id	sid	tid	token	lemma	pos
cana-1171	1	1	communications	communication	NOUN
cana-1171	1	2	on	on	ADP
cana-1171	1	3	applied	apply	VERB
cana-1171	1	4	nonlinear	nonlinear	ADJ
cana-1171	1	5	analysis	analysis	NOUN
cana-1171	1	6	issn	issn	NOUN
cana-1171	1	7	:	:	PUNCT
cana-1171	1	8	1074	1074	NUM
cana-1171	1	9	-	-	PUNCT
cana-1171	1	10	133x	133x	NUM
cana-1171	1	11	vol	vol	NOUN
cana-1171	1	12	31	31	NUM
cana-1171	1	13	no	no	NOUN
cana-1171	1	14	.	.	PUNCT
cana-1171	2	1	6s	6s	NUM
cana-1171	2	2	(	(	PUNCT
cana-1171	2	3	2024	2024	NUM
cana-1171	2	4	)	)	PUNCT
cana-1171	2	5	114	114	NUM
cana-1171	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1171	2	7	revolutionizing	revolutionize	VERB
cana-1171	2	8	electrochemical	electrochemical	ADJ
cana-1171	2	9	kinetics	kinetic	NOUN
cana-1171	2	10	:	:	PUNCT
cana-1171	2	11	homogeneous	homogeneous	ADJ
cana-1171	2	12	redox	redox	NOUN
cana-1171	2	13	catalysis	catalysis	NOUN
cana-1171	2	14	unveiled	unveil	VERB
cana-1171	2	15	through	through	ADP
cana-1171	2	16	an	an	DET
cana-1171	2	17	innovative	innovative	ADJ
cana-1171	2	18	mathematical	mathematical	ADJ
cana-1171	2	19	framework	framework	NOUN
cana-1171	2	20	using	use	VERB
cana-1171	2	21	the	the	DET
cana-1171	2	22	homotopy	homotopy	NOUN
cana-1171	2	23	perturbation	perturbation	NOUN
cana-1171	2	24	method	method	NOUN
cana-1171	2	25	saranya.k1	saranya.k1	PROPN
cana-1171	2	26	,	,	PUNCT
cana-1171	2	27	dr.r	dr.r	NOUN
cana-1171	2	28	.	.	PUNCT
cana-1171	3	1	angel	angel	NOUN
cana-1171	3	2	joy2	joy2	PROPN
cana-1171	3	3	1research	1research	NUM
cana-1171	3	4	scholar	scholar	NOUN
cana-1171	3	5	,	,	PUNCT
cana-1171	3	6	department	department	NOUN
cana-1171	3	7	of	of	ADP
cana-1171	3	8	mathematics	mathematic	NOUN
cana-1171	3	9	,	,	PUNCT
cana-1171	3	10	sri	sri	PROPN
cana-1171	3	11	gvg	gvg	PROPN
cana-1171	3	12	visalakshi	visalakshi	PROPN
cana-1171	3	13	college	college	PROPN
cana-1171	3	14	for	for	ADP
cana-1171	3	15	women	woman	NOUN
cana-1171	3	16	,	,	PUNCT
cana-1171	3	17	udumalpet	udumalpet	ADJ
cana-1171	3	18	.	.	PUNCT
cana-1171	4	1	2associate	2associate	NUM
cana-1171	4	2	professor	professor	NOUN
cana-1171	4	3	&	&	CCONJ
cana-1171	4	4	hod	hod	PROPN
cana-1171	4	5	of	of	ADP
cana-1171	4	6	mathematics	mathematics	PROPN
cana-1171	4	7	,	,	PUNCT
cana-1171	4	8	sri	sri	PROPN
cana-1171	4	9	gvg	gvg	PROPN
cana-1171	4	10	visalakshi	visalakshi	PROPN
cana-1171	4	11	college	college	PROPN
cana-1171	4	12	for	for	ADP
cana-1171	4	13	women	woman	NOUN
cana-1171	4	14	,	,	PUNCT
cana-1171	4	15	udumalpet	udumalpet	ADJ
cana-1171	4	16	.	.	PUNCT
cana-1171	5	1	article	article	NOUN
cana-1171	5	2	history	history	NOUN
cana-1171	5	3	:	:	PUNCT
cana-1171	5	4	received	receive	VERB
cana-1171	5	5	:	:	PUNCT
cana-1171	5	6	25	25	NUM
cana-1171	5	7	-	-	PUNCT
cana-1171	5	8	05	05	NUM
cana-1171	5	9	-	-	PUNCT
cana-1171	5	10	2024	2024	NUM
cana-1171	5	11	revised	revise	VERB
cana-1171	5	12	:	:	PUNCT
cana-1171	5	13	11	11	NUM
cana-1171	5	14	-	-	SYM
cana-1171	5	15	07	07	NUM
cana-1171	5	16	-	-	PUNCT
cana-1171	5	17	2024	2024	NUM
cana-1171	5	18	accepted	accept	VERB
cana-1171	5	19	:	:	PUNCT
cana-1171	5	20	24	24	NUM
cana-1171	5	21	-	-	PUNCT
cana-1171	5	22	07	07	NUM
cana-1171	5	23	-	-	PUNCT
cana-1171	5	24	2024	2024	NUM
cana-1171	5	25	abstract	abstract	NOUN
cana-1171	5	26	:	:	PUNCT
cana-1171	5	27	introduction	introduction	NOUN
cana-1171	5	28	:	:	PUNCT
cana-1171	5	29	in	in	ADP
cana-1171	5	30	redox	redox	ADJ
cana-1171	5	31	homogeneous	homogeneous	ADJ
cana-1171	5	32	catalysis	catalysis	NOUN
cana-1171	5	33	the	the	DET
cana-1171	5	34	catalyst	catalyst	NOUN
cana-1171	5	35	couple	couple	NOUN
cana-1171	5	36	merely	merely	ADV
cana-1171	5	37	plays	play	VERB
cana-1171	5	38	the	the	DET
cana-1171	5	39	role	role	NOUN
cana-1171	5	40	of	of	ADP
cana-1171	5	41	an	an	DET
cana-1171	5	42	electron	electron	NOUN
cana-1171	5	43	in	in	ADP
cana-1171	5	44	contrast	contrast	NOUN
cana-1171	5	45	with	with	ADP
cana-1171	5	46	chemical	chemical	ADJ
cana-1171	5	47	catalysis	catalysis	NOUN
cana-1171	5	48	.	.	PUNCT
cana-1171	6	1	the	the	DET
cana-1171	6	2	mathematical	mathematical	ADJ
cana-1171	6	3	modelling	modelling	NOUN
cana-1171	6	4	of	of	ADP
cana-1171	6	5	homogeneous	homogeneous	ADJ
cana-1171	6	6	redox	redox	ADJ
cana-1171	6	7	catalysis	catalysis	NOUN
cana-1171	6	8	of	of	ADP
cana-1171	6	9	electrochemical	electrochemical	ADJ
cana-1171	6	10	reactions	reaction	NOUN
cana-1171	6	11	for	for	ADP
cana-1171	6	12	the	the	DET
cana-1171	6	13	ec	ec	PROPN
cana-1171	6	14	scheme	scheme	NOUN
cana-1171	6	15	is	be	AUX
cana-1171	6	16	described	describe	VERB
cana-1171	6	17	by	by	ADP
cana-1171	6	18	the	the	DET
cana-1171	6	19	system	system	NOUN
cana-1171	6	20	of	of	ADP
cana-1171	6	21	second	second	ADJ
cana-1171	6	22	order	order	NOUN
cana-1171	6	23	nonlinear	nonlinear	ADJ
cana-1171	6	24	differential	differential	ADJ
cana-1171	6	25	equations	equation	NOUN
cana-1171	6	26	.	.	PUNCT
cana-1171	7	1	this	this	DET
cana-1171	7	2	model	model	NOUN
cana-1171	7	3	was	be	AUX
cana-1171	7	4	initially	initially	ADV
cana-1171	7	5	designed	design	VERB
cana-1171	7	6	using	use	VERB
cana-1171	7	7	the	the	DET
cana-1171	7	8	classical	classical	ADJ
cana-1171	7	9	differential	differential	ADJ
cana-1171	7	10	equations	equation	NOUN
cana-1171	7	11	and	and	CCONJ
cana-1171	7	12	it	it	PRON
cana-1171	7	13	is	be	AUX
cana-1171	7	14	extended	extend	VERB
cana-1171	7	15	to	to	ADP
cana-1171	7	16	the	the	DET
cana-1171	7	17	caputo	caputo	PROPN
cana-1171	7	18	fractional	fractional	PROPN
cana-1171	7	19	derivative	derivative	PROPN
cana-1171	7	20	(	(	PUNCT
cana-1171	7	21	fde	fde	PROPN
cana-1171	7	22	’s	’s	NOUN
cana-1171	7	23	)	)	PUNCT
cana-1171	7	24	of	of	ADP
cana-1171	7	25	order	order	NOUN
cana-1171	7	26	𝛼	𝛼	VERB
cana-1171	7	27	in	in	ADP
cana-1171	7	28	particularly	particularly	ADV
cana-1171	7	29	sequential	sequential	ADJ
cana-1171	7	30	fractional	fractional	ADJ
cana-1171	7	31	case	case	NOUN
cana-1171	7	32	.	.	PUNCT
cana-1171	8	1	the	the	DET
cana-1171	8	2	aim	aim	NOUN
cana-1171	8	3	is	be	AUX
cana-1171	8	4	to	to	PART
cana-1171	8	5	obtain	obtain	VERB
cana-1171	8	6	approximate	approximate	ADJ
cana-1171	8	7	analytical	analytical	ADJ
cana-1171	8	8	solutions	solution	NOUN
cana-1171	8	9	of	of	ADP
cana-1171	8	10	the	the	DET
cana-1171	8	11	system	system	NOUN
cana-1171	8	12	of	of	ADP
cana-1171	8	13	fde	fde	PROPN
cana-1171	8	14	’s	’s	PART
cana-1171	8	15	using	use	VERB
cana-1171	8	16	homotopy	homotopy	NOUN
cana-1171	8	17	perturbation	perturbation	NOUN
cana-1171	8	18	method	method	NOUN
cana-1171	8	19	(	(	PUNCT
cana-1171	8	20	hpm	hpm	NOUN
cana-1171	8	21	)	)	PUNCT
cana-1171	8	22	and	and	CCONJ
cana-1171	8	23	analyze	analyze	VERB
cana-1171	8	24	the	the	DET
cana-1171	8	25	impact	impact	NOUN
cana-1171	8	26	of	of	ADP
cana-1171	8	27	various	various	ADJ
cana-1171	8	28	parameters	parameter	NOUN
cana-1171	8	29	with	with	ADP
cana-1171	8	30	different	different	ADJ
cana-1171	8	31	order	order	NOUN
cana-1171	8	32	of	of	ADP
cana-1171	8	33	𝛼.	𝛼.	NOUN
cana-1171	8	34	in	in	ADP
cana-1171	8	35	addition	addition	NOUN
cana-1171	8	36	,	,	PUNCT
cana-1171	8	37	the	the	DET
cana-1171	8	38	solution	solution	NOUN
cana-1171	8	39	of	of	ADP
cana-1171	8	40	the	the	DET
cana-1171	8	41	sequential	sequential	ADJ
cana-1171	8	42	dynamic	dynamic	ADJ
cana-1171	8	43	equations	equation	NOUN
cana-1171	8	44	yields	yield	VERB
cana-1171	8	45	the	the	DET
cana-1171	8	46	solution	solution	NOUN
cana-1171	8	47	of	of	ADP
cana-1171	8	48	the	the	DET
cana-1171	8	49	corresponding	corresponding	ADJ
cana-1171	8	50	integer	integer	NOUN
cana-1171	8	51	-	-	PUNCT
cana-1171	8	52	order	order	NOUN
cana-1171	8	53	differential	differential	ADJ
cana-1171	8	54	equations	equation	NOUN
cana-1171	8	55	as	as	ADP
cana-1171	8	56	a	a	DET
cana-1171	8	57	special	special	ADJ
cana-1171	8	58	case	case	NOUN
cana-1171	8	59	.	.	PUNCT
cana-1171	9	1	keywords	keyword	NOUN
cana-1171	9	2	:	:	PUNCT
cana-1171	9	3	electrochemical	electrochemical	ADJ
cana-1171	9	4	reaction	reaction	NOUN
cana-1171	9	5	,	,	PUNCT
cana-1171	9	6	fractional	fractional	ADJ
cana-1171	9	7	differential	differential	ADJ
cana-1171	9	8	equations	equation	NOUN
cana-1171	9	9	,	,	PUNCT
cana-1171	9	10	homotopy	homotopy	VERB
cana-1171	9	11	perturbation	perturbation	NOUN
cana-1171	9	12	method	method	NOUN
cana-1171	9	13	.	.	PUNCT
cana-1171	10	1	1	1	X
cana-1171	10	2	.	.	X
cana-1171	10	3	introduction	introduction	NOUN
cana-1171	10	4	fractional	fractional	ADJ
cana-1171	10	5	derivatives	derivative	NOUN
cana-1171	10	6	provide	provide	VERB
cana-1171	10	7	a	a	DET
cana-1171	10	8	special	special	ADJ
cana-1171	10	9	instrument	instrument	NOUN
cana-1171	10	10	for	for	ADP
cana-1171	10	11	the	the	DET
cana-1171	10	12	description	description	NOUN
cana-1171	10	13	of	of	ADP
cana-1171	10	14	the	the	DET
cana-1171	10	15	memory	memory	NOUN
cana-1171	10	16	effects	effect	NOUN
cana-1171	10	17	and	and	CCONJ
cana-1171	10	18	hereditary	hereditary	ADJ
cana-1171	10	19	properties	property	NOUN
cana-1171	10	20	of	of	ADP
cana-1171	10	21	various	various	ADJ
cana-1171	10	22	materials	material	NOUN
cana-1171	10	23	and	and	CCONJ
cana-1171	10	24	processes	process	NOUN
cana-1171	10	25	.	.	PUNCT
cana-1171	11	1	in	in	ADP
cana-1171	11	2	the	the	DET
cana-1171	11	3	comparison	comparison	NOUN
cana-1171	11	4	between	between	ADP
cana-1171	11	5	fractional	fractional	ADJ
cana-1171	11	6	derivatives	derivative	NOUN
cana-1171	11	7	and	and	CCONJ
cana-1171	11	8	integer	integer	NOUN
cana-1171	11	9	-	-	PUNCT
cana-1171	11	10	order	order	NOUN
cana-1171	11	11	derivatives	derivative	NOUN
cana-1171	11	12	,	,	PUNCT
cana-1171	11	13	these	these	DET
cana-1171	11	14	effects	effect	NOUN
cana-1171	11	15	are	be	AUX
cana-1171	11	16	not	not	PART
cana-1171	11	17	taken	take	VERB
cana-1171	11	18	into	into	ADP
cana-1171	11	19	account	account	NOUN
cana-1171	11	20	.	.	PUNCT
cana-1171	12	1	k.b	k.b	PROPN
cana-1171	12	2	.	.	PROPN
cana-1171	12	3	oldham	oldham	PROPN
cana-1171	12	4	et	et	PROPN
cana-1171	12	5	al	al	PROPN
cana-1171	12	6	.	.	PUNCT
cana-1171	13	1	[	[	X
cana-1171	13	2	2	2	X
cana-1171	13	3	]	]	PUNCT
cana-1171	13	4	mentioned	mention	VERB
cana-1171	13	5	in	in	ADP
cana-1171	13	6	their	their	PRON
cana-1171	13	7	book	book	NOUN
cana-1171	13	8	that	that	SCONJ
cana-1171	13	9	applications	application	NOUN
cana-1171	13	10	in	in	ADP
cana-1171	13	11	physics	physics	NOUN
cana-1171	13	12	,	,	PUNCT
cana-1171	13	13	chemistry	chemistry	NOUN
cana-1171	13	14	,	,	PUNCT
cana-1171	13	15	and	and	CCONJ
cana-1171	13	16	engineering	engineering	NOUN
cana-1171	13	17	play	play	VERB
cana-1171	13	18	an	an	DET
cana-1171	13	19	outstanding	outstanding	ADJ
cana-1171	13	20	role	role	NOUN
cana-1171	13	21	in	in	ADP
cana-1171	13	22	the	the	DET
cana-1171	13	23	development	development	NOUN
cana-1171	13	24	of	of	ADP
cana-1171	13	25	the	the	DET
cana-1171	13	26	subject	subject	NOUN
cana-1171	13	27	of	of	ADP
cana-1171	13	28	applied	applied	ADJ
cana-1171	13	29	fractional	fractional	ADJ
cana-1171	13	30	calculus	calculus	NOUN
cana-1171	13	31	.	.	PUNCT
cana-1171	14	1	in	in	ADP
cana-1171	14	2	[	[	X
cana-1171	14	3	1	1	NUM
cana-1171	14	4	]	]	PUNCT
cana-1171	14	5	,	,	PUNCT
cana-1171	14	6	m.	m.	PROPN
cana-1171	14	7	caputo	caputo	PROPN
cana-1171	14	8	published	publish	VERB
cana-1171	14	9	his	his	PRON
cana-1171	14	10	book	book	NOUN
cana-1171	14	11	in	in	ADP
cana-1171	14	12	1969	1969	NUM
cana-1171	14	13	,	,	PUNCT
cana-1171	14	14	in	in	ADP
cana-1171	14	15	which	which	PRON
cana-1171	14	16	he	he	PRON
cana-1171	14	17	systematically	systematically	ADV
cana-1171	14	18	used	use	VERB
cana-1171	14	19	the	the	DET
cana-1171	14	20	original	original	ADJ
cana-1171	14	21	definition	definition	NOUN
cana-1171	14	22	of	of	ADP
cana-1171	14	23	fractional	fractional	ADJ
cana-1171	14	24	differentiation	differentiation	NOUN
cana-1171	14	25	for	for	ADP
cana-1171	14	26	formulating	formulate	VERB
cana-1171	14	27	and	and	CCONJ
cana-1171	14	28	solving	solve	VERB
cana-1171	14	29	various	various	ADJ
cana-1171	14	30	types	type	NOUN
cana-1171	14	31	of	of	ADP
cana-1171	14	32	problems	problem	NOUN
cana-1171	14	33	in	in	ADP
cana-1171	14	34	various	various	ADJ
cana-1171	14	35	applications	application	NOUN
cana-1171	14	36	like	like	ADP
cana-1171	14	37	viscoelasticity	viscoelasticity	NOUN
cana-1171	14	38	,	,	PUNCT
cana-1171	14	39	rheological	rheological	ADJ
cana-1171	14	40	properties	property	NOUN
cana-1171	14	41	of	of	ADP
cana-1171	14	42	rocks	rock	NOUN
cana-1171	14	43	,	,	PUNCT
cana-1171	14	44	and	and	CCONJ
cana-1171	14	45	many	many	ADJ
cana-1171	14	46	other	other	ADJ
cana-1171	14	47	fields	field	NOUN
cana-1171	14	48	.	.	PUNCT
cana-1171	15	1	see	see	VERB
cana-1171	15	2	[	[	X
cana-1171	15	3	14	14	NUM
cana-1171	15	4	,	,	PUNCT
cana-1171	15	5	16	16	NUM
cana-1171	15	6	,	,	PUNCT
cana-1171	15	7	21	21	NUM
cana-1171	15	8	]	]	PUNCT
cana-1171	15	9	.	.	PUNCT
cana-1171	16	1	they	they	PRON
cana-1171	16	2	observed	observe	VERB
cana-1171	16	3	in	in	ADP
cana-1171	16	4	their	their	PRON
cana-1171	16	5	research	research	NOUN
cana-1171	16	6	of	of	ADP
cana-1171	16	7	sequential	sequential	ADJ
cana-1171	16	8	fractional	fractional	ADJ
cana-1171	16	9	differential	differential	ADJ
cana-1171	16	10	equations	equation	NOUN
cana-1171	16	11	with	with	ADP
cana-1171	16	12	boundary	boundary	ADJ
cana-1171	16	13	value	value	NOUN
cana-1171	16	14	problems	problem	NOUN
cana-1171	16	15	and	and	CCONJ
cana-1171	16	16	experiments	experiment	NOUN
cana-1171	16	17	that	that	SCONJ
cana-1171	16	18	the	the	DET
cana-1171	16	19	use	use	NOUN
cana-1171	16	20	of	of	ADP
cana-1171	16	21	half	half	ADJ
cana-1171	16	22	-	-	PUNCT
cana-1171	16	23	order	order	NOUN
cana-1171	16	24	derivatives	derivative	NOUN
cana-1171	16	25	and	and	CCONJ
cana-1171	16	26	integrals	integral	NOUN
cana-1171	16	27	led	lead	VERB
cana-1171	16	28	to	to	ADP
cana-1171	16	29	a	a	DET
cana-1171	16	30	formulation	formulation	NOUN
cana-1171	16	31	of	of	ADP
cana-1171	16	32	certain	certain	ADJ
cana-1171	16	33	electro	electro	ADJ
cana-1171	16	34	-	-	PUNCT
cana-1171	16	35	chemical	chemical	NOUN
cana-1171	16	36	problems	problem	NOUN
cana-1171	16	37	that	that	PRON
cana-1171	16	38	was	be	AUX
cana-1171	16	39	more	more	ADV
cana-1171	16	40	useful	useful	ADJ
cana-1171	16	41	than	than	ADP
cana-1171	16	42	the	the	DET
cana-1171	16	43	classical	classical	ADJ
cana-1171	16	44	approach	approach	NOUN
cana-1171	16	45	.	.	PUNCT
cana-1171	17	1	and	and	CCONJ
cana-1171	17	2	also	also	ADV
cana-1171	17	3	see	see	VERB
cana-1171	17	4	[	[	X
cana-1171	17	5	22	22	NUM
cana-1171	17	6	]	]	PUNCT
cana-1171	17	7	,	,	PUNCT
cana-1171	17	8	where	where	SCONJ
cana-1171	17	9	the	the	DET
cana-1171	17	10	author	author	NOUN
cana-1171	17	11	mentions	mention	VERB
cana-1171	17	12	that	that	SCONJ
cana-1171	17	13	we	we	PRON
cana-1171	17	14	can	can	AUX
cana-1171	17	15	compute	compute	VERB
cana-1171	17	16	the	the	DET
cana-1171	17	17	numerical	numerical	ADJ
cana-1171	17	18	solution	solution	NOUN
cana-1171	17	19	of	of	ADP
cana-1171	17	20	the	the	DET
cana-1171	17	21	sequential	sequential	ADJ
cana-1171	17	22	caputo	caputo	PROPN
cana-1171	17	23	fractional	fractional	PROPN
cana-1171	17	24	equations	equation	NOUN
cana-1171	17	25	with	with	ADP
cana-1171	17	26	boundary	boundary	ADJ
cana-1171	17	27	conditions	condition	NOUN
cana-1171	17	28	tend	tend	VERB
cana-1171	17	29	to	to	ADP
cana-1171	17	30	the	the	DET
cana-1171	17	31	corresponding	corresponding	ADJ
cana-1171	17	32	solution	solution	NOUN
cana-1171	17	33	of	of	ADP
cana-1171	17	34	the	the	DET
cana-1171	17	35	integer	integer	NOUN
cana-1171	17	36	boundary	boundary	ADJ
cana-1171	17	37	value	value	NOUN
cana-1171	17	38	problems	problem	NOUN
cana-1171	17	39	.	.	PUNCT
cana-1171	18	1	otherwise	otherwise	ADV
cana-1171	18	2	,	,	PUNCT
cana-1171	18	3	it	it	PRON
cana-1171	18	4	can	can	AUX
cana-1171	18	5	be	be	AUX
cana-1171	18	6	noted	note	VERB
cana-1171	18	7	that	that	SCONJ
cana-1171	18	8	it	it	PRON
cana-1171	18	9	is	be	AUX
cana-1171	18	10	non	non	ADJ
cana-1171	18	11	-	-	ADJ
cana-1171	18	12	sequential	sequential	ADJ
cana-1171	18	13	.	.	PUNCT
cana-1171	19	1	communications	communication	NOUN
cana-1171	19	2	on	on	ADP
cana-1171	19	3	applied	apply	VERB
cana-1171	19	4	nonlinear	nonlinear	ADJ
cana-1171	19	5	analysis	analysis	NOUN
cana-1171	19	6	issn	issn	NOUN
cana-1171	19	7	:	:	PUNCT
cana-1171	19	8	1074	1074	NUM
cana-1171	19	9	-	-	PUNCT
cana-1171	19	10	133x	133x	NUM
cana-1171	19	11	vol	vol	NOUN
cana-1171	19	12	31	31	NUM
cana-1171	19	13	no	no	NOUN
cana-1171	19	14	.	.	PUNCT
cana-1171	20	1	6s	6s	NUM
cana-1171	20	2	(	(	PUNCT
cana-1171	20	3	2024	2024	NUM
cana-1171	20	4	)	)	PUNCT
cana-1171	20	5	115	115	NUM
cana-1171	20	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1171	20	7	in	in	ADP
cana-1171	20	8	the	the	DET
cana-1171	20	9	early	early	ADJ
cana-1171	20	10	1990s	1990	NOUN
cana-1171	20	11	,	,	PUNCT
cana-1171	20	12	the	the	DET
cana-1171	20	13	perturbation	perturbation	NOUN
cana-1171	20	14	method	method	NOUN
cana-1171	20	15	was	be	AUX
cana-1171	20	16	one	one	NUM
cana-1171	20	17	of	of	ADP
cana-1171	20	18	the	the	DET
cana-1171	20	19	most	most	ADV
cana-1171	20	20	effective	effective	ADJ
cana-1171	20	21	methods	method	NOUN
cana-1171	20	22	.	.	PUNCT
cana-1171	21	1	however	however	ADV
cana-1171	21	2	,	,	PUNCT
cana-1171	21	3	the	the	DET
cana-1171	21	4	solutions	solution	NOUN
cana-1171	21	5	dealt	deal	VERB
cana-1171	21	6	with	with	ADP
cana-1171	21	7	small	small	ADJ
cana-1171	21	8	parameters	parameter	NOUN
cana-1171	21	9	.	.	PUNCT
cana-1171	22	1	the	the	DET
cana-1171	22	2	development	development	NOUN
cana-1171	22	3	of	of	ADP
cana-1171	22	4	a	a	DET
cana-1171	22	5	new	new	ADJ
cana-1171	22	6	method	method	NOUN
cana-1171	22	7	called	call	VERB
cana-1171	22	8	the	the	DET
cana-1171	22	9	homotopy	homotopy	NOUN
cana-1171	22	10	perturbation	perturbation	NOUN
cana-1171	22	11	method	method	NOUN
cana-1171	22	12	(	(	PUNCT
cana-1171	22	13	hpm	hpm	NOUN
cana-1171	22	14	)	)	PUNCT
cana-1171	22	15	has	have	AUX
cana-1171	22	16	been	be	AUX
cana-1171	22	17	done	do	VERB
cana-1171	22	18	to	to	PART
cana-1171	22	19	overcome	overcome	VERB
cana-1171	22	20	this	this	DET
cana-1171	22	21	problem	problem	NOUN
cana-1171	22	22	.	.	PUNCT
cana-1171	23	1	ji	ji	PROPN
cana-1171	23	2	-	-	PROPN
cana-1171	23	3	huan	huan	PROPN
cana-1171	23	4	he	he	PRON
cana-1171	23	5	was	be	AUX
cana-1171	23	6	the	the	DET
cana-1171	23	7	first	first	ADJ
cana-1171	23	8	to	to	PART
cana-1171	23	9	introduce	introduce	VERB
cana-1171	23	10	the	the	DET
cana-1171	23	11	homotopy	homotopy	NOUN
cana-1171	23	12	perturbation	perturbation	NOUN
cana-1171	23	13	method	method	NOUN
cana-1171	23	14	in	in	ADP
cana-1171	23	15	1998	1998	NUM
cana-1171	23	16	.	.	PUNCT
cana-1171	24	1	he	he	PRON
cana-1171	24	2	introduced	introduce	VERB
cana-1171	24	3	this	this	PRON
cana-1171	24	4	as	as	ADP
cana-1171	24	5	a	a	DET
cana-1171	24	6	means	means	NOUN
cana-1171	24	7	of	of	ADP
cana-1171	24	8	resolving	resolve	VERB
cana-1171	24	9	problems	problem	NOUN
cana-1171	24	10	in	in	ADP
cana-1171	24	11	linear	linear	PROPN
cana-1171	24	12	,	,	PUNCT
cana-1171	24	13	non	non	ADJ
cana-1171	24	14	-	-	ADJ
cana-1171	24	15	linear	linear	ADJ
cana-1171	24	16	,	,	PUNCT
cana-1171	24	17	and	and	CCONJ
cana-1171	24	18	coupled	couple	VERB
cana-1171	24	19	differential	differential	ADJ
cana-1171	24	20	equations	equation	NOUN
cana-1171	24	21	in	in	ADP
cana-1171	24	22	ordinary	ordinary	ADJ
cana-1171	24	23	and	and	CCONJ
cana-1171	24	24	partial	partial	ADJ
cana-1171	24	25	differential	differential	ADJ
cana-1171	24	26	equations	equation	NOUN
cana-1171	24	27	with	with	ADP
cana-1171	24	28	boundary	boundary	ADJ
cana-1171	24	29	or	or	CCONJ
cana-1171	24	30	initial	initial	ADJ
cana-1171	24	31	conditions	condition	NOUN
cana-1171	24	32	.	.	PUNCT
cana-1171	25	1	hpm	hpm	PROPN
cana-1171	25	2	is	be	AUX
cana-1171	25	3	a	a	DET
cana-1171	25	4	semi	semi	ADJ
cana-1171	25	5	-	-	ADJ
cana-1171	25	6	analytical	analytical	ADJ
cana-1171	25	7	method	method	NOUN
cana-1171	25	8	that	that	PRON
cana-1171	25	9	is	be	AUX
cana-1171	25	10	widely	widely	ADV
cana-1171	25	11	used	use	VERB
cana-1171	25	12	by	by	ADP
cana-1171	25	13	mathematicians	mathematician	NOUN
cana-1171	25	14	and	and	CCONJ
cana-1171	25	15	engineers	engineer	NOUN
cana-1171	25	16	.	.	PUNCT
cana-1171	26	1	this	this	DET
cana-1171	26	2	method	method	NOUN
cana-1171	26	3	is	be	AUX
cana-1171	26	4	a	a	DET
cana-1171	26	5	highly	highly	ADV
cana-1171	26	6	effective	effective	ADJ
cana-1171	26	7	and	and	CCONJ
cana-1171	26	8	convenient	convenient	ADJ
cana-1171	26	9	way	way	NOUN
cana-1171	26	10	to	to	PART
cana-1171	26	11	overcome	overcome	VERB
cana-1171	26	12	the	the	DET
cana-1171	26	13	difficulties	difficulty	NOUN
cana-1171	26	14	of	of	ADP
cana-1171	26	15	traditional	traditional	ADJ
cana-1171	26	16	methods	method	NOUN
cana-1171	26	17	.	.	PUNCT
cana-1171	27	1	redox	redox	ADJ
cana-1171	27	2	reactions	reaction	NOUN
cana-1171	27	3	generally	generally	ADV
cana-1171	27	4	involve	involve	VERB
cana-1171	27	5	the	the	DET
cana-1171	27	6	transfer	transfer	NOUN
cana-1171	27	7	of	of	ADP
cana-1171	27	8	electrons	electron	NOUN
cana-1171	27	9	between	between	ADP
cana-1171	27	10	species	specie	NOUN
cana-1171	27	11	.	.	PUNCT
cana-1171	28	1	redox	redox	ADJ
cana-1171	28	2	reactions	reaction	NOUN
cana-1171	28	3	are	be	AUX
cana-1171	28	4	part	part	NOUN
cana-1171	28	5	of	of	ADP
cana-1171	28	6	everyday	everyday	ADJ
cana-1171	28	7	activities	activity	NOUN
cana-1171	28	8	such	such	ADJ
cana-1171	28	9	as	as	ADP
cana-1171	28	10	photosynthesis	photosynthesis	NOUN
cana-1171	28	11	,	,	PUNCT
cana-1171	28	12	respiration	respiration	NOUN
cana-1171	28	13	,	,	PUNCT
cana-1171	28	14	coal	coal	NOUN
cana-1171	28	15	combustion	combustion	NOUN
cana-1171	28	16	,	,	PUNCT
cana-1171	28	17	and	and	CCONJ
cana-1171	28	18	fertilizer	fertilizer	NOUN
cana-1171	28	19	production	production	NOUN
cana-1171	28	20	and	and	CCONJ
cana-1171	28	21	use	use	NOUN
cana-1171	28	22	.	.	PUNCT
cana-1171	29	1	homogeneous	homogeneous	ADJ
cana-1171	29	2	redox	redox	ADJ
cana-1171	29	3	catalysis	catalysis	NOUN
cana-1171	29	4	involves	involve	VERB
cana-1171	29	5	analyzing	analyze	VERB
cana-1171	29	6	and	and	CCONJ
cana-1171	29	7	predicting	predict	VERB
cana-1171	29	8	the	the	DET
cana-1171	29	9	effectiveness	effectiveness	NOUN
cana-1171	29	10	of	of	ADP
cana-1171	29	11	catalysis	catalysis	NOUN
cana-1171	29	12	as	as	ADP
cana-1171	29	13	a	a	DET
cana-1171	29	14	function	function	NOUN
cana-1171	29	15	of	of	ADP
cana-1171	29	16	the	the	DET
cana-1171	29	17	potential	potential	ADJ
cana-1171	29	18	separation	separation	NOUN
cana-1171	29	19	of	of	ADP
cana-1171	29	20	the	the	DET
cana-1171	29	21	catalyst	catalyst	NOUN
cana-1171	29	22	,	,	PUNCT
cana-1171	29	23	substrate	substrate	NOUN
cana-1171	29	24	,	,	PUNCT
cana-1171	29	25	and	and	CCONJ
cana-1171	29	26	stationary	stationary	ADJ
cana-1171	29	27	and	and	CCONJ
cana-1171	29	28	quasistationary	quasistationary	ADJ
cana-1171	29	29	methods	method	NOUN
cana-1171	29	30	.	.	PUNCT
cana-1171	30	1	c.p	c.p	PROPN
cana-1171	30	2	.	.	PROPN
cana-1171	30	3	andrieux	andrieux	PROPN
cana-1171	30	4	et	et	PROPN
cana-1171	30	5	al	al	PROPN
cana-1171	30	6	.	.	PUNCT
cana-1171	31	1	[	[	X
cana-1171	31	2	3	3	NUM
cana-1171	31	3	-	-	SYM
cana-1171	31	4	5	5	NUM
cana-1171	31	5	]	]	PUNCT
cana-1171	31	6	discussed	discuss	VERB
cana-1171	31	7	the	the	DET
cana-1171	31	8	mathematical	mathematical	ADJ
cana-1171	31	9	model	model	NOUN
cana-1171	31	10	of	of	ADP
cana-1171	31	11	the	the	DET
cana-1171	31	12	homogeneous	homogeneous	ADJ
cana-1171	31	13	redox	redox	ADJ
cana-1171	31	14	catalysis	catalysis	NOUN
cana-1171	31	15	of	of	ADP
cana-1171	31	16	electrochemical	electrochemical	ADJ
cana-1171	31	17	reactions	reaction	NOUN
cana-1171	31	18	.	.	PUNCT
cana-1171	32	1	a	a	DET
cana-1171	32	2	mathematical	mathematical	ADJ
cana-1171	32	3	model	model	NOUN
cana-1171	32	4	that	that	PRON
cana-1171	32	5	includes	include	VERB
cana-1171	32	6	boundary	boundary	ADJ
cana-1171	32	7	conditions	condition	NOUN
cana-1171	32	8	features	feature	VERB
cana-1171	32	9	a	a	DET
cana-1171	32	10	system	system	NOUN
cana-1171	32	11	of	of	ADP
cana-1171	32	12	second	second	ADJ
cana-1171	32	13	-	-	PUNCT
cana-1171	32	14	order	order	NOUN
cana-1171	32	15	nonlinear	nonlinear	ADJ
cana-1171	32	16	differential	differential	ADJ
cana-1171	32	17	equations	equation	NOUN
cana-1171	32	18	.	.	PUNCT
cana-1171	33	1	this	this	DET
cana-1171	33	2	paper	paper	NOUN
cana-1171	33	3	investigates	investigate	VERB
cana-1171	33	4	the	the	DET
cana-1171	33	5	dynamics	dynamic	NOUN
cana-1171	33	6	of	of	ADP
cana-1171	33	7	the	the	DET
cana-1171	33	8	electrochemical	electrochemical	ADJ
cana-1171	33	9	mechanism	mechanism	NOUN
cana-1171	33	10	model	model	NOUN
cana-1171	33	11	in	in	ADP
cana-1171	33	12	classical	classical	ADJ
cana-1171	33	13	secondorder	secondorder	ADJ
cana-1171	33	14	non	non	ADJ
cana-1171	33	15	-	-	ADJ
cana-1171	33	16	linear	linear	ADJ
cana-1171	33	17	differential	differential	ADJ
cana-1171	33	18	equations	equation	NOUN
cana-1171	33	19	with	with	ADP
cana-1171	33	20	boundary	boundary	ADJ
cana-1171	33	21	value	value	NOUN
cana-1171	33	22	conditions	condition	NOUN
cana-1171	33	23	[	[	X
cana-1171	33	24	4	4	X
cana-1171	33	25	]	]	PUNCT
cana-1171	33	26	initially	initially	ADV
cana-1171	33	27	and	and	CCONJ
cana-1171	33	28	then	then	ADV
cana-1171	33	29	updated	update	VERB
cana-1171	33	30	it	it	PRON
cana-1171	33	31	to	to	ADP
cana-1171	33	32	caputo	caputo	PROPN
cana-1171	33	33	sequential	sequential	ADJ
cana-1171	33	34	fractional	fractional	ADJ
cana-1171	33	35	equations	equation	NOUN
cana-1171	33	36	.	.	PUNCT
cana-1171	34	1	the	the	DET
cana-1171	34	2	homotopy	homotopy	NOUN
cana-1171	34	3	perturbation	perturbation	NOUN
cana-1171	34	4	method	method	NOUN
cana-1171	34	5	(	(	PUNCT
cana-1171	34	6	hpm	hpm	NOUN
cana-1171	34	7	)	)	PUNCT
cana-1171	34	8	is	be	AUX
cana-1171	34	9	used	use	VERB
cana-1171	34	10	to	to	PART
cana-1171	34	11	derive	derive	VERB
cana-1171	34	12	the	the	DET
cana-1171	34	13	approximate	approximate	ADJ
cana-1171	34	14	analytical	analytical	ADJ
cana-1171	34	15	solutions	solution	NOUN
cana-1171	34	16	of	of	ADP
cana-1171	34	17	the	the	DET
cana-1171	34	18	fde	fde	NOUN
cana-1171	34	19	system	system	NOUN
cana-1171	34	20	in	in	ADP
cana-1171	34	21	fractional	fractional	ADJ
cana-1171	34	22	order	order	NOUN
cana-1171	34	23	.	.	PUNCT
cana-1171	35	1	to	to	PART
cana-1171	35	2	analyze	analyze	VERB
cana-1171	35	3	the	the	DET
cana-1171	35	4	effect	effect	NOUN
cana-1171	35	5	of	of	ADP
cana-1171	35	6	various	various	ADJ
cana-1171	35	7	values	value	NOUN
cana-1171	35	8	of	of	ADP
cana-1171	35	9	each	each	DET
cana-1171	35	10	parameter	parameter	NOUN
cana-1171	35	11	with	with	ADP
cana-1171	35	12	different	different	ADJ
cana-1171	35	13	order	order	NOUN
cana-1171	35	14	𝛼	𝛼	NOUN
cana-1171	35	15	on	on	ADP
cana-1171	35	16	the	the	DET
cana-1171	35	17	concentration	concentration	NOUN
cana-1171	35	18	profile	profile	NOUN
cana-1171	35	19	.	.	PUNCT
cana-1171	36	1	additionally	additionally	ADV
cana-1171	36	2	,	,	PUNCT
cana-1171	36	3	the	the	DET
cana-1171	36	4	hpm	hpm	ADJ
cana-1171	36	5	solutions	solution	NOUN
cana-1171	36	6	of	of	ADP
cana-1171	36	7	the	the	DET
cana-1171	36	8	ec	ec	PROPN
cana-1171	36	9	mechanisms	mechanism	NOUN
cana-1171	36	10	of	of	ADP
cana-1171	36	11	fractional	fractional	ADJ
cana-1171	36	12	order	order	NOUN
cana-1171	36	13	tend	tend	VERB
cana-1171	36	14	to	to	ADP
cana-1171	36	15	the	the	DET
cana-1171	36	16	integer	integer	NOUN
cana-1171	36	17	-	-	PUNCT
cana-1171	36	18	order	order	NOUN
cana-1171	36	19	hpm	hpm	NOUN
cana-1171	36	20	solution	solution	NOUN
cana-1171	36	21	of	of	ADP
cana-1171	36	22	the	the	DET
cana-1171	36	23	ec	ec	PROPN
cana-1171	36	24	mechanism	mechanism	NOUN
cana-1171	36	25	as	as	ADP
cana-1171	36	26	a	a	DET
cana-1171	36	27	special	special	ADJ
cana-1171	36	28	case	case	NOUN
cana-1171	36	29	𝛼	𝛼	X
cana-1171	36	30	→	→	SYM
cana-1171	36	31	1	1	NUM
cana-1171	36	32	.	.	PUNCT
cana-1171	36	33	nomenclature	nomenclature	ADJ
cana-1171	36	34	𝑃	𝑃	NOUN
cana-1171	36	35	,	,	PUNCT
cana-1171	36	36	𝑄	𝑄	PROPN
cana-1171	36	37	catalyst	catalyst	NOUN
cana-1171	36	38	couple	couple	NOUN
cana-1171	36	39	.	.	PUNCT
cana-1171	37	1	𝐴	𝐴	NOUN
cana-1171	37	2	substrate	substrate	NOUN
cana-1171	37	3	.	.	PUNCT
cana-1171	38	1	𝐵	𝐵	NOUN
cana-1171	38	2	product	product	NOUN
cana-1171	38	3	.	.	PUNCT
cana-1171	39	1	𝑐𝑃	𝑐𝑃	NOUN
cana-1171	39	2	,	,	PUNCT
cana-1171	39	3	𝑐𝑄	𝑐𝑄	PROPN
cana-1171	39	4	,	,	PUNCT
cana-1171	39	5	𝑐𝐴	𝑐𝐴	PROPN
cana-1171	39	6	,	,	PUNCT
cana-1171	39	7	𝑐𝐵	𝑐𝐵	VERB
cana-1171	39	8	concentration	concentration	NOUN
cana-1171	39	9	of	of	ADP
cana-1171	39	10	𝑃	𝑃	NOUN
cana-1171	39	11	,	,	PUNCT
cana-1171	39	12	𝑄	𝑄	PROPN
cana-1171	39	13	,	,	PUNCT
cana-1171	39	14	𝐴	𝐴	PROPN
cana-1171	39	15	,	,	PUNCT
cana-1171	39	16	𝐵.	𝐵.	PROPN
cana-1171	39	17	𝐷𝑝	𝐷𝑝	PROPN
cana-1171	39	18	,	,	PUNCT
cana-1171	39	19	𝐷𝑄	𝐷𝑄	PROPN
cana-1171	39	20	,	,	PUNCT
cana-1171	39	21	𝐷𝐴	𝐷𝐴	PROPN
cana-1171	39	22	,	,	PUNCT
cana-1171	39	23	𝐷𝐵	𝐷𝐵	PROPN
cana-1171	39	24	diffusion	diffusion	NOUN
cana-1171	39	25	coefficients	coefficient	NOUN
cana-1171	39	26	of	of	ADP
cana-1171	39	27	𝑃	𝑃	NOUN
cana-1171	39	28	,	,	PUNCT
cana-1171	39	29	𝑄	𝑄	PROPN
cana-1171	39	30	,	,	PUNCT
cana-1171	39	31	𝐴	𝐴	PROPN
cana-1171	39	32	,	,	PUNCT
cana-1171	39	33	𝐵	𝐵	NOUN
cana-1171	39	34	in	in	ADP
cana-1171	39	35	𝑐𝑚2𝑠−1	𝑐𝑚2𝑠−1	PROPN
cana-1171	39	36	.	.	PUNCT
cana-1171	40	1	𝐾	𝐾	PROPN
cana-1171	40	2	,	,	PUNCT
cana-1171	40	3	𝐾1	𝐾1	PROPN
cana-1171	40	4	,	,	PUNCT
cana-1171	40	5	𝐾2	𝐾2	ADJ
cana-1171	40	6	rate	rate	NOUN
cana-1171	40	7	constants	constant	NOUN
cana-1171	40	8	.	.	PUNCT
cana-1171	41	1	𝜆	𝜆	X
cana-1171	41	2	,	,	PUNCT
cana-1171	41	3	𝜆1	𝜆1	NOUN
cana-1171	41	4	,	,	PUNCT
cana-1171	41	5	𝜆2	𝜆2	NOUN
cana-1171	41	6	dimensionless	dimensionless	NOUN
cana-1171	41	7	rate	rate	NOUN
cana-1171	41	8	parameters	parameter	NOUN
cana-1171	41	9	.	.	PUNCT
cana-1171	42	1	𝑡	𝑡	NOUN
cana-1171	42	2	time	time	NOUN
cana-1171	42	3	.	.	PUNCT
cana-1171	43	1	𝑥	𝑥	DET
cana-1171	43	2	distance	distance	NOUN
cana-1171	43	3	to	to	ADP
cana-1171	43	4	the	the	DET
cana-1171	43	5	electrode	electrode	NOUN
cana-1171	43	6	.	.	PUNCT
cana-1171	44	1	𝐸	𝐸	ADJ
cana-1171	44	2	electrode	electrode	NOUN
cana-1171	44	3	potential	potential	NOUN
cana-1171	44	4	.	.	PUNCT
cana-1171	45	1	𝐸𝑃𝑄	𝐸𝑃𝑄	PROPN
cana-1171	45	2	𝑜	𝑜	PRON
cana-1171	45	3	standard	standard	ADJ
cana-1171	45	4	potential	potential	NOUN
cana-1171	45	5	of	of	ADP
cana-1171	45	6	the	the	DET
cana-1171	45	7	catalyst	catalyst	NOUN
cana-1171	45	8	.	.	PUNCT
cana-1171	46	1	𝑆	𝑆	PROPN
cana-1171	46	2	electrode	electrode	NOUN
cana-1171	46	3	surface	surface	NOUN
cana-1171	46	4	area	area	NOUN
cana-1171	46	5	.	.	PUNCT
cana-1171	47	1	𝛿	𝛿	PRON
cana-1171	47	2	polarography	polarography	NOUN
cana-1171	47	3	of	of	ADP
cana-1171	47	4	the	the	DET
cana-1171	47	5	diffusion	diffusion	NOUN
cana-1171	47	6	layer	layer	NOUN
cana-1171	47	7	thickness	thickness	NOUN
cana-1171	47	8	.	.	PUNCT
cana-1171	48	1	𝑣	𝑣	DET
cana-1171	48	2	kinetic	kinetic	ADJ
cana-1171	48	3	viscosity	viscosity	NOUN
cana-1171	48	4	in	in	ADP
cana-1171	48	5	𝑐𝑚	𝑐𝑚	PROPN
cana-1171	48	6	𝑠−1	𝑠−1	PROPN
cana-1171	48	7	.	.	PUNCT
cana-1171	48	8	communications	communication	NOUN
cana-1171	48	9	on	on	ADP
cana-1171	48	10	applied	apply	VERB
cana-1171	48	11	nonlinear	nonlinear	ADJ
cana-1171	48	12	analysis	analysis	NOUN
cana-1171	48	13	issn	issn	NOUN
cana-1171	48	14	:	:	PUNCT
cana-1171	48	15	1074	1074	NUM
cana-1171	48	16	-	-	PUNCT
cana-1171	48	17	133x	133x	NUM
cana-1171	48	18	vol	vol	NOUN
cana-1171	48	19	31	31	NUM
cana-1171	48	20	no	no	NOUN
cana-1171	48	21	.	.	PUNCT
cana-1171	49	1	6s	6s	NUM
cana-1171	49	2	(	(	PUNCT
cana-1171	49	3	2024	2024	NUM
cana-1171	49	4	)	)	PUNCT
cana-1171	49	5	116	116	NUM
cana-1171	49	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1171	49	7	2.sequential	2.sequential	NUM
cana-1171	49	8	fractional	fractional	ADJ
cana-1171	49	9	derivatives	derivative	NOUN
cana-1171	49	10	this	this	DET
cana-1171	49	11	approach	approach	NOUN
cana-1171	49	12	is	be	AUX
cana-1171	49	13	based	base	VERB
cana-1171	49	14	on	on	ADP
cana-1171	49	15	the	the	DET
cana-1171	49	16	observation	observation	NOUN
cana-1171	49	17	[	[	X
cana-1171	49	18	2	2	NUM
cana-1171	49	19	,	,	PUNCT
cana-1171	49	20	10	10	NUM
cana-1171	49	21	]	]	PUNCT
cana-1171	49	22	that	that	SCONJ
cana-1171	49	23	the	the	DET
cana-1171	49	24	𝑚-th	𝑚-th	PROPN
cana-1171	49	25	order	order	NOUN
cana-1171	49	26	differentiation	differentiation	NOUN
cana-1171	49	27	is	be	AUX
cana-1171	49	28	simply	simply	ADV
cana-1171	49	29	a	a	DET
cana-1171	49	30	series	series	NOUN
cana-1171	49	31	of	of	ADP
cana-1171	49	32	first	first	ADJ
cana-1171	49	33	order	order	NOUN
cana-1171	49	34	differentiations	differentiation	NOUN
cana-1171	49	35	.	.	PUNCT
cana-1171	50	1	that	that	PRON
cana-1171	50	2	is	be	AUX
cana-1171	50	3	,	,	PUNCT
cana-1171	50	4	𝑑𝑚𝜑(𝑡	𝑑𝑚𝜑(𝑡	PROPN
cana-1171	50	5	)	)	PUNCT
cana-1171	50	6	𝑑𝑡𝑚	𝑑𝑡𝑚	ADV
cana-1171	50	7	=	=	PUNCT
cana-1171	51	1	(	(	PUNCT
cana-1171	51	2	𝑑	𝑑	NOUN
cana-1171	51	3	𝑑𝑡	𝑑𝑡	ADP
cana-1171	51	4	.	.	PUNCT
cana-1171	52	1	𝑑	𝑑	PROPN
cana-1171	52	2	𝑑𝑡	𝑑𝑡	ADP
cana-1171	52	3	…	…	PUNCT
cana-1171	52	4	(	(	PUNCT
cana-1171	52	5	𝑚	𝑚	X
cana-1171	52	6	𝑡𝑖𝑚𝑒𝑠	𝑡𝑖𝑚𝑒𝑠	NOUN
cana-1171	52	7	)	)	PUNCT
cana-1171	52	8	)	)	PUNCT
cana-1171	52	9	𝜑(𝑡	𝜑(𝑡	PROPN
cana-1171	52	10	)	)	PUNCT
cana-1171	52	11	k.s.miller	k.s.miller	NOUN
cana-1171	52	12	and	and	CCONJ
cana-1171	52	13	b.ross	b.ross	ADV
cana-1171	52	14	first	first	ADV
cana-1171	52	15	called	call	VERB
cana-1171	52	16	the	the	DET
cana-1171	52	17	generalized	generalize	VERB
cana-1171	52	18	fractional	fractional	ADJ
cana-1171	52	19	differentiation	differentiation	NOUN
cana-1171	52	20	defined	define	VERB
cana-1171	52	21	by	by	ADP
cana-1171	52	22	𝐷𝛼	𝐷𝛼	PROPN
cana-1171	52	23	is	be	AUX
cana-1171	52	24	the	the	DET
cana-1171	52	25	riemann	riemann	PROPN
cana-1171	52	26	-	-	PUNCT
cana-1171	52	27	lioville	lioville	ADJ
cana-1171	52	28	fractional	fractional	ADJ
cana-1171	52	29	derivative	derivative	ADJ
cana-1171	52	30	and	and	CCONJ
cana-1171	52	31	sequential	sequential	ADJ
cana-1171	52	32	differentiation	differentiation	NOUN
cana-1171	52	33	.	.	PUNCT
cana-1171	53	1	that	that	PRON
cana-1171	53	2	is	be	AUX
cana-1171	53	3	a	a	DET
cana-1171	53	4	suitable	suitable	ADJ
cana-1171	53	5	method	method	NOUN
cana-1171	53	6	for	for	ADP
cana-1171	53	7	replacing	replace	VERB
cana-1171	53	8	𝑑	𝑑	PRON
cana-1171	53	9	𝑑𝑡	𝑑𝑡	ADP
cana-1171	53	10	with	with	ADP
cana-1171	53	11	the	the	DET
cana-1171	53	12	derivative	derivative	NOUN
cana-1171	53	13	of	of	ADP
cana-1171	53	14	non	non	ADJ
cana-1171	53	15	-	-	ADJ
cana-1171	53	16	integer	integer	ADJ
cana-1171	53	17	order	order	NOUN
cana-1171	53	18	𝐷𝛼	𝐷𝛼	NOUN
cana-1171	53	19	where	where	SCONJ
cana-1171	53	20	0	0	NUM
cana-1171	53	21	≤	≤	NUM
cana-1171	53	22	𝛼	𝛼	VERB
cana-1171	53	23	≤	≤	NUM
cana-1171	53	24	1	1	NUM
cana-1171	53	25	.	.	PUNCT
cana-1171	54	1	therefore	therefore	ADV
cana-1171	54	2	,	,	PUNCT
cana-1171	54	3	the	the	DET
cana-1171	54	4	general	general	ADJ
cana-1171	54	5	fractional	fractional	ADJ
cana-1171	54	6	differentiation	differentiation	NOUN
cana-1171	54	7	series	series	NOUN
cana-1171	54	8	is	be	AUX
cana-1171	54	9	written	write	VERB
cana-1171	54	10	as	as	ADP
cana-1171	54	11	𝐷𝑚𝛼𝜑(𝑡	𝐷𝑚𝛼𝜑(𝑡	PROPN
cana-1171	54	12	)	)	PUNCT
cana-1171	54	13	=	=	PUNCT
cana-1171	54	14	(	(	PUNCT
cana-1171	54	15	𝐷𝛼	𝐷𝛼	NOUN
cana-1171	54	16	.	.	PUNCT
cana-1171	55	1	𝐷𝛼	𝐷𝛼	NOUN
cana-1171	55	2	…	…	PUNCT
cana-1171	55	3	(	(	PUNCT
cana-1171	55	4	𝑚	𝑚	X
cana-1171	55	5	𝑡𝑖𝑚𝑒𝑠))𝜑(𝑡	𝑡𝑖𝑚𝑒𝑠))𝜑(𝑡	PROPN
cana-1171	55	6	)	)	PUNCT
cana-1171	55	7	3	3	NUM
cana-1171	55	8	.	.	PUNCT
cana-1171	55	9	preliminaries	preliminary	NOUN
cana-1171	55	10	in	in	ADP
cana-1171	55	11	this	this	DET
cana-1171	55	12	section	section	NOUN
cana-1171	55	13	,	,	PUNCT
cana-1171	55	14	some	some	DET
cana-1171	55	15	basic	basic	ADJ
cana-1171	55	16	definitions	definition	NOUN
cana-1171	55	17	that	that	PRON
cana-1171	55	18	will	will	AUX
cana-1171	55	19	be	be	AUX
cana-1171	55	20	used	use	VERB
cana-1171	55	21	in	in	ADP
cana-1171	55	22	the	the	DET
cana-1171	55	23	remaining	remain	VERB
cana-1171	55	24	sections	section	NOUN
cana-1171	55	25	are	be	AUX
cana-1171	55	26	given	give	VERB
cana-1171	55	27	,	,	PUNCT
cana-1171	55	28	definition	definition	NOUN
cana-1171	55	29	1	1	NUM
cana-1171	55	30	.	.	PUNCT
cana-1171	56	1	a	a	DET
cana-1171	56	2	real	real	ADV
cana-1171	56	3	valued	value	VERB
cana-1171	56	4	function	function	NOUN
cana-1171	56	5	𝜑(𝑡	𝜑(𝑡	PROPN
cana-1171	56	6	)	)	PUNCT
cana-1171	56	7	,	,	PUNCT
cana-1171	56	8	defined	define	VERB
cana-1171	56	9	on	on	ADP
cana-1171	56	10	[	[	X
cana-1171	56	11	𝑎	𝑎	X
cana-1171	56	12	,	,	PUNCT
cana-1171	56	13	𝑏	𝑏	NOUN
cana-1171	56	14	]	]	PUNCT
cana-1171	56	15	lies	lie	VERB
cana-1171	56	16	in	in	ADP
cana-1171	56	17	the	the	DET
cana-1171	56	18	function	function	NOUN
cana-1171	56	19	space	space	NOUN
cana-1171	56	20	ℂ𝜇[𝑎	ℂ𝜇[𝑎	PROPN
cana-1171	56	21	,	,	PUNCT
cana-1171	56	22	𝑏	𝑏	NOUN
cana-1171	56	23	]	]	X
cana-1171	56	24	,	,	PUNCT
cana-1171	56	25	𝜇	𝜇	ADP
cana-1171	56	26	∈	∈	PROPN
cana-1171	56	27	ℝ	ℝ	PROPN
cana-1171	56	28	,	,	PUNCT
cana-1171	56	29	if	if	SCONJ
cana-1171	56	30	there	there	PRON
cana-1171	56	31	exists	exist	VERB
cana-1171	56	32	a	a	DET
cana-1171	56	33	real	real	ADJ
cana-1171	56	34	number	number	NOUN
cana-1171	56	35	𝑘	𝑘	ADP
cana-1171	56	36	>	>	X
cana-1171	56	37	𝜇	𝜇	ADP
cana-1171	56	38	such	such	ADJ
cana-1171	56	39	that	that	SCONJ
cana-1171	56	40	𝜑(𝑡	𝜑(𝑡	PROPN
cana-1171	56	41	)	)	PUNCT
cana-1171	56	42	=	=	PRON
cana-1171	56	43	(	(	PUNCT
cana-1171	56	44	𝑡	𝑡	PROPN
cana-1171	56	45	−	−	PROPN
cana-1171	56	46	𝑎)𝑘	𝑎)𝑘	ADJ
cana-1171	56	47	�	�	PROPN
cana-1171	56	48	̅	̅	NOUN
cana-1171	56	49	�	�	NOUN
cana-1171	56	50	(𝑡	(𝑡	NOUN
cana-1171	56	51	)	)	PUNCT
cana-1171	56	52	,	,	PUNCT
cana-1171	56	53	with	with	ADP
cana-1171	56	54	�	�	NOUN
cana-1171	56	55	̅	̅	NOUN
cana-1171	56	56	�	�	NOUN
cana-1171	56	57	∈	∈	NOUN
cana-1171	56	58	ℂ[𝑎	ℂ[𝑎	NOUN
cana-1171	56	59	,	,	PUNCT
cana-1171	56	60	𝑏	𝑏	NOUN
cana-1171	56	61	]	]	PUNCT
cana-1171	56	62	,	,	PUNCT
cana-1171	56	63	and	and	CCONJ
cana-1171	56	64	it	it	PRON
cana-1171	56	65	is	be	AUX
cana-1171	56	66	said	say	VERB
cana-1171	56	67	to	to	PART
cana-1171	56	68	be	be	AUX
cana-1171	56	69	in	in	ADP
cana-1171	56	70	the	the	DET
cana-1171	56	71	space	space	NOUN
cana-1171	56	72	ℂ𝜇	ℂ𝜇	PROPN
cana-1171	56	73	𝑛	𝑛	NOUN
cana-1171	56	74	if	if	SCONJ
cana-1171	57	1	and	and	CCONJ
cana-1171	57	2	only	only	ADV
cana-1171	57	3	if	if	SCONJ
cana-1171	57	4	𝜑(𝑛	𝜑(𝑛	NUM
cana-1171	57	5	)	)	PUNCT
cana-1171	57	6	∈	∈	PROPN
cana-1171	57	7	ℂ𝜇	ℂ𝜇	PROPN
cana-1171	57	8	,	,	PUNCT
cana-1171	57	9	𝑛	𝑛	PRON
cana-1171	57	10	is	be	AUX
cana-1171	57	11	positive	positive	ADJ
cana-1171	57	12	integer	integer	NOUN
cana-1171	57	13	number	number	NOUN
cana-1171	57	14	with	with	ADP
cana-1171	57	15	zero	zero	NUM
cana-1171	57	16	.	.	PUNCT
cana-1171	58	1	it	it	PRON
cana-1171	58	2	is	be	AUX
cana-1171	58	3	clear	clear	ADJ
cana-1171	58	4	that	that	SCONJ
cana-1171	58	5	ℂ𝜇1	ℂ𝜇1	NOUN
cana-1171	58	6	⊂	⊂	PROPN
cana-1171	58	7	ℂ𝜇2	ℂ𝜇2	VERB
cana-1171	58	8	for	for	ADP
cana-1171	58	9	𝜇1	𝜇1	PROPN
cana-1171	58	10	≤	≤	PROPN
cana-1171	58	11	𝜇2	𝜇2	NOUN
cana-1171	58	12	.	.	PUNCT
cana-1171	59	1	definition	definition	NOUN
cana-1171	59	2	2	2	NUM
cana-1171	59	3	.	.	PUNCT
cana-1171	60	1	the	the	DET
cana-1171	60	2	caputo	caputo	PROPN
cana-1171	60	3	fractional	fractional	PROPN
cana-1171	60	4	derivative	derivative	NOUN
cana-1171	60	5	of	of	ADP
cana-1171	60	6	order	order	NOUN
cana-1171	60	7	𝛼	𝛼	AUX
cana-1171	60	8	∈	∈	NOUN
cana-1171	60	9	ℝ	ℝ	PROPN
cana-1171	60	10	is	be	AUX
cana-1171	60	11	defined	define	VERB
cana-1171	60	12	as	as	ADP
cana-1171	60	13	𝐷𝑡	𝐷𝑡	PROPN
cana-1171	60	14	𝛼	𝛼	NOUN
cana-1171	60	15	0	0	PUNCT
cana-1171	60	16	𝐶	𝐶	PROPN
cana-1171	60	17	𝜑(𝑡	𝜑(𝑡	PROPN
cana-1171	60	18	)	)	PUNCT
cana-1171	60	19	=	=	SYM
cana-1171	60	20	1	1	NUM
cana-1171	60	21	𝛤(𝑛	𝛤(𝑛	NUM
cana-1171	60	22	−	−	PROPN
cana-1171	60	23	𝛼	𝛼	NOUN
cana-1171	60	24	)	)	PUNCT
cana-1171	60	25	∫	∫	PROPN
cana-1171	60	26	(	(	PUNCT
cana-1171	60	27	𝑡	𝑡	PROPN
cana-1171	60	28	−	−	NOUN
cana-1171	60	29	𝜏)𝑛−𝛼−1𝜑(𝑛)(𝜏)𝑑𝜏	𝜏)𝑛−𝛼−1𝜑(𝑛)(𝜏)𝑑𝜏	ADV
cana-1171	60	30	𝑡	𝑡	X
cana-1171	60	31	0	0	NUM
cana-1171	60	32	where	where	SCONJ
cana-1171	60	33	𝛼	𝛼	X
cana-1171	60	34	>	>	X
cana-1171	60	35	0	0	NUM
cana-1171	60	36	.	.	PUNCT
cana-1171	61	1	if	if	SCONJ
cana-1171	61	2	𝛼	𝛼	PRON
cana-1171	61	3	=	=	VERB
cana-1171	61	4	𝑛	𝑛	VERB
cana-1171	61	5	then	then	ADV
cana-1171	61	6	𝐷𝑡	𝐷𝑡	PROPN
cana-1171	61	7	𝛼	𝛼	NOUN
cana-1171	61	8	0	0	PUNCT
cana-1171	61	9	𝐶	𝐶	PROPN
cana-1171	61	10	𝜑(𝑡	𝜑(𝑡	PROPN
cana-1171	61	11	)	)	PUNCT
cana-1171	61	12	=	=	SYM
cana-1171	61	13	𝑑𝑛𝜑(𝑡	𝑑𝑛𝜑(𝑡	VERB
cana-1171	61	14	)	)	PUNCT
cana-1171	61	15	𝑑𝑡𝑛	𝑑𝑡𝑛	NOUN
cana-1171	61	16	.	.	PUNCT
cana-1171	62	1	definition	definition	NOUN
cana-1171	62	2	3	3	X
cana-1171	62	3	.	.	PUNCT
cana-1171	63	1	let	let	VERB
cana-1171	63	2	𝑚𝛼	𝑚𝛼	VERB
cana-1171	63	3	>	>	X
cana-1171	63	4	0	0	NUM
cana-1171	63	5	,	,	PUNCT
cana-1171	63	6	and	and	CCONJ
cana-1171	63	7	𝜑(𝑡	𝜑(𝑡	PROPN
cana-1171	63	8	)	)	PUNCT
cana-1171	63	9	∶	∶	NOUN
cana-1171	63	10	(	(	PUNCT
cana-1171	63	11	0	0	NUM
cana-1171	63	12	,	,	PUNCT
cana-1171	63	13	∞	∞	NUM
cana-1171	63	14	)	)	PUNCT
cana-1171	63	15	→	→	SYM
cana-1171	63	16	ℝ.	ℝ.	PROPN
cana-1171	63	17	then	then	ADV
cana-1171	63	18	,	,	PUNCT
cana-1171	63	19	the	the	DET
cana-1171	63	20	caputo	caputo	PROPN
cana-1171	63	21	derivative	derivative	NOUN
cana-1171	63	22	of	of	ADP
cana-1171	63	23	𝜑(𝑡	𝜑(𝑡	PROPN
cana-1171	63	24	)	)	PUNCT
cana-1171	63	25	of	of	ADP
cana-1171	63	26	order	order	NOUN
cana-1171	63	27	𝑚𝛼	𝑚𝛼	VERB
cana-1171	63	28	is	be	AUX
cana-1171	63	29	given	give	VERB
cana-1171	63	30	by	by	ADP
cana-1171	63	31	𝐷𝑡	𝐷𝑡	PROPN
cana-1171	63	32	𝑚𝛼	𝑚𝛼	ADP
cana-1171	63	33	0	0	NUM
cana-1171	63	34	𝐶	𝐶	PROPN
cana-1171	63	35	𝜑(𝑡	𝜑(𝑡	PROPN
cana-1171	63	36	)	)	PUNCT
cana-1171	63	37	=	=	SYM
cana-1171	63	38	1	1	NUM
cana-1171	63	39	𝛤(𝑛	𝛤(𝑛	NUM
cana-1171	63	40	−	−	PROPN
cana-1171	63	41	𝑚𝛼	𝑚𝛼	NOUN
cana-1171	63	42	)	)	PUNCT
cana-1171	63	43	∫	∫	PROPN
cana-1171	63	44	(	(	PUNCT
cana-1171	63	45	𝑡	𝑡	PROPN
cana-1171	63	46	−	−	PROPN
cana-1171	63	47	𝜏)𝑛−𝑚𝛼−1𝜑(𝑛)(𝜏)𝑑𝜏	𝜏)𝑛−𝑚𝛼−1𝜑(𝑛)(𝜏)𝑑𝜏	PROPN
cana-1171	63	48	𝑡	𝑡	PROPN
cana-1171	63	49	0	0	NUM
cana-1171	64	1	where	where	SCONJ
cana-1171	64	2	𝑚	𝑚	PROPN
cana-1171	64	3	∈	∈	PROPN
cana-1171	64	4	ℕ	ℕ	PROPN
cana-1171	64	5	such	such	ADJ
cana-1171	64	6	that	that	PRON
cana-1171	64	7	(	(	PUNCT
cana-1171	64	8	𝑛	𝑛	PRON
cana-1171	64	9	−	−	PROPN
cana-1171	64	10	1	1	NUM
cana-1171	64	11	)	)	PUNCT
cana-1171	64	12	<	<	X
cana-1171	64	13	𝑚𝛼	𝑚𝛼	ADP
cana-1171	64	14	<	<	X
cana-1171	64	15	𝑛.	𝑛.	NOUN
cana-1171	64	16	in	in	ADP
cana-1171	64	17	particular	particular	ADJ
cana-1171	64	18	,	,	PUNCT
cana-1171	64	19	if	if	SCONJ
cana-1171	64	20	𝛼	𝛼	X
cana-1171	64	21	=	=	SYM
cana-1171	64	22	1	1	NUM
cana-1171	64	23	,	,	PUNCT
cana-1171	64	24	then	then	ADV
cana-1171	64	25	𝑚𝛼	𝑚𝛼	ADP
cana-1171	64	26	=	=	SYM
cana-1171	64	27	𝑚	𝑚	PROPN
cana-1171	64	28	is	be	AUX
cana-1171	64	29	an	an	DET
cana-1171	64	30	integer	integer	NOUN
cana-1171	64	31	and	and	CCONJ
cana-1171	64	32	𝐷𝑡	𝐷𝑡	PROPN
cana-1171	64	33	𝑚𝛼	𝑚𝛼	ADP
cana-1171	64	34	0	0	NUM
cana-1171	64	35	𝐶	𝐶	PROPN
cana-1171	64	36	𝜑(𝑡	𝜑(𝑡	PROPN
cana-1171	64	37	)	)	PUNCT
cana-1171	65	1	=	=	SYM
cana-1171	66	1	𝐷𝑡	𝐷𝑡	PROPN
cana-1171	66	2	𝑚	𝑚	NOUN
cana-1171	66	3	0	0	NUM
cana-1171	66	4	𝐶	𝐶	PROPN
cana-1171	66	5	𝜑(𝑡	𝜑(𝑡	PROPN
cana-1171	66	6	)	)	PUNCT
cana-1171	66	7	and	and	CCONJ
cana-1171	66	8	𝐷𝑡	𝐷𝑡	PROPN
cana-1171	66	9	𝛼	𝛼	NOUN
cana-1171	66	10	0	0	PUNCT
cana-1171	66	11	𝐶	𝐶	PROPN
cana-1171	66	12	𝜑(𝑡	𝜑(𝑡	PROPN
cana-1171	66	13	)	)	PUNCT
cana-1171	66	14	=	=	PUNCT
cana-1171	66	15	𝜑1(𝑡	𝜑1(𝑡	NOUN
cana-1171	66	16	)	)	PUNCT
cana-1171	66	17	.	.	PUNCT
cana-1171	67	1	𝜔	𝜔	ADP
cana-1171	67	2	angular	angular	ADJ
cana-1171	67	3	rotation	rotation	NOUN
cana-1171	67	4	speed	speed	NOUN
cana-1171	67	5	in	in	ADP
cana-1171	67	6	𝑟𝑎𝑑	𝑟𝑎𝑑	ADP
cana-1171	67	7	𝑠−1	𝑠−1	PROPN
cana-1171	67	8	.	.	PROPN
cana-1171	67	9	𝜉	𝜉	PROPN
cana-1171	67	10	dimensionless	dimensionless	ADJ
cana-1171	67	11	potential	potential	ADJ
cana-1171	67	12	scale	scale	NOUN
cana-1171	67	13	.	.	PUNCT
cana-1171	68	1	𝜓∞	𝜓∞	NOUN
cana-1171	68	2	dimensionless	dimensionless	PROPN
cana-1171	68	3	plateau	plateau	PROPN
cana-1171	68	4	current	current	NOUN
cana-1171	68	5	.	.	PUNCT
cana-1171	69	1	𝑖1	𝑖1	PROPN
cana-1171	69	2	catalytic	catalytic	ADJ
cana-1171	69	3	plateau	plateau	NOUN
cana-1171	69	4	current	current	NOUN
cana-1171	69	5	.	.	PUNCT
cana-1171	70	1	𝑖𝑑𝑃	𝑖𝑑𝑃	ADJ
cana-1171	70	2	diffusion	diffusion	NOUN
cana-1171	70	3	-	-	PUNCT
cana-1171	70	4	controlled	control	VERB
cana-1171	70	5	plateau	plateau	NOUN
cana-1171	70	6	current	current	NOUN
cana-1171	70	7	of	of	ADP
cana-1171	70	8	𝑃.	𝑃.	PROPN
cana-1171	70	9	𝑖𝑑𝐴	𝑖𝑑𝐴	PROPN
cana-1171	70	10	diffusion	diffusion	NOUN
cana-1171	70	11	-	-	PUNCT
cana-1171	70	12	controlled	control	VERB
cana-1171	70	13	plateau	plateau	NOUN
cana-1171	70	14	current	current	NOUN
cana-1171	70	15	of	of	ADP
cana-1171	70	16	𝐴.	𝐴.	PROPN
cana-1171	70	17	communications	communication	NOUN
cana-1171	70	18	on	on	ADP
cana-1171	70	19	applied	apply	VERB
cana-1171	70	20	nonlinear	nonlinear	ADJ
cana-1171	70	21	analysis	analysis	NOUN
cana-1171	70	22	issn	issn	NOUN
cana-1171	70	23	:	:	PUNCT
cana-1171	70	24	1074	1074	NUM
cana-1171	70	25	-	-	PUNCT
cana-1171	70	26	133x	133x	NUM
cana-1171	70	27	vol	vol	NOUN
cana-1171	70	28	31	31	NUM
cana-1171	70	29	no	no	NOUN
cana-1171	70	30	.	.	PUNCT
cana-1171	71	1	6s	6s	NUM
cana-1171	71	2	(	(	PUNCT
cana-1171	71	3	2024	2024	NUM
cana-1171	71	4	)	)	PUNCT
cana-1171	71	5	117	117	NUM
cana-1171	71	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1171	71	7	definition	definition	NOUN
cana-1171	71	8	4	4	NUM
cana-1171	71	9	.	.	PUNCT
cana-1171	72	1	the	the	DET
cana-1171	72	2	caputo	caputo	PROPN
cana-1171	72	3	fractional	fractional	PROPN
cana-1171	72	4	derivative	derivative	NOUN
cana-1171	72	5	of	of	ADP
cana-1171	72	6	𝜑(𝑡	𝜑(𝑡	PROPN
cana-1171	72	7	)	)	PUNCT
cana-1171	72	8	of	of	ADP
cana-1171	72	9	order	order	NOUN
cana-1171	72	10	𝑚𝛼	𝑚𝛼	VERB
cana-1171	72	11	for	for	ADP
cana-1171	72	12	(	(	PUNCT
cana-1171	72	13	𝑛	𝑛	PRON
cana-1171	72	14	−	−	PROPN
cana-1171	72	15	1	1	NUM
cana-1171	72	16	)	)	PUNCT
cana-1171	72	17	<	<	X
cana-1171	72	18	𝑚𝛼	𝑚𝛼	ADP
cana-1171	72	19	<	<	X
cana-1171	72	20	𝑛	𝑛	PROPN
cana-1171	72	21	is	be	AUX
cana-1171	72	22	said	say	VERB
cana-1171	72	23	to	to	PART
cana-1171	72	24	be	be	AUX
cana-1171	72	25	the	the	DET
cana-1171	72	26	sequential	sequential	ADJ
cana-1171	72	27	caputo	caputo	PROPN
cana-1171	72	28	fractional	fractional	PROPN
cana-1171	72	29	derivative	derivative	NOUN
cana-1171	72	30	of	of	ADP
cana-1171	72	31	order	order	NOUN
cana-1171	72	32	𝛼	𝛼	NOUN
cana-1171	72	33	if	if	SCONJ
cana-1171	72	34	the	the	DET
cana-1171	72	35	relation	relation	NOUN
cana-1171	72	36	is	be	AUX
cana-1171	72	37	written	write	VERB
cana-1171	72	38	as	as	SCONJ
cana-1171	72	39	𝐷𝑡	𝐷𝑡	PROPN
cana-1171	72	40	𝑚𝛼	𝑚𝛼	ADP
cana-1171	72	41	0	0	NUM
cana-1171	72	42	𝐶	𝐶	PROPN
cana-1171	72	43	𝜑(𝑡	𝜑(𝑡	PROPN
cana-1171	72	44	)	)	PUNCT
cana-1171	72	45	=	=	PUNCT
cana-1171	73	1	𝐷𝑡	𝐷𝑡	NOUN
cana-1171	73	2	𝛼	𝛼	NOUN
cana-1171	73	3	0	0	PUNCT
cana-1171	73	4	𝐶	𝐶	PROPN
cana-1171	73	5	(	(	PUNCT
cana-1171	73	6	𝐷𝑡	𝐷𝑡	PROPN
cana-1171	73	7	(	(	PUNCT
cana-1171	73	8	𝑚−1)𝛼	𝑚−1)𝛼	PROPN
cana-1171	73	9	0	0	NUM
cana-1171	73	10	𝐶	𝐶	PROPN
cana-1171	73	11	)	)	PUNCT
cana-1171	73	12	𝜑(𝑡	𝜑(𝑡	PROPN
cana-1171	73	13	)	)	PUNCT
cana-1171	73	14	holds	hold	VERB
cana-1171	73	15	for	for	ADP
cana-1171	73	16	𝑚	𝑚	NOUN
cana-1171	73	17	=	=	SYM
cana-1171	73	18	2,3	2,3	NUM
cana-1171	73	19	,	,	PUNCT
cana-1171	73	20	…	…	PUNCT
cana-1171	73	21	definition	definition	NOUN
cana-1171	73	22	5	5	NUM
cana-1171	73	23	.	.	PUNCT
cana-1171	74	1	the	the	DET
cana-1171	74	2	riemann	riemann	PROPN
cana-1171	74	3	-	-	PUNCT
cana-1171	74	4	lioville	lioville	ADJ
cana-1171	74	5	fractional	fractional	ADJ
cana-1171	74	6	integral	integral	ADJ
cana-1171	74	7	operator	operator	NOUN
cana-1171	74	8	(	(	PUNCT
cana-1171	74	9	ℐ𝛼	ℐ𝛼	NOUN
cana-1171	74	10	)	)	PUNCT
cana-1171	74	11	of	of	ADP
cana-1171	74	12	order	order	NOUN
cana-1171	74	13	𝛼	𝛼	VERB
cana-1171	74	14	>	>	X
cana-1171	74	15	0	0	NUM
cana-1171	74	16	,	,	PUNCT
cana-1171	74	17	of	of	ADP
cana-1171	74	18	a	a	DET
cana-1171	74	19	function	function	NOUN
cana-1171	74	20	𝜑(𝑡	𝜑(𝑡	PROPN
cana-1171	74	21	)	)	PUNCT
cana-1171	74	22	is	be	AUX
cana-1171	74	23	defined	define	VERB
cana-1171	74	24	as	as	ADP
cana-1171	74	25	ℐ𝛼𝜑(𝑡	ℐ𝛼𝜑(𝑡	NOUN
cana-1171	74	26	)	)	PUNCT
cana-1171	74	27	=	=	SYM
cana-1171	74	28	1	1	NUM
cana-1171	74	29	𝛤(𝛼	𝛤(𝛼	NUM
cana-1171	74	30	)	)	PUNCT
cana-1171	74	31	∫	∫	PROPN
cana-1171	74	32	(	(	PUNCT
cana-1171	74	33	𝑡	𝑡	PROPN
cana-1171	74	34	−	−	NOUN
cana-1171	74	35	𝜏)𝛼−1𝜑(𝜏)𝑑𝜏	𝜏)𝛼−1𝜑(𝜏)𝑑𝜏	NOUN
cana-1171	74	36	𝑡	𝑡	PROPN
cana-1171	74	37	0	0	PUNCT
cana-1171	74	38	(	(	PUNCT
cana-1171	74	39	𝛼	𝛼	X
cana-1171	74	40	>	>	X
cana-1171	74	41	0	0	NUM
cana-1171	74	42	)	)	PUNCT
cana-1171	74	43	,	,	PUNCT
cana-1171	74	44	ℐ0𝜑(𝑡	ℐ0𝜑(𝑡	NOUN
cana-1171	74	45	)	)	PUNCT
cana-1171	74	46	=	=	SYM
cana-1171	74	47	𝜑(𝑡	𝜑(𝑡	X
cana-1171	74	48	)	)	PUNCT
cana-1171	74	49	where	where	SCONJ
cana-1171	74	50	𝛤(𝛼	𝛤(𝛼	X
cana-1171	74	51	)	)	PUNCT
cana-1171	74	52	is	be	AUX
cana-1171	74	53	the	the	DET
cana-1171	74	54	well	well	ADV
cana-1171	74	55	-	-	PUNCT
cana-1171	74	56	known	know	VERB
cana-1171	74	57	gamma	gamma	NOUN
cana-1171	74	58	function	function	NOUN
cana-1171	74	59	.	.	PUNCT
cana-1171	75	1	some	some	PRON
cana-1171	75	2	of	of	ADP
cana-1171	75	3	the	the	DET
cana-1171	75	4	properties	property	NOUN
cana-1171	75	5	for	for	ADP
cana-1171	75	6	ℐ𝛼	ℐ𝛼	PROPN
cana-1171	75	7	and	and	CCONJ
cana-1171	75	8	𝐷𝛼	𝐷𝛼	PROPN
cana-1171	75	9	can	can	AUX
cana-1171	75	10	be	be	AUX
cana-1171	75	11	derived	derive	VERB
cana-1171	75	12	as	as	SCONJ
cana-1171	75	13	follows	follow	VERB
cana-1171	75	14	1	1	NUM
cana-1171	75	15	)	)	PUNCT
cana-1171	76	1	𝐷𝑡	𝐷𝑡	NOUN
cana-1171	76	2	𝛼	𝛼	NOUN
cana-1171	76	3	0	0	PUNCT
cana-1171	76	4	𝐶	𝐶	PROPN
cana-1171	76	5	𝜑𝛿	𝜑𝛿	PROPN
cana-1171	76	6	=	=	SYM
cana-1171	76	7	𝛤(𝛿+1	𝛤(𝛿+1	PROPN
cana-1171	76	8	)	)	PUNCT
cana-1171	76	9	𝛤(𝛿−𝛼+1	𝛤(𝛿−𝛼+1	NOUN
cana-1171	76	10	)	)	PUNCT
cana-1171	77	1	𝜑𝛿−𝛼	𝜑𝛿−𝛼	PROPN
cana-1171	77	2	,	,	PUNCT
cana-1171	77	3	𝛼	𝛼	X
cana-1171	77	4	>	>	X
cana-1171	77	5	0	0	PROPN
cana-1171	77	6	,	,	PUNCT
cana-1171	77	7	𝛿	𝛿	PRON
cana-1171	77	8	>	>	X
cana-1171	77	9	−1	−1	NOUN
cana-1171	77	10	,	,	PUNCT
cana-1171	77	11	𝜑	𝜑	PROPN
cana-1171	77	12	>	>	X
cana-1171	77	13	0	0	NUM
cana-1171	77	14	,	,	PUNCT
cana-1171	77	15	2	2	X
cana-1171	77	16	)	)	PUNCT
cana-1171	77	17	ℐ𝛼𝜑𝛿	ℐ𝛼𝜑𝛿	PROPN
cana-1171	77	18	=	=	SYM
cana-1171	77	19	𝛤(𝛿+1	𝛤(𝛿+1	PROPN
cana-1171	77	20	)	)	PUNCT
cana-1171	77	21	𝛤(𝛿+𝛼+1	𝛤(𝛿+𝛼+1	NOUN
cana-1171	77	22	)	)	PUNCT
cana-1171	77	23	𝜑𝛿+𝛼	𝜑𝛿+𝛼	PROPN
cana-1171	77	24	,	,	PUNCT
cana-1171	77	25	𝛼	𝛼	X
cana-1171	77	26	>	>	X
cana-1171	77	27	0	0	PROPN
cana-1171	77	28	,	,	PUNCT
cana-1171	77	29	𝛿	𝛿	PRON
cana-1171	77	30	>	>	X
cana-1171	77	31	−1	−1	NOUN
cana-1171	77	32	,	,	PUNCT
cana-1171	77	33	𝜑	𝜑	PROPN
cana-1171	77	34	>	>	X
cana-1171	77	35	0	0	NUM
cana-1171	77	36	,	,	PUNCT
cana-1171	77	37	3	3	NUM
cana-1171	77	38	)	)	PUNCT
cana-1171	77	39	ℐ𝛼ℐ𝜗𝜑(𝑡	ℐ𝛼ℐ𝜗𝜑(𝑡	NUM
cana-1171	77	40	)	)	PUNCT
cana-1171	77	41	=	=	SYM
cana-1171	77	42	ℐ𝜗ℐ𝛼𝜑(𝑡	ℐ𝜗ℐ𝛼𝜑(𝑡	PROPN
cana-1171	77	43	)	)	PUNCT
cana-1171	77	44	=	=	SYM
cana-1171	77	45	ℐ𝛼+𝜗𝜑(𝑡	ℐ𝛼+𝜗𝜑(𝑡	PROPN
cana-1171	77	46	)	)	PUNCT
cana-1171	77	47	,	,	PUNCT
cana-1171	77	48	𝛼	𝛼	PROPN
cana-1171	77	49	,	,	PUNCT
cana-1171	77	50	𝜗	𝜗	X
cana-1171	77	51	>	>	X
cana-1171	77	52	0	0	NUM
cana-1171	77	53	,	,	PUNCT
cana-1171	77	54	4	4	X
cana-1171	77	55	)	)	PUNCT
cana-1171	77	56	𝐷𝑏	𝐷𝑏	NOUN
cana-1171	77	57	𝛼	𝛼	NOUN
cana-1171	77	58	𝑎	𝑎	PROPN
cana-1171	77	59	𝐶	𝐶	PROPN
cana-1171	77	60	ℐ𝛼𝜑(𝑡	ℐ𝛼𝜑(𝑡	PROPN
cana-1171	77	61	)	)	PUNCT
cana-1171	77	62	=	=	SYM
cana-1171	77	63	𝜑(𝑡	𝜑(𝑡	PROPN
cana-1171	77	64	)	)	PUNCT
cana-1171	77	65	,	,	PUNCT
cana-1171	77	66	𝑎	𝑎	PROPN
cana-1171	77	67	≤	≤	NUM
cana-1171	77	68	𝑡	𝑡	PROPN
cana-1171	77	69	≤	≤	NOUN
cana-1171	77	70	𝑏	𝑏	NOUN
cana-1171	77	71	,	,	PUNCT
cana-1171	77	72	5	5	NUM
cana-1171	77	73	)	)	PUNCT
cana-1171	77	74	ℐ𝛼	ℐ𝛼	PROPN
cana-1171	77	75	𝐷𝑡	𝐷𝑡	PROPN
cana-1171	77	76	𝛼	𝛼	NOUN
cana-1171	77	77	0	0	PUNCT
cana-1171	77	78	𝐶	𝐶	PROPN
cana-1171	77	79	𝜑(𝑡	𝜑(𝑡	PROPN
cana-1171	77	80	)	)	PUNCT
cana-1171	77	81	=	=	SYM
cana-1171	77	82	𝜑(𝑡	𝜑(𝑡	X
cana-1171	77	83	)	)	PUNCT
cana-1171	77	84	−	−	NOUN
cana-1171	77	85	∑	∑	PUNCT
cana-1171	77	86	𝜑(𝑘)(0	𝜑(𝑘)(0	PROPN
cana-1171	77	87	+	+	PROPN
cana-1171	77	88	)	)	PUNCT
cana-1171	77	89	𝑡𝑘	𝑡𝑘	ADV
cana-1171	77	90	𝑘	𝑘	PROPN
cana-1171	77	91	!	!	PROPN
cana-1171	77	92	,	,	PUNCT
cana-1171	77	93	𝜇−1	𝜇−1	PROPN
cana-1171	77	94	𝑘	𝑘	PRON
cana-1171	77	95	𝜇	𝜇	ADP
cana-1171	77	96	−	−	PROPN
cana-1171	77	97	1	1	NUM
cana-1171	77	98	<	<	X
cana-1171	77	99	𝛼	𝛼	X
cana-1171	77	100	<	<	X
cana-1171	77	101	𝜇	𝜇	X
cana-1171	77	102	,	,	PUNCT
cana-1171	77	103	𝑡	𝑡	X
cana-1171	77	104	>	>	X
cana-1171	77	105	0	0	X
cana-1171	77	106	.	.	PUNCT
cana-1171	78	1	lemma	lemma	PROPN
cana-1171	78	2	1	1	NUM
cana-1171	78	3	.	.	PUNCT
cana-1171	79	1	if	if	SCONJ
cana-1171	79	2	𝑚	𝑚	PROPN
cana-1171	79	3	−	−	PROPN
cana-1171	79	4	1	1	NUM
cana-1171	79	5	<	<	X
cana-1171	79	6	𝛼	𝛼	PROPN
cana-1171	79	7	≤	≤	NUM
cana-1171	79	8	𝑚	𝑚	VERB
cana-1171	79	9	is	be	AUX
cana-1171	79	10	the	the	DET
cana-1171	79	11	order	order	NOUN
cana-1171	79	12	of	of	ADP
cana-1171	79	13	caputo	caputo	PROPN
cana-1171	79	14	fractional	fractional	PROPN
cana-1171	79	15	derivative	derivative	PROPN
cana-1171	79	16	𝐷𝑏	𝐷𝑏	PROPN
cana-1171	79	17	𝛼	𝛼	NOUN
cana-1171	79	18	𝑎	𝑎	PROPN
cana-1171	79	19	𝐶	𝐶	PROPN
cana-1171	79	20	,	,	PUNCT
cana-1171	79	21	then	then	ADV
cana-1171	79	22	it	it	PRON
cana-1171	79	23	is	be	AUX
cana-1171	79	24	consistent	consistent	ADJ
cana-1171	79	25	with	with	ADP
cana-1171	79	26	the	the	DET
cana-1171	79	27	integer	integer	NOUN
cana-1171	79	28	-	-	PUNCT
cana-1171	79	29	order	order	NOUN
cana-1171	79	30	derivative	derivative	ADJ
cana-1171	79	31	𝑑𝑚	𝑑𝑚	NOUN
cana-1171	79	32	𝑑𝑡𝑚	𝑑𝑡𝑚	ADV
cana-1171	79	33	for	for	ADP
cana-1171	79	34	𝑚	𝑚	PROPN
cana-1171	79	35	∈	∈	PROPN
cana-1171	79	36	ℕ.	ℕ.	PROPN
cana-1171	79	37	proof	proof	NOUN
cana-1171	79	38	.	.	PUNCT
cana-1171	80	1	for	for	ADP
cana-1171	80	2	𝜑	𝜑	PRON
cana-1171	80	3	∈	∈	PROPN
cana-1171	80	4	ℂ𝑚+1([0	ℂ𝑚+1([0	NOUN
cana-1171	80	5	,	,	PUNCT
cana-1171	80	6	∞]),then	∞]),then	ADV
cana-1171	81	1	𝐷𝑡	𝐷𝑡	PROPN
cana-1171	81	2	𝛼	𝛼	NOUN
cana-1171	81	3	𝜑0	𝜑0	NOUN
cana-1171	81	4	𝐶	𝐶	PROPN
cana-1171	81	5	(	(	PUNCT
cana-1171	81	6	𝑡	𝑡	NOUN
cana-1171	81	7	)	)	PUNCT
cana-1171	81	8	=	=	SYM
cana-1171	81	9	1	1	NUM
cana-1171	81	10	𝛤(𝑚	𝛤(𝑚	ADV
cana-1171	81	11	−	−	NUM
cana-1171	81	12	𝛼	𝛼	X
cana-1171	81	13	)	)	PUNCT
cana-1171	81	14	∫	∫	PROPN
cana-1171	81	15	𝜑(𝑚)(𝜏	𝜑(𝑚)(𝜏	NUM
cana-1171	81	16	)	)	PUNCT
cana-1171	81	17	(	(	PUNCT
cana-1171	81	18	𝑡	𝑡	PROPN
cana-1171	81	19	−	−	PROPN
cana-1171	81	20	𝜏)1−(𝑚−𝛼	𝜏)1−(𝑚−𝛼	NOUN
cana-1171	81	21	)	)	PUNCT
cana-1171	81	22	𝑑𝜏	𝑑𝜏	PROPN
cana-1171	81	23	𝑡	𝑡	NOUN
cana-1171	81	24	0	0	PUNCT
cana-1171	81	25	=	=	SYM
cana-1171	81	26	1	1	NUM
cana-1171	81	27	𝛤(𝑚	𝛤(𝑚	ADV
cana-1171	81	28	−	−	NUM
cana-1171	81	29	𝛼	𝛼	NOUN
cana-1171	81	30	)	)	PUNCT
cana-1171	82	1	[	[	X
cana-1171	82	2	−	−	X
cana-1171	82	3	(	(	PUNCT
cana-1171	82	4	𝑡	𝑡	X
cana-1171	82	5	−	−	PROPN
cana-1171	82	6	𝜏)𝑚−𝛼	𝜏)𝑚−𝛼	X
cana-1171	83	1	𝑚	𝑚	X
cana-1171	83	2	−	−	PROPN
cana-1171	83	3	𝛼	𝛼	NOUN
cana-1171	83	4	𝜑(𝑚)(𝜏)|𝜏=0	𝜑(𝑚)(𝜏)|𝜏=0	NOUN
cana-1171	84	1	𝜏=𝑡	𝜏=𝑡	PROPN
cana-1171	84	2	+	+	NUM
cana-1171	84	3	∫	∫	PROPN
cana-1171	84	4	(	(	PUNCT
cana-1171	84	5	𝑡	𝑡	X
cana-1171	84	6	−	−	PROPN
cana-1171	84	7	𝜏)𝑚−𝛼	𝜏)𝑚−𝛼	X
cana-1171	85	1	𝑚	𝑚	X
cana-1171	85	2	−	−	PROPN
cana-1171	85	3	𝛼	𝛼	PROPN
cana-1171	85	4	𝜑(𝑚+1)(𝜏)𝑑𝜏	𝜑(𝑚+1)(𝜏)𝑑𝜏	NOUN
cana-1171	85	5	𝑡	𝑡	PROPN
cana-1171	85	6	0	0	PUNCT
cana-1171	85	7	]	]	PUNCT
cana-1171	85	8	=	=	SYM
cana-1171	86	1	1	1	NUM
cana-1171	86	2	𝛤(𝑚	𝛤(𝑚	ADV
cana-1171	86	3	−	−	PROPN
cana-1171	86	4	𝛼	𝛼	NOUN
cana-1171	86	5	+	+	NOUN
cana-1171	86	6	1	1	NUM
cana-1171	86	7	)	)	PUNCT
cana-1171	87	1	[	[	X
cana-1171	87	2	0	0	NUM
cana-1171	87	3	+	+	NUM
cana-1171	87	4	𝑡𝑚−𝛼𝜑(𝑚)(0	𝑡𝑚−𝛼𝜑(𝑚)(0	NOUN
cana-1171	87	5	)	)	PUNCT
cana-1171	88	1	+	+	NUM
cana-1171	88	2	∫	∫	PROPN
cana-1171	88	3	(	(	PUNCT
cana-1171	88	4	𝑡	𝑡	X
cana-1171	88	5	−	−	PROPN
cana-1171	88	6	𝜏)𝑚−𝛼	𝜏)𝑚−𝛼	PROPN
cana-1171	88	7	𝜑(𝑚+1)(𝜏)𝑑𝜏	𝜑(𝑚+1)(𝜏)𝑑𝜏	PROPN
cana-1171	88	8	𝑡	𝑡	PROPN
cana-1171	88	9	0	0	NUM
cana-1171	88	10	]	]	PUNCT
cana-1171	88	11	and	and	CCONJ
cana-1171	88	12	taking	take	VERB
cana-1171	88	13	the	the	DET
cana-1171	88	14	limit	limit	NOUN
cana-1171	88	15	:	:	PUNCT
cana-1171	88	16	𝛼	𝛼	X
cana-1171	88	17	∈	∈	NOUN
cana-1171	88	18	ℝ	ℝ	PROPN
cana-1171	88	19	→	→	SYM
cana-1171	88	20	𝑚	𝑚	PROPN
cana-1171	88	21	∈	∈	PROPN
cana-1171	88	22	ℕ	ℕ	PROPN
cana-1171	88	23	with	with	ADP
cana-1171	88	24	𝑚	𝑚	PROPN
cana-1171	88	25	−	−	PROPN
cana-1171	88	26	1	1	NUM
cana-1171	88	27	≤	≤	NUM
cana-1171	88	28	𝛼	𝛼	PRON
cana-1171	88	29	≤	≤	NOUN
cana-1171	88	30	𝑚	𝑚	ADP
cana-1171	88	31	yields	yield	NOUN
cana-1171	88	32	:	:	PUNCT
cana-1171	88	33	=	=	SYM
cana-1171	88	34	1	1	NUM
cana-1171	88	35	𝛤(1	𝛤(1	NUM
cana-1171	88	36	)	)	PUNCT
cana-1171	89	1	[	[	X
cana-1171	89	2	𝜑(𝑚)(0	𝜑(𝑚)(0	PROPN
cana-1171	89	3	)	)	PUNCT
cana-1171	89	4	+	+	NUM
cana-1171	89	5	∫	∫	PROPN
cana-1171	89	6	𝜑(𝑚+1)(𝜏)𝑑𝜏	𝜑(𝑚+1)(𝜏)𝑑𝜏	PROPN
cana-1171	89	7	𝑡	𝑡	PROPN
cana-1171	89	8	0	0	PUNCT
cana-1171	89	9	]	]	PUNCT
cana-1171	89	10	=	=	SYM
cana-1171	89	11	𝜑(𝑚)(0	𝜑(𝑚)(0	PROPN
cana-1171	89	12	)	)	PUNCT
cana-1171	89	13	+	+	NUM
cana-1171	89	14	𝜑(𝑚)(𝑡	𝜑(𝑚)(𝑡	X
cana-1171	89	15	)	)	PUNCT
cana-1171	89	16	−	−	PROPN
cana-1171	89	17	𝜑(𝑚)(0	𝜑(𝑚)(0	PROPN
cana-1171	89	18	)	)	PUNCT
cana-1171	89	19	=	=	PUNCT
cana-1171	89	20	𝑑𝑚𝜑	𝑑𝑚𝜑	VERB
cana-1171	89	21	𝑑𝑡𝑚	𝑑𝑡𝑚	ADV
cana-1171	89	22	(	(	PUNCT
cana-1171	89	23	𝑡	𝑡	NOUN
cana-1171	89	24	)	)	PUNCT
cana-1171	89	25	.	.	PUNCT
cana-1171	90	1	4	4	X
cana-1171	90	2	.	.	X
cana-1171	90	3	mathematical	mathematical	ADJ
cana-1171	90	4	formulation	formulation	NOUN
cana-1171	90	5	of	of	ADP
cana-1171	90	6	the	the	DET
cana-1171	90	7	problem	problem	NOUN
cana-1171	90	8	the	the	DET
cana-1171	90	9	simplest	simplest	NOUN
cana-1171	90	10	of	of	ADP
cana-1171	90	11	the	the	DET
cana-1171	90	12	reaction	reaction	NOUN
cana-1171	90	13	sequences	sequence	NOUN
cana-1171	90	14	in	in	ADP
cana-1171	90	15	which	which	PRON
cana-1171	90	16	chemical	chemical	ADJ
cana-1171	90	17	reactions	reaction	NOUN
cana-1171	90	18	for	for	ADP
cana-1171	90	19	electrochemical	electrochemical	ADJ
cana-1171	90	20	(	(	PUNCT
cana-1171	90	21	ec	ec	NOUN
cana-1171	90	22	)	)	PUNCT
cana-1171	90	23	mechanism	mechanism	NOUN
cana-1171	90	24	can	can	AUX
cana-1171	90	25	be	be	AUX
cana-1171	90	26	represented	represent	VERB
cana-1171	90	27	in	in	ADP
cana-1171	90	28	[	[	PUNCT
cana-1171	90	29	4	4	NUM
cana-1171	90	30	]	]	PUNCT
cana-1171	90	31	communications	communication	NOUN
cana-1171	90	32	on	on	ADP
cana-1171	90	33	applied	apply	VERB
cana-1171	90	34	nonlinear	nonlinear	ADJ
cana-1171	90	35	analysis	analysis	NOUN
cana-1171	90	36	issn	issn	NOUN
cana-1171	90	37	:	:	PUNCT
cana-1171	90	38	1074	1074	NUM
cana-1171	90	39	-	-	PUNCT
cana-1171	90	40	133x	133x	NUM
cana-1171	90	41	vol	vol	NOUN
cana-1171	90	42	31	31	NUM
cana-1171	90	43	no	no	NOUN
cana-1171	90	44	.	.	PUNCT
cana-1171	91	1	6s	6s	NUM
cana-1171	91	2	(	(	PUNCT
cana-1171	91	3	2024	2024	NUM
cana-1171	91	4	)	)	PUNCT
cana-1171	91	5	118	118	NUM
cana-1171	91	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1171	91	7	electrode	electrode	NOUN
cana-1171	91	8	process	process	NOUN
cana-1171	91	9	𝐴	𝐴	PROPN
cana-1171	91	10	+	+	CCONJ
cana-1171	91	11	1𝑒	1𝑒	NUM
cana-1171	91	12	⇌	⇌	PROPN
cana-1171	91	13	𝐵	𝐵	NOUN
cana-1171	91	14	(	(	PUNCT
cana-1171	91	15	1	1	NUM
cana-1171	91	16	)	)	PUNCT
cana-1171	91	17	redox	redox	ADJ
cana-1171	91	18	catalyzed	catalyze	VERB
cana-1171	91	19	process	process	NOUN
cana-1171	91	20	𝑃	𝑃	NOUN
cana-1171	91	21	+	+	CCONJ
cana-1171	91	22	1𝑒	1𝑒	NUM
cana-1171	91	23	⇌	⇌	PROPN
cana-1171	91	24	𝑄(𝐸𝑃𝑄	𝑄(𝐸𝑃𝑄	NOUN
cana-1171	91	25	0	0	NUM
cana-1171	91	26	)	)	PUNCT
cana-1171	91	27	(	(	PUNCT
cana-1171	91	28	2	2	X
cana-1171	91	29	)	)	PUNCT
cana-1171	91	30	𝑄	𝑄	PROPN
cana-1171	91	31	+	+	CCONJ
cana-1171	91	32	𝐴	𝐴	PROPN
cana-1171	91	33	𝐾1	𝐾1	PROPN
cana-1171	91	34	⇌	⇌	PROPN
cana-1171	91	35	𝐾2	𝐾2	NOUN
cana-1171	91	36	𝑃	𝑃	NOUN
cana-1171	91	37	+	+	CCONJ
cana-1171	91	38	𝐵	𝐵	NOUN
cana-1171	91	39	(	(	PUNCT
cana-1171	91	40	3	3	NUM
cana-1171	91	41	)	)	PUNCT
cana-1171	91	42	𝐵	𝐵	NOUN
cana-1171	91	43	𝐾	𝐾	PROPN
cana-1171	91	44	→	→	SYM
cana-1171	91	45	𝐶	𝐶	PROPN
cana-1171	91	46	(	(	PUNCT
cana-1171	91	47	4	4	NUM
cana-1171	91	48	)	)	PUNCT
cana-1171	91	49	a	a	DET
cana-1171	91	50	reduction	reduction	NOUN
cana-1171	91	51	process	process	NOUN
cana-1171	91	52	of	of	ADP
cana-1171	91	53	the	the	DET
cana-1171	91	54	oxidized	oxidized	ADJ
cana-1171	91	55	form	form	NOUN
cana-1171	91	56	𝑃	𝑃	NOUN
cana-1171	91	57	of	of	ADP
cana-1171	91	58	the	the	DET
cana-1171	91	59	catalyst	catalyst	NOUN
cana-1171	91	60	couple	couple	NOUN
cana-1171	91	61	𝑃	𝑃	NOUN
cana-1171	91	62	𝑄⁄	𝑄⁄	NOUN
cana-1171	91	63	is	be	AUX
cana-1171	91	64	introduced	introduce	VERB
cana-1171	91	65	into	into	ADP
cana-1171	91	66	the	the	DET
cana-1171	91	67	solution	solution	NOUN
cana-1171	91	68	.	.	PUNCT
cana-1171	92	1	here	here	ADV
cana-1171	92	2	,	,	PUNCT
cana-1171	92	3	𝑃	𝑃	NOUN
cana-1171	92	4	𝑄⁄	𝑄⁄	NOUN
cana-1171	92	5	is	be	AUX
cana-1171	92	6	introduced	introduce	VERB
cana-1171	92	7	to	to	PART
cana-1171	92	8	fulfill	fulfill	VERB
cana-1171	92	9	the	the	DET
cana-1171	92	10	following	follow	VERB
cana-1171	92	11	conditions	condition	NOUN
cana-1171	92	12	:	:	PUNCT
cana-1171	92	13	the	the	DET
cana-1171	92	14	standard	standard	ADJ
cana-1171	92	15	potential	potential	ADJ
cana-1171	92	16	𝐸𝑃𝑄	𝐸𝑃𝑄	PROPN
cana-1171	92	17	𝑜	𝑜	NOUN
cana-1171	92	18	is	be	AUX
cana-1171	92	19	positive	positive	ADJ
cana-1171	92	20	for	for	ADP
cana-1171	92	21	the	the	DET
cana-1171	92	22	reduction	reduction	NOUN
cana-1171	92	23	potential	potential	NOUN
cana-1171	92	24	of	of	ADP
cana-1171	92	25	the	the	DET
cana-1171	92	26	substrate	substrate	NOUN
cana-1171	92	27	𝐴	𝐴	PROPN
cana-1171	92	28	;	;	PUNCT
cana-1171	92	29	electron	electron	NOUN
cana-1171	92	30	alteration	alteration	NOUN
cana-1171	92	31	between	between	ADP
cana-1171	92	32	the	the	DET
cana-1171	92	33	electrode	electrode	NOUN
cana-1171	92	34	and	and	CCONJ
cana-1171	92	35	𝑃	𝑃	PROPN
cana-1171	92	36	or	or	CCONJ
cana-1171	92	37	𝑄	𝑄	PROPN
cana-1171	92	38	is	be	AUX
cana-1171	92	39	fast	fast	ADJ
cana-1171	92	40	,	,	PUNCT
cana-1171	92	41	both	both	CCONJ
cana-1171	92	42	𝑃	𝑃	NOUN
cana-1171	92	43	and	and	CCONJ
cana-1171	92	44	𝑄	𝑄	PRON
cana-1171	92	45	are	be	AUX
cana-1171	92	46	chemically	chemically	ADV
cana-1171	92	47	stable	stable	ADJ
cana-1171	92	48	.	.	PUNCT
cana-1171	93	1	in	in	ADP
cana-1171	93	2	[	[	X
cana-1171	93	3	3	3	NUM
cana-1171	93	4	,	,	PUNCT
cana-1171	93	5	4	4	NUM
cana-1171	93	6	]	]	X
cana-1171	93	7	c.p	c.p	PROPN
cana-1171	93	8	.	.	PROPN
cana-1171	93	9	andrieux	andrieux	PROPN
cana-1171	93	10	et.al	et.al	PROPN
cana-1171	93	11	.	.	PUNCT
cana-1171	94	1	treat	treat	VERB
cana-1171	94	2	the	the	DET
cana-1171	94	3	system	system	NOUN
cana-1171	94	4	as	as	SCONJ
cana-1171	94	5	governed	govern	VERB
cana-1171	94	6	by	by	ADP
cana-1171	94	7	a	a	DET
cana-1171	94	8	set	set	NOUN
cana-1171	94	9	of	of	ADP
cana-1171	94	10	differential	differential	ADJ
cana-1171	94	11	equations	equation	NOUN
cana-1171	94	12	with	with	ADP
cana-1171	94	13	boundary	boundary	ADJ
cana-1171	94	14	conditions	condition	NOUN
cana-1171	94	15	and	and	CCONJ
cana-1171	94	16	a	a	DET
cana-1171	94	17	stationary	stationary	ADJ
cana-1171	94	18	-	-	PUNCT
cana-1171	94	19	state	state	NOUN
cana-1171	94	20	assumption	assumption	NOUN
cana-1171	94	21	regarding	regard	VERB
cana-1171	94	22	b	b	NOUN
cana-1171	94	23	:	:	PUNCT
cana-1171	94	24	𝐾1𝑐𝐴𝑐𝑄	𝐾1𝑐𝐴𝑐𝑄	PROPN
cana-1171	94	25	=	=	SYM
cana-1171	94	26	𝐾𝑐𝐵	𝐾𝑐𝐵	PROPN
cana-1171	94	27	+	+	CCONJ
cana-1171	94	28	𝐾2𝑐𝐵𝑐𝑃	𝐾2𝑐𝐵𝑐𝑃	PROPN
cana-1171	94	29	(	(	PUNCT
cana-1171	94	30	5	5	X
cana-1171	94	31	)	)	PUNCT
cana-1171	94	32	introduce	introduce	VERB
cana-1171	94	33	the	the	DET
cana-1171	94	34	dimensionless	dimensionless	NOUN
cana-1171	94	35	variables	variable	NOUN
cana-1171	94	36	as	as	SCONJ
cana-1171	94	37	follows	follow	VERB
cana-1171	94	38	:	:	PUNCT
cana-1171	94	39	𝑦	𝑦	NOUN
cana-1171	94	40	=	=	SYM
cana-1171	94	41	𝑥	𝑥	X
cana-1171	94	42	𝛿⁄	𝛿⁄	PROPN
cana-1171	94	43	,	,	PUNCT
cana-1171	94	44	𝑢	𝑢	X
cana-1171	94	45	=	=	X
cana-1171	94	46	𝑐𝑃	𝑐𝑃	NOUN
cana-1171	94	47	𝑐𝑃	𝑐𝑃	PROPN
cana-1171	94	48	0	0	NUM
cana-1171	94	49	,	,	PUNCT
cana-1171	94	50	𝑣	𝑣	X
cana-1171	94	51	=	=	PUNCT
cana-1171	94	52	𝑐𝑄	𝑐𝑄	X
cana-1171	94	53	𝑐𝑃	𝑐𝑃	NOUN
cana-1171	94	54	0	0	NUM
cana-1171	94	55	,	,	PUNCT
cana-1171	94	56	𝑤	𝑤	X
cana-1171	94	57	=	=	PUNCT
cana-1171	95	1	𝑐𝐴	𝑐𝐴	X
cana-1171	95	2	𝑐𝑃	𝑐𝑃	NOUN
cana-1171	95	3	0	0	NUM
cana-1171	95	4	,	,	PUNCT
cana-1171	95	5	𝑏	𝑏	NOUN
cana-1171	95	6	=	=	SYM
cana-1171	95	7	𝑐𝐵	𝑐𝐵	VERB
cana-1171	95	8	𝑐𝑃	𝑐𝑃	NOUN
cana-1171	95	9	0	0	NUM
cana-1171	95	10	,	,	PUNCT
cana-1171	95	11	𝛾	𝛾	PROPN
cana-1171	95	12	=	=	VERB
cana-1171	95	13	𝑐𝐴	𝑐𝐴	NOUN
cana-1171	95	14	0	0	PUNCT
cana-1171	96	1	𝑐𝑃	𝑐𝑃	NOUN
cana-1171	96	2	0	0	NUM
cana-1171	96	3	,	,	PUNCT
cana-1171	96	4	𝜉	𝜉	NOUN
cana-1171	96	5	=	=	PUNCT
cana-1171	96	6	−(𝐹	−(𝐹	ADJ
cana-1171	96	7	𝑅𝑇⁄	𝑅𝑇⁄	NUM
cana-1171	96	8	)	)	PUNCT
cana-1171	96	9	(	(	PUNCT
cana-1171	96	10	𝐸	𝐸	PROPN
cana-1171	96	11	−	−	PROPN
cana-1171	96	12	𝐸𝑃𝑄	𝐸𝑃𝑄	PROPN
cana-1171	96	13	0	0	NUM
cana-1171	96	14	)	)	PUNCT
cana-1171	96	15	.	.	PUNCT
cana-1171	97	1	(	(	PUNCT
cana-1171	97	2	6	6	X
cana-1171	97	3	)	)	PUNCT
cana-1171	97	4	the	the	DET
cana-1171	97	5	dimensionless	dimensionless	NOUN
cana-1171	97	6	rate	rate	NOUN
cana-1171	97	7	parameters[4	parameters[4	PROPN
cana-1171	97	8	]	]	X
cana-1171	97	9	𝜆1	𝜆1	NOUN
cana-1171	97	10	=	=	PUNCT
cana-1171	97	11	𝐾1𝑐𝑝	𝐾1𝑐𝑝	VERB
cana-1171	97	12	0𝛿2	0𝛿2	NUM
cana-1171	97	13	𝐷	𝐷	NOUN
cana-1171	97	14	,	,	PUNCT
cana-1171	97	15	𝜆2	𝜆2	PROPN
cana-1171	97	16	=	=	SYM
cana-1171	97	17	𝐾2𝑐𝑝	𝐾2𝑐𝑝	X
cana-1171	97	18	0𝛿2	0𝛿2	NUM
cana-1171	98	1	𝐷	𝐷	NOUN
cana-1171	98	2	𝜆	𝜆	NOUN
cana-1171	98	3	=	=	PUNCT
cana-1171	98	4	𝐾𝛿2	𝐾𝛿2	ADJ
cana-1171	98	5	𝐷	𝐷	PROPN
cana-1171	98	6	(	(	PUNCT
cana-1171	98	7	7	7	NUM
cana-1171	98	8	)	)	PUNCT
cana-1171	98	9	substituting	substitute	VERB
cana-1171	98	10	(	(	PUNCT
cana-1171	98	11	6	6	NUM
cana-1171	98	12	)	)	PUNCT
cana-1171	98	13	,	,	PUNCT
cana-1171	98	14	(	(	PUNCT
cana-1171	98	15	7	7	X
cana-1171	98	16	)	)	PUNCT
cana-1171	98	17	in	in	ADP
cana-1171	98	18	[	[	X
cana-1171	98	19	4	4	X
cana-1171	98	20	]	]	PUNCT
cana-1171	98	21	gives	give	VERB
cana-1171	98	22	𝑑2𝑢	𝑑2𝑢	PROPN
cana-1171	98	23	𝑑𝑦2	𝑑𝑦2	X
cana-1171	98	24	=	=	PUNCT
cana-1171	98	25	−𝜆1𝑤𝑣	−𝜆1𝑤𝑣	PROPN
cana-1171	98	26	+	+	CCONJ
cana-1171	98	27	𝜆2𝑏𝑢	𝜆2𝑏𝑢	PUNCT
cana-1171	98	28	(	(	PUNCT
cana-1171	98	29	8)	8)	NUM
cana-1171	98	30	𝑑2𝑣	𝑑2𝑣	X
cana-1171	98	31	𝑑𝑦2	𝑑𝑦2	NOUN
cana-1171	98	32	=	=	SYM
cana-1171	98	33	𝜆1𝑤𝑣	𝜆1𝑤𝑣	PUNCT
cana-1171	98	34	−	−	NOUN
cana-1171	98	35	𝜆2𝑏𝑢	𝜆2𝑏𝑢	PUNCT
cana-1171	98	36	(	(	PUNCT
cana-1171	98	37	9	9	NUM
cana-1171	98	38	)	)	PUNCT
cana-1171	98	39	𝑑2𝑤	𝑑2𝑤	VERB
cana-1171	98	40	𝑑𝑦2	𝑑𝑦2	NOUN
cana-1171	98	41	=	=	SYM
cana-1171	98	42	𝜆1𝑤𝑣	𝜆1𝑤𝑣	PUNCT
cana-1171	98	43	−	−	NOUN
cana-1171	98	44	𝜆2𝑏𝑢	𝜆2𝑏𝑢	PUNCT
cana-1171	98	45	(	(	PUNCT
cana-1171	98	46	10	10	NUM
cana-1171	98	47	)	)	PUNCT
cana-1171	98	48	using	use	VERB
cana-1171	98	49	(	(	PUNCT
cana-1171	98	50	6	6	NUM
cana-1171	98	51	)	)	PUNCT
cana-1171	98	52	and	and	CCONJ
cana-1171	98	53	(	(	PUNCT
cana-1171	98	54	7	7	X
cana-1171	98	55	)	)	PUNCT
cana-1171	98	56	in	in	ADP
cana-1171	98	57	(	(	PUNCT
cana-1171	98	58	5	5	NUM
cana-1171	98	59	)	)	PUNCT
cana-1171	98	60	𝜆𝑏	𝜆𝑏	NOUN
cana-1171	99	1	=	=	SYM
cana-1171	99	2	𝜆1𝑤𝑣	𝜆1𝑤𝑣	PUNCT
cana-1171	100	1	−	−	NOUN
cana-1171	100	2	𝜆2𝑏𝑢	𝜆2𝑏𝑢	NOUN
cana-1171	100	3	or	or	CCONJ
cana-1171	100	4	𝑏	𝑏	NOUN
cana-1171	100	5	=	=	PUNCT
cana-1171	100	6	𝜆1𝑤𝑣	𝜆1𝑤𝑣	PUNCT
cana-1171	100	7	𝜆+𝜆2𝑢	𝜆+𝜆2𝑢	PUNCT
cana-1171	101	1	(	(	PUNCT
cana-1171	101	2	11	11	NUM
cana-1171	101	3	)	)	PUNCT
cana-1171	101	4	when	when	SCONJ
cana-1171	101	5	𝑦	𝑦	NOUN
cana-1171	101	6	=	=	SYM
cana-1171	101	7	1	1	NUM
cana-1171	101	8	:	:	PUNCT
cana-1171	101	9	𝑢	𝑢	X
cana-1171	101	10	=	=	SYM
cana-1171	101	11	1	1	NUM
cana-1171	101	12	,	,	PUNCT
cana-1171	101	13	𝑣	𝑣	X
cana-1171	101	14	=	=	PUNCT
cana-1171	101	15	𝑏	𝑏	NOUN
cana-1171	101	16	=	=	SYM
cana-1171	101	17	0	0	NUM
cana-1171	101	18	,	,	PUNCT
cana-1171	101	19	𝑤	𝑤	X
cana-1171	101	20	=	=	SYM
cana-1171	101	21	𝛾	𝛾	PROPN
cana-1171	101	22	(	(	PUNCT
cana-1171	101	23	12	12	NUM
cana-1171	101	24	)	)	PUNCT
cana-1171	101	25	communications	communication	NOUN
cana-1171	101	26	on	on	ADP
cana-1171	101	27	applied	apply	VERB
cana-1171	101	28	nonlinear	nonlinear	ADJ
cana-1171	101	29	analysis	analysis	NOUN
cana-1171	101	30	issn	issn	NOUN
cana-1171	101	31	:	:	PUNCT
cana-1171	101	32	1074	1074	NUM
cana-1171	101	33	-	-	PUNCT
cana-1171	101	34	133x	133x	NUM
cana-1171	101	35	vol	vol	NOUN
cana-1171	101	36	31	31	NUM
cana-1171	101	37	no	no	NOUN
cana-1171	101	38	.	.	PUNCT
cana-1171	102	1	6s	6s	NUM
cana-1171	102	2	(	(	PUNCT
cana-1171	102	3	2024	2024	NUM
cana-1171	102	4	)	)	PUNCT
cana-1171	102	5	119	119	NUM
cana-1171	102	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1171	102	7	when	when	SCONJ
cana-1171	102	8	𝑦	𝑦	NOUN
cana-1171	102	9	=	=	SYM
cana-1171	102	10	0	0	NUM
cana-1171	102	11	:	:	PUNCT
cana-1171	102	12	(	(	PUNCT
cana-1171	102	13	𝑑𝑢	𝑑𝑢	INTJ
cana-1171	102	14	𝑑𝑦	𝑑𝑦	NOUN
cana-1171	102	15	)	)	PUNCT
cana-1171	103	1	+	+	CCONJ
cana-1171	103	2	(	(	PUNCT
cana-1171	103	3	𝑑𝑣	𝑑𝑣	X
cana-1171	103	4	𝑑𝑦	𝑑𝑦	NOUN
cana-1171	103	5	)	)	PUNCT
cana-1171	104	1	=	=	SYM
cana-1171	104	2	0	0	NUM
cana-1171	104	3	,	,	PUNCT
cana-1171	104	4	𝑢	𝑢	X
cana-1171	104	5	=	=	X
cana-1171	104	6	𝑣	𝑣	PRON
cana-1171	104	7	exp(−𝜉	exp(−𝜉	PROPN
cana-1171	104	8	)	)	PUNCT
cana-1171	104	9	,	,	PUNCT
cana-1171	104	10	(	(	PUNCT
cana-1171	104	11	𝑑𝑤	𝑑𝑤	PROPN
cana-1171	104	12	𝑑𝑦	𝑑𝑦	NOUN
cana-1171	104	13	)	)	PUNCT
cana-1171	105	1	=	=	SYM
cana-1171	105	2	−	−	PROPN
cana-1171	106	1	(	(	PUNCT
cana-1171	106	2	𝑑𝑏	𝑑𝑏	INTJ
cana-1171	106	3	𝑑𝑦	𝑑𝑦	NOUN
cana-1171	106	4	)	)	PUNCT
cana-1171	107	1	=	=	SYM
cana-1171	107	2	0	0	PUNCT
cana-1171	107	3	(	(	PUNCT
cana-1171	107	4	13	13	NUM
cana-1171	107	5	)	)	PUNCT
cana-1171	107	6	from	from	ADP
cana-1171	107	7	equations	equation	NOUN
cana-1171	107	8	(	(	PUNCT
cana-1171	107	9	8)	8)	NUM
cana-1171	107	10	,	,	PUNCT
cana-1171	107	11	(	(	PUNCT
cana-1171	107	12	9	9	NUM
cana-1171	107	13	)	)	PUNCT
cana-1171	107	14	,	,	PUNCT
cana-1171	107	15	(	(	PUNCT
cana-1171	107	16	11	11	NUM
cana-1171	107	17	)	)	PUNCT
cana-1171	107	18	and	and	CCONJ
cana-1171	107	19	(	(	PUNCT
cana-1171	107	20	12	12	NUM
cana-1171	107	21	)	)	PUNCT
cana-1171	107	22	,	,	PUNCT
cana-1171	107	23	it	it	PRON
cana-1171	107	24	is	be	AUX
cana-1171	107	25	clear	clear	ADJ
cana-1171	107	26	that	that	SCONJ
cana-1171	107	27	𝑢	𝑢	VERB
cana-1171	107	28	+	+	X
cana-1171	107	29	𝑣	𝑣	X
cana-1171	107	30	=	=	SYM
cana-1171	107	31	1	1	X
cana-1171	107	32	.	.	PUNCT
cana-1171	108	1	in	in	ADP
cana-1171	108	2	particular	particular	ADJ
cana-1171	108	3	𝑢0	𝑢0	NOUN
cana-1171	108	4	+	+	CCONJ
cana-1171	108	5	𝑣0	𝑣0	PROPN
cana-1171	108	6	=	=	SYM
cana-1171	108	7	1	1	NUM
cana-1171	108	8	and	and	CCONJ
cana-1171	108	9	therefore	therefore	ADV
cana-1171	108	10	,	,	PUNCT
cana-1171	108	11	taking	take	VERB
cana-1171	108	12	(	(	PUNCT
cana-1171	108	13	13	13	NUM
cana-1171	108	14	)	)	PUNCT
cana-1171	108	15	into	into	ADP
cana-1171	108	16	:	:	PUNCT
cana-1171	108	17	𝑢0	𝑢0	PROPN
cana-1171	108	18	=	=	SYM
cana-1171	108	19	1	1	NUM
cana-1171	108	20	1	1	NUM
cana-1171	108	21	+	+	NUM
cana-1171	108	22	exp	exp	NOUN
cana-1171	108	23	(	(	PUNCT
cana-1171	108	24	𝜉	𝜉	NOUN
cana-1171	108	25	)	)	PUNCT
cana-1171	108	26	,	,	PUNCT
cana-1171	108	27	𝑣0	𝑣0	NOUN
cana-1171	108	28	=	=	SYM
cana-1171	108	29	1	1	NUM
cana-1171	108	30	1	1	NUM
cana-1171	108	31	+	+	NUM
cana-1171	108	32	exp	exp	NOUN
cana-1171	108	33	(	(	PUNCT
cana-1171	108	34	−𝜉	−𝜉	NOUN
cana-1171	108	35	)	)	PUNCT
cana-1171	108	36	finally	finally	ADV
cana-1171	108	37	,	,	PUNCT
cana-1171	108	38	the	the	DET
cana-1171	108	39	system	system	NOUN
cana-1171	108	40	of	of	ADP
cana-1171	108	41	second	second	ADJ
cana-1171	108	42	order	order	NOUN
cana-1171	108	43	non	non	ADJ
cana-1171	108	44	-	-	ADJ
cana-1171	108	45	linear	linear	ADJ
cana-1171	108	46	differential	differential	ADJ
cana-1171	108	47	equation	equation	NOUN
cana-1171	108	48	and	and	CCONJ
cana-1171	108	49	substitute	substitute	NOUN
cana-1171	108	50	for	for	ADP
cana-1171	108	51	𝑏	𝑏	PROPN
cana-1171	108	52	(	(	PUNCT
cana-1171	108	53	11	11	NUM
cana-1171	108	54	)	)	PUNCT
cana-1171	108	55	in	in	ADP
cana-1171	108	56	(	(	PUNCT
cana-1171	108	57	8)	8)	NUM
cana-1171	108	58	−	−	NOUN
cana-1171	108	59	(	(	PUNCT
cana-1171	108	60	10	10	NUM
cana-1171	108	61	)	)	PUNCT
cana-1171	108	62	𝑑2𝑢	𝑑2𝑢	VERB
cana-1171	108	63	𝑑𝑦2	𝑑𝑦2	X
cana-1171	109	1	+	+	CCONJ
cana-1171	109	2	𝜆1𝑤𝑣	𝜆1𝑤𝑣	PUNCT
cana-1171	109	3	−	−	PROPN
cana-1171	109	4	𝐶𝑢𝑣𝑤	𝐶𝑢𝑣𝑤	PROPN
cana-1171	109	5	=	=	SYM
cana-1171	109	6	0	0	PUNCT
cana-1171	109	7	(	(	PUNCT
cana-1171	109	8	14	14	NUM
cana-1171	109	9	)	)	PUNCT
cana-1171	109	10	𝑑2𝑣	𝑑2𝑣	VERB
cana-1171	109	11	𝑑𝑦2	𝑑𝑦2	X
cana-1171	109	12	−	−	PROPN
cana-1171	109	13	𝜆1𝑤𝑣	𝜆1𝑤𝑣	PUNCT
cana-1171	110	1	+	+	CCONJ
cana-1171	110	2	𝐶𝑢𝑣𝑤	𝐶𝑢𝑣𝑤	PROPN
cana-1171	110	3	=	=	SYM
cana-1171	110	4	0	0	NUM
cana-1171	110	5	(	(	PUNCT
cana-1171	110	6	15	15	NUM
cana-1171	110	7	)	)	PUNCT
cana-1171	110	8	𝑑2𝑤	𝑑2𝑤	ADP
cana-1171	110	9	𝑑𝑦2	𝑑𝑦2	NOUN
cana-1171	110	10	−	−	PROPN
cana-1171	110	11	𝜆1𝑤𝑣	𝜆1𝑤𝑣	PUNCT
cana-1171	111	1	+	+	CCONJ
cana-1171	111	2	𝐶𝑢𝑣𝑤	𝐶𝑢𝑣𝑤	PROPN
cana-1171	111	3	=	=	SYM
cana-1171	111	4	0	0	PUNCT
cana-1171	111	5	(	(	PUNCT
cana-1171	111	6	16	16	NUM
cana-1171	111	7	)	)	PUNCT
cana-1171	111	8	with	with	ADP
cana-1171	111	9	the	the	DET
cana-1171	111	10	boundary	boundary	ADJ
cana-1171	111	11	conditions	condition	NOUN
cana-1171	111	12	,	,	PUNCT
cana-1171	111	13	𝑦	𝑦	NOUN
cana-1171	111	14	=	=	SYM
cana-1171	111	15	1	1	NUM
cana-1171	111	16	∶	∶	NOUN
cana-1171	111	17	𝑢	𝑢	X
cana-1171	111	18	=	=	SYM
cana-1171	111	19	1	1	NUM
cana-1171	111	20	,	,	PUNCT
cana-1171	111	21	𝑣	𝑣	X
cana-1171	111	22	=	=	SYM
cana-1171	111	23	0	0	NUM
cana-1171	111	24	,	,	PUNCT
cana-1171	111	25	𝑤	𝑤	X
cana-1171	111	26	=	=	SYM
cana-1171	111	27	𝛾	𝛾	PROPN
cana-1171	111	28	(	(	PUNCT
cana-1171	111	29	17	17	NUM
cana-1171	111	30	)	)	PUNCT
cana-1171	111	31	𝑦	𝑦	NOUN
cana-1171	111	32	=	=	SYM
cana-1171	111	33	0	0	NUM
cana-1171	111	34	∶	∶	NOUN
cana-1171	111	35	𝑢	𝑢	X
cana-1171	111	36	=	=	SYM
cana-1171	111	37	1	1	NUM
cana-1171	111	38	[	[	SYM
cana-1171	111	39	1	1	NUM
cana-1171	111	40	+	+	NUM
cana-1171	111	41	𝑒𝑥𝑝(𝜉	𝑒𝑥𝑝(𝜉	NOUN
cana-1171	111	42	)	)	PUNCT
cana-1171	111	43	]	]	PUNCT
cana-1171	111	44	=	=	SYM
cana-1171	111	45	𝑠	𝑠	PROPN
cana-1171	111	46	(	(	PUNCT
cana-1171	111	47	say	say	PROPN
cana-1171	111	48	)	)	PUNCT
cana-1171	111	49	,	,	PUNCT
cana-1171	111	50	𝑑𝑢	𝑑𝑢	PROPN
cana-1171	111	51	𝑑𝑦	𝑑𝑦	INTJ
cana-1171	111	52	+	+	X
cana-1171	111	53	𝑑𝑣	𝑑𝑣	X
cana-1171	111	54	𝑑𝑦	𝑑𝑦	NOUN
cana-1171	111	55	=	=	NOUN
cana-1171	111	56	0	0	PROPN
cana-1171	111	57	,	,	PUNCT
cana-1171	111	58	𝑑𝑤	𝑑𝑤	PROPN
cana-1171	111	59	𝑑𝑦	𝑑𝑦	NOUN
cana-1171	111	60	=	=	SYM
cana-1171	111	61	0	0	PROPN
cana-1171	111	62	(	(	PUNCT
cana-1171	111	63	18	18	NUM
cana-1171	111	64	)	)	PUNCT
cana-1171	111	65	where	where	SCONJ
cana-1171	111	66	𝜆1𝜆2	𝜆1𝜆2	PUNCT
cana-1171	111	67	𝜆+𝜆2	𝜆+𝜆2	NOUN
cana-1171	111	68	=	=	SYM
cana-1171	111	69	𝐶(say	𝐶(say	INTJ
cana-1171	111	70	)	)	PUNCT
cana-1171	111	71	.	.	PUNCT
cana-1171	112	1	a	a	DET
cana-1171	112	2	fractional	fractional	ADJ
cana-1171	112	3	model	model	NOUN
cana-1171	112	4	in	in	ADP
cana-1171	112	5	caputo	caputo	PROPN
cana-1171	112	6	sequential	sequential	PROPN
cana-1171	112	7	derivative	derivative	NOUN
cana-1171	112	8	.	.	PUNCT
cana-1171	113	1	the	the	DET
cana-1171	113	2	fractional	fractional	ADJ
cana-1171	113	3	framework	framework	NOUN
cana-1171	113	4	for	for	ADP
cana-1171	113	5	the	the	DET
cana-1171	113	6	ec	ec	PROPN
cana-1171	113	7	mechanism	mechanism	NOUN
cana-1171	113	8	(	(	PUNCT
cana-1171	113	9	14	14	NUM
cana-1171	113	10	)	)	PUNCT
cana-1171	113	11	−	−	PROPN
cana-1171	114	1	(	(	PUNCT
cana-1171	114	2	16	16	NUM
cana-1171	114	3	)	)	PUNCT
cana-1171	114	4	is	be	AUX
cana-1171	114	5	given	give	VERB
cana-1171	114	6	as	as	SCONJ
cana-1171	114	7	follows	follow	VERB
cana-1171	114	8	:	:	PUNCT
cana-1171	114	9	𝐷𝑦	𝐷𝑦	PROPN
cana-1171	114	10	2𝛼	2𝛼	PROPN
cana-1171	114	11	0	0	NUM
cana-1171	114	12	𝐶𝑆	𝐶𝑆	PROPN
cana-1171	114	13	𝑢(𝑦	𝑢(𝑦	PROPN
cana-1171	114	14	)	)	PUNCT
cana-1171	114	15	+	+	CCONJ
cana-1171	114	16	𝜆1	𝜆1	VERB
cana-1171	114	17	𝛼𝑤𝑣	𝛼𝑤𝑣	NOUN
cana-1171	114	18	−	−	PROPN
cana-1171	114	19	𝐶𝛼𝑢𝑣𝑤	𝐶𝛼𝑢𝑣𝑤	PROPN
cana-1171	114	20	=	=	SYM
cana-1171	114	21	0	0	PUNCT
cana-1171	114	22	(	(	PUNCT
cana-1171	114	23	19	19	NUM
cana-1171	114	24	)	)	PUNCT
cana-1171	115	1	𝐷𝑦	𝐷𝑦	PROPN
cana-1171	115	2	2𝛼	2𝛼	PROPN
cana-1171	115	3	0	0	NUM
cana-1171	115	4	𝐶𝑆	𝐶𝑆	PROPN
cana-1171	115	5	𝑣(𝑦	𝑣(𝑦	PROPN
cana-1171	115	6	)	)	PUNCT
cana-1171	115	7	−	−	NOUN
cana-1171	115	8	𝜆1	𝜆1	VERB
cana-1171	115	9	𝛼𝑤𝑣	𝛼𝑤𝑣	NOUN
cana-1171	115	10	+	+	CCONJ
cana-1171	115	11	𝐶𝛼𝑢𝑣𝑤	𝐶𝛼𝑢𝑣𝑤	PROPN
cana-1171	115	12	=	=	SYM
cana-1171	115	13	0	0	PUNCT
cana-1171	115	14	(	(	PUNCT
cana-1171	115	15	20	20	NUM
cana-1171	115	16	)	)	PUNCT
cana-1171	116	1	𝐷𝑦	𝐷𝑦	PROPN
cana-1171	116	2	2𝛼	2𝛼	PROPN
cana-1171	116	3	0	0	X
cana-1171	116	4	𝐶𝑆	𝐶𝑆	PROPN
cana-1171	116	5	𝑤(𝑦	𝑤(𝑦	PRON
cana-1171	116	6	)	)	PUNCT
cana-1171	117	1	−	−	PROPN
cana-1171	117	2	𝜆1	𝜆1	VERB
cana-1171	117	3	𝛼𝑤𝑣	𝛼𝑤𝑣	NOUN
cana-1171	117	4	+	+	CCONJ
cana-1171	117	5	𝐶𝛼𝑢𝑣𝑤	𝐶𝛼𝑢𝑣𝑤	PROPN
cana-1171	117	6	=	=	SYM
cana-1171	117	7	0	0	PUNCT
cana-1171	117	8	(	(	PUNCT
cana-1171	117	9	21	21	NUM
cana-1171	117	10	)	)	PUNCT
cana-1171	117	11	with	with	ADP
cana-1171	117	12	𝑏	𝑏	NOUN
cana-1171	117	13	=	=	SYM
cana-1171	117	14	𝜆1	𝜆1	VERB
cana-1171	117	15	𝛼𝑤𝑣	𝛼𝑤𝑣	NOUN
cana-1171	117	16	𝜆𝛼+𝜆2	𝜆𝛼+𝜆2	NOUN
cana-1171	117	17	𝛼𝑢	𝛼𝑢	NOUN
cana-1171	117	18	.	.	PUNCT
cana-1171	118	1	(	(	PUNCT
cana-1171	118	2	22	22	NUM
cana-1171	118	3	)	)	PUNCT
cana-1171	118	4	where	where	SCONJ
cana-1171	118	5	𝐷𝑦	𝐷𝑦	PROPN
cana-1171	118	6	2𝛼	2𝛼	PROPN
cana-1171	118	7	0	0	NUM
cana-1171	118	8	𝐶𝑆	𝐶𝑆	NOUN
cana-1171	118	9	represents	represent	VERB
cana-1171	118	10	caputo	caputo	PROPN
cana-1171	118	11	-	-	PUNCT
cana-1171	118	12	sequential	sequential	ADJ
cana-1171	118	13	derivative	derivative	NOUN
cana-1171	118	14	with	with	ADP
cana-1171	118	15	fractional	fractional	ADJ
cana-1171	118	16	order	order	NOUN
cana-1171	119	1	2𝛼.	2𝛼.	NUM
cana-1171	119	2	5	5	NUM
cana-1171	119	3	.	.	PUNCT
cana-1171	120	1	analysis	analysis	NOUN
cana-1171	120	2	of	of	ADP
cana-1171	120	3	pre	pre	NOUN
cana-1171	120	4	-	-	NOUN
cana-1171	120	5	equilibrium	equilibrium	ADJ
cana-1171	120	6	and	and	CCONJ
cana-1171	120	7	stationary	stationary	ADJ
cana-1171	120	8	-	-	PUNCT
cana-1171	120	9	state	state	NOUN
cana-1171	120	10	assumptions	assumption	NOUN
cana-1171	120	11	.	.	PUNCT
cana-1171	121	1	this	this	DET
cana-1171	121	2	section	section	NOUN
cana-1171	121	3	discusses	discuss	VERB
cana-1171	121	4	the	the	DET
cana-1171	121	5	equilibrium	equilibrium	NOUN
cana-1171	121	6	points	point	NOUN
cana-1171	121	7	of	of	ADP
cana-1171	121	8	the	the	DET
cana-1171	121	9	ec	ec	PROPN
cana-1171	121	10	fractional	fractional	ADJ
cana-1171	121	11	model	model	NOUN
cana-1171	121	12	and	and	CCONJ
cana-1171	121	13	the	the	DET
cana-1171	121	14	stationary	stationary	ADJ
cana-1171	121	15	-	-	PUNCT
cana-1171	121	16	state	state	NOUN
cana-1171	121	17	of	of	ADP
cana-1171	121	18	the	the	DET
cana-1171	121	19	model	model	NOUN
cana-1171	121	20	(	(	PUNCT
cana-1171	121	21	14	14	NUM
cana-1171	121	22	)	)	PUNCT
cana-1171	121	23	−	−	PROPN
cana-1171	122	1	(	(	PUNCT
cana-1171	122	2	16	16	NUM
cana-1171	122	3	)	)	PUNCT
cana-1171	122	4	communications	communication	NOUN
cana-1171	122	5	on	on	ADP
cana-1171	122	6	applied	apply	VERB
cana-1171	122	7	nonlinear	nonlinear	ADJ
cana-1171	122	8	analysis	analysis	NOUN
cana-1171	122	9	issn	issn	NOUN
cana-1171	122	10	:	:	PUNCT
cana-1171	122	11	1074	1074	NUM
cana-1171	122	12	-	-	PUNCT
cana-1171	122	13	133x	133x	NUM
cana-1171	122	14	vol	vol	NOUN
cana-1171	122	15	31	31	NUM
cana-1171	122	16	no	no	NOUN
cana-1171	122	17	.	.	PUNCT
cana-1171	123	1	6s	6s	NUM
cana-1171	123	2	(	(	PUNCT
cana-1171	123	3	2024	2024	NUM
cana-1171	123	4	)	)	PUNCT
cana-1171	123	5	120	120	NUM
cana-1171	123	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1171	123	7	(	(	PUNCT
cana-1171	123	8	i	i	NOUN
cana-1171	123	9	)	)	PUNCT
cana-1171	123	10	kinetic	kinetic	ADJ
cana-1171	123	11	control	control	NOUN
cana-1171	123	12	by	by	ADP
cana-1171	123	13	chemical	chemical	ADJ
cana-1171	123	14	reaction	reaction	NOUN
cana-1171	123	15	(	(	PUNCT
cana-1171	123	16	4	4	NUM
cana-1171	123	17	)	)	PUNCT
cana-1171	123	18	with	with	ADP
cana-1171	123	19	electrode	electrode	PROPN
cana-1171	123	20	process(1	process(1	PROPN
cana-1171	123	21	)	)	PUNCT
cana-1171	123	22	acts	act	VERB
cana-1171	123	23	as	as	ADP
cana-1171	123	24	a	a	DET
cana-1171	123	25	pre	pre	NOUN
cana-1171	123	26	-	-	NOUN
cana-1171	123	27	equilibrium	equilibrium	NOUN
cana-1171	123	28	.	.	PUNCT
cana-1171	124	1	in	in	ADP
cana-1171	124	2	the	the	DET
cana-1171	124	3	context	context	NOUN
cana-1171	124	4	of	of	ADP
cana-1171	124	5	homogeneous	homogeneous	ADJ
cana-1171	124	6	redox	redox	NOUN
cana-1171	124	7	catalysis	catalysis	NOUN
cana-1171	124	8	,	,	PUNCT
cana-1171	124	9	when	when	SCONJ
cana-1171	124	10	the	the	DET
cana-1171	124	11	follow	follow	VERB
cana-1171	124	12	-	-	PUNCT
cana-1171	124	13	up	up	ADP
cana-1171	124	14	chemical	chemical	NOUN
cana-1171	124	15	reaction	reaction	NOUN
cana-1171	124	16	(	(	PUNCT
cana-1171	124	17	4	4	X
cana-1171	124	18	)	)	PUNCT
cana-1171	124	19	is	be	AUX
cana-1171	124	20	slower	slow	ADJ
cana-1171	124	21	than	than	ADP
cana-1171	124	22	the	the	DET
cana-1171	124	23	backward	backward	ADJ
cana-1171	124	24	solution	solution	NOUN
cana-1171	124	25	electron	electron	NOUN
cana-1171	124	26	transfer	transfer	NOUN
cana-1171	124	27	(	(	PUNCT
cana-1171	124	28	3	3	NUM
cana-1171	124	29	)	)	PUNCT
cana-1171	124	30	,	,	PUNCT
cana-1171	124	31	the	the	DET
cana-1171	124	32	overall	overall	ADJ
cana-1171	124	33	reaction	reaction	NOUN
cana-1171	124	34	kinetics	kinetic	NOUN
cana-1171	124	35	are	be	AUX
cana-1171	124	36	controlled	control	VERB
cana-1171	124	37	by	by	ADP
cana-1171	124	38	the	the	DET
cana-1171	124	39	follow	follow	VERB
cana-1171	124	40	-	-	PUNCT
cana-1171	124	41	up	up	ADP
cana-1171	124	42	chemical	chemical	NOUN
cana-1171	124	43	reaction	reaction	NOUN
cana-1171	124	44	,	,	PUNCT
cana-1171	124	45	with	with	ADP
cana-1171	124	46	the	the	DET
cana-1171	124	47	reaction	reaction	NOUN
cana-1171	124	48	(	(	PUNCT
cana-1171	124	49	3	3	X
cana-1171	124	50	)	)	PUNCT
cana-1171	124	51	acting	act	VERB
cana-1171	124	52	as	as	ADP
cana-1171	124	53	a	a	DET
cana-1171	124	54	pre	pre	NOUN
cana-1171	124	55	-	-	NOUN
cana-1171	124	56	equilibrium	equilibrium	NOUN
cana-1171	124	57	.	.	PUNCT
cana-1171	125	1	the	the	DET
cana-1171	125	2	proceeding	proceeding	NOUN
cana-1171	125	3	system	system	NOUN
cana-1171	125	4	(	(	PUNCT
cana-1171	125	5	8)	8)	NUM
cana-1171	125	6	−	−	NOUN
cana-1171	125	7	(	(	PUNCT
cana-1171	125	8	10	10	NUM
cana-1171	125	9	)	)	PUNCT
cana-1171	125	10	of	of	ADP
cana-1171	125	11	three	three	NUM
cana-1171	125	12	differential	differential	ADJ
cana-1171	125	13	equations	equation	NOUN
cana-1171	125	14	can	can	AUX
cana-1171	125	15	be	be	AUX
cana-1171	125	16	reduced	reduce	VERB
cana-1171	125	17	into	into	ADP
cana-1171	125	18	a	a	DET
cana-1171	125	19	single	single	ADJ
cana-1171	125	20	differential	differential	NOUN
cana-1171	125	21	equation	equation	NOUN
cana-1171	125	22	that	that	PRON
cana-1171	125	23	is	be	AUX
cana-1171	125	24	𝑑2𝑢	𝑑2𝑢	PROPN
cana-1171	125	25	𝑑𝑦2	𝑑𝑦2	X
cana-1171	125	26	+	+	CCONJ
cana-1171	125	27	(	(	PUNCT
cana-1171	125	28	𝜆𝜆1	𝜆𝜆1	NOUN
cana-1171	125	29	𝜆2	𝜆2	NOUN
cana-1171	125	30	)	)	PUNCT
cana-1171	126	1	[	[	X
cana-1171	126	2	𝜓(𝑦	𝜓(𝑦	ADP
cana-1171	126	3	−	−	NOUN
cana-1171	126	4	1	1	NUM
cana-1171	126	5	)	)	PUNCT
cana-1171	126	6	+	+	CCONJ
cana-1171	126	7	1	1	NUM
cana-1171	126	8	+	+	CCONJ
cana-1171	126	9	𝛾	𝛾	ADP
cana-1171	126	10	−	−	NOUN
cana-1171	126	11	𝑢	𝑢	NOUN
cana-1171	126	12	]	]	X
cana-1171	126	13	(	(	PUNCT
cana-1171	126	14	1	1	NUM
cana-1171	126	15	−	−	PROPN
cana-1171	126	16	𝑢	𝑢	NOUN
cana-1171	126	17	)	)	PUNCT
cana-1171	126	18	𝑢	𝑢	NOUN
cana-1171	126	19	=	=	SYM
cana-1171	126	20	0	0	NUM
cana-1171	126	21	(	(	PUNCT
cana-1171	126	22	23	23	NUM
cana-1171	126	23	)	)	PUNCT
cana-1171	126	24	where	where	SCONJ
cana-1171	126	25	𝜓	𝜓	PROPN
cana-1171	126	26	is	be	AUX
cana-1171	126	27	the	the	DET
cana-1171	126	28	dimensionless	dimensionless	NOUN
cana-1171	126	29	plateau	plateau	NOUN
cana-1171	126	30	current	current	NOUN
cana-1171	126	31	depends	depend	VERB
cana-1171	126	32	upon	upon	SCONJ
cana-1171	126	33	olnly	olnly	ADV
cana-1171	126	34	two	two	NUM
cana-1171	126	35	parameters	parameter	NOUN
cana-1171	126	36	𝛾	𝛾	VERB
cana-1171	126	37	and	and	CCONJ
cana-1171	126	38	𝜆𝜆1	𝜆𝜆1	NOUN
cana-1171	126	39	𝜆2	𝜆2	NOUN
cana-1171	126	40	=	=	SYM
cana-1171	126	41	(	(	PUNCT
cana-1171	126	42	𝑘𝑘1/𝑘2)(𝛿2/𝐷	𝑘𝑘1/𝑘2)(𝛿2/𝐷	PROPN
cana-1171	126	43	)	)	PUNCT
cana-1171	126	44	.	.	PUNCT
cana-1171	127	1	in	in	ADP
cana-1171	127	2	[	[	X
cana-1171	127	3	4	4	NUM
cana-1171	127	4	]	]	PUNCT
cana-1171	127	5	,	,	PUNCT
cana-1171	127	6	which	which	PRON
cana-1171	127	7	corresponds	correspond	VERB
cana-1171	127	8	to	to	ADP
cana-1171	127	9	general	general	ADJ
cana-1171	127	10	cases	case	NOUN
cana-1171	127	11	,	,	PUNCT
cana-1171	127	12	some	some	PRON
cana-1171	127	13	of	of	ADP
cana-1171	127	14	the	the	DET
cana-1171	127	15	observations	observation	NOUN
cana-1171	127	16	are	be	AUX
cana-1171	127	17	represented	represent	VERB
cana-1171	127	18	as	as	SCONJ
cana-1171	127	19	follows	follow	VERB
cana-1171	127	20	:	:	PUNCT
cana-1171	127	21	(	(	PUNCT
cana-1171	127	22	i	i	NOUN
cana-1171	127	23	)	)	PUNCT
cana-1171	127	24	the	the	DET
cana-1171	127	25	system	system	NOUN
cana-1171	127	26	depends	depend	VERB
cana-1171	127	27	on	on	ADP
cana-1171	127	28	two	two	NUM
cana-1171	127	29	kinetic	kinetic	ADJ
cana-1171	127	30	parameters	parameter	NOUN
cana-1171	127	31	and	and	CCONJ
cana-1171	127	32	𝛾	𝛾	ADP
cana-1171	127	33	,	,	PUNCT
cana-1171	127	34	and	and	CCONJ
cana-1171	127	35	for	for	ADP
cana-1171	127	36	high	high	ADJ
cana-1171	127	37	values	value	NOUN
cana-1171	127	38	of	of	ADP
cana-1171	127	39	𝜆𝜆1	𝜆𝜆1	NOUN
cana-1171	127	40	𝜆2	𝜆2	PROPN
cana-1171	127	41	,	,	PUNCT
cana-1171	127	42	the	the	DET
cana-1171	127	43	catalytic	catalytic	ADJ
cana-1171	127	44	efficiency	efficiency	NOUN
cana-1171	127	45	reaches	reach	VERB
cana-1171	127	46	unity	unity	NOUN
cana-1171	127	47	,	,	PUNCT
cana-1171	127	48	and	and	CCONJ
cana-1171	127	49	the	the	DET
cana-1171	127	50	current	current	ADJ
cana-1171	127	51	-	-	PUNCT
cana-1171	127	52	potential	potential	ADJ
cana-1171	127	53	curves	curve	NOUN
cana-1171	127	54	split	split	VERB
cana-1171	127	55	into	into	ADP
cana-1171	127	56	two	two	NUM
cana-1171	127	57	waves	wave	NOUN
cana-1171	127	58	.	.	PUNCT
cana-1171	128	1	(	(	PUNCT
cana-1171	128	2	ii	ii	NOUN
cana-1171	128	3	)	)	PUNCT
cana-1171	128	4	an	an	DET
cana-1171	128	5	increase	increase	NOUN
cana-1171	128	6	in	in	ADP
cana-1171	128	7	δ	δ	NOUN
cana-1171	128	8	shifts	shift	NOUN
cana-1171	128	9	the	the	DET
cana-1171	128	10	catalytic	catalytic	ADJ
cana-1171	128	11	efficiency	efficiency	NOUN
cana-1171	128	12	of	of	ADP
cana-1171	128	13	the	the	DET
cana-1171	128	14	system	system	NOUN
cana-1171	128	15	from	from	ADP
cana-1171	128	16	low	low	ADJ
cana-1171	128	17	to	to	ADP
cana-1171	128	18	high	high	ADJ
cana-1171	128	19	.	.	PUNCT
cana-1171	129	1	(	(	PUNCT
cana-1171	129	2	iii	iii	X
cana-1171	129	3	)	)	PUNCT
cana-1171	129	4	the	the	DET
cana-1171	129	5	catalytic	catalytic	ADJ
cana-1171	129	6	efficiency	efficiency	NOUN
cana-1171	129	7	is	be	AUX
cana-1171	129	8	a	a	DET
cana-1171	129	9	function	function	NOUN
cana-1171	129	10	of	of	ADP
cana-1171	129	11	𝜆1(7	𝜆1(7	PROPN
cana-1171	129	12	)	)	PUNCT
cana-1171	129	13	,	,	PUNCT
cana-1171	129	14	and	and	CCONJ
cana-1171	129	15	an	an	DET
cana-1171	129	16	increase	increase	NOUN
cana-1171	129	17	in	in	ADP
cana-1171	129	18	𝑐0	𝑐0	NOUN
cana-1171	129	19	leads	lead	VERB
cana-1171	129	20	to	to	ADP
cana-1171	129	21	an	an	DET
cana-1171	129	22	increase	increase	NOUN
cana-1171	129	23	in	in	ADP
cana-1171	129	24	𝜆1	𝜆1	NOUN
cana-1171	129	25	,	,	PUNCT
cana-1171	129	26	resulting	result	VERB
cana-1171	129	27	in	in	ADP
cana-1171	129	28	the	the	DET
cana-1171	129	29	function	function	NOUN
cana-1171	129	30	𝜆𝜆1	𝜆𝜆1	NOUN
cana-1171	129	31	𝜆2	𝜆2	NOUN
cana-1171	129	32	=	=	SYM
cana-1171	129	33	(	(	PUNCT
cana-1171	129	34	𝑘𝑘1/𝑘2)(𝛿2/𝐷	𝑘𝑘1/𝑘2)(𝛿2/𝐷	PROPN
cana-1171	129	35	)	)	PUNCT
cana-1171	129	36	independent	independent	NOUN
cana-1171	129	37	of	of	ADP
cana-1171	129	38	𝑐0	𝑐0	PROPN
cana-1171	129	39	.	.	PUNCT
cana-1171	130	1	(	(	PUNCT
cana-1171	130	2	ii	ii	NOUN
cana-1171	130	3	)	)	PUNCT
cana-1171	130	4	the	the	DET
cana-1171	130	5	stationary	stationary	ADJ
cana-1171	130	6	-	-	PUNCT
cana-1171	130	7	state	state	NOUN
cana-1171	130	8	assumption	assumption	NOUN
cana-1171	130	9	regarding	regard	VERB
cana-1171	130	10	b.	b.	PROPN
cana-1171	130	11	suppose	suppose	VERB
cana-1171	130	12	there	there	PRON
cana-1171	130	13	is	be	VERB
cana-1171	130	14	no	no	DET
cana-1171	130	15	chemical	chemical	ADJ
cana-1171	130	16	reaction	reaction	NOUN
cana-1171	130	17	of	of	ADP
cana-1171	130	18	the	the	DET
cana-1171	130	19	electron	electron	NOUN
cana-1171	130	20	-	-	PUNCT
cana-1171	130	21	transfer	transfer	NOUN
cana-1171	130	22	,	,	PUNCT
cana-1171	130	23	i.e.	i.e.	X
cana-1171	130	24	when	when	SCONJ
cana-1171	130	25	𝜆	𝜆	ADP
cana-1171	130	26	=	=	SYM
cana-1171	130	27	0	0	PROPN
cana-1171	130	28	.	.	PUNCT
cana-1171	131	1	then	then	ADV
cana-1171	131	2	the	the	DET
cana-1171	131	3	stationarystate	stationarystate	ADJ
cana-1171	131	4	assumption	assumption	NOUN
cana-1171	131	5	regarding	regard	VERB
cana-1171	131	6	𝐵	𝐵	NOUN
cana-1171	131	7	is	be	AUX
cana-1171	131	8	no	no	ADV
cana-1171	131	9	longer	long	ADV
cana-1171	131	10	valid	valid	ADJ
cana-1171	131	11	.	.	PUNCT
cana-1171	132	1	in	in	ADP
cana-1171	132	2	[	[	X
cana-1171	132	3	4	4	NUM
cana-1171	132	4	]	]	PUNCT
cana-1171	132	5	,	,	PUNCT
cana-1171	132	6	(	(	PUNCT
cana-1171	132	7	i	i	NOUN
cana-1171	132	8	)	)	PUNCT
cana-1171	132	9	the	the	DET
cana-1171	132	10	stationary	stationary	ADJ
cana-1171	132	11	-	-	PUNCT
cana-1171	132	12	state	state	NOUN
cana-1171	132	13	assumption	assumption	NOUN
cana-1171	132	14	is	be	AUX
cana-1171	132	15	valid	valid	ADJ
cana-1171	132	16	when	when	SCONJ
cana-1171	132	17	the	the	DET
cana-1171	132	18	follow	follow	VERB
cana-1171	132	19	-	-	PUNCT
cana-1171	132	20	up	up	ADP
cana-1171	132	21	chemical	chemical	NOUN
cana-1171	132	22	reaction	reaction	NOUN
cana-1171	132	23	is	be	AUX
cana-1171	132	24	slower	slow	ADJ
cana-1171	132	25	than	than	ADP
cana-1171	132	26	the	the	DET
cana-1171	132	27	backward	backward	ADJ
cana-1171	132	28	solution	solution	NOUN
cana-1171	132	29	electron	electron	NOUN
cana-1171	132	30	transfer	transfer	NOUN
cana-1171	132	31	,	,	PUNCT
cana-1171	132	32	and	and	CCONJ
cana-1171	132	33	the	the	DET
cana-1171	132	34	catalytic	catalytic	ADJ
cana-1171	132	35	efficiency	efficiency	NOUN
cana-1171	132	36	is	be	AUX
cana-1171	132	37	low	low	ADJ
cana-1171	132	38	.	.	PUNCT
cana-1171	133	1	(	(	PUNCT
cana-1171	133	2	ii	ii	NOUN
cana-1171	133	3	)	)	PUNCT
cana-1171	133	4	the	the	DET
cana-1171	133	5	stationarystate	stationarystate	PROPN
cana-1171	133	6	assumption	assumption	NOUN
cana-1171	133	7	leads	lead	VERB
cana-1171	133	8	to	to	ADP
cana-1171	133	9	two	two	NUM
cana-1171	133	10	limiting	limit	VERB
cana-1171	133	11	situations	situation	NOUN
cana-1171	133	12	for	for	ADP
cana-1171	133	13	extreme	extreme	ADJ
cana-1171	133	14	values	value	NOUN
cana-1171	133	15	of	of	ADP
cana-1171	133	16	𝑘/𝑘2	𝑘/𝑘2	PRON
cana-1171	133	17	,	,	PUNCT
cana-1171	133	18	which	which	PRON
cana-1171	133	19	involve	involve	VERB
cana-1171	133	20	kinetic	kinetic	ADJ
cana-1171	133	21	control	control	NOUN
cana-1171	133	22	of	of	ADP
cana-1171	133	23	the	the	DET
cana-1171	133	24	overall	overall	ADJ
cana-1171	133	25	reaction	reaction	NOUN
cana-1171	133	26	either	either	CCONJ
cana-1171	133	27	by	by	ADP
cana-1171	133	28	the	the	DET
cana-1171	133	29	forward	forward	ADJ
cana-1171	133	30	reaction	reaction	NOUN
cana-1171	133	31	(	(	PUNCT
cana-1171	133	32	3	3	NUM
cana-1171	133	33	)	)	PUNCT
cana-1171	133	34	or	or	CCONJ
cana-1171	133	35	by	by	ADP
cana-1171	133	36	reaction	reaction	NOUN
cana-1171	133	37	(	(	PUNCT
cana-1171	133	38	4)with	4)with	NUM
cana-1171	133	39	(	(	PUNCT
cana-1171	133	40	3	3	NUM
cana-1171	133	41	)	)	PUNCT
cana-1171	133	42	as	as	ADP
cana-1171	133	43	a	a	DET
cana-1171	133	44	preequilibrium	preequilibrium	NOUN
cana-1171	133	45	.	.	PUNCT
cana-1171	134	1	(	(	PUNCT
cana-1171	134	2	iii	iii	X
cana-1171	134	3	)	)	PUNCT
cana-1171	134	4	the	the	DET
cana-1171	134	5	polarization	polarization	NOUN
cana-1171	134	6	problem	problem	NOUN
cana-1171	134	7	can	can	AUX
cana-1171	134	8	be	be	AUX
cana-1171	134	9	numerically	numerically	ADV
cana-1171	134	10	solved	solve	VERB
cana-1171	134	11	for	for	ADP
cana-1171	134	12	these	these	DET
cana-1171	134	13	two	two	NUM
cana-1171	134	14	limiting	limit	VERB
cana-1171	134	15	cases	case	NOUN
cana-1171	134	16	as	as	ADV
cana-1171	134	17	well	well	ADV
cana-1171	134	18	as	as	ADP
cana-1171	134	19	for	for	ADP
cana-1171	134	20	the	the	DET
cana-1171	134	21	transition	transition	NOUN
cana-1171	134	22	between	between	ADP
cana-1171	134	23	them	they	PRON
cana-1171	134	24	in	in	ADP
cana-1171	134	25	the	the	DET
cana-1171	134	26	context	context	NOUN
cana-1171	134	27	of	of	ADP
cana-1171	134	28	stationary	stationary	ADJ
cana-1171	134	29	or	or	CCONJ
cana-1171	134	30	quasi	quasi	ADJ
cana-1171	134	31	-	-	ADJ
cana-1171	134	32	stationary	stationary	ADJ
cana-1171	134	33	electrochemical	electrochemical	ADJ
cana-1171	134	34	methods	method	NOUN
cana-1171	134	35	.	.	PUNCT
cana-1171	135	1	(	(	PUNCT
cana-1171	135	2	iv	iv	X
cana-1171	135	3	)	)	PUNCT
cana-1171	135	4	the	the	DET
cana-1171	135	5	stationary	stationary	ADJ
cana-1171	135	6	-	-	PUNCT
cana-1171	135	7	state	state	NOUN
cana-1171	135	8	assumption	assumption	NOUN
cana-1171	135	9	reduces	reduce	VERB
cana-1171	135	10	the	the	DET
cana-1171	135	11	number	number	NOUN
cana-1171	135	12	of	of	ADP
cana-1171	135	13	parameters	parameter	NOUN
cana-1171	135	14	needed	need	VERB
cana-1171	135	15	to	to	PART
cana-1171	135	16	describe	describe	VERB
cana-1171	135	17	the	the	DET
cana-1171	135	18	reaction	reaction	NOUN
cana-1171	135	19	kinetics	kinetic	NOUN
cana-1171	135	20	,	,	PUNCT
cana-1171	135	21	making	make	VERB
cana-1171	135	22	it	it	PRON
cana-1171	135	23	easier	easy	ADJ
cana-1171	135	24	to	to	PART
cana-1171	135	25	analyze	analyze	VERB
cana-1171	135	26	and	and	CCONJ
cana-1171	135	27	understand	understand	VERB
cana-1171	135	28	the	the	DET
cana-1171	135	29	kinetics	kinetic	NOUN
cana-1171	135	30	of	of	ADP
cana-1171	135	31	electrochemical	electrochemical	ADJ
cana-1171	135	32	reactions	reaction	NOUN
cana-1171	135	33	under	under	ADP
cana-1171	135	34	homogeneous	homogeneous	ADJ
cana-1171	135	35	redox	redox	NOUN
cana-1171	135	36	catalysis	catalysis	NOUN
cana-1171	135	37	.	.	PUNCT
cana-1171	136	1	(	(	PUNCT
cana-1171	136	2	v	v	NOUN
cana-1171	136	3	)	)	PUNCT
cana-1171	136	4	the	the	DET
cana-1171	136	5	stationary	stationary	ADJ
cana-1171	136	6	-	-	PUNCT
cana-1171	136	7	state	state	NOUN
cana-1171	136	8	assumption	assumption	NOUN
cana-1171	136	9	has	have	VERB
cana-1171	136	10	limitations	limitation	NOUN
cana-1171	136	11	and	and	CCONJ
cana-1171	136	12	is	be	AUX
cana-1171	136	13	only	only	ADV
cana-1171	136	14	valid	valid	ADJ
cana-1171	136	15	for	for	ADP
cana-1171	136	16	certain	certain	ADJ
cana-1171	136	17	ranges	range	NOUN
cana-1171	136	18	of	of	ADP
cana-1171	136	19	catalytic	catalytic	ADJ
cana-1171	136	20	efficiency	efficiency	NOUN
cana-1171	136	21	and	and	CCONJ
cana-1171	136	22	rate	rate	NOUN
cana-1171	136	23	constants	constant	NOUN
cana-1171	136	24	.	.	PUNCT
cana-1171	137	1	the	the	DET
cana-1171	137	2	previously	previously	ADV
cana-1171	137	3	established	establish	VERB
cana-1171	137	4	results	result	NOUN
cana-1171	137	5	concerning	concern	VERB
cana-1171	137	6	pre	pre	NOUN
cana-1171	137	7	-	-	NOUN
cana-1171	137	8	equilibrium	equilibrium	NOUN
cana-1171	137	9	and	and	CCONJ
cana-1171	137	10	the	the	DET
cana-1171	137	11	stationary	stationary	ADJ
cana-1171	137	12	-	-	PUNCT
cana-1171	137	13	state	state	NOUN
cana-1171	137	14	assumption	assumption	NOUN
cana-1171	137	15	are	be	AUX
cana-1171	137	16	relevant	relevant	ADJ
cana-1171	137	17	when	when	SCONJ
cana-1171	137	18	addressing	address	VERB
cana-1171	137	19	fractional	fractional	ADJ
cana-1171	137	20	differential	differential	ADJ
cana-1171	137	21	equations	equation	NOUN
cana-1171	137	22	with	with	ADP
cana-1171	137	23	orders	order	NOUN
cana-1171	137	24	ranging	range	VERB
cana-1171	137	25	from	from	ADP
cana-1171	137	26	0	0	NUM
cana-1171	137	27	to	to	ADP
cana-1171	137	28	1	1	NUM
cana-1171	137	29	.	.	PUNCT
cana-1171	138	1	6.basic	6.basic	NUM
cana-1171	138	2	idea	idea	NOUN
cana-1171	138	3	of	of	ADP
cana-1171	138	4	homotopy	homotopy	NOUN
cana-1171	138	5	perturbation	perturbation	NOUN
cana-1171	138	6	method	method	NOUN
cana-1171	138	7	for	for	ADP
cana-1171	138	8	system	system	NOUN
cana-1171	138	9	of	of	ADP
cana-1171	138	10	fdes	fde	NOUN
cana-1171	138	11	first	first	ADV
cana-1171	138	12	to	to	PART
cana-1171	138	13	illustrate	illustrate	VERB
cana-1171	138	14	the	the	DET
cana-1171	138	15	basic	basic	ADJ
cana-1171	138	16	idea	idea	NOUN
cana-1171	138	17	of	of	ADP
cana-1171	138	18	homotopy	homotopy	NOUN
cana-1171	138	19	perturbation	perturbation	NOUN
cana-1171	138	20	method	method	NOUN
cana-1171	138	21	,	,	PUNCT
cana-1171	138	22	many	many	ADJ
cana-1171	138	23	applications	application	NOUN
cana-1171	138	24	are	be	AUX
cana-1171	138	25	modelled	model	VERB
cana-1171	138	26	by	by	ADP
cana-1171	138	27	systems	system	NOUN
cana-1171	138	28	of	of	ADP
cana-1171	138	29	fractional	fractional	ADJ
cana-1171	138	30	differential	differential	ADJ
cana-1171	138	31	equations	equation	NOUN
cana-1171	138	32	which	which	PRON
cana-1171	138	33	can	can	AUX
cana-1171	138	34	be	be	AUX
cana-1171	138	35	written	write	VERB
cana-1171	138	36	in	in	ADP
cana-1171	138	37	the	the	DET
cana-1171	138	38	form	form	NOUN
cana-1171	138	39	𝐷𝛼1𝜑1(𝑡	𝐷𝛼1𝜑1(𝑡	NOUN
cana-1171	138	40	)	)	PUNCT
cana-1171	138	41	=	=	SYM
cana-1171	138	42	𝑓1(𝑡	𝑓1(𝑡	PROPN
cana-1171	138	43	,	,	PUNCT
cana-1171	138	44	𝜑1	𝜑1	NOUN
cana-1171	138	45	,	,	PUNCT
cana-1171	138	46	𝜑2	𝜑2	NOUN
cana-1171	138	47	,	,	PUNCT
cana-1171	138	48	𝜑3	𝜑3	PROPN
cana-1171	138	49	,	,	PUNCT
cana-1171	138	50	…	…	PUNCT
cana-1171	138	51	,	,	PUNCT
cana-1171	138	52	𝜑𝑛	𝜑𝑛	NOUN
cana-1171	138	53	)	)	PUNCT
cana-1171	138	54	(	(	PUNCT
cana-1171	138	55	25	25	NUM
cana-1171	138	56	)	)	PUNCT
cana-1171	138	57	communications	communication	NOUN
cana-1171	138	58	on	on	ADP
cana-1171	138	59	applied	apply	VERB
cana-1171	138	60	nonlinear	nonlinear	ADJ
cana-1171	138	61	analysis	analysis	NOUN
cana-1171	138	62	issn	issn	NOUN
cana-1171	138	63	:	:	PUNCT
cana-1171	138	64	1074	1074	NUM
cana-1171	138	65	-	-	PUNCT
cana-1171	138	66	133x	133x	NUM
cana-1171	138	67	vol	vol	NOUN
cana-1171	138	68	31	31	NUM
cana-1171	138	69	no	no	NOUN
cana-1171	138	70	.	.	PUNCT
cana-1171	139	1	6s	6s	NUM
cana-1171	139	2	(	(	PUNCT
cana-1171	139	3	2024	2024	NUM
cana-1171	139	4	)	)	PUNCT
cana-1171	139	5	121	121	NUM
cana-1171	139	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1171	139	7	𝐷𝛼2𝜑2(𝑡	𝐷𝛼2𝜑2(𝑡	NOUN
cana-1171	139	8	)	)	PUNCT
cana-1171	139	9	=	=	SYM
cana-1171	140	1	𝑓2(𝑡	𝑓2(𝑡	NOUN
cana-1171	140	2	,	,	PUNCT
cana-1171	140	3	𝜑1	𝜑1	NOUN
cana-1171	140	4	,	,	PUNCT
cana-1171	140	5	𝜑2	𝜑2	NOUN
cana-1171	140	6	,	,	PUNCT
cana-1171	140	7	𝜑3	𝜑3	PROPN
cana-1171	140	8	,	,	PUNCT
cana-1171	140	9	…	…	PUNCT
cana-1171	140	10	,	,	PUNCT
cana-1171	140	11	𝜑𝑛	𝜑𝑛	NOUN
cana-1171	140	12	)	)	PUNCT
cana-1171	140	13	(	(	PUNCT
cana-1171	140	14	26	26	NUM
cana-1171	140	15	)	)	PUNCT
cana-1171	140	16	.	.	PUNCT
cana-1171	140	17	.	.	PUNCT
cana-1171	140	18	.	.	PUNCT
cana-1171	141	1	𝐷𝛼𝑛𝜑𝑛(𝑡	𝐷𝛼𝑛𝜑𝑛(𝑡	X
cana-1171	141	2	)	)	PUNCT
cana-1171	142	1	=	=	SYM
cana-1171	142	2	𝑓𝑛(𝑡	𝑓𝑛(𝑡	X
cana-1171	142	3	,	,	PUNCT
cana-1171	142	4	𝜑1	𝜑1	VERB
cana-1171	142	5	,	,	PUNCT
cana-1171	142	6	𝜑2	𝜑2	NOUN
cana-1171	142	7	,	,	PUNCT
cana-1171	142	8	𝜑3	𝜑3	PROPN
cana-1171	142	9	,	,	PUNCT
cana-1171	142	10	…	…	PUNCT
cana-1171	142	11	,	,	PUNCT
cana-1171	142	12	𝜑𝑛	𝜑𝑛	NOUN
cana-1171	142	13	)	)	PUNCT
cana-1171	142	14	(	(	PUNCT
cana-1171	142	15	27	27	NUM
cana-1171	142	16	)	)	PUNCT
cana-1171	142	17	subject	subject	NOUN
cana-1171	142	18	to	to	ADP
cana-1171	142	19	the	the	DET
cana-1171	142	20	initial	initial	ADJ
cana-1171	142	21	condtions	condtion	NOUN
cana-1171	142	22	:	:	PUNCT
cana-1171	142	23	𝜑𝑛(𝑡	𝜑𝑛(𝑡	NUM
cana-1171	142	24	)	)	PUNCT
cana-1171	142	25	=	=	SYM
cana-1171	142	26	𝑐𝑘	𝑐𝑘	PROPN
cana-1171	142	27	,	,	PUNCT
cana-1171	142	28	𝑘	𝑘	NOUN
cana-1171	142	29	=	=	SYM
cana-1171	142	30	1,2	1,2	NUM
cana-1171	142	31	,	,	PUNCT
cana-1171	142	32	…	…	PUNCT
cana-1171	142	33	,	,	PUNCT
cana-1171	142	34	𝑛.	𝑛.	NOUN
cana-1171	142	35	where	where	SCONJ
cana-1171	142	36	𝐷𝛼𝑖	𝐷𝛼𝑖	PROPN
cana-1171	142	37	is	be	AUX
cana-1171	142	38	the	the	DET
cana-1171	142	39	fractional	fractional	ADJ
cana-1171	142	40	derivative	derivative	NOUN
cana-1171	142	41	of	of	ADP
cana-1171	142	42	order	order	NOUN
cana-1171	142	43	𝛼𝑖	𝛼𝑖	X
cana-1171	142	44	(	(	PUNCT
cana-1171	142	45	𝑚	𝑚	PROPN
cana-1171	142	46	−	−	PROPN
cana-1171	142	47	1	1	NUM
cana-1171	142	48	<	<	X
cana-1171	142	49	𝛼𝑖	𝛼𝑖	ADJ
cana-1171	142	50	≤	≤	NUM
cana-1171	142	51	𝑚	𝑚	NOUN
cana-1171	142	52	)	)	PUNCT
cana-1171	142	53	and	and	CCONJ
cana-1171	142	54	𝑓𝑖	𝑓𝑖	PROPN
cana-1171	142	55	are	be	AUX
cana-1171	142	56	arbitrary	arbitrary	ADJ
cana-1171	142	57	linear	linear	ADJ
cana-1171	142	58	and	and	CCONJ
cana-1171	142	59	nonlinar	nonlinar	ADJ
cana-1171	142	60	functions	function	NOUN
cana-1171	142	61	.	.	PUNCT
cana-1171	143	1	construct	construct	VERB
cana-1171	143	2	the	the	DET
cana-1171	143	3	following	follow	VERB
cana-1171	143	4	homotopy	homotopy	NOUN
cana-1171	143	5	:	:	PUNCT
cana-1171	143	6	𝐷𝛼𝑖𝜑𝑖	𝐷𝛼𝑖𝜑𝑖	PROPN
cana-1171	143	7	=	=	SYM
cana-1171	143	8	𝑝𝑓𝑖(𝑡	𝑝𝑓𝑖(𝑡	PROPN
cana-1171	143	9	,	,	PUNCT
cana-1171	143	10	𝜑1	𝜑1	VERB
cana-1171	143	11	,	,	PUNCT
cana-1171	143	12	𝜑2	𝜑2	NOUN
cana-1171	143	13	,	,	PUNCT
cana-1171	143	14	𝜑3	𝜑3	PROPN
cana-1171	143	15	,	,	PUNCT
cana-1171	143	16	…	…	PUNCT
cana-1171	143	17	,	,	PUNCT
cana-1171	143	18	𝜑𝑛	𝜑𝑛	NOUN
cana-1171	143	19	)	)	PUNCT
cana-1171	143	20	(	(	PUNCT
cana-1171	143	21	28	28	NUM
cana-1171	143	22	)	)	PUNCT
cana-1171	143	23	where	where	SCONJ
cana-1171	143	24	𝑖	𝑖	ADP
cana-1171	143	25	=	=	SYM
cana-1171	143	26	1,2	1,2	NUM
cana-1171	143	27	,	,	PUNCT
cana-1171	143	28	…	…	PUNCT
cana-1171	143	29	,	,	PUNCT
cana-1171	143	30	𝑛	𝑛	PROPN
cana-1171	143	31	and	and	CCONJ
cana-1171	143	32	𝑝	𝑝	PROPN
cana-1171	143	33	is	be	AUX
cana-1171	143	34	an	an	DET
cana-1171	143	35	embedding	embed	VERB
cana-1171	143	36	parameter	parameter	NOUN
cana-1171	143	37	which	which	PRON
cana-1171	143	38	is	be	AUX
cana-1171	143	39	monotonically	monotonically	ADV
cana-1171	143	40	increasing	increase	VERB
cana-1171	143	41	from	from	ADP
cana-1171	143	42	0	0	NUM
cana-1171	143	43	to	to	ADP
cana-1171	143	44	1	1	NUM
cana-1171	143	45	.	.	PUNCT
cana-1171	144	1	using	use	VERB
cana-1171	144	2	the	the	DET
cana-1171	144	3	parameter	parameter	NOUN
cana-1171	144	4	𝑝	𝑝	NOUN
cana-1171	144	5	,	,	PUNCT
cana-1171	144	6	we	we	PRON
cana-1171	144	7	expand	expand	VERB
cana-1171	144	8	the	the	DET
cana-1171	144	9	solution	solution	NOUN
cana-1171	144	10	of	of	ADP
cana-1171	144	11	the	the	DET
cana-1171	144	12	system	system	NOUN
cana-1171	144	13	(	(	PUNCT
cana-1171	144	14	25	25	NUM
cana-1171	144	15	)	)	PUNCT
cana-1171	144	16	−	−	PROPN
cana-1171	145	1	(	(	PUNCT
cana-1171	145	2	27	27	NUM
cana-1171	145	3	)	)	PUNCT
cana-1171	145	4	in	in	ADP
cana-1171	145	5	the	the	DET
cana-1171	145	6	form	form	NOUN
cana-1171	145	7	𝜑𝑖(𝑡	𝜑𝑖(𝑡	PUNCT
cana-1171	145	8	)	)	PUNCT
cana-1171	145	9	=	=	SYM
cana-1171	146	1	𝜑𝑖0	𝜑𝑖0	PROPN
cana-1171	146	2	+	+	CCONJ
cana-1171	146	3	𝑝𝜑𝑖1	𝑝𝜑𝑖1	ADJ
cana-1171	146	4	+	+	CCONJ
cana-1171	146	5	𝑝2𝜑𝑖2	𝑝2𝜑𝑖2	NOUN
cana-1171	146	6	+	+	CCONJ
cana-1171	146	7	𝑝3𝜑𝑖3	𝑝3𝜑𝑖3	NOUN
cana-1171	146	8	+	+	CCONJ
cana-1171	146	9	⋯	⋯	PROPN
cana-1171	146	10	(	(	PUNCT
cana-1171	146	11	29	29	NUM
cana-1171	146	12	)	)	PUNCT
cana-1171	146	13	substituting	substituting	NOUN
cana-1171	146	14	(	(	PUNCT
cana-1171	146	15	29	29	NUM
cana-1171	146	16	)	)	PUNCT
cana-1171	146	17	into	into	ADP
cana-1171	146	18	(	(	PUNCT
cana-1171	146	19	28	28	NUM
cana-1171	146	20	)	)	PUNCT
cana-1171	146	21	and	and	CCONJ
cana-1171	146	22	the	the	DET
cana-1171	146	23	resultant	resultant	NOUN
cana-1171	146	24	equation	equation	NOUN
cana-1171	146	25	is	be	AUX
cana-1171	146	26	in	in	ADP
cana-1171	146	27	terms	term	NOUN
cana-1171	146	28	with	with	ADP
cana-1171	146	29	the	the	DET
cana-1171	146	30	same	same	ADJ
cana-1171	146	31	powers	power	NOUN
cana-1171	146	32	of	of	ADP
cana-1171	146	33	𝑝	𝑝	PROPN
cana-1171	146	34	,	,	PUNCT
cana-1171	146	35	𝑝𝑜	𝑝𝑜	INTJ
cana-1171	146	36	:	:	PUNCT
cana-1171	146	37	𝐷𝛼𝑖𝜑𝑖0	𝐷𝛼𝑖𝜑𝑖0	PROPN
cana-1171	146	38	=	=	SYM
cana-1171	146	39	0	0	NUM
cana-1171	146	40	,	,	PUNCT
cana-1171	146	41	𝑝1	𝑝1	NOUN
cana-1171	146	42	:	:	PUNCT
cana-1171	146	43	𝐷𝛼𝑖𝜑𝑖1	𝐷𝛼𝑖𝜑𝑖1	PROPN
cana-1171	146	44	=	=	SYM
cana-1171	146	45	𝑓𝑖1(𝑡	𝑓𝑖1(𝑡	PROPN
cana-1171	146	46	,	,	PUNCT
cana-1171	146	47	𝜑10	𝜑10	ADJ
cana-1171	146	48	,	,	PUNCT
cana-1171	146	49	𝜑20	𝜑20	ADJ
cana-1171	146	50	,	,	PUNCT
cana-1171	146	51	𝜑30	𝜑30	NOUN
cana-1171	146	52	,	,	PUNCT
cana-1171	146	53	…	…	PUNCT
cana-1171	146	54	,	,	PUNCT
cana-1171	146	55	𝜑𝑛0	𝜑𝑛0	PROPN
cana-1171	146	56	)	)	PUNCT
cana-1171	146	57	,	,	PUNCT
cana-1171	146	58	𝑝2	𝑝2	NOUN
cana-1171	146	59	:	:	PUNCT
cana-1171	146	60	𝐷𝛼𝑖𝜑𝑖2	𝐷𝛼𝑖𝜑𝑖2	PROPN
cana-1171	146	61	=	=	SYM
cana-1171	146	62	𝑓𝑖2(𝑡	𝑓𝑖2(𝑡	PROPN
cana-1171	146	63	,	,	PUNCT
cana-1171	146	64	𝜑10	𝜑10	ADJ
cana-1171	146	65	,	,	PUNCT
cana-1171	146	66	𝜑20	𝜑20	ADJ
cana-1171	146	67	,	,	PUNCT
cana-1171	146	68	𝜑30	𝜑30	NOUN
cana-1171	146	69	,	,	PUNCT
cana-1171	146	70	…	…	PUNCT
cana-1171	146	71	,	,	PUNCT
cana-1171	146	72	𝜑𝑛0	𝜑𝑛0	PROPN
cana-1171	146	73	,	,	PUNCT
cana-1171	146	74	𝜑11	𝜑11	PROPN
cana-1171	146	75	,	,	PUNCT
cana-1171	146	76	𝜑21	𝜑21	NOUN
cana-1171	146	77	,	,	PUNCT
cana-1171	146	78	𝜑31	𝜑31	PROPN
cana-1171	146	79	,	,	PUNCT
cana-1171	146	80	…	…	PUNCT
cana-1171	146	81	,	,	PUNCT
cana-1171	146	82	𝜑𝑛1	𝜑𝑛1	NOUN
cana-1171	146	83	)	)	PUNCT
cana-1171	146	84	,	,	PUNCT
cana-1171	146	85	𝑝3	𝑝3	ADV
cana-1171	146	86	:	:	PUNCT
cana-1171	146	87	𝐷𝛼𝑖𝜑𝑖3	𝐷𝛼𝑖𝜑𝑖3	PROPN
cana-1171	146	88	=	=	SYM
cana-1171	146	89	𝑓𝑖3(𝑡	𝑓𝑖3(𝑡	PROPN
cana-1171	146	90	,	,	PUNCT
cana-1171	146	91	𝜑10	𝜑10	ADJ
cana-1171	146	92	,	,	PUNCT
cana-1171	146	93	𝜑20	𝜑20	ADJ
cana-1171	146	94	,	,	PUNCT
cana-1171	146	95	𝜑30	𝜑30	NOUN
cana-1171	146	96	,	,	PUNCT
cana-1171	146	97	…	…	PUNCT
cana-1171	146	98	,	,	PUNCT
cana-1171	146	99	𝜑𝑛0	𝜑𝑛0	PROPN
cana-1171	146	100	,	,	PUNCT
cana-1171	146	101	𝜑11	𝜑11	PROPN
cana-1171	146	102	,	,	PUNCT
cana-1171	146	103	𝜑21	𝜑21	NOUN
cana-1171	146	104	,	,	PUNCT
cana-1171	146	105	𝜑31	𝜑31	PROPN
cana-1171	146	106	,	,	PUNCT
cana-1171	146	107	…	…	PUNCT
cana-1171	146	108	,	,	PUNCT
cana-1171	146	109	𝜑𝑛1	𝜑𝑛1	NOUN
cana-1171	146	110	,	,	PUNCT
cana-1171	146	111	𝜑11	𝜑11	PROPN
cana-1171	146	112	,	,	PUNCT
cana-1171	146	113	𝜑22	𝜑22	PROPN
cana-1171	146	114	,	,	PUNCT
cana-1171	146	115	𝜑32	𝜑32	ADJ
cana-1171	146	116	,	,	PUNCT
cana-1171	146	117	…	…	PUNCT
cana-1171	146	118	,	,	PUNCT
cana-1171	146	119	𝜑𝑛2	𝜑𝑛2	PROPN
cana-1171	146	120	)	)	PUNCT
cana-1171	146	121	,	,	PUNCT
cana-1171	146	122	etc	etc	X
cana-1171	146	123	.	.	X
cana-1171	146	124	,	,	PUNCT
cana-1171	146	125	where	where	SCONJ
cana-1171	146	126	the	the	DET
cana-1171	146	127	functions	function	NOUN
cana-1171	146	128	satisfies	satisfy	VERB
cana-1171	146	129	the	the	DET
cana-1171	146	130	following	follow	VERB
cana-1171	146	131	equation	equation	NOUN
cana-1171	146	132	𝑓𝑖(𝑡	𝑓𝑖(𝑡	NOUN
cana-1171	146	133	,	,	PUNCT
cana-1171	146	134	𝜑10	𝜑10	ADJ
cana-1171	146	135	+	+	NOUN
cana-1171	146	136	𝑝𝜑11	𝑝𝜑11	PROPN
cana-1171	146	137	+	+	NUM
cana-1171	146	138	𝑝2𝜑12	𝑝2𝜑12	NOUN
cana-1171	147	1	+	+	CCONJ
cana-1171	147	2	⋯	⋯	PROPN
cana-1171	147	3	,	,	PUNCT
cana-1171	147	4	𝜑𝑛0	𝜑𝑛0	PROPN
cana-1171	147	5	+	+	CCONJ
cana-1171	148	1	𝑝𝜑𝑛1	𝑝𝜑𝑛1	PROPN
cana-1171	148	2	+	+	CCONJ
cana-1171	148	3	𝑝2𝜑𝑛2	𝑝2𝜑𝑛2	PROPN
cana-1171	148	4	+	+	CCONJ
cana-1171	148	5	⋯	⋯	NOUN
cana-1171	148	6	)	)	PUNCT
cana-1171	148	7	=	=	SYM
cana-1171	148	8	𝑓𝑖1(𝑡	𝑓𝑖1(𝑡	PROPN
cana-1171	148	9	,	,	PUNCT
cana-1171	148	10	𝜑10	𝜑10	ADJ
cana-1171	148	11	,	,	PUNCT
cana-1171	148	12	𝜑20	𝜑20	ADJ
cana-1171	148	13	,	,	PUNCT
cana-1171	148	14	𝜑30	𝜑30	NOUN
cana-1171	148	15	,	,	PUNCT
cana-1171	148	16	…	…	PUNCT
cana-1171	148	17	,	,	PUNCT
cana-1171	148	18	𝜑𝑛0	𝜑𝑛0	PROPN
cana-1171	148	19	)	)	PUNCT
cana-1171	149	1	+	+	CCONJ
cana-1171	149	2	𝑝𝑓𝑖2(𝑡	𝑝𝑓𝑖2(𝑡	ADJ
cana-1171	149	3	,	,	PUNCT
cana-1171	149	4	𝜑10	𝜑10	ADJ
cana-1171	149	5	,	,	PUNCT
cana-1171	149	6	𝜑20	𝜑20	ADJ
cana-1171	149	7	,	,	PUNCT
cana-1171	149	8	𝜑30	𝜑30	NOUN
cana-1171	149	9	,	,	PUNCT
cana-1171	149	10	…	…	PUNCT
cana-1171	149	11	,	,	PUNCT
cana-1171	149	12	𝜑𝑛0	𝜑𝑛0	PROPN
cana-1171	149	13	,	,	PUNCT
cana-1171	149	14	𝜑11	𝜑11	PROPN
cana-1171	149	15	,	,	PUNCT
cana-1171	149	16	𝜑21	𝜑21	NOUN
cana-1171	149	17	,	,	PUNCT
cana-1171	149	18	𝜑31	𝜑31	PROPN
cana-1171	149	19	,	,	PUNCT
cana-1171	149	20	…	…	PUNCT
cana-1171	149	21	,	,	PUNCT
cana-1171	149	22	𝜑𝑛1	𝜑𝑛1	NOUN
cana-1171	149	23	)	)	PUNCT
cana-1171	150	1	+	+	CCONJ
cana-1171	150	2	𝑝2𝑓𝑖3(𝑡	𝑝2𝑓𝑖3(𝑡	PROPN
cana-1171	150	3	,	,	PUNCT
cana-1171	150	4	𝜑10	𝜑10	ADJ
cana-1171	150	5	,	,	PUNCT
cana-1171	150	6	𝜑20	𝜑20	ADJ
cana-1171	150	7	,	,	PUNCT
cana-1171	150	8	𝜑30	𝜑30	NOUN
cana-1171	150	9	,	,	PUNCT
cana-1171	150	10	…	…	PUNCT
cana-1171	150	11	,	,	PUNCT
cana-1171	150	12	𝜑𝑛0	𝜑𝑛0	PROPN
cana-1171	150	13	,	,	PUNCT
cana-1171	150	14	𝜑11	𝜑11	PROPN
cana-1171	150	15	,	,	PUNCT
cana-1171	150	16	𝜑21	𝜑21	NOUN
cana-1171	150	17	,	,	PUNCT
cana-1171	150	18	𝜑31	𝜑31	PROPN
cana-1171	150	19	,	,	PUNCT
cana-1171	150	20	…	…	PUNCT
cana-1171	150	21	,	,	PUNCT
cana-1171	150	22	𝜑𝑛1	𝜑𝑛1	NOUN
cana-1171	150	23	,	,	PUNCT
cana-1171	150	24	𝜑11	𝜑11	PROPN
cana-1171	150	25	,	,	PUNCT
cana-1171	150	26	𝜑22	𝜑22	PROPN
cana-1171	150	27	,	,	PUNCT
cana-1171	150	28	𝜑32	𝜑32	ADJ
cana-1171	150	29	,	,	PUNCT
cana-1171	150	30	…	…	PUNCT
cana-1171	150	31	,	,	PUNCT
cana-1171	150	32	𝜑𝑛2	𝜑𝑛2	PROPN
cana-1171	150	33	)	)	PUNCT
cana-1171	151	1	+	+	CCONJ
cana-1171	151	2	⋯	⋯	ADP
cana-1171	151	3	it	it	PRON
cana-1171	151	4	can	can	AUX
cana-1171	151	5	be	be	AUX
cana-1171	151	6	easily	easily	ADV
cana-1171	151	7	solve	solve	VERB
cana-1171	151	8	by	by	ADP
cana-1171	151	9	applying	apply	VERB
cana-1171	151	10	the	the	DET
cana-1171	151	11	ℐ𝛼𝑖	ℐ𝛼𝑖	PROPN
cana-1171	151	12	that	that	PRON
cana-1171	151	13	is	be	AUX
cana-1171	151	14	the	the	DET
cana-1171	151	15	inverse	inverse	NOUN
cana-1171	151	16	of	of	ADP
cana-1171	151	17	the	the	DET
cana-1171	151	18	operator	operator	NOUN
cana-1171	151	19	𝐷𝛼𝑖.	𝐷𝛼𝑖.	PROPN
cana-1171	151	20	by	by	ADP
cana-1171	151	21	setting	set	VERB
cana-1171	151	22	𝑝	𝑝	NOUN
cana-1171	151	23	=	=	SYM
cana-1171	151	24	1	1	NUM
cana-1171	151	25	in	in	ADP
cana-1171	151	26	(	(	PUNCT
cana-1171	151	27	28	28	NUM
cana-1171	151	28	)	)	PUNCT
cana-1171	151	29	,	,	PUNCT
cana-1171	151	30	hence	hence	ADV
cana-1171	151	31	the	the	DET
cana-1171	151	32	components	component	NOUN
cana-1171	152	1	𝜑𝑖𝑘(𝑘	𝜑𝑖𝑘(𝑘	NOUN
cana-1171	152	2	=	=	SYM
cana-1171	152	3	0,1,2	0,1,2	NUM
cana-1171	152	4	,	,	PUNCT
cana-1171	152	5	…	…	PUNCT
cana-1171	152	6	)	)	PUNCT
cana-1171	152	7	of	of	ADP
cana-1171	152	8	the	the	DET
cana-1171	152	9	hpm	hpm	NOUN
cana-1171	152	10	solution	solution	NOUN
cana-1171	152	11	can	can	AUX
cana-1171	152	12	be	be	AUX
cana-1171	152	13	determined	determine	VERB
cana-1171	152	14	.	.	PUNCT
cana-1171	153	1	7.the	7.the	DET
cana-1171	153	2	hpm	hpm	NOUN
cana-1171	153	3	of	of	ADP
cana-1171	153	4	solving	solve	VERB
cana-1171	153	5	system	system	NOUN
cana-1171	153	6	of	of	ADP
cana-1171	153	7	fdes	fde	NOUN
cana-1171	153	8	(	(	PUNCT
cana-1171	153	9	19)-(21	19)-(21	ADV
cana-1171	153	10	)	)	PUNCT
cana-1171	153	11	construct	construct	VERB
cana-1171	153	12	the	the	DET
cana-1171	153	13	following	follow	VERB
cana-1171	153	14	homotopy	homotopy	NOUN
cana-1171	153	15	𝐷𝑦	𝐷𝑦	PROPN
cana-1171	153	16	2𝛼	2𝛼	PROPN
cana-1171	153	17	0	0	NUM
cana-1171	153	18	𝐶𝑆	𝐶𝑆	PROPN
cana-1171	153	19	𝑢(𝑦	𝑢(𝑦	NOUN
cana-1171	153	20	)	)	PUNCT
cana-1171	153	21	=	=	SYM
cana-1171	153	22	𝑝(−𝜆1	𝑝(−𝜆1	NOUN
cana-1171	153	23	𝛼𝑤𝑣	𝛼𝑤𝑣	NOUN
cana-1171	153	24	+	+	CCONJ
cana-1171	153	25	𝐶𝛼𝑢𝑣𝑤	𝐶𝛼𝑢𝑣𝑤	PROPN
cana-1171	153	26	)	)	PUNCT
cana-1171	153	27	(	(	PUNCT
cana-1171	153	28	30	30	X
cana-1171	153	29	)	)	PUNCT
cana-1171	154	1	𝐷𝑦	𝐷𝑦	PROPN
cana-1171	154	2	2𝛼	2𝛼	PROPN
cana-1171	154	3	0	0	NUM
cana-1171	154	4	𝐶𝑆	𝐶𝑆	PROPN
cana-1171	154	5	𝑣(𝑦	𝑣(𝑦	PROPN
cana-1171	154	6	)	)	PUNCT
cana-1171	154	7	=	=	PUNCT
cana-1171	154	8	𝑝(𝜆1	𝑝(𝜆1	ADJ
cana-1171	154	9	𝛼𝑤𝑣	𝛼𝑤𝑣	NOUN
cana-1171	154	10	−	−	PROPN
cana-1171	154	11	𝐶𝛼𝑢𝑣𝑤	𝐶𝛼𝑢𝑣𝑤	PROPN
cana-1171	154	12	)	)	PUNCT
cana-1171	154	13	(	(	PUNCT
cana-1171	154	14	31	31	X
cana-1171	154	15	)	)	PUNCT
cana-1171	155	1	𝐷𝑦	𝐷𝑦	PROPN
cana-1171	155	2	2𝛼	2𝛼	PROPN
cana-1171	155	3	0	0	X
cana-1171	155	4	𝐶𝑆	𝐶𝑆	PROPN
cana-1171	155	5	𝑤(𝑦	𝑤(𝑦	PRON
cana-1171	155	6	)	)	PUNCT
cana-1171	155	7	=	=	SYM
cana-1171	155	8	𝑝(𝜆1	𝑝(𝜆1	ADJ
cana-1171	155	9	𝛼𝑤𝑣	𝛼𝑤𝑣	NOUN
cana-1171	155	10	−	−	PROPN
cana-1171	155	11	𝐶𝛼𝑢𝑣𝑤	𝐶𝛼𝑢𝑣𝑤	PROPN
cana-1171	155	12	)	)	PUNCT
cana-1171	155	13	(	(	PUNCT
cana-1171	155	14	32	32	NUM
cana-1171	155	15	)	)	PUNCT
cana-1171	155	16	by	by	ADP
cana-1171	155	17	perturbation	perturbation	NOUN
cana-1171	155	18	technique	technique	NOUN
cana-1171	155	19	,	,	PUNCT
cana-1171	155	20	𝑢	𝑢	X
cana-1171	155	21	,	,	PUNCT
cana-1171	155	22	𝑣	𝑣	X
cana-1171	155	23	and	and	CCONJ
cana-1171	155	24	𝑤	𝑤	X
cana-1171	155	25	can	can	AUX
cana-1171	155	26	be	be	AUX
cana-1171	155	27	written	write	VERB
cana-1171	155	28	as	as	ADP
cana-1171	155	29	a	a	DET
cana-1171	155	30	following	follow	VERB
cana-1171	155	31	series	series	NOUN
cana-1171	155	32	in	in	ADP
cana-1171	155	33	𝑝	𝑝	PROPN
cana-1171	155	34	:	:	PUNCT
cana-1171	155	35	𝑢	𝑢	X
cana-1171	155	36	=	=	X
cana-1171	155	37	𝑢0	𝑢0	PROPN
cana-1171	155	38	+	+	CCONJ
cana-1171	155	39	𝑝𝑢1	𝑝𝑢1	NOUN
cana-1171	155	40	+	+	X
cana-1171	155	41	𝑝2𝑢2	𝑝2𝑢2	X
cana-1171	156	1	+	+	CCONJ
cana-1171	156	2	⋯	⋯	PROPN
cana-1171	156	3	(	(	PUNCT
cana-1171	156	4	33	33	NUM
cana-1171	156	5	)	)	PUNCT
cana-1171	156	6	𝑣	𝑣	NOUN
cana-1171	156	7	=	=	SYM
cana-1171	156	8	𝑣0	𝑣0	PROPN
cana-1171	156	9	+	+	CCONJ
cana-1171	156	10	𝑝𝑣1	𝑝𝑣1	PROPN
cana-1171	156	11	+	+	CCONJ
cana-1171	156	12	𝑝2𝑣2	𝑝2𝑣2	PROPN
cana-1171	156	13	+	+	SYM
cana-1171	156	14	⋯	⋯	PROPN
cana-1171	156	15	(	(	PUNCT
cana-1171	156	16	34	34	NUM
cana-1171	156	17	)	)	PUNCT
cana-1171	156	18	communications	communication	NOUN
cana-1171	156	19	on	on	ADP
cana-1171	156	20	applied	apply	VERB
cana-1171	156	21	nonlinear	nonlinear	ADJ
cana-1171	156	22	analysis	analysis	NOUN
cana-1171	156	23	issn	issn	NOUN
cana-1171	156	24	:	:	PUNCT
cana-1171	156	25	1074	1074	NUM
cana-1171	156	26	-	-	PUNCT
cana-1171	156	27	133x	133x	NUM
cana-1171	156	28	vol	vol	NOUN
cana-1171	156	29	31	31	NUM
cana-1171	156	30	no	no	NOUN
cana-1171	156	31	.	.	PUNCT
cana-1171	157	1	6s	6s	NUM
cana-1171	157	2	(	(	PUNCT
cana-1171	157	3	2024	2024	NUM
cana-1171	157	4	)	)	PUNCT
cana-1171	157	5	122	122	NUM
cana-1171	157	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1171	157	7	𝑤	𝑤	SYM
cana-1171	157	8	=	=	SYM
cana-1171	157	9	𝑤0	𝑤0	PROPN
cana-1171	157	10	+	+	CCONJ
cana-1171	157	11	𝑝𝑤1	𝑝𝑤1	NOUN
cana-1171	157	12	+	+	SYM
cana-1171	157	13	𝑝2𝑤2	𝑝2𝑤2	X
cana-1171	157	14	+	+	CCONJ
cana-1171	157	15	⋯	⋯	PROPN
cana-1171	157	16	(	(	PUNCT
cana-1171	157	17	35	35	NUM
cana-1171	157	18	)	)	PUNCT
cana-1171	157	19	substituting	substituting	NOUN
cana-1171	157	20	(	(	PUNCT
cana-1171	157	21	33	33	NUM
cana-1171	157	22	)	)	PUNCT
cana-1171	157	23	−	−	PROPN
cana-1171	157	24	(	(	PUNCT
cana-1171	157	25	35	35	NUM
cana-1171	157	26	)	)	PUNCT
cana-1171	157	27	into	into	ADP
cana-1171	157	28	(	(	PUNCT
cana-1171	157	29	30	30	NUM
cana-1171	157	30	)	)	PUNCT
cana-1171	157	31	−	−	PROPN
cana-1171	157	32	(	(	PUNCT
cana-1171	157	33	32	32	NUM
cana-1171	157	34	)	)	PUNCT
cana-1171	157	35	and	and	CCONJ
cana-1171	157	36	equating	equate	VERB
cana-1171	157	37	terms	term	NOUN
cana-1171	157	38	of	of	ADP
cana-1171	157	39	the	the	DET
cana-1171	157	40	same	same	ADJ
cana-1171	157	41	powers	power	NOUN
cana-1171	157	42	of	of	ADP
cana-1171	157	43	𝑝	𝑝	NOUN
cana-1171	157	44	yields	yield	NOUN
cana-1171	157	45	the	the	DET
cana-1171	157	46	following	follow	VERB
cana-1171	157	47	three	three	NUM
cana-1171	157	48	sets	set	NOUN
cana-1171	157	49	of	of	ADP
cana-1171	157	50	equations	equation	NOUN
cana-1171	157	51	𝑝0	𝑝0	PROPN
cana-1171	157	52	∶	∶	NOUN
cana-1171	157	53	𝐷𝑦	𝐷𝑦	PROPN
cana-1171	157	54	2𝛼	2𝛼	PROPN
cana-1171	157	55	0	0	NUM
cana-1171	157	56	𝐶𝑆	𝐶𝑆	PROPN
cana-1171	157	57	𝑢0	𝑢0	PROPN
cana-1171	157	58	=	=	SYM
cana-1171	157	59	0	0	NUM
cana-1171	157	60	𝑝0	𝑝0	PROPN
cana-1171	157	61	∶	∶	NOUN
cana-1171	158	1	𝐷𝑦	𝐷𝑦	PROPN
cana-1171	158	2	2𝛼	2𝛼	PROPN
cana-1171	158	3	0	0	NUM
cana-1171	158	4	𝐶𝑆	𝐶𝑆	PROPN
cana-1171	158	5	𝑣0	𝑣0	PROPN
cana-1171	158	6	=	=	SYM
cana-1171	158	7	0	0	NUM
cana-1171	158	8	𝑝1	𝑝1	NOUN
cana-1171	158	9	∶	∶	NOUN
cana-1171	158	10	𝐷𝑦	𝐷𝑦	PROPN
cana-1171	158	11	2𝛼	2𝛼	PROPN
cana-1171	158	12	0	0	NUM
cana-1171	158	13	𝐶𝑆	𝐶𝑆	PROPN
cana-1171	158	14	𝑢1	𝑢1	PROPN
cana-1171	158	15	=	=	PROPN
cana-1171	158	16	−𝜆1	−𝜆1	PROPN
cana-1171	159	1	𝛼𝑤0𝑣0	𝛼𝑤0𝑣0	PROPN
cana-1171	159	2	+	+	NUM
cana-1171	159	3	𝐶𝛼𝑢0𝑣0𝑤0	𝐶𝛼𝑢0𝑣0𝑤0	NUM
cana-1171	159	4	𝑝1	𝑝1	NOUN
cana-1171	159	5	∶	∶	NOUN
cana-1171	159	6	𝐷𝑦	𝐷𝑦	PROPN
cana-1171	159	7	2𝛼	2𝛼	PROPN
cana-1171	159	8	0	0	NUM
cana-1171	159	9	𝐶𝑆	𝐶𝑆	PROPN
cana-1171	159	10	𝑣1	𝑣1	NOUN
cana-1171	159	11	=	=	PRON
cana-1171	159	12	𝜆1	𝜆1	VERB
cana-1171	159	13	𝛼𝑤0𝑣0	𝛼𝑤0𝑣0	PROPN
cana-1171	159	14	−	−	NUM
cana-1171	159	15	𝐶𝛼𝑢0𝑣0𝑤0	𝐶𝛼𝑢0𝑣0𝑤0	ADJ
cana-1171	159	16	⋮	⋮	NOUN
cana-1171	159	17	⋮	⋮	NOUN
cana-1171	159	18	𝑝0	𝑝0	PROPN
cana-1171	159	19	∶	∶	NOUN
cana-1171	160	1	𝐷𝑦	𝐷𝑦	PROPN
cana-1171	160	2	2𝛼	2𝛼	PROPN
cana-1171	160	3	0	0	NUM
cana-1171	160	4	𝐶𝑆	𝐶𝑆	PROPN
cana-1171	160	5	𝑤0	𝑤0	NOUN
cana-1171	160	6	=	=	SYM
cana-1171	160	7	0	0	NUM
cana-1171	160	8	𝑝1	𝑝1	NOUN
cana-1171	160	9	∶	∶	NOUN
cana-1171	160	10	𝐷𝑦	𝐷𝑦	PROPN
cana-1171	160	11	2𝛼	2𝛼	PROPN
cana-1171	160	12	0	0	NUM
cana-1171	160	13	𝐶𝑆	𝐶𝑆	PROPN
cana-1171	160	14	𝑤1	𝑤1	NOUN
cana-1171	160	15	=	=	PUNCT
cana-1171	160	16	𝜆1	𝜆1	VERB
cana-1171	160	17	𝛼𝑤0𝑣0	𝛼𝑤0𝑣0	PROPN
cana-1171	160	18	−	−	PROPN
cana-1171	160	19	𝐶𝛼𝑢0𝑣0𝑤0	𝐶𝛼𝑢0𝑣0𝑤0	ADJ
cana-1171	160	20	⋮	⋮	NOUN
cana-1171	160	21	applying	apply	VERB
cana-1171	160	22	the	the	DET
cana-1171	160	23	operator	operator	NOUN
cana-1171	160	24	of	of	ADP
cana-1171	160	25	ℐ𝛼	ℐ𝛼	PROPN
cana-1171	160	26	which	which	PRON
cana-1171	160	27	is	be	AUX
cana-1171	160	28	inverse	inverse	ADJ
cana-1171	160	29	operator	operator	NOUN
cana-1171	160	30	of	of	ADP
cana-1171	160	31	𝐷𝛼	𝐷𝛼	PROPN
cana-1171	160	32	in	in	ADP
cana-1171	160	33	to	to	ADP
cana-1171	160	34	𝑢0	𝑢0	PROPN
cana-1171	160	35	,	,	PUNCT
cana-1171	160	36	𝑣0	𝑣0	PROPN
cana-1171	160	37	,	,	PUNCT
cana-1171	160	38	𝑤0	𝑤0	PROPN
cana-1171	160	39	,	,	PUNCT
cana-1171	160	40	𝑢1	𝑢1	PROPN
cana-1171	160	41	,	,	PUNCT
cana-1171	160	42	𝑣1	𝑣1	PROPN
cana-1171	160	43	,	,	PUNCT
cana-1171	160	44	𝑤1	𝑤1	VERB
cana-1171	160	45	,	,	PUNCT
cana-1171	160	46	…	…	PUNCT
cana-1171	160	47	𝑢0(𝑦	𝑢0(𝑦	X
cana-1171	160	48	)	)	PUNCT
cana-1171	160	49	=	=	PUNCT
cana-1171	160	50	(	(	PUNCT
cana-1171	160	51	1	1	NUM
cana-1171	160	52	−	−	NOUN
cana-1171	160	53	𝑠)𝑦	𝑠)𝑦	NOUN
cana-1171	160	54	+	+	CCONJ
cana-1171	160	55	𝑠	𝑠	NUM
cana-1171	160	56	,	,	PUNCT
cana-1171	160	57	𝑣0(𝑦	𝑣0(𝑦	X
cana-1171	160	58	)	)	PUNCT
cana-1171	160	59	=	=	SYM
cana-1171	161	1	(	(	PUNCT
cana-1171	161	2	𝑠	𝑠	NUM
cana-1171	161	3	−	−	PROPN
cana-1171	161	4	1)𝑦	1)𝑦	PROPN
cana-1171	161	5	+	+	CCONJ
cana-1171	161	6	(	(	PUNCT
cana-1171	161	7	1	1	NUM
cana-1171	161	8	−	−	PROPN
cana-1171	161	9	𝑠	𝑠	NOUN
cana-1171	161	10	)	)	PUNCT
cana-1171	161	11	,	,	PUNCT
cana-1171	161	12	𝑤0(𝑦	𝑤0(𝑦	NOUN
cana-1171	161	13	)	)	PUNCT
cana-1171	161	14	=	=	PUNCT
cana-1171	161	15	𝛾	𝛾	ADP
cana-1171	161	16	𝑢1(𝑦	𝑢1(𝑦	PROPN
cana-1171	161	17	)	)	PUNCT
cana-1171	161	18	=	=	SYM
cana-1171	162	1	𝛾(1	𝛾(1	NOUN
cana-1171	162	2	−	−	PROPN
cana-1171	162	3	𝑠)[𝐶𝛼𝑠	𝑠)[𝐶𝛼𝑠	PROPN
cana-1171	162	4	−	−	PROPN
cana-1171	162	5	𝜆1	𝜆1	NOUN
cana-1171	162	6	𝛼	𝛼	X
cana-1171	162	7	]	]	X
cana-1171	162	8	𝑦2𝛼	𝑦2𝛼	VERB
cana-1171	162	9	𝛤(2𝛼	𝛤(2𝛼	VERB
cana-1171	162	10	+	+	CCONJ
cana-1171	162	11	1	1	NUM
cana-1171	162	12	)	)	PUNCT
cana-1171	163	1	+	+	CCONJ
cana-1171	163	2	𝛾(𝑠	𝛾(𝑠	PROPN
cana-1171	163	3	−	−	NOUN
cana-1171	163	4	1)[𝐶𝛼(𝑠	1)[𝐶𝛼(𝑠	NUM
cana-1171	163	5	−	−	NOUN
cana-1171	163	6	1	1	NUM
cana-1171	163	7	)	)	PUNCT
cana-1171	163	8	−	−	NOUN
cana-1171	163	9	𝜆1	𝜆1	NOUN
cana-1171	163	10	𝛼	𝛼	PRON
cana-1171	163	11	+	+	CCONJ
cana-1171	163	12	𝐶𝛼𝑠	𝐶𝛼𝑠	PROPN
cana-1171	163	13	]	]	PUNCT
cana-1171	163	14	𝑦2𝛼+1	𝑦2𝛼+1	CCONJ
cana-1171	163	15	𝛤(2𝛼	𝛤(2𝛼	X
cana-1171	163	16	+	+	CCONJ
cana-1171	163	17	2	2	X
cana-1171	163	18	)	)	PUNCT
cana-1171	163	19	−𝐶𝛼𝛾(1	−𝐶𝛼𝛾(1	NOUN
cana-1171	163	20	−	−	NOUN
cana-1171	163	21	𝑠)2	𝑠)2	NOUN
cana-1171	163	22	𝑦2𝛼+2	𝑦2𝛼+2	NOUN
cana-1171	163	23	𝛤(2𝛼	𝛤(2𝛼	X
cana-1171	163	24	+	+	CCONJ
cana-1171	163	25	3	3	X
cana-1171	163	26	)	)	PUNCT
cana-1171	163	27	+	+	CCONJ
cana-1171	163	28	{	{	PUNCT
cana-1171	163	29	−𝛾(1	−𝛾(1	NOUN
cana-1171	163	30	−	−	NOUN
cana-1171	163	31	𝑠)[𝐶𝛼𝑠	𝑠)[𝐶𝛼𝑠	PROPN
cana-1171	163	32	−	−	PROPN
cana-1171	163	33	𝜆1	𝜆1	NOUN
cana-1171	163	34	𝛼	𝛼	X
cana-1171	163	35	]	]	X
cana-1171	163	36	1	1	NUM
cana-1171	163	37	𝛤(2𝛼	𝛤(2𝛼	ADJ
cana-1171	163	38	+	+	CCONJ
cana-1171	163	39	1	1	NUM
cana-1171	163	40	)	)	PUNCT
cana-1171	163	41	−	−	ADP
cana-1171	163	42	𝛾(𝑠	𝛾(𝑠	PROPN
cana-1171	163	43	−	−	PROPN
cana-1171	163	44	1)[𝐶𝛼(𝑠	1)[𝐶𝛼(𝑠	NUM
cana-1171	163	45	−	−	NOUN
cana-1171	163	46	1	1	NUM
cana-1171	163	47	)	)	PUNCT
cana-1171	163	48	−	−	NOUN
cana-1171	163	49	𝜆1	𝜆1	NOUN
cana-1171	163	50	𝛼	𝛼	PRON
cana-1171	164	1	+	+	CCONJ
cana-1171	164	2	𝐶𝛼𝑠	𝐶𝛼𝑠	PROPN
cana-1171	164	3	]	]	X
cana-1171	164	4	1	1	NUM
cana-1171	164	5	𝛤(2𝛼	𝛤(2𝛼	ADJ
cana-1171	164	6	+	+	CCONJ
cana-1171	164	7	2	2	NUM
cana-1171	164	8	)	)	PUNCT
cana-1171	164	9	+	+	CCONJ
cana-1171	164	10	𝛾(1	𝛾(1	NOUN
cana-1171	164	11	−	−	NOUN
cana-1171	164	12	𝑠)2	𝑠)2	NOUN
cana-1171	164	13	2	2	NUM
cana-1171	164	14	𝛤(2𝛼	𝛤(2𝛼	X
cana-1171	164	15	+	+	X
cana-1171	164	16	3	3	NUM
cana-1171	164	17	)	)	PUNCT
cana-1171	164	18	}	}	PUNCT
cana-1171	164	19	𝑦𝛼	𝑦𝛼	ADP
cana-1171	164	20	𝑣1(𝑦	𝑣1(𝑦	PROPN
cana-1171	164	21	)	)	PUNCT
cana-1171	165	1	=	=	SYM
cana-1171	165	2	𝛾(1	𝛾(1	PROPN
cana-1171	165	3	−	−	PROPN
cana-1171	165	4	𝑠)[𝜆1	𝑠)[𝜆1	PROPN
cana-1171	165	5	𝛼	𝛼	PRON
cana-1171	165	6	−	−	PROPN
cana-1171	165	7	𝐶𝛼𝑠	𝐶𝛼𝑠	PROPN
cana-1171	165	8	]	]	PUNCT
cana-1171	165	9	𝑦2𝛼	𝑦2𝛼	VERB
cana-1171	165	10	𝛤(2𝛼	𝛤(2𝛼	VERB
cana-1171	165	11	+	+	CCONJ
cana-1171	165	12	1	1	NUM
cana-1171	165	13	)	)	PUNCT
cana-1171	165	14	+	+	CCONJ
cana-1171	165	15	𝛾(𝑠	𝛾(𝑠	PROPN
cana-1171	165	16	−	−	PROPN
cana-1171	165	17	1)[𝜆1	1)[𝜆1	NUM
cana-1171	165	18	𝛼	𝛼	NOUN
cana-1171	165	19	−	−	PROPN
cana-1171	165	20	𝐶𝛼𝑠	𝐶𝛼𝑠	PROPN
cana-1171	165	21	−	−	NOUN
cana-1171	165	22	𝐶𝛼(𝑠	𝐶𝛼(𝑠	NOUN
cana-1171	165	23	−	−	PROPN
cana-1171	165	24	1	1	NUM
cana-1171	165	25	)	)	PUNCT
cana-1171	165	26	]	]	PUNCT
cana-1171	166	1	𝑦2𝛼+1	𝑦2𝛼+1	CCONJ
cana-1171	166	2	𝛤(2𝛼	𝛤(2𝛼	X
cana-1171	166	3	+	+	CCONJ
cana-1171	166	4	2	2	X
cana-1171	166	5	)	)	PUNCT
cana-1171	166	6	+	+	NOUN
cana-1171	166	7	𝐶𝛼𝛾(1	𝐶𝛼𝛾(1	ADJ
cana-1171	166	8	−	−	NOUN
cana-1171	166	9	𝑠)2	𝑠)2	NOUN
cana-1171	166	10	𝑦2𝛼+2	𝑦2𝛼+2	NOUN
cana-1171	166	11	𝛤(2𝛼	𝛤(2𝛼	X
cana-1171	166	12	+	+	CCONJ
cana-1171	166	13	3	3	X
cana-1171	166	14	)	)	PUNCT
cana-1171	166	15	+	+	CCONJ
cana-1171	166	16	{	{	PUNCT
cana-1171	166	17	−𝛾(1	−𝛾(1	NOUN
cana-1171	166	18	−	−	NOUN
cana-1171	166	19	𝑠)[𝐶𝛼𝑠	𝑠)[𝐶𝛼𝑠	PROPN
cana-1171	166	20	−	−	PROPN
cana-1171	166	21	𝜆1	𝜆1	NOUN
cana-1171	166	22	𝛼	𝛼	X
cana-1171	166	23	]	]	X
cana-1171	166	24	1	1	NUM
cana-1171	166	25	𝛤(2𝛼	𝛤(2𝛼	ADJ
cana-1171	166	26	+	+	CCONJ
cana-1171	166	27	1	1	NUM
cana-1171	166	28	)	)	PUNCT
cana-1171	166	29	−	−	ADP
cana-1171	166	30	𝛾(𝑠	𝛾(𝑠	PROPN
cana-1171	166	31	−	−	PROPN
cana-1171	166	32	1)[𝐶𝛼(𝑠	1)[𝐶𝛼(𝑠	NUM
cana-1171	166	33	−	−	NOUN
cana-1171	166	34	1	1	NUM
cana-1171	166	35	)	)	PUNCT
cana-1171	166	36	−	−	NOUN
cana-1171	166	37	𝜆1	𝜆1	NOUN
cana-1171	166	38	𝛼	𝛼	PRON
cana-1171	166	39	+	+	CCONJ
cana-1171	166	40	𝐶𝛼𝑠	𝐶𝛼𝑠	PROPN
cana-1171	166	41	]	]	X
cana-1171	166	42	1	1	NUM
cana-1171	166	43	𝛤(2𝛼	𝛤(2𝛼	ADJ
cana-1171	166	44	+	+	CCONJ
cana-1171	166	45	2	2	NUM
cana-1171	166	46	)	)	PUNCT
cana-1171	166	47	−	−	PROPN
cana-1171	166	48	𝛾(1	𝛾(1	NOUN
cana-1171	166	49	−	−	NOUN
cana-1171	166	50	𝑠)2	𝑠)2	NOUN
cana-1171	166	51	2	2	NUM
cana-1171	166	52	𝛤(2𝛼	𝛤(2𝛼	X
cana-1171	166	53	+	+	X
cana-1171	166	54	3	3	NUM
cana-1171	166	55	)	)	PUNCT
cana-1171	166	56	}	}	PUNCT
cana-1171	166	57	𝑦𝛼	𝑦𝛼	ADP
cana-1171	166	58	𝑤1(𝑦	𝑤1(𝑦	PROPN
cana-1171	166	59	)	)	PUNCT
cana-1171	166	60	=	=	SYM
cana-1171	166	61	𝛾(1	𝛾(1	PROPN
cana-1171	166	62	−	−	PROPN
cana-1171	166	63	𝑠)[𝜆1	𝑠)[𝜆1	PROPN
cana-1171	166	64	𝛼	𝛼	PRON
cana-1171	166	65	−	−	PROPN
cana-1171	166	66	𝐶𝛼𝑠	𝐶𝛼𝑠	PROPN
cana-1171	166	67	]	]	PUNCT
cana-1171	166	68	𝑦2𝛼	𝑦2𝛼	VERB
cana-1171	166	69	𝛤(2𝛼	𝛤(2𝛼	AUX
cana-1171	166	70	+	+	CCONJ
cana-1171	166	71	1	1	NUM
cana-1171	166	72	)	)	PUNCT
cana-1171	166	73	+	+	CCONJ
cana-1171	166	74	𝛾(𝑠	𝛾(𝑠	PROPN
cana-1171	166	75	−	−	PROPN
cana-1171	166	76	1)[𝜆1	1)[𝜆1	NUM
cana-1171	166	77	𝛼	𝛼	NOUN
cana-1171	166	78	−	−	PROPN
cana-1171	166	79	𝐶𝛼𝑠	𝐶𝛼𝑠	PROPN
cana-1171	166	80	−	−	NOUN
cana-1171	166	81	𝐶𝛼(𝑠	𝐶𝛼(𝑠	NOUN
cana-1171	166	82	−	−	PROPN
cana-1171	166	83	1	1	NUM
cana-1171	166	84	)	)	PUNCT
cana-1171	166	85	]	]	PUNCT
cana-1171	167	1	𝑦2𝛼+1	𝑦2𝛼+1	CCONJ
cana-1171	167	2	𝛤(2𝛼	𝛤(2𝛼	X
cana-1171	167	3	+	+	CCONJ
cana-1171	167	4	2	2	X
cana-1171	167	5	)	)	PUNCT
cana-1171	167	6	+	+	NOUN
cana-1171	167	7	𝐶𝛼𝛾(1	𝐶𝛼𝛾(1	ADJ
cana-1171	167	8	−	−	NOUN
cana-1171	167	9	𝑠)2	𝑠)2	NOUN
cana-1171	167	10	𝑦2𝛼+2	𝑦2𝛼+2	NOUN
cana-1171	167	11	𝛤(2𝛼	𝛤(2𝛼	X
cana-1171	167	12	+	+	CCONJ
cana-1171	167	13	3	3	X
cana-1171	167	14	)	)	PUNCT
cana-1171	167	15	+	+	CCONJ
cana-1171	167	16	{	{	PUNCT
cana-1171	167	17	−𝛾(1	−𝛾(1	NOUN
cana-1171	167	18	−	−	NOUN
cana-1171	167	19	𝑠)[𝐶𝛼𝑠	𝑠)[𝐶𝛼𝑠	PROPN
cana-1171	167	20	−	−	PROPN
cana-1171	167	21	𝜆1	𝜆1	NOUN
cana-1171	167	22	𝛼	𝛼	X
cana-1171	167	23	]	]	X
cana-1171	167	24	1	1	NUM
cana-1171	167	25	𝛤(2𝛼	𝛤(2𝛼	ADJ
cana-1171	167	26	+	+	CCONJ
cana-1171	167	27	1	1	NUM
cana-1171	167	28	)	)	PUNCT
cana-1171	167	29	−	−	ADP
cana-1171	167	30	𝛾(𝑠	𝛾(𝑠	PROPN
cana-1171	167	31	−	−	PROPN
cana-1171	167	32	1)[𝐶𝛼(𝑠	1)[𝐶𝛼(𝑠	NUM
cana-1171	167	33	−	−	NOUN
cana-1171	167	34	1	1	NUM
cana-1171	167	35	)	)	PUNCT
cana-1171	167	36	−	−	NOUN
cana-1171	167	37	𝜆1	𝜆1	NOUN
cana-1171	167	38	𝛼	𝛼	PRON
cana-1171	167	39	+	+	CCONJ
cana-1171	167	40	𝐶𝛼𝑠	𝐶𝛼𝑠	PROPN
cana-1171	167	41	]	]	X
cana-1171	167	42	1	1	NUM
cana-1171	167	43	𝛤(2𝛼	𝛤(2𝛼	ADJ
cana-1171	167	44	+	+	CCONJ
cana-1171	167	45	2	2	NUM
cana-1171	167	46	)	)	PUNCT
cana-1171	167	47	−	−	PROPN
cana-1171	167	48	𝛾(1	𝛾(1	NOUN
cana-1171	167	49	−	−	NOUN
cana-1171	167	50	𝑠)2	𝑠)2	NOUN
cana-1171	167	51	2	2	NUM
cana-1171	167	52	𝛤(2𝛼	𝛤(2𝛼	X
cana-1171	167	53	+	+	X
cana-1171	167	54	3	3	NUM
cana-1171	167	55	)	)	PUNCT
cana-1171	167	56	}	}	PUNCT
cana-1171	167	57	𝑦𝛼	𝑦𝛼	ADP
cana-1171	167	58	letting	let	VERB
cana-1171	167	59	𝑝	𝑝	NOUN
cana-1171	167	60	→	→	SYM
cana-1171	167	61	1	1	NUM
cana-1171	167	62	gives	give	VERB
cana-1171	167	63	therefore	therefore	ADV
cana-1171	167	64	,	,	PUNCT
cana-1171	167	65	communications	communication	NOUN
cana-1171	167	66	on	on	ADP
cana-1171	167	67	applied	apply	VERB
cana-1171	167	68	nonlinear	nonlinear	ADJ
cana-1171	167	69	analysis	analysis	NOUN
cana-1171	167	70	issn	issn	NOUN
cana-1171	167	71	:	:	PUNCT
cana-1171	167	72	1074	1074	NUM
cana-1171	167	73	-	-	PUNCT
cana-1171	167	74	133x	133x	NUM
cana-1171	167	75	vol	vol	NOUN
cana-1171	167	76	31	31	NUM
cana-1171	167	77	no	no	NOUN
cana-1171	167	78	.	.	PUNCT
cana-1171	168	1	6s	6s	NUM
cana-1171	168	2	(	(	PUNCT
cana-1171	168	3	2024	2024	NUM
cana-1171	168	4	)	)	PUNCT
cana-1171	168	5	123	123	NUM
cana-1171	168	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1171	168	7	𝑢(𝑦	𝑢(𝑦	NOUN
cana-1171	168	8	)	)	PUNCT
cana-1171	168	9	=	=	PUNCT
cana-1171	168	10	(	(	PUNCT
cana-1171	168	11	1	1	NUM
cana-1171	168	12	−	−	NOUN
cana-1171	168	13	𝑠)𝑦	𝑠)𝑦	NOUN
cana-1171	168	14	+	+	CCONJ
cana-1171	168	15	𝑠	𝑠	PROPN
cana-1171	168	16	+	+	CCONJ
cana-1171	169	1	𝛾(1	𝛾(1	PROPN
cana-1171	169	2	−	−	PROPN
cana-1171	169	3	𝑠)[𝐶𝛼𝑠	𝑠)[𝐶𝛼𝑠	PROPN
cana-1171	169	4	−	−	PROPN
cana-1171	169	5	𝜆1	𝜆1	NOUN
cana-1171	169	6	𝛼	𝛼	X
cana-1171	169	7	]	]	X
cana-1171	169	8	+	+	CCONJ
cana-1171	169	9	𝛾(𝑠	𝛾(𝑠	PROPN
cana-1171	169	10	−	−	PROPN
cana-1171	169	11	1)[𝐶𝛼(𝑠	1)[𝐶𝛼(𝑠	NUM
cana-1171	169	12	−	−	NOUN
cana-1171	169	13	1	1	NUM
cana-1171	169	14	)	)	PUNCT
cana-1171	169	15	−	−	NOUN
cana-1171	169	16	𝜆1	𝜆1	NOUN
cana-1171	169	17	𝛼	𝛼	PRON
cana-1171	169	18	+	+	CCONJ
cana-1171	169	19	𝐶𝛼𝑠	𝐶𝛼𝑠	PROPN
cana-1171	169	20	]	]	PUNCT
cana-1171	169	21	𝑦2𝛼+1	𝑦2𝛼+1	CCONJ
cana-1171	169	22	𝛤(2𝛼	𝛤(2𝛼	X
cana-1171	169	23	+	+	CCONJ
cana-1171	169	24	2	2	NUM
cana-1171	169	25	)	)	PUNCT
cana-1171	169	26	−	−	NOUN
cana-1171	169	27	𝐶𝛼𝛾(1	𝐶𝛼𝛾(1	NOUN
cana-1171	169	28	−	−	ADP
cana-1171	169	29	𝑠)2	𝑠)2	ADJ
cana-1171	169	30	𝑦2𝛼+2	𝑦2𝛼+2	NOUN
cana-1171	169	31	𝛤(2𝛼	𝛤(2𝛼	X
cana-1171	169	32	+	+	CCONJ
cana-1171	169	33	3	3	X
cana-1171	169	34	)	)	PUNCT
cana-1171	169	35	+	+	CCONJ
cana-1171	169	36	{	{	PUNCT
cana-1171	169	37	−𝛾(1	−𝛾(1	NOUN
cana-1171	169	38	−	−	NOUN
cana-1171	169	39	𝑠)[𝐶𝛼𝑠	𝑠)[𝐶𝛼𝑠	PROPN
cana-1171	169	40	−	−	PROPN
cana-1171	169	41	𝜆1	𝜆1	NOUN
cana-1171	169	42	𝛼	𝛼	X
cana-1171	169	43	]	]	X
cana-1171	169	44	1	1	NUM
cana-1171	169	45	𝛤(2𝛼	𝛤(2𝛼	ADJ
cana-1171	169	46	+	+	CCONJ
cana-1171	169	47	1	1	NUM
cana-1171	169	48	)	)	PUNCT
cana-1171	169	49	−	−	ADP
cana-1171	169	50	𝛾(𝑠	𝛾(𝑠	PROPN
cana-1171	169	51	−	−	PROPN
cana-1171	169	52	1)[𝐶𝛼(𝑠	1)[𝐶𝛼(𝑠	NUM
cana-1171	169	53	−	−	NOUN
cana-1171	169	54	1	1	NUM
cana-1171	169	55	)	)	PUNCT
cana-1171	169	56	−	−	NOUN
cana-1171	169	57	𝜆1	𝜆1	NOUN
cana-1171	169	58	𝛼	𝛼	PRON
cana-1171	170	1	+	+	CCONJ
cana-1171	170	2	𝐶𝛼𝑠	𝐶𝛼𝑠	PROPN
cana-1171	170	3	]	]	X
cana-1171	170	4	1	1	NUM
cana-1171	170	5	𝛤(2𝛼	𝛤(2𝛼	ADJ
cana-1171	170	6	+	+	CCONJ
cana-1171	170	7	2	2	NUM
cana-1171	170	8	)	)	PUNCT
cana-1171	170	9	+	+	CCONJ
cana-1171	170	10	𝛾(1	𝛾(1	NOUN
cana-1171	170	11	−	−	NOUN
cana-1171	170	12	𝑠)2	𝑠)2	NOUN
cana-1171	170	13	2	2	NUM
cana-1171	170	14	𝛤(2𝛼	𝛤(2𝛼	X
cana-1171	170	15	+	+	X
cana-1171	170	16	3	3	NUM
cana-1171	170	17	)	)	PUNCT
cana-1171	170	18	}	}	PUNCT
cana-1171	170	19	𝑦𝛼	𝑦𝛼	PROPN
cana-1171	170	20	(	(	PUNCT
cana-1171	170	21	36	36	NUM
cana-1171	170	22	)	)	PUNCT
cana-1171	170	23	𝑣(𝑦	𝑣(𝑦	PROPN
cana-1171	170	24	)	)	PUNCT
cana-1171	171	1	=	=	PRON
cana-1171	172	1	(	(	PUNCT
cana-1171	172	2	𝑠	𝑠	X
cana-1171	172	3	−	−	PROPN
cana-1171	172	4	1)𝑦	1)𝑦	PROPN
cana-1171	172	5	+	+	CCONJ
cana-1171	172	6	(	(	PUNCT
cana-1171	172	7	1	1	NUM
cana-1171	172	8	−	−	PROPN
cana-1171	172	9	𝑠	𝑠	NUM
cana-1171	172	10	)	)	PUNCT
cana-1171	173	1	+	+	CCONJ
cana-1171	173	2	𝛾(1	𝛾(1	PROPN
cana-1171	173	3	−	−	PROPN
cana-1171	173	4	𝑠)[𝜆1	𝑠)[𝜆1	PROPN
cana-1171	173	5	𝛼	𝛼	PRON
cana-1171	173	6	−	−	PROPN
cana-1171	173	7	𝐶𝛼𝑠	𝐶𝛼𝑠	PROPN
cana-1171	173	8	]	]	PUNCT
cana-1171	173	9	𝑦2𝛼	𝑦2𝛼	VERB
cana-1171	173	10	𝛤(2𝛼	𝛤(2𝛼	VERB
cana-1171	173	11	+	+	CCONJ
cana-1171	173	12	1	1	NUM
cana-1171	173	13	)	)	PUNCT
cana-1171	173	14	+	+	CCONJ
cana-1171	173	15	𝛾(𝑠	𝛾(𝑠	PROPN
cana-1171	173	16	−	−	PROPN
cana-1171	173	17	1)[𝜆1	1)[𝜆1	NUM
cana-1171	173	18	𝛼	𝛼	NOUN
cana-1171	173	19	−	−	PROPN
cana-1171	173	20	𝐶𝛼𝑠	𝐶𝛼𝑠	PROPN
cana-1171	173	21	−	−	NOUN
cana-1171	173	22	𝐶𝛼(𝑠	𝐶𝛼(𝑠	NOUN
cana-1171	173	23	−	−	PROPN
cana-1171	173	24	1	1	NUM
cana-1171	173	25	)	)	PUNCT
cana-1171	173	26	]	]	PUNCT
cana-1171	174	1	𝑦2𝛼+1	𝑦2𝛼+1	CCONJ
cana-1171	174	2	𝛤(2𝛼	𝛤(2𝛼	X
cana-1171	174	3	+	+	CCONJ
cana-1171	174	4	2	2	NUM
cana-1171	174	5	)	)	PUNCT
cana-1171	174	6	+	+	CCONJ
cana-1171	174	7	𝐶𝛼𝛾(1	𝐶𝛼𝛾(1	NUM
cana-1171	174	8	−	−	NOUN
cana-1171	174	9	𝑠)2	𝑠)2	NOUN
cana-1171	174	10	𝑦2𝛼+2	𝑦2𝛼+2	NOUN
cana-1171	174	11	𝛤(2𝛼	𝛤(2𝛼	X
cana-1171	174	12	+	+	CCONJ
cana-1171	174	13	3	3	X
cana-1171	174	14	)	)	PUNCT
cana-1171	174	15	+	+	CCONJ
cana-1171	174	16	{	{	PUNCT
cana-1171	174	17	−𝛾(1	−𝛾(1	NOUN
cana-1171	174	18	−	−	NOUN
cana-1171	174	19	𝑠)[𝐶𝛼𝑠	𝑠)[𝐶𝛼𝑠	PROPN
cana-1171	174	20	−	−	PROPN
cana-1171	174	21	𝜆1	𝜆1	NOUN
cana-1171	174	22	𝛼	𝛼	X
cana-1171	174	23	]	]	X
cana-1171	174	24	1	1	NUM
cana-1171	174	25	𝛤(2𝛼	𝛤(2𝛼	ADJ
cana-1171	174	26	+	+	CCONJ
cana-1171	174	27	1	1	NUM
cana-1171	174	28	)	)	PUNCT
cana-1171	174	29	−	−	ADP
cana-1171	174	30	𝛾(𝑠	𝛾(𝑠	NOUN
cana-1171	174	31	−	−	PROPN
cana-1171	174	32	1	1	NUM
cana-1171	174	33	)	)	PUNCT
cana-1171	175	1	[	[	X
cana-1171	175	2	𝐶𝛼(𝑠	𝐶𝛼(𝑠	ADJ
cana-1171	175	3	−	−	NUM
cana-1171	175	4	1	1	NUM
cana-1171	175	5	)	)	PUNCT
cana-1171	175	6	−	−	NOUN
cana-1171	175	7	𝜆1	𝜆1	NOUN
cana-1171	175	8	𝛼	𝛼	PRON
cana-1171	175	9	+	+	CCONJ
cana-1171	175	10	𝐶𝛼𝑠	𝐶𝛼𝑠	PROPN
cana-1171	175	11	]	]	X
cana-1171	175	12	1	1	NUM
cana-1171	175	13	𝛤(2𝛼	𝛤(2𝛼	ADJ
cana-1171	175	14	+	+	CCONJ
cana-1171	175	15	2	2	NUM
cana-1171	175	16	)	)	PUNCT
cana-1171	175	17	−	−	PROPN
cana-1171	175	18	𝛾(1	𝛾(1	NOUN
cana-1171	175	19	−	−	NOUN
cana-1171	175	20	𝑠)2	𝑠)2	NOUN
cana-1171	175	21	2	2	NUM
cana-1171	175	22	𝛤(2𝛼	𝛤(2𝛼	X
cana-1171	175	23	+	+	X
cana-1171	175	24	3	3	NUM
cana-1171	175	25	)	)	PUNCT
cana-1171	175	26	}	}	PUNCT
cana-1171	175	27	𝑦𝛼	𝑦𝛼	PROPN
cana-1171	175	28	(	(	PUNCT
cana-1171	175	29	37	37	NUM
cana-1171	175	30	)	)	PUNCT
cana-1171	175	31	𝑤(𝑦	𝑤(𝑦	PUNCT
cana-1171	175	32	)	)	PUNCT
cana-1171	175	33	=	=	SYM
cana-1171	176	1	𝛾	𝛾	AUX
cana-1171	176	2	+	+	X
cana-1171	176	3	𝛾(1	𝛾(1	PROPN
cana-1171	176	4	−	−	PROPN
cana-1171	176	5	𝑠)[𝜆1	𝑠)[𝜆1	PROPN
cana-1171	176	6	𝛼	𝛼	PRON
cana-1171	176	7	−	−	PROPN
cana-1171	176	8	𝐶𝛼𝑠	𝐶𝛼𝑠	PROPN
cana-1171	176	9	]	]	PUNCT
cana-1171	176	10	𝑦2𝛼	𝑦2𝛼	VERB
cana-1171	176	11	𝛤(2𝛼	𝛤(2𝛼	VERB
cana-1171	176	12	+	+	CCONJ
cana-1171	176	13	1	1	NUM
cana-1171	176	14	)	)	PUNCT
cana-1171	177	1	+	+	CCONJ
cana-1171	177	2	𝛾(𝑠	𝛾(𝑠	PROPN
cana-1171	177	3	−	−	PROPN
cana-1171	177	4	1)[𝜆1	1)[𝜆1	NUM
cana-1171	177	5	𝛼	𝛼	NOUN
cana-1171	177	6	−	−	PROPN
cana-1171	177	7	𝐶𝛼𝑠	𝐶𝛼𝑠	PROPN
cana-1171	177	8	−	−	NOUN
cana-1171	177	9	𝐶𝛼(𝑠	𝐶𝛼(𝑠	NOUN
cana-1171	177	10	−	−	PROPN
cana-1171	177	11	1	1	NUM
cana-1171	177	12	)	)	PUNCT
cana-1171	177	13	]	]	PUNCT
cana-1171	177	14	𝑦2𝛼+1	𝑦2𝛼+1	CCONJ
cana-1171	177	15	𝛤(2𝛼	𝛤(2𝛼	X
cana-1171	177	16	+	+	CCONJ
cana-1171	177	17	2	2	NUM
cana-1171	177	18	)	)	PUNCT
cana-1171	177	19	+	+	CCONJ
cana-1171	177	20	𝐶𝛼𝛾(1	𝐶𝛼𝛾(1	NUM
cana-1171	177	21	−	−	NOUN
cana-1171	177	22	𝑠)2	𝑠)2	NOUN
cana-1171	177	23	𝑦2𝛼+2	𝑦2𝛼+2	NOUN
cana-1171	177	24	𝛤(2𝛼	𝛤(2𝛼	X
cana-1171	177	25	+	+	CCONJ
cana-1171	177	26	3	3	X
cana-1171	177	27	)	)	PUNCT
cana-1171	177	28	+	+	ADJ
cana-1171	177	29	{	{	PUNCT
cana-1171	177	30	−𝛾(1	−𝛾(1	NOUN
cana-1171	177	31	−	−	NOUN
cana-1171	177	32	𝑠)[𝐶𝛼𝑠	𝑠)[𝐶𝛼𝑠	PROPN
cana-1171	177	33	−	−	PROPN
cana-1171	177	34	𝜆1	𝜆1	NOUN
cana-1171	177	35	𝛼	𝛼	X
cana-1171	177	36	]	]	X
cana-1171	177	37	1	1	NUM
cana-1171	177	38	𝛤(2𝛼	𝛤(2𝛼	ADJ
cana-1171	177	39	+	+	CCONJ
cana-1171	177	40	1	1	NUM
cana-1171	177	41	)	)	PUNCT
cana-1171	177	42	−	−	ADP
cana-1171	177	43	𝛾(𝑠	𝛾(𝑠	PROPN
cana-1171	177	44	−	−	PROPN
cana-1171	177	45	1)[𝐶𝛼(𝑠	1)[𝐶𝛼(𝑠	NUM
cana-1171	177	46	−	−	NOUN
cana-1171	177	47	1	1	NUM
cana-1171	177	48	)	)	PUNCT
cana-1171	177	49	−	−	NOUN
cana-1171	178	1	𝜆1	𝜆1	NOUN
cana-1171	178	2	𝛼	𝛼	PRON
cana-1171	179	1	+	+	CCONJ
cana-1171	179	2	𝐶𝛼𝑠	𝐶𝛼𝑠	PROPN
cana-1171	179	3	]	]	X
cana-1171	179	4	1	1	NUM
cana-1171	179	5	𝛤(2𝛼	𝛤(2𝛼	ADJ
cana-1171	179	6	+	+	CCONJ
cana-1171	179	7	2	2	NUM
cana-1171	179	8	)	)	PUNCT
cana-1171	179	9	−	−	PROPN
cana-1171	179	10	𝛾(1	𝛾(1	NOUN
cana-1171	179	11	−	−	NOUN
cana-1171	179	12	𝑠)2	𝑠)2	NOUN
cana-1171	179	13	2	2	NUM
cana-1171	179	14	𝛤(2𝛼	𝛤(2𝛼	X
cana-1171	179	15	+	+	X
cana-1171	179	16	3	3	NUM
cana-1171	179	17	)	)	PUNCT
cana-1171	179	18	}	}	PUNCT
cana-1171	179	19	(	(	PUNCT
cana-1171	179	20	38	38	NUM
cana-1171	179	21	)	)	PUNCT
cana-1171	179	22	remark	remark	NOUN
cana-1171	179	23	substituting	substitute	VERB
cana-1171	179	24	the	the	DET
cana-1171	179	25	expressions	expression	NOUN
cana-1171	179	26	of	of	ADP
cana-1171	179	27	𝑢(𝑦	𝑢(𝑦	NOUN
cana-1171	179	28	)	)	PUNCT
cana-1171	179	29	,	,	PUNCT
cana-1171	179	30	𝑣(𝑦	𝑣(𝑦	PROPN
cana-1171	179	31	)	)	PUNCT
cana-1171	179	32	and	and	CCONJ
cana-1171	179	33	𝑤(𝑦	𝑤(𝑦	NOUN
cana-1171	179	34	)	)	PUNCT
cana-1171	179	35	in	in	ADP
cana-1171	179	36	(	(	PUNCT
cana-1171	179	37	22	22	NUM
cana-1171	179	38	)	)	PUNCT
cana-1171	179	39	.	.	PUNCT
cana-1171	180	1	the	the	DET
cana-1171	180	2	concentration	concentration	NOUN
cana-1171	180	3	of	of	ADP
cana-1171	180	4	the	the	DET
cana-1171	180	5	product	product	NOUN
cana-1171	180	6	𝐵	𝐵	NOUN
cana-1171	180	7	can	can	AUX
cana-1171	180	8	be	be	AUX
cana-1171	180	9	obtained	obtain	VERB
cana-1171	180	10	as	as	ADP
cana-1171	180	11	𝑏(𝑦	𝑏(𝑦	PROPN
cana-1171	180	12	)	)	PUNCT
cana-1171	180	13	.	.	PUNCT
cana-1171	181	1	8	8	X
cana-1171	181	2	.	.	X
cana-1171	181	3	analysis	analysis	NOUN
cana-1171	181	4	and	and	CCONJ
cana-1171	181	5	discussion	discussion	NOUN
cana-1171	181	6	in	in	ADP
cana-1171	181	7	this	this	DET
cana-1171	181	8	section	section	NOUN
cana-1171	181	9	,	,	PUNCT
cana-1171	181	10	we	we	PRON
cana-1171	181	11	established	establish	VERB
cana-1171	181	12	the	the	DET
cana-1171	181	13	significance	significance	NOUN
cana-1171	181	14	of	of	ADP
cana-1171	181	15	the	the	DET
cana-1171	181	16	parameters	parameter	NOUN
cana-1171	181	17	𝜆	𝜆	ADP
cana-1171	181	18	,	,	PUNCT
cana-1171	181	19	𝐶	𝐶	PROPN
cana-1171	181	20	,	,	PUNCT
cana-1171	181	21	𝛾	𝛾	PROPN
cana-1171	181	22	,	,	PUNCT
cana-1171	181	23	𝜆1	𝜆1	NOUN
cana-1171	181	24	,	,	PUNCT
cana-1171	181	25	𝜆2	𝜆2	NOUN
cana-1171	181	26	and	and	CCONJ
cana-1171	181	27	𝜉	𝜉	X
cana-1171	181	28	on	on	ADP
cana-1171	181	29	the	the	DET
cana-1171	181	30	concentration	concentration	NOUN
cana-1171	181	31	of	of	ADP
cana-1171	181	32	𝑃	𝑃	NOUN
cana-1171	181	33	,	,	PUNCT
cana-1171	181	34	𝑄	𝑄	PROPN
cana-1171	181	35	,	,	PUNCT
cana-1171	181	36	𝐴	𝐴	PROPN
cana-1171	181	37	,	,	PUNCT
cana-1171	181	38	and	and	CCONJ
cana-1171	181	39	𝐵.	𝐵.	PROPN
cana-1171	181	40	communications	communication	NOUN
cana-1171	181	41	on	on	ADP
cana-1171	181	42	applied	apply	VERB
cana-1171	181	43	nonlinear	nonlinear	ADJ
cana-1171	181	44	analysis	analysis	NOUN
cana-1171	181	45	issn	issn	NOUN
cana-1171	181	46	:	:	PUNCT
cana-1171	181	47	1074	1074	NUM
cana-1171	181	48	-	-	PUNCT
cana-1171	181	49	133x	133x	NUM
cana-1171	181	50	vol	vol	NOUN
cana-1171	181	51	31	31	NUM
cana-1171	181	52	no	no	NOUN
cana-1171	181	53	.	.	PUNCT
cana-1171	182	1	6s	6s	NUM
cana-1171	182	2	(	(	PUNCT
cana-1171	182	3	2024	2024	NUM
cana-1171	182	4	)	)	PUNCT
cana-1171	182	5	124	124	NUM
cana-1171	182	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1171	182	7	fig	fig	NOUN
cana-1171	182	8	1	1	NUM
cana-1171	182	9	dimensionless	dimensionless	NOUN
cana-1171	182	10	concentration	concentration	NOUN
cana-1171	182	11	𝑢	𝑢	NOUN
cana-1171	182	12	,	,	PUNCT
cana-1171	182	13	𝑣	𝑣	INTJ
cana-1171	182	14	,	,	PUNCT
cana-1171	182	15	𝑤	𝑤	ADP
cana-1171	182	16	,	,	PUNCT
cana-1171	182	17	𝑏	𝑏	PROPN
cana-1171	182	18	versus	versus	ADP
cana-1171	182	19	dimensionless	dimensionless	NOUN
cana-1171	182	20	distance	distance	NOUN
cana-1171	182	21	𝑦	𝑦	PRON
cana-1171	182	22	computed	compute	VERB
cana-1171	182	23	using	use	VERB
cana-1171	182	24	(	(	PUNCT
cana-1171	182	25	36	36	NUM
cana-1171	182	26	)	)	PUNCT
cana-1171	182	27	to	to	ADP
cana-1171	182	28	(	(	PUNCT
cana-1171	182	29	38	38	NUM
cana-1171	182	30	)	)	PUNCT
cana-1171	182	31	,	,	PUNCT
cana-1171	182	32	(	(	PUNCT
cana-1171	182	33	22	22	NUM
cana-1171	182	34	)	)	PUNCT
cana-1171	182	35	for	for	ADP
cana-1171	182	36	various	various	ADJ
cana-1171	182	37	values	value	NOUN
cana-1171	182	38	of	of	ADP
cana-1171	182	39	𝛼	𝛼	NOUN
cana-1171	182	40	,	,	PUNCT
cana-1171	182	41	and	and	CCONJ
cana-1171	182	42	for	for	ADP
cana-1171	182	43	some	some	DET
cana-1171	182	44	fixed	fix	VERB
cana-1171	182	45	value	value	NOUN
cana-1171	182	46	of	of	ADP
cana-1171	182	47	parameters	parameter	NOUN
cana-1171	182	48	𝜆	𝜆	ADP
cana-1171	182	49	,	,	PUNCT
cana-1171	182	50	𝛾	𝛾	PROPN
cana-1171	182	51	,	,	PUNCT
cana-1171	182	52	𝜆1	𝜆1	NOUN
cana-1171	182	53	,	,	PUNCT
cana-1171	182	54	𝜆2	𝜆2	NOUN
cana-1171	182	55	and	and	CCONJ
cana-1171	182	56	𝜉	𝜉	PROPN
cana-1171	182	57	.	.	PUNCT
cana-1171	183	1	fig	fig	NOUN
cana-1171	183	2	2	2	NUM
cana-1171	183	3	dimensionless	dimensionless	NOUN
cana-1171	183	4	concentration	concentration	NOUN
cana-1171	183	5	𝑢	𝑢	NOUN
cana-1171	183	6	,	,	PUNCT
cana-1171	183	7	𝑣	𝑣	INTJ
cana-1171	183	8	,	,	PUNCT
cana-1171	183	9	𝑤	𝑤	ADP
cana-1171	183	10	,	,	PUNCT
cana-1171	183	11	𝑏	𝑏	PROPN
cana-1171	183	12	versus	versus	ADP
cana-1171	183	13	dimensionless	dimensionless	NOUN
cana-1171	183	14	distance	distance	NOUN
cana-1171	183	15	𝑦	𝑦	PRON
cana-1171	183	16	computed	compute	VERB
cana-1171	183	17	using	use	VERB
cana-1171	183	18	(	(	PUNCT
cana-1171	183	19	36	36	NUM
cana-1171	183	20	)	)	PUNCT
cana-1171	183	21	to	to	ADP
cana-1171	183	22	(	(	PUNCT
cana-1171	183	23	38	38	NUM
cana-1171	183	24	)	)	PUNCT
cana-1171	183	25	,	,	PUNCT
cana-1171	183	26	(	(	PUNCT
cana-1171	183	27	22	22	NUM
cana-1171	183	28	)	)	PUNCT
cana-1171	183	29	for	for	ADP
cana-1171	183	30	various	various	ADJ
cana-1171	183	31	values	value	NOUN
cana-1171	183	32	of	of	ADP
cana-1171	183	33	𝐶	𝐶	PROPN
cana-1171	183	34	,	,	PUNCT
cana-1171	183	35	and	and	CCONJ
cana-1171	183	36	for	for	ADP
cana-1171	183	37	some	some	DET
cana-1171	183	38	fixed	fix	VERB
cana-1171	183	39	value	value	NOUN
cana-1171	183	40	of	of	ADP
cana-1171	183	41	parameters	parameter	NOUN
cana-1171	183	42	𝜆	𝜆	ADP
cana-1171	183	43	,	,	PUNCT
cana-1171	183	44	𝛾	𝛾	PROPN
cana-1171	183	45	,	,	PUNCT
cana-1171	183	46	𝜆1	𝜆1	NOUN
cana-1171	183	47	,	,	PUNCT
cana-1171	183	48	𝜆2	𝜆2	NOUN
cana-1171	183	49	and	and	CCONJ
cana-1171	183	50	𝜉	𝜉	PROPN
cana-1171	183	51	.	.	PUNCT
cana-1171	184	1	communications	communication	NOUN
cana-1171	184	2	on	on	ADP
cana-1171	184	3	applied	apply	VERB
cana-1171	184	4	nonlinear	nonlinear	ADJ
cana-1171	184	5	analysis	analysis	NOUN
cana-1171	184	6	issn	issn	NOUN
cana-1171	184	7	:	:	PUNCT
cana-1171	184	8	1074	1074	NUM
cana-1171	184	9	-	-	PUNCT
cana-1171	184	10	133x	133x	NUM
cana-1171	184	11	vol	vol	NOUN
cana-1171	184	12	31	31	NUM
cana-1171	184	13	no	no	NOUN
cana-1171	184	14	.	.	PUNCT
cana-1171	185	1	6s	6s	NUM
cana-1171	185	2	(	(	PUNCT
cana-1171	185	3	2024	2024	NUM
cana-1171	185	4	)	)	PUNCT
cana-1171	185	5	125	125	NUM
cana-1171	185	6	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-1171	185	7	fig	fig	NOUN
cana-1171	185	8	3	3	NUM
cana-1171	185	9	dimensionless	dimensionless	NOUN
cana-1171	185	10	concentration	concentration	NOUN
cana-1171	185	11	𝑢	𝑢	NOUN
cana-1171	185	12	,	,	PUNCT
cana-1171	185	13	𝑣	𝑣	INTJ
cana-1171	185	14	,	,	PUNCT
cana-1171	185	15	𝑤	𝑤	ADP
cana-1171	185	16	,	,	PUNCT
cana-1171	185	17	𝑏	𝑏	PROPN
cana-1171	185	18	versus	versus	ADP
cana-1171	185	19	dimensionless	dimensionless	NOUN
cana-1171	185	20	distance	distance	NOUN
cana-1171	185	21	𝑦	𝑦	PRON
cana-1171	185	22	computed	compute	VERB
cana-1171	185	23	using	use	VERB
cana-1171	185	24	(	(	PUNCT
cana-1171	185	25	36	36	NUM
cana-1171	185	26	)	)	PUNCT
cana-1171	185	27	to	to	ADP
cana-1171	185	28	(	(	PUNCT
cana-1171	185	29	38	38	NUM
cana-1171	185	30	)	)	PUNCT
cana-1171	185	31	,	,	PUNCT
cana-1171	185	32	(	(	PUNCT
cana-1171	185	33	22	22	NUM
cana-1171	185	34	)	)	PUNCT
cana-1171	185	35	for	for	ADP
cana-1171	185	36	various	various	ADJ
cana-1171	185	37	values	value	NOUN
cana-1171	185	38	of	of	ADP
cana-1171	185	39	dimensionless	dimensionless	NOUN
cana-1171	185	40	potential	potential	ADJ
cana-1171	185	41	𝜉	𝜉	NOUN
cana-1171	185	42	and	and	CCONJ
cana-1171	185	43	for	for	ADP
cana-1171	185	44	some	some	DET
cana-1171	185	45	fixed	fix	VERB
cana-1171	185	46	value	value	NOUN
cana-1171	185	47	of	of	ADP
cana-1171	185	48	parameters	parameter	NOUN
cana-1171	185	49	𝜆	𝜆	ADP
cana-1171	185	50	,	,	PUNCT
cana-1171	185	51	𝐶	𝐶	PROPN
cana-1171	185	52	,	,	PUNCT
cana-1171	185	53	𝜆1	𝜆1	NOUN
cana-1171	185	54	,	,	PUNCT
cana-1171	185	55	𝜆2	𝜆2	NOUN
cana-1171	185	56	and	and	CCONJ
cana-1171	185	57	γ	γ	PROPN
cana-1171	185	58	.	.	PROPN
cana-1171	185	59	fig	fig	NOUN
cana-1171	185	60	4	4	NUM
cana-1171	185	61	dimensionless	dimensionless	NOUN
cana-1171	185	62	concentration	concentration	NOUN
cana-1171	185	63	𝑢	𝑢	NOUN
cana-1171	185	64	,	,	PUNCT
cana-1171	185	65	𝑣	𝑣	INTJ
cana-1171	185	66	,	,	PUNCT
cana-1171	185	67	𝑤	𝑤	ADP
cana-1171	185	68	,	,	PUNCT
cana-1171	185	69	𝑏	𝑏	PROPN
cana-1171	185	70	versus	versus	ADP
cana-1171	185	71	dimensionless	dimensionless	NOUN
cana-1171	185	72	distance	distance	NOUN
cana-1171	185	73	𝑦	𝑦	PRON
cana-1171	185	74	computed	compute	VERB
cana-1171	185	75	using	use	VERB
cana-1171	185	76	(	(	PUNCT
cana-1171	185	77	36	36	NUM
cana-1171	185	78	)	)	PUNCT
cana-1171	185	79	to	to	ADP
cana-1171	185	80	(	(	PUNCT
cana-1171	185	81	38	38	NUM
cana-1171	185	82	)	)	PUNCT
cana-1171	185	83	,	,	PUNCT
cana-1171	185	84	(	(	PUNCT
cana-1171	185	85	22	22	NUM
cana-1171	185	86	)	)	PUNCT
cana-1171	185	87	for	for	ADP
cana-1171	185	88	various	various	ADJ
cana-1171	185	89	values	value	NOUN
cana-1171	185	90	of	of	ADP
cana-1171	185	91	𝜆1	𝜆1	NOUN
cana-1171	185	92	,	,	PUNCT
cana-1171	185	93	and	and	CCONJ
cana-1171	185	94	for	for	ADP
cana-1171	185	95	some	some	DET
cana-1171	185	96	fixed	fix	VERB
cana-1171	185	97	values	value	NOUN
cana-1171	185	98	of	of	ADP
cana-1171	185	99	parameters	parameter	NOUN
cana-1171	185	100	𝜉	𝜉	X
cana-1171	185	101	,	,	PUNCT
cana-1171	185	102	𝐶	𝐶	PROPN
cana-1171	185	103	,	,	PUNCT
cana-1171	185	104	𝜆2	𝜆2	PROPN
cana-1171	185	105	and	and	CCONJ
cana-1171	185	106	γ	γ	PROPN
cana-1171	185	107	.	.	PROPN
cana-1171	185	108	communications	communication	NOUN
cana-1171	185	109	on	on	ADP
cana-1171	185	110	applied	apply	VERB
cana-1171	185	111	nonlinear	nonlinear	ADJ
cana-1171	185	112	analysis	analysis	NOUN
cana-1171	185	113	issn	issn	NOUN
cana-1171	185	114	:	:	PUNCT
cana-1171	185	115	1074	1074	NUM
cana-1171	185	116	-	-	PUNCT
cana-1171	185	117	133x	133x	NUM
cana-1171	185	118	vol	vol	NOUN
cana-1171	185	119	31	31	NUM
cana-1171	185	120	no	no	NOUN
cana-1171	185	121	.	.	PUNCT
cana-1171	186	1	6s	6s	NUM
cana-1171	186	2	(	(	PUNCT
cana-1171	186	3	2024	2024	NUM
cana-1171	186	4	)	)	PUNCT
cana-1171	186	5	126	126	NUM
cana-1171	186	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1171	186	7	fig	fig	NOUN
cana-1171	186	8	5	5	NUM
cana-1171	186	9	the	the	DET
cana-1171	186	10	hpm	hpm	ADJ
cana-1171	186	11	solution	solution	NOUN
cana-1171	186	12	of	of	ADP
cana-1171	186	13	the	the	DET
cana-1171	186	14	caputo	caputo	PROPN
cana-1171	186	15	sequential	sequential	ADJ
cana-1171	186	16	system	system	NOUN
cana-1171	186	17	of	of	ADP
cana-1171	186	18	fractional	fractional	ADJ
cana-1171	186	19	equations(36	equations(36	NOUN
cana-1171	186	20	)	)	PUNCT
cana-1171	186	21	to	to	ADP
cana-1171	186	22	(	(	PUNCT
cana-1171	186	23	38	38	NUM
cana-1171	186	24	)	)	PUNCT
cana-1171	186	25	yields	yield	VERB
cana-1171	186	26	the	the	DET
cana-1171	186	27	solution	solution	NOUN
cana-1171	186	28	of	of	ADP
cana-1171	186	29	the	the	DET
cana-1171	186	30	corresponding	corresponding	ADJ
cana-1171	186	31	integer	integer	NOUN
cana-1171	186	32	-	-	PUNCT
cana-1171	186	33	order	order	NOUN
cana-1171	186	34	differential	differential	NOUN
cana-1171	186	35	equations(𝐴23	equations(𝐴23	PROPN
cana-1171	186	36	)	)	PUNCT
cana-1171	186	37	,	,	PUNCT
cana-1171	186	38	(	(	PUNCT
cana-1171	186	39	𝐴24	𝐴24	NOUN
cana-1171	186	40	)	)	PUNCT
cana-1171	186	41	and	and	CCONJ
cana-1171	186	42	(	(	PUNCT
cana-1171	186	43	𝐴25	𝐴25	PROPN
cana-1171	186	44	)	)	PUNCT
cana-1171	186	45	as	as	ADP
cana-1171	186	46	a	a	DET
cana-1171	186	47	special	special	ADJ
cana-1171	186	48	case	case	NOUN
cana-1171	186	49	𝛼	𝛼	X
cana-1171	186	50	→	→	SYM
cana-1171	186	51	1	1	NUM
cana-1171	186	52	.	.	PUNCT
cana-1171	186	53	equations	equation	NOUN
cana-1171	186	54	(	(	PUNCT
cana-1171	186	55	36	36	NUM
cana-1171	186	56	)	)	PUNCT
cana-1171	186	57	−	−	PROPN
cana-1171	187	1	(	(	PUNCT
cana-1171	187	2	38	38	NUM
cana-1171	187	3	)	)	PUNCT
cana-1171	187	4	and	and	CCONJ
cana-1171	187	5	the	the	DET
cana-1171	187	6	remark	remark	NOUN
cana-1171	187	7	represents	represent	VERB
cana-1171	187	8	the	the	DET
cana-1171	187	9	analytical	analytical	ADJ
cana-1171	187	10	expressions	expression	NOUN
cana-1171	187	11	for	for	ADP
cana-1171	187	12	the	the	DET
cana-1171	187	13	dimensionless	dimensionless	NOUN
cana-1171	187	14	concentration	concentration	NOUN
cana-1171	187	15	profile	profile	NOUN
cana-1171	187	16	for	for	ADP
cana-1171	187	17	catalyst	catalyst	NOUN
cana-1171	187	18	𝑃	𝑃	NOUN
cana-1171	187	19	and	and	CCONJ
cana-1171	187	20	𝑄	𝑄	PROPN
cana-1171	187	21	,	,	PUNCT
cana-1171	187	22	and	and	CCONJ
cana-1171	187	23	the	the	DET
cana-1171	187	24	substrate	substrate	NOUN
cana-1171	187	25	𝐴	𝐴	PROPN
cana-1171	187	26	and	and	CCONJ
cana-1171	187	27	the	the	DET
cana-1171	187	28	product	product	NOUN
cana-1171	187	29	𝐵	𝐵	NOUN
cana-1171	187	30	for	for	ADP
cana-1171	187	31	the	the	DET
cana-1171	187	32	different	different	ADJ
cana-1171	187	33	values	value	NOUN
cana-1171	187	34	of	of	ADP
cana-1171	187	35	the	the	DET
cana-1171	187	36	parameters	parameter	NOUN
cana-1171	187	37	𝜉	𝜉	ADP
cana-1171	187	38	,	,	PUNCT
cana-1171	187	39	𝜆1	𝜆1	NOUN
cana-1171	187	40	,	,	PUNCT
cana-1171	187	41	𝛾	𝛾	ADP
cana-1171	187	42	,	,	PUNCT
cana-1171	187	43	𝐶	𝐶	PROPN
cana-1171	187	44	,	,	PUNCT
cana-1171	187	45	𝜆	𝜆	NOUN
cana-1171	187	46	,	,	PUNCT
cana-1171	187	47	𝜆2	𝜆2	NOUN
cana-1171	187	48	with	with	ADP
cana-1171	187	49	the	the	DET
cana-1171	187	50	different	different	ADJ
cana-1171	187	51	non	non	ADJ
cana-1171	187	52	-	-	ADJ
cana-1171	187	53	integer	integer	ADJ
cana-1171	187	54	order	order	NOUN
cana-1171	187	55	.	.	PUNCT
cana-1171	188	1	in	in	ADP
cana-1171	188	2	figures(1	figures(1	NOUN
cana-1171	188	3	)	)	PUNCT
cana-1171	188	4	,	,	PUNCT
cana-1171	188	5	demonstrate	demonstrate	VERB
cana-1171	188	6	the	the	DET
cana-1171	188	7	dimensionless	dimensionless	NOUN
cana-1171	188	8	concentration	concentration	NOUN
cana-1171	188	9	of	of	ADP
cana-1171	188	10	𝑃	𝑃	NOUN
cana-1171	188	11	,	,	PUNCT
cana-1171	188	12	𝑄	𝑄	PROPN
cana-1171	188	13	,	,	PUNCT
cana-1171	188	14	𝐴	𝐴	PROPN
cana-1171	188	15	,	,	PUNCT
cana-1171	188	16	𝐵	𝐵	NOUN
cana-1171	188	17	for	for	ADP
cana-1171	188	18	some	some	DET
cana-1171	188	19	fixed	fix	VERB
cana-1171	188	20	values	value	NOUN
cana-1171	188	21	of	of	ADP
cana-1171	188	22	parameter	parameter	NOUN
cana-1171	188	23	with	with	ADP
cana-1171	188	24	different	different	ADJ
cana-1171	188	25	values	value	NOUN
cana-1171	188	26	of	of	ADP
cana-1171	188	27	fractional	fractional	ADJ
cana-1171	188	28	order	order	NOUN
cana-1171	188	29	𝛼.	𝛼.	NOUN
cana-1171	188	30	this	this	DET
cana-1171	188	31	figures	figure	NOUN
cana-1171	188	32	gives	give	VERB
cana-1171	188	33	more	more	ADV
cana-1171	188	34	accurate	accurate	ADJ
cana-1171	188	35	results	result	NOUN
cana-1171	188	36	compared	compare	VERB
cana-1171	188	37	to	to	ADP
cana-1171	188	38	classical	classical	ADJ
cana-1171	188	39	model	model	NOUN
cana-1171	188	40	.	.	PUNCT
cana-1171	189	1	in	in	ADP
cana-1171	189	2	figures(2	figures(2	NOUN
cana-1171	189	3	)	)	PUNCT
cana-1171	189	4	,	,	PUNCT
cana-1171	189	5	shows	show	VERB
cana-1171	189	6	that	that	SCONJ
cana-1171	189	7	the	the	DET
cana-1171	189	8	concentration	concentration	NOUN
cana-1171	189	9	of	of	ADP
cana-1171	189	10	the	the	DET
cana-1171	189	11	catalyst	catalyst	NOUN
cana-1171	189	12	𝑄	𝑄	PROPN
cana-1171	189	13	,	,	PUNCT
cana-1171	189	14	the	the	DET
cana-1171	189	15	substrate	substrate	NOUN
cana-1171	189	16	𝐴	𝐴	PROPN
cana-1171	189	17	and	and	CCONJ
cana-1171	189	18	the	the	DET
cana-1171	189	19	product	product	NOUN
cana-1171	189	20	𝐵	𝐵	NOUN
cana-1171	189	21	are	be	AUX
cana-1171	189	22	directly	directly	ADV
cana-1171	189	23	proportional	proportional	ADJ
cana-1171	189	24	to	to	ADP
cana-1171	189	25	𝐶	𝐶	PROPN
cana-1171	189	26	but	but	CCONJ
cana-1171	189	27	concentration	concentration	NOUN
cana-1171	189	28	of	of	ADP
cana-1171	189	29	the	the	DET
cana-1171	189	30	catalyst	catalyst	NOUN
cana-1171	189	31	𝑃	𝑃	NOUN
cana-1171	189	32	is	be	AUX
cana-1171	189	33	inversely	inversely	ADV
cana-1171	189	34	proportional	proportional	ADJ
cana-1171	189	35	to	to	ADP
cana-1171	189	36	𝐶.	𝐶.	PROPN
cana-1171	189	37	in	in	ADP
cana-1171	189	38	figures(3	figures(3	NOUN
cana-1171	189	39	)	)	PUNCT
cana-1171	189	40	,	,	PUNCT
cana-1171	189	41	catalyst	catalyst	NOUN
cana-1171	189	42	𝑃	𝑃	PROPN
cana-1171	189	43	initially	initially	ADV
cana-1171	189	44	exhibits	exhibit	VERB
cana-1171	189	45	direct	direct	ADJ
cana-1171	189	46	proportionality	proportionality	NOUN
cana-1171	189	47	to	to	ADP
cana-1171	189	48	potentialξ	potentialξ	PROPN
cana-1171	189	49	,	,	PUNCT
cana-1171	189	50	changing	change	VERB
cana-1171	189	51	to	to	ADP
cana-1171	189	52	inverse	inverse	ADJ
cana-1171	189	53	proportionality	proportionality	NOUN
cana-1171	189	54	at	at	ADP
cana-1171	189	55	specific	specific	ADJ
cana-1171	189	56	points	point	NOUN
cana-1171	189	57	.	.	PUNCT
cana-1171	190	1	similarly	similarly	ADV
cana-1171	190	2	,	,	PUNCT
cana-1171	190	3	catalyst	catalyst	NOUN
cana-1171	190	4	𝑄	𝑄	PROPN
cana-1171	190	5	initially	initially	ADV
cana-1171	190	6	increases	increase	VERB
cana-1171	190	7	with	with	ADP
cana-1171	190	8	ξ	ξ	PROPN
cana-1171	190	9	up	up	ADP
cana-1171	190	10	to	to	ADP
cana-1171	190	11	a	a	DET
cana-1171	190	12	certain	certain	ADJ
cana-1171	190	13	point	point	NOUN
cana-1171	190	14	,	,	PUNCT
cana-1171	190	15	then	then	ADV
cana-1171	190	16	decreases	decrease	VERB
cana-1171	190	17	.	.	PUNCT
cana-1171	191	1	simultaneously	simultaneously	ADV
cana-1171	191	2	,	,	PUNCT
cana-1171	191	3	product	product	NOUN
cana-1171	191	4	𝐵	𝐵	NOUN
cana-1171	191	5	undergoes	undergo	VERB
cana-1171	191	6	a	a	DET
cana-1171	191	7	slight	slight	ADJ
cana-1171	191	8	increase	increase	NOUN
cana-1171	191	9	followed	follow	VERB
cana-1171	191	10	by	by	ADP
cana-1171	191	11	a	a	DET
cana-1171	191	12	more	more	ADV
cana-1171	191	13	significant	significant	ADJ
cana-1171	191	14	decrease	decrease	NOUN
cana-1171	191	15	.	.	PUNCT
cana-1171	192	1	in	in	ADP
cana-1171	192	2	figures(4	figures(4	NOUN
cana-1171	192	3	)	)	PUNCT
cana-1171	192	4	,	,	PUNCT
cana-1171	192	5	shows	show	VERB
cana-1171	192	6	that	that	SCONJ
cana-1171	192	7	the	the	DET
cana-1171	192	8	concentration	concentration	NOUN
cana-1171	192	9	of	of	ADP
cana-1171	192	10	the	the	DET
cana-1171	192	11	catalyst	catalyst	NOUN
cana-1171	192	12	𝑃	𝑃	NOUN
cana-1171	192	13	is	be	AUX
cana-1171	192	14	directly	directly	ADV
cana-1171	192	15	proportional	proportional	ADJ
cana-1171	192	16	to	to	ADP
cana-1171	192	17	𝜆1,but	𝜆1,but	NOUN
cana-1171	192	18	concentration	concentration	NOUN
cana-1171	192	19	of	of	ADP
cana-1171	192	20	the	the	DET
cana-1171	192	21	catalyst	catalyst	NOUN
cana-1171	192	22	𝑄	𝑄	PROPN
cana-1171	192	23	,	,	PUNCT
cana-1171	192	24	the	the	DET
cana-1171	192	25	substrate	substrate	NOUN
cana-1171	192	26	𝐴	𝐴	PROPN
cana-1171	192	27	and	and	CCONJ
cana-1171	192	28	the	the	DET
cana-1171	192	29	product	product	NOUN
cana-1171	192	30	𝐵	𝐵	NOUN
cana-1171	192	31	are	be	AUX
cana-1171	192	32	inversely	inversely	ADV
cana-1171	192	33	proportional	proportional	ADJ
cana-1171	192	34	to	to	AUX
cana-1171	192	35	𝜆1	𝜆1	VERB
cana-1171	192	36	.	.	PUNCT
cana-1171	193	1	in	in	ADP
cana-1171	193	2	figures(5	figures(5	PROPN
cana-1171	193	3	)	)	PUNCT
cana-1171	193	4	,	,	PUNCT
cana-1171	193	5	shows	show	VERB
cana-1171	193	6	that	that	SCONJ
cana-1171	193	7	the	the	DET
cana-1171	193	8	fractional	fractional	ADJ
cana-1171	193	9	hpm	hpm	NOUN
cana-1171	193	10	yields	yield	VERB
cana-1171	193	11	the	the	DET
cana-1171	193	12	solution	solution	NOUN
cana-1171	193	13	of	of	ADP
cana-1171	193	14	the	the	DET
cana-1171	193	15	corresponding	correspond	VERB
cana-1171	193	16	integerorder	integerorder	NOUN
cana-1171	193	17	differential	differential	PROPN
cana-1171	193	18	equations(𝐴23	equations(𝐴23	PROPN
cana-1171	193	19	)	)	PUNCT
cana-1171	193	20	,	,	PUNCT
cana-1171	193	21	(	(	PUNCT
cana-1171	193	22	𝐴24	𝐴24	NOUN
cana-1171	193	23	)	)	PUNCT
cana-1171	193	24	and	and	CCONJ
cana-1171	193	25	(	(	PUNCT
cana-1171	193	26	𝐴25	𝐴25	PROPN
cana-1171	193	27	)	)	PUNCT
cana-1171	193	28	as	as	ADP
cana-1171	193	29	a	a	DET
cana-1171	193	30	special	special	ADJ
cana-1171	193	31	case	case	NOUN
cana-1171	193	32	.	.	PUNCT
cana-1171	194	1	9	9	X
cana-1171	194	2	.	.	X
cana-1171	194	3	conclusion	conclusion	NOUN
cana-1171	194	4	in	in	ADP
cana-1171	194	5	this	this	DET
cana-1171	194	6	paper	paper	NOUN
cana-1171	194	7	,	,	PUNCT
cana-1171	194	8	a	a	DET
cana-1171	194	9	new	new	ADJ
cana-1171	194	10	mathematical	mathematical	ADJ
cana-1171	194	11	model	model	NOUN
cana-1171	194	12	based	base	VERB
cana-1171	194	13	on	on	ADP
cana-1171	194	14	the	the	DET
cana-1171	194	15	caputo	caputo	NOUN
cana-1171	194	16	-	-	PUNCT
cana-1171	194	17	sequential	sequential	ADJ
cana-1171	194	18	fractional	fractional	ADJ
cana-1171	194	19	differential	differential	NOUN
cana-1171	194	20	systems	system	NOUN
cana-1171	194	21	of	of	ADP
cana-1171	194	22	the	the	DET
cana-1171	194	23	ec	ec	PROPN
cana-1171	194	24	mechanism	mechanism	NOUN
cana-1171	194	25	was	be	AUX
cana-1171	194	26	investigated	investigate	VERB
cana-1171	194	27	with	with	ADP
cana-1171	194	28	steady	steady	ADJ
cana-1171	194	29	-	-	PUNCT
cana-1171	194	30	state	state	NOUN
cana-1171	194	31	assumptions	assumption	NOUN
cana-1171	194	32	.	.	PUNCT
cana-1171	195	1	the	the	DET
cana-1171	195	2	fractional	fractional	ADJ
cana-1171	195	3	model	model	NOUN
cana-1171	195	4	of	of	ADP
cana-1171	195	5	the	the	DET
cana-1171	195	6	ec	ec	PROPN
cana-1171	195	7	mechanism	mechanism	NOUN
cana-1171	195	8	gives	give	VERB
cana-1171	195	9	more	more	ADV
cana-1171	195	10	accurate	accurate	ADJ
cana-1171	195	11	results	result	NOUN
cana-1171	195	12	as	as	ADP
cana-1171	195	13	compared	compare	VERB
cana-1171	195	14	to	to	ADP
cana-1171	195	15	the	the	DET
cana-1171	195	16	classical	classical	ADJ
cana-1171	195	17	integer	integer	NOUN
cana-1171	195	18	-	-	PUNCT
cana-1171	195	19	order	order	NOUN
cana-1171	195	20	model	model	NOUN
cana-1171	195	21	.	.	PUNCT
cana-1171	196	1	communications	communication	NOUN
cana-1171	196	2	on	on	ADP
cana-1171	196	3	applied	apply	VERB
cana-1171	196	4	nonlinear	nonlinear	ADJ
cana-1171	196	5	analysis	analysis	NOUN
cana-1171	196	6	issn	issn	NOUN
cana-1171	196	7	:	:	PUNCT
cana-1171	196	8	1074	1074	NUM
cana-1171	196	9	-	-	PUNCT
cana-1171	196	10	133x	133x	NUM
cana-1171	196	11	vol	vol	NOUN
cana-1171	196	12	31	31	NUM
cana-1171	196	13	no	no	NOUN
cana-1171	196	14	.	.	PUNCT
cana-1171	197	1	6s	6s	NUM
cana-1171	197	2	(	(	PUNCT
cana-1171	197	3	2024	2024	NUM
cana-1171	197	4	)	)	PUNCT
cana-1171	197	5	127	127	NUM
cana-1171	197	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1171	198	1	the	the	DET
cana-1171	198	2	dynamic	dynamic	ADJ
cana-1171	198	3	system	system	NOUN
cana-1171	198	4	of	of	ADP
cana-1171	198	5	non	non	ADJ
cana-1171	198	6	-	-	ADJ
cana-1171	198	7	linear	linear	ADJ
cana-1171	198	8	equations	equation	NOUN
cana-1171	198	9	with	with	ADP
cana-1171	198	10	fractional	fractional	ADJ
cana-1171	198	11	order	order	NOUN
cana-1171	198	12	has	have	AUX
cana-1171	198	13	been	be	AUX
cana-1171	198	14	solved	solve	VERB
cana-1171	198	15	by	by	ADP
cana-1171	198	16	the	the	DET
cana-1171	198	17	semianalytical	semianalytical	ADJ
cana-1171	198	18	method	method	NOUN
cana-1171	198	19	,	,	PUNCT
cana-1171	198	20	that	that	ADV
cana-1171	198	21	is	is	ADV
cana-1171	198	22	,	,	PUNCT
cana-1171	198	23	hpm	hpm	PROPN
cana-1171	198	24	,	,	PUNCT
cana-1171	198	25	which	which	PRON
cana-1171	198	26	has	have	VERB
cana-1171	198	27	very	very	ADV
cana-1171	198	28	high	high	ADJ
cana-1171	198	29	accuracy	accuracy	NOUN
cana-1171	198	30	.	.	PUNCT
cana-1171	199	1	this	this	DET
cana-1171	199	2	method	method	NOUN
cana-1171	199	3	is	be	AUX
cana-1171	199	4	effective	effective	ADJ
cana-1171	199	5	and	and	CCONJ
cana-1171	199	6	efficient	efficient	ADJ
cana-1171	199	7	not	not	PART
cana-1171	199	8	only	only	ADV
cana-1171	199	9	for	for	ADP
cana-1171	199	10	classical	classical	ADJ
cana-1171	199	11	differential	differential	ADJ
cana-1171	199	12	equations	equation	NOUN
cana-1171	199	13	but	but	CCONJ
cana-1171	199	14	also	also	ADV
cana-1171	199	15	for	for	ADP
cana-1171	199	16	fractional	fractional	ADJ
cana-1171	199	17	derivatives	derivative	NOUN
cana-1171	199	18	.	.	PUNCT
cana-1171	200	1	the	the	DET
cana-1171	200	2	influence	influence	NOUN
cana-1171	200	3	of	of	ADP
cana-1171	200	4	the	the	DET
cana-1171	200	5	various	various	ADJ
cana-1171	200	6	parameters	parameter	NOUN
cana-1171	200	7	on	on	ADP
cana-1171	200	8	catalytic	catalytic	ADJ
cana-1171	200	9	efficiency	efficiency	NOUN
cana-1171	200	10	was	be	AUX
cana-1171	200	11	discussed	discuss	VERB
cana-1171	200	12	.	.	PUNCT
cana-1171	201	1	additionally	additionally	ADV
cana-1171	201	2	,	,	PUNCT
cana-1171	201	3	we	we	PRON
cana-1171	201	4	demonstrate	demonstrate	VERB
cana-1171	201	5	that	that	SCONJ
cana-1171	201	6	the	the	DET
cana-1171	201	7	sequential	sequential	ADJ
cana-1171	201	8	system	system	NOUN
cana-1171	201	9	of	of	ADP
cana-1171	201	10	fractional	fractional	ADJ
cana-1171	201	11	equations	equation	NOUN
cana-1171	201	12	yields	yield	VERB
cana-1171	201	13	the	the	DET
cana-1171	201	14	solution	solution	NOUN
cana-1171	201	15	of	of	ADP
cana-1171	201	16	the	the	DET
cana-1171	201	17	integer	integer	NOUN
cana-1171	201	18	-	-	PUNCT
cana-1171	201	19	order	order	NOUN
cana-1171	201	20	differential	differential	ADJ
cana-1171	201	21	equations	equation	NOUN
cana-1171	201	22	as	as	ADP
cana-1171	201	23	a	a	DET
cana-1171	201	24	special	special	ADJ
cana-1171	201	25	case	case	NOUN
cana-1171	201	26	as	as	ADP
cana-1171	201	27	𝛼	𝛼	X
cana-1171	201	28	→	→	SYM
cana-1171	201	29	1	1	NUM
cana-1171	201	30	.	.	X
cana-1171	201	31	appendix	appendix	VERB
cana-1171	201	32	a	a	DET
cana-1171	201	33	the	the	DET
cana-1171	201	34	homotopy	homotopy	NOUN
cana-1171	201	35	perturbation	perturbation	NOUN
cana-1171	201	36	method	method	NOUN
cana-1171	201	37	of	of	ADP
cana-1171	201	38	solving	solve	VERB
cana-1171	201	39	system	system	NOUN
cana-1171	201	40	of	of	ADP
cana-1171	201	41	second	second	ADJ
cana-1171	201	42	order	order	NOUN
cana-1171	201	43	non	non	ADJ
cana-1171	201	44	-	-	ADJ
cana-1171	201	45	linear	linear	ADJ
cana-1171	201	46	differential	differential	ADJ
cana-1171	201	47	equation	equation	NOUN
cana-1171	201	48	of	of	ADP
cana-1171	201	49	ec	ec	PROPN
cana-1171	201	50	mechanism	mechanism	NOUN
cana-1171	201	51	here	here	ADV
cana-1171	201	52	we	we	PRON
cana-1171	201	53	can	can	AUX
cana-1171	201	54	solve	solve	VERB
cana-1171	201	55	the	the	DET
cana-1171	201	56	system	system	NOUN
cana-1171	201	57	of	of	ADP
cana-1171	201	58	second	second	ADJ
cana-1171	201	59	order	order	NOUN
cana-1171	201	60	non	non	ADJ
cana-1171	201	61	-	-	ADJ
cana-1171	201	62	linear	linear	ADJ
cana-1171	201	63	differential	differential	ADJ
cana-1171	201	64	equations	equation	NOUN
cana-1171	201	65	(	(	PUNCT
cana-1171	201	66	14	14	NUM
cana-1171	201	67	)	)	PUNCT
cana-1171	201	68	−	−	PROPN
cana-1171	202	1	(	(	PUNCT
cana-1171	202	2	16	16	NUM
cana-1171	202	3	)	)	PUNCT
cana-1171	202	4	with	with	ADP
cana-1171	202	5	boundary	boundary	ADJ
cana-1171	202	6	conditions	condition	NOUN
cana-1171	202	7	(	(	PUNCT
cana-1171	202	8	17	17	NUM
cana-1171	202	9	)	)	PUNCT
cana-1171	202	10	and	and	CCONJ
cana-1171	202	11	(	(	PUNCT
cana-1171	202	12	18	18	NUM
cana-1171	202	13	)	)	PUNCT
cana-1171	202	14	analytically	analytically	ADV
cana-1171	202	15	using	use	VERB
cana-1171	202	16	homotopy	homotopy	NOUN
cana-1171	202	17	perturbation	perturbation	NOUN
cana-1171	202	18	method	method	NOUN
cana-1171	202	19	[	[	X
cana-1171	202	20	4	4	X
cana-1171	202	21	]	]	PUNCT
cana-1171	202	22	in	in	ADP
cana-1171	202	23	the	the	DET
cana-1171	202	24	following	following	ADJ
cana-1171	202	25	way	way	NOUN
cana-1171	202	26	.	.	PUNCT
cana-1171	203	1	using	use	VERB
cana-1171	203	2	homotopy	homotopy	NOUN
cana-1171	203	3	for	for	ADP
cana-1171	203	4	the	the	DET
cana-1171	203	5	equations	equation	NOUN
cana-1171	203	6	(	(	PUNCT
cana-1171	203	7	14	14	NUM
cana-1171	203	8	)	)	PUNCT
cana-1171	203	9	to	to	ADP
cana-1171	203	10	(	(	PUNCT
cana-1171	203	11	16	16	NUM
cana-1171	203	12	)	)	PUNCT
cana-1171	203	13	are	be	AUX
cana-1171	203	14	(	(	PUNCT
cana-1171	203	15	1	1	NUM
cana-1171	203	16	−	−	PROPN
cana-1171	203	17	𝑝	𝑝	NOUN
cana-1171	203	18	)	)	PUNCT
cana-1171	203	19	(	(	PUNCT
cana-1171	203	20	𝑑2𝑢	𝑑2𝑢	NOUN
cana-1171	203	21	𝑑𝑦2	𝑑𝑦2	X
cana-1171	203	22	)	)	PUNCT
cana-1171	204	1	+	+	CCONJ
cana-1171	204	2	𝑝	𝑝	X
cana-1171	204	3	[	[	PUNCT
cana-1171	204	4	𝑑2𝑢	𝑑2𝑢	NOUN
cana-1171	204	5	𝑑𝑦2	𝑑𝑦2	X
cana-1171	204	6	+	+	CCONJ
cana-1171	204	7	𝜆1𝑤𝑣	𝜆1𝑤𝑣	PUNCT
cana-1171	204	8	−	−	PROPN
cana-1171	204	9	𝐶𝑢𝑣𝑤	𝐶𝑢𝑣𝑤	PROPN
cana-1171	204	10	]	]	X
cana-1171	204	11	=	=	SYM
cana-1171	204	12	0	0	NUM
cana-1171	204	13	𝑑2𝑢	𝑑2𝑢	NOUN
cana-1171	204	14	𝑑𝑦2	𝑑𝑦2	X
cana-1171	205	1	+	+	CCONJ
cana-1171	205	2	𝑝𝜆1𝑤𝑣	𝑝𝜆1𝑤𝑣	NUM
cana-1171	205	3	−	−	PROPN
cana-1171	205	4	𝑝𝐶𝑢𝑣𝑤	𝑝𝐶𝑢𝑣𝑤	PROPN
cana-1171	205	5	=	=	SYM
cana-1171	205	6	0	0	PUNCT
cana-1171	206	1	(	(	PUNCT
cana-1171	206	2	𝐴1	𝐴1	PROPN
cana-1171	206	3	)	)	PUNCT
cana-1171	206	4	(	(	PUNCT
cana-1171	206	5	1	1	NUM
cana-1171	206	6	−	−	PROPN
cana-1171	206	7	𝑝	𝑝	NOUN
cana-1171	206	8	)	)	PUNCT
cana-1171	206	9	(	(	PUNCT
cana-1171	206	10	𝑑2𝑣	𝑑2𝑣	X
cana-1171	206	11	𝑑𝑦2	𝑑𝑦2	X
cana-1171	206	12	)	)	PUNCT
cana-1171	207	1	+	+	CCONJ
cana-1171	207	2	𝑝	𝑝	PROPN
cana-1171	207	3	[	[	PUNCT
cana-1171	207	4	𝑑2𝑣	𝑑2𝑣	X
cana-1171	207	5	𝑑𝑦2	𝑑𝑦2	NOUN
cana-1171	207	6	−	−	PROPN
cana-1171	207	7	𝜆1𝑤𝑣	𝜆1𝑤𝑣	PUNCT
cana-1171	208	1	+	+	PUNCT
cana-1171	208	2	𝐶𝑢𝑣𝑤	𝐶𝑢𝑣𝑤	PROPN
cana-1171	208	3	]	]	X
cana-1171	208	4	=	=	SYM
cana-1171	208	5	0	0	NUM
cana-1171	208	6	𝑑2𝑣	𝑑2𝑣	VERB
cana-1171	208	7	𝑑𝑦2	𝑑𝑦2	X
cana-1171	208	8	−	−	PROPN
cana-1171	208	9	𝑝𝜆1𝑤𝑣	𝑝𝜆1𝑤𝑣	NOUN
cana-1171	209	1	+	+	CCONJ
cana-1171	209	2	𝑝𝐶𝑢𝑣𝑤	𝑝𝐶𝑢𝑣𝑤	PROPN
cana-1171	209	3	=	=	SYM
cana-1171	209	4	0	0	PUNCT
cana-1171	209	5	(	(	PUNCT
cana-1171	209	6	𝐴2	𝐴2	PROPN
cana-1171	209	7	)	)	PUNCT
cana-1171	209	8	(	(	PUNCT
cana-1171	209	9	1	1	NUM
cana-1171	209	10	−	−	PROPN
cana-1171	209	11	𝑝	𝑝	NOUN
cana-1171	209	12	)	)	PUNCT
cana-1171	209	13	(	(	PUNCT
cana-1171	209	14	𝑑2𝑤	𝑑2𝑤	ADP
cana-1171	209	15	𝑑𝑦2	𝑑𝑦2	X
cana-1171	209	16	)	)	PUNCT
cana-1171	210	1	+	+	PUNCT
cana-1171	210	2	𝑝	𝑝	NOUN
cana-1171	210	3	[	[	PUNCT
cana-1171	210	4	𝑑2𝑤	𝑑2𝑤	ADP
cana-1171	210	5	𝑑𝑦2	𝑑𝑦2	NOUN
cana-1171	210	6	−	−	PROPN
cana-1171	210	7	𝜆1𝑤𝑣	𝜆1𝑤𝑣	PUNCT
cana-1171	211	1	+	+	PUNCT
cana-1171	211	2	𝐶𝑢𝑣𝑤	𝐶𝑢𝑣𝑤	PROPN
cana-1171	211	3	]	]	X
cana-1171	211	4	=	=	SYM
cana-1171	211	5	0	0	PUNCT
cana-1171	211	6	𝑑2𝑤	𝑑2𝑤	ADP
cana-1171	211	7	𝑑𝑦2	𝑑𝑦2	NOUN
cana-1171	211	8	−	−	PROPN
cana-1171	211	9	𝑝𝜆1𝑤𝑣	𝑝𝜆1𝑤𝑣	NOUN
cana-1171	212	1	+	+	CCONJ
cana-1171	212	2	𝑝𝐶𝑢𝑣𝑤	𝑝𝐶𝑢𝑣𝑤	PROPN
cana-1171	212	3	=	=	SYM
cana-1171	212	4	0	0	NUM
cana-1171	212	5	(	(	PUNCT
cana-1171	212	6	𝐴3	𝐴3	PROPN
cana-1171	212	7	)	)	PUNCT
cana-1171	212	8	by	by	ADP
cana-1171	212	9	perturbation	perturbation	NOUN
cana-1171	212	10	technique	technique	NOUN
cana-1171	212	11	,	,	PUNCT
cana-1171	212	12	𝑢	𝑢	X
cana-1171	212	13	,	,	PUNCT
cana-1171	212	14	𝑣	𝑣	X
cana-1171	212	15	and	and	CCONJ
cana-1171	212	16	𝑤	𝑤	AUX
cana-1171	212	17	can	can	AUX
cana-1171	212	18	be	be	AUX
cana-1171	212	19	written	write	VERB
cana-1171	212	20	as	as	ADP
cana-1171	212	21	a	a	DET
cana-1171	212	22	series	series	NOUN
cana-1171	212	23	in	in	ADP
cana-1171	212	24	𝑝	𝑝	PROPN
cana-1171	212	25	as	as	SCONJ
cana-1171	212	26	follows	follow	VERB
cana-1171	212	27	:	:	PUNCT
cana-1171	212	28	𝑢	𝑢	X
cana-1171	212	29	=	=	X
cana-1171	212	30	𝑢0	𝑢0	PROPN
cana-1171	212	31	+	+	CCONJ
cana-1171	212	32	𝑝𝑢1	𝑝𝑢1	NOUN
cana-1171	212	33	+	+	X
cana-1171	212	34	𝑝2𝑢2	𝑝2𝑢2	X
cana-1171	213	1	+	+	CCONJ
cana-1171	213	2	⋯	⋯	PROPN
cana-1171	213	3	(	(	PUNCT
cana-1171	213	4	𝐴4	𝐴4	PROPN
cana-1171	213	5	)	)	PUNCT
cana-1171	213	6	𝑣	𝑣	ADP
cana-1171	213	7	=	=	PUNCT
cana-1171	213	8	𝑣0	𝑣0	PROPN
cana-1171	213	9	+	+	CCONJ
cana-1171	213	10	𝑝𝑣1	𝑝𝑣1	PROPN
cana-1171	213	11	+	+	CCONJ
cana-1171	213	12	𝑝2𝑣2	𝑝2𝑣2	PROPN
cana-1171	213	13	+	+	SYM
cana-1171	213	14	⋯	⋯	PROPN
cana-1171	213	15	(	(	PUNCT
cana-1171	213	16	𝐴5	𝐴5	PROPN
cana-1171	213	17	)	)	PUNCT
cana-1171	213	18	𝑤	𝑤	PROPN
cana-1171	213	19	=	=	SYM
cana-1171	213	20	𝑤0	𝑤0	PROPN
cana-1171	214	1	+	+	CCONJ
cana-1171	214	2	𝑝𝑤1	𝑝𝑤1	NOUN
cana-1171	214	3	+	+	SYM
cana-1171	214	4	𝑝2𝑤2	𝑝2𝑤2	X
cana-1171	214	5	+	+	CCONJ
cana-1171	214	6	⋯	⋯	PROPN
cana-1171	214	7	(	(	PUNCT
cana-1171	214	8	𝐴6	𝐴6	PROPN
cana-1171	214	9	)	)	PUNCT
cana-1171	214	10	equating	equate	VERB
cana-1171	214	11	the	the	DET
cana-1171	214	12	identical	identical	ADJ
cana-1171	214	13	powers	power	NOUN
cana-1171	214	14	of	of	ADP
cana-1171	214	15	𝑝	𝑝	NOUN
cana-1171	214	16	on	on	ADP
cana-1171	214	17	both	both	DET
cana-1171	214	18	sides	side	NOUN
cana-1171	214	19	of	of	ADP
cana-1171	214	20	equation	equation	NOUN
cana-1171	214	21	(	(	PUNCT
cana-1171	214	22	𝐴1	𝐴1	PROPN
cana-1171	214	23	)	)	PUNCT
cana-1171	214	24	and	and	CCONJ
cana-1171	214	25	(	(	PUNCT
cana-1171	214	26	𝐴4	𝐴4	PROPN
cana-1171	214	27	)	)	PUNCT
cana-1171	214	28	to	to	ADP
cana-1171	214	29	(	(	PUNCT
cana-1171	214	30	𝐴6	𝐴6	PROPN
cana-1171	214	31	)	)	PUNCT
cana-1171	214	32	gives	give	VERB
cana-1171	214	33	,	,	PUNCT
cana-1171	214	34	communications	communication	NOUN
cana-1171	214	35	on	on	ADP
cana-1171	214	36	applied	apply	VERB
cana-1171	214	37	nonlinear	nonlinear	ADJ
cana-1171	214	38	analysis	analysis	NOUN
cana-1171	214	39	issn	issn	NOUN
cana-1171	214	40	:	:	PUNCT
cana-1171	214	41	1074	1074	NUM
cana-1171	214	42	-	-	PUNCT
cana-1171	214	43	133x	133x	NUM
cana-1171	214	44	vol	vol	NOUN
cana-1171	214	45	31	31	NUM
cana-1171	214	46	no	no	NOUN
cana-1171	214	47	.	.	PUNCT
cana-1171	215	1	6s	6s	NUM
cana-1171	215	2	(	(	PUNCT
cana-1171	215	3	2024	2024	NUM
cana-1171	215	4	)	)	PUNCT
cana-1171	215	5	128	128	NUM
cana-1171	215	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1171	215	7	𝑝0	𝑝0	NOUN
cana-1171	215	8	∶	∶	NOUN
cana-1171	215	9	𝑑2𝑢0	𝑑2𝑢0	PUNCT
cana-1171	215	10	𝑑𝑦2	𝑑𝑦2	X
cana-1171	215	11	=	=	SYM
cana-1171	215	12	0	0	NUM
cana-1171	215	13	(	(	PUNCT
cana-1171	215	14	𝐴7	𝐴7	PROPN
cana-1171	215	15	)	)	PUNCT
cana-1171	215	16	𝑝1	𝑝1	NOUN
cana-1171	215	17	∶	∶	NOUN
cana-1171	215	18	𝑑2𝑢1	𝑑2𝑢1	PUNCT
cana-1171	215	19	𝑑𝑦2	𝑑𝑦2	X
cana-1171	215	20	+	+	CCONJ
cana-1171	215	21	𝜆1𝑤0𝑣0	𝜆1𝑤0𝑣0	ADJ
cana-1171	215	22	−	−	PROPN
cana-1171	215	23	𝐶𝑢0𝑤0	𝐶𝑢0𝑤0	NUM
cana-1171	215	24	(	(	PUNCT
cana-1171	215	25	𝐴8	𝐴8	PROPN
cana-1171	215	26	)	)	PUNCT
cana-1171	215	27	⋮	⋮	NOUN
cana-1171	215	28	at	at	ADP
cana-1171	215	29	𝑦	𝑦	NOUN
cana-1171	215	30	=	=	SYM
cana-1171	215	31	1	1	NUM
cana-1171	215	32	,	,	PUNCT
cana-1171	215	33	𝑢0	𝑢0	NOUN
cana-1171	215	34	=	=	SYM
cana-1171	215	35	1	1	NUM
cana-1171	215	36	,	,	PUNCT
cana-1171	215	37	𝑢𝑖	𝑢𝑖	PRON
cana-1171	215	38	=	=	SYM
cana-1171	215	39	0	0	NUM
cana-1171	215	40	∀	∀	NOUN
cana-1171	215	41	𝑖	𝑖	NOUN
cana-1171	216	1	=	=	NOUN
cana-1171	216	2	1,2,3	1,2,3	NUM
cana-1171	216	3	,	,	PUNCT
cana-1171	216	4	…	…	PUNCT
cana-1171	216	5	(	(	PUNCT
cana-1171	216	6	𝐴9	𝐴9	PROPN
cana-1171	216	7	)	)	PUNCT
cana-1171	217	1	at	at	ADP
cana-1171	217	2	𝑦	𝑦	NOUN
cana-1171	217	3	=	=	SYM
cana-1171	217	4	0	0	NUM
cana-1171	217	5	,	,	PUNCT
cana-1171	217	6	𝑢0	𝑢0	PROPN
cana-1171	217	7	=	=	SYM
cana-1171	217	8	𝑠	𝑠	PROPN
cana-1171	217	9	,	,	PUNCT
cana-1171	217	10	𝑢𝑖	𝑢𝑖	NOUN
cana-1171	217	11	=	=	SYM
cana-1171	217	12	0	0	NUM
cana-1171	217	13	∀	∀	NOUN
cana-1171	217	14	𝑖	𝑖	NOUN
cana-1171	217	15	=	=	NOUN
cana-1171	217	16	1,2,3	1,2,3	NUM
cana-1171	217	17	,	,	PUNCT
cana-1171	217	18	…	…	PUNCT
cana-1171	217	19	(	(	PUNCT
cana-1171	217	20	𝐴10	𝐴10	PROPN
cana-1171	217	21	)	)	PUNCT
cana-1171	217	22	equating	equate	VERB
cana-1171	217	23	the	the	DET
cana-1171	217	24	identical	identical	ADJ
cana-1171	217	25	powers	power	NOUN
cana-1171	217	26	of	of	ADP
cana-1171	217	27	𝑝	𝑝	NOUN
cana-1171	217	28	on	on	ADP
cana-1171	217	29	both	both	DET
cana-1171	217	30	sides	side	NOUN
cana-1171	217	31	of	of	ADP
cana-1171	217	32	equation	equation	NOUN
cana-1171	217	33	(	(	PUNCT
cana-1171	217	34	𝐴2	𝐴2	PROPN
cana-1171	217	35	)	)	PUNCT
cana-1171	217	36	and	and	CCONJ
cana-1171	217	37	(	(	PUNCT
cana-1171	217	38	𝐴4	𝐴4	PROPN
cana-1171	217	39	)	)	PUNCT
cana-1171	217	40	to	to	ADP
cana-1171	217	41	(	(	PUNCT
cana-1171	217	42	𝐴6	𝐴6	PROPN
cana-1171	217	43	)	)	PUNCT
cana-1171	217	44	gives	give	VERB
cana-1171	217	45	,	,	PUNCT
cana-1171	217	46	𝑝0	𝑝0	PROPN
cana-1171	217	47	∶	∶	NOUN
cana-1171	217	48	𝑑2𝑣0	𝑑2𝑣0	VERB
cana-1171	217	49	𝑑𝑦2	𝑑𝑦2	X
cana-1171	217	50	=	=	SYM
cana-1171	217	51	0	0	NUM
cana-1171	217	52	(	(	PUNCT
cana-1171	217	53	𝐴11	𝐴11	PROPN
cana-1171	217	54	)	)	PUNCT
cana-1171	217	55	𝑝1	𝑝1	NOUN
cana-1171	217	56	∶	∶	NOUN
cana-1171	217	57	𝑑2𝑣1	𝑑2𝑣1	NOUN
cana-1171	217	58	𝑑𝑦2	𝑑𝑦2	NOUN
cana-1171	217	59	−	−	PROPN
cana-1171	217	60	𝜆1𝑤0𝑣0	𝜆1𝑤0𝑣0	PROPN
cana-1171	217	61	+	+	PROPN
cana-1171	217	62	𝐶𝑢0𝑤0𝑣0	𝐶𝑢0𝑤0𝑣0	PROPN
cana-1171	217	63	=	=	SYM
cana-1171	217	64	0	0	PUNCT
cana-1171	217	65	(	(	PUNCT
cana-1171	217	66	𝐴12	𝐴12	PROPN
cana-1171	217	67	)	)	PUNCT
cana-1171	217	68	⋮	⋮	NOUN
cana-1171	217	69	at	at	ADP
cana-1171	217	70	𝑦	𝑦	NOUN
cana-1171	217	71	=	=	SYM
cana-1171	217	72	1	1	NUM
cana-1171	217	73	,	,	PUNCT
cana-1171	217	74	𝑣0	𝑣0	NOUN
cana-1171	217	75	=	=	SYM
cana-1171	217	76	0	0	NUM
cana-1171	217	77	∀	∀	NOUN
cana-1171	217	78	𝑖	𝑖	NOUN
cana-1171	217	79	=	=	NOUN
cana-1171	217	80	0,1,2,3	0,1,2,3	NUM
cana-1171	217	81	,	,	PUNCT
cana-1171	217	82	…	…	PUNCT
cana-1171	217	83	(	(	PUNCT
cana-1171	217	84	𝐴13	𝐴13	PROPN
cana-1171	217	85	)	)	PUNCT
cana-1171	217	86	at	at	ADP
cana-1171	217	87	𝑦	𝑦	NOUN
cana-1171	217	88	=	=	SYM
cana-1171	217	89	0	0	NUM
cana-1171	217	90	,	,	PUNCT
cana-1171	217	91	𝑑𝑢𝑖	𝑑𝑢𝑖	PRON
cana-1171	217	92	𝑑𝑦	𝑑𝑦	ADP
cana-1171	217	93	+	+	NUM
cana-1171	217	94	𝑑𝑣𝑖	𝑑𝑣𝑖	NOUN
cana-1171	217	95	𝑑𝑦	𝑑𝑦	NOUN
cana-1171	217	96	=	=	NOUN
cana-1171	217	97	0	0	NUM
cana-1171	217	98	∀	∀	NOUN
cana-1171	217	99	𝑖	𝑖	SYM
cana-1171	217	100	=	=	NOUN
cana-1171	217	101	0,1,2,3	0,1,2,3	NUM
cana-1171	217	102	(	(	PUNCT
cana-1171	217	103	𝐴14	𝐴14	NOUN
cana-1171	217	104	)	)	PUNCT
cana-1171	217	105	equating	equate	VERB
cana-1171	217	106	the	the	DET
cana-1171	217	107	identical	identical	ADJ
cana-1171	217	108	powers	power	NOUN
cana-1171	217	109	of	of	ADP
cana-1171	217	110	p	p	NOUN
cana-1171	217	111	on	on	ADP
cana-1171	217	112	both	both	DET
cana-1171	217	113	sides	side	NOUN
cana-1171	217	114	of	of	ADP
cana-1171	217	115	equation	equation	NOUN
cana-1171	217	116	(	(	PUNCT
cana-1171	217	117	𝐴3	𝐴3	PROPN
cana-1171	217	118	)	)	PUNCT
cana-1171	217	119	and	and	CCONJ
cana-1171	217	120	(	(	PUNCT
cana-1171	217	121	𝐴4	𝐴4	PROPN
cana-1171	217	122	)	)	PUNCT
cana-1171	217	123	to	to	ADP
cana-1171	217	124	(	(	PUNCT
cana-1171	217	125	𝐴6	𝐴6	PROPN
cana-1171	217	126	)	)	PUNCT
cana-1171	217	127	gives	give	VERB
cana-1171	217	128	,	,	PUNCT
cana-1171	217	129	𝑝0	𝑝0	PROPN
cana-1171	217	130	∶	∶	PROPN
cana-1171	217	131	𝑑2𝑤0	𝑑2𝑤0	NOUN
cana-1171	217	132	𝑑𝑦2	𝑑𝑦2	X
cana-1171	217	133	=	=	SYM
cana-1171	217	134	0	0	PUNCT
cana-1171	217	135	(	(	PUNCT
cana-1171	217	136	𝐴15	𝐴15	PROPN
cana-1171	217	137	)	)	PUNCT
cana-1171	217	138	𝑝1	𝑝1	NOUN
cana-1171	217	139	∶	∶	PROPN
cana-1171	217	140	𝑑2𝑤1	𝑑2𝑤1	NOUN
cana-1171	217	141	𝑑𝑦2	𝑑𝑦2	NOUN
cana-1171	217	142	−	−	PROPN
cana-1171	218	1	𝜆1𝑤0𝑣0	𝜆1𝑤0𝑣0	NOUN
cana-1171	219	1	+	+	CCONJ
cana-1171	219	2	𝐶𝑢0𝑤0	𝐶𝑢0𝑤0	NUM
cana-1171	219	3	(	(	PUNCT
cana-1171	219	4	𝐴16	𝐴16	PROPN
cana-1171	219	5	)	)	PUNCT
cana-1171	219	6	⋮	⋮	NOUN
cana-1171	219	7	at	at	ADP
cana-1171	219	8	𝑦	𝑦	NOUN
cana-1171	219	9	=	=	SYM
cana-1171	219	10	1	1	NUM
cana-1171	219	11	,	,	PUNCT
cana-1171	219	12	𝑤0	𝑤0	NOUN
cana-1171	219	13	=	=	PUNCT
cana-1171	220	1	𝛾	𝛾	PROPN
cana-1171	220	2	𝑤𝑖	𝑤𝑖	NOUN
cana-1171	220	3	=	=	SYM
cana-1171	220	4	0	0	NUM
cana-1171	220	5	∀	∀	NOUN
cana-1171	220	6	𝑖	𝑖	NOUN
cana-1171	221	1	=	=	NOUN
cana-1171	221	2	1,2,3	1,2,3	NUM
cana-1171	221	3	,	,	PUNCT
cana-1171	221	4	…	…	PUNCT
cana-1171	221	5	(	(	PUNCT
cana-1171	221	6	𝐴17	𝐴17	X
cana-1171	221	7	)	)	PUNCT
cana-1171	221	8	at	at	ADP
cana-1171	221	9	𝑦	𝑦	NOUN
cana-1171	221	10	=	=	SYM
cana-1171	221	11	0	0	NUM
cana-1171	221	12	,	,	PUNCT
cana-1171	221	13	𝑑𝑤𝑖	𝑑𝑤𝑖	NOUN
cana-1171	221	14	𝑑𝑦	𝑑𝑦	NOUN
cana-1171	222	1	=	=	SYM
cana-1171	222	2	0	0	NUM
cana-1171	222	3	∀	∀	NOUN
cana-1171	222	4	𝑖	𝑖	NOUN
cana-1171	222	5	=	=	NOUN
cana-1171	222	6	0,1,2,3	0,1,2,3	NUM
cana-1171	222	7	,	,	PUNCT
cana-1171	222	8	…	…	PUNCT
cana-1171	222	9	(	(	PUNCT
cana-1171	222	10	𝐴18	𝐴18	PROPN
cana-1171	222	11	)	)	PUNCT
cana-1171	222	12	integrating	integrating	NOUN
cana-1171	222	13	(	(	PUNCT
cana-1171	222	14	𝐴7	𝐴7	PROPN
cana-1171	222	15	)	)	PUNCT
cana-1171	222	16	,	,	PUNCT
cana-1171	222	17	(	(	PUNCT
cana-1171	222	18	𝐴8	𝐴8	PROPN
cana-1171	222	19	)	)	PUNCT
cana-1171	222	20	,	,	PUNCT
cana-1171	222	21	(	(	PUNCT
cana-1171	222	22	𝐴11	𝐴11	PROPN
cana-1171	222	23	)	)	PUNCT
cana-1171	222	24	,	,	PUNCT
cana-1171	222	25	(	(	PUNCT
cana-1171	222	26	𝐴12	𝐴12	PROPN
cana-1171	222	27	)	)	PUNCT
cana-1171	222	28	,	,	PUNCT
cana-1171	222	29	(	(	PUNCT
cana-1171	222	30	𝐴15	𝐴15	PROPN
cana-1171	222	31	)	)	PUNCT
cana-1171	222	32	,	,	PUNCT
cana-1171	222	33	(	(	PUNCT
cana-1171	222	34	𝐴16	𝐴16	PROPN
cana-1171	222	35	)	)	PUNCT
cana-1171	222	36	with	with	ADP
cana-1171	222	37	respect	respect	NOUN
cana-1171	222	38	to	to	ADP
cana-1171	222	39	y	y	PROPN
cana-1171	222	40	,	,	PUNCT
cana-1171	222	41	𝑢0(𝑦	𝑢0(𝑦	PROPN
cana-1171	222	42	)	)	PUNCT
cana-1171	222	43	=	=	SYM
cana-1171	222	44	𝑦(1	𝑦(1	NOUN
cana-1171	222	45	−	−	PROPN
cana-1171	222	46	𝑠	𝑠	NOUN
cana-1171	222	47	)	)	PUNCT
cana-1171	223	1	+	+	CCONJ
cana-1171	223	2	𝑠	𝑠	X
cana-1171	223	3	;	;	PUNCT
cana-1171	223	4	𝑣0(𝑦	𝑣0(𝑦	X
cana-1171	223	5	)	)	PUNCT
cana-1171	223	6	=	=	SYM
cana-1171	224	1	(	(	PUNCT
cana-1171	224	2	𝑠	𝑠	NUM
cana-1171	224	3	−	−	PROPN
cana-1171	224	4	1)𝑦	1)𝑦	PROPN
cana-1171	224	5	+	+	CCONJ
cana-1171	224	6	(	(	PUNCT
cana-1171	224	7	1	1	NUM
cana-1171	224	8	−	−	PROPN
cana-1171	224	9	𝑠	𝑠	NOUN
cana-1171	224	10	)	)	PUNCT
cana-1171	224	11	;	;	PUNCT
cana-1171	224	12	𝑤0(𝑦	𝑤0(𝑦	X
cana-1171	224	13	)	)	PUNCT
cana-1171	225	1	=	=	SYM
cana-1171	225	2	𝛾	𝛾	X
cana-1171	225	3	(	(	PUNCT
cana-1171	225	4	𝐴19	𝐴19	PROPN
cana-1171	225	5	)	)	PUNCT
cana-1171	225	6	𝑢1(𝑦	𝑢1(𝑦	PROPN
cana-1171	225	7	)	)	PUNCT
cana-1171	225	8	=	=	SYM
cana-1171	225	9	𝐶𝛾(2𝑠	𝐶𝛾(2𝑠	PROPN
cana-1171	225	10	−	−	NOUN
cana-1171	225	11	𝑠2	𝑠2	NOUN
cana-1171	225	12	−	−	PROPN
cana-1171	225	13	1	1	NUM
cana-1171	225	14	)	)	PUNCT
cana-1171	225	15	12	12	NUM
cana-1171	225	16	𝑦4	𝑦4	NOUN
cana-1171	225	17	+	+	CCONJ
cana-1171	225	18	𝛾(2𝐶𝑠2	𝛾(2𝐶𝑠2	NOUN
cana-1171	225	19	−	−	PROPN
cana-1171	225	20	3𝐶𝑠	3𝐶𝑠	PROPN
cana-1171	225	21	+	+	CCONJ
cana-1171	225	22	𝐶	𝐶	PROPN
cana-1171	225	23	−	−	PROPN
cana-1171	225	24	𝜆1𝑠	𝜆1𝑠	PUNCT
cana-1171	225	25	+	+	NUM
cana-1171	225	26	𝜆1	𝜆1	NOUN
cana-1171	225	27	)	)	PUNCT
cana-1171	225	28	6	6	NUM
cana-1171	225	29	𝑦3	𝑦3	PROPN
cana-1171	225	30	+	+	CCONJ
cana-1171	225	31	𝛾(𝐶𝑠	𝛾(𝐶𝑠	NOUN
cana-1171	225	32	−	−	NOUN
cana-1171	225	33	𝐶𝑠2	𝐶𝑠2	NOUN
cana-1171	225	34	−	−	PROPN
cana-1171	225	35	𝜆1	𝜆1	NOUN
cana-1171	225	36	+	+	CCONJ
cana-1171	225	37	𝜆1𝑠	𝜆1𝑠	NOUN
cana-1171	225	38	)	)	PUNCT
cana-1171	225	39	2	2	NUM
cana-1171	225	40	𝑦2	𝑦2	NOUN
cana-1171	225	41	+	+	CCONJ
cana-1171	225	42	(	(	PUNCT
cana-1171	225	43	3𝐶𝑠2𝛾	3𝐶𝑠2𝛾	PRON
cana-1171	225	44	−	−	PROPN
cana-1171	225	45	2𝐶𝑠𝛾	2𝐶𝑠𝛾	NOUN
cana-1171	226	1	−	−	PROPN
cana-1171	226	2	𝐶𝛾	𝐶𝛾	NOUN
cana-1171	226	3	−	−	PROPN
cana-1171	226	4	4𝜆1𝑠𝛾	4𝜆1𝑠𝛾	NUM
cana-1171	227	1	+	+	CCONJ
cana-1171	227	2	4𝜆1𝛾	4𝜆1𝛾	NUM
cana-1171	227	3	)	)	PUNCT
cana-1171	227	4	12	12	NUM
cana-1171	227	5	(	(	PUNCT
cana-1171	227	6	𝐴20	𝐴20	NOUN
cana-1171	227	7	)	)	PUNCT
cana-1171	227	8	communications	communication	NOUN
cana-1171	227	9	on	on	ADP
cana-1171	227	10	applied	apply	VERB
cana-1171	227	11	nonlinear	nonlinear	ADJ
cana-1171	227	12	analysis	analysis	NOUN
cana-1171	227	13	issn	issn	NOUN
cana-1171	227	14	:	:	PUNCT
cana-1171	227	15	1074	1074	NUM
cana-1171	227	16	-	-	PUNCT
cana-1171	227	17	133x	133x	NUM
cana-1171	227	18	vol	vol	NOUN
cana-1171	227	19	31	31	NUM
cana-1171	227	20	no	no	NOUN
cana-1171	227	21	.	.	PUNCT
cana-1171	228	1	6s	6s	NUM
cana-1171	228	2	(	(	PUNCT
cana-1171	228	3	2024	2024	NUM
cana-1171	228	4	)	)	PUNCT
cana-1171	228	5	129	129	NUM
cana-1171	228	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1171	228	7	𝑣1(𝑦	𝑣1(𝑦	AUX
cana-1171	228	8	)	)	PUNCT
cana-1171	228	9	=	=	SYM
cana-1171	228	10	𝐶𝛾(𝑠2	𝐶𝛾(𝑠2	PROPN
cana-1171	229	1	−	−	NOUN
cana-1171	229	2	2𝑠	2𝑠	NOUN
cana-1171	229	3	+	+	CCONJ
cana-1171	229	4	1	1	X
cana-1171	229	5	)	)	PUNCT
cana-1171	229	6	12	12	NUM
cana-1171	229	7	𝑦4	𝑦4	NOUN
cana-1171	229	8	+	+	CCONJ
cana-1171	229	9	𝛾(3𝐶𝑠	𝛾(3𝐶𝑠	ADP
cana-1171	229	10	−	−	PROPN
cana-1171	229	11	2𝐶𝑠2	2𝐶𝑠2	NOUN
cana-1171	229	12	−	−	PROPN
cana-1171	229	13	𝐶	𝐶	PROPN
cana-1171	229	14	+	+	CCONJ
cana-1171	229	15	𝜆1𝑠	𝜆1𝑠	NOUN
cana-1171	229	16	−	−	PROPN
cana-1171	229	17	𝜆1	𝜆1	NOUN
cana-1171	229	18	)	)	PUNCT
cana-1171	229	19	6	6	NUM
cana-1171	229	20	𝑦3	𝑦3	PROPN
cana-1171	229	21	+	+	NUM
cana-1171	229	22	𝛾(𝐶𝑠2	𝛾(𝐶𝑠2	PROPN
cana-1171	229	23	−	−	PROPN
cana-1171	230	1	𝐶𝑠	𝐶𝑠	PROPN
cana-1171	230	2	+	+	PROPN
cana-1171	230	3	𝜆1	𝜆1	VERB
cana-1171	230	4	−	−	PROPN
cana-1171	230	5	𝜆1𝑠	𝜆1𝑠	NOUN
cana-1171	230	6	)	)	PUNCT
cana-1171	230	7	2	2	NUM
cana-1171	230	8	𝑦2	𝑦2	NOUN
cana-1171	230	9	+	+	CCONJ
cana-1171	230	10	(	(	PUNCT
cana-1171	230	11	2𝐶𝑠𝛾	2𝐶𝑠𝛾	NUM
cana-1171	230	12	−	−	NOUN
cana-1171	231	1	3𝐶𝑠2𝛾	3𝐶𝑠2𝛾	NOUN
cana-1171	232	1	+	+	CCONJ
cana-1171	232	2	𝐶𝛾	𝐶𝛾	PROPN
cana-1171	232	3	−	−	PROPN
cana-1171	232	4	4𝜆1𝑠𝛾	4𝜆1𝑠𝛾	NUM
cana-1171	232	5	+	+	CCONJ
cana-1171	232	6	4𝜆1𝛾	4𝜆1𝛾	NUM
cana-1171	232	7	)	)	PUNCT
cana-1171	232	8	12	12	NUM
cana-1171	232	9	𝑦	𝑦	NOUN
cana-1171	232	10	(	(	PUNCT
cana-1171	232	11	𝐴21	𝐴21	PROPN
cana-1171	232	12	)	)	PUNCT
cana-1171	232	13	𝑤1(𝑦	𝑤1(𝑦	PROPN
cana-1171	232	14	)	)	PUNCT
cana-1171	232	15	=	=	SYM
cana-1171	232	16	𝐶𝛾(𝑠2	𝐶𝛾(𝑠2	PROPN
cana-1171	232	17	−	−	NOUN
cana-1171	232	18	2𝑠	2𝑠	NOUN
cana-1171	233	1	+	+	CCONJ
cana-1171	234	1	1	1	X
cana-1171	234	2	)	)	PUNCT
cana-1171	234	3	12	12	NUM
cana-1171	234	4	𝑦4	𝑦4	NOUN
cana-1171	234	5	+	+	CCONJ
cana-1171	234	6	𝛾(3𝐶𝑠	𝛾(3𝐶𝑠	ADP
cana-1171	234	7	−	−	PROPN
cana-1171	234	8	2𝐶𝑠2	2𝐶𝑠2	NOUN
cana-1171	234	9	−	−	PROPN
cana-1171	234	10	𝐶	𝐶	PROPN
cana-1171	234	11	+	+	CCONJ
cana-1171	234	12	𝜆1𝑠	𝜆1𝑠	NOUN
cana-1171	234	13	−	−	PROPN
cana-1171	234	14	𝜆1	𝜆1	NOUN
cana-1171	234	15	)	)	PUNCT
cana-1171	234	16	6	6	NUM
cana-1171	234	17	𝑦3	𝑦3	PROPN
cana-1171	234	18	+	+	NUM
cana-1171	234	19	𝛾(𝐶𝑠2	𝛾(𝐶𝑠2	PROPN
cana-1171	234	20	−	−	PROPN
cana-1171	235	1	𝐶𝑠	𝐶𝑠	PROPN
cana-1171	235	2	+	+	PROPN
cana-1171	235	3	𝜆1	𝜆1	VERB
cana-1171	235	4	−	−	PROPN
cana-1171	235	5	𝜆1𝑠	𝜆1𝑠	NOUN
cana-1171	235	6	)	)	PUNCT
cana-1171	235	7	2	2	NUM
cana-1171	235	8	𝑦2	𝑦2	NOUN
cana-1171	236	1	+	+	CCONJ
cana-1171	237	1	2𝐶𝑠𝛾	2𝐶𝑠𝛾	NUM
cana-1171	238	1	−	−	PROPN
cana-1171	239	1	3𝐶𝑠2𝛾	3𝐶𝑠2𝛾	NOUN
cana-1171	240	1	+	+	CCONJ
cana-1171	241	1	𝐶𝛾	𝐶𝛾	AUX
cana-1171	241	2	+	+	PROPN
cana-1171	241	3	4𝜆1𝑠𝛾	4𝜆1𝑠𝛾	NUM
cana-1171	241	4	−	−	NOUN
cana-1171	241	5	4𝜆1𝛾	4𝜆1𝛾	NOUN
cana-1171	241	6	12	12	NUM
cana-1171	241	7	(	(	PUNCT
cana-1171	241	8	𝐴22	𝐴22	X
cana-1171	241	9	)	)	PUNCT
cana-1171	241	10	letting	let	VERB
cana-1171	241	11	𝑝	𝑝	ADP
cana-1171	241	12	→	→	SYM
cana-1171	241	13	1	1	NUM
cana-1171	241	14	gives	give	NOUN
cana-1171	241	15	,	,	PUNCT
cana-1171	241	16	therefore	therefore	ADV
cana-1171	241	17	𝑢(𝑦	𝑢(𝑦	ADJ
cana-1171	241	18	)	)	PUNCT
cana-1171	242	1	=	=	SYM
cana-1171	242	2	𝑠	𝑠	PROPN
cana-1171	243	1	+	+	CCONJ
cana-1171	243	2	(	(	PUNCT
cana-1171	243	3	12	12	NUM
cana-1171	243	4	−	−	NUM
cana-1171	243	5	12𝑠	12𝑠	NUM
cana-1171	244	1	+	+	CCONJ
cana-1171	245	1	3𝐶𝑠2𝛾	3𝐶𝑠2𝛾	NUM
cana-1171	245	2	−	−	NUM
cana-1171	245	3	2𝐶𝑠𝛾	2𝐶𝑠𝛾	NOUN
cana-1171	245	4	−	−	PROPN
cana-1171	246	1	𝐶𝛾	𝐶𝛾	NOUN
cana-1171	246	2	−	−	PROPN
cana-1171	246	3	4𝜆1𝑠𝛾	4𝜆1𝑠𝛾	NUM
cana-1171	247	1	+	+	CCONJ
cana-1171	247	2	4𝜆1𝛾	4𝜆1𝛾	NUM
cana-1171	247	3	)	)	PUNCT
cana-1171	247	4	12	12	NUM
cana-1171	247	5	𝑦	𝑦	NOUN
cana-1171	247	6	+	+	NUM
cana-1171	247	7	𝛾(𝐶𝑠	𝛾(𝐶𝑠	NOUN
cana-1171	247	8	−	−	NOUN
cana-1171	247	9	𝐶𝑠2	𝐶𝑠2	NOUN
cana-1171	247	10	−	−	PROPN
cana-1171	247	11	𝜆1	𝜆1	NOUN
cana-1171	247	12	+	+	CCONJ
cana-1171	247	13	𝜆1𝑠	𝜆1𝑠	NOUN
cana-1171	247	14	)	)	PUNCT
cana-1171	247	15	2	2	NUM
cana-1171	247	16	𝑦2	𝑦2	NOUN
cana-1171	247	17	+	+	CCONJ
cana-1171	247	18	𝛾(2𝐶𝑠2	𝛾(2𝐶𝑠2	PROPN
cana-1171	247	19	−	−	PROPN
cana-1171	247	20	3𝐶𝑠	3𝐶𝑠	PROPN
cana-1171	247	21	+	+	CCONJ
cana-1171	247	22	𝐶	𝐶	PROPN
cana-1171	247	23	−	−	PROPN
cana-1171	247	24	𝜆1𝑠	𝜆1𝑠	PUNCT
cana-1171	248	1	+	+	NUM
cana-1171	248	2	𝜆1	𝜆1	NOUN
cana-1171	248	3	)	)	PUNCT
cana-1171	248	4	6	6	NUM
cana-1171	248	5	𝑦3	𝑦3	PROPN
cana-1171	248	6	+	+	CCONJ
cana-1171	248	7	𝐶𝛾(2𝑠	𝐶𝛾(2𝑠	PROPN
cana-1171	248	8	−	−	NOUN
cana-1171	248	9	𝑠2	𝑠2	NOUN
cana-1171	248	10	−	−	PROPN
cana-1171	248	11	1	1	NUM
cana-1171	248	12	)	)	PUNCT
cana-1171	248	13	12	12	NUM
cana-1171	248	14	𝑦4	𝑦4	NOUN
cana-1171	248	15	(	(	PUNCT
cana-1171	248	16	𝐴23	𝐴23	PROPN
cana-1171	248	17	)	)	PUNCT
cana-1171	248	18	𝑣(𝑦	𝑣(𝑦	PROPN
cana-1171	248	19	)	)	PUNCT
cana-1171	248	20	=	=	NOUN
cana-1171	249	1	1	1	NUM
cana-1171	249	2	−	−	NUM
cana-1171	249	3	𝑠	𝑠	INTJ
cana-1171	249	4	−	−	PROPN
cana-1171	249	5	(	(	PUNCT
cana-1171	249	6	12	12	NUM
cana-1171	249	7	−	−	NUM
cana-1171	249	8	12𝑠	12𝑠	NUM
cana-1171	250	1	+	+	CCONJ
cana-1171	250	2	3𝐶𝑠2	3𝐶𝑠2	NUM
cana-1171	250	3	−	−	NUM
cana-1171	250	4	2𝐶𝑠𝛾	2𝐶𝑠𝛾	NOUN
cana-1171	250	5	−	−	NOUN
cana-1171	251	1	𝐶𝛾	𝐶𝛾	NOUN
cana-1171	251	2	−	−	PROPN
cana-1171	251	3	4𝜆1𝑠𝛾	4𝜆1𝑠𝛾	NUM
cana-1171	252	1	+	+	CCONJ
cana-1171	252	2	4𝜆1𝛾	4𝜆1𝛾	NUM
cana-1171	252	3	)	)	PUNCT
cana-1171	253	1	12	12	NUM
cana-1171	253	2	𝑦	𝑦	NOUN
cana-1171	253	3	−	−	PROPN
cana-1171	253	4	𝛾(𝐶𝑠	𝛾(𝐶𝑠	NOUN
cana-1171	253	5	−	−	NOUN
cana-1171	253	6	𝐶𝑠2	𝐶𝑠2	NOUN
cana-1171	253	7	−	−	PROPN
cana-1171	253	8	𝜆1	𝜆1	NOUN
cana-1171	253	9	+	+	CCONJ
cana-1171	253	10	𝜆1𝑠	𝜆1𝑠	NOUN
cana-1171	253	11	)	)	PUNCT
cana-1171	253	12	2	2	NUM
cana-1171	253	13	𝑦2	𝑦2	NOUN
cana-1171	253	14	−	−	PROPN
cana-1171	253	15	𝛾(2𝐶𝑠2	𝛾(2𝐶𝑠2	PROPN
cana-1171	253	16	−	−	PROPN
cana-1171	253	17	3𝐶𝑠	3𝐶𝑠	PROPN
cana-1171	253	18	+	+	CCONJ
cana-1171	253	19	𝐶	𝐶	PROPN
cana-1171	253	20	−	−	PROPN
cana-1171	253	21	𝜆1𝑠	𝜆1𝑠	PUNCT
cana-1171	253	22	+	+	NUM
cana-1171	253	23	𝜆1	𝜆1	NOUN
cana-1171	253	24	)	)	PUNCT
cana-1171	253	25	6	6	NUM
cana-1171	253	26	𝑦3	𝑦3	PROPN
cana-1171	253	27	−	−	PROPN
cana-1171	253	28	𝐶𝛾(2𝑠	𝐶𝛾(2𝑠	PROPN
cana-1171	253	29	−	−	PROPN
cana-1171	253	30	𝑠2	𝑠2	NOUN
cana-1171	253	31	−	−	PROPN
cana-1171	253	32	1	1	NUM
cana-1171	253	33	)	)	PUNCT
cana-1171	253	34	12	12	NUM
cana-1171	253	35	𝑦4	𝑦4	NOUN
cana-1171	253	36	(	(	PUNCT
cana-1171	253	37	𝐴24	𝐴24	NOUN
cana-1171	253	38	)	)	PUNCT
cana-1171	253	39	𝑤(𝑦	𝑤(𝑦	PUNCT
cana-1171	253	40	)	)	PUNCT
cana-1171	253	41	=	=	SYM
cana-1171	253	42	(	(	PUNCT
cana-1171	253	43	12𝛾	12𝛾	X
cana-1171	253	44	+	+	CCONJ
cana-1171	253	45	2𝐶𝑠𝛾	2𝐶𝑠𝛾	NUM
cana-1171	253	46	−	−	NOUN
cana-1171	254	1	3𝐶𝑠2𝛾	3𝐶𝑠2𝛾	NOUN
cana-1171	255	1	+	+	CCONJ
cana-1171	255	2	𝐶𝛾	𝐶𝛾	PROPN
cana-1171	255	3	+	+	NOUN
cana-1171	255	4	4𝜆1𝑠𝛾	4𝜆1𝑠𝛾	NUM
cana-1171	255	5	−	−	NOUN
cana-1171	255	6	4𝜆1𝛾	4𝜆1𝛾	NUM
cana-1171	255	7	)	)	PUNCT
cana-1171	255	8	12	12	NUM
cana-1171	255	9	−	−	NOUN
cana-1171	255	10	𝛾(𝐶𝑠	𝛾(𝐶𝑠	NOUN
cana-1171	255	11	−	−	NOUN
cana-1171	255	12	𝐶𝑠2	𝐶𝑠2	NOUN
cana-1171	255	13	−	−	PROPN
cana-1171	255	14	𝜆1	𝜆1	NOUN
cana-1171	255	15	+	+	CCONJ
cana-1171	255	16	𝜆1𝑠	𝜆1𝑠	NOUN
cana-1171	255	17	)	)	PUNCT
cana-1171	255	18	2	2	NUM
cana-1171	255	19	𝑦2	𝑦2	NOUN
cana-1171	255	20	−	−	PROPN
cana-1171	255	21	𝛾(2𝐶𝑠2	𝛾(2𝐶𝑠2	PROPN
cana-1171	255	22	−	−	PROPN
cana-1171	255	23	3𝐶𝑠	3𝐶𝑠	PROPN
cana-1171	256	1	+	+	CCONJ
cana-1171	256	2	𝐶	𝐶	PROPN
cana-1171	256	3	−	−	PROPN
cana-1171	256	4	𝜆1𝑠	𝜆1𝑠	PUNCT
cana-1171	256	5	+	+	NUM
cana-1171	256	6	𝜆1	𝜆1	NOUN
cana-1171	256	7	)	)	PUNCT
cana-1171	256	8	6	6	NUM
cana-1171	256	9	𝑦3	𝑦3	PROPN
cana-1171	256	10	−	−	PROPN
cana-1171	256	11	𝐶𝛾(2𝑠	𝐶𝛾(2𝑠	PROPN
cana-1171	256	12	−	−	PROPN
cana-1171	256	13	𝑠2	𝑠2	NOUN
cana-1171	256	14	−	−	PROPN
cana-1171	256	15	1	1	NUM
cana-1171	256	16	)	)	PUNCT
cana-1171	256	17	12	12	NUM
cana-1171	256	18	𝑦4	𝑦4	NOUN
cana-1171	256	19	(	(	PUNCT
cana-1171	256	20	𝐴25	𝐴25	PROPN
cana-1171	256	21	)	)	PUNCT
cana-1171	256	22	the	the	DET
cana-1171	256	23	equations	equation	NOUN
cana-1171	256	24	(	(	PUNCT
cana-1171	256	25	𝐴23	𝐴23	PROPN
cana-1171	256	26	)	)	PUNCT
cana-1171	256	27	,	,	PUNCT
cana-1171	256	28	(	(	PUNCT
cana-1171	256	29	𝐴24	𝐴24	NOUN
cana-1171	256	30	)	)	PUNCT
cana-1171	256	31	and	and	CCONJ
cana-1171	256	32	(	(	PUNCT
cana-1171	256	33	𝐴25	𝐴25	PROPN
cana-1171	256	34	)	)	PUNCT
cana-1171	256	35	gives	give	VERB
cana-1171	256	36	the	the	DET
cana-1171	256	37	approximate	approximate	ADJ
cana-1171	256	38	analytical	analytical	ADJ
cana-1171	256	39	solution	solution	NOUN
cana-1171	256	40	of	of	ADP
cana-1171	256	41	the	the	DET
cana-1171	256	42	system	system	NOUN
cana-1171	256	43	(	(	PUNCT
cana-1171	256	44	14	14	NUM
cana-1171	256	45	)	)	PUNCT
cana-1171	256	46	−	−	PROPN
cana-1171	257	1	(	(	PUNCT
cana-1171	257	2	16	16	NUM
cana-1171	257	3	)	)	PUNCT
cana-1171	257	4	.	.	PUNCT
cana-1171	258	1	remark	remark	NOUN
cana-1171	258	2	substituting	substitute	VERB
cana-1171	258	3	the	the	DET
cana-1171	258	4	expressions	expression	NOUN
cana-1171	258	5	of	of	ADP
cana-1171	258	6	𝑢(𝑦	𝑢(𝑦	NOUN
cana-1171	258	7	)	)	PUNCT
cana-1171	258	8	,	,	PUNCT
cana-1171	258	9	𝑣(𝑦	𝑣(𝑦	PROPN
cana-1171	258	10	)	)	PUNCT
cana-1171	258	11	and	and	CCONJ
cana-1171	258	12	𝑤(𝑦	𝑤(𝑦	NOUN
cana-1171	258	13	)	)	PUNCT
cana-1171	258	14	in	in	ADP
cana-1171	258	15	(	(	PUNCT
cana-1171	258	16	11	11	NUM
cana-1171	258	17	)	)	PUNCT
cana-1171	258	18	.	.	PUNCT
cana-1171	259	1	the	the	DET
cana-1171	259	2	concentration	concentration	NOUN
cana-1171	259	3	of	of	ADP
cana-1171	259	4	the	the	DET
cana-1171	259	5	product	product	NOUN
cana-1171	259	6	𝐵	𝐵	NOUN
cana-1171	259	7	can	can	AUX
cana-1171	259	8	be	be	AUX
cana-1171	259	9	obtained	obtain	VERB
cana-1171	259	10	as	as	ADP
cana-1171	259	11	𝑏(𝑦	𝑏(𝑦	PROPN
cana-1171	259	12	)	)	PUNCT
cana-1171	259	13	.	.	PUNCT
cana-1171	260	1	reference	reference	NOUN
cana-1171	260	2	:	:	PUNCT
cana-1171	261	1	[	[	X
cana-1171	261	2	1	1	NUM
cana-1171	261	3	]	]	X
cana-1171	261	4	m.caputo	m.caputo	ADJ
cana-1171	261	5	,	,	PUNCT
cana-1171	261	6	‘	'	PUNCT
cana-1171	261	7	elasticità	elasticità	NOUN
cana-1171	261	8	e	e	X
cana-1171	261	9	dissipazione	dissipazione	NOUN
cana-1171	261	10	’	'	PUNCT
cana-1171	261	11	,	,	PUNCT
cana-1171	261	12	zanichelli	zanichelli	PROPN
cana-1171	261	13	,	,	PUNCT
cana-1171	261	14	bologna	bologna	NOUN
cana-1171	261	15	,	,	PUNCT
cana-1171	261	16	1969	1969	NUM
cana-1171	261	17	.	.	PUNCT
cana-1171	262	1	[	[	X
cana-1171	262	2	2	2	NUM
cana-1171	262	3	]	]	PUNCT
cana-1171	262	4	oldham.b	oldham.b	NUM
cana-1171	262	5	,	,	PUNCT
cana-1171	262	6	spanier.j	spanier.j	NOUN
cana-1171	262	7	,	,	PUNCT
cana-1171	262	8	‘	'	PUNCT
cana-1171	262	9	the	the	DET
cana-1171	262	10	fractional	fractional	ADJ
cana-1171	262	11	calculus	calculus	NOUN
cana-1171	262	12	’	'	PUNCT
cana-1171	262	13	,	,	PUNCT
cana-1171	262	14	academic	academic	ADJ
cana-1171	262	15	press	press	NOUN
cana-1171	262	16	,	,	PUNCT
cana-1171	262	17	new	new	PROPN
cana-1171	262	18	york	york	PROPN
cana-1171	262	19	,	,	PUNCT
cana-1171	262	20	ny	ny	PROPN
cana-1171	262	21	,	,	PUNCT
cana-1171	262	22	usa	usa	PROPN
cana-1171	262	23	,	,	PUNCT
cana-1171	262	24	london	london	PROPN
cana-1171	262	25	,	,	PUNCT
cana-1171	262	26	uk	uk	PROPN
cana-1171	262	27	,	,	PUNCT
cana-1171	262	28	1974	1974	NUM
cana-1171	262	29	.	.	PUNCT
cana-1171	263	1	[	[	X
cana-1171	263	2	3	3	NUM
cana-1171	263	3	]	]	X
cana-1171	263	4	c.p.andrieux	c.p.andrieux	NOUN
cana-1171	263	5	,	,	PUNCT
cana-1171	263	6	j.m.dumas	j.m.duma	NOUN
cana-1171	263	7	-	-	PUNCT
cana-1171	263	8	bouchiat	bouchiat	NOUN
cana-1171	263	9	,	,	PUNCT
cana-1171	263	10	j.m.saveant	j.m.saveant	ADJ
cana-1171	263	11	,	,	PUNCT
cana-1171	263	12	‘	'	PUNCT
cana-1171	263	13	homogeneous	homogeneous	ADJ
cana-1171	263	14	redox	redox	ADJ
cana-1171	263	15	catalysis	catalysis	NOUN
cana-1171	263	16	of	of	ADP
cana-1171	263	17	electrochemical	electrochemical	ADJ
cana-1171	263	18	reaction	reaction	NOUN
cana-1171	263	19	part	part	NOUN
cana-1171	263	20	i.	i.	PROPN
cana-1171	263	21	introduction	introduction	PROPN
cana-1171	263	22	’	'	PUNCT
cana-1171	263	23	,	,	PUNCT
cana-1171	263	24	j.	j.	PROPN
cana-1171	263	25	electroanal	electroanal	PROPN
cana-1171	263	26	.	.	PUNCT
cana-1171	264	1	chem	chem	PROPN
cana-1171	264	2	.	.	PUNCT
cana-1171	264	3	,87(1978	,87(1978	PUNCT
cana-1171	264	4	)	)	PUNCT
cana-1171	264	5	39	39	NUM
cana-1171	264	6	-	-	SYM
cana-1171	264	7	53	53	NUM
cana-1171	264	8	.	.	PUNCT
cana-1171	265	1	communications	communication	NOUN
cana-1171	265	2	on	on	ADP
cana-1171	265	3	applied	apply	VERB
cana-1171	265	4	nonlinear	nonlinear	ADJ
cana-1171	265	5	analysis	analysis	NOUN
cana-1171	265	6	issn	issn	NOUN
cana-1171	265	7	:	:	PUNCT
cana-1171	265	8	1074	1074	NUM
cana-1171	265	9	-	-	PUNCT
cana-1171	265	10	133x	133x	NUM
cana-1171	265	11	vol	vol	NOUN
cana-1171	265	12	31	31	NUM
cana-1171	265	13	no	no	NOUN
cana-1171	265	14	.	.	PUNCT
cana-1171	266	1	6s	6s	NUM
cana-1171	266	2	(	(	PUNCT
cana-1171	266	3	2024	2024	NUM
cana-1171	266	4	)	)	PUNCT
cana-1171	266	5	130	130	NUM
cana-1171	266	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1171	267	1	[	[	X
cana-1171	267	2	4	4	NUM
cana-1171	267	3	]	]	X
cana-1171	267	4	c.p.andrieux	c.p.andrieux	NOUN
cana-1171	267	5	,	,	PUNCT
cana-1171	267	6	j.m.dumas	j.m.duma	NOUN
cana-1171	267	7	-	-	PUNCT
cana-1171	267	8	bouchiat	bouchiat	NOUN
cana-1171	267	9	,	,	PUNCT
cana-1171	267	10	j.m.saveant	j.m.saveant	ADJ
cana-1171	267	11	,	,	PUNCT
cana-1171	267	12	‘	'	PUNCT
cana-1171	267	13	homogeneous	homogeneous	ADJ
cana-1171	267	14	redox	redox	ADJ
cana-1171	267	15	catalysis	catalysis	NOUN
cana-1171	267	16	of	of	ADP
cana-1171	267	17	electrochemical	electrochemical	ADJ
cana-1171	267	18	reaction	reaction	NOUN
cana-1171	267	19	,	,	PUNCT
cana-1171	267	20	part	part	NOUN
cana-1171	267	21	iv.kinetic	iv.kinetic	ADJ
cana-1171	267	22	controls	control	NOUN
cana-1171	267	23	in	in	ADP
cana-1171	267	24	the	the	DET
cana-1171	267	25	homogeneous	homogeneous	ADJ
cana-1171	267	26	process	process	NOUN
cana-1171	267	27	as	as	SCONJ
cana-1171	267	28	characterized	characterize	VERB
cana-1171	267	29	by	by	ADP
cana-1171	267	30	stationary	stationary	ADJ
cana-1171	267	31	and	and	CCONJ
cana-1171	267	32	quasi	quasi	ADJ
cana-1171	267	33	-	-	ADJ
cana-1171	267	34	stationary	stationary	ADJ
cana-1171	267	35	electrochemical	electrochemical	ADJ
cana-1171	267	36	techniques	technique	NOUN
cana-1171	267	37	’	'	PUNCT
cana-1171	267	38	,	,	PUNCT
cana-1171	267	39	j.electroanal	j.electroanal	PROPN
cana-1171	267	40	.	.	PUNCT
cana-1171	267	41	chem	chem	PROPN
cana-1171	267	42	.	.	PUNCT
cana-1171	267	43	,113(1980	,113(1980	PUNCT
cana-1171	267	44	)	)	PUNCT
cana-1171	267	45	1	1	NUM
cana-1171	267	46	-	-	SYM
cana-1171	267	47	18	18	NUM
cana-1171	267	48	.	.	PUNCT
cana-1171	268	1	[	[	X
cana-1171	268	2	5	5	NUM
cana-1171	268	3	]	]	SYM
cana-1171	268	4	c.p.andrieux	c.p.andrieux	NOUN
cana-1171	268	5	,	,	PUNCT
cana-1171	268	6	c.blocman	c.blocman	NOUN
cana-1171	268	7	,	,	PUNCT
cana-1171	268	8	j.m.dumas	j.m.duma	NOUN
cana-1171	268	9	-	-	PUNCT
cana-1171	268	10	bouchiat	bouchiat	NOUN
cana-1171	268	11	,	,	PUNCT
cana-1171	268	12	f.m.halla	f.m.halla	NOUN
cana-1171	268	13	,	,	PUNCT
cana-1171	268	14	j.m.saveant	j.m.saveant	ADJ
cana-1171	268	15	,	,	PUNCT
cana-1171	268	16	‘	'	PUNCT
cana-1171	268	17	homogeneous	homogeneous	ADJ
cana-1171	268	18	redox	redox	ADJ
cana-1171	268	19	catalysis	catalysis	NOUN
cana-1171	268	20	of	of	ADP
cana-1171	268	21	electrochemical	electrochemical	ADJ
cana-1171	268	22	reaction	reaction	NOUN
cana-1171	268	23	part	part	NOUN
cana-1171	268	24	v.	v.	ADP
cana-1171	268	25	cyclic	cyclic	ADJ
cana-1171	268	26	voltammetry	voltammetry	NOUN
cana-1171	268	27	’	'	PUNCT
cana-1171	268	28	,	,	PUNCT
cana-1171	269	1	j.electroanal	j.electroanal	PROPN
cana-1171	269	2	.	.	PUNCT
cana-1171	269	3	chem	chem	PROPN
cana-1171	269	4	.	.	PUNCT
cana-1171	270	1	,113(1980	,113(1980	PUNCT
cana-1171	270	2	)	)	PUNCT
cana-1171	270	3	19	19	NUM
cana-1171	270	4	-	-	SYM
cana-1171	270	5	40	40	NUM
cana-1171	270	6	.	.	PUNCT
cana-1171	271	1	[	[	X
cana-1171	271	2	6	6	NUM
cana-1171	271	3	]	]	SYM
cana-1171	271	4	k.s.miller	k.s.miller	NOUN
cana-1171	271	5	and	and	CCONJ
cana-1171	271	6	b.ross	b.ross	NOUN
cana-1171	271	7	,	,	PUNCT
cana-1171	271	8	‘	'	PUNCT
cana-1171	271	9	an	an	DET
cana-1171	271	10	introduction	introduction	NOUN
cana-1171	271	11	to	to	ADP
cana-1171	271	12	the	the	DET
cana-1171	271	13	fractional	fractional	ADJ
cana-1171	271	14	calculus	calculus	NOUN
cana-1171	271	15	and	and	CCONJ
cana-1171	271	16	fractional	fractional	ADJ
cana-1171	271	17	differential	differential	ADJ
cana-1171	271	18	equations	equation	NOUN
cana-1171	271	19	’	'	PUNCT
cana-1171	271	20	,	,	PUNCT
cana-1171	271	21	john	john	PROPN
cana-1171	271	22	wiley	wiley	PROPN
cana-1171	271	23	&	&	CCONJ
cana-1171	271	24	sons	sons	PROPN
cana-1171	271	25	inc	inc	PROPN
cana-1171	271	26	.	.	PROPN
cana-1171	271	27	,	,	PUNCT
cana-1171	271	28	newyork	newyork	PROPN
cana-1171	271	29	,	,	PUNCT
cana-1171	271	30	1993	1993	NUM
cana-1171	271	31	.	.	PUNCT
cana-1171	272	1	[	[	X
cana-1171	272	2	7	7	X
cana-1171	272	3	]	]	X
cana-1171	272	4	ji	ji	PROPN
cana-1171	272	5	-	-	PROPN
cana-1171	272	6	huan	huan	PROPN
cana-1171	272	7	he	he	PRON
cana-1171	272	8	,	,	PUNCT
cana-1171	272	9	‘	'	PUNCT
cana-1171	272	10	homotopy	homotopy	VERB
cana-1171	272	11	perturbation	perturbation	NOUN
cana-1171	272	12	technique’,comput	technique’,comput	NOUN
cana-1171	272	13	.	.	PUNCT
cana-1171	273	1	methods	method	NOUN
cana-1171	273	2	appl	appl	PROPN
cana-1171	273	3	.	.	PROPN
cana-1171	273	4	mech	mech	PROPN
cana-1171	273	5	.	.	PUNCT
cana-1171	274	1	engrg	engrg	PROPN
cana-1171	274	2	.	.	PUNCT
cana-1171	275	1	178(1999	178(1999	NUM
cana-1171	275	2	)	)	PUNCT
cana-1171	275	3	257	257	NUM
cana-1171	275	4	-	-	SYM
cana-1171	275	5	262	262	NUM
cana-1171	275	6	.	.	PUNCT
cana-1171	276	1	[	[	X
cana-1171	276	2	8	8	NUM
cana-1171	276	3	]	]	PUNCT
cana-1171	276	4	i.podlubny	i.podlubny	ADP
cana-1171	276	5	,	,	PUNCT
cana-1171	276	6	‘	'	PUNCT
cana-1171	276	7	fractional	fractional	ADJ
cana-1171	276	8	differential	differential	ADJ
cana-1171	276	9	equations	equation	NOUN
cana-1171	276	10	’	'	PUNCT
cana-1171	276	11	,	,	PUNCT
cana-1171	276	12	mathematics	mathematic	NOUN
cana-1171	276	13	in	in	ADP
cana-1171	276	14	science	science	NOUN
cana-1171	276	15	and	and	CCONJ
cana-1171	276	16	engineering	engineering	NOUN
cana-1171	276	17	,	,	PUNCT
cana-1171	276	18	volume	volume	NOUN
cana-1171	276	19	198	198	NUM
cana-1171	276	20	(	(	PUNCT
cana-1171	276	21	1999	1999	NUM
cana-1171	276	22	)	)	PUNCT
cana-1171	276	23	.	.	PUNCT
cana-1171	277	1	[	[	X
cana-1171	277	2	9	9	NUM
cana-1171	277	3	]	]	SYM
cana-1171	277	4	a.c	a.c	PROPN
cana-1171	277	5	.	.	PROPN
cana-1171	277	6	king	king	PROPN
cana-1171	277	7	,	,	PUNCT
cana-1171	277	8	j.	j.	PROPN
cana-1171	277	9	billingham	billingham	PROPN
cana-1171	277	10	,	,	PUNCT
cana-1171	277	11	s.r	s.r	PROPN
cana-1171	277	12	.	.	PROPN
cana-1171	277	13	otto	otto	PROPN
cana-1171	277	14	,	,	PUNCT
cana-1171	277	15	‘	'	PUNCT
cana-1171	277	16	differential	differential	ADJ
cana-1171	277	17	equations	equation	NOUN
cana-1171	277	18	:	:	PUNCT
cana-1171	277	19	linear	linear	ADJ
cana-1171	277	20	,	,	PUNCT
cana-1171	277	21	nonlinear	nonlinear	ADJ
cana-1171	277	22	,	,	PUNCT
cana-1171	277	23	ordinary	ordinary	ADJ
cana-1171	277	24	’	'	PUNCT
cana-1171	277	25	,	,	PUNCT
cana-1171	277	26	partial	partial	ADJ
cana-1171	277	27	,	,	PUNCT
cana-1171	277	28	cambridge	cambridge	PROPN
cana-1171	277	29	university	university	PROPN
cana-1171	277	30	press	press	PROPN
cana-1171	277	31	2005	2005	NUM
cana-1171	277	32	.	.	PUNCT
cana-1171	278	1	[	[	X
cana-1171	278	2	10	10	NUM
cana-1171	278	3	]	]	SYM
cana-1171	278	4	a.a.kilbas	a.a.kilbas	PROPN
cana-1171	278	5	,	,	PUNCT
cana-1171	278	6	h.m	h.m	PROPN
cana-1171	278	7	.	.	PROPN
cana-1171	278	8	srivastava	srivastava	PROPN
cana-1171	278	9	,	,	PUNCT
cana-1171	278	10	j.j	j.j	PROPN
cana-1171	278	11	.	.	PROPN
cana-1171	278	12	trujillo	trujillo	PROPN
cana-1171	278	13	,	,	PUNCT
cana-1171	278	14	‘	'	PUNCT
cana-1171	278	15	theory	theory	NOUN
cana-1171	278	16	and	and	CCONJ
cana-1171	278	17	applications	application	NOUN
cana-1171	278	18	of	of	ADP
cana-1171	278	19	fractional	fractional	ADJ
cana-1171	278	20	differential	differential	ADJ
cana-1171	278	21	equations	equation	NOUN
cana-1171	278	22	’	'	PUNCT
cana-1171	278	23	,	,	PUNCT
cana-1171	278	24	northholland	northholland	NOUN
cana-1171	278	25	mathematics	mathematics	PROPN
cana-1171	278	26	studies	study	NOUN
cana-1171	278	27	,	,	PUNCT
cana-1171	278	28	1st	1st	ADJ
cana-1171	278	29	edition	edition	NOUN
cana-1171	278	30	,	,	PUNCT
cana-1171	278	31	jan	jan	PROPN
cana-1171	278	32	12	12	NUM
cana-1171	278	33	,	,	PUNCT
cana-1171	278	34	2006	2006	NUM
cana-1171	278	35	.	.	PUNCT
cana-1171	279	1	[	[	X
cana-1171	279	2	11	11	NUM
cana-1171	279	3	]	]	X
cana-1171	279	4	ji	ji	PROPN
cana-1171	279	5	-	-	PROPN
cana-1171	279	6	huan	huan	PROPN
cana-1171	279	7	he	he	PRON
cana-1171	279	8	,	,	PUNCT
cana-1171	279	9	‘	'	PUNCT
cana-1171	279	10	homotopy	homotopy	VERB
cana-1171	279	11	perturbation	perturbation	NOUN
cana-1171	279	12	method	method	NOUN
cana-1171	279	13	for	for	ADP
cana-1171	279	14	solving	solve	VERB
cana-1171	279	15	boundary	boundary	ADJ
cana-1171	279	16	value	value	NOUN
cana-1171	279	17	problems	problem	NOUN
cana-1171	279	18	’	'	PUNCT
cana-1171	279	19	,	,	PUNCT
cana-1171	279	20	physics	physics	NOUN
cana-1171	279	21	letters	letter	NOUN
cana-1171	279	22	a	a	DET
cana-1171	279	23	350	350	NUM
cana-1171	279	24	(	(	PUNCT
cana-1171	279	25	2006	2006	NUM
cana-1171	279	26	)	)	PUNCT
cana-1171	279	27	87	87	NUM
cana-1171	279	28	-	-	SYM
cana-1171	279	29	88	88	NUM
cana-1171	279	30	.	.	PUNCT
cana-1171	280	1	[	[	X
cana-1171	280	2	12	12	NUM
cana-1171	280	3	]	]	PUNCT
cana-1171	280	4	dehghani.r	dehghani.r	PROPN
cana-1171	280	5	,	,	PUNCT
cana-1171	280	6	ghanbari.k	ghanbari.k	PROPN
cana-1171	280	7	,	,	PUNCT
cana-1171	280	8	asadzadeh.m	asadzadeh.m	NOUN
cana-1171	280	9	,	,	PUNCT
cana-1171	280	10	‘	'	PUNCT
cana-1171	280	11	triple	triple	ADJ
cana-1171	280	12	positive	positive	ADJ
cana-1171	280	13	solutions	solution	NOUN
cana-1171	280	14	for	for	ADP
cana-1171	280	15	boundary	boundary	ADJ
cana-1171	280	16	value	value	NOUN
cana-1171	280	17	problem	problem	NOUN
cana-1171	280	18	of	of	ADP
cana-1171	280	19	a	a	DET
cana-1171	280	20	nonlinear	nonlinear	ADJ
cana-1171	280	21	fractional	fractional	ADJ
cana-1171	280	22	differential	differential	ADJ
cana-1171	280	23	equation	equation	NOUN
cana-1171	280	24	’	'	PUNCT
cana-1171	280	25	,	,	PUNCT
cana-1171	280	26	springer	springer	NOUN
cana-1171	280	27	,	,	PUNCT
cana-1171	280	28	berlin	berlin	PROPN
cana-1171	280	29	,	,	PUNCT
cana-1171	280	30	germany	germany	PROPN
cana-1171	280	31	,	,	PUNCT
cana-1171	280	32	2007	2007	NUM
cana-1171	280	33	.	.	PUNCT
cana-1171	281	1	[	[	X
cana-1171	281	2	13	13	NUM
cana-1171	281	3	]	]	PUNCT
cana-1171	281	4	o.abdulaziz	o.abdulaziz	ADJ
cana-1171	281	5	,	,	PUNCT
cana-1171	281	6	i.hashim	i.hashim	PRON
cana-1171	281	7	,	,	PUNCT
cana-1171	281	8	s.momani	s.momani	NOUN
cana-1171	281	9	,	,	PUNCT
cana-1171	281	10	‘	'	PUNCT
cana-1171	281	11	solving	solve	VERB
cana-1171	281	12	system	system	NOUN
cana-1171	281	13	of	of	ADP
cana-1171	281	14	fractional	fractional	ADJ
cana-1171	281	15	differential	differential	ADJ
cana-1171	281	16	equations	equation	NOUN
cana-1171	281	17	by	by	ADP
cana-1171	281	18	homotopy	homotopy	NOUN
cana-1171	281	19	perturbation	perturbation	NOUN
cana-1171	281	20	method	method	NOUN
cana-1171	281	21	’	'	PUNCT
cana-1171	281	22	,	,	PUNCT
cana-1171	281	23	elsevier	elsevier	NOUN
cana-1171	281	24	,	,	PUNCT
cana-1171	281	25	physics	physics	NOUN
cana-1171	281	26	letters	letter	NOUN
cana-1171	281	27	a	a	PRON
cana-1171	281	28	,	,	PUNCT
cana-1171	281	29	372	372	NUM
cana-1171	281	30	(	(	PUNCT
cana-1171	281	31	2008	2008	NUM
cana-1171	281	32	)	)	PUNCT
cana-1171	281	33	,	,	PUNCT
cana-1171	281	34	451	451	NUM
cana-1171	281	35	-	-	SYM
cana-1171	281	36	459	459	NUM
cana-1171	281	37	.	.	PUNCT
cana-1171	282	1	[	[	X
cana-1171	282	2	14	14	NUM
cana-1171	282	3	]	]	SYM
cana-1171	282	4	chikrii.a	chikrii.a	NUM
cana-1171	282	5	,	,	PUNCT
cana-1171	282	6	matychyn.i	matychyn.i	NOUN
cana-1171	282	7	,	,	PUNCT
cana-1171	282	8	‘	'	PUNCT
cana-1171	282	9	riemann	riemann	PROPN
cana-1171	282	10	-	-	PUNCT
cana-1171	282	11	lioville	lioville	PROPN
cana-1171	282	12	,	,	PUNCT
cana-1171	282	13	caputo	caputo	NOUN
cana-1171	282	14	and	and	CCONJ
cana-1171	282	15	sequential	sequential	ADJ
cana-1171	282	16	fractional	fractional	ADJ
cana-1171	282	17	derivative	derivative	NOUN
cana-1171	282	18	in	in	ADP
cana-1171	282	19	differential	differential	ADJ
cana-1171	282	20	games	game	NOUN
cana-1171	282	21	’	'	PUNCT
cana-1171	282	22	,	,	PUNCT
cana-1171	282	23	birkhauser	birkhauser	PROPN
cana-1171	282	24	,	,	PUNCT
cana-1171	282	25	boston	boston	PROPN
cana-1171	282	26	,	,	PUNCT
cana-1171	282	27	ma	ma	PROPN
cana-1171	282	28	,	,	PUNCT
cana-1171	282	29	usa	usa	PROPN
cana-1171	282	30	,	,	PUNCT
cana-1171	282	31	2011	2011	NUM
cana-1171	282	32	.	.	PUNCT
cana-1171	283	1	[	[	X
cana-1171	283	2	15	15	NUM
cana-1171	283	3	]	]	X
cana-1171	283	4	partha	partha	PROPN
cana-1171	283	5	s.mallick	s.mallick	PROPN
cana-1171	283	6	,	,	PUNCT
cana-1171	283	7	‘	'	PUNCT
cana-1171	283	8	matlab	matlab	PROPN
cana-1171	283	9	and	and	CCONJ
cana-1171	283	10	simulink	simulink	PROPN
cana-1171	283	11	introduction	introduction	NOUN
cana-1171	283	12	to	to	ADP
cana-1171	283	13	applications	application	NOUN
cana-1171	283	14	’	'	PUNCT
cana-1171	283	15	,	,	PUNCT
cana-1171	283	16	fourth	fourth	PROPN
cana-1171	283	17	edition	edition	NOUN
cana-1171	283	18	,	,	PUNCT
cana-1171	283	19	30	30	NUM
cana-1171	283	20	sep	sep	NOUN
cana-1171	283	21	2011	2011	NUM
cana-1171	283	22	.	.	PUNCT
cana-1171	284	1	[	[	X
cana-1171	284	2	16	16	NUM
cana-1171	284	3	]	]	SYM
cana-1171	284	4	bashir.a	bashir.a	PROPN
cana-1171	284	5	,	,	PUNCT
cana-1171	284	6	nieto.j.j	nieto.j.j	PROPN
cana-1171	284	7	,	,	PUNCT
cana-1171	284	8	‘	'	PUNCT
cana-1171	284	9	sequential	sequential	ADJ
cana-1171	284	10	fractional	fractional	ADJ
cana-1171	284	11	differential	differential	ADJ
cana-1171	284	12	equations	equation	NOUN
cana-1171	284	13	with	with	ADP
cana-1171	284	14	three	three	NUM
cana-1171	284	15	-	-	PUNCT
cana-1171	284	16	point	point	NOUN
cana-1171	284	17	boundary	boundary	ADJ
cana-1171	284	18	conditions	condition	NOUN
cana-1171	284	19	’	'	PUNCT
cana-1171	284	20	,	,	PUNCT
cana-1171	284	21	comput	comput	NOUN
cana-1171	284	22	.	.	PUNCT
cana-1171	285	1	math.appl	math.appl	NOUN
cana-1171	285	2	.	.	PROPN
cana-1171	285	3	2012	2012	NUM
cana-1171	285	4	,	,	PUNCT
cana-1171	285	5	64	64	NUM
cana-1171	285	6	,	,	PUNCT
cana-1171	285	7	3046	3046	NUM
cana-1171	285	8	-	-	SYM
cana-1171	285	9	3052	3052	NUM
cana-1171	285	10	.	.	PUNCT
cana-1171	286	1	[	[	X
cana-1171	286	2	17	17	NUM
cana-1171	286	3	]	]	X
cana-1171	286	4	ahmad	ahmad	PROPN
cana-1171	286	5	el	el	PROPN
cana-1171	286	6	-	-	PUNCT
cana-1171	286	7	ajou,.o	ajou,.o	NOUN
cana-1171	286	8	,	,	PUNCT
cana-1171	286	9	arqub.a	arqub.a	PROPN
cana-1171	286	10	,	,	PUNCT
cana-1171	286	11	momani.s	momani.s	PROPN
cana-1171	286	12	,	,	PUNCT
cana-1171	286	13	‘	'	PUNCT
cana-1171	286	14	solving	solve	VERB
cana-1171	286	15	fractional	fractional	ADJ
cana-1171	286	16	two	two	NUM
cana-1171	286	17	-	-	PUNCT
cana-1171	286	18	point	point	NOUN
cana-1171	286	19	boundary	boundary	ADJ
cana-1171	286	20	value	value	NOUN
cana-1171	286	21	problems	problem	NOUN
cana-1171	286	22	using	use	VERB
cana-1171	286	23	continuous	continuous	ADJ
cana-1171	286	24	analytic	analytic	ADJ
cana-1171	286	25	method	method	NOUN
cana-1171	286	26	’	'	PUNCT
cana-1171	286	27	,	,	PUNCT
cana-1171	286	28	ain	ain	PROPN
cana-1171	286	29	shams	sham	NOUN
cana-1171	286	30	eng.j	eng.j	PROPN
cana-1171	286	31	,	,	PUNCT
cana-1171	286	32	2013	2013	NUM
cana-1171	286	33	,	,	PUNCT
cana-1171	286	34	4	4	NUM
cana-1171	286	35	,	,	PUNCT
cana-1171	286	36	539	539	NUM
cana-1171	286	37	-	-	SYM
cana-1171	286	38	547	547	NUM
cana-1171	286	39	.	.	PUNCT
cana-1171	287	1	[	[	X
cana-1171	287	2	18	18	NUM
cana-1171	287	3	]	]	X
cana-1171	287	4	a.s.yakimov	a.s.yakimov	PROPN
cana-1171	287	5	,	,	PUNCT
cana-1171	287	6	‘	'	PUNCT
cana-1171	287	7	analytical	analytical	ADJ
cana-1171	287	8	solution	solution	NOUN
cana-1171	287	9	methods	method	NOUN
cana-1171	287	10	for	for	ADP
cana-1171	287	11	boundary	boundary	ADJ
cana-1171	287	12	value	value	NOUN
cana-1171	287	13	problems	problem	NOUN
cana-1171	287	14	’	'	PUNCT
cana-1171	287	15	,	,	PUNCT
cana-1171	287	16	academic	academic	ADJ
cana-1171	287	17	press	press	NOUN
cana-1171	287	18	,	,	PUNCT
cana-1171	287	19	2016	2016	NUM
cana-1171	287	20	.	.	PUNCT
cana-1171	288	1	[	[	X
cana-1171	288	2	19	19	NUM
cana-1171	288	3	]	]	PUNCT
cana-1171	288	4	i.ates	i.ate	NOUN
cana-1171	288	5	,	,	PUNCT
cana-1171	288	6	p.a.zegeling	p.a.zegeling	NOUN
cana-1171	288	7	,	,	PUNCT
cana-1171	288	8	‘	'	PUNCT
cana-1171	288	9	a	a	DET
cana-1171	288	10	homotopy	homotopy	NOUN
cana-1171	288	11	perturbation	perturbation	NOUN
cana-1171	288	12	method	method	NOUN
cana-1171	288	13	for	for	ADP
cana-1171	288	14	fractional	fractional	ADJ
cana-1171	288	15	-	-	PUNCT
cana-1171	288	16	order	order	NOUN
cana-1171	288	17	advection	advection	NOUN
cana-1171	288	18	-	-	PUNCT
cana-1171	288	19	diffusion	diffusion	NOUN
cana-1171	288	20	-	-	PUNCT
cana-1171	288	21	reaction	reaction	NOUN
cana-1171	288	22	boundaryvalue	boundaryvalue	NOUN
cana-1171	288	23	problems	problem	NOUN
cana-1171	288	24	’	'	PUNCT
cana-1171	288	25	,	,	PUNCT
cana-1171	288	26	elsevier	elsevier	PROPN
cana-1171	288	27	,	,	PUNCT
cana-1171	288	28	applied	apply	VERB
cana-1171	288	29	mathematical	mathematical	ADJ
cana-1171	288	30	modelling	modelling	NOUN
cana-1171	288	31	,	,	PUNCT
cana-1171	288	32	47	47	NUM
cana-1171	288	33	(	(	PUNCT
cana-1171	288	34	2017	2017	NUM
cana-1171	288	35	)	)	PUNCT
cana-1171	288	36	,	,	PUNCT
cana-1171	288	37	425	425	NUM
cana-1171	288	38	-	-	SYM
cana-1171	288	39	441	441	NUM
cana-1171	288	40	.	.	PUNCT
cana-1171	289	1	[	[	X
cana-1171	289	2	20	20	NUM
cana-1171	289	3	]	]	PUNCT
cana-1171	289	4	n.alghamdi	n.alghamdi	PROPN
cana-1171	289	5	,	,	PUNCT
cana-1171	289	6	b.	b.	PROPN
cana-1171	289	7	ahmad	ahmad	PROPN
cana-1171	289	8	,	,	PUNCT
cana-1171	289	9	s.k	s.k	PROPN
cana-1171	289	10	.	.	PROPN
cana-1171	289	11	ntouyas	ntouyas	PROPN
cana-1171	289	12	and	and	CCONJ
cana-1171	289	13	a.	a.	NOUN
cana-1171	289	14	alsaedi	alsaedi	PROPN
cana-1171	289	15	,	,	PUNCT
cana-1171	289	16	‘	'	PUNCT
cana-1171	289	17	sequential	sequential	ADJ
cana-1171	289	18	fractional	fractional	ADJ
cana-1171	289	19	equations	equation	NOUN
cana-1171	289	20	with	with	ADP
cana-1171	289	21	non	non	ADJ
cana-1171	289	22	-	-	ADJ
cana-1171	289	23	local	local	ADJ
cana-1171	289	24	boundary	boundary	ADJ
cana-1171	289	25	conditions	condition	NOUN
cana-1171	289	26	on	on	ADP
cana-1171	289	27	an	an	DET
cana-1171	289	28	arbitrary	arbitrary	ADJ
cana-1171	289	29	interval	interval	NOUN
cana-1171	289	30	’	'	PUNCT
cana-1171	289	31	,	,	PUNCT
cana-1171	289	32	advance	advance	NOUN
cana-1171	289	33	in	in	ADP
cana-1171	289	34	difference	difference	NOUN
cana-1171	289	35	equations	equation	NOUN
cana-1171	289	36	(	(	PUNCT
cana-1171	289	37	2017	2017	NUM
cana-1171	289	38	)	)	PUNCT
cana-1171	289	39	.	.	PUNCT
cana-1171	290	1	doi	doi	NOUN
cana-1171	290	2	:	:	PUNCT
cana-1171	290	3	10.11861513662	10.11861513662	NUM
cana-1171	290	4	-	-	SYM
cana-1171	290	5	017	017	NUM
cana-1171	290	6	-	-	PUNCT
cana-1171	290	7	1303	1303	NUM
cana-1171	290	8	-	-	SYM
cana-1171	290	9	2	2	NUM
cana-1171	290	10	.	.	PUNCT
cana-1171	291	1	[	[	X
cana-1171	291	2	21	21	NUM
cana-1171	291	3	]	]	PUNCT
cana-1171	291	4	tariboon.j	tariboon.j	NOUN
cana-1171	291	5	,	,	PUNCT
cana-1171	291	6	cuntavepanit.a	cuntavepanit.a	NOUN
cana-1171	291	7	,	,	PUNCT
cana-1171	291	8	ntouyas.s.k	ntouyas.s.k	ADV
cana-1171	291	9	,	,	PUNCT
cana-1171	291	10	nithiarayaphaks.w	nithiarayaphaks.w	NUM
cana-1171	291	11	,	,	PUNCT
cana-1171	291	12	‘	'	PUNCT
cana-1171	291	13	separated	separate	VERB
cana-1171	291	14	boundary	boundary	ADJ
cana-1171	291	15	value	value	NOUN
cana-1171	291	16	problems	problem	NOUN
cana-1171	291	17	of	of	ADP
cana-1171	291	18	sequential	sequential	ADJ
cana-1171	291	19	caputo	caputo	PROPN
cana-1171	291	20	and	and	CCONJ
cana-1171	291	21	hadamard	hadamard	ADJ
cana-1171	291	22	fractional	fractional	ADJ
cana-1171	291	23	differential	differential	NOUN
cana-1171	291	24	equations	equation	NOUN
cana-1171	291	25	’	'	PUNCT
cana-1171	291	26	,	,	PUNCT
cana-1171	291	27	j.funct	j.funct	NOUN
cana-1171	291	28	.	.	PUNCT
cana-1171	292	1	spaces	space	VERB
cana-1171	292	2	2018	2018	NUM
cana-1171	292	3	,	,	PUNCT
cana-1171	292	4	6974046	6974046	NUM
cana-1171	292	5	.	.	PUNCT
cana-1171	293	1	[	[	X
cana-1171	293	2	22	22	NUM
cana-1171	293	3	]	]	PUNCT
cana-1171	293	4	a.s.vatsala	a.s.vatsala	NOUN
cana-1171	293	5	,	,	PUNCT
cana-1171	293	6	g.pageni	g.pageni	NOUN
cana-1171	293	7	,	,	PUNCT
cana-1171	293	8	v.a.vijesh	v.a.vijesh	NOUN
cana-1171	293	9	,	,	PUNCT
cana-1171	293	10	‘	'	PUNCT
cana-1171	293	11	analysis	analysis	NOUN
cana-1171	293	12	of	of	ADP
cana-1171	293	13	sequential	sequential	ADJ
cana-1171	293	14	caputo	caputo	PROPN
cana-1171	293	15	fractional	fractional	ADJ
cana-1171	293	16	differenial	differenial	ADJ
cana-1171	293	17	equations	equation	NOUN
cana-1171	293	18	versus	versus	ADP
cana-1171	293	19	nonsequential	nonsequential	PROPN
cana-1171	293	20	caputo	caputo	PROPN
cana-1171	293	21	fractional	fractional	PROPN
cana-1171	293	22	differential	differential	PROPN
cana-1171	293	23	equations	equation	NOUN
cana-1171	293	24	with	with	ADP
cana-1171	293	25	applications	application	NOUN
cana-1171	293	26	’	'	PUNCT
cana-1171	293	27	,	,	PUNCT
cana-1171	293	28	foundations	foundation	NOUN
cana-1171	293	29	(	(	PUNCT
cana-1171	293	30	2022	2022	NUM
cana-1171	293	31	)	)	PUNCT
cana-1171	293	32	,	,	PUNCT
cana-1171	293	33	2	2	NUM
cana-1171	293	34	,	,	PUNCT
cana-1171	293	35	1129	1129	NUM
cana-1171	293	36	-	-	SYM
cana-1171	293	37	1142	1142	NUM
cana-1171	293	38	.	.	PUNCT
cana-1171	294	1	[	[	X
cana-1171	294	2	23	23	NUM
cana-1171	294	3	]	]	X
cana-1171	294	4	xiao	xiao	PROPN
cana-1171	294	5	-	-	PUNCT
cana-1171	294	6	ping	ping	PROPN
cana-1171	294	7	li	li	PROPN
cana-1171	294	8	,	,	PUNCT
cana-1171	294	9	et.al	et.al	PROPN
cana-1171	294	10	.	.	PROPN
cana-1171	294	11	,	,	PUNCT
cana-1171	294	12	‘	'	PUNCT
cana-1171	294	13	application	application	NOUN
cana-1171	294	14	of	of	ADP
cana-1171	294	15	piecewise	piecewise	NOUN
cana-1171	294	16	fractional	fractional	ADJ
cana-1171	294	17	differential	differential	ADJ
cana-1171	294	18	equation	equation	NOUN
cana-1171	294	19	to	to	ADP
cana-1171	294	20	covid-19	covid-19	PROPN
cana-1171	294	21	infection	infection	NOUN
cana-1171	294	22	dynamics	dynamic	NOUN
cana-1171	294	23	’	'	PUNCT
cana-1171	294	24	,	,	PUNCT
cana-1171	294	25	elsevier	elsevier	NOUN
cana-1171	294	26	,	,	PUNCT
cana-1171	294	27	results	result	NOUN
cana-1171	294	28	in	in	ADP
cana-1171	294	29	physics	physics	NOUN
cana-1171	294	30	39(2022	39(2022	PROPN
cana-1171	294	31	)	)	PUNCT
cana-1171	294	32	,	,	PUNCT
cana-1171	294	33	105685	105685	NUM
cana-1171	294	34	.	.	PUNCT
cana-1171	295	1	[	[	X
cana-1171	295	2	24	24	NUM
cana-1171	295	3	]	]	PUNCT
cana-1171	295	4	sadia	sadia	PROPN
cana-1171	295	5	arshad	arshad	PROPN
cana-1171	295	6	,	,	PUNCT
cana-1171	295	7	imran	imran	PROPN
cana-1171	295	8	siddique	siddique	PROPN
cana-1171	295	9	,	,	PUNCT
cana-1171	295	10	et.al	et.al	PROPN
cana-1171	295	11	.	.	PROPN
cana-1171	295	12	,	,	PUNCT
cana-1171	295	13	‘	'	PUNCT
cana-1171	295	14	dynamics	dynamic	NOUN
cana-1171	295	15	of	of	ADP
cana-1171	295	16	a	a	DET
cana-1171	295	17	fractional	fractional	ADJ
cana-1171	295	18	order	order	NOUN
cana-1171	295	19	mathematical	mathematical	ADJ
cana-1171	295	20	model	model	NOUN
cana-1171	295	21	for	for	ADP
cana-1171	295	22	covid-19	covid-19	PROPN
cana-1171	295	23	epidemic	epidemic	NOUN
cana-1171	295	24	transmission	transmission	NOUN
cana-1171	295	25	’	'	PUNCT
cana-1171	295	26	,	,	PUNCT
cana-1171	295	27	elsevier	elsevier	PROPN
cana-1171	295	28	,	,	PUNCT
cana-1171	295	29	physica	physica	VERB
cana-1171	295	30	a	a	DET
cana-1171	295	31	609(2023	609(2023	NUM
cana-1171	295	32	)	)	PUNCT
cana-1171	295	33	,	,	PUNCT
cana-1171	295	34	128383	128383	NUM
cana-1171	295	35	.	.	PUNCT