id	sid	tid	token	lemma	pos
ejde-1812	1	1	electronic	electronic	ADJ
ejde-1812	1	2	journal	journal	NOUN
ejde-1812	1	3	of	of	ADP
ejde-1812	1	4	differential	differential	ADJ
ejde-1812	1	5	equations	equation	NOUN
ejde-1812	1	6	,	,	PUNCT
ejde-1812	1	7	vol	vol	NOUN
ejde-1812	1	8	.	.	PUNCT
ejde-1812	1	9	2025	2025	NUM
ejde-1812	1	10	(	(	PUNCT
ejde-1812	1	11	2025	2025	NUM
ejde-1812	1	12	)	)	PUNCT
ejde-1812	1	13	,	,	PUNCT
ejde-1812	1	14	no	no	INTJ
ejde-1812	1	15	.	.	NOUN
ejde-1812	1	16	109	109	NUM
ejde-1812	1	17	,	,	PUNCT
ejde-1812	1	18	pp	pp	ADJ
ejde-1812	1	19	.	.	PUNCT
ejde-1812	2	1	1–17	1–17	NOUN
ejde-1812	2	2	.	.	PUNCT
ejde-1812	3	1	issn	issn	PROPN
ejde-1812	3	2	:	:	PUNCT
ejde-1812	3	3	1072	1072	NUM
ejde-1812	3	4	-	-	SYM
ejde-1812	3	5	6691	6691	NUM
ejde-1812	3	6	.	.	PUNCT
ejde-1812	4	1	url	url	PROPN
ejde-1812	4	2	:	:	PUNCT
ejde-1812	4	3	https://ejde.math.txstate.edu	https://ejde.math.txstate.edu	PROPN
ejde-1812	4	4	,	,	PUNCT
ejde-1812	4	5	doi	doi	NOUN
ejde-1812	4	6	:	:	PUNCT
ejde-1812	4	7	10.58997	10.58997	NUM
ejde-1812	4	8	/	/	SYM
ejde-1812	4	9	ejde.2025.109	ejde.2025.109	VERB
ejde-1812	4	10	evolution	evolution	NOUN
ejde-1812	4	11	ψ	ψ	NOUN
ejde-1812	4	12	-	-	ADJ
ejde-1812	4	13	hilfer	hilfer	NOUN
ejde-1812	4	14	fractional	fractional	ADJ
ejde-1812	4	15	differential	differential	ADJ
ejde-1812	4	16	equations	equation	NOUN
ejde-1812	4	17	in	in	ADP
ejde-1812	4	18	banach	banach	NOUN
ejde-1812	4	19	spaces	space	NOUN
ejde-1812	4	20	jin	jin	PROPN
ejde-1812	4	21	liang	liang	PROPN
ejde-1812	4	22	,	,	PUNCT
ejde-1812	4	23	yunyi	yunyi	PROPN
ejde-1812	4	24	mu	mu	PROPN
ejde-1812	4	25	,	,	PUNCT
ejde-1812	4	26	ti	ti	PROPN
ejde-1812	4	27	-	-	PROPN
ejde-1812	4	28	jun	jun	PROPN
ejde-1812	4	29	xiao	xiao	PROPN
ejde-1812	4	30	abstract	abstract	PROPN
ejde-1812	4	31	.	.	PUNCT
ejde-1812	5	1	this	this	DET
ejde-1812	5	2	article	article	NOUN
ejde-1812	5	3	concerns	concern	VERB
ejde-1812	5	4	evolution	evolution	NOUN
ejde-1812	5	5	equations	equation	NOUN
ejde-1812	5	6	involving	involve	VERB
ejde-1812	5	7	ψ	ψ	NOUN
ejde-1812	5	8	-	-	ADJ
ejde-1812	5	9	hilfer	hilfer	NOUN
ejde-1812	5	10	fractional	fractional	ADJ
ejde-1812	5	11	derivative	derivative	NOUN
ejde-1812	5	12	in	in	ADP
ejde-1812	5	13	a	a	DET
ejde-1812	5	14	banach	banach	NOUN
ejde-1812	5	15	space	space	NOUN
ejde-1812	5	16	.	.	PUNCT
ejde-1812	6	1	by	by	ADP
ejde-1812	6	2	using	use	VERB
ejde-1812	6	3	the	the	DET
ejde-1812	6	4	theory	theory	NOUN
ejde-1812	6	5	of	of	ADP
ejde-1812	6	6	fractional	fractional	ADJ
ejde-1812	6	7	calculus	calculus	NOUN
ejde-1812	6	8	and	and	CCONJ
ejde-1812	6	9	ψ	ψ	NOUN
ejde-1812	6	10	-	-	ADJ
ejde-1812	6	11	laplace	laplace	ADJ
ejde-1812	6	12	transform	transform	NOUN
ejde-1812	6	13	,	,	PUNCT
ejde-1812	6	14	we	we	PRON
ejde-1812	6	15	firstly	firstly	ADV
ejde-1812	6	16	derive	derive	VERB
ejde-1812	6	17	a	a	DET
ejde-1812	6	18	definition	definition	NOUN
ejde-1812	6	19	of	of	ADP
ejde-1812	6	20	mild	mild	ADJ
ejde-1812	6	21	solutions	solution	NOUN
ejde-1812	6	22	for	for	ADP
ejde-1812	6	23	these	these	DET
ejde-1812	6	24	equations	equation	NOUN
ejde-1812	6	25	.	.	PUNCT
ejde-1812	7	1	then	then	ADV
ejde-1812	7	2	we	we	PRON
ejde-1812	7	3	establish	establish	VERB
ejde-1812	7	4	theorems	theorem	NOUN
ejde-1812	7	5	for	for	ADP
ejde-1812	7	6	the	the	DET
ejde-1812	7	7	existence	existence	NOUN
ejde-1812	7	8	and	and	CCONJ
ejde-1812	7	9	uniqueness	uniqueness	NOUN
ejde-1812	7	10	of	of	ADP
ejde-1812	7	11	solutions	solution	NOUN
ejde-1812	7	12	and	and	CCONJ
ejde-1812	7	13	the	the	DET
ejde-1812	7	14	approximate	approximate	ADJ
ejde-1812	7	15	controllability	controllability	NOUN
ejde-1812	7	16	(	(	PUNCT
ejde-1812	7	17	not	not	PART
ejde-1812	7	18	the	the	DET
ejde-1812	7	19	exact	exact	ADJ
ejde-1812	7	20	controllability	controllability	NOUN
ejde-1812	7	21	)	)	PUNCT
ejde-1812	7	22	of	of	ADP
ejde-1812	7	23	the	the	DET
ejde-1812	7	24	ψ	ψ	NOUN
ejde-1812	7	25	-	-	ADJ
ejde-1812	7	26	hilfer	hilfer	NOUN
ejde-1812	7	27	fractional	fractional	ADJ
ejde-1812	7	28	differential	differential	NOUN
ejde-1812	7	29	system	system	NOUN
ejde-1812	7	30	under	under	ADP
ejde-1812	7	31	appropriate	appropriate	ADJ
ejde-1812	7	32	conditions	condition	NOUN
ejde-1812	7	33	.	.	PUNCT
ejde-1812	8	1	we	we	PRON
ejde-1812	8	2	focus	focus	VERB
ejde-1812	8	3	on	on	ADP
ejde-1812	8	4	the	the	DET
ejde-1812	8	5	approximate	approximate	ADJ
ejde-1812	8	6	controllability	controllability	NOUN
ejde-1812	8	7	rather	rather	ADV
ejde-1812	8	8	than	than	ADP
ejde-1812	8	9	the	the	DET
ejde-1812	8	10	exact	exact	ADJ
ejde-1812	8	11	controllability	controllability	NOUN
ejde-1812	8	12	because	because	SCONJ
ejde-1812	8	13	the	the	DET
ejde-1812	8	14	exact	exact	ADJ
ejde-1812	8	15	controllability	controllability	NOUN
ejde-1812	8	16	can	can	AUX
ejde-1812	8	17	not	not	PART
ejde-1812	8	18	be	be	AUX
ejde-1812	8	19	achieved	achieve	VERB
ejde-1812	8	20	generally	generally	ADV
ejde-1812	8	21	for	for	ADP
ejde-1812	8	22	the	the	DET
ejde-1812	8	23	system	system	NOUN
ejde-1812	8	24	in	in	ADP
ejde-1812	8	25	infinite	infinite	ADJ
ejde-1812	8	26	-	-	PUNCT
ejde-1812	8	27	dimensional	dimensional	ADJ
ejde-1812	8	28	spaces	space	NOUN
ejde-1812	8	29	.	.	PUNCT
ejde-1812	9	1	we	we	PRON
ejde-1812	9	2	present	present	VERB
ejde-1812	9	3	a	a	DET
ejde-1812	9	4	new	new	ADJ
ejde-1812	9	5	multidimensional	multidimensional	ADJ
ejde-1812	9	6	gronwall	gronwall	ADJ
ejde-1812	9	7	-	-	PUNCT
ejde-1812	9	8	type	type	NOUN
ejde-1812	9	9	inequality	inequality	NOUN
ejde-1812	9	10	with	with	ADP
ejde-1812	9	11	multiple	multiple	ADJ
ejde-1812	9	12	singular	singular	ADJ
ejde-1812	9	13	kernels	kernel	NOUN
ejde-1812	9	14	involving	involve	VERB
ejde-1812	9	15	exponential	exponential	ADJ
ejde-1812	9	16	factors	factor	NOUN
ejde-1812	9	17	,	,	PUNCT
ejde-1812	9	18	which	which	PRON
ejde-1812	9	19	extends	extend	VERB
ejde-1812	9	20	essentially	essentially	ADV
ejde-1812	9	21	many	many	ADJ
ejde-1812	9	22	existing	exist	VERB
ejde-1812	9	23	results	result	NOUN
ejde-1812	9	24	.	.	PUNCT
ejde-1812	10	1	we	we	PRON
ejde-1812	10	2	also	also	ADV
ejde-1812	10	3	use	use	VERB
ejde-1812	10	4	the	the	DET
ejde-1812	10	5	new	new	ADJ
ejde-1812	10	6	gronwall	gronwall	ADJ
ejde-1812	10	7	-	-	PUNCT
ejde-1812	10	8	type	type	NOUN
ejde-1812	10	9	inequality	inequality	NOUN
ejde-1812	10	10	to	to	PART
ejde-1812	10	11	study	study	VERB
ejde-1812	10	12	the	the	DET
ejde-1812	10	13	dependence	dependence	NOUN
ejde-1812	10	14	of	of	ADP
ejde-1812	10	15	the	the	DET
ejde-1812	10	16	solution	solution	NOUN
ejde-1812	10	17	on	on	ADP
ejde-1812	10	18	the	the	DET
ejde-1812	10	19	order	order	NOUN
ejde-1812	10	20	and	and	CCONJ
ejde-1812	10	21	the	the	DET
ejde-1812	10	22	initial	initial	ADJ
ejde-1812	10	23	condition	condition	NOUN
ejde-1812	10	24	for	for	ADP
ejde-1812	10	25	the	the	DET
ejde-1812	10	26	fractional	fractional	ADJ
ejde-1812	10	27	integro	integro	ADJ
ejde-1812	10	28	-	-	PUNCT
ejde-1812	10	29	differential	differential	NOUN
ejde-1812	10	30	equations	equation	NOUN
ejde-1812	10	31	involving	involve	VERB
ejde-1812	10	32	ψ	ψ	NOUN
ejde-1812	10	33	-	-	ADJ
ejde-1812	10	34	hilfer	hilfer	NOUN
ejde-1812	10	35	fractional	fractional	ADJ
ejde-1812	10	36	derivative	derivative	NOUN
ejde-1812	10	37	.	.	PUNCT
ejde-1812	11	1	finally	finally	ADV
ejde-1812	11	2	,	,	PUNCT
ejde-1812	11	3	an	an	DET
ejde-1812	11	4	example	example	NOUN
ejde-1812	11	5	is	be	AUX
ejde-1812	11	6	given	give	VERB
ejde-1812	11	7	to	to	PART
ejde-1812	11	8	illustrate	illustrate	VERB
ejde-1812	11	9	our	our	PRON
ejde-1812	11	10	main	main	ADJ
ejde-1812	11	11	results	result	NOUN
ejde-1812	11	12	.	.	PUNCT
ejde-1812	12	1	1	1	X
ejde-1812	12	2	.	.	X
ejde-1812	12	3	introduction	introduction	NOUN
ejde-1812	12	4	in	in	ADP
ejde-1812	12	5	the	the	DET
ejde-1812	12	6	past	past	ADJ
ejde-1812	12	7	decades	decade	NOUN
ejde-1812	12	8	,	,	PUNCT
ejde-1812	12	9	applications	application	NOUN
ejde-1812	12	10	of	of	ADP
ejde-1812	12	11	fractional	fractional	ADJ
ejde-1812	12	12	calculus	calculus	NOUN
ejde-1812	12	13	have	have	AUX
ejde-1812	12	14	gradually	gradually	ADV
ejde-1812	12	15	expanded	expand	VERB
ejde-1812	12	16	and	and	CCONJ
ejde-1812	12	17	covered	cover	VERB
ejde-1812	12	18	fields	field	NOUN
ejde-1812	12	19	such	such	ADJ
ejde-1812	12	20	as	as	ADP
ejde-1812	12	21	fluid	fluid	ADJ
ejde-1812	12	22	mechanics	mechanic	NOUN
ejde-1812	12	23	,	,	PUNCT
ejde-1812	12	24	rheology	rheology	NOUN
ejde-1812	12	25	,	,	PUNCT
ejde-1812	12	26	viscoelasticity	viscoelasticity	NOUN
ejde-1812	12	27	,	,	PUNCT
ejde-1812	12	28	fractional	fractional	ADJ
ejde-1812	12	29	control	control	NOUN
ejde-1812	12	30	systems	system	NOUN
ejde-1812	12	31	and	and	CCONJ
ejde-1812	12	32	controllers	controller	NOUN
ejde-1812	12	33	,	,	PUNCT
ejde-1812	12	34	electroanalytical	electroanalytical	ADJ
ejde-1812	12	35	chemistry	chemistry	NOUN
ejde-1812	12	36	,	,	PUNCT
ejde-1812	12	37	electrical	electrical	ADJ
ejde-1812	12	38	conductivity	conductivity	NOUN
ejde-1812	12	39	in	in	ADP
ejde-1812	12	40	biological	biological	ADJ
ejde-1812	12	41	systems	system	NOUN
ejde-1812	12	42	,	,	PUNCT
ejde-1812	12	43	fractional	fractional	ADJ
ejde-1812	12	44	models	model	NOUN
ejde-1812	12	45	of	of	ADP
ejde-1812	12	46	nerves	nerve	NOUN
ejde-1812	12	47	,	,	PUNCT
ejde-1812	12	48	fractional	fractional	ADJ
ejde-1812	12	49	regression	regression	NOUN
ejde-1812	12	50	models	model	NOUN
ejde-1812	12	51	,	,	PUNCT
ejde-1812	12	52	etc	etc	X
ejde-1812	12	53	.	.	X
ejde-1812	12	54	when	when	SCONJ
ejde-1812	12	55	using	use	VERB
ejde-1812	12	56	fractional	fractional	ADJ
ejde-1812	12	57	order	order	NOUN
ejde-1812	12	58	derivatives	derivative	NOUN
ejde-1812	12	59	instead	instead	ADV
ejde-1812	12	60	of	of	ADP
ejde-1812	12	61	traditional	traditional	ADJ
ejde-1812	12	62	integer	integer	NOUN
ejde-1812	12	63	order	order	NOUN
ejde-1812	12	64	derivatives	derivative	NOUN
ejde-1812	12	65	to	to	PART
ejde-1812	12	66	describe	describe	VERB
ejde-1812	12	67	problems	problem	NOUN
ejde-1812	12	68	involving	involve	VERB
ejde-1812	12	69	hereditary	hereditary	ADJ
ejde-1812	12	70	or	or	CCONJ
ejde-1812	12	71	memory	memory	NOUN
ejde-1812	12	72	properties	property	NOUN
ejde-1812	12	73	,	,	PUNCT
ejde-1812	12	74	it	it	PRON
ejde-1812	12	75	often	often	ADV
ejde-1812	12	76	not	not	PART
ejde-1812	12	77	only	only	ADV
ejde-1812	12	78	simplifies	simplify	VERB
ejde-1812	12	79	the	the	DET
ejde-1812	12	80	differential	differential	ADJ
ejde-1812	12	81	equations	equation	NOUN
ejde-1812	12	82	but	but	CCONJ
ejde-1812	12	83	also	also	ADV
ejde-1812	12	84	yields	yield	VERB
ejde-1812	12	85	results	result	NOUN
ejde-1812	12	86	that	that	PRON
ejde-1812	12	87	are	be	AUX
ejde-1812	12	88	closer	close	ADJ
ejde-1812	12	89	to	to	ADP
ejde-1812	12	90	reality	reality	NOUN
ejde-1812	12	91	.	.	PUNCT
ejde-1812	13	1	we	we	PRON
ejde-1812	13	2	refer	refer	VERB
ejde-1812	13	3	the	the	DET
ejde-1812	13	4	readers	reader	NOUN
ejde-1812	13	5	to	to	ADP
ejde-1812	13	6	[	[	X
ejde-1812	13	7	1	1	NUM
ejde-1812	13	8	,	,	PUNCT
ejde-1812	13	9	2	2	NUM
ejde-1812	13	10	,	,	PUNCT
ejde-1812	13	11	5	5	NUM
ejde-1812	13	12	,	,	PUNCT
ejde-1812	13	13	6	6	NUM
ejde-1812	13	14	,	,	PUNCT
ejde-1812	13	15	7	7	NUM
ejde-1812	13	16	,	,	PUNCT
ejde-1812	13	17	8	8	NUM
ejde-1812	13	18	,	,	PUNCT
ejde-1812	13	19	9	9	NUM
ejde-1812	13	20	,	,	PUNCT
ejde-1812	13	21	11	11	NUM
ejde-1812	13	22	,	,	PUNCT
ejde-1812	13	23	10	10	NUM
ejde-1812	13	24	,	,	PUNCT
ejde-1812	13	25	12	12	NUM
ejde-1812	13	26	,	,	PUNCT
ejde-1812	13	27	16	16	NUM
ejde-1812	13	28	,	,	PUNCT
ejde-1812	13	29	19	19	NUM
ejde-1812	13	30	,	,	PUNCT
ejde-1812	13	31	20	20	NUM
ejde-1812	13	32	,	,	PUNCT
ejde-1812	13	33	22	22	NUM
ejde-1812	13	34	,	,	PUNCT
ejde-1812	13	35	23	23	NUM
ejde-1812	13	36	,	,	PUNCT
ejde-1812	13	37	24	24	NUM
ejde-1812	13	38	,	,	PUNCT
ejde-1812	13	39	25	25	NUM
ejde-1812	13	40	,	,	PUNCT
ejde-1812	13	41	26	26	NUM
ejde-1812	13	42	,	,	PUNCT
ejde-1812	13	43	32	32	NUM
ejde-1812	13	44	,	,	PUNCT
ejde-1812	13	45	33	33	NUM
ejde-1812	13	46	,	,	PUNCT
ejde-1812	13	47	35	35	NUM
ejde-1812	13	48	,	,	PUNCT
ejde-1812	13	49	36	36	NUM
ejde-1812	13	50	,	,	PUNCT
ejde-1812	13	51	39	39	NUM
ejde-1812	13	52	]	]	PUNCT
ejde-1812	13	53	and	and	CCONJ
ejde-1812	13	54	the	the	DET
ejde-1812	13	55	reference	reference	NOUN
ejde-1812	13	56	therein	therein	ADV
ejde-1812	13	57	for	for	ADP
ejde-1812	13	58	theory	theory	NOUN
ejde-1812	13	59	and	and	CCONJ
ejde-1812	13	60	applications	application	NOUN
ejde-1812	13	61	on	on	ADP
ejde-1812	13	62	fractional	fractional	ADJ
ejde-1812	13	63	calculus	calculus	NOUN
ejde-1812	13	64	.	.	PUNCT
ejde-1812	14	1	the	the	DET
ejde-1812	14	2	widely	widely	ADV
ejde-1812	14	3	studied	study	VERB
ejde-1812	14	4	fractional	fractional	ADJ
ejde-1812	14	5	derivatives	derivative	NOUN
ejde-1812	14	6	include	include	VERB
ejde-1812	14	7	riemann	riemann	PROPN
ejde-1812	14	8	-	-	PUNCT
ejde-1812	14	9	liouville	liouville	VERB
ejde-1812	14	10	fractional	fractional	ADJ
ejde-1812	14	11	derivatives	derivative	NOUN
ejde-1812	14	12	and	and	CCONJ
ejde-1812	14	13	caputo	caputo	PROPN
ejde-1812	14	14	fractional	fractional	ADJ
ejde-1812	14	15	derivatives	derivative	NOUN
ejde-1812	14	16	,	,	PUNCT
ejde-1812	14	17	and	and	CCONJ
ejde-1812	14	18	the	the	DET
ejde-1812	14	19	solutions	solution	NOUN
ejde-1812	14	20	of	of	ADP
ejde-1812	14	21	equations	equation	NOUN
ejde-1812	14	22	containing	contain	VERB
ejde-1812	14	23	these	these	DET
ejde-1812	14	24	two	two	NUM
ejde-1812	14	25	types	type	NOUN
ejde-1812	14	26	of	of	ADP
ejde-1812	14	27	derivative	derivative	ADJ
ejde-1812	14	28	operators	operator	NOUN
ejde-1812	14	29	have	have	VERB
ejde-1812	14	30	significantly	significantly	ADV
ejde-1812	14	31	different	different	ADJ
ejde-1812	14	32	properties	property	NOUN
ejde-1812	14	33	.	.	PUNCT
ejde-1812	15	1	in	in	ADP
ejde-1812	15	2	[	[	X
ejde-1812	15	3	16	16	NUM
ejde-1812	15	4	]	]	PUNCT
ejde-1812	15	5	,	,	PUNCT
ejde-1812	15	6	hilfer	hilfer	NOUN
ejde-1812	15	7	combined	combine	VERB
ejde-1812	15	8	the	the	DET
ejde-1812	15	9	riemannliouville	riemannliouville	NOUN
ejde-1812	15	10	fractional	fractional	ADJ
ejde-1812	15	11	derivative	derivative	NOUN
ejde-1812	15	12	and	and	CCONJ
ejde-1812	15	13	the	the	DET
ejde-1812	15	14	caputo	caputo	PROPN
ejde-1812	15	15	fractional	fractional	PROPN
ejde-1812	15	16	derivative	derivative	PROPN
ejde-1812	15	17	to	to	PART
ejde-1812	15	18	obtain	obtain	VERB
ejde-1812	15	19	a	a	DET
ejde-1812	15	20	derivative	derivative	NOUN
ejde-1812	15	21	,	,	PUNCT
ejde-1812	15	22	which	which	PRON
ejde-1812	15	23	is	be	AUX
ejde-1812	15	24	later	later	ADV
ejde-1812	15	25	referred	refer	VERB
ejde-1812	15	26	to	to	ADP
ejde-1812	15	27	as	as	ADP
ejde-1812	15	28	the	the	DET
ejde-1812	15	29	hilfer	hilfer	NOUN
ejde-1812	15	30	fractional	fractional	ADJ
ejde-1812	15	31	derivative	derivative	NOUN
ejde-1812	15	32	in	in	ADP
ejde-1812	15	33	many	many	ADJ
ejde-1812	15	34	literature	literature	NOUN
ejde-1812	15	35	.	.	PUNCT
ejde-1812	16	1	this	this	DET
ejde-1812	16	2	derivative	derivative	NOUN
ejde-1812	16	3	is	be	AUX
ejde-1812	16	4	an	an	DET
ejde-1812	16	5	interpolation	interpolation	NOUN
ejde-1812	16	6	of	of	ADP
ejde-1812	16	7	the	the	DET
ejde-1812	16	8	riemann	riemann	PROPN
ejde-1812	16	9	-	-	PUNCT
ejde-1812	16	10	liouville	liouville	VERB
ejde-1812	16	11	fractional	fractional	ADJ
ejde-1812	16	12	derivative	derivative	NOUN
ejde-1812	16	13	and	and	CCONJ
ejde-1812	16	14	the	the	DET
ejde-1812	16	15	caputo	caputo	PROPN
ejde-1812	16	16	fractional	fractional	PROPN
ejde-1812	16	17	derivative	derivative	PROPN
ejde-1812	16	18	,	,	PUNCT
ejde-1812	16	19	and	and	CCONJ
ejde-1812	16	20	he	he	PRON
ejde-1812	16	21	studied	study	VERB
ejde-1812	16	22	differential	differential	ADJ
ejde-1812	16	23	equations	equation	NOUN
ejde-1812	16	24	involving	involve	VERB
ejde-1812	16	25	this	this	PRON
ejde-1812	16	26	derivative([17	derivative([17	PROPN
ejde-1812	16	27	]	]	PUNCT
ejde-1812	16	28	)	)	PUNCT
ejde-1812	16	29	.	.	PUNCT
ejde-1812	17	1	in	in	ADP
ejde-1812	17	2	[	[	X
ejde-1812	17	3	13	13	NUM
ejde-1812	17	4	]	]	PUNCT
ejde-1812	17	5	,	,	PUNCT
ejde-1812	17	6	the	the	DET
ejde-1812	17	7	authors	author	NOUN
ejde-1812	17	8	studied	study	VERB
ejde-1812	17	9	a	a	DET
ejde-1812	17	10	class	class	NOUN
ejde-1812	17	11	of	of	ADP
ejde-1812	17	12	evolution	evolution	NOUN
ejde-1812	17	13	equations	equation	NOUN
ejde-1812	17	14	containing	contain	VERB
ejde-1812	17	15	hilfer	hilfer	NOUN
ejde-1812	17	16	fractional	fractional	ADJ
ejde-1812	17	17	derivatives	derivative	NOUN
ejde-1812	17	18	in	in	ADP
ejde-1812	17	19	banach	banach	NOUN
ejde-1812	17	20	spaces	space	NOUN
ejde-1812	17	21	.	.	PUNCT
ejde-1812	18	1	they	they	PRON
ejde-1812	18	2	introduced	introduce	VERB
ejde-1812	18	3	the	the	DET
ejde-1812	18	4	definition	definition	NOUN
ejde-1812	18	5	of	of	ADP
ejde-1812	18	6	mild	mild	ADJ
ejde-1812	18	7	solutions	solution	NOUN
ejde-1812	18	8	for	for	ADP
ejde-1812	18	9	these	these	DET
ejde-1812	18	10	equations	equation	NOUN
ejde-1812	18	11	through	through	ADP
ejde-1812	18	12	laplace	laplace	NOUN
ejde-1812	18	13	transform	transform	NOUN
ejde-1812	18	14	and	and	CCONJ
ejde-1812	18	15	the	the	DET
ejde-1812	18	16	density	density	NOUN
ejde-1812	18	17	function	function	NOUN
ejde-1812	18	18	,	,	PUNCT
ejde-1812	18	19	and	and	CCONJ
ejde-1812	18	20	obtained	obtain	VERB
ejde-1812	18	21	an	an	DET
ejde-1812	18	22	existence	existence	NOUN
ejde-1812	18	23	theorem	theorem	VERB
ejde-1812	18	24	for	for	ADP
ejde-1812	18	25	mild	mild	ADJ
ejde-1812	18	26	solutions	solution	NOUN
ejde-1812	18	27	using	use	VERB
ejde-1812	18	28	non	non	ADJ
ejde-1812	18	29	-	-	ADJ
ejde-1812	18	30	compactness	compactness	ADJ
ejde-1812	18	31	measures	measure	NOUN
ejde-1812	18	32	and	and	CCONJ
ejde-1812	18	33	the	the	DET
ejde-1812	18	34	ascoli	ascoli	PROPN
ejde-1812	18	35	-	-	PUNCT
ejde-1812	18	36	arzela	arzela	PROPN
ejde-1812	18	37	theorem	theorem	VERB
ejde-1812	18	38	.	.	PUNCT
ejde-1812	19	1	in	in	ADP
ejde-1812	19	2	[	[	X
ejde-1812	19	3	41	41	NUM
ejde-1812	19	4	]	]	PUNCT
ejde-1812	19	5	,	,	PUNCT
ejde-1812	19	6	the	the	DET
ejde-1812	19	7	authors	author	NOUN
ejde-1812	19	8	introduced	introduce	VERB
ejde-1812	19	9	ψ	ψ	NOUN
ejde-1812	19	10	-	-	ADJ
ejde-1812	19	11	hilfer	hilfer	NOUN
ejde-1812	19	12	fractional	fractional	ADJ
ejde-1812	19	13	derivatives	derivative	NOUN
ejde-1812	19	14	and	and	CCONJ
ejde-1812	19	15	studied	study	VERB
ejde-1812	19	16	equations	equation	NOUN
ejde-1812	19	17	involving	involve	VERB
ejde-1812	19	18	such	such	ADJ
ejde-1812	19	19	derivatives	derivative	NOUN
ejde-1812	19	20	.	.	PUNCT
ejde-1812	20	1	compared	compare	VERB
ejde-1812	20	2	to	to	ADP
ejde-1812	20	3	traditional	traditional	ADJ
ejde-1812	20	4	derivatives	derivative	NOUN
ejde-1812	20	5	,	,	PUNCT
ejde-1812	20	6	derivatives	derivative	NOUN
ejde-1812	20	7	containing	contain	VERB
ejde-1812	20	8	an	an	DET
ejde-1812	20	9	arbitrary	arbitrary	ADJ
ejde-1812	20	10	function	function	NOUN
ejde-1812	20	11	ψ(t	ψ(t	PROPN
ejde-1812	20	12	)	)	PUNCT
ejde-1812	20	13	are	be	AUX
ejde-1812	20	14	more	more	ADV
ejde-1812	20	15	widely	widely	ADV
ejde-1812	20	16	used	use	VERB
ejde-1812	20	17	.	.	PUNCT
ejde-1812	21	1	the	the	DET
ejde-1812	21	2	concept	concept	NOUN
ejde-1812	21	3	of	of	ADP
ejde-1812	21	4	exact	exact	ADJ
ejde-1812	21	5	controllability	controllability	NOUN
ejde-1812	21	6	was	be	AUX
ejde-1812	21	7	first	first	ADV
ejde-1812	21	8	proposed	propose	VERB
ejde-1812	21	9	by	by	ADP
ejde-1812	21	10	kalman	kalman	PROPN
ejde-1812	21	11	(	(	PUNCT
ejde-1812	21	12	[	[	X
ejde-1812	21	13	18	18	NUM
ejde-1812	21	14	]	]	SYM
ejde-1812	21	15	)	)	PUNCT
ejde-1812	21	16	in	in	ADP
ejde-1812	21	17	1963	1963	NUM
ejde-1812	21	18	and	and	CCONJ
ejde-1812	21	19	gradually	gradually	ADV
ejde-1812	21	20	became	become	VERB
ejde-1812	21	21	an	an	DET
ejde-1812	21	22	active	active	ADJ
ejde-1812	21	23	research	research	NOUN
ejde-1812	21	24	field	field	NOUN
ejde-1812	21	25	due	due	ADP
ejde-1812	21	26	to	to	ADP
ejde-1812	21	27	its	its	PRON
ejde-1812	21	28	enormous	enormous	ADJ
ejde-1812	21	29	applications	application	NOUN
ejde-1812	21	30	in	in	ADP
ejde-1812	21	31	the	the	DET
ejde-1812	21	32	field	field	NOUN
ejde-1812	21	33	of	of	ADP
ejde-1812	21	34	physics	physics	NOUN
ejde-1812	21	35	.	.	PUNCT
ejde-1812	22	1	the	the	DET
ejde-1812	22	2	application	application	NOUN
ejde-1812	22	3	of	of	ADP
ejde-1812	22	4	certain	certain	ADJ
ejde-1812	22	5	control	control	NOUN
ejde-1812	22	6	to	to	ADP
ejde-1812	22	7	a	a	DET
ejde-1812	22	8	natural	natural	ADJ
ejde-1812	22	9	or	or	CCONJ
ejde-1812	22	10	artificial	artificial	ADJ
ejde-1812	22	11	system	system	NOUN
ejde-1812	22	12	to	to	PART
ejde-1812	22	13	influence	influence	VERB
ejde-1812	22	14	its	its	PRON
ejde-1812	22	15	behavior	behavior	NOUN
ejde-1812	22	16	to	to	PART
ejde-1812	22	17	meet	meet	VERB
ejde-1812	22	18	predetermined	predetermined	ADJ
ejde-1812	22	19	goals	goal	NOUN
ejde-1812	22	20	is	be	AUX
ejde-1812	22	21	called	call	VERB
ejde-1812	22	22	a	a	DET
ejde-1812	22	23	control	control	NOUN
ejde-1812	22	24	system	system	NOUN
ejde-1812	22	25	.	.	PUNCT
ejde-1812	23	1	the	the	DET
ejde-1812	23	2	controllability	controllability	NOUN
ejde-1812	23	3	of	of	ADP
ejde-1812	23	4	control	control	NOUN
ejde-1812	23	5	systems	system	NOUN
ejde-1812	23	6	is	be	AUX
ejde-1812	23	7	one	one	NUM
ejde-1812	23	8	of	of	ADP
ejde-1812	23	9	2020	2020	NUM
ejde-1812	23	10	mathematics	mathematic	NOUN
ejde-1812	23	11	subject	subject	ADJ
ejde-1812	23	12	classification	classification	NOUN
ejde-1812	23	13	.	.	PUNCT
ejde-1812	24	1	34k37	34k37	NUM
ejde-1812	24	2	,	,	PUNCT
ejde-1812	24	3	34a08	34a08	NUM
ejde-1812	24	4	,	,	PUNCT
ejde-1812	24	5	45g05	45g05	NUM
ejde-1812	24	6	,	,	PUNCT
ejde-1812	24	7	45e05	45e05	NUM
ejde-1812	24	8	.	.	PUNCT
ejde-1812	25	1	key	key	ADJ
ejde-1812	25	2	words	word	NOUN
ejde-1812	25	3	and	and	CCONJ
ejde-1812	25	4	phrases	phrase	NOUN
ejde-1812	25	5	.	.	PUNCT
ejde-1812	26	1	ψ	ψ	X
ejde-1812	26	2	-	-	NOUN
ejde-1812	26	3	hilfer	hilfer	NOUN
ejde-1812	26	4	;	;	PUNCT
ejde-1812	26	5	mild	mild	ADJ
ejde-1812	26	6	solution	solution	NOUN
ejde-1812	26	7	;	;	PUNCT
ejde-1812	26	8	approximate	approximate	ADJ
ejde-1812	26	9	controllability	controllability	NOUN
ejde-1812	26	10	;	;	PUNCT
ejde-1812	26	11	gronwall	gronwall	ADJ
ejde-1812	26	12	-	-	PUNCT
ejde-1812	26	13	type	type	NOUN
ejde-1812	26	14	inequality	inequality	NOUN
ejde-1812	26	15	.	.	PUNCT
ejde-1812	27	1	©	©	PROPN
ejde-1812	27	2	2025	2025	NUM
ejde-1812	27	3	.	.	PUNCT
ejde-1812	28	1	this	this	DET
ejde-1812	28	2	work	work	NOUN
ejde-1812	28	3	is	be	AUX
ejde-1812	28	4	licensed	license	VERB
ejde-1812	28	5	under	under	ADP
ejde-1812	28	6	a	a	DET
ejde-1812	28	7	cc	cc	NOUN
ejde-1812	28	8	by	by	ADP
ejde-1812	28	9	4.0	4.0	NUM
ejde-1812	28	10	license	license	NOUN
ejde-1812	28	11	.	.	PUNCT
ejde-1812	29	1	submitted	submit	VERB
ejde-1812	29	2	october	october	PROPN
ejde-1812	29	3	11	11	NUM
ejde-1812	29	4	,	,	PUNCT
ejde-1812	29	5	2025	2025	NUM
ejde-1812	29	6	.	.	PUNCT
ejde-1812	30	1	published	publish	VERB
ejde-1812	30	2	november	november	PROPN
ejde-1812	30	3	18	18	NUM
ejde-1812	30	4	,	,	PUNCT
ejde-1812	30	5	2025	2025	NUM
ejde-1812	30	6	.	.	PUNCT
ejde-1812	31	1	1	1	NUM
ejde-1812	31	2	2	2	NUM
ejde-1812	31	3	j.	j.	PROPN
ejde-1812	31	4	liang	liang	PROPN
ejde-1812	31	5	,	,	PUNCT
ejde-1812	31	6	y.	y.	PROPN
ejde-1812	31	7	mu	mu	PROPN
ejde-1812	31	8	,	,	PUNCT
ejde-1812	31	9	t.-j	t.-j	PROPN
ejde-1812	31	10	.	.	PUNCT
ejde-1812	32	1	xiao	xiao	PROPN
ejde-1812	32	2	ejde-2025/109	ejde-2025/109	VERB
ejde-1812	32	3	the	the	DET
ejde-1812	32	4	fundamental	fundamental	ADJ
ejde-1812	32	5	concepts	concept	NOUN
ejde-1812	32	6	in	in	ADP
ejde-1812	32	7	control	control	NOUN
ejde-1812	32	8	theory	theory	NOUN
ejde-1812	32	9	,	,	PUNCT
ejde-1812	32	10	which	which	PRON
ejde-1812	32	11	is	be	AUX
ejde-1812	32	12	the	the	DET
ejde-1812	32	13	basis	basis	NOUN
ejde-1812	32	14	for	for	ADP
ejde-1812	32	15	studying	study	VERB
ejde-1812	32	16	optimal	optimal	ADJ
ejde-1812	32	17	control	control	NOUN
ejde-1812	32	18	and	and	CCONJ
ejde-1812	32	19	estimation	estimation	NOUN
ejde-1812	32	20	.	.	PUNCT
ejde-1812	33	1	at	at	ADP
ejde-1812	33	2	present	present	ADJ
ejde-1812	33	3	,	,	PUNCT
ejde-1812	33	4	the	the	DET
ejde-1812	33	5	controllability	controllability	NOUN
ejde-1812	33	6	problem	problem	NOUN
ejde-1812	33	7	of	of	ADP
ejde-1812	33	8	differential	differential	NOUN
ejde-1812	33	9	systems	system	NOUN
ejde-1812	33	10	described	describe	VERB
ejde-1812	33	11	by	by	ADP
ejde-1812	33	12	differential	differential	ADJ
ejde-1812	33	13	equations	equation	NOUN
ejde-1812	33	14	has	have	AUX
ejde-1812	33	15	been	be	AUX
ejde-1812	33	16	studied	study	VERB
ejde-1812	33	17	by	by	ADP
ejde-1812	33	18	many	many	ADJ
ejde-1812	33	19	scholars	scholar	NOUN
ejde-1812	33	20	.	.	PUNCT
ejde-1812	34	1	the	the	DET
ejde-1812	34	2	controllability	controllability	NOUN
ejde-1812	34	3	problem	problem	NOUN
ejde-1812	34	4	of	of	ADP
ejde-1812	34	5	differential	differential	ADJ
ejde-1812	34	6	systems	system	NOUN
ejde-1812	34	7	in	in	ADP
ejde-1812	34	8	banach	banach	NOUN
ejde-1812	34	9	space	space	NOUN
ejde-1812	34	10	is	be	AUX
ejde-1812	34	11	often	often	ADV
ejde-1812	34	12	transformed	transform	VERB
ejde-1812	34	13	into	into	ADP
ejde-1812	34	14	a	a	DET
ejde-1812	34	15	fixed	fix	VERB
ejde-1812	34	16	point	point	NOUN
ejde-1812	34	17	problem	problem	NOUN
ejde-1812	34	18	of	of	ADP
ejde-1812	34	19	operators	operator	NOUN
ejde-1812	34	20	,	,	PUNCT
ejde-1812	34	21	and	and	CCONJ
ejde-1812	34	22	the	the	DET
ejde-1812	34	23	condition	condition	NOUN
ejde-1812	34	24	of	of	ADP
ejde-1812	34	25	compactness	compactness	NOUN
ejde-1812	34	26	is	be	AUX
ejde-1812	34	27	often	often	ADV
ejde-1812	34	28	indispensable	indispensable	ADJ
ejde-1812	34	29	when	when	SCONJ
ejde-1812	34	30	applying	apply	VERB
ejde-1812	34	31	the	the	DET
ejde-1812	34	32	fixed	fix	VERB
ejde-1812	34	33	point	point	NOUN
ejde-1812	34	34	theorem	theorem	VERB
ejde-1812	34	35	.	.	PUNCT
ejde-1812	35	1	it	it	PRON
ejde-1812	35	2	is	be	AUX
ejde-1812	35	3	well	well	ADV
ejde-1812	35	4	known	know	VERB
ejde-1812	35	5	that	that	SCONJ
ejde-1812	35	6	the	the	DET
ejde-1812	35	7	exact	exact	ADJ
ejde-1812	35	8	controllability	controllability	NOUN
ejde-1812	35	9	can	can	AUX
ejde-1812	35	10	not	not	PART
ejde-1812	35	11	be	be	AUX
ejde-1812	35	12	achieved	achieve	VERB
ejde-1812	35	13	generally	generally	ADV
ejde-1812	35	14	for	for	ADP
ejde-1812	35	15	control	control	NOUN
ejde-1812	35	16	systems	system	NOUN
ejde-1812	35	17	in	in	ADP
ejde-1812	35	18	infinite	infinite	ADJ
ejde-1812	35	19	-	-	PUNCT
ejde-1812	35	20	dimensional	dimensional	ADJ
ejde-1812	35	21	spaces	space	NOUN
ejde-1812	35	22	.	.	PUNCT
ejde-1812	36	1	therefore	therefore	ADV
ejde-1812	36	2	,	,	PUNCT
ejde-1812	36	3	in	in	ADP
ejde-1812	36	4	addition	addition	NOUN
ejde-1812	36	5	to	to	ADP
ejde-1812	36	6	exact	exact	ADJ
ejde-1812	36	7	controllability	controllability	NOUN
ejde-1812	36	8	,	,	PUNCT
ejde-1812	36	9	there	there	PRON
ejde-1812	36	10	is	be	VERB
ejde-1812	36	11	also	also	ADV
ejde-1812	36	12	a	a	DET
ejde-1812	36	13	more	more	ADV
ejde-1812	36	14	widely	widely	ADV
ejde-1812	36	15	used	use	VERB
ejde-1812	36	16	concept	concept	NOUN
ejde-1812	36	17	of	of	ADP
ejde-1812	36	18	approximate	approximate	ADJ
ejde-1812	36	19	controllability	controllability	NOUN
ejde-1812	36	20	in	in	ADP
ejde-1812	36	21	the	the	DET
ejde-1812	36	22	controllability	controllability	NOUN
ejde-1812	36	23	of	of	ADP
ejde-1812	36	24	differential	differential	ADJ
ejde-1812	36	25	systems	system	NOUN
ejde-1812	36	26	.	.	PUNCT
ejde-1812	37	1	exact	exact	ADJ
ejde-1812	37	2	controllability	controllability	NOUN
ejde-1812	37	3	refers	refer	VERB
ejde-1812	37	4	to	to	ADP
ejde-1812	37	5	the	the	DET
ejde-1812	37	6	ability	ability	NOUN
ejde-1812	37	7	of	of	ADP
ejde-1812	37	8	a	a	DET
ejde-1812	37	9	system	system	NOUN
ejde-1812	37	10	to	to	PART
ejde-1812	37	11	achieve	achieve	VERB
ejde-1812	37	12	the	the	DET
ejde-1812	37	13	expected	expect	VERB
ejde-1812	37	14	precise	precise	ADJ
ejde-1812	37	15	value	value	NOUN
ejde-1812	37	16	under	under	ADP
ejde-1812	37	17	the	the	DET
ejde-1812	37	18	influence	influence	NOUN
ejde-1812	37	19	of	of	ADP
ejde-1812	37	20	control	control	NOUN
ejde-1812	37	21	functions	function	NOUN
ejde-1812	37	22	,	,	PUNCT
ejde-1812	37	23	while	while	SCONJ
ejde-1812	37	24	approximate	approximate	ADJ
ejde-1812	37	25	controllability	controllability	NOUN
ejde-1812	37	26	does	do	AUX
ejde-1812	37	27	not	not	PART
ejde-1812	37	28	require	require	VERB
ejde-1812	37	29	precise	precise	ADJ
ejde-1812	37	30	achievement	achievement	NOUN
ejde-1812	37	31	,	,	PUNCT
ejde-1812	37	32	but	but	CCONJ
ejde-1812	37	33	only	only	ADV
ejde-1812	37	34	requires	require	VERB
ejde-1812	37	35	the	the	DET
ejde-1812	37	36	system	system	NOUN
ejde-1812	37	37	to	to	PART
ejde-1812	37	38	reach	reach	VERB
ejde-1812	37	39	a	a	DET
ejde-1812	37	40	region	region	NOUN
ejde-1812	37	41	near	near	ADP
ejde-1812	37	42	the	the	DET
ejde-1812	37	43	expected	expect	VERB
ejde-1812	37	44	value	value	NOUN
ejde-1812	37	45	.	.	PUNCT
ejde-1812	38	1	for	for	ADP
ejde-1812	38	2	more	more	ADJ
ejde-1812	38	3	research	research	NOUN
ejde-1812	38	4	on	on	ADP
ejde-1812	38	5	the	the	DET
ejde-1812	38	6	controllability	controllability	NOUN
ejde-1812	38	7	of	of	ADP
ejde-1812	38	8	differential	differential	NOUN
ejde-1812	38	9	systems	system	NOUN
ejde-1812	38	10	,	,	PUNCT
ejde-1812	38	11	please	please	INTJ
ejde-1812	38	12	refer	refer	VERB
ejde-1812	38	13	to	to	ADP
ejde-1812	38	14	[	[	X
ejde-1812	38	15	3	3	NUM
ejde-1812	38	16	,	,	PUNCT
ejde-1812	38	17	4	4	NUM
ejde-1812	38	18	,	,	PUNCT
ejde-1812	38	19	6	6	NUM
ejde-1812	38	20	,	,	PUNCT
ejde-1812	38	21	14	14	NUM
ejde-1812	38	22	,	,	PUNCT
ejde-1812	38	23	21	21	NUM
ejde-1812	38	24	,	,	PUNCT
ejde-1812	38	25	30	30	NUM
ejde-1812	38	26	,	,	PUNCT
ejde-1812	38	27	31	31	NUM
ejde-1812	38	28	]	]	PUNCT
ejde-1812	38	29	and	and	CCONJ
ejde-1812	38	30	the	the	DET
ejde-1812	38	31	references	reference	NOUN
ejde-1812	38	32	therein	therein	ADV
ejde-1812	38	33	.	.	PUNCT
ejde-1812	39	1	integral	integral	ADJ
ejde-1812	39	2	inequalities	inequality	NOUN
ejde-1812	39	3	serve	serve	VERB
ejde-1812	39	4	as	as	ADP
ejde-1812	39	5	fundamental	fundamental	ADJ
ejde-1812	39	6	tools	tool	NOUN
ejde-1812	39	7	for	for	ADP
ejde-1812	39	8	quantitatively	quantitatively	ADV
ejde-1812	39	9	analyzing	analyze	VERB
ejde-1812	39	10	solutions	solution	NOUN
ejde-1812	39	11	to	to	PART
ejde-1812	39	12	differential	differential	VERB
ejde-1812	39	13	and	and	CCONJ
ejde-1812	39	14	integral	integral	ADJ
ejde-1812	39	15	equations	equation	NOUN
ejde-1812	39	16	.	.	PUNCT
ejde-1812	40	1	among	among	ADP
ejde-1812	40	2	these	these	PRON
ejde-1812	40	3	,	,	PUNCT
ejde-1812	40	4	the	the	DET
ejde-1812	40	5	gronwall	gronwall	ADJ
ejde-1812	40	6	-	-	PUNCT
ejde-1812	40	7	bellman	bellman	NOUN
ejde-1812	40	8	inequality	inequality	NOUN
ejde-1812	40	9	has	have	AUX
ejde-1812	40	10	demonstrated	demonstrate	VERB
ejde-1812	40	11	wide	wide	ADJ
ejde-1812	40	12	applications	application	NOUN
ejde-1812	40	13	in	in	ADP
ejde-1812	40	14	deriving	derive	VERB
ejde-1812	40	15	estimates	estimate	NOUN
ejde-1812	40	16	across	across	ADP
ejde-1812	40	17	ordinary	ordinary	ADJ
ejde-1812	40	18	differential	differential	ADJ
ejde-1812	40	19	equations	equation	NOUN
ejde-1812	40	20	,	,	PUNCT
ejde-1812	40	21	partial	partial	ADJ
ejde-1812	40	22	differential	differential	NOUN
ejde-1812	40	23	equations	equation	NOUN
ejde-1812	40	24	,	,	PUNCT
ejde-1812	40	25	stochastic	stochastic	ADJ
ejde-1812	40	26	differential	differential	ADJ
ejde-1812	40	27	equations	equation	NOUN
ejde-1812	40	28	,	,	PUNCT
ejde-1812	40	29	and	and	CCONJ
ejde-1812	40	30	integral	integral	ADJ
ejde-1812	40	31	-	-	PUNCT
ejde-1812	40	32	differential	differential	NOUN
ejde-1812	40	33	equations	equation	NOUN
ejde-1812	40	34	,	,	PUNCT
ejde-1812	40	35	as	as	SCONJ
ejde-1812	40	36	it	it	PRON
ejde-1812	40	37	provides	provide	VERB
ejde-1812	40	38	explicit	explicit	ADJ
ejde-1812	40	39	bounds	bound	NOUN
ejde-1812	40	40	of	of	ADP
ejde-1812	40	41	unknown	unknown	ADJ
ejde-1812	40	42	functions	function	NOUN
ejde-1812	40	43	x(t	x(t	PROPN
ejde-1812	40	44	)	)	PUNCT
ejde-1812	40	45	.	.	PUNCT
ejde-1812	41	1	given	give	VERB
ejde-1812	41	2	its	its	PRON
ejde-1812	41	3	broad	broad	ADJ
ejde-1812	41	4	applicability	applicability	NOUN
ejde-1812	41	5	and	and	CCONJ
ejde-1812	41	6	significance	significance	NOUN
ejde-1812	41	7	,	,	PUNCT
ejde-1812	41	8	numerous	numerous	ADJ
ejde-1812	41	9	extensions	extension	NOUN
ejde-1812	41	10	of	of	ADP
ejde-1812	41	11	this	this	DET
ejde-1812	41	12	classical	classical	ADJ
ejde-1812	41	13	inequality	inequality	NOUN
ejde-1812	41	14	have	have	AUX
ejde-1812	41	15	been	be	AUX
ejde-1812	41	16	developed	develop	VERB
ejde-1812	41	17	.	.	PUNCT
ejde-1812	42	1	for	for	ADP
ejde-1812	42	2	works	work	NOUN
ejde-1812	42	3	on	on	ADP
ejde-1812	42	4	generalized	generalized	ADJ
ejde-1812	42	5	gronwall	gronwall	ADJ
ejde-1812	42	6	-	-	PUNCT
ejde-1812	42	7	bellman	bellman	NOUN
ejde-1812	42	8	inequalities	inequality	NOUN
ejde-1812	42	9	,	,	PUNCT
ejde-1812	42	10	gronwall	gronwall	ADJ
ejde-1812	42	11	-	-	PUNCT
ejde-1812	42	12	type	type	NOUN
ejde-1812	42	13	inequalities	inequality	NOUN
ejde-1812	42	14	,	,	PUNCT
ejde-1812	42	15	and	and	CCONJ
ejde-1812	42	16	their	their	PRON
ejde-1812	42	17	applications	application	NOUN
ejde-1812	42	18	,	,	PUNCT
ejde-1812	42	19	we	we	PRON
ejde-1812	42	20	refer	refer	VERB
ejde-1812	42	21	readers	reader	NOUN
ejde-1812	42	22	to	to	ADP
ejde-1812	42	23	[	[	X
ejde-1812	42	24	4	4	NUM
ejde-1812	42	25	,	,	PUNCT
ejde-1812	42	26	5	5	NUM
ejde-1812	42	27	,	,	PUNCT
ejde-1812	42	28	6	6	NUM
ejde-1812	42	29	,	,	PUNCT
ejde-1812	42	30	7	7	NUM
ejde-1812	42	31	,	,	PUNCT
ejde-1812	42	32	15	15	NUM
ejde-1812	42	33	,	,	PUNCT
ejde-1812	42	34	26	26	NUM
ejde-1812	42	35	,	,	PUNCT
ejde-1812	42	36	27	27	NUM
ejde-1812	42	37	,	,	PUNCT
ejde-1812	42	38	28	28	NUM
ejde-1812	42	39	,	,	PUNCT
ejde-1812	42	40	29	29	NUM
ejde-1812	42	41	,	,	PUNCT
ejde-1812	42	42	34	34	NUM
ejde-1812	42	43	,	,	PUNCT
ejde-1812	42	44	38	38	NUM
ejde-1812	42	45	,	,	PUNCT
ejde-1812	42	46	40	40	NUM
ejde-1812	42	47	,	,	PUNCT
ejde-1812	42	48	42	42	NUM
ejde-1812	42	49	,	,	PUNCT
ejde-1812	42	50	43	43	NUM
ejde-1812	42	51	]	]	PUNCT
ejde-1812	42	52	and	and	CCONJ
ejde-1812	42	53	the	the	DET
ejde-1812	42	54	references	reference	NOUN
ejde-1812	42	55	therein	therein	ADV
ejde-1812	42	56	.	.	PUNCT
ejde-1812	43	1	the	the	DET
ejde-1812	43	2	research	research	NOUN
ejde-1812	43	3	on	on	ADP
ejde-1812	43	4	evolution	evolution	NOUN
ejde-1812	43	5	differential	differential	NOUN
ejde-1812	43	6	equations	equation	NOUN
ejde-1812	43	7	with	with	ADP
ejde-1812	43	8	ψ	ψ	NOUN
ejde-1812	43	9	-	-	ADJ
ejde-1812	43	10	hilfer	hilfer	NOUN
ejde-1812	43	11	fractional	fractional	ADJ
ejde-1812	43	12	derivatives	derivative	NOUN
ejde-1812	43	13	in	in	ADP
ejde-1812	43	14	banach	banach	NOUN
ejde-1812	43	15	spaces	space	NOUN
ejde-1812	43	16	is	be	AUX
ejde-1812	43	17	blank	blank	ADJ
ejde-1812	43	18	,	,	PUNCT
ejde-1812	43	19	and	and	CCONJ
ejde-1812	43	20	this	this	DET
ejde-1812	43	21	paper	paper	NOUN
ejde-1812	43	22	fills	fill	VERB
ejde-1812	43	23	this	this	DET
ejde-1812	43	24	gap	gap	NOUN
ejde-1812	43	25	.	.	PUNCT
ejde-1812	44	1	the	the	DET
ejde-1812	44	2	rest	rest	NOUN
ejde-1812	44	3	of	of	ADP
ejde-1812	44	4	this	this	DET
ejde-1812	44	5	paper	paper	NOUN
ejde-1812	44	6	is	be	AUX
ejde-1812	44	7	organized	organize	VERB
ejde-1812	44	8	as	as	SCONJ
ejde-1812	44	9	follows	follow	VERB
ejde-1812	44	10	.	.	PUNCT
ejde-1812	45	1	in	in	ADP
ejde-1812	45	2	section	section	NOUN
ejde-1812	45	3	2	2	NUM
ejde-1812	45	4	,	,	PUNCT
ejde-1812	45	5	we	we	PRON
ejde-1812	45	6	introduce	introduce	VERB
ejde-1812	45	7	some	some	DET
ejde-1812	45	8	notations	notation	NOUN
ejde-1812	45	9	,	,	PUNCT
ejde-1812	45	10	recall	recall	VERB
ejde-1812	45	11	some	some	DET
ejde-1812	45	12	basic	basic	ADJ
ejde-1812	45	13	known	know	VERB
ejde-1812	45	14	results	result	NOUN
ejde-1812	45	15	,	,	PUNCT
ejde-1812	45	16	and	and	CCONJ
ejde-1812	45	17	derive	derive	VERB
ejde-1812	45	18	a	a	DET
ejde-1812	45	19	definition	definition	NOUN
ejde-1812	45	20	of	of	ADP
ejde-1812	45	21	mild	mild	ADJ
ejde-1812	45	22	solutions	solution	NOUN
ejde-1812	45	23	for	for	ADP
ejde-1812	45	24	the	the	DET
ejde-1812	45	25	evolution	evolution	NOUN
ejde-1812	45	26	equations	equation	NOUN
ejde-1812	45	27	involving	involve	VERB
ejde-1812	45	28	ψ	ψ	VERB
ejde-1812	45	29	-	-	ADJ
ejde-1812	45	30	hilfer	hilfer	NOUN
ejde-1812	45	31	fractional	fractional	ADJ
ejde-1812	45	32	derivatives	derivative	NOUN
ejde-1812	45	33	.	.	PUNCT
ejde-1812	46	1	in	in	ADP
ejde-1812	46	2	section	section	NOUN
ejde-1812	46	3	3	3	NUM
ejde-1812	46	4	,	,	PUNCT
ejde-1812	46	5	we	we	PRON
ejde-1812	46	6	develop	develop	VERB
ejde-1812	46	7	the	the	DET
ejde-1812	46	8	existence	existence	NOUN
ejde-1812	46	9	and	and	CCONJ
ejde-1812	46	10	uniqueness	uniqueness	NOUN
ejde-1812	46	11	theorem	theorem	NOUN
ejde-1812	46	12	of	of	ADP
ejde-1812	46	13	mild	mild	ADJ
ejde-1812	46	14	solutions	solution	NOUN
ejde-1812	46	15	for	for	ADP
ejde-1812	46	16	ψ	ψ	NOUN
ejde-1812	46	17	-	-	ADJ
ejde-1812	46	18	hilfer	hilfer	NOUN
ejde-1812	46	19	fractional	fractional	ADJ
ejde-1812	46	20	system	system	NOUN
ejde-1812	46	21	,	,	PUNCT
ejde-1812	46	22	and	and	CCONJ
ejde-1812	46	23	discuss	discuss	VERB
ejde-1812	46	24	the	the	DET
ejde-1812	46	25	approximate	approximate	ADJ
ejde-1812	46	26	controllability	controllability	NOUN
ejde-1812	46	27	of	of	ADP
ejde-1812	46	28	the	the	DET
ejde-1812	46	29	control	control	NOUN
ejde-1812	46	30	problem	problem	NOUN
ejde-1812	46	31	in	in	ADP
ejde-1812	46	32	the	the	DET
ejde-1812	46	33	weighted	weighted	ADJ
ejde-1812	46	34	space	space	NOUN
ejde-1812	46	35	c1−α−β(1−α);ψ	c1−α−β(1−α);ψ	PUNCT
ejde-1812	46	36	under	under	ADP
ejde-1812	46	37	suitable	suitable	ADJ
ejde-1812	46	38	conditions	condition	NOUN
ejde-1812	46	39	.	.	PUNCT
ejde-1812	47	1	in	in	ADP
ejde-1812	47	2	section	section	NOUN
ejde-1812	47	3	4	4	NUM
ejde-1812	47	4	,	,	PUNCT
ejde-1812	47	5	we	we	PRON
ejde-1812	47	6	establish	establish	VERB
ejde-1812	47	7	a	a	DET
ejde-1812	47	8	new	new	ADJ
ejde-1812	47	9	multidimensional	multidimensional	ADJ
ejde-1812	47	10	gronwall	gronwall	ADJ
ejde-1812	47	11	-	-	PUNCT
ejde-1812	47	12	type	type	NOUN
ejde-1812	47	13	inequality	inequality	NOUN
ejde-1812	47	14	involving	involve	VERB
ejde-1812	47	15	multiple	multiple	ADJ
ejde-1812	47	16	singular	singular	ADJ
ejde-1812	47	17	kernels	kernel	NOUN
ejde-1812	47	18	and	and	CCONJ
ejde-1812	47	19	exponential	exponential	ADJ
ejde-1812	47	20	factors	factor	NOUN
ejde-1812	47	21	,	,	PUNCT
ejde-1812	47	22	and	and	CCONJ
ejde-1812	47	23	use	use	VERB
ejde-1812	47	24	it	it	PRON
ejde-1812	47	25	to	to	PART
ejde-1812	47	26	study	study	VERB
ejde-1812	47	27	the	the	DET
ejde-1812	47	28	dependence	dependence	NOUN
ejde-1812	47	29	of	of	ADP
ejde-1812	47	30	solution	solution	NOUN
ejde-1812	47	31	on	on	ADP
ejde-1812	47	32	the	the	DET
ejde-1812	47	33	order	order	NOUN
ejde-1812	47	34	and	and	CCONJ
ejde-1812	47	35	the	the	DET
ejde-1812	47	36	initial	initial	ADJ
ejde-1812	47	37	condition	condition	NOUN
ejde-1812	47	38	for	for	ADP
ejde-1812	47	39	the	the	DET
ejde-1812	47	40	fractional	fractional	ADJ
ejde-1812	47	41	integrodifferential	integrodifferential	ADJ
ejde-1812	47	42	ψ	ψ	NOUN
ejde-1812	47	43	-	-	ADJ
ejde-1812	47	44	hilfer	hilfer	NOUN
ejde-1812	47	45	fractional	fractional	ADJ
ejde-1812	47	46	equations	equation	NOUN
ejde-1812	47	47	.	.	PUNCT
ejde-1812	48	1	finally	finally	ADV
ejde-1812	48	2	,	,	PUNCT
ejde-1812	48	3	in	in	ADP
ejde-1812	48	4	section	section	NOUN
ejde-1812	48	5	5	5	NUM
ejde-1812	48	6	,	,	PUNCT
ejde-1812	48	7	an	an	DET
ejde-1812	48	8	example	example	NOUN
ejde-1812	48	9	is	be	AUX
ejde-1812	48	10	given	give	VERB
ejde-1812	48	11	to	to	PART
ejde-1812	48	12	illustrate	illustrate	VERB
ejde-1812	48	13	the	the	DET
ejde-1812	48	14	main	main	ADJ
ejde-1812	48	15	results	result	NOUN
ejde-1812	48	16	.	.	PUNCT
ejde-1812	49	1	2	2	X
ejde-1812	49	2	.	.	X
ejde-1812	49	3	definition	definition	NOUN
ejde-1812	49	4	of	of	ADP
ejde-1812	49	5	mild	mild	ADJ
ejde-1812	49	6	solutions	solution	NOUN
ejde-1812	49	7	we	we	PRON
ejde-1812	49	8	begin	begin	VERB
ejde-1812	49	9	this	this	DET
ejde-1812	49	10	part	part	NOUN
ejde-1812	49	11	by	by	ADP
ejde-1812	49	12	setting	set	VERB
ejde-1812	49	13	some	some	DET
ejde-1812	49	14	notation	notation	NOUN
ejde-1812	49	15	.	.	PUNCT
ejde-1812	49	16	suppose	suppose	VERB
ejde-1812	49	17	that	that	SCONJ
ejde-1812	49	18	ψ(t	ψ(t	PROPN
ejde-1812	49	19	)	)	PUNCT
ejde-1812	49	20	∈	∈	PROPN
ejde-1812	49	21	c1[0,∞	c1[0,∞	PROPN
ejde-1812	49	22	)	)	PUNCT
ejde-1812	49	23	is	be	AUX
ejde-1812	49	24	strictly	strictly	ADV
ejde-1812	49	25	increasing	increase	VERB
ejde-1812	49	26	and	and	CCONJ
ejde-1812	49	27	satisfies	satisfie	NOUN
ejde-1812	49	28	that	that	PRON
ejde-1812	49	29	ψ(0	ψ(0	NOUN
ejde-1812	49	30	)	)	PUNCT
ejde-1812	49	31	=	=	SYM
ejde-1812	49	32	0	0	NUM
ejde-1812	49	33	and	and	CCONJ
ejde-1812	49	34	limt→∞ψ(t	limt→∞ψ(t	PROPN
ejde-1812	49	35	)	)	PUNCT
ejde-1812	50	1	=	=	NOUN
ejde-1812	50	2	∞.	∞.	PROPN
ejde-1812	50	3	let	let	AUX
ejde-1812	50	4	ζ(t	ζ(t	VERB
ejde-1812	50	5	)	)	PUNCT
ejde-1812	50	6	be	be	AUX
ejde-1812	50	7	the	the	DET
ejde-1812	50	8	inverse	inverse	ADJ
ejde-1812	50	9	function	function	NOUN
ejde-1812	50	10	of	of	ADP
ejde-1812	50	11	the	the	DET
ejde-1812	50	12	function	function	NOUN
ejde-1812	50	13	ψ(t	ψ(t	PROPN
ejde-1812	50	14	)	)	PUNCT
ejde-1812	50	15	.	.	PUNCT
ejde-1812	51	1	denote	denote	VERB
ejde-1812	51	2	by	by	ADP
ejde-1812	51	3	x	x	DET
ejde-1812	51	4	a	a	DET
ejde-1812	51	5	banach	banach	NOUN
ejde-1812	51	6	space	space	NOUN
ejde-1812	51	7	with	with	ADP
ejde-1812	51	8	norm	norm	NOUN
ejde-1812	51	9	∥·∥.	∥·∥.	X
ejde-1812	51	10	we	we	PRON
ejde-1812	51	11	denote	denote	VERB
ejde-1812	51	12	by	by	ADP
ejde-1812	51	13	c(j	c(j	PROPN
ejde-1812	51	14	,	,	PUNCT
ejde-1812	51	15	x	x	X
ejde-1812	51	16	)	)	PUNCT
ejde-1812	51	17	the	the	DET
ejde-1812	51	18	space	space	NOUN
ejde-1812	51	19	of	of	ADP
ejde-1812	51	20	all	all	DET
ejde-1812	51	21	x	x	ADJ
ejde-1812	51	22	-	-	VERB
ejde-1812	51	23	valued	value	VERB
ejde-1812	51	24	continuous	continuous	ADJ
ejde-1812	51	25	functions	function	NOUN
ejde-1812	51	26	on	on	ADP
ejde-1812	51	27	j	j	PROPN
ejde-1812	51	28	with	with	ADP
ejde-1812	51	29	the	the	DET
ejde-1812	51	30	natural	natural	ADJ
ejde-1812	51	31	norm	norm	NOUN
ejde-1812	51	32	∥x∥c(j	∥x∥c(j	ADJ
ejde-1812	51	33	,	,	PUNCT
ejde-1812	51	34	x	x	X
ejde-1812	51	35	)	)	PUNCT
ejde-1812	51	36	=	=	SYM
ejde-1812	51	37	supt∈j	supt∈j	PROPN
ejde-1812	51	38	∥x(t)∥.	∥x(t)∥.	ADV
ejde-1812	51	39	let	let	VERB
ejde-1812	51	40	c1−γ;ψ(j	c1−γ;ψ(j	ADV
ejde-1812	51	41	,	,	PUNCT
ejde-1812	51	42	x	x	X
ejde-1812	51	43	)	)	PUNCT
ejde-1812	52	1	=	=	PRON
ejde-1812	52	2	{	{	PUNCT
ejde-1812	52	3	x	x	X
ejde-1812	52	4	:	:	PUNCT
ejde-1812	52	5	ψ1−γ(t)x(t	ψ1−γ(t)x(t	NUM
ejde-1812	52	6	)	)	PUNCT
ejde-1812	52	7	∈	∈	PROPN
ejde-1812	52	8	c(j	c(j	PROPN
ejde-1812	52	9	,	,	PUNCT
ejde-1812	52	10	x	x	NOUN
ejde-1812	52	11	)	)	PUNCT
ejde-1812	52	12	}	}	PUNCT
ejde-1812	52	13	(	(	PUNCT
ejde-1812	52	14	γ	γ	X
ejde-1812	52	15	∈	∈	PROPN
ejde-1812	52	16	(	(	PUNCT
ejde-1812	52	17	0	0	NUM
ejde-1812	52	18	,	,	PUNCT
ejde-1812	52	19	1	1	NUM
ejde-1812	52	20	)	)	PUNCT
ejde-1812	52	21	)	)	PUNCT
ejde-1812	52	22	with	with	ADP
ejde-1812	52	23	the	the	DET
ejde-1812	52	24	norm	norm	NOUN
ejde-1812	52	25	∥x∥c1−γ;ψ	∥x∥c1−γ;ψ	NOUN
ejde-1812	52	26	=	=	SYM
ejde-1812	52	27	sup	sup	NOUN
ejde-1812	52	28	{	{	PUNCT
ejde-1812	52	29	ψ1−γ(t)∥x(t)∥	ψ1−γ(t)∥x(t)∥	X
ejde-1812	52	30	:	:	PUNCT
ejde-1812	52	31	t	t	PROPN
ejde-1812	52	32	∈	∈	PROPN
ejde-1812	52	33	j	j	PROPN
ejde-1812	52	34	}	}	PUNCT
ejde-1812	52	35	.	.	PUNCT
ejde-1812	53	1	obviously	obviously	ADV
ejde-1812	53	2	,	,	PUNCT
ejde-1812	53	3	the	the	DET
ejde-1812	53	4	space	space	NOUN
ejde-1812	53	5	c1−γ;ψ(j	c1−γ;ψ(j	ADV
ejde-1812	53	6	,	,	PUNCT
ejde-1812	53	7	x	x	X
ejde-1812	53	8	)	)	PUNCT
ejde-1812	53	9	is	be	AUX
ejde-1812	53	10	a	a	DET
ejde-1812	53	11	banach	banach	NOUN
ejde-1812	53	12	space	space	NOUN
ejde-1812	53	13	.	.	PUNCT
ejde-1812	54	1	throughout	throughout	ADP
ejde-1812	54	2	this	this	DET
ejde-1812	54	3	article	article	NOUN
ejde-1812	54	4	,	,	PUNCT
ejde-1812	54	5	we	we	PRON
ejde-1812	54	6	assume	assume	VERB
ejde-1812	54	7	that	that	SCONJ
ejde-1812	54	8	the	the	DET
ejde-1812	54	9	semigroup	semigroup	PROPN
ejde-1812	54	10	{	{	PUNCT
ejde-1812	54	11	t	t	PROPN
ejde-1812	54	12	(	(	PUNCT
ejde-1812	54	13	t)}t≥0	t)}t≥0	NOUN
ejde-1812	54	14	is	be	AUX
ejde-1812	54	15	differentiable	differentiable	ADJ
ejde-1812	54	16	and	and	CCONJ
ejde-1812	54	17	uniformly	uniformly	ADV
ejde-1812	54	18	bounded	bound	VERB
ejde-1812	54	19	,	,	PUNCT
ejde-1812	54	20	that	that	ADV
ejde-1812	54	21	is	is	ADV
ejde-1812	54	22	,	,	PUNCT
ejde-1812	54	23	there	there	PRON
ejde-1812	54	24	is	be	VERB
ejde-1812	54	25	a	a	DET
ejde-1812	54	26	constant	constant	ADJ
ejde-1812	54	27	m	m	NOUN
ejde-1812	54	28	>	>	X
ejde-1812	54	29	0	0	NUM
ejde-1812	55	1	such	such	ADJ
ejde-1812	55	2	that	that	SCONJ
ejde-1812	55	3	∥t	∥t	PROPN
ejde-1812	55	4	(	(	PUNCT
ejde-1812	55	5	t)∥	t)∥	NUM
ejde-1812	55	6	≤m	≤m	NOUN
ejde-1812	55	7	,	,	PUNCT
ejde-1812	55	8	∀t	∀t	PROPN
ejde-1812	55	9	≥	≥	NOUN
ejde-1812	55	10	0	0	NUM
ejde-1812	55	11	.	.	PUNCT
ejde-1812	56	1	definition	definition	NOUN
ejde-1812	56	2	2.1	2.1	NUM
ejde-1812	56	3	(	(	PUNCT
ejde-1812	56	4	[	[	X
ejde-1812	56	5	16	16	NUM
ejde-1812	56	6	]	]	PUNCT
ejde-1812	56	7	)	)	PUNCT
ejde-1812	56	8	.	.	PUNCT
ejde-1812	57	1	the	the	DET
ejde-1812	57	2	fractional	fractional	ADJ
ejde-1812	57	3	integral	integral	NOUN
ejde-1812	57	4	of	of	ADP
ejde-1812	57	5	order	order	NOUN
ejde-1812	57	6	α(0	α(0	PROPN
ejde-1812	57	7	<	<	X
ejde-1812	57	8	α	α	X
ejde-1812	57	9	<	<	X
ejde-1812	57	10	1	1	NUM
ejde-1812	57	11	)	)	PUNCT
ejde-1812	57	12	involving	involve	VERB
ejde-1812	57	13	a	a	DET
ejde-1812	57	14	general	general	ADJ
ejde-1812	57	15	function	function	NOUN
ejde-1812	57	16	ψ	ψ	NOUN
ejde-1812	57	17	for	for	ADP
ejde-1812	57	18	a	a	DET
ejde-1812	57	19	function	function	NOUN
ejde-1812	57	20	f	f	PROPN
ejde-1812	57	21	is	be	AUX
ejde-1812	57	22	defined	define	VERB
ejde-1812	57	23	by	by	ADP
ejde-1812	57	24	iα;ψf(t	iα;ψf(t	NOUN
ejde-1812	57	25	)	)	PUNCT
ejde-1812	57	26	=	=	SYM
ejde-1812	57	27	1	1	NUM
ejde-1812	57	28	γ(α	γ(α	NOUN
ejde-1812	57	29	)	)	PUNCT
ejde-1812	58	1	∫	∫	PROPN
ejde-1812	58	2	t	t	PROPN
ejde-1812	58	3	0	0	NUM
ejde-1812	59	1	(	(	PUNCT
ejde-1812	59	2	ψ(t)−	ψ(t)−	PROPN
ejde-1812	59	3	ψ(s))α−1f(s)ψ′(s)ds	ψ(s))α−1f(s)ψ′(s)ds	AUX
ejde-1812	59	4	.	.	PROPN
ejde-1812	59	5	remark	remark	PROPN
ejde-1812	59	6	2.2	2.2	NUM
ejde-1812	59	7	.	.	PUNCT
ejde-1812	60	1	when	when	SCONJ
ejde-1812	60	2	ψ(t	ψ(t	X
ejde-1812	60	3	)	)	PUNCT
ejde-1812	60	4	=	=	SYM
ejde-1812	60	5	t	t	PROPN
ejde-1812	60	6	,	,	PUNCT
ejde-1812	60	7	the	the	DET
ejde-1812	60	8	fractional	fractional	ADJ
ejde-1812	60	9	integral	integral	ADJ
ejde-1812	60	10	iα;ψ	iα;ψ	NOUN
ejde-1812	60	11	becomes	become	VERB
ejde-1812	60	12	the	the	DET
ejde-1812	60	13	riemann	riemann	PROPN
ejde-1812	60	14	-	-	PUNCT
ejde-1812	60	15	liouville	liouville	VERB
ejde-1812	60	16	fractional	fractional	ADJ
ejde-1812	60	17	integral	integral	ADJ
ejde-1812	60	18	iα([16	iα([16	PROPN
ejde-1812	60	19	]	]	NOUN
ejde-1812	60	20	)	)	PUNCT
ejde-1812	60	21	.	.	PUNCT
ejde-1812	61	1	ejde-2025/109	ejde-2025/109	ADP
ejde-1812	61	2	evolution	evolution	NOUN
ejde-1812	61	3	ψ	ψ	NOUN
ejde-1812	61	4	-	-	ADJ
ejde-1812	61	5	hilfer	hilfer	NOUN
ejde-1812	61	6	fractional	fractional	ADJ
ejde-1812	61	7	differential	differential	ADJ
ejde-1812	61	8	equations	equation	NOUN
ejde-1812	61	9	3	3	NUM
ejde-1812	61	10	definition	definition	NOUN
ejde-1812	61	11	2.3	2.3	NUM
ejde-1812	61	12	.	.	PUNCT
ejde-1812	62	1	[	[	X
ejde-1812	62	2	41	41	NUM
ejde-1812	62	3	]	]	PUNCT
ejde-1812	62	4	for	for	ADP
ejde-1812	62	5	any	any	DET
ejde-1812	62	6	0	0	PUNCT
ejde-1812	62	7	<	<	X
ejde-1812	62	8	α	α	PROPN
ejde-1812	62	9	≤	≤	NUM
ejde-1812	62	10	1	1	NUM
ejde-1812	62	11	,	,	PUNCT
ejde-1812	62	12	0	0	NUM
ejde-1812	62	13	≤	≤	NUM
ejde-1812	62	14	β	β	X
ejde-1812	62	15	≤	≤	NUM
ejde-1812	62	16	1	1	NUM
ejde-1812	62	17	,	,	PUNCT
ejde-1812	62	18	ψ	ψ	NOUN
ejde-1812	62	19	is	be	AUX
ejde-1812	62	20	differentiable	differentiable	ADJ
ejde-1812	62	21	,	,	PUNCT
ejde-1812	62	22	the	the	DET
ejde-1812	62	23	ψ	ψ	NOUN
ejde-1812	62	24	-	-	ADJ
ejde-1812	62	25	hilfer	hilfer	NOUN
ejde-1812	62	26	fractional	fractional	ADJ
ejde-1812	62	27	derivative	derivative	NOUN
ejde-1812	62	28	of	of	ADP
ejde-1812	62	29	order	order	NOUN
ejde-1812	62	30	α	α	NOUN
ejde-1812	62	31	and	and	CCONJ
ejde-1812	62	32	type	type	NOUN
ejde-1812	62	33	β	β	NOUN
ejde-1812	62	34	for	for	ADP
ejde-1812	62	35	a	a	DET
ejde-1812	62	36	function	function	NOUN
ejde-1812	62	37	f	f	PROPN
ejde-1812	62	38	is	be	AUX
ejde-1812	62	39	defined	define	VERB
ejde-1812	62	40	by	by	ADP
ejde-1812	62	41	dα	dα	NOUN
ejde-1812	62	42	,	,	PUNCT
ejde-1812	62	43	β;ψf(t	β;ψf(t	PROPN
ejde-1812	62	44	)	)	PUNCT
ejde-1812	62	45	=	=	VERB
ejde-1812	62	46	iβ(1−α);ψ	iβ(1−α);ψ	ADJ
ejde-1812	62	47	1	1	NUM
ejde-1812	62	48	ψ′(t	ψ′(t	NOUN
ejde-1812	62	49	)	)	PUNCT
ejde-1812	62	50	d	d	NOUN
ejde-1812	62	51	dt	dt	PUNCT
ejde-1812	62	52	i(1−β)(1−α);ψf(t	i(1−β)(1−α);ψf(t	NOUN
ejde-1812	62	53	)	)	PUNCT
ejde-1812	62	54	.	.	PUNCT
ejde-1812	63	1	remark	remark	PROPN
ejde-1812	63	2	2.4	2.4	NUM
ejde-1812	63	3	.	.	PUNCT
ejde-1812	64	1	when	when	SCONJ
ejde-1812	64	2	ψ(t	ψ(t	X
ejde-1812	64	3	)	)	PUNCT
ejde-1812	64	4	=	=	SYM
ejde-1812	64	5	t	t	PROPN
ejde-1812	64	6	,	,	PUNCT
ejde-1812	64	7	the	the	DET
ejde-1812	64	8	ψ	ψ	NOUN
ejde-1812	64	9	-	-	ADJ
ejde-1812	64	10	hilfer	hilfer	NOUN
ejde-1812	64	11	fractional	fractional	ADJ
ejde-1812	64	12	derivative	derivative	NOUN
ejde-1812	64	13	becomes	become	VERB
ejde-1812	64	14	the	the	DET
ejde-1812	64	15	hilfer	hilfer	NOUN
ejde-1812	64	16	fractional	fractional	ADJ
ejde-1812	64	17	derivative	derivative	NOUN
ejde-1812	64	18	(	(	PUNCT
ejde-1812	64	19	[	[	X
ejde-1812	64	20	16	16	NUM
ejde-1812	64	21	]	]	SYM
ejde-1812	64	22	)	)	PUNCT
ejde-1812	64	23	.	.	PUNCT
ejde-1812	65	1	definition	definition	NOUN
ejde-1812	65	2	2.5	2.5	NUM
ejde-1812	65	3	(	(	PUNCT
ejde-1812	65	4	[	[	X
ejde-1812	65	5	27	27	NUM
ejde-1812	65	6	]	]	NUM
ejde-1812	65	7	)	)	PUNCT
ejde-1812	65	8	.	.	PUNCT
ejde-1812	66	1	for	for	ADP
ejde-1812	66	2	f	f	PROPN
ejde-1812	66	3	∈	∈	PROPN
ejde-1812	66	4	l1	l1	PROPN
ejde-1812	66	5	loc(r+	loc(r+	PROPN
ejde-1812	66	6	,	,	PUNCT
ejde-1812	66	7	x	x	NOUN
ejde-1812	66	8	)	)	PUNCT
ejde-1812	66	9	and	and	CCONJ
ejde-1812	66	10	λ	λ	X
ejde-1812	66	11	∈	∈	PROPN
ejde-1812	66	12	c	c	NOUN
ejde-1812	66	13	,	,	PUNCT
ejde-1812	66	14	the	the	DET
ejde-1812	66	15	ψ	ψ	NOUN
ejde-1812	66	16	-	-	ADJ
ejde-1812	66	17	laplace	laplace	ADJ
ejde-1812	66	18	transform	transform	NOUN
ejde-1812	66	19	of	of	ADP
ejde-1812	66	20	f	f	PROPN
ejde-1812	66	21	is	be	AUX
ejde-1812	66	22	defined	define	VERB
ejde-1812	66	23	as	as	ADP
ejde-1812	66	24	lψ[f	lψ[f	NOUN
ejde-1812	66	25	]	]	X
ejde-1812	66	26	(	(	PUNCT
ejde-1812	66	27	λ	λ	NOUN
ejde-1812	66	28	)	)	PUNCT
ejde-1812	66	29	=	=	SYM
ejde-1812	66	30	f̃(λ	f̃(λ	PROPN
ejde-1812	66	31	)	)	PUNCT
ejde-1812	67	1	:	:	PUNCT
ejde-1812	68	1	=	=	SYM
ejde-1812	68	2	∫	∫	PROPN
ejde-1812	68	3	∞	∞	PROPN
ejde-1812	68	4	0	0	X
ejde-1812	69	1	e−λψ(t)f(t)ψ′(t)dt	e−λψ(t)f(t)ψ′(t)dt	NOUN
ejde-1812	69	2	,	,	PUNCT
ejde-1812	69	3	as	as	ADV
ejde-1812	69	4	long	long	ADV
ejde-1812	69	5	as	as	SCONJ
ejde-1812	69	6	the	the	DET
ejde-1812	69	7	integral	integral	ADJ
ejde-1812	69	8	on	on	ADP
ejde-1812	69	9	the	the	DET
ejde-1812	69	10	right	right	ADJ
ejde-1812	69	11	hand	hand	NOUN
ejde-1812	69	12	exists	exist	VERB
ejde-1812	69	13	as	as	ADP
ejde-1812	69	14	a	a	DET
ejde-1812	69	15	bochner	bochner	NOUN
ejde-1812	69	16	integral	integral	ADJ
ejde-1812	69	17	.	.	PUNCT
ejde-1812	70	1	lemma	lemma	PROPN
ejde-1812	70	2	2.6	2.6	NUM
ejde-1812	70	3	.	.	PUNCT
ejde-1812	71	1	let	let	VERB
ejde-1812	71	2	0	0	NUM
ejde-1812	71	3	<	<	X
ejde-1812	71	4	α	α	X
ejde-1812	71	5	<	<	X
ejde-1812	71	6	1	1	NUM
ejde-1812	71	7	and	and	CCONJ
ejde-1812	71	8	0	0	NUM
ejde-1812	71	9	≤	≤	NUM
ejde-1812	71	10	β	β	X
ejde-1812	71	11	≤	≤	NUM
ejde-1812	71	12	1	1	NUM
ejde-1812	71	13	.	.	PUNCT
ejde-1812	72	1	if	if	SCONJ
ejde-1812	72	2	x	x	PROPN
ejde-1812	72	3	∈	∈	PROPN
ejde-1812	72	4	c1−α−β(1−α);ψ(j	c1−α−β(1−α);ψ(j	NOUN
ejde-1812	72	5	,	,	PUNCT
ejde-1812	72	6	x	x	X
ejde-1812	72	7	)	)	PUNCT
ejde-1812	72	8	and	and	CCONJ
ejde-1812	72	9	x	x	X
ejde-1812	72	10	is	be	AUX
ejde-1812	72	11	a	a	DET
ejde-1812	72	12	solution	solution	NOUN
ejde-1812	72	13	of	of	ADP
ejde-1812	72	14	the	the	DET
ejde-1812	72	15	equations	equation	NOUN
ejde-1812	72	16	(	(	PUNCT
ejde-1812	72	17	dα	dα	ADP
ejde-1812	72	18	,	,	PUNCT
ejde-1812	72	19	β;ψx	β;ψx	PROPN
ejde-1812	72	20	)	)	PUNCT
ejde-1812	72	21	(	(	PUNCT
ejde-1812	72	22	t	t	NOUN
ejde-1812	72	23	)	)	PUNCT
ejde-1812	72	24	=	=	PUNCT
ejde-1812	72	25	ax(t	ax(t	NUM
ejde-1812	72	26	)	)	PUNCT
ejde-1812	72	27	+	+	CCONJ
ejde-1812	73	1	g(t	g(t	PROPN
ejde-1812	73	2	)	)	PUNCT
ejde-1812	73	3	,	,	PUNCT
ejde-1812	73	4	t	t	PROPN
ejde-1812	73	5	∈	∈	PROPN
ejde-1812	73	6	j	j	PROPN
ejde-1812	73	7	′	′	NUM
ejde-1812	73	8	,	,	PUNCT
ejde-1812	73	9	i(1−α)(1−β);ψx(0	i(1−α)(1−β);ψx(0	NOUN
ejde-1812	73	10	)	)	PUNCT
ejde-1812	74	1	=	=	SYM
ejde-1812	74	2	x0	x0	PROPN
ejde-1812	74	3	,	,	PUNCT
ejde-1812	74	4	(	(	PUNCT
ejde-1812	74	5	2.1	2.1	NUM
ejde-1812	74	6	)	)	PUNCT
ejde-1812	74	7	then	then	ADV
ejde-1812	74	8	x	x	PRON
ejde-1812	74	9	satisfies	satisfy	VERB
ejde-1812	74	10	the	the	DET
ejde-1812	74	11	equation	equation	NOUN
ejde-1812	74	12	x(t	x(t	PROPN
ejde-1812	74	13	)	)	PUNCT
ejde-1812	75	1	=	=	PRON
ejde-1812	75	2	(	(	PUNCT
ejde-1812	75	3	iβ(1−α)kα	iβ(1−α)kα	PROPN
ejde-1812	75	4	)	)	PUNCT
ejde-1812	76	1	(	(	PUNCT
ejde-1812	76	2	ψ(t))x0	ψ(t))x0	PROPN
ejde-1812	76	3	+	+	CCONJ
ejde-1812	76	4	∫	∫	PROPN
ejde-1812	76	5	t	t	PROPN
ejde-1812	76	6	0	0	NUM
ejde-1812	76	7	kα(ψ(t)−	kα(ψ(t)−	PROPN
ejde-1812	76	8	ψ(s))g(s)ψ′(s)ds	ψ(s))g(s)ψ′(s)ds	PROPN
ejde-1812	76	9	,	,	PUNCT
ejde-1812	76	10	where	where	SCONJ
ejde-1812	76	11	kα(t	kα(t	NOUN
ejde-1812	76	12	)	)	PUNCT
ejde-1812	76	13	=	=	PUNCT
ejde-1812	77	1	α	α	NOUN
ejde-1812	77	2	∫	∫	PROPN
ejde-1812	77	3	∞	∞	NOUN
ejde-1812	77	4	0	0	NUM
ejde-1812	78	1	tα−1σξα(σ)t	tα−1σξα(σ)t	NOUN
ejde-1812	78	2	(	(	PUNCT
ejde-1812	78	3	σt	σt	ADP
ejde-1812	78	4	α)dσ	α)dσ	PROPN
ejde-1812	78	5	,	,	PUNCT
ejde-1812	78	6	ξq(σ	ξq(σ	NUM
ejde-1812	78	7	)	)	PUNCT
ejde-1812	78	8	=	=	SYM
ejde-1812	78	9	1	1	NUM
ejde-1812	78	10	q	q	NOUN
ejde-1812	78	11	ϖq(σ	ϖq(σ	VERB
ejde-1812	78	12	−	−	NUM
ejde-1812	78	13	1	1	NUM
ejde-1812	78	14	q	q	NOUN
ejde-1812	78	15	)	)	PUNCT
ejde-1812	78	16	,	,	PUNCT
ejde-1812	78	17	σ	σ	PROPN
ejde-1812	78	18	∈	∈	PROPN
ejde-1812	78	19	(	(	PUNCT
ejde-1812	78	20	0,∞	0,∞	NOUN
ejde-1812	78	21	)	)	PUNCT
ejde-1812	78	22	,	,	PUNCT
ejde-1812	78	23	ϖq(τ	ϖq(τ	X
ejde-1812	78	24	)	)	PUNCT
ejde-1812	78	25	=	=	SYM
ejde-1812	79	1	1	1	NUM
ejde-1812	79	2	π	π	PROPN
ejde-1812	79	3	∞∑	∞∑	NUM
ejde-1812	79	4	n=1	n=1	NUM
ejde-1812	79	5	(	(	PUNCT
ejde-1812	79	6	−1)n−1τ−qn−1γ(qn+	−1)n−1τ−qn−1γ(qn+	INTJ
ejde-1812	79	7	1	1	NUM
ejde-1812	79	8	)	)	PUNCT
ejde-1812	79	9	n	n	CCONJ
ejde-1812	79	10	!	!	NOUN
ejde-1812	79	11	sin(nπq	sin(nπq	NOUN
ejde-1812	79	12	)	)	PUNCT
ejde-1812	79	13	,	,	PUNCT
ejde-1812	79	14	τ	τ	PROPN
ejde-1812	79	15	∈	∈	PROPN
ejde-1812	79	16	(	(	PUNCT
ejde-1812	79	17	0,∞	0,∞	NOUN
ejde-1812	79	18	)	)	PUNCT
ejde-1812	79	19	.	.	PUNCT
ejde-1812	80	1	proof	proof	NOUN
ejde-1812	80	2	.	.	PUNCT
ejde-1812	81	1	set	set	VERB
ejde-1812	81	2	ρ(λ	ρ(λ	PROPN
ejde-1812	81	3	)	)	PUNCT
ejde-1812	81	4	=	=	SYM
ejde-1812	82	1	∫	∫	PROPN
ejde-1812	83	1	∞	∞	PROPN
ejde-1812	83	2	0	0	PROPN
ejde-1812	83	3	e−λψ(t)g(t)ψ′(t)dt	e−λψ(t)g(t)ψ′(t)dt	NOUN
ejde-1812	83	4	.	.	PUNCT
ejde-1812	84	1	applying	apply	VERB
ejde-1812	84	2	the	the	DET
ejde-1812	84	3	ψ	ψ	NOUN
ejde-1812	84	4	-	-	ADJ
ejde-1812	84	5	laplace	laplace	ADJ
ejde-1812	84	6	transform	transform	NOUN
ejde-1812	84	7	to	to	ADP
ejde-1812	84	8	both	both	DET
ejde-1812	84	9	sides	side	NOUN
ejde-1812	84	10	of	of	ADP
ejde-1812	84	11	the	the	DET
ejde-1812	84	12	first	first	ADJ
ejde-1812	84	13	equation	equation	NOUN
ejde-1812	84	14	of	of	ADP
ejde-1812	84	15	(	(	PUNCT
ejde-1812	84	16	2.1	2.1	NUM
ejde-1812	84	17	)	)	PUNCT
ejde-1812	84	18	,	,	PUNCT
ejde-1812	84	19	we	we	PRON
ejde-1812	84	20	obtain	obtain	VERB
ejde-1812	84	21	λαlψ[x](λ)−	λαlψ[x](λ)−	PROPN
ejde-1812	84	22	λβ(α−1)i(1−α)(1−β);ψx(0	λβ(α−1)i(1−α)(1−β);ψx(0	NOUN
ejde-1812	84	23	)	)	PUNCT
ejde-1812	84	24	=	=	SYM
ejde-1812	84	25	alψ[x](λ	alψ[x](λ	PROPN
ejde-1812	84	26	)	)	PUNCT
ejde-1812	85	1	+	+	CCONJ
ejde-1812	85	2	ρ(λ	ρ(λ	PROPN
ejde-1812	85	3	)	)	PUNCT
ejde-1812	85	4	.	.	PUNCT
ejde-1812	86	1	then	then	ADV
ejde-1812	86	2	(	(	PUNCT
ejde-1812	86	3	λαi	λαi	NOUN
ejde-1812	86	4	−a)x̃(λ	−a)x̃(λ	NOUN
ejde-1812	86	5	)	)	PUNCT
ejde-1812	87	1	=	=	SYM
ejde-1812	87	2	λβ(α−1)x0	λβ(α−1)x0	PROPN
ejde-1812	87	3	+	+	CCONJ
ejde-1812	87	4	ρ(λ	ρ(λ	PROPN
ejde-1812	87	5	)	)	PUNCT
ejde-1812	87	6	;	;	PUNCT
ejde-1812	87	7	thus	thus	ADV
ejde-1812	87	8	ũ(λ	ũ(λ	PROPN
ejde-1812	87	9	)	)	PUNCT
ejde-1812	87	10	=	=	SYM
ejde-1812	88	1	λβ(α−1)(λαi	λβ(α−1)(λαi	NUM
ejde-1812	88	2	−a)−1x0	−a)−1x0	NOUN
ejde-1812	88	3	+	+	CCONJ
ejde-1812	88	4	(	(	PUNCT
ejde-1812	88	5	λαi	λαi	VERB
ejde-1812	88	6	−a)−1ρ(λ	−a)−1ρ(λ	PROPN
ejde-1812	88	7	)	)	PUNCT
ejde-1812	89	1	=	=	SYM
ejde-1812	89	2	λβ(α−1	λβ(α−1	PROPN
ejde-1812	89	3	)	)	PUNCT
ejde-1812	89	4	∫	∫	PROPN
ejde-1812	90	1	∞	∞	NUM
ejde-1812	90	2	0	0	NUM
ejde-1812	91	1	e−λ	e−λ	PRON
ejde-1812	91	2	αst	αst	VERB
ejde-1812	91	3	(	(	PUNCT
ejde-1812	91	4	s)x0ds+	s)x0ds+	ADJ
ejde-1812	91	5	∫	∫	PROPN
ejde-1812	91	6	∞	∞	NUM
ejde-1812	91	7	0	0	NUM
ejde-1812	91	8	e−λ	e−λ	PRON
ejde-1812	91	9	αst	αst	VERB
ejde-1812	91	10	(	(	PUNCT
ejde-1812	91	11	s)ρ(λ)ds	s)ρ(λ)d	VERB
ejde-1812	91	12	.	.	PUNCT
ejde-1812	92	1	we	we	PRON
ejde-1812	92	2	consider	consider	VERB
ejde-1812	92	3	the	the	DET
ejde-1812	92	4	one	one	NUM
ejde-1812	92	5	-	-	PUNCT
ejde-1812	92	6	sided	sided	ADJ
ejde-1812	92	7	stable	stable	ADJ
ejde-1812	92	8	probability	probability	NOUN
ejde-1812	92	9	density	density	NOUN
ejde-1812	92	10	function	function	NOUN
ejde-1812	92	11	in	in	ADP
ejde-1812	92	12	r+	r+	NOUN
ejde-1812	92	13	as	as	ADP
ejde-1812	92	14	ϖα(σ	ϖα(σ	X
ejde-1812	92	15	)	)	PUNCT
ejde-1812	92	16	=	=	SYM
ejde-1812	93	1	1	1	NUM
ejde-1812	93	2	π	π	PROPN
ejde-1812	93	3	∞∑	∞∑	NUM
ejde-1812	93	4	n=1	n=1	PUNCT
ejde-1812	93	5	(	(	PUNCT
ejde-1812	93	6	−1)n−1σ−nα−1γ(nα+	−1)n−1σ−nα−1γ(nα+	NOUN
ejde-1812	93	7	1	1	NUM
ejde-1812	93	8	)	)	PUNCT
ejde-1812	93	9	n	n	CCONJ
ejde-1812	93	10	!	!	PUNCT
ejde-1812	93	11	sin(nπα	sin(nπα	NOUN
ejde-1812	93	12	)	)	PUNCT
ejde-1812	93	13	,	,	PUNCT
ejde-1812	93	14	σ	σ	PROPN
ejde-1812	93	15	∈	∈	PROPN
ejde-1812	93	16	(	(	PUNCT
ejde-1812	93	17	0,∞	0,∞	NOUN
ejde-1812	93	18	)	)	PUNCT
ejde-1812	93	19	,	,	PUNCT
ejde-1812	93	20	whose	whose	DET
ejde-1812	93	21	laplace	laplace	NOUN
ejde-1812	93	22	transform	transform	NOUN
ejde-1812	93	23	is	be	AUX
ejde-1812	93	24	∫	∫	PROPN
ejde-1812	93	25	∞	∞	NUM
ejde-1812	93	26	0	0	PUNCT
ejde-1812	93	27	e−λσϖα(σ)dσ	e−λσϖα(σ)dσ	NOUN
ejde-1812	93	28	=	=	SYM
ejde-1812	93	29	e−λ	e−λ	NOUN
ejde-1812	93	30	α	α	NOUN
ejde-1812	93	31	,	,	PUNCT
ejde-1812	93	32	α	α	PROPN
ejde-1812	93	33	∈	∈	PROPN
ejde-1812	93	34	(	(	PUNCT
ejde-1812	93	35	0	0	NUM
ejde-1812	93	36	,	,	PUNCT
ejde-1812	93	37	1	1	NUM
ejde-1812	93	38	)	)	PUNCT
ejde-1812	93	39	.	.	PUNCT
ejde-1812	94	1	(	(	PUNCT
ejde-1812	94	2	2.2	2.2	NUM
ejde-1812	94	3	)	)	PUNCT
ejde-1812	94	4	then	then	ADV
ejde-1812	94	5	,	,	PUNCT
ejde-1812	94	6	using	use	VERB
ejde-1812	94	7	(	(	PUNCT
ejde-1812	94	8	2.2	2.2	NUM
ejde-1812	94	9	)	)	PUNCT
ejde-1812	94	10	we	we	PRON
ejde-1812	94	11	obtain∫	obtain∫	VERB
ejde-1812	94	12	∞	∞	PROPN
ejde-1812	94	13	0	0	NUM
ejde-1812	94	14	e−λ	e−λ	PROPN
ejde-1812	94	15	αst	αst	VERB
ejde-1812	94	16	(	(	PUNCT
ejde-1812	94	17	s)x0ds	s)x0ds	NOUN
ejde-1812	94	18	=	=	PUNCT
ejde-1812	94	19	∫	∫	PROPN
ejde-1812	95	1	∞	∞	PROPN
ejde-1812	95	2	0	0	NUM
ejde-1812	96	1	∫	∫	PROPN
ejde-1812	96	2	∞	∞	NOUN
ejde-1812	96	3	0	0	NUM
ejde-1812	97	1	e−λtσαtα−1ϖα(σ)t	e−λtσαtα−1ϖα(σ)t	PROPN
ejde-1812	97	2	(	(	PUNCT
ejde-1812	97	3	t	t	PROPN
ejde-1812	97	4	α)x0dσdt	α)x0dσdt	NUM
ejde-1812	98	1	=	=	SYM
ejde-1812	98	2	∫	∫	PROPN
ejde-1812	98	3	∞	∞	PROPN
ejde-1812	98	4	0	0	PROPN
ejde-1812	98	5	e−λt	e−λt	NOUN
ejde-1812	98	6	[	[	PUNCT
ejde-1812	98	7	α	α	NOUN
ejde-1812	98	8	∫	∫	PROPN
ejde-1812	98	9	∞	∞	NUM
ejde-1812	98	10	0	0	NUM
ejde-1812	99	1	tα−1	tα−1	NOUN
ejde-1812	99	2	σα	σα	PRON
ejde-1812	99	3	ϖα(σ)t	ϖα(σ)t	X
ejde-1812	100	1	(	(	PUNCT
ejde-1812	100	2	tα	tα	PROPN
ejde-1812	100	3	σα	σα	PROPN
ejde-1812	100	4	)	)	PUNCT
ejde-1812	101	1	x0dσ	x0dσ	X
ejde-1812	101	2	]	]	PUNCT
ejde-1812	102	1	dt	dt	X
ejde-1812	102	2	4	4	NUM
ejde-1812	102	3	j.	j.	PROPN
ejde-1812	102	4	liang	liang	PROPN
ejde-1812	102	5	,	,	PUNCT
ejde-1812	102	6	y.	y.	PROPN
ejde-1812	102	7	mu	mu	PROPN
ejde-1812	102	8	,	,	PUNCT
ejde-1812	102	9	t.-j	t.-j	PROPN
ejde-1812	102	10	.	.	PUNCT
ejde-1812	103	1	xiao	xiao	PROPN
ejde-1812	103	2	ejde-2025/109	ejde-2025/109	PUNCT
ejde-1812	104	1	=	=	PUNCT
ejde-1812	104	2	∫	∫	PROPN
ejde-1812	104	3	∞	∞	PROPN
ejde-1812	104	4	0	0	NUM
ejde-1812	104	5	e−λψ(t	e−λψ(t	NUM
ejde-1812	104	6	)	)	PUNCT
ejde-1812	104	7	[	[	PUNCT
ejde-1812	104	8	α	α	X
ejde-1812	104	9	∫	∫	PROPN
ejde-1812	104	10	∞	∞	NOUN
ejde-1812	104	11	0	0	PUNCT
ejde-1812	105	1	ψα−1(t	ψα−1(t	ADJ
ejde-1812	105	2	)	)	PUNCT
ejde-1812	106	1	σα	σα	PROPN
ejde-1812	106	2	ϖα(σ)t	ϖα(σ)t	X
ejde-1812	106	3	(	(	PUNCT
ejde-1812	106	4	ψα(t	ψα(t	NOUN
ejde-1812	106	5	)	)	PUNCT
ejde-1812	106	6	σα	σα	NOUN
ejde-1812	106	7	)	)	PUNCT
ejde-1812	106	8	x0dσ	x0dσ	X
ejde-1812	106	9	]	]	PUNCT
ejde-1812	107	1	ψ′(t)dt	ψ′(t)dt	PROPN
ejde-1812	107	2	,	,	PUNCT
ejde-1812	107	3	and∫	and∫	ADV
ejde-1812	107	4	∞	∞	NUM
ejde-1812	107	5	0	0	NUM
ejde-1812	107	6	e−λ	e−λ	PRON
ejde-1812	107	7	αst	αst	NUM
ejde-1812	107	8	(	(	PUNCT
ejde-1812	107	9	s)ρ(λ)ds	s)ρ(λ)ds	PROPN
ejde-1812	107	10	=	=	SYM
ejde-1812	107	11	∫	∫	PROPN
ejde-1812	107	12	∞	∞	PROPN
ejde-1812	107	13	0	0	NUM
ejde-1812	107	14	∫	∫	PROPN
ejde-1812	107	15	∞	∞	PROPN
ejde-1812	107	16	0	0	NUM
ejde-1812	107	17	e−λτσατα−1ϖα(σ)t	e−λτσατα−1ϖα(σ)t	PROPN
ejde-1812	107	18	(	(	PUNCT
ejde-1812	107	19	τ	τ	PROPN
ejde-1812	107	20	α	α	PROPN
ejde-1812	107	21	)	)	PUNCT
ejde-1812	107	22	(	(	PUNCT
ejde-1812	107	23	∫	∫	PROPN
ejde-1812	107	24	∞	∞	PROPN
ejde-1812	107	25	0	0	NUM
ejde-1812	107	26	e−λtg(ζ(t))dt	e−λtg(ζ(t))dt	NOUN
ejde-1812	107	27	)	)	PUNCT
ejde-1812	107	28	dσdτ	dσdτ	NOUN
ejde-1812	107	29	=	=	PROPN
ejde-1812	107	30	α	α	NOUN
ejde-1812	107	31	∫	∫	PROPN
ejde-1812	107	32	∞	∞	NUM
ejde-1812	107	33	0	0	NUM
ejde-1812	107	34	∫	∫	PROPN
ejde-1812	107	35	∞	∞	PROPN
ejde-1812	107	36	0	0	NUM
ejde-1812	107	37	e−λϑ	e−λϑ	PROPN
ejde-1812	107	38	ϑα−1	ϑα−1	PROPN
ejde-1812	107	39	σα	σα	PRON
ejde-1812	107	40	ϖα(σ)t	ϖα(σ)t	X
ejde-1812	107	41	(	(	PUNCT
ejde-1812	107	42	ϑα	ϑα	ADP
ejde-1812	107	43	σα	σα	PROPN
ejde-1812	107	44	)	)	PUNCT
ejde-1812	107	45	(	(	PUNCT
ejde-1812	107	46	∫	∫	PROPN
ejde-1812	107	47	∞	∞	PROPN
ejde-1812	107	48	0	0	NUM
ejde-1812	107	49	e−λtg(ζ(t))dt	e−λtg(ζ(t))dt	NOUN
ejde-1812	107	50	)	)	PUNCT
ejde-1812	107	51	dϑdσ	dϑdσ	NOUN
ejde-1812	107	52	=	=	PUNCT
ejde-1812	107	53	α	α	NOUN
ejde-1812	107	54	∫	∫	PROPN
ejde-1812	107	55	∞	∞	NUM
ejde-1812	107	56	0	0	NUM
ejde-1812	108	1	(	(	PUNCT
ejde-1812	108	2	∫	∫	PROPN
ejde-1812	108	3	∞	∞	PROPN
ejde-1812	108	4	0	0	NUM
ejde-1812	108	5	∫	∫	PROPN
ejde-1812	108	6	τ	τ	PROPN
ejde-1812	108	7	0	0	NUM
ejde-1812	108	8	e−λτ	e−λτ	PROPN
ejde-1812	108	9	(	(	PUNCT
ejde-1812	108	10	τ	τ	X
ejde-1812	108	11	−	−	PROPN
ejde-1812	108	12	t)α−1	t)α−1	VERB
ejde-1812	108	13	σα	σα	PRON
ejde-1812	108	14	ϖα(σ)t	ϖα(σ)t	X
ejde-1812	108	15	(	(	PUNCT
ejde-1812	108	16	(	(	PUNCT
ejde-1812	108	17	τ	τ	PROPN
ejde-1812	108	18	−	−	PROPN
ejde-1812	108	19	t)α	t)α	NOUN
ejde-1812	108	20	σα	σα	PROPN
ejde-1812	108	21	)	)	PUNCT
ejde-1812	108	22	g(ζ(t))dtdτ	g(ζ(t))dtdτ	NOUN
ejde-1812	108	23	)	)	PUNCT
ejde-1812	109	1	dσ	dσ	PROPN
ejde-1812	109	2	=	=	SYM
ejde-1812	109	3	∫	∫	PROPN
ejde-1812	109	4	∞	∞	PROPN
ejde-1812	109	5	0	0	NUM
ejde-1812	109	6	e−λψ(t	e−λψ(t	NUM
ejde-1812	109	7	)	)	PUNCT
ejde-1812	109	8	[	[	PUNCT
ejde-1812	109	9	α	α	X
ejde-1812	109	10	∫	∫	PROPN
ejde-1812	109	11	ψ(t	ψ(t	PROPN
ejde-1812	109	12	)	)	PUNCT
ejde-1812	109	13	0	0	NUM
ejde-1812	110	1	∫	∫	PROPN
ejde-1812	110	2	∞	∞	PROPN
ejde-1812	110	3	0	0	NUM
ejde-1812	111	1	(	(	PUNCT
ejde-1812	111	2	ψ(t)−	ψ(t)−	PROPN
ejde-1812	111	3	s)α−1	s)α−1	VERB
ejde-1812	111	4	σα	σα	PROPN
ejde-1812	111	5	ϖα(σ)t	ϖα(σ)t	X
ejde-1812	112	1	(	(	PUNCT
ejde-1812	112	2	(	(	PUNCT
ejde-1812	112	3	ψ(t)−	ψ(t)−	PROPN
ejde-1812	112	4	s)α	s)α	VERB
ejde-1812	112	5	σα	σα	PROPN
ejde-1812	112	6	)	)	PUNCT
ejde-1812	112	7	g(ζ(s))dσds	g(ζ(s))dσds	PROPN
ejde-1812	112	8	]	]	PUNCT
ejde-1812	112	9	×	×	PROPN
ejde-1812	112	10	ψ′(t)dt	ψ′(t)dt	PROPN
ejde-1812	112	11	=	=	PUNCT
ejde-1812	113	1	∫	∫	PROPN
ejde-1812	114	1	∞	∞	PROPN
ejde-1812	114	2	0	0	NUM
ejde-1812	114	3	e−λψ(t	e−λψ(t	NUM
ejde-1812	114	4	)	)	PUNCT
ejde-1812	114	5	[	[	PUNCT
ejde-1812	114	6	α	α	X
ejde-1812	114	7	∫	∫	PROPN
ejde-1812	114	8	t	t	PROPN
ejde-1812	114	9	0	0	NUM
ejde-1812	114	10	∫	∫	PROPN
ejde-1812	114	11	∞	∞	PROPN
ejde-1812	114	12	0	0	NUM
ejde-1812	114	13	(	(	PUNCT
ejde-1812	114	14	ψ(t)−	ψ(t)−	PROPN
ejde-1812	114	15	ψ(s))α−1σξα(σ)t	ψ(s))α−1σξα(σ)t	PROPN
ejde-1812	114	16	(	(	PUNCT
ejde-1812	114	17	σ(ψ(t)−	σ(ψ(t)−	PROPN
ejde-1812	114	18	ψ(s))α)g(s)ψ′(s)dσds	ψ(s))α)g(s)ψ′(s)dσds	X
ejde-1812	114	19	]	]	PUNCT
ejde-1812	114	20	ψ′(t)dt	ψ′(t)dt	PROPN
ejde-1812	114	21	.	.	PUNCT
ejde-1812	115	1	set	set	VERB
ejde-1812	115	2	kα(t	kα(t	NOUN
ejde-1812	115	3	)	)	PUNCT
ejde-1812	115	4	=	=	PUNCT
ejde-1812	116	1	α	α	NOUN
ejde-1812	116	2	∫	∫	PROPN
ejde-1812	116	3	∞	∞	NOUN
ejde-1812	116	4	0	0	NUM
ejde-1812	117	1	tα−1σξα(σ)t	tα−1σξα(σ)t	NOUN
ejde-1812	117	2	(	(	PUNCT
ejde-1812	117	3	σt	σt	ADP
ejde-1812	117	4	α)dσ	α)dσ	PROPN
ejde-1812	117	5	.	.	PROPN
ejde-1812	118	1	since	since	SCONJ
ejde-1812	118	2	the	the	DET
ejde-1812	118	3	laplace	laplace	NOUN
ejde-1812	118	4	transform	transform	NOUN
ejde-1812	118	5	of	of	ADP
ejde-1812	118	6	f(t	f(t	PROPN
ejde-1812	118	7	)	)	PUNCT
ejde-1812	118	8	:	:	PUNCT
ejde-1812	118	9	=	=	PUNCT
ejde-1812	118	10	tβ(1−α)−1	tβ(1−α)−1	NOUN
ejde-1812	118	11	γ(β(1−	γ(β(1−	PROPN
ejde-1812	118	12	α	α	NOUN
ejde-1812	118	13	)	)	PUNCT
ejde-1812	118	14	)	)	PUNCT
ejde-1812	118	15	(	(	PUNCT
ejde-1812	118	16	0	0	NUM
ejde-1812	118	17	<	<	X
ejde-1812	118	18	β	β	X
ejde-1812	118	19	≤	≤	NUM
ejde-1812	118	20	1	1	NUM
ejde-1812	118	21	)	)	PUNCT
ejde-1812	118	22	is	be	AUX
ejde-1812	118	23	l[f(t)](λ	l[f(t)](λ	PRON
ejde-1812	118	24	)	)	PUNCT
ejde-1812	118	25	=	=	SYM
ejde-1812	118	26	λβ(α−1	λβ(α−1	PROPN
ejde-1812	118	27	)	)	PUNCT
ejde-1812	118	28	,	,	PUNCT
ejde-1812	118	29	we	we	PRON
ejde-1812	118	30	have	have	VERB
ejde-1812	118	31	that	that	PRON
ejde-1812	118	32	for	for	ADP
ejde-1812	118	33	0	0	NUM
ejde-1812	118	34	<	<	X
ejde-1812	118	35	β	β	X
ejde-1812	118	36	≤	≤	NUM
ejde-1812	118	37	1	1	NUM
ejde-1812	118	38	,	,	PUNCT
ejde-1812	118	39	λβ(α−1	λβ(α−1	NOUN
ejde-1812	118	40	)	)	PUNCT
ejde-1812	118	41	∫	∫	PROPN
ejde-1812	119	1	∞	∞	NUM
ejde-1812	119	2	0	0	NUM
ejde-1812	119	3	e−λ	e−λ	PRON
ejde-1812	119	4	αst	αst	VERB
ejde-1812	119	5	(	(	PUNCT
ejde-1812	119	6	s)x0ds	s)x0ds	NOUN
ejde-1812	119	7	=	=	PUNCT
ejde-1812	119	8	l[f(t)](λ)l[kα(t)](λ)x0	l[f(t)](λ)l[kα(t)](λ)x0	PUNCT
ejde-1812	119	9	=	=	PUNCT
ejde-1812	119	10	l	l	PUNCT
ejde-1812	120	1	[	[	X
ejde-1812	120	2	(	(	PUNCT
ejde-1812	120	3	f	f	PROPN
ejde-1812	120	4	∗kα)(t	∗kα)(t	PROPN
ejde-1812	120	5	)	)	PUNCT
ejde-1812	120	6	]	]	PUNCT
ejde-1812	121	1	(	(	PUNCT
ejde-1812	121	2	λ)x0	λ)x0	PROPN
ejde-1812	121	3	=	=	SYM
ejde-1812	121	4	lψ	lψ	PROPN
ejde-1812	122	1	[	[	X
ejde-1812	122	2	(	(	PUNCT
ejde-1812	122	3	iβ(1−α)kα	iβ(1−α)kα	PROPN
ejde-1812	122	4	)	)	PUNCT
ejde-1812	122	5	(	(	PUNCT
ejde-1812	122	6	ψ(t	ψ(t	PROPN
ejde-1812	122	7	)	)	PUNCT
ejde-1812	122	8	)	)	PUNCT
ejde-1812	122	9	]	]	PUNCT
ejde-1812	123	1	(	(	PUNCT
ejde-1812	123	2	λ)x0	λ)x0	PROPN
ejde-1812	123	3	.	.	PROPN
ejde-1812	123	4	observe	observe	VERB
ejde-1812	123	5	that∫	that∫	NOUN
ejde-1812	123	6	∞	∞	NOUN
ejde-1812	123	7	0	0	NUM
ejde-1812	124	1	e−λ	e−λ	PRON
ejde-1812	124	2	αst	αst	VERB
ejde-1812	124	3	(	(	PUNCT
ejde-1812	124	4	s)ρ(λ)ds	s)ρ(λ)ds	PROPN
ejde-1812	124	5	=	=	SYM
ejde-1812	124	6	∫	∫	PROPN
ejde-1812	124	7	∞	∞	PROPN
ejde-1812	124	8	0	0	NUM
ejde-1812	124	9	e−λψ(t	e−λψ(t	NUM
ejde-1812	124	10	)	)	PUNCT
ejde-1812	124	11	[	[	PUNCT
ejde-1812	124	12	∫	∫	PROPN
ejde-1812	124	13	t	t	PROPN
ejde-1812	124	14	0	0	PROPN
ejde-1812	124	15	kα(ψ(t)−	kα(ψ(t)−	PROPN
ejde-1812	124	16	ψ(s))g(s)ψ′(s)ds	ψ(s))g(s)ψ′(s)ds	PROPN
ejde-1812	124	17	]	]	PUNCT
ejde-1812	124	18	ψ′(t)dt	ψ′(t)dt	PROPN
ejde-1812	124	19	.	.	PUNCT
ejde-1812	125	1	(	(	PUNCT
ejde-1812	125	2	2.3	2.3	NUM
ejde-1812	125	3	)	)	PUNCT
ejde-1812	125	4	when	when	SCONJ
ejde-1812	125	5	β	β	X
ejde-1812	125	6	=	=	SYM
ejde-1812	125	7	0	0	NUM
ejde-1812	125	8	,	,	PUNCT
ejde-1812	125	9	(	(	PUNCT
ejde-1812	125	10	2.3	2.3	NUM
ejde-1812	125	11	)	)	PUNCT
ejde-1812	125	12	also	also	ADV
ejde-1812	125	13	holds	hold	VERB
ejde-1812	125	14	if	if	SCONJ
ejde-1812	125	15	we	we	PRON
ejde-1812	125	16	keep	keep	VERB
ejde-1812	125	17	in	in	ADP
ejde-1812	125	18	mind	mind	NOUN
ejde-1812	125	19	that	that	SCONJ
ejde-1812	125	20	i0kα	i0kα	PUNCT
ejde-1812	126	1	=	=	SYM
ejde-1812	126	2	kα	kα	PROPN
ejde-1812	126	3	.	.	PUNCT
ejde-1812	127	1	therefore	therefore	ADV
ejde-1812	127	2	,	,	PUNCT
ejde-1812	127	3	for	for	ADP
ejde-1812	127	4	0	0	NUM
ejde-1812	127	5	<	<	X
ejde-1812	127	6	α	α	X
ejde-1812	127	7	<	<	X
ejde-1812	127	8	1	1	NUM
ejde-1812	127	9	and	and	CCONJ
ejde-1812	127	10	0	0	NUM
ejde-1812	127	11	≤	≤	NUM
ejde-1812	127	12	β	β	X
ejde-1812	127	13	≤	≤	NUM
ejde-1812	127	14	1	1	NUM
ejde-1812	127	15	,	,	PUNCT
ejde-1812	127	16	we	we	PRON
ejde-1812	127	17	have	have	VERB
ejde-1812	127	18	x(t	x(t	PROPN
ejde-1812	127	19	)	)	PUNCT
ejde-1812	127	20	=	=	PRON
ejde-1812	127	21	(	(	PUNCT
ejde-1812	127	22	iβ(1−α)kα	iβ(1−α)kα	PROPN
ejde-1812	127	23	)	)	PUNCT
ejde-1812	128	1	(	(	PUNCT
ejde-1812	128	2	ψ(t))x0	ψ(t))x0	PROPN
ejde-1812	128	3	+	+	CCONJ
ejde-1812	128	4	∫	∫	PROPN
ejde-1812	128	5	t	t	PROPN
ejde-1812	128	6	0	0	PROPN
ejde-1812	128	7	kα(ψ(t)−	kα(ψ(t)−	PROPN
ejde-1812	128	8	ψ(s))g(s)ψ′(s)ds	ψ(s))g(s)ψ′(s)ds	PROPN
ejde-1812	128	9	,	,	PUNCT
ejde-1812	128	10	which	which	PRON
ejde-1812	128	11	completes	complete	VERB
ejde-1812	128	12	the	the	DET
ejde-1812	128	13	proof	proof	NOUN
ejde-1812	128	14	.	.	PUNCT
ejde-1812	129	1	□	□	PUNCT
ejde-1812	129	2	remark	remark	NOUN
ejde-1812	129	3	2.7	2.7	NUM
ejde-1812	129	4	.	.	PUNCT
ejde-1812	130	1	(	(	PUNCT
ejde-1812	130	2	i	i	NOUN
ejde-1812	130	3	)	)	PUNCT
ejde-1812	130	4	from	from	ADP
ejde-1812	130	5	[	[	X
ejde-1812	130	6	11	11	NUM
ejde-1812	130	7	]	]	PUNCT
ejde-1812	130	8	we	we	PRON
ejde-1812	130	9	have	have	VERB
ejde-1812	130	10	∥kα(t)∥	∥kα(t)∥	NOUN
ejde-1812	130	11	≤	≤	NUM
ejde-1812	130	12	mtα−1	mtα−1	PROPN
ejde-1812	130	13	γ(α	γ(α	PROPN
ejde-1812	130	14	)	)	PUNCT
ejde-1812	130	15	,	,	PUNCT
ejde-1812	130	16	t	t	X
ejde-1812	130	17	>	>	X
ejde-1812	130	18	0	0	NUM
ejde-1812	130	19	.	.	PUNCT
ejde-1812	131	1	(	(	PUNCT
ejde-1812	131	2	ii	ii	NOUN
ejde-1812	131	3	)	)	PUNCT
ejde-1812	131	4	∥	∥	PROPN
ejde-1812	131	5	(	(	PUNCT
ejde-1812	131	6	iβ(1−α)kα	iβ(1−α)kα	PROPN
ejde-1812	131	7	)	)	PUNCT
ejde-1812	131	8	(	(	PUNCT
ejde-1812	132	1	t)∥	t)∥	NUM
ejde-1812	132	2	≤	≤	NUM
ejde-1812	132	3	mtα+β(1−α)−1	mtα+β(1−α)−1	PROPN
ejde-1812	132	4	γ(α+	γ(α+	DET
ejde-1812	132	5	β(1−	β(1−	NOUN
ejde-1812	132	6	α	α	X
ejde-1812	132	7	)	)	PUNCT
ejde-1812	132	8	)	)	PUNCT
ejde-1812	132	9	,	,	PUNCT
ejde-1812	132	10	t	t	X
ejde-1812	132	11	>	>	X
ejde-1812	132	12	0	0	X
ejde-1812	132	13	.	.	PUNCT
ejde-1812	132	14	proof	proof	NOUN
ejde-1812	132	15	.	.	PUNCT
ejde-1812	133	1	∥	∥	X
ejde-1812	133	2	(	(	PUNCT
ejde-1812	133	3	iβ(1−α)kα	iβ(1−α)kα	PROPN
ejde-1812	133	4	)	)	PUNCT
ejde-1812	133	5	(	(	PUNCT
ejde-1812	133	6	t)∥	t)∥	X
ejde-1812	133	7	=	=	SYM
ejde-1812	133	8	∥∥	∥∥	X
ejde-1812	133	9	1	1	NUM
ejde-1812	133	10	γ(β(1−	γ(β(1−	PROPN
ejde-1812	133	11	α	α	NOUN
ejde-1812	133	12	)	)	PUNCT
ejde-1812	133	13	)	)	PUNCT
ejde-1812	134	1	∫	∫	PROPN
ejde-1812	135	1	t	t	PROPN
ejde-1812	135	2	0	0	NUM
ejde-1812	135	3	(	(	PUNCT
ejde-1812	135	4	t−	t−	PROPN
ejde-1812	135	5	s)β(1−α)−1kα(s)ds	s)β(1−α)−1kα(s)ds	ADV
ejde-1812	135	6	∥∥	∥∥	PUNCT
ejde-1812	135	7	ejde-2025/109	ejde-2025/109	ADP
ejde-1812	135	8	evolution	evolution	NOUN
ejde-1812	135	9	ψ	ψ	NOUN
ejde-1812	135	10	-	-	ADJ
ejde-1812	135	11	hilfer	hilfer	NOUN
ejde-1812	135	12	fractional	fractional	ADJ
ejde-1812	135	13	differential	differential	ADJ
ejde-1812	135	14	equations	equation	NOUN
ejde-1812	135	15	5	5	NUM
ejde-1812	135	16	≤	≤	NUM
ejde-1812	135	17	m	m	VERB
ejde-1812	135	18	γ(α)γ(β(1−	γ(α)γ(β(1−	PUNCT
ejde-1812	135	19	α	α	NOUN
ejde-1812	135	20	)	)	PUNCT
ejde-1812	135	21	)	)	PUNCT
ejde-1812	136	1	∫	∫	PROPN
ejde-1812	136	2	t	t	PROPN
ejde-1812	136	3	0	0	NUM
ejde-1812	137	1	(	(	PUNCT
ejde-1812	137	2	t−	t−	PROPN
ejde-1812	137	3	s)β(1−α)−1sα−1ds	s)β(1−α)−1sα−1ds	PROPN
ejde-1812	137	4	=	=	SYM
ejde-1812	137	5	mtα+β(1−α)−1	mtα+β(1−α)−1	PROPN
ejde-1812	137	6	γ(α+	γ(α+	DET
ejde-1812	137	7	β(1−	β(1−	NOUN
ejde-1812	137	8	α	α	X
ejde-1812	137	9	)	)	PUNCT
ejde-1812	137	10	)	)	PUNCT
ejde-1812	137	11	.	.	PUNCT
ejde-1812	138	1	□	□	PUNCT
ejde-1812	138	2	3	3	X
ejde-1812	138	3	.	.	NUM
ejde-1812	138	4	approximate	approximate	ADJ
ejde-1812	138	5	controllability	controllability	NOUN
ejde-1812	138	6	in	in	ADP
ejde-1812	138	7	this	this	DET
ejde-1812	138	8	section	section	NOUN
ejde-1812	138	9	,	,	PUNCT
ejde-1812	138	10	we	we	PRON
ejde-1812	138	11	consider	consider	VERB
ejde-1812	138	12	the	the	DET
ejde-1812	138	13	approximate	approximate	ADJ
ejde-1812	138	14	controllability	controllability	NOUN
ejde-1812	138	15	of	of	ADP
ejde-1812	138	16	the	the	DET
ejde-1812	138	17	following	following	ADJ
ejde-1812	138	18	ψ	ψ	NOUN
ejde-1812	138	19	-	-	ADJ
ejde-1812	138	20	hilfer	hilfer	NOUN
ejde-1812	138	21	fractional	fractional	ADJ
ejde-1812	138	22	control	control	NOUN
ejde-1812	138	23	system	system	NOUN
ejde-1812	138	24	in	in	ADP
ejde-1812	138	25	a	a	DET
ejde-1812	138	26	banach	banach	NOUN
ejde-1812	138	27	space	space	NOUN
ejde-1812	138	28	x	x	X
ejde-1812	138	29	:(	:(	X
ejde-1812	138	30	dα	dα	NOUN
ejde-1812	138	31	,	,	PUNCT
ejde-1812	138	32	β;ψx	β;ψx	PROPN
ejde-1812	138	33	)	)	PUNCT
ejde-1812	138	34	(	(	PUNCT
ejde-1812	138	35	t	t	NOUN
ejde-1812	138	36	)	)	PUNCT
ejde-1812	138	37	=	=	SYM
ejde-1812	138	38	ax(t	ax(t	NUM
ejde-1812	138	39	)	)	PUNCT
ejde-1812	139	1	+	+	NOUN
ejde-1812	139	2	bu(t	bu(t	X
ejde-1812	139	3	)	)	PUNCT
ejde-1812	139	4	+	+	CCONJ
ejde-1812	139	5	f(t	f(t	NOUN
ejde-1812	139	6	,	,	PUNCT
ejde-1812	139	7	x(t	x(t	PROPN
ejde-1812	139	8	)	)	PUNCT
ejde-1812	139	9	)	)	PUNCT
ejde-1812	139	10	,	,	PUNCT
ejde-1812	139	11	t	t	PROPN
ejde-1812	139	12	∈	∈	PROPN
ejde-1812	139	13	j	j	PROPN
ejde-1812	139	14	′	′	NUM
ejde-1812	139	15	,	,	PUNCT
ejde-1812	139	16	i(1−α)(1−β);ψx(0	i(1−α)(1−β);ψx(0	NOUN
ejde-1812	139	17	)	)	PUNCT
ejde-1812	139	18	=	=	SYM
ejde-1812	139	19	x0	x0	PROPN
ejde-1812	139	20	,	,	PUNCT
ejde-1812	139	21	(	(	PUNCT
ejde-1812	139	22	3.1	3.1	NUM
ejde-1812	139	23	)	)	PUNCT
ejde-1812	139	24	where	where	SCONJ
ejde-1812	139	25	dα	dα	NOUN
ejde-1812	139	26	,	,	PUNCT
ejde-1812	139	27	β;ψ	β;ψ	PRON
ejde-1812	139	28	,	,	PUNCT
ejde-1812	139	29	α	α	PROPN
ejde-1812	139	30	∈	∈	PROPN
ejde-1812	139	31	(	(	PUNCT
ejde-1812	139	32	0	0	NUM
ejde-1812	139	33	,	,	PUNCT
ejde-1812	139	34	1	1	NUM
ejde-1812	139	35	)	)	PUNCT
ejde-1812	139	36	,	,	PUNCT
ejde-1812	139	37	β	β	X
ejde-1812	139	38	∈	∈	PROPN
ejde-1812	140	1	[	[	X
ejde-1812	140	2	0	0	NUM
ejde-1812	140	3	,	,	PUNCT
ejde-1812	140	4	1	1	NUM
ejde-1812	140	5	]	]	PUNCT
ejde-1812	140	6	,	,	PUNCT
ejde-1812	140	7	is	be	AUX
ejde-1812	140	8	the	the	DET
ejde-1812	140	9	ψ	ψ	NOUN
ejde-1812	140	10	-	-	ADJ
ejde-1812	140	11	hilfer	hilfer	NOUN
ejde-1812	140	12	fractional	fractional	ADJ
ejde-1812	140	13	derivative	derivative	NOUN
ejde-1812	140	14	of	of	ADP
ejde-1812	140	15	order	order	NOUN
ejde-1812	140	16	α	α	NOUN
ejde-1812	140	17	and	and	CCONJ
ejde-1812	140	18	type	type	NOUN
ejde-1812	140	19	β	β	NOUN
ejde-1812	140	20	with	with	ADP
ejde-1812	140	21	the	the	DET
ejde-1812	140	22	lower	low	ADJ
ejde-1812	140	23	limit	limit	NOUN
ejde-1812	140	24	0	0	NUM
ejde-1812	140	25	;	;	PUNCT
ejde-1812	140	26	b	b	X
ejde-1812	140	27	>	>	X
ejde-1812	140	28	0	0	NUM
ejde-1812	140	29	is	be	AUX
ejde-1812	140	30	a	a	DET
ejde-1812	140	31	constant	constant	ADJ
ejde-1812	140	32	,	,	PUNCT
ejde-1812	140	33	j	j	X
ejde-1812	141	1	=	=	PUNCT
ejde-1812	142	1	[	[	X
ejde-1812	142	2	0	0	NUM
ejde-1812	142	3	,	,	PUNCT
ejde-1812	142	4	b	b	NOUN
ejde-1812	142	5	]	]	X
ejde-1812	142	6	,	,	PUNCT
ejde-1812	142	7	j	j	PROPN
ejde-1812	142	8	′	′	NUM
ejde-1812	142	9	=	=	SYM
ejde-1812	142	10	(	(	PUNCT
ejde-1812	142	11	0	0	NUM
ejde-1812	142	12	,	,	PUNCT
ejde-1812	142	13	b	b	NOUN
ejde-1812	142	14	]	]	X
ejde-1812	142	15	;	;	PUNCT
ejde-1812	142	16	closed	close	VERB
ejde-1812	142	17	unbounded	unbounded	ADJ
ejde-1812	142	18	operator	operator	NOUN
ejde-1812	142	19	a	a	DET
ejde-1812	142	20	(	(	PUNCT
ejde-1812	142	21	d(a	d(a	PROPN
ejde-1812	142	22	)	)	PUNCT
ejde-1812	142	23	⊆	⊆	NUM
ejde-1812	142	24	x	x	SYM
ejde-1812	142	25	)	)	PUNCT
ejde-1812	142	26	generates	generate	VERB
ejde-1812	142	27	a	a	DET
ejde-1812	142	28	c0	c0	PROPN
ejde-1812	142	29	semigroup	semigroup	PROPN
ejde-1812	142	30	t	t	PROPN
ejde-1812	142	31	(	(	PUNCT
ejde-1812	142	32	t	t	PROPN
ejde-1812	142	33	)	)	PUNCT
ejde-1812	142	34	on	on	ADP
ejde-1812	142	35	[	[	X
ejde-1812	142	36	0,∞	0,∞	NOUN
ejde-1812	142	37	)	)	PUNCT
ejde-1812	142	38	;	;	PUNCT
ejde-1812	142	39	the	the	DET
ejde-1812	142	40	semilinear	semilinear	PROPN
ejde-1812	142	41	function	function	NOUN
ejde-1812	142	42	f	f	PROPN
ejde-1812	142	43	:	:	PUNCT
ejde-1812	142	44	j	j	PROPN
ejde-1812	142	45	×	×	NOUN
ejde-1812	142	46	x	x	INTJ
ejde-1812	142	47	→	→	PUNCT
ejde-1812	142	48	x	x	X
ejde-1812	142	49	is	be	AUX
ejde-1812	142	50	a	a	DET
ejde-1812	142	51	given	give	VERB
ejde-1812	142	52	function	function	NOUN
ejde-1812	142	53	to	to	PART
ejde-1812	142	54	be	be	AUX
ejde-1812	142	55	specified	specify	VERB
ejde-1812	142	56	later	later	ADV
ejde-1812	142	57	;	;	PUNCT
ejde-1812	142	58	x0	x0	PROPN
ejde-1812	142	59	∈	∈	PROPN
ejde-1812	143	1	x	x	X
ejde-1812	143	2	;	;	PUNCT
ejde-1812	143	3	the	the	DET
ejde-1812	143	4	control	control	NOUN
ejde-1812	143	5	function	function	NOUN
ejde-1812	143	6	u	u	NOUN
ejde-1812	143	7	takes	take	VERB
ejde-1812	143	8	its	its	PRON
ejde-1812	143	9	value	value	NOUN
ejde-1812	143	10	in	in	ADP
ejde-1812	143	11	v	v	NOUN
ejde-1812	143	12	=	=	SYM
ejde-1812	143	13	lr(j	lr(j	X
ejde-1812	143	14	,	,	PUNCT
ejde-1812	143	15	u	u	NOUN
ejde-1812	143	16	)	)	PUNCT
ejde-1812	143	17	(	(	PUNCT
ejde-1812	143	18	r	r	NOUN
ejde-1812	143	19	>	>	X
ejde-1812	143	20	1	1	NUM
ejde-1812	143	21	α	α	NOUN
ejde-1812	143	22	)	)	PUNCT
ejde-1812	143	23	,	,	PUNCT
ejde-1812	143	24	and	and	CCONJ
ejde-1812	143	25	u	u	NOUN
ejde-1812	143	26	is	be	AUX
ejde-1812	143	27	a	a	DET
ejde-1812	143	28	banach	banach	NOUN
ejde-1812	143	29	space	space	NOUN
ejde-1812	143	30	;	;	PUNCT
ejde-1812	143	31	b	b	X
ejde-1812	143	32	:	:	PUNCT
ejde-1812	143	33	v	v	NOUN
ejde-1812	143	34	→	→	SYM
ejde-1812	143	35	lr(j	lr(j	X
ejde-1812	143	36	,	,	PUNCT
ejde-1812	143	37	x	x	X
ejde-1812	143	38	)	)	PUNCT
ejde-1812	143	39	is	be	AUX
ejde-1812	143	40	a	a	DET
ejde-1812	143	41	linear	linear	ADJ
ejde-1812	143	42	operator	operator	NOUN
ejde-1812	143	43	.	.	PUNCT
ejde-1812	144	1	according	accord	VERB
ejde-1812	144	2	to	to	ADP
ejde-1812	144	3	lemma	lemma	PROPN
ejde-1812	144	4	2.6	2.6	NUM
ejde-1812	144	5	,	,	PUNCT
ejde-1812	144	6	we	we	PRON
ejde-1812	144	7	give	give	VERB
ejde-1812	144	8	the	the	DET
ejde-1812	144	9	following	follow	VERB
ejde-1812	144	10	definition	definition	NOUN
ejde-1812	144	11	.	.	PUNCT
ejde-1812	145	1	definition	definition	NOUN
ejde-1812	145	2	3.1	3.1	NUM
ejde-1812	145	3	.	.	PUNCT
ejde-1812	146	1	a	a	DET
ejde-1812	146	2	function	function	NOUN
ejde-1812	146	3	x	x	X
ejde-1812	146	4	∈	∈	PROPN
ejde-1812	146	5	c1−α−β(1−α);ψ(j	c1−α−β(1−α);ψ(j	PROPN
ejde-1812	146	6	,	,	PUNCT
ejde-1812	146	7	x	x	X
ejde-1812	146	8	)	)	PUNCT
ejde-1812	146	9	is	be	AUX
ejde-1812	146	10	called	call	VERB
ejde-1812	146	11	a	a	DET
ejde-1812	146	12	mild	mild	ADJ
ejde-1812	146	13	solution	solution	NOUN
ejde-1812	146	14	of	of	ADP
ejde-1812	146	15	problem	problem	NOUN
ejde-1812	146	16	(	(	PUNCT
ejde-1812	146	17	3.1	3.1	NUM
ejde-1812	146	18	)	)	PUNCT
ejde-1812	146	19	if	if	SCONJ
ejde-1812	146	20	it	it	PRON
ejde-1812	146	21	satisfies	satisfy	VERB
ejde-1812	146	22	the	the	DET
ejde-1812	146	23	integral	integral	ADJ
ejde-1812	146	24	equation	equation	NOUN
ejde-1812	146	25	x(t	x(t	PROPN
ejde-1812	146	26	)	)	PUNCT
ejde-1812	146	27	=	=	PRON
ejde-1812	146	28	(	(	PUNCT
ejde-1812	146	29	iβ(1−α)kα	iβ(1−α)kα	PROPN
ejde-1812	146	30	)	)	PUNCT
ejde-1812	147	1	(	(	PUNCT
ejde-1812	147	2	ψ(t))x0	ψ(t))x0	PROPN
ejde-1812	147	3	+	+	CCONJ
ejde-1812	147	4	∫	∫	PROPN
ejde-1812	147	5	t	t	PROPN
ejde-1812	147	6	0	0	NUM
ejde-1812	147	7	kα(ψ(t)−	kα(ψ(t)−	PROPN
ejde-1812	147	8	ψ(s))[bu(s	ψ(s))[bu(s	PROPN
ejde-1812	147	9	)	)	PUNCT
ejde-1812	147	10	+	+	NUM
ejde-1812	147	11	f(s	f(	NOUN
ejde-1812	147	12	,	,	PUNCT
ejde-1812	147	13	x(s))]ψ′(s)ds	x(s))]ψ′(s)ds	PROPN
ejde-1812	147	14	.	.	PUNCT
ejde-1812	147	15	definition	definition	NOUN
ejde-1812	147	16	3.2	3.2	NUM
ejde-1812	147	17	.	.	PUNCT
ejde-1812	148	1	let	let	AUX
ejde-1812	148	2	x(·;u	x(·;u	X
ejde-1812	148	3	)	)	PUNCT
ejde-1812	148	4	be	be	AUX
ejde-1812	148	5	a	a	DET
ejde-1812	148	6	mild	mild	ADJ
ejde-1812	148	7	solution	solution	NOUN
ejde-1812	148	8	of	of	ADP
ejde-1812	148	9	problem	problem	NOUN
ejde-1812	148	10	(	(	PUNCT
ejde-1812	148	11	3.1	3.1	NUM
ejde-1812	148	12	)	)	PUNCT
ejde-1812	148	13	corresponding	correspond	VERB
ejde-1812	148	14	to	to	ADP
ejde-1812	148	15	the	the	DET
ejde-1812	148	16	control	control	NOUN
ejde-1812	148	17	u	u	NOUN
ejde-1812	148	18	(	(	PUNCT
ejde-1812	148	19	·	·	PUNCT
ejde-1812	148	20	)	)	PUNCT
ejde-1812	148	21	∈	∈	PROPN
ejde-1812	148	22	v	v	NOUN
ejde-1812	148	23	and	and	CCONJ
ejde-1812	148	24	the	the	DET
ejde-1812	148	25	initial	initial	ADJ
ejde-1812	148	26	value	value	NOUN
ejde-1812	148	27	x0	x0	PROPN
ejde-1812	148	28	∈	∈	PROPN
ejde-1812	148	29	x.	x.	NOUN
ejde-1812	149	1	the	the	DET
ejde-1812	149	2	set	set	NOUN
ejde-1812	149	3	kb(f	kb(f	NOUN
ejde-1812	149	4	)	)	PUNCT
ejde-1812	149	5	:	:	PUNCT
ejde-1812	150	1	=	=	X
ejde-1812	150	2	{	{	PUNCT
ejde-1812	150	3	x(b;u	x(b;u	PROPN
ejde-1812	150	4	)	)	PUNCT
ejde-1812	150	5	:	:	PUNCT
ejde-1812	150	6	u	u	NOUN
ejde-1812	150	7	(	(	PUNCT
ejde-1812	150	8	·	·	PUNCT
ejde-1812	150	9	)	)	PUNCT
ejde-1812	150	10	∈	∈	NOUN
ejde-1812	150	11	v	v	NOUN
ejde-1812	150	12	}	}	PUNCT
ejde-1812	150	13	is	be	AUX
ejde-1812	150	14	called	call	VERB
ejde-1812	150	15	the	the	DET
ejde-1812	150	16	reachable	reachable	ADJ
ejde-1812	150	17	set	set	NOUN
ejde-1812	150	18	of	of	ADP
ejde-1812	150	19	problem	problem	NOUN
ejde-1812	150	20	(	(	PUNCT
ejde-1812	150	21	3.1	3.1	NUM
ejde-1812	150	22	)	)	PUNCT
ejde-1812	150	23	at	at	ADP
ejde-1812	150	24	terminal	terminal	ADJ
ejde-1812	150	25	time	time	PROPN
ejde-1812	150	26	b.	b.	PROPN
ejde-1812	150	27	if	if	SCONJ
ejde-1812	150	28	kb(f	kb(f	NOUN
ejde-1812	150	29	)	)	PUNCT
ejde-1812	150	30	=	=	SYM
ejde-1812	151	1	x	x	X
ejde-1812	151	2	,	,	PUNCT
ejde-1812	151	3	problem	problem	NOUN
ejde-1812	151	4	(	(	PUNCT
ejde-1812	151	5	3.1	3.1	NUM
ejde-1812	151	6	)	)	PUNCT
ejde-1812	151	7	is	be	AUX
ejde-1812	151	8	said	say	VERB
ejde-1812	151	9	to	to	PART
ejde-1812	151	10	be	be	AUX
ejde-1812	151	11	approximately	approximately	ADV
ejde-1812	151	12	controllable	controllable	ADJ
ejde-1812	151	13	on	on	ADP
ejde-1812	151	14	j	j	PROPN
ejde-1812	151	15	.	.	PUNCT
ejde-1812	152	1	before	before	SCONJ
ejde-1812	152	2	we	we	PRON
ejde-1812	152	3	give	give	VERB
ejde-1812	152	4	the	the	DET
ejde-1812	152	5	existence	existence	NOUN
ejde-1812	152	6	and	and	CCONJ
ejde-1812	152	7	uniqueness	uniqueness	VERB
ejde-1812	152	8	lemma	lemma	PROPN
ejde-1812	152	9	of	of	ADP
ejde-1812	152	10	mild	mild	ADJ
ejde-1812	152	11	solutions	solution	NOUN
ejde-1812	152	12	of	of	ADP
ejde-1812	152	13	problem	problem	NOUN
ejde-1812	152	14	(	(	PUNCT
ejde-1812	152	15	3.1	3.1	NUM
ejde-1812	152	16	)	)	PUNCT
ejde-1812	152	17	,	,	PUNCT
ejde-1812	152	18	we	we	PRON
ejde-1812	152	19	pose	pose	VERB
ejde-1812	152	20	the	the	DET
ejde-1812	152	21	following	following	ADJ
ejde-1812	152	22	assumptions	assumption	NOUN
ejde-1812	152	23	:	:	PUNCT
ejde-1812	152	24	(	(	PUNCT
ejde-1812	152	25	h1	h1	PROPN
ejde-1812	152	26	)	)	PUNCT
ejde-1812	152	27	there	there	PRON
ejde-1812	152	28	exist	exist	VERB
ejde-1812	152	29	a	a	DET
ejde-1812	152	30	function	function	NOUN
ejde-1812	152	31	µ	µ	X
ejde-1812	152	32	(	(	PUNCT
ejde-1812	152	33	·	·	PUNCT
ejde-1812	152	34	)	)	PUNCT
ejde-1812	152	35	∈	∈	PROPN
ejde-1812	152	36	lr(j	lr(j	NOUN
ejde-1812	152	37	,	,	PUNCT
ejde-1812	152	38	r+	r+	X
ejde-1812	152	39	)	)	PUNCT
ejde-1812	152	40	and	and	CCONJ
ejde-1812	152	41	a	a	DET
ejde-1812	152	42	positive	positive	ADJ
ejde-1812	152	43	constant	constant	ADJ
ejde-1812	152	44	ℓ1	ℓ1	NOUN
ejde-1812	152	45	such	such	ADJ
ejde-1812	152	46	that	that	DET
ejde-1812	152	47	∥f(t	∥f(t	NOUN
ejde-1812	152	48	,	,	PUNCT
ejde-1812	152	49	x)∥	x)∥	SYM
ejde-1812	152	50	≤	≤	PROPN
ejde-1812	152	51	µ(t	µ(t	ADJ
ejde-1812	152	52	)	)	PUNCT
ejde-1812	152	53	+	+	CCONJ
ejde-1812	152	54	ℓ1ψ	ℓ1ψ	PROPN
ejde-1812	152	55	1−α−β(1−α)(t)∥x∥	1−α−β(1−α)(t)∥x∥	NUM
ejde-1812	152	56	,	,	PUNCT
ejde-1812	152	57	for	for	ADP
ejde-1812	152	58	a.e	a.e	PROPN
ejde-1812	152	59	.	.	PROPN
ejde-1812	152	60	t	t	PROPN
ejde-1812	152	61	∈	∈	PROPN
ejde-1812	152	62	j	j	PROPN
ejde-1812	152	63	and	and	CCONJ
ejde-1812	152	64	each	each	DET
ejde-1812	152	65	x	x	SYM
ejde-1812	152	66	∈	∈	PROPN
ejde-1812	152	67	x.	x.	NOUN
ejde-1812	152	68	(	(	PUNCT
ejde-1812	152	69	h2	h2	PROPN
ejde-1812	152	70	)	)	PUNCT
ejde-1812	152	71	there	there	PRON
ejde-1812	152	72	exists	exist	VERB
ejde-1812	152	73	a	a	DET
ejde-1812	152	74	positive	positive	ADJ
ejde-1812	152	75	constant	constant	ADJ
ejde-1812	152	76	ℓ2	ℓ2	NOUN
ejde-1812	152	77	such	such	ADJ
ejde-1812	152	78	that	that	DET
ejde-1812	152	79	∥f(t	∥f(t	NOUN
ejde-1812	152	80	,	,	PUNCT
ejde-1812	152	81	x1)−	x1)−	PROPN
ejde-1812	152	82	f(t	f(t	PROPN
ejde-1812	152	83	,	,	PUNCT
ejde-1812	152	84	x2)∥	x2)∥	SYM
ejde-1812	152	85	≤	≤	NUM
ejde-1812	152	86	ℓ2∥x1	ℓ2∥x1	NOUN
ejde-1812	152	87	−	−	PROPN
ejde-1812	152	88	x2∥	x2∥	PROPN
ejde-1812	152	89	,	,	PUNCT
ejde-1812	152	90	∀xi	∀xi	PROPN
ejde-1812	152	91	∈	∈	PROPN
ejde-1812	152	92	x(i	x(i	PROPN
ejde-1812	152	93	=	=	SYM
ejde-1812	152	94	1	1	NUM
ejde-1812	152	95	,	,	PUNCT
ejde-1812	152	96	2	2	NUM
ejde-1812	152	97	)	)	PUNCT
ejde-1812	152	98	.	.	PUNCT
ejde-1812	153	1	lemma	lemma	PROPN
ejde-1812	153	2	3.3	3.3	NUM
ejde-1812	153	3	.	.	PUNCT
ejde-1812	154	1	if	if	SCONJ
ejde-1812	154	2	(	(	PUNCT
ejde-1812	154	3	h1	h1	PROPN
ejde-1812	154	4	)	)	PUNCT
ejde-1812	154	5	,	,	PUNCT
ejde-1812	154	6	(	(	PUNCT
ejde-1812	154	7	h2	h2	NOUN
ejde-1812	154	8	)	)	PUNCT
ejde-1812	154	9	are	be	AUX
ejde-1812	154	10	satisfied	satisfied	ADJ
ejde-1812	154	11	,	,	PUNCT
ejde-1812	154	12	then	then	ADV
ejde-1812	154	13	for	for	ADP
ejde-1812	154	14	any	any	DET
ejde-1812	154	15	control	control	NOUN
ejde-1812	154	16	function	function	NOUN
ejde-1812	154	17	u	u	PROPN
ejde-1812	154	18	(	(	PUNCT
ejde-1812	154	19	·	·	PUNCT
ejde-1812	154	20	)	)	PUNCT
ejde-1812	154	21	∈	∈	PROPN
ejde-1812	154	22	v	v	NOUN
ejde-1812	154	23	,	,	PUNCT
ejde-1812	154	24	there	there	PRON
ejde-1812	154	25	exists	exist	VERB
ejde-1812	154	26	a	a	DET
ejde-1812	154	27	unique	unique	ADJ
ejde-1812	154	28	mild	mild	ADJ
ejde-1812	154	29	solution	solution	NOUN
ejde-1812	154	30	for	for	ADP
ejde-1812	154	31	the	the	DET
ejde-1812	154	32	control	control	NOUN
ejde-1812	154	33	problem	problem	NOUN
ejde-1812	154	34	(	(	PUNCT
ejde-1812	154	35	3.1	3.1	NUM
ejde-1812	154	36	)	)	PUNCT
ejde-1812	154	37	on	on	ADP
ejde-1812	154	38	c1−α−β(1−α);ψ(j	c1−α−β(1−α);ψ(j	ADJ
ejde-1812	154	39	,	,	PUNCT
ejde-1812	154	40	x	x	NOUN
ejde-1812	154	41	)	)	PUNCT
ejde-1812	154	42	.	.	PUNCT
ejde-1812	155	1	proof	proof	NOUN
ejde-1812	155	2	.	.	PUNCT
ejde-1812	156	1	define	define	VERB
ejde-1812	156	2	the	the	DET
ejde-1812	156	3	operator	operator	NOUN
ejde-1812	156	4	t	t	PROPN
ejde-1812	156	5	as	as	SCONJ
ejde-1812	156	6	follows	follow	VERB
ejde-1812	156	7	:	:	PUNCT
ejde-1812	156	8	(	(	PUNCT
ejde-1812	156	9	tx)(t	tx)(t	PROPN
ejde-1812	156	10	)	)	PUNCT
ejde-1812	156	11	=	=	PRON
ejde-1812	156	12	(	(	PUNCT
ejde-1812	156	13	iβ(1−α)kα	iβ(1−α)kα	PROPN
ejde-1812	156	14	)	)	PUNCT
ejde-1812	157	1	(	(	PUNCT
ejde-1812	157	2	ψ(t))x0	ψ(t))x0	PROPN
ejde-1812	157	3	+	+	CCONJ
ejde-1812	157	4	∫	∫	PROPN
ejde-1812	157	5	t	t	PROPN
ejde-1812	157	6	0	0	NUM
ejde-1812	157	7	kα(ψ(t)−	kα(ψ(t)−	PROPN
ejde-1812	157	8	ψ(s))[bu(s	ψ(s))[bu(s	PROPN
ejde-1812	157	9	)	)	PUNCT
ejde-1812	157	10	+	+	NUM
ejde-1812	157	11	f(s	f(	NOUN
ejde-1812	157	12	,	,	PUNCT
ejde-1812	157	13	x(s))]ψ′(s)ds	x(s))]ψ′(s)ds	PROPN
ejde-1812	157	14	.	.	PUNCT
ejde-1812	157	15	(	(	PUNCT
ejde-1812	157	16	3.2	3.2	NUM
ejde-1812	157	17	)	)	PUNCT
ejde-1812	157	18	from	from	ADP
ejde-1812	157	19	our	our	PRON
ejde-1812	157	20	hypotheses	hypothesis	NOUN
ejde-1812	157	21	,	,	PUNCT
ejde-1812	157	22	it	it	PRON
ejde-1812	157	23	follows	follow	VERB
ejde-1812	157	24	that	that	SCONJ
ejde-1812	157	25	t	t	PROPN
ejde-1812	157	26	maps	maps	PROPN
ejde-1812	157	27	c1−α−β(1−α);ψ(j	c1−α−β(1−α);ψ(j	PROPN
ejde-1812	157	28	,	,	PUNCT
ejde-1812	157	29	x	x	X
ejde-1812	157	30	)	)	PUNCT
ejde-1812	157	31	into	into	ADP
ejde-1812	157	32	itself	itself	PRON
ejde-1812	157	33	.	.	PUNCT
ejde-1812	158	1	then	then	ADV
ejde-1812	158	2	,	,	PUNCT
ejde-1812	158	3	we	we	PRON
ejde-1812	158	4	show	show	VERB
ejde-1812	158	5	that	that	SCONJ
ejde-1812	158	6	tn	tn	PROPN
ejde-1812	158	7	is	be	AUX
ejde-1812	158	8	a	a	DET
ejde-1812	158	9	contraction	contraction	NOUN
ejde-1812	158	10	mapping	mapping	NOUN
ejde-1812	158	11	on	on	ADP
ejde-1812	158	12	c1−α−β(1−α);ψ(j	c1−α−β(1−α);ψ(j	NUM
ejde-1812	158	13	,	,	PUNCT
ejde-1812	158	14	x	x	NOUN
ejde-1812	158	15	)	)	PUNCT
ejde-1812	158	16	.	.	PUNCT
ejde-1812	159	1	as	as	ADP
ejde-1812	159	2	a	a	DET
ejde-1812	159	3	matter	matter	NOUN
ejde-1812	159	4	of	of	ADP
ejde-1812	159	5	fact	fact	NOUN
ejde-1812	159	6	,	,	PUNCT
ejde-1812	159	7	for	for	ADP
ejde-1812	159	8	each	each	DET
ejde-1812	159	9	x1	x1	PROPN
ejde-1812	159	10	,	,	PUNCT
ejde-1812	159	11	x2	x2	PROPN
ejde-1812	159	12	∈	∈	PROPN
ejde-1812	159	13	c1−α−β(1−α);ψ(j	c1−α−β(1−α);ψ(j	PROPN
ejde-1812	159	14	,	,	PUNCT
ejde-1812	159	15	x	x	PRON
ejde-1812	159	16	)	)	PUNCT
ejde-1812	159	17	and	and	CCONJ
ejde-1812	159	18	t	t	PROPN
ejde-1812	159	19	∈	∈	PROPN
ejde-1812	159	20	j	j	PROPN
ejde-1812	159	21	,	,	PUNCT
ejde-1812	159	22	we	we	PRON
ejde-1812	159	23	can	can	AUX
ejde-1812	159	24	obtain	obtain	VERB
ejde-1812	159	25	ψ1−α−β(1−α)(t)∥(tx1)(t)−	ψ1−α−β(1−α)(t)∥(tx1)(t)−	PROPN
ejde-1812	159	26	(	(	PUNCT
ejde-1812	159	27	tx2)(t)∥	tx2)(t)∥	PRON
ejde-1812	159	28	≤	≤	NUM
ejde-1812	159	29	ψ1−α−β(1−α)(t	ψ1−α−β(1−α)(t	NOUN
ejde-1812	159	30	)	)	PUNCT
ejde-1812	160	1	∫	∫	PROPN
ejde-1812	160	2	t	t	NOUN
ejde-1812	160	3	0	0	NUM
ejde-1812	161	1	∥kα(ψ(t)−	∥kα(ψ(t)−	ADJ
ejde-1812	161	2	ψ(s))[f(s	ψ(s))[f(	NOUN
ejde-1812	161	3	,	,	PUNCT
ejde-1812	161	4	x1(s))−	x1(s))−	PUNCT
ejde-1812	161	5	f(s	f(	NOUN
ejde-1812	161	6	,	,	PUNCT
ejde-1812	161	7	x2(s))]∥ψ′(s)ds	x2(s))]∥ψ′(s)ds	PROPN
ejde-1812	161	8	≤	≤	PROPN
ejde-1812	161	9	mℓ2	mℓ2	PROPN
ejde-1812	161	10	γ(α	γ(α	NOUN
ejde-1812	161	11	)	)	PUNCT
ejde-1812	161	12	ψ1−α−β(1−α)(t	ψ1−α−β(1−α)(t	NOUN
ejde-1812	161	13	)	)	PUNCT
ejde-1812	161	14	∫	∫	PROPN
ejde-1812	161	15	t	t	PROPN
ejde-1812	161	16	0	0	NUM
ejde-1812	161	17	(	(	PUNCT
ejde-1812	161	18	ψ(t)−	ψ(t)−	PROPN
ejde-1812	161	19	ψ(s))α−1ψα+β(1−α)−1(s	ψ(s))α−1ψα+β(1−α)−1(s	PROPN
ejde-1812	161	20	)	)	PUNCT
ejde-1812	161	21	6	6	NUM
ejde-1812	161	22	j.	j.	PROPN
ejde-1812	161	23	liang	liang	PROPN
ejde-1812	161	24	,	,	PUNCT
ejde-1812	161	25	y.	y.	PROPN
ejde-1812	161	26	mu	mu	PROPN
ejde-1812	161	27	,	,	PUNCT
ejde-1812	161	28	t.-j	t.-j	PROPN
ejde-1812	161	29	.	.	PUNCT
ejde-1812	162	1	xiao	xiao	PROPN
ejde-1812	162	2	ejde-2025/109	ejde-2025/109	PROPN
ejde-1812	163	1	×	×	PROPN
ejde-1812	163	2	ψ1−α−β(1−α)(s)∥x1(s)−	ψ1−α−β(1−α)(s)∥x1(s)−	PUNCT
ejde-1812	163	3	x2(s)∥ψ′(s)ds	x2(s)∥ψ′(s)ds	PROPN
ejde-1812	163	4	≤	≤	NOUN
ejde-1812	163	5	γ(α+	γ(α+	DET
ejde-1812	163	6	β(1−	β(1−	NOUN
ejde-1812	163	7	α))mℓ2ψ	α))mℓ2ψ	NUM
ejde-1812	163	8	α(t	α(t	PROPN
ejde-1812	163	9	)	)	PUNCT
ejde-1812	164	1	γ(2α+	γ(2α+	PROPN
ejde-1812	164	2	β(1−	β(1−	PROPN
ejde-1812	164	3	α	α	X
ejde-1812	164	4	)	)	PUNCT
ejde-1812	164	5	)	)	PUNCT
ejde-1812	164	6	∥x1	∥x1	NOUN
ejde-1812	164	7	−	−	PROPN
ejde-1812	164	8	x2∥c1−α−β(1−α);ψ	x2∥c1−α−β(1−α);ψ	PROPN
ejde-1812	164	9	.	.	PUNCT
ejde-1812	165	1	(	(	PUNCT
ejde-1812	165	2	3.3	3.3	NUM
ejde-1812	165	3	)	)	PUNCT
ejde-1812	165	4	using	use	VERB
ejde-1812	165	5	(	(	PUNCT
ejde-1812	165	6	3.2	3.2	NUM
ejde-1812	165	7	)	)	PUNCT
ejde-1812	165	8	,	,	PUNCT
ejde-1812	165	9	(	(	PUNCT
ejde-1812	165	10	3.3	3.3	NUM
ejde-1812	165	11	)	)	PUNCT
ejde-1812	165	12	,	,	PUNCT
ejde-1812	165	13	and	and	CCONJ
ejde-1812	165	14	arguing	argue	VERB
ejde-1812	165	15	by	by	ADP
ejde-1812	165	16	induction	induction	NOUN
ejde-1812	165	17	on	on	ADP
ejde-1812	165	18	n	n	CCONJ
ejde-1812	165	19	,	,	PUNCT
ejde-1812	165	20	we	we	PRON
ejde-1812	165	21	easily	easily	ADV
ejde-1812	165	22	see	see	VERB
ejde-1812	165	23	that	that	SCONJ
ejde-1812	165	24	ψ1−α−β(1−α)(t)∥(tnx1)(t)−	ψ1−α−β(1−α)(t)∥(tnx1)(t)−	PROPN
ejde-1812	165	25	(	(	PUNCT
ejde-1812	165	26	tnx2)(t)∥	tnx2)(t)∥	NOUN
ejde-1812	165	27	≤	≤	NOUN
ejde-1812	166	1	γ(α+	γ(α+	PRON
ejde-1812	166	2	β(1−	β(1−	NOUN
ejde-1812	166	3	α	α	X
ejde-1812	166	4	)	)	PUNCT
ejde-1812	166	5	)	)	PUNCT
ejde-1812	166	6	(	(	PUNCT
ejde-1812	166	7	mℓ2ψ	mℓ2ψ	NOUN
ejde-1812	166	8	α(t	α(t	PROPN
ejde-1812	166	9	)	)	PUNCT
ejde-1812	166	10	)	)	PUNCT
ejde-1812	167	1	n	n	CCONJ
ejde-1812	167	2	γ((n+	γ((n+	NOUN
ejde-1812	167	3	1)α+	1)α+	NUM
ejde-1812	167	4	β(1−	β(1−	NOUN
ejde-1812	167	5	α	α	X
ejde-1812	167	6	)	)	PUNCT
ejde-1812	167	7	)	)	PUNCT
ejde-1812	167	8	∥x1	∥x1	NOUN
ejde-1812	167	9	−	−	PROPN
ejde-1812	167	10	x2∥c1−α−β(1−α);ψ	x2∥c1−α−β(1−α);ψ	PROPN
ejde-1812	167	11	.	.	PUNCT
ejde-1812	168	1	hence	hence	ADV
ejde-1812	168	2	,	,	PUNCT
ejde-1812	168	3	we	we	PRON
ejde-1812	168	4	can	can	AUX
ejde-1812	168	5	obtain	obtain	VERB
ejde-1812	168	6	∥(tnx1)(t)−	∥(tnx1)(t)−	PROPN
ejde-1812	168	7	(	(	PUNCT
ejde-1812	168	8	tnx2)(t)∥c1−α−β(1−α);ψ	tnx2)(t)∥c1−α−β(1−α);ψ	VERB
ejde-1812	168	9	≤	≤	NOUN
ejde-1812	168	10	γ(α+	γ(α+	DET
ejde-1812	168	11	β(1−	β(1−	NOUN
ejde-1812	168	12	α	α	X
ejde-1812	168	13	)	)	PUNCT
ejde-1812	168	14	)	)	PUNCT
ejde-1812	169	1	(	(	PUNCT
ejde-1812	169	2	mℓ2ψ	mℓ2ψ	NOUN
ejde-1812	169	3	α(t	α(t	PROPN
ejde-1812	169	4	)	)	PUNCT
ejde-1812	169	5	)	)	PUNCT
ejde-1812	170	1	n	n	CCONJ
ejde-1812	170	2	γ((n+	γ((n+	NOUN
ejde-1812	170	3	1)α+	1)α+	NUM
ejde-1812	170	4	β(1−	β(1−	NOUN
ejde-1812	170	5	α	α	X
ejde-1812	170	6	)	)	PUNCT
ejde-1812	170	7	)	)	PUNCT
ejde-1812	170	8	∥x1	∥x1	NOUN
ejde-1812	170	9	−	−	PROPN
ejde-1812	170	10	x2∥c1−α−β(1−α);ψ	x2∥c1−α−β(1−α);ψ	PROPN
ejde-1812	170	11	.	.	PUNCT
ejde-1812	171	1	because	because	SCONJ
ejde-1812	171	2	lim	lim	PROPN
ejde-1812	171	3	n→∞	n→∞	X
ejde-1812	171	4	(	(	PUNCT
ejde-1812	171	5	mℓ2ψ	mℓ2ψ	NOUN
ejde-1812	171	6	α(t	α(t	PROPN
ejde-1812	171	7	)	)	PUNCT
ejde-1812	171	8	)	)	PUNCT
ejde-1812	171	9	n	n	CCONJ
ejde-1812	171	10	γ((n+	γ((n+	NOUN
ejde-1812	171	11	1)α+	1)α+	NUM
ejde-1812	171	12	β(1−	β(1−	NOUN
ejde-1812	171	13	α	α	X
ejde-1812	171	14	)	)	PUNCT
ejde-1812	171	15	)	)	PUNCT
ejde-1812	172	1	=	=	SYM
ejde-1812	172	2	0	0	X
ejde-1812	172	3	,	,	PUNCT
ejde-1812	172	4	there	there	PRON
ejde-1812	172	5	exists	exist	VERB
ejde-1812	172	6	a	a	DET
ejde-1812	172	7	positive	positive	ADJ
ejde-1812	172	8	integer	integer	NOUN
ejde-1812	172	9	n	n	CCONJ
ejde-1812	172	10	such	such	ADJ
ejde-1812	172	11	that	that	SCONJ
ejde-1812	172	12	γ(α+	γ(α+	NUM
ejde-1812	172	13	β(1−	β(1−	NOUN
ejde-1812	172	14	α	α	X
ejde-1812	172	15	)	)	PUNCT
ejde-1812	172	16	)	)	PUNCT
ejde-1812	172	17	(	(	PUNCT
ejde-1812	172	18	mℓ2ψ	mℓ2ψ	NOUN
ejde-1812	172	19	α(t	α(t	PROPN
ejde-1812	172	20	)	)	PUNCT
ejde-1812	172	21	)	)	PUNCT
ejde-1812	173	1	n	n	CCONJ
ejde-1812	173	2	γ((n	γ((n	NOUN
ejde-1812	174	1	+	+	CCONJ
ejde-1812	174	2	1)α+	1)α+	NUM
ejde-1812	174	3	β(1−	β(1−	NOUN
ejde-1812	174	4	α	α	X
ejde-1812	174	5	)	)	PUNCT
ejde-1812	174	6	)	)	PUNCT
ejde-1812	174	7	<	<	X
ejde-1812	174	8	1	1	X
ejde-1812	174	9	.	.	PUNCT
ejde-1812	175	1	so	so	ADV
ejde-1812	175	2	tn	tn	PROPN
ejde-1812	175	3	is	be	AUX
ejde-1812	175	4	a	a	DET
ejde-1812	175	5	contraction	contraction	NOUN
ejde-1812	175	6	mapping	mapping	NOUN
ejde-1812	175	7	on	on	ADP
ejde-1812	175	8	c1−α−β(1−α);ψ(j	c1−α−β(1−α);ψ(j	NUM
ejde-1812	175	9	,	,	PUNCT
ejde-1812	175	10	x	x	NOUN
ejde-1812	175	11	)	)	PUNCT
ejde-1812	175	12	.	.	PUNCT
ejde-1812	176	1	then	then	ADV
ejde-1812	176	2	by	by	ADP
ejde-1812	176	3	a	a	DET
ejde-1812	176	4	well	well	ADV
ejde-1812	176	5	-	-	PUNCT
ejde-1812	176	6	known	know	VERB
ejde-1812	176	7	extension	extension	NOUN
ejde-1812	176	8	of	of	ADP
ejde-1812	176	9	the	the	DET
ejde-1812	176	10	banach	banach	NOUN
ejde-1812	176	11	contraction	contraction	NOUN
ejde-1812	176	12	mapping	mapping	NOUN
ejde-1812	176	13	theorem	theorem	NOUN
ejde-1812	176	14	,	,	PUNCT
ejde-1812	176	15	t	t	PROPN
ejde-1812	176	16	has	have	VERB
ejde-1812	176	17	a	a	DET
ejde-1812	176	18	unique	unique	ADJ
ejde-1812	176	19	fixed	fix	VERB
ejde-1812	176	20	point	point	NOUN
ejde-1812	176	21	x(t	x(t	PROPN
ejde-1812	176	22	)	)	PUNCT
ejde-1812	176	23	on	on	ADP
ejde-1812	176	24	c1−α−β(1−α);ψ(j	c1−α−β(1−α);ψ(j	ADJ
ejde-1812	176	25	,	,	PUNCT
ejde-1812	176	26	x	x	NOUN
ejde-1812	176	27	)	)	PUNCT
ejde-1812	176	28	,	,	PUNCT
ejde-1812	176	29	which	which	PRON
ejde-1812	176	30	is	be	AUX
ejde-1812	176	31	the	the	DET
ejde-1812	176	32	unique	unique	ADJ
ejde-1812	176	33	mild	mild	ADJ
ejde-1812	176	34	solution	solution	NOUN
ejde-1812	176	35	of	of	ADP
ejde-1812	176	36	problem	problem	NOUN
ejde-1812	176	37	(	(	PUNCT
ejde-1812	176	38	3.1	3.1	NUM
ejde-1812	176	39	)	)	PUNCT
ejde-1812	176	40	.	.	PUNCT
ejde-1812	177	1	□	□	PUNCT
ejde-1812	177	2	next	next	ADV
ejde-1812	177	3	,	,	PUNCT
ejde-1812	177	4	we	we	PRON
ejde-1812	177	5	study	study	VERB
ejde-1812	177	6	the	the	DET
ejde-1812	177	7	approximate	approximate	ADJ
ejde-1812	177	8	controllability	controllability	NOUN
ejde-1812	177	9	of	of	ADP
ejde-1812	177	10	the	the	DET
ejde-1812	177	11	evolution	evolution	NOUN
ejde-1812	177	12	ψ	ψ	NOUN
ejde-1812	177	13	-	-	ADJ
ejde-1812	177	14	hilfer	hilfer	NOUN
ejde-1812	177	15	fractional	fractional	ADJ
ejde-1812	177	16	differential	differential	ADJ
ejde-1812	177	17	equations	equation	NOUN
ejde-1812	177	18	(	(	PUNCT
ejde-1812	177	19	3.1	3.1	NUM
ejde-1812	177	20	)	)	PUNCT
ejde-1812	177	21	in	in	ADP
ejde-1812	177	22	the	the	DET
ejde-1812	177	23	banach	banach	NOUN
ejde-1812	177	24	space	space	NOUN
ejde-1812	177	25	x.	x.	NOUN
ejde-1812	178	1	we	we	PRON
ejde-1812	178	2	denote	denote	VERB
ejde-1812	178	3	the	the	DET
ejde-1812	178	4	nemytskil	nemytskil	NOUN
ejde-1812	178	5	operator	operator	NOUN
ejde-1812	178	6	associated	associate	VERB
ejde-1812	178	7	with	with	ADP
ejde-1812	178	8	the	the	DET
ejde-1812	178	9	semilinear	semilinear	ADJ
ejde-1812	178	10	function	function	NOUN
ejde-1812	178	11	f	f	PROPN
ejde-1812	178	12	by	by	ADP
ejde-1812	178	13	nf	nf	INTJ
ejde-1812	178	14	:	:	PUNCT
ejde-1812	178	15	c1−α−β(1−α);ψ(j	c1−α−β(1−α);ψ(j	NUM
ejde-1812	178	16	,	,	PUNCT
ejde-1812	178	17	x	x	X
ejde-1812	178	18	)	)	PUNCT
ejde-1812	178	19	→	→	SYM
ejde-1812	178	20	lr(j	lr(j	X
ejde-1812	178	21	,	,	PUNCT
ejde-1812	178	22	x	x	X
ejde-1812	178	23	)	)	PUNCT
ejde-1812	178	24	,	,	PUNCT
ejde-1812	178	25	nf	nf	INTJ
ejde-1812	178	26	(	(	PUNCT
ejde-1812	178	27	x)(t	x)(t	NUM
ejde-1812	178	28	)	)	PUNCT
ejde-1812	178	29	=	=	PUNCT
ejde-1812	179	1	f(t	f(t	NOUN
ejde-1812	179	2	,	,	PUNCT
ejde-1812	179	3	x(t	x(t	PROPN
ejde-1812	179	4	)	)	PUNCT
ejde-1812	179	5	)	)	PUNCT
ejde-1812	179	6	.	.	PUNCT
ejde-1812	180	1	the	the	DET
ejde-1812	180	2	linear	linear	PROPN
ejde-1812	180	3	bounded	bound	VERB
ejde-1812	180	4	operator	operator	NOUN
ejde-1812	180	5	h	h	NOUN
ejde-1812	180	6	:	:	PUNCT
ejde-1812	180	7	lr(j	lr(j	X
ejde-1812	180	8	,	,	PUNCT
ejde-1812	180	9	x	x	X
ejde-1812	180	10	)	)	PUNCT
ejde-1812	180	11	→	→	PUNCT
ejde-1812	180	12	x	x	X
ejde-1812	180	13	is	be	AUX
ejde-1812	180	14	defined	define	VERB
ejde-1812	180	15	as	as	ADP
ejde-1812	180	16	hg	hg	PROPN
ejde-1812	180	17	=	=	PUNCT
ejde-1812	180	18	∫	∫	PROPN
ejde-1812	180	19	b	b	PROPN
ejde-1812	180	20	0	0	NUM
ejde-1812	180	21	kα(ψ(b)−	kα(ψ(b)−	PROPN
ejde-1812	180	22	ψ(s))ψ′(s)g(s)ds	ψ(s))ψ′(s)g(s)ds	PROPN
ejde-1812	180	23	,	,	PUNCT
ejde-1812	180	24	g	g	PROPN
ejde-1812	180	25	(	(	PUNCT
ejde-1812	180	26	·	·	PUNCT
ejde-1812	180	27	)	)	PUNCT
ejde-1812	180	28	∈	∈	PROPN
ejde-1812	180	29	lr(j	lr(j	NOUN
ejde-1812	180	30	,	,	PUNCT
ejde-1812	180	31	x	x	NOUN
ejde-1812	180	32	)	)	PUNCT
ejde-1812	180	33	.	.	PUNCT
ejde-1812	181	1	by	by	ADP
ejde-1812	181	2	definition	definition	NOUN
ejde-1812	181	3	3.2	3.2	NUM
ejde-1812	181	4	,	,	PUNCT
ejde-1812	181	5	we	we	PRON
ejde-1812	181	6	easily	easily	ADV
ejde-1812	181	7	know	know	VERB
ejde-1812	181	8	that	that	SCONJ
ejde-1812	181	9	if	if	SCONJ
ejde-1812	181	10	for	for	ADP
ejde-1812	181	11	any	any	DET
ejde-1812	181	12	x0	x0	PROPN
ejde-1812	181	13	∈	∈	PROPN
ejde-1812	181	14	x	x	X
ejde-1812	181	15	and	and	CCONJ
ejde-1812	181	16	u	u	NOUN
ejde-1812	181	17	(	(	PUNCT
ejde-1812	181	18	·	·	PUNCT
ejde-1812	181	19	)	)	PUNCT
ejde-1812	181	20	∈	∈	PROPN
ejde-1812	181	21	v	v	NOUN
ejde-1812	181	22	,	,	PUNCT
ejde-1812	181	23	kb(f	kb(f	NOUN
ejde-1812	181	24	)	)	PUNCT
ejde-1812	181	25	=	=	SYM
ejde-1812	182	1	x	x	X
ejde-1812	182	2	,	,	PUNCT
ejde-1812	182	3	then	then	ADV
ejde-1812	182	4	problem	problem	NOUN
ejde-1812	182	5	(	(	PUNCT
ejde-1812	182	6	3.1	3.1	NUM
ejde-1812	182	7	)	)	PUNCT
ejde-1812	182	8	is	be	AUX
ejde-1812	182	9	approximately	approximately	ADV
ejde-1812	182	10	controllable	controllable	ADJ
ejde-1812	182	11	on	on	ADP
ejde-1812	182	12	j	j	PROPN
ejde-1812	182	13	.	.	PUNCT
ejde-1812	183	1	therefore	therefore	ADV
ejde-1812	183	2	,	,	PUNCT
ejde-1812	183	3	if	if	SCONJ
ejde-1812	183	4	for	for	ADP
ejde-1812	183	5	any	any	DET
ejde-1812	183	6	target	target	NOUN
ejde-1812	183	7	state	state	NOUN
ejde-1812	183	8	ξ	ξ	X
ejde-1812	183	9	∈	∈	PROPN
ejde-1812	183	10	x	x	X
ejde-1812	183	11	and	and	CCONJ
ejde-1812	183	12	each	each	DET
ejde-1812	183	13	ε	ε	PROPN
ejde-1812	183	14	>	>	X
ejde-1812	183	15	0	0	PROPN
ejde-1812	183	16	,	,	PUNCT
ejde-1812	183	17	there	there	PRON
ejde-1812	183	18	exists	exist	VERB
ejde-1812	183	19	a	a	DET
ejde-1812	183	20	control	control	NOUN
ejde-1812	183	21	function	function	NOUN
ejde-1812	183	22	uε	uε	PROPN
ejde-1812	183	23	(	(	PUNCT
ejde-1812	183	24	·	·	PUNCT
ejde-1812	183	25	)	)	PUNCT
ejde-1812	183	26	∈	∈	PROPN
ejde-1812	183	27	v	v	NOUN
ejde-1812	183	28	,	,	PUNCT
ejde-1812	183	29	such	such	ADJ
ejde-1812	183	30	that	that	SCONJ
ejde-1812	183	31	the	the	DET
ejde-1812	183	32	mild	mild	ADJ
ejde-1812	183	33	solution	solution	NOUN
ejde-1812	183	34	of	of	ADP
ejde-1812	183	35	problem	problem	NOUN
ejde-1812	183	36	(	(	PUNCT
ejde-1812	183	37	3.1	3.1	NUM
ejde-1812	183	38	)	)	PUNCT
ejde-1812	183	39	satisfies∥∥ξ	satisfies∥∥ξ	PROPN
ejde-1812	183	40	−	−	PROPN
ejde-1812	183	41	(	(	PUNCT
ejde-1812	183	42	iβ(1−α)kα	iβ(1−α)kα	PROPN
ejde-1812	183	43	)	)	PUNCT
ejde-1812	183	44	(	(	PUNCT
ejde-1812	183	45	ψ(b))x0	ψ(b))x0	VERB
ejde-1812	183	46	−hnf	−hnf	NOUN
ejde-1812	183	47	(	(	PUNCT
ejde-1812	183	48	xε)−hbuε	xε)−hbuε	PROPN
ejde-1812	183	49	∥∥	∥∥	X
ejde-1812	183	50	<	<	X
ejde-1812	183	51	ε	ε	PROPN
ejde-1812	183	52	,	,	PUNCT
ejde-1812	183	53	(	(	PUNCT
ejde-1812	183	54	3.4	3.4	NUM
ejde-1812	183	55	)	)	PUNCT
ejde-1812	183	56	where	where	SCONJ
ejde-1812	183	57	xε(t	xε(t	X
ejde-1812	183	58	)	)	PUNCT
ejde-1812	183	59	=	=	SYM
ejde-1812	183	60	x(t;uε	x(t;uε	PROPN
ejde-1812	183	61	)	)	PUNCT
ejde-1812	183	62	,	,	PUNCT
ejde-1812	183	63	t	t	PROPN
ejde-1812	183	64	∈	∈	PROPN
ejde-1812	183	65	(	(	PUNCT
ejde-1812	183	66	0	0	NUM
ejde-1812	183	67	,	,	PUNCT
ejde-1812	183	68	b	b	NOUN
ejde-1812	183	69	]	]	X
ejde-1812	183	70	,	,	PUNCT
ejde-1812	183	71	then	then	ADV
ejde-1812	183	72	problem	problem	NOUN
ejde-1812	183	73	(	(	PUNCT
ejde-1812	183	74	3.1	3.1	NUM
ejde-1812	183	75	)	)	PUNCT
ejde-1812	183	76	is	be	AUX
ejde-1812	183	77	approximately	approximately	ADV
ejde-1812	183	78	controllable	controllable	ADJ
ejde-1812	183	79	on	on	ADP
ejde-1812	183	80	j	j	PROPN
ejde-1812	183	81	.	.	PUNCT
ejde-1812	184	1	to	to	PART
ejde-1812	184	2	analyze	analyze	VERB
ejde-1812	184	3	the	the	DET
ejde-1812	184	4	approximate	approximate	ADJ
ejde-1812	184	5	controllability	controllability	NOUN
ejde-1812	184	6	of	of	ADP
ejde-1812	184	7	problem	problem	NOUN
ejde-1812	184	8	(	(	PUNCT
ejde-1812	184	9	3.1	3.1	NUM
ejde-1812	184	10	)	)	PUNCT
ejde-1812	184	11	,	,	PUNCT
ejde-1812	184	12	we	we	PRON
ejde-1812	184	13	introduce	introduce	VERB
ejde-1812	184	14	the	the	DET
ejde-1812	184	15	assumption	assumption	NOUN
ejde-1812	184	16	(	(	PUNCT
ejde-1812	184	17	h3	h3	NOUN
ejde-1812	184	18	)	)	PUNCT
ejde-1812	184	19	there	there	PRON
ejde-1812	184	20	exists	exist	VERB
ejde-1812	184	21	a	a	DET
ejde-1812	184	22	positive	positive	ADJ
ejde-1812	184	23	constant	constant	ADJ
ejde-1812	184	24	ℓ3	ℓ3	NOUN
ejde-1812	184	25	such	such	ADJ
ejde-1812	184	26	that	that	SCONJ
ejde-1812	184	27	∥f(t	∥f(t	NOUN
ejde-1812	184	28	,	,	PUNCT
ejde-1812	184	29	x1)−	x1)−	PROPN
ejde-1812	184	30	f(t	f(t	PROPN
ejde-1812	184	31	,	,	PUNCT
ejde-1812	184	32	x2)∥	x2)∥	PUNCT
ejde-1812	184	33	≤	≤	X
ejde-1812	184	34	ℓ3ψ	ℓ3ψ	NOUN
ejde-1812	184	35	1−α−β(1−α)(t)∥x1	1−α−β(1−α)(t)∥x1	NUM
ejde-1812	184	36	−	−	NOUN
ejde-1812	184	37	x2∥	x2∥	NOUN
ejde-1812	184	38	,	,	PUNCT
ejde-1812	184	39	∀xi	∀xi	PROPN
ejde-1812	184	40	∈	∈	PROPN
ejde-1812	184	41	x(i	x(i	PROPN
ejde-1812	184	42	=	=	SYM
ejde-1812	184	43	1	1	NUM
ejde-1812	184	44	,	,	PUNCT
ejde-1812	184	45	2	2	NUM
ejde-1812	184	46	)	)	PUNCT
ejde-1812	184	47	,	,	PUNCT
ejde-1812	184	48	t	t	PROPN
ejde-1812	184	49	∈	∈	PROPN
ejde-1812	185	1	j.	j.	PROPN
ejde-1812	185	2	the	the	DET
ejde-1812	185	3	following	follow	VERB
ejde-1812	185	4	lemma	lemma	PROPN
ejde-1812	185	5	will	will	AUX
ejde-1812	185	6	be	be	AUX
ejde-1812	185	7	used	use	VERB
ejde-1812	185	8	to	to	PART
ejde-1812	185	9	establish	establish	VERB
ejde-1812	185	10	the	the	DET
ejde-1812	185	11	approximate	approximate	ADJ
ejde-1812	185	12	controllability	controllability	NOUN
ejde-1812	185	13	of	of	ADP
ejde-1812	185	14	problem	problem	NOUN
ejde-1812	185	15	(	(	PUNCT
ejde-1812	185	16	3.1	3.1	NUM
ejde-1812	185	17	)	)	PUNCT
ejde-1812	185	18	.	.	PUNCT
ejde-1812	186	1	lemma	lemma	PROPN
ejde-1812	186	2	3.4	3.4	NUM
ejde-1812	186	3	.	.	PUNCT
ejde-1812	187	1	if	if	SCONJ
ejde-1812	187	2	(	(	PUNCT
ejde-1812	187	3	h1	h1	PROPN
ejde-1812	187	4	)	)	PUNCT
ejde-1812	187	5	and	and	CCONJ
ejde-1812	187	6	(	(	PUNCT
ejde-1812	187	7	h3	h3	NOUN
ejde-1812	187	8	)	)	PUNCT
ejde-1812	187	9	are	be	AUX
ejde-1812	187	10	satisfied	satisfied	ADJ
ejde-1812	187	11	,	,	PUNCT
ejde-1812	187	12	then	then	ADV
ejde-1812	187	13	∥x∥c1−α−β(1−α);ψ	∥x∥c1−α−β(1−α);ψ	VERB
ejde-1812	187	14	≤	≤	NOUN
ejde-1812	187	15	σeα	σeα	NOUN
ejde-1812	187	16	(	(	PUNCT
ejde-1812	187	17	mℓ1ψ	mℓ1ψ	PROPN
ejde-1812	187	18	1−β(1−α)(b	1−β(1−α)(b	NUM
ejde-1812	187	19	)	)	PUNCT
ejde-1812	187	20	)	)	PUNCT
ejde-1812	187	21	,	,	PUNCT
ejde-1812	188	1	∥x−	∥x−	PROPN
ejde-1812	188	2	y∥c1−α−β(1−α);ψ	y∥c1−α−β(1−α);ψ	NOUN
ejde-1812	188	3	≤	≤	NOUN
ejde-1812	188	4	ϕeα	ϕeα	NOUN
ejde-1812	188	5	(	(	PUNCT
ejde-1812	188	6	mℓ3ψ	mℓ3ψ	PROPN
ejde-1812	188	7	1−β(1−α)(b	1−β(1−α)(b	NUM
ejde-1812	188	8	)	)	PUNCT
ejde-1812	188	9	)	)	PUNCT
ejde-1812	189	1	∥bu−bv∥lr(j	∥bu−bv∥lr(j	PROPN
ejde-1812	189	2	,	,	PUNCT
ejde-1812	189	3	x	x	NOUN
ejde-1812	189	4	)	)	PUNCT
ejde-1812	189	5	,	,	PUNCT
ejde-1812	189	6	where	where	SCONJ
ejde-1812	189	7	x	x	PRON
ejde-1812	189	8	and	and	CCONJ
ejde-1812	189	9	y	y	PROPN
ejde-1812	189	10	are	be	AUX
ejde-1812	189	11	the	the	DET
ejde-1812	189	12	unique	unique	ADJ
ejde-1812	189	13	mild	mild	ADJ
ejde-1812	189	14	solutions	solution	NOUN
ejde-1812	189	15	of	of	ADP
ejde-1812	189	16	problem	problem	NOUN
ejde-1812	189	17	(	(	PUNCT
ejde-1812	189	18	3.1	3.1	NUM
ejde-1812	189	19	)	)	PUNCT
ejde-1812	189	20	with	with	ADP
ejde-1812	189	21	respect	respect	NOUN
ejde-1812	189	22	to	to	ADP
ejde-1812	189	23	u	u	NOUN
ejde-1812	189	24	and	and	CCONJ
ejde-1812	189	25	v	v	NOUN
ejde-1812	189	26	(	(	PUNCT
ejde-1812	189	27	u	u	NOUN
ejde-1812	189	28	,	,	PUNCT
ejde-1812	189	29	v	v	NOUN
ejde-1812	189	30	∈	∈	PROPN
ejde-1812	189	31	v	v	NOUN
ejde-1812	189	32	)	)	PUNCT
ejde-1812	189	33	,	,	PUNCT
ejde-1812	189	34	respectively	respectively	ADV
ejde-1812	189	35	,	,	PUNCT
ejde-1812	189	36	eα	eα	PROPN
ejde-1812	189	37	is	be	AUX
ejde-1812	189	38	the	the	DET
ejde-1812	189	39	mittag	mittag	ADJ
ejde-1812	189	40	-	-	PUNCT
ejde-1812	189	41	leffler	leffler	NOUN
ejde-1812	189	42	function	function	NOUN
ejde-1812	189	43	defined	define	VERB
ejde-1812	189	44	by	by	ADP
ejde-1812	189	45	eα(z	eα(z	NOUN
ejde-1812	189	46	)	)	PUNCT
ejde-1812	189	47	=	=	NOUN
ejde-1812	190	1	∞∑	∞∑	NUM
ejde-1812	190	2	i=0	i=0	PROPN
ejde-1812	190	3	zk	zk	X
ejde-1812	190	4	γ(kα+	γ(kα+	PRON
ejde-1812	190	5	1	1	NUM
ejde-1812	190	6	)	)	PUNCT
ejde-1812	190	7	,	,	PUNCT
ejde-1812	190	8	ejde-2025/109	ejde-2025/109	ADP
ejde-1812	190	9	evolution	evolution	PROPN
ejde-1812	190	10	ψ	ψ	NOUN
ejde-1812	190	11	-	-	ADJ
ejde-1812	190	12	hilfer	hilfer	NOUN
ejde-1812	190	13	fractional	fractional	ADJ
ejde-1812	190	14	differential	differential	ADJ
ejde-1812	190	15	equations	equation	NOUN
ejde-1812	190	16	7	7	NUM
ejde-1812	190	17	ϕ	ϕ	NOUN
ejde-1812	190	18	=	=	NOUN
ejde-1812	190	19	mψ1−1	mψ1−1	ADJ
ejde-1812	190	20	/	/	SYM
ejde-1812	190	21	r(b	r(b	NOUN
ejde-1812	190	22	)	)	PUNCT
ejde-1812	190	23	γ(α	γ(α	NOUN
ejde-1812	190	24	)	)	PUNCT
ejde-1812	190	25	(	(	PUNCT
ejde-1812	190	26	r	r	NOUN
ejde-1812	190	27	−	−	PROPN
ejde-1812	190	28	1	1	NUM
ejde-1812	190	29	rα−	rα−	SYM
ejde-1812	190	30	1	1	NUM
ejde-1812	190	31	)	)	PUNCT
ejde-1812	190	32	1−1	1−1	NUM
ejde-1812	190	33	/	/	SYM
ejde-1812	190	34	r	r	NOUN
ejde-1812	190	35	,	,	PUNCT
ejde-1812	190	36	σ	σ	NOUN
ejde-1812	190	37	=	=	PUNCT
ejde-1812	190	38	m	m	VERB
ejde-1812	190	39	γ(α+	γ(α+	NUM
ejde-1812	190	40	β(1−	β(1−	NOUN
ejde-1812	190	41	α	α	X
ejde-1812	190	42	)	)	PUNCT
ejde-1812	190	43	)	)	PUNCT
ejde-1812	190	44	∥x0∥+	∥x0∥+	NOUN
ejde-1812	190	45	mψ1−1	mψ1−1	ADJ
ejde-1812	190	46	/	/	SYM
ejde-1812	190	47	r(b	r(b	NOUN
ejde-1812	190	48	)	)	PUNCT
ejde-1812	190	49	γ(α	γ(α	NOUN
ejde-1812	190	50	)	)	PUNCT
ejde-1812	190	51	(	(	PUNCT
ejde-1812	190	52	r	r	NOUN
ejde-1812	190	53	−	−	PROPN
ejde-1812	190	54	1	1	NUM
ejde-1812	190	55	rα−	rα−	SYM
ejde-1812	190	56	1	1	NUM
ejde-1812	190	57	)	)	PUNCT
ejde-1812	190	58	1−1	1−1	NUM
ejde-1812	190	59	/	/	SYM
ejde-1812	190	60	r	r	NOUN
ejde-1812	190	61	(	(	PUNCT
ejde-1812	190	62	∥bu∥lr(j	∥bu∥lr(j	PROPN
ejde-1812	190	63	,	,	PUNCT
ejde-1812	190	64	x	x	X
ejde-1812	190	65	)	)	PUNCT
ejde-1812	190	66	+	+	SYM
ejde-1812	190	67	∥µ∥lr(j	∥µ∥lr(j	PROPN
ejde-1812	190	68	,	,	PUNCT
ejde-1812	190	69	x	x	NOUN
ejde-1812	190	70	)	)	PUNCT
ejde-1812	190	71	)	)	PUNCT
ejde-1812	190	72	.	.	PUNCT
ejde-1812	191	1	proof	proof	NOUN
ejde-1812	191	2	.	.	PUNCT
ejde-1812	192	1	since	since	SCONJ
ejde-1812	192	2	x	x	PRON
ejde-1812	192	3	is	be	AUX
ejde-1812	192	4	the	the	DET
ejde-1812	192	5	unique	unique	ADJ
ejde-1812	192	6	mild	mild	ADJ
ejde-1812	192	7	solution	solution	NOUN
ejde-1812	192	8	of	of	ADP
ejde-1812	192	9	(	(	PUNCT
ejde-1812	192	10	3.1	3.1	NUM
ejde-1812	192	11	)	)	PUNCT
ejde-1812	192	12	with	with	ADP
ejde-1812	192	13	respect	respect	NOUN
ejde-1812	192	14	to	to	ADP
ejde-1812	192	15	u	u	NOUN
ejde-1812	192	16	∈	∈	PROPN
ejde-1812	192	17	v	v	NOUN
ejde-1812	192	18	in	in	ADP
ejde-1812	192	19	c1−α−β(1−α);ψ(j	c1−α−β(1−α);ψ(j	PROPN
ejde-1812	192	20	,	,	PUNCT
ejde-1812	192	21	x	x	X
ejde-1812	192	22	)	)	PUNCT
ejde-1812	192	23	,	,	PUNCT
ejde-1812	192	24	we	we	PRON
ejde-1812	192	25	have	have	VERB
ejde-1812	192	26	x(t	x(t	PROPN
ejde-1812	192	27	)	)	PUNCT
ejde-1812	192	28	=	=	PRON
ejde-1812	192	29	(	(	PUNCT
ejde-1812	192	30	iβ(1−α)kα	iβ(1−α)kα	PROPN
ejde-1812	192	31	)	)	PUNCT
ejde-1812	193	1	(	(	PUNCT
ejde-1812	193	2	ψ(t))x0	ψ(t))x0	PROPN
ejde-1812	193	3	+	+	CCONJ
ejde-1812	193	4	∫	∫	PROPN
ejde-1812	193	5	t	t	PROPN
ejde-1812	193	6	0	0	NUM
ejde-1812	193	7	kα(ψ(t)−	kα(ψ(t)−	PROPN
ejde-1812	193	8	ψ(s))[bu(s	ψ(s))[bu(s	PROPN
ejde-1812	193	9	)	)	PUNCT
ejde-1812	193	10	+	+	NUM
ejde-1812	193	11	f(s	f(	NOUN
ejde-1812	193	12	,	,	PUNCT
ejde-1812	193	13	x(s))]ψ′(s)ds	x(s))]ψ′(s)ds	PROPN
ejde-1812	193	14	.	.	PROPN
ejde-1812	194	1	for	for	ADP
ejde-1812	194	2	t	t	PROPN
ejde-1812	194	3	∈	∈	PROPN
ejde-1812	194	4	j	j	PROPN
ejde-1812	194	5	,	,	PUNCT
ejde-1812	194	6	we	we	PRON
ejde-1812	194	7	have	have	VERB
ejde-1812	194	8	ψ1−α−β(1−α)(t)∥x(t)∥	ψ1−α−β(1−α)(t)∥x(t)∥	NOUN
ejde-1812	194	9	≤	≤	NUM
ejde-1812	194	10	ψ1−α−β(1−α)(t)∥	ψ1−α−β(1−α)(t)∥	NOUN
ejde-1812	194	11	(	(	PUNCT
ejde-1812	194	12	iβ(1−α)kα	iβ(1−α)kα	PROPN
ejde-1812	194	13	)	)	PUNCT
ejde-1812	194	14	(	(	PUNCT
ejde-1812	194	15	ψ(t))x0∥+	ψ(t))x0∥+	NOUN
ejde-1812	194	16	ψ1−α−β(1−α)(t	ψ1−α−β(1−α)(t	ADJ
ejde-1812	194	17	)	)	PUNCT
ejde-1812	195	1	×	×	NOUN
ejde-1812	195	2	∫	∫	PROPN
ejde-1812	195	3	t	t	PROPN
ejde-1812	195	4	0	0	NUM
ejde-1812	196	1	∥kα(ψ(t)−	∥kα(ψ(t)−	PROPN
ejde-1812	196	2	ψ(s))ψ′(s)bu(s)∥	ψ(s))ψ′(s)bu(s)∥	PROPN
ejde-1812	196	3	ds	ds	ADJ
ejde-1812	196	4	+	+	CCONJ
ejde-1812	196	5	ψ1−α−β(1−α)(t	ψ1−α−β(1−α)(t	ADJ
ejde-1812	196	6	)	)	PUNCT
ejde-1812	196	7	∫	∫	PROPN
ejde-1812	197	1	t	t	NOUN
ejde-1812	197	2	0	0	NUM
ejde-1812	198	1	∥kα(ψ(t)−	∥kα(ψ(t)−	PROPN
ejde-1812	198	2	ψ(s))ψ′(s)f(s	ψ(s))ψ′(s)f(s	VERB
ejde-1812	198	3	,	,	PUNCT
ejde-1812	198	4	x(s))∥	x(s))∥	X
ejde-1812	198	5	ds	ds	PROPN
ejde-1812	198	6	≤	≤	NUM
ejde-1812	198	7	m	m	VERB
ejde-1812	198	8	γ(α+	γ(α+	X
ejde-1812	198	9	β(1−	β(1−	NOUN
ejde-1812	198	10	α	α	NUM
ejde-1812	198	11	)	)	PUNCT
ejde-1812	198	12	)	)	PUNCT
ejde-1812	199	1	∥x0∥+	∥x0∥+	PROPN
ejde-1812	199	2	m	m	PROPN
ejde-1812	199	3	γ(α	γ(α	NOUN
ejde-1812	199	4	)	)	PUNCT
ejde-1812	199	5	ψ1−α−β(1−α)(t	ψ1−α−β(1−α)(t	NOUN
ejde-1812	199	6	)	)	PUNCT
ejde-1812	199	7	∫	∫	PROPN
ejde-1812	199	8	t	t	PROPN
ejde-1812	199	9	0	0	NUM
ejde-1812	199	10	(	(	PUNCT
ejde-1812	199	11	ψ(t)−	ψ(t)−	PROPN
ejde-1812	199	12	ψ(s))1−αψ′(s	ψ(s))1−αψ′(s	PROPN
ejde-1812	199	13	)	)	PUNCT
ejde-1812	199	14	×	×	PROPN
ejde-1812	199	15	∥bu(s)∥ds+	∥bu(s)∥ds+	PROPN
ejde-1812	199	16	m	m	NOUN
ejde-1812	199	17	γ(α	γ(α	NOUN
ejde-1812	199	18	)	)	PUNCT
ejde-1812	199	19	ψ1−α−β(1−α)(t	ψ1−α−β(1−α)(t	NOUN
ejde-1812	199	20	)	)	PUNCT
ejde-1812	199	21	∫	∫	PROPN
ejde-1812	200	1	t	t	PROPN
ejde-1812	200	2	0	0	NUM
ejde-1812	200	3	(	(	PUNCT
ejde-1812	200	4	ψ(t)−	ψ(t)−	PROPN
ejde-1812	200	5	ψ(s))α−1ψ′(s	ψ(s))α−1ψ′(s	PROPN
ejde-1812	200	6	)	)	PUNCT
ejde-1812	200	7	×	×	NOUN
ejde-1812	200	8	[	[	PUNCT
ejde-1812	200	9	µ(s	µ(s	X
ejde-1812	200	10	)	)	PUNCT
ejde-1812	200	11	+	+	CCONJ
ejde-1812	200	12	ℓ1ψ	ℓ1ψ	PROPN
ejde-1812	200	13	1−α−β(1−α)(s)∥x(s)∥	1−α−β(1−α)(s)∥x(s)∥	NUM
ejde-1812	200	14	]	]	PUNCT
ejde-1812	200	15	ds	ds	PROPN
ejde-1812	200	16	≤	≤	NUM
ejde-1812	200	17	m	m	VERB
ejde-1812	200	18	γ(α+	γ(α+	X
ejde-1812	200	19	β(1−	β(1−	NOUN
ejde-1812	200	20	α	α	NUM
ejde-1812	200	21	)	)	PUNCT
ejde-1812	200	22	)	)	PUNCT
ejde-1812	200	23	∥x0∥+	∥x0∥+	NOUN
ejde-1812	200	24	mψ1−1	mψ1−1	ADJ
ejde-1812	200	25	/	/	SYM
ejde-1812	200	26	r(b	r(b	NOUN
ejde-1812	200	27	)	)	PUNCT
ejde-1812	200	28	γ(α	γ(α	NOUN
ejde-1812	200	29	)	)	PUNCT
ejde-1812	200	30	×	×	NOUN
ejde-1812	200	31	(	(	PUNCT
ejde-1812	200	32	r	r	NOUN
ejde-1812	200	33	−	−	PROPN
ejde-1812	200	34	1	1	NUM
ejde-1812	200	35	rα−	rα−	SYM
ejde-1812	200	36	1	1	NUM
ejde-1812	200	37	)	)	PUNCT
ejde-1812	200	38	1−1	1−1	NUM
ejde-1812	200	39	/	/	SYM
ejde-1812	200	40	r	r	NOUN
ejde-1812	200	41	(	(	PUNCT
ejde-1812	200	42	∥bu∥lr(j	∥bu∥lr(j	PROPN
ejde-1812	200	43	,	,	PUNCT
ejde-1812	200	44	x	x	X
ejde-1812	200	45	)	)	PUNCT
ejde-1812	200	46	+	+	SYM
ejde-1812	200	47	∥µ∥lr(j	∥µ∥lr(j	PROPN
ejde-1812	200	48	,	,	PUNCT
ejde-1812	200	49	x	x	NOUN
ejde-1812	200	50	)	)	PUNCT
ejde-1812	200	51	)	)	PUNCT
ejde-1812	201	1	+	+	CCONJ
ejde-1812	201	2	mℓ1ψ	mℓ1ψ	PROPN
ejde-1812	201	3	1−α−β(1−α)(b	1−α−β(1−α)(b	PROPN
ejde-1812	201	4	)	)	PUNCT
ejde-1812	201	5	γ(α	γ(α	PROPN
ejde-1812	201	6	)	)	PUNCT
ejde-1812	202	1	∫	∫	PROPN
ejde-1812	202	2	t	t	PROPN
ejde-1812	202	3	0	0	NUM
ejde-1812	203	1	(	(	PUNCT
ejde-1812	203	2	ψ(t)−	ψ(t)−	PROPN
ejde-1812	203	3	ψ(s))α−1ψ′(s)ψ1−α−β(1−α)(s)∥x(s)∥ds	ψ(s))α−1ψ′(s)ψ1−α−β(1−α)(s)∥x(s)∥ds	VERB
ejde-1812	203	4	.	.	PUNCT
ejde-1812	204	1	setting	set	VERB
ejde-1812	204	2	m(t	m(t	NOUN
ejde-1812	204	3	)	)	PUNCT
ejde-1812	204	4	=	=	SYM
ejde-1812	205	1	ψ1−α−β(1−α)(t)∥x(t)∥	ψ1−α−β(1−α)(t)∥x(t)∥	PROPN
ejde-1812	205	2	,	,	PUNCT
ejde-1812	205	3	in	in	ADP
ejde-1812	205	4	the	the	DET
ejde-1812	205	5	above	above	ADJ
ejde-1812	205	6	inequality	inequality	NOUN
ejde-1812	205	7	we	we	PRON
ejde-1812	205	8	obtain	obtain	VERB
ejde-1812	205	9	m(t	m(t	NOUN
ejde-1812	205	10	)	)	PUNCT
ejde-1812	206	1	≤	≤	NUM
ejde-1812	206	2	σ	σ	PROPN
ejde-1812	206	3	+	+	PROPN
ejde-1812	206	4	mℓ1ψ	mℓ1ψ	PROPN
ejde-1812	206	5	1−α−β(1−α)(b	1−α−β(1−α)(b	PROPN
ejde-1812	206	6	)	)	PUNCT
ejde-1812	206	7	γ(α	γ(α	PROPN
ejde-1812	206	8	)	)	PUNCT
ejde-1812	207	1	∫	∫	PROPN
ejde-1812	207	2	t	t	PROPN
ejde-1812	207	3	0	0	NUM
ejde-1812	208	1	(	(	PUNCT
ejde-1812	208	2	ψ(t)−	ψ(t)−	PROPN
ejde-1812	208	3	ψ(s))α−1ψ′(s)m(s)ds	ψ(s))α−1ψ′(s)m(s)ds	PROPN
ejde-1812	208	4	.	.	PUNCT
ejde-1812	209	1	by	by	ADP
ejde-1812	209	2	[	[	X
ejde-1812	209	3	27	27	NUM
ejde-1812	209	4	,	,	PUNCT
ejde-1812	209	5	theorem	theorem	VERB
ejde-1812	209	6	3	3	NUM
ejde-1812	209	7	]	]	PUNCT
ejde-1812	209	8	,	,	PUNCT
ejde-1812	209	9	we	we	PRON
ejde-1812	209	10	can	can	AUX
ejde-1812	209	11	obtain	obtain	VERB
ejde-1812	209	12	m(t	m(t	NOUN
ejde-1812	209	13	)	)	PUNCT
ejde-1812	209	14	≤	≤	NOUN
ejde-1812	209	15	σeα	σeα	NOUN
ejde-1812	209	16	(	(	PUNCT
ejde-1812	209	17	mℓ1ψ	mℓ1ψ	PROPN
ejde-1812	209	18	1−α−β(1−α)(b)ψα(t	1−α−β(1−α)(b)ψα(t	NUM
ejde-1812	209	19	)	)	PUNCT
ejde-1812	209	20	)	)	PUNCT
ejde-1812	209	21	≤	≤	NOUN
ejde-1812	209	22	σeα	σeα	NOUN
ejde-1812	209	23	(	(	PUNCT
ejde-1812	209	24	mℓ1ψ	mℓ1ψ	PROPN
ejde-1812	209	25	1−β(1−α)(b	1−β(1−α)(b	NUM
ejde-1812	209	26	)	)	PUNCT
ejde-1812	209	27	)	)	PUNCT
ejde-1812	209	28	.	.	PUNCT
ejde-1812	210	1	so	so	ADV
ejde-1812	210	2	∥x∥c1−α−β(1−α);ψ	∥x∥c1−α−β(1−α);ψ	NOUN
ejde-1812	210	3	=	=	PUNCT
ejde-1812	210	4	sup	sup	NOUN
ejde-1812	210	5	t∈j	t∈j	NOUN
ejde-1812	210	6	ψ1−α−β(1−α)(t)∥x(t)∥	ψ1−α−β(1−α)(t)∥x(t)∥	NOUN
ejde-1812	210	7	≤	≤	ADJ
ejde-1812	210	8	σeα	σeα	NOUN
ejde-1812	210	9	(	(	PUNCT
ejde-1812	210	10	mℓ1ψ	mℓ1ψ	PROPN
ejde-1812	210	11	1−β(1−α)(b	1−β(1−α)(b	NUM
ejde-1812	210	12	)	)	PUNCT
ejde-1812	210	13	)	)	PUNCT
ejde-1812	210	14	.	.	PUNCT
ejde-1812	211	1	a	a	DET
ejde-1812	211	2	parallel	parallel	ADJ
ejde-1812	211	3	argument	argument	NOUN
ejde-1812	211	4	yields	yield	VERB
ejde-1812	211	5	∥x−	∥x−	PROPN
ejde-1812	211	6	y∥c1−α−β(1−α);ψ	y∥c1−α−β(1−α);ψ	PROPN
ejde-1812	211	7	≤	≤	NOUN
ejde-1812	211	8	ϕeα	ϕeα	NOUN
ejde-1812	211	9	(	(	PUNCT
ejde-1812	211	10	mℓ3ψ	mℓ3ψ	PROPN
ejde-1812	211	11	1−β(1−α)(b	1−β(1−α)(b	NUM
ejde-1812	211	12	)	)	PUNCT
ejde-1812	211	13	)	)	PUNCT
ejde-1812	212	1	∥bu−bv∥lr(j	∥bu−bv∥lr(j	PROPN
ejde-1812	212	2	,	,	PUNCT
ejde-1812	212	3	x	x	NOUN
ejde-1812	212	4	)	)	PUNCT
ejde-1812	212	5	.	.	PUNCT
ejde-1812	213	1	this	this	PRON
ejde-1812	213	2	completes	complete	VERB
ejde-1812	213	3	the	the	DET
ejde-1812	213	4	proof	proof	NOUN
ejde-1812	213	5	.	.	PUNCT
ejde-1812	214	1	□	□	PUNCT
ejde-1812	214	2	moreover	moreover	ADV
ejde-1812	214	3	,	,	PUNCT
ejde-1812	214	4	to	to	PART
ejde-1812	214	5	discuss	discuss	VERB
ejde-1812	214	6	the	the	DET
ejde-1812	214	7	approximate	approximate	ADJ
ejde-1812	214	8	controllability	controllability	NOUN
ejde-1812	214	9	of	of	ADP
ejde-1812	214	10	problem	problem	NOUN
ejde-1812	214	11	(	(	PUNCT
ejde-1812	214	12	3.1	3.1	NUM
ejde-1812	214	13	)	)	PUNCT
ejde-1812	214	14	,	,	PUNCT
ejde-1812	214	15	we	we	PRON
ejde-1812	214	16	assume	assume	VERB
ejde-1812	214	17	that	that	SCONJ
ejde-1812	214	18	(	(	PUNCT
ejde-1812	214	19	h4	h4	PROPN
ejde-1812	214	20	)	)	PUNCT
ejde-1812	214	21	for	for	ADP
ejde-1812	214	22	each	each	DET
ejde-1812	214	23	ε	ε	PROPN
ejde-1812	214	24	>	>	X
ejde-1812	214	25	0	0	PUNCT
ejde-1812	214	26	and	and	CCONJ
ejde-1812	214	27	δ	δ	PROPN
ejde-1812	214	28	∈	∈	PROPN
ejde-1812	214	29	lr(j	lr(j	NOUN
ejde-1812	214	30	,	,	PUNCT
ejde-1812	214	31	x	x	X
ejde-1812	214	32	)	)	PUNCT
ejde-1812	214	33	,	,	PUNCT
ejde-1812	214	34	there	there	PRON
ejde-1812	214	35	exists	exist	VERB
ejde-1812	214	36	a	a	DET
ejde-1812	214	37	control	control	NOUN
ejde-1812	214	38	function	function	NOUN
ejde-1812	214	39	u	u	PROPN
ejde-1812	214	40	∈	∈	PROPN
ejde-1812	214	41	lr(j	lr(j	X
ejde-1812	214	42	,	,	PUNCT
ejde-1812	214	43	u	u	NOUN
ejde-1812	214	44	)	)	PUNCT
ejde-1812	214	45	such	such	ADJ
ejde-1812	214	46	that	that	SCONJ
ejde-1812	214	47	∥hδ	∥hδ	NUM
ejde-1812	214	48	−hbu∥	−hbu∥	NOUN
ejde-1812	214	49	<	<	X
ejde-1812	214	50	ε	ε	PROPN
ejde-1812	214	51	,	,	PUNCT
ejde-1812	214	52	(	(	PUNCT
ejde-1812	214	53	3.5	3.5	NUM
ejde-1812	214	54	)	)	PUNCT
ejde-1812	214	55	∥bu∥lr(j	∥bu∥lr(j	PROPN
ejde-1812	214	56	,	,	PUNCT
ejde-1812	214	57	x	x	X
ejde-1812	214	58	)	)	PUNCT
ejde-1812	214	59	<	<	X
ejde-1812	214	60	c∥δ∥lr(j	c∥δ∥lr(j	NOUN
ejde-1812	214	61	,	,	PUNCT
ejde-1812	214	62	x	x	NOUN
ejde-1812	214	63	)	)	PUNCT
ejde-1812	214	64	,	,	PUNCT
ejde-1812	214	65	(	(	PUNCT
ejde-1812	214	66	3.6	3.6	NUM
ejde-1812	214	67	)	)	PUNCT
ejde-1812	214	68	8	8	NUM
ejde-1812	214	69	j.	j.	PROPN
ejde-1812	214	70	liang	liang	PROPN
ejde-1812	214	71	,	,	PUNCT
ejde-1812	214	72	y.	y.	PROPN
ejde-1812	214	73	mu	mu	PROPN
ejde-1812	214	74	,	,	PUNCT
ejde-1812	214	75	t.-j	t.-j	PROPN
ejde-1812	214	76	.	.	PUNCT
ejde-1812	215	1	xiao	xiao	PROPN
ejde-1812	215	2	ejde-2025/109	ejde-2025/109	ADP
ejde-1812	215	3	where	where	SCONJ
ejde-1812	215	4	c	c	PROPN
ejde-1812	215	5	is	be	AUX
ejde-1812	215	6	a	a	DET
ejde-1812	215	7	positive	positive	ADJ
ejde-1812	215	8	constant	constant	ADJ
ejde-1812	215	9	independent	independent	NOUN
ejde-1812	215	10	of	of	ADP
ejde-1812	215	11	δ	δ	PROPN
ejde-1812	215	12	∈	∈	PROPN
ejde-1812	215	13	lr(j	lr(j	NOUN
ejde-1812	215	14	,	,	PUNCT
ejde-1812	215	15	x	x	NOUN
ejde-1812	215	16	)	)	PUNCT
ejde-1812	215	17	,	,	PUNCT
ejde-1812	215	18	and	and	CCONJ
ejde-1812	215	19	cℓ3eα	cℓ3eα	NUM
ejde-1812	215	20	(	(	PUNCT
ejde-1812	215	21	mℓ3ψ	mℓ3ψ	PROPN
ejde-1812	215	22	1−β(1−α)(b	1−β(1−α)(b	NUM
ejde-1812	215	23	)	)	PUNCT
ejde-1812	215	24	)	)	PUNCT
ejde-1812	215	25	mψ1−1	mψ1−1	ADJ
ejde-1812	215	26	/	/	SYM
ejde-1812	215	27	r(b	r(b	NOUN
ejde-1812	215	28	)	)	PUNCT
ejde-1812	215	29	γ(α	γ(α	NOUN
ejde-1812	215	30	)	)	PUNCT
ejde-1812	216	1	(	(	PUNCT
ejde-1812	216	2	r	r	NOUN
ejde-1812	216	3	−	−	PROPN
ejde-1812	216	4	1	1	NUM
ejde-1812	216	5	rα−	rα−	SYM
ejde-1812	216	6	1	1	NUM
ejde-1812	216	7	)	)	PUNCT
ejde-1812	216	8	1−1	1−1	NUM
ejde-1812	216	9	/	/	SYM
ejde-1812	216	10	r	r	NOUN
ejde-1812	216	11	<	<	X
ejde-1812	216	12	1	1	NUM
ejde-1812	216	13	.	.	PUNCT
ejde-1812	216	14	(	(	PUNCT
ejde-1812	216	15	3.7	3.7	NUM
ejde-1812	216	16	)	)	PUNCT
ejde-1812	216	17	theorem	theorem	VERB
ejde-1812	216	18	3.5	3.5	NUM
ejde-1812	216	19	.	.	PUNCT
ejde-1812	217	1	suppose	suppose	VERB
ejde-1812	217	2	that	that	SCONJ
ejde-1812	217	3	the	the	DET
ejde-1812	217	4	hypotheses	hypothesis	NOUN
ejde-1812	217	5	of	of	ADP
ejde-1812	217	6	lemma	lemma	PROPN
ejde-1812	217	7	3.4	3.4	NUM
ejde-1812	217	8	and	and	CCONJ
ejde-1812	217	9	(	(	PUNCT
ejde-1812	217	10	h4	h4	PROPN
ejde-1812	217	11	)	)	PUNCT
ejde-1812	217	12	hold	hold	NOUN
ejde-1812	217	13	.	.	PUNCT
ejde-1812	218	1	then	then	ADV
ejde-1812	218	2	problem	problem	NOUN
ejde-1812	218	3	(	(	PUNCT
ejde-1812	218	4	3.1	3.1	NUM
ejde-1812	218	5	)	)	PUNCT
ejde-1812	218	6	is	be	AUX
ejde-1812	218	7	approximately	approximately	ADV
ejde-1812	218	8	controllable	controllable	ADJ
ejde-1812	218	9	on	on	ADP
ejde-1812	218	10	j	j	PROPN
ejde-1812	218	11	.	.	PUNCT
ejde-1812	219	1	proof	proof	NOUN
ejde-1812	219	2	.	.	PUNCT
ejde-1812	220	1	as	as	SCONJ
ejde-1812	220	2	the	the	DET
ejde-1812	220	3	domain	domain	NOUN
ejde-1812	220	4	d(a	d(a	PROPN
ejde-1812	220	5	)	)	PUNCT
ejde-1812	220	6	of	of	ADP
ejde-1812	220	7	the	the	DET
ejde-1812	220	8	operator	operator	NOUN
ejde-1812	220	9	a	a	PRON
ejde-1812	220	10	is	be	AUX
ejde-1812	220	11	dense	dense	ADJ
ejde-1812	220	12	in	in	ADP
ejde-1812	220	13	x	x	PRON
ejde-1812	220	14	,	,	PUNCT
ejde-1812	220	15	we	we	PRON
ejde-1812	220	16	need	need	AUX
ejde-1812	220	17	only	only	ADV
ejde-1812	220	18	prove	prove	VERB
ejde-1812	220	19	that	that	SCONJ
ejde-1812	220	20	d(a	d(a	PROPN
ejde-1812	220	21	)	)	PUNCT
ejde-1812	220	22	⊂	⊂	PROPN
ejde-1812	220	23	kb(f	kb(f	NOUN
ejde-1812	220	24	)	)	PUNCT
ejde-1812	220	25	,	,	PUNCT
ejde-1812	220	26	i.e.	i.e.	X
ejde-1812	220	27	,	,	PUNCT
ejde-1812	220	28	for	for	ADP
ejde-1812	220	29	any	any	DET
ejde-1812	220	30	ξ	ξ	PROPN
ejde-1812	220	31	∈	∈	PROPN
ejde-1812	220	32	d(a	d(a	PROPN
ejde-1812	220	33	)	)	PUNCT
ejde-1812	220	34	and	and	CCONJ
ejde-1812	220	35	each	each	DET
ejde-1812	220	36	ε	ε	PROPN
ejde-1812	220	37	>	>	X
ejde-1812	220	38	0	0	PROPN
ejde-1812	220	39	,	,	PUNCT
ejde-1812	220	40	there	there	PRON
ejde-1812	220	41	exits	exit	VERB
ejde-1812	220	42	a	a	DET
ejde-1812	220	43	uε	uε	PROPN
ejde-1812	220	44	∈	∈	PROPN
ejde-1812	220	45	v	v	NOUN
ejde-1812	220	46	,	,	PUNCT
ejde-1812	221	1	such	such	ADJ
ejde-1812	221	2	that	that	SCONJ
ejde-1812	221	3	∥ξ	∥ξ	PROPN
ejde-1812	221	4	−	−	PROPN
ejde-1812	221	5	(	(	PUNCT
ejde-1812	221	6	iβ(1−α)kα	iβ(1−α)kα	PROPN
ejde-1812	221	7	)	)	PUNCT
ejde-1812	221	8	(	(	PUNCT
ejde-1812	221	9	ψ(b))x0	ψ(b))x0	VERB
ejde-1812	221	10	−hnf	−hnf	ADV
ejde-1812	221	11	(	(	PUNCT
ejde-1812	221	12	xε)−hbuε∥	xε)−hbuε∥	X
ejde-1812	221	13	<	<	X
ejde-1812	221	14	ε	ε	PROPN
ejde-1812	221	15	,	,	PUNCT
ejde-1812	221	16	(	(	PUNCT
ejde-1812	221	17	3.8	3.8	NUM
ejde-1812	221	18	)	)	PUNCT
ejde-1812	221	19	where	where	SCONJ
ejde-1812	221	20	xε(t	xε(t	X
ejde-1812	221	21	)	)	PUNCT
ejde-1812	221	22	=	=	SYM
ejde-1812	221	23	x(t;uε	x(t;uε	PROPN
ejde-1812	221	24	)	)	PUNCT
ejde-1812	221	25	,	,	PUNCT
ejde-1812	221	26	t	t	PROPN
ejde-1812	221	27	∈	∈	PROPN
ejde-1812	221	28	(	(	PUNCT
ejde-1812	221	29	0	0	NUM
ejde-1812	221	30	,	,	PUNCT
ejde-1812	221	31	b	b	NOUN
ejde-1812	221	32	]	]	X
ejde-1812	221	33	.	.	PUNCT
ejde-1812	222	1	first	first	ADV
ejde-1812	222	2	,	,	PUNCT
ejde-1812	222	3	for	for	ADP
ejde-1812	222	4	each	each	DET
ejde-1812	222	5	x0	x0	PROPN
ejde-1812	222	6	∈	∈	PROPN
ejde-1812	222	7	x	x	NOUN
ejde-1812	222	8	,	,	PUNCT
ejde-1812	222	9	due	due	ADP
ejde-1812	222	10	to	to	ADP
ejde-1812	222	11	the	the	DET
ejde-1812	222	12	differentiability	differentiability	NOUN
ejde-1812	222	13	of	of	ADP
ejde-1812	222	14	the	the	DET
ejde-1812	222	15	c0	c0	PROPN
ejde-1812	222	16	-	-	PUNCT
ejde-1812	222	17	semigroup	semigroup	PROPN
ejde-1812	222	18	t	t	PROPN
ejde-1812	222	19	(	(	PUNCT
ejde-1812	222	20	t)(t	t)(t	PROPN
ejde-1812	222	21	>	>	X
ejde-1812	222	22	0	0	NUM
ejde-1812	222	23	)	)	PUNCT
ejde-1812	222	24	,	,	PUNCT
ejde-1812	222	25	we	we	PRON
ejde-1812	222	26	know	know	VERB
ejde-1812	222	27	that	that	SCONJ
ejde-1812	222	28	(	(	PUNCT
ejde-1812	222	29	iβ(1−α)kα)(ψ(b))x0	iβ(1−α)kα)(ψ(b))x0	NOUN
ejde-1812	222	30	∈	∈	PROPN
ejde-1812	222	31	d(a	d(a	PROPN
ejde-1812	222	32	)	)	PUNCT
ejde-1812	222	33	.	.	PUNCT
ejde-1812	223	1	so	so	ADV
ejde-1812	223	2	,	,	PUNCT
ejde-1812	223	3	for	for	ADP
ejde-1812	223	4	any	any	DET
ejde-1812	223	5	given	give	VERB
ejde-1812	223	6	ξ	ξ	PROPN
ejde-1812	223	7	∈	∈	PROPN
ejde-1812	223	8	d(a	d(a	PROPN
ejde-1812	223	9	)	)	PUNCT
ejde-1812	223	10	,	,	PUNCT
ejde-1812	223	11	there	there	PRON
ejde-1812	223	12	exists	exist	VERB
ejde-1812	223	13	a	a	DET
ejde-1812	223	14	function	function	NOUN
ejde-1812	223	15	ω	ω	PROPN
ejde-1812	223	16	∈	∈	PROPN
ejde-1812	223	17	lr(j	lr(j	X
ejde-1812	223	18	,	,	PUNCT
ejde-1812	223	19	x	x	NOUN
ejde-1812	223	20	)	)	PUNCT
ejde-1812	223	21	such	such	ADJ
ejde-1812	223	22	that	that	SCONJ
ejde-1812	223	23	hω	hω	ADP
ejde-1812	223	24	=	=	SYM
ejde-1812	223	25	ξ	ξ	PROPN
ejde-1812	223	26	−	−	PROPN
ejde-1812	223	27	(	(	PUNCT
ejde-1812	223	28	iβ(1−α)kα	iβ(1−α)kα	PROPN
ejde-1812	223	29	)	)	PUNCT
ejde-1812	223	30	(	(	PUNCT
ejde-1812	223	31	ψ(b))x0	ψ(b))x0	NOUN
ejde-1812	223	32	,	,	PUNCT
ejde-1812	223	33	for	for	ADP
ejde-1812	223	34	example	example	NOUN
ejde-1812	223	35	,	,	PUNCT
ejde-1812	223	36	we	we	PRON
ejde-1812	223	37	can	can	AUX
ejde-1812	223	38	take	take	VERB
ejde-1812	223	39	ω(t	ω(t	NOUN
ejde-1812	223	40	)	)	PUNCT
ejde-1812	223	41	=	=	PUNCT
ejde-1812	224	1	[	[	X
ejde-1812	224	2	γ(α)]2(ψ(b)−	γ(α)]2(ψ(b)−	X
ejde-1812	224	3	ψ(t))1−α	ψ(t))1−α	SYM
ejde-1812	224	4	ψ(b	ψ(b	NOUN
ejde-1812	224	5	)	)	PUNCT
ejde-1812	224	6	[	[	PUNCT
ejde-1812	224	7	wα(ψ(b)−	wα(ψ(b)−	NOUN
ejde-1812	224	8	ψ(t	ψ(t	PROPN
ejde-1812	224	9	)	)	PUNCT
ejde-1812	224	10	)	)	PUNCT
ejde-1812	225	1	+	+	CCONJ
ejde-1812	225	2	2ψ(t	2ψ(t	X
ejde-1812	225	3	)	)	PUNCT
ejde-1812	225	4	dwα(ψ(b)−	dwα(ψ(b)−	PROPN
ejde-1812	225	5	ψ(t	ψ(t	PROPN
ejde-1812	225	6	)	)	PUNCT
ejde-1812	225	7	)	)	PUNCT
ejde-1812	225	8	dt	dt	X
ejde-1812	225	9	]	]	X
ejde-1812	225	10	×	×	X
ejde-1812	225	11	[	[	PUNCT
ejde-1812	225	12	ξ	ξ	X
ejde-1812	225	13	−	−	PROPN
ejde-1812	225	14	(	(	PUNCT
ejde-1812	225	15	iβ(1−α)kα)(ψ(b))x0	iβ(1−α)kα)(ψ(b))x0	NOUN
ejde-1812	225	16	]	]	PUNCT
ejde-1812	225	17	,	,	PUNCT
ejde-1812	225	18	t	t	PROPN
ejde-1812	225	19	∈	∈	PROPN
ejde-1812	225	20	(	(	PUNCT
ejde-1812	225	21	0	0	NUM
ejde-1812	225	22	,	,	PUNCT
ejde-1812	225	23	b	b	NOUN
ejde-1812	225	24	)	)	PUNCT
ejde-1812	225	25	,	,	PUNCT
ejde-1812	225	26	where	where	SCONJ
ejde-1812	225	27	wα(t	wα(t	X
ejde-1812	225	28	)	)	PUNCT
ejde-1812	225	29	=	=	SYM
ejde-1812	225	30	t1−αkα(t	t1−αkα(t	PROPN
ejde-1812	225	31	)	)	PUNCT
ejde-1812	225	32	.	.	PUNCT
ejde-1812	226	1	now	now	ADV
ejde-1812	226	2	,	,	PUNCT
ejde-1812	226	3	we	we	PRON
ejde-1812	226	4	show	show	VERB
ejde-1812	226	5	that	that	SCONJ
ejde-1812	226	6	there	there	PRON
ejde-1812	226	7	exists	exist	VERB
ejde-1812	226	8	a	a	DET
ejde-1812	226	9	control	control	NOUN
ejde-1812	226	10	function	function	NOUN
ejde-1812	226	11	uε	uε	PROPN
ejde-1812	226	12	∈	∈	PROPN
ejde-1812	226	13	v	v	ADP
ejde-1812	226	14	such	such	DET
ejde-1812	226	15	that	that	SCONJ
ejde-1812	226	16	the	the	DET
ejde-1812	226	17	inequality	inequality	NOUN
ejde-1812	226	18	(	(	PUNCT
ejde-1812	226	19	3.8	3.8	NUM
ejde-1812	226	20	)	)	PUNCT
ejde-1812	226	21	holds	hold	VERB
ejde-1812	226	22	.	.	PUNCT
ejde-1812	227	1	indeed	indeed	ADV
ejde-1812	227	2	,	,	PUNCT
ejde-1812	227	3	for	for	ADP
ejde-1812	227	4	any	any	DET
ejde-1812	227	5	given	give	VERB
ejde-1812	227	6	ε	ε	PROPN
ejde-1812	227	7	>	>	PUNCT
ejde-1812	227	8	0	0	PUNCT
ejde-1812	227	9	and	and	CCONJ
ejde-1812	227	10	u1	u1	PROPN
ejde-1812	227	11	∈	∈	PROPN
ejde-1812	227	12	v	v	NOUN
ejde-1812	227	13	,	,	PUNCT
ejde-1812	227	14	by	by	ADP
ejde-1812	227	15	(	(	PUNCT
ejde-1812	227	16	h4	h4	PROPN
ejde-1812	227	17	)	)	PUNCT
ejde-1812	227	18	,	,	PUNCT
ejde-1812	227	19	there	there	PRON
ejde-1812	227	20	exists	exist	VERB
ejde-1812	227	21	a	a	DET
ejde-1812	227	22	u2	u2	PROPN
ejde-1812	227	23	∈	∈	PROPN
ejde-1812	227	24	v	v	NOUN
ejde-1812	227	25	,	,	PUNCT
ejde-1812	227	26	such	such	ADJ
ejde-1812	227	27	that	that	SCONJ
ejde-1812	227	28	∥ξ	∥ξ	PROPN
ejde-1812	227	29	−	−	PROPN
ejde-1812	227	30	(	(	PUNCT
ejde-1812	227	31	iβ(1−α)kα	iβ(1−α)kα	PROPN
ejde-1812	227	32	)	)	PUNCT
ejde-1812	227	33	(	(	PUNCT
ejde-1812	227	34	ψ(b))x0	ψ(b))x0	VERB
ejde-1812	227	35	−hnf	−hnf	ADV
ejde-1812	227	36	(	(	PUNCT
ejde-1812	227	37	x1)−hbu2∥	x1)−hbu2∥	PROPN
ejde-1812	227	38	<	<	X
ejde-1812	227	39	ε	ε	PROPN
ejde-1812	227	40	22	22	NUM
ejde-1812	227	41	,	,	PUNCT
ejde-1812	227	42	where	where	SCONJ
ejde-1812	227	43	x1(t	x1(t	PUNCT
ejde-1812	227	44	)	)	PUNCT
ejde-1812	227	45	=	=	SYM
ejde-1812	227	46	x(t;u1	x(t;u1	PROPN
ejde-1812	227	47	)	)	PUNCT
ejde-1812	227	48	,	,	PUNCT
ejde-1812	227	49	t	t	PROPN
ejde-1812	227	50	∈	∈	PROPN
ejde-1812	227	51	(	(	PUNCT
ejde-1812	227	52	0	0	NUM
ejde-1812	227	53	,	,	PUNCT
ejde-1812	227	54	b	b	NOUN
ejde-1812	227	55	]	]	PUNCT
ejde-1812	227	56	.	.	PUNCT
ejde-1812	228	1	denote	denote	VERB
ejde-1812	228	2	x2(t	x2(t	PRON
ejde-1812	228	3	)	)	PUNCT
ejde-1812	228	4	=	=	PUNCT
ejde-1812	229	1	x(t;u2	x(t;u2	PROPN
ejde-1812	229	2	)	)	PUNCT
ejde-1812	230	1	,	,	PUNCT
ejde-1812	230	2	t	t	PROPN
ejde-1812	230	3	∈	∈	PROPN
ejde-1812	230	4	(	(	PUNCT
ejde-1812	230	5	0	0	NUM
ejde-1812	230	6	,	,	PUNCT
ejde-1812	230	7	b	b	NOUN
ejde-1812	230	8	]	]	PUNCT
ejde-1812	230	9	.	.	PUNCT
ejde-1812	231	1	using	use	VERB
ejde-1812	231	2	hypothesis	hypothesis	NOUN
ejde-1812	231	3	(	(	PUNCT
ejde-1812	231	4	h4	h4	PROPN
ejde-1812	231	5	)	)	PUNCT
ejde-1812	231	6	and	and	CCONJ
ejde-1812	231	7	lemma	lemma	PROPN
ejde-1812	231	8	3.4	3.4	NUM
ejde-1812	231	9	again	again	ADV
ejde-1812	231	10	,	,	PUNCT
ejde-1812	231	11	we	we	PRON
ejde-1812	231	12	have	have	VERB
ejde-1812	231	13	that	that	SCONJ
ejde-1812	231	14	there	there	PRON
ejde-1812	231	15	exists	exist	VERB
ejde-1812	231	16	v2	v2	PROPN
ejde-1812	231	17	∈	∈	PROPN
ejde-1812	231	18	v	v	ADP
ejde-1812	231	19	such	such	ADJ
ejde-1812	231	20	that	that	SCONJ
ejde-1812	232	1	∥hbv2	∥hbv2	PROPN
ejde-1812	232	2	−	−	PROPN
ejde-1812	233	1	[	[	X
ejde-1812	233	2	hnf	hnf	X
ejde-1812	233	3	(	(	PUNCT
ejde-1812	233	4	x2)−hnf	x2)−hnf	PROPN
ejde-1812	233	5	(	(	PUNCT
ejde-1812	233	6	x1)]∥	x1)]∥	X
ejde-1812	233	7	<	<	X
ejde-1812	233	8	ε	ε	PROPN
ejde-1812	233	9	23	23	NUM
ejde-1812	233	10	.	.	PUNCT
ejde-1812	234	1	and	and	CCONJ
ejde-1812	234	2	∥bv2∥lr(j	∥bv2∥lr(j	PROPN
ejde-1812	234	3	,	,	PUNCT
ejde-1812	234	4	x	x	NOUN
ejde-1812	234	5	)	)	PUNCT
ejde-1812	234	6	≤	≤	NUM
ejde-1812	235	1	c	c	NOUN
ejde-1812	235	2	∥nf	∥nf	PROPN
ejde-1812	235	3	(	(	PUNCT
ejde-1812	235	4	x2)(·)−nf	x2)(·)−nf	PROPN
ejde-1812	235	5	(	(	PUNCT
ejde-1812	235	6	x1)(·)∥	x1)(·)∥	X
ejde-1812	235	7	≤	≤	X
ejde-1812	235	8	cℓ3∥x2	cℓ3∥x2	NOUN
ejde-1812	235	9	−	−	PROPN
ejde-1812	235	10	x1∥c1−α−β(1−α);ψ	x1∥c1−α−β(1−α);ψ	PUNCT
ejde-1812	235	11	≤	≤	NUM
ejde-1812	235	12	cℓ3eα	cℓ3eα	NUM
ejde-1812	235	13	(	(	PUNCT
ejde-1812	235	14	mℓ3ψ	mℓ3ψ	PROPN
ejde-1812	235	15	1−β(1−α)(b	1−β(1−α)(b	NUM
ejde-1812	235	16	)	)	PUNCT
ejde-1812	235	17	)	)	PUNCT
ejde-1812	235	18	mψ1−1	mψ1−1	ADJ
ejde-1812	235	19	/	/	SYM
ejde-1812	235	20	r(b	r(b	NOUN
ejde-1812	235	21	)	)	PUNCT
ejde-1812	235	22	γ(α	γ(α	NOUN
ejde-1812	235	23	)	)	PUNCT
ejde-1812	235	24	(	(	PUNCT
ejde-1812	235	25	r	r	NOUN
ejde-1812	235	26	−	−	PROPN
ejde-1812	235	27	1	1	NUM
ejde-1812	235	28	rα−	rα−	SYM
ejde-1812	235	29	1	1	NUM
ejde-1812	235	30	)	)	PUNCT
ejde-1812	235	31	1−1	1−1	NUM
ejde-1812	235	32	/	/	SYM
ejde-1812	235	33	r∥bu2	r∥bu2	PROPN
ejde-1812	235	34	−bu1∥lr(j	−bu1∥lr(j	PROPN
ejde-1812	235	35	,	,	PUNCT
ejde-1812	235	36	x	x	NOUN
ejde-1812	235	37	)	)	PUNCT
ejde-1812	235	38	.	.	PUNCT
ejde-1812	236	1	let	let	VERB
ejde-1812	236	2	u3(t	u3(t	PRON
ejde-1812	236	3	)	)	PUNCT
ejde-1812	236	4	=	=	SYM
ejde-1812	236	5	u2(t)−	u2(t)−	PROPN
ejde-1812	237	1	v2(t	v2(t	NOUN
ejde-1812	237	2	)	)	PUNCT
ejde-1812	237	3	,	,	PUNCT
ejde-1812	237	4	u3	u3	NOUN
ejde-1812	237	5	∈	∈	PROPN
ejde-1812	237	6	v	v	NOUN
ejde-1812	237	7	.	.	PUNCT
ejde-1812	238	1	then	then	ADV
ejde-1812	238	2	∥ξ	∥ξ	PROPN
ejde-1812	238	3	−	−	PROPN
ejde-1812	238	4	(	(	PUNCT
ejde-1812	238	5	iβ(1−α)kα	iβ(1−α)kα	PROPN
ejde-1812	238	6	)	)	PUNCT
ejde-1812	238	7	(	(	PUNCT
ejde-1812	238	8	ψ(b))x0	ψ(b))x0	VERB
ejde-1812	238	9	−hnf	−hnf	PRON
ejde-1812	238	10	(	(	PUNCT
ejde-1812	238	11	x2)−hbu3∥	x2)−hbu3∥	PUNCT
ejde-1812	238	12	≤	≤	PROPN
ejde-1812	239	1	∥ξ	∥ξ	PROPN
ejde-1812	239	2	−	−	PROPN
ejde-1812	239	3	(	(	PUNCT
ejde-1812	239	4	iβ(1−α)kα	iβ(1−α)kα	PROPN
ejde-1812	239	5	)	)	PUNCT
ejde-1812	239	6	(	(	PUNCT
ejde-1812	239	7	ψ(b))x0	ψ(b))x0	VERB
ejde-1812	239	8	−hnf	−hnf	ADV
ejde-1812	239	9	(	(	PUNCT
ejde-1812	239	10	x1)−hbu2∥+	x1)−hbu2∥+	NUM
ejde-1812	239	11	∥hbv2	∥hbv2	X
ejde-1812	239	12	−	−	PROPN
ejde-1812	240	1	[	[	X
ejde-1812	240	2	hnf	hnf	X
ejde-1812	240	3	(	(	PUNCT
ejde-1812	240	4	x2)−hnf	x2)−hnf	PROPN
ejde-1812	240	5	(	(	PUNCT
ejde-1812	240	6	x1)]∥	x1)]∥	PROPN
ejde-1812	240	7	≤	≤	PROPN
ejde-1812	240	8	(	(	PUNCT
ejde-1812	240	9	1	1	NUM
ejde-1812	240	10	22	22	NUM
ejde-1812	240	11	+	+	CCONJ
ejde-1812	240	12	1	1	NUM
ejde-1812	240	13	23	23	NUM
ejde-1812	240	14	)	)	PUNCT
ejde-1812	240	15	ε	ε	PROPN
ejde-1812	240	16	.	.	PUNCT
ejde-1812	240	17	by	by	ADP
ejde-1812	240	18	induction	induction	NOUN
ejde-1812	240	19	we	we	PRON
ejde-1812	240	20	can	can	AUX
ejde-1812	240	21	obtain	obtain	VERB
ejde-1812	240	22	a	a	DET
ejde-1812	240	23	sequence	sequence	NOUN
ejde-1812	240	24	{	{	PUNCT
ejde-1812	240	25	un	un	PROPN
ejde-1812	240	26	(	(	PUNCT
ejde-1812	240	27	·	·	PUNCT
ejde-1812	240	28	)	)	PUNCT
ejde-1812	240	29	}	}	PUNCT
ejde-1812	241	1	⊂	⊂	PROPN
ejde-1812	241	2	v	v	ADP
ejde-1812	241	3	satisfying	satisfy	VERB
ejde-1812	241	4	∥ξ	∥ξ	PROPN
ejde-1812	241	5	−	−	PROPN
ejde-1812	241	6	(	(	PUNCT
ejde-1812	241	7	iβ(1−α)kα	iβ(1−α)kα	PROPN
ejde-1812	241	8	)	)	PUNCT
ejde-1812	241	9	(	(	PUNCT
ejde-1812	241	10	ψ(b))x0	ψ(b))x0	VERB
ejde-1812	241	11	−hnf	−hnf	ADV
ejde-1812	241	12	(	(	PUNCT
ejde-1812	241	13	xn)−hbun+1∥	xn)−hbun+1∥	PROPN
ejde-1812	241	14	<	<	X
ejde-1812	241	15	(	(	PUNCT
ejde-1812	241	16	1	1	NUM
ejde-1812	241	17	22	22	NUM
ejde-1812	241	18	+	+	CCONJ
ejde-1812	241	19	·	·	PUNCT
ejde-1812	241	20	·	·	PUNCT
ejde-1812	241	21	·	·	PUNCT
ejde-1812	241	22	+	+	NUM
ejde-1812	241	23	1	1	NUM
ejde-1812	241	24	2n+1	2n+1	PROPN
ejde-1812	241	25	)	)	PUNCT
ejde-1812	241	26	ε	ε	PROPN
ejde-1812	241	27	,	,	PUNCT
ejde-1812	241	28	where	where	SCONJ
ejde-1812	241	29	xn(t	xn(t	NUM
ejde-1812	241	30	)	)	PUNCT
ejde-1812	241	31	=	=	SYM
ejde-1812	241	32	x(t;un	x(t;un	X
ejde-1812	241	33	)	)	PUNCT
ejde-1812	241	34	,	,	PUNCT
ejde-1812	241	35	t	t	PROPN
ejde-1812	241	36	∈	∈	PROPN
ejde-1812	241	37	(	(	PUNCT
ejde-1812	241	38	0	0	NUM
ejde-1812	241	39	,	,	PUNCT
ejde-1812	241	40	b	b	NOUN
ejde-1812	241	41	]	]	X
ejde-1812	241	42	,	,	PUNCT
ejde-1812	241	43	and	and	CCONJ
ejde-1812	241	44	∥bun+1	∥bun+1	ADJ
ejde-1812	241	45	−bun∥lr(j	−bun∥lr(j	PROPN
ejde-1812	241	46	,	,	PUNCT
ejde-1812	241	47	x	x	NOUN
ejde-1812	241	48	)	)	PUNCT
ejde-1812	241	49	≤	≤	NOUN
ejde-1812	241	50	cℓ3eα	cℓ3eα	NUM
ejde-1812	241	51	(	(	PUNCT
ejde-1812	241	52	mℓ3ψ	mℓ3ψ	PROPN
ejde-1812	241	53	1−β(1−α)(b	1−β(1−α)(b	NUM
ejde-1812	241	54	)	)	PUNCT
ejde-1812	241	55	)	)	PUNCT
ejde-1812	241	56	mψ1−1	mψ1−1	ADJ
ejde-1812	241	57	/	/	SYM
ejde-1812	241	58	r(b	r(b	NOUN
ejde-1812	241	59	)	)	PUNCT
ejde-1812	241	60	γ(α	γ(α	NOUN
ejde-1812	241	61	)	)	PUNCT
ejde-1812	241	62	(	(	PUNCT
ejde-1812	242	1	r	r	NOUN
ejde-1812	242	2	−	−	PROPN
ejde-1812	242	3	1	1	NUM
ejde-1812	242	4	rα−	rα−	SYM
ejde-1812	242	5	1	1	NUM
ejde-1812	242	6	)	)	PUNCT
ejde-1812	242	7	1−1	1−1	NUM
ejde-1812	242	8	/	/	SYM
ejde-1812	242	9	r	r	NOUN
ejde-1812	242	10	∥bun	∥bun	NOUN
ejde-1812	242	11	−bun−1∥lr(j	−bun−1∥lr(j	ADJ
ejde-1812	242	12	,	,	PUNCT
ejde-1812	242	13	x	x	NOUN
ejde-1812	242	14	)	)	PUNCT
ejde-1812	242	15	.	.	PUNCT
ejde-1812	243	1	ejde-2025/109	ejde-2025/109	ADP
ejde-1812	243	2	evolution	evolution	NOUN
ejde-1812	243	3	ψ	ψ	NOUN
ejde-1812	243	4	-	-	ADJ
ejde-1812	243	5	hilfer	hilfer	NOUN
ejde-1812	243	6	fractional	fractional	ADJ
ejde-1812	243	7	differential	differential	ADJ
ejde-1812	243	8	equations	equation	NOUN
ejde-1812	243	9	9	9	NUM
ejde-1812	243	10	from	from	ADP
ejde-1812	243	11	(	(	PUNCT
ejde-1812	243	12	3.7	3.7	NUM
ejde-1812	243	13	)	)	PUNCT
ejde-1812	243	14	,	,	PUNCT
ejde-1812	243	15	we	we	PRON
ejde-1812	243	16	see	see	VERB
ejde-1812	243	17	that	that	SCONJ
ejde-1812	243	18	the	the	DET
ejde-1812	243	19	sequence	sequence	NOUN
ejde-1812	243	20	{	{	PUNCT
ejde-1812	243	21	bun	bun	NOUN
ejde-1812	243	22	:	:	PUNCT
ejde-1812	243	23	n	n	CCONJ
ejde-1812	243	24	∈	∈	PROPN
ejde-1812	243	25	n+	n+	PROPN
ejde-1812	243	26	}	}	PUNCT
ejde-1812	243	27	is	be	AUX
ejde-1812	243	28	a	a	DET
ejde-1812	243	29	cauchy	cauchy	ADJ
ejde-1812	243	30	sequence	sequence	NOUN
ejde-1812	243	31	in	in	ADP
ejde-1812	243	32	the	the	DET
ejde-1812	243	33	banach	banach	NOUN
ejde-1812	243	34	space	space	NOUN
ejde-1812	243	35	lr(j	lr(j	PROPN
ejde-1812	243	36	,	,	PUNCT
ejde-1812	243	37	x	x	NOUN
ejde-1812	243	38	)	)	PUNCT
ejde-1812	243	39	.	.	PUNCT
ejde-1812	244	1	hence	hence	ADV
ejde-1812	244	2	,	,	PUNCT
ejde-1812	244	3	there	there	PRON
ejde-1812	244	4	exists	exist	VERB
ejde-1812	244	5	a	a	DET
ejde-1812	244	6	function	function	NOUN
ejde-1812	244	7	τ	τ	X
ejde-1812	244	8	(	(	PUNCT
ejde-1812	244	9	·	·	PUNCT
ejde-1812	244	10	)	)	PUNCT
ejde-1812	244	11	∈	∈	PROPN
ejde-1812	244	12	lr(j	lr(j	NOUN
ejde-1812	244	13	,	,	PUNCT
ejde-1812	244	14	x	x	X
ejde-1812	244	15	)	)	PUNCT
ejde-1812	244	16	,	,	PUNCT
ejde-1812	244	17	such	such	ADJ
ejde-1812	244	18	that	that	DET
ejde-1812	244	19	bun	bun	PROPN
ejde-1812	244	20	(	(	PUNCT
ejde-1812	244	21	·	·	PUNCT
ejde-1812	244	22	)	)	PUNCT
ejde-1812	244	23	=	=	SYM
ejde-1812	244	24	τ	τ	X
ejde-1812	244	25	(	(	PUNCT
ejde-1812	244	26	·	·	PUNCT
ejde-1812	244	27	)	)	PUNCT
ejde-1812	244	28	in	in	ADP
ejde-1812	244	29	lr(j	lr(j	PROPN
ejde-1812	244	30	,	,	PUNCT
ejde-1812	244	31	x	x	NOUN
ejde-1812	244	32	)	)	PUNCT
ejde-1812	244	33	,	,	PUNCT
ejde-1812	244	34	which	which	PRON
ejde-1812	244	35	implies	imply	VERB
ejde-1812	244	36	that	that	SCONJ
ejde-1812	244	37	for	for	ADP
ejde-1812	244	38	each	each	DET
ejde-1812	244	39	ε	ε	PROPN
ejde-1812	244	40	>	>	X
ejde-1812	244	41	0	0	PROPN
ejde-1812	244	42	,	,	PUNCT
ejde-1812	244	43	there	there	PRON
ejde-1812	244	44	exists	exist	VERB
ejde-1812	244	45	an	an	DET
ejde-1812	244	46	integer	integer	NOUN
ejde-1812	244	47	n	n	CCONJ
ejde-1812	244	48	>	>	X
ejde-1812	244	49	0	0	NUM
ejde-1812	244	50	,	,	PUNCT
ejde-1812	244	51	such	such	ADJ
ejde-1812	244	52	that	that	SCONJ
ejde-1812	244	53	∥hbun+1	∥hbun+1	PROPN
ejde-1812	244	54	−hbun∥	−hbun∥	PROPN
ejde-1812	244	55	≤	≤	NUM
ejde-1812	244	56	ε	ε	PROPN
ejde-1812	244	57	2	2	NUM
ejde-1812	244	58	.	.	PUNCT
ejde-1812	245	1	therefore	therefore	ADV
ejde-1812	245	2	,	,	PUNCT
ejde-1812	245	3	∥ξ	∥ξ	PROPN
ejde-1812	245	4	−	−	PROPN
ejde-1812	245	5	(	(	PUNCT
ejde-1812	245	6	iβ(1−α)kα	iβ(1−α)kα	PROPN
ejde-1812	245	7	)	)	PUNCT
ejde-1812	245	8	(	(	PUNCT
ejde-1812	245	9	ψ(b))x0	ψ(b))x0	VERB
ejde-1812	245	10	−hnf	−hnf	ADV
ejde-1812	245	11	(	(	PUNCT
ejde-1812	245	12	xn	xn	X
ejde-1812	245	13	)	)	PUNCT
ejde-1812	245	14	−hbun∥	−hbun∥	PROPN
ejde-1812	245	15	≤	≤	PUNCT
ejde-1812	246	1	∥ξ	∥ξ	PROPN
ejde-1812	246	2	−	−	PROPN
ejde-1812	246	3	(	(	PUNCT
ejde-1812	246	4	iβ(1−α)kα	iβ(1−α)kα	PROPN
ejde-1812	246	5	)	)	PUNCT
ejde-1812	246	6	(	(	PUNCT
ejde-1812	246	7	ψ(b))x0	ψ(b))x0	VERB
ejde-1812	246	8	−hnf	−hnf	ADV
ejde-1812	246	9	(	(	PUNCT
ejde-1812	246	10	xn	xn	NUM
ejde-1812	246	11	)	)	PUNCT
ejde-1812	246	12	−hbun+1∥+	−hbun+1∥+	PROPN
ejde-1812	246	13	∥hbun+1	∥hbun+1	PROPN
ejde-1812	246	14	−hbun∥	−hbun∥	PROPN
ejde-1812	246	15	≤	≤	NUM
ejde-1812	246	16	(	(	PUNCT
ejde-1812	246	17	1	1	NUM
ejde-1812	246	18	22	22	NUM
ejde-1812	246	19	+	+	CCONJ
ejde-1812	246	20	·	·	PUNCT
ejde-1812	246	21	·	·	PUNCT
ejde-1812	246	22	·	·	PUNCT
ejde-1812	246	23	+	+	NUM
ejde-1812	246	24	1	1	NUM
ejde-1812	246	25	2n+1	2n+1	PROPN
ejde-1812	246	26	)	)	PUNCT
ejde-1812	246	27	ε+	ε+	X
ejde-1812	246	28	ε	ε	PROPN
ejde-1812	246	29	2	2	NUM
ejde-1812	246	30	<	<	X
ejde-1812	246	31	ε	ε	PROPN
ejde-1812	246	32	,	,	PUNCT
ejde-1812	246	33	which	which	PRON
ejde-1812	246	34	yields	yield	VERB
ejde-1812	246	35	the	the	DET
ejde-1812	246	36	approximate	approximate	ADJ
ejde-1812	246	37	controllability	controllability	NOUN
ejde-1812	246	38	of	of	ADP
ejde-1812	246	39	problem	problem	NOUN
ejde-1812	246	40	(	(	PUNCT
ejde-1812	246	41	3.1	3.1	NUM
ejde-1812	246	42	)	)	PUNCT
ejde-1812	246	43	.	.	PUNCT
ejde-1812	247	1	□	□	PUNCT
ejde-1812	247	2	4	4	X
ejde-1812	247	3	.	.	X
ejde-1812	247	4	a	a	DET
ejde-1812	247	5	new	new	ADJ
ejde-1812	247	6	gronwall	gronwall	ADJ
ejde-1812	247	7	-	-	PUNCT
ejde-1812	247	8	type	type	NOUN
ejde-1812	247	9	inequality	inequality	NOUN
ejde-1812	247	10	and	and	CCONJ
ejde-1812	247	11	the	the	DET
ejde-1812	247	12	dependence	dependence	NOUN
ejde-1812	247	13	of	of	ADP
ejde-1812	247	14	solution	solution	NOUN
ejde-1812	247	15	on	on	ADP
ejde-1812	247	16	the	the	DET
ejde-1812	247	17	order	order	NOUN
ejde-1812	247	18	and	and	CCONJ
ejde-1812	247	19	the	the	DET
ejde-1812	247	20	initial	initial	ADJ
ejde-1812	247	21	condition	condition	NOUN
ejde-1812	247	22	first	first	ADV
ejde-1812	247	23	,	,	PUNCT
ejde-1812	247	24	we	we	PRON
ejde-1812	247	25	present	present	VERB
ejde-1812	247	26	the	the	DET
ejde-1812	247	27	following	follow	VERB
ejde-1812	247	28	multivariate	multivariate	VERB
ejde-1812	247	29	gronwall	gronwall	ADJ
ejde-1812	247	30	-	-	PUNCT
ejde-1812	247	31	type	type	NOUN
ejde-1812	247	32	inequality	inequality	NOUN
ejde-1812	247	33	with	with	ADP
ejde-1812	247	34	multiple	multiple	ADJ
ejde-1812	247	35	different	different	ADJ
ejde-1812	247	36	singular	singular	ADJ
ejde-1812	247	37	kernels	kernel	NOUN
ejde-1812	247	38	involving	involve	VERB
ejde-1812	247	39	exponential	exponential	ADJ
ejde-1812	247	40	factors	factor	NOUN
ejde-1812	247	41	,	,	PUNCT
ejde-1812	247	42	which	which	PRON
ejde-1812	247	43	generalizes	generalize	VERB
ejde-1812	247	44	many	many	ADJ
ejde-1812	247	45	existing	exist	VERB
ejde-1812	247	46	results	result	NOUN
ejde-1812	247	47	.	.	PUNCT
ejde-1812	248	1	theorem	theorem	VERB
ejde-1812	248	2	4.1	4.1	NUM
ejde-1812	248	3	.	.	PUNCT
ejde-1812	249	1	suppose	suppose	VERB
ejde-1812	249	2	that	that	SCONJ
ejde-1812	249	3	m	m	PROPN
ejde-1812	249	4	,	,	PUNCT
ejde-1812	249	5	p	p	PROPN
ejde-1812	249	6	∈	∈	PROPN
ejde-1812	249	7	n	n	CCONJ
ejde-1812	249	8	,	,	PUNCT
ejde-1812	249	9	βki	βki	ADP
ejde-1812	249	10	>	>	X
ejde-1812	249	11	0	0	NUM
ejde-1812	249	12	,	,	PUNCT
ejde-1812	249	13	ai	ai	VERB
ejde-1812	249	14	≥	≥	NOUN
ejde-1812	249	15	0	0	NUM
ejde-1812	249	16	,	,	PUNCT
ejde-1812	249	17	ψi(t	ψi(t	PUNCT
ejde-1812	249	18	)	)	PUNCT
ejde-1812	249	19	is	be	AUX
ejde-1812	249	20	an	an	DET
ejde-1812	249	21	increasing	increase	VERB
ejde-1812	249	22	and	and	CCONJ
ejde-1812	249	23	positive	positive	ADJ
ejde-1812	249	24	monotone	monotone	ADJ
ejde-1812	249	25	differentiable	differentiable	ADJ
ejde-1812	249	26	function	function	NOUN
ejde-1812	249	27	on	on	ADP
ejde-1812	249	28	(	(	PUNCT
ejde-1812	249	29	ai	ai	VERB
ejde-1812	249	30	,	,	PUNCT
ejde-1812	249	31	ti	ti	NOUN
ejde-1812	249	32	]	]	X
ejde-1812	249	33	,	,	PUNCT
ejde-1812	249	34	ζi(t	ζi(t	X
ejde-1812	249	35	)	)	PUNCT
ejde-1812	249	36	is	be	AUX
ejde-1812	249	37	a	a	DET
ejde-1812	249	38	locally	locally	ADV
ejde-1812	249	39	integrable	integrable	ADJ
ejde-1812	249	40	function	function	NOUN
ejde-1812	249	41	on	on	ADP
ejde-1812	249	42	(	(	PUNCT
ejde-1812	249	43	ai	ai	VERB
ejde-1812	249	44	,	,	PUNCT
ejde-1812	249	45	ti	ti	NOUN
ejde-1812	249	46	]	]	X
ejde-1812	249	47	(	(	PUNCT
ejde-1812	249	48	1	1	NUM
ejde-1812	249	49	≤	≤	NUM
ejde-1812	249	50	i	i	X
ejde-1812	249	51	≤	≤	NOUN
ejde-1812	249	52	m	m	ADP
ejde-1812	249	53	,	,	PUNCT
ejde-1812	250	1	1	1	NUM
ejde-1812	250	2	≤	≤	NUM
ejde-1812	250	3	k	k	NOUN
ejde-1812	250	4	≤	≤	PROPN
ejde-1812	250	5	p	p	X
ejde-1812	250	6	)	)	PUNCT
ejde-1812	250	7	,	,	PUNCT
ejde-1812	250	8	a(t1	a(t1	PROPN
ejde-1812	250	9	,	,	PUNCT
ejde-1812	250	10	t2	t2	NOUN
ejde-1812	250	11	,	,	PUNCT
ejde-1812	250	12	.	.	PUNCT
ejde-1812	250	13	.	.	PUNCT
ejde-1812	250	14	.	.	PUNCT
ejde-1812	251	1	,	,	PUNCT
ejde-1812	251	2	tm	tm	PROPN
ejde-1812	251	3	)	)	PUNCT
ejde-1812	251	4	is	be	AUX
ejde-1812	251	5	a	a	DET
ejde-1812	251	6	nonnegative	nonnegative	ADJ
ejde-1812	251	7	locally	locally	ADV
ejde-1812	251	8	integrable	integrable	ADJ
ejde-1812	251	9	function	function	NOUN
ejde-1812	251	10	on	on	ADP
ejde-1812	251	11	[	[	X
ejde-1812	251	12	a1	a1	NOUN
ejde-1812	251	13	,	,	PUNCT
ejde-1812	251	14	t1)×	t1)×	ADP
ejde-1812	252	1	[	[	X
ejde-1812	252	2	a2	a2	NOUN
ejde-1812	252	3	,	,	PUNCT
ejde-1812	252	4	t2)×	t2)×	X
ejde-1812	252	5	·	·	PUNCT
ejde-1812	252	6	·	·	PUNCT
ejde-1812	252	7	·	·	PUNCT
ejde-1812	252	8	×	×	NOUN
ejde-1812	252	9	[	[	X
ejde-1812	252	10	am	am	NOUN
ejde-1812	252	11	,	,	PUNCT
ejde-1812	252	12	tm	tm	NOUN
ejde-1812	252	13	)	)	PUNCT
ejde-1812	252	14	(	(	PUNCT
ejde-1812	252	15	some	some	DET
ejde-1812	252	16	ti	ti	NOUN
ejde-1812	252	17	≤	≤	X
ejde-1812	252	18	+	+	NOUN
ejde-1812	252	19	∞	∞	NUM
ejde-1812	252	20	)	)	PUNCT
ejde-1812	252	21	and	and	CCONJ
ejde-1812	252	22	gk(t1	gk(t1	NOUN
ejde-1812	252	23	,	,	PUNCT
ejde-1812	252	24	t2	t2	NOUN
ejde-1812	252	25	,	,	PUNCT
ejde-1812	252	26	.	.	PUNCT
ejde-1812	252	27	.	.	PUNCT
ejde-1812	253	1	.	.	PUNCT
ejde-1812	254	1	,	,	PUNCT
ejde-1812	254	2	tm)(1	tm)(1	NOUN
ejde-1812	254	3	≤	≤	NUM
ejde-1812	254	4	k	k	NOUN
ejde-1812	254	5	≤	≤	PROPN
ejde-1812	254	6	p	p	X
ejde-1812	254	7	)	)	PUNCT
ejde-1812	254	8	is	be	AUX
ejde-1812	254	9	a	a	DET
ejde-1812	254	10	nonnegative	nonnegative	ADJ
ejde-1812	254	11	,	,	PUNCT
ejde-1812	254	12	nondecreasing	nondecrease	VERB
ejde-1812	254	13	continuous	continuous	ADJ
ejde-1812	254	14	function	function	NOUN
ejde-1812	254	15	defined	define	VERB
ejde-1812	254	16	on	on	ADP
ejde-1812	254	17	[	[	X
ejde-1812	254	18	a1	a1	NOUN
ejde-1812	254	19	,	,	PUNCT
ejde-1812	254	20	t1)×	t1)×	ADP
ejde-1812	255	1	[	[	X
ejde-1812	255	2	a2	a2	PROPN
ejde-1812	255	3	,	,	PUNCT
ejde-1812	255	4	t2)×	t2)×	AUX
ejde-1812	255	5	·	·	PUNCT
ejde-1812	255	6	·	·	PUNCT
ejde-1812	255	7	·	·	PUNCT
ejde-1812	255	8	×	×	NOUN
ejde-1812	255	9	[	[	X
ejde-1812	255	10	am	am	NOUN
ejde-1812	255	11	,	,	PUNCT
ejde-1812	255	12	tm	tm	NOUN
ejde-1812	255	13	)	)	PUNCT
ejde-1812	255	14	,	,	PUNCT
ejde-1812	255	15	gk(t1	gk(t1	NOUN
ejde-1812	255	16	,	,	PUNCT
ejde-1812	255	17	t2	t2	NOUN
ejde-1812	255	18	,	,	PUNCT
ejde-1812	255	19	.	.	PUNCT
ejde-1812	255	20	.	.	PUNCT
ejde-1812	256	1	.	.	PUNCT
ejde-1812	257	1	,	,	PUNCT
ejde-1812	257	2	tm	tm	NOUN
ejde-1812	257	3	)	)	PUNCT
ejde-1812	258	1	≤	≤	NUM
ejde-1812	258	2	c	c	X
ejde-1812	258	3	(	(	PUNCT
ejde-1812	258	4	constant	constant	ADJ
ejde-1812	258	5	)	)	PUNCT
ejde-1812	258	6	,	,	PUNCT
ejde-1812	258	7	and	and	CCONJ
ejde-1812	258	8	suppose	suppose	VERB
ejde-1812	258	9	u(t1	u(t1	NOUN
ejde-1812	258	10	,	,	PUNCT
ejde-1812	258	11	t2	t2	NOUN
ejde-1812	258	12	,	,	PUNCT
ejde-1812	258	13	.	.	PUNCT
ejde-1812	258	14	.	.	PUNCT
ejde-1812	258	15	.	.	PUNCT
ejde-1812	259	1	,	,	PUNCT
ejde-1812	259	2	tm	tm	PROPN
ejde-1812	259	3	)	)	PUNCT
ejde-1812	259	4	is	be	AUX
ejde-1812	259	5	nonnegative	nonnegative	ADJ
ejde-1812	259	6	and	and	CCONJ
ejde-1812	259	7	locally	locally	ADV
ejde-1812	259	8	integrable	integrable	ADJ
ejde-1812	259	9	on	on	ADP
ejde-1812	259	10	[	[	X
ejde-1812	259	11	a1	a1	NOUN
ejde-1812	259	12	,	,	PUNCT
ejde-1812	259	13	t1	t1	NOUN
ejde-1812	259	14	)	)	PUNCT
ejde-1812	260	1	×	×	NOUN
ejde-1812	260	2	[	[	X
ejde-1812	260	3	a2	a2	PROPN
ejde-1812	260	4	,	,	PUNCT
ejde-1812	260	5	t2	t2	NOUN
ejde-1812	260	6	)	)	PUNCT
ejde-1812	260	7	×	×	NOUN
ejde-1812	260	8	·	·	PUNCT
ejde-1812	260	9	·	·	PUNCT
ejde-1812	261	1	·	·	PUNCT
ejde-1812	261	2	×	×	NOUN
ejde-1812	261	3	[	[	X
ejde-1812	261	4	am	am	NOUN
ejde-1812	261	5	,	,	PUNCT
ejde-1812	261	6	tm	tm	NOUN
ejde-1812	261	7	)	)	PUNCT
ejde-1812	261	8	with	with	ADP
ejde-1812	261	9	u(t1	u(t1	NOUN
ejde-1812	261	10	,	,	PUNCT
ejde-1812	261	11	t2	t2	NOUN
ejde-1812	261	12	,	,	PUNCT
ejde-1812	261	13	.	.	PUNCT
ejde-1812	261	14	.	.	PUNCT
ejde-1812	262	1	.	.	PUNCT
ejde-1812	263	1	,	,	PUNCT
ejde-1812	263	2	tm	tm	NOUN
ejde-1812	263	3	)	)	PUNCT
ejde-1812	263	4	≤	≤	NUM
ejde-1812	263	5	a(t1	a(t1	NOUN
ejde-1812	263	6	,	,	PUNCT
ejde-1812	263	7	t2	t2	NOUN
ejde-1812	263	8	,	,	PUNCT
ejde-1812	263	9	.	.	PUNCT
ejde-1812	263	10	.	.	PUNCT
ejde-1812	263	11	.	.	PUNCT
ejde-1812	264	1	,	,	PUNCT
ejde-1812	264	2	tm	tm	PROPN
ejde-1812	264	3	)	)	PUNCT
ejde-1812	265	1	+	+	NUM
ejde-1812	265	2	p∑	p∑	X
ejde-1812	265	3	k=1	k=1	PROPN
ejde-1812	265	4	gk(t1	gk(t1	PROPN
ejde-1812	265	5	,	,	PUNCT
ejde-1812	265	6	t2	t2	NOUN
ejde-1812	265	7	,	,	PUNCT
ejde-1812	265	8	.	.	PUNCT
ejde-1812	265	9	.	.	PUNCT
ejde-1812	265	10	.	.	PUNCT
ejde-1812	266	1	,	,	PUNCT
ejde-1812	266	2	tm	tm	PROPN
ejde-1812	266	3	)	)	PUNCT
ejde-1812	266	4	∫	∫	PROPN
ejde-1812	266	5	tm	tm	PROPN
ejde-1812	266	6	am	am	PROPN
ejde-1812	266	7	·	·	PUNCT
ejde-1812	266	8	·	·	PUNCT
ejde-1812	266	9	·	·	PUNCT
ejde-1812	266	10	∫	∫	PROPN
ejde-1812	266	11	t2	t2	PROPN
ejde-1812	266	12	a2	a2	PROPN
ejde-1812	266	13	∫	∫	PROPN
ejde-1812	266	14	t1	t1	PROPN
ejde-1812	266	15	a1	a1	PROPN
ejde-1812	266	16	m∏	m∏	PROPN
ejde-1812	266	17	i=1	i=1	PROPN
ejde-1812	266	18	eζ(si)−ζi(ti)ψ′	eζ(si)−ζi(ti)ψ′	ADJ
ejde-1812	266	19	i(si	i(si	PROPN
ejde-1812	266	20	)	)	PUNCT
ejde-1812	266	21	×	×	NOUN
ejde-1812	266	22	(	(	PUNCT
ejde-1812	266	23	ψi(ti)−	ψi(ti)−	PROPN
ejde-1812	266	24	ψi(si	ψi(si	PROPN
ejde-1812	266	25	)	)	PUNCT
ejde-1812	266	26	)	)	PUNCT
ejde-1812	267	1	βki−1u(s1	βki−1u(s1	PROPN
ejde-1812	267	2	,	,	PUNCT
ejde-1812	267	3	s2	s2	NOUN
ejde-1812	267	4	,	,	PUNCT
ejde-1812	267	5	.	.	PUNCT
ejde-1812	267	6	.	.	PUNCT
ejde-1812	267	7	.	.	PUNCT
ejde-1812	268	1	,	,	PUNCT
ejde-1812	268	2	sm)ds1	sm)ds1	PROPN
ejde-1812	268	3	.	.	PUNCT
ejde-1812	268	4	.	.	PUNCT
ejde-1812	268	5	.	.	PUNCT
ejde-1812	269	1	dsm	dsm	PROPN
ejde-1812	269	2	,	,	PUNCT
ejde-1812	269	3	on	on	ADP
ejde-1812	269	4	[	[	X
ejde-1812	269	5	a1	a1	NOUN
ejde-1812	269	6	,	,	PUNCT
ejde-1812	269	7	t1)×	t1)×	ADP
ejde-1812	270	1	[	[	X
ejde-1812	270	2	a2	a2	NOUN
ejde-1812	270	3	,	,	PUNCT
ejde-1812	270	4	t2)×	t2)×	X
ejde-1812	270	5	·	·	PUNCT
ejde-1812	270	6	·	·	PUNCT
ejde-1812	270	7	·	·	PUNCT
ejde-1812	270	8	×	×	NOUN
ejde-1812	270	9	[	[	X
ejde-1812	270	10	am	am	NOUN
ejde-1812	270	11	,	,	PUNCT
ejde-1812	270	12	tm	tm	NOUN
ejde-1812	270	13	)	)	PUNCT
ejde-1812	270	14	.	.	PUNCT
ejde-1812	271	1	then	then	ADV
ejde-1812	271	2	u(t1	u(t1	VERB
ejde-1812	271	3	,	,	PUNCT
ejde-1812	271	4	t2	t2	NOUN
ejde-1812	271	5	,	,	PUNCT
ejde-1812	271	6	.	.	PUNCT
ejde-1812	271	7	.	.	PUNCT
ejde-1812	271	8	.	.	PUNCT
ejde-1812	272	1	,	,	PUNCT
ejde-1812	272	2	tm	tm	NOUN
ejde-1812	272	3	)	)	PUNCT
ejde-1812	272	4	≤	≤	NUM
ejde-1812	272	5	a(t1	a(t1	NOUN
ejde-1812	272	6	,	,	PUNCT
ejde-1812	272	7	t2	t2	NOUN
ejde-1812	272	8	,	,	PUNCT
ejde-1812	272	9	.	.	PUNCT
ejde-1812	272	10	.	.	PUNCT
ejde-1812	272	11	.	.	PUNCT
ejde-1812	273	1	,	,	PUNCT
ejde-1812	273	2	tm	tm	PROPN
ejde-1812	273	3	)	)	PUNCT
ejde-1812	274	1	+	+	CCONJ
ejde-1812	275	1	∞∑	∞∑	NUM
ejde-1812	275	2	n=1	n=1	PROPN
ejde-1812	275	3	∑	∑	PROPN
ejde-1812	275	4	0≤l1,	0≤l1,	PROPN
ejde-1812	275	5	...	...	PUNCT
ejde-1812	275	6	,lp≤n	,lp≤n	PUNCT
ejde-1812	275	7	l1+···+lp	l1+···+lp	PROPN
ejde-1812	275	8	=	=	SYM
ejde-1812	275	9	n	n	CCONJ
ejde-1812	275	10	(	(	PUNCT
ejde-1812	275	11	n	n	PRON
ejde-1812	275	12	l1	l1	PROPN
ejde-1812	275	13	,	,	PUNCT
ejde-1812	275	14	.	.	PUNCT
ejde-1812	275	15	.	.	PUNCT
ejde-1812	275	16	.	.	PUNCT
ejde-1812	276	1	,	,	PUNCT
ejde-1812	276	2	lp	lp	X
ejde-1812	276	3	)	)	PUNCT
ejde-1812	277	1	p∏	p∏	PROPN
ejde-1812	277	2	k=1	k=1	X
ejde-1812	277	3	(	(	PUNCT
ejde-1812	277	4	gk(t1	gk(t1	NOUN
ejde-1812	277	5	,	,	PUNCT
ejde-1812	277	6	t2	t2	NOUN
ejde-1812	277	7	,	,	PUNCT
ejde-1812	277	8	.	.	PUNCT
ejde-1812	277	9	.	.	PUNCT
ejde-1812	277	10	.	.	PUNCT
ejde-1812	278	1	,	,	PUNCT
ejde-1812	278	2	tm))lk	tm))lk	PROPN
ejde-1812	278	3	×	×	ADJ
ejde-1812	278	4	∫	∫	PROPN
ejde-1812	278	5	tm	tm	PROPN
ejde-1812	278	6	am	am	PROPN
ejde-1812	279	1	·	·	PUNCT
ejde-1812	279	2	·	·	PUNCT
ejde-1812	279	3	·	·	PUNCT
ejde-1812	279	4	∫	∫	PROPN
ejde-1812	279	5	t2	t2	PROPN
ejde-1812	279	6	a2	a2	PROPN
ejde-1812	279	7	∫	∫	PROPN
ejde-1812	279	8	t1	t1	PROPN
ejde-1812	279	9	a1	a1	PROPN
ejde-1812	279	10	m∏	m∏	PROPN
ejde-1812	279	11	i=1	i=1	PART
ejde-1812	280	1	eζi(si)−ζi(ti)ψ′	eζi(si)−ζi(ti)ψ′	PROPN
ejde-1812	280	2	i(si	i(si	PROPN
ejde-1812	280	3	)	)	PUNCT
ejde-1812	280	4	×	×	NOUN
ejde-1812	281	1	[	[	X
ejde-1812	281	2	∏p	∏p	NOUN
ejde-1812	281	3	k=1(γ(βki	k=1(γ(βki	NOUN
ejde-1812	281	4	)	)	PUNCT
ejde-1812	281	5	)	)	PUNCT
ejde-1812	282	1	lk	lk	PROPN
ejde-1812	282	2	γ	γ	X
ejde-1812	282	3	(	(	PUNCT
ejde-1812	282	4	∑p	∑p	PROPN
ejde-1812	282	5	k=1	k=1	PROPN
ejde-1812	282	6	lkβki	lkβki	PROPN
ejde-1812	282	7	)	)	PUNCT
ejde-1812	282	8	(	(	PUNCT
ejde-1812	282	9	ψi(ti)−	ψi(ti)−	PROPN
ejde-1812	282	10	ψi(si	ψi(si	PROPN
ejde-1812	282	11	)	)	PUNCT
ejde-1812	282	12	)	)	PUNCT
ejde-1812	283	1	∑p	∑p	PROPN
ejde-1812	283	2	k=1	k=1	X
ejde-1812	283	3	lkβki−1	lkβki−1	X
ejde-1812	283	4	]	]	PUNCT
ejde-1812	283	5	×	×	PROPN
ejde-1812	283	6	a(s1	a(s1	NOUN
ejde-1812	283	7	,	,	PUNCT
ejde-1812	283	8	s2	s2	NOUN
ejde-1812	283	9	,	,	PUNCT
ejde-1812	283	10	.	.	PUNCT
ejde-1812	283	11	.	.	PUNCT
ejde-1812	284	1	.	.	PUNCT
ejde-1812	285	1	,	,	PUNCT
ejde-1812	285	2	sm)ds1	sm)ds1	PROPN
ejde-1812	285	3	.	.	PUNCT
ejde-1812	285	4	.	.	PUNCT
ejde-1812	285	5	.	.	PUNCT
ejde-1812	286	1	dsm	dsm	PROPN
ejde-1812	286	2	,	,	PUNCT
ejde-1812	286	3	ai	ai	VERB
ejde-1812	286	4	≤	≤	ADJ
ejde-1812	286	5	ti	ti	NOUN
ejde-1812	286	6	<	<	X
ejde-1812	286	7	ti	ti	X
ejde-1812	286	8	(	(	PUNCT
ejde-1812	286	9	1	1	NUM
ejde-1812	286	10	≤	≤	NUM
ejde-1812	286	11	i	i	PRON
ejde-1812	286	12	≤	≤	NOUN
ejde-1812	286	13	m	m	PROPN
ejde-1812	286	14	)	)	PUNCT
ejde-1812	286	15	,	,	PUNCT
ejde-1812	286	16	(	(	PUNCT
ejde-1812	286	17	4.1	4.1	NUM
ejde-1812	286	18	)	)	PUNCT
ejde-1812	286	19	where	where	SCONJ
ejde-1812	286	20	(	(	PUNCT
ejde-1812	286	21	n	n	X
ejde-1812	286	22	l1	l1	PROPN
ejde-1812	286	23	,	,	PUNCT
ejde-1812	286	24	.	.	PUNCT
ejde-1812	286	25	.	.	PUNCT
ejde-1812	287	1	.	.	PUNCT
ejde-1812	288	1	,	,	PUNCT
ejde-1812	288	2	lp	lp	X
ejde-1812	288	3	)	)	PUNCT
ejde-1812	288	4	=	=	SYM
ejde-1812	288	5	n	n	X
ejde-1812	288	6	!	!	PUNCT
ejde-1812	288	7	l1	l1	PROPN
ejde-1812	288	8	!	!	PUNCT
ejde-1812	288	9	.	.	PUNCT
ejde-1812	288	10	.	.	PUNCT
ejde-1812	288	11	.	.	PUNCT
ejde-1812	289	1	lp	lp	INTJ
ejde-1812	289	2	!	!	PROPN
ejde-1812	289	3	,	,	PUNCT
ejde-1812	289	4	l1	l1	PROPN
ejde-1812	289	5	+	+	CCONJ
ejde-1812	289	6	·	·	PUNCT
ejde-1812	289	7	·	·	PUNCT
ejde-1812	289	8	·	·	PUNCT
ejde-1812	289	9	+	+	NUM
ejde-1812	289	10	lp	lp	ADJ
ejde-1812	289	11	=	=	PUNCT
ejde-1812	289	12	n.	n.	NOUN
ejde-1812	289	13	proof	proof	NOUN
ejde-1812	289	14	.	.	PUNCT
ejde-1812	290	1	define	define	VERB
ejde-1812	290	2	an	an	DET
ejde-1812	290	3	operator	operator	NOUN
ejde-1812	290	4	p	p	NOUN
ejde-1812	290	5	by	by	ADP
ejde-1812	290	6	(	(	PUNCT
ejde-1812	290	7	pu)(t1	pu)(t1	PROPN
ejde-1812	290	8	,	,	PUNCT
ejde-1812	290	9	t2	t2	NOUN
ejde-1812	290	10	,	,	PUNCT
ejde-1812	290	11	.	.	PUNCT
ejde-1812	290	12	.	.	PUNCT
ejde-1812	291	1	.	.	PUNCT
ejde-1812	292	1	,	,	PUNCT
ejde-1812	292	2	tm	tm	NOUN
ejde-1812	292	3	)	)	PUNCT
ejde-1812	292	4	=	=	PUNCT
ejde-1812	293	1	p∑	p∑	X
ejde-1812	294	1	k=1	k=1	PROPN
ejde-1812	294	2	gk(t1	gk(t1	PROPN
ejde-1812	294	3	,	,	PUNCT
ejde-1812	294	4	t2	t2	NOUN
ejde-1812	294	5	,	,	PUNCT
ejde-1812	294	6	.	.	PUNCT
ejde-1812	294	7	.	.	PUNCT
ejde-1812	294	8	.	.	PUNCT
ejde-1812	295	1	,	,	PUNCT
ejde-1812	295	2	tm	tm	PROPN
ejde-1812	295	3	)	)	PUNCT
ejde-1812	295	4	∫	∫	PROPN
ejde-1812	295	5	tm	tm	PROPN
ejde-1812	295	6	am	am	PROPN
ejde-1812	295	7	·	·	PUNCT
ejde-1812	295	8	·	·	PUNCT
ejde-1812	295	9	·	·	PUNCT
ejde-1812	295	10	∫	∫	PROPN
ejde-1812	295	11	t2	t2	PROPN
ejde-1812	295	12	a2	a2	PROPN
ejde-1812	295	13	∫	∫	PROPN
ejde-1812	295	14	t1	t1	PROPN
ejde-1812	295	15	a1	a1	PROPN
ejde-1812	295	16	m∏	m∏	PROPN
ejde-1812	295	17	i=1	i=1	PROPN
ejde-1812	295	18	eζ(si)−ζi(ti)ψ′	eζ(si)−ζi(ti)ψ′	ADJ
ejde-1812	295	19	i(si	i(si	PROPN
ejde-1812	295	20	)	)	PUNCT
ejde-1812	295	21	×	×	NOUN
ejde-1812	295	22	(	(	PUNCT
ejde-1812	295	23	ψi(ti)−	ψi(ti)−	PROPN
ejde-1812	295	24	ψi(si	ψi(si	PROPN
ejde-1812	295	25	)	)	PUNCT
ejde-1812	295	26	)	)	PUNCT
ejde-1812	296	1	βki−1u(s1	βki−1u(s1	PROPN
ejde-1812	296	2	,	,	PUNCT
ejde-1812	296	3	s2	s2	NOUN
ejde-1812	296	4	,	,	PUNCT
ejde-1812	296	5	.	.	PUNCT
ejde-1812	296	6	.	.	PUNCT
ejde-1812	296	7	.	.	PUNCT
ejde-1812	297	1	,	,	PUNCT
ejde-1812	297	2	sm)ds1	sm)ds1	PROPN
ejde-1812	297	3	.	.	PUNCT
ejde-1812	297	4	.	.	PUNCT
ejde-1812	297	5	.	.	PUNCT
ejde-1812	298	1	dsm	dsm	PROPN
ejde-1812	298	2	,	,	PUNCT
ejde-1812	298	3	10	10	NUM
ejde-1812	298	4	j.	j.	PROPN
ejde-1812	298	5	liang	liang	PROPN
ejde-1812	298	6	,	,	PUNCT
ejde-1812	298	7	y.	y.	PROPN
ejde-1812	298	8	mu	mu	PROPN
ejde-1812	298	9	,	,	PUNCT
ejde-1812	298	10	t.-j	t.-j	PROPN
ejde-1812	298	11	.	.	PUNCT
ejde-1812	299	1	xiao	xiao	PROPN
ejde-1812	299	2	ejde-2025/109	ejde-2025/109	PROPN
ejde-1812	299	3	for	for	ADP
ejde-1812	299	4	each	each	DET
ejde-1812	299	5	locally	locally	ADV
ejde-1812	299	6	integrable	integrable	ADJ
ejde-1812	299	7	function	function	NOUN
ejde-1812	299	8	u(t1	u(t1	NOUN
ejde-1812	299	9	,	,	PUNCT
ejde-1812	299	10	t2	t2	NOUN
ejde-1812	299	11	,	,	PUNCT
ejde-1812	299	12	.	.	PUNCT
ejde-1812	299	13	.	.	PUNCT
ejde-1812	299	14	.	.	PUNCT
ejde-1812	300	1	,	,	PUNCT
ejde-1812	300	2	tm	tm	NOUN
ejde-1812	300	3	)	)	PUNCT
ejde-1812	300	4	.	.	PUNCT
ejde-1812	301	1	then	then	ADV
ejde-1812	301	2	the	the	DET
ejde-1812	301	3	fact	fact	NOUN
ejde-1812	301	4	u(t1	u(t1	NOUN
ejde-1812	301	5	,	,	PUNCT
ejde-1812	301	6	t2	t2	NOUN
ejde-1812	301	7	,	,	PUNCT
ejde-1812	301	8	.	.	PUNCT
ejde-1812	301	9	.	.	PUNCT
ejde-1812	301	10	.	.	PUNCT
ejde-1812	302	1	,	,	PUNCT
ejde-1812	302	2	tm	tm	NOUN
ejde-1812	302	3	)	)	PUNCT
ejde-1812	302	4	≤	≤	NUM
ejde-1812	302	5	f(t1	f(t1	NOUN
ejde-1812	302	6	,	,	PUNCT
ejde-1812	302	7	t2	t2	NOUN
ejde-1812	302	8	,	,	PUNCT
ejde-1812	302	9	.	.	PUNCT
ejde-1812	302	10	.	.	PUNCT
ejde-1812	302	11	.	.	PUNCT
ejde-1812	303	1	,	,	PUNCT
ejde-1812	303	2	tm	tm	PROPN
ejde-1812	303	3	)	)	PUNCT
ejde-1812	303	4	+	+	CCONJ
ejde-1812	303	5	(	(	PUNCT
ejde-1812	303	6	pu)(t1	pu)(t1	PROPN
ejde-1812	303	7	,	,	PUNCT
ejde-1812	303	8	t2	t2	NOUN
ejde-1812	303	9	,	,	PUNCT
ejde-1812	303	10	.	.	PUNCT
ejde-1812	303	11	.	.	PUNCT
ejde-1812	303	12	.	.	PUNCT
ejde-1812	304	1	,	,	PUNCT
ejde-1812	304	2	tm	tm	PROPN
ejde-1812	304	3	)	)	PUNCT
ejde-1812	304	4	implies	imply	VERB
ejde-1812	304	5	u(t1	u(t1	NOUN
ejde-1812	304	6	,	,	PUNCT
ejde-1812	304	7	t2	t2	NOUN
ejde-1812	304	8	,	,	PUNCT
ejde-1812	304	9	.	.	PUNCT
ejde-1812	304	10	.	.	PUNCT
ejde-1812	305	1	.	.	PUNCT
ejde-1812	306	1	,	,	PUNCT
ejde-1812	306	2	tm	tm	NOUN
ejde-1812	306	3	)	)	PUNCT
ejde-1812	306	4	≤	≤	NOUN
ejde-1812	307	1	n∑	n∑	PROPN
ejde-1812	307	2	i=0	i=0	PROPN
ejde-1812	307	3	(	(	PUNCT
ejde-1812	307	4	p	p	NOUN
ejde-1812	307	5	if)(t1	if)(t1	NOUN
ejde-1812	307	6	,	,	PUNCT
ejde-1812	307	7	t2	t2	NOUN
ejde-1812	307	8	,	,	PUNCT
ejde-1812	307	9	.	.	PUNCT
ejde-1812	307	10	.	.	PUNCT
ejde-1812	307	11	.	.	PUNCT
ejde-1812	308	1	,	,	PUNCT
ejde-1812	308	2	tm	tm	PROPN
ejde-1812	308	3	)	)	PUNCT
ejde-1812	309	1	+	+	CCONJ
ejde-1812	309	2	(	(	PUNCT
ejde-1812	309	3	pn+1u)(t1	pn+1u)(t1	NOUN
ejde-1812	309	4	,	,	PUNCT
ejde-1812	309	5	t2	t2	NOUN
ejde-1812	309	6	,	,	PUNCT
ejde-1812	309	7	.	.	PUNCT
ejde-1812	309	8	.	.	PUNCT
ejde-1812	309	9	.	.	PUNCT
ejde-1812	310	1	,	,	PUNCT
ejde-1812	310	2	tm	tm	PROPN
ejde-1812	310	3	)	)	PUNCT
ejde-1812	310	4	,	,	PUNCT
ejde-1812	310	5	(	(	PUNCT
ejde-1812	310	6	4.2	4.2	NUM
ejde-1812	310	7	)	)	PUNCT
ejde-1812	310	8	for	for	ADP
ejde-1812	310	9	all	all	PRON
ejde-1812	310	10	n	n	DET
ejde-1812	310	11	∈	∈	PROPN
ejde-1812	310	12	n.	n.	NOUN
ejde-1812	310	13	next	next	ADV
ejde-1812	310	14	,	,	PUNCT
ejde-1812	310	15	we	we	PRON
ejde-1812	310	16	want	want	VERB
ejde-1812	310	17	to	to	PART
ejde-1812	310	18	prove	prove	VERB
ejde-1812	310	19	the	the	DET
ejde-1812	310	20	following	follow	VERB
ejde-1812	310	21	(	(	PUNCT
ejde-1812	310	22	4.3	4.3	NUM
ejde-1812	310	23	)	)	PUNCT
ejde-1812	310	24	by	by	ADP
ejde-1812	310	25	induction	induction	NOUN
ejde-1812	310	26	:	:	PUNCT
ejde-1812	310	27	(	(	PUNCT
ejde-1812	310	28	pnu)(t1	pnu)(t1	PROPN
ejde-1812	310	29	,	,	PUNCT
ejde-1812	310	30	t2	t2	NOUN
ejde-1812	310	31	,	,	PUNCT
ejde-1812	310	32	.	.	PUNCT
ejde-1812	310	33	.	.	PUNCT
ejde-1812	311	1	.	.	PUNCT
ejde-1812	312	1	,	,	PUNCT
ejde-1812	312	2	tm	tm	NOUN
ejde-1812	312	3	)	)	PUNCT
ejde-1812	312	4	≤	≤	NOUN
ejde-1812	312	5	∑	∑	PUNCT
ejde-1812	312	6	0≤l1,	0≤l1,	PROPN
ejde-1812	312	7	...	...	PUNCT
ejde-1812	312	8	,lp≤n	,lp≤n	PUNCT
ejde-1812	313	1	l1+···+lp	l1+···+lp	PROPN
ejde-1812	313	2	=	=	SYM
ejde-1812	313	3	n	n	CCONJ
ejde-1812	313	4	(	(	PUNCT
ejde-1812	313	5	n	n	PRON
ejde-1812	313	6	l1	l1	PROPN
ejde-1812	313	7	,	,	PUNCT
ejde-1812	313	8	.	.	PUNCT
ejde-1812	313	9	.	.	PUNCT
ejde-1812	314	1	.	.	PUNCT
ejde-1812	315	1	,	,	PUNCT
ejde-1812	315	2	lp	lp	X
ejde-1812	315	3	)	)	PUNCT
ejde-1812	316	1	p∏	p∏	PROPN
ejde-1812	316	2	k=1	k=1	X
ejde-1812	316	3	(	(	PUNCT
ejde-1812	316	4	gk(t1	gk(t1	NOUN
ejde-1812	316	5	,	,	PUNCT
ejde-1812	316	6	t2	t2	NOUN
ejde-1812	316	7	,	,	PUNCT
ejde-1812	316	8	.	.	PUNCT
ejde-1812	316	9	.	.	PUNCT
ejde-1812	316	10	.	.	PUNCT
ejde-1812	317	1	,	,	PUNCT
ejde-1812	317	2	tm))lk	tm))lk	PROPN
ejde-1812	317	3	×	×	ADJ
ejde-1812	317	4	∫	∫	PROPN
ejde-1812	317	5	tm	tm	PROPN
ejde-1812	317	6	am	am	PROPN
ejde-1812	318	1	·	·	PUNCT
ejde-1812	318	2	·	·	PUNCT
ejde-1812	318	3	·	·	PUNCT
ejde-1812	318	4	∫	∫	PROPN
ejde-1812	318	5	t2	t2	PROPN
ejde-1812	318	6	a2	a2	PROPN
ejde-1812	318	7	∫	∫	PROPN
ejde-1812	318	8	t1	t1	PROPN
ejde-1812	318	9	a1	a1	PROPN
ejde-1812	318	10	m∏	m∏	PROPN
ejde-1812	318	11	i=1	i=1	PART
ejde-1812	319	1	eζi(si)−ζi(ti)ψ′	eζi(si)−ζi(ti)ψ′	PROPN
ejde-1812	319	2	i(si	i(si	PROPN
ejde-1812	319	3	)	)	PUNCT
ejde-1812	320	1	[	[	X
ejde-1812	320	2	∏p	∏p	X
ejde-1812	320	3	k=1(γ(βki	k=1(γ(βki	NOUN
ejde-1812	320	4	)	)	PUNCT
ejde-1812	320	5	)	)	PUNCT
ejde-1812	321	1	lk	lk	PROPN
ejde-1812	321	2	γ	γ	X
ejde-1812	321	3	(	(	PUNCT
ejde-1812	321	4	∑p	∑p	PROPN
ejde-1812	321	5	k=1	k=1	PROPN
ejde-1812	321	6	lkβki	lkβki	PROPN
ejde-1812	321	7	)	)	PUNCT
ejde-1812	321	8	]	]	PUNCT
ejde-1812	322	1	×	×	NOUN
ejde-1812	322	2	(	(	PUNCT
ejde-1812	322	3	ψi(ti)−	ψi(ti)−	PROPN
ejde-1812	322	4	ψi(si	ψi(si	PROPN
ejde-1812	322	5	)	)	PUNCT
ejde-1812	322	6	)	)	PUNCT
ejde-1812	323	1	∑p	∑p	PROPN
ejde-1812	323	2	k=1	k=1	PUNCT
ejde-1812	323	3	lkβki−1u(s1	lkβki−1u(s1	PROPN
ejde-1812	323	4	,	,	PUNCT
ejde-1812	323	5	s2	s2	PROPN
ejde-1812	323	6	,	,	PUNCT
ejde-1812	323	7	.	.	PUNCT
ejde-1812	323	8	.	.	PUNCT
ejde-1812	324	1	.	.	PUNCT
ejde-1812	325	1	,	,	PUNCT
ejde-1812	325	2	sm)ds1	sm)ds1	PROPN
ejde-1812	325	3	.	.	PUNCT
ejde-1812	325	4	.	.	PUNCT
ejde-1812	325	5	.	.	PUNCT
ejde-1812	326	1	dsm	dsm	PROPN
ejde-1812	326	2	,	,	PUNCT
ejde-1812	326	3	(	(	PUNCT
ejde-1812	326	4	4.3	4.3	NUM
ejde-1812	326	5	)	)	PUNCT
ejde-1812	326	6	for	for	ADP
ejde-1812	326	7	all	all	PRON
ejde-1812	326	8	n	n	DET
ejde-1812	326	9	∈	∈	PROPN
ejde-1812	326	10	n.	n.	NOUN
ejde-1812	326	11	clearly	clearly	ADV
ejde-1812	326	12	,	,	PUNCT
ejde-1812	326	13	(	(	PUNCT
ejde-1812	326	14	4.3	4.3	NUM
ejde-1812	326	15	)	)	PUNCT
ejde-1812	326	16	is	be	AUX
ejde-1812	326	17	true	true	ADJ
ejde-1812	326	18	for	for	ADP
ejde-1812	326	19	n	n	NOUN
ejde-1812	326	20	=	=	SYM
ejde-1812	326	21	1	1	X
ejde-1812	326	22	.	.	PUNCT
ejde-1812	326	23	suppose	suppose	VERB
ejde-1812	326	24	that	that	SCONJ
ejde-1812	326	25	(	(	PUNCT
ejde-1812	326	26	4.3	4.3	NUM
ejde-1812	326	27	)	)	PUNCT
ejde-1812	326	28	holds	hold	VERB
ejde-1812	326	29	for	for	ADP
ejde-1812	326	30	n	n	NOUN
ejde-1812	326	31	=	=	SYM
ejde-1812	326	32	l.	l.	NOUN
ejde-1812	326	33	we	we	PRON
ejde-1812	326	34	want	want	VERB
ejde-1812	326	35	to	to	PART
ejde-1812	326	36	prove	prove	VERB
ejde-1812	326	37	that	that	SCONJ
ejde-1812	326	38	(	(	PUNCT
ejde-1812	326	39	4.3	4.3	NUM
ejde-1812	326	40	)	)	PUNCT
ejde-1812	326	41	also	also	ADV
ejde-1812	326	42	holds	hold	VERB
ejde-1812	326	43	for	for	ADP
ejde-1812	326	44	n	n	NOUN
ejde-1812	326	45	=	=	SYM
ejde-1812	326	46	l	l	NOUN
ejde-1812	327	1	+	+	NOUN
ejde-1812	327	2	1	1	X
ejde-1812	327	3	.	.	PUNCT
ejde-1812	327	4	in	in	ADP
ejde-1812	327	5	fact	fact	NOUN
ejde-1812	327	6	,	,	PUNCT
ejde-1812	327	7	we	we	PRON
ejde-1812	327	8	have	have	VERB
ejde-1812	327	9	(	(	PUNCT
ejde-1812	327	10	p	p	NOUN
ejde-1812	327	11	l+1u)(t	l+1u)(t	NOUN
ejde-1812	327	12	)	)	PUNCT
ejde-1812	327	13	=	=	SYM
ejde-1812	328	1	p∑	p∑	NOUN
ejde-1812	329	1	j=1	j=1	PROPN
ejde-1812	329	2	gj(t1	gj(t1	PROPN
ejde-1812	329	3	,	,	PUNCT
ejde-1812	329	4	t2	t2	NOUN
ejde-1812	329	5	,	,	PUNCT
ejde-1812	329	6	.	.	PUNCT
ejde-1812	329	7	.	.	PUNCT
ejde-1812	329	8	.	.	PUNCT
ejde-1812	330	1	,	,	PUNCT
ejde-1812	330	2	tm	tm	PROPN
ejde-1812	330	3	)	)	PUNCT
ejde-1812	330	4	∫	∫	PROPN
ejde-1812	330	5	tm	tm	PROPN
ejde-1812	330	6	am	am	PROPN
ejde-1812	331	1	·	·	PUNCT
ejde-1812	331	2	·	·	PUNCT
ejde-1812	331	3	·	·	PUNCT
ejde-1812	331	4	∫	∫	PROPN
ejde-1812	331	5	t2	t2	PROPN
ejde-1812	331	6	a2	a2	PROPN
ejde-1812	331	7	∫	∫	PROPN
ejde-1812	331	8	t1	t1	PROPN
ejde-1812	331	9	a1	a1	PROPN
ejde-1812	331	10	m∏	m∏	PROPN
ejde-1812	331	11	i=1	i=1	PART
ejde-1812	332	1	eζi(si)−ζi(ti)ψ′	eζi(si)−ζi(ti)ψ′	PROPN
ejde-1812	332	2	i(si	i(si	PROPN
ejde-1812	332	3	)	)	PUNCT
ejde-1812	332	4	×	×	NOUN
ejde-1812	332	5	(	(	PUNCT
ejde-1812	332	6	ψi(ti)−	ψi(ti)−	PROPN
ejde-1812	332	7	ψi(si	ψi(si	PROPN
ejde-1812	332	8	)	)	PUNCT
ejde-1812	332	9	)	)	PUNCT
ejde-1812	332	10	βji−1(p	βji−1(p	PUNCT
ejde-1812	333	1	lu)(s1	lu)(s1	NOUN
ejde-1812	333	2	,	,	PUNCT
ejde-1812	333	3	s2	s2	PROPN
ejde-1812	333	4	,	,	PUNCT
ejde-1812	333	5	.	.	PUNCT
ejde-1812	333	6	.	.	PUNCT
ejde-1812	333	7	.	.	PUNCT
ejde-1812	334	1	,	,	PUNCT
ejde-1812	334	2	sm)ds1	sm)ds1	PROPN
ejde-1812	334	3	.	.	PUNCT
ejde-1812	334	4	.	.	PUNCT
ejde-1812	334	5	.	.	PUNCT
ejde-1812	335	1	dsm	dsm	PROPN
ejde-1812	335	2	≤	≤	PUNCT
ejde-1812	335	3	p∑	p∑	X
ejde-1812	336	1	j=1	j=1	NOUN
ejde-1812	336	2	∑	∑	PROPN
ejde-1812	336	3	0≤l1,	0≤l1,	PROPN
ejde-1812	336	4	...	...	PUNCT
ejde-1812	336	5	,lp≤l	,lp≤l	PUNCT
ejde-1812	336	6	l1+···+lp	l1+···+lp	ADJ
ejde-1812	336	7	=	=	SYM
ejde-1812	336	8	l	l	NOUN
ejde-1812	336	9	(	(	PUNCT
ejde-1812	336	10	l	l	PROPN
ejde-1812	336	11	l1	l1	PROPN
ejde-1812	336	12	,	,	PUNCT
ejde-1812	336	13	.	.	PUNCT
ejde-1812	336	14	.	.	PUNCT
ejde-1812	337	1	.	.	PUNCT
ejde-1812	338	1	,	,	PUNCT
ejde-1812	338	2	lp	lp	X
ejde-1812	338	3	)	)	PUNCT
ejde-1812	338	4	gj(t1	gj(t1	PROPN
ejde-1812	338	5	,	,	PUNCT
ejde-1812	338	6	t2	t2	NOUN
ejde-1812	338	7	,	,	PUNCT
ejde-1812	338	8	.	.	PUNCT
ejde-1812	338	9	.	.	PUNCT
ejde-1812	338	10	.	.	PUNCT
ejde-1812	339	1	,	,	PUNCT
ejde-1812	339	2	tm	tm	PROPN
ejde-1812	339	3	)	)	PUNCT
ejde-1812	339	4	∫	∫	PROPN
ejde-1812	339	5	tm	tm	PROPN
ejde-1812	339	6	am	am	PROPN
ejde-1812	339	7	·	·	PUNCT
ejde-1812	339	8	·	·	PUNCT
ejde-1812	339	9	·	·	PUNCT
ejde-1812	339	10	∫	∫	PROPN
ejde-1812	339	11	t2	t2	PROPN
ejde-1812	339	12	a2	a2	PROPN
ejde-1812	339	13	∫	∫	PROPN
ejde-1812	339	14	t1	t1	PROPN
ejde-1812	339	15	a1	a1	PROPN
ejde-1812	339	16	m∏	m∏	PROPN
ejde-1812	339	17	i=1	i=1	PART
ejde-1812	339	18	eζi(si)−ζi(ti	eζi(si)−ζi(ti	PROPN
ejde-1812	339	19	)	)	PUNCT
ejde-1812	339	20	×	×	NOUN
ejde-1812	339	21	ψ′	ψ′	PUNCT
ejde-1812	339	22	i(si)(ψi(ti)−	i(si)(ψi(ti)−	PROPN
ejde-1812	339	23	ψi(si	ψi(si	PROPN
ejde-1812	339	24	)	)	PUNCT
ejde-1812	339	25	)	)	PUNCT
ejde-1812	340	1	βji−1	βji−1	PUNCT
ejde-1812	341	1	p∏	p∏	PROPN
ejde-1812	341	2	k=1	k=1	X
ejde-1812	341	3	(	(	PUNCT
ejde-1812	341	4	gk(s1	gk(s1	NOUN
ejde-1812	341	5	,	,	PUNCT
ejde-1812	341	6	s2	s2	PROPN
ejde-1812	341	7	,	,	PUNCT
ejde-1812	341	8	.	.	PUNCT
ejde-1812	341	9	.	.	PUNCT
ejde-1812	341	10	.	.	PUNCT
ejde-1812	342	1	,	,	PUNCT
ejde-1812	342	2	sm))lk	sm))lk	PROPN
ejde-1812	342	3	∫	∫	PROPN
ejde-1812	342	4	sm	sm	PROPN
ejde-1812	342	5	am	be	AUX
ejde-1812	342	6	·	·	PUNCT
ejde-1812	342	7	·	·	PUNCT
ejde-1812	342	8	·	·	PUNCT
ejde-1812	342	9	∫	∫	PROPN
ejde-1812	342	10	s2	s2	PROPN
ejde-1812	342	11	a2	a2	PROPN
ejde-1812	342	12	∫	∫	PROPN
ejde-1812	342	13	s1	s1	PROPN
ejde-1812	342	14	a1	a1	NOUN
ejde-1812	342	15	×	×	PROPN
ejde-1812	342	16	m∏	m∏	PROPN
ejde-1812	342	17	i=1	i=1	PART
ejde-1812	343	1	eζi(τi)−ζi(si)ψ′	eζi(τi)−ζi(si)ψ′	NOUN
ejde-1812	343	2	i(τi	i(τi	NOUN
ejde-1812	343	3	)	)	PUNCT
ejde-1812	344	1	[	[	X
ejde-1812	344	2	∏p	∏p	X
ejde-1812	344	3	k=1(γ(βki	k=1(γ(βki	NOUN
ejde-1812	344	4	)	)	PUNCT
ejde-1812	344	5	)	)	PUNCT
ejde-1812	345	1	lk	lk	PROPN
ejde-1812	345	2	γ	γ	X
ejde-1812	345	3	(	(	PUNCT
ejde-1812	345	4	∑p	∑p	PROPN
ejde-1812	345	5	k=1	k=1	PROPN
ejde-1812	345	6	lkβki	lkβki	PROPN
ejde-1812	345	7	)	)	PUNCT
ejde-1812	345	8	(	(	PUNCT
ejde-1812	345	9	ψi(si)−	ψi(si)−	NOUN
ejde-1812	345	10	ψi(τi	ψi(τi	NOUN
ejde-1812	345	11	)	)	PUNCT
ejde-1812	345	12	)	)	PUNCT
ejde-1812	346	1	∑p	∑p	PROPN
ejde-1812	346	2	k=1	k=1	X
ejde-1812	346	3	lkβki−1	lkβki−1	X
ejde-1812	346	4	]	]	PUNCT
ejde-1812	346	5	×	×	NOUN
ejde-1812	346	6	u(τ1	u(τ1	NOUN
ejde-1812	346	7	,	,	PUNCT
ejde-1812	346	8	τ2	τ2	NOUN
ejde-1812	346	9	,	,	PUNCT
ejde-1812	346	10	.	.	PUNCT
ejde-1812	346	11	.	.	PUNCT
ejde-1812	347	1	.	.	PUNCT
ejde-1812	348	1	,	,	PUNCT
ejde-1812	348	2	τm)dτ1	τm)dτ1	PROPN
ejde-1812	348	3	.	.	PUNCT
ejde-1812	348	4	.	.	PUNCT
ejde-1812	348	5	.	.	PUNCT
ejde-1812	349	1	dτmds1	dτmds1	INTJ
ejde-1812	349	2	.	.	PUNCT
ejde-1812	349	3	.	.	PUNCT
ejde-1812	349	4	.	.	PUNCT
ejde-1812	350	1	dsm	dsm	PROPN
ejde-1812	350	2	.	.	PUNCT
ejde-1812	351	1	by	by	ADP
ejde-1812	351	2	exchanging	exchange	VERB
ejde-1812	351	3	the	the	DET
ejde-1812	351	4	integration	integration	NOUN
ejde-1812	351	5	order	order	NOUN
ejde-1812	351	6	and	and	CCONJ
ejde-1812	351	7	noting	note	VERB
ejde-1812	351	8	that	that	SCONJ
ejde-1812	351	9	the	the	DET
ejde-1812	351	10	functions	function	NOUN
ejde-1812	351	11	gi	gi	VERB
ejde-1812	351	12	are	be	AUX
ejde-1812	351	13	nondecreasing	nondecrease	VERB
ejde-1812	351	14	,	,	PUNCT
ejde-1812	351	15	we	we	PRON
ejde-1812	351	16	obtain∫	obtain∫	VERB
ejde-1812	351	17	t1	t1	NOUN
ejde-1812	351	18	a1	a1	NOUN
ejde-1812	351	19	eζ1(s1)−ζ1(t1)ψ′	eζ1(s1)−ζ1(t1)ψ′	PROPN
ejde-1812	351	20	1(s1)(ψ1(t1)−	1(s1)(ψ1(t1)−	PROPN
ejde-1812	351	21	ψ1(s1	ψ1(s1	NOUN
ejde-1812	351	22	)	)	PUNCT
ejde-1812	351	23	)	)	PUNCT
ejde-1812	351	24	βj1−1	βj1−1	VERB
ejde-1812	352	1	p∏	p∏	PROPN
ejde-1812	352	2	k=1	k=1	X
ejde-1812	353	1	(	(	PUNCT
ejde-1812	353	2	gk(s1	gk(s1	NOUN
ejde-1812	353	3	,	,	PUNCT
ejde-1812	353	4	s2	s2	PROPN
ejde-1812	353	5	,	,	PUNCT
ejde-1812	353	6	.	.	PUNCT
ejde-1812	353	7	.	.	PUNCT
ejde-1812	354	1	.	.	PUNCT
ejde-1812	355	1	,	,	PUNCT
ejde-1812	356	1	sm))lk	sm))lk	PROPN
ejde-1812	356	2	×	×	NOUN
ejde-1812	356	3	∫	∫	NOUN
ejde-1812	356	4	s1	s1	NOUN
ejde-1812	356	5	a1	a1	NOUN
ejde-1812	356	6	eζ1(τ1)−ζ1(s1)ψ′	eζ1(τ1)−ζ1(s1)ψ′	PROPN
ejde-1812	356	7	1(τ1	1(τ1	NUM
ejde-1812	356	8	)	)	PUNCT
ejde-1812	357	1	[	[	X
ejde-1812	357	2	∏p	∏p	NOUN
ejde-1812	357	3	k=1(γ(βk1	k=1(γ(βk1	NOUN
ejde-1812	357	4	)	)	PUNCT
ejde-1812	357	5	)	)	PUNCT
ejde-1812	358	1	lk	lk	PROPN
ejde-1812	358	2	γ	γ	X
ejde-1812	358	3	(	(	PUNCT
ejde-1812	358	4	∑p	∑p	ADJ
ejde-1812	358	5	k=1	k=1	NOUN
ejde-1812	358	6	lkβk1	lkβk1	NOUN
ejde-1812	358	7	)	)	PUNCT
ejde-1812	358	8	(	(	PUNCT
ejde-1812	358	9	ψ1(s1)−	ψ1(s1)−	NOUN
ejde-1812	358	10	ψ1(τ1	ψ1(τ1	NOUN
ejde-1812	358	11	)	)	PUNCT
ejde-1812	358	12	)	)	PUNCT
ejde-1812	359	1	∑p	∑p	PROPN
ejde-1812	360	1	k=1	k=1	NOUN
ejde-1812	360	2	lkβk1−1	lkβk1−1	ADJ
ejde-1812	360	3	]	]	PUNCT
ejde-1812	360	4	×	×	NOUN
ejde-1812	360	5	u(τ1	u(τ1	NOUN
ejde-1812	360	6	,	,	PUNCT
ejde-1812	360	7	τ2	τ2	NOUN
ejde-1812	360	8	,	,	PUNCT
ejde-1812	360	9	.	.	PUNCT
ejde-1812	360	10	.	.	PUNCT
ejde-1812	360	11	.	.	PUNCT
ejde-1812	361	1	,	,	PUNCT
ejde-1812	361	2	τm)dτ1ds1	τm)dτ1ds1	PROPN
ejde-1812	361	3	≤	≤	NUM
ejde-1812	361	4	p∏	p∏	PROPN
ejde-1812	361	5	k=1	k=1	X
ejde-1812	361	6	(	(	PUNCT
ejde-1812	361	7	gk(t1	gk(t1	NOUN
ejde-1812	361	8	,	,	PUNCT
ejde-1812	361	9	s2	s2	NOUN
ejde-1812	361	10	,	,	PUNCT
ejde-1812	361	11	.	.	PUNCT
ejde-1812	361	12	.	.	PUNCT
ejde-1812	361	13	.	.	PUNCT
ejde-1812	361	14	,	,	PUNCT
ejde-1812	362	1	sm))lk	sm))lk	PROPN
ejde-1812	362	2	[	[	PUNCT
ejde-1812	362	3	∏	∏	PROPN
ejde-1812	362	4	k	k	PROPN
ejde-1812	362	5	̸=j(γ(βk1	̸=j(γ(βk1	PROPN
ejde-1812	362	6	)	)	PUNCT
ejde-1812	362	7	)	)	PUNCT
ejde-1812	363	1	lk	lk	X
ejde-1812	363	2	]	]	X
ejde-1812	363	3	(	(	PUNCT
ejde-1812	363	4	γ(βj1	γ(βj1	NOUN
ejde-1812	363	5	)	)	PUNCT
ejde-1812	363	6	)	)	PUNCT
ejde-1812	363	7	lj+1	lj+1	PROPN
ejde-1812	363	8	γ	γ	X
ejde-1812	363	9	(	(	PUNCT
ejde-1812	363	10	∑	∑	PROPN
ejde-1812	363	11	k	k	X
ejde-1812	363	12	̸=j	̸=j	PROPN
ejde-1812	363	13	lkβk1	lkβk1	NOUN
ejde-1812	363	14	+	+	CCONJ
ejde-1812	363	15	(	(	PUNCT
ejde-1812	363	16	lj	lj	PROPN
ejde-1812	363	17	+	+	NUM
ejde-1812	363	18	1)βj1	1)βj1	NUM
ejde-1812	363	19	)	)	PUNCT
ejde-1812	363	20	×	×	NOUN
ejde-1812	363	21	∫	∫	PROPN
ejde-1812	363	22	t1	t1	NOUN
ejde-1812	363	23	a1	a1	PROPN
ejde-1812	363	24	eζ1(s1)−ζ1(t1)ψ′	eζ1(s1)−ζ1(t1)ψ′	PROPN
ejde-1812	363	25	1(s1)(ψ1(t1)−	1(s1)(ψ1(t1)−	PROPN
ejde-1812	363	26	ψ1(s1	ψ1(s1	NOUN
ejde-1812	363	27	)	)	PUNCT
ejde-1812	363	28	)	)	PUNCT
ejde-1812	363	29	βj1	βj1	NOUN
ejde-1812	363	30	+	+	CCONJ
ejde-1812	363	31	∑p	∑p	ADJ
ejde-1812	363	32	k=1	k=1	X
ejde-1812	363	33	lkβk1−1u(s1	lkβk1−1u(s1	NOUN
ejde-1812	363	34	,	,	PUNCT
ejde-1812	363	35	τ2	τ2	NOUN
ejde-1812	363	36	,	,	PUNCT
ejde-1812	363	37	.	.	PUNCT
ejde-1812	363	38	.	.	PUNCT
ejde-1812	363	39	.	.	PUNCT
ejde-1812	364	1	,	,	PUNCT
ejde-1812	364	2	τm)ds1	τm)ds1	PROPN
ejde-1812	364	3	,	,	PUNCT
ejde-1812	364	4	where	where	SCONJ
ejde-1812	364	5	we	we	PRON
ejde-1812	364	6	use	use	VERB
ejde-1812	364	7	that∫	that∫	NOUN
ejde-1812	364	8	t1	t1	NOUN
ejde-1812	364	9	τ1	τ1	PROPN
ejde-1812	364	10	(	(	PUNCT
ejde-1812	364	11	ψ1(t1)−	ψ1(t1)−	NOUN
ejde-1812	364	12	ψ1(s1	ψ1(s1	PROPN
ejde-1812	364	13	)	)	PUNCT
ejde-1812	364	14	)	)	PUNCT
ejde-1812	365	1	βj1−1(ψ1(s1)−	βj1−1(ψ1(s1)−	NOUN
ejde-1812	365	2	ψ1(τ1	ψ1(τ1	PROPN
ejde-1812	365	3	)	)	PUNCT
ejde-1812	365	4	)	)	PUNCT
ejde-1812	366	1	∑p	∑p	SCONJ
ejde-1812	366	2	k=1	k=1	PUNCT
ejde-1812	367	1	lkβk1−1ψ′	lkβk1−1ψ′	NUM
ejde-1812	367	2	1(s)ds	1(s)ds	NUM
ejde-1812	367	3	=	=	SYM
ejde-1812	367	4	(	(	PUNCT
ejde-1812	367	5	ψ1(t1)−	ψ1(t1)−	NOUN
ejde-1812	367	6	ψ1(τ1	ψ1(τ1	PROPN
ejde-1812	367	7	)	)	PUNCT
ejde-1812	367	8	)	)	PUNCT
ejde-1812	367	9	βj1	βj1	NOUN
ejde-1812	367	10	+	+	CCONJ
ejde-1812	367	11	∑p	∑p	ADJ
ejde-1812	367	12	k=1	k=1	NOUN
ejde-1812	367	13	lkβk1−1b(βj1	lkβk1−1b(βj1	NOUN
ejde-1812	367	14	,	,	PUNCT
ejde-1812	367	15	p∑	p∑	X
ejde-1812	367	16	k=1	k=1	X
ejde-1812	367	17	lkβk1	lkβk1	NOUN
ejde-1812	367	18	)	)	PUNCT
ejde-1812	367	19	ejde-2025/109	ejde-2025/109	ADP
ejde-1812	367	20	evolution	evolution	NOUN
ejde-1812	367	21	ψ	ψ	NOUN
ejde-1812	367	22	-	-	ADJ
ejde-1812	367	23	hilfer	hilfer	NOUN
ejde-1812	367	24	fractional	fractional	ADJ
ejde-1812	367	25	differential	differential	ADJ
ejde-1812	367	26	equations	equation	NOUN
ejde-1812	367	27	11	11	NUM
ejde-1812	367	28	and	and	CCONJ
ejde-1812	367	29	b(βj1	b(βj1	NOUN
ejde-1812	367	30	,	,	PUNCT
ejde-1812	367	31	p∑	p∑	X
ejde-1812	367	32	k=1	k=1	X
ejde-1812	367	33	lkβk1	lkβk1	NOUN
ejde-1812	367	34	)	)	PUNCT
ejde-1812	367	35	=	=	SYM
ejde-1812	368	1	γ(βj1)γ	γ(βj1)γ	NOUN
ejde-1812	368	2	(	(	PUNCT
ejde-1812	368	3	∑p	∑p	ADJ
ejde-1812	368	4	k=1	k=1	ADJ
ejde-1812	368	5	lkβk1	lkβk1	NOUN
ejde-1812	368	6	)	)	PUNCT
ejde-1812	368	7	γ	γ	PROPN
ejde-1812	368	8	(	(	PUNCT
ejde-1812	368	9	∑	∑	PROPN
ejde-1812	368	10	k	k	X
ejde-1812	368	11	̸=j	̸=j	PROPN
ejde-1812	368	12	lkβk1	lkβk1	NOUN
ejde-1812	368	13	+	+	CCONJ
ejde-1812	368	14	(	(	PUNCT
ejde-1812	368	15	lj	lj	PROPN
ejde-1812	368	16	+	+	NUM
ejde-1812	368	17	1)βj1	1)βj1	NUM
ejde-1812	368	18	)	)	PUNCT
ejde-1812	368	19	.	.	PUNCT
ejde-1812	369	1	repeating	repeat	VERB
ejde-1812	369	2	this	this	DET
ejde-1812	369	3	process	process	NOUN
ejde-1812	369	4	for	for	ADP
ejde-1812	369	5	m	m	PROPN
ejde-1812	369	6	times	time	NOUN
ejde-1812	369	7	,	,	PUNCT
ejde-1812	369	8	we	we	PRON
ejde-1812	369	9	obtain	obtain	VERB
ejde-1812	369	10	(	(	PUNCT
ejde-1812	369	11	p	p	NOUN
ejde-1812	369	12	l+1u)(t	l+1u)(t	NOUN
ejde-1812	369	13	)	)	PUNCT
ejde-1812	369	14	≤	≤	PUNCT
ejde-1812	369	15	p∑	p∑	NOUN
ejde-1812	370	1	j=1	j=1	NOUN
ejde-1812	370	2	∑	∑	PROPN
ejde-1812	370	3	0≤l1,	0≤l1,	PROPN
ejde-1812	370	4	...	...	PUNCT
ejde-1812	370	5	,lp≤l	,lp≤l	PUNCT
ejde-1812	370	6	l1+···+lp	l1+···+lp	ADJ
ejde-1812	370	7	=	=	SYM
ejde-1812	370	8	l	l	NOUN
ejde-1812	370	9	(	(	PUNCT
ejde-1812	370	10	l	l	PROPN
ejde-1812	370	11	l1	l1	PROPN
ejde-1812	370	12	,	,	PUNCT
ejde-1812	370	13	.	.	PUNCT
ejde-1812	370	14	.	.	PUNCT
ejde-1812	371	1	.	.	PUNCT
ejde-1812	372	1	,	,	PUNCT
ejde-1812	372	2	lp	lp	INTJ
ejde-1812	372	3	)	)	PUNCT
ejde-1812	373	1	[	[	X
ejde-1812	373	2	∏	∏	X
ejde-1812	373	3	k	k	X
ejde-1812	373	4	̸=j	̸=j	PROPN
ejde-1812	373	5	(	(	PUNCT
ejde-1812	373	6	gk(t1	gk(t1	NOUN
ejde-1812	373	7	,	,	PUNCT
ejde-1812	373	8	s2	s2	NOUN
ejde-1812	373	9	,	,	PUNCT
ejde-1812	373	10	.	.	PUNCT
ejde-1812	373	11	.	.	PUNCT
ejde-1812	373	12	.	.	PUNCT
ejde-1812	373	13	,	,	PUNCT
ejde-1812	374	1	sm))lk	sm))lk	PROPN
ejde-1812	374	2	]	]	PUNCT
ejde-1812	374	3	(	(	PUNCT
ejde-1812	374	4	gj(t1	gj(t1	PROPN
ejde-1812	374	5	,	,	PUNCT
ejde-1812	374	6	s2	s2	PROPN
ejde-1812	374	7	,	,	PUNCT
ejde-1812	374	8	.	.	PUNCT
ejde-1812	374	9	.	.	PUNCT
ejde-1812	374	10	.	.	PUNCT
ejde-1812	375	1	,	,	PUNCT
ejde-1812	375	2	sm))lj+1	sm))lj+1	PROPN
ejde-1812	376	1	×	×	NOUN
ejde-1812	376	2	∫	∫	INTJ
ejde-1812	376	3	tm	tm	PROPN
ejde-1812	376	4	am	am	PROPN
ejde-1812	376	5	·	·	PUNCT
ejde-1812	376	6	·	·	PUNCT
ejde-1812	376	7	·	·	PUNCT
ejde-1812	376	8	∫	∫	PROPN
ejde-1812	376	9	t2	t2	PROPN
ejde-1812	376	10	a2	a2	PROPN
ejde-1812	376	11	∫	∫	PROPN
ejde-1812	376	12	t1	t1	PROPN
ejde-1812	376	13	a1	a1	PROPN
ejde-1812	376	14	m∏	m∏	PROPN
ejde-1812	376	15	i=1	i=1	X
ejde-1812	377	1	[	[	PUNCT
ejde-1812	377	2	∏	∏	PROPN
ejde-1812	377	3	k	k	PROPN
ejde-1812	377	4	̸=j(γ(βki	̸=j(γ(βki	PROPN
ejde-1812	377	5	)	)	PUNCT
ejde-1812	377	6	)	)	PUNCT
ejde-1812	378	1	lk	lk	X
ejde-1812	378	2	]	]	X
ejde-1812	378	3	(	(	PUNCT
ejde-1812	378	4	γ(βji	γ(βji	NOUN
ejde-1812	378	5	)	)	PUNCT
ejde-1812	378	6	)	)	PUNCT
ejde-1812	378	7	lj+1	lj+1	PROPN
ejde-1812	378	8	γ	γ	X
ejde-1812	378	9	(	(	PUNCT
ejde-1812	378	10	∑	∑	PROPN
ejde-1812	378	11	k	k	PROPN
ejde-1812	378	12	̸=j	̸=j	PROPN
ejde-1812	378	13	lkβki	lkβki	NOUN
ejde-1812	378	14	+	+	CCONJ
ejde-1812	378	15	(	(	PUNCT
ejde-1812	378	16	lj	lj	PROPN
ejde-1812	378	17	+	+	NUM
ejde-1812	378	18	1)βji	1)βji	NUM
ejde-1812	378	19	)	)	PUNCT
ejde-1812	378	20	eζi(si)−ζi(ti)ψ′	eζi(si)−ζi(ti)ψ′	PROPN
ejde-1812	378	21	i(si	i(si	PROPN
ejde-1812	378	22	)	)	PUNCT
ejde-1812	378	23	×	×	NOUN
ejde-1812	378	24	(	(	PUNCT
ejde-1812	378	25	ψi(ti)−	ψi(ti)−	PROPN
ejde-1812	378	26	ψi(si	ψi(si	PROPN
ejde-1812	378	27	)	)	PUNCT
ejde-1812	378	28	)	)	PUNCT
ejde-1812	379	1	∑	∑	PUNCT
ejde-1812	380	1	k	k	PROPN
ejde-1812	380	2	̸=j	̸=j	PROPN
ejde-1812	380	3	lkβki+(lj+1)βji−1u(s1	lkβki+(lj+1)βji−1u(s1	PROPN
ejde-1812	380	4	,	,	PUNCT
ejde-1812	380	5	s2	s2	PROPN
ejde-1812	380	6	,	,	PUNCT
ejde-1812	380	7	.	.	PUNCT
ejde-1812	380	8	.	.	PUNCT
ejde-1812	380	9	.	.	PUNCT
ejde-1812	381	1	,	,	PUNCT
ejde-1812	381	2	sm)ds1	sm)ds1	PROPN
ejde-1812	381	3	.	.	PUNCT
ejde-1812	381	4	.	.	PUNCT
ejde-1812	381	5	.	.	PUNCT
ejde-1812	382	1	dsm	dsm	PROPN
ejde-1812	382	2	.	.	PUNCT
ejde-1812	383	1	therefore	therefore	ADV
ejde-1812	383	2	,	,	PUNCT
ejde-1812	383	3	(	(	PUNCT
ejde-1812	383	4	p	p	NOUN
ejde-1812	383	5	l+1u)(t	l+1u)(t	PROPN
ejde-1812	383	6	)	)	PUNCT
ejde-1812	383	7	=	=	SYM
ejde-1812	383	8	∑	∑	PUNCT
ejde-1812	383	9	0≤l1,	0≤l1,	PROPN
ejde-1812	383	10	...	...	PUNCT
ejde-1812	383	11	,lp≤l+1	,lp≤l+1	PUNCT
ejde-1812	383	12	l1+···+lp	l1+···+lp	NOUN
ejde-1812	383	13	=	=	SYM
ejde-1812	383	14	l+1	l+1	X
ejde-1812	383	15	p∑	p∑	NOUN
ejde-1812	384	1	j=1	j=1	NOUN
ejde-1812	385	1	(	(	PUNCT
ejde-1812	385	2	l	l	PROPN
ejde-1812	385	3	l1	l1	PROPN
ejde-1812	385	4	,	,	PUNCT
ejde-1812	385	5	.	.	PUNCT
ejde-1812	385	6	.	.	PUNCT
ejde-1812	385	7	.	.	PUNCT
ejde-1812	386	1	,	,	PUNCT
ejde-1812	386	2	lj−1	lj−1	PROPN
ejde-1812	386	3	,	,	PUNCT
ejde-1812	386	4	lj	lj	PROPN
ejde-1812	386	5	−	−	PROPN
ejde-1812	386	6	1	1	NUM
ejde-1812	386	7	,	,	PUNCT
ejde-1812	386	8	lj+1	lj+1	PROPN
ejde-1812	386	9	,	,	PUNCT
ejde-1812	386	10	.	.	PUNCT
ejde-1812	386	11	.	.	PUNCT
ejde-1812	386	12	.	.	PUNCT
ejde-1812	387	1	,	,	PUNCT
ejde-1812	387	2	lp	lp	X
ejde-1812	387	3	)	)	PUNCT
ejde-1812	388	1	p∏	p∏	PROPN
ejde-1812	388	2	k=1	k=1	X
ejde-1812	388	3	(	(	PUNCT
ejde-1812	388	4	gk(t1	gk(t1	NOUN
ejde-1812	388	5	,	,	PUNCT
ejde-1812	388	6	s2	s2	NOUN
ejde-1812	388	7	,	,	PUNCT
ejde-1812	388	8	.	.	PUNCT
ejde-1812	388	9	.	.	PUNCT
ejde-1812	388	10	.	.	PUNCT
ejde-1812	389	1	,	,	PUNCT
ejde-1812	389	2	sm))lk	sm))lk	PROPN
ejde-1812	389	3	×	×	NOUN
ejde-1812	389	4	∫	∫	PROPN
ejde-1812	389	5	tm	tm	PROPN
ejde-1812	389	6	am	am	PROPN
ejde-1812	389	7	·	·	PUNCT
ejde-1812	390	1	·	·	PUNCT
ejde-1812	390	2	·	·	PUNCT
ejde-1812	390	3	∫	∫	PROPN
ejde-1812	390	4	t2	t2	PROPN
ejde-1812	390	5	a2	a2	PROPN
ejde-1812	390	6	∫	∫	PROPN
ejde-1812	390	7	t1	t1	PROPN
ejde-1812	390	8	a1	a1	PROPN
ejde-1812	390	9	m∏	m∏	PROPN
ejde-1812	390	10	i=1	i=1	PROPN
ejde-1812	390	11	∏p	∏p	PROPN
ejde-1812	390	12	k=1(γ(βki	k=1(γ(βki	NOUN
ejde-1812	390	13	)	)	PUNCT
ejde-1812	390	14	)	)	PUNCT
ejde-1812	391	1	lk	lk	PROPN
ejde-1812	391	2	γ	γ	X
ejde-1812	391	3	(	(	PUNCT
ejde-1812	391	4	∑p	∑p	ADJ
ejde-1812	391	5	k=1	k=1	PROPN
ejde-1812	391	6	lkβki	lkβki	PROPN
ejde-1812	391	7	)	)	PUNCT
ejde-1812	391	8	eζi(si)−ζi(ti)ψ′	eζi(si)−ζi(ti)ψ′	PROPN
ejde-1812	391	9	i(si	i(si	PROPN
ejde-1812	391	10	)	)	PUNCT
ejde-1812	391	11	×	×	NOUN
ejde-1812	391	12	(	(	PUNCT
ejde-1812	391	13	ψi(ti)−	ψi(ti)−	PROPN
ejde-1812	391	14	ψi(si	ψi(si	PROPN
ejde-1812	391	15	)	)	PUNCT
ejde-1812	391	16	)	)	PUNCT
ejde-1812	392	1	∑p	∑p	PROPN
ejde-1812	392	2	k=1	k=1	PUNCT
ejde-1812	392	3	lkβki−1u(s1	lkβki−1u(s1	PROPN
ejde-1812	392	4	,	,	PUNCT
ejde-1812	392	5	s2	s2	PROPN
ejde-1812	392	6	,	,	PUNCT
ejde-1812	392	7	.	.	PUNCT
ejde-1812	392	8	.	.	PUNCT
ejde-1812	393	1	.	.	PUNCT
ejde-1812	394	1	,	,	PUNCT
ejde-1812	394	2	sm)ds1	sm)ds1	PROPN
ejde-1812	394	3	.	.	PUNCT
ejde-1812	394	4	.	.	PUNCT
ejde-1812	394	5	.	.	PUNCT
ejde-1812	395	1	dsm	dsm	PROPN
ejde-1812	395	2	=	=	SYM
ejde-1812	395	3	∑	∑	PROPN
ejde-1812	395	4	0≤l1,	0≤l1,	PROPN
ejde-1812	395	5	...	...	PUNCT
ejde-1812	395	6	,lp≤l+1	,lp≤l+1	PUNCT
ejde-1812	395	7	l1+···+lp	l1+···+lp	PROPN
ejde-1812	395	8	=	=	SYM
ejde-1812	395	9	l+1	l+1	X
ejde-1812	395	10	(	(	PUNCT
ejde-1812	395	11	l	l	NOUN
ejde-1812	395	12	+	+	NOUN
ejde-1812	395	13	1	1	NUM
ejde-1812	395	14	l1	l1	NOUN
ejde-1812	395	15	,	,	PUNCT
ejde-1812	395	16	.	.	PUNCT
ejde-1812	395	17	.	.	PUNCT
ejde-1812	395	18	.	.	PUNCT
ejde-1812	396	1	,	,	PUNCT
ejde-1812	396	2	lp	lp	X
ejde-1812	396	3	)	)	PUNCT
ejde-1812	397	1	p∏	p∏	PROPN
ejde-1812	397	2	k=1	k=1	X
ejde-1812	397	3	(	(	PUNCT
ejde-1812	397	4	gk(t1	gk(t1	NOUN
ejde-1812	397	5	,	,	PUNCT
ejde-1812	397	6	s2	s2	NOUN
ejde-1812	397	7	,	,	PUNCT
ejde-1812	397	8	.	.	PUNCT
ejde-1812	397	9	.	.	PUNCT
ejde-1812	397	10	.	.	PUNCT
ejde-1812	398	1	,	,	PUNCT
ejde-1812	398	2	sm))lk	sm))lk	PROPN
ejde-1812	398	3	×	×	NOUN
ejde-1812	398	4	∫	∫	PROPN
ejde-1812	398	5	tm	tm	PROPN
ejde-1812	398	6	am	am	PROPN
ejde-1812	398	7	·	·	PUNCT
ejde-1812	399	1	·	·	PUNCT
ejde-1812	399	2	·	·	PUNCT
ejde-1812	399	3	∫	∫	PROPN
ejde-1812	399	4	t2	t2	PROPN
ejde-1812	399	5	a2	a2	PROPN
ejde-1812	399	6	∫	∫	PROPN
ejde-1812	399	7	t1	t1	PROPN
ejde-1812	399	8	a1	a1	PROPN
ejde-1812	399	9	m∏	m∏	PROPN
ejde-1812	399	10	i=1	i=1	PROPN
ejde-1812	399	11	∏p	∏p	PROPN
ejde-1812	399	12	k=1(γ(βki	k=1(γ(βki	NOUN
ejde-1812	399	13	)	)	PUNCT
ejde-1812	399	14	)	)	PUNCT
ejde-1812	400	1	lk	lk	PROPN
ejde-1812	400	2	γ	γ	X
ejde-1812	400	3	(	(	PUNCT
ejde-1812	400	4	∑p	∑p	ADJ
ejde-1812	400	5	k=1	k=1	PROPN
ejde-1812	400	6	lkβki	lkβki	PROPN
ejde-1812	400	7	)	)	PUNCT
ejde-1812	400	8	eζi(si)−ζi(ti)ψ′	eζi(si)−ζi(ti)ψ′	PROPN
ejde-1812	400	9	i(si	i(si	PROPN
ejde-1812	400	10	)	)	PUNCT
ejde-1812	400	11	×	×	NOUN
ejde-1812	400	12	(	(	PUNCT
ejde-1812	400	13	ψi(ti)−	ψi(ti)−	PROPN
ejde-1812	400	14	ψi(si	ψi(si	PROPN
ejde-1812	400	15	)	)	PUNCT
ejde-1812	400	16	)	)	PUNCT
ejde-1812	401	1	∑p	∑p	PROPN
ejde-1812	401	2	k=1	k=1	PUNCT
ejde-1812	401	3	lkβki−1u(s1	lkβki−1u(s1	PROPN
ejde-1812	401	4	,	,	PUNCT
ejde-1812	401	5	s2	s2	PROPN
ejde-1812	401	6	,	,	PUNCT
ejde-1812	401	7	.	.	PUNCT
ejde-1812	401	8	.	.	PUNCT
ejde-1812	402	1	.	.	PUNCT
ejde-1812	403	1	,	,	PUNCT
ejde-1812	403	2	sm)ds1	sm)ds1	PROPN
ejde-1812	403	3	.	.	PUNCT
ejde-1812	403	4	.	.	PUNCT
ejde-1812	403	5	.	.	PUNCT
ejde-1812	404	1	dsm	dsm	PROPN
ejde-1812	404	2	,	,	PUNCT
ejde-1812	404	3	where	where	SCONJ
ejde-1812	404	4	we	we	PRON
ejde-1812	404	5	have	have	AUX
ejde-1812	404	6	used	use	VERB
ejde-1812	404	7	m∑	m∑	ADV
ejde-1812	404	8	j=1	j=1	PROPN
ejde-1812	404	9	(	(	PUNCT
ejde-1812	404	10	n	n	X
ejde-1812	404	11	l1	l1	PROPN
ejde-1812	404	12	,	,	PUNCT
ejde-1812	404	13	.	.	PUNCT
ejde-1812	404	14	.	.	PUNCT
ejde-1812	404	15	.	.	PUNCT
ejde-1812	405	1	,	,	PUNCT
ejde-1812	405	2	lj−1	lj−1	PROPN
ejde-1812	405	3	,	,	PUNCT
ejde-1812	405	4	lj	lj	PROPN
ejde-1812	405	5	−	−	PROPN
ejde-1812	405	6	1	1	NUM
ejde-1812	405	7	,	,	PUNCT
ejde-1812	405	8	lj+1	lj+1	PROPN
ejde-1812	405	9	,	,	PUNCT
ejde-1812	405	10	.	.	PUNCT
ejde-1812	405	11	.	.	PUNCT
ejde-1812	405	12	.	.	PUNCT
ejde-1812	406	1	,	,	PUNCT
ejde-1812	406	2	lm	lm	INTJ
ejde-1812	406	3	)	)	PUNCT
ejde-1812	406	4	=	=	SYM
ejde-1812	407	1	(	(	PUNCT
ejde-1812	407	2	n+	n+	NUM
ejde-1812	407	3	1	1	NUM
ejde-1812	407	4	l1	l1	PROPN
ejde-1812	407	5	,	,	PUNCT
ejde-1812	407	6	.	.	PUNCT
ejde-1812	407	7	.	.	PUNCT
ejde-1812	407	8	.	.	PUNCT
ejde-1812	408	1	,	,	PUNCT
ejde-1812	408	2	lm	lm	INTJ
ejde-1812	408	3	)	)	PUNCT
ejde-1812	408	4	,	,	PUNCT
ejde-1812	408	5	in	in	ADP
ejde-1812	408	6	which	which	PRON
ejde-1812	408	7	∑m	∑m	PROPN
ejde-1812	408	8	j=1	j=1	NOUN
ejde-1812	409	1	lj	lj	PROPN
ejde-1812	409	2	=	=	SYM
ejde-1812	409	3	n+	n+	PUNCT
ejde-1812	409	4	1	1	NUM
ejde-1812	409	5	,	,	PUNCT
ejde-1812	409	6	and	and	CCONJ
ejde-1812	409	7	we	we	PRON
ejde-1812	409	8	take	take	VERB
ejde-1812	409	9	(	(	PUNCT
ejde-1812	409	10	n	n	DET
ejde-1812	409	11	l1	l1	PROPN
ejde-1812	409	12	,	,	PUNCT
ejde-1812	409	13	.	.	PUNCT
ejde-1812	409	14	.	.	PUNCT
ejde-1812	409	15	.	.	PUNCT
ejde-1812	410	1	,	,	PUNCT
ejde-1812	410	2	lm	lm	INTJ
ejde-1812	410	3	)	)	PUNCT
ejde-1812	411	1	=	=	SYM
ejde-1812	411	2	0	0	PUNCT
ejde-1812	411	3	when	when	SCONJ
ejde-1812	411	4	li	li	PROPN
ejde-1812	411	5	=	=	VERB
ejde-1812	411	6	−1	−1	NOUN
ejde-1812	411	7	for	for	ADP
ejde-1812	411	8	some	some	DET
ejde-1812	411	9	i.	i.	NOUN
ejde-1812	411	10	thus	thus	ADV
ejde-1812	411	11	we	we	PRON
ejde-1812	411	12	show	show	VERB
ejde-1812	411	13	that	that	SCONJ
ejde-1812	411	14	(	(	PUNCT
ejde-1812	411	15	4.3	4.3	NUM
ejde-1812	411	16	)	)	PUNCT
ejde-1812	411	17	also	also	ADV
ejde-1812	411	18	holds	hold	VERB
ejde-1812	411	19	for	for	ADP
ejde-1812	411	20	n	n	NOUN
ejde-1812	411	21	=	=	SYM
ejde-1812	411	22	l	l	NOUN
ejde-1812	412	1	+	+	NOUN
ejde-1812	412	2	1	1	X
ejde-1812	412	3	.	.	X
ejde-1812	412	4	therefore	therefore	ADV
ejde-1812	412	5	,	,	PUNCT
ejde-1812	412	6	(	(	PUNCT
ejde-1812	412	7	4.3	4.3	NUM
ejde-1812	412	8	)	)	PUNCT
ejde-1812	412	9	is	be	AUX
ejde-1812	412	10	true	true	ADJ
ejde-1812	412	11	.	.	PUNCT
ejde-1812	413	1	by	by	ADP
ejde-1812	413	2	(	(	PUNCT
ejde-1812	413	3	4.3	4.3	NUM
ejde-1812	413	4	)	)	PUNCT
ejde-1812	413	5	we	we	PRON
ejde-1812	413	6	can	can	AUX
ejde-1812	413	7	see	see	VERB
ejde-1812	413	8	that	that	DET
ejde-1812	413	9	(	(	PUNCT
ejde-1812	413	10	pnu)(t	pnu)(t	NOUN
ejde-1812	413	11	)	)	PUNCT
ejde-1812	413	12	→	→	SYM
ejde-1812	413	13	0	0	NUM
ejde-1812	413	14	as	as	ADP
ejde-1812	413	15	n	n	NOUN
ejde-1812	413	16	→	→	SYM
ejde-1812	413	17	∞.	∞.	PROPN
ejde-1812	413	18	from	from	ADP
ejde-1812	413	19	(	(	PUNCT
ejde-1812	413	20	4.2	4.2	NUM
ejde-1812	413	21	)	)	PUNCT
ejde-1812	413	22	and	and	CCONJ
ejde-1812	413	23	(	(	PUNCT
ejde-1812	413	24	4.3	4.3	NUM
ejde-1812	413	25	)	)	PUNCT
ejde-1812	413	26	,	,	PUNCT
ejde-1812	413	27	we	we	PRON
ejde-1812	413	28	see	see	VERB
ejde-1812	413	29	that	that	SCONJ
ejde-1812	413	30	(	(	PUNCT
ejde-1812	413	31	4.1	4.1	NUM
ejde-1812	413	32	)	)	PUNCT
ejde-1812	413	33	holds	hold	VERB
ejde-1812	413	34	.	.	PUNCT
ejde-1812	414	1	the	the	DET
ejde-1812	414	2	proof	proof	NOUN
ejde-1812	414	3	is	be	AUX
ejde-1812	414	4	complete	complete	ADJ
ejde-1812	414	5	□	□	PUNCT
ejde-1812	414	6	remark	remark	NOUN
ejde-1812	414	7	4.2	4.2	NUM
ejde-1812	414	8	.	.	PUNCT
ejde-1812	415	1	theorem	theorem	VERB
ejde-1812	415	2	4.1	4.1	NUM
ejde-1812	415	3	extends	extend	VERB
ejde-1812	415	4	essentially	essentially	ADV
ejde-1812	415	5	many	many	ADJ
ejde-1812	415	6	existing	exist	VERB
ejde-1812	415	7	results	result	NOUN
ejde-1812	415	8	.	.	PUNCT
ejde-1812	416	1	for	for	ADP
ejde-1812	416	2	example	example	NOUN
ejde-1812	416	3	,	,	PUNCT
ejde-1812	416	4	taking	take	VERB
ejde-1812	416	5	ζi	ζi	PROPN
ejde-1812	416	6	≡	≡	PROPN
ejde-1812	416	7	0	0	PUNCT
ejde-1812	417	1	(	(	PUNCT
ejde-1812	417	2	1	1	NUM
ejde-1812	417	3	≤	≤	NUM
ejde-1812	417	4	i	i	X
ejde-1812	417	5	≤	≤	NUM
ejde-1812	417	6	m	m	VERB
ejde-1812	417	7	)	)	PUNCT
ejde-1812	417	8	in	in	ADP
ejde-1812	417	9	theorem	theorem	NOUN
ejde-1812	417	10	4.1	4.1	NUM
ejde-1812	417	11	,	,	PUNCT
ejde-1812	417	12	we	we	PRON
ejde-1812	417	13	obtain	obtain	VERB
ejde-1812	417	14	the	the	DET
ejde-1812	417	15	following	follow	VERB
ejde-1812	417	16	inequality	inequality	NOUN
ejde-1812	417	17	in	in	ADP
ejde-1812	417	18	[	[	X
ejde-1812	417	19	27	27	NUM
ejde-1812	417	20	]	]	PUNCT
ejde-1812	417	21	,	,	PUNCT
ejde-1812	417	22	while	while	SCONJ
ejde-1812	417	23	taking	take	VERB
ejde-1812	417	24	ζi	ζi	PROPN
ejde-1812	417	25	≡	≡	PROPN
ejde-1812	417	26	0	0	PUNCT
ejde-1812	418	1	(	(	PUNCT
ejde-1812	418	2	1	1	NUM
ejde-1812	418	3	≤	≤	NUM
ejde-1812	418	4	i	i	PRON
ejde-1812	418	5	≤	≤	NOUN
ejde-1812	418	6	m	m	VERB
ejde-1812	418	7	)	)	PUNCT
ejde-1812	418	8	and	and	CCONJ
ejde-1812	418	9	p	p	X
ejde-1812	418	10	=	=	NOUN
ejde-1812	418	11	1	1	NUM
ejde-1812	418	12	in	in	ADP
ejde-1812	418	13	theorem	theorem	NOUN
ejde-1812	418	14	4.1	4.1	NUM
ejde-1812	418	15	,	,	PUNCT
ejde-1812	418	16	we	we	PRON
ejde-1812	418	17	obtain	obtain	VERB
ejde-1812	418	18	the	the	DET
ejde-1812	418	19	inequality	inequality	NOUN
ejde-1812	418	20	in	in	ADP
ejde-1812	418	21	[	[	X
ejde-1812	418	22	26	26	NUM
ejde-1812	418	23	]	]	PUNCT
ejde-1812	418	24	;	;	PUNCT
ejde-1812	418	25	taking	take	VERB
ejde-1812	418	26	m	m	NOUN
ejde-1812	418	27	=	=	PUNCT
ejde-1812	418	28	p	p	NOUN
ejde-1812	418	29	=	=	NOUN
ejde-1812	418	30	1	1	NUM
ejde-1812	418	31	,	,	PUNCT
ejde-1812	418	32	a	a	DET
ejde-1812	418	33	=	=	SYM
ejde-1812	418	34	0	0	NUM
ejde-1812	418	35	,	,	PUNCT
ejde-1812	418	36	ζ	ζ	PROPN
ejde-1812	418	37	≡	≡	PROPN
ejde-1812	418	38	0	0	NUM
ejde-1812	418	39	,	,	PUNCT
ejde-1812	418	40	and	and	CCONJ
ejde-1812	418	41	ψ(t	ψ(t	PROPN
ejde-1812	418	42	)	)	PUNCT
ejde-1812	419	1	=	=	SYM
ejde-1812	419	2	t	t	PROPN
ejde-1812	419	3	in	in	ADP
ejde-1812	419	4	theorem	theorem	NOUN
ejde-1812	419	5	4.1	4.1	NUM
ejde-1812	419	6	,	,	PUNCT
ejde-1812	419	7	we	we	PRON
ejde-1812	419	8	obtain	obtain	VERB
ejde-1812	419	9	the	the	DET
ejde-1812	419	10	inequality	inequality	NOUN
ejde-1812	419	11	in	in	ADP
ejde-1812	419	12	[	[	X
ejde-1812	419	13	43	43	NUM
ejde-1812	419	14	]	]	PUNCT
ejde-1812	419	15	;	;	PUNCT
ejde-1812	419	16	and	and	CCONJ
ejde-1812	419	17	taking	take	VERB
ejde-1812	419	18	m	m	NOUN
ejde-1812	419	19	=	=	PUNCT
ejde-1812	419	20	p	p	NOUN
ejde-1812	419	21	=	=	SYM
ejde-1812	419	22	1	1	NUM
ejde-1812	419	23	,	,	PUNCT
ejde-1812	419	24	g(t	g(t	PROPN
ejde-1812	419	25	)	)	PUNCT
ejde-1812	419	26	≡	≡	PROPN
ejde-1812	419	27	b	b	PROPN
ejde-1812	419	28	,	,	PUNCT
ejde-1812	419	29	a	a	DET
ejde-1812	419	30	=	=	SYM
ejde-1812	419	31	0	0	NUM
ejde-1812	419	32	,	,	PUNCT
ejde-1812	419	33	ζ	ζ	PROPN
ejde-1812	419	34	≡	≡	PROPN
ejde-1812	419	35	0	0	NUM
ejde-1812	419	36	,	,	PUNCT
ejde-1812	419	37	and	and	CCONJ
ejde-1812	419	38	ψ(t	ψ(t	PROPN
ejde-1812	419	39	)	)	PUNCT
ejde-1812	420	1	=	=	SYM
ejde-1812	420	2	t	t	PROPN
ejde-1812	420	3	in	in	ADP
ejde-1812	420	4	theorem	theorem	NOUN
ejde-1812	420	5	4.1	4.1	NUM
ejde-1812	420	6	,	,	PUNCT
ejde-1812	420	7	we	we	PRON
ejde-1812	420	8	obtain	obtain	VERB
ejde-1812	420	9	the	the	DET
ejde-1812	420	10	inequality	inequality	NOUN
ejde-1812	420	11	in	in	ADP
ejde-1812	420	12	[	[	X
ejde-1812	420	13	15	15	NUM
ejde-1812	420	14	]	]	PUNCT
ejde-1812	420	15	.	.	PUNCT
ejde-1812	421	1	corollary	corollary	NOUN
ejde-1812	421	2	4.3	4.3	NUM
ejde-1812	421	3	.	.	PUNCT
ejde-1812	422	1	suppose	suppose	VERB
ejde-1812	422	2	that	that	SCONJ
ejde-1812	422	3	m	m	PROPN
ejde-1812	422	4	,	,	PUNCT
ejde-1812	422	5	p	p	PROPN
ejde-1812	422	6	∈	∈	PROPN
ejde-1812	422	7	n	n	CCONJ
ejde-1812	422	8	,	,	PUNCT
ejde-1812	422	9	βki	βki	ADP
ejde-1812	422	10	>	>	X
ejde-1812	422	11	0	0	NUM
ejde-1812	422	12	,	,	PUNCT
ejde-1812	422	13	ai	ai	VERB
ejde-1812	422	14	≥	≥	NOUN
ejde-1812	422	15	0	0	NUM
ejde-1812	422	16	,	,	PUNCT
ejde-1812	422	17	ψi(t	ψi(t	PUNCT
ejde-1812	422	18	)	)	PUNCT
ejde-1812	422	19	is	be	AUX
ejde-1812	422	20	an	an	DET
ejde-1812	422	21	increasing	increase	VERB
ejde-1812	422	22	and	and	CCONJ
ejde-1812	422	23	positive	positive	ADJ
ejde-1812	422	24	monotone	monotone	ADJ
ejde-1812	422	25	differentiable	differentiable	ADJ
ejde-1812	422	26	function	function	NOUN
ejde-1812	422	27	on	on	ADP
ejde-1812	422	28	(	(	PUNCT
ejde-1812	422	29	ai	ai	VERB
ejde-1812	422	30	,	,	PUNCT
ejde-1812	422	31	ti	ti	NOUN
ejde-1812	422	32	]	]	X
ejde-1812	422	33	(	(	PUNCT
ejde-1812	422	34	1	1	NUM
ejde-1812	422	35	≤	≤	NUM
ejde-1812	422	36	i	i	X
ejde-1812	422	37	≤	≤	NOUN
ejde-1812	422	38	m	m	ADP
ejde-1812	422	39	,	,	PUNCT
ejde-1812	423	1	1	1	NUM
ejde-1812	423	2	≤	≤	NUM
ejde-1812	423	3	k	k	NOUN
ejde-1812	423	4	≤	≤	PROPN
ejde-1812	423	5	p	p	X
ejde-1812	423	6	)	)	PUNCT
ejde-1812	423	7	,	,	PUNCT
ejde-1812	423	8	a(t1	a(t1	PROPN
ejde-1812	423	9	,	,	PUNCT
ejde-1812	423	10	t2	t2	NOUN
ejde-1812	423	11	,	,	PUNCT
ejde-1812	423	12	.	.	PUNCT
ejde-1812	423	13	.	.	PUNCT
ejde-1812	423	14	.	.	PUNCT
ejde-1812	424	1	,	,	PUNCT
ejde-1812	424	2	tm	tm	PROPN
ejde-1812	424	3	)	)	PUNCT
ejde-1812	424	4	is	be	AUX
ejde-1812	424	5	a	a	DET
ejde-1812	424	6	nonnegative	nonnegative	ADJ
ejde-1812	424	7	locally	locally	ADV
ejde-1812	424	8	integrable	integrable	ADJ
ejde-1812	424	9	function	function	NOUN
ejde-1812	424	10	on	on	ADP
ejde-1812	424	11	[	[	X
ejde-1812	424	12	a1	a1	NOUN
ejde-1812	424	13	,	,	PUNCT
ejde-1812	424	14	t1	t1	NOUN
ejde-1812	424	15	)	)	PUNCT
ejde-1812	424	16	×	×	NOUN
ejde-1812	425	1	[	[	X
ejde-1812	425	2	a2	a2	PROPN
ejde-1812	425	3	,	,	PUNCT
ejde-1812	425	4	t2	t2	NOUN
ejde-1812	425	5	)	)	PUNCT
ejde-1812	425	6	×	×	NOUN
ejde-1812	425	7	·	·	PUNCT
ejde-1812	425	8	·	·	PUNCT
ejde-1812	425	9	·	·	PUNCT
ejde-1812	425	10	×	×	NOUN
ejde-1812	426	1	[	[	X
ejde-1812	426	2	am	am	NOUN
ejde-1812	426	3	,	,	PUNCT
ejde-1812	426	4	tm	tm	NOUN
ejde-1812	426	5	)	)	PUNCT
ejde-1812	426	6	(	(	PUNCT
ejde-1812	426	7	some	some	DET
ejde-1812	426	8	ti	ti	NOUN
ejde-1812	426	9	≤	≤	X
ejde-1812	426	10	+	+	NOUN
ejde-1812	426	11	∞	∞	NUM
ejde-1812	426	12	)	)	PUNCT
ejde-1812	426	13	and	and	CCONJ
ejde-1812	426	14	gk(t1	gk(t1	NOUN
ejde-1812	426	15	,	,	PUNCT
ejde-1812	426	16	t2	t2	NOUN
ejde-1812	426	17	,	,	PUNCT
ejde-1812	426	18	.	.	PUNCT
ejde-1812	426	19	.	.	PUNCT
ejde-1812	426	20	.	.	PUNCT
ejde-1812	427	1	,	,	PUNCT
ejde-1812	427	2	tm)(1	tm)(1	NOUN
ejde-1812	427	3	≤	≤	NUM
ejde-1812	427	4	k	k	NOUN
ejde-1812	427	5	≤	≤	PROPN
ejde-1812	427	6	p	p	X
ejde-1812	427	7	)	)	PUNCT
ejde-1812	427	8	is	be	AUX
ejde-1812	427	9	a	a	DET
ejde-1812	427	10	nonnegative	nonnegative	ADJ
ejde-1812	427	11	,	,	PUNCT
ejde-1812	427	12	nondecreasing	nondecrease	VERB
ejde-1812	427	13	continuous	continuous	ADJ
ejde-1812	427	14	function	function	NOUN
ejde-1812	427	15	defined	define	VERB
ejde-1812	427	16	on	on	ADP
ejde-1812	427	17	12	12	NUM
ejde-1812	427	18	j.	j.	PROPN
ejde-1812	427	19	liang	liang	PROPN
ejde-1812	427	20	,	,	PUNCT
ejde-1812	427	21	y.	y.	PROPN
ejde-1812	427	22	mu	mu	PROPN
ejde-1812	427	23	,	,	PUNCT
ejde-1812	427	24	t.-j	t.-j	PROPN
ejde-1812	427	25	.	.	PUNCT
ejde-1812	428	1	xiao	xiao	PROPN
ejde-1812	428	2	ejde-2025/109	ejde-2025/109	PUNCT
ejde-1812	429	1	[	[	X
ejde-1812	429	2	a1	a1	NOUN
ejde-1812	429	3	,	,	PUNCT
ejde-1812	429	4	t1)×	t1)×	ADP
ejde-1812	430	1	[	[	X
ejde-1812	430	2	a2	a2	NOUN
ejde-1812	430	3	,	,	PUNCT
ejde-1812	430	4	t2)×	t2)×	X
ejde-1812	430	5	·	·	PUNCT
ejde-1812	430	6	·	·	PUNCT
ejde-1812	430	7	·	·	PUNCT
ejde-1812	430	8	×	×	NOUN
ejde-1812	431	1	[	[	X
ejde-1812	431	2	am	am	NOUN
ejde-1812	431	3	,	,	PUNCT
ejde-1812	431	4	tm	tm	NOUN
ejde-1812	431	5	)	)	PUNCT
ejde-1812	431	6	,	,	PUNCT
ejde-1812	431	7	gk(t1	gk(t1	NOUN
ejde-1812	431	8	,	,	PUNCT
ejde-1812	431	9	t2	t2	NOUN
ejde-1812	431	10	,	,	PUNCT
ejde-1812	431	11	.	.	PUNCT
ejde-1812	431	12	.	.	PUNCT
ejde-1812	431	13	.	.	PUNCT
ejde-1812	432	1	,	,	PUNCT
ejde-1812	432	2	tm	tm	NOUN
ejde-1812	432	3	)	)	PUNCT
ejde-1812	433	1	≤	≤	NUM
ejde-1812	433	2	c	c	X
ejde-1812	433	3	(	(	PUNCT
ejde-1812	433	4	constant	constant	ADJ
ejde-1812	433	5	)	)	PUNCT
ejde-1812	433	6	,	,	PUNCT
ejde-1812	433	7	and	and	CCONJ
ejde-1812	433	8	suppose	suppose	VERB
ejde-1812	433	9	u(t1	u(t1	NOUN
ejde-1812	433	10	,	,	PUNCT
ejde-1812	433	11	t2	t2	NOUN
ejde-1812	433	12	,	,	PUNCT
ejde-1812	433	13	.	.	PUNCT
ejde-1812	433	14	.	.	PUNCT
ejde-1812	433	15	.	.	PUNCT
ejde-1812	434	1	,	,	PUNCT
ejde-1812	434	2	tm	tm	PROPN
ejde-1812	434	3	)	)	PUNCT
ejde-1812	434	4	is	be	AUX
ejde-1812	434	5	nonnegative	nonnegative	ADJ
ejde-1812	434	6	and	and	CCONJ
ejde-1812	434	7	locally	locally	ADV
ejde-1812	434	8	integrable	integrable	ADJ
ejde-1812	434	9	on	on	ADP
ejde-1812	434	10	[	[	X
ejde-1812	434	11	a1	a1	NOUN
ejde-1812	434	12	,	,	PUNCT
ejde-1812	434	13	t1)×	t1)×	ADP
ejde-1812	435	1	[	[	X
ejde-1812	435	2	a2	a2	NOUN
ejde-1812	435	3	,	,	PUNCT
ejde-1812	435	4	t2)×	t2)×	X
ejde-1812	435	5	·	·	PUNCT
ejde-1812	435	6	·	·	PUNCT
ejde-1812	435	7	·	·	PUNCT
ejde-1812	435	8	×	×	NOUN
ejde-1812	435	9	[	[	X
ejde-1812	435	10	am	am	NOUN
ejde-1812	435	11	,	,	PUNCT
ejde-1812	435	12	tm	tm	NOUN
ejde-1812	435	13	)	)	PUNCT
ejde-1812	435	14	with	with	ADP
ejde-1812	435	15	u(t1	u(t1	NOUN
ejde-1812	435	16	,	,	PUNCT
ejde-1812	435	17	t2	t2	NOUN
ejde-1812	435	18	,	,	PUNCT
ejde-1812	435	19	.	.	PUNCT
ejde-1812	435	20	.	.	PUNCT
ejde-1812	436	1	.	.	PUNCT
ejde-1812	437	1	,	,	PUNCT
ejde-1812	437	2	tm	tm	NOUN
ejde-1812	437	3	)	)	PUNCT
ejde-1812	437	4	≤	≤	NUM
ejde-1812	437	5	a(t1	a(t1	NOUN
ejde-1812	437	6	,	,	PUNCT
ejde-1812	437	7	t2	t2	NOUN
ejde-1812	437	8	,	,	PUNCT
ejde-1812	437	9	.	.	PUNCT
ejde-1812	437	10	.	.	PUNCT
ejde-1812	437	11	.	.	PUNCT
ejde-1812	438	1	,	,	PUNCT
ejde-1812	438	2	tm	tm	PROPN
ejde-1812	438	3	)	)	PUNCT
ejde-1812	439	1	+	+	NUM
ejde-1812	439	2	p∑	p∑	X
ejde-1812	439	3	k=1	k=1	PROPN
ejde-1812	439	4	gk(t1	gk(t1	PROPN
ejde-1812	439	5	,	,	PUNCT
ejde-1812	439	6	t2	t2	NOUN
ejde-1812	439	7	,	,	PUNCT
ejde-1812	439	8	.	.	PUNCT
ejde-1812	439	9	.	.	PUNCT
ejde-1812	439	10	.	.	PUNCT
ejde-1812	440	1	,	,	PUNCT
ejde-1812	440	2	tm	tm	PROPN
ejde-1812	440	3	)	)	PUNCT
ejde-1812	440	4	∫	∫	PROPN
ejde-1812	440	5	tm	tm	PROPN
ejde-1812	440	6	am	am	PROPN
ejde-1812	440	7	·	·	PUNCT
ejde-1812	441	1	·	·	PUNCT
ejde-1812	441	2	·	·	PUNCT
ejde-1812	441	3	∫	∫	PROPN
ejde-1812	441	4	t2	t2	PROPN
ejde-1812	441	5	a2	a2	PROPN
ejde-1812	441	6	∫	∫	PROPN
ejde-1812	441	7	t1	t1	PROPN
ejde-1812	441	8	a1	a1	PROPN
ejde-1812	441	9	m∏	m∏	PROPN
ejde-1812	441	10	i=1	i=1	PROPN
ejde-1812	441	11	ψ′	ψ′	PROPN
ejde-1812	441	12	i(si)(ψi(ti)−	i(si)(ψi(ti)−	PROPN
ejde-1812	441	13	ψi(si	ψi(si	PROPN
ejde-1812	441	14	)	)	PUNCT
ejde-1812	441	15	)	)	PUNCT
ejde-1812	442	1	βki−1	βki−1	PROPN
ejde-1812	442	2	×	×	NOUN
ejde-1812	442	3	u(s1	u(s1	NOUN
ejde-1812	442	4	,	,	PUNCT
ejde-1812	442	5	s2	s2	PROPN
ejde-1812	442	6	,	,	PUNCT
ejde-1812	442	7	.	.	PUNCT
ejde-1812	442	8	.	.	PUNCT
ejde-1812	442	9	.	.	PUNCT
ejde-1812	442	10	,	,	PUNCT
ejde-1812	442	11	sm)ds1	sm)ds1	PROPN
ejde-1812	442	12	.	.	PUNCT
ejde-1812	442	13	.	.	PUNCT
ejde-1812	442	14	.	.	PUNCT
ejde-1812	443	1	dsm	dsm	PROPN
ejde-1812	443	2	,	,	PUNCT
ejde-1812	443	3	on	on	ADP
ejde-1812	443	4	[	[	X
ejde-1812	443	5	a1	a1	NOUN
ejde-1812	443	6	,	,	PUNCT
ejde-1812	443	7	t1)×	t1)×	ADP
ejde-1812	444	1	[	[	X
ejde-1812	444	2	a2	a2	NOUN
ejde-1812	444	3	,	,	PUNCT
ejde-1812	444	4	t2)×	t2)×	X
ejde-1812	444	5	·	·	PUNCT
ejde-1812	444	6	·	·	PUNCT
ejde-1812	444	7	·	·	PUNCT
ejde-1812	444	8	×	×	NOUN
ejde-1812	444	9	[	[	X
ejde-1812	444	10	am	am	NOUN
ejde-1812	444	11	,	,	PUNCT
ejde-1812	444	12	tm	tm	NOUN
ejde-1812	444	13	)	)	PUNCT
ejde-1812	444	14	.	.	PUNCT
ejde-1812	445	1	then	then	ADV
ejde-1812	445	2	u(t1	u(t1	VERB
ejde-1812	445	3	,	,	PUNCT
ejde-1812	445	4	t2	t2	NOUN
ejde-1812	445	5	,	,	PUNCT
ejde-1812	445	6	.	.	PUNCT
ejde-1812	445	7	.	.	PUNCT
ejde-1812	445	8	.	.	PUNCT
ejde-1812	446	1	,	,	PUNCT
ejde-1812	446	2	tm	tm	NOUN
ejde-1812	446	3	)	)	PUNCT
ejde-1812	446	4	≤	≤	NUM
ejde-1812	446	5	a(t1	a(t1	NOUN
ejde-1812	446	6	,	,	PUNCT
ejde-1812	446	7	t2	t2	NOUN
ejde-1812	446	8	,	,	PUNCT
ejde-1812	446	9	.	.	PUNCT
ejde-1812	446	10	.	.	PUNCT
ejde-1812	446	11	.	.	PUNCT
ejde-1812	447	1	,	,	PUNCT
ejde-1812	447	2	tm	tm	PROPN
ejde-1812	447	3	)	)	PUNCT
ejde-1812	448	1	+	+	CCONJ
ejde-1812	449	1	∞∑	∞∑	NUM
ejde-1812	449	2	n=1	n=1	PROPN
ejde-1812	449	3	∑	∑	PROPN
ejde-1812	449	4	0≤l1,	0≤l1,	PROPN
ejde-1812	449	5	...	...	PUNCT
ejde-1812	449	6	,lp≤n	,lp≤n	PUNCT
ejde-1812	449	7	l1+···+lp	l1+···+lp	PROPN
ejde-1812	449	8	=	=	SYM
ejde-1812	449	9	n	n	CCONJ
ejde-1812	449	10	(	(	PUNCT
ejde-1812	449	11	n	n	PRON
ejde-1812	449	12	l1	l1	PROPN
ejde-1812	449	13	,	,	PUNCT
ejde-1812	449	14	.	.	PUNCT
ejde-1812	449	15	.	.	PUNCT
ejde-1812	449	16	.	.	PUNCT
ejde-1812	450	1	,	,	PUNCT
ejde-1812	450	2	lp	lp	X
ejde-1812	450	3	)	)	PUNCT
ejde-1812	451	1	p∏	p∏	PROPN
ejde-1812	451	2	k=1	k=1	X
ejde-1812	451	3	(	(	PUNCT
ejde-1812	451	4	gk(t1	gk(t1	NOUN
ejde-1812	451	5	,	,	PUNCT
ejde-1812	451	6	t2	t2	NOUN
ejde-1812	451	7	,	,	PUNCT
ejde-1812	451	8	.	.	PUNCT
ejde-1812	451	9	.	.	PUNCT
ejde-1812	451	10	.	.	PUNCT
ejde-1812	452	1	,	,	PUNCT
ejde-1812	452	2	tm))lk	tm))lk	PROPN
ejde-1812	452	3	×	×	ADJ
ejde-1812	452	4	∫	∫	PROPN
ejde-1812	452	5	tm	tm	PROPN
ejde-1812	452	6	am	am	PROPN
ejde-1812	452	7	·	·	PUNCT
ejde-1812	452	8	·	·	PUNCT
ejde-1812	452	9	·	·	PUNCT
ejde-1812	452	10	∫	∫	PROPN
ejde-1812	452	11	t2	t2	PROPN
ejde-1812	452	12	a2	a2	PROPN
ejde-1812	452	13	∫	∫	PROPN
ejde-1812	452	14	t1	t1	PROPN
ejde-1812	452	15	a1	a1	PROPN
ejde-1812	452	16	m∏	m∏	PROPN
ejde-1812	452	17	i=1	i=1	PROPN
ejde-1812	452	18	ψ′	ψ′	NUM
ejde-1812	452	19	i(si	i(si	NUM
ejde-1812	452	20	)	)	PUNCT
ejde-1812	453	1	[	[	X
ejde-1812	453	2	∏p	∏p	X
ejde-1812	453	3	k=1(γ(βki	k=1(γ(βki	NOUN
ejde-1812	453	4	)	)	PUNCT
ejde-1812	453	5	)	)	PUNCT
ejde-1812	454	1	lk	lk	PROPN
ejde-1812	454	2	γ	γ	X
ejde-1812	454	3	(	(	PUNCT
ejde-1812	454	4	∑p	∑p	PROPN
ejde-1812	454	5	k=1	k=1	PROPN
ejde-1812	454	6	lkβki	lkβki	PROPN
ejde-1812	454	7	)	)	PUNCT
ejde-1812	454	8	(	(	PUNCT
ejde-1812	454	9	ψi(ti)−	ψi(ti)−	PROPN
ejde-1812	454	10	ψi(si	ψi(si	PROPN
ejde-1812	454	11	)	)	PUNCT
ejde-1812	454	12	)	)	PUNCT
ejde-1812	455	1	∑p	∑p	PROPN
ejde-1812	455	2	k=1	k=1	X
ejde-1812	455	3	lkβki−1	lkβki−1	X
ejde-1812	455	4	]	]	PUNCT
ejde-1812	455	5	×	×	PROPN
ejde-1812	455	6	a(s1	a(s1	NOUN
ejde-1812	455	7	,	,	PUNCT
ejde-1812	455	8	s2	s2	NOUN
ejde-1812	455	9	,	,	PUNCT
ejde-1812	455	10	.	.	PUNCT
ejde-1812	455	11	.	.	PUNCT
ejde-1812	456	1	.	.	PUNCT
ejde-1812	457	1	,	,	PUNCT
ejde-1812	457	2	sm)ds1	sm)ds1	PROPN
ejde-1812	457	3	.	.	PUNCT
ejde-1812	457	4	.	.	PUNCT
ejde-1812	457	5	.	.	PUNCT
ejde-1812	458	1	dsm	dsm	PROPN
ejde-1812	458	2	,	,	PUNCT
ejde-1812	458	3	ai	ai	VERB
ejde-1812	458	4	≤	≤	ADJ
ejde-1812	458	5	ti	ti	NOUN
ejde-1812	458	6	<	<	X
ejde-1812	458	7	ti	ti	X
ejde-1812	458	8	(	(	PUNCT
ejde-1812	458	9	1	1	NUM
ejde-1812	458	10	≤	≤	NUM
ejde-1812	458	11	i	i	PRON
ejde-1812	458	12	≤	≤	NOUN
ejde-1812	458	13	m	m	VERB
ejde-1812	458	14	)	)	PUNCT
ejde-1812	458	15	,	,	PUNCT
ejde-1812	458	16	where	where	SCONJ
ejde-1812	458	17	(	(	PUNCT
ejde-1812	458	18	n	n	DET
ejde-1812	458	19	l1	l1	PROPN
ejde-1812	458	20	,	,	PUNCT
ejde-1812	458	21	.	.	PUNCT
ejde-1812	458	22	.	.	PUNCT
ejde-1812	459	1	.	.	PUNCT
ejde-1812	460	1	,	,	PUNCT
ejde-1812	460	2	lp	lp	X
ejde-1812	460	3	)	)	PUNCT
ejde-1812	460	4	=	=	SYM
ejde-1812	460	5	n	n	X
ejde-1812	460	6	!	!	PUNCT
ejde-1812	460	7	l1	l1	PROPN
ejde-1812	460	8	!	!	PUNCT
ejde-1812	460	9	.	.	PUNCT
ejde-1812	460	10	.	.	PUNCT
ejde-1812	460	11	.	.	PUNCT
ejde-1812	461	1	lp	lp	INTJ
ejde-1812	461	2	!	!	PROPN
ejde-1812	461	3	,	,	PUNCT
ejde-1812	461	4	l1	l1	PROPN
ejde-1812	461	5	+	+	CCONJ
ejde-1812	461	6	·	·	PUNCT
ejde-1812	461	7	·	·	PUNCT
ejde-1812	461	8	·	·	PUNCT
ejde-1812	461	9	+	+	NUM
ejde-1812	461	10	lp	lp	NOUN
ejde-1812	461	11	=	=	PUNCT
ejde-1812	461	12	n.	n.	NOUN
ejde-1812	461	13	using	use	VERB
ejde-1812	461	14	theorem	theorem	NOUN
ejde-1812	461	15	4.1	4.1	NUM
ejde-1812	461	16	,	,	PUNCT
ejde-1812	461	17	we	we	PRON
ejde-1812	461	18	obtain	obtain	VERB
ejde-1812	461	19	the	the	DET
ejde-1812	461	20	following	following	ADJ
ejde-1812	461	21	result	result	NOUN
ejde-1812	461	22	of	of	ADP
ejde-1812	461	23	the	the	DET
ejde-1812	461	24	dependence	dependence	NOUN
ejde-1812	461	25	of	of	ADP
ejde-1812	461	26	the	the	DET
ejde-1812	461	27	solution	solution	NOUN
ejde-1812	461	28	on	on	ADP
ejde-1812	461	29	the	the	DET
ejde-1812	461	30	order	order	NOUN
ejde-1812	461	31	and	and	CCONJ
ejde-1812	461	32	the	the	DET
ejde-1812	461	33	initial	initial	ADJ
ejde-1812	461	34	condition	condition	NOUN
ejde-1812	461	35	for	for	ADP
ejde-1812	461	36	the	the	DET
ejde-1812	461	37	fractional	fractional	PROPN
ejde-1812	461	38	cauchy	cauchy	PROPN
ejde-1812	461	39	problem	problem	NOUN
ejde-1812	461	40	.	.	PUNCT
ejde-1812	462	1	theorem	theorem	VERB
ejde-1812	462	2	4.4	4.4	NUM
ejde-1812	462	3	.	.	PUNCT
ejde-1812	463	1	let	let	VERB
ejde-1812	463	2	f	f	NOUN
ejde-1812	463	3	:	:	PUNCT
ejde-1812	464	1	[	[	X
ejde-1812	464	2	0	0	NUM
ejde-1812	464	3	,	,	PUNCT
ejde-1812	464	4	b	b	NOUN
ejde-1812	464	5	]	]	X
ejde-1812	464	6	×x	×x	X
ejde-1812	464	7	×x	×x	X
ejde-1812	464	8	→	→	SYM
ejde-1812	464	9	x	x	PART
ejde-1812	464	10	be	be	AUX
ejde-1812	464	11	a	a	DET
ejde-1812	464	12	bounded	bounded	ADJ
ejde-1812	464	13	function	function	NOUN
ejde-1812	464	14	and	and	CCONJ
ejde-1812	464	15	satisfy	satisfy	VERB
ejde-1812	464	16	the	the	DET
ejde-1812	464	17	lipschitz	lipschitz	ADJ
ejde-1812	464	18	-	-	PUNCT
ejde-1812	464	19	type	type	NOUN
ejde-1812	464	20	condition	condition	NOUN
ejde-1812	464	21	with	with	ADP
ejde-1812	464	22	respect	respect	NOUN
ejde-1812	464	23	to	to	ADP
ejde-1812	464	24	the	the	DET
ejde-1812	464	25	second	second	ADJ
ejde-1812	464	26	and	and	CCONJ
ejde-1812	464	27	third	third	ADJ
ejde-1812	464	28	variable	variable	NOUN
ejde-1812	464	29	,	,	PUNCT
ejde-1812	464	30	i.e.	i.e.	X
ejde-1812	464	31	,	,	PUNCT
ejde-1812	464	32	for	for	ADP
ejde-1812	464	33	any	any	DET
ejde-1812	464	34	t	t	NOUN
ejde-1812	464	35	∈	∈	PROPN
ejde-1812	465	1	[	[	X
ejde-1812	465	2	0	0	NUM
ejde-1812	465	3	,	,	PUNCT
ejde-1812	465	4	b	b	NOUN
ejde-1812	465	5	]	]	X
ejde-1812	465	6	,	,	PUNCT
ejde-1812	465	7	xi	xi	PROPN
ejde-1812	465	8	,	,	PUNCT
ejde-1812	465	9	yi	yi	PROPN
ejde-1812	465	10	∈	∈	PROPN
ejde-1812	465	11	x	x	X
ejde-1812	465	12	(	(	PUNCT
ejde-1812	465	13	i	i	NOUN
ejde-1812	465	14	=	=	NOUN
ejde-1812	465	15	1	1	NUM
ejde-1812	465	16	,	,	PUNCT
ejde-1812	465	17	2	2	NUM
ejde-1812	465	18	)	)	PUNCT
ejde-1812	465	19	,	,	PUNCT
ejde-1812	465	20	there	there	PRON
ejde-1812	465	21	exist	exist	VERB
ejde-1812	465	22	a	a	DET
ejde-1812	465	23	l	l	NOUN
ejde-1812	465	24	>	>	X
ejde-1812	465	25	0	0	PUNCT
ejde-1812	466	1	and	and	CCONJ
ejde-1812	466	2	an	an	DET
ejde-1812	466	3	integrable	integrable	ADJ
ejde-1812	466	4	function	function	NOUN
ejde-1812	466	5	ζ(t	ζ(t	NOUN
ejde-1812	466	6	)	)	PUNCT
ejde-1812	466	7	≤	≤	NOUN
ejde-1812	466	8	0	0	NUM
ejde-1812	466	9	,	,	PUNCT
ejde-1812	466	10	a.e	a.e	PROPN
ejde-1812	466	11	.	.	PROPN
ejde-1812	466	12	t	t	PROPN
ejde-1812	466	13	∈	∈	PROPN
ejde-1812	467	1	[	[	X
ejde-1812	467	2	0	0	NUM
ejde-1812	467	3	,	,	PUNCT
ejde-1812	467	4	b	b	NOUN
ejde-1812	467	5	]	]	X
ejde-1812	467	6	such	such	ADJ
ejde-1812	467	7	that	that	SCONJ
ejde-1812	467	8	∥f(t	∥f(t	NOUN
ejde-1812	467	9	,	,	PUNCT
ejde-1812	467	10	x1	x1	NUM
ejde-1812	467	11	,	,	PUNCT
ejde-1812	467	12	x2)−	x2)−	ADJ
ejde-1812	467	13	f(t	f(t	NOUN
ejde-1812	467	14	,	,	PUNCT
ejde-1812	467	15	y1	y1	NOUN
ejde-1812	467	16	,	,	PUNCT
ejde-1812	467	17	y2)|	y2)|	PROPN
ejde-1812	467	18	≤	≤	PROPN
ejde-1812	467	19	leζ(t	leζ(t	PROPN
ejde-1812	467	20	)	)	PUNCT
ejde-1812	467	21	(	(	PUNCT
ejde-1812	467	22	∥x1	∥x1	X
ejde-1812	467	23	−	−	PROPN
ejde-1812	467	24	y1∥+	y1∥+	PROPN
ejde-1812	467	25	∥x2	∥x2	NOUN
ejde-1812	468	1	−	−	PROPN
ejde-1812	468	2	y2∥	y2∥	PROPN
ejde-1812	468	3	)	)	PUNCT
ejde-1812	468	4	.	.	PUNCT
ejde-1812	469	1	assume	assume	VERB
ejde-1812	469	2	that	that	SCONJ
ejde-1812	469	3	x(t	x(t	PROPN
ejde-1812	469	4	)	)	PUNCT
ejde-1812	469	5	and	and	CCONJ
ejde-1812	469	6	y(t	y(t	NUM
ejde-1812	469	7	)	)	PUNCT
ejde-1812	469	8	are	be	AUX
ejde-1812	469	9	the	the	DET
ejde-1812	469	10	solutions	solution	NOUN
ejde-1812	469	11	of	of	ADP
ejde-1812	469	12	the	the	DET
ejde-1812	469	13	following	following	ADJ
ejde-1812	469	14	initial	initial	ADJ
ejde-1812	469	15	-	-	PUNCT
ejde-1812	469	16	value	value	NOUN
ejde-1812	469	17	integro	integro	ADJ
ejde-1812	469	18	-	-	PUNCT
ejde-1812	469	19	differential	differential	NOUN
ejde-1812	469	20	equations	equation	NOUN
ejde-1812	469	21	(	(	PUNCT
ejde-1812	469	22	4.4	4.4	NUM
ejde-1812	469	23	)	)	PUNCT
ejde-1812	469	24	and	and	CCONJ
ejde-1812	469	25	(	(	PUNCT
ejde-1812	469	26	4.5	4.5	NUM
ejde-1812	469	27	)	)	PUNCT
ejde-1812	469	28	,	,	PUNCT
ejde-1812	469	29	respectively	respectively	ADV
ejde-1812	469	30	:(	:(	PUNCT
ejde-1812	469	31	dα	dα	NOUN
ejde-1812	469	32	,	,	PUNCT
ejde-1812	469	33	β;ψx	β;ψx	PROPN
ejde-1812	469	34	)	)	PUNCT
ejde-1812	469	35	(	(	PUNCT
ejde-1812	469	36	t	t	NOUN
ejde-1812	469	37	)	)	PUNCT
ejde-1812	469	38	=	=	PUNCT
ejde-1812	469	39	ax(t	ax(t	NUM
ejde-1812	469	40	)	)	PUNCT
ejde-1812	470	1	+	+	CCONJ
ejde-1812	470	2	f	f	X
ejde-1812	470	3	(	(	PUNCT
ejde-1812	470	4	t	t	PROPN
ejde-1812	470	5	,	,	PUNCT
ejde-1812	470	6	x(t	x(t	PROPN
ejde-1812	470	7	)	)	PUNCT
ejde-1812	470	8	,	,	PUNCT
ejde-1812	470	9	∫	∫	PROPN
ejde-1812	470	10	t	t	PROPN
ejde-1812	470	11	0	0	NUM
ejde-1812	470	12	ρ(t	ρ(t	NUM
ejde-1812	470	13	,	,	PUNCT
ejde-1812	470	14	s)x(s)ds	s)x(s)ds	NOUN
ejde-1812	470	15	)	)	PUNCT
ejde-1812	470	16	,	,	PUNCT
ejde-1812	470	17	0	0	NUM
ejde-1812	470	18	<	<	X
ejde-1812	470	19	α	α	X
ejde-1812	470	20	<	<	X
ejde-1812	470	21	1	1	NUM
ejde-1812	470	22	,	,	PUNCT
ejde-1812	470	23	0	0	NUM
ejde-1812	470	24	≤	≤	NUM
ejde-1812	471	1	β	β	X
ejde-1812	471	2	≤	≤	NUM
ejde-1812	471	3	1	1	NUM
ejde-1812	471	4	,	,	PUNCT
ejde-1812	471	5	t	t	PROPN
ejde-1812	471	6	∈	∈	PROPN
ejde-1812	471	7	(	(	PUNCT
ejde-1812	471	8	0	0	NUM
ejde-1812	471	9	,	,	PUNCT
ejde-1812	471	10	b	b	NOUN
ejde-1812	471	11	]	]	X
ejde-1812	471	12	,	,	PUNCT
ejde-1812	471	13	i1−γ;ψx(0	i1−γ;ψx(0	NUM
ejde-1812	471	14	)	)	PUNCT
ejde-1812	471	15	=	=	SYM
ejde-1812	471	16	x0	x0	PROPN
ejde-1812	471	17	,	,	PUNCT
ejde-1812	471	18	α	α	PROPN
ejde-1812	471	19	≤	≤	NOUN
ejde-1812	471	20	γ	γ	X
ejde-1812	471	21	=	=	X
ejde-1812	471	22	α+	α+	NOUN
ejde-1812	471	23	β	β	X
ejde-1812	471	24	−	−	NOUN
ejde-1812	471	25	αβ	αβ	INTJ
ejde-1812	471	26	<	<	X
ejde-1812	471	27	1	1	NUM
ejde-1812	471	28	,	,	PUNCT
ejde-1812	471	29	(	(	PUNCT
ejde-1812	471	30	4.4	4.4	NUM
ejde-1812	471	31	)	)	PUNCT
ejde-1812	471	32	and	and	CCONJ
ejde-1812	471	33	(	(	PUNCT
ejde-1812	471	34	dα′,β′;ψy	dα′,β′;ψy	NOUN
ejde-1812	471	35	)	)	PUNCT
ejde-1812	471	36	(	(	PUNCT
ejde-1812	471	37	t	t	NOUN
ejde-1812	471	38	)	)	PUNCT
ejde-1812	471	39	=	=	PUNCT
ejde-1812	471	40	ay(t	ay(t	PUNCT
ejde-1812	471	41	)	)	PUNCT
ejde-1812	472	1	+	+	CCONJ
ejde-1812	472	2	f	f	X
ejde-1812	472	3	(	(	PUNCT
ejde-1812	472	4	t	t	PROPN
ejde-1812	472	5	,	,	PUNCT
ejde-1812	472	6	y(t	y(t	PROPN
ejde-1812	472	7	)	)	PUNCT
ejde-1812	472	8	,	,	PUNCT
ejde-1812	472	9	∫	∫	PROPN
ejde-1812	472	10	t	t	PROPN
ejde-1812	472	11	0	0	NUM
ejde-1812	472	12	ρ(t	ρ(t	NUM
ejde-1812	472	13	,	,	PUNCT
ejde-1812	472	14	s)y(s)ds	s)y(s)ds	PROPN
ejde-1812	472	15	)	)	PUNCT
ejde-1812	472	16	,	,	PUNCT
ejde-1812	472	17	0	0	PUNCT
ejde-1812	472	18	<	<	X
ejde-1812	472	19	α′	α′	X
ejde-1812	472	20	<	<	X
ejde-1812	472	21	1	1	NUM
ejde-1812	472	22	,	,	PUNCT
ejde-1812	472	23	0	0	NUM
ejde-1812	472	24	≤	≤	NUM
ejde-1812	472	25	β′	β′	NUM
ejde-1812	472	26	≤	≤	NUM
ejde-1812	472	27	1	1	NUM
ejde-1812	472	28	,	,	PUNCT
ejde-1812	472	29	t	t	PROPN
ejde-1812	472	30	∈	∈	PROPN
ejde-1812	472	31	(	(	PUNCT
ejde-1812	472	32	0	0	NUM
ejde-1812	472	33	,	,	PUNCT
ejde-1812	472	34	b	b	NOUN
ejde-1812	472	35	]	]	X
ejde-1812	472	36	,	,	PUNCT
ejde-1812	472	37	i1−γ	i1−γ	PROPN
ejde-1812	472	38	′;ψy(0	′;ψy(0	PROPN
ejde-1812	472	39	)	)	PUNCT
ejde-1812	472	40	=	=	SYM
ejde-1812	472	41	y0	y0	NOUN
ejde-1812	472	42	,	,	PUNCT
ejde-1812	472	43	α′	α′	ADV
ejde-1812	472	44	≤	≤	NUM
ejde-1812	472	45	γ′	γ′	X
ejde-1812	472	46	=	=	PUNCT
ejde-1812	472	47	α′	α′	NUM
ejde-1812	472	48	+	+	CCONJ
ejde-1812	472	49	β′	β′	NUM
ejde-1812	472	50	−	−	PROPN
ejde-1812	473	1	α′β′	α′β′	VERB
ejde-1812	473	2	<	<	X
ejde-1812	473	3	1	1	NUM
ejde-1812	473	4	,	,	PUNCT
ejde-1812	473	5	(	(	PUNCT
ejde-1812	473	6	4.5	4.5	NUM
ejde-1812	473	7	)	)	PUNCT
ejde-1812	473	8	where	where	SCONJ
ejde-1812	473	9	b	b	X
ejde-1812	473	10	>	>	X
ejde-1812	473	11	0	0	NUM
ejde-1812	473	12	,	,	PUNCT
ejde-1812	473	13	and	and	CCONJ
ejde-1812	473	14	ρ(t	ρ(t	NUM
ejde-1812	473	15	,	,	PUNCT
ejde-1812	473	16	s	s	X
ejde-1812	473	17	)	)	PUNCT
ejde-1812	473	18	=	=	SYM
ejde-1812	473	19	eζ(s)−ζ(t)(ψ(t)−	eζ(s)−ζ(t)(ψ(t)−	PROPN
ejde-1812	473	20	ψ(s))r−1ψ′(s	ψ(s))r−1ψ′(s	PROPN
ejde-1812	473	21	)	)	PUNCT
ejde-1812	473	22	(	(	PUNCT
ejde-1812	473	23	r	r	NOUN
ejde-1812	473	24	∈	∈	PROPN
ejde-1812	473	25	(	(	PUNCT
ejde-1812	473	26	0	0	NUM
ejde-1812	473	27	,	,	PUNCT
ejde-1812	473	28	1	1	NUM
ejde-1812	473	29	]	]	NUM
ejde-1812	473	30	)	)	PUNCT
ejde-1812	473	31	.	.	PUNCT
ejde-1812	474	1	then	then	ADV
ejde-1812	474	2	,	,	PUNCT
ejde-1812	474	3	for	for	ADP
ejde-1812	474	4	t	t	PROPN
ejde-1812	474	5	∈	∈	PROPN
ejde-1812	474	6	(	(	PUNCT
ejde-1812	474	7	0	0	NUM
ejde-1812	474	8	,	,	PUNCT
ejde-1812	474	9	b	b	NOUN
ejde-1812	474	10	]	]	X
ejde-1812	474	11	,	,	PUNCT
ejde-1812	474	12	∥x(t)−	∥x(t)−	PROPN
ejde-1812	474	13	y(t)∥	y(t)∥	NOUN
ejde-1812	474	14	≤	≤	NUM
ejde-1812	474	15	a(t	a(t	NOUN
ejde-1812	474	16	)	)	PUNCT
ejde-1812	475	1	+	+	CCONJ
ejde-1812	475	2	∞∑	∞∑	NUM
ejde-1812	475	3	n=1	n=1	PROPN
ejde-1812	475	4	(	(	PUNCT
ejde-1812	475	5	lm)n	lm)n	PROPN
ejde-1812	475	6	∞∑	∞∑	PROPN
ejde-1812	475	7	k=0	k=0	PROPN
ejde-1812	475	8	ckn	ckn	NOUN
ejde-1812	475	9	(	(	PUNCT
ejde-1812	475	10	γ(r))n−k	γ(r))n−k	X
ejde-1812	475	11	(	(	PUNCT
ejde-1812	475	12	γ(α′))k(γ(α′	γ(α′))k(γ(α′	NOUN
ejde-1812	475	13	+	+	CCONJ
ejde-1812	475	14	r))n−k	r))n−k	PROPN
ejde-1812	476	1	×	×	PROPN
ejde-1812	476	2	∫	∫	PROPN
ejde-1812	476	3	t	t	PROPN
ejde-1812	476	4	0	0	NUM
ejde-1812	476	5	eζ(s)−ζ(t)(ψ(t)−	eζ(s)−ζ(t)(ψ(t)−	PROPN
ejde-1812	476	6	ψ(s))nα	ψ(s))nα	PUNCT
ejde-1812	477	1	′+(n−k)r−1a(s)ψ′(s)ds	′+(n−k)r−1a(s)ψ′(s)d	VERB
ejde-1812	477	2	,	,	PUNCT
ejde-1812	477	3	where	where	SCONJ
ejde-1812	477	4	a(t	a(t	NOUN
ejde-1812	477	5	)	)	PUNCT
ejde-1812	477	6	=	=	SYM
ejde-1812	478	1	∥	∥	PROPN
ejde-1812	478	2	(	(	PUNCT
ejde-1812	478	3	iβ(1−α)kα	iβ(1−α)kα	PROPN
ejde-1812	478	4	)	)	PUNCT
ejde-1812	478	5	(	(	PUNCT
ejde-1812	478	6	ψ(t))x0	ψ(t))x0	PROPN
ejde-1812	478	7	−	−	PROPN
ejde-1812	478	8	(	(	PUNCT
ejde-1812	478	9	iβ(1−α)kα	iβ(1−α)kα	PROPN
ejde-1812	478	10	)	)	PUNCT
ejde-1812	478	11	(	(	PUNCT
ejde-1812	478	12	ψ(t))y0∥	ψ(t))y0∥	NOUN
ejde-1812	478	13	+	+	CCONJ
ejde-1812	478	14	∫	∫	PROPN
ejde-1812	478	15	t	t	NOUN
ejde-1812	478	16	0	0	NUM
ejde-1812	479	1	∥kα(ψ(t)−	∥kα(ψ(t)−	PROPN
ejde-1812	479	2	ψ(s))−kα′(ψ(t)−	ψ(s))−kα′(ψ(t)−	PROPN
ejde-1812	479	3	ψ(s))∥ψ′(s)ds	ψ(s))∥ψ′(s)ds	ADV
ejde-1812	479	4	·	·	PUNCT
ejde-1812	479	5	∥f∥	∥f∥	ADJ
ejde-1812	479	6	,	,	PUNCT
ejde-1812	479	7	and	and	CCONJ
ejde-1812	479	8	∥f∥	∥f∥	PROPN
ejde-1812	479	9	=	=	SYM
ejde-1812	479	10	sup(t	sup(t	PROPN
ejde-1812	479	11	,	,	PUNCT
ejde-1812	479	12	x1,x2)∈(0,b]×x×x∥f(t	x1,x2)∈(0,b]×x×x∥f(t	NOUN
ejde-1812	479	13	,	,	PUNCT
ejde-1812	479	14	x1	x1	PROPN
ejde-1812	479	15	,	,	PUNCT
ejde-1812	479	16	x2)∥.	x2)∥.	PROPN
ejde-1812	479	17	ejde-2025/109	ejde-2025/109	ADJ
ejde-1812	479	18	evolution	evolution	PROPN
ejde-1812	479	19	ψ	ψ	NOUN
ejde-1812	479	20	-	-	ADJ
ejde-1812	479	21	hilfer	hilfer	NOUN
ejde-1812	479	22	fractional	fractional	ADJ
ejde-1812	479	23	differential	differential	ADJ
ejde-1812	479	24	equations	equation	NOUN
ejde-1812	479	25	13	13	NUM
ejde-1812	479	26	proof	proof	NOUN
ejde-1812	479	27	.	.	PUNCT
ejde-1812	480	1	by	by	ADP
ejde-1812	480	2	lemma	lemma	PROPN
ejde-1812	480	3	2.6	2.6	NUM
ejde-1812	480	4	,	,	PUNCT
ejde-1812	480	5	the	the	DET
ejde-1812	480	6	solution	solution	NOUN
ejde-1812	480	7	of	of	ADP
ejde-1812	480	8	(	(	PUNCT
ejde-1812	480	9	4.4	4.4	NUM
ejde-1812	480	10	)	)	PUNCT
ejde-1812	480	11	satisfies	satisfie	NOUN
ejde-1812	480	12	x(t	x(t	PROPN
ejde-1812	480	13	)	)	PUNCT
ejde-1812	480	14	=	=	PRON
ejde-1812	480	15	(	(	PUNCT
ejde-1812	480	16	iβ(1−α)kα	iβ(1−α)kα	PROPN
ejde-1812	480	17	)	)	PUNCT
ejde-1812	481	1	(	(	PUNCT
ejde-1812	481	2	ψ(t))x0	ψ(t))x0	PROPN
ejde-1812	481	3	+	+	CCONJ
ejde-1812	481	4	∫	∫	PROPN
ejde-1812	481	5	t	t	PROPN
ejde-1812	481	6	0	0	NUM
ejde-1812	481	7	kα(ψ(t)−	kα(ψ(t)−	PROPN
ejde-1812	482	1	ψ(s))f	ψ(s))f	PROPN
ejde-1812	482	2	(	(	PUNCT
ejde-1812	482	3	s	s	PROPN
ejde-1812	482	4	,	,	PUNCT
ejde-1812	482	5	x(s	x(s	PROPN
ejde-1812	482	6	)	)	PUNCT
ejde-1812	482	7	,	,	PUNCT
ejde-1812	482	8	∫	∫	PROPN
ejde-1812	482	9	s	s	PART
ejde-1812	482	10	0	0	NUM
ejde-1812	482	11	ρ(s	ρ(s	NOUN
ejde-1812	482	12	,	,	PUNCT
ejde-1812	482	13	τ)x(τ)dτ	τ)x(τ)dτ	PROPN
ejde-1812	482	14	)	)	PUNCT
ejde-1812	482	15	ψ′(s)ds	ψ′(s)ds	PROPN
ejde-1812	482	16	.	.	PUNCT
ejde-1812	482	17	also	also	ADV
ejde-1812	482	18	bylemma	bylemma	PROPN
ejde-1812	482	19	2.6	2.6	NUM
ejde-1812	482	20	,	,	PUNCT
ejde-1812	482	21	the	the	DET
ejde-1812	482	22	solution	solution	NOUN
ejde-1812	482	23	of	of	ADP
ejde-1812	482	24	(	(	PUNCT
ejde-1812	482	25	4.5	4.5	NUM
ejde-1812	482	26	)	)	PUNCT
ejde-1812	482	27	satisfies	satisfie	NOUN
ejde-1812	482	28	y(t	y(t	NUM
ejde-1812	482	29	)	)	PUNCT
ejde-1812	483	1	=	=	PUNCT
ejde-1812	483	2	(	(	PUNCT
ejde-1812	483	3	iβ	iβ	ADP
ejde-1812	483	4	′(1−α′)kα′	′(1−α′)kα′	PROPN
ejde-1812	483	5	)	)	PUNCT
ejde-1812	483	6	(	(	PUNCT
ejde-1812	483	7	ψ(t))y0	ψ(t))y0	NOUN
ejde-1812	484	1	+	+	CCONJ
ejde-1812	484	2	∫	∫	PROPN
ejde-1812	484	3	t	t	PROPN
ejde-1812	484	4	0	0	NUM
ejde-1812	484	5	kα′(ψ(t)−	kα′(ψ(t)−	PROPN
ejde-1812	484	6	ψ(s))f	ψ(s))f	PROPN
ejde-1812	484	7	(	(	PUNCT
ejde-1812	484	8	s	s	PROPN
ejde-1812	484	9	,	,	PUNCT
ejde-1812	484	10	y(s	y(s	PROPN
ejde-1812	484	11	)	)	PUNCT
ejde-1812	484	12	,	,	PUNCT
ejde-1812	484	13	∫	∫	PROPN
ejde-1812	484	14	s	s	PART
ejde-1812	484	15	0	0	NUM
ejde-1812	484	16	ρ(s	ρ(s	NOUN
ejde-1812	484	17	,	,	PUNCT
ejde-1812	484	18	τ)y(τ)dτ	τ)y(τ)dτ	NOUN
ejde-1812	484	19	)	)	PUNCT
ejde-1812	484	20	ψ′(s)ds	ψ′(s)ds	PROPN
ejde-1812	484	21	.	.	PUNCT
ejde-1812	485	1	then	then	ADV
ejde-1812	485	2	we	we	PRON
ejde-1812	485	3	have	have	VERB
ejde-1812	485	4	∥x(t)−	∥x(t)−	PROPN
ejde-1812	485	5	y(t)∥	y(t)∥	NOUN
ejde-1812	485	6	≤	≤	ADV
ejde-1812	485	7	∥	∥	NUM
ejde-1812	485	8	(	(	PUNCT
ejde-1812	485	9	iβ(1−α)kα	iβ(1−α)kα	PROPN
ejde-1812	485	10	)	)	PUNCT
ejde-1812	485	11	(	(	PUNCT
ejde-1812	485	12	ψ(t))x0	ψ(t))x0	PROPN
ejde-1812	485	13	−	−	PROPN
ejde-1812	485	14	(	(	PUNCT
ejde-1812	485	15	iβ	iβ	ADP
ejde-1812	485	16	′(1−α′)kα′	′(1−α′)kα′	PROPN
ejde-1812	485	17	)	)	PUNCT
ejde-1812	485	18	(	(	PUNCT
ejde-1812	485	19	ψ(t))y0∥	ψ(t))y0∥	NOUN
ejde-1812	485	20	+	+	CCONJ
ejde-1812	486	1	∫	∫	PROPN
ejde-1812	486	2	t	t	NOUN
ejde-1812	486	3	0	0	PUNCT
ejde-1812	487	1	∥kα(ψ(t)−	∥kα(ψ(t)−	PROPN
ejde-1812	487	2	ψ(s))−kα′(ψ(t)−	ψ(s))−kα′(ψ(t)−	PROPN
ejde-1812	487	3	ψ(s))∥	ψ(s))∥	VERB
ejde-1812	487	4	∥∥f(s	∥∥f(	NOUN
ejde-1812	487	5	,	,	PUNCT
ejde-1812	487	6	x(s),∫	x(s),∫	PROPN
ejde-1812	487	7	s	s	PART
ejde-1812	487	8	0	0	NUM
ejde-1812	487	9	ρ(s	ρ(s	NOUN
ejde-1812	487	10	,	,	PUNCT
ejde-1812	487	11	τ)x(τ)dτ	τ)x(τ)dτ	PROPN
ejde-1812	487	12	)	)	PUNCT
ejde-1812	487	13	∥∥ψ′(s)ds	∥∥ψ′(s)ds	PROPN
ejde-1812	487	14	+	+	CCONJ
ejde-1812	488	1	∫	∫	PROPN
ejde-1812	488	2	t	t	PROPN
ejde-1812	488	3	0	0	NUM
ejde-1812	489	1	∥kα′(ψ(t)−	∥kα′(ψ(t)−	PROPN
ejde-1812	489	2	ψ(s))∥	ψ(s))∥	VERB
ejde-1812	489	3	∥∥f(s	∥∥f(	NOUN
ejde-1812	489	4	,	,	PUNCT
ejde-1812	489	5	x(s),∫	x(s),∫	PROPN
ejde-1812	489	6	s	s	PART
ejde-1812	489	7	0	0	NUM
ejde-1812	489	8	ρ(s	ρ(s	NOUN
ejde-1812	489	9	,	,	PUNCT
ejde-1812	489	10	τ)x(τ)dτ	τ)x(τ)dτ	PROPN
ejde-1812	489	11	)	)	PUNCT
ejde-1812	490	1	−	−	PROPN
ejde-1812	490	2	f	f	X
ejde-1812	490	3	(	(	PUNCT
ejde-1812	490	4	s	s	PROPN
ejde-1812	490	5	,	,	PUNCT
ejde-1812	490	6	y(s	y(s	PROPN
ejde-1812	490	7	)	)	PUNCT
ejde-1812	490	8	,	,	PUNCT
ejde-1812	490	9	∫	∫	PROPN
ejde-1812	490	10	s	s	PART
ejde-1812	490	11	0	0	NUM
ejde-1812	490	12	ρ(s	ρ(s	NOUN
ejde-1812	490	13	,	,	PUNCT
ejde-1812	490	14	τ)y(τ)dτ	τ)y(τ)dτ	NOUN
ejde-1812	490	15	)	)	PUNCT
ejde-1812	490	16	ψ′(s)ds	ψ′(s)ds	PROPN
ejde-1812	490	17	∥∥	∥∥	PRON
ejde-1812	490	18	≤	≤	NUM
ejde-1812	490	19	a(t	a(t	NOUN
ejde-1812	490	20	)	)	PUNCT
ejde-1812	491	1	+	+	NUM
ejde-1812	491	2	lm	lm	X
ejde-1812	491	3	γ(α′	γ(α′	PROPN
ejde-1812	491	4	)	)	PUNCT
ejde-1812	492	1	∫	∫	PROPN
ejde-1812	492	2	t	t	PROPN
ejde-1812	492	3	0	0	NUM
ejde-1812	492	4	eζ(s)−ζ(t)(ψ(t)−	eζ(s)−ζ(t)(ψ(t)−	PROPN
ejde-1812	493	1	ψ(s))α	ψ(s))α	PROPN
ejde-1812	493	2	′−1∥x(s)−	′−1∥x(s)−	PROPN
ejde-1812	493	3	y(s)∥ψ′(s)ds	y(s)∥ψ′(s)ds	PROPN
ejde-1812	493	4	+	+	CCONJ
ejde-1812	493	5	lm	lm	PROPN
ejde-1812	493	6	γ(α′	γ(α′	PROPN
ejde-1812	493	7	)	)	PUNCT
ejde-1812	494	1	∫	∫	PROPN
ejde-1812	494	2	t	t	PROPN
ejde-1812	494	3	0	0	NUM
ejde-1812	494	4	eζ(s)−ζ(t)(ψ(t)−	eζ(s)−ζ(t)(ψ(t)−	PROPN
ejde-1812	494	5	ψ(s))α	ψ(s))α	PROPN
ejde-1812	494	6	′−1	′−1	PUNCT
ejde-1812	494	7	×	×	NOUN
ejde-1812	494	8	[	[	PUNCT
ejde-1812	494	9	∫	∫	PROPN
ejde-1812	494	10	s	s	PART
ejde-1812	494	11	0	0	NUM
ejde-1812	494	12	eζ(τ)−ζ(s)(ψ(s)−	eζ(τ)−ζ(s)(ψ(s)−	ADP
ejde-1812	494	13	ψ(τ))r−1∥x(τ)−	ψ(τ))r−1∥x(τ)−	NOUN
ejde-1812	494	14	y(τ)∥ψ′(τ)dτ	y(τ)∥ψ′(τ)dτ	PROPN
ejde-1812	494	15	]	]	PUNCT
ejde-1812	495	1	ψ′(s)ds	ψ′(s)ds	PROPN
ejde-1812	495	2	≤	≤	PROPN
ejde-1812	495	3	a(t	a(t	PROPN
ejde-1812	495	4	)	)	PUNCT
ejde-1812	496	1	+	+	NUM
ejde-1812	496	2	lm	lm	X
ejde-1812	496	3	γ(α′	γ(α′	PROPN
ejde-1812	496	4	)	)	PUNCT
ejde-1812	497	1	∫	∫	PROPN
ejde-1812	497	2	t	t	PROPN
ejde-1812	497	3	0	0	NUM
ejde-1812	497	4	eζ(s)−ζ(t)(ψ(t)−	eζ(s)−ζ(t)(ψ(t)−	PROPN
ejde-1812	498	1	ψ(s))α	ψ(s))α	PROPN
ejde-1812	498	2	′−1∥x(s)−	′−1∥x(s)−	PROPN
ejde-1812	498	3	y(s)∥ψ′(s)ds	y(s)∥ψ′(s)ds	PROPN
ejde-1812	498	4	+	+	CCONJ
ejde-1812	498	5	lmγ(r	lmγ(r	PROPN
ejde-1812	498	6	)	)	PUNCT
ejde-1812	498	7	γ(α′	γ(α′	NOUN
ejde-1812	498	8	+	+	CCONJ
ejde-1812	498	9	r	r	X
ejde-1812	498	10	)	)	PUNCT
ejde-1812	498	11	∫	∫	PROPN
ejde-1812	498	12	t	t	PROPN
ejde-1812	498	13	0	0	NUM
ejde-1812	499	1	eζ(s)−ζ(t)(ψ(t)−	eζ(s)−ζ(t)(ψ(t)−	PROPN
ejde-1812	499	2	ψ(s))α	ψ(s))α	PROPN
ejde-1812	499	3	′+r−1∥x(s)−	′+r−1∥x(s)−	VERB
ejde-1812	499	4	y(s)∥ψ′(s)ds	y(s)∥ψ′(s)ds	PROPN
ejde-1812	499	5	,	,	PUNCT
ejde-1812	499	6	where	where	SCONJ
ejde-1812	499	7	a(t	a(t	NOUN
ejde-1812	499	8	)	)	PUNCT
ejde-1812	499	9	=	=	SYM
ejde-1812	500	1	∥	∥	PROPN
ejde-1812	500	2	(	(	PUNCT
ejde-1812	500	3	iβ(1−α)kα	iβ(1−α)kα	PROPN
ejde-1812	500	4	)	)	PUNCT
ejde-1812	500	5	(	(	PUNCT
ejde-1812	500	6	ψ(t))x0	ψ(t))x0	PROPN
ejde-1812	500	7	−	−	PROPN
ejde-1812	500	8	(	(	PUNCT
ejde-1812	500	9	iβ	iβ	ADP
ejde-1812	500	10	′(1−α′)kα′	′(1−α′)kα′	PROPN
ejde-1812	500	11	)	)	PUNCT
ejde-1812	500	12	(	(	PUNCT
ejde-1812	500	13	ψ(t))y0∥	ψ(t))y0∥	NOUN
ejde-1812	500	14	+	+	CCONJ
ejde-1812	500	15	∫	∫	PROPN
ejde-1812	500	16	t	t	NOUN
ejde-1812	500	17	0	0	NUM
ejde-1812	501	1	∥kα(ψ(t)−	∥kα(ψ(t)−	PROPN
ejde-1812	501	2	ψ(s))−kα′(ψ(t)−	ψ(s))−kα′(ψ(t)−	PROPN
ejde-1812	501	3	ψ(s))∥ψ′(s)ds	ψ(s))∥ψ′(s)ds	PROPN
ejde-1812	501	4	·	·	PUNCT
ejde-1812	501	5	∥f∥.	∥f∥.	ADV
ejde-1812	501	6	an	an	DET
ejde-1812	501	7	application	application	NOUN
ejde-1812	501	8	of	of	ADP
ejde-1812	501	9	theorem	theorem	ADJ
ejde-1812	501	10	4.1	4.1	NUM
ejde-1812	501	11	(	(	PUNCT
ejde-1812	501	12	with	with	ADP
ejde-1812	501	13	m	m	PROPN
ejde-1812	501	14	=	=	SYM
ejde-1812	501	15	1	1	NUM
ejde-1812	501	16	and	and	CCONJ
ejde-1812	501	17	p	p	NOUN
ejde-1812	501	18	=	=	ADJ
ejde-1812	501	19	2	2	X
ejde-1812	501	20	)	)	PUNCT
ejde-1812	501	21	yields	yield	VERB
ejde-1812	501	22	∥x(t)−	∥x(t)−	PROPN
ejde-1812	501	23	y(t)∥	y(t)∥	NOUN
ejde-1812	501	24	≤	≤	NUM
ejde-1812	501	25	a(t	a(t	NOUN
ejde-1812	501	26	)	)	PUNCT
ejde-1812	502	1	+	+	CCONJ
ejde-1812	502	2	∞∑	∞∑	NUM
ejde-1812	502	3	n=1	n=1	PROPN
ejde-1812	502	4	(	(	PUNCT
ejde-1812	502	5	lm)n	lm)n	PROPN
ejde-1812	502	6	∞∑	∞∑	PROPN
ejde-1812	502	7	k=0	k=0	PROPN
ejde-1812	502	8	ckn	ckn	NOUN
ejde-1812	502	9	(	(	PUNCT
ejde-1812	502	10	γ(r))n−k	γ(r))n−k	X
ejde-1812	502	11	(	(	PUNCT
ejde-1812	502	12	γ(α′))k(γ(α′	γ(α′))k(γ(α′	NOUN
ejde-1812	502	13	+	+	CCONJ
ejde-1812	502	14	r))n−k	r))n−k	PROPN
ejde-1812	503	1	×	×	PROPN
ejde-1812	503	2	∫	∫	PROPN
ejde-1812	503	3	t	t	PROPN
ejde-1812	503	4	0	0	NUM
ejde-1812	503	5	eζ(s)−ζ(t)(ψ(t)−	eζ(s)−ζ(t)(ψ(t)−	PROPN
ejde-1812	503	6	ψ(s))nα	ψ(s))nα	PUNCT
ejde-1812	504	1	′+(n−k)r−1a(s)ψ′(s)ds	′+(n−k)r−1a(s)ψ′(s)d	VERB
ejde-1812	504	2	,	,	PUNCT
ejde-1812	504	3	where	where	SCONJ
ejde-1812	504	4	cmn	cmn	NOUN
ejde-1812	504	5	=	=	SYM
ejde-1812	504	6	n	n	X
ejde-1812	504	7	!	!	PUNCT
ejde-1812	505	1	m!(n−m	m!(n−m	NOUN
ejde-1812	505	2	)	)	PUNCT
ejde-1812	505	3	!	!	PUNCT
ejde-1812	506	1	is	be	AUX
ejde-1812	506	2	a	a	DET
ejde-1812	506	3	binomial	binomial	ADJ
ejde-1812	506	4	coefficient	coefficient	NOUN
ejde-1812	506	5	.	.	PUNCT
ejde-1812	507	1	thus	thus	ADV
ejde-1812	507	2	,	,	PUNCT
ejde-1812	507	3	the	the	DET
ejde-1812	507	4	proof	proof	NOUN
ejde-1812	507	5	is	be	AUX
ejde-1812	507	6	complete	complete	ADJ
ejde-1812	507	7	.	.	PUNCT
ejde-1812	508	1	□	□	PUNCT
ejde-1812	508	2	remark	remark	NOUN
ejde-1812	508	3	4.5	4.5	NUM
ejde-1812	508	4	.	.	PUNCT
ejde-1812	509	1	in	in	ADP
ejde-1812	509	2	theorem	theorem	NOUN
ejde-1812	509	3	4.4	4.4	NUM
ejde-1812	509	4	,	,	PUNCT
ejde-1812	509	5	we	we	PRON
ejde-1812	509	6	do	do	AUX
ejde-1812	509	7	not	not	PART
ejde-1812	509	8	require	require	VERB
ejde-1812	509	9	the	the	DET
ejde-1812	509	10	function	function	NOUN
ejde-1812	509	11	ζ(t	ζ(t	VERB
ejde-1812	509	12	)	)	PUNCT
ejde-1812	509	13	to	to	PART
ejde-1812	509	14	be	be	AUX
ejde-1812	509	15	nondecreasing	nondecrease	VERB
ejde-1812	509	16	on	on	ADP
ejde-1812	509	17	[	[	X
ejde-1812	509	18	0	0	NUM
ejde-1812	509	19	,	,	PUNCT
ejde-1812	509	20	b	b	NOUN
ejde-1812	509	21	]	]	X
ejde-1812	509	22	,	,	PUNCT
ejde-1812	509	23	so	so	ADV
ejde-1812	509	24	using	use	VERB
ejde-1812	509	25	corollary	corollary	NOUN
ejde-1812	509	26	4.3	4.3	NUM
ejde-1812	509	27	without	without	ADP
ejde-1812	509	28	exponential	exponential	ADJ
ejde-1812	509	29	factors	factor	NOUN
ejde-1812	509	30	can	can	AUX
ejde-1812	509	31	not	not	PART
ejde-1812	509	32	lead	lead	VERB
ejde-1812	509	33	to	to	ADP
ejde-1812	509	34	the	the	DET
ejde-1812	509	35	conclusion	conclusion	NOUN
ejde-1812	509	36	of	of	ADP
ejde-1812	509	37	theorem	theorem	NOUN
ejde-1812	509	38	4.4	4.4	NUM
ejde-1812	509	39	.	.	PUNCT
ejde-1812	510	1	corollary	corollary	ADJ
ejde-1812	510	2	4.6	4.6	NUM
ejde-1812	510	3	.	.	PUNCT
ejde-1812	511	1	under	under	ADP
ejde-1812	511	2	the	the	DET
ejde-1812	511	3	hypotheses	hypothesis	NOUN
ejde-1812	511	4	of	of	ADP
ejde-1812	511	5	theorem	theorem	NOUN
ejde-1812	511	6	4.4	4.4	NUM
ejde-1812	511	7	,	,	PUNCT
ejde-1812	511	8	if	if	SCONJ
ejde-1812	511	9	α	α	NOUN
ejde-1812	511	10	=	=	SYM
ejde-1812	511	11	α′	α′	NOUN
ejde-1812	511	12	and	and	CCONJ
ejde-1812	511	13	β	β	X
ejde-1812	511	14	=	=	SYM
ejde-1812	511	15	β′	β′	NUM
ejde-1812	511	16	,	,	PUNCT
ejde-1812	511	17	then	then	ADV
ejde-1812	511	18	∥x(t)−	∥x(t)−	PROPN
ejde-1812	511	19	y(t)∥	y(t)∥	NOUN
ejde-1812	511	20	≤	≤	ADV
ejde-1812	511	21	1	1	NUM
ejde-1812	511	22	γ(α+	γ(α+	PRON
ejde-1812	511	23	β(1−	β(1−	NOUN
ejde-1812	511	24	α	α	X
ejde-1812	511	25	)	)	PUNCT
ejde-1812	511	26	)	)	PUNCT
ejde-1812	512	1	[	[	PUNCT
ejde-1812	512	2	m(ψ(t))α+β(1−α)−1	m(ψ(t))α+β(1−α)−1	NOUN
ejde-1812	512	3	+	+	CCONJ
ejde-1812	512	4	∞∑	∞∑	NUM
ejde-1812	512	5	n=1	n=1	PROPN
ejde-1812	512	6	lnmn+1	lnmn+1	VERB
ejde-1812	512	7	∞∑	∞∑	ADJ
ejde-1812	512	8	k=0	k=0	PROPN
ejde-1812	512	9	ckn	ckn	NOUN
ejde-1812	512	10	×	×	NOUN
ejde-1812	512	11	(	(	PUNCT
ejde-1812	512	12	γ(r))n−k	γ(r))n−k	X
ejde-1812	512	13	(	(	PUNCT
ejde-1812	512	14	γ(α))k(γ(α+	γ(α))k(γ(α+	NOUN
ejde-1812	512	15	r))n−k	r))n−k	PROPN
ejde-1812	512	16	∫	∫	PROPN
ejde-1812	512	17	t	t	PROPN
ejde-1812	512	18	0	0	NUM
ejde-1812	512	19	eζ(s)−ζ(t)(ψ(t)−	eζ(s)−ζ(t)(ψ(t)−	PROPN
ejde-1812	513	1	ψ(s))nα+(n−k)r−1	ψ(s))nα+(n−k)r−1	PROPN
ejde-1812	513	2	14	14	NUM
ejde-1812	513	3	j.	j.	PROPN
ejde-1812	513	4	liang	liang	PROPN
ejde-1812	513	5	,	,	PUNCT
ejde-1812	513	6	y.	y.	PROPN
ejde-1812	513	7	mu	mu	PROPN
ejde-1812	513	8	,	,	PUNCT
ejde-1812	513	9	t.-j	t.-j	PROPN
ejde-1812	513	10	.	.	PUNCT
ejde-1812	514	1	xiao	xiao	PROPN
ejde-1812	514	2	ejde-2025/109	ejde-2025/109	VERB
ejde-1812	514	3	×	×	PROPN
ejde-1812	514	4	(	(	PUNCT
ejde-1812	514	5	ψ(s))α+β(1−α)−1ψ′(s)ds	ψ(s))α+β(1−α)−1ψ′(s)ds	PROPN
ejde-1812	514	6	]	]	PUNCT
ejde-1812	514	7	∥x0	∥x0	NOUN
ejde-1812	514	8	−	−	PROPN
ejde-1812	514	9	y0∥	y0∥	PROPN
ejde-1812	514	10	,	,	PUNCT
ejde-1812	514	11	for	for	ADP
ejde-1812	514	12	t	t	PROPN
ejde-1812	514	13	∈	∈	PROPN
ejde-1812	514	14	(	(	PUNCT
ejde-1812	514	15	0	0	NUM
ejde-1812	514	16	,	,	PUNCT
ejde-1812	514	17	b	b	NOUN
ejde-1812	514	18	]	]	PUNCT
ejde-1812	514	19	.	.	PUNCT
ejde-1812	515	1	proof	proof	NOUN
ejde-1812	515	2	.	.	PUNCT
ejde-1812	516	1	if	if	SCONJ
ejde-1812	516	2	α	α	NOUN
ejde-1812	516	3	=	=	SYM
ejde-1812	516	4	α′	α′	NUM
ejde-1812	516	5	and	and	CCONJ
ejde-1812	516	6	β	β	X
ejde-1812	516	7	=	=	SYM
ejde-1812	516	8	β′	β′	NUM
ejde-1812	516	9	,	,	PUNCT
ejde-1812	516	10	then	then	ADV
ejde-1812	516	11	a(t	a(t	NOUN
ejde-1812	516	12	)	)	PUNCT
ejde-1812	517	1	=	=	SYM
ejde-1812	517	2	∥	∥	PROPN
ejde-1812	517	3	(	(	PUNCT
ejde-1812	517	4	iβ(1−α)kα	iβ(1−α)kα	PROPN
ejde-1812	517	5	)	)	PUNCT
ejde-1812	518	1	(	(	PUNCT
ejde-1812	518	2	ψ(t))(x0	ψ(t))(x0	PROPN
ejde-1812	518	3	−	−	PROPN
ejde-1812	518	4	y0)∥	y0)∥	X
ejde-1812	518	5	≤	≤	PROPN
ejde-1812	518	6	m(ψ(t))α+β(1−α)−1	m(ψ(t))α+β(1−α)−1	VERB
ejde-1812	518	7	γ(α+	γ(α+	X
ejde-1812	518	8	β(1−	β(1−	PROPN
ejde-1812	518	9	α	α	NUM
ejde-1812	518	10	)	)	PUNCT
ejde-1812	518	11	)	)	PUNCT
ejde-1812	518	12	∥x0	∥x0	NOUN
ejde-1812	518	13	−	−	NOUN
ejde-1812	518	14	y0∥.	y0∥.	PROPN
ejde-1812	518	15	by	by	ADP
ejde-1812	518	16	theorem	theorem	NOUN
ejde-1812	518	17	4.4	4.4	NUM
ejde-1812	518	18	,	,	PUNCT
ejde-1812	518	19	we	we	PRON
ejde-1812	518	20	have	have	VERB
ejde-1812	518	21	∥x(t)−	∥x(t)−	PROPN
ejde-1812	518	22	y(t)∥	y(t)∥	NOUN
ejde-1812	518	23	≤	≤	NUM
ejde-1812	518	24	a(t	a(t	NOUN
ejde-1812	518	25	)	)	PUNCT
ejde-1812	519	1	+	+	CCONJ
ejde-1812	519	2	∞∑	∞∑	NUM
ejde-1812	519	3	n=1	n=1	PROPN
ejde-1812	519	4	(	(	PUNCT
ejde-1812	519	5	lm)n	lm)n	PROPN
ejde-1812	519	6	∞∑	∞∑	PROPN
ejde-1812	519	7	k=0	k=0	PROPN
ejde-1812	519	8	ckn	ckn	NOUN
ejde-1812	519	9	(	(	PUNCT
ejde-1812	519	10	γ(r))n−k	γ(r))n−k	X
ejde-1812	519	11	(	(	PUNCT
ejde-1812	519	12	γ(α))k(γ(α+	γ(α))k(γ(α+	NOUN
ejde-1812	519	13	r))n−k	r))n−k	PROPN
ejde-1812	519	14	×	×	PROPN
ejde-1812	519	15	∫	∫	PROPN
ejde-1812	519	16	t	t	PROPN
ejde-1812	519	17	0	0	NUM
ejde-1812	519	18	eζ(s)−ζ(t)(ψ(t)−	eζ(s)−ζ(t)(ψ(t)−	PROPN
ejde-1812	519	19	ψ(s))nα+(n−k)r−1a(s)ψ′(s)ds	ψ(s))nα+(n−k)r−1a(s)ψ′(s)ds	PROPN
ejde-1812	519	20	=	=	PUNCT
ejde-1812	519	21	1	1	NUM
ejde-1812	519	22	γ(α+	γ(α+	PRON
ejde-1812	519	23	β(1−	β(1−	NOUN
ejde-1812	519	24	α	α	X
ejde-1812	519	25	)	)	PUNCT
ejde-1812	519	26	)	)	PUNCT
ejde-1812	519	27	[	[	PUNCT
ejde-1812	519	28	m(ψ(t))α+β(1−α)−1	m(ψ(t))α+β(1−α)−1	NOUN
ejde-1812	519	29	+	+	CCONJ
ejde-1812	519	30	∞∑	∞∑	NUM
ejde-1812	519	31	n=1	n=1	PROPN
ejde-1812	519	32	lnmn+1	lnmn+1	VERB
ejde-1812	520	1	∞∑	∞∑	ADJ
ejde-1812	520	2	k=0	k=0	PROPN
ejde-1812	520	3	ckn	ckn	NOUN
ejde-1812	520	4	×	×	NOUN
ejde-1812	520	5	(	(	PUNCT
ejde-1812	520	6	γ(r))n−k	γ(r))n−k	X
ejde-1812	520	7	(	(	PUNCT
ejde-1812	520	8	γ(α))k(γ(α+	γ(α))k(γ(α+	NOUN
ejde-1812	520	9	r))n−k	r))n−k	PROPN
ejde-1812	520	10	∫	∫	PROPN
ejde-1812	520	11	t	t	PROPN
ejde-1812	520	12	0	0	NUM
ejde-1812	520	13	eζ(s)−ζ(t)(ψ(t)−	eζ(s)−ζ(t)(ψ(t)−	PROPN
ejde-1812	521	1	ψ(s))nα+(n−k)r−1	ψ(s))nα+(n−k)r−1	PROPN
ejde-1812	521	2	×	×	NOUN
ejde-1812	521	3	(	(	PUNCT
ejde-1812	521	4	ψ(s))α+β(1−α)−1ψ′(s)ds	ψ(s))α+β(1−α)−1ψ′(s)ds	PROPN
ejde-1812	521	5	]	]	PUNCT
ejde-1812	521	6	∥x0	∥x0	NOUN
ejde-1812	521	7	−	−	PROPN
ejde-1812	521	8	y0∥	y0∥	PROPN
ejde-1812	521	9	,	,	PUNCT
ejde-1812	521	10	for	for	ADP
ejde-1812	521	11	t	t	PROPN
ejde-1812	521	12	∈	∈	PROPN
ejde-1812	521	13	(	(	PUNCT
ejde-1812	521	14	0	0	NUM
ejde-1812	521	15	,	,	PUNCT
ejde-1812	521	16	b	b	NOUN
ejde-1812	521	17	]	]	X
ejde-1812	521	18	.	.	PUNCT
ejde-1812	522	1	the	the	DET
ejde-1812	522	2	proof	proof	NOUN
ejde-1812	522	3	is	be	AUX
ejde-1812	522	4	complete	complete	ADJ
ejde-1812	522	5	.	.	PUNCT
ejde-1812	523	1	□	□	PUNCT
ejde-1812	523	2	5	5	X
ejde-1812	523	3	.	.	PUNCT
ejde-1812	523	4	an	an	DET
ejde-1812	523	5	example	example	NOUN
ejde-1812	523	6	in	in	ADP
ejde-1812	523	7	this	this	DET
ejde-1812	523	8	section	section	NOUN
ejde-1812	523	9	,	,	PUNCT
ejde-1812	523	10	we	we	PRON
ejde-1812	523	11	give	give	VERB
ejde-1812	523	12	an	an	DET
ejde-1812	523	13	example	example	NOUN
ejde-1812	523	14	to	to	PART
ejde-1812	523	15	show	show	VERB
ejde-1812	523	16	the	the	DET
ejde-1812	523	17	applicability	applicability	NOUN
ejde-1812	523	18	of	of	ADP
ejde-1812	523	19	the	the	DET
ejde-1812	523	20	results	result	NOUN
ejde-1812	523	21	obtained	obtain	VERB
ejde-1812	523	22	in	in	ADP
ejde-1812	523	23	previous	previous	ADJ
ejde-1812	523	24	sections	section	NOUN
ejde-1812	523	25	.	.	PUNCT
ejde-1812	524	1	let	let	VERB
ejde-1812	524	2	x	x	PUNCT
ejde-1812	524	3	=	=	PRON
ejde-1812	524	4	{	{	PUNCT
ejde-1812	524	5	u(t	u(t	PROPN
ejde-1812	524	6	)	)	PUNCT
ejde-1812	524	7	:	:	PUNCT
ejde-1812	524	8	u(t	u(t	NOUN
ejde-1812	524	9	)	)	PUNCT
ejde-1812	524	10	∈	∈	PROPN
ejde-1812	524	11	l2[0	l2[0	PROPN
ejde-1812	524	12	,	,	PUNCT
ejde-1812	524	13	π	π	NOUN
ejde-1812	524	14	]	]	X
ejde-1812	524	15	,	,	PUNCT
ejde-1812	524	16	u(t	u(t	NOUN
ejde-1812	524	17	)	)	PUNCT
ejde-1812	524	18	is	be	AUX
ejde-1812	524	19	a	a	DET
ejde-1812	524	20	real	real	ADJ
ejde-1812	524	21	function	function	NOUN
ejde-1812	524	22	}	}	PUNCT
ejde-1812	524	23	and	and	CCONJ
ejde-1812	525	1	u	u	X
ejde-1812	525	2	=	=	NOUN
ejde-1812	525	3	x.	x.	NOUN
ejde-1812	525	4	we	we	PRON
ejde-1812	525	5	define	define	VERB
ejde-1812	525	6	the	the	DET
ejde-1812	525	7	inner	inner	ADJ
ejde-1812	525	8	product	product	NOUN
ejde-1812	525	9	and	and	CCONJ
ejde-1812	525	10	norm	norm	NOUN
ejde-1812	525	11	on	on	ADP
ejde-1812	525	12	x	x	PUNCT
ejde-1812	525	13	respectively	respectively	ADV
ejde-1812	525	14	,	,	PUNCT
ejde-1812	525	15	for	for	ADP
ejde-1812	525	16	u1	u1	NOUN
ejde-1812	525	17	,	,	PUNCT
ejde-1812	525	18	u2	u2	PROPN
ejde-1812	525	19	∈	∈	PROPN
ejde-1812	525	20	x	x	X
ejde-1812	525	21	,	,	PUNCT
ejde-1812	525	22	by	by	ADP
ejde-1812	525	23	⟨u1	⟨u1	NOUN
ejde-1812	525	24	,	,	PUNCT
ejde-1812	525	25	u2⟩	u2⟩	PRON
ejde-1812	525	26	=	=	SYM
ejde-1812	526	1	∫	∫	PROPN
ejde-1812	526	2	π	π	NOUN
ejde-1812	526	3	0	0	X
ejde-1812	526	4	u1(t)u2(t)dt	u1(t)u2(t)dt	PROPN
ejde-1812	526	5	,	,	PUNCT
ejde-1812	526	6	∥u1∥x	∥u1∥x	PROPN
ejde-1812	526	7	=	=	PUNCT
ejde-1812	526	8	(	(	PUNCT
ejde-1812	526	9	∫	∫	PROPN
ejde-1812	526	10	π	π	PROPN
ejde-1812	526	11	0	0	NUM
ejde-1812	526	12	u21(t)dt	u21(t)dt	PROPN
ejde-1812	526	13	)	)	PUNCT
ejde-1812	526	14	1/2	1/2	NUM
ejde-1812	526	15	.	.	PUNCT
ejde-1812	527	1	we	we	PRON
ejde-1812	527	2	define	define	VERB
ejde-1812	527	3	the	the	DET
ejde-1812	527	4	operator	operator	NOUN
ejde-1812	527	5	a	a	DET
ejde-1812	527	6	:	:	PUNCT
ejde-1812	527	7	d(a	d(a	PROPN
ejde-1812	527	8	)	)	PUNCT
ejde-1812	528	1	⊂	⊂	PROPN
ejde-1812	528	2	x	x	PUNCT
ejde-1812	528	3	→	→	PUNCT
ejde-1812	528	4	x	x	X
ejde-1812	528	5	by	by	ADP
ejde-1812	528	6	d(a	d(a	PROPN
ejde-1812	528	7	)	)	PUNCT
ejde-1812	528	8	:	:	PUNCT
ejde-1812	528	9	=	=	SYM
ejde-1812	528	10	{	{	PUNCT
ejde-1812	528	11	v	v	NUM
ejde-1812	528	12	∈	∈	NOUN
ejde-1812	528	13	x	x	X
ejde-1812	528	14	:	:	PUNCT
ejde-1812	528	15	v′′	v′′	VERB
ejde-1812	528	16	∈	∈	PROPN
ejde-1812	528	17	x	x	NOUN
ejde-1812	528	18	,	,	PUNCT
ejde-1812	528	19	v(0	v(0	PROPN
ejde-1812	528	20	)	)	PUNCT
ejde-1812	528	21	=	=	SYM
ejde-1812	528	22	v(π	v(π	NOUN
ejde-1812	528	23	)	)	PUNCT
ejde-1812	528	24	=	=	PUNCT
ejde-1812	529	1	0	0	NUM
ejde-1812	529	2	}	}	PUNCT
ejde-1812	529	3	,	,	PUNCT
ejde-1812	529	4	au	au	X
ejde-1812	529	5	=	=	SYM
ejde-1812	529	6	∂2u	∂2u	PROPN
ejde-1812	529	7	∂x2	∂x2	PROPN
ejde-1812	529	8	.	.	PUNCT
ejde-1812	530	1	from	from	ADP
ejde-1812	530	2	[	[	X
ejde-1812	530	3	34	34	NUM
ejde-1812	530	4	]	]	PUNCT
ejde-1812	530	5	we	we	PRON
ejde-1812	530	6	know	know	VERB
ejde-1812	530	7	that	that	DET
ejde-1812	530	8	−a	−a	NOUN
ejde-1812	530	9	has	have	VERB
ejde-1812	530	10	eigenvalues	eigenvalue	NOUN
ejde-1812	530	11	of	of	ADP
ejde-1812	530	12	the	the	DET
ejde-1812	530	13	form	form	NOUN
ejde-1812	530	14	n2	n2	NOUN
ejde-1812	530	15	(	(	PUNCT
ejde-1812	530	16	n	n	X
ejde-1812	530	17	∈	∈	PROPN
ejde-1812	530	18	n+	n+	PROPN
ejde-1812	530	19	)	)	PUNCT
ejde-1812	530	20	,	,	PUNCT
ejde-1812	530	21	and	and	CCONJ
ejde-1812	530	22	the	the	DET
ejde-1812	530	23	corresponding	corresponding	ADJ
ejde-1812	530	24	normalized	normalize	VERB
ejde-1812	530	25	eigenfunctions	eigenfunction	NOUN
ejde-1812	530	26	are	be	AUX
ejde-1812	530	27	given	give	VERB
ejde-1812	530	28	by	by	ADP
ejde-1812	530	29	en	en	X
ejde-1812	530	30	=	=	NOUN
ejde-1812	530	31	√	√	PROPN
ejde-1812	530	32	2	2	NUM
ejde-1812	530	33	π	π	NOUN
ejde-1812	530	34	sin(nx	sin(nx	NOUN
ejde-1812	530	35	)	)	PUNCT
ejde-1812	530	36	(	(	PUNCT
ejde-1812	530	37	n	n	X
ejde-1812	530	38	∈	∈	PROPN
ejde-1812	530	39	n+	n+	PROPN
ejde-1812	530	40	)	)	PUNCT
ejde-1812	530	41	.	.	PUNCT
ejde-1812	531	1	moreover	moreover	ADV
ejde-1812	531	2	,	,	PUNCT
ejde-1812	531	3	a	a	PRON
ejde-1812	531	4	generates	generate	VERB
ejde-1812	531	5	a	a	DET
ejde-1812	531	6	compact	compact	ADJ
ejde-1812	531	7	analytic	analytic	ADJ
ejde-1812	531	8	semigroup	semigroup	NOUN
ejde-1812	531	9	{	{	PUNCT
ejde-1812	531	10	t	t	NOUN
ejde-1812	531	11	(	(	PUNCT
ejde-1812	531	12	t)}t≥0	t)}t≥0	NOUN
ejde-1812	531	13	on	on	ADP
ejde-1812	531	14	x	x	NOUN
ejde-1812	531	15	,	,	PUNCT
ejde-1812	531	16	and	and	CCONJ
ejde-1812	531	17	t	t	PROPN
ejde-1812	531	18	(	(	PUNCT
ejde-1812	531	19	t)u	t)u	X
ejde-1812	531	20	=	=	PUNCT
ejde-1812	531	21	∞∑	∞∑	NUM
ejde-1812	531	22	n=1	n=1	PROPN
ejde-1812	531	23	e−n	e−n	PROPN
ejde-1812	531	24	2t⟨u	2t⟨u	NUM
ejde-1812	531	25	,	,	PUNCT
ejde-1812	531	26	en⟩en	en⟩en	NUM
ejde-1812	531	27	.	.	PUNCT
ejde-1812	532	1	we	we	PRON
ejde-1812	532	2	can	can	AUX
ejde-1812	532	3	verify	verify	VERB
ejde-1812	532	4	that	that	SCONJ
ejde-1812	532	5	∥t	∥t	PROPN
ejde-1812	532	6	(	(	PUNCT
ejde-1812	532	7	t)∥	t)∥	NUM
ejde-1812	532	8	≤	≤	NUM
ejde-1812	532	9	e−t	e−t	NOUN
ejde-1812	532	10	for	for	ADP
ejde-1812	532	11	all	all	DET
ejde-1812	532	12	t	t	PROPN
ejde-1812	532	13	≥	≥	NOUN
ejde-1812	532	14	0	0	NUM
ejde-1812	532	15	,	,	PUNCT
ejde-1812	532	16	and	and	CCONJ
ejde-1812	532	17	take	take	VERB
ejde-1812	532	18	m	m	NOUN
ejde-1812	532	19	=	=	NOUN
ejde-1812	532	20	1	1	X
ejde-1812	532	21	.	.	PUNCT
ejde-1812	533	1	furthermore	furthermore	ADV
ejde-1812	533	2	,	,	PUNCT
ejde-1812	533	3	by	by	ADP
ejde-1812	533	4	[	[	X
ejde-1812	533	5	37	37	NUM
ejde-1812	533	6	]	]	PUNCT
ejde-1812	533	7	we	we	PRON
ejde-1812	533	8	know	know	VERB
ejde-1812	533	9	that	that	SCONJ
ejde-1812	533	10	{	{	PUNCT
ejde-1812	533	11	t	t	NOUN
ejde-1812	533	12	(	(	PUNCT
ejde-1812	533	13	t)}t≥0	t)}t≥0	NOUN
ejde-1812	533	14	is	be	AUX
ejde-1812	533	15	continuous	continuous	ADJ
ejde-1812	533	16	in	in	ADP
ejde-1812	533	17	the	the	DET
ejde-1812	533	18	uniform	uniform	ADJ
ejde-1812	533	19	operator	operator	NOUN
ejde-1812	533	20	topology	topology	NOUN
ejde-1812	533	21	for	for	ADP
ejde-1812	533	22	t	t	PROPN
ejde-1812	533	23	>	>	X
ejde-1812	533	24	0	0	X
ejde-1812	533	25	.	.	PUNCT
ejde-1812	534	1	for	for	ADP
ejde-1812	534	2	each	each	DET
ejde-1812	534	3	u	u	NOUN
ejde-1812	534	4	(	(	PUNCT
ejde-1812	534	5	·	·	PUNCT
ejde-1812	534	6	)	)	PUNCT
ejde-1812	534	7	∈	∈	NOUN
ejde-1812	534	8	v	v	NOUN
ejde-1812	534	9	=	=	SYM
ejde-1812	534	10	l2(j	l2(j	PROPN
ejde-1812	534	11	,	,	PUNCT
ejde-1812	534	12	u	u	NOUN
ejde-1812	534	13	)	)	PUNCT
ejde-1812	534	14	,	,	PUNCT
ejde-1812	534	15	we	we	PRON
ejde-1812	534	16	have	have	VERB
ejde-1812	534	17	u(t	u(t	NOUN
ejde-1812	534	18	)	)	PUNCT
ejde-1812	534	19	=	=	NOUN
ejde-1812	535	1	∞∑	∞∑	NUM
ejde-1812	535	2	n=1	n=1	NOUN
ejde-1812	535	3	un(t)en	un(t)en	NOUN
ejde-1812	535	4	,	,	PUNCT
ejde-1812	535	5	un(t	un(t	NUM
ejde-1812	535	6	)	)	PUNCT
ejde-1812	536	1	=	=	NOUN
ejde-1812	536	2	<	<	X
ejde-1812	536	3	u(t	u(t	NOUN
ejde-1812	536	4	)	)	PUNCT
ejde-1812	536	5	,	,	PUNCT
ejde-1812	536	6	en	en	X
ejde-1812	536	7	>	>	X
ejde-1812	536	8	.	.	PUNCT
ejde-1812	537	1	the	the	DET
ejde-1812	537	2	operator	operator	NOUN
ejde-1812	537	3	b	b	NOUN
ejde-1812	537	4	is	be	AUX
ejde-1812	537	5	defined	define	VERB
ejde-1812	537	6	by	by	ADP
ejde-1812	537	7	bu(t	bu(t	NOUN
ejde-1812	537	8	)	)	PUNCT
ejde-1812	537	9	=	=	PUNCT
ejde-1812	538	1	∞∑	∞∑	NUM
ejde-1812	538	2	n=1	n=1	PROPN
ejde-1812	538	3	vn(t)en	vn(t)en	ADV
ejde-1812	538	4	,	,	PUNCT
ejde-1812	538	5	where	where	SCONJ
ejde-1812	538	6	vn(t	vn(t	NUM
ejde-1812	538	7	)	)	PUNCT
ejde-1812	539	1	=	=	PRON
ejde-1812	539	2	{	{	PUNCT
ejde-1812	539	3	0	0	NUM
ejde-1812	539	4	,	,	PUNCT
ejde-1812	539	5	t	t	PROPN
ejde-1812	539	6	∈	∈	PROPN
ejde-1812	540	1	[	[	X
ejde-1812	540	2	0	0	NUM
ejde-1812	540	3	,	,	PUNCT
ejde-1812	540	4	1−	1−	NUM
ejde-1812	540	5	1	1	NUM
ejde-1812	540	6	n3	n3	NOUN
ejde-1812	540	7	]	]	PUNCT
ejde-1812	540	8	,	,	PUNCT
ejde-1812	540	9	un(t	un(t	NUM
ejde-1812	540	10	)	)	PUNCT
ejde-1812	540	11	,	,	PUNCT
ejde-1812	540	12	t	t	PROPN
ejde-1812	540	13	∈	∈	PROPN
ejde-1812	540	14	(	(	PUNCT
ejde-1812	540	15	1−	1−	NUM
ejde-1812	540	16	1	1	NUM
ejde-1812	540	17	n3	n3	NOUN
ejde-1812	540	18	,	,	PUNCT
ejde-1812	540	19	1	1	NUM
ejde-1812	540	20	]	]	PUNCT
ejde-1812	540	21	,	,	PUNCT
ejde-1812	540	22	where	where	SCONJ
ejde-1812	540	23	n	n	X
ejde-1812	540	24	∈	∈	PROPN
ejde-1812	540	25	n+	n+	PROPN
ejde-1812	540	26	.	.	PUNCT
ejde-1812	541	1	then	then	ADV
ejde-1812	541	2	we	we	PRON
ejde-1812	541	3	can	can	AUX
ejde-1812	541	4	see	see	VERB
ejde-1812	541	5	that	that	SCONJ
ejde-1812	541	6	∥bu(·)∥	∥bu(·)∥	PROPN
ejde-1812	541	7	≤	≤	NUM
ejde-1812	541	8	∥u(·)∥	∥u(·)∥	NOUN
ejde-1812	541	9	,	,	PUNCT
ejde-1812	541	10	which	which	PRON
ejde-1812	541	11	means	mean	VERB
ejde-1812	541	12	that	that	SCONJ
ejde-1812	541	13	b	b	X
ejde-1812	541	14	∈	∈	ADJ
ejde-1812	541	15	l	l	NOUN
ejde-1812	541	16	(	(	PUNCT
ejde-1812	541	17	v	v	NOUN
ejde-1812	541	18	,	,	PUNCT
ejde-1812	541	19	l2(j	l2(j	PROPN
ejde-1812	541	20	,	,	PUNCT
ejde-1812	541	21	x	x	NOUN
ejde-1812	541	22	)	)	PUNCT
ejde-1812	541	23	)	)	PUNCT
ejde-1812	541	24	.	.	PUNCT
ejde-1812	542	1	ejde-2025/109	ejde-2025/109	ADP
ejde-1812	542	2	evolution	evolution	NOUN
ejde-1812	542	3	ψ	ψ	NOUN
ejde-1812	542	4	-	-	ADJ
ejde-1812	542	5	hilfer	hilfer	NOUN
ejde-1812	542	6	fractional	fractional	ADJ
ejde-1812	542	7	differential	differential	ADJ
ejde-1812	542	8	equations	equation	NOUN
ejde-1812	542	9	15	15	NUM
ejde-1812	542	10	we	we	PRON
ejde-1812	542	11	consider	consider	VERB
ejde-1812	542	12	the	the	DET
ejde-1812	542	13	following	follow	VERB
ejde-1812	542	14	fractional	fractional	ADJ
ejde-1812	542	15	differential	differential	NOUN
ejde-1812	542	16	control	control	NOUN
ejde-1812	542	17	problem	problem	NOUN
ejde-1812	542	18	involving	involve	VERB
ejde-1812	542	19	ψ	ψ	NOUN
ejde-1812	542	20	-	-	ADJ
ejde-1812	542	21	hilfer	hilfer	NOUN
ejde-1812	542	22	fractional	fractional	ADJ
ejde-1812	542	23	derivative	derivative	NOUN
ejde-1812	542	24	:	:	PUNCT
ejde-1812	542	25	(	(	PUNCT
ejde-1812	542	26	dα	dα	NOUN
ejde-1812	542	27	,	,	PUNCT
ejde-1812	542	28	β;ψx)(t	β;ψx)(t	NUM
ejde-1812	542	29	)	)	PUNCT
ejde-1812	542	30	=	=	NOUN
ejde-1812	542	31	ax(t	ax(t	NUM
ejde-1812	542	32	)	)	PUNCT
ejde-1812	543	1	+	+	CCONJ
ejde-1812	543	2	f(t	f(t	NOUN
ejde-1812	543	3	,	,	PUNCT
ejde-1812	543	4	x(t	x(t	PROPN
ejde-1812	543	5	)	)	PUNCT
ejde-1812	543	6	)	)	PUNCT
ejde-1812	544	1	+	+	ADJ
ejde-1812	544	2	bu(t	bu(t	NOUN
ejde-1812	544	3	)	)	PUNCT
ejde-1812	544	4	,	,	PUNCT
ejde-1812	544	5	t	t	PROPN
ejde-1812	544	6	∈	∈	PROPN
ejde-1812	545	1	j	j	NOUN
ejde-1812	545	2	′	′	NUM
ejde-1812	546	1	=	=	SYM
ejde-1812	546	2	(	(	PUNCT
ejde-1812	546	3	0	0	NUM
ejde-1812	546	4	,	,	PUNCT
ejde-1812	546	5	1	1	NUM
ejde-1812	546	6	]	]	PUNCT
ejde-1812	546	7	,	,	PUNCT
ejde-1812	546	8	i(1−α)(1−β);ψx(0	i(1−α)(1−β);ψx(0	NOUN
ejde-1812	546	9	)	)	PUNCT
ejde-1812	547	1	=	=	SYM
ejde-1812	547	2	x0	x0	PROPN
ejde-1812	547	3	,	,	PUNCT
ejde-1812	547	4	(	(	PUNCT
ejde-1812	547	5	5.1	5.1	NUM
ejde-1812	547	6	)	)	PUNCT
ejde-1812	547	7	where	where	SCONJ
ejde-1812	547	8	α	α	NOUN
ejde-1812	547	9	=	=	NOUN
ejde-1812	547	10	4	4	NUM
ejde-1812	547	11	5	5	NUM
ejde-1812	547	12	,	,	PUNCT
ejde-1812	547	13	β	β	X
ejde-1812	547	14	=	=	SYM
ejde-1812	547	15	3	3	NUM
ejde-1812	547	16	4	4	NUM
ejde-1812	547	17	,	,	PUNCT
ejde-1812	547	18	x0	x0	PROPN
ejde-1812	547	19	∈	∈	PROPN
ejde-1812	547	20	x	x	NOUN
ejde-1812	547	21	,	,	PUNCT
ejde-1812	547	22	ψ(t	ψ(t	PROPN
ejde-1812	547	23	)	)	PUNCT
ejde-1812	547	24	=	=	SYM
ejde-1812	547	25	t3	t3	PROPN
ejde-1812	547	26	,	,	PUNCT
ejde-1812	547	27	and	and	CCONJ
ejde-1812	547	28	f(t	f(t	NOUN
ejde-1812	547	29	,	,	PUNCT
ejde-1812	547	30	x	x	NOUN
ejde-1812	547	31	)	)	PUNCT
ejde-1812	547	32	=	=	SYM
ejde-1812	547	33	lt3/20	lt3/20	X
ejde-1812	547	34	sin(x	sin(x	PROPN
ejde-1812	547	35	)	)	PUNCT
ejde-1812	547	36	,	,	PUNCT
ejde-1812	547	37	t	t	PROPN
ejde-1812	547	38	∈	∈	PROPN
ejde-1812	547	39	(	(	PUNCT
ejde-1812	547	40	0	0	NUM
ejde-1812	547	41	,	,	PUNCT
ejde-1812	547	42	1	1	NUM
ejde-1812	547	43	]	]	PUNCT
ejde-1812	547	44	.	.	PUNCT
ejde-1812	548	1	next	next	ADV
ejde-1812	548	2	,	,	PUNCT
ejde-1812	548	3	we	we	PRON
ejde-1812	548	4	verify	verify	VERB
ejde-1812	548	5	that	that	DET
ejde-1812	548	6	hypothesis	hypothesis	NOUN
ejde-1812	548	7	(	(	PUNCT
ejde-1812	548	8	h4	h4	PROPN
ejde-1812	548	9	)	)	PUNCT
ejde-1812	548	10	holds	hold	VERB
ejde-1812	548	11	.	.	PUNCT
ejde-1812	549	1	to	to	PART
ejde-1812	549	2	do	do	VERB
ejde-1812	549	3	this	this	PRON
ejde-1812	549	4	,	,	PUNCT
ejde-1812	549	5	for	for	ADP
ejde-1812	549	6	each	each	DET
ejde-1812	549	7	h	h	NOUN
ejde-1812	549	8	(	(	PUNCT
ejde-1812	549	9	·	·	PUNCT
ejde-1812	549	10	)	)	PUNCT
ejde-1812	549	11	∈	∈	PROPN
ejde-1812	549	12	l2(j	l2(j	PROPN
ejde-1812	549	13	,	,	PUNCT
ejde-1812	549	14	x	x	NOUN
ejde-1812	549	15	)	)	PUNCT
ejde-1812	549	16	,	,	PUNCT
ejde-1812	549	17	let	let	VERB
ejde-1812	549	18	l	l	NOUN
ejde-1812	549	19	=	=	SYM
ejde-1812	550	1	∫	∫	PROPN
ejde-1812	550	2	1	1	NUM
ejde-1812	550	3	0	0	NUM
ejde-1812	550	4	kα(ψ(1)−	kα(ψ(1)−	PROPN
ejde-1812	550	5	ψ(s))ψ′(s)h(s)ds	ψ(s))ψ′(s)h(s)ds	NOUN
ejde-1812	550	6	=	=	NOUN
ejde-1812	550	7	∞∑	∞∑	NUM
ejde-1812	550	8	n=1	n=1	PROPN
ejde-1812	550	9	lnen	lnen	NOUN
ejde-1812	550	10	,	,	PUNCT
ejde-1812	550	11	where	where	SCONJ
ejde-1812	550	12	ln	ln	ADJ
ejde-1812	550	13	=	=	NOUN
ejde-1812	550	14	⟨l	⟨l	NOUN
ejde-1812	550	15	,	,	PUNCT
ejde-1812	550	16	en⟩.	en⟩.	VERB
ejde-1812	550	17	we	we	PRON
ejde-1812	550	18	can	can	AUX
ejde-1812	550	19	take	take	VERB
ejde-1812	550	20	un(t	un(t	NOUN
ejde-1812	550	21	)	)	PUNCT
ejde-1812	550	22	=	=	PUNCT
ejde-1812	551	1	3n3	3n3	NUM
ejde-1812	551	2	1−	1−	NUM
ejde-1812	551	3	e−ψ(3	e−ψ(3	PROPN
ejde-1812	551	4	)	)	PUNCT
ejde-1812	551	5	lne	lne	PROPN
ejde-1812	551	6	−n3(1−ψ(t	−n3(1−ψ(t	PROPN
ejde-1812	551	7	)	)	PUNCT
ejde-1812	551	8	)	)	PUNCT
ejde-1812	551	9	,	,	PUNCT
ejde-1812	551	10	1−	1−	NUM
ejde-1812	551	11	1	1	NUM
ejde-1812	551	12	n3	n3	PROPN
ejde-1812	551	13	≤	≤	PROPN
ejde-1812	551	14	t	t	PROPN
ejde-1812	551	15	≤	≤	NOUN
ejde-1812	551	16	1	1	NUM
ejde-1812	551	17	,	,	PUNCT
ejde-1812	551	18	ln	ln	NOUN
ejde-1812	551	19	=	=	PUNCT
ejde-1812	551	20	∫	∫	PROPN
ejde-1812	551	21	1	1	NUM
ejde-1812	551	22	1−	1−	NUM
ejde-1812	551	23	1	1	NUM
ejde-1812	552	1	n3	n3	NOUN
ejde-1812	552	2	∫	∫	PROPN
ejde-1812	552	3	∞	∞	PROPN
ejde-1812	552	4	0	0	NUM
ejde-1812	553	1	(	(	PUNCT
ejde-1812	553	2	1−	1−	NUM
ejde-1812	553	3	ψ(t))−	ψ(t))−	NOUN
ejde-1812	553	4	1	1	NUM
ejde-1812	553	5	5σξ	5σξ	ADJ
ejde-1812	553	6	4	4	NUM
ejde-1812	553	7	5	5	NUM
ejde-1812	553	8	e−n	e−n	PROPN
ejde-1812	553	9	3σ(1−ψ(t	3σ(1−ψ(t	NUM
ejde-1812	553	10	)	)	PUNCT
ejde-1812	553	11	)	)	PUNCT
ejde-1812	553	12	4	4	NUM
ejde-1812	553	13	5	5	NUM
ejde-1812	553	14	u(t)ψ′(t)dσdt	u(t)ψ′(t)dσdt	NOUN
ejde-1812	553	15	.	.	PUNCT
ejde-1812	554	1	and	and	CCONJ
ejde-1812	554	2	define	define	VERB
ejde-1812	554	3	u(t	u(t	NOUN
ejde-1812	554	4	)	)	PUNCT
ejde-1812	555	1	:	:	PUNCT
ejde-1812	555	2	=	=	NOUN
ejde-1812	555	3	∞∑	∞∑	NUM
ejde-1812	555	4	n=1	n=1	ADJ
ejde-1812	555	5	ũn(t)en	ũn(t)en	NOUN
ejde-1812	555	6	,	,	PUNCT
ejde-1812	555	7	where	where	SCONJ
ejde-1812	555	8	ũn(t	ũn(t	NOUN
ejde-1812	555	9	)	)	PUNCT
ejde-1812	555	10	=	=	PRON
ejde-1812	555	11	{	{	PUNCT
ejde-1812	555	12	0	0	NUM
ejde-1812	555	13	,	,	PUNCT
ejde-1812	555	14	t	t	PROPN
ejde-1812	555	15	∈	∈	PROPN
ejde-1812	556	1	[	[	X
ejde-1812	556	2	0	0	NUM
ejde-1812	556	3	,	,	PUNCT
ejde-1812	556	4	1−	1−	NUM
ejde-1812	556	5	1	1	NUM
ejde-1812	556	6	n3	n3	NOUN
ejde-1812	556	7	]	]	PUNCT
ejde-1812	556	8	,	,	PUNCT
ejde-1812	556	9	un(t	un(t	NUM
ejde-1812	556	10	)	)	PUNCT
ejde-1812	556	11	,	,	PUNCT
ejde-1812	556	12	t	t	PROPN
ejde-1812	556	13	∈	∈	PROPN
ejde-1812	556	14	(	(	PUNCT
ejde-1812	556	15	1−	1−	NUM
ejde-1812	556	16	1	1	NUM
ejde-1812	556	17	n3	n3	NOUN
ejde-1812	556	18	,	,	PUNCT
ejde-1812	556	19	1	1	NUM
ejde-1812	556	20	]	]	PUNCT
ejde-1812	556	21	,	,	PUNCT
ejde-1812	556	22	for	for	ADP
ejde-1812	556	23	n	n	PRON
ejde-1812	556	24	∈	∈	PROPN
ejde-1812	556	25	n+	n+	PROPN
ejde-1812	556	26	.	.	PUNCT
ejde-1812	557	1	so	so	ADV
ejde-1812	557	2	,	,	PUNCT
ejde-1812	557	3	for	for	ADP
ejde-1812	557	4	each	each	DET
ejde-1812	557	5	given	give	VERB
ejde-1812	557	6	function	function	NOUN
ejde-1812	557	7	h	h	PROPN
ejde-1812	557	8	(	(	PUNCT
ejde-1812	557	9	·	·	PUNCT
ejde-1812	557	10	)	)	PUNCT
ejde-1812	557	11	∈	∈	PROPN
ejde-1812	557	12	l2(j	l2(j	PROPN
ejde-1812	557	13	,	,	PUNCT
ejde-1812	557	14	x	x	NOUN
ejde-1812	557	15	)	)	PUNCT
ejde-1812	557	16	,	,	PUNCT
ejde-1812	557	17	there	there	PRON
ejde-1812	557	18	exists	exist	VERB
ejde-1812	557	19	u	u	NOUN
ejde-1812	557	20	(	(	PUNCT
ejde-1812	557	21	·	·	PUNCT
ejde-1812	557	22	)	)	PUNCT
ejde-1812	557	23	∈	∈	NOUN
ejde-1812	557	24	v	v	ADP
ejde-1812	557	25	such	such	ADJ
ejde-1812	557	26	that∫	that∫	NOUN
ejde-1812	557	27	1	1	NUM
ejde-1812	557	28	0	0	NUM
ejde-1812	558	1	kα(1−	kα(1−	PROPN
ejde-1812	558	2	ψ(s))ψ′(s)bu(s)ds	ψ(s))ψ′(s)bu(s)ds	PROPN
ejde-1812	558	3	=	=	SYM
ejde-1812	558	4	∫	∫	PROPN
ejde-1812	558	5	1	1	NUM
ejde-1812	558	6	0	0	NUM
ejde-1812	558	7	kα(1−	kα(1−	PROPN
ejde-1812	558	8	ψ(s))ψ′(s)h(s)ds	ψ(s))ψ′(s)h(s)ds	PROPN
ejde-1812	558	9	,	,	PUNCT
ejde-1812	558	10	which	which	PRON
ejde-1812	558	11	implies	imply	VERB
ejde-1812	558	12	that	that	SCONJ
ejde-1812	558	13	condition	condition	NOUN
ejde-1812	558	14	(	(	PUNCT
ejde-1812	558	15	3.5	3.5	NUM
ejde-1812	558	16	)	)	PUNCT
ejde-1812	558	17	of	of	ADP
ejde-1812	558	18	(	(	PUNCT
ejde-1812	558	19	h4	h4	NOUN
ejde-1812	558	20	)	)	PUNCT
ejde-1812	558	21	holds	hold	VERB
ejde-1812	558	22	.	.	PUNCT
ejde-1812	559	1	moreover	moreover	ADV
ejde-1812	559	2	,	,	PUNCT
ejde-1812	559	3	we	we	PRON
ejde-1812	559	4	can	can	AUX
ejde-1812	559	5	obtain	obtain	VERB
ejde-1812	559	6	∥bu(·)∥2	∥bu(·)∥2	NOUN
ejde-1812	559	7	=	=	NOUN
ejde-1812	560	1	∞∑	∞∑	NUM
ejde-1812	560	2	n=1	n=1	NUM
ejde-1812	560	3	∫	∫	PROPN
ejde-1812	560	4	1	1	NUM
ejde-1812	560	5	1−	1−	NUM
ejde-1812	560	6	1	1	NUM
ejde-1812	560	7	n3	n3	NOUN
ejde-1812	560	8	|u(t)|2dt	|u(t)|2dt	NOUN
ejde-1812	560	9	=	=	PUNCT
ejde-1812	560	10	(	(	PUNCT
ejde-1812	560	11	1−	1−	NUM
ejde-1812	560	12	e−ψ(3	e−ψ(3	NOUN
ejde-1812	560	13	)	)	PUNCT
ejde-1812	560	14	)	)	PUNCT
ejde-1812	560	15	−1	−1	NOUN
ejde-1812	561	1	∞∑	∞∑	NUM
ejde-1812	561	2	n=1	n=1	PUNCT
ejde-1812	561	3	3n3l2n	3n3l2n	NUM
ejde-1812	561	4	=	=	SYM
ejde-1812	561	5	4	4	NUM
ejde-1812	561	6	3	3	NUM
ejde-1812	561	7	(	(	PUNCT
ejde-1812	561	8	1−	1−	NUM
ejde-1812	561	9	e−ψ(3	e−ψ(3	NOUN
ejde-1812	561	10	)	)	PUNCT
ejde-1812	561	11	)	)	PUNCT
ejde-1812	561	12	−1	−1	NOUN
ejde-1812	562	1	∞∑	∞∑	NUM
ejde-1812	562	2	n=1	n=1	PROPN
ejde-1812	562	3	(	(	PUNCT
ejde-1812	562	4	1−	1−	NUM
ejde-1812	562	5	e−ψ(3)n	e−ψ(3)n	ADP
ejde-1812	562	6	3	3	NUM
ejde-1812	562	7	)	)	PUNCT
ejde-1812	562	8	∫	∫	PROPN
ejde-1812	563	1	1	1	NUM
ejde-1812	563	2	0	0	NUM
ejde-1812	563	3	|hn(t)|2dt	|hn(t)|2dt	NUM
ejde-1812	563	4	≤	≤	NUM
ejde-1812	563	5	4	4	NUM
ejde-1812	563	6	3	3	NUM
ejde-1812	563	7	(	(	PUNCT
ejde-1812	563	8	1−	1−	NUM
ejde-1812	563	9	e−ψ(3	e−ψ(3	NOUN
ejde-1812	563	10	)	)	PUNCT
ejde-1812	563	11	)	)	PUNCT
ejde-1812	563	12	−1	−1	NOUN
ejde-1812	563	13	|h(·)|2	|h(·)|2	NOUN
ejde-1812	563	14	.	.	PUNCT
ejde-1812	564	1	hence	hence	ADV
ejde-1812	564	2	,	,	PUNCT
ejde-1812	564	3	condition	condition	NOUN
ejde-1812	564	4	(	(	PUNCT
ejde-1812	564	5	3.6	3.6	NUM
ejde-1812	564	6	)	)	PUNCT
ejde-1812	564	7	of	of	ADP
ejde-1812	564	8	(	(	PUNCT
ejde-1812	564	9	h4	h4	NOUN
ejde-1812	564	10	)	)	PUNCT
ejde-1812	564	11	is	be	AUX
ejde-1812	564	12	also	also	ADV
ejde-1812	564	13	satisfied	satisfied	ADJ
ejde-1812	564	14	,	,	PUNCT
ejde-1812	564	15	and	and	CCONJ
ejde-1812	564	16	if	if	SCONJ
ejde-1812	564	17	4	4	NUM
ejde-1812	564	18	√	√	VERB
ejde-1812	564	19	15	15	NUM
ejde-1812	564	20	9(1−	9(1−	NUM
ejde-1812	564	21	e−ψ(3))γ	e−ψ(3))γ	NOUN
ejde-1812	564	22	(	(	PUNCT
ejde-1812	564	23	45	45	NUM
ejde-1812	564	24	)	)	PUNCT
ejde-1812	564	25	ℓ3e	ℓ3e	ADV
ejde-1812	564	26	4	4	NUM
ejde-1812	564	27	5	5	NUM
ejde-1812	564	28	(	(	PUNCT
ejde-1812	564	29	ℓ3	ℓ3	PROPN
ejde-1812	564	30	)	)	PUNCT
ejde-1812	564	31	<	<	X
ejde-1812	564	32	1	1	NUM
ejde-1812	564	33	,	,	PUNCT
ejde-1812	564	34	then	then	ADV
ejde-1812	564	35	problem	problem	NOUN
ejde-1812	564	36	(	(	PUNCT
ejde-1812	564	37	5.1	5.1	NUM
ejde-1812	564	38	)	)	PUNCT
ejde-1812	564	39	is	be	AUX
ejde-1812	564	40	approximately	approximately	ADV
ejde-1812	564	41	controllable	controllable	ADJ
ejde-1812	564	42	on	on	ADP
ejde-1812	564	43	j	j	PROPN
ejde-1812	564	44	.	.	PUNCT
ejde-1812	565	1	acknowledgments	acknowledgment	NOUN
ejde-1812	565	2	.	.	PUNCT
ejde-1812	566	1	the	the	DET
ejde-1812	566	2	authors	author	NOUN
ejde-1812	566	3	would	would	AUX
ejde-1812	566	4	like	like	VERB
ejde-1812	566	5	to	to	PART
ejde-1812	566	6	thank	thank	VERB
ejde-1812	566	7	the	the	DET
ejde-1812	566	8	anonymous	anonymous	ADJ
ejde-1812	566	9	referee	referee	NOUN
ejde-1812	566	10	for	for	ADP
ejde-1812	566	11	the	the	DET
ejde-1812	566	12	valuable	valuable	ADJ
ejde-1812	566	13	comments	comment	NOUN
ejde-1812	566	14	and	and	CCONJ
ejde-1812	566	15	suggestions	suggestion	NOUN
ejde-1812	566	16	.	.	PUNCT
ejde-1812	567	1	the	the	DET
ejde-1812	567	2	work	work	NOUN
ejde-1812	567	3	was	be	AUX
ejde-1812	567	4	supported	support	VERB
ejde-1812	567	5	partly	partly	ADV
ejde-1812	567	6	by	by	ADP
ejde-1812	567	7	the	the	DET
ejde-1812	567	8	nsf	nsf	PROPN
ejde-1812	567	9	of	of	ADP
ejde-1812	567	10	china	china	PROPN
ejde-1812	567	11	(	(	PUNCT
ejde-1812	567	12	12371116	12371116	NUM
ejde-1812	567	13	,	,	PUNCT
ejde-1812	567	14	12171094	12171094	NUM
ejde-1812	567	15	)	)	PUNCT
ejde-1812	567	16	,	,	PUNCT
ejde-1812	567	17	and	and	CCONJ
ejde-1812	567	18	by	by	ADP
ejde-1812	567	19	the	the	DET
ejde-1812	567	20	shanghai	shanghai	PROPN
ejde-1812	567	21	key	key	PROPN
ejde-1812	567	22	laboratory	laboratory	PROPN
ejde-1812	567	23	for	for	ADP
ejde-1812	567	24	contemporary	contemporary	ADJ
ejde-1812	567	25	applied	apply	VERB
ejde-1812	567	26	mathematics	mathematic	NOUN
ejde-1812	567	27	(	(	PUNCT
ejde-1812	567	28	08dz2271900	08dz2271900	NUM
ejde-1812	567	29	)	)	PUNCT
ejde-1812	567	30	.	.	PUNCT
ejde-1812	568	1	16	16	NUM
ejde-1812	568	2	j.	j.	PROPN
ejde-1812	568	3	liang	liang	PROPN
ejde-1812	568	4	,	,	PUNCT
ejde-1812	568	5	y.	y.	PROPN
ejde-1812	568	6	mu	mu	PROPN
ejde-1812	568	7	,	,	PUNCT
ejde-1812	568	8	t.-j	t.-j	PROPN
ejde-1812	568	9	.	.	PUNCT
ejde-1812	569	1	xiao	xiao	PROPN
ejde-1812	569	2	ejde-2025/109	ejde-2025/109	ADJ
ejde-1812	569	3	references	reference	NOUN
ejde-1812	569	4	[	[	X
ejde-1812	569	5	1	1	NUM
ejde-1812	569	6	]	]	PUNCT
ejde-1812	569	7	r.	r.	PROPN
ejde-1812	569	8	almeida	almeida	PROPN
ejde-1812	569	9	;	;	PUNCT
ejde-1812	569	10	a	a	DET
ejde-1812	569	11	caputo	caputo	PROPN
ejde-1812	569	12	fractional	fractional	PROPN
ejde-1812	569	13	derivative	derivative	NOUN
ejde-1812	569	14	of	of	ADP
ejde-1812	569	15	a	a	DET
ejde-1812	569	16	function	function	NOUN
ejde-1812	569	17	with	with	ADP
ejde-1812	569	18	respect	respect	NOUN
ejde-1812	569	19	to	to	ADP
ejde-1812	569	20	another	another	DET
ejde-1812	569	21	function	function	NOUN
ejde-1812	569	22	,	,	PUNCT
ejde-1812	569	23	commun	commun	PROPN
ejde-1812	569	24	.	.	PUNCT
ejde-1812	570	1	nonlinear	nonlinear	PROPN
ejde-1812	570	2	.	.	PUNCT
ejde-1812	571	1	sci	sci	PROPN
ejde-1812	571	2	.	.	PUNCT
ejde-1812	571	3	numer	numer	PROPN
ejde-1812	571	4	.	.	PUNCT
ejde-1812	572	1	simulat	simulat	NOUN
ejde-1812	572	2	.	.	PUNCT
ejde-1812	573	1	44	44	NUM
ejde-1812	573	2	(	(	PUNCT
ejde-1812	573	3	2017	2017	NUM
ejde-1812	573	4	)	)	PUNCT
ejde-1812	573	5	,	,	PUNCT
ejde-1812	573	6	460	460	NUM
ejde-1812	573	7	-	-	SYM
ejde-1812	573	8	481	481	NUM
ejde-1812	573	9	.	.	PUNCT
ejde-1812	574	1	[	[	X
ejde-1812	574	2	2	2	NUM
ejde-1812	574	3	]	]	X
ejde-1812	574	4	d.	d.	PROPN
ejde-1812	574	5	baleanu	baleanu	PROPN
ejde-1812	574	6	,	,	PUNCT
ejde-1812	574	7	s.	s.	PROPN
ejde-1812	574	8	i.	i.	PROPN
ejde-1812	574	9	muslih	muslih	PROPN
ejde-1812	574	10	;	;	PUNCT
ejde-1812	574	11	about	about	ADP
ejde-1812	574	12	fractional	fractional	ADJ
ejde-1812	574	13	supersymmetric	supersymmetric	ADJ
ejde-1812	574	14	quantum	quantum	NOUN
ejde-1812	574	15	mechanics	mechanic	NOUN
ejde-1812	574	16	,	,	PUNCT
ejde-1812	574	17	czech	czech	PROPN
ejde-1812	574	18	.	.	PUNCT
ejde-1812	575	1	j.	j.	PROPN
ejde-1812	575	2	physics	physics	PROPN
ejde-1812	575	3	,	,	PUNCT
ejde-1812	575	4	(	(	PUNCT
ejde-1812	575	5	9	9	X
ejde-1812	575	6	)	)	PUNCT
ejde-1812	575	7	55	55	NUM
ejde-1812	575	8	(	(	PUNCT
ejde-1812	575	9	2005	2005	NUM
ejde-1812	575	10	)	)	PUNCT
ejde-1812	575	11	,	,	PUNCT
ejde-1812	575	12	1063	1063	NUM
ejde-1812	575	13	-	-	SYM
ejde-1812	575	14	1066	1066	NUM
ejde-1812	575	15	.	.	PUNCT
ejde-1812	576	1	[	[	X
ejde-1812	576	2	3	3	X
ejde-1812	576	3	]	]	X
ejde-1812	576	4	d.	d.	PROPN
ejde-1812	576	5	n.	n.	PROPN
ejde-1812	576	6	chalishajar	chalishajar	PROPN
ejde-1812	576	7	,	,	PUNCT
ejde-1812	576	8	f.	f.	PROPN
ejde-1812	576	9	s.	s.	PROPN
ejde-1812	576	10	acharya	acharya	PROPN
ejde-1812	576	11	;	;	PUNCT
ejde-1812	576	12	controllability	controllability	NOUN
ejde-1812	576	13	of	of	ADP
ejde-1812	576	14	second	second	ADJ
ejde-1812	576	15	order	order	NOUN
ejde-1812	576	16	semi	semi	ADJ
ejde-1812	576	17	-	-	ADJ
ejde-1812	576	18	linear	linear	ADJ
ejde-1812	576	19	neutral	neutral	ADJ
ejde-1812	576	20	impulsive	impulsive	ADJ
ejde-1812	576	21	differential	differential	ADJ
ejde-1812	576	22	inclusions	inclusion	NOUN
ejde-1812	576	23	on	on	ADP
ejde-1812	576	24	unbounded	unbounded	ADJ
ejde-1812	576	25	domain	domain	NOUN
ejde-1812	576	26	with	with	ADP
ejde-1812	576	27	infinite	infinite	ADJ
ejde-1812	576	28	delay	delay	NOUN
ejde-1812	576	29	in	in	ADP
ejde-1812	576	30	banach	banach	NOUN
ejde-1812	576	31	spaces	space	NOUN
ejde-1812	576	32	,	,	PUNCT
ejde-1812	576	33	bull	bull	NOUN
ejde-1812	576	34	.	.	PUNCT
ejde-1812	577	1	korean	korean	ADJ
ejde-1812	577	2	math	math	PROPN
ejde-1812	577	3	.	.	PUNCT
ejde-1812	578	1	soc	soc	PROPN
ejde-1812	578	2	.	.	PUNCT
ejde-1812	579	1	48	48	NUM
ejde-1812	579	2	(	(	PUNCT
ejde-1812	579	3	2011	2011	NUM
ejde-1812	579	4	)	)	PUNCT
ejde-1812	579	5	,	,	PUNCT
ejde-1812	579	6	813	813	NUM
ejde-1812	579	7	-	-	SYM
ejde-1812	579	8	838	838	NUM
ejde-1812	579	9	.	.	PUNCT
ejde-1812	580	1	[	[	X
ejde-1812	580	2	4	4	X
ejde-1812	580	3	]	]	X
ejde-1812	580	4	d.	d.	PROPN
ejde-1812	580	5	n.	n.	PROPN
ejde-1812	580	6	chalishajar	chalishajar	PROPN
ejde-1812	580	7	,	,	PUNCT
ejde-1812	580	8	a.	a.	NOUN
ejde-1812	580	9	anguraj	anguraj	PROPN
ejde-1812	580	10	,	,	PUNCT
ejde-1812	580	11	k.	k.	PROPN
ejde-1812	580	12	malar	malar	PROPN
ejde-1812	580	13	,	,	PUNCT
ejde-1812	580	14	k.	k.	PROPN
ejde-1812	580	15	karthikeyan	karthikeyan	PROPN
ejde-1812	580	16	;	;	PUNCT
ejde-1812	580	17	a	a	DET
ejde-1812	580	18	study	study	NOUN
ejde-1812	580	19	of	of	ADP
ejde-1812	580	20	controllability	controllability	NOUN
ejde-1812	580	21	of	of	ADP
ejde-1812	580	22	impulsive	impulsive	ADJ
ejde-1812	580	23	neutral	neutral	ADJ
ejde-1812	580	24	evolution	evolution	NOUN
ejde-1812	580	25	integro	integro	ADJ
ejde-1812	580	26	-	-	PUNCT
ejde-1812	580	27	differential	differential	NOUN
ejde-1812	580	28	equations	equation	NOUN
ejde-1812	580	29	with	with	ADP
ejde-1812	580	30	state	state	NOUN
ejde-1812	580	31	-	-	PUNCT
ejde-1812	580	32	dependent	dependent	ADJ
ejde-1812	580	33	delay	delay	NOUN
ejde-1812	580	34	in	in	ADP
ejde-1812	580	35	banach	banach	NOUN
ejde-1812	580	36	spaces	space	NOUN
ejde-1812	580	37	,	,	PUNCT
ejde-1812	580	38	mathematics	mathematic	NOUN
ejde-1812	580	39	,	,	PUNCT
ejde-1812	580	40	4	4	NUM
ejde-1812	580	41	(	(	PUNCT
ejde-1812	580	42	2016	2016	NUM
ejde-1812	580	43	)	)	PUNCT
ejde-1812	580	44	,	,	PUNCT
ejde-1812	580	45	60	60	NUM
ejde-1812	580	46	,	,	PUNCT
ejde-1812	580	47	doi	doi	NOUN
ejde-1812	580	48	:	:	PUNCT
ejde-1812	580	49	10.3390	10.3390	NUM
ejde-1812	580	50	/	/	SYM
ejde-1812	580	51	math4040060	math4040060	PROPN
ejde-1812	580	52	.	.	PUNCT
ejde-1812	581	1	[	[	X
ejde-1812	581	2	5	5	X
ejde-1812	581	3	]	]	PUNCT
ejde-1812	581	4	d.	d.	PROPN
ejde-1812	581	5	n.	n.	PROPN
ejde-1812	581	6	chalishajar	chalishajar	PROPN
ejde-1812	581	7	,	,	PUNCT
ejde-1812	581	8	k.	k.	PROPN
ejde-1812	581	9	karthikeyan	karthikeyan	PROPN
ejde-1812	581	10	;	;	PUNCT
ejde-1812	581	11	boundary	boundary	ADJ
ejde-1812	581	12	value	value	NOUN
ejde-1812	581	13	problems	problem	NOUN
ejde-1812	581	14	for	for	ADP
ejde-1812	581	15	impulsive	impulsive	ADJ
ejde-1812	581	16	fractional	fractional	ADJ
ejde-1812	581	17	evolution	evolution	NOUN
ejde-1812	581	18	integrodifferential	integrodifferential	ADJ
ejde-1812	581	19	equations	equation	NOUN
ejde-1812	581	20	with	with	ADP
ejde-1812	581	21	gronwall	gronwall	PROPN
ejde-1812	581	22	’s	’s	PART
ejde-1812	581	23	inequality	inequality	NOUN
ejde-1812	581	24	in	in	ADP
ejde-1812	581	25	banach	banach	NOUN
ejde-1812	581	26	spaces	space	NOUN
ejde-1812	581	27	,	,	PUNCT
ejde-1812	581	28	discontin	discontin	PROPN
ejde-1812	581	29	.	.	PUNCT
ejde-1812	581	30	nonlinearity	nonlinearity	NOUN
ejde-1812	581	31	complex	complex	NOUN
ejde-1812	581	32	.	.	PUNCT
ejde-1812	582	1	3	3	NUM
ejde-1812	582	2	(	(	PUNCT
ejde-1812	582	3	2014	2014	NUM
ejde-1812	582	4	)	)	PUNCT
ejde-1812	582	5	,	,	PUNCT
ejde-1812	582	6	33	33	NUM
ejde-1812	582	7	-	-	SYM
ejde-1812	582	8	48	48	NUM
ejde-1812	582	9	.	.	PUNCT
ejde-1812	583	1	[	[	X
ejde-1812	583	2	6	6	NUM
ejde-1812	583	3	]	]	PUNCT
ejde-1812	583	4	d.	d.	PROPN
ejde-1812	583	5	n.	n.	PROPN
ejde-1812	583	6	chalishajar	chalishajar	PROPN
ejde-1812	583	7	,	,	PUNCT
ejde-1812	583	8	k.	k.	PROPN
ejde-1812	583	9	ravikumar	ravikumar	PROPN
ejde-1812	583	10	,	,	PUNCT
ejde-1812	583	11	k.	k.	PROPN
ejde-1812	583	12	ramkumar	ramkumar	PROPN
ejde-1812	583	13	,	,	PUNCT
ejde-1812	583	14	a.	a.	NOUN
ejde-1812	583	15	anguraj	anguraj	PROPN
ejde-1812	583	16	;	;	PUNCT
ejde-1812	583	17	null	null	ADJ
ejde-1812	583	18	controllability	controllability	NOUN
ejde-1812	583	19	of	of	ADP
ejde-1812	583	20	hilfer	hilfer	NOUN
ejde-1812	583	21	fractional	fractional	ADJ
ejde-1812	583	22	stochastic	stochastic	ADJ
ejde-1812	583	23	differential	differential	ADJ
ejde-1812	583	24	equations	equation	NOUN
ejde-1812	583	25	with	with	ADP
ejde-1812	583	26	nonlocal	nonlocal	ADJ
ejde-1812	583	27	conditions	condition	NOUN
ejde-1812	583	28	,	,	PUNCT
ejde-1812	583	29	numer	numer	NOUN
ejde-1812	583	30	.	.	PUNCT
ejde-1812	584	1	algebra	algebra	PROPN
ejde-1812	584	2	control	control	PROPN
ejde-1812	584	3	optim	optim	PROPN
ejde-1812	584	4	.	.	PUNCT
ejde-1812	585	1	(	(	PUNCT
ejde-1812	585	2	2	2	NUM
ejde-1812	585	3	)	)	PUNCT
ejde-1812	585	4	14	14	NUM
ejde-1812	585	5	(	(	PUNCT
ejde-1812	585	6	2024	2024	NUM
ejde-1812	585	7	)	)	PUNCT
ejde-1812	585	8	,	,	PUNCT
ejde-1812	585	9	3	3	NUM
ejde-1812	585	10	22	22	NUM
ejde-1812	585	11	-	-	SYM
ejde-1812	585	12	338	338	NUM
ejde-1812	585	13	.	.	PUNCT
ejde-1812	586	1	[	[	X
ejde-1812	586	2	7	7	X
ejde-1812	586	3	]	]	X
ejde-1812	586	4	d.	d.	PROPN
ejde-1812	586	5	n.	n.	PROPN
ejde-1812	586	6	chalishajar	chalishajar	PROPN
ejde-1812	586	7	,	,	PUNCT
ejde-1812	586	8	d.	d.	PROPN
ejde-1812	586	9	kasinathan	kasinathan	PROPN
ejde-1812	586	10	,	,	PUNCT
ejde-1812	586	11	r.	r.	PROPN
ejde-1812	586	12	kasinathan	kasinathan	PROPN
ejde-1812	586	13	,	,	PUNCT
ejde-1812	586	14	r.	r.	PROPN
ejde-1812	586	15	kasinathan	kasinathan	PROPN
ejde-1812	586	16	;	;	PUNCT
ejde-1812	586	17	ulam	ulam	PROPN
ejde-1812	586	18	-	-	PUNCT
ejde-1812	586	19	hyers	hyer	NOUN
ejde-1812	586	20	-	-	PUNCT
ejde-1812	586	21	rassias	rassias	PROPN
ejde-1812	586	22	stability	stability	NOUN
ejde-1812	586	23	of	of	ADP
ejde-1812	586	24	hilfer	hilfer	NOUN
ejde-1812	586	25	fractional	fractional	ADJ
ejde-1812	586	26	stochastic	stochastic	ADJ
ejde-1812	586	27	impulsive	impulsive	ADJ
ejde-1812	586	28	differential	differential	ADJ
ejde-1812	586	29	equations	equation	NOUN
ejde-1812	586	30	with	with	ADP
ejde-1812	586	31	non	non	ADJ
ejde-1812	586	32	-	-	ADJ
ejde-1812	586	33	local	local	ADJ
ejde-1812	586	34	condition	condition	NOUN
ejde-1812	586	35	via	via	ADP
ejde-1812	586	36	time	time	NOUN
ejde-1812	586	37	-	-	PUNCT
ejde-1812	586	38	changed	change	VERB
ejde-1812	586	39	brownian	brownian	ADJ
ejde-1812	586	40	motion	motion	NOUN
ejde-1812	586	41	followed	follow	VERB
ejde-1812	586	42	by	by	ADP
ejde-1812	586	43	the	the	DET
ejde-1812	586	44	currency	currency	NOUN
ejde-1812	586	45	options	option	NOUN
ejde-1812	586	46	pricing	pricing	NOUN
ejde-1812	586	47	model	model	NOUN
ejde-1812	586	48	,	,	PUNCT
ejde-1812	586	49	chaos	chaos	NOUN
ejde-1812	586	50	solitons	soliton	NOUN
ejde-1812	586	51	fractals	fractal	NOUN
ejde-1812	586	52	,	,	PUNCT
ejde-1812	586	53	197	197	NUM
ejde-1812	586	54	(	(	PUNCT
ejde-1812	586	55	2025	2025	NUM
ejde-1812	586	56	)	)	PUNCT
ejde-1812	586	57	.	.	PUNCT
ejde-1812	587	1	[	[	X
ejde-1812	587	2	8	8	NUM
ejde-1812	587	3	]	]	PUNCT
ejde-1812	587	4	a.	a.	NOUN
ejde-1812	587	5	chatterjee	chatterjee	PROPN
ejde-1812	587	6	;	;	PUNCT
ejde-1812	587	7	statistical	statistical	ADJ
ejde-1812	587	8	origins	origin	NOUN
ejde-1812	587	9	of	of	ADP
ejde-1812	587	10	fractional	fractional	ADJ
ejde-1812	587	11	derivatives	derivative	NOUN
ejde-1812	587	12	in	in	ADP
ejde-1812	587	13	viscoelasticity	viscoelasticity	NOUN
ejde-1812	587	14	,	,	PUNCT
ejde-1812	587	15	j.	j.	PROPN
ejde-1812	587	16	sound	sound	PROPN
ejde-1812	587	17	vib	vib	PROPN
ejde-1812	587	18	.	.	PROPN
ejde-1812	587	19	284	284	NUM
ejde-1812	587	20	(	(	PUNCT
ejde-1812	587	21	2005	2005	NUM
ejde-1812	587	22	)	)	PUNCT
ejde-1812	587	23	,	,	PUNCT
ejde-1812	587	24	12401245	12401245	NUM
ejde-1812	587	25	.	.	PUNCT
ejde-1812	588	1	[	[	X
ejde-1812	588	2	9	9	NUM
ejde-1812	588	3	]	]	X
ejde-1812	588	4	c.	c.	PROPN
ejde-1812	588	5	cuevas	cuevas	PROPN
ejde-1812	588	6	,	,	PUNCT
ejde-1812	588	7	j.	j.	PROPN
ejde-1812	588	8	c.	c.	PROPN
ejde-1812	588	9	de	de	PROPN
ejde-1812	588	10	souza	souza	PROPN
ejde-1812	588	11	;	;	PUNCT
ejde-1812	588	12	s	s	X
ejde-1812	588	13	-	-	PUNCT
ejde-1812	588	14	asymptotically	asymptotically	ADV
ejde-1812	588	15	ω	ω	ADJ
ejde-1812	588	16	-	-	ADJ
ejde-1812	588	17	periodic	periodic	ADJ
ejde-1812	588	18	solutions	solution	NOUN
ejde-1812	588	19	of	of	ADP
ejde-1812	588	20	semilinear	semilinear	ADJ
ejde-1812	588	21	fractional	fractional	ADJ
ejde-1812	588	22	integro	integro	ADJ
ejde-1812	588	23	-	-	PUNCT
ejde-1812	588	24	differential	differential	NOUN
ejde-1812	588	25	equations	equation	NOUN
ejde-1812	588	26	,	,	PUNCT
ejde-1812	588	27	appl	appl	PROPN
ejde-1812	588	28	.	.	PROPN
ejde-1812	588	29	math	math	PROPN
ejde-1812	588	30	.	.	PUNCT
ejde-1812	589	1	lett	lett	PROPN
ejde-1812	589	2	.	.	PUNCT
ejde-1812	590	1	22	22	NUM
ejde-1812	590	2	(	(	PUNCT
ejde-1812	590	3	2009	2009	NUM
ejde-1812	590	4	)	)	PUNCT
ejde-1812	590	5	,	,	PUNCT
ejde-1812	590	6	865	865	NUM
ejde-1812	590	7	-	-	SYM
ejde-1812	590	8	870	870	NUM
ejde-1812	590	9	.	.	PUNCT
ejde-1812	591	1	[	[	X
ejde-1812	591	2	10	10	NUM
ejde-1812	591	3	]	]	X
ejde-1812	591	4	v.	v.	PROPN
ejde-1812	591	5	del	del	PROPN
ejde-1812	591	6	,	,	PUNCT
ejde-1812	591	7	a.	a.	NOUN
ejde-1812	591	8	ciarmiello	ciarmiello	PROPN
ejde-1812	591	9	,	,	PUNCT
ejde-1812	591	10	l.	l.	PROPN
ejde-1812	591	11	pace	pace	PROPN
ejde-1812	591	12	,	,	PUNCT
ejde-1812	591	13	m.	m.	NOUN
ejde-1812	591	14	potena	potena	PROPN
ejde-1812	591	15	,	,	PUNCT
ejde-1812	591	16	m.	m.	NOUN
ejde-1812	591	17	carriero	carriero	NOUN
ejde-1812	591	18	;	;	PUNCT
ejde-1812	591	19	existence	existence	NOUN
ejde-1812	591	20	and	and	CCONJ
ejde-1812	591	21	uniqueness	uniqueness	NOUN
ejde-1812	591	22	of	of	ADP
ejde-1812	591	23	mild	mild	ADJ
ejde-1812	591	24	solution	solution	NOUN
ejde-1812	591	25	for	for	ADP
ejde-1812	591	26	an	an	DET
ejde-1812	591	27	impulsive	impulsive	ADJ
ejde-1812	591	28	neutral	neutral	ADJ
ejde-1812	591	29	fractional	fractional	ADJ
ejde-1812	591	30	integro	integro	ADJ
ejde-1812	591	31	-	-	PUNCT
ejde-1812	591	32	differential	differential	NOUN
ejde-1812	591	33	equation	equation	NOUN
ejde-1812	591	34	with	with	ADP
ejde-1812	591	35	infinite	infinite	ADJ
ejde-1812	591	36	delay	delay	NOUN
ejde-1812	591	37	,	,	PUNCT
ejde-1812	591	38	math	math	NOUN
ejde-1812	591	39	.	.	PUNCT
ejde-1812	592	1	comput	comput	NOUN
ejde-1812	592	2	.	.	PUNCT
ejde-1812	593	1	modell	modell	PROPN
ejde-1812	593	2	.	.	PUNCT
ejde-1812	594	1	57	57	NUM
ejde-1812	594	2	(	(	PUNCT
ejde-1812	594	3	2013	2013	NUM
ejde-1812	594	4	)	)	PUNCT
ejde-1812	594	5	,	,	PUNCT
ejde-1812	594	6	3	3	NUM
ejde-1812	594	7	-	-	SYM
ejde-1812	594	8	4	4	NUM
ejde-1812	594	9	:	:	SYM
ejde-1812	594	10	754	754	NUM
ejde-1812	594	11	-	-	SYM
ejde-1812	594	12	763	763	NUM
ejde-1812	594	13	.	.	PUNCT
ejde-1812	595	1	[	[	X
ejde-1812	595	2	11	11	NUM
ejde-1812	595	3	]	]	PUNCT
ejde-1812	595	4	m.	m.	NOUN
ejde-1812	595	5	el	el	PROPN
ejde-1812	595	6	-	-	PUNCT
ejde-1812	595	7	borai	borai	NOUN
ejde-1812	595	8	;	;	PUNCT
ejde-1812	595	9	some	some	DET
ejde-1812	595	10	probability	probability	NOUN
ejde-1812	595	11	densities	density	NOUN
ejde-1812	595	12	and	and	CCONJ
ejde-1812	595	13	fundamental	fundamental	ADJ
ejde-1812	595	14	solutions	solution	NOUN
ejde-1812	595	15	of	of	ADP
ejde-1812	595	16	fractional	fractional	ADJ
ejde-1812	595	17	evolution	evolution	NOUN
ejde-1812	595	18	equations	equation	NOUN
ejde-1812	595	19	,	,	PUNCT
ejde-1812	595	20	chaos	chaos	NOUN
ejde-1812	595	21	solitons	soliton	NOUN
ejde-1812	595	22	fractals	fractal	NOUN
ejde-1812	595	23	,	,	PUNCT
ejde-1812	595	24	14	14	NUM
ejde-1812	595	25	(	(	PUNCT
ejde-1812	595	26	2002	2002	NUM
ejde-1812	595	27	)	)	PUNCT
ejde-1812	595	28	,	,	PUNCT
ejde-1812	595	29	433	433	NUM
ejde-1812	595	30	-	-	SYM
ejde-1812	595	31	440	440	NUM
ejde-1812	595	32	.	.	PUNCT
ejde-1812	596	1	[	[	X
ejde-1812	596	2	12	12	NUM
ejde-1812	596	3	]	]	X
ejde-1812	596	4	w.	w.	PROPN
ejde-1812	596	5	g.	g.	PROPN
ejde-1812	596	6	glöckle	glöckle	PROPN
ejde-1812	596	7	,	,	PUNCT
ejde-1812	596	8	t.	t.	PROPN
ejde-1812	596	9	f.	f.	PROPN
ejde-1812	596	10	nonnenmacher	nonnenmacher	PROPN
ejde-1812	596	11	;	;	PUNCT
ejde-1812	596	12	a	a	DET
ejde-1812	596	13	fractional	fractional	ADJ
ejde-1812	596	14	calculus	calculus	NOUN
ejde-1812	596	15	approach	approach	NOUN
ejde-1812	596	16	to	to	ADP
ejde-1812	596	17	self	self	NOUN
ejde-1812	596	18	-	-	PUNCT
ejde-1812	596	19	similar	similar	ADJ
ejde-1812	596	20	protein	protein	NOUN
ejde-1812	596	21	dynamics	dynamic	NOUN
ejde-1812	596	22	,	,	PUNCT
ejde-1812	596	23	biophysical	biophysical	ADJ
ejde-1812	596	24	j.	j.	PROPN
ejde-1812	596	25	,	,	PUNCT
ejde-1812	596	26	68	68	NUM
ejde-1812	596	27	(	(	PUNCT
ejde-1812	596	28	1995	1995	NUM
ejde-1812	596	29	)	)	PUNCT
ejde-1812	596	30	,	,	PUNCT
ejde-1812	596	31	46	46	NUM
ejde-1812	596	32	-	-	SYM
ejde-1812	596	33	53	53	NUM
ejde-1812	596	34	.	.	PUNCT
ejde-1812	597	1	[	[	X
ejde-1812	597	2	13	13	NUM
ejde-1812	597	3	]	]	X
ejde-1812	597	4	h.	h.	PROPN
ejde-1812	597	5	gu	gu	PROPN
ejde-1812	597	6	,	,	PUNCT
ejde-1812	597	7	j.	j.	PROPN
ejde-1812	597	8	j.	j.	PROPN
ejde-1812	597	9	trujillo	trujillo	PROPN
ejde-1812	597	10	;	;	PUNCT
ejde-1812	597	11	existence	existence	NOUN
ejde-1812	597	12	of	of	ADP
ejde-1812	597	13	mild	mild	ADJ
ejde-1812	597	14	solution	solution	NOUN
ejde-1812	597	15	for	for	ADP
ejde-1812	597	16	evolution	evolution	NOUN
ejde-1812	597	17	equation	equation	NOUN
ejde-1812	597	18	with	with	ADP
ejde-1812	597	19	hilfer	hilfer	NOUN
ejde-1812	597	20	fractional	fractional	ADJ
ejde-1812	597	21	derivative	derivative	ADJ
ejde-1812	597	22	,	,	PUNCT
ejde-1812	597	23	appl	appl	PROPN
ejde-1812	597	24	.	.	PROPN
ejde-1812	597	25	math	math	PROPN
ejde-1812	597	26	.	.	PUNCT
ejde-1812	598	1	comput	comput	NOUN
ejde-1812	598	2	.	.	PUNCT
ejde-1812	598	3	,	,	PUNCT
ejde-1812	598	4	257	257	NUM
ejde-1812	598	5	(	(	PUNCT
ejde-1812	598	6	2015	2015	NUM
ejde-1812	598	7	)	)	PUNCT
ejde-1812	598	8	,	,	PUNCT
ejde-1812	598	9	344	344	NUM
ejde-1812	598	10	-	-	SYM
ejde-1812	598	11	354	354	NUM
ejde-1812	598	12	.	.	PUNCT
ejde-1812	599	1	[	[	X
ejde-1812	599	2	14	14	NUM
ejde-1812	599	3	]	]	PUNCT
ejde-1812	599	4	m.	m.	NOUN
ejde-1812	599	5	guo	guo	PROPN
ejde-1812	599	6	,	,	PUNCT
ejde-1812	599	7	x.	x.	PROPN
ejde-1812	599	8	xue	xue	PROPN
ejde-1812	599	9	,	,	PUNCT
ejde-1812	599	10	r.	r.	PROPN
ejde-1812	599	11	li	li	PROPN
ejde-1812	599	12	;	;	PUNCT
ejde-1812	599	13	controllability	controllability	NOUN
ejde-1812	599	14	of	of	ADP
ejde-1812	599	15	impulsive	impulsive	ADJ
ejde-1812	599	16	evolution	evolution	NOUN
ejde-1812	599	17	inclusions	inclusion	NOUN
ejde-1812	599	18	with	with	ADP
ejde-1812	599	19	nonlocal	nonlocal	ADJ
ejde-1812	599	20	conditions	condition	NOUN
ejde-1812	599	21	,	,	PUNCT
ejde-1812	599	22	j.	j.	PROPN
ejde-1812	599	23	optim	optim	PROPN
ejde-1812	599	24	.	.	PUNCT
ejde-1812	600	1	theory	theory	NOUN
ejde-1812	600	2	appl	appl	PROPN
ejde-1812	600	3	.	.	PROPN
ejde-1812	601	1	,	,	PUNCT
ejde-1812	601	2	120	120	NUM
ejde-1812	601	3	(	(	PUNCT
ejde-1812	601	4	2004	2004	NUM
ejde-1812	601	5	)	)	PUNCT
ejde-1812	601	6	,	,	PUNCT
ejde-1812	601	7	no	no	INTJ
ejde-1812	601	8	.	.	NOUN
ejde-1812	601	9	2	2	NUM
ejde-1812	601	10	,	,	PUNCT
ejde-1812	601	11	355	355	NUM
ejde-1812	601	12	-	-	SYM
ejde-1812	601	13	374	374	NUM
ejde-1812	601	14	.	.	PUNCT
ejde-1812	602	1	[	[	X
ejde-1812	602	2	15	15	NUM
ejde-1812	602	3	]	]	X
ejde-1812	602	4	d.	d.	PROPN
ejde-1812	602	5	henry	henry	PROPN
ejde-1812	602	6	;	;	PUNCT
ejde-1812	602	7	geometric	geometric	ADJ
ejde-1812	602	8	theory	theory	NOUN
ejde-1812	602	9	of	of	ADP
ejde-1812	602	10	semilinear	semilinear	PROPN
ejde-1812	602	11	parabolic	parabolic	PROPN
ejde-1812	602	12	equations	equation	NOUN
ejde-1812	602	13	,	,	PUNCT
ejde-1812	602	14	lecture	lecture	NOUN
ejde-1812	602	15	notes	note	NOUN
ejde-1812	602	16	in	in	ADP
ejde-1812	602	17	math	math	NOUN
ejde-1812	602	18	.	.	PUNCT
ejde-1812	603	1	vol	vol	NOUN
ejde-1812	603	2	.	.	PUNCT
ejde-1812	604	1	840	840	NUM
ejde-1812	604	2	,	,	PUNCT
ejde-1812	604	3	springerverlag	springerverlag	NOUN
ejde-1812	604	4	,	,	PUNCT
ejde-1812	604	5	new	new	PROPN
ejde-1812	604	6	york	york	PROPN
ejde-1812	604	7	/	/	SYM
ejde-1812	604	8	berlin	berlin	PROPN
ejde-1812	604	9	,	,	PUNCT
ejde-1812	604	10	1981	1981	NUM
ejde-1812	604	11	.	.	PUNCT
ejde-1812	605	1	[	[	X
ejde-1812	605	2	16	16	NUM
ejde-1812	605	3	]	]	X
ejde-1812	605	4	r.	r.	NOUN
ejde-1812	605	5	hilfer	hilfer	PROPN
ejde-1812	605	6	;	;	PUNCT
ejde-1812	605	7	applications	application	NOUN
ejde-1812	605	8	of	of	ADP
ejde-1812	605	9	fractional	fractional	ADJ
ejde-1812	605	10	calculus	calculus	NOUN
ejde-1812	605	11	in	in	ADP
ejde-1812	605	12	physics	physics	PROPN
ejde-1812	605	13	,	,	PUNCT
ejde-1812	605	14	world	world	NOUN
ejde-1812	605	15	scientific	scientific	PROPN
ejde-1812	605	16	,	,	PUNCT
ejde-1812	605	17	singapore	singapore	PROPN
ejde-1812	605	18	,	,	PUNCT
ejde-1812	605	19	2000	2000	NUM
ejde-1812	605	20	.	.	PUNCT
ejde-1812	606	1	[	[	X
ejde-1812	606	2	17	17	NUM
ejde-1812	606	3	]	]	X
ejde-1812	606	4	r.	r.	NOUN
ejde-1812	606	5	hilfer	hilfer	PROPN
ejde-1812	606	6	,	,	PUNCT
ejde-1812	606	7	y.	y.	PROPN
ejde-1812	606	8	luchko	luchko	PROPN
ejde-1812	606	9	,	,	PUNCT
ejde-1812	606	10	z.	z.	PROPN
ejde-1812	606	11	tomovski	tomovski	PROPN
ejde-1812	606	12	;	;	PUNCT
ejde-1812	606	13	operational	operational	ADJ
ejde-1812	606	14	method	method	NOUN
ejde-1812	606	15	for	for	ADP
ejde-1812	606	16	the	the	DET
ejde-1812	606	17	solution	solution	NOUN
ejde-1812	606	18	of	of	ADP
ejde-1812	606	19	fractional	fractional	ADJ
ejde-1812	606	20	differential	differential	ADJ
ejde-1812	606	21	equations	equation	NOUN
ejde-1812	606	22	with	with	ADP
ejde-1812	606	23	generalized	generalized	ADJ
ejde-1812	606	24	riemann	riemann	PROPN
ejde-1812	606	25	-	-	PUNCT
ejde-1812	606	26	liouville	liouville	VERB
ejde-1812	606	27	fractional	fractional	ADJ
ejde-1812	606	28	derivatives	derivative	NOUN
ejde-1812	606	29	,	,	PUNCT
ejde-1812	606	30	fract	fract	NOUN
ejde-1812	606	31	.	.	PUNCT
ejde-1812	607	1	calc	calc	PROPN
ejde-1812	607	2	.	.	PUNCT
ejde-1812	608	1	appl	appl	PROPN
ejde-1812	608	2	.	.	PROPN
ejde-1812	608	3	,	,	PUNCT
ejde-1812	608	4	12	12	NUM
ejde-1812	608	5	(	(	PUNCT
ejde-1812	608	6	2009	2009	NUM
ejde-1812	608	7	)	)	PUNCT
ejde-1812	608	8	,	,	PUNCT
ejde-1812	609	1	no	no	INTJ
ejde-1812	609	2	.	.	NOUN
ejde-1812	609	3	3	3	NUM
ejde-1812	609	4	,	,	PUNCT
ejde-1812	609	5	299	299	NUM
ejde-1812	609	6	-	-	SYM
ejde-1812	609	7	318	318	NUM
ejde-1812	609	8	.	.	PUNCT
ejde-1812	610	1	[	[	X
ejde-1812	610	2	18	18	NUM
ejde-1812	610	3	]	]	X
ejde-1812	610	4	r.	r.	PROPN
ejde-1812	610	5	e.	e.	PROPN
ejde-1812	610	6	kalman	kalman	PROPN
ejde-1812	610	7	;	;	PUNCT
ejde-1812	610	8	controllability	controllability	NOUN
ejde-1812	610	9	of	of	ADP
ejde-1812	610	10	linear	linear	PROPN
ejde-1812	610	11	dynamical	dynamical	ADJ
ejde-1812	610	12	systems	system	NOUN
ejde-1812	610	13	,	,	PUNCT
ejde-1812	610	14	contrib	contrib	PROPN
ejde-1812	610	15	.	.	PROPN
ejde-1812	610	16	diff	diff	PROPN
ejde-1812	610	17	.	.	PUNCT
ejde-1812	611	1	equ	equ	PROPN
ejde-1812	611	2	.	.	PUNCT
ejde-1812	612	1	(	(	PUNCT
ejde-1812	612	2	1	1	X
ejde-1812	612	3	)	)	PUNCT
ejde-1812	612	4	1	1	NUM
ejde-1812	612	5	(	(	PUNCT
ejde-1812	612	6	1963	1963	NUM
ejde-1812	612	7	)	)	PUNCT
ejde-1812	612	8	,	,	PUNCT
ejde-1812	612	9	189	189	NUM
ejde-1812	612	10	-	-	SYM
ejde-1812	612	11	213	213	NUM
ejde-1812	612	12	.	.	PUNCT
ejde-1812	613	1	[	[	X
ejde-1812	613	2	19	19	NUM
ejde-1812	613	3	]	]	PUNCT
ejde-1812	613	4	a.	a.	NOUN
ejde-1812	613	5	a.	a.	NOUN
ejde-1812	613	6	kilbas	kilbas	PROPN
ejde-1812	613	7	,	,	PUNCT
ejde-1812	613	8	h.	h.	PROPN
ejde-1812	613	9	m.	m.	PROPN
ejde-1812	613	10	srivastava	srivastava	PROPN
ejde-1812	613	11	,	,	PUNCT
ejde-1812	613	12	j.	j.	PROPN
ejde-1812	613	13	j.	j.	PROPN
ejde-1812	613	14	trujillo	trujillo	PROPN
ejde-1812	613	15	;	;	PUNCT
ejde-1812	613	16	theory	theory	NOUN
ejde-1812	613	17	and	and	CCONJ
ejde-1812	613	18	applications	application	NOUN
ejde-1812	613	19	of	of	ADP
ejde-1812	613	20	fractional	fractional	ADJ
ejde-1812	613	21	differential	differential	ADJ
ejde-1812	613	22	equaations	equaation	NOUN
ejde-1812	613	23	.	.	PUNCT
ejde-1812	614	1	in	in	ADP
ejde-1812	614	2	:	:	PUNCT
ejde-1812	614	3	north	north	NOUN
ejde-1812	614	4	-	-	PUNCT
ejde-1812	614	5	holland	holland	PROPN
ejde-1812	614	6	mathematics	mathematics	PROPN
ejde-1812	614	7	studies	study	NOUN
ejde-1812	614	8	,	,	PUNCT
ejde-1812	614	9	vol.204	vol.204	PROPN
ejde-1812	614	10	.	.	PUNCT
ejde-1812	615	1	elsevier	elsevier	PROPN
ejde-1812	615	2	,	,	PUNCT
ejde-1812	615	3	amsterdam	amsterdam	PROPN
ejde-1812	615	4	,	,	PUNCT
ejde-1812	615	5	2006	2006	NUM
ejde-1812	615	6	.	.	PUNCT
ejde-1812	616	1	[	[	X
ejde-1812	616	2	20	20	NUM
ejde-1812	616	3	]	]	PUNCT
ejde-1812	616	4	m.	m.	NOUN
ejde-1812	616	5	k]”of	k]”of	PROPN
ejde-1812	616	6	,	,	PUNCT
ejde-1812	616	7	c.	c.	PROPN
ejde-1812	616	8	corinth	corinth	PROPN
ejde-1812	616	9	,	,	PUNCT
ejde-1812	616	10	o.	o.	PROPN
ejde-1812	616	11	haferkamp	haferkamp	PROPN
ejde-1812	616	12	,	,	PUNCT
ejde-1812	616	13	t.	t.	PROPN
ejde-1812	616	14	f.	f.	PROPN
ejde-1812	616	15	nonnenmacher	nonnenmacher	PROPN
ejde-1812	616	16	;	;	PUNCT
ejde-1812	616	17	anomalous	anomalous	ADJ
ejde-1812	616	18	diffusion	diffusion	NOUN
ejde-1812	616	19	of	of	ADP
ejde-1812	616	20	water	water	NOUN
ejde-1812	616	21	in	in	ADP
ejde-1812	616	22	biological	biological	ADJ
ejde-1812	616	23	tissues	tissue	NOUN
ejde-1812	616	24	,	,	PUNCT
ejde-1812	616	25	biophysical	biophysical	ADJ
ejde-1812	616	26	j.	j.	PROPN
ejde-1812	616	27	70	70	NUM
ejde-1812	616	28	(	(	PUNCT
ejde-1812	616	29	1996	1996	NUM
ejde-1812	616	30	)	)	PUNCT
ejde-1812	616	31	,	,	PUNCT
ejde-1812	616	32	2950	2950	NUM
ejde-1812	616	33	-	-	SYM
ejde-1812	616	34	2958	2958	NUM
ejde-1812	616	35	.	.	PUNCT
ejde-1812	617	1	[	[	X
ejde-1812	617	2	21	21	NUM
ejde-1812	617	3	]	]	PUNCT
ejde-1812	617	4	s.	s.	PROPN
ejde-1812	617	5	kumar	kumar	PROPN
ejde-1812	617	6	,	,	PUNCT
ejde-1812	617	7	n.	n.	PROPN
ejde-1812	617	8	sukavanam	sukavanam	NOUN
ejde-1812	617	9	;	;	PUNCT
ejde-1812	617	10	approximate	approximate	ADJ
ejde-1812	617	11	controllability	controllability	NOUN
ejde-1812	617	12	of	of	ADP
ejde-1812	617	13	fractional	fractional	ADJ
ejde-1812	617	14	order	order	NOUN
ejde-1812	617	15	semilinear	semilinear	NOUN
ejde-1812	617	16	systems	system	NOUN
ejde-1812	617	17	with	with	ADP
ejde-1812	617	18	bounded	bounded	ADJ
ejde-1812	617	19	delay	delay	NOUN
ejde-1812	617	20	,	,	PUNCT
ejde-1812	617	21	j.	j.	PROPN
ejde-1812	617	22	diff	diff	PROPN
ejde-1812	617	23	.	.	PUNCT
ejde-1812	618	1	equ	equ	PROPN
ejde-1812	618	2	.	.	PROPN
ejde-1812	619	1	252	252	NUM
ejde-1812	619	2	(	(	PUNCT
ejde-1812	619	3	2012	2012	NUM
ejde-1812	619	4	)	)	PUNCT
ejde-1812	619	5	,	,	PUNCT
ejde-1812	619	6	6163	6163	NUM
ejde-1812	619	7	-	-	SYM
ejde-1812	619	8	6174	6174	NUM
ejde-1812	619	9	.	.	PUNCT
ejde-1812	620	1	[	[	X
ejde-1812	620	2	22	22	NUM
ejde-1812	620	3	]	]	X
ejde-1812	620	4	n.	n.	NOUN
ejde-1812	620	5	laskin	laskin	PROPN
ejde-1812	620	6	;	;	PUNCT
ejde-1812	620	7	fractional	fractional	ADJ
ejde-1812	620	8	quantum	quantum	ADJ
ejde-1812	620	9	mechanics	mechanic	NOUN
ejde-1812	620	10	and	and	CCONJ
ejde-1812	620	11	lévy	lévy	NUM
ejde-1812	620	12	path	path	NOUN
ejde-1812	620	13	integrals	integral	NOUN
ejde-1812	620	14	,	,	PUNCT
ejde-1812	620	15	phys	phy	NOUN
ejde-1812	620	16	.	.	PUNCT
ejde-1812	621	1	lett	lett	PROPN
ejde-1812	621	2	.	.	PUNCT
ejde-1812	622	1	a	a	DET
ejde-1812	622	2	268	268	NUM
ejde-1812	622	3	(	(	PUNCT
ejde-1812	622	4	2000	2000	NUM
ejde-1812	622	5	)	)	PUNCT
ejde-1812	622	6	,	,	PUNCT
ejde-1812	622	7	298	298	NUM
ejde-1812	622	8	-	-	SYM
ejde-1812	622	9	305	305	NUM
ejde-1812	622	10	.	.	PUNCT
ejde-1812	623	1	[	[	X
ejde-1812	623	2	23	23	NUM
ejde-1812	623	3	]	]	X
ejde-1812	623	4	f.	f.	PROPN
ejde-1812	623	5	li	li	PROPN
ejde-1812	623	6	,	,	PUNCT
ejde-1812	623	7	j.	j.	PROPN
ejde-1812	623	8	liang	liang	PROPN
ejde-1812	623	9	,	,	PUNCT
ejde-1812	623	10	t.	t.	PROPN
ejde-1812	623	11	t.	t.	PROPN
ejde-1812	623	12	lu	lu	PROPN
ejde-1812	623	13	,	,	PUNCT
ejde-1812	623	14	h.	h.	PROPN
ejde-1812	623	15	zhu	zhu	PROPN
ejde-1812	623	16	;	;	PUNCT
ejde-1812	623	17	a	a	DET
ejde-1812	623	18	nonlocal	nonlocal	ADJ
ejde-1812	623	19	cauchy	cauchy	NOUN
ejde-1812	623	20	problem	problem	NOUN
ejde-1812	623	21	for	for	ADP
ejde-1812	623	22	fractional	fractional	ADJ
ejde-1812	623	23	integro	integro	ADJ
ejde-1812	623	24	-	-	PUNCT
ejde-1812	623	25	differential	differential	NOUN
ejde-1812	623	26	equations	equation	NOUN
ejde-1812	623	27	,	,	PUNCT
ejde-1812	623	28	j.	j.	PROPN
ejde-1812	623	29	appl	appl	PROPN
ejde-1812	623	30	.	.	PROPN
ejde-1812	623	31	math	math	PROPN
ejde-1812	623	32	.	.	PUNCT
ejde-1812	624	1	2012	2012	NUM
ejde-1812	624	2	(	(	PUNCT
ejde-1812	624	3	2012	2012	NUM
ejde-1812	624	4	)	)	PUNCT
ejde-1812	624	5	,	,	PUNCT
ejde-1812	624	6	article	article	NOUN
ejde-1812	624	7	i	i	PROPN
ejde-1812	624	8	d	d	PROPN
ejde-1812	624	9	901942	901942	NUM
ejde-1812	624	10	.	.	PUNCT
ejde-1812	625	1	[	[	X
ejde-1812	625	2	24	24	NUM
ejde-1812	625	3	]	]	X
ejde-1812	625	4	f.	f.	PROPN
ejde-1812	625	5	li	li	PROPN
ejde-1812	625	6	,	,	PUNCT
ejde-1812	625	7	j.	j.	PROPN
ejde-1812	625	8	liang	liang	PROPN
ejde-1812	625	9	,	,	PUNCT
ejde-1812	625	10	h.	h.	PROPN
ejde-1812	625	11	k.	k.	PROPN
ejde-1812	625	12	xu	xu	PROPN
ejde-1812	625	13	;	;	PUNCT
ejde-1812	625	14	existence	existence	NOUN
ejde-1812	625	15	of	of	ADP
ejde-1812	625	16	mild	mild	ADJ
ejde-1812	625	17	solutions	solution	NOUN
ejde-1812	625	18	for	for	ADP
ejde-1812	625	19	fractional	fractional	ADJ
ejde-1812	625	20	integrodifferential	integrodifferential	ADJ
ejde-1812	625	21	equations	equation	NOUN
ejde-1812	625	22	of	of	ADP
ejde-1812	625	23	sobolev	sobolev	ADJ
ejde-1812	625	24	type	type	NOUN
ejde-1812	625	25	with	with	ADP
ejde-1812	625	26	nonlocal	nonlocal	ADJ
ejde-1812	625	27	conditions	condition	NOUN
ejde-1812	625	28	,	,	PUNCT
ejde-1812	625	29	j.	j.	PROPN
ejde-1812	625	30	math	math	PROPN
ejde-1812	625	31	.	.	PUNCT
ejde-1812	626	1	anal	anal	PROPN
ejde-1812	626	2	.	.	PUNCT
ejde-1812	627	1	appl	appl	PROPN
ejde-1812	627	2	.	.	PROPN
ejde-1812	628	1	391	391	NUM
ejde-1812	628	2	(	(	PUNCT
ejde-1812	628	3	2012	2012	NUM
ejde-1812	628	4	)	)	PUNCT
ejde-1812	628	5	,	,	PUNCT
ejde-1812	628	6	510	510	NUM
ejde-1812	628	7	-	-	SYM
ejde-1812	628	8	525	525	NUM
ejde-1812	628	9	.	.	PUNCT
ejde-1812	629	1	[	[	X
ejde-1812	629	2	25	25	NUM
ejde-1812	629	3	]	]	X
ejde-1812	629	4	f.	f.	PROPN
ejde-1812	629	5	li	li	PROPN
ejde-1812	629	6	,	,	PUNCT
ejde-1812	629	7	j.	j.	PROPN
ejde-1812	629	8	liang	liang	PROPN
ejde-1812	629	9	,	,	PUNCT
ejde-1812	629	10	h.	h.	PROPN
ejde-1812	629	11	wang	wang	PROPN
ejde-1812	629	12	;	;	PUNCT
ejde-1812	629	13	s	s	X
ejde-1812	629	14	-	-	PUNCT
ejde-1812	629	15	asymptotically	asymptotically	ADV
ejde-1812	629	16	ω	ω	ADJ
ejde-1812	629	17	-	-	ADJ
ejde-1812	629	18	periodic	periodic	ADJ
ejde-1812	629	19	solution	solution	NOUN
ejde-1812	629	20	for	for	ADP
ejde-1812	629	21	fractional	fractional	ADJ
ejde-1812	629	22	differential	differential	ADJ
ejde-1812	629	23	equations	equation	NOUN
ejde-1812	629	24	of	of	ADP
ejde-1812	629	25	oder	oder	PROPN
ejde-1812	629	26	q	q	PROPN
ejde-1812	629	27	∈	∈	PROPN
ejde-1812	629	28	(	(	PUNCT
ejde-1812	629	29	0	0	NUM
ejde-1812	629	30	,	,	PUNCT
ejde-1812	629	31	1	1	NUM
ejde-1812	629	32	)	)	PUNCT
ejde-1812	629	33	with	with	ADP
ejde-1812	629	34	finite	finite	ADJ
ejde-1812	629	35	delay	delay	NOUN
ejde-1812	629	36	,	,	PUNCT
ejde-1812	629	37	adv	adv	PROPN
ejde-1812	629	38	.	.	PUNCT
ejde-1812	629	39	diff	diff	PROPN
ejde-1812	629	40	.	.	PUNCT
ejde-1812	630	1	equ	equ	PROPN
ejde-1812	630	2	.	.	PUNCT
ejde-1812	631	1	(	(	PUNCT
ejde-1812	631	2	2017	2017	NUM
ejde-1812	631	3	)	)	PUNCT
ejde-1812	631	4	,	,	PUNCT
ejde-1812	631	5	2017:83	2017:83	NUM
ejde-1812	631	6	.	.	PUNCT
ejde-1812	632	1	[	[	X
ejde-1812	632	2	26	26	NUM
ejde-1812	632	3	]	]	PUNCT
ejde-1812	632	4	j.	j.	PROPN
ejde-1812	632	5	liang	liang	PROPN
ejde-1812	632	6	,	,	PUNCT
ejde-1812	632	7	y.	y.	PROPN
ejde-1812	632	8	mu	mu	PROPN
ejde-1812	632	9	,	,	PUNCT
ejde-1812	632	10	t.	t.	PROPN
ejde-1812	632	11	j.	j.	PROPN
ejde-1812	632	12	xiao	xiao	PROPN
ejde-1812	632	13	;	;	PUNCT
ejde-1812	632	14	initial	initial	ADJ
ejde-1812	632	15	-	-	PUNCT
ejde-1812	632	16	value	value	NOUN
ejde-1812	632	17	/	/	SYM
ejde-1812	632	18	nonlocal	nonlocal	ADJ
ejde-1812	632	19	cauchy	cauchy	NOUN
ejde-1812	632	20	problems	problem	NOUN
ejde-1812	632	21	for	for	ADP
ejde-1812	632	22	fractional	fractional	ADJ
ejde-1812	632	23	differential	differential	ADJ
ejde-1812	632	24	equations	equation	NOUN
ejde-1812	632	25	involving	involve	VERB
ejde-1812	632	26	ψ	ψ	NOUN
ejde-1812	632	27	-	-	ADJ
ejde-1812	632	28	hilfer	hilfer	NOUN
ejde-1812	632	29	multivariable	multivariable	ADJ
ejde-1812	632	30	operators	operator	NOUN
ejde-1812	632	31	,	,	PUNCT
ejde-1812	632	32	fract	fract	PROPN
ejde-1812	632	33	.	.	PUNCT
ejde-1812	632	34	calc	calc	PROPN
ejde-1812	632	35	.	.	PUNCT
ejde-1812	633	1	appl	appl	PROPN
ejde-1812	633	2	.	.	PUNCT
ejde-1812	634	1	anal	anal	PROPN
ejde-1812	634	2	.	.	PUNCT
ejde-1812	635	1	23	23	NUM
ejde-1812	635	2	(	(	PUNCT
ejde-1812	635	3	2020	2020	NUM
ejde-1812	635	4	)	)	PUNCT
ejde-1812	635	5	,	,	PUNCT
ejde-1812	635	6	no	no	INTJ
ejde-1812	635	7	.	.	NOUN
ejde-1812	635	8	4	4	NUM
ejde-1812	635	9	,	,	PUNCT
ejde-1812	635	10	1090	1090	NUM
ejde-1812	635	11	-	-	SYM
ejde-1812	635	12	1124	1124	NUM
ejde-1812	635	13	.	.	PUNCT
ejde-1812	636	1	[	[	X
ejde-1812	636	2	27	27	NUM
ejde-1812	636	3	]	]	PUNCT
ejde-1812	636	4	j.	j.	PROPN
ejde-1812	636	5	liang	liang	PROPN
ejde-1812	636	6	,	,	PUNCT
ejde-1812	636	7	y.	y.	PROPN
ejde-1812	636	8	mu	mu	PROPN
ejde-1812	636	9	,	,	PUNCT
ejde-1812	636	10	t.	t.	PROPN
ejde-1812	636	11	j.	j.	PROPN
ejde-1812	636	12	xiao	xiao	PROPN
ejde-1812	636	13	;	;	PUNCT
ejde-1812	636	14	nonlocal	nonlocal	ADJ
ejde-1812	636	15	integro	integro	ADJ
ejde-1812	636	16	-	-	PUNCT
ejde-1812	636	17	differential	differential	NOUN
ejde-1812	636	18	equations	equation	NOUN
ejde-1812	636	19	of	of	ADP
ejde-1812	636	20	sobolev	sobolev	ADJ
ejde-1812	636	21	type	type	NOUN
ejde-1812	636	22	in	in	ADP
ejde-1812	636	23	banach	banach	NOUN
ejde-1812	636	24	spaces	space	NOUN
ejde-1812	636	25	involving	involve	VERB
ejde-1812	636	26	ψ	ψ	PROPN
ejde-1812	636	27	-	-	ADJ
ejde-1812	636	28	caputo	caputo	ADJ
ejde-1812	636	29	fractional	fractional	PROPN
ejde-1812	636	30	derivative	derivative	NOUN
ejde-1812	636	31	,	,	PUNCT
ejde-1812	636	32	banach	banach	NOUN
ejde-1812	636	33	j.	j.	PROPN
ejde-1812	636	34	math	math	PROPN
ejde-1812	636	35	.	.	PUNCT
ejde-1812	637	1	anal	anal	PROPN
ejde-1812	637	2	.	.	PUNCT
ejde-1812	638	1	(	(	PUNCT
ejde-1812	638	2	2022	2022	NUM
ejde-1812	638	3	)	)	PUNCT
ejde-1812	638	4	,	,	PUNCT
ejde-1812	639	1	16:3	16:3	NUM
ejde-1812	639	2	.	.	PUNCT
ejde-1812	640	1	[	[	X
ejde-1812	640	2	28	28	NUM
ejde-1812	640	3	]	]	PUNCT
ejde-1812	640	4	j.	j.	PROPN
ejde-1812	640	5	liang	liang	PROPN
ejde-1812	640	6	,	,	PUNCT
ejde-1812	640	7	t.	t.	PROPN
ejde-1812	640	8	j.	j.	PROPN
ejde-1812	640	9	xiao	xiao	PROPN
ejde-1812	640	10	;	;	PUNCT
ejde-1812	640	11	solutions	solution	NOUN
ejde-1812	640	12	to	to	ADP
ejde-1812	640	13	abstract	abstract	ADJ
ejde-1812	640	14	integral	integral	ADJ
ejde-1812	640	15	equations	equation	NOUN
ejde-1812	640	16	and	and	CCONJ
ejde-1812	640	17	infinite	infinite	ADJ
ejde-1812	640	18	delay	delay	NOUN
ejde-1812	640	19	evolution	evolution	NOUN
ejde-1812	640	20	equations	equation	NOUN
ejde-1812	640	21	,	,	PUNCT
ejde-1812	640	22	bull	bull	NOUN
ejde-1812	640	23	.	.	PUNCT
ejde-1812	641	1	belg	belg	PROPN
ejde-1812	641	2	.	.	PUNCT
ejde-1812	642	1	math	math	NOUN
ejde-1812	642	2	.	.	PUNCT
ejde-1812	643	1	soc	soc	PROPN
ejde-1812	643	2	.	.	PUNCT
ejde-1812	644	1	simon	simon	PROPN
ejde-1812	644	2	stevin	stevin	PROPN
ejde-1812	644	3	,	,	PUNCT
ejde-1812	644	4	18	18	NUM
ejde-1812	644	5	(	(	PUNCT
ejde-1812	644	6	2011	2011	NUM
ejde-1812	644	7	)	)	PUNCT
ejde-1812	644	8	,	,	PUNCT
ejde-1812	644	9	793	793	NUM
ejde-1812	644	10	-	-	SYM
ejde-1812	644	11	804	804	NUM
ejde-1812	644	12	.	.	PUNCT
ejde-1812	645	1	[	[	X
ejde-1812	645	2	29	29	NUM
ejde-1812	645	3	]	]	X
ejde-1812	645	4	o.	o.	NOUN
ejde-1812	645	5	lipovan	lipovan	PROPN
ejde-1812	645	6	;	;	PUNCT
ejde-1812	645	7	a	a	DET
ejde-1812	645	8	retarded	retarded	ADJ
ejde-1812	645	9	integral	integral	ADJ
ejde-1812	645	10	inequality	inequality	NOUN
ejde-1812	645	11	and	and	CCONJ
ejde-1812	645	12	its	its	PRON
ejde-1812	645	13	applications	application	NOUN
ejde-1812	645	14	,	,	PUNCT
ejde-1812	645	15	j.	j.	PROPN
ejde-1812	645	16	math	math	PROPN
ejde-1812	645	17	.	.	PUNCT
ejde-1812	646	1	anal	anal	PROPN
ejde-1812	646	2	.	.	PUNCT
ejde-1812	647	1	appl	appl	PROPN
ejde-1812	647	2	.	.	PROPN
ejde-1812	647	3	,	,	PUNCT
ejde-1812	647	4	285	285	NUM
ejde-1812	647	5	(	(	PUNCT
ejde-1812	647	6	2003	2003	NUM
ejde-1812	647	7	)	)	PUNCT
ejde-1812	647	8	,	,	PUNCT
ejde-1812	647	9	436	436	NUM
ejde-1812	647	10	-	-	SYM
ejde-1812	647	11	443	443	NUM
ejde-1812	647	12	.	.	PUNCT
ejde-1812	648	1	[	[	X
ejde-1812	648	2	30	30	NUM
ejde-1812	648	3	]	]	X
ejde-1812	648	4	b.	b.	PROPN
ejde-1812	648	5	liu	liu	PROPN
ejde-1812	648	6	;	;	PUNCT
ejde-1812	648	7	controllability	controllability	NOUN
ejde-1812	648	8	of	of	ADP
ejde-1812	648	9	nonlinear	nonlinear	ADJ
ejde-1812	648	10	neutral	neutral	ADJ
ejde-1812	648	11	evolution	evolution	NOUN
ejde-1812	648	12	integro	integro	ADJ
ejde-1812	648	13	-	-	PUNCT
ejde-1812	648	14	differential	differential	NOUN
ejde-1812	648	15	systems	system	NOUN
ejde-1812	648	16	with	with	ADP
ejde-1812	648	17	infinite	infinite	ADJ
ejde-1812	648	18	delay	delay	NOUN
ejde-1812	648	19	,	,	PUNCT
ejde-1812	648	20	j.	j.	PROPN
ejde-1812	648	21	optim	optim	PROPN
ejde-1812	648	22	.	.	PUNCT
ejde-1812	649	1	theory	theory	NOUN
ejde-1812	649	2	appl	appl	PROPN
ejde-1812	649	3	.	.	PUNCT
ejde-1812	650	1	122	122	NUM
ejde-1812	650	2	(	(	PUNCT
ejde-1812	650	3	2004	2004	NUM
ejde-1812	650	4	)	)	PUNCT
ejde-1812	650	5	,	,	PUNCT
ejde-1812	650	6	80	80	NUM
ejde-1812	650	7	-	-	SYM
ejde-1812	650	8	109	109	NUM
ejde-1812	650	9	.	.	PUNCT
ejde-1812	651	1	[	[	X
ejde-1812	651	2	31	31	NUM
ejde-1812	651	3	]	]	X
ejde-1812	651	4	n.	n.	PROPN
ejde-1812	651	5	mahmudov	mahmudov	PROPN
ejde-1812	651	6	,	,	PUNCT
ejde-1812	651	7	s.	s.	PROPN
ejde-1812	651	8	zorlu	zorlu	PROPN
ejde-1812	651	9	;	;	PUNCT
ejde-1812	651	10	on	on	ADP
ejde-1812	651	11	the	the	DET
ejde-1812	651	12	approximate	approximate	ADJ
ejde-1812	651	13	controllability	controllability	NOUN
ejde-1812	651	14	of	of	ADP
ejde-1812	651	15	fractional	fractional	ADJ
ejde-1812	651	16	evolution	evolution	NOUN
ejde-1812	651	17	equations	equation	NOUN
ejde-1812	651	18	with	with	ADP
ejde-1812	651	19	compact	compact	ADJ
ejde-1812	651	20	analytic	analytic	ADJ
ejde-1812	651	21	semigroup	semigroup	NOUN
ejde-1812	651	22	,	,	PUNCT
ejde-1812	651	23	j.	j.	PROPN
ejde-1812	651	24	comput	comput	PROPN
ejde-1812	651	25	.	.	PUNCT
ejde-1812	652	1	appl	appl	PROPN
ejde-1812	652	2	.	.	PROPN
ejde-1812	652	3	math	math	PROPN
ejde-1812	652	4	.	.	PUNCT
ejde-1812	653	1	,	,	PUNCT
ejde-1812	653	2	259	259	NUM
ejde-1812	653	3	(	(	PUNCT
ejde-1812	653	4	2014	2014	NUM
ejde-1812	653	5	)	)	PUNCT
ejde-1812	653	6	,	,	PUNCT
ejde-1812	653	7	194	194	NUM
ejde-1812	653	8	-	-	SYM
ejde-1812	653	9	204	204	NUM
ejde-1812	653	10	.	.	PUNCT
ejde-1812	654	1	ejde-2025/109	ejde-2025/109	ADP
ejde-1812	654	2	evolution	evolution	PROPN
ejde-1812	654	3	ψ	ψ	NOUN
ejde-1812	654	4	-	-	ADJ
ejde-1812	654	5	hilfer	hilfer	NOUN
ejde-1812	654	6	fractional	fractional	ADJ
ejde-1812	654	7	differential	differential	ADJ
ejde-1812	654	8	equations	equation	NOUN
ejde-1812	654	9	17	17	NUM
ejde-1812	654	10	[	[	SYM
ejde-1812	654	11	32	32	NUM
ejde-1812	654	12	]	]	PUNCT
ejde-1812	654	13	f.	f.	PROPN
ejde-1812	654	14	mainardi	mainardi	PROPN
ejde-1812	654	15	;	;	PUNCT
ejde-1812	654	16	fractional	fractional	ADJ
ejde-1812	654	17	calculus	calculus	NOUN
ejde-1812	654	18	,	,	PUNCT
ejde-1812	654	19	some	some	DET
ejde-1812	654	20	basic	basic	ADJ
ejde-1812	654	21	problems	problem	NOUN
ejde-1812	654	22	in	in	ADP
ejde-1812	654	23	continuum	continuum	ADJ
ejde-1812	654	24	and	and	CCONJ
ejde-1812	654	25	statistical	statistical	ADJ
ejde-1812	654	26	mechanics	mechanic	NOUN
ejde-1812	654	27	,	,	PUNCT
ejde-1812	654	28	springerverlag	springerverlag	NOUN
ejde-1812	654	29	,	,	PUNCT
ejde-1812	654	30	wien	wien	NOUN
ejde-1812	654	31	,	,	PUNCT
ejde-1812	654	32	1997	1997	NUM
ejde-1812	654	33	,	,	PUNCT
ejde-1812	654	34	pp	pp	ADP
ejde-1812	654	35	291	291	NUM
ejde-1812	654	36	-	-	SYM
ejde-1812	654	37	348	348	NUM
ejde-1812	654	38	.	.	PUNCT
ejde-1812	655	1	[	[	X
ejde-1812	655	2	33	33	NUM
ejde-1812	655	3	]	]	PUNCT
ejde-1812	655	4	r.	r.	PROPN
ejde-1812	655	5	metzler	metzler	PROPN
ejde-1812	655	6	,	,	PUNCT
ejde-1812	655	7	t.	t.	PROPN
ejde-1812	655	8	f.	f.	PROPN
ejde-1812	655	9	nonnenmacher	nonnenmacher	PROPN
ejde-1812	655	10	;	;	PUNCT
ejde-1812	655	11	fractional	fractional	ADJ
ejde-1812	655	12	relaxation	relaxation	NOUN
ejde-1812	655	13	processes	process	NOUN
ejde-1812	655	14	and	and	CCONJ
ejde-1812	655	15	fractional	fractional	ADJ
ejde-1812	655	16	rheological	rheological	ADJ
ejde-1812	655	17	models	model	NOUN
ejde-1812	655	18	for	for	ADP
ejde-1812	655	19	the	the	DET
ejde-1812	655	20	description	description	NOUN
ejde-1812	655	21	of	of	ADP
ejde-1812	655	22	a	a	DET
ejde-1812	655	23	class	class	NOUN
ejde-1812	655	24	of	of	ADP
ejde-1812	655	25	viscoelastic	viscoelastic	ADJ
ejde-1812	655	26	materials	material	NOUN
ejde-1812	655	27	,	,	PUNCT
ejde-1812	655	28	int	int	NOUN
ejde-1812	655	29	.	.	PUNCT
ejde-1812	656	1	j.	j.	PROPN
ejde-1812	656	2	plast	plast	PROPN
ejde-1812	656	3	.	.	PUNCT
ejde-1812	657	1	19	19	NUM
ejde-1812	657	2	(	(	PUNCT
ejde-1812	657	3	2003	2003	NUM
ejde-1812	657	4	)	)	PUNCT
ejde-1812	657	5	,	,	PUNCT
ejde-1812	657	6	941	941	NUM
ejde-1812	657	7	-	-	SYM
ejde-1812	657	8	959	959	NUM
ejde-1812	657	9	.	.	PUNCT
ejde-1812	658	1	[	[	X
ejde-1812	658	2	34	34	NUM
ejde-1812	658	3	]	]	X
ejde-1812	658	4	g.	g.	PROPN
ejde-1812	658	5	m.	m.	PROPN
ejde-1812	658	6	mophou	mophou	PROPN
ejde-1812	658	7	,	,	PUNCT
ejde-1812	658	8	g.	g.	PROPN
ejde-1812	658	9	m.	m.	PROPN
ejde-1812	658	10	n’guérékata	n’guérékata	PROPN
ejde-1812	658	11	;	;	PUNCT
ejde-1812	658	12	existence	existence	NOUN
ejde-1812	658	13	of	of	ADP
ejde-1812	658	14	mild	mild	ADJ
ejde-1812	658	15	solutions	solution	NOUN
ejde-1812	658	16	for	for	ADP
ejde-1812	658	17	some	some	DET
ejde-1812	658	18	fractional	fractional	ADJ
ejde-1812	658	19	differential	differential	ADJ
ejde-1812	658	20	equations	equation	NOUN
ejde-1812	658	21	with	with	ADP
ejde-1812	658	22	nonlocal	nonlocal	ADJ
ejde-1812	658	23	conditions	condition	NOUN
ejde-1812	658	24	,	,	PUNCT
ejde-1812	658	25	semigroup	semigroup	PROPN
ejde-1812	658	26	forum	forum	PROPN
ejde-1812	658	27	,	,	PUNCT
ejde-1812	658	28	79	79	NUM
ejde-1812	658	29	(	(	PUNCT
ejde-1812	658	30	2009	2009	NUM
ejde-1812	658	31	)	)	PUNCT
ejde-1812	658	32	,	,	PUNCT
ejde-1812	658	33	315	315	NUM
ejde-1812	658	34	-	-	SYM
ejde-1812	658	35	322	322	NUM
ejde-1812	658	36	.	.	PUNCT
ejde-1812	659	1	[	[	X
ejde-1812	659	2	35	35	NUM
ejde-1812	659	3	]	]	X
ejde-1812	659	4	r.	r.	PROPN
ejde-1812	659	5	r.	r.	PROPN
ejde-1812	659	6	nigmatullin	nigmatullin	PROPN
ejde-1812	659	7	,	,	PUNCT
ejde-1812	659	8	s.	s.	PROPN
ejde-1812	659	9	i.	i.	PROPN
ejde-1812	659	10	osokin	osokin	PROPN
ejde-1812	659	11	;	;	PUNCT
ejde-1812	659	12	signal	signal	NOUN
ejde-1812	659	13	processing	processing	NOUN
ejde-1812	659	14	and	and	CCONJ
ejde-1812	659	15	recognition	recognition	NOUN
ejde-1812	659	16	of	of	ADP
ejde-1812	659	17	true	true	ADJ
ejde-1812	659	18	kinetic	kinetic	ADJ
ejde-1812	659	19	equations	equation	NOUN
ejde-1812	659	20	containing	contain	VERB
ejde-1812	659	21	noninteger	noninteger	NOUN
ejde-1812	659	22	derivatives	derivative	NOUN
ejde-1812	659	23	from	from	ADP
ejde-1812	659	24	raw	raw	ADJ
ejde-1812	659	25	dielectric	dielectric	ADJ
ejde-1812	659	26	data	datum	NOUN
ejde-1812	659	27	,	,	PUNCT
ejde-1812	659	28	signal	signal	ADJ
ejde-1812	659	29	processing	processing	NOUN
ejde-1812	659	30	,	,	PUNCT
ejde-1812	659	31	(	(	PUNCT
ejde-1812	659	32	11	11	NUM
ejde-1812	659	33	)	)	SYM
ejde-1812	659	34	83	83	NUM
ejde-1812	659	35	(	(	PUNCT
ejde-1812	659	36	2003	2003	NUM
ejde-1812	659	37	)	)	PUNCT
ejde-1812	659	38	,	,	PUNCT
ejde-1812	659	39	2433	2433	NUM
ejde-1812	659	40	-	-	SYM
ejde-1812	659	41	2453	2453	NUM
ejde-1812	659	42	.	.	PUNCT
ejde-1812	660	1	[	[	X
ejde-1812	660	2	36	36	NUM
ejde-1812	660	3	]	]	PUNCT
ejde-1812	660	4	m.	m.	PROPN
ejde-1812	660	5	d.	d.	PROPN
ejde-1812	660	6	ortigueira	ortigueira	PROPN
ejde-1812	660	7	;	;	PUNCT
ejde-1812	660	8	on	on	ADP
ejde-1812	660	9	the	the	DET
ejde-1812	660	10	initial	initial	ADJ
ejde-1812	660	11	conditions	condition	NOUN
ejde-1812	660	12	in	in	ADP
ejde-1812	660	13	continuous	continuous	ADJ
ejde-1812	660	14	-	-	PUNCT
ejde-1812	660	15	time	time	NOUN
ejde-1812	660	16	fractional	fractional	ADJ
ejde-1812	660	17	linear	linear	NOUN
ejde-1812	660	18	systems	system	NOUN
ejde-1812	660	19	,	,	PUNCT
ejde-1812	660	20	signal	signal	ADJ
ejde-1812	660	21	processing	processing	NOUN
ejde-1812	660	22	(	(	PUNCT
ejde-1812	660	23	11	11	NUM
ejde-1812	660	24	)	)	SYM
ejde-1812	660	25	83	83	NUM
ejde-1812	660	26	(	(	PUNCT
ejde-1812	660	27	2003	2003	NUM
ejde-1812	660	28	)	)	PUNCT
ejde-1812	660	29	,	,	PUNCT
ejde-1812	660	30	2301	2301	NUM
ejde-1812	660	31	-	-	SYM
ejde-1812	660	32	2309	2309	NUM
ejde-1812	660	33	.	.	PUNCT
ejde-1812	661	1	[	[	X
ejde-1812	661	2	37	37	NUM
ejde-1812	661	3	]	]	PUNCT
ejde-1812	661	4	a.	a.	NOUN
ejde-1812	661	5	pazy	pazy	NOUN
ejde-1812	661	6	;	;	PUNCT
ejde-1812	661	7	semigroups	semigroup	NOUN
ejde-1812	661	8	of	of	ADP
ejde-1812	661	9	linear	linear	PROPN
ejde-1812	661	10	operators	operator	NOUN
ejde-1812	661	11	and	and	CCONJ
ejde-1812	661	12	applications	application	NOUN
ejde-1812	661	13	to	to	ADP
ejde-1812	661	14	partial	partial	ADJ
ejde-1812	661	15	differential	differential	NOUN
ejde-1812	661	16	equations	equation	NOUN
ejde-1812	661	17	,	,	PUNCT
ejde-1812	661	18	springer	springer	NOUN
ejde-1812	661	19	,	,	PUNCT
ejde-1812	661	20	new	new	PROPN
ejde-1812	661	21	york	york	PROPN
ejde-1812	661	22	,	,	PUNCT
ejde-1812	661	23	1986	1986	NUM
ejde-1812	661	24	.	.	PUNCT
ejde-1812	662	1	[	[	X
ejde-1812	662	2	38	38	NUM
ejde-1812	662	3	]	]	PUNCT
ejde-1812	662	4	b.	b.	PROPN
ejde-1812	662	5	g.	g.	PROPN
ejde-1812	662	6	pachpatte	pachpatte	PROPN
ejde-1812	662	7	;	;	PUNCT
ejde-1812	662	8	inequalities	inequality	NOUN
ejde-1812	662	9	for	for	ADP
ejde-1812	662	10	differential	differential	ADJ
ejde-1812	662	11	and	and	CCONJ
ejde-1812	662	12	integral	integral	ADJ
ejde-1812	662	13	equations	equation	NOUN
ejde-1812	662	14	,	,	PUNCT
ejde-1812	662	15	academic	academic	ADJ
ejde-1812	662	16	press	press	NOUN
ejde-1812	662	17	,	,	PUNCT
ejde-1812	662	18	new	new	PROPN
ejde-1812	662	19	york	york	PROPN
ejde-1812	662	20	,	,	PUNCT
ejde-1812	662	21	1998	1998	NUM
ejde-1812	662	22	.	.	PUNCT
ejde-1812	663	1	[	[	X
ejde-1812	663	2	39	39	NUM
ejde-1812	663	3	]	]	PUNCT
ejde-1812	663	4	i.	i.	NOUN
ejde-1812	663	5	podlubny	podlubny	PROPN
ejde-1812	663	6	;	;	PUNCT
ejde-1812	663	7	fractional	fractional	ADJ
ejde-1812	663	8	differential	differential	ADJ
ejde-1812	663	9	equations	equation	NOUN
ejde-1812	663	10	,	,	PUNCT
ejde-1812	663	11	in	in	ADP
ejde-1812	663	12	:	:	PUNCT
ejde-1812	663	13	mathematicas	mathematica	NOUN
ejde-1812	663	14	in	in	ADP
ejde-1812	663	15	science	science	NOUN
ejde-1812	663	16	and	and	CCONJ
ejde-1812	663	17	engineering	engineering	NOUN
ejde-1812	663	18	,	,	PUNCT
ejde-1812	663	19	vol	vol	NOUN
ejde-1812	663	20	.	.	PROPN
ejde-1812	663	21	198	198	NUM
ejde-1812	663	22	,	,	PUNCT
ejde-1812	663	23	academic	academic	ADJ
ejde-1812	663	24	press	press	NOUN
ejde-1812	663	25	,	,	PUNCT
ejde-1812	663	26	new	new	PROPN
ejde-1812	663	27	york	york	PROPN
ejde-1812	663	28	,	,	PUNCT
ejde-1812	663	29	1999	1999	NUM
ejde-1812	663	30	.	.	PUNCT
ejde-1812	664	1	[	[	X
ejde-1812	664	2	40	40	NUM
ejde-1812	664	3	]	]	PUNCT
ejde-1812	664	4	s.	s.	PROPN
ejde-1812	664	5	h.	h.	PROPN
ejde-1812	664	6	saker	saker	PROPN
ejde-1812	664	7	;	;	PUNCT
ejde-1812	664	8	some	some	DET
ejde-1812	664	9	nonlinear	nonlinear	ADJ
ejde-1812	664	10	dynamic	dynamic	ADJ
ejde-1812	664	11	inequalities	inequality	NOUN
ejde-1812	664	12	on	on	ADP
ejde-1812	664	13	time	time	NOUN
ejde-1812	664	14	scales	scale	NOUN
ejde-1812	664	15	,	,	PUNCT
ejde-1812	664	16	math	math	NOUN
ejde-1812	664	17	.	.	PUNCT
ejde-1812	665	1	inequal	inequal	PROPN
ejde-1812	665	2	.	.	PUNCT
ejde-1812	666	1	appl	appl	PROPN
ejde-1812	666	2	.	.	PROPN
ejde-1812	666	3	,	,	PUNCT
ejde-1812	666	4	14	14	NUM
ejde-1812	666	5	(	(	PUNCT
ejde-1812	666	6	2011	2011	NUM
ejde-1812	666	7	)	)	PUNCT
ejde-1812	666	8	,	,	PUNCT
ejde-1812	666	9	633	633	NUM
ejde-1812	666	10	-	-	SYM
ejde-1812	666	11	645	645	NUM
ejde-1812	666	12	.	.	PUNCT
ejde-1812	667	1	[	[	X
ejde-1812	667	2	41	41	NUM
ejde-1812	667	3	]	]	X
ejde-1812	667	4	j.	j.	PROPN
ejde-1812	667	5	v.	v.	PROPN
ejde-1812	667	6	c.	c.	PROPN
ejde-1812	667	7	sousa	sousa	PROPN
ejde-1812	667	8	,	,	PUNCT
ejde-1812	667	9	e.	e.	PROPN
ejde-1812	667	10	c.	c.	PROPN
ejde-1812	667	11	oliveira	oliveira	PROPN
ejde-1812	667	12	;	;	PUNCT
ejde-1812	667	13	on	on	ADP
ejde-1812	667	14	the	the	DET
ejde-1812	667	15	ψ	ψ	NOUN
ejde-1812	667	16	-	-	ADJ
ejde-1812	667	17	hilfer	hilfer	NOUN
ejde-1812	667	18	fractional	fractional	ADJ
ejde-1812	667	19	derivative	derivative	NOUN
ejde-1812	667	20	,	,	PUNCT
ejde-1812	667	21	commun	commun	PROPN
ejde-1812	667	22	.	.	PUNCT
ejde-1812	668	1	nonlinear	nonlinear	PROPN
ejde-1812	668	2	sci	sci	PROPN
ejde-1812	668	3	.	.	PUNCT
ejde-1812	668	4	numer	numer	PROPN
ejde-1812	668	5	.	.	PUNCT
ejde-1812	669	1	simul	simul	PROPN
ejde-1812	669	2	.	.	PROPN
ejde-1812	669	3	,	,	PUNCT
ejde-1812	669	4	(	(	PUNCT
ejde-1812	669	5	1	1	X
ejde-1812	669	6	)	)	SYM
ejde-1812	669	7	60	60	NUM
ejde-1812	669	8	(	(	PUNCT
ejde-1812	669	9	2018	2018	NUM
ejde-1812	669	10	)	)	PUNCT
ejde-1812	669	11	,	,	PUNCT
ejde-1812	669	12	72	72	NUM
ejde-1812	669	13	-	-	SYM
ejde-1812	669	14	91	91	NUM
ejde-1812	669	15	.	.	PUNCT
ejde-1812	670	1	[	[	X
ejde-1812	670	2	42	42	NUM
ejde-1812	670	3	]	]	PUNCT
ejde-1812	670	4	t.	t.	PROPN
ejde-1812	670	5	j.	j.	PROPN
ejde-1812	670	6	xiao	xiao	PROPN
ejde-1812	670	7	,	,	PUNCT
ejde-1812	670	8	j.	j.	PROPN
ejde-1812	670	9	liang	liang	PROPN
ejde-1812	670	10	;	;	PUNCT
ejde-1812	670	11	blow	blow	NOUN
ejde-1812	670	12	-	-	PUNCT
ejde-1812	670	13	up	up	NOUN
ejde-1812	670	14	and	and	CCONJ
ejde-1812	670	15	global	global	ADJ
ejde-1812	670	16	existence	existence	NOUN
ejde-1812	670	17	of	of	ADP
ejde-1812	670	18	solutions	solution	NOUN
ejde-1812	670	19	to	to	ADP
ejde-1812	670	20	integral	integral	ADJ
ejde-1812	670	21	equations	equation	NOUN
ejde-1812	670	22	with	with	ADP
ejde-1812	670	23	infinite	infinite	ADJ
ejde-1812	670	24	delay	delay	NOUN
ejde-1812	670	25	in	in	ADP
ejde-1812	670	26	banach	banach	NOUN
ejde-1812	670	27	spaces	space	NOUN
ejde-1812	670	28	,	,	PUNCT
ejde-1812	670	29	nonlinear	nonlinear	ADJ
ejde-1812	670	30	anal	anal	NOUN
ejde-1812	670	31	.	.	PUNCT
ejde-1812	670	32	,	,	PUNCT
ejde-1812	670	33	71	71	NUM
ejde-1812	670	34	(	(	PUNCT
ejde-1812	670	35	2009	2009	NUM
ejde-1812	670	36	)	)	PUNCT
ejde-1812	670	37	,	,	PUNCT
ejde-1812	670	38	1442	1442	NUM
ejde-1812	670	39	-	-	SYM
ejde-1812	670	40	1447	1447	NUM
ejde-1812	670	41	.	.	PUNCT
ejde-1812	671	1	[	[	X
ejde-1812	671	2	43	43	NUM
ejde-1812	671	3	]	]	X
ejde-1812	671	4	h.	h.	PROPN
ejde-1812	671	5	ye	ye	PROPN
ejde-1812	671	6	,	,	PUNCT
ejde-1812	671	7	j.	j.	PROPN
ejde-1812	671	8	gao	gao	PROPN
ejde-1812	671	9	,	,	PUNCT
ejde-1812	671	10	y.	y.	PROPN
ejde-1812	671	11	ding	ding	PROPN
ejde-1812	671	12	;	;	PUNCT
ejde-1812	671	13	a	a	DET
ejde-1812	671	14	generalized	generalized	ADJ
ejde-1812	671	15	gronwall	gronwall	ADJ
ejde-1812	671	16	inequality	inequality	NOUN
ejde-1812	671	17	and	and	CCONJ
ejde-1812	671	18	its	its	PRON
ejde-1812	671	19	application	application	NOUN
ejde-1812	671	20	to	to	ADP
ejde-1812	671	21	a	a	DET
ejde-1812	671	22	fractional	fractional	ADJ
ejde-1812	671	23	differential	differential	NOUN
ejde-1812	671	24	equation	equation	NOUN
ejde-1812	671	25	,	,	PUNCT
ejde-1812	671	26	j.	j.	PROPN
ejde-1812	671	27	math	math	PROPN
ejde-1812	671	28	.	.	PUNCT
ejde-1812	672	1	anal	anal	PROPN
ejde-1812	672	2	.	.	PUNCT
ejde-1812	673	1	appl	appl	PROPN
ejde-1812	673	2	.	.	PROPN
ejde-1812	673	3	,	,	PUNCT
ejde-1812	673	4	328	328	NUM
ejde-1812	673	5	(	(	PUNCT
ejde-1812	673	6	2007	2007	NUM
ejde-1812	673	7	)	)	PUNCT
ejde-1812	673	8	,	,	PUNCT
ejde-1812	673	9	no	no	INTJ
ejde-1812	673	10	.	.	NOUN
ejde-1812	673	11	2	2	NUM
ejde-1812	673	12	,	,	PUNCT
ejde-1812	673	13	1075	1075	NUM
ejde-1812	673	14	-	-	SYM
ejde-1812	673	15	1081	1081	NUM
ejde-1812	673	16	.	.	PUNCT
ejde-1812	674	1	jin	jin	PROPN
ejde-1812	674	2	liang	liang	PROPN
ejde-1812	674	3	school	school	PROPN
ejde-1812	674	4	of	of	ADP
ejde-1812	674	5	mathematical	mathematical	ADJ
ejde-1812	674	6	sciences	sciences	PROPN
ejde-1812	674	7	,	,	PUNCT
ejde-1812	674	8	shanghai	shanghai	PROPN
ejde-1812	674	9	jiao	jiao	PROPN
ejde-1812	674	10	tong	tong	PROPN
ejde-1812	674	11	university	university	PROPN
ejde-1812	674	12	,	,	PUNCT
ejde-1812	674	13	shanghai	shanghai	PROPN
ejde-1812	674	14	200240	200240	NUM
ejde-1812	674	15	,	,	PUNCT
ejde-1812	674	16	china	china	PROPN
ejde-1812	674	17	email	email	NOUN
ejde-1812	674	18	address	address	NOUN
ejde-1812	674	19	:	:	PUNCT
ejde-1812	674	20	jinliang@sjtu.edu.cn	jinliang@sjtu.edu.cn	NUM
ejde-1812	674	21	yunyi	yunyi	PROPN
ejde-1812	674	22	mu	mu	PROPN
ejde-1812	674	23	(	(	PUNCT
ejde-1812	674	24	corresponding	corresponding	ADJ
ejde-1812	674	25	author	author	NOUN
ejde-1812	674	26	)	)	PUNCT
ejde-1812	674	27	school	school	NOUN
ejde-1812	674	28	of	of	ADP
ejde-1812	674	29	arts	art	NOUN
ejde-1812	674	30	and	and	CCONJ
ejde-1812	674	31	sciences	science	NOUN
ejde-1812	674	32	,	,	PUNCT
ejde-1812	674	33	shanghai	shanghai	PROPN
ejde-1812	674	34	dianji	dianji	PROPN
ejde-1812	674	35	university	university	PROPN
ejde-1812	674	36	,	,	PUNCT
ejde-1812	674	37	shanghai	shanghai	PROPN
ejde-1812	674	38	201306	201306	NUM
ejde-1812	674	39	,	,	PUNCT
ejde-1812	674	40	china	china	PROPN
ejde-1812	674	41	email	email	PROPN
ejde-1812	674	42	address	address	NOUN
ejde-1812	674	43	:	:	PUNCT
ejde-1812	674	44	muyy@sdju.edu.cn	muyy@sdju.edu.cn	ADJ
ejde-1812	674	45	ti	ti	PROPN
ejde-1812	674	46	-	-	PROPN
ejde-1812	674	47	jun	jun	PROPN
ejde-1812	674	48	xiao	xiao	PROPN
ejde-1812	674	49	shanghai	shanghai	PROPN
ejde-1812	674	50	key	key	PROPN
ejde-1812	674	51	laboratory	laboratory	PROPN
ejde-1812	674	52	for	for	ADP
ejde-1812	674	53	contemporary	contemporary	ADJ
ejde-1812	674	54	applied	apply	VERB
ejde-1812	674	55	mathematics	mathematic	NOUN
ejde-1812	674	56	,	,	PUNCT
ejde-1812	674	57	school	school	NOUN
ejde-1812	674	58	of	of	ADP
ejde-1812	674	59	mathematical	mathematical	ADJ
ejde-1812	674	60	sciences	sciences	PROPN
ejde-1812	674	61	,	,	PUNCT
ejde-1812	674	62	fudan	fudan	PROPN
ejde-1812	674	63	university	university	PROPN
ejde-1812	674	64	,	,	PUNCT
ejde-1812	674	65	shanghai	shanghai	PROPN
ejde-1812	674	66	200433	200433	NUM
ejde-1812	674	67	,	,	PUNCT
ejde-1812	674	68	china	china	PROPN
ejde-1812	674	69	email	email	NOUN
ejde-1812	674	70	address	address	NOUN
ejde-1812	674	71	:	:	PUNCT
ejde-1812	674	72	tjxiao@fudan.edu.cn	tjxiao@fudan.edu.cn	PROPN
ejde-1812	675	1	1	1	NUM
ejde-1812	675	2	.	.	PUNCT
ejde-1812	675	3	introduction	introduction	NOUN
ejde-1812	675	4	2	2	NUM
ejde-1812	675	5	.	.	PUNCT
ejde-1812	675	6	definition	definition	NOUN
ejde-1812	675	7	of	of	ADP
ejde-1812	675	8	mild	mild	ADJ
ejde-1812	675	9	solutions	solution	NOUN
ejde-1812	675	10	3	3	NUM
ejde-1812	675	11	.	.	NOUN
ejde-1812	675	12	approximate	approximate	ADJ
ejde-1812	675	13	controllability	controllability	NOUN
ejde-1812	675	14	4	4	NUM
ejde-1812	675	15	.	.	PUNCT
ejde-1812	676	1	a	a	DET
ejde-1812	676	2	new	new	ADJ
ejde-1812	676	3	gronwall	gronwall	ADJ
ejde-1812	676	4	-	-	PUNCT
ejde-1812	676	5	type	type	NOUN
ejde-1812	676	6	inequality	inequality	NOUN
ejde-1812	676	7	and	and	CCONJ
ejde-1812	676	8	the	the	DET
ejde-1812	676	9	dependence	dependence	NOUN
ejde-1812	676	10	of	of	ADP
ejde-1812	676	11	solution	solution	NOUN
ejde-1812	676	12	on	on	ADP
ejde-1812	676	13	the	the	DET
ejde-1812	676	14	order	order	NOUN
ejde-1812	676	15	and	and	CCONJ
ejde-1812	676	16	the	the	DET
ejde-1812	676	17	initial	initial	ADJ
ejde-1812	676	18	condition	condition	NOUN
ejde-1812	676	19	5	5	NUM
ejde-1812	676	20	.	.	PUNCT
ejde-1812	677	1	an	an	DET
ejde-1812	677	2	example	example	NOUN
ejde-1812	677	3	acknowledgments	acknowledgment	NOUN
ejde-1812	677	4	references	reference	NOUN