id	sid	tid	token	lemma	pos
ssh-7883	1	1	bcp	bcp	VERB
ssh-7883	1	2	social	social	PROPN
ssh-7883	1	3	sciences	sciences	PROPN
ssh-7883	1	4	&	&	CCONJ
ssh-7883	1	5	humanities	humanities	PROPN
ssh-7883	1	6	erss	erss	VERB
ssh-7883	1	7	2024	2024	NUM
ssh-7883	1	8	volume	volume	NOUN
ssh-7883	1	9	23	23	NUM
ssh-7883	1	10	(	(	PUNCT
ssh-7883	1	11	2024	2024	NUM
ssh-7883	1	12	)	)	PUNCT
ssh-7883	1	13	1	1	NUM
ssh-7883	1	14	study	study	NOUN
ssh-7883	1	15	of	of	ADP
ssh-7883	1	16	the	the	DET
ssh-7883	1	17	relationship	relationship	NOUN
ssh-7883	1	18	between	between	ADP
ssh-7883	1	19	two	two	NUM
ssh-7883	1	20	types	type	NOUN
ssh-7883	1	21	of	of	ADP
ssh-7883	1	22	mixed	mixed	ADJ
ssh-7883	1	23	-	-	PUNCT
ssh-7883	1	24	order	order	NOUN
ssh-7883	1	25	evolution	evolution	NOUN
ssh-7883	1	26	equations	equation	NOUN
ssh-7883	1	27	and	and	CCONJ
ssh-7883	1	28	the	the	DET
ssh-7883	1	29	existence	existence	NOUN
ssh-7883	1	30	of	of	ADP
ssh-7883	1	31	their	their	PRON
ssh-7883	1	32	solutions	solution	NOUN
ssh-7883	1	33	haoshan	haoshan	ADP
ssh-7883	1	34	yuan	yuan	PROPN
ssh-7883	1	35	*	*	PUNCT
ssh-7883	2	1	the	the	DET
ssh-7883	2	2	high	high	ADJ
ssh-7883	2	3	school	school	NOUN
ssh-7883	2	4	attached	attach	VERB
ssh-7883	2	5	to	to	ADP
ssh-7883	2	6	hunan	hunan	PROPN
ssh-7883	2	7	normal	normal	PROPN
ssh-7883	2	8	university	university	PROPN
ssh-7883	2	9	,	,	PUNCT
ssh-7883	2	10	changsha	changsha	PROPN
ssh-7883	2	11	hunan	hunan	PROPN
ssh-7883	2	12	,	,	PUNCT
ssh-7883	2	13	410000	410000	NUM
ssh-7883	2	14	,	,	PUNCT
ssh-7883	2	15	china	china	PROPN
ssh-7883	2	16	*	*	PUNCT
ssh-7883	2	17	corresponding	correspond	VERB
ssh-7883	2	18	author	author	NOUN
ssh-7883	2	19	email	email	NOUN
ssh-7883	2	20	:	:	PUNCT
ssh-7883	2	21	1217594171@qq.com	1217594171@qq.com	NUM
ssh-7883	2	22	abstract	abstract	NOUN
ssh-7883	2	23	.	.	PUNCT
ssh-7883	3	1	the	the	DET
ssh-7883	3	2	purpose	purpose	NOUN
ssh-7883	3	3	of	of	ADP
ssh-7883	3	4	this	this	DET
ssh-7883	3	5	article	article	NOUN
ssh-7883	3	6	is	be	AUX
ssh-7883	3	7	to	to	PART
ssh-7883	3	8	study	study	VERB
ssh-7883	3	9	the	the	DET
ssh-7883	3	10	relationship	relationship	NOUN
ssh-7883	3	11	between	between	ADP
ssh-7883	3	12	two	two	NUM
ssh-7883	3	13	types	type	NOUN
ssh-7883	3	14	of	of	ADP
ssh-7883	3	15	mixed	mixed	ADJ
ssh-7883	3	16	-	-	PUNCT
ssh-7883	3	17	order	order	NOUN
ssh-7883	3	18	evolution	evolution	NOUN
ssh-7883	3	19	equations	equation	NOUN
ssh-7883	3	20	and	and	CCONJ
ssh-7883	3	21	the	the	DET
ssh-7883	3	22	existence	existence	NOUN
ssh-7883	3	23	of	of	ADP
ssh-7883	3	24	their	their	PRON
ssh-7883	3	25	solutions	solution	NOUN
ssh-7883	3	26	.	.	PUNCT
ssh-7883	4	1	initially	initially	ADV
ssh-7883	4	2	,	,	PUNCT
ssh-7883	4	3	the	the	DET
ssh-7883	4	4	mild	mild	ADJ
ssh-7883	4	5	solutions	solution	NOUN
ssh-7883	4	6	of	of	ADP
ssh-7883	4	7	the	the	DET
ssh-7883	4	8	two	two	NUM
ssh-7883	4	9	system	system	NOUN
ssh-7883	4	10	are	be	AUX
ssh-7883	4	11	obtained	obtain	VERB
ssh-7883	4	12	by	by	ADP
ssh-7883	4	13	laplace	laplace	NOUN
ssh-7883	4	14	transform	transform	NOUN
ssh-7883	4	15	.	.	PUNCT
ssh-7883	5	1	then	then	ADV
ssh-7883	5	2	,	,	PUNCT
ssh-7883	5	3	we	we	PRON
ssh-7883	5	4	use	use	VERB
ssh-7883	5	5	semigroup	semigroup	PROPN
ssh-7883	5	6	theorem	theorem	NOUN
ssh-7883	5	7	and	and	CCONJ
ssh-7883	5	8	sector	sector	NOUN
ssh-7883	5	9	operator	operator	NOUN
ssh-7883	5	10	theorem	theorem	VERB
ssh-7883	5	11	to	to	PART
ssh-7883	5	12	get	get	VERB
ssh-7883	5	13	the	the	DET
ssh-7883	5	14	norm	norm	NOUN
ssh-7883	5	15	estimation	estimation	NOUN
ssh-7883	5	16	results	result	NOUN
ssh-7883	5	17	of	of	ADP
ssh-7883	5	18	understanding	understand	VERB
ssh-7883	5	19	operator	operator	NOUN
ssh-7883	5	20	through	through	ADP
ssh-7883	5	21	special	special	ADJ
ssh-7883	5	22	paths	path	NOUN
ssh-7883	5	23	in	in	ADP
ssh-7883	5	24	the	the	DET
ssh-7883	5	25	complex	complex	ADJ
ssh-7883	5	26	plane	plane	NOUN
ssh-7883	5	27	.	.	PUNCT
ssh-7883	6	1	further	far	ADV
ssh-7883	6	2	,	,	PUNCT
ssh-7883	6	3	the	the	DET
ssh-7883	6	4	sufficient	sufficient	ADJ
ssh-7883	6	5	conditions	condition	NOUN
ssh-7883	6	6	for	for	ADP
ssh-7883	6	7	existence	existence	NOUN
ssh-7883	6	8	and	and	CCONJ
ssh-7883	6	9	uniqueness	uniqueness	NOUN
ssh-7883	6	10	of	of	ADP
ssh-7883	6	11	mild	mild	ADJ
ssh-7883	6	12	solution	solution	NOUN
ssh-7883	6	13	of	of	ADP
ssh-7883	6	14	the	the	DET
ssh-7883	6	15	proposed	propose	VERB
ssh-7883	6	16	system	system	NOUN
ssh-7883	6	17	are	be	AUX
ssh-7883	6	18	verified	verify	VERB
ssh-7883	6	19	by	by	ADP
ssh-7883	6	20	applying	apply	VERB
ssh-7883	6	21	fixed	fix	VERB
ssh-7883	6	22	point	point	NOUN
ssh-7883	6	23	theorems	theorem	NOUN
ssh-7883	6	24	.	.	PUNCT
ssh-7883	7	1	finally	finally	ADV
ssh-7883	7	2	,	,	PUNCT
ssh-7883	7	3	examples	example	NOUN
ssh-7883	7	4	are	be	AUX
ssh-7883	7	5	provided	provide	VERB
ssh-7883	7	6	to	to	PART
ssh-7883	7	7	illustrate	illustrate	VERB
ssh-7883	7	8	the	the	DET
ssh-7883	7	9	main	main	ADJ
ssh-7883	7	10	results	result	NOUN
ssh-7883	7	11	.	.	PUNCT
ssh-7883	8	1	keywords	keyword	NOUN
ssh-7883	8	2	:	:	PUNCT
ssh-7883	8	3	mixed	mixed	ADJ
ssh-7883	8	4	-	-	PUNCT
ssh-7883	8	5	order	order	NOUN
ssh-7883	8	6	evolution	evolution	NOUN
ssh-7883	8	7	equation	equation	NOUN
ssh-7883	8	8	;	;	PUNCT
ssh-7883	8	9	mild	mild	ADJ
ssh-7883	8	10	solution	solution	NOUN
ssh-7883	8	11	;	;	PUNCT
ssh-7883	8	12	sectorial	sectorial	ADJ
ssh-7883	8	13	operator	operator	NOUN
ssh-7883	8	14	.	.	PUNCT
ssh-7883	9	1	1	1	X
ssh-7883	9	2	.	.	X
ssh-7883	9	3	introduction	introduction	NOUN
ssh-7883	9	4	fractional	fractional	ADJ
ssh-7883	9	5	calculus	calculus	NOUN
ssh-7883	9	6	is	be	AUX
ssh-7883	9	7	a	a	DET
ssh-7883	9	8	theory	theory	NOUN
ssh-7883	9	9	about	about	ADP
ssh-7883	9	10	arbitrary	arbitrary	ADJ
ssh-7883	9	11	-	-	PUNCT
ssh-7883	9	12	order	order	NOUN
ssh-7883	9	13	differentiation	differentiation	NOUN
ssh-7883	9	14	and	and	CCONJ
ssh-7883	9	15	integral	integral	ADJ
ssh-7883	9	16	,	,	PUNCT
ssh-7883	9	17	and	and	CCONJ
ssh-7883	9	18	it	it	PRON
ssh-7883	9	19	is	be	AUX
ssh-7883	9	20	a	a	DET
ssh-7883	9	21	generalization	generalization	NOUN
ssh-7883	9	22	of	of	ADP
ssh-7883	9	23	integer	integer	NOUN
ssh-7883	9	24	-	-	PUNCT
ssh-7883	9	25	order	order	NOUN
ssh-7883	9	26	calculus	calculus	NOUN
ssh-7883	9	27	.	.	PUNCT
ssh-7883	10	1	in	in	ADP
ssh-7883	10	2	recent	recent	ADJ
ssh-7883	10	3	years	year	NOUN
ssh-7883	10	4	,	,	PUNCT
ssh-7883	10	5	fractional	fractional	ADJ
ssh-7883	10	6	order	order	NOUN
ssh-7883	10	7	derivatives	derivative	NOUN
ssh-7883	10	8	have	have	AUX
ssh-7883	10	9	become	become	VERB
ssh-7883	10	10	an	an	DET
ssh-7883	10	11	important	important	ADJ
ssh-7883	10	12	tool	tool	NOUN
ssh-7883	10	13	for	for	ADP
ssh-7883	10	14	describing	describe	VERB
ssh-7883	10	15	various	various	ADJ
ssh-7883	10	16	complex	complex	ADJ
ssh-7883	10	17	mechanical	mechanical	ADJ
ssh-7883	10	18	behaviors	behavior	NOUN
ssh-7883	10	19	,	,	PUNCT
ssh-7883	10	20	physical	physical	ADJ
ssh-7883	10	21	behaviors	behavior	NOUN
ssh-7883	10	22	and	and	CCONJ
ssh-7883	10	23	other	other	ADJ
ssh-7883	10	24	relevant	relevant	ADJ
ssh-7883	10	25	behavioral	behavioral	ADJ
ssh-7883	10	26	features	feature	NOUN
ssh-7883	10	27	[	[	X
ssh-7883	10	28	1–4	1–4	NOUN
ssh-7883	10	29	]	]	X
ssh-7883	10	30	.	.	PUNCT
ssh-7883	11	1	as	as	ADP
ssh-7883	11	2	a	a	DET
ssh-7883	11	3	research	research	NOUN
ssh-7883	11	4	direction	direction	NOUN
ssh-7883	11	5	with	with	ADP
ssh-7883	11	6	practical	practical	ADJ
ssh-7883	11	7	significance	significance	NOUN
ssh-7883	11	8	,	,	PUNCT
ssh-7883	11	9	the	the	DET
ssh-7883	11	10	fractional	fractional	ADJ
ssh-7883	11	11	order	order	NOUN
ssh-7883	11	12	differential	differential	NOUN
ssh-7883	11	13	equations	equation	NOUN
ssh-7883	11	14	have	have	AUX
ssh-7883	11	15	been	be	AUX
ssh-7883	11	16	of	of	ADP
ssh-7883	11	17	great	great	ADJ
ssh-7883	11	18	concern	concern	NOUN
ssh-7883	11	19	to	to	ADP
ssh-7883	11	20	researchers	researcher	NOUN
ssh-7883	11	21	.	.	PUNCT
ssh-7883	12	1	many	many	ADJ
ssh-7883	12	2	researchers	researcher	NOUN
ssh-7883	12	3	have	have	AUX
ssh-7883	12	4	studied	study	VERB
ssh-7883	12	5	riemann	riemann	PROPN
ssh-7883	12	6	-	-	PUNCT
ssh-7883	12	7	liuville	liuville	VERB
ssh-7883	12	8	fractional	fractional	ADJ
ssh-7883	12	9	order	order	NOUN
ssh-7883	12	10	differential	differential	ADJ
ssh-7883	12	11	equations	equation	NOUN
ssh-7883	12	12	and	and	CCONJ
ssh-7883	12	13	caputo	caputo	PROPN
ssh-7883	12	14	fractional	fractional	PROPN
ssh-7883	12	15	order	order	NOUN
ssh-7883	12	16	differential	differential	NOUN
ssh-7883	12	17	equations	equation	NOUN
ssh-7883	12	18	,	,	PUNCT
ssh-7883	12	19	and	and	CCONJ
ssh-7883	12	20	have	have	AUX
ssh-7883	12	21	achieved	achieve	VERB
ssh-7883	12	22	significant	significant	ADJ
ssh-7883	12	23	results	result	NOUN
ssh-7883	12	24	[	[	X
ssh-7883	12	25	5–9	5–9	X
ssh-7883	12	26	]	]	X
ssh-7883	12	27	.	.	PUNCT
ssh-7883	13	1	for	for	ADP
ssh-7883	13	2	example	example	NOUN
ssh-7883	13	3	,	,	PUNCT
ssh-7883	13	4	arara	arara	NOUN
ssh-7883	13	5	,	,	PUNCT
ssh-7883	13	6	a	a	DET
ssh-7883	13	7	et	et	NOUN
ssh-7883	13	8	al	al	PROPN
ssh-7883	13	9	.	.	PUNCT
ssh-7883	14	1	[	[	X
ssh-7883	14	2	8	8	NUM
ssh-7883	14	3	]	]	PUNCT
ssh-7883	14	4	used	use	VERB
ssh-7883	14	5	the	the	DET
ssh-7883	14	6	fixed	fix	VERB
ssh-7883	14	7	point	point	NOUN
ssh-7883	14	8	theorem	theorem	NOUN
ssh-7883	14	9	of	of	ADP
ssh-7883	14	10	schauder	schauder	NOUN
ssh-7883	14	11	combined	combine	VERB
ssh-7883	14	12	with	with	ADP
ssh-7883	14	13	the	the	DET
ssh-7883	14	14	diagonalization	diagonalization	NOUN
ssh-7883	14	15	method	method	NOUN
ssh-7883	14	16	to	to	PART
ssh-7883	14	17	prove	prove	VERB
ssh-7883	14	18	the	the	DET
ssh-7883	14	19	existence	existence	NOUN
ssh-7883	14	20	of	of	ADP
ssh-7883	14	21	bounded	bounded	ADJ
ssh-7883	14	22	solutions	solution	NOUN
ssh-7883	14	23	of	of	ADP
ssh-7883	14	24	a	a	DET
ssh-7883	14	25	boundary	boundary	ADJ
ssh-7883	14	26	value	value	NOUN
ssh-7883	14	27	problem	problem	NOUN
ssh-7883	14	28	on	on	ADP
ssh-7883	14	29	an	an	DET
ssh-7883	14	30	unbounded	unbounded	ADJ
ssh-7883	14	31	domain	domain	NOUN
ssh-7883	14	32	for	for	ADP
ssh-7883	14	33	differential	differential	ADJ
ssh-7883	14	34	equations	equation	NOUN
ssh-7883	14	35	involving	involve	VERB
ssh-7883	14	36	the	the	DET
ssh-7883	14	37	caputo	caputo	PROPN
ssh-7883	14	38	fractional	fractional	PROPN
ssh-7883	14	39	derivative	derivative	PROPN
ssh-7883	14	40	.	.	PUNCT
ssh-7883	15	1	shu	shu	PROPN
ssh-7883	15	2	et	et	PROPN
ssh-7883	15	3	al	al	PROPN
ssh-7883	15	4	.	.	PUNCT
ssh-7883	16	1	[	[	X
ssh-7883	16	2	9	9	NUM
ssh-7883	16	3	]	]	PUNCT
ssh-7883	16	4	investigated	investigate	VERB
ssh-7883	16	5	the	the	DET
ssh-7883	16	6	existence	existence	NOUN
ssh-7883	16	7	of	of	ADP
ssh-7883	16	8	the	the	DET
ssh-7883	16	9	extremal	extremal	ADJ
ssh-7883	16	10	solutions	solution	NOUN
ssh-7883	16	11	for	for	ADP
ssh-7883	16	12	a	a	DET
ssh-7883	16	13	class	class	NOUN
ssh-7883	16	14	of	of	ADP
ssh-7883	16	15	fractional	fractional	ADJ
ssh-7883	16	16	partial	partial	ADJ
ssh-7883	16	17	differential	differential	NOUN
ssh-7883	16	18	equations	equation	NOUN
ssh-7883	16	19	with	with	ADP
ssh-7883	16	20	order	order	NOUN
ssh-7883	16	21	1	1	NUM
ssh-7883	16	22	<	<	X
ssh-7883	16	23	α	α	X
ssh-7883	16	24	<	<	X
ssh-7883	16	25	2	2	NUM
ssh-7883	16	26	by	by	ADP
ssh-7883	16	27	upper	upper	ADJ
ssh-7883	16	28	and	and	CCONJ
ssh-7883	16	29	lower	low	ADJ
ssh-7883	16	30	solution	solution	NOUN
ssh-7883	16	31	method	method	NOUN
ssh-7883	16	32	.	.	PUNCT
ssh-7883	17	1	in	in	ADP
ssh-7883	17	2	this	this	DET
ssh-7883	17	3	article	article	NOUN
ssh-7883	17	4	,	,	PUNCT
ssh-7883	17	5	we	we	PRON
ssh-7883	17	6	study	study	VERB
ssh-7883	17	7	the	the	DET
ssh-7883	17	8	relationship	relationship	NOUN
ssh-7883	17	9	between	between	ADP
ssh-7883	17	10	two	two	NUM
ssh-7883	17	11	types	type	NOUN
ssh-7883	17	12	of	of	ADP
ssh-7883	17	13	mixed	mixed	ADJ
ssh-7883	17	14	-	-	PUNCT
ssh-7883	17	15	order	order	NOUN
ssh-7883	17	16	development	development	NOUN
ssh-7883	17	17	equations	equation	NOUN
ssh-7883	17	18	and	and	CCONJ
ssh-7883	17	19	existence	existence	NOUN
ssh-7883	17	20	of	of	ADP
ssh-7883	17	21	their	their	PRON
ssh-7883	17	22	solutions	solution	NOUN
ssh-7883	17	23	.	.	PUNCT
ssh-7883	18	1	in	in	ADP
ssh-7883	18	2	addition	addition	NOUN
ssh-7883	18	3	,	,	PUNCT
ssh-7883	18	4	with	with	ADP
ssh-7883	18	5	the	the	DET
ssh-7883	18	6	development	development	NOUN
ssh-7883	18	7	of	of	ADP
ssh-7883	18	8	operator	operator	NOUN
ssh-7883	18	9	theory	theory	NOUN
ssh-7883	18	10	,	,	PUNCT
ssh-7883	18	11	people	people	NOUN
ssh-7883	18	12	are	be	AUX
ssh-7883	18	13	no	no	ADV
ssh-7883	18	14	longer	long	ADV
ssh-7883	18	15	limited	limit	VERB
ssh-7883	18	16	to	to	ADP
ssh-7883	18	17	the	the	DET
ssh-7883	18	18	study	study	NOUN
ssh-7883	18	19	of	of	ADP
ssh-7883	18	20	linear	linear	ADJ
ssh-7883	18	21	fractional	fractional	ADJ
ssh-7883	18	22	differential	differential	NOUN
ssh-7883	18	23	equations	equation	NOUN
ssh-7883	18	24	,	,	PUNCT
ssh-7883	18	25	and	and	CCONJ
ssh-7883	18	26	the	the	DET
ssh-7883	18	27	research	research	NOUN
ssh-7883	18	28	for	for	ADP
ssh-7883	18	29	a	a	DET
ssh-7883	18	30	class	class	NOUN
ssh-7883	18	31	of	of	ADP
ssh-7883	18	32	fractional	fractional	ADJ
ssh-7883	18	33	semilinear	semilinear	ADJ
ssh-7883	18	34	integrodifferential	integrodifferential	ADJ
ssh-7883	18	35	equation	equation	NOUN
ssh-7883	18	36	has	have	AUX
ssh-7883	18	37	also	also	ADV
ssh-7883	18	38	attracted	attract	VERB
ssh-7883	18	39	widespread	widespread	ADJ
ssh-7883	18	40	attention	attention	NOUN
ssh-7883	18	41	,	,	PUNCT
ssh-7883	18	42	and	and	CCONJ
ssh-7883	18	43	a	a	DET
ssh-7883	18	44	lot	lot	NOUN
ssh-7883	18	45	of	of	ADP
ssh-7883	18	46	scholars	scholar	NOUN
ssh-7883	18	47	have	have	AUX
ssh-7883	18	48	done	do	VERB
ssh-7883	18	49	relevant	relevant	ADJ
ssh-7883	18	50	researches	research	NOUN
ssh-7883	19	1	[	[	X
ssh-7883	19	2	10	10	NUM
ssh-7883	19	3	–	–	PUNCT
ssh-7883	19	4	14	14	NUM
ssh-7883	19	5	]	]	PUNCT
ssh-7883	19	6	.	.	PUNCT
ssh-7883	20	1	although	although	SCONJ
ssh-7883	20	2	many	many	ADJ
ssh-7883	20	3	scholars	scholar	NOUN
ssh-7883	20	4	have	have	AUX
ssh-7883	20	5	studied	study	VERB
ssh-7883	20	6	many	many	ADJ
ssh-7883	20	7	kinds	kind	NOUN
ssh-7883	20	8	of	of	ADP
ssh-7883	20	9	differential	differential	ADJ
ssh-7883	20	10	equations	equation	NOUN
ssh-7883	20	11	,	,	PUNCT
ssh-7883	20	12	there	there	PRON
ssh-7883	20	13	are	be	VERB
ssh-7883	20	14	still	still	ADV
ssh-7883	20	15	parts	part	NOUN
ssh-7883	20	16	waiting	wait	VERB
ssh-7883	20	17	to	to	PART
ssh-7883	20	18	be	be	AUX
ssh-7883	20	19	explored	explore	VERB
ssh-7883	20	20	.	.	PUNCT
ssh-7883	21	1	moreover	moreover	ADV
ssh-7883	21	2	,	,	PUNCT
ssh-7883	21	3	shu	shu	PROPN
ssh-7883	21	4	etal.[12	etal.[12	PROPN
ssh-7883	21	5	]	]	PUNCT
ssh-7883	21	6	have	have	AUX
ssh-7883	21	7	studied	study	VERB
ssh-7883	21	8	a	a	DET
ssh-7883	21	9	class	class	NOUN
ssh-7883	21	10	of	of	ADP
ssh-7883	21	11	fractional	fractional	ADJ
ssh-7883	21	12	differential	differential	ADJ
ssh-7883	21	13	equations	equation	NOUN
ssh-7883	21	14	with	with	ADP
ssh-7883	21	15	nolocal	nolocal	ADJ
ssh-7883	21	16	conditions	condition	NOUN
ssh-7883	21	17	of	of	ADP
ssh-7883	21	18	order	order	NOUN
ssh-7883	21	19	1	1	NUM
ssh-7883	21	20	<	<	X
ssh-7883	21	21	α	α	X
ssh-7883	21	22	<	<	X
ssh-7883	21	23	2	2	NUM
ssh-7883	21	24	and	and	CCONJ
ssh-7883	21	25	obtain	obtain	VERB
ssh-7883	21	26	the	the	DET
ssh-7883	21	27	existence	existence	NOUN
ssh-7883	21	28	results	result	NOUN
ssh-7883	21	29	by	by	ADP
ssh-7883	21	30	the	the	DET
ssh-7883	21	31	fixed	fix	VERB
ssh-7883	21	32	point	point	NOUN
ssh-7883	21	33	theorem	theorem	VERB
ssh-7883	21	34	combined	combine	VERB
ssh-7883	21	35	with	with	ADP
ssh-7883	21	36	solutions	solution	NOUN
ssh-7883	21	37	operator	operator	NOUN
ssh-7883	21	38	theorems	theorem	NOUN
ssh-7883	21	39	.	.	PUNCT
ssh-7883	22	1	the	the	DET
ssh-7883	22	2	system	system	NOUN
ssh-7883	22	3	is	be	AUX
ssh-7883	22	4	as	as	SCONJ
ssh-7883	22	5	follows	follow	VERB
ssh-7883	22	6	:	:	PUNCT
ssh-7883	22	7	ds	ds	ADJ
ssh-7883	22	8	,	,	PUNCT
ssh-7883	22	9	t	t	PROPN
ssh-7883	22	10	∈	∈	PROPN
ssh-7883	23	1	the	the	DET
ssh-7883	23	2	system	system	NOUN
ssh-7883	23	3	is	be	AUX
ssh-7883	23	4	on	on	ADP
ssh-7883	23	5	banach	banach	NOUN
ssh-7883	23	6	space	space	NOUN
ssh-7883	23	7	x	x	NOUN
ssh-7883	23	8	and	and	CCONJ
ssh-7883	23	9	dtα	dtα	NOUN
ssh-7883	23	10	is	be	AUX
ssh-7883	23	11	caputo	caputo	PROPN
ssh-7883	23	12	’s	’s	PART
ssh-7883	23	13	fractional	fractional	ADJ
ssh-7883	23	14	derivative	derivative	NOUN
ssh-7883	23	15	of	of	ADP
ssh-7883	23	16	1	1	NUM
ssh-7883	23	17	<	<	X
ssh-7883	23	18	α	α	X
ssh-7883	23	19	<	<	X
ssh-7883	23	20	2	2	NUM
ssh-7883	23	21	,	,	PUNCT
ssh-7883	23	22	a	a	PRON
ssh-7883	23	23	is	be	AUX
ssh-7883	23	24	a	a	DET
ssh-7883	23	25	sectorial	sectorial	ADJ
ssh-7883	23	26	operator	operator	NOUN
ssh-7883	23	27	of	of	ADP
ssh-7883	23	28	type	type	NOUN
ssh-7883	23	29	(	(	PUNCT
ssh-7883	23	30	m	m	PROPN
ssh-7883	23	31	,	,	PUNCT
ssh-7883	23	32	θ	θ	PROPN
ssh-7883	23	33	,	,	PUNCT
ssh-7883	23	34	α,µ	α,µ	ADJ
ssh-7883	23	35	)	)	PUNCT
ssh-7883	23	36	.	.	PUNCT
ssh-7883	24	1	motivated	motivate	VERB
ssh-7883	24	2	by	by	ADP
ssh-7883	24	3	the	the	DET
ssh-7883	24	4	literature	literature	NOUN
ssh-7883	24	5	above	above	ADV
ssh-7883	24	6	,	,	PUNCT
ssh-7883	24	7	on	on	ADP
ssh-7883	24	8	a	a	DET
ssh-7883	24	9	banach	banach	NOUN
ssh-7883	24	10	space	space	NOUN
ssh-7883	24	11	x	x	NOUN
ssh-7883	24	12	,	,	PUNCT
ssh-7883	24	13	we	we	PRON
ssh-7883	24	14	study	study	VERB
ssh-7883	24	15	the	the	DET
ssh-7883	24	16	relationship	relationship	NOUN
ssh-7883	24	17	between	between	ADP
ssh-7883	24	18	following	follow	VERB
ssh-7883	24	19	two	two	NUM
ssh-7883	24	20	types	type	NOUN
ssh-7883	24	21	of	of	ADP
ssh-7883	24	22	mixed	mixed	ADJ
ssh-7883	24	23	-	-	PUNCT
ssh-7883	24	24	order	order	NOUN
ssh-7883	24	25	development	development	NOUN
ssh-7883	24	26	equations	equation	NOUN
ssh-7883	24	27	and	and	CCONJ
ssh-7883	24	28	the	the	DET
ssh-7883	24	29	existence	existence	NOUN
ssh-7883	24	30	of	of	ADP
ssh-7883	24	31	the	the	DET
ssh-7883	24	32	solution	solution	NOUN
ssh-7883	24	33	:	:	PUNCT
ssh-7883	24	34	(	(	PUNCT
ssh-7883	24	35	1.1	1.1	NUM
ssh-7883	24	36	)	)	PUNCT
ssh-7883	24	37	bcp	bcp	VERB
ssh-7883	24	38	social	social	PROPN
ssh-7883	24	39	sciences	sciences	PROPN
ssh-7883	24	40	&	&	CCONJ
ssh-7883	24	41	humanities	humanities	PROPN
ssh-7883	24	42	erss	erss	VERB
ssh-7883	24	43	2024	2024	NUM
ssh-7883	24	44	volume	volume	NOUN
ssh-7883	24	45	23	23	NUM
ssh-7883	24	46	(	(	PUNCT
ssh-7883	24	47	2024	2024	NUM
ssh-7883	24	48	)	)	PUNCT
ssh-7883	24	49	2	2	NUM
ssh-7883	24	50	and	and	CCONJ
ssh-7883	24	51	(	(	PUNCT
ssh-7883	24	52	1.2	1.2	NUM
ssh-7883	24	53	)	)	PUNCT
ssh-7883	24	54	where	where	SCONJ
ssh-7883	24	55	t	t	PROPN
ssh-7883	24	56	∈	∈	PROPN
ssh-7883	24	57	j	j	PROPN
ssh-7883	25	1	=	=	PUNCT
ssh-7883	26	1	[	[	X
ssh-7883	26	2	0	0	NUM
ssh-7883	26	3	,	,	PUNCT
ssh-7883	26	4	∞	∞	PROPN
ssh-7883	26	5	)	)	PUNCT
ssh-7883	26	6	,	,	PUNCT
ssh-7883	26	7	0	0	NUM
ssh-7883	26	8	<	<	X
ssh-7883	26	9	α	α	X
ssh-7883	26	10	<	<	X
ssh-7883	26	11	1	1	NUM
ssh-7883	26	12	,	,	PUNCT
ssh-7883	26	13	0	0	PUNCT
ssh-7883	26	14	<	<	X
ssh-7883	26	15	β	β	X
ssh-7883	26	16	<	<	X
ssh-7883	26	17	1	1	NUM
ssh-7883	26	18	,	,	PUNCT
ssh-7883	26	19	1	1	NUM
ssh-7883	26	20	<	<	X
ssh-7883	26	21	α+β	α+β	X
ssh-7883	26	22	<	<	X
ssh-7883	26	23	2	2	NUM
ssh-7883	26	24	.	.	PUNCT
ssh-7883	26	25	here	here	ADV
ssh-7883	26	26	d0α+	d0α+	PROPN
ssh-7883	26	27	denotes	denote	VERB
ssh-7883	26	28	riemann	riemann	PROPN
ssh-7883	26	29	-	-	PUNCT
ssh-7883	26	30	liouville	liouville	VERB
ssh-7883	26	31	fractional	fractional	ADJ
ssh-7883	26	32	order	order	NOUN
ssh-7883	26	33	derivative	derivative	NOUN
ssh-7883	26	34	of	of	ADP
ssh-7883	26	35	order	order	NOUN
ssh-7883	26	36	α	α	NOUN
ssh-7883	26	37	with	with	ADP
ssh-7883	26	38	lower	low	ADJ
ssh-7883	26	39	limit	limit	NOUN
ssh-7883	26	40	zero(see	zero(see	NOUN
ssh-7883	26	41	definition	definition	NOUN
ssh-7883	26	42	2.2),and	2.2),and	NUM
ssh-7883	26	43	cd0	cd0	NOUN
ssh-7883	26	44	β	β	NOUN
ssh-7883	27	1	+	+	CCONJ
ssh-7883	27	2	denotes	denote	NOUN
ssh-7883	27	3	caputo	caputo	PROPN
ssh-7883	27	4	fractonal	fractonal	ADJ
ssh-7883	27	5	order	order	NOUN
ssh-7883	27	6	derivative	derivative	NOUN
ssh-7883	27	7	of	of	ADP
ssh-7883	27	8	order	order	NOUN
ssh-7883	27	9	β	β	X
ssh-7883	27	10	lower	low	ADJ
ssh-7883	27	11	limit	limit	VERB
ssh-7883	27	12	zero(see	zero(see	PROPN
ssh-7883	27	13	definition	definition	NOUN
ssh-7883	27	14	2.3	2.3	NUM
ssh-7883	27	15	)	)	PUNCT
ssh-7883	27	16	;	;	PUNCT
ssh-7883	27	17	let	let	VERB
ssh-7883	27	18	a	a	DET
ssh-7883	27	19	:	:	PUNCT
ssh-7883	27	20	d(a	d(a	PROPN
ssh-7883	27	21	)	)	PUNCT
ssh-7883	28	1	⊆	⊆	NUM
ssh-7883	28	2	x	x	SYM
ssh-7883	28	3	→	→	PUNCT
ssh-7883	28	4	x	x	PUNCT
ssh-7883	28	5	be	be	AUX
ssh-7883	28	6	a	a	DET
ssh-7883	28	7	sectorial	sectorial	ADJ
ssh-7883	28	8	operator	operator	NOUN
ssh-7883	28	9	of	of	ADP
ssh-7883	28	10	type	type	NOUN
ssh-7883	28	11	(	(	PUNCT
ssh-7883	28	12	m	m	PROPN
ssh-7883	28	13	,	,	PUNCT
ssh-7883	28	14	θ	θ	NOUN
ssh-7883	28	15	,	,	PUNCT
ssh-7883	28	16	α+β,µ)(see	α+β,µ)(see	ADJ
ssh-7883	28	17	definition	definition	NOUN
ssh-7883	28	18	2.4	2.4	NUM
ssh-7883	28	19	)	)	PUNCT
ssh-7883	28	20	,	,	PUNCT
ssh-7883	28	21	and	and	CCONJ
ssh-7883	28	22	the	the	DET
ssh-7883	28	23	nonlinear	nonlinear	ADJ
ssh-7883	28	24	map	map	NOUN
ssh-7883	28	25	f	f	X
ssh-7883	28	26	:	:	PUNCT
ssh-7883	28	27	j	j	PROPN
ssh-7883	28	28	×	×	NOUN
ssh-7883	28	29	x	x	INTJ
ssh-7883	28	30	→	→	PUNCT
ssh-7883	28	31	x	x	X
ssh-7883	28	32	is	be	AUX
ssh-7883	28	33	a	a	DET
ssh-7883	28	34	continious	continious	ADJ
ssh-7883	28	35	function	function	NOUN
ssh-7883	28	36	satisfying	satisfy	VERB
ssh-7883	28	37	some	some	DET
ssh-7883	28	38	conditions	condition	NOUN
ssh-7883	28	39	given	give	VERB
ssh-7883	28	40	later	later	ADV
ssh-7883	28	41	.	.	PUNCT
ssh-7883	29	1	the	the	DET
ssh-7883	29	2	motives	motive	NOUN
ssh-7883	29	3	and	and	CCONJ
ssh-7883	29	4	highlights	highlight	NOUN
ssh-7883	29	5	in	in	ADP
ssh-7883	29	6	this	this	DET
ssh-7883	29	7	paper	paper	NOUN
ssh-7883	29	8	are	be	AUX
ssh-7883	29	9	as	as	SCONJ
ssh-7883	29	10	follows	follow	VERB
ssh-7883	29	11	:	:	PUNCT
ssh-7883	29	12	for	for	ADP
ssh-7883	29	13	equation	equation	NOUN
ssh-7883	29	14	(	(	PUNCT
ssh-7883	29	15	1	1	NUM
ssh-7883	29	16	)	)	PUNCT
ssh-7883	29	17	and	and	CCONJ
ssh-7883	29	18	(	(	PUNCT
ssh-7883	29	19	2	2	NUM
ssh-7883	29	20	)	)	PUNCT
ssh-7883	29	21	,	,	PUNCT
ssh-7883	29	22	instead	instead	ADV
ssh-7883	29	23	of	of	ADP
ssh-7883	29	24	just	just	ADV
ssh-7883	29	25	using	use	VERB
ssh-7883	29	26	riemann	riemann	PROPN
ssh-7883	29	27	-	-	PUNCT
ssh-7883	29	28	liouville	liouville	VERB
ssh-7883	29	29	fractional	fractional	ADJ
ssh-7883	29	30	derivative	derivative	NOUN
ssh-7883	29	31	or	or	CCONJ
ssh-7883	29	32	caputo	caputo	PROPN
ssh-7883	29	33	fractional	fractional	PROPN
ssh-7883	29	34	derivative	derivative	NOUN
ssh-7883	29	35	,	,	PUNCT
ssh-7883	29	36	it	it	PRON
ssh-7883	29	37	combines	combine	VERB
ssh-7883	29	38	two	two	NUM
ssh-7883	29	39	differentials	differential	NOUN
ssh-7883	29	40	to	to	PART
ssh-7883	29	41	construct	construct	VERB
ssh-7883	29	42	a	a	DET
ssh-7883	29	43	new	new	ADJ
ssh-7883	29	44	class	class	NOUN
ssh-7883	29	45	of	of	ADP
ssh-7883	29	46	equations	equation	NOUN
ssh-7883	29	47	.	.	PUNCT
ssh-7883	30	1	meanwhile	meanwhile	ADV
ssh-7883	30	2	,	,	PUNCT
ssh-7883	30	3	we	we	PRON
ssh-7883	30	4	obtain	obtain	VERB
ssh-7883	30	5	the	the	DET
ssh-7883	30	6	solution	solution	NOUN
ssh-7883	30	7	of	of	ADP
ssh-7883	30	8	equation	equation	NOUN
ssh-7883	30	9	(	(	PUNCT
ssh-7883	30	10	1.1	1.1	NUM
ssh-7883	30	11	)	)	PUNCT
ssh-7883	30	12	and	and	CCONJ
ssh-7883	30	13	(	(	PUNCT
ssh-7883	30	14	1.2	1.2	NUM
ssh-7883	30	15	)	)	PUNCT
ssh-7883	30	16	not	not	PART
ssh-7883	30	17	by	by	ADP
ssh-7883	30	18	the	the	DET
ssh-7883	30	19	traditional	traditional	ADJ
ssh-7883	30	20	integral	integral	ADJ
ssh-7883	30	21	operator	operator	NOUN
ssh-7883	30	22	sequentially	sequentially	ADV
ssh-7883	30	23	acting	act	VERB
ssh-7883	30	24	on	on	ADP
ssh-7883	30	25	the	the	DET
ssh-7883	30	26	equation	equation	NOUN
ssh-7883	30	27	,	,	PUNCT
ssh-7883	30	28	but	but	CCONJ
ssh-7883	30	29	by	by	ADP
ssh-7883	30	30	using	use	VERB
ssh-7883	30	31	the	the	DET
ssh-7883	30	32	properties	property	NOUN
ssh-7883	30	33	of	of	ADP
ssh-7883	30	34	the	the	DET
ssh-7883	30	35	laplace	laplace	NOUN
ssh-7883	30	36	operator	operator	NOUN
ssh-7883	30	37	and	and	CCONJ
ssh-7883	30	38	the	the	DET
ssh-7883	30	39	sectorial	sectorial	ADJ
ssh-7883	30	40	operator	operator	NOUN
ssh-7883	30	41	to	to	PART
ssh-7883	30	42	obtain	obtain	VERB
ssh-7883	30	43	the	the	DET
ssh-7883	30	44	mild	mild	ADJ
ssh-7883	30	45	solution	solution	NOUN
ssh-7883	30	46	of	of	ADP
ssh-7883	30	47	the	the	DET
ssh-7883	30	48	equation	equation	NOUN
ssh-7883	30	49	,	,	PUNCT
ssh-7883	30	50	which	which	PRON
ssh-7883	30	51	is	be	AUX
ssh-7883	30	52	different	different	ADJ
ssh-7883	30	53	from	from	ADP
ssh-7883	30	54	the	the	DET
ssh-7883	30	55	research	research	NOUN
ssh-7883	30	56	methods	method	NOUN
ssh-7883	30	57	of	of	ADP
ssh-7883	30	58	previous	previous	ADJ
ssh-7883	30	59	researchers	researcher	NOUN
ssh-7883	30	60	.	.	PUNCT
ssh-7883	31	1	2	2	X
ssh-7883	31	2	.	.	X
ssh-7883	31	3	preliminaries	preliminary	NOUN
ssh-7883	31	4	in	in	ADP
ssh-7883	31	5	this	this	DET
ssh-7883	31	6	section	section	NOUN
ssh-7883	31	7	,	,	PUNCT
ssh-7883	31	8	we	we	PRON
ssh-7883	31	9	will	will	AUX
ssh-7883	31	10	present	present	VERB
ssh-7883	31	11	some	some	DET
ssh-7883	31	12	primary	primary	ADJ
ssh-7883	31	13	components	component	NOUN
ssh-7883	31	14	,	,	PUNCT
ssh-7883	31	15	including	include	VERB
ssh-7883	31	16	notations	notation	NOUN
ssh-7883	31	17	,	,	PUNCT
ssh-7883	31	18	definitions	definition	NOUN
ssh-7883	31	19	,	,	PUNCT
ssh-7883	31	20	lemmas	lemmas	PROPN
ssh-7883	31	21	,	,	PUNCT
ssh-7883	31	22	theorems	theorem	NOUN
ssh-7883	31	23	,	,	PUNCT
ssh-7883	31	24	and	and	CCONJ
ssh-7883	31	25	so	so	ADV
ssh-7883	31	26	on	on	ADV
ssh-7883	31	27	,	,	PUNCT
ssh-7883	31	28	which	which	PRON
ssh-7883	31	29	are	be	AUX
ssh-7883	31	30	required	require	VERB
ssh-7883	31	31	in	in	ADP
ssh-7883	31	32	the	the	DET
ssh-7883	31	33	process	process	NOUN
ssh-7883	31	34	to	to	PART
ssh-7883	31	35	prove	prove	VERB
ssh-7883	31	36	our	our	PRON
ssh-7883	31	37	main	main	ADJ
ssh-7883	31	38	results	result	NOUN
ssh-7883	31	39	.	.	PUNCT
ssh-7883	32	1	in	in	ADP
ssh-7883	32	2	this	this	DET
ssh-7883	32	3	paper	paper	NOUN
ssh-7883	32	4	,	,	PUNCT
ssh-7883	32	5	c(j	c(j	PROPN
ssh-7883	32	6	,	,	PUNCT
ssh-7883	32	7	x	x	X
ssh-7883	32	8	)	)	PUNCT
ssh-7883	32	9	is	be	AUX
ssh-7883	32	10	the	the	DET
ssh-7883	32	11	banach	banach	NOUN
ssh-7883	32	12	space	space	NOUN
ssh-7883	32	13	of	of	ADP
ssh-7883	32	14	all	all	DET
ssh-7883	32	15	continuous	continuous	ADJ
ssh-7883	32	16	functions	function	NOUN
ssh-7883	32	17	from	from	ADP
ssh-7883	32	18	j	j	PROPN
ssh-7883	32	19	=	=	PUNCT
ssh-7883	33	1	[	[	X
ssh-7883	33	2	0	0	NUM
ssh-7883	33	3	,	,	PUNCT
ssh-7883	33	4	∞	∞	PROPN
ssh-7883	33	5	)	)	PUNCT
ssh-7883	33	6	into	into	ADP
ssh-7883	33	7	x	x	PRON
ssh-7883	33	8	,	,	PUNCT
ssh-7883	33	9	furnished	furnish	VERB
ssh-7883	33	10	with	with	ADP
ssh-7883	33	11	the	the	DET
ssh-7883	33	12	uniform	uniform	ADJ
ssh-7883	33	13	convergence	convergence	NOUN
ssh-7883	33	14	norm	norm	NOUN
ssh-7883	33	15	//u	//u	PUNCT
ssh-7883	33	16	//∞	//∞	PUNCT
ssh-7883	33	17	,	,	PUNCT
ssh-7883	33	18	and	and	CCONJ
ssh-7883	33	19	denote	denote	VERB
ssh-7883	33	20	cb	cb	PROPN
ssh-7883	33	21	(	(	PUNCT
ssh-7883	33	22	j	j	PROPN
ssh-7883	33	23	,	,	PUNCT
ssh-7883	33	24	x	x	NOUN
ssh-7883	33	25	)	)	PUNCT
ssh-7883	33	26	=	=	PRON
ssh-7883	33	27	{	{	PUNCT
ssh-7883	33	28	f	f	PROPN
ssh-7883	33	29	∈	∈	PROPN
ssh-7883	33	30	c(j	c(j	PROPN
ssh-7883	33	31	,	,	PUNCT
ssh-7883	33	32	x	x	NOUN
ssh-7883	33	33	)	)	PUNCT
ssh-7883	33	34	:	:	PUNCT
ssh-7883	33	35	f	f	PROPN
ssh-7883	33	36	is	be	AUX
ssh-7883	33	37	bounded	bound	VERB
ssh-7883	33	38	.	.	PUNCT
ssh-7883	33	39	}	}	PUNCT
ssh-7883	33	40	,	,	PUNCT
ssh-7883	33	41	endowed	endow	VERB
ssh-7883	33	42	with	with	ADP
ssh-7883	33	43	the	the	DET
ssh-7883	33	44	norm	norm	NOUN
ssh-7883	33	45	of	of	ADP
ssh-7883	33	46	uniformly	uniformly	ADJ
ssh-7883	33	47	convergence	convergence	NOUN
ssh-7883	33	48	as	as	ADV
ssh-7883	33	49	well	well	ADV
ssh-7883	33	50	.	.	PUNCT
ssh-7883	34	1	definition	definition	NOUN
ssh-7883	34	2	2.1	2.1	NUM
ssh-7883	34	3	[	[	X
ssh-7883	34	4	5](riemann	5](riemann	NUM
ssh-7883	34	5	-	-	PUNCT
ssh-7883	34	6	liouville	liouville	VERB
ssh-7883	34	7	fractional	fractional	ADJ
ssh-7883	34	8	integral	integral	ADJ
ssh-7883	34	9	)	)	PUNCT
ssh-7883	34	10	the	the	DET
ssh-7883	34	11	riemann	riemann	PROPN
ssh-7883	34	12	-	-	PUNCT
ssh-7883	34	13	liouville	liouville	VERB
ssh-7883	34	14	fractional	fractional	ADJ
ssh-7883	34	15	integral	integral	ADJ
ssh-7883	34	16	of	of	ADP
ssh-7883	34	17	order	order	NOUN
ssh-7883	34	18	α	α	X
ssh-7883	34	19	∈	∈	PROPN
ssh-7883	34	20	r+	r+	PUNCT
ssh-7883	34	21	afunction	afunction	NOUN
ssh-7883	34	22	u	u	PROPN
ssh-7883	34	23	∈	∈	PROPN
ssh-7883	34	24	l1	l1	PROPN
ssh-7883	34	25	(	(	PUNCT
ssh-7883	34	26	[	[	X
ssh-7883	34	27	0	0	NUM
ssh-7883	34	28	,	,	PUNCT
ssh-7883	34	29	∞);r+	∞);r+	PROPN
ssh-7883	34	30	)	)	PUNCT
ssh-7883	34	31	of	of	ADP
ssh-7883	34	32	oreder	oreder	NOUN
ssh-7883	34	33	α	α	PROPN
ssh-7883	34	34	∈	∈	PROPN
ssh-7883	34	35	r+	r+	NOUN
ssh-7883	34	36	is	be	AUX
ssh-7883	34	37	defined	define	VERB
ssh-7883	34	38	by	by	ADP
ssh-7883	34	39	where	where	SCONJ
ssh-7883	34	40	γ	γ	X
ssh-7883	34	41	(	(	PUNCT
ssh-7883	34	42	.	.	PUNCT
ssh-7883	34	43	)	)	PUNCT
ssh-7883	34	44	is	be	AUX
ssh-7883	34	45	the	the	DET
ssh-7883	34	46	gamma	gamma	PROPN
ssh-7883	34	47	function	function	NOUN
ssh-7883	34	48	.	.	PUNCT
ssh-7883	35	1	definition	definition	NOUN
ssh-7883	35	2	2.2	2.2	NUM
ssh-7883	35	3	[	[	X
ssh-7883	35	4	5](riemann	5](riemann	NUM
ssh-7883	35	5	-	-	PUNCT
ssh-7883	35	6	liouville	liouville	VERB
ssh-7883	35	7	fractional	fractional	ADJ
ssh-7883	35	8	order	order	NOUN
ssh-7883	35	9	derivative	derivative	NOUN
ssh-7883	35	10	)	)	PUNCT
ssh-7883	35	11	the	the	DET
ssh-7883	35	12	riemann	riemann	PROPN
ssh-7883	35	13	-	-	PUNCT
ssh-7883	35	14	liouville	liouville	VERB
ssh-7883	35	15	fractional	fractional	ADJ
ssh-7883	35	16	order	order	NOUN
ssh-7883	35	17	derivative	derivative	NOUN
ssh-7883	35	18	of	of	ADP
ssh-7883	35	19	order	order	NOUN
ssh-7883	35	20	α	α	X
ssh-7883	35	21	∈	∈	PROPN
ssh-7883	35	22	r+	r+	NOUN
ssh-7883	35	23	of	of	ADP
ssh-7883	35	24	a	a	DET
ssh-7883	35	25	function	function	NOUN
ssh-7883	35	26	f	f	NOUN
ssh-7883	35	27	given	give	VERB
ssh-7883	35	28	on	on	ADP
ssh-7883	35	29	the	the	DET
ssh-7883	35	30	interval	interval	NOUN
ssh-7883	35	31	[	[	X
ssh-7883	35	32	0	0	NUM
ssh-7883	35	33	,	,	PUNCT
ssh-7883	35	34	∞	∞	NUM
ssh-7883	35	35	)	)	PUNCT
ssh-7883	35	36	is	be	AUX
ssh-7883	35	37	defined	define	VERB
ssh-7883	35	38	by	by	ADP
ssh-7883	35	39	where	where	SCONJ
ssh-7883	35	40	α	α	PROPN
ssh-7883	35	41	∈	∈	PROPN
ssh-7883	35	42	(	(	PUNCT
ssh-7883	35	43	n	n	CCONJ
ssh-7883	35	44	−	−	PROPN
ssh-7883	35	45	1	1	NUM
ssh-7883	35	46	,	,	PUNCT
ssh-7883	35	47	n	n	CCONJ
ssh-7883	35	48	)	)	PUNCT
ssh-7883	35	49	,	,	PUNCT
ssh-7883	35	50	n	n	PROPN
ssh-7883	35	51	∈	∈	PROPN
ssh-7883	35	52	n.	n.	NOUN
ssh-7883	35	53	definition	definition	NOUN
ssh-7883	35	54	2.3	2.3	NUM
ssh-7883	35	55	[	[	X
ssh-7883	35	56	5](caputo	5](caputo	NUM
ssh-7883	35	57	fractonal	fractonal	ADJ
ssh-7883	35	58	order	order	NOUN
ssh-7883	35	59	derivative	derivative	NOUN
ssh-7883	35	60	)	)	PUNCT
ssh-7883	35	61	the	the	DET
ssh-7883	35	62	caputo	caputo	PROPN
ssh-7883	35	63	fractional	fractional	PROPN
ssh-7883	35	64	order	order	NOUN
ssh-7883	35	65	derivative	derivative	NOUN
ssh-7883	35	66	of	of	ADP
ssh-7883	35	67	order	order	NOUN
ssh-7883	35	68	α	α	X
ssh-7883	35	69	∈	∈	PROPN
ssh-7883	35	70	r+	r+	NOUN
ssh-7883	35	71	of	of	ADP
ssh-7883	35	72	a	a	DET
ssh-7883	35	73	function	function	NOUN
ssh-7883	35	74	u	u	NOUN
ssh-7883	35	75	given	give	VERB
ssh-7883	35	76	on	on	ADP
ssh-7883	35	77	the	the	DET
ssh-7883	35	78	interval	interval	NOUN
ssh-7883	35	79	[	[	X
ssh-7883	35	80	0	0	NUM
ssh-7883	35	81	,	,	PUNCT
ssh-7883	35	82	∞	∞	NUM
ssh-7883	35	83	)	)	PUNCT
ssh-7883	35	84	is	be	AUX
ssh-7883	35	85	defined	define	VERB
ssh-7883	35	86	by	by	ADP
ssh-7883	35	87	where	where	SCONJ
ssh-7883	35	88	α	α	PROPN
ssh-7883	35	89	∈	∈	PROPN
ssh-7883	35	90	(	(	PUNCT
ssh-7883	35	91	n	n	CCONJ
ssh-7883	35	92	−	−	PROPN
ssh-7883	35	93	1	1	NUM
ssh-7883	35	94	,	,	PUNCT
ssh-7883	35	95	n	n	CCONJ
ssh-7883	35	96	)	)	PUNCT
ssh-7883	35	97	,	,	PUNCT
ssh-7883	35	98	n	n	PROPN
ssh-7883	35	99	∈	∈	PROPN
ssh-7883	35	100	n.	n.	NOUN
ssh-7883	35	101	definition	definition	NOUN
ssh-7883	35	102	2.4	2.4	NUM
ssh-7883	36	1	[	[	X
ssh-7883	36	2	12	12	NUM
ssh-7883	36	3	]	]	PUNCT
ssh-7883	36	4	a	a	PRON
ssh-7883	36	5	:	:	PUNCT
ssh-7883	36	6	d(a	d(a	PROPN
ssh-7883	36	7	)	)	PUNCT
ssh-7883	37	1	⊂	⊂	PROPN
ssh-7883	37	2	x	x	PUNCT
ssh-7883	37	3	→	→	PUNCT
ssh-7883	37	4	x	x	PUNCT
ssh-7883	37	5	be	be	AUX
ssh-7883	37	6	a	a	DET
ssh-7883	37	7	closed	closed	ADJ
ssh-7883	37	8	linear	linear	NOUN
ssh-7883	37	9	operator.a	operator.a	ADP
ssh-7883	37	10	is	be	AUX
ssh-7883	37	11	said	say	VERB
ssh-7883	37	12	to	to	PART
ssh-7883	37	13	be	be	AUX
ssh-7883	37	14	sectorial	sectorial	ADJ
ssh-7883	37	15	operator	operator	NOUN
ssh-7883	37	16	of	of	ADP
ssh-7883	37	17	type	type	NOUN
ssh-7883	37	18	(	(	PUNCT
ssh-7883	37	19	m	m	PROPN
ssh-7883	37	20	,	,	PUNCT
ssh-7883	37	21	θ	θ	PROPN
ssh-7883	37	22	,	,	PUNCT
ssh-7883	37	23	α,µ	α,µ	ADJ
ssh-7883	37	24	)	)	PUNCT
ssh-7883	37	25	if	if	SCONJ
ssh-7883	37	26	there	there	PRON
ssh-7883	37	27	exist	exist	VERB
ssh-7883	37	28	0	0	NUM
ssh-7883	37	29	that	that	SCONJ
ssh-7883	37	30	the	the	DET
ssh-7883	37	31	α	α	NOUN
ssh-7883	37	32	-	-	NOUN
ssh-7883	37	33	resolvent	resolvent	NOUN
ssh-7883	37	34	of	of	ADP
ssh-7883	37	35	a	a	DET
ssh-7883	37	36	exsits	exsit	NOUN
ssh-7883	37	37	outside	outside	ADP
ssh-7883	37	38	the	the	DET
ssh-7883	37	39	sector	sector	NOUN
ssh-7883	37	40	µ	µ	X
ssh-7883	37	41	+	+	CCONJ
ssh-7883	37	42	sθ	sθ	ADP
ssh-7883	37	43	=	=	SYM
ssh-7883	37	44	{	{	PUNCT
ssh-7883	37	45	µ	µ	PROPN
ssh-7883	37	46	+	+	X
ssh-7883	37	47	λα	λα	X
ssh-7883	37	48	:	:	PUNCT
ssh-7883	37	49	λ	λ	X
ssh-7883	37	50	∈	∈	PROPN
ssh-7883	37	51	c	c	X
ssh-7883	37	52	,	,	PUNCT
ssh-7883	37	53	|arg(−λα	|arg(−λα	PROPN
ssh-7883	37	54	)	)	PUNCT
ssh-7883	37	55	|	|	CCONJ
ssh-7883	37	56	<	<	X
ssh-7883	37	57	θ	θ	X
ssh-7883	37	58	}	}	PUNCT
ssh-7883	37	59	,	,	PUNCT
ssh-7883	37	60	and	and	CCONJ
ssh-7883	37	61	let	let	VERB
ssh-7883	37	62	r(λα	r(λα	NOUN
ssh-7883	37	63	,	,	PUNCT
ssh-7883	37	64	a	a	PRON
ssh-7883	37	65	)	)	PUNCT
ssh-7883	38	1	=	=	SYM
ssh-7883	38	2	(	(	PUNCT
ssh-7883	38	3	λα	λα	NOUN
ssh-7883	38	4	i	i	PRON
ssh-7883	38	5	−	−	PROPN
ssh-7883	38	6	a)−1	a)−1	NOUN
ssh-7883	38	7	,	,	PUNCT
ssh-7883	38	8	the	the	DET
ssh-7883	38	9	following	follow	VERB
ssh-7883	38	10	relationship	relationship	NOUN
ssh-7883	38	11	is	be	AUX
ssh-7883	38	12	established	establish	VERB
ssh-7883	38	13	µ	µ	NOUN
ssh-7883	38	14	+	+	CCONJ
ssh-7883	38	15	sθ	sθ	NOUN
ssh-7883	38	16	.	.	PUNCT
ssh-7883	39	1	lemma	lemma	PROPN
ssh-7883	39	2	2.1	2.1	NUM
ssh-7883	40	1	[	[	X
ssh-7883	40	2	7	7	X
ssh-7883	40	3	]	]	X
ssh-7883	40	4	if	if	SCONJ
ssh-7883	40	5	re(α	re(α	NOUN
ssh-7883	40	6	)	)	PUNCT
ssh-7883	40	7	>	>	X
ssh-7883	41	1	0	0	NUM
ssh-7883	41	2	,	,	PUNCT
ssh-7883	41	3	n	n	NOUN
ssh-7883	41	4	=	=	SYM
ssh-7883	42	1	[	[	X
ssh-7883	42	2	re(α	re(α	NOUN
ssh-7883	42	3	)	)	PUNCT
ssh-7883	42	4	]	]	PUNCT
ssh-7883	43	1	+	+	CCONJ
ssh-7883	43	2	1	1	NUM
ssh-7883	43	3	,	,	PUNCT
ssh-7883	43	4	u(t	u(t	NOUN
ssh-7883	43	5	)	)	PUNCT
ssh-7883	43	6	∈	∈	PROPN
ssh-7883	43	7	acn	acn	NOUN
ssh-7883	44	1	[	[	X
ssh-7883	44	2	0	0	NUM
ssh-7883	44	3	,	,	PUNCT
ssh-7883	44	4	b	b	NOUN
ssh-7883	44	5	]	]	X
ssh-7883	44	6	,	,	PUNCT
ssh-7883	44	7	∀b	∀b	X
ssh-7883	44	8	>	>	X
ssh-7883	44	9	0	0	PUNCT
ssh-7883	44	10	and	and	CCONJ
ssh-7883	44	11	|u(t)|	|u(t)|	PROPN
ssh-7883	44	12	≤	≤	NUM
ssh-7883	44	13	beq0	beq0	PROPN
ssh-7883	44	14	t	t	PROPN
ssh-7883	44	15	(	(	PUNCT
ssh-7883	44	16	t	t	PROPN
ssh-7883	44	17	>	>	X
ssh-7883	44	18	b	b	X
ssh-7883	44	19	>	>	X
ssh-7883	44	20	0	0	NUM
ssh-7883	44	21	)	)	PUNCT
ssh-7883	44	22	for	for	ADP
ssh-7883	44	23	b	b	PROPN
ssh-7883	44	24	>	>	X
ssh-7883	44	25	0	0	PROPN
ssh-7883	44	26	,	,	PUNCT
ssh-7883	44	27	q0	q0	VERB
ssh-7883	44	28	>	>	X
ssh-7883	44	29	0	0	NUM
ssh-7883	44	30	,	,	PUNCT
ssh-7883	44	31	and	and	CCONJ
ssh-7883	44	32	there	there	PRON
ssh-7883	44	33	exists	exist	VERB
ssh-7883	44	34	the	the	DET
ssh-7883	44	35	finite	finite	PROPN
ssh-7883	44	36	limits	limit	NOUN
ssh-7883	44	37	bcp	bcp	VERB
ssh-7883	44	38	social	social	PROPN
ssh-7883	44	39	sciences	sciences	PROPN
ssh-7883	44	40	&	&	CCONJ
ssh-7883	44	41	humanities	humanities	PROPN
ssh-7883	44	42	erss	erss	VERB
ssh-7883	44	43	2024	2024	NUM
ssh-7883	44	44	volume	volume	NOUN
ssh-7883	44	45	23	23	NUM
ssh-7883	44	46	(	(	PUNCT
ssh-7883	44	47	2024	2024	NUM
ssh-7883	44	48	)	)	PUNCT
ssh-7883	44	49	3	3	NUM
ssh-7883	44	50	and	and	CCONJ
ssh-7883	44	51	then	then	ADV
ssh-7883	44	52	lemma	lemma	PROPN
ssh-7883	44	53	2.2	2.2	NUM
ssh-7883	44	54	[	[	X
ssh-7883	44	55	7	7	NUM
ssh-7883	44	56	]	]	PUNCT
ssh-7883	44	57	let	let	VERB
ssh-7883	44	58	α	α	PRON
ssh-7883	44	59	>	>	X
ssh-7883	44	60	0	0	PROPN
ssh-7883	44	61	,	,	PUNCT
ssh-7883	44	62	n−1	n−1	PROPN
ssh-7883	44	63	<	<	X
ssh-7883	44	64	α	α	PROPN
ssh-7883	44	65	≤	≤	PUNCT
ssh-7883	44	66	n(n	n(n	PROPN
ssh-7883	44	67	∈	∈	PROPN
ssh-7883	44	68	n	n	CCONJ
ssh-7883	44	69	)	)	PUNCT
ssh-7883	44	70	be	be	AUX
ssh-7883	44	71	such	such	ADJ
ssh-7883	44	72	that	that	SCONJ
ssh-7883	44	73	u(t	u(t	NOUN
ssh-7883	44	74	)	)	PUNCT
ssh-7883	44	75	∈	∈	PROPN
ssh-7883	44	76	cn	cn	PROPN
ssh-7883	44	77	(	(	PUNCT
ssh-7883	44	78	r+	r+	NOUN
ssh-7883	44	79	)	)	PUNCT
ssh-7883	44	80	,	,	PUNCT
ssh-7883	44	81	u(n)(t	u(n)(t	SYM
ssh-7883	44	82	)	)	PUNCT
ssh-7883	44	83	∈	∈	PROPN
ssh-7883	44	84	l1	l1	PROPN
ssh-7883	44	85	(	(	PUNCT
ssh-7883	44	86	0	0	NUM
ssh-7883	44	87	,	,	PUNCT
ssh-7883	44	88	b	b	NOUN
ssh-7883	44	89	)	)	PUNCT
ssh-7883	44	90	,	,	PUNCT
ssh-7883	44	91	∀b	∀b	X
ssh-7883	44	92	>	>	X
ssh-7883	44	93	0	0	NUM
ssh-7883	44	94	,	,	PUNCT
ssh-7883	44	95	and	and	CCONJ
ssh-7883	44	96	|u(t)|	|u(t)|	PROPN
ssh-7883	44	97	≤	≤	PROPN
ssh-7883	44	98	beq0	beq0	PROPN
ssh-7883	44	99	t	t	PROPN
ssh-7883	44	100	(	(	PUNCT
ssh-7883	44	101	t	t	PROPN
ssh-7883	44	102	>	>	X
ssh-7883	44	103	b	b	X
ssh-7883	44	104	>	>	X
ssh-7883	44	105	0	0	NUM
ssh-7883	44	106	)	)	PUNCT
ssh-7883	44	107	for	for	ADP
ssh-7883	44	108	b	b	PROPN
ssh-7883	44	109	>	>	X
ssh-7883	44	110	0	0	PROPN
ssh-7883	44	111	,	,	PUNCT
ssh-7883	44	112	q0	q0	VERB
ssh-7883	44	113	>	>	X
ssh-7883	44	114	0,the	0,the	PRON
ssh-7883	44	115	laplace	laplace	NOUN
ssh-7883	44	116	transforms	transform	VERB
ssh-7883	44	117	(	(	PUNCT
ssh-7883	44	118	lu)(λ	lu)(λ	NOUN
ssh-7883	44	119	)	)	PUNCT
ssh-7883	44	120	and	and	CCONJ
ssh-7883	44	121	(	(	PUNCT
ssh-7883	44	122	ldnu)(λ	ldnu)(λ	NOUN
ssh-7883	44	123	)	)	PUNCT
ssh-7883	44	124	exist	exist	VERB
ssh-7883	44	125	,	,	PUNCT
ssh-7883	44	126	and	and	CCONJ
ssh-7883	44	127	then	then	ADV
ssh-7883	44	128	the	the	DET
ssh-7883	44	129	following	follow	VERB
ssh-7883	44	130	relation	relation	NOUN
ssh-7883	44	131	holds	hold	VERB
ssh-7883	44	132	:	:	PUNCT
ssh-7883	44	133	theorem	theorem	VERB
ssh-7883	44	134	2.1	2.1	NUM
ssh-7883	45	1	[	[	SYM
ssh-7883	45	2	15	15	NUM
ssh-7883	45	3	]	]	X
ssh-7883	45	4	(	(	PUNCT
ssh-7883	45	5	banach	banach	ADV
ssh-7883	45	6	’s	’s	PART
ssh-7883	45	7	fixed	fix	VERB
ssh-7883	45	8	point	point	NOUN
ssh-7883	45	9	theorem	theorem	ADJ
ssh-7883	45	10	)	)	PUNCT
ssh-7883	45	11	let	let	VERB
ssh-7883	45	12	x	x	PRON
ssh-7883	45	13	be	be	AUX
ssh-7883	45	14	a	a	DET
ssh-7883	45	15	nonempty	nonempty	ADJ
ssh-7883	45	16	complete	complete	ADJ
ssh-7883	45	17	metric	metric	ADJ
ssh-7883	45	18	space	space	NOUN
ssh-7883	45	19	,	,	PUNCT
ssh-7883	45	20	t	t	PROPN
ssh-7883	45	21	:	:	PUNCT
ssh-7883	45	22	x	x	SYM
ssh-7883	45	23	→	→	PUNCT
ssh-7883	45	24	x	x	X
ssh-7883	45	25	is	be	AUX
ssh-7883	45	26	a	a	DET
ssh-7883	45	27	compression	compression	NOUN
ssh-7883	45	28	map	map	NOUN
ssh-7883	45	29	,	,	PUNCT
ssh-7883	45	30	then	then	ADV
ssh-7883	45	31	t	t	PROPN
ssh-7883	45	32	must	must	AUX
ssh-7883	45	33	have	have	VERB
ssh-7883	45	34	a	a	DET
ssh-7883	45	35	unique	unique	ADJ
ssh-7883	45	36	fixed	fix	VERB
ssh-7883	45	37	point	point	NOUN
ssh-7883	45	38	.	.	PUNCT
ssh-7883	46	1	in	in	ADP
ssh-7883	46	2	the	the	DET
ssh-7883	46	3	following	following	ADJ
ssh-7883	46	4	pages	page	NOUN
ssh-7883	46	5	,	,	PUNCT
ssh-7883	46	6	what	what	PRON
ssh-7883	46	7	we	we	PRON
ssh-7883	46	8	hope	hope	VERB
ssh-7883	46	9	is	be	AUX
ssh-7883	46	10	to	to	PART
ssh-7883	46	11	be	be	AUX
ssh-7883	46	12	able	able	ADJ
ssh-7883	46	13	to	to	PART
ssh-7883	46	14	study	study	VERB
ssh-7883	46	15	the	the	DET
ssh-7883	46	16	relationship	relationship	NOUN
ssh-7883	46	17	and	and	CCONJ
ssh-7883	46	18	the	the	DET
ssh-7883	46	19	existence	existence	NOUN
ssh-7883	46	20	of	of	ADP
ssh-7883	46	21	the	the	DET
ssh-7883	46	22	mild	mild	ADJ
ssh-7883	46	23	solutions	solution	NOUN
ssh-7883	46	24	of	of	ADP
ssh-7883	46	25	the	the	DET
ssh-7883	46	26	two	two	NUM
ssh-7883	46	27	types	type	NOUN
ssh-7883	46	28	of	of	ADP
ssh-7883	46	29	mixed	mixed	ADJ
ssh-7883	46	30	-	-	PUNCT
ssh-7883	46	31	order	order	NOUN
ssh-7883	46	32	fractional	fractional	ADJ
ssh-7883	46	33	differential	differential	NOUN
ssh-7883	46	34	equation	equation	NOUN
ssh-7883	46	35	(	(	PUNCT
ssh-7883	46	36	1.1	1.1	NUM
ssh-7883	46	37	)	)	PUNCT
ssh-7883	46	38	and	and	CCONJ
ssh-7883	46	39	(	(	PUNCT
ssh-7883	46	40	1.2	1.2	NUM
ssh-7883	46	41	)	)	PUNCT
ssh-7883	46	42	.	.	PUNCT
ssh-7883	47	1	we	we	PRON
ssh-7883	47	2	first	first	ADV
ssh-7883	47	3	consider	consider	VERB
ssh-7883	47	4	the	the	DET
ssh-7883	47	5	definition	definition	NOUN
ssh-7883	47	6	of	of	ADP
ssh-7883	47	7	mild	mild	ADJ
ssh-7883	47	8	solutions	solution	NOUN
ssh-7883	47	9	to	to	ADP
ssh-7883	47	10	system	system	NOUN
ssh-7883	47	11	(	(	PUNCT
ssh-7883	47	12	1.1	1.1	NUM
ssh-7883	47	13	)	)	PUNCT
ssh-7883	47	14	and	and	CCONJ
ssh-7883	47	15	system	system	NOUN
ssh-7883	47	16	(	(	PUNCT
ssh-7883	47	17	2.2	2.2	NUM
ssh-7883	47	18	)	)	PUNCT
ssh-7883	47	19	,	,	PUNCT
ssh-7883	47	20	and	and	CCONJ
ssh-7883	47	21	operator	operator	NOUN
ssh-7883	47	22	estimation	estimation	NOUN
ssh-7883	47	23	is	be	AUX
ssh-7883	47	24	made	make	VERB
ssh-7883	47	25	on	on	ADP
ssh-7883	47	26	the	the	DET
ssh-7883	47	27	solution	solution	NOUN
ssh-7883	47	28	operator	operator	NOUN
ssh-7883	47	29	of	of	ADP
ssh-7883	47	30	the	the	DET
ssh-7883	47	31	mild	mild	ADJ
ssh-7883	47	32	solutions	solution	NOUN
ssh-7883	47	33	.	.	PUNCT
ssh-7883	48	1	then	then	ADV
ssh-7883	48	2	,	,	PUNCT
ssh-7883	48	3	we	we	PRON
ssh-7883	48	4	define	define	VERB
ssh-7883	48	5	an	an	DET
ssh-7883	48	6	operator	operator	NOUN
ssh-7883	48	7	g	g	NOUN
ssh-7883	48	8	according	accord	VERB
ssh-7883	48	9	to	to	ADP
ssh-7883	48	10	the	the	DET
ssh-7883	48	11	mild	mild	ADJ
ssh-7883	48	12	solutions	solution	NOUN
ssh-7883	48	13	obtained	obtain	VERB
ssh-7883	48	14	,	,	PUNCT
ssh-7883	48	15	and	and	CCONJ
ssh-7883	48	16	the	the	DET
ssh-7883	48	17	main	main	ADJ
ssh-7883	48	18	existence	existence	NOUN
ssh-7883	48	19	results	result	NOUN
ssh-7883	48	20	can	can	AUX
ssh-7883	48	21	be	be	AUX
ssh-7883	48	22	acquired	acquire	VERB
ssh-7883	48	23	by	by	ADP
ssh-7883	48	24	applying	apply	VERB
ssh-7883	48	25	the	the	DET
ssh-7883	48	26	fixed	fix	VERB
ssh-7883	48	27	-	-	PUNCT
ssh-7883	48	28	point	point	NOUN
ssh-7883	48	29	theorem	theorem	NOUN
ssh-7883	48	30	.	.	PROPN
ssh-7883	49	1	3	3	X
ssh-7883	49	2	.	.	X
ssh-7883	49	3	definition	definition	NOUN
ssh-7883	49	4	of	of	ADP
ssh-7883	49	5	a	a	DET
ssh-7883	49	6	mild	mild	ADJ
ssh-7883	49	7	solution	solution	NOUN
ssh-7883	49	8	to	to	ADP
ssh-7883	49	9	the	the	DET
ssh-7883	49	10	mixed	mix	VERB
ssh-7883	49	11	-	-	PUNCT
ssh-7883	49	12	order	order	NOUN
ssh-7883	49	13	fractional	fractional	ADJ
ssh-7883	49	14	evolution	evolution	NOUN
ssh-7883	49	15	equation	equation	NOUN
ssh-7883	49	16	(	(	PUNCT
ssh-7883	49	17	1.1	1.1	NUM
ssh-7883	49	18	)	)	PUNCT
ssh-7883	49	19	firstly	firstly	ADV
ssh-7883	49	20	,	,	PUNCT
ssh-7883	49	21	we	we	PRON
ssh-7883	49	22	consider	consider	VERB
ssh-7883	49	23	the	the	DET
ssh-7883	49	24	following	follow	VERB
ssh-7883	49	25	cauchy	cauchy	PROPN
ssh-7883	49	26	problem	problem	NOUN
ssh-7883	49	27	(	(	PUNCT
ssh-7883	49	28	3.1	3.1	NUM
ssh-7883	49	29	)	)	PUNCT
ssh-7883	49	30	where	where	SCONJ
ssh-7883	49	31	a	a	PRON
ssh-7883	49	32	is	be	AUX
ssh-7883	49	33	a	a	DET
ssh-7883	49	34	sectorial	sectorial	ADJ
ssh-7883	49	35	operator	operator	NOUN
ssh-7883	49	36	of	of	ADP
ssh-7883	49	37	type	type	NOUN
ssh-7883	49	38	(	(	PUNCT
ssh-7883	49	39	m	m	PROPN
ssh-7883	49	40	,	,	PUNCT
ssh-7883	49	41	θ	θ	PROPN
ssh-7883	49	42	,	,	PUNCT
ssh-7883	49	43	α	α	PROPN
ssh-7883	49	44	+	+	X
ssh-7883	49	45	β	β	X
ssh-7883	49	46	,	,	PUNCT
ssh-7883	49	47	µ	µ	NOUN
ssh-7883	49	48	)	)	PUNCT
ssh-7883	49	49	.	.	PUNCT
ssh-7883	50	1	theorem	theorem	VERB
ssh-7883	50	2	3.1	3.1	NUM
ssh-7883	50	3	the	the	DET
ssh-7883	50	4	function	function	NOUN
ssh-7883	50	5	f	f	PROPN
ssh-7883	50	6	satisfies	satisfy	VERB
ssh-7883	50	7	the	the	DET
ssh-7883	50	8	consistent	consistent	ADJ
ssh-7883	50	9	holder	holder	NOUN
ssh-7883	50	10	condition	condition	NOUN
ssh-7883	50	11	,	,	PUNCT
ssh-7883	50	12	then	then	ADV
ssh-7883	50	13	the	the	DET
ssh-7883	50	14	unique	unique	ADJ
ssh-7883	50	15	solution	solution	NOUN
ssh-7883	50	16	of	of	ADP
ssh-7883	50	17	cauchy	cauchy	ADJ
ssh-7883	50	18	problem	problem	NOUN
ssh-7883	50	19	(	(	PUNCT
ssh-7883	50	20	3.1	3.1	NUM
ssh-7883	50	21	)	)	PUNCT
ssh-7883	50	22	is	be	AUX
ssh-7883	50	23	given	give	VERB
ssh-7883	50	24	by	by	ADP
ssh-7883	50	25	u(t	u(t	NOUN
ssh-7883	50	26	)	)	PUNCT
ssh-7883	50	27	=	=	PRON
ssh-7883	51	1	sα+β(t)u0	sα+β(t)u0	NOUN
ssh-7883	51	2	+	+	X
ssh-7883	51	3	tα+β(t)r0	tα+β(t)r0	X
ssh-7883	51	4	+	+	CCONJ
ssh-7883	51	5	tα+β(t	tα+β(t	NOUN
ssh-7883	51	6	−	−	PROPN
ssh-7883	51	7	s)f(s)ds	s)f(s)ds	NOUN
ssh-7883	51	8	,	,	PUNCT
ssh-7883	51	9	(	(	PUNCT
ssh-7883	51	10	3.2	3.2	NUM
ssh-7883	51	11	)	)	PUNCT
ssh-7883	51	12	where	where	SCONJ
ssh-7883	51	13	with	with	ADP
ssh-7883	51	14	c	c	PROPN
ssh-7883	51	15	being	be	AUX
ssh-7883	51	16	a	a	DET
ssh-7883	51	17	suitable	suitable	ADJ
ssh-7883	51	18	path	path	NOUN
ssh-7883	51	19	such	such	ADJ
ssh-7883	51	20	that	that	SCONJ
ssh-7883	51	21	λα+β	λα+β	PROPN
ssh-7883	51	22	µ	µ	NOUN
ssh-7883	51	23	+	+	CCONJ
ssh-7883	51	24	sθ	sθ	ADP
ssh-7883	51	25	for	for	ADP
ssh-7883	51	26	λα+β	λα+β	PROPN
ssh-7883	51	27	∈	∈	PROPN
ssh-7883	51	28	c.	c.	PROPN
ssh-7883	51	29	bcp	bcp	PROPN
ssh-7883	51	30	social	social	PROPN
ssh-7883	51	31	sciences	sciences	PROPN
ssh-7883	51	32	&	&	CCONJ
ssh-7883	51	33	humanities	humanities	PROPN
ssh-7883	51	34	erss	erss	VERB
ssh-7883	51	35	2024	2024	NUM
ssh-7883	51	36	volume	volume	NOUN
ssh-7883	51	37	23	23	NUM
ssh-7883	51	38	(	(	PUNCT
ssh-7883	51	39	2024	2024	NUM
ssh-7883	51	40	)	)	PUNCT
ssh-7883	51	41	4	4	NUM
ssh-7883	51	42	remark	remark	NOUN
ssh-7883	51	43	1	1	NUM
ssh-7883	51	44	we	we	PRON
ssh-7883	51	45	can	can	AUX
ssh-7883	51	46	observe	observe	VERB
ssh-7883	51	47	that	that	SCONJ
ssh-7883	51	48	a	a	PRON
ssh-7883	51	49	is	be	AUX
ssh-7883	51	50	the	the	DET
ssh-7883	51	51	infinitesimal	infinitesimal	ADJ
ssh-7883	51	52	generator	generator	NOUN
ssh-7883	51	53	of	of	ADP
ssh-7883	51	54	a	a	DET
ssh-7883	51	55	α	α	NOUN
ssh-7883	51	56	+	+	CCONJ
ssh-7883	51	57	β	β	ADJ
ssh-7883	51	58	-	-	ADJ
ssh-7883	51	59	reslovent	reslovent	NOUN
ssh-7883	51	60	family	family	NOUN
ssh-7883	51	61	{	{	PUNCT
ssh-7883	51	62	tα+β(t)}t≥0	tα+β(t)}t≥0	X
ssh-7883	51	63	and	and	CCONJ
ssh-7883	51	64	{	{	PUNCT
ssh-7883	51	65	sα+β(t)}t≥0	sα+β(t)}t≥0	NOUN
ssh-7883	51	66	in	in	ADP
ssh-7883	51	67	bananch	bananch	NOUN
ssh-7883	51	68	space	space	NOUN
ssh-7883	51	69	,	,	PUNCT
ssh-7883	51	70	and	and	CCONJ
ssh-7883	51	71	tα+β(t	tα+β(t	NOUN
ssh-7883	51	72	)	)	PUNCT
ssh-7883	51	73	and	and	CCONJ
ssh-7883	51	74	sα+β(t	sα+β(t	PROPN
ssh-7883	51	75	)	)	PUNCT
ssh-7883	51	76	are	be	AUX
ssh-7883	51	77	well	well	ADJ
ssh-7883	51	78	definitions	definition	NOUN
ssh-7883	51	79	.	.	PUNCT
ssh-7883	52	1	proof	proof	NOUN
ssh-7883	52	2	.	.	PUNCT
ssh-7883	53	1	we	we	PRON
ssh-7883	53	2	perform	perform	VERB
ssh-7883	53	3	the	the	DET
ssh-7883	53	4	laplace	laplace	NOUN
ssh-7883	53	5	transform	transform	NOUN
ssh-7883	53	6	on	on	ADP
ssh-7883	53	7	the	the	DET
ssh-7883	53	8	left	left	ADJ
ssh-7883	53	9	side	side	NOUN
ssh-7883	53	10	of	of	ADP
ssh-7883	53	11	the	the	DET
ssh-7883	53	12	equation	equation	NOUN
ssh-7883	53	13	=	=	PRON
ssh-7883	53	14	λα	λα	PROPN
ssh-7883	53	15	+	+	CCONJ
ssh-7883	53	16	βlu	βlu	NOUN
ssh-7883	53	17	−	−	PROPN
ssh-7883	53	18	λα	λα	PROPN
ssh-7883	54	1	+	+	X
ssh-7883	54	2	β	β	PROPN
ssh-7883	54	3	−	−	NOUN
ssh-7883	54	4	1u(0	1u(0	NUM
ssh-7883	54	5	)	)	PUNCT
ssh-7883	54	6	−	−	PROPN
ssh-7883	55	1	i0	i0	PROPN
ssh-7883	55	2	1	1	NUM
ssh-7883	55	3	α	α	NOUN
ssh-7883	55	4	(	(	PUNCT
ssh-7883	55	5	cd0	cd0	NOUN
ssh-7883	55	6	β	β	X
ssh-7883	55	7	+	+	NOUN
ssh-7883	55	8	u)(t	u)(t	NOUN
ssh-7883	55	9	)	)	PUNCT
ssh-7883	55	10	it	it	PRON
ssh-7883	55	11	follows	follow	VERB
ssh-7883	55	12	that	that	SCONJ
ssh-7883	55	13	λα	λα	PROPN
ssh-7883	56	1	+	+	CCONJ
ssh-7883	56	2	β(lu)(λ	β(lu)(λ	ADJ
ssh-7883	56	3	)	)	PUNCT
ssh-7883	57	1	−	−	PROPN
ssh-7883	57	2	λα	λα	PROPN
ssh-7883	58	1	+	+	CCONJ
ssh-7883	58	2	β	β	PROPN
ssh-7883	58	3	−	−	NOUN
ssh-7883	58	4	1u(0	1u(0	NUM
ssh-7883	58	5	)	)	PUNCT
ssh-7883	58	6	−	−	PROPN
ssh-7883	59	1	i0	i0	PROPN
ssh-7883	59	2	1	1	NUM
ssh-7883	59	3	α	α	NOUN
ssh-7883	59	4	(	(	PUNCT
ssh-7883	59	5	cd0	cd0	NOUN
ssh-7883	59	6	β	β	X
ssh-7883	59	7	+	+	NOUN
ssh-7883	59	8	u)(t	u)(t	ADJ
ssh-7883	59	9	)	)	PUNCT
ssh-7883	59	10	=	=	SYM
ssh-7883	59	11	l[au(t	l[au(t	PROPN
ssh-7883	59	12	)	)	PUNCT
ssh-7883	59	13	+	+	NUM
ssh-7883	59	14	f(t)](λ	f(t)](λ	NUM
ssh-7883	59	15	)	)	PUNCT
ssh-7883	59	16	(	(	PUNCT
ssh-7883	59	17	λα	λα	NOUN
ssh-7883	60	1	+	+	CCONJ
ssh-7883	60	2	βi	βi	PROPN
ssh-7883	60	3	−	−	NOUN
ssh-7883	60	4	a)(lu)(λ	a)(lu)(λ	PROPN
ssh-7883	60	5	)	)	PUNCT
ssh-7883	60	6	=	=	SYM
ssh-7883	61	1	λα	λα	PROPN
ssh-7883	62	1	+	+	ADJ
ssh-7883	62	2	β	β	X
ssh-7883	62	3	−	−	NOUN
ssh-7883	62	4	1u0	1u0	NUM
ssh-7883	63	1	+	+	CCONJ
ssh-7883	63	2	r0	r0	NOUN
ssh-7883	63	3	+	+	CCONJ
ssh-7883	63	4	(	(	PUNCT
ssh-7883	63	5	lf)(λ	lf)(λ	PROPN
ssh-7883	63	6	)	)	PUNCT
ssh-7883	63	7	let	let	VERB
ssh-7883	63	8	r(λα	r(λα	NOUN
ssh-7883	63	9	+	+	ADP
ssh-7883	63	10	β	β	NOUN
ssh-7883	63	11	,	,	PUNCT
ssh-7883	63	12	a	a	PRON
ssh-7883	63	13	)	)	PUNCT
ssh-7883	63	14	=	=	SYM
ssh-7883	64	1	(	(	PUNCT
ssh-7883	64	2	λα	λα	PROPN
ssh-7883	65	1	+	+	CCONJ
ssh-7883	65	2	βi	βi	PROPN
ssh-7883	65	3	−	−	PROPN
ssh-7883	65	4	a)−	a)−	PROPN
ssh-7883	65	5	1	1	NUM
ssh-7883	65	6	(	(	PUNCT
ssh-7883	65	7	lu)(λ	lu)(λ	NOUN
ssh-7883	65	8	)	)	PUNCT
ssh-7883	65	9	=	=	PUNCT
ssh-7883	66	1	r(λα	r(λα	NOUN
ssh-7883	66	2	+	+	ADP
ssh-7883	66	3	β	β	X
ssh-7883	66	4	,	,	PUNCT
ssh-7883	66	5	a)(λα	a)(λα	VERB
ssh-7883	66	6	+	+	PUNCT
ssh-7883	67	1	β	β	NUM
ssh-7883	67	2	−	−	NOUN
ssh-7883	67	3	1u0	1u0	NUM
ssh-7883	68	1	+	+	CCONJ
ssh-7883	68	2	r0	r0	NOUN
ssh-7883	68	3	+	+	CCONJ
ssh-7883	68	4	(	(	PUNCT
ssh-7883	68	5	lf)(λ	lf)(λ	NOUN
ssh-7883	68	6	)	)	PUNCT
ssh-7883	68	7	)	)	PUNCT
ssh-7883	68	8	u(t	u(t	NOUN
ssh-7883	68	9	)	)	PUNCT
ssh-7883	69	1	=	=	SYM
ssh-7883	69	2	l−	l−	PROPN
ssh-7883	69	3	1r(λα	1r(λα	NUM
ssh-7883	69	4	+	+	CCONJ
ssh-7883	69	5	β	β	X
ssh-7883	69	6	,	,	PUNCT
ssh-7883	69	7	a)(λα	a)(λα	VERB
ssh-7883	69	8	+	+	PUNCT
ssh-7883	70	1	β	β	NUM
ssh-7883	70	2	−	−	NOUN
ssh-7883	70	3	1u0	1u0	NUM
ssh-7883	70	4	+	+	CCONJ
ssh-7883	70	5	r0	r0	NOUN
ssh-7883	70	6	)	)	PUNCT
ssh-7883	71	1	+	+	CCONJ
ssh-7883	71	2	l−	l−	PROPN
ssh-7883	71	3	1r(λα	1r(λα	NUM
ssh-7883	71	4	+	+	CCONJ
ssh-7883	71	5	β	β	NOUN
ssh-7883	71	6	,	,	PUNCT
ssh-7883	71	7	a)lf	a)lf	PROPN
ssh-7883	71	8	now	now	ADV
ssh-7883	71	9	we	we	PRON
ssh-7883	71	10	can	can	AUX
ssh-7883	71	11	get	get	VERB
ssh-7883	71	12	(	(	PUNCT
ssh-7883	71	13	3.2	3.2	NUM
ssh-7883	71	14	)	)	PUNCT
ssh-7883	71	15	easily	easily	ADV
ssh-7883	71	16	by	by	ADP
ssh-7883	71	17	converting	convert	VERB
ssh-7883	71	18	the	the	DET
ssh-7883	71	19	above	above	ADJ
ssh-7883	71	20	equation	equation	NOUN
ssh-7883	71	21	.	.	PUNCT
ssh-7883	72	1	theorem	theorem	VERB
ssh-7883	72	2	3.2	3.2	NUM
ssh-7883	72	3	the	the	DET
ssh-7883	72	4	function	function	NOUN
ssh-7883	72	5	f	f	PROPN
ssh-7883	72	6	satisfies	satisfy	VERB
ssh-7883	72	7	the	the	DET
ssh-7883	72	8	consistent	consistent	ADJ
ssh-7883	72	9	holder	holder	NOUN
ssh-7883	72	10	condition	condition	NOUN
ssh-7883	72	11	,	,	PUNCT
ssh-7883	72	12	then	then	ADV
ssh-7883	72	13	the	the	DET
ssh-7883	72	14	solutions	solution	NOUN
ssh-7883	72	15	of	of	ADP
ssh-7883	72	16	the	the	DET
ssh-7883	72	17	cauchy	cauchy	ADJ
ssh-7883	72	18	problem	problem	NOUN
ssh-7883	72	19	(	(	PUNCT
ssh-7883	72	20	1.1	1.1	NUM
ssh-7883	72	21	)	)	PUNCT
ssh-7883	72	22	are	be	AUX
ssh-7883	72	23	fixed	fix	VERB
ssh-7883	72	24	points	point	NOUN
ssh-7883	72	25	of	of	ADP
ssh-7883	72	26	operator	operator	NOUN
ssh-7883	72	27	equation	equation	NOUN
ssh-7883	72	28	u(t	u(t	NOUN
ssh-7883	72	29	)	)	PUNCT
ssh-7883	72	30	=	=	PRON
ssh-7883	73	1	sα+β(t)u0	sα+β(t)u0	NOUN
ssh-7883	73	2	+	+	X
ssh-7883	73	3	tα+β(t)r0	tα+β(t)r0	X
ssh-7883	73	4	+	+	NOUN
ssh-7883	73	5	tα+β(t	tα+β(t	NOUN
ssh-7883	73	6	-	-	PUNCT
ssh-7883	73	7	s)f(s	s)f(s	PROPN
ssh-7883	73	8	,	,	PUNCT
ssh-7883	73	9	u(s))ds	u(s))ds	PROPN
ssh-7883	73	10	,	,	PUNCT
ssh-7883	73	11	theorem	theorem	VERB
ssh-7883	73	12	3.2	3.2	NUM
ssh-7883	73	13	leads	lead	VERB
ssh-7883	73	14	the	the	DET
ssh-7883	73	15	following	follow	VERB
ssh-7883	73	16	appropriate	appropriate	ADJ
ssh-7883	73	17	definition	definition	NOUN
ssh-7883	73	18	of	of	ADP
ssh-7883	73	19	a	a	DET
ssh-7883	73	20	mild	mild	ADJ
ssh-7883	73	21	solution	solution	NOUN
ssh-7883	73	22	to	to	ADP
ssh-7883	73	23	(	(	PUNCT
ssh-7883	73	24	1.1	1.1	NUM
ssh-7883	73	25	)	)	PUNCT
ssh-7883	73	26	.	.	PUNCT
ssh-7883	74	1	definition	definition	NOUN
ssh-7883	74	2	3.1	3.1	NUM
ssh-7883	74	3	afunction	afunction	NOUN
ssh-7883	74	4	u	u	PROPN
ssh-7883	74	5	∈	∈	PROPN
ssh-7883	74	6	c(j	c(j	PROPN
ssh-7883	74	7	,	,	PUNCT
ssh-7883	74	8	x	x	X
ssh-7883	74	9	)	)	PUNCT
ssh-7883	74	10	is	be	AUX
ssh-7883	74	11	called	call	VERB
ssh-7883	74	12	a	a	DET
ssh-7883	74	13	mild	mild	ADJ
ssh-7883	74	14	solution	solution	NOUN
ssh-7883	74	15	of	of	ADP
ssh-7883	74	16	(	(	PUNCT
ssh-7883	74	17	1.1	1.1	NUM
ssh-7883	74	18	)	)	PUNCT
ssh-7883	74	19	when	when	SCONJ
ssh-7883	74	20	it	it	PRON
ssh-7883	74	21	satifies	satifie	VERB
ssh-7883	74	22	the	the	DET
ssh-7883	74	23	operator	operator	NOUN
ssh-7883	74	24	equation	equation	NOUN
ssh-7883	74	25	u(t	u(t	NOUN
ssh-7883	74	26	)	)	PUNCT
ssh-7883	74	27	=	=	PRON
ssh-7883	75	1	sα+β(t)u0	sα+β(t)u0	NOUN
ssh-7883	75	2	+	+	X
ssh-7883	75	3	tα+β(t)r0	tα+β(t)r0	X
ssh-7883	75	4	+	+	CCONJ
ssh-7883	75	5	tα+β(t	tα+β(t	NOUN
ssh-7883	75	6	−	−	NOUN
ssh-7883	75	7	s)f(s	s)f(	NOUN
ssh-7883	75	8	,	,	PUNCT
ssh-7883	75	9	u(s))ds	u(s))ds	PROPN
ssh-7883	75	10	,	,	PUNCT
ssh-7883	75	11	(	(	PUNCT
ssh-7883	75	12	3.3	3.3	NUM
ssh-7883	75	13	)	)	PUNCT
ssh-7883	75	14	4	4	NUM
ssh-7883	75	15	.	.	PUNCT
ssh-7883	75	16	definition	definition	NOUN
ssh-7883	75	17	of	of	ADP
ssh-7883	75	18	a	a	DET
ssh-7883	75	19	mild	mild	ADJ
ssh-7883	75	20	solution	solution	NOUN
ssh-7883	75	21	to	to	ADP
ssh-7883	75	22	the	the	DET
ssh-7883	75	23	mixed	mix	VERB
ssh-7883	75	24	-	-	PUNCT
ssh-7883	75	25	order	order	NOUN
ssh-7883	75	26	fractional	fractional	ADJ
ssh-7883	75	27	evolution	evolution	NOUN
ssh-7883	75	28	equation	equation	NOUN
ssh-7883	75	29	(	(	PUNCT
ssh-7883	75	30	1.2	1.2	NUM
ssh-7883	75	31	)	)	PUNCT
ssh-7883	75	32	similarly	similarly	ADV
ssh-7883	75	33	,	,	PUNCT
ssh-7883	75	34	we	we	PRON
ssh-7883	75	35	consider	consider	VERB
ssh-7883	75	36	the	the	DET
ssh-7883	75	37	following	follow	VERB
ssh-7883	75	38	cauchy	cauchy	PROPN
ssh-7883	75	39	problem	problem	NOUN
ssh-7883	75	40	(	(	PUNCT
ssh-7883	75	41	4.1	4.1	NUM
ssh-7883	75	42	)	)	PUNCT
ssh-7883	75	43	where	where	SCONJ
ssh-7883	75	44	a	a	PRON
ssh-7883	75	45	is	be	AUX
ssh-7883	75	46	a	a	DET
ssh-7883	75	47	sectorial	sectorial	ADJ
ssh-7883	75	48	operator	operator	NOUN
ssh-7883	75	49	of	of	ADP
ssh-7883	75	50	type	type	NOUN
ssh-7883	75	51	(	(	PUNCT
ssh-7883	75	52	m	m	PROPN
ssh-7883	75	53	,	,	PUNCT
ssh-7883	75	54	θ	θ	PROPN
ssh-7883	75	55	,	,	PUNCT
ssh-7883	75	56	α	α	NOUN
ssh-7883	75	57	+	+	X
ssh-7883	75	58	β,µ	β,µ	ADJ
ssh-7883	75	59	)	)	PUNCT
ssh-7883	75	60	.	.	PUNCT
ssh-7883	76	1	theorem	theorem	VERB
ssh-7883	76	2	4.1	4.1	NUM
ssh-7883	76	3	the	the	DET
ssh-7883	76	4	function	function	NOUN
ssh-7883	76	5	f	f	PROPN
ssh-7883	76	6	satisfies	satisfy	VERB
ssh-7883	76	7	the	the	DET
ssh-7883	76	8	consistent	consistent	ADJ
ssh-7883	76	9	holder	holder	NOUN
ssh-7883	76	10	condition	condition	NOUN
ssh-7883	76	11	,	,	PUNCT
ssh-7883	76	12	then	then	ADV
ssh-7883	76	13	the	the	DET
ssh-7883	76	14	unique	unique	ADJ
ssh-7883	76	15	solution	solution	NOUN
ssh-7883	76	16	of	of	ADP
ssh-7883	76	17	cauchy	cauchy	ADJ
ssh-7883	76	18	problem	problem	NOUN
ssh-7883	76	19	(	(	PUNCT
ssh-7883	76	20	4.1	4.1	NUM
ssh-7883	76	21	)	)	PUNCT
ssh-7883	76	22	is	be	AUX
ssh-7883	76	23	given	give	VERB
ssh-7883	76	24	by	by	ADP
ssh-7883	76	25	u(t	u(t	NOUN
ssh-7883	76	26	)	)	PUNCT
ssh-7883	76	27	=	=	SYM
ssh-7883	76	28	sα+β	sα+β	PROPN
ssh-7883	76	29	,	,	PUNCT
ssh-7883	76	30	β	β	X
ssh-7883	76	31	(	(	PUNCT
ssh-7883	76	32	t)u1	t)u1	NOUN
ssh-7883	76	33	+	+	CCONJ
ssh-7883	76	34	sα+β	sα+β	NOUN
ssh-7883	76	35	,	,	PUNCT
ssh-7883	76	36	β−1(t)r1	β−1(t)r1	NUM
ssh-7883	77	1	+	+	CCONJ
ssh-7883	77	2	tα+β	tα+β	NOUN
ssh-7883	77	3	(	(	PUNCT
ssh-7883	77	4	t	t	PROPN
ssh-7883	77	5	−	−	PROPN
ssh-7883	77	6	s)f(s)ds	s)f(s)ds	PROPN
ssh-7883	77	7	.	.	PUNCT
ssh-7883	78	1	(	(	PUNCT
ssh-7883	78	2	4.2	4.2	NUM
ssh-7883	78	3	)	)	PUNCT
ssh-7883	78	4	where	where	SCONJ
ssh-7883	78	5	bcp	bcp	X
ssh-7883	78	6	social	social	PROPN
ssh-7883	78	7	sciences	sciences	PROPN
ssh-7883	78	8	&	&	CCONJ
ssh-7883	78	9	humanities	humanities	PROPN
ssh-7883	78	10	erss	erss	VERB
ssh-7883	78	11	2024	2024	NUM
ssh-7883	78	12	volume	volume	NOUN
ssh-7883	78	13	23	23	NUM
ssh-7883	78	14	(	(	PUNCT
ssh-7883	78	15	2024	2024	NUM
ssh-7883	78	16	)	)	PUNCT
ssh-7883	78	17	5	5	NUM
ssh-7883	78	18	with	with	ADP
ssh-7883	78	19	c	c	PROPN
ssh-7883	78	20	being	be	AUX
ssh-7883	78	21	a	a	DET
ssh-7883	78	22	suitable	suitable	ADJ
ssh-7883	78	23	path	path	NOUN
ssh-7883	78	24	such	such	ADJ
ssh-7883	78	25	that	that	SCONJ
ssh-7883	78	26	λα+β	λα+β	PROPN
ssh-7883	78	27	µ	µ	NOUN
ssh-7883	78	28	+	+	CCONJ
ssh-7883	78	29	sθ	sθ	ADP
ssh-7883	78	30	,	,	PUNCT
ssh-7883	78	31	for	for	ADP
ssh-7883	78	32	λα+β	λα+β	PROPN
ssh-7883	78	33	∈	∈	PROPN
ssh-7883	78	34	c.	c.	NOUN
ssh-7883	78	35	remark	remark	NOUN
ssh-7883	78	36	2	2	NUM
ssh-7883	78	37	similarly	similarly	ADV
ssh-7883	78	38	,	,	PUNCT
ssh-7883	78	39	we	we	PRON
ssh-7883	78	40	can	can	AUX
ssh-7883	78	41	also	also	ADV
ssh-7883	78	42	see	see	VERB
ssh-7883	78	43	that	that	SCONJ
ssh-7883	78	44	a	a	PRON
ssh-7883	78	45	is	be	AUX
ssh-7883	78	46	the	the	DET
ssh-7883	78	47	infinitesimal	infinitesimal	ADJ
ssh-7883	78	48	generator	generator	NOUN
ssh-7883	78	49	of	of	ADP
ssh-7883	78	50	a	a	DET
ssh-7883	78	51	α	α	NOUN
ssh-7883	78	52	+	+	X
ssh-7883	78	53	β	β	X
ssh-7883	78	54	reslovent	reslovent	NOUN
ssh-7883	78	55	family	family	NOUN
ssh-7883	78	56	{	{	PUNCT
ssh-7883	78	57	sα+β	sα+β	PROPN
ssh-7883	78	58	,	,	PUNCT
ssh-7883	78	59	β(t)}t≥0	β(t)}t≥0	NOUN
ssh-7883	78	60	,	,	PUNCT
ssh-7883	78	61	{	{	PUNCT
ssh-7883	78	62	sα+β	sα+β	NOUN
ssh-7883	78	63	,	,	PUNCT
ssh-7883	78	64	β−1(t)}t≥0	β−1(t)}t≥0	PROPN
ssh-7883	78	65	and	and	CCONJ
ssh-7883	78	66	{	{	PUNCT
ssh-7883	78	67	tα+β(t)}t≥0	tα+β(t)}t≥0	VERB
ssh-7883	78	68	in	in	ADP
ssh-7883	78	69	bananch	bananch	NOUN
ssh-7883	78	70	space	space	NOUN
ssh-7883	78	71	,	,	PUNCT
ssh-7883	78	72	and	and	CCONJ
ssh-7883	78	73	sα+β	sα+β	NOUN
ssh-7883	78	74	,	,	PUNCT
ssh-7883	78	75	β	β	X
ssh-7883	78	76	(	(	PUNCT
ssh-7883	78	77	t),sα+β	t),sα+β	NOUN
ssh-7883	78	78	,	,	PUNCT
ssh-7883	78	79	β−1(t	β−1(t	PUNCT
ssh-7883	78	80	)	)	PUNCT
ssh-7883	78	81	and	and	CCONJ
ssh-7883	78	82	tα+β	tα+β	NOUN
ssh-7883	78	83	(	(	PUNCT
ssh-7883	78	84	t	t	NOUN
ssh-7883	78	85	)	)	PUNCT
ssh-7883	78	86	are	be	AUX
ssh-7883	78	87	well	well	ADJ
ssh-7883	78	88	definitions	definition	NOUN
ssh-7883	78	89	.	.	PUNCT
ssh-7883	79	1	proof	proof	NOUN
ssh-7883	79	2	.	.	PUNCT
ssh-7883	80	1	we	we	PRON
ssh-7883	80	2	perform	perform	VERB
ssh-7883	80	3	the	the	DET
ssh-7883	80	4	laplace	laplace	NOUN
ssh-7883	80	5	transform	transform	NOUN
ssh-7883	80	6	on	on	ADP
ssh-7883	80	7	the	the	DET
ssh-7883	80	8	left	left	ADJ
ssh-7883	80	9	side	side	NOUN
ssh-7883	80	10	of	of	ADP
ssh-7883	80	11	the	the	DET
ssh-7883	80	12	equation	equation	NOUN
ssh-7883	80	13	it	it	PRON
ssh-7883	80	14	follows	follow	VERB
ssh-7883	80	15	that	that	SCONJ
ssh-7883	80	16	λα	λα	PROPN
ssh-7883	80	17	+	+	NUM
ssh-7883	80	18	βlu	βlu	NOUN
ssh-7883	81	1	−	−	NOUN
ssh-7883	81	2	λβ	λβ	ADP
ssh-7883	81	3	−	−	PROPN
ssh-7883	81	4	1i0	1i0	NUM
ssh-7883	81	5	1	1	NUM
ssh-7883	81	6	α	α	DET
ssh-7883	81	7	u(0	u(0	PROPN
ssh-7883	81	8	+	+	PROPN
ssh-7883	81	9	)	)	PUNCT
ssh-7883	81	10	−	−	NOUN
ssh-7883	82	1	λβ	λβ	ADP
ssh-7883	82	2	−	−	PROPN
ssh-7883	82	3	1(ld0	1(ld0	NUM
ssh-7883	82	4	α	α	NOUN
ssh-7883	82	5	+	+	NOUN
ssh-7883	82	6	u)(0	u)(0	NOUN
ssh-7883	82	7	)	)	PUNCT
ssh-7883	82	8	=	=	SYM
ssh-7883	82	9	l[au(t	l[au(t	PROPN
ssh-7883	82	10	)	)	PUNCT
ssh-7883	82	11	+	+	NUM
ssh-7883	82	12	f(t)](λ	f(t)](λ	NUM
ssh-7883	82	13	)	)	PUNCT
ssh-7883	82	14	(	(	PUNCT
ssh-7883	82	15	λα	λα	NOUN
ssh-7883	82	16	+	+	CCONJ
ssh-7883	82	17	βi	βi	PROPN
ssh-7883	82	18	−	−	NOUN
ssh-7883	82	19	a)(lu)(λ	a)(lu)(λ	PROPN
ssh-7883	82	20	)	)	PUNCT
ssh-7883	82	21	=	=	SYM
ssh-7883	83	1	λβ	λβ	ADP
ssh-7883	83	2	u1	u1	NOUN
ssh-7883	83	3	+	+	CCONJ
ssh-7883	83	4	λβ	λβ	ADP
ssh-7883	83	5	−	−	NUM
ssh-7883	83	6	1r1	1r1	NUM
ssh-7883	83	7	+	+	CCONJ
ssh-7883	83	8	(	(	PUNCT
ssh-7883	83	9	lf)(λ	lf)(λ	NOUN
ssh-7883	83	10	)	)	PUNCT
ssh-7883	83	11	let	let	VERB
ssh-7883	83	12	r(λα	r(λα	NOUN
ssh-7883	83	13	+	+	ADP
ssh-7883	83	14	β	β	NOUN
ssh-7883	83	15	,	,	PUNCT
ssh-7883	83	16	a	a	PRON
ssh-7883	83	17	)	)	PUNCT
ssh-7883	83	18	=	=	SYM
ssh-7883	84	1	(	(	PUNCT
ssh-7883	84	2	λα	λα	PROPN
ssh-7883	85	1	+	+	CCONJ
ssh-7883	85	2	βi	βi	PROPN
ssh-7883	85	3	−	−	PROPN
ssh-7883	85	4	a)−	a)−	PROPN
ssh-7883	85	5	1	1	NUM
ssh-7883	85	6	(	(	PUNCT
ssh-7883	85	7	lu)(λ	lu)(λ	NOUN
ssh-7883	85	8	)	)	PUNCT
ssh-7883	85	9	=	=	PUNCT
ssh-7883	86	1	r(λα	r(λα	NOUN
ssh-7883	86	2	+	+	ADP
ssh-7883	86	3	β	β	X
ssh-7883	86	4	,	,	PUNCT
ssh-7883	86	5	a)(λβ	a)(λβ	NUM
ssh-7883	86	6	u1	u1	NOUN
ssh-7883	86	7	+	+	CCONJ
ssh-7883	86	8	λβ	λβ	ADP
ssh-7883	86	9	−	−	NUM
ssh-7883	86	10	1r1	1r1	NUM
ssh-7883	86	11	+	+	CCONJ
ssh-7883	86	12	(	(	PUNCT
ssh-7883	86	13	lf)(λ	lf)(λ	NOUN
ssh-7883	86	14	)	)	PUNCT
ssh-7883	86	15	)	)	PUNCT
ssh-7883	86	16	u(t	u(t	NOUN
ssh-7883	86	17	)	)	PUNCT
ssh-7883	86	18	=	=	SYM
ssh-7883	87	1	l−	l−	PROPN
ssh-7883	87	2	1r(λα	1r(λα	NUM
ssh-7883	87	3	+	+	CCONJ
ssh-7883	87	4	β	β	X
ssh-7883	87	5	,	,	PUNCT
ssh-7883	87	6	a)(λβ	a)(λβ	NUM
ssh-7883	87	7	u1	u1	NOUN
ssh-7883	87	8	+	+	CCONJ
ssh-7883	87	9	λβ	λβ	ADP
ssh-7883	87	10	−	−	PROPN
ssh-7883	87	11	1r1	1r1	NUM
ssh-7883	87	12	)	)	PUNCT
ssh-7883	88	1	+	+	CCONJ
ssh-7883	88	2	l−	l−	PROPN
ssh-7883	88	3	1r(λα	1r(λα	NUM
ssh-7883	88	4	+	+	CCONJ
ssh-7883	88	5	β	β	X
ssh-7883	88	6	,	,	PUNCT
ssh-7883	88	7	a)lf	a)lf	PROPN
ssh-7883	88	8	now	now	ADV
ssh-7883	88	9	we	we	PRON
ssh-7883	88	10	can	can	AUX
ssh-7883	88	11	get	get	VERB
ssh-7883	88	12	(	(	PUNCT
ssh-7883	88	13	3.1	3.1	NUM
ssh-7883	88	14	)	)	PUNCT
ssh-7883	88	15	easily	easily	ADV
ssh-7883	88	16	by	by	ADP
ssh-7883	88	17	converting	convert	VERB
ssh-7883	88	18	the	the	DET
ssh-7883	88	19	above	above	ADJ
ssh-7883	88	20	equation	equation	NOUN
ssh-7883	88	21	.	.	PUNCT
ssh-7883	89	1	theorem	theorem	VERB
ssh-7883	89	2	4.2	4.2	NUM
ssh-7883	89	3	the	the	DET
ssh-7883	89	4	function	function	NOUN
ssh-7883	89	5	f	f	PROPN
ssh-7883	89	6	satisfies	satisfy	VERB
ssh-7883	89	7	the	the	DET
ssh-7883	89	8	consistent	consistent	ADJ
ssh-7883	89	9	holder	holder	NOUN
ssh-7883	89	10	condition	condition	NOUN
ssh-7883	89	11	and	and	CCONJ
ssh-7883	89	12	a	a	PRON
ssh-7883	89	13	is	be	AUX
ssh-7883	89	14	a	a	DET
ssh-7883	89	15	sectorial	sectorial	ADJ
ssh-7883	89	16	operator	operator	NOUN
ssh-7883	89	17	of	of	ADP
ssh-7883	89	18	type	type	NOUN
ssh-7883	89	19	(	(	PUNCT
ssh-7883	89	20	m	m	PROPN
ssh-7883	89	21	,	,	PUNCT
ssh-7883	89	22	θ	θ	PROPN
ssh-7883	89	23	,	,	PUNCT
ssh-7883	89	24	α	α	NOUN
ssh-7883	90	1	+	+	X
ssh-7883	90	2	β,µ	β,µ	NOUN
ssh-7883	90	3	)	)	PUNCT
ssh-7883	90	4	,	,	PUNCT
ssh-7883	90	5	then	then	ADV
ssh-7883	90	6	the	the	DET
ssh-7883	90	7	solutions	solution	NOUN
ssh-7883	90	8	of	of	ADP
ssh-7883	90	9	the	the	DET
ssh-7883	90	10	cauchy	cauchy	ADJ
ssh-7883	90	11	problem	problem	NOUN
ssh-7883	90	12	(	(	PUNCT
ssh-7883	90	13	1.2	1.2	NUM
ssh-7883	90	14	)	)	PUNCT
ssh-7883	90	15	are	be	AUX
ssh-7883	90	16	fixed	fix	VERB
ssh-7883	90	17	points	point	NOUN
ssh-7883	90	18	of	of	ADP
ssh-7883	90	19	operator	operator	NOUN
ssh-7883	90	20	equation	equation	NOUN
ssh-7883	90	21	u(t	u(t	NOUN
ssh-7883	90	22	)	)	PUNCT
ssh-7883	90	23	=	=	SYM
ssh-7883	90	24	sα+β	sα+β	PROPN
ssh-7883	90	25	,	,	PUNCT
ssh-7883	90	26	β	β	X
ssh-7883	90	27	(	(	PUNCT
ssh-7883	90	28	t)u1	t)u1	NOUN
ssh-7883	90	29	+	+	CCONJ
ssh-7883	90	30	sα+β	sα+β	NOUN
ssh-7883	90	31	,	,	PUNCT
ssh-7883	90	32	β−1(t)r1	β−1(t)r1	NUM
ssh-7883	91	1	+	+	CCONJ
ssh-7883	91	2	tα+β	tα+β	NOUN
ssh-7883	91	3	(	(	PUNCT
ssh-7883	91	4	t	t	NOUN
ssh-7883	91	5	−	−	NOUN
ssh-7883	91	6	s)f(s	s)f(s	PROPN
ssh-7883	91	7	,	,	PUNCT
ssh-7883	91	8	u(s))ds	u(s))ds	PROPN
ssh-7883	91	9	.	.	PUNCT
ssh-7883	92	1	(	(	PUNCT
ssh-7883	92	2	4.3	4.3	NUM
ssh-7883	92	3	)	)	PUNCT
ssh-7883	92	4	theorem	theorem	VERB
ssh-7883	92	5	4.2	4.2	NUM
ssh-7883	92	6	leads	lead	VERB
ssh-7883	92	7	the	the	DET
ssh-7883	92	8	following	follow	VERB
ssh-7883	92	9	appropriate	appropriate	ADJ
ssh-7883	92	10	definition	definition	NOUN
ssh-7883	92	11	of	of	ADP
ssh-7883	92	12	a	a	DET
ssh-7883	92	13	mild	mild	ADJ
ssh-7883	92	14	solution	solution	NOUN
ssh-7883	92	15	to	to	ADP
ssh-7883	92	16	(	(	PUNCT
ssh-7883	92	17	1.2	1.2	NUM
ssh-7883	92	18	)	)	PUNCT
ssh-7883	92	19	.	.	PUNCT
ssh-7883	93	1	definition	definition	NOUN
ssh-7883	93	2	4.1	4.1	NUM
ssh-7883	93	3	afunction	afunction	NOUN
ssh-7883	93	4	u	u	PROPN
ssh-7883	93	5	∈	∈	PROPN
ssh-7883	93	6	c(j	c(j	PROPN
ssh-7883	93	7	,	,	PUNCT
ssh-7883	93	8	x	x	X
ssh-7883	93	9	)	)	PUNCT
ssh-7883	93	10	is	be	AUX
ssh-7883	93	11	called	call	VERB
ssh-7883	93	12	a	a	DET
ssh-7883	93	13	mild	mild	ADJ
ssh-7883	93	14	solution	solution	NOUN
ssh-7883	93	15	of	of	ADP
ssh-7883	93	16	(	(	PUNCT
ssh-7883	93	17	1.2	1.2	NUM
ssh-7883	93	18	)	)	PUNCT
ssh-7883	93	19	when	when	SCONJ
ssh-7883	93	20	it	it	PRON
ssh-7883	93	21	satifies	satifie	VERB
ssh-7883	93	22	the	the	DET
ssh-7883	93	23	operator	operator	NOUN
ssh-7883	93	24	equation	equation	NOUN
ssh-7883	93	25	u(t	u(t	NOUN
ssh-7883	93	26	)	)	PUNCT
ssh-7883	93	27	=	=	SYM
ssh-7883	93	28	sα+β	sα+β	PROPN
ssh-7883	93	29	,	,	PUNCT
ssh-7883	93	30	β	β	X
ssh-7883	93	31	(	(	PUNCT
ssh-7883	93	32	t)u1	t)u1	NOUN
ssh-7883	93	33	+	+	CCONJ
ssh-7883	93	34	sα+β	sα+β	NOUN
ssh-7883	93	35	,	,	PUNCT
ssh-7883	93	36	β−1(t)r1	β−1(t)r1	NUM
ssh-7883	94	1	+	+	CCONJ
ssh-7883	94	2	tα+β	tα+β	NOUN
ssh-7883	94	3	(	(	PUNCT
ssh-7883	94	4	t	t	NOUN
ssh-7883	94	5	−	−	NOUN
ssh-7883	94	6	s)f(s	s)f(s	PROPN
ssh-7883	94	7	,	,	PUNCT
ssh-7883	94	8	u(s))ds	u(s))ds	PROPN
ssh-7883	94	9	.	.	PUNCT
ssh-7883	94	10	(	(	PUNCT
ssh-7883	94	11	4.4	4.4	NUM
ssh-7883	94	12	)	)	PUNCT
ssh-7883	94	13	by	by	ADP
ssh-7883	94	14	observing	observe	VERB
ssh-7883	94	15	the	the	DET
ssh-7883	94	16	expression	expression	NOUN
ssh-7883	94	17	forms	form	NOUN
ssh-7883	94	18	of	of	ADP
ssh-7883	94	19	the	the	DET
ssh-7883	94	20	solutions	solution	NOUN
ssh-7883	94	21	of	of	ADP
ssh-7883	94	22	these	these	DET
ssh-7883	94	23	two	two	NUM
ssh-7883	94	24	types	type	NOUN
ssh-7883	94	25	of	of	ADP
ssh-7883	94	26	mixed	mixed	ADJ
ssh-7883	94	27	fractional	fractional	ADJ
ssh-7883	94	28	order	order	NOUN
ssh-7883	94	29	evolution	evolution	NOUN
ssh-7883	94	30	equations	equation	NOUN
ssh-7883	94	31	,	,	PUNCT
ssh-7883	94	32	the	the	DET
ssh-7883	94	33	solution	solution	NOUN
ssh-7883	94	34	operator	operator	NOUN
ssh-7883	94	35	forms	form	NOUN
ssh-7883	94	36	of	of	ADP
ssh-7883	94	37	these	these	DET
ssh-7883	94	38	mixed	mix	VERB
ssh-7883	94	39	fractional	fractional	ADJ
ssh-7883	94	40	equations	equation	NOUN
ssh-7883	94	41	are	be	AUX
ssh-7883	94	42	different	different	ADJ
ssh-7883	94	43	after	after	SCONJ
ssh-7883	94	44	the	the	DET
ssh-7883	94	45	differential	differential	ADJ
ssh-7883	94	46	order	order	NOUN
ssh-7883	94	47	is	be	AUX
ssh-7883	94	48	exchanged	exchange	VERB
ssh-7883	94	49	.	.	PUNCT
ssh-7883	95	1	therefore	therefore	ADV
ssh-7883	95	2	,	,	PUNCT
ssh-7883	95	3	we	we	PRON
ssh-7883	95	4	perform	perform	VERB
ssh-7883	95	5	a	a	DET
ssh-7883	95	6	norm	norm	NOUN
ssh-7883	95	7	estimation	estimation	NOUN
ssh-7883	95	8	of	of	ADP
ssh-7883	95	9	its	its	PRON
ssh-7883	95	10	solution	solution	NOUN
ssh-7883	95	11	operator	operator	NOUN
ssh-7883	95	12	.	.	PUNCT
ssh-7883	96	1	5	5	X
ssh-7883	96	2	.	.	X
ssh-7883	96	3	norm	norm	NOUN
ssh-7883	96	4	estimations	estimation	NOUN
ssh-7883	96	5	theorem	theorem	VERB
ssh-7883	96	6	5.1	5.1	NUM
ssh-7883	96	7	let	let	VERB
ssh-7883	96	8	a	a	PRON
ssh-7883	96	9	be	be	AUX
ssh-7883	96	10	an	an	DET
ssh-7883	96	11	operator	operator	NOUN
ssh-7883	96	12	with	with	ADP
ssh-7883	96	13	type	type	NOUN
ssh-7883	96	14	(	(	PUNCT
ssh-7883	96	15	m	m	PROPN
ssh-7883	96	16	,	,	PUNCT
ssh-7883	96	17	θ	θ	PROPN
ssh-7883	96	18	,	,	PUNCT
ssh-7883	96	19	α	α	NOUN
ssh-7883	96	20	+	+	X
ssh-7883	96	21	β,µ	β,µ	ADJ
ssh-7883	96	22	)	)	PUNCT
ssh-7883	96	23	.	.	PUNCT
ssh-7883	97	1	then	then	ADV
ssh-7883	97	2	we	we	PRON
ssh-7883	97	3	can	can	AUX
ssh-7883	97	4	show	show	VERB
ssh-7883	97	5	the	the	DET
ssh-7883	97	6	following	follow	VERB
ssh-7883	97	7	estimates	estimate	NOUN
ssh-7883	97	8	on	on	ADP
ssh-7883	97	9	//sα+β	//sα+β	PUNCT
ssh-7883	97	10	,	,	PUNCT
ssh-7883	97	11	β(t	β(t	PROPN
ssh-7883	97	12	)	)	PUNCT
ssh-7883	97	13	//	//	NOUN
ssh-7883	97	14	.	.	PUNCT
ssh-7883	98	1	(	(	PUNCT
ssh-7883	98	2	i	i	NOUN
ssh-7883	98	3	)	)	PUNCT
ssh-7883	98	4	when	when	SCONJ
ssh-7883	98	5	µ	µ	X
ssh-7883	98	6	≥	≥	X
ssh-7883	98	7	0	0	NUM
ssh-7883	98	8	,	,	PUNCT
ssh-7883	98	9	for	for	ADP
ssh-7883	98	10	ϕ	ϕ	PROPN
ssh-7883	98	11	∈	∈	PROPN
ssh-7883	98	12	(	(	PUNCT
ssh-7883	98	13	0,π	0,π	PROPN
ssh-7883	98	14	)	)	PUNCT
ssh-7883	98	15	,	,	PUNCT
ssh-7883	98	16	we	we	PRON
ssh-7883	98	17	have	have	VERB
ssh-7883	98	18	(	(	PUNCT
ssh-7883	98	19	ii	ii	NOUN
ssh-7883	98	20	)	)	PUNCT
ssh-7883	98	21	when	when	SCONJ
ssh-7883	98	22	µ	µ	X
ssh-7883	98	23	<	<	X
ssh-7883	98	24	0	0	NUM
ssh-7883	98	25	.	.	PUNCT
ssh-7883	99	1	for	for	ADP
ssh-7883	99	2	φ	φ	PROPN
ssh-7883	99	3	∈	∈	PROPN
ssh-7883	99	4	(	(	PUNCT
ssh-7883	99	5	0	0	NUM
ssh-7883	99	6	,	,	PUNCT
ssh-7883	99	7	π	π	PROPN
ssh-7883	99	8	)	)	PUNCT
ssh-7883	99	9	,	,	PUNCT
ssh-7883	99	10	we	we	PRON
ssh-7883	99	11	have	have	VERB
ssh-7883	99	12	bcp	bcp	VERB
ssh-7883	99	13	social	social	PROPN
ssh-7883	99	14	sciences	sciences	PROPN
ssh-7883	99	15	&	&	CCONJ
ssh-7883	99	16	humanities	humanities	PROPN
ssh-7883	99	17	erss	erss	VERB
ssh-7883	99	18	2024	2024	NUM
ssh-7883	99	19	volume	volume	NOUN
ssh-7883	99	20	23	23	NUM
ssh-7883	99	21	(	(	PUNCT
ssh-7883	99	22	2024	2024	NUM
ssh-7883	99	23	)	)	PUNCT
ssh-7883	99	24	6	6	NUM
ssh-7883	99	25	proof	proof	NOUN
ssh-7883	99	26	.	.	PUNCT
ssh-7883	100	1	give	give	VERB
ssh-7883	100	2	a	a	DET
ssh-7883	100	3	ϕ	ϕ	X
ssh-7883	100	4	∈	∈	PROPN
ssh-7883	100	5	(	(	PUNCT
ssh-7883	100	6	0,π	0,π	NOUN
ssh-7883	100	7	)	)	PUNCT
ssh-7883	100	8	,	,	PUNCT
ssh-7883	100	9	define	define	VERB
ssh-7883	100	10	sϕ	sϕ	NOUN
ssh-7883	100	11	=	=	PUNCT
ssh-7883	100	12	{	{	PUNCT
ssh-7883	100	13	λ	λ	X
ssh-7883	100	14	∈	∈	PROPN
ssh-7883	100	15	c	c	NOUN
ssh-7883	100	16	:	:	PUNCT
ssh-7883	100	17	|arg(−λ)|	|arg(−λ)|	PUNCT
ssh-7883	100	18	<	<	X
ssh-7883	100	19	ϕ	ϕ	X
ssh-7883	100	20	}	}	PUNCT
ssh-7883	100	21	.	.	PUNCT
ssh-7883	101	1	first	first	ADV
ssh-7883	101	2	,	,	PUNCT
ssh-7883	101	3	we	we	PRON
ssh-7883	101	4	prove	prove	VERB
ssh-7883	101	5	(	(	PUNCT
ssh-7883	101	6	i	i	NOUN
ssh-7883	101	7	)	)	PUNCT
ssh-7883	101	8	.	.	PUNCT
ssh-7883	102	1	for	for	ADP
ssh-7883	102	2	t	t	PROPN
ssh-7883	102	3	>	>	X
ssh-7883	102	4	0	0	NUM
ssh-7883	102	5	,	,	PUNCT
ssh-7883	102	6	consider	consider	VERB
ssh-7883	102	7	the	the	DET
ssh-7883	102	8	positively	positively	ADV
ssh-7883	102	9	oriented	orient	VERB
ssh-7883	102	10	path	path	NOUN
ssh-7883	102	11	c	c	NOUN
ssh-7883	102	12	which	which	PRON
ssh-7883	102	13	is	be	AUX
ssh-7883	102	14	the	the	DET
ssh-7883	102	15	image	image	NOUN
ssh-7883	102	16	of	of	ADP
ssh-7883	102	17	the	the	DET
ssh-7883	102	18	boundary	boundary	NOUN
ssh-7883	102	19	of	of	ADP
ssh-7883	102	20	(	(	PUNCT
ssh-7883	102	21	µ	µ	X
ssh-7883	102	22	+	+	X
ssh-7883	102	23	+	+	CCONJ
ssh-7883	102	24	sθ	sθ	ADJ
ssh-7883	102	25	)	)	PUNCT
ssh-7883	102	26	∪	∪	ADP
ssh-7883	102	27	sϕ	sϕ	NOUN
ssh-7883	102	28	under	under	ADP
ssh-7883	102	29	the	the	DET
ssh-7883	102	30	function	function	NOUN
ssh-7883	102	31	p	p	X
ssh-7883	102	32	(	(	PUNCT
ssh-7883	102	33	)	)	PUNCT
ssh-7883	102	34	,	,	PUNCT
ssh-7883	102	35	here	here	ADV
ssh-7883	102	36	we	we	PRON
ssh-7883	102	37	require	require	VERB
ssh-7883	102	38	ϕ	ϕ	X
ssh-7883	102	39	>	>	X
ssh-7883	102	40	θ	θ	PROPN
ssh-7883	102	41	so	so	SCONJ
ssh-7883	102	42	that	that	SCONJ
ssh-7883	102	43	sϕ	sϕ	PROPN
ssh-7883	102	44	⊂	⊂	PROPN
ssh-7883	102	45	̸	̸	PUNCT
ssh-7883	102	46	(	(	PUNCT
ssh-7883	102	47	µ+	µ+	X
ssh-7883	102	48	+	+	ADJ
ssh-7883	102	49	sθ	sθ	NOUN
ssh-7883	102	50	)	)	PUNCT
ssh-7883	102	51	(	(	PUNCT
ssh-7883	102	52	as	as	ADP
ssh-7883	102	53	show	show	NOUN
ssh-7883	102	54	in	in	ADP
ssh-7883	102	55	fig.1	fig.1	PROPN
ssh-7883	102	56	)	)	PUNCT
ssh-7883	102	57	.	.	PUNCT
ssh-7883	103	1	then	then	ADV
ssh-7883	103	2	along	along	ADP
ssh-7883	103	3	c	c	PROPN
ssh-7883	103	4	,	,	PUNCT
ssh-7883	103	5	the	the	DET
ssh-7883	103	6	resolvent	resolvent	ADJ
ssh-7883	103	7	(	(	PUNCT
ssh-7883	103	8	λα+βi	λα+βi	X
ssh-7883	103	9	−a	−a	NOUN
ssh-7883	103	10	)	)	PUNCT
ssh-7883	103	11	is	be	AUX
ssh-7883	103	12	well	well	ADV
ssh-7883	103	13	defined	define	VERB
ssh-7883	103	14	,	,	PUNCT
ssh-7883	103	15	and	and	CCONJ
ssh-7883	103	16	then	then	ADV
ssh-7883	103	17	the	the	DET
ssh-7883	103	18	representation	representation	NOUN
ssh-7883	103	19	of	of	ADP
ssh-7883	103	20	sα+β	sα+β	NOUN
ssh-7883	103	21	,	,	PUNCT
ssh-7883	103	22	β(t	β(t	PROPN
ssh-7883	103	23	)	)	PUNCT
ssh-7883	103	24	is	be	AUX
ssh-7883	103	25	meaningful	meaningful	ADJ
ssh-7883	103	26	.	.	PUNCT
ssh-7883	104	1	now	now	ADV
ssh-7883	104	2	,	,	PUNCT
ssh-7883	104	3	we	we	PRON
ssh-7883	104	4	let	let	VERB
ssh-7883	104	5	c1	c1	PROPN
ssh-7883	104	6	be	be	AUX
ssh-7883	104	7	the	the	DET
ssh-7883	104	8	part	part	NOUN
ssh-7883	104	9	of	of	ADP
ssh-7883	104	10	c	c	PROPN
ssh-7883	104	11	associated	associate	VERB
ssh-7883	104	12	with	with	ADP
ssh-7883	104	13	the	the	DET
ssh-7883	104	14	part	part	NOUN
ssh-7883	104	15	on	on	ADP
ssh-7883	104	16	the	the	DET
ssh-7883	104	17	boundary	boundary	NOUN
ssh-7883	104	18	from	from	ADP
ssh-7883	104	19	zt	zt	PROPN
ssh-7883	104	20	to	to	ADP
ssh-7883	104	21	zt	zt	PROPN
ssh-7883	104	22	,	,	PUNCT
ssh-7883	104	23	and	and	CCONJ
ssh-7883	104	24	c21	c21	NOUN
ssh-7883	104	25	and	and	CCONJ
ssh-7883	104	26	c22	c22	NOUN
ssh-7883	104	27	be	be	AUX
ssh-7883	104	28	the	the	DET
ssh-7883	104	29	parts	part	NOUN
ssh-7883	104	30	of	of	ADP
ssh-7883	104	31	c	c	PROPN
ssh-7883	104	32	associated	associate	VERB
ssh-7883	104	33	with	with	ADP
ssh-7883	104	34	the	the	DET
ssh-7883	104	35	parts	part	NOUN
ssh-7883	104	36	on	on	ADP
ssh-7883	104	37	the	the	DET
ssh-7883	104	38	boundary	boundary	NOUN
ssh-7883	104	39	from	from	ADP
ssh-7883	104	40	infinity	infinity	NOUN
ssh-7883	104	41	to	to	ADP
ssh-7883	104	42	zt	zt	PROPN
ssh-7883	104	43	and	and	CCONJ
ssh-7883	104	44	from	from	ADP
ssh-7883	104	45	zt	zt	PROPN
ssh-7883	104	46	to	to	ADP
ssh-7883	104	47	infinity	infinity	NOUN
ssh-7883	104	48	,	,	PUNCT
ssh-7883	104	49	where	where	SCONJ
ssh-7883	104	50	zt	zt	PROPN
ssh-7883	104	51	and	and	CCONJ
ssh-7883	104	52	zt	zt	PROPN
ssh-7883	104	53	are	be	AUX
ssh-7883	104	54	the	the	DET
ssh-7883	104	55	intersection	intersection	NOUN
ssh-7883	104	56	points	point	NOUN
ssh-7883	104	57	of	of	ADP
ssh-7883	104	58	the	the	DET
ssh-7883	104	59	boundaries	boundary	NOUN
ssh-7883	104	60	of	of	ADP
ssh-7883	104	61	µ	µ	NOUN
ssh-7883	104	62	+	+	NOUN
ssh-7883	104	63	+	+	CCONJ
ssh-7883	104	64	sθ	sθ	NOUN
ssh-7883	104	65	and	and	CCONJ
ssh-7883	104	66	sϕ	sϕ	NOUN
ssh-7883	104	67	.	.	PUNCT
ssh-7883	105	1	in	in	ADP
ssh-7883	105	2	this	this	DET
ssh-7883	105	3	case	case	NOUN
ssh-7883	105	4	,	,	PUNCT
ssh-7883	105	5	we	we	PRON
ssh-7883	105	6	divide	divide	VERB
ssh-7883	105	7	sα+β	sα+β	PROPN
ssh-7883	105	8	,	,	PUNCT
ssh-7883	105	9	β(t	β(t	PROPN
ssh-7883	105	10	)	)	PUNCT
ssh-7883	105	11	into	into	ADP
ssh-7883	105	12	two	two	NUM
ssh-7883	105	13	parts	part	NOUN
ssh-7883	105	14	:	:	PUNCT
ssh-7883	105	15	sα+β	sα+β	NOUN
ssh-7883	105	16	,	,	PUNCT
ssh-7883	105	17	β(t	β(t	NOUN
ssh-7883	105	18	)	)	PUNCT
ssh-7883	105	19	=	=	PROPN
ssh-7883	105	20	i1	i1	PROPN
ssh-7883	105	21	(	(	PUNCT
ssh-7883	105	22	t	t	PROPN
ssh-7883	105	23	)	)	PUNCT
ssh-7883	105	24	+	+	NUM
ssh-7883	105	25	i2	i2	PROPN
ssh-7883	105	26	(	(	PUNCT
ssh-7883	105	27	t	t	PROPN
ssh-7883	105	28	)	)	PUNCT
ssh-7883	105	29	,	,	PUNCT
ssh-7883	105	30	here	here	ADV
ssh-7883	105	31	fig	fig	NOUN
ssh-7883	105	32	1	1	NUM
ssh-7883	105	33	.	.	PUNCT
ssh-7883	106	1	a	a	DET
ssh-7883	106	2	particular	particular	ADJ
ssh-7883	106	3	path	path	NOUN
ssh-7883	106	4	for	for	ADP
ssh-7883	106	5	estimating	estimate	VERB
ssh-7883	106	6	//sα+β	//sα+β	NOUN
ssh-7883	106	7	,	,	PUNCT
ssh-7883	106	8	β(t	β(t	PROPN
ssh-7883	106	9	)	)	PUNCT
ssh-7883	107	1	//	//	X
ssh-7883	107	2	when	when	SCONJ
ssh-7883	107	3	µ	µ	PRON
ssh-7883	107	4	≥	≥	X
ssh-7883	107	5	0	0	NUM
ssh-7883	107	6	and	and	CCONJ
ssh-7883	107	7	for	for	ADP
ssh-7883	107	8	λ	λ	PROPN
ssh-7883	107	9	∈	∈	PROPN
ssh-7883	107	10	c1	c1	PROPN
ssh-7883	107	11	,	,	PUNCT
ssh-7883	107	12	one	one	PRON
ssh-7883	107	13	can	can	AUX
ssh-7883	107	14	easily	easily	ADV
ssh-7883	107	15	see	see	VERB
ssh-7883	107	16	from	from	ADP
ssh-7883	107	17	the	the	DET
ssh-7883	107	18	fig.1	fig.1	PROPN
ssh-7883	107	19	that	that	PRON
ssh-7883	107	20	and	and	CCONJ
ssh-7883	107	21	it	it	PRON
ssh-7883	107	22	is	be	AUX
ssh-7883	107	23	obvious	obvious	ADJ
ssh-7883	107	24	that	that	SCONJ
ssh-7883	107	25	c1	c1	PROPN
ssh-7883	107	26	is	be	AUX
ssh-7883	107	27	symmetric	symmetric	ADJ
ssh-7883	107	28	about	about	ADP
ssh-7883	107	29	the	the	DET
ssh-7883	107	30	real	real	ADJ
ssh-7883	107	31	axis	axis	NOUN
ssh-7883	107	32	and	and	CCONJ
ssh-7883	107	33	the	the	DET
ssh-7883	107	34	part	part	NOUN
ssh-7883	107	35	above	above	ADP
ssh-7883	107	36	the	the	DET
ssh-7883	107	37	real	real	ADJ
ssh-7883	107	38	axis	axis	NOUN
ssh-7883	107	39	is	be	AUX
ssh-7883	107	40	parameterized	parameterized	ADJ
ssh-7883	108	1	then	then	ADV
ssh-7883	108	2	therefore	therefore	ADV
ssh-7883	108	3	,	,	PUNCT
ssh-7883	108	4	bcp	bcp	VERB
ssh-7883	108	5	social	social	PROPN
ssh-7883	108	6	sciences	sciences	PROPN
ssh-7883	108	7	&	&	CCONJ
ssh-7883	108	8	humanities	humanities	PROPN
ssh-7883	108	9	erss	erss	VERB
ssh-7883	108	10	2024	2024	NUM
ssh-7883	108	11	volume	volume	NOUN
ssh-7883	108	12	23	23	NUM
ssh-7883	108	13	(	(	PUNCT
ssh-7883	108	14	2024	2024	NUM
ssh-7883	108	15	)	)	PUNCT
ssh-7883	108	16	7	7	NUM
ssh-7883	108	17	now	now	ADV
ssh-7883	108	18	we	we	PRON
ssh-7883	108	19	come	come	VERB
ssh-7883	108	20	to	to	PART
ssh-7883	108	21	estimate	estimate	VERB
ssh-7883	108	22	//i2	//i2	PUNCT
ssh-7883	108	23	(	(	PUNCT
ssh-7883	108	24	t	t	PROPN
ssh-7883	108	25	)	)	PUNCT
ssh-7883	108	26	//	//	NOUN
ssh-7883	108	27	.	.	PUNCT
ssh-7883	109	1	note	note	VERB
ssh-7883	109	2	that	that	SCONJ
ssh-7883	109	3	for	for	ADP
ssh-7883	109	4	t	t	PROPN
ssh-7883	109	5	>	>	X
ssh-7883	109	6	0	0	NUM
ssh-7883	109	7	,	,	PUNCT
ssh-7883	109	8	|zt	|zt	NUM
ssh-7883	110	1	|	|	NOUN
ssh-7883	111	1	=	=	SYM
ssh-7883	112	1	|	|	ADV
ssh-7883	112	2	sinθ	sinθ	PROPN
ssh-7883	112	3	,	,	PUNCT
ssh-7883	112	4	t	t	X
ssh-7883	112	5	>	>	X
ssh-7883	112	6	0	0	PUNCT
ssh-7883	112	7	and	and	CCONJ
ssh-7883	112	8	for	for	ADP
ssh-7883	112	9	λ	λ	PROPN
ssh-7883	112	10	∈	∈	PROPN
ssh-7883	112	11	c2	c2	PROPN
ssh-7883	112	12	=	=	PUNCT
ssh-7883	112	13	c21	c21	PROPN
ssh-7883	112	14	∪	∪	PROPN
ssh-7883	112	15	c22	c22	PROPN
ssh-7883	112	16	,	,	PUNCT
ssh-7883	112	17	|λα+β	|λα+β	ADP
ssh-7883	112	18	−	−	PROPN
ssh-7883	112	19	µ|	µ|	PROPN
ssh-7883	112	20	≥	≥	NUM
ssh-7883	112	21	|zt	|zt	NUM
ssh-7883	112	22	|sinϕ	|sinϕ	ADJ
ssh-7883	112	23	=	=	PUNCT
ssh-7883	112	24	|	|	NOUN
ssh-7883	112	25	zt	zt	PROPN
ssh-7883	112	26	|sinϕ	|sinϕ	VERB
ssh-7883	112	27	in	in	ADP
ssh-7883	112	28	the	the	DET
ssh-7883	112	29	above	above	NOUN
ssh-7883	112	30	,	,	PUNCT
ssh-7883	112	31	we	we	PRON
ssh-7883	112	32	require	require	VERB
ssh-7883	112	33	cos	cos	ADP
ssh-7883	112	34	α	α	NOUN
ssh-7883	112	35	π	π	X
ssh-7883	112	36	β	β	X
ssh-7883	112	37	ϕ	ϕ	X
ssh-7883	112	38	<	<	X
ssh-7883	112	39	0	0	NUM
ssh-7883	112	40	or	or	CCONJ
ssh-7883	112	41	equivalently	equivalently	ADV
ssh-7883	112	42	π	π	X
ssh-7883	112	43	ϕ	ϕ	PROPN
ssh-7883	112	44	∈	∈	PROPN
ssh-7883	112	45	(	(	PUNCT
ssh-7883	112	46	2	2	NUM
ssh-7883	112	47	π	π	NOUN
ssh-7883	112	48	,	,	PUNCT
ssh-7883	112	49	π	π	PROPN
ssh-7883	112	50	)	)	PUNCT
ssh-7883	112	51	.	.	PUNCT
ssh-7883	113	1	therefore	therefore	ADV
ssh-7883	113	2	,	,	PUNCT
ssh-7883	113	3	by	by	ADP
ssh-7883	113	4	combing	comb	VERB
ssh-7883	113	5	the	the	DET
ssh-7883	113	6	estimates	estimate	NOUN
ssh-7883	113	7	of	of	ADP
ssh-7883	113	8	//i1	//i1	PUNCT
ssh-7883	113	9	(	(	PUNCT
ssh-7883	113	10	t	t	PROPN
ssh-7883	113	11	)	)	PUNCT
ssh-7883	113	12	//	//	NOUN
ssh-7883	113	13	and	and	CCONJ
ssh-7883	113	14	//i2	//i2	NUM
ssh-7883	113	15	(	(	PUNCT
ssh-7883	113	16	t	t	PROPN
ssh-7883	113	17	)	)	PUNCT
ssh-7883	113	18	//	//	NOUN
ssh-7883	113	19	,	,	PUNCT
ssh-7883	113	20	we	we	PRON
ssh-7883	113	21	get	get	VERB
ssh-7883	113	22	the	the	DET
ssh-7883	113	23	conclusion	conclusion	NOUN
ssh-7883	113	24	.	.	PUNCT
ssh-7883	114	1	now	now	ADV
ssh-7883	114	2	we	we	PRON
ssh-7883	114	3	turn	turn	VERB
ssh-7883	114	4	to	to	PART
ssh-7883	114	5	prove	prove	VERB
ssh-7883	114	6	(	(	PUNCT
ssh-7883	114	7	ii	ii	NOUN
ssh-7883	114	8	)	)	PUNCT
ssh-7883	114	9	.	.	PUNCT
ssh-7883	115	1	the	the	DET
ssh-7883	115	2	porove	porove	NOUN
ssh-7883	115	3	is	be	AUX
ssh-7883	115	4	similar	similar	ADJ
ssh-7883	115	5	to	to	ADP
ssh-7883	115	6	that	that	PRON
ssh-7883	115	7	of	of	ADP
ssh-7883	115	8	(	(	PUNCT
ssh-7883	115	9	i	i	PROPN
ssh-7883	115	10	)	)	PUNCT
ssh-7883	115	11	.	.	PUNCT
ssh-7883	116	1	in	in	ADP
ssh-7883	116	2	this	this	DET
ssh-7883	116	3	case	case	NOUN
ssh-7883	116	4	,	,	PUNCT
ssh-7883	116	5	we	we	PRON
ssh-7883	116	6	consider	consider	VERB
ssh-7883	116	7	the	the	DET
ssh-7883	116	8	path	path	NOUN
ssh-7883	116	9	of	of	ADP
ssh-7883	116	10	c	c	NOUN
ssh-7883	116	11	,	,	PUNCT
ssh-7883	116	12	whose	whose	DET
ssh-7883	116	13	image	image	NOUN
ssh-7883	116	14	under	under	ADP
ssh-7883	116	15	the	the	DET
ssh-7883	116	16	p(zα+β	p(zα+β	NOUN
ssh-7883	116	17	)	)	PUNCT
ssh-7883	116	18	is	be	AUX
ssh-7883	116	19	the	the	DET
ssh-7883	116	20	boundary	boundary	NOUN
ssh-7883	116	21	of	of	ADP
ssh-7883	116	22	(	(	PUNCT
ssh-7883	116	23	tα	tα	PROPN
ssh-7883	116	24	β	β	PROPN
ssh-7883	116	25	+	+	CCONJ
ssh-7883	116	26	sϕ	sϕ	NOUN
ssh-7883	116	27	−	−	PROPN
ssh-7883	116	28	2	2	NUM
ssh-7883	116	29	π	π	NOUN
ssh-7883	116	30	)	)	PUNCT
ssh-7883	116	31	∪	∪	ADP
ssh-7883	116	32	sϕ	sϕ	NOUN
ssh-7883	116	33	,	,	PUNCT
ssh-7883	116	34	here	here	ADV
ssh-7883	116	35	we	we	PRON
ssh-7883	116	36	require	require	VERB
ssh-7883	116	37	ϕ	ϕ	PROPN
ssh-7883	116	38	∈	∈	PROPN
ssh-7883	116	39	(	(	PUNCT
ssh-7883	116	40	2	2	NUM
ssh-7883	116	41	π	π	NOUN
ssh-7883	116	42	,	,	PUNCT
ssh-7883	116	43	π)(as	π)(as	DET
ssh-7883	116	44	show	show	NOUN
ssh-7883	116	45	in	in	ADP
ssh-7883	116	46	fig	fig	NOUN
ssh-7883	116	47	2	2	NUM
ssh-7883	116	48	)	)	PUNCT
ssh-7883	116	49	.	.	PUNCT
ssh-7883	117	1	as	as	ADV
ssh-7883	117	2	same	same	ADJ
ssh-7883	117	3	as	as	ADP
ssh-7883	117	4	the	the	DET
ssh-7883	117	5	before	before	ADV
ssh-7883	117	6	,	,	PUNCT
ssh-7883	117	7	let	let	VERB
ssh-7883	117	8	c1	c1	PROPN
ssh-7883	117	9	be	be	AUX
ssh-7883	117	10	the	the	DET
ssh-7883	117	11	path	path	NOUN
ssh-7883	117	12	of	of	ADP
ssh-7883	117	13	c1	c1	PROPN
ssh-7883	117	14	be	be	AUX
ssh-7883	117	15	the	the	DET
ssh-7883	117	16	part	part	NOUN
ssh-7883	117	17	of	of	ADP
ssh-7883	117	18	c	c	PROPN
ssh-7883	117	19	associated	associate	VERB
ssh-7883	117	20	with	with	ADP
ssh-7883	117	21	the	the	DET
ssh-7883	117	22	part	part	NOUN
ssh-7883	117	23	on	on	ADP
ssh-7883	117	24	the	the	DET
ssh-7883	117	25	boundary	boundary	NOUN
ssh-7883	117	26	from	from	ADP
ssh-7883	117	27	zt	zt	PROPN
ssh-7883	117	28	to	to	ADP
ssh-7883	117	29	zt	zt	PROPN
ssh-7883	117	30	,	,	PUNCT
ssh-7883	117	31	and	and	CCONJ
ssh-7883	117	32	c21	c21	NOUN
ssh-7883	117	33	and	and	CCONJ
ssh-7883	117	34	c22	c22	PROPN
ssh-7883	117	35	respectively	respectively	ADV
ssh-7883	117	36	represent	represent	VERB
ssh-7883	117	37	the	the	DET
ssh-7883	117	38	parts	part	NOUN
ssh-7883	117	39	of	of	ADP
ssh-7883	117	40	c	c	PROPN
ssh-7883	117	41	associated	associate	VERB
ssh-7883	117	42	with	with	ADP
ssh-7883	117	43	the	the	DET
ssh-7883	117	44	parts	part	NOUN
ssh-7883	117	45	on	on	ADP
ssh-7883	117	46	the	the	DET
ssh-7883	117	47	boundary	boundary	NOUN
ssh-7883	117	48	from	from	ADP
ssh-7883	117	49	infinity	infinity	NOUN
ssh-7883	117	50	to	to	ADP
ssh-7883	117	51	zt	zt	PROPN
ssh-7883	117	52	and	and	CCONJ
ssh-7883	117	53	from	from	ADP
ssh-7883	117	54	zt	zt	PROPN
ssh-7883	117	55	to	to	ADP
ssh-7883	117	56	infinity	infinity	NOUN
ssh-7883	117	57	,	,	PUNCT
ssh-7883	117	58	where	where	SCONJ
ssh-7883	117	59	zt	zt	PROPN
ssh-7883	117	60	and	and	CCONJ
ssh-7883	117	61	zt	zt	PROPN
ssh-7883	117	62	are	be	AUX
ssh-7883	117	63	the	the	DET
ssh-7883	117	64	intersection	intersection	NOUN
ssh-7883	117	65	points	point	NOUN
ssh-7883	117	66	of	of	ADP
ssh-7883	117	67	the	the	DET
ssh-7883	117	68	boundaries	boundary	NOUN
ssh-7883	117	69	of	of	ADP
ssh-7883	117	70	+	+	NOUN
ssh-7883	117	71	sϕ	sϕ	PROPN
ssh-7883	117	72	−	−	PROPN
ssh-7883	117	73	and	and	CCONJ
ssh-7883	117	74	sϕ.	sϕ.	VERB
ssh-7883	117	75	for	for	ADP
ssh-7883	117	76	λ	λ	PROPN
ssh-7883	117	77	∈	∈	PROPN
ssh-7883	117	78	c1	c1	PROPN
ssh-7883	117	79	,	,	PUNCT
ssh-7883	117	80	combine	combine	VERB
ssh-7883	117	81	with	with	ADP
ssh-7883	117	82	the	the	DET
ssh-7883	117	83	fig.2	fig.2	PROPN
ssh-7883	117	84	above	above	ADV
ssh-7883	117	85	,	,	PUNCT
ssh-7883	117	86	we	we	PRON
ssh-7883	117	87	can	can	AUX
ssh-7883	117	88	get	get	AUX
ssh-7883	117	89	easily	easily	ADV
ssh-7883	117	90	see	see	VERB
ssh-7883	117	91	that	that	PRON
ssh-7883	117	92	and	and	CCONJ
ssh-7883	117	93	note	note	VERB
ssh-7883	117	94	that	that	SCONJ
ssh-7883	117	95	c1	c1	PROPN
ssh-7883	117	96	is	be	AUX
ssh-7883	117	97	the	the	DET
ssh-7883	117	98	symmetric	symmetric	ADJ
ssh-7883	117	99	about	about	ADP
ssh-7883	117	100	the	the	DET
ssh-7883	117	101	real	real	ADJ
ssh-7883	117	102	axis	axis	NOUN
ssh-7883	117	103	and	and	CCONJ
ssh-7883	117	104	the	the	DET
ssh-7883	117	105	part	part	NOUN
ssh-7883	117	106	above	above	ADP
ssh-7883	117	107	the	the	DET
ssh-7883	117	108	real	real	NOUN
ssh-7883	117	109	has	have	VERB
ssh-7883	117	110	the	the	DET
ssh-7883	117	111	parametrization	parametrization	NOUN
ssh-7883	117	112	,	,	PUNCT
ssh-7883	117	113	let	let	VERB
ssh-7883	117	114	π	π	PROPN
ssh-7883	117	115	sinθ	sinθ	PROPN
ssh-7883	117	116	bcp	bcp	PROPN
ssh-7883	117	117	social	social	PROPN
ssh-7883	117	118	sciences	sciences	PROPN
ssh-7883	117	119	&	&	CCONJ
ssh-7883	117	120	humanities	humanities	PROPN
ssh-7883	117	121	erss	erss	VERB
ssh-7883	117	122	2024	2024	NUM
ssh-7883	117	123	volume	volume	NOUN
ssh-7883	117	124	23	23	NUM
ssh-7883	117	125	(	(	PUNCT
ssh-7883	117	126	2024	2024	NUM
ssh-7883	117	127	)	)	PUNCT
ssh-7883	117	128	8	8	NUM
ssh-7883	117	129	fig	fig	NOUN
ssh-7883	117	130	2	2	NUM
ssh-7883	117	131	.	.	PUNCT
ssh-7883	118	1	a	a	DET
ssh-7883	118	2	particular	particular	ADJ
ssh-7883	118	3	path	path	NOUN
ssh-7883	118	4	for	for	ADP
ssh-7883	118	5	estimating	estimate	VERB
ssh-7883	118	6	//sα+β	//sα+β	NOUN
ssh-7883	118	7	,	,	PUNCT
ssh-7883	118	8	β(t	β(t	PROPN
ssh-7883	118	9	)	)	PUNCT
ssh-7883	119	1	//	//	X
ssh-7883	119	2	when	when	SCONJ
ssh-7883	119	3	<	<	X
ssh-7883	119	4	0	0	X
ssh-7883	119	5	then	then	ADV
ssh-7883	119	6	it	it	PRON
ssh-7883	119	7	follows	follow	VERB
ssh-7883	119	8	that	that	SCONJ
ssh-7883	119	9	on	on	ADP
ssh-7883	119	10	the	the	DET
ssh-7883	119	11	other	other	ADJ
ssh-7883	119	12	hand	hand	NOUN
ssh-7883	119	13	,	,	PUNCT
ssh-7883	119	14	for	for	ADP
ssh-7883	119	15	∈	∈	PROPN
ssh-7883	119	16	c2	c2	PROPN
ssh-7883	119	17	,	,	PUNCT
ssh-7883	119	18	we	we	PRON
ssh-7883	119	19	have	have	VERB
ssh-7883	119	20	then	then	ADV
ssh-7883	119	21	,	,	PUNCT
ssh-7883	119	22	we	we	PRON
ssh-7883	119	23	have	have	VERB
ssh-7883	119	24	bcp	bcp	VERB
ssh-7883	119	25	social	social	PROPN
ssh-7883	119	26	sciences	sciences	PROPN
ssh-7883	119	27	&	&	CCONJ
ssh-7883	119	28	humanities	humanities	PROPN
ssh-7883	119	29	erss	erss	VERB
ssh-7883	119	30	2024	2024	NUM
ssh-7883	119	31	volume	volume	NOUN
ssh-7883	119	32	23	23	NUM
ssh-7883	119	33	(	(	PUNCT
ssh-7883	119	34	2024	2024	NUM
ssh-7883	119	35	)	)	PUNCT
ssh-7883	119	36	9	9	NUM
ssh-7883	119	37	therefore	therefore	ADV
ssh-7883	119	38	,	,	PUNCT
ssh-7883	119	39	we	we	PRON
ssh-7883	119	40	complete	complete	VERB
ssh-7883	119	41	the	the	DET
ssh-7883	119	42	proof	proof	NOUN
ssh-7883	119	43	of	of	ADP
ssh-7883	119	44	conclusion	conclusion	NOUN
ssh-7883	119	45	(	(	PUNCT
ssh-7883	119	46	ii	ii	NOUN
ssh-7883	119	47	)	)	PUNCT
ssh-7883	119	48	.	.	PUNCT
ssh-7883	120	1	similarly	similarly	ADV
ssh-7883	120	2	,	,	PUNCT
ssh-7883	120	3	we	we	PRON
ssh-7883	120	4	can	can	AUX
ssh-7883	120	5	prove	prove	VERB
ssh-7883	120	6	the	the	DET
ssh-7883	120	7	following	follow	VERB
ssh-7883	120	8	estimates	estimate	NOUN
ssh-7883	120	9	on	on	ADP
ssh-7883	120	10	//sα+β	//sα+β	ADV
ssh-7883	120	11	,	,	PUNCT
ssh-7883	120	12	β−1(t	β−1(t	PROPN
ssh-7883	120	13	)	)	PUNCT
ssh-7883	120	14	//	//	NOUN
ssh-7883	120	15	and	and	CCONJ
ssh-7883	120	16	//tα+β(t	//tα+β(t	NUM
ssh-7883	120	17	)	)	PUNCT
ssh-7883	121	1	//	//	PROPN
ssh-7883	121	2	.	.	PUNCT
ssh-7883	122	1	theorem	theorem	VERB
ssh-7883	122	2	5.2	5.2	NUM
ssh-7883	122	3	let	let	VERB
ssh-7883	122	4	a	a	PRON
ssh-7883	122	5	be	be	AUX
ssh-7883	122	6	an	an	DET
ssh-7883	122	7	operator	operator	NOUN
ssh-7883	122	8	with	with	ADP
ssh-7883	122	9	type	type	NOUN
ssh-7883	122	10	(	(	PUNCT
ssh-7883	122	11	m	m	PROPN
ssh-7883	122	12	,	,	PUNCT
ssh-7883	122	13	θ	θ	PROPN
ssh-7883	122	14	,	,	PUNCT
ssh-7883	122	15	α	α	NOUN
ssh-7883	122	16	+	+	X
ssh-7883	122	17	β,µ	β,µ	ADJ
ssh-7883	122	18	)	)	PUNCT
ssh-7883	122	19	.	.	PUNCT
ssh-7883	123	1	then	then	ADV
ssh-7883	123	2	we	we	PRON
ssh-7883	123	3	can	can	AUX
ssh-7883	123	4	show	show	VERB
ssh-7883	123	5	the	the	DET
ssh-7883	123	6	following	follow	VERB
ssh-7883	123	7	estimates	estimate	NOUN
ssh-7883	123	8	on	on	ADP
ssh-7883	123	9	//sα+β	//sα+β	ADV
ssh-7883	123	10	,	,	PUNCT
ssh-7883	123	11	β−1(t	β−1(t	PROPN
ssh-7883	123	12	)	)	PUNCT
ssh-7883	123	13	//	//	NOUN
ssh-7883	123	14	and	and	CCONJ
ssh-7883	123	15	//tα+β(t)//	//tα+β(t)//	PUNCT
ssh-7883	123	16	.	.	PUNCT
ssh-7883	124	1	(	(	PUNCT
ssh-7883	124	2	i	i	NOUN
ssh-7883	124	3	)	)	PUNCT
ssh-7883	124	4	when	when	SCONJ
ssh-7883	124	5	µ	µ	X
ssh-7883	124	6	≥	≥	X
ssh-7883	124	7	0	0	NUM
ssh-7883	124	8	,	,	PUNCT
ssh-7883	124	9	for	for	ADP
ssh-7883	124	10	ϕ	ϕ	PROPN
ssh-7883	124	11	∈	∈	PROPN
ssh-7883	124	12	(	(	PUNCT
ssh-7883	124	13	0,π	0,π	PROPN
ssh-7883	124	14	)	)	PUNCT
ssh-7883	124	15	,	,	PUNCT
ssh-7883	124	16	we	we	PRON
ssh-7883	124	17	have	have	VERB
ssh-7883	124	18	and	and	CCONJ
ssh-7883	124	19	(	(	PUNCT
ssh-7883	124	20	ii	ii	NOUN
ssh-7883	124	21	)	)	PUNCT
ssh-7883	124	22	when	when	SCONJ
ssh-7883	124	23	µ	µ	X
ssh-7883	124	24	<	<	X
ssh-7883	124	25	0	0	NUM
ssh-7883	124	26	.	.	PUNCT
ssh-7883	125	1	for	for	ADP
ssh-7883	125	2	φ	φ	PROPN
ssh-7883	125	3	∈	∈	PROPN
ssh-7883	125	4	(	(	PUNCT
ssh-7883	125	5	0,π	0,π	PROPN
ssh-7883	125	6	)	)	PUNCT
ssh-7883	125	7	,	,	PUNCT
ssh-7883	125	8	we	we	PRON
ssh-7883	125	9	have	have	VERB
ssh-7883	125	10	π|cosϕ|	π|cosϕ|	PROPN
ssh-7883	125	11	1	1	NUM
ssh-7883	125	12	+	+	NUM
ssh-7883	125	13	π|cosϕ||cos	π|cosϕ||co	NOUN
ssh-7883	125	14	|	|	NOUN
ssh-7883	125	15	α+β	α+β	NUM
ssh-7883	125	16	1	1	NUM
ssh-7883	125	17	+	+	CCONJ
ssh-7883	125	18	|µ|tα+β	|µ|tα+β	NOUN
ssh-7883	125	19	,	,	PUNCT
ssh-7883	125	20	and	and	CCONJ
ssh-7883	125	21	fort	fort	NOUN
ssh-7883	125	22	>	>	X
ssh-7883	125	23	0	0	PROPN
ssh-7883	125	24	,	,	PUNCT
ssh-7883	125	25	where	where	SCONJ
ssh-7883	125	26	k1	k1	X
ssh-7883	125	27	(	(	PUNCT
ssh-7883	125	28	θ,ϕ	θ,ϕ	PROPN
ssh-7883	125	29	)	)	PUNCT
ssh-7883	125	30	=	=	SYM
ssh-7883	125	31	max{1	max{1	NOUN
ssh-7883	125	32	,	,	PUNCT
ssh-7883	125	33	}	}	PUNCT
ssh-7883	125	34	.	.	PUNCT
ssh-7883	126	1	6	6	X
ssh-7883	126	2	.	.	X
ssh-7883	126	3	existence	existence	NOUN
ssh-7883	126	4	of	of	ADP
ssh-7883	126	5	mild	mild	ADJ
ssh-7883	126	6	solutions	solution	NOUN
ssh-7883	126	7	next	next	ADV
ssh-7883	126	8	,	,	PUNCT
ssh-7883	126	9	we	we	PRON
ssh-7883	126	10	present	present	VERB
ssh-7883	126	11	existence	existence	NOUN
ssh-7883	126	12	and	and	CCONJ
ssh-7883	126	13	uniqueness	uniqueness	NOUN
ssh-7883	126	14	result	result	NOUN
ssh-7883	126	15	for	for	ADP
ssh-7883	126	16	system	system	NOUN
ssh-7883	126	17	(	(	PUNCT
ssh-7883	126	18	1.1	1.1	NUM
ssh-7883	126	19	)	)	PUNCT
ssh-7883	126	20	and	and	CCONJ
ssh-7883	126	21	system	system	NOUN
ssh-7883	126	22	(	(	PUNCT
ssh-7883	126	23	1.2	1.2	NUM
ssh-7883	126	24	)	)	PUNCT
ssh-7883	126	25	based	base	VERB
ssh-7883	126	26	on	on	ADP
ssh-7883	126	27	banach	banach	ADV
ssh-7883	126	28	fixed	fix	VERB
ssh-7883	126	29	theorem	theorem	VERB
ssh-7883	126	30	.	.	PUNCT
ssh-7883	127	1	in	in	ADP
ssh-7883	127	2	order	order	NOUN
ssh-7883	127	3	to	to	PART
ssh-7883	127	4	prove	prove	VERB
ssh-7883	127	5	the	the	DET
ssh-7883	127	6	desired	desire	VERB
ssh-7883	127	7	results	result	NOUN
ssh-7883	127	8	about	about	ADP
ssh-7883	127	9	the	the	DET
ssh-7883	127	10	fractional	fractional	ADJ
ssh-7883	127	11	equation	equation	NOUN
ssh-7883	127	12	in	in	ADP
ssh-7883	127	13	this	this	DET
ssh-7883	127	14	paper	paper	NOUN
ssh-7883	127	15	,	,	PUNCT
ssh-7883	127	16	from	from	ADP
ssh-7883	127	17	the	the	DET
ssh-7883	127	18	estimates	estimate	NOUN
ssh-7883	127	19	on	on	ADP
ssh-7883	127	20	//sα+β(t	//sα+β(t	PROPN
ssh-7883	127	21	)	)	PUNCT
ssh-7883	127	22	//	//	NOUN
ssh-7883	127	23	,	,	PUNCT
ssh-7883	127	24	//sα+β	//sα+β	INTJ
ssh-7883	127	25	,	,	PUNCT
ssh-7883	127	26	β(t	β(t	PROPN
ssh-7883	127	27	)	)	PUNCT
ssh-7883	127	28	//	//	NOUN
ssh-7883	127	29	,	,	PUNCT
ssh-7883	127	30	//sα+β	//sα+β	INTJ
ssh-7883	127	31	,	,	PUNCT
ssh-7883	127	32	β−1(t	β−1(t	PROPN
ssh-7883	127	33	)	)	PUNCT
ssh-7883	127	34	//	//	NOUN
ssh-7883	127	35	and	and	CCONJ
ssh-7883	127	36	|tα+β(t	|tα+β(t	NUM
ssh-7883	127	37	)	)	PUNCT
ssh-7883	127	38	//	//	NOUN
ssh-7883	127	39	,	,	PUNCT
ssh-7883	127	40	we	we	PRON
ssh-7883	127	41	make	make	VERB
ssh-7883	127	42	the	the	DET
ssh-7883	127	43	following	follow	VERB
ssh-7883	127	44	assumptions	assumption	NOUN
ssh-7883	127	45	:	:	PUNCT
ssh-7883	127	46	(	(	PUNCT
ssh-7883	127	47	h1	h1	NOUN
ssh-7883	127	48	):	):	PUNCT
ssh-7883	127	49	the	the	DET
ssh-7883	127	50	operators	operator	NOUN
ssh-7883	127	51	sα+β(t	sα+β(t	PROPN
ssh-7883	127	52	)	)	PUNCT
ssh-7883	127	53	,	,	PUNCT
ssh-7883	127	54	sα+β	sα+β	NOUN
ssh-7883	127	55	,	,	PUNCT
ssh-7883	127	56	β(t	β(t	PROPN
ssh-7883	127	57	)	)	PUNCT
ssh-7883	127	58	,	,	PUNCT
ssh-7883	127	59	sα+β	sα+β	NOUN
ssh-7883	127	60	,	,	PUNCT
ssh-7883	127	61	β−1(t	β−1(t	ADV
ssh-7883	127	62	)	)	PUNCT
ssh-7883	127	63	,	,	PUNCT
ssh-7883	127	64	and	and	CCONJ
ssh-7883	127	65	tα+β(t	tα+β(t	NOUN
ssh-7883	127	66	)	)	PUNCT
ssh-7883	127	67	generated	generate	VERB
ssh-7883	127	68	by	by	ADP
ssh-7883	127	69	a	a	DET
ssh-7883	127	70	are	be	AUX
ssh-7883	127	71	compact	compact	ADJ
ssh-7883	127	72	in	in	ADP
ssh-7883	127	73	d(a	d(a	PROPN
ssh-7883	127	74	)	)	PUNCT
ssh-7883	127	75	when	when	SCONJ
ssh-7883	127	76	t	t	PROPN
ssh-7883	127	77	≥	≥	NOUN
ssh-7883	127	78	0	0	NUM
ssh-7883	127	79	and	and	CCONJ
ssh-7883	127	80	bcp	bcp	PROPN
ssh-7883	127	81	social	social	PROPN
ssh-7883	127	82	sciences	sciences	PROPN
ssh-7883	127	83	&	&	CCONJ
ssh-7883	127	84	humanities	humanities	PROPN
ssh-7883	127	85	erss	erss	VERB
ssh-7883	127	86	2024	2024	NUM
ssh-7883	127	87	volume	volume	NOUN
ssh-7883	127	88	23	23	NUM
ssh-7883	127	89	(	(	PUNCT
ssh-7883	127	90	2024	2024	NUM
ssh-7883	127	91	)	)	PUNCT
ssh-7883	127	92	10	10	NUM
ssh-7883	127	93	sup	sup	NOUN
ssh-7883	127	94	//sα+β(t	//sα+β(t	PUNCT
ssh-7883	127	95	)	)	PUNCT
ssh-7883	127	96	//	//	PUNCT
ssh-7883	128	1	≤	≤	PROPN
ssh-7883	128	2	m1	m1	NOUN
ssh-7883	128	3	,	,	PUNCT
ssh-7883	128	4	sup	sup	INTJ
ssh-7883	128	5	//sα+β	//sα+β	NOUN
ssh-7883	128	6	,	,	PUNCT
ssh-7883	128	7	β(t	β(t	PROPN
ssh-7883	128	8	)	)	PUNCT
ssh-7883	128	9	//	//	PUNCT
ssh-7883	128	10	≤	≤	PROPN
ssh-7883	128	11	m1	m1	NOUN
ssh-7883	128	12	,	,	PUNCT
ssh-7883	128	13	sup	sup	INTJ
ssh-7883	128	14	//sα+β	//sα+β	NOUN
ssh-7883	128	15	,	,	PUNCT
ssh-7883	128	16	β−1(t	β−1(t	PROPN
ssh-7883	128	17	)	)	PUNCT
ssh-7883	128	18	//	//	PUNCT
ssh-7883	128	19	≤	≤	PROPN
ssh-7883	128	20	m1	m1	NOUN
ssh-7883	128	21	,	,	PUNCT
ssh-7883	128	22	sup	sup	NOUN
ssh-7883	128	23	//tα+β(t	//tα+β(t	PROPN
ssh-7883	128	24	)	)	PUNCT
ssh-7883	128	25	//	//	PUNCT
ssh-7883	129	1	≤	≤	PROPN
ssh-7883	129	2	m1	m1	PROPN
ssh-7883	129	3	t∈j	t∈j	NOUN
ssh-7883	129	4	t∈j	t∈j	VERB
ssh-7883	129	5	t∈j	t∈j	NOUN
ssh-7883	129	6	t∈j	t∈j	NOUN
ssh-7883	129	7	(	(	PUNCT
ssh-7883	129	8	h2	h2	PROPN
ssh-7883	129	9	):	):	PUNCT
ssh-7883	129	10	there	there	PRON
ssh-7883	129	11	exists	exist	VERB
ssh-7883	129	12	a	a	DET
ssh-7883	129	13	continuous	continuous	ADJ
ssh-7883	129	14	function	function	NOUN
ssh-7883	129	15	l(t	l(t	NOUN
ssh-7883	129	16	)	)	PUNCT
ssh-7883	129	17	making	make	VERB
ssh-7883	129	18	the	the	DET
ssh-7883	129	19	continuous	continuous	ADJ
ssh-7883	129	20	function	function	NOUN
ssh-7883	129	21	f	f	NOUN
ssh-7883	129	22	:	:	PUNCT
ssh-7883	129	23	j	j	PROPN
ssh-7883	129	24	×	×	NOUN
ssh-7883	129	25	x	x	INTJ
ssh-7883	129	26	→	→	SYM
ssh-7883	129	27	x	x	AUX
ssh-7883	129	28	satisfy	satisfy	VERB
ssh-7883	129	29	the	the	DET
ssh-7883	129	30	lipschitz	lipschitz	NOUN
ssh-7883	129	31	condition	condition	NOUN
ssh-7883	129	32	:	:	PUNCT
ssh-7883	129	33	//f(t	//f(t	NUM
ssh-7883	129	34	,	,	PUNCT
ssh-7883	129	35	u1	u1	NOUN
ssh-7883	129	36	(	(	PUNCT
ssh-7883	129	37	t	t	PROPN
ssh-7883	129	38	)	)	PUNCT
ssh-7883	129	39	)	)	PUNCT
ssh-7883	130	1	−	−	ADP
ssh-7883	130	2	f(t	f(t	PROPN
ssh-7883	130	3	,	,	PUNCT
ssh-7883	130	4	u2	u2	PROPN
ssh-7883	130	5	(	(	PUNCT
ssh-7883	130	6	t	t	PROPN
ssh-7883	130	7	)	)	PUNCT
ssh-7883	130	8	)	)	PUNCT
ssh-7883	131	1	//	//	NUM
ssh-7883	131	2	≤	≤	NUM
ssh-7883	131	3	l(t	l(t	PROPN
ssh-7883	131	4	)	)	PUNCT
ssh-7883	131	5	//u1	//u1	PUNCT
ssh-7883	132	1	(	(	PUNCT
ssh-7883	132	2	t	t	PROPN
ssh-7883	132	3	)	)	PUNCT
ssh-7883	132	4	−	−	PROPN
ssh-7883	132	5	u2	u2	PROPN
ssh-7883	132	6	(	(	PUNCT
ssh-7883	132	7	t	t	PROPN
ssh-7883	132	8	)	)	PUNCT
ssh-7883	132	9	//	//	NOUN
ssh-7883	132	10	,	,	PUNCT
ssh-7883	132	11	t	t	PROPN
ssh-7883	132	12	∈	∈	PROPN
ssh-7883	132	13	j	j	PROPN
ssh-7883	132	14	,	,	PUNCT
ssh-7883	132	15	u1	u1	PROPN
ssh-7883	132	16	(	(	PUNCT
ssh-7883	132	17	t	t	PROPN
ssh-7883	132	18	)	)	PUNCT
ssh-7883	132	19	,	,	PUNCT
ssh-7883	132	20	u2	u2	PROPN
ssh-7883	132	21	(	(	PUNCT
ssh-7883	132	22	t	t	PROPN
ssh-7883	132	23	)	)	PUNCT
ssh-7883	132	24	∈	∈	PROPN
ssh-7883	132	25	x.	x.	NOUN
ssh-7883	132	26	(	(	PUNCT
ssh-7883	132	27	h3	h3	NOUN
ssh-7883	132	28	):	):	PUNCT
ssh-7883	132	29	l(t	l(t	PROPN
ssh-7883	132	30	)	)	PUNCT
ssh-7883	132	31	and	and	CCONJ
ssh-7883	132	32	f(s	f(s	PROPN
ssh-7883	132	33	,	,	PUNCT
ssh-7883	132	34	o	o	NOUN
ssh-7883	132	35	)	)	PUNCT
ssh-7883	132	36	are	be	AUX
ssh-7883	132	37	continuous	continuous	ADJ
ssh-7883	132	38	functions	function	NOUN
ssh-7883	132	39	,	,	PUNCT
ssh-7883	132	40	so	so	SCONJ
ssh-7883	132	41	we	we	PRON
ssh-7883	132	42	can	can	AUX
ssh-7883	132	43	assume	assume	VERB
ssh-7883	132	44	that	that	SCONJ
ssh-7883	132	45	there	there	PRON
ssh-7883	132	46	exist	exist	VERB
ssh-7883	132	47	constants	constant	NOUN
ssh-7883	132	48	l	l	NOUN
ssh-7883	132	49	and	and	CCONJ
ssh-7883	132	50	f	f	X
ssh-7883	132	51	satisfying	satisfying	NOUN
ssh-7883	132	52	//l(t	//l(t	PUNCT
ssh-7883	132	53	)	)	PUNCT
ssh-7883	132	54	//	//	PUNCT
ssh-7883	133	1	≤	≤	NUM
ssh-7883	133	2	l	l	NOUN
ssh-7883	133	3	and	and	CCONJ
ssh-7883	133	4	//f(s,0	//f(s,0	PROPN
ssh-7883	133	5	)	)	PUNCT
ssh-7883	133	6	//	//	PUNCT
ssh-7883	134	1	≤	≤	NUM
ssh-7883	134	2	f	f	PROPN
ssh-7883	134	3	for	for	ADP
ssh-7883	134	4	t	t	PROPN
ssh-7883	134	5	∈	∈	PROPN
ssh-7883	135	1	[	[	X
ssh-7883	135	2	0	0	NUM
ssh-7883	135	3	,	,	PUNCT
ssh-7883	135	4	t	t	PROPN
ssh-7883	135	5	]	]	PUNCT
ssh-7883	135	6	,	,	PUNCT
ssh-7883	135	7	and	and	CCONJ
ssh-7883	135	8	lt	lt	PRON
ssh-7883	135	9	<	<	X
ssh-7883	135	10	1	1	NUM
ssh-7883	135	11	.	.	PUNCT
ssh-7883	135	12	theorem	theorem	ADJ
ssh-7883	135	13	6.1	6.1	NUM
ssh-7883	135	14	assume	assume	VERB
ssh-7883	135	15	that	that	SCONJ
ssh-7883	135	16	(	(	PUNCT
ssh-7883	135	17	h1	h1	PROPN
ssh-7883	135	18	)	)	PUNCT
ssh-7883	135	19	,	,	PUNCT
ssh-7883	135	20	(	(	PUNCT
ssh-7883	135	21	h2	h2	PROPN
ssh-7883	135	22	)	)	PUNCT
ssh-7883	135	23	,	,	PUNCT
ssh-7883	135	24	(	(	PUNCT
ssh-7883	135	25	h3	h3	NOUN
ssh-7883	135	26	)	)	PUNCT
ssh-7883	135	27	hold	hold	VERB
ssh-7883	135	28	,	,	PUNCT
ssh-7883	135	29	then	then	ADV
ssh-7883	135	30	the	the	DET
ssh-7883	135	31	system	system	NOUN
ssh-7883	135	32	(	(	PUNCT
ssh-7883	135	33	1.1	1.1	NUM
ssh-7883	135	34	)	)	PUNCT
ssh-7883	135	35	has	have	VERB
ssh-7883	135	36	a	a	DET
ssh-7883	135	37	unique	unique	ADJ
ssh-7883	135	38	mild	mild	ADJ
ssh-7883	135	39	solution	solution	NOUN
ssh-7883	135	40	u	u	NOUN
ssh-7883	135	41	on	on	ADP
ssh-7883	135	42	the	the	DET
ssh-7883	135	43	interval	interval	NOUN
ssh-7883	135	44	j.	j.	PROPN
ssh-7883	135	45	proof	proof	PROPN
ssh-7883	135	46	.	.	PUNCT
ssh-7883	136	1	define	define	VERB
ssh-7883	136	2	a	a	DET
ssh-7883	136	3	function	function	NOUN
ssh-7883	136	4	g	g	NOUN
ssh-7883	136	5	:	:	PUNCT
ssh-7883	136	6	cb	cb	PROPN
ssh-7883	136	7	(	(	PUNCT
ssh-7883	136	8	j	j	PROPN
ssh-7883	136	9	,	,	PUNCT
ssh-7883	136	10	x	x	NOUN
ssh-7883	136	11	)	)	PUNCT
ssh-7883	136	12	→	→	SYM
ssh-7883	136	13	cb	cb	PROPN
ssh-7883	136	14	(	(	PUNCT
ssh-7883	136	15	j	j	PROPN
ssh-7883	136	16	,	,	PUNCT
ssh-7883	136	17	x	x	X
ssh-7883	136	18	)	)	PUNCT
ssh-7883	136	19	by	by	ADP
ssh-7883	136	20	(	(	PUNCT
ssh-7883	136	21	gu)(t	gu)(t	NOUN
ssh-7883	136	22	)	)	PUNCT
ssh-7883	136	23	=	=	PRON
ssh-7883	137	1	sα+β(t)u0	sα+β(t)u0	NOUN
ssh-7883	137	2	+	+	X
ssh-7883	137	3	tα+β(t)r0	tα+β(t)r0	X
ssh-7883	137	4	+	+	CCONJ
ssh-7883	137	5	tα+β(t	tα+β(t	NOUN
ssh-7883	137	6	−	−	NOUN
ssh-7883	137	7	s)f(s	s)f(	NOUN
ssh-7883	137	8	,	,	PUNCT
ssh-7883	137	9	u(s))ds	u(s))ds	PROPN
ssh-7883	137	10	.	.	PUNCT
ssh-7883	138	1	firstly	firstly	ADV
ssh-7883	138	2	,	,	PUNCT
ssh-7883	138	3	we	we	PRON
ssh-7883	138	4	show	show	VERB
ssh-7883	138	5	that	that	SCONJ
ssh-7883	138	6	if	if	SCONJ
ssh-7883	138	7	u	u	PROPN
ssh-7883	138	8	∈	∈	PROPN
ssh-7883	138	9	cb	cb	X
ssh-7883	138	10	(	(	PUNCT
ssh-7883	138	11	j	j	PROPN
ssh-7883	138	12	,	,	PUNCT
ssh-7883	138	13	x	x	NOUN
ssh-7883	138	14	)	)	PUNCT
ssh-7883	138	15	,	,	PUNCT
ssh-7883	138	16	then	then	ADV
ssh-7883	138	17	g(u	g(u	PROPN
ssh-7883	138	18	)	)	PUNCT
ssh-7883	138	19	∈	∈	PROPN
ssh-7883	138	20	cb	cb	PROPN
ssh-7883	138	21	(	(	PUNCT
ssh-7883	138	22	j	j	PROPN
ssh-7883	138	23	,	,	PUNCT
ssh-7883	138	24	x	x	NOUN
ssh-7883	138	25	)	)	PUNCT
ssh-7883	138	26	.	.	PUNCT
ssh-7883	139	1	≤	≤	ADJ
ssh-7883	139	2	m1	m1	NOUN
ssh-7883	139	3	(	(	PUNCT
ssh-7883	139	4	|uo	|uo	X
ssh-7883	139	5	|	|	NOUN
ssh-7883	139	6	+	+	CCONJ
ssh-7883	139	7	|r0	|r0	ADP
ssh-7883	139	8	|	|	ADV
ssh-7883	139	9	+	+	CCONJ
ssh-7883	139	10	lt	lt	PROPN
ssh-7883	139	11	//u	//u	PUNCT
ssh-7883	139	12	//	//	PROPN
ssh-7883	139	13	+	+	NUM
ssh-7883	139	14	ft	ft	NOUN
ssh-7883	139	15	)	)	PUNCT
ssh-7883	139	16	.	.	PUNCT
ssh-7883	140	1	obviously	obviously	ADV
ssh-7883	140	2	,	,	PUNCT
ssh-7883	140	3	it	it	PRON
ssh-7883	140	4	means	mean	VERB
ssh-7883	140	5	g	g	NOUN
ssh-7883	140	6	:	:	PUNCT
ssh-7883	140	7	cb	cb	PROPN
ssh-7883	140	8	(	(	PUNCT
ssh-7883	140	9	j	j	PROPN
ssh-7883	140	10	,	,	PUNCT
ssh-7883	140	11	x	x	NOUN
ssh-7883	140	12	)	)	PUNCT
ssh-7883	140	13	→	→	SYM
ssh-7883	140	14	cb	cb	PROPN
ssh-7883	140	15	(	(	PUNCT
ssh-7883	140	16	j	j	PROPN
ssh-7883	140	17	,	,	PUNCT
ssh-7883	140	18	x	x	NOUN
ssh-7883	140	19	)	)	PUNCT
ssh-7883	140	20	.	.	PUNCT
ssh-7883	141	1	then	then	ADV
ssh-7883	141	2	,	,	PUNCT
ssh-7883	141	3	we	we	PRON
ssh-7883	141	4	need	need	VERB
ssh-7883	141	5	to	to	PART
ssh-7883	141	6	prove	prove	VERB
ssh-7883	141	7	that	that	SCONJ
ssh-7883	141	8	g	g	PROPN
ssh-7883	141	9	is	be	AUX
ssh-7883	141	10	a	a	DET
ssh-7883	141	11	compression	compression	NOUN
ssh-7883	141	12	mapping	mapping	NOUN
ssh-7883	141	13	in	in	ADP
ssh-7883	141	14	g.	g.	PROPN
ssh-7883	141	15	for	for	ADP
ssh-7883	141	16	u1	u1	NOUN
ssh-7883	141	17	,	,	PUNCT
ssh-7883	141	18	u2	u2	PROPN
ssh-7883	141	19	∈	∈	PROPN
ssh-7883	141	20	c	c	X
ssh-7883	141	21	,	,	PUNCT
ssh-7883	141	22	we	we	PRON
ssh-7883	141	23	have	have	VERB
ssh-7883	141	24	//gu1	//gu1	PUNCT
ssh-7883	142	1	(	(	PUNCT
ssh-7883	142	2	t	t	NOUN
ssh-7883	142	3	)	)	PUNCT
ssh-7883	142	4	−	−	PROPN
ssh-7883	142	5	gu2	gu2	NOUN
ssh-7883	142	6	(	(	PUNCT
ssh-7883	142	7	t	t	PROPN
ssh-7883	142	8	)	)	PUNCT
ssh-7883	142	9	//	//	X
ssh-7883	143	1	=	=	SYM
ssh-7883	143	2	//	//	PUNCT
ssh-7883	143	3	tα+β	tα+β	PROPN
ssh-7883	143	4	(	(	PUNCT
ssh-7883	143	5	t	t	PROPN
ssh-7883	143	6	−	−	PROPN
ssh-7883	143	7	s)[f(s	s)[f(s	ADJ
ssh-7883	143	8	,	,	PUNCT
ssh-7883	143	9	u1	u1	NOUN
ssh-7883	143	10	(	(	PUNCT
ssh-7883	143	11	s	s	NOUN
ssh-7883	143	12	)	)	PUNCT
ssh-7883	143	13	)	)	PUNCT
ssh-7883	143	14	−	−	PROPN
ssh-7883	144	1	f(s	f(	NOUN
ssh-7883	144	2	,	,	PUNCT
ssh-7883	144	3	u2	u2	PROPN
ssh-7883	144	4	(	(	PUNCT
ssh-7883	144	5	s))]ds	s))]ds	PROPN
ssh-7883	144	6	//	//	NUM
ssh-7883	144	7	≤	≤	NUM
ssh-7883	144	8	lt	lt	PRON
ssh-7883	144	9	//u1	//u1	PUNCT
ssh-7883	144	10	−	−	PROPN
ssh-7883	144	11	u2	u2	PROPN
ssh-7883	144	12	//	//	NOUN
ssh-7883	144	13	according	accord	VERB
ssh-7883	144	14	to	to	ADP
ssh-7883	144	15	bananch	bananch	PROPN
ssh-7883	144	16	’s	’s	PART
ssh-7883	144	17	fixed	fix	VERB
ssh-7883	144	18	point	point	NOUN
ssh-7883	144	19	theorem	theorem	VERB
ssh-7883	144	20	,	,	PUNCT
ssh-7883	144	21	we	we	PRON
ssh-7883	144	22	know	know	VERB
ssh-7883	144	23	there	there	PRON
ssh-7883	144	24	is	be	VERB
ssh-7883	144	25	a	a	DET
ssh-7883	144	26	fixed	fix	VERB
ssh-7883	144	27	point	point	NOUN
ssh-7883	144	28	in	in	ADP
ssh-7883	144	29	cb	cb	PROPN
ssh-7883	144	30	(	(	PUNCT
ssh-7883	144	31	j	j	PROPN
ssh-7883	144	32	,	,	PUNCT
ssh-7883	144	33	x	x	NOUN
ssh-7883	144	34	)	)	PUNCT
ssh-7883	144	35	,	,	PUNCT
ssh-7883	144	36	which	which	PRON
ssh-7883	144	37	is	be	AUX
ssh-7883	144	38	the	the	DET
ssh-7883	144	39	mild	mild	ADJ
ssh-7883	144	40	solution	solution	NOUN
ssh-7883	144	41	of	of	ADP
ssh-7883	144	42	system	system	NOUN
ssh-7883	144	43	(	(	PUNCT
ssh-7883	144	44	1.1	1.1	NUM
ssh-7883	144	45	)	)	PUNCT
ssh-7883	144	46	similarly	similarly	ADV
ssh-7883	144	47	,	,	PUNCT
ssh-7883	144	48	we	we	PRON
ssh-7883	144	49	can	can	AUX
ssh-7883	144	50	get	get	VERB
ssh-7883	144	51	the	the	DET
ssh-7883	144	52	following	follow	VERB
ssh-7883	144	53	conclusion	conclusion	NOUN
ssh-7883	144	54	:	:	PUNCT
ssh-7883	144	55	theorem	theorem	VERB
ssh-7883	144	56	6.2	6.2	NUM
ssh-7883	144	57	assume	assume	VERB
ssh-7883	144	58	that	that	SCONJ
ssh-7883	144	59	(	(	PUNCT
ssh-7883	144	60	h1	h1	PROPN
ssh-7883	144	61	)	)	PUNCT
ssh-7883	144	62	,	,	PUNCT
ssh-7883	144	63	(	(	PUNCT
ssh-7883	144	64	h2	h2	NOUN
ssh-7883	144	65	)	)	PUNCT
ssh-7883	144	66	,	,	PUNCT
ssh-7883	144	67	(	(	PUNCT
ssh-7883	144	68	h3	h3	NOUN
ssh-7883	144	69	)	)	PUNCT
ssh-7883	144	70	hold	hold	VERB
ssh-7883	144	71	,	,	PUNCT
ssh-7883	144	72	then	then	ADV
ssh-7883	144	73	the	the	DET
ssh-7883	144	74	system	system	NOUN
ssh-7883	144	75	(	(	PUNCT
ssh-7883	144	76	1.2	1.2	NUM
ssh-7883	144	77	)	)	PUNCT
ssh-7883	144	78	has	have	VERB
ssh-7883	144	79	a	a	DET
ssh-7883	144	80	unique	unique	ADJ
ssh-7883	144	81	mild	mild	ADJ
ssh-7883	144	82	solution	solution	NOUN
ssh-7883	144	83	u	u	NOUN
ssh-7883	144	84	on	on	ADP
ssh-7883	144	85	the	the	DET
ssh-7883	144	86	interval	interval	NOUN
ssh-7883	144	87	j.	j.	PROPN
ssh-7883	144	88	7	7	PROPN
ssh-7883	144	89	.	.	PROPN
ssh-7883	144	90	example	example	NOUN
ssh-7883	144	91	example	example	NOUN
ssh-7883	144	92	1	1	NUM
ssh-7883	144	93	.	.	PUNCT
ssh-7883	145	1	as	as	ADP
ssh-7883	145	2	an	an	DET
ssh-7883	145	3	application	application	NOUN
ssh-7883	145	4	of	of	ADP
ssh-7883	145	5	our	our	PRON
ssh-7883	145	6	obtained	obtain	VERB
ssh-7883	145	7	results	result	NOUN
ssh-7883	145	8	,	,	PUNCT
ssh-7883	145	9	suppose	suppose	VERB
ssh-7883	145	10	that	that	SCONJ
ssh-7883	145	11	ω	ω	PROPN
ssh-7883	145	12	⊂	⊂	PROPN
ssh-7883	145	13	r2	r2	PROPN
ssh-7883	145	14	is	be	AUX
ssh-7883	145	15	a	a	DET
ssh-7883	145	16	unit	unit	NOUN
ssh-7883	145	17	circular	circular	ADJ
ssh-7883	145	18	domain	domain	NOUN
ssh-7883	145	19	with	with	ADP
ssh-7883	145	20	respect	respect	NOUN
ssh-7883	145	21	to	to	ADP
ssh-7883	145	22	the	the	DET
ssh-7883	145	23	origin	origin	NOUN
ssh-7883	145	24	.	.	PUNCT
ssh-7883	146	1	consider	consider	VERB
ssh-7883	146	2	the	the	DET
ssh-7883	146	3	following	follow	VERB
ssh-7883	146	4	fractional	fractional	ADJ
ssh-7883	146	5	partial	partial	ADJ
ssh-7883	146	6	differential	differential	NOUN
ssh-7883	146	7	equation	equation	NOUN
ssh-7883	146	8	:	:	PUNCT
ssh-7883	146	9	,	,	PUNCT
ssh-7883	146	10	1	1	X
ssh-7883	146	11	<	<	X
ssh-7883	146	12	α	α	PROPN
ssh-7883	147	1	+	+	X
ssh-7883	147	2	β	β	X
ssh-7883	147	3	<	<	X
ssh-7883	147	4	2	2	NUM
ssh-7883	147	5	,	,	PUNCT
ssh-7883	147	6	t	t	PROPN
ssh-7883	147	7	∈	∈	PROPN
ssh-7883	147	8	,	,	PUNCT
ssh-7883	147	9	x	x	PUNCT
ssh-7883	147	10	∈	∈	PROPN
ssh-7883	147	11	ω	ω	NOUN
ssh-7883	147	12	,	,	PUNCT
ssh-7883	147	13	let	let	VERB
ssh-7883	147	14	x	x	SYM
ssh-7883	147	15	=	=	SYM
ssh-7883	147	16	l2	l2	NOUN
ssh-7883	147	17	(	(	PUNCT
ssh-7883	147	18	ω	ω	NOUN
ssh-7883	147	19	)	)	PUNCT
ssh-7883	147	20	,	,	PUNCT
ssh-7883	147	21	0	0	NUM
ssh-7883	147	22	<	<	X
ssh-7883	147	23	α	α	X
ssh-7883	147	24	<	<	X
ssh-7883	147	25	1	1	NUM
ssh-7883	147	26	,	,	PUNCT
ssh-7883	147	27	0	0	PUNCT
ssh-7883	147	28	<	<	X
ssh-7883	147	29	β	β	X
ssh-7883	147	30	<	<	X
ssh-7883	147	31	1	1	NUM
ssh-7883	147	32	,	,	PUNCT
ssh-7883	147	33	1	1	NUM
ssh-7883	147	34	<	<	X
ssh-7883	147	35	α	α	PROPN
ssh-7883	147	36	+	+	X
ssh-7883	147	37	β	β	X
ssh-7883	147	38	<	<	X
ssh-7883	147	39	2	2	NUM
ssh-7883	147	40	,	,	PUNCT
ssh-7883	147	41	define	define	VERB
ssh-7883	147	42	the	the	DET
ssh-7883	147	43	operator	operator	NOUN
ssh-7883	147	44	a	a	DET
ssh-7883	147	45	:	:	PUNCT
ssh-7883	147	46	d(a	d(a	PROPN
ssh-7883	147	47	)	)	PUNCT
ssh-7883	147	48	⊆	⊆	NUM
ssh-7883	147	49	x	x	SYM
ssh-7883	147	50	→	→	SYM
ssh-7883	147	51	x	x	PUNCT
ssh-7883	147	52	by	by	ADP
ssh-7883	147	53	au	au	NOUN
ssh-7883	147	54	=	=	SYM
ssh-7883	147	55	∂2	∂2	NOUN
ssh-7883	147	56	x	x	SYM
ssh-7883	147	57	(	(	PUNCT
ssh-7883	147	58	,	,	PUNCT
ssh-7883	147	59	x	x	NOUN
ssh-7883	147	60	)	)	PUNCT
ssh-7883	147	61	−	−	PROPN
ssh-7883	147	62	u(t	u(t	NOUN
ssh-7883	147	63	,	,	PUNCT
ssh-7883	147	64	x	x	NOUN
ssh-7883	147	65	)	)	PUNCT
ssh-7883	147	66	with	with	ADP
ssh-7883	147	67	d(a	d(a	PROPN
ssh-7883	147	68	)	)	PUNCT
ssh-7883	147	69	=	=	SYM
ssh-7883	147	70	h2	h2	PROPN
ssh-7883	147	71	(	(	PUNCT
ssh-7883	147	72	ω	ω	NOUN
ssh-7883	147	73	)	)	PUNCT
ssh-7883	147	74	∩	∩	PROPN
ssh-7883	147	75	h0	h0	NOUN
ssh-7883	147	76	1(ω	1(ω	NUM
ssh-7883	147	77	)	)	PUNCT
ssh-7883	147	78	.	.	PUNCT
ssh-7883	148	1	then	then	ADV
ssh-7883	148	2	a	a	PRON
ssh-7883	148	3	is	be	AUX
ssh-7883	148	4	a	a	DET
ssh-7883	148	5	sectorial	sectorial	ADJ
ssh-7883	148	6	operator	operator	NOUN
ssh-7883	148	7	of	of	ADP
ssh-7883	148	8	type	type	NOUN
ssh-7883	148	9	(	(	PUNCT
ssh-7883	148	10	m;θ;α	m;θ;α	NOUN
ssh-7883	148	11	+	+	NOUN
ssh-7883	148	12	β;µ	β;µ	NUM
ssh-7883	148	13	)	)	PUNCT
ssh-7883	148	14	with	with	ADP
ssh-7883	148	15	µ	µ	NOUN
ssh-7883	148	16	=	=	SYM
ssh-7883	148	17	−1	−1	NOUN
ssh-7883	148	18	,	,	PUNCT
ssh-7883	148	19	so	so	SCONJ
ssh-7883	148	20	the	the	DET
ssh-7883	148	21	results	result	NOUN
ssh-7883	148	22	in	in	ADP
ssh-7883	148	23	the	the	DET
ssh-7883	148	24	theorem	theorem	ADJ
ssh-7883	148	25	3.1	3.1	NUM
ssh-7883	148	26	and	and	CCONJ
ssh-7883	148	27	the	the	DET
ssh-7883	148	28	theorem	theorem	ADJ
ssh-7883	148	29	3.3	3.3	NUM
ssh-7883	148	30	hold	hold	NOUN
ssh-7883	148	31	.	.	PUNCT
ssh-7883	149	1	bcp	bcp	VERB
ssh-7883	149	2	social	social	PROPN
ssh-7883	149	3	sciences	sciences	PROPN
ssh-7883	149	4	&	&	CCONJ
ssh-7883	149	5	humanities	humanities	PROPN
ssh-7883	149	6	erss	erss	VERB
ssh-7883	149	7	2024	2024	NUM
ssh-7883	149	8	volume	volume	NOUN
ssh-7883	149	9	23	23	NUM
ssh-7883	149	10	(	(	PUNCT
ssh-7883	149	11	2024	2024	NUM
ssh-7883	149	12	)	)	PUNCT
ssh-7883	149	13	11	11	NUM
ssh-7883	149	14	let	let	VERB
ssh-7883	149	15	u	u	PRON
ssh-7883	149	16	and	and	CCONJ
ssh-7883	149	17	define	define	VERB
ssh-7883	149	18	f	f	X
ssh-7883	149	19	:	:	PUNCT
ssh-7883	149	20	j	j	PROPN
ssh-7883	149	21	×	×	NOUN
ssh-7883	149	22	x	x	INTJ
ssh-7883	149	23	→	→	SYM
ssh-7883	149	24	x	x	X
ssh-7883	149	25	by	by	ADP
ssh-7883	149	26	f	f	PROPN
ssh-7883	149	27	.	.	PUNCT
ssh-7883	150	1	set	set	VERB
ssh-7883	150	2	ω	ω	PROPN
ssh-7883	150	3	=	=	SYM
ssh-7883	150	4	1	1	NUM
ssh-7883	150	5	,	,	PUNCT
ssh-7883	150	6	,	,	PUNCT
ssh-7883	150	7	t	t	PROPN
ssh-7883	150	8	∈	∈	PROPN
ssh-7883	151	1	j.	j.	PROPN
ssh-7883	151	2	it	it	PRON
ssh-7883	151	3	is	be	AUX
ssh-7883	151	4	obvious	obvious	ADJ
ssh-7883	151	5	to	to	PART
ssh-7883	151	6	observe	observe	VERB
ssh-7883	151	7	that	that	PRON
ssh-7883	151	8	and	and	CCONJ
ssh-7883	151	9	we	we	PRON
ssh-7883	151	10	can	can	AUX
ssh-7883	151	11	get	get	VERB
ssh-7883	151	12	,	,	PUNCT
ssh-7883	151	13	.	.	PUNCT
ssh-7883	152	1	now	now	ADV
ssh-7883	152	2	all	all	DET
ssh-7883	152	3	the	the	DET
ssh-7883	152	4	assumptions	assumption	NOUN
ssh-7883	152	5	of	of	ADP
ssh-7883	152	6	theorem	theorem	ADJ
ssh-7883	152	7	3.3	3.3	NUM
ssh-7883	152	8	are	be	AUX
ssh-7883	152	9	satisfied	satisfied	ADJ
ssh-7883	152	10	,	,	PUNCT
ssh-7883	152	11	so	so	ADV
ssh-7883	152	12	the	the	DET
ssh-7883	152	13	system	system	NOUN
ssh-7883	152	14	has	have	VERB
ssh-7883	152	15	a	a	DET
ssh-7883	152	16	unique	unique	ADJ
ssh-7883	152	17	solution	solution	NOUN
ssh-7883	152	18	on	on	ADP
ssh-7883	152	19	[	[	X
ssh-7883	152	20	0	0	NUM
ssh-7883	152	21	,	,	PUNCT
ssh-7883	152	22	t	t	PROPN
ssh-7883	152	23	]	]	PUNCT
ssh-7883	152	24	.	.	PUNCT
ssh-7883	153	1	references	reference	NOUN
ssh-7883	153	2	[	[	X
ssh-7883	153	3	1	1	X
ssh-7883	153	4	]	]	PUNCT
ssh-7883	153	5	vasily	vasily	NOUN
ssh-7883	153	6	e	e	NOUN
ssh-7883	153	7	tarasov	tarasov	NOUN
ssh-7883	153	8	.	.	PUNCT
ssh-7883	154	1	fractional	fractional	ADJ
ssh-7883	154	2	dynamics	dynamic	NOUN
ssh-7883	154	3	:	:	PUNCT
ssh-7883	154	4	applications	application	NOUN
ssh-7883	154	5	of	of	ADP
ssh-7883	154	6	fractional	fractional	ADJ
ssh-7883	154	7	calculus	calculus	NOUN
ssh-7883	154	8	to	to	ADP
ssh-7883	154	9	dynamics	dynamic	NOUN
ssh-7883	154	10	of	of	ADP
ssh-7883	154	11	particles	particle	NOUN
ssh-7883	154	12	,	,	PUNCT
ssh-7883	154	13	fields	field	NOUN
ssh-7883	154	14	and	and	CCONJ
ssh-7883	154	15	media	medium	NOUN
ssh-7883	154	16	.	.	PUNCT
ssh-7883	155	1	springer	springer	NOUN
ssh-7883	155	2	science	science	PROPN
ssh-7883	155	3	&	&	CCONJ
ssh-7883	155	4	business	business	NOUN
ssh-7883	155	5	media	medium	NOUN
ssh-7883	155	6	,	,	PUNCT
ssh-7883	155	7	2011	2011	NUM
ssh-7883	155	8	.	.	PUNCT
ssh-7883	156	1	[	[	X
ssh-7883	156	2	2	2	NUM
ssh-7883	156	3	]	]	PUNCT
ssh-7883	156	4	lokenath	lokenath	NOUN
ssh-7883	156	5	debnath	debnath	PROPN
ssh-7883	156	6	etal	etal	PROPN
ssh-7883	156	7	.	.	PUNCT
ssh-7883	157	1	recent	recent	ADJ
ssh-7883	157	2	applications	application	NOUN
ssh-7883	157	3	of	of	ADP
ssh-7883	157	4	fractional	fractional	ADJ
ssh-7883	157	5	calculus	calculus	NOUN
ssh-7883	157	6	to	to	ADP
ssh-7883	157	7	science	science	NOUN
ssh-7883	157	8	and	and	CCONJ
ssh-7883	157	9	engineering	engineering	NOUN
ssh-7883	157	10	.	.	PUNCT
ssh-7883	158	1	international	international	ADJ
ssh-7883	158	2	journal	journal	PROPN
ssh-7883	158	3	of	of	ADP
ssh-7883	158	4	mathematics	mathematics	PROPN
ssh-7883	158	5	and	and	CCONJ
ssh-7883	158	6	mathematical	mathematical	ADJ
ssh-7883	158	7	sciences	science	NOUN
ssh-7883	158	8	,	,	PUNCT
ssh-7883	158	9	2003:3413–3442	2003:3413–3442	NUM
ssh-7883	158	10	,	,	PUNCT
ssh-7883	158	11	2003	2003	NUM
ssh-7883	158	12	.	.	PUNCT
ssh-7883	159	1	[	[	X
ssh-7883	159	2	3	3	X
ssh-7883	159	3	]	]	X
ssh-7883	159	4	roberto	roberto	PROPN
ssh-7883	159	5	garrappa	garrappa	PROPN
ssh-7883	159	6	and	and	CCONJ
ssh-7883	159	7	marina	marina	PROPN
ssh-7883	159	8	popolizio	popolizio	PROPN
ssh-7883	159	9	.	.	PUNCT
ssh-7883	160	1	on	on	ADP
ssh-7883	160	2	accurate	accurate	ADJ
ssh-7883	160	3	product	product	NOUN
ssh-7883	160	4	integration	integration	NOUN
ssh-7883	160	5	rules	rule	NOUN
ssh-7883	160	6	for	for	ADP
ssh-7883	160	7	linear	linear	ADJ
ssh-7883	160	8	fractional	fractional	ADJ
ssh-7883	160	9	differential	differential	ADJ
ssh-7883	160	10	equations	equation	NOUN
ssh-7883	160	11	.	.	PUNCT
ssh-7883	161	1	journal	journal	NOUN
ssh-7883	161	2	of	of	ADP
ssh-7883	161	3	computational	computational	ADJ
ssh-7883	161	4	and	and	CCONJ
ssh-7883	161	5	applied	applied	ADJ
ssh-7883	161	6	mathematics	mathematic	NOUN
ssh-7883	161	7	,	,	PUNCT
ssh-7883	161	8	235(5):1085–1097	235(5):1085–1097	NUM
ssh-7883	161	9	,	,	PUNCT
ssh-7883	161	10	2011	2011	NUM
ssh-7883	161	11	.	.	PUNCT
ssh-7883	162	1	[	[	X
ssh-7883	162	2	4	4	NUM
ssh-7883	162	3	]	]	X
ssh-7883	162	4	alexander	alexander	NOUN
ssh-7883	162	5	i	i	PRON
ssh-7883	162	6	saichev	saichev	VERB
ssh-7883	162	7	and	and	CCONJ
ssh-7883	162	8	george	george	PROPN
ssh-7883	162	9	m	m	PROPN
ssh-7883	162	10	zaslavsky	zaslavsky	PROPN
ssh-7883	162	11	.	.	PUNCT
ssh-7883	163	1	fractional	fractional	ADJ
ssh-7883	163	2	kinetic	kinetic	ADJ
ssh-7883	163	3	equations	equation	NOUN
ssh-7883	163	4	:	:	PUNCT
ssh-7883	163	5	solutions	solution	NOUN
ssh-7883	163	6	and	and	CCONJ
ssh-7883	163	7	applications	application	NOUN
ssh-7883	163	8	.	.	PUNCT
ssh-7883	164	1	chaos	chaos	NOUN
ssh-7883	164	2	:	:	PUNCT
ssh-7883	164	3	an	an	DET
ssh-7883	164	4	interdisciplinary	interdisciplinary	ADJ
ssh-7883	164	5	journal	journal	NOUN
ssh-7883	164	6	of	of	ADP
ssh-7883	164	7	nonlinear	nonlinear	ADJ
ssh-7883	164	8	science	science	NOUN
ssh-7883	164	9	,	,	PUNCT
ssh-7883	164	10	7(4):753–764	7(4):753–764	NUM
ssh-7883	164	11	,	,	PUNCT
ssh-7883	164	12	1997	1997	NUM
ssh-7883	164	13	.	.	PUNCT
ssh-7883	165	1	[	[	X
ssh-7883	165	2	5	5	NUM
ssh-7883	165	3	]	]	PUNCT
ssh-7883	165	4	anatoly	anatoly	PROPN
ssh-7883	165	5	a	a	DET
ssh-7883	165	6	kilbas	kilbas	PROPN
ssh-7883	165	7	,	,	PUNCT
ssh-7883	165	8	oleg	oleg	PROPN
ssh-7883	165	9	i	i	PRON
ssh-7883	165	10	marichev	marichev	PROPN
ssh-7883	165	11	,	,	PUNCT
ssh-7883	165	12	and	and	CCONJ
ssh-7883	165	13	stefan	stefan	PROPN
ssh-7883	165	14	g	g	PROPN
ssh-7883	165	15	samko	samko	PROPN
ssh-7883	165	16	.	.	PUNCT
ssh-7883	166	1	fractional	fractional	ADJ
ssh-7883	166	2	integrals	integral	NOUN
ssh-7883	166	3	and	and	CCONJ
ssh-7883	166	4	derivatives	derivative	NOUN
ssh-7883	166	5	(	(	PUNCT
ssh-7883	166	6	theory	theory	NOUN
ssh-7883	166	7	and	and	CCONJ
ssh-7883	166	8	applications	application	NOUN
ssh-7883	166	9	)	)	PUNCT
ssh-7883	166	10	,	,	PUNCT
ssh-7883	166	11	1993	1993	NUM
ssh-7883	166	12	.	.	PUNCT
ssh-7883	167	1	[	[	X
ssh-7883	167	2	6	6	NUM
ssh-7883	167	3	]	]	PUNCT
ssh-7883	167	4	yu	yu	PROPN
ssh-7883	167	5	f	f	PROPN
ssh-7883	167	6	luchko	luchko	VERB
ssh-7883	167	7	and	and	CCONJ
ssh-7883	167	8	h	h	NOUN
ssh-7883	167	9	m	m	PROPN
ssh-7883	167	10	srivastava	srivastava	PROPN
ssh-7883	167	11	.	.	PUNCT
ssh-7883	168	1	the	the	DET
ssh-7883	168	2	exact	exact	ADJ
ssh-7883	168	3	solution	solution	NOUN
ssh-7883	168	4	of	of	ADP
ssh-7883	168	5	certain	certain	ADJ
ssh-7883	168	6	differential	differential	ADJ
ssh-7883	168	7	equations	equation	NOUN
ssh-7883	168	8	of	of	ADP
ssh-7883	168	9	fractional	fractional	ADJ
ssh-7883	168	10	order	order	NOUN
ssh-7883	168	11	by	by	ADP
ssh-7883	168	12	using	use	VERB
ssh-7883	168	13	operational	operational	ADJ
ssh-7883	168	14	calculus	calculus	NOUN
ssh-7883	168	15	.	.	PUNCT
ssh-7883	169	1	computers	computer	NOUN
ssh-7883	169	2	&	&	CCONJ
ssh-7883	169	3	mathematics	mathematics	PROPN
ssh-7883	169	4	with	with	ADP
ssh-7883	169	5	applications	application	NOUN
ssh-7883	169	6	,	,	PUNCT
ssh-7883	169	7	29(8):73–85	29(8):73–85	NUM
ssh-7883	169	8	,	,	PUNCT
ssh-7883	169	9	1995	1995	NUM
ssh-7883	169	10	.	.	PUNCT
ssh-7883	170	1	[	[	X
ssh-7883	170	2	7	7	X
ssh-7883	170	3	]	]	PUNCT
ssh-7883	170	4	anatoli˘ı	anatoli˘ı	NOUN
ssh-7883	170	5	aleksandrovich	aleksandrovich	PROPN
ssh-7883	170	6	kilbas	kilbas	PROPN
ssh-7883	170	7	,	,	PUNCT
ssh-7883	170	8	hari	hari	PROPN
ssh-7883	170	9	m	m	PROPN
ssh-7883	170	10	srivastava	srivastava	PROPN
ssh-7883	170	11	,	,	PUNCT
ssh-7883	170	12	and	and	CCONJ
ssh-7883	170	13	juan	juan	PROPN
ssh-7883	170	14	j	j	PROPN
ssh-7883	170	15	trujillo	trujillo	PROPN
ssh-7883	170	16	.	.	PUNCT
ssh-7883	170	17	theory	theory	NOUN
ssh-7883	170	18	and	and	CCONJ
ssh-7883	170	19	applications	application	NOUN
ssh-7883	170	20	of	of	ADP
ssh-7883	170	21	fractional	fractional	ADJ
ssh-7883	170	22	differential	differential	ADJ
ssh-7883	170	23	equations	equation	NOUN
ssh-7883	170	24	,	,	PUNCT
ssh-7883	170	25	volume	volume	NOUN
ssh-7883	170	26	204	204	NUM
ssh-7883	170	27	.	.	PUNCT
ssh-7883	171	1	elsevier	elsevier	NOUN
ssh-7883	171	2	,	,	PUNCT
ssh-7883	171	3	2006	2006	NUM
ssh-7883	171	4	.	.	PUNCT
ssh-7883	172	1	[	[	X
ssh-7883	172	2	8	8	NUM
ssh-7883	172	3	]	]	PUNCT
ssh-7883	172	4	a	a	DET
ssh-7883	172	5	arara	arara	NOUN
ssh-7883	172	6	,	,	PUNCT
ssh-7883	172	7	m	m	NOUN
ssh-7883	172	8	benchohra	benchohra	NOUN
ssh-7883	172	9	,	,	PUNCT
ssh-7883	172	10	n	n	PRON
ssh-7883	172	11	hamidi	hamidi	NOUN
ssh-7883	172	12	,	,	PUNCT
ssh-7883	172	13	and	and	CCONJ
ssh-7883	172	14	jj	jj	PROPN
ssh-7883	172	15	nieto	nieto	PROPN
ssh-7883	172	16	.	.	PUNCT
ssh-7883	173	1	fractional	fractional	ADJ
ssh-7883	173	2	order	order	NOUN
ssh-7883	173	3	differential	differential	ADJ
ssh-7883	173	4	equations	equation	NOUN
ssh-7883	173	5	on	on	ADP
ssh-7883	173	6	an	an	DET
ssh-7883	173	7	unbounded	unbounded	ADJ
ssh-7883	173	8	domain	domain	NOUN
ssh-7883	173	9	.	.	PUNCT
ssh-7883	174	1	nonlinear	nonlinear	ADJ
ssh-7883	174	2	analysis	analysis	NOUN
ssh-7883	174	3	:	:	PUNCT
ssh-7883	174	4	theory	theory	NOUN
ssh-7883	174	5	,	,	PUNCT
ssh-7883	174	6	methods	method	NOUN
ssh-7883	174	7	&	&	CCONJ
ssh-7883	174	8	applications	application	NOUN
ssh-7883	174	9	,	,	PUNCT
ssh-7883	174	10	72(2):580–586	72(2):580–586	PROPN
ssh-7883	174	11	,	,	PUNCT
ssh-7883	174	12	2010	2010	NUM
ssh-7883	174	13	.	.	PUNCT
ssh-7883	175	1	[	[	X
ssh-7883	175	2	9	9	NUM
ssh-7883	175	3	]	]	SYM
ssh-7883	175	4	xiaobao	xiaobao	PROPN
ssh-7883	175	5	shu	shu	PROPN
ssh-7883	175	6	and	and	CCONJ
ssh-7883	175	7	fei	fei	PROPN
ssh-7883	175	8	xu	xu	PROPN
ssh-7883	175	9	.	.	PUNCT
ssh-7883	176	1	upper	upper	ADJ
ssh-7883	176	2	and	and	CCONJ
ssh-7883	176	3	lower	low	ADJ
ssh-7883	176	4	solution	solution	NOUN
ssh-7883	176	5	method	method	NOUN
ssh-7883	176	6	for	for	ADP
ssh-7883	176	7	fractional	fractional	ADJ
ssh-7883	176	8	evolution	evolution	NOUN
ssh-7883	176	9	equations	equation	NOUN
ssh-7883	176	10	with	with	ADP
ssh-7883	176	11	order	order	NOUN
ssh-7883	176	12	1	1	NUM
ssh-7883	176	13	<	<	X
ssh-7883	176	14	α	α	X
ssh-7883	176	15	<	<	PROPN
ssh-7883	176	16	2	2	NUM
ssh-7883	176	17	.	.	NOUN
ssh-7883	176	18	journal	journal	NOUN
ssh-7883	176	19	of	of	ADP
ssh-7883	176	20	the	the	DET
ssh-7883	176	21	korean	korean	PROPN
ssh-7883	176	22	mathematical	mathematical	ADJ
ssh-7883	176	23	society	society	NOUN
ssh-7883	176	24	,	,	PUNCT
ssh-7883	176	25	51(6):1123–1139	51(6):1123–1139	NUM
ssh-7883	176	26	,	,	PUNCT
ssh-7883	176	27	2014	2014	NUM
ssh-7883	176	28	.	.	PUNCT
ssh-7883	177	1	[	[	X
ssh-7883	177	2	10	10	NUM
ssh-7883	177	3	]	]	X
ssh-7883	177	4	claudio	claudio	NOUN
ssh-7883	177	5	cuevas	cuevas	NOUN
ssh-7883	177	6	and	and	CCONJ
ssh-7883	177	7	manuel	manuel	PROPN
ssh-7883	177	8	pinto	pinto	PROPN
ssh-7883	177	9	jim´enez	jim´enez	PROPN
ssh-7883	177	10	.	.	PUNCT
ssh-7883	178	1	existence	existence	NOUN
ssh-7883	178	2	and	and	CCONJ
ssh-7883	178	3	uniqueness	uniqueness	NOUN
ssh-7883	178	4	of	of	ADP
ssh-7883	178	5	pseudo	pseudo	NOUN
ssh-7883	178	6	almost	almost	ADV
ssh-7883	178	7	periodic	periodic	ADJ
ssh-7883	178	8	solutions	solution	NOUN
ssh-7883	178	9	of	of	ADP
ssh-7883	178	10	semilinear	semilinear	PROPN
ssh-7883	178	11	cauchy	cauchy	PROPN
ssh-7883	178	12	problems	problem	NOUN
ssh-7883	178	13	with	with	ADP
ssh-7883	178	14	non	non	ADJ
ssh-7883	178	15	-	-	ADJ
ssh-7883	178	16	dense	dense	ADJ
ssh-7883	178	17	domain	domain	NOUN
ssh-7883	178	18	.	.	PUNCT
ssh-7883	179	1	2001	2001	NUM
ssh-7883	179	2	.	.	PUNCT
ssh-7883	180	1	[	[	X
ssh-7883	180	2	11	11	NUM
ssh-7883	180	3	]	]	X
ssh-7883	180	4	gisele	gisele	PROPN
ssh-7883	180	5	m	m	PROPN
ssh-7883	180	6	mophou	mophou	NOUN
ssh-7883	180	7	and	and	CCONJ
ssh-7883	180	8	gaston	gaston	PROPN
ssh-7883	180	9	m	m	PROPN
ssh-7883	180	10	n’guerekata	n’guerekata	PROPN
ssh-7883	180	11	.	.	PUNCT
ssh-7883	181	1	mild	mild	ADJ
ssh-7883	181	2	solutions	solution	NOUN
ssh-7883	181	3	for	for	ADP
ssh-7883	181	4	semilinear	semilinear	ADJ
ssh-7883	181	5	fractional	fractional	ADJ
ssh-7883	181	6	differential	differential	ADJ
ssh-7883	181	7	equations	equation	NOUN
ssh-7883	181	8	.	.	PUNCT
ssh-7883	182	1	electronic	electronic	ADJ
ssh-7883	182	2	journal	journal	NOUN
ssh-7883	182	3	of	of	ADP
ssh-7883	182	4	differential	differential	ADJ
ssh-7883	182	5	equations	equation	NOUN
ssh-7883	182	6	(	(	PUNCT
ssh-7883	182	7	ejde	ejde	NOUN
ssh-7883	182	8	)	)	PUNCT
ssh-7883	183	1	[	[	X
ssh-7883	183	2	electronic	electronic	ADJ
ssh-7883	183	3	only	only	ADV
ssh-7883	183	4	]	]	PUNCT
ssh-7883	183	5	,	,	PUNCT
ssh-7883	183	6	2009	2009	NUM
ssh-7883	183	7	:	:	PUNCT
ssh-7883	183	8	paper	paper	NOUN
ssh-7883	183	9	–	–	PUNCT
ssh-7883	183	10	no	no	NOUN
ssh-7883	183	11	,	,	PUNCT
ssh-7883	183	12	2009	2009	NUM
ssh-7883	183	13	.	.	PUNCT
ssh-7883	184	1	[	[	X
ssh-7883	184	2	12	12	NUM
ssh-7883	184	3	]	]	PUNCT
ssh-7883	184	4	xiaobao	xiaobao	PROPN
ssh-7883	184	5	shu	shu	PROPN
ssh-7883	184	6	and	and	CCONJ
ssh-7883	184	7	qianqian	qianqian	PROPN
ssh-7883	184	8	wang	wang	PROPN
ssh-7883	184	9	.	.	PUNCT
ssh-7883	185	1	the	the	DET
ssh-7883	185	2	existence	existence	NOUN
ssh-7883	185	3	and	and	CCONJ
ssh-7883	185	4	uniqueness	uniqueness	NOUN
ssh-7883	185	5	of	of	ADP
ssh-7883	185	6	mild	mild	ADJ
ssh-7883	185	7	solutions	solution	NOUN
ssh-7883	185	8	for	for	ADP
ssh-7883	185	9	fractional	fractional	ADJ
ssh-7883	185	10	differential	differential	ADJ
ssh-7883	185	11	equations	equation	NOUN
ssh-7883	185	12	with	with	ADP
ssh-7883	185	13	nonlocal	nonlocal	ADJ
ssh-7883	185	14	conditions	condition	NOUN
ssh-7883	185	15	of	of	ADP
ssh-7883	185	16	order	order	NOUN
ssh-7883	185	17	1	1	NUM
ssh-7883	185	18	<	<	X
ssh-7883	185	19	α	α	X
ssh-7883	185	20	<	<	X
ssh-7883	185	21	2	2	NUM
ssh-7883	185	22	.	.	PUNCT
ssh-7883	185	23	computers	computer	NOUN
ssh-7883	185	24	&	&	CCONJ
ssh-7883	185	25	mathematics	mathematics	PROPN
ssh-7883	185	26	with	with	ADP
ssh-7883	185	27	applications	application	NOUN
ssh-7883	185	28	,	,	PUNCT
ssh-7883	185	29	64(6):2100–2110	64(6):2100–2110	NOUN
ssh-7883	185	30	,	,	PUNCT
ssh-7883	185	31	2012	2012	NUM
ssh-7883	185	32	.	.	PUNCT
ssh-7883	186	1	[	[	X
ssh-7883	186	2	13	13	NUM
ssh-7883	186	3	]	]	PUNCT
ssh-7883	186	4	lulu	lulu	PROPN
ssh-7883	186	5	ren	ren	PROPN
ssh-7883	186	6	,	,	PUNCT
ssh-7883	186	7	jinrong	jinrong	PROPN
ssh-7883	186	8	wang	wang	PROPN
ssh-7883	186	9	,	,	PUNCT
ssh-7883	186	10	and	and	CCONJ
ssh-7883	186	11	michal	michal	PROPN
ssh-7883	186	12	feˇckan	feˇckan	PROPN
ssh-7883	186	13	.	.	PUNCT
ssh-7883	187	1	asymptotically	asymptotically	ADV
ssh-7883	187	2	periodic	periodic	ADJ
ssh-7883	187	3	solutions	solution	NOUN
ssh-7883	187	4	for	for	ADP
ssh-7883	187	5	caputo	caputo	PROPN
ssh-7883	187	6	type	type	PROPN
ssh-7883	187	7	fractional	fractional	ADJ
ssh-7883	187	8	evolution	evolution	NOUN
ssh-7883	187	9	equations	equation	NOUN
ssh-7883	187	10	.	.	PUNCT
ssh-7883	188	1	fractional	fractional	ADJ
ssh-7883	188	2	calculus	calculus	NOUN
ssh-7883	188	3	and	and	CCONJ
ssh-7883	188	4	applied	apply	VERB
ssh-7883	188	5	analysis	analysis	NOUN
ssh-7883	188	6	,	,	PUNCT
ssh-7883	188	7	21(5):1294–1312	21(5):1294–1312	NUM
ssh-7883	188	8	,	,	PUNCT
ssh-7883	188	9	2018	2018	NUM
ssh-7883	188	10	.	.	PUNCT
ssh-7883	189	1	[	[	X
ssh-7883	189	2	14	14	NUM
ssh-7883	189	3	]	]	PUNCT
ssh-7883	189	4	lulu	lulu	PROPN
ssh-7883	189	5	ren	ren	PROPN
ssh-7883	189	6	,	,	PUNCT
ssh-7883	189	7	jinrong	jinrong	PROPN
ssh-7883	189	8	wang	wang	PROPN
ssh-7883	189	9	,	,	PUNCT
ssh-7883	189	10	and	and	CCONJ
ssh-7883	189	11	donal	donal	ADJ
ssh-7883	189	12	o	o	NOUN
ssh-7883	189	13	’	'	PUNCT
ssh-7883	189	14	regan	regan	PROPN
ssh-7883	189	15	.	.	PUNCT
ssh-7883	190	1	asymptotically	asymptotically	ADV
ssh-7883	190	2	periodic	periodic	ADJ
ssh-7883	190	3	behavior	behavior	NOUN
ssh-7883	190	4	of	of	ADP
ssh-7883	190	5	solutions	solution	NOUN
ssh-7883	190	6	of	of	ADP
ssh-7883	190	7	fractional	fractional	ADJ
ssh-7883	190	8	evolution	evolution	NOUN
ssh-7883	190	9	equations	equation	NOUN
ssh-7883	190	10	of	of	ADP
ssh-7883	190	11	order	order	NOUN
ssh-7883	190	12	1	1	NUM
ssh-7883	190	13	<	<	X
ssh-7883	190	14	α	α	X
ssh-7883	190	15	<	<	X
ssh-7883	190	16	2	2	NUM
ssh-7883	190	17	.	.	PUNCT
ssh-7883	190	18	mathematica	mathematica	PROPN
ssh-7883	190	19	slovaca	slovaca	PROPN
ssh-7883	190	20	,	,	PUNCT
ssh-7883	190	21	69(3):599–610	69(3):599–610	PROPN
ssh-7883	190	22	,	,	PUNCT
ssh-7883	190	23	2019	2019	NUM
ssh-7883	190	24	.	.	PUNCT
ssh-7883	191	1	[	[	X
ssh-7883	191	2	15	15	NUM
ssh-7883	191	3	]	]	PUNCT
ssh-7883	191	4	gongqing	gongqe	VERB
ssh-7883	191	5	zhang	zhang	PROPN
ssh-7883	191	6	and	and	CCONJ
ssh-7883	191	7	yuanqu	yuanqu	PROPN
ssh-7883	191	8	lin	lin	PROPN
ssh-7883	191	9	.	.	PUNCT
ssh-7883	192	1	lecture	lecture	NOUN
ssh-7883	192	2	notes	note	NOUN
ssh-7883	192	3	on	on	ADP
ssh-7883	192	4	functional	functional	ADJ
ssh-7883	192	5	analysis	analysis	NOUN
ssh-7883	192	6	.	.	PUNCT
ssh-7883	193	1	previous	previous	ADJ
ssh-7883	193	2	.	.	PUNCT
ssh-7883	194	1	peking	peking	PROPN
ssh-7883	194	2	university	university	PROPN
ssh-7883	194	3	press	press	NOUN
ssh-7883	194	4	,	,	PUNCT
ssh-7883	194	5	2005	2005	NUM
ssh-7883	194	6	.	.	PUNCT
ssh-7883	195	1	[	[	X
ssh-7883	195	2	16	16	NUM
ssh-7883	195	3	]	]	PUNCT
ssh-7883	195	4	amnon	amnon	PROPN
ssh-7883	195	5	pazy	pazy	NOUN
ssh-7883	195	6	.	.	PUNCT
ssh-7883	196	1	semigroups	semigroup	NOUN
ssh-7883	196	2	of	of	ADP
ssh-7883	196	3	linear	linear	PROPN
ssh-7883	196	4	operators	operator	NOUN
ssh-7883	196	5	and	and	CCONJ
ssh-7883	196	6	applications	application	NOUN
ssh-7883	196	7	to	to	ADP
ssh-7883	196	8	partial	partial	ADJ
ssh-7883	196	9	differential	differential	NOUN
ssh-7883	196	10	equations	equation	NOUN
ssh-7883	196	11	,	,	PUNCT
ssh-7883	196	12	volume	volume	NOUN
ssh-7883	196	13	44	44	NUM
ssh-7883	196	14	.	.	PUNCT
ssh-7883	197	1	springer	springer	PROPN
ssh-7883	197	2	science	science	PROPN
ssh-7883	197	3	&	&	CCONJ
ssh-7883	197	4	business	business	NOUN
ssh-7883	197	5	media	medium	NOUN
ssh-7883	197	6	,	,	PUNCT
ssh-7883	197	7	2012	2012	NUM
ssh-7883	197	8	.	.	PUNCT