	PUNCT
ejde-745	102	15	inf{t	inf{t	VERB
ejde-745	102	16	>	>	X
ejde-745	102	17	0	0	NUM
ejde-745	103	1	:	:	PUNCT
ejde-745	103	2	there	there	PRON
ejde-745	103	3	exists	exist	VERB
ejde-745	103	4	c	c	NOUN
ejde-745	103	5	∈	∈	NOUN
ejde-745	103	6	kω	kω	VERB
ejde-745	103	7	such	such	DET
ejde-745	103	8	that	that	SCONJ
ejde-745	103	9	a	a	DET
ejde-745	103	10	⊂	⊂	X
ejde-745	103	11	c	c	X
ejde-745	103	12	+	+	CCONJ
ejde-745	103	13	tb0	tb0	NOUN
ejde-745	103	14	}	}	PUNCT
ejde-745	103	15	where	where	SCONJ
ejde-745	103	16	kω	kω	PROPN
ejde-745	103	17	is	be	AUX
ejde-745	103	18	the	the	DET
ejde-745	103	19	set	set	NOUN
ejde-745	103	20	of	of	ADP
ejde-745	103	21	weakly	weakly	ADJ
ejde-745	103	22	compact	compact	ADJ
ejde-745	103	23	subsets	subset	NOUN
ejde-745	103	24	of	of	ADP
ejde-745	103	25	e	e	NOUN
ejde-745	103	26	and	and	CCONJ
ejde-745	103	27	b0	b0	NOUN
ejde-745	103	28	is	be	AUX
ejde-745	103	29	the	the	DET
ejde-745	103	30	norm	norm	NOUN
ejde-745	103	31	unit	unit	NOUN
ejde-745	103	32	ball	ball	PROPN
ejde-745	103	33	in	in	ADP
ejde-745	103	34	e.	e.	PROPN
ejde-745	103	35	the	the	DET
ejde-745	103	36	properties	property	NOUN
ejde-745	103	37	of	of	ADP
ejde-745	103	38	the	the	DET
ejde-745	103	39	measure	measure	NOUN
ejde-745	103	40	of	of	ADP
ejde-745	103	41	noncompactness	noncompactness	ADJ
ejde-745	103	42	β(a	β(a	NOUN
ejde-745	103	43	)	)	PUNCT
ejde-745	103	44	are	be	AUX
ejde-745	103	45	as	as	SCONJ
ejde-745	103	46	follows	follow	VERB
ejde-745	103	47	:	:	PUNCT
ejde-745	103	48	(	(	PUNCT
ejde-745	103	49	i	i	NOUN
ejde-745	103	50	)	)	PUNCT
ejde-745	103	51	if	if	SCONJ
ejde-745	103	52	a	a	DET
ejde-745	103	53	⊂	⊂	PROPN
ejde-745	103	54	b	b	PROPN
ejde-745	103	55	then	then	ADV
ejde-745	103	56	β(a	β(a	PROPN
ejde-745	103	57	)	)	PUNCT
ejde-745	103	58	≤	≤	NOUN
ejde-745	103	59	β(b	β(b	PUNCT
ejde-745	103	60	)	)	PUNCT
ejde-745	103	61	;	;	PUNCT
ejde-745	103	62	(	(	PUNCT
ejde-745	103	63	ii	ii	NOUN
ejde-745	103	64	)	)	PUNCT
ejde-745	103	65	β(a	β(a	PROPN
ejde-745	103	66	)	)	PUNCT
ejde-745	103	67	=	=	SYM
ejde-745	103	68	0	0	PUNCT
ejde-745	104	1	if	if	SCONJ
ejde-745	104	2	and	and	CCONJ
ejde-745	104	3	only	only	ADV
ejde-745	104	4	if	if	SCONJ
ejde-745	104	5	a	a	PRON
ejde-745	104	6	is	be	AUX
ejde-745	104	7	relatively	relatively	ADV
ejde-745	104	8	weakly	weakly	ADJ
ejde-745	104	9	compact	compact	ADJ
ejde-745	104	10	;	;	PUNCT
ejde-745	104	11	(	(	PUNCT
ejde-745	104	12	iii	iii	X
ejde-745	104	13	)	)	PUNCT
ejde-745	104	14	β(a	β(a	NOUN
ejde-745	104	15	∪b	∪b	X
ejde-745	104	16	)	)	PUNCT
ejde-745	104	17	=	=	SYM
ejde-745	104	18	max{β(a	max{β(a	PROPN
ejde-745	104	19	)	)	PUNCT
ejde-745	104	20	,	,	PUNCT
ejde-745	104	21	β(b	β(b	PUNCT
ejde-745	104	22	)	)	PUNCT
ejde-745	104	23	}	}	PUNCT
ejde-745	104	24	;	;	PUNCT
ejde-745	104	25	(	(	PUNCT
ejde-745	104	26	iv	iv	X
ejde-745	104	27	)	)	PUNCT
ejde-745	104	28	β(āω	β(āω	NUM
ejde-745	104	29	)	)	PUNCT
ejde-745	105	1	=	=	SYM
ejde-745	105	2	β(a	β(a	PROPN
ejde-745	105	3	)	)	PUNCT
ejde-745	105	4	,	,	PUNCT
ejde-745	105	5	where	where	SCONJ
ejde-745	105	6	āω	āω	PROPN
ejde-745	105	7	denotes	denote	VERB
ejde-745	105	8	the	the	DET
ejde-745	105	9	weak	weak	ADJ
ejde-745	105	10	closure	closure	NOUN
ejde-745	105	11	of	of	ADP
ejde-745	105	12	a	a	DET
ejde-745	105	13	(	(	PUNCT
ejde-745	105	14	v	v	NOUN
ejde-745	105	15	)	)	PUNCT
ejde-745	105	16	β(λa	β(λa	NUM
ejde-745	105	17	)	)	PUNCT
ejde-745	105	18	=	=	SYM
ejde-745	105	19	|λ|β(a	|λ|β(a	PROPN
ejde-745	105	20	)	)	PUNCT
ejde-745	105	21	,	,	PUNCT
ejde-745	105	22	(	(	PUNCT
ejde-745	105	23	λ	λ	X
ejde-745	105	24	∈	∈	PROPN
ejde-745	105	25	r	r	NOUN
ejde-745	105	26	)	)	PUNCT
ejde-745	105	27	;	;	PUNCT
ejde-745	105	28	(	(	PUNCT
ejde-745	105	29	vi	vi	NOUN
ejde-745	105	30	)	)	PUNCT
ejde-745	105	31	β(a+b	β(a+b	PUNCT
ejde-745	105	32	)	)	PUNCT
ejde-745	105	33	≤	≤	NUM
ejde-745	105	34	β(a	β(a	PROPN
ejde-745	105	35	)	)	PUNCT
ejde-745	106	1	+	+	CCONJ
ejde-745	106	2	β(b	β(b	NUM
ejde-745	106	3	)	)	PUNCT
ejde-745	106	4	;	;	PUNCT
ejde-745	106	5	(	(	PUNCT
ejde-745	106	6	vii	vii	PROPN
ejde-745	106	7	)	)	PUNCT
ejde-745	106	8	β(conv(a	β(conv(a	PROPN
ejde-745	106	9	)	)	PUNCT
ejde-745	106	10	)	)	PUNCT
ejde-745	107	1	=	=	SYM
ejde-745	107	2	β(a	β(a	PROPN
ejde-745	107	3	)	)	PUNCT
ejde-745	107	4	,	,	PUNCT
ejde-745	107	5	where	where	SCONJ
ejde-745	107	6	conv(a	conv(a	NOUN
ejde-745	107	7	)	)	PUNCT
ejde-745	107	8	denotes	denote	VERB
ejde-745	107	9	the	the	DET
ejde-745	107	10	convex	convex	PROPN
ejde-745	107	11	extension	extension	NOUN
ejde-745	107	12	of	of	ADP
ejde-745	107	13	a.	a.	NOUN
ejde-745	107	14	theorem	theorem	NOUN
ejde-745	107	15	2.10	2.10	NUM
ejde-745	107	16	(	(	PUNCT
ejde-745	107	17	[	[	X
ejde-745	107	18	15	15	NUM
ejde-745	107	19	]	]	NUM
ejde-745	107	20	)	)	PUNCT
ejde-745	107	21	.	.	PUNCT
ejde-745	108	1	let	let	VERB
ejde-745	108	2	h	h	PROPN
ejde-745	108	3	⊂	⊂	PROPN
ejde-745	108	4	c(ia	c(ia	PROPN
ejde-745	108	5	,	,	PUNCT
ejde-745	108	6	e	e	NOUN
ejde-745	108	7	)	)	PUNCT
ejde-745	108	8	be	be	AUX
ejde-745	108	9	a	a	DET
ejde-745	108	10	family	family	NOUN
ejde-745	108	11	of	of	ADP
ejde-745	108	12	strongly	strongly	ADV
ejde-745	108	13	equicontinuous	equicontinuous	ADJ
ejde-745	108	14	functions	function	NOUN
ejde-745	108	15	.	.	PUNCT
ejde-745	109	1	let	let	VERB
ejde-745	109	2	h(t	h(t	PRON
ejde-745	109	3	)	)	PUNCT
ejde-745	110	1	=	=	PRON
ejde-745	110	2	{	{	PUNCT
ejde-745	110	3	h(t	h(t	PROPN
ejde-745	110	4	)	)	PUNCT
ejde-745	110	5	∈	∈	PROPN
ejde-745	110	6	e	e	NOUN
ejde-745	110	7	,	,	PUNCT
ejde-745	110	8	h	h	PROPN
ejde-745	110	9	∈	∈	PROPN
ejde-745	110	10	h	h	NOUN
ejde-745	110	11	}	}	PUNCT
ejde-745	110	12	,	,	PUNCT
ejde-745	110	13	for	for	ADP
ejde-745	110	14	t	t	PROPN
ejde-745	110	15	∈	∈	PROPN
ejde-745	110	16	ia	ia	PROPN
ejde-745	110	17	and	and	CCONJ
ejde-745	110	18	h(ia	h(ia	PROPN
ejde-745	110	19	)	)	PUNCT
ejde-745	110	20	=	=	PUNCT
ejde-745	111	1	⋃	⋃	ADP
ejde-745	111	2	t∈ia	t∈ia	NOUN
ejde-745	111	3	h(t	h(t	PROPN
ejde-745	111	4	)	)	PUNCT
ejde-745	111	5	.	.	PUNCT
ejde-745	112	1	then	then	ADV
ejde-745	112	2	βc(h	βc(h	PUNCT
ejde-745	112	3	)	)	PUNCT
ejde-745	112	4	=	=	SYM
ejde-745	112	5	sup	sup	NOUN
ejde-745	112	6	t∈ia	t∈ia	NOUN
ejde-745	112	7	β(h(t	β(h(t	PROPN
ejde-745	112	8	)	)	PUNCT
ejde-745	112	9	)	)	PUNCT
ejde-745	113	1	=	=	PUNCT
ejde-745	113	2	β(h(ia	β(h(ia	X
ejde-745	113	3	)	)	PUNCT
ejde-745	113	4	)	)	PUNCT
ejde-745	113	5	where	where	SCONJ
ejde-745	113	6	βc(h	βc(h	NUM
ejde-745	113	7	)	)	PUNCT
ejde-745	113	8	denotes	denote	VERB
ejde-745	113	9	the	the	DET
ejde-745	113	10	measure	measure	NOUN
ejde-745	113	11	of	of	ADP
ejde-745	113	12	weak	weak	ADJ
ejde-745	113	13	noncompactness	noncompactness	NOUN
ejde-745	113	14	in	in	ADP
ejde-745	113	15	c(ia	c(ia	PROPN
ejde-745	113	16	,	,	PUNCT
ejde-745	113	17	e	e	NOUN
ejde-745	113	18	)	)	PUNCT
ejde-745	113	19	,	,	PUNCT
ejde-745	113	20	and	and	CCONJ
ejde-745	113	21	the	the	DET
ejde-745	113	22	function	function	NOUN
ejde-745	113	23	t	t	PROPN
ejde-745	113	24	7→	7→	NUM
ejde-745	113	25	β(h(t	β(h(t	PROPN
ejde-745	113	26	)	)	PUNCT
ejde-745	113	27	)	)	PUNCT
ejde-745	113	28	is	be	AUX
ejde-745	113	29	continuous	continuous	ADJ
ejde-745	113	30	.	.	PUNCT
ejde-745	114	1	ejde-2024/36	ejde-2024/36	NOUN
ejde-745	114	2	existence	existence	NOUN
ejde-745	114	3	of	of	ADP
ejde-745	114	4	pseudosolutions	pseudosolution	NOUN
ejde-745	114	5	5	5	NUM
ejde-745	114	6	definition	definition	NOUN
ejde-745	114	7	2.11	2.11	NUM
ejde-745	114	8	.	.	PUNCT
ejde-745	115	1	a	a	DET
ejde-745	115	2	function	function	NOUN
ejde-745	115	3	f	f	NOUN
ejde-745	115	4	:	:	PUNCT
ejde-745	115	5	ia	ia	PROPN
ejde-745	115	6	→	→	SYM
ejde-745	115	7	e	e	PROPN
ejde-745	115	8	is	be	AUX
ejde-745	115	9	said	say	VERB
ejde-745	115	10	to	to	PART
ejde-745	115	11	be	be	AUX
ejde-745	115	12	weakly	weakly	ADV
ejde-745	115	13	continuous	continuous	ADJ
ejde-745	115	14	if	if	SCONJ
ejde-745	115	15	it	it	PRON
ejde-745	115	16	is	be	AUX
ejde-745	115	17	continuous	continuous	ADJ
ejde-745	115	18	from	from	ADP
ejde-745	115	19	ia	ia	PROPN
ejde-745	115	20	to	to	PART
ejde-745	115	21	e	e	PRON
ejde-745	115	22	endowed	endow	VERB
ejde-745	115	23	with	with	ADP
ejde-745	115	24	its	its	PRON
ejde-745	115	25	weak	weak	ADJ
ejde-745	115	26	topology	topology	NOUN
ejde-745	115	27	.	.	PUNCT
ejde-745	116	1	a	a	DET
ejde-745	116	2	function	function	NOUN
ejde-745	116	3	g	g	NOUN
ejde-745	116	4	:	:	PUNCT
ejde-745	116	5	e	e	X
ejde-745	116	6	→	→	PUNCT
ejde-745	116	7	e1	e1	VERB
ejde-745	116	8	where	where	SCONJ
ejde-745	116	9	e	e	NOUN
ejde-745	116	10	and	and	CCONJ
ejde-745	116	11	e1	e1	PROPN
ejde-745	116	12	are	be	AUX
ejde-745	116	13	banach	banach	ADV
ejde-745	116	14	spaces	space	NOUN
ejde-745	116	15	,	,	PUNCT
ejde-745	116	16	is	be	AUX
ejde-745	116	17	said	say	VERB
ejde-745	116	18	to	to	PART
ejde-745	116	19	be	be	AUX
ejde-745	116	20	weakly	weakly	ADV
ejde-745	116	21	sequentially	sequentially	ADV
ejde-745	116	22	continuous	continuous	ADJ
ejde-745	116	23	if	if	SCONJ
ejde-745	116	24	for	for	ADP
ejde-745	116	25	each	each	DET
ejde-745	116	26	weakly	weakly	ADJ
ejde-745	116	27	convergent	convergent	NOUN
ejde-745	116	28	sequence	sequence	NOUN
ejde-745	116	29	(	(	PUNCT
ejde-745	116	30	xn	xn	X
ejde-745	116	31	)	)	PUNCT
ejde-745	116	32	in	in	ADP
ejde-745	116	33	e	e	NOUN
ejde-745	116	34	,	,	PUNCT
ejde-745	116	35	the	the	DET
ejde-745	116	36	sequence	sequence	NOUN
ejde-745	116	37	(	(	PUNCT
ejde-745	116	38	g(xn	g(xn	NOUN
ejde-745	116	39	)	)	PUNCT
ejde-745	116	40	)	)	PUNCT
ejde-745	116	41	is	be	AUX
ejde-745	116	42	weakly	weakly	ADJ
ejde-745	116	43	convergent	convergent	NOUN
ejde-745	116	44	in	in	ADP
ejde-745	116	45	e1	e1	PROPN
ejde-745	116	46	.	.	PUNCT
ejde-745	117	1	when	when	SCONJ
ejde-745	117	2	the	the	DET
ejde-745	117	3	sequence	sequence	NOUN
ejde-745	117	4	xn	xn	PROPN
ejde-745	117	5	tends	tend	VERB
ejde-745	117	6	weakly	weakly	ADJ
ejde-745	117	7	to	to	ADP
ejde-745	117	8	x0	x0	PROPN
ejde-745	117	9	in	in	ADP
ejde-745	117	10	e	e	NOUN
ejde-745	117	11	,	,	PUNCT
ejde-745	117	12	we	we	PRON
ejde-745	117	13	will	will	AUX
ejde-745	117	14	write	write	VERB
ejde-745	117	15	xn	xn	PROPN
ejde-745	118	1	ω→	ω→	PROPN
ejde-745	119	1	x0	x0	PROPN
ejde-745	119	2	.	.	PUNCT
ejde-745	120	1	definition	definition	NOUN
ejde-745	120	2	2.12	2.12	NUM
ejde-745	120	3	(	(	PUNCT
ejde-745	120	4	[	[	X
ejde-745	120	5	12	12	NUM
ejde-745	120	6	]	]	NUM
ejde-745	120	7	)	)	PUNCT
ejde-745	120	8	.	.	PUNCT
ejde-745	121	1	a	a	DET
ejde-745	121	2	family	family	NOUN
ejde-745	121	3	f	f	PROPN
ejde-745	121	4	of	of	ADP
ejde-745	121	5	functions	function	NOUN
ejde-745	121	6	f	f	PROPN
ejde-745	121	7	is	be	AUX
ejde-745	121	8	said	say	VERB
ejde-745	121	9	to	to	PART
ejde-745	121	10	be	be	AUX
ejde-745	121	11	uniformly	uniformly	ADV
ejde-745	121	12	absolutely	absolutely	ADV
ejde-745	121	13	continuous	continuous	ADJ
ejde-745	121	14	in	in	ADP
ejde-745	121	15	the	the	DET
ejde-745	121	16	restricted	restricted	ADJ
ejde-745	121	17	sense	sense	NOUN
ejde-745	121	18	on	on	ADP
ejde-745	121	19	a	a	DET
ejde-745	121	20	or	or	CCONJ
ejde-745	121	21	in	in	ADP
ejde-745	121	22	short	short	ADJ
ejde-745	121	23	uniformly	uniformly	ADV
ejde-745	121	24	ac∗(a	ac∗(a	ADJ
ejde-745	121	25	)	)	PUNCT
ejde-745	121	26	,	,	PUNCT
ejde-745	121	27	if	if	SCONJ
ejde-745	121	28	for	for	ADP
ejde-745	121	29	every	every	DET
ejde-745	121	30	ϵ	ϵ	X
ejde-745	121	31	>	>	X
ejde-745	121	32	0	0	PUNCT
ejde-745	122	1	there	there	PRON
ejde-745	122	2	is	be	VERB
ejde-745	122	3	η	η	PROPN
ejde-745	122	4	>	>	X
ejde-745	122	5	0	0	PROPN
ejde-745	122	6	,	,	PUNCT
ejde-745	122	7	such	such	ADJ
ejde-745	122	8	that	that	PRON
ejde-745	122	9	for	for	ADP
ejde-745	122	10	every	every	DET
ejde-745	122	11	f	f	PROPN
ejde-745	122	12	in	in	ADP
ejde-745	122	13	f	f	PROPN
ejde-745	122	14	and	and	CCONJ
ejde-745	122	15	for	for	ADP
ejde-745	122	16	every	every	DET
ejde-745	122	17	finite	finite	NOUN
ejde-745	122	18	or	or	CCONJ
ejde-745	122	19	infinite	infinite	ADJ
ejde-745	122	20	sequence	sequence	NOUN
ejde-745	122	21	of	of	ADP
ejde-745	122	22	nonoverlapping	nonoverlapping	ADJ
ejde-745	122	23	intervals	interval	NOUN
ejde-745	122	24	{	{	PUNCT
ejde-745	122	25	[	[	X
ejde-745	122	26	ai	ai	NOUN
ejde-745	122	27	,	,	PUNCT
ejde-745	122	28	bi	bi	NOUN
ejde-745	122	29	]	]	X
ejde-745	122	30	}	}	PUNCT
ejde-745	122	31	with	with	ADP
ejde-745	122	32	ai	ai	PROPN
ejde-745	122	33	,	,	PUNCT
ejde-745	122	34	bi	bi	NOUN
ejde-745	122	35	∈	∈	PROPN
ejde-745	122	36	a	a	PRON
ejde-745	122	37	,	,	PUNCT
ejde-745	122	38	and	and	CCONJ
ejde-745	122	39	satisfying	satisfy	VERB
ejde-745	122	40	∑	∑	PUNCT
ejde-745	122	41	i	i	PRON
ejde-745	122	42	|bi	|bi	PUNCT
ejde-745	122	43	−	−	PROPN
ejde-745	122	44	ai|	ai|	PROPN
ejde-745	122	45	<	<	X
ejde-745	122	46	η	η	PROPN
ejde-745	122	47	,	,	PUNCT
ejde-745	122	48	we	we	PRON
ejde-745	122	49	have	have	VERB
ejde-745	122	50	∑	∑	PROPN
ejde-745	122	51	i	i	PRON
ejde-745	122	52	ω(f	ω(f	ADJ
ejde-745	122	53	,	,	PUNCT
ejde-745	122	54	[	[	X
ejde-745	122	55	ai	ai	NOUN
ejde-745	122	56	,	,	PUNCT
ejde-745	122	57	bi	bi	NOUN
ejde-745	122	58	]	]	X
ejde-745	122	59	)	)	PUNCT
ejde-745	122	60	<	<	X
ejde-745	123	1	ϵ	ϵ	X
ejde-745	123	2	where	where	SCONJ
ejde-745	123	3	ω	ω	PROPN
ejde-745	123	4	denotes	denote	VERB
ejde-745	123	5	the	the	DET
ejde-745	123	6	oscillation	oscillation	NOUN
ejde-745	123	7	of	of	ADP
ejde-745	123	8	f	f	PROPN
ejde-745	123	9	over	over	ADP
ejde-745	123	10	[	[	X
ejde-745	123	11	ai	ai	NOUN
ejde-745	123	12	,	,	PUNCT
ejde-745	123	13	bi	bi	NOUN
ejde-745	123	14	]	]	X
ejde-745	123	15	.	.	PUNCT
ejde-745	124	1	a	a	DET
ejde-745	124	2	family	family	NOUN
ejde-745	124	3	f	f	PROPN
ejde-745	124	4	of	of	ADP
ejde-745	124	5	functions	function	NOUN
ejde-745	124	6	f	f	PROPN
ejde-745	124	7	is	be	AUX
ejde-745	124	8	said	say	VERB
ejde-745	124	9	to	to	PART
ejde-745	124	10	be	be	AUX
ejde-745	124	11	uniformly	uniformly	ADV
ejde-745	124	12	generalized	generalize	VERB
ejde-745	124	13	absolutely	absolutely	ADV
ejde-745	124	14	continuous	continuous	ADJ
ejde-745	124	15	in	in	ADP
ejde-745	124	16	the	the	DET
ejde-745	124	17	restricted	restricted	ADJ
ejde-745	124	18	sense	sense	NOUN
ejde-745	124	19	on	on	ADP
ejde-745	124	20	[	[	X
ejde-745	124	21	a	a	X
ejde-745	124	22	,	,	PUNCT
ejde-745	124	23	b	b	NOUN
ejde-745	124	24	]	]	PUNCT
ejde-745	124	25	or	or	CCONJ
ejde-745	124	26	uniformly	uniformly	ADJ
ejde-745	124	27	acg∗([a	acg∗([a	NOUN
ejde-745	124	28	,	,	PUNCT
ejde-745	124	29	b	b	NOUN
ejde-745	124	30	]	]	X
ejde-745	124	31	)	)	PUNCT
ejde-745	124	32	if	if	SCONJ
ejde-745	124	33	[	[	X
ejde-745	124	34	a	a	X
ejde-745	124	35	,	,	PUNCT
ejde-745	124	36	b	b	X
ejde-745	124	37	]	]	X
ejde-745	124	38	is	be	AUX
ejde-745	124	39	the	the	DET
ejde-745	124	40	union	union	NOUN
ejde-745	124	41	of	of	ADP
ejde-745	124	42	a	a	DET
ejde-745	124	43	sequence	sequence	NOUN
ejde-745	124	44	of	of	ADP
ejde-745	124	45	closed	closed	ADJ
ejde-745	124	46	sets	set	NOUN
ejde-745	124	47	ai	ai	VERB
ejde-745	124	48	such	such	ADJ
ejde-745	124	49	that	that	SCONJ
ejde-745	124	50	on	on	ADP
ejde-745	124	51	each	each	PRON
ejde-745	124	52	ai	ai	VERB
ejde-745	124	53	the	the	DET
ejde-745	124	54	function	function	NOUN
ejde-745	124	55	f	f	PROPN
ejde-745	124	56	is	be	AUX
ejde-745	124	57	uniformly	uniformly	ADV
ejde-745	124	58	ac∗(ai	ac∗(ai	NOUN
ejde-745	124	59	)	)	PUNCT
ejde-745	124	60	.	.	PUNCT
ejde-745	125	1	in	in	ADP
ejde-745	125	2	the	the	DET
ejde-745	125	3	proof	proof	NOUN
ejde-745	125	4	of	of	ADP
ejde-745	125	5	the	the	DET
ejde-745	125	6	main	main	ADJ
ejde-745	125	7	theorem	theorem	NOUN
ejde-745	125	8	we	we	PRON
ejde-745	125	9	will	will	AUX
ejde-745	125	10	apply	apply	VERB
ejde-745	125	11	the	the	DET
ejde-745	125	12	following	following	ADJ
ejde-745	125	13	fixed	fix	VERB
ejde-745	125	14	point	point	NOUN
ejde-745	125	15	theorem	theorem	VERB
ejde-745	125	16	.	.	PUNCT
ejde-745	125	17	theorem	theorem	NOUN
ejde-745	125	18	2.13	2.13	NUM
ejde-745	125	19	(	(	PUNCT
ejde-745	125	20	[	[	X
ejde-745	125	21	14	14	NUM
ejde-745	125	22	]	]	NUM
ejde-745	125	23	)	)	PUNCT
ejde-745	125	24	.	.	PUNCT
ejde-745	126	1	let	let	VERB
ejde-745	126	2	x	x	PRON
ejde-745	126	3	be	be	AUX
ejde-745	126	4	a	a	DET
ejde-745	126	5	metrizable	metrizable	ADJ
ejde-745	126	6	locally	locally	ADV
ejde-745	126	7	convex	convex	ADJ
ejde-745	126	8	topological	topological	ADJ
ejde-745	126	9	vector	vector	NOUN
ejde-745	126	10	space	space	NOUN
ejde-745	126	11	.	.	PUNCT
ejde-745	127	1	let	let	VERB
ejde-745	127	2	d	d	PRON
ejde-745	127	3	be	be	AUX
ejde-745	127	4	a	a	DET
ejde-745	127	5	closed	closed	ADJ
ejde-745	127	6	convex	convex	NOUN
ejde-745	127	7	subset	subset	NOUN
ejde-745	127	8	of	of	ADP
ejde-745	127	9	x	x	X
ejde-745	127	10	,	,	PUNCT
ejde-745	127	11	and	and	CCONJ
ejde-745	127	12	let	let	VERB
ejde-745	127	13	f	f	PRON
ejde-745	127	14	be	be	AUX
ejde-745	127	15	a	a	DET
ejde-745	127	16	weakly	weakly	ADV
ejde-745	127	17	-	-	PUNCT
ejde-745	127	18	weakly	weakly	ADV
ejde-745	127	19	sequentially	sequentially	ADV
ejde-745	127	20	continuous	continuous	ADJ
ejde-745	127	21	map	map	NOUN
ejde-745	127	22	from	from	ADP
ejde-745	127	23	d	d	PROPN
ejde-745	127	24	into	into	ADP
ejde-745	127	25	itself	itself	PRON
ejde-745	127	26	.	.	PUNCT
ejde-745	128	1	if	if	SCONJ
ejde-745	128	2	for	for	ADP
ejde-745	128	3	some	some	DET
ejde-745	128	4	x	x	SYM
ejde-745	128	5	∈	∈	PROPN
ejde-745	129	1	d	d	X
ejde-745	129	2	the	the	DET
ejde-745	129	3	implication	implication	NOUN
ejde-745	129	4	that	that	SCONJ
ejde-745	129	5	v̄	v̄	NOUN
ejde-745	129	6	=	=	SYM
ejde-745	129	7	conv({x	conv({x	PROPN
ejde-745	129	8	}	}	PUNCT
ejde-745	129	9	∪	∪	VERB
ejde-745	129	10	f	f	PROPN
ejde-745	129	11	(	(	PUNCT
ejde-745	129	12	v	v	NOUN
ejde-745	129	13	)	)	PUNCT
ejde-745	129	14	)	)	PUNCT
ejde-745	130	1	=	=	PRON
ejde-745	130	2	⇒	⇒	NOUN
ejde-745	130	3	v	v	NOUN
ejde-745	130	4	is	be	AUX
ejde-745	130	5	relatively	relatively	ADV
ejde-745	130	6	weakly	weakly	ADJ
ejde-745	130	7	compact	compact	ADJ
ejde-745	130	8	,	,	PUNCT
ejde-745	130	9	(	(	PUNCT
ejde-745	130	10	2.1	2.1	NUM
ejde-745	130	11	)	)	PUNCT
ejde-745	130	12	holds	hold	VERB
ejde-745	130	13	for	for	ADP
ejde-745	130	14	every	every	DET
ejde-745	130	15	subset	subset	NOUN
ejde-745	130	16	v	v	NOUN
ejde-745	130	17	of	of	ADP
ejde-745	130	18	d	d	PROPN
ejde-745	130	19	,	,	PUNCT
ejde-745	130	20	then	then	ADV
ejde-745	130	21	f	f	PROPN
ejde-745	130	22	has	have	VERB
ejde-745	130	23	a	a	DET
ejde-745	130	24	fixed	fix	VERB
ejde-745	130	25	point	point	NOUN
ejde-745	130	26	.	.	PUNCT
ejde-745	131	1	3	3	X
ejde-745	131	2	.	.	X
ejde-745	131	3	main	main	ADJ
ejde-745	131	4	problem	problem	NOUN
ejde-745	131	5	now	now	ADV
ejde-745	131	6	we	we	PRON
ejde-745	131	7	will	will	AUX
ejde-745	131	8	consider	consider	VERB
ejde-745	131	9	the	the	DET
ejde-745	131	10	integral	integral	ADJ
ejde-745	131	11	problem	problem	NOUN
ejde-745	131	12	x(t	x(t	PROPN
ejde-745	131	13	)	)	PUNCT
ejde-745	132	1	=	=	PUNCT
ejde-745	133	1	x0	x0	PROPN
ejde-745	133	2	+	+	CCONJ
ejde-745	133	3	1	1	NUM
ejde-745	133	4	γ(α	γ(α	NOUN
ejde-745	133	5	)	)	PUNCT
ejde-745	134	1	∫	∫	PROPN
ejde-745	135	1	t	t	PROPN
ejde-745	135	2	0	0	NUM
ejde-745	135	3	(	(	PUNCT
ejde-745	135	4	t−	t−	PROPN
ejde-745	135	5	s)α−1f(s	s)α−1f(s	X
ejde-745	135	6	,	,	PUNCT
ejde-745	135	7	x(s))∆s	x(s))∆s	ADV
ejde-745	135	8	,	,	PUNCT
ejde-745	135	9	for	for	ADP
ejde-745	135	10	t	t	PROPN
ejde-745	135	11	∈	∈	PROPN
ejde-745	135	12	ia	ia	PROPN
ejde-745	135	13	,	,	PUNCT
ejde-745	135	14	(	(	PUNCT
ejde-745	135	15	3.1	3.1	NUM
ejde-745	135	16	)	)	PUNCT
ejde-745	135	17	where	where	SCONJ
ejde-745	135	18	f	f	X
ejde-745	135	19	:	:	PUNCT
ejde-745	135	20	ia	ia	PROPN
ejde-745	135	21	×	×	PROPN
ejde-745	135	22	e	e	PROPN
ejde-745	135	23	→	→	SYM
ejde-745	135	24	e	e	PROPN
ejde-745	135	25	,	,	PUNCT
ejde-745	135	26	t	t	PROPN
ejde-745	135	27	denotes	denote	VERB
ejde-745	135	28	a	a	DET
ejde-745	135	29	time	time	NOUN
ejde-745	135	30	scale	scale	NOUN
ejde-745	135	31	(	(	PUNCT
ejde-745	135	32	nonempty	nonempty	X
ejde-745	135	33	closed	close	VERB
ejde-745	135	34	subset	subset	NOUN
ejde-745	135	35	of	of	ADP
ejde-745	135	36	real	real	ADJ
ejde-745	135	37	numbers	number	NOUN
ejde-745	135	38	r	r	NOUN
ejde-745	135	39	)	)	PUNCT
ejde-745	135	40	,	,	PUNCT
ejde-745	135	41	0	0	NUM
ejde-745	135	42	∈	∈	PROPN
ejde-745	135	43	t	t	PROPN
ejde-745	135	44	,	,	PUNCT
ejde-745	135	45	ia	ia	PROPN
ejde-745	135	46	denotes	denote	VERB
ejde-745	135	47	a	a	DET
ejde-745	135	48	time	time	NOUN
ejde-745	135	49	scale	scale	NOUN
ejde-745	135	50	interval	interval	NOUN
ejde-745	135	51	,	,	PUNCT
ejde-745	135	52	(	(	PUNCT
ejde-745	135	53	e	e	NOUN
ejde-745	135	54	,	,	PUNCT
ejde-745	135	55	∥	∥	X
ejde-745	135	56	·	·	PUNCT
ejde-745	135	57	∥	∥	X
ejde-745	135	58	)	)	PUNCT
ejde-745	135	59	is	be	AUX
ejde-745	135	60	a	a	DET
ejde-745	135	61	banach	banach	NOUN
ejde-745	135	62	space	space	NOUN
ejde-745	135	63	and	and	CCONJ
ejde-745	135	64	integral	integral	ADJ
ejde-745	135	65	is	be	AUX
ejde-745	135	66	taken	take	VERB
ejde-745	135	67	in	in	ADP
ejde-745	135	68	the	the	DET
ejde-745	135	69	sense	sense	NOUN
ejde-745	135	70	of	of	ADP
ejde-745	135	71	∆−hkp	∆−hkp	NOUN
ejde-745	135	72	.	.	PUNCT
ejde-745	136	1	fix	fix	VERB
ejde-745	136	2	x∗	x∗	PROPN
ejde-745	136	3	∈	∈	PROPN
ejde-745	136	4	e∗	e∗	NOUN
ejde-745	136	5	and	and	CCONJ
ejde-745	136	6	consider	consider	VERB
ejde-745	136	7	the	the	DET
ejde-745	136	8	problem	problem	NOUN
ejde-745	136	9	c	c	PROPN
ejde-745	136	10	t∆	t∆	PROPN
ejde-745	136	11	α(x∗x)(t	α(x∗x)(t	PROPN
ejde-745	136	12	)	)	PUNCT
ejde-745	136	13	=	=	SYM
ejde-745	136	14	x∗(f(t	x∗(f(t	PROPN
ejde-745	136	15	,	,	PUNCT
ejde-745	136	16	x(t	x(t	PROPN
ejde-745	136	17	)	)	PUNCT
ejde-745	136	18	)	)	PUNCT
ejde-745	136	19	)	)	PUNCT
ejde-745	137	1	(	(	PUNCT
ejde-745	137	2	3.2	3.2	NUM
ejde-745	137	3	)	)	PUNCT
ejde-745	137	4	definition	definition	NOUN
ejde-745	137	5	3.1	3.1	NUM
ejde-745	137	6	.	.	PUNCT
ejde-745	138	1	let	let	VERB
ejde-745	138	2	f	f	NOUN
ejde-745	138	3	:	:	PUNCT
ejde-745	138	4	i	i	PROPN
ejde-745	138	5	→	→	SYM
ejde-745	138	6	e	e	NOUN
ejde-745	138	7	and	and	CCONJ
ejde-745	138	8	let	let	VERB
ejde-745	138	9	a	a	DET
ejde-745	138	10	⊂	⊂	PROPN
ejde-745	138	11	i.	i.	NOUN
ejde-745	138	12	the	the	DET
ejde-745	138	13	function	function	NOUN
ejde-745	139	1	f	f	NOUN
ejde-745	139	2	:	:	PUNCT
ejde-745	139	3	a	a	DET
ejde-745	139	4	→	→	SYM
ejde-745	139	5	e	e	NOUN
ejde-745	139	6	is	be	AUX
ejde-745	139	7	a	a	DET
ejde-745	139	8	fractional	fractional	ADJ
ejde-745	139	9	pseudo	pseudo	NOUN
ejde-745	139	10	∆-derivative	∆-derivative	NOUN
ejde-745	139	11	of	of	ADP
ejde-745	139	12	f	f	PROPN
ejde-745	139	13	on	on	ADP
ejde-745	139	14	a	a	DET
ejde-745	139	15	if	if	NOUN
ejde-745	139	16	for	for	ADP
ejde-745	139	17	each	each	DET
ejde-745	139	18	x∗	x∗	PROPN
ejde-745	139	19	∈	∈	PROPN
ejde-745	139	20	e∗	e∗	PROPN
ejde-745	139	21	the	the	DET
ejde-745	139	22	real	real	ADV
ejde-745	139	23	-	-	PUNCT
ejde-745	139	24	valued	value	VERB
ejde-745	139	25	function	function	NOUN
ejde-745	139	26	x∗f	x∗f	NUM
ejde-745	139	27	is	be	AUX
ejde-745	139	28	c	c	PROPN
ejde-745	139	29	t∆	t∆	PROPN
ejde-745	139	30	α	α	PROPN
ejde-745	139	31	-	-	ADJ
ejde-745	139	32	differentiable	differentiable	ADJ
ejde-745	139	33	µ∆	µ∆	NOUN
ejde-745	139	34	almost	almost	ADV
ejde-745	139	35	everywhere	everywhere	ADV
ejde-745	139	36	on	on	ADP
ejde-745	139	37	a	a	DET
ejde-745	139	38	and	and	CCONJ
ejde-745	139	39	c	c	NOUN
ejde-745	139	40	t∆	t∆	NOUN
ejde-745	139	41	α(x∗f	α(x∗f	ADV
ejde-745	139	42	)	)	PUNCT
ejde-745	140	1	=	=	SYM
ejde-745	140	2	x∗f	x∗f	NUM
ejde-745	140	3	µ∆	µ∆	NOUN
ejde-745	140	4	almost	almost	ADV
ejde-745	140	5	everywhere	everywhere	ADV
ejde-745	140	6	on	on	ADP
ejde-745	140	7	a.	a.	NOUN
ejde-745	140	8	regarding	regard	VERB
ejde-745	140	9	the	the	DET
ejde-745	140	10	above	above	ADJ
ejde-745	140	11	definition	definition	NOUN
ejde-745	140	12	it	it	PRON
ejde-745	140	13	is	be	AUX
ejde-745	140	14	clear	clear	ADJ
ejde-745	140	15	that	that	SCONJ
ejde-745	140	16	the	the	DET
ejde-745	140	17	left	left	ADJ
ejde-745	140	18	-	-	PUNCT
ejde-745	140	19	hand	hand	NOUN
ejde-745	140	20	side	side	NOUN
ejde-745	140	21	of	of	ADP
ejde-745	140	22	(	(	PUNCT
ejde-745	140	23	3.2	3.2	NUM
ejde-745	140	24	)	)	PUNCT
ejde-745	140	25	can	can	AUX
ejde-745	140	26	be	be	AUX
ejde-745	140	27	rewritten	rewrite	VERB
ejde-745	140	28	to	to	ADP
ejde-745	140	29	the	the	DET
ejde-745	140	30	form	form	NOUN
ejde-745	140	31	x∗(ct∆	x∗(ct∆	NOUN
ejde-745	140	32	αx(t	αx(t	NOUN
ejde-745	140	33	)	)	PUNCT
ejde-745	140	34	)	)	PUNCT
ejde-745	140	35	,	,	PUNCT
ejde-745	140	36	where	where	SCONJ
ejde-745	140	37	c	c	PROPN
ejde-745	140	38	t∆	t∆	PROPN
ejde-745	140	39	α	α	PROPN
ejde-745	140	40	denotes	denote	VERB
ejde-745	140	41	the	the	DET
ejde-745	140	42	fractional	fractional	ADJ
ejde-745	140	43	pseudo	pseudo	NOUN
ejde-745	140	44	∆-derivative	∆-derivative	NOUN
ejde-745	140	45	.	.	PUNCT
ejde-745	141	1	to	to	PART
ejde-745	141	2	obtain	obtain	VERB
ejde-745	141	3	the	the	DET
ejde-745	141	4	existence	existence	NOUN
ejde-745	141	5	result	result	VERB
ejde-745	141	6	for	for	ADP
ejde-745	141	7	our	our	PRON
ejde-745	141	8	problem	problem	NOUN
ejde-745	141	9	it	it	PRON
ejde-745	141	10	is	be	AUX
ejde-745	141	11	necessary	necessary	ADJ
ejde-745	141	12	to	to	PART
ejde-745	141	13	define	define	VERB
ejde-745	141	14	a	a	DET
ejde-745	141	15	notion	notion	NOUN
ejde-745	141	16	of	of	ADP
ejde-745	141	17	a	a	DET
ejde-745	141	18	solution	solution	NOUN
ejde-745	141	19	.	.	PUNCT
ejde-745	142	1	definition	definition	NOUN
ejde-745	142	2	3.2	3.2	NUM
ejde-745	142	3	.	.	PUNCT
ejde-745	143	1	a	a	DET
ejde-745	143	2	function	function	NOUN
ejde-745	143	3	x	x	X
ejde-745	143	4	:	:	PUNCT
ejde-745	143	5	ia	ia	PROPN
ejde-745	143	6	→	→	SYM
ejde-745	143	7	e	e	PROPN
ejde-745	143	8	is	be	AUX
ejde-745	143	9	said	say	VERB
ejde-745	143	10	to	to	PART
ejde-745	143	11	be	be	AUX
ejde-745	143	12	a	a	DET
ejde-745	143	13	pseudosolution	pseudosolution	NOUN
ejde-745	143	14	of	of	ADP
ejde-745	143	15	problem	problem	NOUN
ejde-745	143	16	(	(	PUNCT
ejde-745	143	17	1.1	1.1	NUM
ejde-745	143	18	)	)	PUNCT
ejde-745	143	19	if	if	SCONJ
ejde-745	143	20	it	it	PRON
ejde-745	143	21	satisfies	satisfy	VERB
ejde-745	143	22	the	the	DET
ejde-745	143	23	following	follow	VERB
ejde-745	143	24	conditions	condition	NOUN
ejde-745	143	25	:	:	PUNCT
ejde-745	143	26	(	(	PUNCT
ejde-745	143	27	1	1	X
ejde-745	143	28	)	)	PUNCT
ejde-745	143	29	x	x	NOUN
ejde-745	143	30	(	(	PUNCT
ejde-745	143	31	·	·	PUNCT
ejde-745	143	32	)	)	PUNCT
ejde-745	143	33	is	be	AUX
ejde-745	143	34	acg∗	acg∗	NOUN
ejde-745	143	35	function	function	NOUN
ejde-745	143	36	,	,	PUNCT
ejde-745	143	37	(	(	PUNCT
ejde-745	143	38	2	2	X
ejde-745	143	39	)	)	PUNCT
ejde-745	143	40	x(0	x(0	PROPN
ejde-745	143	41	)	)	PUNCT
ejde-745	144	1	=	=	PUNCT
ejde-745	144	2	x0	x0	PROPN
ejde-745	144	3	,	,	PUNCT
ejde-745	144	4	6	6	NUM
ejde-745	144	5	a.	a.	NOUN
ejde-745	144	6	sikorska	sikorska	PROPN
ejde-745	144	7	-	-	PUNCT
ejde-745	144	8	nowak	nowak	PROPN
ejde-745	144	9	ejde-2024/36	ejde-2024/36	NOUN
ejde-745	144	10	(	(	PUNCT
ejde-745	144	11	3	3	NUM
ejde-745	144	12	)	)	PUNCT
ejde-745	144	13	for	for	ADP
ejde-745	144	14	each	each	DET
ejde-745	144	15	x∗	x∗	PROPN
ejde-745	144	16	∈	∈	PROPN
ejde-745	144	17	e∗	e∗	PROPN
ejde-745	144	18	there	there	PRON
ejde-745	144	19	exists	exist	VERB
ejde-745	144	20	a	a	DET
ejde-745	144	21	set	set	NOUN
ejde-745	144	22	a(x∗	a(x∗	NOUN
ejde-745	144	23	)	)	PUNCT
ejde-745	144	24	with	with	ADP
ejde-745	144	25	µ∆	µ∆	NOUN
ejde-745	144	26	measure	measure	NOUN
ejde-745	144	27	zero	zero	NUM
ejde-745	144	28	,	,	PUNCT
ejde-745	144	29	such	such	ADJ
ejde-745	144	30	that	that	PRON
ejde-745	144	31	for	for	ADP
ejde-745	144	32	each	each	DET
ejde-745	144	33	t	t	NOUN
ejde-745	144	34	/∈	/∈	PUNCT
ejde-745	144	35	a(x∗	a(x∗	ADV
ejde-745	144	36	)	)	PUNCT
ejde-745	144	37	,	,	PUNCT
ejde-745	144	38	c	c	PROPN
ejde-745	144	39	t∆	t∆	PROPN
ejde-745	144	40	α(x∗x)(t	α(x∗x)(t	PROPN
ejde-745	144	41	)	)	PUNCT
ejde-745	144	42	=	=	SYM
ejde-745	144	43	x∗(f(t	x∗(f(t	PROPN
ejde-745	144	44	,	,	PUNCT
ejde-745	144	45	x(t	x(t	PROPN
ejde-745	144	46	)	)	PUNCT
ejde-745	144	47	)	)	PUNCT
ejde-745	144	48	)	)	PUNCT
ejde-745	144	49	.	.	PUNCT
ejde-745	145	1	definition	definition	NOUN
ejde-745	145	2	3.3	3.3	NUM
ejde-745	145	3	.	.	PUNCT
ejde-745	146	1	a	a	DET
ejde-745	146	2	continuous	continuous	ADJ
ejde-745	146	3	function	function	NOUN
ejde-745	146	4	x	x	INTJ
ejde-745	146	5	:	:	PUNCT
ejde-745	146	6	ia	ia	PROPN
ejde-745	146	7	→	→	SYM
ejde-745	146	8	e	e	PROPN
ejde-745	146	9	is	be	AUX
ejde-745	146	10	said	say	VERB
ejde-745	146	11	to	to	PART
ejde-745	146	12	be	be	AUX
ejde-745	146	13	a	a	DET
ejde-745	146	14	solution	solution	NOUN
ejde-745	146	15	to	to	ADP
ejde-745	146	16	problem	problem	NOUN
ejde-745	146	17	(	(	PUNCT
ejde-745	146	18	3.1	3.1	NUM
ejde-745	146	19	)	)	PUNCT
ejde-745	146	20	if	if	SCONJ
ejde-745	146	21	it	it	PRON
ejde-745	146	22	satisfies	satisfy	VERB
ejde-745	146	23	(	(	PUNCT
ejde-745	146	24	3.1	3.1	NUM
ejde-745	146	25	)	)	PUNCT
ejde-745	146	26	for	for	ADP
ejde-745	146	27	every	every	DET
ejde-745	146	28	t	t	PROPN
ejde-745	146	29	∈	∈	PROPN
ejde-745	146	30	ia	ia	PROPN
ejde-745	146	31	.	.	PROPN
ejde-745	146	32	let	let	VERB
ejde-745	146	33	b	b	NOUN
ejde-745	146	34	=	=	PRON
ejde-745	146	35	{	{	PUNCT
ejde-745	146	36	x	x	SYM
ejde-745	146	37	∈	∈	PROPN
ejde-745	146	38	e	e	NOUN
ejde-745	146	39	:	:	PUNCT
ejde-745	146	40	∥x∥	∥x∥	NOUN
ejde-745	146	41	≤	≤	ADJ
ejde-745	146	42	∥x0∥+	∥x0∥+	PROPN
ejde-745	146	43	p	p	NOUN
ejde-745	146	44	,	,	PUNCT
ejde-745	146	45	p	p	X
ejde-745	146	46	>	>	X
ejde-745	146	47	0	0	NUM
ejde-745	146	48	}	}	PUNCT
ejde-745	146	49	,	,	PUNCT
ejde-745	146	50	b̃	b̃	PROPN
ejde-745	146	51	=	=	PRON
ejde-745	146	52	{	{	PUNCT
ejde-745	146	53	x	x	SYM
ejde-745	146	54	∈	∈	PROPN
ejde-745	146	55	(	(	PUNCT
ejde-745	146	56	c(ia	c(ia	PROPN
ejde-745	146	57	,	,	PUNCT
ejde-745	146	58	e	e	NOUN
ejde-745	146	59	)	)	PUNCT
ejde-745	146	60	,	,	PUNCT
ejde-745	146	61	ω	ω	NOUN
ejde-745	146	62	)	)	PUNCT
ejde-745	146	63	:	:	PUNCT
ejde-745	147	1	x(0	x(0	PROPN
ejde-745	147	2	)	)	PUNCT
ejde-745	147	3	=	=	PUNCT
ejde-745	147	4	x0	x0	PROPN
ejde-745	147	5	,	,	PUNCT
ejde-745	147	6	∥x∥	∥x∥	NOUN
ejde-745	147	7	≤	≤	ADJ
ejde-745	147	8	∥x0∥+	∥x0∥+	PROPN
ejde-745	147	9	p	p	NOUN
ejde-745	147	10	,	,	PUNCT
ejde-745	147	11	p	p	X
ejde-745	147	12	>	>	X
ejde-745	147	13	0	0	NUM
ejde-745	147	14	}	}	PUNCT
ejde-745	147	15	,	,	PUNCT
ejde-745	147	16	f	f	X
ejde-745	147	17	(	(	PUNCT
ejde-745	147	18	x)(t	x)(t	PROPN
ejde-745	147	19	)	)	PUNCT
ejde-745	147	20	=	=	PUNCT
ejde-745	148	1	x0	x0	PROPN
ejde-745	148	2	+	+	CCONJ
ejde-745	148	3	1	1	NUM
ejde-745	148	4	γ(α	γ(α	NOUN
ejde-745	148	5	)	)	PUNCT
ejde-745	148	6	∫	∫	PROPN
ejde-745	149	1	t	t	PROPN
ejde-745	149	2	0	0	NUM
ejde-745	149	3	(	(	PUNCT
ejde-745	149	4	t−	t−	PROPN
ejde-745	149	5	s)α−1f(s	s)α−1f(s	X
ejde-745	149	6	,	,	PUNCT
ejde-745	149	7	x(s))∆s	x(s))∆s	ADV
ejde-745	149	8	,	,	PUNCT
ejde-745	149	9	for	for	ADP
ejde-745	149	10	t	t	PROPN
ejde-745	149	11	∈	∈	PROPN
ejde-745	149	12	ia	ia	PROPN
ejde-745	149	13	,	,	PUNCT
ejde-745	149	14	k	k	PROPN
ejde-745	149	15	=	=	PRON
ejde-745	149	16	{	{	PUNCT
ejde-745	149	17	f	f	X
ejde-745	149	18	(	(	PUNCT
ejde-745	149	19	x	x	NOUN
ejde-745	149	20	)	)	PUNCT
ejde-745	149	21	:	:	PUNCT
ejde-745	150	1	x	x	PUNCT
ejde-745	150	2	∈	∈	PROPN
ejde-745	150	3	b	b	NOUN
ejde-745	150	4	}	}	PUNCT
ejde-745	150	5	.	.	PUNCT
ejde-745	151	1	theorem	theorem	VERB
ejde-745	151	2	3.4	3.4	NUM
ejde-745	151	3	.	.	PUNCT
ejde-745	152	1	assume	assume	VERB
ejde-745	152	2	that	that	SCONJ
ejde-745	152	3	for	for	ADP
ejde-745	152	4	each	each	DET
ejde-745	152	5	acg∗	acg∗	NOUN
ejde-745	152	6	function	function	NOUN
ejde-745	152	7	x	x	X
ejde-745	152	8	:	:	PUNCT
ejde-745	152	9	ia	ia	PROPN
ejde-745	152	10	→	→	SYM
ejde-745	152	11	e	e	PROPN
ejde-745	152	12	,	,	PUNCT
ejde-745	152	13	f	f	X
ejde-745	152	14	(	(	PUNCT
ejde-745	152	15	·	·	PUNCT
ejde-745	152	16	,	,	PUNCT
ejde-745	152	17	x	x	X
ejde-745	152	18	(	(	PUNCT
ejde-745	152	19	·	·	PUNCT
ejde-745	152	20	)	)	PUNCT
ejde-745	152	21	)	)	PUNCT
ejde-745	152	22	is	be	AUX
ejde-745	152	23	fractionale	fractionale	NOUN
ejde-745	152	24	∆-hkp	∆-hkp	NOUN
ejde-745	152	25	integrable	integrable	ADJ
ejde-745	152	26	,	,	PUNCT
ejde-745	152	27	f(t	f(t	NOUN
ejde-745	152	28	,	,	PUNCT
ejde-745	152	29	·	·	PUNCT
ejde-745	152	30	)	)	PUNCT
ejde-745	152	31	is	be	AUX
ejde-745	152	32	weakly	weakly	ADV
ejde-745	152	33	-	-	PUNCT
ejde-745	152	34	weakly	weakly	ADV
ejde-745	152	35	sequentially	sequentially	ADV
ejde-745	152	36	continuous	continuous	ADJ
ejde-745	152	37	.	.	PUNCT
ejde-745	153	1	suppose	suppose	VERB
ejde-745	153	2	,	,	PUNCT
ejde-745	153	3	that	that	SCONJ
ejde-745	153	4	there	there	PRON
ejde-745	153	5	exists	exist	VERB
ejde-745	153	6	a	a	DET
ejde-745	153	7	constans	constans	PROPN
ejde-745	153	8	c	c	PROPN
ejde-745	153	9	>	>	X
ejde-745	153	10	0	0	NUM
ejde-745	153	11	such	such	ADJ
ejde-745	153	12	that	that	SCONJ
ejde-745	153	13	β(f(i	β(f(i	PROPN
ejde-745	153	14	×x	×x	NUM
ejde-745	153	15	)	)	PUNCT
ejde-745	153	16	)	)	PUNCT
ejde-745	153	17	≤	≤	NUM
ejde-745	153	18	cβ(x	cβ(x	NOUN
ejde-745	153	19	)	)	PUNCT
ejde-745	153	20	,	,	PUNCT
ejde-745	153	21	0	0	PUNCT
ejde-745	153	22	<	<	X
ejde-745	153	23	c	c	PROPN
ejde-745	153	24	γ(α	γ(α	PROPN
ejde-745	153	25	)	)	PUNCT
ejde-745	154	1	∫	∫	PROPN
ejde-745	154	2	t	t	PROPN
ejde-745	154	3	0	0	NUM
ejde-745	154	4	(	(	PUNCT
ejde-745	154	5	t−	t−	PROPN
ejde-745	154	6	s)α−1∆s	s)α−1∆s	PROPN
ejde-745	154	7	<	<	X
ejde-745	154	8	1	1	NUM
ejde-745	154	9	,	,	PUNCT
ejde-745	154	10	t	t	PROPN
ejde-745	154	11	∈	∈	PROPN
ejde-745	155	1	i	i	PRON
ejde-745	155	2	,	,	PUNCT
ejde-745	155	3	(	(	PUNCT
ejde-745	155	4	3.3	3.3	NUM
ejde-745	155	5	)	)	PUNCT
ejde-745	155	6	for	for	ADP
ejde-745	155	7	each	each	DET
ejde-745	155	8	bounded	bound	VERB
ejde-745	155	9	subset	subset	VERB
ejde-745	155	10	x	x	X
ejde-745	155	11	⊂	⊂	PROPN
ejde-745	155	12	b	b	PROPN
ejde-745	155	13	and	and	CCONJ
ejde-745	155	14	for	for	ADP
ejde-745	155	15	each	each	DET
ejde-745	155	16	subinterval	subinterval	NOUN
ejde-745	155	17	i	i	PRON
ejde-745	155	18	of	of	ADP
ejde-745	155	19	ia	ia	PROPN
ejde-745	155	20	.	.	PROPN
ejde-745	155	21	suppose	suppose	VERB
ejde-745	155	22	that	that	SCONJ
ejde-745	155	23	the	the	DET
ejde-745	155	24	set	set	NOUN
ejde-745	155	25	k	k	PROPN
ejde-745	155	26	is	be	AUX
ejde-745	155	27	equicontinuous	equicontinuous	ADJ
ejde-745	155	28	,	,	PUNCT
ejde-745	155	29	equibounded	equibounded	ADJ
ejde-745	155	30	and	and	CCONJ
ejde-745	155	31	weakly	weakly	ADJ
ejde-745	155	32	uniformly	uniformly	ADJ
ejde-745	155	33	acg∗	acg∗	NOUN
ejde-745	155	34	on	on	ADP
ejde-745	155	35	ia	ia	PROPN
ejde-745	155	36	.	.	PUNCT
ejde-745	156	1	then	then	ADV
ejde-745	156	2	there	there	PRON
ejde-745	156	3	exists	exist	VERB
ejde-745	156	4	at	at	ADP
ejde-745	156	5	least	least	ADV
ejde-745	156	6	one	one	NUM
ejde-745	156	7	pseudo	pseudo	NOUN
ejde-745	156	8	solution	solution	NOUN
ejde-745	156	9	of	of	ADP
ejde-745	156	10	problem	problem	NOUN
ejde-745	156	11	(	(	PUNCT
ejde-745	156	12	1.1	1.1	NUM
ejde-745	156	13	)	)	PUNCT
ejde-745	156	14	on	on	ADP
ejde-745	156	15	i	i	PROPN
ejde-745	156	16	d	d	PROPN
ejde-745	156	17	,	,	PUNCT
ejde-745	156	18	for	for	ADP
ejde-745	156	19	some	some	DET
ejde-745	156	20	number	number	NOUN
ejde-745	156	21	d	d	PROPN
ejde-745	156	22	∈	∈	PROPN
ejde-745	156	23	t	t	PROPN
ejde-745	156	24	,	,	PUNCT
ejde-745	156	25	0	0	PUNCT
ejde-745	156	26	<	<	X
ejde-745	156	27	d	d	X
ejde-745	156	28	≤	≤	NUM
ejde-745	156	29	a.	a.	NOUN
ejde-745	156	30	proof	proof	NOUN
ejde-745	156	31	.	.	PUNCT
ejde-745	157	1	we	we	PRON
ejde-745	157	2	will	will	AUX
ejde-745	157	3	prove	prove	VERB
ejde-745	157	4	,	,	PUNCT
ejde-745	157	5	in	in	ADP
ejde-745	157	6	fact	fact	NOUN
ejde-745	157	7	,	,	PUNCT
ejde-745	157	8	the	the	DET
ejde-745	157	9	existence	existence	NOUN
ejde-745	157	10	of	of	ADP
ejde-745	157	11	a	a	DET
ejde-745	157	12	solution	solution	NOUN
ejde-745	157	13	for	for	ADP
ejde-745	157	14	problem	problem	NOUN
ejde-745	157	15	(	(	PUNCT
ejde-745	157	16	3.1	3.1	NUM
ejde-745	157	17	)	)	PUNCT
ejde-745	157	18	because	because	SCONJ
ejde-745	157	19	each	each	DET
ejde-745	157	20	solution	solution	NOUN
ejde-745	157	21	of	of	ADP
ejde-745	157	22	problem	problem	NOUN
ejde-745	157	23	(	(	PUNCT
ejde-745	157	24	3.1	3.1	NUM
ejde-745	157	25	)	)	PUNCT
ejde-745	157	26	is	be	AUX
ejde-745	157	27	a	a	DET
ejde-745	157	28	solution	solution	NOUN
ejde-745	157	29	of	of	ADP
ejde-745	157	30	problem	problem	NOUN
ejde-745	157	31	(	(	PUNCT
ejde-745	157	32	1.1	1.1	NUM
ejde-745	157	33	)	)	PUNCT
ejde-745	157	34	.	.	PUNCT
ejde-745	158	1	let	let	VERB
ejde-745	158	2	x	x	PRON
ejde-745	158	3	be	be	AUX
ejde-745	158	4	a	a	DET
ejde-745	158	5	continuous	continuous	ADJ
ejde-745	158	6	solution	solution	NOUN
ejde-745	158	7	of	of	ADP
ejde-745	158	8	(	(	PUNCT
ejde-745	158	9	3.1	3.1	NUM
ejde-745	158	10	)	)	PUNCT
ejde-745	158	11	.	.	PUNCT
ejde-745	159	1	fix	fix	VERB
ejde-745	159	2	an	an	DET
ejde-745	159	3	arbitrary	arbitrary	ADJ
ejde-745	159	4	p	p	NOUN
ejde-745	159	5	≥	≥	NOUN
ejde-745	159	6	0	0	NUM
ejde-745	159	7	.	.	PUNCT
ejde-745	160	1	recall	recall	NOUN
ejde-745	160	2	,	,	PUNCT
ejde-745	160	3	that	that	SCONJ
ejde-745	160	4	the	the	DET
ejde-745	160	5	set	set	NOUN
ejde-745	160	6	k	k	PROPN
ejde-745	160	7	of	of	ADP
ejde-745	160	8	continuous	continuous	ADJ
ejde-745	160	9	function	function	NOUN
ejde-745	160	10	f	f	PROPN
ejde-745	160	11	(	(	PUNCT
ejde-745	160	12	x	x	X
ejde-745	160	13	)	)	PUNCT
ejde-745	160	14	∈	∈	PROPN
ejde-745	160	15	k	k	PROPN
ejde-745	160	16	defined	define	VERB
ejde-745	160	17	on	on	ADP
ejde-745	160	18	a	a	DET
ejde-745	160	19	time	time	NOUN
ejde-745	160	20	scale	scale	NOUN
ejde-745	160	21	interval	interval	NOUN
ejde-745	160	22	ia	ia	PROPN
ejde-745	160	23	is	be	AUX
ejde-745	160	24	equicontinuous	equicontinuous	ADJ
ejde-745	160	25	on	on	ADP
ejde-745	160	26	ia	ia	PROPN
ejde-745	160	27	if	if	SCONJ
ejde-745	160	28	for	for	ADP
ejde-745	160	29	each	each	PRON
ejde-745	161	1	ϵ	ϵ	X
ejde-745	161	2	>	>	X
ejde-745	161	3	0	0	PUNCT
ejde-745	162	1	there	there	PRON
ejde-745	162	2	exists	exist	VERB
ejde-745	162	3	δ	δ	PROPN
ejde-745	162	4	>	>	X
ejde-745	162	5	0	0	NUM
ejde-745	163	1	such	such	ADJ
ejde-745	163	2	that	that	SCONJ
ejde-745	163	3	∥f	∥f	PROPN
ejde-745	163	4	(	(	PUNCT
ejde-745	163	5	x)(t)−	x)(t)−	PROPN
ejde-745	163	6	f	f	PROPN
ejde-745	163	7	(	(	PUNCT
ejde-745	163	8	x)(τ)∥	x)(τ)∥	PROPN
ejde-745	163	9	<	<	X
ejde-745	164	1	ϵ	ϵ	X
ejde-745	164	2	for	for	ADP
ejde-745	164	3	all	all	DET
ejde-745	164	4	x	x	SYM
ejde-745	164	5	∈	∈	PROPN
ejde-745	164	6	b̃	b̃	PROPN
ejde-745	164	7	whenever	whenever	SCONJ
ejde-745	164	8	|t−	|t−	PROPN
ejde-745	164	9	τ	τ	PROPN
ejde-745	164	10	|	|	ADV
ejde-745	164	11	<	<	X
ejde-745	164	12	δ	δ	PROPN
ejde-745	164	13	,	,	PUNCT
ejde-745	164	14	t	t	PROPN
ejde-745	164	15	,	,	PUNCT
ejde-745	164	16	τ	τ	PROPN
ejde-745	164	17	∈	∈	PROPN
ejde-745	164	18	ia	ia	PROPN
ejde-745	164	19	,	,	PUNCT
ejde-745	164	20	for	for	ADP
ejde-745	164	21	each	each	DET
ejde-745	164	22	f	f	X
ejde-745	164	23	(	(	PUNCT
ejde-745	164	24	x	x	X
ejde-745	164	25	)	)	PUNCT
ejde-745	164	26	∈	∈	PROPN
ejde-745	164	27	k.	k.	PROPN
ejde-745	165	1	thus	thus	ADV
ejde-745	165	2	,	,	PUNCT
ejde-745	165	3	for	for	ADP
ejde-745	165	4	each	each	PRON
ejde-745	165	5	ϵ	ϵ	X
ejde-745	165	6	>	>	X
ejde-745	165	7	0	0	PUNCT
ejde-745	165	8	there	there	PRON
ejde-745	165	9	exists	exist	VERB
ejde-745	165	10	δ	δ	PROPN
ejde-745	165	11	>	>	X
ejde-745	165	12	0	0	NUM
ejde-745	165	13	such	such	ADJ
ejde-745	165	14	that	that	SCONJ
ejde-745	165	15	∥	∥	PROPN
ejde-745	165	16	∫	∫	PROPN
ejde-745	165	17	t	t	PROPN
ejde-745	165	18	τ	τ	PROPN
ejde-745	165	19	(	(	PUNCT
ejde-745	165	20	t−s)α−1f(s	t−s)α−1f(s	ADJ
ejde-745	165	21	,	,	PUNCT
ejde-745	165	22	x(s))∆s∥	x(s))∆s∥	X
ejde-745	165	23	<	<	X
ejde-745	165	24	ϵ	ϵ	X
ejde-745	165	25	,	,	PUNCT
ejde-745	165	26	for	for	ADP
ejde-745	165	27	all	all	DET
ejde-745	165	28	x	x	SYM
ejde-745	165	29	∈	∈	PROPN
ejde-745	165	30	b̃	b̃	PROPN
ejde-745	165	31	,	,	PUNCT
ejde-745	165	32	whenever	whenever	SCONJ
ejde-745	165	33	|t−τ	|t−τ	NOUN
ejde-745	165	34	|	|	ADV
ejde-745	165	35	<	<	X
ejde-745	165	36	δ	δ	PROPN
ejde-745	165	37	and	and	CCONJ
ejde-745	165	38	t	t	PROPN
ejde-745	165	39	,	,	PUNCT
ejde-745	165	40	τ	τ	PROPN
ejde-745	165	41	∈	∈	PROPN
ejde-745	165	42	ia	ia	PROPN
ejde-745	165	43	.	.	PROPN
ejde-745	166	1	as	as	ADP
ejde-745	166	2	a	a	DET
ejde-745	166	3	result	result	NOUN
ejde-745	166	4	,	,	PUNCT
ejde-745	166	5	there	there	PRON
ejde-745	166	6	exists	exist	VERB
ejde-745	166	7	a	a	DET
ejde-745	166	8	number	number	NOUN
ejde-745	166	9	d	d	NOUN
ejde-745	166	10	,	,	PUNCT
ejde-745	166	11	0	0	PUNCT
ejde-745	166	12	<	<	X
ejde-745	166	13	d	d	X
ejde-745	166	14	≤	≤	PROPN
ejde-745	166	15	a	a	PRON
ejde-745	166	16	,	,	PUNCT
ejde-745	166	17	such	such	ADJ
ejde-745	166	18	that	that	SCONJ
ejde-745	166	19	∥	∥	NUM
ejde-745	166	20	∫	∫	PROPN
ejde-745	166	21	t	t	NOUN
ejde-745	166	22	0	0	NUM
ejde-745	166	23	(	(	PUNCT
ejde-745	166	24	t−s)α−1f(s	t−s)α−1f(s	ADJ
ejde-745	166	25	,	,	PUNCT
ejde-745	166	26	x(s))∆s∥	x(s))∆s∥	PUNCT
ejde-745	167	1	≤	≤	PROPN
ejde-745	168	1	p	p	X
ejde-745	168	2	,	,	PUNCT
ejde-745	168	3	t	t	PROPN
ejde-745	168	4	∈	∈	PROPN
ejde-745	169	1	i	i	PROPN
ejde-745	169	2	d	d	PROPN
ejde-745	169	3	,	,	PUNCT
ejde-745	169	4	x	x	SYM
ejde-745	169	5	∈	∈	NOUN
ejde-745	169	6	b̃.	b̃.	NOUN
ejde-745	169	7	we	we	PRON
ejde-745	169	8	will	will	AUX
ejde-745	169	9	show	show	VERB
ejde-745	169	10	that	that	SCONJ
ejde-745	169	11	the	the	DET
ejde-745	169	12	operator	operator	NOUN
ejde-745	169	13	f	f	X
ejde-745	169	14	is	be	AUX
ejde-745	169	15	well	well	ADV
ejde-745	169	16	defined	define	VERB
ejde-745	169	17	and	and	CCONJ
ejde-745	169	18	maps	map	VERB
ejde-745	169	19	b̃	b̃	PROPN
ejde-745	169	20	into	into	ADP
ejde-745	169	21	b̃.	b̃.	NOUN
ejde-745	169	22	to	to	PART
ejde-745	169	23	see	see	VERB
ejde-745	169	24	this	this	PRON
ejde-745	169	25	,	,	PUNCT
ejde-745	169	26	note	note	VERB
ejde-745	169	27	for	for	ADP
ejde-745	169	28	any	any	DET
ejde-745	169	29	x∗	x∗	PROPN
ejde-745	169	30	∈	∈	PROPN
ejde-745	169	31	e∗	e∗	PROPN
ejde-745	169	32	,	,	PUNCT
ejde-745	169	33	such	such	ADJ
ejde-745	169	34	that	that	PRON
ejde-745	169	35	∥x∗∥	∥x∗∥	VERB
ejde-745	169	36	≤	≤	NUM
ejde-745	169	37	1	1	NUM
ejde-745	169	38	,	,	PUNCT
ejde-745	169	39	for	for	ADP
ejde-745	169	40	each	each	DET
ejde-745	169	41	x	x	SYM
ejde-745	169	42	∈	∈	PROPN
ejde-745	169	43	b̃	b̃	PROPN
ejde-745	169	44	and	and	CCONJ
ejde-745	169	45	t	t	NOUN
ejde-745	169	46	∈	∈	PROPN
ejde-745	170	1	i	i	PRON
ejde-745	170	2	d	d	NOUN
ejde-745	170	3	we	we	PRON
ejde-745	170	4	have	have	VERB
ejde-745	170	5	|x∗f	|x∗f	NOUN
ejde-745	170	6	(	(	PUNCT
ejde-745	170	7	x)(t)|	x)(t)|	PROPN
ejde-745	170	8	=	=	SYM
ejde-745	170	9	|x∗x0|+	|x∗x0|+	NOUN
ejde-745	170	10	∣∣x∗	∣∣x∗	NOUN
ejde-745	170	11	(	(	PUNCT
ejde-745	170	12	1	1	NUM
ejde-745	170	13	γ(α	γ(α	NOUN
ejde-745	170	14	)	)	PUNCT
ejde-745	170	15	∫	∫	PROPN
ejde-745	171	1	t	t	PROPN
ejde-745	171	2	0	0	NUM
ejde-745	171	3	(	(	PUNCT
ejde-745	171	4	t−	t−	PROPN
ejde-745	171	5	s)α−1f(s	s)α−1f(s	X
ejde-745	171	6	,	,	PUNCT
ejde-745	171	7	x(s))∆s	x(s))∆s	PUNCT
ejde-745	171	8	)	)	PUNCT
ejde-745	171	9	∣∣	∣∣	PROPN
ejde-745	171	10	≤	≤	NUM
ejde-745	171	11	∥x∗∥∥x0∥+	∥x∗∥∥x0∥+	PROPN
ejde-745	171	12	∥x∗∥	∥x∗∥	VERB
ejde-745	171	13	∥∥	∥∥	PROPN
ejde-745	171	14	1	1	NUM
ejde-745	171	15	γ(α	γ(α	NOUN
ejde-745	171	16	)	)	PUNCT
ejde-745	172	1	∫	∫	PROPN
ejde-745	172	2	t	t	PROPN
ejde-745	172	3	0	0	NUM
ejde-745	172	4	(	(	PUNCT
ejde-745	172	5	t−	t−	PROPN
ejde-745	172	6	s)α−1f(s	s)α−1f(s	PROPN
ejde-745	172	7	,	,	PUNCT
ejde-745	172	8	x(s))∆s	x(s))∆s	ADV
ejde-745	172	9	∥∥	∥∥	X
ejde-745	172	10	≤	≤	ADJ
ejde-745	172	11	∥x0∥+	∥x0∥+	NOUN
ejde-745	172	12	|	|	NOUN
ejde-745	172	13	1	1	NUM
ejde-745	172	14	γ(α	γ(α	NOUN
ejde-745	172	15	)	)	PUNCT
ejde-745	172	16	|p	|p	VERB
ejde-745	172	17	≤	≤	ADJ
ejde-745	172	18	∥x0∥+	∥x0∥+	NOUN
ejde-745	172	19	p	p	NOUN
ejde-745	172	20	so	so	ADV
ejde-745	172	21	sup{|x∗f	sup{|x∗f	INTJ
ejde-745	172	22	(	(	PUNCT
ejde-745	172	23	x)(t)|	x)(t)|	NUM
ejde-745	172	24	:	:	PUNCT
ejde-745	172	25	x∗	x∗	PROPN
ejde-745	172	26	∈	∈	PROPN
ejde-745	172	27	e∗	e∗	PROPN
ejde-745	172	28	,	,	PUNCT
ejde-745	172	29	∥x∗∥	∥x∗∥	VERB
ejde-745	172	30	≤	≤	NUM
ejde-745	172	31	1	1	NUM
ejde-745	172	32	}	}	PUNCT
ejde-745	172	33	≤	≤	NUM
ejde-745	173	1	∥x0∥+	∥x0∥+	NOUN
ejde-745	174	1	p.	p.	NOUN
ejde-745	174	2	and	and	CCONJ
ejde-745	174	3	as	as	ADP
ejde-745	174	4	a	a	DET
ejde-745	174	5	result	result	NOUN
ejde-745	175	1	∥f	∥f	PROPN
ejde-745	175	2	(	(	PUNCT
ejde-745	175	3	x)(t)∥	x)(t)∥	PROPN
ejde-745	175	4	≤	≤	NUM
ejde-745	175	5	∥x0∥	∥x0∥	PROPN
ejde-745	175	6	+	+	CCONJ
ejde-745	176	1	p.	p.	NOUN
ejde-745	176	2	thus	thus	ADV
ejde-745	176	3	f	f	X
ejde-745	176	4	(	(	PUNCT
ejde-745	176	5	x)(t	x)(t	PROPN
ejde-745	176	6	)	)	PUNCT
ejde-745	176	7	∈	∈	PROPN
ejde-745	176	8	b̃.	b̃.	NOUN
ejde-745	176	9	we	we	PRON
ejde-745	176	10	will	will	AUX
ejde-745	176	11	show	show	VERB
ejde-745	176	12	,	,	PUNCT
ejde-745	176	13	that	that	SCONJ
ejde-745	176	14	the	the	DET
ejde-745	176	15	operator	operator	NOUN
ejde-745	176	16	f	f	PROPN
ejde-745	176	17	is	be	AUX
ejde-745	176	18	weakly	weakly	ADV
ejde-745	176	19	-	-	PUNCT
ejde-745	176	20	weakly	weakly	ADV
ejde-745	176	21	sequentially	sequentially	ADV
ejde-745	176	22	continuous	continuous	ADJ
ejde-745	176	23	.	.	PUNCT
ejde-745	177	1	by	by	ADP
ejde-745	177	2	[	[	X
ejde-745	177	3	18	18	NUM
ejde-745	177	4	,	,	PUNCT
ejde-745	177	5	lemma	lemma	PROPN
ejde-745	177	6	9	9	NUM
ejde-745	177	7	]	]	PUNCT
ejde-745	177	8	a	a	DET
ejde-745	177	9	sequence	sequence	NOUN
ejde-745	177	10	ejde-2024/36	ejde-2024/36	NOUN
ejde-745	177	11	existence	existence	NOUN
ejde-745	177	12	of	of	ADP
ejde-745	177	13	pseudosolutions	pseudosolution	NOUN
ejde-745	177	14	7	7	NUM
ejde-745	177	15	xn	xn	SYM
ejde-745	177	16	(	(	PUNCT
ejde-745	177	17	·	·	PUNCT
ejde-745	177	18	)	)	PUNCT
ejde-745	177	19	is	be	AUX
ejde-745	177	20	weakly	weakly	ADJ
ejde-745	177	21	convergent	convergent	NOUN
ejde-745	177	22	in	in	ADP
ejde-745	177	23	c(id	c(id	PROPN
ejde-745	177	24	,	,	PUNCT
ejde-745	177	25	e	e	NOUN
ejde-745	177	26	)	)	PUNCT
ejde-745	177	27	to	to	ADP
ejde-745	177	28	x	x	SYM
ejde-745	177	29	(	(	PUNCT
ejde-745	177	30	·	·	PUNCT
ejde-745	177	31	)	)	PUNCT
ejde-745	178	1	if	if	SCONJ
ejde-745	178	2	and	and	CCONJ
ejde-745	178	3	only	only	ADV
ejde-745	178	4	if	if	SCONJ
ejde-745	178	5	xn(t	xn(t	NOUN
ejde-745	178	6	)	)	PUNCT
ejde-745	178	7	tends	tend	VERB
ejde-745	178	8	weakly	weakly	ADJ
ejde-745	178	9	to	to	ADP
ejde-745	178	10	x(t	x(t	PROPN
ejde-745	178	11	)	)	PUNCT
ejde-745	178	12	for	for	ADP
ejde-745	178	13	each	each	DET
ejde-745	178	14	t	t	NOUN
ejde-745	178	15	∈	∈	PROPN
ejde-745	178	16	i	i	PROPN
ejde-745	178	17	d	d	PROPN
ejde-745	178	18	,	,	PUNCT
ejde-745	178	19	so	so	SCONJ
ejde-745	178	20	if	if	SCONJ
ejde-745	178	21	xn	xn	PROPN
ejde-745	178	22	ω→	ω→	PUNCT
ejde-745	178	23	x	x	PUNCT
ejde-745	178	24	in	in	ADP
ejde-745	178	25	c(id	c(id	PROPN
ejde-745	178	26	,	,	PUNCT
ejde-745	178	27	e	e	NOUN
ejde-745	178	28	)	)	PUNCT
ejde-745	178	29	then	then	ADV
ejde-745	178	30	f(s	f(	VERB
ejde-745	178	31	,	,	PUNCT
ejde-745	178	32	xn(s	xn(s	NUM
ejde-745	178	33	)	)	PUNCT
ejde-745	178	34	)	)	PUNCT
ejde-745	179	1	ω→	ω→	PUNCT
ejde-745	179	2	f(s	f(s	PROPN
ejde-745	179	3	,	,	PUNCT
ejde-745	179	4	x(s	x(s	PROPN
ejde-745	179	5	)	)	PUNCT
ejde-745	179	6	)	)	PUNCT
ejde-745	179	7	in	in	ADP
ejde-745	179	8	e	e	PROPN
ejde-745	179	9	for	for	ADP
ejde-745	179	10	t	t	PROPN
ejde-745	179	11	∈	∈	PROPN
ejde-745	179	12	i	i	PROPN
ejde-745	179	13	d	d	PROPN
ejde-745	179	14	and	and	CCONJ
ejde-745	179	15	by	by	ADP
ejde-745	179	16	theorem	theorem	NOUN
ejde-745	179	17	2.6	2.6	NUM
ejde-745	179	18	we	we	PRON
ejde-745	179	19	have	have	VERB
ejde-745	179	20	f	f	X
ejde-745	179	21	(	(	PUNCT
ejde-745	179	22	xn)(t	xn)(t	PROPN
ejde-745	179	23	)	)	PUNCT
ejde-745	179	24	→	→	SYM
ejde-745	179	25	f	f	X
ejde-745	179	26	(	(	PUNCT
ejde-745	179	27	x)(t	x)(t	ADJ
ejde-745	179	28	)	)	PUNCT
ejde-745	179	29	weakly	weakly	ADV
ejde-745	179	30	in	in	ADP
ejde-745	179	31	e	e	PROPN
ejde-745	179	32	for	for	ADP
ejde-745	179	33	each	each	DET
ejde-745	179	34	t	t	NOUN
ejde-745	179	35	∈	∈	PROPN
ejde-745	180	1	i	i	PROPN
ejde-745	180	2	d	d	PROPN
ejde-745	180	3	,	,	PUNCT
ejde-745	181	1	so	so	SCONJ
ejde-745	181	2	f	f	X
ejde-745	181	3	(	(	PUNCT
ejde-745	181	4	xn	xn	PROPN
ejde-745	181	5	)	)	PUNCT
ejde-745	181	6	→	→	SYM
ejde-745	181	7	f	f	X
ejde-745	181	8	(	(	PUNCT
ejde-745	181	9	x	x	X
ejde-745	181	10	)	)	PUNCT
ejde-745	181	11	in	in	ADP
ejde-745	181	12	c(id	c(id	PROPN
ejde-745	181	13	,	,	PUNCT
ejde-745	181	14	e	e	NOUN
ejde-745	181	15	)	)	PUNCT
ejde-745	181	16	with	with	ADP
ejde-745	181	17	its	its	PRON
ejde-745	181	18	weak	weak	ADJ
ejde-745	181	19	topology	topology	NOUN
ejde-745	181	20	.	.	PUNCT
ejde-745	181	21	suppose	suppose	VERB
ejde-745	181	22	that	that	SCONJ
ejde-745	181	23	v	v	X
ejde-745	181	24	⊂	⊂	PROPN
ejde-745	181	25	b̃	b̃	PROPN
ejde-745	181	26	satisfies	satisfy	VERB
ejde-745	181	27	the	the	DET
ejde-745	181	28	condition	condition	NOUN
ejde-745	181	29	v	v	ADP
ejde-745	181	30	=	=	SYM
ejde-745	181	31	conv({x	conv({x	X
ejde-745	181	32	}	}	PUNCT
ejde-745	181	33	∪	∪	VERB
ejde-745	181	34	f	f	PROPN
ejde-745	181	35	(	(	PUNCT
ejde-745	181	36	v	v	NOUN
ejde-745	181	37	)	)	PUNCT
ejde-745	181	38	)	)	PUNCT
ejde-745	181	39	.	.	PUNCT
ejde-745	182	1	we	we	PRON
ejde-745	182	2	will	will	AUX
ejde-745	182	3	prove	prove	VERB
ejde-745	182	4	that	that	SCONJ
ejde-745	182	5	v	v	NOUN
ejde-745	182	6	is	be	AUX
ejde-745	182	7	relatively	relatively	ADV
ejde-745	182	8	weakly	weakly	ADJ
ejde-745	182	9	compact	compact	ADJ
ejde-745	182	10	and	and	CCONJ
ejde-745	182	11	so	so	ADV
ejde-745	182	12	(	(	PUNCT
ejde-745	182	13	2.1	2.1	NUM
ejde-745	182	14	)	)	PUNCT
ejde-745	182	15	is	be	AUX
ejde-745	182	16	satisfied	satisfied	ADJ
ejde-745	182	17	.	.	PUNCT
ejde-745	183	1	since	since	SCONJ
ejde-745	183	2	v	v	NUM
ejde-745	183	3	⊂	⊂	PROPN
ejde-745	183	4	b̃	b̃	PROPN
ejde-745	183	5	,	,	PUNCT
ejde-745	183	6	f	f	PROPN
ejde-745	183	7	(	(	PUNCT
ejde-745	183	8	v	v	NOUN
ejde-745	183	9	)	)	PUNCT
ejde-745	184	1	⊂	⊂	PROPN
ejde-745	184	2	k.	k.	PROPN
ejde-745	185	1	then	then	ADV
ejde-745	185	2	v	v	ADP
ejde-745	185	3	⊂	⊂	PROPN
ejde-745	185	4	v	v	X
ejde-745	185	5	=	=	SYM
ejde-745	185	6	conv({x}∪f	conv({x}∪f	NOUN
ejde-745	185	7	(	(	PUNCT
ejde-745	185	8	v	v	NOUN
ejde-745	185	9	)	)	PUNCT
ejde-745	185	10	)	)	PUNCT
ejde-745	185	11	is	be	AUX
ejde-745	185	12	equicontinuous	equicontinuous	ADJ
ejde-745	185	13	.	.	PUNCT
ejde-745	186	1	by	by	ADP
ejde-745	186	2	theorem	theorem	NOUN
ejde-745	186	3	2.10	2.10	NUM
ejde-745	186	4	t	t	NOUN
ejde-745	186	5	7→	7→	NUM
ejde-745	186	6	v(t	v(t	NUM
ejde-745	186	7	)	)	PUNCT
ejde-745	186	8	=	=	SYM
ejde-745	186	9	β(v	β(v	PROPN
ejde-745	186	10	(	(	PUNCT
ejde-745	186	11	t	t	PROPN
ejde-745	186	12	)	)	PUNCT
ejde-745	186	13	)	)	PUNCT
ejde-745	186	14	is	be	AUX
ejde-745	186	15	continuous	continuous	ADJ
ejde-745	186	16	on	on	ADP
ejde-745	186	17	i	i	PROPN
ejde-745	186	18	d.	d.	PROPN
ejde-745	186	19	for	for	ADP
ejde-745	186	20	fixed	fix	VERB
ejde-745	186	21	t	t	PROPN
ejde-745	186	22	∈	∈	PROPN
ejde-745	187	1	i	i	PRON
ejde-745	187	2	d	d	NOUN
ejde-745	187	3	we	we	PRON
ejde-745	187	4	divide	divide	VERB
ejde-745	187	5	the	the	DET
ejde-745	187	6	interval	interval	NOUN
ejde-745	187	7	[	[	X
ejde-745	187	8	0	0	NUM
ejde-745	187	9	,	,	PUNCT
ejde-745	187	10	t	t	PROPN
ejde-745	187	11	]	]	PUNCT
ejde-745	187	12	into	into	ADP
ejde-745	187	13	m	m	PROPN
ejde-745	187	14	parts	part	NOUN
ejde-745	187	15	in	in	ADP
ejde-745	187	16	the	the	DET
ejde-745	187	17	following	following	ADJ
ejde-745	187	18	way	way	NOUN
ejde-745	187	19	:	:	PUNCT
ejde-745	187	20	t0	t0	NOUN
ejde-745	187	21	=	=	SYM
ejde-745	187	22	0	0	NUM
ejde-745	187	23	,	,	PUNCT
ejde-745	187	24	t1	t1	NOUN
ejde-745	187	25	=	=	PUNCT
ejde-745	188	1	sups∈ia{s	sups∈ia{s	ADJ
ejde-745	188	2	:	:	PUNCT
ejde-745	189	1	s	s	X
ejde-745	189	2	≥	≥	X
ejde-745	189	3	t0	t0	NOUN
ejde-745	189	4	,	,	PUNCT
ejde-745	189	5	s−	s−	PROPN
ejde-745	189	6	t0	t0	PROPN
ejde-745	189	7	<	<	X
ejde-745	189	8	δ	δ	X
ejde-745	189	9	}	}	PUNCT
ejde-745	189	10	,	,	PUNCT
ejde-745	189	11	t2	t2	NOUN
ejde-745	189	12	=	=	SYM
ejde-745	189	13	sup	sup	NOUN
ejde-745	189	14	s∈ia	s∈ia	NOUN
ejde-745	189	15	{	{	PUNCT
ejde-745	189	16	s	s	X
ejde-745	189	17	:	:	PUNCT
ejde-745	189	18	s	s	PART
ejde-745	189	19	≥	≥	NOUN
ejde-745	189	20	t1	t1	NOUN
ejde-745	189	21	,	,	PUNCT
ejde-745	189	22	s−	s−	PROPN
ejde-745	189	23	t1	t1	VERB
ejde-745	189	24	<	<	X
ejde-745	189	25	δ	δ	PROPN
ejde-745	189	26	}	}	PUNCT
ejde-745	189	27	,	,	PUNCT
ejde-745	189	28	.	.	PUNCT
ejde-745	189	29	.	.	PUNCT
ejde-745	189	30	.	.	PUNCT
ejde-745	190	1	,	,	PUNCT
ejde-745	190	2	tm	tm	NOUN
ejde-745	190	3	=	=	NOUN
ejde-745	190	4	sup	sup	NOUN
ejde-745	190	5	s∈ia	s∈ia	NOUN
ejde-745	190	6	{	{	PUNCT
ejde-745	190	7	s	s	X
ejde-745	190	8	:	:	PUNCT
ejde-745	190	9	s	s	PART
ejde-745	190	10	≥	≥	NOUN
ejde-745	190	11	tm−1	tm−1	NOUN
ejde-745	190	12	,	,	PUNCT
ejde-745	190	13	s−	s−	PROPN
ejde-745	190	14	tm−1	tm−1	PROPN
ejde-745	190	15	<	<	X
ejde-745	190	16	δ	δ	PROPN
ejde-745	190	17	}	}	PUNCT
ejde-745	190	18	.	.	PUNCT
ejde-745	191	1	since	since	SCONJ
ejde-745	191	2	t	t	PROPN
ejde-745	191	3	is	be	AUX
ejde-745	191	4	closed	closed	ADJ
ejde-745	191	5	,	,	PUNCT
ejde-745	191	6	we	we	PRON
ejde-745	191	7	have	have	VERB
ejde-745	191	8	ti	ti	PROPN
ejde-745	191	9	∈	∈	PROPN
ejde-745	191	10	ia	ia	PROPN
ejde-745	191	11	.	.	PUNCT
ejde-745	192	1	if	if	SCONJ
ejde-745	192	2	some	some	PRON
ejde-745	192	3	ti+1	ti+1	NOUN
ejde-745	192	4	=	=	SYM
ejde-745	192	5	ti	ti	NOUN
ejde-745	192	6	then	then	ADV
ejde-745	192	7	ti+2	ti+2	NUM
ejde-745	193	1	=	=	SYM
ejde-745	193	2	{	{	PUNCT
ejde-745	193	3	inf	inf	NOUN
ejde-745	193	4	t	t	PROPN
ejde-745	193	5	∈	∈	PROPN
ejde-745	193	6	t	t	PROPN
ejde-745	193	7	:	:	PUNCT
ejde-745	193	8	t	t	PROPN
ejde-745	193	9	≥	≥	NOUN
ejde-745	193	10	ti+1	ti+1	ADV
ejde-745	193	11	}	}	PUNCT
ejde-745	193	12	.	.	PUNCT
ejde-745	194	1	f	f	PROPN
ejde-745	194	2	(	(	PUNCT
ejde-745	194	3	x)(t	x)(t	PROPN
ejde-745	194	4	)	)	PUNCT
ejde-745	194	5	=	=	PUNCT
ejde-745	195	1	x0	x0	PROPN
ejde-745	195	2	+	+	CCONJ
ejde-745	195	3	1	1	NUM
ejde-745	195	4	γ(α	γ(α	NOUN
ejde-745	195	5	)	)	PUNCT
ejde-745	195	6	∫	∫	PROPN
ejde-745	196	1	t	t	PROPN
ejde-745	196	2	0	0	NUM
ejde-745	196	3	(	(	PUNCT
ejde-745	196	4	t−	t−	PROPN
ejde-745	196	5	s)α−1f(s	s)α−1f(s	X
ejde-745	196	6	,	,	PUNCT
ejde-745	196	7	x(s))∆s	x(s))∆s	PUNCT
ejde-745	196	8	=	=	PUNCT
ejde-745	197	1	x0	x0	PROPN
ejde-745	197	2	+	+	CCONJ
ejde-745	197	3	1	1	NUM
ejde-745	197	4	γ(α	γ(α	NOUN
ejde-745	197	5	)	)	PUNCT
ejde-745	198	1	m−1∑	m−1∑	PROPN
ejde-745	198	2	i=0	i=0	PROPN
ejde-745	198	3	∫	∫	PROPN
ejde-745	198	4	ji	ji	PROPN
ejde-745	198	5	(	(	PUNCT
ejde-745	198	6	t−	t−	PROPN
ejde-745	198	7	s)α−1f(s	s)α−1f(s	PROPN
ejde-745	198	8	,	,	PUNCT
ejde-745	198	9	x(s))∆s	x(s))∆s	PROPN
ejde-745	199	1	∈	∈	PROPN
ejde-745	200	1	x0	x0	PROPN
ejde-745	200	2	+	+	CCONJ
ejde-745	200	3	1	1	NUM
ejde-745	200	4	γ(α	γ(α	NOUN
ejde-745	200	5	)	)	PUNCT
ejde-745	200	6	m−1∑	m−1∑	NUM
ejde-745	200	7	i=0	i=0	PROPN
ejde-745	200	8	µ∆(ji	µ∆(ji	NOUN
ejde-745	200	9	)	)	PUNCT
ejde-745	200	10	sup	sup	NOUN
ejde-745	200	11	si∈ji	si∈ji	X
ejde-745	200	12	(	(	PUNCT
ejde-745	200	13	t−	t−	PROPN
ejde-745	200	14	si	si	PROPN
ejde-745	200	15	)	)	PUNCT
ejde-745	200	16	α−1conv(f(ji	α−1conv(f(ji	PROPN
ejde-745	200	17	,	,	PUNCT
ejde-745	200	18	v	v	PROPN
ejde-745	200	19	(	(	PUNCT
ejde-745	200	20	ji	ji	NOUN
ejde-745	200	21	)	)	PUNCT
ejde-745	200	22	)	)	PUNCT
ejde-745	200	23	)	)	PUNCT
ejde-745	201	1	where	where	SCONJ
ejde-745	201	2	ji	ji	PROPN
ejde-745	201	3	=	=	PUNCT
ejde-745	202	1	[	[	X
ejde-745	202	2	ti	ti	X
ejde-745	202	3	,	,	PUNCT
ejde-745	202	4	ti+1	ti+1	NOUN
ejde-745	202	5	]	]	PUNCT
ejde-745	202	6	,	,	PUNCT
ejde-745	202	7	i	i	PRON
ejde-745	202	8	=	=	NOUN
ejde-745	202	9	0	0	NUM
ejde-745	202	10	,	,	PUNCT
ejde-745	202	11	1	1	NUM
ejde-745	202	12	,	,	PUNCT
ejde-745	202	13	.	.	PUNCT
ejde-745	202	14	.	.	PUNCT
ejde-745	202	15	.	.	PUNCT
ejde-745	203	1	,	,	PUNCT
ejde-745	203	2	m−	m−	PROPN
ejde-745	203	3	1	1	NUM
ejde-745	203	4	.	.	PUNCT
ejde-745	204	1	using	use	VERB
ejde-745	204	2	(	(	PUNCT
ejde-745	204	3	3.3	3.3	NUM
ejde-745	204	4	)	)	PUNCT
ejde-745	204	5	and	and	CCONJ
ejde-745	204	6	properties	property	NOUN
ejde-745	204	7	of	of	ADP
ejde-745	204	8	the	the	DET
ejde-745	204	9	measure	measure	NOUN
ejde-745	204	10	of	of	ADP
ejde-745	204	11	weak	weak	ADJ
ejde-745	204	12	noncompactness	noncompactness	ADV
ejde-745	204	13	we	we	PRON
ejde-745	204	14	obtain	obtain	VERB
ejde-745	204	15	β(f	β(f	PROPN
ejde-745	204	16	(	(	PUNCT
ejde-745	204	17	v	v	NOUN
ejde-745	204	18	(	(	PUNCT
ejde-745	204	19	t	t	PROPN
ejde-745	204	20	)	)	PUNCT
ejde-745	204	21	)	)	PUNCT
ejde-745	204	22	)	)	PUNCT
ejde-745	205	1	≤	≤	ADV
ejde-745	205	2	1	1	NUM
ejde-745	205	3	γ(α	γ(α	NOUN
ejde-745	205	4	)	)	PUNCT
ejde-745	206	1	m−1∑	m−1∑	PROPN
ejde-745	206	2	i=0	i=0	PROPN
ejde-745	206	3	µ∆(ji)(t−	µ∆(ji)(t−	NOUN
ejde-745	206	4	qi	qi	PROPN
ejde-745	206	5	)	)	PUNCT
ejde-745	206	6	α−1β(f(ji	α−1β(f(ji	NUM
ejde-745	206	7	,	,	PUNCT
ejde-745	206	8	v	v	X
ejde-745	206	9	(	(	PUNCT
ejde-745	206	10	ji	ji	NOUN
ejde-745	206	11	)	)	PUNCT
ejde-745	206	12	)	)	PUNCT
ejde-745	206	13	)	)	PUNCT
ejde-745	207	1	≤	≤	ADV
ejde-745	207	2	1	1	NUM
ejde-745	207	3	γ(α	γ(α	NOUN
ejde-745	207	4	)	)	PUNCT
ejde-745	207	5	m−1∑	m−1∑	PROPN
ejde-745	207	6	i=0	i=0	PROPN
ejde-745	207	7	µ∆(ji)(t−	µ∆(ji)(t−	NOUN
ejde-745	207	8	qi	qi	PROPN
ejde-745	207	9	)	)	PUNCT
ejde-745	207	10	α−1	α−1	PROPN
ejde-745	207	11	·	·	PUNCT
ejde-745	207	12	c	c	X
ejde-745	207	13	·	·	PUNCT
ejde-745	207	14	β(v	β(v	NOUN
ejde-745	207	15	(	(	PUNCT
ejde-745	207	16	i	i	PROPN
ejde-745	207	17	d	d	PROPN
ejde-745	207	18	)	)	PUNCT
ejde-745	207	19	)	)	PUNCT
ejde-745	207	20	≤	≤	NUM
ejde-745	208	1	c	c	NOUN
ejde-745	208	2	·	·	PUNCT
ejde-745	208	3	β(v	β(v	NOUN
ejde-745	208	4	(	(	PUNCT
ejde-745	208	5	i	i	PROPN
ejde-745	208	6	d	d	PROPN
ejde-745	208	7	)	)	PUNCT
ejde-745	208	8	)	)	PUNCT
ejde-745	208	9	γ(α	γ(α	PROPN
ejde-745	208	10	)	)	PUNCT
ejde-745	209	1	∫	∫	PROPN
ejde-745	209	2	t	t	PROPN
ejde-745	209	3	0	0	NUM
ejde-745	209	4	(	(	PUNCT
ejde-745	209	5	t−	t−	PROPN
ejde-745	209	6	s)α−1∆s	s)α−1∆s	PROPN
ejde-745	209	7	.	.	PUNCT
ejde-745	210	1	since	since	SCONJ
ejde-745	210	2	v	v	NUM
ejde-745	210	3	⊂	⊂	PROPN
ejde-745	210	4	v	v	X
ejde-745	210	5	=	=	SYM
ejde-745	210	6	conv({x	conv({x	X
ejde-745	210	7	}	}	PUNCT
ejde-745	210	8	∪	∪	VERB
ejde-745	210	9	f	f	PROPN
ejde-745	210	10	(	(	PUNCT
ejde-745	210	11	v	v	NOUN
ejde-745	210	12	)	)	PUNCT
ejde-745	210	13	)	)	PUNCT
ejde-745	210	14	,	,	PUNCT
ejde-745	210	15	β(v	β(v	PROPN
ejde-745	210	16	(	(	PUNCT
ejde-745	210	17	t	t	NOUN
ejde-745	210	18	)	)	PUNCT
ejde-745	210	19	)	)	PUNCT
ejde-745	210	20	≤	≤	PROPN
ejde-745	210	21	c·β(v	c·β(v	PROPN
ejde-745	210	22	(	(	PUNCT
ejde-745	210	23	i	i	PROPN
ejde-745	210	24	d	d	PROPN
ejde-745	210	25	)	)	PUNCT
ejde-745	210	26	)	)	PUNCT
ejde-745	210	27	γ(α	γ(α	PROPN
ejde-745	210	28	)	)	PUNCT
ejde-745	210	29	∫	∫	PROPN
ejde-745	210	30	t	t	PROPN
ejde-745	210	31	0	0	NUM
ejde-745	210	32	(	(	PUNCT
ejde-745	210	33	t	t	PROPN
ejde-745	210	34	−	−	PROPN
ejde-745	210	35	s)α−1∆s	s)α−1∆s	PROPN
ejde-745	210	36	.	.	PUNCT
ejde-745	210	37	using	use	VERB
ejde-745	210	38	theorem	theorem	NOUN
ejde-745	210	39	2.6	2.6	NUM
ejde-745	210	40	we	we	PRON
ejde-745	210	41	obtain	obtain	VERB
ejde-745	210	42	β(v	β(v	ADP
ejde-745	210	43	(	(	PUNCT
ejde-745	210	44	i	i	PROPN
ejde-745	210	45	d	d	PROPN
ejde-745	210	46	)	)	PUNCT
ejde-745	210	47	)	)	PUNCT
ejde-745	210	48	≤	≤	NUM
ejde-745	210	49	c	c	NOUN
ejde-745	210	50	·	·	PUNCT
ejde-745	210	51	β(v	β(v	NOUN
ejde-745	210	52	(	(	PUNCT
ejde-745	210	53	i	i	PROPN
ejde-745	210	54	d	d	PROPN
ejde-745	210	55	)	)	PUNCT
ejde-745	210	56	)	)	PUNCT
ejde-745	210	57	γ(α	γ(α	PROPN
ejde-745	210	58	)	)	PUNCT
ejde-745	211	1	∫	∫	PROPN
ejde-745	211	2	t	t	PROPN
ejde-745	211	3	0	0	NUM
ejde-745	211	4	(	(	PUNCT
ejde-745	211	5	t−	t−	PROPN
ejde-745	211	6	s)α−1∆s	s)α−1∆s	PROPN
ejde-745	211	7	since	since	SCONJ
ejde-745	211	8	c	c	PROPN
ejde-745	211	9	γ(α	γ(α	PROPN
ejde-745	211	10	)	)	PUNCT
ejde-745	212	1	∫	∫	PROPN
ejde-745	212	2	t	t	PROPN
ejde-745	212	3	0	0	NUM
ejde-745	213	1	(	(	PUNCT
ejde-745	213	2	t	t	PROPN
ejde-745	213	3	−	−	PROPN
ejde-745	213	4	s)α−1∆s	s)α−1∆s	PROPN
ejde-745	213	5	<	<	X
ejde-745	213	6	1	1	NUM
ejde-745	213	7	,	,	PUNCT
ejde-745	213	8	we	we	PRON
ejde-745	213	9	obtain	obtain	VERB
ejde-745	213	10	v(t	v(t	NOUN
ejde-745	213	11	)	)	PUNCT
ejde-745	213	12	=	=	SYM
ejde-745	214	1	β(v	β(v	PROPN
ejde-745	214	2	(	(	PUNCT
ejde-745	214	3	t	t	NOUN
ejde-745	214	4	)	)	PUNCT
ejde-745	214	5	)	)	PUNCT
ejde-745	215	1	=	=	PUNCT
ejde-745	215	2	0	0	NUM
ejde-745	215	3	,	,	PUNCT
ejde-745	215	4	for	for	ADP
ejde-745	215	5	t	t	PROPN
ejde-745	215	6	∈	∈	PROPN
ejde-745	216	1	i	i	PRON
ejde-745	216	2	d.	d.	NOUN
ejde-745	216	3	using	use	VERB
ejde-745	216	4	ascoli‘s	ascoli‘s	PROPN
ejde-745	216	5	theorem	theorem	VERB
ejde-745	216	6	,	,	PUNCT
ejde-745	216	7	v	v	NOUN
ejde-745	216	8	is	be	AUX
ejde-745	216	9	relatively	relatively	ADV
ejde-745	216	10	weakly	weakly	ADJ
ejde-745	216	11	compact	compact	ADJ
ejde-745	216	12	.	.	PUNCT
ejde-745	217	1	by	by	ADP
ejde-745	217	2	theorem	theorem	NOUN
ejde-745	217	3	2.13	2.13	NUM
ejde-745	217	4	the	the	DET
ejde-745	217	5	operator	operator	NOUN
ejde-745	217	6	f	f	PROPN
ejde-745	217	7	has	have	VERB
ejde-745	217	8	a	a	DET
ejde-745	217	9	fixed	fix	VERB
ejde-745	217	10	point	point	NOUN
ejde-745	217	11	.	.	PUNCT
ejde-745	218	1	then	then	ADV
ejde-745	218	2	there	there	PRON
ejde-745	218	3	exists	exist	VERB
ejde-745	218	4	a	a	DET
ejde-745	218	5	pseudosolution	pseudosolution	NOUN
ejde-745	218	6	to	to	PART
ejde-745	218	7	problem	problem	NOUN
ejde-745	218	8	(	(	PUNCT
ejde-745	218	9	1.1	1.1	NUM
ejde-745	218	10	)	)	PUNCT
ejde-745	218	11	.	.	PUNCT
ejde-745	219	1	□	□	PUNCT
ejde-745	219	2	references	reference	NOUN
ejde-745	219	3	[	[	X
ejde-745	219	4	1	1	NUM
ejde-745	219	5	]	]	X
ejde-745	219	6	abbas	abbas	PROPN
ejde-745	219	7	,	,	PUNCT
ejde-745	219	8	s.	s.	PROPN
ejde-745	219	9	;	;	PUNCT
ejde-745	219	10	benchohra	benchohra	NOUN
ejde-745	219	11	,	,	PUNCT
ejde-745	219	12	m.	m.	NOUN
ejde-745	219	13	;	;	PUNCT
ejde-745	219	14	henderson	henderson	PROPN
ejde-745	219	15	,	,	PUNCT
ejde-745	219	16	j.	j.	PROPN
ejde-745	219	17	;	;	PUNCT
ejde-745	219	18	weak	weak	ADJ
ejde-745	219	19	solutions	solution	NOUN
ejde-745	219	20	for	for	ADP
ejde-745	219	21	implicit	implicit	ADJ
ejde-745	219	22	fractional	fractional	ADJ
ejde-745	219	23	differential	differential	ADJ
ejde-745	219	24	equations	equation	NOUN
ejde-745	219	25	of	of	ADP
ejde-745	219	26	hadamard	hadamard	ADJ
ejde-745	219	27	type	type	NOUN
ejde-745	219	28	.	.	PUNCT
ejde-745	220	1	adv	adv	PROPN
ejde-745	220	2	.	.	PUNCT
ejde-745	221	1	dyn	dyn	PROPN
ejde-745	221	2	.	.	PUNCT
ejde-745	222	1	syst	syst	PROPN
ejde-745	222	2	.	.	PUNCT
ejde-745	223	1	appl	appl	PROPN
ejde-745	223	2	.	.	PROPN
ejde-745	223	3	,	,	PUNCT
ejde-745	223	4	vol	vol	NOUN
ejde-745	223	5	.	.	PROPN
ejde-745	223	6	11	11	NUM
ejde-745	223	7	(	(	PUNCT
ejde-745	223	8	2016	2016	NUM
ejde-745	223	9	)	)	PUNCT
ejde-745	223	10	,	,	PUNCT
ejde-745	223	11	pp	pp	PROPN
ejde-745	223	12	.	.	PUNCT
ejde-745	224	1	1–13	1–13	NOUN
ejde-745	224	2	.	.	PUNCT
ejde-745	224	3	8	8	NUM
ejde-745	224	4	a.	a.	NOUN
ejde-745	224	5	sikorska	sikorska	PROPN
ejde-745	224	6	-	-	PUNCT
ejde-745	224	7	nowak	nowak	PROPN
ejde-745	224	8	ejde-2024/36	ejde-2024/36	NOUN
ejde-745	224	9	[	[	X
ejde-745	224	10	2	2	NUM
ejde-745	224	11	]	]	PUNCT
ejde-745	224	12	agarwal	agarwal	PROPN
ejde-745	224	13	,	,	PUNCT
ejde-745	224	14	r.	r.	PROPN
ejde-745	224	15	p.	p.	PROPN
ejde-745	224	16	;	;	PUNCT
ejde-745	224	17	bohner	bohner	NOUN
ejde-745	224	18	,	,	PUNCT
ejde-745	224	19	m.	m.	NOUN
ejde-745	224	20	;	;	PUNCT
ejde-745	224	21	basic	basic	ADJ
ejde-745	224	22	calculus	calculus	NOUN
ejde-745	224	23	on	on	ADP
ejde-745	224	24	time	time	NOUN
ejde-745	224	25	scales	scale	NOUN
ejde-745	224	26	and	and	CCONJ
ejde-745	224	27	some	some	PRON
ejde-745	224	28	of	of	ADP
ejde-745	224	29	its	its	PRON
ejde-745	224	30	applications	application	NOUN
ejde-745	224	31	.	.	PUNCT
ejde-745	225	1	result	result	PROPN
ejde-745	225	2	math	math	PROPN
ejde-745	225	3	.	.	PUNCT
ejde-745	226	1	,	,	PUNCT
ejde-745	226	2	vol	vol	NOUN
ejde-745	226	3	.	.	PROPN
ejde-745	226	4	35	35	NUM
ejde-745	226	5	(	(	PUNCT
ejde-745	226	6	1999	1999	NUM
ejde-745	226	7	)	)	PUNCT
ejde-745	226	8	,	,	PUNCT
ejde-745	226	9	pp	pp	ADP
ejde-745	226	10	.	.	PUNCT
ejde-745	227	1	3	3	NUM
ejde-745	227	2	-	-	SYM
ejde-745	227	3	22	22	NUM
ejde-745	227	4	.	.	PUNCT
ejde-745	228	1	[	[	X
ejde-745	228	2	3	3	NUM
ejde-745	228	3	]	]	X
ejde-745	228	4	agarwal	agarwal	PROPN
ejde-745	228	5	,	,	PUNCT
ejde-745	228	6	r.	r.	PROPN
ejde-745	228	7	p.	p.	PROPN
ejde-745	228	8	;	;	PUNCT
ejde-745	228	9	bohner	bohner	NOUN
ejde-745	228	10	,	,	PUNCT
ejde-745	228	11	m.	m.	NOUN
ejde-745	228	12	;	;	PUNCT
ejde-745	228	13	peterson	peterson	PROPN
ejde-745	228	14	,	,	PUNCT
ejde-745	228	15	a.	a.	PROPN
ejde-745	228	16	;	;	PUNCT
ejde-745	228	17	inequalities	inequality	NOUN
ejde-745	228	18	on	on	ADP
ejde-745	228	19	time	time	NOUN
ejde-745	228	20	scales	scale	NOUN
ejde-745	228	21	:	:	PUNCT
ejde-745	228	22	a	a	DET
ejde-745	228	23	survey	survey	NOUN
ejde-745	228	24	.	.	PUNCT
ejde-745	229	1	math	math	NOUN
ejde-745	229	2	.	.	PUNCT
ejde-745	230	1	inequal	inequal	PROPN
ejde-745	230	2	.	.	PUNCT
ejde-745	231	1	appl	appl	PROPN
ejde-745	231	2	.	.	PROPN
ejde-745	231	3	,	,	PUNCT
ejde-745	231	4	vol	vol	NOUN
ejde-745	231	5	.	.	PROPN
ejde-745	231	6	4	4	NUM
ejde-745	231	7	,	,	PUNCT
ejde-745	231	8	no	no	INTJ
ejde-745	231	9	.	.	NOUN
ejde-745	231	10	4	4	NUM
ejde-745	231	11	(	(	PUNCT
ejde-745	231	12	2021	2021	NUM
ejde-745	231	13	)	)	PUNCT
ejde-745	231	14	,	,	PUNCT
ejde-745	231	15	pp	pp	ADP
ejde-745	231	16	.	.	PUNCT
ejde-745	232	1	535	535	NUM
ejde-745	232	2	-	-	SYM
ejde-745	232	3	557	557	NUM
ejde-745	232	4	.	.	PUNCT
ejde-745	233	1	[	[	X
ejde-745	233	2	4	4	NUM
ejde-745	233	3	]	]	X
ejde-745	233	4	agarwal	agarwal	PROPN
ejde-745	233	5	,	,	PUNCT
ejde-745	233	6	r.	r.	PROPN
ejde-745	233	7	p.	p.	PROPN
ejde-745	233	8	;	;	PUNCT
ejde-745	233	9	lupulescu	lupulescu	PROPN
ejde-745	233	10	,	,	PUNCT
ejde-745	233	11	v.	v.	ADV
ejde-745	233	12	;	;	PUNCT
ejde-745	233	13	o’regan	o’regan	PROPN
ejde-745	233	14	,	,	PUNCT
ejde-745	233	15	d.	d.	PROPN
ejde-745	233	16	;	;	PUNCT
ejde-745	233	17	rahman	rahman	PROPN
ejde-745	233	18	,	,	PUNCT
ejde-745	233	19	g.	g.	PROPN
ejde-745	233	20	;	;	PUNCT
ejde-745	233	21	weak	weak	ADJ
ejde-745	233	22	solutions	solution	NOUN
ejde-745	233	23	for	for	ADP
ejde-745	233	24	fractional	fractional	ADJ
ejde-745	233	25	differential	differential	ADJ
ejde-745	233	26	equations	equation	NOUN
ejde-745	233	27	in	in	ADP
ejde-745	233	28	nonreflexive	nonreflexive	ADJ
ejde-745	233	29	banach	banach	NOUN
ejde-745	233	30	spaces	space	NOUN
ejde-745	233	31	via	via	ADP
ejde-745	233	32	riemann	riemann	PROPN
ejde-745	233	33	–	–	PUNCT
ejde-745	233	34	pettis	pettis	NOUN
ejde-745	233	35	integrals	integral	NOUN
ejde-745	233	36	.	.	PUNCT
ejde-745	234	1	math	math	NOUN
ejde-745	234	2	.	.	PUNCT
ejde-745	235	1	nachr	nachr	PROPN
ejde-745	235	2	.	.	PUNCT
ejde-745	235	3	,	,	PUNCT
ejde-745	236	1	vol	vol	NOUN
ejde-745	236	2	.	.	PROPN
ejde-745	237	1	289	289	NUM
ejde-745	237	2	(	(	PUNCT
ejde-745	237	3	2016	2016	NUM
ejde-745	237	4	)	)	PUNCT
ejde-745	237	5	,	,	PUNCT
ejde-745	237	6	pp	pp	ADP
ejde-745	237	7	.	.	PUNCT
ejde-745	238	1	395–409	395–409	NUM
ejde-745	238	2	.	.	PUNCT
ejde-745	238	3	doi	doi	PROPN
ejde-745	238	4	10.1002	10.1002	NUM
ejde-745	238	5	/	/	SYM
ejde-745	238	6	mana.201400010	mana.201400010	PROPN
ejde-745	239	1	[	[	X
ejde-745	239	2	5	5	NUM
ejde-745	239	3	]	]	PUNCT
ejde-745	239	4	ball	ball	NOUN
ejde-745	239	5	,	,	PUNCT
ejde-745	239	6	j.	j.	PROPN
ejde-745	239	7	m.	m.	PROPN
ejde-745	239	8	;	;	PUNCT
ejde-745	239	9	weak	weak	ADJ
ejde-745	239	10	continuity	continuity	NOUN
ejde-745	239	11	properties	property	NOUN
ejde-745	239	12	of	of	ADP
ejde-745	239	13	mappings	mapping	NOUN
ejde-745	239	14	and	and	CCONJ
ejde-745	239	15	semigroups	semigroup	NOUN
ejde-745	239	16	.	.	PUNCT
ejde-745	240	1	proc	proc	PROPN
ejde-745	240	2	.	.	PUNCT
ejde-745	241	1	royal	royal	ADJ
ejde-745	241	2	soc	soc	PROPN
ejde-745	241	3	.	.	PUNCT
ejde-745	242	1	edinburgh	edinburgh	NOUN
ejde-745	242	2	sect	sect	PROPN
ejde-745	242	3	.	.	PUNCT
ejde-745	243	1	a	a	DET
ejde-745	243	2	,	,	PUNCT
ejde-745	243	3	vol	vol	NOUN
ejde-745	243	4	.	.	PROPN
ejde-745	243	5	72	72	NUM
ejde-745	243	6	(	(	PUNCT
ejde-745	243	7	1979	1979	NUM
ejde-745	243	8	)	)	PUNCT
ejde-745	243	9	,	,	PUNCT
ejde-745	243	10	pp	pp	ADP
ejde-745	243	11	.	.	PUNCT
ejde-745	244	1	275–280	275–280	NUM
ejde-745	244	2	.	.	PUNCT
ejde-745	245	1	[	[	X
ejde-745	245	2	6	6	NUM
ejde-745	245	3	]	]	X
ejde-745	245	4	belmor	belmor	NOUN
ejde-745	245	5	,	,	PUNCT
ejde-745	245	6	s.	s.	PROPN
ejde-745	245	7	;	;	PUNCT
ejde-745	245	8	ravichandran	ravichandran	NOUN
ejde-745	245	9	,	,	PUNCT
ejde-745	245	10	c.	c.	PROPN
ejde-745	245	11	;	;	PUNCT
ejde-745	245	12	jarad	jarad	PROPN
ejde-745	245	13	,	,	PUNCT
ejde-745	245	14	f.	f.	PROPN
ejde-745	245	15	;	;	PUNCT
ejde-745	245	16	nonlinear	nonlinear	ADJ
ejde-745	245	17	generalized	generalize	VERB
ejde-745	245	18	fractional	fractional	ADJ
ejde-745	245	19	differential	differential	ADJ
ejde-745	245	20	equations	equation	NOUN
ejde-745	245	21	with	with	ADP
ejde-745	245	22	generalized	generalized	ADJ
ejde-745	245	23	fractional	fractional	ADJ
ejde-745	245	24	integral	integral	ADJ
ejde-745	245	25	conditions	condition	NOUN
ejde-745	245	26	.	.	PUNCT
ejde-745	246	1	j.	j.	PROPN
ejde-745	246	2	taibah	taibah	PROPN
ejde-745	246	3	uni	uni	PROPN
ejde-745	246	4	.	.	PUNCT
ejde-745	247	1	sci	sci	PROPN
ejde-745	247	2	.	.	PROPN
ejde-745	247	3	,	,	PUNCT
ejde-745	247	4	vol	vol	NOUN
ejde-745	247	5	.	.	PROPN
ejde-745	247	6	14	14	NUM
ejde-745	247	7	(	(	PUNCT
ejde-745	247	8	2020	2020	NUM
ejde-745	247	9	)	)	PUNCT
ejde-745	247	10	,	,	PUNCT
ejde-745	247	11	pp	pp	ADP
ejde-745	247	12	.	.	PUNCT
ejde-745	248	1	114–123	114–123	NUM
ejde-745	248	2	.	.	PUNCT
ejde-745	248	3	doi	doi	NOUN
ejde-745	248	4	10.1080/16583655.2019.1709265	10.1080/16583655.2019.1709265	NUM
ejde-745	248	5	[	[	X
ejde-745	248	6	7	7	NUM
ejde-745	248	7	]	]	X
ejde-745	248	8	bohner	bohner	NOUN
ejde-745	248	9	,	,	PUNCT
ejde-745	248	10	m.	m.	NOUN
ejde-745	248	11	;	;	PUNCT
ejde-745	248	12	peterson	peterson	PROPN
ejde-745	248	13	,	,	PUNCT
ejde-745	248	14	a.	a.	PROPN
ejde-745	248	15	;	;	PUNCT
ejde-745	248	16	advances	advance	NOUN
ejde-745	248	17	in	in	ADP
ejde-745	248	18	dynamic	dynamic	ADJ
ejde-745	248	19	equations	equation	NOUN
ejde-745	248	20	on	on	ADP
ejde-745	248	21	time	time	NOUN
ejde-745	248	22	scales	scale	NOUN
ejde-745	248	23	.	.	PUNCT
ejde-745	249	1	birkhäuser	birkhäuser	NOUN
ejde-745	249	2	,	,	PUNCT
ejde-745	249	3	boston	boston	PROPN
ejde-745	249	4	,	,	PUNCT
ejde-745	249	5	2003	2003	NUM
ejde-745	249	6	.	.	PUNCT
ejde-745	250	1	[	[	X
ejde-745	250	2	8	8	NUM
ejde-745	250	3	]	]	X
ejde-745	250	4	cabada	cabada	PROPN
ejde-745	250	5	,	,	PUNCT
ejde-745	250	6	a.	a.	PROPN
ejde-745	250	7	;	;	PUNCT
ejde-745	250	8	vivero	vivero	PROPN
ejde-745	250	9	,	,	PUNCT
ejde-745	250	10	d.	d.	PROPN
ejde-745	250	11	r.	r.	PROPN
ejde-745	250	12	;	;	PUNCT
ejde-745	250	13	expression	expression	NOUN
ejde-745	250	14	of	of	ADP
ejde-745	250	15	the	the	DET
ejde-745	250	16	lebesgue	lebesgue	NOUN
ejde-745	250	17	∆-integral	∆-integral	NOUN
ejde-745	250	18	on	on	ADP
ejde-745	250	19	time	time	NOUN
ejde-745	250	20	scales	scale	NOUN
ejde-745	250	21	as	as	ADP
ejde-745	250	22	a	a	DET
ejde-745	250	23	usual	usual	ADJ
ejde-745	250	24	lebesgue	lebesgue	NOUN
ejde-745	250	25	integral	integral	ADJ
ejde-745	250	26	;	;	PUNCT
ejde-745	250	27	applications	application	NOUN
ejde-745	250	28	of	of	ADP
ejde-745	250	29	the	the	DET
ejde-745	250	30	calculus	calculus	NOUN
ejde-745	250	31	of	of	ADP
ejde-745	250	32	∆-antiderivatives	∆-antiderivative	NOUN
ejde-745	250	33	.	.	PUNCT
ejde-745	251	1	math	math	NOUN
ejde-745	251	2	.	.	PUNCT
ejde-745	252	1	comp	comp	PROPN
ejde-745	252	2	.	.	PUNCT
ejde-745	253	1	modell	modell	PROPN
ejde-745	253	2	.	.	PUNCT
ejde-745	254	1	,	,	PUNCT
ejde-745	254	2	vol	vol	NOUN
ejde-745	254	3	.	.	PROPN
ejde-745	255	1	43	43	NUM
ejde-745	255	2	(	(	PUNCT
ejde-745	255	3	2006	2006	NUM
ejde-745	255	4	)	)	PUNCT
ejde-745	255	5	,	,	PUNCT
ejde-745	256	1	pp	pp	PROPN
ejde-745	256	2	.	.	PUNCT
ejde-745	257	1	194	194	NUM
ejde-745	257	2	-	-	SYM
ejde-745	257	3	207	207	NUM
ejde-745	257	4	.	.	PUNCT
ejde-745	258	1	[	[	X
ejde-745	258	2	9	9	NUM
ejde-745	258	3	]	]	PUNCT
ejde-745	258	4	cichoń	cichoń	NOUN
ejde-745	258	5	,	,	PUNCT
ejde-745	258	6	m.	m.	NOUN
ejde-745	258	7	;	;	PUNCT
ejde-745	258	8	on	on	ADP
ejde-745	258	9	integrals	integral	NOUN
ejde-745	258	10	of	of	ADP
ejde-745	258	11	vector	vector	NOUN
ejde-745	258	12	-	-	PUNCT
ejde-745	258	13	valued	value	VERB
ejde-745	258	14	functions	function	NOUN
ejde-745	258	15	on	on	ADP
ejde-745	258	16	time	time	NOUN
ejde-745	258	17	scales	scale	NOUN
ejde-745	258	18	.	.	PUNCT
ejde-745	259	1	commun	commun	PROPN
ejde-745	259	2	.	.	PUNCT
ejde-745	260	1	math	math	PROPN
ejde-745	260	2	.	.	PUNCT
ejde-745	261	1	anal	anal	PROPN
ejde-745	261	2	.	.	PUNCT
ejde-745	261	3	,	,	PUNCT
ejde-745	261	4	vol	vol	NOUN
ejde-745	261	5	.	.	PROPN
ejde-745	262	1	11	11	NUM
ejde-745	262	2	,	,	PUNCT
ejde-745	262	3	no	no	INTJ
ejde-745	262	4	.	.	NOUN
ejde-745	262	5	1	1	NUM
ejde-745	262	6	(	(	PUNCT
ejde-745	262	7	2011	2011	NUM
ejde-745	262	8	)	)	PUNCT
ejde-745	262	9	,	,	PUNCT
ejde-745	263	1	pp	pp	ADP
ejde-745	263	2	.	.	PUNCT
ejde-745	264	1	94	94	NUM
ejde-745	264	2	-	-	SYM
ejde-745	264	3	110	110	NUM
ejde-745	264	4	.	.	PUNCT
ejde-745	265	1	[	[	X
ejde-745	265	2	10	10	NUM
ejde-745	265	3	]	]	X
ejde-745	265	4	cichoń	cichoń	NOUN
ejde-745	265	5	,	,	PUNCT
ejde-745	265	6	m.	m.	NOUN
ejde-745	265	7	;	;	PUNCT
ejde-745	265	8	salem	salem	PROPN
ejde-745	265	9	,	,	PUNCT
ejde-745	265	10	h.	h.	PROPN
ejde-745	265	11	a.	a.	PROPN
ejde-745	265	12	h.	h.	PROPN
ejde-745	265	13	;	;	PUNCT
ejde-745	265	14	on	on	ADP
ejde-745	265	15	the	the	DET
ejde-745	265	16	solutions	solution	NOUN
ejde-745	265	17	of	of	ADP
ejde-745	265	18	caputo	caputo	PROPN
ejde-745	265	19	–	–	PUNCT
ejde-745	265	20	hadamard	hadamard	ADJ
ejde-745	265	21	pettis	pettis	NOUN
ejde-745	265	22	-	-	PUNCT
ejde-745	265	23	type	type	NOUN
ejde-745	265	24	fractional	fractional	ADJ
ejde-745	265	25	differential	differential	NOUN
ejde-745	265	26	equations	equation	NOUN
ejde-745	265	27	.	.	PUNCT
ejde-745	266	1	racsam	racsam	PROPN
ejde-745	266	2	rev	rev	PROPN
ejde-745	266	3	.	.	PROPN
ejde-745	266	4	r.	r.	PROPN
ejde-745	266	5	acad	acad	PROPN
ejde-745	266	6	.	.	PUNCT
ejde-745	267	1	cienc	cienc	PROPN
ejde-745	267	2	.	.	PUNCT
ejde-745	268	1	exactas	exactas	PROPN
ejde-745	268	2	f́ıs	f́ıs	PROPN
ejde-745	268	3	.	.	PUNCT
ejde-745	269	1	nat	nat	PROPN
ejde-745	269	2	.	.	PUNCT
ejde-745	270	1	ser	ser	PROPN
ejde-745	270	2	.	.	PUNCT
ejde-745	271	1	a	a	DET
ejde-745	271	2	mat	mat	NOUN
ejde-745	271	3	.	.	NOUN
ejde-745	271	4	,	,	PUNCT
ejde-745	271	5	vol	vol	NOUN
ejde-745	271	6	.	.	PROPN
ejde-745	271	7	113	113	NUM
ejde-745	271	8	(	(	PUNCT
ejde-745	271	9	2019	2019	NUM
ejde-745	271	10	)	)	PUNCT
ejde-745	271	11	,	,	PUNCT
ejde-745	271	12	pp	pp	ADJ
ejde-745	271	13	.	.	PUNCT
ejde-745	272	1	3031–3053	3031–3053	NUM
ejde-745	272	2	.	.	PUNCT
ejde-745	273	1	doi	doi	NOUN
ejde-745	273	2	10.1007	10.1007	NUM
ejde-745	273	3	/	/	SYM
ejde-745	273	4	s13398	s13398	NOUN
ejde-745	273	5	-	-	PUNCT
ejde-745	273	6	015	015	NUM
ejde-745	273	7	-	-	PUNCT
ejde-745	273	8	0228	0228	NUM
ejde-745	273	9	-	-	PUNCT
ejde-745	273	10	4	4	NUM
ejde-745	274	1	[	[	SYM
ejde-745	274	2	11	11	NUM
ejde-745	274	3	]	]	X
ejde-745	274	4	gou	gou	PROPN
ejde-745	274	5	,	,	PUNCT
ejde-745	274	6	h.	h.	PROPN
ejde-745	274	7	;	;	PUNCT
ejde-745	274	8	li	li	PROPN
ejde-745	274	9	,	,	PUNCT
ejde-745	274	10	y.	y.	PROPN
ejde-745	274	11	;	;	PUNCT
ejde-745	274	12	weak	weak	ADJ
ejde-745	274	13	solutions	solution	NOUN
ejde-745	274	14	for	for	ADP
ejde-745	274	15	fractional	fractional	ADJ
ejde-745	274	16	differential	differential	ADJ
ejde-745	274	17	equations	equation	NOUN
ejde-745	274	18	via	via	ADP
ejde-745	274	19	henstock	henstock	PROPN
ejde-745	274	20	–	–	PUNCT
ejde-745	274	21	kurzweil	kurzweil	PROPN
ejde-745	274	22	–	–	PUNCT
ejde-745	274	23	pettis	pettis	NOUN
ejde-745	274	24	integrals	integral	NOUN
ejde-745	274	25	.	.	PUNCT
ejde-745	275	1	ijnsns	ijnsns	NOUN
ejde-745	275	2	,	,	PUNCT
ejde-745	275	3	2019	2019	NUM
ejde-745	275	4	.	.	PUNCT
ejde-745	276	1	doi	doi	NOUN
ejde-745	276	2	10.1515	10.1515	NUM
ejde-745	276	3	/	/	SYM
ejde-745	276	4	ijnsns-2018	ijnsns-2018	NOUN
ejde-745	276	5	-	-	NUM
ejde-745	276	6	0174	0174	NUM
ejde-745	277	1	[	[	X
ejde-745	277	2	12	12	NUM
ejde-745	277	3	]	]	X
ejde-745	277	4	henstock	henstock	PROPN
ejde-745	277	5	,	,	PUNCT
ejde-745	277	6	r.	r.	PROPN
ejde-745	277	7	;	;	PUNCT
ejde-745	277	8	the	the	DET
ejde-745	277	9	general	general	ADJ
ejde-745	277	10	theory	theory	NOUN
ejde-745	277	11	of	of	ADP
ejde-745	277	12	integration	integration	NOUN
ejde-745	277	13	.	.	PUNCT
ejde-745	278	1	oxford	oxford	PROPN
ejde-745	278	2	math	math	PROPN
ejde-745	278	3	.	.	PUNCT
ejde-745	279	1	monographs	monograph	NOUN
ejde-745	279	2	,	,	PUNCT
ejde-745	279	3	clarendon	clarendon	PROPN
ejde-745	279	4	press	press	NOUN
ejde-745	279	5	,	,	PUNCT
ejde-745	279	6	oxford	oxford	NOUN
ejde-745	279	7	,	,	PUNCT
ejde-745	279	8	1991	1991	NUM
ejde-745	279	9	.	.	PUNCT
ejde-745	280	1	[	[	X
ejde-745	280	2	13	13	NUM
ejde-745	280	3	]	]	PUNCT
ejde-745	280	4	hilger	hilger	NOUN
ejde-745	280	5	,	,	PUNCT
ejde-745	280	6	s.	s.	PROPN
ejde-745	280	7	;	;	PUNCT
ejde-745	281	1	ein	ein	PROPN
ejde-745	281	2	makettenkalkül	makettenkalkül	PROPN
ejde-745	281	3	mit	mit	PROPN
ejde-745	281	4	anwendung	anwendung	PROPN
ejde-745	281	5	auf	auf	PROPN
ejde-745	281	6	zentrumsmannigfaltigkeiten	zentrumsmannigfaltigkeiten	PROPN
ejde-745	281	7	.	.	PUNCT
ejde-745	281	8	ph.d	ph.d	PROPN
ejde-745	281	9	.	.	PUNCT
ejde-745	282	1	thesis	thesis	NOUN
ejde-745	282	2	,	,	PUNCT
ejde-745	282	3	universität	universität	PROPN
ejde-745	282	4	würzburg	würzburg	PROPN
ejde-745	282	5	,	,	PUNCT
ejde-745	282	6	germany	germany	PROPN
ejde-745	282	7	,	,	PUNCT
ejde-745	282	8	1988	1988	NUM
ejde-745	282	9	.	.	PUNCT
ejde-745	283	1	[	[	X
ejde-745	283	2	14	14	NUM
ejde-745	283	3	]	]	X
ejde-745	283	4	kubiaczyk	kubiaczyk	NOUN
ejde-745	283	5	,	,	PUNCT
ejde-745	283	6	i.	i.	NOUN
ejde-745	283	7	;	;	PUNCT
ejde-745	283	8	kneser	kneser	NOUN
ejde-745	283	9	type	type	NOUN
ejde-745	283	10	theorems	theorem	NOUN
ejde-745	283	11	for	for	ADP
ejde-745	283	12	ordinary	ordinary	ADJ
ejde-745	283	13	differential	differential	ADJ
ejde-745	283	14	equations	equation	NOUN
ejde-745	283	15	in	in	ADP
ejde-745	283	16	banach	banach	NOUN
ejde-745	283	17	spaces	space	NOUN
ejde-745	283	18	.	.	PUNCT
ejde-745	284	1	journal	journal	PROPN
ejde-745	284	2	of	of	ADP
ejde-745	284	3	differential	differential	ADJ
ejde-745	284	4	equations	equation	NOUN
ejde-745	284	5	,	,	PUNCT
ejde-745	284	6	vol	vol	NOUN
ejde-745	284	7	.	.	PROPN
ejde-745	285	1	45	45	NUM
ejde-745	285	2	,	,	PUNCT
ejde-745	285	3	no	no	INTJ
ejde-745	285	4	.	.	NOUN
ejde-745	285	5	2	2	NUM
ejde-745	285	6	(	(	PUNCT
ejde-745	285	7	1982	1982	NUM
ejde-745	285	8	)	)	PUNCT
ejde-745	285	9	,	,	PUNCT
ejde-745	285	10	pp	pp	ADP
ejde-745	285	11	.	.	PUNCT
ejde-745	286	1	139	139	NUM
ejde-745	286	2	-	-	SYM
ejde-745	286	3	146	146	NUM
ejde-745	286	4	.	.	PUNCT
ejde-745	287	1	[	[	X
ejde-745	287	2	15	15	NUM
ejde-745	287	3	]	]	X
ejde-745	287	4	kubiaczyk	kubiaczyk	NOUN
ejde-745	287	5	,	,	PUNCT
ejde-745	287	6	i.	i.	NOUN
ejde-745	287	7	;	;	PUNCT
ejde-745	287	8	sikorska	sikorska	ADJ
ejde-745	287	9	-	-	PUNCT
ejde-745	287	10	nowak	nowak	PROPN
ejde-745	287	11	,	,	PUNCT
ejde-745	287	12	a.	a.	NOUN
ejde-745	287	13	;	;	PUNCT
ejde-745	287	14	existence	existence	NOUN
ejde-745	287	15	of	of	ADP
ejde-745	287	16	solutions	solution	NOUN
ejde-745	287	17	of	of	ADP
ejde-745	287	18	the	the	DET
ejde-745	287	19	dynamic	dynamic	ADJ
ejde-745	287	20	cauchy	cauchy	ADJ
ejde-745	287	21	problem	problem	NOUN
ejde-745	287	22	of	of	ADP
ejde-745	287	23	infinite	infinite	ADJ
ejde-745	287	24	time	time	NOUN
ejde-745	287	25	scale	scale	NOUN
ejde-745	287	26	intervals	interval	NOUN
ejde-745	287	27	.	.	PUNCT
ejde-745	288	1	discuss	discuss	PROPN
ejde-745	288	2	.	.	PUNCT
ejde-745	289	1	math	math	PROPN
ejde-745	289	2	.	.	PUNCT
ejde-745	290	1	differ	differ	VERB
ejde-745	290	2	.	.	PUNCT
ejde-745	291	1	incl	incl	NOUN
ejde-745	291	2	.	.	PUNCT
ejde-745	292	1	,	,	PUNCT
ejde-745	292	2	vol	vol	NOUN
ejde-745	292	3	.	.	PROPN
ejde-745	292	4	29	29	NUM
ejde-745	292	5	(	(	PUNCT
ejde-745	292	6	2009	2009	NUM
ejde-745	292	7	)	)	PUNCT
ejde-745	292	8	,	,	PUNCT
ejde-745	293	1	pp	pp	ADJ
ejde-745	293	2	.	.	PUNCT
ejde-745	294	1	113–126	113–126	NUM
ejde-745	294	2	.	.	PUNCT
ejde-745	295	1	[	[	X
ejde-745	295	2	16	16	NUM
ejde-745	295	3	]	]	X
ejde-745	295	4	kumar	kumar	PROPN
ejde-745	295	5	,	,	PUNCT
ejde-745	295	6	v.	v.	PROPN
ejde-745	295	7	;	;	PUNCT
ejde-745	295	8	malik	malik	PROPN
ejde-745	295	9	,	,	PUNCT
ejde-745	295	10	m.	m.	NOUN
ejde-745	295	11	;	;	PUNCT
ejde-745	295	12	existence	existence	NOUN
ejde-745	295	13	and	and	CCONJ
ejde-745	295	14	stability	stability	NOUN
ejde-745	295	15	results	result	NOUN
ejde-745	295	16	of	of	ADP
ejde-745	295	17	nonlinear	nonlinear	ADJ
ejde-745	295	18	fractional	fractional	ADJ
ejde-745	295	19	differential	differential	ADJ
ejde-745	295	20	equations	equation	NOUN
ejde-745	295	21	with	with	ADP
ejde-745	295	22	nonlinear	nonlinear	ADJ
ejde-745	295	23	integral	integral	ADJ
ejde-745	295	24	boundary	boundary	ADJ
ejde-745	295	25	condition	condition	NOUN
ejde-745	295	26	on	on	ADP
ejde-745	295	27	time	time	NOUN
ejde-745	295	28	scales	scale	NOUN
ejde-745	295	29	.	.	PUNCT
ejde-745	296	1	aam	aam	PROPN
ejde-745	296	2	,	,	PUNCT
ejde-745	296	3	vol	vol	NOUN
ejde-745	296	4	.	.	PROPN
ejde-745	296	5	15	15	NUM
ejde-745	296	6	,	,	PUNCT
ejde-745	296	7	no	no	INTJ
ejde-745	296	8	.	.	NOUN
ejde-745	296	9	3	3	NUM
ejde-745	296	10	(	(	PUNCT
ejde-745	296	11	2020	2020	NUM
ejde-745	296	12	)	)	PUNCT
ejde-745	296	13	,	,	PUNCT
ejde-745	296	14	special	special	ADJ
ejde-745	296	15	issue	issue	NOUN
ejde-745	296	16	6	6	NUM
ejde-745	296	17	,	,	PUNCT
ejde-745	296	18	art	art	NOUN
ejde-745	296	19	.	.	PUNCT
ejde-745	297	1	10	10	NUM
ejde-745	297	2	.	.	PUNCT
ejde-745	298	1	[	[	X
ejde-745	298	2	17	17	NUM
ejde-745	298	3	]	]	PUNCT
ejde-745	298	4	lazreg	lazreg	PROPN
ejde-745	298	5	,	,	PUNCT
ejde-745	298	6	j.	j.	PROPN
ejde-745	298	7	e.	e.	PROPN
ejde-745	298	8	;	;	PUNCT
ejde-745	298	9	benkhettou	benkhettou	PROPN
ejde-745	298	10	,	,	PUNCT
ejde-745	298	11	n.	n.	PROPN
ejde-745	298	12	;	;	PUNCT
ejde-745	298	13	benchora	benchora	PROPN
ejde-745	298	14	,	,	PUNCT
ejde-745	298	15	m.	m.	NOUN
ejde-745	298	16	;	;	PUNCT
ejde-745	298	17	karapinar	karapinar	PROPN
ejde-745	298	18	,	,	PUNCT
ejde-745	298	19	e.	e.	PROPN
ejde-745	298	20	;	;	PUNCT
ejde-745	298	21	neutral	neutral	ADJ
ejde-745	298	22	functional	functional	ADJ
ejde-745	298	23	sequential	sequential	ADJ
ejde-745	298	24	differential	differential	ADJ
ejde-745	298	25	equations	equation	NOUN
ejde-745	298	26	with	with	ADP
ejde-745	298	27	caputo	caputo	PROPN
ejde-745	298	28	fractional	fractional	PROPN
ejde-745	298	29	derivative	derivative	NOUN
ejde-745	298	30	on	on	ADP
ejde-745	298	31	time	time	NOUN
ejde-745	298	32	scales	scale	NOUN
ejde-745	298	33	.	.	PUNCT
ejde-745	299	1	fixed	fix	VERB
ejde-745	299	2	point	point	NOUN
ejde-745	299	3	theory	theory	NOUN
ejde-745	299	4	algorithms	algorithms	PROPN
ejde-745	299	5	sci	sci	PROPN
ejde-745	299	6	.	.	PUNCT
ejde-745	300	1	eng	eng	PROPN
ejde-745	300	2	.	.	PROPN
ejde-745	300	3	,	,	PUNCT
ejde-745	300	4	,	,	PUNCT
ejde-745	300	5	article	article	NOUN
ejde-745	300	6	6	6	NUM
ejde-745	300	7	(	(	PUNCT
ejde-745	300	8	2022	2022	NUM
ejde-745	300	9	)	)	PUNCT
ejde-745	300	10	.	.	PUNCT
ejde-745	301	1	doi	doi	PROPN
ejde-745	301	2	10.1186	10.1186	NUM
ejde-745	301	3	/	/	SYM
ejde-745	301	4	s13663	s13663	PROPN
ejde-745	301	5	-	-	PUNCT
ejde-745	301	6	022	022	NUM
ejde-745	301	7	-	-	PUNCT
ejde-745	301	8	00716	00716	NUM
ejde-745	301	9	-	-	SYM
ejde-745	301	10	9	9	NUM
ejde-745	301	11	[	[	SYM
ejde-745	301	12	18	18	NUM
ejde-745	301	13	]	]	X
ejde-745	301	14	mitchell	mitchell	PROPN
ejde-745	301	15	,	,	PUNCT
ejde-745	301	16	a.	a.	PROPN
ejde-745	301	17	r.	r.	PROPN
ejde-745	301	18	;	;	PUNCT
ejde-745	301	19	smith	smith	PROPN
ejde-745	301	20	,	,	PUNCT
ejde-745	301	21	c.	c.	PROPN
ejde-745	301	22	;	;	PUNCT
ejde-745	301	23	an	an	DET
ejde-745	301	24	existence	existence	NOUN
ejde-745	301	25	theorem	theorem	VERB
ejde-745	301	26	for	for	ADP
ejde-745	301	27	weak	weak	ADJ
ejde-745	301	28	solutions	solution	NOUN
ejde-745	301	29	of	of	ADP
ejde-745	301	30	differential	differential	ADJ
ejde-745	301	31	equations	equation	NOUN
ejde-745	301	32	in	in	ADP
ejde-745	301	33	banach	banach	NOUN
ejde-745	301	34	spaces	space	NOUN
ejde-745	301	35	.	.	PUNCT
ejde-745	302	1	in	in	ADP
ejde-745	302	2	:	:	PUNCT
ejde-745	302	3	nonlinear	nonlinear	ADJ
ejde-745	302	4	equations	equation	NOUN
ejde-745	302	5	in	in	ADP
ejde-745	302	6	abstract	abstract	ADJ
ejde-745	302	7	spaces	space	NOUN
ejde-745	302	8	,	,	PUNCT
ejde-745	302	9	proceedings	proceeding	NOUN
ejde-745	302	10	of	of	ADP
ejde-745	302	11	the	the	DET
ejde-745	302	12	international	international	ADJ
ejde-745	302	13	symposium	symposium	NOUN
ejde-745	302	14	,	,	PUNCT
ejde-745	302	15	university	university	PROPN
ejde-745	302	16	of	of	ADP
ejde-745	302	17	texas	texas	PROPN
ejde-745	302	18	,	,	PUNCT
ejde-745	302	19	arlington	arlington	PROPN
ejde-745	302	20	,	,	PUNCT
ejde-745	302	21	texas	texas	PROPN
ejde-745	302	22	,	,	PUNCT
ejde-745	302	23	1977	1977	NUM
ejde-745	302	24	,	,	PUNCT
ejde-745	302	25	v.	v.	ADP
ejde-745	302	26	lakshmikantham	lakshmikantham	ADJ
ejde-745	302	27	(	(	PUNCT
ejde-745	302	28	ed	ed	NOUN
ejde-745	302	29	.	.	PUNCT
ejde-745	302	30	)	)	PUNCT
ejde-745	302	31	,	,	PUNCT
ejde-745	302	32	pp	pp	PROPN
ejde-745	302	33	.	.	PUNCT
ejde-745	303	1	387	387	NUM
ejde-745	303	2	-	-	SYM
ejde-745	303	3	403	403	NUM
ejde-745	303	4	,	,	PUNCT
ejde-745	303	5	academic	academic	ADJ
ejde-745	303	6	press	press	NOUN
ejde-745	303	7	,	,	PUNCT
ejde-745	303	8	new	new	PROPN
ejde-745	303	9	york	york	PROPN
ejde-745	303	10	,	,	PUNCT
ejde-745	303	11	ny	ny	PROPN
ejde-745	303	12	,	,	PUNCT
ejde-745	303	13	usa	usa	PROPN
ejde-745	303	14	,	,	PUNCT
ejde-745	303	15	1978	1978	NUM
ejde-745	303	16	.	.	PUNCT
ejde-745	304	1	[	[	X
ejde-745	304	2	19	19	NUM
ejde-745	304	3	]	]	X
ejde-745	304	4	nisar	nisar	PROPN
ejde-745	304	5	,	,	PUNCT
ejde-745	304	6	k.	k.	PROPN
ejde-745	304	7	s.	s.	PROPN
ejde-745	304	8	;	;	PUNCT
ejde-745	304	9	jothimani	jothimani	PROPN
ejde-745	304	10	,	,	PUNCT
ejde-745	304	11	k.	k.	PROPN
ejde-745	304	12	;	;	PUNCT
ejde-745	304	13	ravichandran	ravichandran	NOUN
ejde-745	304	14	,	,	PUNCT
ejde-745	304	15	c.	c.	PROPN
ejde-745	304	16	;	;	PUNCT
ejde-745	304	17	baleanu	baleanu	PROPN
ejde-745	304	18	,	,	PUNCT
ejde-745	304	19	d.	d.	PROPN
ejde-745	304	20	;	;	PUNCT
ejde-745	304	21	kumar	kumar	PROPN
ejde-745	304	22	,	,	PUNCT
ejde-745	304	23	d.	d.	PROPN
ejde-745	304	24	;	;	PUNCT
ejde-745	304	25	new	new	ADJ
ejde-745	304	26	approach	approach	NOUN
ejde-745	304	27	on	on	ADP
ejde-745	304	28	controllability	controllability	NOUN
ejde-745	304	29	of	of	ADP
ejde-745	304	30	hilfer	hilfer	NOUN
ejde-745	304	31	fractional	fractional	ADJ
ejde-745	304	32	derivatives	derivative	NOUN
ejde-745	304	33	with	with	ADP
ejde-745	304	34	nondense	nondense	NOUN
ejde-745	304	35	domain	domain	NOUN
ejde-745	304	36	.	.	PUNCT
ejde-745	305	1	aims	aim	VERB
ejde-745	305	2	math	math	NOUN
ejde-745	305	3	.	.	PUNCT
ejde-745	306	1	,	,	PUNCT
ejde-745	306	2	vol	vol	NOUN
ejde-745	306	3	.	.	PROPN
ejde-745	306	4	7	7	NUM
ejde-745	306	5	(	(	PUNCT
ejde-745	306	6	2022	2022	NUM
ejde-745	306	7	)	)	PUNCT
ejde-745	306	8	,	,	PUNCT
ejde-745	307	1	pp	pp	ADP
ejde-745	307	2	.	.	PUNCT
ejde-745	308	1	10079–10095.doi	10079–10095.doi	NUM
ejde-745	308	2	10.3934	10.3934	NUM
ejde-745	308	3	/	/	SYM
ejde-745	308	4	math.2022561	math.2022561	PROPN
ejde-745	308	5	[	[	X
ejde-745	308	6	20	20	NUM
ejde-745	308	7	]	]	SYM
ejde-745	308	8	podlubny	podlubny	NOUN
ejde-745	308	9	,	,	PUNCT
ejde-745	308	10	i.	i.	NOUN
ejde-745	308	11	;	;	PUNCT
ejde-745	308	12	fractional	fractional	ADJ
ejde-745	308	13	differential	differential	ADJ
ejde-745	308	14	equations	equation	NOUN
ejde-745	308	15	:	:	PUNCT
ejde-745	308	16	an	an	DET
ejde-745	308	17	introduction	introduction	NOUN
ejde-745	308	18	to	to	ADP
ejde-745	308	19	fractional	fractional	ADJ
ejde-745	308	20	derivatives	derivative	NOUN
ejde-745	308	21	,	,	PUNCT
ejde-745	308	22	fractional	fractional	ADJ
ejde-745	308	23	differential	differential	ADJ
ejde-745	308	24	equations	equation	NOUN
ejde-745	308	25	,	,	PUNCT
ejde-745	308	26	to	to	ADP
ejde-745	308	27	methods	method	NOUN
ejde-745	308	28	of	of	ADP
ejde-745	308	29	their	their	PRON
ejde-745	308	30	solution	solution	NOUN
ejde-745	308	31	and	and	CCONJ
ejde-745	308	32	some	some	PRON
ejde-745	308	33	of	of	ADP
ejde-745	308	34	their	their	PRON
ejde-745	308	35	applications	application	NOUN
ejde-745	308	36	.	.	PUNCT
ejde-745	309	1	san	san	PROPN
ejde-745	309	2	diego	diego	PROPN
ejde-745	309	3	:	:	PUNCT
ejde-745	309	4	academic	academic	ADJ
ejde-745	309	5	press	press	NOUN
ejde-745	309	6	,	,	PUNCT
ejde-745	309	7	1999	1999	NUM
ejde-745	309	8	.	.	PUNCT
ejde-745	310	1	[	[	X
ejde-745	310	2	21	21	NUM
ejde-745	310	3	]	]	X
ejde-745	310	4	ravichandran	ravichandran	NOUN
ejde-745	310	5	,	,	PUNCT
ejde-745	310	6	c.	c.	NOUN
ejde-745	310	7	;	;	PUNCT
ejde-745	310	8	sowbakiya	sowbakiya	PROPN
ejde-745	310	9	,	,	PUNCT
ejde-745	310	10	v.	v.	ADV
ejde-745	310	11	;	;	PUNCT
ejde-745	310	12	nisar	nisar	PROPN
ejde-745	310	13	,	,	PUNCT
ejde-745	310	14	k.	k.	PROPN
ejde-745	310	15	s.	s.	PROPN
ejde-745	310	16	;	;	PUNCT
ejde-745	310	17	study	study	NOUN
ejde-745	310	18	on	on	ADP
ejde-745	310	19	existence	existence	NOUN
ejde-745	310	20	and	and	CCONJ
ejde-745	310	21	data	datum	NOUN
ejde-745	310	22	dependence	dependence	NOUN
ejde-745	310	23	results	result	NOUN
ejde-745	310	24	for	for	ADP
ejde-745	310	25	fractional	fractional	ADJ
ejde-745	310	26	order	order	NOUN
ejde-745	310	27	differential	differential	NOUN
ejde-745	310	28	equations	equation	NOUN
ejde-745	310	29	.	.	PUNCT
ejde-745	311	1	chaos	chaos	NOUN
ejde-745	311	2	,	,	PUNCT
ejde-745	311	3	solitons	soliton	NOUN
ejde-745	311	4	,	,	PUNCT
ejde-745	311	5	fractals	fractal	NOUN
ejde-745	311	6	,	,	PUNCT
ejde-745	311	7	vol	vol	NOUN
ejde-745	311	8	.	.	NOUN
ejde-745	311	9	160	160	NUM
ejde-745	311	10	(	(	PUNCT
ejde-745	311	11	2022	2022	NUM
ejde-745	311	12	)	)	PUNCT
ejde-745	311	13	,	,	PUNCT
ejde-745	311	14	112232	112232	NUM
ejde-745	311	15	.	.	PUNCT
ejde-745	312	1	doi	doi	PROPN
ejde-745	312	2	10.1016	10.1016	NUM
ejde-745	312	3	/	/	SYM
ejde-745	312	4	j.chaos.2022.112232	j.chaos.2022.112232	NOUN
ejde-745	313	1	[	[	X
ejde-745	313	2	22	22	NUM
ejde-745	313	3	]	]	X
ejde-745	313	4	salem	salem	NOUN
ejde-745	313	5	,	,	PUNCT
ejde-745	313	6	h.	h.	PROPN
ejde-745	313	7	a.	a.	PROPN
ejde-745	313	8	h.	h.	PROPN
ejde-745	313	9	;	;	PUNCT
ejde-745	313	10	hadamard	hadamard	ADJ
ejde-745	313	11	-	-	PUNCT
ejde-745	313	12	type	type	NOUN
ejde-745	313	13	fractional	fractional	ADJ
ejde-745	313	14	calculus	calculus	NOUN
ejde-745	313	15	in	in	ADP
ejde-745	313	16	banach	banach	NOUN
ejde-745	313	17	spaces	space	NOUN
ejde-745	313	18	.	.	PUNCT
ejde-745	314	1	racsam	racsam	PROPN
ejde-745	314	2	rev	rev	PROPN
ejde-745	314	3	.	.	PROPN
ejde-745	314	4	r.	r.	PROPN
ejde-745	314	5	acad	acad	PROPN
ejde-745	314	6	.	.	PUNCT
ejde-745	315	1	cienc	cienc	PROPN
ejde-745	315	2	.	.	PUNCT
ejde-745	316	1	exactas	exactas	PROPN
ejde-745	316	2	f́ıs	f́ıs	PROPN
ejde-745	316	3	.	.	PUNCT
ejde-745	317	1	nat	nat	PROPN
ejde-745	317	2	.	.	PUNCT
ejde-745	318	1	ser	ser	PROPN
ejde-745	318	2	.	.	PUNCT
ejde-745	319	1	a	a	DET
ejde-745	319	2	mat	mat	NOUN
ejde-745	319	3	.	.	NOUN
ejde-745	319	4	,	,	PUNCT
ejde-745	319	5	vol	vol	NOUN
ejde-745	319	6	.	.	PROPN
ejde-745	319	7	113	113	NUM
ejde-745	319	8	(	(	PUNCT
ejde-745	319	9	2019	2019	NUM
ejde-745	319	10	)	)	PUNCT
ejde-745	319	11	,	,	PUNCT
ejde-745	320	1	pp	pp	ADP
ejde-745	320	2	.	.	PUNCT
ejde-745	321	1	987–1006	987–1006	NUM
ejde-745	321	2	,	,	PUNCT
ejde-745	321	3	doi	doi	X
ejde-745	321	4	10.1007	10.1007	NUM
ejde-745	321	5	/	/	SYM
ejde-745	321	6	s13398	s13398	NOUN
ejde-745	321	7	-	-	PUNCT
ejde-745	321	8	018	018	NUM
ejde-745	321	9	-	-	PUNCT
ejde-745	321	10	0531	0531	NUM
ejde-745	321	11	-	-	PUNCT
ejde-745	321	12	y	y	NOUN
ejde-745	322	1	[	[	X
ejde-745	322	2	23	23	NUM
ejde-745	322	3	]	]	X
ejde-745	322	4	salem	salem	NOUN
ejde-745	322	5	,	,	PUNCT
ejde-745	322	6	h.	h.	PROPN
ejde-745	322	7	a.	a.	PROPN
ejde-745	322	8	h.	h.	PROPN
ejde-745	322	9	;	;	PUNCT
ejde-745	323	1	el	el	PROPN
ejde-745	323	2	-	-	PUNCT
ejde-745	323	3	sayed	sayed	PROPN
ejde-745	323	4	,	,	PUNCT
ejde-745	323	5	a.	a.	PROPN
ejde-745	323	6	m.	m.	PROPN
ejde-745	323	7	a.	a.	PROPN
ejde-745	323	8	;	;	PUNCT
ejde-745	323	9	moustafa	moustafa	PROPN
ejde-745	323	10	,	,	PUNCT
ejde-745	323	11	o.	o.	PROPN
ejde-745	323	12	l.	l.	PROPN
ejde-745	323	13	;	;	PUNCT
ejde-745	323	14	a	a	DET
ejde-745	323	15	note	note	NOUN
ejde-745	323	16	on	on	ADP
ejde-745	323	17	the	the	DET
ejde-745	323	18	fractional	fractional	ADJ
ejde-745	323	19	calculus	calculus	NOUN
ejde-745	323	20	in	in	ADP
ejde-745	323	21	banach	banach	NOUN
ejde-745	323	22	spaces	space	NOUN
ejde-745	323	23	.	.	PUNCT
ejde-745	324	1	studia	studia	PROPN
ejde-745	324	2	scientiarum	scientiarum	PROPN
ejde-745	324	3	mathematicarum	mathematicarum	PROPN
ejde-745	324	4	hungarica	hungarica	PROPN
ejde-745	324	5	,	,	PUNCT
ejde-745	324	6	vol	vol	NOUN
ejde-745	324	7	.	.	PROPN
ejde-745	325	1	42	42	NUM
ejde-745	325	2	(	(	PUNCT
ejde-745	325	3	2005	2005	NUM
ejde-745	325	4	)	)	PUNCT
ejde-745	325	5	,	,	PUNCT
ejde-745	325	6	pp	pp	ADP
ejde-745	325	7	.	.	PUNCT
ejde-745	326	1	115–130	115–130	NUM
ejde-745	326	2	.	.	PUNCT
ejde-745	327	1	[	[	X
ejde-745	327	2	24	24	NUM
ejde-745	327	3	]	]	SYM
ejde-745	327	4	salem	salem	NOUN
ejde-745	327	5	,	,	PUNCT
ejde-745	327	6	h.	h.	PROPN
ejde-745	327	7	a.	a.	PROPN
ejde-745	327	8	h.	h.	PROPN
ejde-745	327	9	;	;	PUNCT
ejde-745	327	10	on	on	ADP
ejde-745	327	11	the	the	DET
ejde-745	327	12	fractional	fractional	ADJ
ejde-745	327	13	order	order	NOUN
ejde-745	327	14	m	m	NOUN
ejde-745	327	15	-	-	PUNCT
ejde-745	327	16	point	point	NOUN
ejde-745	327	17	boundary	boundary	ADJ
ejde-745	327	18	value	value	NOUN
ejde-745	327	19	problem	problem	NOUN
ejde-745	327	20	in	in	ADP
ejde-745	327	21	reflexive	reflexive	ADJ
ejde-745	327	22	banach	banach	NOUN
ejde-745	327	23	spaces	space	NOUN
ejde-745	327	24	and	and	CCONJ
ejde-745	327	25	weak	weak	ADJ
ejde-745	327	26	topologies	topology	NOUN
ejde-745	327	27	.	.	PUNCT
ejde-745	328	1	j.	j.	PROPN
ejde-745	328	2	comput	comput	PROPN
ejde-745	328	3	.	.	PUNCT
ejde-745	329	1	appl	appl	PROPN
ejde-745	329	2	.	.	PROPN
ejde-745	329	3	math	math	PROPN
ejde-745	329	4	.	.	PUNCT
ejde-745	330	1	,	,	PUNCT
ejde-745	330	2	vol	vol	NOUN
ejde-745	330	3	.	.	PROPN
ejde-745	331	1	224	224	NUM
ejde-745	331	2	(	(	PUNCT
ejde-745	331	3	2009	2009	NUM
ejde-745	331	4	)	)	PUNCT
ejde-745	331	5	,	,	PUNCT
ejde-745	331	6	pp	pp	ADP
ejde-745	331	7	.	.	PUNCT
ejde-745	332	1	565–572	565–572	NUM
ejde-745	332	2	.	.	PUNCT
ejde-745	333	1	ejde-2024/36	ejde-2024/36	NOUN
ejde-745	333	2	existence	existence	NOUN
ejde-745	333	3	of	of	ADP
ejde-745	333	4	pseudosolutions	pseudosolution	NOUN
ejde-745	333	5	9	9	NUM
ejde-745	333	6	[	[	X
ejde-745	333	7	25	25	NUM
ejde-745	333	8	]	]	PUNCT
ejde-745	333	9	salem	salem	NOUN
ejde-745	333	10	,	,	PUNCT
ejde-745	333	11	h.	h.	PROPN
ejde-745	333	12	a.	a.	PROPN
ejde-745	333	13	h.	h.	PROPN
ejde-745	333	14	;	;	PUNCT
ejde-745	333	15	on	on	ADP
ejde-745	333	16	the	the	DET
ejde-745	333	17	fractional	fractional	ADJ
ejde-745	333	18	calculus	calculus	NOUN
ejde-745	333	19	in	in	ADP
ejde-745	333	20	abstract	abstract	ADJ
ejde-745	333	21	spaces	space	NOUN
ejde-745	333	22	and	and	CCONJ
ejde-745	333	23	their	their	PRON
ejde-745	333	24	applications	application	NOUN
ejde-745	333	25	to	to	ADP
ejde-745	333	26	the	the	DET
ejde-745	333	27	dirichlet	dirichlet	NOUN
ejde-745	333	28	-	-	PUNCT
ejde-745	333	29	type	type	NOUN
ejde-745	333	30	problem	problem	NOUN
ejde-745	333	31	of	of	ADP
ejde-745	333	32	fractional	fractional	ADJ
ejde-745	333	33	order	order	NOUN
ejde-745	333	34	.	.	PUNCT
ejde-745	334	1	comput	comput	NOUN
ejde-745	334	2	.	.	PUNCT
ejde-745	335	1	math	math	NOUN
ejde-745	335	2	.	.	PUNCT
ejde-745	336	1	appl	appl	PROPN
ejde-745	336	2	.	.	PROPN
ejde-745	336	3	,	,	PUNCT
ejde-745	336	4	vol	vol	NOUN
ejde-745	336	5	.	.	PROPN
ejde-745	336	6	59	59	NUM
ejde-745	336	7	(	(	PUNCT
ejde-745	336	8	2010	2010	NUM
ejde-745	336	9	)	)	PUNCT
ejde-745	336	10	,	,	PUNCT
ejde-745	337	1	pp	pp	ADP
ejde-745	337	2	.	.	PUNCT
ejde-745	338	1	1278–1293	1278–1293	NUM
ejde-745	338	2	.	.	PUNCT
ejde-745	339	1	[	[	X
ejde-745	339	2	26	26	NUM
ejde-745	339	3	]	]	X
ejde-745	339	4	salem	salem	NOUN
ejde-745	339	5	,	,	PUNCT
ejde-745	339	6	h.	h.	PROPN
ejde-745	339	7	a.	a.	PROPN
ejde-745	339	8	h.	h.	PROPN
ejde-745	339	9	;	;	PUNCT
ejde-745	339	10	cichoń	cichoń	NOUN
ejde-745	339	11	,	,	PUNCT
ejde-745	339	12	m.	m.	NOUN
ejde-745	339	13	;	;	PUNCT
ejde-745	339	14	on	on	ADP
ejde-745	339	15	solutions	solution	NOUN
ejde-745	339	16	of	of	ADP
ejde-745	339	17	fractional	fractional	ADJ
ejde-745	339	18	order	order	NOUN
ejde-745	339	19	boundary	boundary	ADJ
ejde-745	339	20	value	value	NOUN
ejde-745	339	21	problems	problem	NOUN
ejde-745	339	22	with	with	ADP
ejde-745	339	23	integral	integral	ADJ
ejde-745	339	24	boundary	boundary	ADJ
ejde-745	339	25	conditions	condition	NOUN
ejde-745	339	26	in	in	ADP
ejde-745	339	27	banach	banach	NOUN
ejde-745	339	28	spaces	space	NOUN
ejde-745	339	29	.	.	PUNCT
ejde-745	340	1	j.	j.	PROPN
ejde-745	340	2	funct	funct	PROPN
ejde-745	340	3	.	.	PUNCT
ejde-745	341	1	spaces	space	NOUN
ejde-745	341	2	appl	appl	PROPN
ejde-745	341	3	.	.	PROPN
ejde-745	341	4	,	,	PUNCT
ejde-745	341	5	vol	vol	NOUN
ejde-745	341	6	.	.	PROPN
ejde-745	342	1	2013	2013	NUM
ejde-745	342	2	(	(	PUNCT
ejde-745	342	3	2013	2013	NUM
ejde-745	342	4	)	)	PUNCT
ejde-745	342	5	,	,	PUNCT
ejde-745	342	6	article	article	NOUN
ejde-745	342	7	i	i	PROPN
ejde-745	342	8	d	d	PROPN
ejde-745	342	9	428094	428094	NUM
ejde-745	342	10	.	.	PUNCT
ejde-745	343	1	doi	doi	X
ejde-745	343	2	10.1155/2013/428094	10.1155/2013/428094	NUM
ejde-745	343	3	aneta	aneta	PROPN
ejde-745	343	4	sikorska	sikorska	PROPN
ejde-745	343	5	-	-	PUNCT
ejde-745	343	6	nowak	nowak	PROPN
ejde-745	343	7	faculty	faculty	NOUN
ejde-745	343	8	of	of	ADP
ejde-745	343	9	mathematics	mathematic	NOUN
ejde-745	343	10	and	and	CCONJ
ejde-745	343	11	computer	computer	NOUN
ejde-745	343	12	science	science	NOUN
ejde-745	343	13	,	,	PUNCT
ejde-745	343	14	adam	adam	PROPN
ejde-745	343	15	mickiewicz	mickiewicz	PROPN
ejde-745	343	16	university	university	PROPN
ejde-745	343	17	,	,	PUNCT
ejde-745	343	18	uniwersytetu	uniwersytetu	ADJ
ejde-745	343	19	poznańskiego	poznańskiego	NOUN
ejde-745	343	20	4	4	NUM
ejde-745	343	21	,	,	PUNCT
ejde-745	343	22	61	61	NUM
ejde-745	343	23	-	-	SYM
ejde-745	343	24	614	614	NUM
ejde-745	343	25	poznań	poznań	NOUN
ejde-745	343	26	,	,	PUNCT
ejde-745	343	27	poland	poland	PROPN
ejde-745	343	28	email	email	NOUN
ejde-745	343	29	address	address	NOUN
ejde-745	343	30	:	:	PUNCT
ejde-745	343	31	anetas@amu.edu.pl	anetas@amu.edu.pl	PROPN
ejde-745	343	32	1	1	NUM
ejde-745	343	33	.	.	PUNCT
ejde-745	344	1	introduction	introduction	NOUN
ejde-745	344	2	2	2	NUM
ejde-745	344	3	.	.	PUNCT
ejde-745	344	4	preliminaries	preliminary	NOUN
ejde-745	344	5	3	3	NUM
ejde-745	344	6	.	.	X
ejde-745	344	7	main	main	ADJ
ejde-745	344	8	problem	problem	NOUN
ejde-745	344	9	references	reference	NOUN