id	sid	tid	token	lemma	pos
ejpam-84	1	1	european	european	PROPN
ejpam-84	1	2	journal	journal	PROPN
ejpam-84	1	3	of	of	ADP
ejpam-84	1	4	pure	pure	ADJ
ejpam-84	1	5	and	and	CCONJ
ejpam-84	1	6	applied	apply	VERB
ejpam-84	1	7	mathematics	mathematic	NOUN
ejpam-84	1	8	vol	vol	NOUN
ejpam-84	1	9	.	.	PROPN
ejpam-84	2	1	1	1	NUM
ejpam-84	2	2	,	,	PUNCT
ejpam-84	2	3	no	no	INTJ
ejpam-84	2	4	.	.	NOUN
ejpam-84	2	5	1	1	NUM
ejpam-84	2	6	,	,	PUNCT
ejpam-84	2	7	2008	2008	NUM
ejpam-84	2	8	,	,	PUNCT
ejpam-84	2	9	(	(	PUNCT
ejpam-84	2	10	38	38	NUM
ejpam-84	2	11	-	-	SYM
ejpam-84	2	12	45	45	NUM
ejpam-84	2	13	)	)	PUNCT
ejpam-84	2	14	issn	issn	PROPN
ejpam-84	2	15	1307	1307	NUM
ejpam-84	2	16	-	-	SYM
ejpam-84	2	17	5543	5543	NUM
ejpam-84	2	18	–	–	PUNCT
ejpam-84	2	19	www.ejpam.com	www.ejpam.com	X
ejpam-84	2	20	honorary	honorary	PROPN
ejpam-84	2	21	invited	invite	VERB
ejpam-84	2	22	paper	paper	NOUN
ejpam-84	2	23	theory	theory	NOUN
ejpam-84	2	24	of	of	ADP
ejpam-84	2	25	fractional	fractional	ADJ
ejpam-84	2	26	differential	differential	ADJ
ejpam-84	2	27	equations	equation	NOUN
ejpam-84	2	28	in	in	ADP
ejpam-84	2	29	a	a	DET
ejpam-84	2	30	banach	banach	NOUN
ejpam-84	2	31	space	space	NOUN
ejpam-84	2	32	v.	v.	ADP
ejpam-84	2	33	lakshmikantham1,∗	lakshmikantham1,∗	PROPN
ejpam-84	2	34	,	,	PUNCT
ejpam-84	2	35	j.	j.	PROPN
ejpam-84	2	36	vasundhara	vasundhara	PROPN
ejpam-84	2	37	devi2	devi2	NOUN
ejpam-84	3	1	1	1	NUM
ejpam-84	3	2	department	department	NOUN
ejpam-84	3	3	of	of	ADP
ejpam-84	3	4	mathematical	mathematical	ADJ
ejpam-84	3	5	sciences	sciences	PROPN
ejpam-84	3	6	,	,	PUNCT
ejpam-84	3	7	florida	florida	PROPN
ejpam-84	3	8	institute	institute	PROPN
ejpam-84	3	9	of	of	ADP
ejpam-84	3	10	technology	technology	PROPN
ejpam-84	3	11	,	,	PUNCT
ejpam-84	3	12	melbourne	melbourne	PROPN
ejpam-84	3	13	,	,	PUNCT
ejpam-84	3	14	fl	fl	PROPN
ejpam-84	3	15	32901	32901	NUM
ejpam-84	3	16	usa	usa	PROPN
ejpam-84	3	17	2	2	NUM
ejpam-84	3	18	gvp	gvp	NOUN
ejpam-84	3	19	institute	institute	NOUN
ejpam-84	3	20	for	for	ADP
ejpam-84	3	21	advanced	advanced	ADJ
ejpam-84	3	22	studies	study	NOUN
ejpam-84	3	23	,	,	PUNCT
ejpam-84	3	24	visakhapatnam	visakhapatnam	PROPN
ejpam-84	3	25	,	,	PUNCT
ejpam-84	3	26	india	india	PROPN
ejpam-84	3	27	abstract	abstract	NOUN
ejpam-84	3	28	.	.	PUNCT
ejpam-84	4	1	in	in	ADP
ejpam-84	4	2	this	this	DET
ejpam-84	4	3	paper	paper	NOUN
ejpam-84	4	4	,	,	PUNCT
ejpam-84	4	5	the	the	DET
ejpam-84	4	6	basic	basic	ADJ
ejpam-84	4	7	theory	theory	NOUN
ejpam-84	4	8	of	of	ADP
ejpam-84	4	9	fractional	fractional	ADJ
ejpam-84	4	10	differential	differential	ADJ
ejpam-84	4	11	equations	equation	NOUN
ejpam-84	4	12	in	in	ADP
ejpam-84	4	13	a	a	DET
ejpam-84	4	14	banach	banach	NOUN
ejpam-84	4	15	space	space	NOUN
ejpam-84	4	16	is	be	AUX
ejpam-84	4	17	discussed	discuss	VERB
ejpam-84	4	18	including	include	VERB
ejpam-84	4	19	flow	flow	NOUN
ejpam-84	4	20	invariance	invariance	NOUN
ejpam-84	4	21	and	and	CCONJ
ejpam-84	4	22	theory	theory	NOUN
ejpam-84	4	23	of	of	ADP
ejpam-84	4	24	inequalities	inequality	NOUN
ejpam-84	4	25	in	in	ADP
ejpam-84	4	26	cones	cone	NOUN
ejpam-84	4	27	.	.	PUNCT
ejpam-84	5	1	ams	am	NOUN
ejpam-84	5	2	subject	subject	ADJ
ejpam-84	5	3	classifications	classification	NOUN
ejpam-84	5	4	:	:	PUNCT
ejpam-84	5	5	34l30	34l30	NUM
ejpam-84	5	6	,	,	PUNCT
ejpam-84	5	7	34a12	34a12	NUM
ejpam-84	5	8	,	,	PUNCT
ejpam-84	5	9	34a40	34a40	NUM
ejpam-84	5	10	.	.	PUNCT
ejpam-84	6	1	key	key	ADJ
ejpam-84	6	2	words	word	NOUN
ejpam-84	6	3	:	:	PUNCT
ejpam-84	6	4	fractional	fractional	ADJ
ejpam-84	6	5	differential	differential	ADJ
ejpam-84	6	6	equations	equation	NOUN
ejpam-84	6	7	in	in	ADP
ejpam-84	6	8	a	a	DET
ejpam-84	6	9	banach	banach	NOUN
ejpam-84	6	10	space	space	NOUN
ejpam-84	6	11	,	,	PUNCT
ejpam-84	6	12	basic	basic	ADJ
ejpam-84	6	13	existence	existence	NOUN
ejpam-84	6	14	theory	theory	NOUN
ejpam-84	6	15	,	,	PUNCT
ejpam-84	6	16	flow	flow	NOUN
ejpam-84	6	17	invariance	invariance	NOUN
ejpam-84	6	18	.	.	PUNCT
ejpam-84	7	1	1	1	X
ejpam-84	7	2	.	.	X
ejpam-84	7	3	introduction	introduction	NOUN
ejpam-84	7	4	the	the	DET
ejpam-84	7	5	concept	concept	NOUN
ejpam-84	7	6	of	of	ADP
ejpam-84	7	7	fractional	fractional	ADJ
ejpam-84	7	8	derivative	derivative	NOUN
ejpam-84	7	9	and	and	CCONJ
ejpam-84	7	10	the	the	DET
ejpam-84	7	11	corresponding	corresponding	ADJ
ejpam-84	7	12	fractional	fractional	ADJ
ejpam-84	7	13	voltera	voltera	NOUN
ejpam-84	7	14	integral	integral	ADJ
ejpam-84	7	15	are	be	AUX
ejpam-84	7	16	nonlocal	nonlocal	ADJ
ejpam-84	7	17	[	[	X
ejpam-84	7	18	14	14	NUM
ejpam-84	7	19	]	]	PUNCT
ejpam-84	7	20	compared	compare	VERB
ejpam-84	7	21	to	to	ADP
ejpam-84	7	22	the	the	DET
ejpam-84	7	23	usual	usual	ADJ
ejpam-84	7	24	standard	standard	ADJ
ejpam-84	7	25	notions	notion	NOUN
ejpam-84	7	26	.	.	PUNCT
ejpam-84	8	1	as	as	ADP
ejpam-84	8	2	a	a	DET
ejpam-84	8	3	result	result	NOUN
ejpam-84	8	4	,	,	PUNCT
ejpam-84	8	5	the	the	DET
ejpam-84	8	6	change	change	NOUN
ejpam-84	8	7	of	of	ADP
ejpam-84	8	8	initial	initial	ADJ
ejpam-84	8	9	value	value	NOUN
ejpam-84	8	10	in	in	ADP
ejpam-84	8	11	time	time	NOUN
ejpam-84	8	12	from	from	ADP
ejpam-84	8	13	zero	zero	NUM
ejpam-84	8	14	to	to	ADP
ejpam-84	8	15	any	any	DET
ejpam-84	8	16	t0	t0	PROPN
ejpam-84	8	17	>	>	X
ejpam-84	8	18	0	0	PUNCT
ejpam-84	8	19	changes	change	VERB
ejpam-84	8	20	the	the	DET
ejpam-84	8	21	fractional	fractional	ADJ
ejpam-84	8	22	dynamic	dynamic	ADJ
ejpam-84	8	23	systems	system	NOUN
ejpam-84	8	24	which	which	PRON
ejpam-84	8	25	needs	need	VERB
ejpam-84	8	26	to	to	PART
ejpam-84	8	27	be	be	AUX
ejpam-84	8	28	considered	consider	VERB
ejpam-84	8	29	depending	depend	VERB
ejpam-84	8	30	on	on	ADP
ejpam-84	8	31	the	the	DET
ejpam-84	8	32	requirement	requirement	NOUN
ejpam-84	8	33	of	of	ADP
ejpam-84	8	34	the	the	DET
ejpam-84	8	35	properties	property	NOUN
ejpam-84	8	36	of	of	ADP
ejpam-84	8	37	solutions	solution	NOUN
ejpam-84	8	38	of	of	ADP
ejpam-84	8	39	such	such	ADJ
ejpam-84	8	40	equations	equation	NOUN
ejpam-84	8	41	.	.	PUNCT
ejpam-84	9	1	recently	recently	ADV
ejpam-84	9	2	[	[	X
ejpam-84	9	3	9][12	9][12	NOUN
ejpam-84	9	4	]	]	PUNCT
ejpam-84	9	5	,	,	PUNCT
ejpam-84	9	6	we	we	PRON
ejpam-84	9	7	have	have	AUX
ejpam-84	9	8	investigated	investigate	VERB
ejpam-84	9	9	the	the	DET
ejpam-84	9	10	fundamental	fundamental	ADJ
ejpam-84	9	11	theory	theory	NOUN
ejpam-84	9	12	of	of	ADP
ejpam-84	9	13	the	the	DET
ejpam-84	9	14	initial	initial	ADJ
ejpam-84	9	15	value	value	NOUN
ejpam-84	9	16	problem	problem	NOUN
ejpam-84	9	17	for	for	ADP
ejpam-84	9	18	fractional	fractional	ADJ
ejpam-84	9	19	differential	differential	ADJ
ejpam-84	9	20	equations	equation	NOUN
ejpam-84	9	21	involving	involve	VERB
ejpam-84	9	22	riemann	riemann	PROPN
ejpam-84	9	23	-	-	PUNCT
ejpam-84	9	24	liouville	liouville	VERB
ejpam-84	9	25	differential	differential	NOUN
ejpam-84	9	26	operators	operator	NOUN
ejpam-84	9	27	of	of	ADP
ejpam-84	9	28	arbitrary	arbitrary	ADJ
ejpam-84	9	29	order	order	NOUN
ejpam-84	9	30	0	0	PUNCT
ejpam-84	9	31	<	<	X
ejpam-84	9	32	q	q	X
ejpam-84	9	33	<	<	X
ejpam-84	9	34	1	1	NUM
ejpam-84	9	35	,	,	PUNCT
ejpam-84	9	36	because	because	SCONJ
ejpam-84	9	37	such	such	ADJ
ejpam-84	9	38	dynamic	dynamic	ADJ
ejpam-84	9	39	systems	system	NOUN
ejpam-84	9	40	are	be	AUX
ejpam-84	9	41	important	important	ADJ
ejpam-84	9	42	in	in	ADP
ejpam-84	9	43	modeling	model	VERB
ejpam-84	9	44	a	a	DET
ejpam-84	9	45	variety	variety	NOUN
ejpam-84	9	46	of	of	ADP
ejpam-84	9	47	real	real	ADJ
ejpam-84	9	48	world	world	NOUN
ejpam-84	9	49	problems	problem	NOUN
ejpam-84	10	1	[	[	X
ejpam-84	10	2	1][6	1][6	X
ejpam-84	10	3	]	]	X
ejpam-84	10	4	,	,	PUNCT
ejpam-84	11	1	[	[	X
ejpam-84	11	2	13][15	13][15	X
ejpam-84	11	3	]	]	X
ejpam-84	11	4	.	.	PUNCT
ejpam-84	12	1	we	we	PRON
ejpam-84	12	2	followed	follow	VERB
ejpam-84	12	3	the	the	DET
ejpam-84	12	4	classical	classical	ADJ
ejpam-84	12	5	approach	approach	NOUN
ejpam-84	12	6	of	of	ADP
ejpam-84	12	7	the	the	DET
ejpam-84	12	8	theory	theory	NOUN
ejpam-84	12	9	of	of	ADP
ejpam-84	12	10	differential	differential	ADJ
ejpam-84	12	11	equations	equation	NOUN
ejpam-84	12	12	of	of	ADP
ejpam-84	12	13	integer	integer	NOUN
ejpam-84	12	14	order	order	NOUN
ejpam-84	12	15	in	in	ADP
ejpam-84	12	16	order	order	NOUN
ejpam-84	12	17	to	to	PART
ejpam-84	12	18	compare	compare	VERB
ejpam-84	12	19	and	and	CCONJ
ejpam-84	12	20	contrast	contrast	VERB
ejpam-84	12	21	the	the	DET
ejpam-84	12	22	differences	difference	NOUN
ejpam-84	12	23	and	and	CCONJ
ejpam-84	12	24	intricacies	intricacy	NOUN
ejpam-84	12	25	that	that	PRON
ejpam-84	12	26	might	might	AUX
ejpam-84	12	27	result	result	VERB
ejpam-84	12	28	in	in	ADP
ejpam-84	12	29	the	the	DET
ejpam-84	12	30	development	development	NOUN
ejpam-84	12	31	[	[	X
ejpam-84	12	32	7	7	NUM
ejpam-84	12	33	]	]	PUNCT
ejpam-84	12	34	.	.	PUNCT
ejpam-84	13	1	in	in	ADP
ejpam-84	13	2	this	this	DET
ejpam-84	13	3	paper	paper	NOUN
ejpam-84	13	4	,	,	PUNCT
ejpam-84	13	5	we	we	PRON
ejpam-84	13	6	discuss	discuss	VERB
ejpam-84	13	7	the	the	DET
ejpam-84	13	8	theory	theory	NOUN
ejpam-84	13	9	of	of	ADP
ejpam-84	13	10	fractional	fractional	ADJ
ejpam-84	13	11	differential	differential	ADJ
ejpam-84	13	12	equations	equation	NOUN
ejpam-84	13	13	in	in	ADP
ejpam-84	13	14	a	a	DET
ejpam-84	13	15	banach	banach	NOUN
ejpam-84	13	16	space	space	NOUN
ejpam-84	13	17	parallel	parallel	NOUN
ejpam-84	13	18	to	to	ADP
ejpam-84	13	19	[	[	X
ejpam-84	13	20	8	8	NUM
ejpam-84	13	21	]	]	PUNCT
ejpam-84	13	22	utilizing	utilize	VERB
ejpam-84	13	23	the	the	DET
ejpam-84	13	24	initial	initial	ADJ
ejpam-84	13	25	time	time	NOUN
ejpam-84	13	26	t0	t0	PROPN
ejpam-84	13	27	≥	≥	NUM
ejpam-84	13	28	0	0	NUM
ejpam-84	13	29	.	.	PUNCT
ejpam-84	14	1	we	we	PRON
ejpam-84	14	2	prove	prove	VERB
ejpam-84	14	3	general	general	ADJ
ejpam-84	14	4	existence	existence	NOUN
ejpam-84	14	5	and	and	CCONJ
ejpam-84	14	6	uniqueness	uniqueness	NOUN
ejpam-84	14	7	,	,	PUNCT
ejpam-84	14	8	continuous	continuous	ADJ
ejpam-84	14	9	dependence	dependence	NOUN
ejpam-84	14	10	,	,	PUNCT
ejpam-84	14	11	fractional	fractional	ADJ
ejpam-84	14	12	differential	differential	ADJ
ejpam-84	14	13	inequalities	inequality	NOUN
ejpam-84	14	14	in	in	ADP
ejpam-84	14	15	cones	cone	NOUN
ejpam-84	14	16	and	and	CCONJ
ejpam-84	14	17	flow	flow	NOUN
ejpam-84	14	18	invariance	invariance	NOUN
ejpam-84	14	19	.	.	PUNCT
ejpam-84	15	1	although	although	SCONJ
ejpam-84	15	2	the	the	DET
ejpam-84	15	3	developed	develop	VERB
ejpam-84	15	4	theory	theory	NOUN
ejpam-84	15	5	includes	include	VERB
ejpam-84	15	6	as	as	ADP
ejpam-84	15	7	a	a	DET
ejpam-84	15	8	special	special	ADJ
ejpam-84	15	9	case	case	NOUN
ejpam-84	15	10	,	,	PUNCT
ejpam-84	15	11	fractional	fractional	ADJ
ejpam-84	15	12	differential	differential	NOUN
ejpam-84	15	13	systems	system	NOUN
ejpam-84	15	14	in	in	ADP
ejpam-84	15	15	rn	rn	PROPN
ejpam-84	15	16	,	,	PUNCT
ejpam-84	15	17	it	it	PRON
ejpam-84	15	18	does	do	AUX
ejpam-84	15	19	not	not	PART
ejpam-84	15	20	cover	cover	VERB
ejpam-84	15	21	the	the	DET
ejpam-84	15	22	case	case	NOUN
ejpam-84	15	23	when	when	SCONJ
ejpam-84	15	24	each	each	DET
ejpam-84	15	25	component	component	NOUN
ejpam-84	15	26	or	or	CCONJ
ejpam-84	15	27	a	a	DET
ejpam-84	15	28	group	group	NOUN
ejpam-84	15	29	of	of	ADP
ejpam-84	15	30	components	component	NOUN
ejpam-84	15	31	of	of	ADP
ejpam-84	15	32	the	the	DET
ejpam-84	15	33	vector	vector	NOUN
ejpam-84	15	34	in	in	ADP
ejpam-84	15	35	rn	rn	PROPN
ejpam-84	15	36	,	,	PUNCT
ejpam-84	15	37	has	have	VERB
ejpam-84	15	38	a	a	DET
ejpam-84	15	39	different	different	ADJ
ejpam-84	15	40	arbitrary	arbitrary	ADJ
ejpam-84	15	41	order	order	NOUN
ejpam-84	15	42	.	.	PUNCT
ejpam-84	16	1	this	this	DET
ejpam-84	16	2	case	case	NOUN
ejpam-84	16	3	needs	need	VERB
ejpam-84	16	4	a	a	DET
ejpam-84	16	5	different	different	ADJ
ejpam-84	16	6	consideration	consideration	NOUN
ejpam-84	16	7	such	such	ADJ
ejpam-84	16	8	as	as	ADP
ejpam-84	16	9	employed	employ	VERB
ejpam-84	16	10	in	in	ADP
ejpam-84	16	11	the	the	DET
ejpam-84	16	12	study	study	NOUN
ejpam-84	16	13	of	of	ADP
ejpam-84	16	14	large	large	ADJ
ejpam-84	16	15	scale	scale	NOUN
ejpam-84	16	16	systems	system	NOUN
ejpam-84	16	17	,	,	PUNCT
ejpam-84	16	18	which	which	PRON
ejpam-84	16	19	will	will	AUX
ejpam-84	16	20	be	be	AUX
ejpam-84	16	21	taken	take	VERB
ejpam-84	16	22	up	up	ADP
ejpam-84	16	23	later	later	ADV
ejpam-84	16	24	.	.	PUNCT
ejpam-84	17	1	∗corresponding	∗corresponde	VERB
ejpam-84	17	2	author	author	NOUN
ejpam-84	17	3	.	.	PUNCT
ejpam-84	18	1	email	email	NOUN
ejpam-84	18	2	addresses	address	NOUN
ejpam-84	18	3	:	:	PUNCT
ejpam-84	18	4	lakshmik@fit.edu	lakshmik@fit.edu	NOUN
ejpam-84	18	5	(	(	PUNCT
ejpam-84	18	6	v.lakshmikantham	v.lakshmikantham	PROPN
ejpam-84	18	7	)	)	PUNCT
ejpam-84	18	8	,	,	PUNCT
ejpam-84	18	9	jvdevi@gmail.com	jvdevi@gmail.com	X
ejpam-84	18	10	(	(	PUNCT
ejpam-84	18	11	j.devi	j.devi	PROPN
ejpam-84	18	12	)	)	PUNCT
ejpam-84	18	13	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-84	19	1	38	38	NUM
ejpam-84	20	1	c	c	X
ejpam-84	20	2	©	©	PROPN
ejpam-84	20	3	2007	2007	NUM
ejpam-84	20	4	ejpam	ejpam	NOUN
ejpam-84	20	5	all	all	DET
ejpam-84	20	6	rights	right	NOUN
ejpam-84	20	7	reserved	reserve	VERB
ejpam-84	20	8	.	.	PUNCT
ejpam-84	21	1	v.lakshmikantham	v.lakshmikantham	PROPN
ejpam-84	21	2	,	,	PUNCT
ejpam-84	21	3	j.devi	j.devi	PROPN
ejpam-84	21	4	/	/	SYM
ejpam-84	21	5	eur	eur	PROPN
ejpam-84	21	6	.	.	PUNCT
ejpam-84	22	1	j.	j.	PROPN
ejpam-84	22	2	pure	pure	PROPN
ejpam-84	22	3	appl	appl	PROPN
ejpam-84	22	4	.	.	PROPN
ejpam-84	22	5	math	math	PROPN
ejpam-84	22	6	,	,	PUNCT
ejpam-84	22	7	1	1	NUM
ejpam-84	22	8	(	(	PUNCT
ejpam-84	22	9	2008	2008	NUM
ejpam-84	22	10	)	)	PUNCT
ejpam-84	22	11	,	,	PUNCT
ejpam-84	22	12	(	(	PUNCT
ejpam-84	22	13	38	38	NUM
ejpam-84	22	14	-	-	SYM
ejpam-84	22	15	45	45	NUM
ejpam-84	22	16	)	)	PUNCT
ejpam-84	22	17	39	39	NUM
ejpam-84	22	18	2	2	NUM
ejpam-84	22	19	.	.	PUNCT
ejpam-84	23	1	uniqueness	uniqueness	NOUN
ejpam-84	23	2	and	and	CCONJ
ejpam-84	23	3	continuous	continuous	ADJ
ejpam-84	23	4	dependence	dependence	NOUN
ejpam-84	23	5	let	let	VERB
ejpam-84	23	6	e	e	PRON
ejpam-84	23	7	be	be	AUX
ejpam-84	23	8	a	a	DET
ejpam-84	23	9	real	real	ADJ
ejpam-84	23	10	banach	banach	NOUN
ejpam-84	23	11	space	space	NOUN
ejpam-84	23	12	with	with	ADP
ejpam-84	23	13	the	the	DET
ejpam-84	23	14	norm	norm	NOUN
ejpam-84	23	15	|	|	ADV
ejpam-84	23	16	·	·	PUNCT
ejpam-84	24	1	|	|	INTJ
ejpam-84	24	2	.	.	PUNCT
ejpam-84	25	1	let	let	VERB
ejpam-84	25	2	0	0	NUM
ejpam-84	25	3	<	<	X
ejpam-84	25	4	q	q	X
ejpam-84	26	1	<	<	X
ejpam-84	26	2	1	1	NUM
ejpam-84	26	3	and	and	CCONJ
ejpam-84	26	4	p	p	NOUN
ejpam-84	26	5	=	=	NOUN
ejpam-84	26	6	1	1	NUM
ejpam-84	26	7	−	−	NOUN
ejpam-84	26	8	q.	q.	NOUN
ejpam-84	26	9	we	we	PRON
ejpam-84	26	10	let	let	VERB
ejpam-84	26	11	cp([t0	cp([t0	NOUN
ejpam-84	26	12	,	,	PUNCT
ejpam-84	26	13	t0	t0	PROPN
ejpam-84	26	14	+	+	CCONJ
ejpam-84	27	1	a	a	DET
ejpam-84	27	2	]	]	X
ejpam-84	27	3	,	,	PUNCT
ejpam-84	27	4	e	e	NOUN
ejpam-84	27	5	)	)	PUNCT
ejpam-84	27	6	=	=	NOUN
ejpam-84	28	1	[	[	X
ejpam-84	28	2	u	u	X
ejpam-84	28	3	:	:	PUNCT
ejpam-84	28	4	c((t0	c((t0	PROPN
ejpam-84	28	5	,	,	PUNCT
ejpam-84	28	6	t0	t0	PROPN
ejpam-84	28	7	+	+	CCONJ
ejpam-84	28	8	a	a	DET
ejpam-84	28	9	]	]	X
ejpam-84	28	10	,	,	PUNCT
ejpam-84	28	11	e	e	NOUN
ejpam-84	28	12	)	)	PUNCT
ejpam-84	28	13	and	and	CCONJ
ejpam-84	28	14	(	(	PUNCT
ejpam-84	28	15	t	t	PROPN
ejpam-84	28	16	−	−	PROPN
ejpam-84	28	17	t0)1−qu(t	t0)1−qu(t	PROPN
ejpam-84	28	18	)	)	PUNCT
ejpam-84	28	19	∈	∈	PROPN
ejpam-84	28	20	c([t0	c([t0	NOUN
ejpam-84	28	21	,	,	PUNCT
ejpam-84	28	22	t0	t0	PROPN
ejpam-84	28	23	+	+	CCONJ
ejpam-84	28	24	a	a	DET
ejpam-84	28	25	]	]	X
ejpam-84	28	26	,	,	PUNCT
ejpam-84	28	27	e	e	NOUN
ejpam-84	28	28	)	)	PUNCT
ejpam-84	28	29	]	]	PUNCT
ejpam-84	28	30	.	.	PUNCT
ejpam-84	29	1	let	let	VERB
ejpam-84	29	2	us	we	PRON
ejpam-84	29	3	consider	consider	VERB
ejpam-84	29	4	the	the	DET
ejpam-84	29	5	initial	initial	ADJ
ejpam-84	29	6	value	value	NOUN
ejpam-84	29	7	problem	problem	NOUN
ejpam-84	29	8	(	(	PUNCT
ejpam-84	29	9	ivp	ivp	NOUN
ejpam-84	29	10	)	)	PUNCT
ejpam-84	29	11	for	for	ADP
ejpam-84	29	12	fractional	fractional	ADJ
ejpam-84	29	13	differential	differential	ADJ
ejpam-84	29	14	equations	equation	NOUN
ejpam-84	29	15	in	in	ADP
ejpam-84	29	16	e	e	NOUN
ejpam-84	29	17	given	give	VERB
ejpam-84	29	18	by	by	ADP
ejpam-84	29	19	dqx	dqx	NOUN
ejpam-84	29	20	=	=	SYM
ejpam-84	29	21	f(t	f(t	NOUN
ejpam-84	29	22	,	,	PUNCT
ejpam-84	29	23	x	x	NOUN
ejpam-84	29	24	)	)	PUNCT
ejpam-84	29	25	,	,	PUNCT
ejpam-84	29	26	x(t)(t−	x(t)(t−	PUNCT
ejpam-84	30	1	t0)1−q|t	t0)1−q|t	NUM
ejpam-84	30	2	=	=	SYM
ejpam-84	30	3	t0	t0	NOUN
ejpam-84	30	4	=	=	PUNCT
ejpam-84	30	5	x0	x0	PROPN
ejpam-84	30	6	,	,	PUNCT
ejpam-84	30	7	(	(	PUNCT
ejpam-84	30	8	2.1	2.1	NUM
ejpam-84	30	9	)	)	PUNCT
ejpam-84	30	10	where	where	SCONJ
ejpam-84	30	11	f	f	PROPN
ejpam-84	30	12	∈	∈	PROPN
ejpam-84	30	13	c[r0	c[r0	VERB
ejpam-84	30	14	,	,	PUNCT
ejpam-84	30	15	e	e	X
ejpam-84	30	16	]	]	PUNCT
ejpam-84	30	17	with	with	ADP
ejpam-84	30	18	r0	r0	NOUN
ejpam-84	30	19	=	=	PUNCT
ejpam-84	31	1	[	[	X
ejpam-84	31	2	(	(	PUNCT
ejpam-84	31	3	t	t	PROPN
ejpam-84	31	4	,	,	PUNCT
ejpam-84	31	5	x	x	NOUN
ejpam-84	31	6	)	)	PUNCT
ejpam-84	31	7	:	:	PUNCT
ejpam-84	31	8	t0	t0	PROPN
ejpam-84	31	9	≤	≤	PROPN
ejpam-84	31	10	t	t	PROPN
ejpam-84	31	11	≤	≤	NUM
ejpam-84	31	12	t0	t0	PROPN
ejpam-84	31	13	+	+	CCONJ
ejpam-84	31	14	a	a	PRON
ejpam-84	31	15	and	and	CCONJ
ejpam-84	31	16	b(x0	b(x0	NOUN
ejpam-84	31	17	,	,	PUNCT
ejpam-84	31	18	b	b	NOUN
ejpam-84	31	19	)	)	PUNCT
ejpam-84	31	20	]	]	PUNCT
ejpam-84	31	21	,	,	PUNCT
ejpam-84	31	22	dqx	dqx	NOUN
ejpam-84	31	23	is	be	AUX
ejpam-84	31	24	the	the	DET
ejpam-84	31	25	fractional	fractional	ADJ
ejpam-84	31	26	derivative	derivative	NOUN
ejpam-84	31	27	of	of	ADP
ejpam-84	31	28	x	x	PUNCT
ejpam-84	31	29	of	of	ADP
ejpam-84	31	30	order	order	NOUN
ejpam-84	31	31	0	0	PUNCT
ejpam-84	31	32	<	<	X
ejpam-84	31	33	q	q	X
ejpam-84	31	34	<	<	X
ejpam-84	31	35	1	1	NUM
ejpam-84	31	36	and	and	CCONJ
ejpam-84	31	37	x0(t	x0(t	NUM
ejpam-84	31	38	)	)	PUNCT
ejpam-84	31	39	=	=	SYM
ejpam-84	31	40	x0(t−t0)q−1	x0(t−t0)q−1	X
ejpam-84	31	41	γ(q	γ(q	NOUN
ejpam-84	31	42	)	)	PUNCT
ejpam-84	31	43	.	.	PUNCT
ejpam-84	32	1	since	since	SCONJ
ejpam-84	32	2	f	f	PROPN
ejpam-84	32	3	is	be	AUX
ejpam-84	32	4	assumed	assume	VERB
ejpam-84	32	5	continuous	continuous	ADJ
ejpam-84	32	6	,	,	PUNCT
ejpam-84	32	7	the	the	DET
ejpam-84	32	8	ivp	ivp	NOUN
ejpam-84	32	9	(	(	PUNCT
ejpam-84	32	10	2.1	2.1	NUM
ejpam-84	32	11	)	)	PUNCT
ejpam-84	32	12	is	be	AUX
ejpam-84	32	13	equivalent	equivalent	ADJ
ejpam-84	32	14	to	to	ADP
ejpam-84	32	15	the	the	DET
ejpam-84	32	16	following	follow	VERB
ejpam-84	32	17	fractional	fractional	ADJ
ejpam-84	32	18	volterra	volterra	PROPN
ejpam-84	32	19	integral	integral	ADJ
ejpam-84	32	20	x(t	x(t	PROPN
ejpam-84	32	21	)	)	PUNCT
ejpam-84	32	22	=	=	SYM
ejpam-84	33	1	x0(t	x0(t	PROPN
ejpam-84	33	2	)	)	PUNCT
ejpam-84	33	3	+	+	CCONJ
ejpam-84	33	4	1	1	NUM
ejpam-84	33	5	γ(q	γ(q	NOUN
ejpam-84	33	6	)	)	PUNCT
ejpam-84	33	7	∫	∫	PROPN
ejpam-84	33	8	t	t	PROPN
ejpam-84	33	9	t0	t0	PROPN
ejpam-84	33	10	(	(	PUNCT
ejpam-84	33	11	t−	t−	PROPN
ejpam-84	33	12	s)q−1f(s	s)q−1f(	NOUN
ejpam-84	33	13	,	,	PUNCT
ejpam-84	33	14	x(s))ds	x(s))ds	PROPN
ejpam-84	33	15	,	,	PUNCT
ejpam-84	33	16	t0	t0	PROPN
ejpam-84	33	17	≤	≤	PROPN
ejpam-84	33	18	t	t	PROPN
ejpam-84	33	19	≤	≤	NUM
ejpam-84	33	20	t0	t0	PROPN
ejpam-84	33	21	+	+	CCONJ
ejpam-84	33	22	a	a	X
ejpam-84	33	23	;	;	PUNCT
ejpam-84	33	24	(	(	PUNCT
ejpam-84	33	25	2.2	2.2	NUM
ejpam-84	33	26	)	)	PUNCT
ejpam-84	33	27	that	that	PRON
ejpam-84	33	28	is	is	ADV
ejpam-84	33	29	,	,	PUNCT
ejpam-84	33	30	every	every	DET
ejpam-84	33	31	solution	solution	NOUN
ejpam-84	33	32	of	of	ADP
ejpam-84	33	33	(	(	PUNCT
ejpam-84	33	34	2.2	2.2	NUM
ejpam-84	33	35	)	)	PUNCT
ejpam-84	33	36	is	be	AUX
ejpam-84	33	37	a	a	DET
ejpam-84	33	38	solution	solution	NOUN
ejpam-84	33	39	of	of	ADP
ejpam-84	33	40	(	(	PUNCT
ejpam-84	33	41	2.1	2.1	NUM
ejpam-84	33	42	)	)	PUNCT
ejpam-84	33	43	and	and	CCONJ
ejpam-84	33	44	vice	vice	ADV
ejpam-84	33	45	versa	versa	ADV
ejpam-84	33	46	.	.	PUNCT
ejpam-84	34	1	here	here	ADV
ejpam-84	34	2	and	and	CCONJ
ejpam-84	34	3	in	in	ADP
ejpam-84	34	4	what	what	PRON
ejpam-84	34	5	follows	follow	VERB
ejpam-84	34	6	γ	γ	PROPN
ejpam-84	34	7	is	be	AUX
ejpam-84	34	8	the	the	DET
ejpam-84	34	9	gamma	gamma	PROPN
ejpam-84	34	10	function	function	NOUN
ejpam-84	34	11	.	.	PUNCT
ejpam-84	35	1	remark	remark	VERB
ejpam-84	35	2	2.1	2.1	NUM
ejpam-84	35	3	:	:	PUNCT
ejpam-84	35	4	when	when	SCONJ
ejpam-84	35	5	we	we	PRON
ejpam-84	35	6	change	change	VERB
ejpam-84	35	7	the	the	DET
ejpam-84	35	8	initial	initial	ADJ
ejpam-84	35	9	condition	condition	NOUN
ejpam-84	35	10	in	in	ADP
ejpam-84	35	11	time	time	NOUN
ejpam-84	35	12	from	from	ADP
ejpam-84	35	13	zero	zero	NUM
ejpam-84	35	14	to	to	ADP
ejpam-84	35	15	t0	t0	PROPN
ejpam-84	35	16	≥	≥	NUM
ejpam-84	35	17	0	0	NUM
ejpam-84	35	18	,	,	PUNCT
ejpam-84	35	19	we	we	PRON
ejpam-84	35	20	need	need	VERB
ejpam-84	35	21	to	to	PART
ejpam-84	35	22	change	change	VERB
ejpam-84	35	23	the	the	DET
ejpam-84	35	24	same	same	ADJ
ejpam-84	35	25	in	in	ADP
ejpam-84	35	26	(	(	PUNCT
ejpam-84	35	27	2.2	2.2	NUM
ejpam-84	35	28	)	)	PUNCT
ejpam-84	35	29	.	.	PUNCT
ejpam-84	36	1	in	in	ADP
ejpam-84	36	2	some	some	DET
ejpam-84	36	3	earlier	early	ADJ
ejpam-84	36	4	papers	paper	NOUN
ejpam-84	36	5	[	[	X
ejpam-84	36	6	9][11	9][11	X
ejpam-84	36	7	]	]	PUNCT
ejpam-84	36	8	,	,	PUNCT
ejpam-84	36	9	we	we	PRON
ejpam-84	36	10	did	do	AUX
ejpam-84	36	11	use	use	VERB
ejpam-84	36	12	t0	t0	NOUN
ejpam-84	36	13	=	=	SYM
ejpam-84	36	14	0	0	NUM
ejpam-84	36	15	for	for	ADP
ejpam-84	36	16	convenience	convenience	NOUN
ejpam-84	36	17	.	.	PUNCT
ejpam-84	37	1	however	however	ADV
ejpam-84	37	2	,	,	PUNCT
ejpam-84	37	3	in	in	ADP
ejpam-84	37	4	dealing	deal	VERB
ejpam-84	37	5	with	with	ADP
ejpam-84	37	6	,	,	PUNCT
ejpam-84	37	7	for	for	ADP
ejpam-84	37	8	example	example	NOUN
ejpam-84	37	9	,	,	PUNCT
ejpam-84	37	10	the	the	DET
ejpam-84	37	11	continuous	continuous	ADJ
ejpam-84	37	12	dependence	dependence	NOUN
ejpam-84	37	13	of	of	ADP
ejpam-84	37	14	solutions	solution	NOUN
ejpam-84	37	15	with	with	ADP
ejpam-84	37	16	respect	respect	NOUN
ejpam-84	37	17	to	to	ADP
ejpam-84	37	18	initial	initial	ADJ
ejpam-84	37	19	values	value	NOUN
ejpam-84	37	20	(	(	PUNCT
ejpam-84	37	21	t0	t0	NOUN
ejpam-84	37	22	,	,	PUNCT
ejpam-84	37	23	x0	x0	PROPN
ejpam-84	37	24	)	)	PUNCT
ejpam-84	37	25	,	,	PUNCT
ejpam-84	37	26	as	as	ADV
ejpam-84	37	27	well	well	ADV
ejpam-84	37	28	as	as	ADP
ejpam-84	37	29	discussing	discuss	VERB
ejpam-84	37	30	the	the	DET
ejpam-84	37	31	qualitative	qualitative	ADJ
ejpam-84	37	32	theory	theory	NOUN
ejpam-84	37	33	including	include	VERB
ejpam-84	37	34	lyapunov	lyapunov	ADJ
ejpam-84	37	35	stability	stability	NOUN
ejpam-84	37	36	theory	theory	NOUN
ejpam-84	37	37	,	,	PUNCT
ejpam-84	37	38	we	we	PRON
ejpam-84	37	39	need	need	VERB
ejpam-84	37	40	to	to	PART
ejpam-84	37	41	employ	employ	VERB
ejpam-84	37	42	nonzero	nonzero	NOUN
ejpam-84	37	43	initial	initial	ADJ
ejpam-84	37	44	time	time	NOUN
ejpam-84	37	45	t0	t0	PROPN
ejpam-84	37	46	>	>	X
ejpam-84	37	47	0	0	PUNCT
ejpam-84	38	1	instead	instead	ADV
ejpam-84	38	2	of	of	ADP
ejpam-84	38	3	only	only	ADV
ejpam-84	38	4	t0	t0	PROPN
ejpam-84	39	1	=	=	PUNCT
ejpam-84	39	2	0	0	X
ejpam-84	39	3	.	.	PUNCT
ejpam-84	40	1	the	the	DET
ejpam-84	40	2	difference	difference	NOUN
ejpam-84	40	3	in	in	ADP
ejpam-84	40	4	such	such	DET
ejpam-84	40	5	a	a	DET
ejpam-84	40	6	change	change	NOUN
ejpam-84	40	7	appears	appear	VERB
ejpam-84	40	8	only	only	ADV
ejpam-84	40	9	when	when	SCONJ
ejpam-84	40	10	we	we	PRON
ejpam-84	40	11	have	have	VERB
ejpam-84	40	12	to	to	PART
ejpam-84	40	13	utilize	utilize	VERB
ejpam-84	40	14	the	the	DET
ejpam-84	40	15	gamma	gamma	NOUN
ejpam-84	40	16	and	and	CCONJ
ejpam-84	40	17	beta	beta	NOUN
ejpam-84	40	18	functions	function	NOUN
ejpam-84	40	19	,	,	PUNCT
ejpam-84	40	20	in	in	ADP
ejpam-84	40	21	which	which	DET
ejpam-84	40	22	case	case	NOUN
ejpam-84	40	23	,	,	PUNCT
ejpam-84	40	24	the	the	DET
ejpam-84	40	25	limits	limit	NOUN
ejpam-84	40	26	of	of	ADP
ejpam-84	40	27	the	the	DET
ejpam-84	40	28	transformed	transform	VERB
ejpam-84	40	29	integral	integral	NOUN
ejpam-84	40	30	is	be	AUX
ejpam-84	40	31	required	require	VERB
ejpam-84	40	32	to	to	PART
ejpam-84	40	33	be	be	AUX
ejpam-84	40	34	zero	zero	NUM
ejpam-84	40	35	to	to	ADP
ejpam-84	40	36	one	one	NUM
ejpam-84	40	37	.	.	PUNCT
ejpam-84	41	1	a	a	DET
ejpam-84	41	2	suitable	suitable	ADJ
ejpam-84	41	3	transformation	transformation	NOUN
ejpam-84	41	4	does	do	VERB
ejpam-84	41	5	the	the	DET
ejpam-84	41	6	trick	trick	NOUN
ejpam-84	41	7	,	,	PUNCT
ejpam-84	41	8	that	that	ADV
ejpam-84	41	9	is	is	ADV
ejpam-84	41	10	,	,	PUNCT
ejpam-84	41	11	setting	set	VERB
ejpam-84	41	12	s	s	AUX
ejpam-84	41	13	=	=	X
ejpam-84	41	14	t0	t0	PROPN
ejpam-84	41	15	+	+	CCONJ
ejpam-84	41	16	(	(	PUNCT
ejpam-84	41	17	t−	t−	PROPN
ejpam-84	41	18	t0)σ	t0)σ	PROPN
ejpam-84	41	19	.	.	PUNCT
ejpam-84	42	1	we	we	PRON
ejpam-84	42	2	need	need	VERB
ejpam-84	42	3	the	the	DET
ejpam-84	42	4	following	follow	VERB
ejpam-84	42	5	known	know	VERB
ejpam-84	42	6	results	result	NOUN
ejpam-84	42	7	[	[	X
ejpam-84	42	8	10	10	NUM
ejpam-84	42	9	]	]	PUNCT
ejpam-84	42	10	,	,	PUNCT
ejpam-84	42	11	[	[	X
ejpam-84	42	12	11	11	NUM
ejpam-84	42	13	]	]	PUNCT
ejpam-84	42	14	before	before	SCONJ
ejpam-84	42	15	we	we	PRON
ejpam-84	42	16	proceed	proceed	VERB
ejpam-84	42	17	further	far	ADV
ejpam-84	42	18	.	.	PUNCT
ejpam-84	43	1	lemma	lemma	PROPN
ejpam-84	43	2	2.1	2.1	NUM
ejpam-84	43	3	:	:	PUNCT
ejpam-84	43	4	let	let	VERB
ejpam-84	43	5	m	m	PRON
ejpam-84	43	6	:	:	PUNCT
ejpam-84	43	7	r+	r+	NOUN
ejpam-84	43	8	→	→	PUNCT
ejpam-84	43	9	r	r	NOUN
ejpam-84	43	10	be	be	AUX
ejpam-84	43	11	locally	locally	ADV
ejpam-84	43	12	hölder	hölder	NOUN
ejpam-84	43	13	continuous	continuous	ADJ
ejpam-84	43	14	such	such	ADJ
ejpam-84	43	15	that	that	PRON
ejpam-84	43	16	for	for	ADP
ejpam-84	43	17	any	any	DET
ejpam-84	43	18	t1	t1	NOUN
ejpam-84	43	19	∈	∈	PROPN
ejpam-84	44	1	[	[	X
ejpam-84	44	2	t0,∞	t0,∞	NUM
ejpam-84	44	3	)	)	PUNCT
ejpam-84	44	4	,	,	PUNCT
ejpam-84	44	5	one	one	PRON
ejpam-84	44	6	has	have	VERB
ejpam-84	44	7	m(t1	m(t1	NOUN
ejpam-84	44	8	)	)	PUNCT
ejpam-84	44	9	=	=	SYM
ejpam-84	44	10	0	0	NUM
ejpam-84	44	11	and	and	CCONJ
ejpam-84	44	12	m(t	m(t	NOUN
ejpam-84	44	13	)	)	PUNCT
ejpam-84	44	14	≤	≤	NUM
ejpam-84	44	15	0	0	NUM
ejpam-84	44	16	or	or	CCONJ
ejpam-84	44	17	m(t	m(t	NOUN
ejpam-84	44	18	)	)	PUNCT
ejpam-84	44	19	≥	≥	X
ejpam-84	44	20	0	0	NUM
ejpam-84	44	21	for	for	ADP
ejpam-84	44	22	t0	t0	PROPN
ejpam-84	44	23	≤	≤	PROPN
ejpam-84	44	24	t	t	PROPN
ejpam-84	44	25	≤	≤	NUM
ejpam-84	44	26	t1	t1	PROPN
ejpam-84	44	27	.	.	PUNCT
ejpam-84	45	1	then	then	ADV
ejpam-84	45	2	it	it	PRON
ejpam-84	45	3	follows	follow	VERB
ejpam-84	45	4	that	that	SCONJ
ejpam-84	45	5	dqm(t1	dqm(t1	NOUN
ejpam-84	45	6	)	)	PUNCT
ejpam-84	45	7	≥	≥	NOUN
ejpam-84	45	8	0	0	NUM
ejpam-84	45	9	or	or	CCONJ
ejpam-84	45	10	dqm(t1	dqm(t1	NOUN
ejpam-84	45	11	)	)	PUNCT
ejpam-84	45	12	≤	≤	NOUN
ejpam-84	45	13	0	0	NUM
ejpam-84	45	14	respectively	respectively	ADV
ejpam-84	45	15	.	.	PUNCT
ejpam-84	46	1	lemma	lemma	PROPN
ejpam-84	46	2	2.2	2.2	NUM
ejpam-84	46	3	:	:	PUNCT
ejpam-84	46	4	let	let	VERB
ejpam-84	46	5	{	{	PUNCT
ejpam-84	46	6	xε(t	xε(t	NOUN
ejpam-84	46	7	)	)	PUNCT
ejpam-84	46	8	}	}	PUNCT
ejpam-84	46	9	be	be	AUX
ejpam-84	46	10	a	a	DET
ejpam-84	46	11	family	family	NOUN
ejpam-84	46	12	of	of	ADP
ejpam-84	46	13	continuous	continuous	ADJ
ejpam-84	46	14	functions	function	NOUN
ejpam-84	46	15	on	on	ADP
ejpam-84	46	16	[	[	X
ejpam-84	46	17	t0	t0	NOUN
ejpam-84	46	18	,	,	PUNCT
ejpam-84	46	19	t0	t0	PROPN
ejpam-84	47	1	+	+	PROPN
ejpam-84	47	2	t	t	X
ejpam-84	47	3	]	]	PUNCT
ejpam-84	47	4	,	,	PUNCT
ejpam-84	47	5	for	for	ADP
ejpam-84	47	6	each	each	DET
ejpam-84	47	7	ε	ε	PROPN
ejpam-84	47	8	>	>	X
ejpam-84	47	9	0	0	NUM
ejpam-84	47	10	where	where	SCONJ
ejpam-84	47	11	dqxε(t	dqxε(t	ADP
ejpam-84	47	12	)	)	PUNCT
ejpam-84	47	13	=	=	PUNCT
ejpam-84	48	1	f(t	f(t	NOUN
ejpam-84	48	2	,	,	PUNCT
ejpam-84	48	3	xε(t	xε(t	NOUN
ejpam-84	48	4	)	)	PUNCT
ejpam-84	48	5	)	)	PUNCT
ejpam-84	48	6	,	,	PUNCT
ejpam-84	48	7	x0	x0	PROPN
ejpam-84	48	8	ε	ε	PROPN
ejpam-84	48	9	=	=	PUNCT
ejpam-84	48	10	xε(t)(t	xε(t)(t	PROPN
ejpam-84	48	11	−	−	ADP
ejpam-84	48	12	t0)1−q|t	t0)1−q|t	NUM
ejpam-84	48	13	=	=	SYM
ejpam-84	48	14	t0	t0	PROPN
ejpam-84	48	15	and	and	CCONJ
ejpam-84	48	16	|f(t	|f(t	PROPN
ejpam-84	48	17	,	,	PUNCT
ejpam-84	48	18	xε(t))|	xε(t))|	PROPN
ejpam-84	48	19	≤	≤	NUM
ejpam-84	48	20	m	m	VERB
ejpam-84	48	21	for	for	ADP
ejpam-84	48	22	t0	t0	PROPN
ejpam-84	48	23	≤	≤	PROPN
ejpam-84	48	24	t	t	PROPN
ejpam-84	48	25	≤	≤	NUM
ejpam-84	48	26	t0	t0	PROPN
ejpam-84	48	27	+	+	CCONJ
ejpam-84	48	28	t	t	PROPN
ejpam-84	48	29	.	.	PUNCT
ejpam-84	49	1	then	then	ADV
ejpam-84	49	2	the	the	DET
ejpam-84	49	3	family	family	NOUN
ejpam-84	49	4	{	{	PUNCT
ejpam-84	49	5	xε(t	xε(t	NOUN
ejpam-84	49	6	)	)	PUNCT
ejpam-84	49	7	}	}	PUNCT
ejpam-84	49	8	is	be	AUX
ejpam-84	49	9	equicontinuous	equicontinuous	ADJ
ejpam-84	49	10	on	on	ADP
ejpam-84	49	11	t0	t0	PROPN
ejpam-84	49	12	≤	≤	PROPN
ejpam-84	49	13	t	t	PROPN
ejpam-84	49	14	≤	≤	NUM
ejpam-84	49	15	t0	t0	PROPN
ejpam-84	49	16	+	+	PROPN
ejpam-84	49	17	t	t	PROPN
ejpam-84	49	18	.	.	PUNCT
ejpam-84	50	1	lemma	lemma	PROPN
ejpam-84	50	2	2.3	2.3	NUM
ejpam-84	50	3	:	:	PUNCT
ejpam-84	50	4	assume	assume	VERB
ejpam-84	50	5	that	that	SCONJ
ejpam-84	50	6	g	g	PROPN
ejpam-84	50	7	∈	∈	PROPN
ejpam-84	50	8	c[ω	c[ω	PROPN
ejpam-84	50	9	,	,	PUNCT
ejpam-84	50	10	r	r	X
ejpam-84	50	11	]	]	X
ejpam-84	50	12	where	where	SCONJ
ejpam-84	50	13	ω	ω	PROPN
ejpam-84	50	14	is	be	AUX
ejpam-84	50	15	an	an	DET
ejpam-84	50	16	open	open	ADJ
ejpam-84	50	17	(	(	PUNCT
ejpam-84	50	18	t	t	PROPN
ejpam-84	50	19	,	,	PUNCT
ejpam-84	50	20	u)-set	u)-set	NOUN
ejpam-84	50	21	in	in	ADP
ejpam-84	50	22	r2	r2	PROPN
ejpam-84	50	23	and	and	CCONJ
ejpam-84	50	24	(	(	PUNCT
ejpam-84	50	25	t0	t0	PROPN
ejpam-84	50	26	,	,	PUNCT
ejpam-84	50	27	u0	u0	ADJ
ejpam-84	50	28	)	)	PUNCT
ejpam-84	50	29	∈	∈	PROPN
ejpam-84	50	30	ω	ω	PROPN
ejpam-84	50	31	.	.	PUNCT
ejpam-84	50	32	suppose	suppose	VERB
ejpam-84	51	1	that	that	SCONJ
ejpam-84	52	1	[	[	X
ejpam-84	52	2	t0	t0	NOUN
ejpam-84	52	3	,	,	PUNCT
ejpam-84	52	4	t0	t0	PROPN
ejpam-84	52	5	+	+	CCONJ
ejpam-84	52	6	a	a	X
ejpam-84	52	7	)	)	PUNCT
ejpam-84	52	8	is	be	AUX
ejpam-84	52	9	the	the	DET
ejpam-84	52	10	largest	large	ADJ
ejpam-84	52	11	interval	interval	NOUN
ejpam-84	52	12	of	of	ADP
ejpam-84	52	13	existence	existence	NOUN
ejpam-84	52	14	of	of	ADP
ejpam-84	52	15	the	the	DET
ejpam-84	52	16	maximal	maximal	ADJ
ejpam-84	52	17	solution	solution	NOUN
ejpam-84	52	18	r(t	r(t	NOUN
ejpam-84	52	19	)	)	PUNCT
ejpam-84	52	20	of	of	ADP
ejpam-84	52	21	dqu	dqu	ADJ
ejpam-84	52	22	=	=	SYM
ejpam-84	52	23	g(t	g(t	PROPN
ejpam-84	52	24	,	,	PUNCT
ejpam-84	52	25	u	u	NOUN
ejpam-84	52	26	)	)	PUNCT
ejpam-84	52	27	,	,	PUNCT
ejpam-84	52	28	u(t)(t	u(t)(t	NUM
ejpam-84	52	29	−	−	ADP
ejpam-84	52	30	t0)1−q|t	t0)1−q|t	NUM
ejpam-84	52	31	=	=	SYM
ejpam-84	52	32	t0	t0	NOUN
ejpam-84	52	33	=	=	SYM
ejpam-84	52	34	u0	u0	PROPN
ejpam-84	52	35	.	.	PUNCT
ejpam-84	53	1	let	let	VERB
ejpam-84	54	1	[	[	X
ejpam-84	54	2	t0	t0	NOUN
ejpam-84	54	3	,	,	PUNCT
ejpam-84	54	4	t1	t1	PROPN
ejpam-84	54	5	]	]	PUNCT
ejpam-84	54	6	be	be	AUX
ejpam-84	54	7	a	a	DET
ejpam-84	54	8	compact	compact	ADJ
ejpam-84	54	9	interval	interval	NOUN
ejpam-84	54	10	of	of	ADP
ejpam-84	54	11	[	[	X
ejpam-84	54	12	t0	t0	PROPN
ejpam-84	54	13	,	,	PUNCT
ejpam-84	54	14	t0	t0	PROPN
ejpam-84	54	15	+	+	CCONJ
ejpam-84	54	16	a	a	X
ejpam-84	54	17	)	)	PUNCT
ejpam-84	54	18	.	.	PUNCT
ejpam-84	55	1	then	then	ADV
ejpam-84	55	2	there	there	PRON
ejpam-84	55	3	is	be	VERB
ejpam-84	55	4	an	an	DET
ejpam-84	55	5	ε0	ε0	PROPN
ejpam-84	55	6	>	>	X
ejpam-84	55	7	0	0	NUM
ejpam-84	55	8	such	such	ADJ
ejpam-84	55	9	that	that	PRON
ejpam-84	55	10	for	for	ADP
ejpam-84	55	11	0	0	NUM
ejpam-84	55	12	<	<	X
ejpam-84	55	13	ε	ε	PROPN
ejpam-84	55	14	<	<	X
ejpam-84	55	15	ε0	ε0	PROPN
ejpam-84	55	16	,	,	PUNCT
ejpam-84	55	17	the	the	DET
ejpam-84	55	18	maximal	maximal	ADJ
ejpam-84	55	19	solution	solution	NOUN
ejpam-84	55	20	r(t	r(t	NOUN
ejpam-84	55	21	,	,	PUNCT
ejpam-84	55	22	ε	ε	PROPN
ejpam-84	55	23	)	)	PUNCT
ejpam-84	55	24	of	of	ADP
ejpam-84	55	25	dqu	dqu	ADJ
ejpam-84	55	26	=	=	SYM
ejpam-84	55	27	g(t	g(t	PROPN
ejpam-84	55	28	,	,	PUNCT
ejpam-84	55	29	u	u	NOUN
ejpam-84	55	30	)	)	PUNCT
ejpam-84	55	31	+	+	CCONJ
ejpam-84	55	32	ε	ε	PROPN
ejpam-84	55	33	,	,	PUNCT
ejpam-84	55	34	u(t)(t−	u(t)(t−	INTJ
ejpam-84	55	35	t0)1−q	t0)1−q	ADJ
ejpam-84	55	36	+	+	PUNCT
ejpam-84	55	37	ε|t	ε|t	ADJ
ejpam-84	55	38	=	=	ADJ
ejpam-84	55	39	t0	t0	NOUN
ejpam-84	55	40	=	=	SYM
ejpam-84	55	41	u0	u0	PROPN
ejpam-84	55	42	+	+	CCONJ
ejpam-84	55	43	ε	ε	PROPN
ejpam-84	55	44	exists	exist	VERB
ejpam-84	55	45	on	on	ADP
ejpam-84	55	46	[	[	X
ejpam-84	55	47	t0	t0	NOUN
ejpam-84	55	48	,	,	PUNCT
ejpam-84	55	49	t1	t1	NOUN
ejpam-84	55	50	]	]	PUNCT
ejpam-84	55	51	and	and	CCONJ
ejpam-84	55	52	limε→∞	limε→∞	PROPN
ejpam-84	55	53	r(t	r(t	NOUN
ejpam-84	55	54	,	,	PUNCT
ejpam-84	55	55	ε	ε	PROPN
ejpam-84	55	56	)	)	PUNCT
ejpam-84	55	57	=	=	SYM
ejpam-84	55	58	r(t	r(t	NOUN
ejpam-84	55	59	)	)	PUNCT
ejpam-84	55	60	uniformly	uniformly	ADV
ejpam-84	55	61	on	on	ADP
ejpam-84	55	62	[	[	X
ejpam-84	55	63	t0	t0	NOUN
ejpam-84	55	64	,	,	PUNCT
ejpam-84	55	65	t1	t1	PROPN
ejpam-84	55	66	]	]	X
ejpam-84	55	67	.	.	PUNCT
ejpam-84	56	1	lemma	lemma	PROPN
ejpam-84	56	2	2.4	2.4	NUM
ejpam-84	56	3	:	:	PUNCT
ejpam-84	56	4	assume	assume	VERB
ejpam-84	56	5	that	that	SCONJ
ejpam-84	56	6	m	m	PRON
ejpam-84	56	7	:	:	PUNCT
ejpam-84	57	1	[	[	X
ejpam-84	57	2	t0	t0	NOUN
ejpam-84	57	3	,	,	PUNCT
ejpam-84	57	4	t0	t0	PROPN
ejpam-84	57	5	+	+	CCONJ
ejpam-84	57	6	a	a	X
ejpam-84	57	7	]	]	X
ejpam-84	57	8	→	→	PUNCT
ejpam-84	57	9	r+	r+	NOUN
ejpam-84	57	10	be	be	AUX
ejpam-84	57	11	locally	locally	ADV
ejpam-84	57	12	hölder	hölder	NOUN
ejpam-84	57	13	continuous	continuous	ADJ
ejpam-84	57	14	,	,	PUNCT
ejpam-84	57	15	g	g	PROPN
ejpam-84	57	16	∈	∈	PROPN
ejpam-84	57	17	c([t0	c([t0	PROPN
ejpam-84	57	18	,	,	PUNCT
ejpam-84	57	19	t0	t0	PROPN
ejpam-84	57	20	+	+	CCONJ
ejpam-84	57	21	a]×r+	a]×r+	PROPN
ejpam-84	57	22	,	,	PUNCT
ejpam-84	57	23	r+	r+	PUNCT
ejpam-84	57	24	)	)	PUNCT
ejpam-84	57	25	and	and	CCONJ
ejpam-84	57	26	for	for	ADP
ejpam-84	57	27	t0	t0	PROPN
ejpam-84	57	28	≤	≤	PROPN
ejpam-84	57	29	t	t	PROPN
ejpam-84	57	30	≤	≤	NUM
ejpam-84	57	31	t0	t0	PROPN
ejpam-84	57	32	+	+	CCONJ
ejpam-84	57	33	a	a	DET
ejpam-84	57	34	,	,	PUNCT
ejpam-84	57	35	dqm(t	dqm(t	PROPN
ejpam-84	57	36	)	)	PUNCT
ejpam-84	57	37	≤	≤	NOUN
ejpam-84	57	38	g(t	g(t	PROPN
ejpam-84	57	39	,	,	PUNCT
ejpam-84	57	40	m(t	m(t	NOUN
ejpam-84	57	41	)	)	PUNCT
ejpam-84	57	42	)	)	PUNCT
ejpam-84	57	43	,	,	PUNCT
ejpam-84	57	44	m0	m0	PROPN
ejpam-84	57	45	=	=	PUNCT
ejpam-84	57	46	m(t)(t−	m(t)(t−	PROPN
ejpam-84	57	47	t0)1−q|t	t0)1−q|t	NUM
ejpam-84	57	48	=	=	ADJ
ejpam-84	57	49	t0	t0	PROPN
ejpam-84	57	50	.	.	PUNCT
ejpam-84	58	1	let	let	VERB
ejpam-84	58	2	r(t	r(t	NOUN
ejpam-84	58	3	)	)	PUNCT
ejpam-84	58	4	be	be	VERB
ejpam-84	58	5	the	the	DET
ejpam-84	58	6	maximal	maximal	ADJ
ejpam-84	58	7	solution	solution	NOUN
ejpam-84	58	8	of	of	ADP
ejpam-84	58	9	dqu	dqu	ADJ
ejpam-84	58	10	=	=	SYM
ejpam-84	58	11	g(t	g(t	PROPN
ejpam-84	58	12	,	,	PUNCT
ejpam-84	58	13	u	u	NOUN
ejpam-84	58	14	)	)	PUNCT
ejpam-84	58	15	,	,	PUNCT
ejpam-84	58	16	u(t)(t−	u(t)(t−	NOUN
ejpam-84	58	17	t0)1−q|t	t0)1−q|t	NUM
ejpam-84	58	18	=	=	SYM
ejpam-84	58	19	t0	t0	NOUN
ejpam-84	58	20	=	=	SYM
ejpam-84	58	21	u0	u0	ADJ
ejpam-84	58	22	≥	≥	PROPN
ejpam-84	58	23	0	0	NUM
ejpam-84	58	24	,	,	PUNCT
ejpam-84	58	25	v.lakshmikantham	v.lakshmikantham	PROPN
ejpam-84	58	26	,	,	PUNCT
ejpam-84	58	27	j.devi	j.devi	PROPN
ejpam-84	58	28	/	/	SYM
ejpam-84	58	29	eur	eur	PROPN
ejpam-84	58	30	.	.	PUNCT
ejpam-84	59	1	j.	j.	PROPN
ejpam-84	59	2	pure	pure	PROPN
ejpam-84	59	3	appl	appl	PROPN
ejpam-84	59	4	.	.	PROPN
ejpam-84	59	5	math	math	PROPN
ejpam-84	59	6	,	,	PUNCT
ejpam-84	59	7	1	1	NUM
ejpam-84	59	8	(	(	PUNCT
ejpam-84	59	9	2008	2008	NUM
ejpam-84	59	10	)	)	PUNCT
ejpam-84	59	11	,	,	PUNCT
ejpam-84	59	12	(	(	PUNCT
ejpam-84	59	13	38	38	NUM
ejpam-84	59	14	-	-	SYM
ejpam-84	59	15	45	45	NUM
ejpam-84	59	16	)	)	PUNCT
ejpam-84	59	17	40	40	NUM
ejpam-84	59	18	existing	exist	VERB
ejpam-84	59	19	on	on	ADP
ejpam-84	59	20	[	[	X
ejpam-84	59	21	t0	t0	NOUN
ejpam-84	59	22	,	,	PUNCT
ejpam-84	59	23	t0	t0	PROPN
ejpam-84	59	24	+	+	CCONJ
ejpam-84	59	25	a	a	DET
ejpam-84	59	26	]	]	X
ejpam-84	59	27	.	.	PUNCT
ejpam-84	60	1	then	then	ADV
ejpam-84	60	2	we	we	PRON
ejpam-84	60	3	have	have	VERB
ejpam-84	60	4	m(t	m(t	NOUN
ejpam-84	60	5	)	)	PUNCT
ejpam-84	60	6	≤	≤	NOUN
ejpam-84	60	7	r(t	r(t	NOUN
ejpam-84	60	8	)	)	PUNCT
ejpam-84	60	9	,	,	PUNCT
ejpam-84	60	10	t0	t0	PROPN
ejpam-84	60	11	≤	≤	PROPN
ejpam-84	60	12	t	t	PROPN
ejpam-84	60	13	≤	≤	NUM
ejpam-84	60	14	t0	t0	PROPN
ejpam-84	61	1	+	+	CCONJ
ejpam-84	61	2	a.	a.	NOUN
ejpam-84	61	3	we	we	PRON
ejpam-84	61	4	are	be	AUX
ejpam-84	61	5	now	now	ADV
ejpam-84	61	6	in	in	ADP
ejpam-84	61	7	a	a	DET
ejpam-84	61	8	position	position	NOUN
ejpam-84	61	9	to	to	PART
ejpam-84	61	10	prove	prove	VERB
ejpam-84	61	11	the	the	DET
ejpam-84	61	12	following	follow	VERB
ejpam-84	61	13	general	general	ADJ
ejpam-84	61	14	existence	existence	NOUN
ejpam-84	61	15	and	and	CCONJ
ejpam-84	61	16	uniqueness	uniqueness	NOUN
ejpam-84	61	17	result	result	NOUN
ejpam-84	61	18	.	.	PUNCT
ejpam-84	62	1	theorem	theorem	VERB
ejpam-84	62	2	2.1	2.1	NUM
ejpam-84	62	3	:	:	PUNCT
ejpam-84	63	1	assume	assume	VERB
ejpam-84	63	2	that	that	SCONJ
ejpam-84	63	3	(	(	PUNCT
ejpam-84	63	4	a	a	X
ejpam-84	63	5	)	)	PUNCT
ejpam-84	63	6	f	f	PROPN
ejpam-84	63	7	∈	∈	PROPN
ejpam-84	63	8	c(r0	c(r0	NOUN
ejpam-84	63	9	,	,	PUNCT
ejpam-84	63	10	e	e	NOUN
ejpam-84	63	11	)	)	PUNCT
ejpam-84	63	12	and	and	CCONJ
ejpam-84	63	13	|f(t	|f(t	PROPN
ejpam-84	63	14	,	,	PUNCT
ejpam-84	63	15	x)|	x)|	PROPN
ejpam-84	63	16	≤	≤	NOUN
ejpam-84	63	17	m0	m0	NOUN
ejpam-84	63	18	on	on	ADP
ejpam-84	63	19	r0	r0	NOUN
ejpam-84	63	20	;	;	PUNCT
ejpam-84	63	21	(	(	PUNCT
ejpam-84	63	22	b	b	X
ejpam-84	63	23	)	)	PUNCT
ejpam-84	63	24	g	g	PROPN
ejpam-84	63	25	∈	∈	PROPN
ejpam-84	63	26	c([t0	c([t0	PROPN
ejpam-84	63	27	,	,	PUNCT
ejpam-84	63	28	t0	t0	PROPN
ejpam-84	63	29	+	+	CCONJ
ejpam-84	63	30	a]×	a]×	PROPN
ejpam-84	63	31	[	[	X
ejpam-84	63	32	0	0	NUM
ejpam-84	63	33	,	,	PUNCT
ejpam-84	63	34	2b	2b	NOUN
ejpam-84	63	35	]	]	PUNCT
ejpam-84	63	36	,	,	PUNCT
ejpam-84	63	37	r+	r+	X
ejpam-84	63	38	)	)	PUNCT
ejpam-84	63	39	,	,	PUNCT
ejpam-84	63	40	g(t	g(t	PROPN
ejpam-84	63	41	,	,	PUNCT
ejpam-84	63	42	u	u	NOUN
ejpam-84	63	43	)	)	PUNCT
ejpam-84	63	44	≤	≤	NOUN
ejpam-84	63	45	m1	m1	NOUN
ejpam-84	63	46	on	on	ADP
ejpam-84	63	47	[	[	X
ejpam-84	63	48	t0	t0	NOUN
ejpam-84	63	49	,	,	PUNCT
ejpam-84	63	50	t0	t0	PROPN
ejpam-84	63	51	+	+	CCONJ
ejpam-84	63	52	a]×	a]×	PROPN
ejpam-84	63	53	[	[	X
ejpam-84	63	54	0	0	NUM
ejpam-84	63	55	,	,	PUNCT
ejpam-84	63	56	2b	2b	NOUN
ejpam-84	63	57	]	]	PUNCT
ejpam-84	63	58	,	,	PUNCT
ejpam-84	63	59	g(t	g(t	PROPN
ejpam-84	63	60	,	,	PUNCT
ejpam-84	63	61	0	0	NUM
ejpam-84	63	62	)	)	PUNCT
ejpam-84	63	63	≡	≡	PROPN
ejpam-84	63	64	0	0	NUM
ejpam-84	63	65	,	,	PUNCT
ejpam-84	63	66	g(t	g(t	PROPN
ejpam-84	63	67	,	,	PUNCT
ejpam-84	63	68	u	u	NOUN
ejpam-84	63	69	)	)	PUNCT
ejpam-84	63	70	is	be	AUX
ejpam-84	63	71	nondecreasing	nondecrease	VERB
ejpam-84	63	72	in	in	ADP
ejpam-84	63	73	u	u	NOUN
ejpam-84	63	74	for	for	ADP
ejpam-84	63	75	each	each	DET
ejpam-84	63	76	t	t	PROPN
ejpam-84	63	77	and	and	CCONJ
ejpam-84	63	78	u(t	u(t	NOUN
ejpam-84	63	79	)	)	PUNCT
ejpam-84	63	80	≡	≡	PROPN
ejpam-84	63	81	0	0	NUM
ejpam-84	63	82	is	be	AUX
ejpam-84	63	83	the	the	DET
ejpam-84	63	84	only	only	ADJ
ejpam-84	63	85	solution	solution	NOUN
ejpam-84	63	86	of	of	ADP
ejpam-84	63	87	dqu	dqu	ADJ
ejpam-84	63	88	=	=	SYM
ejpam-84	63	89	g(t	g(t	PROPN
ejpam-84	63	90	,	,	PUNCT
ejpam-84	63	91	u	u	NOUN
ejpam-84	63	92	)	)	PUNCT
ejpam-84	63	93	,	,	PUNCT
ejpam-84	63	94	u(t)[t−	u(t)[t−	ADJ
ejpam-84	63	95	t0)1−q|t	t0)1−q|t	NUM
ejpam-84	63	96	=	=	SYM
ejpam-84	63	97	t0	t0	NOUN
ejpam-84	63	98	=	=	SYM
ejpam-84	63	99	0	0	NUM
ejpam-84	63	100	,	,	PUNCT
ejpam-84	63	101	(	(	PUNCT
ejpam-84	63	102	2.3	2.3	NUM
ejpam-84	63	103	)	)	PUNCT
ejpam-84	63	104	on	on	ADP
ejpam-84	63	105	[	[	X
ejpam-84	63	106	t0	t0	NOUN
ejpam-84	63	107	,	,	PUNCT
ejpam-84	63	108	t0	t0	PROPN
ejpam-84	63	109	+	+	CCONJ
ejpam-84	63	110	a	a	DET
ejpam-84	63	111	]	]	X
ejpam-84	63	112	;	;	PUNCT
ejpam-84	63	113	(	(	PUNCT
ejpam-84	63	114	c	c	X
ejpam-84	63	115	)	)	PUNCT
ejpam-84	63	116	|f(t	|f(t	PROPN
ejpam-84	63	117	,	,	PUNCT
ejpam-84	63	118	x)−	x)−	PROPN
ejpam-84	63	119	f(t	f(t	PROPN
ejpam-84	63	120	,	,	PUNCT
ejpam-84	63	121	y)|	y)|	PROPN
ejpam-84	63	122	≤	≤	PROPN
ejpam-84	63	123	g(t	g(t	PROPN
ejpam-84	63	124	,	,	PUNCT
ejpam-84	63	125	|x−	|x−	NOUN
ejpam-84	63	126	y|	y|	NOUN
ejpam-84	63	127	)	)	PUNCT
ejpam-84	63	128	on	on	ADP
ejpam-84	63	129	r0	r0	NOUN
ejpam-84	63	130	.	.	PUNCT
ejpam-84	64	1	then	then	ADV
ejpam-84	64	2	,	,	PUNCT
ejpam-84	64	3	the	the	DET
ejpam-84	64	4	successive	successive	ADJ
ejpam-84	64	5	approximation	approximation	NOUN
ejpam-84	64	6	defined	define	VERB
ejpam-84	64	7	by	by	ADP
ejpam-84	64	8	xn+1(t	xn+1(t	PROPN
ejpam-84	64	9	)	)	PUNCT
ejpam-84	65	1	=	=	SYM
ejpam-84	65	2	x0(t	x0(t	PROPN
ejpam-84	65	3	)	)	PUNCT
ejpam-84	65	4	+	+	CCONJ
ejpam-84	65	5	1	1	NUM
ejpam-84	65	6	γ(q	γ(q	NOUN
ejpam-84	65	7	)	)	PUNCT
ejpam-84	65	8	∫	∫	PROPN
ejpam-84	65	9	t	t	PROPN
ejpam-84	65	10	t0	t0	PROPN
ejpam-84	65	11	(	(	PUNCT
ejpam-84	65	12	t−	t−	PROPN
ejpam-84	65	13	s)q−1f(s	s)q−1f(	NOUN
ejpam-84	65	14	,	,	PUNCT
ejpam-84	65	15	xn(s))ds	xn(s))ds	PROPN
ejpam-84	65	16	,	,	PUNCT
ejpam-84	65	17	n	n	NOUN
ejpam-84	65	18	=	=	SYM
ejpam-84	65	19	0	0	NUM
ejpam-84	65	20	,	,	PUNCT
ejpam-84	65	21	1	1	NUM
ejpam-84	65	22	,	,	PUNCT
ejpam-84	65	23	2	2	NUM
ejpam-84	65	24	,	,	PUNCT
ejpam-84	65	25	...	...	PUNCT
ejpam-84	65	26	(	(	PUNCT
ejpam-84	65	27	2.4	2.4	NUM
ejpam-84	65	28	)	)	PUNCT
ejpam-84	65	29	on	on	ADP
ejpam-84	65	30	[	[	X
ejpam-84	65	31	t0	t0	NOUN
ejpam-84	65	32	,	,	PUNCT
ejpam-84	65	33	t0	t0	PROPN
ejpam-84	65	34	+	+	CCONJ
ejpam-84	65	35	α	α	X
ejpam-84	65	36	]	]	X
ejpam-84	65	37	,	,	PUNCT
ejpam-84	65	38	where	where	SCONJ
ejpam-84	65	39	α	α	PROPN
ejpam-84	65	40	=	=	SYM
ejpam-84	65	41	min	min	PROPN
ejpam-84	65	42	(	(	PUNCT
ejpam-84	65	43	a	a	PRON
ejpam-84	65	44	,	,	PUNCT
ejpam-84	65	45	[	[	PUNCT
ejpam-84	65	46	bγ(q+1	bγ(q+1	PROPN
ejpam-84	65	47	)	)	PUNCT
ejpam-84	65	48	m	m	VERB
ejpam-84	65	49	]	]	PUNCT
ejpam-84	65	50	1	1	NUM
ejpam-84	65	51	q	q	NOUN
ejpam-84	65	52	)	)	PUNCT
ejpam-84	65	53	,	,	PUNCT
ejpam-84	65	54	m	m	VERB
ejpam-84	65	55	=	=	SYM
ejpam-84	65	56	max(m0,m1	max(m0,m1	PROPN
ejpam-84	65	57	)	)	PUNCT
ejpam-84	65	58	,	,	PUNCT
ejpam-84	65	59	are	be	AUX
ejpam-84	65	60	continuous	continuous	ADJ
ejpam-84	65	61	and	and	CCONJ
ejpam-84	65	62	converge	converge	VERB
ejpam-84	65	63	uniformly	uniformly	ADV
ejpam-84	65	64	to	to	ADP
ejpam-84	65	65	the	the	DET
ejpam-84	65	66	unique	unique	ADJ
ejpam-84	65	67	solution	solution	NOUN
ejpam-84	65	68	x(t	x(t	PROPN
ejpam-84	65	69	)	)	PUNCT
ejpam-84	65	70	of	of	ADP
ejpam-84	65	71	the	the	DET
ejpam-84	65	72	ivp	ivp	NOUN
ejpam-84	65	73	(	(	PUNCT
ejpam-84	65	74	2.1	2.1	NUM
ejpam-84	65	75	)	)	PUNCT
ejpam-84	65	76	on	on	ADP
ejpam-84	65	77	[	[	X
ejpam-84	65	78	t0	t0	NOUN
ejpam-84	65	79	,	,	PUNCT
ejpam-84	65	80	t0	t0	PROPN
ejpam-84	65	81	+	+	CCONJ
ejpam-84	65	82	α	α	X
ejpam-84	65	83	]	]	X
ejpam-84	65	84	.	.	PUNCT
ejpam-84	66	1	proof	proof	NOUN
ejpam-84	66	2	:	:	PUNCT
ejpam-84	66	3	for	for	ADP
ejpam-84	66	4	t0	t0	PROPN
ejpam-84	66	5	≤	≤	NUM
ejpam-84	66	6	t1	t1	PROPN
ejpam-84	66	7	≤	≤	PUNCT
ejpam-84	66	8	t2	t2	PROPN
ejpam-84	66	9	≤	≤	NUM
ejpam-84	66	10	t0	t0	PROPN
ejpam-84	66	11	+	+	CCONJ
ejpam-84	66	12	α	α	X
ejpam-84	66	13	,	,	PUNCT
ejpam-84	66	14	we	we	PRON
ejpam-84	66	15	find	find	VERB
ejpam-84	66	16	|x1(t1)−	|x1(t1)−	NOUN
ejpam-84	66	17	x0(t1)−	x0(t1)−	PROPN
ejpam-84	66	18	x1(t2	x1(t2	PROPN
ejpam-84	66	19	)	)	PUNCT
ejpam-84	66	20	+	+	CCONJ
ejpam-84	66	21	x0(t2)|	x0(t2)|	X
ejpam-84	66	22	≤	≤	NUM
ejpam-84	66	23	m	m	NUM
ejpam-84	66	24	γ(q	γ(q	NOUN
ejpam-84	66	25	)	)	PUNCT
ejpam-84	66	26	∣∣∣∣	∣∣∣∣	NOUN
ejpam-84	66	27	∫	∫	PROPN
ejpam-84	66	28	t	t	PROPN
ejpam-84	66	29	t0	t0	PROPN
ejpam-84	67	1	[	[	X
ejpam-84	67	2	(	(	PUNCT
ejpam-84	67	3	t1	t1	NOUN
ejpam-84	67	4	−	−	PROPN
ejpam-84	67	5	s)q−1	s)q−1	PRON
ejpam-84	67	6	−	−	PROPN
ejpam-84	68	1	(	(	PUNCT
ejpam-84	68	2	t2	t2	NOUN
ejpam-84	68	3	−	−	PROPN
ejpam-84	68	4	s)q−1]ds	s)q−1]ds	PROPN
ejpam-84	68	5	+	+	CCONJ
ejpam-84	68	6	∫	∫	PROPN
ejpam-84	68	7	t2	t2	PROPN
ejpam-84	68	8	t1	t1	NOUN
ejpam-84	68	9	(	(	PUNCT
ejpam-84	68	10	t2	t2	PROPN
ejpam-84	68	11	−	−	PROPN
ejpam-84	68	12	s)q−1ds	s)q−1ds	PROPN
ejpam-84	68	13	∣∣∣∣	∣∣∣∣	PROPN
ejpam-84	68	14	≤	≤	NUM
ejpam-84	68	15	m	m	NOUN
ejpam-84	68	16	γ(q	γ(q	NOUN
ejpam-84	69	1	+	+	CCONJ
ejpam-84	69	2	1	1	NUM
ejpam-84	69	3	)	)	PUNCT
ejpam-84	70	1	[	[	X
ejpam-84	70	2	(	(	PUNCT
ejpam-84	70	3	t1	t1	NOUN
ejpam-84	70	4	−	−	PROPN
ejpam-84	70	5	t0)q	t0)q	PROPN
ejpam-84	70	6	−	−	PROPN
ejpam-84	71	1	(	(	PUNCT
ejpam-84	71	2	t2	t2	PROPN
ejpam-84	71	3	−	−	PROPN
ejpam-84	71	4	t0)q	t0)q	PROPN
ejpam-84	71	5	+	+	CCONJ
ejpam-84	71	6	2(t2	2(t2	NUM
ejpam-84	71	7	−	−	NOUN
ejpam-84	71	8	t1)q	t1)q	NOUN
ejpam-84	71	9	]	]	PUNCT
ejpam-84	71	10	≤	≤	NUM
ejpam-84	71	11	2	2	NUM
ejpam-84	71	12	m	m	NOUN
ejpam-84	71	13	γ(q	γ(q	NOUN
ejpam-84	71	14	+	+	CCONJ
ejpam-84	71	15	1	1	NUM
ejpam-84	71	16	)	)	PUNCT
ejpam-84	71	17	(	(	PUNCT
ejpam-84	71	18	t2	t2	NOUN
ejpam-84	71	19	−	−	PROPN
ejpam-84	71	20	t1)q	t1)q	NOUN
ejpam-84	71	21	<	<	X
ejpam-84	71	22	ε	ε	PROPN
ejpam-84	71	23	,	,	PUNCT
ejpam-84	71	24	provided	provide	VERB
ejpam-84	71	25	|t2	|t2	ADP
ejpam-84	71	26	−	−	PROPN
ejpam-84	71	27	t1|	t1|	PROPN
ejpam-84	71	28	<	<	X
ejpam-84	71	29	δ	δ	PROPN
ejpam-84	71	30	,	,	PUNCT
ejpam-84	71	31	where	where	SCONJ
ejpam-84	71	32	δ	δ	PROPN
ejpam-84	71	33	=	=	X
ejpam-84	71	34	[	[	PUNCT
ejpam-84	71	35	εγ(q+1	εγ(q+1	PROPN
ejpam-84	71	36	)	)	PUNCT
ejpam-84	71	37	2	2	NUM
ejpam-84	71	38	m	m	NOUN
ejpam-84	71	39	]	]	PUNCT
ejpam-84	71	40	1	1	NUM
ejpam-84	71	41	q	q	NOUN
ejpam-84	71	42	,	,	PUNCT
ejpam-84	71	43	proving	prove	VERB
ejpam-84	71	44	that	that	PRON
ejpam-84	71	45	x1(t	x1(t	PUNCT
ejpam-84	71	46	)	)	PUNCT
ejpam-84	71	47	is	be	AUX
ejpam-84	71	48	continuous	continuous	ADJ
ejpam-84	71	49	on	on	ADP
ejpam-84	71	50	[	[	X
ejpam-84	71	51	t0	t0	NOUN
ejpam-84	71	52	,	,	PUNCT
ejpam-84	71	53	t0	t0	PROPN
ejpam-84	71	54	+	+	CCONJ
ejpam-84	71	55	α	α	X
ejpam-84	71	56	]	]	X
ejpam-84	71	57	.	.	PUNCT
ejpam-84	72	1	similarly	similarly	ADV
ejpam-84	72	2	,	,	PUNCT
ejpam-84	72	3	|x1(t)−	|x1(t)−	PROPN
ejpam-84	72	4	x0(t)|	x0(t)|	PROPN
ejpam-84	72	5	≤	≤	NUM
ejpam-84	72	6	1	1	NUM
ejpam-84	72	7	γ(q	γ(q	NOUN
ejpam-84	72	8	)	)	PUNCT
ejpam-84	72	9	∫	∫	PROPN
ejpam-84	72	10	t	t	PROPN
ejpam-84	72	11	t0	t0	PROPN
ejpam-84	72	12	(	(	PUNCT
ejpam-84	72	13	t−	t−	PROPN
ejpam-84	72	14	s)q−1|f(s	s)q−1|f(	NOUN
ejpam-84	72	15	,	,	PUNCT
ejpam-84	72	16	x0)|ds	x0)|ds	PROPN
ejpam-84	72	17	≤	≤	NUM
ejpam-84	72	18	m(t−	m(t−	PUNCT
ejpam-84	72	19	t0)q	t0)q	PROPN
ejpam-84	72	20	γ(q	γ(q	PROPN
ejpam-84	73	1	+	+	CCONJ
ejpam-84	73	2	1	1	NUM
ejpam-84	73	3	)	)	PUNCT
ejpam-84	73	4	≤	≤	NOUN
ejpam-84	74	1	mαq	mαq	PROPN
ejpam-84	74	2	γ(q	γ(q	PROPN
ejpam-84	74	3	+	+	CCONJ
ejpam-84	74	4	1	1	NUM
ejpam-84	74	5	)	)	PUNCT
ejpam-84	74	6	≤	≤	NOUN
ejpam-84	74	7	b.	b.	PROPN
ejpam-84	75	1	hence	hence	ADV
ejpam-84	75	2	it	it	PRON
ejpam-84	75	3	is	be	AUX
ejpam-84	75	4	easily	easily	ADV
ejpam-84	75	5	seen	see	VERB
ejpam-84	75	6	by	by	ADP
ejpam-84	75	7	induction	induction	NOUN
ejpam-84	75	8	that	that	SCONJ
ejpam-84	75	9	the	the	DET
ejpam-84	75	10	successive	successive	ADJ
ejpam-84	75	11	approximations	approximation	NOUN
ejpam-84	75	12	are	be	AUX
ejpam-84	75	13	continuous	continuous	ADJ
ejpam-84	75	14	and	and	CCONJ
ejpam-84	75	15	satisfy	satisfy	VERB
ejpam-84	75	16	|xn(t)−	|xn(t)−	PROPN
ejpam-84	75	17	x0|	x0|	PROPN
ejpam-84	76	1	≤	≤	PROPN
ejpam-84	76	2	b	b	PROPN
ejpam-84	76	3	,	,	PUNCT
ejpam-84	76	4	n	n	NOUN
ejpam-84	76	5	=	=	SYM
ejpam-84	76	6	0	0	NUM
ejpam-84	76	7	,	,	PUNCT
ejpam-84	76	8	1	1	NUM
ejpam-84	76	9	,	,	PUNCT
ejpam-84	76	10	2	2	NUM
ejpam-84	76	11	,	,	PUNCT
ejpam-84	76	12	3	3	NUM
ejpam-84	76	13	,	,	PUNCT
ejpam-84	76	14	...	...	PUNCT
ejpam-84	77	1	we	we	PRON
ejpam-84	77	2	shall	shall	AUX
ejpam-84	77	3	next	next	ADV
ejpam-84	77	4	define	define	VERB
ejpam-84	77	5	the	the	DET
ejpam-84	77	6	successive	successive	ADJ
ejpam-84	77	7	approximations	approximation	NOUN
ejpam-84	77	8	for	for	ADP
ejpam-84	77	9	the	the	DET
ejpam-84	77	10	ivp	ivp	NOUN
ejpam-84	77	11	(	(	PUNCT
ejpam-84	77	12	2.3	2.3	NUM
ejpam-84	77	13	)	)	PUNCT
ejpam-84	77	14	as	as	SCONJ
ejpam-84	77	15	follows	follow	VERB
ejpam-84	77	16	:	:	PUNCT
ejpam-84	77	17	u0(t	u0(t	X
ejpam-84	77	18	)	)	PUNCT
ejpam-84	77	19	=	=	SYM
ejpam-84	77	20	m(t−	m(t−	PROPN
ejpam-84	77	21	t0)q	t0)q	PROPN
ejpam-84	77	22	γ(q	γ(q	PROPN
ejpam-84	78	1	+	+	CCONJ
ejpam-84	78	2	1	1	X
ejpam-84	78	3	)	)	PUNCT
ejpam-84	78	4	un+1	un+1	NOUN
ejpam-84	78	5	=	=	SYM
ejpam-84	78	6	1	1	NUM
ejpam-84	78	7	γ(q	γ(q	PROPN
ejpam-84	78	8	)	)	PUNCT
ejpam-84	79	1	∫	∫	PROPN
ejpam-84	79	2	t	t	PROPN
ejpam-84	79	3	t0	t0	PROPN
ejpam-84	79	4	(	(	PUNCT
ejpam-84	79	5	t−	t−	PROPN
ejpam-84	79	6	s)q−1g(s	s)q−1g(s	ADJ
ejpam-84	79	7	,	,	PUNCT
ejpam-84	79	8	un(s))ds	un(s))ds	PROPN
ejpam-84	79	9	,	,	PUNCT
ejpam-84	79	10	t0	t0	PROPN
ejpam-84	79	11	≤	≤	PROPN
ejpam-84	79	12	t	t	PROPN
ejpam-84	79	13	≤	≤	NUM
ejpam-84	79	14	t0	t0	PROPN
ejpam-84	79	15	+	+	CCONJ
ejpam-84	79	16	α	α	X
ejpam-84	79	17	.	.	PUNCT
ejpam-84	80	1	(	(	PUNCT
ejpam-84	80	2	2.5	2.5	NUM
ejpam-84	80	3	)	)	PUNCT
ejpam-84	80	4	v.lakshmikantham	v.lakshmikantham	PROPN
ejpam-84	80	5	,	,	PUNCT
ejpam-84	80	6	j.devi	j.devi	PROPN
ejpam-84	80	7	/	/	SYM
ejpam-84	80	8	eur	eur	PROPN
ejpam-84	80	9	.	.	PUNCT
ejpam-84	81	1	j.	j.	PROPN
ejpam-84	81	2	pure	pure	PROPN
ejpam-84	81	3	appl	appl	PROPN
ejpam-84	81	4	.	.	PROPN
ejpam-84	81	5	math	math	PROPN
ejpam-84	81	6	,	,	PUNCT
ejpam-84	81	7	1	1	NUM
ejpam-84	81	8	(	(	PUNCT
ejpam-84	81	9	2008	2008	NUM
ejpam-84	81	10	)	)	PUNCT
ejpam-84	81	11	,	,	PUNCT
ejpam-84	81	12	(	(	PUNCT
ejpam-84	81	13	38	38	NUM
ejpam-84	81	14	-	-	SYM
ejpam-84	81	15	45	45	NUM
ejpam-84	81	16	)	)	PUNCT
ejpam-84	81	17	41	41	NUM
ejpam-84	81	18	since	since	SCONJ
ejpam-84	81	19	g(t	g(t	PROPN
ejpam-84	81	20	,	,	PUNCT
ejpam-84	81	21	u	u	NOUN
ejpam-84	81	22	)	)	PUNCT
ejpam-84	81	23	is	be	AUX
ejpam-84	81	24	assumed	assume	VERB
ejpam-84	81	25	to	to	PART
ejpam-84	81	26	be	be	AUX
ejpam-84	81	27	nondecreasing	nondecrease	VERB
ejpam-84	81	28	in	in	ADP
ejpam-84	81	29	u	u	NOUN
ejpam-84	81	30	for	for	ADP
ejpam-84	81	31	each	each	DET
ejpam-84	81	32	t	t	PROPN
ejpam-84	81	33	,	,	PUNCT
ejpam-84	81	34	an	an	DET
ejpam-84	81	35	easy	easy	ADJ
ejpam-84	81	36	induction	induction	NOUN
ejpam-84	81	37	shows	show	VERB
ejpam-84	81	38	that	that	SCONJ
ejpam-84	81	39	the	the	DET
ejpam-84	81	40	successive	successive	ADJ
ejpam-84	81	41	approximations	approximation	NOUN
ejpam-84	81	42	(	(	PUNCT
ejpam-84	81	43	2.5	2.5	NUM
ejpam-84	81	44	)	)	PUNCT
ejpam-84	81	45	are	be	AUX
ejpam-84	81	46	well	well	ADV
ejpam-84	81	47	defined	define	VERB
ejpam-84	81	48	and	and	CCONJ
ejpam-84	81	49	satisfy	satisfy	VERB
ejpam-84	81	50	0	0	NUM
ejpam-84	81	51	≤	≤	ADJ
ejpam-84	81	52	un+1(t	un+1(t	ADJ
ejpam-84	81	53	)	)	PUNCT
ejpam-84	81	54	≤	≤	NOUN
ejpam-84	81	55	un(t	un(t	NUM
ejpam-84	81	56	)	)	PUNCT
ejpam-84	81	57	,	,	PUNCT
ejpam-84	81	58	t0	t0	PROPN
ejpam-84	81	59	≤	≤	PROPN
ejpam-84	81	60	t	t	PROPN
ejpam-84	81	61	≤	≤	NUM
ejpam-84	81	62	t0	t0	PROPN
ejpam-84	81	63	+	+	CCONJ
ejpam-84	81	64	α	α	X
ejpam-84	81	65	.	.	PUNCT
ejpam-84	82	1	moreover	moreover	ADV
ejpam-84	82	2	,	,	PUNCT
ejpam-84	82	3	|dqun(t)|	|dqun(t)|	PROPN
ejpam-84	82	4	=	=	SYM
ejpam-84	82	5	g(t	g(t	PROPN
ejpam-84	82	6	,	,	PUNCT
ejpam-84	82	7	un−1(t	un−1(t	ADJ
ejpam-84	82	8	)	)	PUNCT
ejpam-84	82	9	)	)	PUNCT
ejpam-84	82	10	≤	≤	NUM
ejpam-84	82	11	m	m	VERB
ejpam-84	82	12	and	and	CCONJ
ejpam-84	82	13	therefore	therefore	ADV
ejpam-84	82	14	,	,	PUNCT
ejpam-84	82	15	we	we	PRON
ejpam-84	82	16	can	can	AUX
ejpam-84	82	17	conclude	conclude	VERB
ejpam-84	82	18	by	by	ADP
ejpam-84	82	19	ascoli	ascoli	PROPN
ejpam-84	82	20	-	-	PUNCT
ejpam-84	82	21	arzela	arzela	PROPN
ejpam-84	82	22	theorem	theorem	NOUN
ejpam-84	82	23	and	and	CCONJ
ejpam-84	82	24	the	the	DET
ejpam-84	82	25	monotonicity	monotonicity	NOUN
ejpam-84	82	26	of	of	ADP
ejpam-84	82	27	the	the	DET
ejpam-84	82	28	sequence	sequence	NOUN
ejpam-84	82	29	{	{	PUNCT
ejpam-84	82	30	un(t	un(t	NUM
ejpam-84	82	31	)	)	PUNCT
ejpam-84	82	32	}	}	PUNCT
ejpam-84	82	33	that	that	SCONJ
ejpam-84	82	34	limn→∞	limn→∞	PROPN
ejpam-84	82	35	un(t	un(t	X
ejpam-84	82	36	)	)	PUNCT
ejpam-84	82	37	=	=	SYM
ejpam-84	82	38	u(t	u(t	NOUN
ejpam-84	82	39	)	)	PUNCT
ejpam-84	82	40	uniformly	uniformly	ADV
ejpam-84	82	41	on	on	ADP
ejpam-84	82	42	[	[	X
ejpam-84	82	43	t0	t0	NOUN
ejpam-84	82	44	,	,	PUNCT
ejpam-84	82	45	t0+α	t0+α	PROPN
ejpam-84	82	46	]	]	PUNCT
ejpam-84	82	47	.	.	PUNCT
ejpam-84	83	1	it	it	PRON
ejpam-84	83	2	is	be	AUX
ejpam-84	83	3	also	also	ADV
ejpam-84	83	4	clear	clear	ADJ
ejpam-84	83	5	that	that	SCONJ
ejpam-84	83	6	u(t	u(t	NOUN
ejpam-84	83	7	)	)	PUNCT
ejpam-84	83	8	satisfies	satisfy	VERB
ejpam-84	83	9	the	the	DET
ejpam-84	83	10	ivp	ivp	NOUN
ejpam-84	83	11	(	(	PUNCT
ejpam-84	83	12	2.3	2.3	NUM
ejpam-84	83	13	)	)	PUNCT
ejpam-84	83	14	and	and	CCONJ
ejpam-84	83	15	hence	hence	ADV
ejpam-84	83	16	by	by	ADP
ejpam-84	83	17	(	(	PUNCT
ejpam-84	83	18	b	b	NOUN
ejpam-84	83	19	)	)	PUNCT
ejpam-84	83	20	u(t	u(t	NOUN
ejpam-84	83	21	)	)	PUNCT
ejpam-84	83	22	≡	≡	PROPN
ejpam-84	83	23	0	0	NUM
ejpam-84	84	1	on	on	ADP
ejpam-84	84	2	[	[	X
ejpam-84	84	3	t0	t0	NOUN
ejpam-84	84	4	,	,	PUNCT
ejpam-84	84	5	t0+α	t0+α	PROPN
ejpam-84	84	6	]	]	PUNCT
ejpam-84	84	7	.	.	PUNCT
ejpam-84	85	1	to	to	PART
ejpam-84	85	2	get	get	VERB
ejpam-84	85	3	the	the	DET
ejpam-84	85	4	equicontinuity	equicontinuity	NOUN
ejpam-84	85	5	of	of	ADP
ejpam-84	85	6	the	the	DET
ejpam-84	85	7	sequence	sequence	NOUN
ejpam-84	85	8	{	{	PUNCT
ejpam-84	85	9	un(t	un(t	NOUN
ejpam-84	85	10	)	)	PUNCT
ejpam-84	85	11	}	}	PUNCT
ejpam-84	85	12	,	,	PUNCT
ejpam-84	85	13	one	one	PRON
ejpam-84	85	14	can	can	AUX
ejpam-84	85	15	use	use	VERB
ejpam-84	85	16	lemma	lemma	PROPN
ejpam-84	85	17	2.2	2.2	NUM
ejpam-84	85	18	.	.	PUNCT
ejpam-84	86	1	now	now	ADV
ejpam-84	86	2	from	from	ADP
ejpam-84	86	3	the	the	DET
ejpam-84	86	4	earlier	early	ADJ
ejpam-84	86	5	estimate	estimate	NOUN
ejpam-84	86	6	|x1(t)−	|x1(t)−	PROPN
ejpam-84	87	1	x0(t)|	x0(t)|	PROPN
ejpam-84	87	2	≤	≤	PROPN
ejpam-84	88	1	m(t−	m(t−	PROPN
ejpam-84	88	2	t0)q	t0)q	PROPN
ejpam-84	88	3	γ(q	γ(q	PROPN
ejpam-84	88	4	+	+	CCONJ
ejpam-84	88	5	1	1	NUM
ejpam-84	88	6	)	)	PUNCT
ejpam-84	88	7	=	=	PUNCT
ejpam-84	88	8	u0(t	u0(t	PROPN
ejpam-84	88	9	)	)	PUNCT
ejpam-84	88	10	.	.	PUNCT
ejpam-84	89	1	assume	assume	VERB
ejpam-84	89	2	that	that	SCONJ
ejpam-84	89	3	|xk(t)−	|xk(t)−	PROPN
ejpam-84	89	4	xk−1(t)|	xk−1(t)|	ADV
ejpam-84	89	5	≤	≤	ADJ
ejpam-84	89	6	uk−1(t	uk−1(t	NOUN
ejpam-84	89	7	)	)	PUNCT
ejpam-84	89	8	for	for	ADP
ejpam-84	89	9	some	some	DET
ejpam-84	89	10	given	give	VERB
ejpam-84	89	11	k.	k.	PROPN
ejpam-84	89	12	since	since	SCONJ
ejpam-84	89	13	|xk+1(t)−	|xk+1(t)−	PROPN
ejpam-84	89	14	xk(t)|	xk(t)|	PUNCT
ejpam-84	90	1	=	=	SYM
ejpam-84	90	2	1	1	NUM
ejpam-84	90	3	γ(q	γ(q	PROPN
ejpam-84	90	4	)	)	PUNCT
ejpam-84	90	5	∣∣∣∣	∣∣∣∣	NOUN
ejpam-84	90	6	∫	∫	PROPN
ejpam-84	90	7	t	t	PROPN
ejpam-84	90	8	t0	t0	PROPN
ejpam-84	90	9	(	(	PUNCT
ejpam-84	90	10	t−	t−	PROPN
ejpam-84	90	11	s)q−1f(s	s)q−1f(	NOUN
ejpam-84	90	12	,	,	PUNCT
ejpam-84	90	13	xk(s))ds−	xk(s))ds−	PROPN
ejpam-84	90	14	∫	∫	PROPN
ejpam-84	90	15	t	t	PROPN
ejpam-84	90	16	t0	t0	PROPN
ejpam-84	90	17	(	(	PUNCT
ejpam-84	90	18	t−	t−	PROPN
ejpam-84	90	19	s)q−1f(s	s)q−1f(	NOUN
ejpam-84	90	20	,	,	PUNCT
ejpam-84	90	21	xk−1(s))ds	xk−1(s))ds	PROPN
ejpam-84	90	22	∣∣∣∣	∣∣∣∣	PROPN
ejpam-84	90	23	≤	≤	NUM
ejpam-84	90	24	1	1	NUM
ejpam-84	90	25	γ(q	γ(q	NOUN
ejpam-84	90	26	)	)	PUNCT
ejpam-84	90	27	∫	∫	PROPN
ejpam-84	90	28	t	t	PROPN
ejpam-84	90	29	t0	t0	PROPN
ejpam-84	90	30	(	(	PUNCT
ejpam-84	90	31	t−	t−	PROPN
ejpam-84	90	32	s)q−1|f(s	s)q−1|f(s	PROPN
ejpam-84	90	33	,	,	PUNCT
ejpam-84	90	34	xk(s))−	xk(s))−	PROPN
ejpam-84	90	35	f(s	f(s	PROPN
ejpam-84	90	36	,	,	PUNCT
ejpam-84	90	37	xk−1(s))|ds	xk−1(s))|ds	PROPN
ejpam-84	90	38	,	,	PUNCT
ejpam-84	90	39	using	use	VERB
ejpam-84	90	40	condition	condition	NOUN
ejpam-84	90	41	(	(	PUNCT
ejpam-84	90	42	c	c	NOUN
ejpam-84	90	43	)	)	PUNCT
ejpam-84	90	44	and	and	CCONJ
ejpam-84	90	45	the	the	DET
ejpam-84	90	46	monotone	monotone	ADJ
ejpam-84	90	47	character	character	NOUN
ejpam-84	90	48	of	of	ADP
ejpam-84	90	49	g(t	g(t	PROPN
ejpam-84	90	50	,	,	PUNCT
ejpam-84	90	51	u	u	NOUN
ejpam-84	90	52	)	)	PUNCT
ejpam-84	90	53	,	,	PUNCT
ejpam-84	90	54	we	we	PRON
ejpam-84	90	55	get	get	VERB
ejpam-84	90	56	|xk+1(t)−	|xk+1(t)−	PUNCT
ejpam-84	90	57	xk(t)|	xk(t)|	PUNCT
ejpam-84	90	58	≤	≤	NUM
ejpam-84	90	59	1	1	NUM
ejpam-84	90	60	γ(q	γ(q	NOUN
ejpam-84	90	61	)	)	PUNCT
ejpam-84	91	1	∫	∫	PROPN
ejpam-84	91	2	t	t	PROPN
ejpam-84	91	3	t0	t0	PROPN
ejpam-84	91	4	(	(	PUNCT
ejpam-84	91	5	t−	t−	PROPN
ejpam-84	91	6	s)q−1g(s	s)q−1g(s	ADJ
ejpam-84	91	7	,	,	PUNCT
ejpam-84	91	8	|xk(s)−	|xk(s)−	PROPN
ejpam-84	91	9	xk−1(s)|)ds	xk−1(s)|)ds	PROPN
ejpam-84	91	10	=	=	PUNCT
ejpam-84	91	11	uk(t	uk(t	X
ejpam-84	91	12	)	)	PUNCT
ejpam-84	91	13	.	.	PUNCT
ejpam-84	92	1	thus	thus	ADV
ejpam-84	92	2	by	by	ADP
ejpam-84	92	3	induction	induction	NOUN
ejpam-84	92	4	,	,	PUNCT
ejpam-84	92	5	the	the	DET
ejpam-84	92	6	inequality	inequality	NOUN
ejpam-84	92	7	|xn+1(t)−	|xn+1(t)−	PROPN
ejpam-84	92	8	xn(t)|	xn(t)|	ADV
ejpam-84	92	9	≤	≤	NUM
ejpam-84	92	10	un(t	un(t	NUM
ejpam-84	92	11	)	)	PUNCT
ejpam-84	92	12	,	,	PUNCT
ejpam-84	92	13	t0	t0	PROPN
ejpam-84	92	14	≤	≤	PROPN
ejpam-84	92	15	t	t	PROPN
ejpam-84	92	16	≤	≤	NUM
ejpam-84	92	17	t0	t0	PROPN
ejpam-84	92	18	+	+	CCONJ
ejpam-84	92	19	α	α	PROPN
ejpam-84	92	20	,	,	PUNCT
ejpam-84	92	21	holds	hold	VERB
ejpam-84	92	22	for	for	ADP
ejpam-84	92	23	all	all	DET
ejpam-84	92	24	n.	n.	NOUN
ejpam-84	92	25	also	also	ADV
ejpam-84	92	26	,	,	PUNCT
ejpam-84	92	27	|dqxn+1(t)−dqxn(t)|	|dqxn+1(t)−dqxn(t)|	ADJ
ejpam-84	92	28	≤	≤	NUM
ejpam-84	92	29	|f(t	|f(t	NOUN
ejpam-84	92	30	,	,	PUNCT
ejpam-84	92	31	xn(t))−	xn(t))−	NOUN
ejpam-84	92	32	f(t	f(t	NOUN
ejpam-84	92	33	,	,	PUNCT
ejpam-84	92	34	xn−1(t))|	xn−1(t))|	PROPN
ejpam-84	92	35	≤	≤	PROPN
ejpam-84	92	36	g(t	g(t	PROPN
ejpam-84	92	37	,	,	PUNCT
ejpam-84	92	38	|xn(t)−	|xn(t)−	PROPN
ejpam-84	92	39	xn−1(t)|	xn−1(t)|	NUM
ejpam-84	92	40	)	)	PUNCT
ejpam-84	92	41	≤	≤	NUM
ejpam-84	92	42	g(t	g(t	PROPN
ejpam-84	92	43	,	,	PUNCT
ejpam-84	92	44	un(t	un(t	NUM
ejpam-84	92	45	)	)	PUNCT
ejpam-84	92	46	)	)	PUNCT
ejpam-84	92	47	.	.	PUNCT
ejpam-84	93	1	let	let	VERB
ejpam-84	93	2	n	n	PRON
ejpam-84	93	3	≤	≤	ADJ
ejpam-84	93	4	m.	m.	NOUN
ejpam-84	93	5	then	then	ADV
ejpam-84	93	6	we	we	PRON
ejpam-84	93	7	can	can	AUX
ejpam-84	93	8	easily	easily	ADV
ejpam-84	93	9	obtain	obtain	VERB
ejpam-84	93	10	d+q|xn(t)−	d+q|xn(t)−	PROPN
ejpam-84	93	11	xm(t)|	xm(t)|	PUNCT
ejpam-84	93	12	≤	≤	PROPN
ejpam-84	93	13	|dqxn(t)−dqxm(t)|	|dqxn(t)−dqxm(t)|	VERB
ejpam-84	93	14	≤	≤	NUM
ejpam-84	93	15	g(t	g(t	PROPN
ejpam-84	93	16	,	,	PUNCT
ejpam-84	93	17	un−1(t	un−1(t	ADJ
ejpam-84	93	18	)	)	PUNCT
ejpam-84	93	19	)	)	PUNCT
ejpam-84	94	1	+	+	CCONJ
ejpam-84	94	2	g(t	g(t	PROPN
ejpam-84	94	3	,	,	PUNCT
ejpam-84	94	4	um−1(t	um−1(t	ADJ
ejpam-84	94	5	)	)	PUNCT
ejpam-84	94	6	)	)	PUNCT
ejpam-84	95	1	+	+	CCONJ
ejpam-84	95	2	g(t	g(t	PROPN
ejpam-84	95	3	,	,	PUNCT
ejpam-84	95	4	|xn(t)−	|xn(t)−	PROPN
ejpam-84	95	5	xm(t)|	xm(t)|	NUM
ejpam-84	95	6	)	)	PUNCT
ejpam-84	95	7	.	.	PUNCT
ejpam-84	96	1	since	since	SCONJ
ejpam-84	96	2	un+1(t	un+1(t	ADJ
ejpam-84	96	3	)	)	PUNCT
ejpam-84	96	4	≤	≤	NOUN
ejpam-84	96	5	un(t	un(t	NOUN
ejpam-84	96	6	)	)	PUNCT
ejpam-84	96	7	for	for	ADP
ejpam-84	96	8	all	all	DET
ejpam-84	96	9	n	n	CCONJ
ejpam-84	96	10	,	,	PUNCT
ejpam-84	96	11	it	it	PRON
ejpam-84	96	12	follows	follow	VERB
ejpam-84	96	13	that	that	SCONJ
ejpam-84	96	14	d+q|xn(t)−	d+q|xn(t)−	PROPN
ejpam-84	96	15	xm(t)|	xm(t)|	PUNCT
ejpam-84	96	16	≤	≤	PROPN
ejpam-84	97	1	g(t	g(t	PROPN
ejpam-84	97	2	,	,	PUNCT
ejpam-84	97	3	|xn(t)−	|xn(t)−	PROPN
ejpam-84	97	4	xm(t)|	xm(t)|	PUNCT
ejpam-84	97	5	)	)	PUNCT
ejpam-84	98	1	+	+	CCONJ
ejpam-84	98	2	2g(t	2g(t	NUM
ejpam-84	98	3	,	,	PUNCT
ejpam-84	98	4	un−1(t	un−1(t	ADJ
ejpam-84	98	5	)	)	PUNCT
ejpam-84	98	6	)	)	PUNCT
ejpam-84	98	7	,	,	PUNCT
ejpam-84	98	8	where	where	SCONJ
ejpam-84	98	9	d+q	d+q	PROPN
ejpam-84	98	10	denotes	denote	VERB
ejpam-84	98	11	the	the	DET
ejpam-84	98	12	corresponding	correspond	VERB
ejpam-84	98	13	dini	dini	NOUN
ejpam-84	98	14	derivative	derivative	NOUN
ejpam-84	98	15	to	to	ADP
ejpam-84	98	16	d+	d+	NOUN
ejpam-84	98	17	.	.	PUNCT
ejpam-84	99	1	an	an	DET
ejpam-84	99	2	application	application	NOUN
ejpam-84	99	3	of	of	ADP
ejpam-84	99	4	comparison	comparison	NOUN
ejpam-84	99	5	result	result	VERB
ejpam-84	99	6	lemma	lemma	PROPN
ejpam-84	99	7	2.4	2.4	NUM
ejpam-84	99	8	gives	give	VERB
ejpam-84	99	9	|xn(t)−	|xn(t)−	PROPN
ejpam-84	99	10	xm(t)|	xm(t)|	PUNCT
ejpam-84	99	11	≤	≤	NUM
ejpam-84	99	12	rn(t	rn(t	NUM
ejpam-84	99	13	)	)	PUNCT
ejpam-84	99	14	,	,	PUNCT
ejpam-84	99	15	t0	t0	PROPN
ejpam-84	99	16	≤	≤	PROPN
ejpam-84	99	17	t	t	PROPN
ejpam-84	99	18	≤	≤	NUM
ejpam-84	99	19	t0	t0	PROPN
ejpam-84	99	20	+	+	CCONJ
ejpam-84	99	21	α	α	PROPN
ejpam-84	99	22	,	,	PUNCT
ejpam-84	99	23	v.lakshmikantham	v.lakshmikantham	PROPN
ejpam-84	99	24	,	,	PUNCT
ejpam-84	99	25	j.devi	j.devi	PROPN
ejpam-84	99	26	/	/	SYM
ejpam-84	99	27	eur	eur	PROPN
ejpam-84	99	28	.	.	PUNCT
ejpam-84	100	1	j.	j.	PROPN
ejpam-84	100	2	pure	pure	PROPN
ejpam-84	100	3	appl	appl	PROPN
ejpam-84	100	4	.	.	PROPN
ejpam-84	100	5	math	math	PROPN
ejpam-84	100	6	,	,	PUNCT
ejpam-84	100	7	1	1	NUM
ejpam-84	100	8	(	(	PUNCT
ejpam-84	100	9	2008	2008	NUM
ejpam-84	100	10	)	)	PUNCT
ejpam-84	100	11	,	,	PUNCT
ejpam-84	100	12	(	(	PUNCT
ejpam-84	100	13	38	38	NUM
ejpam-84	100	14	-	-	SYM
ejpam-84	100	15	45	45	NUM
ejpam-84	100	16	)	)	PUNCT
ejpam-84	100	17	42	42	NUM
ejpam-84	100	18	where	where	SCONJ
ejpam-84	100	19	rn(t	rn(t	NUM
ejpam-84	100	20	)	)	PUNCT
ejpam-84	100	21	is	be	AUX
ejpam-84	100	22	the	the	DET
ejpam-84	100	23	maximal	maximal	ADJ
ejpam-84	100	24	solution	solution	NOUN
ejpam-84	100	25	of	of	ADP
ejpam-84	100	26	the	the	DET
ejpam-84	100	27	ivp	ivp	ADJ
ejpam-84	100	28	dqv	dqv	PROPN
ejpam-84	100	29	=	=	SYM
ejpam-84	100	30	g(t	g(t	PROPN
ejpam-84	100	31	,	,	PUNCT
ejpam-84	100	32	v	v	NOUN
ejpam-84	100	33	)	)	PUNCT
ejpam-84	100	34	+	+	CCONJ
ejpam-84	100	35	2g(t	2g(t	NUM
ejpam-84	100	36	,	,	PUNCT
ejpam-84	100	37	un−1(t	un−1(t	ADJ
ejpam-84	100	38	)	)	PUNCT
ejpam-84	100	39	)	)	PUNCT
ejpam-84	100	40	,	,	PUNCT
ejpam-84	100	41	v(t)(t−	v(t)(t−	NOUN
ejpam-84	100	42	t0)1−q|t	t0)1−q|t	NUM
ejpam-84	100	43	=	=	SYM
ejpam-84	100	44	t0	t0	NOUN
ejpam-84	100	45	=	=	SYM
ejpam-84	100	46	0	0	NUM
ejpam-84	100	47	,	,	PUNCT
ejpam-84	100	48	for	for	ADP
ejpam-84	100	49	each	each	DET
ejpam-84	100	50	n.	n.	NOUN
ejpam-84	100	51	since	since	SCONJ
ejpam-84	100	52	as	as	ADP
ejpam-84	100	53	n	n	X
ejpam-84	100	54	→∞	→∞	PROPN
ejpam-84	100	55	,	,	PUNCT
ejpam-84	100	56	2g(t	2g(t	NUM
ejpam-84	100	57	,	,	PUNCT
ejpam-84	100	58	un−1(t	un−1(t	ADJ
ejpam-84	100	59	)	)	PUNCT
ejpam-84	100	60	)	)	PUNCT
ejpam-84	101	1	→	→	SYM
ejpam-84	101	2	0	0	NUM
ejpam-84	101	3	uniformly	uniformly	ADV
ejpam-84	101	4	on	on	ADP
ejpam-84	101	5	[	[	X
ejpam-84	101	6	t0	t0	NOUN
ejpam-84	101	7	,	,	PUNCT
ejpam-84	101	8	t0	t0	PROPN
ejpam-84	101	9	+	+	CCONJ
ejpam-84	101	10	α	α	X
ejpam-84	101	11	]	]	X
ejpam-84	101	12	,	,	PUNCT
ejpam-84	101	13	it	it	PRON
ejpam-84	101	14	follows	follow	VERB
ejpam-84	101	15	by	by	ADP
ejpam-84	101	16	lemma	lemma	PROPN
ejpam-84	101	17	2.3	2.3	NUM
ejpam-84	101	18	that	that	DET
ejpam-84	101	19	rn(t	rn(t	NUM
ejpam-84	101	20	)	)	PUNCT
ejpam-84	101	21	→	→	SYM
ejpam-84	101	22	0	0	NUM
ejpam-84	101	23	uniformly	uniformly	ADV
ejpam-84	101	24	on	on	ADP
ejpam-84	101	25	[	[	X
ejpam-84	101	26	t0	t0	NOUN
ejpam-84	101	27	,	,	PUNCT
ejpam-84	101	28	t0	t0	PROPN
ejpam-84	101	29	+	+	CCONJ
ejpam-84	101	30	α	α	X
ejpam-84	101	31	]	]	X
ejpam-84	101	32	.	.	PUNCT
ejpam-84	102	1	this	this	PRON
ejpam-84	102	2	implies	imply	VERB
ejpam-84	102	3	that	that	SCONJ
ejpam-84	102	4	{	{	PUNCT
ejpam-84	102	5	xn(t	xn(t	NUM
ejpam-84	102	6	)	)	PUNCT
ejpam-84	102	7	}	}	PUNCT
ejpam-84	102	8	converges	converge	VERB
ejpam-84	102	9	uniformly	uniformly	ADV
ejpam-84	102	10	to	to	ADP
ejpam-84	102	11	x(t	x(t	PROPN
ejpam-84	102	12	)	)	PUNCT
ejpam-84	102	13	and	and	CCONJ
ejpam-84	102	14	it	it	PRON
ejpam-84	102	15	is	be	AUX
ejpam-84	102	16	now	now	ADV
ejpam-84	102	17	easy	easy	ADJ
ejpam-84	102	18	to	to	PART
ejpam-84	102	19	show	show	VERB
ejpam-84	102	20	that	that	SCONJ
ejpam-84	102	21	x(t	x(t	PROPN
ejpam-84	102	22	)	)	PUNCT
ejpam-84	102	23	is	be	AUX
ejpam-84	102	24	a	a	DET
ejpam-84	102	25	solution	solution	NOUN
ejpam-84	102	26	of	of	ADP
ejpam-84	102	27	ivp	ivp	NOUN
ejpam-84	102	28	(	(	PUNCT
ejpam-84	102	29	2.1	2.1	NUM
ejpam-84	102	30	)	)	PUNCT
ejpam-84	102	31	.	.	PUNCT
ejpam-84	103	1	to	to	PART
ejpam-84	103	2	show	show	VERB
ejpam-84	103	3	that	that	SCONJ
ejpam-84	103	4	this	this	DET
ejpam-84	103	5	solution	solution	NOUN
ejpam-84	103	6	x(t	x(t	PROPN
ejpam-84	103	7	)	)	PUNCT
ejpam-84	103	8	is	be	AUX
ejpam-84	103	9	unique	unique	ADJ
ejpam-84	103	10	,	,	PUNCT
ejpam-84	103	11	let	let	VERB
ejpam-84	103	12	y(t	y(t	NUM
ejpam-84	103	13	)	)	PUNCT
ejpam-84	103	14	be	be	AUX
ejpam-84	103	15	another	another	DET
ejpam-84	103	16	solution	solution	NOUN
ejpam-84	103	17	of	of	ADP
ejpam-84	103	18	the	the	DET
ejpam-84	103	19	ivp	ivp	NOUN
ejpam-84	103	20	(	(	PUNCT
ejpam-84	103	21	2.1	2.1	NUM
ejpam-84	103	22	)	)	PUNCT
ejpam-84	103	23	on	on	ADP
ejpam-84	103	24	[	[	X
ejpam-84	103	25	t0	t0	NOUN
ejpam-84	103	26	,	,	PUNCT
ejpam-84	103	27	t0	t0	PROPN
ejpam-84	103	28	+	+	CCONJ
ejpam-84	103	29	α	α	X
ejpam-84	103	30	]	]	X
ejpam-84	103	31	.	.	PUNCT
ejpam-84	104	1	define	define	VERB
ejpam-84	104	2	m(t	m(t	NOUN
ejpam-84	104	3	)	)	PUNCT
ejpam-84	105	1	=	=	PUNCT
ejpam-84	105	2	|x(t)−	|x(t)−	X
ejpam-84	105	3	y(t)|	y(t)|	PROPN
ejpam-84	105	4	and	and	CCONJ
ejpam-84	105	5	note	note	VERB
ejpam-84	105	6	that	that	SCONJ
ejpam-84	105	7	m(t0	m(t0	NOUN
ejpam-84	105	8	)	)	PUNCT
ejpam-84	106	1	=	=	SYM
ejpam-84	106	2	0	0	X
ejpam-84	106	3	.	.	PUNCT
ejpam-84	107	1	then	then	ADV
ejpam-84	107	2	d+qm(t	d+qm(t	NOUN
ejpam-84	107	3	)	)	PUNCT
ejpam-84	107	4	≤	≤	NUM
ejpam-84	107	5	|dqx(t)−	|dqx(t)−	PUNCT
ejpam-84	108	1	dqy(t)|	dqy(t)|	ADJ
ejpam-84	108	2	≤	≤	PUNCT
ejpam-84	108	3	|f(t	|f(t	PROPN
ejpam-84	108	4	,	,	PUNCT
ejpam-84	108	5	x(t	x(t	PROPN
ejpam-84	108	6	)	)	PUNCT
ejpam-84	108	7	)	)	PUNCT
ejpam-84	109	1	−	−	ADP
ejpam-84	109	2	f(t	f(t	NOUN
ejpam-84	109	3	,	,	PUNCT
ejpam-84	109	4	y(t))|	y(t))|	PROPN
ejpam-84	109	5	≤	≤	PROPN
ejpam-84	109	6	g(t	g(t	PROPN
ejpam-84	109	7	,	,	PUNCT
ejpam-84	109	8	m(t	m(t	NOUN
ejpam-84	109	9	)	)	PUNCT
ejpam-84	109	10	)	)	PUNCT
ejpam-84	109	11	,	,	PUNCT
ejpam-84	109	12	using	use	VERB
ejpam-84	109	13	condition	condition	NOUN
ejpam-84	109	14	(	(	PUNCT
ejpam-84	109	15	c	c	NOUN
ejpam-84	109	16	)	)	PUNCT
ejpam-84	109	17	.	.	PUNCT
ejpam-84	110	1	again	again	ADV
ejpam-84	110	2	applying	apply	VERB
ejpam-84	110	3	the	the	DET
ejpam-84	110	4	comparison	comparison	NOUN
ejpam-84	110	5	result	result	VERB
ejpam-84	110	6	lemma	lemma	PROPN
ejpam-84	110	7	2.4	2.4	NUM
ejpam-84	110	8	,	,	PUNCT
ejpam-84	110	9	we	we	PRON
ejpam-84	110	10	have	have	VERB
ejpam-84	110	11	m(t	m(t	NOUN
ejpam-84	110	12	)	)	PUNCT
ejpam-84	110	13	≤	≤	NOUN
ejpam-84	110	14	r(t	r(t	NOUN
ejpam-84	110	15	)	)	PUNCT
ejpam-84	110	16	,	,	PUNCT
ejpam-84	110	17	t0	t0	PROPN
ejpam-84	110	18	≤	≤	PROPN
ejpam-84	110	19	t	t	PROPN
ejpam-84	110	20	≤	≤	NUM
ejpam-84	110	21	t0	t0	PROPN
ejpam-84	110	22	+	+	CCONJ
ejpam-84	110	23	α	α	NOUN
ejpam-84	110	24	,	,	PUNCT
ejpam-84	110	25	where	where	SCONJ
ejpam-84	110	26	r(t	r(t	NOUN
ejpam-84	110	27	)	)	PUNCT
ejpam-84	110	28	is	be	AUX
ejpam-84	110	29	the	the	DET
ejpam-84	110	30	maximal	maximal	ADJ
ejpam-84	110	31	solution	solution	NOUN
ejpam-84	110	32	of	of	ADP
ejpam-84	110	33	ivp	ivp	NOUN
ejpam-84	110	34	(	(	PUNCT
ejpam-84	110	35	2.3	2.3	NUM
ejpam-84	110	36	)	)	PUNCT
ejpam-84	110	37	.	.	PUNCT
ejpam-84	111	1	by	by	ADP
ejpam-84	111	2	assumption	assumption	NOUN
ejpam-84	111	3	(	(	PUNCT
ejpam-84	111	4	b	b	NOUN
ejpam-84	111	5	)	)	PUNCT
ejpam-84	111	6	,	,	PUNCT
ejpam-84	111	7	r(t	r(t	NOUN
ejpam-84	111	8	)	)	PUNCT
ejpam-84	111	9	≡	≡	PROPN
ejpam-84	111	10	0	0	PUNCT
ejpam-84	111	11	and	and	CCONJ
ejpam-84	111	12	this	this	PRON
ejpam-84	111	13	proves	prove	VERB
ejpam-84	111	14	that	that	SCONJ
ejpam-84	111	15	x(t	x(t	PROPN
ejpam-84	111	16	)	)	PUNCT
ejpam-84	111	17	=	=	SYM
ejpam-84	111	18	y(t	y(t	PROPN
ejpam-84	111	19	)	)	PUNCT
ejpam-84	111	20	on	on	ADP
ejpam-84	111	21	[	[	X
ejpam-84	111	22	t0	t0	NOUN
ejpam-84	111	23	,	,	PUNCT
ejpam-84	111	24	t0	t0	PROPN
ejpam-84	111	25	+	+	CCONJ
ejpam-84	111	26	α	α	X
ejpam-84	111	27	]	]	X
ejpam-84	111	28	.	.	PUNCT
ejpam-84	112	1	hence	hence	ADV
ejpam-84	112	2	the	the	DET
ejpam-84	112	3	proof	proof	NOUN
ejpam-84	112	4	is	be	AUX
ejpam-84	112	5	complete	complete	ADJ
ejpam-84	112	6	.	.	PUNCT
ejpam-84	113	1	corollary	corollary	ADJ
ejpam-84	113	2	2.1	2.1	NUM
ejpam-84	113	3	:	:	PUNCT
ejpam-84	113	4	the	the	DET
ejpam-84	113	5	function	function	PROPN
ejpam-84	113	6	g(t	g(t	PROPN
ejpam-84	113	7	,	,	PUNCT
ejpam-84	113	8	u	u	NOUN
ejpam-84	113	9	)	)	PUNCT
ejpam-84	113	10	=	=	SYM
ejpam-84	113	11	lu	lu	PROPN
ejpam-84	113	12	,	,	PUNCT
ejpam-84	113	13	l	l	NOUN
ejpam-84	113	14	>	>	X
ejpam-84	113	15	0	0	PUNCT
ejpam-84	113	16	is	be	AUX
ejpam-84	113	17	admissible	admissible	ADJ
ejpam-84	113	18	in	in	ADP
ejpam-84	113	19	theorem	theorem	NOUN
ejpam-84	113	20	2.1	2.1	NUM
ejpam-84	113	21	.	.	PUNCT
ejpam-84	114	1	let	let	VERB
ejpam-84	114	2	us	we	PRON
ejpam-84	114	3	note	note	VERB
ejpam-84	114	4	first	first	ADV
ejpam-84	114	5	that	that	SCONJ
ejpam-84	114	6	when	when	SCONJ
ejpam-84	114	7	the	the	DET
ejpam-84	114	8	initial	initial	ADJ
ejpam-84	114	9	time	time	NOUN
ejpam-84	114	10	is	be	AUX
ejpam-84	114	11	changed	change	VERB
ejpam-84	114	12	the	the	DET
ejpam-84	114	13	corresponding	corresponding	ADJ
ejpam-84	114	14	fractional	fractional	ADJ
ejpam-84	114	15	differential	differential	NOUN
ejpam-84	114	16	equation	equation	NOUN
ejpam-84	114	17	becomes	become	VERB
ejpam-84	114	18	different	different	ADJ
ejpam-84	114	19	because	because	SCONJ
ejpam-84	114	20	the	the	DET
ejpam-84	114	21	notion	notion	NOUN
ejpam-84	114	22	of	of	ADP
ejpam-84	114	23	fractional	fractional	ADJ
ejpam-84	114	24	derivative	derivative	NOUN
ejpam-84	114	25	is	be	AUX
ejpam-84	114	26	nonlocal	nonlocal	ADJ
ejpam-84	114	27	.	.	PUNCT
ejpam-84	115	1	we	we	PRON
ejpam-84	115	2	are	be	AUX
ejpam-84	115	3	therefore	therefore	ADV
ejpam-84	115	4	content	content	ADJ
ejpam-84	115	5	with	with	ADP
ejpam-84	115	6	proving	prove	VERB
ejpam-84	115	7	the	the	DET
ejpam-84	115	8	continuous	continuous	ADJ
ejpam-84	115	9	dependence	dependence	NOUN
ejpam-84	115	10	of	of	ADP
ejpam-84	115	11	solutions	solution	NOUN
ejpam-84	115	12	x(t	x(t	PROPN
ejpam-84	115	13	,	,	PUNCT
ejpam-84	115	14	t0	t0	PROPN
ejpam-84	115	15	,	,	PUNCT
ejpam-84	115	16	x0	x0	PROPN
ejpam-84	115	17	)	)	PUNCT
ejpam-84	115	18	of	of	ADP
ejpam-84	115	19	ivp	ivp	PROPN
ejpam-84	115	20	(	(	PUNCT
ejpam-84	115	21	2.1	2.1	NUM
ejpam-84	115	22	)	)	PUNCT
ejpam-84	115	23	with	with	ADP
ejpam-84	115	24	respect	respect	NOUN
ejpam-84	115	25	to	to	ADP
ejpam-84	115	26	x0	x0	PROPN
ejpam-84	115	27	only	only	ADV
ejpam-84	115	28	.	.	PUNCT
ejpam-84	116	1	theorem	theorem	VERB
ejpam-84	116	2	2.2	2.2	NUM
ejpam-84	116	3	:	:	PUNCT
ejpam-84	116	4	let	let	VERB
ejpam-84	116	5	f	f	PROPN
ejpam-84	116	6	∈	∈	PROPN
ejpam-84	116	7	c(r+	c(r+	X
ejpam-84	116	8	×e	×e	NOUN
ejpam-84	116	9	,	,	PUNCT
ejpam-84	116	10	e	e	NOUN
ejpam-84	116	11	)	)	PUNCT
ejpam-84	116	12	and	and	CCONJ
ejpam-84	116	13	for	for	ADP
ejpam-84	116	14	(	(	PUNCT
ejpam-84	116	15	t	t	PROPN
ejpam-84	116	16	,	,	PUNCT
ejpam-84	116	17	x	x	NOUN
ejpam-84	116	18	)	)	PUNCT
ejpam-84	117	1	=	=	PUNCT
ejpam-84	117	2	r+	r+	PUNCT
ejpam-84	117	3	×	×	PROPN
ejpam-84	117	4	e	e	NOUN
ejpam-84	117	5	,	,	PUNCT
ejpam-84	117	6	|f(t	|f(t	PROPN
ejpam-84	117	7	,	,	PUNCT
ejpam-84	117	8	x)−	x)−	PROPN
ejpam-84	117	9	f(t	f(t	PROPN
ejpam-84	117	10	,	,	PUNCT
ejpam-84	117	11	y)|	y)|	PROPN
ejpam-84	117	12	≤	≤	PROPN
ejpam-84	117	13	g(t	g(t	PROPN
ejpam-84	117	14	,	,	PUNCT
ejpam-84	117	15	|x−	|x−	NOUN
ejpam-84	117	16	y|	y|	NOUN
ejpam-84	117	17	)	)	PUNCT
ejpam-84	117	18	(	(	PUNCT
ejpam-84	117	19	2.6	2.6	NUM
ejpam-84	117	20	)	)	PUNCT
ejpam-84	117	21	where	where	SCONJ
ejpam-84	117	22	g	g	PROPN
ejpam-84	117	23	∈	∈	PROPN
ejpam-84	117	24	c(r2	c(r2	NOUN
ejpam-84	118	1	+	+	NOUN
ejpam-84	118	2	,	,	PUNCT
ejpam-84	118	3	r+	r+	X
ejpam-84	118	4	)	)	PUNCT
ejpam-84	118	5	.	.	PUNCT
ejpam-84	119	1	assume	assume	VERB
ejpam-84	119	2	that	that	SCONJ
ejpam-84	119	3	u(t	u(t	NOUN
ejpam-84	119	4	)	)	PUNCT
ejpam-84	119	5	≡	≡	PROPN
ejpam-84	119	6	0	0	NUM
ejpam-84	119	7	is	be	AUX
ejpam-84	119	8	the	the	DET
ejpam-84	119	9	unique	unique	ADJ
ejpam-84	119	10	solution	solution	NOUN
ejpam-84	119	11	of	of	ADP
ejpam-84	119	12	the	the	DET
ejpam-84	119	13	fractional	fractional	ADJ
ejpam-84	119	14	differential	differential	ADJ
ejpam-84	119	15	equation	equation	NOUN
ejpam-84	119	16	dqu	dqu	NOUN
ejpam-84	119	17	=	=	SYM
ejpam-84	119	18	g(t	g(t	PROPN
ejpam-84	119	19	,	,	PUNCT
ejpam-84	119	20	u	u	NOUN
ejpam-84	119	21	)	)	PUNCT
ejpam-84	119	22	(	(	PUNCT
ejpam-84	119	23	2.7	2.7	NUM
ejpam-84	119	24	)	)	PUNCT
ejpam-84	119	25	with	with	ADP
ejpam-84	119	26	u(t)(t−	u(t)(t−	PRON
ejpam-84	119	27	t0)1−q|t	t0)1−q|t	NUM
ejpam-84	119	28	=	=	SYM
ejpam-84	119	29	t0	t0	NOUN
ejpam-84	119	30	=	=	SYM
ejpam-84	120	1	0	0	X
ejpam-84	120	2	.	.	PUNCT
ejpam-84	121	1	then	then	ADV
ejpam-84	121	2	,	,	PUNCT
ejpam-84	121	3	if	if	SCONJ
ejpam-84	121	4	the	the	DET
ejpam-84	121	5	solutions	solution	NOUN
ejpam-84	121	6	u(t	u(t	NOUN
ejpam-84	121	7	,	,	PUNCT
ejpam-84	121	8	t0	t0	PROPN
ejpam-84	121	9	,	,	PUNCT
ejpam-84	121	10	u0	u0	PROPN
ejpam-84	121	11	)	)	PUNCT
ejpam-84	121	12	where	where	SCONJ
ejpam-84	121	13	u0	u0	ADJ
ejpam-84	121	14	=	=	NOUN
ejpam-84	121	15	u(t)(t−	u(t)(t−	ADJ
ejpam-84	121	16	t0)1−q|t	t0)1−q|t	NUM
ejpam-84	121	17	=	=	SYM
ejpam-84	121	18	t0	t0	X
ejpam-84	121	19	of	of	ADP
ejpam-84	121	20	(	(	PUNCT
ejpam-84	121	21	2.7	2.7	NUM
ejpam-84	121	22	)	)	PUNCT
ejpam-84	121	23	are	be	AUX
ejpam-84	121	24	continuous	continuous	ADJ
ejpam-84	121	25	with	with	ADP
ejpam-84	121	26	respect	respect	NOUN
ejpam-84	121	27	to	to	ADP
ejpam-84	121	28	the	the	DET
ejpam-84	121	29	initial	initial	ADJ
ejpam-84	121	30	condition	condition	NOUN
ejpam-84	121	31	u0	u0	PROPN
ejpam-84	121	32	,	,	PUNCT
ejpam-84	121	33	the	the	DET
ejpam-84	121	34	solutions	solution	NOUN
ejpam-84	121	35	x(t	x(t	PROPN
ejpam-84	121	36	,	,	PUNCT
ejpam-84	121	37	t0	t0	PROPN
ejpam-84	121	38	,	,	PUNCT
ejpam-84	121	39	x0	x0	PROPN
ejpam-84	121	40	)	)	PUNCT
ejpam-84	121	41	of	of	ADP
ejpam-84	121	42	(	(	PUNCT
ejpam-84	121	43	2.1	2.1	NUM
ejpam-84	121	44	)	)	PUNCT
ejpam-84	121	45	are	be	AUX
ejpam-84	121	46	unique	unique	ADJ
ejpam-84	121	47	and	and	CCONJ
ejpam-84	121	48	continuous	continuous	ADJ
ejpam-84	121	49	relative	relative	NOUN
ejpam-84	121	50	to	to	ADP
ejpam-84	121	51	x0	x0	PROPN
ejpam-84	121	52	.	.	PUNCT
ejpam-84	122	1	proof	proof	NOUN
ejpam-84	122	2	:	:	PUNCT
ejpam-84	122	3	since	since	SCONJ
ejpam-84	122	4	uniqueness	uniqueness	NOUN
ejpam-84	122	5	follows	follow	VERB
ejpam-84	122	6	from	from	ADP
ejpam-84	122	7	theorem	theorem	ADJ
ejpam-84	122	8	2.1	2.1	NUM
ejpam-84	122	9	,	,	PUNCT
ejpam-84	122	10	we	we	PRON
ejpam-84	122	11	have	have	VERB
ejpam-84	122	12	to	to	PART
ejpam-84	122	13	consider	consider	VERB
ejpam-84	122	14	continuity	continuity	NOUN
ejpam-84	122	15	part	part	NOUN
ejpam-84	122	16	only	only	ADV
ejpam-84	122	17	.	.	PUNCT
ejpam-84	123	1	to	to	ADP
ejpam-84	123	2	the	the	DET
ejpam-84	123	3	end	end	NOUN
ejpam-84	123	4	,	,	PUNCT
ejpam-84	123	5	let	let	VERB
ejpam-84	123	6	x(t	x(t	PROPN
ejpam-84	123	7	,	,	PUNCT
ejpam-84	123	8	t0	t0	PROPN
ejpam-84	123	9	,	,	PUNCT
ejpam-84	123	10	x0	x0	PROPN
ejpam-84	123	11	)	)	PUNCT
ejpam-84	123	12	,	,	PUNCT
ejpam-84	123	13	y(t	y(t	PROPN
ejpam-84	123	14	,	,	PUNCT
ejpam-84	123	15	t0	t0	PROPN
ejpam-84	123	16	,	,	PUNCT
ejpam-84	123	17	y0	y0	PROPN
ejpam-84	123	18	)	)	PUNCT
ejpam-84	123	19	be	be	VERB
ejpam-84	123	20	the	the	DET
ejpam-84	123	21	two	two	NUM
ejpam-84	123	22	solutions	solution	NOUN
ejpam-84	123	23	of	of	ADP
ejpam-84	123	24	(	(	PUNCT
ejpam-84	123	25	2.1	2.1	NUM
ejpam-84	123	26	)	)	PUNCT
ejpam-84	123	27	through	through	ADP
ejpam-84	123	28	(	(	PUNCT
ejpam-84	123	29	t0	t0	PROPN
ejpam-84	123	30	,	,	PUNCT
ejpam-84	123	31	x0	x0	PROPN
ejpam-84	123	32	)	)	PUNCT
ejpam-84	123	33	,	,	PUNCT
ejpam-84	123	34	(	(	PUNCT
ejpam-84	123	35	t0	t0	NOUN
ejpam-84	123	36	,	,	PUNCT
ejpam-84	123	37	y0	y0	NOUN
ejpam-84	123	38	)	)	PUNCT
ejpam-84	123	39	respectively	respectively	ADV
ejpam-84	123	40	.	.	PUNCT
ejpam-84	124	1	defining	define	VERB
ejpam-84	124	2	m(t	m(t	NOUN
ejpam-84	124	3	)	)	PUNCT
ejpam-84	124	4	=	=	SYM
ejpam-84	124	5	|x(t	|x(t	PROPN
ejpam-84	124	6	,	,	PUNCT
ejpam-84	124	7	t0	t0	PROPN
ejpam-84	124	8	,	,	PUNCT
ejpam-84	124	9	x0)−	x0)−	PROPN
ejpam-84	124	10	y(t	y(t	PROPN
ejpam-84	124	11	,	,	PUNCT
ejpam-84	124	12	t0	t0	PROPN
ejpam-84	124	13	,	,	PUNCT
ejpam-84	124	14	y0)|	y0)|	NOUN
ejpam-84	124	15	,	,	PUNCT
ejpam-84	124	16	condition	condition	NOUN
ejpam-84	124	17	(	(	PUNCT
ejpam-84	124	18	2.6	2.6	NUM
ejpam-84	124	19	)	)	PUNCT
ejpam-84	124	20	implies	imply	VERB
ejpam-84	124	21	the	the	DET
ejpam-84	124	22	inequality	inequality	NOUN
ejpam-84	124	23	d+qm(t	d+qm(t	NOUN
ejpam-84	124	24	)	)	PUNCT
ejpam-84	124	25	≤	≤	NUM
ejpam-84	125	1	g(t	g(t	PROPN
ejpam-84	125	2	,	,	PUNCT
ejpam-84	125	3	m(t	m(t	NOUN
ejpam-84	125	4	)	)	PUNCT
ejpam-84	125	5	)	)	PUNCT
ejpam-84	125	6	,	,	PUNCT
ejpam-84	125	7	and	and	CCONJ
ejpam-84	125	8	by	by	ADP
ejpam-84	125	9	lemma	lemma	PROPN
ejpam-84	125	10	2.4	2.4	NUM
ejpam-84	125	11	,	,	PUNCT
ejpam-84	125	12	we	we	PRON
ejpam-84	125	13	get	get	VERB
ejpam-84	125	14	m(t	m(t	NOUN
ejpam-84	125	15	)	)	PUNCT
ejpam-84	125	16	≤	≤	NOUN
ejpam-84	125	17	r(t	r(t	NOUN
ejpam-84	125	18	,	,	PUNCT
ejpam-84	125	19	t0	t0	PROPN
ejpam-84	125	20	,	,	PUNCT
ejpam-84	125	21	|x0	|x0	NOUN
ejpam-84	125	22	−	−	PROPN
ejpam-84	125	23	y0|	y0|	PROPN
ejpam-84	125	24	)	)	PUNCT
ejpam-84	125	25	,	,	PUNCT
ejpam-84	125	26	t	t	PROPN
ejpam-84	125	27	≥	≥	PROPN
ejpam-84	125	28	t0	t0	PROPN
ejpam-84	125	29	,	,	PUNCT
ejpam-84	125	30	where	where	SCONJ
ejpam-84	125	31	r(t	r(t	NOUN
ejpam-84	125	32	,	,	PUNCT
ejpam-84	125	33	t0	t0	PROPN
ejpam-84	125	34	,	,	PUNCT
ejpam-84	125	35	u0	u0	ADJ
ejpam-84	125	36	)	)	PUNCT
ejpam-84	125	37	is	be	AUX
ejpam-84	125	38	the	the	DET
ejpam-84	125	39	maximal	maximal	ADJ
ejpam-84	125	40	solution	solution	NOUN
ejpam-84	125	41	of	of	ADP
ejpam-84	125	42	(	(	PUNCT
ejpam-84	125	43	2.7	2.7	NUM
ejpam-84	125	44	)	)	PUNCT
ejpam-84	125	45	such	such	ADJ
ejpam-84	125	46	that	that	DET
ejpam-84	125	47	u0	u0	ADJ
ejpam-84	125	48	=	=	PUNCT
ejpam-84	125	49	|x0	|x0	PROPN
ejpam-84	125	50	−	−	PROPN
ejpam-84	125	51	y0|	y0|	PROPN
ejpam-84	125	52	.	.	PUNCT
ejpam-84	126	1	since	since	SCONJ
ejpam-84	126	2	the	the	DET
ejpam-84	126	3	solutions	solution	NOUN
ejpam-84	126	4	u(t	u(t	NOUN
ejpam-84	126	5	,	,	PUNCT
ejpam-84	126	6	t0	t0	PROPN
ejpam-84	126	7	,	,	PUNCT
ejpam-84	126	8	u0	u0	ADJ
ejpam-84	126	9	)	)	PUNCT
ejpam-84	126	10	are	be	AUX
ejpam-84	126	11	assumed	assume	VERB
ejpam-84	126	12	to	to	PART
ejpam-84	126	13	be	be	AUX
ejpam-84	126	14	continuous	continuous	ADJ
ejpam-84	126	15	relative	relative	ADJ
ejpam-84	126	16	to	to	ADP
ejpam-84	126	17	u0	u0	VERB
ejpam-84	126	18	,	,	PUNCT
ejpam-84	126	19	it	it	PRON
ejpam-84	126	20	follows	follow	VERB
ejpam-84	126	21	that	that	SCONJ
ejpam-84	126	22	limx0→y0	limx0→y0	NOUN
ejpam-84	126	23	r(t	r(t	NOUN
ejpam-84	126	24	,	,	PUNCT
ejpam-84	126	25	t0	t0	PROPN
ejpam-84	126	26	,	,	PUNCT
ejpam-84	126	27	|x0	|x0	NOUN
ejpam-84	126	28	−	−	PROPN
ejpam-84	126	29	y0|	y0|	PROPN
ejpam-84	126	30	)	)	PUNCT
ejpam-84	127	1	=	=	SYM
ejpam-84	127	2	r(t	r(t	NOUN
ejpam-84	127	3	,	,	PUNCT
ejpam-84	127	4	t0	t0	PROPN
ejpam-84	127	5	,	,	PUNCT
ejpam-84	127	6	0	0	NUM
ejpam-84	127	7	)	)	PUNCT
ejpam-84	127	8	≡	≡	PROPN
ejpam-84	127	9	0	0	NUM
ejpam-84	127	10	by	by	ADP
ejpam-84	127	11	hypothesis	hypothesis	NOUN
ejpam-84	127	12	.	.	PUNCT
ejpam-84	128	1	it	it	PRON
ejpam-84	128	2	then	then	ADV
ejpam-84	128	3	follows	follow	VERB
ejpam-84	128	4	that	that	SCONJ
ejpam-84	128	5	limx0→y0	limx0→y0	NOUN
ejpam-84	128	6	x(t	x(t	PROPN
ejpam-84	128	7	,	,	PUNCT
ejpam-84	128	8	t0	t0	PROPN
ejpam-84	128	9	,	,	PUNCT
ejpam-84	128	10	x0	x0	PROPN
ejpam-84	128	11	)	)	PUNCT
ejpam-84	129	1	=	=	SYM
ejpam-84	129	2	y(t	y(t	PROPN
ejpam-84	129	3	,	,	PUNCT
ejpam-84	129	4	t0	t0	PROPN
ejpam-84	129	5	,	,	PUNCT
ejpam-84	129	6	y0	y0	PROPN
ejpam-84	129	7	)	)	PUNCT
ejpam-84	129	8	,	,	PUNCT
ejpam-84	129	9	proving	prove	VERB
ejpam-84	129	10	the	the	DET
ejpam-84	129	11	continuity	continuity	NOUN
ejpam-84	129	12	with	with	ADP
ejpam-84	129	13	respect	respect	NOUN
ejpam-84	129	14	to	to	ADP
ejpam-84	129	15	x0	x0	PROPN
ejpam-84	129	16	.	.	PUNCT
ejpam-84	130	1	the	the	DET
ejpam-84	130	2	proof	proof	NOUN
ejpam-84	130	3	is	be	AUX
ejpam-84	130	4	complete	complete	ADJ
ejpam-84	130	5	.	.	PUNCT
ejpam-84	131	1	v.lakshmikantham	v.lakshmikantham	PROPN
ejpam-84	131	2	,	,	PUNCT
ejpam-84	131	3	j.devi	j.devi	PROPN
ejpam-84	131	4	/	/	SYM
ejpam-84	131	5	eur	eur	PROPN
ejpam-84	131	6	.	.	PUNCT
ejpam-84	132	1	j.	j.	PROPN
ejpam-84	132	2	pure	pure	PROPN
ejpam-84	132	3	appl	appl	PROPN
ejpam-84	132	4	.	.	PROPN
ejpam-84	132	5	math	math	PROPN
ejpam-84	132	6	,	,	PUNCT
ejpam-84	132	7	1	1	NUM
ejpam-84	132	8	(	(	PUNCT
ejpam-84	132	9	2008	2008	NUM
ejpam-84	132	10	)	)	PUNCT
ejpam-84	132	11	,	,	PUNCT
ejpam-84	132	12	(	(	PUNCT
ejpam-84	132	13	38	38	NUM
ejpam-84	132	14	-	-	SYM
ejpam-84	132	15	45	45	NUM
ejpam-84	132	16	)	)	PUNCT
ejpam-84	132	17	43	43	NUM
ejpam-84	132	18	3	3	NUM
ejpam-84	132	19	.	.	PUNCT
ejpam-84	132	20	flow	flow	NOUN
ejpam-84	132	21	invariance	invariance	NOUN
ejpam-84	132	22	and	and	CCONJ
ejpam-84	132	23	inequalities	inequality	NOUN
ejpam-84	132	24	in	in	ADP
ejpam-84	132	25	cones	cone	NOUN
ejpam-84	132	26	the	the	DET
ejpam-84	132	27	definition	definition	NOUN
ejpam-84	132	28	of	of	ADP
ejpam-84	132	29	the	the	DET
ejpam-84	132	30	fractional	fractional	ADJ
ejpam-84	132	31	derivative	derivative	NOUN
ejpam-84	132	32	of	of	ADP
ejpam-84	132	33	an	an	DET
ejpam-84	132	34	arbitrary	arbitrary	ADJ
ejpam-84	132	35	order	order	NOUN
ejpam-84	132	36	0	0	PUNCT
ejpam-84	132	37	<	<	X
ejpam-84	132	38	q	q	X
ejpam-84	132	39	<	<	X
ejpam-84	132	40	1	1	NUM
ejpam-84	132	41	of	of	ADP
ejpam-84	132	42	a	a	DET
ejpam-84	132	43	function	function	NOUN
ejpam-84	132	44	x	x	SYM
ejpam-84	132	45	∈	∈	NOUN
ejpam-84	132	46	c([t0,∞	c([t0,∞	NOUN
ejpam-84	132	47	)	)	PUNCT
ejpam-84	132	48	,	,	PUNCT
ejpam-84	132	49	e	e	X
ejpam-84	132	50	)	)	PUNCT
ejpam-84	132	51	is	be	AUX
ejpam-84	132	52	given	give	VERB
ejpam-84	132	53	by	by	ADP
ejpam-84	132	54	[	[	X
ejpam-84	132	55	14	14	NUM
ejpam-84	132	56	]	]	X
ejpam-84	132	57	dqx(t	dqx(t	PROPN
ejpam-84	132	58	)	)	PUNCT
ejpam-84	132	59	=	=	PROPN
ejpam-84	132	60	lim	lim	PROPN
ejpam-84	132	61	h→0	h→0	NOUN
ejpam-84	132	62	nh=(t−t0	nh=(t−t0	NOUN
ejpam-84	132	63	)	)	PUNCT
ejpam-84	132	64	h−q	h−q	NOUN
ejpam-84	133	1	n∑	n∑	PROPN
ejpam-84	134	1	η=0	η=0	PROPN
ejpam-84	135	1	(	(	PUNCT
ejpam-84	135	2	−1)η(q	−1)η(q	NOUN
ejpam-84	135	3	η)×	η)×	X
ejpam-84	135	4	(	(	PUNCT
ejpam-84	135	5	t−	t−	PROPN
ejpam-84	135	6	ηh	ηh	PROPN
ejpam-84	135	7	)	)	PUNCT
ejpam-84	136	1	=	=	VERB
ejpam-84	136	2	lim	lim	PROPN
ejpam-84	136	3	h→0	h→0	NOUN
ejpam-84	136	4	nh=(t−t0	nh=(t−t0	NOUN
ejpam-84	136	5	)	)	PUNCT
ejpam-84	136	6	x(q)h(t	x(q)h(t	ADJ
ejpam-84	136	7	)	)	PUNCT
ejpam-84	136	8	,	,	PUNCT
ejpam-84	136	9	(	(	PUNCT
ejpam-84	136	10	3.1	3.1	NUM
ejpam-84	136	11	)	)	PUNCT
ejpam-84	136	12	where	where	SCONJ
ejpam-84	136	13	x	x	X
ejpam-84	136	14	(	(	PUNCT
ejpam-84	136	15	q	q	NOUN
ejpam-84	136	16	)	)	PUNCT
ejpam-84	136	17	h	h	NOUN
ejpam-84	136	18	(	(	PUNCT
ejpam-84	136	19	t	t	NOUN
ejpam-84	136	20	)	)	PUNCT
ejpam-84	136	21	=	=	NOUN
ejpam-84	137	1	h−q	h−q	NOUN
ejpam-84	137	2	n∑	n∑	PRON
ejpam-84	137	3	η=0	η=0	PROPN
ejpam-84	137	4	(	(	PUNCT
ejpam-84	137	5	−1)η(q	−1)η(q	NOUN
ejpam-84	137	6	η)×	η)×	X
ejpam-84	137	7	(	(	PUNCT
ejpam-84	137	8	t−	t−	PROPN
ejpam-84	137	9	ηh	ηh	NOUN
ejpam-84	137	10	)	)	PUNCT
ejpam-84	137	11	.	.	PUNCT
ejpam-84	138	1	(	(	PUNCT
ejpam-84	138	2	3.2	3.2	NUM
ejpam-84	138	3	)	)	PUNCT
ejpam-84	138	4	this	this	PRON
ejpam-84	138	5	implies	imply	VERB
ejpam-84	138	6	,	,	PUNCT
ejpam-84	138	7	on	on	ADP
ejpam-84	138	8	expanding	expand	VERB
ejpam-84	138	9	x	x	X
ejpam-84	138	10	(	(	PUNCT
ejpam-84	138	11	q	q	NOUN
ejpam-84	138	12	)	)	PUNCT
ejpam-84	138	13	h	h	NOUN
ejpam-84	138	14	(	(	PUNCT
ejpam-84	138	15	t	t	NOUN
ejpam-84	138	16	)	)	PUNCT
ejpam-84	138	17	=	=	SYM
ejpam-84	139	1	1	1	NUM
ejpam-84	139	2	hq	hq	NOUN
ejpam-84	139	3	[	[	PUNCT
ejpam-84	139	4	x(t)−	x(t)−	PROPN
ejpam-84	139	5	qx(t−	qx(t−	INTJ
ejpam-84	139	6	h	h	NOUN
ejpam-84	139	7	)	)	PUNCT
ejpam-84	139	8	+	+	CCONJ
ejpam-84	139	9	q(q	q(q	NOUN
ejpam-84	139	10	−	−	PROPN
ejpam-84	139	11	1	1	NUM
ejpam-84	139	12	)	)	PUNCT
ejpam-84	139	13	2	2	NUM
ejpam-84	139	14	!	!	PUNCT
ejpam-84	139	15	x(t−	x(t−	PROPN
ejpam-84	140	1	2h)−	2h)−	ADP
ejpam-84	140	2	q(q	q(q	PROPN
ejpam-84	140	3	−	−	PROPN
ejpam-84	140	4	1)(q	1)(q	NUM
ejpam-84	140	5	−	−	NOUN
ejpam-84	140	6	2	2	NUM
ejpam-84	140	7	)	)	PUNCT
ejpam-84	140	8	3	3	NUM
ejpam-84	140	9	!	!	PUNCT
ejpam-84	140	10	x(t−	x(t−	PROPN
ejpam-84	141	1	3h	3h	NUM
ejpam-84	141	2	)	)	PUNCT
ejpam-84	142	1	+	+	CCONJ
ejpam-84	142	2	...	...	PUNCT
ejpam-84	142	3	]	]	PUNCT
ejpam-84	143	1	=	=	PUNCT
ejpam-84	143	2	1	1	NUM
ejpam-84	143	3	hq	hq	NOUN
ejpam-84	144	1	[	[	X
ejpam-84	144	2	x(t)−	x(t)−	PROPN
ejpam-84	144	3	s(t	s(t	PROPN
ejpam-84	144	4	,	,	PUNCT
ejpam-84	144	5	h	h	NOUN
ejpam-84	144	6	,	,	PUNCT
ejpam-84	144	7	q	q	NOUN
ejpam-84	144	8	)	)	PUNCT
ejpam-84	144	9	]	]	PUNCT
ejpam-84	144	10	.	.	PUNCT
ejpam-84	145	1	(	(	PUNCT
ejpam-84	145	2	3.3	3.3	NUM
ejpam-84	145	3	)	)	PUNCT
ejpam-84	145	4	let	let	VERB
ejpam-84	145	5	us	we	PRON
ejpam-84	145	6	consider	consider	VERB
ejpam-84	145	7	the	the	DET
ejpam-84	145	8	ivp	ivp	NOUN
ejpam-84	145	9	for	for	ADP
ejpam-84	145	10	fractional	fractional	ADJ
ejpam-84	145	11	differential	differential	ADJ
ejpam-84	145	12	equation	equation	NOUN
ejpam-84	145	13	dqx	dqx	NOUN
ejpam-84	145	14	=	=	SYM
ejpam-84	145	15	f(t	f(t	NOUN
ejpam-84	145	16	,	,	PUNCT
ejpam-84	145	17	x	x	NOUN
ejpam-84	145	18	)	)	PUNCT
ejpam-84	145	19	,	,	PUNCT
ejpam-84	145	20	x(t)(t−	x(t)(t−	PUNCT
ejpam-84	146	1	t0)1−q|t	t0)1−q|t	NUM
ejpam-84	146	2	=	=	SYM
ejpam-84	146	3	t0	t0	NOUN
ejpam-84	146	4	=	=	NOUN
ejpam-84	147	1	x0	x0	PROPN
ejpam-84	147	2	∈	∈	PROPN
ejpam-84	147	3	f	f	X
ejpam-84	147	4	,	,	PUNCT
ejpam-84	147	5	(	(	PUNCT
ejpam-84	147	6	3.4	3.4	NUM
ejpam-84	147	7	)	)	PUNCT
ejpam-84	147	8	where	where	SCONJ
ejpam-84	147	9	f	f	PROPN
ejpam-84	147	10	∈	∈	PROPN
ejpam-84	147	11	c([t0,∞)×e	c([t0,∞)×e	PROPN
ejpam-84	147	12	,	,	PUNCT
ejpam-84	147	13	e	e	NOUN
ejpam-84	147	14	)	)	PUNCT
ejpam-84	147	15	and	and	CCONJ
ejpam-84	147	16	f	f	PROPN
ejpam-84	147	17	⊂	⊂	PROPN
ejpam-84	147	18	e	e	X
ejpam-84	147	19	is	be	AUX
ejpam-84	147	20	a	a	DET
ejpam-84	147	21	closed	closed	ADJ
ejpam-84	147	22	set	set	NOUN
ejpam-84	147	23	.	.	PUNCT
ejpam-84	148	1	we	we	PRON
ejpam-84	148	2	define	define	VERB
ejpam-84	148	3	lim	lim	PROPN
ejpam-84	148	4	h→∞	h→∞	NUM
ejpam-84	148	5	1	1	NUM
ejpam-84	148	6	hq	hq	NOUN
ejpam-84	148	7	d[x−	d[x−	PROPN
ejpam-84	148	8	hqf(t	hqf(t	PROPN
ejpam-84	148	9	,	,	PUNCT
ejpam-84	148	10	x	x	NOUN
ejpam-84	148	11	)	)	PUNCT
ejpam-84	148	12	,	,	PUNCT
ejpam-84	148	13	f	f	X
ejpam-84	148	14	]	]	X
ejpam-84	149	1	=	=	PUNCT
ejpam-84	149	2	0	0	NUM
ejpam-84	149	3	,	,	PUNCT
ejpam-84	149	4	(	(	PUNCT
ejpam-84	149	5	3.5	3.5	NUM
ejpam-84	149	6	)	)	PUNCT
ejpam-84	149	7	where	where	SCONJ
ejpam-84	149	8	d(x	d(x	NOUN
ejpam-84	149	9	,	,	PUNCT
ejpam-84	149	10	f	f	PROPN
ejpam-84	149	11	)	)	PUNCT
ejpam-84	150	1	=	=	PUNCT
ejpam-84	150	2	infy∈f	infy∈f	ADJ
ejpam-84	150	3	|x	|x	NOUN
ejpam-84	150	4	−	−	PROPN
ejpam-84	150	5	y|	y|	NOUN
ejpam-84	150	6	.	.	PUNCT
ejpam-84	151	1	the	the	DET
ejpam-84	151	2	set	set	NOUN
ejpam-84	151	3	f	f	PROPN
ejpam-84	151	4	is	be	AUX
ejpam-84	151	5	said	say	VERB
ejpam-84	151	6	to	to	PART
ejpam-84	151	7	be	be	AUX
ejpam-84	151	8	flow	flow	VERB
ejpam-84	151	9	invariant	invariant	ADJ
ejpam-84	151	10	relative	relative	NOUN
ejpam-84	151	11	to	to	ADP
ejpam-84	151	12	f	f	PROPN
ejpam-84	151	13	,	,	PUNCT
ejpam-84	151	14	if	if	SCONJ
ejpam-84	151	15	every	every	DET
ejpam-84	151	16	solution	solution	NOUN
ejpam-84	151	17	x(t	x(t	PROPN
ejpam-84	151	18	)	)	PUNCT
ejpam-84	151	19	of	of	ADP
ejpam-84	151	20	ivp	ivp	PROPN
ejpam-84	151	21	(	(	PUNCT
ejpam-84	151	22	3.4	3.4	NUM
ejpam-84	151	23	)	)	PUNCT
ejpam-84	151	24	on	on	ADP
ejpam-84	151	25	[	[	X
ejpam-84	151	26	t0,∞	t0,∞	NUM
ejpam-84	151	27	)	)	PUNCT
ejpam-84	151	28	is	be	AUX
ejpam-84	151	29	such	such	ADJ
ejpam-84	151	30	that	that	SCONJ
ejpam-84	151	31	x(t	x(t	PROPN
ejpam-84	151	32	)	)	PUNCT
ejpam-84	151	33	∈	∈	PROPN
ejpam-84	151	34	f	f	PROPN
ejpam-84	151	35	for	for	ADP
ejpam-84	151	36	t0	t0	PROPN
ejpam-84	151	37	≤	≤	PROPN
ejpam-84	151	38	t	t	PROPN
ejpam-84	151	39	<	<	X
ejpam-84	151	40	∞.	∞.	PROPN
ejpam-84	151	41	a	a	DET
ejpam-84	151	42	set	set	NOUN
ejpam-84	151	43	a	a	DET
ejpam-84	151	44	⊂	⊂	PROPN
ejpam-84	151	45	e	e	PROPN
ejpam-84	151	46	is	be	AUX
ejpam-84	151	47	called	call	VERB
ejpam-84	151	48	a	a	DET
ejpam-84	151	49	distance	distance	NOUN
ejpam-84	151	50	set	set	NOUN
ejpam-84	151	51	,	,	PUNCT
ejpam-84	151	52	if	if	SCONJ
ejpam-84	151	53	to	to	ADP
ejpam-84	151	54	each	each	DET
ejpam-84	151	55	x	x	SYM
ejpam-84	151	56	∈	∈	PROPN
ejpam-84	151	57	e	e	NOUN
ejpam-84	151	58	there	there	PRON
ejpam-84	151	59	corresponds	correspond	VERB
ejpam-84	151	60	a	a	DET
ejpam-84	151	61	point	point	NOUN
ejpam-84	151	62	y	y	PROPN
ejpam-84	151	63	∈	∈	PROPN
ejpam-84	151	64	a	a	DET
ejpam-84	151	65	such	such	ADJ
ejpam-84	151	66	that	that	DET
ejpam-84	151	67	d(x	d(x	PROPN
ejpam-84	151	68	,	,	PUNCT
ejpam-84	151	69	a	a	PRON
ejpam-84	151	70	)	)	PUNCT
ejpam-84	151	71	=	=	SYM
ejpam-84	151	72	|x	|x	NOUN
ejpam-84	151	73	−	−	PROPN
ejpam-84	151	74	y|	y|	NOUN
ejpam-84	151	75	.	.	PUNCT
ejpam-84	152	1	a	a	DET
ejpam-84	152	2	function	function	NOUN
ejpam-84	152	3	g	g	PROPN
ejpam-84	152	4	∈	∈	PROPN
ejpam-84	152	5	(	(	PUNCT
ejpam-84	152	6	[	[	X
ejpam-84	152	7	t0,∞	t0,∞	NUM
ejpam-84	152	8	)	)	PUNCT
ejpam-84	152	9	×	×	NOUN
ejpam-84	152	10	r+	r+	NOUN
ejpam-84	152	11	,	,	PUNCT
ejpam-84	152	12	r+	r+	X
ejpam-84	152	13	)	)	PUNCT
ejpam-84	152	14	is	be	AUX
ejpam-84	152	15	said	say	VERB
ejpam-84	152	16	to	to	PART
ejpam-84	152	17	be	be	AUX
ejpam-84	152	18	a	a	DET
ejpam-84	152	19	uniqueness	uniqueness	NOUN
ejpam-84	152	20	function	function	NOUN
ejpam-84	152	21	,	,	PUNCT
ejpam-84	152	22	if	if	SCONJ
ejpam-84	152	23	the	the	DET
ejpam-84	152	24	following	follow	VERB
ejpam-84	152	25	holds	hold	VERB
ejpam-84	152	26	:	:	PUNCT
ejpam-84	152	27	if	if	SCONJ
ejpam-84	152	28	m	m	PROPN
ejpam-84	152	29	∈	∈	NOUN
ejpam-84	152	30	c([t0,∞	c([t0,∞	NOUN
ejpam-84	152	31	)	)	PUNCT
ejpam-84	152	32	,	,	PUNCT
ejpam-84	152	33	r+	r+	X
ejpam-84	152	34	)	)	PUNCT
ejpam-84	152	35	is	be	AUX
ejpam-84	152	36	such	such	ADJ
ejpam-84	152	37	that	that	SCONJ
ejpam-84	152	38	m(t)(t	m(t)(t	PROPN
ejpam-84	152	39	−	−	NUM
ejpam-84	152	40	t0)1−q|t	t0)1−q|t	NUM
ejpam-84	152	41	=	=	SYM
ejpam-84	152	42	t0	t0	NOUN
ejpam-84	152	43	≤	≤	NOUN
ejpam-84	152	44	0	0	NUM
ejpam-84	152	45	and	and	CCONJ
ejpam-84	152	46	dqm(t	dqm(t	PROPN
ejpam-84	152	47	)	)	PUNCT
ejpam-84	152	48	≤	≤	NOUN
ejpam-84	152	49	g(t	g(t	PROPN
ejpam-84	152	50	,	,	PUNCT
ejpam-84	152	51	m(t	m(t	NOUN
ejpam-84	152	52	)	)	PUNCT
ejpam-84	152	53	)	)	PUNCT
ejpam-84	152	54	,	,	PUNCT
ejpam-84	152	55	wherever	wherever	SCONJ
ejpam-84	152	56	m(t	m(t	NOUN
ejpam-84	152	57	)	)	PUNCT
ejpam-84	152	58	>	>	X
ejpam-84	152	59	0	0	NUM
ejpam-84	152	60	,	,	PUNCT
ejpam-84	152	61	then	then	ADV
ejpam-84	152	62	m(t	m(t	NOUN
ejpam-84	152	63	)	)	PUNCT
ejpam-84	152	64	≤	≤	NOUN
ejpam-84	152	65	0	0	NUM
ejpam-84	153	1	for	for	ADP
ejpam-84	153	2	t0	t0	PROPN
ejpam-84	153	3	≤	≤	PROPN
ejpam-84	153	4	t	t	PROPN
ejpam-84	153	5	<	<	X
ejpam-84	153	6	∞.	∞.	PROPN
ejpam-84	153	7	we	we	PRON
ejpam-84	153	8	are	be	AUX
ejpam-84	153	9	now	now	ADV
ejpam-84	153	10	in	in	ADP
ejpam-84	153	11	a	a	DET
ejpam-84	153	12	position	position	NOUN
ejpam-84	153	13	to	to	PART
ejpam-84	153	14	prove	prove	VERB
ejpam-84	153	15	the	the	DET
ejpam-84	153	16	following	following	ADJ
ejpam-84	153	17	result	result	NOUN
ejpam-84	153	18	on	on	ADP
ejpam-84	153	19	flow	flow	NOUN
ejpam-84	153	20	invariance	invariance	NOUN
ejpam-84	153	21	of	of	ADP
ejpam-84	153	22	f	f	PROPN
ejpam-84	153	23	.	.	PUNCT
ejpam-84	154	1	theorem	theorem	VERB
ejpam-84	154	2	3.1	3.1	NUM
ejpam-84	154	3	:	:	PUNCT
ejpam-84	154	4	let	let	VERB
ejpam-84	154	5	f	f	PROPN
ejpam-84	154	6	⊂	⊂	PROPN
ejpam-84	154	7	e	e	X
ejpam-84	154	8	be	be	AUX
ejpam-84	154	9	a	a	DET
ejpam-84	154	10	closed	closed	ADJ
ejpam-84	154	11	and	and	CCONJ
ejpam-84	154	12	distance	distance	NOUN
ejpam-84	154	13	set	set	NOUN
ejpam-84	154	14	.	.	PUNCT
ejpam-84	155	1	assume	assume	VERB
ejpam-84	155	2	further	far	ADV
ejpam-84	155	3	that	that	SCONJ
ejpam-84	155	4	(	(	PUNCT
ejpam-84	155	5	i	i	NOUN
ejpam-84	155	6	)	)	PUNCT
ejpam-84	155	7	limh→0	limh→0	PROPN
ejpam-84	155	8	1	1	NUM
ejpam-84	155	9	hq	hq	NOUN
ejpam-84	155	10	d[x−	d[x−	PROPN
ejpam-84	155	11	hqf(t	hqf(t	PROPN
ejpam-84	155	12	,	,	PUNCT
ejpam-84	155	13	x	x	NOUN
ejpam-84	155	14	)	)	PUNCT
ejpam-84	155	15	,	,	PUNCT
ejpam-84	155	16	f	f	X
ejpam-84	155	17	]	]	X
ejpam-84	156	1	=	=	PUNCT
ejpam-84	156	2	0	0	NUM
ejpam-84	156	3	,	,	PUNCT
ejpam-84	156	4	t	t	PROPN
ejpam-84	156	5	∈	∈	PROPN
ejpam-84	157	1	[	[	X
ejpam-84	157	2	t0,∞	t0,∞	NUM
ejpam-84	157	3	)	)	PUNCT
ejpam-84	157	4	,	,	PUNCT
ejpam-84	157	5	x	x	PUNCT
ejpam-84	157	6	∈	∈	NOUN
ejpam-84	157	7	ϕf	ϕf	NOUN
ejpam-84	157	8	(	(	PUNCT
ejpam-84	157	9	ii	ii	NOUN
ejpam-84	157	10	)	)	PUNCT
ejpam-84	157	11	|f(t	|f(t	PROPN
ejpam-84	157	12	,	,	PUNCT
ejpam-84	157	13	x)−	x)−	PROPN
ejpam-84	157	14	f(t	f(t	PROPN
ejpam-84	157	15	,	,	PUNCT
ejpam-84	157	16	y)|	y)|	PROPN
ejpam-84	157	17	≤	≤	PROPN
ejpam-84	157	18	g(t	g(t	PROPN
ejpam-84	157	19	,	,	PUNCT
ejpam-84	157	20	|x−	|x−	NOUN
ejpam-84	157	21	y|	y|	PROPN
ejpam-84	157	22	)	)	PUNCT
ejpam-84	157	23	,	,	PUNCT
ejpam-84	158	1	x	x	PUNCT
ejpam-84	158	2	∈	∈	PROPN
ejpam-84	158	3	e	e	NOUN
ejpam-84	158	4	−	−	PROPN
ejpam-84	159	1	f	f	X
ejpam-84	159	2	,	,	PUNCT
ejpam-84	159	3	y	y	PROPN
ejpam-84	159	4	∈	∈	PROPN
ejpam-84	160	1	ϕf	ϕf	INTJ
ejpam-84	160	2	,	,	PUNCT
ejpam-84	160	3	where	where	SCONJ
ejpam-84	160	4	g(t	g(t	PROPN
ejpam-84	160	5	,	,	PUNCT
ejpam-84	160	6	u	u	NOUN
ejpam-84	160	7	)	)	PUNCT
ejpam-84	160	8	is	be	AUX
ejpam-84	160	9	a	a	DET
ejpam-84	160	10	uniqueness	uniqueness	NOUN
ejpam-84	160	11	function	function	NOUN
ejpam-84	160	12	.	.	PUNCT
ejpam-84	161	1	then	then	ADV
ejpam-84	161	2	f	f	PROPN
ejpam-84	161	3	is	be	AUX
ejpam-84	161	4	flow	flow	NOUN
ejpam-84	161	5	invariant	invariant	ADJ
ejpam-84	161	6	with	with	ADP
ejpam-84	161	7	respect	respect	NOUN
ejpam-84	161	8	to	to	ADP
ejpam-84	161	9	f	f	PROPN
ejpam-84	161	10	.	.	PUNCT
ejpam-84	162	1	proof	proof	NOUN
ejpam-84	162	2	:	:	PUNCT
ejpam-84	162	3	let	let	VERB
ejpam-84	162	4	x(t	x(t	PROPN
ejpam-84	162	5	)	)	PUNCT
ejpam-84	162	6	be	be	VERB
ejpam-84	162	7	a	a	DET
ejpam-84	162	8	solution	solution	NOUN
ejpam-84	162	9	of	of	ADP
ejpam-84	162	10	(	(	PUNCT
ejpam-84	162	11	3.4	3.4	NUM
ejpam-84	162	12	)	)	PUNCT
ejpam-84	162	13	.	.	PUNCT
ejpam-84	163	1	suppose	suppose	VERB
ejpam-84	163	2	that	that	SCONJ
ejpam-84	163	3	x(t	x(t	PROPN
ejpam-84	163	4	)	)	PUNCT
ejpam-84	163	5	∈	∈	PROPN
ejpam-84	163	6	f	f	PROPN
ejpam-84	163	7	for	for	ADP
ejpam-84	163	8	t0	t0	PROPN
ejpam-84	163	9	≤	≤	PROPN
ejpam-84	163	10	t	t	PROPN
ejpam-84	163	11	≤	≤	NUM
ejpam-84	163	12	t0	t0	PROPN
ejpam-84	163	13	+	+	CCONJ
ejpam-84	163	14	a	a	X
ejpam-84	163	15	,	,	PUNCT
ejpam-84	163	16	where	where	SCONJ
ejpam-84	163	17	t0	t0	PROPN
ejpam-84	163	18	+	+	CCONJ
ejpam-84	163	19	a	a	DET
ejpam-84	163	20	<	<	X
ejpam-84	163	21	∞	∞	PROPN
ejpam-84	163	22	is	be	AUX
ejpam-84	163	23	maximal	maximal	ADJ
ejpam-84	163	24	,	,	PUNCT
ejpam-84	163	25	that	that	ADV
ejpam-84	163	26	is	be	AUX
ejpam-84	163	27	,	,	PUNCT
ejpam-84	163	28	x(t	x(t	PROPN
ejpam-84	163	29	)	)	PUNCT
ejpam-84	163	30	leaves	leave	VERB
ejpam-84	163	31	the	the	DET
ejpam-84	163	32	set	set	NOUN
ejpam-84	163	33	f	f	PROPN
ejpam-84	163	34	at	at	ADP
ejpam-84	163	35	t	t	PROPN
ejpam-84	163	36	=	=	SYM
ejpam-84	163	37	t0	t0	PROPN
ejpam-84	163	38	+	+	CCONJ
ejpam-84	163	39	a	a	PRON
ejpam-84	163	40	for	for	ADP
ejpam-84	163	41	the	the	DET
ejpam-84	163	42	first	first	ADJ
ejpam-84	163	43	time	time	NOUN
ejpam-84	163	44	.	.	PUNCT
ejpam-84	164	1	let	let	VERB
ejpam-84	164	2	t1	t1	PROPN
ejpam-84	164	3	∈	∈	PROPN
ejpam-84	164	4	(	(	PUNCT
ejpam-84	164	5	t0	t0	NOUN
ejpam-84	164	6	+	+	CCONJ
ejpam-84	164	7	a,∞	a,∞	PROPN
ejpam-84	164	8	)	)	PUNCT
ejpam-84	164	9	and	and	CCONJ
ejpam-84	164	10	x(t1	x(t1	NOUN
ejpam-84	164	11	)	)	PUNCT
ejpam-84	165	1	6∈	6∈	PROPN
ejpam-84	165	2	f	f	PROPN
ejpam-84	166	1	and	and	CCONJ
ejpam-84	166	2	let	let	VERB
ejpam-84	166	3	y0	y0	PRON
ejpam-84	166	4	∈	∈	NOUN
ejpam-84	166	5	ϕf	ϕf	INTJ
ejpam-84	166	6	be	be	AUX
ejpam-84	166	7	such	such	ADJ
ejpam-84	166	8	that	that	DET
ejpam-84	166	9	d(x(t1	d(x(t1	PROPN
ejpam-84	166	10	)	)	PUNCT
ejpam-84	166	11	,	,	PUNCT
ejpam-84	166	12	f	f	PROPN
ejpam-84	166	13	)	)	PUNCT
ejpam-84	167	1	=	=	SYM
ejpam-84	167	2	|x(t1	|x(t1	NOUN
ejpam-84	167	3	)	)	PUNCT
ejpam-84	168	1	−	−	PROPN
ejpam-84	168	2	y0|	y0|	PROPN
ejpam-84	168	3	.	.	PUNCT
ejpam-84	169	1	set	set	PROPN
ejpam-84	169	2	v.lakshmikantham	v.lakshmikantham	PROPN
ejpam-84	169	3	,	,	PUNCT
ejpam-84	169	4	j.devi	j.devi	PROPN
ejpam-84	169	5	/	/	SYM
ejpam-84	169	6	eur	eur	PROPN
ejpam-84	169	7	.	.	PUNCT
ejpam-84	170	1	j.	j.	PROPN
ejpam-84	170	2	pure	pure	PROPN
ejpam-84	170	3	appl	appl	PROPN
ejpam-84	170	4	.	.	PROPN
ejpam-84	170	5	math	math	PROPN
ejpam-84	170	6	,	,	PUNCT
ejpam-84	170	7	1	1	NUM
ejpam-84	170	8	(	(	PUNCT
ejpam-84	170	9	2008	2008	NUM
ejpam-84	170	10	)	)	PUNCT
ejpam-84	170	11	,	,	PUNCT
ejpam-84	170	12	(	(	PUNCT
ejpam-84	170	13	38	38	NUM
ejpam-84	170	14	-	-	SYM
ejpam-84	170	15	45	45	NUM
ejpam-84	170	16	)	)	PUNCT
ejpam-84	170	17	44	44	NUM
ejpam-84	170	18	for	for	ADP
ejpam-84	170	19	t	t	PROPN
ejpam-84	170	20	∈	∈	PROPN
ejpam-84	171	1	[	[	X
ejpam-84	171	2	t0,∞	t0,∞	NUM
ejpam-84	171	3	)	)	PUNCT
ejpam-84	171	4	m(t	m(t	NOUN
ejpam-84	171	5	)	)	PUNCT
ejpam-84	171	6	=	=	SYM
ejpam-84	171	7	d[x(t	d[x(t	NOUN
ejpam-84	171	8	)	)	PUNCT
ejpam-84	171	9	,	,	PUNCT
ejpam-84	171	10	f	f	X
ejpam-84	171	11	]	]	PUNCT
ejpam-84	171	12	and	and	CCONJ
ejpam-84	171	13	v(t	v(t	NOUN
ejpam-84	171	14	)	)	PUNCT
ejpam-84	171	15	=	=	SYM
ejpam-84	171	16	|x(t	|x(t	PROPN
ejpam-84	171	17	)	)	PUNCT
ejpam-84	171	18	−	−	PROPN
ejpam-84	171	19	y0|	y0|	PROPN
ejpam-84	171	20	.	.	PUNCT
ejpam-84	172	1	for	for	ADP
ejpam-84	172	2	sufficiently	sufficiently	ADV
ejpam-84	172	3	small	small	ADJ
ejpam-84	172	4	h	h	NOUN
ejpam-84	172	5	>	>	X
ejpam-84	172	6	0	0	NUM
ejpam-84	172	7	,	,	PUNCT
ejpam-84	172	8	letting	let	VERB
ejpam-84	172	9	x	x	PUNCT
ejpam-84	172	10	=	=	PUNCT
ejpam-84	172	11	x(t1	x(t1	NOUN
ejpam-84	172	12	)	)	PUNCT
ejpam-84	172	13	,	,	PUNCT
ejpam-84	172	14	we	we	PRON
ejpam-84	172	15	have	have	VERB
ejpam-84	172	16	d[s(t1	d[s(t1	NOUN
ejpam-84	172	17	,	,	PUNCT
ejpam-84	172	18	h	h	NOUN
ejpam-84	172	19	,	,	PUNCT
ejpam-84	172	20	q	q	NOUN
ejpam-84	172	21	)	)	PUNCT
ejpam-84	172	22	,	,	PUNCT
ejpam-84	172	23	f	f	X
ejpam-84	172	24	]	]	PUNCT
ejpam-84	172	25	≥	≥	PROPN
ejpam-84	172	26	d[x−	d[x−	NUM
ejpam-84	172	27	hqf(t1	hqf(t1	PROPN
ejpam-84	172	28	,	,	PUNCT
ejpam-84	172	29	x	x	NOUN
ejpam-84	172	30	)	)	PUNCT
ejpam-84	172	31	,	,	PUNCT
ejpam-84	172	32	f	f	X
ejpam-84	173	1	]	]	X
ejpam-84	173	2	−	−	X
ejpam-84	173	3	ε(hq	ε(hq	NOUN
ejpam-84	173	4	)	)	PUNCT
ejpam-84	173	5	=	=	PUNCT
ejpam-84	174	1	d[x−	d[x−	NUM
ejpam-84	174	2	y0	y0	PROPN
ejpam-84	174	3	−	−	PROPN
ejpam-84	174	4	hq(f(t1	hq(f(t1	PROPN
ejpam-84	174	5	,	,	PUNCT
ejpam-84	174	6	x)−	x)−	PROPN
ejpam-84	174	7	f(t1	f(t1	NOUN
ejpam-84	174	8	,	,	PUNCT
ejpam-84	174	9	y0	y0	NOUN
ejpam-84	174	10	)	)	PUNCT
ejpam-84	174	11	)	)	PUNCT
ejpam-84	174	12	,	,	PUNCT
ejpam-84	174	13	f	f	X
ejpam-84	174	14	]	]	X
ejpam-84	174	15	−	−	PROPN
ejpam-84	174	16	d[x−	d[x−	SYM
ejpam-84	174	17	y0	y0	PROPN
ejpam-84	174	18	−	−	PROPN
ejpam-84	174	19	hq(f(t1	hq(f(t1	NOUN
ejpam-84	174	20	,	,	PUNCT
ejpam-84	174	21	x)−	x)−	PROPN
ejpam-84	174	22	f(t1	f(t1	NOUN
ejpam-84	174	23	,	,	PUNCT
ejpam-84	174	24	y0	y0	NOUN
ejpam-84	174	25	)	)	PUNCT
ejpam-84	174	26	)	)	PUNCT
ejpam-84	174	27	,	,	PUNCT
ejpam-84	174	28	f	f	X
ejpam-84	174	29	]	]	PUNCT
ejpam-84	175	1	+	+	CCONJ
ejpam-84	175	2	d[x−	d[x−	NUM
ejpam-84	175	3	hqf(t1	hqf(t1	PROPN
ejpam-84	175	4	,	,	PUNCT
ejpam-84	175	5	x	x	NOUN
ejpam-84	175	6	)	)	PUNCT
ejpam-84	175	7	,	,	PUNCT
ejpam-84	175	8	f	f	X
ejpam-84	175	9	]	]	X
ejpam-84	175	10	−	−	PROPN
ejpam-84	175	11	ε(hq	ε(hq	NOUN
ejpam-84	175	12	)	)	PUNCT
ejpam-84	175	13	≥	≥	NOUN
ejpam-84	175	14	d[x−	d[x−	NUM
ejpam-84	175	15	y0	y0	PROPN
ejpam-84	175	16	−	−	PROPN
ejpam-84	175	17	hq(f(t1	hq(f(t1	NOUN
ejpam-84	175	18	,	,	PUNCT
ejpam-84	175	19	x)−	x)−	PROPN
ejpam-84	175	20	f(t1	f(t1	NOUN
ejpam-84	175	21	,	,	PUNCT
ejpam-84	175	22	y0	y0	NOUN
ejpam-84	175	23	)	)	PUNCT
ejpam-84	175	24	)	)	PUNCT
ejpam-84	175	25	,	,	PUNCT
ejpam-84	175	26	f	f	X
ejpam-84	175	27	]	]	X
ejpam-84	175	28	−	−	PROPN
ejpam-84	175	29	d[y0	d[y0	NOUN
ejpam-84	175	30	−	−	PROPN
ejpam-84	175	31	hqf(t1	hqf(t1	PROPN
ejpam-84	175	32	,	,	PUNCT
ejpam-84	175	33	y0	y0	PROPN
ejpam-84	175	34	,	,	PUNCT
ejpam-84	175	35	f	f	NOUN
ejpam-84	175	36	)	)	PUNCT
ejpam-84	175	37	]	]	X
ejpam-84	175	38	−	−	PART
ejpam-84	175	39	ε(hq	ε(hq	NOUN
ejpam-84	175	40	)	)	PUNCT
ejpam-84	175	41	≥	≥	NOUN
ejpam-84	175	42	−hq|f(t1	−hq|f(t1	PROPN
ejpam-84	175	43	,	,	PUNCT
ejpam-84	175	44	x)−	x)−	PROPN
ejpam-84	175	45	f(t1	f(t1	NOUN
ejpam-84	175	46	,	,	PUNCT
ejpam-84	175	47	y0)|	y0)|	NOUN
ejpam-84	175	48	−	−	PROPN
ejpam-84	175	49	ε(hq	ε(hq	NOUN
ejpam-84	175	50	)	)	PUNCT
ejpam-84	175	51	+	+	CCONJ
ejpam-84	175	52	d[x	d[x	PROPN
ejpam-84	175	53	,	,	PUNCT
ejpam-84	175	54	f	f	X
ejpam-84	175	55	]	]	PUNCT
ejpam-84	175	56	.	.	PUNCT
ejpam-84	176	1	(	(	PUNCT
ejpam-84	176	2	3.6	3.6	NUM
ejpam-84	176	3	)	)	PUNCT
ejpam-84	176	4	since	since	SCONJ
ejpam-84	176	5	m(t1	m(t1	NOUN
ejpam-84	176	6	)	)	PUNCT
ejpam-84	176	7	=	=	SYM
ejpam-84	176	8	v(t1	v(t1	NOUN
ejpam-84	176	9	)	)	PUNCT
ejpam-84	176	10	>	>	SYM
ejpam-84	176	11	0	0	PUNCT
ejpam-84	176	12	and	and	CCONJ
ejpam-84	176	13	m(t1	m(t1	NOUN
ejpam-84	176	14	)	)	PUNCT
ejpam-84	176	15	=	=	SYM
ejpam-84	176	16	d[x	d[x	PROPN
ejpam-84	176	17	,	,	PUNCT
ejpam-84	176	18	f	f	X
ejpam-84	176	19	]	]	X
ejpam-84	176	20	=	=	PUNCT
ejpam-84	177	1	|x(t1)−	|x(t1)−	PROPN
ejpam-84	177	2	y0|	y0|	PROPN
ejpam-84	177	3	,	,	PUNCT
ejpam-84	177	4	we	we	PRON
ejpam-84	177	5	find	find	VERB
ejpam-84	177	6	|x(t1)−	|x(t1)−	PROPN
ejpam-84	177	7	y0|	y0|	PROPN
ejpam-84	177	8	−	−	PROPN
ejpam-84	178	1	d[s(t1	d[s(t1	PROPN
ejpam-84	178	2	,	,	PUNCT
ejpam-84	178	3	h	h	NOUN
ejpam-84	178	4	,	,	PUNCT
ejpam-84	178	5	q	q	NOUN
ejpam-84	178	6	)	)	PUNCT
ejpam-84	178	7	,	,	PUNCT
ejpam-84	178	8	f	f	X
ejpam-84	178	9	]	]	PUNCT
ejpam-84	178	10	≤	≤	PROPN
ejpam-84	178	11	hq|f(t1	hq|f(t1	PROPN
ejpam-84	178	12	,	,	PUNCT
ejpam-84	178	13	x)−	x)−	PROPN
ejpam-84	178	14	f(t1	f(t1	NOUN
ejpam-84	178	15	,	,	PUNCT
ejpam-84	178	16	y0)|	y0)|	NOUN
ejpam-84	178	17	−	−	PROPN
ejpam-84	178	18	ε(hq	ε(hq	NOUN
ejpam-84	178	19	)	)	PUNCT
ejpam-84	178	20	,	,	PUNCT
ejpam-84	178	21	which	which	PRON
ejpam-84	178	22	yields	yield	VERB
ejpam-84	178	23	the	the	DET
ejpam-84	178	24	inequality	inequality	NOUN
ejpam-84	178	25	dqm(t1	dqm(t1	NOUN
ejpam-84	178	26	)	)	PUNCT
ejpam-84	178	27	≤	≤	NOUN
ejpam-84	178	28	g(t1,m(t1	g(t1,m(t1	PROPN
ejpam-84	178	29	)	)	PUNCT
ejpam-84	178	30	)	)	PUNCT
ejpam-84	178	31	.	.	PUNCT
ejpam-84	179	1	this	this	PRON
ejpam-84	179	2	gives	give	VERB
ejpam-84	179	3	,	,	PUNCT
ejpam-84	179	4	in	in	ADP
ejpam-84	179	5	view	view	NOUN
ejpam-84	179	6	of	of	ADP
ejpam-84	179	7	the	the	DET
ejpam-84	179	8	facts	fact	NOUN
ejpam-84	179	9	that	that	SCONJ
ejpam-84	179	10	g	g	PROPN
ejpam-84	179	11	is	be	AUX
ejpam-84	179	12	the	the	DET
ejpam-84	179	13	uniqueness	uniqueness	NOUN
ejpam-84	179	14	function	function	NOUN
ejpam-84	179	15	and	and	CCONJ
ejpam-84	179	16	m(t)(t−	m(t)(t−	NOUN
ejpam-84	179	17	t0)1−q|t	t0)1−q|t	NUM
ejpam-84	179	18	=	=	SYM
ejpam-84	179	19	t0	t0	NOUN
ejpam-84	179	20	=	=	SYM
ejpam-84	179	21	0	0	PROPN
ejpam-84	179	22	,	,	PUNCT
ejpam-84	179	23	the	the	DET
ejpam-84	179	24	relation	relation	NOUN
ejpam-84	179	25	m(t	m(t	NOUN
ejpam-84	179	26	)	)	PUNCT
ejpam-84	179	27	≤	≤	NOUN
ejpam-84	179	28	0	0	NUM
ejpam-84	179	29	,	,	PUNCT
ejpam-84	179	30	t0	t0	PROPN
ejpam-84	179	31	≤	≤	PROPN
ejpam-84	179	32	t	t	PROPN
ejpam-84	179	33	<	<	X
ejpam-84	179	34	∞.	∞.	PROPN
ejpam-84	179	35	but	but	CCONJ
ejpam-84	179	36	,	,	PUNCT
ejpam-84	179	37	d[x(t1	d[x(t1	PROPN
ejpam-84	179	38	)	)	PUNCT
ejpam-84	179	39	,	,	PUNCT
ejpam-84	179	40	f	f	X
ejpam-84	179	41	]	]	X
ejpam-84	180	1	=	=	SYM
ejpam-84	180	2	m(t1	m(t1	NOUN
ejpam-84	180	3	)	)	PUNCT
ejpam-84	180	4	>	>	X
ejpam-84	180	5	0	0	NUM
ejpam-84	180	6	,	,	PUNCT
ejpam-84	180	7	which	which	PRON
ejpam-84	180	8	is	be	AUX
ejpam-84	180	9	a	a	DET
ejpam-84	180	10	contradiction	contradiction	NOUN
ejpam-84	180	11	.	.	PUNCT
ejpam-84	181	1	hence	hence	ADV
ejpam-84	181	2	the	the	DET
ejpam-84	181	3	set	set	NOUN
ejpam-84	181	4	f	f	PROPN
ejpam-84	181	5	is	be	AUX
ejpam-84	181	6	flow	flow	ADJ
ejpam-84	181	7	invariant	invariant	ADJ
ejpam-84	181	8	relative	relative	NOUN
ejpam-84	181	9	to	to	ADP
ejpam-84	181	10	f(t	f(t	PROPN
ejpam-84	181	11	,	,	PUNCT
ejpam-84	181	12	x	x	NOUN
ejpam-84	181	13	)	)	PUNCT
ejpam-84	181	14	and	and	CCONJ
ejpam-84	181	15	the	the	DET
ejpam-84	181	16	proof	proof	NOUN
ejpam-84	181	17	is	be	AUX
ejpam-84	181	18	complete	complete	ADJ
ejpam-84	181	19	.	.	PUNCT
ejpam-84	182	1	we	we	PRON
ejpam-84	182	2	shall	shall	AUX
ejpam-84	182	3	next	next	ADV
ejpam-84	182	4	develop	develop	VERB
ejpam-84	182	5	the	the	DET
ejpam-84	182	6	theory	theory	NOUN
ejpam-84	182	7	fractional	fractional	ADJ
ejpam-84	182	8	differential	differential	NOUN
ejpam-84	182	9	inequalities	inequality	NOUN
ejpam-84	182	10	.	.	PUNCT
ejpam-84	183	1	to	to	PART
ejpam-84	183	2	do	do	VERB
ejpam-84	183	3	this	this	PRON
ejpam-84	183	4	,	,	PUNCT
ejpam-84	183	5	we	we	PRON
ejpam-84	183	6	need	need	VERB
ejpam-84	183	7	the	the	DET
ejpam-84	183	8	concept	concept	NOUN
ejpam-84	183	9	of	of	ADP
ejpam-84	183	10	a	a	DET
ejpam-84	183	11	cone	cone	NOUN
ejpam-84	183	12	which	which	PRON
ejpam-84	183	13	induces	induce	VERB
ejpam-84	183	14	a	a	DET
ejpam-84	183	15	partial	partial	ADJ
ejpam-84	183	16	order	order	NOUN
ejpam-84	183	17	in	in	ADP
ejpam-84	183	18	e.	e.	PROPN
ejpam-84	183	19	a	a	DET
ejpam-84	183	20	proper	proper	ADJ
ejpam-84	183	21	subset	subset	NOUN
ejpam-84	183	22	k	k	PROPN
ejpam-84	183	23	of	of	ADP
ejpam-84	183	24	e	e	PROPN
ejpam-84	183	25	is	be	AUX
ejpam-84	183	26	said	say	VERB
ejpam-84	183	27	to	to	PART
ejpam-84	183	28	be	be	AUX
ejpam-84	183	29	a	a	DET
ejpam-84	183	30	cone	cone	NOUN
ejpam-84	183	31	if	if	SCONJ
ejpam-84	183	32	λk	λk	ADP
ejpam-84	183	33	⊂	⊂	PROPN
ejpam-84	183	34	k	k	PROPN
ejpam-84	183	35	,	,	PUNCT
ejpam-84	183	36	λ	λ	X
ejpam-84	183	37	≥	≥	NOUN
ejpam-84	183	38	0	0	NUM
ejpam-84	183	39	,	,	PUNCT
ejpam-84	183	40	k	k	PROPN
ejpam-84	184	1	+	+	CCONJ
ejpam-84	184	2	k	k	PROPN
ejpam-84	184	3	⊂	⊂	PROPN
ejpam-84	184	4	k	k	PROPN
ejpam-84	184	5	,	,	PUNCT
ejpam-84	184	6	k	k	PROPN
ejpam-84	184	7	=	=	SYM
ejpam-84	184	8	k	k	PROPN
ejpam-84	184	9	and	and	CCONJ
ejpam-84	184	10	k	k	PROPN
ejpam-84	184	11	∩	∩	PROPN
ejpam-84	184	12	{	{	PUNCT
ejpam-84	184	13	−k	−k	ADJ
ejpam-84	184	14	}	}	PUNCT
ejpam-84	184	15	=	=	SYM
ejpam-84	184	16	0	0	NUM
ejpam-84	184	17	,	,	PUNCT
ejpam-84	184	18	where	where	SCONJ
ejpam-84	184	19	0	0	NUM
ejpam-84	184	20	denotes	denote	VERB
ejpam-84	184	21	the	the	DET
ejpam-84	184	22	null	null	ADJ
ejpam-84	184	23	element	element	NOUN
ejpam-84	184	24	of	of	ADP
ejpam-84	184	25	e	e	PROPN
ejpam-84	184	26	and	and	CCONJ
ejpam-84	184	27	k	k	PROPN
ejpam-84	184	28	is	be	AUX
ejpam-84	184	29	the	the	DET
ejpam-84	184	30	closure	closure	NOUN
ejpam-84	184	31	of	of	ADP
ejpam-84	184	32	k.	k.	PROPN
ejpam-84	184	33	let	let	VERB
ejpam-84	184	34	k0	k0	PROPN
ejpam-84	184	35	denote	denote	VERB
ejpam-84	184	36	the	the	DET
ejpam-84	184	37	interior	interior	NOUN
ejpam-84	184	38	of	of	ADP
ejpam-84	184	39	k	k	PROPN
ejpam-84	184	40	and	and	CCONJ
ejpam-84	184	41	assume	assume	VERB
ejpam-84	184	42	that	that	SCONJ
ejpam-84	184	43	k0	k0	PROPN
ejpam-84	184	44	is	be	AUX
ejpam-84	184	45	nonempty	nonempty	ADJ
ejpam-84	184	46	.	.	PUNCT
ejpam-84	185	1	the	the	DET
ejpam-84	185	2	cone	cone	NOUN
ejpam-84	185	3	k	k	PROPN
ejpam-84	185	4	induces	induce	VERB
ejpam-84	185	5	the	the	DET
ejpam-84	185	6	order	order	NOUN
ejpam-84	185	7	relations	relation	NOUN
ejpam-84	185	8	in	in	ADP
ejpam-84	185	9	e	e	NOUN
ejpam-84	185	10	defined	define	VERB
ejpam-84	185	11	by	by	ADP
ejpam-84	185	12	x	x	SYM
ejpam-84	185	13	≤	≤	PROPN
ejpam-84	185	14	y	y	PROPN
ejpam-84	185	15	iff	iff	PROPN
ejpam-84	185	16	y	y	PROPN
ejpam-84	185	17	−	−	PROPN
ejpam-84	185	18	x	x	SYM
ejpam-84	185	19	∈	∈	PROPN
ejpam-84	185	20	k	k	PROPN
ejpam-84	185	21	and	and	CCONJ
ejpam-84	185	22	x	x	X
ejpam-84	185	23	<	<	X
ejpam-84	185	24	y	y	PROPN
ejpam-84	185	25	iff	iff	PROPN
ejpam-84	185	26	y	y	PROPN
ejpam-84	185	27	−	−	PROPN
ejpam-84	185	28	k	k	PROPN
ejpam-84	185	29	∈	∈	PROPN
ejpam-84	185	30	k0	k0	PROPN
ejpam-84	185	31	.	.	PUNCT
ejpam-84	186	1	let	let	VERB
ejpam-84	186	2	k∗	k∗	PROPN
ejpam-84	186	3	be	be	AUX
ejpam-84	186	4	the	the	DET
ejpam-84	186	5	set	set	NOUN
ejpam-84	186	6	of	of	ADP
ejpam-84	186	7	all	all	DET
ejpam-84	186	8	continuous	continuous	ADJ
ejpam-84	186	9	linear	linear	NOUN
ejpam-84	186	10	functionals	functional	NOUN
ejpam-84	186	11	c	c	NOUN
ejpam-84	186	12	on	on	ADP
ejpam-84	186	13	e	e	ADP
ejpam-84	186	14	such	such	ADJ
ejpam-84	186	15	that	that	DET
ejpam-84	186	16	cx	cx	PROPN
ejpam-84	186	17	≥	≥	NOUN
ejpam-84	186	18	0	0	NUM
ejpam-84	186	19	for	for	ADP
ejpam-84	186	20	all	all	DET
ejpam-84	186	21	x	x	SYM
ejpam-84	186	22	∈	∈	PROPN
ejpam-84	186	23	k	k	NOUN
ejpam-84	186	24	and	and	CCONJ
ejpam-84	186	25	let	let	VERB
ejpam-84	186	26	k∗0	k∗0	NOUN
ejpam-84	186	27	be	be	AUX
ejpam-84	186	28	the	the	DET
ejpam-84	186	29	set	set	NOUN
ejpam-84	186	30	such	such	ADJ
ejpam-84	186	31	that	that	DET
ejpam-84	186	32	cx	cx	PROPN
ejpam-84	186	33	>	>	X
ejpam-84	186	34	0	0	PUNCT
ejpam-84	187	1	for	for	ADP
ejpam-84	187	2	all	all	DET
ejpam-84	187	3	x	x	PROPN
ejpam-84	187	4	∈	∈	PROPN
ejpam-84	187	5	k0	k0	PROPN
ejpam-84	187	6	.	.	PUNCT
ejpam-84	188	1	a	a	DET
ejpam-84	188	2	function	function	NOUN
ejpam-84	188	3	f	f	NOUN
ejpam-84	188	4	:	:	PUNCT
ejpam-84	188	5	e	e	X
ejpam-84	188	6	→	→	PUNCT
ejpam-84	188	7	e	e	X
ejpam-84	188	8	is	be	AUX
ejpam-84	188	9	said	say	VERB
ejpam-84	188	10	to	to	PART
ejpam-84	188	11	be	be	AUX
ejpam-84	188	12	quasimonotone	quasimonotone	NOUN
ejpam-84	188	13	nondecreasing	nondecrease	VERB
ejpam-84	188	14	if	if	SCONJ
ejpam-84	188	15	x	x	PROPN
ejpam-84	188	16	≤	≤	ADJ
ejpam-84	188	17	y	y	NOUN
ejpam-84	188	18	and	and	CCONJ
ejpam-84	188	19	cx	cx	PROPN
ejpam-84	189	1	=	=	PUNCT
ejpam-84	189	2	cy	cy	PROPN
ejpam-84	189	3	for	for	ADP
ejpam-84	189	4	some	some	DET
ejpam-84	189	5	c	c	NOUN
ejpam-84	189	6	∈	∈	PROPN
ejpam-84	189	7	k∗0	k∗0	NOUN
ejpam-84	189	8	,	,	PUNCT
ejpam-84	189	9	then	then	ADV
ejpam-84	189	10	cf(x	cf(x	NOUN
ejpam-84	189	11	)	)	PUNCT
ejpam-84	189	12	≤	≤	NOUN
ejpam-84	189	13	cf(y	cf(y	NUM
ejpam-84	189	14	)	)	PUNCT
ejpam-84	189	15	.	.	PUNCT
ejpam-84	190	1	theorem	theorem	ADJ
ejpam-84	190	2	3.2	3.2	NUM
ejpam-84	190	3	:	:	PUNCT
ejpam-84	190	4	let	let	VERB
ejpam-84	190	5	k	k	PRON
ejpam-84	190	6	be	be	AUX
ejpam-84	190	7	a	a	DET
ejpam-84	190	8	cone	cone	NOUN
ejpam-84	190	9	with	with	ADP
ejpam-84	190	10	nonempty	nonempty	ADJ
ejpam-84	190	11	interior	interior	NOUN
ejpam-84	190	12	.	.	PUNCT
ejpam-84	191	1	assume	assume	VERB
ejpam-84	191	2	that	that	SCONJ
ejpam-84	191	3	(	(	PUNCT
ejpam-84	191	4	a	a	X
ejpam-84	191	5	)	)	PUNCT
ejpam-84	191	6	u	u	NOUN
ejpam-84	191	7	,	,	PUNCT
ejpam-84	191	8	v	v	PROPN
ejpam-84	191	9	∈	∈	PROPN
ejpam-84	191	10	c[r+	c[r+	NOUN
ejpam-84	191	11	,	,	PUNCT
ejpam-84	191	12	e	e	X
ejpam-84	191	13	]	]	X
ejpam-84	191	14	such	such	ADJ
ejpam-84	191	15	that	that	SCONJ
ejpam-84	191	16	dqv	dqv	PROPN
ejpam-84	191	17	,	,	PUNCT
ejpam-84	191	18	dqu	dqu	ADJ
ejpam-84	191	19	exist	exist	NOUN
ejpam-84	191	20	,	,	PUNCT
ejpam-84	191	21	f	f	PROPN
ejpam-84	191	22	∈	∈	PROPN
ejpam-84	191	23	c[r+×e	c[r+×e	NOUN
ejpam-84	191	24	,	,	PUNCT
ejpam-84	191	25	e	e	NOUN
ejpam-84	191	26	]	]	X
ejpam-84	191	27	and	and	CCONJ
ejpam-84	191	28	f(t	f(t	NOUN
ejpam-84	191	29	,	,	PUNCT
ejpam-84	191	30	x	x	X
ejpam-84	191	31	)	)	PUNCT
ejpam-84	191	32	is	be	AUX
ejpam-84	191	33	quasimonotone	quasimonotone	NOUN
ejpam-84	191	34	nondecreasing	nondecrease	VERB
ejpam-84	191	35	in	in	ADP
ejpam-84	191	36	x	x	PUNCT
ejpam-84	191	37	for	for	ADP
ejpam-84	191	38	each	each	DET
ejpam-84	191	39	t	t	PROPN
ejpam-84	191	40	∈	∈	PROPN
ejpam-84	191	41	r+	r+	ADV
ejpam-84	191	42	;	;	PUNCT
ejpam-84	191	43	(	(	PUNCT
ejpam-84	191	44	b	b	X
ejpam-84	191	45	)	)	PUNCT
ejpam-84	191	46	dqu(t)−	dqu(t)−	PROPN
ejpam-84	191	47	f(t	f(t	PROPN
ejpam-84	191	48	,	,	PUNCT
ejpam-84	191	49	u(t	u(t	NOUN
ejpam-84	191	50	)	)	PUNCT
ejpam-84	191	51	)	)	PUNCT
ejpam-84	192	1	<	<	X
ejpam-84	192	2	dqv(t)−	dqv(t)−	PROPN
ejpam-84	192	3	f(t	f(t	PROPN
ejpam-84	192	4	,	,	PUNCT
ejpam-84	192	5	v(t	v(t	NOUN
ejpam-84	192	6	)	)	PUNCT
ejpam-84	192	7	)	)	PUNCT
ejpam-84	192	8	,	,	PUNCT
ejpam-84	192	9	t	t	PROPN
ejpam-84	192	10	∈	∈	PROPN
ejpam-84	193	1	[	[	X
ejpam-84	193	2	t0,∞	t0,∞	NUM
ejpam-84	193	3	)	)	PUNCT
ejpam-84	193	4	.	.	PUNCT
ejpam-84	194	1	then	then	ADV
ejpam-84	194	2	v0	v0	VERB
ejpam-84	194	3	<	<	X
ejpam-84	194	4	w0	w0	PROPN
ejpam-84	194	5	implies	imply	VERB
ejpam-84	194	6	that	that	SCONJ
ejpam-84	194	7	u(t	u(t	NOUN
ejpam-84	194	8	)	)	PUNCT
ejpam-84	194	9	<	<	X
ejpam-84	194	10	v(t	v(t	NOUN
ejpam-84	194	11	)	)	PUNCT
ejpam-84	194	12	,	,	PUNCT
ejpam-84	194	13	t0	t0	PROPN
ejpam-84	194	14	≤	≤	PROPN
ejpam-84	194	15	t	t	PROPN
ejpam-84	194	16	<	<	X
ejpam-84	194	17	∞.	∞.	PROPN
ejpam-84	194	18	proof	proof	NOUN
ejpam-84	194	19	:	:	PUNCT
ejpam-84	194	20	suppose	suppose	VERB
ejpam-84	194	21	that	that	SCONJ
ejpam-84	194	22	the	the	DET
ejpam-84	194	23	assertion	assertion	NOUN
ejpam-84	194	24	of	of	ADP
ejpam-84	194	25	the	the	DET
ejpam-84	194	26	theorem	theorem	NOUN
ejpam-84	194	27	is	be	AUX
ejpam-84	194	28	false	false	ADJ
ejpam-84	194	29	.	.	PUNCT
ejpam-84	195	1	then	then	ADV
ejpam-84	195	2	there	there	PRON
ejpam-84	195	3	exists	exist	VERB
ejpam-84	195	4	a	a	DET
ejpam-84	195	5	t1	t1	NOUN
ejpam-84	195	6	>	>	X
ejpam-84	195	7	t0	t0	NOUN
ejpam-84	195	8	such	such	ADJ
ejpam-84	195	9	that	that	SCONJ
ejpam-84	195	10	v(t1)−	v(t1)−	PROPN
ejpam-84	195	11	u(t1	u(t1	NOUN
ejpam-84	195	12	)	)	PUNCT
ejpam-84	195	13	∈	∈	PROPN
ejpam-84	195	14	ϕk	ϕk	NOUN
ejpam-84	196	1	and	and	CCONJ
ejpam-84	196	2	v(t)−	v(t)−	PROPN
ejpam-84	196	3	u(t	u(t	PROPN
ejpam-84	196	4	)	)	PUNCT
ejpam-84	196	5	∈	∈	PROPN
ejpam-84	196	6	k0	k0	PROPN
ejpam-84	196	7	,	,	PUNCT
ejpam-84	196	8	t	t	PROPN
ejpam-84	196	9	∈	∈	PROPN
ejpam-84	197	1	[	[	X
ejpam-84	197	2	t0	t0	PROPN
ejpam-84	197	3	,	,	PUNCT
ejpam-84	197	4	t1	t1	NOUN
ejpam-84	197	5	)	)	PUNCT
ejpam-84	197	6	.	.	PUNCT
ejpam-84	198	1	by	by	ADP
ejpam-84	198	2	mazur	mazur	PROPN
ejpam-84	198	3	’s	’s	PART
ejpam-84	198	4	lemma	lemma	PROPN
ejpam-84	198	5	,	,	PUNCT
ejpam-84	198	6	there	there	PRON
ejpam-84	198	7	exists	exist	VERB
ejpam-84	198	8	a	a	DET
ejpam-84	198	9	c	c	PROPN
ejpam-84	198	10	∈	∈	PROPN
ejpam-84	198	11	k∗0	k∗0	NOUN
ejpam-84	198	12	with	with	ADP
ejpam-84	198	13	cv(t1)−cu(t1	cv(t1)−cu(t1	NOUN
ejpam-84	198	14	)	)	PUNCT
ejpam-84	199	1	=	=	PUNCT
ejpam-84	199	2	0	0	X
ejpam-84	199	3	.	.	X
ejpam-84	200	1	setting	set	VERB
ejpam-84	200	2	m(t	m(t	NOUN
ejpam-84	200	3	)	)	PUNCT
ejpam-84	200	4	=	=	PUNCT
ejpam-84	200	5	c(v(t)−u(t	c(v(t)−u(t	PROPN
ejpam-84	200	6	)	)	PUNCT
ejpam-84	200	7	)	)	PUNCT
ejpam-84	200	8	,	,	PUNCT
ejpam-84	200	9	we	we	PRON
ejpam-84	200	10	see	see	VERB
ejpam-84	200	11	that	that	SCONJ
ejpam-84	200	12	m(t	m(t	NOUN
ejpam-84	200	13	)	)	PUNCT
ejpam-84	200	14	>	>	X
ejpam-84	200	15	0	0	PUNCT
ejpam-84	201	1	for	for	ADP
ejpam-84	201	2	t0	t0	PROPN
ejpam-84	201	3	≤	≤	PROPN
ejpam-84	201	4	t	t	PROPN
ejpam-84	201	5	≤	≤	NUM
ejpam-84	201	6	t1	t1	NOUN
ejpam-84	201	7	and	and	CCONJ
ejpam-84	201	8	m(t1	m(t1	NOUN
ejpam-84	201	9	)	)	PUNCT
ejpam-84	201	10	=	=	SYM
ejpam-84	201	11	0	0	X
ejpam-84	201	12	.	.	PUNCT
ejpam-84	201	13	consequently	consequently	ADV
ejpam-84	201	14	,	,	PUNCT
ejpam-84	201	15	by	by	ADP
ejpam-84	201	16	lemma	lemma	PROPN
ejpam-84	201	17	2.1	2.1	NUM
ejpam-84	201	18	,	,	PUNCT
ejpam-84	201	19	we	we	PRON
ejpam-84	201	20	references	reference	VERB
ejpam-84	201	21	45	45	NUM
ejpam-84	201	22	get	get	NOUN
ejpam-84	201	23	dqm(t1	dqm(t1	NOUN
ejpam-84	201	24	)	)	PUNCT
ejpam-84	201	25	≤	≤	NOUN
ejpam-84	201	26	0	0	NUM
ejpam-84	201	27	.	.	PUNCT
ejpam-84	202	1	at	at	ADP
ejpam-84	202	2	t	t	PROPN
ejpam-84	202	3	=	=	SYM
ejpam-84	202	4	t1	t1	PROPN
ejpam-84	202	5	,	,	PUNCT
ejpam-84	202	6	we	we	PRON
ejpam-84	202	7	have	have	VERB
ejpam-84	202	8	u(t1	u(t1	NOUN
ejpam-84	202	9	)	)	PUNCT
ejpam-84	202	10	≤	≤	NOUN
ejpam-84	202	11	v(t1	v(t1	NOUN
ejpam-84	202	12	)	)	PUNCT
ejpam-84	202	13	and	and	CCONJ
ejpam-84	202	14	c(u(t1	c(u(t1	NOUN
ejpam-84	202	15	)	)	PUNCT
ejpam-84	202	16	)	)	PUNCT
ejpam-84	203	1	=	=	SYM
ejpam-84	203	2	c(v(t1	c(v(t1	PROPN
ejpam-84	203	3	)	)	PUNCT
ejpam-84	203	4	)	)	PUNCT
ejpam-84	203	5	.	.	PUNCT
ejpam-84	204	1	hence	hence	ADV
ejpam-84	204	2	using	use	VERB
ejpam-84	204	3	quasimonotone	quasimonotone	ADJ
ejpam-84	204	4	property	property	NOUN
ejpam-84	204	5	of	of	ADP
ejpam-84	204	6	f	f	PROPN
ejpam-84	204	7	and	and	CCONJ
ejpam-84	204	8	(	(	PUNCT
ejpam-84	204	9	b	b	NOUN
ejpam-84	204	10	)	)	PUNCT
ejpam-84	204	11	,	,	PUNCT
ejpam-84	204	12	it	it	PRON
ejpam-84	204	13	follows	follow	VERB
ejpam-84	204	14	that	that	SCONJ
ejpam-84	204	15	dqm(t1	dqm(t1	VERB
ejpam-84	204	16	)	)	PUNCT
ejpam-84	204	17	=	=	SYM
ejpam-84	204	18	c(dqv(t1)−dqu(t1	c(dqv(t1)−dqu(t1	NOUN
ejpam-84	204	19	)	)	PUNCT
ejpam-84	204	20	)	)	PUNCT
ejpam-84	204	21	>	>	X
ejpam-84	205	1	c(f(t1	c(f(t1	PROPN
ejpam-84	205	2	,	,	PUNCT
ejpam-84	205	3	v(t1))−	v(t1))−	NOUN
ejpam-84	205	4	f(t1	f(t1	NOUN
ejpam-84	205	5	,	,	PUNCT
ejpam-84	205	6	u(t1	u(t1	NOUN
ejpam-84	205	7	)	)	PUNCT
ejpam-84	205	8	)	)	PUNCT
ejpam-84	205	9	)	)	PUNCT
ejpam-84	205	10	≥	≥	NOUN
ejpam-84	205	11	0	0	NUM
ejpam-84	205	12	.	.	PUNCT
ejpam-84	206	1	this	this	DET
ejpam-84	206	2	contradiction	contradiction	NOUN
ejpam-84	206	3	proves	prove	VERB
ejpam-84	206	4	the	the	DET
ejpam-84	206	5	theorem	theorem	PROPN
ejpam-84	206	6	.	.	PROPN
ejpam-84	206	7	remark	remark	PROPN
ejpam-84	206	8	3.1	3.1	NUM
ejpam-84	206	9	:	:	PUNCT
ejpam-84	206	10	observe	observe	VERB
ejpam-84	206	11	that	that	SCONJ
ejpam-84	206	12	theorem	theorem	VERB
ejpam-84	206	13	3.1	3.1	NUM
ejpam-84	206	14	is	be	AUX
ejpam-84	206	15	true	true	ADJ
ejpam-84	206	16	when	when	SCONJ
ejpam-84	206	17	f	f	PROPN
ejpam-84	206	18	=	=	SYM
ejpam-84	206	19	k.	k.	PROPN
ejpam-84	206	20	although	although	SCONJ
ejpam-84	206	21	k0	k0	PROPN
ejpam-84	206	22	is	be	AUX
ejpam-84	206	23	not	not	PART
ejpam-84	206	24	assumed	assume	VERB
ejpam-84	206	25	to	to	PART
ejpam-84	206	26	have	have	VERB
ejpam-84	206	27	nonempty	nonempty	ADJ
ejpam-84	206	28	interior	interior	NOUN
ejpam-84	206	29	,	,	PUNCT
ejpam-84	206	30	theorem	theorem	VERB
ejpam-84	206	31	3.1	3.1	NUM
ejpam-84	206	32	requires	require	VERB
ejpam-84	206	33	that	that	SCONJ
ejpam-84	206	34	k	k	PROPN
ejpam-84	206	35	must	must	AUX
ejpam-84	206	36	be	be	AUX
ejpam-84	206	37	a	a	DET
ejpam-84	206	38	distance	distance	NOUN
ejpam-84	206	39	set	set	NOUN
ejpam-84	206	40	.	.	PUNCT
ejpam-84	207	1	this	this	DET
ejpam-84	207	2	,	,	PUNCT
ejpam-84	207	3	however	however	ADV
ejpam-84	207	4	,	,	PUNCT
ejpam-84	207	5	a	a	DET
ejpam-84	207	6	weaker	weak	ADJ
ejpam-84	207	7	assumption	assumption	NOUN
ejpam-84	207	8	because	because	SCONJ
ejpam-84	207	9	the	the	DET
ejpam-84	207	10	cones	cone	NOUN
ejpam-84	207	11	in	in	ADP
ejpam-84	207	12	lp	lp	NOUN
ejpam-84	207	13	-	-	PUNCT
ejpam-84	207	14	spaces	space	NOUN
ejpam-84	207	15	are	be	AUX
ejpam-84	207	16	distance	distance	NOUN
ejpam-84	207	17	sets	set	NOUN
ejpam-84	207	18	whose	whose	DET
ejpam-84	207	19	interior	interior	NOUN
ejpam-84	207	20	is	be	AUX
ejpam-84	207	21	empty	empty	ADJ
ejpam-84	207	22	.	.	PUNCT
ejpam-84	208	1	we	we	PRON
ejpam-84	208	2	note	note	VERB
ejpam-84	208	3	also	also	ADV
ejpam-84	208	4	that	that	SCONJ
ejpam-84	208	5	every	every	DET
ejpam-84	208	6	closed	close	VERB
ejpam-84	208	7	convex	convex	NOUN
ejpam-84	208	8	set	set	VERB
ejpam-84	208	9	in	in	ADP
ejpam-84	208	10	a	a	DET
ejpam-84	208	11	reflexive	reflexive	ADJ
ejpam-84	208	12	banach	banach	NOUN
ejpam-84	208	13	space	space	NOUN
ejpam-84	208	14	is	be	AUX
ejpam-84	208	15	a	a	DET
ejpam-84	208	16	distance	distance	NOUN
ejpam-84	208	17	set	set	NOUN
ejpam-84	208	18	.	.	PUNCT
ejpam-84	209	1	references	reference	NOUN
ejpam-84	209	2	[	[	X
ejpam-84	209	3	1	1	NUM
ejpam-84	209	4	]	]	X
ejpam-84	209	5	caputo	caputo	PROPN
ejpam-84	209	6	,	,	PUNCT
ejpam-84	209	7	m.	m.	NOUN
ejpam-84	209	8	“	"	PUNCT
ejpam-84	209	9	linear	linear	ADJ
ejpam-84	209	10	models	model	NOUN
ejpam-84	209	11	of	of	ADP
ejpam-84	209	12	dissipation	dissipation	NOUN
ejpam-84	209	13	whose	whose	DET
ejpam-84	209	14	q	q	NOUN
ejpam-84	209	15	is	be	AUX
ejpam-84	209	16	almost	almost	ADV
ejpam-84	209	17	independent	independent	ADJ
ejpam-84	209	18	,	,	PUNCT
ejpam-84	209	19	ii	ii	NOUN
ejpam-84	209	20	.	.	PUNCT
ejpam-84	209	21	”	"	PUNCT
ejpam-84	210	1	geophy	geophy	NOUN
ejpam-84	210	2	.	.	PUNCT
ejpam-84	211	1	j.	j.	PROPN
ejpam-84	211	2	roy	roy	PROPN
ejpam-84	211	3	.	.	PROPN
ejpam-84	211	4	astronom	astronom	PROPN
ejpam-84	211	5	13	13	NUM
ejpam-84	211	6	(	(	PUNCT
ejpam-84	211	7	1967	1967	NUM
ejpam-84	211	8	):	):	PUNCT
ejpam-84	211	9	529	529	NUM
ejpam-84	211	10	-	-	SYM
ejpam-84	211	11	539	539	NUM
ejpam-84	211	12	.	.	PUNCT
ejpam-84	212	1	[	[	X
ejpam-84	212	2	2	2	NUM
ejpam-84	212	3	]	]	X
ejpam-84	212	4	glöckle	glöckle	PROPN
ejpam-84	212	5	,	,	PUNCT
ejpam-84	212	6	w.g	w.g	PROPN
ejpam-84	212	7	.	.	PROPN
ejpam-84	212	8	and	and	CCONJ
ejpam-84	212	9	t.f	t.f	PROPN
ejpam-84	212	10	.	.	PROPN
ejpam-84	212	11	nonnenmacher	nonnenmacher	PROPN
ejpam-84	212	12	.	.	PUNCT
ejpam-84	213	1	“	"	PUNCT
ejpam-84	213	2	a	a	DET
ejpam-84	213	3	fractional	fractional	ADJ
ejpam-84	213	4	calculus	calculus	NOUN
ejpam-84	213	5	approach	approach	NOUN
ejpam-84	213	6	to	to	ADP
ejpam-84	213	7	self	self	NOUN
ejpam-84	213	8	similar	similar	ADJ
ejpam-84	213	9	protein	protein	NOUN
ejpam-84	213	10	dynamics	dynamic	NOUN
ejpam-84	213	11	.	.	PUNCT
ejpam-84	213	12	”	"	PUNCT
ejpam-84	213	13	biophy	biophy	NOUN
ejpam-84	213	14	.	.	PUNCT
ejpam-84	214	1	j.	j.	PROPN
ejpam-84	214	2	68	68	NUM
ejpam-84	214	3	(	(	PUNCT
ejpam-84	214	4	1995	1995	NUM
ejpam-84	214	5	):	):	PUNCT
ejpam-84	214	6	46	46	NUM
ejpam-84	214	7	-	-	SYM
ejpam-84	214	8	53	53	NUM
ejpam-84	214	9	.	.	PUNCT
ejpam-84	215	1	[	[	X
ejpam-84	215	2	3	3	NUM
ejpam-84	215	3	]	]	X
ejpam-84	215	4	diethelm	diethelm	NOUN
ejpam-84	215	5	,	,	PUNCT
ejpam-84	215	6	k	k	PROPN
ejpam-84	215	7	and	and	CCONJ
ejpam-84	215	8	n.j	n.j	PROPN
ejpam-84	215	9	.	.	PROPN
ejpam-84	215	10	ford	ford	PROPN
ejpam-84	215	11	.	.	PUNCT
ejpam-84	216	1	“	"	PUNCT
ejpam-84	216	2	analysis	analysis	NOUN
ejpam-84	216	3	of	of	ADP
ejpam-84	216	4	fractional	fractional	ADJ
ejpam-84	216	5	differential	differential	ADJ
ejpam-84	216	6	equations	equation	NOUN
ejpam-84	216	7	.	.	PUNCT
ejpam-84	216	8	”	"	PUNCT
ejpam-84	216	9	jmaa	jmaa	VERB
ejpam-84	216	10	265	265	NUM
ejpam-84	216	11	(	(	PUNCT
ejpam-84	216	12	2002	2002	NUM
ejpam-84	216	13	):	):	PUNCT
ejpam-84	216	14	229248	229248	NUM
ejpam-84	216	15	.	.	PUNCT
ejpam-84	217	1	[	[	X
ejpam-84	217	2	4	4	NUM
ejpam-84	217	3	]	]	X
ejpam-84	217	4	diethelm	diethelm	NOUN
ejpam-84	217	5	,	,	PUNCT
ejpam-84	217	6	k.	k.	PROPN
ejpam-84	217	7	and	and	CCONJ
ejpam-84	217	8	n.j	n.j	PROPN
ejpam-84	217	9	.	.	PROPN
ejpam-84	217	10	ford	ford	PROPN
ejpam-84	217	11	.	.	PUNCT
ejpam-84	218	1	“	"	PUNCT
ejpam-84	218	2	multi	multi	ADJ
ejpam-84	218	3	-	-	ADJ
ejpam-84	218	4	order	order	ADJ
ejpam-84	218	5	fractional	fractional	ADJ
ejpam-84	218	6	differential	differential	ADJ
ejpam-84	218	7	equations	equation	NOUN
ejpam-84	218	8	and	and	CCONJ
ejpam-84	218	9	their	their	PRON
ejpam-84	218	10	numerical	numerical	ADJ
ejpam-84	218	11	solution	solution	NOUN
ejpam-84	218	12	.	.	PUNCT
ejpam-84	218	13	”	"	PUNCT
ejpam-84	219	1	amc	amc	PROPN
ejpam-84	219	2	154	154	NUM
ejpam-84	219	3	(	(	PUNCT
ejpam-84	219	4	2004	2004	NUM
ejpam-84	219	5	):	):	PUNCT
ejpam-84	219	6	621	621	NUM
ejpam-84	219	7	-	-	SYM
ejpam-84	219	8	640	640	NUM
ejpam-84	219	9	.	.	PUNCT
ejpam-84	220	1	[	[	X
ejpam-84	220	2	5	5	NUM
ejpam-84	220	3	]	]	SYM
ejpam-84	220	4	diethelm	diethelm	NOUN
ejpam-84	220	5	,	,	PUNCT
ejpam-84	220	6	k.	k.	PROPN
ejpam-84	220	7	and	and	CCONJ
ejpam-84	220	8	a.d	a.d	PROPN
ejpam-84	220	9	.	.	PROPN
ejpam-84	220	10	freed	freed	PROPN
ejpam-84	220	11	.	.	PUNCT
ejpam-84	221	1	“	"	PUNCT
ejpam-84	221	2	on	on	ADP
ejpam-84	221	3	the	the	DET
ejpam-84	221	4	solution	solution	NOUN
ejpam-84	221	5	of	of	ADP
ejpam-84	221	6	nonlinear	nonlinear	ADJ
ejpam-84	221	7	fractional	fractional	ADJ
ejpam-84	221	8	differential	differential	ADJ
ejpam-84	221	9	equations	equation	NOUN
ejpam-84	221	10	used	use	VERB
ejpam-84	221	11	in	in	ADP
ejpam-84	221	12	the	the	DET
ejpam-84	221	13	modeling	modeling	NOUN
ejpam-84	221	14	of	of	ADP
ejpam-84	221	15	viscoplasticity	viscoplasticity	NOUN
ejpam-84	221	16	.	.	PUNCT
ejpam-84	221	17	”	"	PUNCT
ejpam-84	221	18	scientific	scientific	ADJ
ejpam-84	221	19	computing	computing	NOUN
ejpam-84	221	20	in	in	ADP
ejpam-84	221	21	chemical	chemical	PROPN
ejpam-84	221	22	engineering	engineering	PROPN
ejpam-84	221	23	ii	ii	PROPN
ejpam-84	221	24	:	:	PUNCT
ejpam-84	221	25	computational	computational	ADJ
ejpam-84	221	26	fluid	fluid	ADJ
ejpam-84	221	27	dynamics	dynamic	NOUN
ejpam-84	221	28	,	,	PUNCT
ejpam-84	221	29	reaction	reaction	NOUN
ejpam-84	221	30	engineering	engineering	NOUN
ejpam-84	221	31	,	,	PUNCT
ejpam-84	221	32	and	and	CCONJ
ejpam-84	221	33	molecular	molecular	ADJ
ejpam-84	221	34	properties	property	NOUN
ejpam-84	221	35	eds	ed	NOUN
ejpam-84	221	36	.	.	PUNCT
ejpam-84	221	37	f.	f.	PROPN
ejpam-84	221	38	keil	keil	PROPN
ejpam-84	221	39	,	,	PUNCT
ejpam-84	221	40	w.	w.	PROPN
ejpam-84	221	41	mackens	macken	VERB
ejpam-84	221	42	,	,	PUNCT
ejpam-84	221	43	h.	h.	PROPN
ejpam-84	221	44	vob	vob	PROPN
ejpam-84	221	45	,	,	PUNCT
ejpam-84	221	46	and	and	CCONJ
ejpam-84	221	47	j.	j.	PROPN
ejpam-84	221	48	werther	werther	PROPN
ejpam-84	221	49	.	.	PUNCT
ejpam-84	222	1	heidelberg	heidelberg	PROPN
ejpam-84	222	2	:	:	PUNCT
ejpam-84	222	3	springer	springer	NOUN
ejpam-84	222	4	,	,	PUNCT
ejpam-84	222	5	1999	1999	NUM
ejpam-84	222	6	.	.	PUNCT
ejpam-84	223	1	217	217	NUM
ejpam-84	223	2	-	-	SYM
ejpam-84	223	3	224	224	NUM
ejpam-84	223	4	.	.	PUNCT
ejpam-84	224	1	[	[	X
ejpam-84	224	2	6	6	NUM
ejpam-84	224	3	]	]	SYM
ejpam-84	224	4	kiryakova	kiryakova	X
ejpam-84	224	5	,	,	PUNCT
ejpam-84	224	6	v.	v.	ADP
ejpam-84	224	7	“	"	PUNCT
ejpam-84	224	8	generalized	generalize	VERB
ejpam-84	224	9	fractional	fractional	ADJ
ejpam-84	224	10	calculus	calculus	NOUN
ejpam-84	224	11	and	and	CCONJ
ejpam-84	224	12	applications	application	NOUN
ejpam-84	224	13	.	.	PUNCT
ejpam-84	224	14	”	"	PUNCT
ejpam-84	224	15	pitman	pitman	NOUN
ejpam-84	224	16	res	re	NOUN
ejpam-84	224	17	.	.	PROPN
ejpam-84	225	1	notes	note	VERB
ejpam-84	225	2	math	math	PROPN
ejpam-84	225	3	.	.	PUNCT
ejpam-84	226	1	ser	ser	PROPN
ejpam-84	226	2	.	.	PUNCT
ejpam-84	227	1	vol	vol	NOUN
ejpam-84	227	2	301	301	NUM
ejpam-84	227	3	.	.	PUNCT
ejpam-84	228	1	new	new	PROPN
ejpam-84	228	2	york	york	PROPN
ejpam-84	228	3	:	:	PUNCT
ejpam-84	228	4	longman	longman	NOUN
ejpam-84	228	5	-	-	PUNCT
ejpam-84	228	6	wiley	wiley	NOUN
ejpam-84	228	7	,	,	PUNCT
ejpam-84	228	8	1994	1994	NUM
ejpam-84	228	9	.	.	PUNCT
ejpam-84	229	1	[	[	X
ejpam-84	229	2	7	7	NUM
ejpam-84	229	3	]	]	SYM
ejpam-84	229	4	lakshmikantham	lakshmikantham	ADV
ejpam-84	229	5	,	,	PUNCT
ejpam-84	229	6	v.	v.	PROPN
ejpam-84	229	7	and	and	CCONJ
ejpam-84	229	8	s.	s.	PROPN
ejpam-84	229	9	leela	leela	PROPN
ejpam-84	229	10	.	.	PUNCT
ejpam-84	230	1	differential	differential	PROPN
ejpam-84	230	2	and	and	CCONJ
ejpam-84	230	3	integral	integral	ADJ
ejpam-84	230	4	inequalities	inequality	NOUN
ejpam-84	230	5	vol	vol	NOUN
ejpam-84	230	6	.	.	PUNCT
ejpam-84	231	1	i	i	PRON
ejpam-84	231	2	and	and	CCONJ
ejpam-84	231	3	vol	vol	NOUN
ejpam-84	231	4	.	.	PUNCT
ejpam-84	231	5	ii	ii	PROPN
ejpam-84	231	6	.	.	PUNCT
ejpam-84	232	1	new	new	PROPN
ejpam-84	232	2	york	york	PROPN
ejpam-84	232	3	:	:	PUNCT
ejpam-84	232	4	academic	academic	ADJ
ejpam-84	232	5	press	press	NOUN
ejpam-84	232	6	,	,	PUNCT
ejpam-84	232	7	1969	1969	NUM
ejpam-84	232	8	.	.	PUNCT
ejpam-84	233	1	[	[	X
ejpam-84	233	2	8	8	NUM
ejpam-84	233	3	]	]	SYM
ejpam-84	233	4	lakshmikantham	lakshmikantham	ADV
ejpam-84	233	5	,	,	PUNCT
ejpam-84	233	6	v.	v.	PROPN
ejpam-84	233	7	and	and	CCONJ
ejpam-84	233	8	s.	s.	PROPN
ejpam-84	233	9	leela	leela	PROPN
ejpam-84	233	10	.	.	PUNCT
ejpam-84	234	1	nonlinear	nonlinear	ADJ
ejpam-84	234	2	differential	differential	ADJ
ejpam-84	234	3	equations	equation	NOUN
ejpam-84	234	4	in	in	ADP
ejpam-84	234	5	abstract	abstract	ADJ
ejpam-84	234	6	spaces	space	NOUN
ejpam-84	234	7	oxford	oxford	NOUN
ejpam-84	234	8	:	:	PUNCT
ejpam-84	234	9	pergamon	pergamon	PROPN
ejpam-84	234	10	press	press	PROPN
ejpam-84	234	11	,	,	PUNCT
ejpam-84	234	12	1981	1981	NUM
ejpam-84	234	13	.	.	PUNCT
ejpam-84	235	1	[	[	X
ejpam-84	235	2	9	9	NUM
ejpam-84	235	3	]	]	SYM
ejpam-84	235	4	lakshmikantham	lakshmikantham	ADV
ejpam-84	235	5	,	,	PUNCT
ejpam-84	235	6	v.	v.	PROPN
ejpam-84	235	7	and	and	CCONJ
ejpam-84	235	8	a.s	a.s	PROPN
ejpam-84	235	9	.	.	PROPN
ejpam-84	235	10	vatsala	vatsala	PROPN
ejpam-84	235	11	.	.	PUNCT
ejpam-84	236	1	“	"	PUNCT
ejpam-84	236	2	basic	basic	ADJ
ejpam-84	236	3	theory	theory	NOUN
ejpam-84	236	4	of	of	ADP
ejpam-84	236	5	fractional	fractional	ADJ
ejpam-84	236	6	differential	differential	ADJ
ejpam-84	236	7	equations	equation	NOUN
ejpam-84	236	8	.	.	PUNCT
ejpam-84	236	9	”	"	PUNCT
ejpam-84	237	1	nonlinear	nonlinear	ADJ
ejpam-84	237	2	analysis	analysis	NOUN
ejpam-84	237	3	:	:	PUNCT
ejpam-84	237	4	theory	theory	NOUN
ejpam-84	237	5	,	,	PUNCT
ejpam-84	237	6	methods	method	NOUN
ejpam-84	237	7	,	,	PUNCT
ejpam-84	237	8	and	and	CCONJ
ejpam-84	237	9	applications	application	NOUN
ejpam-84	237	10	to	to	PART
ejpam-84	237	11	appear	appear	VERB
ejpam-84	237	12	.	.	PUNCT
ejpam-84	238	1	[	[	X
ejpam-84	238	2	10	10	NUM
ejpam-84	238	3	]	]	X
ejpam-84	238	4	lakshmikantham	lakshmikantham	ADV
ejpam-84	238	5	,	,	PUNCT
ejpam-84	238	6	v.	v.	PROPN
ejpam-84	238	7	and	and	CCONJ
ejpam-84	238	8	a.s	a.s	PROPN
ejpam-84	238	9	.	.	PROPN
ejpam-84	238	10	vatsala	vatsala	PROPN
ejpam-84	238	11	.	.	PUNCT
ejpam-84	239	1	“	"	PUNCT
ejpam-84	239	2	theory	theory	NOUN
ejpam-84	239	3	of	of	ADP
ejpam-84	239	4	fractional	fractional	ADJ
ejpam-84	239	5	differential	differential	ADJ
ejpam-84	239	6	inequalities	inequality	NOUN
ejpam-84	239	7	and	and	CCONJ
ejpam-84	239	8	applications	application	NOUN
ejpam-84	239	9	”	"	PUNCT
ejpam-84	239	10	communications	communication	NOUN
ejpam-84	239	11	is	be	AUX
ejpam-84	239	12	applied	apply	VERB
ejpam-84	239	13	analysis	analysis	NOUN
ejpam-84	239	14	to	to	PART
ejpam-84	239	15	appear	appear	VERB
ejpam-84	239	16	.	.	PUNCT
ejpam-84	240	1	[	[	X
ejpam-84	240	2	11	11	NUM
ejpam-84	240	3	]	]	SYM
ejpam-84	240	4	lakshmikantham	lakshmikantham	ADV
ejpam-84	240	5	,	,	PUNCT
ejpam-84	240	6	v.	v.	PROPN
ejpam-84	240	7	and	and	CCONJ
ejpam-84	240	8	a.s	a.s	PROPN
ejpam-84	240	9	.	.	PROPN
ejpam-84	240	10	vatsala	vatsala	PROPN
ejpam-84	240	11	.	.	PUNCT
ejpam-84	241	1	“	"	PUNCT
ejpam-84	241	2	general	general	ADJ
ejpam-84	241	3	uniqueness	uniqueness	NOUN
ejpam-84	241	4	and	and	CCONJ
ejpam-84	241	5	monotone	monotone	ADJ
ejpam-84	241	6	iterative	iterative	NOUN
ejpam-84	241	7	technique	technique	NOUN
ejpam-84	241	8	for	for	ADP
ejpam-84	241	9	fractional	fractional	ADJ
ejpam-84	241	10	differential	differential	ADJ
ejpam-84	241	11	equations	equation	NOUN
ejpam-84	241	12	”	"	PUNCT
ejpam-84	241	13	math	math	NOUN
ejpam-84	241	14	letters	letter	NOUN
ejpam-84	241	15	to	to	PART
ejpam-84	241	16	appear	appear	VERB
ejpam-84	241	17	.	.	PUNCT
ejpam-84	242	1	[	[	X
ejpam-84	242	2	12	12	NUM
ejpam-84	242	3	]	]	X
ejpam-84	242	4	lakshmikantham	lakshmikantham	ADV
ejpam-84	242	5	,	,	PUNCT
ejpam-84	242	6	v.	v.	ADP
ejpam-84	242	7	“	"	PUNCT
ejpam-84	242	8	theory	theory	NOUN
ejpam-84	242	9	of	of	ADP
ejpam-84	242	10	fractional	fractional	ADJ
ejpam-84	242	11	functional	functional	ADJ
ejpam-84	242	12	differential	differential	ADJ
ejpam-84	242	13	equations	equation	NOUN
ejpam-84	242	14	”	"	PUNCT
ejpam-84	242	15	nonlinear	nonlinear	ADJ
ejpam-84	242	16	analysis	analysis	NOUN
ejpam-84	242	17	:	:	PUNCT
ejpam-84	242	18	theory	theory	NOUN
ejpam-84	242	19	,	,	PUNCT
ejpam-84	242	20	methods	method	NOUN
ejpam-84	242	21	,	,	PUNCT
ejpam-84	242	22	and	and	CCONJ
ejpam-84	242	23	applications	application	NOUN
ejpam-84	242	24	to	to	PART
ejpam-84	242	25	appear	appear	VERB
ejpam-84	242	26	.	.	PUNCT
ejpam-84	243	1	[	[	X
ejpam-84	243	2	13	13	NUM
ejpam-84	243	3	]	]	X
ejpam-84	243	4	metzler	metzler	NOUN
ejpam-84	243	5	,	,	PUNCT
ejpam-84	243	6	r.	r.	PROPN
ejpam-84	243	7	,	,	PUNCT
ejpam-84	243	8	w.	w.	PROPN
ejpam-84	243	9	schick	schick	PROPN
ejpam-84	243	10	,	,	PUNCT
ejpam-84	243	11	h.g	h.g	PROPN
ejpam-84	243	12	.	.	PROPN
ejpam-84	243	13	kilian	kilian	PROPN
ejpam-84	243	14	,	,	PUNCT
ejpam-84	243	15	and	and	CCONJ
ejpam-84	243	16	t.f	t.f	PROPN
ejpam-84	243	17	.	.	PROPN
ejpam-84	243	18	nonnenmacher	nonnenmacher	PROPN
ejpam-84	243	19	.	.	PUNCT
ejpam-84	244	1	“	"	PUNCT
ejpam-84	244	2	relaxation	relaxation	NOUN
ejpam-84	244	3	in	in	ADP
ejpam-84	244	4	filled	fill	VERB
ejpam-84	244	5	polymers	polymer	NOUN
ejpam-84	244	6	:	:	PUNCT
ejpam-84	244	7	a	a	DET
ejpam-84	244	8	fractional	fractional	ADJ
ejpam-84	244	9	calculus	calculus	NOUN
ejpam-84	244	10	approach	approach	NOUN
ejpam-84	244	11	.	.	PUNCT
ejpam-84	244	12	”	"	PUNCT
ejpam-84	245	1	j.	j.	PROPN
ejpam-84	245	2	chem	chem	PROPN
ejpam-84	245	3	.	.	PUNCT
ejpam-84	246	1	phy	phy	PROPN
ejpam-84	246	2	.	.	PROPN
ejpam-84	246	3	103	103	NUM
ejpam-84	246	4	(	(	PUNCT
ejpam-84	246	5	1995	1995	NUM
ejpam-84	246	6	):	):	PUNCT
ejpam-84	246	7	7180	7180	NUM
ejpam-84	246	8	-	-	SYM
ejpam-84	246	9	7186	7186	NUM
ejpam-84	246	10	.	.	PUNCT
ejpam-84	247	1	[	[	X
ejpam-84	247	2	14	14	NUM
ejpam-84	247	3	]	]	SYM
ejpam-84	247	4	podlubny	podlubny	NOUN
ejpam-84	247	5	,	,	PUNCT
ejpam-84	247	6	i.	i.	NOUN
ejpam-84	247	7	fractional	fractional	PROPN
ejpam-84	247	8	differential	differential	PROPN
ejpam-84	247	9	equations	equation	NOUN
ejpam-84	247	10	san	san	PROPN
ejpam-84	247	11	diego	diego	PROPN
ejpam-84	247	12	:	:	PUNCT
ejpam-84	247	13	academic	academic	ADJ
ejpam-84	247	14	press	press	NOUN
ejpam-84	247	15	,	,	PUNCT
ejpam-84	247	16	1999	1999	NUM
ejpam-84	247	17	.	.	PUNCT
ejpam-84	248	1	[	[	X
ejpam-84	248	2	15	15	NUM
ejpam-84	248	3	]	]	X
ejpam-84	248	4	samko	samko	NOUN
ejpam-84	248	5	,	,	PUNCT
ejpam-84	248	6	s.g	s.g	PROPN
ejpam-84	248	7	.	.	PROPN
ejpam-84	248	8	,	,	PUNCT
ejpam-84	248	9	a.a	a.a	PROPN
ejpam-84	248	10	.	.	PROPN
ejpam-84	248	11	kilbas	kilbas	PROPN
ejpam-84	248	12	,	,	PUNCT
ejpam-84	248	13	and	and	CCONJ
ejpam-84	248	14	o.i	o.i	PROPN
ejpam-84	248	15	.	.	PUNCT
ejpam-84	248	16	marichev	marichev	PROPN
ejpam-84	248	17	.	.	PUNCT
ejpam-84	249	1	fractional	fractional	ADJ
ejpam-84	249	2	integrals	integral	NOUN
ejpam-84	249	3	and	and	CCONJ
ejpam-84	249	4	derivatives	derivative	NOUN
ejpam-84	249	5	,	,	PUNCT
ejpam-84	249	6	theory	theory	NOUN
ejpam-84	249	7	and	and	CCONJ
ejpam-84	249	8	applications	application	NOUN
ejpam-84	249	9	yverdon	yverdon	PROPN
ejpam-84	249	10	:	:	PUNCT
ejpam-84	249	11	gordon	gordon	PROPN
ejpam-84	249	12	and	and	CCONJ
ejpam-84	249	13	breach	breach	NOUN
ejpam-84	249	14	,	,	PUNCT
ejpam-84	249	15	1993	1993	NUM
ejpam-84	249	16	.	.	PUNCT