id	sid	tid	token	lemma	pos
cana-1739	1	1	communications	communication	NOUN
cana-1739	1	2	on	on	ADP
cana-1739	1	3	applied	apply	VERB
cana-1739	1	4	nonlinear	nonlinear	ADJ
cana-1739	1	5	analysis	analysis	NOUN
cana-1739	1	6	issn	issn	NOUN
cana-1739	1	7	:	:	PUNCT
cana-1739	1	8	1074	1074	NUM
cana-1739	1	9	-	-	PUNCT
cana-1739	1	10	133x	133x	NUM
cana-1739	1	11	vol	vol	NOUN
cana-1739	1	12	32	32	NUM
cana-1739	1	13	no	no	NOUN
cana-1739	1	14	.	.	NOUN
cana-1739	1	15	2	2	NUM
cana-1739	1	16	(	(	PUNCT
cana-1739	1	17	2025	2025	NUM
cana-1739	1	18	)	)	PUNCT
cana-1739	1	19	231	231	NUM
cana-1739	1	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1739	1	21	dynamic	dynamic	ADJ
cana-1739	1	22	effect	effect	NOUN
cana-1739	1	23	of	of	ADP
cana-1739	1	24	green	green	ADJ
cana-1739	1	25	building	building	NOUN
cana-1739	1	26	concept	concept	NOUN
cana-1739	1	27	for	for	ADP
cana-1739	1	28	sustainable	sustainable	ADJ
cana-1739	1	29	cities	city	NOUN
cana-1739	1	30	under	under	ADP
cana-1739	1	31	climate	climate	NOUN
cana-1739	1	32	change	change	NOUN
cana-1739	1	33	via	via	ADP
cana-1739	1	34	variable	variable	ADJ
cana-1739	1	35	-	-	PUNCT
cana-1739	1	36	order	order	NOUN
cana-1739	1	37	fractional	fractional	ADJ
cana-1739	1	38	derivatives	derivative	NOUN
cana-1739	1	39	t.saradhadevi1	t.saradhadevi1	NOUN
cana-1739	1	40	,	,	PUNCT
cana-1739	1	41	a.kalavathi2	a.kalavathi2	PROPN
cana-1739	1	42	1research	1research	NUM
cana-1739	1	43	scholar	scholar	NOUN
cana-1739	1	44	,	,	PUNCT
cana-1739	1	45	department	department	NOUN
cana-1739	1	46	of	of	ADP
cana-1739	1	47	mathematics	mathematics	PROPN
cana-1739	1	48	,	,	PUNCT
cana-1739	1	49	sri	sri	NOUN
cana-1739	1	50	gvg	gvg	NOUN
cana-1739	1	51	,	,	PUNCT
cana-1739	1	52	visalakshi	visalakshi	PROPN
cana-1739	1	53	college	college	NOUN
cana-1739	1	54	for	for	ADP
cana-1739	1	55	women	woman	NOUN
cana-1739	1	56	,	,	PUNCT
cana-1739	1	57	udumalpet	udumalpet	ADJ
cana-1739	1	58	,	,	PUNCT
cana-1739	1	59	tamilnadu	tamilnadu	NOUN
cana-1739	1	60	,	,	PUNCT
cana-1739	1	61	india	india	PROPN
cana-1739	1	62	,	,	PUNCT
cana-1739	1	63	email	email	NOUN
cana-1739	1	64	id:search2saradha@gmail.com	id:search2saradha@gmail.com	NOUN
cana-1739	2	1	2assistant	2assistant	NUM
cana-1739	2	2	professor	professor	NOUN
cana-1739	2	3	,	,	PUNCT
cana-1739	2	4	department	department	NOUN
cana-1739	2	5	of	of	ADP
cana-1739	2	6	mathematics	mathematics	PROPN
cana-1739	2	7	,	,	PUNCT
cana-1739	2	8	sri	sri	NOUN
cana-1739	2	9	gvg	gvg	NOUN
cana-1739	2	10	,	,	PUNCT
cana-1739	2	11	visalakshi	visalakshi	PROPN
cana-1739	2	12	college	college	NOUN
cana-1739	2	13	for	for	ADP
cana-1739	2	14	women	woman	NOUN
cana-1739	2	15	,	,	PUNCT
cana-1739	2	16	udumalpet	udumalpet	ADJ
cana-1739	2	17	,	,	PUNCT
cana-1739	2	18	tamilnadu	tamilnadu	NOUN
cana-1739	2	19	,	,	PUNCT
cana-1739	2	20	india	india	PROPN
cana-1739	2	21	,	,	PUNCT
cana-1739	2	22	email	email	NOUN
cana-1739	2	23	i	i	PROPN
cana-1739	2	24	d	d	PROPN
cana-1739	2	25	:	:	PUNCT
cana-1739	2	26	kalavathigvg2018@gmail.com	kalavathigvg2018@gmail.com	PROPN
cana-1739	2	27	article	article	PROPN
cana-1739	2	28	history	history	NOUN
cana-1739	2	29	:	:	PUNCT
cana-1739	2	30	received	receive	VERB
cana-1739	2	31	:	:	PUNCT
cana-1739	2	32	31	31	NUM
cana-1739	2	33	-	-	SYM
cana-1739	2	34	07	07	NUM
cana-1739	2	35	-	-	PUNCT
cana-1739	2	36	2024	2024	NUM
cana-1739	2	37	revised	revise	VERB
cana-1739	2	38	:	:	PUNCT
cana-1739	2	39	09	09	NUM
cana-1739	2	40	-	-	SYM
cana-1739	2	41	09	09	NUM
cana-1739	2	42	-	-	PUNCT
cana-1739	2	43	2024	2024	NUM
cana-1739	2	44	accepted	accept	VERB
cana-1739	2	45	:	:	PUNCT
cana-1739	2	46	18	18	NUM
cana-1739	2	47	-	-	SYM
cana-1739	2	48	09	09	NUM
cana-1739	2	49	-	-	PUNCT
cana-1739	2	50	2024	2024	NUM
cana-1739	2	51	abstract	abstract	NOUN
cana-1739	2	52	:	:	PUNCT
cana-1739	2	53	this	this	DET
cana-1739	2	54	study	study	NOUN
cana-1739	2	55	introduces	introduce	VERB
cana-1739	2	56	an	an	DET
cana-1739	2	57	innovative	innovative	ADJ
cana-1739	2	58	fractional	fractional	ADJ
cana-1739	2	59	order	order	NOUN
cana-1739	2	60	model	model	NOUN
cana-1739	2	61	that	that	PRON
cana-1739	2	62	delves	delve	VERB
cana-1739	2	63	into	into	ADP
cana-1739	2	64	the	the	DET
cana-1739	2	65	core	core	ADJ
cana-1739	2	66	principles	principle	NOUN
cana-1739	2	67	of	of	ADP
cana-1739	2	68	sustainable	sustainable	ADJ
cana-1739	2	69	constructions	construction	NOUN
cana-1739	2	70	,	,	PUNCT
cana-1739	2	71	incorporating	incorporate	VERB
cana-1739	2	72	liouville	liouville	NOUN
cana-1739	2	73	-	-	PUNCT
cana-1739	2	74	caputo	caputo	PROPN
cana-1739	2	75	,	,	PUNCT
cana-1739	2	76	caputo	caputo	PROPN
cana-1739	2	77	-	-	PUNCT
cana-1739	2	78	fabrizio	fabrizio	PROPN
cana-1739	2	79	,	,	PUNCT
cana-1739	2	80	and	and	CCONJ
cana-1739	2	81	atangana	atangana	PROPN
cana-1739	2	82	-	-	PUNCT
cana-1739	2	83	baleanu	baleanu	ADJ
cana-1739	2	84	derivatives	derivative	NOUN
cana-1739	2	85	.	.	PUNCT
cana-1739	3	1	it	it	PRON
cana-1739	3	2	examines	examine	VERB
cana-1739	3	3	the	the	DET
cana-1739	3	4	increasing	increase	VERB
cana-1739	3	5	adoption	adoption	NOUN
cana-1739	3	6	of	of	ADP
cana-1739	3	7	eco	eco	PROPN
cana-1739	3	8	-	-	PUNCT
cana-1739	3	9	friendly	friendly	ADJ
cana-1739	3	10	buildings	building	NOUN
cana-1739	3	11	in	in	ADP
cana-1739	3	12	india	india	PROPN
cana-1739	3	13	as	as	ADP
cana-1739	3	14	a	a	DET
cana-1739	3	15	crucial	crucial	ADJ
cana-1739	3	16	remedy	remedy	NOUN
cana-1739	3	17	against	against	ADP
cana-1739	3	18	climate	climate	NOUN
cana-1739	3	19	change	change	NOUN
cana-1739	3	20	.	.	PUNCT
cana-1739	4	1	by	by	ADP
cana-1739	4	2	revealing	reveal	VERB
cana-1739	4	3	innovative	innovative	ADJ
cana-1739	4	4	perspectives	perspective	NOUN
cana-1739	4	5	on	on	ADP
cana-1739	4	6	fractional	fractional	ADJ
cana-1739	4	7	solutions	solution	NOUN
cana-1739	4	8	,	,	PUNCT
cana-1739	4	9	encompassing	encompass	VERB
cana-1739	4	10	their	their	PRON
cana-1739	4	11	validity	validity	NOUN
cana-1739	4	12	and	and	CCONJ
cana-1739	4	13	distinctiveness	distinctiveness	NOUN
cana-1739	4	14	,	,	PUNCT
cana-1739	4	15	the	the	DET
cana-1739	4	16	research	research	NOUN
cana-1739	4	17	conducts	conduct	VERB
cana-1739	4	18	computational	computational	ADJ
cana-1739	4	19	analyses	analysis	NOUN
cana-1739	4	20	to	to	PART
cana-1739	4	21	evaluate	evaluate	VERB
cana-1739	4	22	the	the	DET
cana-1739	4	23	impacts	impact	NOUN
cana-1739	4	24	of	of	ADP
cana-1739	4	25	greenhouse	greenhouse	NOUN
cana-1739	4	26	gas	gas	NOUN
cana-1739	4	27	(	(	PUNCT
cana-1739	4	28	ghg	ghg	PROPN
cana-1739	4	29	)	)	PUNCT
cana-1739	4	30	elements	element	NOUN
cana-1739	4	31	.	.	PUNCT
cana-1739	5	1	visual	visual	ADJ
cana-1739	5	2	representations	representation	NOUN
cana-1739	5	3	demonstrate	demonstrate	VERB
cana-1739	5	4	the	the	DET
cana-1739	5	5	dynamics	dynamic	NOUN
cana-1739	5	6	of	of	ADP
cana-1739	5	7	the	the	DET
cana-1739	5	8	model	model	NOUN
cana-1739	5	9	,	,	PUNCT
cana-1739	5	10	emphasizing	emphasize	VERB
cana-1739	5	11	the	the	DET
cana-1739	5	12	influences	influence	NOUN
cana-1739	5	13	of	of	ADP
cana-1739	5	14	various	various	ADJ
cana-1739	5	15	fractional	fractional	ADJ
cana-1739	5	16	order	order	NOUN
cana-1739	5	17	parameters	parameter	NOUN
cana-1739	5	18	across	across	ADP
cana-1739	5	19	different	different	ADJ
cana-1739	5	20	scenarios	scenario	NOUN
cana-1739	5	21	.	.	PUNCT
cana-1739	6	1	keywords	keyword	NOUN
cana-1739	6	2	:	:	PUNCT
cana-1739	6	3	fractional	fractional	ADJ
cana-1739	6	4	variable	variable	ADJ
cana-1739	6	5	-	-	PUNCT
cana-1739	6	6	order	order	NOUN
cana-1739	6	7	model	model	NOUN
cana-1739	6	8	,	,	PUNCT
cana-1739	6	9	liouville	liouville	NOUN
cana-1739	6	10	-	-	PUNCT
cana-1739	6	11	caputo	caputo	PROPN
cana-1739	6	12	,	,	PUNCT
cana-1739	6	13	caputo	caputo	PROPN
cana-1739	6	14	-	-	PUNCT
cana-1739	6	15	fabrizio	fabrizio	PROPN
cana-1739	6	16	,	,	PUNCT
cana-1739	6	17	atangana	atangana	PROPN
cana-1739	6	18	-	-	PUNCT
cana-1739	6	19	baleanu	baleanu	PROPN
cana-1739	6	20	,	,	PUNCT
cana-1739	6	21	numerical	numerical	ADJ
cana-1739	6	22	simulations	simulation	NOUN
cana-1739	6	23	.	.	PUNCT
cana-1739	7	1	1	1	X
cana-1739	7	2	.	.	X
cana-1739	7	3	introduction	introduction	NOUN
cana-1739	7	4	in	in	ADP
cana-1739	7	5	recent	recent	ADJ
cana-1739	7	6	years	year	NOUN
cana-1739	7	7	,	,	PUNCT
cana-1739	7	8	there	there	PRON
cana-1739	7	9	has	have	AUX
cana-1739	7	10	been	be	AUX
cana-1739	7	11	a	a	DET
cana-1739	7	12	notable	notable	ADJ
cana-1739	7	13	global	global	ADJ
cana-1739	7	14	increase	increase	NOUN
cana-1739	7	15	in	in	ADP
cana-1739	7	16	the	the	DET
cana-1739	7	17	utilization	utilization	NOUN
cana-1739	7	18	of	of	ADP
cana-1739	7	19	sustainable	sustainable	ADJ
cana-1739	7	20	construction	construction	NOUN
cana-1739	7	21	methods	method	NOUN
cana-1739	7	22	as	as	ADP
cana-1739	7	23	a	a	DET
cana-1739	7	24	key	key	ADJ
cana-1739	7	25	approach	approach	NOUN
cana-1739	7	26	to	to	ADP
cana-1739	7	27	tackling	tackle	VERB
cana-1739	7	28	the	the	DET
cana-1739	7	29	issues	issue	NOUN
cana-1739	7	30	related	relate	VERB
cana-1739	7	31	to	to	ADP
cana-1739	7	32	climate	climate	NOUN
cana-1739	7	33	change	change	NOUN
cana-1739	7	34	.	.	PUNCT
cana-1739	8	1	currently	currently	ADV
cana-1739	8	2	,	,	PUNCT
cana-1739	8	3	buildings	building	NOUN
cana-1739	8	4	contribute	contribute	VERB
cana-1739	8	5	to	to	ADP
cana-1739	8	6	7.85	7.85	NUM
cana-1739	8	7	gigatons	gigaton	NOUN
cana-1739	8	8	(	(	PUNCT
cana-1739	8	9	gt	gt	INTJ
cana-1739	8	10	)	)	PUNCT
cana-1739	8	11	or	or	CCONJ
cana-1739	8	12	33	33	NUM
cana-1739	8	13	%	%	NOUN
cana-1739	8	14	of	of	ADP
cana-1739	8	15	all	all	DET
cana-1739	8	16	energy	energy	NOUN
cana-1739	8	17	-	-	PUNCT
cana-1739	8	18	linked	link	VERB
cana-1739	8	19	co2	co2	NOUN
cana-1739	8	20	emissions	emission	NOUN
cana-1739	8	21	worldwide	worldwide	ADV
cana-1739	8	22	.	.	PUNCT
cana-1739	9	1	forecasts	forecast	NOUN
cana-1739	9	2	suggest	suggest	VERB
cana-1739	9	3	that	that	SCONJ
cana-1739	9	4	by	by	ADP
cana-1739	9	5	2030	2030	NUM
cana-1739	9	6	,	,	PUNCT
cana-1739	9	7	these	these	DET
cana-1739	9	8	emissions	emission	NOUN
cana-1739	9	9	could	could	AUX
cana-1739	9	10	potentially	potentially	ADV
cana-1739	9	11	rise	rise	VERB
cana-1739	9	12	to	to	ADP
cana-1739	9	13	between	between	ADP
cana-1739	9	14	11	11	NUM
cana-1739	9	15	and	and	CCONJ
cana-1739	9	16	15.6	15.6	NUM
cana-1739	9	17	gt	gt	PROPN
cana-1739	9	18	.	.	PUNCT
cana-1739	10	1	specifically	specifically	ADV
cana-1739	10	2	,	,	PUNCT
cana-1739	10	3	developed	develop	VERB
cana-1739	10	4	nations	nation	NOUN
cana-1739	10	5	observe	observe	VERB
cana-1739	10	6	buildings	building	NOUN
cana-1739	10	7	consuming	consume	VERB
cana-1739	10	8	over	over	ADP
cana-1739	10	9	41	41	NUM
cana-1739	10	10	%	%	NOUN
cana-1739	10	11	of	of	ADP
cana-1739	10	12	total	total	ADJ
cana-1739	10	13	energy	energy	NOUN
cana-1739	10	14	usage	usage	NOUN
cana-1739	10	15	.	.	PUNCT
cana-1739	11	1	in	in	ADP
cana-1739	11	2	india	india	PROPN
cana-1739	11	3	,	,	PUNCT
cana-1739	11	4	the	the	DET
cana-1739	11	5	rapid	rapid	ADJ
cana-1739	11	6	growth	growth	NOUN
cana-1739	11	7	in	in	ADP
cana-1739	11	8	urbanization	urbanization	NOUN
cana-1739	11	9	,	,	PUNCT
cana-1739	11	10	population	population	NOUN
cana-1739	11	11	expansion	expansion	NOUN
cana-1739	11	12	,	,	PUNCT
cana-1739	11	13	and	and	CCONJ
cana-1739	11	14	the	the	DET
cana-1739	11	15	flourishing	flourish	VERB
cana-1739	11	16	it	it	PRON
cana-1739	11	17	sector	sector	NOUN
cana-1739	11	18	and	and	CCONJ
cana-1739	11	19	its	its	PRON
cana-1739	11	20	related	related	ADJ
cana-1739	11	21	industries	industry	NOUN
cana-1739	11	22	are	be	AUX
cana-1739	11	23	major	major	ADJ
cana-1739	11	24	factors	factor	NOUN
cana-1739	11	25	contributing	contribute	VERB
cana-1739	11	26	to	to	ADP
cana-1739	11	27	the	the	DET
cana-1739	11	28	escalating	escalate	VERB
cana-1739	11	29	energy	energy	NOUN
cana-1739	11	30	needs	need	NOUN
cana-1739	11	31	.	.	PUNCT
cana-1739	12	1	green	green	ADJ
cana-1739	12	2	structures	structure	NOUN
cana-1739	12	3	are	be	AUX
cana-1739	12	4	created	create	VERB
cana-1739	12	5	,	,	PUNCT
cana-1739	12	6	constructed	construct	VERB
cana-1739	12	7	,	,	PUNCT
cana-1739	12	8	and	and	CCONJ
cana-1739	12	9	managed	manage	VERB
cana-1739	12	10	with	with	ADP
cana-1739	12	11	the	the	DET
cana-1739	12	12	aim	aim	NOUN
cana-1739	12	13	of	of	ADP
cana-1739	12	14	minimizing	minimize	VERB
cana-1739	12	15	their	their	PRON
cana-1739	12	16	ecological	ecological	ADJ
cana-1739	12	17	impact	impact	NOUN
cana-1739	12	18	while	while	SCONJ
cana-1739	12	19	enhancing	enhance	VERB
cana-1739	12	20	efficiency	efficiency	NOUN
cana-1739	12	21	and	and	CCONJ
cana-1739	12	22	functionality	functionality	NOUN
cana-1739	12	23	.	.	PUNCT
cana-1739	13	1	this	this	PRON
cana-1739	13	2	involves	involve	VERB
cana-1739	13	3	strategies	strategy	NOUN
cana-1739	13	4	like	like	ADP
cana-1739	13	5	water	water	NOUN
cana-1739	13	6	preservation	preservation	NOUN
cana-1739	13	7	,	,	PUNCT
cana-1739	13	8	reducing	reduce	VERB
cana-1739	13	9	energy	energy	NOUN
cana-1739	13	10	usage	usage	NOUN
cana-1739	13	11	,	,	PUNCT
cana-1739	13	12	and	and	CCONJ
cana-1739	13	13	employing	employ	VERB
cana-1739	13	14	sustainable	sustainable	ADJ
cana-1739	13	15	resources	resource	NOUN
cana-1739	13	16	.	.	PUNCT
cana-1739	14	1	in	in	ADP
cana-1739	14	2	india	india	PROPN
cana-1739	14	3	,	,	PUNCT
cana-1739	14	4	there	there	PRON
cana-1739	14	5	has	have	AUX
cana-1739	14	6	been	be	AUX
cana-1739	14	7	a	a	DET
cana-1739	14	8	significant	significant	ADJ
cana-1739	14	9	rise	rise	NOUN
cana-1739	14	10	in	in	ADP
cana-1739	14	11	the	the	DET
cana-1739	14	12	volume	volume	NOUN
cana-1739	14	13	of	of	ADP
cana-1739	14	14	environmentally	environmentally	ADV
cana-1739	14	15	friendly	friendly	ADJ
cana-1739	14	16	building	building	NOUN
cana-1739	14	17	space	space	NOUN
cana-1739	14	18	,	,	PUNCT
cana-1739	14	19	with	with	ADP
cana-1739	14	20	the	the	DET
cana-1739	14	21	indian	indian	ADJ
cana-1739	14	22	green	green	PROPN
cana-1739	14	23	building	building	PROPN
cana-1739	14	24	council	council	PROPN
cana-1739	14	25	(	(	PUNCT
cana-1739	14	26	igbc	igbc	PROPN
cana-1739	14	27	)	)	PUNCT
cana-1739	14	28	certifying	certify	VERB
cana-1739	14	29	over	over	ADP
cana-1739	14	30	7.6	7.6	NUM
cana-1739	14	31	billion	billion	NUM
cana-1739	14	32	square	square	ADJ
cana-1739	14	33	feet	foot	NOUN
cana-1739	14	34	of	of	ADP
cana-1739	14	35	green	green	ADJ
cana-1739	14	36	building	building	NOUN
cana-1739	14	37	space	space	NOUN
cana-1739	14	38	as	as	ADP
cana-1739	14	39	of	of	ADP
cana-1739	14	40	august	august	PROPN
cana-1739	14	41	2023	2023	NUM
cana-1739	14	42	.	.	PUNCT
cana-1739	15	1	this	this	PRON
cana-1739	15	2	reflects	reflect	VERB
cana-1739	15	3	a	a	DET
cana-1739	15	4	notable	notable	ADJ
cana-1739	15	5	increase	increase	NOUN
cana-1739	15	6	from	from	ADP
cana-1739	15	7	the	the	DET
cana-1739	15	8	3.6	3.6	NUM
cana-1739	15	9	billion	billion	NUM
cana-1739	15	10	square	square	ADJ
cana-1739	15	11	feet	foot	NOUN
cana-1739	15	12	of	of	ADP
cana-1739	15	13	certified	certify	VERB
cana-1739	15	14	green	green	ADJ
cana-1739	15	15	building	building	NOUN
cana-1739	15	16	space	space	NOUN
cana-1739	15	17	in	in	ADP
cana-1739	15	18	2018	2018	NUM
cana-1739	15	19	.	.	PUNCT
cana-1739	16	1	the	the	DET
cana-1739	16	2	expansion	expansion	NOUN
cana-1739	16	3	of	of	ADP
cana-1739	16	4	sustainable	sustainable	ADJ
cana-1739	16	5	construction	construction	NOUN
cana-1739	16	6	in	in	ADP
cana-1739	16	7	india	india	PROPN
cana-1739	16	8	is	be	AUX
cana-1739	16	9	being	be	AUX
cana-1739	16	10	primarily	primarily	ADV
cana-1739	16	11	influenced	influence	VERB
cana-1739	16	12	by	by	ADP
cana-1739	16	13	several	several	ADJ
cana-1739	16	14	factors	factor	NOUN
cana-1739	16	15	,	,	PUNCT
cana-1739	16	16	including	include	VERB
cana-1739	16	17	governmental	governmental	ADJ
cana-1739	16	18	efforts	effort	NOUN
cana-1739	16	19	,	,	PUNCT
cana-1739	16	20	rising	rise	VERB
cana-1739	16	21	consumer	consumer	NOUN
cana-1739	16	22	awareness	awareness	NOUN
cana-1739	16	23	,	,	PUNCT
cana-1739	16	24	and	and	CCONJ
cana-1739	16	25	growing	grow	VERB
cana-1739	16	26	demand	demand	NOUN
cana-1739	16	27	from	from	ADP
cana-1739	16	28	multinational	multinational	ADJ
cana-1739	16	29	corporations	corporation	NOUN
cana-1739	16	30	.	.	PUNCT
cana-1739	17	1	this	this	DET
cana-1739	17	2	growth	growth	NOUN
cana-1739	17	3	is	be	AUX
cana-1739	17	4	resulting	result	VERB
cana-1739	17	5	in	in	ADP
cana-1739	17	6	numerous	numerous	ADJ
cana-1739	17	7	favourable	favourable	ADJ
cana-1739	17	8	outcomes	outcome	NOUN
cana-1739	17	9	,	,	PUNCT
cana-1739	17	10	such	such	ADJ
cana-1739	17	11	as	as	ADP
cana-1739	17	12	the	the	DET
cana-1739	17	13	conservation	conservation	NOUN
cana-1739	17	14	of	of	ADP
cana-1739	17	15	communications	communication	NOUN
cana-1739	17	16	on	on	ADP
cana-1739	17	17	applied	apply	VERB
cana-1739	17	18	nonlinear	nonlinear	ADJ
cana-1739	17	19	analysis	analysis	NOUN
cana-1739	17	20	issn	issn	NOUN
cana-1739	17	21	:	:	PUNCT
cana-1739	17	22	1074	1074	NUM
cana-1739	17	23	-	-	PUNCT
cana-1739	17	24	133x	133x	NUM
cana-1739	17	25	vol	vol	NOUN
cana-1739	17	26	32	32	NUM
cana-1739	17	27	no	no	NOUN
cana-1739	17	28	.	.	NOUN
cana-1739	17	29	2	2	NUM
cana-1739	17	30	(	(	PUNCT
cana-1739	17	31	2025	2025	NUM
cana-1739	17	32	)	)	PUNCT
cana-1739	17	33	232	232	NUM
cana-1739	17	34	https://internationalpubls.com	https://internationalpubls.com	X
cana-1739	17	35	resources	resource	NOUN
cana-1739	17	36	,	,	PUNCT
cana-1739	17	37	decreased	decrease	VERB
cana-1739	17	38	greenhouse	greenhouse	NOUN
cana-1739	17	39	gas	gas	NOUN
cana-1739	17	40	emissions	emission	NOUN
cana-1739	17	41	,	,	PUNCT
cana-1739	17	42	enhanced	enhance	VERB
cana-1739	17	43	indoor	indoor	ADJ
cana-1739	17	44	air	air	NOUN
cana-1739	17	45	quality	quality	NOUN
cana-1739	17	46	,	,	PUNCT
cana-1739	17	47	and	and	CCONJ
cana-1739	17	48	the	the	DET
cana-1739	17	49	creation	creation	NOUN
cana-1739	17	50	of	of	ADP
cana-1739	17	51	employment	employment	NOUN
cana-1739	17	52	opportunities	opportunity	NOUN
cana-1739	17	53	.	.	PUNCT
cana-1739	18	1	recently	recently	ADV
cana-1739	18	2	,	,	PUNCT
cana-1739	18	3	the	the	DET
cana-1739	18	4	indian	indian	ADJ
cana-1739	18	5	government	government	NOUN
cana-1739	18	6	has	have	AUX
cana-1739	18	7	displayed	display	VERB
cana-1739	18	8	a	a	DET
cana-1739	18	9	stronger	strong	ADJ
cana-1739	18	10	dedication	dedication	NOUN
cana-1739	18	11	to	to	ADP
cana-1739	18	12	encouraging	encourage	VERB
cana-1739	18	13	eco	eco	NOUN
cana-1739	18	14	-	-	PUNCT
cana-1739	18	15	friendly	friendly	ADJ
cana-1739	18	16	building	building	NOUN
cana-1739	18	17	practices	practice	NOUN
cana-1739	18	18	,	,	PUNCT
cana-1739	18	19	while	while	SCONJ
cana-1739	18	20	indian	indian	ADJ
cana-1739	18	21	consumers	consumer	NOUN
cana-1739	18	22	are	be	AUX
cana-1739	18	23	growing	grow	VERB
cana-1739	18	24	more	more	ADV
cana-1739	18	25	knowledgeable	knowledgeable	ADJ
cana-1739	18	26	about	about	ADP
cana-1739	18	27	the	the	DET
cana-1739	18	28	benefits	benefit	NOUN
cana-1739	18	29	of	of	ADP
cana-1739	18	30	environmentally	environmentally	ADV
cana-1739	18	31	conscious	conscious	ADJ
cana-1739	18	32	constructions	construction	NOUN
cana-1739	18	33	.	.	PUNCT
cana-1739	19	1	as	as	ADP
cana-1739	19	2	of	of	ADP
cana-1739	19	3	october	october	PROPN
cana-1739	19	4	21	21	NUM
cana-1739	19	5	,	,	PUNCT
cana-1739	19	6	2023	2023	NUM
cana-1739	19	7	,	,	PUNCT
cana-1739	19	8	there	there	PRON
cana-1739	19	9	are	be	VERB
cana-1739	19	10	more	more	ADJ
cana-1739	19	11	than	than	ADP
cana-1739	19	12	3,088	3,088	NUM
cana-1739	19	13	building	building	NOUN
cana-1739	19	14	projects	project	NOUN
cana-1739	19	15	in	in	ADP
cana-1739	19	16	india	india	PROPN
cana-1739	19	17	,	,	PUNCT
cana-1739	19	18	encompassing	encompass	VERB
cana-1739	19	19	a	a	DET
cana-1739	19	20	total	total	ADJ
cana-1739	19	21	area	area	NOUN
cana-1739	19	22	of	of	ADP
cana-1739	19	23	over	over	ADP
cana-1739	19	24	1,315	1,315	NUM
cana-1739	19	25	million	million	NUM
cana-1739	19	26	square	square	ADJ
cana-1739	19	27	feet	foot	NOUN
cana-1739	19	28	(	(	PUNCT
cana-1739	19	29	122.2×10	122.2×10	NUM
cana-1739	19	30	^	^	SYM
cana-1739	19	31	6	6	NUM
cana-1739	19	32	m^2	m^2	NOUN
cana-1739	19	33	)	)	PUNCT
cana-1739	19	34	of	of	ADP
cana-1739	19	35	certified	certified	ADJ
cana-1739	19	36	space	space	NOUN
cana-1739	19	37	.	.	PUNCT
cana-1739	20	1	these	these	DET
cana-1739	20	2	initiatives	initiative	NOUN
cana-1739	20	3	have	have	AUX
cana-1739	20	4	been	be	AUX
cana-1739	20	5	approved	approve	VERB
cana-1739	20	6	by	by	ADP
cana-1739	20	7	the	the	DET
cana-1739	20	8	indian	indian	ADJ
cana-1739	20	9	green	green	PROPN
cana-1739	20	10	building	building	PROPN
cana-1739	20	11	council	council	PROPN
cana-1739	20	12	(	(	PUNCT
cana-1739	20	13	igbc	igbc	PROPN
cana-1739	20	14	)	)	PUNCT
cana-1739	20	15	,	,	PUNCT
cana-1739	20	16	the	the	DET
cana-1739	20	17	primary	primary	ADJ
cana-1739	20	18	green	green	ADJ
cana-1739	20	19	building	building	NOUN
cana-1739	20	20	assessment	assessment	NOUN
cana-1739	20	21	system	system	NOUN
cana-1739	20	22	in	in	ADP
cana-1739	20	23	the	the	DET
cana-1739	20	24	nation	nation	NOUN
cana-1739	20	25	.	.	PUNCT
cana-1739	21	1	it	it	PRON
cana-1739	21	2	is	be	AUX
cana-1739	21	3	approximated	approximate	VERB
cana-1739	21	4	that	that	SCONJ
cana-1739	21	5	less	less	ADJ
cana-1739	21	6	than	than	ADP
cana-1739	21	7	10	10	NUM
cana-1739	21	8	%	%	NOUN
cana-1739	21	9	of	of	ADP
cana-1739	21	10	buildings	building	NOUN
cana-1739	21	11	in	in	ADP
cana-1739	21	12	india	india	PROPN
cana-1739	21	13	conform	conform	VERB
cana-1739	21	14	to	to	ADP
cana-1739	21	15	sustainable	sustainable	ADJ
cana-1739	21	16	standards	standard	NOUN
cana-1739	21	17	,	,	PUNCT
cana-1739	21	18	a	a	DET
cana-1739	21	19	stark	stark	ADJ
cana-1739	21	20	contrast	contrast	NOUN
cana-1739	21	21	to	to	ADP
cana-1739	21	22	developed	develop	VERB
cana-1739	21	23	countries	country	NOUN
cana-1739	21	24	like	like	ADP
cana-1739	21	25	the	the	DET
cana-1739	21	26	united	united	PROPN
cana-1739	21	27	states	states	PROPN
cana-1739	21	28	,	,	PUNCT
cana-1739	21	29	where	where	SCONJ
cana-1739	21	30	over	over	ADP
cana-1739	21	31	30	30	NUM
cana-1739	21	32	%	%	NOUN
cana-1739	21	33	of	of	ADP
cana-1739	21	34	buildings	building	NOUN
cana-1739	21	35	are	be	AUX
cana-1739	21	36	considered	consider	VERB
cana-1739	21	37	environmentally	environmentally	ADV
cana-1739	21	38	friendly	friendly	ADJ
cana-1739	21	39	.	.	PUNCT
cana-1739	22	1	a	a	DET
cana-1739	22	2	green	green	ADJ
cana-1739	22	3	building	building	NOUN
cana-1739	22	4	is	be	AUX
cana-1739	22	5	characterized	characterize	VERB
cana-1739	22	6	as	as	ADP
cana-1739	22	7	one	one	NUM
cana-1739	22	8	that	that	PRON
cana-1739	22	9	utilizes	utilize	VERB
cana-1739	22	10	less	less	ADJ
cana-1739	22	11	water	water	NOUN
cana-1739	22	12	,	,	PUNCT
cana-1739	22	13	enhances	enhance	VERB
cana-1739	22	14	energy	energy	NOUN
cana-1739	22	15	efficiency	efficiency	NOUN
cana-1739	22	16	,	,	PUNCT
cana-1739	22	17	safeguards	safeguard	VERB
cana-1739	22	18	natural	natural	ADJ
cana-1739	22	19	resources	resource	NOUN
cana-1739	22	20	,	,	PUNCT
cana-1739	22	21	minimizes	minimize	NOUN
cana-1739	22	22	waste	waste	NOUN
cana-1739	22	23	,	,	PUNCT
cana-1739	22	24	and	and	CCONJ
cana-1739	22	25	provides	provide	VERB
cana-1739	22	26	healthier	healthy	ADJ
cana-1739	22	27	environments	environment	NOUN
cana-1739	22	28	for	for	ADP
cana-1739	22	29	occupants	occupant	NOUN
cana-1739	22	30	compared	compare	VERB
cana-1739	22	31	to	to	ADP
cana-1739	22	32	a	a	DET
cana-1739	22	33	traditional	traditional	ADJ
cana-1739	22	34	building	building	NOUN
cana-1739	22	35	.	.	PUNCT
cana-1739	23	1	it	it	PRON
cana-1739	23	2	is	be	AUX
cana-1739	23	3	commonly	commonly	ADV
cana-1739	23	4	known	know	VERB
cana-1739	23	5	as	as	ADP
cana-1739	23	6	a	a	DET
cana-1739	23	7	'	'	PUNCT
cana-1739	23	8	high	high	ADJ
cana-1739	23	9	-	-	PUNCT
cana-1739	23	10	performance	performance	NOUN
cana-1739	23	11	'	'	PUNCT
cana-1739	23	12	or	or	CCONJ
cana-1739	23	13	sustainable	sustainable	ADJ
cana-1739	23	14	structure	structure	NOUN
cana-1739	23	15	[	[	X
cana-1739	23	16	1	1	NUM
cana-1739	23	17	]	]	PUNCT
cana-1739	23	18	.	.	PUNCT
cana-1739	24	1	environmental	environmental	ADJ
cana-1739	24	2	issues	issue	NOUN
cana-1739	24	3	are	be	AUX
cana-1739	24	4	intertwined	intertwine	VERB
cana-1739	24	5	with	with	ADP
cana-1739	24	6	economic	economic	ADJ
cana-1739	24	7	and	and	CCONJ
cana-1739	24	8	population	population	NOUN
cana-1739	24	9	growth	growth	NOUN
cana-1739	24	10	.	.	PUNCT
cana-1739	25	1	to	to	PART
cana-1739	25	2	achieve	achieve	VERB
cana-1739	25	3	sustainability	sustainability	NOUN
cana-1739	25	4	,	,	PUNCT
cana-1739	25	5	india	india	PROPN
cana-1739	25	6	needs	need	VERB
cana-1739	25	7	to	to	PART
cana-1739	25	8	effectively	effectively	ADV
cana-1739	25	9	waste	waste	VERB
cana-1739	25	10	that	that	PRON
cana-1739	25	11	contaminates	contaminate	VERB
cana-1739	25	12	the	the	DET
cana-1739	25	13	ecosystem	ecosystem	NOUN
cana-1739	26	1	[	[	X
cana-1739	26	2	2	2	NUM
cana-1739	26	3	]	]	PUNCT
cana-1739	26	4	.	.	PUNCT
cana-1739	27	1	through	through	ADP
cana-1739	27	2	life	life	NOUN
cana-1739	27	3	cycle	cycle	NOUN
cana-1739	27	4	analysis	analysis	NOUN
cana-1739	27	5	,	,	PUNCT
cana-1739	27	6	eco	eco	NOUN
cana-1739	27	7	-	-	PUNCT
cana-1739	27	8	friendly	friendly	ADJ
cana-1739	27	9	buildings	building	NOUN
cana-1739	27	10	will	will	AUX
cana-1739	27	11	preserve	preserve	VERB
cana-1739	27	12	resources	resource	NOUN
cana-1739	27	13	and	and	CCONJ
cana-1739	27	14	mitigate	mitigate	VERB
cana-1739	27	15	climate	climate	NOUN
cana-1739	27	16	change	change	NOUN
cana-1739	27	17	[	[	X
cana-1739	27	18	3	3	NUM
cana-1739	27	19	]	]	PUNCT
cana-1739	27	20	.	.	PUNCT
cana-1739	28	1	the	the	DET
cana-1739	28	2	idea	idea	NOUN
cana-1739	28	3	of	of	ADP
cana-1739	28	4	green	green	ADJ
cana-1739	28	5	buildings	building	NOUN
cana-1739	28	6	has	have	AUX
cana-1739	28	7	developed	develop	VERB
cana-1739	28	8	in	in	ADP
cana-1739	28	9	a	a	DET
cana-1739	28	10	surprising	surprising	ADJ
cana-1739	28	11	manner	manner	NOUN
cana-1739	28	12	to	to	PART
cana-1739	28	13	achieve	achieve	VERB
cana-1739	28	14	a	a	DET
cana-1739	28	15	more	more	ADV
cana-1739	28	16	realistic	realistic	ADJ
cana-1739	28	17	sequence	sequence	NOUN
cana-1739	28	18	of	of	ADP
cana-1739	28	19	events	event	NOUN
cana-1739	28	20	[	[	X
cana-1739	28	21	4	4	NUM
cana-1739	28	22	-	-	SYM
cana-1739	28	23	6	6	NUM
cana-1739	28	24	]	]	PUNCT
cana-1739	28	25	.	.	PUNCT
cana-1739	29	1	sustainable	sustainable	ADJ
cana-1739	29	2	buildings	building	NOUN
cana-1739	29	3	offer	offer	VERB
cana-1739	29	4	reduced	reduce	VERB
cana-1739	29	5	energy	energy	NOUN
cana-1739	29	6	consumption	consumption	NOUN
cana-1739	29	7	and	and	CCONJ
cana-1739	29	8	minimized	minimize	VERB
cana-1739	29	9	negative	negative	ADJ
cana-1739	29	10	environmental	environmental	ADJ
cana-1739	29	11	impacts	impact	NOUN
cana-1739	29	12	however	however	ADV
cana-1739	29	13	,	,	PUNCT
cana-1739	29	14	one	one	NUM
cana-1739	29	15	of	of	ADP
cana-1739	29	16	the	the	DET
cana-1739	29	17	causes	cause	NOUN
cana-1739	29	18	of	of	ADP
cana-1739	29	19	preventable	preventable	ADJ
cana-1739	29	20	health	health	NOUN
cana-1739	29	21	issues	issue	NOUN
cana-1739	29	22	,	,	PUNCT
cana-1739	29	23	increased	increase	VERB
cana-1739	29	24	consumption	consumption	NOUN
cana-1739	29	25	costs	cost	NOUN
cana-1739	29	26	,	,	PUNCT
cana-1739	29	27	and	and	CCONJ
cana-1739	29	28	decreased	decrease	VERB
cana-1739	29	29	productivity	productivity	NOUN
cana-1739	29	30	is	be	AUX
cana-1739	29	31	the	the	DET
cana-1739	29	32	incapacity	incapacity	NOUN
cana-1739	29	33	to	to	PART
cana-1739	29	34	adopt	adopt	VERB
cana-1739	29	35	a	a	DET
cana-1739	29	36	"	"	PUNCT
cana-1739	29	37	green	green	ADJ
cana-1739	29	38	"	"	PUNCT
cana-1739	29	39	lifestyle	lifestyle	NOUN
cana-1739	30	1	[	[	X
cana-1739	30	2	7	7	NUM
cana-1739	30	3	]	]	PUNCT
cana-1739	30	4	.	.	PUNCT
cana-1739	31	1	while	while	SCONJ
cana-1739	31	2	recent	recent	ADJ
cana-1739	31	3	research	research	NOUN
cana-1739	31	4	studies	study	NOUN
cana-1739	31	5	[	[	X
cana-1739	31	6	8	8	NUM
cana-1739	31	7	,	,	PUNCT
cana-1739	31	8	9	9	NUM
cana-1739	31	9	]	]	PUNCT
cana-1739	31	10	have	have	AUX
cana-1739	31	11	advised	advise	VERB
cana-1739	31	12	the	the	DET
cana-1739	31	13	utilization	utilization	NOUN
cana-1739	31	14	of	of	ADP
cana-1739	31	15	innovative	innovative	ADJ
cana-1739	31	16	technology	technology	NOUN
cana-1739	31	17	to	to	PART
cana-1739	31	18	enhance	enhance	VERB
cana-1739	31	19	the	the	DET
cana-1739	31	20	state	state	NOUN
cana-1739	31	21	of	of	ADP
cana-1739	31	22	buildings	building	NOUN
cana-1739	31	23	constructed	construct	VERB
cana-1739	31	24	from	from	ADP
cana-1739	31	25	locally	locally	ADV
cana-1739	31	26	sourced	source	VERB
cana-1739	31	27	materials	material	NOUN
cana-1739	31	28	,	,	PUNCT
cana-1739	31	29	this	this	DET
cana-1739	31	30	recommendation	recommendation	NOUN
cana-1739	31	31	has	have	VERB
cana-1739	31	32	yet	yet	ADV
cana-1739	31	33	to	to	PART
cana-1739	31	34	be	be	AUX
cana-1739	31	35	implemented	implement	VERB
cana-1739	31	36	.	.	PUNCT
cana-1739	32	1	concerning	concern	VERB
cana-1739	32	2	thermal	thermal	ADJ
cana-1739	32	3	comfort	comfort	NOUN
cana-1739	32	4	,	,	PUNCT
cana-1739	32	5	dwellings	dwelling	NOUN
cana-1739	32	6	featuring	feature	VERB
cana-1739	32	7	thatched	thatch	VERB
cana-1739	32	8	roofs	roof	NOUN
cana-1739	32	9	,	,	PUNCT
cana-1739	32	10	bamboo	bamboo	NOUN
cana-1739	32	11	cladding	cladding	NOUN
cana-1739	32	12	,	,	PUNCT
cana-1739	32	13	and	and	CCONJ
cana-1739	32	14	mud	mud	NOUN
cana-1739	32	15	bricks	brick	NOUN
cana-1739	32	16	tend	tend	VERB
cana-1739	32	17	to	to	PART
cana-1739	32	18	be	be	AUX
cana-1739	32	19	more	more	ADV
cana-1739	32	20	appealing	appealing	ADJ
cana-1739	32	21	to	to	ADP
cana-1739	32	22	residents	resident	NOUN
cana-1739	32	23	compared	compare	VERB
cana-1739	32	24	to	to	ADP
cana-1739	32	25	traditional	traditional	ADJ
cana-1739	32	26	,	,	PUNCT
cana-1739	32	27	unsustainable	unsustainable	ADJ
cana-1739	32	28	edifices	edifice	NOUN
cana-1739	32	29	.	.	PUNCT
cana-1739	33	1	enhancing	enhance	VERB
cana-1739	33	2	greenery	greenery	PROPN
cana-1739	33	3	cover	cover	NOUN
cana-1739	33	4	to	to	PART
cana-1739	33	5	implement	implement	VERB
cana-1739	33	6	nature	nature	NOUN
cana-1739	33	7	-	-	PUNCT
cana-1739	33	8	based	base	VERB
cana-1739	33	9	strategies	strategy	NOUN
cana-1739	33	10	for	for	ADP
cana-1739	33	11	mitigating	mitigate	VERB
cana-1739	33	12	heat	heat	NOUN
cana-1739	33	13	can	can	AUX
cana-1739	33	14	significantly	significantly	ADV
cana-1739	33	15	reduce	reduce	VERB
cana-1739	33	16	energy	energy	NOUN
cana-1739	33	17	consumption	consumption	NOUN
cana-1739	33	18	,	,	PUNCT
cana-1739	33	19	as	as	ADV
cana-1739	33	20	well	well	ADV
cana-1739	33	21	as	as	ADP
cana-1739	33	22	the	the	DET
cana-1739	33	23	associated	associated	ADJ
cana-1739	33	24	risks	risk	NOUN
cana-1739	33	25	of	of	ADP
cana-1739	33	26	mortality	mortality	NOUN
cana-1739	33	27	and	and	CCONJ
cana-1739	33	28	heat	heat	NOUN
cana-1739	33	29	-	-	PUNCT
cana-1739	33	30	related	relate	VERB
cana-1739	33	31	ailments	ailment	NOUN
cana-1739	33	32	[	[	X
cana-1739	33	33	10	10	NUM
cana-1739	33	34	]	]	PUNCT
cana-1739	33	35	.	.	PUNCT
cana-1739	34	1	the	the	DET
cana-1739	34	2	rise	rise	NOUN
cana-1739	34	3	in	in	ADP
cana-1739	34	4	green	green	ADJ
cana-1739	34	5	building	building	NOUN
cana-1739	34	6	construction	construction	NOUN
cana-1739	34	7	in	in	ADP
cana-1739	34	8	urban	urban	ADJ
cana-1739	34	9	areas	area	NOUN
cana-1739	34	10	is	be	AUX
cana-1739	34	11	closely	closely	ADV
cana-1739	34	12	linked	link	VERB
cana-1739	34	13	to	to	ADP
cana-1739	34	14	the	the	DET
cana-1739	34	15	pressing	press	VERB
cana-1739	34	16	need	need	NOUN
cana-1739	34	17	for	for	ADP
cana-1739	34	18	economic	economic	ADJ
cana-1739	34	19	development	development	NOUN
cana-1739	34	20	as	as	SCONJ
cana-1739	34	21	cities	city	NOUN
cana-1739	34	22	strive	strive	VERB
cana-1739	34	23	to	to	PART
cana-1739	34	24	develop	develop	VERB
cana-1739	34	25	intelligent	intelligent	ADJ
cana-1739	34	26	,	,	PUNCT
cana-1739	34	27	eco	eco	NOUN
cana-1739	34	28	-	-	PUNCT
cana-1739	34	29	friendly	friendly	ADJ
cana-1739	34	30	,	,	PUNCT
cana-1739	34	31	and	and	CCONJ
cana-1739	34	32	sustainable	sustainable	ADJ
cana-1739	34	33	environment	environment	NOUN
cana-1739	35	1	[	[	X
cana-1739	35	2	11	11	NUM
cana-1739	35	3	-	-	SYM
cana-1739	35	4	13	13	NUM
cana-1739	35	5	]	]	PUNCT
cana-1739	35	6	.	.	PUNCT
cana-1739	36	1	the	the	DET
cana-1739	36	2	transition	transition	NOUN
cana-1739	36	3	from	from	ADP
cana-1739	36	4	integer	integer	NOUN
cana-1739	36	5	-	-	PUNCT
cana-1739	36	6	order	order	NOUN
cana-1739	36	7	differential	differential	ADJ
cana-1739	36	8	equations	equation	NOUN
cana-1739	36	9	to	to	PART
cana-1739	36	10	fractional	fractional	ADJ
cana-1739	36	11	differential	differential	ADJ
cana-1739	36	12	equations	equation	NOUN
cana-1739	36	13	represents	represent	VERB
cana-1739	36	14	a	a	DET
cana-1739	36	15	broadening	broadening	NOUN
cana-1739	36	16	of	of	ADP
cana-1739	36	17	mathematical	mathematical	ADJ
cana-1739	36	18	frameworks	framework	NOUN
cana-1739	36	19	.	.	PUNCT
cana-1739	37	1	fractional	fractional	ADJ
cana-1739	37	2	calculus	calculus	NOUN
cana-1739	37	3	,	,	PUNCT
cana-1739	37	4	widely	widely	ADV
cana-1739	37	5	utilized	utilize	VERB
cana-1739	37	6	by	by	ADP
cana-1739	37	7	scholars	scholar	NOUN
cana-1739	37	8	and	and	CCONJ
cana-1739	37	9	mathematicians	mathematician	NOUN
cana-1739	37	10	,	,	PUNCT
cana-1739	37	11	serves	serve	VERB
cana-1739	37	12	as	as	ADP
cana-1739	37	13	a	a	DET
cana-1739	37	14	powerful	powerful	ADJ
cana-1739	37	15	tool	tool	NOUN
cana-1739	37	16	for	for	ADP
cana-1739	37	17	modeling	model	VERB
cana-1739	37	18	real	real	ADJ
cana-1739	37	19	-	-	PUNCT
cana-1739	37	20	world	world	NOUN
cana-1739	37	21	scenarios	scenario	NOUN
cana-1739	37	22	[	[	X
cana-1739	37	23	18	18	NUM
cana-1739	37	24	-	-	SYM
cana-1739	37	25	22	22	NUM
cana-1739	37	26	,	,	PUNCT
cana-1739	37	27	33	33	NUM
cana-1739	37	28	,	,	PUNCT
cana-1739	37	29	34	34	NUM
cana-1739	37	30	]	]	PUNCT
cana-1739	37	31	.	.	PUNCT
cana-1739	38	1	the	the	DET
cana-1739	38	2	growing	grow	VERB
cana-1739	38	3	significance	significance	NOUN
cana-1739	38	4	of	of	ADP
cana-1739	38	5	variable	variable	ADJ
cana-1739	38	6	-	-	PUNCT
cana-1739	38	7	order	order	NOUN
cana-1739	38	8	fractional	fractional	ADJ
cana-1739	38	9	calculus	calculus	NOUN
cana-1739	38	10	is	be	AUX
cana-1739	38	11	evident	evident	ADJ
cana-1739	38	12	due	due	ADP
cana-1739	38	13	to	to	ADP
cana-1739	38	14	its	its	PRON
cana-1739	38	15	diverse	diverse	ADJ
cana-1739	38	16	applications	application	NOUN
cana-1739	38	17	across	across	ADP
cana-1739	38	18	science	science	NOUN
cana-1739	38	19	and	and	CCONJ
cana-1739	38	20	engineering	engineering	NOUN
cana-1739	38	21	fields	field	NOUN
cana-1739	38	22	.	.	PUNCT
cana-1739	39	1	these	these	DET
cana-1739	39	2	fractional	fractional	ADJ
cana-1739	39	3	operators	operator	NOUN
cana-1739	39	4	with	with	ADP
cana-1739	39	5	variable	variable	ADJ
cana-1739	39	6	orders	order	NOUN
cana-1739	39	7	demonstrate	demonstrate	VERB
cana-1739	39	8	intriguing	intriguing	ADJ
cana-1739	39	9	practical	practical	ADJ
cana-1739	39	10	uses	use	NOUN
cana-1739	39	11	[	[	X
cana-1739	39	12	23	23	NUM
cana-1739	39	13	-	-	SYM
cana-1739	39	14	30	30	NUM
cana-1739	39	15	]	]	PUNCT
cana-1739	39	16	.	.	PUNCT
cana-1739	40	1	in	in	ADP
cana-1739	40	2	view	view	NOUN
cana-1739	40	3	of	of	ADP
cana-1739	40	4	the	the	DET
cana-1739	40	5	above	above	ADJ
cana-1739	40	6	,	,	PUNCT
cana-1739	40	7	this	this	DET
cana-1739	40	8	study	study	NOUN
cana-1739	40	9	is	be	AUX
cana-1739	40	10	driven	drive	VERB
cana-1739	40	11	by	by	ADP
cana-1739	40	12	the	the	DET
cana-1739	40	13	need	need	NOUN
cana-1739	40	14	to	to	PART
cana-1739	40	15	comprehend	comprehend	VERB
cana-1739	40	16	the	the	DET
cana-1739	40	17	dynamic	dynamic	ADJ
cana-1739	40	18	effects	effect	NOUN
cana-1739	40	19	of	of	ADP
cana-1739	40	20	the	the	DET
cana-1739	40	21	green	green	ADJ
cana-1739	40	22	building	building	NOUN
cana-1739	40	23	concept	concept	NOUN
cana-1739	40	24	for	for	ADP
cana-1739	40	25	sustainable	sustainable	ADJ
cana-1739	40	26	cities	city	NOUN
cana-1739	40	27	under	under	ADP
cana-1739	40	28	climate	climate	NOUN
cana-1739	40	29	change	change	NOUN
cana-1739	40	30	through	through	ADP
cana-1739	40	31	the	the	DET
cana-1739	40	32	application	application	NOUN
cana-1739	40	33	of	of	ADP
cana-1739	40	34	the	the	DET
cana-1739	40	35	variableorder	variableorder	NOUN
cana-1739	40	36	fractional	fractional	ADJ
cana-1739	40	37	derivative	derivative	NOUN
cana-1739	40	38	in	in	ADP
cana-1739	40	39	the	the	DET
cana-1739	40	40	liouville	liouville	PROPN
cana-1739	40	41	-	-	PUNCT
cana-1739	40	42	caputo	caputo	PROPN
cana-1739	40	43	,	,	PUNCT
cana-1739	40	44	caputo	caputo	PROPN
cana-1739	40	45	-	-	PUNCT
cana-1739	40	46	fabrizio	fabrizio	PROPN
cana-1739	40	47	,	,	PUNCT
cana-1739	40	48	and	and	CCONJ
cana-1739	40	49	atangana	atangana	PROPN
cana-1739	40	50	-	-	PUNCT
cana-1739	40	51	baleanu	baleanu	PROPN
cana-1739	40	52	senses	sense	NOUN
cana-1739	40	53	.	.	PUNCT
cana-1739	41	1	in	in	ADP
cana-1739	41	2	section	section	NOUN
cana-1739	41	3	2	2	NUM
cana-1739	41	4	,	,	PUNCT
cana-1739	41	5	the	the	DET
cana-1739	41	6	necessary	necessary	ADJ
cana-1739	41	7	preliminary	preliminary	ADJ
cana-1739	41	8	information	information	NOUN
cana-1739	41	9	for	for	ADP
cana-1739	41	10	the	the	DET
cana-1739	41	11	fractional	fractional	ADJ
cana-1739	41	12	model	model	NOUN
cana-1739	41	13	are	be	AUX
cana-1739	41	14	provided	provide	VERB
cana-1739	41	15	.	.	PUNCT
cana-1739	42	1	section	section	NOUN
cana-1739	42	2	3	3	NUM
cana-1739	42	3	presents	present	VERB
cana-1739	42	4	a	a	DET
cana-1739	42	5	detailed	detailed	ADJ
cana-1739	42	6	description	description	NOUN
cana-1739	42	7	of	of	ADP
cana-1739	42	8	the	the	DET
cana-1739	42	9	model	model	NOUN
cana-1739	42	10	in	in	ADP
cana-1739	42	11	the	the	DET
cana-1739	42	12	classical	classical	ADJ
cana-1739	42	13	version	version	NOUN
cana-1739	42	14	of	of	ADP
cana-1739	42	15	the	the	DET
cana-1739	42	16	"	"	PUNCT
cana-1739	42	17	green	green	ADJ
cana-1739	42	18	building	building	NOUN
cana-1739	42	19	concept	concept	NOUN
cana-1739	42	20	for	for	ADP
cana-1739	42	21	sustainable	sustainable	ADJ
cana-1739	42	22	cities	city	NOUN
cana-1739	42	23	"	"	PUNCT
cana-1739	42	24	and	and	CCONJ
cana-1739	42	25	its	its	PRON
cana-1739	42	26	corresponding	corresponding	ADJ
cana-1739	42	27	fractional	fractional	ADJ
cana-1739	42	28	order	order	NOUN
cana-1739	42	29	version	version	NOUN
cana-1739	42	30	.	.	PUNCT
cana-1739	43	1	the	the	DET
cana-1739	43	2	uniqueness	uniqueness	NOUN
cana-1739	43	3	and	and	CCONJ
cana-1739	43	4	existence	existence	NOUN
cana-1739	43	5	of	of	ADP
cana-1739	43	6	fractional	fractional	ADJ
cana-1739	43	7	solutions	solution	NOUN
cana-1739	43	8	are	be	AUX
cana-1739	43	9	explained	explain	VERB
cana-1739	43	10	in	in	ADP
cana-1739	43	11	section	section	NOUN
cana-1739	43	12	5	5	NUM
cana-1739	43	13	.	.	PUNCT
cana-1739	43	14	section	section	NOUN
cana-1739	43	15	6	6	NUM
cana-1739	43	16	provides	provide	VERB
cana-1739	43	17	detailed	detailed	ADJ
cana-1739	43	18	numerical	numerical	ADJ
cana-1739	43	19	results	result	NOUN
cana-1739	43	20	and	and	CCONJ
cana-1739	43	21	communications	communication	NOUN
cana-1739	43	22	on	on	ADP
cana-1739	43	23	applied	apply	VERB
cana-1739	43	24	nonlinear	nonlinear	ADJ
cana-1739	43	25	analysis	analysis	NOUN
cana-1739	43	26	issn	issn	NOUN
cana-1739	43	27	:	:	PUNCT
cana-1739	43	28	1074	1074	NUM
cana-1739	43	29	-	-	PUNCT
cana-1739	43	30	133x	133x	NUM
cana-1739	43	31	vol	vol	NOUN
cana-1739	43	32	32	32	NUM
cana-1739	43	33	no	no	NOUN
cana-1739	43	34	.	.	NOUN
cana-1739	43	35	2	2	NUM
cana-1739	43	36	(	(	PUNCT
cana-1739	43	37	2025	2025	NUM
cana-1739	43	38	)	)	PUNCT
cana-1739	43	39	233	233	NUM
cana-1739	43	40	https://internationalpubls.com	https://internationalpubls.com	X
cana-1739	43	41	simulations	simulation	NOUN
cana-1739	43	42	for	for	ADP
cana-1739	43	43	the	the	DET
cana-1739	43	44	suggested	suggest	VERB
cana-1739	43	45	model	model	NOUN
cana-1739	43	46	on	on	ADP
cana-1739	43	47	liouville	liouville	PROPN
cana-1739	43	48	caputo	caputo	PROPN
cana-1739	43	49	,	,	PUNCT
cana-1739	43	50	caputo	caputo	PROPN
cana-1739	43	51	-	-	PUNCT
cana-1739	43	52	fabrizio	fabrizio	PROPN
cana-1739	43	53	,	,	PUNCT
cana-1739	43	54	and	and	CCONJ
cana-1739	43	55	atangana	atangana	PROPN
cana-1739	43	56	-	-	PUNCT
cana-1739	43	57	baleanu	baleanu	ADJ
cana-1739	43	58	derivatives	derivative	NOUN
cana-1739	43	59	.	.	PUNCT
cana-1739	44	1	all	all	PRON
cana-1739	44	2	obtained	obtain	VERB
cana-1739	44	3	results	result	NOUN
cana-1739	44	4	of	of	ADP
cana-1739	44	5	the	the	DET
cana-1739	44	6	work	work	NOUN
cana-1739	44	7	are	be	AUX
cana-1739	44	8	concluded	conclude	VERB
cana-1739	44	9	in	in	ADP
cana-1739	44	10	the	the	DET
cana-1739	44	11	final	final	ADJ
cana-1739	44	12	section	section	NOUN
cana-1739	44	13	.	.	PUNCT
cana-1739	45	1	2	2	X
cana-1739	45	2	.	.	X
cana-1739	45	3	prelminaries	prelminarie	NOUN
cana-1739	45	4	this	this	DET
cana-1739	45	5	section	section	NOUN
cana-1739	45	6	provides	provide	VERB
cana-1739	45	7	some	some	DET
cana-1739	45	8	basic	basic	ADJ
cana-1739	45	9	definitions	definition	NOUN
cana-1739	45	10	of	of	ADP
cana-1739	45	11	variable	variable	ADJ
cana-1739	45	12	order	order	NOUN
cana-1739	45	13	fractional	fractional	ADJ
cana-1739	45	14	derivatives	derivative	NOUN
cana-1739	45	15	which	which	PRON
cana-1739	45	16	are	be	AUX
cana-1739	45	17	used	use	VERB
cana-1739	45	18	in	in	ADP
cana-1739	45	19	subsequent	subsequent	ADJ
cana-1739	45	20	sections	section	NOUN
cana-1739	45	21	.	.	PUNCT
cana-1739	46	1	definition	definition	NOUN
cana-1739	46	2	2.1	2.1	NUM
cana-1739	46	3	:	:	PUNCT
cana-1739	46	4	the	the	DET
cana-1739	46	5	liouville	liouville	NOUN
cana-1739	46	6	–	–	PUNCT
cana-1739	46	7	caputo	caputo	PROPN
cana-1739	46	8	(	(	PUNCT
cana-1739	46	9	lc	lc	PROPN
cana-1739	46	10	)	)	PUNCT
cana-1739	46	11	fractional	fractional	ADJ
cana-1739	46	12	derivative	derivative	NOUN
cana-1739	46	13	with	with	ADP
cana-1739	46	14	variable	variable	ADJ
cana-1739	46	15	-	-	PUNCT
cana-1739	46	16	order	order	NOUN
cana-1739	46	17	ν(t	ν(t	NOUN
cana-1739	46	18	)	)	PUNCT
cana-1739	46	19	is	be	AUX
cana-1739	46	20	defined	define	VERB
cana-1739	46	21	as	as	ADP
cana-1739	46	22	[	[	X
cana-1739	46	23	32	32	NUM
cana-1739	46	24	]	]	X
cana-1739	46	25	𝐷𝑡	𝐷𝑡	PROPN
cana-1739	46	26	ν(t	ν(t	NOUN
cana-1739	46	27	)	)	PUNCT
cana-1739	46	28	0	0	NUM
cana-1739	47	1	𝐿𝐶	𝐿𝐶	PROPN
cana-1739	47	2	𝑓(𝑡	𝑓(𝑡	NOUN
cana-1739	47	3	)	)	PUNCT
cana-1739	47	4	=	=	SYM
cana-1739	47	5	1	1	NUM
cana-1739	47	6	⎾	⎾	NUM
cana-1739	47	7	1−ν(t	1−ν(t	NUM
cana-1739	47	8	)	)	PUNCT
cana-1739	47	9	∫	∫	PROPN
cana-1739	47	10	(	(	PUNCT
cana-1739	47	11	𝑡	𝑡	PROPN
cana-1739	47	12	−	−	PROPN
cana-1739	47	13	𝑢)−ν(t)𝑡	𝑢)−ν(t)𝑡	NOUN
cana-1739	47	14	0	0	NUM
cana-1739	47	15	𝑓(𝑢)𝑑𝑢	𝑓(𝑢)𝑑𝑢	NOUN
cana-1739	47	16	,	,	PUNCT
cana-1739	48	1	0	0	NUM
cana-1739	48	2	<	<	X
cana-1739	48	3	ν(t	ν(t	NOUN
cana-1739	48	4	)	)	PUNCT
cana-1739	48	5	≤	≤	NUM
cana-1739	48	6	1	1	NUM
cana-1739	48	7	definition	definition	NOUN
cana-1739	48	8	2.2	2.2	NUM
cana-1739	48	9	:	:	PUNCT
cana-1739	48	10	the	the	DET
cana-1739	48	11	caputo	caputo	PROPN
cana-1739	48	12	–	–	PUNCT
cana-1739	48	13	fabrizio	fabrizio	PROPN
cana-1739	48	14	(	(	PUNCT
cana-1739	48	15	cf	cf	NOUN
cana-1739	48	16	)	)	PUNCT
cana-1739	48	17	derivative	derivative	NOUN
cana-1739	48	18	with	with	ADP
cana-1739	48	19	variable	variable	ADJ
cana-1739	48	20	-	-	PUNCT
cana-1739	48	21	order	order	NOUN
cana-1739	48	22	ν(t	ν(t	NOUN
cana-1739	48	23	)	)	PUNCT
cana-1739	48	24	in	in	ADP
cana-1739	48	25	liouville	liouville	NOUN
cana-1739	48	26	–	–	PUNCT
cana-1739	48	27	caputo	caputo	NOUN
cana-1739	48	28	sense	sense	NOUN
cana-1739	48	29	is	be	AUX
cana-1739	48	30	defined	define	VERB
cana-1739	48	31	as	as	SCONJ
cana-1739	48	32	follows	follow	VERB
cana-1739	48	33	𝐷𝑡	𝐷𝑡	PROPN
cana-1739	48	34	ν(t	ν(t	NOUN
cana-1739	48	35	)	)	PUNCT
cana-1739	48	36	0	0	NUM
cana-1739	49	1	𝐶𝐹	𝐶𝐹	PROPN
cana-1739	49	2	𝑓(𝑡	𝑓(𝑡	PROPN
cana-1739	49	3	)	)	PUNCT
cana-1739	49	4	=	=	SYM
cana-1739	49	5	(	(	PUNCT
cana-1739	49	6	2−ν(t))𝑀(ν(t	2−ν(t))𝑀(ν(t	NUM
cana-1739	49	7	)	)	PUNCT
cana-1739	49	8	)	)	PUNCT
cana-1739	49	9	2(1−ν(t	2(1−ν(t	NOUN
cana-1739	49	10	)	)	PUNCT
cana-1739	49	11	)	)	PUNCT
cana-1739	50	1	∫	∫	PROPN
cana-1739	50	2	exp	exp	X
cana-1739	50	3	[	[	PUNCT
cana-1739	50	4	−ν(t	−ν(t	NOUN
cana-1739	50	5	)	)	PUNCT
cana-1739	50	6	(	(	PUNCT
cana-1739	50	7	1−ν(t	1−ν(t	NUM
cana-1739	50	8	)	)	PUNCT
cana-1739	50	9	)	)	PUNCT
cana-1739	51	1	𝑡	𝑡	X
cana-1739	51	2	0	0	NUM
cana-1739	51	3	(	(	PUNCT
cana-1739	51	4	𝑡	𝑡	PROPN
cana-1739	51	5	−	−	PROPN
cana-1739	51	6	𝑢)]𝑓′(𝑢)𝑑𝑢	𝑢)]𝑓′(𝑢)𝑑𝑢	PROPN
cana-1739	51	7	,	,	PUNCT
cana-1739	51	8	0	0	NUM
cana-1739	51	9	<	<	X
cana-1739	51	10	ν(t	ν(t	NOUN
cana-1739	51	11	)	)	PUNCT
cana-1739	51	12	<	<	X
cana-1739	51	13	1	1	NUM
cana-1739	51	14	where	where	SCONJ
cana-1739	51	15	𝑀(ν(t	𝑀(ν(t	NOUN
cana-1739	51	16	)	)	PUNCT
cana-1739	51	17	)	)	PUNCT
cana-1739	52	1	=	=	SYM
cana-1739	52	2	2	2	NUM
cana-1739	52	3	2−ν(t	2−ν(t	NUM
cana-1739	52	4	)	)	PUNCT
cana-1739	52	5	is	be	AUX
cana-1739	52	6	a	a	DET
cana-1739	52	7	normalization	normalization	NOUN
cana-1739	52	8	function	function	NOUN
cana-1739	52	9	.	.	PUNCT
cana-1739	53	1	definition	definition	NOUN
cana-1739	53	2	2.3	2.3	NUM
cana-1739	53	3	:	:	PUNCT
cana-1739	53	4	the	the	DET
cana-1739	53	5	atangana	atangana	PROPN
cana-1739	53	6	–	–	PUNCT
cana-1739	53	7	baleanu	baleanu	PROPN
cana-1739	53	8	(	(	PUNCT
cana-1739	53	9	ab	ab	NOUN
cana-1739	53	10	)	)	PUNCT
cana-1739	53	11	fractional	fractional	ADJ
cana-1739	53	12	derivative	derivative	NOUN
cana-1739	53	13	with	with	ADP
cana-1739	53	14	variable	variable	ADJ
cana-1739	53	15	-	-	PUNCT
cana-1739	53	16	order	order	NOUN
cana-1739	53	17	ν(t	ν(t	NOUN
cana-1739	53	18	)	)	PUNCT
cana-1739	53	19	in	in	ADP
cana-1739	53	20	liouville	liouville	NOUN
cana-1739	53	21	–	–	PUNCT
cana-1739	53	22	caputo	caputo	NOUN
cana-1739	53	23	sense	sense	NOUN
cana-1739	53	24	is	be	AUX
cana-1739	53	25	defined	define	VERB
cana-1739	53	26	as	as	SCONJ
cana-1739	53	27	follows	follow	VERB
cana-1739	53	28	[	[	X
cana-1739	53	29	17	17	NUM
cana-1739	53	30	]	]	X
cana-1739	53	31	𝐷𝑡	𝐷𝑡	PROPN
cana-1739	53	32	ν(t	ν(t	NOUN
cana-1739	53	33	)	)	PUNCT
cana-1739	53	34	0	0	NUM
cana-1739	54	1	𝐴𝐵	𝐴𝐵	PROPN
cana-1739	54	2	𝑓(𝑡	𝑓(𝑡	PROPN
cana-1739	54	3	)	)	PUNCT
cana-1739	54	4	=	=	SYM
cana-1739	54	5	𝐵(ν(t	𝐵(ν(t	NOUN
cana-1739	54	6	)	)	PUNCT
cana-1739	54	7	)	)	PUNCT
cana-1739	54	8	(	(	PUNCT
cana-1739	54	9	1−ν(t	1−ν(t	NUM
cana-1739	54	10	)	)	PUNCT
cana-1739	54	11	)	)	PUNCT
cana-1739	55	1	∫	∫	PROPN
cana-1739	55	2	𝐸ν(t	𝐸ν(t	PROPN
cana-1739	55	3	)	)	PUNCT
cana-1739	55	4	[	[	PUNCT
cana-1739	55	5	−ν(t	−ν(t	X
cana-1739	55	6	)	)	PUNCT
cana-1739	55	7	(	(	PUNCT
cana-1739	55	8	1−ν(t	1−ν(t	NUM
cana-1739	55	9	)	)	PUNCT
cana-1739	55	10	)	)	PUNCT
cana-1739	56	1	𝑡	𝑡	X
cana-1739	56	2	0	0	PUNCT
cana-1739	56	3	(	(	PUNCT
cana-1739	56	4	𝑡	𝑡	NOUN
cana-1739	56	5	−	−	NOUN
cana-1739	56	6	𝑢)ν(t)]𝑓′(𝑢)𝑑𝑢	𝑢)ν(t)]𝑓′(𝑢)𝑑𝑢	NOUN
cana-1739	56	7	,	,	PUNCT
cana-1739	56	8	0	0	NUM
cana-1739	56	9	<	<	X
cana-1739	56	10	ν(t	ν(t	NOUN
cana-1739	56	11	)	)	PUNCT
cana-1739	56	12	≤	≤	NOUN
cana-1739	56	13	1	1	NUM
cana-1739	56	14	where	where	SCONJ
cana-1739	56	15	𝐵(ν(t	𝐵(ν(t	NOUN
cana-1739	56	16	)	)	PUNCT
cana-1739	56	17	)	)	PUNCT
cana-1739	57	1	=	=	SYM
cana-1739	57	2	1	1	NUM
cana-1739	57	3	−	−	NOUN
cana-1739	57	4	ν(t	ν(t	NOUN
cana-1739	57	5	)	)	PUNCT
cana-1739	58	1	+	+	NUM
cana-1739	58	2	ν(t	ν(t	NOUN
cana-1739	58	3	)	)	PUNCT
cana-1739	58	4	⎾	⎾	NUM
cana-1739	58	5	ν(t	ν(t	NOUN
cana-1739	58	6	)	)	PUNCT
cana-1739	58	7	is	be	AUX
cana-1739	58	8	a	a	DET
cana-1739	58	9	normalization	normalization	NOUN
cana-1739	58	10	function	function	NOUN
cana-1739	58	11	.	.	PUNCT
cana-1739	59	1	remark	remark	NOUN
cana-1739	59	2	:	:	PUNCT
cana-1739	59	3	when	when	SCONJ
cana-1739	59	4	ν(t	ν(t	NOUN
cana-1739	59	5	)	)	PUNCT
cana-1739	59	6	is	be	AUX
cana-1739	59	7	a	a	DET
cana-1739	59	8	constant	constant	ADJ
cana-1739	59	9	,	,	PUNCT
cana-1739	59	10	then	then	ADV
cana-1739	59	11	we	we	PRON
cana-1739	59	12	retrieve	retrieve	VERB
cana-1739	59	13	the	the	DET
cana-1739	59	14	constant	constant	ADJ
cana-1739	59	15	-	-	PUNCT
cana-1739	59	16	order	order	NOUN
cana-1739	59	17	fractional	fractional	ADJ
cana-1739	59	18	derivative	derivative	NOUN
cana-1739	59	19	in	in	ADP
cana-1739	59	20	liouville	liouville	PROPN
cana-1739	59	21	-	-	PUNCT
cana-1739	59	22	caputo	caputo	PROPN
cana-1739	59	23	,	,	PUNCT
cana-1739	59	24	caputo	caputo	PROPN
cana-1739	59	25	-	-	PUNCT
cana-1739	59	26	fabrizio	fabrizio	PROPN
cana-1739	59	27	and	and	CCONJ
cana-1739	59	28	atangana	atangana	PROPN
cana-1739	59	29	-	-	PUNCT
cana-1739	59	30	baleanu	baleanu	PROPN
cana-1739	59	31	sense	sense	NOUN
cana-1739	59	32	.	.	PUNCT
cana-1739	60	1	3	3	X
cana-1739	60	2	.	.	X
cana-1739	60	3	model	model	NOUN
cana-1739	60	4	formulation	formulation	NOUN
cana-1739	60	5	in	in	ADP
cana-1739	60	6	classical	classical	ADJ
cana-1739	60	7	and	and	CCONJ
cana-1739	60	8	fractional	fractional	ADJ
cana-1739	60	9	sense	sense	NOUN
cana-1739	60	10	3.1	3.1	NUM
cana-1739	60	11	classical	classical	ADJ
cana-1739	60	12	model	model	NOUN
cana-1739	60	13	of	of	ADP
cana-1739	60	14	green	green	ADJ
cana-1739	60	15	building	building	NOUN
cana-1739	60	16	concept	concept	NOUN
cana-1739	60	17	for	for	ADP
cana-1739	60	18	sustainable	sustainable	ADJ
cana-1739	60	19	cities	city	NOUN
cana-1739	60	20	under	under	ADP
cana-1739	60	21	climate	climate	NOUN
cana-1739	60	22	change	change	NOUN
cana-1739	60	23	a	a	DET
cana-1739	60	24	mathematical	mathematical	ADJ
cana-1739	60	25	model	model	NOUN
cana-1739	60	26	[	[	X
cana-1739	60	27	15	15	NUM
cana-1739	60	28	]	]	PUNCT
cana-1739	60	29	has	have	AUX
cana-1739	60	30	been	be	AUX
cana-1739	60	31	developed	develop	VERB
cana-1739	60	32	to	to	PART
cana-1739	60	33	examine	examine	VERB
cana-1739	60	34	the	the	DET
cana-1739	60	35	effects	effect	NOUN
cana-1739	60	36	of	of	ADP
cana-1739	60	37	global	global	ADJ
cana-1739	60	38	warming	warm	VERB
cana-1739	60	39	excessive	excessive	ADJ
cana-1739	60	40	greenhouse	greenhouse	NOUN
cana-1739	60	41	gas	gas	NOUN
cana-1739	60	42	emissions	emission	NOUN
cana-1739	60	43	on	on	ADP
cana-1739	60	44	sustainable	sustainable	ADJ
cana-1739	60	45	urban	urban	ADJ
cana-1739	60	46	.	.	PUNCT
cana-1739	61	1	this	this	DET
cana-1739	61	2	model	model	NOUN
cana-1739	61	3	considers	consider	VERB
cana-1739	61	4	four	four	NUM
cana-1739	61	5	key	key	ADJ
cana-1739	61	6	variables	variable	NOUN
cana-1739	61	7	:	:	PUNCT
cana-1739	61	8	g(t	g(t	PROPN
cana-1739	61	9	)	)	PUNCT
cana-1739	61	10	represents	represent	VERB
cana-1739	61	11	the	the	DET
cana-1739	61	12	quantity	quantity	NOUN
cana-1739	61	13	of	of	ADP
cana-1739	61	14	green	green	ADJ
cana-1739	61	15	buildings	building	NOUN
cana-1739	61	16	at	at	ADP
cana-1739	61	17	any	any	DET
cana-1739	61	18	given	give	VERB
cana-1739	61	19	time	time	NOUN
cana-1739	61	20	t	t	PROPN
cana-1739	61	21	,	,	PUNCT
cana-1739	61	22	c(t	c(t	PROPN
cana-1739	61	23	)	)	PUNCT
cana-1739	61	24	signifies	signify	VERB
cana-1739	61	25	the	the	DET
cana-1739	61	26	level	level	NOUN
cana-1739	61	27	of	of	ADP
cana-1739	61	28	ghgs	ghg	VERB
cana-1739	61	29	at	at	ADP
cana-1739	61	30	time	time	NOUN
cana-1739	61	31	t	t	PROPN
cana-1739	61	32	,	,	PUNCT
cana-1739	61	33	i(t	i(t	PROPN
cana-1739	61	34	)	)	PUNCT
cana-1739	61	35	denotes	denote	VERB
cana-1739	61	36	the	the	DET
cana-1739	61	37	energy	energy	NOUN
cana-1739	61	38	generated	generate	VERB
cana-1739	61	39	by	by	ADP
cana-1739	61	40	green	green	ADJ
cana-1739	61	41	buildings	building	NOUN
cana-1739	61	42	at	at	ADP
cana-1739	61	43	time	time	NOUN
cana-1739	61	44	t	t	PROPN
cana-1739	61	45	,	,	PUNCT
cana-1739	61	46	and	and	CCONJ
cana-1739	61	47	h(t	h(t	NUM
cana-1739	61	48	)	)	PUNCT
cana-1739	61	49	reflects	reflect	VERB
cana-1739	61	50	the	the	DET
cana-1739	61	51	human	human	ADJ
cana-1739	61	52	populations	population	NOUN
cana-1739	61	53	in	in	ADP
cana-1739	61	54	a	a	DET
cana-1739	61	55	specific	specific	ADJ
cana-1739	61	56	region	region	NOUN
cana-1739	61	57	at	at	ADP
cana-1739	61	58	time	time	NOUN
cana-1739	61	59	t.	t.	PROPN
cana-1739	61	60	𝑑𝐺	𝑑𝐺	PROPN
cana-1739	61	61	𝑑𝑡	𝑑𝑡	ADP
cana-1739	61	62	=	=	SYM
cana-1739	61	63	𝛬	𝛬	PROPN
cana-1739	61	64	+	+	NUM
cana-1739	61	65	𝑝1𝐺(𝑡)𝐶(𝑡	𝑝1𝐺(𝑡)𝐶(𝑡	ADJ
cana-1739	61	66	)	)	PUNCT
cana-1739	61	67	−	−	PROPN
cana-1739	61	68	𝑝2𝐺(𝑡	𝑝2𝐺(𝑡	PROPN
cana-1739	61	69	)	)	PUNCT
cana-1739	61	70	𝑑𝐶	𝑑𝐶	NOUN
cana-1739	61	71	𝑑𝑡	𝑑𝑡	ADP
cana-1739	61	72	=	=	SYM
cana-1739	61	73	𝛺	𝛺	PROPN
cana-1739	61	74	−	−	NOUN
cana-1739	61	75	𝑝1𝐺(𝑡)𝐶(𝑡	𝑝1𝐺(𝑡)𝐶(𝑡	NOUN
cana-1739	61	76	)	)	PUNCT
cana-1739	62	1	+	+	CCONJ
cana-1739	62	2	𝑝3𝐻(𝑡)𝐶(𝑡	𝑝3𝐻(𝑡)𝐶(𝑡	ADJ
cana-1739	62	3	)	)	PUNCT
cana-1739	62	4	−	−	PROPN
cana-1739	62	5	𝑝4𝐶(𝑡	𝑝4𝐶(𝑡	ADJ
cana-1739	62	6	)	)	PUNCT
cana-1739	62	7	(	(	PUNCT
cana-1739	62	8	1	1	X
cana-1739	62	9	)	)	PUNCT
cana-1739	62	10	𝑑𝐼	𝑑𝐼	ADJ
cana-1739	62	11	𝑑𝑡	𝑑𝑡	ADP
cana-1739	62	12	=	=	PUNCT
cana-1739	62	13	𝑝5𝐺(𝑡)𝐼(𝑡	𝑝5𝐺(𝑡)𝐼(𝑡	PROPN
cana-1739	62	14	)	)	PUNCT
cana-1739	62	15	−	−	PROPN
cana-1739	62	16	𝑝6𝐻(𝑡)𝐼(𝑡	𝑝6𝐻(𝑡)𝐼(𝑡	NOUN
cana-1739	62	17	)	)	PUNCT
cana-1739	63	1	−	−	PROPN
cana-1739	63	2	𝑝7𝐼(𝑡	𝑝7𝐼(𝑡	X
cana-1739	63	3	)	)	PUNCT
cana-1739	63	4	𝑑𝐻	𝑑𝐻	VERB
cana-1739	63	5	𝑑𝑡	𝑑𝑡	ADP
cana-1739	63	6	=	=	SYM
cana-1739	63	7	𝛹	𝛹	PROPN
cana-1739	63	8	+	+	NUM
cana-1739	63	9	𝑝6𝐻(𝑡)𝐼(𝑡	𝑝6𝐻(𝑡)𝐼(𝑡	PROPN
cana-1739	63	10	)	)	PUNCT
cana-1739	63	11	−	−	PROPN
cana-1739	63	12	𝑝8𝐻(𝑡	𝑝8𝐻(𝑡	NOUN
cana-1739	63	13	)	)	PUNCT
cana-1739	63	14	communications	communication	NOUN
cana-1739	63	15	on	on	ADP
cana-1739	63	16	applied	apply	VERB
cana-1739	63	17	nonlinear	nonlinear	ADJ
cana-1739	63	18	analysis	analysis	NOUN
cana-1739	63	19	issn	issn	NOUN
cana-1739	63	20	:	:	PUNCT
cana-1739	63	21	1074	1074	NUM
cana-1739	63	22	-	-	PUNCT
cana-1739	63	23	133x	133x	NUM
cana-1739	63	24	vol	vol	NOUN
cana-1739	63	25	32	32	NUM
cana-1739	63	26	no	no	NOUN
cana-1739	63	27	.	.	NOUN
cana-1739	63	28	2	2	NUM
cana-1739	63	29	(	(	PUNCT
cana-1739	63	30	2025	2025	NUM
cana-1739	63	31	)	)	PUNCT
cana-1739	63	32	234	234	NUM
cana-1739	63	33	https://internationalpubls.com	https://internationalpubls.com	X
cana-1739	63	34	with	with	ADP
cana-1739	63	35	initial	initial	ADJ
cana-1739	63	36	conditions	condition	NOUN
cana-1739	63	37	𝐺(0	𝐺(0	NUM
cana-1739	63	38	)	)	PUNCT
cana-1739	63	39	=	=	SYM
cana-1739	63	40	𝐺0	𝐺0	X
cana-1739	63	41	≥	≥	NOUN
cana-1739	63	42	0	0	NUM
cana-1739	63	43	;	;	PUNCT
cana-1739	63	44	𝐶(0	𝐶(0	X
cana-1739	63	45	)	)	PUNCT
cana-1739	63	46	=	=	SYM
cana-1739	63	47	𝐶0	𝐶0	X
cana-1739	63	48	>	>	X
cana-1739	63	49	0	0	NUM
cana-1739	63	50	;	;	PUNCT
cana-1739	63	51	𝐼(0	𝐼(0	X
cana-1739	63	52	)	)	PUNCT
cana-1739	63	53	=	=	SYM
cana-1739	63	54	𝐼0	𝐼0	ADJ
cana-1739	63	55	;	;	PUNCT
cana-1739	63	56	𝐻(0	𝐻(0	X
cana-1739	63	57	)	)	PUNCT
cana-1739	63	58	=	=	VERB
cana-1739	63	59	𝐻0	𝐻0	PROPN
cana-1739	63	60	≥	≥	NOUN
cana-1739	63	61	0	0	NUM
cana-1739	63	62	where	where	SCONJ
cana-1739	63	63	𝛬	𝛬	PRON
cana-1739	63	64	refers	refer	VERB
cana-1739	63	65	the	the	DET
cana-1739	63	66	amount	amount	NOUN
cana-1739	63	67	of	of	ADP
cana-1739	63	68	green	green	ADJ
cana-1739	63	69	building	building	NOUN
cana-1739	63	70	,	,	PUNCT
cana-1739	63	71	𝑝1	𝑝1	NOUN
cana-1739	63	72	is	be	AUX
cana-1739	63	73	the	the	DET
cana-1739	63	74	rate	rate	NOUN
cana-1739	63	75	at	at	ADP
cana-1739	63	76	which	which	PRON
cana-1739	63	77	ghgs	ghg	VERB
cana-1739	63	78	are	be	AUX
cana-1739	63	79	absorbed	absorb	VERB
cana-1739	63	80	by	by	ADP
cana-1739	63	81	green	green	ADJ
cana-1739	63	82	buildings	building	NOUN
cana-1739	63	83	,	,	PUNCT
cana-1739	63	84	𝑝2	𝑝2	NOUN
cana-1739	63	85	is	be	AUX
cana-1739	63	86	the	the	DET
cana-1739	63	87	reduction	reduction	NOUN
cana-1739	63	88	rate	rate	NOUN
cana-1739	63	89	of	of	ADP
cana-1739	63	90	green	green	ADJ
cana-1739	63	91	building	building	NOUN
cana-1739	63	92	,	,	PUNCT
cana-1739	63	93	ghgs	ghg	VERB
cana-1739	63	94	are	be	AUX
cana-1739	63	95	measured	measure	VERB
cana-1739	63	96	by	by	ADP
cana-1739	63	97	𝛺	𝛺	PROPN
cana-1739	63	98	,	,	PUNCT
cana-1739	63	99	𝑝3	𝑝3	ADV
cana-1739	63	100	is	be	AUX
cana-1739	63	101	the	the	DET
cana-1739	63	102	rate	rate	NOUN
cana-1739	63	103	of	of	ADP
cana-1739	63	104	human	human	ADJ
cana-1739	63	105	originated	originated	NOUN
cana-1739	63	106	ghgs	ghg	VERB
cana-1739	63	107	,	,	PUNCT
cana-1739	63	108	𝑝4	𝑝4	NOUN
cana-1739	63	109	represents	represent	VERB
cana-1739	63	110	rate	rate	NOUN
cana-1739	63	111	of	of	ADP
cana-1739	63	112	reduction	reduction	NOUN
cana-1739	63	113	of	of	ADP
cana-1739	63	114	ghgs	ghgs	NOUN
cana-1739	63	115	,	,	PUNCT
cana-1739	63	116	an	an	DET
cana-1739	63	117	ingredient	ingredient	NOUN
cana-1739	63	118	production	production	NOUN
cana-1739	63	119	rate	rate	NOUN
cana-1739	63	120	by	by	ADP
cana-1739	63	121	green	green	ADJ
cana-1739	63	122	buildings	building	NOUN
cana-1739	63	123	is	be	AUX
cana-1739	63	124	measured	measure	VERB
cana-1739	63	125	by	by	ADP
cana-1739	63	126	𝑝5	𝑝5	NOUN
cana-1739	63	127	,	,	PUNCT
cana-1739	63	128	𝑝6	𝑝6	NOUN
cana-1739	63	129	is	be	AUX
cana-1739	63	130	the	the	DET
cana-1739	63	131	adoption	adoption	NOUN
cana-1739	63	132	rate	rate	NOUN
cana-1739	63	133	of	of	ADP
cana-1739	63	134	ingredients	ingredient	NOUN
cana-1739	63	135	by	by	ADP
cana-1739	63	136	human	human	ADJ
cana-1739	63	137	communities	community	NOUN
cana-1739	63	138	,	,	PUNCT
cana-1739	63	139	the	the	DET
cana-1739	63	140	reduction	reduction	NOUN
cana-1739	63	141	rate	rate	NOUN
cana-1739	63	142	of	of	ADP
cana-1739	63	143	ingredients	ingredient	NOUN
cana-1739	63	144	is	be	AUX
cana-1739	63	145	defined	define	VERB
cana-1739	63	146	as	as	ADP
cana-1739	63	147	𝑝7	𝑝7	PROPN
cana-1739	63	148	,	,	PUNCT
cana-1739	63	149	𝛹	𝛹	PROPN
cana-1739	63	150	is	be	AUX
cana-1739	63	151	the	the	DET
cana-1739	63	152	amount	amount	NOUN
cana-1739	63	153	of	of	ADP
cana-1739	63	154	human	human	ADJ
cana-1739	63	155	community	community	NOUN
cana-1739	63	156	and	and	CCONJ
cana-1739	63	157	𝑝8	𝑝8	PROPN
cana-1739	63	158	is	be	AUX
cana-1739	63	159	the	the	DET
cana-1739	63	160	reduction	reduction	NOUN
cana-1739	63	161	rate	rate	NOUN
cana-1739	63	162	of	of	ADP
cana-1739	63	163	human	human	ADJ
cana-1739	63	164	communities	community	NOUN
cana-1739	63	165	.	.	PUNCT
cana-1739	64	1	3.2	3.2	NUM
cana-1739	64	2	fractional	fractional	ADJ
cana-1739	64	3	version	version	NOUN
cana-1739	64	4	of	of	ADP
cana-1739	64	5	the	the	DET
cana-1739	64	6	classical	classical	ADJ
cana-1739	64	7	model	model	NOUN
cana-1739	64	8	by	by	ADP
cana-1739	64	9	substituting	substitute	VERB
cana-1739	64	10	the	the	DET
cana-1739	64	11	classical	classical	ADJ
cana-1739	64	12	derivative	derivative	NOUN
cana-1739	64	13	with	with	ADP
cana-1739	64	14	the	the	DET
cana-1739	64	15	operator	operator	NOUN
cana-1739	64	16	𝑑ν(t)𝑓(𝑡	𝑑ν(t)𝑓(𝑡	VERB
cana-1739	64	17	)	)	PUNCT
cana-1739	64	18	𝑑𝑡	𝑑𝑡	ADP
cana-1739	64	19	,	,	PUNCT
cana-1739	64	20	the	the	DET
cana-1739	64	21	fractional	fractional	ADJ
cana-1739	64	22	model	model	NOUN
cana-1739	64	23	of	of	ADP
cana-1739	64	24	system	system	NOUN
cana-1739	64	25	(	(	PUNCT
cana-1739	64	26	1	1	X
cana-1739	64	27	)	)	PUNCT
cana-1739	64	28	is	be	AUX
cana-1739	64	29	obtained	obtain	VERB
cana-1739	64	30	.	.	PUNCT
cana-1739	65	1	𝑑ν(t)𝐺	𝑑ν(t)𝐺	VERB
cana-1739	65	2	𝑑𝑡	𝑑𝑡	ADP
cana-1739	65	3	=	=	SYM
cana-1739	65	4	𝛬	𝛬	PROPN
cana-1739	65	5	+	+	PROPN
cana-1739	65	6	𝑝1	𝑝1	NOUN
cana-1739	65	7	ν(t)𝐺(𝑡)𝐶(𝑡	ν(t)𝐺(𝑡)𝐶(𝑡	PROPN
cana-1739	65	8	)	)	PUNCT
cana-1739	65	9	−	−	PROPN
cana-1739	65	10	𝑝2	𝑝2	PROPN
cana-1739	65	11	ν(t)𝐺(𝑡	ν(t)𝐺(𝑡	PROPN
cana-1739	65	12	)	)	PUNCT
cana-1739	65	13	𝑑ν(t)𝐶	𝑑ν(t)𝐶	ADJ
cana-1739	65	14	𝑑𝑡	𝑑𝑡	ADP
cana-1739	65	15	=	=	PUNCT
cana-1739	65	16	𝛺	𝛺	PROPN
cana-1739	65	17	−	−	PROPN
cana-1739	65	18	𝑝1	𝑝1	NOUN
cana-1739	65	19	ν(t)𝐺(𝑡)𝐶(𝑡	ν(t)𝐺(𝑡)𝐶(𝑡	PROPN
cana-1739	65	20	)	)	PUNCT
cana-1739	65	21	+	+	CCONJ
cana-1739	65	22	𝑝3	𝑝3	ADV
cana-1739	65	23	ν(t)𝐻(𝑡)𝐶(𝑡	ν(t)𝐻(𝑡)𝐶(𝑡	ADJ
cana-1739	65	24	)	)	PUNCT
cana-1739	65	25	−	−	PROPN
cana-1739	65	26	𝑝4	𝑝4	NOUN
cana-1739	65	27	ν(t)𝐶(𝑡	ν(t)𝐶(𝑡	NOUN
cana-1739	65	28	)	)	PUNCT
cana-1739	65	29	𝑑ν(t)𝐼	𝑑ν(t)𝐼	VERB
cana-1739	65	30	𝑑𝑡	𝑑𝑡	ADP
cana-1739	65	31	=	=	PROPN
cana-1739	65	32	𝑝5	𝑝5	PROPN
cana-1739	65	33	ν(t)𝐺(𝑡)𝐼(𝑡	ν(t)𝐺(𝑡)𝐼(𝑡	PROPN
cana-1739	65	34	)	)	PUNCT
cana-1739	65	35	−	−	PROPN
cana-1739	65	36	𝑝6	𝑝6	NOUN
cana-1739	65	37	ν(t)𝐻(𝑡)𝐼(𝑡	ν(t)𝐻(𝑡)𝐼(𝑡	PROPN
cana-1739	65	38	)	)	PUNCT
cana-1739	65	39	−	−	PROPN
cana-1739	65	40	𝑝7	𝑝7	PROPN
cana-1739	65	41	ν(t)𝐼(𝑡	ν(t)𝐼(𝑡	PROPN
cana-1739	65	42	)	)	PUNCT
cana-1739	65	43	(	(	PUNCT
cana-1739	65	44	2	2	X
cana-1739	65	45	)	)	PUNCT
cana-1739	65	46	𝑑ν(t)𝐻	𝑑ν(t)𝐻	NOUN
cana-1739	65	47	𝑑𝑡	𝑑𝑡	ADP
cana-1739	65	48	=	=	SYM
cana-1739	65	49	𝛹	𝛹	PROPN
cana-1739	65	50	+	+	NUM
cana-1739	65	51	𝑝6	𝑝6	PROPN
cana-1739	65	52	ν(t)𝐻(𝑡)𝐼(𝑡	ν(t)𝐻(𝑡)𝐼(𝑡	PROPN
cana-1739	65	53	)	)	PUNCT
cana-1739	65	54	−	−	PROPN
cana-1739	65	55	𝑝8	𝑝8	PROPN
cana-1739	65	56	ν(t)𝐻(𝑡	ν(t)𝐻(𝑡	PROPN
cana-1739	65	57	)	)	PUNCT
cana-1739	65	58	with	with	ADP
cana-1739	65	59	𝐺(0	𝐺(0	NOUN
cana-1739	65	60	)	)	PUNCT
cana-1739	65	61	=	=	SYM
cana-1739	65	62	𝐺0	𝐺0	X
cana-1739	65	63	≥	≥	NOUN
cana-1739	65	64	0	0	NUM
cana-1739	65	65	;	;	PUNCT
cana-1739	65	66	𝐶(0	𝐶(0	X
cana-1739	65	67	)	)	PUNCT
cana-1739	65	68	=	=	SYM
cana-1739	65	69	𝐶0	𝐶0	X
cana-1739	65	70	>	>	X
cana-1739	65	71	0	0	NUM
cana-1739	65	72	;	;	PUNCT
cana-1739	65	73	(	(	PUNCT
cana-1739	65	74	0	0	X
cana-1739	65	75	)	)	PUNCT
cana-1739	65	76	=	=	SYM
cana-1739	65	77	𝐼0	𝐼0	ADJ
cana-1739	65	78	;	;	PUNCT
cana-1739	65	79	𝐻(0	𝐻(0	X
cana-1739	65	80	)	)	PUNCT
cana-1739	65	81	=	=	VERB
cana-1739	65	82	𝐻0	𝐻0	PROPN
cana-1739	65	83	≥	≥	NOUN
cana-1739	65	84	0	0	NUM
cana-1739	65	85	the	the	DET
cana-1739	65	86	equilibria	equilibrium	NOUN
cana-1739	65	87	of	of	ADP
cana-1739	65	88	the	the	DET
cana-1739	65	89	above	above	ADJ
cana-1739	65	90	fractional	fractional	ADJ
cana-1739	65	91	-	-	PUNCT
cana-1739	65	92	order	order	NOUN
cana-1739	65	93	model	model	NOUN
cana-1739	65	94	can	can	AUX
cana-1739	65	95	be	be	AUX
cana-1739	65	96	obtained	obtain	VERB
cana-1739	65	97	from	from	ADP
cana-1739	65	98	𝑑ν(t)𝐺(𝑡	𝑑ν(t)𝐺(𝑡	NUM
cana-1739	65	99	)	)	PUNCT
cana-1739	65	100	𝑑𝑡	𝑑𝑡	ADP
cana-1739	65	101	=	=	NOUN
cana-1739	65	102	0	0	NUM
cana-1739	65	103	𝑑ν(t)𝐶(𝑡	𝑑ν(t)𝐶(𝑡	NUM
cana-1739	65	104	)	)	PUNCT
cana-1739	65	105	𝑑𝑡	𝑑𝑡	ADP
cana-1739	65	106	=	=	SYM
cana-1739	65	107	0	0	NUM
cana-1739	65	108	,	,	PUNCT
cana-1739	65	109	𝑑ν(t)𝐼(𝑡	𝑑ν(t)𝐼(𝑡	NUM
cana-1739	65	110	)	)	PUNCT
cana-1739	65	111	𝑑𝑡	𝑑𝑡	ADP
cana-1739	65	112	=	=	NOUN
cana-1739	65	113	0	0	NUM
cana-1739	65	114	and	and	CCONJ
cana-1739	65	115	𝑑ν(t)𝐻(𝑡	𝑑ν(t)𝐻(𝑡	NUM
cana-1739	65	116	)	)	PUNCT
cana-1739	65	117	𝑑𝑡	𝑑𝑡	ADP
cana-1739	65	118	=	=	NOUN
cana-1739	65	119	0	0	NUM
cana-1739	65	120	.	.	PUNCT
cana-1739	66	1	it	it	PRON
cana-1739	66	2	was	be	AUX
cana-1739	66	3	observed	observe	VERB
cana-1739	66	4	that	that	SCONJ
cana-1739	66	5	the	the	DET
cana-1739	66	6	system	system	NOUN
cana-1739	66	7	(	(	PUNCT
cana-1739	66	8	1	1	X
cana-1739	66	9	)	)	PUNCT
cana-1739	66	10	has	have	VERB
cana-1739	66	11	two	two	NUM
cana-1739	66	12	equilibria	equilibrium	NOUN
cana-1739	66	13	,	,	PUNCT
cana-1739	66	14	one	one	NUM
cana-1739	66	15	of	of	ADP
cana-1739	66	16	them	they	PRON
cana-1739	66	17	is	be	AUX
cana-1739	66	18	trivial	trivial	ADJ
cana-1739	66	19	equilibrium	equilibrium	NOUN
cana-1739	66	20	𝐸𝑇𝐸	𝐸𝑇𝐸	PROPN
cana-1739	66	21	=(	=(	NOUN
cana-1739	66	22	𝐺0	𝐺0	PROPN
cana-1739	66	23	,	,	PUNCT
cana-1739	66	24	𝐶0	𝐶0	PROPN
cana-1739	66	25	,	,	PUNCT
cana-1739	66	26	𝐼0	𝐼0	PROPN
cana-1739	66	27	,	,	PUNCT
cana-1739	66	28	𝐻0	𝐻0	PROPN
cana-1739	66	29	)	)	PUNCT
cana-1739	66	30	and	and	CCONJ
cana-1739	66	31	the	the	DET
cana-1739	66	32	other	other	ADJ
cana-1739	66	33	is	be	AUX
cana-1739	66	34	global	global	ADJ
cana-1739	66	35	equilibrium	equilibrium	NOUN
cana-1739	66	36	𝐸𝐺𝐸	𝐸𝐺𝐸	PROPN
cana-1739	66	37	=	=	SYM
cana-1739	66	38	(	(	PUNCT
cana-1739	66	39	𝐺∗	𝐺∗	PROPN
cana-1739	66	40	,	,	PUNCT
cana-1739	66	41	𝐶∗	𝐶∗	NOUN
cana-1739	66	42	,	,	PUNCT
cana-1739	66	43	𝐼∗	𝐼∗	PROPN
cana-1739	66	44	,	,	PUNCT
cana-1739	66	45	𝐻∗	𝐻∗	PROPN
cana-1739	66	46	)	)	PUNCT
cana-1739	66	47	.	.	PUNCT
cana-1739	67	1	where	where	SCONJ
cana-1739	67	2	𝐺∗	𝐺∗	NOUN
cana-1739	67	3	=	=	SYM
cana-1739	67	4	α	α	PROPN
cana-1739	67	5	=	=	SYM
cana-1739	67	6	𝛬𝑝3	𝛬𝑝3	X
cana-1739	67	7	𝜈(𝑡	𝜈(𝑡	PROPN
cana-1739	67	8	)	)	PUNCT
cana-1739	67	9	𝑝7	𝑝7	PROPN
cana-1739	67	10	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	67	11	)	)	PUNCT
cana-1739	68	1	+	+	NUM
cana-1739	68	2	𝛬𝑝4	𝛬𝑝4	NOUN
cana-1739	68	3	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	68	4	)	)	PUNCT
cana-1739	68	5	𝑝6	𝑝6	NOUN
cana-1739	68	6	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	68	7	)	)	PUNCT
cana-1739	69	1	[	[	X
cana-1739	69	2	(	(	PUNCT
cana-1739	69	3	𝑝2	𝑝2	NOUN
cana-1739	69	4	𝜈(𝑡	𝜈(𝑡	PROPN
cana-1739	69	5	)	)	PUNCT
cana-1739	69	6	𝑝3	𝑝3	ADV
cana-1739	69	7	𝜈(𝑡	𝜈(𝑡	ADJ
cana-1739	69	8	)	)	PUNCT
cana-1739	69	9	𝑝7	𝑝7	PROPN
cana-1739	69	10	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	69	11	)	)	PUNCT
cana-1739	70	1	+	+	NUM
cana-1739	70	2	𝑝2	𝑝2	NOUN
cana-1739	70	3	𝜈(𝑡	𝜈(𝑡	PROPN
cana-1739	70	4	)	)	PUNCT
cana-1739	70	5	𝑝4	𝑝4	NOUN
cana-1739	70	6	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	70	7	)	)	PUNCT
cana-1739	70	8	𝑝6	𝑝6	NOUN
cana-1739	70	9	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	70	10	)	)	PUNCT
cana-1739	70	11	)	)	PUNCT
cana-1739	71	1	+	+	CCONJ
cana-1739	71	2	(	(	PUNCT
cana-1739	71	3	𝛬𝑝3	𝛬𝑝3	X
cana-1739	71	4	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	71	5	)	)	PUNCT
cana-1739	71	6	𝑝5	𝑝5	NOUN
cana-1739	71	7	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	71	8	)	)	PUNCT
cana-1739	71	9	−	−	NOUN
cana-1739	71	10	𝛬𝑝1	𝛬𝑝1	NOUN
cana-1739	71	11	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	71	12	)	)	PUNCT
cana-1739	71	13	𝑝6	𝑝6	NOUN
cana-1739	71	14	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	71	15	)	)	PUNCT
cana-1739	71	16	)	)	PUNCT
cana-1739	72	1	−	−	PROPN
cana-1739	72	2	𝑝1	𝑝1	NOUN
cana-1739	72	3	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	72	4	)	)	PUNCT
cana-1739	72	5	𝛺𝑝6	𝛺𝑝6	ADV
cana-1739	72	6	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	72	7	)	)	PUNCT
cana-1739	72	8	]	]	PUNCT
cana-1739	72	9	𝐶∗	𝐶∗	NOUN
cana-1739	72	10	=	=	SYM
cana-1739	72	11	𝛺𝑝6	𝛺𝑝6	ADV
cana-1739	72	12	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	72	13	)	)	PUNCT
cana-1739	72	14	(	(	PUNCT
cana-1739	72	15	𝑝3	𝑝3	ADV
cana-1739	72	16	𝜈(𝑡	𝜈(𝑡	ADJ
cana-1739	72	17	)	)	PUNCT
cana-1739	72	18	𝑝7	𝑝7	PROPN
cana-1739	72	19	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	72	20	)	)	PUNCT
cana-1739	73	1	+	+	CCONJ
cana-1739	73	2	𝑝4	𝑝4	PROPN
cana-1739	73	3	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	73	4	)	)	PUNCT
cana-1739	73	5	𝑝6	𝑝6	NOUN
cana-1739	73	6	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	73	7	)	)	PUNCT
cana-1739	73	8	)	)	PUNCT
cana-1739	73	9	−	−	PROPN
cana-1739	73	10	α(𝑝3	α(𝑝3	NOUN
cana-1739	73	11	𝜈(𝑡	𝜈(𝑡	ADJ
cana-1739	73	12	)	)	PUNCT
cana-1739	73	13	𝑝5	𝑝5	NOUN
cana-1739	73	14	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	73	15	)	)	PUNCT
cana-1739	74	1	+	+	CCONJ
cana-1739	74	2	𝑝1	𝑝1	NOUN
cana-1739	74	3	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	74	4	)	)	PUNCT
cana-1739	74	5	𝑝6	𝑝6	NOUN
cana-1739	74	6	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	74	7	)	)	PUNCT
cana-1739	74	8	)	)	PUNCT
cana-1739	74	9	𝐼∗	𝐼∗	NOUN
cana-1739	75	1	=	=	SYM
cana-1739	75	2	𝑝5	𝑝5	VERB
cana-1739	75	3	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	75	4	)	)	PUNCT
cana-1739	75	5	𝑝8	𝑝8	NOUN
cana-1739	75	6	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	75	7	)	)	PUNCT
cana-1739	75	8	α−𝑝7	α−𝑝7	VERB
cana-1739	75	9	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	75	10	)	)	PUNCT
cana-1739	75	11	𝑝8	𝑝8	NOUN
cana-1739	75	12	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	75	13	)	)	PUNCT
cana-1739	75	14	−ψ𝑝6	−ψ𝑝6	ADP
cana-1739	76	1	𝜈(𝑡	𝜈(𝑡	ADJ
cana-1739	76	2	)	)	PUNCT
cana-1739	76	3	𝑝6	𝑝6	NOUN
cana-1739	76	4	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	76	5	)	)	PUNCT
cana-1739	76	6	(	(	PUNCT
cana-1739	76	7	𝑝5	𝑝5	VERB
cana-1739	76	8	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	76	9	)	)	PUNCT
cana-1739	76	10	α−𝑝7	α−𝑝7	X
cana-1739	76	11	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	76	12	)	)	PUNCT
cana-1739	76	13	)	)	PUNCT
cana-1739	76	14	𝐻∗	𝐻∗	PROPN
cana-1739	76	15	=	=	SYM
cana-1739	76	16	𝑝5	𝑝5	VERB
cana-1739	76	17	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	76	18	)	)	PUNCT
cana-1739	76	19	α	α	PROPN
cana-1739	76	20	−	−	PROPN
cana-1739	76	21	𝑝7	𝑝7	PROPN
cana-1739	76	22	𝜈(𝑡	𝜈(𝑡	ADV
cana-1739	76	23	)	)	PUNCT
cana-1739	76	24	𝑝6	𝑝6	NOUN
cana-1739	76	25	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	76	26	)	)	PUNCT
cana-1739	76	27	the	the	DET
cana-1739	76	28	eigen	eigen	PROPN
cana-1739	76	29	values	value	NOUN
cana-1739	76	30	are	be	AUX
cana-1739	76	31	the	the	DET
cana-1739	76	32	solutions	solution	NOUN
cana-1739	76	33	of	of	ADP
cana-1739	76	34	the	the	DET
cana-1739	76	35	characteristic	characteristic	ADJ
cana-1739	76	36	equation	equation	NOUN
cana-1739	76	37	det(𝐴𝑖	det(𝐴𝑖	PROPN
cana-1739	76	38	−	−	PROPN
cana-1739	76	39	𝜆𝐼	𝜆𝐼	NOUN
cana-1739	76	40	)	)	PUNCT
cana-1739	76	41	=	=	SYM
cana-1739	77	1	0	0	X
cana-1739	77	2	.	.	PUNCT
cana-1739	77	3	where	where	SCONJ
cana-1739	77	4	the	the	DET
cana-1739	77	5	matrix	matrix	NOUN
cana-1739	77	6	𝐴𝑖	𝐴𝑖	PROPN
cana-1739	77	7	and	and	CCONJ
cana-1739	77	8	the	the	DET
cana-1739	77	9	unit	unit	NOUN
cana-1739	77	10	matrix	matrix	NOUN
cana-1739	77	11	is	be	AUX
cana-1739	77	12	i	i	PRON
cana-1739	77	13	with	with	ADP
cana-1739	77	14	the	the	DET
cana-1739	77	15	eigen	eigen	PROPN
cana-1739	77	16	values	value	NOUN
cana-1739	77	17	calculated	calculate	VERB
cana-1739	77	18	at	at	ADP
cana-1739	77	19	𝐸𝑇𝐸	𝐸𝑇𝐸	PROPN
cana-1739	77	20	and	and	CCONJ
cana-1739	77	21	𝐸𝐺𝐸	𝐸𝐺𝐸	PROPN
cana-1739	77	22	.	.	PUNCT
cana-1739	78	1	for	for	ADP
cana-1739	78	2	further	further	ADJ
cana-1739	78	3	details	detail	NOUN
cana-1739	78	4	of	of	ADP
cana-1739	78	5	the	the	DET
cana-1739	78	6	results	result	NOUN
cana-1739	78	7	can	can	AUX
cana-1739	78	8	be	be	AUX
cana-1739	78	9	found	find	VERB
cana-1739	78	10	in	in	ADP
cana-1739	78	11	[	[	X
cana-1739	78	12	15	15	NUM
cana-1739	78	13	]	]	X
cana-1739	78	14	communications	communication	NOUN
cana-1739	78	15	on	on	ADP
cana-1739	78	16	applied	apply	VERB
cana-1739	78	17	nonlinear	nonlinear	ADJ
cana-1739	78	18	analysis	analysis	NOUN
cana-1739	78	19	issn	issn	NOUN
cana-1739	78	20	:	:	PUNCT
cana-1739	78	21	1074	1074	NUM
cana-1739	78	22	-	-	PUNCT
cana-1739	78	23	133x	133x	NUM
cana-1739	78	24	vol	vol	NOUN
cana-1739	78	25	32	32	NUM
cana-1739	78	26	no	no	NOUN
cana-1739	78	27	.	.	NOUN
cana-1739	78	28	2	2	NUM
cana-1739	78	29	(	(	PUNCT
cana-1739	78	30	2025	2025	NUM
cana-1739	78	31	)	)	PUNCT
cana-1739	78	32	235	235	NUM
cana-1739	78	33	https://internationalpubls.com	https://internationalpubls.com	X
cana-1739	78	34	since	since	SCONJ
cana-1739	78	35	the	the	DET
cana-1739	78	36	parameters	parameter	NOUN
cana-1739	78	37	are	be	AUX
cana-1739	78	38	dimensionless	dimensionless	NOUN
cana-1739	78	39	,	,	PUNCT
cana-1739	78	40	the	the	DET
cana-1739	78	41	fractional	fractional	ADJ
cana-1739	78	42	models	model	NOUN
cana-1739	78	43	within	within	ADP
cana-1739	78	44	lc	lc	PROPN
cana-1739	78	45	,	,	PUNCT
cana-1739	78	46	cf	cf	NOUN
cana-1739	78	47	and	and	CCONJ
cana-1739	78	48	ab	ab	PROPN
cana-1739	78	49	sense	sense	NOUN
cana-1739	78	50	will	will	AUX
cana-1739	78	51	be	be	AUX
cana-1739	78	52	the	the	DET
cana-1739	78	53	same	same	ADJ
cana-1739	78	54	and	and	CCONJ
cana-1739	78	55	it	it	PRON
cana-1739	78	56	will	will	AUX
cana-1739	78	57	not	not	PART
cana-1739	78	58	be	be	AUX
cana-1739	78	59	necessary	necessary	ADJ
cana-1739	78	60	to	to	PART
cana-1739	78	61	investigate	investigate	VERB
cana-1739	78	62	again	again	ADV
cana-1739	78	63	.	.	PUNCT
cana-1739	79	1	the	the	DET
cana-1739	79	2	jacobian	jacobian	ADJ
cana-1739	79	3	matrix	matrix	NOUN
cana-1739	79	4	of	of	ADP
cana-1739	79	5	the	the	DET
cana-1739	79	6	system	system	NOUN
cana-1739	79	7	(	(	PUNCT
cana-1739	79	8	2	2	X
cana-1739	79	9	)	)	PUNCT
cana-1739	79	10	is	be	AUX
cana-1739	79	11	as	as	SCONJ
cana-1739	79	12	follows	follow	VERB
cana-1739	79	13	j=	j=	NOUN
cana-1739	79	14	[	[	PUNCT
cana-1739	79	15	𝑝1	𝑝1	NOUN
cana-1739	79	16	ν(t)𝐶	ν(t)𝐶	PROPN
cana-1739	80	1	−	−	PROPN
cana-1739	80	2	𝑝2	𝑝2	NOUN
cana-1739	80	3	ν(t	ν(t	NOUN
cana-1739	80	4	)	)	PUNCT
cana-1739	80	5	𝑝1	𝑝1	NOUN
cana-1739	80	6	ν(t)𝐺	ν(t)𝐺	NOUN
cana-1739	80	7	0	0	NUM
cana-1739	80	8	0	0	NUM
cana-1739	81	1	−𝑝1	−𝑝1	NOUN
cana-1739	81	2	ν(t)𝐶	ν(t)𝐶	PROPN
cana-1739	82	1	−𝑝1	−𝑝1	INTJ
cana-1739	82	2	ν(t)𝐺	ν(t)𝐺	PROPN
cana-1739	83	1	+	+	CCONJ
cana-1739	83	2	𝑝3	𝑝3	ADV
cana-1739	83	3	ν(t)𝐻	ν(t)𝐻	NUM
cana-1739	83	4	−	−	NOUN
cana-1739	83	5	𝑝4	𝑝4	PROPN
cana-1739	83	6	ν(t	ν(t	NOUN
cana-1739	83	7	)	)	PUNCT
cana-1739	83	8	0	0	NUM
cana-1739	84	1	𝑝3	𝑝3	ADP
cana-1739	84	2	ν(t)𝐶	ν(t)𝐶	NUM
cana-1739	84	3	𝑝5	𝑝5	NOUN
cana-1739	85	1	ν(t)𝐼	ν(t)𝐼	PROPN
cana-1739	85	2	0	0	NUM
cana-1739	85	3	𝑝5	𝑝5	NOUN
cana-1739	85	4	ν(t)𝐺	ν(t)𝐺	NUM
cana-1739	85	5	−	−	PROPN
cana-1739	86	1	𝑝6	𝑝6	NOUN
cana-1739	86	2	ν(t)𝐻	ν(t)𝐻	PROPN
cana-1739	86	3	−	−	PROPN
cana-1739	86	4	𝑝7	𝑝7	PROPN
cana-1739	86	5	ν(t	ν(t	PROPN
cana-1739	86	6	)	)	PUNCT
cana-1739	86	7	−𝑝6	−𝑝6	PROPN
cana-1739	86	8	ν(t)𝐼	ν(t)𝐼	PROPN
cana-1739	86	9	0	0	SYM
cana-1739	86	10	0	0	NUM
cana-1739	86	11	𝑝6	𝑝6	NOUN
cana-1739	86	12	ν(t)𝐻	ν(t)𝐻	PROPN
cana-1739	87	1	𝑝6	𝑝6	NOUN
cana-1739	88	1	ν(t)𝐼	ν(t)𝐼	PROPN
cana-1739	89	1	−	−	PROPN
cana-1739	89	2	𝑝8	𝑝8	PROPN
cana-1739	89	3	ν(t)𝐻	ν(t)𝐻	PROPN
cana-1739	89	4	]	]	X
cana-1739	89	5	4	4	NUM
cana-1739	89	6	.	.	NOUN
cana-1739	89	7	existence	existence	NOUN
cana-1739	89	8	and	and	CCONJ
cana-1739	89	9	uniqueness	uniqueness	NOUN
cana-1739	89	10	of	of	ADP
cana-1739	89	11	fractional	fractional	ADJ
cana-1739	89	12	solutions	solution	NOUN
cana-1739	89	13	4.1	4.1	NUM
cana-1739	89	14	existence	existence	NOUN
cana-1739	89	15	and	and	CCONJ
cana-1739	89	16	uniqueness	uniqueness	NOUN
cana-1739	89	17	of	of	ADP
cana-1739	89	18	fractional	fractional	ADJ
cana-1739	89	19	solutions	solution	NOUN
cana-1739	89	20	by	by	ADP
cana-1739	89	21	the	the	DET
cana-1739	89	22	liouville	liouville	PROPN
cana-1739	89	23	-	-	PUNCT
cana-1739	89	24	caputo	caputo	PROPN
cana-1739	89	25	model	model	NOUN
cana-1739	89	26	in	in	ADP
cana-1739	89	27	this	this	DET
cana-1739	89	28	section	section	NOUN
cana-1739	89	29	,	,	PUNCT
cana-1739	89	30	we	we	PRON
cana-1739	89	31	establish	establish	VERB
cana-1739	89	32	the	the	DET
cana-1739	89	33	existence	existence	NOUN
cana-1739	89	34	and	and	CCONJ
cana-1739	89	35	uniqueness	uniqueness	NOUN
cana-1739	89	36	of	of	ADP
cana-1739	89	37	solutions	solution	NOUN
cana-1739	89	38	of	of	ADP
cana-1739	89	39	the	the	DET
cana-1739	89	40	liouvillecaputo	liouvillecaputo	NOUN
cana-1739	89	41	model	model	NOUN
cana-1739	89	42	.	.	PUNCT
cana-1739	90	1	let	let	VERB
cana-1739	90	2	us	we	PRON
cana-1739	90	3	construct	construct	VERB
cana-1739	90	4	the	the	DET
cana-1739	90	5	system	system	NOUN
cana-1739	90	6	(	(	PUNCT
cana-1739	90	7	2	2	NUM
cana-1739	90	8	)	)	PUNCT
cana-1739	90	9	as	as	ADP
cana-1739	90	10	𝐷𝑡	𝐷𝑡	PROPN
cana-1739	90	11	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	90	12	)	)	PUNCT
cana-1739	90	13	0	0	NUM
cana-1739	91	1	𝐿𝐶	𝐿𝐶	PROPN
cana-1739	91	2	[	[	X
cana-1739	91	3	𝐺(𝑡	𝐺(𝑡	NOUN
cana-1739	91	4	)	)	PUNCT
cana-1739	91	5	]	]	PUNCT
cana-1739	91	6	=	=	PUNCT
cana-1739	91	7	𝐹1(𝑡	𝐹1(𝑡	PROPN
cana-1739	91	8	,	,	PUNCT
cana-1739	91	9	𝐺	𝐺	NOUN
cana-1739	91	10	)	)	PUNCT
cana-1739	91	11	=	=	SYM
cana-1739	92	1	𝛬	𝛬	NOUN
cana-1739	92	2	+	+	NUM
cana-1739	92	3	𝑝1	𝑝1	NOUN
cana-1739	92	4	ν(t)𝐺(𝑡)𝐶(𝑡	ν(t)𝐺(𝑡)𝐶(𝑡	PROPN
cana-1739	92	5	)	)	PUNCT
cana-1739	92	6	−	−	PROPN
cana-1739	92	7	𝑝2	𝑝2	PROPN
cana-1739	92	8	ν(t)𝐺(𝑡	ν(t)𝐺(𝑡	PROPN
cana-1739	92	9	)	)	PUNCT
cana-1739	93	1	𝐷𝑡	𝐷𝑡	NOUN
cana-1739	93	2	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	93	3	)	)	PUNCT
cana-1739	93	4	0	0	NUM
cana-1739	94	1	𝐿𝐶	𝐿𝐶	PROPN
cana-1739	94	2	[	[	X
cana-1739	94	3	𝐶(𝑡	𝐶(𝑡	NOUN
cana-1739	94	4	)	)	PUNCT
cana-1739	94	5	]	]	PUNCT
cana-1739	95	1	=	=	PUNCT
cana-1739	95	2	𝐹2(𝑡	𝐹2(𝑡	PROPN
cana-1739	95	3	,	,	PUNCT
cana-1739	95	4	𝐶	𝐶	PROPN
cana-1739	95	5	)	)	PUNCT
cana-1739	95	6	=	=	PUNCT
cana-1739	96	1	𝛺	𝛺	ADP
cana-1739	96	2	−	−	PROPN
cana-1739	96	3	𝑝1	𝑝1	NOUN
cana-1739	96	4	ν(t)𝐺(𝑡)𝐶(𝑡	ν(t)𝐺(𝑡)𝐶(𝑡	PROPN
cana-1739	96	5	)	)	PUNCT
cana-1739	96	6	+	+	CCONJ
cana-1739	96	7	𝑝3	𝑝3	ADV
cana-1739	96	8	ν(t)𝐻(𝑡)𝐶(𝑡	ν(t)𝐻(𝑡)𝐶(𝑡	ADJ
cana-1739	96	9	)	)	PUNCT
cana-1739	96	10	−	−	PROPN
cana-1739	96	11	𝑝4	𝑝4	NOUN
cana-1739	96	12	ν(t)𝐶(𝑡	ν(t)𝐶(𝑡	NOUN
cana-1739	96	13	)	)	PUNCT
cana-1739	97	1	𝐷𝑡	𝐷𝑡	NOUN
cana-1739	97	2	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	97	3	)	)	PUNCT
cana-1739	97	4	0	0	NUM
cana-1739	98	1	𝐿𝐶	𝐿𝐶	PROPN
cana-1739	98	2	[	[	X
cana-1739	98	3	𝐼(𝑡	𝐼(𝑡	NUM
cana-1739	98	4	)	)	PUNCT
cana-1739	98	5	]	]	PUNCT
cana-1739	99	1	=	=	SYM
cana-1739	99	2	𝐹3(𝑡	𝐹3(𝑡	PROPN
cana-1739	99	3	,	,	PUNCT
cana-1739	99	4	𝐼	𝐼	PROPN
cana-1739	99	5	)	)	PUNCT
cana-1739	99	6	=	=	SYM
cana-1739	99	7	𝑝5	𝑝5	PROPN
cana-1739	99	8	ν(t)𝐺(𝑡)𝐼(𝑡	ν(t)𝐺(𝑡)𝐼(𝑡	PROPN
cana-1739	99	9	)	)	PUNCT
cana-1739	99	10	−	−	PROPN
cana-1739	99	11	𝑝6	𝑝6	NOUN
cana-1739	99	12	ν(t)𝐻(𝑡)𝐼(𝑡	ν(t)𝐻(𝑡)𝐼(𝑡	PROPN
cana-1739	99	13	)	)	PUNCT
cana-1739	100	1	−	−	PROPN
cana-1739	100	2	𝑝7	𝑝7	PROPN
cana-1739	100	3	ν(t)𝐼(𝑡	ν(t)𝐼(𝑡	PROPN
cana-1739	100	4	)	)	PUNCT
cana-1739	100	5	(	(	PUNCT
cana-1739	100	6	3	3	X
cana-1739	100	7	)	)	PUNCT
cana-1739	100	8	𝐷𝑡	𝐷𝑡	PROPN
cana-1739	100	9	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	100	10	)	)	PUNCT
cana-1739	100	11	0	0	NUM
cana-1739	101	1	𝐿𝐶	𝐿𝐶	PROPN
cana-1739	101	2	[	[	X
cana-1739	101	3	𝐻(𝑡	𝐻(𝑡	NOUN
cana-1739	101	4	)	)	PUNCT
cana-1739	101	5	]	]	PUNCT
cana-1739	102	1	=	=	PUNCT
cana-1739	102	2	𝐹4(𝑡	𝐹4(𝑡	X
cana-1739	102	3	,	,	PUNCT
cana-1739	102	4	𝐻	𝐻	NOUN
cana-1739	102	5	)	)	PUNCT
cana-1739	102	6	=	=	SYM
cana-1739	102	7	𝛹	𝛹	PROPN
cana-1739	102	8	+	+	NUM
cana-1739	102	9	𝑝6	𝑝6	PROPN
cana-1739	102	10	ν(t)𝐻(𝑡)𝐼(𝑡	ν(t)𝐻(𝑡)𝐼(𝑡	PROPN
cana-1739	102	11	)	)	PUNCT
cana-1739	102	12	−	−	PROPN
cana-1739	102	13	𝑝8	𝑝8	PROPN
cana-1739	102	14	ν(t)𝐻(𝑡	ν(t)𝐻(𝑡	PRON
cana-1739	102	15	)	)	PUNCT
cana-1739	102	16	by	by	ADP
cana-1739	102	17	using	use	VERB
cana-1739	102	18	liouville	liouville	PROPN
cana-1739	102	19	-	-	PUNCT
cana-1739	102	20	caputo	caputo	PROPN
cana-1739	102	21	fractional	fractional	ADJ
cana-1739	102	22	integral	integral	ADJ
cana-1739	102	23	operator	operator	NOUN
cana-1739	102	24	to	to	ADP
cana-1739	102	25	the	the	DET
cana-1739	102	26	above	above	ADJ
cana-1739	102	27	system	system	NOUN
cana-1739	102	28	,	,	PUNCT
cana-1739	102	29	we	we	PRON
cana-1739	102	30	get	get	VERB
cana-1739	102	31	𝐺(𝑡	𝐺(𝑡	NOUN
cana-1739	102	32	)	)	PUNCT
cana-1739	102	33	−	−	NUM
cana-1739	102	34	𝐺(0	𝐺(0	NUM
cana-1739	102	35	)	)	PUNCT
cana-1739	102	36	=	=	SYM
cana-1739	102	37	1	1	NUM
cana-1739	102	38	⎾	⎾	NUM
cana-1739	102	39	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	102	40	)	)	PUNCT
cana-1739	102	41	∫	∫	PROPN
cana-1739	102	42	(	(	PUNCT
cana-1739	102	43	𝑡	𝑡	PROPN
cana-1739	102	44	−	−	PROPN
cana-1739	102	45	𝑘)𝜈(𝑡)−1𝑡	𝑘)𝜈(𝑡)−1𝑡	PROPN
cana-1739	102	46	0	0	SYM
cana-1739	102	47	𝐹1(𝐾	𝐹1(𝐾	NOUN
cana-1739	102	48	,	,	PUNCT
cana-1739	102	49	𝐺(𝑡))𝑑𝑘	𝐺(𝑡))𝑑𝑘	NUM
cana-1739	102	50	𝐶(𝑡	𝐶(𝑡	NOUN
cana-1739	102	51	)	)	PUNCT
cana-1739	102	52	−	−	NUM
cana-1739	102	53	𝐶(0	𝐶(0	NOUN
cana-1739	102	54	)	)	PUNCT
cana-1739	102	55	=	=	SYM
cana-1739	102	56	1	1	NUM
cana-1739	102	57	⎾	⎾	NUM
cana-1739	102	58	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	102	59	)	)	PUNCT
cana-1739	102	60	∫	∫	PROPN
cana-1739	102	61	(	(	PUNCT
cana-1739	102	62	𝑡	𝑡	PROPN
cana-1739	102	63	−	−	PROPN
cana-1739	102	64	𝑘)𝜈(𝑡)−1𝑡	𝑘)𝜈(𝑡)−1𝑡	PROPN
cana-1739	102	65	0	0	NUM
cana-1739	102	66	𝐹2(𝐾	𝐹2(𝐾	NOUN
cana-1739	102	67	,	,	PUNCT
cana-1739	102	68	𝐶(𝑡))𝑑𝑘	𝐶(𝑡))𝑑𝑘	PROPN
cana-1739	102	69	𝐼(𝑡	𝐼(𝑡	NOUN
cana-1739	102	70	)	)	PUNCT
cana-1739	102	71	−	−	NOUN
cana-1739	102	72	𝐼(0	𝐼(0	NOUN
cana-1739	102	73	)	)	PUNCT
cana-1739	102	74	=	=	SYM
cana-1739	102	75	1	1	NUM
cana-1739	102	76	⎾	⎾	NUM
cana-1739	102	77	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	102	78	)	)	PUNCT
cana-1739	102	79	∫	∫	PROPN
cana-1739	102	80	(	(	PUNCT
cana-1739	102	81	𝑡	𝑡	PROPN
cana-1739	102	82	−	−	PROPN
cana-1739	102	83	𝑘)𝜈(𝑡)−1𝑡	𝑘)𝜈(𝑡)−1𝑡	PROPN
cana-1739	102	84	0	0	NUM
cana-1739	102	85	𝐹3(𝐾	𝐹3(𝐾	ADJ
cana-1739	102	86	,	,	PUNCT
cana-1739	102	87	𝐼(𝑡))𝑑𝑘	𝐼(𝑡))𝑑𝑘	NUM
cana-1739	102	88	𝐻(𝑡	𝐻(𝑡	NOUN
cana-1739	102	89	)	)	PUNCT
cana-1739	102	90	−	−	PROPN
cana-1739	102	91	𝐻(0	𝐻(0	CCONJ
cana-1739	102	92	)	)	PUNCT
cana-1739	102	93	=	=	SYM
cana-1739	102	94	1	1	NUM
cana-1739	102	95	⎾	⎾	NUM
cana-1739	102	96	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	102	97	)	)	PUNCT
cana-1739	102	98	∫	∫	PROPN
cana-1739	102	99	(	(	PUNCT
cana-1739	102	100	𝑡	𝑡	PROPN
cana-1739	102	101	−	−	PROPN
cana-1739	102	102	𝑘)𝜈(𝑡)−1𝑡	𝑘)𝜈(𝑡)−1𝑡	NOUN
cana-1739	102	103	0	0	NUM
cana-1739	103	1	𝐹4(𝐾,𝐻(𝑡))𝑑𝑘	𝐹4(𝐾,𝐻(𝑡))𝑑𝑘	ADJ
cana-1739	103	2	we	we	PRON
cana-1739	103	3	will	will	AUX
cana-1739	103	4	show	show	VERB
cana-1739	103	5	that	that	SCONJ
cana-1739	103	6	the	the	DET
cana-1739	103	7	kernel	kernel	NOUN
cana-1739	103	8	𝐹𝑖	𝐹𝑖	PROPN
cana-1739	103	9	for	for	ADP
cana-1739	103	10	𝑖	𝑖	NOUN
cana-1739	103	11	=	=	SYM
cana-1739	103	12	1,2,3,4	1,2,3,4	NUM
cana-1739	103	13	follows	follow	VERB
cana-1739	103	14	the	the	DET
cana-1739	103	15	lipschitz	lipschitz	NOUN
cana-1739	103	16	condition	condition	NOUN
cana-1739	103	17	and	and	CCONJ
cana-1739	103	18	contraction	contraction	NOUN
cana-1739	103	19	.	.	PUNCT
cana-1739	104	1	theorem	theorem	VERB
cana-1739	104	2	4.1.1	4.1.1	PROPN
cana-1739	104	3	the	the	DET
cana-1739	104	4	kernel	kernel	PROPN
cana-1739	104	5	𝐹𝑖(𝐾	𝐹𝑖(𝐾	PROPN
cana-1739	104	6	,	,	PUNCT
cana-1739	104	7	𝐺	𝐺	NOUN
cana-1739	104	8	)	)	PUNCT
cana-1739	104	9	for	for	ADP
cana-1739	104	10	𝑖	𝑖	NOUN
cana-1739	104	11	=	=	SYM
cana-1739	104	12	1,2,3,4	1,2,3,4	NUM
cana-1739	104	13	satisfies	satisfie	NOUN
cana-1739	104	14	lipschitz	lipschitz	VERB
cana-1739	104	15	condition	condition	NOUN
cana-1739	104	16	and	and	CCONJ
cana-1739	104	17	contraction	contraction	NOUN
cana-1739	104	18	if	if	SCONJ
cana-1739	104	19	the	the	DET
cana-1739	104	20	following	follow	VERB
cana-1739	104	21	inequality	inequality	NOUN
cana-1739	104	22	0	0	NUM
cana-1739	104	23	≤	≤	NUM
cana-1739	104	24	𝑟𝑖	𝑟𝑖	ADP
cana-1739	104	25	<	<	X
cana-1739	104	26	1	1	NUM
cana-1739	104	27	holds	hold	NOUN
cana-1739	104	28	.	.	PUNCT
cana-1739	105	1	proof	proof	NOUN
cana-1739	105	2	consider	consider	VERB
cana-1739	105	3	two	two	NUM
cana-1739	105	4	functions	function	NOUN
cana-1739	105	5	𝐺	𝐺	PROPN
cana-1739	105	6	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-1739	105	7	�	�	PROPN
cana-1739	105	8	̅	̅	NOUN
cana-1739	105	9	�	�	PROPN
cana-1739	105	10	‖𝐹1(𝑡	‖𝐹1(𝑡	NOUN
cana-1739	105	11	,	,	PUNCT
cana-1739	105	12	𝐺	𝐺	NOUN
cana-1739	105	13	)	)	PUNCT
cana-1739	105	14	−	−	PROPN
cana-1739	105	15	𝐹1(𝑡	𝐹1(𝑡	PROPN
cana-1739	105	16	,	,	PUNCT
cana-1739	105	17	�	�	PROPN
cana-1739	105	18	̅	̅	NOUN
cana-1739	105	19	�	�	NOUN
cana-1739	105	20	)‖	)‖	NOUN
cana-1739	105	21	≤	≤	ADJ
cana-1739	105	22	𝑝1	𝑝1	NOUN
cana-1739	105	23	ν(t)‖𝐶‖‖𝐺	ν(t)‖𝐶‖‖𝐺	PROPN
cana-1739	106	1	−	−	PROPN
cana-1739	106	2	�	�	PROPN
cana-1739	106	3	̅	̅	NOUN
cana-1739	106	4	�	�	NOUN
cana-1739	106	5	‖	‖	PROPN
cana-1739	106	6	−	−	PROPN
cana-1739	106	7	𝑝2	𝑝2	NOUN
cana-1739	106	8	ν(t)‖𝐺	ν(t)‖𝐺	PROPN
cana-1739	106	9	−	−	PROPN
cana-1739	106	10	�	�	PROPN
cana-1739	106	11	̅	̅	NOUN
cana-1739	106	12	�	�	NOUN
cana-1739	106	13	‖	‖	ADJ
cana-1739	106	14	≤	≤	PUNCT
cana-1739	107	1	[	[	PUNCT
cana-1739	107	2	𝑝1	𝑝1	NOUN
cana-1739	107	3	ν(t)𝑢2	ν(t)𝑢2	NOUN
cana-1739	107	4	−	−	PROPN
cana-1739	107	5	𝑝2	𝑝2	NOUN
cana-1739	107	6	ν(t)]‖𝐺	ν(t)]‖𝐺	NOUN
cana-1739	107	7	−	−	PROPN
cana-1739	107	8	�	�	PROPN
cana-1739	107	9	̅	̅	NOUN
cana-1739	107	10	�	�	NOUN
cana-1739	107	11	‖	‖	ADJ
cana-1739	107	12	≤	≤	NOUN
cana-1739	107	13	𝑟1‖𝐺	𝑟1‖𝐺	NOUN
cana-1739	107	14	−	−	PROPN
cana-1739	107	15	�	�	NOUN
cana-1739	107	16	̅	̅	NOUN
cana-1739	107	17	�	�	NOUN
cana-1739	107	18	‖	‖	VERB
cana-1739	107	19	(	(	PUNCT
cana-1739	107	20	4	4	NUM
cana-1739	107	21	)	)	PUNCT
cana-1739	107	22	communications	communication	NOUN
cana-1739	107	23	on	on	ADP
cana-1739	107	24	applied	apply	VERB
cana-1739	107	25	nonlinear	nonlinear	ADJ
cana-1739	107	26	analysis	analysis	NOUN
cana-1739	107	27	issn	issn	NOUN
cana-1739	107	28	:	:	PUNCT
cana-1739	107	29	1074	1074	NUM
cana-1739	107	30	-	-	PUNCT
cana-1739	107	31	133x	133x	NUM
cana-1739	107	32	vol	vol	NOUN
cana-1739	107	33	32	32	NUM
cana-1739	107	34	no	no	NOUN
cana-1739	107	35	.	.	NOUN
cana-1739	107	36	2	2	NUM
cana-1739	107	37	(	(	PUNCT
cana-1739	107	38	2025	2025	NUM
cana-1739	107	39	)	)	PUNCT
cana-1739	107	40	236	236	NUM
cana-1739	107	41	https://internationalpubls.com	https://internationalpubls.com	X
cana-1739	107	42	where	where	SCONJ
cana-1739	107	43	‖𝐺(𝑡)‖	‖𝐺(𝑡)‖	NOUN
cana-1739	107	44	≤	≤	NUM
cana-1739	107	45	𝑢1	𝑢1	NOUN
cana-1739	107	46	,	,	PUNCT
cana-1739	107	47	‖𝐶(𝑡)‖	‖𝐶(𝑡)‖	PROPN
cana-1739	107	48	≤	≤	PUNCT
cana-1739	107	49	𝑢2	𝑢2	PROPN
cana-1739	107	50	,	,	PUNCT
cana-1739	107	51	‖𝐼(𝑡)‖	‖𝐼(𝑡)‖	ADJ
cana-1739	107	52	≤	≤	NUM
cana-1739	107	53	𝑢3	𝑢3	NOUN
cana-1739	107	54	,	,	PUNCT
cana-1739	107	55	‖𝐻(𝑡)‖	‖𝐻(𝑡)‖	NOUN
cana-1739	107	56	≤	≤	ADJ
cana-1739	107	57	𝑢4	𝑢4	NOUN
cana-1739	107	58	and	and	CCONJ
cana-1739	107	59	𝑟1	𝑟1	NOUN
cana-1739	107	60	=	=	SYM
cana-1739	107	61	𝑝1	𝑝1	NOUN
cana-1739	107	62	ν(t)𝑢2	ν(t)𝑢2	NOUN
cana-1739	107	63	−	−	PROPN
cana-1739	107	64	𝑝2	𝑝2	NOUN
cana-1739	107	65	ν(t	ν(t	NOUN
cana-1739	107	66	)	)	PUNCT
cana-1739	107	67	are	be	AUX
cana-1739	107	68	positive	positive	ADJ
cana-1739	107	69	constants	constant	NOUN
cana-1739	107	70	.as	.as	PUNCT
cana-1739	108	1	a	a	DET
cana-1739	108	2	result	result	NOUN
cana-1739	108	3	,	,	PUNCT
cana-1739	108	4	the	the	DET
cana-1739	108	5	lipschitz	lipschitz	NOUN
cana-1739	108	6	condition	condition	NOUN
cana-1739	108	7	is	be	AUX
cana-1739	108	8	met	meet	VERB
cana-1739	108	9	for	for	ADP
cana-1739	108	10	𝑟1and	𝑟1and	NOUN
cana-1739	108	11	if	if	SCONJ
cana-1739	108	12	0	0	NUM
cana-1739	108	13	≤	≤	NUM
cana-1739	108	14	𝑟1	𝑟1	NOUN
cana-1739	108	15	<	<	X
cana-1739	108	16	1,then	1,then	PROPN
cana-1739	108	17	𝑟1follows	𝑟1follow	VERB
cana-1739	108	18	contraction	contraction	NOUN
cana-1739	108	19	.	.	PUNCT
cana-1739	109	1	similarly	similarly	ADV
cana-1739	109	2	,	,	PUNCT
cana-1739	109	3	it	it	PRON
cana-1739	109	4	can	can	AUX
cana-1739	109	5	be	be	AUX
cana-1739	109	6	exihibited	exihibite	VERB
cana-1739	109	7	and	and	CCONJ
cana-1739	109	8	demonstrated	demonstrate	VERB
cana-1739	109	9	in	in	ADP
cana-1739	109	10	the	the	DET
cana-1739	109	11	other	other	ADJ
cana-1739	109	12	equations	equation	NOUN
cana-1739	109	13	as	as	SCONJ
cana-1739	109	14	follows	follow	VERB
cana-1739	109	15	‖𝐹2(𝑡	‖𝐹2(𝑡	PROPN
cana-1739	109	16	,	,	PUNCT
cana-1739	109	17	𝐶	𝐶	PROPN
cana-1739	109	18	)	)	PUNCT
cana-1739	109	19	−	−	PROPN
cana-1739	110	1	𝐹2(𝑡	𝐹2(𝑡	NOUN
cana-1739	110	2	,	,	PUNCT
cana-1739	110	3	𝐶̅)‖	𝐶̅)‖	NOUN
cana-1739	110	4	≤	≤	NOUN
cana-1739	111	1	𝑟2‖𝐶	𝑟2‖𝐶	ADP
cana-1739	111	2	−	−	PROPN
cana-1739	111	3	𝐶̅‖	𝐶̅‖	PROPN
cana-1739	111	4	‖𝐹3(𝑡	‖𝐹3(𝑡	PROPN
cana-1739	111	5	,	,	PUNCT
cana-1739	111	6	𝐼	𝐼	PROPN
cana-1739	111	7	)	)	PUNCT
cana-1739	111	8	−	−	PROPN
cana-1739	111	9	𝐹3(𝑡	𝐹3(𝑡	PROPN
cana-1739	111	10	,	,	PUNCT
cana-1739	111	11	𝐼)̅‖	𝐼)̅‖	ADJ
cana-1739	111	12	≤	≤	NOUN
cana-1739	111	13	𝑟3‖𝐼	𝑟3‖𝐼	NOUN
cana-1739	112	1	−	−	PROPN
cana-1739	112	2	𝐼‖̅	𝐼‖̅	PROPN
cana-1739	112	3	‖𝐹4(𝑡	‖𝐹4(𝑡	PROPN
cana-1739	112	4	,	,	PUNCT
cana-1739	112	5	𝐻	𝐻	PROPN
cana-1739	112	6	)	)	PUNCT
cana-1739	112	7	−	−	PROPN
cana-1739	113	1	𝐹3(𝑡	𝐹3(𝑡	PROPN
cana-1739	113	2	,	,	PUNCT
cana-1739	113	3	�	�	PROPN
cana-1739	113	4	̅	̅	NOUN
cana-1739	113	5	�	�	NOUN
cana-1739	113	6	)‖	)‖	NOUN
cana-1739	113	7	≤	≤	NUM
cana-1739	113	8	𝑟4‖𝐻	𝑟4‖𝐻	NOUN
cana-1739	113	9	−	−	ADP
cana-1739	113	10	�	�	NOUN
cana-1739	113	11	̅	̅	NOUN
cana-1739	113	12	�	�	NOUN
cana-1739	113	13	‖	‖	ADJ
cana-1739	113	14	therefore	therefore	ADV
cana-1739	113	15	𝐹𝑖	𝐹𝑖	PROPN
cana-1739	113	16	satisfies	satisfie	NOUN
cana-1739	113	17	lipschitz	lipschitz	NOUN
cana-1739	113	18	condition	condition	NOUN
cana-1739	113	19	.	.	PUNCT
cana-1739	114	1	also	also	ADV
cana-1739	114	2	,	,	PUNCT
cana-1739	114	3	if	if	SCONJ
cana-1739	114	4	0	0	NUM
cana-1739	114	5	≤	≤	NUM
cana-1739	114	6	𝑟𝑖	𝑟𝑖	ADV
cana-1739	114	7	<	<	X
cana-1739	114	8	1	1	NUM
cana-1739	114	9	,	,	PUNCT
cana-1739	114	10	then	then	ADV
cana-1739	114	11	the	the	DET
cana-1739	114	12	kernels	kernel	NOUN
cana-1739	114	13	follows	follow	VERB
cana-1739	114	14	contractions	contraction	NOUN
cana-1739	114	15	.	.	PUNCT
cana-1739	115	1	from	from	ADP
cana-1739	115	2	system	system	NOUN
cana-1739	115	3	(	(	PUNCT
cana-1739	115	4	3	3	NUM
cana-1739	115	5	)	)	PUNCT
cana-1739	115	6	,	,	PUNCT
cana-1739	115	7	the	the	DET
cana-1739	115	8	recurrent	recurrent	ADJ
cana-1739	115	9	form	form	NOUN
cana-1739	115	10	can	can	AUX
cana-1739	115	11	be	be	AUX
cana-1739	115	12	written	write	VERB
cana-1739	115	13	as	as	SCONJ
cana-1739	115	14	follows	follow	VERB
cana-1739	115	15	𝛷1𝑛	𝛷1𝑛	PROPN
cana-1739	115	16	=	=	PUNCT
cana-1739	115	17	𝐺𝑛(𝑡	𝐺𝑛(𝑡	PROPN
cana-1739	115	18	)	)	PUNCT
cana-1739	115	19	−	−	ADP
cana-1739	115	20	𝐺𝑛−1(𝑡	𝐺𝑛−1(𝑡	NOUN
cana-1739	115	21	)	)	PUNCT
cana-1739	115	22	=	=	SYM
cana-1739	115	23	1	1	NUM
cana-1739	115	24	⎾	⎾	NUM
cana-1739	115	25	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	115	26	)	)	PUNCT
cana-1739	116	1	∫(𝑡	∫(𝑡	ADJ
cana-1739	116	2	−	−	PROPN
cana-1739	116	3	𝑘)𝜈(𝑡)−1	𝑘)𝜈(𝑡)−1	NOUN
cana-1739	116	4	𝑡	𝑡	NOUN
cana-1739	116	5	0	0	PUNCT
cana-1739	117	1	[	[	X
cana-1739	117	2	𝐹1(𝐾	𝐹1(𝐾	PROPN
cana-1739	117	3	,	,	PUNCT
cana-1739	117	4	𝐺𝑛−1	𝐺𝑛−1	NUM
cana-1739	117	5	)	)	PUNCT
cana-1739	118	1	−	−	PROPN
cana-1739	118	2	𝐹1(𝐾	𝐹1(𝐾	PROPN
cana-1739	118	3	,	,	PUNCT
cana-1739	118	4	𝐺𝑛−2)]𝑑𝑘	𝐺𝑛−2)]𝑑𝑘	ADP
cana-1739	118	5	𝛷2𝑛	𝛷2𝑛	PROPN
cana-1739	118	6	=	=	SYM
cana-1739	118	7	𝐶𝑛(𝑡	𝐶𝑛(𝑡	PROPN
cana-1739	118	8	)	)	PUNCT
cana-1739	118	9	−	−	NUM
cana-1739	118	10	𝐶𝑛−1(𝑡	𝐶𝑛−1(𝑡	NOUN
cana-1739	118	11	)	)	PUNCT
cana-1739	118	12	=	=	SYM
cana-1739	118	13	1	1	NUM
cana-1739	118	14	⎾	⎾	NUM
cana-1739	118	15	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	118	16	)	)	PUNCT
cana-1739	118	17	∫(𝑡	∫(𝑡	ADJ
cana-1739	118	18	−	−	PROPN
cana-1739	118	19	𝑘)𝜈(𝑡)−1	𝑘)𝜈(𝑡)−1	NOUN
cana-1739	118	20	𝑡	𝑡	NOUN
cana-1739	118	21	0	0	PUNCT
cana-1739	119	1	[	[	X
cana-1739	119	2	𝐹2(𝐾	𝐹2(𝐾	NOUN
cana-1739	119	3	,	,	PUNCT
cana-1739	119	4	𝐶𝑛−1	𝐶𝑛−1	NOUN
cana-1739	119	5	)	)	PUNCT
cana-1739	120	1	−	−	PROPN
cana-1739	120	2	𝐹2(𝐾	𝐹2(𝐾	NOUN
cana-1739	120	3	,	,	PUNCT
cana-1739	120	4	𝐶𝑛−2)]𝑑𝑘	𝐶𝑛−2)]𝑑𝑘	NUM
cana-1739	120	5	𝛷3𝑛	𝛷3𝑛	PROPN
cana-1739	120	6	=	=	PUNCT
cana-1739	120	7	𝐼𝑛(𝑡	𝐼𝑛(𝑡	PROPN
cana-1739	120	8	)	)	PUNCT
cana-1739	120	9	−	−	NOUN
cana-1739	120	10	𝐼𝑛−1(𝑡	𝐼𝑛−1(𝑡	SYM
cana-1739	120	11	)	)	PUNCT
cana-1739	120	12	=	=	SYM
cana-1739	120	13	1	1	NUM
cana-1739	120	14	⎾	⎾	NUM
cana-1739	120	15	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	120	16	)	)	PUNCT
cana-1739	120	17	∫	∫	PROPN
cana-1739	120	18	(	(	PUNCT
cana-1739	120	19	𝑡	𝑡	PROPN
cana-1739	120	20	−	−	PROPN
cana-1739	120	21	𝑘)𝜈(𝑡)−1𝑡	𝑘)𝜈(𝑡)−1𝑡	NOUN
cana-1739	120	22	0	0	PUNCT
cana-1739	121	1	[	[	X
cana-1739	121	2	𝐹3(𝐾	𝐹3(𝐾	ADJ
cana-1739	121	3	,	,	PUNCT
cana-1739	121	4	𝐼𝑛−1	𝐼𝑛−1	PROPN
cana-1739	121	5	)	)	PUNCT
cana-1739	122	1	−	−	PROPN
cana-1739	122	2	𝐹3(𝐾	𝐹3(𝐾	PROPN
cana-1739	122	3	,	,	PUNCT
cana-1739	122	4	𝐼𝑛−2)]𝑑𝑘	𝐼𝑛−2)]𝑑𝑘	ADP
cana-1739	122	5	𝛷4𝑛	𝛷4𝑛	PROPN
cana-1739	122	6	=	=	PUNCT
cana-1739	122	7	𝐻𝑛(𝑡	𝐻𝑛(𝑡	PROPN
cana-1739	122	8	)	)	PUNCT
cana-1739	122	9	−	−	NOUN
cana-1739	122	10	𝐻𝑛−1(𝑡	𝐻𝑛−1(𝑡	NOUN
cana-1739	122	11	)	)	PUNCT
cana-1739	122	12	=	=	SYM
cana-1739	122	13	1	1	NUM
cana-1739	122	14	⎾	⎾	NUM
cana-1739	122	15	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	122	16	)	)	PUNCT
cana-1739	123	1	∫(𝑡	∫(𝑡	ADJ
cana-1739	123	2	−	−	PROPN
cana-1739	123	3	𝑘)𝜈(𝑡)−1	𝑘)𝜈(𝑡)−1	NOUN
cana-1739	123	4	𝑡	𝑡	NOUN
cana-1739	123	5	0	0	PUNCT
cana-1739	124	1	[	[	X
cana-1739	124	2	𝐹4(𝐾	𝐹4(𝐾	X
cana-1739	124	3	,	,	PUNCT
cana-1739	124	4	𝐻𝑛−1	𝐻𝑛−1	PROPN
cana-1739	124	5	)	)	PUNCT
cana-1739	124	6	−	−	NUM
cana-1739	124	7	𝐹4(𝐾,𝐻𝑛−2)]𝑑𝑘	𝐹4(𝐾,𝐻𝑛−2)]𝑑𝑘	ADP
cana-1739	124	8	using	use	VERB
cana-1739	124	9	the	the	DET
cana-1739	124	10	initial	initial	ADJ
cana-1739	124	11	conditions	condition	NOUN
cana-1739	124	12	𝐺(𝑡	𝐺(𝑡	NOUN
cana-1739	124	13	)	)	PUNCT
cana-1739	124	14	=	=	PUNCT
cana-1739	124	15	𝐺(0),𝐶(𝑡	𝐺(0),𝐶(𝑡	ADJ
cana-1739	124	16	)	)	PUNCT
cana-1739	124	17	=	=	SYM
cana-1739	124	18	𝐶(0	𝐶(0	NOUN
cana-1739	124	19	)	)	PUNCT
cana-1739	124	20	,	,	PUNCT
cana-1739	124	21	𝐼(𝑡	𝐼(𝑡	NUM
cana-1739	124	22	)	)	PUNCT
cana-1739	124	23	=	=	SYM
cana-1739	124	24	𝐼(0	𝐼(0	NOUN
cana-1739	124	25	)	)	PUNCT
cana-1739	124	26	,	,	PUNCT
cana-1739	124	27	𝐻(𝑡	𝐻(𝑡	NOUN
cana-1739	124	28	)	)	PUNCT
cana-1739	124	29	=	=	PUNCT
cana-1739	124	30	𝐻(0	𝐻(0	PROPN
cana-1739	124	31	)	)	PUNCT
cana-1739	124	32	for	for	ADP
cana-1739	124	33	the	the	DET
cana-1739	124	34	above	above	ADJ
cana-1739	124	35	equation	equation	NOUN
cana-1739	124	36	and	and	CCONJ
cana-1739	124	37	taking	take	VERB
cana-1739	124	38	norm	norm	NOUN
cana-1739	124	39	,	,	PUNCT
cana-1739	124	40	we	we	PRON
cana-1739	124	41	get	get	VERB
cana-1739	124	42	‖𝛷1𝑛(𝑡)‖	‖𝛷1𝑛(𝑡)‖	PROPN
cana-1739	124	43	=	=	SYM
cana-1739	124	44	‖𝐺𝑛(𝑡	‖𝐺𝑛(𝑡	PROPN
cana-1739	124	45	)	)	PUNCT
cana-1739	124	46	−	−	VERB
cana-1739	125	1	𝐺𝑛−1(𝑡)‖	𝐺𝑛−1(𝑡)‖	ADJ
cana-1739	125	2	=	=	SYM
cana-1739	125	3	‖	‖	PROPN
cana-1739	125	4	1	1	NUM
cana-1739	125	5	⎾	⎾	NUM
cana-1739	125	6	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	125	7	)	)	PUNCT
cana-1739	126	1	∫(𝑡	∫(𝑡	ADJ
cana-1739	126	2	−	−	PROPN
cana-1739	126	3	𝑘)𝜈(𝑡)−1	𝑘)𝜈(𝑡)−1	NOUN
cana-1739	126	4	𝑡	𝑡	NOUN
cana-1739	126	5	0	0	PUNCT
cana-1739	127	1	[	[	X
cana-1739	127	2	𝐹1(𝐾	𝐹1(𝐾	PROPN
cana-1739	127	3	,	,	PUNCT
cana-1739	127	4	𝐺𝑛−1	𝐺𝑛−1	NUM
cana-1739	127	5	)	)	PUNCT
cana-1739	128	1	−	−	PROPN
cana-1739	128	2	𝐹1(𝐾	𝐹1(𝐾	NOUN
cana-1739	128	3	,	,	PUNCT
cana-1739	128	4	𝐺𝑛−2)]𝑑𝑘‖	𝐺𝑛−2)]𝑑𝑘‖	NOUN
cana-1739	128	5	now	now	ADV
cana-1739	128	6	using	use	VERB
cana-1739	128	7	lipschitz	lipschitz	NOUN
cana-1739	128	8	condition	condition	NOUN
cana-1739	128	9	in	in	ADP
cana-1739	128	10	the	the	DET
cana-1739	128	11	above	above	ADJ
cana-1739	128	12	equation	equation	NOUN
cana-1739	128	13	,	,	PUNCT
cana-1739	128	14	we	we	PRON
cana-1739	128	15	obtain	obtain	VERB
cana-1739	128	16	‖𝛷1𝑛(𝑡)‖	‖𝛷1𝑛(𝑡)‖	PROPN
cana-1739	128	17	≤	≤	ADJ
cana-1739	128	18	𝑟1	𝑟1	NOUN
cana-1739	128	19	⎾	⎾	NUM
cana-1739	128	20	𝜈(𝑡	𝜈(𝑡	X
cana-1739	128	21	)	)	PUNCT
cana-1739	128	22	∫‖𝛷1(𝑛−1)(𝑘)‖𝑑𝑘	∫‖𝛷1(𝑛−1)(𝑘)‖𝑑𝑘	AUX
cana-1739	128	23	𝑡	𝑡	X
cana-1739	128	24	0	0	NUM
cana-1739	128	25	similarly	similarly	ADV
cana-1739	128	26	,	,	PUNCT
cana-1739	128	27	‖𝛷2𝑛(𝑡)‖	‖𝛷2𝑛(𝑡)‖	PROPN
cana-1739	128	28	≤	≤	NUM
cana-1739	128	29	𝑟2	𝑟2	NOUN
cana-1739	128	30	⎾	⎾	NOUN
cana-1739	128	31	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	128	32	)	)	PUNCT
cana-1739	128	33	∫‖𝛷2(𝑛−1)(𝑘)‖𝑑𝑘	∫‖𝛷2(𝑛−1)(𝑘)‖𝑑𝑘	X
cana-1739	128	34	𝑡	𝑡	X
cana-1739	128	35	0	0	NUM
cana-1739	128	36	‖𝛷3𝑛(𝑡)‖	‖𝛷3𝑛(𝑡)‖	PROPN
cana-1739	128	37	≤	≤	NUM
cana-1739	128	38	𝑟3	𝑟3	NOUN
cana-1739	128	39	⎾	⎾	X
cana-1739	128	40	𝜈(𝑡	𝜈(𝑡	ADJ
cana-1739	128	41	)	)	PUNCT
cana-1739	128	42	∫	∫	PROPN
cana-1739	128	43	‖𝛷3(𝑛−1)(𝑘)‖𝑑𝑘	‖𝛷3(𝑛−1)(𝑘)‖𝑑𝑘	X
cana-1739	128	44	𝑡	𝑡	PROPN
cana-1739	128	45	0	0	NUM
cana-1739	128	46	‖𝛷4𝑛(𝑡)‖	‖𝛷4𝑛(𝑡)‖	ADJ
cana-1739	128	47	≤	≤	NUM
cana-1739	128	48	𝑟4	𝑟4	PROPN
cana-1739	128	49	⎾	⎾	NUM
cana-1739	128	50	𝜈(𝑡	𝜈(𝑡	X
cana-1739	128	51	)	)	PUNCT
cana-1739	128	52	∫	∫	PROPN
cana-1739	128	53	‖𝛷4(𝑛−1)(𝑘)‖𝑑𝑘	‖𝛷4(𝑛−1)(𝑘)‖𝑑𝑘	ADV
cana-1739	128	54	𝑡	𝑡	PROPN
cana-1739	128	55	0	0	NUM
cana-1739	128	56	(	(	PUNCT
cana-1739	128	57	5	5	NUM
cana-1739	128	58	)	)	PUNCT
cana-1739	128	59	communications	communication	NOUN
cana-1739	128	60	on	on	ADP
cana-1739	128	61	applied	apply	VERB
cana-1739	128	62	nonlinear	nonlinear	ADJ
cana-1739	128	63	analysis	analysis	NOUN
cana-1739	128	64	issn	issn	NOUN
cana-1739	128	65	:	:	PUNCT
cana-1739	128	66	1074	1074	NUM
cana-1739	128	67	-	-	PUNCT
cana-1739	128	68	133x	133x	NUM
cana-1739	128	69	vol	vol	NOUN
cana-1739	128	70	32	32	NUM
cana-1739	128	71	no	no	NOUN
cana-1739	128	72	.	.	NOUN
cana-1739	128	73	2	2	NUM
cana-1739	128	74	(	(	PUNCT
cana-1739	128	75	2025	2025	NUM
cana-1739	128	76	)	)	PUNCT
cana-1739	128	77	237	237	NUM
cana-1739	128	78	https://internationalpubls.com	https://internationalpubls.com	X
cana-1739	128	79	which	which	PRON
cana-1739	128	80	implies	imply	VERB
cana-1739	128	81	that	that	SCONJ
cana-1739	128	82	it	it	PRON
cana-1739	128	83	can	can	AUX
cana-1739	128	84	be	be	AUX
cana-1739	128	85	written	write	VERB
cana-1739	128	86	as	as	ADP
cana-1739	128	87	𝐺𝑛(𝑡	𝐺𝑛(𝑡	PROPN
cana-1739	128	88	)	)	PUNCT
cana-1739	128	89	=	=	SYM
cana-1739	128	90	∑	∑	PUNCT
cana-1739	128	91	𝛷1𝑖(𝑡	𝛷1𝑖(𝑡	ADJ
cana-1739	128	92	)	)	PUNCT
cana-1739	129	1	𝑛	𝑛	PRON
cana-1739	129	2	𝑖=1	𝑖=1	PROPN
cana-1739	129	3	;	;	PUNCT
cana-1739	129	4	𝐶𝑛(𝑡	𝐶𝑛(𝑡	X
cana-1739	129	5	)	)	PUNCT
cana-1739	129	6	=	=	PUNCT
cana-1739	129	7	∑	∑	PUNCT
cana-1739	129	8	𝛷2𝑖	𝛷2𝑖	PROPN
cana-1739	129	9	𝑛	𝑛	PRON
cana-1739	129	10	𝑖=1	𝑖=1	PROPN
cana-1739	129	11	(	(	PUNCT
cana-1739	129	12	𝑡	𝑡	NOUN
cana-1739	129	13	)	)	PUNCT
cana-1739	129	14	,	,	PUNCT
cana-1739	129	15	𝐼𝑛(𝑡	𝐼𝑛(𝑡	X
cana-1739	129	16	)	)	PUNCT
cana-1739	129	17	=	=	SYM
cana-1739	129	18	∑	∑	PUNCT
cana-1739	129	19	𝛷3𝑖(𝑡	𝛷3𝑖(𝑡	NOUN
cana-1739	129	20	)	)	PUNCT
cana-1739	129	21	𝑛	𝑛	PRON
cana-1739	129	22	𝑖=1	𝑖=1	PROPN
cana-1739	129	23	,	,	PUNCT
cana-1739	129	24	𝐻𝑛(𝑡	𝐻𝑛(𝑡	PROPN
cana-1739	129	25	)	)	PUNCT
cana-1739	129	26	=	=	SYM
cana-1739	129	27	∑	∑	PUNCT
cana-1739	129	28	𝛷4𝑖(𝑡	𝛷4𝑖(𝑡	NUM
cana-1739	129	29	)	)	PUNCT
cana-1739	130	1	𝑛	𝑛	DET
cana-1739	130	2	𝑖=1	𝑖=1	PROPN
cana-1739	130	3	theorem	theorem	VERB
cana-1739	130	4	4.1.2	4.1.2	NUM
cana-1739	130	5	the	the	DET
cana-1739	130	6	liouville	liouville	NOUN
cana-1739	130	7	-caputo	-caputo	PROPN
cana-1739	130	8	model	model	NOUN
cana-1739	130	9	(	(	PUNCT
cana-1739	130	10	3	3	X
cana-1739	130	11	)	)	PUNCT
cana-1739	130	12	has	have	VERB
cana-1739	130	13	system	system	NOUN
cana-1739	130	14	of	of	ADP
cana-1739	130	15	solutions	solution	NOUN
cana-1739	130	16	if	if	SCONJ
cana-1739	130	17	there	there	PRON
cana-1739	130	18	exists	exist	VERB
cana-1739	130	19	t	t	PROPN
cana-1739	130	20	>	>	X
cana-1739	130	21	1	1	NUM
cana-1739	130	22	such	such	ADJ
cana-1739	130	23	that	that	PRON
cana-1739	130	24	𝑟𝑖𝑡	𝑟𝑖𝑡	VERB
cana-1739	130	25	⎾	⎾	NUM
cana-1739	130	26	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	130	27	)	)	PUNCT
cana-1739	130	28	≤	≤	NUM
cana-1739	130	29	1	1	NUM
cana-1739	130	30	for	for	ADP
cana-1739	130	31	i=1	i=1	PRON
cana-1739	130	32	,	,	PUNCT
cana-1739	130	33	2	2	NUM
cana-1739	130	34	,	,	PUNCT
cana-1739	130	35	3	3	NUM
cana-1739	130	36	,	,	PUNCT
cana-1739	130	37	4	4	NUM
cana-1739	130	38	proof	proof	NOUN
cana-1739	130	39	consider	consider	VERB
cana-1739	130	40	,	,	PUNCT
cana-1739	130	41	‖𝛷1𝑛(𝑡)‖	‖𝛷1𝑛(𝑡)‖	PROPN
cana-1739	130	42	≤	≤	ADJ
cana-1739	130	43	𝑟1	𝑟1	NOUN
cana-1739	130	44	⎾	⎾	NUM
cana-1739	130	45	𝜈(𝑡	𝜈(𝑡	X
cana-1739	130	46	)	)	PUNCT
cana-1739	130	47	∫‖𝛷1(𝑛−1)(𝑘)‖𝑑𝑘	∫‖𝛷1(𝑛−1)(𝑘)‖𝑑𝑘	AUX
cana-1739	130	48	𝑡	𝑡	AUX
cana-1739	130	49	0	0	NUM
cana-1739	130	50	replacing	replace	VERB
cana-1739	130	51	n	n	ADV
cana-1739	130	52	by	by	ADP
cana-1739	130	53	n-1	n-1	NOUN
cana-1739	130	54	in	in	ADP
cana-1739	130	55	the	the	DET
cana-1739	130	56	above	above	ADJ
cana-1739	130	57	inequality	inequality	NOUN
cana-1739	130	58	‖𝛷1(𝑛−1)(𝑡)‖	‖𝛷1(𝑛−1)(𝑡)‖	VERB
cana-1739	130	59	≤	≤	ADJ
cana-1739	130	60	𝑟1	𝑟1	NOUN
cana-1739	130	61	⎾	⎾	NUM
cana-1739	130	62	𝜈(𝑡	𝜈(𝑡	ADJ
cana-1739	130	63	)	)	PUNCT
cana-1739	130	64	∫	∫	PROPN
cana-1739	130	65	‖𝛷1(𝑛−2)(𝑘)‖𝑑𝑘	‖𝛷1(𝑛−2)(𝑘)‖𝑑𝑘	NUM
cana-1739	130	66	𝑡	𝑡	PROPN
cana-1739	130	67	0	0	NUM
cana-1739	130	68	≤	≤	NOUN
cana-1739	130	69	[	[	PUNCT
cana-1739	130	70	𝑟1	𝑟1	NOUN
cana-1739	130	71	⎾	⎾	X
cana-1739	130	72	𝜈(𝑡	𝜈(𝑡	X
cana-1739	130	73	)	)	PUNCT
cana-1739	130	74	]	]	PUNCT
cana-1739	130	75	2	2	NUM
cana-1739	130	76	∫	∫	NOUN
cana-1739	130	77	‖𝛷1(𝑛−2)(𝑘)‖𝑑𝑘	‖𝛷1(𝑛−2)(𝑘)‖𝑑𝑘	NUM
cana-1739	130	78	𝑡	𝑡	PROPN
cana-1739	130	79	0	0	VERB
cana-1739	130	80	again	again	ADV
cana-1739	130	81	,	,	PUNCT
cana-1739	130	82	replacing	replace	VERB
cana-1739	130	83	n	n	ADV
cana-1739	130	84	by	by	ADP
cana-1739	130	85	n-2	n-2	NOUN
cana-1739	130	86	in	in	ADP
cana-1739	130	87	the	the	DET
cana-1739	130	88	given	give	VERB
cana-1739	130	89	inequality	inequality	NOUN
cana-1739	130	90	‖𝛷1(𝑛−2)(𝑡)‖	‖𝛷1(𝑛−2)(𝑡)‖	PUNCT
cana-1739	130	91	≤	≤	NOUN
cana-1739	130	92	[	[	PUNCT
cana-1739	130	93	𝑟1	𝑟1	NOUN
cana-1739	130	94	⎾	⎾	X
cana-1739	130	95	𝜈(𝑡	𝜈(𝑡	X
cana-1739	130	96	)	)	PUNCT
cana-1739	130	97	]	]	PUNCT
cana-1739	130	98	3	3	NUM
cana-1739	130	99	∫‖𝛷1(𝑛−3)(𝑘)‖𝑑𝑘	∫‖𝛷1(𝑛−3)(𝑘)‖𝑑𝑘	NOUN
cana-1739	130	100	𝑡	𝑡	X
cana-1739	130	101	0	0	NUM
cana-1739	130	102	on	on	ADP
cana-1739	130	103	substituting	substitute	VERB
cana-1739	130	104	in	in	ADP
cana-1739	130	105	this	this	DET
cana-1739	130	106	way	way	NOUN
cana-1739	130	107	and	and	CCONJ
cana-1739	130	108	use	use	VERB
cana-1739	130	109	the	the	DET
cana-1739	130	110	initial	initial	ADJ
cana-1739	130	111	condition	condition	NOUN
cana-1739	130	112	we	we	PRON
cana-1739	130	113	obtain	obtain	VERB
cana-1739	130	114	‖𝛷1𝑛(𝑡)‖	‖𝛷1𝑛(𝑡)‖	PROPN
cana-1739	130	115	≤	≤	NUM
cana-1739	130	116	‖𝐺𝑛(0)‖	‖𝐺𝑛(0)‖	NOUN
cana-1739	130	117	[	[	PUNCT
cana-1739	130	118	𝑟1𝑡	𝑟1𝑡	PROPN
cana-1739	130	119	⎾	⎾	NUM
cana-1739	130	120	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	130	121	)	)	PUNCT
cana-1739	130	122	]	]	PUNCT
cana-1739	130	123	𝑛	𝑛	PRON
cana-1739	130	124	similarly	similarly	ADV
cana-1739	130	125	,	,	PUNCT
cana-1739	130	126	we	we	PRON
cana-1739	130	127	get	get	VERB
cana-1739	130	128	ν(t	ν(t	NOUN
cana-1739	130	129	)	)	PUNCT
cana-1739	130	130	‖𝛷2𝑛(𝑡)‖	‖𝛷2𝑛(𝑡)‖	PROPN
cana-1739	130	131	≤	≤	PROPN
cana-1739	130	132	‖𝐶𝑛(0)‖	‖𝐶𝑛(0)‖	PROPN
cana-1739	130	133	[	[	PUNCT
cana-1739	130	134	𝑟2𝑡	𝑟2𝑡	X
cana-1739	130	135	⎾	⎾	NUM
cana-1739	130	136	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	130	137	)	)	PUNCT
cana-1739	130	138	]	]	PUNCT
cana-1739	130	139	𝑛	𝑛	PROPN
cana-1739	130	140	‖𝛷3𝑛(𝑡)‖	‖𝛷3𝑛(𝑡)‖	PROPN
cana-1739	130	141	≤	≤	NUM
cana-1739	130	142	‖𝐼𝑛(0)‖	‖𝐼𝑛(0)‖	NOUN
cana-1739	130	143	[	[	PUNCT
cana-1739	130	144	𝑟3𝑡	𝑟3𝑡	NOUN
cana-1739	130	145	⎾	⎾	NUM
cana-1739	130	146	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	130	147	)	)	PUNCT
cana-1739	130	148	]	]	PUNCT
cana-1739	130	149	𝑛	𝑛	DET
cana-1739	130	150	‖𝛷4𝑛(𝑡)‖	‖𝛷4𝑛(𝑡)‖	PROPN
cana-1739	130	151	≤	≤	NUM
cana-1739	130	152	‖𝐻𝑛(0)‖	‖𝐻𝑛(0)‖	NOUN
cana-1739	130	153	[	[	PUNCT
cana-1739	130	154	𝑟4𝑡	𝑟4𝑡	NOUN
cana-1739	130	155	⎾	⎾	NUM
cana-1739	130	156	𝜈(𝑡	𝜈(𝑡	X
cana-1739	130	157	)	)	PUNCT
cana-1739	130	158	]	]	PUNCT
cana-1739	131	1	𝑛	𝑛	ADP
cana-1739	131	2	this	this	DET
cana-1739	131	3	result	result	NOUN
cana-1739	131	4	proved	prove	VERB
cana-1739	131	5	the	the	DET
cana-1739	131	6	existence	existence	NOUN
cana-1739	131	7	and	and	CCONJ
cana-1739	131	8	continuity	continuity	NOUN
cana-1739	131	9	of	of	ADP
cana-1739	131	10	solutions	solution	NOUN
cana-1739	131	11	to	to	PART
cana-1739	131	12	show	show	VERB
cana-1739	131	13	that	that	SCONJ
cana-1739	131	14	g(t	g(t	PROPN
cana-1739	131	15	)	)	PUNCT
cana-1739	131	16	,	,	PUNCT
cana-1739	131	17	c(t	c(t	PROPN
cana-1739	131	18	)	)	PUNCT
cana-1739	131	19	,	,	PUNCT
cana-1739	131	20	i(t	i(t	PROPN
cana-1739	131	21	)	)	PUNCT
cana-1739	131	22	and	and	CCONJ
cana-1739	131	23	h(t	h(t	PROPN
cana-1739	131	24	)	)	PUNCT
cana-1739	131	25	are	be	AUX
cana-1739	131	26	the	the	DET
cana-1739	131	27	solutions	solution	NOUN
cana-1739	131	28	of	of	ADP
cana-1739	131	29	(	(	PUNCT
cana-1739	131	30	3	3	NUM
cana-1739	131	31	)	)	PUNCT
cana-1739	131	32	,	,	PUNCT
cana-1739	131	33	we	we	PRON
cana-1739	131	34	consider	consider	VERB
cana-1739	131	35	the	the	DET
cana-1739	131	36	following	follow	VERB
cana-1739	131	37	equations	equation	NOUN
cana-1739	131	38	𝐺(𝑡	𝐺(𝑡	VERB
cana-1739	131	39	)	)	PUNCT
cana-1739	131	40	−	−	NUM
cana-1739	131	41	𝐺(0	𝐺(0	NUM
cana-1739	131	42	)	)	PUNCT
cana-1739	131	43	=	=	SYM
cana-1739	131	44	𝐺𝑛(𝑡	𝐺𝑛(𝑡	NOUN
cana-1739	131	45	)	)	PUNCT
cana-1739	132	1	−	−	PROPN
cana-1739	132	2	𝑅1𝑛(𝑡	𝑅1𝑛(𝑡	NOUN
cana-1739	132	3	)	)	PUNCT
cana-1739	132	4	𝐶(𝑡	𝐶(𝑡	NOUN
cana-1739	132	5	)	)	PUNCT
cana-1739	132	6	−	−	NUM
cana-1739	132	7	𝐶(0	𝐶(0	NOUN
cana-1739	132	8	)	)	PUNCT
cana-1739	132	9	=	=	SYM
cana-1739	132	10	𝐶𝑛(𝑡	𝐶𝑛(𝑡	NOUN
cana-1739	132	11	)	)	PUNCT
cana-1739	132	12	−	−	ADP
cana-1739	132	13	𝑅2𝑛(𝑡	𝑅2𝑛(𝑡	NOUN
cana-1739	132	14	)	)	PUNCT
cana-1739	132	15	𝐼(𝑡	𝐼(𝑡	NUM
cana-1739	132	16	)	)	PUNCT
cana-1739	132	17	−	−	NOUN
cana-1739	132	18	𝐼(0	𝐼(0	NOUN
cana-1739	132	19	)	)	PUNCT
cana-1739	132	20	=	=	SYM
cana-1739	132	21	𝐼𝑛(𝑡	𝐼𝑛(𝑡	PROPN
cana-1739	132	22	)	)	PUNCT
cana-1739	132	23	−	−	ADP
cana-1739	132	24	𝑅3𝑛(𝑡	𝑅3𝑛(𝑡	NUM
cana-1739	132	25	)	)	PUNCT
cana-1739	132	26	(	(	PUNCT
cana-1739	132	27	6	6	X
cana-1739	132	28	)	)	PUNCT
cana-1739	132	29	communications	communication	NOUN
cana-1739	132	30	on	on	ADP
cana-1739	132	31	applied	apply	VERB
cana-1739	132	32	nonlinear	nonlinear	ADJ
cana-1739	132	33	analysis	analysis	NOUN
cana-1739	132	34	issn	issn	NOUN
cana-1739	132	35	:	:	PUNCT
cana-1739	132	36	1074	1074	NUM
cana-1739	132	37	-	-	PUNCT
cana-1739	132	38	133x	133x	NUM
cana-1739	132	39	vol	vol	NOUN
cana-1739	132	40	32	32	NUM
cana-1739	132	41	no	no	NOUN
cana-1739	132	42	.	.	NOUN
cana-1739	132	43	2	2	NUM
cana-1739	132	44	(	(	PUNCT
cana-1739	132	45	2025	2025	NUM
cana-1739	132	46	)	)	PUNCT
cana-1739	132	47	238	238	NUM
cana-1739	132	48	https://internationalpubls.com	https://internationalpubls.com	X
cana-1739	132	49	𝐻(𝑡	𝐻(𝑡	NOUN
cana-1739	132	50	)	)	PUNCT
cana-1739	132	51	−	−	NUM
cana-1739	132	52	𝐻(0	𝐻(0	NUM
cana-1739	132	53	)	)	PUNCT
cana-1739	132	54	=	=	SYM
cana-1739	132	55	𝐻𝑛(𝑡	𝐻𝑛(𝑡	PROPN
cana-1739	132	56	)	)	PUNCT
cana-1739	132	57	−	−	NOUN
cana-1739	132	58	𝑅4𝑛(𝑡	𝑅4𝑛(𝑡	NOUN
cana-1739	132	59	)	)	PUNCT
cana-1739	132	60	‖𝑅1𝑛(𝑡)‖	‖𝑅1𝑛(𝑡)‖	PROPN
cana-1739	132	61	=	=	SYM
cana-1739	132	62	‖	‖	PROPN
cana-1739	132	63	1	1	NUM
cana-1739	132	64	⎾	⎾	NUM
cana-1739	132	65	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	132	66	)	)	PUNCT
cana-1739	132	67	∫[𝐹1(𝐾	∫[𝐹1(𝐾	ADP
cana-1739	132	68	,	,	PUNCT
cana-1739	132	69	𝐺𝑛	𝐺𝑛	NOUN
cana-1739	132	70	)	)	PUNCT
cana-1739	132	71	−	−	ADP
cana-1739	132	72	𝐹1(𝐾	𝐹1(𝐾	PROPN
cana-1739	132	73	,	,	PUNCT
cana-1739	132	74	𝐺𝑛−1	𝐺𝑛−1	NUM
cana-1739	132	75	)	)	PUNCT
cana-1739	132	76	]	]	PUNCT
cana-1739	133	1	𝑡	𝑡	X
cana-1739	133	2	0	0	NUM
cana-1739	133	3	𝑑𝑘‖	𝑑𝑘‖	ADP
cana-1739	133	4	≤	≤	NUM
cana-1739	133	5	1	1	NUM
cana-1739	133	6	⎾	⎾	NUM
cana-1739	133	7	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	133	8	)	)	PUNCT
cana-1739	133	9	∫	∫	PROPN
cana-1739	133	10	‖[𝐹1(𝐾	‖[𝐹1(𝐾	SYM
cana-1739	133	11	,	,	PUNCT
cana-1739	133	12	𝐺𝑛	𝐺𝑛	NOUN
cana-1739	133	13	)	)	PUNCT
cana-1739	133	14	−	−	ADP
cana-1739	133	15	𝐹1(𝐾	𝐹1(𝐾	PROPN
cana-1739	133	16	,	,	PUNCT
cana-1739	133	17	𝐺𝑛−1)]‖	𝐺𝑛−1)]‖	PROPN
cana-1739	133	18	𝑡	𝑡	X
cana-1739	133	19	0	0	NUM
cana-1739	133	20	𝑑𝑘	𝑑𝑘	ADV
cana-1739	133	21	≤	≤	NUM
cana-1739	133	22	1	1	NUM
cana-1739	133	23	⎾	⎾	NUM
cana-1739	133	24	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	133	25	)	)	PUNCT
cana-1739	134	1	𝑟1‖𝐺𝑛	𝑟1‖𝐺𝑛	PROPN
cana-1739	134	2	−	−	PROPN
cana-1739	135	1	𝐺𝑛−1‖𝑡	𝐺𝑛−1‖𝑡	NUM
cana-1739	135	2	applying	apply	VERB
cana-1739	135	3	the	the	DET
cana-1739	135	4	above	above	ADJ
cana-1739	135	5	process	process	NOUN
cana-1739	135	6	recursively	recursively	ADV
cana-1739	135	7	,	,	PUNCT
cana-1739	135	8	‖𝑅1𝑛(𝑡)‖	‖𝑅1𝑛(𝑡)‖	PROPN
cana-1739	135	9	=	=	SYM
cana-1739	135	10	[	[	PUNCT
cana-1739	135	11	𝑟1𝑡	𝑟1𝑡	PROPN
cana-1739	135	12	⎾	⎾	NUM
cana-1739	135	13	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	135	14	)	)	PUNCT
cana-1739	135	15	]	]	PUNCT
cana-1739	136	1	𝑛+1	𝑛+1	PROPN
cana-1739	136	2	.	.	PUNCT
cana-1739	137	1	𝑀	𝑀	PROPN
cana-1739	137	2	where	where	SCONJ
cana-1739	137	3	m	m	NOUN
cana-1739	137	4	is	be	AUX
cana-1739	137	5	the	the	DET
cana-1739	137	6	lipschitz	lipschitz	NOUN
cana-1739	137	7	constant	constant	ADJ
cana-1739	137	8	when	when	SCONJ
cana-1739	137	9	𝑛	𝑛	PROPN
cana-1739	137	10	→	→	SYM
cana-1739	137	11	∞	∞	PROPN
cana-1739	137	12	,	,	PUNCT
cana-1739	137	13	‖𝑅1𝑛(𝑡)‖	‖𝑅1𝑛(𝑡)‖	PROPN
cana-1739	137	14	→	→	SYM
cana-1739	137	15	0	0	NUM
cana-1739	137	16	similarly	similarly	ADV
cana-1739	137	17	we	we	PRON
cana-1739	137	18	prove	prove	VERB
cana-1739	137	19	for	for	ADP
cana-1739	137	20	‖𝑅2𝑛(𝑡)‖	‖𝑅2𝑛(𝑡)‖	PROPN
cana-1739	137	21	→	→	SYM
cana-1739	137	22	0	0	NUM
cana-1739	137	23	,	,	PUNCT
cana-1739	137	24	‖𝑅3𝑛(𝑡)‖	‖𝑅3𝑛(𝑡)‖	PROPN
cana-1739	137	25	→	→	SYM
cana-1739	137	26	0	0	NUM
cana-1739	137	27	𝑎𝑛𝑑‖𝑅4𝑛(𝑡)‖	𝑎𝑛𝑑‖𝑅4𝑛(𝑡)‖	PROPN
cana-1739	137	28	→	→	SYM
cana-1739	137	29	0	0	PUNCT
cana-1739	137	30	as	as	ADP
cana-1739	137	31	𝑛	𝑛	PROPN
cana-1739	137	32	→	→	SYM
cana-1739	137	33	∞	∞	PROPN
cana-1739	137	34	hence	hence	ADV
cana-1739	137	35	the	the	DET
cana-1739	137	36	proof	proof	NOUN
cana-1739	137	37	.	.	PUNCT
cana-1739	138	1	theorem	theorem	VERB
cana-1739	138	2	4.1.3	4.1.3	NUM
cana-1739	138	3	if	if	SCONJ
cana-1739	138	4	the	the	DET
cana-1739	138	5	condition	condition	NOUN
cana-1739	138	6	[	[	X
cana-1739	138	7	1	1	NUM
cana-1739	138	8	−	−	PRON
cana-1739	138	9	𝑟𝑖𝑡	𝑟𝑖𝑡	NOUN
cana-1739	138	10	⎾	⎾	NUM
cana-1739	138	11	𝜈(𝑡	𝜈(𝑡	X
cana-1739	138	12	)	)	PUNCT
cana-1739	138	13	]	]	PUNCT
cana-1739	138	14	≥	≥	NOUN
cana-1739	138	15	0	0	NUM
cana-1739	138	16	,	,	PUNCT
cana-1739	138	17	for	for	ADP
cana-1739	138	18	𝑖	𝑖	PRON
cana-1739	138	19	=	=	SYM
cana-1739	138	20	1,2,3,4	1,2,3,4	NUM
cana-1739	138	21	holds	hold	VERB
cana-1739	138	22	then	then	ADV
cana-1739	138	23	caputo	caputo	PROPN
cana-1739	138	24	model	model	PROPN
cana-1739	138	25	have	have	VERB
cana-1739	138	26	unique	unique	ADJ
cana-1739	138	27	solution	solution	NOUN
cana-1739	138	28	.	.	PUNCT
cana-1739	139	1	proof	proof	NOUN
cana-1739	139	2	to	to	PART
cana-1739	139	3	establish	establish	VERB
cana-1739	139	4	the	the	DET
cana-1739	139	5	uniqueness	uniqueness	NOUN
cana-1739	139	6	for	for	ADP
cana-1739	139	7	a	a	DET
cana-1739	139	8	solution	solution	NOUN
cana-1739	139	9	of	of	ADP
cana-1739	139	10	the	the	DET
cana-1739	139	11	system	system	NOUN
cana-1739	139	12	(	(	PUNCT
cana-1739	139	13	3	3	NUM
cana-1739	139	14	)	)	PUNCT
cana-1739	139	15	,	,	PUNCT
cana-1739	139	16	consider	consider	VERB
cana-1739	139	17	the	the	DET
cana-1739	139	18	different	different	ADJ
cana-1739	139	19	set	set	NOUN
cana-1739	139	20	of	of	ADP
cana-1739	139	21	solutions	solution	NOUN
cana-1739	139	22	for	for	ADP
cana-1739	139	23	the	the	DET
cana-1739	139	24	system	system	NOUN
cana-1739	139	25	(	(	PUNCT
cana-1739	139	26	3	3	NUM
cana-1739	139	27	)	)	PUNCT
cana-1739	139	28	,	,	PUNCT
cana-1739	139	29	say	say	VERB
cana-1739	139	30	𝐺	𝐺	PROPN
cana-1739	139	31	̅	̅	NOUN
cana-1739	139	32	,	,	PUNCT
cana-1739	139	33	𝐶	𝐶	PROPN
cana-1739	139	34	̅	̅	NOUN
cana-1739	139	35	𝐼	𝐼	ADP
cana-1739	139	36	̅	̅	NOUN
cana-1739	139	37	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-1739	139	38	𝐻	𝐻	PROPN
cana-1739	139	39	̅̅	̅̅	NOUN
cana-1739	139	40	̅	̅	NOUN
cana-1739	139	41	.	.	PUNCT
cana-1739	140	1	then	then	ADV
cana-1739	140	2	as	as	ADP
cana-1739	140	3	an	an	DET
cana-1739	140	4	outcome	outcome	NOUN
cana-1739	140	5	of	of	ADP
cana-1739	140	6	the	the	DET
cana-1739	140	7	first	first	ADJ
cana-1739	140	8	equation	equation	NOUN
cana-1739	140	9	of	of	ADP
cana-1739	140	10	(	(	PUNCT
cana-1739	140	11	3	3	NUM
cana-1739	140	12	)	)	PUNCT
cana-1739	140	13	,	,	PUNCT
cana-1739	140	14	we	we	PRON
cana-1739	140	15	write	write	VERB
cana-1739	140	16	𝐺(𝑡	𝐺(𝑡	VERB
cana-1739	140	17	)	)	PUNCT
cana-1739	140	18	−	−	ADP
cana-1739	140	19	�	�	PROPN
cana-1739	140	20	̅	̅	NOUN
cana-1739	140	21	�	�	NOUN
cana-1739	140	22	(𝑡	(𝑡	NOUN
cana-1739	140	23	)	)	PUNCT
cana-1739	140	24	=	=	SYM
cana-1739	140	25	1	1	NUM
cana-1739	140	26	⎾	⎾	NUM
cana-1739	140	27	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	140	28	)	)	PUNCT
cana-1739	140	29	∫[𝐹1(𝐾	∫[𝐹1(𝐾	ADP
cana-1739	140	30	,	,	PUNCT
cana-1739	140	31	𝐺	𝐺	NOUN
cana-1739	140	32	)	)	PUNCT
cana-1739	140	33	−	−	ADP
cana-1739	140	34	𝐹1(𝐾	𝐹1(𝐾	PROPN
cana-1739	140	35	,	,	PUNCT
cana-1739	140	36	�	�	NOUN
cana-1739	140	37	̅	̅	NOUN
cana-1739	140	38	�	�	NOUN
cana-1739	140	39	)	)	PUNCT
cana-1739	140	40	]	]	PUNCT
cana-1739	141	1	𝑡	𝑡	X
cana-1739	141	2	0	0	NUM
cana-1739	141	3	𝑑𝑘	𝑑𝑘	ADP
cana-1739	141	4	using	use	VERB
cana-1739	141	5	the	the	DET
cana-1739	141	6	norm	norm	NOUN
cana-1739	141	7	of	of	ADP
cana-1739	141	8	above	above	ADP
cana-1739	141	9	equation	equation	NOUN
cana-1739	141	10	‖𝐺(𝑡	‖𝐺(𝑡	NOUN
cana-1739	141	11	)	)	PUNCT
cana-1739	141	12	−	−	ADP
cana-1739	141	13	�	�	NOUN
cana-1739	141	14	̅	̅	NOUN
cana-1739	141	15	�	�	NOUN
cana-1739	141	16	(𝑡)‖	(𝑡)‖	NOUN
cana-1739	141	17	=	=	SYM
cana-1739	141	18	‖	‖	PROPN
cana-1739	141	19	1	1	NUM
cana-1739	141	20	⎾	⎾	NUM
cana-1739	141	21	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	141	22	)	)	PUNCT
cana-1739	141	23	∫[𝐹1(𝐾	∫[𝐹1(𝐾	ADP
cana-1739	141	24	,	,	PUNCT
cana-1739	141	25	𝐺	𝐺	NOUN
cana-1739	141	26	)	)	PUNCT
cana-1739	141	27	−	−	ADP
cana-1739	141	28	𝐹1(𝐾	𝐹1(𝐾	PROPN
cana-1739	141	29	,	,	PUNCT
cana-1739	141	30	�	�	NOUN
cana-1739	141	31	̅	̅	NOUN
cana-1739	141	32	�	�	NOUN
cana-1739	141	33	)	)	PUNCT
cana-1739	141	34	]	]	PUNCT
cana-1739	142	1	𝑡	𝑡	X
cana-1739	142	2	0	0	NUM
cana-1739	142	3	𝑑𝑘‖	𝑑𝑘‖	ADP
cana-1739	142	4	now	now	ADV
cana-1739	142	5	by	by	ADP
cana-1739	142	6	applying	apply	VERB
cana-1739	142	7	lipschitz	lipschitz	NOUN
cana-1739	142	8	condition	condition	NOUN
cana-1739	142	9	,	,	PUNCT
cana-1739	142	10	‖𝐺(𝑡	‖𝐺(𝑡	NOUN
cana-1739	142	11	)	)	PUNCT
cana-1739	142	12	−	−	PROPN
cana-1739	142	13	�	�	NOUN
cana-1739	142	14	̅	̅	NOUN
cana-1739	142	15	�	�	NOUN
cana-1739	142	16	(𝑡)‖	(𝑡)‖	NOUN
cana-1739	142	17	=	=	SYM
cana-1739	142	18	1	1	NUM
cana-1739	142	19	⎾	⎾	NUM
cana-1739	142	20	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	142	21	)	)	PUNCT
cana-1739	142	22	𝑟1𝑡‖𝐺(𝑡	𝑟1𝑡‖𝐺(𝑡	NUM
cana-1739	142	23	)	)	PUNCT
cana-1739	142	24	−	−	PROPN
cana-1739	142	25	�	�	NOUN
cana-1739	142	26	̅	̅	VERB
cana-1739	142	27	�	�	NOUN
cana-1739	142	28	(𝑡)‖	(𝑡)‖	PRON
cana-1739	142	29	consequently	consequently	ADV
cana-1739	142	30	,	,	PUNCT
cana-1739	142	31	‖𝐺(𝑡	‖𝐺(𝑡	PROPN
cana-1739	142	32	)	)	PUNCT
cana-1739	142	33	−	−	PROPN
cana-1739	142	34	�	�	PROPN
cana-1739	142	35	̅	̅	NOUN
cana-1739	142	36	�	�	NOUN
cana-1739	142	37	(𝑡)‖	(𝑡)‖	NOUN
cana-1739	142	38	−	−	PROPN
cana-1739	142	39	1	1	NUM
cana-1739	142	40	⎾	⎾	NUM
cana-1739	142	41	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	142	42	)	)	PUNCT
cana-1739	142	43	𝑟1𝑡‖𝐺(𝑡	𝑟1𝑡‖𝐺(𝑡	NUM
cana-1739	142	44	)	)	PUNCT
cana-1739	142	45	−	−	PROPN
cana-1739	142	46	�	�	NOUN
cana-1739	142	47	̅	̅	VERB
cana-1739	142	48	�	�	NOUN
cana-1739	142	49	(𝑡)‖	(𝑡)‖	NOUN
cana-1739	142	50	≤	≤	ADJ
cana-1739	142	51	0	0	NUM
cana-1739	142	52	communications	communication	NOUN
cana-1739	142	53	on	on	ADP
cana-1739	142	54	applied	apply	VERB
cana-1739	142	55	nonlinear	nonlinear	ADJ
cana-1739	142	56	analysis	analysis	NOUN
cana-1739	142	57	issn	issn	NOUN
cana-1739	142	58	:	:	PUNCT
cana-1739	142	59	1074	1074	NUM
cana-1739	142	60	-	-	PUNCT
cana-1739	142	61	133x	133x	NUM
cana-1739	142	62	vol	vol	NOUN
cana-1739	142	63	32	32	NUM
cana-1739	142	64	no	no	NOUN
cana-1739	142	65	.	.	NOUN
cana-1739	142	66	2	2	NUM
cana-1739	142	67	(	(	PUNCT
cana-1739	142	68	2025	2025	NUM
cana-1739	142	69	)	)	PUNCT
cana-1739	142	70	239	239	NUM
cana-1739	142	71	https://internationalpubls.com	https://internationalpubls.com	X
cana-1739	142	72	‖𝐺(𝑡	‖𝐺(𝑡	NOUN
cana-1739	142	73	)	)	PUNCT
cana-1739	142	74	−	−	ADP
cana-1739	142	75	�	�	PROPN
cana-1739	142	76	̅	̅	NOUN
cana-1739	142	77	�	�	NOUN
cana-1739	142	78	(𝑡)‖[1	(𝑡)‖[1	PUNCT
cana-1739	142	79	−	−	PROPN
cana-1739	142	80	1	1	NUM
cana-1739	142	81	⎾	⎾	NUM
cana-1739	142	82	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	142	83	)	)	PUNCT
cana-1739	142	84	𝑟1𝑡	𝑟1𝑡	PROPN
cana-1739	142	85	]	]	PUNCT
cana-1739	142	86	≤	≤	NUM
cana-1739	142	87	0	0	NUM
cana-1739	142	88	(	(	PUNCT
cana-1739	142	89	7	7	NUM
cana-1739	142	90	)	)	PUNCT
cana-1739	142	91	since	since	SCONJ
cana-1739	142	92	[	[	X
cana-1739	142	93	1	1	NUM
cana-1739	142	94	−	−	NUM
cana-1739	142	95	1	1	NUM
cana-1739	142	96	⎾	⎾	NUM
cana-1739	142	97	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	142	98	)	)	PUNCT
cana-1739	143	1	𝑟𝑖𝑡	𝑟𝑖𝑡	PROPN
cana-1739	143	2	]	]	PUNCT
cana-1739	143	3	>	>	X
cana-1739	143	4	0	0	PUNCT
cana-1739	143	5	,	,	PUNCT
cana-1739	143	6	equation	equation	NOUN
cana-1739	143	7	(	(	PUNCT
cana-1739	143	8	7	7	X
cana-1739	143	9	)	)	PUNCT
cana-1739	143	10	becomes	become	VERB
cana-1739	143	11	the	the	DET
cana-1739	143	12	form	form	NOUN
cana-1739	143	13	‖𝐺(𝑡	‖𝐺(𝑡	NOUN
cana-1739	143	14	)	)	PUNCT
cana-1739	143	15	−	−	ADP
cana-1739	143	16	�	�	NOUN
cana-1739	143	17	̅	̅	NOUN
cana-1739	143	18	�	�	NOUN
cana-1739	143	19	(𝑡)‖	(𝑡)‖	SYM
cana-1739	143	20	=	=	SYM
cana-1739	143	21	0	0	NUM
cana-1739	143	22	therefore	therefore	ADV
cana-1739	143	23	,	,	PUNCT
cana-1739	143	24	𝐺(𝑡	𝐺(𝑡	NOUN
cana-1739	143	25	)	)	PUNCT
cana-1739	143	26	=	=	SYM
cana-1739	143	27	�	�	PROPN
cana-1739	143	28	̅	̅	NOUN
cana-1739	143	29	�	�	NOUN
cana-1739	143	30	(𝑡	(𝑡	NOUN
cana-1739	143	31	)	)	PUNCT
cana-1739	143	32	similarly	similarly	ADV
cana-1739	143	33	,	,	PUNCT
cana-1739	143	34	we	we	PRON
cana-1739	143	35	prove	prove	VERB
cana-1739	143	36	𝐶(𝑡	𝐶(𝑡	ADP
cana-1739	143	37	)	)	PUNCT
cana-1739	143	38	=	=	PUNCT
cana-1739	143	39	𝐶̅(𝑡	𝐶̅(𝑡	ADV
cana-1739	143	40	)	)	PUNCT
cana-1739	143	41	,	,	PUNCT
cana-1739	143	42	𝐼(𝑡	𝐼(𝑡	NUM
cana-1739	143	43	)	)	PUNCT
cana-1739	143	44	=	=	SYM
cana-1739	143	45	𝐼(̅𝑡	𝐼(̅𝑡	PROPN
cana-1739	143	46	)	)	PUNCT
cana-1739	143	47	and	and	CCONJ
cana-1739	143	48	𝐻(𝑡	𝐻(𝑡	NOUN
cana-1739	143	49	)	)	PUNCT
cana-1739	143	50	=	=	SYM
cana-1739	143	51	�	�	PROPN
cana-1739	143	52	̅	̅	NOUN
cana-1739	143	53	�	�	NOUN
cana-1739	143	54	(𝑡	(𝑡	NOUN
cana-1739	143	55	)	)	PUNCT
cana-1739	143	56	4.2	4.2	NUM
cana-1739	143	57	existence	existence	NOUN
cana-1739	143	58	and	and	CCONJ
cana-1739	143	59	uniqueness	uniqueness	NOUN
cana-1739	143	60	of	of	ADP
cana-1739	143	61	fractional	fractional	ADJ
cana-1739	143	62	solutions	solution	NOUN
cana-1739	143	63	by	by	ADP
cana-1739	143	64	the	the	DET
cana-1739	143	65	caputo	caputo	PROPN
cana-1739	143	66	-	-	PUNCT
cana-1739	143	67	fabrizio	fabrizio	PROPN
cana-1739	143	68	model	model	NOUN
cana-1739	143	69	let	let	VERB
cana-1739	143	70	us	we	PRON
cana-1739	143	71	construct	construct	VERB
cana-1739	143	72	the	the	DET
cana-1739	143	73	system	system	NOUN
cana-1739	143	74	(	(	PUNCT
cana-1739	143	75	2	2	NUM
cana-1739	143	76	)	)	PUNCT
cana-1739	143	77	in	in	ADP
cana-1739	143	78	the	the	DET
cana-1739	143	79	sense	sense	NOUN
cana-1739	143	80	of	of	ADP
cana-1739	143	81	caputo	caputo	PROPN
cana-1739	143	82	-	-	PUNCT
cana-1739	143	83	fabrizio	fabrizio	PROPN
cana-1739	143	84	,	,	PUNCT
cana-1739	143	85	we	we	PRON
cana-1739	143	86	have	have	VERB
cana-1739	143	87	𝐷𝑡	𝐷𝑡	PROPN
cana-1739	143	88	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	143	89	)	)	PUNCT
cana-1739	143	90	0	0	NUM
cana-1739	144	1	𝐶𝐹	𝐶𝐹	PROPN
cana-1739	145	1	[	[	X
cana-1739	145	2	𝐺(𝑡	𝐺(𝑡	NOUN
cana-1739	145	3	)	)	PUNCT
cana-1739	145	4	]	]	PUNCT
cana-1739	145	5	=	=	PUNCT
cana-1739	145	6	𝐹1(𝑡	𝐹1(𝑡	PROPN
cana-1739	145	7	,	,	PUNCT
cana-1739	145	8	𝐺	𝐺	NOUN
cana-1739	145	9	)	)	PUNCT
cana-1739	145	10	=	=	SYM
cana-1739	146	1	𝛬	𝛬	NOUN
cana-1739	146	2	+	+	NUM
cana-1739	146	3	𝑝1	𝑝1	NOUN
cana-1739	146	4	ν(t)𝐺(𝑡)𝐶(𝑡	ν(t)𝐺(𝑡)𝐶(𝑡	PROPN
cana-1739	146	5	)	)	PUNCT
cana-1739	146	6	−	−	PROPN
cana-1739	146	7	𝑝2	𝑝2	PROPN
cana-1739	146	8	ν(t)𝐺(𝑡	ν(t)𝐺(𝑡	PROPN
cana-1739	146	9	)	)	PUNCT
cana-1739	147	1	𝐷𝑡	𝐷𝑡	NOUN
cana-1739	147	2	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	147	3	)	)	PUNCT
cana-1739	147	4	0	0	NUM
cana-1739	147	5	𝐶𝐹	𝐶𝐹	PROPN
cana-1739	148	1	[	[	X
cana-1739	148	2	𝐶(𝑡	𝐶(𝑡	NUM
cana-1739	148	3	)	)	PUNCT
cana-1739	148	4	]	]	PUNCT
cana-1739	148	5	=	=	PUNCT
cana-1739	148	6	𝐹2(𝑡	𝐹2(𝑡	PROPN
cana-1739	148	7	,	,	PUNCT
cana-1739	148	8	𝐶	𝐶	PROPN
cana-1739	148	9	)	)	PUNCT
cana-1739	149	1	=	=	PUNCT
cana-1739	149	2	𝛺	𝛺	ADP
cana-1739	149	3	−	−	PROPN
cana-1739	149	4	𝑝1	𝑝1	NOUN
cana-1739	149	5	ν(t)𝐺(𝑡)𝐶(𝑡	ν(t)𝐺(𝑡)𝐶(𝑡	PROPN
cana-1739	149	6	)	)	PUNCT
cana-1739	149	7	+	+	CCONJ
cana-1739	149	8	𝑝3	𝑝3	ADV
cana-1739	149	9	ν(t)𝐻(𝑡)𝐶(𝑡	ν(t)𝐻(𝑡)𝐶(𝑡	ADJ
cana-1739	149	10	)	)	PUNCT
cana-1739	149	11	−	−	PROPN
cana-1739	149	12	𝑝4	𝑝4	NOUN
cana-1739	149	13	ν(t)𝐶(𝑡	ν(t)𝐶(𝑡	PROPN
cana-1739	149	14	)	)	PUNCT
cana-1739	149	15	(	(	PUNCT
cana-1739	149	16	8)	8)	NUM
cana-1739	149	17	𝐷𝑡	𝐷𝑡	PROPN
cana-1739	149	18	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	149	19	)	)	PUNCT
cana-1739	149	20	0	0	NUM
cana-1739	150	1	𝐶𝐹	𝐶𝐹	PROPN
cana-1739	151	1	[	[	X
cana-1739	151	2	𝐼(𝑡	𝐼(𝑡	NUM
cana-1739	151	3	)	)	PUNCT
cana-1739	151	4	]	]	PUNCT
cana-1739	152	1	=	=	SYM
cana-1739	152	2	𝐹3(𝑡	𝐹3(𝑡	PROPN
cana-1739	152	3	,	,	PUNCT
cana-1739	152	4	𝐼	𝐼	PROPN
cana-1739	152	5	)	)	PUNCT
cana-1739	152	6	=	=	SYM
cana-1739	152	7	𝑝5	𝑝5	PROPN
cana-1739	152	8	ν(t)𝐺(𝑡)𝐼(𝑡	ν(t)𝐺(𝑡)𝐼(𝑡	PROPN
cana-1739	152	9	)	)	PUNCT
cana-1739	152	10	−	−	PROPN
cana-1739	152	11	𝑝6	𝑝6	NOUN
cana-1739	152	12	ν(t)𝐻(𝑡)𝐼(𝑡	ν(t)𝐻(𝑡)𝐼(𝑡	PROPN
cana-1739	152	13	)	)	PUNCT
cana-1739	153	1	−	−	PROPN
cana-1739	153	2	𝑝7	𝑝7	PROPN
cana-1739	153	3	ν(t)𝐼(𝑡	ν(t)𝐼(𝑡	PROPN
cana-1739	153	4	)	)	PUNCT
cana-1739	154	1	𝐷𝑡	𝐷𝑡	PROPN
cana-1739	154	2	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	154	3	)	)	PUNCT
cana-1739	154	4	0	0	NUM
cana-1739	154	5	𝐶𝐹	𝐶𝐹	PROPN
cana-1739	154	6	[	[	X
cana-1739	154	7	𝐻(𝑡	𝐻(𝑡	NOUN
cana-1739	154	8	)	)	PUNCT
cana-1739	154	9	]	]	PUNCT
cana-1739	155	1	=	=	PUNCT
cana-1739	155	2	𝐹4(𝑡	𝐹4(𝑡	X
cana-1739	155	3	,	,	PUNCT
cana-1739	155	4	𝐻	𝐻	NOUN
cana-1739	155	5	)	)	PUNCT
cana-1739	155	6	=	=	SYM
cana-1739	155	7	𝛹	𝛹	PROPN
cana-1739	155	8	+	+	NUM
cana-1739	155	9	𝑝6	𝑝6	PROPN
cana-1739	155	10	ν(t)𝐻(𝑡)𝐼(𝑡	ν(t)𝐻(𝑡)𝐼(𝑡	PROPN
cana-1739	155	11	)	)	PUNCT
cana-1739	155	12	−	−	PROPN
cana-1739	155	13	𝑝8	𝑝8	PROPN
cana-1739	155	14	ν(t)𝐻(𝑡	ν(t)𝐻(𝑡	PRON
cana-1739	155	15	)	)	PUNCT
cana-1739	155	16	the	the	DET
cana-1739	155	17	caputo	caputo	PROPN
cana-1739	155	18	-	-	PUNCT
cana-1739	155	19	fabrizio	fabrizio	PROPN
cana-1739	155	20	integral	integral	ADJ
cana-1739	155	21	form	form	NOUN
cana-1739	155	22	of	of	ADP
cana-1739	155	23	the	the	DET
cana-1739	155	24	above	above	ADJ
cana-1739	155	25	system	system	NOUN
cana-1739	155	26	is	be	AUX
cana-1739	155	27	𝐺(𝑡	𝐺(𝑡	NOUN
cana-1739	155	28	)	)	PUNCT
cana-1739	155	29	−	−	NUM
cana-1739	155	30	𝐺(0	𝐺(0	NUM
cana-1739	155	31	)	)	PUNCT
cana-1739	155	32	=	=	SYM
cana-1739	156	1	1−𝜈(𝑡	1−𝜈(𝑡	NUM
cana-1739	156	2	)	)	PUNCT
cana-1739	156	3	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	156	4	)	)	PUNCT
cana-1739	156	5	)	)	PUNCT
cana-1739	157	1	𝐹1(𝑡	𝐹1(𝑡	PROPN
cana-1739	157	2	,	,	PUNCT
cana-1739	157	3	𝐺	𝐺	NOUN
cana-1739	157	4	)	)	PUNCT
cana-1739	157	5	+	+	CCONJ
cana-1739	157	6	𝜈(𝑡	𝜈(𝑡	ADJ
cana-1739	157	7	)	)	PUNCT
cana-1739	157	8	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	157	9	)	)	PUNCT
cana-1739	157	10	)	)	PUNCT
cana-1739	157	11	∫	∫	PROPN
cana-1739	157	12	𝐹1(𝜏	𝐹1(𝜏	PROPN
cana-1739	157	13	,	,	PUNCT
cana-1739	157	14	𝐺)𝑑𝜏	𝐺)𝑑𝜏	PROPN
cana-1739	157	15	𝑡	𝑡	PROPN
cana-1739	157	16	0	0	PUNCT
cana-1739	157	17	𝐶(𝑡	𝐶(𝑡	NOUN
cana-1739	157	18	)	)	PUNCT
cana-1739	157	19	−	−	NUM
cana-1739	157	20	𝐶(0	𝐶(0	NOUN
cana-1739	157	21	)	)	PUNCT
cana-1739	157	22	=	=	SYM
cana-1739	157	23	1−𝜈(𝑡	1−𝜈(𝑡	NUM
cana-1739	157	24	)	)	PUNCT
cana-1739	157	25	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	157	26	)	)	PUNCT
cana-1739	157	27	)	)	PUNCT
cana-1739	158	1	𝐹2(𝑡	𝐹2(𝑡	NOUN
cana-1739	158	2	,	,	PUNCT
cana-1739	158	3	𝑋	𝑋	PROPN
cana-1739	158	4	)	)	PUNCT
cana-1739	158	5	+	+	NUM
cana-1739	158	6	𝜈(𝑡	𝜈(𝑡	ADJ
cana-1739	158	7	)	)	PUNCT
cana-1739	158	8	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	158	9	)	)	PUNCT
cana-1739	158	10	)	)	PUNCT
cana-1739	158	11	∫	∫	PROPN
cana-1739	159	1	𝐹2(𝜏	𝐹2(𝜏	PROPN
cana-1739	159	2	,	,	PUNCT
cana-1739	159	3	𝐶)𝑑𝜏	𝐶)𝑑𝜏	PROPN
cana-1739	159	4	𝑡	𝑡	PROPN
cana-1739	159	5	0	0	NUM
cana-1739	159	6	𝐼(𝑡	𝐼(𝑡	NUM
cana-1739	159	7	)	)	PUNCT
cana-1739	159	8	−	−	NOUN
cana-1739	159	9	𝐼(0	𝐼(0	NOUN
cana-1739	159	10	)	)	PUNCT
cana-1739	159	11	=	=	SYM
cana-1739	159	12	1−𝜈(𝑡	1−𝜈(𝑡	NUM
cana-1739	159	13	)	)	PUNCT
cana-1739	159	14	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	159	15	)	)	PUNCT
cana-1739	159	16	)	)	PUNCT
cana-1739	160	1	𝐹3(𝑡	𝐹3(𝑡	PROPN
cana-1739	160	2	,	,	PUNCT
cana-1739	160	3	𝐼	𝐼	PROPN
cana-1739	160	4	)	)	PUNCT
cana-1739	160	5	+	+	CCONJ
cana-1739	160	6	𝜈(𝑡	𝜈(𝑡	ADJ
cana-1739	160	7	)	)	PUNCT
cana-1739	160	8	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	160	9	)	)	PUNCT
cana-1739	160	10	)	)	PUNCT
cana-1739	160	11	∫	∫	PROPN
cana-1739	161	1	𝐹3(𝜏	𝐹3(𝜏	PROPN
cana-1739	161	2	,	,	PUNCT
cana-1739	161	3	𝐼)𝑑𝜏	𝐼)𝑑𝜏	PROPN
cana-1739	161	4	𝑡	𝑡	PROPN
cana-1739	161	5	0	0	NUM
cana-1739	161	6	(	(	PUNCT
cana-1739	161	7	9	9	NUM
cana-1739	161	8	)	)	PUNCT
cana-1739	161	9	𝐻(𝑡	𝐻(𝑡	NOUN
cana-1739	161	10	)	)	PUNCT
cana-1739	161	11	−	−	NUM
cana-1739	161	12	𝐻(0	𝐻(0	CCONJ
cana-1739	161	13	)	)	PUNCT
cana-1739	161	14	=	=	SYM
cana-1739	161	15	1−𝜈(𝑡	1−𝜈(𝑡	NUM
cana-1739	161	16	)	)	PUNCT
cana-1739	161	17	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	161	18	)	)	PUNCT
cana-1739	161	19	)	)	PUNCT
cana-1739	162	1	𝐹3(𝑡	𝐹3(𝑡	PROPN
cana-1739	162	2	,	,	PUNCT
cana-1739	162	3	𝐻	𝐻	PROPN
cana-1739	162	4	)	)	PUNCT
cana-1739	162	5	+	+	CCONJ
cana-1739	162	6	𝜈(𝑡	𝜈(𝑡	ADJ
cana-1739	162	7	)	)	PUNCT
cana-1739	162	8	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	162	9	)	)	PUNCT
cana-1739	162	10	)	)	PUNCT
cana-1739	162	11	∫	∫	PROPN
cana-1739	163	1	𝐹4(𝜏	𝐹4(𝜏	PROPN
cana-1739	163	2	,	,	PUNCT
cana-1739	163	3	𝐻)𝑑𝜏	𝐻)𝑑𝜏	PROPN
cana-1739	163	4	𝑡	𝑡	PROPN
cana-1739	163	5	0	0	NUM
cana-1739	163	6	here	here	ADV
cana-1739	163	7	we	we	PRON
cana-1739	163	8	have	have	VERB
cana-1739	163	9	to	to	PART
cana-1739	163	10	prove	prove	VERB
cana-1739	163	11	the	the	DET
cana-1739	163	12	kernel	kernel	NOUN
cana-1739	164	1	𝐹𝑖	𝐹𝑖	PROPN
cana-1739	164	2	for	for	ADP
cana-1739	164	3	𝑖	𝑖	NOUN
cana-1739	164	4	=	=	SYM
cana-1739	164	5	1,2,3,4	1,2,3,4	NUM
cana-1739	164	6	follows	follow	VERB
cana-1739	164	7	the	the	DET
cana-1739	164	8	lipschitz	lipschitz	NOUN
cana-1739	164	9	condition	condition	NOUN
cana-1739	164	10	and	and	CCONJ
cana-1739	164	11	a	a	DET
cana-1739	164	12	contraction	contraction	NOUN
cana-1739	164	13	.	.	PUNCT
cana-1739	165	1	theorem	theorem	VERB
cana-1739	165	2	4.2.1	4.2.1	NUM
cana-1739	165	3	the	the	DET
cana-1739	165	4	kernel	kernel	PROPN
cana-1739	165	5	𝐹𝑖(𝜏	𝐹𝑖(𝜏	PROPN
cana-1739	165	6	,	,	PUNCT
cana-1739	165	7	𝐺	𝐺	PROPN
cana-1739	165	8	)	)	PUNCT
cana-1739	165	9	,	,	PUNCT
cana-1739	165	10	for	for	SCONJ
cana-1739	165	11	𝑖	𝑖	PRON
cana-1739	165	12	=	=	SYM
cana-1739	165	13	1,2,3,4	1,2,3,4	NUM
cana-1739	165	14	satisfies	satisfie	NOUN
cana-1739	165	15	the	the	DET
cana-1739	165	16	lipschitz	lipschitz	NOUN
cana-1739	165	17	condition	condition	NOUN
cana-1739	165	18	and	and	CCONJ
cana-1739	165	19	a	a	DET
cana-1739	165	20	contraction	contraction	NOUN
cana-1739	165	21	if	if	SCONJ
cana-1739	165	22	the	the	DET
cana-1739	165	23	following	follow	VERB
cana-1739	165	24	inequality	inequality	NOUN
cana-1739	165	25	0	0	NUM
cana-1739	165	26	≤	≤	NUM
cana-1739	165	27	𝜌𝑖	𝜌𝑖	ADP
cana-1739	165	28	<	<	X
cana-1739	165	29	1	1	NUM
cana-1739	165	30	holds	hold	NOUN
cana-1739	165	31	.	.	PUNCT
cana-1739	166	1	proof	proof	NOUN
cana-1739	166	2	this	this	DET
cana-1739	166	3	theorem	theorem	NOUN
cana-1739	166	4	is	be	AUX
cana-1739	166	5	proved	prove	VERB
cana-1739	166	6	as	as	ADV
cana-1739	166	7	similar	similar	ADJ
cana-1739	166	8	as	as	ADP
cana-1739	166	9	theorem	theorem	VERB
cana-1739	166	10	4.1.1	4.1.1	NUM
cana-1739	166	11	the	the	DET
cana-1739	166	12	recurrent	recurrent	ADJ
cana-1739	166	13	form	form	NOUN
cana-1739	166	14	of	of	ADP
cana-1739	166	15	(	(	PUNCT
cana-1739	166	16	9	9	NUM
cana-1739	166	17	)	)	PUNCT
cana-1739	166	18	for	for	ADP
cana-1739	166	19	the	the	DET
cana-1739	166	20	first	first	ADJ
cana-1739	166	21	equation	equation	NOUN
cana-1739	166	22	is	be	AUX
cana-1739	166	23	𝜓1𝑛	𝜓1𝑛	PROPN
cana-1739	166	24	=	=	SYM
cana-1739	166	25	𝐺𝑛(𝑡	𝐺𝑛(𝑡	NOUN
cana-1739	166	26	)	)	PUNCT
cana-1739	166	27	−	−	ADP
cana-1739	166	28	𝐺𝑛−1(𝑡	𝐺𝑛−1(𝑡	NOUN
cana-1739	166	29	)	)	PUNCT
cana-1739	166	30	communications	communication	NOUN
cana-1739	166	31	on	on	ADP
cana-1739	166	32	applied	apply	VERB
cana-1739	166	33	nonlinear	nonlinear	ADJ
cana-1739	166	34	analysis	analysis	NOUN
cana-1739	166	35	issn	issn	NOUN
cana-1739	166	36	:	:	PUNCT
cana-1739	166	37	1074	1074	NUM
cana-1739	166	38	-	-	PUNCT
cana-1739	166	39	133x	133x	NUM
cana-1739	166	40	vol	vol	NOUN
cana-1739	166	41	32	32	NUM
cana-1739	166	42	no	no	NOUN
cana-1739	166	43	.	.	NOUN
cana-1739	166	44	2	2	NUM
cana-1739	166	45	(	(	PUNCT
cana-1739	166	46	2025	2025	NUM
cana-1739	166	47	)	)	PUNCT
cana-1739	166	48	240	240	NUM
cana-1739	166	49	https://internationalpubls.com	https://internationalpubls.com	X
cana-1739	166	50	=	=	SYM
cana-1739	167	1	1	1	NUM
cana-1739	167	2	−	−	NOUN
cana-1739	167	3	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	167	4	)	)	PUNCT
cana-1739	167	5	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	167	6	)	)	PUNCT
cana-1739	167	7	)	)	PUNCT
cana-1739	168	1	[	[	X
cana-1739	168	2	𝐹1(𝑡	𝐹1(𝑡	X
cana-1739	168	3	,	,	PUNCT
cana-1739	168	4	𝐺𝑛−1	𝐺𝑛−1	NUM
cana-1739	168	5	)	)	PUNCT
cana-1739	169	1	−	−	PROPN
cana-1739	169	2	𝐹1(𝑡	𝐹1(𝑡	PROPN
cana-1739	169	3	,	,	PUNCT
cana-1739	169	4	𝐺𝑛−2	𝐺𝑛−2	PROPN
cana-1739	169	5	)	)	PUNCT
cana-1739	169	6	]	]	PUNCT
cana-1739	170	1	+	+	CCONJ
cana-1739	170	2	𝜈(𝑡	𝜈(𝑡	X
cana-1739	170	3	)	)	PUNCT
cana-1739	170	4	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	170	5	)	)	PUNCT
cana-1739	170	6	)	)	PUNCT
cana-1739	170	7	∫[𝐹1(𝜏	∫[𝐹1(𝜏	PROPN
cana-1739	170	8	,	,	PUNCT
cana-1739	170	9	𝐺𝑛−1	𝐺𝑛−1	NUM
cana-1739	170	10	)	)	PUNCT
cana-1739	170	11	−	−	ADP
cana-1739	170	12	𝐹1(𝜏	𝐹1(𝜏	NOUN
cana-1739	170	13	,	,	PUNCT
cana-1739	170	14	𝐺𝑛−2)]𝑑𝜏	𝐺𝑛−2)]𝑑𝜏	NUM
cana-1739	170	15	𝑡	𝑡	X
cana-1739	170	16	0	0	NUM
cana-1739	170	17	similarly	similarly	ADV
cana-1739	170	18	𝜓2𝑛	𝜓2𝑛	ADJ
cana-1739	170	19	and	and	CCONJ
cana-1739	170	20	𝜓3𝑛	𝜓3𝑛	NUM
cana-1739	170	21	are	be	AUX
cana-1739	170	22	also	also	ADV
cana-1739	170	23	be	be	AUX
cana-1739	170	24	derived	derive	VERB
cana-1739	170	25	using	use	VERB
cana-1739	170	26	the	the	DET
cana-1739	170	27	initial	initial	ADJ
cana-1739	170	28	condition	condition	NOUN
cana-1739	170	29	and	and	CCONJ
cana-1739	170	30	taking	take	VERB
cana-1739	170	31	norm	norm	NOUN
cana-1739	170	32	,	,	PUNCT
cana-1739	170	33	we	we	PRON
cana-1739	170	34	get	get	VERB
cana-1739	170	35	‖𝜓1𝑛‖	‖𝜓1𝑛‖	NOUN
cana-1739	170	36	≤	≤	ADJ
cana-1739	170	37	1−𝜈(𝑡	1−𝜈(𝑡	NUM
cana-1739	170	38	)	)	PUNCT
cana-1739	170	39	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	170	40	)	)	PUNCT
cana-1739	170	41	)	)	PUNCT
cana-1739	170	42	‖[𝐹1(𝑡	‖[𝐹1(𝑡	PROPN
cana-1739	170	43	,	,	PUNCT
cana-1739	170	44	𝐺𝑛−1	𝐺𝑛−1	NUM
cana-1739	170	45	)	)	PUNCT
cana-1739	171	1	−	−	PROPN
cana-1739	172	1	𝐹1(𝑡	𝐹1(𝑡	PROPN
cana-1739	172	2	,	,	PUNCT
cana-1739	172	3	𝐺𝑛−2)]‖	𝐺𝑛−2)]‖	PROPN
cana-1739	172	4	+	+	CCONJ
cana-1739	172	5	𝜈(𝑡	𝜈(𝑡	ADJ
cana-1739	172	6	)	)	PUNCT
cana-1739	172	7	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	172	8	)	)	PUNCT
cana-1739	172	9	)	)	PUNCT
cana-1739	172	10	∫	∫	PROPN
cana-1739	172	11	‖[𝐹1(𝜏	‖[𝐹1(𝜏	PROPN
cana-1739	172	12	,	,	PUNCT
cana-1739	172	13	𝐺𝑛−1	𝐺𝑛−1	NUM
cana-1739	172	14	)	)	PUNCT
cana-1739	172	15	−	−	ADP
cana-1739	172	16	𝐹1(𝜏	𝐹1(𝜏	NOUN
cana-1739	172	17	,	,	PUNCT
cana-1739	172	18	𝐺𝑛−2)]‖	𝐺𝑛−2)]‖	PROPN
cana-1739	172	19	𝑡	𝑡	PROPN
cana-1739	172	20	0	0	NUM
cana-1739	172	21	𝑑𝜏	𝑑𝜏	NOUN
cana-1739	172	22	since	since	SCONJ
cana-1739	172	23	𝜌1satisfies	𝜌1satisfie	NOUN
cana-1739	172	24	lipschitz	lipschitz	VERB
cana-1739	172	25	condition	condition	NOUN
cana-1739	172	26	‖𝜓1𝑛(𝑡)‖	‖𝜓1𝑛(𝑡)‖	PUNCT
cana-1739	172	27	≤	≤	NOUN
cana-1739	172	28	1−𝜈(𝑡	1−𝜈(𝑡	NUM
cana-1739	172	29	)	)	PUNCT
cana-1739	172	30	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	172	31	)	)	PUNCT
cana-1739	172	32	)	)	PUNCT
cana-1739	173	1	𝜌1‖[𝜓1(𝑛−1)(𝑡)]‖	𝜌1‖[𝜓1(𝑛−1)(𝑡)]‖	PROPN
cana-1739	173	2	+	+	CCONJ
cana-1739	173	3	𝜈(𝑡	𝜈(𝑡	ADJ
cana-1739	173	4	)	)	PUNCT
cana-1739	173	5	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	173	6	)	)	PUNCT
cana-1739	173	7	)	)	PUNCT
cana-1739	174	1	𝜌1	𝜌1	NOUN
cana-1739	174	2	∫	∫	PROPN
cana-1739	174	3	‖𝜓1(𝑛−1)(𝜏)‖	‖𝜓1(𝑛−1)(𝜏)‖	PROPN
cana-1739	174	4	𝑡	𝑡	PROPN
cana-1739	174	5	0	0	NUM
cana-1739	174	6	𝑑𝜏	𝑑𝜏	NOUN
cana-1739	174	7	(	(	PUNCT
cana-1739	174	8	10	10	NUM
cana-1739	174	9	)	)	PUNCT
cana-1739	174	10	similarly	similarly	ADV
cana-1739	174	11	‖𝜓2𝑛(𝑡)‖	‖𝜓2𝑛(𝑡)‖	PUNCT
cana-1739	174	12	,	,	PUNCT
cana-1739	174	13	‖𝜓3𝑛(𝑡)‖	‖𝜓3𝑛(𝑡)‖	PUNCT
cana-1739	174	14	and	and	CCONJ
cana-1739	174	15	‖𝜓4𝑛(𝑡)‖can	‖𝜓4𝑛(𝑡)‖can	PROPN
cana-1739	174	16	also	also	ADV
cana-1739	174	17	be	be	AUX
cana-1739	174	18	obtained	obtain	VERB
cana-1739	174	19	.	.	PUNCT
cana-1739	175	1	therefore	therefore	ADV
cana-1739	175	2	,	,	PUNCT
cana-1739	175	3	𝐺𝑛(𝑡	𝐺𝑛(𝑡	PROPN
cana-1739	175	4	)	)	PUNCT
cana-1739	175	5	=	=	SYM
cana-1739	175	6	∑	∑	PUNCT
cana-1739	175	7	𝜓1𝑖(𝑡	𝜓1𝑖(𝑡	PROPN
cana-1739	175	8	)	)	PUNCT
cana-1739	175	9	,	,	PUNCT
cana-1739	175	10	𝑛	𝑛	PRON
cana-1739	175	11	𝑖=1	𝑖=1	PROPN
cana-1739	175	12	𝐶𝑛(𝑡	𝐶𝑛(𝑡	NOUN
cana-1739	175	13	)	)	PUNCT
cana-1739	175	14	=	=	PUNCT
cana-1739	175	15	∑	∑	PUNCT
cana-1739	175	16	𝜓2𝑖(𝑡	𝜓2𝑖(𝑡	NOUN
cana-1739	175	17	)	)	PUNCT
cana-1739	175	18	,	,	PUNCT
cana-1739	175	19	𝑛	𝑛	DET
cana-1739	175	20	𝑖=1	𝑖=1	PROPN
cana-1739	175	21	𝐼𝑛(𝑡	𝐼𝑛(𝑡	PROPN
cana-1739	175	22	)	)	PUNCT
cana-1739	175	23	=	=	SYM
cana-1739	175	24	∑	∑	PUNCT
cana-1739	175	25	𝜓3𝑖(𝑡	𝜓3𝑖(𝑡	PROPN
cana-1739	175	26	)	)	PUNCT
cana-1739	175	27	𝑛	𝑛	PRON
cana-1739	175	28	𝑖=1	𝑖=1	PROPN
cana-1739	175	29	,	,	PUNCT
cana-1739	175	30	𝐻𝑛(𝑡	𝐻𝑛(𝑡	PROPN
cana-1739	175	31	)	)	PUNCT
cana-1739	175	32	=	=	SYM
cana-1739	175	33	∑	∑	PUNCT
cana-1739	175	34	𝜓4𝑖(𝑡	𝜓4𝑖(𝑡	PROPN
cana-1739	175	35	)	)	PUNCT
cana-1739	175	36	𝑛	𝑛	DET
cana-1739	175	37	𝑖=1	𝑖=1	PROPN
cana-1739	175	38	theorem	theorem	VERB
cana-1739	175	39	4.2.2	4.2.2	NUM
cana-1739	175	40	the	the	DET
cana-1739	175	41	caputo	caputo	PROPN
cana-1739	175	42	fabrizio	fabrizio	PROPN
cana-1739	175	43	fractional	fractional	PROPN
cana-1739	175	44	derivative	derivative	ADJ
cana-1739	175	45	model	model	NOUN
cana-1739	175	46	(	(	PUNCT
cana-1739	175	47	8)	8)	NOUN
cana-1739	175	48	has	have	VERB
cana-1739	175	49	system	system	NOUN
cana-1739	175	50	of	of	ADP
cana-1739	175	51	solutions	solution	NOUN
cana-1739	175	52	if	if	SCONJ
cana-1739	175	53	there	there	PRON
cana-1739	175	54	exists	exist	VERB
cana-1739	175	55	𝑣	𝑣	ADP
cana-1739	175	56	>	>	X
cana-1739	175	57	1	1	NUM
cana-1739	175	58	such	such	ADJ
cana-1739	175	59	that	that	SCONJ
cana-1739	175	60	[	[	PUNCT
cana-1739	175	61	1−𝜈(𝑡	1−𝜈(𝑡	NUM
cana-1739	175	62	)	)	PUNCT
cana-1739	175	63	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	175	64	)	)	PUNCT
cana-1739	175	65	)	)	PUNCT
cana-1739	175	66	𝜌𝑖	𝜌𝑖	ADP
cana-1739	175	67	+	+	CCONJ
cana-1739	175	68	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	175	69	)	)	PUNCT
cana-1739	175	70	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	175	71	)	)	PUNCT
cana-1739	175	72	)	)	PUNCT
cana-1739	175	73	𝜌𝑖	𝜌𝑖	ADP
cana-1739	175	74	𝑣	𝑣	NOUN
cana-1739	175	75	]	]	PUNCT
cana-1739	175	76	≤	≤	NUM
cana-1739	175	77	1	1	NUM
cana-1739	175	78	,	,	PUNCT
cana-1739	175	79	for	for	ADP
cana-1739	175	80	i=1,2,3,4	i=1,2,3,4	ADJ
cana-1739	175	81	proof	proof	NOUN
cana-1739	175	82	operating	operate	VERB
cana-1739	175	83	(	(	PUNCT
cana-1739	175	84	10	10	NUM
cana-1739	175	85	)	)	PUNCT
cana-1739	175	86	recursively	recursively	ADV
cana-1739	175	87	and	and	CCONJ
cana-1739	175	88	using	use	VERB
cana-1739	175	89	the	the	DET
cana-1739	175	90	initial	initial	ADJ
cana-1739	175	91	conditions	condition	NOUN
cana-1739	175	92	,	,	PUNCT
cana-1739	175	93	we	we	PRON
cana-1739	175	94	have	have	VERB
cana-1739	175	95	‖𝜓1𝑛(𝑡)‖	‖𝜓1𝑛(𝑡)‖	ADV
cana-1739	175	96	≤	≤	NUM
cana-1739	175	97	‖𝐺𝑛(0)‖	‖𝐺𝑛(0)‖	NOUN
cana-1739	175	98	[	[	PUNCT
cana-1739	175	99	1−𝜈(𝑡	1−𝜈(𝑡	NUM
cana-1739	175	100	)	)	PUNCT
cana-1739	175	101	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	175	102	)	)	PUNCT
cana-1739	175	103	)	)	PUNCT
cana-1739	176	1	𝜌1	𝜌1	NOUN
cana-1739	176	2	+	+	PUNCT
cana-1739	176	3	𝜈(𝑡	𝜈(𝑡	ADJ
cana-1739	176	4	)	)	PUNCT
cana-1739	176	5	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	176	6	)	)	PUNCT
cana-1739	176	7	)	)	PUNCT
cana-1739	177	1	𝜌1𝑣	𝜌1𝑣	ADP
cana-1739	177	2	]	]	PUNCT
cana-1739	177	3	𝑛	𝑛	PRON
cana-1739	177	4	similarly	similarly	ADV
cana-1739	177	5	,	,	PUNCT
cana-1739	177	6	we	we	PRON
cana-1739	177	7	have	have	VERB
cana-1739	177	8	for	for	ADP
cana-1739	177	9	‖𝜓2𝑛(𝑡)‖	‖𝜓2𝑛(𝑡)‖	NOUN
cana-1739	177	10	,	,	PUNCT
cana-1739	177	11	‖𝜓3𝑛(𝑡)‖	‖𝜓3𝑛(𝑡)‖	PUNCT
cana-1739	177	12	and	and	CCONJ
cana-1739	177	13	‖𝜓4𝑛(𝑡)‖this	‖𝜓4𝑛(𝑡)‖this	PRON
cana-1739	177	14	result	result	NOUN
cana-1739	177	15	proved	prove	VERB
cana-1739	177	16	the	the	DET
cana-1739	177	17	existence	existence	NOUN
cana-1739	177	18	and	and	CCONJ
cana-1739	177	19	continuity	continuity	NOUN
cana-1739	177	20	of	of	ADP
cana-1739	177	21	solution	solution	NOUN
cana-1739	177	22	.	.	PUNCT
cana-1739	178	1	to	to	PART
cana-1739	178	2	show	show	VERB
cana-1739	178	3	that	that	SCONJ
cana-1739	178	4	g(𝑡	g(𝑡	NOUN
cana-1739	178	5	)	)	PUNCT
cana-1739	178	6	,	,	PUNCT
cana-1739	178	7	𝐶(𝑡	𝐶(𝑡	NOUN
cana-1739	178	8	)	)	PUNCT
cana-1739	178	9	,	,	PUNCT
cana-1739	178	10	𝐼(𝑡	𝐼(𝑡	NUM
cana-1739	178	11	)	)	PUNCT
cana-1739	178	12	and	and	CCONJ
cana-1739	178	13	𝐻(𝑡	𝐻(𝑡	PRON
cana-1739	178	14	)	)	PUNCT
cana-1739	178	15	are	be	AUX
cana-1739	178	16	solutions	solution	NOUN
cana-1739	178	17	of	of	ADP
cana-1739	178	18	(	(	PUNCT
cana-1739	178	19	8)	8)	NUM
cana-1739	178	20	,	,	PUNCT
cana-1739	178	21	consider	consider	VERB
cana-1739	178	22	,	,	PUNCT
cana-1739	178	23	𝐺(𝑡	𝐺(𝑡	ADJ
cana-1739	178	24	)	)	PUNCT
cana-1739	178	25	−	−	NUM
cana-1739	178	26	𝐺(0	𝐺(0	NUM
cana-1739	178	27	)	)	PUNCT
cana-1739	178	28	=	=	SYM
cana-1739	178	29	𝐺𝑛(𝑡	𝐺𝑛(𝑡	NOUN
cana-1739	178	30	)	)	PUNCT
cana-1739	178	31	−	−	ADP
cana-1739	178	32	𝐷1𝑛(𝑡	𝐷1𝑛(𝑡	NOUN
cana-1739	178	33	)	)	PUNCT
cana-1739	178	34	𝐶(𝑡	𝐶(𝑡	NOUN
cana-1739	178	35	)	)	PUNCT
cana-1739	178	36	−	−	NUM
cana-1739	178	37	𝐶(0	𝐶(0	NOUN
cana-1739	178	38	)	)	PUNCT
cana-1739	178	39	=	=	SYM
cana-1739	178	40	𝐶𝑛(𝑡	𝐶𝑛(𝑡	NOUN
cana-1739	178	41	)	)	PUNCT
cana-1739	178	42	−	−	PROPN
cana-1739	178	43	𝐷2𝑛(𝑡	𝐷2𝑛(𝑡	NOUN
cana-1739	178	44	)	)	PUNCT
cana-1739	178	45	𝐼(𝑡	𝐼(𝑡	NOUN
cana-1739	178	46	)	)	PUNCT
cana-1739	178	47	−	−	NOUN
cana-1739	178	48	𝐼(0	𝐼(0	NOUN
cana-1739	178	49	)	)	PUNCT
cana-1739	178	50	=	=	SYM
cana-1739	178	51	𝐼𝑛(𝑡	𝐼𝑛(𝑡	PROPN
cana-1739	178	52	)	)	PUNCT
cana-1739	178	53	−	−	PROPN
cana-1739	178	54	𝐷3𝑛(𝑡	𝐷3𝑛(𝑡	PROPN
cana-1739	178	55	)	)	PUNCT
cana-1739	178	56	𝐻(𝑡	𝐻(𝑡	NOUN
cana-1739	178	57	)	)	PUNCT
cana-1739	178	58	−	−	NUM
cana-1739	178	59	𝐻(0	𝐻(0	NUM
cana-1739	178	60	)	)	PUNCT
cana-1739	178	61	=	=	SYM
cana-1739	178	62	𝐻𝑛(𝑡	𝐻𝑛(𝑡	PROPN
cana-1739	178	63	)	)	PUNCT
cana-1739	178	64	−	−	PROPN
cana-1739	178	65	𝐷3𝑛(𝑡	𝐷3𝑛(𝑡	NOUN
cana-1739	178	66	)	)	PUNCT
cana-1739	178	67	now	now	ADV
cana-1739	178	68	,	,	PUNCT
cana-1739	178	69	‖𝐷1𝑛(𝑡)‖	‖𝐷1𝑛(𝑡)‖	PROPN
cana-1739	178	70	≤	≤	NOUN
cana-1739	178	71	1−𝜈(𝑡	1−𝜈(𝑡	NUM
cana-1739	178	72	)	)	PUNCT
cana-1739	178	73	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	178	74	)	)	PUNCT
cana-1739	178	75	)	)	PUNCT
cana-1739	178	76	‖[𝐹1(𝑡	‖[𝐹1(𝑡	NOUN
cana-1739	178	77	,	,	PUNCT
cana-1739	178	78	𝐺𝑛	𝐺𝑛	NOUN
cana-1739	178	79	)	)	PUNCT
cana-1739	178	80	−	−	NOUN
cana-1739	178	81	𝐹1(𝑡	𝐹1(𝑡	PROPN
cana-1739	178	82	,	,	PUNCT
cana-1739	178	83	𝐺𝑛−1)]‖	𝐺𝑛−1)]‖	X
cana-1739	178	84	+	+	CCONJ
cana-1739	178	85	𝜈(𝑡	𝜈(𝑡	ADJ
cana-1739	178	86	)	)	PUNCT
cana-1739	178	87	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	178	88	)	)	PUNCT
cana-1739	178	89	)	)	PUNCT
cana-1739	179	1	∫	∫	PROPN
cana-1739	179	2	‖[𝐹1(𝜏	‖[𝐹1(𝜏	PROPN
cana-1739	179	3	,	,	PUNCT
cana-1739	179	4	𝐺𝑛	𝐺𝑛	NOUN
cana-1739	179	5	)	)	PUNCT
cana-1739	179	6	−	−	ADP
cana-1739	179	7	𝐹1(𝜏	𝐹1(𝜏	NOUN
cana-1739	179	8	,	,	PUNCT
cana-1739	179	9	𝐺𝑛−1)]‖	𝐺𝑛−1)]‖	PROPN
cana-1739	179	10	𝑡	𝑡	X
cana-1739	179	11	0	0	NUM
cana-1739	179	12	𝑑𝜏	𝑑𝜏	PROPN
cana-1739	179	13	≤	≤	NOUN
cana-1739	179	14	1−𝜈(𝑡	1−𝜈(𝑡	NUM
cana-1739	179	15	)	)	PUNCT
cana-1739	179	16	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	179	17	)	)	PUNCT
cana-1739	179	18	)	)	PUNCT
cana-1739	180	1	𝜌1‖𝐺𝑛	𝜌1‖𝐺𝑛	PROPN
cana-1739	180	2	−	−	PROPN
cana-1739	180	3	𝐺𝑛−1‖	𝐺𝑛−1‖	PROPN
cana-1739	180	4	+	+	CCONJ
cana-1739	180	5	𝜈(𝑡	𝜈(𝑡	ADJ
cana-1739	180	6	)	)	PUNCT
cana-1739	180	7	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	180	8	)	)	PUNCT
cana-1739	180	9	)	)	PUNCT
cana-1739	181	1	𝜌1	𝜌1	NOUN
cana-1739	181	2	‖𝐺𝑛	‖𝐺𝑛	NOUN
cana-1739	181	3	−	−	PROPN
cana-1739	181	4	𝐺𝑛−1‖𝑣	𝐺𝑛−1‖𝑣	X
cana-1739	181	5	≤	≤	NOUN
cana-1739	181	6	[	[	PUNCT
cana-1739	181	7	1−𝜈(𝑡	1−𝜈(𝑡	NUM
cana-1739	181	8	)	)	PUNCT
cana-1739	181	9	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	181	10	)	)	PUNCT
cana-1739	181	11	)	)	PUNCT
cana-1739	182	1	𝜌1	𝜌1	NOUN
cana-1739	182	2	+	+	PUNCT
cana-1739	182	3	𝜈(𝑡	𝜈(𝑡	ADJ
cana-1739	182	4	)	)	PUNCT
cana-1739	182	5	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	182	6	)	)	PUNCT
cana-1739	182	7	)	)	PUNCT
cana-1739	183	1	𝜌1𝑣	𝜌1𝑣	ADP
cana-1739	183	2	]	]	PUNCT
cana-1739	183	3	‖𝐺𝑛	‖𝐺𝑛	PROPN
cana-1739	183	4	−	−	PROPN
cana-1739	183	5	𝐺𝑛−1‖	𝐺𝑛−1‖	PROPN
cana-1739	183	6	applying	apply	VERB
cana-1739	183	7	the	the	DET
cana-1739	183	8	above	above	ADJ
cana-1739	183	9	process	process	NOUN
cana-1739	183	10	recursively	recursively	ADJ
cana-1739	183	11	communications	communication	NOUN
cana-1739	183	12	on	on	ADP
cana-1739	183	13	applied	apply	VERB
cana-1739	183	14	nonlinear	nonlinear	ADJ
cana-1739	183	15	analysis	analysis	NOUN
cana-1739	183	16	issn	issn	AUX
cana-1739	183	17	:	:	PUNCT
cana-1739	183	18	1074	1074	NUM
cana-1739	183	19	-	-	PUNCT
cana-1739	183	20	133x	133x	NUM
cana-1739	183	21	vol	vol	NOUN
cana-1739	183	22	32	32	NUM
cana-1739	183	23	no	no	NOUN
cana-1739	183	24	.	.	NOUN
cana-1739	183	25	2	2	NUM
cana-1739	183	26	(	(	PUNCT
cana-1739	183	27	2025	2025	NUM
cana-1739	183	28	)	)	PUNCT
cana-1739	183	29	241	241	NUM
cana-1739	183	30	https://internationalpubls.com	https://internationalpubls.com	X
cana-1739	183	31	‖𝐷1𝑛(𝑡)‖	‖𝐷1𝑛(𝑡)‖	PROPN
cana-1739	183	32	≤	≤	PROPN
cana-1739	183	33	[	[	PUNCT
cana-1739	183	34	1	1	NUM
cana-1739	183	35	−	−	NOUN
cana-1739	183	36	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	183	37	)	)	PUNCT
cana-1739	183	38	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	183	39	)	)	PUNCT
cana-1739	183	40	)	)	PUNCT
cana-1739	183	41	𝜌1	𝜌1	NOUN
cana-1739	183	42	+	+	PUNCT
cana-1739	183	43	𝜈(𝑡	𝜈(𝑡	ADJ
cana-1739	183	44	)	)	PUNCT
cana-1739	183	45	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	183	46	)	)	PUNCT
cana-1739	183	47	)	)	PUNCT
cana-1739	184	1	𝜌1𝑣	𝜌1𝑣	ADP
cana-1739	184	2	]	]	PUNCT
cana-1739	184	3	𝑛+1	𝑛+1	X
cana-1739	184	4	.	.	PUNCT
cana-1739	185	1	𝑆	𝑆	PROPN
cana-1739	185	2	where	where	SCONJ
cana-1739	185	3	s	s	VERB
cana-1739	185	4	is	be	AUX
cana-1739	185	5	the	the	DET
cana-1739	185	6	lipschitz	lipschitz	NOUN
cana-1739	185	7	constant	constant	ADJ
cana-1739	185	8	,	,	PUNCT
cana-1739	185	9	when	when	SCONJ
cana-1739	185	10	𝑛	𝑛	ADP
cana-1739	185	11	→	→	SYM
cana-1739	185	12	∞	∞	NUM
cana-1739	185	13	,	,	PUNCT
cana-1739	185	14	‖𝐷1𝑛‖	‖𝐷1𝑛‖	NOUN
cana-1739	185	15	→	→	SYM
cana-1739	185	16	0	0	NUM
cana-1739	185	17	similarly	similarly	ADV
cana-1739	185	18	,	,	PUNCT
cana-1739	185	19	we	we	PRON
cana-1739	185	20	prove	prove	VERB
cana-1739	185	21	for‖𝐷2𝑛‖	for‖𝐷2𝑛‖	NOUN
cana-1739	185	22	→	→	SYM
cana-1739	185	23	0	0	NUM
cana-1739	185	24	,	,	PUNCT
cana-1739	185	25	‖𝐷3𝑛‖	‖𝐷3𝑛‖	NOUN
cana-1739	185	26	→	→	SYM
cana-1739	185	27	0	0	NUM
cana-1739	185	28	and	and	CCONJ
cana-1739	185	29	‖𝐷4𝑛‖	‖𝐷4𝑛‖	NOUN
cana-1739	185	30	→	→	SYM
cana-1739	185	31	0	0	PUNCT
cana-1739	185	32	as	as	ADP
cana-1739	185	33	𝑛	𝑛	PROPN
cana-1739	185	34	→	→	SYM
cana-1739	185	35	∞	∞	NOUN
cana-1739	185	36	hence	hence	ADV
cana-1739	185	37	the	the	DET
cana-1739	185	38	proof	proof	NOUN
cana-1739	185	39	theorem	theorem	VERB
cana-1739	185	40	4.2.3	4.2.3	NUM
cana-1739	185	41	if	if	SCONJ
cana-1739	185	42	the	the	DET
cana-1739	185	43	condition	condition	NOUN
cana-1739	185	44	[	[	X
cana-1739	185	45	1	1	NUM
cana-1739	185	46	−	−	PROPN
cana-1739	185	47	[	[	PUNCT
cana-1739	185	48	1−𝜈(𝑡	1−𝜈(𝑡	NUM
cana-1739	185	49	)	)	PUNCT
cana-1739	185	50	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	185	51	)	)	PUNCT
cana-1739	185	52	)	)	PUNCT
cana-1739	185	53	𝜌𝑖	𝜌𝑖	ADP
cana-1739	185	54	+	+	CCONJ
cana-1739	185	55	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	185	56	)	)	PUNCT
cana-1739	185	57	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	185	58	)	)	PUNCT
cana-1739	185	59	)	)	PUNCT
cana-1739	185	60	𝜌𝑖𝑣	𝜌𝑖𝑣	NOUN
cana-1739	185	61	]	]	PUNCT
cana-1739	185	62	]	]	X
cana-1739	185	63	≥	≥	X
cana-1739	185	64	0	0	NUM
cana-1739	185	65	,	,	PUNCT
cana-1739	185	66	for	for	ADP
cana-1739	185	67	i=1,2,3,4	i=1,2,3,4	ADJ
cana-1739	185	68	holds	hold	NOUN
cana-1739	185	69	then	then	ADV
cana-1739	185	70	the	the	DET
cana-1739	185	71	caputo	caputo	PROPN
cana-1739	185	72	-	-	PUNCT
cana-1739	185	73	fabrizio	fabrizio	PROPN
cana-1739	185	74	fractional	fractional	ADJ
cana-1739	185	75	derivative	derivative	ADJ
cana-1739	185	76	model	model	NOUN
cana-1739	185	77	have	have	VERB
cana-1739	185	78	unique	unique	ADJ
cana-1739	185	79	solutions	solution	NOUN
cana-1739	185	80	.	.	PUNCT
cana-1739	186	1	proof	proof	NOUN
cana-1739	186	2	suppose	suppose	VERB
cana-1739	186	3	the	the	DET
cana-1739	186	4	system	system	NOUN
cana-1739	186	5	(	(	PUNCT
cana-1739	186	6	8)	8)	NUM
cana-1739	186	7	has	have	VERB
cana-1739	186	8	another	another	DET
cana-1739	186	9	solution	solution	NOUN
cana-1739	186	10	�	�	NOUN
cana-1739	186	11	̅	̅	NOUN
cana-1739	186	12	�	�	NOUN
cana-1739	186	13	,	,	PUNCT
cana-1739	186	14	𝐶̅	𝐶̅	NOUN
cana-1739	186	15	,	,	PUNCT
cana-1739	186	16	𝐼,̅	𝐼,̅	ADJ
cana-1739	186	17	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-1739	186	18	�	�	PROPN
cana-1739	186	19	̅	̅	NOUN
cana-1739	186	20	�	�	PROPN
cana-1739	186	21	𝐺(𝑡	𝐺(𝑡	NOUN
cana-1739	186	22	)	)	PUNCT
cana-1739	186	23	−	−	ADP
cana-1739	186	24	�	�	PROPN
cana-1739	186	25	̅	̅	NOUN
cana-1739	186	26	�	�	NOUN
cana-1739	186	27	(𝑡	(𝑡	NOUN
cana-1739	186	28	)	)	PUNCT
cana-1739	186	29	=	=	SYM
cana-1739	186	30	1−𝜈(𝑡	1−𝜈(𝑡	NUM
cana-1739	186	31	)	)	PUNCT
cana-1739	186	32	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	186	33	)	)	PUNCT
cana-1739	186	34	)	)	PUNCT
cana-1739	187	1	[	[	X
cana-1739	187	2	𝐹1(𝑡	𝐹1(𝑡	X
cana-1739	187	3	,	,	PUNCT
cana-1739	187	4	𝐺	𝐺	PROPN
cana-1739	187	5	)	)	PUNCT
cana-1739	187	6	−	−	PROPN
cana-1739	187	7	𝐹1(𝑡	𝐹1(𝑡	PROPN
cana-1739	187	8	,	,	PUNCT
cana-1739	187	9	�	�	PROPN
cana-1739	187	10	̅	̅	NOUN
cana-1739	187	11	�	�	NOUN
cana-1739	187	12	)	)	PUNCT
cana-1739	187	13	]	]	PUNCT
cana-1739	188	1	+	+	CCONJ
cana-1739	188	2	𝜈(𝑡	𝜈(𝑡	X
cana-1739	188	3	)	)	PUNCT
cana-1739	188	4	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	188	5	)	)	PUNCT
cana-1739	188	6	)	)	PUNCT
cana-1739	189	1	∫	∫	PROPN
cana-1739	190	1	[	[	X
cana-1739	190	2	𝐹1(𝜏	𝐹1(𝜏	NOUN
cana-1739	190	3	,	,	PUNCT
cana-1739	190	4	𝐺	𝐺	NOUN
cana-1739	190	5	)	)	PUNCT
cana-1739	191	1	−	−	ADP
cana-1739	191	2	𝐹1(𝜏	𝐹1(𝜏	NOUN
cana-1739	191	3	,	,	PUNCT
cana-1739	191	4	�	�	NOUN
cana-1739	191	5	̅	̅	NOUN
cana-1739	191	6	�	�	NOUN
cana-1739	191	7	)	)	PUNCT
cana-1739	191	8	]	]	PUNCT
cana-1739	192	1	𝑡	𝑡	PROPN
cana-1739	192	2	0	0	PROPN
cana-1739	192	3	𝑑𝜏	𝑑𝜏	NOUN
cana-1739	192	4	using	use	VERB
cana-1739	192	5	norm	norm	NOUN
cana-1739	192	6	and	and	CCONJ
cana-1739	192	7	applying	apply	VERB
cana-1739	192	8	lipschitz	lipschitz	NOUN
cana-1739	192	9	condition	condition	NOUN
cana-1739	192	10	‖𝐺(𝑡	‖𝐺(𝑡	NOUN
cana-1739	192	11	)	)	PUNCT
cana-1739	192	12	−	−	PRON
cana-1739	192	13	�	�	PROPN
cana-1739	192	14	̅	̅	VERB
cana-1739	192	15	�	�	NOUN
cana-1739	192	16	(𝑡)‖	(𝑡)‖	NOUN
cana-1739	192	17	≤	≤	X
cana-1739	192	18	[	[	PUNCT
cana-1739	192	19	1	1	NUM
cana-1739	192	20	−	−	NOUN
cana-1739	192	21	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	192	22	)	)	PUNCT
cana-1739	192	23	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	192	24	)	)	PUNCT
cana-1739	192	25	)	)	PUNCT
cana-1739	192	26	𝜌1	𝜌1	NOUN
cana-1739	192	27	+	+	PUNCT
cana-1739	192	28	𝜈(𝑡	𝜈(𝑡	ADJ
cana-1739	192	29	)	)	PUNCT
cana-1739	192	30	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	192	31	)	)	PUNCT
cana-1739	192	32	)	)	PUNCT
cana-1739	193	1	𝜌1𝑣	𝜌1𝑣	ADP
cana-1739	193	2	]	]	X
cana-1739	193	3	‖𝐺(𝑡	‖𝐺(𝑡	NOUN
cana-1739	193	4	)	)	PUNCT
cana-1739	193	5	−	−	PROPN
cana-1739	193	6	�	�	NOUN
cana-1739	193	7	̅	̅	NOUN
cana-1739	193	8	�	�	NOUN
cana-1739	193	9	(𝑡)‖	(𝑡)‖	PRON
cana-1739	193	10	consequently	consequently	ADV
cana-1739	193	11	,	,	PUNCT
cana-1739	193	12	we	we	PRON
cana-1739	193	13	have	have	VERB
cana-1739	193	14	‖𝐺(𝑡	‖𝐺(𝑡	NOUN
cana-1739	193	15	)	)	PUNCT
cana-1739	194	1	−	−	ADP
cana-1739	194	2	�	�	PROPN
cana-1739	194	3	̅	̅	NOUN
cana-1739	194	4	�	�	NOUN
cana-1739	194	5	(𝑡)‖	(𝑡)‖	NOUN
cana-1739	194	6	[	[	X
cana-1739	194	7	1	1	NUM
cana-1739	194	8	−	−	NOUN
cana-1739	194	9	[	[	PUNCT
cana-1739	194	10	1	1	NUM
cana-1739	194	11	−	−	NOUN
cana-1739	194	12	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	194	13	)	)	PUNCT
cana-1739	194	14	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	194	15	)	)	PUNCT
cana-1739	194	16	)	)	PUNCT
cana-1739	194	17	𝜌1	𝜌1	NOUN
cana-1739	194	18	+	+	PUNCT
cana-1739	194	19	𝜈(𝑡	𝜈(𝑡	ADJ
cana-1739	194	20	)	)	PUNCT
cana-1739	194	21	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	194	22	)	)	PUNCT
cana-1739	194	23	)	)	PUNCT
cana-1739	195	1	𝜌1𝑣	𝜌1𝑣	ADP
cana-1739	195	2	]	]	PUNCT
cana-1739	195	3	]	]	X
cana-1739	195	4	≤	≤	NUM
cana-1739	195	5	0	0	PUNCT
cana-1739	195	6	since	since	SCONJ
cana-1739	195	7	[	[	X
cana-1739	195	8	1	1	NUM
cana-1739	195	9	−	−	PROPN
cana-1739	195	10	[	[	PUNCT
cana-1739	195	11	1−𝜈(𝑡	1−𝜈(𝑡	NUM
cana-1739	195	12	)	)	PUNCT
cana-1739	195	13	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	195	14	)	)	PUNCT
cana-1739	195	15	)	)	PUNCT
cana-1739	195	16	𝜌𝑖	𝜌𝑖	ADP
cana-1739	195	17	+	+	CCONJ
cana-1739	195	18	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	195	19	)	)	PUNCT
cana-1739	195	20	𝑀(𝜈(𝑡	𝑀(𝜈(𝑡	NOUN
cana-1739	195	21	)	)	PUNCT
cana-1739	195	22	)	)	PUNCT
cana-1739	195	23	𝜌𝑖𝑣	𝜌𝑖𝑣	NOUN
cana-1739	195	24	]	]	PUNCT
cana-1739	195	25	]	]	PUNCT
cana-1739	195	26	>	>	X
cana-1739	195	27	0,we	0,we	PRON
cana-1739	195	28	have	have	VERB
cana-1739	195	29	‖𝐺(𝑡	‖𝐺(𝑡	NOUN
cana-1739	195	30	)	)	PUNCT
cana-1739	195	31	−	−	ADP
cana-1739	195	32	�	�	NOUN
cana-1739	195	33	̅	̅	NOUN
cana-1739	195	34	�	�	NOUN
cana-1739	195	35	(𝑡)‖	(𝑡)‖	SYM
cana-1739	195	36	=	=	SYM
cana-1739	195	37	0	0	NUM
cana-1739	195	38	therefore	therefore	ADV
cana-1739	195	39	𝐺(𝑡	𝐺(𝑡	ADJ
cana-1739	195	40	)	)	PUNCT
cana-1739	195	41	=	=	SYM
cana-1739	195	42	�	�	PROPN
cana-1739	195	43	̅	̅	NOUN
cana-1739	195	44	�	�	NOUN
cana-1739	195	45	(𝑡	(𝑡	NOUN
cana-1739	195	46	)	)	PUNCT
cana-1739	195	47	similarly	similarly	ADV
cana-1739	195	48	we	we	PRON
cana-1739	195	49	prove	prove	VERB
cana-1739	195	50	𝐶(𝑡	𝐶(𝑡	ADP
cana-1739	195	51	)	)	PUNCT
cana-1739	195	52	=	=	PUNCT
cana-1739	195	53	𝐶̅(𝑡	𝐶̅(𝑡	ADV
cana-1739	195	54	)	)	PUNCT
cana-1739	195	55	,	,	PUNCT
cana-1739	195	56	𝐼(𝑡	𝐼(𝑡	NUM
cana-1739	195	57	)	)	PUNCT
cana-1739	195	58	=	=	SYM
cana-1739	195	59	𝐼(̅𝑡	𝐼(̅𝑡	PROPN
cana-1739	195	60	)	)	PUNCT
cana-1739	195	61	and	and	CCONJ
cana-1739	195	62	𝐻(𝑡	𝐻(𝑡	NOUN
cana-1739	195	63	)	)	PUNCT
cana-1739	195	64	=	=	SYM
cana-1739	195	65	�	�	PROPN
cana-1739	195	66	̅	̅	NOUN
cana-1739	195	67	�	�	NOUN
cana-1739	195	68	(𝑡	(𝑡	NOUN
cana-1739	195	69	)	)	PUNCT
cana-1739	195	70	hence	hence	ADV
cana-1739	195	71	the	the	DET
cana-1739	195	72	proof	proof	NOUN
cana-1739	195	73	4.3	4.3	NUM
cana-1739	195	74	existence	existence	NOUN
cana-1739	195	75	and	and	CCONJ
cana-1739	195	76	uniqueness	uniqueness	NOUN
cana-1739	195	77	of	of	ADP
cana-1739	195	78	solutions	solution	NOUN
cana-1739	195	79	for	for	ADP
cana-1739	195	80	the	the	DET
cana-1739	195	81	atangana	atangana	PROPN
cana-1739	195	82	-	-	PUNCT
cana-1739	195	83	baleanu	baleanu	ADJ
cana-1739	195	84	fractional	fractional	ADJ
cana-1739	195	85	model	model	NOUN
cana-1739	195	86	let	let	VERB
cana-1739	195	87	us	we	PRON
cana-1739	195	88	construct	construct	VERB
cana-1739	195	89	(	(	PUNCT
cana-1739	195	90	2	2	NUM
cana-1739	195	91	)	)	PUNCT
cana-1739	195	92	in	in	ADP
cana-1739	195	93	atangana	atangana	PROPN
cana-1739	195	94	baleanu	baleanu	PROPN
cana-1739	195	95	fractional	fractional	ADJ
cana-1739	195	96	derivative	derivative	NOUN
cana-1739	195	97	in	in	ADP
cana-1739	195	98	caputo	caputo	PROPN
cana-1739	195	99	sense	sense	NOUN
cana-1739	195	100	𝐷𝑡	𝐷𝑡	PROPN
cana-1739	195	101	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	195	102	)	)	PUNCT
cana-1739	195	103	0	0	NUM
cana-1739	196	1	𝐴𝐵	𝐴𝐵	NOUN
cana-1739	197	1	[	[	X
cana-1739	197	2	𝐺(𝑡	𝐺(𝑡	NOUN
cana-1739	197	3	)	)	PUNCT
cana-1739	197	4	]	]	PUNCT
cana-1739	197	5	=	=	PUNCT
cana-1739	197	6	𝐹1(𝑡	𝐹1(𝑡	PROPN
cana-1739	197	7	,	,	PUNCT
cana-1739	197	8	𝐺	𝐺	NOUN
cana-1739	197	9	)	)	PUNCT
cana-1739	197	10	=	=	SYM
cana-1739	198	1	𝛬	𝛬	NOUN
cana-1739	198	2	+	+	NUM
cana-1739	198	3	𝑝1	𝑝1	NOUN
cana-1739	198	4	ν(t)𝐺(𝑡)𝐶(𝑡	ν(t)𝐺(𝑡)𝐶(𝑡	PROPN
cana-1739	198	5	)	)	PUNCT
cana-1739	198	6	−	−	PROPN
cana-1739	198	7	𝑝2	𝑝2	PROPN
cana-1739	198	8	ν(t)𝐺(𝑡	ν(t)𝐺(𝑡	PROPN
cana-1739	198	9	)	)	PUNCT
cana-1739	199	1	𝐷𝑡	𝐷𝑡	NOUN
cana-1739	199	2	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	199	3	)	)	PUNCT
cana-1739	199	4	0	0	NUM
cana-1739	199	5	𝐴𝐵	𝐴𝐵	NOUN
cana-1739	200	1	[	[	X
cana-1739	200	2	𝐶(𝑡	𝐶(𝑡	NUM
cana-1739	200	3	)	)	PUNCT
cana-1739	200	4	]	]	PUNCT
cana-1739	200	5	=	=	PUNCT
cana-1739	200	6	𝐹2(𝑡	𝐹2(𝑡	PROPN
cana-1739	200	7	,	,	PUNCT
cana-1739	200	8	𝐶	𝐶	PROPN
cana-1739	200	9	)	)	PUNCT
cana-1739	200	10	=	=	PUNCT
cana-1739	201	1	𝛺	𝛺	ADP
cana-1739	201	2	−	−	PROPN
cana-1739	201	3	𝑝1	𝑝1	NOUN
cana-1739	201	4	ν(t)𝐺(𝑡)𝐶(𝑡	ν(t)𝐺(𝑡)𝐶(𝑡	PROPN
cana-1739	201	5	)	)	PUNCT
cana-1739	201	6	+	+	CCONJ
cana-1739	201	7	𝑝3	𝑝3	ADV
cana-1739	201	8	ν(t)𝐻(𝑡)𝐶(𝑡	ν(t)𝐻(𝑡)𝐶(𝑡	ADJ
cana-1739	201	9	)	)	PUNCT
cana-1739	201	10	−	−	PROPN
cana-1739	201	11	𝑝4	𝑝4	NOUN
cana-1739	201	12	ν(t)𝐶(𝑡	ν(t)𝐶(𝑡	NOUN
cana-1739	201	13	)	)	PUNCT
cana-1739	202	1	𝐷𝑡	𝐷𝑡	NOUN
cana-1739	202	2	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	202	3	)	)	PUNCT
cana-1739	202	4	0	0	NUM
cana-1739	202	5	𝐴𝐵	𝐴𝐵	NOUN
cana-1739	203	1	[	[	X
cana-1739	203	2	𝐼(𝑡	𝐼(𝑡	NOUN
cana-1739	203	3	)	)	PUNCT
cana-1739	203	4	]	]	PUNCT
cana-1739	203	5	=	=	SYM
cana-1739	203	6	𝐹3(𝑡	𝐹3(𝑡	PROPN
cana-1739	203	7	,	,	PUNCT
cana-1739	203	8	𝐼	𝐼	PROPN
cana-1739	203	9	)	)	PUNCT
cana-1739	203	10	=	=	SYM
cana-1739	203	11	𝑝5	𝑝5	PROPN
cana-1739	203	12	ν(t)𝐺(𝑡)𝐼(𝑡	ν(t)𝐺(𝑡)𝐼(𝑡	PROPN
cana-1739	203	13	)	)	PUNCT
cana-1739	203	14	−	−	PROPN
cana-1739	203	15	𝑝6	𝑝6	NOUN
cana-1739	203	16	ν(t)𝐻(𝑡)𝐼(𝑡	ν(t)𝐻(𝑡)𝐼(𝑡	PROPN
cana-1739	203	17	)	)	PUNCT
cana-1739	204	1	−	−	PROPN
cana-1739	204	2	𝑝7	𝑝7	PROPN
cana-1739	204	3	ν(t)𝐼(𝑡	ν(t)𝐼(𝑡	PROPN
cana-1739	204	4	)	)	PUNCT
cana-1739	205	1	𝐷𝑡	𝐷𝑡	PROPN
cana-1739	205	2	𝜈(𝑡	𝜈(𝑡	NUM
cana-1739	205	3	)	)	PUNCT
cana-1739	205	4	0	0	NUM
cana-1739	205	5	𝐴𝐵	𝐴𝐵	NOUN
cana-1739	206	1	[	[	X
cana-1739	206	2	𝐻(𝑡	𝐻(𝑡	NOUN
cana-1739	206	3	)	)	PUNCT
cana-1739	206	4	]	]	PUNCT
cana-1739	207	1	=	=	PUNCT
cana-1739	207	2	𝐹4(𝑡	𝐹4(𝑡	X
cana-1739	207	3	,	,	PUNCT
cana-1739	207	4	𝐻	𝐻	NOUN
cana-1739	207	5	)	)	PUNCT
cana-1739	207	6	=	=	SYM
cana-1739	207	7	𝛹	𝛹	PROPN
cana-1739	207	8	+	+	NUM
cana-1739	207	9	𝑝6	𝑝6	PROPN
cana-1739	207	10	ν(t)𝐻(𝑡)𝐼(𝑡	ν(t)𝐻(𝑡)𝐼(𝑡	PROPN
cana-1739	207	11	)	)	PUNCT
cana-1739	207	12	−	−	PROPN
cana-1739	207	13	𝑝8	𝑝8	PROPN
cana-1739	207	14	ν(t)𝐻(𝑡	ν(t)𝐻(𝑡	PRON
cana-1739	207	15	)	)	PUNCT
cana-1739	207	16	(	(	PUNCT
cana-1739	207	17	11	11	X
cana-1739	207	18	)	)	PUNCT
cana-1739	207	19	communications	communication	NOUN
cana-1739	207	20	on	on	ADP
cana-1739	207	21	applied	apply	VERB
cana-1739	207	22	nonlinear	nonlinear	ADJ
cana-1739	207	23	analysis	analysis	NOUN
cana-1739	207	24	issn	issn	NOUN
cana-1739	207	25	:	:	PUNCT
cana-1739	207	26	1074	1074	NUM
cana-1739	207	27	-	-	PUNCT
cana-1739	207	28	133x	133x	NUM
cana-1739	207	29	vol	vol	NOUN
cana-1739	207	30	32	32	NUM
cana-1739	207	31	no	no	NOUN
cana-1739	207	32	.	.	NOUN
cana-1739	207	33	2	2	NUM
cana-1739	207	34	(	(	PUNCT
cana-1739	207	35	2025	2025	NUM
cana-1739	207	36	)	)	PUNCT
cana-1739	207	37	242	242	NUM
cana-1739	207	38	https://internationalpubls.com	https://internationalpubls.com	X
cana-1739	207	39	the	the	DET
cana-1739	207	40	atangana	atangana	PROPN
cana-1739	207	41	-	-	PUNCT
cana-1739	207	42	baleanu	baleanu	ADJ
cana-1739	207	43	integral	integral	ADJ
cana-1739	207	44	form	form	NOUN
cana-1739	207	45	of	of	ADP
cana-1739	207	46	the	the	DET
cana-1739	207	47	above	above	ADJ
cana-1739	207	48	system	system	NOUN
cana-1739	207	49	is	be	AUX
cana-1739	207	50	𝐺(𝑡	𝐺(𝑡	NOUN
cana-1739	207	51	)	)	PUNCT
cana-1739	207	52	−	−	NUM
cana-1739	207	53	𝐺(0	𝐺(0	NUM
cana-1739	207	54	)	)	PUNCT
cana-1739	207	55	=	=	SYM
cana-1739	207	56	1−𝜈(𝑡	1−𝜈(𝑡	X
cana-1739	207	57	)	)	PUNCT
cana-1739	207	58	𝐴𝐵(𝜈(𝑡	𝐴𝐵(𝜈(𝑡	NOUN
cana-1739	207	59	)	)	PUNCT
cana-1739	207	60	)	)	PUNCT
cana-1739	208	1	𝐹1(𝑡	𝐹1(𝑡	PROPN
cana-1739	208	2	,	,	PUNCT
cana-1739	208	3	𝐺	𝐺	NOUN
cana-1739	208	4	)	)	PUNCT
cana-1739	209	1	+	+	CCONJ
cana-1739	209	2	𝜈(𝑡	𝜈(𝑡	X
cana-1739	209	3	)	)	PUNCT
cana-1739	209	4	𝐴𝐵(𝜈(𝑡))	𝐴𝐵(𝜈(𝑡))	PROPN
cana-1739	209	5	⎾	⎾	NUM
cana-1739	209	6	𝜈(𝑡	𝜈(𝑡	PRON
cana-1739	209	7	)	)	PUNCT
cana-1739	209	8	∫	∫	PROPN
cana-1739	209	9	(	(	PUNCT
cana-1739	209	10	𝑡	𝑡	PROPN
cana-1739	209	11	−	−	PROPN
cana-1739	209	12	𝛾)𝜈(𝑡)−1𝐹1(𝛾	𝛾)𝜈(𝑡)−1𝐹1(𝛾	SYM
cana-1739	209	13	,	,	PUNCT
cana-1739	209	14	𝐺)𝑑𝛾	𝐺)𝑑𝛾	VERB
cana-1739	209	15	𝑡	𝑡	X
cana-1739	209	16	0	0	PUNCT
cana-1739	209	17	𝐶(𝑡	𝐶(𝑡	NUM
cana-1739	209	18	)	)	PUNCT
cana-1739	209	19	−	−	NUM
cana-1739	209	20	𝐶(0	𝐶(0	NOUN
cana-1739	209	21	)	)	PUNCT
cana-1739	209	22	=	=	SYM
cana-1739	209	23	1−𝜈(𝑡	1−𝜈(𝑡	X
cana-1739	209	24	)	)	PUNCT
cana-1739	209	25	𝐴𝐵(𝜈(𝑡	𝐴𝐵(𝜈(𝑡	NOUN
cana-1739	209	26	)	)	PUNCT
cana-1739	209	27	)	)	PUNCT
cana-1739	210	1	𝐹2(𝑡	𝐹2(𝑡	PROPN
cana-1739	210	2	,	,	PUNCT
cana-1739	210	3	𝐶	𝐶	PROPN
cana-1739	210	4	)	)	PUNCT
cana-1739	210	5	+	+	CCONJ
cana-1739	210	6	𝜈(𝑡	𝜈(𝑡	X
cana-1739	210	7	)	)	PUNCT
cana-1739	210	8	𝐴𝐵(𝜈(𝑡))	𝐴𝐵(𝜈(𝑡))	PROPN
cana-1739	210	9	⎾	⎾	NUM
cana-1739	210	10	𝜈(𝑡	𝜈(𝑡	PRON
cana-1739	210	11	)	)	PUNCT
cana-1739	210	12	∫	∫	PROPN
cana-1739	210	13	(	(	PUNCT
cana-1739	210	14	𝑡	𝑡	PROPN
cana-1739	210	15	−	−	NOUN
cana-1739	210	16	𝛾)𝜈(𝑡)−1𝐹2(𝛾	𝛾)𝜈(𝑡)−1𝐹2(𝛾	ADJ
cana-1739	210	17	,	,	PUNCT
cana-1739	210	18	𝐶)𝑑𝛾	𝐶)𝑑𝛾	PROPN
cana-1739	210	19	𝑡	𝑡	NOUN
cana-1739	210	20	0	0	NUM
cana-1739	210	21	(	(	PUNCT
cana-1739	210	22	12	12	NUM
cana-1739	210	23	)	)	PUNCT
cana-1739	210	24	𝐼(𝑡	𝐼(𝑡	NUM
cana-1739	210	25	)	)	PUNCT
cana-1739	210	26	−	−	NOUN
cana-1739	210	27	𝐼(0	𝐼(0	NOUN
cana-1739	210	28	)	)	PUNCT
cana-1739	210	29	=	=	SYM
cana-1739	210	30	1−𝜈(𝑡	1−𝜈(𝑡	X
cana-1739	210	31	)	)	PUNCT
cana-1739	210	32	𝐴𝐵(𝜈(𝑡	𝐴𝐵(𝜈(𝑡	NOUN
cana-1739	210	33	)	)	PUNCT
cana-1739	210	34	)	)	PUNCT
cana-1739	211	1	𝐹3(𝑡	𝐹3(𝑡	PROPN
cana-1739	211	2	,	,	PUNCT
cana-1739	211	3	𝐼	𝐼	PROPN
cana-1739	211	4	)	)	PUNCT
cana-1739	211	5	+	+	CCONJ
cana-1739	211	6	𝜈(𝑡	𝜈(𝑡	X
cana-1739	211	7	)	)	PUNCT
cana-1739	211	8	𝐴𝐵(𝜈(𝑡))	𝐴𝐵(𝜈(𝑡))	PROPN
cana-1739	211	9	⎾	⎾	NUM
cana-1739	211	10	𝜈(𝑡	𝜈(𝑡	PRON
cana-1739	211	11	)	)	PUNCT
cana-1739	211	12	∫	∫	PROPN
cana-1739	211	13	(	(	PUNCT
cana-1739	211	14	𝑡	𝑡	PROPN
cana-1739	211	15	−	−	PROPN
cana-1739	211	16	𝛾)𝜈(𝑡)−1𝐹3(𝛾	𝛾)𝜈(𝑡)−1𝐹3(𝛾	SYM
cana-1739	211	17	,	,	PUNCT
cana-1739	211	18	𝐼)𝑑𝛾	𝐼)𝑑𝛾	PROPN
cana-1739	211	19	𝑡	𝑡	PROPN
cana-1739	211	20	0	0	PUNCT
cana-1739	211	21	𝐻(𝑡	𝐻(𝑡	NOUN
cana-1739	211	22	)	)	PUNCT
cana-1739	211	23	−	−	NUM
cana-1739	211	24	𝐻(0	𝐻(0	CCONJ
cana-1739	211	25	)	)	PUNCT
cana-1739	211	26	=	=	SYM
cana-1739	211	27	1−𝜈(𝑡	1−𝜈(𝑡	X
cana-1739	211	28	)	)	PUNCT
cana-1739	211	29	𝐴𝐵(𝜈(𝑡	𝐴𝐵(𝜈(𝑡	NOUN
cana-1739	211	30	)	)	PUNCT
cana-1739	211	31	)	)	PUNCT
cana-1739	212	1	𝐹4(𝑡	𝐹4(𝑡	NOUN
cana-1739	212	2	,	,	PUNCT
cana-1739	212	3	𝐻	𝐻	PROPN
cana-1739	212	4	)	)	PUNCT
cana-1739	212	5	+	+	CCONJ
cana-1739	212	6	𝜈(𝑡	𝜈(𝑡	X
cana-1739	212	7	)	)	PUNCT
cana-1739	212	8	𝐴𝐵(𝜈(𝑡))	𝐴𝐵(𝜈(𝑡))	PROPN
cana-1739	212	9	⎾	⎾	NUM
cana-1739	212	10	𝜈(𝑡	𝜈(𝑡	PRON
cana-1739	212	11	)	)	PUNCT
cana-1739	212	12	∫	∫	PROPN
cana-1739	212	13	(	(	PUNCT
cana-1739	212	14	𝑡	𝑡	PROPN
cana-1739	212	15	−	−	PROPN
cana-1739	212	16	𝛾)𝜈(𝑡)−1𝐹4(𝛾	𝛾)𝜈(𝑡)−1𝐹4(𝛾	PROPN
cana-1739	212	17	,	,	PUNCT
cana-1739	212	18	𝐻)𝑑𝛾	𝐻)𝑑𝛾	PROPN
cana-1739	212	19	𝑡	𝑡	PROPN
cana-1739	212	20	0	0	PUNCT
cana-1739	212	21	now	now	ADV
cana-1739	212	22	to	to	PART
cana-1739	212	23	prove	prove	VERB
cana-1739	212	24	the	the	DET
cana-1739	212	25	kernel	kernel	NOUN
cana-1739	213	1	𝐹𝑖	𝐹𝑖	PROPN
cana-1739	213	2	for	for	ADP
cana-1739	213	3	𝑖	𝑖	NOUN
cana-1739	213	4	=	=	SYM
cana-1739	213	5	1,2,3,4	1,2,3,4	NUM
cana-1739	213	6	follows	follow	VERB
cana-1739	213	7	the	the	DET
cana-1739	213	8	lipschitz	lipschitz	NOUN
cana-1739	213	9	condition	condition	NOUN
cana-1739	213	10	and	and	CCONJ
cana-1739	213	11	contraction	contraction	NOUN
cana-1739	213	12	.	.	PUNCT
cana-1739	214	1	theorem	theorem	VERB
cana-1739	214	2	4.3.1	4.3.1	NUM
cana-1739	214	3	the	the	DET
cana-1739	214	4	kernel	kernel	NOUN
cana-1739	214	5	𝐹𝑖(𝛾	𝐹𝑖(𝛾	PROPN
cana-1739	214	6	,	,	PUNCT
cana-1739	214	7	𝐺	𝐺	PROPN
cana-1739	214	8	)	)	PUNCT
cana-1739	214	9	,	,	PUNCT
cana-1739	214	10	for	for	SCONJ
cana-1739	214	11	𝑖	𝑖	PRON
cana-1739	214	12	=	=	SYM
cana-1739	214	13	1,2,3,4	1,2,3,4	NUM
cana-1739	214	14	satisfies	satisfie	NOUN
cana-1739	214	15	the	the	DET
cana-1739	214	16	lipschitz	lipschitz	NOUN
cana-1739	214	17	condition	condition	NOUN
cana-1739	214	18	and	and	CCONJ
cana-1739	214	19	contraction	contraction	NOUN
cana-1739	214	20	if	if	SCONJ
cana-1739	214	21	0	0	NUM
cana-1739	214	22	≤	≤	NUM
cana-1739	214	23	𝛿𝑖	𝛿𝑖	ADP
cana-1739	214	24	<	<	X
cana-1739	214	25	1	1	NUM
cana-1739	214	26	holds	hold	NOUN
cana-1739	214	27	.	.	PUNCT
cana-1739	215	1	proof	proof	NOUN
cana-1739	215	2	the	the	DET
cana-1739	215	3	proof	proof	NOUN
cana-1739	215	4	is	be	AUX
cana-1739	215	5	similar	similar	ADJ
cana-1739	215	6	to	to	ADP
cana-1739	215	7	the	the	DET
cana-1739	215	8	proof	proof	NOUN
cana-1739	215	9	of	of	ADP
cana-1739	215	10	4.1.1	4.1.1	NUM
cana-1739	215	11	.	.	PUNCT
cana-1739	216	1	now	now	ADV
cana-1739	216	2	the	the	DET
cana-1739	216	3	recurrent	recurrent	ADJ
cana-1739	216	4	form	form	NOUN
cana-1739	216	5	of	of	ADP
cana-1739	216	6	(	(	PUNCT
cana-1739	216	7	12	12	NUM
cana-1739	216	8	)	)	PUNCT
cana-1739	216	9	is	be	AUX
cana-1739	216	10	𝜃1𝑛	𝜃1𝑛	NOUN
cana-1739	216	11	=	=	SYM
cana-1739	216	12	𝐺𝑛(𝑡	𝐺𝑛(𝑡	NOUN
cana-1739	216	13	)	)	PUNCT
cana-1739	216	14	−	−	ADP
cana-1739	216	15	𝐺𝑛−1(𝑡	𝐺𝑛−1(𝑡	NOUN
cana-1739	216	16	)	)	PUNCT
cana-1739	216	17	=	=	SYM
cana-1739	216	18	1−𝜈(𝑡	1−𝜈(𝑡	NUM
cana-1739	216	19	)	)	PUNCT
cana-1739	216	20	𝐴𝐵(𝜈(𝑡	𝐴𝐵(𝜈(𝑡	NOUN
cana-1739	216	21	)	)	PUNCT
cana-1739	216	22	)	)	PUNCT
cana-1739	217	1	[	[	X
cana-1739	217	2	𝐹1(𝑡	𝐹1(𝑡	X
cana-1739	217	3	,	,	PUNCT
cana-1739	217	4	𝐺𝑛−1	𝐺𝑛−1	NUM
cana-1739	217	5	)	)	PUNCT
cana-1739	218	1	−	−	PROPN
cana-1739	218	2	𝐹1(𝑡	𝐹1(𝑡	PROPN
cana-1739	218	3	,	,	PUNCT
cana-1739	218	4	𝐺𝑛−2	𝐺𝑛−2	PROPN
cana-1739	218	5	)	)	PUNCT
cana-1739	218	6	]	]	PUNCT
cana-1739	219	1	+	+	CCONJ
cana-1739	219	2	𝜈(𝑡	𝜈(𝑡	X
cana-1739	219	3	)	)	PUNCT
cana-1739	219	4	𝐴𝐵(𝜈(𝑡))	𝐴𝐵(𝜈(𝑡))	PROPN
cana-1739	219	5	⎾	⎾	NUM
cana-1739	219	6	𝜈(𝑡	𝜈(𝑡	PRON
cana-1739	219	7	)	)	PUNCT
cana-1739	219	8	∫	∫	PROPN
cana-1739	219	9	(	(	PUNCT
cana-1739	219	10	𝑡	𝑡	PROPN
cana-1739	219	11	−	−	NOUN
cana-1739	219	12	𝛾)𝜈(𝑡)−1[𝐹1(𝛾	𝛾)𝜈(𝑡)−1[𝐹1(𝛾	ADP
cana-1739	219	13	,	,	PUNCT
cana-1739	219	14	𝐺𝑛−1	𝐺𝑛−1	NUM
cana-1739	219	15	)	)	PUNCT
cana-1739	219	16	−	−	PROPN
cana-1739	219	17	𝑡	𝑡	PROPN
cana-1739	219	18	0	0	PROPN
cana-1739	219	19	𝐹1(𝛾	𝐹1(𝛾	PROPN
cana-1739	219	20	,	,	PUNCT
cana-1739	219	21	𝐺𝑛−2)]𝑑𝛾	𝐺𝑛−2)]𝑑𝛾	X
cana-1739	219	22	similarly	similarly	ADV
cana-1739	219	23	𝜃2𝑛	𝜃2𝑛	PUNCT
cana-1739	219	24	,	,	PUNCT
cana-1739	219	25	𝜃3𝑛	𝜃3𝑛	X
cana-1739	219	26	and	and	CCONJ
cana-1739	219	27	𝜃4𝑛are	𝜃4𝑛are	NOUN
cana-1739	219	28	also	also	ADV
cana-1739	219	29	be	be	AUX
cana-1739	219	30	derived	derive	VERB
cana-1739	219	31	.	.	PUNCT
cana-1739	220	1	using	use	VERB
cana-1739	220	2	the	the	DET
cana-1739	220	3	initial	initial	ADJ
cana-1739	220	4	condition	condition	NOUN
cana-1739	220	5	and	and	CCONJ
cana-1739	220	6	taking	take	VERB
cana-1739	220	7	norm	norm	NOUN
cana-1739	220	8	,	,	PUNCT
cana-1739	220	9	we	we	PRON
cana-1739	220	10	get	get	VERB
cana-1739	220	11	‖𝜃1𝑛‖	‖𝜃1𝑛‖	NOUN
cana-1739	220	12	≤	≤	NUM
cana-1739	220	13	1−𝜈(𝑡	1−𝜈(𝑡	NUM
cana-1739	220	14	)	)	PUNCT
cana-1739	220	15	𝐴𝐵(𝜈(𝑡	𝐴𝐵(𝜈(𝑡	NOUN
cana-1739	220	16	)	)	PUNCT
cana-1739	220	17	)	)	PUNCT
cana-1739	221	1	‖[𝐹1(𝑡	‖[𝐹1(𝑡	PROPN
cana-1739	221	2	,	,	PUNCT
cana-1739	221	3	𝐺𝑛−1	𝐺𝑛−1	NUM
cana-1739	221	4	)	)	PUNCT
cana-1739	221	5	−	−	PROPN
cana-1739	222	1	𝐹1(𝑡	𝐹1(𝑡	PROPN
cana-1739	222	2	,	,	PUNCT
cana-1739	222	3	𝐺𝑛−2)]‖	𝐺𝑛−2)]‖	PROPN
cana-1739	222	4	+	+	CCONJ
cana-1739	222	5	𝜈(𝑡	𝜈(𝑡	ADJ
cana-1739	222	6	)	)	PUNCT
cana-1739	222	7	𝐴𝐵(𝜈(𝑡))	𝐴𝐵(𝜈(𝑡))	PROPN
cana-1739	222	8	⎾	⎾	NUM
cana-1739	222	9	𝜈(𝑡	𝜈(𝑡	PRON
cana-1739	222	10	)	)	PUNCT
cana-1739	222	11	∫	∫	PROPN
cana-1739	222	12	(	(	PUNCT
cana-1739	222	13	𝑡	𝑡	X
cana-1739	222	14	−	−	NOUN
cana-1739	222	15	𝛾)𝜈(𝑡)−1‖[𝐹1(𝛾	𝛾)𝜈(𝑡)−1‖[𝐹1(𝛾	ADJ
cana-1739	222	16	,	,	PUNCT
cana-1739	222	17	𝐺𝑛−1	𝐺𝑛−1	NUM
cana-1739	222	18	)	)	PUNCT
cana-1739	222	19	−	−	PROPN
cana-1739	222	20	𝑡	𝑡	PROPN
cana-1739	222	21	0	0	PROPN
cana-1739	222	22	𝐹1(𝛾	𝐹1(𝛾	PROPN
cana-1739	222	23	,	,	PUNCT
cana-1739	222	24	𝐺𝑛−2)]‖	𝐺𝑛−2)]‖	PROPN
cana-1739	222	25	𝑑𝛾	𝑑𝛾	PROPN
cana-1739	222	26	since	since	SCONJ
cana-1739	222	27	𝛿1	𝛿1	NOUN
cana-1739	222	28	satisfies	satisfie	NOUN
cana-1739	222	29	lipschitz	lipschitz	VERB
cana-1739	222	30	condition	condition	NOUN
cana-1739	222	31	‖𝜃1𝑛‖	‖𝜃1𝑛‖	NOUN
cana-1739	222	32	≤	≤	NUM
cana-1739	222	33	1−𝜈(𝑡	1−𝜈(𝑡	NUM
cana-1739	222	34	)	)	PUNCT
cana-1739	222	35	𝐴𝐵(𝜈(𝑡	𝐴𝐵(𝜈(𝑡	NOUN
cana-1739	222	36	)	)	PUNCT
cana-1739	222	37	)	)	PUNCT
cana-1739	223	1	𝛿1‖𝜃1(𝑛−1)‖	𝛿1‖𝜃1(𝑛−1)‖	VERB
cana-1739	223	2	+	+	X
cana-1739	223	3	𝜈(𝑡	𝜈(𝑡	X
cana-1739	223	4	)	)	PUNCT
cana-1739	223	5	𝐴𝐵(𝜈(𝑡))	𝐴𝐵(𝜈(𝑡))	PROPN
cana-1739	223	6	⎾	⎾	NUM
cana-1739	223	7	𝜈(𝑡	𝜈(𝑡	PRON
cana-1739	223	8	)	)	PUNCT
cana-1739	223	9	𝛿1	𝛿1	NOUN
cana-1739	223	10	∫	∫	PROPN
cana-1739	223	11	(	(	PUNCT
cana-1739	223	12	𝑡	𝑡	PROPN
cana-1739	223	13	−	−	PROPN
cana-1739	223	14	𝛾)𝜈(𝑡)−1‖𝜃1(𝑛−1)(𝛾)‖	𝛾)𝜈(𝑡)−1‖𝜃1(𝑛−1)(𝛾)‖	PROPN
cana-1739	223	15	𝑡	𝑡	PROPN
cana-1739	223	16	0	0	NUM
cana-1739	223	17	𝑑𝛾	𝑑𝛾	NOUN
cana-1739	223	18	similarly	similarly	ADV
cana-1739	223	19	for‖𝜃2𝑛‖	for‖𝜃2𝑛‖	NOUN
cana-1739	223	20	,	,	PUNCT
cana-1739	223	21	‖𝜃3𝑛‖	‖𝜃3𝑛‖	NOUN
cana-1739	223	22	and	and	CCONJ
cana-1739	223	23	‖𝜃4𝑛‖	‖𝜃4𝑛‖	NOUN
cana-1739	223	24	which	which	PRON
cana-1739	223	25	implies	imply	VERB
cana-1739	223	26	that	that	SCONJ
cana-1739	223	27	it	it	PRON
cana-1739	223	28	can	can	AUX
cana-1739	223	29	be	be	AUX
cana-1739	223	30	written	write	VERB
cana-1739	223	31	as	as	ADP
cana-1739	223	32	𝐺𝑛(𝑡	𝐺𝑛(𝑡	PROPN
cana-1739	223	33	)	)	PUNCT
cana-1739	223	34	=	=	SYM
cana-1739	223	35	∑	∑	PUNCT
cana-1739	223	36	𝜃1𝑖(𝑡	𝜃1𝑖(𝑡	PROPN
cana-1739	223	37	)	)	PUNCT
cana-1739	223	38	,	,	PUNCT
cana-1739	223	39	𝑛	𝑛	PRON
cana-1739	223	40	𝑖=1	𝑖=1	PROPN
cana-1739	223	41	𝐶𝑛(𝑡	𝐶𝑛(𝑡	NOUN
cana-1739	223	42	)	)	PUNCT
cana-1739	223	43	=	=	SYM
cana-1739	223	44	∑	∑	PUNCT
cana-1739	223	45	𝜃2𝑖(𝑡	𝜃2𝑖(𝑡	NUM
cana-1739	223	46	)	)	PUNCT
cana-1739	223	47	,	,	PUNCT
cana-1739	223	48	𝑛	𝑛	DET
cana-1739	223	49	𝑖=1	𝑖=1	PROPN
cana-1739	223	50	𝐼𝑛(𝑡	𝐼𝑛(𝑡	PROPN
cana-1739	223	51	)	)	PUNCT
cana-1739	223	52	=	=	SYM
cana-1739	223	53	∑	∑	PUNCT
cana-1739	223	54	𝜃3𝑖(𝑡	𝜃3𝑖(𝑡	PROPN
cana-1739	223	55	)	)	PUNCT
cana-1739	223	56	𝑛	𝑛	PART
cana-1739	223	57	𝑖=1	𝑖=1	PROPN
cana-1739	223	58	,	,	PUNCT
cana-1739	223	59	𝐻𝑛(𝑡	𝐻𝑛(𝑡	PROPN
cana-1739	223	60	)	)	PUNCT
cana-1739	223	61	=	=	SYM
cana-1739	223	62	∑	∑	PUNCT
cana-1739	223	63	𝜃4𝑖(𝑡	𝜃4𝑖(𝑡	PROPN
cana-1739	223	64	)	)	PUNCT
cana-1739	223	65	𝑛	𝑛	PRON
cana-1739	223	66	𝑖=1	𝑖=1	PROPN
cana-1739	223	67	(	(	PUNCT
cana-1739	223	68	13	13	NUM
cana-1739	223	69	)	)	PUNCT
cana-1739	223	70	theorem	theorem	VERB
cana-1739	223	71	4.3.2	4.3.2	NUM
cana-1739	223	72	the	the	DET
cana-1739	223	73	atanganabaleanu	atanganabaleanu	NOUN
cana-1739	223	74	derivative	derivative	ADJ
cana-1739	223	75	model	model	NOUN
cana-1739	223	76	(	(	PUNCT
cana-1739	223	77	11	11	NUM
cana-1739	223	78	)	)	PUNCT
cana-1739	223	79	have	have	VERB
cana-1739	223	80	system	system	NOUN
cana-1739	223	81	of	of	ADP
cana-1739	223	82	solutions	solution	NOUN
cana-1739	223	83	,	,	PUNCT
cana-1739	223	84	if	if	SCONJ
cana-1739	223	85	there	there	PRON
cana-1739	223	86	exists	exist	VERB
cana-1739	223	87	𝜇	𝜇	ADP
cana-1739	223	88	>	>	X
cana-1739	223	89	1such	1such	NUM
cana-1739	223	90	that	that	SCONJ
cana-1739	223	91	[	[	PUNCT
cana-1739	223	92	1−𝜈(𝑡	1−𝜈(𝑡	NUM
cana-1739	223	93	)	)	PUNCT
cana-1739	223	94	𝐴𝐵(𝜈(𝑡	𝐴𝐵(𝜈(𝑡	NOUN
cana-1739	223	95	)	)	PUNCT
cana-1739	223	96	)	)	PUNCT
cana-1739	223	97	𝛿𝑖	𝛿𝑖	ADP
cana-1739	223	98	+	+	SYM
cana-1739	223	99	𝜈(𝑡	𝜈(𝑡	X
cana-1739	223	100	)	)	PUNCT
cana-1739	223	101	𝐴𝐵(𝜈(𝑡))	𝐴𝐵(𝜈(𝑡))	PROPN
cana-1739	223	102	⎾	⎾	NUM
cana-1739	223	103	𝜈(𝑡	𝜈(𝑡	PRON
cana-1739	223	104	)	)	PUNCT
cana-1739	223	105	𝛿𝑖𝜇	𝛿𝑖𝜇	NOUN
cana-1739	223	106	]	]	PUNCT
cana-1739	223	107	≤	≤	NOUN
cana-1739	223	108	1	1	NUM
cana-1739	224	1	𝑓𝑜𝑟	𝑓𝑜𝑟	NOUN
cana-1739	224	2	𝑖	𝑖	NOUN
cana-1739	224	3	=	=	NOUN
cana-1739	224	4	1,2,3,4	1,2,3,4	NUM
cana-1739	224	5	proof	proof	NOUN
cana-1739	224	6	consider	consider	VERB
cana-1739	224	7	,	,	PUNCT
cana-1739	224	8	‖𝜃1𝑛‖	‖𝜃1𝑛‖	NOUN
cana-1739	224	9	≤	≤	NOUN
cana-1739	224	10	‖𝐺𝑛(0)‖	‖𝐺𝑛(0)‖	NOUN
cana-1739	224	11	[	[	PUNCT
cana-1739	224	12	1	1	NUM
cana-1739	224	13	−	−	NOUN
cana-1739	224	14	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	224	15	)	)	PUNCT
cana-1739	224	16	𝐴𝐵(𝜈(𝑡	𝐴𝐵(𝜈(𝑡	NOUN
cana-1739	224	17	)	)	PUNCT
cana-1739	224	18	)	)	PUNCT
cana-1739	225	1	𝛿𝑖	𝛿𝑖	ADP
cana-1739	225	2	+	+	SYM
cana-1739	225	3	𝜈(𝑡	𝜈(𝑡	X
cana-1739	225	4	)	)	PUNCT
cana-1739	225	5	𝐴𝐵(𝜈(𝑡))	𝐴𝐵(𝜈(𝑡))	PROPN
cana-1739	225	6	⎾	⎾	NUM
cana-1739	225	7	𝜈(𝑡	𝜈(𝑡	PRON
cana-1739	225	8	)	)	PUNCT
cana-1739	225	9	𝛿𝑖𝜇	𝛿𝑖𝜇	PROPN
cana-1739	225	10	]	]	PUNCT
cana-1739	225	11	𝑛	𝑛	PRON
cana-1739	225	12	similarly,‖𝜃2𝑛‖	similarly,‖𝜃2𝑛‖	NOUN
cana-1739	225	13	,	,	PUNCT
cana-1739	225	14	‖𝜃3𝑛‖	‖𝜃3𝑛‖	NOUN
cana-1739	225	15	and	and	CCONJ
cana-1739	225	16	‖𝜃4𝑛‖	‖𝜃4𝑛‖	NOUN
cana-1739	225	17	can	can	AUX
cana-1739	225	18	also	also	ADV
cana-1739	225	19	be	be	AUX
cana-1739	225	20	obtained	obtain	VERB
cana-1739	225	21	communications	communication	NOUN
cana-1739	225	22	on	on	ADP
cana-1739	225	23	applied	apply	VERB
cana-1739	225	24	nonlinear	nonlinear	ADJ
cana-1739	225	25	analysis	analysis	NOUN
cana-1739	225	26	issn	issn	NOUN
cana-1739	225	27	:	:	PUNCT
cana-1739	225	28	1074	1074	NUM
cana-1739	225	29	-	-	PUNCT
cana-1739	225	30	133x	133x	NUM
cana-1739	225	31	vol	vol	NOUN
cana-1739	225	32	32	32	NUM
cana-1739	225	33	no	no	NOUN
cana-1739	225	34	.	.	NOUN
cana-1739	225	35	2	2	NUM
cana-1739	225	36	(	(	PUNCT
cana-1739	225	37	2025	2025	NUM
cana-1739	225	38	)	)	PUNCT
cana-1739	225	39	243	243	NUM
cana-1739	225	40	https://internationalpubls.com	https://internationalpubls.com	X
cana-1739	225	41	these	these	DET
cana-1739	225	42	results	result	NOUN
cana-1739	225	43	proved	prove	VERB
cana-1739	225	44	the	the	DET
cana-1739	225	45	existence	existence	NOUN
cana-1739	225	46	and	and	CCONJ
cana-1739	225	47	continuity	continuity	NOUN
cana-1739	225	48	of	of	ADP
cana-1739	225	49	solution	solution	NOUN
cana-1739	225	50	.	.	PUNCT
cana-1739	226	1	now	now	ADV
cana-1739	226	2	to	to	PART
cana-1739	226	3	show	show	VERB
cana-1739	226	4	that	that	SCONJ
cana-1739	226	5	𝐺(𝑡	𝐺(𝑡	NOUN
cana-1739	226	6	)	)	PUNCT
cana-1739	226	7	,	,	PUNCT
cana-1739	226	8	𝐶(𝑡	𝐶(𝑡	NOUN
cana-1739	226	9	)	)	PUNCT
cana-1739	226	10	,	,	PUNCT
cana-1739	226	11	𝐼(𝑡	𝐼(𝑡	NUM
cana-1739	226	12	)	)	PUNCT
cana-1739	226	13	and	and	CCONJ
cana-1739	226	14	𝐻(𝑡	𝐻(𝑡	PRON
cana-1739	226	15	)	)	PUNCT
cana-1739	226	16	are	be	AUX
cana-1739	226	17	solutions	solution	NOUN
cana-1739	226	18	of	of	ADP
cana-1739	226	19	(	(	PUNCT
cana-1739	226	20	11	11	NUM
cana-1739	226	21	)	)	PUNCT
cana-1739	226	22	consider	consider	VERB
cana-1739	226	23	𝐺(𝑡	𝐺(𝑡	NOUN
cana-1739	226	24	)	)	PUNCT
cana-1739	226	25	−	−	NUM
cana-1739	226	26	𝐺(0	𝐺(0	NUM
cana-1739	226	27	)	)	PUNCT
cana-1739	226	28	=	=	SYM
cana-1739	226	29	𝐺𝑛(𝑡	𝐺𝑛(𝑡	NOUN
cana-1739	226	30	)	)	PUNCT
cana-1739	226	31	−	−	PROPN
cana-1739	226	32	𝐸1𝑛(𝑡	𝐸1𝑛(𝑡	PROPN
cana-1739	226	33	)	)	PUNCT
cana-1739	226	34	𝐶(𝑡	𝐶(𝑡	NOUN
cana-1739	226	35	)	)	PUNCT
cana-1739	226	36	−	−	NUM
cana-1739	226	37	𝐶(0	𝐶(0	NOUN
cana-1739	226	38	)	)	PUNCT
cana-1739	226	39	=	=	SYM
cana-1739	226	40	𝐶𝑛(𝑡	𝐶𝑛(𝑡	NOUN
cana-1739	226	41	)	)	PUNCT
cana-1739	226	42	−	−	ADP
cana-1739	226	43	𝐸2𝑛(𝑡	𝐸2𝑛(𝑡	SYM
cana-1739	226	44	)	)	PUNCT
cana-1739	226	45	𝐼(𝑡	𝐼(𝑡	NOUN
cana-1739	226	46	)	)	PUNCT
cana-1739	226	47	−	−	NOUN
cana-1739	226	48	𝐼(0	𝐼(0	NOUN
cana-1739	226	49	)	)	PUNCT
cana-1739	226	50	=	=	SYM
cana-1739	226	51	𝐼𝑛(𝑡	𝐼𝑛(𝑡	PROPN
cana-1739	226	52	)	)	PUNCT
cana-1739	226	53	−	−	ADP
cana-1739	226	54	𝐸3𝑛(𝑡	𝐸3𝑛(𝑡	PROPN
cana-1739	226	55	)	)	PUNCT
cana-1739	226	56	𝐻(𝑡	𝐻(𝑡	NOUN
cana-1739	226	57	)	)	PUNCT
cana-1739	226	58	−	−	NUM
cana-1739	226	59	𝐻(0	𝐻(0	NUM
cana-1739	226	60	)	)	PUNCT
cana-1739	226	61	=	=	SYM
cana-1739	226	62	𝐻𝑛(𝑡	𝐻𝑛(𝑡	PROPN
cana-1739	226	63	)	)	PUNCT
cana-1739	226	64	−	−	NOUN
cana-1739	226	65	𝐸4𝑛(𝑡	𝐸4𝑛(𝑡	NOUN
cana-1739	226	66	)	)	PUNCT
cana-1739	226	67	now	now	ADV
cana-1739	226	68	‖𝐸1𝑛(𝑡)‖	‖𝐸1𝑛(𝑡)‖	PROPN
cana-1739	226	69	≤	≤	NOUN
cana-1739	226	70	1−𝜈(𝑡	1−𝜈(𝑡	NUM
cana-1739	226	71	)	)	PUNCT
cana-1739	226	72	𝐴𝐵(𝜈(𝑡	𝐴𝐵(𝜈(𝑡	NOUN
cana-1739	226	73	)	)	PUNCT
cana-1739	226	74	)	)	PUNCT
cana-1739	226	75	‖[𝐹1(𝑡	‖[𝐹1(𝑡	NOUN
cana-1739	226	76	,	,	PUNCT
cana-1739	226	77	𝐺𝑛	𝐺𝑛	NOUN
cana-1739	226	78	)	)	PUNCT
cana-1739	226	79	−	−	NOUN
cana-1739	227	1	𝐹1(𝑡	𝐹1(𝑡	PROPN
cana-1739	227	2	,	,	PUNCT
cana-1739	227	3	𝐺𝑛−1)]‖	𝐺𝑛−1)]‖	X
cana-1739	227	4	+	+	CCONJ
cana-1739	227	5	𝜈(𝑡	𝜈(𝑡	ADJ
cana-1739	227	6	)	)	PUNCT
cana-1739	227	7	𝐴𝐵(𝜈(𝑡))	𝐴𝐵(𝜈(𝑡))	PROPN
cana-1739	227	8	⎾	⎾	NUM
cana-1739	227	9	𝜈(𝑡	𝜈(𝑡	PRON
cana-1739	227	10	)	)	PUNCT
cana-1739	227	11	∫	∫	PROPN
cana-1739	227	12	(	(	PUNCT
cana-1739	227	13	𝑡	𝑡	PROPN
cana-1739	227	14	−	−	PROPN
cana-1739	227	15	𝛾)𝛼(𝑡)−1‖[𝐹1(𝛾	𝛾)𝛼(𝑡)−1‖[𝐹1(𝛾	ADJ
cana-1739	227	16	,	,	PUNCT
cana-1739	227	17	𝐺𝑛	𝐺𝑛	NOUN
cana-1739	227	18	)	)	PUNCT
cana-1739	227	19	−	−	PROPN
cana-1739	227	20	𝑡	𝑡	PROPN
cana-1739	227	21	0	0	PROPN
cana-1739	227	22	𝐹1(𝛾	𝐹1(𝛾	PROPN
cana-1739	227	23	,	,	PUNCT
cana-1739	227	24	𝐺𝑛−1)]‖	𝐺𝑛−1)]‖	PROPN
cana-1739	227	25	𝑑𝛾	𝑑𝛾	PROPN
cana-1739	227	26	≤	≤	NUM
cana-1739	227	27	1−𝜈(𝑡	1−𝜈(𝑡	NUM
cana-1739	227	28	)	)	PUNCT
cana-1739	227	29	𝐴𝐵(𝜈(𝑡	𝐴𝐵(𝜈(𝑡	NOUN
cana-1739	227	30	)	)	PUNCT
cana-1739	227	31	)	)	PUNCT
cana-1739	228	1	𝛿1‖𝐺𝑛	𝛿1‖𝐺𝑛	PROPN
cana-1739	228	2	−	−	PROPN
cana-1739	228	3	𝐺𝑛−1‖	𝐺𝑛−1‖	PROPN
cana-1739	228	4	+	+	CCONJ
cana-1739	228	5	𝜈(𝑡	𝜈(𝑡	ADJ
cana-1739	228	6	)	)	PUNCT
cana-1739	228	7	𝐴𝐵(𝜈(𝑡))	𝐴𝐵(𝜈(𝑡))	PROPN
cana-1739	228	8	⎾	⎾	NUM
cana-1739	228	9	𝜈(𝑡	𝜈(𝑡	X
cana-1739	228	10	)	)	PUNCT
cana-1739	228	11	𝛿1‖𝐺𝑛	𝛿1‖𝐺𝑛	PROPN
cana-1739	228	12	−	−	NOUN
cana-1739	228	13	𝐺𝑛−1‖𝜇	𝐺𝑛−1‖𝜇	X
cana-1739	228	14	≤	≤	PROPN
cana-1739	228	15	[	[	PUNCT
cana-1739	228	16	1−𝜈(𝑡	1−𝜈(𝑡	NUM
cana-1739	228	17	)	)	PUNCT
cana-1739	228	18	𝐴𝐵(𝜈(𝑡	𝐴𝐵(𝜈(𝑡	NOUN
cana-1739	228	19	)	)	PUNCT
cana-1739	228	20	)	)	PUNCT
cana-1739	228	21	𝛿1	𝛿1	NOUN
cana-1739	228	22	+	+	CCONJ
cana-1739	228	23	𝜈(𝑡	𝜈(𝑡	ADJ
cana-1739	228	24	)	)	PUNCT
cana-1739	228	25	𝐴𝐵(𝜈(𝑡))	𝐴𝐵(𝜈(𝑡))	PROPN
cana-1739	228	26	⎾	⎾	NUM
cana-1739	228	27	𝜈(𝑡	𝜈(𝑡	X
cana-1739	228	28	)	)	PUNCT
cana-1739	228	29	𝛿1𝜇	𝛿1𝜇	PROPN
cana-1739	228	30	]	]	X
cana-1739	228	31	‖𝐺𝑛	‖𝐺𝑛	PROPN
cana-1739	228	32	−	−	PROPN
cana-1739	228	33	𝐺𝑛−1‖	𝐺𝑛−1‖	PROPN
cana-1739	228	34	applying	apply	VERB
cana-1739	228	35	the	the	DET
cana-1739	228	36	above	above	ADJ
cana-1739	228	37	process	process	NOUN
cana-1739	228	38	recursively	recursively	ADV
cana-1739	228	39	‖𝐸1𝑛(𝑡)‖	‖𝐸1𝑛(𝑡)‖	PROPN
cana-1739	228	40	≤	≤	NOUN
cana-1739	228	41	[	[	PUNCT
cana-1739	228	42	1	1	NUM
cana-1739	228	43	−	−	NOUN
cana-1739	228	44	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	228	45	)	)	PUNCT
cana-1739	228	46	𝐴𝐵(𝜈(𝑡	𝐴𝐵(𝜈(𝑡	NOUN
cana-1739	228	47	)	)	PUNCT
cana-1739	228	48	)	)	PUNCT
cana-1739	228	49	𝛿1	𝛿1	NOUN
cana-1739	228	50	+	+	CCONJ
cana-1739	228	51	𝜈(𝑡	𝜈(𝑡	ADJ
cana-1739	228	52	)	)	PUNCT
cana-1739	228	53	𝐴𝐵(𝜈(𝑡))	𝐴𝐵(𝜈(𝑡))	PROPN
cana-1739	228	54	⎾	⎾	NUM
cana-1739	228	55	𝜈(𝑡	𝜈(𝑡	X
cana-1739	228	56	)	)	PUNCT
cana-1739	228	57	𝛿1𝜇	𝛿1𝜇	PROPN
cana-1739	228	58	]	]	X
cana-1739	228	59	𝑛+1	𝑛+1	PROPN
cana-1739	228	60	.𝑊	.𝑊	PROPN
cana-1739	228	61	where	where	SCONJ
cana-1739	228	62	w	w	NOUN
cana-1739	228	63	is	be	AUX
cana-1739	228	64	the	the	DET
cana-1739	228	65	lipschitz	lipschitz	NOUN
cana-1739	228	66	constant	constant	ADJ
cana-1739	228	67	when	when	SCONJ
cana-1739	228	68	𝑛	𝑛	PROPN
cana-1739	228	69	→	→	SYM
cana-1739	228	70	∞	∞	PROPN
cana-1739	228	71	,	,	PUNCT
cana-1739	228	72	‖𝐸1𝑛‖	‖𝐸1𝑛‖	NOUN
cana-1739	228	73	→	→	SYM
cana-1739	228	74	0	0	NUM
cana-1739	228	75	similarly	similarly	ADV
cana-1739	228	76	we	we	PRON
cana-1739	228	77	prove	prove	VERB
cana-1739	228	78	for	for	ADP
cana-1739	228	79	‖𝐸2𝑛‖	‖𝐸2𝑛‖	NOUN
cana-1739	228	80	→	→	SYM
cana-1739	228	81	0	0	NUM
cana-1739	228	82	,	,	PUNCT
cana-1739	228	83	‖𝐸3𝑛‖	‖𝐸3𝑛‖	ADJ
cana-1739	228	84	→	→	SYM
cana-1739	228	85	0	0	NUM
cana-1739	228	86	and	and	CCONJ
cana-1739	228	87	‖𝐸4𝑛‖	‖𝐸4𝑛‖	NUM
cana-1739	228	88	→	→	SYM
cana-1739	228	89	0	0	NUM
cana-1739	228	90	as	as	ADP
cana-1739	228	91	𝑛	𝑛	PROPN
cana-1739	228	92	→	→	SYM
cana-1739	228	93	∞	∞	PROPN
cana-1739	228	94	hence	hence	ADV
cana-1739	228	95	the	the	DET
cana-1739	228	96	proof	proof	NOUN
cana-1739	228	97	.	.	PUNCT
cana-1739	229	1	theorem	theorem	VERB
cana-1739	229	2	4.3.3	4.3.3	NUM
cana-1739	229	3	if	if	SCONJ
cana-1739	229	4	the	the	DET
cana-1739	229	5	condition	condition	NOUN
cana-1739	229	6	[	[	X
cana-1739	229	7	1	1	NUM
cana-1739	229	8	−	−	PROPN
cana-1739	229	9	[	[	PUNCT
cana-1739	229	10	1−𝜈(𝑡	1−𝜈(𝑡	NUM
cana-1739	229	11	)	)	PUNCT
cana-1739	229	12	𝐴𝐵(𝜈(𝑡	𝐴𝐵(𝜈(𝑡	NOUN
cana-1739	229	13	)	)	PUNCT
cana-1739	229	14	)	)	PUNCT
cana-1739	229	15	𝛿𝑖	𝛿𝑖	ADP
cana-1739	229	16	+	+	SYM
cana-1739	229	17	𝜈(𝑡	𝜈(𝑡	X
cana-1739	229	18	)	)	PUNCT
cana-1739	229	19	𝐴𝐵(𝜈(𝑡))	𝐴𝐵(𝜈(𝑡))	PROPN
cana-1739	229	20	⎾	⎾	NUM
cana-1739	229	21	𝜈(𝑡	𝜈(𝑡	PRON
cana-1739	229	22	)	)	PUNCT
cana-1739	229	23	𝛿𝑖𝜇	𝛿𝑖𝜇	NOUN
cana-1739	229	24	]	]	X
cana-1739	229	25	]	]	X
cana-1739	229	26	≥	≥	X
cana-1739	229	27	0	0	NUM
cana-1739	229	28	for	for	ADP
cana-1739	229	29	i=1,2,3,4	i=1,2,3,4	ADJ
cana-1739	229	30	holds	hold	NOUN
cana-1739	229	31	then	then	ADV
cana-1739	229	32	the	the	DET
cana-1739	229	33	atanganabaleanu	atanganabaleanu	NOUN
cana-1739	229	34	fractional	fractional	ADJ
cana-1739	229	35	derivative	derivative	ADJ
cana-1739	229	36	model	model	NOUN
cana-1739	229	37	have	have	VERB
cana-1739	229	38	unique	unique	ADJ
cana-1739	229	39	solutions	solution	NOUN
cana-1739	229	40	.	.	PUNCT
cana-1739	230	1	proof	proof	NOUN
cana-1739	230	2	suppose	suppose	VERB
cana-1739	230	3	the	the	DET
cana-1739	230	4	system	system	NOUN
cana-1739	230	5	(	(	PUNCT
cana-1739	230	6	16	16	NUM
cana-1739	230	7	)	)	PUNCT
cana-1739	230	8	has	have	VERB
cana-1739	230	9	another	another	DET
cana-1739	230	10	solution	solution	NOUN
cana-1739	230	11	𝐺	𝐺	NOUN
cana-1739	230	12	̅	̅	NOUN
cana-1739	230	13	,	,	PUNCT
cana-1739	230	14	𝐶	𝐶	PROPN
cana-1739	230	15	̅	̅	NOUN
cana-1739	230	16	,	,	PUNCT
cana-1739	230	17	𝐼	𝐼	ADP
cana-1739	230	18	̅	̅	NOUN
cana-1739	230	19	and	and	CCONJ
cana-1739	230	20	𝐻	𝐻	PROPN
cana-1739	230	21	̅̅	̅̅	NOUN
cana-1739	230	22	̅then	̅then	ADV
cana-1739	230	23	𝐺(𝑡	𝐺(𝑡	ADJ
cana-1739	230	24	)	)	PUNCT
cana-1739	230	25	−	−	ADP
cana-1739	230	26	�	�	PROPN
cana-1739	230	27	̅	̅	NOUN
cana-1739	230	28	�	�	NOUN
cana-1739	230	29	(𝑡	(𝑡	NOUN
cana-1739	230	30	)	)	PUNCT
cana-1739	230	31	=	=	SYM
cana-1739	230	32	1	1	NUM
cana-1739	230	33	−	−	NOUN
cana-1739	230	34	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	230	35	)	)	PUNCT
cana-1739	230	36	𝐴𝐵(𝜈(𝑡	𝐴𝐵(𝜈(𝑡	NOUN
cana-1739	230	37	)	)	PUNCT
cana-1739	230	38	)	)	PUNCT
cana-1739	231	1	[	[	X
cana-1739	231	2	𝐹1(𝑡	𝐹1(𝑡	X
cana-1739	231	3	,	,	PUNCT
cana-1739	231	4	𝐺	𝐺	PROPN
cana-1739	231	5	)	)	PUNCT
cana-1739	231	6	−	−	PROPN
cana-1739	231	7	𝐹1(𝑡	𝐹1(𝑡	PROPN
cana-1739	231	8	,	,	PUNCT
cana-1739	231	9	�	�	PROPN
cana-1739	231	10	̅	̅	NOUN
cana-1739	231	11	�	�	NOUN
cana-1739	231	12	)	)	PUNCT
cana-1739	231	13	]	]	PUNCT
cana-1739	232	1	+	+	CCONJ
cana-1739	232	2	𝜈(𝑡	𝜈(𝑡	X
cana-1739	232	3	)	)	PUNCT
cana-1739	232	4	𝐴𝐵(𝜈(𝑡))	𝐴𝐵(𝜈(𝑡))	PROPN
cana-1739	232	5	⎾	⎾	NUM
cana-1739	232	6	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	232	7	)	)	PUNCT
cana-1739	233	1	∫(𝑡	∫(𝑡	ADJ
cana-1739	233	2	−	−	PROPN
cana-1739	233	3	𝛾)𝛼(𝑡)−1[𝐹1(𝛾	𝛾)𝛼(𝑡)−1[𝐹1(𝛾	NOUN
cana-1739	233	4	,	,	PUNCT
cana-1739	233	5	𝐺	𝐺	NOUN
cana-1739	233	6	)	)	PUNCT
cana-1739	233	7	−	−	PROPN
cana-1739	233	8	𝐹1(𝛾	𝐹1(𝛾	PROPN
cana-1739	233	9	,	,	PUNCT
cana-1739	233	10	�	�	PROPN
cana-1739	233	11	̅	̅	NOUN
cana-1739	233	12	�	�	NOUN
cana-1739	233	13	)]𝑑𝛾	)]𝑑𝛾	PUNCT
cana-1739	233	14	𝑡	𝑡	X
cana-1739	233	15	0	0	PUNCT
cana-1739	233	16	using	use	VERB
cana-1739	233	17	norm	norm	NOUN
cana-1739	233	18	and	and	CCONJ
cana-1739	233	19	apply	apply	VERB
cana-1739	233	20	lipschitz	lipschitz	NOUN
cana-1739	233	21	condition	condition	NOUN
cana-1739	233	22	communications	communication	NOUN
cana-1739	233	23	on	on	ADP
cana-1739	233	24	applied	apply	VERB
cana-1739	233	25	nonlinear	nonlinear	ADJ
cana-1739	233	26	analysis	analysis	NOUN
cana-1739	233	27	issn	issn	NOUN
cana-1739	233	28	:	:	PUNCT
cana-1739	233	29	1074	1074	NUM
cana-1739	233	30	-	-	PUNCT
cana-1739	233	31	133x	133x	NUM
cana-1739	233	32	vol	vol	NOUN
cana-1739	233	33	32	32	NUM
cana-1739	233	34	no	no	NOUN
cana-1739	233	35	.	.	NOUN
cana-1739	233	36	2	2	NUM
cana-1739	233	37	(	(	PUNCT
cana-1739	233	38	2025	2025	NUM
cana-1739	233	39	)	)	PUNCT
cana-1739	233	40	244	244	NUM
cana-1739	233	41	https://internationalpubls.com	https://internationalpubls.com	X
cana-1739	233	42	‖𝐺(𝑡	‖𝐺(𝑡	NOUN
cana-1739	233	43	)	)	PUNCT
cana-1739	233	44	−	−	ADP
cana-1739	233	45	�	�	NOUN
cana-1739	233	46	̅	̅	VERB
cana-1739	233	47	�	�	NOUN
cana-1739	233	48	(𝑡)‖	(𝑡)‖	NOUN
cana-1739	233	49	≤	≤	NUM
cana-1739	233	50	(	(	PUNCT
cana-1739	233	51	[	[	PUNCT
cana-1739	233	52	1−𝜈(𝑡	1−𝜈(𝑡	NUM
cana-1739	233	53	)	)	PUNCT
cana-1739	233	54	𝐴𝐵(𝜈(𝑡	𝐴𝐵(𝜈(𝑡	NOUN
cana-1739	233	55	)	)	PUNCT
cana-1739	233	56	)	)	PUNCT
cana-1739	234	1	𝛿1	𝛿1	NOUN
cana-1739	234	2	+	+	CCONJ
cana-1739	234	3	𝜈(𝑡	𝜈(𝑡	ADJ
cana-1739	234	4	)	)	PUNCT
cana-1739	234	5	𝐴𝐵(𝜈(𝑡))	𝐴𝐵(𝜈(𝑡))	PROPN
cana-1739	234	6	⎾	⎾	NUM
cana-1739	234	7	𝜈(𝑡	𝜈(𝑡	X
cana-1739	234	8	)	)	PUNCT
cana-1739	234	9	𝛿1𝜇	𝛿1𝜇	PROPN
cana-1739	234	10	]	]	X
cana-1739	234	11	‖𝐺(𝑡	‖𝐺(𝑡	NOUN
cana-1739	234	12	)	)	PUNCT
cana-1739	234	13	−	−	PROPN
cana-1739	234	14	�	�	SYM
cana-1739	234	15	̅	̅	NOUN
cana-1739	234	16	�	�	NOUN
cana-1739	234	17	(𝑡)‖	(𝑡)‖	NOUN
cana-1739	234	18	)	)	PUNCT
cana-1739	234	19	consequently	consequently	ADV
cana-1739	234	20	we	we	PRON
cana-1739	234	21	have	have	VERB
cana-1739	234	22	[	[	X
cana-1739	234	23	1	1	NUM
cana-1739	234	24	−	−	NOUN
cana-1739	234	25	[	[	PUNCT
cana-1739	234	26	1	1	NUM
cana-1739	234	27	−	−	NOUN
cana-1739	234	28	𝜈(𝑡	𝜈(𝑡	NOUN
cana-1739	234	29	)	)	PUNCT
cana-1739	234	30	𝐴𝐵(𝜈(𝑡	𝐴𝐵(𝜈(𝑡	NOUN
cana-1739	234	31	)	)	PUNCT
cana-1739	234	32	)	)	PUNCT
cana-1739	235	1	𝛿1	𝛿1	NOUN
cana-1739	235	2	+	+	CCONJ
cana-1739	235	3	𝜈(𝑡	𝜈(𝑡	ADJ
cana-1739	235	4	)	)	PUNCT
cana-1739	235	5	𝐴𝐵(𝜈(𝑡))	𝐴𝐵(𝜈(𝑡))	PROPN
cana-1739	235	6	⎾	⎾	NUM
cana-1739	235	7	𝜈(𝑡	𝜈(𝑡	X
cana-1739	235	8	)	)	PUNCT
cana-1739	235	9	𝛿1𝜇	𝛿1𝜇	PROPN
cana-1739	235	10	]	]	X
cana-1739	235	11	]	]	X
cana-1739	235	12	‖𝐺(𝑡	‖𝐺(𝑡	NOUN
cana-1739	235	13	)	)	PUNCT
cana-1739	235	14	−	−	PROPN
cana-1739	235	15	�	�	NOUN
cana-1739	235	16	̅	̅	VERB
cana-1739	235	17	�	�	NOUN
cana-1739	235	18	(𝑡)‖	(𝑡)‖	NOUN
cana-1739	235	19	≤	≤	NUM
cana-1739	235	20	0	0	NUM
cana-1739	236	1	since[1	since[1	NUM
cana-1739	236	2	−	−	PROPN
cana-1739	236	3	[	[	PUNCT
cana-1739	236	4	1−𝜈(𝑡	1−𝜈(𝑡	NUM
cana-1739	236	5	)	)	PUNCT
cana-1739	236	6	𝐴𝐵(𝜈(𝑡	𝐴𝐵(𝜈(𝑡	NOUN
cana-1739	236	7	)	)	PUNCT
cana-1739	236	8	)	)	PUNCT
cana-1739	237	1	𝛿𝑖	𝛿𝑖	ADP
cana-1739	237	2	+	+	SYM
cana-1739	237	3	𝜈(𝑡	𝜈(𝑡	X
cana-1739	237	4	)	)	PUNCT
cana-1739	237	5	𝐴𝐵(𝜈(𝑡))	𝐴𝐵(𝜈(𝑡))	PROPN
cana-1739	237	6	⎾	⎾	NUM
cana-1739	237	7	𝜈(𝑡	𝜈(𝑡	PRON
cana-1739	237	8	)	)	PUNCT
cana-1739	237	9	𝛿𝑖𝜇	𝛿𝑖𝜇	NOUN
cana-1739	237	10	]	]	X
cana-1739	237	11	]	]	PUNCT
cana-1739	238	1	>	>	X
cana-1739	238	2	0,we	0,we	PRON
cana-1739	238	3	have	have	VERB
cana-1739	238	4	‖𝐺(𝑡	‖𝐺(𝑡	NOUN
cana-1739	238	5	)	)	PUNCT
cana-1739	239	1	−	−	ADP
cana-1739	239	2	�	�	NOUN
cana-1739	239	3	̅	̅	NOUN
cana-1739	239	4	�	�	NOUN
cana-1739	239	5	(𝑡)‖	(𝑡)‖	SYM
cana-1739	239	6	=	=	SYM
cana-1739	239	7	0	0	NUM
cana-1739	239	8	therefore	therefore	ADV
cana-1739	239	9	,	,	PUNCT
cana-1739	239	10	𝐺(𝑡	𝐺(𝑡	NOUN
cana-1739	239	11	)	)	PUNCT
cana-1739	239	12	=	=	SYM
cana-1739	239	13	�	�	PROPN
cana-1739	239	14	̅	̅	NOUN
cana-1739	239	15	�	�	NOUN
cana-1739	239	16	(𝑡	(𝑡	NOUN
cana-1739	239	17	)	)	PUNCT
cana-1739	239	18	similarly	similarly	ADV
cana-1739	239	19	,	,	PUNCT
cana-1739	239	20	we	we	PRON
cana-1739	239	21	prove	prove	VERB
cana-1739	239	22	𝐶(𝑡	𝐶(𝑡	ADP
cana-1739	239	23	)	)	PUNCT
cana-1739	239	24	=	=	PUNCT
cana-1739	239	25	𝐶̅(𝑡	𝐶̅(𝑡	ADV
cana-1739	239	26	)	)	PUNCT
cana-1739	239	27	,	,	PUNCT
cana-1739	239	28	𝐼(𝑡	𝐼(𝑡	NUM
cana-1739	239	29	)	)	PUNCT
cana-1739	239	30	=	=	SYM
cana-1739	239	31	𝐼(̅𝑡	𝐼(̅𝑡	PROPN
cana-1739	239	32	)	)	PUNCT
cana-1739	239	33	and	and	CCONJ
cana-1739	239	34	𝐻(𝑡	𝐻(𝑡	NOUN
cana-1739	239	35	)	)	PUNCT
cana-1739	239	36	=	=	PUNCT
cana-1739	239	37	𝐻(𝑡	𝐻(𝑡	NOUN
cana-1739	239	38	)	)	PUNCT
cana-1739	239	39	hence	hence	ADV
cana-1739	239	40	the	the	DET
cana-1739	239	41	proof	proof	NOUN
cana-1739	239	42	5	5	NUM
cana-1739	239	43	.	.	PUNCT
cana-1739	239	44	numerical	numerical	ADJ
cana-1739	239	45	scheme	scheme	NOUN
cana-1739	239	46	in	in	ADP
cana-1739	239	47	this	this	DET
cana-1739	239	48	section	section	NOUN
cana-1739	239	49	numerical	numerical	ADJ
cana-1739	239	50	scheme	scheme	NOUN
cana-1739	240	1	[	[	X
cana-1739	240	2	31	31	NUM
cana-1739	240	3	]	]	PUNCT
cana-1739	240	4	is	be	AUX
cana-1739	240	5	considered	consider	VERB
cana-1739	240	6	in	in	ADP
cana-1739	240	7	the	the	DET
cana-1739	240	8	sense	sense	NOUN
cana-1739	240	9	of	of	ADP
cana-1739	240	10	liouville	liouville	NOUN
cana-1739	240	11	-	-	PUNCT
cana-1739	240	12	caputo	caputo	PROPN
cana-1739	240	13	,	,	PUNCT
cana-1739	240	14	caputofabrizio	caputofabrizio	PROPN
cana-1739	240	15	and	and	CCONJ
cana-1739	240	16	atangana	atangana	NOUN
cana-1739	240	17	–	–	PUNCT
cana-1739	240	18	baleanu	baleanu	ADJ
cana-1739	240	19	fractional	fractional	ADJ
cana-1739	240	20	derivatives	derivative	NOUN
cana-1739	240	21	.	.	PUNCT
cana-1739	241	1	let	let	VERB
cana-1739	241	2	us	we	PRON
cana-1739	241	3	consider	consider	VERB
cana-1739	241	4	our	our	PRON
cana-1739	241	5	fractional	fractional	ADJ
cana-1739	241	6	model	model	NOUN
cana-1739	241	7	as	as	ADP
cana-1739	241	8	𝐷𝑡	𝐷𝑡	PROPN
cana-1739	241	9	𝛼	𝛼	NOUN
cana-1739	241	10	0	0	NUM
cana-1739	241	11	∗	∗	NOUN
cana-1739	241	12	𝑢(𝑡	𝑢(𝑡	NOUN
cana-1739	241	13	)	)	PUNCT
cana-1739	242	1	=	=	SYM
cana-1739	242	2	𝑓(𝑡	𝑓(𝑡	NOUN
cana-1739	242	3	,	,	PUNCT
cana-1739	242	4	𝑢(𝑡	𝑢(𝑡	NOUN
cana-1739	242	5	)	)	PUNCT
cana-1739	242	6	)	)	PUNCT
cana-1739	242	7	where	where	SCONJ
cana-1739	242	8	*	*	PUNCT
cana-1739	242	9	denotes	denote	NOUN
cana-1739	242	10	lc	lc	PROPN
cana-1739	242	11	,	,	PUNCT
cana-1739	242	12	cf	cf	NOUN
cana-1739	242	13	and	and	CCONJ
cana-1739	242	14	ab	ab	PROPN
cana-1739	242	15	terms	term	NOUN
cana-1739	242	16	and	and	CCONJ
cana-1739	242	17	𝑢(𝑡	𝑢(𝑡	NOUN
cana-1739	242	18	)	)	PUNCT
cana-1739	242	19	=	=	PUNCT
cana-1739	242	20	(	(	PUNCT
cana-1739	242	21	𝐺(𝑡	𝐺(𝑡	NOUN
cana-1739	242	22	)	)	PUNCT
cana-1739	242	23	,	,	PUNCT
cana-1739	242	24	𝐶(𝑡	𝐶(𝑡	NOUN
cana-1739	242	25	)	)	PUNCT
cana-1739	242	26	,	,	PUNCT
cana-1739	242	27	𝐼(𝑡	𝐼(𝑡	PROPN
cana-1739	242	28	)	)	PUNCT
cana-1739	242	29	,	,	PUNCT
cana-1739	242	30	𝐻(𝑡	𝐻(𝑡	NOUN
cana-1739	242	31	)	)	PUNCT
cana-1739	242	32	)	)	PUNCT
cana-1739	242	33	.	.	PUNCT
cana-1739	243	1	now	now	ADV
cana-1739	243	2	we	we	PRON
cana-1739	243	3	use	use	VERB
cana-1739	243	4	the	the	DET
cana-1739	243	5	numerical	numerical	ADJ
cana-1739	243	6	scheme	scheme	NOUN
cana-1739	244	1	[	[	X
cana-1739	244	2	31	31	NUM
cana-1739	244	3	]	]	PUNCT
cana-1739	244	4	represented	represent	VERB
cana-1739	244	5	for	for	ADP
cana-1739	244	6	liouville	liouville	NOUN
cana-1739	244	7	-	-	PUNCT
cana-1739	244	8	caputo	caputo	PROPN
cana-1739	244	9	(	(	PUNCT
cana-1739	244	10	14	14	NUM
cana-1739	244	11	)	)	PUNCT
cana-1739	244	12	,	,	PUNCT
cana-1739	244	13	caputo	caputo	PROPN
cana-1739	244	14	-	-	PUNCT
cana-1739	244	15	fabrizio(15	fabrizio(15	NOUN
cana-1739	244	16	)	)	PUNCT
cana-1739	244	17	and	and	CCONJ
cana-1739	244	18	atangana	atangana	PROPN
cana-1739	244	19	-	-	PUNCT
cana-1739	244	20	baleanu(16	baleanu(16	NOUN
cana-1739	244	21	)	)	PUNCT
cana-1739	244	22	fractional	fractional	ADJ
cana-1739	244	23	derivatives	derivative	NOUN
cana-1739	244	24	in	in	ADP
cana-1739	244	25	(	(	PUNCT
cana-1739	244	26	2	2	NUM
cana-1739	244	27	)	)	PUNCT
cana-1739	244	28	𝑢𝑛+1(𝑡	𝑢𝑛+1(𝑡	PROPN
cana-1739	244	29	)	)	PUNCT
cana-1739	244	30	=	=	SYM
cana-1739	244	31	𝑢(0	𝑢(0	PROPN
cana-1739	244	32	)	)	PUNCT
cana-1739	244	33	+	+	CCONJ
cana-1739	244	34	1	1	NUM
cana-1739	244	35	⎾	⎾	NUM
cana-1739	244	36	ν(t	ν(t	NOUN
cana-1739	244	37	)	)	PUNCT
cana-1739	244	38	∑	∑	PROPN
cana-1739	244	39	(	(	PUNCT
cana-1739	244	40	ℎν(t)𝑓(𝑡𝑚	ℎν(t)𝑓(𝑡𝑚	PROPN
cana-1739	244	41	,	,	PUNCT
cana-1739	244	42	𝑢𝑚	𝑢𝑚	NOUN
cana-1739	244	43	)	)	PUNCT
cana-1739	244	44	ν(t)(ν(t)+1	ν(t)(ν(t)+1	NOUN
cana-1739	244	45	)	)	PUNCT
cana-1739	244	46	(	(	PUNCT
cana-1739	244	47	(	(	PUNCT
cana-1739	244	48	𝑛	𝑛	PRON
cana-1739	244	49	−	−	NOUN
cana-1739	244	50	𝑚	𝑚	NOUN
cana-1739	244	51	+	+	CCONJ
cana-1739	244	52	2	2	NUM
cana-1739	244	53	+	+	NUM
cana-1739	244	54	2𝛼	2𝛼	NUM
cana-1739	244	55	)	)	PUNCT
cana-1739	244	56	−	−	PROPN
cana-1739	244	57	ℎν(t)𝑓(𝑡𝑚−1	ℎν(t)𝑓(𝑡𝑚−1	PROPN
cana-1739	244	58	,	,	PUNCT
cana-1739	244	59	𝑢𝑚−1	𝑢𝑚−1	PROPN
cana-1739	244	60	)	)	PUNCT
cana-1739	244	61	ν(t)(ν(t)+1	ν(t)(ν(t)+1	NOUN
cana-1739	244	62	)	)	PUNCT
cana-1739	244	63	(	(	PUNCT
cana-1739	244	64	(	(	PUNCT
cana-1739	244	65	𝑛	𝑛	X
cana-1739	244	66	+	+	SYM
cana-1739	244	67	1	1	NUM
cana-1739	244	68	−	−	NOUN
cana-1739	244	69	𝑚)ν(t)+1	𝑚)ν(t)+1	NOUN
cana-1739	244	70	−	−	PROPN
cana-1739	244	71	(	(	PUNCT
cana-1739	244	72	𝑛	𝑛	PROPN
cana-1739	244	73	−	−	NOUN
cana-1739	244	74	𝑚)ν(t)(𝑛	𝑚)ν(t)(𝑛	NOUN
cana-1739	244	75	−	−	NOUN
cana-1739	244	76	𝑚	𝑚	NOUN
cana-1739	244	77	+	+	NOUN
cana-1739	244	78	1	1	NUM
cana-1739	244	79	+	+	NUM
cana-1739	244	80	ν(t	ν(t	NOUN
cana-1739	244	81	)	)	PUNCT
cana-1739	244	82	)	)	PUNCT
cana-1739	244	83	)	)	PUNCT
cana-1739	245	1	𝑛	𝑛	DET
cana-1739	245	2	𝑚=0	𝑚=0	PUNCT
cana-1739	245	3	(	(	PUNCT
cana-1739	245	4	14	14	NUM
cana-1739	245	5	)	)	PUNCT
cana-1739	245	6	(	(	PUNCT
cana-1739	245	7	𝑢𝑛+1	𝑢𝑛+1	X
cana-1739	245	8	)	)	PUNCT
cana-1739	245	9	=	=	PUNCT
cana-1739	245	10	(	(	PUNCT
cana-1739	245	11	𝑢𝑛	𝑢𝑛	NOUN
cana-1739	245	12	)	)	PUNCT
cana-1739	245	13	+	+	CCONJ
cana-1739	245	14	[	[	PUNCT
cana-1739	245	15	(	(	PUNCT
cana-1739	245	16	2−ν(t))(1−ν(t	2−ν(t))(1−ν(t	NOUN
cana-1739	245	17	)	)	PUNCT
cana-1739	245	18	)	)	PUNCT
cana-1739	245	19	2	2	NUM
cana-1739	246	1	+	+	NUM
cana-1739	246	2	3ℎ	3ℎ	NUM
cana-1739	246	3	4	4	NUM
cana-1739	246	4	ν(t)(2	ν(t)(2	NOUN
cana-1739	246	5	−	−	NOUN
cana-1739	246	6	ν(t	ν(t	NOUN
cana-1739	246	7	)	)	PUNCT
cana-1739	246	8	)	)	PUNCT
cana-1739	246	9	]	]	PUNCT
cana-1739	247	1	𝑓(𝑡𝑛	𝑓(𝑡𝑛	NOUN
cana-1739	247	2	,	,	PUNCT
cana-1739	247	3	𝑢𝑛	𝑢𝑛	NOUN
cana-1739	247	4	)	)	PUNCT
cana-1739	247	5	−	−	PROPN
cana-1739	247	6	[	[	PUNCT
cana-1739	247	7	(	(	PUNCT
cana-1739	247	8	2−ν(t))(1−ν(t	2−ν(t))(1−ν(t	NOUN
cana-1739	247	9	)	)	PUNCT
cana-1739	247	10	)	)	PUNCT
cana-1739	247	11	2	2	NUM
cana-1739	248	1	+	+	CCONJ
cana-1739	248	2	ℎ	ℎ	PROPN
cana-1739	248	3	4	4	NUM
cana-1739	248	4	ν(t	ν(t	NOUN
cana-1739	248	5	)	)	PUNCT
cana-1739	248	6	(	(	PUNCT
cana-1739	248	7	2	2	NUM
cana-1739	248	8	−	−	NOUN
cana-1739	248	9	ν(t	ν(t	NOUN
cana-1739	248	10	)	)	PUNCT
cana-1739	248	11	)	)	PUNCT
cana-1739	248	12	]	]	PUNCT
cana-1739	248	13	𝑓(𝑡𝑛−1	𝑓(𝑡𝑛−1	NOUN
cana-1739	248	14	,	,	PUNCT
cana-1739	248	15	𝑢𝑛−1	𝑢𝑛−1	NOUN
cana-1739	248	16	)	)	PUNCT
cana-1739	248	17	𝑢𝑛+1(𝑡	𝑢𝑛+1(𝑡	PROPN
cana-1739	248	18	)	)	PUNCT
cana-1739	248	19	=	=	SYM
cana-1739	248	20	𝑢(0	𝑢(0	PROPN
cana-1739	248	21	)	)	PUNCT
cana-1739	248	22	+	+	NUM
cana-1739	248	23	⎾	⎾	NUM
cana-1739	248	24	ν(t)(1−ν(t	ν(t)(1−ν(t	NUM
cana-1739	248	25	)	)	PUNCT
cana-1739	248	26	)	)	PUNCT
cana-1739	249	1	⎾	⎾	NUM
cana-1739	250	1	ν(t)(1−ν(t))+ν(t	ν(t)(1−ν(t))+ν(t	NOUN
cana-1739	250	2	)	)	PUNCT
cana-1739	250	3	𝑓(𝑡𝑛	𝑓(𝑡𝑛	NOUN
cana-1739	250	4	,	,	PUNCT
cana-1739	250	5	𝑢𝑛	𝑢𝑛	NOUN
cana-1739	250	6	)	)	PUNCT
cana-1739	250	7	(	(	PUNCT
cana-1739	250	8	15	15	X
cana-1739	250	9	)	)	PUNCT
cana-1739	250	10	communications	communication	NOUN
cana-1739	250	11	on	on	ADP
cana-1739	250	12	applied	apply	VERB
cana-1739	250	13	nonlinear	nonlinear	ADJ
cana-1739	250	14	analysis	analysis	NOUN
cana-1739	250	15	issn	issn	NOUN
cana-1739	250	16	:	:	PUNCT
cana-1739	250	17	1074	1074	NUM
cana-1739	250	18	-	-	PUNCT
cana-1739	250	19	133x	133x	NUM
cana-1739	250	20	vol	vol	NOUN
cana-1739	250	21	32	32	NUM
cana-1739	250	22	no	no	NOUN
cana-1739	250	23	.	.	NOUN
cana-1739	250	24	2	2	NUM
cana-1739	250	25	(	(	PUNCT
cana-1739	250	26	2025	2025	NUM
cana-1739	250	27	)	)	PUNCT
cana-1739	250	28	245	245	NUM
cana-1739	250	29	https://internationalpubls.com	https://internationalpubls.com	X
cana-1739	250	30	+	+	CCONJ
cana-1739	250	31	1	1	NUM
cana-1739	250	32	(	(	PUNCT
cana-1739	250	33	ν(t)+1)((1−ν(t))	ν(t)+1)((1−ν(t))	PROPN
cana-1739	250	34	⎾	⎾	NUM
cana-1739	250	35	ν(t))+ν(t	ν(t))+ν(t	NOUN
cana-1739	250	36	)	)	PUNCT
cana-1739	250	37	∑	∑	PUNCT
cana-1739	250	38	(	(	PUNCT
cana-1739	250	39	ℎν(t)𝑓(𝑡𝑚	ℎν(t)𝑓(𝑡𝑚	NOUN
cana-1739	250	40	,	,	PUNCT
cana-1739	250	41	𝑢𝑚	𝑢𝑚	NOUN
cana-1739	250	42	)	)	PUNCT
cana-1739	250	43	(	(	PUNCT
cana-1739	250	44	(	(	PUNCT
cana-1739	250	45	𝑛	𝑛	X
cana-1739	250	46	+	+	NOUN
cana-1739	250	47	1	1	NUM
cana-1739	250	48	−	−	NUM
cana-1739	250	49	𝑚)ν(t	𝑚)ν(t	NUM
cana-1739	250	50	)	)	PUNCT
cana-1739	250	51	(	(	PUNCT
cana-1739	250	52	𝑛	𝑛	PRON
cana-1739	250	53	−	−	NOUN
cana-1739	250	54	𝑚	𝑚	NOUN
cana-1739	250	55	+	+	CCONJ
cana-1739	250	56	2	2	NUM
cana-1739	250	57	+	+	NUM
cana-1739	250	58	ν(t	ν(t	NOUN
cana-1739	250	59	)	)	PUNCT
cana-1739	250	60	)	)	PUNCT
cana-1739	250	61	−	−	PROPN
cana-1739	251	1	(	(	PUNCT
cana-1739	251	2	𝑛	𝑛	PROPN
cana-1739	251	3	−	−	NOUN
cana-1739	251	4	𝑚)ν(t)(𝑛	𝑚)ν(t)(𝑛	NOUN
cana-1739	251	5	−	−	NOUN
cana-1739	251	6	𝑚	𝑚	NOUN
cana-1739	251	7	+	+	NOUN
cana-1739	251	8	2	2	NUM
cana-1739	251	9	+	+	NUM
cana-1739	251	10	2𝛼(𝑡	2𝛼(𝑡	NUM
cana-1739	251	11	)	)	PUNCT
cana-1739	251	12	)	)	PUNCT
cana-1739	252	1	−ℎν(t)𝑓(𝑡𝑚−1	−ℎν(t)𝑓(𝑡𝑚−1	PROPN
cana-1739	252	2	,	,	PUNCT
cana-1739	252	3	𝑢𝑚−1	𝑢𝑚−1	PROPN
cana-1739	252	4	)	)	PUNCT
cana-1739	252	5	(	(	PUNCT
cana-1739	252	6	(	(	PUNCT
cana-1739	252	7	𝑛	𝑛	X
cana-1739	252	8	+	+	SYM
cana-1739	252	9	1	1	NUM
cana-1739	252	10	−	−	NOUN
cana-1739	252	11	𝑚)ν(t)+1	𝑚)ν(t)+1	NOUN
cana-1739	252	12	−	−	PROPN
cana-1739	253	1	(	(	PUNCT
cana-1739	253	2	𝑛	𝑛	DET
cana-1739	253	3	−	−	NOUN
cana-1739	253	4	𝑚)ν(t	𝑚)ν(t	NUM
cana-1739	253	5	)	)	PUNCT
cana-1739	253	6	(	(	PUNCT
cana-1739	253	7	𝑛	𝑛	PRON
cana-1739	253	8	−	−	NOUN
cana-1739	253	9	𝑚	𝑚	NOUN
cana-1739	253	10	+	+	PROPN
cana-1739	253	11	1	1	NUM
cana-1739	253	12	+	+	NUM
cana-1739	253	13	ν(t	ν(t	NOUN
cana-1739	253	14	)	)	PUNCT
cana-1739	253	15	)	)	PUNCT
cana-1739	253	16	)	)	PUNCT
cana-1739	253	17	)	)	PUNCT
cana-1739	254	1	𝑛	𝑛	DET
cana-1739	254	2	𝑚=0	𝑚=0	PUNCT
cana-1739	254	3	(	(	PUNCT
cana-1739	254	4	16	16	NUM
cana-1739	254	5	)	)	PUNCT
cana-1739	254	6	6	6	NUM
cana-1739	254	7	.	.	PUNCT
cana-1739	254	8	results	result	NOUN
cana-1739	254	9	and	and	CCONJ
cana-1739	254	10	discussions	discussion	NOUN
cana-1739	254	11	the	the	DET
cana-1739	254	12	primary	primary	ADJ
cana-1739	254	13	aim	aim	NOUN
cana-1739	254	14	of	of	ADP
cana-1739	254	15	our	our	PRON
cana-1739	254	16	model	model	NOUN
cana-1739	254	17	is	be	AUX
cana-1739	254	18	to	to	PART
cana-1739	254	19	effectively	effectively	ADV
cana-1739	254	20	address	address	VERB
cana-1739	254	21	the	the	DET
cana-1739	254	22	adverse	adverse	ADJ
cana-1739	254	23	effects	effect	NOUN
cana-1739	254	24	of	of	ADP
cana-1739	254	25	greenhouse	greenhouse	NOUN
cana-1739	254	26	gases	gas	NOUN
cana-1739	254	27	(	(	PUNCT
cana-1739	254	28	ghgs	ghg	VERB
cana-1739	254	29	)	)	PUNCT
cana-1739	254	30	by	by	ADP
cana-1739	254	31	integrating	integrate	VERB
cana-1739	254	32	them	they	PRON
cana-1739	254	33	into	into	ADP
cana-1739	254	34	green	green	ADJ
cana-1739	254	35	building	building	NOUN
cana-1739	254	36	systems	system	NOUN
cana-1739	254	37	using	use	VERB
cana-1739	254	38	a	a	DET
cana-1739	254	39	fractional	fractional	ADJ
cana-1739	254	40	model	model	NOUN
cana-1739	254	41	.	.	PUNCT
cana-1739	255	1	existence	existence	NOUN
cana-1739	255	2	and	and	CCONJ
cana-1739	255	3	uniqueness	uniqueness	NOUN
cana-1739	255	4	of	of	ADP
cana-1739	255	5	the	the	DET
cana-1739	255	6	fractional	fractional	ADJ
cana-1739	255	7	operators	operator	NOUN
cana-1739	255	8	are	be	AUX
cana-1739	255	9	established	establish	VERB
cana-1739	255	10	.	.	PUNCT
cana-1739	256	1	numerical	numerical	PROPN
cana-1739	256	2	or	or	CCONJ
cana-1739	256	3	computer	computer	NOUN
cana-1739	256	4	simulations	simulation	NOUN
cana-1739	256	5	are	be	AUX
cana-1739	256	6	considered	consider	VERB
cana-1739	256	7	the	the	DET
cana-1739	256	8	most	most	ADV
cana-1739	256	9	appropriate	appropriate	ADJ
cana-1739	256	10	method	method	NOUN
cana-1739	256	11	to	to	PART
cana-1739	256	12	accurately	accurately	ADV
cana-1739	256	13	represent	represent	VERB
cana-1739	256	14	the	the	DET
cana-1739	256	15	solution	solution	NOUN
cana-1739	256	16	.	.	PUNCT
cana-1739	257	1	we	we	PRON
cana-1739	257	2	employed	employ	VERB
cana-1739	257	3	matlab	matlab	NOUN
cana-1739	257	4	r2023a	r2023a	ADJ
cana-1739	257	5	programming	programming	NOUN
cana-1739	257	6	language	language	NOUN
cana-1739	257	7	to	to	PART
cana-1739	257	8	conduct	conduct	VERB
cana-1739	257	9	numerical	numerical	ADJ
cana-1739	257	10	simulations	simulation	NOUN
cana-1739	257	11	of	of	ADP
cana-1739	257	12	the	the	DET
cana-1739	257	13	proposed	propose	VERB
cana-1739	257	14	fractional	fractional	ADJ
cana-1739	257	15	model	model	NOUN
cana-1739	257	16	.	.	PUNCT
cana-1739	258	1	these	these	DET
cana-1739	258	2	simulations	simulation	NOUN
cana-1739	258	3	aim	aim	VERB
cana-1739	258	4	to	to	PART
cana-1739	258	5	demonstrate	demonstrate	VERB
cana-1739	258	6	the	the	DET
cana-1739	258	7	dynamic	dynamic	ADJ
cana-1739	258	8	behavior	behavior	NOUN
cana-1739	258	9	of	of	ADP
cana-1739	258	10	green	green	ADJ
cana-1739	258	11	building	building	NOUN
cana-1739	258	12	dynamics	dynamic	NOUN
cana-1739	258	13	in	in	ADP
cana-1739	258	14	order	order	NOUN
cana-1739	258	15	to	to	PART
cana-1739	258	16	mitigate	mitigate	VERB
cana-1739	258	17	ghg	ghg	PROPN
cana-1739	258	18	emissions	emission	NOUN
cana-1739	258	19	and	and	CCONJ
cana-1739	258	20	gain	gain	VERB
cana-1739	258	21	a	a	DET
cana-1739	258	22	comprehensive	comprehensive	ADJ
cana-1739	258	23	understanding	understanding	NOUN
cana-1739	258	24	of	of	ADP
cana-1739	258	25	the	the	DET
cana-1739	258	26	impact	impact	NOUN
cana-1739	258	27	on	on	ADP
cana-1739	258	28	human	human	ADJ
cana-1739	258	29	communities	community	NOUN
cana-1739	258	30	.	.	PUNCT
cana-1739	259	1	human	human	ADJ
cana-1739	259	2	communities	community	NOUN
cana-1739	259	3	are	be	AUX
cana-1739	259	4	significant	significant	ADJ
cana-1739	259	5	contributors	contributor	NOUN
cana-1739	259	6	to	to	ADP
cana-1739	259	7	unwanted	unwanted	ADJ
cana-1739	259	8	ghg	ghg	PROPN
cana-1739	259	9	emissions	emission	NOUN
cana-1739	259	10	.	.	PUNCT
cana-1739	260	1	the	the	DET
cana-1739	260	2	rise	rise	NOUN
cana-1739	260	3	in	in	ADP
cana-1739	260	4	these	these	DET
cana-1739	260	5	emissions	emission	NOUN
cana-1739	260	6	due	due	ADP
cana-1739	260	7	to	to	ADP
cana-1739	260	8	various	various	ADJ
cana-1739	260	9	human	human	ADJ
cana-1739	260	10	activities	activity	NOUN
cana-1739	260	11	poses	pose	VERB
cana-1739	260	12	a	a	DET
cana-1739	260	13	threat	threat	NOUN
cana-1739	260	14	to	to	ADP
cana-1739	260	15	the	the	DET
cana-1739	260	16	well	well	ADV
cana-1739	260	17	-	-	PUNCT
cana-1739	260	18	being	being	NOUN
cana-1739	260	19	of	of	ADP
cana-1739	260	20	all	all	DET
cana-1739	260	21	organisms	organism	NOUN
cana-1739	260	22	.	.	PUNCT
cana-1739	261	1	the	the	DET
cana-1739	261	2	continuous	continuous	ADJ
cana-1739	261	3	increase	increase	NOUN
cana-1739	261	4	in	in	ADP
cana-1739	261	5	the	the	DET
cana-1739	261	6	human	human	ADJ
cana-1739	261	7	population	population	NOUN
cana-1739	261	8	leads	lead	VERB
cana-1739	261	9	to	to	ADP
cana-1739	261	10	higher	high	ADJ
cana-1739	261	11	levels	level	NOUN
cana-1739	261	12	of	of	ADP
cana-1739	261	13	these	these	DET
cana-1739	261	14	harmful	harmful	ADJ
cana-1739	261	15	gases	gas	NOUN
cana-1739	261	16	.	.	PUNCT
cana-1739	262	1	in	in	ADP
cana-1739	262	2	cases	case	NOUN
cana-1739	262	3	of	of	ADP
cana-1739	262	4	rapid	rapid	ADJ
cana-1739	262	5	emission	emission	NOUN
cana-1739	262	6	of	of	ADP
cana-1739	262	7	these	these	DET
cana-1739	262	8	gases	gas	NOUN
cana-1739	262	9	by	by	ADP
cana-1739	262	10	human	human	ADJ
cana-1739	262	11	societies	society	NOUN
cana-1739	262	12	,	,	PUNCT
cana-1739	262	13	green	green	ADJ
cana-1739	262	14	constructions	construction	NOUN
cana-1739	262	15	utilize	utilize	VERB
cana-1739	262	16	their	their	PRON
cana-1739	262	17	advanced	advanced	ADJ
cana-1739	262	18	technologies	technology	NOUN
cana-1739	262	19	to	to	PART
cana-1739	262	20	tackle	tackle	VERB
cana-1739	262	21	the	the	DET
cana-1739	262	22	issue	issue	NOUN
cana-1739	262	23	.	.	PUNCT
cana-1739	263	1	consequently	consequently	ADV
cana-1739	263	2	,	,	PUNCT
cana-1739	263	3	green	green	ADJ
cana-1739	263	4	buildings	building	NOUN
cana-1739	263	5	offer	offer	VERB
cana-1739	263	6	a	a	DET
cana-1739	263	7	range	range	NOUN
cana-1739	263	8	of	of	ADP
cana-1739	263	9	advantages	advantage	NOUN
cana-1739	263	10	while	while	SCONJ
cana-1739	263	11	effectively	effectively	ADV
cana-1739	263	12	addressing	address	VERB
cana-1739	263	13	the	the	DET
cana-1739	263	14	problem	problem	NOUN
cana-1739	263	15	of	of	ADP
cana-1739	263	16	ghgs	ghgs	NOUN
cana-1739	263	17	.	.	PUNCT
cana-1739	264	1	by	by	ADP
cana-1739	264	2	incorporating	incorporate	VERB
cana-1739	264	3	sustainable	sustainable	ADJ
cana-1739	264	4	practices	practice	NOUN
cana-1739	264	5	,	,	PUNCT
cana-1739	264	6	energy	energy	NOUN
cana-1739	264	7	-	-	PUNCT
cana-1739	264	8	efficient	efficient	ADJ
cana-1739	264	9	designs	design	NOUN
cana-1739	264	10	,	,	PUNCT
cana-1739	264	11	and	and	CCONJ
cana-1739	264	12	innovative	innovative	ADJ
cana-1739	264	13	technologies	technology	NOUN
cana-1739	264	14	,	,	PUNCT
cana-1739	264	15	these	these	DET
cana-1739	264	16	buildings	building	NOUN
cana-1739	264	17	help	help	VERB
cana-1739	264	18	to	to	PART
cana-1739	264	19	create	create	VERB
cana-1739	264	20	a	a	DET
cana-1739	264	21	more	more	ADV
cana-1739	264	22	environmentally	environmentally	ADV
cana-1739	264	23	friendly	friendly	ADJ
cana-1739	264	24	and	and	CCONJ
cana-1739	264	25	sustainable	sustainable	ADJ
cana-1739	264	26	built	build	VERB
cana-1739	264	27	environment	environment	NOUN
cana-1739	264	28	.	.	PUNCT
cana-1739	265	1	these	these	DET
cana-1739	265	2	energy	energy	NOUN
cana-1739	265	3	-	-	PUNCT
cana-1739	265	4	efficient	efficient	ADJ
cana-1739	265	5	structures	structure	NOUN
cana-1739	265	6	also	also	ADV
cana-1739	265	7	provide	provide	VERB
cana-1739	265	8	benefits	benefit	NOUN
cana-1739	265	9	to	to	ADP
cana-1739	265	10	human	human	ADJ
cana-1739	265	11	societies	society	NOUN
cana-1739	265	12	.	.	PUNCT
cana-1739	266	1	the	the	DET
cana-1739	266	2	fractional	fractional	ADJ
cana-1739	266	3	order	order	NOUN
cana-1739	266	4	model	model	NOUN
cana-1739	266	5	is	be	AUX
cana-1739	266	6	ideal	ideal	ADJ
cana-1739	266	7	for	for	ADP
cana-1739	266	8	illustrating	illustrate	VERB
cana-1739	266	9	the	the	DET
cana-1739	266	10	memory	memory	NOUN
cana-1739	266	11	effect	effect	NOUN
cana-1739	266	12	/	/	SYM
cana-1739	266	13	history	history	NOUN
cana-1739	266	14	of	of	ADP
cana-1739	266	15	increasing	increase	VERB
cana-1739	266	16	ghgs	ghg	VERB
cana-1739	266	17	on	on	ADP
cana-1739	266	18	green	green	ADJ
cana-1739	266	19	building	building	NOUN
cana-1739	266	20	systems	system	NOUN
cana-1739	266	21	to	to	PART
cana-1739	266	22	enhance	enhance	VERB
cana-1739	266	23	their	their	PRON
cana-1739	266	24	efficiency	efficiency	NOUN
cana-1739	266	25	.	.	PUNCT
cana-1739	267	1	case	case	NOUN
cana-1739	267	2	1(variable	1(variable	ADJ
cana-1739	267	3	-	-	PUNCT
cana-1739	267	4	order	order	NOUN
cana-1739	267	5	case	case	NOUN
cana-1739	267	6	):	):	PUNCT
cana-1739	267	7	the	the	DET
cana-1739	267	8	rate	rate	NOUN
cana-1739	267	9	of	of	ADP
cana-1739	267	10	green	green	ADJ
cana-1739	267	11	building	building	NOUN
cana-1739	267	12	projects	project	NOUN
cana-1739	267	13	varies	vary	VERB
cana-1739	267	14	due	due	ADJ
cana-1739	267	15	to	to	ADP
cana-1739	267	16	a	a	DET
cana-1739	267	17	multitude	multitude	NOUN
cana-1739	267	18	of	of	ADP
cana-1739	267	19	factors	factor	NOUN
cana-1739	267	20	.	.	PUNCT
cana-1739	268	1	these	these	PRON
cana-1739	268	2	include	include	VERB
cana-1739	268	3	the	the	DET
cana-1739	268	4	progression	progression	NOUN
cana-1739	268	5	of	of	ADP
cana-1739	268	6	eco	eco	PROPN
cana-1739	268	7	-	-	PUNCT
cana-1739	268	8	friendly	friendly	ADJ
cana-1739	268	9	building	building	NOUN
cana-1739	268	10	initiatives	initiative	NOUN
cana-1739	268	11	,	,	PUNCT
cana-1739	268	12	government	government	NOUN
cana-1739	268	13	policies	policy	NOUN
cana-1739	268	14	,	,	PUNCT
cana-1739	268	15	public	public	ADJ
cana-1739	268	16	awareness	awareness	NOUN
cana-1739	268	17	,	,	PUNCT
cana-1739	268	18	and	and	CCONJ
cana-1739	268	19	technological	technological	ADJ
cana-1739	268	20	advancements	advancement	NOUN
cana-1739	268	21	.	.	PUNCT
cana-1739	269	1	additionally	additionally	ADV
cana-1739	269	2	,	,	PUNCT
cana-1739	269	3	economic	economic	ADJ
cana-1739	269	4	incentives	incentive	NOUN
cana-1739	269	5	,	,	PUNCT
cana-1739	269	6	market	market	NOUN
cana-1739	269	7	demand	demand	NOUN
cana-1739	269	8	,	,	PUNCT
cana-1739	269	9	industry	industry	NOUN
cana-1739	269	10	standards	standard	NOUN
cana-1739	269	11	,	,	PUNCT
cana-1739	269	12	access	access	NOUN
cana-1739	269	13	to	to	ADP
cana-1739	269	14	resources	resource	NOUN
cana-1739	269	15	,	,	PUNCT
cana-1739	269	16	regulatory	regulatory	ADJ
cana-1739	269	17	environment	environment	NOUN
cana-1739	269	18	,	,	PUNCT
cana-1739	269	19	collaboration	collaboration	NOUN
cana-1739	269	20	,	,	PUNCT
cana-1739	269	21	and	and	CCONJ
cana-1739	269	22	public	public	ADJ
cana-1739	269	23	perception	perception	NOUN
cana-1739	269	24	play	play	VERB
cana-1739	269	25	crucial	crucial	ADJ
cana-1739	269	26	roles	role	NOUN
cana-1739	269	27	.	.	PUNCT
cana-1739	270	1	variable	variable	ADJ
cana-1739	270	2	order	order	NOUN
cana-1739	270	3	study	study	NOUN
cana-1739	270	4	of	of	ADP
cana-1739	270	5	the	the	DET
cana-1739	270	6	green	green	ADJ
cana-1739	270	7	building	building	NOUN
cana-1739	270	8	concept	concept	NOUN
cana-1739	270	9	allows	allow	VERB
cana-1739	270	10	for	for	ADP
cana-1739	270	11	a	a	DET
cana-1739	270	12	more	more	ADV
cana-1739	270	13	comprehensive	comprehensive	ADJ
cana-1739	270	14	understanding	understanding	NOUN
cana-1739	270	15	of	of	ADP
cana-1739	270	16	its	its	PRON
cana-1739	270	17	dynamics	dynamic	NOUN
cana-1739	270	18	and	and	CCONJ
cana-1739	270	19	complexities	complexity	NOUN
cana-1739	270	20	.	.	PUNCT
cana-1739	271	1	the	the	DET
cana-1739	271	2	variable	variable	ADJ
cana-1739	271	3	order	order	NOUN
cana-1739	271	4	of	of	ADP
cana-1739	271	5	𝐺(𝑡	𝐺(𝑡	NOUN
cana-1739	271	6	)	)	PUNCT
cana-1739	271	7	can	can	AUX
cana-1739	271	8	be	be	AUX
cana-1739	271	9	represented	represent	VERB
cana-1739	271	10	as	as	ADP
cana-1739	271	11	ν(t)=	ν(t)=	PROPN
cana-1739	271	12	l/(1+exp(k(t	l/(1+exp(k(t	PROPN
cana-1739	271	13	-	-	PUNCT
cana-1739	271	14	t0	t0	NOUN
cana-1739	271	15	)	)	PUNCT
cana-1739	271	16	)	)	PUNCT
cana-1739	271	17	,	,	PUNCT
cana-1739	271	18	where	where	SCONJ
cana-1739	271	19	l	l	NOUN
cana-1739	271	20	is	be	AUX
cana-1739	271	21	the	the	DET
cana-1739	271	22	highest	high	ADJ
cana-1739	271	23	percentage	percentage	NOUN
cana-1739	271	24	value	value	NOUN
cana-1739	271	25	of	of	ADP
cana-1739	271	26	buildings	building	NOUN
cana-1739	271	27	that	that	PRON
cana-1739	271	28	are	be	AUX
cana-1739	271	29	deemed	deem	VERB
cana-1739	271	30	to	to	PART
cana-1739	271	31	be	be	AUX
cana-1739	271	32	green	green	ADJ
cana-1739	271	33	,	,	PUNCT
cana-1739	271	34	k	k	PROPN
cana-1739	271	35	is	be	AUX
cana-1739	271	36	the	the	DET
cana-1739	271	37	logistic	logistic	ADJ
cana-1739	271	38	growth	growth	NOUN
cana-1739	271	39	rate	rate	NOUN
cana-1739	271	40	and	and	CCONJ
cana-1739	271	41	t0	t0	PROPN
cana-1739	271	42	is	be	AUX
cana-1739	271	43	the	the	DET
cana-1739	271	44	time	time	NOUN
cana-1739	271	45	at	at	ADP
cana-1739	271	46	which	which	PRON
cana-1739	271	47	the	the	DET
cana-1739	271	48	growth	growth	NOUN
cana-1739	271	49	is	be	AUX
cana-1739	271	50	halfway	halfway	ADV
cana-1739	271	51	between	between	ADP
cana-1739	271	52	its	its	PRON
cana-1739	271	53	starting	starting	NOUN
cana-1739	271	54	and	and	CCONJ
cana-1739	271	55	ending	end	VERB
cana-1739	271	56	values	value	NOUN
cana-1739	271	57	.	.	PUNCT
cana-1739	272	1	various	various	ADJ
cana-1739	272	2	factors	factor	NOUN
cana-1739	272	3	,	,	PUNCT
cana-1739	272	4	including	include	VERB
cana-1739	272	5	building	build	VERB
cana-1739	272	6	materials	material	NOUN
cana-1739	272	7	,	,	PUNCT
cana-1739	272	8	energy	energy	NOUN
cana-1739	272	9	sources	source	NOUN
cana-1739	272	10	,	,	PUNCT
cana-1739	272	11	energy	energy	NOUN
cana-1739	272	12	efficiency	efficiency	NOUN
cana-1739	272	13	measures	measure	NOUN
cana-1739	272	14	,	,	PUNCT
cana-1739	272	15	occupant	occupant	ADJ
cana-1739	272	16	behavior	behavior	NOUN
cana-1739	272	17	,	,	PUNCT
cana-1739	272	18	and	and	CCONJ
cana-1739	272	19	maintenance	maintenance	NOUN
cana-1739	272	20	practices	practice	NOUN
cana-1739	272	21	,	,	PUNCT
cana-1739	272	22	may	may	AUX
cana-1739	272	23	have	have	VERB
cana-1739	272	24	an	an	DET
cana-1739	272	25	impact	impact	NOUN
cana-1739	272	26	on	on	ADP
cana-1739	272	27	the	the	DET
cana-1739	272	28	function	function	NOUN
cana-1739	272	29	of	of	ADP
cana-1739	272	30	greenhouse	greenhouse	NOUN
cana-1739	272	31	gas	gas	NOUN
cana-1739	272	32	emission	emission	NOUN
cana-1739	272	33	rates	rate	NOUN
cana-1739	272	34	in	in	ADP
cana-1739	272	35	green	green	ADJ
cana-1739	272	36	buildings	building	NOUN
cana-1739	272	37	.	.	PUNCT
cana-1739	273	1	communications	communication	NOUN
cana-1739	273	2	on	on	ADP
cana-1739	273	3	applied	apply	VERB
cana-1739	273	4	nonlinear	nonlinear	ADJ
cana-1739	273	5	analysis	analysis	NOUN
cana-1739	273	6	issn	issn	NOUN
cana-1739	273	7	:	:	PUNCT
cana-1739	273	8	1074	1074	NUM
cana-1739	273	9	-	-	PUNCT
cana-1739	273	10	133x	133x	NUM
cana-1739	273	11	vol	vol	NOUN
cana-1739	273	12	32	32	NUM
cana-1739	273	13	no	no	NOUN
cana-1739	273	14	.	.	NOUN
cana-1739	273	15	2	2	NUM
cana-1739	273	16	(	(	PUNCT
cana-1739	273	17	2025	2025	NUM
cana-1739	273	18	)	)	PUNCT
cana-1739	273	19	246	246	NUM
cana-1739	273	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1739	273	21	𝐶(𝑡	𝐶(𝑡	NOUN
cana-1739	273	22	)	)	PUNCT
cana-1739	273	23	takes	take	VERB
cana-1739	273	24	the	the	DET
cana-1739	273	25	variable	variable	ADJ
cana-1739	273	26	order	order	NOUN
cana-1739	273	27	as	as	ADP
cana-1739	273	28	a	a	DET
cana-1739	273	29	linear	linear	ADJ
cana-1739	273	30	function	function	NOUN
cana-1739	273	31	ν(t)=	ν(t)=	PUNCT
cana-1739	273	32	r0-𝜆t	r0-𝜆t	PROPN
cana-1739	273	33	,	,	PUNCT
cana-1739	273	34	where	where	SCONJ
cana-1739	273	35	r0	r0	NOUN
cana-1739	273	36	represents	represent	VERB
cana-1739	273	37	the	the	DET
cana-1739	273	38	starting	starting	NOUN
cana-1739	273	39	point	point	NOUN
cana-1739	273	40	of	of	ADP
cana-1739	273	41	greenhouse	greenhouse	NOUN
cana-1739	273	42	gas	gas	NOUN
cana-1739	273	43	emissions	emission	NOUN
cana-1739	273	44	and	and	CCONJ
cana-1739	273	45	𝜆	𝜆	X
cana-1739	273	46	is	be	AUX
cana-1739	273	47	the	the	DET
cana-1739	273	48	decreasing	decrease	VERB
cana-1739	273	49	rate	rate	NOUN
cana-1739	273	50	of	of	ADP
cana-1739	273	51	ghgs	ghg	VERB
cana-1739	273	52	in	in	ADP
cana-1739	273	53	green	green	ADJ
cana-1739	273	54	buildings	building	NOUN
cana-1739	273	55	.	.	PUNCT
cana-1739	274	1	the	the	DET
cana-1739	274	2	usage	usage	NOUN
cana-1739	274	3	of	of	ADP
cana-1739	274	4	ingredients	ingredient	NOUN
cana-1739	274	5	in	in	ADP
cana-1739	274	6	green	green	ADJ
cana-1739	274	7	buildings	building	NOUN
cana-1739	274	8	𝐼(𝑡	𝐼(𝑡	NUM
cana-1739	274	9	)	)	PUNCT
cana-1739	274	10	can	can	AUX
cana-1739	274	11	be	be	AUX
cana-1739	274	12	represented	represent	VERB
cana-1739	274	13	in	in	ADP
cana-1739	274	14	variable	variable	ADJ
cana-1739	274	15	order	order	NOUN
cana-1739	274	16	as	as	ADP
cana-1739	274	17	ν(t)=s0+𝜇t	ν(t)=s0+𝜇t	PROPN
cana-1739	274	18	,	,	PUNCT
cana-1739	274	19	where	where	SCONJ
cana-1739	274	20	s0	s0	PROPN
cana-1739	274	21	symbolizes	symbolize	VERB
cana-1739	274	22	the	the	DET
cana-1739	274	23	initial	initial	ADJ
cana-1739	274	24	adoption	adoption	NOUN
cana-1739	274	25	of	of	ADP
cana-1739	274	26	eco	eco	NOUN
cana-1739	274	27	-	-	PUNCT
cana-1739	274	28	friendly	friendly	ADJ
cana-1739	274	29	components	component	NOUN
cana-1739	274	30	and	and	CCONJ
cana-1739	274	31	𝜇	𝜇	ADP
cana-1739	274	32	denotes	denote	NOUN
cana-1739	274	33	the	the	DET
cana-1739	274	34	speed	speed	NOUN
cana-1739	274	35	of	of	ADP
cana-1739	274	36	growth	growth	NOUN
cana-1739	274	37	in	in	ADP
cana-1739	274	38	usage	usage	NOUN
cana-1739	274	39	.	.	PUNCT
cana-1739	275	1	these	these	DET
cana-1739	275	2	components	component	NOUN
cana-1739	275	3	might	might	AUX
cana-1739	275	4	include	include	VERB
cana-1739	275	5	things	thing	NOUN
cana-1739	275	6	like	like	ADP
cana-1739	275	7	renewable	renewable	ADJ
cana-1739	275	8	energy	energy	NOUN
cana-1739	275	9	sources	source	NOUN
cana-1739	275	10	and	and	CCONJ
cana-1739	275	11	other	other	ADJ
cana-1739	275	12	elements	element	NOUN
cana-1739	275	13	that	that	PRON
cana-1739	275	14	enhance	enhance	VERB
cana-1739	275	15	a	a	DET
cana-1739	275	16	building	building	NOUN
cana-1739	275	17	's	's	PART
cana-1739	275	18	green	green	ADJ
cana-1739	275	19	features	feature	NOUN
cana-1739	275	20	.	.	PUNCT
cana-1739	276	1	when	when	SCONJ
cana-1739	276	2	new	new	ADJ
cana-1739	276	3	technologies	technology	NOUN
cana-1739	276	4	are	be	AUX
cana-1739	276	5	created	create	VERB
cana-1739	276	6	,	,	PUNCT
cana-1739	276	7	building	building	NOUN
cana-1739	276	8	codes	code	NOUN
cana-1739	276	9	are	be	AUX
cana-1739	276	10	updated	update	VERB
cana-1739	276	11	,	,	PUNCT
cana-1739	276	12	and	and	CCONJ
cana-1739	276	13	societal	societal	ADJ
cana-1739	276	14	priorities	priority	NOUN
cana-1739	276	15	change	change	VERB
cana-1739	276	16	over	over	ADP
cana-1739	276	17	time	time	NOUN
cana-1739	276	18	,	,	PUNCT
cana-1739	276	19	the	the	DET
cana-1739	276	20	function	function	NOUN
cana-1739	276	21	may	may	AUX
cana-1739	276	22	change	change	VERB
cana-1739	276	23	.	.	PUNCT
cana-1739	277	1	the	the	DET
cana-1739	277	2	growth	growth	NOUN
cana-1739	277	3	rate	rate	NOUN
cana-1739	277	4	of	of	ADP
cana-1739	277	5	a	a	DET
cana-1739	277	6	human	human	ADJ
cana-1739	277	7	community	community	NOUN
cana-1739	277	8	in	in	ADP
cana-1739	277	9	green	green	ADJ
cana-1739	277	10	buildings	building	NOUN
cana-1739	277	11	is	be	AUX
cana-1739	277	12	determined	determine	VERB
cana-1739	277	13	by	by	ADP
cana-1739	277	14	various	various	ADJ
cana-1739	277	15	factors	factor	NOUN
cana-1739	277	16	,	,	PUNCT
cana-1739	277	17	including	include	VERB
cana-1739	277	18	population	population	NOUN
cana-1739	277	19	dynamics	dynamic	NOUN
cana-1739	277	20	,	,	PUNCT
cana-1739	277	21	urbanization	urbanization	NOUN
cana-1739	277	22	trends	trend	NOUN
cana-1739	277	23	,	,	PUNCT
cana-1739	277	24	economic	economic	ADJ
cana-1739	277	25	conditions	condition	NOUN
cana-1739	277	26	,	,	PUNCT
cana-1739	277	27	and	and	CCONJ
cana-1739	277	28	the	the	DET
cana-1739	277	29	availability	availability	NOUN
cana-1739	277	30	of	of	ADP
cana-1739	277	31	green	green	ADJ
cana-1739	277	32	buildings	building	NOUN
cana-1739	277	33	.here	.here	ADP
cana-1739	277	34	the	the	DET
cana-1739	277	35	variable	variable	ADJ
cana-1739	277	36	order	order	NOUN
cana-1739	277	37	of	of	ADP
cana-1739	277	38	𝐻(𝑡	𝐻(𝑡	NOUN
cana-1739	277	39	)	)	PUNCT
cana-1739	277	40	can	can	AUX
cana-1739	277	41	be	be	AUX
cana-1739	277	42	represented	represent	VERB
cana-1739	277	43	as	as	ADP
cana-1739	277	44	ν(t)=𝜗+α	ν(t)=𝜗+α	NOUN
cana-1739	277	45	exp((ω)(t)(m)),where	exp((ω)(t)(m)),where	NOUN
cana-1739	277	46	𝜗	𝜗	PROPN
cana-1739	277	47	denotes	denote	VERB
cana-1739	277	48	the	the	DET
cana-1739	277	49	baseline	baseline	NOUN
cana-1739	277	50	growth	growth	NOUN
cana-1739	277	51	factor	factor	NOUN
cana-1739	277	52	,	,	PUNCT
cana-1739	277	53	α	α	PRON
cana-1739	277	54	represents	represent	VERB
cana-1739	277	55	a	a	DET
cana-1739	277	56	coefficient	coefficient	NOUN
cana-1739	277	57	scaling	scaling	NOUN
cana-1739	277	58	of	of	ADP
cana-1739	277	59	the	the	DET
cana-1739	277	60	exponential	exponential	ADJ
cana-1739	277	61	growth	growth	NOUN
cana-1739	277	62	,	,	PUNCT
cana-1739	277	63	ω	ω	PROPN
cana-1739	277	64	indicates	indicate	VERB
cana-1739	277	65	the	the	DET
cana-1739	277	66	decay	decay	NOUN
cana-1739	277	67	rate	rate	NOUN
cana-1739	277	68	coefficient	coefficient	NOUN
cana-1739	277	69	of	of	ADP
cana-1739	277	70	the	the	DET
cana-1739	277	71	exponential	exponential	ADJ
cana-1739	277	72	growth	growth	NOUN
cana-1739	277	73	and	and	CCONJ
cana-1739	277	74	m	m	NOUN
cana-1739	277	75	represents	represent	VERB
cana-1739	277	76	a	a	DET
cana-1739	277	77	coefficient	coefficient	NOUN
cana-1739	277	78	affecting	affect	VERB
cana-1739	277	79	the	the	DET
cana-1739	277	80	speed	speed	NOUN
cana-1739	277	81	at	at	ADP
cana-1739	277	82	which	which	PRON
cana-1739	277	83	the	the	DET
cana-1739	277	84	growth	growth	NOUN
cana-1739	277	85	function	function	NOUN
cana-1739	277	86	approaches	approach	VERB
cana-1739	277	87	zero	zero	NUM
cana-1739	277	88	as	as	ADP
cana-1739	277	89	t	t	NOUN
cana-1739	277	90	increases	increase	NOUN
cana-1739	277	91	.	.	PUNCT
cana-1739	278	1	fig	fig	NOUN
cana-1739	278	2	1	1	NUM
cana-1739	278	3	:	:	PUNCT
cana-1739	278	4	comparison	comparison	NOUN
cana-1739	278	5	graph	graph	NOUN
cana-1739	278	6	of	of	ADP
cana-1739	278	7	𝐺(𝑡	𝐺(𝑡	NOUN
cana-1739	278	8	)	)	PUNCT
cana-1739	278	9	via	via	ADP
cana-1739	278	10	lc	lc	PROPN
cana-1739	278	11	,	,	PUNCT
cana-1739	278	12	cf	cf	NOUN
cana-1739	278	13	and	and	CCONJ
cana-1739	278	14	ab	ab	PROPN
cana-1739	278	15	fig	fig	NOUN
cana-1739	278	16	1	1	NUM
cana-1739	278	17	illustrates	illustrate	VERB
cana-1739	278	18	the	the	DET
cana-1739	278	19	growth	growth	NOUN
cana-1739	278	20	rate	rate	NOUN
cana-1739	278	21	of	of	ADP
cana-1739	278	22	green	green	ADJ
cana-1739	278	23	buildings	building	NOUN
cana-1739	278	24	with	with	ADP
cana-1739	278	25	a	a	DET
cana-1739	278	26	variable	variable	ADJ
cana-1739	278	27	order	order	NOUN
cana-1739	278	28	represented	represent	VERB
cana-1739	278	29	by	by	ADP
cana-1739	278	30	ν(t)=0.90/(1+exp(0.1(t-10	ν(t)=0.90/(1+exp(0.1(t-10	NOUN
cana-1739	278	31	)	)	PUNCT
cana-1739	278	32	)	)	PUNCT
cana-1739	278	33	.	.	PUNCT
cana-1739	279	1	here,0.90	here,0.90	PROPN
cana-1739	279	2	represents	represent	VERB
cana-1739	279	3	buildings	building	NOUN
cana-1739	279	4	with	with	ADP
cana-1739	279	5	the	the	DET
cana-1739	279	6	highest	high	ADJ
cana-1739	279	7	percentage	percentage	NOUN
cana-1739	279	8	of	of	ADP
cana-1739	279	9	green	green	ADJ
cana-1739	279	10	features,0.1	features,0.1	NOUN
cana-1739	279	11	represents	represent	VERB
cana-1739	279	12	the	the	DET
cana-1739	279	13	rate	rate	NOUN
cana-1739	279	14	of	of	ADP
cana-1739	279	15	logistic	logistic	ADJ
cana-1739	279	16	growth	growth	NOUN
cana-1739	279	17	and	and	CCONJ
cana-1739	279	18	10	10	NUM
cana-1739	279	19	indicates	indicate	VERB
cana-1739	279	20	the	the	DET
cana-1739	279	21	growth	growth	NOUN
cana-1739	279	22	reaches	reach	VERB
cana-1739	279	23	a	a	DET
cana-1739	279	24	point	point	NOUN
cana-1739	279	25	midway	midway	NOUN
cana-1739	279	26	between	between	ADP
cana-1739	279	27	its	its	PRON
cana-1739	279	28	initial	initial	ADJ
cana-1739	279	29	and	and	CCONJ
cana-1739	279	30	final	final	ADJ
cana-1739	279	31	values	value	NOUN
cana-1739	279	32	.	.	PUNCT
cana-1739	280	1	it	it	PRON
cana-1739	280	2	is	be	AUX
cana-1739	280	3	observed	observe	VERB
cana-1739	280	4	that	that	SCONJ
cana-1739	280	5	in	in	ADP
cana-1739	280	6	all	all	DET
cana-1739	280	7	cases	case	NOUN
cana-1739	280	8	of	of	ADP
cana-1739	280	9	lc	lc	NOUN
cana-1739	280	10	,	,	PUNCT
cana-1739	280	11	cf	cf	NOUN
cana-1739	280	12	and	and	CCONJ
cana-1739	280	13	ab	ab	X
cana-1739	280	14	the	the	DET
cana-1739	280	15	growth	growth	NOUN
cana-1739	280	16	rate	rate	NOUN
cana-1739	280	17	of	of	ADP
cana-1739	280	18	green	green	ADJ
cana-1739	280	19	buildings	building	NOUN
cana-1739	280	20	rises	rise	VERB
cana-1739	280	21	accordingly	accordingly	ADV
cana-1739	280	22	when	when	SCONJ
cana-1739	280	23	time	time	NOUN
cana-1739	280	24	increases	increase	VERB
cana-1739	280	25	.	.	PUNCT
cana-1739	281	1	communications	communication	NOUN
cana-1739	281	2	on	on	ADP
cana-1739	281	3	applied	apply	VERB
cana-1739	281	4	nonlinear	nonlinear	ADJ
cana-1739	281	5	analysis	analysis	NOUN
cana-1739	281	6	issn	issn	NOUN
cana-1739	281	7	:	:	PUNCT
cana-1739	281	8	1074	1074	NUM
cana-1739	281	9	-	-	PUNCT
cana-1739	281	10	133x	133x	NUM
cana-1739	281	11	vol	vol	NOUN
cana-1739	281	12	32	32	NUM
cana-1739	281	13	no	no	NOUN
cana-1739	281	14	.	.	NOUN
cana-1739	281	15	2	2	NUM
cana-1739	281	16	(	(	PUNCT
cana-1739	281	17	2025	2025	NUM
cana-1739	281	18	)	)	PUNCT
cana-1739	281	19	247	247	NUM
cana-1739	281	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1739	281	21	fig	fig	NOUN
cana-1739	281	22	2	2	NUM
cana-1739	281	23	:	:	PUNCT
cana-1739	281	24	comparison	comparison	NOUN
cana-1739	281	25	graph	graph	NOUN
cana-1739	281	26	of	of	ADP
cana-1739	281	27	𝐶(𝑡	𝐶(𝑡	NOUN
cana-1739	281	28	)	)	PUNCT
cana-1739	281	29	via	via	ADP
cana-1739	281	30	lc	lc	PROPN
cana-1739	281	31	,	,	PUNCT
cana-1739	281	32	cf	cf	NOUN
cana-1739	281	33	and	and	CCONJ
cana-1739	281	34	ab	ab	PROPN
cana-1739	281	35	fig	fig	NOUN
cana-1739	281	36	2	2	NUM
cana-1739	281	37	depicts	depict	VERB
cana-1739	281	38	the	the	DET
cana-1739	281	39	change	change	NOUN
cana-1739	281	40	of	of	ADP
cana-1739	281	41	ghgs	ghg	VERB
cana-1739	281	42	rate	rate	NOUN
cana-1739	281	43	with	with	ADP
cana-1739	281	44	a	a	DET
cana-1739	281	45	variable	variable	ADJ
cana-1739	281	46	order	order	NOUN
cana-1739	282	1	ν(t)=	ν(t)=	NOUN
cana-1739	282	2	0.1-0.5t.where	0.1-0.5t.where	NOUN
cana-1739	282	3	0.1	0.1	NUM
cana-1739	282	4	signifies	signify	VERB
cana-1739	282	5	the	the	DET
cana-1739	282	6	initial	initial	ADJ
cana-1739	282	7	stage	stage	NOUN
cana-1739	282	8	of	of	ADP
cana-1739	282	9	greenhouse	greenhouse	NOUN
cana-1739	282	10	gas	gas	NOUN
cana-1739	282	11	emissions.0.5	emissions.0.5	PROPN
cana-1739	282	12	indicates	indicate	VERB
cana-1739	282	13	the	the	DET
cana-1739	282	14	rate	rate	NOUN
cana-1739	282	15	at	at	ADP
cana-1739	282	16	which	which	PRON
cana-1739	282	17	greenhouse	greenhouse	NOUN
cana-1739	282	18	gas	gas	NOUN
cana-1739	282	19	emission	emission	NOUN
cana-1739	282	20	decreases	decrease	VERB
cana-1739	282	21	.	.	PUNCT
cana-1739	283	1	by	by	ADP
cana-1739	283	2	operating	operate	VERB
cana-1739	283	3	the	the	DET
cana-1739	283	4	above	above	ADJ
cana-1739	283	5	function	function	NOUN
cana-1739	283	6	using	use	VERB
cana-1739	283	7	lc	lc	NOUN
cana-1739	283	8	,	,	PUNCT
cana-1739	283	9	cf	cf	NOUN
cana-1739	283	10	and	and	CCONJ
cana-1739	283	11	ab	ab	PROPN
cana-1739	283	12	,	,	PUNCT
cana-1739	283	13	ab	ab	PROPN
cana-1739	283	14	gives	give	VERB
cana-1739	283	15	declination	declination	NOUN
cana-1739	283	16	of	of	ADP
cana-1739	283	17	ghgs	ghg	VERB
cana-1739	283	18	in	in	ADP
cana-1739	283	19	green	green	ADJ
cana-1739	283	20	buildings	building	NOUN
cana-1739	283	21	more	more	ADV
cana-1739	283	22	appropriately	appropriately	ADV
cana-1739	283	23	as	as	ADP
cana-1739	283	24	in	in	ADP
cana-1739	283	25	[	[	X
cana-1739	283	26	15	15	NUM
cana-1739	283	27	]	]	PUNCT
cana-1739	283	28	than	than	ADP
cana-1739	283	29	lc	lc	PROPN
cana-1739	283	30	and	and	CCONJ
cana-1739	283	31	cf	cf	NOUN
cana-1739	283	32	.	.	PUNCT
cana-1739	284	1	gradually	gradually	ADV
cana-1739	284	2	,	,	PUNCT
cana-1739	284	3	as	as	SCONJ
cana-1739	284	4	green	green	ADJ
cana-1739	284	5	technologies	technology	NOUN
cana-1739	284	6	and	and	CCONJ
cana-1739	284	7	practices	practice	NOUN
cana-1739	284	8	are	be	AUX
cana-1739	284	9	adopted	adopt	VERB
cana-1739	284	10	and	and	CCONJ
cana-1739	284	11	refined	refine	VERB
cana-1739	284	12	,	,	PUNCT
cana-1739	284	13	the	the	DET
cana-1739	284	14	rate	rate	NOUN
cana-1739	284	15	of	of	ADP
cana-1739	284	16	greenhouse	greenhouse	NOUN
cana-1739	284	17	gas	gas	NOUN
cana-1739	284	18	emissions	emission	NOUN
cana-1739	284	19	declines	decline	VERB
cana-1739	284	20	.	.	PUNCT
cana-1739	285	1	fig	fig	NOUN
cana-1739	285	2	3	3	NUM
cana-1739	285	3	:	:	PUNCT
cana-1739	285	4	comparison	comparison	NOUN
cana-1739	285	5	graph	graph	NOUN
cana-1739	285	6	of	of	ADP
cana-1739	285	7	𝐼(𝑡	𝐼(𝑡	PROPN
cana-1739	285	8	)	)	PUNCT
cana-1739	285	9	via	via	ADP
cana-1739	285	10	lc	lc	PROPN
cana-1739	285	11	,	,	PUNCT
cana-1739	285	12	cf	cf	NOUN
cana-1739	285	13	and	and	CCONJ
cana-1739	285	14	ab	ab	PROPN
cana-1739	285	15	fig	fig	NOUN
cana-1739	285	16	3	3	NUM
cana-1739	285	17	displays	display	VERB
cana-1739	285	18	the	the	DET
cana-1739	285	19	growth	growth	NOUN
cana-1739	285	20	rate	rate	NOUN
cana-1739	285	21	of	of	ADP
cana-1739	285	22	ingredients	ingredient	NOUN
cana-1739	285	23	by	by	ADP
cana-1739	285	24	the	the	DET
cana-1739	285	25	variable	variable	ADJ
cana-1739	285	26	order	order	NOUN
cana-1739	285	27	ν(t	ν(t	NOUN
cana-1739	285	28	)	)	PUNCT
cana-1739	285	29	=	=	SYM
cana-1739	285	30	0.5	0.5	NUM
cana-1739	285	31	+	+	NUM
cana-1739	285	32	0.05	0.05	NUM
cana-1739	285	33	t.	t.	NOUN
cana-1739	285	34	here	here	ADV
cana-1739	285	35	,	,	PUNCT
cana-1739	285	36	0.5	0.5	NUM
cana-1739	285	37	represents	represent	VERB
cana-1739	285	38	the	the	DET
cana-1739	285	39	initial	initial	ADJ
cana-1739	285	40	usage	usage	NOUN
cana-1739	285	41	of	of	ADP
cana-1739	285	42	green	green	ADJ
cana-1739	285	43	ingredients	ingredient	NOUN
cana-1739	285	44	and	and	CCONJ
cana-1739	285	45	0.05	0.05	NUM
cana-1739	285	46	represents	represent	VERB
cana-1739	285	47	the	the	DET
cana-1739	285	48	rate	rate	NOUN
cana-1739	285	49	of	of	ADP
cana-1739	285	50	increase	increase	NOUN
cana-1739	285	51	in	in	ADP
cana-1739	285	52	usage	usage	NOUN
cana-1739	285	53	.	.	PUNCT
cana-1739	286	1	using	use	VERB
cana-1739	286	2	lc	lc	NOUN
cana-1739	286	3	,	,	PUNCT
cana-1739	286	4	cf	cf	NOUN
cana-1739	286	5	and	and	CCONJ
cana-1739	286	6	ab	ab	PROPN
cana-1739	286	7	for	for	ADP
cana-1739	286	8	observing	observe	VERB
cana-1739	286	9	the	the	DET
cana-1739	286	10	considered	consider	VERB
cana-1739	286	11	function	function	NOUN
cana-1739	286	12	,	,	PUNCT
cana-1739	286	13	the	the	DET
cana-1739	286	14	growth	growth	NOUN
cana-1739	286	15	rate	rate	NOUN
cana-1739	286	16	of	of	ADP
cana-1739	286	17	ingredients	ingredient	NOUN
cana-1739	286	18	gradually	gradually	ADV
cana-1739	286	19	rises	rise	VERB
cana-1739	286	20	over	over	ADP
cana-1739	286	21	time	time	NOUN
cana-1739	286	22	.	.	PUNCT
cana-1739	287	1	also	also	ADV
cana-1739	287	2	cf	cf	VERB
cana-1739	287	3	,	,	PUNCT
cana-1739	287	4	ab	ab	PROPN
cana-1739	287	5	have	have	VERB
cana-1739	287	6	better	well	ADJ
cana-1739	287	7	memory	memory	NOUN
cana-1739	287	8	effect	effect	NOUN
cana-1739	287	9	than	than	ADP
cana-1739	287	10	lc	lc	PROPN
cana-1739	287	11	.	.	PUNCT
cana-1739	287	12	communications	communication	NOUN
cana-1739	287	13	on	on	ADP
cana-1739	287	14	applied	apply	VERB
cana-1739	287	15	nonlinear	nonlinear	ADJ
cana-1739	287	16	analysis	analysis	NOUN
cana-1739	287	17	issn	issn	NOUN
cana-1739	287	18	:	:	PUNCT
cana-1739	287	19	1074	1074	NUM
cana-1739	287	20	-	-	PUNCT
cana-1739	287	21	133x	133x	NUM
cana-1739	287	22	vol	vol	NOUN
cana-1739	287	23	32	32	NUM
cana-1739	287	24	no	no	NOUN
cana-1739	287	25	.	.	NOUN
cana-1739	287	26	2	2	NUM
cana-1739	287	27	(	(	PUNCT
cana-1739	287	28	2025	2025	NUM
cana-1739	287	29	)	)	PUNCT
cana-1739	287	30	248	248	NUM
cana-1739	287	31	https://internationalpubls.com	https://internationalpubls.com	X
cana-1739	287	32	fig	fig	NOUN
cana-1739	287	33	4	4	NUM
cana-1739	287	34	:	:	PUNCT
cana-1739	287	35	comparison	comparison	NOUN
cana-1739	287	36	graph	graph	NOUN
cana-1739	287	37	of	of	ADP
cana-1739	287	38	𝐻(𝑡	𝐻(𝑡	NOUN
cana-1739	287	39	)	)	PUNCT
cana-1739	287	40	via	via	ADP
cana-1739	287	41	lc	lc	PROPN
cana-1739	287	42	,	,	PUNCT
cana-1739	287	43	cf	cf	NOUN
cana-1739	287	44	and	and	CCONJ
cana-1739	287	45	ab	ab	PROPN
cana-1739	287	46	fig	fig	NOUN
cana-1739	287	47	4	4	NUM
cana-1739	287	48	provides	provide	VERB
cana-1739	287	49	a	a	DET
cana-1739	287	50	graph	graph	NOUN
cana-1739	287	51	of	of	ADP
cana-1739	287	52	the	the	DET
cana-1739	287	53	variable	variable	ADJ
cana-1739	287	54	order	order	NOUN
cana-1739	287	55	function	function	VERB
cana-1739	287	56	ν(t)=1	ν(t)=1	ADP
cana-1739	287	57	+	+	NOUN
cana-1739	287	58	0.1exp(-(0.1)(t)(0.50)),where	0.1exp(-(0.1)(t)(0.50)),where	NUM
cana-1739	287	59	1	1	NUM
cana-1739	287	60	represents	represent	VERB
cana-1739	287	61	the	the	DET
cana-1739	287	62	fundamental	fundamental	ADJ
cana-1739	287	63	growth	growth	NOUN
cana-1739	287	64	element	element	NOUN
cana-1739	287	65	,	,	PUNCT
cana-1739	287	66	0.1	0.1	NUM
cana-1739	287	67	denotes	denote	VERB
cana-1739	287	68	the	the	DET
cana-1739	287	69	growth	growth	NOUN
cana-1739	287	70	and	and	CCONJ
cana-1739	287	71	decay	decay	NOUN
cana-1739	287	72	rate	rate	NOUN
cana-1739	287	73	coefficient	coefficient	NOUN
cana-1739	287	74	of	of	ADP
cana-1739	287	75	human	human	ADJ
cana-1739	287	76	community	community	NOUN
cana-1739	287	77	and	and	CCONJ
cana-1739	287	78	0.50	0.50	NUM
cana-1739	287	79	indicates	indicate	VERB
cana-1739	287	80	how	how	SCONJ
cana-1739	287	81	quickly	quickly	ADV
cana-1739	287	82	the	the	DET
cana-1739	287	83	growth	growth	NOUN
cana-1739	287	84	function	function	NOUN
cana-1739	287	85	approaches	approach	VERB
cana-1739	287	86	zero	zero	NUM
cana-1739	287	87	as	as	ADP
cana-1739	287	88	time	time	NOUN
cana-1739	287	89	t	t	NOUN
cana-1739	287	90	increases	increase	NOUN
cana-1739	287	91	.	.	PUNCT
cana-1739	288	1	here	here	ADV
cana-1739	288	2	the	the	DET
cana-1739	288	3	growth	growth	NOUN
cana-1739	288	4	rate	rate	NOUN
cana-1739	288	5	of	of	ADP
cana-1739	288	6	human	human	ADJ
cana-1739	288	7	community	community	NOUN
cana-1739	288	8	in	in	ADP
cana-1739	288	9	green	green	ADJ
cana-1739	288	10	buildings	building	NOUN
cana-1739	288	11	progressively	progressively	ADV
cana-1739	288	12	rises	rise	VERB
cana-1739	288	13	over	over	ADP
cana-1739	288	14	time	time	NOUN
cana-1739	288	15	in	in	ADP
cana-1739	288	16	all	all	DET
cana-1739	288	17	cases	case	NOUN
cana-1739	288	18	of	of	ADP
cana-1739	288	19	lc	lc	NOUN
cana-1739	288	20	,	,	PUNCT
cana-1739	288	21	cf	cf	NOUN
cana-1739	288	22	and	and	CCONJ
cana-1739	288	23	ab	ab	PROPN
cana-1739	288	24	.	.	PUNCT
cana-1739	289	1	(	(	PUNCT
cana-1739	289	2	a	a	X
cana-1739	289	3	)	)	PUNCT
cana-1739	289	4	(	(	PUNCT
cana-1739	289	5	b	b	X
cana-1739	289	6	)	)	PUNCT
cana-1739	289	7	communications	communication	NOUN
cana-1739	289	8	on	on	ADP
cana-1739	289	9	applied	apply	VERB
cana-1739	289	10	nonlinear	nonlinear	ADJ
cana-1739	289	11	analysis	analysis	NOUN
cana-1739	289	12	issn	issn	NOUN
cana-1739	289	13	:	:	PUNCT
cana-1739	289	14	1074	1074	NUM
cana-1739	289	15	-	-	PUNCT
cana-1739	289	16	133x	133x	NUM
cana-1739	289	17	vol	vol	NOUN
cana-1739	289	18	32	32	NUM
cana-1739	289	19	no	no	NOUN
cana-1739	289	20	.	.	NOUN
cana-1739	289	21	2	2	NUM
cana-1739	289	22	(	(	PUNCT
cana-1739	289	23	2025	2025	NUM
cana-1739	289	24	)	)	PUNCT
cana-1739	289	25	249	249	NUM
cana-1739	289	26	https://internationalpubls.com	https://internationalpubls.com	X
cana-1739	289	27	(	(	PUNCT
cana-1739	289	28	c	c	NOUN
cana-1739	289	29	)	)	PUNCT
cana-1739	289	30	(	(	PUNCT
cana-1739	289	31	d	d	X
cana-1739	289	32	)	)	PUNCT
cana-1739	289	33	fig5.numerical	fig5.numerical	PROPN
cana-1739	289	34	simulation	simulation	NOUN
cana-1739	289	35	of	of	ADP
cana-1739	289	36	green	green	ADJ
cana-1739	289	37	buildings	building	NOUN
cana-1739	289	38	for	for	ADP
cana-1739	289	39	various	various	ADJ
cana-1739	289	40	values	value	NOUN
cana-1739	289	41	of	of	ADP
cana-1739	289	42	ν=0.65,0.75,0.85	ν=0.65,0.75,0.85	PROPN
cana-1739	289	43	and	and	CCONJ
cana-1739	289	44	0.95	0.95	NUM
cana-1739	289	45	in	in	ADP
cana-1739	289	46	liouville	liouville	PROPN
cana-1739	289	47	-	-	PUNCT
cana-1739	289	48	caputo	caputo	PROPN
cana-1739	289	49	sense	sense	NOUN
cana-1739	289	50	(	(	PUNCT
cana-1739	289	51	a	a	NOUN
cana-1739	289	52	)	)	PUNCT
cana-1739	289	53	(	(	PUNCT
cana-1739	289	54	b	b	X
cana-1739	289	55	)	)	PUNCT
cana-1739	289	56	communications	communication	NOUN
cana-1739	289	57	on	on	ADP
cana-1739	289	58	applied	apply	VERB
cana-1739	289	59	nonlinear	nonlinear	ADJ
cana-1739	289	60	analysis	analysis	NOUN
cana-1739	289	61	issn	issn	NOUN
cana-1739	289	62	:	:	PUNCT
cana-1739	289	63	1074	1074	NUM
cana-1739	289	64	-	-	PUNCT
cana-1739	289	65	133x	133x	NUM
cana-1739	289	66	vol	vol	NOUN
cana-1739	289	67	32	32	NUM
cana-1739	289	68	no	no	NOUN
cana-1739	289	69	.	.	NOUN
cana-1739	289	70	2	2	NUM
cana-1739	289	71	(	(	PUNCT
cana-1739	289	72	2025	2025	NUM
cana-1739	289	73	)	)	PUNCT
cana-1739	289	74	250	250	NUM
cana-1739	289	75	https://internationalpubls.com	https://internationalpubls.com	X
cana-1739	289	76	(	(	PUNCT
cana-1739	289	77	c	c	NOUN
cana-1739	289	78	)	)	PUNCT
cana-1739	289	79	(	(	PUNCT
cana-1739	289	80	d	d	X
cana-1739	289	81	)	)	PUNCT
cana-1739	289	82	fig	fig	NOUN
cana-1739	289	83	6.numerical	6.numerical	NUM
cana-1739	289	84	simulation	simulation	NOUN
cana-1739	289	85	of	of	ADP
cana-1739	289	86	green	green	ADJ
cana-1739	289	87	buildings	building	NOUN
cana-1739	289	88	for	for	ADP
cana-1739	289	89	various	various	ADJ
cana-1739	289	90	values	value	NOUN
cana-1739	289	91	of	of	ADP
cana-1739	289	92	ν=0.65,0.75,0.85	ν=0.65,0.75,0.85	PROPN
cana-1739	289	93	and	and	CCONJ
cana-1739	289	94	0.95	0.95	NUM
cana-1739	289	95	in	in	ADP
cana-1739	289	96	caputo	caputo	PROPN
cana-1739	289	97	-	-	PUNCT
cana-1739	289	98	fabrizio	fabrizio	PROPN
cana-1739	289	99	sense	sense	NOUN
cana-1739	289	100	.	.	PUNCT
cana-1739	290	1	(	(	PUNCT
cana-1739	290	2	a	a	X
cana-1739	290	3	)	)	PUNCT
cana-1739	290	4	(	(	PUNCT
cana-1739	290	5	b	b	X
cana-1739	290	6	)	)	PUNCT
cana-1739	290	7	communications	communication	NOUN
cana-1739	290	8	on	on	ADP
cana-1739	290	9	applied	apply	VERB
cana-1739	290	10	nonlinear	nonlinear	ADJ
cana-1739	290	11	analysis	analysis	NOUN
cana-1739	290	12	issn	issn	NOUN
cana-1739	290	13	:	:	PUNCT
cana-1739	290	14	1074	1074	NUM
cana-1739	290	15	-	-	PUNCT
cana-1739	290	16	133x	133x	NUM
cana-1739	290	17	vol	vol	NOUN
cana-1739	290	18	32	32	NUM
cana-1739	290	19	no	no	NOUN
cana-1739	290	20	.	.	NOUN
cana-1739	290	21	2	2	NUM
cana-1739	290	22	(	(	PUNCT
cana-1739	290	23	2025	2025	NUM
cana-1739	290	24	)	)	PUNCT
cana-1739	290	25	251	251	NUM
cana-1739	290	26	https://internationalpubls.com	https://internationalpubls.com	X
cana-1739	290	27	(	(	PUNCT
cana-1739	290	28	c	c	NOUN
cana-1739	290	29	)	)	PUNCT
cana-1739	290	30	(	(	PUNCT
cana-1739	290	31	d	d	X
cana-1739	290	32	)	)	PUNCT
cana-1739	290	33	fig	fig	NOUN
cana-1739	290	34	7.numerical	7.numerical	NUM
cana-1739	290	35	simulation	simulation	NOUN
cana-1739	290	36	of	of	ADP
cana-1739	290	37	green	green	ADJ
cana-1739	290	38	buildings	building	NOUN
cana-1739	290	39	for	for	ADP
cana-1739	290	40	various	various	ADJ
cana-1739	290	41	values	value	NOUN
cana-1739	290	42	of	of	ADP
cana-1739	290	43	ν=0.65,0.75,0.85	ν=0.65,0.75,0.85	PROPN
cana-1739	290	44	and	and	CCONJ
cana-1739	290	45	0.95	0.95	NUM
cana-1739	290	46	in	in	ADP
cana-1739	290	47	atangana	atangana	PROPN
cana-1739	290	48	-	-	PUNCT
cana-1739	290	49	baleanu	baleanu	PROPN
cana-1739	290	50	sense	sense	NOUN
cana-1739	290	51	.	.	PUNCT
cana-1739	291	1	case	case	NOUN
cana-1739	291	2	2(fractional	2(fractional	ADJ
cana-1739	291	3	order	order	NOUN
cana-1739	291	4	case):fig[5	case):fig[5	NOUN
cana-1739	291	5	]	]	PUNCT
cana-1739	291	6	shows	show	VERB
cana-1739	291	7	that	that	SCONJ
cana-1739	291	8	when	when	SCONJ
cana-1739	291	9	ν	ν	NOUN
cana-1739	291	10	increases	increase	NOUN
cana-1739	291	11	,	,	PUNCT
cana-1739	291	12	the	the	DET
cana-1739	291	13	growth	growth	NOUN
cana-1739	291	14	rate	rate	NOUN
cana-1739	291	15	of	of	ADP
cana-1739	291	16	green	green	ADJ
cana-1739	291	17	buildings	building	NOUN
cana-1739	291	18	absorbing	absorb	VERB
cana-1739	291	19	greenhouse	greenhouse	NOUN
cana-1739	291	20	gases	gas	NOUN
cana-1739	291	21	also	also	ADV
cana-1739	291	22	increases	increase	VERB
cana-1739	291	23	drastically	drastically	ADV
cana-1739	291	24	,	,	PUNCT
cana-1739	291	25	but	but	CCONJ
cana-1739	291	26	in	in	ADP
cana-1739	291	27	fig	fig	NOUN
cana-1739	291	28	6	6	NUM
cana-1739	291	29	and	and	CCONJ
cana-1739	291	30	7	7	NUM
cana-1739	291	31	,	,	PUNCT
cana-1739	291	32	it	it	PRON
cana-1739	291	33	increases	increase	VERB
cana-1739	291	34	more	more	ADV
cana-1739	291	35	gradually	gradually	ADV
cana-1739	291	36	over	over	ADP
cana-1739	291	37	time	time	NOUN
cana-1739	291	38	,	,	PUNCT
cana-1739	291	39	which	which	PRON
cana-1739	291	40	is	be	AUX
cana-1739	291	41	more	more	ADJ
cana-1739	291	42	in	in	ADP
cana-1739	291	43	line	line	NOUN
cana-1739	291	44	with	with	ADP
cana-1739	291	45	real	real	ADJ
cana-1739	291	46	world	world	NOUN
cana-1739	291	47	circumstances.in	circumstances.in	X
cana-1739	291	48	fig[5	fig[5	NOUN
cana-1739	291	49	-	-	SYM
cana-1739	291	50	7	7	NUM
cana-1739	291	51	]	]	PUNCT
cana-1739	291	52	,	,	PUNCT
cana-1739	291	53	ghg	ghg	PROPN
cana-1739	291	54	emissions	emission	NOUN
cana-1739	291	55	decrease	decrease	VERB
cana-1739	291	56	gradually	gradually	ADV
cana-1739	291	57	over	over	ADP
cana-1739	291	58	time	time	NOUN
cana-1739	291	59	as	as	ADP
cana-1739	291	60	ν	ν	NOUN
cana-1739	291	61	increases	increase	NOUN
cana-1739	291	62	.	.	PUNCT
cana-1739	292	1	according	accord	VERB
cana-1739	292	2	to	to	ADP
cana-1739	292	3	fig	fig	NOUN
cana-1739	292	4	6	6	NUM
cana-1739	292	5	and	and	CCONJ
cana-1739	292	6	7	7	NUM
cana-1739	292	7	,	,	PUNCT
cana-1739	292	8	green	green	ADJ
cana-1739	292	9	buildings	building	NOUN
cana-1739	292	10	can	can	AUX
cana-1739	292	11	produce	produce	VERB
cana-1739	292	12	ingredients	ingredient	NOUN
cana-1739	292	13	proportionally	proportionally	ADV
cana-1739	292	14	with	with	ADP
cana-1739	292	15	increasing	increase	VERB
cana-1739	292	16	v	v	ADP
cana-1739	292	17	due	due	ADP
cana-1739	292	18	to	to	ADP
cana-1739	292	19	their	their	PRON
cana-1739	292	20	high	high	ADJ
cana-1739	292	21	absorption	absorption	NOUN
cana-1739	292	22	of	of	ADP
cana-1739	292	23	greenhouse	greenhouse	NOUN
cana-1739	292	24	gases	gas	NOUN
cana-1739	292	25	,	,	PUNCT
cana-1739	292	26	whereas	whereas	SCONJ
cana-1739	292	27	in	in	ADP
cana-1739	292	28	fig	fig	NOUN
cana-1739	292	29	5	5	NUM
cana-1739	292	30	,	,	PUNCT
cana-1739	292	31	as	as	ADP
cana-1739	292	32	ν	ν	X
cana-1739	292	33	close	close	ADJ
cana-1739	292	34	to	to	ADP
cana-1739	292	35	1	1	NUM
cana-1739	292	36	,	,	PUNCT
cana-1739	292	37	the	the	DET
cana-1739	292	38	production	production	NOUN
cana-1739	292	39	of	of	ADP
cana-1739	292	40	ingredients	ingredient	NOUN
cana-1739	292	41	reaches	reach	VERB
cana-1739	292	42	a	a	DET
cana-1739	292	43	peak	peak	NOUN
cana-1739	292	44	and	and	CCONJ
cana-1739	292	45	then	then	ADV
cana-1739	292	46	falls	fall	VERB
cana-1739	292	47	rapidly	rapidly	ADV
cana-1739	292	48	,	,	PUNCT
cana-1739	292	49	this	this	PRON
cana-1739	292	50	is	be	AUX
cana-1739	292	51	because	because	SCONJ
cana-1739	292	52	of	of	ADP
cana-1739	292	53	lc	lc	PROPN
cana-1739	292	54	's	's	PART
cana-1739	292	55	singularity	singularity	NOUN
cana-1739	292	56	behavior	behavior	NOUN
cana-1739	292	57	.	.	PUNCT
cana-1739	293	1	fig	fig	NOUN
cana-1739	293	2	6	6	NUM
cana-1739	293	3	and	and	CCONJ
cana-1739	293	4	7	7	NUM
cana-1739	293	5	show	show	VERB
cana-1739	293	6	that	that	SCONJ
cana-1739	293	7	the	the	DET
cana-1739	293	8	human	human	ADJ
cana-1739	293	9	community	community	NOUN
cana-1739	293	10	will	will	AUX
cana-1739	293	11	benefit	benefit	VERB
cana-1739	293	12	from	from	ADP
cana-1739	293	13	receiving	receive	VERB
cana-1739	293	14	the	the	DET
cana-1739	293	15	ingredients	ingredient	NOUN
cana-1739	293	16	,	,	PUNCT
cana-1739	293	17	hence	hence	ADV
cana-1739	293	18	it	it	PRON
cana-1739	293	19	rises	rise	VERB
cana-1739	293	20	proportionally	proportionally	ADV
cana-1739	293	21	in	in	ADP
cana-1739	293	22	cases	case	NOUN
cana-1739	293	23	of	of	ADP
cana-1739	293	24	cf	cf	NOUN
cana-1739	293	25	and	and	CCONJ
cana-1739	293	26	ab	ab	PROPN
cana-1739	293	27	,	,	PUNCT
cana-1739	293	28	whereas	whereas	SCONJ
cana-1739	293	29	in	in	ADP
cana-1739	293	30	fig	fig	NOUN
cana-1739	293	31	5	5	NUM
cana-1739	293	32	,	,	PUNCT
cana-1739	293	33	we	we	PRON
cana-1739	293	34	see	see	VERB
cana-1739	293	35	that	that	SCONJ
cana-1739	293	36	for	for	ADP
cana-1739	293	37	small	small	ADJ
cana-1739	293	38	values	value	NOUN
cana-1739	293	39	of	of	ADP
cana-1739	293	40	ν	ν	NOUN
cana-1739	293	41	,	,	PUNCT
cana-1739	293	42	the	the	DET
cana-1739	293	43	human	human	ADJ
cana-1739	293	44	community	community	NOUN
cana-1739	293	45	remains	remain	VERB
cana-1739	293	46	stable	stable	ADJ
cana-1739	293	47	,	,	PUNCT
cana-1739	293	48	which	which	PRON
cana-1739	293	49	violates	violate	VERB
cana-1739	293	50	the	the	DET
cana-1739	293	51	real	real	ADJ
cana-1739	293	52	-	-	PUNCT
cana-1739	293	53	time	time	NOUN
cana-1739	293	54	scenario	scenario	NOUN
cana-1739	293	55	.	.	PUNCT
cana-1739	294	1	hence	hence	ADV
cana-1739	294	2	cf	cf	NOUN
cana-1739	294	3	and	and	CCONJ
cana-1739	294	4	ab	ab	PROPN
cana-1739	294	5	approaches	approach	NOUN
cana-1739	294	6	give	give	VERB
cana-1739	294	7	better	well	ADJ
cana-1739	294	8	results	result	NOUN
cana-1739	294	9	than	than	ADP
cana-1739	294	10	the	the	DET
cana-1739	294	11	lc	lc	PROPN
cana-1739	294	12	approach	approach	NOUN
cana-1739	294	13	.	.	PUNCT
cana-1739	295	1	conclusion	conclusion	NOUN
cana-1739	295	2	this	this	DET
cana-1739	295	3	study	study	NOUN
cana-1739	295	4	developed	develop	VERB
cana-1739	295	5	a	a	DET
cana-1739	295	6	fractional	fractional	ADJ
cana-1739	295	7	variable	variable	ADJ
cana-1739	295	8	-	-	PUNCT
cana-1739	295	9	order	order	NOUN
cana-1739	295	10	model	model	NOUN
cana-1739	295	11	using	use	VERB
cana-1739	295	12	liouville	liouville	PROPN
cana-1739	295	13	-	-	PUNCT
cana-1739	295	14	caputo	caputo	PROPN
cana-1739	295	15	,	,	PUNCT
cana-1739	295	16	caputo	caputo	PROPN
cana-1739	295	17	-	-	PUNCT
cana-1739	295	18	fabrizio	fabrizio	PROPN
cana-1739	295	19	,	,	PUNCT
cana-1739	295	20	and	and	CCONJ
cana-1739	295	21	atangana	atangana	PROPN
cana-1739	295	22	-	-	PUNCT
cana-1739	295	23	baleanu	baleanu	ADJ
cana-1739	295	24	derivatives	derivative	NOUN
cana-1739	295	25	to	to	PART
cana-1739	295	26	explore	explore	VERB
cana-1739	295	27	sustainable	sustainable	ADJ
cana-1739	295	28	building	building	NOUN
cana-1739	295	29	practices	practice	NOUN
cana-1739	295	30	in	in	ADP
cana-1739	295	31	india	india	PROPN
cana-1739	295	32	,	,	PUNCT
cana-1739	295	33	focusing	focus	VERB
cana-1739	295	34	on	on	ADP
cana-1739	295	35	their	their	PRON
cana-1739	295	36	impact	impact	NOUN
cana-1739	295	37	on	on	ADP
cana-1739	295	38	greenhouse	greenhouse	NOUN
cana-1739	295	39	gas	gas	NOUN
cana-1739	295	40	(	(	PUNCT
cana-1739	295	41	ghg	ghg	PROPN
cana-1739	295	42	)	)	PUNCT
cana-1739	295	43	emissions	emission	NOUN
cana-1739	295	44	.	.	PUNCT
cana-1739	296	1	numerical	numerical	ADJ
cana-1739	296	2	simulations	simulation	NOUN
cana-1739	296	3	showed	show	VERB
cana-1739	296	4	that	that	SCONJ
cana-1739	296	5	green	green	ADJ
cana-1739	296	6	buildings	building	NOUN
cana-1739	296	7	can	can	AUX
cana-1739	296	8	effectively	effectively	ADV
cana-1739	296	9	reduce	reduce	VERB
cana-1739	296	10	ghgs	ghg	VERB
cana-1739	296	11	,	,	PUNCT
cana-1739	296	12	with	with	ADP
cana-1739	296	13	the	the	DET
cana-1739	296	14	caputo	caputo	PROPN
cana-1739	296	15	-	-	PUNCT
cana-1739	296	16	fabrizio	fabrizio	PROPN
cana-1739	296	17	and	and	CCONJ
cana-1739	296	18	atangana	atangana	PROPN
cana-1739	296	19	-	-	PUNCT
cana-1739	296	20	baleanu	baleanu	PROPN
cana-1739	296	21	approaches	approach	NOUN
cana-1739	296	22	providing	provide	VERB
cana-1739	296	23	more	more	ADV
cana-1739	296	24	realistic	realistic	ADJ
cana-1739	296	25	and	and	CCONJ
cana-1739	296	26	accurate	accurate	ADJ
cana-1739	296	27	results	result	NOUN
cana-1739	296	28	compared	compare	VERB
cana-1739	296	29	to	to	ADP
cana-1739	296	30	the	the	DET
cana-1739	296	31	liouville	liouville	PROPN
cana-1739	296	32	-	-	PUNCT
cana-1739	296	33	caputo	caputo	PROPN
cana-1739	296	34	method	method	NOUN
cana-1739	296	35	.	.	PUNCT
cana-1739	297	1	the	the	DET
cana-1739	297	2	findings	finding	NOUN
cana-1739	297	3	highlight	highlight	VERB
cana-1739	297	4	the	the	DET
cana-1739	297	5	potential	potential	NOUN
cana-1739	297	6	of	of	ADP
cana-1739	297	7	green	green	ADJ
cana-1739	297	8	buildings	building	NOUN
cana-1739	297	9	in	in	ADP
cana-1739	297	10	fostering	foster	VERB
cana-1739	297	11	sustainable	sustainable	ADJ
cana-1739	297	12	communities	community	NOUN
cana-1739	297	13	,	,	PUNCT
cana-1739	297	14	where	where	SCONJ
cana-1739	297	15	gradual	gradual	ADJ
cana-1739	297	16	ghg	ghg	PROPN
cana-1739	297	17	absorption	absorption	NOUN
cana-1739	297	18	and	and	CCONJ
cana-1739	297	19	the	the	DET
cana-1739	297	20	growth	growth	NOUN
cana-1739	297	21	of	of	ADP
cana-1739	297	22	eco	eco	PROPN
cana-1739	297	23	-	-	PUNCT
cana-1739	297	24	friendly	friendly	ADJ
cana-1739	297	25	components	component	NOUN
cana-1739	297	26	align	align	VERB
cana-1739	297	27	with	with	ADP
cana-1739	297	28	real	real	ADJ
cana-1739	297	29	-	-	PUNCT
cana-1739	297	30	world	world	NOUN
cana-1739	297	31	scenarios	scenario	NOUN
cana-1739	297	32	.	.	PUNCT
cana-1739	298	1	references	reference	NOUN
cana-1739	298	2	[	[	X
cana-1739	298	3	1	1	NUM
cana-1739	298	4	]	]	X
cana-1739	298	5	mohammad	mohammad	PROPN
cana-1739	298	6	qasim	qasim	PROPN
cana-1739	298	7	,	,	PUNCT
cana-1739	298	8	shalilka	shalilka	PROPN
cana-1739	298	9	mehta	mehta	PROPN
cana-1739	298	10	,	,	PUNCT
cana-1739	298	11	sandeep	sandeep	PROPN
cana-1739	298	12	salhotra	salhotra	PROPN
cana-1739	298	13	,	,	PUNCT
cana-1739	298	14	“	"	PUNCT
cana-1739	298	15	cost	cost	NOUN
cana-1739	298	16	optimization	optimization	NOUN
cana-1739	298	17	of	of	ADP
cana-1739	298	18	a	a	DET
cana-1739	298	19	building	building	NOUN
cana-1739	298	20	using	use	VERB
cana-1739	298	21	sustainable	sustainable	ADJ
cana-1739	298	22	building	building	NOUN
cana-1739	298	23	concept	concept	NOUN
cana-1739	298	24	,	,	PUNCT
cana-1739	298	25	”	"	PUNCT
cana-1739	298	26	ijitee	ijitee	NOUN
cana-1739	298	27	,	,	PUNCT
cana-1739	298	28	vol-8,issue-8,2019	vol-8,issue-8,2019	PROPN
cana-1739	298	29	.	.	PUNCT
cana-1739	299	1	communications	communication	NOUN
cana-1739	299	2	on	on	ADP
cana-1739	299	3	applied	apply	VERB
cana-1739	299	4	nonlinear	nonlinear	ADJ
cana-1739	299	5	analysis	analysis	NOUN
cana-1739	299	6	issn	issn	NOUN
cana-1739	299	7	:	:	PUNCT
cana-1739	299	8	1074	1074	NUM
cana-1739	299	9	-	-	PUNCT
cana-1739	299	10	133x	133x	NUM
cana-1739	299	11	vol	vol	NOUN
cana-1739	299	12	32	32	NUM
cana-1739	299	13	no	no	NOUN
cana-1739	299	14	.	.	NOUN
cana-1739	299	15	2	2	NUM
cana-1739	299	16	(	(	PUNCT
cana-1739	299	17	2025	2025	NUM
cana-1739	299	18	)	)	PUNCT
cana-1739	300	1	252	252	NUM
cana-1739	300	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-1739	300	3	[	[	X
cana-1739	300	4	2	2	NUM
cana-1739	300	5	]	]	X
cana-1739	300	6	alnaser	alnaser	NOUN
cana-1739	300	7	,	,	PUNCT
cana-1739	300	8	n.	n.	PROPN
cana-1739	300	9	w.	w.	PROPN
cana-1739	300	10	,	,	PUNCT
cana-1739	300	11	r.	r.	PROPN
cana-1739	300	12	flanagan	flanagan	PROPN
cana-1739	300	13	,	,	PUNCT
cana-1739	300	14	and	and	CCONJ
cana-1739	300	15	w.	w.	PROPN
cana-1739	300	16	e.	e.	PROPN
cana-1739	300	17	alnaser	alnaser	PROPN
cana-1739	300	18	.	.	PUNCT
cana-1739	301	1	"	"	PUNCT
cana-1739	301	2	potential	potential	NOUN
cana-1739	301	3	of	of	ADP
cana-1739	301	4	making	make	VERB
cana-1739	301	5	—	—	PUNCT
cana-1739	301	6	over	over	ADP
cana-1739	301	7	to	to	ADP
cana-1739	301	8	sustainable	sustainable	ADJ
cana-1739	301	9	buildings	building	NOUN
cana-1739	301	10	in	in	ADP
cana-1739	301	11	the	the	DET
cana-1739	301	12	kingdom	kingdom	NOUN
cana-1739	301	13	of	of	ADP
cana-1739	301	14	bahrain	bahrain	NOUN
cana-1739	301	15	.	.	PUNCT
cana-1739	301	16	"	"	PUNCT
cana-1739	302	1	energy	energy	NOUN
cana-1739	302	2	and	and	CCONJ
cana-1739	302	3	buildings	building	NOUN
cana-1739	302	4	,	,	PUNCT
cana-1739	302	5	40	40	NUM
cana-1739	302	6	,	,	PUNCT
cana-1739	302	7	no.7,1304	no.7,1304	PROPN
cana-1739	302	8	-	-	PUNCT
cana-1739	302	9	1323,2008	1323,2008	PROPN
cana-1739	302	10	.	.	PUNCT
cana-1739	303	1	[	[	X
cana-1739	303	2	3	3	NUM
cana-1739	303	3	]	]	X
cana-1739	303	4	zuo	zuo	PROPN
cana-1739	303	5	,	,	PUNCT
cana-1739	303	6	jian	jian	PROPN
cana-1739	303	7	,	,	PUNCT
cana-1739	303	8	and	and	CCONJ
cana-1739	303	9	zhen	zhen	PROPN
cana-1739	303	10	-	-	PUNCT
cana-1739	303	11	yu	yu	PROPN
cana-1739	303	12	zhao	zhao	PROPN
cana-1739	303	13	.	.	PUNCT
cana-1739	304	1	"	"	PUNCT
cana-1739	304	2	green	green	ADJ
cana-1739	304	3	building	building	NOUN
cana-1739	304	4	research	research	NOUN
cana-1739	304	5	–	–	PUNCT
cana-1739	304	6	current	current	ADJ
cana-1739	304	7	status	status	NOUN
cana-1739	304	8	and	and	CCONJ
cana-1739	304	9	future	future	ADJ
cana-1739	304	10	agenda	agenda	NOUN
cana-1739	304	11	:	:	PUNCT
cana-1739	304	12	a	a	DET
cana-1739	304	13	review	review	NOUN
cana-1739	304	14	.	.	PUNCT
cana-1739	304	15	"	"	PUNCT
cana-1739	305	1	renewable	renewable	ADJ
cana-1739	305	2	and	and	CCONJ
cana-1739	305	3	sustainable	sustainable	ADJ
cana-1739	305	4	energy	energy	NOUN
cana-1739	305	5	reviews	review	NOUN
cana-1739	305	6	,	,	PUNCT
cana-1739	305	7	30,271	30,271	NUM
cana-1739	305	8	-	-	SYM
cana-1739	305	9	281,2014	281,2014	NUM
cana-1739	305	10	.	.	PUNCT
cana-1739	306	1	[	[	X
cana-1739	306	2	4	4	NUM
cana-1739	306	3	]	]	X
cana-1739	306	4	kibert	kibert	PROPN
cana-1739	306	5	,	,	PUNCT
cana-1739	306	6	charles	charles	PROPN
cana-1739	306	7	j.	j.	PROPN
cana-1739	306	8	“	"	PUNCT
cana-1739	306	9	green	green	ADJ
cana-1739	306	10	buildings	building	NOUN
cana-1739	306	11	:	:	PUNCT
cana-1739	306	12	an	an	DET
cana-1739	306	13	overview	overview	NOUN
cana-1739	306	14	of	of	ADP
cana-1739	306	15	progress	progress	NOUN
cana-1739	306	16	.	.	PUNCT
cana-1739	306	17	”	"	PUNCT
cana-1739	307	1	journal	journal	NOUN
cana-1739	307	2	of	of	ADP
cana-1739	307	3	land	land	NOUN
cana-1739	307	4	use	use	NOUN
cana-1739	307	5	&	&	CCONJ
cana-1739	307	6	environmental	environmental	ADJ
cana-1739	307	7	law	law	NOUN
cana-1739	307	8	19	19	NUM
cana-1739	307	9	,	,	PUNCT
cana-1739	307	10	no	no	INTJ
cana-1739	307	11	.	.	NOUN
cana-1739	307	12	2	2	NUM
cana-1739	307	13	,	,	PUNCT
cana-1739	307	14	491–502,2004	491–502,2004	NUM
cana-1739	307	15	.	.	PUNCT
cana-1739	308	1	[	[	X
cana-1739	308	2	5	5	NUM
cana-1739	308	3	]	]	SYM
cana-1739	308	4	hamid	hamid	PROPN
cana-1739	308	5	,	,	PUNCT
cana-1739	308	6	zuhairi	zuhairi	PROPN
cana-1739	308	7	abd	abd	PROPN
cana-1739	308	8	,	,	PUNCT
cana-1739	308	9	a.	a.	PROPN
cana-1739	308	10	f.	f.	PROPN
cana-1739	308	11	roslan	roslan	PROPN
cana-1739	308	12	,	,	PUNCT
cana-1739	308	13	m.	m.	PROPN
cana-1739	308	14	c.	c.	PROPN
cana-1739	308	15	ali	ali	PROPN
cana-1739	308	16	,	,	PUNCT
cana-1739	308	17	f.	f.	PROPN
cana-1739	308	18	c.	c.	PROPN
cana-1739	308	19	hung	hung	PROPN
cana-1739	308	20	,	,	PUNCT
cana-1739	308	21	m.	m.	NOUN
cana-1739	308	22	s.	s.	PROPN
cana-1739	308	23	m.	m.	PROPN
cana-1739	308	24	noor	noor	PROPN
cana-1739	308	25	,	,	PUNCT
cana-1739	308	26	and	and	CCONJ
cana-1739	308	27	nurulhuda	nurulhuda	NOUN
cana-1739	308	28	mat	mat	NOUN
cana-1739	308	29	kilau	kilau	NOUN
cana-1739	308	30	.	.	PUNCT
cana-1739	309	1	"towards	"towards	AUX
cana-1739	309	2	a	a	DET
cana-1739	309	3	national	national	ADJ
cana-1739	309	4	green	green	ADJ
cana-1739	309	5	building	building	NOUN
cana-1739	309	6	rating	rating	NOUN
cana-1739	309	7	system	system	NOUN
cana-1739	309	8	for	for	ADP
cana-1739	309	9	malaysia	malaysia	PROPN
cana-1739	309	10	.	.	PUNCT
cana-1739	309	11	"	"	PUNCT
cana-1739	310	1	malaysian	malaysian	ADJ
cana-1739	310	2	construction	construction	PROPN
cana-1739	310	3	research	research	PROPN
cana-1739	310	4	journal	journal	PROPN
cana-1739	310	5	14	14	NUM
cana-1739	310	6	,	,	PUNCT
cana-1739	310	7	no	no	INTJ
cana-1739	310	8	.	.	NOUN
cana-1739	310	9	1,116,2014	1,116,2014	NUM
cana-1739	310	10	.	.	PUNCT
cana-1739	311	1	[	[	X
cana-1739	311	2	6	6	NUM
cana-1739	311	3	]	]	X
cana-1739	311	4	bradley	bradley	PROPN
cana-1739	311	5	guy	guy	PROPN
cana-1739	311	6	,	,	PUNCT
cana-1739	311	7	g.	g.	PROPN
cana-1739	311	8	,	,	PUNCT
cana-1739	311	9	and	and	CCONJ
cana-1739	311	10	charles	charles	PROPN
cana-1739	311	11	j.	j.	PROPN
cana-1739	311	12	kibert	kibert	PROPN
cana-1739	311	13	.	.	PUNCT
cana-1739	312	1	"	"	PUNCT
cana-1739	312	2	developing	develop	VERB
cana-1739	312	3	indicators	indicator	NOUN
cana-1739	312	4	of	of	ADP
cana-1739	312	5	sustainability	sustainability	NOUN
cana-1739	312	6	:	:	PUNCT
cana-1739	312	7	us	us	PROPN
cana-1739	312	8	experience	experience	NOUN
cana-1739	312	9	.	.	PUNCT
cana-1739	312	10	"	"	PUNCT
cana-1739	313	1	building	build	VERB
cana-1739	313	2	research	research	NOUN
cana-1739	313	3	&	&	CCONJ
cana-1739	313	4	information	information	NOUN
cana-1739	313	5	26	26	NUM
cana-1739	313	6	,	,	PUNCT
cana-1739	313	7	no	no	INTJ
cana-1739	313	8	.	.	PUNCT
cana-1739	314	1	1,39	1,39	NUM
cana-1739	314	2	-	-	SYM
cana-1739	314	3	45,1998	45,1998	NUM
cana-1739	314	4	.	.	PUNCT
cana-1739	315	1	[	[	X
cana-1739	315	2	7	7	NUM
cana-1739	315	3	]	]	X
cana-1739	315	4	zhou	zhou	PROPN
cana-1739	315	5	,	,	PUNCT
cana-1739	315	6	lei	lei	PROPN
cana-1739	315	7	,	,	PUNCT
cana-1739	315	8	and	and	CCONJ
cana-1739	315	9	d.	d.	PROPN
cana-1739	315	10	j.	j.	PROPN
cana-1739	315	11	lowe	lowe	PROPN
cana-1739	315	12	.	.	PUNCT
cana-1739	316	1	"	"	PUNCT
cana-1739	316	2	economic	economic	ADJ
cana-1739	316	3	challenges	challenge	NOUN
cana-1739	316	4	of	of	ADP
cana-1739	316	5	sustainable	sustainable	ADJ
cana-1739	316	6	construction	construction	NOUN
cana-1739	316	7	.	.	PUNCT
cana-1739	317	1	"in	"in	X
cana-1739	317	2	proceedings	proceeding	NOUN
cana-1739	317	3	of	of	ADP
cana-1739	317	4	rics	rics	PROPN
cana-1739	317	5	\	\	PROPN
cana-1739	317	6	cobra	cobra	PROPN
cana-1739	317	7	foundation	foundation	NOUN
cana-1739	317	8	construction	construction	NOUN
cana-1739	317	9	and	and	CCONJ
cana-1739	317	10	building	build	VERB
cana-1739	317	11	research	research	NOUN
cana-1739	317	12	conference	conference	NOUN
cana-1739	317	13	,	,	PUNCT
cana-1739	317	14	pp	pp	ADJ
cana-1739	317	15	.	.	PUNCT
cana-1739	318	1	1	1	NUM
cana-1739	318	2	-	-	SYM
cana-1739	318	3	2	2	NUM
cana-1739	318	4	.	.	PUNCT
cana-1739	318	5	wolverhampton	wolverhampton	PROPN
cana-1739	318	6	,	,	PUNCT
cana-1739	318	7	uk	uk	PROPN
cana-1739	318	8	:	:	PUNCT
cana-1739	318	9	university	university	NOUN
cana-1739	318	10	of	of	ADP
cana-1739	318	11	wolverhampton	wolverhampton	PROPN
cana-1739	318	12	,	,	PUNCT
cana-1739	318	13	2003	2003	NUM
cana-1739	318	14	.	.	PUNCT
cana-1739	319	1	[	[	X
cana-1739	319	2	8	8	NUM
cana-1739	319	3	]	]	SYM
cana-1739	319	4	hayles	hayle	NOUN
cana-1739	319	5	,	,	PUNCT
cana-1739	319	6	c.	c.	PROPN
cana-1739	319	7	s.	s.	PROPN
cana-1739	319	8	,	,	PUNCT
cana-1739	319	9	and	and	CCONJ
cana-1739	319	10	t.	t.	PROPN
cana-1739	319	11	kooloos	kooloos	PROPN
cana-1739	319	12	.	.	PUNCT
cana-1739	320	1	"	"	PUNCT
cana-1739	320	2	the	the	DET
cana-1739	320	3	challenges	challenge	NOUN
cana-1739	320	4	and	and	CCONJ
cana-1739	320	5	opportunities	opportunity	NOUN
cana-1739	320	6	for	for	ADP
cana-1739	320	7	sustainable	sustainable	ADJ
cana-1739	320	8	building	building	NOUN
cana-1739	320	9	practices	practice	NOUN
cana-1739	320	10	”	"	PUNCT
cana-1739	320	11	benefits	benefit	NOUN
cana-1739	320	12	2	2	NUM
cana-1739	320	13	,	,	PUNCT
cana-1739	320	14	19,2005	19,2005	NUM
cana-1739	320	15	.	.	PUNCT
cana-1739	321	1	[	[	X
cana-1739	321	2	9	9	NUM
cana-1739	321	3	]	]	PUNCT
cana-1739	321	4	du	du	NOUN
cana-1739	321	5	plessis	plessis	NOUN
cana-1739	321	6	,	,	PUNCT
cana-1739	321	7	chrisna	chrisna	NOUN
cana-1739	321	8	.	.	PUNCT
cana-1739	322	1	"	"	PUNCT
cana-1739	322	2	agenda	agenda	NOUN
cana-1739	322	3	21	21	NUM
cana-1739	322	4	for	for	ADP
cana-1739	322	5	sustainable	sustainable	ADJ
cana-1739	322	6	construction	construction	NOUN
cana-1739	322	7	in	in	ADP
cana-1739	322	8	developing	develop	VERB
cana-1739	322	9	countries	country	NOUN
cana-1739	322	10	.	.	PUNCT
cana-1739	322	11	"	"	PUNCT
cana-1739	323	1	csir	csir	PROPN
cana-1739	323	2	report	report	NOUN
cana-1739	323	3	boue	boue	NOUN
cana-1739	323	4	204,25,2004	204,25,2004	NUM
cana-1739	323	5	.	.	PUNCT
cana-1739	324	1	[	[	X
cana-1739	324	2	10	10	NUM
cana-1739	324	3	]	]	X
cana-1739	324	4	santamouris	santamouri	NOUN
cana-1739	324	5	,	,	PUNCT
cana-1739	324	6	m.	m.	NOUN
cana-1739	324	7	,	,	PUNCT
cana-1739	324	8	r.	r.	PROPN
cana-1739	324	9	paolini	paolini	PROPN
cana-1739	324	10	,	,	PUNCT
cana-1739	324	11	s.	s.	PROPN
cana-1739	324	12	haddad	haddad	PROPN
cana-1739	324	13	,	,	PUNCT
cana-1739	324	14	a.	a.	NOUN
cana-1739	324	15	synnefa	synnefa	PROPN
cana-1739	324	16	,	,	PUNCT
cana-1739	324	17	s.	s.	PROPN
cana-1739	324	18	garshasbi	garshasbi	PROPN
cana-1739	324	19	,	,	PUNCT
cana-1739	324	20	g.	g.	PROPN
cana-1739	324	21	hatvani	hatvani	PROPN
cana-1739	324	22	-	-	PUNCT
cana-1739	324	23	kovacs	kovacs	PROPN
cana-1739	324	24	,	,	PUNCT
cana-1739	324	25	k.	k.	PROPN
cana-1739	324	26	gobakis	gobakis	PROPN
cana-1739	324	27	et	et	PROPN
cana-1739	324	28	al	al	PROPN
cana-1739	324	29	.	.	PUNCT
cana-1739	325	1	"	"	PUNCT
cana-1739	325	2	heat	heat	NOUN
cana-1739	325	3	mitigation	mitigation	NOUN
cana-1739	325	4	technologies	technology	NOUN
cana-1739	325	5	can	can	AUX
cana-1739	325	6	improve	improve	VERB
cana-1739	325	7	sustainability	sustainability	NOUN
cana-1739	325	8	in	in	ADP
cana-1739	325	9	cities	city	NOUN
cana-1739	325	10	.	.	PUNCT
cana-1739	326	1	an	an	DET
cana-1739	326	2	holistic	holistic	ADJ
cana-1739	326	3	experimental	experimental	ADJ
cana-1739	326	4	and	and	CCONJ
cana-1739	326	5	numerical	numerical	ADJ
cana-1739	326	6	impact	impact	NOUN
cana-1739	326	7	assessment	assessment	NOUN
cana-1739	326	8	of	of	ADP
cana-1739	326	9	urban	urban	ADJ
cana-1739	326	10	overheating	overheating	ADJ
cana-1739	326	11	and	and	CCONJ
cana-1739	326	12	related	related	ADJ
cana-1739	326	13	heat	heat	NOUN
cana-1739	326	14	mitigation	mitigation	NOUN
cana-1739	326	15	strategies	strategy	NOUN
cana-1739	326	16	on	on	ADP
cana-1739	326	17	energy	energy	NOUN
cana-1739	326	18	consumption	consumption	NOUN
cana-1739	326	19	,	,	PUNCT
cana-1739	326	20	indoor	indoor	ADJ
cana-1739	326	21	comfort	comfort	NOUN
cana-1739	326	22	,	,	PUNCT
cana-1739	326	23	vulnerability	vulnerability	NOUN
cana-1739	326	24	and	and	CCONJ
cana-1739	326	25	heat	heat	NOUN
cana-1739	326	26	-	-	PUNCT
cana-1739	326	27	related	relate	VERB
cana-1739	326	28	mortality	mortality	NOUN
cana-1739	326	29	and	and	CCONJ
cana-1739	326	30	morbidity	morbidity	NOUN
cana-1739	326	31	in	in	ADP
cana-1739	326	32	cities	city	NOUN
cana-1739	326	33	.	.	PUNCT
cana-1739	326	34	"	"	PUNCT
cana-1739	327	1	energy	energy	NOUN
cana-1739	327	2	and	and	CCONJ
cana-1739	327	3	buildings	building	NOUN
cana-1739	327	4	217	217	NUM
cana-1739	327	5	,	,	PUNCT
cana-1739	327	6	110002	110002	NUM
cana-1739	327	7	,	,	PUNCT
cana-1739	327	8	2020	2020	NUM
cana-1739	327	9	.	.	PUNCT
cana-1739	328	1	[	[	X
cana-1739	328	2	11	11	NUM
cana-1739	328	3	]	]	PUNCT
cana-1739	328	4	kremer	kremer	PROPN
cana-1739	328	5	,	,	PUNCT
cana-1739	328	6	peleg	peleg	PROPN
cana-1739	328	7	,	,	PUNCT
cana-1739	328	8	annegret	annegret	NOUN
cana-1739	328	9	haase	haase	NOUN
cana-1739	328	10	,	,	PUNCT
cana-1739	328	11	and	and	CCONJ
cana-1739	328	12	dagmar	dagmar	PROPN
cana-1739	328	13	haase	haase	PROPN
cana-1739	328	14	.	.	PUNCT
cana-1739	329	1	"	"	PUNCT
cana-1739	329	2	the	the	DET
cana-1739	329	3	future	future	NOUN
cana-1739	329	4	of	of	ADP
cana-1739	329	5	urban	urban	ADJ
cana-1739	329	6	sustainability	sustainability	NOUN
cana-1739	329	7	:	:	PUNCT
cana-1739	329	8	smart	smart	ADJ
cana-1739	329	9	,	,	PUNCT
cana-1739	329	10	efficient	efficient	ADJ
cana-1739	329	11	,	,	PUNCT
cana-1739	329	12	green	green	ADJ
cana-1739	329	13	or	or	CCONJ
cana-1739	329	14	just	just	ADV
cana-1739	329	15	?	?	PUNCT
cana-1739	330	1	introduction	introduction	NOUN
cana-1739	330	2	to	to	ADP
cana-1739	330	3	the	the	DET
cana-1739	330	4	special	special	ADJ
cana-1739	330	5	issue	issue	NOUN
cana-1739	330	6	.	.	PUNCT
cana-1739	330	7	"	"	PUNCT
cana-1739	331	1	sustainable	sustainable	ADJ
cana-1739	331	2	cities	city	NOUN
cana-1739	331	3	and	and	CCONJ
cana-1739	331	4	society	society	NOUN
cana-1739	331	5	51,101761,2019	51,101761,2019	NUM
cana-1739	331	6	.	.	PUNCT
cana-1739	332	1	[	[	X
cana-1739	332	2	12	12	NUM
cana-1739	332	3	]	]	PUNCT
cana-1739	332	4	illankoon	illankoon	NOUN
cana-1739	332	5	,	,	PUNCT
cana-1739	332	6	i	i	PRON
cana-1739	332	7	m	m	VERB
cana-1739	332	8	chethana	chethana	PROPN
cana-1739	332	9	s.	s.	PROPN
cana-1739	332	10	,	,	PUNCT
cana-1739	332	11	vivian	vivian	PROPN
cana-1739	332	12	wy	wy	PROPN
cana-1739	332	13	tam	tam	PROPN
cana-1739	332	14	,	,	PUNCT
cana-1739	332	15	khoa	khoa	PROPN
cana-1739	332	16	n.	n.	PROPN
cana-1739	332	17	le	le	PROPN
cana-1739	332	18	,	,	PUNCT
cana-1739	332	19	and	and	CCONJ
cana-1739	332	20	liyin	liyin	PROPN
cana-1739	332	21	shen	shen	NOUN
cana-1739	332	22	.	.	PUNCT
cana-1739	333	1	"	"	PUNCT
cana-1739	333	2	key	key	ADJ
cana-1739	333	3	credit	credit	NOUN
cana-1739	333	4	criteria	criterion	NOUN
cana-1739	333	5	among	among	ADP
cana-1739	333	6	international	international	ADJ
cana-1739	333	7	green	green	ADJ
cana-1739	333	8	building	building	NOUN
cana-1739	333	9	rating	rating	NOUN
cana-1739	333	10	tools	tool	NOUN
cana-1739	333	11	.	.	PUNCT
cana-1739	333	12	"	"	PUNCT
cana-1739	334	1	journal	journal	NOUN
cana-1739	334	2	of	of	ADP
cana-1739	334	3	cleaner	clean	ADJ
cana-1739	334	4	production	production	NOUN
cana-1739	334	5	164	164	NUM
cana-1739	334	6	,	,	PUNCT
cana-1739	334	7	209	209	NUM
cana-1739	334	8	-	-	PUNCT
cana-1739	334	9	220,2017	220,2017	NUM
cana-1739	334	10	.	.	PUNCT
cana-1739	335	1	[	[	X
cana-1739	335	2	13	13	NUM
cana-1739	335	3	]	]	SYM
cana-1739	335	4	harvey	harvey	NOUN
cana-1739	335	5	,	,	PUNCT
cana-1739	335	6	steve	steve	PROPN
cana-1739	335	7	,	,	PUNCT
cana-1739	335	8	e.	e.	PROPN
cana-1739	335	9	kevin	kevin	PROPN
cana-1739	335	10	kelloway	kelloway	PROPN
cana-1739	335	11	,	,	PUNCT
cana-1739	335	12	and	and	CCONJ
cana-1739	335	13	leslie	leslie	PROPN
cana-1739	335	14	duncan	duncan	PROPN
cana-1739	335	15	-	-	PUNCT
cana-1739	335	16	leiper	leiper	NOUN
cana-1739	335	17	.	.	PUNCT
cana-1739	336	1	"	"	PUNCT
cana-1739	336	2	trust	trust	NOUN
cana-1739	336	3	in	in	ADP
cana-1739	336	4	management	management	NOUN
cana-1739	336	5	as	as	ADP
cana-1739	336	6	a	a	DET
cana-1739	336	7	buffer	buffer	NOUN
cana-1739	336	8	of	of	ADP
cana-1739	336	9	the	the	DET
cana-1739	336	10	relationships	relationship	NOUN
cana-1739	336	11	between	between	ADP
cana-1739	336	12	overload	overload	NOUN
cana-1739	336	13	and	and	CCONJ
cana-1739	336	14	strain	strain	NOUN
cana-1739	336	15	.	.	PUNCT
cana-1739	336	16	"	"	PUNCT
cana-1739	337	1	journal	journal	NOUN
cana-1739	337	2	of	of	ADP
cana-1739	337	3	occupational	occupational	ADJ
cana-1739	337	4	health	health	NOUN
cana-1739	337	5	psychology	psychology	NOUN
cana-1739	337	6	8	8	NUM
cana-1739	337	7	,	,	PUNCT
cana-1739	337	8	no	no	INTJ
cana-1739	337	9	.	.	PUNCT
cana-1739	337	10	4,306,2003	4,306,2003	NUM
cana-1739	337	11	.	.	PUNCT
cana-1739	338	1	[	[	X
cana-1739	338	2	14	14	NUM
cana-1739	338	3	]	]	X
cana-1739	338	4	mahmoud	mahmoud	PROPN
cana-1739	338	5	,	,	PUNCT
cana-1739	338	6	sherif	sherif	PROPN
cana-1739	338	7	,	,	PUNCT
cana-1739	338	8	tarek	tarek	PROPN
cana-1739	338	9	zayed	zayed	PROPN
cana-1739	338	10	,	,	PUNCT
cana-1739	338	11	and	and	CCONJ
cana-1739	338	12	mohammad	mohammad	PROPN
cana-1739	338	13	fahmy	fahmy	PROPN
cana-1739	338	14	.	.	PUNCT
cana-1739	339	1	"	"	PUNCT
cana-1739	339	2	development	development	NOUN
cana-1739	339	3	of	of	ADP
cana-1739	339	4	sustainability	sustainability	NOUN
cana-1739	339	5	assessment	assessment	NOUN
cana-1739	339	6	tool	tool	NOUN
cana-1739	339	7	for	for	ADP
cana-1739	339	8	existing	exist	VERB
cana-1739	339	9	buildings	building	NOUN
cana-1739	339	10	.	.	PUNCT
cana-1739	339	11	"	"	PUNCT
cana-1739	340	1	sustainable	sustainable	ADJ
cana-1739	340	2	cities	city	NOUN
cana-1739	340	3	and	and	CCONJ
cana-1739	340	4	society	society	NOUN
cana-1739	340	5	44,99	44,99	PROPN
cana-1739	340	6	-	-	PUNCT
cana-1739	340	7	119,2019	119,2019	NUM
cana-1739	340	8	.	.	PUNCT
cana-1739	341	1	[	[	X
cana-1739	341	2	15	15	NUM
cana-1739	341	3	]	]	X
cana-1739	341	4	biswas	biswas	PROPN
cana-1739	341	5	,	,	PUNCT
cana-1739	341	6	md	md	PROPN
cana-1739	341	7	haider	haider	PROPN
cana-1739	341	8	ali	ali	PROPN
cana-1739	341	9	,	,	PUNCT
cana-1739	341	10	pinky	pinky	PROPN
cana-1739	341	11	rani	rani	PROPN
cana-1739	341	12	dey	dey	PROPN
cana-1739	341	13	,	,	PUNCT
cana-1739	341	14	md	md	PROPN
cana-1739	341	15	sirajul	sirajul	PROPN
cana-1739	341	16	islam	islam	PROPN
cana-1739	341	17	,	,	PUNCT
cana-1739	341	18	and	and	CCONJ
cana-1739	341	19	sajib	sajib	ADJ
cana-1739	341	20	mandal	mandal	NOUN
cana-1739	341	21	.	.	PUNCT
cana-1739	342	1	"mathematical	"mathematical	ADJ
cana-1739	342	2	model	model	NOUN
cana-1739	342	3	applied	apply	VERB
cana-1739	342	4	to	to	ADP
cana-1739	342	5	green	green	ADJ
cana-1739	342	6	building	building	NOUN
cana-1739	342	7	concept	concept	NOUN
cana-1739	342	8	for	for	ADP
cana-1739	342	9	sustainable	sustainable	ADJ
cana-1739	342	10	cities	city	NOUN
cana-1739	342	11	under	under	ADP
cana-1739	342	12	climate	climate	NOUN
cana-1739	342	13	change	change	NOUN
cana-1739	342	14	.	.	PUNCT
cana-1739	342	15	"	"	PUNCT
cana-1739	343	1	journal	journal	PROPN
cana-1739	343	2	of	of	ADP
cana-1739	343	3	contemporary	contemporary	PROPN
cana-1739	343	4	urban	urban	PROPN
cana-1739	343	5	affairs	affair	NOUN
cana-1739	343	6	6	6	NUM
cana-1739	343	7	,	,	PUNCT
cana-1739	343	8	no	no	INTJ
cana-1739	343	9	.	.	PUNCT
cana-1739	344	1	1,36	1,36	NUM
cana-1739	344	2	-	-	PUNCT
cana-1739	344	3	50,2022	50,2022	NOUN
cana-1739	344	4	.	.	PUNCT
cana-1739	345	1	[	[	X
cana-1739	345	2	16	16	NUM
cana-1739	345	3	]	]	X
cana-1739	345	4	caputo	caputo	PROPN
cana-1739	345	5	,	,	PUNCT
cana-1739	345	6	michele	michele	PROPN
cana-1739	345	7	,	,	PUNCT
cana-1739	345	8	and	and	CCONJ
cana-1739	345	9	mauro	mauro	PROPN
cana-1739	345	10	fabrizio	fabrizio	PROPN
cana-1739	345	11	.	.	PUNCT
cana-1739	346	1	"	"	PUNCT
cana-1739	346	2	a	a	DET
cana-1739	346	3	new	new	ADJ
cana-1739	346	4	definition	definition	NOUN
cana-1739	346	5	of	of	ADP
cana-1739	346	6	fractional	fractional	ADJ
cana-1739	346	7	derivative	derivative	NOUN
cana-1739	346	8	without	without	ADP
cana-1739	346	9	singular	singular	ADJ
cana-1739	346	10	kernel	kernel	NOUN
cana-1739	346	11	.	.	PUNCT
cana-1739	346	12	"	"	PUNCT
cana-1739	347	1	progress	progress	NOUN
cana-1739	347	2	in	in	ADP
cana-1739	347	3	fractional	fractional	ADJ
cana-1739	347	4	differentiation	differentiation	NOUN
cana-1739	347	5	&	&	CCONJ
cana-1739	347	6	applications	application	NOUN
cana-1739	347	7	1	1	NUM
cana-1739	347	8	,	,	PUNCT
cana-1739	347	9	no	no	DET
cana-1739	347	10	2	2	NUM
cana-1739	347	11	,	,	PUNCT
cana-1739	347	12	73	73	NUM
cana-1739	347	13	-	-	SYM
cana-1739	347	14	85,2015	85,2015	NUM
cana-1739	347	15	.	.	PUNCT
cana-1739	348	1	[	[	X
cana-1739	348	2	17	17	NUM
cana-1739	348	3	]	]	PUNCT
cana-1739	348	4	atangana	atangana	PROPN
cana-1739	348	5	,	,	PUNCT
cana-1739	348	6	abdon	abdon	PROPN
cana-1739	348	7	,	,	PUNCT
cana-1739	348	8	and	and	CCONJ
cana-1739	348	9	dumitru	dumitru	PROPN
cana-1739	348	10	baleanu	baleanu	NOUN
cana-1739	348	11	.	.	PUNCT
cana-1739	349	1	"	"	PUNCT
cana-1739	349	2	new	new	ADJ
cana-1739	349	3	fractional	fractional	ADJ
cana-1739	349	4	derivatives	derivative	NOUN
cana-1739	349	5	with	with	ADP
cana-1739	349	6	nonlocal	nonlocal	ADJ
cana-1739	349	7	and	and	CCONJ
cana-1739	349	8	non	non	ADJ
cana-1739	349	9	-	-	ADJ
cana-1739	349	10	singular	singular	ADJ
cana-1739	349	11	kernel	kernel	NOUN
cana-1739	349	12	:	:	PUNCT
cana-1739	349	13	theory	theory	NOUN
cana-1739	349	14	and	and	CCONJ
cana-1739	349	15	application	application	NOUN
cana-1739	349	16	to	to	PART
cana-1739	349	17	heat	heat	NOUN
cana-1739	349	18	transfer	transfer	NOUN
cana-1739	349	19	model	model	NOUN
cana-1739	349	20	.	.	PUNCT
cana-1739	349	21	"	"	PUNCT
cana-1739	350	1	arxiv	arxiv	PROPN
cana-1739	350	2	preprintarxiv:1602.03408	preprintarxiv:1602.03408	NUM
cana-1739	350	3	,	,	PUNCT
cana-1739	350	4	2016	2016	NUM
cana-1739	350	5	.	.	PUNCT
cana-1739	351	1	[	[	X
cana-1739	351	2	18	18	NUM
cana-1739	351	3	]	]	PUNCT
cana-1739	351	4	owolabi	owolabi	NOUN
cana-1739	351	5	,	,	PUNCT
cana-1739	351	6	kolade	kolade	ADJ
cana-1739	351	7	m.	m.	NOUN
cana-1739	351	8	"	"	PUNCT
cana-1739	351	9	mathematical	mathematical	ADJ
cana-1739	351	10	modelling	modelling	NOUN
cana-1739	351	11	and	and	CCONJ
cana-1739	351	12	analysis	analysis	NOUN
cana-1739	351	13	of	of	ADP
cana-1739	351	14	two	two	NUM
cana-1739	351	15	-	-	PUNCT
cana-1739	351	16	component	component	NOUN
cana-1739	351	17	system	system	NOUN
cana-1739	351	18	with	with	ADP
cana-1739	351	19	caputo	caputo	PROPN
cana-1739	351	20	fractional	fractional	ADJ
cana-1739	351	21	derivative	derivative	ADJ
cana-1739	351	22	order	order	NOUN
cana-1739	351	23	.	.	PUNCT
cana-1739	351	24	"	"	PUNCT
cana-1739	352	1	chaos	chaos	NOUN
cana-1739	352	2	,	,	PUNCT
cana-1739	352	3	solitons	soliton	NOUN
cana-1739	352	4	&	&	CCONJ
cana-1739	352	5	fractals	fractal	VERB
cana-1739	352	6	103,544	103,544	NUM
cana-1739	352	7	-	-	SYM
cana-1739	352	8	554,2017	554,2017	NUM
cana-1739	352	9	.	.	PUNCT
cana-1739	353	1	[	[	X
cana-1739	353	2	19	19	NUM
cana-1739	353	3	]	]	PUNCT
cana-1739	353	4	owolabi	owolabi	NOUN
cana-1739	353	5	,	,	PUNCT
cana-1739	353	6	kolade	kolade	ADJ
cana-1739	353	7	m.	m.	NOUN
cana-1739	353	8	"	"	PUNCT
cana-1739	353	9	robust	robust	ADJ
cana-1739	353	10	and	and	CCONJ
cana-1739	353	11	adaptive	adaptive	ADJ
cana-1739	353	12	techniques	technique	NOUN
cana-1739	353	13	for	for	ADP
cana-1739	353	14	numerical	numerical	ADJ
cana-1739	353	15	simulation	simulation	NOUN
cana-1739	353	16	of	of	ADP
cana-1739	353	17	nonlinear	nonlinear	ADJ
cana-1739	353	18	partial	partial	ADJ
cana-1739	353	19	differential	differential	ADJ
cana-1739	353	20	equations	equation	NOUN
cana-1739	353	21	of	of	ADP
cana-1739	353	22	fractional	fractional	ADJ
cana-1739	353	23	order	order	NOUN
cana-1739	353	24	.	.	PUNCT
cana-1739	353	25	"	"	PUNCT
cana-1739	354	1	communications	communication	NOUN
cana-1739	354	2	in	in	ADP
cana-1739	354	3	nonlinear	nonlinear	ADJ
cana-1739	354	4	science	science	NOUN
cana-1739	354	5	and	and	CCONJ
cana-1739	354	6	numerical	numerical	PROPN
cana-1739	354	7	simulation	simulation	PROPN
cana-1739	354	8	44	44	NUM
cana-1739	354	9	,	,	PUNCT
cana-1739	354	10	304	304	NUM
cana-1739	354	11	-	-	SYM
cana-1739	354	12	317,2017	317,2017	NUM
cana-1739	354	13	.	.	PUNCT
cana-1739	355	1	[	[	X
cana-1739	355	2	20	20	NUM
cana-1739	355	3	]	]	X
cana-1739	355	4	guo	guo	PROPN
cana-1739	355	5	,	,	PUNCT
cana-1739	355	6	yong‐mei	yong‐mei	PROPN
cana-1739	355	7	,	,	PUNCT
cana-1739	355	8	yang	yang	PROPN
cana-1739	355	9	zhao	zhao	PROPN
cana-1739	355	10	,	,	PUNCT
cana-1739	355	11	yao‐ming	yao‐me	VERB
cana-1739	355	12	zhou	zhou	PROPN
cana-1739	355	13	,	,	PUNCT
cana-1739	355	14	zhong‐bin	zhong‐bin	PROPN
cana-1739	355	15	xiao	xiao	PROPN
cana-1739	355	16	,	,	PUNCT
cana-1739	355	17	and	and	CCONJ
cana-1739	355	18	xiao‐jun	xiao‐jun	PROPN
cana-1739	355	19	yang	yang	PROPN
cana-1739	355	20	.	.	PUNCT
cana-1739	355	21	"on	"on	PROPN
cana-1739	356	1	the	the	DET
cana-1739	356	2	local	local	ADJ
cana-1739	356	3	fractional	fractional	ADJ
cana-1739	356	4	lwr	lwr	PROPN
cana-1739	356	5	model	model	PROPN
cana-1739	356	6	in	in	ADP
cana-1739	356	7	fractal	fractal	ADJ
cana-1739	356	8	traffic	traffic	NOUN
cana-1739	356	9	flows	flow	NOUN
cana-1739	356	10	in	in	ADP
cana-1739	356	11	the	the	DET
cana-1739	356	12	entropy	entropy	NOUN
cana-1739	356	13	condition	condition	NOUN
cana-1739	356	14	.	.	PUNCT
cana-1739	356	15	"	"	PUNCT
cana-1739	357	1	mathematical	mathematical	ADJ
cana-1739	357	2	methods	method	NOUN
cana-1739	357	3	in	in	ADP
cana-1739	357	4	the	the	DET
cana-1739	357	5	applied	apply	VERB
cana-1739	357	6	sciences	science	NOUN
cana-1739	357	7	40	40	NUM
cana-1739	357	8	,	,	PUNCT
cana-1739	357	9	no	no	INTJ
cana-1739	357	10	.	.	PUNCT
cana-1739	358	1	17,6127	17,6127	NUM
cana-1739	358	2	-	-	SYM
cana-1739	358	3	6132,2017	6132,2017	NUM
cana-1739	358	4	.	.	PUNCT
cana-1739	359	1	[	[	X
cana-1739	359	2	21	21	NUM
cana-1739	359	3	]	]	X
cana-1739	359	4	kumar	kumar	PROPN
cana-1739	359	5	,	,	PUNCT
cana-1739	359	6	sunil	sunil	PROPN
cana-1739	359	7	,	,	PUNCT
cana-1739	359	8	amit	amit	PROPN
cana-1739	359	9	kumar	kumar	PROPN
cana-1739	359	10	,	,	PUNCT
cana-1739	359	11	and	and	CCONJ
cana-1739	359	12	dumitru	dumitru	PROPN
cana-1739	359	13	baleanu	baleanu	NOUN
cana-1739	359	14	.	.	PUNCT
cana-1739	360	1	"	"	PUNCT
cana-1739	360	2	two	two	NUM
cana-1739	360	3	analytical	analytical	ADJ
cana-1739	360	4	methods	method	NOUN
cana-1739	360	5	for	for	ADP
cana-1739	360	6	timefractional	timefractional	ADJ
cana-1739	360	7	nonlinear	nonlinear	ADJ
cana-1739	360	8	coupled	couple	VERB
cana-1739	360	9	boussinesq	boussinesq	ADJ
cana-1739	360	10	–	–	PUNCT
cana-1739	360	11	burger	burger	NOUN
cana-1739	360	12	’s	’s	PART
cana-1739	360	13	equations	equation	NOUN
cana-1739	360	14	arise	arise	VERB
cana-1739	360	15	in	in	ADP
cana-1739	360	16	propagation	propagation	NOUN
cana-1739	360	17	of	of	ADP
cana-1739	360	18	shallow	shallow	ADJ
cana-1739	360	19	water	water	NOUN
cana-1739	360	20	waves	wave	NOUN
cana-1739	360	21	.	.	PUNCT
cana-1739	360	22	"	"	PUNCT
cana-1739	361	1	nonlinear	nonlinear	ADJ
cana-1739	361	2	dynamics	dynamic	NOUN
cana-1739	361	3	85,699715,2016	85,699715,2016	NUM
cana-1739	361	4	.	.	PUNCT
cana-1739	362	1	[	[	X
cana-1739	362	2	22	22	NUM
cana-1739	362	3	]	]	PUNCT
cana-1739	362	4	atangana	atangana	PROPN
cana-1739	362	5	,	,	PUNCT
cana-1739	362	6	abdon	abdon	PROPN
cana-1739	362	7	,	,	PUNCT
cana-1739	362	8	and	and	CCONJ
cana-1739	362	9	josé	josé	PROPN
cana-1739	362	10	francisco	francisco	PROPN
cana-1739	362	11	gómez	gómez	PROPN
cana-1739	362	12	-	-	PUNCT
cana-1739	362	13	aguilar	aguilar	PROPN
cana-1739	362	14	.	.	PUNCT
cana-1739	363	1	"	"	PUNCT
cana-1739	363	2	decolonisation	decolonisation	NOUN
cana-1739	363	3	of	of	ADP
cana-1739	363	4	fractional	fractional	ADJ
cana-1739	363	5	calculus	calculus	NOUN
cana-1739	363	6	rules	rule	NOUN
cana-1739	363	7	:	:	PUNCT
cana-1739	363	8	breaking	break	VERB
cana-1739	363	9	commutativity	commutativity	NOUN
cana-1739	363	10	and	and	CCONJ
cana-1739	363	11	associativity	associativity	NOUN
cana-1739	363	12	to	to	PART
cana-1739	363	13	capture	capture	VERB
cana-1739	363	14	more	more	ADJ
cana-1739	363	15	natural	natural	ADJ
cana-1739	363	16	phenomena	phenomenon	NOUN
cana-1739	363	17	.	.	PUNCT
cana-1739	363	18	"	"	PUNCT
cana-1739	364	1	the	the	DET
cana-1739	364	2	european	european	PROPN
cana-1739	364	3	physical	physical	PROPN
cana-1739	364	4	journal	journal	PROPN
cana-1739	364	5	plus	plus	CCONJ
cana-1739	364	6	133,122,2018	133,122,2018	PROPN
cana-1739	364	7	.	.	PUNCT
cana-1739	365	1	communications	communication	NOUN
cana-1739	365	2	on	on	ADP
cana-1739	365	3	applied	apply	VERB
cana-1739	365	4	nonlinear	nonlinear	ADJ
cana-1739	365	5	analysis	analysis	NOUN
cana-1739	365	6	issn	issn	NOUN
cana-1739	365	7	:	:	PUNCT
cana-1739	365	8	1074	1074	NUM
cana-1739	365	9	-	-	PUNCT
cana-1739	365	10	133x	133x	NUM
cana-1739	365	11	vol	vol	NOUN
cana-1739	365	12	32	32	NUM
cana-1739	365	13	no	no	NOUN
cana-1739	365	14	.	.	NOUN
cana-1739	365	15	2	2	NUM
cana-1739	365	16	(	(	PUNCT
cana-1739	365	17	2025	2025	NUM
cana-1739	365	18	)	)	PUNCT
cana-1739	366	1	253	253	NUM
cana-1739	366	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-1739	366	3	[	[	X
cana-1739	366	4	23	23	NUM
cana-1739	366	5	]	]	X
cana-1739	366	6	alkahtani	alkahtani	PROPN
cana-1739	366	7	,	,	PUNCT
cana-1739	366	8	badr	badr	PROPN
cana-1739	366	9	saad	saad	PROPN
cana-1739	366	10	t.	t.	PROPN
cana-1739	366	11	,	,	PUNCT
cana-1739	366	12	ilknur	ilknur	PROPN
cana-1739	366	13	koca	koca	PROPN
cana-1739	366	14	,	,	PUNCT
cana-1739	366	15	and	and	CCONJ
cana-1739	366	16	abdon	abdon	PROPN
cana-1739	366	17	atangana	atangana	PROPN
cana-1739	366	18	.	.	PUNCT
cana-1739	367	1	"	"	PUNCT
cana-1739	367	2	a	a	DET
cana-1739	367	3	novel	novel	ADJ
cana-1739	367	4	approach	approach	NOUN
cana-1739	367	5	of	of	ADP
cana-1739	367	6	variable	variable	ADJ
cana-1739	367	7	order	order	NOUN
cana-1739	367	8	derivative	derivative	NOUN
cana-1739	367	9	:	:	PUNCT
cana-1739	367	10	theory	theory	NOUN
cana-1739	367	11	and	and	CCONJ
cana-1739	367	12	methods	method	NOUN
cana-1739	367	13	.	.	PUNCT
cana-1739	367	14	"	"	PUNCT
cana-1739	368	1	j.	j.	PROPN
cana-1739	368	2	nonlinear	nonlinear	PROPN
cana-1739	368	3	sci	sci	PROPN
cana-1739	368	4	.	.	PUNCT
cana-1739	368	5	appl	appl	PROPN
cana-1739	368	6	9	9	NUM
cana-1739	368	7	,	,	PUNCT
cana-1739	368	8	no	no	INTJ
cana-1739	368	9	.	.	NOUN
cana-1739	368	10	6	6	NUM
cana-1739	368	11	,	,	PUNCT
cana-1739	368	12	48674876,2016	48674876,2016	PROPN
cana-1739	368	13	.	.	PUNCT
cana-1739	369	1	[	[	X
cana-1739	369	2	24	24	NUM
cana-1739	369	3	]	]	PUNCT
cana-1739	369	4	atangana	atangana	PROPN
cana-1739	369	5	,	,	PUNCT
cana-1739	369	6	abdon	abdon	PROPN
cana-1739	369	7	.	.	PUNCT
cana-1739	370	1	"	"	PUNCT
cana-1739	370	2	on	on	ADP
cana-1739	370	3	the	the	DET
cana-1739	370	4	stability	stability	NOUN
cana-1739	370	5	and	and	CCONJ
cana-1739	370	6	convergence	convergence	NOUN
cana-1739	370	7	of	of	ADP
cana-1739	370	8	the	the	DET
cana-1739	370	9	time	time	NOUN
cana-1739	370	10	-	-	PUNCT
cana-1739	370	11	fractional	fractional	ADJ
cana-1739	370	12	variable	variable	ADJ
cana-1739	370	13	order	order	NOUN
cana-1739	370	14	telegraph	telegraph	NOUN
cana-1739	370	15	equation	equation	NOUN
cana-1739	370	16	.	.	PUNCT
cana-1739	370	17	"	"	PUNCT
cana-1739	370	18	journal	journal	NOUN
cana-1739	370	19	of	of	ADP
cana-1739	370	20	computational	computational	ADJ
cana-1739	370	21	physics	physic	NOUN
cana-1739	370	22	293	293	NUM
cana-1739	370	23	,	,	PUNCT
cana-1739	370	24	104	104	NUM
cana-1739	370	25	-	-	SYM
cana-1739	370	26	114,2015	114,2015	NUM
cana-1739	370	27	.	.	PUNCT
cana-1739	371	1	[	[	X
cana-1739	371	2	25	25	NUM
cana-1739	371	3	]	]	X
cana-1739	371	4	sun	sun	NOUN
cana-1739	371	5	,	,	PUNCT
cana-1739	371	6	hongguang	hongguang	PROPN
cana-1739	371	7	,	,	PUNCT
cana-1739	371	8	wen	wen	PROPN
cana-1739	371	9	chen	chen	PROPN
cana-1739	371	10	,	,	PUNCT
cana-1739	371	11	changpin	changpin	PROPN
cana-1739	371	12	li	li	PROPN
cana-1739	371	13	,	,	PUNCT
cana-1739	371	14	and	and	CCONJ
cana-1739	371	15	yangquan	yangquan	PROPN
cana-1739	371	16	chen	chen	PROPN
cana-1739	371	17	.	.	PUNCT
cana-1739	372	1	"	"	PUNCT
cana-1739	372	2	fractional	fractional	ADJ
cana-1739	372	3	differential	differential	NOUN
cana-1739	372	4	models	model	NOUN
cana-1739	372	5	for	for	ADP
cana-1739	372	6	anomalous	anomalous	ADJ
cana-1739	372	7	diffusion	diffusion	NOUN
cana-1739	372	8	.	.	PUNCT
cana-1739	372	9	"	"	PUNCT
cana-1739	373	1	physica	physica	VERB
cana-1739	373	2	a	a	DET
cana-1739	373	3	:	:	PUNCT
cana-1739	373	4	statistical	statistical	ADJ
cana-1739	373	5	mechanics	mechanic	NOUN
cana-1739	373	6	and	and	CCONJ
cana-1739	373	7	its	its	PRON
cana-1739	373	8	applications	application	NOUN
cana-1739	373	9	389	389	NUM
cana-1739	373	10	,	,	PUNCT
cana-1739	373	11	no	no	INTJ
cana-1739	373	12	.	.	NOUN
cana-1739	373	13	14	14	NUM
cana-1739	373	14	,	,	PUNCT
cana-1739	373	15	2719	2719	NUM
cana-1739	373	16	-	-	SYM
cana-1739	373	17	2724,2010	2724,2010	NUM
cana-1739	373	18	.	.	PUNCT
cana-1739	374	1	[	[	X
cana-1739	374	2	26	26	NUM
cana-1739	374	3	]	]	PUNCT
cana-1739	374	4	atangana	atangana	PROPN
cana-1739	374	5	,	,	PUNCT
cana-1739	374	6	abdon	abdon	PROPN
cana-1739	374	7	,	,	PUNCT
cana-1739	374	8	and	and	CCONJ
cana-1739	374	9	joseph	joseph	PROPN
cana-1739	374	10	francois	francois	PROPN
cana-1739	374	11	botha	botha	PROPN
cana-1739	374	12	.	.	PUNCT
cana-1739	375	1	"	"	PUNCT
cana-1739	375	2	a	a	DET
cana-1739	375	3	generalized	generalized	ADJ
cana-1739	375	4	groundwater	groundwater	NOUN
cana-1739	375	5	flow	flow	NOUN
cana-1739	375	6	equation	equation	NOUN
cana-1739	375	7	using	use	VERB
cana-1739	375	8	the	the	DET
cana-1739	375	9	concept	concept	NOUN
cana-1739	375	10	of	of	ADP
cana-1739	375	11	variable	variable	ADJ
cana-1739	375	12	-	-	PUNCT
cana-1739	375	13	order	order	NOUN
cana-1739	375	14	derivative	derivative	NOUN
cana-1739	375	15	.	.	PUNCT
cana-1739	375	16	"	"	PUNCT
cana-1739	376	1	boundary	boundary	ADJ
cana-1739	376	2	value	value	NOUN
cana-1739	376	3	problems	problem	NOUN
cana-1739	376	4	2013,1	2013,1	PROPN
cana-1739	376	5	-	-	PUNCT
cana-1739	376	6	11,2013	11,2013	NUM
cana-1739	376	7	.	.	PUNCT
cana-1739	377	1	[	[	X
cana-1739	377	2	27	27	NUM
cana-1739	377	3	]	]	PUNCT
cana-1739	377	4	atangana	atangana	PROPN
cana-1739	377	5	,	,	PUNCT
cana-1739	377	6	abdon	abdon	NOUN
cana-1739	377	7	,	,	PUNCT
cana-1739	377	8	and	and	CCONJ
cana-1739	377	9	rubayyi	rubayyi	ADJ
cana-1739	377	10	t.	t.	PROPN
cana-1739	377	11	alqahtani	alqahtani	PROPN
cana-1739	377	12	.	.	PUNCT
cana-1739	378	1	"	"	PUNCT
cana-1739	378	2	stability	stability	NOUN
cana-1739	378	3	analysis	analysis	NOUN
cana-1739	378	4	of	of	ADP
cana-1739	378	5	nonlinear	nonlinear	ADJ
cana-1739	378	6	thin	thin	ADJ
cana-1739	378	7	viscous	viscous	ADJ
cana-1739	378	8	fluid	fluid	NOUN
cana-1739	378	9	sheet	sheet	NOUN
cana-1739	378	10	flow	flow	NOUN
cana-1739	378	11	equation	equation	NOUN
cana-1739	378	12	with	with	ADP
cana-1739	378	13	local	local	ADJ
cana-1739	378	14	fractional	fractional	ADJ
cana-1739	378	15	variable	variable	ADJ
cana-1739	378	16	order	order	NOUN
cana-1739	378	17	derivative	derivative	NOUN
cana-1739	378	18	.	.	PUNCT
cana-1739	378	19	"	"	PUNCT
cana-1739	378	20	journal	journal	NOUN
cana-1739	378	21	of	of	ADP
cana-1739	378	22	computational	computational	ADJ
cana-1739	378	23	and	and	CCONJ
cana-1739	378	24	theoretical	theoretical	ADJ
cana-1739	378	25	nanoscience	nanoscience	NOUN
cana-1739	378	26	13	13	NUM
cana-1739	378	27	,	,	PUNCT
cana-1739	378	28	no	no	INTJ
cana-1739	378	29	.	.	NOUN
cana-1739	378	30	5	5	NUM
cana-1739	378	31	,	,	PUNCT
cana-1739	378	32	27102717,2016	27102717,2016	NUM
cana-1739	378	33	.	.	PUNCT
cana-1739	379	1	[	[	X
cana-1739	379	2	28	28	NUM
cana-1739	379	3	]	]	X
cana-1739	379	4	gómez	gómez	NOUN
cana-1739	379	5	-	-	PUNCT
cana-1739	379	6	aguilar	aguilar	PROPN
cana-1739	379	7	,	,	PUNCT
cana-1739	379	8	j.	j.	PROPN
cana-1739	379	9	f.	f.	PROPN
cana-1739	380	1	"	"	PUNCT
cana-1739	380	2	analytical	analytical	ADJ
cana-1739	380	3	and	and	CCONJ
cana-1739	380	4	numerical	numerical	ADJ
cana-1739	380	5	solutions	solution	NOUN
cana-1739	380	6	of	of	ADP
cana-1739	380	7	a	a	DET
cana-1739	380	8	nonlinear	nonlinear	ADJ
cana-1739	380	9	alcoholism	alcoholism	NOUN
cana-1739	380	10	model	model	NOUN
cana-1739	380	11	via	via	ADP
cana-1739	380	12	variable	variable	ADJ
cana-1739	380	13	-	-	PUNCT
cana-1739	380	14	order	order	NOUN
cana-1739	380	15	fractional	fractional	ADJ
cana-1739	380	16	differential	differential	ADJ
cana-1739	380	17	equations	equation	NOUN
cana-1739	380	18	.	.	PUNCT
cana-1739	380	19	"	"	PUNCT
cana-1739	381	1	physica	physica	VERB
cana-1739	381	2	a	a	DET
cana-1739	381	3	:	:	PUNCT
cana-1739	381	4	statisticalmechanics	statisticalmechanic	NOUN
cana-1739	381	5	and	and	CCONJ
cana-1739	381	6	its	its	PRON
cana-1739	381	7	applications	application	NOUN
cana-1739	381	8	494	494	NUM
cana-1739	381	9	,	,	PUNCT
cana-1739	381	10	52	52	NUM
cana-1739	381	11	-	-	SYM
cana-1739	381	12	75,2018	75,2018	NUM
cana-1739	381	13	.	.	PUNCT
cana-1739	382	1	[	[	X
cana-1739	382	2	29	29	NUM
cana-1739	382	3	]	]	X
cana-1739	382	4	coronel	coronel	NOUN
cana-1739	382	5	-	-	PUNCT
cana-1739	382	6	escamilla	escamilla	NOUN
cana-1739	382	7	,	,	PUNCT
cana-1739	382	8	a.	a.	PROPN
cana-1739	382	9	,	,	PUNCT
cana-1739	382	10	josé	josé	PROPN
cana-1739	382	11	francisco	francisco	PROPN
cana-1739	382	12	gómez	gómez	PROPN
cana-1739	382	13	-	-	PUNCT
cana-1739	382	14	aguilar	aguilar	ADJ
cana-1739	382	15	,	,	PUNCT
cana-1739	382	16	lizeth	lizeth	NOUN
cana-1739	382	17	torres	torre	NOUN
cana-1739	382	18	,	,	PUNCT
cana-1739	382	19	and	and	CCONJ
cana-1739	382	20	ricardo	ricardo	PROPN
cana-1739	382	21	fabricio	fabricio	PROPN
cana-1739	382	22	escobar	escobar	PROPN
cana-1739	382	23	-	-	PUNCT
cana-1739	382	24	jiménez	jiménez	PROPN
cana-1739	382	25	.	.	PUNCT
cana-1739	383	1	"	"	PUNCT
cana-1739	383	2	a	a	DET
cana-1739	383	3	numerical	numerical	ADJ
cana-1739	383	4	solution	solution	NOUN
cana-1739	383	5	for	for	ADP
cana-1739	383	6	a	a	DET
cana-1739	383	7	variable	variable	ADJ
cana-1739	383	8	-	-	PUNCT
cana-1739	383	9	order	order	NOUN
cana-1739	383	10	reaction	reaction	NOUN
cana-1739	383	11	-	-	PUNCT
cana-1739	383	12	diffusion	diffusion	NOUN
cana-1739	383	13	model	model	NOUN
cana-1739	383	14	by	by	ADP
cana-1739	383	15	using	use	VERB
cana-1739	383	16	fractional	fractional	ADJ
cana-1739	383	17	derivatives	derivative	NOUN
cana-1739	383	18	with	with	ADP
cana-1739	383	19	non	non	ADJ
cana-1739	383	20	local	local	ADJ
cana-1739	383	21	and	and	CCONJ
cana-1739	383	22	non	non	ADJ
cana-1739	383	23	-	-	ADJ
cana-1739	383	24	singular	singular	ADJ
cana-1739	383	25	kernel	kernel	NOUN
cana-1739	383	26	.	.	PUNCT
cana-1739	383	27	"	"	PUNCT
cana-1739	384	1	physica	physica	VERB
cana-1739	384	2	a	a	DET
cana-1739	384	3	:	:	PUNCT
cana-1739	384	4	statistical	statistical	ADJ
cana-1739	384	5	mechanics	mechanic	NOUN
cana-1739	384	6	and	and	CCONJ
cana-1739	384	7	its	its	PRON
cana-1739	384	8	applications	application	NOUN
cana-1739	384	9	491,406	491,406	NUM
cana-1739	384	10	-	-	SYM
cana-1739	384	11	424,2018	424,2018	NUM
cana-1739	384	12	.	.	PUNCT
cana-1739	385	1	[	[	X
cana-1739	385	2	30	30	NUM
cana-1739	385	3	]	]	X
cana-1739	385	4	solís	solís	NOUN
cana-1739	385	5	-	-	PUNCT
cana-1739	385	6	pérez	pérez	NOUN
cana-1739	385	7	,	,	PUNCT
cana-1739	385	8	j.	j.	PROPN
cana-1739	385	9	e.	e.	PROPN
cana-1739	385	10	,	,	PUNCT
cana-1739	385	11	j.	j.	PROPN
cana-1739	385	12	f.	f.	PROPN
cana-1739	385	13	gómez	gómez	PROPN
cana-1739	385	14	-	-	PUNCT
cana-1739	385	15	aguilar	aguilar	PROPN
cana-1739	385	16	,	,	PUNCT
cana-1739	385	17	and	and	CCONJ
cana-1739	385	18	a.	a.	PROPN
cana-1739	385	19	atangana	atangana	PROPN
cana-1739	385	20	.	.	PUNCT
cana-1739	386	1	"	"	PUNCT
cana-1739	386	2	novel	novel	ADJ
cana-1739	386	3	numerical	numerical	ADJ
cana-1739	386	4	method	method	NOUN
cana-1739	386	5	for	for	ADP
cana-1739	386	6	solving	solve	VERB
cana-1739	386	7	variable	variable	ADJ
cana-1739	386	8	-	-	PUNCT
cana-1739	386	9	order	order	NOUN
cana-1739	386	10	fractional	fractional	ADJ
cana-1739	386	11	differential	differential	ADJ
cana-1739	386	12	equations	equation	NOUN
cana-1739	386	13	with	with	ADP
cana-1739	386	14	power	power	NOUN
cana-1739	386	15	,	,	PUNCT
cana-1739	386	16	exponential	exponential	ADJ
cana-1739	386	17	and	and	CCONJ
cana-1739	386	18	mittag	mittag	ADJ
cana-1739	386	19	-	-	PUNCT
cana-1739	386	20	leffler	leffler	NOUN
cana-1739	386	21	laws	law	NOUN
cana-1739	386	22	.	.	PUNCT
cana-1739	386	23	"	"	PUNCT
cana-1739	387	1	chaos	chaos	NOUN
cana-1739	387	2	,	,	PUNCT
cana-1739	387	3	solitons	soliton	NOUN
cana-1739	387	4	&	&	CCONJ
cana-1739	387	5	fractals	fractal	NOUN
cana-1739	387	6	114	114	NUM
cana-1739	387	7	,	,	PUNCT
cana-1739	387	8	175	175	NUM
cana-1739	387	9	-	-	NOUN
cana-1739	387	10	185,2018	185,2018	NUM
cana-1739	387	11	.	.	PUNCT
cana-1739	388	1	[	[	X
cana-1739	388	2	31	31	NUM
cana-1739	388	3	]	]	PUNCT
cana-1739	388	4	moghaddam	moghaddam	NOUN
cana-1739	388	5	,	,	PUNCT
cana-1739	388	6	b.	b.	PROPN
cana-1739	388	7	parsa	parsa	PROPN
cana-1739	388	8	,	,	PUNCT
cana-1739	388	9	sh	sh	PROPN
cana-1739	388	10	yaghoobi	yaghoobi	NOUN
cana-1739	388	11	,	,	PUNCT
cana-1739	388	12	and	and	CCONJ
cana-1739	388	13	j.	j.	PROPN
cana-1739	388	14	a.	a.	PROPN
cana-1739	388	15	tenreiro	tenreiro	PROPN
cana-1739	388	16	machado	machado	PROPN
cana-1739	388	17	.	.	PUNCT
cana-1739	389	1	"	"	PUNCT
cana-1739	389	2	an	an	DET
cana-1739	389	3	extended	extended	ADJ
cana-1739	389	4	predictor	predictor	NOUN
cana-1739	389	5	–	–	PUNCT
cana-1739	389	6	corrector	corrector	NOUN
cana-1739	389	7	algorithm	algorithm	NOUN
cana-1739	389	8	for	for	ADP
cana-1739	389	9	variable	variable	ADJ
cana-1739	389	10	-	-	PUNCT
cana-1739	389	11	order	order	NOUN
cana-1739	389	12	fractional	fractional	ADJ
cana-1739	389	13	delay	delay	NOUN
cana-1739	389	14	differential	differential	ADJ
cana-1739	389	15	equations	equation	NOUN
cana-1739	389	16	.	.	PUNCT
cana-1739	389	17	"	"	PUNCT
cana-1739	389	18	journal	journal	NOUN
cana-1739	389	19	of	of	ADP
cana-1739	389	20	computational	computational	ADJ
cana-1739	389	21	and	and	CCONJ
cana-1739	389	22	nonlinear	nonlinear	ADJ
cana-1739	389	23	dynamics	dynamic	NOUN
cana-1739	389	24	11	11	NUM
cana-1739	389	25	,	,	PUNCT
cana-1739	389	26	no	no	INTJ
cana-1739	389	27	.	.	NOUN
cana-1739	389	28	6	6	NUM
cana-1739	389	29	,	,	PUNCT
cana-1739	389	30	2016	2016	NUM
cana-1739	389	31	.	.	PUNCT
cana-1739	390	1	[	[	X
cana-1739	390	2	32	32	NUM
cana-1739	390	3	]	]	SYM
cana-1739	390	4	wu	wu	PROPN
cana-1739	390	5	,	,	PUNCT
cana-1739	390	6	jianjun	jianjun	PROPN
cana-1739	390	7	,	,	PUNCT
cana-1739	390	8	and	and	CCONJ
cana-1739	390	9	lu	lu	PROPN
cana-1739	390	10	xia	xia	PROPN
cana-1739	390	11	.	.	PUNCT
cana-1739	391	1	"	"	PUNCT
cana-1739	391	2	sliding	slide	VERB
cana-1739	391	3	mode	mode	NOUN
cana-1739	391	4	control	control	NOUN
cana-1739	391	5	design	design	NOUN
cana-1739	391	6	and	and	CCONJ
cana-1739	391	7	stability	stability	NOUN
cana-1739	391	8	analysis	analysis	NOUN
cana-1739	391	9	of	of	ADP
cana-1739	391	10	a	a	DET
cana-1739	391	11	class	class	NOUN
cana-1739	391	12	of	of	ADP
cana-1739	391	13	financial	financial	ADJ
cana-1739	391	14	fractional	fractional	ADJ
cana-1739	391	15	-	-	PUNCT
cana-1739	391	16	order	order	NOUN
cana-1739	391	17	chaotic	chaotic	ADJ
cana-1739	391	18	mathematical	mathematical	ADJ
cana-1739	391	19	model	model	NOUN
cana-1739	391	20	.	.	PUNCT
cana-1739	391	21	"	"	PUNCT
cana-1739	391	22	economics	economic	NOUN
cana-1739	391	23	1	1	NUM
cana-1739	391	24	:	:	PUNCT
cana-1739	391	25	4,2024	4,2024	NUM
cana-1739	391	26	.	.	PUNCT
cana-1739	392	1	[	[	X
cana-1739	392	2	33	33	NUM
cana-1739	392	3	]	]	X
cana-1739	392	4	thakur	thakur	PROPN
cana-1739	392	5	,	,	PUNCT
cana-1739	392	6	bharti	bharti	PROPN
cana-1739	392	7	,	,	PUNCT
cana-1739	392	8	and	and	CCONJ
cana-1739	392	9	sandipan	sandipan	ADJ
cana-1739	392	10	gupta	gupta	PROPN
cana-1739	392	11	.	.	PUNCT
cana-1739	393	1	"	"	PUNCT
cana-1739	393	2	an	an	DET
cana-1739	393	3	iterative	iterative	NOUN
cana-1739	393	4	algorithm	algorithm	NOUN
cana-1739	393	5	for	for	ADP
cana-1739	393	6	numerical	numerical	ADJ
cana-1739	393	7	solution	solution	NOUN
cana-1739	393	8	of	of	ADP
cana-1739	393	9	nonlinear	nonlinear	ADJ
cana-1739	393	10	fractional	fractional	ADJ
cana-1739	393	11	differential	differential	NOUN
cana-1739	393	12	equation	equation	NOUN
cana-1739	393	13	using	use	VERB
cana-1739	393	14	legendre	legendre	PROPN
cana-1739	393	15	wavelet	wavelet	PROPN
cana-1739	393	16	method	method	NOUN
cana-1739	393	17	.	.	PUNCT
cana-1739	393	18	"	"	PUNCT
cana-1739	394	1	iaeng	iaeng	PROPN
cana-1739	394	2	international	international	PROPN
cana-1739	394	3	journal	journal	NOUN
cana-1739	394	4	of	of	ADP
cana-1739	394	5	applied	apply	VERB
cana-1739	394	6	mathematics	mathematic	NOUN
cana-1739	394	7	54	54	NUM
cana-1739	394	8	,	,	PUNCT
cana-1739	394	9	no	no	INTJ
cana-1739	394	10	.	.	NOUN
cana-1739	394	11	3	3	NUM
cana-1739	394	12	,	,	PUNCT
cana-1739	394	13	2024	2024	NUM
cana-1739	394	14	.	.	PUNCT