id	sid	tid	token	lemma	pos
ejpam-1858	1	1	compile	compile	NOUN
ejpam-1858	1	2	/	/	SYM
ejpam-1858	1	3	output.dvi	output.dvi	NOUN
ejpam-1858	1	4	european	european	ADJ
ejpam-1858	1	5	journal	journal	NOUN
ejpam-1858	1	6	of	of	ADP
ejpam-1858	1	7	pure	pure	ADJ
ejpam-1858	1	8	and	and	CCONJ
ejpam-1858	1	9	applied	apply	VERB
ejpam-1858	1	10	mathematics	mathematic	NOUN
ejpam-1858	1	11	vol	vol	NOUN
ejpam-1858	1	12	.	.	PUNCT
ejpam-1858	2	1	7	7	NUM
ejpam-1858	2	2	,	,	PUNCT
ejpam-1858	2	3	no	no	INTJ
ejpam-1858	2	4	.	.	NOUN
ejpam-1858	2	5	2	2	NUM
ejpam-1858	2	6	,	,	PUNCT
ejpam-1858	2	7	2014	2014	NUM
ejpam-1858	2	8	,	,	PUNCT
ejpam-1858	2	9	115	115	NUM
ejpam-1858	2	10	-	-	SYM
ejpam-1858	2	11	128	128	NUM
ejpam-1858	2	12	issn	issn	PROPN
ejpam-1858	2	13	1307	1307	NUM
ejpam-1858	2	14	-	-	SYM
ejpam-1858	2	15	5543	5543	NUM
ejpam-1858	2	16	–	–	PUNCT
ejpam-1858	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1858	2	18	on	on	ADP
ejpam-1858	2	19	hybrid	hybrid	ADJ
ejpam-1858	2	20	caputo	caputo	PROPN
ejpam-1858	2	21	fractional	fractional	PROPN
ejpam-1858	2	22	differential	differential	ADJ
ejpam-1858	2	23	equations	equation	NOUN
ejpam-1858	2	24	with	with	ADP
ejpam-1858	2	25	variable	variable	ADJ
ejpam-1858	2	26	moments	moment	NOUN
ejpam-1858	2	27	of	of	ADP
ejpam-1858	2	28	impulse	impulse	ADJ
ejpam-1858	2	29	j.	j.	PROPN
ejpam-1858	2	30	vasundhara	vasundhara	PROPN
ejpam-1858	2	31	devi	devi	PROPN
ejpam-1858	2	32	,	,	PUNCT
ejpam-1858	2	33	n.giribabu∗	n.giribabu∗	PROPN
ejpam-1858	2	34	department	department	NOUN
ejpam-1858	2	35	of	of	ADP
ejpam-1858	2	36	mathematics	mathematics	PROPN
ejpam-1858	2	37	,	,	PUNCT
ejpam-1858	2	38	gvp-prof.v.lakshmikantham	gvp-prof.v.lakshmikantham	PROPN
ejpam-1858	2	39	institute	institute	VERB
ejpam-1858	2	40	for	for	ADP
ejpam-1858	2	41	advanced	advanced	ADJ
ejpam-1858	2	42	studies	study	NOUN
ejpam-1858	2	43	,	,	PUNCT
ejpam-1858	2	44	gvp	gvp	PROPN
ejpam-1858	2	45	college	college	PROPN
ejpam-1858	2	46	of	of	ADP
ejpam-1858	2	47	engineering	engineering	PROPN
ejpam-1858	2	48	,	,	PUNCT
ejpam-1858	2	49	visakhapatnam	visakhapatnam	PROPN
ejpam-1858	2	50	,	,	PUNCT
ejpam-1858	2	51	ap	ap	PROPN
ejpam-1858	2	52	,	,	PUNCT
ejpam-1858	2	53	india	india	PROPN
ejpam-1858	2	54	.	.	PUNCT
ejpam-1858	3	1	abstract	abstract	PROPN
ejpam-1858	3	2	.	.	PUNCT
ejpam-1858	4	1	in	in	ADP
ejpam-1858	4	2	this	this	DET
ejpam-1858	4	3	paper	paper	NOUN
ejpam-1858	4	4	existence	existence	NOUN
ejpam-1858	4	5	and	and	CCONJ
ejpam-1858	4	6	continuation	continuation	NOUN
ejpam-1858	4	7	results	result	NOUN
ejpam-1858	4	8	for	for	ADP
ejpam-1858	4	9	hybrid	hybrid	ADJ
ejpam-1858	4	10	caputo	caputo	PROPN
ejpam-1858	4	11	fractional	fractional	PROPN
ejpam-1858	4	12	differential	differential	ADJ
ejpam-1858	4	13	equations	equation	NOUN
ejpam-1858	4	14	of	of	ADP
ejpam-1858	4	15	order	order	NOUN
ejpam-1858	4	16	q	q	X
ejpam-1858	4	17	∈	∈	PROPN
ejpam-1858	4	18	(	(	PUNCT
ejpam-1858	4	19	0,1	0,1	NUM
ejpam-1858	4	20	)	)	PUNCT
ejpam-1858	4	21	with	with	ADP
ejpam-1858	4	22	variable	variable	ADJ
ejpam-1858	4	23	moments	moment	NOUN
ejpam-1858	4	24	of	of	ADP
ejpam-1858	4	25	impulse	impulse	ADJ
ejpam-1858	4	26	are	be	AUX
ejpam-1858	4	27	established	establish	VERB
ejpam-1858	4	28	under	under	ADP
ejpam-1858	4	29	the	the	DET
ejpam-1858	4	30	weakened	weaken	VERB
ejpam-1858	4	31	hypothesis	hypothesis	NOUN
ejpam-1858	4	32	of	of	ADP
ejpam-1858	4	33	cq	cq	NOUN
ejpam-1858	4	34	continuity	continuity	NOUN
ejpam-1858	4	35	.	.	PUNCT
ejpam-1858	5	1	2010	2010	NUM
ejpam-1858	5	2	mathematics	mathematic	NOUN
ejpam-1858	5	3	subject	subject	NOUN
ejpam-1858	5	4	classifications	classification	NOUN
ejpam-1858	5	5	:	:	PUNCT
ejpam-1858	5	6	34a12,34a08,34a37	34a12,34a08,34a37	NUM
ejpam-1858	5	7	,	,	PUNCT
ejpam-1858	5	8	34k07	34k07	NUM
ejpam-1858	5	9	key	key	ADJ
ejpam-1858	5	10	words	word	NOUN
ejpam-1858	5	11	and	and	CCONJ
ejpam-1858	5	12	phrases	phrase	NOUN
ejpam-1858	5	13	:	:	PUNCT
ejpam-1858	5	14	hybrid	hybrid	PROPN
ejpam-1858	5	15	caputo	caputo	PROPN
ejpam-1858	5	16	fractional	fractional	PROPN
ejpam-1858	5	17	differential	differential	PROPN
ejpam-1858	5	18	equations	equation	NOUN
ejpam-1858	5	19	,	,	PUNCT
ejpam-1858	5	20	existence	existence	NOUN
ejpam-1858	5	21	,	,	PUNCT
ejpam-1858	5	22	continuation	continuation	NOUN
ejpam-1858	5	23	1	1	NUM
ejpam-1858	5	24	.	.	PUNCT
ejpam-1858	5	25	introduction	introduction	NOUN
ejpam-1858	5	26	the	the	DET
ejpam-1858	5	27	concept	concept	NOUN
ejpam-1858	5	28	of	of	ADP
ejpam-1858	5	29	a	a	DET
ejpam-1858	5	30	fractional	fractional	ADJ
ejpam-1858	5	31	derivative	derivative	NOUN
ejpam-1858	5	32	,	,	PUNCT
ejpam-1858	5	33	as	as	SCONJ
ejpam-1858	5	34	is	be	AUX
ejpam-1858	5	35	well	well	ADV
ejpam-1858	5	36	known	know	VERB
ejpam-1858	5	37	,	,	PUNCT
ejpam-1858	5	38	has	have	VERB
ejpam-1858	5	39	its	its	PRON
ejpam-1858	5	40	inception	inception	NOUN
ejpam-1858	5	41	in	in	ADP
ejpam-1858	5	42	a	a	DET
ejpam-1858	5	43	question	question	NOUN
ejpam-1858	5	44	posed	pose	VERB
ejpam-1858	5	45	during	during	ADP
ejpam-1858	5	46	a	a	DET
ejpam-1858	5	47	communication	communication	NOUN
ejpam-1858	5	48	between	between	ADP
ejpam-1858	5	49	leibnitz	leibnitz	PROPN
ejpam-1858	5	50	and	and	CCONJ
ejpam-1858	5	51	l’hospital	l’hospital	PROPN
ejpam-1858	5	52	.	.	PUNCT
ejpam-1858	6	1	the	the	DET
ejpam-1858	6	2	five	five	NUM
ejpam-1858	6	3	century	century	NOUN
ejpam-1858	6	4	old	old	ADJ
ejpam-1858	6	5	question	question	NOUN
ejpam-1858	6	6	has	have	AUX
ejpam-1858	6	7	become	become	VERB
ejpam-1858	6	8	a	a	DET
ejpam-1858	6	9	major	major	ADJ
ejpam-1858	6	10	area	area	NOUN
ejpam-1858	6	11	of	of	ADP
ejpam-1858	6	12	research	research	NOUN
ejpam-1858	6	13	both	both	CCONJ
ejpam-1858	6	14	in	in	ADP
ejpam-1858	6	15	the	the	DET
ejpam-1858	6	16	realm	realm	NOUN
ejpam-1858	6	17	of	of	ADP
ejpam-1858	6	18	applications	application	NOUN
ejpam-1858	6	19	and	and	CCONJ
ejpam-1858	6	20	in	in	ADP
ejpam-1858	6	21	the	the	DET
ejpam-1858	6	22	theoretical	theoretical	ADJ
ejpam-1858	6	23	set	set	NOUN
ejpam-1858	6	24	up	up	ADP
ejpam-1858	6	25	.	.	PUNCT
ejpam-1858	7	1	the	the	DET
ejpam-1858	7	2	potential	potential	NOUN
ejpam-1858	7	3	it	it	PRON
ejpam-1858	7	4	offers	offer	VERB
ejpam-1858	7	5	in	in	ADP
ejpam-1858	7	6	both	both	DET
ejpam-1858	7	7	these	these	DET
ejpam-1858	7	8	branches	branch	NOUN
ejpam-1858	7	9	has	have	AUX
ejpam-1858	7	10	attracted	attract	VERB
ejpam-1858	7	11	the	the	DET
ejpam-1858	7	12	attention	attention	NOUN
ejpam-1858	7	13	of	of	ADP
ejpam-1858	7	14	both	both	CCONJ
ejpam-1858	7	15	theoretical	theoretical	ADJ
ejpam-1858	7	16	and	and	CCONJ
ejpam-1858	7	17	applied	apply	VERB
ejpam-1858	7	18	scientists	scientist	NOUN
ejpam-1858	7	19	as	as	ADV
ejpam-1858	7	20	well	well	ADV
ejpam-1858	7	21	as	as	ADP
ejpam-1858	7	22	engineers	engineer	NOUN
ejpam-1858	7	23	and	and	CCONJ
ejpam-1858	7	24	other	other	ADJ
ejpam-1858	7	25	technologists	technologist	NOUN
ejpam-1858	7	26	.	.	PUNCT
ejpam-1858	8	1	the	the	DET
ejpam-1858	8	2	major	major	ADJ
ejpam-1858	8	3	contributions	contribution	NOUN
ejpam-1858	8	4	in	in	ADP
ejpam-1858	8	5	this	this	DET
ejpam-1858	8	6	field	field	NOUN
ejpam-1858	8	7	are	be	AUX
ejpam-1858	8	8	given	give	VERB
ejpam-1858	8	9	in	in	ADP
ejpam-1858	8	10	[	[	X
ejpam-1858	8	11	6	6	NUM
ejpam-1858	8	12	,	,	PUNCT
ejpam-1858	8	13	8	8	NUM
ejpam-1858	8	14	,	,	PUNCT
ejpam-1858	8	15	9	9	NUM
ejpam-1858	8	16	,	,	PUNCT
ejpam-1858	8	17	11–14	11–14	NUM
ejpam-1858	8	18	]	]	PUNCT
ejpam-1858	8	19	and	and	CCONJ
ejpam-1858	8	20	the	the	DET
ejpam-1858	8	21	references	reference	NOUN
ejpam-1858	8	22	therein	therein	ADV
ejpam-1858	8	23	.	.	PUNCT
ejpam-1858	9	1	in	in	ADP
ejpam-1858	9	2	[	[	X
ejpam-1858	9	3	6	6	NUM
ejpam-1858	9	4	]	]	PUNCT
ejpam-1858	9	5	diethelm	diethelm	NOUN
ejpam-1858	9	6	gave	give	VERB
ejpam-1858	9	7	a	a	DET
ejpam-1858	9	8	simple	simple	ADJ
ejpam-1858	9	9	example	example	NOUN
ejpam-1858	9	10	which	which	PRON
ejpam-1858	9	11	naturally	naturally	ADV
ejpam-1858	9	12	introduces	introduce	VERB
ejpam-1858	9	13	the	the	DET
ejpam-1858	9	14	fractional	fractional	ADJ
ejpam-1858	9	15	derivative	derivative	NOUN
ejpam-1858	9	16	.	.	PUNCT
ejpam-1858	10	1	we	we	PRON
ejpam-1858	10	2	briefly	briefly	ADV
ejpam-1858	10	3	introduce	introduce	VERB
ejpam-1858	10	4	it	it	PRON
ejpam-1858	10	5	here	here	ADV
ejpam-1858	10	6	,	,	PUNCT
ejpam-1858	10	7	so	so	SCONJ
ejpam-1858	10	8	as	as	SCONJ
ejpam-1858	10	9	to	to	PART
ejpam-1858	10	10	connect	connect	VERB
ejpam-1858	10	11	it	it	PRON
ejpam-1858	10	12	later	later	ADV
ejpam-1858	10	13	,	,	PUNCT
ejpam-1858	10	14	to	to	ADP
ejpam-1858	10	15	the	the	DET
ejpam-1858	10	16	problem	problem	NOUN
ejpam-1858	10	17	considered	consider	VERB
ejpam-1858	10	18	in	in	ADP
ejpam-1858	10	19	this	this	DET
ejpam-1858	10	20	paper	paper	NOUN
ejpam-1858	10	21	.	.	PUNCT
ejpam-1858	11	1	consider	consider	VERB
ejpam-1858	11	2	the	the	DET
ejpam-1858	11	3	stress	stress	NOUN
ejpam-1858	11	4	σ(t	σ(t	NOUN
ejpam-1858	11	5	)	)	PUNCT
ejpam-1858	11	6	and	and	CCONJ
ejpam-1858	11	7	strain	strain	VERB
ejpam-1858	11	8	ε(t	ε(t	NOUN
ejpam-1858	11	9	)	)	PUNCT
ejpam-1858	11	10	of	of	ADP
ejpam-1858	11	11	a	a	DET
ejpam-1858	11	12	viscous	viscous	ADJ
ejpam-1858	11	13	liquid	liquid	NOUN
ejpam-1858	11	14	.	.	PUNCT
ejpam-1858	12	1	it	it	PRON
ejpam-1858	12	2	is	be	AUX
ejpam-1858	12	3	known	know	VERB
ejpam-1858	12	4	that	that	SCONJ
ejpam-1858	12	5	the	the	DET
ejpam-1858	12	6	newton	newton	PROPN
ejpam-1858	12	7	’s	’s	PART
ejpam-1858	12	8	law	law	NOUN
ejpam-1858	12	9	σ(t	σ(t	PROPN
ejpam-1858	12	10	)	)	PUNCT
ejpam-1858	12	11	=	=	PUNCT
ejpam-1858	12	12	ηd1ε(t	ηd1ε(t	NOUN
ejpam-1858	12	13	)	)	PUNCT
ejpam-1858	12	14	,	,	PUNCT
ejpam-1858	12	15	(	(	PUNCT
ejpam-1858	12	16	1	1	X
ejpam-1858	12	17	)	)	PUNCT
ejpam-1858	12	18	describes	describe	VERB
ejpam-1858	12	19	the	the	DET
ejpam-1858	12	20	relation	relation	NOUN
ejpam-1858	12	21	between	between	ADP
ejpam-1858	12	22	stress	stress	NOUN
ejpam-1858	12	23	and	and	CCONJ
ejpam-1858	12	24	strain	strain	VERB
ejpam-1858	12	25	for	for	ADP
ejpam-1858	12	26	a	a	DET
ejpam-1858	12	27	viscous	viscous	ADJ
ejpam-1858	12	28	liquid	liquid	NOUN
ejpam-1858	12	29	,	,	PUNCT
ejpam-1858	12	30	where	where	SCONJ
ejpam-1858	12	31	η	η	PROPN
ejpam-1858	12	32	is	be	AUX
ejpam-1858	12	33	the	the	DET
ejpam-1858	12	34	viscosity	viscosity	NOUN
ejpam-1858	12	35	of	of	ADP
ejpam-1858	12	36	the	the	DET
ejpam-1858	12	37	material	material	NOUN
ejpam-1858	12	38	.	.	PUNCT
ejpam-1858	13	1	the	the	DET
ejpam-1858	13	2	hooke	hooke	PROPN
ejpam-1858	13	3	’s	’s	PART
ejpam-1858	13	4	law	law	NOUN
ejpam-1858	13	5	states	state	VERB
ejpam-1858	13	6	the	the	DET
ejpam-1858	13	7	stress	stress	NOUN
ejpam-1858	13	8	-	-	PUNCT
ejpam-1858	13	9	strain	strain	NOUN
ejpam-1858	13	10	relationship	relationship	NOUN
ejpam-1858	13	11	for	for	ADP
ejpam-1858	13	12	elastic	elastic	ADJ
ejpam-1858	13	13	solid	solid	ADJ
ejpam-1858	13	14	and	and	CCONJ
ejpam-1858	13	15	is	be	AUX
ejpam-1858	13	16	given	give	VERB
ejpam-1858	13	17	by	by	ADP
ejpam-1858	13	18	σ(t	σ(t	NOUN
ejpam-1858	13	19	)	)	PUNCT
ejpam-1858	14	1	=	=	SYM
ejpam-1858	14	2	e	e	X
ejpam-1858	14	3	d0ε(t	d0ε(t	NOUN
ejpam-1858	14	4	)	)	PUNCT
ejpam-1858	14	5	,	,	PUNCT
ejpam-1858	14	6	(	(	PUNCT
ejpam-1858	14	7	2	2	X
ejpam-1858	14	8	)	)	PUNCT
ejpam-1858	14	9	∗corresponding	∗corresponde	VERB
ejpam-1858	14	10	author	author	NOUN
ejpam-1858	14	11	.	.	PUNCT
ejpam-1858	15	1	email	email	NOUN
ejpam-1858	15	2	addresses	address	NOUN
ejpam-1858	15	3	:	:	PUNCT
ejpam-1858	15	4	jvdevi@gmail.com	jvdevi@gmail.com	X
ejpam-1858	15	5	(	(	PUNCT
ejpam-1858	15	6	j.	j.	PROPN
ejpam-1858	15	7	devi	devi	PROPN
ejpam-1858	15	8	)	)	PUNCT
ejpam-1858	15	9	,	,	PUNCT
ejpam-1858	15	10	giri.hcu.gvpcoe@gmail.com	giri.hcu.gvpcoe@gmail.com	PROPN
ejpam-1858	15	11	(	(	PUNCT
ejpam-1858	15	12	n.	n.	PROPN
ejpam-1858	15	13	giribabu	giribabu	PROPN
ejpam-1858	15	14	)	)	PUNCT
ejpam-1858	15	15	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1858	16	1	115	115	NUM
ejpam-1858	17	1	c	c	X
ejpam-1858	17	2	©	©	NOUN
ejpam-1858	17	3	2014	2014	NUM
ejpam-1858	17	4	ejpam	ejpam	NOUN
ejpam-1858	17	5	all	all	DET
ejpam-1858	17	6	rights	right	NOUN
ejpam-1858	17	7	reserved	reserve	VERB
ejpam-1858	17	8	.	.	PUNCT
ejpam-1858	18	1	j.	j.	PROPN
ejpam-1858	18	2	devi	devi	PROPN
ejpam-1858	18	3	,	,	PUNCT
ejpam-1858	18	4	n.	n.	PROPN
ejpam-1858	18	5	giribabu	giribabu	PROPN
ejpam-1858	18	6	/	/	SYM
ejpam-1858	18	7	eur	eur	PROPN
ejpam-1858	18	8	.	.	PUNCT
ejpam-1858	19	1	j.	j.	PROPN
ejpam-1858	19	2	pure	pure	PROPN
ejpam-1858	19	3	appl	appl	PROPN
ejpam-1858	19	4	.	.	PROPN
ejpam-1858	19	5	math	math	PROPN
ejpam-1858	19	6	,	,	PUNCT
ejpam-1858	19	7	7	7	NUM
ejpam-1858	19	8	(	(	PUNCT
ejpam-1858	19	9	2014	2014	NUM
ejpam-1858	19	10	)	)	PUNCT
ejpam-1858	19	11	,	,	PUNCT
ejpam-1858	19	12	115	115	NUM
ejpam-1858	19	13	-	-	SYM
ejpam-1858	19	14	128	128	NUM
ejpam-1858	19	15	116	116	NUM
ejpam-1858	19	16	where	where	SCONJ
ejpam-1858	19	17	e	e	NOUN
ejpam-1858	19	18	is	be	AUX
ejpam-1858	19	19	the	the	DET
ejpam-1858	19	20	modulus	modulus	NOUN
ejpam-1858	19	21	of	of	ADP
ejpam-1858	19	22	elasticity	elasticity	NOUN
ejpam-1858	19	23	of	of	ADP
ejpam-1858	19	24	the	the	DET
ejpam-1858	19	25	material	material	NOUN
ejpam-1858	19	26	.	.	PUNCT
ejpam-1858	20	1	now	now	ADV
ejpam-1858	20	2	it	it	PRON
ejpam-1858	20	3	can	can	AUX
ejpam-1858	20	4	be	be	AUX
ejpam-1858	20	5	naturally	naturally	ADV
ejpam-1858	20	6	concluded	conclude	VERB
ejpam-1858	20	7	that	that	SCONJ
ejpam-1858	20	8	the	the	DET
ejpam-1858	20	9	behaviour	behaviour	NOUN
ejpam-1858	20	10	of	of	ADP
ejpam-1858	20	11	viscoelastic	viscoelastic	ADJ
ejpam-1858	20	12	material	material	NOUN
ejpam-1858	20	13	must	must	AUX
ejpam-1858	20	14	have	have	VERB
ejpam-1858	20	15	a	a	DET
ejpam-1858	20	16	behaviour	behaviour	NOUN
ejpam-1858	20	17	that	that	PRON
ejpam-1858	20	18	is	be	AUX
ejpam-1858	20	19	modeled	model	VERB
ejpam-1858	20	20	by	by	ADP
ejpam-1858	20	21	an	an	DET
ejpam-1858	20	22	equation	equation	NOUN
ejpam-1858	20	23	having	have	VERB
ejpam-1858	20	24	derivative	derivative	NOUN
ejpam-1858	20	25	of	of	ADP
ejpam-1858	20	26	order	order	NOUN
ejpam-1858	20	27	k	k	PROPN
ejpam-1858	20	28	∈	∈	PROPN
ejpam-1858	20	29	(	(	PUNCT
ejpam-1858	20	30	0,1	0,1	NOUN
ejpam-1858	20	31	)	)	PUNCT
ejpam-1858	20	32	that	that	PRON
ejpam-1858	20	33	lies	lie	VERB
ejpam-1858	20	34	in	in	ADP
ejpam-1858	20	35	betweeen	betweeen	VERB
ejpam-1858	20	36	the	the	DET
ejpam-1858	20	37	equations	equation	NOUN
ejpam-1858	20	38	of	of	ADP
ejpam-1858	20	39	(	(	PUNCT
ejpam-1858	20	40	1	1	NUM
ejpam-1858	20	41	)	)	PUNCT
ejpam-1858	20	42	and	and	CCONJ
ejpam-1858	20	43	(	(	PUNCT
ejpam-1858	20	44	2	2	NUM
ejpam-1858	20	45	)	)	PUNCT
ejpam-1858	20	46	and	and	CCONJ
ejpam-1858	20	47	is	be	AUX
ejpam-1858	20	48	given	give	VERB
ejpam-1858	20	49	by	by	ADP
ejpam-1858	20	50	σ(t	σ(t	NOUN
ejpam-1858	20	51	)	)	PUNCT
ejpam-1858	20	52	=	=	SYM
ejpam-1858	21	1	νdkε(t	νdkε(t	PROPN
ejpam-1858	21	2	)	)	PUNCT
ejpam-1858	21	3	,	,	PUNCT
ejpam-1858	21	4	(	(	PUNCT
ejpam-1858	21	5	3	3	X
ejpam-1858	21	6	)	)	PUNCT
ejpam-1858	21	7	where	where	SCONJ
ejpam-1858	21	8	ν	ν	NOUN
ejpam-1858	21	9	is	be	AUX
ejpam-1858	21	10	the	the	DET
ejpam-1858	21	11	constant	constant	ADJ
ejpam-1858	21	12	of	of	ADP
ejpam-1858	21	13	the	the	DET
ejpam-1858	21	14	material	material	NOUN
ejpam-1858	21	15	and	and	CCONJ
ejpam-1858	21	16	k	k	PROPN
ejpam-1858	21	17	∈	∈	PROPN
ejpam-1858	21	18	(	(	PUNCT
ejpam-1858	21	19	0,1	0,1	NUM
ejpam-1858	21	20	)	)	PUNCT
ejpam-1858	21	21	.	.	PUNCT
ejpam-1858	22	1	the	the	DET
ejpam-1858	22	2	relation	relation	NOUN
ejpam-1858	22	3	(	(	PUNCT
ejpam-1858	22	4	3	3	NUM
ejpam-1858	22	5	)	)	PUNCT
ejpam-1858	22	6	in	in	ADP
ejpam-1858	22	7	a	a	DET
ejpam-1858	22	8	slightly	slightly	ADV
ejpam-1858	22	9	different	different	ADJ
ejpam-1858	22	10	set	set	NOUN
ejpam-1858	22	11	up	up	ADP
ejpam-1858	22	12	is	be	AUX
ejpam-1858	22	13	called	call	VERB
ejpam-1858	22	14	as	as	ADP
ejpam-1858	22	15	nutting	nutting	NOUN
ejpam-1858	22	16	’s	’s	PART
ejpam-1858	22	17	law	law	NOUN
ejpam-1858	22	18	.	.	PUNCT
ejpam-1858	23	1	it	it	PRON
ejpam-1858	23	2	has	have	AUX
ejpam-1858	23	3	been	be	AUX
ejpam-1858	23	4	observed	observe	VERB
ejpam-1858	23	5	in	in	ADP
ejpam-1858	23	6	[	[	X
ejpam-1858	23	7	9	9	NUM
ejpam-1858	23	8	]	]	PUNCT
ejpam-1858	23	9	that	that	SCONJ
ejpam-1858	23	10	viscoelastic	viscoelastic	ADJ
ejpam-1858	23	11	materials	material	NOUN
ejpam-1858	23	12	like	like	ADP
ejpam-1858	23	13	polymers	polymer	NOUN
ejpam-1858	23	14	,	,	PUNCT
ejpam-1858	23	15	some	some	DET
ejpam-1858	23	16	biological	biological	ADJ
ejpam-1858	23	17	tissue	tissue	NOUN
ejpam-1858	23	18	etc	etc	X
ejpam-1858	23	19	.	.	X
ejpam-1858	23	20	may	may	AUX
ejpam-1858	23	21	follow	follow	VERB
ejpam-1858	23	22	the	the	DET
ejpam-1858	23	23	relation	relation	NOUN
ejpam-1858	23	24	(	(	PUNCT
ejpam-1858	23	25	3	3	NUM
ejpam-1858	23	26	)	)	PUNCT
ejpam-1858	23	27	.	.	PUNCT
ejpam-1858	24	1	the	the	DET
ejpam-1858	24	2	operator	operator	NOUN
ejpam-1858	24	3	dk	dk	NOUN
ejpam-1858	24	4	is	be	AUX
ejpam-1858	24	5	called	call	VERB
ejpam-1858	24	6	as	as	ADP
ejpam-1858	24	7	the	the	DET
ejpam-1858	24	8	fractional	fractional	ADJ
ejpam-1858	24	9	derivative	derivative	NOUN
ejpam-1858	24	10	and	and	CCONJ
ejpam-1858	24	11	is	be	AUX
ejpam-1858	24	12	described	describe	VERB
ejpam-1858	24	13	in	in	ADP
ejpam-1858	24	14	section	section	NOUN
ejpam-1858	24	15	2	2	NUM
ejpam-1858	24	16	.	.	PUNCT
ejpam-1858	25	1	it	it	PRON
ejpam-1858	25	2	has	have	AUX
ejpam-1858	25	3	been	be	AUX
ejpam-1858	25	4	observed	observe	VERB
ejpam-1858	25	5	that	that	SCONJ
ejpam-1858	25	6	the	the	DET
ejpam-1858	25	7	theory	theory	NOUN
ejpam-1858	25	8	of	of	ADP
ejpam-1858	25	9	ordinary	ordinary	ADJ
ejpam-1858	25	10	differential	differential	ADJ
ejpam-1858	25	11	equations	equation	NOUN
ejpam-1858	25	12	is	be	AUX
ejpam-1858	25	13	being	be	AUX
ejpam-1858	25	14	systematically	systematically	ADV
ejpam-1858	25	15	extended	extend	VERB
ejpam-1858	25	16	to	to	ADP
ejpam-1858	25	17	the	the	DET
ejpam-1858	25	18	set	set	NOUN
ejpam-1858	25	19	up	up	ADP
ejpam-1858	25	20	of	of	ADP
ejpam-1858	25	21	fractional	fractional	ADJ
ejpam-1858	25	22	differential	differential	ADJ
ejpam-1858	25	23	equations	equation	NOUN
ejpam-1858	25	24	.	.	PUNCT
ejpam-1858	26	1	further	far	ADV
ejpam-1858	26	2	an	an	DET
ejpam-1858	26	3	effort	effort	NOUN
ejpam-1858	26	4	is	be	AUX
ejpam-1858	26	5	being	be	AUX
ejpam-1858	26	6	put	put	VERB
ejpam-1858	26	7	to	to	PART
ejpam-1858	26	8	obtain	obtain	VERB
ejpam-1858	26	9	better	well	ADJ
ejpam-1858	26	10	results	result	NOUN
ejpam-1858	26	11	by	by	ADP
ejpam-1858	26	12	using	use	VERB
ejpam-1858	26	13	fractional	fractional	ADJ
ejpam-1858	26	14	derivatives	derivative	NOUN
ejpam-1858	26	15	in	in	ADP
ejpam-1858	26	16	place	place	NOUN
ejpam-1858	26	17	of	of	ADP
ejpam-1858	26	18	ordinary	ordinary	ADJ
ejpam-1858	26	19	derivatives	derivative	NOUN
ejpam-1858	26	20	,	,	PUNCT
ejpam-1858	26	21	where	where	SCONJ
ejpam-1858	26	22	there	there	PRON
ejpam-1858	26	23	is	be	VERB
ejpam-1858	26	24	nonlocality	nonlocality	NOUN
ejpam-1858	26	25	or	or	CCONJ
ejpam-1858	26	26	memory	memory	NOUN
ejpam-1858	26	27	involved	involve	VERB
ejpam-1858	26	28	.	.	PUNCT
ejpam-1858	27	1	it	it	PRON
ejpam-1858	27	2	is	be	AUX
ejpam-1858	27	3	known	know	VERB
ejpam-1858	27	4	that	that	SCONJ
ejpam-1858	27	5	many	many	ADJ
ejpam-1858	27	6	evolutionary	evolutionary	ADJ
ejpam-1858	27	7	processes	process	NOUN
ejpam-1858	27	8	experience	experience	VERB
ejpam-1858	27	9	a	a	DET
ejpam-1858	27	10	change	change	NOUN
ejpam-1858	27	11	of	of	ADP
ejpam-1858	27	12	state	state	NOUN
ejpam-1858	27	13	abruptly	abruptly	ADV
ejpam-1858	27	14	.	.	PUNCT
ejpam-1858	28	1	these	these	PRON
ejpam-1858	28	2	undergo	undergo	VERB
ejpam-1858	28	3	short	short	ADJ
ejpam-1858	28	4	term	term	NOUN
ejpam-1858	28	5	perturbations	perturbation	NOUN
ejpam-1858	28	6	,	,	PUNCT
ejpam-1858	28	7	where	where	SCONJ
ejpam-1858	28	8	the	the	DET
ejpam-1858	28	9	time	time	NOUN
ejpam-1858	28	10	span	span	NOUN
ejpam-1858	28	11	is	be	AUX
ejpam-1858	28	12	negligible	negligible	ADJ
ejpam-1858	28	13	with	with	ADP
ejpam-1858	28	14	respect	respect	NOUN
ejpam-1858	28	15	to	to	ADP
ejpam-1858	28	16	the	the	DET
ejpam-1858	28	17	duration	duration	NOUN
ejpam-1858	28	18	of	of	ADP
ejpam-1858	28	19	the	the	DET
ejpam-1858	28	20	process	process	NOUN
ejpam-1858	28	21	.	.	PUNCT
ejpam-1858	29	1	thus	thus	ADV
ejpam-1858	29	2	,	,	PUNCT
ejpam-1858	29	3	it	it	PRON
ejpam-1858	29	4	is	be	AUX
ejpam-1858	29	5	natural	natural	ADJ
ejpam-1858	29	6	to	to	PART
ejpam-1858	29	7	assume	assume	VERB
ejpam-1858	29	8	that	that	SCONJ
ejpam-1858	29	9	the	the	DET
ejpam-1858	29	10	perturbations	perturbation	NOUN
ejpam-1858	29	11	act	act	VERB
ejpam-1858	29	12	instantaneously	instantaneously	ADV
ejpam-1858	29	13	and	and	CCONJ
ejpam-1858	29	14	hence	hence	ADV
ejpam-1858	29	15	can	can	AUX
ejpam-1858	29	16	be	be	AUX
ejpam-1858	29	17	modelled	model	VERB
ejpam-1858	29	18	as	as	ADP
ejpam-1858	29	19	impulses	impulse	NOUN
ejpam-1858	29	20	.	.	PUNCT
ejpam-1858	30	1	these	these	DET
ejpam-1858	30	2	perturbations	perturbation	NOUN
ejpam-1858	30	3	or	or	CCONJ
ejpam-1858	30	4	impulses	impulse	NOUN
ejpam-1858	30	5	can	can	AUX
ejpam-1858	30	6	be	be	AUX
ejpam-1858	30	7	considered	consider	VERB
ejpam-1858	30	8	as	as	ADP
ejpam-1858	30	9	of	of	ADP
ejpam-1858	30	10	two	two	NUM
ejpam-1858	30	11	types	type	NOUN
ejpam-1858	30	12	.	.	PUNCT
ejpam-1858	31	1	the	the	DET
ejpam-1858	31	2	moments	moment	NOUN
ejpam-1858	31	3	of	of	ADP
ejpam-1858	31	4	impulse	impulse	ADJ
ejpam-1858	31	5	can	can	AUX
ejpam-1858	31	6	be	be	AUX
ejpam-1858	31	7	decided	decide	VERB
ejpam-1858	31	8	in	in	ADP
ejpam-1858	31	9	advance	advance	NOUN
ejpam-1858	31	10	or	or	CCONJ
ejpam-1858	31	11	can	can	AUX
ejpam-1858	31	12	depend	depend	VERB
ejpam-1858	31	13	on	on	ADP
ejpam-1858	31	14	the	the	DET
ejpam-1858	31	15	solution	solution	NOUN
ejpam-1858	31	16	of	of	ADP
ejpam-1858	31	17	the	the	DET
ejpam-1858	31	18	model	model	NOUN
ejpam-1858	31	19	described	describe	VERB
ejpam-1858	31	20	by	by	ADP
ejpam-1858	31	21	the	the	DET
ejpam-1858	31	22	physical	physical	ADJ
ejpam-1858	31	23	phenomenon	phenomenon	NOUN
ejpam-1858	31	24	.	.	PUNCT
ejpam-1858	32	1	some	some	DET
ejpam-1858	32	2	examples	example	NOUN
ejpam-1858	32	3	that	that	PRON
ejpam-1858	32	4	can	can	AUX
ejpam-1858	32	5	be	be	AUX
ejpam-1858	32	6	modelled	model	VERB
ejpam-1858	32	7	in	in	ADP
ejpam-1858	32	8	this	this	DET
ejpam-1858	32	9	set	set	VERB
ejpam-1858	32	10	up	up	ADP
ejpam-1858	32	11	are	be	AUX
ejpam-1858	32	12	biological	biological	ADJ
ejpam-1858	32	13	phenomena	phenomenon	NOUN
ejpam-1858	32	14	involving	involve	VERB
ejpam-1858	32	15	thresholds	threshold	NOUN
ejpam-1858	32	16	,	,	PUNCT
ejpam-1858	32	17	bursting	burst	VERB
ejpam-1858	32	18	rhythmic	rhythmic	ADJ
ejpam-1858	32	19	models	model	NOUN
ejpam-1858	32	20	in	in	ADP
ejpam-1858	32	21	biology	biology	NOUN
ejpam-1858	32	22	and	and	CCONJ
ejpam-1858	32	23	medicine	medicine	NOUN
ejpam-1858	32	24	,	,	PUNCT
ejpam-1858	32	25	optimal	optimal	ADJ
ejpam-1858	32	26	control	control	NOUN
ejpam-1858	32	27	in	in	ADP
ejpam-1858	32	28	economics	economic	NOUN
ejpam-1858	32	29	,	,	PUNCT
ejpam-1858	32	30	to	to	PART
ejpam-1858	32	31	name	name	VERB
ejpam-1858	32	32	a	a	DET
ejpam-1858	32	33	few	few	ADJ
ejpam-1858	32	34	.	.	PUNCT
ejpam-1858	33	1	in	in	ADP
ejpam-1858	33	2	some	some	PRON
ejpam-1858	33	3	of	of	ADP
ejpam-1858	33	4	the	the	DET
ejpam-1858	33	5	afore	afore	ADV
ejpam-1858	33	6	mentioned	mention	VERB
ejpam-1858	33	7	models	model	NOUN
ejpam-1858	33	8	,	,	PUNCT
ejpam-1858	33	9	the	the	DET
ejpam-1858	33	10	occurrence	occurrence	NOUN
ejpam-1858	33	11	of	of	ADP
ejpam-1858	33	12	a	a	DET
ejpam-1858	33	13	change	change	NOUN
ejpam-1858	33	14	of	of	ADP
ejpam-1858	33	15	state	state	NOUN
ejpam-1858	33	16	or	or	CCONJ
ejpam-1858	33	17	perturbation	perturbation	NOUN
ejpam-1858	33	18	depends	depend	VERB
ejpam-1858	33	19	on	on	ADP
ejpam-1858	33	20	the	the	DET
ejpam-1858	33	21	solution	solution	NOUN
ejpam-1858	33	22	.	.	PUNCT
ejpam-1858	34	1	also	also	ADV
ejpam-1858	34	2	,	,	PUNCT
ejpam-1858	34	3	the	the	DET
ejpam-1858	34	4	constraints	constraint	NOUN
ejpam-1858	34	5	of	of	ADP
ejpam-1858	34	6	any	any	DET
ejpam-1858	34	7	physical	physical	ADJ
ejpam-1858	34	8	model	model	NOUN
ejpam-1858	34	9	can	can	AUX
ejpam-1858	34	10	be	be	AUX
ejpam-1858	34	11	considered	consider	VERB
ejpam-1858	34	12	as	as	ADP
ejpam-1858	34	13	a	a	DET
ejpam-1858	34	14	barrier	barrier	NOUN
ejpam-1858	34	15	or	or	CCONJ
ejpam-1858	34	16	a	a	DET
ejpam-1858	34	17	surface	surface	NOUN
ejpam-1858	34	18	.	.	PUNCT
ejpam-1858	35	1	if	if	SCONJ
ejpam-1858	35	2	a	a	DET
ejpam-1858	35	3	solution	solution	NOUN
ejpam-1858	35	4	of	of	ADP
ejpam-1858	35	5	the	the	DET
ejpam-1858	35	6	model	model	NOUN
ejpam-1858	35	7	encounters	encounter	VERB
ejpam-1858	35	8	the	the	DET
ejpam-1858	35	9	surface	surface	NOUN
ejpam-1858	35	10	,	,	PUNCT
ejpam-1858	35	11	it	it	PRON
ejpam-1858	35	12	must	must	AUX
ejpam-1858	35	13	be	be	AUX
ejpam-1858	35	14	given	give	VERB
ejpam-1858	35	15	an	an	DET
ejpam-1858	35	16	impulse	impulse	NOUN
ejpam-1858	35	17	or	or	CCONJ
ejpam-1858	35	18	a	a	DET
ejpam-1858	35	19	perturbation	perturbation	NOUN
ejpam-1858	35	20	to	to	PART
ejpam-1858	35	21	avoid	avoid	VERB
ejpam-1858	35	22	it	it	PRON
ejpam-1858	35	23	or	or	CCONJ
ejpam-1858	35	24	to	to	PART
ejpam-1858	35	25	get	get	VERB
ejpam-1858	35	26	out	out	ADP
ejpam-1858	35	27	of	of	ADP
ejpam-1858	35	28	it	it	PRON
ejpam-1858	35	29	.	.	PUNCT
ejpam-1858	36	1	thus	thus	ADV
ejpam-1858	36	2	a	a	DET
ejpam-1858	36	3	mathematical	mathematical	ADJ
ejpam-1858	36	4	model	model	NOUN
ejpam-1858	36	5	involving	involve	VERB
ejpam-1858	36	6	differential	differential	ADJ
ejpam-1858	36	7	equation	equation	NOUN
ejpam-1858	36	8	with	with	ADP
ejpam-1858	36	9	variable	variable	ADJ
ejpam-1858	36	10	moments	moment	NOUN
ejpam-1858	36	11	of	of	ADP
ejpam-1858	36	12	impulse	impulse	ADJ
ejpam-1858	36	13	is	be	AUX
ejpam-1858	36	14	a	a	DET
ejpam-1858	36	15	system	system	NOUN
ejpam-1858	36	16	worth	worth	ADJ
ejpam-1858	36	17	studying	study	VERB
ejpam-1858	36	18	.	.	PUNCT
ejpam-1858	37	1	this	this	DET
ejpam-1858	37	2	model	model	NOUN
ejpam-1858	37	3	exhibits	exhibit	VERB
ejpam-1858	37	4	many	many	ADJ
ejpam-1858	37	5	interesting	interesting	ADJ
ejpam-1858	37	6	phenomena	phenomenon	NOUN
ejpam-1858	37	7	which	which	PRON
ejpam-1858	37	8	are	be	AUX
ejpam-1858	37	9	discussed	discuss	VERB
ejpam-1858	37	10	in	in	ADP
ejpam-1858	37	11	[	[	X
ejpam-1858	37	12	9	9	NUM
ejpam-1858	37	13	]	]	PUNCT
ejpam-1858	37	14	.	.	PUNCT
ejpam-1858	38	1	the	the	DET
ejpam-1858	38	2	momentum	momentum	NOUN
ejpam-1858	38	3	that	that	SCONJ
ejpam-1858	38	4	the	the	DET
ejpam-1858	38	5	research	research	NOUN
ejpam-1858	38	6	on	on	ADP
ejpam-1858	38	7	fractional	fractional	ADJ
ejpam-1858	38	8	differential	differential	ADJ
ejpam-1858	38	9	equation	equation	NOUN
ejpam-1858	38	10	is	be	AUX
ejpam-1858	38	11	gaining	gain	VERB
ejpam-1858	38	12	had	have	AUX
ejpam-1858	38	13	prompted	prompt	VERB
ejpam-1858	38	14	us	we	PRON
ejpam-1858	38	15	to	to	PART
ejpam-1858	38	16	take	take	VERB
ejpam-1858	38	17	up	up	ADP
ejpam-1858	38	18	the	the	DET
ejpam-1858	38	19	study	study	NOUN
ejpam-1858	38	20	of	of	ADP
ejpam-1858	38	21	fractional	fractional	ADJ
ejpam-1858	38	22	differential	differential	ADJ
ejpam-1858	38	23	equations	equation	NOUN
ejpam-1858	38	24	with	with	ADP
ejpam-1858	38	25	variable	variable	ADJ
ejpam-1858	38	26	moments	moment	NOUN
ejpam-1858	38	27	of	of	ADP
ejpam-1858	38	28	impulse	impulse	ADJ
ejpam-1858	38	29	,	,	PUNCT
ejpam-1858	38	30	in	in	ADP
ejpam-1858	38	31	this	this	DET
ejpam-1858	38	32	paper	paper	NOUN
ejpam-1858	38	33	.	.	PUNCT
ejpam-1858	39	1	we	we	PRON
ejpam-1858	39	2	proceeded	proceed	VERB
ejpam-1858	39	3	along	along	ADP
ejpam-1858	39	4	the	the	DET
ejpam-1858	39	5	lines	line	NOUN
ejpam-1858	39	6	of	of	ADP
ejpam-1858	39	7	the	the	DET
ejpam-1858	39	8	theory	theory	NOUN
ejpam-1858	39	9	established	establish	VERB
ejpam-1858	39	10	in	in	ADP
ejpam-1858	39	11	[	[	X
ejpam-1858	39	12	9	9	NUM
ejpam-1858	39	13	]	]	PUNCT
ejpam-1858	39	14	and	and	CCONJ
ejpam-1858	39	15	have	have	AUX
ejpam-1858	39	16	constructed	construct	VERB
ejpam-1858	39	17	examples	example	NOUN
ejpam-1858	39	18	in	in	ADP
ejpam-1858	39	19	the	the	DET
ejpam-1858	39	20	present	present	NOUN
ejpam-1858	39	21	set	set	VERB
ejpam-1858	39	22	up	up	ADP
ejpam-1858	39	23	.	.	PUNCT
ejpam-1858	40	1	the	the	DET
ejpam-1858	40	2	fact	fact	NOUN
ejpam-1858	40	3	that	that	SCONJ
ejpam-1858	40	4	there	there	PRON
ejpam-1858	40	5	are	be	VERB
ejpam-1858	40	6	many	many	ADJ
ejpam-1858	40	7	physical	physical	ADJ
ejpam-1858	40	8	phenomena	phenomenon	NOUN
ejpam-1858	40	9	that	that	PRON
ejpam-1858	40	10	can	can	AUX
ejpam-1858	40	11	be	be	AUX
ejpam-1858	40	12	modeled	model	VERB
ejpam-1858	40	13	using	use	VERB
ejpam-1858	40	14	fractional	fractional	ADJ
ejpam-1858	40	15	derivatives	derivative	NOUN
ejpam-1858	40	16	had	have	AUX
ejpam-1858	40	17	encouraged	encourage	VERB
ejpam-1858	40	18	us	we	PRON
ejpam-1858	40	19	to	to	PART
ejpam-1858	40	20	obtain	obtain	VERB
ejpam-1858	40	21	conditions	condition	NOUN
ejpam-1858	40	22	using	use	VERB
ejpam-1858	40	23	fractional	fractional	ADJ
ejpam-1858	40	24	derivatives	derivative	NOUN
ejpam-1858	40	25	.	.	PUNCT
ejpam-1858	41	1	the	the	DET
ejpam-1858	41	2	remaining	remain	VERB
ejpam-1858	41	3	part	part	NOUN
ejpam-1858	41	4	of	of	ADP
ejpam-1858	41	5	the	the	DET
ejpam-1858	41	6	paper	paper	NOUN
ejpam-1858	41	7	is	be	AUX
ejpam-1858	41	8	organized	organize	VERB
ejpam-1858	41	9	as	as	SCONJ
ejpam-1858	41	10	follows	follow	VERB
ejpam-1858	41	11	.	.	PUNCT
ejpam-1858	42	1	in	in	ADP
ejpam-1858	42	2	section	section	NOUN
ejpam-1858	42	3	2	2	NUM
ejpam-1858	42	4	,	,	PUNCT
ejpam-1858	42	5	we	we	PRON
ejpam-1858	42	6	deal	deal	VERB
ejpam-1858	42	7	with	with	ADP
ejpam-1858	42	8	the	the	DET
ejpam-1858	42	9	preliminaries	preliminary	NOUN
ejpam-1858	42	10	of	of	ADP
ejpam-1858	42	11	fractional	fractional	ADJ
ejpam-1858	42	12	differential	differential	ADJ
ejpam-1858	42	13	equations	equation	NOUN
ejpam-1858	42	14	.	.	PUNCT
ejpam-1858	43	1	adapting	adapt	VERB
ejpam-1858	43	2	the	the	DET
ejpam-1858	43	3	description	description	NOUN
ejpam-1858	43	4	of	of	ADP
ejpam-1858	43	5	solution	solution	NOUN
ejpam-1858	43	6	of	of	ADP
ejpam-1858	43	7	an	an	DET
ejpam-1858	43	8	evolutionary	evolutionary	ADJ
ejpam-1858	43	9	process	process	NOUN
ejpam-1858	43	10	in	in	ADP
ejpam-1858	43	11	[	[	X
ejpam-1858	43	12	9]we	9]we	NUM
ejpam-1858	43	13	described	describe	VERB
ejpam-1858	43	14	the	the	DET
ejpam-1858	43	15	solution	solution	NOUN
ejpam-1858	43	16	of	of	ADP
ejpam-1858	43	17	an	an	DET
ejpam-1858	43	18	impulsive	impulsive	ADJ
ejpam-1858	43	19	or	or	CCONJ
ejpam-1858	43	20	a	a	DET
ejpam-1858	43	21	hybrid	hybrid	ADJ
ejpam-1858	43	22	fractional	fractional	ADJ
ejpam-1858	43	23	differential	differential	ADJ
ejpam-1858	43	24	equation	equation	NOUN
ejpam-1858	43	25	in	in	ADP
ejpam-1858	43	26	section	section	NOUN
ejpam-1858	43	27	3	3	NUM
ejpam-1858	43	28	.	.	PUNCT
ejpam-1858	44	1	an	an	DET
ejpam-1858	44	2	example	example	NOUN
ejpam-1858	44	3	illustrating	illustrate	VERB
ejpam-1858	44	4	the	the	DET
ejpam-1858	44	5	proposed	propose	VERB
ejpam-1858	44	6	system	system	NOUN
ejpam-1858	44	7	is	be	AUX
ejpam-1858	44	8	given	give	VERB
ejpam-1858	44	9	in	in	ADP
ejpam-1858	44	10	section	section	NOUN
ejpam-1858	44	11	4	4	NUM
ejpam-1858	44	12	.	.	PUNCT
ejpam-1858	45	1	in	in	ADP
ejpam-1858	45	2	section	section	NOUN
ejpam-1858	45	3	5	5	NUM
ejpam-1858	45	4	we	we	PRON
ejpam-1858	45	5	deal	deal	VERB
ejpam-1858	45	6	with	with	ADP
ejpam-1858	45	7	existence	existence	NOUN
ejpam-1858	45	8	and	and	CCONJ
ejpam-1858	45	9	continuation	continuation	NOUN
ejpam-1858	45	10	of	of	ADP
ejpam-1858	45	11	solutions	solution	NOUN
ejpam-1858	45	12	.	.	PUNCT
ejpam-1858	46	1	section	section	NOUN
ejpam-1858	46	2	6	6	NUM
ejpam-1858	46	3	concludes	conclude	VERB
ejpam-1858	46	4	the	the	DET
ejpam-1858	46	5	work	work	NOUN
ejpam-1858	46	6	done	do	VERB
ejpam-1858	46	7	in	in	ADP
ejpam-1858	46	8	the	the	DET
ejpam-1858	46	9	paper	paper	NOUN
ejpam-1858	46	10	.	.	PUNCT
ejpam-1858	47	1	j.	j.	PROPN
ejpam-1858	47	2	devi	devi	PROPN
ejpam-1858	47	3	,	,	PUNCT
ejpam-1858	47	4	n.	n.	PROPN
ejpam-1858	47	5	giribabu	giribabu	PROPN
ejpam-1858	47	6	/	/	SYM
ejpam-1858	47	7	eur	eur	PROPN
ejpam-1858	47	8	.	.	PUNCT
ejpam-1858	48	1	j.	j.	PROPN
ejpam-1858	48	2	pure	pure	PROPN
ejpam-1858	48	3	appl	appl	PROPN
ejpam-1858	48	4	.	.	PROPN
ejpam-1858	48	5	math	math	PROPN
ejpam-1858	48	6	,	,	PUNCT
ejpam-1858	48	7	7	7	NUM
ejpam-1858	48	8	(	(	PUNCT
ejpam-1858	48	9	2014	2014	NUM
ejpam-1858	48	10	)	)	PUNCT
ejpam-1858	48	11	,	,	PUNCT
ejpam-1858	48	12	115	115	NUM
ejpam-1858	48	13	-	-	SYM
ejpam-1858	48	14	128	128	NUM
ejpam-1858	48	15	117	117	NUM
ejpam-1858	48	16	2	2	NUM
ejpam-1858	48	17	.	.	PUNCT
ejpam-1858	48	18	preliminaries	preliminary	NOUN
ejpam-1858	48	19	in	in	ADP
ejpam-1858	48	20	this	this	DET
ejpam-1858	48	21	section	section	NOUN
ejpam-1858	48	22	,	,	PUNCT
ejpam-1858	48	23	we	we	PRON
ejpam-1858	48	24	introduce	introduce	VERB
ejpam-1858	48	25	notations	notation	NOUN
ejpam-1858	48	26	,	,	PUNCT
ejpam-1858	48	27	definitions	definition	NOUN
ejpam-1858	48	28	,	,	PUNCT
ejpam-1858	48	29	results	result	NOUN
ejpam-1858	48	30	and	and	CCONJ
ejpam-1858	48	31	preliminary	preliminary	ADJ
ejpam-1858	48	32	facts	fact	NOUN
ejpam-1858	48	33	from	from	ADP
ejpam-1858	48	34	[	[	X
ejpam-1858	48	35	10	10	NUM
ejpam-1858	48	36	]	]	PUNCT
ejpam-1858	48	37	,	,	PUNCT
ejpam-1858	48	38	[	[	X
ejpam-1858	48	39	4	4	X
ejpam-1858	48	40	]	]	PUNCT
ejpam-1858	48	41	that	that	PRON
ejpam-1858	48	42	are	be	AUX
ejpam-1858	48	43	required	require	VERB
ejpam-1858	48	44	in	in	ADP
ejpam-1858	48	45	the	the	DET
ejpam-1858	48	46	remainder	remainder	NOUN
ejpam-1858	48	47	of	of	ADP
ejpam-1858	48	48	this	this	DET
ejpam-1858	48	49	paper	paper	NOUN
ejpam-1858	48	50	.	.	PUNCT
ejpam-1858	49	1	definition	definition	NOUN
ejpam-1858	49	2	1	1	NUM
ejpam-1858	49	3	.	.	PUNCT
ejpam-1858	50	1	the	the	DET
ejpam-1858	50	2	riemann	riemann	PROPN
ejpam-1858	50	3	-	-	PUNCT
ejpam-1858	50	4	liouville	liouville	VERB
ejpam-1858	50	5	fractional	fractional	ADJ
ejpam-1858	50	6	integral	integral	ADJ
ejpam-1858	50	7	of	of	ADP
ejpam-1858	50	8	order	order	NOUN
ejpam-1858	50	9	q	q	NOUN
ejpam-1858	50	10	,	,	PUNCT
ejpam-1858	50	11	where	where	SCONJ
ejpam-1858	50	12	q	q	NOUN
ejpam-1858	50	13	is	be	AUX
ejpam-1858	50	14	a	a	DET
ejpam-1858	50	15	positive	positive	ADJ
ejpam-1858	50	16	real	real	ADJ
ejpam-1858	50	17	number	number	NOUN
ejpam-1858	50	18	,	,	PUNCT
ejpam-1858	50	19	of	of	ADP
ejpam-1858	50	20	a	a	DET
ejpam-1858	50	21	function	function	NOUN
ejpam-1858	50	22	x	x	PUNCT
ejpam-1858	50	23	given	give	VERB
ejpam-1858	50	24	on	on	ADP
ejpam-1858	50	25	the	the	DET
ejpam-1858	50	26	interval	interval	NOUN
ejpam-1858	50	27	[	[	X
ejpam-1858	50	28	t0	t0	PROPN
ejpam-1858	50	29	,	,	PUNCT
ejpam-1858	50	30	t	t	PROPN
ejpam-1858	50	31	]	]	PUNCT
ejpam-1858	50	32	,	,	PUNCT
ejpam-1858	50	33	t0	t0	PROPN
ejpam-1858	50	34	≥	≥	NUM
ejpam-1858	50	35	0	0	NUM
ejpam-1858	50	36	is	be	AUX
ejpam-1858	50	37	defined	define	VERB
ejpam-1858	50	38	as	as	ADP
ejpam-1858	50	39	d−q	d−q	PROPN
ejpam-1858	50	40	x(t	x(t	PROPN
ejpam-1858	50	41	)	)	PUNCT
ejpam-1858	51	1	=	=	SYM
ejpam-1858	51	2	1	1	NUM
ejpam-1858	51	3	γ(q	γ(q	PROPN
ejpam-1858	51	4	)	)	PUNCT
ejpam-1858	51	5	t	t	NOUN
ejpam-1858	51	6	∫	∫	PROPN
ejpam-1858	51	7	t0	t0	PROPN
ejpam-1858	51	8	(	(	PUNCT
ejpam-1858	51	9	t	t	PROPN
ejpam-1858	51	10	−	−	PROPN
ejpam-1858	51	11	s)q−1	s)q−1	PROPN
ejpam-1858	51	12	x(s)ds	x(s)ds	PROPN
ejpam-1858	51	13	,	,	PUNCT
ejpam-1858	51	14	t0	t0	PROPN
ejpam-1858	51	15	≤	≤	PROPN
ejpam-1858	51	16	t	t	PROPN
ejpam-1858	51	17	≤	≤	PROPN
ejpam-1858	51	18	t	t	PROPN
ejpam-1858	51	19	,	,	PUNCT
ejpam-1858	51	20	where	where	SCONJ
ejpam-1858	51	21	γ	γ	PROPN
ejpam-1858	51	22	is	be	AUX
ejpam-1858	51	23	the	the	DET
ejpam-1858	51	24	gamma	gamma	PROPN
ejpam-1858	51	25	function	function	NOUN
ejpam-1858	51	26	.	.	PUNCT
ejpam-1858	52	1	definition	definition	NOUN
ejpam-1858	52	2	2	2	NUM
ejpam-1858	52	3	.	.	PUNCT
ejpam-1858	53	1	the	the	DET
ejpam-1858	53	2	riemann	riemann	PROPN
ejpam-1858	53	3	-	-	PUNCT
ejpam-1858	53	4	liouville	liouville	VERB
ejpam-1858	53	5	fractional	fractional	ADJ
ejpam-1858	53	6	derivative	derivative	NOUN
ejpam-1858	53	7	of	of	ADP
ejpam-1858	53	8	order	order	NOUN
ejpam-1858	53	9	q	q	NOUN
ejpam-1858	53	10	,	,	PUNCT
ejpam-1858	53	11	where	where	SCONJ
ejpam-1858	53	12	q	q	NOUN
ejpam-1858	53	13	is	be	AUX
ejpam-1858	53	14	a	a	DET
ejpam-1858	53	15	positive	positive	ADJ
ejpam-1858	53	16	real	real	ADJ
ejpam-1858	53	17	number	number	NOUN
ejpam-1858	53	18	,	,	PUNCT
ejpam-1858	53	19	of	of	ADP
ejpam-1858	53	20	a	a	DET
ejpam-1858	53	21	function	function	NOUN
ejpam-1858	53	22	x	x	PUNCT
ejpam-1858	53	23	given	give	VERB
ejpam-1858	53	24	on	on	ADP
ejpam-1858	53	25	the	the	DET
ejpam-1858	53	26	interval	interval	NOUN
ejpam-1858	53	27	[	[	X
ejpam-1858	53	28	t0	t0	PROPN
ejpam-1858	53	29	,	,	PUNCT
ejpam-1858	53	30	t	t	PROPN
ejpam-1858	53	31	]	]	PUNCT
ejpam-1858	53	32	,	,	PUNCT
ejpam-1858	53	33	t0	t0	PROPN
ejpam-1858	53	34	≥	≥	NUM
ejpam-1858	53	35	0	0	NUM
ejpam-1858	53	36	is	be	AUX
ejpam-1858	53	37	defined	define	VERB
ejpam-1858	53	38	as	as	ADP
ejpam-1858	53	39	dq	dq	ADP
ejpam-1858	53	40	x(t	x(t	PROPN
ejpam-1858	53	41	)	)	PUNCT
ejpam-1858	54	1	=	=	SYM
ejpam-1858	54	2	1	1	NUM
ejpam-1858	54	3	γ(p	γ(p	NOUN
ejpam-1858	54	4	)	)	PUNCT
ejpam-1858	55	1	dm	dm	PROPN
ejpam-1858	55	2	d	d	NOUN
ejpam-1858	55	3	tm	tm	PRON
ejpam-1858	55	4			PROPN
ejpam-1858	55	5			PROPN
ejpam-1858	55	6			DET
ejpam-1858	55	7			PROPN
ejpam-1858	55	8			PROPN
ejpam-1858	55	9	t	t	PROPN
ejpam-1858	55	10	∫	∫	PROPN
ejpam-1858	55	11	t0	t0	PROPN
ejpam-1858	55	12	(	(	PUNCT
ejpam-1858	55	13	t	t	PROPN
ejpam-1858	55	14	−	−	PROPN
ejpam-1858	55	15	s)p−1	s)p−1	VERB
ejpam-1858	55	16	x(s)ds	x(s)ds	PROPN
ejpam-1858	55	17			PROPN
ejpam-1858	55	18			PROPN
ejpam-1858	56	1			PROPN
ejpam-1858	56	2			ADJ
ejpam-1858	56	3			NOUN
ejpam-1858	56	4	,	,	PUNCT
ejpam-1858	56	5	t0	t0	PROPN
ejpam-1858	56	6	≤	≤	PROPN
ejpam-1858	56	7	t	t	PROPN
ejpam-1858	56	8	≤	≤	PROPN
ejpam-1858	56	9	t	t	PROPN
ejpam-1858	56	10	,	,	PUNCT
ejpam-1858	56	11	where	where	SCONJ
ejpam-1858	56	12	m−	m−	PROPN
ejpam-1858	56	13	p	p	X
ejpam-1858	56	14	=	=	X
ejpam-1858	56	15	q	q	PROPN
ejpam-1858	56	16	and	and	CCONJ
ejpam-1858	56	17	m	m	PROPN
ejpam-1858	56	18	is	be	AUX
ejpam-1858	56	19	the	the	DET
ejpam-1858	56	20	least	least	ADV
ejpam-1858	56	21	positive	positive	ADJ
ejpam-1858	56	22	integer	integer	NOUN
ejpam-1858	56	23	greater	great	ADJ
ejpam-1858	56	24	than	than	ADP
ejpam-1858	56	25	q	q	NOUN
ejpam-1858	56	26	so	so	SCONJ
ejpam-1858	56	27	that	that	SCONJ
ejpam-1858	56	28	0	0	NUM
ejpam-1858	56	29	<	<	X
ejpam-1858	56	30	p	p	X
ejpam-1858	56	31	≤	≤	NUM
ejpam-1858	56	32	1	1	NUM
ejpam-1858	56	33	.	.	PUNCT
ejpam-1858	57	1	definition	definition	NOUN
ejpam-1858	57	2	3	3	NUM
ejpam-1858	57	3	.	.	PUNCT
ejpam-1858	58	1	the	the	DET
ejpam-1858	58	2	caputo	caputo	PROPN
ejpam-1858	58	3	’s	’s	PART
ejpam-1858	58	4	fractional	fractional	ADJ
ejpam-1858	58	5	derivative	derivative	NOUN
ejpam-1858	58	6	of	of	ADP
ejpam-1858	58	7	order	order	NOUN
ejpam-1858	58	8	q	q	NOUN
ejpam-1858	58	9	,	,	PUNCT
ejpam-1858	58	10	where	where	SCONJ
ejpam-1858	58	11	q	q	NOUN
ejpam-1858	58	12	is	be	AUX
ejpam-1858	58	13	a	a	DET
ejpam-1858	58	14	positive	positive	ADJ
ejpam-1858	58	15	real	real	ADJ
ejpam-1858	58	16	number	number	NOUN
ejpam-1858	58	17	,	,	PUNCT
ejpam-1858	58	18	of	of	ADP
ejpam-1858	58	19	a	a	DET
ejpam-1858	58	20	function	function	NOUN
ejpam-1858	58	21	x	x	PUNCT
ejpam-1858	58	22	given	give	VERB
ejpam-1858	58	23	on	on	ADP
ejpam-1858	58	24	the	the	DET
ejpam-1858	58	25	interval	interval	NOUN
ejpam-1858	58	26	[	[	X
ejpam-1858	58	27	t0	t0	PROPN
ejpam-1858	58	28	,	,	PUNCT
ejpam-1858	58	29	t	t	PROPN
ejpam-1858	58	30	]	]	PUNCT
ejpam-1858	58	31	,	,	PUNCT
ejpam-1858	58	32	t0	t0	PROPN
ejpam-1858	58	33	≥	≥	NUM
ejpam-1858	58	34	0	0	NUM
ejpam-1858	58	35	is	be	AUX
ejpam-1858	58	36	defined	define	VERB
ejpam-1858	58	37	as	as	ADP
ejpam-1858	58	38	c	c	PROPN
ejpam-1858	58	39	dq	dq	ADP
ejpam-1858	58	40	x(t	x(t	PROPN
ejpam-1858	58	41	)	)	PUNCT
ejpam-1858	59	1	=	=	SYM
ejpam-1858	59	2	1	1	NUM
ejpam-1858	59	3	γ(n−	γ(n−	PROPN
ejpam-1858	59	4	q	q	PROPN
ejpam-1858	59	5	)	)	PUNCT
ejpam-1858	59	6	t	t	PROPN
ejpam-1858	59	7	∫	∫	PROPN
ejpam-1858	59	8	t0	t0	PROPN
ejpam-1858	59	9	(	(	PUNCT
ejpam-1858	59	10	t	t	PROPN
ejpam-1858	59	11	−	−	PROPN
ejpam-1858	59	12	s)n−q−1	s)n−q−1	PROPN
ejpam-1858	59	13	x	x	SYM
ejpam-1858	59	14	(	(	PUNCT
ejpam-1858	59	15	n)(s)ds	n)(s)ds	NOUN
ejpam-1858	59	16	,	,	PUNCT
ejpam-1858	59	17	t0	t0	PROPN
ejpam-1858	59	18	≤	≤	PROPN
ejpam-1858	59	19	t	t	PROPN
ejpam-1858	59	20	≤	≤	PROPN
ejpam-1858	59	21	t	t	PROPN
ejpam-1858	59	22	,	,	PUNCT
ejpam-1858	59	23	where	where	SCONJ
ejpam-1858	59	24	n	n	PRON
ejpam-1858	59	25	is	be	AUX
ejpam-1858	59	26	a	a	DET
ejpam-1858	59	27	positive	positive	ADJ
ejpam-1858	59	28	integer	integer	NOUN
ejpam-1858	59	29	such	such	DET
ejpam-1858	59	30	that	that	DET
ejpam-1858	59	31	n−	n−	NOUN
ejpam-1858	59	32	1	1	NUM
ejpam-1858	59	33	<	<	X
ejpam-1858	59	34	q	q	X
ejpam-1858	59	35	<	<	X
ejpam-1858	59	36	n.	n.	NOUN
ejpam-1858	59	37	in	in	ADP
ejpam-1858	59	38	particular	particular	ADJ
ejpam-1858	59	39	,	,	PUNCT
ejpam-1858	59	40	the	the	DET
ejpam-1858	59	41	caputo	caputo	PROPN
ejpam-1858	59	42	’s	’s	PART
ejpam-1858	59	43	fractional	fractional	ADJ
ejpam-1858	59	44	derivative	derivative	NOUN
ejpam-1858	59	45	of	of	ADP
ejpam-1858	59	46	order	order	NOUN
ejpam-1858	59	47	q	q	NOUN
ejpam-1858	59	48	,	,	PUNCT
ejpam-1858	59	49	where	where	SCONJ
ejpam-1858	59	50	0	0	X
ejpam-1858	59	51	<	<	X
ejpam-1858	59	52	q	q	X
ejpam-1858	59	53	<	<	X
ejpam-1858	59	54	1	1	NUM
ejpam-1858	59	55	is	be	AUX
ejpam-1858	59	56	defined	define	VERB
ejpam-1858	59	57	as	as	ADP
ejpam-1858	59	58	c	c	PROPN
ejpam-1858	59	59	dq	dq	ADP
ejpam-1858	59	60	x(t	x(t	PROPN
ejpam-1858	59	61	)	)	PUNCT
ejpam-1858	59	62	=	=	SYM
ejpam-1858	59	63	1	1	NUM
ejpam-1858	59	64	γ(1−	γ(1−	NOUN
ejpam-1858	59	65	q	q	X
ejpam-1858	59	66	)	)	PUNCT
ejpam-1858	59	67	t	t	PROPN
ejpam-1858	59	68	∫	∫	PROPN
ejpam-1858	59	69	t0	t0	PROPN
ejpam-1858	59	70	(	(	PUNCT
ejpam-1858	59	71	t	t	PROPN
ejpam-1858	59	72	−	−	PROPN
ejpam-1858	59	73	s)−q	s)−q	PROPN
ejpam-1858	59	74	x	x	SYM
ejpam-1858	59	75	′(s)ds	′(s)ds	PROPN
ejpam-1858	59	76	,	,	PUNCT
ejpam-1858	59	77	t0	t0	PROPN
ejpam-1858	59	78	≤	≤	PROPN
ejpam-1858	59	79	t	t	PROPN
ejpam-1858	59	80	≤	≤	ADJ
ejpam-1858	59	81	t.	t.	NOUN
ejpam-1858	59	82	definition	definition	NOUN
ejpam-1858	59	83	4	4	NUM
ejpam-1858	59	84	.	.	PUNCT
ejpam-1858	60	1	a	a	DET
ejpam-1858	60	2	function	function	NOUN
ejpam-1858	60	3	u	u	NOUN
ejpam-1858	60	4	is	be	AUX
ejpam-1858	60	5	said	say	VERB
ejpam-1858	60	6	to	to	PART
ejpam-1858	60	7	be	be	AUX
ejpam-1858	60	8	cp	cp	INTJ
ejpam-1858	60	9	continuous	continuous	ADJ
ejpam-1858	60	10	i.e.	i.e.	X
ejpam-1858	60	11	,	,	PUNCT
ejpam-1858	60	12	u	u	PROPN
ejpam-1858	60	13	∈	∈	PROPN
ejpam-1858	60	14	cp	cp	INTJ
ejpam-1858	60	15	�	�	PROPN
ejpam-1858	60	16	[	[	X
ejpam-1858	60	17	t0	t0	PROPN
ejpam-1858	60	18	,	,	PUNCT
ejpam-1858	60	19	t0	t0	PROPN
ejpam-1858	60	20	+	+	CCONJ
ejpam-1858	60	21	a],r	a],r	VERB
ejpam-1858	60	22	�	�	PROPN
ejpam-1858	60	23	if	if	SCONJ
ejpam-1858	60	24	and	and	CCONJ
ejpam-1858	60	25	only	only	ADV
ejpam-1858	60	26	if	if	SCONJ
ejpam-1858	60	27	u	u	PROPN
ejpam-1858	60	28	∈	∈	PROPN
ejpam-1858	60	29	c((t0	c((t0	NOUN
ejpam-1858	60	30	,	,	PUNCT
ejpam-1858	60	31	t0	t0	PROPN
ejpam-1858	60	32	+	+	CCONJ
ejpam-1858	60	33	a],r	a],r	PROPN
ejpam-1858	60	34	)	)	PUNCT
ejpam-1858	60	35	and	and	CCONJ
ejpam-1858	60	36	(	(	PUNCT
ejpam-1858	60	37	t	t	PROPN
ejpam-1858	60	38	−	−	PROPN
ejpam-1858	60	39	t0	t0	PROPN
ejpam-1858	60	40	)	)	PUNCT
ejpam-1858	60	41	pu(t	pu(t	X
ejpam-1858	60	42	)	)	PUNCT
ejpam-1858	60	43	∈	∈	PROPN
ejpam-1858	60	44	c([t0	c([t0	PROPN
ejpam-1858	60	45	,	,	PUNCT
ejpam-1858	60	46	t0	t0	PROPN
ejpam-1858	60	47	+	+	CCONJ
ejpam-1858	60	48	a],r	a],r	PROPN
ejpam-1858	60	49	)	)	PUNCT
ejpam-1858	60	50	with	with	ADP
ejpam-1858	60	51	p+	p+	NOUN
ejpam-1858	60	52	q	q	X
ejpam-1858	60	53	=	=	SYM
ejpam-1858	60	54	1	1	NUM
ejpam-1858	60	55	,	,	PUNCT
ejpam-1858	60	56	0	0	PUNCT
ejpam-1858	60	57	<	<	X
ejpam-1858	60	58	q	q	X
ejpam-1858	60	59	<	<	X
ejpam-1858	60	60	1	1	NUM
ejpam-1858	60	61	.	.	PUNCT
ejpam-1858	60	62	definition	definition	NOUN
ejpam-1858	60	63	5	5	NUM
ejpam-1858	60	64	.	.	PUNCT
ejpam-1858	61	1	a	a	DET
ejpam-1858	61	2	function	function	NOUN
ejpam-1858	61	3	u	u	NOUN
ejpam-1858	61	4	is	be	AUX
ejpam-1858	61	5	said	say	VERB
ejpam-1858	61	6	to	to	PART
ejpam-1858	61	7	be	be	AUX
ejpam-1858	61	8	cq	cq	ADP
ejpam-1858	61	9	continuous	continuous	ADJ
ejpam-1858	61	10	i.e.	i.e.	X
ejpam-1858	61	11	,	,	PUNCT
ejpam-1858	61	12	u	u	PROPN
ejpam-1858	61	13	∈	∈	PROPN
ejpam-1858	61	14	cq	cq	PROPN
ejpam-1858	61	15	�	�	PROPN
ejpam-1858	61	16	[	[	X
ejpam-1858	61	17	t0	t0	PROPN
ejpam-1858	61	18	,	,	PUNCT
ejpam-1858	61	19	t],r	t],r	PUNCT
ejpam-1858	61	20	�	�	PROPN
ejpam-1858	61	21	if	if	SCONJ
ejpam-1858	61	22	and	and	CCONJ
ejpam-1858	61	23	only	only	ADV
ejpam-1858	61	24	if	if	SCONJ
ejpam-1858	61	25	the	the	DET
ejpam-1858	61	26	caputo	caputo	PROPN
ejpam-1858	61	27	derivative	derivative	NOUN
ejpam-1858	61	28	c	c	PROPN
ejpam-1858	61	29	dqu(t	dqu(t	PROPN
ejpam-1858	61	30	)	)	PUNCT
ejpam-1858	61	31	exists	exist	VERB
ejpam-1858	61	32	and	and	CCONJ
ejpam-1858	61	33	satisfies	satisfie	NOUN
ejpam-1858	61	34	c	c	X
ejpam-1858	61	35	dqu(t	dqu(t	PROPN
ejpam-1858	61	36	)	)	PUNCT
ejpam-1858	61	37	=	=	SYM
ejpam-1858	61	38	1	1	NUM
ejpam-1858	61	39	γ(1−	γ(1−	NOUN
ejpam-1858	61	40	q	q	X
ejpam-1858	61	41	)	)	PUNCT
ejpam-1858	62	1	t	t	PROPN
ejpam-1858	62	2	∫	∫	PROPN
ejpam-1858	62	3	t0	t0	PROPN
ejpam-1858	62	4	(	(	PUNCT
ejpam-1858	62	5	t	t	PROPN
ejpam-1858	62	6	−	−	PROPN
ejpam-1858	62	7	s)−qu′(s)ds	s)−qu′(s)d	VERB
ejpam-1858	62	8	,	,	PUNCT
ejpam-1858	62	9	t0	t0	PROPN
ejpam-1858	62	10	≤	≤	PROPN
ejpam-1858	62	11	t	t	PROPN
ejpam-1858	62	12	≤	≤	PROPN
ejpam-1858	62	13	t.	t.	PROPN
ejpam-1858	62	14	j.	j.	PROPN
ejpam-1858	62	15	devi	devi	PROPN
ejpam-1858	62	16	,	,	PUNCT
ejpam-1858	62	17	n.	n.	PROPN
ejpam-1858	62	18	giribabu	giribabu	PROPN
ejpam-1858	62	19	/	/	SYM
ejpam-1858	62	20	eur	eur	PROPN
ejpam-1858	62	21	.	.	PUNCT
ejpam-1858	63	1	j.	j.	PROPN
ejpam-1858	63	2	pure	pure	PROPN
ejpam-1858	63	3	appl	appl	PROPN
ejpam-1858	63	4	.	.	PROPN
ejpam-1858	63	5	math	math	PROPN
ejpam-1858	63	6	,	,	PUNCT
ejpam-1858	63	7	7	7	NUM
ejpam-1858	63	8	(	(	PUNCT
ejpam-1858	63	9	2014	2014	NUM
ejpam-1858	63	10	)	)	PUNCT
ejpam-1858	63	11	,	,	PUNCT
ejpam-1858	63	12	115	115	NUM
ejpam-1858	63	13	-	-	SYM
ejpam-1858	63	14	128	128	NUM
ejpam-1858	63	15	118	118	NUM
ejpam-1858	63	16	we	we	PRON
ejpam-1858	63	17	observe	observe	VERB
ejpam-1858	63	18	that	that	SCONJ
ejpam-1858	63	19	u	u	PROPN
ejpam-1858	63	20	∈	∈	PROPN
ejpam-1858	63	21	cq	cq	PROPN
ejpam-1858	63	22	�	�	PROPN
ejpam-1858	63	23	[	[	X
ejpam-1858	63	24	t0	t0	PROPN
ejpam-1858	63	25	,	,	PUNCT
ejpam-1858	63	26	t0	t0	PROPN
ejpam-1858	63	27	+	+	CCONJ
ejpam-1858	63	28	a],r	a],r	PROPN
ejpam-1858	63	29	�	�	PROPN
ejpam-1858	63	30	,	,	PUNCT
ejpam-1858	63	31	implies	imply	VERB
ejpam-1858	63	32	that	that	SCONJ
ejpam-1858	63	33	u	u	PRON
ejpam-1858	63	34	is	be	AUX
ejpam-1858	63	35	continuous	continuous	ADJ
ejpam-1858	63	36	and	and	CCONJ
ejpam-1858	63	37	differentiable	differentiable	ADJ
ejpam-1858	63	38	.	.	PUNCT
ejpam-1858	64	1	next	next	ADV
ejpam-1858	64	2	we	we	PRON
ejpam-1858	64	3	state	state	VERB
ejpam-1858	64	4	the	the	DET
ejpam-1858	64	5	following	following	ADJ
ejpam-1858	64	6	result	result	NOUN
ejpam-1858	64	7	from	from	ADP
ejpam-1858	64	8	[	[	X
ejpam-1858	64	9	10	10	NUM
ejpam-1858	64	10	]	]	PUNCT
ejpam-1858	64	11	,	,	PUNCT
ejpam-1858	64	12	which	which	PRON
ejpam-1858	64	13	is	be	AUX
ejpam-1858	64	14	used	use	VERB
ejpam-1858	64	15	in	in	ADP
ejpam-1858	64	16	section	section	NOUN
ejpam-1858	64	17	5	5	NUM
ejpam-1858	64	18	.	.	PUNCT
ejpam-1858	65	1	lemma	lemma	PROPN
ejpam-1858	65	2	1	1	NUM
ejpam-1858	65	3	.	.	PUNCT
ejpam-1858	65	4	x(t	x(t	PROPN
ejpam-1858	65	5	)	)	PUNCT
ejpam-1858	65	6	∈	∈	PROPN
ejpam-1858	65	7	cq([t0	cq([t0	NOUN
ejpam-1858	65	8	,	,	PUNCT
ejpam-1858	65	9	t0	t0	PROPN
ejpam-1858	65	10	+	+	CCONJ
ejpam-1858	65	11	a],r	a],r	PROPN
ejpam-1858	65	12	)	)	PUNCT
ejpam-1858	65	13	is	be	AUX
ejpam-1858	65	14	solution	solution	NOUN
ejpam-1858	65	15	of	of	ADP
ejpam-1858	65	16	the	the	DET
ejpam-1858	65	17	initial	initial	ADJ
ejpam-1858	65	18	value	value	NOUN
ejpam-1858	65	19	problem	problem	NOUN
ejpam-1858	65	20	c	c	NOUN
ejpam-1858	65	21	dq	dq	NOUN
ejpam-1858	65	22	x	x	SYM
ejpam-1858	65	23	=	=	SYM
ejpam-1858	65	24	f	f	PROPN
ejpam-1858	65	25	(	(	PUNCT
ejpam-1858	65	26	t	t	PROPN
ejpam-1858	65	27	,	,	PUNCT
ejpam-1858	65	28	x	x	NOUN
ejpam-1858	65	29	)	)	PUNCT
ejpam-1858	65	30	,	,	PUNCT
ejpam-1858	65	31	x(t0	x(t0	PROPN
ejpam-1858	65	32	)	)	PUNCT
ejpam-1858	66	1	=	=	PUNCT
ejpam-1858	66	2	x0	x0	PROPN
ejpam-1858	66	3	,	,	PUNCT
ejpam-1858	66	4	0	0	PUNCT
ejpam-1858	66	5	<	<	X
ejpam-1858	66	6	q	q	X
ejpam-1858	66	7	<	<	X
ejpam-1858	66	8	1	1	NUM
ejpam-1858	66	9	if	if	SCONJ
ejpam-1858	66	10	and	and	CCONJ
ejpam-1858	66	11	only	only	ADV
ejpam-1858	66	12	if	if	SCONJ
ejpam-1858	66	13	it	it	PRON
ejpam-1858	66	14	satisfies	satisfy	VERB
ejpam-1858	66	15	corresponding	correspond	VERB
ejpam-1858	66	16	volterra	volterra	PROPN
ejpam-1858	66	17	fractional	fractional	ADJ
ejpam-1858	66	18	integral	integral	ADJ
ejpam-1858	66	19	equation	equation	NOUN
ejpam-1858	66	20	x(t	x(t	PROPN
ejpam-1858	66	21	)	)	PUNCT
ejpam-1858	66	22	=	=	PUNCT
ejpam-1858	67	1	x0	x0	PROPN
ejpam-1858	67	2	+	+	CCONJ
ejpam-1858	67	3	1	1	NUM
ejpam-1858	67	4	γ(q	γ(q	NOUN
ejpam-1858	67	5	)	)	PUNCT
ejpam-1858	67	6	t	t	NOUN
ejpam-1858	67	7	∫	∫	PROPN
ejpam-1858	67	8	t0	t0	PROPN
ejpam-1858	67	9	(	(	PUNCT
ejpam-1858	67	10	t	t	PROPN
ejpam-1858	67	11	−	−	PROPN
ejpam-1858	67	12	s)q−1	s)q−1	NOUN
ejpam-1858	67	13	f	f	PROPN
ejpam-1858	67	14	(	(	PUNCT
ejpam-1858	67	15	s	s	PROPN
ejpam-1858	67	16	,	,	PUNCT
ejpam-1858	67	17	x(s))ds	x(s))ds	PROPN
ejpam-1858	67	18	,	,	PUNCT
ejpam-1858	67	19	t0	t0	PROPN
ejpam-1858	67	20	≤	≤	PROPN
ejpam-1858	67	21	t	t	PROPN
ejpam-1858	67	22	≤	≤	NUM
ejpam-1858	67	23	t0	t0	PROPN
ejpam-1858	67	24	+	+	CCONJ
ejpam-1858	67	25	a.	a.	NOUN
ejpam-1858	67	26	finally	finally	ADV
ejpam-1858	67	27	,	,	PUNCT
ejpam-1858	67	28	we	we	PRON
ejpam-1858	67	29	state	state	VERB
ejpam-1858	67	30	the	the	DET
ejpam-1858	67	31	following	follow	VERB
ejpam-1858	67	32	lemma	lemma	PROPN
ejpam-1858	68	1	[	[	X
ejpam-1858	68	2	1	1	NUM
ejpam-1858	68	3	]	]	PUNCT
ejpam-1858	68	4	,	,	PUNCT
ejpam-1858	68	5	which	which	PRON
ejpam-1858	68	6	is	be	AUX
ejpam-1858	68	7	used	use	VERB
ejpam-1858	68	8	in	in	ADP
ejpam-1858	68	9	section	section	NOUN
ejpam-1858	68	10	5	5	NUM
ejpam-1858	68	11	and	and	CCONJ
ejpam-1858	68	12	section	section	NOUN
ejpam-1858	68	13	6	6	NUM
ejpam-1858	68	14	to	to	PART
ejpam-1858	68	15	prove	prove	VERB
ejpam-1858	68	16	our	our	PRON
ejpam-1858	68	17	main	main	ADJ
ejpam-1858	68	18	results	result	NOUN
ejpam-1858	68	19	.	.	PUNCT
ejpam-1858	69	1	lemma	lemma	PROPN
ejpam-1858	69	2	2	2	X
ejpam-1858	69	3	.	.	PUNCT
ejpam-1858	70	1	let	let	VERB
ejpam-1858	70	2	0	0	NUM
ejpam-1858	70	3	<	<	X
ejpam-1858	70	4	q	q	X
ejpam-1858	70	5	<	<	X
ejpam-1858	70	6	1	1	NUM
ejpam-1858	70	7	.	.	PUNCT
ejpam-1858	71	1	consider	consider	VERB
ejpam-1858	71	2	the	the	DET
ejpam-1858	71	3	caputo	caputo	PROPN
ejpam-1858	71	4	fractional	fractional	PROPN
ejpam-1858	71	5	differential	differential	NOUN
ejpam-1858	71	6	equation	equation	NOUN
ejpam-1858	71	7	c	c	NOUN
ejpam-1858	71	8	d	d	X
ejpam-1858	71	9	q	q	PROPN
ejpam-1858	71	10	t0	t0	PROPN
ejpam-1858	71	11	u(t	u(t	PROPN
ejpam-1858	71	12	)	)	PUNCT
ejpam-1858	71	13	=	=	SYM
ejpam-1858	71	14	g(t	g(t	PROPN
ejpam-1858	71	15	,	,	PUNCT
ejpam-1858	71	16	u(t	u(t	NOUN
ejpam-1858	71	17	)	)	PUNCT
ejpam-1858	71	18	)	)	PUNCT
ejpam-1858	71	19	,	,	PUNCT
ejpam-1858	71	20	t	t	PROPN
ejpam-1858	71	21	≥	≥	PROPN
ejpam-1858	71	22	t0	t0	PROPN
ejpam-1858	71	23	,	,	PUNCT
ejpam-1858	71	24	where	where	SCONJ
ejpam-1858	71	25	g(t	g(t	PROPN
ejpam-1858	71	26	,	,	PUNCT
ejpam-1858	71	27	u	u	NOUN
ejpam-1858	71	28	)	)	PUNCT
ejpam-1858	71	29	≥	≥	NOUN
ejpam-1858	71	30	0	0	NUM
ejpam-1858	71	31	and	and	CCONJ
ejpam-1858	71	32	t0	t0	PROPN
ejpam-1858	71	33	∈	∈	PROPN
ejpam-1858	71	34	r.	r.	PROPN
ejpam-1858	71	35	if	if	SCONJ
ejpam-1858	71	36	the	the	DET
ejpam-1858	71	37	solutions	solution	NOUN
ejpam-1858	71	38	exist	exist	VERB
ejpam-1858	71	39	and	and	CCONJ
ejpam-1858	71	40	u(t0	u(t0	ADJ
ejpam-1858	71	41	)	)	PUNCT
ejpam-1858	71	42	≥	≥	NOUN
ejpam-1858	71	43	0	0	NUM
ejpam-1858	71	44	,	,	PUNCT
ejpam-1858	71	45	then	then	ADV
ejpam-1858	71	46	they	they	PRON
ejpam-1858	71	47	are	be	AUX
ejpam-1858	71	48	nonnegative	nonnegative	ADJ
ejpam-1858	71	49	.	.	PUNCT
ejpam-1858	72	1	furthermore	furthermore	ADV
ejpam-1858	72	2	,	,	PUNCT
ejpam-1858	72	3	if	if	SCONJ
ejpam-1858	72	4	g(t	g(t	PROPN
ejpam-1858	72	5	,	,	PUNCT
ejpam-1858	72	6	u	u	NOUN
ejpam-1858	72	7	)	)	PUNCT
ejpam-1858	72	8	=	=	SYM
ejpam-1858	72	9	λu	λu	PROPN
ejpam-1858	72	10	for	for	ADP
ejpam-1858	72	11	λ	λ	PROPN
ejpam-1858	72	12	≥	≥	NOUN
ejpam-1858	72	13	0	0	NUM
ejpam-1858	72	14	,	,	PUNCT
ejpam-1858	72	15	then	then	ADV
ejpam-1858	72	16	the	the	DET
ejpam-1858	72	17	solutions	solution	NOUN
ejpam-1858	72	18	are	be	AUX
ejpam-1858	72	19	nondecreasing	nondecrease	VERB
ejpam-1858	72	20	in	in	ADP
ejpam-1858	72	21	t.	t.	PROPN
ejpam-1858	72	22	3	3	NUM
ejpam-1858	72	23	.	.	PUNCT
ejpam-1858	72	24	hybrid	hybrid	PROPN
ejpam-1858	72	25	caputo	caputo	PROPN
ejpam-1858	72	26	fractional	fractional	PROPN
ejpam-1858	72	27	differential	differential	NOUN
ejpam-1858	72	28	equations	equation	NOUN
ejpam-1858	72	29	as	as	SCONJ
ejpam-1858	72	30	observed	observe	VERB
ejpam-1858	72	31	in	in	ADP
ejpam-1858	72	32	the	the	DET
ejpam-1858	72	33	introduction	introduction	NOUN
ejpam-1858	72	34	it	it	PRON
ejpam-1858	72	35	is	be	AUX
ejpam-1858	72	36	natural	natural	ADJ
ejpam-1858	72	37	to	to	PART
ejpam-1858	72	38	expect	expect	VERB
ejpam-1858	72	39	viscoelastic	viscoelastic	ADJ
ejpam-1858	72	40	materials	material	NOUN
ejpam-1858	72	41	to	to	PART
ejpam-1858	72	42	be	be	AUX
ejpam-1858	72	43	modeled	model	VERB
ejpam-1858	72	44	after	after	ADP
ejpam-1858	72	45	fractional	fractional	ADJ
ejpam-1858	72	46	differential	differential	ADJ
ejpam-1858	72	47	equations	equation	NOUN
ejpam-1858	72	48	.	.	PUNCT
ejpam-1858	73	1	let	let	VERB
ejpam-1858	73	2	the	the	DET
ejpam-1858	73	3	natural	natural	ADJ
ejpam-1858	73	4	constraints	constraint	NOUN
ejpam-1858	73	5	that	that	PRON
ejpam-1858	73	6	arise	arise	VERB
ejpam-1858	73	7	in	in	ADP
ejpam-1858	73	8	the	the	DET
ejpam-1858	73	9	model	model	NOUN
ejpam-1858	73	10	be	be	AUX
ejpam-1858	73	11	construed	construe	VERB
ejpam-1858	73	12	as	as	ADP
ejpam-1858	73	13	a	a	DET
ejpam-1858	73	14	barrier	barrier	NOUN
ejpam-1858	73	15	or	or	CCONJ
ejpam-1858	73	16	a	a	DET
ejpam-1858	73	17	threshold	threshold	NOUN
ejpam-1858	73	18	.	.	PUNCT
ejpam-1858	74	1	when	when	SCONJ
ejpam-1858	74	2	the	the	DET
ejpam-1858	74	3	solution	solution	NOUN
ejpam-1858	74	4	of	of	ADP
ejpam-1858	74	5	the	the	DET
ejpam-1858	74	6	model	model	NOUN
ejpam-1858	74	7	,	,	PUNCT
ejpam-1858	74	8	come	come	VERB
ejpam-1858	74	9	into	into	ADP
ejpam-1858	74	10	contact	contact	NOUN
ejpam-1858	74	11	with	with	ADP
ejpam-1858	74	12	the	the	DET
ejpam-1858	74	13	barrier	barrier	NOUN
ejpam-1858	74	14	,	,	PUNCT
ejpam-1858	74	15	some	some	DET
ejpam-1858	74	16	additional	additional	ADJ
ejpam-1858	74	17	input	input	NOUN
ejpam-1858	74	18	or	or	CCONJ
ejpam-1858	74	19	impulse	impulse	ADJ
ejpam-1858	74	20	must	must	AUX
ejpam-1858	74	21	be	be	AUX
ejpam-1858	74	22	given	give	VERB
ejpam-1858	74	23	for	for	ADP
ejpam-1858	74	24	the	the	DET
ejpam-1858	74	25	solution	solution	NOUN
ejpam-1858	74	26	to	to	PART
ejpam-1858	74	27	get	get	VERB
ejpam-1858	74	28	out	out	ADP
ejpam-1858	74	29	of	of	ADP
ejpam-1858	74	30	the	the	DET
ejpam-1858	74	31	barrier	barrier	NOUN
ejpam-1858	74	32	.	.	PUNCT
ejpam-1858	75	1	this	this	DET
ejpam-1858	75	2	general	general	ADJ
ejpam-1858	75	3	behaviour	behaviour	NOUN
ejpam-1858	75	4	can	can	AUX
ejpam-1858	75	5	be	be	AUX
ejpam-1858	75	6	understood	understand	VERB
ejpam-1858	75	7	through	through	ADP
ejpam-1858	75	8	an	an	DET
ejpam-1858	75	9	evolutionary	evolutionary	ADJ
ejpam-1858	75	10	process	process	NOUN
ejpam-1858	75	11	of	of	ADP
ejpam-1858	75	12	a	a	DET
ejpam-1858	75	13	physical	physical	ADJ
ejpam-1858	75	14	phenomenon	phenomenon	NOUN
ejpam-1858	75	15	given	give	VERB
ejpam-1858	75	16	below	below	ADV
ejpam-1858	75	17	.	.	PUNCT
ejpam-1858	76	1	we	we	PRON
ejpam-1858	76	2	adapt	adapt	VERB
ejpam-1858	76	3	the	the	DET
ejpam-1858	76	4	process	process	NOUN
ejpam-1858	76	5	given	give	VERB
ejpam-1858	76	6	in	in	ADP
ejpam-1858	76	7	[	[	NOUN
ejpam-1858	76	8	9	9	NUM
ejpam-1858	76	9	]	]	PUNCT
ejpam-1858	76	10	to	to	ADP
ejpam-1858	76	11	the	the	DET
ejpam-1858	76	12	set	set	NOUN
ejpam-1858	76	13	up	up	ADP
ejpam-1858	76	14	of	of	ADP
ejpam-1858	76	15	fractional	fractional	ADJ
ejpam-1858	76	16	differential	differential	ADJ
ejpam-1858	76	17	equations	equation	NOUN
ejpam-1858	76	18	.	.	PUNCT
ejpam-1858	77	1	consider	consider	VERB
ejpam-1858	77	2	an	an	DET
ejpam-1858	77	3	evolutionary	evolutionary	ADJ
ejpam-1858	77	4	process	process	NOUN
ejpam-1858	77	5	or	or	CCONJ
ejpam-1858	77	6	a	a	DET
ejpam-1858	77	7	physical	physical	ADJ
ejpam-1858	77	8	phenomenon	phenomenon	NOUN
ejpam-1858	77	9	that	that	PRON
ejpam-1858	77	10	exhibits	exhibit	VERB
ejpam-1858	77	11	behaviour	behaviour	NOUN
ejpam-1858	77	12	which	which	PRON
ejpam-1858	77	13	can	can	AUX
ejpam-1858	77	14	be	be	AUX
ejpam-1858	77	15	described	describe	VERB
ejpam-1858	77	16	by	by	ADP
ejpam-1858	77	17	(	(	PUNCT
ejpam-1858	77	18	i	i	NOUN
ejpam-1858	77	19	)	)	PUNCT
ejpam-1858	77	20	a	a	DET
ejpam-1858	77	21	caputo	caputo	PROPN
ejpam-1858	77	22	fractional	fractional	PROPN
ejpam-1858	77	23	differential	differential	ADJ
ejpam-1858	77	24	equation	equation	NOUN
ejpam-1858	77	25	of	of	ADP
ejpam-1858	77	26	order	order	NOUN
ejpam-1858	77	27	q	q	X
ejpam-1858	77	28	∈	∈	PROPN
ejpam-1858	77	29	(	(	PUNCT
ejpam-1858	77	30	0,1	0,1	NUM
ejpam-1858	77	31	)	)	PUNCT
ejpam-1858	77	32	c	c	NOUN
ejpam-1858	77	33	dq	dq	NOUN
ejpam-1858	77	34	x	x	SYM
ejpam-1858	77	35	=	=	SYM
ejpam-1858	77	36	f	f	PROPN
ejpam-1858	77	37	(	(	PUNCT
ejpam-1858	77	38	t	t	PROPN
ejpam-1858	77	39	,	,	PUNCT
ejpam-1858	77	40	x	x	NOUN
ejpam-1858	77	41	)	)	PUNCT
ejpam-1858	77	42	,	,	PUNCT
ejpam-1858	77	43	(	(	PUNCT
ejpam-1858	77	44	4	4	X
ejpam-1858	77	45	)	)	PUNCT
ejpam-1858	77	46	where	where	SCONJ
ejpam-1858	77	47	f	f	NOUN
ejpam-1858	77	48	:	:	PUNCT
ejpam-1858	77	49	r+×ω→	r+×ω→	PROPN
ejpam-1858	77	50	r	r	PROPN
ejpam-1858	77	51	,	,	PUNCT
ejpam-1858	77	52	ω	ω	NOUN
ejpam-1858	77	53	⊂	⊂	PROPN
ejpam-1858	77	54	r	r	NOUN
ejpam-1858	77	55	is	be	AUX
ejpam-1858	77	56	an	an	DET
ejpam-1858	77	57	open	open	ADJ
ejpam-1858	77	58	set	set	NOUN
ejpam-1858	77	59	,	,	PUNCT
ejpam-1858	77	60	and	and	CCONJ
ejpam-1858	77	61	r	r	NOUN
ejpam-1858	77	62	is	be	AUX
ejpam-1858	77	63	the	the	DET
ejpam-1858	77	64	space	space	NOUN
ejpam-1858	77	65	of	of	ADP
ejpam-1858	77	66	real	real	ADJ
ejpam-1858	77	67	numbers	number	NOUN
ejpam-1858	77	68	and	and	CCONJ
ejpam-1858	77	69	r+	r+	NOUN
ejpam-1858	77	70	is	be	AUX
ejpam-1858	77	71	the	the	DET
ejpam-1858	77	72	nonnegative	nonnegative	ADJ
ejpam-1858	77	73	real	real	ADJ
ejpam-1858	77	74	line	line	NOUN
ejpam-1858	77	75	;	;	PUNCT
ejpam-1858	77	76	(	(	PUNCT
ejpam-1858	77	77	ii	ii	X
ejpam-1858	77	78	)	)	PUNCT
ejpam-1858	77	79	the	the	DET
ejpam-1858	77	80	sets	set	NOUN
ejpam-1858	77	81	m(t	m(t	NOUN
ejpam-1858	77	82	)	)	PUNCT
ejpam-1858	77	83	,	,	PUNCT
ejpam-1858	77	84	n(t	n(t	PROPN
ejpam-1858	77	85	)	)	PUNCT
ejpam-1858	77	86	⊂	⊂	PROPN
ejpam-1858	77	87	ω	ω	PROPN
ejpam-1858	77	88	for	for	ADP
ejpam-1858	77	89	each	each	DET
ejpam-1858	77	90	t	t	PROPN
ejpam-1858	77	91	∈	∈	PROPN
ejpam-1858	77	92	r+	r+	NOUN
ejpam-1858	77	93	;	;	PUNCT
ejpam-1858	77	94	and	and	CCONJ
ejpam-1858	77	95	(	(	PUNCT
ejpam-1858	77	96	iii	iii	X
ejpam-1858	77	97	)	)	PUNCT
ejpam-1858	77	98	the	the	DET
ejpam-1858	77	99	operator	operator	NOUN
ejpam-1858	77	100	a(t	a(t	NOUN
ejpam-1858	77	101	)	)	PUNCT
ejpam-1858	77	102	:	:	PUNCT
ejpam-1858	77	103	m(t)→	m(t)→	PROPN
ejpam-1858	77	104	n(t	n(t	PROPN
ejpam-1858	77	105	)	)	PUNCT
ejpam-1858	77	106	for	for	ADP
ejpam-1858	77	107	each	each	DET
ejpam-1858	77	108	t	t	PROPN
ejpam-1858	77	109	∈	∈	PROPN
ejpam-1858	77	110	r+	r+	NOUN
ejpam-1858	77	111	.	.	PUNCT
ejpam-1858	78	1	j.	j.	PROPN
ejpam-1858	78	2	devi	devi	PROPN
ejpam-1858	78	3	,	,	PUNCT
ejpam-1858	78	4	n.	n.	PROPN
ejpam-1858	78	5	giribabu	giribabu	PROPN
ejpam-1858	78	6	/	/	SYM
ejpam-1858	78	7	eur	eur	PROPN
ejpam-1858	78	8	.	.	PUNCT
ejpam-1858	79	1	j.	j.	PROPN
ejpam-1858	79	2	pure	pure	PROPN
ejpam-1858	79	3	appl	appl	PROPN
ejpam-1858	79	4	.	.	PROPN
ejpam-1858	79	5	math	math	PROPN
ejpam-1858	79	6	,	,	PUNCT
ejpam-1858	79	7	7	7	NUM
ejpam-1858	79	8	(	(	PUNCT
ejpam-1858	79	9	2014	2014	NUM
ejpam-1858	79	10	)	)	PUNCT
ejpam-1858	79	11	,	,	PUNCT
ejpam-1858	79	12	115	115	NUM
ejpam-1858	79	13	-	-	SYM
ejpam-1858	79	14	128	128	NUM
ejpam-1858	79	15	119	119	NUM
ejpam-1858	79	16	let	let	VERB
ejpam-1858	79	17	x(t	x(t	PROPN
ejpam-1858	79	18	)	)	PUNCT
ejpam-1858	79	19	=	=	SYM
ejpam-1858	79	20	x(t	x(t	PROPN
ejpam-1858	79	21	,	,	PUNCT
ejpam-1858	79	22	t0	t0	PROPN
ejpam-1858	79	23	,	,	PUNCT
ejpam-1858	79	24	x0	x0	PROPN
ejpam-1858	79	25	)	)	PUNCT
ejpam-1858	79	26	be	be	VERB
ejpam-1858	79	27	any	any	DET
ejpam-1858	79	28	solution	solution	NOUN
ejpam-1858	79	29	of	of	ADP
ejpam-1858	79	30	(	(	PUNCT
ejpam-1858	79	31	4	4	NUM
ejpam-1858	79	32	)	)	PUNCT
ejpam-1858	79	33	starting	start	VERB
ejpam-1858	79	34	at	at	ADP
ejpam-1858	79	35	(	(	PUNCT
ejpam-1858	79	36	t0	t0	PROPN
ejpam-1858	79	37	,	,	PUNCT
ejpam-1858	79	38	x0	x0	PROPN
ejpam-1858	79	39	)	)	PUNCT
ejpam-1858	79	40	.	.	PUNCT
ejpam-1858	80	1	the	the	DET
ejpam-1858	80	2	behaviour	behaviour	NOUN
ejpam-1858	80	3	of	of	ADP
ejpam-1858	80	4	the	the	DET
ejpam-1858	80	5	evolutionary	evolutionary	ADJ
ejpam-1858	80	6	process	process	NOUN
ejpam-1858	80	7	or	or	CCONJ
ejpam-1858	80	8	the	the	DET
ejpam-1858	80	9	physical	physical	ADJ
ejpam-1858	80	10	phenomenon	phenomenon	NOUN
ejpam-1858	80	11	can	can	AUX
ejpam-1858	80	12	be	be	AUX
ejpam-1858	80	13	described	describe	VERB
ejpam-1858	80	14	by	by	ADP
ejpam-1858	80	15	the	the	DET
ejpam-1858	80	16	point	point	NOUN
ejpam-1858	80	17	pt	pt	X
ejpam-1858	80	18	=	=	SYM
ejpam-1858	80	19	(	(	PUNCT
ejpam-1858	80	20	t	t	PROPN
ejpam-1858	80	21	,	,	PUNCT
ejpam-1858	80	22	x(t	x(t	PROPN
ejpam-1858	80	23	)	)	PUNCT
ejpam-1858	80	24	)	)	PUNCT
ejpam-1858	80	25	starting	start	VERB
ejpam-1858	80	26	at	at	ADP
ejpam-1858	80	27	pt0	pt0	NOUN
ejpam-1858	80	28	=	=	SYM
ejpam-1858	80	29	(	(	PUNCT
ejpam-1858	80	30	t0	t0	PROPN
ejpam-1858	80	31	,	,	PUNCT
ejpam-1858	80	32	x0	x0	PROPN
ejpam-1858	80	33	)	)	PUNCT
ejpam-1858	80	34	,	,	PUNCT
ejpam-1858	80	35	it	it	PRON
ejpam-1858	80	36	moves	move	VERB
ejpam-1858	80	37	along	along	ADP
ejpam-1858	80	38	the	the	DET
ejpam-1858	80	39	curve	curve	NOUN
ejpam-1858	80	40	{	{	PUNCT
ejpam-1858	80	41	(	(	PUNCT
ejpam-1858	80	42	t	t	PROPN
ejpam-1858	80	43	,	,	PUNCT
ejpam-1858	80	44	x	x	NOUN
ejpam-1858	80	45	)	)	PUNCT
ejpam-1858	80	46	:	:	PUNCT
ejpam-1858	81	1	t	t	PROPN
ejpam-1858	81	2	≥	≥	PROPN
ejpam-1858	81	3	t0	t0	PROPN
ejpam-1858	81	4	,	,	PUNCT
ejpam-1858	81	5	x	x	X
ejpam-1858	81	6	=	=	SYM
ejpam-1858	81	7	x(t	x(t	PROPN
ejpam-1858	81	8	)	)	PUNCT
ejpam-1858	81	9	}	}	PUNCT
ejpam-1858	81	10	until	until	SCONJ
ejpam-1858	81	11	the	the	DET
ejpam-1858	81	12	point	point	NOUN
ejpam-1858	81	13	pt	pt	NOUN
ejpam-1858	81	14	meets	meet	VERB
ejpam-1858	81	15	the	the	DET
ejpam-1858	81	16	set	set	NOUN
ejpam-1858	81	17	m(t	m(t	NOUN
ejpam-1858	81	18	)	)	PUNCT
ejpam-1858	81	19	at	at	ADP
ejpam-1858	81	20	t	t	PROPN
ejpam-1858	81	21	=	=	SYM
ejpam-1858	81	22	t1	t1	PROPN
ejpam-1858	81	23	.	.	PUNCT
ejpam-1858	82	1	then	then	ADV
ejpam-1858	82	2	at	at	ADP
ejpam-1858	82	3	the	the	DET
ejpam-1858	82	4	point	point	NOUN
ejpam-1858	82	5	t	t	NOUN
ejpam-1858	82	6	=	=	SYM
ejpam-1858	82	7	t1	t1	PROPN
ejpam-1858	82	8	,	,	PUNCT
ejpam-1858	82	9	the	the	DET
ejpam-1858	82	10	operator	operator	NOUN
ejpam-1858	82	11	a(t	a(t	NOUN
ejpam-1858	82	12	)	)	PUNCT
ejpam-1858	82	13	transfers	transfer	NOUN
ejpam-1858	82	14	the	the	DET
ejpam-1858	82	15	point	point	NOUN
ejpam-1858	82	16	pt1	pt1	PROPN
ejpam-1858	82	17	=	=	SYM
ejpam-1858	82	18	(	(	PUNCT
ejpam-1858	82	19	t1	t1	PROPN
ejpam-1858	82	20	,	,	PUNCT
ejpam-1858	82	21	x(t1	x(t1	PROPN
ejpam-1858	82	22	)	)	PUNCT
ejpam-1858	82	23	)	)	PUNCT
ejpam-1858	83	1	∈	∈	PROPN
ejpam-1858	83	2	m(t1	m(t1	NOUN
ejpam-1858	83	3	)	)	PUNCT
ejpam-1858	83	4	to	to	ADP
ejpam-1858	83	5	the	the	DET
ejpam-1858	83	6	position	position	NOUN
ejpam-1858	83	7	pt1	pt1	PROPN
ejpam-1858	83	8	+	+	PROPN
ejpam-1858	83	9	=	=	SYM
ejpam-1858	83	10	(	(	PUNCT
ejpam-1858	83	11	t1	t1	PROPN
ejpam-1858	83	12	,	,	PUNCT
ejpam-1858	83	13	x+	x+	X
ejpam-1858	83	14	1	1	X
ejpam-1858	83	15	)	)	PUNCT
ejpam-1858	83	16	∈	∈	PROPN
ejpam-1858	83	17	n(t1	n(t1	NOUN
ejpam-1858	83	18	)	)	PUNCT
ejpam-1858	83	19	where	where	SCONJ
ejpam-1858	83	20	x+	x+	SYM
ejpam-1858	83	21	1	1	NUM
ejpam-1858	83	22	=	=	SYM
ejpam-1858	83	23	a(t1)x(t1	a(t1)x(t1	PROPN
ejpam-1858	83	24	)	)	PUNCT
ejpam-1858	83	25	.	.	PUNCT
ejpam-1858	84	1	now	now	ADV
ejpam-1858	84	2	the	the	DET
ejpam-1858	84	3	motion	motion	NOUN
ejpam-1858	84	4	of	of	ADP
ejpam-1858	84	5	the	the	DET
ejpam-1858	84	6	point	point	NOUN
ejpam-1858	84	7	pt	pt	NOUN
ejpam-1858	84	8	continues	continue	VERB
ejpam-1858	84	9	forward	forward	ADV
ejpam-1858	84	10	from	from	ADP
ejpam-1858	84	11	pt+	pt+	NOUN
ejpam-1858	84	12	1	1	NUM
ejpam-1858	84	13	along	along	ADP
ejpam-1858	84	14	the	the	DET
ejpam-1858	84	15	the	the	DET
ejpam-1858	84	16	curve	curve	NOUN
ejpam-1858	84	17	{	{	PUNCT
ejpam-1858	84	18	(	(	PUNCT
ejpam-1858	84	19	t	t	PROPN
ejpam-1858	84	20	,	,	PUNCT
ejpam-1858	84	21	x	x	NOUN
ejpam-1858	84	22	)	)	PUNCT
ejpam-1858	84	23	:	:	PUNCT
ejpam-1858	85	1	t	t	PROPN
ejpam-1858	85	2	≥	≥	NOUN
ejpam-1858	85	3	t1	t1	NOUN
ejpam-1858	85	4	,	,	PUNCT
ejpam-1858	85	5	x	x	PUNCT
ejpam-1858	85	6	=	=	SYM
ejpam-1858	85	7	x(t	x(t	PROPN
ejpam-1858	85	8	,	,	PUNCT
ejpam-1858	85	9	t1	t1	NOUN
ejpam-1858	85	10	,	,	PUNCT
ejpam-1858	85	11	x+	x+	X
ejpam-1858	85	12	1	1	NUM
ejpam-1858	85	13	)	)	PUNCT
ejpam-1858	85	14	}	}	PUNCT
ejpam-1858	85	15	as	as	ADP
ejpam-1858	85	16	the	the	DET
ejpam-1858	85	17	solution	solution	NOUN
ejpam-1858	85	18	of	of	ADP
ejpam-1858	85	19	(	(	PUNCT
ejpam-1858	85	20	4	4	NUM
ejpam-1858	85	21	)	)	PUNCT
ejpam-1858	85	22	with	with	ADP
ejpam-1858	85	23	starting	start	VERB
ejpam-1858	85	24	point	point	NOUN
ejpam-1858	85	25	(	(	PUNCT
ejpam-1858	85	26	t1	t1	NOUN
ejpam-1858	85	27	,	,	PUNCT
ejpam-1858	85	28	x+	x+	X
ejpam-1858	85	29	1	1	NUM
ejpam-1858	85	30	)	)	PUNCT
ejpam-1858	85	31	until	until	SCONJ
ejpam-1858	85	32	it	it	PRON
ejpam-1858	85	33	again	again	ADV
ejpam-1858	85	34	meets	meet	VERB
ejpam-1858	85	35	the	the	DET
ejpam-1858	85	36	set	set	NOUN
ejpam-1858	85	37	m(t	m(t	NOUN
ejpam-1858	85	38	)	)	PUNCT
ejpam-1858	85	39	at	at	ADP
ejpam-1858	85	40	t	t	NOUN
ejpam-1858	85	41	=	=	SYM
ejpam-1858	85	42	t2	t2	PROPN
ejpam-1858	85	43	.	.	PUNCT
ejpam-1858	86	1	this	this	DET
ejpam-1858	86	2	again	again	ADV
ejpam-1858	86	3	yields	yield	VERB
ejpam-1858	86	4	,	,	PUNCT
ejpam-1858	86	5	by	by	ADP
ejpam-1858	86	6	the	the	DET
ejpam-1858	86	7	effect	effect	NOUN
ejpam-1858	86	8	of	of	ADP
ejpam-1858	86	9	operator	operator	NOUN
ejpam-1858	86	10	a(t	a(t	NOUN
ejpam-1858	86	11	)	)	PUNCT
ejpam-1858	86	12	,	,	PUNCT
ejpam-1858	86	13	that	that	SCONJ
ejpam-1858	86	14	the	the	DET
ejpam-1858	86	15	point	point	NOUN
ejpam-1858	86	16	pt2	pt2	NOUN
ejpam-1858	86	17	=	=	SYM
ejpam-1858	86	18	(	(	PUNCT
ejpam-1858	86	19	t2	t2	NOUN
ejpam-1858	86	20	,	,	PUNCT
ejpam-1858	86	21	x(t2	x(t2	ADJ
ejpam-1858	86	22	)	)	PUNCT
ejpam-1858	86	23	)	)	PUNCT
ejpam-1858	86	24	is	be	AUX
ejpam-1858	86	25	transferred	transfer	VERB
ejpam-1858	86	26	to	to	ADP
ejpam-1858	86	27	the	the	DET
ejpam-1858	86	28	position	position	NOUN
ejpam-1858	86	29	pt2	pt2	NOUN
ejpam-1858	87	1	+	+	X
ejpam-1858	87	2	=	=	SYM
ejpam-1858	87	3	(	(	PUNCT
ejpam-1858	87	4	t2	t2	NOUN
ejpam-1858	87	5	,	,	PUNCT
ejpam-1858	87	6	x+	x+	X
ejpam-1858	87	7	2	2	X
ejpam-1858	87	8	)	)	PUNCT
ejpam-1858	87	9	where	where	SCONJ
ejpam-1858	87	10	x+	x+	ADJ
ejpam-1858	87	11	2	2	NUM
ejpam-1858	87	12	=	=	SYM
ejpam-1858	87	13	a(t2)x(t2	a(t2)x(t2	NOUN
ejpam-1858	87	14	)	)	PUNCT
ejpam-1858	87	15	∈	∈	PROPN
ejpam-1858	87	16	n(t2	n(t2	NOUN
ejpam-1858	87	17	)	)	PUNCT
ejpam-1858	87	18	.	.	PUNCT
ejpam-1858	88	1	from	from	ADP
ejpam-1858	88	2	then	then	ADV
ejpam-1858	88	3	on	on	ADV
ejpam-1858	88	4	,	,	PUNCT
ejpam-1858	88	5	the	the	DET
ejpam-1858	88	6	motion	motion	NOUN
ejpam-1858	88	7	of	of	ADP
ejpam-1858	88	8	the	the	DET
ejpam-1858	88	9	evolutionary	evolutionary	ADJ
ejpam-1858	88	10	process	process	NOUN
ejpam-1858	88	11	moves	move	VERB
ejpam-1858	88	12	the	the	DET
ejpam-1858	88	13	point	point	NOUN
ejpam-1858	88	14	pt	pt	INTJ
ejpam-1858	88	15	forward	forward	ADV
ejpam-1858	88	16	following	follow	VERB
ejpam-1858	88	17	the	the	DET
ejpam-1858	88	18	equation	equation	NOUN
ejpam-1858	88	19	c	c	NOUN
ejpam-1858	88	20	dq	dq	NOUN
ejpam-1858	88	21	x	x	SYM
ejpam-1858	88	22	=	=	SYM
ejpam-1858	88	23	f	f	PROPN
ejpam-1858	88	24	(	(	PUNCT
ejpam-1858	88	25	t	t	PROPN
ejpam-1858	88	26	,	,	PUNCT
ejpam-1858	88	27	x	x	NOUN
ejpam-1858	88	28	)	)	PUNCT
ejpam-1858	88	29	till	till	SCONJ
ejpam-1858	88	30	it	it	PRON
ejpam-1858	88	31	touches	touch	VERB
ejpam-1858	88	32	m(t	m(t	NOUN
ejpam-1858	88	33	)	)	PUNCT
ejpam-1858	88	34	at	at	ADP
ejpam-1858	88	35	t	t	PROPN
ejpam-1858	88	36	=	=	SYM
ejpam-1858	88	37	t3	t3	PROPN
ejpam-1858	88	38	.	.	PUNCT
ejpam-1858	89	1	this	this	DET
ejpam-1858	89	2	process	process	NOUN
ejpam-1858	89	3	can	can	AUX
ejpam-1858	89	4	be	be	AUX
ejpam-1858	89	5	continued	continue	VERB
ejpam-1858	89	6	forward	forward	ADV
ejpam-1858	89	7	as	as	ADV
ejpam-1858	89	8	long	long	ADV
ejpam-1858	89	9	as	as	SCONJ
ejpam-1858	89	10	the	the	DET
ejpam-1858	89	11	solution	solution	NOUN
ejpam-1858	89	12	of	of	ADP
ejpam-1858	89	13	(	(	PUNCT
ejpam-1858	89	14	4	4	NUM
ejpam-1858	89	15	)	)	PUNCT
ejpam-1858	89	16	exists	exist	VERB
ejpam-1858	89	17	.	.	PUNCT
ejpam-1858	90	1	the	the	DET
ejpam-1858	90	2	set	set	NOUN
ejpam-1858	90	3	up	up	ADP
ejpam-1858	90	4	given	give	VERB
ejpam-1858	90	5	by	by	ADP
ejpam-1858	90	6	(	(	PUNCT
ejpam-1858	90	7	i	i	NOUN
ejpam-1858	90	8	)	)	PUNCT
ejpam-1858	90	9	,	,	PUNCT
ejpam-1858	90	10	(	(	PUNCT
ejpam-1858	90	11	ii	ii	NOUN
ejpam-1858	90	12	)	)	PUNCT
ejpam-1858	90	13	,	,	PUNCT
ejpam-1858	90	14	(	(	PUNCT
ejpam-1858	90	15	iii	iii	NOUN
ejpam-1858	90	16	)	)	PUNCT
ejpam-1858	90	17	characterizes	characterize	VERB
ejpam-1858	90	18	the	the	DET
ejpam-1858	90	19	considered	consider	VERB
ejpam-1858	90	20	evolutionary	evolutionary	ADJ
ejpam-1858	90	21	process	process	NOUN
ejpam-1858	90	22	as	as	ADP
ejpam-1858	90	23	a	a	DET
ejpam-1858	90	24	hybrid	hybrid	ADJ
ejpam-1858	90	25	caputo	caputo	PROPN
ejpam-1858	90	26	fractional	fractional	PROPN
ejpam-1858	90	27	differential	differential	NOUN
ejpam-1858	90	28	system	system	NOUN
ejpam-1858	90	29	.	.	PUNCT
ejpam-1858	91	1	the	the	DET
ejpam-1858	91	2	motion	motion	NOUN
ejpam-1858	91	3	of	of	ADP
ejpam-1858	91	4	the	the	DET
ejpam-1858	91	5	point	point	NOUN
ejpam-1858	91	6	pt	pt	NOUN
ejpam-1858	91	7	is	be	AUX
ejpam-1858	91	8	a	a	DET
ejpam-1858	91	9	curve	curve	NOUN
ejpam-1858	91	10	represents	represent	VERB
ejpam-1858	91	11	the	the	DET
ejpam-1858	91	12	solution	solution	NOUN
ejpam-1858	91	13	curve	curve	NOUN
ejpam-1858	91	14	of	of	ADP
ejpam-1858	91	15	the	the	DET
ejpam-1858	91	16	hybrid	hybrid	ADJ
ejpam-1858	91	17	caputo	caputo	PROPN
ejpam-1858	91	18	fractional	fractional	PROPN
ejpam-1858	91	19	differential	differential	NOUN
ejpam-1858	91	20	equation	equation	NOUN
ejpam-1858	91	21	(	(	PUNCT
ejpam-1858	91	22	hcfde	hcfde	NOUN
ejpam-1858	91	23	for	for	ADP
ejpam-1858	91	24	short	short	ADJ
ejpam-1858	91	25	)	)	PUNCT
ejpam-1858	91	26	.	.	PUNCT
ejpam-1858	92	1	thus	thus	ADV
ejpam-1858	92	2	a	a	DET
ejpam-1858	92	3	solution	solution	NOUN
ejpam-1858	92	4	of	of	ADP
ejpam-1858	92	5	a	a	DET
ejpam-1858	92	6	hybrid	hybrid	ADJ
ejpam-1858	92	7	caputo	caputo	PROPN
ejpam-1858	92	8	fractional	fractional	PROPN
ejpam-1858	92	9	differential	differential	NOUN
ejpam-1858	92	10	equation	equation	NOUN
ejpam-1858	92	11	may	may	AUX
ejpam-1858	92	12	exhibit	exhibit	VERB
ejpam-1858	92	13	a	a	DET
ejpam-1858	92	14	variety	variety	NOUN
ejpam-1858	92	15	of	of	ADP
ejpam-1858	92	16	behaviour	behaviour	NOUN
ejpam-1858	92	17	as	as	SCONJ
ejpam-1858	92	18	given	give	VERB
ejpam-1858	92	19	below	below	ADV
ejpam-1858	92	20	.	.	PUNCT
ejpam-1858	93	1	(	(	PUNCT
ejpam-1858	93	2	i	i	NOUN
ejpam-1858	93	3	)	)	PUNCT
ejpam-1858	93	4	the	the	DET
ejpam-1858	93	5	solution	solution	NOUN
ejpam-1858	93	6	may	may	AUX
ejpam-1858	93	7	be	be	AUX
ejpam-1858	93	8	a	a	DET
ejpam-1858	93	9	continuous	continuous	ADJ
ejpam-1858	93	10	function	function	NOUN
ejpam-1858	93	11	,	,	PUNCT
ejpam-1858	93	12	if	if	SCONJ
ejpam-1858	93	13	the	the	DET
ejpam-1858	93	14	integral	integral	ADJ
ejpam-1858	93	15	curve	curve	NOUN
ejpam-1858	93	16	does	do	AUX
ejpam-1858	93	17	not	not	PART
ejpam-1858	93	18	intersect	intersect	VERB
ejpam-1858	93	19	m(t	m(t	NOUN
ejpam-1858	93	20	)	)	PUNCT
ejpam-1858	93	21	or	or	CCONJ
ejpam-1858	93	22	hits	hit	VERB
ejpam-1858	93	23	it	it	PRON
ejpam-1858	93	24	at	at	ADP
ejpam-1858	93	25	the	the	DET
ejpam-1858	93	26	fixed	fix	VERB
ejpam-1858	93	27	points	point	NOUN
ejpam-1858	93	28	of	of	ADP
ejpam-1858	93	29	the	the	DET
ejpam-1858	93	30	operator	operator	NOUN
ejpam-1858	93	31	a(t	a(t	NOUN
ejpam-1858	93	32	)	)	PUNCT
ejpam-1858	93	33	.	.	PUNCT
ejpam-1858	94	1	(	(	PUNCT
ejpam-1858	94	2	ii	ii	X
ejpam-1858	94	3	)	)	PUNCT
ejpam-1858	94	4	the	the	DET
ejpam-1858	94	5	solution	solution	NOUN
ejpam-1858	94	6	can	can	AUX
ejpam-1858	94	7	be	be	AUX
ejpam-1858	94	8	a	a	DET
ejpam-1858	94	9	piecewise	piecewise	NOUN
ejpam-1858	94	10	continuous	continuous	ADJ
ejpam-1858	94	11	function	function	NOUN
ejpam-1858	94	12	having	have	VERB
ejpam-1858	94	13	a	a	DET
ejpam-1858	94	14	finite	finite	ADJ
ejpam-1858	94	15	number	number	NOUN
ejpam-1858	94	16	of	of	ADP
ejpam-1858	94	17	discontinuities	discontinuity	NOUN
ejpam-1858	94	18	of	of	ADP
ejpam-1858	94	19	first	first	ADJ
ejpam-1858	94	20	kind	kind	NOUN
ejpam-1858	94	21	which	which	PRON
ejpam-1858	94	22	are	be	AUX
ejpam-1858	94	23	are	be	AUX
ejpam-1858	94	24	not	not	PART
ejpam-1858	94	25	fixed	fix	VERB
ejpam-1858	94	26	points	point	NOUN
ejpam-1858	94	27	of	of	ADP
ejpam-1858	94	28	the	the	DET
ejpam-1858	94	29	operator	operator	NOUN
ejpam-1858	94	30	a(t	a(t	NOUN
ejpam-1858	94	31	)	)	PUNCT
ejpam-1858	94	32	.	.	PUNCT
ejpam-1858	95	1	(	(	PUNCT
ejpam-1858	95	2	iii	iii	X
ejpam-1858	95	3	)	)	PUNCT
ejpam-1858	95	4	the	the	DET
ejpam-1858	95	5	solution	solution	NOUN
ejpam-1858	95	6	may	may	AUX
ejpam-1858	95	7	also	also	ADV
ejpam-1858	95	8	have	have	VERB
ejpam-1858	95	9	a	a	DET
ejpam-1858	95	10	countable	countable	ADJ
ejpam-1858	95	11	number	number	NOUN
ejpam-1858	95	12	of	of	ADP
ejpam-1858	95	13	discontinuities	discontinuity	NOUN
ejpam-1858	95	14	of	of	ADP
ejpam-1858	95	15	first	first	ADJ
ejpam-1858	95	16	kind	kind	NOUN
ejpam-1858	95	17	.	.	PUNCT
ejpam-1858	96	1	then	then	ADV
ejpam-1858	96	2	the	the	DET
ejpam-1858	96	3	solution	solution	NOUN
ejpam-1858	96	4	is	be	AUX
ejpam-1858	96	5	a	a	DET
ejpam-1858	96	6	piecewise	piecewise	NOUN
ejpam-1858	96	7	continuous	continuous	ADJ
ejpam-1858	96	8	function	function	NOUN
ejpam-1858	96	9	with	with	ADP
ejpam-1858	96	10	a	a	DET
ejpam-1858	96	11	countable	countable	ADJ
ejpam-1858	96	12	number	number	NOUN
ejpam-1858	96	13	of	of	ADP
ejpam-1858	96	14	discontinuities	discontinuity	NOUN
ejpam-1858	96	15	.	.	PUNCT
ejpam-1858	97	1	clearly	clearly	ADV
ejpam-1858	97	2	all	all	DET
ejpam-1858	97	3	these	these	DET
ejpam-1858	97	4	points	point	NOUN
ejpam-1858	97	5	are	be	AUX
ejpam-1858	97	6	not	not	PART
ejpam-1858	97	7	fixed	fix	VERB
ejpam-1858	97	8	points	point	NOUN
ejpam-1858	97	9	of	of	ADP
ejpam-1858	97	10	the	the	DET
ejpam-1858	97	11	operator	operator	NOUN
ejpam-1858	97	12	a(t	a(t	NOUN
ejpam-1858	97	13	)	)	PUNCT
ejpam-1858	97	14	.	.	PUNCT
ejpam-1858	98	1	the	the	DET
ejpam-1858	98	2	question	question	NOUN
ejpam-1858	98	3	of	of	ADP
ejpam-1858	98	4	uncountable	uncountable	ADJ
ejpam-1858	98	5	number	number	NOUN
ejpam-1858	98	6	of	of	ADP
ejpam-1858	98	7	discontinuities	discontinuity	NOUN
ejpam-1858	98	8	does	do	AUX
ejpam-1858	98	9	not	not	PART
ejpam-1858	98	10	arise	arise	VERB
ejpam-1858	98	11	as	as	SCONJ
ejpam-1858	98	12	we	we	PRON
ejpam-1858	98	13	have	have	AUX
ejpam-1858	98	14	assumed	assume	VERB
ejpam-1858	98	15	x(t	x(t	PROPN
ejpam-1858	98	16	)	)	PUNCT
ejpam-1858	98	17	is	be	AUX
ejpam-1858	98	18	a	a	DET
ejpam-1858	98	19	solution	solution	NOUN
ejpam-1858	98	20	of	of	ADP
ejpam-1858	98	21	(	(	PUNCT
ejpam-1858	98	22	4	4	NUM
ejpam-1858	98	23	)	)	PUNCT
ejpam-1858	98	24	.	.	PUNCT
ejpam-1858	99	1	the	the	DET
ejpam-1858	99	2	moments	moment	NOUN
ejpam-1858	99	3	of	of	ADP
ejpam-1858	99	4	time	time	NOUN
ejpam-1858	99	5	at	at	ADP
ejpam-1858	99	6	which	which	PRON
ejpam-1858	99	7	the	the	DET
ejpam-1858	99	8	integral	integral	ADJ
ejpam-1858	99	9	curve	curve	NOUN
ejpam-1858	99	10	hits	hit	VERB
ejpam-1858	99	11	the	the	DET
ejpam-1858	99	12	set	set	NOUN
ejpam-1858	99	13	m(t	m(t	NOUN
ejpam-1858	99	14	)	)	PUNCT
ejpam-1858	99	15	are	be	AUX
ejpam-1858	99	16	called	call	VERB
ejpam-1858	99	17	as	as	ADP
ejpam-1858	99	18	the	the	DET
ejpam-1858	99	19	moments	moment	NOUN
ejpam-1858	99	20	of	of	ADP
ejpam-1858	99	21	the	the	DET
ejpam-1858	99	22	impulse	impulse	NOUN
ejpam-1858	99	23	and	and	CCONJ
ejpam-1858	99	24	are	be	AUX
ejpam-1858	99	25	denoted	denote	VERB
ejpam-1858	99	26	by	by	ADP
ejpam-1858	99	27	t	t	PROPN
ejpam-1858	99	28	=	=	SYM
ejpam-1858	99	29	tk	tk	PROPN
ejpam-1858	99	30	.	.	PROPN
ejpam-1858	100	1	following	follow	VERB
ejpam-1858	100	2	the	the	DET
ejpam-1858	100	3	standard	standard	ADJ
ejpam-1858	100	4	notation	notation	NOUN
ejpam-1858	100	5	in	in	ADP
ejpam-1858	100	6	impulsive	impulsive	ADJ
ejpam-1858	100	7	differential	differential	ADJ
ejpam-1858	100	8	equations	equation	NOUN
ejpam-1858	100	9	[	[	X
ejpam-1858	100	10	9	9	NUM
ejpam-1858	100	11	]	]	PUNCT
ejpam-1858	100	12	,	,	PUNCT
ejpam-1858	100	13	we	we	PRON
ejpam-1858	100	14	assume	assume	VERB
ejpam-1858	100	15	that	that	SCONJ
ejpam-1858	100	16	the	the	DET
ejpam-1858	100	17	solution	solution	NOUN
ejpam-1858	100	18	of	of	ADP
ejpam-1858	100	19	the	the	DET
ejpam-1858	100	20	hcfde	hcfde	NOUN
ejpam-1858	100	21	is	be	AUX
ejpam-1858	100	22	left	leave	VERB
ejpam-1858	100	23	continuous	continuous	ADJ
ejpam-1858	100	24	at	at	ADP
ejpam-1858	100	25	t	t	PROPN
ejpam-1858	100	26	=	=	SYM
ejpam-1858	100	27	tk	tk	PROPN
ejpam-1858	100	28	,	,	PUNCT
ejpam-1858	100	29	k	k	PROPN
ejpam-1858	100	30	=	=	PUNCT
ejpam-1858	100	31	1,2,3	1,2,3	NUM
ejpam-1858	100	32	,	,	PUNCT
ejpam-1858	100	33	.	.	PUNCT
ejpam-1858	100	34	.	.	PUNCT
ejpam-1858	100	35	.	.	PUNCT
ejpam-1858	101	1	that	that	PRON
ejpam-1858	101	2	is	be	AUX
ejpam-1858	101	3	x(t−	x(t−	PROPN
ejpam-1858	101	4	k	k	NOUN
ejpam-1858	101	5	)	)	PUNCT
ejpam-1858	102	1	=	=	SYM
ejpam-1858	102	2	limh→0	limh→0	PROPN
ejpam-1858	102	3	+	+	SYM
ejpam-1858	102	4	x(tk	x(tk	PROPN
ejpam-1858	102	5	−	−	NOUN
ejpam-1858	102	6	h	h	NOUN
ejpam-1858	102	7	)	)	PUNCT
ejpam-1858	102	8	=	=	SYM
ejpam-1858	102	9	x(tk	x(tk	PROPN
ejpam-1858	102	10	)	)	PUNCT
ejpam-1858	102	11	.	.	PUNCT
ejpam-1858	103	1	the	the	DET
ejpam-1858	103	2	generality	generality	NOUN
ejpam-1858	103	3	in	in	ADP
ejpam-1858	103	4	the	the	DET
ejpam-1858	103	5	above	above	ADJ
ejpam-1858	103	6	set	set	VERB
ejpam-1858	103	7	up	up	ADP
ejpam-1858	103	8	,	,	PUNCT
ejpam-1858	103	9	gives	give	VERB
ejpam-1858	103	10	rise	rise	NOUN
ejpam-1858	103	11	to	to	ADP
ejpam-1858	103	12	two	two	NUM
ejpam-1858	103	13	types	type	NOUN
ejpam-1858	103	14	of	of	ADP
ejpam-1858	103	15	hcfde	hcfde	NOUN
ejpam-1858	103	16	known	know	VERB
ejpam-1858	103	17	as	as	ADP
ejpam-1858	103	18	hcfde	hcfde	NOUN
ejpam-1858	103	19	with	with	ADP
ejpam-1858	103	20	fixed	fix	VERB
ejpam-1858	103	21	moments	moment	NOUN
ejpam-1858	103	22	of	of	ADP
ejpam-1858	103	23	impulse	impulse	ADJ
ejpam-1858	103	24	and	and	CCONJ
ejpam-1858	103	25	the	the	DET
ejpam-1858	103	26	other	other	ADJ
ejpam-1858	103	27	by	by	ADP
ejpam-1858	103	28	hcfde	hcfde	NOUN
ejpam-1858	103	29	with	with	ADP
ejpam-1858	103	30	variable	variable	ADJ
ejpam-1858	103	31	moments	moment	NOUN
ejpam-1858	103	32	of	of	ADP
ejpam-1858	103	33	impulse	impulse	ADJ
ejpam-1858	103	34	.	.	PUNCT
ejpam-1858	104	1	the	the	DET
ejpam-1858	104	2	former	former	ADJ
ejpam-1858	104	3	is	be	AUX
ejpam-1858	104	4	quite	quite	ADV
ejpam-1858	104	5	popular	popular	ADJ
ejpam-1858	104	6	and	and	CCONJ
ejpam-1858	104	7	runs	run	VERB
ejpam-1858	104	8	parallel	parallel	ADJ
ejpam-1858	104	9	to	to	ADP
ejpam-1858	104	10	ordinary	ordinary	ADJ
ejpam-1858	104	11	differential	differential	ADJ
ejpam-1858	104	12	equations	equation	NOUN
ejpam-1858	104	13	with	with	ADP
ejpam-1858	104	14	fixed	fix	VERB
ejpam-1858	104	15	moments	moment	NOUN
ejpam-1858	104	16	of	of	ADP
ejpam-1858	104	17	impulse	impulse	ADJ
ejpam-1858	104	18	.	.	PUNCT
ejpam-1858	105	1	there	there	PRON
ejpam-1858	105	2	are	be	VERB
ejpam-1858	105	3	many	many	ADJ
ejpam-1858	105	4	papers	paper	NOUN
ejpam-1858	105	5	on	on	ADP
ejpam-1858	105	6	fractional	fractional	ADJ
ejpam-1858	105	7	differential	differential	ADJ
ejpam-1858	105	8	equations	equation	NOUN
ejpam-1858	105	9	with	with	ADP
ejpam-1858	105	10	fixed	fix	VERB
ejpam-1858	105	11	moments	moment	NOUN
ejpam-1858	105	12	of	of	ADP
ejpam-1858	105	13	impulse	impulse	ADJ
ejpam-1858	105	14	,	,	PUNCT
ejpam-1858	105	15	of	of	ADP
ejpam-1858	105	16	which	which	PRON
ejpam-1858	105	17	some	some	PRON
ejpam-1858	105	18	are	be	AUX
ejpam-1858	105	19	[	[	X
ejpam-1858	105	20	2	2	NUM
ejpam-1858	105	21	,	,	PUNCT
ejpam-1858	105	22	3	3	NUM
ejpam-1858	105	23	,	,	PUNCT
ejpam-1858	105	24	5	5	NUM
ejpam-1858	105	25	,	,	PUNCT
ejpam-1858	105	26	7	7	NUM
ejpam-1858	105	27	]	]	PUNCT
ejpam-1858	105	28	.	.	PUNCT
ejpam-1858	106	1	the	the	DET
ejpam-1858	106	2	latter	latter	ADJ
ejpam-1858	106	3	gives	give	VERB
ejpam-1858	106	4	rise	rise	VERB
ejpam-1858	106	5	to	to	ADP
ejpam-1858	106	6	very	very	ADV
ejpam-1858	106	7	interesting	interesting	ADJ
ejpam-1858	106	8	phenomenon	phenomenon	NOUN
ejpam-1858	106	9	and	and	CCONJ
ejpam-1858	106	10	exhibits	exhibit	VERB
ejpam-1858	106	11	complex	complex	ADJ
ejpam-1858	106	12	behaviour	behaviour	NOUN
ejpam-1858	106	13	.	.	PUNCT
ejpam-1858	107	1	we	we	PRON
ejpam-1858	107	2	concentrate	concentrate	VERB
ejpam-1858	107	3	on	on	ADP
ejpam-1858	107	4	the	the	DET
ejpam-1858	107	5	latter	latter	ADJ
ejpam-1858	107	6	types	type	NOUN
ejpam-1858	107	7	of	of	ADP
ejpam-1858	107	8	equations	equation	NOUN
ejpam-1858	107	9	in	in	ADP
ejpam-1858	107	10	this	this	DET
ejpam-1858	107	11	paper	paper	NOUN
ejpam-1858	107	12	.	.	PUNCT
ejpam-1858	108	1	j.	j.	PROPN
ejpam-1858	108	2	devi	devi	PROPN
ejpam-1858	108	3	,	,	PUNCT
ejpam-1858	108	4	n.	n.	PROPN
ejpam-1858	108	5	giribabu	giribabu	PROPN
ejpam-1858	108	6	/	/	SYM
ejpam-1858	108	7	eur	eur	PROPN
ejpam-1858	108	8	.	.	PUNCT
ejpam-1858	109	1	j.	j.	PROPN
ejpam-1858	109	2	pure	pure	PROPN
ejpam-1858	109	3	appl	appl	PROPN
ejpam-1858	109	4	.	.	PROPN
ejpam-1858	109	5	math	math	PROPN
ejpam-1858	109	6	,	,	PUNCT
ejpam-1858	109	7	7	7	NUM
ejpam-1858	109	8	(	(	PUNCT
ejpam-1858	109	9	2014	2014	NUM
ejpam-1858	109	10	)	)	PUNCT
ejpam-1858	109	11	,	,	PUNCT
ejpam-1858	109	12	115	115	NUM
ejpam-1858	109	13	-	-	SYM
ejpam-1858	109	14	128	128	NUM
ejpam-1858	109	15	120	120	NUM
ejpam-1858	109	16	4	4	NUM
ejpam-1858	109	17	.	.	PUNCT
ejpam-1858	109	18	hcfde	hcfde	NOUN
ejpam-1858	109	19	with	with	ADP
ejpam-1858	109	20	variable	variable	ADJ
ejpam-1858	109	21	moments	moment	NOUN
ejpam-1858	109	22	of	of	ADP
ejpam-1858	109	23	impulse	impulse	ADJ
ejpam-1858	109	24	consider	consider	VERB
ejpam-1858	109	25	a	a	DET
ejpam-1858	109	26	sequence	sequence	NOUN
ejpam-1858	109	27	of	of	ADP
ejpam-1858	109	28	surfaces	surface	NOUN
ejpam-1858	109	29	{	{	PUNCT
ejpam-1858	109	30	sk	sk	PART
ejpam-1858	109	31	}	}	PUNCT
ejpam-1858	109	32	given	give	VERB
ejpam-1858	109	33	by	by	ADP
ejpam-1858	109	34	sk	sk	NOUN
ejpam-1858	109	35	:	:	PUNCT
ejpam-1858	109	36	t	t	NOUN
ejpam-1858	109	37	=	=	PUNCT
ejpam-1858	109	38	τk(x	τk(x	X
ejpam-1858	109	39	)	)	PUNCT
ejpam-1858	109	40	,	,	PUNCT
ejpam-1858	109	41	k	k	X
ejpam-1858	110	1	=	=	PUNCT
ejpam-1858	110	2	1,2,3	1,2,3	NUM
ejpam-1858	110	3	,	,	PUNCT
ejpam-1858	110	4	.	.	PUNCT
ejpam-1858	110	5	.	.	PUNCT
ejpam-1858	111	1	.	.	PUNCT
ejpam-1858	112	1	,	,	PUNCT
ejpam-1858	112	2	τk	τk	ADP
ejpam-1858	112	3	:	:	PUNCT
ejpam-1858	112	4	r→	r→	VERB
ejpam-1858	112	5	r	r	NOUN
ejpam-1858	112	6	such	such	ADJ
ejpam-1858	112	7	that	that	PRON
ejpam-1858	112	8	τk(x	τk(x	PUNCT
ejpam-1858	112	9	)	)	PUNCT
ejpam-1858	112	10	<	<	X
ejpam-1858	112	11	τk+1(x	τk+1(x	PROPN
ejpam-1858	112	12	)	)	PUNCT
ejpam-1858	112	13	and	and	CCONJ
ejpam-1858	112	14	limk→∞	limk→∞	PROPN
ejpam-1858	112	15	τk(x	τk(x	PUNCT
ejpam-1858	112	16	)	)	PUNCT
ejpam-1858	113	1	=	=	PRON
ejpam-1858	113	2	∞.	∞.	PROPN
ejpam-1858	113	3	then	then	ADV
ejpam-1858	113	4	the	the	DET
ejpam-1858	113	5	hcfde	hcfde	NOUN
ejpam-1858	113	6	with	with	ADP
ejpam-1858	113	7	variable	variable	ADJ
ejpam-1858	113	8	moments	moment	NOUN
ejpam-1858	113	9	of	of	ADP
ejpam-1858	113	10	impulse	impulse	ADJ
ejpam-1858	113	11	is	be	AUX
ejpam-1858	113	12	given	give	VERB
ejpam-1858	113	13	by	by	ADP
ejpam-1858	113	14	c	c	PROPN
ejpam-1858	113	15	dq	dq	PROPN
ejpam-1858	113	16	x	x	SYM
ejpam-1858	113	17	=	=	SYM
ejpam-1858	113	18	f	f	PROPN
ejpam-1858	113	19	(	(	PUNCT
ejpam-1858	113	20	t	t	PROPN
ejpam-1858	113	21	,	,	PUNCT
ejpam-1858	113	22	x	x	NOUN
ejpam-1858	113	23	)	)	PUNCT
ejpam-1858	113	24	,	,	PUNCT
ejpam-1858	113	25	t	t	PROPN
ejpam-1858	113	26	6=	6=	NUM
ejpam-1858	113	27	τk(x	τk(x	NOUN
ejpam-1858	113	28	)	)	PUNCT
ejpam-1858	113	29	,	,	PUNCT
ejpam-1858	113	30	x(t+	x(t+	NUM
ejpam-1858	113	31	)	)	PUNCT
ejpam-1858	114	1	=	=	SYM
ejpam-1858	114	2	x(t	x(t	X
ejpam-1858	114	3	)	)	PUNCT
ejpam-1858	114	4	+	+	SYM
ejpam-1858	114	5	ik(x(t	ik(x(t	NOUN
ejpam-1858	114	6	)	)	PUNCT
ejpam-1858	114	7	)	)	PUNCT
ejpam-1858	114	8	,	,	PUNCT
ejpam-1858	114	9	t	t	PROPN
ejpam-1858	114	10	=	=	PUNCT
ejpam-1858	114	11	τk(x	τk(x	X
ejpam-1858	114	12	)	)	PUNCT
ejpam-1858	114	13	,	,	PUNCT
ejpam-1858	114	14	(	(	PUNCT
ejpam-1858	114	15	5	5	X
ejpam-1858	114	16	)	)	PUNCT
ejpam-1858	114	17	where	where	SCONJ
ejpam-1858	114	18	f	f	X
ejpam-1858	114	19	:	:	PUNCT
ejpam-1858	114	20	r+	r+	PUNCT
ejpam-1858	114	21	×ω→	×ω→	PROPN
ejpam-1858	114	22	r	r	PROPN
ejpam-1858	114	23	,	,	PUNCT
ejpam-1858	114	24	ω	ω	PROPN
ejpam-1858	114	25	⊂	⊂	PROPN
ejpam-1858	114	26	r	r	NOUN
ejpam-1858	114	27	is	be	AUX
ejpam-1858	114	28	an	an	DET
ejpam-1858	114	29	open	open	ADJ
ejpam-1858	114	30	set	set	NOUN
ejpam-1858	114	31	,	,	PUNCT
ejpam-1858	114	32	τk	τk	ADP
ejpam-1858	114	33	∈	∈	PROPN
ejpam-1858	114	34	c[ω	c[ω	NOUN
ejpam-1858	114	35	,	,	PUNCT
ejpam-1858	114	36	(	(	PUNCT
ejpam-1858	114	37	0,∞	0,∞	NOUN
ejpam-1858	114	38	)	)	PUNCT
ejpam-1858	114	39	]	]	PUNCT
ejpam-1858	114	40	,	,	PUNCT
ejpam-1858	114	41	k	k	X
ejpam-1858	114	42	=	=	PUNCT
ejpam-1858	114	43	1,2,3	1,2,3	NUM
ejpam-1858	114	44	,	,	PUNCT
ejpam-1858	114	45	.	.	PUNCT
ejpam-1858	114	46	.	.	PUNCT
ejpam-1858	115	1	.	.	PUNCT
ejpam-1858	116	1	,	,	PUNCT
ejpam-1858	116	2	ik(x(t	ik(x(t	NOUN
ejpam-1858	116	3	)	)	PUNCT
ejpam-1858	116	4	)	)	PUNCT
ejpam-1858	117	1	=	=	SYM
ejpam-1858	117	2	∆(x(t	∆(x(t	NOUN
ejpam-1858	117	3	)	)	PUNCT
ejpam-1858	117	4	)	)	PUNCT
ejpam-1858	118	1	=	=	PUNCT
ejpam-1858	119	1	x(t+)−	x(t+)−	PROPN
ejpam-1858	119	2	x(t−	x(t−	PROPN
ejpam-1858	119	3	)	)	PUNCT
ejpam-1858	119	4	,	,	PUNCT
ejpam-1858	119	5	and	and	CCONJ
ejpam-1858	119	6	ik	ik	PROPN
ejpam-1858	119	7	∈	∈	PROPN
ejpam-1858	119	8	c[ω	c[ω	PROPN
ejpam-1858	119	9	,	,	PUNCT
ejpam-1858	119	10	r	r	NOUN
ejpam-1858	119	11	]	]	PUNCT
ejpam-1858	119	12	.	.	PUNCT
ejpam-1858	120	1	in	in	ADP
ejpam-1858	120	2	this	this	DET
ejpam-1858	120	3	case	case	NOUN
ejpam-1858	120	4	,	,	PUNCT
ejpam-1858	120	5	the	the	DET
ejpam-1858	120	6	moments	moment	NOUN
ejpam-1858	120	7	of	of	ADP
ejpam-1858	120	8	the	the	DET
ejpam-1858	120	9	impulsive	impulsive	ADJ
ejpam-1858	120	10	effect	effect	NOUN
ejpam-1858	120	11	for	for	ADP
ejpam-1858	120	12	the	the	DET
ejpam-1858	120	13	system	system	NOUN
ejpam-1858	120	14	(	(	PUNCT
ejpam-1858	120	15	5	5	X
ejpam-1858	120	16	)	)	PUNCT
ejpam-1858	120	17	depend	depend	VERB
ejpam-1858	120	18	on	on	ADP
ejpam-1858	120	19	the	the	DET
ejpam-1858	120	20	solutions	solution	NOUN
ejpam-1858	120	21	satisfying	satisfy	VERB
ejpam-1858	120	22	tk	tk	PROPN
ejpam-1858	120	23	=	=	PUNCT
ejpam-1858	120	24	τk(x(tk	τk(x(tk	PROPN
ejpam-1858	120	25	)	)	PUNCT
ejpam-1858	120	26	)	)	PUNCT
ejpam-1858	120	27	,	,	PUNCT
ejpam-1858	120	28	for	for	ADP
ejpam-1858	120	29	each	each	DET
ejpam-1858	120	30	k.	k.	PROPN
ejpam-1858	121	1	thus	thus	ADV
ejpam-1858	121	2	,	,	PUNCT
ejpam-1858	121	3	the	the	DET
ejpam-1858	121	4	solutions	solution	NOUN
ejpam-1858	121	5	starting	start	VERB
ejpam-1858	121	6	at	at	ADP
ejpam-1858	121	7	different	different	ADJ
ejpam-1858	121	8	points	point	NOUN
ejpam-1858	121	9	will	will	AUX
ejpam-1858	121	10	have	have	VERB
ejpam-1858	121	11	different	different	ADJ
ejpam-1858	121	12	points	point	NOUN
ejpam-1858	121	13	of	of	ADP
ejpam-1858	121	14	discontinuity	discontinuity	NOUN
ejpam-1858	121	15	.	.	PUNCT
ejpam-1858	122	1	also	also	ADV
ejpam-1858	122	2	a	a	DET
ejpam-1858	122	3	solution	solution	NOUN
ejpam-1858	122	4	may	may	AUX
ejpam-1858	122	5	hit	hit	VERB
ejpam-1858	122	6	the	the	DET
ejpam-1858	122	7	same	same	ADJ
ejpam-1858	122	8	surface	surface	NOUN
ejpam-1858	122	9	t	t	NOUN
ejpam-1858	122	10	=	=	PUNCT
ejpam-1858	122	11	τk(x	τk(x	PRON
ejpam-1858	122	12	)	)	PUNCT
ejpam-1858	122	13	several	several	ADJ
ejpam-1858	122	14	times	time	NOUN
ejpam-1858	122	15	and	and	CCONJ
ejpam-1858	122	16	we	we	PRON
ejpam-1858	122	17	shall	shall	AUX
ejpam-1858	122	18	call	call	VERB
ejpam-1858	122	19	such	such	DET
ejpam-1858	122	20	a	a	DET
ejpam-1858	122	21	behaviour	behaviour	NOUN
ejpam-1858	122	22	as	as	ADP
ejpam-1858	122	23	“	"	PUNCT
ejpam-1858	122	24	pulse	pulse	NOUN
ejpam-1858	122	25	phenomena	phenomenon	NOUN
ejpam-1858	122	26	”	"	PUNCT
ejpam-1858	122	27	.	.	PUNCT
ejpam-1858	123	1	in	in	ADP
ejpam-1858	123	2	addition	addition	NOUN
ejpam-1858	123	3	,	,	PUNCT
ejpam-1858	123	4	different	different	ADJ
ejpam-1858	123	5	solutions	solution	NOUN
ejpam-1858	123	6	may	may	AUX
ejpam-1858	123	7	coincide	coincide	VERB
ejpam-1858	123	8	after	after	ADP
ejpam-1858	123	9	some	some	DET
ejpam-1858	123	10	time	time	NOUN
ejpam-1858	123	11	and	and	CCONJ
ejpam-1858	123	12	behaves	behave	VERB
ejpam-1858	123	13	as	as	ADP
ejpam-1858	123	14	a	a	DET
ejpam-1858	123	15	single	single	ADJ
ejpam-1858	123	16	solution	solution	NOUN
ejpam-1858	123	17	there	there	ADV
ejpam-1858	123	18	after	after	ADP
ejpam-1858	123	19	.	.	PUNCT
ejpam-1858	124	1	this	this	DET
ejpam-1858	124	2	phenomena	phenomena	NOUN
ejpam-1858	124	3	is	be	AUX
ejpam-1858	124	4	called	call	VERB
ejpam-1858	124	5	“	"	PUNCT
ejpam-1858	124	6	confluence	confluence	NOUN
ejpam-1858	124	7	”	"	PUNCT
ejpam-1858	124	8	.	.	PUNCT
ejpam-1858	125	1	in	in	ADP
ejpam-1858	125	2	the	the	DET
ejpam-1858	125	3	following	follow	VERB
ejpam-1858	125	4	example	example	NOUN
ejpam-1858	125	5	,	,	PUNCT
ejpam-1858	125	6	the	the	DET
ejpam-1858	125	7	different	different	ADJ
ejpam-1858	125	8	solutions	solution	NOUN
ejpam-1858	125	9	that	that	PRON
ejpam-1858	125	10	arise	arise	VERB
ejpam-1858	125	11	in	in	ADP
ejpam-1858	125	12	this	this	DET
ejpam-1858	125	13	context	context	NOUN
ejpam-1858	125	14	are	be	AUX
ejpam-1858	125	15	described	describe	VERB
ejpam-1858	125	16	and	and	CCONJ
ejpam-1858	125	17	the	the	DET
ejpam-1858	125	18	graphs	graph	NOUN
ejpam-1858	125	19	are	be	AUX
ejpam-1858	125	20	drawn	draw	VERB
ejpam-1858	125	21	.	.	PUNCT
ejpam-1858	126	1	consider	consider	VERB
ejpam-1858	126	2	the	the	DET
ejpam-1858	126	3	hybrid	hybrid	ADJ
ejpam-1858	126	4	caputo	caputo	PROPN
ejpam-1858	126	5	fractional	fractional	PROPN
ejpam-1858	126	6	differential	differential	NOUN
ejpam-1858	126	7	equation	equation	NOUN
ejpam-1858	126	8	with	with	ADP
ejpam-1858	126	9	variable	variable	ADJ
ejpam-1858	126	10	moments	moment	NOUN
ejpam-1858	126	11	of	of	ADP
ejpam-1858	126	12	impulse	impulse	ADJ
ejpam-1858	126	13	c	c	NOUN
ejpam-1858	126	14	dq	dq	NOUN
ejpam-1858	126	15	x	x	SYM
ejpam-1858	126	16	=	=	NOUN
ejpam-1858	126	17	0	0	NUM
ejpam-1858	126	18	,	,	PUNCT
ejpam-1858	126	19	t	t	PROPN
ejpam-1858	126	20	6=	6=	NUM
ejpam-1858	126	21	τk(x	τk(x	PROPN
ejpam-1858	126	22	)	)	PUNCT
ejpam-1858	126	23	,	,	PUNCT
ejpam-1858	126	24	t	t	PROPN
ejpam-1858	126	25	≥	≥	NUM
ejpam-1858	126	26	0	0	NUM
ejpam-1858	126	27	,	,	PUNCT
ejpam-1858	126	28	x(t+	x(t+	NUM
ejpam-1858	126	29	)	)	PUNCT
ejpam-1858	127	1	=	=	SYM
ejpam-1858	127	2	x2	x2	NOUN
ejpam-1858	127	3	sgn	sgn	NOUN
ejpam-1858	127	4	x	x	NOUN
ejpam-1858	127	5	,	,	PUNCT
ejpam-1858	127	6	t	t	NOUN
ejpam-1858	127	7	=	=	PUNCT
ejpam-1858	127	8	τk(x	τk(x	X
ejpam-1858	127	9	)	)	PUNCT
ejpam-1858	127	10	,	,	PUNCT
ejpam-1858	127	11	k	k	X
ejpam-1858	127	12	=	=	PUNCT
ejpam-1858	127	13	1,2,3	1,2,3	NUM
ejpam-1858	127	14	,	,	PUNCT
ejpam-1858	127	15	.	.	PUNCT
ejpam-1858	127	16	.	.	PUNCT
ejpam-1858	127	17	.	.	PUNCT
ejpam-1858	128	1	(	(	PUNCT
ejpam-1858	128	2	6	6	NUM
ejpam-1858	128	3	)	)	PUNCT
ejpam-1858	128	4	where	where	SCONJ
ejpam-1858	128	5	τk(x	τk(x	PUNCT
ejpam-1858	128	6	)	)	PUNCT
ejpam-1858	128	7	=	=	SYM
ejpam-1858	129	1	x2	x2	PROPN
ejpam-1858	130	1	+	+	CCONJ
ejpam-1858	130	2	20(k	20(k	NUM
ejpam-1858	130	3	−	−	NOUN
ejpam-1858	130	4	1	1	NUM
ejpam-1858	130	5	)	)	PUNCT
ejpam-1858	130	6	for	for	ADP
ejpam-1858	130	7	|x	|x	NOUN
ejpam-1858	130	8	|	|	ADV
ejpam-1858	130	9	<	<	X
ejpam-1858	130	10	6	6	NUM
ejpam-1858	130	11	describe	describe	VERB
ejpam-1858	130	12	the	the	DET
ejpam-1858	130	13	surfaces	surface	NOUN
ejpam-1858	130	14	sk	sk	INTJ
ejpam-1858	130	15	:	:	PUNCT
ejpam-1858	130	16	t	t	PROPN
ejpam-1858	130	17	=	=	PUNCT
ejpam-1858	130	18	τk(x	τk(x	X
ejpam-1858	130	19	)	)	PUNCT
ejpam-1858	130	20	.	.	PUNCT
ejpam-1858	131	1	here	here	ADV
ejpam-1858	131	2	ik(x	ik(x	NOUN
ejpam-1858	131	3	)	)	PUNCT
ejpam-1858	131	4	=	=	SYM
ejpam-1858	131	5	∆(x	∆(x	NOUN
ejpam-1858	131	6	)	)	PUNCT
ejpam-1858	131	7	=	=	SYM
ejpam-1858	131	8	x2	x2	PROPN
ejpam-1858	131	9	sgn	sgn	NOUN
ejpam-1858	131	10	x	x	X
ejpam-1858	131	11	−	−	PROPN
ejpam-1858	131	12	x	x	X
ejpam-1858	131	13	.	.	PUNCT
ejpam-1858	132	1	if	if	SCONJ
ejpam-1858	132	2	c	c	X
ejpam-1858	132	3	dq	dq	VERB
ejpam-1858	132	4	x	x	SYM
ejpam-1858	132	5	=	=	SYM
ejpam-1858	132	6	0	0	PUNCT
ejpam-1858	132	7	then	then	ADV
ejpam-1858	132	8	x(t	x(t	PROPN
ejpam-1858	132	9	)	)	PUNCT
ejpam-1858	132	10	=	=	PUNCT
ejpam-1858	132	11	x0	x0	PROPN
ejpam-1858	132	12	,	,	PUNCT
ejpam-1858	132	13	a	a	DET
ejpam-1858	132	14	constant	constant	ADJ
ejpam-1858	132	15	.	.	PUNCT
ejpam-1858	133	1	case	case	NOUN
ejpam-1858	133	2	(	(	PUNCT
ejpam-1858	133	3	1	1	X
ejpam-1858	133	4	)	)	PUNCT
ejpam-1858	133	5	the	the	DET
ejpam-1858	133	6	solutions	solution	NOUN
ejpam-1858	133	7	x(t	x(t	PROPN
ejpam-1858	133	8	)	)	PUNCT
ejpam-1858	133	9	with	with	ADP
ejpam-1858	133	10	initial	initial	ADJ
ejpam-1858	133	11	condition	condition	NOUN
ejpam-1858	133	12	x(0	x(0	PROPN
ejpam-1858	133	13	)	)	PUNCT
ejpam-1858	134	1	=	=	PUNCT
ejpam-1858	134	2	x0	x0	PROPN
ejpam-1858	134	3	,	,	PUNCT
ejpam-1858	134	4	|x0|	|x0|	PROPN
ejpam-1858	134	5	≥	≥	NUM
ejpam-1858	134	6	6	6	NUM
ejpam-1858	134	7	are	be	AUX
ejpam-1858	134	8	free	free	ADJ
ejpam-1858	134	9	from	from	ADP
ejpam-1858	134	10	impulsive	impulsive	ADJ
ejpam-1858	134	11	effect	effect	NOUN
ejpam-1858	134	12	since	since	SCONJ
ejpam-1858	134	13	they	they	PRON
ejpam-1858	134	14	do	do	AUX
ejpam-1858	134	15	not	not	PART
ejpam-1858	134	16	intersect	intersect	VERB
ejpam-1858	134	17	the	the	DET
ejpam-1858	134	18	surfaces	surface	NOUN
ejpam-1858	134	19	sk	sk	VERB
ejpam-1858	134	20	for	for	ADP
ejpam-1858	134	21	any	any	DET
ejpam-1858	134	22	k.	k.	NOUN
ejpam-1858	134	23	for	for	ADP
ejpam-1858	134	24	example	example	NOUN
ejpam-1858	134	25	,	,	PUNCT
ejpam-1858	134	26	consider	consider	VERB
ejpam-1858	134	27	the	the	DET
ejpam-1858	134	28	solution	solution	NOUN
ejpam-1858	134	29	x(t	x(t	PROPN
ejpam-1858	134	30	)	)	PUNCT
ejpam-1858	134	31	of	of	ADP
ejpam-1858	134	32	(	(	PUNCT
ejpam-1858	134	33	6	6	NUM
ejpam-1858	134	34	)	)	PUNCT
ejpam-1858	134	35	starting	start	VERB
ejpam-1858	134	36	at	at	ADP
ejpam-1858	134	37	the	the	DET
ejpam-1858	134	38	point	point	NOUN
ejpam-1858	134	39	(	(	PUNCT
ejpam-1858	134	40	0,8.5	0,8.5	NUM
ejpam-1858	134	41	)	)	PUNCT
ejpam-1858	134	42	.	.	PUNCT
ejpam-1858	135	1	it	it	PRON
ejpam-1858	135	2	does	do	AUX
ejpam-1858	135	3	not	not	PART
ejpam-1858	135	4	hit	hit	VERB
ejpam-1858	135	5	any	any	DET
ejpam-1858	135	6	surface	surface	NOUN
ejpam-1858	135	7	,	,	PUNCT
ejpam-1858	135	8	see	see	VERB
ejpam-1858	135	9	figure	figure	NOUN
ejpam-1858	135	10	1a	1a	NOUN
ejpam-1858	135	11	.	.	PUNCT
ejpam-1858	136	1	case	case	NOUN
ejpam-1858	136	2	(	(	PUNCT
ejpam-1858	136	3	2	2	X
ejpam-1858	136	4	)	)	PUNCT
ejpam-1858	136	5	the	the	DET
ejpam-1858	136	6	solutions	solution	NOUN
ejpam-1858	136	7	starting	start	VERB
ejpam-1858	136	8	at	at	ADP
ejpam-1858	136	9	the	the	DET
ejpam-1858	136	10	points	point	NOUN
ejpam-1858	136	11	(	(	PUNCT
ejpam-1858	136	12	0	0	NUM
ejpam-1858	136	13	,	,	PUNCT
ejpam-1858	136	14	x0	x0	PROPN
ejpam-1858	136	15	)	)	PUNCT
ejpam-1858	136	16	where	where	SCONJ
ejpam-1858	136	17	1	1	NUM
ejpam-1858	136	18	<	<	X
ejpam-1858	136	19	x0	x0	PROPN
ejpam-1858	136	20	<	<	X
ejpam-1858	136	21	6	6	NUM
ejpam-1858	136	22	or	or	CCONJ
ejpam-1858	136	23	−6	−6	NOUN
ejpam-1858	136	24	<	<	X
ejpam-1858	136	25	x0	x0	PROPN
ejpam-1858	136	26	<	<	X
ejpam-1858	136	27	−1	−1	NOUN
ejpam-1858	136	28	,	,	PUNCT
ejpam-1858	136	29	undergo	undergo	VERB
ejpam-1858	136	30	impulsive	impulsive	ADJ
ejpam-1858	136	31	effect	effect	NOUN
ejpam-1858	136	32	a	a	DET
ejpam-1858	136	33	finite	finite	ADJ
ejpam-1858	136	34	number	number	NOUN
ejpam-1858	136	35	of	of	ADP
ejpam-1858	136	36	times	time	NOUN
ejpam-1858	136	37	.	.	PUNCT
ejpam-1858	137	1	for	for	ADP
ejpam-1858	137	2	example	example	NOUN
ejpam-1858	137	3	,	,	PUNCT
ejpam-1858	137	4	consider	consider	VERB
ejpam-1858	137	5	the	the	DET
ejpam-1858	137	6	solution	solution	NOUN
ejpam-1858	137	7	x(t	x(t	PROPN
ejpam-1858	137	8	)	)	PUNCT
ejpam-1858	137	9	with	with	ADP
ejpam-1858	137	10	initial	initial	ADJ
ejpam-1858	137	11	condition	condition	NOUN
ejpam-1858	137	12	x(0	x(0	PROPN
ejpam-1858	137	13	)	)	PUNCT
ejpam-1858	138	1	=	=	PUNCT
ejpam-1858	139	1	p	p	NOUN
ejpam-1858	139	2	2	2	NUM
ejpam-1858	139	3	.	.	PUNCT
ejpam-1858	140	1	the	the	DET
ejpam-1858	140	2	point	point	NOUN
ejpam-1858	140	3	pt	pt	X
ejpam-1858	140	4	=	=	SYM
ejpam-1858	140	5	(	(	PUNCT
ejpam-1858	140	6	t	t	PROPN
ejpam-1858	140	7	,	,	PUNCT
ejpam-1858	140	8	x(t	x(t	PROPN
ejpam-1858	140	9	)	)	PUNCT
ejpam-1858	140	10	)	)	PUNCT
ejpam-1858	140	11	starts	start	VERB
ejpam-1858	140	12	its	its	PRON
ejpam-1858	140	13	motion	motion	NOUN
ejpam-1858	140	14	from	from	ADP
ejpam-1858	140	15	(	(	PUNCT
ejpam-1858	140	16	t0	t0	PROPN
ejpam-1858	140	17	,	,	PUNCT
ejpam-1858	140	18	x0	x0	PROPN
ejpam-1858	140	19	)	)	PUNCT
ejpam-1858	141	1	=	=	SYM
ejpam-1858	141	2	(	(	PUNCT
ejpam-1858	141	3	0	0	NUM
ejpam-1858	141	4	,	,	PUNCT
ejpam-1858	141	5	p	p	NOUN
ejpam-1858	141	6	2	2	NUM
ejpam-1858	141	7	)	)	PUNCT
ejpam-1858	141	8	and	and	CCONJ
ejpam-1858	141	9	moves	move	NOUN
ejpam-1858	141	10	along	along	ADP
ejpam-1858	141	11	the	the	DET
ejpam-1858	141	12	curve	curve	NOUN
ejpam-1858	141	13	{	{	PUNCT
ejpam-1858	141	14	(	(	PUNCT
ejpam-1858	141	15	t	t	PROPN
ejpam-1858	141	16	,	,	PUNCT
ejpam-1858	141	17	x	x	NOUN
ejpam-1858	141	18	)	)	PUNCT
ejpam-1858	141	19	:	:	PUNCT
ejpam-1858	141	20	t	t	X
ejpam-1858	141	21	≥	≥	NUM
ejpam-1858	141	22	0	0	NUM
ejpam-1858	141	23	,	,	PUNCT
ejpam-1858	141	24	x	x	SYM
ejpam-1858	141	25	=	=	PUNCT
ejpam-1858	141	26	x(t)}=	x(t)}=	X
ejpam-1858	141	27	{	{	PUNCT
ejpam-1858	141	28	(	(	PUNCT
ejpam-1858	141	29	t	t	PROPN
ejpam-1858	141	30	,	,	PUNCT
ejpam-1858	141	31	x)t	x)t	X
ejpam-1858	141	32	≥	≥	NOUN
ejpam-1858	141	33	0	0	NUM
ejpam-1858	141	34	,	,	PUNCT
ejpam-1858	141	35	x	x	PUNCT
ejpam-1858	142	1	=	=	PUNCT
ejpam-1858	142	2	p	p	VERB
ejpam-1858	142	3	2	2	NUM
ejpam-1858	142	4	}	}	PUNCT
ejpam-1858	142	5	until	until	ADP
ejpam-1858	142	6	the	the	DET
ejpam-1858	142	7	time	time	NOUN
ejpam-1858	142	8	t1	t1	NOUN
ejpam-1858	142	9	=	=	SYM
ejpam-1858	142	10	2	2	NUM
ejpam-1858	142	11	>	>	PUNCT
ejpam-1858	142	12	t0	t0	PROPN
ejpam-1858	142	13	=	=	PUNCT
ejpam-1858	142	14	0	0	PUNCT
ejpam-1858	142	15	at	at	ADP
ejpam-1858	142	16	which	which	PRON
ejpam-1858	142	17	the	the	DET
ejpam-1858	142	18	point	point	NOUN
ejpam-1858	142	19	pt	pt	NOUN
ejpam-1858	142	20	meets	meet	VERB
ejpam-1858	142	21	the	the	DET
ejpam-1858	142	22	surface	surface	NOUN
ejpam-1858	142	23	s1	s1	NOUN
ejpam-1858	142	24	:	:	PUNCT
ejpam-1858	143	1	t	t	X
ejpam-1858	143	2	=	=	SYM
ejpam-1858	143	3	x2	x2	PROPN
ejpam-1858	143	4	.	.	PUNCT
ejpam-1858	144	1	the	the	DET
ejpam-1858	144	2	point	point	NOUN
ejpam-1858	144	3	pt1	pt1	PROPN
ejpam-1858	144	4	=	=	SYM
ejpam-1858	144	5	(	(	PUNCT
ejpam-1858	144	6	t1	t1	PROPN
ejpam-1858	144	7	,	,	PUNCT
ejpam-1858	144	8	x1	x1	PROPN
ejpam-1858	144	9	)	)	PUNCT
ejpam-1858	144	10	=	=	SYM
ejpam-1858	144	11	(	(	PUNCT
ejpam-1858	144	12	2	2	NUM
ejpam-1858	144	13	,	,	PUNCT
ejpam-1858	144	14	p	p	NOUN
ejpam-1858	144	15	2	2	NUM
ejpam-1858	144	16	)	)	PUNCT
ejpam-1858	144	17	which	which	PRON
ejpam-1858	144	18	lies	lie	VERB
ejpam-1858	144	19	on	on	ADP
ejpam-1858	144	20	the	the	DET
ejpam-1858	144	21	surface	surface	NOUN
ejpam-1858	144	22	s1	s1	NOUN
ejpam-1858	144	23	is	be	AUX
ejpam-1858	144	24	transferred	transfer	VERB
ejpam-1858	144	25	to	to	ADP
ejpam-1858	144	26	the	the	DET
ejpam-1858	144	27	point	point	NOUN
ejpam-1858	144	28	pt+	pt+	NOUN
ejpam-1858	144	29	1	1	NUM
ejpam-1858	144	30	=	=	SYM
ejpam-1858	144	31	(	(	PUNCT
ejpam-1858	144	32	t1	t1	PROPN
ejpam-1858	144	33	,	,	PUNCT
ejpam-1858	144	34	x+	x+	X
ejpam-1858	144	35	1	1	X
ejpam-1858	144	36	)	)	PUNCT
ejpam-1858	144	37	=	=	SYM
ejpam-1858	144	38	(	(	PUNCT
ejpam-1858	144	39	2,2	2,2	NUM
ejpam-1858	144	40	)	)	PUNCT
ejpam-1858	145	1	where	where	SCONJ
ejpam-1858	145	2	x+	x+	SYM
ejpam-1858	145	3	1	1	NUM
ejpam-1858	145	4	=	=	SYM
ejpam-1858	145	5	x2	x2	PROPN
ejpam-1858	145	6	1	1	NUM
ejpam-1858	145	7	sgn	sgn	NOUN
ejpam-1858	145	8	x1	x1	NOUN
ejpam-1858	145	9	=	=	SYM
ejpam-1858	145	10	2	2	X
ejpam-1858	145	11	.	.	PUNCT
ejpam-1858	145	12	then	then	ADV
ejpam-1858	145	13	the	the	DET
ejpam-1858	145	14	point	point	NOUN
ejpam-1858	145	15	pt	pt	PROPN
ejpam-1858	145	16	continues	continue	VERB
ejpam-1858	145	17	to	to	PART
ejpam-1858	145	18	move	move	VERB
ejpam-1858	145	19	further	far	ADV
ejpam-1858	145	20	along	along	ADP
ejpam-1858	145	21	the	the	DET
ejpam-1858	145	22	curve	curve	NOUN
ejpam-1858	145	23	with	with	ADP
ejpam-1858	145	24	x(t	x(t	PROPN
ejpam-1858	145	25	)	)	PUNCT
ejpam-1858	145	26	=	=	SYM
ejpam-1858	146	1	x(t	x(t	PROPN
ejpam-1858	146	2	;	;	PUNCT
ejpam-1858	146	3	t1	t1	NOUN
ejpam-1858	146	4	,	,	PUNCT
ejpam-1858	146	5	x+	x+	X
ejpam-1858	146	6	1	1	NUM
ejpam-1858	146	7	)	)	PUNCT
ejpam-1858	146	8	as	as	ADP
ejpam-1858	146	9	the	the	DET
ejpam-1858	146	10	solution	solution	NOUN
ejpam-1858	146	11	of	of	ADP
ejpam-1858	146	12	(	(	PUNCT
ejpam-1858	146	13	6	6	NUM
ejpam-1858	146	14	)	)	PUNCT
ejpam-1858	146	15	starting	start	VERB
ejpam-1858	146	16	at	at	ADP
ejpam-1858	146	17	(	(	PUNCT
ejpam-1858	146	18	t1	t1	NOUN
ejpam-1858	146	19	,	,	PUNCT
ejpam-1858	146	20	x+	x+	X
ejpam-1858	146	21	1	1	NUM
ejpam-1858	146	22	)	)	PUNCT
ejpam-1858	146	23	until	until	SCONJ
ejpam-1858	146	24	it	it	PRON
ejpam-1858	146	25	hits	hit	VERB
ejpam-1858	146	26	the	the	DET
ejpam-1858	146	27	same	same	ADJ
ejpam-1858	146	28	surface	surface	NOUN
ejpam-1858	146	29	s1	s1	NOUN
ejpam-1858	146	30	at	at	ADP
ejpam-1858	146	31	the	the	DET
ejpam-1858	146	32	next	next	ADJ
ejpam-1858	146	33	moment	moment	NOUN
ejpam-1858	146	34	t2	t2	NOUN
ejpam-1858	146	35	=	=	PROPN
ejpam-1858	146	36	4	4	NUM
ejpam-1858	146	37	>	>	SYM
ejpam-1858	146	38	t1	t1	NOUN
ejpam-1858	146	39	=	=	SYM
ejpam-1858	146	40	2	2	X
ejpam-1858	146	41	.	.	PUNCT
ejpam-1858	147	1	then	then	ADV
ejpam-1858	147	2	once	once	ADV
ejpam-1858	147	3	again	again	ADV
ejpam-1858	147	4	j.	j.	PROPN
ejpam-1858	147	5	devi	devi	PROPN
ejpam-1858	147	6	,	,	PUNCT
ejpam-1858	147	7	n.	n.	PROPN
ejpam-1858	147	8	giribabu	giribabu	PROPN
ejpam-1858	147	9	/	/	SYM
ejpam-1858	147	10	eur	eur	PROPN
ejpam-1858	147	11	.	.	PUNCT
ejpam-1858	148	1	j.	j.	PROPN
ejpam-1858	148	2	pure	pure	PROPN
ejpam-1858	148	3	appl	appl	PROPN
ejpam-1858	148	4	.	.	PROPN
ejpam-1858	148	5	math	math	PROPN
ejpam-1858	148	6	,	,	PUNCT
ejpam-1858	148	7	7	7	NUM
ejpam-1858	148	8	(	(	PUNCT
ejpam-1858	148	9	2014	2014	NUM
ejpam-1858	148	10	)	)	PUNCT
ejpam-1858	148	11	,	,	PUNCT
ejpam-1858	148	12	115	115	NUM
ejpam-1858	148	13	-	-	SYM
ejpam-1858	148	14	128	128	NUM
ejpam-1858	148	15	121	121	NUM
ejpam-1858	148	16	the	the	DET
ejpam-1858	148	17	point	point	NOUN
ejpam-1858	148	18	pt2	pt2	NOUN
ejpam-1858	148	19	=	=	SYM
ejpam-1858	148	20	(	(	PUNCT
ejpam-1858	148	21	t2	t2	PROPN
ejpam-1858	148	22	,	,	PUNCT
ejpam-1858	148	23	x2	x2	PROPN
ejpam-1858	148	24	)	)	PUNCT
ejpam-1858	148	25	=	=	SYM
ejpam-1858	148	26	(	(	PUNCT
ejpam-1858	148	27	4,2	4,2	NOUN
ejpam-1858	148	28	)	)	PUNCT
ejpam-1858	148	29	is	be	AUX
ejpam-1858	148	30	transferred	transfer	VERB
ejpam-1858	148	31	to	to	ADP
ejpam-1858	148	32	the	the	DET
ejpam-1858	148	33	point	point	NOUN
ejpam-1858	148	34	pt+	pt+	NOUN
ejpam-1858	148	35	2	2	X
ejpam-1858	148	36	=	=	SYM
ejpam-1858	148	37	(	(	PUNCT
ejpam-1858	148	38	t2	t2	NOUN
ejpam-1858	148	39	,	,	PUNCT
ejpam-1858	148	40	x+	x+	X
ejpam-1858	148	41	2	2	X
ejpam-1858	148	42	)	)	PUNCT
ejpam-1858	148	43	=	=	SYM
ejpam-1858	148	44	(	(	PUNCT
ejpam-1858	148	45	4,4	4,4	NOUN
ejpam-1858	148	46	)	)	PUNCT
ejpam-1858	148	47	where	where	SCONJ
ejpam-1858	148	48	x+	x+	ADJ
ejpam-1858	148	49	2	2	NUM
ejpam-1858	148	50	=	=	SYM
ejpam-1858	148	51	x2	x2	SYM
ejpam-1858	148	52	2	2	NUM
ejpam-1858	148	53	sgn	sgn	NOUN
ejpam-1858	148	54	x2	x2	NOUN
ejpam-1858	148	55	.	.	PUNCT
ejpam-1858	149	1	as	as	ADP
ejpam-1858	149	2	before	before	ADP
ejpam-1858	149	3	the	the	DET
ejpam-1858	149	4	point	point	NOUN
ejpam-1858	149	5	pt	pt	NOUN
ejpam-1858	149	6	continuous	continuous	ADJ
ejpam-1858	149	7	to	to	PART
ejpam-1858	149	8	move	move	VERB
ejpam-1858	149	9	forward	forward	ADV
ejpam-1858	149	10	with	with	ADP
ejpam-1858	149	11	x(t	x(t	PROPN
ejpam-1858	149	12	)	)	PUNCT
ejpam-1858	150	1	=	=	SYM
ejpam-1858	150	2	x(t	x(t	PROPN
ejpam-1858	150	3	,	,	PUNCT
ejpam-1858	150	4	t2	t2	NOUN
ejpam-1858	150	5	,	,	PUNCT
ejpam-1858	150	6	x+	x+	X
ejpam-1858	150	7	2	2	X
ejpam-1858	150	8	)	)	PUNCT
ejpam-1858	150	9	=	=	SYM
ejpam-1858	150	10	x(t	x(t	PROPN
ejpam-1858	150	11	,	,	PUNCT
ejpam-1858	150	12	4	4	NUM
ejpam-1858	150	13	,	,	PUNCT
ejpam-1858	150	14	4	4	NUM
ejpam-1858	150	15	)	)	PUNCT
ejpam-1858	150	16	as	as	ADP
ejpam-1858	150	17	the	the	DET
ejpam-1858	150	18	solution	solution	NOUN
ejpam-1858	150	19	of	of	ADP
ejpam-1858	150	20	(	(	PUNCT
ejpam-1858	150	21	6	6	NUM
ejpam-1858	150	22	)	)	PUNCT
ejpam-1858	150	23	starting	start	VERB
ejpam-1858	150	24	at	at	ADP
ejpam-1858	150	25	(	(	PUNCT
ejpam-1858	150	26	t2	t2	NOUN
ejpam-1858	150	27	,	,	PUNCT
ejpam-1858	150	28	x+	x+	X
ejpam-1858	150	29	2	2	X
ejpam-1858	150	30	)	)	PUNCT
ejpam-1858	150	31	=	=	SYM
ejpam-1858	150	32	(	(	PUNCT
ejpam-1858	150	33	4,4	4,4	NUM
ejpam-1858	150	34	)	)	PUNCT
ejpam-1858	150	35	until	until	SCONJ
ejpam-1858	150	36	it	it	PRON
ejpam-1858	150	37	hits	hit	VERB
ejpam-1858	150	38	the	the	DET
ejpam-1858	150	39	same	same	ADJ
ejpam-1858	150	40	surface	surface	NOUN
ejpam-1858	150	41	s1	s1	NOUN
ejpam-1858	150	42	at	at	ADP
ejpam-1858	150	43	the	the	DET
ejpam-1858	150	44	moment	moment	NOUN
ejpam-1858	150	45	t3	t3	NOUN
ejpam-1858	150	46	=	=	PUNCT
ejpam-1858	150	47	16	16	NUM
ejpam-1858	150	48	>	>	X
ejpam-1858	150	49	t2	t2	NOUN
ejpam-1858	150	50	=	=	SYM
ejpam-1858	150	51	4	4	X
ejpam-1858	150	52	.	.	PUNCT
ejpam-1858	151	1	then	then	ADV
ejpam-1858	151	2	the	the	DET
ejpam-1858	151	3	point	point	NOUN
ejpam-1858	151	4	(	(	PUNCT
ejpam-1858	151	5	t3	t3	NOUN
ejpam-1858	151	6	,	,	PUNCT
ejpam-1858	151	7	x3	x3	ADJ
ejpam-1858	151	8	)	)	PUNCT
ejpam-1858	151	9	=	=	SYM
ejpam-1858	152	1	(	(	PUNCT
ejpam-1858	152	2	16,4	16,4	NUM
ejpam-1858	152	3	)	)	PUNCT
ejpam-1858	152	4	is	be	AUX
ejpam-1858	152	5	transferred	transfer	VERB
ejpam-1858	152	6	to	to	ADP
ejpam-1858	152	7	the	the	DET
ejpam-1858	152	8	point	point	NOUN
ejpam-1858	152	9	pt+	pt+	NOUN
ejpam-1858	152	10	3	3	X
ejpam-1858	152	11	=	=	SYM
ejpam-1858	152	12	(	(	PUNCT
ejpam-1858	152	13	t3	t3	PROPN
ejpam-1858	152	14	,	,	PUNCT
ejpam-1858	152	15	x+	x+	X
ejpam-1858	152	16	3	3	X
ejpam-1858	152	17	)	)	PUNCT
ejpam-1858	152	18	=	=	PUNCT
ejpam-1858	152	19	(	(	PUNCT
ejpam-1858	152	20	16,16	16,16	NOUN
ejpam-1858	152	21	)	)	PUNCT
ejpam-1858	152	22	,	,	PUNCT
ejpam-1858	153	1	where	where	SCONJ
ejpam-1858	153	2	x+	x+	ADJ
ejpam-1858	153	3	3	3	NUM
ejpam-1858	153	4	=	=	SYM
ejpam-1858	153	5	x2	x2	PROPN
ejpam-1858	153	6	3	3	NUM
ejpam-1858	153	7	sgn	sgn	NOUN
ejpam-1858	153	8	x3	x3	ADJ
ejpam-1858	153	9	and	and	CCONJ
ejpam-1858	153	10	it	it	PRON
ejpam-1858	153	11	does	do	AUX
ejpam-1858	153	12	not	not	PART
ejpam-1858	153	13	encounter	encounter	VERB
ejpam-1858	153	14	any	any	DET
ejpam-1858	153	15	surface	surface	NOUN
ejpam-1858	153	16	,	,	PUNCT
ejpam-1858	153	17	beyond	beyond	ADP
ejpam-1858	153	18	time	time	NOUN
ejpam-1858	153	19	t3	t3	PROPN
ejpam-1858	153	20	=	=	PROPN
ejpam-1858	154	1	16	16	NUM
ejpam-1858	154	2	.	.	PUNCT
ejpam-1858	155	1	in	in	ADP
ejpam-1858	155	2	this	this	DET
ejpam-1858	155	3	case	case	NOUN
ejpam-1858	155	4	the	the	DET
ejpam-1858	155	5	solution	solution	NOUN
ejpam-1858	155	6	x(t	x(t	PROPN
ejpam-1858	155	7	)	)	PUNCT
ejpam-1858	155	8	is	be	AUX
ejpam-1858	155	9	a	a	DET
ejpam-1858	155	10	piecewise	piecewise	NOUN
ejpam-1858	155	11	continuous	continuous	ADJ
ejpam-1858	155	12	function	function	NOUN
ejpam-1858	155	13	having	have	VERB
ejpam-1858	155	14	finite	finite	ADJ
ejpam-1858	155	15	number	number	NOUN
ejpam-1858	155	16	of	of	ADP
ejpam-1858	155	17	discontinuities	discontinuity	NOUN
ejpam-1858	155	18	of	of	ADP
ejpam-1858	155	19	the	the	DET
ejpam-1858	155	20	first	first	ADJ
ejpam-1858	155	21	kind	kind	NOUN
ejpam-1858	155	22	since	since	SCONJ
ejpam-1858	155	23	the	the	DET
ejpam-1858	155	24	integral	integral	ADJ
ejpam-1858	155	25	curve	curve	NOUN
ejpam-1858	155	26	meets	meet	VERB
ejpam-1858	155	27	the	the	DET
ejpam-1858	155	28	surfaces	surface	NOUN
ejpam-1858	155	29	at	at	ADP
ejpam-1858	155	30	a	a	DET
ejpam-1858	155	31	finite	finite	ADJ
ejpam-1858	155	32	number	number	NOUN
ejpam-1858	155	33	of	of	ADP
ejpam-1858	155	34	times	time	NOUN
ejpam-1858	155	35	which	which	PRON
ejpam-1858	155	36	are	be	AUX
ejpam-1858	155	37	not	not	PART
ejpam-1858	155	38	the	the	DET
ejpam-1858	155	39	fixed	fix	VERB
ejpam-1858	155	40	points	point	NOUN
ejpam-1858	155	41	of	of	ADP
ejpam-1858	155	42	the	the	DET
ejpam-1858	155	43	operator	operator	NOUN
ejpam-1858	155	44	a(t	a(t	NOUN
ejpam-1858	155	45	)	)	PUNCT
ejpam-1858	155	46	given	give	VERB
ejpam-1858	155	47	by	by	ADP
ejpam-1858	155	48	a(t)x	a(t)x	NOUN
ejpam-1858	155	49	=	=	SYM
ejpam-1858	155	50	x2	x2	PROPN
ejpam-1858	155	51	sgn	sgn	NOUN
ejpam-1858	155	52	x	x	X
ejpam-1858	155	53	.	.	PUNCT
ejpam-1858	156	1	in	in	ADP
ejpam-1858	156	2	this	this	DET
ejpam-1858	156	3	case	case	NOUN
ejpam-1858	156	4	the	the	DET
ejpam-1858	156	5	solution	solution	NOUN
ejpam-1858	156	6	hit	hit	VERB
ejpam-1858	156	7	the	the	DET
ejpam-1858	156	8	same	same	ADJ
ejpam-1858	156	9	surface	surface	NOUN
ejpam-1858	156	10	s1	s1	NOUN
ejpam-1858	156	11	three	three	NUM
ejpam-1858	156	12	times	time	NOUN
ejpam-1858	156	13	exhibiting	exhibit	VERB
ejpam-1858	156	14	pulse	pulse	NOUN
ejpam-1858	156	15	phenomenon	phenomenon	NOUN
ejpam-1858	156	16	,	,	PUNCT
ejpam-1858	156	17	see	see	VERB
ejpam-1858	156	18	figure	figure	NOUN
ejpam-1858	156	19	1b	1b	NUM
ejpam-1858	156	20	.	.	PUNCT
ejpam-1858	157	1	case	case	NOUN
ejpam-1858	157	2	(	(	PUNCT
ejpam-1858	157	3	3	3	X
ejpam-1858	157	4	)	)	PUNCT
ejpam-1858	157	5	the	the	DET
ejpam-1858	157	6	solutions	solution	NOUN
ejpam-1858	157	7	x(t	x(t	PROPN
ejpam-1858	157	8	)	)	PUNCT
ejpam-1858	157	9	starting	start	VERB
ejpam-1858	157	10	at	at	ADP
ejpam-1858	157	11	the	the	DET
ejpam-1858	157	12	points	point	NOUN
ejpam-1858	157	13	(	(	PUNCT
ejpam-1858	157	14	0	0	NUM
ejpam-1858	157	15	,	,	PUNCT
ejpam-1858	157	16	x0	x0	PROPN
ejpam-1858	157	17	)	)	PUNCT
ejpam-1858	157	18	,	,	PUNCT
ejpam-1858	157	19	0	0	PUNCT
ejpam-1858	157	20	<	<	X
ejpam-1858	157	21	x0	x0	PROPN
ejpam-1858	157	22	<	<	X
ejpam-1858	157	23	1	1	NUM
ejpam-1858	157	24	,	,	PUNCT
ejpam-1858	157	25	meets	meet	VERB
ejpam-1858	157	26	the	the	DET
ejpam-1858	157	27	surfaces	surface	NOUN
ejpam-1858	157	28	sk	sk	VERB
ejpam-1858	157	29	at	at	ADP
ejpam-1858	157	30	an	an	DET
ejpam-1858	157	31	infinite	infinite	ADJ
ejpam-1858	157	32	number	number	NOUN
ejpam-1858	157	33	of	of	ADP
ejpam-1858	157	34	times	time	NOUN
ejpam-1858	157	35	tk	tk	PROPN
ejpam-1858	158	1	and	and	CCONJ
ejpam-1858	158	2	we	we	PRON
ejpam-1858	158	3	have	have	VERB
ejpam-1858	158	4	tk→∞	tk→∞	NUM
ejpam-1858	158	5	as	as	ADV
ejpam-1858	158	6	k→∞	k→∞	ADV
ejpam-1858	158	7	as	as	ADV
ejpam-1858	158	8	well	well	ADV
ejpam-1858	158	9	as	as	ADP
ejpam-1858	158	10	limk→∞	limk→∞	ADJ
ejpam-1858	158	11	x(tk	x(tk	PROPN
ejpam-1858	158	12	)	)	PUNCT
ejpam-1858	159	1	=	=	SYM
ejpam-1858	159	2	0	0	X
ejpam-1858	159	3	.	.	X
ejpam-1858	160	1	for	for	ADP
ejpam-1858	160	2	example	example	NOUN
ejpam-1858	160	3	,	,	PUNCT
ejpam-1858	160	4	let	let	VERB
ejpam-1858	160	5	us	we	PRON
ejpam-1858	160	6	take	take	VERB
ejpam-1858	160	7	x0	x0	PROPN
ejpam-1858	160	8	=	=	PUNCT
ejpam-1858	160	9	0.9	0.9	NUM
ejpam-1858	160	10	.	.	PUNCT
ejpam-1858	161	1	the	the	DET
ejpam-1858	161	2	solution	solution	NOUN
ejpam-1858	161	3	x(t	x(t	PROPN
ejpam-1858	161	4	)	)	PUNCT
ejpam-1858	161	5	begins	begin	VERB
ejpam-1858	161	6	its	its	PRON
ejpam-1858	161	7	motion	motion	NOUN
ejpam-1858	161	8	at	at	ADP
ejpam-1858	161	9	(	(	PUNCT
ejpam-1858	161	10	0,0.9	0,0.9	NOUN
ejpam-1858	161	11	)	)	PUNCT
ejpam-1858	161	12	and	and	CCONJ
ejpam-1858	161	13	continuous	continuous	ADJ
ejpam-1858	161	14	to	to	PART
ejpam-1858	161	15	move	move	VERB
ejpam-1858	161	16	along	along	ADP
ejpam-1858	161	17	the	the	DET
ejpam-1858	161	18	curve	curve	NOUN
ejpam-1858	161	19	x	x	PUNCT
ejpam-1858	162	1	=	=	PUNCT
ejpam-1858	162	2	0.9	0.9	NUM
ejpam-1858	162	3	until	until	SCONJ
ejpam-1858	162	4	it	it	PRON
ejpam-1858	162	5	hits	hit	VERB
ejpam-1858	162	6	the	the	DET
ejpam-1858	162	7	surface	surface	NOUN
ejpam-1858	162	8	s1	s1	NOUN
ejpam-1858	163	1	:	:	PUNCT
ejpam-1858	163	2	t	t	X
ejpam-1858	163	3	=	=	PUNCT
ejpam-1858	164	1	x2	x2	PROPN
ejpam-1858	164	2	at	at	ADP
ejpam-1858	164	3	(	(	PUNCT
ejpam-1858	164	4	0.81,0.9	0.81,0.9	NOUN
ejpam-1858	164	5	)	)	PUNCT
ejpam-1858	164	6	.	.	PUNCT
ejpam-1858	165	1	this	this	DET
ejpam-1858	165	2	point	point	NOUN
ejpam-1858	165	3	(	(	PUNCT
ejpam-1858	165	4	0.81,0.9	0.81,0.9	NOUN
ejpam-1858	165	5	)	)	PUNCT
ejpam-1858	165	6	is	be	AUX
ejpam-1858	165	7	transferred	transfer	VERB
ejpam-1858	165	8	to	to	ADP
ejpam-1858	165	9	(	(	PUNCT
ejpam-1858	165	10	0.81,0.81	0.81,0.81	NUM
ejpam-1858	165	11	)	)	PUNCT
ejpam-1858	165	12	.	.	PUNCT
ejpam-1858	166	1	then	then	ADV
ejpam-1858	166	2	the	the	DET
ejpam-1858	166	3	solution	solution	NOUN
ejpam-1858	166	4	starts	start	VERB
ejpam-1858	166	5	at	at	ADP
ejpam-1858	166	6	(	(	PUNCT
ejpam-1858	166	7	0.81,0.81	0.81,0.81	NUM
ejpam-1858	166	8	)	)	PUNCT
ejpam-1858	166	9	and	and	CCONJ
ejpam-1858	166	10	continuous	continuous	ADJ
ejpam-1858	166	11	to	to	PART
ejpam-1858	166	12	move	move	VERB
ejpam-1858	166	13	along	along	ADP
ejpam-1858	166	14	the	the	DET
ejpam-1858	166	15	line	line	NOUN
ejpam-1858	166	16	x	x	PUNCT
ejpam-1858	166	17	=	=	PUNCT
ejpam-1858	166	18	0.81	0.81	NUM
ejpam-1858	166	19	until	until	SCONJ
ejpam-1858	166	20	it	it	PRON
ejpam-1858	166	21	hits	hit	VERB
ejpam-1858	166	22	the	the	DET
ejpam-1858	166	23	surface	surface	NOUN
ejpam-1858	166	24	s2	s2	NOUN
ejpam-1858	166	25	:	:	PUNCT
ejpam-1858	166	26	t	t	X
ejpam-1858	166	27	=	=	PUNCT
ejpam-1858	167	1	x2	x2	PROPN
ejpam-1858	168	1	+	+	CCONJ
ejpam-1858	168	2	20	20	NUM
ejpam-1858	168	3	at	at	ADP
ejpam-1858	168	4	(	(	PUNCT
ejpam-1858	168	5	20.6561,0.81	20.6561,0.81	NUM
ejpam-1858	168	6	)	)	PUNCT
ejpam-1858	168	7	.	.	PUNCT
ejpam-1858	169	1	it	it	PRON
ejpam-1858	169	2	is	be	AUX
ejpam-1858	169	3	then	then	ADV
ejpam-1858	169	4	transferred	transfer	VERB
ejpam-1858	169	5	to	to	ADP
ejpam-1858	169	6	(	(	PUNCT
ejpam-1858	169	7	20.6561,0.6561	20.6561,0.6561	NOUN
ejpam-1858	169	8	)	)	PUNCT
ejpam-1858	169	9	.	.	PUNCT
ejpam-1858	170	1	the	the	DET
ejpam-1858	170	2	solution	solution	NOUN
ejpam-1858	170	3	then	then	ADV
ejpam-1858	170	4	starts	start	VERB
ejpam-1858	170	5	at	at	ADP
ejpam-1858	170	6	(	(	PUNCT
ejpam-1858	170	7	20.6561,0.6561	20.6561,0.6561	NOUN
ejpam-1858	170	8	)	)	PUNCT
ejpam-1858	170	9	and	and	CCONJ
ejpam-1858	170	10	continuous	continuous	ADJ
ejpam-1858	170	11	to	to	PART
ejpam-1858	170	12	move	move	VERB
ejpam-1858	170	13	until	until	SCONJ
ejpam-1858	170	14	it	it	PRON
ejpam-1858	170	15	hits	hit	VERB
ejpam-1858	170	16	the	the	DET
ejpam-1858	170	17	surface	surface	NOUN
ejpam-1858	170	18	s3	s3	PROPN
ejpam-1858	170	19	:	:	PUNCT
ejpam-1858	170	20	t	t	NOUN
ejpam-1858	170	21	=	=	SYM
ejpam-1858	170	22	x2	x2	PROPN
ejpam-1858	171	1	+	+	PROPN
ejpam-1858	171	2	40	40	NUM
ejpam-1858	171	3	at	at	ADP
ejpam-1858	171	4	(	(	PUNCT
ejpam-1858	171	5	40.43047,0.6561	40.43047,0.6561	NOUN
ejpam-1858	171	6	)	)	PUNCT
ejpam-1858	171	7	and	and	CCONJ
ejpam-1858	171	8	so	so	ADV
ejpam-1858	171	9	on	on	ADV
ejpam-1858	171	10	.	.	PUNCT
ejpam-1858	172	1	as	as	SCONJ
ejpam-1858	172	2	k→∞we	k→∞we	PROPN
ejpam-1858	172	3	have	have	VERB
ejpam-1858	172	4	limk→∞	limk→∞	NOUN
ejpam-1858	172	5	x(tk	x(tk	PROPN
ejpam-1858	172	6	)	)	PUNCT
ejpam-1858	172	7	=	=	SYM
ejpam-1858	173	1	0	0	X
ejpam-1858	173	2	.	.	PUNCT
ejpam-1858	174	1	in	in	ADP
ejpam-1858	174	2	this	this	DET
ejpam-1858	174	3	case	case	NOUN
ejpam-1858	174	4	the	the	DET
ejpam-1858	174	5	solution	solution	NOUN
ejpam-1858	174	6	undergo	undergo	VERB
ejpam-1858	174	7	an	an	DET
ejpam-1858	174	8	impulsive	impulsive	ADJ
ejpam-1858	174	9	effect	effect	NOUN
ejpam-1858	174	10	an	an	DET
ejpam-1858	174	11	infinite	infinite	ADJ
ejpam-1858	174	12	number	number	NOUN
ejpam-1858	174	13	of	of	ADP
ejpam-1858	174	14	times	time	NOUN
ejpam-1858	174	15	,	,	PUNCT
ejpam-1858	174	16	see	see	VERB
ejpam-1858	174	17	figure	figure	NOUN
ejpam-1858	174	18	1c	1c	NOUN
ejpam-1858	174	19	.	.	PUNCT
ejpam-1858	175	1	case	case	NOUN
ejpam-1858	175	2	(	(	PUNCT
ejpam-1858	175	3	4	4	X
ejpam-1858	175	4	)	)	PUNCT
ejpam-1858	175	5	the	the	DET
ejpam-1858	175	6	solutions	solution	NOUN
ejpam-1858	175	7	starting	start	VERB
ejpam-1858	175	8	at	at	ADP
ejpam-1858	175	9	(	(	PUNCT
ejpam-1858	175	10	0,0	0,0	NOUN
ejpam-1858	175	11	)	)	PUNCT
ejpam-1858	175	12	,	,	PUNCT
ejpam-1858	175	13	(	(	PUNCT
ejpam-1858	175	14	0,1	0,1	NOUN
ejpam-1858	175	15	)	)	PUNCT
ejpam-1858	175	16	and	and	CCONJ
ejpam-1858	175	17	(	(	PUNCT
ejpam-1858	175	18	0,−1	0,−1	NUM
ejpam-1858	175	19	)	)	PUNCT
ejpam-1858	175	20	hit	hit	VERB
ejpam-1858	175	21	the	the	DET
ejpam-1858	175	22	surface	surface	NOUN
ejpam-1858	175	23	sk	sk	NOUN
ejpam-1858	175	24	at	at	ADP
ejpam-1858	175	25	times	times	PROPN
ejpam-1858	175	26	tk	tk	PROPN
ejpam-1858	175	27	,	,	PUNCT
ejpam-1858	175	28	(	(	PUNCT
ejpam-1858	175	29	k	k	NOUN
ejpam-1858	175	30	=	=	SYM
ejpam-1858	175	31	0,1,2,3	0,1,2,3	NUM
ejpam-1858	175	32	,	,	PUNCT
ejpam-1858	175	33	.	.	PUNCT
ejpam-1858	175	34	.	.	PUNCT
ejpam-1858	176	1	.	.	PUNCT
ejpam-1858	176	2	)	)	PUNCT
ejpam-1858	177	1	which	which	PRON
ejpam-1858	177	2	are	be	AUX
ejpam-1858	177	3	the	the	DET
ejpam-1858	177	4	fixed	fix	VERB
ejpam-1858	177	5	points	point	NOUN
ejpam-1858	177	6	of	of	ADP
ejpam-1858	177	7	the	the	DET
ejpam-1858	177	8	operator	operator	NOUN
ejpam-1858	177	9	a(t	a(t	NOUN
ejpam-1858	177	10	)	)	PUNCT
ejpam-1858	178	1	x	x	X
ejpam-1858	178	2	=	=	SYM
ejpam-1858	178	3	x2	x2	PROPN
ejpam-1858	178	4	sgn	sgn	NOUN
ejpam-1858	178	5	x	x	X
ejpam-1858	178	6	,	,	PUNCT
ejpam-1858	178	7	and	and	CCONJ
ejpam-1858	178	8	there	there	PRON
ejpam-1858	178	9	is	be	VERB
ejpam-1858	178	10	no	no	DET
ejpam-1858	178	11	impulsive	impulsive	ADJ
ejpam-1858	178	12	effect	effect	NOUN
ejpam-1858	178	13	,	,	PUNCT
ejpam-1858	178	14	see	see	VERB
ejpam-1858	178	15	figure	figure	NOUN
ejpam-1858	178	16	1d	1d	NUM
ejpam-1858	178	17	.	.	PUNCT
ejpam-1858	179	1	case	case	NOUN
ejpam-1858	179	2	(	(	PUNCT
ejpam-1858	179	3	5	5	X
ejpam-1858	179	4	)	)	PUNCT
ejpam-1858	179	5	the	the	DET
ejpam-1858	179	6	solutions	solution	NOUN
ejpam-1858	179	7	starting	start	VERB
ejpam-1858	179	8	at	at	ADP
ejpam-1858	179	9	�	�	PROPN
ejpam-1858	179	10	0,2	0,2	NUM
ejpam-1858	179	11	1	1	NUM
ejpam-1858	179	12	8	8	NUM
ejpam-1858	179	13	�	�	PROPN
ejpam-1858	179	14	,	,	PUNCT
ejpam-1858	179	15	�	�	PROPN
ejpam-1858	179	16	0,2	0,2	NUM
ejpam-1858	179	17	1	1	NUM
ejpam-1858	179	18	4	4	NUM
ejpam-1858	179	19	�	�	PROPN
ejpam-1858	179	20	,	,	PUNCT
ejpam-1858	179	21	�	�	PROPN
ejpam-1858	179	22	0,2	0,2	NUM
ejpam-1858	179	23	1	1	NUM
ejpam-1858	179	24	2	2	NUM
ejpam-1858	179	25	�	�	NOUN
ejpam-1858	179	26	unite	unite	VERB
ejpam-1858	179	27	for	for	ADP
ejpam-1858	179	28	t	t	PROPN
ejpam-1858	179	29	≥	≥	NOUN
ejpam-1858	179	30	p2	p2	PROPN
ejpam-1858	179	31	and	and	CCONJ
ejpam-1858	179	32	thus	thus	ADV
ejpam-1858	179	33	exhibit	exhibit	VERB
ejpam-1858	179	34	the	the	DET
ejpam-1858	179	35	phenomenon	phenomenon	NOUN
ejpam-1858	179	36	of	of	ADP
ejpam-1858	179	37	confluence	confluence	NOUN
ejpam-1858	179	38	,	,	PUNCT
ejpam-1858	179	39	see	see	VERB
ejpam-1858	179	40	figure	figure	NOUN
ejpam-1858	179	41	1e	1e	NOUN
ejpam-1858	179	42	.	.	PUNCT
ejpam-1858	180	1	j.	j.	PROPN
ejpam-1858	180	2	devi	devi	PROPN
ejpam-1858	180	3	,	,	PUNCT
ejpam-1858	180	4	n.	n.	PROPN
ejpam-1858	180	5	giribabu	giribabu	PROPN
ejpam-1858	180	6	/	/	SYM
ejpam-1858	180	7	eur	eur	PROPN
ejpam-1858	180	8	.	.	PUNCT
ejpam-1858	181	1	j.	j.	PROPN
ejpam-1858	181	2	pure	pure	PROPN
ejpam-1858	181	3	appl	appl	PROPN
ejpam-1858	181	4	.	.	PROPN
ejpam-1858	181	5	math	math	PROPN
ejpam-1858	181	6	,	,	PUNCT
ejpam-1858	181	7	7	7	NUM
ejpam-1858	181	8	(	(	PUNCT
ejpam-1858	181	9	2014	2014	NUM
ejpam-1858	181	10	)	)	PUNCT
ejpam-1858	181	11	,	,	PUNCT
ejpam-1858	181	12	115	115	NUM
ejpam-1858	181	13	-	-	SYM
ejpam-1858	181	14	128	128	NUM
ejpam-1858	181	15	122	122	NUM
ejpam-1858	181	16	0	0	NUM
ejpam-1858	181	17	50	50	NUM
ejpam-1858	181	18	100	100	NUM
ejpam-1858	181	19	150	150	NUM
ejpam-1858	181	20	−10	−10	NOUN
ejpam-1858	182	1	−8	−8	X
ejpam-1858	183	1	−6	−6	INTJ
ejpam-1858	184	1	−4	−4	X
ejpam-1858	185	1	−2	−2	NOUN
ejpam-1858	185	2	0	0	NUM
ejpam-1858	185	3	2	2	NUM
ejpam-1858	185	4	4	4	NUM
ejpam-1858	185	5	6	6	NUM
ejpam-1858	185	6	8	8	NUM
ejpam-1858	185	7	10	10	NUM
ejpam-1858	185	8	t−axis	t−axis	NOUN
ejpam-1858	185	9	x−	x−	NOUN
ejpam-1858	185	10	ax	ax	NOUN
ejpam-1858	185	11	is	be	AUX
ejpam-1858	185	12	s	s	PROPN
ejpam-1858	185	13	1	1	NUM
ejpam-1858	185	14	s	s	NUM
ejpam-1858	185	15	2	2	NUM
ejpam-1858	185	16	s	s	PART
ejpam-1858	185	17	3	3	NUM
ejpam-1858	185	18	s	s	PART
ejpam-1858	185	19	4	4	NUM
ejpam-1858	185	20	s	s	NOUN
ejpam-1858	185	21	5	5	NUM
ejpam-1858	185	22	x	x	NOUN
ejpam-1858	185	23	=	=	NOUN
ejpam-1858	185	24	x(t,0,8.5	x(t,0,8.5	X
ejpam-1858	185	25	)	)	PUNCT
ejpam-1858	185	26	(	(	PUNCT
ejpam-1858	185	27	a	a	X
ejpam-1858	185	28	)	)	PUNCT
ejpam-1858	185	29	case	case	NOUN
ejpam-1858	185	30	(	(	PUNCT
ejpam-1858	185	31	1	1	NUM
ejpam-1858	185	32	)	)	PUNCT
ejpam-1858	185	33	0	0	NUM
ejpam-1858	185	34	50	50	NUM
ejpam-1858	185	35	100	100	NUM
ejpam-1858	185	36	150	150	NUM
ejpam-1858	185	37	−10	−10	NOUN
ejpam-1858	186	1	−8	−8	X
ejpam-1858	187	1	−6	−6	INTJ
ejpam-1858	188	1	−4	−4	X
ejpam-1858	189	1	−2	−2	NOUN
ejpam-1858	189	2	0	0	NUM
ejpam-1858	189	3	2	2	NUM
ejpam-1858	189	4	4	4	NUM
ejpam-1858	189	5	6	6	NUM
ejpam-1858	189	6	8	8	NUM
ejpam-1858	189	7	10	10	NUM
ejpam-1858	189	8	t−axis	t−axis	NOUN
ejpam-1858	189	9	x−	x−	NOUN
ejpam-1858	189	10	ax	ax	NOUN
ejpam-1858	189	11	is	be	AUX
ejpam-1858	189	12	s	s	PROPN
ejpam-1858	189	13	1	1	NUM
ejpam-1858	189	14	s	s	NUM
ejpam-1858	189	15	2	2	NUM
ejpam-1858	189	16	s	s	PART
ejpam-1858	189	17	3	3	NUM
ejpam-1858	189	18	s	s	PART
ejpam-1858	189	19	4	4	NUM
ejpam-1858	189	20	s	s	NOUN
ejpam-1858	189	21	5	5	NUM
ejpam-1858	189	22	(	(	PUNCT
ejpam-1858	189	23	b	b	NOUN
ejpam-1858	189	24	)	)	PUNCT
ejpam-1858	189	25	case	case	NOUN
ejpam-1858	189	26	(	(	PUNCT
ejpam-1858	189	27	2	2	NUM
ejpam-1858	189	28	)	)	PUNCT
ejpam-1858	189	29	0	0	NUM
ejpam-1858	189	30	50	50	NUM
ejpam-1858	189	31	100	100	NUM
ejpam-1858	189	32	150	150	NUM
ejpam-1858	189	33	−10	−10	NOUN
ejpam-1858	190	1	−8	−8	X
ejpam-1858	191	1	−6	−6	INTJ
ejpam-1858	192	1	−4	−4	X
ejpam-1858	193	1	−2	−2	NOUN
ejpam-1858	193	2	0	0	NUM
ejpam-1858	193	3	2	2	NUM
ejpam-1858	193	4	4	4	NUM
ejpam-1858	193	5	6	6	NUM
ejpam-1858	193	6	8	8	NUM
ejpam-1858	193	7	10	10	NUM
ejpam-1858	193	8	t−axis	t−axis	NOUN
ejpam-1858	193	9	x−	x−	NOUN
ejpam-1858	193	10	ax	ax	NOUN
ejpam-1858	193	11	is	be	AUX
ejpam-1858	193	12	s	s	PROPN
ejpam-1858	193	13	1	1	NUM
ejpam-1858	193	14	s	s	NUM
ejpam-1858	193	15	2	2	NUM
ejpam-1858	193	16	s	s	PART
ejpam-1858	193	17	3	3	NUM
ejpam-1858	193	18	s	s	PART
ejpam-1858	193	19	4	4	NUM
ejpam-1858	193	20	s	s	NOUN
ejpam-1858	193	21	5	5	NUM
ejpam-1858	193	22	(	(	PUNCT
ejpam-1858	193	23	c	c	NOUN
ejpam-1858	193	24	)	)	PUNCT
ejpam-1858	193	25	case	case	NOUN
ejpam-1858	193	26	(	(	PUNCT
ejpam-1858	193	27	3	3	NUM
ejpam-1858	193	28	)	)	PUNCT
ejpam-1858	193	29	0	0	NUM
ejpam-1858	193	30	50	50	NUM
ejpam-1858	193	31	100	100	NUM
ejpam-1858	193	32	150	150	NUM
ejpam-1858	193	33	−10	−10	NOUN
ejpam-1858	194	1	−8	−8	X
ejpam-1858	195	1	−6	−6	INTJ
ejpam-1858	196	1	−4	−4	X
ejpam-1858	197	1	−2	−2	NOUN
ejpam-1858	197	2	0	0	NUM
ejpam-1858	197	3	2	2	NUM
ejpam-1858	197	4	4	4	NUM
ejpam-1858	197	5	6	6	NUM
ejpam-1858	197	6	8	8	NUM
ejpam-1858	197	7	10	10	NUM
ejpam-1858	197	8	t−axis	t−axis	NOUN
ejpam-1858	197	9	x−	x−	NOUN
ejpam-1858	197	10	ax	ax	NOUN
ejpam-1858	197	11	is	be	AUX
ejpam-1858	197	12	s	s	PROPN
ejpam-1858	197	13	1	1	NUM
ejpam-1858	197	14	s	s	NUM
ejpam-1858	197	15	2	2	NUM
ejpam-1858	197	16	s	s	PART
ejpam-1858	197	17	3	3	NUM
ejpam-1858	197	18	s	s	PART
ejpam-1858	197	19	4	4	NUM
ejpam-1858	197	20	s	s	NOUN
ejpam-1858	197	21	5	5	NUM
ejpam-1858	197	22	(	(	PUNCT
ejpam-1858	197	23	d	d	NOUN
ejpam-1858	197	24	)	)	PUNCT
ejpam-1858	197	25	case	case	NOUN
ejpam-1858	197	26	(	(	PUNCT
ejpam-1858	197	27	4	4	NUM
ejpam-1858	197	28	)	)	PUNCT
ejpam-1858	197	29	0	0	NUM
ejpam-1858	197	30	50	50	NUM
ejpam-1858	197	31	100	100	NUM
ejpam-1858	197	32	150	150	NUM
ejpam-1858	197	33	−10	−10	NOUN
ejpam-1858	198	1	−8	−8	X
ejpam-1858	199	1	−6	−6	INTJ
ejpam-1858	200	1	−4	−4	X
ejpam-1858	201	1	−2	−2	NOUN
ejpam-1858	201	2	0	0	NUM
ejpam-1858	201	3	2	2	NUM
ejpam-1858	201	4	4	4	NUM
ejpam-1858	201	5	6	6	NUM
ejpam-1858	201	6	8	8	NUM
ejpam-1858	201	7	10	10	NUM
ejpam-1858	201	8	t−axis	t−axis	NOUN
ejpam-1858	201	9	x−	x−	NOUN
ejpam-1858	201	10	ax	ax	NOUN
ejpam-1858	201	11	is	be	AUX
ejpam-1858	201	12	s	s	PROPN
ejpam-1858	201	13	1	1	NUM
ejpam-1858	201	14	s	s	NUM
ejpam-1858	201	15	2	2	NUM
ejpam-1858	201	16	s	s	PART
ejpam-1858	201	17	3	3	NUM
ejpam-1858	201	18	s	s	PART
ejpam-1858	201	19	4	4	NUM
ejpam-1858	201	20	s	s	NOUN
ejpam-1858	201	21	5	5	NUM
ejpam-1858	201	22	(	(	PUNCT
ejpam-1858	201	23	e	e	NOUN
ejpam-1858	201	24	)	)	PUNCT
ejpam-1858	201	25	case	case	NOUN
ejpam-1858	201	26	(	(	PUNCT
ejpam-1858	201	27	5	5	NUM
ejpam-1858	201	28	)	)	PUNCT
ejpam-1858	201	29	figure	figure	NOUN
ejpam-1858	201	30	1	1	NUM
ejpam-1858	201	31	:	:	PUNCT
ejpam-1858	201	32	solutions	solution	NOUN
ejpam-1858	201	33	to	to	ADP
ejpam-1858	201	34	(	(	PUNCT
ejpam-1858	201	35	6	6	NUM
ejpam-1858	201	36	)	)	PUNCT
ejpam-1858	201	37	j.	j.	PROPN
ejpam-1858	201	38	devi	devi	PROPN
ejpam-1858	201	39	,	,	PUNCT
ejpam-1858	201	40	n.	n.	PROPN
ejpam-1858	201	41	giribabu	giribabu	PROPN
ejpam-1858	201	42	/	/	SYM
ejpam-1858	201	43	eur	eur	PROPN
ejpam-1858	201	44	.	.	PUNCT
ejpam-1858	202	1	j.	j.	PROPN
ejpam-1858	202	2	pure	pure	PROPN
ejpam-1858	202	3	appl	appl	PROPN
ejpam-1858	202	4	.	.	PROPN
ejpam-1858	202	5	math	math	PROPN
ejpam-1858	202	6	,	,	PUNCT
ejpam-1858	202	7	7	7	NUM
ejpam-1858	202	8	(	(	PUNCT
ejpam-1858	202	9	2014	2014	NUM
ejpam-1858	202	10	)	)	PUNCT
ejpam-1858	202	11	,	,	PUNCT
ejpam-1858	202	12	115	115	NUM
ejpam-1858	202	13	-	-	SYM
ejpam-1858	202	14	128	128	NUM
ejpam-1858	202	15	123	123	NUM
ejpam-1858	202	16	5	5	NUM
ejpam-1858	202	17	.	.	PUNCT
ejpam-1858	203	1	existence	existence	NOUN
ejpam-1858	203	2	and	and	CCONJ
ejpam-1858	203	3	continuation	continuation	NOUN
ejpam-1858	203	4	of	of	ADP
ejpam-1858	203	5	solutions	solution	NOUN
ejpam-1858	203	6	the	the	DET
ejpam-1858	203	7	example	example	NOUN
ejpam-1858	203	8	in	in	ADP
ejpam-1858	203	9	section	section	NOUN
ejpam-1858	203	10	3	3	NUM
ejpam-1858	203	11	,	,	PUNCT
ejpam-1858	203	12	points	point	VERB
ejpam-1858	203	13	to	to	ADP
ejpam-1858	203	14	the	the	DET
ejpam-1858	203	15	rich	rich	ADJ
ejpam-1858	203	16	potential	potential	NOUN
ejpam-1858	203	17	that	that	SCONJ
ejpam-1858	203	18	caputo	caputo	PROPN
ejpam-1858	203	19	fractional	fractional	PROPN
ejpam-1858	203	20	differential	differential	ADJ
ejpam-1858	203	21	equation	equation	NOUN
ejpam-1858	203	22	with	with	ADP
ejpam-1858	203	23	variable	variable	ADJ
ejpam-1858	203	24	moments	moment	NOUN
ejpam-1858	203	25	of	of	ADP
ejpam-1858	203	26	impulse	impulse	ADJ
ejpam-1858	203	27	offers	offer	NOUN
ejpam-1858	203	28	.	.	PUNCT
ejpam-1858	204	1	the	the	DET
ejpam-1858	204	2	first	first	ADJ
ejpam-1858	204	3	question	question	NOUN
ejpam-1858	204	4	that	that	SCONJ
ejpam-1858	204	5	one	one	NOUN
ejpam-1858	204	6	comes	come	VERB
ejpam-1858	204	7	across	across	ADV
ejpam-1858	204	8	is	be	AUX
ejpam-1858	204	9	to	to	PART
ejpam-1858	204	10	discuss	discuss	VERB
ejpam-1858	204	11	the	the	DET
ejpam-1858	204	12	meaning	meaning	NOUN
ejpam-1858	204	13	of	of	ADP
ejpam-1858	204	14	a	a	DET
ejpam-1858	204	15	solution	solution	NOUN
ejpam-1858	204	16	of	of	ADP
ejpam-1858	204	17	this	this	DET
ejpam-1858	204	18	equation	equation	NOUN
ejpam-1858	204	19	and	and	CCONJ
ejpam-1858	204	20	obtain	obtain	VERB
ejpam-1858	204	21	an	an	DET
ejpam-1858	204	22	existence	existence	NOUN
ejpam-1858	204	23	result	result	NOUN
ejpam-1858	204	24	.	.	PUNCT
ejpam-1858	205	1	in	in	ADP
ejpam-1858	205	2	this	this	DET
ejpam-1858	205	3	section	section	NOUN
ejpam-1858	205	4	we	we	PRON
ejpam-1858	205	5	answer	answer	VERB
ejpam-1858	205	6	this	this	DET
ejpam-1858	205	7	question	question	NOUN
ejpam-1858	205	8	.	.	PUNCT
ejpam-1858	206	1	we	we	PRON
ejpam-1858	206	2	define	define	VERB
ejpam-1858	206	3	the	the	DET
ejpam-1858	206	4	solution	solution	NOUN
ejpam-1858	206	5	of	of	ADP
ejpam-1858	206	6	caputo	caputo	PROPN
ejpam-1858	206	7	fractional	fractional	PROPN
ejpam-1858	206	8	differential	differential	NOUN
ejpam-1858	206	9	equation	equation	NOUN
ejpam-1858	206	10	with	with	ADP
ejpam-1858	206	11	variable	variable	ADJ
ejpam-1858	206	12	moments	moment	NOUN
ejpam-1858	206	13	of	of	ADP
ejpam-1858	206	14	impulse	impulse	ADJ
ejpam-1858	206	15	and	and	CCONJ
ejpam-1858	206	16	proceed	proceed	VERB
ejpam-1858	206	17	to	to	PART
ejpam-1858	206	18	prove	prove	VERB
ejpam-1858	206	19	an	an	DET
ejpam-1858	206	20	existence	existence	NOUN
ejpam-1858	206	21	result	result	NOUN
ejpam-1858	206	22	.	.	PUNCT
ejpam-1858	207	1	consider	consider	VERB
ejpam-1858	207	2	an	an	DET
ejpam-1858	207	3	open	open	ADJ
ejpam-1858	207	4	set	set	NOUN
ejpam-1858	207	5	ω	ω	PROPN
ejpam-1858	207	6	⊂	⊂	PROPN
ejpam-1858	207	7	r	r	NOUN
ejpam-1858	207	8	and	and	CCONJ
ejpam-1858	207	9	set	set	VERB
ejpam-1858	207	10	d	d	NOUN
ejpam-1858	207	11	=	=	PUNCT
ejpam-1858	207	12	r+	r+	NOUN
ejpam-1858	207	13	×ω	×ω	X
ejpam-1858	207	14	.	.	PUNCT
ejpam-1858	207	15	suppose	suppose	VERB
ejpam-1858	207	16	that	that	SCONJ
ejpam-1858	207	17	for	for	ADP
ejpam-1858	207	18	each	each	PRON
ejpam-1858	207	19	k	k	NOUN
ejpam-1858	207	20	=	=	PUNCT
ejpam-1858	207	21	1,2,3	1,2,3	NUM
ejpam-1858	207	22	,	,	PUNCT
ejpam-1858	207	23	.	.	PUNCT
ejpam-1858	207	24	.	.	PUNCT
ejpam-1858	208	1	.	.	PUNCT
ejpam-1858	209	1	,	,	PUNCT
ejpam-1858	209	2	τk	τk	ADP
ejpam-1858	209	3	∈	∈	PROPN
ejpam-1858	209	4	c[ω	c[ω	PROPN
ejpam-1858	209	5	,	,	PUNCT
ejpam-1858	209	6	(	(	PUNCT
ejpam-1858	209	7	0,∞	0,∞	NOUN
ejpam-1858	209	8	)	)	PUNCT
ejpam-1858	209	9	]	]	PUNCT
ejpam-1858	209	10	,	,	PUNCT
ejpam-1858	209	11	τk(x	τk(x	PUNCT
ejpam-1858	209	12	)	)	PUNCT
ejpam-1858	209	13	<	<	X
ejpam-1858	209	14	τk+1(x	τk+1(x	PROPN
ejpam-1858	209	15	)	)	PUNCT
ejpam-1858	209	16	and	and	CCONJ
ejpam-1858	209	17	limk→∞	limk→∞	PROPN
ejpam-1858	209	18	τk(x	τk(x	PUNCT
ejpam-1858	209	19	)	)	PUNCT
ejpam-1858	209	20	=	=	SYM
ejpam-1858	209	21	∞	∞	NUM
ejpam-1858	209	22	for	for	ADP
ejpam-1858	209	23	x	x	PROPN
ejpam-1858	209	24	∈	∈	PROPN
ejpam-1858	209	25	ω	ω	PROPN
ejpam-1858	209	26	.	.	PUNCT
ejpam-1858	209	27	suppose	suppose	VERB
ejpam-1858	209	28	that	that	SCONJ
ejpam-1858	209	29	k	k	PROPN
ejpam-1858	209	30	varies	vary	VERB
ejpam-1858	209	31	from	from	ADP
ejpam-1858	209	32	1	1	NUM
ejpam-1858	209	33	to∞.	to∞.	NOUN
ejpam-1858	209	34	also	also	ADV
ejpam-1858	209	35	assume	assume	VERB
ejpam-1858	209	36	that	that	SCONJ
ejpam-1858	209	37	sk	sk	X
ejpam-1858	209	38	:	:	PUNCT
ejpam-1858	209	39	t	t	PROPN
ejpam-1858	209	40	=	=	PUNCT
ejpam-1858	209	41	τk(x	τk(x	X
ejpam-1858	209	42	)	)	PUNCT
ejpam-1858	209	43	are	be	AUX
ejpam-1858	209	44	the	the	DET
ejpam-1858	209	45	surfaces	surface	NOUN
ejpam-1858	209	46	.	.	PUNCT
ejpam-1858	210	1	consider	consider	VERB
ejpam-1858	210	2	the	the	DET
ejpam-1858	210	3	initial	initial	ADJ
ejpam-1858	210	4	value	value	NOUN
ejpam-1858	210	5	problem	problem	NOUN
ejpam-1858	210	6	(	(	PUNCT
ejpam-1858	210	7	ivp	ivp	NOUN
ejpam-1858	210	8	)	)	PUNCT
ejpam-1858	210	9	for	for	ADP
ejpam-1858	210	10	the	the	DET
ejpam-1858	210	11	hybrid	hybrid	PROPN
ejpam-1858	210	12	caputo	caputo	PROPN
ejpam-1858	210	13	fractional	fractional	PROPN
ejpam-1858	210	14	differential	differential	NOUN
ejpam-1858	210	15	equation	equation	NOUN
ejpam-1858	210	16	with	with	ADP
ejpam-1858	210	17	variable	variable	ADJ
ejpam-1858	210	18	moments	moment	NOUN
ejpam-1858	210	19	of	of	ADP
ejpam-1858	210	20	impulse	impulse	ADJ
ejpam-1858	210	21	c	c	NOUN
ejpam-1858	210	22	dq	dq	NOUN
ejpam-1858	210	23	x	x	SYM
ejpam-1858	210	24	=	=	SYM
ejpam-1858	210	25	f	f	PROPN
ejpam-1858	210	26	(	(	PUNCT
ejpam-1858	210	27	t	t	PROPN
ejpam-1858	210	28	,	,	PUNCT
ejpam-1858	210	29	x	x	NOUN
ejpam-1858	210	30	)	)	PUNCT
ejpam-1858	210	31	,	,	PUNCT
ejpam-1858	210	32	t	t	PROPN
ejpam-1858	210	33	6=	6=	NUM
ejpam-1858	210	34	τk(x	τk(x	NOUN
ejpam-1858	210	35	)	)	PUNCT
ejpam-1858	210	36	x(t+	x(t+	NUM
ejpam-1858	210	37	)	)	PUNCT
ejpam-1858	211	1	=	=	SYM
ejpam-1858	211	2	x(t	x(t	PROPN
ejpam-1858	211	3	)	)	PUNCT
ejpam-1858	211	4	+	+	SYM
ejpam-1858	211	5	ik(x(t	ik(x(t	NOUN
ejpam-1858	211	6	)	)	PUNCT
ejpam-1858	211	7	)	)	PUNCT
ejpam-1858	211	8	,	,	PUNCT
ejpam-1858	211	9	t	t	PROPN
ejpam-1858	211	10	=	=	PUNCT
ejpam-1858	211	11	τk(x	τk(x	X
ejpam-1858	211	12	)	)	PUNCT
ejpam-1858	211	13	x(t+	x(t+	PROPN
ejpam-1858	211	14	0	0	NUM
ejpam-1858	211	15	)	)	PUNCT
ejpam-1858	211	16	=	=	SYM
ejpam-1858	211	17	x0	x0	PROPN
ejpam-1858	211	18	,	,	PUNCT
ejpam-1858	211	19	t0	t0	PROPN
ejpam-1858	211	20	≥	≥	NUM
ejpam-1858	211	21	0	0	NUM
ejpam-1858	211	22			PROPN
ejpam-1858	211	23			PROPN
ejpam-1858	211	24			NOUN
ejpam-1858	211	25	(	(	PUNCT
ejpam-1858	211	26	7	7	NUM
ejpam-1858	211	27	)	)	PUNCT
ejpam-1858	211	28	where	where	SCONJ
ejpam-1858	211	29	f	f	X
ejpam-1858	211	30	:	:	PUNCT
ejpam-1858	211	31	d→	d→	VERB
ejpam-1858	211	32	r	r	NOUN
ejpam-1858	211	33	and	and	CCONJ
ejpam-1858	211	34	ik	ik	PROPN
ejpam-1858	211	35	:	:	PUNCT
ejpam-1858	211	36	ω→	ω→	PUNCT
ejpam-1858	211	37	r.	r.	PROPN
ejpam-1858	211	38	a	a	DET
ejpam-1858	211	39	function	function	NOUN
ejpam-1858	211	40	x	x	X
ejpam-1858	211	41	:	:	PUNCT
ejpam-1858	212	1	[	[	X
ejpam-1858	212	2	t0	t0	NOUN
ejpam-1858	212	3	,	,	PUNCT
ejpam-1858	212	4	t0	t0	PROPN
ejpam-1858	212	5	+	+	CCONJ
ejpam-1858	212	6	a)→	a)→	PROPN
ejpam-1858	212	7	r	r	PROPN
ejpam-1858	212	8	,	,	PUNCT
ejpam-1858	212	9	t0	t0	PROPN
ejpam-1858	212	10	≥	≥	NUM
ejpam-1858	212	11	0	0	NUM
ejpam-1858	212	12	,	,	PUNCT
ejpam-1858	212	13	a	a	DET
ejpam-1858	212	14	>	>	X
ejpam-1858	212	15	0	0	NUM
ejpam-1858	212	16	is	be	AUX
ejpam-1858	212	17	said	say	VERB
ejpam-1858	212	18	to	to	PART
ejpam-1858	212	19	be	be	AUX
ejpam-1858	212	20	a	a	DET
ejpam-1858	212	21	solution	solution	NOUN
ejpam-1858	212	22	of	of	ADP
ejpam-1858	212	23	(	(	PUNCT
ejpam-1858	212	24	7	7	NUM
ejpam-1858	212	25	)	)	PUNCT
ejpam-1858	212	26	if	if	SCONJ
ejpam-1858	212	27	(	(	PUNCT
ejpam-1858	212	28	i	i	NOUN
ejpam-1858	212	29	)	)	PUNCT
ejpam-1858	212	30	x(t+	x(t+	PROPN
ejpam-1858	212	31	0	0	NUM
ejpam-1858	212	32	)	)	PUNCT
ejpam-1858	213	1	=	=	SYM
ejpam-1858	213	2	x0	x0	PROPN
ejpam-1858	213	3	and	and	CCONJ
ejpam-1858	213	4	(	(	PUNCT
ejpam-1858	213	5	t	t	PROPN
ejpam-1858	213	6	,	,	PUNCT
ejpam-1858	213	7	x(t	x(t	PROPN
ejpam-1858	213	8	)	)	PUNCT
ejpam-1858	213	9	)	)	PUNCT
ejpam-1858	214	1	∈	∈	PROPN
ejpam-1858	214	2	d	d	NOUN
ejpam-1858	214	3	for	for	ADP
ejpam-1858	214	4	t	t	PROPN
ejpam-1858	214	5	∈	∈	PROPN
ejpam-1858	214	6	[	[	X
ejpam-1858	214	7	t0	t0	PROPN
ejpam-1858	214	8	,	,	PUNCT
ejpam-1858	214	9	t0	t0	PROPN
ejpam-1858	214	10	+	+	CCONJ
ejpam-1858	214	11	a	a	X
ejpam-1858	214	12	)	)	PUNCT
ejpam-1858	214	13	,	,	PUNCT
ejpam-1858	214	14	(	(	PUNCT
ejpam-1858	214	15	ii	ii	NOUN
ejpam-1858	214	16	)	)	PUNCT
ejpam-1858	214	17	x(t	x(t	PROPN
ejpam-1858	214	18	)	)	PUNCT
ejpam-1858	214	19	∈	∈	PROPN
ejpam-1858	214	20	cq([t0	cq([t0	NOUN
ejpam-1858	214	21	,	,	PUNCT
ejpam-1858	214	22	t0	t0	PROPN
ejpam-1858	214	23	+	+	CCONJ
ejpam-1858	214	24	a),r	a),r	PROPN
ejpam-1858	214	25	)	)	PUNCT
ejpam-1858	214	26	,	,	PUNCT
ejpam-1858	214	27	c	c	NOUN
ejpam-1858	214	28	dq	dq	ADP
ejpam-1858	214	29	x(t	x(t	PROPN
ejpam-1858	214	30	)	)	PUNCT
ejpam-1858	214	31	is	be	AUX
ejpam-1858	214	32	continuous	continuous	ADJ
ejpam-1858	214	33	,	,	PUNCT
ejpam-1858	214	34	and	and	CCONJ
ejpam-1858	214	35	x(t	x(t	PROPN
ejpam-1858	214	36	)	)	PUNCT
ejpam-1858	214	37	satisfies	satisfy	VERB
ejpam-1858	214	38	c	c	X
ejpam-1858	214	39	dq	dq	NOUN
ejpam-1858	214	40	x	x	SYM
ejpam-1858	215	1	=	=	SYM
ejpam-1858	215	2	f	f	PROPN
ejpam-1858	215	3	(	(	PUNCT
ejpam-1858	215	4	t	t	PROPN
ejpam-1858	215	5	,	,	PUNCT
ejpam-1858	215	6	x	x	NOUN
ejpam-1858	215	7	)	)	PUNCT
ejpam-1858	215	8	for	for	ADP
ejpam-1858	215	9	t	t	PROPN
ejpam-1858	215	10	∈	∈	PROPN
ejpam-1858	215	11	[	[	X
ejpam-1858	215	12	t0	t0	PROPN
ejpam-1858	215	13	,	,	PUNCT
ejpam-1858	215	14	t0	t0	PROPN
ejpam-1858	215	15	+	+	CCONJ
ejpam-1858	215	16	a	a	X
ejpam-1858	215	17	)	)	PUNCT
ejpam-1858	215	18	and	and	CCONJ
ejpam-1858	215	19	t	t	PROPN
ejpam-1858	215	20	6=	6=	ADP
ejpam-1858	215	21	τk(x(t	τk(x(t	NOUN
ejpam-1858	215	22	)	)	PUNCT
ejpam-1858	215	23	)	)	PUNCT
ejpam-1858	215	24	,	,	PUNCT
ejpam-1858	215	25	(	(	PUNCT
ejpam-1858	215	26	iii	iii	X
ejpam-1858	215	27	)	)	PUNCT
ejpam-1858	215	28	if	if	SCONJ
ejpam-1858	215	29	t	t	PROPN
ejpam-1858	215	30	∈	∈	PROPN
ejpam-1858	215	31	[	[	X
ejpam-1858	215	32	t0	t0	PROPN
ejpam-1858	215	33	,	,	PUNCT
ejpam-1858	215	34	t0	t0	PROPN
ejpam-1858	215	35	+	+	CCONJ
ejpam-1858	215	36	a	a	X
ejpam-1858	215	37	)	)	PUNCT
ejpam-1858	215	38	and	and	CCONJ
ejpam-1858	215	39	t	t	NOUN
ejpam-1858	215	40	=	=	PUNCT
ejpam-1858	215	41	τk(x(t	τk(x(t	NUM
ejpam-1858	215	42	)	)	PUNCT
ejpam-1858	215	43	)	)	PUNCT
ejpam-1858	215	44	,	,	PUNCT
ejpam-1858	215	45	then	then	ADV
ejpam-1858	215	46	x(t+	x(t+	NUM
ejpam-1858	215	47	)	)	PUNCT
ejpam-1858	215	48	=	=	SYM
ejpam-1858	215	49	x(t	x(t	PROPN
ejpam-1858	215	50	)	)	PUNCT
ejpam-1858	215	51	+	+	SYM
ejpam-1858	215	52	ik(x(t	ik(x(t	NOUN
ejpam-1858	215	53	)	)	PUNCT
ejpam-1858	215	54	)	)	PUNCT
ejpam-1858	215	55	,	,	PUNCT
ejpam-1858	215	56	and	and	CCONJ
ejpam-1858	215	57	at	at	ADP
ejpam-1858	215	58	such	such	ADJ
ejpam-1858	215	59	t	t	PROPN
ejpam-1858	215	60	’s	’	VERB
ejpam-1858	215	61	we	we	PRON
ejpam-1858	215	62	always	always	ADV
ejpam-1858	215	63	assume	assume	VERB
ejpam-1858	215	64	that	that	SCONJ
ejpam-1858	215	65	x(t	x(t	PROPN
ejpam-1858	215	66	)	)	PUNCT
ejpam-1858	215	67	is	be	AUX
ejpam-1858	215	68	left	leave	VERB
ejpam-1858	215	69	continuous	continuous	ADJ
ejpam-1858	215	70	and	and	CCONJ
ejpam-1858	215	71	s	s	X
ejpam-1858	215	72	6=	6=	PROPN
ejpam-1858	215	73	τ	τ	PROPN
ejpam-1858	215	74	j(x(s	j(x(s	PROPN
ejpam-1858	215	75	)	)	PUNCT
ejpam-1858	215	76	)	)	PUNCT
ejpam-1858	215	77	for	for	ADP
ejpam-1858	215	78	any	any	DET
ejpam-1858	215	79	j	j	PROPN
ejpam-1858	215	80	,	,	PUNCT
ejpam-1858	215	81	t	t	X
ejpam-1858	215	82	<	<	X
ejpam-1858	215	83	s	s	X
ejpam-1858	215	84	<	<	X
ejpam-1858	215	85	t	t	PROPN
ejpam-1858	215	86	+	+	CCONJ
ejpam-1858	215	87	δ	δ	PROPN
ejpam-1858	215	88	,	,	PUNCT
ejpam-1858	215	89	for	for	ADP
ejpam-1858	215	90	some	some	DET
ejpam-1858	215	91	δ	δ	PROPN
ejpam-1858	215	92	>	>	X
ejpam-1858	215	93	0	0	X
ejpam-1858	215	94	.	.	PUNCT
ejpam-1858	216	1	whenever	whenever	SCONJ
ejpam-1858	216	2	t0	t0	PROPN
ejpam-1858	216	3	6=	6=	PRON
ejpam-1858	216	4	τk(x0	τk(x0	NUM
ejpam-1858	216	5	)	)	PUNCT
ejpam-1858	216	6	for	for	ADP
ejpam-1858	216	7	any	any	DET
ejpam-1858	216	8	k	k	NOUN
ejpam-1858	216	9	,	,	PUNCT
ejpam-1858	216	10	we	we	PRON
ejpam-1858	216	11	mean	mean	VERB
ejpam-1858	216	12	the	the	DET
ejpam-1858	216	13	initial	initial	ADJ
ejpam-1858	216	14	condition	condition	NOUN
ejpam-1858	216	15	x(t+	x(t+	PROPN
ejpam-1858	216	16	0	0	NUM
ejpam-1858	216	17	)	)	PUNCT
ejpam-1858	217	1	=	=	SYM
ejpam-1858	217	2	x0	x0	PROPN
ejpam-1858	217	3	in	in	ADP
ejpam-1858	217	4	the	the	DET
ejpam-1858	217	5	usual	usual	ADJ
ejpam-1858	217	6	sense	sense	NOUN
ejpam-1858	217	7	,	,	PUNCT
ejpam-1858	217	8	that	that	ADV
ejpam-1858	217	9	is	is	ADV
ejpam-1858	217	10	,	,	PUNCT
ejpam-1858	217	11	x(t0	x(t0	PROPN
ejpam-1858	217	12	)	)	PUNCT
ejpam-1858	218	1	=	=	PUNCT
ejpam-1858	218	2	x0	x0	PROPN
ejpam-1858	218	3	.	.	PUNCT
ejpam-1858	219	1	if	if	SCONJ
ejpam-1858	219	2	t0	t0	PROPN
ejpam-1858	219	3	=	=	PUNCT
ejpam-1858	219	4	τk(x0	τk(x0	NUM
ejpam-1858	219	5	)	)	PUNCT
ejpam-1858	219	6	for	for	ADP
ejpam-1858	219	7	some	some	DET
ejpam-1858	219	8	k	k	PROPN
ejpam-1858	219	9	then	then	ADV
ejpam-1858	219	10	x(t+	x(t+	PROPN
ejpam-1858	219	11	0	0	NUM
ejpam-1858	219	12	)	)	PUNCT
ejpam-1858	220	1	=	=	SYM
ejpam-1858	220	2	x0	x0	PROPN
ejpam-1858	220	3	,	,	PUNCT
ejpam-1858	220	4	which	which	PRON
ejpam-1858	220	5	,	,	PUNCT
ejpam-1858	220	6	in	in	ADP
ejpam-1858	220	7	general	general	ADJ
ejpam-1858	220	8	,	,	PUNCT
ejpam-1858	220	9	is	be	AUX
ejpam-1858	220	10	natural	natural	ADJ
ejpam-1858	220	11	for	for	ADP
ejpam-1858	220	12	the	the	DET
ejpam-1858	220	13	system	system	NOUN
ejpam-1858	220	14	(	(	PUNCT
ejpam-1858	220	15	7	7	NUM
ejpam-1858	220	16	)	)	PUNCT
ejpam-1858	220	17	,	,	PUNCT
ejpam-1858	220	18	since	since	SCONJ
ejpam-1858	220	19	(	(	PUNCT
ejpam-1858	220	20	t0	t0	PROPN
ejpam-1858	220	21	,	,	PUNCT
ejpam-1858	220	22	x0	x0	PROPN
ejpam-1858	220	23	)	)	PUNCT
ejpam-1858	220	24	may	may	AUX
ejpam-1858	220	25	be	be	AUX
ejpam-1858	220	26	such	such	ADJ
ejpam-1858	220	27	that	that	SCONJ
ejpam-1858	220	28	t0	t0	PROPN
ejpam-1858	220	29	=	=	PUNCT
ejpam-1858	220	30	τk(x0	τk(x0	NUM
ejpam-1858	220	31	)	)	PUNCT
ejpam-1858	220	32	unlike	unlike	ADP
ejpam-1858	220	33	ordinary	ordinary	ADJ
ejpam-1858	220	34	fractional	fractional	ADJ
ejpam-1858	220	35	differential	differential	ADJ
ejpam-1858	220	36	equations	equation	NOUN
ejpam-1858	220	37	,	,	PUNCT
ejpam-1858	220	38	the	the	DET
ejpam-1858	220	39	system	system	NOUN
ejpam-1858	220	40	(	(	PUNCT
ejpam-1858	220	41	7	7	X
ejpam-1858	220	42	)	)	PUNCT
ejpam-1858	220	43	may	may	AUX
ejpam-1858	220	44	not	not	PART
ejpam-1858	220	45	possess	possess	VERB
ejpam-1858	220	46	any	any	DET
ejpam-1858	220	47	solution	solution	NOUN
ejpam-1858	220	48	at	at	ADV
ejpam-1858	220	49	all	all	ADV
ejpam-1858	220	50	,	,	PUNCT
ejpam-1858	220	51	even	even	ADV
ejpam-1858	220	52	if	if	SCONJ
ejpam-1858	220	53	,	,	PUNCT
ejpam-1858	220	54	f	f	PROPN
ejpam-1858	220	55	is	be	AUX
ejpam-1858	220	56	continuous	continuous	ADJ
ejpam-1858	220	57	(	(	PUNCT
ejpam-1858	220	58	or	or	CCONJ
ejpam-1858	220	59	continuously	continuously	ADV
ejpam-1858	220	60	differentiable	differentiable	ADJ
ejpam-1858	220	61	)	)	PUNCT
ejpam-1858	220	62	since	since	SCONJ
ejpam-1858	220	63	the	the	DET
ejpam-1858	220	64	only	only	ADJ
ejpam-1858	220	65	solution	solution	NOUN
ejpam-1858	220	66	x(t	x(t	PROPN
ejpam-1858	220	67	)	)	PUNCT
ejpam-1858	220	68	of	of	ADP
ejpam-1858	220	69	the	the	DET
ejpam-1858	220	70	problem	problem	NOUN
ejpam-1858	220	71	c	c	NOUN
ejpam-1858	220	72	dq	dq	NOUN
ejpam-1858	220	73	x	x	SYM
ejpam-1858	220	74	=	=	SYM
ejpam-1858	220	75	f	f	PROPN
ejpam-1858	220	76	(	(	PUNCT
ejpam-1858	220	77	t	t	PROPN
ejpam-1858	220	78	,	,	PUNCT
ejpam-1858	220	79	x	x	NOUN
ejpam-1858	220	80	)	)	PUNCT
ejpam-1858	220	81	,	,	PUNCT
ejpam-1858	220	82	x(t0	x(t0	PROPN
ejpam-1858	220	83	)	)	PUNCT
ejpam-1858	221	1	=	=	PUNCT
ejpam-1858	221	2	x0	x0	PROPN
ejpam-1858	221	3	,	,	PUNCT
ejpam-1858	221	4	may	may	AUX
ejpam-1858	221	5	totally	totally	ADV
ejpam-1858	221	6	lie	lie	VERB
ejpam-1858	221	7	on	on	ADP
ejpam-1858	221	8	a	a	DET
ejpam-1858	221	9	surface	surface	NOUN
ejpam-1858	221	10	and	and	CCONJ
ejpam-1858	221	11	hence	hence	ADV
ejpam-1858	221	12	by	by	ADP
ejpam-1858	221	13	the	the	DET
ejpam-1858	221	14	definition	definition	NOUN
ejpam-1858	221	15	,	,	PUNCT
ejpam-1858	221	16	we	we	PRON
ejpam-1858	221	17	conclude	conclude	VERB
ejpam-1858	221	18	that	that	SCONJ
ejpam-1858	221	19	the	the	DET
ejpam-1858	221	20	caputo	caputo	PROPN
ejpam-1858	221	21	fractional	fractional	PROPN
ejpam-1858	221	22	differential	differential	ADJ
ejpam-1858	221	23	equation	equation	NOUN
ejpam-1858	221	24	with	with	ADP
ejpam-1858	221	25	variable	variable	ADJ
ejpam-1858	221	26	moments	moment	NOUN
ejpam-1858	221	27	of	of	ADP
ejpam-1858	221	28	impulse	impulse	ADJ
ejpam-1858	221	29	does	do	AUX
ejpam-1858	221	30	not	not	PART
ejpam-1858	221	31	have	have	VERB
ejpam-1858	221	32	any	any	DET
ejpam-1858	221	33	solution	solution	NOUN
ejpam-1858	221	34	for	for	ADP
ejpam-1858	221	35	all	all	DET
ejpam-1858	221	36	t	t	NOUN
ejpam-1858	221	37	∈	∈	PROPN
ejpam-1858	222	1	[	[	X
ejpam-1858	222	2	t0	t0	PROPN
ejpam-1858	222	3	,	,	PUNCT
ejpam-1858	222	4	t	t	PROPN
ejpam-1858	222	5	]	]	PUNCT
ejpam-1858	222	6	.	.	PUNCT
ejpam-1858	223	1	example	example	NOUN
ejpam-1858	224	1	1	1	X
ejpam-1858	224	2	.	.	X
ejpam-1858	224	3	consider	consider	VERB
ejpam-1858	224	4	the	the	DET
ejpam-1858	224	5	following	follow	VERB
ejpam-1858	224	6	ivp	ivp	X
ejpam-1858	224	7	of	of	ADP
ejpam-1858	224	8	caputo	caputo	PROPN
ejpam-1858	224	9	fractional	fractional	PROPN
ejpam-1858	224	10	differential	differential	NOUN
ejpam-1858	224	11	equation	equation	NOUN
ejpam-1858	224	12	with	with	ADP
ejpam-1858	224	13	q	q	NOUN
ejpam-1858	224	14	=	=	SYM
ejpam-1858	224	15	1	1	NUM
ejpam-1858	224	16	2	2	NUM
ejpam-1858	224	17	c	c	NOUN
ejpam-1858	224	18	d	d	SYM
ejpam-1858	224	19	1	1	NUM
ejpam-1858	224	20	2	2	NUM
ejpam-1858	224	21	x	x	SYM
ejpam-1858	224	22	=	=	NOUN
ejpam-1858	224	23	1	1	NUM
ejpam-1858	224	24	,	,	PUNCT
ejpam-1858	224	25	t	t	PROPN
ejpam-1858	224	26	6=	6=	NUM
ejpam-1858	224	27	τk(x	τk(x	PROPN
ejpam-1858	224	28	)	)	PUNCT
ejpam-1858	224	29	,	,	PUNCT
ejpam-1858	224	30	∆x	∆x	PROPN
ejpam-1858	224	31	=	=	AUX
ejpam-1858	224	32	ik(x	ik(x	X
ejpam-1858	224	33	)	)	PUNCT
ejpam-1858	224	34	=	=	PUNCT
ejpam-1858	225	1	π	π	NOUN
ejpam-1858	225	2	4	4	NUM
ejpam-1858	225	3	(	(	PUNCT
ejpam-1858	225	4	x	x	SYM
ejpam-1858	225	5	−	−	PROPN
ejpam-1858	225	6	1)2	1)2	NUM
ejpam-1858	225	7	+	+	CCONJ
ejpam-1858	225	8	1−	1−	NUM
ejpam-1858	225	9	x	x	NOUN
ejpam-1858	225	10	,	,	PUNCT
ejpam-1858	225	11	t	t	NOUN
ejpam-1858	225	12	=	=	PUNCT
ejpam-1858	225	13	τk(x	τk(x	X
ejpam-1858	225	14	)	)	PUNCT
ejpam-1858	225	15	x(1	x(1	PROPN
ejpam-1858	226	1	+	+	PROPN
ejpam-1858	226	2	)	)	PUNCT
ejpam-1858	227	1	=	=	SYM
ejpam-1858	227	2	1	1	NUM
ejpam-1858	227	3	where	where	SCONJ
ejpam-1858	227	4	sk	sk	X
ejpam-1858	227	5	:	:	PUNCT
ejpam-1858	227	6	τk(x	τk(x	NUM
ejpam-1858	227	7	)	)	PUNCT
ejpam-1858	227	8	=	=	PUNCT
ejpam-1858	228	1	π	π	NOUN
ejpam-1858	228	2	4	4	NUM
ejpam-1858	228	3	(	(	PUNCT
ejpam-1858	228	4	x	x	SYM
ejpam-1858	228	5	−	−	PROPN
ejpam-1858	228	6	1)2	1)2	NUM
ejpam-1858	229	1	+	+	CCONJ
ejpam-1858	229	2	k	k	X
ejpam-1858	229	3	,	,	PUNCT
ejpam-1858	229	4	k	k	NOUN
ejpam-1858	229	5	=	=	SYM
ejpam-1858	229	6	1,2	1,2	NUM
ejpam-1858	229	7	,	,	PUNCT
ejpam-1858	229	8	.	.	PUNCT
ejpam-1858	229	9	.	.	PUNCT
ejpam-1858	229	10	.	.	PUNCT
ejpam-1858	230	1	(	(	PUNCT
ejpam-1858	230	2	8)	8)	NUM
ejpam-1858	230	3	j.	j.	PROPN
ejpam-1858	230	4	devi	devi	PROPN
ejpam-1858	230	5	,	,	PUNCT
ejpam-1858	230	6	n.	n.	PROPN
ejpam-1858	230	7	giribabu	giribabu	PROPN
ejpam-1858	230	8	/	/	SYM
ejpam-1858	230	9	eur	eur	PROPN
ejpam-1858	230	10	.	.	PUNCT
ejpam-1858	231	1	j.	j.	PROPN
ejpam-1858	231	2	pure	pure	PROPN
ejpam-1858	231	3	appl	appl	PROPN
ejpam-1858	231	4	.	.	PROPN
ejpam-1858	231	5	math	math	PROPN
ejpam-1858	231	6	,	,	PUNCT
ejpam-1858	231	7	7	7	NUM
ejpam-1858	231	8	(	(	PUNCT
ejpam-1858	231	9	2014	2014	NUM
ejpam-1858	231	10	)	)	PUNCT
ejpam-1858	231	11	,	,	PUNCT
ejpam-1858	231	12	115	115	NUM
ejpam-1858	231	13	-	-	SYM
ejpam-1858	231	14	128	128	NUM
ejpam-1858	231	15	124	124	NUM
ejpam-1858	231	16	there	there	PRON
ejpam-1858	231	17	is	be	VERB
ejpam-1858	231	18	no	no	DET
ejpam-1858	231	19	solution	solution	NOUN
ejpam-1858	231	20	to	to	ADP
ejpam-1858	231	21	the	the	DET
ejpam-1858	231	22	above	above	ADJ
ejpam-1858	231	23	system	system	NOUN
ejpam-1858	231	24	8	8	NUM
ejpam-1858	231	25	passing	pass	VERB
ejpam-1858	231	26	though	though	ADV
ejpam-1858	231	27	(	(	PUNCT
ejpam-1858	231	28	1,1	1,1	NUM
ejpam-1858	231	29	)	)	PUNCT
ejpam-1858	231	30	,	,	PUNCT
ejpam-1858	231	31	since	since	SCONJ
ejpam-1858	231	32	c	c	PROPN
ejpam-1858	231	33	d	d	PROPN
ejpam-1858	231	34	1	1	NUM
ejpam-1858	231	35	2	2	NUM
ejpam-1858	231	36	x	x	SYM
ejpam-1858	231	37	=	=	NOUN
ejpam-1858	231	38	1⇔	1⇔	PROPN
ejpam-1858	231	39	x(t	x(t	PROPN
ejpam-1858	231	40	)	)	PUNCT
ejpam-1858	232	1	=	=	PUNCT
ejpam-1858	233	1	x0	x0	PROPN
ejpam-1858	233	2	+	+	CCONJ
ejpam-1858	233	3	1	1	NUM
ejpam-1858	233	4	γ(q	γ(q	NOUN
ejpam-1858	233	5	)	)	PUNCT
ejpam-1858	233	6	t	t	NOUN
ejpam-1858	233	7	∫	∫	PROPN
ejpam-1858	233	8	t0	t0	PROPN
ejpam-1858	233	9	f	f	PROPN
ejpam-1858	233	10	(	(	PUNCT
ejpam-1858	233	11	s	s	PROPN
ejpam-1858	233	12	,	,	PUNCT
ejpam-1858	233	13	x(s	x(s	PROPN
ejpam-1858	233	14	)	)	PUNCT
ejpam-1858	233	15	)	)	PUNCT
ejpam-1858	234	1	(	(	PUNCT
ejpam-1858	234	2	t−s)1−q	t−s)1−q	NUM
ejpam-1858	234	3	ds	ds	NOUN
ejpam-1858	234	4	.	.	NOUN
ejpam-1858	234	5	now	now	ADV
ejpam-1858	234	6	x(t	x(t	PROPN
ejpam-1858	234	7	)	)	PUNCT
ejpam-1858	235	1	=	=	SYM
ejpam-1858	235	2	x0	x0	PROPN
ejpam-1858	235	3	+	+	CCONJ
ejpam-1858	235	4	1	1	NUM
ejpam-1858	235	5	γ(q	γ(q	NOUN
ejpam-1858	235	6	)	)	PUNCT
ejpam-1858	236	1	t	t	NOUN
ejpam-1858	236	2	∫	∫	PROPN
ejpam-1858	236	3	t0	t0	PROPN
ejpam-1858	236	4	f	f	PROPN
ejpam-1858	236	5	(	(	PUNCT
ejpam-1858	236	6	s	s	PROPN
ejpam-1858	236	7	,	,	PUNCT
ejpam-1858	236	8	x(s	x(s	PROPN
ejpam-1858	236	9	)	)	PUNCT
ejpam-1858	236	10	)	)	PUNCT
ejpam-1858	237	1	(	(	PUNCT
ejpam-1858	237	2	t	t	X
ejpam-1858	237	3	−	−	NOUN
ejpam-1858	237	4	s)1−q	s)1−q	NOUN
ejpam-1858	237	5	ds	ds	PROPN
ejpam-1858	237	6	=	=	NOUN
ejpam-1858	237	7	1	1	NUM
ejpam-1858	237	8	+	+	NUM
ejpam-1858	237	9	1	1	NUM
ejpam-1858	237	10	γ	γ	X
ejpam-1858	237	11	�	�	PROPN
ejpam-1858	237	12	1	1	NUM
ejpam-1858	237	13	2	2	NUM
ejpam-1858	237	14	�	�	PROPN
ejpam-1858	237	15	t	t	PROPN
ejpam-1858	237	16	∫	∫	PROPN
ejpam-1858	237	17	1	1	NUM
ejpam-1858	237	18	1	1	NUM
ejpam-1858	237	19	(	(	PUNCT
ejpam-1858	237	20	t	t	NOUN
ejpam-1858	237	21	−	−	PROPN
ejpam-1858	237	22	s)1−	s)1−	PROPN
ejpam-1858	237	23	�	�	PROPN
ejpam-1858	237	24	1	1	NUM
ejpam-1858	237	25	2	2	NUM
ejpam-1858	237	26	�	�	NOUN
ejpam-1858	237	27	ds	ds	ADJ
ejpam-1858	237	28	=	=	NOUN
ejpam-1858	237	29	1	1	NUM
ejpam-1858	237	30	+	+	NUM
ejpam-1858	237	31	1p	1p	NUM
ejpam-1858	237	32	π	π	PROPN
ejpam-1858	237	33	t	t	PROPN
ejpam-1858	237	34	∫	∫	PROPN
ejpam-1858	237	35	1	1	NUM
ejpam-1858	237	36	(	(	PUNCT
ejpam-1858	237	37	t	t	PROPN
ejpam-1858	237	38	−	−	PROPN
ejpam-1858	237	39	s)−	s)−	PROPN
ejpam-1858	237	40	�	�	PROPN
ejpam-1858	237	41	1	1	NUM
ejpam-1858	237	42	2	2	NUM
ejpam-1858	237	43	�	�	NOUN
ejpam-1858	237	44	ds	ds	ADJ
ejpam-1858	237	45	=	=	NOUN
ejpam-1858	237	46	1	1	NUM
ejpam-1858	237	47	+	+	NUM
ejpam-1858	237	48	1p	1p	NUM
ejpam-1858	237	49	π	π	PROPN
ejpam-1858	237	50	�	�	PROPN
ejpam-1858	237	51	(	(	PUNCT
ejpam-1858	237	52	−1	−1	NOUN
ejpam-1858	237	53	)	)	PUNCT
ejpam-1858	237	54	(	(	PUNCT
ejpam-1858	237	55	t	t	PROPN
ejpam-1858	237	56	−	−	PROPN
ejpam-1858	237	57	s	s	PART
ejpam-1858	237	58	)	)	PUNCT
ejpam-1858	237	59	1	1	NUM
ejpam-1858	237	60	2	2	NUM
ejpam-1858	237	61	�	�	NOUN
ejpam-1858	237	62	1	1	NUM
ejpam-1858	237	63	2	2	NUM
ejpam-1858	237	64	�	�	PROPN
ejpam-1858	237	65	�	�	PROPN
ejpam-1858	237	66	s	s	PART
ejpam-1858	237	67	=	=	NOUN
ejpam-1858	237	68	t	t	X
ejpam-1858	237	69	s=1	s=1	NOUN
ejpam-1858	237	70	=	=	NOUN
ejpam-1858	237	71	1	1	NUM
ejpam-1858	237	72	+	+	NUM
ejpam-1858	237	73	1p	1p	NUM
ejpam-1858	237	74	π	π	PROPN
ejpam-1858	237	75	�	�	PROPN
ejpam-1858	237	76	0	0	NUM
ejpam-1858	237	77	+	+	CCONJ
ejpam-1858	237	78	(	(	PUNCT
ejpam-1858	237	79	t	t	PROPN
ejpam-1858	237	80	−	−	PROPN
ejpam-1858	237	81	1	1	NUM
ejpam-1858	237	82	)	)	SYM
ejpam-1858	237	83	1	1	NUM
ejpam-1858	237	84	2	2	NUM
ejpam-1858	237	85	�	�	NOUN
ejpam-1858	237	86	1	1	NUM
ejpam-1858	237	87	2	2	NUM
ejpam-1858	237	88	�	�	PROPN
ejpam-1858	237	89	�	�	PROPN
ejpam-1858	237	90	=	=	NOUN
ejpam-1858	237	91	1	1	NUM
ejpam-1858	237	92	+	+	NUM
ejpam-1858	237	93	2p	2p	NUM
ejpam-1858	237	94	π	π	PROPN
ejpam-1858	237	95	p	p	PROPN
ejpam-1858	237	96	t	t	PROPN
ejpam-1858	237	97	−	−	PROPN
ejpam-1858	237	98	1	1	NUM
ejpam-1858	237	99	⇒	⇒	NOUN
ejpam-1858	237	100	x(t	x(t	PROPN
ejpam-1858	237	101	)	)	PUNCT
ejpam-1858	238	1	=	=	SYM
ejpam-1858	238	2	1	1	NUM
ejpam-1858	238	3	+	+	NUM
ejpam-1858	238	4	2p	2p	NUM
ejpam-1858	238	5	π	π	PROPN
ejpam-1858	238	6	p	p	PROPN
ejpam-1858	238	7	t	t	PROPN
ejpam-1858	238	8	−	−	PROPN
ejpam-1858	238	9	1	1	NUM
ejpam-1858	238	10	,	,	PUNCT
ejpam-1858	238	11	which	which	PRON
ejpam-1858	238	12	lies	lie	VERB
ejpam-1858	238	13	entirely	entirely	ADV
ejpam-1858	238	14	on	on	ADP
ejpam-1858	238	15	the	the	DET
ejpam-1858	238	16	surface	surface	NOUN
ejpam-1858	238	17	s1	s1	NOUN
ejpam-1858	238	18	.	.	PUNCT
ejpam-1858	239	1	the	the	DET
ejpam-1858	239	2	above	above	ADJ
ejpam-1858	239	3	example	example	NOUN
ejpam-1858	239	4	clearly	clearly	ADV
ejpam-1858	239	5	shows	show	VERB
ejpam-1858	239	6	that	that	SCONJ
ejpam-1858	239	7	we	we	PRON
ejpam-1858	239	8	need	need	VERB
ejpam-1858	239	9	to	to	PART
ejpam-1858	239	10	obtain	obtain	VERB
ejpam-1858	239	11	some	some	DET
ejpam-1858	239	12	conditions	condition	NOUN
ejpam-1858	239	13	that	that	PRON
ejpam-1858	239	14	will	will	AUX
ejpam-1858	239	15	guarantee	guarantee	VERB
ejpam-1858	239	16	that	that	SCONJ
ejpam-1858	239	17	the	the	DET
ejpam-1858	239	18	solution	solution	NOUN
ejpam-1858	239	19	will	will	AUX
ejpam-1858	239	20	exist	exist	VERB
ejpam-1858	239	21	after	after	SCONJ
ejpam-1858	239	22	it	it	PRON
ejpam-1858	239	23	hits	hit	VERB
ejpam-1858	239	24	a	a	DET
ejpam-1858	239	25	surface	surface	NOUN
ejpam-1858	239	26	or	or	CCONJ
ejpam-1858	239	27	a	a	DET
ejpam-1858	239	28	barrier	barrier	NOUN
ejpam-1858	239	29	.	.	PUNCT
ejpam-1858	240	1	as	as	SCONJ
ejpam-1858	240	2	the	the	DET
ejpam-1858	240	3	solution	solution	NOUN
ejpam-1858	240	4	satisfies	satisfy	VERB
ejpam-1858	240	5	the	the	DET
ejpam-1858	240	6	caputo	caputo	PROPN
ejpam-1858	240	7	fractional	fractional	PROPN
ejpam-1858	240	8	differential	differential	NOUN
ejpam-1858	240	9	equation	equation	NOUN
ejpam-1858	240	10	,	,	PUNCT
ejpam-1858	240	11	it	it	PRON
ejpam-1858	240	12	is	be	AUX
ejpam-1858	240	13	natural	natural	ADJ
ejpam-1858	240	14	that	that	SCONJ
ejpam-1858	240	15	the	the	DET
ejpam-1858	240	16	conditions	condition	NOUN
ejpam-1858	240	17	must	must	AUX
ejpam-1858	240	18	be	be	AUX
ejpam-1858	240	19	in	in	ADP
ejpam-1858	240	20	terms	term	NOUN
ejpam-1858	240	21	of	of	ADP
ejpam-1858	240	22	the	the	DET
ejpam-1858	240	23	fractional	fractional	ADJ
ejpam-1858	240	24	derivatives	derivative	NOUN
ejpam-1858	240	25	.	.	PUNCT
ejpam-1858	241	1	this	this	PRON
ejpam-1858	241	2	is	be	AUX
ejpam-1858	241	3	done	do	VERB
ejpam-1858	241	4	in	in	ADP
ejpam-1858	241	5	the	the	DET
ejpam-1858	241	6	following	following	NOUN
ejpam-1858	241	7	theorem	theorem	VERB
ejpam-1858	241	8	,	,	PUNCT
ejpam-1858	241	9	and	and	CCONJ
ejpam-1858	241	10	the	the	DET
ejpam-1858	241	11	criteria	criterion	NOUN
ejpam-1858	241	12	obtained	obtain	VERB
ejpam-1858	241	13	are	be	AUX
ejpam-1858	241	14	not	not	PART
ejpam-1858	241	15	only	only	ADV
ejpam-1858	241	16	new	new	ADJ
ejpam-1858	241	17	but	but	CCONJ
ejpam-1858	241	18	are	be	AUX
ejpam-1858	241	19	very	very	ADV
ejpam-1858	241	20	interesting	interesting	ADJ
ejpam-1858	241	21	.	.	PUNCT
ejpam-1858	242	1	hence	hence	ADV
ejpam-1858	242	2	we	we	PRON
ejpam-1858	242	3	need	need	VERB
ejpam-1858	242	4	some	some	DET
ejpam-1858	242	5	extra	extra	ADJ
ejpam-1858	242	6	conditions	condition	NOUN
ejpam-1858	242	7	on	on	ADP
ejpam-1858	242	8	τk	τk	ADP
ejpam-1858	242	9	and	and	CCONJ
ejpam-1858	242	10	f	f	PROPN
ejpam-1858	242	11	,	,	PUNCT
ejpam-1858	242	12	τk	τk	ADP
ejpam-1858	242	13	or	or	CCONJ
ejpam-1858	242	14	f	f	X
ejpam-1858	242	15	besides	besides	SCONJ
ejpam-1858	242	16	continuity	continuity	NOUN
ejpam-1858	242	17	in	in	ADP
ejpam-1858	242	18	order	order	NOUN
ejpam-1858	242	19	to	to	PART
ejpam-1858	242	20	establish	establish	VERB
ejpam-1858	242	21	any	any	DET
ejpam-1858	242	22	general	general	ADJ
ejpam-1858	242	23	existence	existence	NOUN
ejpam-1858	242	24	theory	theory	NOUN
ejpam-1858	242	25	for	for	ADP
ejpam-1858	242	26	the	the	DET
ejpam-1858	242	27	system	system	NOUN
ejpam-1858	242	28	(	(	PUNCT
ejpam-1858	242	29	7	7	NUM
ejpam-1858	242	30	)	)	PUNCT
ejpam-1858	242	31	.	.	PUNCT
ejpam-1858	243	1	we	we	PRON
ejpam-1858	243	2	now	now	ADV
ejpam-1858	243	3	proceed	proceed	VERB
ejpam-1858	243	4	to	to	ADP
ejpam-1858	243	5	state	state	NOUN
ejpam-1858	243	6	and	and	CCONJ
ejpam-1858	243	7	prove	prove	VERB
ejpam-1858	243	8	a	a	DET
ejpam-1858	243	9	result	result	NOUN
ejpam-1858	243	10	on	on	ADP
ejpam-1858	243	11	existence	existence	NOUN
ejpam-1858	243	12	of	of	ADP
ejpam-1858	243	13	a	a	DET
ejpam-1858	243	14	solution	solution	NOUN
ejpam-1858	243	15	for	for	ADP
ejpam-1858	243	16	the	the	DET
ejpam-1858	243	17	considered	consider	VERB
ejpam-1858	243	18	ivp	ivp	NOUN
ejpam-1858	243	19	.	.	PUNCT
ejpam-1858	244	1	the	the	DET
ejpam-1858	244	2	proof	proof	NOUN
ejpam-1858	244	3	of	of	ADP
ejpam-1858	244	4	the	the	DET
ejpam-1858	244	5	theorem	theorem	NOUN
ejpam-1858	244	6	is	be	AUX
ejpam-1858	244	7	analogous	analogous	ADJ
ejpam-1858	244	8	to	to	ADP
ejpam-1858	244	9	the	the	DET
ejpam-1858	244	10	proof	proof	NOUN
ejpam-1858	244	11	of	of	ADP
ejpam-1858	244	12	the	the	DET
ejpam-1858	244	13	corresponding	corresponding	ADJ
ejpam-1858	244	14	theorem	theorem	ADJ
ejpam-1858	244	15	1.2.1	1.2.1	NUM
ejpam-1858	244	16	in	in	ADP
ejpam-1858	244	17	[	[	X
ejpam-1858	244	18	9	9	NUM
ejpam-1858	244	19	]	]	PUNCT
ejpam-1858	244	20	.	.	PUNCT
ejpam-1858	245	1	theorem	theorem	NOUN
ejpam-1858	245	2	1	1	NUM
ejpam-1858	245	3	.	.	PUNCT
ejpam-1858	245	4	assume	assume	VERB
ejpam-1858	245	5	that	that	SCONJ
ejpam-1858	245	6	(	(	PUNCT
ejpam-1858	245	7	i	i	NOUN
ejpam-1858	245	8	)	)	PUNCT
ejpam-1858	245	9	f	f	PROPN
ejpam-1858	245	10	:	:	PUNCT
ejpam-1858	245	11	d→	d→	PUNCT
ejpam-1858	245	12	r	r	NOUN
ejpam-1858	245	13	is	be	AUX
ejpam-1858	245	14	continuous	continuous	ADJ
ejpam-1858	245	15	at	at	ADP
ejpam-1858	245	16	t	t	PROPN
ejpam-1858	245	17	6=	6=	NUM
ejpam-1858	245	18	τk(x	τk(x	NOUN
ejpam-1858	245	19	)	)	PUNCT
ejpam-1858	245	20	,	,	PUNCT
ejpam-1858	246	1	k	k	X
ejpam-1858	246	2	=	=	SYM
ejpam-1858	246	3	1,2	1,2	NUM
ejpam-1858	246	4	,	,	PUNCT
ejpam-1858	246	5	.	.	PUNCT
ejpam-1858	246	6	.	.	PUNCT
ejpam-1858	246	7	.	.	PUNCT
ejpam-1858	247	1	,	,	PUNCT
ejpam-1858	247	2	.	.	PUNCT
ejpam-1858	248	1	(	(	PUNCT
ejpam-1858	248	2	ii	ii	NOUN
ejpam-1858	248	3	)	)	PUNCT
ejpam-1858	248	4	for	for	ADP
ejpam-1858	248	5	each	each	PRON
ejpam-1858	248	6	(	(	PUNCT
ejpam-1858	248	7	t	t	PROPN
ejpam-1858	248	8	,	,	PUNCT
ejpam-1858	248	9	x	x	NOUN
ejpam-1858	248	10	)	)	PUNCT
ejpam-1858	248	11	∈	∈	PROPN
ejpam-1858	249	1	d	d	NOUN
ejpam-1858	249	2	there	there	PRON
ejpam-1858	249	3	exists	exist	VERB
ejpam-1858	249	4	a	a	DET
ejpam-1858	249	5	function	function	NOUN
ejpam-1858	249	6	ℓ	ℓ	PROPN
ejpam-1858	249	7	∈	∈	PROPN
ejpam-1858	249	8	l1	l1	PROPN
ejpam-1858	249	9	loc	loc	PROPN
ejpam-1858	249	10	such	such	ADJ
ejpam-1858	249	11	that	that	SCONJ
ejpam-1858	249	12	|	|	ADV
ejpam-1858	249	13	f	f	X
ejpam-1858	249	14	(	(	PUNCT
ejpam-1858	249	15	s	s	PROPN
ejpam-1858	249	16	,	,	PUNCT
ejpam-1858	249	17	y	y	NOUN
ejpam-1858	249	18	)	)	PUNCT
ejpam-1858	249	19	|≤	|≤	PROPN
ejpam-1858	249	20	ℓ(s	ℓ(s	PROPN
ejpam-1858	249	21	)	)	PUNCT
ejpam-1858	249	22	in	in	ADP
ejpam-1858	249	23	a	a	DET
ejpam-1858	249	24	neighbourhood	neighbourhood	NOUN
ejpam-1858	249	25	of	of	ADP
ejpam-1858	249	26	(	(	PUNCT
ejpam-1858	249	27	t	t	PROPN
ejpam-1858	249	28	,	,	PUNCT
ejpam-1858	249	29	x	x	NOUN
ejpam-1858	249	30	)	)	PUNCT
ejpam-1858	249	31	.	.	PUNCT
ejpam-1858	250	1	(	(	PUNCT
ejpam-1858	250	2	iii	iii	X
ejpam-1858	250	3	)	)	PUNCT
ejpam-1858	250	4	t1	t1	NOUN
ejpam-1858	250	5	=	=	SYM
ejpam-1858	250	6	τk(x1	τk(x1	X
ejpam-1858	250	7	)	)	PUNCT
ejpam-1858	250	8	for	for	ADP
ejpam-1858	250	9	any	any	DET
ejpam-1858	250	10	k	k	PROPN
ejpam-1858	250	11	≥	≥	NUM
ejpam-1858	250	12	1	1	NUM
ejpam-1858	250	13	implies	imply	VERB
ejpam-1858	250	14	that	that	SCONJ
ejpam-1858	250	15	there	there	PRON
ejpam-1858	250	16	exists	exist	VERB
ejpam-1858	250	17	δ	δ	PROPN
ejpam-1858	250	18	>	>	X
ejpam-1858	250	19	0	0	NUM
ejpam-1858	250	20	such	such	ADJ
ejpam-1858	250	21	that	that	DET
ejpam-1858	250	22	t	t	PROPN
ejpam-1858	250	23	6=	6=	PROPN
ejpam-1858	250	24	τk(x	τk(x	NOUN
ejpam-1858	250	25	)	)	PUNCT
ejpam-1858	250	26	for	for	ADP
ejpam-1858	250	27	any	any	DET
ejpam-1858	250	28	(	(	PUNCT
ejpam-1858	250	29	t	t	PROPN
ejpam-1858	250	30	,	,	PUNCT
ejpam-1858	250	31	x	x	NOUN
ejpam-1858	250	32	)	)	PUNCT
ejpam-1858	250	33	with	with	ADP
ejpam-1858	250	34	0	0	NUM
ejpam-1858	250	35	<	<	X
ejpam-1858	250	36	t	t	PROPN
ejpam-1858	250	37	−	−	PROPN
ejpam-1858	250	38	t1	t1	NOUN
ejpam-1858	250	39	<	<	X
ejpam-1858	250	40	δ	δ	PROPN
ejpam-1858	250	41	and	and	CCONJ
ejpam-1858	250	42	|	|	ADV
ejpam-1858	250	43	x	x	PRON
ejpam-1858	250	44	−	−	NOUN
ejpam-1858	251	1	x1	x1	INTJ
ejpam-1858	252	1	|	|	ADV
ejpam-1858	252	2	<	<	X
ejpam-1858	252	3	δ	δ	PROPN
ejpam-1858	252	4	.	.	PUNCT
ejpam-1858	252	5	j.	j.	PROPN
ejpam-1858	252	6	devi	devi	PROPN
ejpam-1858	252	7	,	,	PUNCT
ejpam-1858	252	8	n.	n.	PROPN
ejpam-1858	252	9	giribabu	giribabu	PROPN
ejpam-1858	252	10	/	/	SYM
ejpam-1858	252	11	eur	eur	PROPN
ejpam-1858	252	12	.	.	PUNCT
ejpam-1858	253	1	j.	j.	PROPN
ejpam-1858	253	2	pure	pure	PROPN
ejpam-1858	253	3	appl	appl	PROPN
ejpam-1858	253	4	.	.	PROPN
ejpam-1858	253	5	math	math	PROPN
ejpam-1858	253	6	,	,	PUNCT
ejpam-1858	253	7	7	7	NUM
ejpam-1858	253	8	(	(	PUNCT
ejpam-1858	253	9	2014	2014	NUM
ejpam-1858	253	10	)	)	PUNCT
ejpam-1858	253	11	,	,	PUNCT
ejpam-1858	253	12	115	115	NUM
ejpam-1858	253	13	-	-	SYM
ejpam-1858	253	14	128	128	NUM
ejpam-1858	253	15	125	125	NUM
ejpam-1858	253	16	then	then	ADV
ejpam-1858	253	17	for	for	ADP
ejpam-1858	253	18	each	each	DET
ejpam-1858	253	19	(	(	PUNCT
ejpam-1858	253	20	t0	t0	PROPN
ejpam-1858	253	21	,	,	PUNCT
ejpam-1858	253	22	x0	x0	PROPN
ejpam-1858	253	23	)	)	PUNCT
ejpam-1858	254	1	∈	∈	PROPN
ejpam-1858	254	2	d	d	NOUN
ejpam-1858	254	3	,	,	PUNCT
ejpam-1858	254	4	there	there	PRON
ejpam-1858	254	5	exists	exist	VERB
ejpam-1858	254	6	a	a	DET
ejpam-1858	254	7	solution	solution	NOUN
ejpam-1858	254	8	x	x	X
ejpam-1858	254	9	:	:	PUNCT
ejpam-1858	254	10	[	[	X
ejpam-1858	254	11	t0	t0	NOUN
ejpam-1858	254	12	,	,	PUNCT
ejpam-1858	254	13	t0+α)→	t0+α)→	NOUN
ejpam-1858	254	14	r	r	NOUN
ejpam-1858	254	15	of	of	ADP
ejpam-1858	254	16	the	the	DET
ejpam-1858	254	17	initial	initial	ADJ
ejpam-1858	254	18	value	value	NOUN
ejpam-1858	254	19	problem	problem	NOUN
ejpam-1858	254	20	(	(	PUNCT
ejpam-1858	254	21	7	7	NUM
ejpam-1858	254	22	)	)	PUNCT
ejpam-1858	254	23	for	for	ADP
ejpam-1858	254	24	some	some	DET
ejpam-1858	254	25	α	α	NOUN
ejpam-1858	254	26	>	>	X
ejpam-1858	254	27	0	0	PROPN
ejpam-1858	254	28	.	.	PUNCT
ejpam-1858	255	1	proof	proof	NOUN
ejpam-1858	255	2	.	.	PUNCT
ejpam-1858	256	1	if	if	SCONJ
ejpam-1858	256	2	t0	t0	PROPN
ejpam-1858	256	3	6=	6=	PRON
ejpam-1858	256	4	τk(x0	τk(x0	NOUN
ejpam-1858	256	5	)	)	PUNCT
ejpam-1858	256	6	for	for	ADP
ejpam-1858	256	7	all	all	DET
ejpam-1858	256	8	k	k	PROPN
ejpam-1858	256	9	≥	≥	NUM
ejpam-1858	256	10	1	1	NUM
ejpam-1858	256	11	then	then	ADV
ejpam-1858	256	12	there	there	PRON
ejpam-1858	256	13	exists	exist	VERB
ejpam-1858	256	14	δ1	δ1	NOUN
ejpam-1858	256	15	>	>	X
ejpam-1858	256	16	0	0	NUM
ejpam-1858	257	1	such	such	ADJ
ejpam-1858	257	2	that	that	DET
ejpam-1858	257	3	s	s	PROPN
ejpam-1858	257	4	6=	6=	NUM
ejpam-1858	257	5	τi(x(s	τi(x(s	NOUN
ejpam-1858	257	6	)	)	PUNCT
ejpam-1858	257	7	)	)	PUNCT
ejpam-1858	258	1	for	for	ADP
ejpam-1858	258	2	all	all	PRON
ejpam-1858	258	3	i	i	PRON
ejpam-1858	258	4	≥	≥	VERB
ejpam-1858	258	5	1	1	NUM
ejpam-1858	258	6	,	,	PUNCT
ejpam-1858	258	7	t0	t0	X
ejpam-1858	258	8	<	<	X
ejpam-1858	258	9	s	s	X
ejpam-1858	258	10	<	<	X
ejpam-1858	258	11	t0	t0	X
ejpam-1858	258	12	+	+	CCONJ
ejpam-1858	258	13	δ1	δ1	NOUN
ejpam-1858	258	14	.	.	PUNCT
ejpam-1858	259	1	the	the	DET
ejpam-1858	259	2	continuity	continuity	NOUN
ejpam-1858	259	3	of	of	ADP
ejpam-1858	259	4	f	f	PROPN
ejpam-1858	259	5	imply	imply	VERB
ejpam-1858	259	6	the	the	DET
ejpam-1858	259	7	existence	existence	NOUN
ejpam-1858	259	8	of	of	ADP
ejpam-1858	259	9	a	a	DET
ejpam-1858	259	10	local	local	ADJ
ejpam-1858	259	11	solution	solution	NOUN
ejpam-1858	259	12	x(t	x(t	PROPN
ejpam-1858	259	13	)	)	PUNCT
ejpam-1858	259	14	of	of	ADP
ejpam-1858	259	15	c	c	PROPN
ejpam-1858	259	16	dq	dq	PROPN
ejpam-1858	259	17	x	x	SYM
ejpam-1858	259	18	=	=	SYM
ejpam-1858	259	19	f	f	PROPN
ejpam-1858	259	20	(	(	PUNCT
ejpam-1858	259	21	t	t	PROPN
ejpam-1858	259	22	,	,	PUNCT
ejpam-1858	259	23	x	x	NOUN
ejpam-1858	259	24	)	)	PUNCT
ejpam-1858	259	25	and	and	CCONJ
ejpam-1858	259	26	x(t0	x(t0	NOUN
ejpam-1858	259	27	)	)	PUNCT
ejpam-1858	260	1	=	=	PUNCT
ejpam-1858	260	2	x0	x0	PROPN
ejpam-1858	260	3	.	.	PUNCT
ejpam-1858	261	1	hence	hence	ADV
ejpam-1858	261	2	x(t	x(t	PROPN
ejpam-1858	261	3	)	)	PUNCT
ejpam-1858	261	4	is	be	AUX
ejpam-1858	261	5	a	a	DET
ejpam-1858	261	6	local	local	ADJ
ejpam-1858	261	7	solution	solution	NOUN
ejpam-1858	261	8	of	of	ADP
ejpam-1858	261	9	the	the	DET
ejpam-1858	261	10	system	system	NOUN
ejpam-1858	261	11	(	(	PUNCT
ejpam-1858	261	12	7	7	NUM
ejpam-1858	261	13	)	)	PUNCT
ejpam-1858	261	14	.	.	PUNCT
ejpam-1858	262	1	if	if	SCONJ
ejpam-1858	262	2	t0	t0	PROPN
ejpam-1858	262	3	=	=	PUNCT
ejpam-1858	262	4	τk(x0	τk(x0	NUM
ejpam-1858	262	5	)	)	PUNCT
ejpam-1858	262	6	for	for	ADP
ejpam-1858	262	7	some	some	DET
ejpam-1858	262	8	k	k	PROPN
ejpam-1858	262	9	≥	≥	NUM
ejpam-1858	262	10	1	1	NUM
ejpam-1858	262	11	,	,	PUNCT
ejpam-1858	262	12	then	then	ADV
ejpam-1858	262	13	x(t+	x(t+	PROPN
ejpam-1858	262	14	0	0	NUM
ejpam-1858	262	15	)	)	PUNCT
ejpam-1858	263	1	=	=	NOUN
ejpam-1858	263	2	x(t0)+	x(t0)+	PROPN
ejpam-1858	263	3	ik(x(t0	ik(x(t0	PROPN
ejpam-1858	263	4	)	)	PUNCT
ejpam-1858	263	5	)	)	PUNCT
ejpam-1858	263	6	.	.	PUNCT
ejpam-1858	264	1	the	the	DET
ejpam-1858	264	2	continuity	continuity	NOUN
ejpam-1858	264	3	of	of	ADP
ejpam-1858	264	4	f	f	PROPN
ejpam-1858	264	5	and	and	CCONJ
ejpam-1858	264	6	the	the	DET
ejpam-1858	264	7	condition	condition	NOUN
ejpam-1858	264	8	(	(	PUNCT
ejpam-1858	264	9	ii	ii	NOUN
ejpam-1858	264	10	)	)	PUNCT
ejpam-1858	264	11	imply	imply	VERB
ejpam-1858	264	12	the	the	DET
ejpam-1858	264	13	existence	existence	NOUN
ejpam-1858	264	14	of	of	ADP
ejpam-1858	264	15	a	a	DET
ejpam-1858	264	16	local	local	ADJ
ejpam-1858	264	17	solution	solution	NOUN
ejpam-1858	264	18	x(t	x(t	PROPN
ejpam-1858	264	19	)	)	PUNCT
ejpam-1858	264	20	of	of	ADP
ejpam-1858	264	21	c	c	PROPN
ejpam-1858	264	22	dq	dq	PROPN
ejpam-1858	264	23	x	x	SYM
ejpam-1858	264	24	=	=	SYM
ejpam-1858	264	25	f	f	PROPN
ejpam-1858	264	26	(	(	PUNCT
ejpam-1858	264	27	t	t	PROPN
ejpam-1858	264	28	,	,	PUNCT
ejpam-1858	264	29	x	x	NOUN
ejpam-1858	264	30	)	)	PUNCT
ejpam-1858	264	31	and	and	CCONJ
ejpam-1858	264	32	x(t+	x(t+	PROPN
ejpam-1858	264	33	0	0	NUM
ejpam-1858	264	34	)	)	PUNCT
ejpam-1858	264	35	=	=	SYM
ejpam-1858	264	36	x(t0	x(t0	PROPN
ejpam-1858	264	37	)	)	PUNCT
ejpam-1858	265	1	+	+	CCONJ
ejpam-1858	265	2	ik(x(t0	ik(x(t0	PROPN
ejpam-1858	265	3	)	)	PUNCT
ejpam-1858	265	4	)	)	PUNCT
ejpam-1858	265	5	.	.	PUNCT
ejpam-1858	266	1	since	since	SCONJ
ejpam-1858	266	2	τi(x	τi(x	NUM
ejpam-1858	266	3	)	)	PUNCT
ejpam-1858	266	4	<	<	X
ejpam-1858	266	5	τ	τ	PROPN
ejpam-1858	266	6	j(x	j(x	PROPN
ejpam-1858	266	7	)	)	PUNCT
ejpam-1858	266	8	for	for	ADP
ejpam-1858	266	9	i	i	PRON
ejpam-1858	266	10	<	<	X
ejpam-1858	266	11	j	j	PROPN
ejpam-1858	266	12	and	and	CCONJ
ejpam-1858	266	13	,	,	PUNCT
ejpam-1858	266	14	t0	t0	PROPN
ejpam-1858	266	15	=	=	PUNCT
ejpam-1858	266	16	τk(x0	τk(x0	NUM
ejpam-1858	266	17	)	)	PUNCT
ejpam-1858	266	18	we	we	PRON
ejpam-1858	266	19	have	have	VERB
ejpam-1858	266	20	t	t	PROPN
ejpam-1858	266	21	6=	6=	NUM
ejpam-1858	266	22	τ	τ	PROPN
ejpam-1858	266	23	j(x(t	j(x(t	PROPN
ejpam-1858	266	24	)	)	PUNCT
ejpam-1858	266	25	)	)	PUNCT
ejpam-1858	267	1	for	for	ADP
ejpam-1858	267	2	j	j	PROPN
ejpam-1858	267	3	6=	6=	PROPN
ejpam-1858	267	4	k	k	PROPN
ejpam-1858	267	5	and	and	CCONJ
ejpam-1858	267	6	t	t	PROPN
ejpam-1858	267	7	sufficiently	sufficiently	ADV
ejpam-1858	267	8	close	close	ADJ
ejpam-1858	267	9	to	to	ADP
ejpam-1858	267	10	t0	t0	NOUN
ejpam-1858	267	11	.	.	PUNCT
ejpam-1858	268	1	since	since	SCONJ
ejpam-1858	268	2	t0	t0	PROPN
ejpam-1858	268	3	=	=	PUNCT
ejpam-1858	268	4	τk(x0	τk(x0	NUM
ejpam-1858	268	5	)	)	PUNCT
ejpam-1858	268	6	,	,	PUNCT
ejpam-1858	268	7	by	by	ADP
ejpam-1858	268	8	condition	condition	NOUN
ejpam-1858	268	9	(	(	PUNCT
ejpam-1858	268	10	iii	iii	X
ejpam-1858	268	11	)	)	PUNCT
ejpam-1858	268	12	there	there	PRON
ejpam-1858	268	13	exists	exist	VERB
ejpam-1858	268	14	δ	δ	PROPN
ejpam-1858	268	15	>	>	X
ejpam-1858	268	16	0	0	NUM
ejpam-1858	268	17	such	such	ADJ
ejpam-1858	268	18	that	that	DET
ejpam-1858	268	19	t	t	PROPN
ejpam-1858	268	20	6=	6=	PROPN
ejpam-1858	268	21	τk(x	τk(x	NOUN
ejpam-1858	268	22	)	)	PUNCT
ejpam-1858	268	23	for	for	ADP
ejpam-1858	268	24	all	all	DET
ejpam-1858	268	25	(	(	PUNCT
ejpam-1858	268	26	t	t	PROPN
ejpam-1858	268	27	,	,	PUNCT
ejpam-1858	268	28	x	x	NOUN
ejpam-1858	268	29	)	)	PUNCT
ejpam-1858	268	30	with	with	ADP
ejpam-1858	268	31	0	0	NUM
ejpam-1858	268	32	<	<	X
ejpam-1858	268	33	t−	t−	PROPN
ejpam-1858	268	34	t0	t0	PROPN
ejpam-1858	268	35	<	<	X
ejpam-1858	268	36	δ	δ	PROPN
ejpam-1858	268	37	and	and	CCONJ
ejpam-1858	268	38	|	|	ADV
ejpam-1858	268	39	x−	x−	PROPN
ejpam-1858	268	40	x0	x0	PROPN
ejpam-1858	269	1	|	|	ADV
ejpam-1858	269	2	<	<	X
ejpam-1858	269	3	δ	δ	PROPN
ejpam-1858	269	4	.	.	PUNCT
ejpam-1858	270	1	therefore	therefore	ADV
ejpam-1858	270	2	,	,	PUNCT
ejpam-1858	270	3	s	s	PROPN
ejpam-1858	270	4	6=	6=	NUM
ejpam-1858	270	5	τi(x(s	τi(x(s	NOUN
ejpam-1858	270	6	)	)	PUNCT
ejpam-1858	270	7	)	)	PUNCT
ejpam-1858	270	8	for	for	ADP
ejpam-1858	270	9	all	all	DET
ejpam-1858	270	10	i	i	PRON
ejpam-1858	270	11	,	,	PUNCT
ejpam-1858	270	12	t0	t0	PROPN
ejpam-1858	270	13	<	<	X
ejpam-1858	270	14	s	s	X
ejpam-1858	270	15	<	<	X
ejpam-1858	270	16	t0	t0	PROPN
ejpam-1858	270	17	+	+	CCONJ
ejpam-1858	270	18	δ	δ	PROPN
ejpam-1858	270	19	,	,	PUNCT
ejpam-1858	270	20	for	for	ADP
ejpam-1858	270	21	some	some	DET
ejpam-1858	270	22	δ	δ	PROPN
ejpam-1858	270	23	>	>	X
ejpam-1858	270	24	0	0	PROPN
ejpam-1858	270	25	.	.	PUNCT
ejpam-1858	271	1	hence	hence	ADV
ejpam-1858	271	2	x(t	x(t	PROPN
ejpam-1858	271	3	)	)	PUNCT
ejpam-1858	271	4	is	be	AUX
ejpam-1858	271	5	a	a	DET
ejpam-1858	271	6	local	local	ADJ
ejpam-1858	271	7	solution	solution	NOUN
ejpam-1858	271	8	of	of	ADP
ejpam-1858	271	9	the	the	DET
ejpam-1858	271	10	system	system	NOUN
ejpam-1858	271	11	(	(	PUNCT
ejpam-1858	271	12	7	7	NUM
ejpam-1858	271	13	)	)	PUNCT
ejpam-1858	271	14	.	.	PUNCT
ejpam-1858	272	1	remark	remark	PROPN
ejpam-1858	272	2	1	1	NUM
ejpam-1858	272	3	.	.	PUNCT
ejpam-1858	273	1	the	the	DET
ejpam-1858	273	2	condition	condition	NOUN
ejpam-1858	273	3	(	(	PUNCT
ejpam-1858	273	4	iii	iii	NOUN
ejpam-1858	273	5	)	)	PUNCT
ejpam-1858	273	6	in	in	ADP
ejpam-1858	273	7	theorem	theorem	NOUN
ejpam-1858	273	8	1	1	NUM
ejpam-1858	273	9	is	be	AUX
ejpam-1858	273	10	possible	possible	ADJ
ejpam-1858	273	11	for	for	ADP
ejpam-1858	273	12	only	only	ADV
ejpam-1858	273	13	irregular	irregular	ADJ
ejpam-1858	273	14	functions	function	NOUN
ejpam-1858	273	15	τk(x	τk(x	PUNCT
ejpam-1858	273	16	)	)	PUNCT
ejpam-1858	273	17	since	since	SCONJ
ejpam-1858	273	18	the	the	DET
ejpam-1858	273	19	theory	theory	NOUN
ejpam-1858	273	20	of	of	ADP
ejpam-1858	273	21	implicit	implicit	ADJ
ejpam-1858	273	22	functions	function	NOUN
ejpam-1858	273	23	implies	imply	VERB
ejpam-1858	273	24	that	that	SCONJ
ejpam-1858	273	25	if	if	SCONJ
ejpam-1858	273	26	τk	τk	ADV
ejpam-1858	273	27	is	be	AUX
ejpam-1858	273	28	differentiable	differentiable	ADJ
ejpam-1858	273	29	at	at	ADP
ejpam-1858	273	30	x0	x0	PROPN
ejpam-1858	273	31	and	and	CCONJ
ejpam-1858	274	1	τ′	τ′	PUNCT
ejpam-1858	274	2	k	k	X
ejpam-1858	274	3	(	(	PUNCT
ejpam-1858	274	4	x0	x0	PROPN
ejpam-1858	274	5	)	)	PUNCT
ejpam-1858	274	6	6=	6=	ADP
ejpam-1858	274	7	0	0	NUM
ejpam-1858	274	8	,	,	PUNCT
ejpam-1858	274	9	then	then	ADV
ejpam-1858	274	10	the	the	DET
ejpam-1858	274	11	condition	condition	NOUN
ejpam-1858	274	12	(	(	PUNCT
ejpam-1858	274	13	iii	iii	NOUN
ejpam-1858	274	14	)	)	PUNCT
ejpam-1858	274	15	can	can	AUX
ejpam-1858	274	16	never	never	ADV
ejpam-1858	274	17	hold	hold	VERB
ejpam-1858	274	18	.	.	PUNCT
ejpam-1858	275	1	we	we	PRON
ejpam-1858	275	2	now	now	ADV
ejpam-1858	275	3	proceed	proceed	VERB
ejpam-1858	275	4	to	to	ADP
ejpam-1858	275	5	state	state	NOUN
ejpam-1858	275	6	and	and	CCONJ
ejpam-1858	275	7	prove	prove	VERB
ejpam-1858	275	8	a	a	DET
ejpam-1858	275	9	result	result	NOUN
ejpam-1858	275	10	on	on	ADP
ejpam-1858	275	11	existence	existence	NOUN
ejpam-1858	275	12	of	of	ADP
ejpam-1858	275	13	a	a	DET
ejpam-1858	275	14	solution	solution	NOUN
ejpam-1858	275	15	for	for	ADP
ejpam-1858	275	16	the	the	DET
ejpam-1858	275	17	considered	consider	VERB
ejpam-1858	275	18	ivp	ivp	NOUN
ejpam-1858	275	19	with	with	ADP
ejpam-1858	275	20	some	some	DET
ejpam-1858	275	21	regularity	regularity	NOUN
ejpam-1858	275	22	conditions	condition	NOUN
ejpam-1858	275	23	on	on	ADP
ejpam-1858	275	24	τk(x	τk(x	NOUN
ejpam-1858	275	25	)	)	PUNCT
ejpam-1858	275	26	.	.	PUNCT
ejpam-1858	276	1	the	the	DET
ejpam-1858	276	2	condition	condition	NOUN
ejpam-1858	276	3	on	on	ADP
ejpam-1858	276	4	τk(x	τk(x	NOUN
ejpam-1858	276	5	)	)	PUNCT
ejpam-1858	276	6	is	be	AUX
ejpam-1858	276	7	given	give	VERB
ejpam-1858	276	8	in	in	ADP
ejpam-1858	276	9	terms	term	NOUN
ejpam-1858	276	10	of	of	ADP
ejpam-1858	276	11	fractional	fractional	ADJ
ejpam-1858	276	12	derivative	derivative	NOUN
ejpam-1858	276	13	.	.	PUNCT
ejpam-1858	277	1	this	this	PRON
ejpam-1858	277	2	is	be	AUX
ejpam-1858	277	3	natural	natural	ADJ
ejpam-1858	277	4	as	as	SCONJ
ejpam-1858	277	5	the	the	DET
ejpam-1858	277	6	solution	solution	NOUN
ejpam-1858	277	7	follows	follow	VERB
ejpam-1858	277	8	the	the	DET
ejpam-1858	277	9	fractional	fractional	ADJ
ejpam-1858	277	10	differential	differential	ADJ
ejpam-1858	277	11	equation	equation	NOUN
ejpam-1858	277	12	model	model	NOUN
ejpam-1858	277	13	.	.	PUNCT
ejpam-1858	278	1	this	this	DET
ejpam-1858	278	2	result	result	NOUN
ejpam-1858	278	3	is	be	AUX
ejpam-1858	278	4	new	new	ADJ
ejpam-1858	278	5	and	and	CCONJ
ejpam-1858	278	6	has	have	AUX
ejpam-1858	278	7	been	be	AUX
ejpam-1858	278	8	developed	develop	VERB
ejpam-1858	278	9	for	for	ADP
ejpam-1858	278	10	hybrid	hybrid	ADJ
ejpam-1858	278	11	caputo	caputo	PROPN
ejpam-1858	278	12	fractional	fractional	PROPN
ejpam-1858	278	13	differential	differential	NOUN
ejpam-1858	278	14	equation	equation	NOUN
ejpam-1858	278	15	with	with	ADP
ejpam-1858	278	16	variable	variable	ADJ
ejpam-1858	278	17	moments	moment	NOUN
ejpam-1858	278	18	of	of	ADP
ejpam-1858	278	19	impulse	impulse	ADJ
ejpam-1858	278	20	.	.	PUNCT
ejpam-1858	279	1	theorem	theorem	NOUN
ejpam-1858	279	2	2	2	NUM
ejpam-1858	280	1	.	.	X
ejpam-1858	280	2	assume	assume	VERB
ejpam-1858	280	3	that	that	SCONJ
ejpam-1858	280	4	(	(	PUNCT
ejpam-1858	280	5	i	i	NOUN
ejpam-1858	280	6	)	)	PUNCT
ejpam-1858	280	7	f	f	PROPN
ejpam-1858	280	8	:	:	PUNCT
ejpam-1858	281	1	d→	d→	PUNCT
ejpam-1858	281	2	r	r	NOUN
ejpam-1858	281	3	is	be	AUX
ejpam-1858	281	4	continuous	continuous	ADJ
ejpam-1858	281	5	.	.	PUNCT
ejpam-1858	282	1	(	(	PUNCT
ejpam-1858	282	2	ii	ii	NOUN
ejpam-1858	282	3	)	)	PUNCT
ejpam-1858	282	4	c	c	PROPN
ejpam-1858	282	5	dqτk(x	dqτk(x	PROPN
ejpam-1858	282	6	)	)	PUNCT
ejpam-1858	282	7	exists	exist	VERB
ejpam-1858	282	8	,	,	PUNCT
ejpam-1858	282	9	τk	τk	ADP
ejpam-1858	282	10	:	:	PUNCT
ejpam-1858	282	11	ω→	ω→	X
ejpam-1858	282	12	(	(	PUNCT
ejpam-1858	282	13	0,∞	0,∞	NOUN
ejpam-1858	282	14	)	)	PUNCT
ejpam-1858	282	15	are	be	AUX
ejpam-1858	282	16	differentiable	differentiable	ADJ
ejpam-1858	282	17	and	and	CCONJ
ejpam-1858	282	18	linear	linear	ADJ
ejpam-1858	282	19	surfaces	surface	NOUN
ejpam-1858	282	20	for	for	ADP
ejpam-1858	282	21	all	all	DET
ejpam-1858	282	22	k	k	PROPN
ejpam-1858	282	23	≥	≥	NUM
ejpam-1858	282	24	1	1	NUM
ejpam-1858	282	25	.	.	PUNCT
ejpam-1858	283	1	(	(	PUNCT
ejpam-1858	283	2	iii	iii	X
ejpam-1858	283	3	)	)	PUNCT
ejpam-1858	283	4	if	if	SCONJ
ejpam-1858	283	5	t1	t1	NOUN
ejpam-1858	283	6	=	=	SYM
ejpam-1858	283	7	τk(x1	τk(x1	X
ejpam-1858	283	8	)	)	PUNCT
ejpam-1858	283	9	for	for	ADP
ejpam-1858	283	10	some(t1	some(t1	NOUN
ejpam-1858	283	11	,	,	PUNCT
ejpam-1858	283	12	x1	x1	X
ejpam-1858	284	1	)	)	PUNCT
ejpam-1858	284	2	∈	∈	PROPN
ejpam-1858	284	3	d	d	NOUN
ejpam-1858	284	4	and	and	CCONJ
ejpam-1858	284	5	k	k	PROPN
ejpam-1858	284	6	≥	≥	NUM
ejpam-1858	284	7	1	1	NUM
ejpam-1858	284	8	,	,	PUNCT
ejpam-1858	284	9	then	then	ADV
ejpam-1858	284	10	there	there	PRON
ejpam-1858	284	11	existsδ	existsδ	VERB
ejpam-1858	284	12	>	>	X
ejpam-1858	284	13	0	0	NUM
ejpam-1858	284	14	such	such	ADJ
ejpam-1858	284	15	that	that	DET
ejpam-1858	284	16	∂	∂	NUM
ejpam-1858	284	17	τk(x	τk(x	NUM
ejpam-1858	284	18	)	)	PUNCT
ejpam-1858	284	19	∂	∂	NUM
ejpam-1858	285	1	x	x	NOUN
ejpam-1858	285	2	.	.	PUNCT
ejpam-1858	286	1	f	f	PROPN
ejpam-1858	286	2	(	(	PUNCT
ejpam-1858	286	3	t	t	PROPN
ejpam-1858	286	4	,	,	PUNCT
ejpam-1858	286	5	x	x	X
ejpam-1858	286	6	)	)	PUNCT
ejpam-1858	286	7	6=	6=	ADP
ejpam-1858	286	8	(	(	PUNCT
ejpam-1858	286	9	t−t1	t−t1	NUM
ejpam-1858	286	10	)	)	PUNCT
ejpam-1858	286	11	(	(	PUNCT
ejpam-1858	286	12	1−q	1−q	NUM
ejpam-1858	286	13	)	)	PUNCT
ejpam-1858	286	14	γ(2−q	γ(2−q	ADJ
ejpam-1858	286	15	)	)	PUNCT
ejpam-1858	286	16	for	for	ADP
ejpam-1858	286	17	(	(	PUNCT
ejpam-1858	286	18	t	t	PROPN
ejpam-1858	286	19	,	,	PUNCT
ejpam-1858	286	20	x	x	NOUN
ejpam-1858	286	21	)	)	PUNCT
ejpam-1858	286	22	∈	∈	PROPN
ejpam-1858	286	23	d	d	NOUN
ejpam-1858	286	24	with	with	ADP
ejpam-1858	286	25	|	|	NOUN
ejpam-1858	286	26	x	x	ADP
ejpam-1858	286	27	−	−	NOUN
ejpam-1858	287	1	x1	x1	INTJ
ejpam-1858	287	2	|	|	NOUN
ejpam-1858	287	3	<	<	X
ejpam-1858	287	4	δ	δ	PROPN
ejpam-1858	287	5	and	and	CCONJ
ejpam-1858	287	6	0	0	NUM
ejpam-1858	287	7	<	<	X
ejpam-1858	287	8	t	t	PROPN
ejpam-1858	288	1	−	−	PROPN
ejpam-1858	288	2	t1	t1	NOUN
ejpam-1858	288	3	<	<	X
ejpam-1858	288	4	δ	δ	PROPN
ejpam-1858	288	5	.	.	PUNCT
ejpam-1858	289	1	then	then	ADV
ejpam-1858	289	2	for	for	ADP
ejpam-1858	289	3	each	each	DET
ejpam-1858	289	4	(	(	PUNCT
ejpam-1858	289	5	t0	t0	PROPN
ejpam-1858	289	6	,	,	PUNCT
ejpam-1858	289	7	x0	x0	PROPN
ejpam-1858	289	8	)	)	PUNCT
ejpam-1858	289	9	∈	∈	PROPN
ejpam-1858	290	1	d	d	NOUN
ejpam-1858	290	2	,	,	PUNCT
ejpam-1858	290	3	there	there	PRON
ejpam-1858	290	4	exists	exist	VERB
ejpam-1858	290	5	a	a	DET
ejpam-1858	290	6	solution	solution	NOUN
ejpam-1858	290	7	x	x	X
ejpam-1858	290	8	:	:	PUNCT
ejpam-1858	290	9	[	[	X
ejpam-1858	290	10	t0	t0	NOUN
ejpam-1858	290	11	,	,	PUNCT
ejpam-1858	290	12	t0+α)→	t0+α)→	NOUN
ejpam-1858	290	13	r	r	NOUN
ejpam-1858	290	14	of	of	ADP
ejpam-1858	290	15	the	the	DET
ejpam-1858	290	16	system	system	NOUN
ejpam-1858	290	17	(	(	PUNCT
ejpam-1858	290	18	7	7	NUM
ejpam-1858	290	19	)	)	PUNCT
ejpam-1858	290	20	for	for	ADP
ejpam-1858	290	21	some	some	DET
ejpam-1858	290	22	α	α	NOUN
ejpam-1858	290	23	>	>	X
ejpam-1858	290	24	0	0	PROPN
ejpam-1858	290	25	.	.	PUNCT
ejpam-1858	291	1	proof	proof	NOUN
ejpam-1858	291	2	.	.	PUNCT
ejpam-1858	292	1	if	if	SCONJ
ejpam-1858	292	2	t0	t0	PROPN
ejpam-1858	292	3	6=	6=	PRON
ejpam-1858	292	4	τk(x0	τk(x0	NOUN
ejpam-1858	292	5	)	)	PUNCT
ejpam-1858	292	6	for	for	ADP
ejpam-1858	292	7	all	all	DET
ejpam-1858	292	8	k	k	PROPN
ejpam-1858	292	9	≥	≥	NUM
ejpam-1858	292	10	1	1	NUM
ejpam-1858	292	11	then	then	ADV
ejpam-1858	292	12	there	there	PRON
ejpam-1858	292	13	exists	exist	VERB
ejpam-1858	292	14	δ1	δ1	NOUN
ejpam-1858	292	15	>	>	X
ejpam-1858	292	16	0	0	NUM
ejpam-1858	293	1	such	such	ADJ
ejpam-1858	293	2	that	that	DET
ejpam-1858	293	3	s	s	PROPN
ejpam-1858	293	4	6=	6=	NUM
ejpam-1858	293	5	τi(x(s	τi(x(s	NOUN
ejpam-1858	293	6	)	)	PUNCT
ejpam-1858	293	7	)	)	PUNCT
ejpam-1858	293	8	for	for	ADP
ejpam-1858	293	9	all	all	DET
ejpam-1858	293	10	i	i	PRON
ejpam-1858	293	11	,	,	PUNCT
ejpam-1858	293	12	t0	t0	PROPN
ejpam-1858	293	13	<	<	X
ejpam-1858	293	14	s	s	X
ejpam-1858	293	15	<	<	X
ejpam-1858	293	16	t0	t0	X
ejpam-1858	293	17	+	+	CCONJ
ejpam-1858	293	18	δ1	δ1	NOUN
ejpam-1858	293	19	.	.	PUNCT
ejpam-1858	294	1	the	the	DET
ejpam-1858	294	2	continuity	continuity	NOUN
ejpam-1858	294	3	of	of	ADP
ejpam-1858	294	4	f	f	PROPN
ejpam-1858	294	5	imply	imply	VERB
ejpam-1858	294	6	the	the	DET
ejpam-1858	294	7	existence	existence	NOUN
ejpam-1858	294	8	of	of	ADP
ejpam-1858	294	9	a	a	DET
ejpam-1858	294	10	local	local	ADJ
ejpam-1858	294	11	solution	solution	NOUN
ejpam-1858	294	12	x(t	x(t	PROPN
ejpam-1858	294	13	)	)	PUNCT
ejpam-1858	294	14	of	of	ADP
ejpam-1858	294	15	c	c	PROPN
ejpam-1858	294	16	dq	dq	PROPN
ejpam-1858	294	17	x	x	SYM
ejpam-1858	294	18	=	=	SYM
ejpam-1858	294	19	f	f	PROPN
ejpam-1858	294	20	(	(	PUNCT
ejpam-1858	294	21	t	t	PROPN
ejpam-1858	294	22	,	,	PUNCT
ejpam-1858	294	23	x	x	NOUN
ejpam-1858	294	24	)	)	PUNCT
ejpam-1858	294	25	and	and	CCONJ
ejpam-1858	294	26	x(t0	x(t0	NOUN
ejpam-1858	294	27	)	)	PUNCT
ejpam-1858	295	1	=	=	PUNCT
ejpam-1858	295	2	x0	x0	PROPN
ejpam-1858	295	3	.	.	PUNCT
ejpam-1858	296	1	hence	hence	ADV
ejpam-1858	296	2	x(t	x(t	PROPN
ejpam-1858	296	3	)	)	PUNCT
ejpam-1858	296	4	is	be	AUX
ejpam-1858	296	5	a	a	DET
ejpam-1858	296	6	local	local	ADJ
ejpam-1858	296	7	solution	solution	NOUN
ejpam-1858	296	8	of	of	ADP
ejpam-1858	296	9	the	the	DET
ejpam-1858	296	10	system	system	NOUN
ejpam-1858	296	11	(	(	PUNCT
ejpam-1858	296	12	7	7	NUM
ejpam-1858	296	13	)	)	PUNCT
ejpam-1858	296	14	.	.	PUNCT
ejpam-1858	297	1	if	if	SCONJ
ejpam-1858	297	2	t0	t0	PROPN
ejpam-1858	297	3	=	=	PUNCT
ejpam-1858	297	4	τk(x0	τk(x0	NUM
ejpam-1858	297	5	)	)	PUNCT
ejpam-1858	297	6	for	for	ADP
ejpam-1858	297	7	some	some	DET
ejpam-1858	297	8	k	k	PROPN
ejpam-1858	297	9	≥	≥	NUM
ejpam-1858	297	10	1	1	NUM
ejpam-1858	297	11	,	,	PUNCT
ejpam-1858	297	12	then	then	ADV
ejpam-1858	297	13	x(t+	x(t+	PROPN
ejpam-1858	297	14	0	0	NUM
ejpam-1858	297	15	)	)	PUNCT
ejpam-1858	297	16	=	=	SYM
ejpam-1858	297	17	x(t0	x(t0	PROPN
ejpam-1858	297	18	)	)	PUNCT
ejpam-1858	298	1	+	+	CCONJ
ejpam-1858	298	2	ik(x(t0	ik(x(t0	PROPN
ejpam-1858	298	3	)	)	PUNCT
ejpam-1858	298	4	)	)	PUNCT
ejpam-1858	298	5	.	.	PUNCT
ejpam-1858	299	1	the	the	DET
ejpam-1858	299	2	continuity	continuity	NOUN
ejpam-1858	299	3	of	of	ADP
ejpam-1858	299	4	f	f	PROPN
ejpam-1858	299	5	imply	imply	VERB
ejpam-1858	299	6	the	the	DET
ejpam-1858	299	7	existence	existence	NOUN
ejpam-1858	299	8	of	of	ADP
ejpam-1858	299	9	a	a	DET
ejpam-1858	299	10	local	local	ADJ
ejpam-1858	299	11	solution	solution	NOUN
ejpam-1858	299	12	x(t	x(t	PROPN
ejpam-1858	299	13	)	)	PUNCT
ejpam-1858	299	14	of	of	ADP
ejpam-1858	299	15	c	c	PROPN
ejpam-1858	299	16	dq	dq	PROPN
ejpam-1858	299	17	x	x	SYM
ejpam-1858	299	18	=	=	SYM
ejpam-1858	299	19	f	f	PROPN
ejpam-1858	299	20	(	(	PUNCT
ejpam-1858	299	21	t	t	PROPN
ejpam-1858	299	22	,	,	PUNCT
ejpam-1858	299	23	x	x	NOUN
ejpam-1858	299	24	)	)	PUNCT
ejpam-1858	299	25	and	and	CCONJ
ejpam-1858	299	26	x(t+o	x(t+o	NUM
ejpam-1858	299	27	)	)	PUNCT
ejpam-1858	300	1	=	=	SYM
ejpam-1858	300	2	x(t0	x(t0	PROPN
ejpam-1858	300	3	)	)	PUNCT
ejpam-1858	301	1	+	+	CCONJ
ejpam-1858	301	2	ik(x(t0	ik(x(t0	PROPN
ejpam-1858	301	3	)	)	PUNCT
ejpam-1858	301	4	)	)	PUNCT
ejpam-1858	301	5	.	.	PUNCT
ejpam-1858	302	1	set	set	VERB
ejpam-1858	302	2	σ(t	σ(t	PROPN
ejpam-1858	302	3	)	)	PUNCT
ejpam-1858	303	1	=	=	SYM
ejpam-1858	303	2	t	t	PROPN
ejpam-1858	303	3	−	−	NUM
ejpam-1858	303	4	τk(x(t	τk(x(t	NOUN
ejpam-1858	303	5	)	)	PUNCT
ejpam-1858	303	6	,	,	PUNCT
ejpam-1858	303	7	then	then	ADV
ejpam-1858	303	8	σ(t0	σ(t0	NUM
ejpam-1858	303	9	)	)	PUNCT
ejpam-1858	304	1	=	=	SYM
ejpam-1858	304	2	0	0	NUM
ejpam-1858	304	3	,	,	PUNCT
ejpam-1858	304	4	since	since	SCONJ
ejpam-1858	304	5	t0	t0	PROPN
ejpam-1858	304	6	=	=	PUNCT
ejpam-1858	304	7	τk(x0	τk(x0	NUM
ejpam-1858	304	8	)	)	PUNCT
ejpam-1858	304	9	.	.	PUNCT
ejpam-1858	305	1	then	then	ADV
ejpam-1858	305	2	by	by	ADP
ejpam-1858	305	3	using	use	VERB
ejpam-1858	305	4	the	the	DET
ejpam-1858	305	5	fact	fact	NOUN
ejpam-1858	305	6	that	that	SCONJ
ejpam-1858	305	7	τk(x	τk(x	PUNCT
ejpam-1858	305	8	)	)	PUNCT
ejpam-1858	305	9	are	be	AUX
ejpam-1858	305	10	linear	linear	ADJ
ejpam-1858	305	11	surfaces	surface	NOUN
ejpam-1858	305	12	,	,	PUNCT
ejpam-1858	305	13	and	and	CCONJ
ejpam-1858	305	14	the	the	DET
ejpam-1858	305	15	hypothesis	hypothesis	NOUN
ejpam-1858	305	16	in	in	ADP
ejpam-1858	305	17	a	a	DET
ejpam-1858	305	18	small	small	ADJ
ejpam-1858	305	19	right	right	ADJ
ejpam-1858	305	20	neighborhood	neighborhood	NOUN
ejpam-1858	305	21	of	of	ADP
ejpam-1858	305	22	t0	t0	PRON
ejpam-1858	305	23	we	we	PRON
ejpam-1858	305	24	obtain	obtain	VERB
ejpam-1858	305	25	c	c	X
ejpam-1858	305	26	dqσ(t	dqσ(t	PROPN
ejpam-1858	305	27	)	)	PUNCT
ejpam-1858	306	1	=	=	PUNCT
ejpam-1858	306	2	c	c	X
ejpam-1858	306	3	dq[t	dq[t	PROPN
ejpam-1858	306	4	−τk(x(t	−τk(x(t	PROPN
ejpam-1858	306	5	)	)	PUNCT
ejpam-1858	306	6	]	]	PUNCT
ejpam-1858	306	7	j.	j.	PROPN
ejpam-1858	306	8	devi	devi	PROPN
ejpam-1858	306	9	,	,	PUNCT
ejpam-1858	306	10	n.	n.	PROPN
ejpam-1858	306	11	giribabu	giribabu	PROPN
ejpam-1858	306	12	/	/	SYM
ejpam-1858	306	13	eur	eur	PROPN
ejpam-1858	306	14	.	.	PUNCT
ejpam-1858	307	1	j.	j.	PROPN
ejpam-1858	307	2	pure	pure	PROPN
ejpam-1858	307	3	appl	appl	PROPN
ejpam-1858	307	4	.	.	PROPN
ejpam-1858	307	5	math	math	PROPN
ejpam-1858	307	6	,	,	PUNCT
ejpam-1858	307	7	7	7	NUM
ejpam-1858	307	8	(	(	PUNCT
ejpam-1858	307	9	2014	2014	NUM
ejpam-1858	307	10	)	)	PUNCT
ejpam-1858	307	11	,	,	PUNCT
ejpam-1858	307	12	115	115	NUM
ejpam-1858	307	13	-	-	SYM
ejpam-1858	307	14	128	128	NUM
ejpam-1858	307	15	126	126	NUM
ejpam-1858	307	16	=	=	SYM
ejpam-1858	307	17	c	c	PROPN
ejpam-1858	307	18	dq(t)−	dq(t)−	PROPN
ejpam-1858	307	19	c	c	PROPN
ejpam-1858	307	20	dq[τk(x(t	dq[τk(x(t	PROPN
ejpam-1858	307	21	)	)	PUNCT
ejpam-1858	307	22	)	)	PUNCT
ejpam-1858	307	23	]	]	PUNCT
ejpam-1858	308	1	=	=	SYM
ejpam-1858	308	2	1	1	NUM
ejpam-1858	308	3	γ(1−	γ(1−	NOUN
ejpam-1858	308	4	q	q	X
ejpam-1858	308	5	)	)	PUNCT
ejpam-1858	308	6	∫	∫	PROPN
ejpam-1858	308	7	t	t	PROPN
ejpam-1858	308	8	t0	t0	PROPN
ejpam-1858	308	9	(	(	PUNCT
ejpam-1858	308	10	t	t	PROPN
ejpam-1858	308	11	−	−	PROPN
ejpam-1858	308	12	s)−qds−	s)−qds−	PROPN
ejpam-1858	308	13	1	1	NUM
ejpam-1858	308	14	γ(1−	γ(1−	NOUN
ejpam-1858	308	15	q	q	X
ejpam-1858	308	16	)	)	PUNCT
ejpam-1858	308	17	∫	∫	PROPN
ejpam-1858	308	18	t	t	PROPN
ejpam-1858	308	19	t0	t0	PROPN
ejpam-1858	308	20	(	(	PUNCT
ejpam-1858	308	21	t	t	NOUN
ejpam-1858	308	22	−	−	PROPN
ejpam-1858	309	1	s)−q	s)−q	PROPN
ejpam-1858	309	2	d	d	X
ejpam-1858	309	3	ds	ds	X
ejpam-1858	309	4	[	[	X
ejpam-1858	309	5	τk(x(s)]ds	τk(x(s)]ds	PUNCT
ejpam-1858	309	6	=	=	SYM
ejpam-1858	309	7	1	1	NUM
ejpam-1858	309	8	γ(1−	γ(1−	NOUN
ejpam-1858	309	9	q	q	X
ejpam-1858	309	10	)	)	PUNCT
ejpam-1858	309	11	�	�	PROPN
ejpam-1858	309	12	−(t	−(t	PROPN
ejpam-1858	309	13	−	−	PROPN
ejpam-1858	309	14	s)1−q	s)1−q	NOUN
ejpam-1858	309	15	1−	1−	NUM
ejpam-1858	309	16	q	q	PROPN
ejpam-1858	309	17	�	�	PROPN
ejpam-1858	309	18	t	t	PROPN
ejpam-1858	309	19	t0	t0	NOUN
ejpam-1858	309	20	−	−	PROPN
ejpam-1858	309	21	1	1	NUM
ejpam-1858	309	22	γ(1−	γ(1−	PROPN
ejpam-1858	309	23	q	q	X
ejpam-1858	309	24	)	)	PUNCT
ejpam-1858	309	25	∫	∫	PROPN
ejpam-1858	309	26	t	t	PROPN
ejpam-1858	309	27	t0	t0	PROPN
ejpam-1858	309	28	(	(	PUNCT
ejpam-1858	309	29	t	t	PROPN
ejpam-1858	309	30	−	−	PROPN
ejpam-1858	309	31	s)−q	s)−q	PROPN
ejpam-1858	309	32	∂	∂	NOUN
ejpam-1858	309	33	∂	∂	NOUN
ejpam-1858	309	34	x	x	PUNCT
ejpam-1858	310	1	[	[	X
ejpam-1858	310	2	τk(x	τk(x	NOUN
ejpam-1858	310	3	)	)	PUNCT
ejpam-1858	310	4	]	]	PUNCT
ejpam-1858	311	1	x	x	PUNCT
ejpam-1858	311	2	′(s)ds	′(s)ds	NOUN
ejpam-1858	311	3	=	=	SYM
ejpam-1858	311	4	1	1	NUM
ejpam-1858	311	5	γ(1−	γ(1−	NOUN
ejpam-1858	311	6	q	q	NOUN
ejpam-1858	311	7	)	)	PUNCT
ejpam-1858	311	8	(	(	PUNCT
ejpam-1858	311	9	t	t	PROPN
ejpam-1858	311	10	−	−	PROPN
ejpam-1858	311	11	t0	t0	PROPN
ejpam-1858	311	12	)	)	PUNCT
ejpam-1858	311	13	1−q	1−q	NUM
ejpam-1858	311	14	1−	1−	NUM
ejpam-1858	311	15	q	q	NOUN
ejpam-1858	312	1	−	−	PROPN
ejpam-1858	312	2	∂	∂	NUM
ejpam-1858	312	3	∂	∂	NOUN
ejpam-1858	312	4	x	x	PUNCT
ejpam-1858	313	1	[	[	X
ejpam-1858	313	2	τk(x	τk(x	NOUN
ejpam-1858	313	3	)	)	PUNCT
ejpam-1858	313	4	]	]	PUNCT
ejpam-1858	314	1	c	c	X
ejpam-1858	314	2	dq	dq	NOUN
ejpam-1858	314	3	x	x	SYM
ejpam-1858	314	4	=	=	PRON
ejpam-1858	314	5	(	(	PUNCT
ejpam-1858	314	6	t	t	PROPN
ejpam-1858	314	7	−	−	PROPN
ejpam-1858	314	8	t0	t0	PROPN
ejpam-1858	314	9	)	)	PUNCT
ejpam-1858	314	10	1−q	1−q	NUM
ejpam-1858	314	11	γ(2−	γ(2−	PROPN
ejpam-1858	314	12	q	q	NOUN
ejpam-1858	314	13	)	)	PUNCT
ejpam-1858	314	14	−	−	PROPN
ejpam-1858	314	15	∂	∂	NUM
ejpam-1858	314	16	∂	∂	NOUN
ejpam-1858	314	17	x	x	PUNCT
ejpam-1858	315	1	[	[	X
ejpam-1858	315	2	τk(x	τk(x	NOUN
ejpam-1858	315	3	)	)	PUNCT
ejpam-1858	315	4	]	]	PUNCT
ejpam-1858	316	1	f	f	X
ejpam-1858	316	2	(	(	PUNCT
ejpam-1858	316	3	t	t	PROPN
ejpam-1858	316	4	,	,	PUNCT
ejpam-1858	316	5	x	x	X
ejpam-1858	316	6	)	)	PUNCT
ejpam-1858	316	7	6=	6=	ADP
ejpam-1858	316	8	0	0	NUM
ejpam-1858	316	9	since	since	SCONJ
ejpam-1858	316	10	c	c	PROPN
ejpam-1858	316	11	dqσ	dqσ	VERB
ejpam-1858	316	12	6=	6=	ADP
ejpam-1858	316	13	0	0	NUM
ejpam-1858	316	14	in	in	ADP
ejpam-1858	316	15	a	a	DET
ejpam-1858	316	16	small	small	ADJ
ejpam-1858	316	17	right	right	ADJ
ejpam-1858	316	18	neighborhood	neighborhood	NOUN
ejpam-1858	316	19	of	of	ADP
ejpam-1858	316	20	t0	t0	PROPN
ejpam-1858	316	21	and	and	CCONJ
ejpam-1858	316	22	σ(t0	σ(t0	NOUN
ejpam-1858	316	23	)	)	PUNCT
ejpam-1858	317	1	=	=	SYM
ejpam-1858	317	2	0	0	NUM
ejpam-1858	317	3	,	,	PUNCT
ejpam-1858	317	4	we	we	PRON
ejpam-1858	317	5	have	have	VERB
ejpam-1858	317	6	by	by	ADP
ejpam-1858	317	7	lemma	lemma	PROPN
ejpam-1858	317	8	2	2	NUM
ejpam-1858	317	9	,	,	PUNCT
ejpam-1858	317	10	σ(t	σ(t	PROPN
ejpam-1858	317	11	)	)	PUNCT
ejpam-1858	317	12	is	be	AUX
ejpam-1858	317	13	either	either	CCONJ
ejpam-1858	317	14	strictly	strictly	ADV
ejpam-1858	317	15	increasing	increase	VERB
ejpam-1858	317	16	or	or	CCONJ
ejpam-1858	317	17	decreasing	decrease	VERB
ejpam-1858	317	18	in	in	ADP
ejpam-1858	317	19	that	that	DET
ejpam-1858	317	20	neighbourhood	neighbourhood	NOUN
ejpam-1858	317	21	and	and	CCONJ
ejpam-1858	317	22	therefore	therefore	ADV
ejpam-1858	317	23	,	,	PUNCT
ejpam-1858	317	24	t	t	PROPN
ejpam-1858	317	25	6=	6=	NUM
ejpam-1858	317	26	τk(x(t	τk(x(t	NOUN
ejpam-1858	317	27	)	)	PUNCT
ejpam-1858	317	28	)	)	PUNCT
ejpam-1858	317	29	for	for	ADP
ejpam-1858	317	30	0	0	NUM
ejpam-1858	317	31	<	<	X
ejpam-1858	317	32	t	t	X
ejpam-1858	317	33	−	−	PROPN
ejpam-1858	317	34	t0	t0	PROPN
ejpam-1858	317	35	<	<	X
ejpam-1858	317	36	δ2	δ2	VERB
ejpam-1858	317	37	for	for	ADP
ejpam-1858	317	38	some	some	DET
ejpam-1858	317	39	δ2	δ2	VERB
ejpam-1858	317	40	>	>	X
ejpam-1858	317	41	0	0	X
ejpam-1858	317	42	.	.	PUNCT
ejpam-1858	318	1	since	since	SCONJ
ejpam-1858	318	2	τi(x	τi(x	NUM
ejpam-1858	318	3	)	)	PUNCT
ejpam-1858	318	4	<	<	X
ejpam-1858	318	5	τ	τ	PROPN
ejpam-1858	318	6	j(x	j(x	PROPN
ejpam-1858	318	7	)	)	PUNCT
ejpam-1858	318	8	for	for	ADP
ejpam-1858	318	9	i	i	PRON
ejpam-1858	318	10	<	<	X
ejpam-1858	318	11	j	j	PROPN
ejpam-1858	318	12	and	and	CCONJ
ejpam-1858	318	13	t0	t0	PROPN
ejpam-1858	318	14	=	=	PUNCT
ejpam-1858	318	15	τk(x0	τk(x0	NUM
ejpam-1858	318	16	)	)	PUNCT
ejpam-1858	318	17	we	we	PRON
ejpam-1858	318	18	have	have	VERB
ejpam-1858	318	19	t	t	PROPN
ejpam-1858	318	20	6=	6=	NUM
ejpam-1858	318	21	τ	τ	PROPN
ejpam-1858	318	22	j(x(t	j(x(t	PROPN
ejpam-1858	318	23	)	)	PUNCT
ejpam-1858	318	24	)	)	PUNCT
ejpam-1858	319	1	for	for	ADP
ejpam-1858	319	2	j	j	PROPN
ejpam-1858	319	3	6=	6=	PROPN
ejpam-1858	319	4	k	k	PROPN
ejpam-1858	319	5	and	and	CCONJ
ejpam-1858	319	6	t	t	PROPN
ejpam-1858	319	7	sufficiently	sufficiently	ADV
ejpam-1858	319	8	close	close	ADJ
ejpam-1858	319	9	to	to	ADP
ejpam-1858	319	10	t0	t0	NOUN
ejpam-1858	319	11	.	.	PUNCT
ejpam-1858	320	1	therefore	therefore	ADV
ejpam-1858	320	2	,	,	PUNCT
ejpam-1858	320	3	s	s	PROPN
ejpam-1858	320	4	6=	6=	NUM
ejpam-1858	320	5	τi(x(s	τi(x(s	NOUN
ejpam-1858	320	6	)	)	PUNCT
ejpam-1858	320	7	)	)	PUNCT
ejpam-1858	321	1	for	for	ADP
ejpam-1858	321	2	any	any	DET
ejpam-1858	321	3	i	i	PROPN
ejpam-1858	321	4	,	,	PUNCT
ejpam-1858	321	5	t0	t0	PROPN
ejpam-1858	321	6	<	<	X
ejpam-1858	321	7	s	s	X
ejpam-1858	321	8	<	<	X
ejpam-1858	321	9	t0	t0	PROPN
ejpam-1858	321	10	+	+	CCONJ
ejpam-1858	321	11	δ	δ	PROPN
ejpam-1858	321	12	,	,	PUNCT
ejpam-1858	321	13	for	for	ADP
ejpam-1858	321	14	some	some	DET
ejpam-1858	321	15	δ	δ	PROPN
ejpam-1858	321	16	>	>	X
ejpam-1858	321	17	0	0	PROPN
ejpam-1858	321	18	.	.	PUNCT
ejpam-1858	322	1	hence	hence	ADV
ejpam-1858	322	2	x(t	x(t	PROPN
ejpam-1858	322	3	)	)	PUNCT
ejpam-1858	322	4	is	be	AUX
ejpam-1858	322	5	a	a	DET
ejpam-1858	322	6	local	local	ADJ
ejpam-1858	322	7	solution	solution	NOUN
ejpam-1858	322	8	of	of	ADP
ejpam-1858	322	9	the	the	DET
ejpam-1858	322	10	system	system	NOUN
ejpam-1858	322	11	(	(	PUNCT
ejpam-1858	322	12	7	7	NUM
ejpam-1858	322	13	)	)	PUNCT
ejpam-1858	322	14	.	.	PUNCT
ejpam-1858	323	1	regarding	regard	VERB
ejpam-1858	323	2	the	the	DET
ejpam-1858	323	3	initial	initial	ADJ
ejpam-1858	323	4	value	value	NOUN
ejpam-1858	323	5	problem	problem	NOUN
ejpam-1858	323	6	(	(	PUNCT
ejpam-1858	323	7	7	7	X
ejpam-1858	323	8	)	)	PUNCT
ejpam-1858	323	9	we	we	PRON
ejpam-1858	323	10	have	have	VERB
ejpam-1858	323	11	the	the	DET
ejpam-1858	323	12	following	follow	VERB
ejpam-1858	323	13	two	two	NUM
ejpam-1858	323	14	cases	case	NOUN
ejpam-1858	323	15	:	:	PUNCT
ejpam-1858	323	16	(	(	PUNCT
ejpam-1858	323	17	i	i	NOUN
ejpam-1858	323	18	)	)	PUNCT
ejpam-1858	323	19	if	if	SCONJ
ejpam-1858	323	20	t0	t0	PROPN
ejpam-1858	323	21	6=	6=	PRON
ejpam-1858	323	22	τk(x0	τk(x0	NOUN
ejpam-1858	323	23	)	)	PUNCT
ejpam-1858	323	24	,	,	PUNCT
ejpam-1858	323	25	for	for	ADP
ejpam-1858	323	26	all	all	DET
ejpam-1858	323	27	k	k	PROPN
ejpam-1858	323	28	≥	≥	NUM
ejpam-1858	323	29	1	1	NUM
ejpam-1858	323	30	,	,	PUNCT
ejpam-1858	323	31	then	then	ADV
ejpam-1858	323	32	a	a	DET
ejpam-1858	323	33	solution	solution	NOUN
ejpam-1858	323	34	of	of	ADP
ejpam-1858	323	35	(	(	PUNCT
ejpam-1858	323	36	7	7	NUM
ejpam-1858	323	37	)	)	PUNCT
ejpam-1858	323	38	is	be	AUX
ejpam-1858	323	39	understood	understand	VERB
ejpam-1858	323	40	in	in	ADP
ejpam-1858	323	41	the	the	DET
ejpam-1858	323	42	classical	classical	ADJ
ejpam-1858	323	43	sense	sense	NOUN
ejpam-1858	323	44	;	;	PUNCT
ejpam-1858	323	45	(	(	PUNCT
ejpam-1858	323	46	ii	ii	NOUN
ejpam-1858	323	47	)	)	PUNCT
ejpam-1858	323	48	if	if	SCONJ
ejpam-1858	323	49	t0	t0	PROPN
ejpam-1858	323	50	=	=	PUNCT
ejpam-1858	323	51	τk(x0	τk(x0	NUM
ejpam-1858	323	52	)	)	PUNCT
ejpam-1858	323	53	,	,	PUNCT
ejpam-1858	323	54	for	for	ADP
ejpam-1858	323	55	some	some	DET
ejpam-1858	323	56	k	k	PROPN
ejpam-1858	323	57	≥	≥	NUM
ejpam-1858	323	58	1	1	NUM
ejpam-1858	323	59	,	,	PUNCT
ejpam-1858	323	60	then	then	ADV
ejpam-1858	323	61	a	a	DET
ejpam-1858	323	62	solution	solution	NOUN
ejpam-1858	323	63	of	of	ADP
ejpam-1858	323	64	(	(	PUNCT
ejpam-1858	323	65	7	7	NUM
ejpam-1858	323	66	)	)	PUNCT
ejpam-1858	323	67	is	be	AUX
ejpam-1858	323	68	understood	understand	VERB
ejpam-1858	323	69	in	in	ADP
ejpam-1858	323	70	some	some	DET
ejpam-1858	323	71	extended	extended	ADJ
ejpam-1858	323	72	sense	sense	NOUN
ejpam-1858	323	73	depending	depend	VERB
ejpam-1858	323	74	on	on	ADP
ejpam-1858	323	75	the	the	DET
ejpam-1858	323	76	smoothness	smoothness	NOUN
ejpam-1858	323	77	of	of	ADP
ejpam-1858	323	78	f	f	PROPN
ejpam-1858	323	79	.	.	PUNCT
ejpam-1858	324	1	a	a	DET
ejpam-1858	324	2	solution	solution	NOUN
ejpam-1858	324	3	x(t	x(t	PROPN
ejpam-1858	324	4	,	,	PUNCT
ejpam-1858	324	5	t0	t0	PROPN
ejpam-1858	324	6	,	,	PUNCT
ejpam-1858	324	7	x0	x0	PROPN
ejpam-1858	324	8	)	)	PUNCT
ejpam-1858	324	9	of	of	ADP
ejpam-1858	324	10	(	(	PUNCT
ejpam-1858	324	11	7	7	X
ejpam-1858	324	12	)	)	PUNCT
ejpam-1858	324	13	existing	exist	VERB
ejpam-1858	324	14	on	on	ADP
ejpam-1858	324	15	some	some	DET
ejpam-1858	324	16	interval	interval	NOUN
ejpam-1858	324	17	[	[	X
ejpam-1858	324	18	t0	t0	NOUN
ejpam-1858	324	19	,	,	PUNCT
ejpam-1858	324	20	t0	t0	PROPN
ejpam-1858	324	21	+	+	CCONJ
ejpam-1858	324	22	a	a	X
ejpam-1858	324	23	)	)	PUNCT
ejpam-1858	324	24	and	and	CCONJ
ejpam-1858	324	25	experiencing	experience	VERB
ejpam-1858	324	26	impulses	impulse	NOUN
ejpam-1858	324	27	at	at	ADP
ejpam-1858	324	28	the	the	DET
ejpam-1858	324	29	points	point	NOUN
ejpam-1858	324	30	{	{	PUNCT
ejpam-1858	324	31	t	t	X
ejpam-1858	324	32	i	i	X
ejpam-1858	324	33	}	}	PUNCT
ejpam-1858	324	34	,	,	PUNCT
ejpam-1858	324	35	t0	t0	PROPN
ejpam-1858	324	36	<	<	X
ejpam-1858	325	1	t	t	X
ejpam-1858	325	2	i	i	PRON
ejpam-1858	325	3	<	<	X
ejpam-1858	325	4	t0	t0	PROPN
ejpam-1858	325	5	+	+	CCONJ
ejpam-1858	325	6	a	a	X
ejpam-1858	325	7	,	,	PUNCT
ejpam-1858	325	8	t	t	X
ejpam-1858	326	1	i	i	PRON
ejpam-1858	326	2	<	<	X
ejpam-1858	326	3	t	t	PROPN
ejpam-1858	326	4	j	j	PROPN
ejpam-1858	326	5	for	for	ADP
ejpam-1858	326	6	i	i	PRON
ejpam-1858	326	7	<	<	X
ejpam-1858	326	8	j	j	PROPN
ejpam-1858	326	9	,	,	PUNCT
ejpam-1858	326	10	is	be	AUX
ejpam-1858	326	11	described	describe	VERB
ejpam-1858	326	12	as	as	SCONJ
ejpam-1858	326	13	follows	follow	VERB
ejpam-1858	326	14	:	:	PUNCT
ejpam-1858	326	15	x(t	x(t	PROPN
ejpam-1858	326	16	,	,	PUNCT
ejpam-1858	326	17	t0	t0	PROPN
ejpam-1858	326	18	,	,	PUNCT
ejpam-1858	326	19	x0	x0	PROPN
ejpam-1858	326	20	)	)	PUNCT
ejpam-1858	327	1	=	=	PUNCT
ejpam-1858	327	2			PROPN
ejpam-1858	327	3			X
ejpam-1858	327	4			PROPN
ejpam-1858	327	5			PROPN
ejpam-1858	327	6			PROPN
ejpam-1858	327	7			PROPN
ejpam-1858	327	8			PROPN
ejpam-1858	327	9			PROPN
ejpam-1858	327	10			PROPN
ejpam-1858	327	11			PROPN
ejpam-1858	327	12			PROPN
ejpam-1858	327	13			NOUN
ejpam-1858	327	14			PROPN
ejpam-1858	327	15			PROPN
ejpam-1858	327	16			PROPN
ejpam-1858	327	17			PROPN
ejpam-1858	327	18			PROPN
ejpam-1858	327	19			PROPN
ejpam-1858	327	20			PROPN
ejpam-1858	327	21			PROPN
ejpam-1858	327	22			PROPN
ejpam-1858	327	23			PROPN
ejpam-1858	327	24			NOUN
ejpam-1858	327	25	x(t	x(t	PROPN
ejpam-1858	327	26	,	,	PUNCT
ejpam-1858	327	27	t0	t0	PROPN
ejpam-1858	327	28	,	,	PUNCT
ejpam-1858	327	29	x0	x0	PROPN
ejpam-1858	327	30	)	)	PUNCT
ejpam-1858	327	31	,	,	PUNCT
ejpam-1858	327	32	t0	t0	PROPN
ejpam-1858	327	33	≤	≤	PROPN
ejpam-1858	327	34	t	t	PROPN
ejpam-1858	327	35	≤	≤	NUM
ejpam-1858	327	36	t1	t1	PROPN
ejpam-1858	327	37	,	,	PUNCT
ejpam-1858	327	38	x(t	x(t	PROPN
ejpam-1858	327	39	,	,	PUNCT
ejpam-1858	327	40	t1	t1	PROPN
ejpam-1858	327	41	,	,	PUNCT
ejpam-1858	327	42	x+	x+	X
ejpam-1858	327	43	1	1	NUM
ejpam-1858	327	44	)	)	PUNCT
ejpam-1858	328	1	,	,	PUNCT
ejpam-1858	328	2	t1	t1	NOUN
ejpam-1858	328	3	<	<	X
ejpam-1858	328	4	t	t	PROPN
ejpam-1858	328	5	≤	≤	NUM
ejpam-1858	328	6	t2	t2	NOUN
ejpam-1858	328	7	,	,	PUNCT
ejpam-1858	328	8	.	.	PUNCT
ejpam-1858	328	9	.	.	PUNCT
ejpam-1858	328	10	.	.	PUNCT
ejpam-1858	328	11	.	.	PUNCT
ejpam-1858	328	12	.	.	PUNCT
ejpam-1858	328	13	.	.	PUNCT
ejpam-1858	328	14	.	.	PUNCT
ejpam-1858	328	15	.	.	PUNCT
ejpam-1858	328	16	.	.	PUNCT
ejpam-1858	328	17	.	.	PUNCT
ejpam-1858	328	18	.	.	PUNCT
ejpam-1858	328	19	.	.	PUNCT
ejpam-1858	329	1	x(t	x(t	PROPN
ejpam-1858	329	2	,	,	PUNCT
ejpam-1858	329	3	t	t	PROPN
ejpam-1858	329	4	i	i	PRON
ejpam-1858	329	5	,	,	PUNCT
ejpam-1858	329	6	x+	x+	PROPN
ejpam-1858	329	7	i	i	PROPN
ejpam-1858	329	8	)	)	PUNCT
ejpam-1858	329	9	,	,	PUNCT
ejpam-1858	329	10	t	t	X
ejpam-1858	330	1	i	i	PRON
ejpam-1858	330	2	<	<	X
ejpam-1858	330	3	t	t	X
ejpam-1858	330	4	≤	≤	X
ejpam-1858	330	5	t	t	PROPN
ejpam-1858	330	6	i+1	i+1	NOUN
ejpam-1858	330	7	,	,	PUNCT
ejpam-1858	330	8	.	.	PUNCT
ejpam-1858	330	9	.	.	PUNCT
ejpam-1858	330	10	.	.	PUNCT
ejpam-1858	330	11	.	.	PUNCT
ejpam-1858	330	12	.	.	PUNCT
ejpam-1858	330	13	.	.	PUNCT
ejpam-1858	330	14	.	.	PUNCT
ejpam-1858	330	15	.	.	PUNCT
ejpam-1858	330	16	.	.	PUNCT
ejpam-1858	330	17	.	.	PUNCT
ejpam-1858	330	18	.	.	PUNCT
ejpam-1858	330	19	.	.	PUNCT
ejpam-1858	330	20	.	.	PUNCT
ejpam-1858	331	1	where	where	SCONJ
ejpam-1858	331	2	x+	x+	PUNCT
ejpam-1858	331	3	i	i	NOUN
ejpam-1858	331	4	=	=	PUNCT
ejpam-1858	331	5	x	x	VERB
ejpam-1858	331	6	i	i	PRON
ejpam-1858	331	7	+	+	X
ejpam-1858	331	8	ik(x	ik(x	X
ejpam-1858	331	9	i	i	NOUN
ejpam-1858	331	10	)	)	PUNCT
ejpam-1858	331	11	and	and	CCONJ
ejpam-1858	331	12	x	x	X
ejpam-1858	331	13	i	i	NOUN
ejpam-1858	331	14	=	=	PUNCT
ejpam-1858	331	15	x(t	x(t	PROPN
ejpam-1858	331	16	i	i	PRON
ejpam-1858	331	17	)	)	PUNCT
ejpam-1858	331	18	.	.	PUNCT
ejpam-1858	332	1	consequently	consequently	ADV
ejpam-1858	332	2	,	,	PUNCT
ejpam-1858	332	3	even	even	ADV
ejpam-1858	332	4	when	when	SCONJ
ejpam-1858	332	5	t0	t0	PROPN
ejpam-1858	332	6	6=	6=	PRON
ejpam-1858	332	7	τk(x0	τk(x0	NOUN
ejpam-1858	332	8	)	)	PUNCT
ejpam-1858	332	9	,	,	PUNCT
ejpam-1858	332	10	for	for	ADP
ejpam-1858	332	11	any	any	DET
ejpam-1858	332	12	k	k	PROPN
ejpam-1858	332	13	≥	≥	NUM
ejpam-1858	332	14	1	1	NUM
ejpam-1858	332	15	,	,	PUNCT
ejpam-1858	332	16	it	it	PRON
ejpam-1858	332	17	is	be	AUX
ejpam-1858	332	18	possible	possible	ADJ
ejpam-1858	332	19	that	that	SCONJ
ejpam-1858	332	20	for	for	ADP
ejpam-1858	332	21	some	some	DET
ejpam-1858	332	22	i	i	PROPN
ejpam-1858	332	23	,	,	PUNCT
ejpam-1858	332	24	(	(	PUNCT
ejpam-1858	332	25	t	t	NOUN
ejpam-1858	332	26	i	i	PRON
ejpam-1858	332	27	,	,	PUNCT
ejpam-1858	332	28	x+	x+	PROPN
ejpam-1858	332	29	i	i	PROPN
ejpam-1858	332	30	)	)	PUNCT
ejpam-1858	332	31	lies	lie	VERB
ejpam-1858	332	32	on	on	ADP
ejpam-1858	332	33	a	a	DET
ejpam-1858	332	34	surface	surface	NOUN
ejpam-1858	332	35	s	s	PROPN
ejpam-1858	332	36	j	j	PROPN
ejpam-1858	332	37	.	.	PUNCT
ejpam-1858	333	1	in	in	ADP
ejpam-1858	333	2	that	that	DET
ejpam-1858	333	3	case	case	NOUN
ejpam-1858	333	4	,	,	PUNCT
ejpam-1858	333	5	that	that	DET
ejpam-1858	333	6	part	part	NOUN
ejpam-1858	333	7	of	of	ADP
ejpam-1858	333	8	the	the	DET
ejpam-1858	333	9	solution	solution	NOUN
ejpam-1858	333	10	x(t	x(t	PROPN
ejpam-1858	333	11	,	,	PUNCT
ejpam-1858	333	12	t0	t0	PROPN
ejpam-1858	333	13	,	,	PUNCT
ejpam-1858	333	14	x0	x0	PROPN
ejpam-1858	333	15	)	)	PUNCT
ejpam-1858	333	16	on	on	ADP
ejpam-1858	333	17	the	the	DET
ejpam-1858	333	18	interval	interval	NOUN
ejpam-1858	333	19	(	(	PUNCT
ejpam-1858	333	20	t	t	NOUN
ejpam-1858	333	21	i	i	PRON
ejpam-1858	333	22	,	,	PUNCT
ejpam-1858	333	23	t	t	PROPN
ejpam-1858	333	24	i+1	i+1	ADV
ejpam-1858	333	25	]	]	PUNCT
ejpam-1858	333	26	consists	consist	VERB
ejpam-1858	333	27	of	of	ADP
ejpam-1858	333	28	x(t	x(t	PROPN
ejpam-1858	333	29	,	,	PUNCT
ejpam-1858	333	30	t	t	PROPN
ejpam-1858	333	31	i	i	PRON
ejpam-1858	333	32	,	,	PUNCT
ejpam-1858	333	33	x+	x+	PROPN
ejpam-1858	333	34	i	i	PROPN
ejpam-1858	333	35	)	)	PUNCT
ejpam-1858	333	36	which	which	PRON
ejpam-1858	333	37	is	be	AUX
ejpam-1858	333	38	a	a	DET
ejpam-1858	333	39	solution	solution	NOUN
ejpam-1858	333	40	of	of	ADP
ejpam-1858	333	41	(	(	PUNCT
ejpam-1858	333	42	7	7	NUM
ejpam-1858	333	43	)	)	PUNCT
ejpam-1858	333	44	on	on	ADP
ejpam-1858	333	45	[	[	X
ejpam-1858	333	46	t	t	X
ejpam-1858	333	47	i	i	PRON
ejpam-1858	333	48	,	,	PUNCT
ejpam-1858	333	49	t	t	PROPN
ejpam-1858	333	50	i+1	i+1	X
ejpam-1858	333	51	]	]	X
ejpam-1858	333	52	in	in	ADP
ejpam-1858	333	53	the	the	DET
ejpam-1858	333	54	extended	extended	ADJ
ejpam-1858	333	55	sense	sense	NOUN
ejpam-1858	333	56	.	.	PUNCT
ejpam-1858	334	1	given	give	VERB
ejpam-1858	334	2	a	a	DET
ejpam-1858	334	3	solution	solution	NOUN
ejpam-1858	334	4	x(t	x(t	PROPN
ejpam-1858	334	5	)	)	PUNCT
ejpam-1858	334	6	of	of	ADP
ejpam-1858	334	7	(	(	PUNCT
ejpam-1858	334	8	7	7	NUM
ejpam-1858	334	9	)	)	PUNCT
ejpam-1858	334	10	,	,	PUNCT
ejpam-1858	334	11	defined	define	VERB
ejpam-1858	334	12	on	on	ADP
ejpam-1858	334	13	[	[	X
ejpam-1858	334	14	t0	t0	NOUN
ejpam-1858	334	15	,	,	PUNCT
ejpam-1858	334	16	t0	t0	PROPN
ejpam-1858	334	17	+	+	CCONJ
ejpam-1858	334	18	a	a	X
ejpam-1858	334	19	)	)	PUNCT
ejpam-1858	334	20	with	with	ADP
ejpam-1858	334	21	a	a	DET
ejpam-1858	334	22	>	>	X
ejpam-1858	334	23	0	0	NUM
ejpam-1858	334	24	,	,	PUNCT
ejpam-1858	334	25	we	we	PRON
ejpam-1858	334	26	say	say	VERB
ejpam-1858	334	27	that	that	SCONJ
ejpam-1858	334	28	a	a	DET
ejpam-1858	334	29	solution	solution	NOUN
ejpam-1858	334	30	y(t	y(t	NUM
ejpam-1858	334	31	)	)	PUNCT
ejpam-1858	334	32	of	of	ADP
ejpam-1858	334	33	(	(	PUNCT
ejpam-1858	334	34	7	7	X
ejpam-1858	334	35	)	)	PUNCT
ejpam-1858	334	36	is	be	AUX
ejpam-1858	334	37	a	a	DET
ejpam-1858	334	38	proper	proper	ADJ
ejpam-1858	334	39	continuation	continuation	NOUN
ejpam-1858	334	40	to	to	ADP
ejpam-1858	334	41	the	the	DET
ejpam-1858	334	42	right	right	NOUN
ejpam-1858	334	43	of	of	ADP
ejpam-1858	334	44	x(t	x(t	PROPN
ejpam-1858	334	45	)	)	PUNCT
ejpam-1858	334	46	if	if	SCONJ
ejpam-1858	334	47	y(t	y(t	NUM
ejpam-1858	334	48	)	)	PUNCT
ejpam-1858	334	49	is	be	AUX
ejpam-1858	334	50	defined	define	VERB
ejpam-1858	334	51	on	on	ADP
ejpam-1858	334	52	[	[	X
ejpam-1858	334	53	t0	t0	NOUN
ejpam-1858	334	54	,	,	PUNCT
ejpam-1858	334	55	t0	t0	PROPN
ejpam-1858	334	56	+	+	CCONJ
ejpam-1858	334	57	b	b	X
ejpam-1858	334	58	)	)	PUNCT
ejpam-1858	334	59	for	for	ADP
ejpam-1858	334	60	some	some	DET
ejpam-1858	334	61	b	b	PROPN
ejpam-1858	334	62	>	>	X
ejpam-1858	334	63	a	a	PRON
ejpam-1858	334	64	and	and	CCONJ
ejpam-1858	334	65	x(t	x(t	PROPN
ejpam-1858	334	66	)	)	PUNCT
ejpam-1858	335	1	=	=	SYM
ejpam-1858	335	2	y(t	y(t	PROPN
ejpam-1858	335	3	)	)	PUNCT
ejpam-1858	335	4	for	for	ADP
ejpam-1858	335	5	t	t	PROPN
ejpam-1858	335	6	∈	∈	PROPN
ejpam-1858	335	7	[	[	X
ejpam-1858	335	8	t0	t0	PROPN
ejpam-1858	335	9	,	,	PUNCT
ejpam-1858	335	10	t0	t0	PROPN
ejpam-1858	335	11	+	+	CCONJ
ejpam-1858	335	12	a	a	X
ejpam-1858	335	13	)	)	PUNCT
ejpam-1858	335	14	.	.	PUNCT
ejpam-1858	336	1	the	the	DET
ejpam-1858	336	2	interval	interval	NOUN
ejpam-1858	336	3	[	[	X
ejpam-1858	336	4	t0	t0	NOUN
ejpam-1858	336	5	,	,	PUNCT
ejpam-1858	336	6	t0	t0	PROPN
ejpam-1858	336	7	+	+	CCONJ
ejpam-1858	336	8	a	a	X
ejpam-1858	336	9	)	)	PUNCT
ejpam-1858	336	10	is	be	AUX
ejpam-1858	336	11	called	call	VERB
ejpam-1858	336	12	the	the	DET
ejpam-1858	336	13	maximal	maximal	ADJ
ejpam-1858	336	14	interval	interval	NOUN
ejpam-1858	336	15	of	of	ADP
ejpam-1858	336	16	existence	existence	NOUN
ejpam-1858	336	17	of	of	ADP
ejpam-1858	336	18	a	a	DET
ejpam-1858	336	19	solution	solution	NOUN
ejpam-1858	336	20	x(t	x(t	PROPN
ejpam-1858	336	21	)	)	PUNCT
ejpam-1858	336	22	of	of	ADP
ejpam-1858	336	23	(	(	PUNCT
ejpam-1858	336	24	7	7	NUM
ejpam-1858	336	25	)	)	PUNCT
ejpam-1858	336	26	,	,	PUNCT
ejpam-1858	336	27	if	if	SCONJ
ejpam-1858	336	28	x(t	x(t	PROPN
ejpam-1858	336	29	)	)	PUNCT
ejpam-1858	336	30	is	be	AUX
ejpam-1858	336	31	well	well	ADV
ejpam-1858	336	32	defined	define	VERB
ejpam-1858	336	33	on	on	ADP
ejpam-1858	336	34	references	reference	NOUN
ejpam-1858	336	35	127	127	NUM
ejpam-1858	336	36	[	[	X
ejpam-1858	336	37	t0	t0	PROPN
ejpam-1858	336	38	,	,	PUNCT
ejpam-1858	336	39	t0	t0	PROPN
ejpam-1858	336	40	+	+	CCONJ
ejpam-1858	336	41	a	a	X
ejpam-1858	336	42	)	)	PUNCT
ejpam-1858	336	43	and	and	CCONJ
ejpam-1858	336	44	it	it	PRON
ejpam-1858	336	45	does	do	AUX
ejpam-1858	336	46	not	not	PART
ejpam-1858	336	47	have	have	VERB
ejpam-1858	336	48	any	any	DET
ejpam-1858	336	49	proper	proper	ADJ
ejpam-1858	336	50	continuation	continuation	NOUN
ejpam-1858	336	51	to	to	ADP
ejpam-1858	336	52	the	the	DET
ejpam-1858	336	53	right	right	NOUN
ejpam-1858	336	54	.	.	PUNCT
ejpam-1858	337	1	if	if	SCONJ
ejpam-1858	337	2	x(t	x(t	PROPN
ejpam-1858	337	3	)	)	PUNCT
ejpam-1858	337	4	is	be	AUX
ejpam-1858	337	5	a	a	DET
ejpam-1858	337	6	solution	solution	NOUN
ejpam-1858	337	7	of	of	ADP
ejpam-1858	337	8	the	the	DET
ejpam-1858	337	9	system	system	NOUN
ejpam-1858	337	10	(	(	PUNCT
ejpam-1858	337	11	7	7	NUM
ejpam-1858	337	12	)	)	PUNCT
ejpam-1858	337	13	with	with	ADP
ejpam-1858	337	14	maximal	maximal	ADJ
ejpam-1858	337	15	interval	interval	NOUN
ejpam-1858	337	16	of	of	ADP
ejpam-1858	337	17	existence	existence	NOUN
ejpam-1858	337	18	[	[	X
ejpam-1858	337	19	t0	t0	NOUN
ejpam-1858	337	20	,	,	PUNCT
ejpam-1858	337	21	t0	t0	PROPN
ejpam-1858	337	22	+	+	CCONJ
ejpam-1858	337	23	a	a	X
ejpam-1858	337	24	)	)	PUNCT
ejpam-1858	337	25	and	and	CCONJ
ejpam-1858	337	26	if	if	SCONJ
ejpam-1858	337	27	a	a	DET
ejpam-1858	337	28	<	<	X
ejpam-1858	337	29	∞	∞	NOUN
ejpam-1858	337	30	,	,	PUNCT
ejpam-1858	337	31	then	then	ADV
ejpam-1858	337	32	either	either	CCONJ
ejpam-1858	337	33	x(t	x(t	PROPN
ejpam-1858	337	34	)	)	PUNCT
ejpam-1858	337	35	approaches	approach	VERB
ejpam-1858	337	36	the	the	DET
ejpam-1858	337	37	boundary	boundary	NOUN
ejpam-1858	337	38	of	of	ADP
ejpam-1858	337	39	ω	ω	NUM
ejpam-1858	337	40	or	or	CCONJ
ejpam-1858	337	41	|x(t)|	|x(t)|	PROPN
ejpam-1858	337	42	becomes	become	VERB
ejpam-1858	337	43	unbounded	unbounded	ADJ
ejpam-1858	337	44	as	as	ADP
ejpam-1858	337	45	t	t	PROPN
ejpam-1858	337	46	→	→	SYM
ejpam-1858	337	47	(	(	PUNCT
ejpam-1858	337	48	t0	t0	NOUN
ejpam-1858	337	49	+	+	CCONJ
ejpam-1858	337	50	a)−.	a)−.	NOUN
ejpam-1858	337	51	definition	definition	NOUN
ejpam-1858	337	52	6	6	NUM
ejpam-1858	337	53	(	(	PUNCT
ejpam-1858	337	54	regular	regular	ADJ
ejpam-1858	337	55	and	and	CCONJ
ejpam-1858	337	56	irregular	irregular	ADJ
ejpam-1858	337	57	points	point	NOUN
ejpam-1858	337	58	)	)	PUNCT
ejpam-1858	337	59	.	.	PUNCT
ejpam-1858	338	1	a	a	DET
ejpam-1858	338	2	point	point	NOUN
ejpam-1858	338	3	(	(	PUNCT
ejpam-1858	338	4	t1	t1	NOUN
ejpam-1858	338	5	,	,	PUNCT
ejpam-1858	338	6	x1	x1	PROPN
ejpam-1858	338	7	)	)	PUNCT
ejpam-1858	338	8	is	be	AUX
ejpam-1858	338	9	said	say	VERB
ejpam-1858	338	10	to	to	PART
ejpam-1858	338	11	be	be	AUX
ejpam-1858	338	12	a	a	DET
ejpam-1858	338	13	regular	regular	ADJ
ejpam-1858	338	14	point	point	NOUN
ejpam-1858	338	15	if	if	SCONJ
ejpam-1858	338	16	t1	t1	PROPN
ejpam-1858	338	17	6=	6=	PROPN
ejpam-1858	338	18	τk(x(t1	τk(x(t1	PROPN
ejpam-1858	338	19	)	)	PUNCT
ejpam-1858	338	20	)	)	PUNCT
ejpam-1858	338	21	for	for	ADP
ejpam-1858	338	22	all	all	DET
ejpam-1858	338	23	k	k	PROPN
ejpam-1858	338	24	≥	≥	NUM
ejpam-1858	338	25	1	1	NUM
ejpam-1858	338	26	,	,	PUNCT
ejpam-1858	338	27	otherwise	otherwise	ADV
ejpam-1858	338	28	it	it	PRON
ejpam-1858	338	29	is	be	AUX
ejpam-1858	338	30	said	say	VERB
ejpam-1858	338	31	to	to	PART
ejpam-1858	338	32	be	be	AUX
ejpam-1858	338	33	an	an	DET
ejpam-1858	338	34	irregular	irregular	ADJ
ejpam-1858	338	35	point	point	NOUN
ejpam-1858	338	36	.	.	PUNCT
ejpam-1858	339	1	we	we	PRON
ejpam-1858	339	2	now	now	ADV
ejpam-1858	339	3	proceed	proceed	VERB
ejpam-1858	339	4	to	to	PART
ejpam-1858	339	5	state	state	VERB
ejpam-1858	339	6	a	a	DET
ejpam-1858	339	7	result	result	NOUN
ejpam-1858	339	8	on	on	ADP
ejpam-1858	339	9	continuation	continuation	NOUN
ejpam-1858	339	10	of	of	ADP
ejpam-1858	339	11	solutions	solution	NOUN
ejpam-1858	339	12	of	of	ADP
ejpam-1858	339	13	the	the	DET
ejpam-1858	339	14	caputo	caputo	PROPN
ejpam-1858	339	15	fractional	fractional	PROPN
ejpam-1858	339	16	differential	differential	ADJ
ejpam-1858	339	17	equations	equation	NOUN
ejpam-1858	339	18	with	with	ADP
ejpam-1858	339	19	variable	variable	ADJ
ejpam-1858	339	20	moments	moment	NOUN
ejpam-1858	339	21	of	of	ADP
ejpam-1858	339	22	impulse	impulse	ADJ
ejpam-1858	339	23	.	.	PUNCT
ejpam-1858	340	1	the	the	DET
ejpam-1858	340	2	proof	proof	NOUN
ejpam-1858	340	3	is	be	AUX
ejpam-1858	340	4	parallel	parallel	ADJ
ejpam-1858	340	5	to	to	ADP
ejpam-1858	340	6	the	the	DET
ejpam-1858	340	7	theorem	theorem	ADJ
ejpam-1858	340	8	1.2.3	1.2.3	NUM
ejpam-1858	340	9	in	in	ADP
ejpam-1858	340	10	[	[	X
ejpam-1858	340	11	9	9	NUM
ejpam-1858	340	12	]	]	PUNCT
ejpam-1858	340	13	and	and	CCONJ
ejpam-1858	340	14	hence	hence	ADV
ejpam-1858	340	15	omitted	omit	VERB
ejpam-1858	340	16	.	.	PUNCT
ejpam-1858	341	1	theorem	theorem	NOUN
ejpam-1858	341	2	3	3	NUM
ejpam-1858	342	1	.	.	PUNCT
ejpam-1858	342	2	assume	assume	VERB
ejpam-1858	342	3	that	that	SCONJ
ejpam-1858	342	4	(	(	PUNCT
ejpam-1858	342	5	i	i	NOUN
ejpam-1858	342	6	)	)	PUNCT
ejpam-1858	342	7	f	f	PROPN
ejpam-1858	342	8	:	:	PUNCT
ejpam-1858	343	1	d→	d→	PUNCT
ejpam-1858	343	2	r	r	NOUN
ejpam-1858	343	3	is	be	AUX
ejpam-1858	343	4	continuous	continuous	ADJ
ejpam-1858	343	5	.	.	PUNCT
ejpam-1858	344	1	(	(	PUNCT
ejpam-1858	344	2	ii	ii	NOUN
ejpam-1858	344	3	)	)	PUNCT
ejpam-1858	344	4	ik	ik	PROPN
ejpam-1858	344	5	∈	∈	PROPN
ejpam-1858	344	6	c[r	c[r	PROPN
ejpam-1858	344	7	,	,	PUNCT
ejpam-1858	344	8	r	r	NOUN
ejpam-1858	344	9	]	]	X
ejpam-1858	344	10	,	,	PUNCT
ejpam-1858	344	11	τk	τk	ADP
ejpam-1858	344	12	∈	∈	PROPN
ejpam-1858	344	13	c[r	c[r	PROPN
ejpam-1858	344	14	,	,	PUNCT
ejpam-1858	344	15	r+	r+	X
ejpam-1858	344	16	]	]	PUNCT
ejpam-1858	344	17	for	for	ADP
ejpam-1858	344	18	all	all	DET
ejpam-1858	344	19	k	k	PROPN
ejpam-1858	344	20	≥	≥	NUM
ejpam-1858	344	21	1	1	NUM
ejpam-1858	344	22	.	.	PUNCT
ejpam-1858	345	1	if	if	SCONJ
ejpam-1858	345	2	x(t	x(t	PROPN
ejpam-1858	345	3	)	)	PUNCT
ejpam-1858	345	4	is	be	AUX
ejpam-1858	345	5	any	any	DET
ejpam-1858	345	6	solution	solution	NOUN
ejpam-1858	345	7	of	of	ADP
ejpam-1858	345	8	the	the	DET
ejpam-1858	345	9	system	system	NOUN
ejpam-1858	345	10	(	(	PUNCT
ejpam-1858	345	11	7	7	NUM
ejpam-1858	345	12	)	)	PUNCT
ejpam-1858	345	13	with	with	ADP
ejpam-1858	345	14	a	a	DET
ejpam-1858	345	15	finite	finite	NOUN
ejpam-1858	345	16	[	[	X
ejpam-1858	345	17	t0	t0	NOUN
ejpam-1858	345	18	,	,	PUNCT
ejpam-1858	345	19	b	b	NOUN
ejpam-1858	345	20	)	)	PUNCT
ejpam-1858	345	21	as	as	ADP
ejpam-1858	345	22	its	its	PRON
ejpam-1858	345	23	maximal	maximal	ADJ
ejpam-1858	345	24	interval	interval	NOUN
ejpam-1858	345	25	of	of	ADP
ejpam-1858	345	26	existence	existence	NOUN
ejpam-1858	345	27	,	,	PUNCT
ejpam-1858	345	28	with	with	SCONJ
ejpam-1858	345	29	one	one	NUM
ejpam-1858	345	30	of	of	ADP
ejpam-1858	345	31	the	the	DET
ejpam-1858	345	32	following	follow	VERB
ejpam-1858	345	33	three	three	NUM
ejpam-1858	345	34	conditions	condition	NOUN
ejpam-1858	345	35	is	be	AUX
ejpam-1858	345	36	satisfied	satisfied	ADJ
ejpam-1858	345	37	,	,	PUNCT
ejpam-1858	345	38	a	a	PRON
ejpam-1858	345	39	)	)	PUNCT
ejpam-1858	345	40	if	if	SCONJ
ejpam-1858	345	41	t1	t1	NOUN
ejpam-1858	345	42	=	=	SYM
ejpam-1858	345	43	τk(x1	τk(x1	X
ejpam-1858	345	44	)	)	PUNCT
ejpam-1858	345	45	for	for	ADP
ejpam-1858	345	46	some	some	DET
ejpam-1858	345	47	k	k	PROPN
ejpam-1858	345	48	≥	≥	NOUN
ejpam-1858	345	49	1	1	NUM
ejpam-1858	345	50	then	then	ADV
ejpam-1858	345	51	there	there	PRON
ejpam-1858	345	52	exists	exist	VERB
ejpam-1858	345	53	δ	δ	PROPN
ejpam-1858	345	54	>	>	X
ejpam-1858	345	55	0	0	NUM
ejpam-1858	346	1	such	such	ADJ
ejpam-1858	346	2	that	that	DET
ejpam-1858	346	3	t	t	PROPN
ejpam-1858	346	4	6=	6=	PROPN
ejpam-1858	346	5	τk(x	τk(x	NOUN
ejpam-1858	346	6	)	)	PUNCT
ejpam-1858	346	7	for	for	ADP
ejpam-1858	346	8	all	all	DET
ejpam-1858	346	9	(	(	PUNCT
ejpam-1858	346	10	t	t	PROPN
ejpam-1858	346	11	,	,	PUNCT
ejpam-1858	346	12	x	x	NOUN
ejpam-1858	346	13	)	)	PUNCT
ejpam-1858	346	14	with	with	ADP
ejpam-1858	346	15	0	0	NUM
ejpam-1858	346	16	<	<	X
ejpam-1858	346	17	t	t	PROPN
ejpam-1858	346	18	−	−	PROPN
ejpam-1858	346	19	t1	t1	NOUN
ejpam-1858	346	20	<	<	X
ejpam-1858	346	21	δ	δ	PROPN
ejpam-1858	346	22	and	and	CCONJ
ejpam-1858	346	23	|x	|x	NOUN
ejpam-1858	347	1	−	−	PROPN
ejpam-1858	347	2	x1|	x1|	PROPN
ejpam-1858	347	3	<	<	X
ejpam-1858	347	4	δ	δ	PROPN
ejpam-1858	347	5	.	.	PUNCT
ejpam-1858	348	1	b	b	X
ejpam-1858	348	2	)	)	PUNCT
ejpam-1858	348	3	if	if	SCONJ
ejpam-1858	348	4	t1	t1	NOUN
ejpam-1858	348	5	=	=	SYM
ejpam-1858	348	6	τk(x1	τk(x1	X
ejpam-1858	348	7	)	)	PUNCT
ejpam-1858	348	8	for	for	ADP
ejpam-1858	348	9	some	some	DET
ejpam-1858	348	10	k	k	PROPN
ejpam-1858	348	11	≥	≥	PROPN
ejpam-1858	348	12	1	1	NUM
ejpam-1858	348	13	then	then	ADV
ejpam-1858	348	14	t1	t1	VERB
ejpam-1858	348	15	6=	6=	PROPN
ejpam-1858	349	1	τ	τ	PROPN
ejpam-1858	349	2	j(x1	j(x1	PROPN
ejpam-1858	349	3	+	+	X
ejpam-1858	349	4	ik(x1	ik(x1	NOUN
ejpam-1858	349	5	)	)	PUNCT
ejpam-1858	349	6	)	)	PUNCT
ejpam-1858	349	7	for	for	ADP
ejpam-1858	349	8	all	all	DET
ejpam-1858	349	9	j	j	PROPN
ejpam-1858	349	10	≥	≥	NUM
ejpam-1858	349	11	1	1	NUM
ejpam-1858	349	12	.	.	PUNCT
ejpam-1858	350	1	c	c	X
ejpam-1858	350	2	)	)	PUNCT
ejpam-1858	350	3	if	if	SCONJ
ejpam-1858	350	4	t1	t1	NOUN
ejpam-1858	350	5	=	=	SYM
ejpam-1858	350	6	τk(x1	τk(x1	X
ejpam-1858	350	7	)	)	PUNCT
ejpam-1858	350	8	for	for	SCONJ
ejpam-1858	350	9	some	some	DET
ejpam-1858	350	10	k	k	PROPN
ejpam-1858	350	11	≥	≥	NUM
ejpam-1858	350	12	1	1	NUM
ejpam-1858	350	13	,	,	PUNCT
ejpam-1858	350	14	c	c	PROPN
ejpam-1858	350	15	dqτk(x	dqτk(x	PROPN
ejpam-1858	350	16	)	)	PUNCT
ejpam-1858	350	17	exists	exist	VERB
ejpam-1858	350	18	,	,	PUNCT
ejpam-1858	350	19	τi	τi	ADP
ejpam-1858	350	20	∈	∈	PROPN
ejpam-1858	350	21	c1[r	c1[r	NOUN
ejpam-1858	350	22	,	,	PUNCT
ejpam-1858	350	23	r+	r+	X
ejpam-1858	350	24	]	]	PUNCT
ejpam-1858	350	25	and	and	CCONJ
ejpam-1858	350	26	τi(x	τi(x	NUM
ejpam-1858	350	27	)	)	PUNCT
ejpam-1858	350	28	are	be	AUX
ejpam-1858	350	29	linear	linear	ADJ
ejpam-1858	350	30	surfaces	surface	NOUN
ejpam-1858	350	31	for	for	ADP
ejpam-1858	350	32	all	all	DET
ejpam-1858	350	33	i	i	PRON
ejpam-1858	350	34	≥	≥	VERB
ejpam-1858	350	35	1	1	NUM
ejpam-1858	350	36	then	then	ADV
ejpam-1858	350	37	t1	t1	PROPN
ejpam-1858	350	38	=	=	PUNCT
ejpam-1858	350	39	τ	τ	PROPN
ejpam-1858	350	40	j(x1	j(x1	NOUN
ejpam-1858	350	41	+	+	X
ejpam-1858	350	42	ik(x1	ik(x1	NOUN
ejpam-1858	350	43	)	)	PUNCT
ejpam-1858	350	44	)	)	PUNCT
ejpam-1858	350	45	for	for	ADP
ejpam-1858	350	46	some	some	DET
ejpam-1858	350	47	j	j	PROPN
ejpam-1858	350	48	≥	≥	NUM
ejpam-1858	350	49	1	1	NUM
ejpam-1858	350	50	and	and	CCONJ
ejpam-1858	350	51	∂	∂	NUM
ejpam-1858	350	52	τ	τ	X
ejpam-1858	350	53	j(x	j(x	PROPN
ejpam-1858	350	54	)	)	PUNCT
ejpam-1858	350	55	∂	∂	NUM
ejpam-1858	350	56	x	x	NOUN
ejpam-1858	350	57	.	.	PUNCT
ejpam-1858	351	1	f	f	PROPN
ejpam-1858	351	2	(	(	PUNCT
ejpam-1858	351	3	t	t	PROPN
ejpam-1858	351	4	,	,	PUNCT
ejpam-1858	351	5	x	x	X
ejpam-1858	351	6	)	)	PUNCT
ejpam-1858	351	7	6=	6=	ADP
ejpam-1858	351	8	(	(	PUNCT
ejpam-1858	351	9	t−t1	t−t1	NUM
ejpam-1858	351	10	)	)	PUNCT
ejpam-1858	351	11	(	(	PUNCT
ejpam-1858	351	12	1−q	1−q	NUM
ejpam-1858	351	13	)	)	PUNCT
ejpam-1858	351	14	γ(2−q	γ(2−q	ADJ
ejpam-1858	351	15	)	)	PUNCT
ejpam-1858	351	16	at	at	ADP
ejpam-1858	351	17	(	(	PUNCT
ejpam-1858	351	18	t1	t1	NOUN
ejpam-1858	351	19	,	,	PUNCT
ejpam-1858	351	20	x+	x+	X
ejpam-1858	351	21	1	1	X
ejpam-1858	351	22	)	)	PUNCT
ejpam-1858	351	23	where	where	SCONJ
ejpam-1858	351	24	x+	x+	ADJ
ejpam-1858	351	25	1	1	NUM
ejpam-1858	351	26	=	=	SYM
ejpam-1858	351	27	x1	x1	PROPN
ejpam-1858	351	28	+	+	X
ejpam-1858	351	29	ik(x1	ik(x1	NOUN
ejpam-1858	351	30	)	)	PUNCT
ejpam-1858	351	31	.	.	PUNCT
ejpam-1858	352	1	then	then	ADV
ejpam-1858	352	2	limt→b−	limt→b−	NOUN
ejpam-1858	352	3	|x(t)|=∞.	|x(t)|=∞.	X
ejpam-1858	352	4	6	6	NUM
ejpam-1858	352	5	.	.	PUNCT
ejpam-1858	352	6	conclusion	conclusion	NOUN
ejpam-1858	352	7	in	in	ADP
ejpam-1858	352	8	this	this	DET
ejpam-1858	352	9	paper	paper	NOUN
ejpam-1858	352	10	we	we	PRON
ejpam-1858	352	11	have	have	AUX
ejpam-1858	352	12	introduced	introduce	VERB
ejpam-1858	352	13	hybrid	hybrid	ADJ
ejpam-1858	352	14	caputo	caputo	PROPN
ejpam-1858	352	15	fractional	fractional	PROPN
ejpam-1858	352	16	differential	differential	ADJ
ejpam-1858	352	17	equations	equation	NOUN
ejpam-1858	352	18	of	of	ADP
ejpam-1858	352	19	order	order	NOUN
ejpam-1858	352	20	q	q	X
ejpam-1858	352	21	∈	∈	PROPN
ejpam-1858	352	22	(	(	PUNCT
ejpam-1858	352	23	0,1	0,1	NUM
ejpam-1858	352	24	)	)	PUNCT
ejpam-1858	352	25	with	with	ADP
ejpam-1858	352	26	variable	variable	ADJ
ejpam-1858	352	27	moments	moment	NOUN
ejpam-1858	352	28	of	of	ADP
ejpam-1858	352	29	impulse	impulse	ADJ
ejpam-1858	352	30	and	and	CCONJ
ejpam-1858	352	31	have	have	AUX
ejpam-1858	352	32	shown	show	VERB
ejpam-1858	352	33	by	by	ADP
ejpam-1858	352	34	examples	example	NOUN
ejpam-1858	352	35	the	the	DET
ejpam-1858	352	36	potential	potential	NOUN
ejpam-1858	352	37	it	it	PRON
ejpam-1858	352	38	has	have	VERB
ejpam-1858	352	39	for	for	ADP
ejpam-1858	352	40	further	further	ADJ
ejpam-1858	352	41	work	work	NOUN
ejpam-1858	352	42	.	.	PUNCT
ejpam-1858	353	1	we	we	PRON
ejpam-1858	353	2	have	have	AUX
ejpam-1858	353	3	studied	study	VERB
ejpam-1858	353	4	existence	existence	NOUN
ejpam-1858	353	5	and	and	CCONJ
ejpam-1858	353	6	continuation	continuation	NOUN
ejpam-1858	353	7	of	of	ADP
ejpam-1858	353	8	solutions	solution	NOUN
ejpam-1858	353	9	for	for	ADP
ejpam-1858	353	10	initial	initial	ADJ
ejpam-1858	353	11	value	value	NOUN
ejpam-1858	353	12	problems	problem	NOUN
ejpam-1858	353	13	in	in	ADP
ejpam-1858	353	14	this	this	DET
ejpam-1858	353	15	set	set	VERB
ejpam-1858	353	16	up	up	ADP
ejpam-1858	353	17	.	.	PUNCT
ejpam-1858	354	1	references	reference	NOUN
ejpam-1858	354	2	[	[	X
ejpam-1858	354	3	1	1	X
ejpam-1858	354	4	]	]	X
ejpam-1858	354	5	s.k	s.k	PROPN
ejpam-1858	354	6	.	.	PROPN
ejpam-1858	354	7	choi	choi	PROPN
ejpam-1858	354	8	and	and	CCONJ
ejpam-1858	354	9	n.	n.	PROPN
ejpam-1858	354	10	koo	koo	PROPN
ejpam-1858	354	11	.	.	PUNCT
ejpam-1858	355	1	monotone	monotone	ADJ
ejpam-1858	355	2	property	property	NOUN
ejpam-1858	355	3	and	and	CCONJ
ejpam-1858	355	4	stability	stability	NOUN
ejpam-1858	355	5	of	of	ADP
ejpam-1858	355	6	solutions	solution	NOUN
ejpam-1858	355	7	of	of	ADP
ejpam-1858	355	8	fractional	fractional	ADJ
ejpam-1858	355	9	differential	differential	ADJ
ejpam-1858	355	10	equations	equation	NOUN
ejpam-1858	355	11	,	,	PUNCT
ejpam-1858	355	12	non	non	ADJ
ejpam-1858	355	13	linear	linear	VERB
ejpam-1858	355	14	analysis	analysis	NOUN
ejpam-1858	355	15	74	74	NUM
ejpam-1858	355	16	(	(	PUNCT
ejpam-1858	355	17	2011	2011	NUM
ejpam-1858	355	18	)	)	PUNCT
ejpam-1858	355	19	6530–6536	6530–6536	NUM
ejpam-1858	355	20	.	.	PUNCT
ejpam-1858	356	1	[	[	X
ejpam-1858	356	2	2	2	NUM
ejpam-1858	356	3	]	]	X
ejpam-1858	356	4	e.a	e.a	PROPN
ejpam-1858	356	5	.	.	PROPN
ejpam-1858	356	6	dads	dads	PROPN
ejpam-1858	356	7	,	,	PUNCT
ejpam-1858	356	8	m.	m.	NOUN
ejpam-1858	356	9	benchohra	benchohra	NOUN
ejpam-1858	356	10	,	,	PUNCT
ejpam-1858	356	11	and	and	CCONJ
ejpam-1858	356	12	s.	s.	PROPN
ejpam-1858	356	13	hamani	hamani	PROPN
ejpam-1858	356	14	.	.	PUNCT
ejpam-1858	357	1	impulsive	impulsive	ADJ
ejpam-1858	357	2	fractional	fractional	ADJ
ejpam-1858	357	3	differential	differential	ADJ
ejpam-1858	357	4	inclusions	inclusion	NOUN
ejpam-1858	357	5	involving	involve	VERB
ejpam-1858	357	6	the	the	DET
ejpam-1858	357	7	caputo	caputo	PROPN
ejpam-1858	357	8	fractional	fractional	PROPN
ejpam-1858	357	9	derivative	derivative	ADJ
ejpam-1858	357	10	,	,	PUNCT
ejpam-1858	357	11	fractional	fractional	ADJ
ejpam-1858	357	12	calculus	calculus	NOUN
ejpam-1858	357	13	&	&	CCONJ
ejpam-1858	357	14	applied	apply	VERB
ejpam-1858	357	15	analysis	analysis	NOUN
ejpam-1858	357	16	,	,	PUNCT
ejpam-1858	357	17	volume	volume	NOUN
ejpam-1858	357	18	12	12	NUM
ejpam-1858	357	19	,	,	PUNCT
ejpam-1858	357	20	number	number	NOUN
ejpam-1858	357	21	1	1	NUM
ejpam-1858	357	22	(	(	PUNCT
ejpam-1858	357	23	2009	2009	NUM
ejpam-1858	357	24	)	)	PUNCT
ejpam-1858	357	25	.	.	PUNCT
ejpam-1858	358	1	references	reference	NOUN
ejpam-1858	358	2	128	128	NUM
ejpam-1858	359	1	[	[	X
ejpam-1858	359	2	3	3	NUM
ejpam-1858	359	3	]	]	X
ejpam-1858	359	4	j.v	j.v	PROPN
ejpam-1858	359	5	.	.	PUNCT
ejpam-1858	359	6	devi	devi	PROPN
ejpam-1858	359	7	and	and	CCONJ
ejpam-1858	359	8	m.k	m.k	PROPN
ejpam-1858	359	9	.	.	PROPN
ejpam-1858	359	10	sastry	sastry	PROPN
ejpam-1858	359	11	.	.	PUNCT
ejpam-1858	360	1	monotone	monotone	ADJ
ejpam-1858	360	2	iterative	iterative	NOUN
ejpam-1858	360	3	technique	technique	NOUN
ejpam-1858	360	4	for	for	ADP
ejpam-1858	360	5	hybrid	hybrid	ADJ
ejpam-1858	360	6	caputo	caputo	PROPN
ejpam-1858	360	7	fractional	fractional	PROPN
ejpam-1858	360	8	differential	differential	PROPN
ejpam-1858	360	9	equations	equation	NOUN
ejpam-1858	360	10	,	,	PUNCT
ejpam-1858	360	11	dcdis	dcdis	PROPN
ejpam-1858	360	12	series	series	PROPN
ejpam-1858	360	13	a	a	PRON
ejpam-1858	360	14	:	:	PUNCT
ejpam-1858	360	15	mathematical	mathematical	ADJ
ejpam-1858	360	16	analysis	analysis	NOUN
ejpam-1858	360	17	,	,	PUNCT
ejpam-1858	360	18	volume	volume	NOUN
ejpam-1858	360	19	19	19	NUM
ejpam-1858	360	20	,	,	PUNCT
ejpam-1858	360	21	number	number	NOUN
ejpam-1858	360	22	3	3	NUM
ejpam-1858	360	23	(	(	PUNCT
ejpam-1858	360	24	2012	2012	NUM
ejpam-1858	360	25	)	)	PUNCT
ejpam-1858	360	26	,	,	PUNCT
ejpam-1858	360	27	397	397	NUM
ejpam-1858	360	28	-	-	SYM
ejpam-1858	360	29	411	411	NUM
ejpam-1858	360	30	.	.	PUNCT
ejpam-1858	361	1	[	[	X
ejpam-1858	361	2	4	4	NUM
ejpam-1858	361	3	]	]	X
ejpam-1858	361	4	j.v	j.v	PROPN
ejpam-1858	361	5	.	.	PUNCT
ejpam-1858	361	6	devi	devi	PROPN
ejpam-1858	361	7	,	,	PUNCT
ejpam-1858	361	8	f.a	f.a	PROPN
ejpam-1858	361	9	.	.	PROPN
ejpam-1858	361	10	mcrae	mcrae	PROPN
ejpam-1858	361	11	,	,	PUNCT
ejpam-1858	361	12	and	and	CCONJ
ejpam-1858	361	13	z.	z.	PROPN
ejpam-1858	361	14	drici	drici	NOUN
ejpam-1858	361	15	.	.	PUNCT
ejpam-1858	362	1	variational	variational	ADJ
ejpam-1858	362	2	lyapunov	lyapunov	ADJ
ejpam-1858	362	3	method	method	NOUN
ejpam-1858	362	4	for	for	ADP
ejpam-1858	362	5	fractional	fractional	ADJ
ejpam-1858	362	6	differential	differential	ADJ
ejpam-1858	362	7	equations	equation	NOUN
ejpam-1858	362	8	,	,	PUNCT
ejpam-1858	362	9	computers	computer	NOUN
ejpam-1858	362	10	and	and	CCONJ
ejpam-1858	362	11	mathematics	mathematic	NOUN
ejpam-1858	362	12	with	with	ADP
ejpam-1858	362	13	applications	application	NOUN
ejpam-1858	362	14	(	(	PUNCT
ejpam-1858	362	15	2012	2012	NUM
ejpam-1858	362	16	)	)	PUNCT
ejpam-1858	362	17	,	,	PUNCT
ejpam-1858	362	18	doi:10.1016	doi:10.1016	PROPN
ejpam-1858	362	19	/	/	SYM
ejpam-1858	362	20	j.camwa.2012.01.070	j.camwa.2012.01.070	PROPN
ejpam-1858	362	21	.	.	PUNCT
ejpam-1858	363	1	[	[	X
ejpam-1858	363	2	5	5	NUM
ejpam-1858	363	3	]	]	X
ejpam-1858	363	4	j.v	j.v	PROPN
ejpam-1858	363	5	.	.	PUNCT
ejpam-1858	363	6	devi	devi	PROPN
ejpam-1858	363	7	and	and	CCONJ
ejpam-1858	363	8	v.	v.	ADP
ejpam-1858	363	9	radhika	radhika	PROPN
ejpam-1858	363	10	.	.	PROPN
ejpam-1858	363	11	quasilinearization	quasilinearization	PROPN
ejpam-1858	363	12	for	for	ADP
ejpam-1858	363	13	hybrid	hybrid	NOUN
ejpam-1858	363	14	caputo	caputo	PROPN
ejpam-1858	363	15	fractional	fractional	PROPN
ejpam-1858	363	16	differential	differential	PROPN
ejpam-1858	363	17	equations	equation	NOUN
ejpam-1858	363	18	,	,	PUNCT
ejpam-1858	363	19	dynamics	dynamic	NOUN
ejpam-1858	363	20	of	of	ADP
ejpam-1858	363	21	continuous	continuous	ADJ
ejpam-1858	363	22	,	,	PUNCT
ejpam-1858	363	23	discrete	discrete	ADJ
ejpam-1858	363	24	,	,	PUNCT
ejpam-1858	363	25	and	and	CCONJ
ejpam-1858	363	26	impulsive	impulsive	ADJ
ejpam-1858	363	27	systems	system	NOUN
ejpam-1858	363	28	,	,	PUNCT
ejpam-1858	363	29	volume	volume	NOUN
ejpam-1858	363	30	19	19	NUM
ejpam-1858	363	31	.	.	PUNCT
ejpam-1858	364	1	745–756	745–756	NUM
ejpam-1858	364	2	.	.	NOUN
ejpam-1858	364	3	2012	2012	NUM
ejpam-1858	364	4	.	.	PUNCT
ejpam-1858	365	1	[	[	X
ejpam-1858	365	2	6	6	NUM
ejpam-1858	365	3	]	]	PUNCT
ejpam-1858	365	4	k.	k.	PROPN
ejpam-1858	365	5	diethelm	diethelm	PROPN
ejpam-1858	365	6	.	.	PUNCT
ejpam-1858	366	1	the	the	DET
ejpam-1858	366	2	analysis	analysis	NOUN
ejpam-1858	366	3	of	of	ADP
ejpam-1858	366	4	fractional	fractional	ADJ
ejpam-1858	366	5	differential	differential	ADJ
ejpam-1858	366	6	equations	equation	NOUN
ejpam-1858	366	7	,	,	PUNCT
ejpam-1858	366	8	an	an	DET
ejpam-1858	366	9	application	application	NOUN
ejpam-1858	366	10	-	-	PUNCT
ejpam-1858	366	11	oriented	orient	VERB
ejpam-1858	366	12	exposition	exposition	NOUN
ejpam-1858	366	13	using	use	VERB
ejpam-1858	366	14	differential	differential	ADJ
ejpam-1858	366	15	operators	operator	NOUN
ejpam-1858	366	16	of	of	ADP
ejpam-1858	366	17	caputo	caputo	PROPN
ejpam-1858	366	18	type	type	PROPN
ejpam-1858	366	19	,	,	PUNCT
ejpam-1858	366	20	springer	springer	NOUN
ejpam-1858	366	21	,	,	PUNCT
ejpam-1858	366	22	new	new	ADJ
ejpam-1858	366	23	york,1993	york,1993	NOUN
ejpam-1858	366	24	.	.	PUNCT
ejpam-1858	367	1	[	[	X
ejpam-1858	367	2	7	7	X
ejpam-1858	367	3	]	]	X
ejpam-1858	367	4	z.	z.	PROPN
ejpam-1858	367	5	drici	drici	PROPN
ejpam-1858	367	6	,	,	PUNCT
ejpam-1858	367	7	f.a	f.a	PROPN
ejpam-1858	367	8	.	.	PROPN
ejpam-1858	367	9	mcrae	mcrae	PROPN
ejpam-1858	367	10	,	,	PUNCT
ejpam-1858	367	11	and	and	CCONJ
ejpam-1858	367	12	j.v	j.v	PROPN
ejpam-1858	367	13	.	.	PUNCT
ejpam-1858	367	14	devi	devi	PROPN
ejpam-1858	367	15	.	.	PROPN
ejpam-1858	368	1	on	on	ADP
ejpam-1858	368	2	the	the	DET
ejpam-1858	368	3	existence	existence	NOUN
ejpam-1858	368	4	and	and	CCONJ
ejpam-1858	368	5	stability	stability	NOUN
ejpam-1858	368	6	of	of	ADP
ejpam-1858	368	7	solutions	solution	NOUN
ejpam-1858	368	8	of	of	ADP
ejpam-1858	368	9	hybrid	hybrid	ADJ
ejpam-1858	368	10	caputo	caputo	PROPN
ejpam-1858	368	11	fractional	fractional	PROPN
ejpam-1858	368	12	differential	differential	PROPN
ejpam-1858	368	13	equations	equation	NOUN
ejpam-1858	368	14	,	,	PUNCT
ejpam-1858	368	15	dynamics	dynamic	NOUN
ejpam-1858	368	16	of	of	ADP
ejpam-1858	368	17	continuous	continuous	ADJ
ejpam-1858	368	18	,	,	PUNCT
ejpam-1858	368	19	discrete	discrete	ADJ
ejpam-1858	368	20	,	,	PUNCT
ejpam-1858	368	21	and	and	CCONJ
ejpam-1858	368	22	impulsive	impulsive	ADJ
ejpam-1858	368	23	systems	system	NOUN
ejpam-1858	368	24	series	series	PROPN
ejpam-1858	368	25	a	a	DET
ejpam-1858	368	26	:	:	PUNCT
ejpam-1858	368	27	mathematical	mathematical	ADJ
ejpam-1858	368	28	analysis	analysis	NOUN
ejpam-1858	368	29	,	,	PUNCT
ejpam-1858	368	30	volume	volume	NOUN
ejpam-1858	368	31	19	19	NUM
ejpam-1858	368	32	.	.	PUNCT
ejpam-1858	369	1	501–512	501–512	NUM
ejpam-1858	369	2	.	.	NOUN
ejpam-1858	369	3	2012	2012	NUM
ejpam-1858	369	4	.	.	PUNCT
ejpam-1858	370	1	[	[	X
ejpam-1858	370	2	8	8	NUM
ejpam-1858	370	3	]	]	SYM
ejpam-1858	370	4	a.a	a.a	PROPN
ejpam-1858	370	5	.	.	PROPN
ejpam-1858	370	6	kilbas	kilbas	PROPN
ejpam-1858	370	7	,	,	PUNCT
ejpam-1858	370	8	h.m	h.m	PROPN
ejpam-1858	370	9	.	.	PROPN
ejpam-1858	370	10	srivastava	srivastava	PROPN
ejpam-1858	370	11	,	,	PUNCT
ejpam-1858	370	12	and	and	CCONJ
ejpam-1858	370	13	j.j	j.j	PROPN
ejpam-1858	370	14	.	.	PROPN
ejpam-1858	370	15	trujillo	trujillo	PROPN
ejpam-1858	370	16	.	.	PUNCT
ejpam-1858	370	17	theory	theory	NOUN
ejpam-1858	370	18	and	and	CCONJ
ejpam-1858	370	19	applications	application	NOUN
ejpam-1858	370	20	of	of	ADP
ejpam-1858	370	21	fractional	fractional	ADJ
ejpam-1858	370	22	differential	differential	ADJ
ejpam-1858	370	23	equations	equation	NOUN
ejpam-1858	370	24	,	,	PUNCT
ejpam-1858	370	25	north	north	NOUN
ejpam-1858	370	26	-	-	PUNCT
ejpam-1858	370	27	holland	holland	PROPN
ejpam-1858	370	28	mathematics	mathematics	PROPN
ejpam-1858	370	29	studies	study	NOUN
ejpam-1858	370	30	,	,	PUNCT
ejpam-1858	370	31	204	204	NUM
ejpam-1858	370	32	,	,	PUNCT
ejpam-1858	370	33	elsevier	elsevier	PROPN
ejpam-1858	370	34	science	science	PROPN
ejpam-1858	370	35	,	,	PUNCT
ejpam-1858	370	36	b.v	b.v	PROPN
ejpam-1858	370	37	.	.	PROPN
ejpam-1858	370	38	,	,	PUNCT
ejpam-1858	370	39	amsterdam	amsterdam	PROPN
ejpam-1858	370	40	.	.	PUNCT
ejpam-1858	371	1	2006	2006	NUM
ejpam-1858	371	2	.	.	PUNCT
ejpam-1858	372	1	[	[	X
ejpam-1858	372	2	9	9	NUM
ejpam-1858	372	3	]	]	PUNCT
ejpam-1858	372	4	v.	v.	CCONJ
ejpam-1858	372	5	lakshmikantham	lakshmikantham	ADJ
ejpam-1858	372	6	,	,	PUNCT
ejpam-1858	372	7	d.d	d.d	PROPN
ejpam-1858	372	8	.	.	PROPN
ejpam-1858	372	9	bainov	bainov	PROPN
ejpam-1858	372	10	,	,	PUNCT
ejpam-1858	372	11	and	and	CCONJ
ejpam-1858	372	12	p.s	p.s	PROPN
ejpam-1858	372	13	.	.	PROPN
ejpam-1858	372	14	simeonov	simeonov	PROPN
ejpam-1858	372	15	.	.	PUNCT
ejpam-1858	373	1	theory	theory	NOUN
ejpam-1858	373	2	of	of	ADP
ejpam-1858	373	3	impulsive	impulsive	ADJ
ejpam-1858	373	4	differential	differential	ADJ
ejpam-1858	373	5	equations	equation	NOUN
ejpam-1858	373	6	,	,	PUNCT
ejpam-1858	373	7	words	word	NOUN
ejpam-1858	373	8	scientific	scientific	ADJ
ejpam-1858	373	9	,	,	PUNCT
ejpam-1858	373	10	singapore	singapore	PROPN
ejpam-1858	373	11	,	,	PUNCT
ejpam-1858	373	12	1989	1989	NUM
ejpam-1858	373	13	.	.	PUNCT
ejpam-1858	374	1	[	[	X
ejpam-1858	374	2	10	10	NUM
ejpam-1858	374	3	]	]	X
ejpam-1858	374	4	v.	v.	CCONJ
ejpam-1858	374	5	lakshmikantham	lakshmikantham	PROPN
ejpam-1858	374	6	,	,	PUNCT
ejpam-1858	374	7	s.	s.	PROPN
ejpam-1858	374	8	leela	leela	PROPN
ejpam-1858	374	9	,	,	PUNCT
ejpam-1858	374	10	and	and	CCONJ
ejpam-1858	374	11	j.v	j.v	PROPN
ejpam-1858	374	12	.	.	PUNCT
ejpam-1858	375	1	devi	devi	PROPN
ejpam-1858	375	2	.	.	PUNCT
ejpam-1858	375	3	theory	theory	NOUN
ejpam-1858	375	4	of	of	ADP
ejpam-1858	375	5	fractional	fractional	ADJ
ejpam-1858	375	6	dynamic	dynamic	ADJ
ejpam-1858	375	7	systems	system	NOUN
ejpam-1858	375	8	,	,	PUNCT
ejpam-1858	375	9	cambridge	cambridge	PROPN
ejpam-1858	375	10	scientific	scientific	PROPN
ejpam-1858	375	11	publishers	publishers	PROPN
ejpam-1858	375	12	ltd	ltd	PROPN
ejpam-1858	375	13	,	,	PUNCT
ejpam-1858	375	14	2009	2009	NUM
ejpam-1858	375	15	.	.	PUNCT
ejpam-1858	376	1	[	[	X
ejpam-1858	376	2	11	11	NUM
ejpam-1858	376	3	]	]	X
ejpam-1858	376	4	k.s	k.s	PROPN
ejpam-1858	376	5	.	.	PROPN
ejpam-1858	376	6	miller	miller	PROPN
ejpam-1858	376	7	and	and	CCONJ
ejpam-1858	376	8	b.	b.	PROPN
ejpam-1858	376	9	ross	ross	PROPN
ejpam-1858	376	10	.	.	PUNCT
ejpam-1858	377	1	an	an	DET
ejpam-1858	377	2	introduction	introduction	NOUN
ejpam-1858	377	3	to	to	ADP
ejpam-1858	377	4	the	the	DET
ejpam-1858	377	5	fractional	fractional	ADJ
ejpam-1858	377	6	calculus	calculus	NOUN
ejpam-1858	377	7	and	and	CCONJ
ejpam-1858	377	8	fractional	fractional	ADJ
ejpam-1858	377	9	differential	differential	ADJ
ejpam-1858	377	10	equations	equation	NOUN
ejpam-1858	377	11	,	,	PUNCT
ejpam-1858	377	12	wiley	wiley	NOUN
ejpam-1858	377	13	and	and	CCONJ
ejpam-1858	377	14	sons	son	NOUN
ejpam-1858	377	15	,	,	PUNCT
ejpam-1858	377	16	new	new	PROPN
ejpam-1858	377	17	york	york	PROPN
ejpam-1858	377	18	,	,	PUNCT
ejpam-1858	377	19	1993	1993	NUM
ejpam-1858	377	20	.	.	PUNCT
ejpam-1858	378	1	[	[	X
ejpam-1858	378	2	12	12	NUM
ejpam-1858	378	3	]	]	X
ejpam-1858	378	4	k.b	k.b	PROPN
ejpam-1858	378	5	.	.	PROPN
ejpam-1858	378	6	oldham	oldham	PROPN
ejpam-1858	378	7	and	and	CCONJ
ejpam-1858	378	8	j.	j.	PROPN
ejpam-1858	378	9	spanier	spanier	PROPN
ejpam-1858	378	10	.	.	PUNCT
ejpam-1858	379	1	the	the	DET
ejpam-1858	379	2	fractional	fractional	ADJ
ejpam-1858	379	3	calculus	calculus	NOUN
ejpam-1858	379	4	,	,	PUNCT
ejpam-1858	379	5	academic	academic	ADJ
ejpam-1858	379	6	press	press	NOUN
ejpam-1858	379	7	,	,	PUNCT
ejpam-1858	379	8	new	new	PROPN
ejpam-1858	379	9	york	york	PROPN
ejpam-1858	379	10	london	london	PROPN
ejpam-1858	379	11	,	,	PUNCT
ejpam-1858	379	12	1974	1974	NUM
ejpam-1858	379	13	.	.	PUNCT
ejpam-1858	380	1	[	[	X
ejpam-1858	380	2	13	13	NUM
ejpam-1858	380	3	]	]	PUNCT
ejpam-1858	380	4	i.	i.	NOUN
ejpam-1858	380	5	podlubny	podlubny	PROPN
ejpam-1858	380	6	.	.	PUNCT
ejpam-1858	381	1	fractional	fractional	ADJ
ejpam-1858	381	2	differential	differential	ADJ
ejpam-1858	381	3	equations	equation	NOUN
ejpam-1858	381	4	,	,	PUNCT
ejpam-1858	381	5	academic	academic	ADJ
ejpam-1858	381	6	press	press	NOUN
ejpam-1858	381	7	,	,	PUNCT
ejpam-1858	381	8	san	san	PROPN
ejpam-1858	381	9	diego	diego	PROPN
ejpam-1858	381	10	,	,	PUNCT
ejpam-1858	381	11	1999	1999	NUM
ejpam-1858	381	12	[	[	X
ejpam-1858	381	13	14	14	NUM
ejpam-1858	381	14	]	]	X
ejpam-1858	381	15	r.	r.	PROPN
ejpam-1858	381	16	herrmann	herrmann	PROPN
ejpam-1858	381	17	.	.	PUNCT
ejpam-1858	382	1	fractional	fractional	ADJ
ejpam-1858	382	2	calculus	calculus	PROPN
ejpam-1858	382	3	,	,	PUNCT
ejpam-1858	382	4	gigahedron	gigahedron	NOUN
ejpam-1858	382	5	,	,	PUNCT
ejpam-1858	382	6	germany	germany	PROPN
ejpam-1858	382	7	.	.	PUNCT