id	sid	tid	token	lemma	pos
cana-4138	1	1	communications	communication	NOUN
cana-4138	1	2	on	on	ADP
cana-4138	1	3	applied	apply	VERB
cana-4138	1	4	nonlinear	nonlinear	ADJ
cana-4138	1	5	analysis	analysis	NOUN
cana-4138	1	6	issn	issn	NOUN
cana-4138	1	7	:	:	PUNCT
cana-4138	1	8	1074	1074	NUM
cana-4138	1	9	-	-	PUNCT
cana-4138	1	10	133x	133x	NUM
cana-4138	1	11	vol	vol	NOUN
cana-4138	1	12	32	32	NUM
cana-4138	1	13	no	no	NOUN
cana-4138	1	14	.	.	PUNCT
cana-4138	2	1	9s	9s	NUM
cana-4138	2	2	(	(	PUNCT
cana-4138	2	3	2025	2025	NUM
cana-4138	2	4	)	)	PUNCT
cana-4138	2	5	1303	1303	NUM
cana-4138	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4138	2	7	existence	existence	NOUN
cana-4138	2	8	and	and	CCONJ
cana-4138	2	9	uniqueness	uniqueness	NOUN
cana-4138	2	10	of	of	ADP
cana-4138	2	11	continuous	continuous	ADJ
cana-4138	2	12	solutions	solution	NOUN
cana-4138	2	13	for	for	ADP
cana-4138	2	14	conformable	conformable	ADJ
cana-4138	2	15	fractional	fractional	ADJ
cana-4138	2	16	integro	integro	ADJ
cana-4138	2	17	-	-	PUNCT
cana-4138	2	18	differential	differential	NOUN
cana-4138	2	19	equations	equation	NOUN
cana-4138	2	20	in	in	ADP
cana-4138	2	21	cone	cone	NOUN
cana-4138	2	22	metric	metric	ADJ
cana-4138	2	23	spaces	space	NOUN
cana-4138	2	24	kamble	kamble	PROPN
cana-4138	2	25	rajratna	rajratna	PROPN
cana-4138	2	26	m.a	m.a	PROPN
cana-4138	2	27	,	,	PUNCT
cana-4138	2	28	kulkarni	kulkarni	PROPN
cana-4138	2	29	pramod	pramod	PROPN
cana-4138	2	30	rb	rb	PROPN
cana-4138	2	31	ashri	ashri	PROPN
cana-4138	2	32	vitthal	vitthal	VERB
cana-4138	2	33	rukmini	rukmini	NOUN
cana-4138	2	34	arts	art	NOUN
cana-4138	2	35	,	,	PUNCT
cana-4138	2	36	commerce	commerce	NOUN
cana-4138	2	37	and	and	CCONJ
cana-4138	2	38	science	science	PROPN
cana-4138	2	39	college	college	PROPN
cana-4138	2	40	,	,	PUNCT
cana-4138	2	41	sawana	sawana	PROPN
cana-4138	2	42	,	,	PUNCT
cana-4138	2	43	maharashtra	maharashtra	PROPN
cana-4138	2	44	state	state	PROPN
cana-4138	2	45	,	,	PUNCT
cana-4138	2	46	india	india	PROPN
cana-4138	2	47	.	.	PUNCT
cana-4138	2	48	email	email	NOUN
cana-4138	2	49	:	:	PUNCT
cana-4138	2	50	kamblerajratna2@gmail.com	kamblerajratna2@gmail.com	X
cana-4138	2	51	bscience	bscience	NOUN
cana-4138	2	52	college	college	PROPN
cana-4138	2	53	,	,	PUNCT
cana-4138	2	54	nanded	nanded	PROPN
cana-4138	2	55	,	,	PUNCT
cana-4138	2	56	maharashtra	maharashtra	PROPN
cana-4138	2	57	state	state	PROPN
cana-4138	2	58	,	,	PUNCT
cana-4138	2	59	india	india	PROPN
cana-4138	2	60	.	.	PUNCT
cana-4138	2	61	email	email	NOUN
cana-4138	2	62	:	:	PUNCT
cana-4138	3	1	pramodrkul@gmail.com	pramodrkul@gmail.com	X
cana-4138	3	2	article	article	NOUN
cana-4138	3	3	history	history	NOUN
cana-4138	3	4	:	:	PUNCT
cana-4138	3	5	received	receive	VERB
cana-4138	3	6	:	:	PUNCT
cana-4138	3	7	12	12	NUM
cana-4138	3	8	-	-	SYM
cana-4138	3	9	01	01	NUM
cana-4138	3	10	-	-	PUNCT
cana-4138	3	11	2025	2025	NUM
cana-4138	3	12	revised	revise	VERB
cana-4138	3	13	:	:	PUNCT
cana-4138	3	14	15	15	NUM
cana-4138	3	15	-	-	NUM
cana-4138	3	16	02	02	NUM
cana-4138	3	17	-	-	PUNCT
cana-4138	3	18	2025	2025	NUM
cana-4138	3	19	accepted	accept	VERB
cana-4138	3	20	:	:	PUNCT
cana-4138	3	21	01	01	NUM
cana-4138	3	22	-	-	SYM
cana-4138	3	23	03	03	NUM
cana-4138	3	24	-	-	PUNCT
cana-4138	3	25	2025	2025	NUM
cana-4138	3	26	abstract	abstract	NOUN
cana-4138	3	27	:	:	PUNCT
cana-4138	3	28	in	in	ADP
cana-4138	3	29	this	this	DET
cana-4138	3	30	paper	paper	NOUN
cana-4138	3	31	,	,	PUNCT
cana-4138	3	32	by	by	ADP
cana-4138	3	33	the	the	DET
cana-4138	3	34	application	application	NOUN
cana-4138	3	35	of	of	ADP
cana-4138	3	36	some	some	DET
cana-4138	3	37	extensions	extension	NOUN
cana-4138	3	38	of	of	ADP
cana-4138	3	39	banach	banach	NOUN
cana-4138	3	40	's	's	PART
cana-4138	3	41	contraction	contraction	NOUN
cana-4138	3	42	principle	principle	NOUN
cana-4138	3	43	in	in	ADP
cana-4138	3	44	complete	complete	ADJ
cana-4138	3	45	cone	cone	NOUN
cana-4138	3	46	metric	metric	ADJ
cana-4138	3	47	space	space	NOUN
cana-4138	3	48	,	,	PUNCT
cana-4138	3	49	we	we	PRON
cana-4138	3	50	have	have	AUX
cana-4138	3	51	proved	prove	VERB
cana-4138	3	52	the	the	DET
cana-4138	3	53	existence	existence	NOUN
cana-4138	3	54	and	and	CCONJ
cana-4138	3	55	uniqueness	uniqueness	NOUN
cana-4138	3	56	of	of	ADP
cana-4138	3	57	solutions	solution	NOUN
cana-4138	3	58	to	to	ADP
cana-4138	3	59	fractional	fractional	ADJ
cana-4138	3	60	order	order	NOUN
cana-4138	3	61	integro	integro	ADJ
cana-4138	3	62	-	-	PUNCT
cana-4138	3	63	differential	differential	NOUN
cana-4138	3	64	equations	equation	NOUN
cana-4138	3	65	of	of	ADP
cana-4138	3	66	volterra	volterra	NOUN
cana-4138	3	67	-	-	PUNCT
cana-4138	3	68	fredholm	fredholm	NOUN
cana-4138	3	69	type	type	NOUN
cana-4138	3	70	which	which	PRON
cana-4138	3	71	are	be	AUX
cana-4138	3	72	defined	define	VERB
cana-4138	3	73	in	in	ADP
cana-4138	3	74	a	a	DET
cana-4138	3	75	cone	cone	NOUN
cana-4138	3	76	metric	metric	ADJ
cana-4138	3	77	space	space	NOUN
cana-4138	3	78	.	.	PUNCT
cana-4138	4	1	the	the	DET
cana-4138	4	2	fractional	fractional	ADJ
cana-4138	4	3	order	order	NOUN
cana-4138	4	4	derivative	derivative	NOUN
cana-4138	4	5	defined	define	VERB
cana-4138	4	6	in	in	ADP
cana-4138	4	7	the	the	DET
cana-4138	4	8	integro	integro	ADJ
cana-4138	4	9	-	-	PUNCT
cana-4138	4	10	differential	differential	NOUN
cana-4138	4	11	equation	equation	NOUN
cana-4138	4	12	is	be	AUX
cana-4138	4	13	the	the	DET
cana-4138	4	14	conformable	conformable	ADJ
cana-4138	4	15	fractional	fractional	ADJ
cana-4138	4	16	order	order	NOUN
cana-4138	4	17	derivative	derivative	NOUN
cana-4138	4	18	.	.	PUNCT
cana-4138	5	1	the	the	DET
cana-4138	5	2	obtained	obtain	VERB
cana-4138	5	3	results	result	NOUN
cana-4138	5	4	are	be	AUX
cana-4138	5	5	used	use	VERB
cana-4138	5	6	for	for	ADP
cana-4138	5	7	solving	solve	VERB
cana-4138	5	8	a	a	DET
cana-4138	5	9	couple	couple	NOUN
cana-4138	5	10	of	of	ADP
cana-4138	5	11	fractional	fractional	ADJ
cana-4138	5	12	order	order	NOUN
cana-4138	5	13	integro	integro	ADJ
cana-4138	5	14	-	-	PUNCT
cana-4138	5	15	differential	differential	NOUN
cana-4138	5	16	equations	equation	NOUN
cana-4138	5	17	of	of	ADP
cana-4138	5	18	volterra	volterra	NOUN
cana-4138	5	19	-	-	PUNCT
cana-4138	5	20	fredholm	fredholm	NOUN
cana-4138	5	21	type	type	NOUN
cana-4138	5	22	.	.	PUNCT
cana-4138	6	1	mathematics	mathematic	NOUN
cana-4138	6	2	subject	subject	ADJ
cana-4138	6	3	classification	classification	NOUN
cana-4138	6	4	:	:	PUNCT
cana-4138	6	5	34b05	34b05	NUM
cana-4138	6	6	.	.	PUNCT
cana-4138	7	1	keywords	keyword	NOUN
cana-4138	7	2	:	:	PUNCT
cana-4138	7	3	fractional	fractional	ADJ
cana-4138	7	4	order	order	NOUN
cana-4138	7	5	integro	integro	ADJ
cana-4138	7	6	-	-	PUNCT
cana-4138	7	7	differential	differential	NOUN
cana-4138	7	8	equations	equation	NOUN
cana-4138	7	9	,	,	PUNCT
cana-4138	7	10	cone	cone	NOUN
cana-4138	7	11	metric	metric	ADJ
cana-4138	7	12	space	space	NOUN
cana-4138	7	13	,	,	PUNCT
cana-4138	7	14	contractive	contractive	ADJ
cana-4138	7	15	mapping	mapping	NOUN
cana-4138	7	16	,	,	PUNCT
cana-4138	7	17	ordered	order	VERB
cana-4138	7	18	banach	banach	NOUN
cana-4138	7	19	space	space	NOUN
cana-4138	7	20	.	.	PUNCT
cana-4138	8	1	1	1	X
cana-4138	8	2	.	.	X
cana-4138	8	3	introduction	introduction	NOUN
cana-4138	8	4	numerous	numerous	ADJ
cana-4138	8	5	scientific	scientific	ADJ
cana-4138	8	6	and	and	CCONJ
cana-4138	8	7	engineering	engineering	NOUN
cana-4138	8	8	problems	problem	NOUN
cana-4138	8	9	involve	involve	VERB
cana-4138	8	10	integral	integral	ADJ
cana-4138	8	11	equations	equation	NOUN
cana-4138	8	12	.	.	PUNCT
cana-4138	9	1	volterra	volterra	NOUN
cana-4138	9	2	or	or	CCONJ
cana-4138	9	3	fredholm	fredholm	VERB
cana-4138	9	4	integral	integral	ADJ
cana-4138	9	5	equations	equation	NOUN
cana-4138	9	6	can	can	AUX
cana-4138	9	7	be	be	AUX
cana-4138	9	8	used	use	VERB
cana-4138	9	9	to	to	PART
cana-4138	9	10	solve	solve	VERB
cana-4138	9	11	a	a	DET
cana-4138	9	12	wide	wide	ADJ
cana-4138	9	13	range	range	NOUN
cana-4138	9	14	of	of	ADP
cana-4138	9	15	initial	initial	ADJ
cana-4138	9	16	and	and	CCONJ
cana-4138	9	17	boundary	boundary	ADJ
cana-4138	9	18	value	value	NOUN
cana-4138	9	19	problems	problem	NOUN
cana-4138	9	20	.	.	PUNCT
cana-4138	10	1	more	more	ADJ
cana-4138	10	2	than	than	ADP
cana-4138	10	3	any	any	DET
cana-4138	10	4	other	other	ADJ
cana-4138	10	5	discipline	discipline	NOUN
cana-4138	10	6	,	,	PUNCT
cana-4138	10	7	the	the	DET
cana-4138	10	8	potential	potential	ADJ
cana-4138	10	9	theory	theory	NOUN
cana-4138	10	10	helped	help	VERB
cana-4138	10	11	in	in	ADP
cana-4138	10	12	the	the	DET
cana-4138	10	13	development	development	NOUN
cana-4138	10	14	of	of	ADP
cana-4138	10	15	theory	theory	NOUN
cana-4138	10	16	of	of	ADP
cana-4138	10	17	integral	integral	ADJ
cana-4138	10	18	equations	equation	NOUN
cana-4138	10	19	.	.	PUNCT
cana-4138	11	1	integral	integral	ADJ
cana-4138	11	2	equations	equation	NOUN
cana-4138	11	3	were	be	AUX
cana-4138	11	4	also	also	ADV
cana-4138	11	5	developed	develop	VERB
cana-4138	11	6	using	use	VERB
cana-4138	11	7	mathematical	mathematical	ADJ
cana-4138	11	8	physics	physics	NOUN
cana-4138	11	9	models	model	NOUN
cana-4138	11	10	,	,	PUNCT
cana-4138	11	11	including	include	VERB
cana-4138	11	12	water	water	NOUN
cana-4138	11	13	waves	wave	NOUN
cana-4138	11	14	,	,	PUNCT
cana-4138	11	15	conformal	conformal	ADJ
cana-4138	11	16	mapping	mapping	NOUN
cana-4138	11	17	,	,	PUNCT
cana-4138	11	18	diffraction	diffraction	NOUN
cana-4138	11	19	issues	issue	NOUN
cana-4138	11	20	,	,	PUNCT
cana-4138	11	21	and	and	CCONJ
cana-4138	11	22	scattering	scatter	VERB
cana-4138	11	23	in	in	ADP
cana-4138	11	24	quantum	quantum	ADJ
cana-4138	11	25	mechanics	mechanic	NOUN
cana-4138	11	26	.	.	PUNCT
cana-4138	12	1	integral	integral	ADJ
cana-4138	12	2	equations	equation	NOUN
cana-4138	12	3	or	or	CCONJ
cana-4138	12	4	integro	integro	ADJ
cana-4138	12	5	-	-	PUNCT
cana-4138	12	6	differential	differential	NOUN
cana-4138	12	7	equations	equation	NOUN
cana-4138	12	8	describe	describe	VERB
cana-4138	12	9	a	a	DET
cana-4138	12	10	wide	wide	ADJ
cana-4138	12	11	range	range	NOUN
cana-4138	12	12	of	of	ADP
cana-4138	12	13	additional	additional	ADJ
cana-4138	12	14	applications	application	NOUN
cana-4138	12	15	in	in	ADP
cana-4138	12	16	science	science	NOUN
cana-4138	12	17	and	and	CCONJ
cana-4138	12	18	engineering	engineering	NOUN
cana-4138	12	19	.	.	PUNCT
cana-4138	13	1	integral	integral	ADJ
cana-4138	13	2	equations	equation	NOUN
cana-4138	13	3	address	address	VERB
cana-4138	13	4	a	a	DET
cana-4138	13	5	number	number	NOUN
cana-4138	13	6	of	of	ADP
cana-4138	13	7	topics	topic	NOUN
cana-4138	13	8	,	,	PUNCT
cana-4138	13	9	including	include	VERB
cana-4138	13	10	the	the	DET
cana-4138	13	11	volterra	volterra	NOUN
cana-4138	13	12	population	population	PROPN
cana-4138	13	13	growth	growth	NOUN
cana-4138	13	14	model	model	NOUN
cana-4138	13	15	,	,	PUNCT
cana-4138	13	16	coexisting	coexist	VERB
cana-4138	13	17	biological	biological	ADJ
cana-4138	13	18	species	specie	NOUN
cana-4138	13	19	,	,	PUNCT
cana-4138	13	20	the	the	DET
cana-4138	13	21	spread	spread	NOUN
cana-4138	13	22	of	of	ADP
cana-4138	13	23	stocked	stock	VERB
cana-4138	13	24	fish	fish	NOUN
cana-4138	13	25	in	in	ADP
cana-4138	13	26	a	a	DET
cana-4138	13	27	new	new	ADJ
cana-4138	13	28	lake	lake	NOUN
cana-4138	13	29	,	,	PUNCT
cana-4138	13	30	heat	heat	NOUN
cana-4138	13	31	transport	transport	NOUN
cana-4138	13	32	,	,	PUNCT
cana-4138	13	33	and	and	CCONJ
cana-4138	13	34	heat	heat	NOUN
cana-4138	13	35	radiation	radiation	NOUN
cana-4138	13	36	.	.	PUNCT
cana-4138	14	1	integral	integral	ADJ
cana-4138	14	2	equations	equation	NOUN
cana-4138	14	3	with	with	ADP
cana-4138	14	4	logarithmic	logarithmic	ADJ
cana-4138	14	5	kernels	kernel	NOUN
cana-4138	14	6	arise	arise	NOUN
cana-4138	14	7	in	in	ADP
cana-4138	14	8	many	many	ADJ
cana-4138	14	9	scientific	scientific	ADJ
cana-4138	14	10	problems	problem	NOUN
cana-4138	14	11	.	.	PUNCT
cana-4138	15	1	integral	integral	ADJ
cana-4138	15	2	equations	equation	NOUN
cana-4138	15	3	are	be	AUX
cana-4138	15	4	frequently	frequently	ADV
cana-4138	15	5	used	use	VERB
cana-4138	15	6	in	in	ADP
cana-4138	15	7	electrostatic	electrostatic	ADJ
cana-4138	15	8	,	,	PUNCT
cana-4138	15	9	low	low	ADJ
cana-4138	15	10	frequency	frequency	NOUN
cana-4138	15	11	electromagnetic	electromagnetic	NOUN
cana-4138	15	12	,	,	PUNCT
cana-4138	15	13	electromagnetic	electromagnetic	ADJ
cana-4138	15	14	scattering	scattering	NOUN
cana-4138	15	15	,	,	PUNCT
cana-4138	15	16	and	and	CCONJ
cana-4138	15	17	acoustic	acoustic	ADJ
cana-4138	15	18	and	and	CCONJ
cana-4138	15	19	elastic	elastic	ADJ
cana-4138	15	20	wave	wave	NOUN
cana-4138	15	21	propagation	propagation	NOUN
cana-4138	15	22	problems	problem	NOUN
cana-4138	15	23	.	.	PUNCT
cana-4138	16	1	in	in	ADP
cana-4138	16	2	this	this	DET
cana-4138	16	3	paper	paper	NOUN
cana-4138	16	4	we	we	PRON
cana-4138	16	5	study	study	VERB
cana-4138	16	6	the	the	DET
cana-4138	16	7	existence	existence	NOUN
cana-4138	16	8	and	and	CCONJ
cana-4138	16	9	uniqueness	uniqueness	NOUN
cana-4138	16	10	of	of	ADP
cana-4138	16	11	solutions	solution	NOUN
cana-4138	16	12	for	for	ADP
cana-4138	16	13	the	the	DET
cana-4138	16	14	conformable	conformable	ADJ
cana-4138	16	15	fractional	fractional	ADJ
cana-4138	16	16	order	order	NOUN
cana-4138	16	17	volterra	volterra	NOUN
cana-4138	16	18	-	-	PUNCT
cana-4138	16	19	fredholm	fredholm	NOUN
cana-4138	16	20	type	type	NOUN
cana-4138	16	21	integro	integro	NOUN
cana-4138	16	22	-	-	PUNCT
cana-4138	16	23	differentail	differentail	NOUN
cana-4138	16	24	equations	equation	NOUN
cana-4138	16	25	[	[	X
cana-4138	16	26	1	1	NUM
cana-4138	16	27	,	,	PUNCT
cana-4138	16	28	2	2	NUM
cana-4138	16	29	,	,	PUNCT
cana-4138	16	30	3	3	NUM
cana-4138	16	31	]	]	PUNCT
cana-4138	16	32	of	of	ADP
cana-4138	16	33	the	the	DET
cana-4138	16	34	form	form	NOUN
cana-4138	16	35	𝑑𝛼𝑥(𝑡	𝑑𝛼𝑥(𝑡	NOUN
cana-4138	16	36	)	)	PUNCT
cana-4138	16	37	𝑑𝑡	𝑑𝑡	ADP
cana-4138	16	38	=	=	PUNCT
cana-4138	16	39	𝑓(𝑡	𝑓(𝑡	PROPN
cana-4138	16	40	)	)	PUNCT
cana-4138	17	1	+	+	CCONJ
cana-4138	17	2	∫	∫	PROPN
cana-4138	17	3	𝑝(𝑡	𝑝(𝑡	PROPN
cana-4138	17	4	,	,	PUNCT
cana-4138	17	5	𝑠	𝑠	PROPN
cana-4138	17	6	,	,	PUNCT
cana-4138	17	7	𝑥(𝑠))𝑑𝑠	𝑥(𝑠))𝑑𝑠	PROPN
cana-4138	17	8	+	+	CCONJ
cana-4138	17	9	∫	∫	X
cana-4138	17	10	𝑞(𝑡	𝑞(𝑡	PROPN
cana-4138	17	11	,	,	PUNCT
cana-4138	17	12	𝑠	𝑠	PROPN
cana-4138	17	13	,	,	PUNCT
cana-4138	17	14	𝑥(𝑠))𝑑𝑠	𝑥(𝑠))𝑑𝑠	VERB
cana-4138	17	15	𝑏	𝑏	SYM
cana-4138	17	16	0	0	NUM
cana-4138	17	17	𝑡	𝑡	NOUN
cana-4138	17	18	0	0	NUM
cana-4138	17	19	,	,	PUNCT
cana-4138	17	20	𝑡	𝑡	PROPN
cana-4138	17	21	∈	∈	NOUN
cana-4138	17	22	𝐼	𝐼	ADP
cana-4138	17	23	=	=	SYM
cana-4138	18	1	[	[	X
cana-4138	18	2	0	0	NUM
cana-4138	18	3	,	,	PUNCT
cana-4138	18	4	𝑏	𝑏	NOUN
cana-4138	18	5	]	]	X
cana-4138	18	6	…	…	PUNCT
cana-4138	18	7	(	(	PUNCT
cana-4138	18	8	1	1	X
cana-4138	18	9	)	)	PUNCT
cana-4138	18	10	𝑥(0	𝑥(0	ADJ
cana-4138	18	11	)	)	PUNCT
cana-4138	18	12	=	=	SYM
cana-4138	18	13	𝑥0	𝑥0	NOUN
cana-4138	18	14	…	…	PUNCT
cana-4138	18	15	(	(	PUNCT
cana-4138	18	16	2	2	X
cana-4138	18	17	)	)	PUNCT
cana-4138	18	18	mailto:kamblerajratna2@gmail.com	mailto:kamblerajratna2@gmail.com	PROPN
cana-4138	18	19	mailto:pramodrkul@gmail.com	mailto:pramodrkul@gmail.com	PROPN
cana-4138	19	1	communications	communication	NOUN
cana-4138	19	2	on	on	ADP
cana-4138	19	3	applied	apply	VERB
cana-4138	19	4	nonlinear	nonlinear	ADJ
cana-4138	19	5	analysis	analysis	NOUN
cana-4138	19	6	issn	issn	NOUN
cana-4138	19	7	:	:	PUNCT
cana-4138	19	8	1074	1074	NUM
cana-4138	19	9	-	-	PUNCT
cana-4138	19	10	133x	133x	NUM
cana-4138	19	11	vol	vol	NOUN
cana-4138	19	12	32	32	NUM
cana-4138	19	13	no	no	NOUN
cana-4138	19	14	.	.	PUNCT
cana-4138	20	1	9s	9s	NUM
cana-4138	20	2	(	(	PUNCT
cana-4138	20	3	2025	2025	NUM
cana-4138	20	4	)	)	PUNCT
cana-4138	20	5	1304	1304	NUM
cana-4138	20	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4138	20	7	where	where	SCONJ
cana-4138	20	8	the	the	DET
cana-4138	20	9	term	term	NOUN
cana-4138	20	10	𝑑𝛼𝑥(𝑡	𝑑𝛼𝑥(𝑡	PROPN
cana-4138	20	11	)	)	PUNCT
cana-4138	20	12	𝑑𝑡	𝑑𝑡	VERB
cana-4138	20	13	represents	represent	VERB
cana-4138	20	14	the	the	DET
cana-4138	20	15	conformable	conformable	ADJ
cana-4138	20	16	fractional	fractional	ADJ
cana-4138	20	17	order	order	NOUN
cana-4138	20	18	derivative	derivative	NOUN
cana-4138	20	19	of	of	ADP
cana-4138	20	20	fractional	fractional	ADJ
cana-4138	20	21	order	order	NOUN
cana-4138	20	22	𝛼	𝛼	NOUN
cana-4138	20	23	∈	∈	NOUN
cana-4138	20	24	(	(	PUNCT
cana-4138	20	25	0,1	0,1	NUM
cana-4138	20	26	)	)	PUNCT
cana-4138	20	27	.	.	PUNCT
cana-4138	21	1	,	,	PUNCT
cana-4138	22	1	𝑓	𝑓	X
cana-4138	22	2	:	:	PUNCT
cana-4138	22	3	𝐼	𝐼	PROPN
cana-4138	22	4	→	→	SYM
cana-4138	22	5	𝑋	𝑋	PROPN
cana-4138	22	6	,	,	PUNCT
cana-4138	22	7	𝑝	𝑝	PROPN
cana-4138	22	8	,	,	PUNCT
cana-4138	22	9	𝑞	𝑞	X
cana-4138	22	10	:	:	PUNCT
cana-4138	22	11	𝐼	𝐼	ADP
cana-4138	22	12	×	×	NOUN
cana-4138	22	13	𝐼	𝐼	ADP
cana-4138	22	14	×	×	NOUN
cana-4138	22	15	𝑋	𝑋	NOUN
cana-4138	22	16	→	→	SYM
cana-4138	22	17	𝑋	𝑋	PROPN
cana-4138	22	18	are	be	AUX
cana-4138	22	19	continuous	continuous	ADJ
cana-4138	22	20	functions	function	NOUN
cana-4138	22	21	and	and	CCONJ
cana-4138	22	22	𝑥0	𝑥0	NOUN
cana-4138	22	23	is	be	AUX
cana-4138	22	24	an	an	DET
cana-4138	22	25	element	element	NOUN
cana-4138	22	26	of	of	ADP
cana-4138	22	27	a	a	DET
cana-4138	22	28	real	real	ADJ
cana-4138	22	29	banach	banach	NOUN
cana-4138	22	30	space	space	NOUN
cana-4138	22	31	𝑋	𝑋	NOUN
cana-4138	22	32	,	,	PUNCT
cana-4138	22	33	with	with	ADP
cana-4138	22	34	the	the	DET
cana-4138	22	35	norm	norm	NOUN
cana-4138	22	36	‖.	‖.	INTJ
cana-4138	22	37	‖.	‖.	INTJ
cana-4138	22	38	but	but	CCONJ
cana-4138	22	39	before	before	ADP
cana-4138	22	40	investigating	investigate	VERB
cana-4138	22	41	the	the	DET
cana-4138	22	42	problem	problem	NOUN
cana-4138	22	43	,	,	PUNCT
cana-4138	22	44	we	we	PRON
cana-4138	22	45	will	will	AUX
cana-4138	22	46	take	take	VERB
cana-4138	22	47	a	a	DET
cana-4138	22	48	review	review	NOUN
cana-4138	22	49	of	of	ADP
cana-4138	22	50	the	the	DET
cana-4138	22	51	research	research	NOUN
cana-4138	22	52	work	work	NOUN
cana-4138	22	53	done	do	VERB
cana-4138	22	54	by	by	ADP
cana-4138	22	55	the	the	DET
cana-4138	22	56	mathematicians	mathematician	NOUN
cana-4138	22	57	in	in	ADP
cana-4138	22	58	the	the	DET
cana-4138	22	59	development	development	NOUN
cana-4138	22	60	of	of	ADP
cana-4138	22	61	the	the	DET
cana-4138	22	62	topic	topic	NOUN
cana-4138	22	63	.	.	PUNCT
cana-4138	23	1	in	in	ADP
cana-4138	23	2	[	[	X
cana-4138	23	3	4	4	NUM
cana-4138	23	4	]	]	PUNCT
cana-4138	23	5	,	,	PUNCT
cana-4138	23	6	using	use	VERB
cana-4138	23	7	the	the	DET
cana-4138	23	8	schaefer	schaefer	NOUN
cana-4138	23	9	’s	’s	PART
cana-4138	23	10	fixed	fix	VERB
cana-4138	23	11	point	point	NOUN
cana-4138	23	12	theorem	theorem	ADJ
cana-4138	23	13	,	,	PUNCT
cana-4138	23	14	karouni	karouni	NOUN
cana-4138	23	15	,	,	PUNCT
cana-4138	23	16	a.	a.	NOUN
cana-4138	23	17	et	et	PROPN
cana-4138	23	18	.	.	PUNCT
cana-4138	24	1	al	al	PROPN
cana-4138	24	2	.	.	PROPN
cana-4138	24	3	have	have	AUX
cana-4138	24	4	established	establish	VERB
cana-4138	24	5	the	the	DET
cana-4138	24	6	existence	existence	NOUN
cana-4138	24	7	and	and	CCONJ
cana-4138	24	8	uniqueness	uniqueness	NOUN
cana-4138	24	9	of	of	ADP
cana-4138	24	10	the	the	DET
cana-4138	24	11	continuous	continuous	ADJ
cana-4138	24	12	solution	solution	NOUN
cana-4138	24	13	to	to	ADP
cana-4138	24	14	the	the	DET
cana-4138	24	15	nonlinear	nonlinear	ADJ
cana-4138	24	16	fredholm	fredholm	ADJ
cana-4138	24	17	integral	integral	ADJ
cana-4138	24	18	equation	equation	NOUN
cana-4138	24	19	of	of	ADP
cana-4138	24	20	the	the	DET
cana-4138	24	21	form	form	NOUN
cana-4138	24	22	𝑥(𝑡	𝑥(𝑡	NOUN
cana-4138	24	23	)	)	PUNCT
cana-4138	24	24	=	=	SYM
cana-4138	25	1	𝑓(𝑡	𝑓(𝑡	VERB
cana-4138	25	2	)	)	PUNCT
cana-4138	25	3	+	+	CCONJ
cana-4138	25	4	∫	∫	PROPN
cana-4138	25	5	𝑔(𝑡	𝑔(𝑡	PROPN
cana-4138	25	6	,	,	PUNCT
cana-4138	25	7	𝑠	𝑠	PROPN
cana-4138	25	8	,	,	PUNCT
cana-4138	25	9	𝑥(𝑠))𝑑𝑠	𝑥(𝑠))𝑑𝑠	PROPN
cana-4138	25	10	,	,	PUNCT
cana-4138	25	11	−	−	PROPN
cana-4138	25	12	∞	∞	PROPN
cana-4138	25	13	<	<	X
cana-4138	25	14	𝑎	𝑎	X
cana-4138	25	15	≤	≤	NUM
cana-4138	25	16	𝑡	𝑡	NOUN
cana-4138	25	17	≤	≤	NOUN
cana-4138	25	18	𝑏	𝑏	ADP
cana-4138	25	19	<	<	X
cana-4138	25	20	∞	∞	NUM
cana-4138	25	21	𝑏	𝑏	NOUN
cana-4138	25	22	𝑎	𝑎	NOUN
cana-4138	25	23	where	where	SCONJ
cana-4138	25	24	it	it	PRON
cana-4138	25	25	is	be	AUX
cana-4138	25	26	assumed	assume	VERB
cana-4138	25	27	that	that	SCONJ
cana-4138	25	28	the	the	DET
cana-4138	25	29	function	function	NOUN
cana-4138	25	30	𝑓	𝑓	NOUN
cana-4138	25	31	is	be	AUX
cana-4138	25	32	continuous	continuous	ADJ
cana-4138	25	33	over	over	ADP
cana-4138	25	34	the	the	DET
cana-4138	25	35	interval	interval	NOUN
cana-4138	26	1	[	[	X
cana-4138	26	2	𝑎	𝑎	X
cana-4138	26	3	,	,	PUNCT
cana-4138	26	4	𝑏	𝑏	NOUN
cana-4138	26	5	]	]	PUNCT
cana-4138	26	6	and	and	CCONJ
cana-4138	26	7	bounded	bound	VERB
cana-4138	26	8	over	over	ADP
cana-4138	26	9	a	a	DET
cana-4138	26	10	measurable	measurable	ADJ
cana-4138	26	11	set	set	NOUN
cana-4138	26	12	.	.	PUNCT
cana-4138	27	1	in	in	ADP
cana-4138	27	2	[	[	X
cana-4138	27	3	5	5	NUM
cana-4138	27	4	]	]	PUNCT
cana-4138	27	5	,	,	PUNCT
cana-4138	27	6	claudia	claudia	PROPN
cana-4138	27	7	,	,	PUNCT
cana-4138	27	8	a.	a.	PROPN
cana-4138	27	9	have	have	AUX
cana-4138	27	10	proved	prove	VERB
cana-4138	27	11	,	,	PUNCT
cana-4138	27	12	using	use	VERB
cana-4138	27	13	the	the	DET
cana-4138	27	14	picards	picard	NOUN
cana-4138	27	15	operator	operator	NOUN
cana-4138	27	16	theory	theory	NOUN
cana-4138	27	17	,	,	PUNCT
cana-4138	27	18	the	the	DET
cana-4138	27	19	existence	existence	NOUN
cana-4138	27	20	and	and	CCONJ
cana-4138	27	21	uniqueness	uniqueness	NOUN
cana-4138	27	22	to	to	ADP
cana-4138	27	23	the	the	DET
cana-4138	27	24	solution	solution	NOUN
cana-4138	27	25	of	of	ADP
cana-4138	27	26	the	the	DET
cana-4138	27	27	volterra	volterra	NOUN
cana-4138	27	28	-	-	PUNCT
cana-4138	27	29	fredholm	fredholm	NOUN
cana-4138	27	30	integral	integral	ADJ
cana-4138	27	31	equation	equation	NOUN
cana-4138	27	32	of	of	ADP
cana-4138	27	33	the	the	DET
cana-4138	27	34	form	form	NOUN
cana-4138	27	35	𝑢(𝑥	𝑢(𝑥	PROPN
cana-4138	27	36	,	,	PUNCT
cana-4138	27	37	𝑡	𝑡	X
cana-4138	27	38	)	)	PUNCT
cana-4138	27	39	=	=	SYM
cana-4138	28	1	𝑔(𝑥	𝑔(𝑥	PROPN
cana-4138	28	2	,	,	PUNCT
cana-4138	28	3	𝑡	𝑡	X
cana-4138	28	4	)	)	PUNCT
cana-4138	28	5	+	+	NUM
cana-4138	28	6	∫	∫	PROPN
cana-4138	28	7	∫	∫	PROPN
cana-4138	28	8	𝑘(𝑡	𝑘(𝑡	PROPN
cana-4138	28	9	,	,	PUNCT
cana-4138	28	10	𝑥	𝑥	PROPN
cana-4138	28	11	,	,	PUNCT
cana-4138	28	12	𝑠	𝑠	PROPN
cana-4138	28	13	,	,	PUNCT
cana-4138	28	14	𝑦	𝑦	NOUN
cana-4138	28	15	,	,	PUNCT
cana-4138	28	16	𝑢(𝑠	𝑢(𝑠	NOUN
cana-4138	28	17	,	,	PUNCT
cana-4138	28	18	𝑦))𝑑𝑦𝑑𝑠	𝑦))𝑑𝑦𝑑𝑠	PROPN
cana-4138	28	19	ω	ω	PROPN
cana-4138	28	20	𝑡	𝑡	PROPN
cana-4138	28	21	0	0	PUNCT
cana-4138	28	22	where	where	SCONJ
cana-4138	28	23	(	(	PUNCT
cana-4138	28	24	𝑡	𝑡	NOUN
cana-4138	28	25	,	,	PUNCT
cana-4138	28	26	𝑥	𝑥	NOUN
cana-4138	28	27	)	)	PUNCT
cana-4138	28	28	∈	∈	PROPN
cana-4138	29	1	[	[	X
cana-4138	29	2	0	0	NUM
cana-4138	29	3	,	,	PUNCT
cana-4138	29	4	𝑇	𝑇	PROPN
cana-4138	29	5	]	]	X
cana-4138	29	6	×	×	PROPN
cana-4138	29	7	ω	ω	NUM
cana-4138	29	8	≔	≔	NOUN
cana-4138	29	9	�	�	PROPN
cana-4138	29	10	̅	̅	NOUN
cana-4138	29	11	�	�	NOUN
cana-4138	29	12	,	,	PUNCT
cana-4138	29	13	𝑇	𝑇	PROPN
cana-4138	29	14	>	>	X
cana-4138	29	15	0	0	PROPN
cana-4138	29	16	,	,	PUNCT
cana-4138	29	17	ω	ω	PROPN
cana-4138	29	18	∈	∈	PROPN
cana-4138	30	1	ℝ𝑚	ℝ𝑚	NOUN
cana-4138	30	2	is	be	AUX
cana-4138	30	3	bounded	bound	VERB
cana-4138	30	4	and	and	CCONJ
cana-4138	30	5	closed	closed	ADJ
cana-4138	30	6	.	.	PUNCT
cana-4138	31	1	ahmad	ahmad	PROPN
cana-4138	31	2	et	et	PROPN
cana-4138	31	3	al	al	PROPN
cana-4138	31	4	.	.	PUNCT
cana-4138	32	1	in	in	ADP
cana-4138	32	2	[	[	X
cana-4138	32	3	6	6	NUM
cana-4138	32	4	]	]	PUNCT
cana-4138	32	5	have	have	AUX
cana-4138	32	6	obtained	obtain	VERB
cana-4138	32	7	the	the	DET
cana-4138	32	8	solutions	solution	NOUN
cana-4138	32	9	of	of	ADP
cana-4138	32	10	the	the	DET
cana-4138	32	11	integro	integro	ADJ
cana-4138	32	12	-	-	PUNCT
cana-4138	32	13	differential	differential	NOUN
cana-4138	32	14	equations	equation	NOUN
cana-4138	32	15	with	with	ADP
cana-4138	32	16	non	non	ADJ
cana-4138	32	17	-	-	ADJ
cana-4138	32	18	local	local	ADJ
cana-4138	32	19	four	four	NUM
cana-4138	32	20	point	point	NOUN
cana-4138	32	21	and	and	CCONJ
cana-4138	32	22	strip	strip	VERB
cana-4138	32	23	multipoint	multipoint	NOUN
cana-4138	32	24	boundary	boundary	ADJ
cana-4138	32	25	conditions	condition	NOUN
cana-4138	32	26	.	.	PUNCT
cana-4138	33	1	wang	wang	PROPN
cana-4138	33	2	et	et	PROPN
cana-4138	33	3	al	al	PROPN
cana-4138	33	4	.	.	PUNCT
cana-4138	34	1	[	[	X
cana-4138	34	2	7	7	X
cana-4138	34	3	]	]	PUNCT
cana-4138	34	4	have	have	AUX
cana-4138	34	5	established	establish	VERB
cana-4138	34	6	the	the	DET
cana-4138	34	7	conditions	condition	NOUN
cana-4138	34	8	for	for	ADP
cana-4138	34	9	the	the	DET
cana-4138	34	10	uniqueness	uniqueness	NOUN
cana-4138	34	11	and	and	CCONJ
cana-4138	34	12	existence	existence	NOUN
cana-4138	34	13	of	of	ADP
cana-4138	34	14	the	the	DET
cana-4138	34	15	positive	positive	ADJ
cana-4138	34	16	solutions	solution	NOUN
cana-4138	34	17	of	of	ADP
cana-4138	34	18	the	the	DET
cana-4138	34	19	fractional	fractional	ADJ
cana-4138	34	20	integro	integro	ADJ
cana-4138	34	21	-	-	PUNCT
cana-4138	34	22	differential	differential	NOUN
cana-4138	34	23	equation	equation	NOUN
cana-4138	34	24	𝐷𝛼𝑢(𝑡	𝐷𝛼𝑢(𝑡	NOUN
cana-4138	34	25	)	)	PUNCT
cana-4138	35	1	+	+	CCONJ
cana-4138	35	2	𝑓(𝑡	𝑓(𝑡	NOUN
cana-4138	35	3	,	,	PUNCT
cana-4138	35	4	𝑢(𝑡	𝑢(𝑡	NOUN
cana-4138	35	5	)	)	PUNCT
cana-4138	35	6	,	,	PUNCT
cana-4138	35	7	𝑇𝑢(𝑡	𝑇𝑢(𝑡	NOUN
cana-4138	35	8	)	)	PUNCT
cana-4138	35	9	,	,	PUNCT
cana-4138	35	10	𝑆𝑢(𝑡	𝑆𝑢(𝑡	NOUN
cana-4138	35	11	)	)	PUNCT
cana-4138	35	12	)	)	PUNCT
cana-4138	36	1	=	=	PUNCT
cana-4138	36	2	0	0	NUM
cana-4138	36	3	,	,	PUNCT
cana-4138	36	4	0	0	NUM
cana-4138	36	5	<	<	X
cana-4138	36	6	𝑡	𝑡	X
cana-4138	36	7	<	<	X
cana-4138	36	8	1	1	NUM
cana-4138	36	9	under	under	ADP
cana-4138	36	10	the	the	DET
cana-4138	36	11	boundary	boundary	ADJ
cana-4138	36	12	conditions	condition	NOUN
cana-4138	36	13	given	give	VERB
cana-4138	36	14	by	by	ADP
cana-4138	36	15	𝑢(0	𝑢(0	PROPN
cana-4138	36	16	)	)	PUNCT
cana-4138	36	17	=	=	PROPN
cana-4138	36	18	𝑢0	𝑢0	PROPN
cana-4138	36	19	,	,	PUNCT
cana-4138	36	20	𝑢′(0	𝑢′(0	NOUN
cana-4138	36	21	)	)	PUNCT
cana-4138	36	22	=	=	SYM
cana-4138	36	23	𝑏1	𝑏1	NOUN
cana-4138	36	24	,	,	PUNCT
cana-4138	36	25	…	…	PUNCT
cana-4138	36	26	,	,	PUNCT
cana-4138	36	27	𝑢(𝑛−3)(0	𝑢(𝑛−3)(0	X
cana-4138	36	28	)	)	PUNCT
cana-4138	36	29	=	=	SYM
cana-4138	36	30	𝑏𝑛−3	𝑏𝑛−3	PROPN
cana-4138	36	31	,	,	PUNCT
cana-4138	36	32	𝑢(𝑛−2)(0	𝑢(𝑛−2)(0	NUM
cana-4138	36	33	)	)	PUNCT
cana-4138	36	34	=	=	SYM
cana-4138	36	35	𝑏𝑛−2	𝑏𝑛−2	NOUN
cana-4138	36	36	,	,	PUNCT
cana-4138	36	37	𝑢(𝑛−1)(0	𝑢(𝑛−1)(0	ADJ
cana-4138	36	38	)	)	PUNCT
cana-4138	36	39	=	=	VERB
cana-4138	37	1	𝑏𝑛−1	𝑏𝑛−1	NOUN
cana-4138	37	2	where	where	SCONJ
cana-4138	37	3	𝑛	𝑛	PRON
cana-4138	37	4	−	−	PROPN
cana-4138	37	5	1	1	NUM
cana-4138	37	6	<	<	X
cana-4138	37	7	𝛼	𝛼	PROPN
cana-4138	37	8	≤	≤	NUM
cana-4138	37	9	𝑛	𝑛	NOUN
cana-4138	37	10	,	,	PUNCT
cana-4138	37	11	0	0	NUM
cana-4138	37	12	≤	≤	NOUN
cana-4138	37	13	µ	µ	X
cana-4138	37	14	<	<	X
cana-4138	37	15	𝑛	𝑛	PRON
cana-4138	37	16	−	−	PROPN
cana-4138	37	17	1	1	NUM
cana-4138	37	18	,	,	PUNCT
cana-4138	37	19	𝑛	𝑛	DET
cana-4138	37	20	≥	≥	NOUN
cana-4138	37	21	3	3	NUM
cana-4138	37	22	,	,	PUNCT
cana-4138	37	23	𝑏𝑖	𝑏𝑖	ADP
cana-4138	37	24	≥	≥	NOUN
cana-4138	37	25	0	0	PUNCT
cana-4138	37	26	(	(	PUNCT
cana-4138	37	27	𝑖	𝑖	SYM
cana-4138	37	28	=	=	SYM
cana-4138	37	29	1	1	NUM
cana-4138	37	30	,	,	PUNCT
cana-4138	37	31	2	2	NUM
cana-4138	37	32	,	,	PUNCT
cana-4138	37	33	…	…	PUNCT
cana-4138	37	34	,	,	PUNCT
cana-4138	37	35	𝑛	𝑛	PRON
cana-4138	37	36	−	−	PROPN
cana-4138	37	37	3	3	NUM
cana-4138	37	38	,	,	PUNCT
cana-4138	37	39	𝑛	𝑛	DET
cana-4138	37	40	−	−	PROPN
cana-4138	37	41	2	2	NUM
cana-4138	37	42	,	,	PUNCT
cana-4138	37	43	𝑛	𝑛	PRON
cana-4138	37	44	−	−	PROPN
cana-4138	37	45	1	1	NUM
cana-4138	37	46	)	)	PUNCT
cana-4138	37	47	,	,	PUNCT
cana-4138	37	48	𝐷𝛼	𝐷𝛼	NOUN
cana-4138	37	49	being	be	AUX
cana-4138	37	50	the	the	DET
cana-4138	37	51	caputo	caputo	PROPN
cana-4138	37	52	fractional	fractional	PROPN
cana-4138	37	53	derivative	derivative	NOUN
cana-4138	37	54	of	of	ADP
cana-4138	37	55	order	order	NOUN
cana-4138	37	56	𝛼	𝛼	X
cana-4138	37	57	,	,	PUNCT
cana-4138	37	58	𝑓	𝑓	PRON
cana-4138	37	59	is	be	AUX
cana-4138	37	60	a	a	DET
cana-4138	37	61	continuous	continuous	ADJ
cana-4138	37	62	function	function	NOUN
cana-4138	37	63	from	from	ADP
cana-4138	37	64	[	[	X
cana-4138	37	65	0	0	NUM
cana-4138	37	66	,	,	PUNCT
cana-4138	37	67	1	1	NUM
cana-4138	37	68	]	]	SYM
cana-4138	37	69	×	×	NOUN
cana-4138	37	70	ℝ+	ℝ+	PUNCT
cana-4138	37	71	3	3	NUM
cana-4138	37	72	→	→	SYM
cana-4138	37	73	ℝ+	ℝ+	ADJ
cana-4138	37	74	,	,	PUNCT
cana-4138	37	75	𝑇	𝑇	PROPN
cana-4138	37	76	and	and	CCONJ
cana-4138	37	77	𝑆	𝑆	PROPN
cana-4138	37	78	are	be	AUX
cana-4138	37	79	defined	define	VERB
cana-4138	37	80	by	by	ADP
cana-4138	37	81	(	(	PUNCT
cana-4138	37	82	𝑇𝑥)(𝑡	𝑇𝑥)(𝑡	PROPN
cana-4138	37	83	)	)	PUNCT
cana-4138	37	84	=	=	SYM
cana-4138	38	1	∫	∫	PROPN
cana-4138	38	2	𝐾(𝑡	𝐾(𝑡	PROPN
cana-4138	38	3	,	,	PUNCT
cana-4138	38	4	𝑠	𝑠	NOUN
cana-4138	38	5	)	)	PUNCT
cana-4138	38	6	𝑥(𝑠	𝑥(𝑠	NOUN
cana-4138	38	7	)	)	PUNCT
cana-4138	38	8	𝑑𝑠	𝑑𝑠	NOUN
cana-4138	38	9	,	,	PUNCT
cana-4138	38	10	(	(	PUNCT
cana-4138	38	11	𝑆𝑥)(𝑡	𝑆𝑥)(𝑡	PROPN
cana-4138	38	12	)	)	PUNCT
cana-4138	38	13	=	=	SYM
cana-4138	38	14	1	1	NUM
cana-4138	38	15	0	0	NUM
cana-4138	38	16	∫	∫	PROPN
cana-4138	38	17	𝐻(𝑡	𝐻(𝑡	PROPN
cana-4138	38	18	,	,	PUNCT
cana-4138	38	19	𝑠	𝑠	NOUN
cana-4138	38	20	)	)	PUNCT
cana-4138	38	21	𝑥(𝑠	𝑥(𝑠	NOUN
cana-4138	38	22	)	)	PUNCT
cana-4138	38	23	𝑑𝑠	𝑑𝑠	ADV
cana-4138	38	24	1	1	NUM
cana-4138	38	25	0	0	NUM
cana-4138	38	26	𝐾∗	𝐾∗	NUM
cana-4138	39	1	=	=	SYM
cana-4138	39	2	sup	sup	PROPN
cana-4138	39	3	𝑡∈[0	𝑡∈[0	PROPN
cana-4138	39	4	,	,	PUNCT
cana-4138	39	5	1	1	NUM
cana-4138	39	6	]	]	PUNCT
cana-4138	39	7	∫	∫	PROPN
cana-4138	39	8	𝐾(𝑡	𝐾(𝑡	PROPN
cana-4138	39	9	,	,	PUNCT
cana-4138	39	10	𝑠	𝑠	PROPN
cana-4138	39	11	)	)	PUNCT
cana-4138	39	12	𝑑𝑠	𝑑𝑠	NOUN
cana-4138	39	13	𝑡	𝑡	PROPN
cana-4138	39	14	0	0	NUM
cana-4138	39	15	,	,	PUNCT
cana-4138	39	16	𝐻∗	𝐻∗	NUM
cana-4138	39	17	=	=	SYM
cana-4138	39	18	sup	sup	NOUN
cana-4138	39	19	𝑡∈[0	𝑡∈[0	PROPN
cana-4138	39	20	,	,	PUNCT
cana-4138	39	21	1	1	NUM
cana-4138	39	22	]	]	PUNCT
cana-4138	39	23	∫	∫	PROPN
cana-4138	39	24	𝐻(𝑡	𝐻(𝑡	PROPN
cana-4138	39	25	,	,	PUNCT
cana-4138	39	26	𝑠	𝑠	PROPN
cana-4138	39	27	)	)	PUNCT
cana-4138	39	28	𝑑𝑠	𝑑𝑠	NOUN
cana-4138	39	29	𝑡	𝑡	PROPN
cana-4138	39	30	0	0	NUM
cana-4138	39	31	where	where	SCONJ
cana-4138	39	32	𝐾	𝐾	PROPN
cana-4138	39	33	∈	∈	PROPN
cana-4138	39	34	𝐶(𝐷	𝐶(𝐷	NOUN
cana-4138	39	35	,	,	PUNCT
cana-4138	39	36	ℝ+	ℝ+	NOUN
cana-4138	39	37	)	)	PUNCT
cana-4138	39	38	,	,	PUNCT
cana-4138	39	39	𝐻	𝐻	PROPN
cana-4138	39	40	∈	∈	PROPN
cana-4138	39	41	𝐶([0	𝐶([0	PROPN
cana-4138	39	42	,	,	PUNCT
cana-4138	39	43	1	1	NUM
cana-4138	39	44	]	]	SYM
cana-4138	39	45	×	×	NOUN
cana-4138	39	46	[	[	X
cana-4138	39	47	0	0	NUM
cana-4138	39	48	,	,	PUNCT
cana-4138	39	49	1	1	NUM
cana-4138	39	50	]	]	PUNCT
cana-4138	39	51	,	,	PUNCT
cana-4138	39	52	ℝ+	ℝ+	PUNCT
cana-4138	39	53	)	)	PUNCT
cana-4138	39	54	the	the	DET
cana-4138	39	55	authors	author	NOUN
cana-4138	39	56	in	in	ADP
cana-4138	39	57	[	[	X
cana-4138	39	58	8	8	NUM
cana-4138	39	59	,	,	PUNCT
cana-4138	39	60	9	9	NUM
cana-4138	39	61	]	]	PUNCT
cana-4138	39	62	have	have	AUX
cana-4138	39	63	obtained	obtain	VERB
cana-4138	39	64	the	the	DET
cana-4138	39	65	results	result	NOUN
cana-4138	39	66	stating	state	VERB
cana-4138	39	67	the	the	DET
cana-4138	39	68	existence	existence	NOUN
cana-4138	39	69	and	and	CCONJ
cana-4138	39	70	uniqueness	uniqueness	NOUN
cana-4138	39	71	of	of	ADP
cana-4138	39	72	the	the	DET
cana-4138	39	73	solutions	solution	NOUN
cana-4138	39	74	of	of	ADP
cana-4138	39	75	the	the	DET
cana-4138	39	76	fractional	fractional	ADJ
cana-4138	39	77	integro	integro	ADJ
cana-4138	39	78	-	-	PUNCT
cana-4138	39	79	differential	differential	NOUN
cana-4138	39	80	equations	equation	NOUN
cana-4138	39	81	under	under	ADP
cana-4138	39	82	different	different	ADJ
cana-4138	39	83	boundary	boundary	ADJ
cana-4138	39	84	conditions	condition	NOUN
cana-4138	39	85	.	.	PUNCT
cana-4138	40	1	in	in	ADP
cana-4138	40	2	[	[	X
cana-4138	40	3	10	10	NUM
cana-4138	40	4	]	]	PUNCT
cana-4138	40	5	,	,	PUNCT
cana-4138	40	6	bragdi	bragdi	PROPN
cana-4138	40	7	,	,	PUNCT
cana-4138	40	8	a.	a.	PROPN
cana-4138	40	9	et	et	PROPN
cana-4138	40	10	al	al	PROPN
cana-4138	40	11	.	.	PROPN
cana-4138	40	12	have	have	AUX
cana-4138	40	13	obtained	obtain	VERB
cana-4138	40	14	the	the	DET
cana-4138	40	15	solution	solution	NOUN
cana-4138	40	16	of	of	ADP
cana-4138	40	17	the	the	DET
cana-4138	40	18	bvp	bvp	NOUN
cana-4138	40	19	given	give	VERB
cana-4138	40	20	by	by	ADP
cana-4138	40	21	𝐷𝛼(𝐷𝛽)𝑢(𝑡	𝐷𝛼(𝐷𝛽)𝑢(𝑡	NOUN
cana-4138	40	22	)	)	PUNCT
cana-4138	40	23	=	=	PUNCT
cana-4138	41	1	𝑓(𝑡	𝑓(𝑡	NOUN
cana-4138	41	2	,	,	PUNCT
cana-4138	41	3	𝑢(𝑡	𝑢(𝑡	NOUN
cana-4138	41	4	)	)	PUNCT
cana-4138	41	5	,	,	PUNCT
cana-4138	41	6	𝜙𝑢(𝑡	𝜙𝑢(𝑡	NOUN
cana-4138	41	7	)	)	PUNCT
cana-4138	41	8	,	,	PUNCT
cana-4138	41	9	𝜓𝑢(𝑡	𝜓𝑢(𝑡	NOUN
cana-4138	41	10	)	)	PUNCT
cana-4138	41	11	)	)	PUNCT
cana-4138	41	12	communications	communication	NOUN
cana-4138	41	13	on	on	ADP
cana-4138	41	14	applied	apply	VERB
cana-4138	41	15	nonlinear	nonlinear	ADJ
cana-4138	41	16	analysis	analysis	NOUN
cana-4138	41	17	issn	issn	NOUN
cana-4138	41	18	:	:	PUNCT
cana-4138	41	19	1074	1074	NUM
cana-4138	41	20	-	-	PUNCT
cana-4138	41	21	133x	133x	NUM
cana-4138	41	22	vol	vol	NOUN
cana-4138	41	23	32	32	NUM
cana-4138	41	24	no	no	NOUN
cana-4138	41	25	.	.	PUNCT
cana-4138	42	1	9s	9s	NUM
cana-4138	42	2	(	(	PUNCT
cana-4138	42	3	2025	2025	NUM
cana-4138	42	4	)	)	PUNCT
cana-4138	42	5	1305	1305	NUM
cana-4138	42	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4138	43	1	under	under	ADP
cana-4138	43	2	the	the	DET
cana-4138	43	3	boundary	boundary	ADJ
cana-4138	43	4	conditions	condition	NOUN
cana-4138	43	5	given	give	VERB
cana-4138	43	6	by	by	ADP
cana-4138	43	7	𝑢(1	𝑢(1	NOUN
cana-4138	43	8	)	)	PUNCT
cana-4138	43	9	=	=	SYM
cana-4138	43	10	𝑢(0	𝑢(0	PROPN
cana-4138	43	11	)	)	PUNCT
cana-4138	43	12	=	=	PUNCT
cana-4138	44	1	𝑢′(0	𝑢′(0	NOUN
cana-4138	44	2	)	)	PUNCT
cana-4138	44	3	=	=	SYM
cana-4138	44	4	0	0	NUM
cana-4138	44	5	where	where	SCONJ
cana-4138	44	6	it	it	PRON
cana-4138	44	7	is	be	AUX
cana-4138	44	8	assumed	assume	VERB
cana-4138	44	9	that	that	SCONJ
cana-4138	44	10	1	1	NUM
cana-4138	44	11	<	<	X
cana-4138	44	12	𝛼	𝛼	X
cana-4138	44	13	≤	≤	NUM
cana-4138	44	14	2	2	NUM
cana-4138	44	15	,	,	PUNCT
cana-4138	44	16	0	0	NUM
cana-4138	44	17	<	<	X
cana-4138	44	18	𝛽	𝛽	X
cana-4138	44	19	≤	≤	NUM
cana-4138	44	20	1	1	NUM
cana-4138	44	21	,	,	PUNCT
cana-4138	44	22	𝑓	𝑓	DET
cana-4138	44	23	∶	∶	NOUN
cana-4138	44	24	𝐼	𝐼	ADP
cana-4138	44	25	×	×	PROPN
cana-4138	44	26	ℝ3	ℝ3	PROPN
cana-4138	44	27	→	→	SYM
cana-4138	44	28	ℝ	ℝ	PROPN
cana-4138	44	29	,	,	PUNCT
cana-4138	44	30	𝐼	𝐼	PROPN
cana-4138	44	31	=	=	SYM
cana-4138	45	1	[	[	X
cana-4138	45	2	0	0	NUM
cana-4138	45	3	,	,	PUNCT
cana-4138	45	4	1	1	NUM
cana-4138	45	5	]	]	PUNCT
cana-4138	45	6	,	,	PUNCT
cana-4138	45	7	the	the	DET
cana-4138	45	8	function	function	NOUN
cana-4138	45	9	𝑓	𝑓	NOUN
cana-4138	45	10	is	be	AUX
cana-4138	45	11	continuous	continuous	ADJ
cana-4138	45	12	and	and	CCONJ
cana-4138	45	13	𝜙(𝑢)(𝑡	𝜙(𝑢)(𝑡	PROPN
cana-4138	45	14	)	)	PUNCT
cana-4138	45	15	=	=	SYM
cana-4138	45	16	∫	∫	PROPN
cana-4138	45	17	𝛾(𝑡	𝛾(𝑡	PROPN
cana-4138	45	18	,	,	PUNCT
cana-4138	45	19	𝑠)𝑢(𝑠	𝑠)𝑢(𝑠	PROPN
cana-4138	45	20	)	)	PUNCT
cana-4138	45	21	𝑑𝑠	𝑑𝑠	NOUN
cana-4138	45	22	,	,	PUNCT
cana-4138	45	23	𝑡	𝑡	X
cana-4138	45	24	0	0	NUM
cana-4138	45	25	𝜓(𝑢)(𝑡	𝜓(𝑢)(𝑡	NUM
cana-4138	45	26	)	)	PUNCT
cana-4138	45	27	=	=	SYM
cana-4138	46	1	∫	∫	PROPN
cana-4138	46	2	𝜆(𝑡	𝜆(𝑡	PROPN
cana-4138	46	3	,	,	PUNCT
cana-4138	46	4	𝑠)𝑢(𝑠	𝑠)𝑢(𝑠	PROPN
cana-4138	46	5	)	)	PUNCT
cana-4138	46	6	𝑑𝑠	𝑑𝑠	ADP
cana-4138	46	7	𝑡	𝑡	PROPN
cana-4138	46	8	0	0	PROPN
cana-4138	46	9	𝛾	𝛾	NOUN
cana-4138	46	10	,	,	PUNCT
cana-4138	46	11	𝜆	𝜆	DET
cana-4138	46	12	∶	∶	NOUN
cana-4138	46	13	𝐼	𝐼	ADP
cana-4138	46	14	×	×	NOUN
cana-4138	46	15	𝐼	𝐼	NOUN
cana-4138	46	16	→	→	SYM
cana-4138	46	17	[	[	X
cana-4138	46	18	0	0	NUM
cana-4138	46	19	,	,	PUNCT
cana-4138	46	20	1	1	NUM
cana-4138	46	21	)	)	PUNCT
cana-4138	46	22	,	,	PUNCT
cana-4138	46	23	𝑠𝑢𝑝	𝑠𝑢𝑝	NOUN
cana-4138	46	24	∫	∫	PROPN
cana-4138	46	25	𝜆(𝑡	𝜆(𝑡	PROPN
cana-4138	46	26	,	,	PUNCT
cana-4138	46	27	𝑠	𝑠	PROPN
cana-4138	46	28	)	)	PUNCT
cana-4138	46	29	𝑑𝑠	𝑑𝑠	ADV
cana-4138	46	30	1	1	NUM
cana-4138	46	31	0	0	NUM
cana-4138	46	32	<	<	X
cana-4138	46	33	∞	∞	PROPN
cana-4138	46	34	,	,	PUNCT
cana-4138	46	35	𝑠𝑢𝑝	𝑠𝑢𝑝	NOUN
cana-4138	46	36	∫	∫	PROPN
cana-4138	46	37	𝛾(𝑡	𝛾(𝑡	PROPN
cana-4138	46	38	,	,	PUNCT
cana-4138	46	39	𝑠	𝑠	PROPN
cana-4138	46	40	)	)	PUNCT
cana-4138	46	41	𝑑𝑠	𝑑𝑠	ADV
cana-4138	46	42	1	1	NUM
cana-4138	46	43	0	0	NUM
cana-4138	46	44	<	<	X
cana-4138	46	45	∞.	∞.	PROPN
cana-4138	46	46	ibnelazyz	ibnelazyz	PROPN
cana-4138	46	47	,	,	PUNCT
cana-4138	46	48	l.	l.	PROPN
cana-4138	46	49	et	et	PROPN
cana-4138	46	50	al.[11	al.[11	PROPN
cana-4138	46	51	]	]	PUNCT
cana-4138	46	52	have	have	AUX
cana-4138	46	53	explored	explore	VERB
cana-4138	46	54	the	the	DET
cana-4138	46	55	existence	existence	NOUN
cana-4138	46	56	and	and	CCONJ
cana-4138	46	57	uniqueness	uniqueness	NOUN
cana-4138	46	58	for	for	ADP
cana-4138	46	59	a	a	DET
cana-4138	46	60	nonlinear	nonlinear	ADJ
cana-4138	46	61	fractional	fractional	ADJ
cana-4138	46	62	integrodifferential	integrodifferential	ADJ
cana-4138	46	63	equations	equation	NOUN
cana-4138	46	64	with	with	ADP
cana-4138	46	65	integral	integral	ADJ
cana-4138	46	66	and	and	CCONJ
cana-4138	46	67	anti	anti	ADJ
cana-4138	46	68	-	-	ADJ
cana-4138	46	69	periodic	periodic	ADJ
cana-4138	46	70	boundary	boundary	ADJ
cana-4138	46	71	conditions	condition	NOUN
cana-4138	46	72	where	where	SCONJ
cana-4138	46	73	the	the	DET
cana-4138	46	74	existence	existence	NOUN
cana-4138	46	75	is	be	AUX
cana-4138	46	76	proved	prove	VERB
cana-4138	46	77	by	by	ADP
cana-4138	46	78	means	mean	NOUN
cana-4138	46	79	of	of	ADP
cana-4138	46	80	krasnoselskii	krasnoselskii	PROPN
cana-4138	46	81	’s	’s	PART
cana-4138	46	82	fixed	fix	VERB
cana-4138	46	83	point	point	NOUN
cana-4138	46	84	theorem	theorem	NOUN
cana-4138	46	85	and	and	CCONJ
cana-4138	46	86	the	the	DET
cana-4138	46	87	uniqueness	uniqueness	NOUN
cana-4138	46	88	of	of	ADP
cana-4138	46	89	solutions	solution	NOUN
cana-4138	46	90	is	be	AUX
cana-4138	46	91	established	establish	VERB
cana-4138	46	92	via	via	ADP
cana-4138	46	93	the	the	DET
cana-4138	46	94	banach	banach	NOUN
cana-4138	46	95	’s	’s	PART
cana-4138	46	96	contraction	contraction	NOUN
cana-4138	46	97	principle	principle	NOUN
cana-4138	46	98	.	.	PUNCT
cana-4138	47	1	in	in	ADP
cana-4138	47	2	[	[	X
cana-4138	47	3	12	12	NUM
cana-4138	47	4	]	]	PUNCT
cana-4138	47	5	,	,	PUNCT
cana-4138	47	6	kamble	kamble	PROPN
cana-4138	47	7	,	,	PUNCT
cana-4138	47	8	r.	r.	PROPN
cana-4138	47	9	,	,	PUNCT
cana-4138	47	10	and	and	CCONJ
cana-4138	47	11	kukarni	kukarni	PROPN
cana-4138	47	12	,	,	PUNCT
cana-4138	47	13	p.	p.	PROPN
cana-4138	47	14	have	have	AUX
cana-4138	47	15	proved	prove	VERB
cana-4138	47	16	the	the	DET
cana-4138	47	17	existence	existence	NOUN
cana-4138	47	18	and	and	CCONJ
cana-4138	47	19	uniqueness	uniqueness	NOUN
cana-4138	47	20	of	of	ADP
cana-4138	47	21	solutions	solution	NOUN
cana-4138	47	22	for	for	ADP
cana-4138	47	23	the	the	DET
cana-4138	47	24	following	follow	VERB
cana-4138	47	25	equation	equation	NOUN
cana-4138	47	26	𝐷𝛼𝐷𝛽𝑥(𝜏	𝐷𝛼𝐷𝛽𝑥(𝜏	PROPN
cana-4138	47	27	)	)	PUNCT
cana-4138	48	1	=	=	PUNCT
cana-4138	49	1	𝑓(𝑡	𝑓(𝑡	NOUN
cana-4138	49	2	,	,	PUNCT
cana-4138	49	3	𝑥(𝜏	𝑥(𝜏	PROPN
cana-4138	49	4	)	)	PUNCT
cana-4138	49	5	,	,	PUNCT
cana-4138	49	6	𝜙𝑥(𝜏	𝜙𝑥(𝜏	ADJ
cana-4138	49	7	)	)	PUNCT
cana-4138	49	8	,	,	PUNCT
cana-4138	49	9	𝜓𝑥(𝜏	𝜓𝑥(𝜏	NUM
cana-4138	49	10	)	)	PUNCT
cana-4138	49	11	)	)	PUNCT
cana-4138	49	12	,	,	PUNCT
cana-4138	49	13	𝜏𝜖[0,1	𝜏𝜖[0,1	PROPN
cana-4138	49	14	]	]	PUNCT
cana-4138	49	15	,	,	PUNCT
cana-4138	49	16	𝑥(0	𝑥(0	PROPN
cana-4138	49	17	)	)	PUNCT
cana-4138	50	1	=	=	PUNCT
cana-4138	50	2	𝑥(1	𝑥(1	NOUN
cana-4138	50	3	)	)	PUNCT
cana-4138	50	4	=	=	SYM
cana-4138	50	5	0	0	NUM
cana-4138	50	6	where	where	SCONJ
cana-4138	50	7	0	0	X
cana-4138	50	8	<	<	X
cana-4138	50	9	α	α	PRON
cana-4138	50	10	≤	≤	NUM
cana-4138	50	11	1	1	NUM
cana-4138	50	12	,	,	PUNCT
cana-4138	50	13	0	0	PUNCT
cana-4138	50	14	<	<	X
cana-4138	50	15	β	β	X
cana-4138	50	16	≤	≤	NUM
cana-4138	50	17	1	1	NUM
cana-4138	50	18	,	,	PUNCT
cana-4138	50	19	𝐷𝛼	𝐷𝛼	NOUN
cana-4138	50	20	,	,	PUNCT
cana-4138	50	21	𝐷𝛽	𝐷𝛽	PROPN
cana-4138	50	22	are	be	AUX
cana-4138	50	23	the	the	DET
cana-4138	50	24	caputo	caputo	PROPN
cana-4138	50	25	fractional	fractional	ADJ
cana-4138	50	26	derivatives	derivative	NOUN
cana-4138	50	27	of	of	ADP
cana-4138	50	28	order	order	NOUN
cana-4138	50	29	𝛼	𝛼	X
cana-4138	50	30	,	,	PUNCT
cana-4138	50	31	𝛽	𝛽	PROPN
cana-4138	50	32	,	,	PUNCT
cana-4138	50	33	𝜆	𝜆	NOUN
cana-4138	50	34	,	,	PUNCT
cana-4138	50	35	𝛿	𝛿	ADJ
cana-4138	50	36	:	:	PUNCT
cana-4138	50	37	[	[	X
cana-4138	50	38	0,1	0,1	NUM
cana-4138	50	39	]	]	X
cana-4138	50	40	×	×	NOUN
cana-4138	51	1	[	[	X
cana-4138	51	2	0	0	NUM
cana-4138	51	3	,	,	PUNCT
cana-4138	51	4	1	1	NUM
cana-4138	51	5	]	]	PUNCT
cana-4138	51	6	→	→	PUNCT
cana-4138	52	1	[	[	X
cana-4138	52	2	0	0	NUM
cana-4138	52	3	,	,	PUNCT
cana-4138	52	4	+	+	NOUN
cana-4138	52	5	∞	∞	NOUN
cana-4138	52	6	)	)	PUNCT
cana-4138	52	7	,	,	PUNCT
cana-4138	52	8	f	f	X
cana-4138	52	9	:	:	PUNCT
cana-4138	53	1	[	[	X
cana-4138	53	2	0	0	NUM
cana-4138	53	3	,	,	PUNCT
cana-4138	53	4	1	1	NUM
cana-4138	53	5	]	]	SYM
cana-4138	53	6	×	×	NOUN
cana-4138	53	7	ℝ3	ℝ3	PROPN
cana-4138	53	8	⟶	⟶	NOUN
cana-4138	53	9	ℝ	ℝ	PROPN
cana-4138	53	10	is	be	AUX
cana-4138	53	11	a	a	DET
cana-4138	53	12	continuous	continuous	ADJ
cana-4138	53	13	function	function	NOUN
cana-4138	53	14	,	,	PUNCT
cana-4138	53	15	and	and	CCONJ
cana-4138	53	16	𝜙𝑥(𝜏	𝜙𝑥(𝜏	X
cana-4138	53	17	)	)	PUNCT
cana-4138	54	1	=	=	SYM
cana-4138	55	1	∫	∫	PROPN
cana-4138	55	2	𝜆(𝜏	𝜆(𝜏	PROPN
cana-4138	55	3	,	,	PUNCT
cana-4138	55	4	𝑠)𝑥(𝑠)𝑑𝑠	𝑠)𝑥(𝑠)𝑑𝑠	VERB
cana-4138	55	5	𝜏	𝜏	ADP
cana-4138	55	6	0	0	NUM
cana-4138	55	7	,	,	PUNCT
cana-4138	55	8	𝜓𝑥(𝜏	𝜓𝑥(𝜏	NUM
cana-4138	55	9	)	)	PUNCT
cana-4138	55	10	=	=	SYM
cana-4138	55	11	∫	∫	PROPN
cana-4138	55	12	𝛿(𝜏	𝛿(𝜏	PROPN
cana-4138	55	13	,	,	PUNCT
cana-4138	55	14	𝑠)𝑥(𝑠)𝑑𝑠	𝑠)𝑥(𝑠)𝑑𝑠	VERB
cana-4138	55	15	𝜏	𝜏	PRON
cana-4138	55	16	0	0	NUM
cana-4138	55	17	𝜙∗	𝜙∗	NOUN
cana-4138	55	18	=	=	NOUN
cana-4138	55	19	sup	sup	NOUN
cana-4138	55	20	𝑡∈[0,1	𝑡∈[0,1	NOUN
cana-4138	55	21	]	]	PUNCT
cana-4138	55	22	|∫	|∫	X
cana-4138	55	23	𝜆(𝜏	𝜆(𝜏	PROPN
cana-4138	55	24	,	,	PUNCT
cana-4138	55	25	𝑠)𝑑𝑠	𝑠)𝑑𝑠	PROPN
cana-4138	55	26	𝑡	𝑡	X
cana-4138	55	27	0	0	NUM
cana-4138	56	1	|	|	CCONJ
cana-4138	56	2	<	<	X
cana-4138	56	3	∞	∞	PROPN
cana-4138	56	4	,	,	PUNCT
cana-4138	56	5	𝜓∗	𝜓∗	NOUN
cana-4138	56	6	=	=	SYM
cana-4138	56	7	sup	sup	NOUN
cana-4138	56	8	𝑡∈[0,1	𝑡∈[0,1	NOUN
cana-4138	56	9	]	]	PUNCT
cana-4138	56	10	|∫	|∫	X
cana-4138	56	11	𝛿(𝜏	𝛿(𝜏	NOUN
cana-4138	56	12	,	,	PUNCT
cana-4138	56	13	𝑠)𝑑𝑠	𝑠)𝑑𝑠	PROPN
cana-4138	56	14	𝑡	𝑡	X
cana-4138	56	15	0	0	NUM
cana-4138	57	1	|	|	CCONJ
cana-4138	57	2	<	<	X
cana-4138	57	3	∞	∞	PROPN
cana-4138	57	4	,	,	PUNCT
cana-4138	57	5	2	2	NUM
cana-4138	57	6	.	.	PUNCT
cana-4138	58	1	some	some	DET
cana-4138	58	2	preliminary	preliminary	ADJ
cana-4138	58	3	concepts	concept	NOUN
cana-4138	58	4	in	in	ADP
cana-4138	58	5	fixed	fix	VERB
cana-4138	58	6	point	point	NOUN
cana-4138	58	7	theory	theory	NOUN
cana-4138	58	8	and	and	CCONJ
cana-4138	58	9	results	result	NOUN
cana-4138	58	10	in	in	ADP
cana-4138	58	11	this	this	DET
cana-4138	58	12	section	section	NOUN
cana-4138	58	13	,	,	PUNCT
cana-4138	58	14	we	we	PRON
cana-4138	58	15	take	take	VERB
cana-4138	58	16	a	a	DET
cana-4138	58	17	look	look	NOUN
cana-4138	58	18	on	on	ADP
cana-4138	58	19	the	the	DET
cana-4138	58	20	basic	basic	ADJ
cana-4138	58	21	concepts	concept	NOUN
cana-4138	58	22	in	in	ADP
cana-4138	58	23	fixed	fix	VERB
cana-4138	58	24	point	point	NOUN
cana-4138	58	25	theory	theory	NOUN
cana-4138	58	26	.	.	PUNCT
cana-4138	59	1	definition	definition	NOUN
cana-4138	59	2	2.1	2.1	NUM
cana-4138	59	3	:	:	PUNCT
cana-4138	59	4	let	let	VERB
cana-4138	59	5	𝑋	𝑋	NOUN
cana-4138	59	6	be	be	AUX
cana-4138	59	7	a	a	DET
cana-4138	59	8	banach	banach	NOUN
cana-4138	59	9	space	space	NOUN
cana-4138	59	10	over	over	ADP
cana-4138	59	11	the	the	DET
cana-4138	59	12	set	set	NOUN
cana-4138	59	13	of	of	ADP
cana-4138	59	14	real	real	ADJ
cana-4138	59	15	numbers	number	NOUN
cana-4138	59	16	.	.	PUNCT
cana-4138	60	1	a	a	DET
cana-4138	60	2	subset	subset	ADJ
cana-4138	60	3	𝐸	𝐸	PROPN
cana-4138	60	4	of	of	ADP
cana-4138	60	5	𝑋	𝑋	PROPN
cana-4138	60	6	is	be	AUX
cana-4138	60	7	called	call	VERB
cana-4138	60	8	a	a	DET
cana-4138	60	9	cone	cone	NOUN
cana-4138	60	10	if	if	SCONJ
cana-4138	60	11	1	1	NUM
cana-4138	60	12	)	)	PUNCT
cana-4138	60	13	𝐸	𝐸	PROPN
cana-4138	60	14	is	be	AUX
cana-4138	60	15	closed	close	VERB
cana-4138	60	16	,	,	PUNCT
cana-4138	60	17	non	non	ADJ
cana-4138	60	18	-	-	ADJ
cana-4138	60	19	empty	empty	ADJ
cana-4138	60	20	with	with	ADP
cana-4138	60	21	𝐸	𝐸	PROPN
cana-4138	60	22	≠	≠	PROPN
cana-4138	60	23	{	{	PUNCT
cana-4138	60	24	0	0	NUM
cana-4138	60	25	}	}	SYM
cana-4138	60	26	2	2	NUM
cana-4138	60	27	)	)	PUNCT
cana-4138	61	1	𝑐𝑥	𝑐𝑥	ADV
cana-4138	61	2	+	+	NUM
cana-4138	61	3	𝑑𝑦	𝑑𝑦	NOUN
cana-4138	61	4	∈	∈	PROPN
cana-4138	61	5	𝐸	𝐸	PROPN
cana-4138	61	6	whenever	whenever	SCONJ
cana-4138	61	7	𝑐	𝑐	X
cana-4138	61	8	,	,	PUNCT
cana-4138	61	9	𝑑	𝑑	PROPN
cana-4138	61	10	∈	∈	PROPN
cana-4138	61	11	ℝ	ℝ	PROPN
cana-4138	61	12	and	and	CCONJ
cana-4138	61	13	𝑥	𝑥	NOUN
cana-4138	61	14	,	,	PUNCT
cana-4138	61	15	𝑦	𝑦	PROPN
cana-4138	61	16	∈	∈	NOUN
cana-4138	61	17	𝐸	𝐸	PROPN
cana-4138	61	18	3	3	NUM
cana-4138	61	19	)	)	PUNCT
cana-4138	61	20	𝑥	𝑥	NOUN
cana-4138	62	1	=	=	SYM
cana-4138	62	2	0	0	NUM
cana-4138	62	3	whenever	whenever	SCONJ
cana-4138	62	4	both	both	DET
cana-4138	62	5	𝑥	𝑥	ADP
cana-4138	62	6	,	,	PUNCT
cana-4138	62	7	−𝑥	−𝑥	NOUN
cana-4138	62	8	∈	∈	NOUN
cana-4138	62	9	𝐸	𝐸	PROPN
cana-4138	62	10	definition	definition	NOUN
cana-4138	62	11	2.2	2.2	NUM
cana-4138	62	12	:	:	PUNCT
cana-4138	62	13	for	for	ADP
cana-4138	62	14	a	a	DET
cana-4138	62	15	given	give	VERB
cana-4138	62	16	cone	cone	NOUN
cana-4138	62	17	𝐸	𝐸	PROPN
cana-4138	62	18	⊂	⊂	PROPN
cana-4138	62	19	𝑋	𝑋	PROPN
cana-4138	62	20	,	,	PUNCT
cana-4138	62	21	𝑋	𝑋	PROPN
cana-4138	62	22	being	be	AUX
cana-4138	62	23	a	a	DET
cana-4138	62	24	banach	banach	NOUN
cana-4138	62	25	space	space	NOUN
cana-4138	62	26	over	over	ADP
cana-4138	62	27	the	the	DET
cana-4138	62	28	set	set	NOUN
cana-4138	62	29	of	of	ADP
cana-4138	62	30	real	real	ADJ
cana-4138	62	31	numbers	number	NOUN
cana-4138	62	32	,	,	PUNCT
cana-4138	63	1	the	the	DET
cana-4138	63	2	relation	relation	NOUN
cana-4138	63	3	≤	≤	NUM
cana-4138	63	4	defined	define	VERB
cana-4138	63	5	on	on	ADP
cana-4138	63	6	𝐸	𝐸	PROPN
cana-4138	63	7	by	by	ADP
cana-4138	63	8	𝑥	𝑥	DET
cana-4138	63	9	≤	≤	NUM
cana-4138	63	10	𝑦	𝑦	NUM
cana-4138	63	11	⟺	⟺	NOUN
cana-4138	63	12	𝑦	𝑦	NOUN
cana-4138	63	13	−	−	X
cana-4138	64	1	𝑥	𝑥	PRON
cana-4138	64	2	∈	∈	PROPN
cana-4138	64	3	𝐸	𝐸	PROPN
cana-4138	64	4	is	be	AUX
cana-4138	64	5	a	a	DET
cana-4138	64	6	partial	partial	ADJ
cana-4138	64	7	ordering	ordering	NOUN
cana-4138	64	8	relation	relation	NOUN
cana-4138	64	9	.	.	PUNCT
cana-4138	65	1	the	the	DET
cana-4138	65	2	cone	cone	NOUN
cana-4138	65	3	𝐸	𝐸	PROPN
cana-4138	65	4	is	be	AUX
cana-4138	65	5	said	say	VERB
cana-4138	65	6	to	to	PART
cana-4138	65	7	be	be	AUX
cana-4138	65	8	normal	normal	ADJ
cana-4138	65	9	if	if	SCONJ
cana-4138	65	10	there	there	PRON
cana-4138	65	11	is	be	VERB
cana-4138	65	12	a	a	DET
cana-4138	65	13	real	real	ADJ
cana-4138	65	14	number	number	NOUN
cana-4138	65	15	𝑘	𝑘	ADP
cana-4138	65	16	>	>	X
cana-4138	65	17	0	0	NUM
cana-4138	66	1	such	such	ADJ
cana-4138	66	2	that	that	SCONJ
cana-4138	66	3	‖𝑥‖	‖𝑥‖	PROPN
cana-4138	66	4	≤	≤	ADJ
cana-4138	66	5	𝑘‖𝑦‖	𝑘‖𝑦‖	PROPN
cana-4138	66	6	∀	∀	X
cana-4138	66	7	𝑥	𝑥	NOUN
cana-4138	66	8	,	,	PUNCT
cana-4138	66	9	𝑦	𝑦	PRON
cana-4138	66	10	∈	∈	NOUN
cana-4138	66	11	𝐸.	𝐸.	VERB
cana-4138	66	12	the	the	DET
cana-4138	66	13	least	least	ADV
cana-4138	66	14	positive	positive	ADJ
cana-4138	66	15	number	number	NOUN
cana-4138	66	16	𝑘	𝑘	AUX
cana-4138	66	17	satisfying	satisfying	NOUN
cana-4138	66	18	above	above	ADV
cana-4138	66	19	is	be	AUX
cana-4138	66	20	called	call	VERB
cana-4138	66	21	the	the	DET
cana-4138	66	22	normal	normal	ADJ
cana-4138	66	23	constant	constant	NOUN
cana-4138	66	24	of	of	ADP
cana-4138	66	25	𝐸.	𝐸.	PROPN
cana-4138	66	26	definition	definition	NOUN
cana-4138	66	27	2.3	2.3	NUM
cana-4138	66	28	:	:	PUNCT
cana-4138	66	29	let	let	VERB
cana-4138	66	30	𝑋	𝑋	NOUN
cana-4138	66	31	be	be	AUX
cana-4138	66	32	a	a	DET
cana-4138	66	33	non	non	X
cana-4138	66	34	empty	empty	ADJ
cana-4138	66	35	real	real	ADJ
cana-4138	66	36	banach	banach	NOUN
cana-4138	66	37	space	space	NOUN
cana-4138	66	38	,	,	PUNCT
cana-4138	66	39	𝐸	𝐸	PROPN
cana-4138	66	40	be	be	VERB
cana-4138	66	41	a	a	DET
cana-4138	66	42	normal	normal	ADJ
cana-4138	66	43	cone	cone	NOUN
cana-4138	66	44	in	in	ADP
cana-4138	66	45	𝑋	𝑋	NOUN
cana-4138	66	46	with	with	ADP
cana-4138	66	47	≤	≤	NOUN
cana-4138	66	48	as	as	ADP
cana-4138	66	49	the	the	DET
cana-4138	66	50	partial	partial	ADJ
cana-4138	66	51	ordering	ordering	NOUN
cana-4138	66	52	relation	relation	NOUN
cana-4138	66	53	defined	define	VERB
cana-4138	66	54	on	on	ADP
cana-4138	66	55	𝐸.	𝐸.	PROPN
cana-4138	66	56	then	then	ADV
cana-4138	66	57	the	the	DET
cana-4138	66	58	mapping	mapping	NOUN
cana-4138	66	59	𝑑	𝑑	NOUN
cana-4138	66	60	:	:	PUNCT
cana-4138	66	61	𝑋	𝑋	NOUN
cana-4138	66	62	×	×	NOUN
cana-4138	66	63	𝑋	𝑋	PROPN
cana-4138	66	64	→	→	SYM
cana-4138	66	65	𝐸	𝐸	PROPN
cana-4138	66	66	satisfying	satisfy	VERB
cana-4138	66	67	1	1	NUM
cana-4138	66	68	)	)	PUNCT
cana-4138	66	69	0	0	NUM
cana-4138	67	1	≤	≤	NUM
cana-4138	67	2	𝑑(𝑥	𝑑(𝑥	PROPN
cana-4138	67	3	,	,	PUNCT
cana-4138	67	4	𝑦	𝑦	NOUN
cana-4138	67	5	)	)	PUNCT
cana-4138	67	6	∀	∀	PUNCT
cana-4138	68	1	𝑥	𝑥	NOUN
cana-4138	68	2	,	,	PUNCT
cana-4138	68	3	𝑦	𝑦	PROPN
cana-4138	68	4	∈	∈	NOUN
cana-4138	68	5	𝐸	𝐸	PROPN
cana-4138	68	6	2	2	NUM
cana-4138	68	7	)	)	PUNCT
cana-4138	68	8	𝑑(𝑥	𝑑(𝑥	PROPN
cana-4138	68	9	,	,	PUNCT
cana-4138	68	10	𝑦	𝑦	X
cana-4138	68	11	)	)	PUNCT
cana-4138	68	12	=	=	SYM
cana-4138	68	13	𝑑(𝑦	𝑑(𝑦	NOUN
cana-4138	68	14	,	,	PUNCT
cana-4138	68	15	𝑥	𝑥	NOUN
cana-4138	68	16	)	)	PUNCT
cana-4138	68	17	∀	∀	PUNCT
cana-4138	69	1	𝑥	𝑥	NOUN
cana-4138	69	2	,	,	PUNCT
cana-4138	69	3	𝑦	𝑦	NOUN
cana-4138	69	4	∈	∈	NOUN
cana-4138	69	5	𝐸	𝐸	PROPN
cana-4138	69	6	communications	communication	NOUN
cana-4138	69	7	on	on	ADP
cana-4138	69	8	applied	apply	VERB
cana-4138	69	9	nonlinear	nonlinear	ADJ
cana-4138	69	10	analysis	analysis	NOUN
cana-4138	69	11	issn	issn	NOUN
cana-4138	69	12	:	:	PUNCT
cana-4138	69	13	1074	1074	NUM
cana-4138	69	14	-	-	PUNCT
cana-4138	69	15	133x	133x	NUM
cana-4138	69	16	vol	vol	NOUN
cana-4138	69	17	32	32	NUM
cana-4138	69	18	no	no	NOUN
cana-4138	69	19	.	.	PUNCT
cana-4138	70	1	9s	9s	NUM
cana-4138	70	2	(	(	PUNCT
cana-4138	70	3	2025	2025	NUM
cana-4138	70	4	)	)	PUNCT
cana-4138	70	5	1306	1306	NUM
cana-4138	70	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4138	70	7	3	3	NUM
cana-4138	70	8	)	)	PUNCT
cana-4138	70	9	𝑑(𝑥	𝑑(𝑥	PROPN
cana-4138	70	10	,	,	PUNCT
cana-4138	70	11	𝑦	𝑦	NOUN
cana-4138	70	12	)	)	PUNCT
cana-4138	70	13	≤	≤	NOUN
cana-4138	70	14	𝑑(𝑥	𝑑(𝑥	PROPN
cana-4138	70	15	,	,	PUNCT
cana-4138	70	16	𝑧	𝑧	NOUN
cana-4138	70	17	)	)	PUNCT
cana-4138	70	18	+	+	X
cana-4138	70	19	𝑑(𝑧	𝑑(𝑧	PROPN
cana-4138	70	20	,	,	PUNCT
cana-4138	70	21	𝑦	𝑦	NOUN
cana-4138	70	22	)	)	PUNCT
cana-4138	70	23	)	)	PUNCT
cana-4138	70	24	∀	∀	PUNCT
cana-4138	71	1	𝑥	𝑥	NOUN
cana-4138	71	2	,	,	PUNCT
cana-4138	71	3	𝑦	𝑦	NOUN
cana-4138	71	4	,	,	PUNCT
cana-4138	71	5	𝑧	𝑧	DET
cana-4138	71	6	∈	∈	PROPN
cana-4138	71	7	𝐸	𝐸	PROPN
cana-4138	71	8	is	be	AUX
cana-4138	71	9	called	call	VERB
cana-4138	71	10	a	a	DET
cana-4138	71	11	cone	cone	NOUN
cana-4138	71	12	metric	metric	NOUN
cana-4138	71	13	on	on	ADP
cana-4138	71	14	𝑋	𝑋	PROPN
cana-4138	71	15	and	and	CCONJ
cana-4138	71	16	the	the	DET
cana-4138	71	17	space	space	NOUN
cana-4138	71	18	(	(	PUNCT
cana-4138	71	19	𝑋	𝑋	PROPN
cana-4138	71	20	,	,	PUNCT
cana-4138	71	21	𝑑	𝑑	NOUN
cana-4138	71	22	)	)	PUNCT
cana-4138	71	23	is	be	AUX
cana-4138	71	24	called	call	VERB
cana-4138	71	25	cone	cone	NOUN
cana-4138	71	26	metric	metric	ADJ
cana-4138	71	27	space	space	NOUN
cana-4138	71	28	.	.	PUNCT
cana-4138	72	1	definition	definition	NOUN
cana-4138	72	2	2.4	2.4	NUM
cana-4138	72	3	:	:	PUNCT
cana-4138	72	4	let	let	VERB
cana-4138	72	5	𝑋	𝑋	NOUN
cana-4138	72	6	be	be	AUX
cana-4138	72	7	an	an	DET
cana-4138	72	8	ordered	order	VERB
cana-4138	72	9	space	space	NOUN
cana-4138	72	10	.	.	PUNCT
cana-4138	73	1	a	a	DET
cana-4138	73	2	function	function	NOUN
cana-4138	73	3	𝜑	𝜑	NOUN
cana-4138	73	4	:	:	PUNCT
cana-4138	73	5	𝑋	𝑋	PROPN
cana-4138	73	6	→	→	SYM
cana-4138	73	7	𝑋	𝑋	PROPN
cana-4138	73	8	is	be	AUX
cana-4138	73	9	said	say	VERB
cana-4138	73	10	to	to	ADP
cana-4138	73	11	a	a	DET
cana-4138	73	12	comparison	comparison	NOUN
cana-4138	73	13	function	function	NOUN
cana-4138	73	14	if	if	SCONJ
cana-4138	73	15	for	for	ADP
cana-4138	73	16	every	every	DET
cana-4138	73	17	𝑥	𝑥	PROPN
cana-4138	73	18	,	,	PUNCT
cana-4138	73	19	𝑦	𝑦	NOUN
cana-4138	73	20	∈	∈	PROPN
cana-4138	73	21	𝑋	𝑋	PROPN
cana-4138	73	22	,	,	PUNCT
cana-4138	73	23	𝑥	𝑥	PROPN
cana-4138	73	24	≤	≤	NUM
cana-4138	73	25	𝑦	𝑦	NOUN
cana-4138	73	26	⟹	⟹	NUM
cana-4138	73	27	𝜑(𝑥	𝜑(𝑥	NOUN
cana-4138	73	28	)	)	PUNCT
cana-4138	73	29	≤	≤	NUM
cana-4138	73	30	𝜑(𝑦	𝜑(𝑦	NOUN
cana-4138	73	31	)	)	PUNCT
cana-4138	73	32	,	,	PUNCT
cana-4138	73	33	𝜑(𝑥	𝜑(𝑥	PROPN
cana-4138	73	34	)	)	PUNCT
cana-4138	73	35	≤	≤	NUM
cana-4138	73	36	𝑥	𝑥	PROPN
cana-4138	73	37	and	and	CCONJ
cana-4138	73	38	lim	lim	PROPN
cana-4138	73	39	𝑛→∞	𝑛→∞	NUM
cana-4138	73	40	‖𝜑𝑛(𝑥)‖	‖𝜑𝑛(𝑥)‖	PROPN
cana-4138	73	41	=	=	SYM
cana-4138	73	42	0	0	NUM
cana-4138	73	43	for	for	ADP
cana-4138	73	44	every	every	DET
cana-4138	73	45	𝑥	𝑥	PROPN
cana-4138	73	46	∈	∈	PROPN
cana-4138	73	47	𝑋.	𝑋.	PROPN
cana-4138	73	48	a	a	DET
cana-4138	73	49	more	more	ADV
cana-4138	73	50	detailed	detailed	ADJ
cana-4138	73	51	theory	theory	NOUN
cana-4138	73	52	and	and	CCONJ
cana-4138	73	53	examples	example	NOUN
cana-4138	73	54	on	on	ADP
cana-4138	73	55	cone	cone	NOUN
cana-4138	73	56	metric	metric	ADJ
cana-4138	73	57	spaces	space	NOUN
cana-4138	73	58	and	and	CCONJ
cana-4138	73	59	the	the	DET
cana-4138	73	60	different	different	ADJ
cana-4138	73	61	versions	version	NOUN
cana-4138	73	62	of	of	ADP
cana-4138	73	63	the	the	DET
cana-4138	73	64	fixed	fix	VERB
cana-4138	73	65	points	point	NOUN
cana-4138	73	66	theorems	theorem	NOUN
cana-4138	73	67	can	can	AUX
cana-4138	73	68	be	be	AUX
cana-4138	73	69	obtained	obtain	VERB
cana-4138	73	70	in	in	ADP
cana-4138	73	71	the	the	DET
cana-4138	73	72	books	book	NOUN
cana-4138	73	73	by	by	ADP
cana-4138	73	74	the	the	DET
cana-4138	73	75	authors	author	NOUN
cana-4138	73	76	smart	smart	ADJ
cana-4138	73	77	d.	d.	PROPN
cana-4138	73	78	and	and	CCONJ
cana-4138	73	79	o’regan	o’regan	PROPN
cana-4138	73	80	d	d	PROPN
cana-4138	74	1	[	[	X
cana-4138	74	2	13	13	NUM
cana-4138	74	3	,	,	PUNCT
cana-4138	74	4	14	14	NUM
cana-4138	74	5	]	]	PUNCT
cana-4138	74	6	.	.	PUNCT
cana-4138	75	1	we	we	PRON
cana-4138	75	2	will	will	AUX
cana-4138	75	3	take	take	VERB
cana-4138	75	4	a	a	DET
cana-4138	75	5	small	small	ADJ
cana-4138	75	6	review	review	NOUN
cana-4138	75	7	of	of	ADP
cana-4138	75	8	the	the	DET
cana-4138	75	9	research	research	NOUN
cana-4138	75	10	work	work	NOUN
cana-4138	75	11	on	on	ADP
cana-4138	75	12	cone	cone	NOUN
cana-4138	75	13	metric	metric	ADJ
cana-4138	75	14	spaces	space	NOUN
cana-4138	75	15	.	.	PUNCT
cana-4138	76	1	in	in	ADP
cana-4138	76	2	[	[	X
cana-4138	76	3	15	15	NUM
cana-4138	76	4	]	]	PUNCT
cana-4138	76	5	,	,	PUNCT
cana-4138	76	6	the	the	DET
cana-4138	76	7	authors	author	NOUN
cana-4138	76	8	have	have	AUX
cana-4138	76	9	proved	prove	VERB
cana-4138	76	10	the	the	DET
cana-4138	76	11	following	follow	VERB
cana-4138	76	12	result	result	NOUN
cana-4138	76	13	.	.	PUNCT
cana-4138	77	1	lemma	lemma	PROPN
cana-4138	77	2	2.1	2.1	NUM
cana-4138	77	3	:	:	PUNCT
cana-4138	77	4	let	let	VERB
cana-4138	77	5	(	(	PUNCT
cana-4138	77	6	𝑋	𝑋	NOUN
cana-4138	77	7	,	,	PUNCT
cana-4138	77	8	𝑑	𝑑	NOUN
cana-4138	77	9	)	)	PUNCT
cana-4138	77	10	be	be	VERB
cana-4138	77	11	a	a	DET
cana-4138	77	12	complete	complete	ADJ
cana-4138	77	13	cone	cone	NOUN
cana-4138	77	14	metric	metric	ADJ
cana-4138	77	15	space	space	NOUN
cana-4138	77	16	and	and	CCONJ
cana-4138	77	17	𝑃	𝑃	NOUN
cana-4138	77	18	be	be	VERB
cana-4138	77	19	a	a	DET
cana-4138	77	20	normal	normal	ADJ
cana-4138	77	21	cone	cone	NOUN
cana-4138	77	22	with	with	ADP
cana-4138	77	23	normal	normal	ADJ
cana-4138	77	24	constant	constant	ADJ
cana-4138	77	25	𝐾.	𝐾.	NOUN
cana-4138	77	26	let	let	VERB
cana-4138	77	27	𝑓	𝑓	PRON
cana-4138	77	28	:	:	PUNCT
cana-4138	77	29	𝑋	𝑋	PROPN
cana-4138	77	30	→	→	SYM
cana-4138	77	31	𝑋	𝑋	PROPN
cana-4138	77	32	be	be	VERB
cana-4138	77	33	a	a	DET
cana-4138	77	34	function	function	NOUN
cana-4138	77	35	such	such	ADJ
cana-4138	77	36	that	that	SCONJ
cana-4138	77	37	there	there	PRON
cana-4138	77	38	exists	exist	VERB
cana-4138	77	39	a	a	DET
cana-4138	77	40	comparison	comparison	NOUN
cana-4138	77	41	function	function	NOUN
cana-4138	77	42	𝜙	𝜙	NOUN
cana-4138	77	43	:	:	PUNCT
cana-4138	77	44	𝑃	𝑃	NOUN
cana-4138	77	45	⟶	⟶	NOUN
cana-4138	77	46	𝑃	𝑃	NOUN
cana-4138	77	47	such	such	ADJ
cana-4138	77	48	that	that	DET
cana-4138	77	49	𝑑(𝑓(𝑥	𝑑(𝑓(𝑥	NOUN
cana-4138	77	50	)	)	PUNCT
cana-4138	77	51	,	,	PUNCT
cana-4138	77	52	𝑓(𝑦	𝑓(𝑦	PROPN
cana-4138	77	53	)	)	PUNCT
cana-4138	77	54	)	)	PUNCT
cana-4138	78	1	≤	≤	NUM
cana-4138	78	2	𝜙(𝑑(𝑥	𝜙(𝑑(𝑥	PROPN
cana-4138	78	3	,	,	PUNCT
cana-4138	78	4	𝑦	𝑦	NOUN
cana-4138	78	5	)	)	PUNCT
cana-4138	78	6	∀	∀	PUNCT
cana-4138	79	1	𝑥	𝑥	NOUN
cana-4138	79	2	,	,	PUNCT
cana-4138	79	3	𝑦	𝑦	NOUN
cana-4138	79	4	∈	∈	NOUN
cana-4138	79	5	𝑋	𝑋	NOUN
cana-4138	79	6	then	then	ADV
cana-4138	79	7	the	the	DET
cana-4138	79	8	contraction	contraction	NOUN
cana-4138	79	9	mapping	mapping	NOUN
cana-4138	79	10	𝑓	𝑓	PRON
cana-4138	79	11	has	have	VERB
cana-4138	79	12	a	a	DET
cana-4138	79	13	unique	unique	ADJ
cana-4138	79	14	fixed	fix	VERB
cana-4138	79	15	point	point	NOUN
cana-4138	79	16	in	in	ADP
cana-4138	79	17	𝑋.	𝑋.	PROPN
cana-4138	79	18	in	in	ADP
cana-4138	79	19	[	[	X
cana-4138	79	20	16	16	NUM
cana-4138	79	21	]	]	PUNCT
cana-4138	79	22	,	,	PUNCT
cana-4138	79	23	the	the	DET
cana-4138	79	24	authors	author	NOUN
cana-4138	79	25	ilic	ilic	VERB
cana-4138	79	26	,	,	PUNCT
cana-4138	79	27	d	d	NOUN
cana-4138	79	28	,	,	PUNCT
cana-4138	79	29	and	and	CCONJ
cana-4138	79	30	rakocevic	rakocevic	ADJ
cana-4138	79	31	,	,	PUNCT
cana-4138	79	32	v.	v.	PROPN
cana-4138	79	33	has	have	AUX
cana-4138	79	34	proved	prove	VERB
cana-4138	79	35	the	the	DET
cana-4138	79	36	following	follow	VERB
cana-4138	79	37	result	result	NOUN
cana-4138	79	38	.	.	PUNCT
cana-4138	80	1	lemma	lemma	PROPN
cana-4138	80	2	2.2	2.2	NUM
cana-4138	80	3	:	:	PUNCT
cana-4138	80	4	let	let	VERB
cana-4138	80	5	(	(	PUNCT
cana-4138	80	6	𝑋	𝑋	NOUN
cana-4138	80	7	,	,	PUNCT
cana-4138	80	8	𝑑	𝑑	NOUN
cana-4138	80	9	)	)	PUNCT
cana-4138	80	10	be	be	VERB
cana-4138	80	11	a	a	DET
cana-4138	80	12	complete	complete	ADJ
cana-4138	80	13	cone	cone	NOUN
cana-4138	80	14	metric	metric	ADJ
cana-4138	80	15	space	space	NOUN
cana-4138	80	16	and	and	CCONJ
cana-4138	80	17	let	let	VERB
cana-4138	80	18	𝑃	𝑃	PRON
cana-4138	80	19	be	be	AUX
cana-4138	80	20	a	a	DET
cana-4138	80	21	normal	normal	ADJ
cana-4138	80	22	cone	cone	NOUN
cana-4138	80	23	.	.	PUNCT
cana-4138	81	1	let	let	VERB
cana-4138	81	2	𝑓	𝑓	X
cana-4138	81	3	:	:	PUNCT
cana-4138	81	4	𝑋	𝑋	PROPN
cana-4138	81	5	→	→	SYM
cana-4138	81	6	𝑋	𝑋	PROPN
cana-4138	81	7	,	,	PUNCT
cana-4138	81	8	𝑓2	𝑓2	NOUN
cana-4138	81	9	be	be	VERB
cana-4138	81	10	continuous	continuous	ADJ
cana-4138	81	11	,	,	PUNCT
cana-4138	81	12	𝑔	𝑔	NOUN
cana-4138	81	13	:	:	PUNCT
cana-4138	81	14	𝑓	𝑓	DET
cana-4138	81	15	(	(	PUNCT
cana-4138	81	16	𝑋	𝑋	PROPN
cana-4138	81	17	)	)	PUNCT
cana-4138	81	18	→	→	PUNCT
cana-4138	81	19	𝑋	𝑋	PROPN
cana-4138	81	20	be	be	VERB
cana-4138	81	21	such	such	ADJ
cana-4138	81	22	that	that	SCONJ
cana-4138	81	23	𝑔𝑓(𝑋	𝑔𝑓(𝑋	NOUN
cana-4138	81	24	)	)	PUNCT
cana-4138	81	25	⊆	⊆	NUM
cana-4138	81	26	𝑓2(𝑋	𝑓2(𝑋	NUM
cana-4138	81	27	)	)	PUNCT
cana-4138	81	28	,	,	PUNCT
cana-4138	81	29	and	and	CCONJ
cana-4138	81	30	𝑓(𝑔(𝑥	𝑓(𝑔(𝑥	ADJ
cana-4138	81	31	)	)	PUNCT
cana-4138	81	32	)	)	PUNCT
cana-4138	82	1	=	=	SYM
cana-4138	82	2	𝑔(𝑓(𝑥	𝑔(𝑓(𝑥	NOUN
cana-4138	82	3	)	)	PUNCT
cana-4138	82	4	)	)	PUNCT
cana-4138	83	1	whenever	whenever	SCONJ
cana-4138	83	2	both	both	DET
cana-4138	83	3	sides	side	NOUN
cana-4138	83	4	are	be	AUX
cana-4138	83	5	defined	define	VERB
cana-4138	83	6	.	.	PUNCT
cana-4138	84	1	furthermore	furthermore	ADV
cana-4138	84	2	,	,	PUNCT
cana-4138	84	3	let	let	VERB
cana-4138	84	4	there	there	PRON
cana-4138	84	5	exists	exist	VERB
cana-4138	84	6	𝜆	𝜆	DET
cana-4138	84	7	∈	∈	PROPN
cana-4138	84	8	(	(	PUNCT
cana-4138	84	9	0	0	NUM
cana-4138	84	10	,	,	PUNCT
cana-4138	84	11	1	1	NUM
cana-4138	84	12	)	)	PUNCT
cana-4138	84	13	such	such	ADJ
cana-4138	84	14	that	that	SCONJ
cana-4138	84	15	𝑑(𝑔𝑥	𝑑(𝑔𝑥	PROPN
cana-4138	84	16	,	,	PUNCT
cana-4138	84	17	𝑔𝑦	𝑔𝑦	NOUN
cana-4138	84	18	)	)	PUNCT
cana-4138	84	19	≤	≤	NOUN
cana-4138	84	20	𝜆	𝜆	DET
cana-4138	84	21	𝑢	𝑢	NOUN
cana-4138	84	22	for	for	ADP
cana-4138	84	23	every	every	DET
cana-4138	84	24	𝑥	𝑥	PROPN
cana-4138	84	25	,	,	PUNCT
cana-4138	84	26	𝑦	𝑦	PRON
cana-4138	84	27	∈	∈	ADJ
cana-4138	84	28	𝑓	𝑓	PRON
cana-4138	84	29	(	(	PUNCT
cana-4138	84	30	𝑋	𝑋	PROPN
cana-4138	84	31	)	)	PUNCT
cana-4138	84	32	.	.	PUNCT
cana-4138	85	1	then	then	ADV
cana-4138	85	2	𝑓	𝑓	X
cana-4138	85	3	and	and	CCONJ
cana-4138	85	4	𝑔	𝑔	AUX
cana-4138	85	5	have	have	VERB
cana-4138	85	6	a	a	DET
cana-4138	85	7	common	common	ADJ
cana-4138	85	8	unique	unique	ADJ
cana-4138	85	9	fixed	fix	VERB
cana-4138	85	10	point	point	NOUN
cana-4138	85	11	𝑢	𝑢	NOUN
cana-4138	85	12	in	in	ADP
cana-4138	85	13	𝑋.	𝑋.	PROPN
cana-4138	85	14	3	3	NUM
cana-4138	85	15	.	.	PUNCT
cana-4138	85	16	fractional	fractional	ADJ
cana-4138	85	17	derivative	derivative	ADJ
cana-4138	85	18	and	and	CCONJ
cana-4138	85	19	conformable	conformable	ADJ
cana-4138	85	20	fractional	fractional	ADJ
cana-4138	85	21	derivative	derivative	NOUN
cana-4138	85	22	for	for	ADP
cana-4138	85	23	many	many	ADJ
cana-4138	85	24	centuries	century	NOUN
cana-4138	85	25	,	,	PUNCT
cana-4138	85	26	the	the	DET
cana-4138	85	27	derivative	derivative	NOUN
cana-4138	85	28	of	of	ADP
cana-4138	85	29	non	non	ADJ
cana-4138	85	30	-	-	ADJ
cana-4138	85	31	integer	integer	ADJ
cana-4138	85	32	order	order	NOUN
cana-4138	85	33	has	have	AUX
cana-4138	85	34	been	be	AUX
cana-4138	85	35	an	an	DET
cana-4138	85	36	interesting	interesting	ADJ
cana-4138	85	37	area	area	NOUN
cana-4138	85	38	of	of	ADP
cana-4138	85	39	study	study	NOUN
cana-4138	85	40	.	.	PUNCT
cana-4138	86	1	riemann	riemann	PROPN
cana-4138	86	2	-	-	PUNCT
cana-4138	86	3	liouville	liouville	PROPN
cana-4138	86	4	,	,	PUNCT
cana-4138	86	5	caputo	caputo	PROPN
cana-4138	86	6	,	,	PUNCT
cana-4138	86	7	hadamard	hadamard	NOUN
cana-4138	86	8	,	,	PUNCT
cana-4138	86	9	grunwald	grunwald	NOUN
cana-4138	86	10	-	-	PUNCT
cana-4138	86	11	letnikov	letnikov	ADJ
cana-4138	86	12	,	,	PUNCT
cana-4138	86	13	marchaud	marchaud	NOUN
cana-4138	86	14	,	,	PUNCT
cana-4138	86	15	and	and	CCONJ
cana-4138	86	16	riesz	riesz	PROPN
cana-4138	86	17	were	be	AUX
cana-4138	86	18	among	among	ADP
cana-4138	86	19	the	the	DET
cana-4138	86	20	fractional	fractional	ADJ
cana-4138	86	21	derivative	derivative	ADJ
cana-4138	86	22	types	type	NOUN
cana-4138	86	23	that	that	PRON
cana-4138	86	24	were	be	AUX
cana-4138	86	25	introduced	introduce	VERB
cana-4138	86	26	[	[	X
cana-4138	86	27	17	17	NUM
cana-4138	86	28	,	,	PUNCT
cana-4138	86	29	18	18	NUM
cana-4138	86	30	,	,	PUNCT
cana-4138	86	31	19	19	NUM
cana-4138	86	32	,	,	PUNCT
cana-4138	86	33	20	20	NUM
cana-4138	86	34	,	,	PUNCT
cana-4138	86	35	21	21	NUM
cana-4138	86	36	,	,	PUNCT
cana-4138	86	37	22	22	NUM
cana-4138	86	38	]	]	PUNCT
cana-4138	86	39	.	.	PUNCT
cana-4138	87	1	none	none	NOUN
cana-4138	87	2	of	of	ADP
cana-4138	87	3	these	these	DET
cana-4138	87	4	fractional	fractional	ADJ
cana-4138	87	5	derivatives	derivative	NOUN
cana-4138	87	6	satisfy	satisfy	VERB
cana-4138	87	7	the	the	DET
cana-4138	87	8	properties	property	NOUN
cana-4138	87	9	of	of	ADP
cana-4138	87	10	the	the	DET
cana-4138	87	11	classical	classical	ADJ
cana-4138	87	12	integer	integer	NOUN
cana-4138	87	13	order	order	NOUN
cana-4138	87	14	derivatives	derivative	NOUN
cana-4138	87	15	.	.	PUNCT
cana-4138	88	1	we	we	PRON
cana-4138	88	2	are	be	AUX
cana-4138	88	3	aware	aware	ADJ
cana-4138	88	4	that	that	SCONJ
cana-4138	88	5	the	the	DET
cana-4138	88	6	derivative	derivative	NOUN
cana-4138	88	7	of	of	ADP
cana-4138	88	8	an	an	DET
cana-4138	88	9	integer	integer	NOUN
cana-4138	88	10	order	order	NOUN
cana-4138	88	11	constant	constant	ADJ
cana-4138	88	12	is	be	AUX
cana-4138	88	13	zero	zero	NUM
cana-4138	88	14	,	,	PUNCT
cana-4138	88	15	and	and	CCONJ
cana-4138	88	16	we	we	PRON
cana-4138	88	17	expect	expect	VERB
cana-4138	88	18	fractional	fractional	ADJ
cana-4138	88	19	derivatives	derivative	NOUN
cana-4138	88	20	to	to	PART
cana-4138	88	21	be	be	AUX
cana-4138	88	22	no	no	ADV
cana-4138	88	23	different	different	ADJ
cana-4138	88	24	.	.	PUNCT
cana-4138	89	1	this	this	PRON
cana-4138	89	2	is	be	AUX
cana-4138	89	3	not	not	PART
cana-4138	89	4	the	the	DET
cana-4138	89	5	case	case	NOUN
cana-4138	89	6	for	for	ADP
cana-4138	89	7	most	most	ADJ
cana-4138	89	8	fractional	fractional	ADJ
cana-4138	89	9	derivatives	derivative	NOUN
cana-4138	89	10	,	,	PUNCT
cana-4138	89	11	except	except	SCONJ
cana-4138	89	12	for	for	ADP
cana-4138	89	13	the	the	DET
cana-4138	89	14	caputo	caputo	PROPN
cana-4138	89	15	fractional	fractional	PROPN
cana-4138	89	16	derivative	derivative	PROPN
cana-4138	89	17	.	.	PUNCT
cana-4138	90	1	furthermore	furthermore	ADV
cana-4138	90	2	,	,	PUNCT
cana-4138	90	3	fractional	fractional	ADJ
cana-4138	90	4	derivatives	derivative	NOUN
cana-4138	90	5	do	do	AUX
cana-4138	90	6	not	not	PART
cana-4138	90	7	meet	meet	VERB
cana-4138	90	8	the	the	DET
cana-4138	90	9	requirements	requirement	NOUN
cana-4138	90	10	of	of	ADP
cana-4138	90	11	classical	classical	ADJ
cana-4138	90	12	derivatives	derivative	NOUN
cana-4138	90	13	,	,	PUNCT
cana-4138	90	14	including	include	VERB
cana-4138	90	15	the	the	DET
cana-4138	90	16	mean	mean	ADJ
cana-4138	90	17	value	value	NOUN
cana-4138	90	18	theorems	theorem	NOUN
cana-4138	90	19	of	of	ADP
cana-4138	90	20	rolle	rolle	NOUN
cana-4138	90	21	and	and	CCONJ
cana-4138	90	22	lagrange	lagrange	PROPN
cana-4138	90	23	,	,	PUNCT
cana-4138	90	24	the	the	DET
cana-4138	90	25	product	product	NOUN
cana-4138	90	26	rule	rule	NOUN
cana-4138	90	27	,	,	PUNCT
cana-4138	90	28	the	the	DET
cana-4138	90	29	quotient	quotient	NOUN
cana-4138	90	30	rule	rule	NOUN
cana-4138	90	31	,	,	PUNCT
cana-4138	90	32	and	and	CCONJ
cana-4138	90	33	the	the	DET
cana-4138	90	34	chain	chain	NOUN
cana-4138	90	35	rule	rule	NOUN
cana-4138	90	36	.	.	PUNCT
cana-4138	91	1	many	many	ADJ
cana-4138	91	2	authors	author	NOUN
cana-4138	91	3	,	,	PUNCT
cana-4138	91	4	such	such	ADJ
cana-4138	91	5	as	as	ADP
cana-4138	91	6	r.	r.	PROPN
cana-4138	91	7	khalil	khalil	PROPN
cana-4138	92	1	[	[	X
cana-4138	92	2	23	23	NUM
cana-4138	92	3	]	]	PUNCT
cana-4138	92	4	,	,	PUNCT
cana-4138	92	5	abdljawad	abdljawad	VERB
cana-4138	92	6	et	et	PROPN
cana-4138	92	7	al	al	PROPN
cana-4138	92	8	.	.	PUNCT
cana-4138	93	1	[	[	X
cana-4138	93	2	24	24	NUM
cana-4138	93	3	,	,	PUNCT
cana-4138	93	4	25	25	NUM
cana-4138	93	5	,	,	PUNCT
cana-4138	93	6	26	26	NUM
cana-4138	93	7	]	]	PUNCT
cana-4138	93	8	etc	etc	X
cana-4138	93	9	.	.	X
cana-4138	93	10	have	have	AUX
cana-4138	93	11	made	make	VERB
cana-4138	93	12	important	important	ADJ
cana-4138	93	13	contributions	contribution	NOUN
cana-4138	93	14	in	in	ADP
cana-4138	93	15	this	this	DET
cana-4138	93	16	direction	direction	NOUN
cana-4138	93	17	.	.	PUNCT
cana-4138	94	1	they	they	PRON
cana-4138	94	2	have	have	AUX
cana-4138	94	3	established	establish	VERB
cana-4138	94	4	some	some	PRON
cana-4138	94	5	of	of	ADP
cana-4138	94	6	the	the	DET
cana-4138	94	7	properties	property	NOUN
cana-4138	94	8	that	that	PRON
cana-4138	94	9	the	the	DET
cana-4138	94	10	previous	previous	ADJ
cana-4138	94	11	fractional	fractional	ADJ
cana-4138	94	12	derivatives	derivative	NOUN
cana-4138	94	13	did	do	AUX
cana-4138	94	14	not	not	PART
cana-4138	94	15	meet	meet	VERB
cana-4138	94	16	and	and	CCONJ
cana-4138	94	17	defined	define	VERB
cana-4138	94	18	a	a	DET
cana-4138	94	19	few	few	ADJ
cana-4138	94	20	new	new	ADJ
cana-4138	94	21	fractional	fractional	ADJ
cana-4138	94	22	derivatives	derivative	NOUN
cana-4138	94	23	.	.	PUNCT
cana-4138	95	1	all	all	PRON
cana-4138	95	2	of	of	ADP
cana-4138	95	3	these	these	DET
cana-4138	95	4	conformable	conformable	ADJ
cana-4138	95	5	derivatives	derivative	NOUN
cana-4138	95	6	are	be	AUX
cana-4138	95	7	extensions	extension	NOUN
cana-4138	95	8	of	of	ADP
cana-4138	95	9	the	the	DET
cana-4138	95	10	traditional	traditional	ADJ
cana-4138	95	11	limit	limit	NOUN
cana-4138	95	12	form	form	NOUN
cana-4138	95	13	formulation	formulation	NOUN
cana-4138	95	14	.	.	PUNCT
cana-4138	96	1	the	the	DET
cana-4138	96	2	following	follow	VERB
cana-4138	96	3	definitions	definition	NOUN
cana-4138	96	4	are	be	AUX
cana-4138	96	5	revised	revise	VERB
cana-4138	96	6	from	from	ADP
cana-4138	96	7	these	these	DET
cana-4138	96	8	references	reference	NOUN
cana-4138	96	9	.	.	PUNCT
cana-4138	97	1	definition	definition	NOUN
cana-4138	97	2	3.1	3.1	NUM
cana-4138	97	3	:	:	PUNCT
cana-4138	97	4	let	let	VERB
cana-4138	97	5	:	:	PUNCT
cana-4138	98	1	[	[	X
cana-4138	98	2	0	0	NUM
cana-4138	98	3	,	,	PUNCT
cana-4138	98	4	∞	∞	PROPN
cana-4138	98	5	)	)	PUNCT
cana-4138	98	6	→	→	SYM
cana-4138	98	7	ℝ	ℝ	PROPN
cana-4138	98	8	,	,	PUNCT
cana-4138	98	9	be	be	AUX
cana-4138	98	10	any	any	DET
cana-4138	98	11	function	function	NOUN
cana-4138	98	12	of	of	ADP
cana-4138	98	13	real	real	ADJ
cana-4138	98	14	variable	variable	ADJ
cana-4138	98	15	𝑡.	𝑡.	NOUN
cana-4138	98	16	then	then	ADV
cana-4138	98	17	the	the	DET
cana-4138	98	18	conformable	conformable	ADJ
cana-4138	98	19	fractional	fractional	ADJ
cana-4138	98	20	derivative	derivative	NOUN
cana-4138	98	21	of	of	ADP
cana-4138	98	22	𝑢	𝑢	NOUN
cana-4138	98	23	of	of	ADP
cana-4138	98	24	fractional	fractional	ADJ
cana-4138	98	25	order	order	NOUN
cana-4138	98	26	𝛼	𝛼	NOUN
cana-4138	98	27	,	,	PUNCT
cana-4138	98	28	𝛼	𝛼	PROPN
cana-4138	98	29	∈	∈	PROPN
cana-4138	98	30	(	(	PUNCT
cana-4138	98	31	0,1	0,1	NOUN
cana-4138	98	32	]	]	PUNCT
cana-4138	98	33	at	at	ADP
cana-4138	98	34	𝑡	𝑡	X
cana-4138	98	35	>	>	X
cana-4138	98	36	0	0	NUM
cana-4138	98	37	,	,	PUNCT
cana-4138	98	38	denoted	denote	VERB
cana-4138	98	39	𝐷𝛼𝑢(𝑡	𝐷𝛼𝑢(𝑡	NOUN
cana-4138	98	40	)	)	PUNCT
cana-4138	98	41	,	,	PUNCT
cana-4138	98	42	is	be	AUX
cana-4138	98	43	defined	define	VERB
cana-4138	98	44	by	by	ADP
cana-4138	98	45	the	the	DET
cana-4138	98	46	limit	limit	NOUN
cana-4138	98	47	𝐷𝛼𝑢(𝑡	𝐷𝛼𝑢(𝑡	PRON
cana-4138	98	48	)	)	PUNCT
cana-4138	98	49	=	=	PRON
cana-4138	98	50	𝑙𝑖𝑚	𝑙𝑖𝑚	VERB
cana-4138	98	51	ℎ→0	ℎ→0	ADJ
cana-4138	98	52	𝑢(𝑡	𝑢(𝑡	PROPN
cana-4138	98	53	+	+	SYM
cana-4138	98	54	ℎ𝑡(1−𝛼	ℎ𝑡(1−𝛼	NOUN
cana-4138	98	55	)	)	PUNCT
cana-4138	98	56	)	)	PUNCT
cana-4138	99	1	−	−	ADP
cana-4138	99	2	𝑢(𝑡	𝑢(𝑡	NOUN
cana-4138	99	3	)	)	PUNCT
cana-4138	99	4	ℎ	ℎ	NOUN
cana-4138	99	5	provided	provide	VERB
cana-4138	99	6	the	the	DET
cana-4138	99	7	limit	limit	NOUN
cana-4138	99	8	exists	exist	VERB
cana-4138	99	9	.	.	PUNCT
cana-4138	100	1	communications	communication	NOUN
cana-4138	100	2	on	on	ADP
cana-4138	100	3	applied	apply	VERB
cana-4138	100	4	nonlinear	nonlinear	ADJ
cana-4138	100	5	analysis	analysis	NOUN
cana-4138	100	6	issn	issn	NOUN
cana-4138	100	7	:	:	PUNCT
cana-4138	100	8	1074	1074	NUM
cana-4138	100	9	-	-	PUNCT
cana-4138	100	10	133x	133x	NUM
cana-4138	100	11	vol	vol	NOUN
cana-4138	100	12	32	32	NUM
cana-4138	100	13	no	no	NOUN
cana-4138	100	14	.	.	PUNCT
cana-4138	101	1	9s	9s	NUM
cana-4138	101	2	(	(	PUNCT
cana-4138	101	3	2025	2025	NUM
cana-4138	101	4	)	)	PUNCT
cana-4138	101	5	1307	1307	NUM
cana-4138	101	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4138	101	7	for	for	ADP
cana-4138	101	8	𝑛	𝑛	PRON
cana-4138	101	9	<	<	X
cana-4138	101	10	𝛼	𝛼	X
cana-4138	101	11	≤	≤	NUM
cana-4138	101	12	𝑛	𝑛	PRON
cana-4138	101	13	+	+	NOUN
cana-4138	101	14	1	1	NUM
cana-4138	101	15	,	,	PUNCT
cana-4138	101	16	𝑛	𝑛	DET
cana-4138	101	17	∈	∈	PROPN
cana-4138	101	18	𝑁	𝑁	PROPN
cana-4138	101	19	,	,	PUNCT
cana-4138	101	20	the	the	DET
cana-4138	101	21	conformable	conformable	ADJ
cana-4138	101	22	fractional	fractional	ADJ
cana-4138	101	23	derivative	derivative	NOUN
cana-4138	101	24	is	be	AUX
cana-4138	101	25	defined	define	VERB
cana-4138	101	26	by	by	ADP
cana-4138	101	27	𝐷𝛼(𝑢)(𝑡	𝐷𝛼(𝑢)(𝑡	NOUN
cana-4138	101	28	)	)	PUNCT
cana-4138	102	1	=	=	PRON
cana-4138	102	2	𝑙𝑖𝑚	𝑙𝑖𝑚	VERB
cana-4138	102	3	ℎ→0	ℎ→0	X
cana-4138	102	4	𝑢⌈𝛼⌉−1(𝑡	𝑢⌈𝛼⌉−1(𝑡	NOUN
cana-4138	102	5	+	+	CCONJ
cana-4138	102	6	ℎ𝑡(⌈𝛼⌉−𝛼	ℎ𝑡(⌈𝛼⌉−𝛼	NUM
cana-4138	102	7	)	)	PUNCT
cana-4138	102	8	)	)	PUNCT
cana-4138	103	1	−	−	PROPN
cana-4138	103	2	𝑢⌈𝛼⌉−1(𝑡	𝑢⌈𝛼⌉−1(𝑡	PROPN
cana-4138	103	3	)	)	PUNCT
cana-4138	103	4	ℎ	ℎ	NOUN
cana-4138	103	5	where	where	SCONJ
cana-4138	103	6	⌈α⌉	⌈α⌉	NOUN
cana-4138	103	7	is	be	AUX
cana-4138	103	8	the	the	DET
cana-4138	103	9	smallest	small	ADJ
cana-4138	103	10	integer	integer	NOUN
cana-4138	103	11	greater	great	ADJ
cana-4138	103	12	than	than	ADP
cana-4138	103	13	or	or	CCONJ
cana-4138	103	14	equal	equal	ADJ
cana-4138	103	15	to	to	ADP
cana-4138	103	16	α	α	PRON
cana-4138	103	17	provided	provide	VERB
cana-4138	103	18	the	the	DET
cana-4138	103	19	limit	limit	NOUN
cana-4138	103	20	exist	exist	VERB
cana-4138	103	21	.	.	PUNCT
cana-4138	104	1	definition	definition	NOUN
cana-4138	104	2	3.2	3.2	NUM
cana-4138	104	3	:	:	PUNCT
cana-4138	104	4	let	let	VERB
cana-4138	104	5	𝛼	𝛼	PRON
cana-4138	104	6	∈	∈	PROPN
cana-4138	104	7	(	(	PUNCT
cana-4138	104	8	0	0	NUM
cana-4138	104	9	,	,	PUNCT
cana-4138	104	10	1	1	NUM
cana-4138	104	11	]	]	PUNCT
cana-4138	104	12	and	and	CCONJ
cana-4138	104	13	𝑡	𝑡	X
cana-4138	104	14	>	>	X
cana-4138	104	15	0	0	NUM
cana-4138	104	16	.	.	PUNCT
cana-4138	105	1	the	the	DET
cana-4138	105	2	α	α	PROPN
cana-4138	105	3	conformable	conformable	ADJ
cana-4138	105	4	fractional	fractional	ADJ
cana-4138	105	5	integral	integral	NOUN
cana-4138	105	6	is	be	AUX
cana-4138	105	7	given	give	VERB
cana-4138	105	8	by	by	ADP
cana-4138	105	9	𝐼𝛼𝑢(𝑡	𝐼𝛼𝑢(𝑡	NOUN
cana-4138	105	10	)	)	PUNCT
cana-4138	105	11	=	=	SYM
cana-4138	106	1	∫	∫	NUM
cana-4138	106	2	𝑢(𝑠	𝑢(𝑠	NOUN
cana-4138	106	3	)	)	PUNCT
cana-4138	106	4	𝑠1−𝛼	𝑠1−𝛼	PROPN
cana-4138	106	5	𝑡	𝑡	PROPN
cana-4138	106	6	0	0	NUM
cana-4138	106	7	𝑑𝑠.	𝑑𝑠.	NOUN
cana-4138	106	8	definition	definition	NOUN
cana-4138	106	9	3.3	3.3	NUM
cana-4138	106	10	:	:	PUNCT
cana-4138	106	11	let	let	VERB
cana-4138	106	12	𝐵	𝐵	PROPN
cana-4138	106	13	=	=	SYM
cana-4138	106	14	𝐶(𝐼	𝐶(𝐼	PROPN
cana-4138	106	15	,	,	PUNCT
cana-4138	106	16	𝑋	𝑋	PROPN
cana-4138	106	17	)	)	PUNCT
cana-4138	106	18	be	be	AUX
cana-4138	106	19	the	the	DET
cana-4138	106	20	banach	banach	NOUN
cana-4138	106	21	space	space	NOUN
cana-4138	106	22	of	of	ADP
cana-4138	106	23	all	all	DET
cana-4138	106	24	continuous	continuous	ADJ
cana-4138	106	25	functions	function	NOUN
cana-4138	106	26	defined	define	VERB
cana-4138	106	27	on	on	ADP
cana-4138	106	28	the	the	DET
cana-4138	106	29	set	set	NOUN
cana-4138	106	30	𝐼	𝐼	PROPN
cana-4138	106	31	=	=	PUNCT
cana-4138	107	1	[	[	X
cana-4138	107	2	0	0	NUM
cana-4138	107	3	,	,	PUNCT
cana-4138	107	4	𝑏	𝑏	NOUN
cana-4138	107	5	]	]	PUNCT
cana-4138	107	6	into	into	ADP
cana-4138	107	7	𝑋	𝑋	PROPN
cana-4138	107	8	,	,	PUNCT
cana-4138	107	9	where	where	SCONJ
cana-4138	107	10	the	the	DET
cana-4138	107	11	norm	norm	NOUN
cana-4138	107	12	of	of	ADP
cana-4138	107	13	an	an	DET
cana-4138	107	14	𝑥	𝑥	PROPN
cana-4138	107	15	∈	∈	PROPN
cana-4138	107	16	𝐵	𝐵	NOUN
cana-4138	107	17	is	be	AUX
cana-4138	107	18	defined	define	VERB
cana-4138	107	19	by	by	ADP
cana-4138	107	20	||𝑥||∞	||𝑥||∞	NOUN
cana-4138	107	21	=	=	SYM
cana-4138	107	22	sup{||𝑥(𝑡)||	sup{||𝑥(𝑡)||	NOUN
cana-4138	107	23	:	:	PUNCT
cana-4138	107	24	𝑡	𝑡	NOUN
cana-4138	107	25	}	}	PUNCT
cana-4138	107	26	∈	∈	NOUN
cana-4138	107	27	𝐼	𝐼	PROPN
cana-4138	107	28	define	define	VERB
cana-4138	107	29	a	a	DET
cana-4138	107	30	metric	metric	ADJ
cana-4138	107	31	𝑑	𝑑	NOUN
cana-4138	107	32	:	:	PUNCT
cana-4138	107	33	𝐵	𝐵	NOUN
cana-4138	107	34	×	×	PROPN
cana-4138	107	35	𝐵	𝐵	PROPN
cana-4138	107	36	⟶	⟶	NOUN
cana-4138	107	37	ℝ	ℝ	NOUN
cana-4138	107	38	by	by	ADP
cana-4138	107	39	𝑑(𝑥	𝑑(𝑥	PROPN
cana-4138	107	40	,	,	PUNCT
cana-4138	107	41	𝑦	𝑦	X
cana-4138	107	42	)	)	PUNCT
cana-4138	107	43	=	=	SYM
cana-4138	107	44	(	(	PUNCT
cana-4138	107	45	||𝑥	||𝑥	PROPN
cana-4138	107	46	−	−	PROPN
cana-4138	107	47	𝑦||∞	𝑦||∞	PROPN
cana-4138	107	48	,	,	PUNCT
cana-4138	107	49	𝑎||𝑥	𝑎||𝑥	PROPN
cana-4138	107	50	−	−	PROPN
cana-4138	107	51	𝑦||∞	𝑦||∞	PROPN
cana-4138	107	52	)	)	PUNCT
cana-4138	107	53	∀𝑥	∀𝑥	NOUN
cana-4138	107	54	,	,	PUNCT
cana-4138	107	55	𝑦	𝑦	NOUN
cana-4138	107	56	∈	∈	PROPN
cana-4138	107	57	𝐵	𝐵	PROPN
cana-4138	107	58	,	,	PUNCT
cana-4138	107	59	0	0	PUNCT
cana-4138	107	60	<	<	X
cana-4138	107	61	𝑎	𝑎	X
cana-4138	107	62	<	<	X
cana-4138	107	63	1.then	1.then	NUM
cana-4138	107	64	it	it	PRON
cana-4138	107	65	can	can	AUX
cana-4138	107	66	be	be	AUX
cana-4138	107	67	verified	verify	VERB
cana-4138	107	68	that	that	SCONJ
cana-4138	107	69	(	(	PUNCT
cana-4138	107	70	𝐵	𝐵	NOUN
cana-4138	107	71	,	,	PUNCT
cana-4138	107	72	𝑑	𝑑	NOUN
cana-4138	107	73	)	)	PUNCT
cana-4138	107	74	is	be	AUX
cana-4138	107	75	a	a	DET
cana-4138	107	76	cone	cone	NOUN
cana-4138	107	77	metric	metric	ADJ
cana-4138	107	78	space	space	NOUN
cana-4138	107	79	.	.	PUNCT
cana-4138	108	1	the	the	DET
cana-4138	108	2	function	function	NOUN
cana-4138	108	3	𝑥	𝑥	X
cana-4138	108	4	∈	∈	PROPN
cana-4138	108	5	𝐵	𝐵	NOUN
cana-4138	108	6	is	be	AUX
cana-4138	108	7	called	call	VERB
cana-4138	108	8	as	as	ADP
cana-4138	108	9	a	a	DET
cana-4138	108	10	solution	solution	NOUN
cana-4138	108	11	of	of	ADP
cana-4138	108	12	the	the	DET
cana-4138	108	13	initial	initial	ADJ
cana-4138	108	14	value	value	NOUN
cana-4138	108	15	problem	problem	NOUN
cana-4138	108	16	(	(	PUNCT
cana-4138	108	17	1)—(2	1)—(2	NUM
cana-4138	108	18	)	)	PUNCT
cana-4138	108	19	if	if	SCONJ
cana-4138	108	20	it	it	PRON
cana-4138	108	21	satisfies	satisfy	VERB
cana-4138	108	22	the	the	DET
cana-4138	108	23	condition	condition	NOUN
cana-4138	108	24	𝑥(𝑡	𝑥(𝑡	NOUN
cana-4138	108	25	)	)	PUNCT
cana-4138	108	26	=	=	SYM
cana-4138	108	27	𝑢0	𝑢0	PROPN
cana-4138	108	28	+	+	CCONJ
cana-4138	108	29	∫	∫	PROPN
cana-4138	108	30	𝑓(𝑡	𝑓(𝑡	NOUN
cana-4138	108	31	)	)	PUNCT
cana-4138	108	32	.	.	PUNCT
cana-4138	109	1	𝑡𝛼−1𝑑𝑡	𝑡𝛼−1𝑑𝑡	NUM
cana-4138	109	2	𝑡	𝑡	NOUN
cana-4138	109	3	0	0	NUM
cana-4138	109	4	+	+	NUM
cana-4138	109	5	∫	∫	NUM
cana-4138	109	6	𝑡𝛼−1	𝑡𝛼−1	PROPN
cana-4138	109	7	[	[	X
cana-4138	109	8	∫	∫	PROPN
cana-4138	109	9	𝑘(𝑡	𝑘(𝑡	PROPN
cana-4138	109	10	,	,	PUNCT
cana-4138	109	11	𝑠	𝑠	INTJ
cana-4138	109	12	,	,	PUNCT
cana-4138	109	13	𝑥(𝑠))𝑑𝑠	𝑥(𝑠))𝑑𝑠	VERB
cana-4138	109	14	𝑡	𝑡	NOUN
cana-4138	109	15	0	0	NUM
cana-4138	109	16	]	]	PUNCT
cana-4138	110	1	𝑡	𝑡	X
cana-4138	110	2	0	0	NUM
cana-4138	110	3	𝑑𝑡	𝑑𝑡	ADP
cana-4138	110	4	+	+	ADJ
cana-4138	110	5	∫	∫	PROPN
cana-4138	110	6	𝑡𝛼−1	𝑡𝛼−1	PROPN
cana-4138	110	7	𝑡	𝑡	PROPN
cana-4138	110	8	0	0	PUNCT
cana-4138	111	1	[	[	X
cana-4138	111	2	∫	∫	X
cana-4138	111	3	ℎ(𝑡	ℎ(𝑡	PROPN
cana-4138	111	4	,	,	PUNCT
cana-4138	111	5	𝑠	𝑠	PROPN
cana-4138	111	6	,	,	PUNCT
cana-4138	111	7	𝑥(𝑠))𝑑𝑠	𝑥(𝑠))𝑑𝑠	VERB
cana-4138	111	8	𝑏	𝑏	SYM
cana-4138	111	9	0	0	NUM
cana-4138	111	10	]	]	PUNCT
cana-4138	111	11	𝑑𝑡	𝑑𝑡	ADP
cana-4138	111	12	4	4	NUM
cana-4138	111	13	.	.	PUNCT
cana-4138	111	14	main	main	ADJ
cana-4138	111	15	result	result	NOUN
cana-4138	111	16	now	now	ADV
cana-4138	111	17	we	we	PRON
cana-4138	111	18	have	have	VERB
cana-4138	111	19	enough	enough	ADJ
cana-4138	111	20	material	material	NOUN
cana-4138	111	21	to	to	PART
cana-4138	111	22	prove	prove	VERB
cana-4138	111	23	the	the	DET
cana-4138	111	24	main	main	ADJ
cana-4138	111	25	result	result	NOUN
cana-4138	111	26	.	.	PUNCT
cana-4138	112	1	theorem	theorem	VERB
cana-4138	112	2	4.1	4.1	NUM
cana-4138	112	3	:	:	PUNCT
cana-4138	112	4	the	the	DET
cana-4138	112	5	initial	initial	ADJ
cana-4138	112	6	value	value	NOUN
cana-4138	112	7	problem	problem	NOUN
cana-4138	112	8	(	(	PUNCT
cana-4138	112	9	1)—(2	1)—(2	NUM
cana-4138	112	10	)	)	PUNCT
cana-4138	112	11	has	have	VERB
cana-4138	112	12	a	a	DET
cana-4138	112	13	unique	unique	ADJ
cana-4138	112	14	solution	solution	NOUN
cana-4138	112	15	𝑥	𝑥	NOUN
cana-4138	112	16	in	in	ADP
cana-4138	112	17	𝐼	𝐼	PROPN
cana-4138	112	18	if	if	SCONJ
cana-4138	112	19	the	the	DET
cana-4138	112	20	following	follow	VERB
cana-4138	112	21	conditions	condition	NOUN
cana-4138	112	22	are	be	AUX
cana-4138	112	23	satisfied	satisfied	ADJ
cana-4138	112	24	1	1	NUM
cana-4138	112	25	)	)	PUNCT
cana-4138	112	26	there	there	PRON
cana-4138	112	27	exist	exist	VERB
cana-4138	112	28	continuous	continuous	ADJ
cana-4138	112	29	functions	function	NOUN
cana-4138	112	30	𝑝1	𝑝1	NOUN
cana-4138	112	31	,	,	PUNCT
cana-4138	112	32	𝑝2	𝑝2	NOUN
cana-4138	112	33	:	:	PUNCT
cana-4138	113	1	𝐼	𝐼	ADP
cana-4138	113	2	×	×	NOUN
cana-4138	113	3	𝐼	𝐼	NOUN
cana-4138	113	4	→	→	SYM
cana-4138	113	5	ℝ+	ℝ+	PUNCT
cana-4138	113	6	and	and	CCONJ
cana-4138	113	7	a	a	DET
cana-4138	113	8	comparison	comparison	NOUN
cana-4138	113	9	function	function	NOUN
cana-4138	113	10	𝜙	𝜙	NOUN
cana-4138	113	11	:	:	PUNCT
cana-4138	113	12	ℝ2	ℝ2	PROPN
cana-4138	113	13	→	→	PUNCT
cana-4138	113	14	ℝ2	ℝ2	X
cana-4138	113	15	satisfying	satisfying	ADJ
cana-4138	113	16	(	(	PUNCT
cana-4138	113	17	‖𝑘(𝑡	‖𝑘(𝑡	NOUN
cana-4138	113	18	,	,	PUNCT
cana-4138	113	19	𝑠	𝑠	PROPN
cana-4138	113	20	,	,	PUNCT
cana-4138	113	21	𝑢	𝑢	NOUN
cana-4138	113	22	)	)	PUNCT
cana-4138	113	23	−	−	PROPN
cana-4138	114	1	𝑘(𝑡	𝑘(𝑡	PROPN
cana-4138	114	2	,	,	PUNCT
cana-4138	114	3	𝑠	𝑠	PROPN
cana-4138	114	4	,	,	PUNCT
cana-4138	114	5	𝑣)‖	𝑣)‖	ADJ
cana-4138	114	6	,	,	PUNCT
cana-4138	114	7	𝑎‖𝑘(𝑡	𝑎‖𝑘(𝑡	NOUN
cana-4138	114	8	,	,	PUNCT
cana-4138	114	9	𝑠	𝑠	PROPN
cana-4138	114	10	,	,	PUNCT
cana-4138	114	11	𝑢	𝑢	NOUN
cana-4138	114	12	)	)	PUNCT
cana-4138	114	13	−	−	PROPN
cana-4138	115	1	𝑘(𝑡	𝑘(𝑡	PROPN
cana-4138	115	2	,	,	PUNCT
cana-4138	115	3	𝑠	𝑠	PROPN
cana-4138	115	4	,	,	PUNCT
cana-4138	115	5	𝑣)‖	𝑣)‖	NOUN
cana-4138	115	6	)	)	PUNCT
cana-4138	115	7	≤	≤	NOUN
cana-4138	115	8	𝑝1(𝑡	𝑝1(𝑡	PROPN
cana-4138	115	9	,	,	PUNCT
cana-4138	115	10	𝑠)𝜙(𝑑(𝑢	𝑠)𝜙(𝑑(𝑢	NOUN
cana-4138	115	11	,	,	PUNCT
cana-4138	115	12	𝑣	𝑣	NOUN
cana-4138	115	13	)	)	PUNCT
cana-4138	115	14	)	)	PUNCT
cana-4138	115	15	(	(	PUNCT
cana-4138	115	16	‖ℎ(𝑡	‖ℎ(𝑡	X
cana-4138	115	17	,	,	PUNCT
cana-4138	115	18	𝑠	𝑠	PROPN
cana-4138	115	19	,	,	PUNCT
cana-4138	115	20	𝑢	𝑢	PROPN
cana-4138	115	21	)	)	PUNCT
cana-4138	115	22	−	−	PROPN
cana-4138	115	23	ℎ(𝑡	ℎ(𝑡	PROPN
cana-4138	115	24	,	,	PUNCT
cana-4138	115	25	𝑠	𝑠	PROPN
cana-4138	115	26	,	,	PUNCT
cana-4138	115	27	𝑣)‖	𝑣)‖	ADV
cana-4138	115	28	,	,	PUNCT
cana-4138	115	29	𝑎‖ℎ(𝑡	𝑎‖ℎ(𝑡	PROPN
cana-4138	115	30	,	,	PUNCT
cana-4138	115	31	𝑠	𝑠	PROPN
cana-4138	115	32	,	,	PUNCT
cana-4138	115	33	𝑢	𝑢	PROPN
cana-4138	115	34	)	)	PUNCT
cana-4138	115	35	−	−	PROPN
cana-4138	115	36	ℎ(𝑡	ℎ(𝑡	PROPN
cana-4138	115	37	,	,	PUNCT
cana-4138	115	38	𝑠	𝑠	PROPN
cana-4138	115	39	,	,	PUNCT
cana-4138	115	40	𝑣)‖	𝑣)‖	NOUN
cana-4138	115	41	)	)	PUNCT
cana-4138	115	42	≤	≤	NOUN
cana-4138	115	43	𝑝2(𝑡	𝑝2(𝑡	PROPN
cana-4138	115	44	,	,	PUNCT
cana-4138	115	45	𝑠)𝜙(𝑑(𝑢	𝑠)𝜙(𝑑(𝑢	NOUN
cana-4138	115	46	,	,	PUNCT
cana-4138	115	47	𝑣	𝑣	NOUN
cana-4138	115	48	)	)	PUNCT
cana-4138	115	49	)	)	PUNCT
cana-4138	115	50	where	where	SCONJ
cana-4138	115	51	the	the	DET
cana-4138	115	52	metric	metric	NOUN
cana-4138	115	53	𝑑	𝑑	NOUN
cana-4138	115	54	:	:	PUNCT
cana-4138	115	55	𝐵	𝐵	NOUN
cana-4138	115	56	×	×	PROPN
cana-4138	115	57	𝐵	𝐵	PROPN
cana-4138	115	58	⟶	⟶	NOUN
cana-4138	115	59	ℝ	ℝ	PROPN
cana-4138	115	60	is	be	AUX
cana-4138	115	61	defined	define	VERB
cana-4138	115	62	by	by	ADP
cana-4138	115	63	𝑑(𝑥	𝑑(𝑥	PROPN
cana-4138	115	64	,	,	PUNCT
cana-4138	115	65	𝑦	𝑦	NOUN
cana-4138	115	66	)	)	PUNCT
cana-4138	115	67	=	=	SYM
cana-4138	115	68	(	(	PUNCT
cana-4138	115	69	||𝑥	||𝑥	PROPN
cana-4138	115	70	−	−	PROPN
cana-4138	115	71	𝑦||∞	𝑦||∞	PROPN
cana-4138	115	72	,	,	PUNCT
cana-4138	115	73	𝑎||𝑥	𝑎||𝑥	PROPN
cana-4138	115	74	−	−	PROPN
cana-4138	115	75	𝑦||∞	𝑦||∞	PROPN
cana-4138	115	76	)	)	PUNCT
cana-4138	115	77	∀𝑥	∀𝑥	NOUN
cana-4138	115	78	,	,	PUNCT
cana-4138	115	79	𝑦	𝑦	NOUN
cana-4138	115	80	∈	∈	PROPN
cana-4138	115	81	𝐵	𝐵	NOUN
cana-4138	115	82	2	2	NUM
cana-4138	115	83	)	)	PUNCT
cana-4138	115	84	∫	∫	NOUN
cana-4138	115	85	𝑡𝛼−1	𝑡𝛼−1	PROPN
cana-4138	115	86	[	[	X
cana-4138	115	87	∫[𝑝1(𝑡	∫[𝑝1(𝑡	NOUN
cana-4138	115	88	,	,	PUNCT
cana-4138	115	89	𝑠	𝑠	PROPN
cana-4138	115	90	)	)	PUNCT
cana-4138	115	91	+	+	CCONJ
cana-4138	115	92	𝑝2(𝑡	𝑝2(𝑡	PROPN
cana-4138	115	93	,	,	PUNCT
cana-4138	115	94	𝑠	𝑠	NOUN
cana-4138	115	95	)	)	PUNCT
cana-4138	115	96	]	]	PUNCT
cana-4138	116	1	𝑏	𝑏	X
cana-4138	116	2	0	0	NUM
cana-4138	116	3	𝑑𝑠	𝑑𝑠	NOUN
cana-4138	116	4	]	]	PUNCT
cana-4138	116	5	𝑑𝑡	𝑑𝑡	ADP
cana-4138	116	6	≤	≤	ADV
cana-4138	116	7	1	1	NUM
cana-4138	116	8	𝑏	𝑏	NOUN
cana-4138	116	9	0	0	NUM
cana-4138	116	10	proof	proof	NOUN
cana-4138	116	11	:	:	PUNCT
cana-4138	116	12	we	we	PRON
cana-4138	116	13	define	define	VERB
cana-4138	116	14	the	the	DET
cana-4138	116	15	operator	operator	NOUN
cana-4138	116	16	𝐹	𝐹	PROPN
cana-4138	116	17	by	by	ADP
cana-4138	116	18	𝐹𝑥(𝑡	𝐹𝑥(𝑡	NOUN
cana-4138	116	19	)	)	PUNCT
cana-4138	116	20	=	=	SYM
cana-4138	116	21	𝑥0	𝑥0	NOUN
cana-4138	116	22	+	+	NUM
cana-4138	116	23	∫	∫	PROPN
cana-4138	116	24	𝑓(𝑡	𝑓(𝑡	NOUN
cana-4138	116	25	)	)	PUNCT
cana-4138	116	26	.	.	PUNCT
cana-4138	117	1	𝑡𝛼−1𝑑𝑡	𝑡𝛼−1𝑑𝑡	NUM
cana-4138	117	2	𝑡	𝑡	NOUN
cana-4138	117	3	0	0	NUM
cana-4138	117	4	+	+	NUM
cana-4138	117	5	∫	∫	PROPN
cana-4138	117	6	𝑡𝛼−1	𝑡𝛼−1	PROPN
cana-4138	117	7	𝑡	𝑡	PROPN
cana-4138	117	8	0	0	PUNCT
cana-4138	118	1	[	[	X
cana-4138	118	2	∫	∫	PROPN
cana-4138	118	3	𝑘(𝑡	𝑘(𝑡	PROPN
cana-4138	118	4	,	,	PUNCT
cana-4138	118	5	𝑠	𝑠	INTJ
cana-4138	118	6	,	,	PUNCT
cana-4138	118	7	𝑥(𝑠))𝑑𝑠	𝑥(𝑠))𝑑𝑠	AUX
cana-4138	118	8	𝑡	𝑡	NOUN
cana-4138	118	9	0	0	NUM
cana-4138	118	10	]	]	PUNCT
cana-4138	118	11	𝑑𝑡	𝑑𝑡	ADP
cana-4138	118	12	+	+	CCONJ
cana-4138	118	13	∫	∫	PROPN
cana-4138	118	14	𝑡𝛼−1	𝑡𝛼−1	PROPN
cana-4138	118	15	[	[	X
cana-4138	118	16	∫	∫	PROPN
cana-4138	118	17	ℎ(𝑡	ℎ(𝑡	PROPN
cana-4138	118	18	,	,	PUNCT
cana-4138	118	19	𝑠	𝑠	PROPN
cana-4138	118	20	,	,	PUNCT
cana-4138	118	21	𝑥(𝑠))𝑑𝑠	𝑥(𝑠))𝑑𝑠	VERB
cana-4138	118	22	𝑏	𝑏	SYM
cana-4138	118	23	0	0	NUM
cana-4138	118	24	]	]	PUNCT
cana-4138	118	25	𝑡	𝑡	X
cana-4138	118	26	0	0	NUM
cana-4138	118	27	𝑑𝑡	𝑑𝑡	ADP
cana-4138	118	28	𝐹𝑦(𝑡	𝐹𝑦(𝑡	NUM
cana-4138	118	29	)	)	PUNCT
cana-4138	118	30	=	=	SYM
cana-4138	118	31	𝑦0	𝑦0	NOUN
cana-4138	118	32	+	+	CCONJ
cana-4138	118	33	∫	∫	PROPN
cana-4138	118	34	𝑓(𝑡	𝑓(𝑡	NOUN
cana-4138	118	35	)	)	PUNCT
cana-4138	118	36	.	.	PUNCT
cana-4138	119	1	𝑡𝛼−1𝑑𝑡	𝑡𝛼−1𝑑𝑡	NUM
cana-4138	119	2	𝑡	𝑡	NOUN
cana-4138	119	3	0	0	NUM
cana-4138	119	4	+	+	NUM
cana-4138	119	5	∫	∫	NUM
cana-4138	119	6	𝑡𝛼−1	𝑡𝛼−1	PROPN
cana-4138	119	7	[	[	X
cana-4138	119	8	∫	∫	PROPN
cana-4138	119	9	𝑘(𝑡	𝑘(𝑡	PROPN
cana-4138	119	10	,	,	PUNCT
cana-4138	119	11	𝑠	𝑠	PROPN
cana-4138	119	12	,	,	PUNCT
cana-4138	119	13	𝑦(𝑠))𝑑𝑠	𝑦(𝑠))𝑑𝑠	PROPN
cana-4138	119	14	𝑡	𝑡	PROPN
cana-4138	119	15	0	0	NUM
cana-4138	119	16	]	]	PUNCT
cana-4138	119	17	𝑑𝑡	𝑑𝑡	ADP
cana-4138	119	18	𝑡	𝑡	PROPN
cana-4138	119	19	0	0	PUNCT
cana-4138	120	1	+	+	NUM
cana-4138	121	1	∫	∫	PROPN
cana-4138	121	2	𝑡𝛼−1	𝑡𝛼−1	PROPN
cana-4138	121	3	𝑡	𝑡	PROPN
cana-4138	121	4	0	0	PUNCT
cana-4138	122	1	[	[	X
cana-4138	122	2	∫	∫	X
cana-4138	122	3	ℎ(𝑡	ℎ(𝑡	PROPN
cana-4138	122	4	,	,	PUNCT
cana-4138	122	5	𝑠	𝑠	PROPN
cana-4138	122	6	,	,	PUNCT
cana-4138	122	7	𝑦(𝑠))𝑑𝑠	𝑦(𝑠))𝑑𝑠	PROPN
cana-4138	122	8	𝑏	𝑏	NOUN
cana-4138	122	9	0	0	NUM
cana-4138	122	10	]	]	PUNCT
cana-4138	122	11	𝑑𝑡	𝑑𝑡	ADP
cana-4138	122	12	using	use	VERB
cana-4138	122	13	the	the	DET
cana-4138	122	14	conditions	condition	NOUN
cana-4138	122	15	1	1	NUM
cana-4138	122	16	)	)	PUNCT
cana-4138	122	17	and	and	CCONJ
cana-4138	122	18	2	2	NUM
cana-4138	122	19	)	)	PUNCT
cana-4138	122	20	,	,	PUNCT
cana-4138	122	21	for	for	ADP
cana-4138	122	22	all	all	DET
cana-4138	122	23	𝑥	𝑥	PROPN
cana-4138	122	24	,	,	PUNCT
cana-4138	122	25	𝑦	𝑦	NOUN
cana-4138	122	26	∈	∈	PROPN
cana-4138	122	27	𝐵	𝐵	NOUN
cana-4138	122	28	,	,	PUNCT
cana-4138	122	29	we	we	PRON
cana-4138	122	30	have	have	VERB
cana-4138	122	31	(	(	PUNCT
cana-4138	122	32	‖𝐹𝑥(𝑡	‖𝐹𝑥(𝑡	ADJ
cana-4138	122	33	)	)	PUNCT
cana-4138	122	34	−	−	PROPN
cana-4138	123	1	𝐹𝑦(𝑡)‖	𝐹𝑦(𝑡)‖	ADJ
cana-4138	123	2	,	,	PUNCT
cana-4138	123	3	𝑎‖𝐹𝑥(𝑡	𝑎‖𝐹𝑥(𝑡	PROPN
cana-4138	123	4	)	)	PUNCT
cana-4138	123	5	−	−	ADP
cana-4138	123	6	𝐹𝑦(𝑡)‖	𝐹𝑦(𝑡)‖	NOUN
cana-4138	123	7	)	)	PUNCT
cana-4138	123	8	communications	communication	NOUN
cana-4138	123	9	on	on	ADP
cana-4138	123	10	applied	apply	VERB
cana-4138	123	11	nonlinear	nonlinear	ADJ
cana-4138	123	12	analysis	analysis	NOUN
cana-4138	123	13	issn	issn	NOUN
cana-4138	123	14	:	:	PUNCT
cana-4138	123	15	1074	1074	NUM
cana-4138	123	16	-	-	PUNCT
cana-4138	123	17	133x	133x	NUM
cana-4138	123	18	vol	vol	NOUN
cana-4138	123	19	32	32	NUM
cana-4138	123	20	no	no	NOUN
cana-4138	123	21	.	.	PUNCT
cana-4138	124	1	9s	9s	NUM
cana-4138	124	2	(	(	PUNCT
cana-4138	124	3	2025	2025	NUM
cana-4138	124	4	)	)	PUNCT
cana-4138	124	5	1308	1308	NUM
cana-4138	124	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4138	125	1	=	=	PUNCT
cana-4138	125	2	(	(	PUNCT
cana-4138	125	3	‖𝑥0	‖𝑥0	ADV
cana-4138	125	4	−	−	PROPN
cana-4138	126	1	𝑦0‖	𝑦0‖	PROPN
cana-4138	126	2	+	+	CCONJ
cana-4138	126	3	‖∫	‖∫	PROPN
cana-4138	126	4	𝑡𝛼−1	𝑡𝛼−1	NOUN
cana-4138	126	5	𝑡	𝑡	PROPN
cana-4138	126	6	0	0	PUNCT
cana-4138	127	1	[	[	X
cana-4138	127	2	∫	∫	PROPN
cana-4138	127	3	𝑘(𝑡	𝑘(𝑡	PROPN
cana-4138	127	4	,	,	PUNCT
cana-4138	127	5	𝑠	𝑠	INTJ
cana-4138	127	6	,	,	PUNCT
cana-4138	127	7	𝑥(𝑠))𝑑𝑠	𝑥(𝑠))𝑑𝑠	VERB
cana-4138	127	8	𝑡	𝑡	NOUN
cana-4138	127	9	0	0	NUM
cana-4138	127	10	]	]	PUNCT
cana-4138	127	11	𝑑𝑡	𝑑𝑡	ADP
cana-4138	127	12	+	+	CCONJ
cana-4138	127	13	∫	∫	PROPN
cana-4138	127	14	𝑡𝛼−1	𝑡𝛼−1	PROPN
cana-4138	127	15	𝑡	𝑡	PROPN
cana-4138	127	16	0	0	PUNCT
cana-4138	128	1	[	[	X
cana-4138	128	2	∫	∫	X
cana-4138	128	3	ℎ(𝑡	ℎ(𝑡	PROPN
cana-4138	128	4	,	,	PUNCT
cana-4138	128	5	𝑠	𝑠	PROPN
cana-4138	128	6	,	,	PUNCT
cana-4138	128	7	𝑥(𝑠))𝑑𝑠	𝑥(𝑠))𝑑𝑠	VERB
cana-4138	128	8	𝑏	𝑏	SYM
cana-4138	128	9	0	0	NUM
cana-4138	128	10	]	]	PUNCT
cana-4138	128	11	𝑑𝑡	𝑑𝑡	ADP
cana-4138	128	12	−	−	PROPN
cana-4138	128	13	∫	∫	PROPN
cana-4138	128	14	𝑡𝛼−1	𝑡𝛼−1	PROPN
cana-4138	128	15	𝑡	𝑡	PROPN
cana-4138	128	16	0	0	PUNCT
cana-4138	129	1	[	[	X
cana-4138	129	2	∫	∫	PROPN
cana-4138	129	3	𝑘(𝑡	𝑘(𝑡	PROPN
cana-4138	129	4	,	,	PUNCT
cana-4138	129	5	𝑠	𝑠	PROPN
cana-4138	129	6	,	,	PUNCT
cana-4138	129	7	𝑦(𝑠))𝑑𝑠	𝑦(𝑠))𝑑𝑠	PROPN
cana-4138	129	8	𝑡	𝑡	PROPN
cana-4138	129	9	0	0	NUM
cana-4138	129	10	]	]	PUNCT
cana-4138	129	11	𝑑𝑡	𝑑𝑡	ADP
cana-4138	129	12	−	−	PROPN
cana-4138	129	13	∫	∫	PROPN
cana-4138	129	14	𝑡𝛼−1	𝑡𝛼−1	PROPN
cana-4138	129	15	𝑡	𝑡	PROPN
cana-4138	129	16	0	0	PUNCT
cana-4138	130	1	[	[	X
cana-4138	130	2	∫	∫	X
cana-4138	130	3	ℎ(𝑡	ℎ(𝑡	PROPN
cana-4138	130	4	,	,	PUNCT
cana-4138	130	5	𝑠	𝑠	PROPN
cana-4138	130	6	,	,	PUNCT
cana-4138	130	7	𝑦(𝑠))𝑑𝑠	𝑦(𝑠))𝑑𝑠	PROPN
cana-4138	130	8	𝑏	𝑏	NOUN
cana-4138	130	9	0	0	NUM
cana-4138	130	10	]	]	PUNCT
cana-4138	130	11	𝑑𝑡‖	𝑑𝑡‖	NOUN
cana-4138	130	12	,	,	PUNCT
cana-4138	130	13	𝑎‖𝑥0	𝑎‖𝑥0	PROPN
cana-4138	130	14	−	−	PROPN
cana-4138	131	1	𝑦0‖	𝑦0‖	PROPN
cana-4138	132	1	+	+	CCONJ
cana-4138	132	2	𝑎	𝑎	DET
cana-4138	132	3	‖∫	‖∫	NOUN
cana-4138	132	4	𝑡𝛼−1	𝑡𝛼−1	NOUN
cana-4138	132	5	𝑡	𝑡	PROPN
cana-4138	132	6	0	0	PUNCT
cana-4138	133	1	[	[	X
cana-4138	133	2	∫	∫	PROPN
cana-4138	133	3	𝑘(𝑡	𝑘(𝑡	PROPN
cana-4138	133	4	,	,	PUNCT
cana-4138	133	5	𝑠	𝑠	INTJ
cana-4138	133	6	,	,	PUNCT
cana-4138	133	7	𝑥(𝑠))𝑑𝑠	𝑥(𝑠))𝑑𝑠	VERB
cana-4138	133	8	𝑡	𝑡	NOUN
cana-4138	133	9	0	0	NUM
cana-4138	133	10	]	]	PUNCT
cana-4138	133	11	𝑑𝑡	𝑑𝑡	ADP
cana-4138	133	12	+	+	CCONJ
cana-4138	133	13	∫	∫	PROPN
cana-4138	133	14	𝑡𝛼−1	𝑡𝛼−1	PROPN
cana-4138	133	15	𝑡	𝑡	PROPN
cana-4138	133	16	0	0	PUNCT
cana-4138	134	1	[	[	X
cana-4138	134	2	∫	∫	X
cana-4138	134	3	ℎ(𝑡	ℎ(𝑡	PROPN
cana-4138	134	4	,	,	PUNCT
cana-4138	134	5	𝑠	𝑠	PROPN
cana-4138	134	6	,	,	PUNCT
cana-4138	134	7	𝑥(𝑠))𝑑𝑠	𝑥(𝑠))𝑑𝑠	VERB
cana-4138	134	8	𝑏	𝑏	SYM
cana-4138	134	9	0	0	NUM
cana-4138	134	10	]	]	PUNCT
cana-4138	134	11	𝑑𝑡	𝑑𝑡	ADP
cana-4138	134	12	−	−	PROPN
cana-4138	134	13	∫	∫	PROPN
cana-4138	134	14	𝑡𝛼−1	𝑡𝛼−1	PROPN
cana-4138	134	15	𝑡	𝑡	PROPN
cana-4138	134	16	0	0	PUNCT
cana-4138	135	1	[	[	X
cana-4138	135	2	∫	∫	PROPN
cana-4138	135	3	𝑘(𝑡	𝑘(𝑡	PROPN
cana-4138	135	4	,	,	PUNCT
cana-4138	135	5	𝑠	𝑠	PROPN
cana-4138	135	6	,	,	PUNCT
cana-4138	135	7	𝑦(𝑠))𝑑𝑠	𝑦(𝑠))𝑑𝑠	PROPN
cana-4138	135	8	𝑡	𝑡	PROPN
cana-4138	135	9	0	0	NUM
cana-4138	135	10	]	]	PUNCT
cana-4138	135	11	𝑑𝑡	𝑑𝑡	ADP
cana-4138	135	12	−	−	PROPN
cana-4138	135	13	∫	∫	PROPN
cana-4138	135	14	𝑡𝛼−1	𝑡𝛼−1	PROPN
cana-4138	135	15	𝑡	𝑡	PROPN
cana-4138	135	16	0	0	PUNCT
cana-4138	136	1	[	[	X
cana-4138	136	2	∫	∫	X
cana-4138	136	3	ℎ(𝑡	ℎ(𝑡	PROPN
cana-4138	136	4	,	,	PUNCT
cana-4138	136	5	𝑠	𝑠	PROPN
cana-4138	136	6	,	,	PUNCT
cana-4138	136	7	𝑦(𝑠))𝑑𝑠	𝑦(𝑠))𝑑𝑠	PROPN
cana-4138	136	8	𝑏	𝑏	NOUN
cana-4138	136	9	0	0	NUM
cana-4138	136	10	]	]	PUNCT
cana-4138	136	11	𝑑𝑡‖	𝑑𝑡‖	NOUN
cana-4138	136	12	)	)	PUNCT
cana-4138	136	13	≤	≤	NOUN
cana-4138	136	14	(	(	PUNCT
cana-4138	136	15	‖𝑥0	‖𝑥0	NOUN
cana-4138	136	16	−	−	PROPN
cana-4138	137	1	𝑦0‖	𝑦0‖	PROPN
cana-4138	138	1	+	+	NUM
cana-4138	139	1	∫	∫	PROPN
cana-4138	139	2	𝑡𝛼−1	𝑡𝛼−1	PROPN
cana-4138	139	3	𝑡	𝑡	PROPN
cana-4138	139	4	0	0	PUNCT
cana-4138	140	1	[	[	X
cana-4138	140	2	∫	∫	X
cana-4138	140	3	‖𝑘(𝑡	‖𝑘(𝑡	PUNCT
cana-4138	140	4	,	,	PUNCT
cana-4138	140	5	𝑠	𝑠	INTJ
cana-4138	140	6	,	,	PUNCT
cana-4138	140	7	𝑥(𝑠	𝑥(𝑠	PROPN
cana-4138	140	8	)	)	PUNCT
cana-4138	140	9	)	)	PUNCT
cana-4138	141	1	−	−	PROPN
cana-4138	142	1	𝑘(𝑡	𝑘(𝑡	PROPN
cana-4138	142	2	,	,	PUNCT
cana-4138	142	3	𝑠	𝑠	PROPN
cana-4138	142	4	,	,	PUNCT
cana-4138	142	5	𝑦(𝑠))‖𝑑𝑠	𝑦(𝑠))‖𝑑𝑠	PROPN
cana-4138	142	6	𝑡	𝑡	PROPN
cana-4138	142	7	0	0	NUM
cana-4138	142	8	]	]	PUNCT
cana-4138	142	9	𝑑𝑡	𝑑𝑡	ADP
cana-4138	142	10	+	+	CCONJ
cana-4138	142	11	∫	∫	PROPN
cana-4138	142	12	𝑡𝛼−1	𝑡𝛼−1	PROPN
cana-4138	142	13	[	[	X
cana-4138	142	14	∫	∫	X
cana-4138	142	15	‖ℎ(𝑡	‖ℎ(𝑡	PROPN
cana-4138	142	16	,	,	PUNCT
cana-4138	142	17	𝑠	𝑠	INTJ
cana-4138	142	18	,	,	PUNCT
cana-4138	142	19	𝑥(𝑠	𝑥(𝑠	PROPN
cana-4138	142	20	)	)	PUNCT
cana-4138	142	21	)	)	PUNCT
cana-4138	143	1	−	−	PROPN
cana-4138	143	2	ℎ(𝑡	ℎ(𝑡	PROPN
cana-4138	143	3	,	,	PUNCT
cana-4138	143	4	𝑠	𝑠	PROPN
cana-4138	143	5	,	,	PUNCT
cana-4138	143	6	𝑦(𝑠))‖𝑑𝑠	𝑦(𝑠))‖𝑑𝑠	NOUN
cana-4138	143	7	𝑏	𝑏	PROPN
cana-4138	143	8	0	0	NUM
cana-4138	143	9	]	]	PUNCT
cana-4138	143	10	𝑑𝑡	𝑑𝑡	ADP
cana-4138	143	11	,	,	PUNCT
cana-4138	143	12	𝑡	𝑡	X
cana-4138	143	13	0	0	PUNCT
cana-4138	143	14	𝑎‖𝑥0	𝑎‖𝑥0	PROPN
cana-4138	143	15	−	−	PROPN
cana-4138	144	1	𝑦0‖	𝑦0‖	PROPN
cana-4138	145	1	+	+	CCONJ
cana-4138	145	2	𝑎	𝑎	PRON
cana-4138	145	3	∫	∫	NUM
cana-4138	145	4	𝑡𝛼−1	𝑡𝛼−1	NOUN
cana-4138	145	5	𝑡	𝑡	PROPN
cana-4138	145	6	0	0	PUNCT
cana-4138	146	1	[	[	X
cana-4138	146	2	∫	∫	X
cana-4138	146	3	‖𝑘(𝑡	‖𝑘(𝑡	PUNCT
cana-4138	146	4	,	,	PUNCT
cana-4138	146	5	𝑠	𝑠	INTJ
cana-4138	146	6	,	,	PUNCT
cana-4138	146	7	𝑥(𝑠	𝑥(𝑠	PROPN
cana-4138	146	8	)	)	PUNCT
cana-4138	146	9	)	)	PUNCT
cana-4138	147	1	−	−	PROPN
cana-4138	148	1	𝑘(𝑡	𝑘(𝑡	PROPN
cana-4138	148	2	,	,	PUNCT
cana-4138	148	3	𝑠	𝑠	PROPN
cana-4138	148	4	,	,	PUNCT
cana-4138	148	5	𝑦(𝑠))‖𝑑𝑠	𝑦(𝑠))‖𝑑𝑠	PROPN
cana-4138	148	6	𝑡	𝑡	PROPN
cana-4138	148	7	0	0	NUM
cana-4138	148	8	]	]	PUNCT
cana-4138	148	9	𝑑𝑡	𝑑𝑡	ADP
cana-4138	148	10	+	+	CCONJ
cana-4138	148	11	𝑎	𝑎	DET
cana-4138	148	12	∫	∫	NUM
cana-4138	148	13	𝑡𝛼−1	𝑡𝛼−1	NOUN
cana-4138	148	14	[	[	X
cana-4138	148	15	∫	∫	X
cana-4138	148	16	‖ℎ(𝑡	‖ℎ(𝑡	PROPN
cana-4138	148	17	,	,	PUNCT
cana-4138	148	18	𝑠	𝑠	INTJ
cana-4138	148	19	,	,	PUNCT
cana-4138	148	20	𝑥(𝑠	𝑥(𝑠	PROPN
cana-4138	148	21	)	)	PUNCT
cana-4138	148	22	)	)	PUNCT
cana-4138	149	1	−	−	PROPN
cana-4138	150	1	ℎ(𝑡	ℎ(𝑡	PROPN
cana-4138	150	2	,	,	PUNCT
cana-4138	150	3	𝑠	𝑠	PROPN
cana-4138	150	4	,	,	PUNCT
cana-4138	150	5	𝑦(𝑠))‖𝑑𝑠	𝑦(𝑠))‖𝑑𝑠	NOUN
cana-4138	150	6	𝑏	𝑏	PROPN
cana-4138	150	7	0	0	NUM
cana-4138	150	8	]	]	PUNCT
cana-4138	150	9	𝑑𝑡	𝑑𝑡	ADP
cana-4138	150	10	𝑡	𝑡	PROPN
cana-4138	150	11	0	0	NUM
cana-4138	150	12	)	)	PUNCT
cana-4138	150	13	≤	≤	NOUN
cana-4138	150	14	(	(	PUNCT
cana-4138	150	15	∫	∫	PROPN
cana-4138	150	16	𝑡𝛼−1	𝑡𝛼−1	PROPN
cana-4138	150	17	𝑡	𝑡	PROPN
cana-4138	150	18	0	0	PUNCT
cana-4138	151	1	[	[	X
cana-4138	151	2	∫	∫	X
cana-4138	151	3	‖𝑘(𝑡	‖𝑘(𝑡	PUNCT
cana-4138	151	4	,	,	PUNCT
cana-4138	151	5	𝑠	𝑠	INTJ
cana-4138	151	6	,	,	PUNCT
cana-4138	151	7	𝑥(𝑠	𝑥(𝑠	PROPN
cana-4138	151	8	)	)	PUNCT
cana-4138	151	9	)	)	PUNCT
cana-4138	152	1	−	−	PROPN
cana-4138	153	1	𝑘(𝑡	𝑘(𝑡	PROPN
cana-4138	153	2	,	,	PUNCT
cana-4138	153	3	𝑠	𝑠	PROPN
cana-4138	153	4	,	,	PUNCT
cana-4138	153	5	𝑦(𝑠))‖𝑑𝑠	𝑦(𝑠))‖𝑑𝑠	PROPN
cana-4138	153	6	𝑡	𝑡	PROPN
cana-4138	153	7	0	0	NUM
cana-4138	153	8	]	]	PUNCT
cana-4138	153	9	𝑑𝑡	𝑑𝑡	ADP
cana-4138	153	10	,	,	PUNCT
cana-4138	153	11	𝑎	𝑎	DET
cana-4138	153	12	∫	∫	NUM
cana-4138	153	13	𝑡𝛼−1	𝑡𝛼−1	NOUN
cana-4138	153	14	𝑡	𝑡	PROPN
cana-4138	153	15	0	0	PUNCT
cana-4138	154	1	[	[	X
cana-4138	154	2	∫	∫	X
cana-4138	154	3	‖𝑘(𝑡	‖𝑘(𝑡	PUNCT
cana-4138	154	4	,	,	PUNCT
cana-4138	154	5	𝑠	𝑠	INTJ
cana-4138	154	6	,	,	PUNCT
cana-4138	154	7	𝑥(𝑠	𝑥(𝑠	PROPN
cana-4138	154	8	)	)	PUNCT
cana-4138	154	9	)	)	PUNCT
cana-4138	155	1	𝑡	𝑡	ADP
cana-4138	155	2	0	0	NUM
cana-4138	155	3	−	−	PROPN
cana-4138	156	1	𝑘(𝑡	𝑘(𝑡	PROPN
cana-4138	156	2	,	,	PUNCT
cana-4138	156	3	𝑠	𝑠	PROPN
cana-4138	156	4	,	,	PUNCT
cana-4138	156	5	𝑦(𝑠))‖𝑑𝑠	𝑦(𝑠))‖𝑑𝑠	PROPN
cana-4138	156	6	]	]	PUNCT
cana-4138	156	7	𝑑𝑡	𝑑𝑡	VERB
cana-4138	156	8	)	)	PUNCT
cana-4138	156	9	+	+	CCONJ
cana-4138	156	10	(	(	PUNCT
cana-4138	156	11	∫	∫	INTJ
cana-4138	156	12	𝑡𝛼−1	𝑡𝛼−1	PROPN
cana-4138	156	13	[	[	X
cana-4138	156	14	∫	∫	X
cana-4138	156	15	‖ℎ(𝑡	‖ℎ(𝑡	PROPN
cana-4138	156	16	,	,	PUNCT
cana-4138	156	17	𝑠	𝑠	INTJ
cana-4138	156	18	,	,	PUNCT
cana-4138	156	19	𝑥(𝑠	𝑥(𝑠	PROPN
cana-4138	156	20	)	)	PUNCT
cana-4138	156	21	)	)	PUNCT
cana-4138	157	1	−	−	PROPN
cana-4138	157	2	ℎ(𝑡	ℎ(𝑡	PROPN
cana-4138	157	3	,	,	PUNCT
cana-4138	157	4	𝑠	𝑠	PROPN
cana-4138	157	5	,	,	PUNCT
cana-4138	157	6	𝑦(𝑠))‖𝑑𝑠	𝑦(𝑠))‖𝑑𝑠	NOUN
cana-4138	157	7	𝑏	𝑏	PROPN
cana-4138	157	8	0	0	NUM
cana-4138	157	9	]	]	PUNCT
cana-4138	157	10	𝑑𝑡	𝑑𝑡	ADP
cana-4138	157	11	,	,	PUNCT
cana-4138	157	12	𝑡	𝑡	PROPN
cana-4138	157	13	0	0	NUM
cana-4138	157	14	𝑎	𝑎	DET
cana-4138	157	15	∫	∫	NOUN
cana-4138	157	16	𝑡𝛼−1	𝑡𝛼−1	NOUN
cana-4138	157	17	[	[	X
cana-4138	157	18	∫	∫	X
cana-4138	157	19	‖ℎ(𝑡	‖ℎ(𝑡	PROPN
cana-4138	157	20	,	,	PUNCT
cana-4138	157	21	𝑠	𝑠	INTJ
cana-4138	157	22	,	,	PUNCT
cana-4138	157	23	𝑥(𝑠	𝑥(𝑠	PROPN
cana-4138	157	24	)	)	PUNCT
cana-4138	157	25	)	)	PUNCT
cana-4138	158	1	𝑏	𝑏	NOUN
cana-4138	158	2	0	0	NUM
cana-4138	158	3	𝑡	𝑡	NOUN
cana-4138	158	4	0	0	NUM
cana-4138	158	5	−	−	NOUN
cana-4138	158	6	ℎ(𝑡	ℎ(𝑡	PROPN
cana-4138	158	7	,	,	PUNCT
cana-4138	158	8	𝑠	𝑠	PROPN
cana-4138	158	9	,	,	PUNCT
cana-4138	158	10	𝑦(𝑠))‖𝑑𝑠	𝑦(𝑠))‖𝑑𝑠	PROPN
cana-4138	158	11	]	]	PUNCT
cana-4138	158	12	𝑑𝑡	𝑑𝑡	ADP
cana-4138	158	13	)	)	PUNCT
cana-4138	158	14	≤	≤	NUM
cana-4138	158	15	∫	∫	NOUN
cana-4138	158	16	𝑡𝛼−1	𝑡𝛼−1	PROPN
cana-4138	158	17	[	[	X
cana-4138	158	18	∫	∫	PROPN
cana-4138	158	19	𝑝1(𝑡	𝑝1(𝑡	PROPN
cana-4138	158	20	,	,	PUNCT
cana-4138	158	21	𝑠)𝜙(𝑑(𝑥	𝑠)𝜙(𝑑(𝑥	PROPN
cana-4138	158	22	,	,	PUNCT
cana-4138	158	23	𝑦))𝑑𝑠	𝑦))𝑑𝑠	PROPN
cana-4138	158	24	𝑡	𝑡	X
cana-4138	158	25	0	0	NUM
cana-4138	158	26	]	]	PUNCT
cana-4138	158	27	𝑑𝑡	𝑑𝑡	ADP
cana-4138	158	28	+	+	CCONJ
cana-4138	158	29	∫	∫	PROPN
cana-4138	158	30	𝑡𝛼−1	𝑡𝛼−1	PROPN
cana-4138	158	31	[	[	X
cana-4138	158	32	∫	∫	PROPN
cana-4138	158	33	𝑝2(𝑡	𝑝2(𝑡	PROPN
cana-4138	158	34	,	,	PUNCT
cana-4138	158	35	𝑠)𝜙(𝑑(𝑥	𝑠)𝜙(𝑑(𝑥	PROPN
cana-4138	158	36	,	,	PUNCT
cana-4138	158	37	𝑦))𝑑𝑠	𝑦))𝑑𝑠	PROPN
cana-4138	158	38	𝑏	𝑏	NOUN
cana-4138	158	39	0	0	NUM
cana-4138	158	40	]	]	PUNCT
cana-4138	158	41	𝑑𝑡	𝑑𝑡	ADP
cana-4138	158	42	𝑡	𝑡	PROPN
cana-4138	158	43	0	0	PUNCT
cana-4138	158	44	𝑡	𝑡	SYM
cana-4138	158	45	0	0	NUM
cana-4138	158	46	≤	≤	NUM
cana-4138	158	47	∫	∫	NOUN
cana-4138	158	48	𝑡𝛼−1	𝑡𝛼−1	PROPN
cana-4138	158	49	𝑡	𝑡	PROPN
cana-4138	158	50	0	0	PUNCT
cana-4138	159	1	[	[	X
cana-4138	159	2	∫	∫	PROPN
cana-4138	159	3	𝑝1(𝑡	𝑝1(𝑡	PROPN
cana-4138	159	4	,	,	PUNCT
cana-4138	159	5	𝑠)𝜙(‖𝑥	𝑠)𝜙(‖𝑥	ADJ
cana-4138	159	6	−	−	NOUN
cana-4138	159	7	𝑦‖∞	𝑦‖∞	NOUN
cana-4138	159	8	,	,	PUNCT
cana-4138	159	9	𝑎‖𝑥	𝑎‖𝑥	NOUN
cana-4138	159	10	−	−	NOUN
cana-4138	159	11	𝑦‖∞)𝑑𝑠	𝑦‖∞)𝑑𝑠	PROPN
cana-4138	159	12	𝑡	𝑡	PROPN
cana-4138	159	13	0	0	NUM
cana-4138	159	14	]	]	PUNCT
cana-4138	159	15	𝑑𝑡	𝑑𝑡	ADP
cana-4138	159	16	+	+	CCONJ
cana-4138	159	17	∫	∫	PROPN
cana-4138	159	18	𝑡𝛼−1	𝑡𝛼−1	PROPN
cana-4138	159	19	[	[	X
cana-4138	159	20	∫	∫	PROPN
cana-4138	159	21	𝑝2(𝑡	𝑝2(𝑡	PROPN
cana-4138	159	22	,	,	PUNCT
cana-4138	159	23	𝑠)𝜙(‖𝑥	𝑠)𝜙(‖𝑥	ADJ
cana-4138	159	24	−	−	NOUN
cana-4138	159	25	𝑦‖∞	𝑦‖∞	NOUN
cana-4138	159	26	,	,	PUNCT
cana-4138	159	27	𝑎‖𝑥	𝑎‖𝑥	NOUN
cana-4138	159	28	−	−	PUNCT
cana-4138	159	29	𝑦‖∞)𝑑𝑠	𝑦‖∞)𝑑𝑠	PROPN
cana-4138	159	30	𝑏	𝑏	NOUN
cana-4138	159	31	0	0	NUM
cana-4138	159	32	]	]	PUNCT
cana-4138	159	33	𝑑𝑡	𝑑𝑡	ADP
cana-4138	159	34	𝑡	𝑡	PROPN
cana-4138	159	35	0	0	PROPN
cana-4138	159	36	≤	≤	NUM
cana-4138	159	37	∫	∫	NOUN
cana-4138	159	38	𝑡𝛼−1	𝑡𝛼−1	NOUN
cana-4138	159	39	𝑏	𝑏	SYM
cana-4138	159	40	0	0	NUM
cana-4138	160	1	[	[	X
cana-4138	160	2	∫	∫	PROPN
cana-4138	160	3	𝑝1(𝑡	𝑝1(𝑡	PROPN
cana-4138	160	4	,	,	PUNCT
cana-4138	160	5	𝑠)𝜙(‖𝑥	𝑠)𝜙(‖𝑥	ADJ
cana-4138	160	6	−	−	NOUN
cana-4138	160	7	𝑦‖∞	𝑦‖∞	NOUN
cana-4138	160	8	,	,	PUNCT
cana-4138	160	9	𝑎‖𝑥	𝑎‖𝑥	NOUN
cana-4138	160	10	−	−	PUNCT
cana-4138	160	11	𝑦‖∞)𝑑𝑠	𝑦‖∞)𝑑𝑠	PROPN
cana-4138	160	12	𝑏	𝑏	NOUN
cana-4138	160	13	0	0	NUM
cana-4138	160	14	]	]	PUNCT
cana-4138	160	15	𝑑𝑡	𝑑𝑡	ADP
cana-4138	160	16	+	+	CCONJ
cana-4138	160	17	∫	∫	PROPN
cana-4138	160	18	𝑡𝛼−1	𝑡𝛼−1	PROPN
cana-4138	160	19	[	[	X
cana-4138	160	20	∫	∫	PROPN
cana-4138	160	21	𝑝2(𝑡	𝑝2(𝑡	PROPN
cana-4138	160	22	,	,	PUNCT
cana-4138	160	23	𝑠)𝜙(‖𝑥	𝑠)𝜙(‖𝑥	ADJ
cana-4138	160	24	−	−	NOUN
cana-4138	160	25	𝑦‖∞	𝑦‖∞	NOUN
cana-4138	160	26	,	,	PUNCT
cana-4138	160	27	𝑎‖𝑥	𝑎‖𝑥	NOUN
cana-4138	160	28	−	−	PUNCT
cana-4138	160	29	𝑦‖∞)𝑑𝑠	𝑦‖∞)𝑑𝑠	PROPN
cana-4138	160	30	𝑏	𝑏	NOUN
cana-4138	160	31	0	0	NUM
cana-4138	160	32	]	]	PUNCT
cana-4138	160	33	𝑑𝑡	𝑑𝑡	ADP
cana-4138	160	34	𝑏	𝑏	NOUN
cana-4138	160	35	0	0	NUM
cana-4138	160	36	communications	communication	NOUN
cana-4138	160	37	on	on	ADP
cana-4138	160	38	applied	apply	VERB
cana-4138	160	39	nonlinear	nonlinear	ADJ
cana-4138	160	40	analysis	analysis	NOUN
cana-4138	160	41	issn	issn	NOUN
cana-4138	160	42	:	:	PUNCT
cana-4138	160	43	1074	1074	NUM
cana-4138	160	44	-	-	PUNCT
cana-4138	160	45	133x	133x	NUM
cana-4138	160	46	vol	vol	NOUN
cana-4138	160	47	32	32	NUM
cana-4138	160	48	no	no	NOUN
cana-4138	160	49	.	.	PUNCT
cana-4138	161	1	9s	9s	NUM
cana-4138	161	2	(	(	PUNCT
cana-4138	161	3	2025	2025	NUM
cana-4138	161	4	)	)	PUNCT
cana-4138	161	5	1309	1309	NUM
cana-4138	162	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4138	162	2	≤	≤	PUNCT
cana-4138	162	3	𝜙(‖𝑥	𝜙(‖𝑥	ADP
cana-4138	162	4	−	−	NOUN
cana-4138	162	5	𝑦‖∞	𝑦‖∞	NOUN
cana-4138	162	6	,	,	PUNCT
cana-4138	162	7	𝑎‖𝑥	𝑎‖𝑥	NOUN
cana-4138	162	8	−	−	NOUN
cana-4138	162	9	𝑦‖∞	𝑦‖∞	NOUN
cana-4138	162	10	)	)	PUNCT
cana-4138	162	11	∫	∫	NOUN
cana-4138	162	12	𝑡𝛼−1	𝑡𝛼−1	PROPN
cana-4138	162	13	[	[	X
cana-4138	162	14	∫[𝑝1(𝑡	∫[𝑝1(𝑡	NOUN
cana-4138	162	15	,	,	PUNCT
cana-4138	162	16	𝑠	𝑠	PROPN
cana-4138	162	17	)	)	PUNCT
cana-4138	162	18	+	+	CCONJ
cana-4138	162	19	𝑝2(𝑡	𝑝2(𝑡	PROPN
cana-4138	162	20	,	,	PUNCT
cana-4138	162	21	𝑠	𝑠	NOUN
cana-4138	162	22	)	)	PUNCT
cana-4138	162	23	]	]	PUNCT
cana-4138	163	1	𝑏	𝑏	X
cana-4138	163	2	0	0	NUM
cana-4138	163	3	𝑑𝑠	𝑑𝑠	NOUN
cana-4138	163	4	]	]	PUNCT
cana-4138	163	5	𝑑𝑡	𝑑𝑡	ADP
cana-4138	163	6	𝑏	𝑏	SYM
cana-4138	163	7	0	0	NUM
cana-4138	163	8	≤	≤	NOUN
cana-4138	163	9	𝜙(‖𝑥	𝜙(‖𝑥	PUNCT
cana-4138	163	10	−	−	NOUN
cana-4138	163	11	𝑦‖∞	𝑦‖∞	NOUN
cana-4138	163	12	,	,	PUNCT
cana-4138	163	13	𝑎‖𝑥	𝑎‖𝑥	NOUN
cana-4138	163	14	−	−	NOUN
cana-4138	163	15	𝑦‖∞	𝑦‖∞	NOUN
cana-4138	163	16	)	)	PUNCT
cana-4138	163	17	this	this	PRON
cana-4138	163	18	implies	imply	VERB
cana-4138	163	19	that	that	SCONJ
cana-4138	163	20	𝑑(𝐹(𝑥	𝑑(𝐹(𝑥	NUM
cana-4138	163	21	)	)	PUNCT
cana-4138	163	22	,	,	PUNCT
cana-4138	163	23	𝐹(𝑦	𝐹(𝑦	NOUN
cana-4138	163	24	)	)	PUNCT
cana-4138	163	25	)	)	PUNCT
cana-4138	163	26	≤	≤	PROPN
cana-4138	163	27	𝜙𝑑(𝑥	𝜙𝑑(𝑥	PUNCT
cana-4138	163	28	,	,	PUNCT
cana-4138	163	29	𝑦	𝑦	X
cana-4138	163	30	)	)	PUNCT
cana-4138	163	31	∀	∀	PUNCT
cana-4138	164	1	𝑥	𝑥	NOUN
cana-4138	164	2	,	,	PUNCT
cana-4138	164	3	𝑦	𝑦	PRON
cana-4138	164	4	∈	∈	PROPN
cana-4138	164	5	𝐵.	𝐵.	NOUN
cana-4138	164	6	now	now	ADV
cana-4138	164	7	by	by	ADP
cana-4138	164	8	lemma	lemma	PROPN
cana-4138	164	9	2.1	2.1	NUM
cana-4138	164	10	,	,	PUNCT
cana-4138	164	11	the	the	DET
cana-4138	164	12	operator	operator	NOUN
cana-4138	164	13	𝐹	𝐹	PROPN
cana-4138	164	14	has	have	VERB
cana-4138	164	15	a	a	DET
cana-4138	164	16	unique	unique	ADJ
cana-4138	164	17	fixed	fix	VERB
cana-4138	164	18	point	point	NOUN
cana-4138	164	19	in	in	ADP
cana-4138	164	20	𝐵.	𝐵.	PROPN
cana-4138	164	21	this	this	PRON
cana-4138	164	22	means	mean	VERB
cana-4138	164	23	that	that	SCONJ
cana-4138	164	24	the	the	DET
cana-4138	164	25	initial	initial	ADJ
cana-4138	164	26	value	value	NOUN
cana-4138	164	27	problem	problem	NOUN
cana-4138	164	28	(	(	PUNCT
cana-4138	164	29	1)—(2	1)—(2	NUM
cana-4138	164	30	)	)	PUNCT
cana-4138	164	31	has	have	VERB
cana-4138	164	32	a	a	DET
cana-4138	164	33	unique	unique	ADJ
cana-4138	164	34	solution	solution	NOUN
cana-4138	164	35	𝑥	𝑥	NOUN
cana-4138	164	36	in	in	ADP
cana-4138	164	37	𝐼.	𝐼.	PROPN
cana-4138	164	38	this	this	PRON
cana-4138	164	39	completes	complete	VERB
cana-4138	164	40	the	the	DET
cana-4138	164	41	proof	proof	NOUN
cana-4138	164	42	of	of	ADP
cana-4138	164	43	theorem	theorem	VERB
cana-4138	164	44	.	.	PUNCT
cana-4138	165	1	□	□	SYM
cana-4138	165	2	5	5	X
cana-4138	165	3	.	.	X
cana-4138	165	4	application	application	NOUN
cana-4138	165	5	of	of	ADP
cana-4138	165	6	the	the	DET
cana-4138	165	7	result	result	NOUN
cana-4138	165	8	in	in	ADP
cana-4138	165	9	order	order	NOUN
cana-4138	165	10	to	to	PART
cana-4138	165	11	support	support	VERB
cana-4138	165	12	the	the	DET
cana-4138	165	13	result	result	NOUN
cana-4138	165	14	proved	prove	VERB
cana-4138	165	15	,	,	PUNCT
cana-4138	165	16	now	now	ADV
cana-4138	165	17	we	we	PRON
cana-4138	165	18	will	will	AUX
cana-4138	165	19	present	present	VERB
cana-4138	165	20	an	an	DET
cana-4138	165	21	example	example	NOUN
cana-4138	165	22	.	.	PUNCT
cana-4138	166	1	in	in	ADP
cana-4138	166	2	the	the	DET
cana-4138	166	3	initial	initial	ADJ
cana-4138	166	4	value	value	NOUN
cana-4138	166	5	problem	problem	NOUN
cana-4138	166	6	(	(	PUNCT
cana-4138	166	7	1)—(2	1)—(2	NUM
cana-4138	166	8	)	)	PUNCT
cana-4138	166	9	,	,	PUNCT
cana-4138	166	10	let	let	VERB
cana-4138	166	11	𝑘(𝑡	𝑘(𝑡	PROPN
cana-4138	166	12	,	,	PUNCT
cana-4138	166	13	𝑠	𝑠	PROPN
cana-4138	166	14	,	,	PUNCT
cana-4138	166	15	𝑥	𝑥	NOUN
cana-4138	166	16	)	)	PUNCT
cana-4138	166	17	=	=	PUNCT
cana-4138	167	1	𝑡2𝑠2	𝑡2𝑠2	X
cana-4138	167	2	+	+	ADJ
cana-4138	167	3	𝑥𝑠2	𝑥𝑠2	X
cana-4138	167	4	2	2	NUM
cana-4138	167	5	,	,	PUNCT
cana-4138	167	6	ℎ(𝑡	ℎ(𝑡	PROPN
cana-4138	167	7	,	,	PUNCT
cana-4138	167	8	𝑠	𝑠	PROPN
cana-4138	167	9	,	,	PUNCT
cana-4138	167	10	𝑥	𝑥	NOUN
cana-4138	167	11	)	)	PUNCT
cana-4138	167	12	=	=	PUNCT
cana-4138	168	1	𝑡2𝑠2	𝑡2𝑠2	X
cana-4138	168	2	+	+	NUM
cana-4138	168	3	𝑡2𝑠2𝑥	𝑡2𝑠2𝑥	NUM
cana-4138	168	4	2	2	NUM
cana-4138	168	5	,	,	PUNCT
cana-4138	168	6	𝑠	𝑠	PROPN
cana-4138	168	7	,	,	PUNCT
cana-4138	168	8	𝑡	𝑡	PROPN
cana-4138	168	9	∈	∈	NOUN
cana-4138	168	10	𝐼	𝐼	ADP
cana-4138	168	11	=	=	PUNCT
cana-4138	169	1	[	[	X
cana-4138	169	2	0,1	0,1	NUM
cana-4138	169	3	]	]	PUNCT
cana-4138	169	4	,	,	PUNCT
cana-4138	169	5	𝑥	𝑥	PROPN
cana-4138	169	6	∈	∈	PROPN
cana-4138	169	7	(	(	PUNCT
cana-4138	169	8	𝐶[0,1	𝐶[0,1	ADP
cana-4138	169	9	]	]	PUNCT
cana-4138	169	10	,	,	PUNCT
cana-4138	169	11	ℝ	ℝ	PROPN
cana-4138	169	12	)	)	PUNCT
cana-4138	169	13	,	,	PUNCT
cana-4138	169	14	0	0	PUNCT
cana-4138	169	15	<	<	X
cana-4138	169	16	𝛼	𝛼	X
cana-4138	169	17	<	<	X
cana-4138	169	18	1	1	NUM
cana-4138	169	19	.	.	PUNCT
cana-4138	170	1	we	we	PRON
cana-4138	170	2	define	define	VERB
cana-4138	170	3	the	the	DET
cana-4138	170	4	metric	metric	ADJ
cana-4138	170	5	𝑑(𝑥	𝑑(𝑥	PROPN
cana-4138	170	6	,	,	PUNCT
cana-4138	170	7	𝑦	𝑦	X
cana-4138	170	8	)	)	PUNCT
cana-4138	170	9	=	=	SYM
cana-4138	170	10	(	(	PUNCT
cana-4138	170	11	‖𝑥	‖𝑥	NOUN
cana-4138	170	12	−	−	NOUN
cana-4138	170	13	𝑦‖∞	𝑦‖∞	NOUN
cana-4138	170	14	,	,	PUNCT
cana-4138	170	15	𝑎‖𝑥	𝑎‖𝑥	NOUN
cana-4138	170	16	−	−	NOUN
cana-4138	170	17	𝑦‖∞	𝑦‖∞	NOUN
cana-4138	170	18	)	)	PUNCT
cana-4138	170	19	on	on	ADP
cana-4138	170	20	(	(	PUNCT
cana-4138	170	21	𝐶[0,1	𝐶[0,1	ADV
cana-4138	170	22	]	]	PUNCT
cana-4138	170	23	,	,	PUNCT
cana-4138	170	24	ℝ	ℝ	PROPN
cana-4138	170	25	)	)	PUNCT
cana-4138	170	26	and	and	CCONJ
cana-4138	170	27	𝑎	𝑎	DET
cana-4138	170	28	≥	≥	NOUN
cana-4138	170	29	0	0	NUM
cana-4138	170	30	.	.	PUNCT
cana-4138	171	1	then	then	ADV
cana-4138	171	2	it	it	PRON
cana-4138	171	3	is	be	AUX
cana-4138	171	4	clear	clear	ADJ
cana-4138	171	5	that	that	SCONJ
cana-4138	171	6	(	(	PUNCT
cana-4138	171	7	𝐶[0,1	𝐶[0,1	ADP
cana-4138	171	8	]	]	PUNCT
cana-4138	171	9	,	,	PUNCT
cana-4138	171	10	ℝ	ℝ	PROPN
cana-4138	171	11	)	)	PUNCT
cana-4138	171	12	is	be	AUX
cana-4138	171	13	a	a	DET
cana-4138	171	14	complete	complete	ADJ
cana-4138	171	15	cone	cone	NOUN
cana-4138	171	16	metric	metric	ADJ
cana-4138	171	17	space	space	NOUN
cana-4138	171	18	.	.	PUNCT
cana-4138	172	1	now	now	ADV
cana-4138	172	2	we	we	PRON
cana-4138	172	3	have	have	VERB
cana-4138	172	4	(	(	PUNCT
cana-4138	172	5	|𝑘(𝑡	|𝑘(𝑡	ADJ
cana-4138	172	6	,	,	PUNCT
cana-4138	172	7	𝑠	𝑠	INTJ
cana-4138	172	8	,	,	PUNCT
cana-4138	172	9	𝑥(𝑠	𝑥(𝑠	PROPN
cana-4138	172	10	)	)	PUNCT
cana-4138	172	11	)	)	PUNCT
cana-4138	173	1	−	−	PROPN
cana-4138	174	1	𝑘(𝑡	𝑘(𝑡	PROPN
cana-4138	174	2	,	,	PUNCT
cana-4138	174	3	𝑠	𝑠	PROPN
cana-4138	174	4	,	,	PUNCT
cana-4138	174	5	𝑦(𝑠))|	𝑦(𝑠))|	PROPN
cana-4138	174	6	,	,	PUNCT
cana-4138	174	7	𝑎|𝑘(𝑡	𝑎|𝑘(𝑡	PROPN
cana-4138	174	8	,	,	PUNCT
cana-4138	174	9	𝑠	𝑠	INTJ
cana-4138	174	10	,	,	PUNCT
cana-4138	174	11	𝑥(𝑠	𝑥(𝑠	PROPN
cana-4138	174	12	)	)	PUNCT
cana-4138	174	13	)	)	PUNCT
cana-4138	175	1	−	−	PROPN
cana-4138	176	1	𝑘(𝑡	𝑘(𝑡	PROPN
cana-4138	176	2	,	,	PUNCT
cana-4138	176	3	𝑠	𝑠	PROPN
cana-4138	176	4	,	,	PUNCT
cana-4138	176	5	𝑦(𝑠))|	𝑦(𝑠))|	PROPN
cana-4138	176	6	)	)	PUNCT
cana-4138	176	7	=	=	SYM
cana-4138	176	8	(	(	PUNCT
cana-4138	176	9	|𝑡2𝑠2	|𝑡2𝑠2	PROPN
cana-4138	176	10	+	+	X
cana-4138	176	11	𝑥𝑠2	𝑥𝑠2	X
cana-4138	176	12	2	2	NUM
cana-4138	176	13	−	−	NOUN
cana-4138	176	14	𝑡2𝑠2	𝑡2𝑠2	PRON
cana-4138	176	15	−	−	PROPN
cana-4138	176	16	𝑦𝑠2	𝑦𝑠2	NOUN
cana-4138	176	17	2	2	NUM
cana-4138	176	18	|	|	ADV
cana-4138	176	19	,	,	PUNCT
cana-4138	176	20	𝑎	𝑎	DET
cana-4138	176	21	|𝑡2𝑠2	|𝑡2𝑠2	NOUN
cana-4138	177	1	+	+	X
cana-4138	177	2	𝑥𝑠2	𝑥𝑠2	X
cana-4138	177	3	2	2	NUM
cana-4138	177	4	−	−	NOUN
cana-4138	177	5	𝑡2𝑠2	𝑡2𝑠2	PRON
cana-4138	177	6	−	−	PROPN
cana-4138	177	7	𝑦𝑠2	𝑦𝑠2	NOUN
cana-4138	177	8	2	2	NUM
cana-4138	177	9	|	|	NOUN
cana-4138	177	10	)	)	PUNCT
cana-4138	177	11	=	=	PUNCT
cana-4138	178	1	(	(	PUNCT
cana-4138	178	2	|	|	ADV
cana-4138	178	3	𝑥𝑠2	𝑥𝑠2	NOUN
cana-4138	178	4	2	2	NUM
cana-4138	178	5	−	−	NOUN
cana-4138	178	6	𝑦𝑠2	𝑦𝑠2	NOUN
cana-4138	178	7	2	2	NUM
cana-4138	178	8	|	|	ADV
cana-4138	178	9	,	,	PUNCT
cana-4138	178	10	𝑎	𝑎	PRON
cana-4138	178	11	|	|	NOUN
cana-4138	178	12	𝑥𝑠2	𝑥𝑠2	NOUN
cana-4138	178	13	2	2	NUM
cana-4138	178	14	−	−	NOUN
cana-4138	178	15	𝑦𝑠2	𝑦𝑠2	NOUN
cana-4138	178	16	2	2	NUM
cana-4138	178	17	|	|	NOUN
cana-4138	178	18	)	)	PUNCT
cana-4138	178	19	=	=	SYM
cana-4138	178	20	𝑠2	𝑠2	NOUN
cana-4138	178	21	2	2	NUM
cana-4138	178	22	(	(	PUNCT
cana-4138	178	23	|𝑥	|𝑥	ADP
cana-4138	178	24	−	−	PROPN
cana-4138	178	25	𝑦|	𝑦|	PROPN
cana-4138	178	26	,	,	PUNCT
cana-4138	178	27	𝑎|𝑥	𝑎|𝑥	NOUN
cana-4138	178	28	−	−	PROPN
cana-4138	178	29	𝑦|	𝑦|	PROPN
cana-4138	178	30	)	)	PUNCT
cana-4138	178	31	≤	≤	NOUN
cana-4138	178	32	𝑠2	𝑠2	NOUN
cana-4138	178	33	2	2	NUM
cana-4138	178	34	(	(	PUNCT
cana-4138	178	35	‖𝑥	‖𝑥	NOUN
cana-4138	178	36	−	−	NOUN
cana-4138	178	37	𝑦‖∞	𝑦‖∞	NOUN
cana-4138	178	38	,	,	PUNCT
cana-4138	178	39	𝑎‖𝑥	𝑎‖𝑥	NOUN
cana-4138	178	40	−	−	NOUN
cana-4138	178	41	𝑦‖∞	𝑦‖∞	NOUN
cana-4138	178	42	)	)	PUNCT
cana-4138	179	1	=	=	SYM
cana-4138	179	2	𝑝1	𝑝1	NOUN
cana-4138	179	3	∗𝜙∗(‖𝑥	∗𝜙∗(‖𝑥	NOUN
cana-4138	179	4	−	−	NOUN
cana-4138	179	5	𝑦‖∞	𝑦‖∞	NOUN
cana-4138	179	6	,	,	PUNCT
cana-4138	179	7	𝑎‖𝑥	𝑎‖𝑥	NOUN
cana-4138	179	8	−	−	NOUN
cana-4138	179	9	𝑦‖∞	𝑦‖∞	NOUN
cana-4138	179	10	)	)	PUNCT
cana-4138	179	11	where	where	SCONJ
cana-4138	179	12	𝑝1	𝑝1	NOUN
cana-4138	179	13	∗	∗	NOUN
cana-4138	179	14	=	=	SYM
cana-4138	179	15	𝑠2	𝑠2	NOUN
cana-4138	179	16	,	,	PUNCT
cana-4138	179	17	which	which	PRON
cana-4138	179	18	is	be	AUX
cana-4138	179	19	a	a	DET
cana-4138	179	20	continuous	continuous	ADJ
cana-4138	179	21	function	function	NOUN
cana-4138	179	22	from	from	ADP
cana-4138	179	23	[	[	X
cana-4138	179	24	0,1	0,1	NUM
cana-4138	179	25	]	]	X
cana-4138	179	26	×	×	NOUN
cana-4138	179	27	[	[	X
cana-4138	179	28	0	0	NUM
cana-4138	179	29	,	,	PUNCT
cana-4138	179	30	1	1	NUM
cana-4138	179	31	]	]	PUNCT
cana-4138	179	32	into	into	ADP
cana-4138	179	33	ℝ+	ℝ+	PUNCT
cana-4138	179	34	and	and	CCONJ
cana-4138	179	35	a	a	DET
cana-4138	179	36	comparison	comparison	NOUN
cana-4138	179	37	function	function	NOUN
cana-4138	179	38	𝜙∗(𝑥	𝜙∗(𝑥	PROPN
cana-4138	179	39	,	,	PUNCT
cana-4138	179	40	𝑦	𝑦	NOUN
cana-4138	179	41	)	)	PUNCT
cana-4138	179	42	=	=	SYM
cana-4138	179	43	1	1	NUM
cana-4138	179	44	2	2	NUM
cana-4138	179	45	(	(	PUNCT
cana-4138	179	46	𝑥	𝑥	NOUN
cana-4138	179	47	,	,	PUNCT
cana-4138	179	48	𝑦	𝑦	NOUN
cana-4138	179	49	)	)	PUNCT
cana-4138	179	50	.	.	PUNCT
cana-4138	180	1	similarly	similarly	ADV
cana-4138	180	2	we	we	PRON
cana-4138	180	3	can	can	AUX
cana-4138	180	4	prove	prove	VERB
cana-4138	180	5	that	that	SCONJ
cana-4138	180	6	|ℎ(𝑡	|ℎ(𝑡	PROPN
cana-4138	180	7	,	,	PUNCT
cana-4138	180	8	𝑠	𝑠	INTJ
cana-4138	180	9	,	,	PUNCT
cana-4138	180	10	𝑥(𝑠	𝑥(𝑠	PROPN
cana-4138	180	11	)	)	PUNCT
cana-4138	180	12	)	)	PUNCT
cana-4138	181	1	−	−	PROPN
cana-4138	181	2	ℎ(𝑡	ℎ(𝑡	PROPN
cana-4138	181	3	,	,	PUNCT
cana-4138	181	4	𝑠	𝑠	PROPN
cana-4138	181	5	,	,	PUNCT
cana-4138	181	6	𝑦(𝑠))|	𝑦(𝑠))|	PROPN
cana-4138	181	7	,	,	PUNCT
cana-4138	181	8	𝑎|ℎ(𝑡	𝑎|ℎ(𝑡	PROPN
cana-4138	181	9	,	,	PUNCT
cana-4138	181	10	𝑠	𝑠	INTJ
cana-4138	181	11	,	,	PUNCT
cana-4138	181	12	𝑥(𝑠	𝑥(𝑠	PROPN
cana-4138	181	13	)	)	PUNCT
cana-4138	181	14	)	)	PUNCT
cana-4138	182	1	−	−	PROPN
cana-4138	182	2	ℎ(𝑡	ℎ(𝑡	PROPN
cana-4138	182	3	,	,	PUNCT
cana-4138	182	4	𝑠	𝑠	PROPN
cana-4138	182	5	,	,	PUNCT
cana-4138	182	6	𝑦(𝑠))|	𝑦(𝑠))|	PROPN
cana-4138	182	7	≤	≤	PROPN
cana-4138	182	8	𝑝2	𝑝2	NOUN
cana-4138	182	9	∗𝜙∗(‖𝑥	∗𝜙∗(‖𝑥	NOUN
cana-4138	182	10	−	−	NOUN
cana-4138	182	11	𝑦‖∞	𝑦‖∞	NOUN
cana-4138	182	12	,	,	PUNCT
cana-4138	182	13	𝑎‖𝑥	𝑎‖𝑥	NOUN
cana-4138	182	14	−	−	NOUN
cana-4138	182	15	𝑦‖∞	𝑦‖∞	NOUN
cana-4138	182	16	)	)	PUNCT
cana-4138	182	17	where	where	SCONJ
cana-4138	182	18	𝑝2	𝑝2	NOUN
cana-4138	182	19	∗	∗	NOUN
cana-4138	182	20	=	=	SYM
cana-4138	182	21	𝑠2𝑡2	𝑠2𝑡2	X
cana-4138	182	22	which	which	PRON
cana-4138	182	23	is	be	AUX
cana-4138	182	24	a	a	DET
cana-4138	182	25	continuous	continuous	ADJ
cana-4138	182	26	function	function	NOUN
cana-4138	182	27	of	of	ADP
cana-4138	182	28	[	[	X
cana-4138	182	29	0,1	0,1	NUM
cana-4138	182	30	]	]	X
cana-4138	182	31	×	×	NOUN
cana-4138	182	32	[	[	X
cana-4138	182	33	0	0	NUM
cana-4138	182	34	,	,	PUNCT
cana-4138	182	35	1]into	1]into	NUM
cana-4138	182	36	ℝ+	ℝ+	NOUN
cana-4138	182	37	.	.	PUNCT
cana-4138	183	1	also	also	ADV
cana-4138	183	2	,	,	PUNCT
cana-4138	183	3	we	we	PRON
cana-4138	183	4	note	note	VERB
cana-4138	183	5	that	that	SCONJ
cana-4138	183	6	𝑖𝑓	𝑖𝑓	ADP
cana-4138	183	7	𝛼	𝛼	NOUN
cana-4138	183	8	=	=	NOUN
cana-4138	183	9	1	1	NUM
cana-4138	183	10	2	2	NUM
cana-4138	183	11	then	then	ADV
cana-4138	183	12	∫	∫	PROPN
cana-4138	183	13	𝑡𝛼−1	𝑡𝛼−1	PROPN
cana-4138	183	14	∫	∫	PROPN
cana-4138	183	15	(	(	PUNCT
cana-4138	183	16	𝑝1	𝑝1	NOUN
cana-4138	183	17	∗(𝑡	∗(𝑡	PROPN
cana-4138	183	18	,	,	PUNCT
cana-4138	183	19	𝑠	𝑠	NOUN
cana-4138	183	20	)	)	PUNCT
cana-4138	183	21	+	+	NUM
cana-4138	183	22	𝑝2	𝑝2	NOUN
cana-4138	183	23	∗(𝑡	∗(𝑡	PROPN
cana-4138	183	24	,	,	PUNCT
cana-4138	183	25	𝑠))𝑑𝑠𝑑𝑡	𝑠))𝑑𝑠𝑑𝑡	NOUN
cana-4138	183	26	1	1	NUM
cana-4138	183	27	0	0	NUM
cana-4138	183	28	1	1	NUM
cana-4138	183	29	0	0	NUM
cana-4138	183	30	=	=	SYM
cana-4138	183	31	∫	∫	PROPN
cana-4138	183	32	𝑡𝛼−1	𝑡𝛼−1	PROPN
cana-4138	183	33	∫	∫	PROPN
cana-4138	183	34	(	(	PUNCT
cana-4138	183	35	𝑠2	𝑠2	NOUN
cana-4138	183	36	+	+	CCONJ
cana-4138	183	37	𝑠2𝑡2)𝑑𝑠𝑑𝑡	𝑠2𝑡2)𝑑𝑠𝑑𝑡	ADV
cana-4138	183	38	1	1	NUM
cana-4138	183	39	0	0	NUM
cana-4138	183	40	1	1	NUM
cana-4138	183	41	0	0	NUM
cana-4138	183	42	<	<	X
cana-4138	183	43	1	1	NUM
cana-4138	183	44	with	with	ADP
cana-4138	183	45	these	these	DET
cana-4138	183	46	choices	choice	NOUN
cana-4138	183	47	of	of	ADP
cana-4138	183	48	functions	function	NOUN
cana-4138	183	49	,	,	PUNCT
cana-4138	183	50	all	all	DET
cana-4138	183	51	the	the	DET
cana-4138	183	52	hypothesis	hypothesis	NOUN
cana-4138	183	53	in	in	ADP
cana-4138	183	54	theorem	theorem	NOUN
cana-4138	183	55	4.1	4.1	NUM
cana-4138	183	56	are	be	AUX
cana-4138	183	57	satisfied	satisfied	ADJ
cana-4138	183	58	.	.	PUNCT
cana-4138	184	1	hence	hence	ADV
cana-4138	184	2	the	the	DET
cana-4138	184	3	existence	existence	NOUN
cana-4138	184	4	and	and	CCONJ
cana-4138	184	5	uniqueness	uniqueness	NOUN
cana-4138	184	6	of	of	ADP
cana-4138	184	7	the	the	DET
cana-4138	184	8	solution	solution	NOUN
cana-4138	184	9	is	be	AUX
cana-4138	184	10	verified	verify	VERB
cana-4138	184	11	.	.	PUNCT
cana-4138	185	1	communications	communication	NOUN
cana-4138	185	2	on	on	ADP
cana-4138	185	3	applied	apply	VERB
cana-4138	185	4	nonlinear	nonlinear	ADJ
cana-4138	185	5	analysis	analysis	NOUN
cana-4138	185	6	issn	issn	NOUN
cana-4138	185	7	:	:	PUNCT
cana-4138	185	8	1074	1074	NUM
cana-4138	185	9	-	-	PUNCT
cana-4138	185	10	133x	133x	NUM
cana-4138	185	11	vol	vol	NOUN
cana-4138	185	12	32	32	NUM
cana-4138	185	13	no	no	NOUN
cana-4138	185	14	.	.	PUNCT
cana-4138	186	1	9s	9s	NUM
cana-4138	186	2	(	(	PUNCT
cana-4138	186	3	2025	2025	NUM
cana-4138	186	4	)	)	PUNCT
cana-4138	186	5	1310	1310	NUM
cana-4138	187	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4138	187	2	refrences	refrence	VERB
cana-4138	187	3	[	[	X
cana-4138	187	4	1	1	NUM
cana-4138	187	5	]	]	PUNCT
cana-4138	187	6	.	.	PUNCT
cana-4138	188	1	burton	burton	PROPN
cana-4138	188	2	t	t	PROPN
cana-4138	188	3	a	a	PROPN
cana-4138	188	4	,	,	PUNCT
cana-4138	188	5	volterra	volterra	PROPN
cana-4138	188	6	integral	integral	ADJ
cana-4138	188	7	and	and	CCONJ
cana-4138	188	8	differential	differential	ADJ
cana-4138	188	9	equations	equation	NOUN
cana-4138	188	10	,	,	PUNCT
cana-4138	188	11	academic	academic	ADJ
cana-4138	188	12	press	press	NOUN
cana-4138	188	13	,	,	PUNCT
cana-4138	188	14	new	new	PROPN
cana-4138	188	15	york	york	PROPN
cana-4138	188	16	,	,	PUNCT
cana-4138	188	17	1983	1983	NUM
cana-4138	188	18	.	.	PUNCT
cana-4138	189	1	[	[	X
cana-4138	189	2	2	2	NUM
cana-4138	189	3	]	]	PUNCT
cana-4138	189	4	.	.	PUNCT
cana-4138	190	1	miller	miller	PROPN
cana-4138	190	2	r	r	PROPN
cana-4138	190	3	k	k	PROPN
cana-4138	190	4	,	,	PUNCT
cana-4138	190	5	nonlinear	nonlinear	PROPN
cana-4138	190	6	volterra	volterra	PROPN
cana-4138	190	7	integral	integral	ADJ
cana-4138	190	8	equations	equation	NOUN
cana-4138	190	9	,	,	PUNCT
cana-4138	190	10	w.	w.	PROPN
cana-4138	190	11	a.	a.	PROPN
cana-4138	190	12	benjamin	benjamin	PROPN
cana-4138	190	13	,	,	PUNCT
cana-4138	190	14	menlo	menlo	PROPN
cana-4138	190	15	park	park	PROPN
cana-4138	190	16	,	,	PUNCT
cana-4138	190	17	california	california	PROPN
cana-4138	190	18	,	,	PUNCT
cana-4138	190	19	1971	1971	NUM
cana-4138	190	20	.	.	PUNCT
cana-4138	191	1	[	[	X
cana-4138	191	2	3	3	NUM
cana-4138	191	3	]	]	PUNCT
cana-4138	191	4	.	.	PUNCT
cana-4138	192	1	wazwaz	wazwaz	PROPN
cana-4138	192	2	,	,	PUNCT
cana-4138	192	3	a.	a.	NOUN
cana-4138	192	4	,	,	PUNCT
cana-4138	192	5	linear	linear	ADJ
cana-4138	192	6	and	and	CCONJ
cana-4138	192	7	nonlinear	nonlinear	ADJ
cana-4138	192	8	integral	integral	ADJ
cana-4138	192	9	equations	equation	NOUN
cana-4138	192	10	methods	method	NOUN
cana-4138	192	11	and	and	CCONJ
cana-4138	192	12	applications	application	NOUN
cana-4138	192	13	,	,	PUNCT
cana-4138	192	14	springerverlag	springerverlag	NOUN
cana-4138	192	15	higher	high	ADJ
cana-4138	192	16	education	education	NOUN
cana-4138	192	17	press	press	NOUN
cana-4138	192	18	,	,	PUNCT
cana-4138	192	19	beijing	beijing	PROPN
cana-4138	192	20	,	,	PUNCT
cana-4138	192	21	2011	2011	NUM
cana-4138	192	22	.	.	PUNCT
cana-4138	193	1	[	[	X
cana-4138	193	2	4	4	NUM
cana-4138	193	3	]	]	PUNCT
cana-4138	193	4	.	.	PUNCT
cana-4138	194	1	karoui	karoui	PROPN
cana-4138	194	2	,	,	PUNCT
cana-4138	194	3	a.	a.	PROPN
cana-4138	194	4	,	,	PUNCT
cana-4138	194	5	on	on	ADP
cana-4138	194	6	the	the	DET
cana-4138	194	7	existence	existence	NOUN
cana-4138	194	8	of	of	ADP
cana-4138	194	9	continuous	continuous	ADJ
cana-4138	194	10	solutions	solution	NOUN
cana-4138	194	11	of	of	ADP
cana-4138	194	12	nonlinear	nonlinear	ADJ
cana-4138	194	13	integral	integral	ADJ
cana-4138	194	14	equations	equation	NOUN
cana-4138	194	15	,	,	PUNCT
cana-4138	194	16	applied	apply	VERB
cana-4138	194	17	mathematics	mathematics	NOUN
cana-4138	194	18	letters	letter	NOUN
cana-4138	194	19	,	,	PUNCT
cana-4138	194	20	18	18	NUM
cana-4138	194	21	,	,	PUNCT
cana-4138	194	22	299	299	NUM
cana-4138	194	23	,	,	PUNCT
cana-4138	194	24	2005	2005	NUM
cana-4138	194	25	.	.	PUNCT
cana-4138	195	1	[	[	X
cana-4138	195	2	5	5	NUM
cana-4138	195	3	]	]	PUNCT
cana-4138	195	4	.	.	PUNCT
cana-4138	196	1	claudia	claudia	PROPN
cana-4138	196	2	,	,	PUNCT
cana-4138	196	3	b.	b.	PROPN
cana-4138	196	4	,	,	PUNCT
cana-4138	196	5	volterra	volterra	NOUN
cana-4138	196	6	-	-	PUNCT
cana-4138	196	7	fredholm	fredholm	NOUN
cana-4138	196	8	nonlinear	nonlinear	ADJ
cana-4138	196	9	integral	integral	ADJ
cana-4138	196	10	equations	equation	NOUN
cana-4138	196	11	via	via	ADP
cana-4138	196	12	picard	picard	PROPN
cana-4138	196	13	operators	operator	NOUN
cana-4138	196	14	theory	theory	PROPN
cana-4138	196	15	,	,	PUNCT
cana-4138	196	16	mathematica	mathematica	PROPN
cana-4138	196	17	,	,	PUNCT
cana-4138	196	18	tome	tome	NOUN
cana-4138	196	19	51	51	NUM
cana-4138	196	20	(	(	PUNCT
cana-4138	196	21	74	74	NUM
cana-4138	196	22	)	)	PUNCT
cana-4138	196	23	,	,	PUNCT
cana-4138	196	24	no	no	DET
cana-4138	196	25	1	1	NUM
cana-4138	196	26	,	,	PUNCT
cana-4138	196	27	pp	pp	ADJ
cana-4138	196	28	.	.	PUNCT
cana-4138	197	1	23—30	23—30	NUM
cana-4138	197	2	,	,	PUNCT
cana-4138	197	3	2009	2009	NUM
cana-4138	197	4	.	.	PUNCT
cana-4138	198	1	[	[	X
cana-4138	198	2	6	6	NUM
cana-4138	198	3	]	]	PUNCT
cana-4138	198	4	.	.	PUNCT
cana-4138	199	1	b.	b.	PROPN
cana-4138	199	2	ahmad	ahmad	PROPN
cana-4138	199	3	,	,	PUNCT
cana-4138	199	4	s.	s.	PROPN
cana-4138	199	5	k.	k.	PROPN
cana-4138	199	6	ntouyas	ntouyas	PROPN
cana-4138	199	7	,	,	PUNCT
cana-4138	199	8	r.	r.	PROPN
cana-4138	199	9	p.	p.	PROPN
cana-4138	199	10	agarwal	agarwal	PROPN
cana-4138	199	11	and	and	CCONJ
cana-4138	199	12	a.	a.	NOUN
cana-4138	199	13	alsaedi	alsaedi	PROPN
cana-4138	199	14	,	,	PUNCT
cana-4138	199	15	existence	existence	NOUN
cana-4138	199	16	results	result	VERB
cana-4138	199	17	for	for	ADP
cana-4138	199	18	sequential	sequential	ADJ
cana-4138	199	19	fractional	fractional	ADJ
cana-4138	199	20	integro	integro	ADJ
cana-4138	199	21	-	-	PUNCT
cana-4138	199	22	differential	differential	NOUN
cana-4138	199	23	equations	equation	NOUN
cana-4138	199	24	with	with	ADP
cana-4138	199	25	nonlocal	nonlocal	ADJ
cana-4138	199	26	multi	multi	ADJ
cana-4138	199	27	-	-	NOUN
cana-4138	199	28	point	point	NOUN
cana-4138	199	29	and	and	CCONJ
cana-4138	199	30	strip	strip	NOUN
cana-4138	199	31	conditions	condition	NOUN
cana-4138	199	32	,	,	PUNCT
cana-4138	199	33	boundary	boundary	ADJ
cana-4138	199	34	value	value	NOUN
cana-4138	199	35	problems	problem	NOUN
cana-4138	199	36	,	,	PUNCT
cana-4138	199	37	vol	vol	NOUN
cana-4138	199	38	.	.	PROPN
cana-4138	199	39	2016	2016	NUM
cana-4138	199	40	,	,	PUNCT
cana-4138	199	41	no	no	INTJ
cana-4138	199	42	.	.	NOUN
cana-4138	199	43	1	1	NUM
cana-4138	199	44	,	,	PUNCT
cana-4138	199	45	article	article	NOUN
cana-4138	199	46	i	i	PROPN
cana-4138	199	47	d	d	PROPN
cana-4138	199	48	205	205	NUM
cana-4138	199	49	,	,	PUNCT
cana-4138	199	50	2016	2016	NUM
cana-4138	199	51	.	.	PUNCT
cana-4138	200	1	[	[	X
cana-4138	200	2	7	7	NUM
cana-4138	200	3	]	]	PUNCT
cana-4138	200	4	.	.	PUNCT
cana-4138	201	1	y.	y.	PROPN
cana-4138	201	2	wang	wang	PROPN
cana-4138	201	3	and	and	CCONJ
cana-4138	201	4	l.	l.	PROPN
cana-4138	201	5	liu	liu	PROPN
cana-4138	201	6	,	,	PUNCT
cana-4138	201	7	uniqueness	uniqueness	NOUN
cana-4138	201	8	and	and	CCONJ
cana-4138	201	9	existence	existence	NOUN
cana-4138	201	10	of	of	ADP
cana-4138	201	11	positive	positive	ADJ
cana-4138	201	12	solutions	solution	NOUN
cana-4138	201	13	for	for	ADP
cana-4138	201	14	the	the	DET
cana-4138	201	15	fractional	fractional	ADJ
cana-4138	201	16	integro	integro	ADJ
cana-4138	201	17	-	-	PUNCT
cana-4138	201	18	differential	differential	NOUN
cana-4138	201	19	equation	equation	NOUN
cana-4138	201	20	,	,	PUNCT
cana-4138	201	21	boundary	boundary	ADJ
cana-4138	201	22	value	value	NOUN
cana-4138	201	23	problems	problem	NOUN
cana-4138	201	24	,	,	PUNCT
cana-4138	201	25	vol	vol	NOUN
cana-4138	201	26	.	.	PROPN
cana-4138	201	27	12	12	NUM
cana-4138	201	28	,	,	PUNCT
cana-4138	201	29	2017	2017	NUM
cana-4138	201	30	,	,	PUNCT
cana-4138	201	31	pp	pp	ADJ
cana-4138	201	32	.	.	PUNCT
cana-4138	202	1	1	1	NUM
cana-4138	202	2	-	-	SYM
cana-4138	202	3	17	17	NUM
cana-4138	202	4	.	.	PUNCT
cana-4138	203	1	[	[	X
cana-4138	203	2	8	8	NUM
cana-4138	203	3	]	]	PUNCT
cana-4138	203	4	.	.	PUNCT
cana-4138	204	1	k.	k.	PROPN
cana-4138	204	2	hilal	hilal	PROPN
cana-4138	204	3	,	,	PUNCT
cana-4138	204	4	l.	l.	PROPN
cana-4138	204	5	ibnelazyz	ibnelazyz	PROPN
cana-4138	204	6	,	,	PUNCT
cana-4138	204	7	k.	k.	PROPN
cana-4138	204	8	guida	guida	PROPN
cana-4138	204	9	and	and	CCONJ
cana-4138	204	10	d.	d.	PROPN
cana-4138	204	11	melliani	melliani	PROPN
cana-4138	204	12	,	,	PUNCT
cana-4138	204	13	existence	existence	NOUN
cana-4138	204	14	of	of	ADP
cana-4138	204	15	mild	mild	ADJ
cana-4138	204	16	solutions	solution	NOUN
cana-4138	204	17	for	for	ADP
cana-4138	204	18	an	an	DET
cana-4138	204	19	impulsive	impulsive	ADJ
cana-4138	204	20	fractional	fractional	ADJ
cana-4138	204	21	integro	integro	ADJ
cana-4138	204	22	-	-	PUNCT
cana-4138	204	23	differential	differential	NOUN
cana-4138	204	24	equations	equation	NOUN
cana-4138	204	25	with	with	ADP
cana-4138	204	26	non	non	ADJ
cana-4138	204	27	-	-	ADJ
cana-4138	204	28	local	local	ADJ
cana-4138	204	29	condition	condition	NOUN
cana-4138	204	30	,	,	PUNCT
cana-4138	204	31	springer	springer	NOUN
cana-4138	204	32	nature	nature	PROPN
cana-4138	204	33	switzerland	switzerland	PROPN
cana-4138	204	34	ag	ag	PROPN
cana-4138	204	35	,	,	PUNCT
cana-4138	204	36	2019	2019	NUM
cana-4138	204	37	.	.	PUNCT
cana-4138	205	1	[	[	X
cana-4138	205	2	9	9	NUM
cana-4138	205	3	]	]	PUNCT
cana-4138	205	4	.	.	PUNCT
cana-4138	206	1	d.	d.	PROPN
cana-4138	206	2	baleanu	baleanu	PROPN
cana-4138	206	3	,	,	PUNCT
cana-4138	206	4	k.	k.	PROPN
cana-4138	206	5	ghafarnezhad	ghafarnezhad	VERB
cana-4138	206	6	and	and	CCONJ
cana-4138	206	7	s.	s.	PROPN
cana-4138	206	8	rezapour	rezapour	PROPN
cana-4138	206	9	,	,	PUNCT
cana-4138	206	10	on	on	ADP
cana-4138	206	11	a	a	DET
cana-4138	206	12	three	three	NUM
cana-4138	206	13	step	step	NOUN
cana-4138	206	14	crisis	crisis	NOUN
cana-4138	206	15	integro	integro	ADJ
cana-4138	206	16	-	-	PUNCT
cana-4138	206	17	differential	differential	NOUN
cana-4138	206	18	equation	equation	NOUN
cana-4138	206	19	,	,	PUNCT
cana-4138	206	20	advances	advance	NOUN
cana-4138	206	21	in	in	ADP
cana-4138	206	22	difference	difference	NOUN
cana-4138	206	23	equations	equation	NOUN
cana-4138	206	24	,	,	PUNCT
cana-4138	206	25	vol	vol	NOUN
cana-4138	206	26	.	.	PROPN
cana-4138	206	27	2019	2019	NUM
cana-4138	206	28	,	,	PUNCT
cana-4138	206	29	no	no	INTJ
cana-4138	206	30	.	.	NOUN
cana-4138	206	31	1	1	NUM
cana-4138	206	32	,	,	PUNCT
cana-4138	206	33	article	article	NOUN
cana-4138	206	34	i	i	PROPN
cana-4138	206	35	d	d	PROPN
cana-4138	206	36	153	153	NUM
cana-4138	206	37	,	,	PUNCT
cana-4138	206	38	2019	2019	NUM
cana-4138	206	39	.	.	PUNCT
cana-4138	207	1	[	[	X
cana-4138	207	2	10	10	NUM
cana-4138	207	3	]	]	PUNCT
cana-4138	207	4	.	.	PUNCT
cana-4138	207	5	bragdi	bragdi	PROPN
cana-4138	207	6	,	,	PUNCT
cana-4138	207	7	a.	a.	NOUN
cana-4138	207	8	frioui	frioui	PROPN
cana-4138	207	9	and	and	CCONJ
cana-4138	207	10	a.	a.	NOUN
cana-4138	207	11	guezane	guezane	PROPN
cana-4138	207	12	lakoud	lakoud	PROPN
cana-4138	207	13	,	,	PUNCT
cana-4138	207	14	existence	existence	NOUN
cana-4138	207	15	of	of	ADP
cana-4138	207	16	solutions	solution	NOUN
cana-4138	207	17	for	for	ADP
cana-4138	207	18	non	non	ADJ
cana-4138	207	19	-	-	ADJ
cana-4138	207	20	linear	linear	ADJ
cana-4138	207	21	fractional	fractional	ADJ
cana-4138	207	22	integro	integro	ADJ
cana-4138	207	23	-	-	PUNCT
cana-4138	207	24	differential	differential	NOUN
cana-4138	207	25	equations	equation	NOUN
cana-4138	207	26	,	,	PUNCT
cana-4138	207	27	advances	advance	NOUN
cana-4138	207	28	in	in	ADP
cana-4138	207	29	difference	difference	NOUN
cana-4138	207	30	equations	equation	NOUN
cana-4138	207	31	,	,	PUNCT
cana-4138	207	32	vol	vol	NOUN
cana-4138	207	33	.	.	PUNCT
cana-4138	208	1	2020	2020	NUM
cana-4138	208	2	,	,	PUNCT
cana-4138	208	3	no	no	INTJ
cana-4138	208	4	.	.	NOUN
cana-4138	208	5	1	1	NUM
cana-4138	208	6	,	,	PUNCT
cana-4138	208	7	article	article	NOUN
cana-4138	208	8	i	i	PROPN
cana-4138	208	9	d	d	PROPN
cana-4138	208	10	418,pp	418,pp	PROPN
cana-4138	208	11	.	.	PUNCT
cana-4138	209	1	1	1	NUM
cana-4138	209	2	-	-	SYM
cana-4138	209	3	9	9	NUM
cana-4138	209	4	,	,	PUNCT
cana-4138	209	5	2020	2020	NUM
cana-4138	209	6	.	.	PUNCT
cana-4138	210	1	[	[	X
cana-4138	210	2	11	11	NUM
cana-4138	210	3	]	]	PUNCT
cana-4138	210	4	.	.	PUNCT
cana-4138	210	5	l.	l.	PROPN
cana-4138	210	6	ibnelazyz	ibnelazyz	PROPN
cana-4138	210	7	,	,	PUNCT
cana-4138	210	8	k.	k.	PROPN
cana-4138	210	9	guida	guida	PROPN
cana-4138	210	10	,	,	PUNCT
cana-4138	210	11	k.	k.	PROPN
cana-4138	210	12	hilal	hilal	PROPN
cana-4138	210	13	and	and	CCONJ
cana-4138	210	14	.	.	PUNCT
cana-4138	211	1	melliani	melliani	PROPN
cana-4138	211	2	,	,	PUNCT
cana-4138	211	3	existence	existence	NOUN
cana-4138	211	4	results	result	VERB
cana-4138	211	5	for	for	ADP
cana-4138	211	6	nonlinear	nonlinear	ADJ
cana-4138	211	7	fractional	fractional	ADJ
cana-4138	211	8	integro	integro	ADJ
cana-4138	211	9	-	-	PUNCT
cana-4138	211	10	differential	differential	NOUN
cana-4138	211	11	equations	equation	NOUN
cana-4138	211	12	with	with	ADP
cana-4138	211	13	integral	integral	ADJ
cana-4138	211	14	and	and	CCONJ
cana-4138	211	15	antiperiodic	antiperiodic	ADJ
cana-4138	211	16	boundary	boundary	ADJ
cana-4138	211	17	conditions	condition	NOUN
cana-4138	211	18	,	,	PUNCT
cana-4138	211	19	computational	computational	ADJ
cana-4138	211	20	and	and	CCONJ
cana-4138	211	21	applied	applied	ADJ
cana-4138	211	22	mathematics	mathematic	NOUN
cana-4138	211	23	,	,	PUNCT
cana-4138	211	24	vol	vol	NOUN
cana-4138	211	25	.	.	PROPN
cana-4138	211	26	40	40	NUM
cana-4138	211	27	,	,	PUNCT
cana-4138	211	28	no	no	INTJ
cana-4138	211	29	.	.	NOUN
cana-4138	211	30	1	1	NUM
cana-4138	211	31	,	,	PUNCT
cana-4138	211	32	article	article	NOUN
cana-4138	211	33	33	33	NUM
cana-4138	211	34	,	,	PUNCT
cana-4138	211	35	2021	2021	NUM
cana-4138	211	36	.	.	PUNCT
cana-4138	212	1	[	[	X
cana-4138	212	2	12	12	NUM
cana-4138	212	3	]	]	PUNCT
cana-4138	212	4	.	.	PUNCT
cana-4138	213	1	kamble	kamble	PROPN
cana-4138	213	2	,	,	PUNCT
cana-4138	213	3	r.	r.	PROPN
cana-4138	213	4	m.	m.	PROPN
cana-4138	213	5	and	and	CCONJ
cana-4138	213	6	kulkarni	kulkarni	PROPN
cana-4138	213	7	,	,	PUNCT
cana-4138	213	8	p.	p.	PROPN
cana-4138	213	9	r.	r.	PROPN
cana-4138	213	10	,	,	PUNCT
cana-4138	213	11	‘	'	PUNCT
cana-4138	213	12	on	on	ADP
cana-4138	213	13	some	some	DET
cana-4138	213	14	existence	existence	NOUN
cana-4138	213	15	and	and	CCONJ
cana-4138	213	16	uniqueness	uniqueness	NOUN
cana-4138	213	17	results	result	NOUN
cana-4138	213	18	for	for	ADP
cana-4138	213	19	nonlinear	nonlinear	ADJ
cana-4138	213	20	fractional	fractional	ADJ
cana-4138	213	21	differential	differential	ADJ
cana-4138	213	22	equations	equation	NOUN
cana-4138	213	23	with	with	ADP
cana-4138	213	24	boundary	boundary	ADJ
cana-4138	213	25	conditions	condition	NOUN
cana-4138	213	26	’	'	PUNCT
cana-4138	213	27	,	,	PUNCT
cana-4138	213	28	econophysics	econophysic	NOUN
cana-4138	213	29	,	,	PUNCT
cana-4138	213	30	sociophysics	sociophysic	NOUN
cana-4138	213	31	and	and	CCONJ
cana-4138	213	32	other	other	ADJ
cana-4138	213	33	multidisciplinary	multidisciplinary	ADJ
cana-4138	213	34	sciences	science	NOUN
cana-4138	213	35	journal	journal	NOUN
cana-4138	213	36	,	,	PUNCT
cana-4138	213	37	vol	vol	NOUN
cana-4138	213	38	.	.	PUNCT
cana-4138	213	39	12(1	12(1	NUM
cana-4138	213	40	)	)	PUNCT
cana-4138	213	41	,	,	PUNCT
cana-4138	213	42	2023	2023	NUM
cana-4138	213	43	.	.	PUNCT
cana-4138	214	1	[	[	X
cana-4138	214	2	13	13	NUM
cana-4138	214	3	]	]	PUNCT
cana-4138	214	4	.	.	PUNCT
cana-4138	215	1	d.	d.	PROPN
cana-4138	215	2	r.	r.	PROPN
cana-4138	215	3	smart	smart	PROPN
cana-4138	215	4	,	,	PUNCT
cana-4138	215	5	fixed	fixed	ADJ
cana-4138	215	6	point	point	NOUN
cana-4138	215	7	theorems	theorem	NOUN
cana-4138	215	8	,	,	PUNCT
cana-4138	215	9	cambridge	cambridge	PROPN
cana-4138	215	10	university	university	PROPN
cana-4138	215	11	press	press	NOUN
cana-4138	215	12	,	,	PUNCT
cana-4138	215	13	1980	1980	NUM
cana-4138	215	14	.	.	PUNCT
cana-4138	216	1	[	[	X
cana-4138	216	2	14	14	NUM
cana-4138	216	3	]	]	PUNCT
cana-4138	216	4	.	.	PUNCT
cana-4138	217	1	d.	d.	PROPN
cana-4138	217	2	o’regan	o’regan	PROPN
cana-4138	217	3	,	,	PUNCT
cana-4138	217	4	fixed	fix	VERB
cana-4138	217	5	point	point	NOUN
cana-4138	217	6	theory	theory	NOUN
cana-4138	217	7	and	and	CCONJ
cana-4138	217	8	applications	application	NOUN
cana-4138	217	9	,	,	PUNCT
cana-4138	217	10	cambridge	cambridge	PROPN
cana-4138	217	11	university	university	PROPN
cana-4138	217	12	press	press	PROPN
cana-4138	217	13	,	,	PUNCT
cana-4138	217	14	cambridge	cambridge	PROPN
cana-4138	217	15	,	,	PUNCT
cana-4138	217	16	u.	u.	PROPN
cana-4138	217	17	k.	k.	PROPN
cana-4138	218	1	[	[	X
cana-4138	218	2	15	15	NUM
cana-4138	218	3	]	]	PUNCT
cana-4138	218	4	.	.	PUNCT
cana-4138	219	1	huang	huang	PROPN
cana-4138	219	2	long	long	PROPN
cana-4138	219	3	-	-	PUNCT
cana-4138	219	4	guang	guang	PROPN
cana-4138	219	5	,	,	PUNCT
cana-4138	219	6	zhang	zhang	PROPN
cana-4138	219	7	xian	xian	PROPN
cana-4138	219	8	,	,	PUNCT
cana-4138	219	9	cone	cone	NOUN
cana-4138	219	10	metric	metric	ADJ
cana-4138	219	11	spaces	space	NOUN
cana-4138	219	12	and	and	CCONJ
cana-4138	219	13	fixed	fix	VERB
cana-4138	219	14	point	point	NOUN
cana-4138	219	15	theorems	theorem	NOUN
cana-4138	219	16	of	of	ADP
cana-4138	219	17	contractive	contractive	ADJ
cana-4138	219	18	mappings	mapping	NOUN
cana-4138	219	19	,	,	PUNCT
cana-4138	219	20	journal	journal	NOUN
cana-4138	219	21	of	of	ADP
cana-4138	219	22	mathematical	mathematical	ADJ
cana-4138	219	23	analysis	analysis	NOUN
cana-4138	219	24	and	and	CCONJ
cana-4138	219	25	applications	application	NOUN
cana-4138	219	26	,	,	PUNCT
cana-4138	219	27	vol	vol	NOUN
cana-4138	219	28	.	.	PUNCT
cana-4138	219	29	332	332	NUM
cana-4138	219	30	,	,	PUNCT
cana-4138	219	31	pp	pp	ADP
cana-4138	219	32	1468—1476	1468—1476	NUM
cana-4138	219	33	,	,	PUNCT
cana-4138	219	34	2007	2007	NUM
cana-4138	219	35	.	.	PUNCT
cana-4138	220	1	[	[	X
cana-4138	220	2	16	16	NUM
cana-4138	220	3	]	]	PUNCT
cana-4138	220	4	.	.	PUNCT
cana-4138	221	1	ilic	ilic	PROPN
cana-4138	221	2	,	,	PUNCT
cana-4138	221	3	d	d	NOUN
cana-4138	221	4	,	,	PUNCT
cana-4138	221	5	and	and	CCONJ
cana-4138	221	6	rakocevic	rakocevic	ADJ
cana-4138	221	7	,	,	PUNCT
cana-4138	221	8	v.	v.	ADJ
cana-4138	221	9	,	,	PUNCT
cana-4138	221	10	common	common	ADJ
cana-4138	221	11	fixed	fix	VERB
cana-4138	221	12	points	point	NOUN
cana-4138	221	13	for	for	ADP
cana-4138	221	14	maps	map	NOUN
cana-4138	221	15	on	on	ADP
cana-4138	221	16	cone	cone	NOUN
cana-4138	221	17	metric	metric	ADJ
cana-4138	221	18	space	space	NOUN
cana-4138	221	19	,	,	PUNCT
cana-4138	221	20	journal	journal	NOUN
cana-4138	221	21	of	of	ADP
cana-4138	221	22	mathematical	mathematical	ADJ
cana-4138	221	23	analysis	analysis	NOUN
cana-4138	221	24	and	and	CCONJ
cana-4138	221	25	applications	application	NOUN
cana-4138	221	26	,	,	PUNCT
cana-4138	221	27	341	341	NUM
cana-4138	221	28	,	,	PUNCT
cana-4138	221	29	no.2	no.2	PROPN
cana-4138	221	30	,	,	PUNCT
cana-4138	221	31	876	876	NUM
cana-4138	221	32	,	,	PUNCT
cana-4138	221	33	2008	2008	NUM
cana-4138	221	34	.	.	PUNCT
cana-4138	222	1	[	[	X
cana-4138	222	2	17	17	NUM
cana-4138	222	3	]	]	PUNCT
cana-4138	222	4	.	.	PUNCT
cana-4138	223	1	k.	k.	PROPN
cana-4138	223	2	oldham	oldham	PROPN
cana-4138	223	3	,	,	PUNCT
cana-4138	223	4	j.	j.	PROPN
cana-4138	223	5	spanier	spanier	PROPN
cana-4138	223	6	,	,	PUNCT
cana-4138	223	7	the	the	DET
cana-4138	223	8	fractional	fractional	ADJ
cana-4138	223	9	calculus	calculus	NOUN
cana-4138	223	10	:	:	PUNCT
cana-4138	223	11	theory	theory	NOUN
cana-4138	223	12	and	and	CCONJ
cana-4138	223	13	applications	application	NOUN
cana-4138	223	14	of	of	ADP
cana-4138	223	15	differentiation	differentiation	NOUN
cana-4138	223	16	and	and	CCONJ
cana-4138	223	17	integration	integration	NOUN
cana-4138	223	18	of	of	ADP
cana-4138	223	19	arbitrary	arbitrary	ADJ
cana-4138	223	20	order	order	NOUN
cana-4138	223	21	,	,	PUNCT
cana-4138	223	22	academic	academic	ADJ
cana-4138	223	23	press	press	NOUN
cana-4138	223	24	,	,	PUNCT
cana-4138	223	25	usa	usa	PROPN
cana-4138	223	26	,	,	PUNCT
cana-4138	223	27	1974	1974	NUM
cana-4138	223	28	.	.	PUNCT
cana-4138	224	1	[	[	X
cana-4138	224	2	18	18	NUM
cana-4138	224	3	]	]	PUNCT
cana-4138	224	4	.	.	PUNCT
cana-4138	225	1	k.	k.	PROPN
cana-4138	225	2	s.	s.	PROPN
cana-4138	225	3	miller	miller	PROPN
cana-4138	225	4	and	and	CCONJ
cana-4138	225	5	b.	b.	PROPN
cana-4138	225	6	ross	ross	PROPN
cana-4138	225	7	,	,	PUNCT
cana-4138	225	8	an	an	DET
cana-4138	225	9	introduction	introduction	NOUN
cana-4138	225	10	to	to	ADP
cana-4138	225	11	the	the	DET
cana-4138	225	12	fractional	fractional	ADJ
cana-4138	225	13	calculus	calculus	NOUN
cana-4138	225	14	and	and	CCONJ
cana-4138	225	15	fractional	fractional	ADJ
cana-4138	225	16	differential	differential	ADJ
cana-4138	225	17	equations	equation	NOUN
cana-4138	225	18	,	,	PUNCT
cana-4138	225	19	wiley	wiley	NOUN
cana-4138	225	20	-	-	PUNCT
cana-4138	225	21	interscience	interscience	NOUN
cana-4138	225	22	publications	publication	NOUN
cana-4138	225	23	,	,	PUNCT
cana-4138	225	24	usa	usa	PROPN
cana-4138	225	25	,	,	PUNCT
cana-4138	225	26	1993	1993	NUM
cana-4138	225	27	.	.	PUNCT
cana-4138	226	1	[	[	X
cana-4138	226	2	19	19	NUM
cana-4138	226	3	]	]	PUNCT
cana-4138	226	4	.	.	PUNCT
cana-4138	227	1	podlubny	podlubny	PROPN
cana-4138	227	2	i	i	PRON
cana-4138	227	3	,	,	PUNCT
cana-4138	227	4	fractional	fractional	ADJ
cana-4138	227	5	differential	differential	NOUN
cana-4138	227	6	equations	equation	NOUN
cana-4138	227	7	,	,	PUNCT
cana-4138	227	8	academic	academic	ADJ
cana-4138	227	9	press	press	NOUN
cana-4138	227	10	,	,	PUNCT
cana-4138	227	11	new	new	PROPN
cana-4138	227	12	york	york	PROPN
cana-4138	227	13	,	,	PUNCT
cana-4138	227	14	usa	usa	PROPN
cana-4138	227	15	1999	1999	NUM
cana-4138	227	16	.	.	PUNCT
cana-4138	228	1	communications	communication	NOUN
cana-4138	228	2	on	on	ADP
cana-4138	228	3	applied	apply	VERB
cana-4138	228	4	nonlinear	nonlinear	ADJ
cana-4138	228	5	analysis	analysis	NOUN
cana-4138	228	6	issn	issn	NOUN
cana-4138	228	7	:	:	PUNCT
cana-4138	228	8	1074	1074	NUM
cana-4138	228	9	-	-	PUNCT
cana-4138	228	10	133x	133x	NUM
cana-4138	228	11	vol	vol	NOUN
cana-4138	228	12	32	32	NUM
cana-4138	228	13	no	no	NOUN
cana-4138	228	14	.	.	PUNCT
cana-4138	229	1	9s	9s	NUM
cana-4138	229	2	(	(	PUNCT
cana-4138	229	3	2025	2025	NUM
cana-4138	229	4	)	)	PUNCT
cana-4138	229	5	1311	1311	NUM
cana-4138	229	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4138	230	1	[	[	X
cana-4138	230	2	20	20	NUM
cana-4138	230	3	]	]	PUNCT
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cana-4138	242	28	)	)	PUNCT
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