id	sid	tid	token	lemma	pos
cana-5532	1	1	nonlocal	nonlocal	ADJ
cana-5532	1	2	initial	initial	ADJ
cana-5532	1	3	value	value	NOUN
cana-5532	1	4	problems	problem	NOUN
cana-5532	1	5	for	for	ADP
cana-5532	1	6	hybrid	hybrid	ADJ
cana-5532	1	7	caputo	caputo	PROPN
cana-5532	1	8	fractional	fractional	PROPN
cana-5532	1	9	integro	integro	PROPN
cana-5532	1	10	-	-	PUNCT
cana-5532	1	11	differential	differential	NOUN
cana-5532	1	12	equations	equation	NOUN
cana-5532	1	13	communications	communication	NOUN
cana-5532	1	14	on	on	ADP
cana-5532	1	15	applied	apply	VERB
cana-5532	1	16	nonlinear	nonlinear	ADJ
cana-5532	1	17	analysis	analysis	NOUN
cana-5532	1	18	issn	issn	NOUN
cana-5532	1	19	:	:	PUNCT
cana-5532	1	20	1074	1074	NUM
cana-5532	1	21	-	-	PUNCT
cana-5532	1	22	133x	133x	NUM
cana-5532	1	23	vol	vol	NOUN
cana-5532	1	24	32	32	NUM
cana-5532	1	25	no	no	NOUN
cana-5532	1	26	.	.	NOUN
cana-5532	1	27	3	3	NUM
cana-5532	1	28	(	(	PUNCT
cana-5532	1	29	2025	2025	NUM
cana-5532	1	30	)	)	PUNCT
cana-5532	1	31	985	985	NUM
cana-5532	1	32	https://internationalpubls.com	https://internationalpubls.com	X
cana-5532	1	33	nonlocal	nonlocal	ADJ
cana-5532	1	34	initial	initial	ADJ
cana-5532	1	35	value	value	NOUN
cana-5532	1	36	problems	problem	NOUN
cana-5532	1	37	for	for	ADP
cana-5532	1	38	hybrid	hybrid	ADJ
cana-5532	1	39	caputo	caputo	PROPN
cana-5532	1	40	fractional	fractional	PROPN
cana-5532	1	41	integrodifferential	integrodifferential	ADJ
cana-5532	1	42	equations	equations	PROPN
cana-5532	1	43	dr	dr	PROPN
cana-5532	1	44	.	.	PROPN
cana-5532	1	45	moffek	moffek	PROPN
cana-5532	1	46	hamza	hamza	PROPN
cana-5532	1	47	ecole	ecole	PROPN
cana-5532	1	48	normale	normale	PROPN
cana-5532	1	49	supérieure	supérieure	PROPN
cana-5532	1	50	de	de	PROPN
cana-5532	1	51	ouargla,30000	ouargla,30000	PROPN
cana-5532	1	52	ouargla	ouargla	PROPN
cana-5532	1	53	,	,	PUNCT
cana-5532	1	54	algeria	algeria	PROPN
cana-5532	1	55	,	,	PUNCT
cana-5532	1	56	email	email	NOUN
cana-5532	1	57	:	:	PUNCT
cana-5532	1	58	moffek.hamza@ens-ouargla.dz	moffek.hamza@ens-ouargla.dz	ADJ
cana-5532	1	59	article	article	NOUN
cana-5532	1	60	history	history	NOUN
cana-5532	1	61	:	:	PUNCT
cana-5532	1	62	received	receive	VERB
cana-5532	1	63	:	:	PUNCT
cana-5532	1	64	19	19	NUM
cana-5532	1	65	-	-	PUNCT
cana-5532	1	66	09	09	NUM
cana-5532	1	67	-	-	PUNCT
cana-5532	1	68	2024	2024	NUM
cana-5532	1	69	revised	revise	VERB
cana-5532	1	70	:	:	PUNCT
cana-5532	1	71	24	24	NUM
cana-5532	1	72	-	-	PUNCT
cana-5532	1	73	03	03	NUM
cana-5532	1	74	-	-	PUNCT
cana-5532	1	75	2025	2025	NUM
cana-5532	1	76	accepted	accept	VERB
cana-5532	1	77	:	:	PUNCT
cana-5532	1	78	11	11	NUM
cana-5532	1	79	-	-	PUNCT
cana-5532	1	80	04	04	NUM
cana-5532	1	81	-	-	PUNCT
cana-5532	1	82	2025	2025	NUM
cana-5532	1	83	abstract	abstract	NOUN
cana-5532	1	84	:	:	PUNCT
cana-5532	1	85	this	this	DET
cana-5532	1	86	paper	paper	NOUN
cana-5532	1	87	investigates	investigate	VERB
cana-5532	1	88	nonlocal	nonlocal	ADJ
cana-5532	1	89	initial	initial	ADJ
cana-5532	1	90	value	value	NOUN
cana-5532	1	91	problems	problem	NOUN
cana-5532	1	92	for	for	ADP
cana-5532	1	93	hybrid	hybrid	ADJ
cana-5532	1	94	caputo	caputo	PROPN
cana-5532	1	95	fractional	fractional	PROPN
cana-5532	1	96	integro	integro	PROPN
cana-5532	1	97	-	-	PUNCT
cana-5532	1	98	differential	differential	NOUN
cana-5532	1	99	equations	equation	NOUN
cana-5532	1	100	.	.	PUNCT
cana-5532	2	1	by	by	ADP
cana-5532	2	2	employing	employ	VERB
cana-5532	2	3	a	a	DET
cana-5532	2	4	fixed	fix	VERB
cana-5532	2	5	-	-	PUNCT
cana-5532	2	6	point	point	NOUN
cana-5532	2	7	theorem	theorem	NOUN
cana-5532	2	8	due	due	ADP
cana-5532	2	9	to	to	ADP
cana-5532	2	10	dhage	dhage	NOUN
cana-5532	2	11	,	,	PUNCT
cana-5532	2	12	we	we	PRON
cana-5532	2	13	establish	establish	VERB
cana-5532	2	14	the	the	DET
cana-5532	2	15	existence	existence	NOUN
cana-5532	2	16	of	of	ADP
cana-5532	2	17	solutions	solution	NOUN
cana-5532	2	18	to	to	ADP
cana-5532	2	19	these	these	DET
cana-5532	2	20	problems	problem	NOUN
cana-5532	2	21	.	.	PUNCT
cana-5532	3	1	the	the	DET
cana-5532	3	2	theoretical	theoretical	ADJ
cana-5532	3	3	findings	finding	NOUN
cana-5532	3	4	are	be	AUX
cana-5532	3	5	illustrated	illustrate	VERB
cana-5532	3	6	through	through	ADP
cana-5532	3	7	a	a	DET
cana-5532	3	8	concrete	concrete	ADJ
cana-5532	3	9	example	example	NOUN
cana-5532	3	10	,	,	PUNCT
cana-5532	3	11	showcasing	showcase	VERB
cana-5532	3	12	the	the	DET
cana-5532	3	13	applicability	applicability	NOUN
cana-5532	3	14	of	of	ADP
cana-5532	3	15	our	our	PRON
cana-5532	3	16	results	result	NOUN
cana-5532	3	17	.	.	PUNCT
cana-5532	4	1	keywords	keyword	NOUN
cana-5532	4	2	:	:	PUNCT
cana-5532	4	3	the	the	DET
cana-5532	4	4	fractional	fractional	PROPN
cana-5532	4	5	caputo	caputo	PROPN
cana-5532	4	6	derivative	derivative	PROPN
cana-5532	4	7	,	,	PUNCT
cana-5532	4	8	the	the	DET
cana-5532	4	9	fractional	fractional	ADJ
cana-5532	4	10	integral	integral	ADJ
cana-5532	4	11	,	,	PUNCT
cana-5532	4	12	hybrid	hybrid	NOUN
cana-5532	4	13	,	,	PUNCT
cana-5532	4	14	dhage	dhage	NOUN
cana-5532	4	15	fixed	fix	VERB
cana-5532	4	16	point	point	NOUN
cana-5532	4	17	.	.	PUNCT
cana-5532	5	1	introduction	introduction	NOUN
cana-5532	5	2	fractional	fractional	ADJ
cana-5532	5	3	calculus	calculus	NOUN
cana-5532	5	4	,	,	PUNCT
cana-5532	5	5	an	an	DET
cana-5532	5	6	extension	extension	NOUN
cana-5532	5	7	of	of	ADP
cana-5532	5	8	classical	classical	ADJ
cana-5532	5	9	calculus	calculus	NOUN
cana-5532	5	10	,	,	PUNCT
cana-5532	5	11	has	have	AUX
cana-5532	5	12	garnered	garner	VERB
cana-5532	5	13	significant	significant	ADJ
cana-5532	5	14	attention	attention	NOUN
cana-5532	5	15	in	in	ADP
cana-5532	5	16	recent	recent	ADJ
cana-5532	5	17	years	year	NOUN
cana-5532	5	18	due	due	ADP
cana-5532	5	19	to	to	ADP
cana-5532	5	20	its	its	PRON
cana-5532	5	21	ability	ability	NOUN
cana-5532	5	22	to	to	PART
cana-5532	5	23	describe	describe	VERB
cana-5532	5	24	complex	complex	ADJ
cana-5532	5	25	phenomena	phenomenon	NOUN
cana-5532	5	26	that	that	SCONJ
cana-5532	5	27	integer	integer	NOUN
cana-5532	5	28	-	-	PUNCT
cana-5532	5	29	order	order	NOUN
cana-5532	5	30	derivatives	derivative	NOUN
cana-5532	5	31	and	and	CCONJ
cana-5532	5	32	integrals	integral	NOUN
cana-5532	5	33	fail	fail	VERB
cana-5532	5	34	to	to	PART
cana-5532	5	35	capture	capture	VERB
cana-5532	5	36	accurately	accurately	ADV
cana-5532	5	37	.	.	PUNCT
cana-5532	6	1	this	this	DET
cana-5532	6	2	branch	branch	NOUN
cana-5532	6	3	of	of	ADP
cana-5532	6	4	mathematics	mathematic	NOUN
cana-5532	6	5	has	have	AUX
cana-5532	6	6	proven	prove	VERB
cana-5532	6	7	its	its	PRON
cana-5532	6	8	utility	utility	NOUN
cana-5532	6	9	in	in	ADP
cana-5532	6	10	various	various	ADJ
cana-5532	6	11	domains	domain	NOUN
cana-5532	6	12	,	,	PUNCT
cana-5532	6	13	including	include	VERB
cana-5532	6	14	physics	physics	NOUN
cana-5532	6	15	,	,	PUNCT
cana-5532	6	16	engineering	engineering	NOUN
cana-5532	6	17	,	,	PUNCT
cana-5532	6	18	biology	biology	NOUN
cana-5532	6	19	,	,	PUNCT
cana-5532	6	20	and	and	CCONJ
cana-5532	6	21	economics	economic	NOUN
cana-5532	6	22	.	.	PUNCT
cana-5532	7	1	(	(	PUNCT
cana-5532	7	2	[	[	X
cana-5532	7	3	10],[13],[14],[16],[4],[12	10],[13],[14],[16],[4],[12	NUM
cana-5532	7	4	]	]	PUNCT
cana-5532	7	5	)	)	PUNCT
cana-5532	7	6	.	.	PUNCT
cana-5532	8	1	nonlocal	nonlocal	ADJ
cana-5532	8	2	initial	initial	ADJ
cana-5532	8	3	value	value	NOUN
cana-5532	8	4	problems	problem	NOUN
cana-5532	8	5	(	(	PUNCT
cana-5532	8	6	nivps	nivps	NOUN
cana-5532	8	7	)	)	PUNCT
cana-5532	8	8	represent	represent	VERB
cana-5532	8	9	a	a	DET
cana-5532	8	10	category	category	NOUN
cana-5532	8	11	of	of	ADP
cana-5532	8	12	problems	problem	NOUN
cana-5532	8	13	in	in	ADP
cana-5532	8	14	which	which	PRON
cana-5532	8	15	the	the	DET
cana-5532	8	16	initial	initial	ADJ
cana-5532	8	17	conditions	condition	NOUN
cana-5532	8	18	depend	depend	VERB
cana-5532	8	19	on	on	ADP
cana-5532	8	20	the	the	DET
cana-5532	8	21	values	value	NOUN
cana-5532	8	22	of	of	ADP
cana-5532	8	23	the	the	DET
cana-5532	8	24	unknown	unknown	ADJ
cana-5532	8	25	function	function	NOUN
cana-5532	8	26	at	at	ADP
cana-5532	8	27	multiple	multiple	ADJ
cana-5532	8	28	points	point	NOUN
cana-5532	8	29	rather	rather	ADV
cana-5532	8	30	than	than	ADP
cana-5532	8	31	a	a	DET
cana-5532	8	32	single	single	ADJ
cana-5532	8	33	point	point	NOUN
cana-5532	8	34	.	.	PUNCT
cana-5532	9	1	such	such	ADJ
cana-5532	9	2	problems	problem	NOUN
cana-5532	9	3	naturally	naturally	ADV
cana-5532	9	4	arise	arise	VERB
cana-5532	9	5	in	in	ADP
cana-5532	9	6	numerous	numerous	ADJ
cana-5532	9	7	real	real	ADJ
cana-5532	9	8	-	-	PUNCT
cana-5532	9	9	world	world	NOUN
cana-5532	9	10	applications	application	NOUN
cana-5532	9	11	,	,	PUNCT
cana-5532	9	12	such	such	ADJ
cana-5532	9	13	as	as	ADP
cana-5532	9	14	heat	heat	NOUN
cana-5532	9	15	transfer	transfer	NOUN
cana-5532	9	16	,	,	PUNCT
cana-5532	9	17	viscoelastic	viscoelastic	ADJ
cana-5532	9	18	material	material	NOUN
cana-5532	9	19	behavior	behavior	NOUN
cana-5532	9	20	,	,	PUNCT
cana-5532	9	21	and	and	CCONJ
cana-5532	9	22	control	control	NOUN
cana-5532	9	23	systems	system	NOUN
cana-5532	9	24	.	.	PUNCT
cana-5532	10	1	hybrid	hybrid	ADJ
cana-5532	10	2	differential	differential	ADJ
cana-5532	10	3	equations	equation	NOUN
cana-5532	10	4	,	,	PUNCT
cana-5532	10	5	which	which	PRON
cana-5532	10	6	combine	combine	VERB
cana-5532	10	7	differential	differential	ADJ
cana-5532	10	8	and	and	CCONJ
cana-5532	10	9	integral	integral	ADJ
cana-5532	10	10	operators	operator	NOUN
cana-5532	10	11	,	,	PUNCT
cana-5532	10	12	have	have	AUX
cana-5532	10	13	emerged	emerge	VERB
cana-5532	10	14	as	as	ADP
cana-5532	10	15	a	a	DET
cana-5532	10	16	powerful	powerful	ADJ
cana-5532	10	17	tool	tool	NOUN
cana-5532	10	18	for	for	ADP
cana-5532	10	19	modeling	model	VERB
cana-5532	10	20	complex	complex	ADJ
cana-5532	10	21	systems	system	NOUN
cana-5532	10	22	.	.	PUNCT
cana-5532	11	1	in	in	ADP
cana-5532	11	2	recent	recent	ADJ
cana-5532	11	3	years	year	NOUN
cana-5532	11	4	,	,	PUNCT
cana-5532	11	5	there	there	PRON
cana-5532	11	6	has	have	AUX
cana-5532	11	7	been	be	AUX
cana-5532	11	8	growing	grow	VERB
cana-5532	11	9	interest	interest	NOUN
cana-5532	11	10	in	in	ADP
cana-5532	11	11	studying	study	VERB
cana-5532	11	12	hybrid	hybrid	ADJ
cana-5532	11	13	fractional	fractional	ADJ
cana-5532	11	14	differential	differential	NOUN
cana-5532	11	15	equations	equation	NOUN
cana-5532	11	16	,	,	PUNCT
cana-5532	11	17	which	which	PRON
cana-5532	11	18	incorporate	incorporate	VERB
cana-5532	11	19	fractional	fractional	ADJ
cana-5532	11	20	derivatives	derivative	NOUN
cana-5532	11	21	and	and	CCONJ
cana-5532	11	22	integrals	integral	NOUN
cana-5532	11	23	into	into	ADP
cana-5532	11	24	the	the	DET
cana-5532	11	25	hybrid	hybrid	ADJ
cana-5532	11	26	structure	structure	NOUN
cana-5532	11	27	.	.	PUNCT
cana-5532	12	1	(	(	PUNCT
cana-5532	12	2	[	[	X
cana-5532	12	3	10],[13],[14],[16],[4],[12	10],[13],[14],[16],[4],[12	NUM
cana-5532	12	4	]	]	PUNCT
cana-5532	12	5	)	)	PUNCT
cana-5532	12	6	.	.	PUNCT
cana-5532	13	1	lakshmikanthan	lakshmikanthan	INTJ
cana-5532	13	2	and	and	CCONJ
cana-5532	13	3	dhage	dhage	VERB
cana-5532	13	4	[	[	X
cana-5532	13	5	7	7	X
cana-5532	13	6	]	]	PUNCT
cana-5532	13	7	they	they	PRON
cana-5532	13	8	initiated	initiate	VERB
cana-5532	13	9	the	the	DET
cana-5532	13	10	study	study	NOUN
cana-5532	13	11	of	of	ADP
cana-5532	13	12	hybrid	hybrid	ADJ
cana-5532	13	13	equations	equation	NOUN
cana-5532	13	14	by	by	ADP
cana-5532	13	15	introducing	introduce	VERB
cana-5532	13	16	a	a	DET
cana-5532	13	17	novel	novel	ADJ
cana-5532	13	18	class	class	NOUN
cana-5532	13	19	of	of	ADP
cana-5532	13	20	nonlinear	nonlinear	ADJ
cana-5532	13	21	differential	differential	ADJ
cana-5532	13	22	equations	equation	NOUN
cana-5532	13	23	known	know	VERB
cana-5532	13	24	as	as	ADP
cana-5532	13	25	ordinary	ordinary	ADJ
cana-5532	13	26	hybrid	hybrid	ADJ
cana-5532	13	27	differential	differential	NOUN
cana-5532	13	28	equations	equation	NOUN
cana-5532	13	29	.	.	PUNCT
cana-5532	14	1	{	{	PUNCT
cana-5532	14	2	𝑑	𝑑	NOUN
cana-5532	14	3	𝑑𝑡	𝑑𝑡	ADP
cana-5532	14	4	(	(	PUNCT
cana-5532	14	5	𝑥(𝑡	𝑥(𝑡	NOUN
cana-5532	14	6	)	)	PUNCT
cana-5532	14	7	𝑓(𝑡,𝑥(𝑡	𝑓(𝑡,𝑥(𝑡	NOUN
cana-5532	14	8	)	)	PUNCT
cana-5532	14	9	)	)	PUNCT
cana-5532	14	10	)	)	PUNCT
cana-5532	15	1	=	=	PUNCT
cana-5532	15	2	𝑔(𝑡	𝑔(𝑡	PROPN
cana-5532	15	3	,	,	PUNCT
cana-5532	15	4	𝑥(𝑡	𝑥(𝑡	NOUN
cana-5532	15	5	)	)	PUNCT
cana-5532	15	6	)	)	PUNCT
cana-5532	15	7	,	,	PUNCT
cana-5532	15	8	𝑎.	𝑎.	PROPN
cana-5532	15	9	𝑒.	𝑒.	PROPN
cana-5532	16	1	𝑡	𝑡	PROPN
cana-5532	16	2	∈	∈	PROPN
cana-5532	16	3	𝐼0	𝐼0	PROPN
cana-5532	16	4	,	,	PUNCT
cana-5532	16	5	𝑥(𝑡0	𝑥(𝑡0	NOUN
cana-5532	16	6	)	)	PUNCT
cana-5532	16	7	=	=	SYM
cana-5532	16	8	𝑥0	𝑥0	NOUN
cana-5532	16	9	∈	∈	NOUN
cana-5532	16	10	ℝ	ℝ	NOUN
cana-5532	16	11	they	they	PRON
cana-5532	16	12	formulated	formulate	VERB
cana-5532	16	13	essential	essential	ADJ
cana-5532	16	14	hybrid	hybrid	ADJ
cana-5532	16	15	differential	differential	NOUN
cana-5532	16	16	inequalities	inequality	NOUN
cana-5532	16	17	that	that	PRON
cana-5532	16	18	serve	serve	VERB
cana-5532	16	19	as	as	ADP
cana-5532	16	20	key	key	ADJ
cana-5532	16	21	tools	tool	NOUN
cana-5532	16	22	for	for	ADP
cana-5532	16	23	proving	prove	VERB
cana-5532	16	24	the	the	DET
cana-5532	16	25	existence	existence	NOUN
cana-5532	16	26	of	of	ADP
cana-5532	16	27	extremal	extremal	ADJ
cana-5532	16	28	solutions	solution	NOUN
cana-5532	16	29	.	.	PUNCT
cana-5532	17	1	zhao	zhao	PROPN
cana-5532	17	2	et	et	PROPN
cana-5532	17	3	al	al	PROPN
cana-5532	17	4	.	.	PUNCT
cana-5532	18	1	[	[	X
cana-5532	18	2	18	18	NUM
cana-5532	18	3	]	]	X
cana-5532	18	4	extended	extended	ADJ
cana-5532	18	5	dhage	dhage	NOUN
cana-5532	18	6	’s	’s	PART
cana-5532	18	7	work	work	NOUN
cana-5532	18	8	to	to	ADP
cana-5532	18	9	the	the	DET
cana-5532	18	10	fractional	fractional	ADJ
cana-5532	18	11	-	-	PUNCT
cana-5532	18	12	order	order	NOUN
cana-5532	18	13	case	case	NOUN
cana-5532	18	14	by	by	ADP
cana-5532	18	15	examining	examine	VERB
cana-5532	18	16	boundary	boundary	ADJ
cana-5532	18	17	value	value	NOUN
cana-5532	18	18	problems	problem	NOUN
cana-5532	18	19	involving	involve	VERB
cana-5532	18	20	fractional	fractional	ADJ
cana-5532	18	21	hybrid	hybrid	ADJ
cana-5532	18	22	differential	differential	NOUN
cana-5532	18	23	equations	equation	NOUN
cana-5532	18	24	.	.	PUNCT
cana-5532	19	1	communications	communication	NOUN
cana-5532	19	2	on	on	ADP
cana-5532	19	3	applied	apply	VERB
cana-5532	19	4	nonlinear	nonlinear	ADJ
cana-5532	19	5	analysis	analysis	NOUN
cana-5532	19	6	issn	issn	NOUN
cana-5532	19	7	:	:	PUNCT
cana-5532	19	8	1074	1074	NUM
cana-5532	19	9	-	-	PUNCT
cana-5532	19	10	133x	133x	NUM
cana-5532	19	11	vol	vol	NOUN
cana-5532	19	12	32	32	NUM
cana-5532	19	13	no	no	NOUN
cana-5532	19	14	.	.	NOUN
cana-5532	19	15	3	3	NUM
cana-5532	19	16	(	(	PUNCT
cana-5532	19	17	2025	2025	NUM
cana-5532	19	18	)	)	PUNCT
cana-5532	19	19	986	986	NUM
cana-5532	19	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-5532	19	21	{	{	PUNCT
cana-5532	19	22	𝐷0	𝐷0	PROPN
cana-5532	19	23	+	+	X
cana-5532	19	24	𝛼	𝛼	PROPN
cana-5532	19	25	(	(	PUNCT
cana-5532	19	26	𝑥(𝑡	𝑥(𝑡	NOUN
cana-5532	19	27	)	)	PUNCT
cana-5532	19	28	𝑓(𝑡,𝑥(𝑡	𝑓(𝑡,𝑥(𝑡	NOUN
cana-5532	19	29	)	)	PUNCT
cana-5532	19	30	)	)	PUNCT
cana-5532	19	31	)	)	PUNCT
cana-5532	20	1	=	=	PUNCT
cana-5532	20	2	𝑔(𝑡	𝑔(𝑡	PROPN
cana-5532	20	3	,	,	PUNCT
cana-5532	20	4	𝑥(𝑡	𝑥(𝑡	NOUN
cana-5532	20	5	)	)	PUNCT
cana-5532	20	6	)	)	PUNCT
cana-5532	20	7	,	,	PUNCT
cana-5532	20	8	𝑡	𝑡	PROPN
cana-5532	20	9	∈	∈	PROPN
cana-5532	21	1	[	[	X
cana-5532	21	2	0	0	NUM
cana-5532	21	3	,	,	PUNCT
cana-5532	21	4	𝑇	𝑇	PROPN
cana-5532	21	5	]	]	PUNCT
cana-5532	21	6	,	,	PUNCT
cana-5532	21	7	𝑥(𝑡0	𝑥(𝑡0	NOUN
cana-5532	21	8	)	)	PUNCT
cana-5532	21	9	=	=	SYM
cana-5532	21	10	0	0	NUM
cana-5532	21	11	,	,	PUNCT
cana-5532	21	12	where	where	SCONJ
cana-5532	21	13	𝐷0	𝐷0	NOUN
cana-5532	21	14	+	+	CCONJ
cana-5532	21	15	𝛼	𝛼	NOUN
cana-5532	21	16	is	be	AUX
cana-5532	21	17	the	the	DET
cana-5532	21	18	riemann	riemann	PROPN
cana-5532	21	19	-	-	PUNCT
cana-5532	21	20	liouville	liouville	VERB
cana-5532	21	21	fractional	fractional	ADJ
cana-5532	21	22	derivative	derivative	NOUN
cana-5532	21	23	of	of	ADP
cana-5532	21	24	order	order	NOUN
cana-5532	21	25	0	0	PUNCT
cana-5532	21	26	<	<	X
cana-5532	21	27	𝛼	𝛼	X
cana-5532	21	28	<	<	X
cana-5532	21	29	1	1	NUM
cana-5532	21	30	.	.	PUNCT
cana-5532	21	31	hybrid	hybrid	ADJ
cana-5532	21	32	fractional	fractional	ADJ
cana-5532	21	33	differential	differential	ADJ
cana-5532	21	34	equations	equation	NOUN
cana-5532	21	35	and	and	CCONJ
cana-5532	21	36	inclusions	inclusion	NOUN
cana-5532	21	37	have	have	AUX
cana-5532	21	38	been	be	AUX
cana-5532	21	39	the	the	DET
cana-5532	21	40	focus	focus	NOUN
cana-5532	21	41	of	of	ADP
cana-5532	21	42	considerable	considerable	ADJ
cana-5532	21	43	research	research	NOUN
cana-5532	21	44	in	in	ADP
cana-5532	21	45	recent	recent	ADJ
cana-5532	21	46	years	year	NOUN
cana-5532	21	47	.	.	PUNCT
cana-5532	22	1	prior	prior	ADV
cana-5532	22	2	to	to	ADP
cana-5532	22	3	proceeding	proceeding	NOUN
cana-5532	22	4	,	,	PUNCT
cana-5532	22	5	we	we	PRON
cana-5532	22	6	present	present	VERB
cana-5532	22	7	a	a	DET
cana-5532	22	8	brief	brief	ADJ
cana-5532	22	9	overview	overview	NOUN
cana-5532	22	10	of	of	ADP
cana-5532	22	11	some	some	DET
cana-5532	22	12	relevant	relevant	ADJ
cana-5532	22	13	contributions	contribution	NOUN
cana-5532	22	14	in	in	ADP
cana-5532	22	15	this	this	DET
cana-5532	22	16	field	field	NOUN
cana-5532	22	17	.	.	PUNCT
cana-5532	23	1	ahmad	ahmad	PROPN
cana-5532	23	2	et	et	PROPN
cana-5532	23	3	al	al	PROPN
cana-5532	23	4	.	.	PUNCT
cana-5532	24	1	[	[	X
cana-5532	24	2	2	2	X
cana-5532	24	3	]	]	PUNCT
cana-5532	24	4	examined	examine	VERB
cana-5532	24	5	the	the	DET
cana-5532	24	6	existence	existence	NOUN
cana-5532	24	7	of	of	ADP
cana-5532	24	8	solutions	solution	NOUN
cana-5532	24	9	for	for	ADP
cana-5532	24	10	a	a	DET
cana-5532	24	11	hybrid	hybrid	ADJ
cana-5532	24	12	inclusion	inclusion	NOUN
cana-5532	24	13	problem	problem	NOUN
cana-5532	24	14	involving	involve	VERB
cana-5532	24	15	nonlocal	nonlocal	ADJ
cana-5532	24	16	boundary	boundary	ADJ
cana-5532	24	17	conditions	condition	NOUN
cana-5532	24	18	.	.	PUNCT
cana-5532	25	1	{	{	PUNCT
cana-5532	25	2	𝐶𝐷0	𝐶𝐷0	NOUN
cana-5532	25	3	+	+	NOUN
cana-5532	25	4	𝛼	𝛼	PROPN
cana-5532	25	5	(	(	PUNCT
cana-5532	25	6	𝑥(𝑡)−∑	𝑥(𝑡)−∑	NOUN
cana-5532	25	7	𝐼	𝐼	ADP
cana-5532	25	8	0	0	NUM
cana-5532	25	9	+	+	CCONJ
cana-5532	25	10	𝛽𝑖𝑚	𝛽𝑖𝑚	X
cana-5532	25	11	𝑖=1	𝑖=1	PROPN
cana-5532	25	12	ℎ𝑖(𝑡,𝑥(𝑡	ℎ𝑖(𝑡,𝑥(𝑡	PROPN
cana-5532	25	13	)	)	PUNCT
cana-5532	25	14	)	)	PUNCT
cana-5532	25	15	𝑔(𝑡,𝑥(𝑡	𝑔(𝑡,𝑥(𝑡	X
cana-5532	25	16	)	)	PUNCT
cana-5532	25	17	)	)	PUNCT
cana-5532	25	18	)	)	PUNCT
cana-5532	26	1	∈	∈	PROPN
cana-5532	26	2	𝒢(𝑡	𝒢(𝑡	NOUN
cana-5532	26	3	,	,	PUNCT
cana-5532	26	4	𝑥(𝑡	𝑥(𝑡	NOUN
cana-5532	26	5	)	)	PUNCT
cana-5532	26	6	)	)	PUNCT
cana-5532	26	7	,	,	PUNCT
cana-5532	26	8	𝑎.	𝑎.	PROPN
cana-5532	26	9	𝑒.	𝑒.	PROPN
cana-5532	27	1	𝑡	𝑡	PROPN
cana-5532	27	2	∈	∈	PROPN
cana-5532	28	1	[	[	X
cana-5532	28	2	0,1	0,1	NUM
cana-5532	28	3	]	]	PUNCT
cana-5532	28	4	,	,	PUNCT
cana-5532	28	5	𝑥(0	𝑥(0	PROPN
cana-5532	28	6	)	)	PUNCT
cana-5532	28	7	=	=	PUNCT
cana-5532	29	1	𝜇(𝜉	𝜇(𝜉	PROPN
cana-5532	29	2	)	)	PUNCT
cana-5532	29	3	,	,	PUNCT
cana-5532	29	4	 	 	SPACE
cana-5532	29	5	𝑥(1	𝑥(1	VERB
cana-5532	29	6	)	)	PUNCT
cana-5532	29	7	=	=	PUNCT
cana-5532	30	1	𝑎	𝑎	PRON
cana-5532	30	2	∈	∈	NOUN
cana-5532	30	3	ℝ.	ℝ.	PROPN
cana-5532	30	4	where	where	SCONJ
cana-5532	30	5	𝐶𝐷0	𝐶𝐷0	NOUN
cana-5532	30	6	+	+	CCONJ
cana-5532	30	7	𝛼	𝛼	PROPN
cana-5532	30	8	denotes	denote	VERB
cana-5532	30	9	the	the	DET
cana-5532	30	10	caputo	caputo	PROPN
cana-5532	30	11	fractional	fractional	PROPN
cana-5532	30	12	derivative	derivative	NOUN
cana-5532	30	13	of	of	ADP
cana-5532	30	14	order	order	NOUN
cana-5532	30	15	1	1	NUM
cana-5532	30	16	<	<	X
cana-5532	30	17	𝛼	𝛼	X
cana-5532	30	18	≤	≤	PROPN
cana-5532	30	19	2	2	NUM
cana-5532	30	20	and	and	CCONJ
cana-5532	30	21	𝐼	𝐼	PROPN
cana-5532	30	22	0	0	NUM
cana-5532	30	23	+	+	NUM
cana-5532	30	24	𝛽𝑖	𝛽𝑖	VERB
cana-5532	30	25	is	be	AUX
cana-5532	30	26	the	the	DET
cana-5532	30	27	riemann	riemann	PROPN
cana-5532	30	28	–	–	PUNCT
cana-5532	30	29	liouville	liouville	VERB
cana-5532	30	30	fractional	fractional	ADJ
cana-5532	30	31	integral	integral	ADJ
cana-5532	30	32	of	of	ADP
cana-5532	30	33	order	order	NOUN
cana-5532	30	34	𝛽𝑖	𝛽𝑖	NOUN
cana-5532	30	35	>	>	X
cana-5532	30	36	0	0	PUNCT
cana-5532	31	1	with	with	ADP
cana-5532	31	2	𝑖	𝑖	PRON
cana-5532	31	3	∈	∈	PROPN
cana-5532	31	4	{	{	PUNCT
cana-5532	31	5	1,2,3	1,2,3	NOUN
cana-5532	31	6	.	.	PUNCT
cana-5532	31	7	.	.	PUNCT
cana-5532	31	8	.	.	PUNCT
cana-5532	32	1	,	,	PUNCT
cana-5532	32	2	𝑚	𝑚	X
cana-5532	32	3	}	}	PUNCT
cana-5532	32	4	.	.	PUNCT
cana-5532	33	1	in	in	ADP
cana-5532	33	2	[	[	X
cana-5532	33	3	6	6	NUM
cana-5532	33	4	]	]	PUNCT
cana-5532	33	5	,	,	PUNCT
cana-5532	33	6	derbazi	derbazi	NOUN
cana-5532	33	7	et	et	PROPN
cana-5532	33	8	al	al	PROPN
cana-5532	33	9	.	.	PROPN
cana-5532	33	10	confirmed	confirm	VERB
cana-5532	33	11	the	the	DET
cana-5532	33	12	existence	existence	NOUN
cana-5532	33	13	and	and	CCONJ
cana-5532	33	14	uniqueness	uniqueness	NOUN
cana-5532	33	15	of	of	ADP
cana-5532	33	16	solutions	solution	NOUN
cana-5532	33	17	for	for	ADP
cana-5532	33	18	a	a	DET
cana-5532	33	19	fractional	fractional	ADJ
cana-5532	33	20	hybrid	hybrid	ADJ
cana-5532	33	21	boundary	boundary	ADJ
cana-5532	33	22	value	value	NOUN
cana-5532	33	23	problem	problem	NOUN
cana-5532	33	24	.	.	PUNCT
cana-5532	34	1	{	{	PUNCT
cana-5532	34	2	𝐶𝐷0	𝐶𝐷0	NOUN
cana-5532	34	3	+	+	NOUN
cana-5532	34	4	𝛼	𝛼	PROPN
cana-5532	34	5	(	(	PUNCT
cana-5532	34	6	𝑥(𝑡)−ℎ(𝑡,𝑥(𝑡	𝑥(𝑡)−ℎ(𝑡,𝑥(𝑡	NOUN
cana-5532	34	7	)	)	PUNCT
cana-5532	34	8	)	)	PUNCT
cana-5532	34	9	𝑔(𝑡,𝑥(𝑡	𝑔(𝑡,𝑥(𝑡	X
cana-5532	34	10	)	)	PUNCT
cana-5532	34	11	)	)	PUNCT
cana-5532	34	12	)	)	PUNCT
cana-5532	35	1	=	=	SYM
cana-5532	35	2	θ(𝑡	θ(𝑡	PROPN
cana-5532	35	3	,	,	PUNCT
cana-5532	35	4	𝑥(𝑡	𝑥(𝑡	NOUN
cana-5532	35	5	)	)	PUNCT
cana-5532	35	6	)	)	PUNCT
cana-5532	35	7	,	,	PUNCT
cana-5532	35	8	𝑎.	𝑎.	PROPN
cana-5532	35	9	𝑒.	𝑒.	PROPN
cana-5532	36	1	𝑡	𝑡	PROPN
cana-5532	36	2	∈	∈	PROPN
cana-5532	37	1	[	[	X
cana-5532	37	2	0	0	NUM
cana-5532	37	3	,	,	PUNCT
cana-5532	37	4	𝑇	𝑇	PROPN
cana-5532	37	5	]	]	PUNCT
cana-5532	37	6	,	,	PUNCT
cana-5532	37	7	𝑎1	𝑎1	INTJ
cana-5532	37	8	(	(	PUNCT
cana-5532	37	9	𝑥(𝑡)−ℎ(𝑡,𝑥(𝑡	𝑥(𝑡)−ℎ(𝑡,𝑥(𝑡	NOUN
cana-5532	37	10	)	)	PUNCT
cana-5532	37	11	)	)	PUNCT
cana-5532	37	12	𝑔(𝑡,𝑥(𝑡	𝑔(𝑡,𝑥(𝑡	X
cana-5532	37	13	)	)	PUNCT
cana-5532	37	14	)	)	PUNCT
cana-5532	37	15	)	)	PUNCT
cana-5532	38	1	|𝑡=0	|𝑡=0	PROPN
cana-5532	38	2	+	+	CCONJ
cana-5532	38	3	𝑏1	𝑏1	ADJ
cana-5532	38	4	(	(	PUNCT
cana-5532	38	5	𝑥(𝑡)−ℎ(𝑡,𝑥(𝑡	𝑥(𝑡)−ℎ(𝑡,𝑥(𝑡	NOUN
cana-5532	38	6	)	)	PUNCT
cana-5532	38	7	)	)	PUNCT
cana-5532	38	8	𝑔(𝑡,𝑥(𝑡	𝑔(𝑡,𝑥(𝑡	X
cana-5532	38	9	)	)	PUNCT
cana-5532	38	10	)	)	PUNCT
cana-5532	38	11	)	)	PUNCT
cana-5532	39	1	|𝑡=𝑇	|𝑡=𝑇	NOUN
cana-5532	39	2	=	=	SYM
cana-5532	39	3	𝜆1	𝜆1	PROPN
cana-5532	39	4	,	,	PUNCT
cana-5532	39	5	𝑎2	𝑎2	NOUN
cana-5532	39	6	𝐶𝐷	𝐶𝐷	PROPN
cana-5532	39	7	0	0	NUM
cana-5532	39	8	+	+	NOUN
cana-5532	39	9	𝛽	𝛽	PROPN
cana-5532	39	10	(	(	PUNCT
cana-5532	39	11	𝑥(𝑡)−ℎ(𝑡,𝑥(𝑡	𝑥(𝑡)−ℎ(𝑡,𝑥(𝑡	NOUN
cana-5532	39	12	)	)	PUNCT
cana-5532	39	13	)	)	PUNCT
cana-5532	39	14	𝑔(𝑡,𝑥(𝑡	𝑔(𝑡,𝑥(𝑡	X
cana-5532	39	15	)	)	PUNCT
cana-5532	39	16	)	)	PUNCT
cana-5532	39	17	)	)	PUNCT
cana-5532	39	18	|𝑡=𝜂	|𝑡=𝜂	NOUN
cana-5532	39	19	+	+	SYM
cana-5532	39	20	𝑏2	𝑏2	NOUN
cana-5532	39	21	𝐶𝐷	𝐶𝐷	PROPN
cana-5532	39	22	0	0	NUM
cana-5532	39	23	+	+	NOUN
cana-5532	39	24	𝛽	𝛽	PROPN
cana-5532	39	25	(	(	PUNCT
cana-5532	39	26	𝑥(𝑡)−ℎ(𝑡,𝑥(𝑡	𝑥(𝑡)−ℎ(𝑡,𝑥(𝑡	NOUN
cana-5532	39	27	)	)	PUNCT
cana-5532	39	28	)	)	PUNCT
cana-5532	39	29	𝑔(𝑡,𝑥(𝑡	𝑔(𝑡,𝑥(𝑡	X
cana-5532	39	30	)	)	PUNCT
cana-5532	39	31	)	)	PUNCT
cana-5532	39	32	)	)	PUNCT
cana-5532	40	1	|𝑡=𝑇	|𝑡=𝑇	NOUN
cana-5532	40	2	=	=	PROPN
cana-5532	40	3	𝜆2	𝜆2	PROPN
cana-5532	40	4	.	.	PUNCT
cana-5532	41	1	where	where	SCONJ
cana-5532	41	2	1	1	NUM
cana-5532	41	3	<	<	X
cana-5532	41	4	𝛼	𝛼	VERB
cana-5532	41	5	≤	≤	NUM
cana-5532	41	6	2	2	NUM
cana-5532	41	7	,	,	PUNCT
cana-5532	41	8	0	0	NUM
cana-5532	41	9	<	<	X
cana-5532	41	10	𝛽	𝛽	X
cana-5532	41	11	≤	≤	NUM
cana-5532	41	12	1	1	NUM
cana-5532	41	13	,	,	PUNCT
cana-5532	41	14	𝜂	𝜂	X
cana-5532	41	15	∈	∈	PROPN
cana-5532	42	1	[	[	X
cana-5532	42	2	0	0	NUM
cana-5532	42	3	,	,	PUNCT
cana-5532	42	4	𝑇	𝑇	PROPN
cana-5532	42	5	]	]	PUNCT
cana-5532	42	6	and	and	CCONJ
cana-5532	42	7	𝑎1	𝑎1	PROPN
cana-5532	42	8	,	,	PUNCT
cana-5532	42	9	𝑎2	𝑎2	NOUN
cana-5532	42	10	,	,	PUNCT
cana-5532	42	11	𝑏1	𝑏1	NOUN
cana-5532	42	12	,	,	PUNCT
cana-5532	42	13	𝑏2	𝑏2	NOUN
cana-5532	42	14	,	,	PUNCT
cana-5532	42	15	𝜆1	𝜆1	PROPN
cana-5532	42	16	,	,	PUNCT
cana-5532	42	17	𝜆2	𝜆2	PROPN
cana-5532	42	18	are	be	AUX
cana-5532	42	19	real	real	ADJ
cana-5532	42	20	constants	constant	NOUN
cana-5532	42	21	.	.	PUNCT
cana-5532	42	22	.	.	PUNCT
cana-5532	43	1	baleanu	baleanu	PROPN
cana-5532	43	2	et	et	PROPN
cana-5532	43	3	al	al	PROPN
cana-5532	43	4	.	.	PUNCT
cana-5532	44	1	[	[	X
cana-5532	44	2	3	3	X
cana-5532	44	3	]	]	PUNCT
cana-5532	44	4	they	they	PRON
cana-5532	44	5	employed	employ	VERB
cana-5532	44	6	a	a	DET
cana-5532	44	7	generalized	generalized	ADJ
cana-5532	44	8	version	version	NOUN
cana-5532	44	9	of	of	ADP
cana-5532	44	10	dhage	dhage	NOUN
cana-5532	44	11	’s	’s	PART
cana-5532	44	12	hybrid	hybrid	ADJ
cana-5532	44	13	fixed	fix	VERB
cana-5532	44	14	point	point	NOUN
cana-5532	44	15	theorem	theorem	NOUN
cana-5532	44	16	for	for	ADP
cana-5532	44	17	the	the	DET
cana-5532	44	18	sum	sum	NOUN
cana-5532	44	19	of	of	ADP
cana-5532	44	20	three	three	NUM
cana-5532	44	21	fractional	fractional	ADJ
cana-5532	44	22	operators	operator	NOUN
cana-5532	44	23	to	to	PART
cana-5532	44	24	examine	examine	VERB
cana-5532	44	25	the	the	DET
cana-5532	44	26	existence	existence	NOUN
cana-5532	44	27	of	of	ADP
cana-5532	44	28	solutions	solution	NOUN
cana-5532	44	29	to	to	ADP
cana-5532	44	30	a	a	DET
cana-5532	44	31	fractional	fractional	ADJ
cana-5532	44	32	hybrid	hybrid	ADJ
cana-5532	44	33	integro	integro	ADJ
cana-5532	44	34	-	-	PUNCT
cana-5532	44	35	differential	differential	NOUN
cana-5532	44	36	equation	equation	NOUN
cana-5532	44	37	subject	subject	ADJ
cana-5532	44	38	to	to	ADP
cana-5532	44	39	mixed	mixed	ADJ
cana-5532	44	40	hybrid	hybrid	ADJ
cana-5532	44	41	integral	integral	ADJ
cana-5532	44	42	boundary	boundary	ADJ
cana-5532	44	43	conditions	condition	NOUN
cana-5532	44	44	.	.	PUNCT
cana-5532	45	1	{	{	PUNCT
cana-5532	45	2	𝐶𝐷0	𝐶𝐷0	NOUN
cana-5532	45	3	+	+	NOUN
cana-5532	45	4	𝜔	𝜔	PROPN
cana-5532	45	5	(	(	PUNCT
cana-5532	45	6	𝑥(𝑡)−ℎ(𝑡,𝑥(𝑡),𝐼	𝑥(𝑡)−ℎ(𝑡,𝑥(𝑡),𝐼	NOUN
cana-5532	45	7	0	0	NUM
cana-5532	45	8	+	+	CCONJ
cana-5532	45	9	𝛾1𝑥(𝑡),𝐼	𝛾1𝑥(𝑡),𝐼	ADJ
cana-5532	45	10	0	0	NUM
cana-5532	45	11	+	+	NUM
cana-5532	45	12	𝛾2𝑥(𝑡),	𝛾2𝑥(𝑡),	PROPN
cana-5532	45	13	...	...	PUNCT
cana-5532	45	14	,𝐼	,𝐼	PUNCT
cana-5532	45	15	0	0	PUNCT
cana-5532	45	16	+	+	NUM
cana-5532	45	17	𝛾𝑛𝑥(𝑡	𝛾𝑛𝑥(𝑡	PROPN
cana-5532	45	18	)	)	PUNCT
cana-5532	45	19	)	)	PUNCT
cana-5532	46	1	𝑔(𝑡,𝑥(𝑡),𝐼	𝑔(𝑡,𝑥(𝑡),𝐼	VERB
cana-5532	46	2	0	0	NUM
cana-5532	47	1	+	+	NUM
cana-5532	47	2	𝜇1𝑥(𝑡),𝐼	𝜇1𝑥(𝑡),𝐼	NOUN
cana-5532	47	3	0	0	NUM
cana-5532	47	4	+	+	NUM
cana-5532	47	5	𝜇2𝑥(𝑡),	𝜇2𝑥(𝑡),	PROPN
cana-5532	47	6	...	...	PUNCT
cana-5532	47	7	,𝐼	,𝐼	PUNCT
cana-5532	47	8	0	0	PUNCT
cana-5532	47	9	+	+	NUM
cana-5532	47	10	𝜇𝑚𝑥(𝑡	𝜇𝑚𝑥(𝑡	NOUN
cana-5532	47	11	)	)	PUNCT
cana-5532	47	12	)	)	PUNCT
cana-5532	47	13	)	)	PUNCT
cana-5532	48	1	=	=	SYM
cana-5532	48	2	υ(𝑡	υ(𝑡	PROPN
cana-5532	48	3	,	,	PUNCT
cana-5532	48	4	𝑥(𝑡	𝑥(𝑡	NOUN
cana-5532	48	5	)	)	PUNCT
cana-5532	48	6	)	)	PUNCT
cana-5532	48	7	,	,	PUNCT
cana-5532	48	8	𝑎.	𝑎.	PROPN
cana-5532	48	9	𝑒.	𝑒.	PROPN
cana-5532	49	1	𝑡	𝑡	PROPN
cana-5532	49	2	∈	∈	PROPN
cana-5532	50	1	[	[	X
cana-5532	50	2	0,1	0,1	NUM
cana-5532	50	3	]	]	PUNCT
cana-5532	50	4	,	,	PUNCT
cana-5532	50	5	𝜆1	𝜆1	PROPN
cana-5532	50	6	∫	∫	PROPN
cana-5532	50	7	𝐶	𝐶	PROPN
cana-5532	50	8	1	1	NUM
cana-5532	50	9	0	0	NUM
cana-5532	50	10	𝐷	𝐷	PROPN
cana-5532	50	11	0	0	NUM
cana-5532	50	12	+	+	NOUN
cana-5532	50	13	𝛽1	𝛽1	NOUN
cana-5532	50	14	(	(	PUNCT
cana-5532	50	15	𝑥(𝑠)−ℎ(𝑠,𝑥(𝑠),𝐼𝛾1𝑥(𝑠),𝐼𝛾2𝑥(𝑠),	𝑥(𝑠)−ℎ(𝑠,𝑥(𝑠),𝐼𝛾1𝑥(𝑠),𝐼𝛾2𝑥(𝑠),	PROPN
cana-5532	50	16	...	...	PUNCT
cana-5532	50	17	,𝐼𝛾𝑛𝑥(𝑠	,𝐼𝛾𝑛𝑥(𝑠	PUNCT
cana-5532	50	18	)	)	PUNCT
cana-5532	50	19	)	)	PUNCT
cana-5532	50	20	𝑔(𝑠,𝑥(𝑠),𝐼𝜇1𝑥(𝑠),𝐼𝜇2𝑥(𝑠),	𝑔(𝑠,𝑥(𝑠),𝐼𝜇1𝑥(𝑠),𝐼𝜇2𝑥(𝑠),	PROPN
cana-5532	50	21	...	...	PUNCT
cana-5532	50	22	,𝐼𝜇𝑚𝑥(𝑠	,𝐼𝜇𝑚𝑥(𝑠	PUNCT
cana-5532	50	23	)	)	PUNCT
cana-5532	50	24	)	)	PUNCT
cana-5532	50	25	)	)	PUNCT
cana-5532	51	1	𝑑𝑠	𝑑𝑠	X
cana-5532	51	2	+	+	NOUN
cana-5532	51	3	𝜆2	𝜆2	NOUN
cana-5532	51	4	𝐶𝐷	𝐶𝐷	PROPN
cana-5532	51	5	0	0	NUM
cana-5532	51	6	+	+	NUM
cana-5532	51	7	𝛼1	𝛼1	NOUN
cana-5532	51	8	(	(	PUNCT
cana-5532	51	9	𝑥(𝑡)−ℎ(𝑡,𝑥(𝑡),𝐼	𝑥(𝑡)−ℎ(𝑡,𝑥(𝑡),𝐼	NOUN
cana-5532	51	10	0	0	NUM
cana-5532	52	1	+	+	CCONJ
cana-5532	52	2	𝛾1𝑥(𝑡),𝐼	𝛾1𝑥(𝑡),𝐼	ADJ
cana-5532	52	3	0	0	NUM
cana-5532	52	4	+	+	NUM
cana-5532	52	5	𝛾2𝑥(𝑡),	𝛾2𝑥(𝑡),	PROPN
cana-5532	52	6	...	...	PUNCT
cana-5532	52	7	,𝐼	,𝐼	PUNCT
cana-5532	52	8	0	0	PUNCT
cana-5532	52	9	+	+	NUM
cana-5532	52	10	𝛾𝑛𝑥(𝑡	𝛾𝑛𝑥(𝑡	PROPN
cana-5532	52	11	)	)	PUNCT
cana-5532	52	12	)	)	PUNCT
cana-5532	53	1	𝑔(𝑡,𝑥(𝑡),𝐼	𝑔(𝑡,𝑥(𝑡),𝐼	VERB
cana-5532	53	2	0	0	NUM
cana-5532	54	1	+	+	NUM
cana-5532	54	2	𝜇1𝑥(𝑡),𝐼	𝜇1𝑥(𝑡),𝐼	NOUN
cana-5532	54	3	0	0	NUM
cana-5532	54	4	+	+	NUM
cana-5532	54	5	𝜇2𝑥(𝑡),	𝜇2𝑥(𝑡),	PROPN
cana-5532	54	6	...	...	PUNCT
cana-5532	54	7	,𝐼	,𝐼	PUNCT
cana-5532	54	8	0	0	PUNCT
cana-5532	54	9	+	+	NUM
cana-5532	54	10	𝜇𝑚𝑥(𝑡	𝜇𝑚𝑥(𝑡	NOUN
cana-5532	54	11	)	)	PUNCT
cana-5532	54	12	)	)	PUNCT
cana-5532	54	13	)	)	PUNCT
cana-5532	55	1	|𝑡=1	|𝑡=1	PROPN
cana-5532	55	2	+	+	NOUN
cana-5532	55	3	𝜆3	𝜆3	NOUN
cana-5532	55	4	(	(	PUNCT
cana-5532	55	5	𝑥(𝑡)−ℎ(𝑡,𝑥(𝑡),𝐼	𝑥(𝑡)−ℎ(𝑡,𝑥(𝑡),𝐼	NOUN
cana-5532	55	6	0	0	NUM
cana-5532	55	7	+	+	CCONJ
cana-5532	55	8	𝛾1𝑥(𝑡),𝐼	𝛾1𝑥(𝑡),𝐼	ADJ
cana-5532	55	9	0	0	NUM
cana-5532	55	10	+	+	NUM
cana-5532	55	11	𝛾2𝑥(𝑡),	𝛾2𝑥(𝑡),	PROPN
cana-5532	55	12	...	...	PUNCT
cana-5532	55	13	,𝐼	,𝐼	PUNCT
cana-5532	55	14	0	0	PUNCT
cana-5532	55	15	+	+	NUM
cana-5532	55	16	𝛾𝑛𝑥(𝑡	𝛾𝑛𝑥(𝑡	PROPN
cana-5532	55	17	)	)	PUNCT
cana-5532	55	18	)	)	PUNCT
cana-5532	56	1	𝑔(𝑡,𝑥(𝑡),𝐼	𝑔(𝑡,𝑥(𝑡),𝐼	VERB
cana-5532	56	2	0	0	NUM
cana-5532	57	1	+	+	NUM
cana-5532	57	2	𝜇1𝑥(𝑡),𝐼	𝜇1𝑥(𝑡),𝐼	NOUN
cana-5532	57	3	0	0	NUM
cana-5532	57	4	+	+	NUM
cana-5532	57	5	𝜇2𝑥(𝑡),	𝜇2𝑥(𝑡),	PROPN
cana-5532	57	6	...	...	PUNCT
cana-5532	57	7	,𝐼	,𝐼	PUNCT
cana-5532	57	8	0	0	PUNCT
cana-5532	57	9	+	+	NUM
cana-5532	57	10	𝜇𝑚𝑥(𝑡	𝜇𝑚𝑥(𝑡	NOUN
cana-5532	57	11	)	)	PUNCT
cana-5532	57	12	)	)	PUNCT
cana-5532	57	13	)	)	PUNCT
cana-5532	58	1	|𝑡=0	|𝑡=0	PUNCT
cana-5532	58	2	=	=	SYM
cana-5532	58	3	0	0	NUM
cana-5532	58	4	𝜆4	𝜆4	NOUN
cana-5532	58	5	∫	∫	PROPN
cana-5532	58	6	𝐶	𝐶	PROPN
cana-5532	58	7	1	1	NUM
cana-5532	58	8	0	0	NUM
cana-5532	58	9	𝐷	𝐷	NOUN
cana-5532	58	10	0	0	NUM
cana-5532	58	11	+	+	NOUN
cana-5532	58	12	𝛽2	𝛽2	PROPN
cana-5532	58	13	(	(	PUNCT
cana-5532	58	14	𝑥(𝑠)−ℎ(𝑠,𝑥(𝑠),𝐼𝛾1𝑥(𝑠),𝐼𝛾2𝑥(𝑠),	𝑥(𝑠)−ℎ(𝑠,𝑥(𝑠),𝐼𝛾1𝑥(𝑠),𝐼𝛾2𝑥(𝑠),	PROPN
cana-5532	58	15	...	...	PUNCT
cana-5532	58	16	,𝐼𝛾𝑛𝑥(𝑠	,𝐼𝛾𝑛𝑥(𝑠	PUNCT
cana-5532	58	17	)	)	PUNCT
cana-5532	58	18	)	)	PUNCT
cana-5532	58	19	𝑔(𝑠,𝑥(𝑠),𝐼𝜇1𝑥(𝑠),𝐼𝜇2𝑥(𝑠),	𝑔(𝑠,𝑥(𝑠),𝐼𝜇1𝑥(𝑠),𝐼𝜇2𝑥(𝑠),	PROPN
cana-5532	58	20	...	...	PUNCT
cana-5532	58	21	,𝐼𝜇𝑚𝑥(𝑠	,𝐼𝜇𝑚𝑥(𝑠	PUNCT
cana-5532	58	22	)	)	PUNCT
cana-5532	58	23	)	)	PUNCT
cana-5532	58	24	)	)	PUNCT
cana-5532	59	1	𝑑𝑠	𝑑𝑠	X
cana-5532	60	1	+	+	NOUN
cana-5532	60	2	𝜆5	𝜆5	ADJ
cana-5532	60	3	𝐶𝐷	𝐶𝐷	PROPN
cana-5532	60	4	0	0	NUM
cana-5532	60	5	+	+	NUM
cana-5532	60	6	𝛼2	𝛼2	PROPN
cana-5532	60	7	(	(	PUNCT
cana-5532	60	8	𝑥(𝑡)−ℎ(𝑡,𝑥(𝑡),𝐼	𝑥(𝑡)−ℎ(𝑡,𝑥(𝑡),𝐼	NOUN
cana-5532	60	9	0	0	NUM
cana-5532	60	10	+	+	CCONJ
cana-5532	60	11	𝛾1𝑥(𝑡),𝐼	𝛾1𝑥(𝑡),𝐼	ADJ
cana-5532	60	12	0	0	NUM
cana-5532	60	13	+	+	NUM
cana-5532	60	14	𝛾2𝑥(𝑡),	𝛾2𝑥(𝑡),	PROPN
cana-5532	60	15	...	...	PUNCT
cana-5532	60	16	,𝐼	,𝐼	PUNCT
cana-5532	60	17	0	0	PUNCT
cana-5532	60	18	+	+	NUM
cana-5532	60	19	𝛾𝑛𝑥(𝑡	𝛾𝑛𝑥(𝑡	PROPN
cana-5532	60	20	)	)	PUNCT
cana-5532	60	21	)	)	PUNCT
cana-5532	61	1	𝑔(𝑡,𝑥(𝑡),𝐼	𝑔(𝑡,𝑥(𝑡),𝐼	VERB
cana-5532	61	2	0	0	NUM
cana-5532	62	1	+	+	NUM
cana-5532	62	2	𝜇1𝑥(𝑡),𝐼	𝜇1𝑥(𝑡),𝐼	NOUN
cana-5532	62	3	0	0	NUM
cana-5532	62	4	+	+	NUM
cana-5532	62	5	𝜇2𝑥(𝑡),	𝜇2𝑥(𝑡),	PROPN
cana-5532	62	6	...	...	PUNCT
cana-5532	62	7	,𝐼	,𝐼	PUNCT
cana-5532	62	8	0	0	PUNCT
cana-5532	62	9	+	+	NUM
cana-5532	62	10	𝜇𝑚𝑥(𝑡	𝜇𝑚𝑥(𝑡	NOUN
cana-5532	62	11	)	)	PUNCT
cana-5532	62	12	)	)	PUNCT
cana-5532	62	13	)	)	PUNCT
cana-5532	63	1	|𝑡=1	|𝑡=1	PROPN
cana-5532	63	2	+	+	PROPN
cana-5532	63	3	𝜆6	𝜆6	PROPN
cana-5532	63	4	(	(	PUNCT
cana-5532	63	5	𝑥(𝑡)−ℎ(𝑡,𝑥(𝑡),𝐼	𝑥(𝑡)−ℎ(𝑡,𝑥(𝑡),𝐼	NOUN
cana-5532	63	6	0	0	NUM
cana-5532	63	7	+	+	CCONJ
cana-5532	63	8	𝛾1𝑥(𝑡),𝐼	𝛾1𝑥(𝑡),𝐼	ADJ
cana-5532	63	9	0	0	NUM
cana-5532	63	10	+	+	NUM
cana-5532	63	11	𝛾2𝑥(𝑡),	𝛾2𝑥(𝑡),	PROPN
cana-5532	63	12	...	...	PUNCT
cana-5532	63	13	,𝐼	,𝐼	PUNCT
cana-5532	63	14	0	0	PUNCT
cana-5532	63	15	+	+	NUM
cana-5532	63	16	𝛾𝑛𝑥(𝑡	𝛾𝑛𝑥(𝑡	PROPN
cana-5532	63	17	)	)	PUNCT
cana-5532	63	18	)	)	PUNCT
cana-5532	64	1	𝑔(𝑡,𝑥(𝑡),𝐼	𝑔(𝑡,𝑥(𝑡),𝐼	VERB
cana-5532	64	2	0	0	NUM
cana-5532	65	1	+	+	NUM
cana-5532	65	2	𝜇1𝑥(𝑡),𝐼	𝜇1𝑥(𝑡),𝐼	NOUN
cana-5532	65	3	0	0	NUM
cana-5532	65	4	+	+	NUM
cana-5532	65	5	𝜇2𝑥(𝑡),	𝜇2𝑥(𝑡),	PROPN
cana-5532	65	6	...	...	PUNCT
cana-5532	65	7	,𝐼	,𝐼	PUNCT
cana-5532	65	8	0	0	PUNCT
cana-5532	65	9	+	+	NUM
cana-5532	65	10	𝜇𝑚𝑥(𝑡	𝜇𝑚𝑥(𝑡	NOUN
cana-5532	65	11	)	)	PUNCT
cana-5532	65	12	)	)	PUNCT
cana-5532	65	13	)	)	PUNCT
cana-5532	66	1	|𝑡=0	|𝑡=0	PROPN
cana-5532	66	2	=	=	SYM
cana-5532	66	3	0	0	X
cana-5532	66	4	.	.	PUNCT
cana-5532	66	5	communications	communication	NOUN
cana-5532	66	6	on	on	ADP
cana-5532	66	7	applied	apply	VERB
cana-5532	66	8	nonlinear	nonlinear	ADJ
cana-5532	66	9	analysis	analysis	NOUN
cana-5532	66	10	issn	issn	NOUN
cana-5532	66	11	:	:	PUNCT
cana-5532	66	12	1074	1074	NUM
cana-5532	66	13	-	-	PUNCT
cana-5532	66	14	133x	133x	NUM
cana-5532	66	15	vol	vol	NOUN
cana-5532	66	16	32	32	NUM
cana-5532	66	17	no	no	NOUN
cana-5532	66	18	.	.	NOUN
cana-5532	66	19	3	3	NUM
cana-5532	66	20	(	(	PUNCT
cana-5532	66	21	2025	2025	NUM
cana-5532	66	22	)	)	PUNCT
cana-5532	66	23	987	987	NUM
cana-5532	66	24	https://internationalpubls.com	https://internationalpubls.com	X
cana-5532	66	25	where	where	SCONJ
cana-5532	66	26	1	1	NUM
cana-5532	66	27	<	<	X
cana-5532	66	28	𝜔	𝜔	X
cana-5532	66	29	≤	≤	NUM
cana-5532	66	30	2	2	NUM
cana-5532	66	31	,	,	PUNCT
cana-5532	66	32	𝛽1	𝛽1	NOUN
cana-5532	66	33	,	,	PUNCT
cana-5532	66	34	𝛽2	𝛽2	PROPN
cana-5532	66	35	∈	∈	PROPN
cana-5532	66	36	(	(	PUNCT
cana-5532	66	37	0,1	0,1	NOUN
cana-5532	66	38	]	]	PUNCT
cana-5532	66	39	,	,	PUNCT
cana-5532	66	40	𝛼1	𝛼1	NOUN
cana-5532	66	41	,	,	PUNCT
cana-5532	66	42	𝛼2	𝛼2	PROPN
cana-5532	66	43	∈	∈	PROPN
cana-5532	66	44	(	(	PUNCT
cana-5532	66	45	0,1	0,1	NOUN
cana-5532	66	46	]	]	PUNCT
cana-5532	66	47	,	,	PUNCT
cana-5532	66	48	𝜆1	𝜆1	PROPN
cana-5532	66	49	,	,	PUNCT
cana-5532	66	50	𝜆2	𝜆2	PROPN
cana-5532	66	51	,	,	PUNCT
cana-5532	66	52	𝜆3	𝜆3	NOUN
cana-5532	66	53	,	,	PUNCT
cana-5532	66	54	𝜆4	𝜆4	NOUN
cana-5532	66	55	,	,	PUNCT
cana-5532	66	56	𝜆5	𝜆5	PROPN
cana-5532	66	57	,	,	PUNCT
cana-5532	66	58	𝜆6	𝜆6	PROPN
cana-5532	66	59	∈	∈	PROPN
cana-5532	66	60	ℝ	ℝ	PROPN
cana-5532	66	61	+	+	X
cana-5532	66	62	and	and	CCONJ
cana-5532	66	63	𝛾𝑖	𝛾𝑖	ADV
cana-5532	66	64	>	>	X
cana-5532	66	65	0	0	NUM
cana-5532	66	66	,	,	PUNCT
cana-5532	66	67	𝜇𝑗	𝜇𝑗	ADP
cana-5532	66	68	>	>	X
cana-5532	66	69	0	0	PUNCT
cana-5532	66	70	with	with	ADP
cana-5532	66	71	𝑖	𝑖	PROPN
cana-5532	66	72	∈	∈	PROPN
cana-5532	66	73	{	{	PUNCT
cana-5532	66	74	1,2	1,2	NUM
cana-5532	66	75	,	,	PUNCT
cana-5532	66	76	.	.	PUNCT
cana-5532	66	77	.	.	PUNCT
cana-5532	66	78	.	.	PUNCT
cana-5532	67	1	𝑛	𝑛	X
cana-5532	67	2	}	}	PUNCT
cana-5532	67	3	and	and	CCONJ
cana-5532	67	4	𝑗	𝑗	PROPN
cana-5532	67	5	∈	∈	NOUN
cana-5532	67	6	{	{	PUNCT
cana-5532	67	7	1,2	1,2	NUM
cana-5532	67	8	,	,	PUNCT
cana-5532	67	9	.	.	PUNCT
cana-5532	67	10	.	.	PUNCT
cana-5532	67	11	.	.	PUNCT
cana-5532	68	1	𝑚	𝑚	X
cana-5532	68	2	}	}	PUNCT
cana-5532	68	3	.	.	PUNCT
cana-5532	69	1	building	build	VERB
cana-5532	69	2	upon	upon	SCONJ
cana-5532	69	3	the	the	DET
cana-5532	69	4	previous	previous	ADJ
cana-5532	69	5	works	work	NOUN
cana-5532	69	6	,	,	PUNCT
cana-5532	69	7	we	we	PRON
cana-5532	69	8	establish	establish	VERB
cana-5532	69	9	an	an	DET
cana-5532	69	10	existence	existence	NOUN
cana-5532	69	11	result	result	NOUN
cana-5532	69	12	for	for	ADP
cana-5532	69	13	a	a	DET
cana-5532	69	14	class	class	NOUN
cana-5532	69	15	of	of	ADP
cana-5532	69	16	fractional	fractional	ADJ
cana-5532	69	17	hybrid	hybrid	ADJ
cana-5532	69	18	integro	integro	ADJ
cana-5532	69	19	-	-	PUNCT
cana-5532	69	20	differential	differential	NOUN
cana-5532	69	21	problem	problem	NOUN
cana-5532	69	22	.	.	PUNCT
cana-5532	70	1	𝐶𝐷0	𝐶𝐷0	NOUN
cana-5532	70	2	+	+	NOUN
cana-5532	70	3	𝛼	𝛼	PROPN
cana-5532	70	4	(	(	PUNCT
cana-5532	70	5	𝑢(𝑡	𝑢(𝑡	NOUN
cana-5532	70	6	)	)	PUNCT
cana-5532	70	7	𝑓(𝑡,𝑢(𝑡	𝑓(𝑡,𝑢(𝑡	NOUN
cana-5532	70	8	)	)	PUNCT
cana-5532	70	9	)	)	PUNCT
cana-5532	70	10	)	)	PUNCT
cana-5532	71	1	+	+	CCONJ
cana-5532	71	2	𝑔(𝑡	𝑔(𝑡	PROPN
cana-5532	71	3	,	,	PUNCT
cana-5532	71	4	𝐼	𝐼	PROPN
cana-5532	71	5	0	0	NUM
cana-5532	71	6	+	+	NUM
cana-5532	71	7	𝜇1𝑢(𝑡	𝜇1𝑢(𝑡	NOUN
cana-5532	71	8	)	)	PUNCT
cana-5532	71	9	,	,	PUNCT
cana-5532	71	10	𝐼	𝐼	ADP
cana-5532	71	11	0	0	NUM
cana-5532	71	12	+	+	NUM
cana-5532	71	13	𝜇2𝑢(𝑡	𝜇2𝑢(𝑡	NOUN
cana-5532	71	14	)	)	PUNCT
cana-5532	71	15	,	,	PUNCT
cana-5532	71	16	…	…	PUNCT
cana-5532	71	17	,	,	PUNCT
cana-5532	71	18	𝐼	𝐼	ADP
cana-5532	71	19	0	0	NUM
cana-5532	71	20	+	+	NUM
cana-5532	71	21	𝜇𝑛𝑢(𝑡	𝜇𝑛𝑢(𝑡	NOUN
cana-5532	71	22	)	)	PUNCT
cana-5532	71	23	)	)	PUNCT
cana-5532	72	1	+	+	CCONJ
cana-5532	72	2	∫	∫	X
cana-5532	72	3	𝐾	𝐾	PROPN
cana-5532	72	4	𝑡	𝑡	PROPN
cana-5532	72	5	0	0	NUM
cana-5532	72	6	(	(	PUNCT
cana-5532	72	7	𝑡	𝑡	PROPN
cana-5532	72	8	,	,	PUNCT
cana-5532	72	9	𝑠	𝑠	PROPN
cana-5532	72	10	,	,	PUNCT
cana-5532	72	11	𝑢(𝑠)𝑑𝑠	𝑢(𝑠)𝑑𝑠	PROPN
cana-5532	72	12	=	=	NOUN
cana-5532	72	13	0	0	NUM
cana-5532	72	14	,	,	PUNCT
cana-5532	72	15	𝑡	𝑡	PROPN
cana-5532	72	16	∈	∈	PROPN
cana-5532	72	17	𝐼	𝐼	PROPN
cana-5532	72	18	(	(	PUNCT
cana-5532	72	19	1	1	NUM
cana-5532	72	20	)	)	PUNCT
cana-5532	72	21	𝑢(0	𝑢(0	PROPN
cana-5532	72	22	)	)	PUNCT
cana-5532	72	23	=	=	SYM
cana-5532	72	24	ℎ(𝑢	ℎ(𝑢	PROPN
cana-5532	72	25	)	)	PUNCT
cana-5532	72	26	,	,	PUNCT
cana-5532	72	27	𝑎𝐷	𝑎𝐷	NOUN
cana-5532	72	28	(	(	PUNCT
cana-5532	72	29	𝑢(𝑡	𝑢(𝑡	ADJ
cana-5532	72	30	)	)	PUNCT
cana-5532	72	31	𝑓(𝑡,𝑢(𝑡	𝑓(𝑡,𝑢(𝑡	NOUN
cana-5532	72	32	)	)	PUNCT
cana-5532	72	33	)	)	PUNCT
cana-5532	72	34	)	)	PUNCT
cana-5532	72	35	|𝑡=0	|𝑡=0	PROPN
cana-5532	73	1	+	+	CCONJ
cana-5532	73	2	𝑏	𝑏	DET
cana-5532	73	3	𝐶𝐷0	𝐶𝐷0	PROPN
cana-5532	73	4	+	+	CCONJ
cana-5532	73	5	𝛼	𝛼	PROPN
cana-5532	73	6	(	(	PUNCT
cana-5532	73	7	𝑢(𝑡	𝑢(𝑡	NOUN
cana-5532	73	8	)	)	PUNCT
cana-5532	73	9	𝑓(𝑡,𝑢(𝑡	𝑓(𝑡,𝑢(𝑡	NOUN
cana-5532	73	10	)	)	PUNCT
cana-5532	73	11	)	)	PUNCT
cana-5532	73	12	)	)	PUNCT
cana-5532	74	1	|𝑡=1	|𝑡=1	NOUN
cana-5532	74	2	=	=	SYM
cana-5532	74	3	0	0	PROPN
cana-5532	74	4	.	.	PUNCT
cana-5532	75	1	(	(	PUNCT
cana-5532	75	2	2	2	X
cana-5532	75	3	)	)	PUNCT
cana-5532	75	4	where	where	SCONJ
cana-5532	75	5	𝛼	𝛼	X
cana-5532	75	6	∈	∈	PROPN
cana-5532	75	7	(	(	PUNCT
cana-5532	75	8	1,2	1,2	NUM
cana-5532	75	9	]	]	PUNCT
cana-5532	75	10	,	,	PUNCT
cana-5532	75	11	𝑎	𝑎	X
cana-5532	75	12	,	,	PUNCT
cana-5532	75	13	𝑏	𝑏	PROPN
cana-5532	75	14	∈	∈	PROPN
cana-5532	75	15	ℝ	ℝ	PROPN
cana-5532	75	16	,	,	PUNCT
cana-5532	75	17	𝐼	𝐼	PROPN
cana-5532	75	18	:	:	PUNCT
cana-5532	75	19	=	=	PUNCT
cana-5532	76	1	[	[	X
cana-5532	76	2	0,1	0,1	NUM
cana-5532	76	3	]	]	PUNCT
cana-5532	76	4	.	.	PUNCT
cana-5532	77	1	also	also	ADV
cana-5532	77	2	,	,	PUNCT
cana-5532	77	3	𝐶𝐷0	𝐶𝐷0	PROPN
cana-5532	77	4	+	+	NOUN
cana-5532	77	5	𝛼	𝛼	NOUN
cana-5532	77	6	denotes	denote	VERB
cana-5532	77	7	the	the	DET
cana-5532	77	8	fractional	fractional	PROPN
cana-5532	77	9	caputo	caputo	PROPN
cana-5532	77	10	derivative	derivative	NOUN
cana-5532	77	11	of	of	ADP
cana-5532	77	12	order	order	NOUN
cana-5532	77	13	𝛼	𝛼	NOUN
cana-5532	77	14	,	,	PUNCT
cana-5532	77	15	𝐼	𝐼	PROPN
cana-5532	77	16	0	0	NUM
cana-5532	77	17	+	+	NUM
cana-5532	77	18	𝜇𝑖	𝜇𝑖	ADP
cana-5532	77	19	denotes	denote	NOUN
cana-5532	77	20	the	the	DET
cana-5532	77	21	fractional	fractional	ADJ
cana-5532	77	22	riemann	riemann	PROPN
cana-5532	77	23	–	–	PUNCT
cana-5532	77	24	liouville	liouville	VERB
cana-5532	77	25	integral	integral	ADJ
cana-5532	77	26	of	of	ADP
cana-5532	77	27	order	order	NOUN
cana-5532	77	28	𝜇𝑖	𝜇𝑖	ADP
cana-5532	77	29	>	>	X
cana-5532	77	30	0	0	PUNCT
cana-5532	78	1	for	for	ADP
cana-5532	78	2	all	all	DET
cana-5532	78	3	𝑖	𝑖	SYM
cana-5532	78	4	∈	∈	PROPN
cana-5532	78	5	{	{	PUNCT
cana-5532	78	6	1,2	1,2	NUM
cana-5532	78	7	,	,	PUNCT
cana-5532	78	8	.	.	PUNCT
cana-5532	78	9	.	.	PUNCT
cana-5532	78	10	.	.	PUNCT
cana-5532	79	1	,	,	PUNCT
cana-5532	79	2	𝑛	𝑛	PROPN
cana-5532	79	3	}	}	PUNCT
cana-5532	79	4	,	,	PUNCT
cana-5532	79	5	and	and	CCONJ
cana-5532	79	6	the	the	DET
cana-5532	79	7	maps	map	NOUN
cana-5532	79	8	𝑓	𝑓	X
cana-5532	79	9	:	:	PUNCT
cana-5532	79	10	𝐼	𝐼	ADP
cana-5532	79	11	×	×	NOUN
cana-5532	79	12	ℝ	ℝ	PROPN
cana-5532	79	13	→	→	SYM
cana-5532	79	14	ℝ∗	ℝ∗	NOUN
cana-5532	79	15	,	,	PUNCT
cana-5532	79	16	𝑔	𝑔	NOUN
cana-5532	79	17	:	:	PUNCT
cana-5532	79	18	𝐼	𝐼	ADP
cana-5532	79	19	×	×	PROPN
cana-5532	79	20	ℝ𝑛+1	ℝ𝑛+1	NOUN
cana-5532	79	21	→	→	PUNCT
cana-5532	79	22	ℝ	ℝ	PROPN
cana-5532	79	23	and	and	CCONJ
cana-5532	79	24	𝐾	𝐾	NOUN
cana-5532	79	25	:	:	PUNCT
cana-5532	79	26	𝐼	𝐼	ADP
cana-5532	79	27	×	×	NOUN
cana-5532	79	28	𝐼	𝐼	ADP
cana-5532	79	29	×	×	NOUN
cana-5532	79	30	ℝ	ℝ	PROPN
cana-5532	79	31	→	→	PUNCT
cana-5532	79	32	ℝ	ℝ	PROPN
cana-5532	79	33	are	be	AUX
cana-5532	79	34	continuous	continuous	ADJ
cana-5532	79	35	.	.	PUNCT
cana-5532	80	1	this	this	DET
cana-5532	80	2	paper	paper	NOUN
cana-5532	80	3	proceeds	proceed	NOUN
cana-5532	80	4	as	as	SCONJ
cana-5532	80	5	follows	follow	VERB
cana-5532	80	6	:	:	PUNCT
cana-5532	80	7	some	some	DET
cana-5532	80	8	fundamental	fundamental	ADJ
cana-5532	80	9	preliminaries	preliminary	NOUN
cana-5532	80	10	are	be	AUX
cana-5532	80	11	revisited	revisit	VERB
cana-5532	80	12	in	in	ADP
cana-5532	80	13	section	section	NOUN
cana-5532	80	14	2	2	NUM
cana-5532	80	15	.	.	PUNCT
cana-5532	81	1	in	in	ADP
cana-5532	81	2	section	section	NOUN
cana-5532	81	3	3	3	NUM
cana-5532	81	4	,	,	PUNCT
cana-5532	81	5	we	we	PRON
cana-5532	81	6	present	present	VERB
cana-5532	81	7	the	the	DET
cana-5532	81	8	equivalent	equivalent	ADJ
cana-5532	81	9	fractional	fractional	ADJ
cana-5532	81	10	integral	integral	ADJ
cana-5532	81	11	equation	equation	NOUN
cana-5532	81	12	corresponding	correspond	VERB
cana-5532	81	13	to	to	ADP
cana-5532	81	14	the	the	DET
cana-5532	81	15	linear	linear	ADJ
cana-5532	81	16	part	part	NOUN
cana-5532	81	17	of	of	ADP
cana-5532	81	18	the	the	DET
cana-5532	81	19	hybrid	hybrid	ADJ
cana-5532	81	20	fractional	fractional	ADJ
cana-5532	81	21	differential	differential	NOUN
cana-5532	81	22	equation	equation	NOUN
cana-5532	81	23	(	(	PUNCT
cana-5532	81	24	[	[	X
cana-5532	81	25	1],[2	1],[2	NOUN
cana-5532	81	26	]	]	PUNCT
cana-5532	81	27	)	)	PUNCT
cana-5532	81	28	,	,	PUNCT
cana-5532	81	29	and	and	CCONJ
cana-5532	81	30	we	we	PRON
cana-5532	81	31	prove	prove	VERB
cana-5532	81	32	the	the	DET
cana-5532	81	33	main	main	ADJ
cana-5532	81	34	existence	existence	NOUN
cana-5532	81	35	result	result	NOUN
cana-5532	81	36	of	of	ADP
cana-5532	81	37	this	this	DET
cana-5532	81	38	paper.one	paper.one	X
cana-5532	81	39	example	example	NOUN
cana-5532	81	40	is	be	AUX
cana-5532	81	41	given	give	VERB
cana-5532	81	42	in	in	ADP
cana-5532	81	43	section	section	NOUN
cana-5532	81	44	4	4	NUM
cana-5532	81	45	to	to	PART
cana-5532	81	46	support	support	VERB
cana-5532	81	47	the	the	DET
cana-5532	81	48	established	establish	VERB
cana-5532	81	49	findings	finding	NOUN
cana-5532	81	50	.	.	PUNCT
cana-5532	82	1	preliminaries	preliminary	NOUN
cana-5532	82	2	in	in	ADP
cana-5532	82	3	this	this	DET
cana-5532	82	4	section	section	NOUN
cana-5532	82	5	,	,	PUNCT
cana-5532	82	6	we	we	PRON
cana-5532	82	7	present	present	VERB
cana-5532	82	8	definitions	definition	NOUN
cana-5532	82	9	and	and	CCONJ
cana-5532	82	10	properties	property	NOUN
cana-5532	82	11	of	of	ADP
cana-5532	82	12	fractional	fractional	ADJ
cana-5532	82	13	integration	integration	NOUN
cana-5532	82	14	and	and	CCONJ
cana-5532	82	15	differentiation	differentiation	NOUN
cana-5532	82	16	,	,	PUNCT
cana-5532	82	17	as	as	ADV
cana-5532	82	18	well	well	ADV
cana-5532	82	19	as	as	ADP
cana-5532	82	20	the	the	DET
cana-5532	82	21	fixed	fix	VERB
cana-5532	82	22	point	point	NOUN
cana-5532	82	23	theorem	theorem	VERB
cana-5532	82	24	employed	employ	VERB
cana-5532	82	25	in	in	ADP
cana-5532	82	26	this	this	DET
cana-5532	82	27	work	work	NOUN
cana-5532	82	28	.	.	PUNCT
cana-5532	83	1	for	for	ADP
cana-5532	83	2	further	further	ADJ
cana-5532	83	3	details	detail	NOUN
cana-5532	83	4	,	,	PUNCT
cana-5532	83	5	the	the	DET
cana-5532	83	6	reader	reader	NOUN
cana-5532	83	7	may	may	AUX
cana-5532	83	8	refer	refer	VERB
cana-5532	83	9	to	to	ADP
cana-5532	83	10	references	reference	NOUN
cana-5532	83	11	[	[	PUNCT
cana-5532	83	12	[	[	X
cana-5532	83	13	10	10	NUM
cana-5532	83	14	]	]	PUNCT
cana-5532	83	15	,	,	PUNCT
cana-5532	83	16	[	[	X
cana-5532	83	17	13	13	NUM
cana-5532	83	18	]	]	PUNCT
cana-5532	83	19	,	,	PUNCT
cana-5532	83	20	[	[	X
cana-5532	83	21	14	14	NUM
cana-5532	83	22	]	]	PUNCT
cana-5532	83	23	,	,	PUNCT
cana-5532	83	24	[	[	X
cana-5532	83	25	8	8	NUM
cana-5532	83	26	]	]	SYM
cana-5532	83	27	]	]	PUNCT
cana-5532	83	28	.	.	PUNCT
cana-5532	84	1	definition	definition	NOUN
cana-5532	84	2	1	1	NUM
cana-5532	84	3	.	.	PUNCT
cana-5532	85	1	let	let	VERB
cana-5532	85	2	𝑔	𝑔	PART
cana-5532	85	3	be	be	AUX
cana-5532	85	4	a	a	DET
cana-5532	85	5	real	real	ADJ
cana-5532	85	6	function	function	NOUN
cana-5532	85	7	defined	define	VERB
cana-5532	85	8	on	on	ADP
cana-5532	85	9	[	[	X
cana-5532	85	10	0,1	0,1	NUM
cana-5532	85	11	]	]	PUNCT
cana-5532	85	12	and	and	CCONJ
cana-5532	85	13	𝛼	𝛼	ADJ
cana-5532	85	14	>	>	X
cana-5532	85	15	0	0	NUM
cana-5532	85	16	.	.	PUNCT
cana-5532	86	1	then	then	ADV
cana-5532	86	2	the	the	DET
cana-5532	86	3	left	left	ADJ
cana-5532	86	4	and	and	CCONJ
cana-5532	86	5	right	right	ADJ
cana-5532	86	6	riemannliouville	riemannliouville	NOUN
cana-5532	86	7	fractional	fractional	ADJ
cana-5532	86	8	integrals	integral	NOUN
cana-5532	86	9	of	of	ADP
cana-5532	86	10	order	order	NOUN
cana-5532	86	11	𝛼	𝛼	NOUN
cana-5532	86	12	of	of	ADP
cana-5532	86	13	𝑔	𝑔	PROPN
cana-5532	86	14	are	be	AUX
cana-5532	86	15	defined	define	VERB
cana-5532	86	16	respectively	respectively	ADV
cana-5532	86	17	by	by	ADP
cana-5532	86	18	𝐼0	𝐼0	PROPN
cana-5532	86	19	+	+	PROPN
cana-5532	86	20	𝛼	𝛼	NOUN
cana-5532	86	21	𝑔(𝑡	𝑔(𝑡	NOUN
cana-5532	86	22	)	)	PUNCT
cana-5532	86	23	=	=	SYM
cana-5532	86	24	1	1	NUM
cana-5532	86	25	γ(𝛼	γ(𝛼	NUM
cana-5532	86	26	)	)	PUNCT
cana-5532	86	27	∫	∫	PROPN
cana-5532	86	28	𝑔(𝑠	𝑔(𝑠	NOUN
cana-5532	86	29	)	)	PUNCT
cana-5532	86	30	(	(	PUNCT
cana-5532	86	31	𝑡−𝑠)1−𝛼	𝑡−𝑠)1−𝛼	NUM
cana-5532	86	32	𝑡	𝑡	PROPN
cana-5532	86	33	0	0	NUM
cana-5532	86	34	𝑑𝑠	𝑑𝑠	ADP
cana-5532	86	35	𝐼1−	𝐼1−	PROPN
cana-5532	86	36	𝛼	𝛼	PRON
cana-5532	86	37	𝑔(𝑡	𝑔(𝑡	PROPN
cana-5532	86	38	)	)	PUNCT
cana-5532	86	39	=	=	SYM
cana-5532	86	40	1	1	NUM
cana-5532	86	41	γ(𝛼	γ(𝛼	NUM
cana-5532	86	42	)	)	PUNCT
cana-5532	86	43	∫	∫	PROPN
cana-5532	86	44	𝑔(𝑠	𝑔(𝑠	NOUN
cana-5532	86	45	)	)	PUNCT
cana-5532	86	46	(	(	PUNCT
cana-5532	86	47	𝑠−𝑡)1−𝛼	𝑠−𝑡)1−𝛼	NOUN
cana-5532	86	48	1	1	NUM
cana-5532	86	49	𝑡	𝑡	NOUN
cana-5532	86	50	𝑑𝑠	𝑑𝑠	NOUN
cana-5532	86	51	definition	definition	NOUN
cana-5532	86	52	2	2	NUM
cana-5532	86	53	.	.	PUNCT
cana-5532	87	1	the	the	DET
cana-5532	87	2	left	left	NOUN
cana-5532	87	3	and	and	CCONJ
cana-5532	87	4	the	the	DET
cana-5532	87	5	right	right	PROPN
cana-5532	87	6	caputo	caputo	PROPN
cana-5532	87	7	fractional	fractional	PROPN
cana-5532	87	8	derivative	derivative	NOUN
cana-5532	87	9	of	of	ADP
cana-5532	87	10	order	order	NOUN
cana-5532	87	11	𝛼	𝛼	X
cana-5532	87	12	>	>	X
cana-5532	87	13	0	0	NUM
cana-5532	87	14	,	,	PUNCT
cana-5532	87	15	of	of	ADP
cana-5532	87	16	a	a	DET
cana-5532	87	17	function	function	NOUN
cana-5532	87	18	𝑔	𝑔	PROPN
cana-5532	87	19	are	be	AUX
cana-5532	87	20	,	,	PUNCT
cana-5532	87	21	respectively	respectively	ADV
cana-5532	87	22	𝐶𝐷0	𝐶𝐷0	NOUN
cana-5532	87	23	+	+	CCONJ
cana-5532	87	24	𝛼	𝛼	NOUN
cana-5532	87	25	𝑔(𝑡	𝑔(𝑡	NOUN
cana-5532	87	26	)	)	PUNCT
cana-5532	87	27	=	=	PUNCT
cana-5532	87	28	(	(	PUNCT
cana-5532	87	29	𝐼0	𝐼0	ADJ
cana-5532	87	30	+	+	CCONJ
cana-5532	87	31	𝑛−𝛼	𝑛−𝛼	NUM
cana-5532	87	32	𝑑𝑛	𝑑𝑛	NOUN
cana-5532	87	33	𝑑𝑡𝑛	𝑑𝑡𝑛	NOUN
cana-5532	87	34	𝑔(𝑡	𝑔(𝑡	PROPN
cana-5532	87	35	)	)	PUNCT
cana-5532	87	36	)	)	PUNCT
cana-5532	87	37	𝐶𝐷1−	𝐶𝐷1−	NUM
cana-5532	88	1	𝛼	𝛼	X
cana-5532	88	2	𝑔(𝑡	𝑔(𝑡	PROPN
cana-5532	88	3	)	)	PUNCT
cana-5532	89	1	=	=	SYM
cana-5532	89	2	(	(	PUNCT
cana-5532	89	3	−1)𝑛(𝐼1−	−1)𝑛(𝐼1−	X
cana-5532	89	4	𝑛−𝛼	𝑛−𝛼	NOUN
cana-5532	89	5	𝑑𝑛	𝑑𝑛	NOUN
cana-5532	89	6	𝑑𝑡𝑛	𝑑𝑡𝑛	NOUN
cana-5532	89	7	𝑔(𝑡	𝑔(𝑡	PROPN
cana-5532	89	8	)	)	PUNCT
cana-5532	89	9	)	)	PUNCT
cana-5532	89	10	where	where	SCONJ
cana-5532	89	11	𝑛	𝑛	DET
cana-5532	89	12	−	−	PROPN
cana-5532	89	13	1	1	NUM
cana-5532	89	14	<	<	X
cana-5532	89	15	𝛼	𝛼	X
cana-5532	89	16	<	<	X
cana-5532	89	17	𝑛.	𝑛.	NOUN
cana-5532	89	18	proposition	proposition	NOUN
cana-5532	89	19	3	3	X
cana-5532	89	20	.	.	PUNCT
cana-5532	90	1	let	let	VERB
cana-5532	90	2	𝑛	𝑛	PRON
cana-5532	90	3	−	−	PROPN
cana-5532	90	4	1	1	NUM
cana-5532	90	5	<	<	X
cana-5532	90	6	𝛼	𝛼	X
cana-5532	90	7	<	<	X
cana-5532	90	8	𝑛	𝑛	PROPN
cana-5532	90	9	and	and	CCONJ
cana-5532	90	10	𝑓	𝑓	DET
cana-5532	90	11	∈	∈	PROPN
cana-5532	90	12	𝐿1[0	𝐿1[0	PROPN
cana-5532	90	13	,	,	PUNCT
cana-5532	90	14	1	1	NUM
cana-5532	90	15	]	]	PUNCT
cana-5532	90	16	.	.	PUNCT
cana-5532	91	1	then	then	ADV
cana-5532	91	2	(	(	PUNCT
cana-5532	91	3	1	1	X
cana-5532	91	4	)	)	PUNCT
cana-5532	91	5	𝐼0	𝐼0	PROPN
cana-5532	91	6	+	+	NUM
cana-5532	91	7	𝛼	𝛼	NOUN
cana-5532	91	8	𝐶𝐷0	𝐶𝐷0	NOUN
cana-5532	91	9	+	+	CCONJ
cana-5532	91	10	𝛼	𝛼	NOUN
cana-5532	91	11	𝑓(𝑡	𝑓(𝑡	PROPN
cana-5532	91	12	)	)	PUNCT
cana-5532	91	13	=	=	SYM
cana-5532	91	14	𝑓(𝑡	𝑓(𝑡	PROPN
cana-5532	91	15	)	)	PUNCT
cana-5532	91	16	−	−	PROPN
cana-5532	91	17	∑	∑	PUNCT
cana-5532	91	18	𝑓(𝑘)(0	𝑓(𝑘)(0	PROPN
cana-5532	91	19	)	)	PUNCT
cana-5532	91	20	𝑘	𝑘	X
cana-5532	91	21	!	!	PUNCT
cana-5532	92	1	𝑛−1	𝑛−1	NUM
cana-5532	92	2	𝑘=0	𝑘=0	VERB
cana-5532	92	3	𝑡𝑘	𝑡𝑘	ADV
cana-5532	92	4	(	(	PUNCT
cana-5532	92	5	2	2	X
cana-5532	92	6	)	)	PUNCT
cana-5532	92	7	𝐼1−	𝐼1−	PROPN
cana-5532	92	8	𝛼	𝛼	NUM
cana-5532	92	9	𝐶𝐷1−	𝐶𝐷1−	NUM
cana-5532	92	10	𝛼	𝛼	X
cana-5532	92	11	𝑓(𝑡	𝑓(𝑡	PROPN
cana-5532	92	12	)	)	PUNCT
cana-5532	92	13	=	=	SYM
cana-5532	92	14	𝑓(𝑡	𝑓(𝑡	PROPN
cana-5532	92	15	)	)	PUNCT
cana-5532	92	16	−	−	PROPN
cana-5532	93	1	∑	∑	PROPN
cana-5532	93	2	(	(	PUNCT
cana-5532	93	3	−1)𝑘𝑓(𝑘)(1	−1)𝑘𝑓(𝑘)(1	NOUN
cana-5532	93	4	)	)	PUNCT
cana-5532	93	5	𝑘	𝑘	NOUN
cana-5532	93	6	!	!	PUNCT
cana-5532	94	1	𝑛−1	𝑛−1	NUM
cana-5532	94	2	𝑘=0	𝑘=0	PROPN
cana-5532	94	3	(	(	PUNCT
cana-5532	94	4	1	1	NUM
cana-5532	94	5	−	−	PROPN
cana-5532	94	6	𝑡)𝑘	𝑡)𝑘	PUNCT
cana-5532	94	7	theorem	theorem	VERB
cana-5532	94	8	4	4	NUM
cana-5532	94	9	.	.	PUNCT
cana-5532	94	10	(	(	PUNCT
cana-5532	94	11	dhage	dhage	NOUN
cana-5532	94	12	fixed	fix	VERB
cana-5532	94	13	point	point	NOUN
cana-5532	94	14	theorem)[8	theorem)[8	ADP
cana-5532	94	15	]	]	PUNCT
cana-5532	94	16	)	)	PUNCT
cana-5532	94	17	let	let	VERB
cana-5532	94	18	𝑀	𝑀	PRON
cana-5532	94	19	be	be	AUX
cana-5532	94	20	a	a	DET
cana-5532	94	21	closed	closed	ADJ
cana-5532	94	22	,	,	PUNCT
cana-5532	94	23	bounded	bound	VERB
cana-5532	94	24	,	,	PUNCT
cana-5532	94	25	convex	convex	ADJ
cana-5532	94	26	and	and	CCONJ
cana-5532	94	27	nonempty	nonempty	NOUN
cana-5532	94	28	subset	subset	NOUN
cana-5532	94	29	of	of	ADP
cana-5532	94	30	a	a	DET
cana-5532	94	31	banach	banach	NOUN
cana-5532	94	32	algebra	algebra	NOUN
cana-5532	94	33	(	(	PUNCT
cana-5532	94	34	𝐸	𝐸	PROPN
cana-5532	94	35	,	,	PUNCT
cana-5532	94	36	∥	∥	X
cana-5532	94	37	.	.	PUNCT
cana-5532	95	1	∥	∥	NUM
cana-5532	95	2	)	)	PUNCT
cana-5532	95	3	,	,	PUNCT
cana-5532	96	1	and	and	CCONJ
cana-5532	96	2	let	let	VERB
cana-5532	96	3	𝐴	𝐴	PROPN
cana-5532	96	4	:	:	PUNCT
cana-5532	96	5	𝐸	𝐸	PROPN
cana-5532	96	6	→	→	SYM
cana-5532	96	7	𝐸	𝐸	PROPN
cana-5532	96	8	and	and	CCONJ
cana-5532	96	9	𝐵:𝑀	𝐵:𝑀	PROPN
cana-5532	96	10	→	→	SYM
cana-5532	96	11	𝐸	𝐸	PROPN
cana-5532	96	12	be	be	VERB
cana-5532	96	13	two	two	NUM
cana-5532	96	14	operators	operator	NOUN
cana-5532	96	15	such	such	ADJ
cana-5532	96	16	that	that	SCONJ
cana-5532	96	17	(	(	PUNCT
cana-5532	96	18	i	i	NOUN
cana-5532	96	19	)	)	PUNCT
cana-5532	96	20	𝐴	𝐴	PROPN
cana-5532	96	21	is	be	AUX
cana-5532	96	22	lipschitzian	lipschitzian	ADJ
cana-5532	96	23	with	with	ADP
cana-5532	96	24	lipschitz	lipschitz	NOUN
cana-5532	96	25	constant	constant	ADJ
cana-5532	96	26	𝜆	𝜆	ADP
cana-5532	96	27	,	,	PUNCT
cana-5532	96	28	(	(	PUNCT
cana-5532	96	29	ii	ii	NOUN
cana-5532	96	30	)	)	PUNCT
cana-5532	96	31	𝐵	𝐵	NOUN
cana-5532	96	32	is	be	AUX
cana-5532	96	33	completely	completely	ADV
cana-5532	96	34	continuous	continuous	ADJ
cana-5532	96	35	,	,	PUNCT
cana-5532	96	36	,	,	PUNCT
cana-5532	96	37	(	(	PUNCT
cana-5532	96	38	iii	iii	X
cana-5532	96	39	)	)	PUNCT
cana-5532	96	40	𝑥	𝑥	NOUN
cana-5532	96	41	=	=	PUNCT
cana-5532	96	42	𝐴𝑥𝐵𝑧	𝐴𝑥𝐵𝑧	PROPN
cana-5532	96	43	⇒	⇒	VERB
cana-5532	96	44	𝑥	𝑥	X
cana-5532	96	45	∈	∈	PROPN
cana-5532	96	46	𝑀	𝑀	PROPN
cana-5532	96	47	𝑓𝑜𝑟	𝑓𝑜𝑟	ADV
cana-5532	96	48	𝑎𝑙𝑙	𝑎𝑙𝑙	VERB
cana-5532	96	49	𝑧	𝑧	PRON
cana-5532	96	50	∈	∈	PROPN
cana-5532	96	51	𝑀	𝑀	PROPN
cana-5532	96	52	,	,	PUNCT
cana-5532	96	53	(	(	PUNCT
cana-5532	96	54	iv	iv	X
cana-5532	96	55	)	)	PUNCT
cana-5532	97	1	𝜆𝐿	𝜆𝐿	ADP
cana-5532	97	2	<	<	X
cana-5532	97	3	1	1	NUM
cana-5532	97	4	,	,	PUNCT
cana-5532	97	5	where	where	SCONJ
cana-5532	97	6	𝐿	𝐿	PROPN
cana-5532	97	7	=	=	NOUN
cana-5532	97	8	∥	∥	NOUN
cana-5532	97	9	𝐵(𝑀	𝐵(𝑀	PROPN
cana-5532	97	10	)	)	PUNCT
cana-5532	97	11	∥=	∥=	NOUN
cana-5532	97	12	𝑠𝑢𝑝{∥	𝑠𝑢𝑝{∥	NOUN
cana-5532	97	13	𝐵(𝑥	𝐵(𝑥	PROPN
cana-5532	97	14	)	)	PUNCT
cana-5532	97	15	∥	∥	NUM
cana-5532	97	16	:	:	PUNCT
cana-5532	97	17	𝑥	𝑥	PROPN
cana-5532	97	18	∈	∈	PROPN
cana-5532	97	19	𝑀	𝑀	PROPN
cana-5532	97	20	}	}	PUNCT
cana-5532	97	21	.	.	PUNCT
cana-5532	98	1	then	then	ADV
cana-5532	98	2	the	the	DET
cana-5532	98	3	operator	operator	NOUN
cana-5532	98	4	equation	equation	NOUN
cana-5532	98	5	𝐴𝑦𝐵𝑦	𝐴𝑦𝐵𝑦	PROPN
cana-5532	98	6	=	=	SYM
cana-5532	99	1	𝑦	𝑦	PROPN
cana-5532	99	2	has	have	VERB
cana-5532	99	3	a	a	DET
cana-5532	99	4	solution	solution	NOUN
cana-5532	99	5	in	in	ADP
cana-5532	99	6	𝑀.	𝑀.	NOUN
cana-5532	99	7	communications	communication	NOUN
cana-5532	99	8	on	on	ADP
cana-5532	99	9	applied	apply	VERB
cana-5532	99	10	nonlinear	nonlinear	ADJ
cana-5532	99	11	analysis	analysis	NOUN
cana-5532	99	12	issn	issn	NOUN
cana-5532	99	13	:	:	PUNCT
cana-5532	99	14	1074	1074	NUM
cana-5532	99	15	-	-	PUNCT
cana-5532	99	16	133x	133x	NUM
cana-5532	99	17	vol	vol	NOUN
cana-5532	99	18	32	32	NUM
cana-5532	99	19	no	no	NOUN
cana-5532	99	20	.	.	NOUN
cana-5532	99	21	3	3	NUM
cana-5532	99	22	(	(	PUNCT
cana-5532	99	23	2025	2025	NUM
cana-5532	99	24	)	)	PUNCT
cana-5532	99	25	988	988	NUM
cana-5532	99	26	https://internationalpubls.com	https://internationalpubls.com	X
cana-5532	99	27	main	main	ADJ
cana-5532	99	28	results	result	NOUN
cana-5532	99	29	lemma	lemma	PROPN
cana-5532	99	30	5	5	X
cana-5532	99	31	.	.	PUNCT
cana-5532	100	1	let	let	VERB
cana-5532	100	2	𝑦	𝑦	NOUN
cana-5532	100	3	∈	∈	VERB
cana-5532	100	4	𝐴𝐶([0,1	𝐴𝐶([0,1	NOUN
cana-5532	100	5	]	]	X
cana-5532	100	6	,	,	PUNCT
cana-5532	100	7	ℝ	ℝ	PROPN
cana-5532	100	8	)	)	PUNCT
cana-5532	100	9	then	then	ADV
cana-5532	100	10	𝑢	𝑢	PROPN
cana-5532	100	11	is	be	AUX
cana-5532	100	12	a	a	DET
cana-5532	100	13	solution	solution	NOUN
cana-5532	100	14	of	of	ADP
cana-5532	100	15	the	the	DET
cana-5532	100	16	hybrid	hybrid	ADJ
cana-5532	100	17	fractional	fractional	ADJ
cana-5532	100	18	integrodifferential	integrodifferential	ADJ
cana-5532	100	19	problem	problem	NOUN
cana-5532	100	20	{	{	PUNCT
cana-5532	100	21	𝐶𝐷0	𝐶𝐷0	NOUN
cana-5532	100	22	+	+	NOUN
cana-5532	100	23	𝛼	𝛼	PROPN
cana-5532	100	24	(	(	PUNCT
cana-5532	100	25	𝑢(𝑡	𝑢(𝑡	NOUN
cana-5532	100	26	)	)	PUNCT
cana-5532	100	27	𝑓(𝑡,𝑢(𝑡	𝑓(𝑡,𝑢(𝑡	NOUN
cana-5532	100	28	)	)	PUNCT
cana-5532	100	29	)	)	PUNCT
cana-5532	100	30	)	)	PUNCT
cana-5532	101	1	+	+	CCONJ
cana-5532	101	2	𝑦(𝑡	𝑦(𝑡	NUM
cana-5532	101	3	)	)	PUNCT
cana-5532	101	4	=	=	SYM
cana-5532	101	5	0	0	NUM
cana-5532	101	6	,	,	PUNCT
cana-5532	101	7	 	 	SPACE
cana-5532	101	8	𝑡	𝑡	NOUN
cana-5532	101	9	∈	∈	NOUN
cana-5532	101	10	𝐼	𝐼	ADP
cana-5532	101	11	≔	≔	NOUN
cana-5532	101	12	[	[	NOUN
cana-5532	101	13	0,1	0,1	NUM
cana-5532	101	14	]	]	PUNCT
cana-5532	101	15	,	,	PUNCT
cana-5532	101	16	𝑢(0	𝑢(0	PROPN
cana-5532	101	17	)	)	PUNCT
cana-5532	101	18	=	=	SYM
cana-5532	101	19	ℎ(𝑢	ℎ(𝑢	PROPN
cana-5532	101	20	)	)	PUNCT
cana-5532	101	21	,	,	PUNCT
cana-5532	101	22	𝑎𝐷	𝑎𝐷	NOUN
cana-5532	101	23	(	(	PUNCT
cana-5532	101	24	𝑢(𝑡	𝑢(𝑡	ADJ
cana-5532	101	25	)	)	PUNCT
cana-5532	101	26	𝑓(𝑡,𝑢(𝑡	𝑓(𝑡,𝑢(𝑡	NOUN
cana-5532	101	27	)	)	PUNCT
cana-5532	101	28	)	)	PUNCT
cana-5532	101	29	)	)	PUNCT
cana-5532	102	1	|𝑡=0	|𝑡=0	PROPN
cana-5532	103	1	+	+	CCONJ
cana-5532	103	2	𝑏	𝑏	DET
cana-5532	103	3	𝐶𝐷0	𝐶𝐷0	PROPN
cana-5532	103	4	+	+	CCONJ
cana-5532	103	5	𝛼	𝛼	PROPN
cana-5532	103	6	(	(	PUNCT
cana-5532	103	7	𝑢(𝑡	𝑢(𝑡	NOUN
cana-5532	103	8	)	)	PUNCT
cana-5532	103	9	𝑓(𝑡,𝑢(𝑡	𝑓(𝑡,𝑢(𝑡	NOUN
cana-5532	103	10	)	)	PUNCT
cana-5532	103	11	)	)	PUNCT
cana-5532	103	12	)	)	PUNCT
cana-5532	104	1	|𝑡=1	|𝑡=1	NOUN
cana-5532	104	2	=	=	SYM
cana-5532	104	3	0	0	PROPN
cana-5532	104	4	.	.	PUNCT
cana-5532	105	1	(	(	PUNCT
cana-5532	105	2	3	3	X
cana-5532	105	3	)	)	PUNCT
cana-5532	105	4	if	if	SCONJ
cana-5532	105	5	and	and	CCONJ
cana-5532	105	6	only	only	ADV
cana-5532	105	7	if	if	SCONJ
cana-5532	105	8	𝑢	𝑢	NOUN
cana-5532	105	9	is	be	AUX
cana-5532	105	10	a	a	DET
cana-5532	105	11	solution	solution	NOUN
cana-5532	105	12	for	for	ADP
cana-5532	105	13	the	the	DET
cana-5532	105	14	integral	integral	ADJ
cana-5532	105	15	equation	equation	NOUN
cana-5532	105	16	𝑢(𝑡	𝑢(𝑡	NOUN
cana-5532	105	17	)	)	PUNCT
cana-5532	105	18	=	=	PUNCT
cana-5532	106	1	𝑓(𝑡	𝑓(𝑡	NOUN
cana-5532	106	2	,	,	PUNCT
cana-5532	106	3	𝑢(𝑡	𝑢(𝑡	NOUN
cana-5532	106	4	)	)	PUNCT
cana-5532	106	5	)	)	PUNCT
cana-5532	107	1	[	[	X
cana-5532	107	2	−∫	−∫	NOUN
cana-5532	107	3	(	(	PUNCT
cana-5532	107	4	𝑡−𝜏)𝛼−1	𝑡−𝜏)𝛼−1	NOUN
cana-5532	107	5	γ(𝛼	γ(𝛼	ADV
cana-5532	107	6	)	)	PUNCT
cana-5532	107	7	𝑡	𝑡	PROPN
cana-5532	107	8	0	0	PUNCT
cana-5532	107	9	𝑦(𝜏)𝑑𝜏	𝑦(𝜏)𝑑𝜏	NUM
cana-5532	107	10	+	+	NUM
cana-5532	107	11	γ(3−𝛼)𝑏𝑡	γ(3−𝛼)𝑏𝑡	NUM
cana-5532	107	12	𝑎γ(3−𝛼)+𝑏	𝑎γ(3−𝛼)+𝑏	PROPN
cana-5532	107	13	∫	∫	PROPN
cana-5532	107	14	𝑦	𝑦	NOUN
cana-5532	107	15	1	1	NUM
cana-5532	107	16	0	0	NUM
cana-5532	107	17	(	(	PUNCT
cana-5532	107	18	𝜏)𝑑𝜏	𝜏)𝑑𝜏	PROPN
cana-5532	107	19	+	+	CCONJ
cana-5532	107	20	ℎ(𝑢	ℎ(𝑢	PROPN
cana-5532	107	21	)	)	PUNCT
cana-5532	107	22	𝑓(0,ℎ(𝑢	𝑓(0,ℎ(𝑢	NOUN
cana-5532	107	23	)	)	PUNCT
cana-5532	107	24	)	)	PUNCT
cana-5532	107	25	]	]	PUNCT
cana-5532	107	26	(	(	PUNCT
cana-5532	107	27	4	4	X
cana-5532	107	28	)	)	PUNCT
cana-5532	107	29	proof	proof	NOUN
cana-5532	107	30	.	.	PUNCT
cana-5532	108	1	we	we	PRON
cana-5532	108	2	apply	apply	VERB
cana-5532	108	3	the	the	DET
cana-5532	108	4	right	right	ADJ
cana-5532	108	5	-	-	PUNCT
cana-5532	108	6	hand	hand	NOUN
cana-5532	108	7	side	side	NOUN
cana-5532	108	8	fractional	fractional	ADJ
cana-5532	108	9	integral	integral	ADJ
cana-5532	108	10	𝐼0	𝐼0	NOUN
cana-5532	108	11	+	+	X
cana-5532	108	12	𝛼	𝛼	NOUN
cana-5532	108	13	to	to	ADP
cana-5532	108	14	equation	equation	NOUN
cana-5532	108	15	(	(	PUNCT
cana-5532	108	16	[	[	X
cana-5532	108	17	3]).we	3]).we	NUM
cana-5532	108	18	get	get	VERB
cana-5532	108	19	𝑢(𝑡	𝑢(𝑡	NOUN
cana-5532	108	20	)	)	PUNCT
cana-5532	108	21	𝑓(𝑡,𝑢(𝑡	𝑓(𝑡,𝑢(𝑡	NOUN
cana-5532	108	22	)	)	PUNCT
cana-5532	108	23	)	)	PUNCT
cana-5532	109	1	=	=	PUNCT
cana-5532	109	2	−∫	−∫	NOUN
cana-5532	109	3	(	(	PUNCT
cana-5532	109	4	𝑡−𝜏)𝛼−1	𝑡−𝜏)𝛼−1	NOUN
cana-5532	109	5	γ(𝛼	γ(𝛼	ADV
cana-5532	109	6	)	)	PUNCT
cana-5532	109	7	𝑡	𝑡	PROPN
cana-5532	109	8	0	0	PUNCT
cana-5532	109	9	𝑦(𝜏)𝑑𝜏	𝑦(𝜏)𝑑𝜏	NOUN
cana-5532	109	10	+	+	CCONJ
cana-5532	109	11	𝑐1	𝑐1	NOUN
cana-5532	109	12	+	+	CCONJ
cana-5532	109	13	𝑐2𝑡.	𝑐2𝑡.	INTJ
cana-5532	109	14	(	(	PUNCT
cana-5532	109	15	5	5	NUM
cana-5532	109	16	)	)	PUNCT
cana-5532	109	17	using	use	VERB
cana-5532	109	18	the	the	DET
cana-5532	109	19	conditions	condition	NOUN
cana-5532	109	20	nonlocal	nonlocal	ADJ
cana-5532	109	21	𝑢(0	𝑢(0	PROPN
cana-5532	109	22	)	)	PUNCT
cana-5532	109	23	=	=	SYM
cana-5532	109	24	ℎ(𝑢	ℎ(𝑢	PROPN
cana-5532	109	25	)	)	PUNCT
cana-5532	109	26	,	,	PUNCT
cana-5532	109	27	so	so	CCONJ
cana-5532	109	28	𝑐1	𝑐1	NOUN
cana-5532	109	29	=	=	SYM
cana-5532	109	30	ℎ(𝑢	ℎ(𝑢	PROPN
cana-5532	109	31	)	)	PUNCT
cana-5532	109	32	𝑓(0,ℎ(𝑢	𝑓(0,ℎ(𝑢	NOUN
cana-5532	109	33	)	)	PUNCT
cana-5532	109	34	)	)	PUNCT
cana-5532	109	35	.and	.and	PUNCT
cana-5532	110	1	we	we	PRON
cana-5532	110	2	have	have	VERB
cana-5532	110	3	𝐶𝐷0	𝐶𝐷0	NOUN
cana-5532	110	4	+	+	CCONJ
cana-5532	110	5	𝛼−1	𝛼−1	PROPN
cana-5532	110	6	(	(	PUNCT
cana-5532	110	7	𝑢(𝑡	𝑢(𝑡	NOUN
cana-5532	110	8	)	)	PUNCT
cana-5532	110	9	𝑓(𝑡,𝑢(𝑡	𝑓(𝑡,𝑢(𝑡	NOUN
cana-5532	110	10	)	)	PUNCT
cana-5532	110	11	)	)	PUNCT
cana-5532	110	12	)	)	PUNCT
cana-5532	111	1	=	=	PUNCT
cana-5532	111	2	−∫	−∫	X
cana-5532	111	3	𝑦	𝑦	NOUN
cana-5532	111	4	𝑡	𝑡	X
cana-5532	111	5	0	0	PUNCT
cana-5532	111	6	(	(	PUNCT
cana-5532	111	7	𝜏)𝑑𝜏	𝜏)𝑑𝜏	PROPN
cana-5532	111	8	+	+	NUM
cana-5532	111	9	𝑐2	𝑐2	NOUN
cana-5532	111	10	𝑡2−𝛼	𝑡2−𝛼	PROPN
cana-5532	111	11	γ(3−𝛼	γ(3−𝛼	ADJ
cana-5532	111	12	)	)	PUNCT
cana-5532	111	13	,	,	PUNCT
cana-5532	111	14	and	and	CCONJ
cana-5532	111	15	𝐷	𝐷	PROPN
cana-5532	111	16	𝑢(𝑡	𝑢(𝑡	NOUN
cana-5532	111	17	)	)	PUNCT
cana-5532	111	18	𝑓(𝑡,𝑢(𝑡	𝑓(𝑡,𝑢(𝑡	NOUN
cana-5532	111	19	)	)	PUNCT
cana-5532	111	20	)	)	PUNCT
cana-5532	112	1	=	=	PUNCT
cana-5532	112	2	−∫	−∫	NOUN
cana-5532	112	3	(	(	PUNCT
cana-5532	112	4	𝑡−𝜏)𝛼−2	𝑡−𝜏)𝛼−2	ADP
cana-5532	112	5	γ(𝛼−1	γ(𝛼−1	ADJ
cana-5532	112	6	)	)	PUNCT
cana-5532	112	7	𝑡	𝑡	VERB
cana-5532	112	8	0	0	PUNCT
cana-5532	112	9	𝑦(𝜏)𝑑𝜏	𝑦(𝜏)𝑑𝜏	NUM
cana-5532	112	10	+	+	NUM
cana-5532	112	11	𝑐2	𝑐2	NOUN
cana-5532	112	12	,	,	PUNCT
cana-5532	112	13	so	so	ADV
cana-5532	112	14	𝑎𝐷	𝑎𝐷	ADJ
cana-5532	112	15	(	(	PUNCT
cana-5532	112	16	𝑢(𝑡	𝑢(𝑡	ADJ
cana-5532	112	17	)	)	PUNCT
cana-5532	112	18	𝑓(𝑡,𝑢(𝑡	𝑓(𝑡,𝑢(𝑡	NOUN
cana-5532	112	19	)	)	PUNCT
cana-5532	112	20	)	)	PUNCT
cana-5532	112	21	)	)	PUNCT
cana-5532	113	1	|𝑡=0	|𝑡=0	PROPN
cana-5532	114	1	+	+	CCONJ
cana-5532	114	2	𝑏	𝑏	DET
cana-5532	114	3	𝐶𝐷0	𝐶𝐷0	PROPN
cana-5532	114	4	+	+	CCONJ
cana-5532	114	5	𝛼	𝛼	PROPN
cana-5532	114	6	(	(	PUNCT
cana-5532	114	7	𝑢(𝑡	𝑢(𝑡	NOUN
cana-5532	114	8	)	)	PUNCT
cana-5532	114	9	𝑓(𝑡,𝑢(𝑡	𝑓(𝑡,𝑢(𝑡	NOUN
cana-5532	114	10	)	)	PUNCT
cana-5532	114	11	)	)	PUNCT
cana-5532	114	12	)	)	PUNCT
cana-5532	115	1	|𝑡=1	|𝑡=1	PROPN
cana-5532	115	2	=	=	PRON
cana-5532	115	3	𝑎𝑐2	𝑎𝑐2	VERB
cana-5532	115	4	+	+	CCONJ
cana-5532	115	5	𝑏	𝑏	PROPN
cana-5532	115	6	(	(	PUNCT
cana-5532	115	7	−∫	−∫	X
cana-5532	115	8	𝑦	𝑦	NOUN
cana-5532	115	9	1	1	NUM
cana-5532	115	10	0	0	NUM
cana-5532	115	11	(	(	PUNCT
cana-5532	115	12	𝜏)𝑑𝜏	𝜏)𝑑𝜏	PROPN
cana-5532	115	13	+	+	NUM
cana-5532	115	14	𝑐2	𝑐2	NOUN
cana-5532	115	15	γ(3−𝛼	γ(3−𝛼	NOUN
cana-5532	115	16	)	)	PUNCT
cana-5532	115	17	)	)	PUNCT
cana-5532	116	1	then	then	ADV
cana-5532	116	2	we	we	PRON
cana-5532	116	3	get	get	VERB
cana-5532	116	4	𝑐2	𝑐2	NOUN
cana-5532	116	5	=	=	NUM
cana-5532	116	6	γ(3−𝛼)𝑏	γ(3−𝛼)𝑏	NOUN
cana-5532	117	1	𝑎γ(3−𝛼)+𝑏	𝑎γ(3−𝛼)+𝑏	PROPN
cana-5532	117	2	∫	∫	PROPN
cana-5532	117	3	𝑦	𝑦	NOUN
cana-5532	117	4	1	1	NUM
cana-5532	117	5	0	0	NUM
cana-5532	117	6	(	(	PUNCT
cana-5532	117	7	𝜏)𝑑𝜏	𝜏)𝑑𝜏	PROPN
cana-5532	117	8	substituting	substitute	VERB
cana-5532	117	9	the	the	DET
cana-5532	117	10	values	value	NOUN
cana-5532	117	11	of	of	ADP
cana-5532	117	12	𝑐1	𝑐1	NOUN
cana-5532	117	13	,	,	PUNCT
cana-5532	117	14	𝑐2	𝑐2	NOUN
cana-5532	117	15	in	in	ADP
cana-5532	117	16	(	(	PUNCT
cana-5532	117	17	[	[	X
cana-5532	117	18	5	5	NUM
cana-5532	117	19	]	]	NUM
cana-5532	117	20	)	)	PUNCT
cana-5532	117	21	,	,	PUNCT
cana-5532	117	22	we	we	PRON
cana-5532	117	23	get	get	VERB
cana-5532	117	24	solution	solution	NOUN
cana-5532	117	25	(	(	PUNCT
cana-5532	117	26	[	[	X
cana-5532	117	27	4	4	NUM
cana-5532	117	28	]	]	NUM
cana-5532	117	29	)	)	PUNCT
cana-5532	117	30	.	.	PUNCT
cana-5532	118	1	the	the	DET
cana-5532	118	2	converse	converse	NOUN
cana-5532	118	3	follows	follow	VERB
cana-5532	118	4	by	by	ADP
cana-5532	118	5	direct	direct	ADJ
cana-5532	118	6	computation	computation	NOUN
cana-5532	118	7	.	.	PUNCT
cana-5532	119	1	this	this	PRON
cana-5532	119	2	completes	complete	VERB
cana-5532	119	3	the	the	DET
cana-5532	119	4	proof	proof	NOUN
cana-5532	119	5	.	.	PUNCT
cana-5532	120	1	in	in	ADP
cana-5532	120	2	the	the	DET
cana-5532	120	3	sequel	sequel	NOUN
cana-5532	120	4	,	,	PUNCT
cana-5532	120	5	we	we	PRON
cana-5532	120	6	need	need	VERB
cana-5532	120	7	the	the	DET
cana-5532	120	8	following	follow	VERB
cana-5532	120	9	assumptions	assumption	NOUN
cana-5532	120	10	.	.	PUNCT
cana-5532	121	1	(	(	PUNCT
cana-5532	121	2	h1	h1	PROPN
cana-5532	121	3	)	)	PUNCT
cana-5532	121	4	the	the	DET
cana-5532	121	5	function	function	NOUN
cana-5532	121	6	𝑓	𝑓	X
cana-5532	121	7	:	:	PUNCT
cana-5532	121	8	𝐼	𝐼	ADP
cana-5532	121	9	×	×	NOUN
cana-5532	121	10	ℝ	ℝ	PROPN
cana-5532	121	11	→	→	SYM
cana-5532	121	12	ℝ−	ℝ−	NOUN
cana-5532	121	13	{	{	PUNCT
cana-5532	121	14	0	0	NUM
cana-5532	121	15	}	}	PUNCT
cana-5532	121	16	is	be	AUX
cana-5532	121	17	a	a	DET
cana-5532	121	18	continuous	continuous	ADJ
cana-5532	121	19	function	function	NOUN
cana-5532	121	20	satisfying	satisfy	VERB
cana-5532	121	21	the	the	DET
cana-5532	121	22	lipschitz	lipschitz	NOUN
cana-5532	121	23	condition	condition	NOUN
cana-5532	121	24	for	for	ADP
cana-5532	121	25	a	a	DET
cana-5532	121	26	constant	constant	ADJ
cana-5532	121	27	𝜆𝑓	𝜆𝑓	NOUN
cana-5532	121	28	∣	∣	ADJ
cana-5532	121	29	𝑓(𝑡	𝑓(𝑡	PROPN
cana-5532	121	30	,	,	PUNCT
cana-5532	121	31	𝑢	𝑢	NOUN
cana-5532	121	32	)	)	PUNCT
cana-5532	121	33	−	−	PROPN
cana-5532	122	1	𝑓(𝑡	𝑓(𝑡	NOUN
cana-5532	122	2	,	,	PUNCT
cana-5532	122	3	𝑣	𝑣	NOUN
cana-5532	122	4	)	)	PUNCT
cana-5532	122	5	∣≤	∣≤	PUNCT
cana-5532	122	6	𝜆𝑓	𝜆𝑓	ADP
cana-5532	122	7	∣	∣	PROPN
cana-5532	122	8	𝑢	𝑢	NOUN
cana-5532	122	9	−	−	PROPN
cana-5532	122	10	𝑣	𝑣	ADP
cana-5532	122	11	∣.	∣.	X
cana-5532	122	12	(	(	PUNCT
cana-5532	122	13	h2	h2	PROPN
cana-5532	122	14	)	)	PUNCT
cana-5532	122	15	the	the	DET
cana-5532	122	16	function	function	NOUN
cana-5532	122	17	ℎ:ℝ	ℎ:ℝ	PROPN
cana-5532	122	18	→	→	SYM
cana-5532	122	19	ℝ	ℝ	PROPN
cana-5532	122	20	is	be	AUX
cana-5532	122	21	a	a	DET
cana-5532	122	22	continuous	continuous	ADJ
cana-5532	122	23	function	function	NOUN
cana-5532	122	24	and	and	CCONJ
cana-5532	122	25	there	there	PRON
cana-5532	122	26	exists	exist	VERB
cana-5532	122	27	a	a	DET
cana-5532	122	28	constant	constant	ADJ
cana-5532	122	29	𝑀0	𝑀0	NOUN
cana-5532	122	30	>	>	X
cana-5532	122	31	0	0	NUM
cana-5532	122	32	such	such	ADJ
cana-5532	122	33	that	that	SCONJ
cana-5532	122	34	:	:	PUNCT
cana-5532	122	35	|	|	ADV
cana-5532	122	36	ℎ(𝑢	ℎ(𝑢	NOUN
cana-5532	122	37	)	)	PUNCT
cana-5532	122	38	𝑓(0,ℎ(𝑢	𝑓(0,ℎ(𝑢	NOUN
cana-5532	122	39	)	)	PUNCT
cana-5532	122	40	)	)	PUNCT
cana-5532	123	1	|	|	ADV
cana-5532	123	2	≤	≤	NUM
cana-5532	123	3	𝑀0	𝑀0	NOUN
cana-5532	123	4	.	.	PUNCT
cana-5532	124	1	(	(	PUNCT
cana-5532	124	2	h3	h3	NOUN
cana-5532	124	3	)	)	PUNCT
cana-5532	124	4	the	the	DET
cana-5532	124	5	function	function	NOUN
cana-5532	124	6	𝑔	𝑔	NOUN
cana-5532	124	7	:	:	PUNCT
cana-5532	124	8	𝐼	𝐼	ADP
cana-5532	124	9	×	×	PROPN
cana-5532	124	10	ℝ𝑛+1	ℝ𝑛+1	NOUN
cana-5532	124	11	→	→	PUNCT
cana-5532	124	12	ℝ	ℝ	PROPN
cana-5532	124	13	is	be	AUX
cana-5532	124	14	a	a	DET
cana-5532	124	15	continuous	continuous	ADJ
cana-5532	124	16	function	function	NOUN
cana-5532	124	17	and	and	CCONJ
cana-5532	124	18	there	there	PRON
cana-5532	124	19	exists	exist	VERB
cana-5532	124	20	a	a	DET
cana-5532	124	21	bounded	bounded	ADJ
cana-5532	124	22	mapping	mapping	NOUN
cana-5532	124	23	𝜃	𝜃	NOUN
cana-5532	124	24	:	:	PUNCT
cana-5532	124	25	𝐼	𝐼	ADP
cana-5532	124	26	×→	×→	ADV
cana-5532	124	27	ℝ+	ℝ+	PUNCT
cana-5532	124	28	such	such	ADJ
cana-5532	124	29	that	that	PRON
cana-5532	124	30	for	for	ADP
cana-5532	124	31	all	all	DET
cana-5532	124	32	𝑢𝑖	𝑢𝑖	NOUN
cana-5532	124	33	,	,	PUNCT
cana-5532	124	34	𝑣𝑖	𝑣𝑖	ADP
cana-5532	124	35	∈	∈	PROPN
cana-5532	124	36	𝐸	𝐸	PROPN
cana-5532	124	37	,	,	PUNCT
cana-5532	124	38	communications	communication	NOUN
cana-5532	124	39	on	on	ADP
cana-5532	124	40	applied	apply	VERB
cana-5532	124	41	nonlinear	nonlinear	ADJ
cana-5532	124	42	analysis	analysis	NOUN
cana-5532	124	43	issn	issn	NOUN
cana-5532	124	44	:	:	PUNCT
cana-5532	124	45	1074	1074	NUM
cana-5532	124	46	-	-	PUNCT
cana-5532	124	47	133x	133x	NUM
cana-5532	124	48	vol	vol	NOUN
cana-5532	124	49	32	32	NUM
cana-5532	124	50	no	no	NOUN
cana-5532	124	51	.	.	NOUN
cana-5532	124	52	3	3	NUM
cana-5532	124	53	(	(	PUNCT
cana-5532	124	54	2025	2025	NUM
cana-5532	124	55	)	)	PUNCT
cana-5532	124	56	989	989	NUM
cana-5532	124	57	https://internationalpubls.com	https://internationalpubls.com	X
cana-5532	124	58	∣	∣	PROPN
cana-5532	124	59	𝑔(𝑡	𝑔(𝑡	PROPN
cana-5532	124	60	,	,	PUNCT
cana-5532	124	61	𝑢1(𝑡	𝑢1(𝑡	PROPN
cana-5532	124	62	)	)	PUNCT
cana-5532	124	63	,	,	PUNCT
cana-5532	124	64	𝑢2(𝑡	𝑢2(𝑡	PROPN
cana-5532	124	65	)	)	PUNCT
cana-5532	124	66	,	,	PUNCT
cana-5532	124	67	.	.	PUNCT
cana-5532	124	68	.	.	PUNCT
cana-5532	125	1	.	.	PUNCT
cana-5532	126	1	,	,	PUNCT
cana-5532	126	2	𝑢𝑛+1(𝑡	𝑢𝑛+1(𝑡	PROPN
cana-5532	126	3	)	)	PUNCT
cana-5532	126	4	)	)	PUNCT
cana-5532	127	1	−	−	ADP
cana-5532	127	2	𝑔(𝑡	𝑔(𝑡	PROPN
cana-5532	127	3	,	,	PUNCT
cana-5532	127	4	𝑣1(𝑡	𝑣1(𝑡	NOUN
cana-5532	127	5	)	)	PUNCT
cana-5532	127	6	,	,	PUNCT
cana-5532	127	7	𝑣2(𝑡	𝑣2(𝑡	PROPN
cana-5532	127	8	)	)	PUNCT
cana-5532	127	9	,	,	PUNCT
cana-5532	127	10	.	.	PUNCT
cana-5532	127	11	.	.	PUNCT
cana-5532	128	1	.	.	PUNCT
cana-5532	129	1	,	,	PUNCT
cana-5532	129	2	𝑣𝑛+1(𝑡	𝑣𝑛+1(𝑡	PROPN
cana-5532	129	3	)	)	PUNCT
cana-5532	129	4	)	)	PUNCT
cana-5532	130	1	∣≤	∣≤	VERB
cana-5532	130	2	𝜃(𝑡)∑	𝜃(𝑡)∑	X
cana-5532	130	3	∣𝑛+1	∣𝑛+1	X
cana-5532	130	4	𝑖=1	𝑖=1	PROPN
cana-5532	130	5	𝑢𝑖(𝑡	𝑢𝑖(𝑡	NUM
cana-5532	130	6	)	)	PUNCT
cana-5532	130	7	−	−	ADP
cana-5532	130	8	𝑣𝑖(𝑡	𝑣𝑖(𝑡	NUM
cana-5532	130	9	)	)	PUNCT
cana-5532	130	10	∣	∣	PROPN
cana-5532	130	11	,	,	PUNCT
cana-5532	130	12	(	(	PUNCT
cana-5532	130	13	h4	h4	PROPN
cana-5532	130	14	)	)	PUNCT
cana-5532	130	15	the	the	DET
cana-5532	130	16	function	function	NOUN
cana-5532	130	17	𝐾	𝐾	PROPN
cana-5532	130	18	:	:	PUNCT
cana-5532	130	19	𝐼	𝐼	ADP
cana-5532	130	20	×	×	NOUN
cana-5532	130	21	𝐼	𝐼	ADP
cana-5532	130	22	×	×	NOUN
cana-5532	130	23	ℝ	ℝ	PROPN
cana-5532	130	24	→	→	PUNCT
cana-5532	130	25	ℝ+	ℝ+	PUNCT
cana-5532	130	26	is	be	AUX
cana-5532	130	27	a	a	DET
cana-5532	130	28	continuous	continuous	ADJ
cana-5532	130	29	function	function	NOUN
cana-5532	130	30	and	and	CCONJ
cana-5532	130	31	there	there	PRON
cana-5532	130	32	exists	exist	VERB
cana-5532	130	33	a	a	DET
cana-5532	130	34	constant	constant	ADJ
cana-5532	130	35	𝑀1	𝑀1	NOUN
cana-5532	130	36	>	>	X
cana-5532	130	37	0such	0such	PUNCT
cana-5532	131	1	that	that	PRON
cana-5532	131	2	:	:	PUNCT
cana-5532	131	3	𝑀𝑎𝑥{𝐾(𝑡	𝑀𝑎𝑥{𝐾(𝑡	NOUN
cana-5532	131	4	,	,	PUNCT
cana-5532	131	5	𝑠	𝑠	INTJ
cana-5532	131	6	,	,	PUNCT
cana-5532	131	7	𝑢(𝑠	𝑢(𝑠	NOUN
cana-5532	131	8	)	)	PUNCT
cana-5532	131	9	):	):	PUNCT
cana-5532	131	10	𝑡	𝑡	PROPN
cana-5532	131	11	,	,	PUNCT
cana-5532	131	12	𝑠	𝑠	PROPN
cana-5532	131	13	∈	∈	PROPN
cana-5532	131	14	𝐼	𝐼	PROPN
cana-5532	131	15	;	;	PUNCT
cana-5532	131	16	∣	∣	ADJ
cana-5532	131	17	𝑢(𝑠	𝑢(𝑠	NOUN
cana-5532	131	18	)	)	PUNCT
cana-5532	131	19	∣≤	∣≤	PUNCT
cana-5532	131	20	𝑅	𝑅	PROPN
cana-5532	131	21	}	}	PUNCT
cana-5532	131	22	≤	≤	NOUN
cana-5532	131	23	𝑀1	𝑀1	PROPN
cana-5532	131	24	where	where	SCONJ
cana-5532	131	25	𝑅	𝑅	PROPN
cana-5532	131	26	=	=	PROPN
cana-5532	131	27	𝑀𝑓υ	𝑀𝑓υ	PROPN
cana-5532	131	28	1−𝜆𝑓υ	1−𝜆𝑓υ	NOUN
cana-5532	131	29	and	and	CCONJ
cana-5532	131	30	υ	υ	NOUN
cana-5532	131	31	=	=	PUNCT
cana-5532	132	1	[	[	PUNCT
cana-5532	132	2	1	1	NUM
cana-5532	132	3	γ(𝛼	γ(𝛼	PROPN
cana-5532	132	4	+	+	NUM
cana-5532	132	5	1	1	X
cana-5532	132	6	)	)	PUNCT
cana-5532	132	7	+	+	CCONJ
cana-5532	133	1	𝑏γ(3	𝑏γ(3	PROPN
cana-5532	133	2	−	−	PROPN
cana-5532	133	3	𝛼	𝛼	NOUN
cana-5532	133	4	)	)	PUNCT
cana-5532	133	5	𝑎γ(3	𝑎γ(3	PROPN
cana-5532	133	6	−	−	NUM
cana-5532	133	7	𝛼	𝛼	NOUN
cana-5532	133	8	)	)	PUNCT
cana-5532	133	9	+	+	CCONJ
cana-5532	133	10	𝑏	𝑏	NOUN
cana-5532	133	11	]	]	X
cana-5532	134	1	[	[	X
cana-5532	134	2	𝜃∗𝜉𝑅	𝜃∗𝜉𝑅	X
cana-5532	134	3	+	+	X
cana-5532	134	4	𝐺∗	𝐺∗	NUM
cana-5532	134	5	+	+	NOUN
cana-5532	134	6	𝑀1	𝑀1	X
cana-5532	134	7	]	]	X
cana-5532	134	8	+	+	CCONJ
cana-5532	134	9	𝑀0	𝑀0	ADJ
cana-5532	134	10	where	where	SCONJ
cana-5532	134	11	𝜃∗	𝜃∗	PROPN
cana-5532	134	12	=	=	SYM
cana-5532	134	13	𝑠𝑢𝑝𝑡∈𝐼𝜃(𝑡	𝑠𝑢𝑝𝑡∈𝐼𝜃(𝑡	PROPN
cana-5532	134	14	)	)	PUNCT
cana-5532	134	15	,	,	PUNCT
cana-5532	134	16	𝐺	𝐺	NOUN
cana-5532	134	17	∗	∗	NOUN
cana-5532	134	18	=	=	SYM
cana-5532	134	19	𝑠𝑢𝑝𝑡∈𝐼	𝑠𝑢𝑝𝑡∈𝐼	PROPN
cana-5532	134	20	∣	∣	ADJ
cana-5532	134	21	𝑔(𝑡	𝑔(𝑡	PROPN
cana-5532	134	22	,	,	PUNCT
cana-5532	134	23	0,0	0,0	NOUN
cana-5532	134	24	,	,	PUNCT
cana-5532	134	25	.	.	PUNCT
cana-5532	134	26	.	.	PUNCT
cana-5532	134	27	.	.	PUNCT
cana-5532	135	1	,	,	PUNCT
cana-5532	135	2	0	0	X
cana-5532	135	3	)	)	PUNCT
cana-5532	135	4	∣	∣	NOUN
cana-5532	135	5	,	,	PUNCT
cana-5532	135	6	𝑀𝑓	𝑀𝑓	PROPN
cana-5532	135	7	=	=	SYM
cana-5532	135	8	𝑠𝑢𝑝𝑡∈𝐼𝑓(𝑡	𝑠𝑢𝑝𝑡∈𝐼𝑓(𝑡	ADJ
cana-5532	135	9	,	,	PUNCT
cana-5532	135	10	0	0	NUM
cana-5532	135	11	)	)	PUNCT
cana-5532	135	12	,	,	PUNCT
cana-5532	135	13	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
cana-5532	135	14	𝜉	𝜉	X
cana-5532	135	15	=	=	SYM
cana-5532	135	16	1	1	NUM
cana-5532	135	17	+	+	CCONJ
cana-5532	135	18	∑	∑	PROPN
cana-5532	135	19	1	1	NUM
cana-5532	135	20	γ(1+𝜇𝑖	γ(1+𝜇𝑖	PROPN
cana-5532	135	21	)	)	PUNCT
cana-5532	135	22	𝑛	𝑛	PRON
cana-5532	135	23	𝑖=1	𝑖=1	PROPN
cana-5532	135	24	theorem	theorem	VERB
cana-5532	135	25	6	6	NUM
cana-5532	135	26	.	.	PUNCT
cana-5532	135	27	assume	assume	VERB
cana-5532	135	28	that	that	SCONJ
cana-5532	135	29	conditions	condition	NOUN
cana-5532	135	30	(	(	PUNCT
cana-5532	135	31	h1)–(h4	h1)–(h4	NOUN
cana-5532	135	32	)	)	PUNCT
cana-5532	135	33	hold.and	hold.and	NOUN
cana-5532	135	34	if	if	SCONJ
cana-5532	135	35	𝜆𝑓υ	𝜆𝑓υ	NOUN
cana-5532	135	36	<	<	X
cana-5532	135	37	1.then	1.then	NUM
cana-5532	135	38	the	the	DET
cana-5532	135	39	problem	problem	NOUN
cana-5532	135	40	(	(	PUNCT
cana-5532	135	41	[	[	X
cana-5532	135	42	1]-[2	1]-[2	NUM
cana-5532	135	43	]	]	PUNCT
cana-5532	135	44	)	)	PUNCT
cana-5532	135	45	has	have	VERB
cana-5532	135	46	at	at	ADV
cana-5532	135	47	least	least	ADV
cana-5532	135	48	one	one	NUM
cana-5532	135	49	solution	solution	NOUN
cana-5532	135	50	in	in	ADP
cana-5532	135	51	𝐸	𝐸	PROPN
cana-5532	135	52	=	=	PUNCT
cana-5532	135	53	𝐶([0,1	𝐶([0,1	NOUN
cana-5532	135	54	]	]	PUNCT
cana-5532	135	55	)	)	PUNCT
cana-5532	135	56	proof	proof	NOUN
cana-5532	135	57	.	.	PUNCT
cana-5532	136	1	we	we	PRON
cana-5532	136	2	consider	consider	VERB
cana-5532	136	3	a	a	DET
cana-5532	136	4	subset	subset	NOUN
cana-5532	136	5	ω	ω	NOUN
cana-5532	136	6	of	of	ADP
cana-5532	136	7	𝐸	𝐸	PROPN
cana-5532	136	8	given	give	VERB
cana-5532	136	9	by	by	ADP
cana-5532	136	10	ω	ω	PROPN
cana-5532	136	11	=	=	SYM
cana-5532	136	12	{	{	PUNCT
cana-5532	136	13	𝑢	𝑢	PROPN
cana-5532	136	14	∈	∈	PROPN
cana-5532	136	15	𝐸	𝐸	PROPN
cana-5532	136	16	:	:	PUNCT
cana-5532	136	17	∥	∥	NUM
cana-5532	136	18	𝑢	𝑢	X
cana-5532	136	19	∥𝐸≤	∥𝐸≤	PROPN
cana-5532	136	20	𝑅	𝑅	PROPN
cana-5532	136	21	}	}	PUNCT
cana-5532	136	22	and	and	CCONJ
cana-5532	136	23	we	we	PRON
cana-5532	136	24	define	define	VERB
cana-5532	136	25	the	the	DET
cana-5532	136	26	operators	operator	NOUN
cana-5532	136	27	𝐴:𝐸	𝐴:𝐸	PROPN
cana-5532	136	28	→	→	SYM
cana-5532	136	29	𝐸	𝐸	PROPN
cana-5532	136	30	and	and	CCONJ
cana-5532	136	31	𝐵:ω	𝐵:ω	NOUN
cana-5532	136	32	→	→	SYM
cana-5532	136	33	𝐸	𝐸	PROPN
cana-5532	136	34	as	as	SCONJ
cana-5532	136	35	follows	follow	VERB
cana-5532	136	36	:	:	PUNCT
cana-5532	136	37	𝐴𝑢(𝑡	𝐴𝑢(𝑡	X
cana-5532	136	38	)	)	PUNCT
cana-5532	136	39	=	=	PUNCT
cana-5532	136	40	𝑓(𝑡	𝑓(𝑡	NOUN
cana-5532	136	41	,	,	PUNCT
cana-5532	136	42	𝑢(𝑡	𝑢(𝑡	NOUN
cana-5532	136	43	)	)	PUNCT
cana-5532	136	44	)	)	PUNCT
cana-5532	136	45	.	.	PUNCT
cana-5532	136	46	  	  	SPACE
cana-5532	137	1	𝑡	𝑡	PROPN
cana-5532	137	2	∈	∈	PROPN
cana-5532	137	3	𝐼	𝐼	PROPN
cana-5532	137	4	,	,	PUNCT
cana-5532	137	5	𝐵𝑢(𝑡	𝐵𝑢(𝑡	NUM
cana-5532	137	6	)	)	PUNCT
cana-5532	137	7	=	=	PUNCT
cana-5532	137	8	−∫	−∫	NOUN
cana-5532	137	9	(	(	PUNCT
cana-5532	137	10	𝑡−𝜏)𝛼−1	𝑡−𝜏)𝛼−1	NOUN
cana-5532	137	11	γ(𝛼	γ(𝛼	ADV
cana-5532	137	12	)	)	PUNCT
cana-5532	137	13	𝑡	𝑡	NOUN
cana-5532	137	14	0	0	PUNCT
cana-5532	138	1	[	[	X
cana-5532	138	2	𝑔(𝜏	𝑔(𝜏	PROPN
cana-5532	138	3	,	,	PUNCT
cana-5532	138	4	𝐼	𝐼	PROPN
cana-5532	138	5	0	0	NUM
cana-5532	138	6	+	+	NOUN
cana-5532	138	7	𝜇1𝑢(𝜏	𝜇1𝑢(𝜏	PROPN
cana-5532	138	8	)	)	PUNCT
cana-5532	138	9	,	,	PUNCT
cana-5532	138	10	𝐼	𝐼	PROPN
cana-5532	138	11	0	0	NUM
cana-5532	138	12	+	+	NOUN
cana-5532	138	13	𝜇2𝑢(𝜏	𝜇2𝑢(𝜏	PROPN
cana-5532	138	14	)	)	PUNCT
cana-5532	138	15	,	,	PUNCT
cana-5532	138	16	.	.	PUNCT
cana-5532	138	17	.	.	PUNCT
cana-5532	139	1	.	.	PUNCT
cana-5532	140	1	,	,	PUNCT
cana-5532	140	2	𝐼	𝐼	ADP
cana-5532	140	3	0	0	NUM
cana-5532	140	4	+	+	NUM
cana-5532	140	5	𝜇𝑛𝑢(𝜏	𝜇𝑛𝑢(𝜏	PROPN
cana-5532	140	6	)	)	PUNCT
cana-5532	140	7	)	)	PUNCT
cana-5532	141	1	+	+	CCONJ
cana-5532	141	2	∫	∫	X
cana-5532	141	3	𝐾	𝐾	NOUN
cana-5532	141	4	𝜏	𝜏	PROPN
cana-5532	141	5	0	0	NUM
cana-5532	141	6	(	(	PUNCT
cana-5532	141	7	𝜏	𝜏	NOUN
cana-5532	141	8	,	,	PUNCT
cana-5532	141	9	𝑠	𝑠	PROPN
cana-5532	141	10	,	,	PUNCT
cana-5532	141	11	𝑢(𝑠)𝑑𝑠]𝑑𝜏	𝑢(𝑠)𝑑𝑠]𝑑𝜏	NOUN
cana-5532	141	12	+	+	CCONJ
cana-5532	142	1	𝑏γ(3−𝛼)𝑡	𝑏γ(3−𝛼)𝑡	PROPN
cana-5532	142	2	𝑎γ(3−𝛼)+𝑏	𝑎γ(3−𝛼)+𝑏	PROPN
cana-5532	142	3	∫	∫	PROPN
cana-5532	143	1	[	[	X
cana-5532	143	2	𝑔(𝜏	𝑔(𝜏	PROPN
cana-5532	143	3	,	,	PUNCT
cana-5532	143	4	𝐼0	𝐼0	PROPN
cana-5532	143	5	+	+	ADJ
cana-5532	143	6	𝜇1𝑢(𝜏	𝜇1𝑢(𝜏	PROPN
cana-5532	143	7	)	)	PUNCT
cana-5532	143	8	,	,	PUNCT
cana-5532	143	9	𝐼	𝐼	PROPN
cana-5532	143	10	0	0	NUM
cana-5532	143	11	+	+	NOUN
cana-5532	143	12	𝜇2𝑢(𝜏	𝜇2𝑢(𝜏	PROPN
cana-5532	143	13	)	)	PUNCT
cana-5532	143	14	,	,	PUNCT
cana-5532	143	15	.	.	PUNCT
cana-5532	143	16	.	.	PUNCT
cana-5532	144	1	.	.	PUNCT
cana-5532	145	1	,	,	PUNCT
cana-5532	145	2	𝐼	𝐼	ADP
cana-5532	145	3	0	0	NUM
cana-5532	145	4	+	+	NUM
cana-5532	145	5	𝜇𝑛𝑢(𝜏	𝜇𝑛𝑢(𝜏	PROPN
cana-5532	145	6	)	)	PUNCT
cana-5532	145	7	)	)	PUNCT
cana-5532	146	1	+	+	CCONJ
cana-5532	146	2	∫	∫	X
cana-5532	146	3	𝐾	𝐾	NOUN
cana-5532	146	4	𝜏	𝜏	PROPN
cana-5532	146	5	0	0	NUM
cana-5532	146	6	(	(	PUNCT
cana-5532	146	7	𝜏	𝜏	NOUN
cana-5532	146	8	,	,	PUNCT
cana-5532	146	9	𝑠	𝑠	PROPN
cana-5532	146	10	,	,	PUNCT
cana-5532	146	11	𝑢(𝑠)𝑑𝑠	𝑢(𝑠)𝑑𝑠	PROPN
cana-5532	146	12	]	]	X
cana-5532	146	13	1	1	NUM
cana-5532	146	14	0	0	NUM
cana-5532	146	15	𝑑𝜏	𝑑𝜏	NOUN
cana-5532	146	16	+	+	CCONJ
cana-5532	146	17	ℎ(𝑢	ℎ(𝑢	PROPN
cana-5532	146	18	)	)	PUNCT
cana-5532	146	19	𝑓(0,ℎ(𝑢	𝑓(0,ℎ(𝑢	NOUN
cana-5532	146	20	)	)	PUNCT
cana-5532	146	21	)	)	PUNCT
cana-5532	146	22	.	.	PUNCT
cana-5532	147	1	obviously	obviously	ADV
cana-5532	147	2	,	,	PUNCT
cana-5532	147	3	problem	problem	NOUN
cana-5532	147	4	(	(	PUNCT
cana-5532	147	5	[	[	X
cana-5532	147	6	1]-[2	1]-[2	NUM
cana-5532	147	7	]	]	PUNCT
cana-5532	147	8	)	)	PUNCT
cana-5532	147	9	has	have	VERB
cana-5532	147	10	a	a	DET
cana-5532	147	11	solution	solution	NOUN
cana-5532	147	12	if	if	SCONJ
cana-5532	147	13	and	and	CCONJ
cana-5532	147	14	only	only	ADV
cana-5532	147	15	if	if	SCONJ
cana-5532	147	16	𝐴𝑥𝐵𝑥	𝐴𝑥𝐵𝑥	PROPN
cana-5532	147	17	has	have	VERB
cana-5532	147	18	a	a	DET
cana-5532	147	19	fixed	fix	VERB
cana-5532	147	20	point	point	NOUN
cana-5532	147	21	.	.	PUNCT
cana-5532	148	1	now	now	ADV
cana-5532	148	2	,	,	PUNCT
cana-5532	148	3	we	we	PRON
cana-5532	148	4	show	show	VERB
cana-5532	148	5	that	that	SCONJ
cana-5532	148	6	the	the	DET
cana-5532	148	7	operators	operator	NOUN
cana-5532	148	8	𝐴	𝐴	PROPN
cana-5532	148	9	and	and	CCONJ
cana-5532	148	10	𝐵	𝐵	NOUN
cana-5532	148	11	satisfy	satisfy	VERB
cana-5532	148	12	all	all	DET
cana-5532	148	13	the	the	DET
cana-5532	148	14	conditions	condition	NOUN
cana-5532	148	15	of	of	ADP
cana-5532	148	16	theorem	theorem	NOUN
cana-5532	148	17	4	4	NUM
cana-5532	148	18	in	in	ADP
cana-5532	148	19	a	a	DET
cana-5532	148	20	series	series	NOUN
cana-5532	148	21	of	of	ADP
cana-5532	148	22	steps	step	NOUN
cana-5532	148	23	.	.	PUNCT
cana-5532	149	1	claim	claim	NOUN
cana-5532	149	2	1	1	NUM
cana-5532	149	3	𝐴	𝐴	PROPN
cana-5532	149	4	is	be	AUX
cana-5532	149	5	a	a	DET
cana-5532	149	6	lipschitz	lipschitz	NOUN
cana-5532	149	7	on	on	ADP
cana-5532	149	8	𝐸	𝐸	PROPN
cana-5532	149	9	let	let	VERB
cana-5532	149	10	𝑢	𝑢	NOUN
cana-5532	149	11	,	,	PUNCT
cana-5532	149	12	𝑣	𝑣	PRON
cana-5532	149	13	∈	∈	PROPN
cana-5532	149	14	𝐸	𝐸	PROPN
cana-5532	149	15	for	for	ADP
cana-5532	149	16	all	all	DET
cana-5532	149	17	𝑡	𝑡	ADP
cana-5532	149	18	∈	∈	PROPN
cana-5532	149	19	𝐼.	𝐼.	NOUN
cana-5532	149	20	then	then	ADV
cana-5532	149	21	in	in	ADP
cana-5532	149	22	view	view	NOUN
cana-5532	149	23	of	of	ADP
cana-5532	149	24	condition	condition	NOUN
cana-5532	149	25	(	(	PUNCT
cana-5532	149	26	h1	h1	PROPN
cana-5532	149	27	)	)	PUNCT
cana-5532	149	28	,	,	PUNCT
cana-5532	149	29	we	we	PRON
cana-5532	149	30	get	get	VERB
cana-5532	149	31	∣	∣	ADJ
cana-5532	149	32	𝐴𝑢(𝑡	𝐴𝑢(𝑡	ADJ
cana-5532	149	33	)	)	PUNCT
cana-5532	150	1	−	−	PROPN
cana-5532	150	2	𝐴𝑣(𝑡	𝐴𝑣(𝑡	NOUN
cana-5532	150	3	)	)	PUNCT
cana-5532	150	4	∣=∣	∣=∣	NOUN
cana-5532	150	5	𝑓(𝑡	𝑓(𝑡	NOUN
cana-5532	150	6	,	,	PUNCT
cana-5532	150	7	𝑢(𝑡	𝑢(𝑡	NOUN
cana-5532	150	8	)	)	PUNCT
cana-5532	150	9	)	)	PUNCT
cana-5532	151	1	−	−	PROPN
cana-5532	152	1	𝑓(𝑡	𝑓(𝑡	NOUN
cana-5532	152	2	,	,	PUNCT
cana-5532	152	3	𝑣(𝑡	𝑣(𝑡	NOUN
cana-5532	152	4	)	)	PUNCT
cana-5532	152	5	)	)	PUNCT
cana-5532	152	6	∣≤	∣≤	PUNCT
cana-5532	152	7	𝜆𝑓	𝜆𝑓	ADP
cana-5532	152	8	∣	∣	PROPN
cana-5532	152	9	𝑢	𝑢	PROPN
cana-5532	152	10	−	−	PROPN
cana-5532	152	11	𝑣	𝑣	PART
cana-5532	152	12	∣	∣	NOUN
cana-5532	152	13	then	then	ADV
cana-5532	152	14	,	,	PUNCT
cana-5532	152	15	for	for	ADP
cana-5532	152	16	each	each	DET
cana-5532	152	17	𝑡	𝑡	NOUN
cana-5532	152	18	∈	∈	NOUN
cana-5532	152	19	𝐼	𝐼	SCONJ
cana-5532	152	20	we	we	PRON
cana-5532	152	21	obtain	obtain	VERB
cana-5532	152	22	∥	∥	PUNCT
cana-5532	153	1	𝐴𝑢	𝐴𝑢	AUX
cana-5532	153	2	−	−	NOUN
cana-5532	153	3	𝐴𝑣	𝐴𝑣	VERB
cana-5532	153	4	∥𝐸≤	∥𝐸≤	ADJ
cana-5532	153	5	𝜆𝑓	𝜆𝑓	ADP
cana-5532	153	6	∥	∥	NUM
cana-5532	153	7	𝑢	𝑢	ADP
cana-5532	153	8	−	−	NOUN
cana-5532	153	9	𝑣	𝑣	PRON
cana-5532	153	10	∥𝐸	∥𝐸	NOUN
cana-5532	153	11	claim	claim	NOUN
cana-5532	153	12	2	2	NUM
cana-5532	153	13	𝐵	𝐵	NOUN
cana-5532	153	14	is	be	AUX
cana-5532	153	15	completely	completely	ADV
cana-5532	153	16	continuous	continuous	ADJ
cana-5532	153	17	on	on	ADP
cana-5532	153	18	ω	ω	NUM
cana-5532	153	19	.	.	PUNCT
cana-5532	154	1	we	we	PRON
cana-5532	154	2	firstly	firstly	ADV
cana-5532	154	3	show	show	VERB
cana-5532	154	4	that𝐵	that𝐵	PROPN
cana-5532	154	5	is	be	AUX
cana-5532	154	6	uniformly	uniformly	ADV
cana-5532	154	7	bounded	bound	VERB
cana-5532	154	8	for	for	ADP
cana-5532	154	9	any	any	DET
cana-5532	154	10	𝑢	𝑢	PROPN
cana-5532	154	11	∈	∈	PROPN
cana-5532	154	12	ω	ω	NOUN
cana-5532	154	13	,	,	PUNCT
cana-5532	154	14	by	by	ADP
cana-5532	154	15	(	(	PUNCT
cana-5532	154	16	h2)-(h5	h2)-(h5	PROPN
cana-5532	154	17	)	)	PUNCT
cana-5532	154	18	,	,	PUNCT
cana-5532	154	19	we	we	PRON
cana-5532	154	20	have	have	VERB
cana-5532	154	21	.	.	PUNCT
cana-5532	155	1	communications	communication	NOUN
cana-5532	155	2	on	on	ADP
cana-5532	155	3	applied	apply	VERB
cana-5532	155	4	nonlinear	nonlinear	ADJ
cana-5532	155	5	analysis	analysis	NOUN
cana-5532	155	6	issn	issn	NOUN
cana-5532	155	7	:	:	PUNCT
cana-5532	155	8	1074	1074	NUM
cana-5532	155	9	-	-	PUNCT
cana-5532	155	10	133x	133x	NUM
cana-5532	155	11	vol	vol	NOUN
cana-5532	155	12	32	32	NUM
cana-5532	155	13	no	no	NOUN
cana-5532	155	14	.	.	NOUN
cana-5532	155	15	3	3	NUM
cana-5532	155	16	(	(	PUNCT
cana-5532	155	17	2025	2025	NUM
cana-5532	155	18	)	)	PUNCT
cana-5532	155	19	990	990	NUM
cana-5532	155	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-5532	155	21	∣	∣	PROPN
cana-5532	155	22	𝐵𝑢(𝑡	𝐵𝑢(𝑡	NUM
cana-5532	155	23	)	)	PUNCT
cana-5532	155	24	∣≤	∣≤	NUM
cana-5532	155	25	∫	∫	PROPN
cana-5532	155	26	∣𝑡−𝜏∣𝛼−1	∣𝑡−𝜏∣𝛼−1	PROPN
cana-5532	155	27	γ(𝛼	γ(𝛼	PROPN
cana-5532	155	28	)	)	PUNCT
cana-5532	156	1	𝑡	𝑡	X
cana-5532	156	2	0	0	PUNCT
cana-5532	157	1	[	[	X
cana-5532	157	2	∣	∣	ADJ
cana-5532	157	3	𝑔(𝜏	𝑔(𝜏	PROPN
cana-5532	157	4	,	,	PUNCT
cana-5532	157	5	𝑢(𝜏	𝑢(𝜏	PROPN
cana-5532	157	6	)	)	PUNCT
cana-5532	157	7	,	,	PUNCT
cana-5532	157	8	𝐼	𝐼	ADP
cana-5532	157	9	0	0	NUM
cana-5532	157	10	+	+	NUM
cana-5532	157	11	𝜇1𝑢(𝜏	𝜇1𝑢(𝜏	PROPN
cana-5532	157	12	)	)	PUNCT
cana-5532	157	13	,	,	PUNCT
cana-5532	157	14	𝐼	𝐼	PROPN
cana-5532	157	15	0	0	NUM
cana-5532	157	16	+	+	NOUN
cana-5532	157	17	𝜇2𝑢(𝜏	𝜇2𝑢(𝜏	PROPN
cana-5532	157	18	)	)	PUNCT
cana-5532	157	19	,	,	PUNCT
cana-5532	157	20	.	.	PUNCT
cana-5532	157	21	.	.	PUNCT
cana-5532	158	1	.	.	PUNCT
cana-5532	159	1	,	,	PUNCT
cana-5532	159	2	𝐼	𝐼	ADP
cana-5532	159	3	0	0	NUM
cana-5532	159	4	+	+	NUM
cana-5532	159	5	𝜇𝑛𝑢(𝜏	𝜇𝑛𝑢(𝜏	PROPN
cana-5532	159	6	)	)	PUNCT
cana-5532	159	7	)	)	PUNCT
cana-5532	160	1	∣	∣	PROPN
cana-5532	160	2	+	+	PROPN
cana-5532	160	3	∫	∫	PROPN
cana-5532	160	4	∣	∣	ADJ
cana-5532	160	5	𝜏	𝜏	PROPN
cana-5532	160	6	0	0	NUM
cana-5532	160	7	𝐾(𝜏	𝐾(𝜏	ADJ
cana-5532	160	8	,	,	PUNCT
cana-5532	160	9	𝑠	𝑠	PROPN
cana-5532	160	10	,	,	PUNCT
cana-5532	160	11	𝑢(𝑠)𝑑𝑠	𝑢(𝑠)𝑑𝑠	PROPN
cana-5532	160	12	∣]𝑑𝜏	∣]𝑑𝜏	PROPN
cana-5532	160	13	+	+	CCONJ
cana-5532	161	1	𝑏γ(3−𝛼)𝑡	𝑏γ(3−𝛼)𝑡	PROPN
cana-5532	161	2	𝑎γ(3−𝛼)+𝑏	𝑎γ(3−𝛼)+𝑏	PROPN
cana-5532	161	3	∫	∫	PROPN
cana-5532	162	1	[	[	X
cana-5532	162	2	∣	∣	ADJ
cana-5532	162	3	𝑔(𝜏	𝑔(𝜏	PROPN
cana-5532	162	4	,	,	PUNCT
cana-5532	162	5	𝑢(𝜏	𝑢(𝜏	PROPN
cana-5532	162	6	)	)	PUNCT
cana-5532	162	7	,	,	PUNCT
cana-5532	162	8	𝐼0	𝐼0	PROPN
cana-5532	162	9	+	+	ADJ
cana-5532	162	10	𝜇1𝑢(𝜏	𝜇1𝑢(𝜏	PROPN
cana-5532	162	11	)	)	PUNCT
cana-5532	162	12	,	,	PUNCT
cana-5532	162	13	𝐼	𝐼	PROPN
cana-5532	162	14	0	0	NUM
cana-5532	162	15	+	+	NOUN
cana-5532	162	16	𝜇2𝑢(𝜏	𝜇2𝑢(𝜏	PROPN
cana-5532	162	17	)	)	PUNCT
cana-5532	162	18	,	,	PUNCT
cana-5532	162	19	.	.	PUNCT
cana-5532	162	20	.	.	PUNCT
cana-5532	162	21	.	.	PUNCT
cana-5532	163	1	,	,	PUNCT
cana-5532	163	2	𝐼	𝐼	ADP
cana-5532	163	3	0	0	NUM
cana-5532	163	4	+	+	NUM
cana-5532	163	5	𝜇𝑛𝑢(𝜏	𝜇𝑛𝑢(𝜏	PROPN
cana-5532	163	6	)	)	PUNCT
cana-5532	163	7	)	)	PUNCT
cana-5532	164	1	∣	∣	PROPN
cana-5532	164	2	+	+	PROPN
cana-5532	164	3	∫	∫	PROPN
cana-5532	164	4	∣	∣	ADJ
cana-5532	164	5	𝜏	𝜏	PROPN
cana-5532	164	6	0	0	NUM
cana-5532	164	7	𝐾(𝜏	𝐾(𝜏	ADJ
cana-5532	164	8	,	,	PUNCT
cana-5532	164	9	𝑠	𝑠	PROPN
cana-5532	164	10	,	,	PUNCT
cana-5532	164	11	𝑢(𝑠	𝑢(𝑠	NOUN
cana-5532	164	12	)	)	PUNCT
cana-5532	164	13	∣	∣	VERB
cana-5532	164	14	𝑑𝑠	𝑑𝑠	X
cana-5532	164	15	]	]	X
cana-5532	164	16	1	1	NUM
cana-5532	164	17	0	0	NUM
cana-5532	164	18	𝑑𝜏	𝑑𝜏	NOUN
cana-5532	164	19	+	+	PROPN
cana-5532	164	20	|	|	NOUN
cana-5532	164	21	ℎ(𝑢	ℎ(𝑢	NOUN
cana-5532	164	22	)	)	PUNCT
cana-5532	164	23	𝑓(0,ℎ(𝑢	𝑓(0,ℎ(𝑢	NOUN
cana-5532	164	24	)	)	PUNCT
cana-5532	164	25	)	)	PUNCT
cana-5532	165	1	|	|	ADV
cana-5532	165	2	,	,	PUNCT
cana-5532	165	3	≤	≤	NUM
cana-5532	165	4	∫	∫	PROPN
cana-5532	165	5	∣𝑡−𝜏∣𝛼−1	∣𝑡−𝜏∣𝛼−1	PROPN
cana-5532	165	6	γ(𝛼	γ(𝛼	PROPN
cana-5532	165	7	)	)	PUNCT
cana-5532	165	8	𝑡	𝑡	X
cana-5532	165	9	0	0	PUNCT
cana-5532	166	1	[	[	X
cana-5532	166	2	∣	∣	ADJ
cana-5532	166	3	𝑔(𝜏	𝑔(𝜏	PROPN
cana-5532	166	4	,	,	PUNCT
cana-5532	166	5	𝑢(𝜏	𝑢(𝜏	PROPN
cana-5532	166	6	)	)	PUNCT
cana-5532	166	7	,	,	PUNCT
cana-5532	166	8	𝐼	𝐼	ADP
cana-5532	166	9	0	0	NUM
cana-5532	166	10	+	+	NUM
cana-5532	166	11	𝜇1𝑢(𝜏	𝜇1𝑢(𝜏	PROPN
cana-5532	166	12	)	)	PUNCT
cana-5532	166	13	,	,	PUNCT
cana-5532	166	14	𝐼	𝐼	PROPN
cana-5532	166	15	0	0	NUM
cana-5532	166	16	+	+	NOUN
cana-5532	166	17	𝜇2𝑢(𝜏	𝜇2𝑢(𝜏	PROPN
cana-5532	166	18	)	)	PUNCT
cana-5532	166	19	,	,	PUNCT
cana-5532	166	20	.	.	PUNCT
cana-5532	166	21	.	.	PUNCT
cana-5532	167	1	.	.	PUNCT
cana-5532	168	1	,	,	PUNCT
cana-5532	168	2	𝐼	𝐼	ADP
cana-5532	168	3	0	0	NUM
cana-5532	168	4	+	+	NUM
cana-5532	168	5	𝜇𝑛𝑢(𝜏	𝜇𝑛𝑢(𝜏	PROPN
cana-5532	168	6	)	)	PUNCT
cana-5532	168	7	)	)	PUNCT
cana-5532	169	1	−	−	PROPN
cana-5532	169	2	𝑔(𝑡	𝑔(𝑡	PROPN
cana-5532	169	3	,	,	PUNCT
cana-5532	169	4	0	0	NUM
cana-5532	169	5	,	,	PUNCT
cana-5532	169	6	.	.	PUNCT
cana-5532	169	7	.	.	PUNCT
cana-5532	170	1	.	.	PUNCT
cana-5532	171	1	,	,	PUNCT
cana-5532	171	2	0	0	X
cana-5532	171	3	)	)	PUNCT
cana-5532	171	4	∣	∣	ADJ
cana-5532	171	5	+	+	PROPN
cana-5532	171	6	∣	∣	ADJ
cana-5532	171	7	𝑔(𝑡	𝑔(𝑡	PROPN
cana-5532	171	8	,	,	PUNCT
cana-5532	171	9	0	0	NUM
cana-5532	171	10	,	,	PUNCT
cana-5532	171	11	.	.	PUNCT
cana-5532	171	12	.	.	PUNCT
cana-5532	172	1	.	.	PUNCT
cana-5532	173	1	,	,	PUNCT
cana-5532	173	2	0	0	X
cana-5532	173	3	)	)	PUNCT
cana-5532	174	1	∣	∣	PROPN
cana-5532	174	2	+	+	CCONJ
cana-5532	174	3	∫	∫	PROPN
cana-5532	174	4	∣	∣	PROPN
cana-5532	174	5	𝜏	𝜏	PROPN
cana-5532	174	6	0	0	NUM
cana-5532	174	7	𝐾(𝜏	𝐾(𝜏	ADJ
cana-5532	174	8	,	,	PUNCT
cana-5532	174	9	𝑠	𝑠	PROPN
cana-5532	174	10	,	,	PUNCT
cana-5532	174	11	𝑢(𝑠	𝑢(𝑠	NOUN
cana-5532	174	12	)	)	PUNCT
cana-5532	174	13	∣	∣	ADJ
cana-5532	174	14	𝑑𝑠]𝑑𝜏	𝑑𝑠]𝑑𝜏	NOUN
cana-5532	175	1	+	+	CCONJ
cana-5532	175	2	𝑏γ(3−𝛼)𝑡	𝑏γ(3−𝛼)𝑡	PROPN
cana-5532	175	3	𝑎γ(3−𝛼)+𝑏	𝑎γ(3−𝛼)+𝑏	PROPN
cana-5532	175	4	∫	∫	PROPN
cana-5532	175	5	[	[	PUNCT
cana-5532	175	6	1	1	NUM
cana-5532	175	7	0	0	NUM
cana-5532	175	8	∣	∣	ADJ
cana-5532	175	9	𝑔(𝜏	𝑔(𝜏	PROPN
cana-5532	175	10	,	,	PUNCT
cana-5532	175	11	𝑢(𝜏	𝑢(𝜏	PROPN
cana-5532	175	12	)	)	PUNCT
cana-5532	175	13	,	,	PUNCT
cana-5532	175	14	𝐼	𝐼	ADP
cana-5532	175	15	0	0	NUM
cana-5532	175	16	+	+	NUM
cana-5532	175	17	𝜇1𝑢(𝜏	𝜇1𝑢(𝜏	PROPN
cana-5532	175	18	)	)	PUNCT
cana-5532	175	19	,	,	PUNCT
cana-5532	175	20	𝐼	𝐼	PROPN
cana-5532	175	21	0	0	NUM
cana-5532	175	22	+	+	NOUN
cana-5532	175	23	𝜇2𝑢(𝜏	𝜇2𝑢(𝜏	PROPN
cana-5532	175	24	)	)	PUNCT
cana-5532	175	25	,	,	PUNCT
cana-5532	175	26	.	.	PUNCT
cana-5532	175	27	.	.	PUNCT
cana-5532	175	28	.	.	PUNCT
cana-5532	176	1	,	,	PUNCT
cana-5532	176	2	𝐼	𝐼	ADP
cana-5532	176	3	0	0	NUM
cana-5532	176	4	+	+	NUM
cana-5532	176	5	𝜇𝑛𝑢(𝜏	𝜇𝑛𝑢(𝜏	PROPN
cana-5532	176	6	)	)	PUNCT
cana-5532	176	7	)	)	PUNCT
cana-5532	177	1	−	−	PROPN
cana-5532	177	2	𝑔(𝑡	𝑔(𝑡	PROPN
cana-5532	177	3	,	,	PUNCT
cana-5532	177	4	0	0	NUM
cana-5532	177	5	,	,	PUNCT
cana-5532	177	6	.	.	PUNCT
cana-5532	177	7	.	.	PUNCT
cana-5532	178	1	.	.	PUNCT
cana-5532	179	1	,	,	PUNCT
cana-5532	179	2	0	0	X
cana-5532	179	3	)	)	PUNCT
cana-5532	179	4	∣	∣	ADJ
cana-5532	179	5	+	+	PROPN
cana-5532	179	6	∣	∣	ADJ
cana-5532	179	7	𝑔(𝑡	𝑔(𝑡	PROPN
cana-5532	179	8	,	,	PUNCT
cana-5532	179	9	0	0	NUM
cana-5532	179	10	,	,	PUNCT
cana-5532	179	11	.	.	PUNCT
cana-5532	179	12	.	.	PUNCT
cana-5532	180	1	.	.	PUNCT
cana-5532	181	1	,	,	PUNCT
cana-5532	181	2	0	0	X
cana-5532	181	3	)	)	PUNCT
cana-5532	182	1	∣	∣	PROPN
cana-5532	182	2	+	+	CCONJ
cana-5532	182	3	∫	∫	PROPN
cana-5532	182	4	∣	∣	PROPN
cana-5532	182	5	𝜏	𝜏	PROPN
cana-5532	182	6	0	0	NUM
cana-5532	182	7	𝐾(𝜏	𝐾(𝜏	ADJ
cana-5532	182	8	,	,	PUNCT
cana-5532	182	9	𝑠	𝑠	PROPN
cana-5532	182	10	,	,	PUNCT
cana-5532	182	11	𝑢(𝑠	𝑢(𝑠	NOUN
cana-5532	182	12	)	)	PUNCT
cana-5532	182	13	∣	∣	ADJ
cana-5532	182	14	𝑑𝑠]𝑑𝜏	𝑑𝑠]𝑑𝜏	NOUN
cana-5532	183	1	+	+	PROPN
cana-5532	183	2	|	|	ADV
cana-5532	183	3	ℎ(𝑢	ℎ(𝑢	NOUN
cana-5532	183	4	)	)	PUNCT
cana-5532	183	5	𝑓(0,ℎ(𝑢	𝑓(0,ℎ(𝑢	NOUN
cana-5532	183	6	)	)	PUNCT
cana-5532	183	7	)	)	PUNCT
cana-5532	184	1	|	|	ADV
cana-5532	184	2	,	,	PUNCT
cana-5532	184	3	≤	≤	NOUN
cana-5532	184	4	1	1	NUM
cana-5532	184	5	γ(𝛼+1	γ(𝛼+1	PUNCT
cana-5532	184	6	)	)	PUNCT
cana-5532	185	1	[	[	X
cana-5532	185	2	𝜃∗	𝜃∗	X
cana-5532	185	3	(	(	PUNCT
cana-5532	185	4	1	1	NUM
cana-5532	185	5	+	+	SYM
cana-5532	185	6	1	1	NUM
cana-5532	185	7	γ(𝜇1	γ(𝜇1	NOUN
cana-5532	185	8	+	+	NOUN
cana-5532	185	9	1	1	NUM
cana-5532	185	10	)	)	PUNCT
cana-5532	185	11	+	+	CCONJ
cana-5532	185	12	1	1	NUM
cana-5532	185	13	γ(𝜇2	γ(𝜇2	NOUN
cana-5532	185	14	+	+	NOUN
cana-5532	185	15	1	1	NUM
cana-5532	185	16	)	)	PUNCT
cana-5532	185	17	+	+	PROPN
cana-5532	185	18	.	.	PUNCT
cana-5532	185	19	.	.	PUNCT
cana-5532	185	20	.	.	PUNCT
cana-5532	186	1	+	+	CCONJ
cana-5532	186	2	1	1	NUM
cana-5532	186	3	γ(𝜇𝑛+1	γ(𝜇𝑛+1	ADJ
cana-5532	186	4	)	)	PUNCT
cana-5532	186	5	)	)	PUNCT
cana-5532	187	1	∣	∣	VERB
cana-5532	187	2	𝑢	𝑢	PROPN
cana-5532	187	3	∣	∣	ADJ
cana-5532	187	4	+	+	PROPN
cana-5532	187	5	𝐺∗	𝐺∗	NOUN
cana-5532	188	1	+	+	NOUN
cana-5532	188	2	𝑀1	𝑀1	X
cana-5532	188	3	]	]	X
cana-5532	188	4	+	+	CCONJ
cana-5532	188	5	𝑏γ(3−𝛼	𝑏γ(3−𝛼	ADJ
cana-5532	188	6	)	)	PUNCT
cana-5532	188	7	𝑎γ(3−𝛼)+𝑏	𝑎γ(3−𝛼)+𝑏	PROPN
cana-5532	189	1	[	[	X
cana-5532	189	2	𝜃∗	𝜃∗	PROPN
cana-5532	189	3	(	(	PUNCT
cana-5532	189	4	1	1	NUM
cana-5532	189	5	+	+	SYM
cana-5532	189	6	1	1	NUM
cana-5532	189	7	γ(𝜇1	γ(𝜇1	NOUN
cana-5532	189	8	+	+	NOUN
cana-5532	189	9	1	1	NUM
cana-5532	189	10	)	)	PUNCT
cana-5532	189	11	+	+	CCONJ
cana-5532	189	12	1	1	NUM
cana-5532	189	13	γ(𝜇2	γ(𝜇2	NOUN
cana-5532	189	14	+	+	NOUN
cana-5532	189	15	1	1	NUM
cana-5532	189	16	)	)	PUNCT
cana-5532	189	17	+	+	PROPN
cana-5532	189	18	.	.	PUNCT
cana-5532	189	19	.	.	PUNCT
cana-5532	189	20	.	.	PUNCT
cana-5532	190	1	+	+	CCONJ
cana-5532	190	2	1	1	NUM
cana-5532	190	3	γ(𝜇𝑛+1	γ(𝜇𝑛+1	ADJ
cana-5532	190	4	)	)	PUNCT
cana-5532	190	5	)	)	PUNCT
cana-5532	191	1	∣	∣	VERB
cana-5532	191	2	𝑢	𝑢	PROPN
cana-5532	191	3	∣	∣	ADJ
cana-5532	191	4	+	+	PROPN
cana-5532	191	5	𝐺∗	𝐺∗	NOUN
cana-5532	192	1	+	+	NOUN
cana-5532	192	2	𝑀1	𝑀1	X
cana-5532	192	3	]	]	X
cana-5532	192	4	+	+	CCONJ
cana-5532	192	5	𝑀0	𝑀0	ADJ
cana-5532	192	6	≤	≤	NOUN
cana-5532	192	7	[	[	PUNCT
cana-5532	192	8	1	1	NUM
cana-5532	192	9	γ(𝛼+1	γ(𝛼+1	PUNCT
cana-5532	192	10	)	)	PUNCT
cana-5532	193	1	+	+	PUNCT
cana-5532	193	2	𝑏γ(3−𝛼	𝑏γ(3−𝛼	ADJ
cana-5532	193	3	)	)	PUNCT
cana-5532	193	4	𝑎γ(3−𝛼)+𝑏	𝑎γ(3−𝛼)+𝑏	NOUN
cana-5532	193	5	]	]	PUNCT
cana-5532	194	1	[	[	X
cana-5532	194	2	𝜃∗𝜉𝑅	𝜃∗𝜉𝑅	X
cana-5532	194	3	+	+	X
cana-5532	194	4	𝐺∗	𝐺∗	NUM
cana-5532	194	5	+	+	NOUN
cana-5532	194	6	𝑀1	𝑀1	X
cana-5532	194	7	]	]	X
cana-5532	194	8	+	+	CCONJ
cana-5532	194	9	𝑀0	𝑀0	ADJ
cana-5532	194	10	≤	≤	X
cana-5532	194	11	υ	υ	NOUN
cana-5532	194	12	thus	thus	ADV
cana-5532	194	13	,	,	PUNCT
cana-5532	194	14	we	we	PRON
cana-5532	194	15	get	get	VERB
cana-5532	194	16	∥	∥	PUNCT
cana-5532	195	1	𝐵𝑢	𝐵𝑢	NOUN
cana-5532	195	2	∥𝐸≤	∥𝐸≤	ADP
cana-5532	195	3	υfor	υfor	NOUN
cana-5532	195	4	all	all	PRON
cana-5532	195	5	𝑢	𝑢	PROPN
cana-5532	195	6	∈	∈	PROPN
cana-5532	195	7	ω	ω	PROPN
cana-5532	195	8	,	,	PUNCT
cana-5532	195	9	this	this	PRON
cana-5532	195	10	proves	prove	VERB
cana-5532	195	11	that	that	SCONJ
cana-5532	195	12	𝐵	𝐵	NOUN
cana-5532	195	13	is	be	AUX
cana-5532	195	14	uniformly	uniformly	ADV
cana-5532	195	15	bounded	bound	VERB
cana-5532	195	16	in	in	ADP
cana-5532	195	17	ω	ω	PROPN
cana-5532	195	18	.	.	PUNCT
cana-5532	196	1	next	next	ADV
cana-5532	196	2	we	we	PRON
cana-5532	196	3	show	show	VERB
cana-5532	196	4	that	that	SCONJ
cana-5532	196	5	𝐵	𝐵	NOUN
cana-5532	196	6	is	be	AUX
cana-5532	196	7	continuous	continuous	ADJ
cana-5532	196	8	on	on	ADP
cana-5532	196	9	ω	ω	PROPN
cana-5532	196	10	.	.	PUNCT
cana-5532	197	1	let	let	VERB
cana-5532	197	2	{	{	PUNCT
cana-5532	197	3	𝑢𝑛}𝑛∈ℕ	𝑢𝑛}𝑛∈ℕ	NOUN
cana-5532	197	4	be	be	AUX
cana-5532	197	5	a	a	DET
cana-5532	197	6	sequence	sequence	NOUN
cana-5532	197	7	in	in	ADP
cana-5532	197	8	ω	ω	NUM
cana-5532	197	9	converging	converge	VERB
cana-5532	197	10	to	to	ADP
cana-5532	197	11	a	a	DET
cana-5532	197	12	point	point	NOUN
cana-5532	197	13	𝑢	𝑢	X
cana-5532	197	14	∈	∈	PROPN
cana-5532	197	15	ω.then	ω.then	VERB
cana-5532	197	16	by	by	ADP
cana-5532	197	17	(	(	PUNCT
cana-5532	197	18	h2)-(h4	h2)-(h4	PROPN
cana-5532	197	19	)	)	PUNCT
cana-5532	197	20	,	,	PUNCT
cana-5532	197	21	for	for	ADP
cana-5532	197	22	all	all	PRON
cana-5532	197	23	𝑡	𝑡	ADP
cana-5532	197	24	∈	∈	PROPN
cana-5532	197	25	𝐼	𝐼	PROPN
cana-5532	197	26	,	,	PUNCT
cana-5532	197	27	one	one	PRON
cana-5532	197	28	has	have	VERB
cana-5532	197	29	∣	∣	PROPN
cana-5532	197	30	𝐵𝑢𝑛(𝑡	𝐵𝑢𝑛(𝑡	PROPN
cana-5532	197	31	)	)	PUNCT
cana-5532	198	1	−	−	ADP
cana-5532	198	2	𝐵𝑢(𝑡	𝐵𝑢(𝑡	NOUN
cana-5532	198	3	)	)	PUNCT
cana-5532	198	4	∣≤	∣≤	NUM
cana-5532	198	5	∫	∫	PROPN
cana-5532	198	6	∣𝑡−𝜏∣𝛼−1	∣𝑡−𝜏∣𝛼−1	PROPN
cana-5532	198	7	γ(𝛼	γ(𝛼	PROPN
cana-5532	198	8	)	)	PUNCT
cana-5532	198	9	𝑡	𝑡	X
cana-5532	198	10	0	0	PUNCT
cana-5532	199	1	[	[	X
cana-5532	199	2	∣	∣	ADJ
cana-5532	199	3	𝑔(𝜏	𝑔(𝜏	PROPN
cana-5532	199	4	,	,	PUNCT
cana-5532	199	5	𝑢𝑛	𝑢𝑛	NOUN
cana-5532	199	6	,	,	PUNCT
cana-5532	199	7	𝐼0	𝐼0	PROPN
cana-5532	199	8	+	+	NUM
cana-5532	199	9	𝜇1𝑢𝑛(𝜏	𝜇1𝑢𝑛(𝜏	NOUN
cana-5532	199	10	)	)	PUNCT
cana-5532	199	11	,	,	PUNCT
cana-5532	199	12	𝐼0	𝐼0	PROPN
cana-5532	199	13	+	+	NUM
cana-5532	199	14	𝜇2𝑢𝑛(𝜏	𝜇2𝑢𝑛(𝜏	PROPN
cana-5532	199	15	)	)	PUNCT
cana-5532	199	16	,	,	PUNCT
cana-5532	199	17	.	.	PUNCT
cana-5532	199	18	.	.	PUNCT
cana-5532	200	1	.	.	PUNCT
cana-5532	201	1	,	,	PUNCT
cana-5532	201	2	𝐼0	𝐼0	PROPN
cana-5532	201	3	+	+	NUM
cana-5532	201	4	𝜇𝑛𝑢𝑛(𝜏	𝜇𝑛𝑢𝑛(𝜏	NOUN
cana-5532	201	5	)	)	PUNCT
cana-5532	201	6	)	)	PUNCT
cana-5532	202	1	−𝑔(𝜏	−𝑔(𝜏	PROPN
cana-5532	202	2	,	,	PUNCT
cana-5532	202	3	𝑢(𝜏	𝑢(𝜏	PROPN
cana-5532	202	4	)	)	PUNCT
cana-5532	202	5	,	,	PUNCT
cana-5532	202	6	𝐼	𝐼	ADP
cana-5532	202	7	0	0	NUM
cana-5532	202	8	+	+	NUM
cana-5532	202	9	𝜇1𝑢(𝜏	𝜇1𝑢(𝜏	PROPN
cana-5532	202	10	)	)	PUNCT
cana-5532	202	11	,	,	PUNCT
cana-5532	202	12	𝐼	𝐼	PROPN
cana-5532	202	13	0	0	NUM
cana-5532	202	14	+	+	NOUN
cana-5532	202	15	𝜇2𝑢(𝜏	𝜇2𝑢(𝜏	PROPN
cana-5532	202	16	)	)	PUNCT
cana-5532	202	17	,	,	PUNCT
cana-5532	202	18	…	…	PUNCT
cana-5532	202	19	,	,	PUNCT
cana-5532	202	20	𝐼	𝐼	ADP
cana-5532	202	21	0	0	NUM
cana-5532	202	22	+	+	NUM
cana-5532	202	23	𝜇𝑛𝑢(𝜏	𝜇𝑛𝑢(𝜏	PROPN
cana-5532	202	24	)	)	PUNCT
cana-5532	202	25	)	)	PUNCT
cana-5532	203	1	∣	∣	PROPN
cana-5532	203	2	+	+	PROPN
cana-5532	203	3	∫	∫	PROPN
cana-5532	203	4	∣	∣	ADJ
cana-5532	203	5	𝜏	𝜏	PROPN
cana-5532	203	6	0	0	NUM
cana-5532	203	7	𝐾(𝜏	𝐾(𝜏	ADJ
cana-5532	203	8	,	,	PUNCT
cana-5532	203	9	𝑠	𝑠	NOUN
cana-5532	203	10	,	,	PUNCT
cana-5532	203	11	𝑢𝑛(𝑠	𝑢𝑛(𝑠	PROPN
cana-5532	203	12	)	)	PUNCT
cana-5532	204	1	−	−	PROPN
cana-5532	205	1	𝐾(𝜏	𝐾(𝜏	ADP
cana-5532	205	2	,	,	PUNCT
cana-5532	205	3	𝑠	𝑠	PROPN
cana-5532	205	4	,	,	PUNCT
cana-5532	205	5	𝑢(𝑠	𝑢(𝑠	NOUN
cana-5532	205	6	)	)	PUNCT
cana-5532	205	7	∣	∣	ADJ
cana-5532	205	8	𝑑𝑠]𝑑𝜏	𝑑𝑠]𝑑𝜏	NOUN
cana-5532	206	1	+	+	CCONJ
cana-5532	206	2	𝑏γ(3−𝛼)𝑡	𝑏γ(3−𝛼)𝑡	PROPN
cana-5532	206	3	𝑎γ(3−𝛼)+𝑏	𝑎γ(3−𝛼)+𝑏	PROPN
cana-5532	206	4	∫	∫	PROPN
cana-5532	206	5	[	[	PUNCT
cana-5532	206	6	1	1	NUM
cana-5532	206	7	0	0	NUM
cana-5532	206	8	∣	∣	PROPN
cana-5532	206	9	𝑔(𝜏	𝑔(𝜏	PROPN
cana-5532	206	10	,	,	PUNCT
cana-5532	206	11	𝑢𝑛	𝑢𝑛	NOUN
cana-5532	206	12	,	,	PUNCT
cana-5532	206	13	𝐼0	𝐼0	PROPN
cana-5532	206	14	+	+	NUM
cana-5532	206	15	𝜇1𝑢𝑛(𝜏	𝜇1𝑢𝑛(𝜏	NOUN
cana-5532	206	16	)	)	PUNCT
cana-5532	206	17	,	,	PUNCT
cana-5532	206	18	𝐼0	𝐼0	PROPN
cana-5532	206	19	+	+	NUM
cana-5532	206	20	𝜇2𝑢𝑛(𝜏	𝜇2𝑢𝑛(𝜏	PROPN
cana-5532	206	21	)	)	PUNCT
cana-5532	206	22	,	,	PUNCT
cana-5532	206	23	.	.	PUNCT
cana-5532	206	24	.	.	PUNCT
cana-5532	207	1	.	.	PUNCT
cana-5532	208	1	,	,	PUNCT
cana-5532	208	2	𝐼0	𝐼0	PROPN
cana-5532	208	3	+	+	NUM
cana-5532	208	4	𝜇𝑛𝑢𝑛(𝜏	𝜇𝑛𝑢𝑛(𝜏	NOUN
cana-5532	208	5	)	)	PUNCT
cana-5532	208	6	)	)	PUNCT
cana-5532	209	1	−𝑔(𝜏	−𝑔(𝜏	PROPN
cana-5532	209	2	,	,	PUNCT
cana-5532	209	3	𝑢(𝜏	𝑢(𝜏	PROPN
cana-5532	209	4	)	)	PUNCT
cana-5532	209	5	,	,	PUNCT
cana-5532	209	6	𝐼	𝐼	ADP
cana-5532	209	7	0	0	NUM
cana-5532	209	8	+	+	NUM
cana-5532	209	9	𝜇1𝑢(𝜏	𝜇1𝑢(𝜏	PROPN
cana-5532	209	10	)	)	PUNCT
cana-5532	209	11	,	,	PUNCT
cana-5532	209	12	𝐼	𝐼	PROPN
cana-5532	209	13	0	0	NUM
cana-5532	209	14	+	+	NOUN
cana-5532	209	15	𝜇2𝑢(𝜏	𝜇2𝑢(𝜏	PROPN
cana-5532	209	16	)	)	PUNCT
cana-5532	209	17	,	,	PUNCT
cana-5532	209	18	…	…	PUNCT
cana-5532	209	19	,	,	PUNCT
cana-5532	209	20	𝐼	𝐼	ADP
cana-5532	209	21	0	0	NUM
cana-5532	209	22	+	+	NUM
cana-5532	209	23	𝜇𝑛𝑢(𝜏	𝜇𝑛𝑢(𝜏	PROPN
cana-5532	209	24	)	)	PUNCT
cana-5532	209	25	)	)	PUNCT
cana-5532	210	1	∣	∣	PROPN
cana-5532	210	2	+	+	PROPN
cana-5532	210	3	∫	∫	PROPN
cana-5532	210	4	∣	∣	ADJ
cana-5532	210	5	𝜏	𝜏	PROPN
cana-5532	210	6	0	0	NUM
cana-5532	210	7	𝐾(𝜏	𝐾(𝜏	ADJ
cana-5532	210	8	,	,	PUNCT
cana-5532	210	9	𝑠	𝑠	PROPN
cana-5532	210	10	,	,	PUNCT
cana-5532	210	11	𝑢𝑛	𝑢𝑛	PROPN
cana-5532	210	12	(	(	PUNCT
cana-5532	210	13	𝑠	𝑠	NOUN
cana-5532	210	14	)	)	PUNCT
cana-5532	210	15	−	−	PROPN
cana-5532	211	1	𝐾(𝜏	𝐾(𝜏	ADP
cana-5532	211	2	,	,	PUNCT
cana-5532	211	3	𝑠	𝑠	PROPN
cana-5532	211	4	,	,	PUNCT
cana-5532	211	5	𝑢(𝑠	𝑢(𝑠	NOUN
cana-5532	211	6	)	)	PUNCT
cana-5532	211	7	∣	∣	ADJ
cana-5532	211	8	𝑑𝑠]𝑑𝜏	𝑑𝑠]𝑑𝜏	NOUN
cana-5532	212	1	+	+	X
cana-5532	212	2	|	|	NOUN
cana-5532	212	3	ℎ(𝑢𝑛	ℎ(𝑢𝑛	NOUN
cana-5532	212	4	)	)	PUNCT
cana-5532	212	5	𝑓(0,ℎ(𝑢𝑛	𝑓(0,ℎ(𝑢𝑛	NOUN
cana-5532	212	6	)	)	PUNCT
cana-5532	212	7	)	)	PUNCT
cana-5532	213	1	−	−	ADP
cana-5532	213	2	ℎ(𝑢𝑛	ℎ(𝑢𝑛	NOUN
cana-5532	213	3	)	)	PUNCT
cana-5532	213	4	𝑓(0,ℎ(𝑢𝑛	𝑓(0,ℎ(𝑢𝑛	NOUN
cana-5532	213	5	)	)	PUNCT
cana-5532	213	6	)	)	PUNCT
cana-5532	214	1	|	|	ADV
cana-5532	214	2	,	,	PUNCT
cana-5532	214	3	≤	≤	NOUN
cana-5532	214	4	1	1	NUM
cana-5532	214	5	γ(𝛼+1	γ(𝛼+1	PUNCT
cana-5532	214	6	)	)	PUNCT
cana-5532	215	1	[	[	X
cana-5532	215	2	𝜃∗	𝜃∗	X
cana-5532	215	3	(	(	PUNCT
cana-5532	215	4	1	1	NUM
cana-5532	215	5	+	+	SYM
cana-5532	215	6	1	1	NUM
cana-5532	215	7	γ(𝜇1	γ(𝜇1	NOUN
cana-5532	215	8	+	+	NOUN
cana-5532	215	9	1	1	NUM
cana-5532	215	10	)	)	PUNCT
cana-5532	215	11	+	+	CCONJ
cana-5532	215	12	1	1	NUM
cana-5532	215	13	γ(𝜇2	γ(𝜇2	NOUN
cana-5532	215	14	+	+	NOUN
cana-5532	215	15	1	1	NUM
cana-5532	215	16	)	)	PUNCT
cana-5532	215	17	+	+	PROPN
cana-5532	215	18	.	.	PUNCT
cana-5532	215	19	.	.	PUNCT
cana-5532	215	20	.	.	PUNCT
cana-5532	216	1	+	+	CCONJ
cana-5532	216	2	1	1	NUM
cana-5532	216	3	γ(𝜇𝑛+1	γ(𝜇𝑛+1	ADJ
cana-5532	216	4	)	)	PUNCT
cana-5532	216	5	)	)	PUNCT
cana-5532	217	1	∣	∣	PROPN
cana-5532	217	2	𝑢𝑛	𝑢𝑛	NOUN
cana-5532	217	3	−	−	PROPN
cana-5532	217	4	𝑢	𝑢	PART
cana-5532	217	5	∣	∣	ADJ
cana-5532	217	6	+	+	ADV
cana-5532	217	7	𝑘0	𝑘0	ADJ
cana-5532	217	8	∣	∣	ADJ
cana-5532	217	9	𝑢𝑛	𝑢𝑛	NOUN
cana-5532	217	10	−	−	PROPN
cana-5532	217	11	𝑢	𝑢	NOUN
cana-5532	217	12	∣	∣	NOUN
cana-5532	217	13	]	]	X
cana-5532	217	14	+	+	CCONJ
cana-5532	217	15	𝑏γ(3−𝛼	𝑏γ(3−𝛼	ADJ
cana-5532	217	16	)	)	PUNCT
cana-5532	217	17	𝑎γ(3−𝛼)+𝑏	𝑎γ(3−𝛼)+𝑏	PROPN
cana-5532	218	1	[	[	X
cana-5532	218	2	𝜃∗	𝜃∗	PROPN
cana-5532	218	3	(	(	PUNCT
cana-5532	218	4	1	1	NUM
cana-5532	218	5	+	+	SYM
cana-5532	218	6	1	1	NUM
cana-5532	218	7	γ(𝜇1	γ(𝜇1	NOUN
cana-5532	218	8	+	+	NOUN
cana-5532	218	9	1	1	NUM
cana-5532	218	10	)	)	PUNCT
cana-5532	218	11	+	+	CCONJ
cana-5532	218	12	1	1	NUM
cana-5532	218	13	γ(𝜇2	γ(𝜇2	NOUN
cana-5532	218	14	+	+	NOUN
cana-5532	218	15	1	1	NUM
cana-5532	218	16	)	)	PUNCT
cana-5532	218	17	+	+	PROPN
cana-5532	218	18	.	.	PUNCT
cana-5532	218	19	.	.	PUNCT
cana-5532	218	20	.	.	PUNCT
cana-5532	219	1	+	+	CCONJ
cana-5532	219	2	1	1	NUM
cana-5532	219	3	γ(𝜇𝑛+1	γ(𝜇𝑛+1	ADJ
cana-5532	219	4	)	)	PUNCT
cana-5532	219	5	)	)	PUNCT
cana-5532	220	1	∣	∣	PROPN
cana-5532	220	2	𝑢𝑛	𝑢𝑛	NOUN
cana-5532	220	3	−	−	PROPN
cana-5532	220	4	𝑢	𝑢	PART
cana-5532	220	5	∣	∣	ADJ
cana-5532	220	6	+	+	ADV
cana-5532	220	7	𝑘0	𝑘0	ADJ
cana-5532	220	8	∣	∣	ADJ
cana-5532	220	9	𝑢𝑛	𝑢𝑛	NOUN
cana-5532	220	10	−	−	PROPN
cana-5532	220	11	𝑢	𝑢	NOUN
cana-5532	220	12	∣	∣	NOUN
cana-5532	220	13	]	]	X
cana-5532	221	1	+	+	ADJ
cana-5532	221	2	|	|	NOUN
cana-5532	221	3	ℎ(𝑢𝑛	ℎ(𝑢𝑛	NOUN
cana-5532	221	4	)	)	PUNCT
cana-5532	221	5	𝑓(0,ℎ(𝑢𝑛	𝑓(0,ℎ(𝑢𝑛	NOUN
cana-5532	221	6	)	)	PUNCT
cana-5532	221	7	)	)	PUNCT
cana-5532	222	1	−	−	ADP
cana-5532	222	2	ℎ(𝑢𝑛	ℎ(𝑢𝑛	NOUN
cana-5532	222	3	)	)	PUNCT
cana-5532	222	4	𝑓(0,ℎ(𝑢𝑛	𝑓(0,ℎ(𝑢𝑛	NOUN
cana-5532	222	5	)	)	PUNCT
cana-5532	222	6	)	)	PUNCT
cana-5532	223	1	|	|	ADV
cana-5532	223	2	,	,	PUNCT
cana-5532	223	3	≤	≤	X
cana-5532	223	4	[	[	PUNCT
cana-5532	223	5	1	1	NUM
cana-5532	223	6	γ(𝛼+1	γ(𝛼+1	PRON
cana-5532	223	7	)	)	PUNCT
cana-5532	224	1	+	+	PUNCT
cana-5532	224	2	𝑏γ(3−𝛼	𝑏γ(3−𝛼	ADJ
cana-5532	224	3	)	)	PUNCT
cana-5532	224	4	𝑎γ(3−𝛼)+𝑏	𝑎γ(3−𝛼)+𝑏	NOUN
cana-5532	224	5	]	]	PUNCT
cana-5532	225	1	[	[	X
cana-5532	225	2	𝜃∗𝜉	𝜃∗𝜉	NUM
cana-5532	225	3	+	+	NUM
cana-5532	225	4	𝑘0	𝑘0	PROPN
cana-5532	225	5	]	]	X
cana-5532	225	6	∥	∥	PUNCT
cana-5532	225	7	𝑢𝑛	𝑢𝑛	NOUN
cana-5532	225	8	−	−	PROPN
cana-5532	225	9	𝑢	𝑢	PROPN
cana-5532	225	10	∥𝐸	∥𝐸	NOUN
cana-5532	226	1	+	+	NOUN
cana-5532	226	2	|	|	NOUN
cana-5532	226	3	ℎ(𝑢𝑛	ℎ(𝑢𝑛	NOUN
cana-5532	226	4	)	)	PUNCT
cana-5532	226	5	𝑓(0,ℎ(𝑢𝑛	𝑓(0,ℎ(𝑢𝑛	NOUN
cana-5532	226	6	)	)	PUNCT
cana-5532	226	7	)	)	PUNCT
cana-5532	227	1	−	−	ADP
cana-5532	227	2	ℎ(𝑢𝑛	ℎ(𝑢𝑛	NOUN
cana-5532	227	3	)	)	PUNCT
cana-5532	227	4	𝑓(0,ℎ(𝑢𝑛	𝑓(0,ℎ(𝑢𝑛	NOUN
cana-5532	227	5	)	)	PUNCT
cana-5532	227	6	)	)	PUNCT
cana-5532	228	1	|	|	ADV
cana-5532	228	2	,	,	PUNCT
cana-5532	228	3	since	since	SCONJ
cana-5532	228	4	that	that	DET
cana-5532	228	5	functions	function	NOUN
cana-5532	228	6	ℎ	ℎ	NOUN
cana-5532	228	7	and	and	CCONJ
cana-5532	228	8	𝑓	𝑓	PRON
cana-5532	228	9	are	be	AUX
cana-5532	228	10	continuous	continuous	ADJ
cana-5532	228	11	,	,	PUNCT
cana-5532	228	12	we	we	PRON
cana-5532	228	13	deduce	deduce	VERB
cana-5532	228	14	communications	communication	NOUN
cana-5532	228	15	on	on	ADP
cana-5532	228	16	applied	apply	VERB
cana-5532	228	17	nonlinear	nonlinear	ADJ
cana-5532	228	18	analysis	analysis	NOUN
cana-5532	228	19	issn	issn	NOUN
cana-5532	228	20	:	:	PUNCT
cana-5532	228	21	1074	1074	NUM
cana-5532	228	22	-	-	PUNCT
cana-5532	228	23	133x	133x	NUM
cana-5532	228	24	vol	vol	NOUN
cana-5532	228	25	32	32	NUM
cana-5532	228	26	no	no	NOUN
cana-5532	228	27	.	.	NOUN
cana-5532	228	28	3	3	NUM
cana-5532	228	29	(	(	PUNCT
cana-5532	228	30	2025	2025	NUM
cana-5532	228	31	)	)	PUNCT
cana-5532	228	32	991	991	NUM
cana-5532	229	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5532	229	2	∥	∥	PUNCT
cana-5532	230	1	𝐵𝑢𝑛	𝐵𝑢𝑛	PROPN
cana-5532	230	2	−	−	PUNCT
cana-5532	230	3	𝐵𝑢	𝐵𝑢	PROPN
cana-5532	230	4	∥𝐸→	∥𝐸→	NOUN
cana-5532	230	5	0	0	NUM
cana-5532	230	6	𝑎𝑠	𝑎𝑠	PROPN
cana-5532	230	7	𝑛	𝑛	PROPN
cana-5532	230	8	→	→	SYM
cana-5532	230	9	∞.	∞.	PROPN
cana-5532	230	10	then	then	ADV
cana-5532	230	11	𝐵	𝐵	PROPN
cana-5532	230	12	is	be	AUX
cana-5532	230	13	continuous	continuous	ADJ
cana-5532	230	14	.	.	PUNCT
cana-5532	231	1	next	next	ADV
cana-5532	231	2	we	we	PRON
cana-5532	231	3	prove	prove	VERB
cana-5532	231	4	that	that	SCONJ
cana-5532	231	5	the	the	DET
cana-5532	231	6	operator𝐵	operator𝐵	PROPN
cana-5532	231	7	equicontinuous	equicontinuous	ADJ
cana-5532	231	8	.	.	PUNCT
cana-5532	232	1	let	let	VERB
cana-5532	232	2	𝑢	𝑢	PRON
cana-5532	232	3	∈	∈	PROPN
cana-5532	232	4	ω	ω	PROPN
cana-5532	232	5	and	and	CCONJ
cana-5532	232	6	𝑡1	𝑡1	NOUN
cana-5532	232	7	,	,	PUNCT
cana-5532	232	8	𝑡2	𝑡2	NOUN
cana-5532	232	9	∈	∈	PROPN
cana-5532	232	10	𝐼	𝐼	PROPN
cana-5532	232	11	with	with	ADP
cana-5532	232	12	𝑡1	𝑡1	NOUN
cana-5532	232	13	<	<	X
cana-5532	232	14	𝑡2	𝑡2	NOUN
cana-5532	232	15	then	then	ADV
cana-5532	232	16	we	we	PRON
cana-5532	232	17	have	have	VERB
cana-5532	232	18	∣	∣	ADJ
cana-5532	232	19	𝐵𝑢(𝑡2	𝐵𝑢(𝑡2	PROPN
cana-5532	232	20	)	)	PUNCT
cana-5532	232	21	−	−	PROPN
cana-5532	232	22	𝐵𝑢(𝑡1	𝐵𝑢(𝑡1	PROPN
cana-5532	232	23	)	)	PUNCT
cana-5532	232	24	∣≤	∣≤	PUNCT
cana-5532	233	1	|	|	ADV
cana-5532	233	2	∫	∫	PROPN
cana-5532	233	3	(	(	PUNCT
cana-5532	233	4	𝑡2−𝜏	𝑡2−𝜏	PROPN
cana-5532	233	5	)	)	PUNCT
cana-5532	233	6	𝛼−1	𝛼−1	PRON
cana-5532	233	7	γ(𝛼	γ(𝛼	ADJ
cana-5532	233	8	)	)	PUNCT
cana-5532	233	9	𝑡2	𝑡2	NOUN
cana-5532	233	10	0	0	PUNCT
cana-5532	234	1	[	[	X
cana-5532	234	2	𝑔(𝜏	𝑔(𝜏	PROPN
cana-5532	234	3	,	,	PUNCT
cana-5532	234	4	𝑢(𝜏	𝑢(𝜏	PROPN
cana-5532	234	5	)	)	PUNCT
cana-5532	234	6	,	,	PUNCT
cana-5532	234	7	𝐼	𝐼	ADP
cana-5532	234	8	0	0	NUM
cana-5532	234	9	+	+	NUM
cana-5532	234	10	𝜇1𝑢(𝜏	𝜇1𝑢(𝜏	PROPN
cana-5532	234	11	)	)	PUNCT
cana-5532	234	12	,	,	PUNCT
cana-5532	234	13	𝐼	𝐼	PROPN
cana-5532	234	14	0	0	NUM
cana-5532	234	15	+	+	NOUN
cana-5532	234	16	𝜇2𝑢(𝜏	𝜇2𝑢(𝜏	PROPN
cana-5532	234	17	)	)	PUNCT
cana-5532	234	18	,	,	PUNCT
cana-5532	234	19	.	.	PUNCT
cana-5532	234	20	.	.	PUNCT
cana-5532	235	1	.	.	PUNCT
cana-5532	236	1	,	,	PUNCT
cana-5532	236	2	𝐼	𝐼	ADP
cana-5532	236	3	0	0	NUM
cana-5532	236	4	+	+	NUM
cana-5532	236	5	𝜇𝑛𝑢(𝜏	𝜇𝑛𝑢(𝜏	PROPN
cana-5532	236	6	)	)	PUNCT
cana-5532	236	7	)	)	PUNCT
cana-5532	237	1	+	+	CCONJ
cana-5532	237	2	∫	∫	AUX
cana-5532	237	3	𝐾	𝐾	NOUN
cana-5532	237	4	𝜏	𝜏	PROPN
cana-5532	237	5	0	0	NUM
cana-5532	237	6	(	(	PUNCT
cana-5532	237	7	𝜏	𝜏	NOUN
cana-5532	237	8	,	,	PUNCT
cana-5532	237	9	𝑠	𝑠	PROPN
cana-5532	237	10	,	,	PUNCT
cana-5532	237	11	𝑢(𝑠)𝑑𝑠]𝑑𝜏	𝑢(𝑠)𝑑𝑠]𝑑𝜏	NOUN
cana-5532	237	12	+	+	CCONJ
cana-5532	237	13	𝑏γ(3−𝛼)𝑡2	𝑏γ(3−𝛼)𝑡2	PROPN
cana-5532	237	14	𝑎γ(3−𝛼)+𝑏	𝑎γ(3−𝛼)+𝑏	PROPN
cana-5532	237	15	∫	∫	PROPN
cana-5532	238	1	[	[	X
cana-5532	238	2	𝑔(𝜏	𝑔(𝜏	PROPN
cana-5532	238	3	,	,	PUNCT
cana-5532	238	4	𝑢(𝜏	𝑢(𝜏	PROPN
cana-5532	238	5	)	)	PUNCT
cana-5532	238	6	,	,	PUNCT
cana-5532	238	7	𝐼0	𝐼0	PROPN
cana-5532	238	8	+	+	ADJ
cana-5532	238	9	𝜇1𝑢(𝜏	𝜇1𝑢(𝜏	PROPN
cana-5532	238	10	)	)	PUNCT
cana-5532	238	11	,	,	PUNCT
cana-5532	238	12	𝐼	𝐼	PROPN
cana-5532	238	13	0	0	NUM
cana-5532	238	14	+	+	NOUN
cana-5532	238	15	𝜇2𝑢(𝜏	𝜇2𝑢(𝜏	PROPN
cana-5532	238	16	)	)	PUNCT
cana-5532	238	17	,	,	PUNCT
cana-5532	238	18	.	.	PUNCT
cana-5532	238	19	.	.	PUNCT
cana-5532	239	1	.	.	PUNCT
cana-5532	240	1	,	,	PUNCT
cana-5532	240	2	𝐼	𝐼	ADP
cana-5532	240	3	0	0	NUM
cana-5532	240	4	+	+	NUM
cana-5532	240	5	𝜇𝑛𝑢(𝜏	𝜇𝑛𝑢(𝜏	PROPN
cana-5532	240	6	)	)	PUNCT
cana-5532	240	7	)	)	PUNCT
cana-5532	241	1	+	+	CCONJ
cana-5532	241	2	∫	∫	X
cana-5532	241	3	𝐾	𝐾	NOUN
cana-5532	241	4	𝜏	𝜏	PROPN
cana-5532	241	5	0	0	NUM
cana-5532	241	6	(	(	PUNCT
cana-5532	241	7	𝜏	𝜏	NOUN
cana-5532	241	8	,	,	PUNCT
cana-5532	241	9	𝑠	𝑠	PROPN
cana-5532	241	10	,	,	PUNCT
cana-5532	241	11	𝑢(𝑠)𝑑𝑠	𝑢(𝑠)𝑑𝑠	PROPN
cana-5532	241	12	]	]	X
cana-5532	241	13	1	1	NUM
cana-5532	241	14	0	0	NUM
cana-5532	241	15	𝑑𝜏	𝑑𝜏	PRON
cana-5532	241	16	−∫	−∫	X
cana-5532	241	17	(	(	PUNCT
cana-5532	241	18	𝑡1−𝜏	𝑡1−𝜏	PROPN
cana-5532	241	19	)	)	PUNCT
cana-5532	241	20	𝛼−1	𝛼−1	DET
cana-5532	241	21	γ(𝛼	γ(𝛼	ADJ
cana-5532	241	22	)	)	PUNCT
cana-5532	241	23	𝑡1	𝑡1	NOUN
cana-5532	241	24	0	0	NUM
cana-5532	242	1	[	[	X
cana-5532	242	2	𝑔(𝜏	𝑔(𝜏	PROPN
cana-5532	242	3	,	,	PUNCT
cana-5532	242	4	𝑢(𝜏	𝑢(𝜏	PROPN
cana-5532	242	5	)	)	PUNCT
cana-5532	242	6	,	,	PUNCT
cana-5532	242	7	𝐼	𝐼	ADP
cana-5532	242	8	0	0	NUM
cana-5532	242	9	+	+	NUM
cana-5532	242	10	𝜇1𝑢(𝜏	𝜇1𝑢(𝜏	PROPN
cana-5532	242	11	)	)	PUNCT
cana-5532	242	12	,	,	PUNCT
cana-5532	242	13	𝐼	𝐼	PROPN
cana-5532	242	14	0	0	NUM
cana-5532	242	15	+	+	NOUN
cana-5532	242	16	𝜇2𝑢(𝜏	𝜇2𝑢(𝜏	PROPN
cana-5532	242	17	)	)	PUNCT
cana-5532	242	18	,	,	PUNCT
cana-5532	242	19	.	.	PUNCT
cana-5532	242	20	.	.	PUNCT
cana-5532	243	1	.	.	PUNCT
cana-5532	244	1	,	,	PUNCT
cana-5532	244	2	𝐼	𝐼	ADP
cana-5532	244	3	0	0	NUM
cana-5532	244	4	+	+	NUM
cana-5532	244	5	𝜇𝑛𝑢(𝜏	𝜇𝑛𝑢(𝜏	PROPN
cana-5532	244	6	)	)	PUNCT
cana-5532	244	7	)	)	PUNCT
cana-5532	245	1	+	+	CCONJ
cana-5532	245	2	∫	∫	PROPN
cana-5532	245	3	∣	∣	VERB
cana-5532	245	4	𝜏	𝜏	PROPN
cana-5532	245	5	0	0	NUM
cana-5532	245	6	𝐾(𝜏	𝐾(𝜏	ADJ
cana-5532	245	7	,	,	PUNCT
cana-5532	245	8	𝑠	𝑠	PROPN
cana-5532	245	9	,	,	PUNCT
cana-5532	245	10	𝑢(𝑠)𝑑𝑠]𝑑𝜏	𝑢(𝑠)𝑑𝑠]𝑑𝜏	NOUN
cana-5532	245	11	+	+	CCONJ
cana-5532	245	12	𝑏γ(3−𝛼)𝑡1	𝑏γ(3−𝛼)𝑡1	PROPN
cana-5532	245	13	𝑎γ(3−𝛼)+𝑏	𝑎γ(3−𝛼)+𝑏	PROPN
cana-5532	245	14	∫	∫	PROPN
cana-5532	246	1	[	[	X
cana-5532	246	2	𝑔(𝜏	𝑔(𝜏	PROPN
cana-5532	246	3	,	,	PUNCT
cana-5532	246	4	𝑢(𝜏	𝑢(𝜏	PROPN
cana-5532	246	5	)	)	PUNCT
cana-5532	246	6	,	,	PUNCT
cana-5532	246	7	𝐼0	𝐼0	PROPN
cana-5532	246	8	+	+	ADJ
cana-5532	246	9	𝜇1𝑢(𝜏	𝜇1𝑢(𝜏	PROPN
cana-5532	246	10	)	)	PUNCT
cana-5532	246	11	,	,	PUNCT
cana-5532	246	12	𝐼	𝐼	PROPN
cana-5532	246	13	0	0	NUM
cana-5532	246	14	+	+	NOUN
cana-5532	246	15	𝜇2𝑢(𝜏	𝜇2𝑢(𝜏	PROPN
cana-5532	246	16	)	)	PUNCT
cana-5532	246	17	,	,	PUNCT
cana-5532	246	18	.	.	PUNCT
cana-5532	246	19	.	.	PUNCT
cana-5532	247	1	.	.	PUNCT
cana-5532	248	1	,	,	PUNCT
cana-5532	248	2	𝐼	𝐼	ADP
cana-5532	248	3	0	0	NUM
cana-5532	248	4	+	+	NUM
cana-5532	248	5	𝜇𝑛𝑢(𝜏	𝜇𝑛𝑢(𝜏	PROPN
cana-5532	248	6	)	)	PUNCT
cana-5532	248	7	)	)	PUNCT
cana-5532	249	1	+	+	CCONJ
cana-5532	249	2	∫	∫	X
cana-5532	249	3	𝐾	𝐾	NOUN
cana-5532	249	4	𝜏	𝜏	PROPN
cana-5532	249	5	0	0	NUM
cana-5532	249	6	(	(	PUNCT
cana-5532	249	7	𝜏	𝜏	NOUN
cana-5532	249	8	,	,	PUNCT
cana-5532	249	9	𝑠	𝑠	PROPN
cana-5532	249	10	,	,	PUNCT
cana-5532	249	11	𝑢(𝑠)𝑑𝑠	𝑢(𝑠)𝑑𝑠	PROPN
cana-5532	249	12	]	]	X
cana-5532	249	13	1	1	NUM
cana-5532	249	14	0	0	NUM
cana-5532	249	15	𝑑𝜏|	𝑑𝜏|	PROPN
cana-5532	249	16	≤	≤	PROPN
cana-5532	249	17	∫	∫	PROPN
cana-5532	249	18	|	|	ADV
cana-5532	249	19	𝑡1	𝑡1	NOUN
cana-5532	249	20	0	0	PUNCT
cana-5532	249	21	(	(	PUNCT
cana-5532	249	22	𝑡2−𝜏	𝑡2−𝜏	PROPN
cana-5532	249	23	)	)	PUNCT
cana-5532	249	24	𝛼−1−(𝑡1−𝜏	𝛼−1−(𝑡1−𝜏	AUX
cana-5532	249	25	)	)	PUNCT
cana-5532	249	26	𝛼−1	𝛼−1	DET
cana-5532	249	27	γ(𝛼	γ(𝛼	ADJ
cana-5532	249	28	)	)	PUNCT
cana-5532	249	29	|	|	ADV
cana-5532	249	30	[	[	PUNCT
cana-5532	249	31	|𝑔(𝜏	|𝑔(𝜏	PROPN
cana-5532	249	32	,	,	PUNCT
cana-5532	249	33	𝑢(𝜏	𝑢(𝜏	PROPN
cana-5532	249	34	)	)	PUNCT
cana-5532	249	35	,	,	PUNCT
cana-5532	249	36	𝐼	𝐼	ADP
cana-5532	249	37	0	0	NUM
cana-5532	249	38	+	+	NUM
cana-5532	249	39	𝜇1𝑢(𝜏	𝜇1𝑢(𝜏	PROPN
cana-5532	249	40	)	)	PUNCT
cana-5532	249	41	,	,	PUNCT
cana-5532	249	42	𝐼	𝐼	PROPN
cana-5532	249	43	0	0	NUM
cana-5532	249	44	+	+	NOUN
cana-5532	249	45	𝜇2𝑢(𝜏	𝜇2𝑢(𝜏	PROPN
cana-5532	249	46	)	)	PUNCT
cana-5532	249	47	,	,	PUNCT
cana-5532	249	48	.	.	PUNCT
cana-5532	249	49	.	.	PUNCT
cana-5532	249	50	.	.	PUNCT
cana-5532	250	1	,	,	PUNCT
cana-5532	250	2	𝐼	𝐼	ADP
cana-5532	250	3	0	0	NUM
cana-5532	250	4	+	+	NUM
cana-5532	250	5	𝜇𝑛𝑢(𝜏	𝜇𝑛𝑢(𝜏	PROPN
cana-5532	250	6	)	)	PUNCT
cana-5532	250	7	)	)	PUNCT
cana-5532	251	1	+	+	CCONJ
cana-5532	252	1	∫	∫	X
cana-5532	252	2	𝐾	𝐾	NOUN
cana-5532	252	3	𝜏	𝜏	PROPN
cana-5532	252	4	0	0	NUM
cana-5532	252	5	(	(	PUNCT
cana-5532	252	6	𝜏	𝜏	NOUN
cana-5532	252	7	,	,	PUNCT
cana-5532	252	8	𝑠	𝑠	PROPN
cana-5532	252	9	,	,	PUNCT
cana-5532	252	10	𝑢(𝑠)𝑑𝑠|]𝑑𝜏	𝑢(𝑠)𝑑𝑠|]𝑑𝜏	NOUN
cana-5532	253	1	+	+	NOUN
cana-5532	253	2	∫	∫	PROPN
cana-5532	253	3	|	|	ADJ
cana-5532	253	4	𝑡2	𝑡2	PROPN
cana-5532	253	5	𝑡1	𝑡1	NOUN
cana-5532	253	6	(	(	PUNCT
cana-5532	253	7	𝑡2−𝜏	𝑡2−𝜏	PROPN
cana-5532	253	8	)	)	PUNCT
cana-5532	253	9	𝛼−1	𝛼−1	PRON
cana-5532	253	10	γ(𝛼	γ(𝛼	ADJ
cana-5532	253	11	)	)	PUNCT
cana-5532	253	12	|	|	ADV
cana-5532	253	13	[	[	PUNCT
cana-5532	253	14	|𝑔(𝜏	|𝑔(𝜏	PROPN
cana-5532	253	15	,	,	PUNCT
cana-5532	253	16	𝑢(𝜏	𝑢(𝜏	PROPN
cana-5532	253	17	)	)	PUNCT
cana-5532	253	18	,	,	PUNCT
cana-5532	253	19	𝐼	𝐼	ADP
cana-5532	253	20	0	0	NUM
cana-5532	253	21	+	+	NUM
cana-5532	253	22	𝜇1𝑢(𝜏	𝜇1𝑢(𝜏	PROPN
cana-5532	253	23	)	)	PUNCT
cana-5532	253	24	,	,	PUNCT
cana-5532	253	25	𝐼	𝐼	PROPN
cana-5532	253	26	0	0	NUM
cana-5532	253	27	+	+	NOUN
cana-5532	253	28	𝜇2𝑢(𝜏	𝜇2𝑢(𝜏	PROPN
cana-5532	253	29	)	)	PUNCT
cana-5532	253	30	,	,	PUNCT
cana-5532	253	31	.	.	PUNCT
cana-5532	253	32	.	.	PUNCT
cana-5532	253	33	.	.	PUNCT
cana-5532	254	1	,	,	PUNCT
cana-5532	254	2	𝐼	𝐼	ADP
cana-5532	254	3	0	0	NUM
cana-5532	254	4	+	+	NUM
cana-5532	254	5	𝜇𝑛𝑢(𝜏	𝜇𝑛𝑢(𝜏	PROPN
cana-5532	254	6	)	)	PUNCT
cana-5532	254	7	)	)	PUNCT
cana-5532	255	1	+	+	CCONJ
cana-5532	256	1	∫	∫	X
cana-5532	256	2	𝐾	𝐾	NOUN
cana-5532	256	3	𝜏	𝜏	PROPN
cana-5532	256	4	0	0	NUM
cana-5532	256	5	(	(	PUNCT
cana-5532	256	6	𝜏	𝜏	NOUN
cana-5532	256	7	,	,	PUNCT
cana-5532	256	8	𝑠	𝑠	PROPN
cana-5532	256	9	,	,	PUNCT
cana-5532	256	10	𝑢(𝑠)𝑑𝑠|]𝑑𝜏	𝑢(𝑠)𝑑𝑠|]𝑑𝜏	NOUN
cana-5532	256	11	+	+	CCONJ
cana-5532	256	12	𝑏γ(3−𝛼)∣𝑡2−𝑡1∣	𝑏γ(3−𝛼)∣𝑡2−𝑡1∣	PROPN
cana-5532	256	13	𝑎γ(3−𝛼)+𝑏	𝑎γ(3−𝛼)+𝑏	PROPN
cana-5532	256	14	∫	∫	PROPN
cana-5532	256	15	[	[	PUNCT
cana-5532	256	16	|	|	ADV
cana-5532	256	17	1	1	NUM
cana-5532	256	18	0	0	NUM
cana-5532	256	19	𝑔(𝜏	𝑔(𝜏	PROPN
cana-5532	256	20	,	,	PUNCT
cana-5532	256	21	𝑢(𝜏	𝑢(𝜏	PROPN
cana-5532	256	22	)	)	PUNCT
cana-5532	256	23	,	,	PUNCT
cana-5532	256	24	𝐼	𝐼	ADP
cana-5532	256	25	0	0	NUM
cana-5532	256	26	+	+	NUM
cana-5532	256	27	𝜇1𝑢(𝜏	𝜇1𝑢(𝜏	PROPN
cana-5532	256	28	)	)	PUNCT
cana-5532	256	29	,	,	PUNCT
cana-5532	256	30	𝐼	𝐼	PROPN
cana-5532	256	31	0	0	NUM
cana-5532	256	32	+	+	NOUN
cana-5532	256	33	𝜇2𝑢(𝜏	𝜇2𝑢(𝜏	PROPN
cana-5532	256	34	)	)	PUNCT
cana-5532	256	35	,	,	PUNCT
cana-5532	256	36	.	.	PUNCT
cana-5532	256	37	.	.	PUNCT
cana-5532	256	38	.	.	PUNCT
cana-5532	257	1	,	,	PUNCT
cana-5532	257	2	𝐼	𝐼	ADP
cana-5532	257	3	0	0	NUM
cana-5532	257	4	+	+	NUM
cana-5532	257	5	𝜇𝑛𝑢(𝜏))|	𝜇𝑛𝑢(𝜏))|	NOUN
cana-5532	258	1	+	+	CCONJ
cana-5532	258	2	∫	∫	PROPN
cana-5532	259	1	|	|	ADV
cana-5532	259	2	𝜏	𝜏	NOUN
cana-5532	259	3	0	0	PUNCT
cana-5532	260	1	𝐾(𝜏	𝐾(𝜏	ADJ
cana-5532	260	2	,	,	PUNCT
cana-5532	260	3	𝑠	𝑠	PROPN
cana-5532	260	4	,	,	PUNCT
cana-5532	260	5	𝑢(𝑠)𝑑𝑠|]𝑑𝜏	𝑢(𝑠)𝑑𝑠|]𝑑𝜏	NOUN
cana-5532	260	6	≤	≤	NOUN
cana-5532	260	7	[	[	PUNCT
cana-5532	260	8	𝜃∗𝜉𝑅+𝐺∗+𝑀1	𝜃∗𝜉𝑅+𝐺∗+𝑀1	NOUN
cana-5532	260	9	γ(𝛼+1	γ(𝛼+1	PUNCT
cana-5532	260	10	)	)	PUNCT
cana-5532	260	11	]	]	PUNCT
cana-5532	261	1	[	[	X
cana-5532	261	2	2	2	NUM
cana-5532	261	3	∣	∣	ADJ
cana-5532	261	4	𝑡2	𝑡2	NOUN
cana-5532	261	5	−	−	PROPN
cana-5532	261	6	𝑡1	𝑡1	PROPN
cana-5532	261	7	∣	∣	PROPN
cana-5532	261	8	𝛼+	𝛼+	VERB
cana-5532	261	9	𝑡2	𝑡2	PROPN
cana-5532	261	10	𝛼	𝛼	ADP
cana-5532	261	11	−	−	PROPN
cana-5532	261	12	𝑡1	𝑡1	NOUN
cana-5532	261	13	𝛼	𝛼	NOUN
cana-5532	261	14	]	]	X
cana-5532	261	15	+	+	CCONJ
cana-5532	261	16	𝑏γ(3−𝛼)∣𝑡2−𝑡1∣	𝑏γ(3−𝛼)∣𝑡2−𝑡1∣	PROPN
cana-5532	261	17	𝑎γ(3−𝛼)+𝑏	𝑎γ(3−𝛼)+𝑏	PROPN
cana-5532	261	18	[	[	X
cana-5532	261	19	𝜃∗𝜉𝑅	𝜃∗𝜉𝑅	X
cana-5532	261	20	+	+	X
cana-5532	261	21	𝐺∗	𝐺∗	NUM
cana-5532	261	22	+	+	NOUN
cana-5532	261	23	𝑀1	𝑀1	X
cana-5532	261	24	]	]	X
cana-5532	261	25	which	which	PRON
cana-5532	261	26	is	be	AUX
cana-5532	261	27	independent	independent	ADJ
cana-5532	261	28	of	of	ADP
cana-5532	261	29	𝑢	𝑢	PROPN
cana-5532	261	30	∈	∈	PROPN
cana-5532	261	31	ω	ω	PROPN
cana-5532	261	32	.	.	PUNCT
cana-5532	262	1	as	as	ADP
cana-5532	262	2	𝑡1	𝑡1	PROPN
cana-5532	262	3	→	→	SYM
cana-5532	262	4	𝑡2	𝑡2	PROPN
cana-5532	262	5	,	,	PUNCT
cana-5532	262	6	the	the	DET
cana-5532	262	7	right	right	ADJ
cana-5532	262	8	-	-	PUNCT
cana-5532	262	9	hand	hand	NOUN
cana-5532	262	10	side	side	NOUN
cana-5532	262	11	of	of	ADP
cana-5532	262	12	the	the	DET
cana-5532	262	13	above	above	ADJ
cana-5532	262	14	inequality	inequality	NOUN
cana-5532	262	15	tends	tend	VERB
cana-5532	262	16	to	to	ADP
cana-5532	262	17	zero	zero	NUM
cana-5532	262	18	.	.	PUNCT
cana-5532	263	1	therefore	therefore	ADV
cana-5532	263	2	,	,	PUNCT
cana-5532	263	3	it	it	PRON
cana-5532	263	4	follows	follow	VERB
cana-5532	263	5	from	from	ADP
cana-5532	263	6	the	the	DET
cana-5532	263	7	arzel´a	arzel´a	NOUN
cana-5532	263	8	-	-	PUNCT
cana-5532	263	9	ascoli	ascoli	NOUN
cana-5532	263	10	theorem	theorem	NOUN
cana-5532	263	11	that	that	SCONJ
cana-5532	263	12	𝐵	𝐵	NOUN
cana-5532	263	13	is	be	AUX
cana-5532	263	14	a	a	DET
cana-5532	263	15	completely	completely	ADV
cana-5532	263	16	continuous	continuous	ADJ
cana-5532	263	17	operator	operator	NOUN
cana-5532	263	18	on	on	ADP
cana-5532	263	19	ω	ω	PROPN
cana-5532	263	20	.	.	PUNCT
cana-5532	264	1	claim	claim	NOUN
cana-5532	264	2	3	3	NUM
cana-5532	264	3	now	now	ADV
cana-5532	264	4	we	we	PRON
cana-5532	264	5	show	show	VERB
cana-5532	264	6	that	that	SCONJ
cana-5532	264	7	the	the	DET
cana-5532	264	8	(	(	PUNCT
cana-5532	264	9	iii	iii	NOUN
cana-5532	264	10	)	)	PUNCT
cana-5532	264	11	hypothesis	hypothesis	NOUN
cana-5532	264	12	of	of	ADP
cana-5532	264	13	theorem	theorem	NOUN
cana-5532	264	14	4	4	NUM
cana-5532	264	15	is	be	AUX
cana-5532	264	16	satisfied	satisfied	ADJ
cana-5532	264	17	.	.	PUNCT
cana-5532	265	1	let	let	VERB
cana-5532	265	2	𝑢	𝑢	PRON
cana-5532	265	3	∈	∈	PROPN
cana-5532	265	4	𝐸	𝐸	PROPN
cana-5532	265	5	and	and	CCONJ
cana-5532	265	6	𝑣	𝑣	ADP
cana-5532	265	7	∈	∈	PROPN
cana-5532	265	8	ω	ω	NOUN
cana-5532	265	9	such	such	ADJ
cana-5532	265	10	that	that	SCONJ
cana-5532	265	11	𝑢	𝑢	X
cana-5532	265	12	=	=	X
cana-5532	265	13	𝐴𝑢𝐵𝑣	𝐴𝑢𝐵𝑣	PROPN
cana-5532	265	14	then	then	ADV
cana-5532	265	15	,	,	PUNCT
cana-5532	265	16	for	for	ADP
cana-5532	265	17	𝑡	𝑡	NOUN
cana-5532	265	18	∈	∈	PROPN
cana-5532	265	19	𝐼	𝐼	SCONJ
cana-5532	265	20	we	we	PRON
cana-5532	265	21	have	have	VERB
cana-5532	265	22	∣	∣	ADJ
cana-5532	265	23	𝑢(𝑡	𝑢(𝑡	NOUN
cana-5532	265	24	)	)	PUNCT
cana-5532	265	25	∣≤∣	∣≤∣	NOUN
cana-5532	266	1	𝐴𝑢(𝑡	𝐴𝑢(𝑡	X
cana-5532	266	2	)	)	PUNCT
cana-5532	266	3	∣∣	∣∣	NUM
cana-5532	266	4	𝐵𝑣(𝑡	𝐵𝑣(𝑡	NOUN
cana-5532	266	5	)	)	PUNCT
cana-5532	266	6	∣	∣	ADJ
cana-5532	266	7	≤∣	≤∣	NUM
cana-5532	266	8	𝑓(𝑡	𝑓(𝑡	NOUN
cana-5532	266	9	,	,	PUNCT
cana-5532	266	10	𝑢(𝑡	𝑢(𝑡	NOUN
cana-5532	266	11	)	)	PUNCT
cana-5532	266	12	)	)	PUNCT
cana-5532	266	13	∣	∣	PROPN
cana-5532	266	14	[	[	PUNCT
cana-5532	266	15	|	|	ADV
cana-5532	266	16	−	−	PROPN
cana-5532	266	17	∫	∫	PROPN
cana-5532	266	18	(	(	PUNCT
cana-5532	266	19	𝑡−𝜏)𝛼−1	𝑡−𝜏)𝛼−1	NOUN
cana-5532	266	20	γ(𝛼	γ(𝛼	ADV
cana-5532	266	21	)	)	PUNCT
cana-5532	266	22	𝑡	𝑡	NOUN
cana-5532	266	23	0	0	PUNCT
cana-5532	267	1	[	[	X
cana-5532	267	2	𝑔(𝜏	𝑔(𝜏	PROPN
cana-5532	267	3	,	,	PUNCT
cana-5532	267	4	𝐼	𝐼	PROPN
cana-5532	267	5	0	0	NUM
cana-5532	267	6	+	+	NOUN
cana-5532	267	7	𝜇1𝑢(𝜏	𝜇1𝑢(𝜏	PROPN
cana-5532	267	8	)	)	PUNCT
cana-5532	267	9	,	,	PUNCT
cana-5532	267	10	𝐼	𝐼	PROPN
cana-5532	267	11	0	0	NUM
cana-5532	267	12	+	+	NOUN
cana-5532	267	13	𝜇2𝑢(𝜏	𝜇2𝑢(𝜏	PROPN
cana-5532	267	14	)	)	PUNCT
cana-5532	267	15	,	,	PUNCT
cana-5532	267	16	.	.	PUNCT
cana-5532	267	17	.	.	PUNCT
cana-5532	268	1	.	.	PUNCT
cana-5532	269	1	,	,	PUNCT
cana-5532	269	2	𝐼	𝐼	ADP
cana-5532	269	3	0	0	NUM
cana-5532	269	4	+	+	NUM
cana-5532	269	5	𝜇𝑛𝑢(𝜏	𝜇𝑛𝑢(𝜏	PROPN
cana-5532	269	6	)	)	PUNCT
cana-5532	269	7	)	)	PUNCT
cana-5532	270	1	+	+	CCONJ
cana-5532	270	2	∫	∫	X
cana-5532	270	3	𝐾	𝐾	NOUN
cana-5532	270	4	𝜏	𝜏	PROPN
cana-5532	270	5	0	0	NUM
cana-5532	270	6	(	(	PUNCT
cana-5532	270	7	𝜏	𝜏	NOUN
cana-5532	270	8	,	,	PUNCT
cana-5532	270	9	𝑠	𝑠	PROPN
cana-5532	270	10	,	,	PUNCT
cana-5532	270	11	𝑢(𝑠)𝑑𝑠]𝑑𝜏	𝑢(𝑠)𝑑𝑠]𝑑𝜏	NOUN
cana-5532	270	12	+	+	CCONJ
cana-5532	271	1	𝑏γ(3−𝛼)𝑡	𝑏γ(3−𝛼)𝑡	PROPN
cana-5532	271	2	𝑎γ(3−𝛼)+𝑏	𝑎γ(3−𝛼)+𝑏	PROPN
cana-5532	271	3	∫	∫	PROPN
cana-5532	272	1	[	[	X
cana-5532	272	2	𝑔(𝜏	𝑔(𝜏	PROPN
cana-5532	272	3	,	,	PUNCT
cana-5532	272	4	𝐼0	𝐼0	PROPN
cana-5532	272	5	+	+	ADJ
cana-5532	272	6	𝜇1𝑢(𝜏	𝜇1𝑢(𝜏	PROPN
cana-5532	272	7	)	)	PUNCT
cana-5532	272	8	,	,	PUNCT
cana-5532	272	9	𝐼	𝐼	PROPN
cana-5532	272	10	0	0	NUM
cana-5532	272	11	+	+	NOUN
cana-5532	272	12	𝜇2𝑢(𝜏	𝜇2𝑢(𝜏	PROPN
cana-5532	272	13	)	)	PUNCT
cana-5532	272	14	,	,	PUNCT
cana-5532	272	15	.	.	PUNCT
cana-5532	272	16	.	.	PUNCT
cana-5532	273	1	.	.	PUNCT
cana-5532	274	1	,	,	PUNCT
cana-5532	274	2	𝐼	𝐼	ADP
cana-5532	274	3	0	0	NUM
cana-5532	274	4	+	+	NUM
cana-5532	274	5	𝜇𝑛𝑢(𝜏	𝜇𝑛𝑢(𝜏	PROPN
cana-5532	274	6	)	)	PUNCT
cana-5532	274	7	)	)	PUNCT
cana-5532	275	1	+	+	CCONJ
cana-5532	275	2	∫	∫	X
cana-5532	275	3	𝐾	𝐾	NOUN
cana-5532	275	4	𝜏	𝜏	PROPN
cana-5532	275	5	0	0	NUM
cana-5532	275	6	(	(	PUNCT
cana-5532	275	7	𝜏	𝜏	NOUN
cana-5532	275	8	,	,	PUNCT
cana-5532	275	9	𝑠	𝑠	PROPN
cana-5532	275	10	,	,	PUNCT
cana-5532	275	11	𝑢(𝑠)𝑑𝑠	𝑢(𝑠)𝑑𝑠	PROPN
cana-5532	275	12	]	]	X
cana-5532	275	13	1	1	NUM
cana-5532	275	14	0	0	NUM
cana-5532	275	15	𝑑𝜏	𝑑𝜏	NOUN
cana-5532	275	16	+	+	CCONJ
cana-5532	275	17	ℎ(𝑢	ℎ(𝑢	PROPN
cana-5532	275	18	)	)	PUNCT
cana-5532	275	19	𝑓(0,ℎ(𝑢	𝑓(0,ℎ(𝑢	NOUN
cana-5532	275	20	)	)	PUNCT
cana-5532	275	21	)	)	PUNCT
cana-5532	276	1	|	|	ADV
cana-5532	276	2	]	]	PUNCT
cana-5532	276	3	≤	≤	NOUN
cana-5532	277	1	[	[	X
cana-5532	277	2	∣	∣	ADJ
cana-5532	277	3	𝑓(𝑡	𝑓(𝑡	NOUN
cana-5532	277	4	,	,	PUNCT
cana-5532	277	5	𝑢(𝑡	𝑢(𝑡	NOUN
cana-5532	277	6	)	)	PUNCT
cana-5532	277	7	)	)	PUNCT
cana-5532	277	8	−	−	PROPN
cana-5532	278	1	𝑓(𝑡	𝑓(𝑡	PROPN
cana-5532	278	2	,	,	PUNCT
cana-5532	278	3	0	0	NUM
cana-5532	278	4	)	)	PUNCT
cana-5532	278	5	∣	∣	ADJ
cana-5532	278	6	+	+	PROPN
cana-5532	278	7	∣	∣	ADJ
cana-5532	278	8	𝑓(𝑡	𝑓(𝑡	NOUN
cana-5532	278	9	,	,	PUNCT
cana-5532	278	10	0	0	NUM
cana-5532	278	11	)	)	PUNCT
cana-5532	278	12	∣	∣	NOUN
cana-5532	278	13	]	]	X
cana-5532	278	14	(	(	PUNCT
cana-5532	278	15	[	[	PUNCT
cana-5532	278	16	1	1	NUM
cana-5532	278	17	γ(𝛼+1	γ(𝛼+1	PRON
cana-5532	278	18	)	)	PUNCT
cana-5532	278	19	+	+	PUNCT
cana-5532	278	20	𝑏γ(3−𝛼	𝑏γ(3−𝛼	ADJ
cana-5532	278	21	)	)	PUNCT
cana-5532	278	22	𝑎γ(3−𝛼)+𝑏	𝑎γ(3−𝛼)+𝑏	NOUN
cana-5532	278	23	]	]	PUNCT
cana-5532	279	1	[	[	X
cana-5532	279	2	𝜃∗𝜉𝑅	𝜃∗𝜉𝑅	X
cana-5532	279	3	+	+	X
cana-5532	279	4	𝐺∗	𝐺∗	NUM
cana-5532	279	5	+	+	NOUN
cana-5532	279	6	𝑀1	𝑀1	X
cana-5532	279	7	]	]	X
cana-5532	279	8	+	+	CCONJ
cana-5532	279	9	𝑀0	𝑀0	X
cana-5532	279	10	)	)	PUNCT
cana-5532	279	11	≤	≤	NOUN
cana-5532	280	1	[	[	X
cana-5532	280	2	𝜆𝑓	𝜆𝑓	ADP
cana-5532	280	3	∣	∣	PROPN
cana-5532	280	4	𝑢	𝑢	PROPN
cana-5532	280	5	∣	∣	ADJ
cana-5532	280	6	+	+	ADJ
cana-5532	280	7	𝑀𝑓]υ	𝑀𝑓]υ	PROPN
cana-5532	280	8	.	.	PUNCT
cana-5532	281	1	thus	thus	ADV
cana-5532	281	2	,	,	PUNCT
cana-5532	281	3	we	we	PRON
cana-5532	281	4	obtain	obtain	VERB
cana-5532	281	5	∥	∥	NOUN
cana-5532	281	6	𝑢(𝑡	𝑢(𝑡	NOUN
cana-5532	281	7	)	)	PUNCT
cana-5532	281	8	∥𝐸≤	∥𝐸≤	ADP
cana-5532	281	9	𝑀𝑓υ	𝑀𝑓υ	PROPN
cana-5532	281	10	1	1	NUM
cana-5532	281	11	−	−	NOUN
cana-5532	281	12	𝜆𝑓υ	𝜆𝑓υ	NOUN
cana-5532	282	1	=	=	PUNCT
cana-5532	282	2	𝑅	𝑅	PROPN
cana-5532	282	3	communications	communication	NOUN
cana-5532	282	4	on	on	ADP
cana-5532	282	5	applied	apply	VERB
cana-5532	282	6	nonlinear	nonlinear	ADJ
cana-5532	282	7	analysis	analysis	NOUN
cana-5532	282	8	issn	issn	NOUN
cana-5532	282	9	:	:	PUNCT
cana-5532	282	10	1074	1074	NUM
cana-5532	282	11	-	-	PUNCT
cana-5532	282	12	133x	133x	NUM
cana-5532	282	13	vol	vol	NOUN
cana-5532	282	14	32	32	NUM
cana-5532	282	15	no	no	NOUN
cana-5532	282	16	.	.	NOUN
cana-5532	282	17	3	3	NUM
cana-5532	282	18	(	(	PUNCT
cana-5532	282	19	2025	2025	NUM
cana-5532	282	20	)	)	PUNCT
cana-5532	282	21	992	992	NUM
cana-5532	282	22	https://internationalpubls.com	https://internationalpubls.com	X
cana-5532	282	23	then	then	ADV
cana-5532	282	24	𝑢	𝑢	PROPN
cana-5532	282	25	∈	∈	PROPN
cana-5532	282	26	ω	ω	PROPN
cana-5532	282	27	,	,	PUNCT
cana-5532	282	28	thus	thus	ADV
cana-5532	282	29	the	the	DET
cana-5532	282	30	(	(	PUNCT
cana-5532	282	31	iii	iii	NOUN
cana-5532	282	32	)	)	PUNCT
cana-5532	282	33	hypothesis	hypothesis	NOUN
cana-5532	282	34	of	of	ADP
cana-5532	282	35	theorem	theorem	NOUN
cana-5532	282	36	4	4	NUM
cana-5532	282	37	is	be	AUX
cana-5532	282	38	satisfied	satisfied	ADJ
cana-5532	282	39	.	.	PUNCT
cana-5532	283	1	claim	claim	VERB
cana-5532	283	2	4	4	NUM
cana-5532	283	3	now	now	ADV
cana-5532	283	4	,	,	PUNCT
cana-5532	283	5	we	we	PRON
cana-5532	283	6	show	show	VERB
cana-5532	283	7	that	that	SCONJ
cana-5532	283	8	𝜆𝑓𝐿	𝜆𝑓𝐿	PROPN
cana-5532	283	9	<	<	X
cana-5532	283	10	1	1	NUM
cana-5532	283	11	,	,	PUNCT
cana-5532	283	12	where	where	SCONJ
cana-5532	283	13	𝐿	𝐿	PROPN
cana-5532	283	14	=	=	NOUN
cana-5532	283	15	∥	∥	NOUN
cana-5532	283	16	𝐵(ω	𝐵(ω	NUM
cana-5532	283	17	)	)	PUNCT
cana-5532	283	18	∥𝐸=	∥𝐸=	PROPN
cana-5532	283	19	sup{∥	sup{∥	X
cana-5532	284	1	𝐵𝑢	𝐵𝑢	PROPN
cana-5532	284	2	∥𝐸	∥𝐸	NOUN
cana-5532	284	3	:	:	PUNCT
cana-5532	284	4	𝑢	𝑢	PROPN
cana-5532	284	5	∈	∈	PROPN
cana-5532	284	6	ω	ω	PROPN
cana-5532	284	7	}	}	PUNCT
cana-5532	284	8	since	since	SCONJ
cana-5532	284	9	𝐿	𝐿	PROPN
cana-5532	284	10	=	=	SYM
cana-5532	284	11	sup𝑢∈ω{sup𝑡∈𝐼	sup𝑢∈ω{sup𝑡∈𝐼	PROPN
cana-5532	284	12	∣	∣	PROPN
cana-5532	284	13	𝐵𝑢(𝑡	𝐵𝑢(𝑡	NUM
cana-5532	284	14	)	)	PUNCT
cana-5532	284	15	∣	∣	ADJ
cana-5532	284	16	}	}	PUNCT
cana-5532	284	17	≤	≤	NUM
cana-5532	284	18	υ	υ	NOUN
cana-5532	284	19	,	,	PUNCT
cana-5532	284	20	then	then	ADV
cana-5532	284	21	𝜆𝑓υ	𝜆𝑓υ	VERB
cana-5532	284	22	<	<	X
cana-5532	284	23	1	1	NUM
cana-5532	284	24	,	,	PUNCT
cana-5532	284	25	thus	thus	ADV
cana-5532	284	26	all	all	DET
cana-5532	284	27	the	the	DET
cana-5532	284	28	conditions	condition	NOUN
cana-5532	284	29	of	of	ADP
cana-5532	284	30	theorem	theorem	ADJ
cana-5532	284	31	4	4	NUM
cana-5532	284	32	are	be	AUX
cana-5532	284	33	satisfied	satisfied	ADJ
cana-5532	284	34	and	and	CCONJ
cana-5532	284	35	hence	hence	ADV
cana-5532	284	36	the	the	DET
cana-5532	284	37	operator	operator	NOUN
cana-5532	284	38	equation	equation	NOUN
cana-5532	284	39	𝑢	𝑢	PART
cana-5532	284	40	=	=	X
cana-5532	284	41	𝐴𝑢𝐵𝑢	𝐴𝑢𝐵𝑢	PROPN
cana-5532	284	42	has	have	VERB
cana-5532	284	43	a	a	DET
cana-5532	284	44	solution	solution	NOUN
cana-5532	284	45	in	in	ADP
cana-5532	284	46	ω	ω	PROPN
cana-5532	284	47	.	.	PUNCT
cana-5532	285	1	in	in	ADP
cana-5532	285	2	consequence	consequence	NOUN
cana-5532	285	3	,	,	PUNCT
cana-5532	285	4	problem	problem	NOUN
cana-5532	285	5	(	(	PUNCT
cana-5532	285	6	[	[	X
cana-5532	285	7	1]-[2	1]-[2	NUM
cana-5532	285	8	]	]	PUNCT
cana-5532	285	9	)	)	PUNCT
cana-5532	285	10	has	have	VERB
cana-5532	285	11	a	a	DET
cana-5532	285	12	solution	solution	NOUN
cana-5532	285	13	on	on	ADP
cana-5532	285	14	𝐼.	𝐼.	PROPN
cana-5532	285	15	this	this	PRON
cana-5532	285	16	completes	complete	VERB
cana-5532	285	17	the	the	DET
cana-5532	285	18	proof	proof	NOUN
cana-5532	285	19	an	an	DET
cana-5532	285	20	example	example	NOUN
cana-5532	285	21	this	this	DET
cana-5532	285	22	section	section	NOUN
cana-5532	285	23	includes	include	VERB
cana-5532	285	24	an	an	DET
cana-5532	285	25	example	example	NOUN
cana-5532	285	26	that	that	PRON
cana-5532	285	27	showcases	showcase	VERB
cana-5532	285	28	how	how	SCONJ
cana-5532	285	29	theorem	theorem	ADJ
cana-5532	285	30	6	6	NUM
cana-5532	285	31	can	can	AUX
cana-5532	285	32	be	be	AUX
cana-5532	285	33	applied	apply	VERB
cana-5532	285	34	.	.	PUNCT
cana-5532	286	1	let	let	VERB
cana-5532	286	2	us	we	PRON
cana-5532	286	3	consider	consider	VERB
cana-5532	286	4	the	the	DET
cana-5532	286	5	following	follow	VERB
cana-5532	286	6	boundary	boundary	ADJ
cana-5532	286	7	value	value	NOUN
cana-5532	286	8	problem	problem	NOUN
cana-5532	286	9	:	:	PUNCT
cana-5532	286	10	𝐶𝐷0	𝐶𝐷0	NOUN
cana-5532	286	11	+	+	NOUN
cana-5532	286	12	1.7	1.7	NUM
cana-5532	286	13	[	[	PUNCT
cana-5532	286	14	𝑢(𝑡	𝑢(𝑡	NOUN
cana-5532	286	15	)	)	PUNCT
cana-5532	286	16	𝑓(𝑡,𝑢(𝑡	𝑓(𝑡,𝑢(𝑡	NOUN
cana-5532	286	17	)	)	PUNCT
cana-5532	286	18	)	)	PUNCT
cana-5532	286	19	]	]	PUNCT
cana-5532	287	1	+	+	CCONJ
cana-5532	287	2	𝑔(𝑡	𝑔(𝑡	PROPN
cana-5532	287	3	,	,	PUNCT
cana-5532	287	4	𝑢(𝑡	𝑢(𝑡	NOUN
cana-5532	287	5	)	)	PUNCT
cana-5532	287	6	,	,	PUNCT
cana-5532	287	7	𝐼0	𝐼0	PROPN
cana-5532	287	8	+	+	PROPN
cana-5532	287	9	0.7𝑢(𝑡	0.7𝑢(𝑡	NUM
cana-5532	287	10	)	)	PUNCT
cana-5532	287	11	,	,	PUNCT
cana-5532	287	12	𝐼0	𝐼0	PROPN
cana-5532	287	13	+	+	NUM
cana-5532	287	14	0.2𝑢(𝑡	0.2𝑢(𝑡	NUM
cana-5532	287	15	)	)	PUNCT
cana-5532	287	16	)	)	PUNCT
cana-5532	288	1	+	+	CCONJ
cana-5532	288	2	∫	∫	X
cana-5532	288	3	𝐾	𝐾	PROPN
cana-5532	288	4	𝑡	𝑡	PROPN
cana-5532	288	5	0	0	NUM
cana-5532	288	6	(	(	PUNCT
cana-5532	288	7	𝑡	𝑡	PROPN
cana-5532	288	8	,	,	PUNCT
cana-5532	288	9	𝑠	𝑠	INTJ
cana-5532	288	10	,	,	PUNCT
cana-5532	288	11	𝑢(𝑠)))𝑑𝑠	𝑢(𝑠)))𝑑𝑠	NOUN
cana-5532	288	12	=	=	NUM
cana-5532	288	13	0	0	NUM
cana-5532	288	14	,	,	PUNCT
cana-5532	288	15	𝑡	𝑡	PROPN
cana-5532	288	16	∈	∈	NOUN
cana-5532	288	17	𝐼	𝐼	ADP
cana-5532	288	18	=	=	SYM
cana-5532	289	1	[	[	X
cana-5532	289	2	0	0	NUM
cana-5532	289	3	,	,	PUNCT
cana-5532	289	4	1	1	NUM
cana-5532	289	5	]	]	PUNCT
cana-5532	289	6	.	.	PUNCT
cana-5532	290	1	(	(	PUNCT
cana-5532	290	2	𝟔	𝟔	X
cana-5532	290	3	)	)	PUNCT
cana-5532	290	4	𝑢(0	𝑢(0	PROPN
cana-5532	290	5	)	)	PUNCT
cana-5532	290	6	=	=	SYM
cana-5532	290	7	ℎ(𝑢	ℎ(𝑢	PROPN
cana-5532	290	8	)	)	PUNCT
cana-5532	290	9	,	,	PUNCT
cana-5532	290	10	100𝐷	100𝐷	NUM
cana-5532	290	11	(	(	PUNCT
cana-5532	290	12	𝑢(𝑡	𝑢(𝑡	NOUN
cana-5532	290	13	)	)	PUNCT
cana-5532	290	14	𝑓(𝑡,𝑢(𝑡	𝑓(𝑡,𝑢(𝑡	NOUN
cana-5532	290	15	)	)	PUNCT
cana-5532	290	16	)	)	PUNCT
cana-5532	290	17	)	)	PUNCT
cana-5532	291	1	|𝑡=0	|𝑡=0	PROPN
cana-5532	291	2	+	+	CCONJ
cana-5532	291	3	𝐶𝐷0	𝐶𝐷0	NOUN
cana-5532	291	4	+	+	CCONJ
cana-5532	291	5	0.7	0.7	NUM
cana-5532	291	6	(	(	PUNCT
cana-5532	291	7	𝑢(𝑡	𝑢(𝑡	NOUN
cana-5532	291	8	)	)	PUNCT
cana-5532	291	9	𝑓(𝑡,𝑢(𝑡	𝑓(𝑡,𝑢(𝑡	NOUN
cana-5532	291	10	)	)	PUNCT
cana-5532	291	11	)	)	PUNCT
cana-5532	291	12	)	)	PUNCT
cana-5532	292	1	|𝑡=1	|𝑡=1	NOUN
cana-5532	292	2	=	=	SYM
cana-5532	292	3	0	0	PROPN
cana-5532	292	4	.	.	PUNCT
cana-5532	292	5	(	(	PUNCT
cana-5532	292	6	𝟕	𝟕	X
cana-5532	292	7	)	)	PUNCT
cana-5532	292	8	here	here	ADV
cana-5532	292	9	𝛼	𝛼	X
cana-5532	292	10	=	=	SYM
cana-5532	292	11	1.7	1.7	NUM
cana-5532	292	12	,	,	PUNCT
cana-5532	292	13	𝜇1	𝜇1	NOUN
cana-5532	292	14	=	=	NOUN
cana-5532	292	15	0.7	0.7	NUM
cana-5532	292	16	,	,	PUNCT
cana-5532	292	17	𝜇2	𝜇2	NOUN
cana-5532	292	18	=	=	NOUN
cana-5532	292	19	0.2	0.2	NUM
cana-5532	292	20	,	,	PUNCT
cana-5532	292	21	𝑎	𝑎	PROPN
cana-5532	292	22	=	=	SYM
cana-5532	292	23	100	100	NUM
cana-5532	292	24	and	and	CCONJ
cana-5532	292	25	𝑏	𝑏	NOUN
cana-5532	292	26	=	=	SYM
cana-5532	292	27	1	1	NUM
cana-5532	292	28	.	.	PUNCT
cana-5532	293	1	where	where	SCONJ
cana-5532	293	2	𝑓(𝑡	𝑓(𝑡	NOUN
cana-5532	293	3	,	,	PUNCT
cana-5532	293	4	𝑢(𝑡	𝑢(𝑡	NOUN
cana-5532	293	5	)	)	PUNCT
cana-5532	293	6	)	)	PUNCT
cana-5532	294	1	=	=	SYM
cana-5532	295	1	7𝑒−3𝑡	7𝑒−3𝑡	NOUN
cana-5532	295	2	15(𝑡2	15(𝑡2	NUM
cana-5532	295	3	+	+	ADJ
cana-5532	295	4	2	2	NUM
cana-5532	295	5	)	)	PUNCT
cana-5532	295	6	|𝑢|+1	|𝑢|+1	NOUN
cana-5532	295	7	|𝑢|+2	|𝑢|+2	NOUN
cana-5532	295	8	,	,	PUNCT
cana-5532	295	9	and	and	CCONJ
cana-5532	295	10	ℎ(𝑢	ℎ(𝑢	PROPN
cana-5532	295	11	)	)	PUNCT
cana-5532	295	12	=	=	SYM
cana-5532	295	13	sin(𝑢	sin(𝑢	PROPN
cana-5532	295	14	)	)	PUNCT
cana-5532	295	15	100+𝑢2	100+𝑢2	PROPN
cana-5532	295	16	,	,	PUNCT
cana-5532	295	17	and	and	CCONJ
cana-5532	295	18	𝑔(𝑡	𝑔(𝑡	PROPN
cana-5532	295	19	,	,	PUNCT
cana-5532	295	20	𝑢(𝑡	𝑢(𝑡	PROPN
cana-5532	295	21	)	)	PUNCT
cana-5532	295	22	,	,	PUNCT
cana-5532	295	23	𝐼0	𝐼0	PROPN
cana-5532	295	24	+	+	PROPN
cana-5532	295	25	0.7𝑢(𝑡	0.7𝑢(𝑡	NUM
cana-5532	295	26	)	)	PUNCT
cana-5532	295	27	,	,	PUNCT
cana-5532	295	28	𝐼0	𝐼0	PROPN
cana-5532	295	29	+	+	NUM
cana-5532	295	30	0.2𝑢(𝑡	0.2𝑢(𝑡	NUM
cana-5532	295	31	)	)	PUNCT
cana-5532	295	32	)	)	PUNCT
cana-5532	296	1	=	=	SYM
cana-5532	296	2	3	3	NUM
cana-5532	296	3	100(𝑡2	100(𝑡2	NUM
cana-5532	296	4	+	+	NOUN
cana-5532	296	5	1	1	NUM
cana-5532	296	6	)	)	PUNCT
cana-5532	297	1	[	[	X
cana-5532	297	2	𝑢(𝑡	𝑢(𝑡	X
cana-5532	297	3	)	)	PUNCT
cana-5532	297	4	+	+	CCONJ
cana-5532	297	5	|cos(𝐼0	|cos(𝐼0	ADV
cana-5532	297	6	+	+	X
cana-5532	297	7	0.7𝑢(𝑡	0.7𝑢(𝑡	NUM
cana-5532	297	8	)	)	PUNCT
cana-5532	297	9	)	)	PUNCT
cana-5532	298	1	−	−	ADP
cana-5532	298	2	𝑐ℎ(𝐼0	𝑐ℎ(𝐼0	NOUN
cana-5532	299	1	+	+	SYM
cana-5532	299	2	0.2𝑢(𝑡))|	0.2𝑢(𝑡))|	NOUN
cana-5532	299	3	]	]	X
cana-5532	299	4	+	+	CCONJ
cana-5532	299	5	𝑡	𝑡	PROPN
cana-5532	299	6	100	100	NUM
cana-5532	299	7	,	,	PUNCT
cana-5532	299	8	and	and	CCONJ
cana-5532	299	9	𝐾(𝑡	𝐾(𝑡	NUM
cana-5532	299	10	,	,	PUNCT
cana-5532	299	11	𝑠	𝑠	PROPN
cana-5532	299	12	,	,	PUNCT
cana-5532	299	13	𝑢(𝑠	𝑢(𝑠	NOUN
cana-5532	299	14	)	)	PUNCT
cana-5532	299	15	)	)	PUNCT
cana-5532	300	1	=	=	SYM
cana-5532	300	2	cos(𝑢2)𝑒−𝑡(𝑠2	cos(𝑢2)𝑒−𝑡(𝑠2	PROPN
cana-5532	300	3	+	+	PROPN
cana-5532	300	4	1	1	NUM
cana-5532	300	5	)	)	PUNCT
cana-5532	300	6	100	100	NUM
cana-5532	300	7	note	note	NOUN
cana-5532	300	8	that	that	SCONJ
cana-5532	300	9	𝑀𝑓	𝑀𝑓	PROPN
cana-5532	300	10	=	=	PUNCT
cana-5532	300	11	sup𝑡∈𝐼	sup𝑡∈𝐼	NOUN
cana-5532	300	12	∣	∣	ADJ
cana-5532	300	13	𝑓(𝑡	𝑓(𝑡	PROPN
cana-5532	300	14	,	,	PUNCT
cana-5532	300	15	0	0	NUM
cana-5532	300	16	)	)	PUNCT
cana-5532	300	17	∣=	∣=	NOUN
cana-5532	300	18	7𝑒−3𝑡	7𝑒−3𝑡	NOUN
cana-5532	300	19	30(𝑡2	30(𝑡2	NUM
cana-5532	300	20	+	+	NOUN
cana-5532	300	21	2	2	NUM
cana-5532	300	22	)	)	PUNCT
cana-5532	300	23	=	=	SYM
cana-5532	300	24	7	7	NUM
cana-5532	300	25	60	60	NUM
cana-5532	300	26	and	and	CCONJ
cana-5532	300	27	𝑀0	𝑀0	ADJ
cana-5532	300	28	=	=	SYM
cana-5532	300	29	|	|	NOUN
cana-5532	300	30	ℎ(𝑢(𝑡	ℎ(𝑢(𝑡	PROPN
cana-5532	300	31	)	)	PUNCT
cana-5532	300	32	𝑓(0,ℎ(𝑢(𝑡	𝑓(0,ℎ(𝑢(𝑡	PROPN
cana-5532	300	33	)	)	PUNCT
cana-5532	300	34	)	)	PUNCT
cana-5532	301	1	|	|	ADV
cana-5532	301	2	=	=	SYM
cana-5532	301	3	60	60	NUM
cana-5532	301	4	70	70	NUM
cana-5532	301	5	setting	set	VERB
cana-5532	301	6	𝑀1	𝑀1	NOUN
cana-5532	301	7	=	=	SYM
cana-5532	301	8	2	2	NUM
cana-5532	301	9	100	100	NUM
cana-5532	301	10	,	,	PUNCT
cana-5532	301	11	𝐺∗	𝐺∗	NUM
cana-5532	301	12	=	=	SYM
cana-5532	301	13	sup𝑡∈𝐼	sup𝑡∈𝐼	PROPN
cana-5532	301	14	∣	∣	PROPN
cana-5532	301	15	𝑔(𝑡	𝑔(𝑡	PROPN
cana-5532	301	16	,	,	PUNCT
cana-5532	301	17	0	0	NUM
cana-5532	301	18	,	,	PUNCT
cana-5532	301	19	.	.	PUNCT
cana-5532	301	20	.	.	PUNCT
cana-5532	301	21	.	.	PUNCT
cana-5532	302	1	,	,	PUNCT
cana-5532	302	2	0	0	X
cana-5532	302	3	)	)	PUNCT
cana-5532	303	1	∣=	∣=	NOUN
cana-5532	303	2	0.01	0.01	NUM
cana-5532	303	3	,	,	PUNCT
cana-5532	303	4	and	and	CCONJ
cana-5532	303	5	we	we	PRON
cana-5532	303	6	have	have	VERB
cana-5532	303	7	∣	∣	ADJ
cana-5532	303	8	𝑓(𝑡	𝑓(𝑡	NOUN
cana-5532	303	9	,	,	PUNCT
cana-5532	303	10	𝑢	𝑢	NOUN
cana-5532	303	11	)	)	PUNCT
cana-5532	303	12	−	−	PROPN
cana-5532	304	1	𝑓(𝑡	𝑓(𝑡	NOUN
cana-5532	304	2	,	,	PUNCT
cana-5532	304	3	𝑣	𝑣	NOUN
cana-5532	304	4	)	)	PUNCT
cana-5532	304	5	∣≤	∣≤	NUM
cana-5532	304	6	7𝑒−3𝑡	7𝑒−3𝑡	NOUN
cana-5532	304	7	15(𝑡2	15(𝑡2	NUM
cana-5532	304	8	+	+	NOUN
cana-5532	304	9	2	2	NUM
cana-5532	304	10	)	)	PUNCT
cana-5532	305	1	|	|	ADV
cana-5532	305	2	𝑢+1	𝑢+1	X
cana-5532	305	3	𝑢+2	𝑢+2	X
cana-5532	305	4	−	−	PUNCT
cana-5532	305	5	𝑣+1	𝑣+1	PROPN
cana-5532	305	6	𝑣+2	𝑣+2	NUM
cana-5532	305	7	|	|	ADV
cana-5532	305	8	≤	≤	NUM
cana-5532	305	9	7	7	NUM
cana-5532	305	10	30	30	NUM
cana-5532	305	11	|	|	ADV
cana-5532	305	12	∣𝑣−𝑢∣	∣𝑣−𝑢∣	NOUN
cana-5532	305	13	∣𝑣+2∣∣𝑢+2∣	∣𝑣+2∣∣𝑢+2∣	VERB
cana-5532	305	14	≤	≤	NUM
cana-5532	305	15	7	7	NUM
cana-5532	305	16	30	30	NUM
cana-5532	305	17	∣	∣	NOUN
cana-5532	305	18	𝑣	𝑣	ADP
cana-5532	305	19	−	−	PROPN
cana-5532	305	20	𝑢	𝑢	X
cana-5532	305	21	∣.	∣.	NOUN
cana-5532	306	1	then	then	ADV
cana-5532	306	2	𝜆𝑓	𝜆𝑓	VERB
cana-5532	307	1	=	=	NOUN
cana-5532	307	2	7	7	NUM
cana-5532	307	3	30	30	NUM
cana-5532	307	4	,	,	PUNCT
cana-5532	307	5	for	for	ADP
cana-5532	307	6	𝑢	𝑢	X
cana-5532	307	7	,	,	PUNCT
cana-5532	307	8	𝑣	𝑣	PRON
cana-5532	307	9	∈	∈	PROPN
cana-5532	307	10	ℝ	ℝ	PROPN
cana-5532	307	11	,	,	PUNCT
cana-5532	307	12	we	we	PRON
cana-5532	307	13	have	have	VERB
cana-5532	307	14	∣	∣	ADJ
cana-5532	307	15	𝑔(𝑡	𝑔(𝑡	PROPN
cana-5532	307	16	,	,	PUNCT
cana-5532	307	17	𝑣(𝑡	𝑣(𝑡	NOUN
cana-5532	307	18	)	)	PUNCT
cana-5532	307	19	,	,	PUNCT
cana-5532	307	20	𝐼0	𝐼0	PROPN
cana-5532	307	21	+	+	NUM
cana-5532	307	22	0.7𝑣(𝑡	0.7𝑣(𝑡	NUM
cana-5532	307	23	)	)	PUNCT
cana-5532	307	24	,	,	PUNCT
cana-5532	307	25	𝐼0	𝐼0	PROPN
cana-5532	307	26	+	+	NOUN
cana-5532	307	27	0.2𝑣(𝑡	0.2𝑣(𝑡	NUM
cana-5532	307	28	)	)	PUNCT
cana-5532	307	29	)	)	PUNCT
cana-5532	308	1	−	−	PUNCT
cana-5532	308	2	𝑔(𝑡	𝑔(𝑡	PROPN
cana-5532	308	3	,	,	PUNCT
cana-5532	308	4	𝑢(𝑡	𝑢(𝑡	PROPN
cana-5532	308	5	)	)	PUNCT
cana-5532	308	6	,	,	PUNCT
cana-5532	308	7	𝐼0	𝐼0	PROPN
cana-5532	308	8	+	+	PROPN
cana-5532	308	9	0.7𝑢(𝑡	0.7𝑢(𝑡	NUM
cana-5532	308	10	)	)	PUNCT
cana-5532	308	11	,	,	PUNCT
cana-5532	308	12	𝐼0	𝐼0	PROPN
cana-5532	308	13	+	+	NUM
cana-5532	308	14	0.2𝑢(𝑡	0.2𝑢(𝑡	NUM
cana-5532	308	15	)	)	PUNCT
cana-5532	308	16	)	)	PUNCT
cana-5532	309	1	∣	∣	ADJ
cana-5532	309	2	≤	≤	NUM
cana-5532	309	3	3	3	NUM
cana-5532	309	4	100(𝑡2	100(𝑡2	NUM
cana-5532	309	5	+	+	SYM
cana-5532	309	6	1	1	NUM
cana-5532	309	7	)	)	PUNCT
cana-5532	309	8	(	(	PUNCT
cana-5532	309	9	1	1	NUM
cana-5532	309	10	+	+	CCONJ
cana-5532	309	11	𝑡0.2	𝑡0.2	PROPN
cana-5532	309	12	γ(1.2	γ(1.2	PROPN
cana-5532	309	13	)	)	PUNCT
cana-5532	310	1	+	+	CCONJ
cana-5532	310	2	𝑡0.7	𝑡0.7	PROPN
cana-5532	310	3	γ(1.7	γ(1.7	PROPN
cana-5532	310	4	)	)	PUNCT
cana-5532	310	5	)	)	PUNCT
cana-5532	310	6	∣	∣	VERB
cana-5532	310	7	𝑣	𝑣	ADP
cana-5532	310	8	−	−	PROPN
cana-5532	310	9	𝑢	𝑢	X
cana-5532	310	10	∣	∣	ADJ
cana-5532	310	11	≤	≤	NUM
cana-5532	310	12	3	3	NUM
cana-5532	310	13	100(𝑡2	100(𝑡2	NUM
cana-5532	310	14	+	+	SYM
cana-5532	310	15	1	1	NUM
cana-5532	310	16	)	)	PUNCT
cana-5532	310	17	(	(	PUNCT
cana-5532	310	18	1	1	NUM
cana-5532	310	19	+	+	SYM
cana-5532	310	20	1	1	NUM
cana-5532	310	21	γ(1.2	γ(1.2	NOUN
cana-5532	310	22	)	)	PUNCT
cana-5532	310	23	+	+	CCONJ
cana-5532	310	24	1	1	NUM
cana-5532	310	25	γ(1.7	γ(1.7	PROPN
cana-5532	310	26	)	)	PUNCT
cana-5532	310	27	)	)	PUNCT
cana-5532	310	28	∣	∣	VERB
cana-5532	310	29	𝑣	𝑣	ADP
cana-5532	310	30	−	−	PROPN
cana-5532	310	31	𝑢	𝑢	PROPN
cana-5532	310	32	∣	∣	VERB
cana-5532	310	33	thus	thus	ADV
cana-5532	310	34	,	,	PUNCT
cana-5532	310	35	the	the	DET
cana-5532	310	36	assumption	assumption	NOUN
cana-5532	310	37	(	(	PUNCT
cana-5532	310	38	a2	a2	NOUN
cana-5532	310	39	)	)	PUNCT
cana-5532	310	40	holds	hold	VERB
cana-5532	310	41	true	true	ADJ
cana-5532	310	42	with	with	ADP
cana-5532	310	43	𝜃(𝑡	𝜃(𝑡	PROPN
cana-5532	310	44	)	)	PUNCT
cana-5532	311	1	=	=	PUNCT
cana-5532	312	1	3	3	NUM
cana-5532	312	2	100(𝑡2	100(𝑡2	NUM
cana-5532	312	3	+	+	SYM
cana-5532	312	4	1	1	NUM
cana-5532	312	5	)	)	PUNCT
cana-5532	312	6	and	and	CCONJ
cana-5532	312	7	𝜃∗	𝜃∗	PROPN
cana-5532	312	8	=	=	PUNCT
cana-5532	312	9	0.03	0.03	NUM
cana-5532	312	10	and	and	CCONJ
cana-5532	312	11	𝜉	𝜉	X
cana-5532	312	12	=	=	ADJ
cana-5532	312	13	3.189672	3.189672	NUM
cana-5532	312	14	.	.	PUNCT
cana-5532	313	1	by	by	ADP
cana-5532	313	2	the	the	DET
cana-5532	313	3	above	above	ADJ
cana-5532	313	4	data	datum	NOUN
cana-5532	313	5	,	,	PUNCT
cana-5532	313	6	we	we	PRON
cana-5532	313	7	get	get	VERB
cana-5532	313	8	υ	υ	NOUN
cana-5532	313	9	=	=	SYM
cana-5532	313	10	0.939755	0.939755	NUM
cana-5532	313	11	and	and	CCONJ
cana-5532	313	12	𝜆𝑓υ	𝜆𝑓υ	NOUN
cana-5532	314	1	=	=	SYM
cana-5532	314	2	0.219276	0.219276	NUM
cana-5532	314	3	<	<	X
cana-5532	314	4	1	1	NUM
cana-5532	314	5	..	..	PUNCT
cana-5532	314	6	thus	thus	ADV
cana-5532	314	7	,	,	PUNCT
cana-5532	314	8	we	we	PRON
cana-5532	314	9	can	can	AUX
cana-5532	314	10	choose	choose	VERB
cana-5532	314	11	communications	communication	NOUN
cana-5532	314	12	on	on	ADP
cana-5532	314	13	applied	apply	VERB
cana-5532	314	14	nonlinear	nonlinear	ADJ
cana-5532	314	15	analysis	analysis	NOUN
cana-5532	314	16	issn	issn	NOUN
cana-5532	314	17	:	:	PUNCT
cana-5532	314	18	1074	1074	NUM
cana-5532	314	19	-	-	PUNCT
cana-5532	314	20	133x	133x	NUM
cana-5532	314	21	vol	vol	NOUN
cana-5532	314	22	32	32	NUM
cana-5532	314	23	no	no	NOUN
cana-5532	314	24	.	.	NOUN
cana-5532	314	25	3	3	NUM
cana-5532	314	26	(	(	PUNCT
cana-5532	314	27	2025	2025	NUM
cana-5532	314	28	)	)	PUNCT
cana-5532	314	29	993	993	NUM
cana-5532	315	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5532	315	2	0.935712	0.935712	NUM
cana-5532	315	3	<	<	X
cana-5532	315	4	𝑅	𝑅	PROPN
cana-5532	315	5	<	<	X
cana-5532	315	6	54.19965	54.19965	NUM
cana-5532	315	7	.	.	PUNCT
cana-5532	316	1	accordingly	accordingly	ADV
cana-5532	316	2	,	,	PUNCT
cana-5532	316	3	all	all	DET
cana-5532	316	4	the	the	DET
cana-5532	316	5	conditions	condition	NOUN
cana-5532	316	6	of	of	ADP
cana-5532	316	7	theorem	theorem	NOUN
cana-5532	316	8	6	6	NUM
cana-5532	316	9	are	be	AUX
cana-5532	316	10	fulfilled	fulfil	VERB
cana-5532	316	11	,	,	PUNCT
cana-5532	316	12	the	the	DET
cana-5532	316	13	hybrid	hybrid	ADJ
cana-5532	316	14	fractional	fractional	ADJ
cana-5532	316	15	problem	problem	NOUN
cana-5532	316	16	(	(	PUNCT
cana-5532	316	17	6	6	NUM
cana-5532	316	18	-	-	SYM
cana-5532	316	19	7	7	NUM
cana-5532	316	20	)	)	PUNCT
cana-5532	316	21	has	have	VERB
cana-5532	316	22	at	at	ADV
cana-5532	316	23	least	least	ADV
cana-5532	316	24	one	one	NUM
cana-5532	316	25	solution	solution	NOUN
cana-5532	316	26	on	on	ADP
cana-5532	316	27	[	[	X
cana-5532	316	28	0	0	NUM
cana-5532	316	29	,	,	PUNCT
cana-5532	316	30	1	1	NUM
cana-5532	316	31	]	]	PUNCT
cana-5532	316	32	.	.	PUNCT
cana-5532	317	1	references	reference	NOUN
cana-5532	317	2	[	[	X
cana-5532	317	3	1	1	NUM
cana-5532	317	4	]	]	X
cana-5532	317	5	bashir	bashir	PROPN
cana-5532	317	6	ahmad	ahmad	PROPN
cana-5532	317	7	and	and	CCONJ
cana-5532	317	8	sotiris	sotiris	PROPN
cana-5532	317	9	ntouyas	ntouyas	NOUN
cana-5532	317	10	.	.	PUNCT
cana-5532	318	1	“	"	PUNCT
cana-5532	318	2	an	an	DET
cana-5532	318	3	existence	existence	NOUN
cana-5532	318	4	theorem	theorem	VERB
cana-5532	318	5	for	for	ADP
cana-5532	318	6	fractional	fractional	ADJ
cana-5532	318	7	hybrid	hybrid	ADJ
cana-5532	318	8	differential	differential	ADJ
cana-5532	318	9	inclusions	inclusion	NOUN
cana-5532	318	10	of	of	ADP
cana-5532	318	11	hadamard	hadamard	ADJ
cana-5532	318	12	type	type	NOUN
cana-5532	318	13	”	"	PUNCT
cana-5532	318	14	.	.	PUNCT
cana-5532	319	1	in	in	ADP
cana-5532	319	2	:	:	PUNCT
cana-5532	319	3	discussiones	discussione	NOUN
cana-5532	319	4	mathematicae	mathematicae	VERB
cana-5532	319	5	,	,	PUNCT
cana-5532	319	6	differential	differential	ADJ
cana-5532	319	7	inclusions	inclusion	NOUN
cana-5532	319	8	,	,	PUNCT
cana-5532	319	9	control	control	NOUN
cana-5532	319	10	and	and	CCONJ
cana-5532	319	11	optimization	optimization	NOUN
cana-5532	319	12	34.2	34.2	NUM
cana-5532	319	13	(	(	PUNCT
cana-5532	319	14	2014	2014	NUM
cana-5532	319	15	)	)	PUNCT
cana-5532	319	16	,	,	PUNCT
cana-5532	319	17	pp	pp	ADP
cana-5532	319	18	.	.	PUNCT
cana-5532	320	1	207–218	207–218	NUM
cana-5532	320	2	.	.	PUNCT
cana-5532	321	1	[	[	X
cana-5532	321	2	2	2	NUM
cana-5532	321	3	]	]	X
cana-5532	321	4	bashir	bashir	PROPN
cana-5532	321	5	ahmad	ahmad	PROPN
cana-5532	321	6	,	,	PUNCT
cana-5532	321	7	sotiris	sotiris	NOUN
cana-5532	321	8	k	k	PROPN
cana-5532	321	9	ntouyas	ntouyas	PROPN
cana-5532	321	10	,	,	PUNCT
cana-5532	321	11	and	and	CCONJ
cana-5532	321	12	jessada	jessada	PROPN
cana-5532	321	13	tariboon	tariboon	PROPN
cana-5532	321	14	.	.	PUNCT
cana-5532	322	1	“	"	PUNCT
cana-5532	322	2	on	on	ADP
cana-5532	322	3	hybrid	hybrid	ADJ
cana-5532	322	4	caputo	caputo	PROPN
cana-5532	322	5	fractional	fractional	ADJ
cana-5532	322	6	integrodifferential	integrodifferential	ADJ
cana-5532	322	7	inclusions	inclusion	NOUN
cana-5532	322	8	with	with	ADP
cana-5532	322	9	nonlocal	nonlocal	ADJ
cana-5532	322	10	conditions	condition	NOUN
cana-5532	322	11	”	"	PUNCT
cana-5532	322	12	.	.	PUNCT
cana-5532	323	1	in	in	ADP
cana-5532	323	2	:	:	PUNCT
cana-5532	323	3	j.	j.	PROPN
cana-5532	323	4	nonlinear	nonlinear	PROPN
cana-5532	323	5	sci	sci	PROPN
cana-5532	323	6	.	.	PUNCT
cana-5532	323	7	appl	appl	PROPN
cana-5532	323	8	9.6	9.6	NUM
cana-5532	323	9	(	(	PUNCT
cana-5532	323	10	2016	2016	NUM
cana-5532	323	11	)	)	PUNCT
cana-5532	323	12	,	,	PUNCT
cana-5532	323	13	pp	pp	PROPN
cana-5532	323	14	.	.	PUNCT
cana-5532	323	15	4235	4235	NUM
cana-5532	323	16	–	–	PUNCT
cana-5532	323	17	4246	4246	NUM
cana-5532	323	18	.	.	PUNCT
cana-5532	324	1	[	[	X
cana-5532	324	2	3	3	NUM
cana-5532	324	3	]	]	X
cana-5532	324	4	dumitru	dumitru	NOUN
cana-5532	324	5	baleanu	baleanu	PROPN
cana-5532	324	6	,	,	PUNCT
cana-5532	324	7	s	s	VERB
cana-5532	324	8	etemad	etemad	ADJ
cana-5532	324	9	,	,	PUNCT
cana-5532	324	10	and	and	CCONJ
cana-5532	324	11	sh	sh	PROPN
cana-5532	324	12	rezapour	rezapour	VERB
cana-5532	324	13	.	.	PUNCT
cana-5532	325	1	“	"	PUNCT
cana-5532	325	2	on	on	ADP
cana-5532	325	3	a	a	DET
cana-5532	325	4	fractional	fractional	ADJ
cana-5532	325	5	hybrid	hybrid	ADJ
cana-5532	325	6	integro	integro	ADJ
cana-5532	325	7	-	-	PUNCT
cana-5532	325	8	differential	differential	NOUN
cana-5532	325	9	equation	equation	NOUN
cana-5532	325	10	with	with	ADP
cana-5532	325	11	mixed	mixed	ADJ
cana-5532	325	12	hybrid	hybrid	ADJ
cana-5532	325	13	integral	integral	ADJ
cana-5532	325	14	boundary	boundary	ADJ
cana-5532	325	15	value	value	NOUN
cana-5532	325	16	conditions	condition	NOUN
cana-5532	325	17	by	by	ADP
cana-5532	325	18	using	use	VERB
cana-5532	325	19	three	three	NUM
cana-5532	325	20	operators	operator	NOUN
cana-5532	325	21	”	"	PUNCT
cana-5532	325	22	.	.	PUNCT
cana-5532	326	1	in	in	ADP
cana-5532	326	2	:	:	PUNCT
cana-5532	326	3	alexandria	alexandria	PROPN
cana-5532	326	4	engineering	engineering	PROPN
cana-5532	326	5	journal	journal	PROPN
cana-5532	326	6	59.5	59.5	NUM
cana-5532	326	7	(	(	PUNCT
cana-5532	326	8	2020	2020	NUM
cana-5532	326	9	)	)	PUNCT
cana-5532	326	10	,	,	PUNCT
cana-5532	326	11	pp	pp	PROPN
cana-5532	326	12	.	.	PUNCT
cana-5532	326	13	3019–3027	3019–3027	NUM
cana-5532	326	14	.	.	PUNCT
cana-5532	327	1	[	[	X
cana-5532	327	2	4	4	NUM
cana-5532	327	3	]	]	X
cana-5532	327	4	dumitru	dumitru	PROPN
cana-5532	327	5	baleanu	baleanu	PROPN
cana-5532	327	6	et	et	PROPN
cana-5532	327	7	al	al	PROPN
cana-5532	327	8	.	.	PROPN
cana-5532	327	9	fractional	fractional	PROPN
cana-5532	327	10	calculus	calculus	NOUN
cana-5532	327	11	:	:	PUNCT
cana-5532	327	12	models	model	NOUN
cana-5532	327	13	and	and	CCONJ
cana-5532	327	14	numerical	numerical	ADJ
cana-5532	327	15	methods	method	NOUN
cana-5532	327	16	.	.	PUNCT
cana-5532	328	1	vol	vol	NOUN
cana-5532	328	2	.	.	PROPN
cana-5532	329	1	3	3	X
cana-5532	329	2	.	.	X
cana-5532	329	3	world	world	NOUN
cana-5532	329	4	scientific	scientific	ADJ
cana-5532	329	5	,	,	PUNCT
cana-5532	329	6	2012	2012	NUM
cana-5532	329	7	.	.	PUNCT
cana-5532	330	1	[	[	X
cana-5532	330	2	5	5	NUM
cana-5532	330	3	]	]	X
cana-5532	330	4	josefa	josefa	PROPN
cana-5532	330	5	caballero	caballero	PROPN
cana-5532	330	6	,	,	PUNCT
cana-5532	330	7	mohamed	mohamed	PROPN
cana-5532	330	8	abdalla	abdalla	PROPN
cana-5532	330	9	darwish	darwish	PROPN
cana-5532	330	10	,	,	PUNCT
cana-5532	330	11	and	and	CCONJ
cana-5532	330	12	kishin	kishin	PROPN
cana-5532	330	13	sadarangani	sadarangani	NOUN
cana-5532	330	14	.	.	PUNCT
cana-5532	331	1	“	"	PUNCT
cana-5532	331	2	solvability	solvability	NOUN
cana-5532	331	3	of	of	ADP
cana-5532	331	4	a	a	DET
cana-5532	331	5	fractional	fractional	ADJ
cana-5532	331	6	hybrid	hybrid	ADJ
cana-5532	331	7	initial	initial	ADJ
cana-5532	331	8	value	value	NOUN
cana-5532	331	9	problem	problem	NOUN
cana-5532	331	10	with	with	ADP
cana-5532	331	11	supremum	supremum	NOUN
cana-5532	331	12	by	by	ADP
cana-5532	331	13	using	use	VERB
cana-5532	331	14	measures	measure	NOUN
cana-5532	331	15	of	of	ADP
cana-5532	331	16	noncompactness	noncompactness	ADJ
cana-5532	331	17	in	in	ADP
cana-5532	331	18	banach	banach	NOUN
cana-5532	331	19	algebras	algebra	NOUN
cana-5532	331	20	”	"	PUNCT
cana-5532	331	21	.	.	PUNCT
cana-5532	332	1	in	in	ADP
cana-5532	332	2	:	:	PUNCT
cana-5532	332	3	applied	applied	ADJ
cana-5532	332	4	mathematics	mathematic	NOUN
cana-5532	332	5	and	and	CCONJ
cana-5532	332	6	computation	computation	NOUN
cana-5532	332	7	224	224	NUM
cana-5532	332	8	(	(	PUNCT
cana-5532	332	9	2013	2013	NUM
cana-5532	332	10	)	)	PUNCT
cana-5532	332	11	,	,	PUNCT
cana-5532	332	12	pp	pp	ADP
cana-5532	332	13	.	.	PUNCT
cana-5532	333	1	553–563	553–563	NUM
cana-5532	333	2	.	.	PUNCT
cana-5532	334	1	[	[	X
cana-5532	334	2	6	6	NUM
cana-5532	334	3	]	]	X
cana-5532	334	4	choukri	choukri	PROPN
cana-5532	334	5	derbazi	derbazi	NOUN
cana-5532	334	6	et	et	PROPN
cana-5532	334	7	al	al	PROPN
cana-5532	334	8	.	.	PUNCT
cana-5532	335	1	“	"	PUNCT
cana-5532	335	2	fractional	fractional	ADJ
cana-5532	335	3	hybrid	hybrid	ADJ
cana-5532	335	4	differential	differential	NOUN
cana-5532	335	5	equations	equation	NOUN
cana-5532	335	6	with	with	ADP
cana-5532	335	7	three	three	NUM
cana-5532	335	8	-	-	PUNCT
cana-5532	335	9	point	point	NOUN
cana-5532	335	10	boundary	boundary	ADJ
cana-5532	335	11	hybrid	hybrid	ADJ
cana-5532	335	12	conditions	condition	NOUN
cana-5532	335	13	”	"	PUNCT
cana-5532	335	14	.	.	PUNCT
cana-5532	336	1	in	in	ADP
cana-5532	336	2	:	:	PUNCT
cana-5532	336	3	advances	advance	NOUN
cana-5532	336	4	in	in	ADP
cana-5532	336	5	difference	difference	NOUN
cana-5532	336	6	equations	equation	NOUN
cana-5532	336	7	2019.1	2019.1	NUM
cana-5532	336	8	(	(	PUNCT
cana-5532	336	9	2019	2019	NUM
cana-5532	336	10	)	)	PUNCT
cana-5532	336	11	,	,	PUNCT
cana-5532	336	12	p.	p.	NOUN
cana-5532	336	13	125	125	NUM
cana-5532	336	14	.	.	PUNCT
cana-5532	337	1	[	[	X
cana-5532	337	2	7	7	X
cana-5532	337	3	]	]	PUNCT
cana-5532	337	4	bapurao	bapurao	NOUN
cana-5532	337	5	c	c	NOUN
cana-5532	337	6	dhage	dhage	NOUN
cana-5532	337	7	and	and	CCONJ
cana-5532	337	8	v	v	NOUN
cana-5532	337	9	lakshmikantham	lakshmikantham	NOUN
cana-5532	337	10	.	.	PUNCT
cana-5532	338	1	“	"	PUNCT
cana-5532	338	2	basic	basic	ADJ
cana-5532	338	3	results	result	NOUN
cana-5532	338	4	on	on	ADP
cana-5532	338	5	hybrid	hybrid	ADJ
cana-5532	338	6	differential	differential	ADJ
cana-5532	338	7	equations	equation	NOUN
cana-5532	338	8	”	"	PUNCT
cana-5532	338	9	.	.	PUNCT
cana-5532	339	1	in	in	ADP
cana-5532	339	2	:	:	PUNCT
cana-5532	339	3	nonlinear	nonlinear	ADJ
cana-5532	339	4	analysis	analysis	NOUN
cana-5532	339	5	:	:	PUNCT
cana-5532	339	6	hybrid	hybrid	ADJ
cana-5532	339	7	systems	system	NOUN
cana-5532	339	8	4.3	4.3	NUM
cana-5532	339	9	(	(	PUNCT
cana-5532	339	10	2010	2010	NUM
cana-5532	339	11	)	)	PUNCT
cana-5532	339	12	,	,	PUNCT
cana-5532	339	13	pp	pp	ADP
cana-5532	339	14	.	.	PUNCT
cana-5532	340	1	414–424	414–424	NUM
cana-5532	340	2	.	.	PUNCT
cana-5532	341	1	[	[	X
cana-5532	341	2	8	8	NUM
cana-5532	341	3	]	]	SYM
cana-5532	341	4	bc	bc	PROPN
cana-5532	341	5	dhage	dhage	NOUN
cana-5532	341	6	.	.	PUNCT
cana-5532	342	1	“	"	PUNCT
cana-5532	342	2	fixed	fix	VERB
cana-5532	342	3	point	point	NOUN
cana-5532	342	4	theorems	theorem	NOUN
cana-5532	342	5	in	in	ADP
cana-5532	342	6	ordered	order	VERB
cana-5532	342	7	banach	banach	NOUN
cana-5532	342	8	algebras	algebra	NOUN
cana-5532	342	9	and	and	CCONJ
cana-5532	342	10	applications	application	NOUN
cana-5532	342	11	”	"	PUNCT
cana-5532	342	12	.	.	PUNCT
cana-5532	343	1	in	in	ADP
cana-5532	343	2	:	:	PUNCT
cana-5532	343	3	panamerican	panamerican	PROPN
cana-5532	343	4	mathematical	mathematical	ADJ
cana-5532	343	5	journal	journal	NOUN
cana-5532	343	6	9	9	NUM
cana-5532	343	7	(	(	PUNCT
cana-5532	343	8	1999	1999	NUM
cana-5532	343	9	)	)	PUNCT
cana-5532	343	10	,	,	PUNCT
cana-5532	343	11	pp	pp	ADP
cana-5532	343	12	.	.	PUNCT
cana-5532	344	1	83–102	83–102	X
cana-5532	344	2	.	.	PUNCT
cana-5532	345	1	[	[	X
cana-5532	345	2	9	9	NUM
cana-5532	345	3	]	]	PUNCT
cana-5532	345	4	mohamed	mohamed	PROPN
cana-5532	345	5	ae	ae	PROPN
cana-5532	345	6	herzallah	herzallah	PROPN
cana-5532	345	7	and	and	CCONJ
cana-5532	345	8	dumitru	dumitru	PROPN
cana-5532	345	9	baleanu	baleanu	NOUN
cana-5532	345	10	.	.	PUNCT
cana-5532	346	1	“	"	PUNCT
cana-5532	346	2	on	on	ADP
cana-5532	346	3	fractional	fractional	ADJ
cana-5532	346	4	order	order	NOUN
cana-5532	346	5	hybrid	hybrid	ADJ
cana-5532	346	6	differential	differential	NOUN
cana-5532	346	7	equations	equation	NOUN
cana-5532	346	8	”	"	PUNCT
cana-5532	346	9	.	.	PUNCT
cana-5532	347	1	in	in	ADP
cana-5532	347	2	:	:	PUNCT
cana-5532	347	3	abstract	abstract	ADJ
cana-5532	347	4	and	and	CCONJ
cana-5532	347	5	applied	apply	VERB
cana-5532	347	6	analysis	analysis	NOUN
cana-5532	347	7	.	.	PUNCT
cana-5532	348	1	vol	vol	NOUN
cana-5532	348	2	.	.	PROPN
cana-5532	348	3	2014	2014	NUM
cana-5532	348	4	.	.	PUNCT
cana-5532	349	1	1	1	X
cana-5532	349	2	.	.	X
cana-5532	349	3	wiley	wiley	PROPN
cana-5532	349	4	online	online	PROPN
cana-5532	349	5	library	library	PROPN
cana-5532	349	6	.	.	PUNCT
cana-5532	350	1	2014	2014	NUM
cana-5532	350	2	,	,	PUNCT
cana-5532	350	3	p.	p.	NOUN
cana-5532	350	4	389386	389386	NUM
cana-5532	350	5	.	.	PUNCT
cana-5532	351	1	[	[	X
cana-5532	351	2	10	10	NUM
cana-5532	351	3	]	]	PUNCT
cana-5532	351	4	a.	a.	NOUN
cana-5532	351	5	aleksandrovich	aleksandrovich	PROPN
cana-5532	351	6	kilbas	kilbas	PROPN
cana-5532	351	7	,	,	PUNCT
cana-5532	351	8	hari	hari	PROPN
cana-5532	351	9	m	m	PROPN
cana-5532	351	10	srivastava	srivastava	PROPN
cana-5532	351	11	,	,	PUNCT
cana-5532	351	12	and	and	CCONJ
cana-5532	351	13	juan	juan	PROPN
cana-5532	351	14	j	j	PROPN
cana-5532	351	15	trujillo	trujillo	PROPN
cana-5532	351	16	.	.	PUNCT
cana-5532	351	17	theory	theory	NOUN
cana-5532	351	18	and	and	CCONJ
cana-5532	351	19	applications	application	NOUN
cana-5532	351	20	of	of	ADP
cana-5532	351	21	fractional	fractional	ADJ
cana-5532	351	22	differential	differential	ADJ
cana-5532	351	23	equations	equation	NOUN
cana-5532	351	24	.	.	PUNCT
cana-5532	352	1	vol	vol	NOUN
cana-5532	352	2	.	.	PUNCT
cana-5532	353	1	204	204	NUM
cana-5532	353	2	.	.	PUNCT
cana-5532	354	1	elsevier	elsevier	NOUN
cana-5532	354	2	,	,	PUNCT
cana-5532	354	3	2006	2006	NUM
cana-5532	354	4	.	.	PUNCT
cana-5532	355	1	[	[	X
cana-5532	355	2	11	11	NUM
cana-5532	355	3	]	]	X
cana-5532	355	4	nazim	nazim	PROPN
cana-5532	355	5	mahmudov	mahmudov	PROPN
cana-5532	355	6	and	and	CCONJ
cana-5532	355	7	mohammed	mohammed	PROPN
cana-5532	355	8	m	m	PROPN
cana-5532	355	9	matar	matar	NOUN
cana-5532	355	10	.	.	PUNCT
cana-5532	356	1	“	"	PUNCT
cana-5532	356	2	existence	existence	NOUN
cana-5532	356	3	of	of	ADP
cana-5532	356	4	mild	mild	ADJ
cana-5532	356	5	solution	solution	NOUN
cana-5532	356	6	for	for	ADP
cana-5532	356	7	hybrid	hybrid	ADJ
cana-5532	356	8	differential	differential	ADJ
cana-5532	356	9	equations	equation	NOUN
cana-5532	356	10	with	with	ADP
cana-5532	356	11	arbitrary	arbitrary	ADJ
cana-5532	356	12	fractional	fractional	ADJ
cana-5532	356	13	order	order	NOUN
cana-5532	356	14	”	"	PUNCT
cana-5532	356	15	.	.	PUNCT
cana-5532	357	1	in	in	ADP
cana-5532	357	2	:	:	PUNCT
cana-5532	357	3	twms	twms	PROPN
cana-5532	357	4	journal	journal	PROPN
cana-5532	357	5	of	of	ADP
cana-5532	357	6	pure	pure	ADJ
cana-5532	357	7	and	and	CCONJ
cana-5532	357	8	applied	applied	ADJ
cana-5532	357	9	mathematics	mathematic	NOUN
cana-5532	357	10	8.2	8.2	NUM
cana-5532	357	11	(	(	PUNCT
cana-5532	357	12	2017	2017	NUM
cana-5532	357	13	)	)	PUNCT
cana-5532	357	14	,	,	PUNCT
cana-5532	357	15	pp	pp	ADP
cana-5532	357	16	.	.	PUNCT
cana-5532	358	1	160–169	160–169	NUM
cana-5532	358	2	.	.	PUNCT
cana-5532	359	1	[	[	X
cana-5532	359	2	12	12	NUM
cana-5532	359	3	]	]	X
cana-5532	359	4	francesco	francesco	PROPN
cana-5532	359	5	mainardi	mainardi	PROPN
cana-5532	359	6	.	.	PUNCT
cana-5532	360	1	fractional	fractional	ADJ
cana-5532	360	2	calculus	calculus	NOUN
cana-5532	360	3	and	and	CCONJ
cana-5532	360	4	waves	wave	NOUN
cana-5532	360	5	in	in	ADP
cana-5532	360	6	linear	linear	PROPN
cana-5532	360	7	viscoelasticity	viscoelasticity	NOUN
cana-5532	360	8	:	:	PUNCT
cana-5532	360	9	an	an	DET
cana-5532	360	10	introduction	introduction	NOUN
cana-5532	360	11	to	to	ADP
cana-5532	360	12	mathematical	mathematical	ADJ
cana-5532	360	13	models	model	NOUN
cana-5532	360	14	.	.	PUNCT
cana-5532	361	1	world	world	NOUN
cana-5532	361	2	scientific	scientific	ADJ
cana-5532	361	3	,	,	PUNCT
cana-5532	361	4	2022	2022	NUM
cana-5532	361	5	.	.	PUNCT
cana-5532	362	1	[	[	X
cana-5532	362	2	13	13	NUM
cana-5532	362	3	]	]	X
cana-5532	362	4	kenneth	kenneth	PROPN
cana-5532	362	5	s	s	PROPN
cana-5532	362	6	miller	miller	PROPN
cana-5532	362	7	and	and	CCONJ
cana-5532	362	8	bertram	bertram	PROPN
cana-5532	362	9	ross	ross	PROPN
cana-5532	362	10	.	.	PUNCT
cana-5532	363	1	“	"	PUNCT
cana-5532	363	2	an	an	DET
cana-5532	363	3	introduction	introduction	NOUN
cana-5532	363	4	to	to	ADP
cana-5532	363	5	the	the	DET
cana-5532	363	6	fractional	fractional	ADJ
cana-5532	363	7	calculus	calculus	NOUN
cana-5532	363	8	and	and	CCONJ
cana-5532	363	9	fractional	fractional	ADJ
cana-5532	363	10	differential	differential	ADJ
cana-5532	363	11	equations	equation	NOUN
cana-5532	363	12	”	"	PUNCT
cana-5532	363	13	.	.	PUNCT
cana-5532	364	1	in	in	ADP
cana-5532	364	2	:	:	PUNCT
cana-5532	364	3	(	(	PUNCT
cana-5532	364	4	no	no	DET
cana-5532	364	5	title	title	NOUN
cana-5532	364	6	)	)	PUNCT
cana-5532	364	7	(	(	PUNCT
cana-5532	364	8	1993	1993	NUM
cana-5532	364	9	)	)	PUNCT
cana-5532	364	10	.	.	PUNCT
cana-5532	365	1	communications	communication	NOUN
cana-5532	365	2	on	on	ADP
cana-5532	365	3	applied	apply	VERB
cana-5532	365	4	nonlinear	nonlinear	ADJ
cana-5532	365	5	analysis	analysis	NOUN
cana-5532	365	6	issn	issn	NOUN
cana-5532	365	7	:	:	PUNCT
cana-5532	365	8	1074	1074	NUM
cana-5532	365	9	-	-	PUNCT
cana-5532	365	10	133x	133x	NUM
cana-5532	365	11	vol	vol	NOUN
cana-5532	365	12	32	32	NUM
cana-5532	365	13	no	no	NOUN
cana-5532	365	14	.	.	NOUN
cana-5532	365	15	3	3	NUM
cana-5532	365	16	(	(	PUNCT
cana-5532	365	17	2025	2025	NUM
cana-5532	365	18	)	)	PUNCT
cana-5532	365	19	994	994	NUM
cana-5532	365	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-5532	366	1	[	[	X
cana-5532	366	2	14	14	NUM
cana-5532	366	3	]	]	X
cana-5532	366	4	igor	igor	NOUN
cana-5532	366	5	podlubny	podlubny	PROPN
cana-5532	366	6	.	.	PUNCT
cana-5532	367	1	fractional	fractional	ADJ
cana-5532	367	2	differential	differential	ADJ
cana-5532	367	3	equations	equation	NOUN
cana-5532	367	4	:	:	PUNCT
cana-5532	367	5	an	an	DET
cana-5532	367	6	introduction	introduction	NOUN
cana-5532	367	7	to	to	ADP
cana-5532	367	8	fractional	fractional	ADJ
cana-5532	367	9	derivatives	derivative	NOUN
cana-5532	367	10	,	,	PUNCT
cana-5532	367	11	fractional	fractional	ADJ
cana-5532	367	12	differential	differential	ADJ
cana-5532	367	13	equations	equation	NOUN
cana-5532	367	14	,	,	PUNCT
cana-5532	367	15	to	to	ADP
cana-5532	367	16	methods	method	NOUN
cana-5532	367	17	of	of	ADP
cana-5532	367	18	their	their	PRON
cana-5532	367	19	solution	solution	NOUN
cana-5532	367	20	and	and	CCONJ
cana-5532	367	21	some	some	PRON
cana-5532	367	22	of	of	ADP
cana-5532	367	23	their	their	PRON
cana-5532	367	24	applications	application	NOUN
cana-5532	367	25	.	.	PUNCT
cana-5532	368	1	vol	vol	NOUN
cana-5532	368	2	.	.	PROPN
cana-5532	369	1	198	198	NUM
cana-5532	369	2	.	.	PUNCT
cana-5532	370	1	elsevier	elsevier	NOUN
cana-5532	370	2	,	,	PUNCT
cana-5532	370	3	1998	1998	NUM
cana-5532	370	4	.	.	PUNCT
cana-5532	371	1	[	[	X
cana-5532	371	2	15	15	NUM
cana-5532	371	3	]	]	X
cana-5532	371	4	surang	surang	PROPN
cana-5532	371	5	sitho	sitho	PROPN
cana-5532	371	6	,	,	PUNCT
cana-5532	371	7	sotiris	sotiris	NOUN
cana-5532	371	8	k	k	PROPN
cana-5532	371	9	ntouyas	ntouyas	PROPN
cana-5532	371	10	,	,	PUNCT
cana-5532	371	11	and	and	CCONJ
cana-5532	371	12	jessada	jessada	PROPN
cana-5532	371	13	tariboon	tariboon	NOUN
cana-5532	371	14	.	.	PUNCT
cana-5532	372	1	“	"	PUNCT
cana-5532	372	2	existence	existence	NOUN
cana-5532	372	3	results	result	VERB
cana-5532	372	4	for	for	ADP
cana-5532	372	5	hybrid	hybrid	ADJ
cana-5532	372	6	fractional	fractional	ADJ
cana-5532	372	7	integro	integro	ADJ
cana-5532	372	8	-	-	PUNCT
cana-5532	372	9	differential	differential	NOUN
cana-5532	372	10	equations	equation	NOUN
cana-5532	372	11	”	"	PUNCT
cana-5532	372	12	.	.	PUNCT
cana-5532	373	1	in	in	ADP
cana-5532	373	2	:	:	PUNCT
cana-5532	373	3	boundary	boundary	ADJ
cana-5532	373	4	value	value	NOUN
cana-5532	373	5	problems	problem	NOUN
cana-5532	373	6	2015	2015	NUM
cana-5532	373	7	(	(	PUNCT
cana-5532	373	8	2015	2015	NUM
cana-5532	373	9	)	)	PUNCT
cana-5532	373	10	,	,	PUNCT
cana-5532	373	11	pp	pp	PROPN
cana-5532	373	12	.	.	PUNCT
cana-5532	373	13	1–13	1–13	NOUN
cana-5532	373	14	.	.	PUNCT
cana-5532	374	1	[	[	X
cana-5532	374	2	16	16	NUM
cana-5532	374	3	]	]	X
cana-5532	374	4	hari	hari	PROPN
cana-5532	374	5	mohan	mohan	PROPN
cana-5532	374	6	srivastava	srivastava	PROPN
cana-5532	374	7	and	and	CCONJ
cana-5532	374	8	khaled	khaled	PROPN
cana-5532	374	9	m	m	PROPN
cana-5532	374	10	saad	saad	PROPN
cana-5532	374	11	.	.	PUNCT
cana-5532	375	1	“	"	PUNCT
cana-5532	375	2	some	some	DET
cana-5532	375	3	new	new	ADJ
cana-5532	375	4	models	model	NOUN
cana-5532	375	5	of	of	ADP
cana-5532	375	6	the	the	DET
cana-5532	375	7	time	time	NOUN
cana-5532	375	8	-	-	PUNCT
cana-5532	375	9	fractional	fractional	ADJ
cana-5532	375	10	gas	gas	NOUN
cana-5532	375	11	dynamics	dynamic	NOUN
cana-5532	375	12	equation	equation	NOUN
cana-5532	375	13	”	"	PUNCT
cana-5532	375	14	.	.	PUNCT
cana-5532	376	1	in	in	ADP
cana-5532	376	2	:	:	PUNCT
cana-5532	376	3	adv	adv	PROPN
cana-5532	376	4	.	.	PUNCT
cana-5532	376	5	math	math	PROPN
cana-5532	376	6	.	.	PUNCT
cana-5532	377	1	models	model	NOUN
cana-5532	377	2	appl	appl	PROPN
cana-5532	377	3	3.1	3.1	NUM
cana-5532	377	4	(	(	PUNCT
cana-5532	377	5	2018	2018	NUM
cana-5532	377	6	)	)	PUNCT
cana-5532	377	7	,	,	PUNCT
cana-5532	377	8	pp	pp	PROPN
cana-5532	377	9	.	.	PUNCT
cana-5532	378	1	5–17	5–17	NOUN
cana-5532	378	2	.	.	PUNCT
cana-5532	379	1	[	[	X
cana-5532	379	2	17	17	NUM
cana-5532	379	3	]	]	X
cana-5532	379	4	zakir	zakir	PROPN
cana-5532	379	5	ullah	ullah	PROPN
cana-5532	379	6	et	et	PROPN
cana-5532	379	7	al	al	PROPN
cana-5532	379	8	.	.	PUNCT
cana-5532	380	1	“	"	PUNCT
cana-5532	380	2	existence	existence	NOUN
cana-5532	380	3	results	result	VERB
cana-5532	380	4	to	to	ADP
cana-5532	380	5	a	a	DET
cana-5532	380	6	class	class	NOUN
cana-5532	380	7	of	of	ADP
cana-5532	380	8	hybrid	hybrid	ADJ
cana-5532	380	9	fractional	fractional	ADJ
cana-5532	380	10	differential	differential	NOUN
cana-5532	380	11	equations	equation	NOUN
cana-5532	380	12	”	"	PUNCT
cana-5532	380	13	.	.	PUNCT
cana-5532	381	1	in	in	ADP
cana-5532	381	2	:	:	PUNCT
cana-5532	381	3	matrix	matrix	NOUN
cana-5532	381	4	sci	sci	PROPN
cana-5532	381	5	.	.	PUNCT
cana-5532	381	6	math	math	PROPN
cana-5532	381	7	2.1	2.1	NUM
cana-5532	381	8	(	(	PUNCT
cana-5532	381	9	2018	2018	NUM
cana-5532	381	10	)	)	PUNCT
cana-5532	381	11	,	,	PUNCT
cana-5532	381	12	pp	pp	ADJ
cana-5532	381	13	.	.	PUNCT
cana-5532	381	14	13–17	13–17	NUM
cana-5532	381	15	.	.	PUNCT
cana-5532	382	1	[	[	X
cana-5532	382	2	18	18	NUM
cana-5532	382	3	]	]	PUNCT
cana-5532	382	4	yige	yige	PROPN
cana-5532	382	5	zhao	zhao	PROPN
cana-5532	382	6	et	et	PROPN
cana-5532	382	7	al	al	PROPN
cana-5532	382	8	.	.	PUNCT
cana-5532	383	1	“	"	PUNCT
cana-5532	383	2	theory	theory	NOUN
cana-5532	383	3	of	of	ADP
cana-5532	383	4	fractional	fractional	ADJ
cana-5532	383	5	hybrid	hybrid	ADJ
cana-5532	383	6	differential	differential	NOUN
cana-5532	383	7	equations	equation	NOUN
cana-5532	383	8	”	"	PUNCT
cana-5532	383	9	.	.	PUNCT
cana-5532	384	1	in	in	ADP
cana-5532	384	2	:	:	PUNCT
cana-5532	384	3	computers	computer	NOUN
cana-5532	384	4	&	&	CCONJ
cana-5532	384	5	mathematics	mathematic	NOUN
cana-5532	384	6	with	with	ADP
cana-5532	384	7	applications	application	NOUN
cana-5532	384	8	62.3	62.3	NUM
cana-5532	384	9	(	(	PUNCT
cana-5532	384	10	2011	2011	NUM
cana-5532	384	11	)	)	PUNCT
cana-5532	384	12	,	,	PUNCT
cana-5532	384	13	pp	pp	ADP
cana-5532	384	14	.	.	PUNCT
cana-5532	385	1	1312–1324	1312–1324	NUM
cana-5532	385	2	.	.	PUNCT