id	sid	tid	token	lemma	pos
ejpam-6411	1	1	european	european	PROPN
ejpam-6411	1	2	journal	journal	PROPN
ejpam-6411	1	3	of	of	ADP
ejpam-6411	1	4	pure	pure	ADJ
ejpam-6411	1	5	and	and	CCONJ
ejpam-6411	1	6	applied	applied	ADJ
ejpam-6411	1	7	mathematics	mathematic	NOUN
ejpam-6411	1	8	2025	2025	NUM
ejpam-6411	1	9	,	,	PUNCT
ejpam-6411	1	10	vol	vol	NOUN
ejpam-6411	1	11	.	.	PROPN
ejpam-6411	1	12	18	18	NUM
ejpam-6411	1	13	,	,	PUNCT
ejpam-6411	1	14	issue	issue	NOUN
ejpam-6411	1	15	4	4	NUM
ejpam-6411	1	16	,	,	PUNCT
ejpam-6411	1	17	article	article	NOUN
ejpam-6411	1	18	number	number	NOUN
ejpam-6411	1	19	6411	6411	NUM
ejpam-6411	1	20	issn	issn	PROPN
ejpam-6411	1	21	1307	1307	NUM
ejpam-6411	1	22	-	-	SYM
ejpam-6411	1	23	5543	5543	NUM
ejpam-6411	1	24	–	–	PUNCT
ejpam-6411	1	25	ejpam.com	ejpam.com	X
ejpam-6411	1	26	published	publish	VERB
ejpam-6411	1	27	by	by	ADP
ejpam-6411	1	28	new	new	PROPN
ejpam-6411	1	29	york	york	PROPN
ejpam-6411	1	30	business	business	PROPN
ejpam-6411	1	31	global	global	PROPN
ejpam-6411	1	32	a	a	DET
ejpam-6411	1	33	study	study	NOUN
ejpam-6411	1	34	of	of	ADP
ejpam-6411	1	35	a	a	DET
ejpam-6411	1	36	coupled	couple	VERB
ejpam-6411	1	37	system	system	NOUN
ejpam-6411	1	38	of	of	ADP
ejpam-6411	1	39	fractional	fractional	ADJ
ejpam-6411	1	40	differential	differential	ADJ
ejpam-6411	1	41	equations	equation	NOUN
ejpam-6411	1	42	with	with	ADP
ejpam-6411	1	43	two	two	NUM
ejpam-6411	1	44	points	point	NOUN
ejpam-6411	1	45	integral	integral	ADJ
ejpam-6411	1	46	boundary	boundary	ADJ
ejpam-6411	1	47	conditions	condition	NOUN
ejpam-6411	1	48	shaher	shaher	VERB
ejpam-6411	1	49	momani1,2	momani1,2	PROPN
ejpam-6411	1	50	,	,	PUNCT
ejpam-6411	1	51	hamzeh	hamzeh	NOUN
ejpam-6411	1	52	zureigat3	zureigat3	NOUN
ejpam-6411	1	53	,	,	PUNCT
ejpam-6411	1	54	shrideh	shrideh	PROPN
ejpam-6411	1	55	al	al	PROPN
ejpam-6411	1	56	-	-	PUNCT
ejpam-6411	1	57	omari4,∗	omari4,∗	PROPN
ejpam-6411	1	58	,	,	PUNCT
ejpam-6411	1	59	mona	mona	PROPN
ejpam-6411	1	60	mohammad	mohammad	PROPN
ejpam-6411	1	61	khandaqji5	khandaqji5	PROPN
ejpam-6411	1	62	,	,	PUNCT
ejpam-6411	1	63	mohammed	mohammed	PROPN
ejpam-6411	1	64	al	al	PROPN
ejpam-6411	1	65	-	-	PUNCT
ejpam-6411	1	66	smadi2,6,7	smadi2,6,7	NOUN
ejpam-6411	1	67	1	1	NUM
ejpam-6411	1	68	department	department	NOUN
ejpam-6411	1	69	of	of	ADP
ejpam-6411	1	70	mathematics	mathematic	NOUN
ejpam-6411	1	71	,	,	PUNCT
ejpam-6411	1	72	faculty	faculty	NOUN
ejpam-6411	1	73	of	of	ADP
ejpam-6411	1	74	science	science	NOUN
ejpam-6411	1	75	,	,	PUNCT
ejpam-6411	1	76	the	the	DET
ejpam-6411	1	77	university	university	PROPN
ejpam-6411	1	78	of	of	ADP
ejpam-6411	1	79	jordan	jordan	PROPN
ejpam-6411	1	80	,	,	PUNCT
ejpam-6411	1	81	amman	amman	PROPN
ejpam-6411	1	82	11942	11942	NUM
ejpam-6411	1	83	,	,	PUNCT
ejpam-6411	1	84	jordan	jordan	PROPN
ejpam-6411	1	85	2	2	NUM
ejpam-6411	1	86	nonlinear	nonlinear	ADJ
ejpam-6411	1	87	dynamics	dynamic	NOUN
ejpam-6411	1	88	research	research	NOUN
ejpam-6411	1	89	center	center	NOUN
ejpam-6411	1	90	(	(	PUNCT
ejpam-6411	1	91	ndrc	ndrc	PROPN
ejpam-6411	1	92	)	)	PUNCT
ejpam-6411	1	93	,	,	PUNCT
ejpam-6411	1	94	ajman	ajman	PROPN
ejpam-6411	1	95	university	university	PROPN
ejpam-6411	1	96	,	,	PUNCT
ejpam-6411	1	97	ajman	ajman	NOUN
ejpam-6411	1	98	20550	20550	NUM
ejpam-6411	1	99	,	,	PUNCT
ejpam-6411	1	100	uae	uae	PROPN
ejpam-6411	1	101	3	3	NUM
ejpam-6411	1	102	department	department	NOUN
ejpam-6411	1	103	of	of	ADP
ejpam-6411	1	104	mathematics	mathematic	NOUN
ejpam-6411	1	105	,	,	PUNCT
ejpam-6411	1	106	faculty	faculty	NOUN
ejpam-6411	1	107	of	of	ADP
ejpam-6411	1	108	science	science	NOUN
ejpam-6411	1	109	and	and	CCONJ
ejpam-6411	1	110	technology	technology	NOUN
ejpam-6411	1	111	,	,	PUNCT
ejpam-6411	1	112	jadara	jadara	PROPN
ejpam-6411	1	113	university	university	PROPN
ejpam-6411	1	114	,	,	PUNCT
ejpam-6411	1	115	21110	21110	NUM
ejpam-6411	1	116	irbid	irbid	NOUN
ejpam-6411	1	117	,	,	PUNCT
ejpam-6411	1	118	jordan	jordan	PROPN
ejpam-6411	1	119	4	4	NUM
ejpam-6411	1	120	department	department	NOUN
ejpam-6411	1	121	of	of	ADP
ejpam-6411	1	122	mathematics	mathematic	NOUN
ejpam-6411	1	123	,	,	PUNCT
ejpam-6411	1	124	faculty	faculty	NOUN
ejpam-6411	1	125	of	of	ADP
ejpam-6411	1	126	science	science	NOUN
ejpam-6411	1	127	,	,	PUNCT
ejpam-6411	1	128	al	al	PROPN
ejpam-6411	1	129	-	-	PUNCT
ejpam-6411	1	130	balqa	balqa	NOUN
ejpam-6411	1	131	applied	apply	VERB
ejpam-6411	1	132	university	university	NOUN
ejpam-6411	1	133	,	,	PUNCT
ejpam-6411	1	134	salt	salt	NOUN
ejpam-6411	1	135	11134	11134	NUM
ejpam-6411	1	136	,	,	PUNCT
ejpam-6411	1	137	jordan	jordan	PROPN
ejpam-6411	1	138	5	5	NUM
ejpam-6411	1	139	department	department	NOUN
ejpam-6411	1	140	of	of	ADP
ejpam-6411	1	141	basic	basic	ADJ
ejpam-6411	1	142	science	science	NOUN
ejpam-6411	1	143	,	,	PUNCT
ejpam-6411	1	144	faculty	faculty	NOUN
ejpam-6411	1	145	of	of	ADP
ejpam-6411	1	146	arts	art	NOUN
ejpam-6411	1	147	and	and	CCONJ
ejpam-6411	1	148	science	science	NOUN
ejpam-6411	1	149	,	,	PUNCT
ejpam-6411	1	150	applied	apply	VERB
ejpam-6411	1	151	science	science	NOUN
ejpam-6411	1	152	private	private	ADJ
ejpam-6411	1	153	university	university	NOUN
ejpam-6411	1	154	,	,	PUNCT
ejpam-6411	1	155	amman	amman	PROPN
ejpam-6411	1	156	11931	11931	NUM
ejpam-6411	1	157	,	,	PUNCT
ejpam-6411	1	158	jordan	jordan	PROPN
ejpam-6411	1	159	6	6	NUM
ejpam-6411	1	160	college	college	PROPN
ejpam-6411	1	161	of	of	ADP
ejpam-6411	1	162	commerce	commerce	PROPN
ejpam-6411	1	163	and	and	CCONJ
ejpam-6411	1	164	business	business	NOUN
ejpam-6411	1	165	,	,	PUNCT
ejpam-6411	1	166	lusail	lusail	PROPN
ejpam-6411	1	167	university	university	PROPN
ejpam-6411	1	168	,	,	PUNCT
ejpam-6411	1	169	lusail	lusail	NOUN
ejpam-6411	1	170	,	,	PUNCT
ejpam-6411	1	171	qatar	qatar	PROPN
ejpam-6411	1	172	7	7	NUM
ejpam-6411	1	173	department	department	NOUN
ejpam-6411	1	174	of	of	ADP
ejpam-6411	1	175	applied	apply	VERB
ejpam-6411	1	176	science	science	NOUN
ejpam-6411	1	177	,	,	PUNCT
ejpam-6411	1	178	ajloun	ajloun	PROPN
ejpam-6411	1	179	college	college	NOUN
ejpam-6411	1	180	,	,	PUNCT
ejpam-6411	1	181	al	al	PROPN
ejpam-6411	1	182	balqa	balqa	NOUN
ejpam-6411	1	183	applied	apply	VERB
ejpam-6411	1	184	university	university	NOUN
ejpam-6411	1	185	,	,	PUNCT
ejpam-6411	1	186	ajloun	ajloun	ADJ
ejpam-6411	1	187	,	,	PUNCT
ejpam-6411	1	188	26816	26816	NUM
ejpam-6411	1	189	,	,	PUNCT
ejpam-6411	1	190	jordan	jordan	PROPN
ejpam-6411	1	191	abstract	abstract	PROPN
ejpam-6411	1	192	.	.	PUNCT
ejpam-6411	2	1	in	in	ADP
ejpam-6411	2	2	this	this	DET
ejpam-6411	2	3	paper	paper	NOUN
ejpam-6411	2	4	,	,	PUNCT
ejpam-6411	2	5	a	a	DET
ejpam-6411	2	6	certain	certain	ADJ
ejpam-6411	2	7	system	system	NOUN
ejpam-6411	2	8	of	of	ADP
ejpam-6411	2	9	fractional	fractional	ADJ
ejpam-6411	2	10	differential	differential	ADJ
ejpam-6411	2	11	equations	equation	NOUN
ejpam-6411	2	12	of	of	ADP
ejpam-6411	2	13	integral	integral	ADJ
ejpam-6411	2	14	boundary	boundary	ADJ
ejpam-6411	2	15	conditions	condition	NOUN
ejpam-6411	2	16	bcs	bc	NOUN
ejpam-6411	2	17	at	at	ADP
ejpam-6411	2	18	two	two	NUM
ejpam-6411	2	19	points	point	NOUN
ejpam-6411	2	20	is	be	AUX
ejpam-6411	2	21	discussed	discuss	VERB
ejpam-6411	2	22	.	.	PUNCT
ejpam-6411	3	1	the	the	DET
ejpam-6411	3	2	presented	present	VERB
ejpam-6411	3	3	coupled	couple	VERB
ejpam-6411	3	4	fractional	fractional	ADJ
ejpam-6411	3	5	system	system	NOUN
ejpam-6411	3	6	are	be	AUX
ejpam-6411	3	7	useful	useful	ADJ
ejpam-6411	3	8	for	for	ADP
ejpam-6411	3	9	describing	describe	VERB
ejpam-6411	3	10	real	real	ADJ
ejpam-6411	3	11	-	-	PUNCT
ejpam-6411	3	12	world	world	NOUN
ejpam-6411	3	13	phenomena	phenomenon	NOUN
ejpam-6411	3	14	,	,	PUNCT
ejpam-6411	3	15	such	such	ADJ
ejpam-6411	3	16	as	as	ADP
ejpam-6411	3	17	in	in	ADP
ejpam-6411	3	18	physics	physics	NOUN
ejpam-6411	3	19	,	,	PUNCT
ejpam-6411	3	20	biology	biology	NOUN
ejpam-6411	3	21	,	,	PUNCT
ejpam-6411	3	22	and	and	CCONJ
ejpam-6411	3	23	engineering	engineering	NOUN
ejpam-6411	3	24	.	.	PUNCT
ejpam-6411	4	1	by	by	ADP
ejpam-6411	4	2	utilizing	utilize	VERB
ejpam-6411	4	3	the	the	DET
ejpam-6411	4	4	contraction	contraction	NOUN
ejpam-6411	4	5	mapping	mapping	NOUN
ejpam-6411	4	6	principle	principle	NOUN
ejpam-6411	4	7	,	,	PUNCT
ejpam-6411	4	8	we	we	PRON
ejpam-6411	4	9	demonstrate	demonstrate	VERB
ejpam-6411	4	10	uniqueness	uniqueness	NOUN
ejpam-6411	4	11	of	of	ADP
ejpam-6411	4	12	certain	certain	ADJ
ejpam-6411	4	13	solutions	solution	NOUN
ejpam-6411	4	14	of	of	ADP
ejpam-6411	4	15	the	the	DET
ejpam-6411	4	16	given	give	VERB
ejpam-6411	4	17	system	system	NOUN
ejpam-6411	4	18	.	.	PUNCT
ejpam-6411	5	1	next	next	ADV
ejpam-6411	5	2	,	,	PUNCT
ejpam-6411	5	3	we	we	PRON
ejpam-6411	5	4	utilize	utilize	VERB
ejpam-6411	5	5	the	the	DET
ejpam-6411	5	6	contraction	contraction	NOUN
ejpam-6411	5	7	mapping	mapping	NOUN
ejpam-6411	5	8	principle	principle	NOUN
ejpam-6411	5	9	to	to	PART
ejpam-6411	5	10	prove	prove	VERB
ejpam-6411	5	11	uniqueness	uniqueness	NOUN
ejpam-6411	5	12	of	of	ADP
ejpam-6411	5	13	each	each	DET
ejpam-6411	5	14	solution	solution	NOUN
ejpam-6411	5	15	.	.	PUNCT
ejpam-6411	6	1	further	far	ADV
ejpam-6411	6	2	,	,	PUNCT
ejpam-6411	6	3	we	we	PRON
ejpam-6411	6	4	address	address	VERB
ejpam-6411	6	5	the	the	DET
ejpam-6411	6	6	hyers	hyers	PROPN
ejpam-6411	6	7	-	-	PUNCT
ejpam-6411	6	8	ulam	ulam	ADJ
ejpam-6411	6	9	stability	stability	NOUN
ejpam-6411	6	10	and	and	CCONJ
ejpam-6411	6	11	provide	provide	VERB
ejpam-6411	6	12	its	its	PRON
ejpam-6411	6	13	conditions	condition	NOUN
ejpam-6411	6	14	to	to	PART
ejpam-6411	6	15	show	show	VERB
ejpam-6411	6	16	that	that	SCONJ
ejpam-6411	6	17	small	small	ADJ
ejpam-6411	6	18	changes	change	NOUN
ejpam-6411	6	19	in	in	ADP
ejpam-6411	6	20	the	the	DET
ejpam-6411	6	21	input	input	NOUN
ejpam-6411	6	22	lead	lead	NOUN
ejpam-6411	6	23	to	to	ADP
ejpam-6411	6	24	small	small	ADJ
ejpam-6411	6	25	changes	change	NOUN
ejpam-6411	6	26	in	in	ADP
ejpam-6411	6	27	the	the	DET
ejpam-6411	6	28	result	result	NOUN
ejpam-6411	6	29	.	.	PUNCT
ejpam-6411	7	1	moreover	moreover	ADV
ejpam-6411	7	2	,	,	PUNCT
ejpam-6411	7	3	we	we	PRON
ejpam-6411	7	4	provide	provide	VERB
ejpam-6411	7	5	numerical	numerical	ADJ
ejpam-6411	7	6	examples	example	NOUN
ejpam-6411	7	7	to	to	PART
ejpam-6411	7	8	support	support	VERB
ejpam-6411	7	9	and	and	CCONJ
ejpam-6411	7	10	demonstrate	demonstrate	VERB
ejpam-6411	7	11	our	our	PRON
ejpam-6411	7	12	theoretical	theoretical	ADJ
ejpam-6411	7	13	results	result	NOUN
ejpam-6411	7	14	.	.	PUNCT
ejpam-6411	8	1	2020	2020	NUM
ejpam-6411	8	2	mathematics	mathematic	NOUN
ejpam-6411	8	3	subject	subject	NOUN
ejpam-6411	8	4	classifications	classification	NOUN
ejpam-6411	8	5	:	:	PUNCT
ejpam-6411	8	6	34a08	34a08	NUM
ejpam-6411	8	7	,	,	PUNCT
ejpam-6411	8	8	34a12	34a12	NUM
ejpam-6411	8	9	,	,	PUNCT
ejpam-6411	8	10	26a33	26a33	NUM
ejpam-6411	8	11	,	,	PUNCT
ejpam-6411	8	12	47h10	47h10	DET
ejpam-6411	8	13	key	key	ADJ
ejpam-6411	8	14	words	word	NOUN
ejpam-6411	8	15	and	and	CCONJ
ejpam-6411	8	16	phrases	phrase	NOUN
ejpam-6411	8	17	:	:	PUNCT
ejpam-6411	8	18	coupled	couple	VERB
ejpam-6411	8	19	system	system	NOUN
ejpam-6411	8	20	,	,	PUNCT
ejpam-6411	8	21	fractional	fractional	ADJ
ejpam-6411	8	22	differential	differential	NOUN
ejpam-6411	8	23	equation	equation	NOUN
ejpam-6411	8	24	,	,	PUNCT
ejpam-6411	8	25	fractional	fractional	ADJ
ejpam-6411	8	26	derivative	derivative	NOUN
ejpam-6411	8	27	,	,	PUNCT
ejpam-6411	8	28	hyers	hyers	PROPN
ejpam-6411	8	29	-	-	PUNCT
ejpam-6411	8	30	ulam	ulam	PROPN
ejpam-6411	8	31	stability	stability	NOUN
ejpam-6411	8	32	∗corresponding	∗corresponde	VERB
ejpam-6411	8	33	author	author	NOUN
ejpam-6411	8	34	.	.	PUNCT
ejpam-6411	9	1	doi	doi	NOUN
ejpam-6411	9	2	:	:	PUNCT
ejpam-6411	9	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6411	https://doi.org/10.29020/nybg.ejpam.v18i4.6411	VERB
ejpam-6411	9	4	email	email	NOUN
ejpam-6411	9	5	addresses	address	VERB
ejpam-6411	9	6	:	:	PUNCT
ejpam-6411	10	1	shahermm@yahoo.com	shahermm@yahoo.com	X
ejpam-6411	10	2	(	(	PUNCT
ejpam-6411	10	3	s.	s.	PROPN
ejpam-6411	10	4	momani	momani	PROPN
ejpam-6411	10	5	)	)	PUNCT
ejpam-6411	10	6	,	,	PUNCT
ejpam-6411	10	7	hamzeh.zu@jadara.edu.jo	hamzeh.zu@jadara.edu.jo	ADV
ejpam-6411	10	8	(	(	PUNCT
ejpam-6411	10	9	h.	h.	PROPN
ejpam-6411	10	10	zureigat	zureigat	PROPN
ejpam-6411	10	11	)	)	PUNCT
ejpam-6411	10	12	,	,	PUNCT
ejpam-6411	10	13	shrideh@bau.edu.jo	shrideh@bau.edu.jo	PROPN
ejpam-6411	10	14	(	(	PUNCT
ejpam-6411	10	15	s.	s.	PROPN
ejpam-6411	10	16	al	al	PROPN
ejpam-6411	10	17	-	-	PUNCT
ejpam-6411	10	18	omari	omari	PROPN
ejpam-6411	10	19	)	)	PUNCT
ejpam-6411	10	20	,	,	PUNCT
ejpam-6411	10	21	m_khandakji@asu.edu.jo	m_khandakji@asu.edu.jo	NUM
ejpam-6411	10	22	(	(	PUNCT
ejpam-6411	10	23	m.	m.	NOUN
ejpam-6411	10	24	m.	m.	NOUN
ejpam-6411	10	25	khandaqji	khandaqji	PROPN
ejpam-6411	10	26	)	)	PUNCT
ejpam-6411	10	27	,	,	PUNCT
ejpam-6411	10	28	malsmadi@lu.edu.qa	malsmadi@lu.edu.qa	PROPN
ejpam-6411	10	29	(	(	PUNCT
ejpam-6411	10	30	m.	m.	NOUN
ejpam-6411	10	31	al	al	PROPN
ejpam-6411	10	32	-	-	PUNCT
ejpam-6411	10	33	smadi	smadi	NOUN
ejpam-6411	10	34	)	)	PUNCT
ejpam-6411	10	35	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6411	11	1	1	1	NUM
ejpam-6411	11	2	copyright	copyright	NOUN
ejpam-6411	11	3	:	:	PUNCT
ejpam-6411	11	4	©	©	PROPN
ejpam-6411	11	5	2025	2025	NUM
ejpam-6411	11	6	the	the	DET
ejpam-6411	11	7	author(s	author(s	NOUN
ejpam-6411	11	8	)	)	PUNCT
ejpam-6411	11	9	.	.	PUNCT
ejpam-6411	12	1	(	(	PUNCT
ejpam-6411	12	2	cc	cc	NOUN
ejpam-6411	12	3	by	by	ADP
ejpam-6411	12	4	-	-	PUNCT
ejpam-6411	12	5	nc	nc	PROPN
ejpam-6411	12	6	4.0	4.0	NUM
ejpam-6411	12	7	)	)	PUNCT
ejpam-6411	12	8	s.	s.	PROPN
ejpam-6411	12	9	momani	momani	PROPN
ejpam-6411	12	10	et	et	PROPN
ejpam-6411	12	11	al	al	PROPN
ejpam-6411	12	12	.	.	PUNCT
ejpam-6411	12	13	/	/	SYM
ejpam-6411	12	14	eur	eur	PROPN
ejpam-6411	12	15	.	.	PUNCT
ejpam-6411	13	1	j.	j.	PROPN
ejpam-6411	13	2	pure	pure	PROPN
ejpam-6411	13	3	appl	appl	PROPN
ejpam-6411	13	4	.	.	PROPN
ejpam-6411	13	5	math	math	PROPN
ejpam-6411	13	6	,	,	PUNCT
ejpam-6411	13	7	18	18	NUM
ejpam-6411	13	8	(	(	PUNCT
ejpam-6411	13	9	4	4	NUM
ejpam-6411	13	10	)	)	PUNCT
ejpam-6411	13	11	(	(	PUNCT
ejpam-6411	13	12	2025	2025	NUM
ejpam-6411	13	13	)	)	PUNCT
ejpam-6411	13	14	,	,	PUNCT
ejpam-6411	13	15	6411	6411	NUM
ejpam-6411	13	16	2	2	NUM
ejpam-6411	13	17	of	of	ADP
ejpam-6411	13	18	16	16	NUM
ejpam-6411	13	19	1	1	NUM
ejpam-6411	13	20	.	.	PUNCT
ejpam-6411	14	1	introduction	introduction	NOUN
ejpam-6411	14	2	due	due	ADP
ejpam-6411	14	3	to	to	ADP
ejpam-6411	14	4	their	their	PRON
ejpam-6411	14	5	numerous	numerous	ADJ
ejpam-6411	14	6	applications	application	NOUN
ejpam-6411	14	7	in	in	ADP
ejpam-6411	14	8	the	the	DET
ejpam-6411	14	9	natural	natural	ADJ
ejpam-6411	14	10	sciences	science	NOUN
ejpam-6411	14	11	and	and	CCONJ
ejpam-6411	14	12	engineering	engineering	NOUN
ejpam-6411	14	13	[	[	X
ejpam-6411	14	14	1	1	NUM
ejpam-6411	14	15	,	,	PUNCT
ejpam-6411	14	16	2	2	NUM
ejpam-6411	14	17	]	]	PUNCT
ejpam-6411	14	18	,	,	PUNCT
ejpam-6411	14	19	fractional	fractional	ADJ
ejpam-6411	14	20	differential	differential	ADJ
ejpam-6411	14	21	equations	equation	NOUN
ejpam-6411	14	22	(	(	PUNCT
ejpam-6411	14	23	fdes	fde	NOUN
ejpam-6411	14	24	)	)	PUNCT
ejpam-6411	14	25	have	have	AUX
ejpam-6411	14	26	garnered	garner	VERB
ejpam-6411	14	27	more	more	ADJ
ejpam-6411	14	28	attention	attention	NOUN
ejpam-6411	14	29	recently	recently	ADV
ejpam-6411	14	30	[	[	X
ejpam-6411	14	31	3	3	NUM
ejpam-6411	14	32	,	,	PUNCT
ejpam-6411	14	33	4	4	NUM
ejpam-6411	14	34	]	]	PUNCT
ejpam-6411	14	35	.	.	PUNCT
ejpam-6411	15	1	in	in	ADP
ejpam-6411	15	2	the	the	DET
ejpam-6411	15	3	last	last	ADJ
ejpam-6411	15	4	decade	decade	NOUN
ejpam-6411	15	5	,	,	PUNCT
ejpam-6411	15	6	the	the	DET
ejpam-6411	15	7	study	study	NOUN
ejpam-6411	15	8	of	of	ADP
ejpam-6411	15	9	fdes	fde	NOUN
ejpam-6411	15	10	has	have	AUX
ejpam-6411	15	11	garnered	garner	VERB
ejpam-6411	15	12	significant	significant	ADJ
ejpam-6411	15	13	attention	attention	NOUN
ejpam-6411	15	14	,	,	PUNCT
ejpam-6411	15	15	resulting	result	VERB
ejpam-6411	15	16	in	in	ADP
ejpam-6411	15	17	a	a	DET
ejpam-6411	15	18	fundamental	fundamental	ADJ
ejpam-6411	15	19	of	of	ADP
ejpam-6411	15	20	articles	article	NOUN
ejpam-6411	15	21	in	in	ADP
ejpam-6411	15	22	many	many	ADJ
ejpam-6411	15	23	applications	application	NOUN
ejpam-6411	15	24	across	across	ADP
ejpam-6411	15	25	various	various	ADJ
ejpam-6411	15	26	fields	field	NOUN
ejpam-6411	15	27	in	in	ADP
ejpam-6411	15	28	mathematical	mathematical	ADJ
ejpam-6411	15	29	modelling	modelling	NOUN
ejpam-6411	15	30	of	of	ADP
ejpam-6411	15	31	complex	complex	ADJ
ejpam-6411	15	32	systems	system	NOUN
ejpam-6411	15	33	[	[	X
ejpam-6411	15	34	5	5	NUM
ejpam-6411	15	35	,	,	PUNCT
ejpam-6411	15	36	6	6	NUM
ejpam-6411	15	37	]	]	PUNCT
ejpam-6411	15	38	.	.	PUNCT
ejpam-6411	16	1	such	such	ADJ
ejpam-6411	16	2	type	type	NOUN
ejpam-6411	16	3	of	of	ADP
ejpam-6411	16	4	equations	equation	NOUN
ejpam-6411	16	5	have	have	AUX
ejpam-6411	16	6	been	be	AUX
ejpam-6411	16	7	successfully	successfully	ADV
ejpam-6411	16	8	applied	apply	VERB
ejpam-6411	16	9	to	to	PART
ejpam-6411	16	10	address	address	VERB
ejpam-6411	16	11	real	real	ADJ
ejpam-6411	16	12	-	-	PUNCT
ejpam-6411	16	13	life	life	NOUN
ejpam-6411	16	14	problems	problem	NOUN
ejpam-6411	16	15	that	that	PRON
ejpam-6411	16	16	often	often	ADV
ejpam-6411	16	17	involve	involve	VERB
ejpam-6411	16	18	integral	integral	ADJ
ejpam-6411	16	19	bcs	bc	NOUN
ejpam-6411	16	20	of	of	ADP
ejpam-6411	16	21	blood	blood	NOUN
ejpam-6411	16	22	flow	flow	NOUN
ejpam-6411	16	23	dynamics	dynamic	NOUN
ejpam-6411	17	1	[	[	X
ejpam-6411	17	2	7	7	NUM
ejpam-6411	17	3	]	]	X
ejpam-6411	17	4	,	,	PUNCT
ejpam-6411	17	5	underground	underground	ADJ
ejpam-6411	17	6	water	water	NOUN
ejpam-6411	17	7	flow	flow	NOUN
ejpam-6411	17	8	[	[	X
ejpam-6411	17	9	8	8	NUM
ejpam-6411	17	10	]	]	PUNCT
ejpam-6411	17	11	,	,	PUNCT
ejpam-6411	17	12	and	and	CCONJ
ejpam-6411	17	13	population	population	NOUN
ejpam-6411	17	14	dynamics	dynamic	NOUN
ejpam-6411	17	15	[	[	X
ejpam-6411	17	16	9	9	NUM
ejpam-6411	17	17	,	,	PUNCT
ejpam-6411	17	18	10	10	NUM
ejpam-6411	17	19	]	]	PUNCT
ejpam-6411	17	20	.	.	PUNCT
ejpam-6411	18	1	a	a	DET
ejpam-6411	18	2	coupled	couple	VERB
ejpam-6411	18	3	system	system	NOUN
ejpam-6411	18	4	of	of	ADP
ejpam-6411	18	5	fdes	fde	NOUN
ejpam-6411	18	6	with	with	ADP
ejpam-6411	18	7	boundary	boundary	ADJ
ejpam-6411	18	8	conditions	condition	NOUN
ejpam-6411	18	9	bcs	bcs	NOUN
ejpam-6411	18	10	is	be	AUX
ejpam-6411	18	11	a	a	DET
ejpam-6411	18	12	complex	complex	ADJ
ejpam-6411	18	13	mathematical	mathematical	ADJ
ejpam-6411	18	14	model	model	NOUN
ejpam-6411	18	15	used	use	VERB
ejpam-6411	18	16	to	to	PART
ejpam-6411	18	17	describe	describe	VERB
ejpam-6411	18	18	biological	biological	ADJ
ejpam-6411	18	19	[	[	X
ejpam-6411	18	20	11	11	NUM
ejpam-6411	18	21	]	]	PUNCT
ejpam-6411	18	22	,	,	PUNCT
ejpam-6411	18	23	different	different	ADJ
ejpam-6411	18	24	physical	physical	ADJ
ejpam-6411	18	25	[	[	X
ejpam-6411	18	26	12	12	NUM
ejpam-6411	18	27	,	,	PUNCT
ejpam-6411	18	28	13	13	NUM
ejpam-6411	18	29	]	]	PUNCT
ejpam-6411	18	30	,	,	PUNCT
ejpam-6411	18	31	and	and	CCONJ
ejpam-6411	18	32	engineering	engineering	NOUN
ejpam-6411	18	33	processes	process	NOUN
ejpam-6411	18	34	[	[	X
ejpam-6411	18	35	14	14	NUM
ejpam-6411	18	36	,	,	PUNCT
ejpam-6411	18	37	15	15	NUM
ejpam-6411	18	38	]	]	PUNCT
ejpam-6411	18	39	.	.	PUNCT
ejpam-6411	19	1	unlike	unlike	ADP
ejpam-6411	19	2	regular	regular	ADJ
ejpam-6411	19	3	differential	differential	ADJ
ejpam-6411	19	4	equations	equation	NOUN
ejpam-6411	19	5	,	,	PUNCT
ejpam-6411	19	6	the	the	DET
ejpam-6411	19	7	fdes	fde	NOUN
ejpam-6411	19	8	use	use	VERB
ejpam-6411	19	9	derivatives	derivative	NOUN
ejpam-6411	19	10	of	of	ADP
ejpam-6411	19	11	non	non	ADJ
ejpam-6411	19	12	-	-	ADJ
ejpam-6411	19	13	integer	integer	ADJ
ejpam-6411	19	14	orders	order	NOUN
ejpam-6411	19	15	to	to	PART
ejpam-6411	19	16	provide	provide	VERB
ejpam-6411	19	17	a	a	DET
ejpam-6411	19	18	better	well	ADJ
ejpam-6411	19	19	capture	capture	NOUN
ejpam-6411	19	20	the	the	DET
ejpam-6411	19	21	memory	memory	NOUN
ejpam-6411	19	22	and	and	CCONJ
ejpam-6411	19	23	history	history	NOUN
ejpam-6411	19	24	of	of	ADP
ejpam-6411	19	25	a	a	DET
ejpam-6411	19	26	system	system	NOUN
ejpam-6411	19	27	.	.	PUNCT
ejpam-6411	20	1	when	when	SCONJ
ejpam-6411	20	2	these	these	DET
ejpam-6411	20	3	equations	equation	NOUN
ejpam-6411	20	4	are	be	AUX
ejpam-6411	20	5	coupled	couple	VERB
ejpam-6411	20	6	,	,	PUNCT
ejpam-6411	20	7	it	it	PRON
ejpam-6411	20	8	means	mean	VERB
ejpam-6411	20	9	they	they	PRON
ejpam-6411	20	10	are	be	AUX
ejpam-6411	20	11	linked	link	VERB
ejpam-6411	20	12	together	together	ADV
ejpam-6411	20	13	and	and	CCONJ
ejpam-6411	20	14	must	must	AUX
ejpam-6411	20	15	be	be	AUX
ejpam-6411	20	16	solved	solve	VERB
ejpam-6411	20	17	at	at	ADP
ejpam-6411	20	18	the	the	DET
ejpam-6411	20	19	same	same	ADJ
ejpam-6411	20	20	time	time	NOUN
ejpam-6411	20	21	because	because	SCONJ
ejpam-6411	20	22	the	the	DET
ejpam-6411	20	23	variables	variable	NOUN
ejpam-6411	20	24	affect	affect	VERB
ejpam-6411	20	25	each	each	DET
ejpam-6411	20	26	other	other	ADJ
ejpam-6411	20	27	.	.	PUNCT
ejpam-6411	21	1	to	to	PART
ejpam-6411	21	2	ensure	ensure	VERB
ejpam-6411	21	3	that	that	SCONJ
ejpam-6411	21	4	the	the	DET
ejpam-6411	21	5	solutions	solution	NOUN
ejpam-6411	21	6	to	to	ADP
ejpam-6411	21	7	real	real	ADJ
ejpam-6411	21	8	-	-	PUNCT
ejpam-6411	21	9	life	life	NOUN
ejpam-6411	21	10	problems	problem	NOUN
ejpam-6411	21	11	are	be	AUX
ejpam-6411	21	12	realistic	realistic	ADJ
ejpam-6411	21	13	,	,	PUNCT
ejpam-6411	21	14	mathematicians	mathematician	NOUN
ejpam-6411	21	15	used	use	VERB
ejpam-6411	21	16	the	the	DET
ejpam-6411	21	17	bcs	bcs	NOUN
ejpam-6411	21	18	to	to	PART
ejpam-6411	21	19	show	show	VERB
ejpam-6411	21	20	how	how	SCONJ
ejpam-6411	21	21	the	the	DET
ejpam-6411	21	22	solution	solution	NOUN
ejpam-6411	21	23	should	should	AUX
ejpam-6411	21	24	behave	behave	VERB
ejpam-6411	21	25	at	at	ADP
ejpam-6411	21	26	the	the	DET
ejpam-6411	21	27	edges	edge	NOUN
ejpam-6411	21	28	of	of	ADP
ejpam-6411	21	29	the	the	DET
ejpam-6411	21	30	problem	problem	NOUN
ejpam-6411	21	31	domain	domain	NOUN
ejpam-6411	21	32	[	[	X
ejpam-6411	21	33	16	16	NUM
ejpam-6411	21	34	,	,	PUNCT
ejpam-6411	21	35	17	17	NUM
ejpam-6411	21	36	]	]	PUNCT
ejpam-6411	21	37	.	.	PUNCT
ejpam-6411	22	1	these	these	DET
ejpam-6411	22	2	models	model	NOUN
ejpam-6411	22	3	are	be	AUX
ejpam-6411	22	4	important	important	ADJ
ejpam-6411	22	5	in	in	ADP
ejpam-6411	22	6	fields	field	NOUN
ejpam-6411	22	7	like	like	ADP
ejpam-6411	22	8	materials	material	NOUN
ejpam-6411	22	9	science	science	NOUN
ejpam-6411	22	10	since	since	SCONJ
ejpam-6411	22	11	[	[	X
ejpam-6411	22	12	18	18	NUM
ejpam-6411	22	13	]	]	PUNCT
ejpam-6411	22	14	they	they	PRON
ejpam-6411	22	15	explain	explain	VERB
ejpam-6411	22	16	how	how	SCONJ
ejpam-6411	22	17	materials	material	NOUN
ejpam-6411	22	18	behave	behave	VERB
ejpam-6411	22	19	over	over	ADP
ejpam-6411	22	20	time	time	NOUN
ejpam-6411	22	21	and	and	CCONJ
ejpam-6411	22	22	in	in	ADP
ejpam-6411	22	23	control	control	NOUN
ejpam-6411	22	24	systems	system	NOUN
ejpam-6411	22	25	where	where	SCONJ
ejpam-6411	22	26	they	they	PRON
ejpam-6411	22	27	manage	manage	VERB
ejpam-6411	22	28	complex	complex	ADJ
ejpam-6411	22	29	systems	system	NOUN
ejpam-6411	22	30	.	.	PUNCT
ejpam-6411	23	1	solving	solve	VERB
ejpam-6411	23	2	these	these	DET
ejpam-6411	23	3	equations	equation	NOUN
ejpam-6411	23	4	is	be	AUX
ejpam-6411	23	5	challenging	challenge	VERB
ejpam-6411	23	6	and	and	CCONJ
ejpam-6411	23	7	requires	require	VERB
ejpam-6411	23	8	advanced	advanced	ADJ
ejpam-6411	23	9	mathematical	mathematical	ADJ
ejpam-6411	23	10	methods	method	NOUN
ejpam-6411	23	11	.	.	PUNCT
ejpam-6411	24	1	in	in	ADP
ejpam-6411	24	2	the	the	DET
ejpam-6411	24	3	last	last	ADJ
ejpam-6411	24	4	decade	decade	NOUN
ejpam-6411	24	5	,	,	PUNCT
ejpam-6411	24	6	many	many	ADJ
ejpam-6411	24	7	mathematicians	mathematician	NOUN
ejpam-6411	24	8	studied	study	VERB
ejpam-6411	24	9	a	a	DET
ejpam-6411	24	10	coupled	couple	VERB
ejpam-6411	24	11	system	system	NOUN
ejpam-6411	24	12	of	of	ADP
ejpam-6411	24	13	fdes	fde	NOUN
ejpam-6411	24	14	of	of	ADP
ejpam-6411	24	15	certain	certain	ADJ
ejpam-6411	24	16	integral	integral	ADJ
ejpam-6411	24	17	bcs	bc	NOUN
ejpam-6411	24	18	.	.	PUNCT
ejpam-6411	25	1	ntouyas	ntouyas	NOUN
ejpam-6411	25	2	and	and	CCONJ
ejpam-6411	25	3	obaid	obaid	X
ejpam-6411	26	1	[	[	X
ejpam-6411	26	2	19	19	NUM
ejpam-6411	26	3	]	]	PUNCT
ejpam-6411	26	4	discussed	discuss	VERB
ejpam-6411	26	5	a	a	DET
ejpam-6411	26	6	system	system	NOUN
ejpam-6411	26	7	of	of	ADP
ejpam-6411	26	8	fdes	fde	NOUN
ejpam-6411	26	9	of	of	ADP
ejpam-6411	26	10	coupled	couple	VERB
ejpam-6411	26	11	equations	equation	NOUN
ejpam-6411	26	12	with	with	ADP
ejpam-6411	26	13	nonlocal	nonlocal	ADJ
ejpam-6411	26	14	integral	integral	ADJ
ejpam-6411	26	15	boundaries	boundary	NOUN
ejpam-6411	26	16	.	.	PUNCT
ejpam-6411	27	1	the	the	DET
ejpam-6411	27	2	banach	banach	NOUN
ejpam-6411	27	3	’s	’s	PART
ejpam-6411	27	4	fixed	fix	VERB
ejpam-6411	27	5	-	-	PUNCT
ejpam-6411	27	6	point	point	NOUN
ejpam-6411	27	7	theorem	theorem	NOUN
ejpam-6411	27	8	and	and	CCONJ
ejpam-6411	27	9	schauder	schauder	NOUN
ejpam-6411	27	10	’s	’s	PART
ejpam-6411	27	11	alternative	alternative	NOUN
ejpam-6411	27	12	are	be	AUX
ejpam-6411	27	13	discussed	discuss	VERB
ejpam-6411	27	14	and	and	CCONJ
ejpam-6411	27	15	implemented	implement	VERB
ejpam-6411	27	16	to	to	PART
ejpam-6411	27	17	investigate	investigate	VERB
ejpam-6411	27	18	both	both	DET
ejpam-6411	27	19	uniqueness	uniqueness	NOUN
ejpam-6411	27	20	and	and	CCONJ
ejpam-6411	27	21	existence	existence	NOUN
ejpam-6411	27	22	of	of	ADP
ejpam-6411	27	23	solutions	solution	NOUN
ejpam-6411	27	24	for	for	ADP
ejpam-6411	27	25	the	the	DET
ejpam-6411	27	26	proposed	propose	VERB
ejpam-6411	27	27	coupled	couple	VERB
ejpam-6411	27	28	fdes	fde	NOUN
ejpam-6411	27	29	under	under	ADP
ejpam-6411	27	30	riemann	riemann	PROPN
ejpam-6411	27	31	-	-	PUNCT
ejpam-6411	27	32	liouville	liouville	VERB
ejpam-6411	27	33	integral	integral	ADJ
ejpam-6411	27	34	bcs	bc	NOUN
ejpam-6411	27	35	.	.	PUNCT
ejpam-6411	28	1	ahmed	ahmed	PROPN
ejpam-6411	28	2	and	and	CCONJ
ejpam-6411	28	3	ntouyas	ntouyas	NOUN
ejpam-6411	28	4	[	[	X
ejpam-6411	28	5	20	20	NUM
ejpam-6411	28	6	]	]	X
ejpam-6411	28	7	utilized	utilize	VERB
ejpam-6411	28	8	schauder	schauder	NOUN
ejpam-6411	28	9	’s	’s	PART
ejpam-6411	28	10	fixed	fix	VERB
ejpam-6411	28	11	-	-	PUNCT
ejpam-6411	28	12	point	point	NOUN
ejpam-6411	28	13	and	and	CCONJ
ejpam-6411	28	14	banach	banach	NOUN
ejpam-6411	28	15	’s	’s	PART
ejpam-6411	28	16	fixed	fix	VERB
ejpam-6411	28	17	-	-	PUNCT
ejpam-6411	28	18	point	point	NOUN
ejpam-6411	28	19	theorems	theorem	NOUN
ejpam-6411	28	20	to	to	PART
ejpam-6411	28	21	demonstrate	demonstrate	VERB
ejpam-6411	28	22	the	the	DET
ejpam-6411	28	23	existence	existence	NOUN
ejpam-6411	28	24	of	of	ADP
ejpam-6411	28	25	solutions	solution	NOUN
ejpam-6411	28	26	for	for	ADP
ejpam-6411	28	27	coupled	couple	VERB
ejpam-6411	28	28	fractional	fractional	ADJ
ejpam-6411	28	29	des	des	PROPN
ejpam-6411	28	30	.	.	PUNCT
ejpam-6411	29	1	these	these	DET
ejpam-6411	29	2	equations	equation	NOUN
ejpam-6411	29	3	have	have	VERB
ejpam-6411	29	4	different	different	ADJ
ejpam-6411	29	5	cases	case	NOUN
ejpam-6411	29	6	including	include	VERB
ejpam-6411	29	7	those	those	PRON
ejpam-6411	29	8	with	with	ADP
ejpam-6411	29	9	coupled	couple	VERB
ejpam-6411	29	10	integral	integral	ADJ
ejpam-6411	29	11	boundary	boundary	ADJ
ejpam-6411	29	12	conditions	condition	NOUN
ejpam-6411	29	13	.	.	PUNCT
ejpam-6411	30	1	the	the	DET
ejpam-6411	30	2	banach	banach	ADV
ejpam-6411	30	3	fixed	fix	VERB
ejpam-6411	30	4	-	-	PUNCT
ejpam-6411	30	5	point	point	NOUN
ejpam-6411	30	6	theorem	theorem	NOUN
ejpam-6411	30	7	and	and	CCONJ
ejpam-6411	30	8	the	the	DET
ejpam-6411	30	9	leray	leray	ADJ
ejpam-6411	30	10	-	-	PUNCT
ejpam-6411	30	11	schauder	schauder	NOUN
ejpam-6411	30	12	alternative	alternative	NOUN
ejpam-6411	30	13	considered	consider	VERB
ejpam-6411	30	14	important	important	ADJ
ejpam-6411	30	15	proof	proof	ADJ
ejpam-6411	30	16	techniques	technique	NOUN
ejpam-6411	30	17	of	of	ADP
ejpam-6411	30	18	coupled	couple	VERB
ejpam-6411	30	19	systems	system	NOUN
ejpam-6411	30	20	of	of	ADP
ejpam-6411	30	21	nonlinear	nonlinear	ADJ
ejpam-6411	30	22	fdes	fde	NOUN
ejpam-6411	30	23	due	due	ADP
ejpam-6411	30	24	to	to	ADP
ejpam-6411	30	25	their	their	PRON
ejpam-6411	30	26	effectiveness	effectiveness	NOUN
ejpam-6411	30	27	in	in	ADP
ejpam-6411	30	28	investigating	investigate	VERB
ejpam-6411	30	29	existence	existence	NOUN
ejpam-6411	30	30	and	and	CCONJ
ejpam-6411	30	31	uniqueness	uniqueness	NOUN
ejpam-6411	30	32	of	of	ADP
ejpam-6411	30	33	solutions	solution	NOUN
ejpam-6411	30	34	for	for	ADP
ejpam-6411	30	35	coupled	couple	VERB
ejpam-6411	30	36	systems	system	NOUN
ejpam-6411	30	37	of	of	ADP
ejpam-6411	30	38	nonlinear	nonlinear	ADJ
ejpam-6411	30	39	fdes	fde	NOUN
ejpam-6411	30	40	in	in	ADP
ejpam-6411	30	41	those	those	DET
ejpam-6411	30	42	coupled	couple	VERB
ejpam-6411	30	43	systems	system	NOUN
ejpam-6411	30	44	that	that	PRON
ejpam-6411	30	45	involve	involve	VERB
ejpam-6411	30	46	complex	complex	ADJ
ejpam-6411	30	47	bcs	bc	NOUN
ejpam-6411	30	48	.	.	PUNCT
ejpam-6411	31	1	the	the	DET
ejpam-6411	31	2	banach	banach	NOUN
ejpam-6411	31	3	’s	’s	PART
ejpam-6411	31	4	fixed	fix	VERB
ejpam-6411	31	5	-	-	PUNCT
ejpam-6411	31	6	point	point	NOUN
ejpam-6411	31	7	theorem	theorem	NOUN
ejpam-6411	31	8	is	be	AUX
ejpam-6411	31	9	valuable	valuable	ADJ
ejpam-6411	31	10	for	for	ADP
ejpam-6411	31	11	proving	prove	VERB
ejpam-6411	31	12	uniqueness	uniqueness	NOUN
ejpam-6411	31	13	since	since	SCONJ
ejpam-6411	31	14	it	it	PRON
ejpam-6411	31	15	ensures	ensure	VERB
ejpam-6411	31	16	a	a	DET
ejpam-6411	31	17	unique	unique	ADJ
ejpam-6411	31	18	fixed	fix	VERB
ejpam-6411	31	19	point	point	NOUN
ejpam-6411	31	20	for	for	ADP
ejpam-6411	31	21	contraction	contraction	NOUN
ejpam-6411	31	22	mappings	mapping	NOUN
ejpam-6411	31	23	on	on	ADP
ejpam-6411	31	24	a	a	DET
ejpam-6411	31	25	complete	complete	ADJ
ejpam-6411	31	26	metric	metric	ADJ
ejpam-6411	31	27	space	space	NOUN
ejpam-6411	31	28	.	.	PUNCT
ejpam-6411	32	1	in	in	ADP
ejpam-6411	32	2	contrast	contrast	NOUN
ejpam-6411	32	3	,	,	PUNCT
ejpam-6411	32	4	the	the	DET
ejpam-6411	32	5	leray	leray	NOUN
ejpam-6411	32	6	-	-	PUNCT
ejpam-6411	32	7	schauder	schauder	NOUN
ejpam-6411	32	8	is	be	AUX
ejpam-6411	32	9	used	use	VERB
ejpam-6411	32	10	to	to	PART
ejpam-6411	32	11	prove	prove	VERB
ejpam-6411	32	12	existence	existence	NOUN
ejpam-6411	32	13	by	by	ADP
ejpam-6411	32	14	dealing	deal	VERB
ejpam-6411	32	15	with	with	ADP
ejpam-6411	32	16	compact	compact	ADJ
ejpam-6411	32	17	and	and	CCONJ
ejpam-6411	32	18	continuous	continuous	ADJ
ejpam-6411	32	19	mappings	mapping	NOUN
ejpam-6411	32	20	that	that	PRON
ejpam-6411	32	21	may	may	AUX
ejpam-6411	32	22	not	not	PART
ejpam-6411	32	23	be	be	AUX
ejpam-6411	32	24	strict	strict	ADJ
ejpam-6411	32	25	contractions	contraction	NOUN
ejpam-6411	32	26	.	.	PUNCT
ejpam-6411	33	1	this	this	PRON
ejpam-6411	33	2	led	lead	VERB
ejpam-6411	33	3	to	to	ADP
ejpam-6411	33	4	extending	extend	VERB
ejpam-6411	33	5	the	the	DET
ejpam-6411	33	6	applicability	applicability	NOUN
ejpam-6411	33	7	of	of	ADP
ejpam-6411	33	8	the	the	DET
ejpam-6411	33	9	fixed	fix	VERB
ejpam-6411	33	10	-	-	PUNCT
ejpam-6411	33	11	point	point	NOUN
ejpam-6411	33	12	theory	theory	NOUN
ejpam-6411	33	13	.	.	PUNCT
ejpam-6411	34	1	these	these	DET
ejpam-6411	34	2	theorems	theorem	NOUN
ejpam-6411	34	3	provide	provide	VERB
ejpam-6411	34	4	strong	strong	ADJ
ejpam-6411	34	5	and	and	CCONJ
ejpam-6411	34	6	dependable	dependable	ADJ
ejpam-6411	34	7	techniques	technique	NOUN
ejpam-6411	34	8	that	that	PRON
ejpam-6411	34	9	have	have	AUX
ejpam-6411	34	10	been	be	AUX
ejpam-6411	34	11	demonstrated	demonstrate	VERB
ejpam-6411	34	12	in	in	ADP
ejpam-6411	34	13	the	the	DET
ejpam-6411	34	14	literature	literature	NOUN
ejpam-6411	34	15	,	,	PUNCT
ejpam-6411	34	16	making	make	VERB
ejpam-6411	34	17	them	they	PRON
ejpam-6411	34	18	ideal	ideal	ADJ
ejpam-6411	34	19	for	for	ADP
ejpam-6411	34	20	nonlinear	nonlinear	ADJ
ejpam-6411	34	21	situations	situation	NOUN
ejpam-6411	34	22	without	without	ADP
ejpam-6411	34	23	the	the	DET
ejpam-6411	34	24	need	need	NOUN
ejpam-6411	34	25	for	for	ADP
ejpam-6411	34	26	linearisation	linearisation	NOUN
ejpam-6411	34	27	.	.	PUNCT
ejpam-6411	35	1	using	use	VERB
ejpam-6411	35	2	fixedpoint	fixedpoint	NOUN
ejpam-6411	35	3	theorems	theorem	NOUN
ejpam-6411	35	4	of	of	ADP
ejpam-6411	35	5	banach	banach	NOUN
ejpam-6411	35	6	and	and	CCONJ
ejpam-6411	35	7	the	the	DET
ejpam-6411	35	8	leray	leray	ADJ
ejpam-6411	35	9	-	-	PUNCT
ejpam-6411	35	10	schauder	schauder	NOUN
ejpam-6411	35	11	alternative	alternative	NOUN
ejpam-6411	35	12	together	together	ADV
ejpam-6411	35	13	takes	take	VERB
ejpam-6411	35	14	advantage	advantage	NOUN
ejpam-6411	35	15	of	of	ADP
ejpam-6411	35	16	their	their	PRON
ejpam-6411	35	17	strengths	strength	NOUN
ejpam-6411	35	18	which	which	PRON
ejpam-6411	35	19	offers	offer	VERB
ejpam-6411	35	20	a	a	DET
ejpam-6411	35	21	complete	complete	ADJ
ejpam-6411	35	22	approach	approach	NOUN
ejpam-6411	35	23	to	to	ADP
ejpam-6411	35	24	handling	handle	VERB
ejpam-6411	35	25	the	the	DET
ejpam-6411	35	26	complexity	complexity	NOUN
ejpam-6411	35	27	of	of	ADP
ejpam-6411	35	28	a	a	DET
ejpam-6411	35	29	coupled	couple	VERB
ejpam-6411	35	30	system	system	NOUN
ejpam-6411	35	31	of	of	ADP
ejpam-6411	35	32	fractional	fractional	PROPN
ejpam-6411	35	33	des	des	PROPN
ejpam-6411	35	34	.	.	PROPN
ejpam-6411	35	35	such	such	ADJ
ejpam-6411	35	36	flexibility	flexibility	NOUN
ejpam-6411	35	37	and	and	CCONJ
ejpam-6411	35	38	dependability	dependability	NOUN
ejpam-6411	35	39	make	make	VERB
ejpam-6411	35	40	them	they	PRON
ejpam-6411	35	41	perfect	perfect	ADJ
ejpam-6411	35	42	for	for	SCONJ
ejpam-6411	35	43	the	the	DET
ejpam-6411	35	44	theoretical	theoretical	ADJ
ejpam-6411	35	45	framework	framework	NOUN
ejpam-6411	35	46	needed	need	VERB
ejpam-6411	35	47	to	to	PART
ejpam-6411	35	48	manage	manage	VERB
ejpam-6411	35	49	the	the	DET
ejpam-6411	35	50	detailed	detailed	ADJ
ejpam-6411	35	51	behavior	behavior	NOUN
ejpam-6411	35	52	of	of	ADP
ejpam-6411	35	53	the	the	DET
ejpam-6411	35	54	coupled	couple	VERB
ejpam-6411	35	55	system	system	NOUN
ejpam-6411	35	56	of	of	ADP
ejpam-6411	35	57	fractional	fractional	PROPN
ejpam-6411	35	58	des	des	PROPN
ejpam-6411	35	59	.	.	PUNCT
ejpam-6411	35	60	studying	study	VERB
ejpam-6411	35	61	coupled	couple	VERB
ejpam-6411	35	62	systems	system	NOUN
ejpam-6411	35	63	of	of	ADP
ejpam-6411	35	64	fdes	fde	NOUN
ejpam-6411	35	65	with	with	ADP
ejpam-6411	35	66	integral	integral	ADJ
ejpam-6411	35	67	bcs	bcs	NOUN
ejpam-6411	35	68	is	be	AUX
ejpam-6411	35	69	crucial	crucial	ADJ
ejpam-6411	35	70	for	for	ADP
ejpam-6411	35	71	theoretical	theoretical	ADJ
ejpam-6411	35	72	mathes	mathe	NOUN
ejpam-6411	35	73	.	.	PUNCT
ejpam-6411	36	1	momani	momani	PROPN
ejpam-6411	36	2	et	et	PROPN
ejpam-6411	36	3	al	al	PROPN
ejpam-6411	36	4	.	.	PUNCT
ejpam-6411	36	5	/	/	SYM
ejpam-6411	36	6	eur	eur	PROPN
ejpam-6411	36	7	.	.	PUNCT
ejpam-6411	37	1	j.	j.	PROPN
ejpam-6411	37	2	pure	pure	PROPN
ejpam-6411	37	3	appl	appl	PROPN
ejpam-6411	37	4	.	.	PROPN
ejpam-6411	37	5	math	math	PROPN
ejpam-6411	37	6	,	,	PUNCT
ejpam-6411	37	7	18	18	NUM
ejpam-6411	37	8	(	(	PUNCT
ejpam-6411	37	9	4	4	NUM
ejpam-6411	37	10	)	)	PUNCT
ejpam-6411	37	11	(	(	PUNCT
ejpam-6411	37	12	2025	2025	NUM
ejpam-6411	37	13	)	)	PUNCT
ejpam-6411	37	14	,	,	PUNCT
ejpam-6411	37	15	6411	6411	NUM
ejpam-6411	37	16	3	3	NUM
ejpam-6411	37	17	of	of	ADP
ejpam-6411	37	18	16	16	NUM
ejpam-6411	37	19	matics	matic	NOUN
ejpam-6411	37	20	and	and	CCONJ
ejpam-6411	37	21	practical	practical	ADJ
ejpam-6411	37	22	applications	application	NOUN
ejpam-6411	37	23	.	.	PUNCT
ejpam-6411	38	1	these	these	DET
ejpam-6411	38	2	systems	system	NOUN
ejpam-6411	38	3	arise	arise	VERB
ejpam-6411	38	4	in	in	ADP
ejpam-6411	38	5	various	various	ADJ
ejpam-6411	38	6	fields	field	NOUN
ejpam-6411	38	7	such	such	ADJ
ejpam-6411	38	8	as	as	ADP
ejpam-6411	38	9	population	population	NOUN
ejpam-6411	38	10	dynamics	dynamic	NOUN
ejpam-6411	38	11	and	and	CCONJ
ejpam-6411	38	12	heat	heat	NOUN
ejpam-6411	38	13	conduction	conduction	NOUN
ejpam-6411	38	14	[	[	X
ejpam-6411	38	15	21	21	NUM
ejpam-6411	38	16	,	,	PUNCT
ejpam-6411	38	17	22	22	NUM
ejpam-6411	38	18	]	]	PUNCT
ejpam-6411	38	19	.	.	PUNCT
ejpam-6411	39	1	by	by	ADP
ejpam-6411	39	2	considering	consider	VERB
ejpam-6411	39	3	integral	integral	ADJ
ejpam-6411	39	4	bcs	bc	NOUN
ejpam-6411	39	5	,	,	PUNCT
ejpam-6411	39	6	we	we	PRON
ejpam-6411	39	7	capture	capture	VERB
ejpam-6411	39	8	more	more	ADV
ejpam-6411	39	9	realistic	realistic	ADJ
ejpam-6411	39	10	behavior	behavior	NOUN
ejpam-6411	39	11	and	and	CCONJ
ejpam-6411	39	12	improve	improve	VERB
ejpam-6411	39	13	accuracy	accuracy	NOUN
ejpam-6411	39	14	in	in	ADP
ejpam-6411	39	15	modeling	model	VERB
ejpam-6411	39	16	real	real	ADJ
ejpam-6411	39	17	-	-	PUNCT
ejpam-6411	39	18	world	world	NOUN
ejpam-6411	39	19	phenomena	phenomenon	NOUN
ejpam-6411	39	20	[	[	X
ejpam-6411	39	21	23	23	NUM
ejpam-6411	39	22	]	]	PUNCT
ejpam-6411	39	23	.	.	PUNCT
ejpam-6411	40	1	solutions	solution	NOUN
ejpam-6411	40	2	to	to	ADP
ejpam-6411	40	3	these	these	DET
ejpam-6411	40	4	systems	system	NOUN
ejpam-6411	40	5	provide	provide	VERB
ejpam-6411	40	6	insights	insight	NOUN
ejpam-6411	40	7	into	into	ADP
ejpam-6411	40	8	physical	physical	ADJ
ejpam-6411	40	9	processes	process	NOUN
ejpam-6411	40	10	and	and	CCONJ
ejpam-6411	40	11	optimal	optimal	ADJ
ejpam-6411	40	12	control	control	NOUN
ejpam-6411	40	13	strategies	strategy	NOUN
ejpam-6411	40	14	[	[	X
ejpam-6411	40	15	24	24	NUM
ejpam-6411	40	16	]	]	PUNCT
ejpam-6411	40	17	.	.	PUNCT
ejpam-6411	41	1	this	this	DET
ejpam-6411	41	2	field	field	NOUN
ejpam-6411	41	3	provides	provide	VERB
ejpam-6411	41	4	our	our	PRON
ejpam-6411	41	5	understanding	understanding	NOUN
ejpam-6411	41	6	of	of	ADP
ejpam-6411	41	7	complex	complex	ADJ
ejpam-6411	41	8	dynamics	dynamic	NOUN
ejpam-6411	41	9	and	and	CCONJ
ejpam-6411	41	10	contributes	contribute	VERB
ejpam-6411	41	11	to	to	ADP
ejpam-6411	41	12	scientific	scientific	ADJ
ejpam-6411	41	13	advancements	advancement	NOUN
ejpam-6411	41	14	.	.	PUNCT
ejpam-6411	42	1	thus	thus	ADV
ejpam-6411	42	2	,	,	PUNCT
ejpam-6411	42	3	it	it	PRON
ejpam-6411	42	4	is	be	AUX
ejpam-6411	42	5	crucial	crucial	ADJ
ejpam-6411	42	6	to	to	PART
ejpam-6411	42	7	concentrate	concentrate	VERB
ejpam-6411	42	8	on	on	ADP
ejpam-6411	42	9	studying	study	VERB
ejpam-6411	42	10	the	the	DET
ejpam-6411	42	11	coupled	couple	VERB
ejpam-6411	42	12	systems	system	NOUN
ejpam-6411	42	13	of	of	ADP
ejpam-6411	42	14	fdes	fde	NOUN
ejpam-6411	42	15	with	with	ADP
ejpam-6411	42	16	integral	integral	ADJ
ejpam-6411	42	17	bcs	bc	NOUN
ejpam-6411	42	18	in	in	ADP
ejpam-6411	42	19	order	order	NOUN
ejpam-6411	42	20	to	to	PART
ejpam-6411	42	21	define	define	VERB
ejpam-6411	42	22	complete	complete	ADJ
ejpam-6411	42	23	and	and	CCONJ
ejpam-6411	42	24	realistic	realistic	ADJ
ejpam-6411	42	25	models	model	NOUN
ejpam-6411	42	26	,	,	PUNCT
ejpam-6411	42	27	fill	fill	VERB
ejpam-6411	42	28	in	in	ADP
ejpam-6411	42	29	research	research	NOUN
ejpam-6411	42	30	gaps	gap	NOUN
ejpam-6411	42	31	,	,	PUNCT
ejpam-6411	42	32	and	and	CCONJ
ejpam-6411	42	33	improve	improve	VERB
ejpam-6411	42	34	our	our	PRON
ejpam-6411	42	35	comprehension	comprehension	NOUN
ejpam-6411	42	36	of	of	ADP
ejpam-6411	42	37	stability	stability	NOUN
ejpam-6411	42	38	and	and	CCONJ
ejpam-6411	42	39	control	control	NOUN
ejpam-6411	42	40	in	in	ADP
ejpam-6411	42	41	these	these	DET
ejpam-6411	42	42	systems	system	NOUN
ejpam-6411	42	43	.	.	PUNCT
ejpam-6411	43	1	in	in	ADP
ejpam-6411	43	2	this	this	DET
ejpam-6411	43	3	paper	paper	NOUN
ejpam-6411	43	4	,	,	PUNCT
ejpam-6411	43	5	the	the	DET
ejpam-6411	43	6	coupled	couple	VERB
ejpam-6411	43	7	system	system	NOUN
ejpam-6411	43	8	of	of	ADP
ejpam-6411	43	9	nonlinear	nonlinear	ADJ
ejpam-6411	43	10	fdes	fde	NOUN
ejpam-6411	43	11	with	with	ADP
ejpam-6411	43	12	two	two	NUM
ejpam-6411	43	13	points	point	NOUN
ejpam-6411	43	14	integral	integral	ADJ
ejpam-6411	43	15	coupled	couple	VERB
ejpam-6411	43	16	bcs	bcs	NOUN
ejpam-6411	43	17	is	be	AUX
ejpam-6411	43	18	defined	define	VERB
ejpam-6411	43	19	as	as	SCONJ
ejpam-6411	43	20	follows	follow	VERB
ejpam-6411	43	21	:	:	PUNCT
ejpam-6411	43	22	{	{	PUNCT
ejpam-6411	44	1	cdα	cdα	NOUN
ejpam-6411	44	2	(	(	PUNCT
ejpam-6411	44	3	t	t	NOUN
ejpam-6411	44	4	)	)	PUNCT
ejpam-6411	44	5	=	=	SYM
ejpam-6411	44	6	u	u	NOUN
ejpam-6411	44	7	(	(	PUNCT
ejpam-6411	44	8	τ	τ	PROPN
ejpam-6411	44	9	,	,	PUNCT
ejpam-6411	44	10	υ	υ	PROPN
ejpam-6411	44	11	(	(	PUNCT
ejpam-6411	44	12	τ	τ	PROPN
ejpam-6411	44	13	)	)	PUNCT
ejpam-6411	44	14	,	,	PUNCT
ejpam-6411	44	15	ω	ω	PROPN
ejpam-6411	44	16	(	(	PUNCT
ejpam-6411	44	17	τ	τ	PROPN
ejpam-6411	44	18	)	)	PUNCT
ejpam-6411	44	19	)	)	PUNCT
ejpam-6411	44	20	,	,	PUNCT
ejpam-6411	44	21	τ	τ	PROPN
ejpam-6411	44	22	∈	∈	PROPN
ejpam-6411	45	1	[	[	X
ejpam-6411	45	2	0,h	0,h	X
ejpam-6411	45	3	]	]	X
ejpam-6411	45	4	,	,	PUNCT
ejpam-6411	45	5	1	1	NUM
ejpam-6411	45	6	<	<	X
ejpam-6411	45	7	α	α	PROPN
ejpam-6411	45	8	≤	≤	NUM
ejpam-6411	45	9	2	2	NUM
ejpam-6411	45	10	,	,	PUNCT
ejpam-6411	45	11	cdβ	cdβ	X
ejpam-6411	45	12	(	(	PUNCT
ejpam-6411	45	13	t	t	NOUN
ejpam-6411	45	14	)	)	PUNCT
ejpam-6411	45	15	=	=	SYM
ejpam-6411	45	16	h	h	PROPN
ejpam-6411	45	17	(	(	PUNCT
ejpam-6411	45	18	t	t	PROPN
ejpam-6411	45	19	,	,	PUNCT
ejpam-6411	45	20	υ	υ	X
ejpam-6411	45	21	(	(	PUNCT
ejpam-6411	45	22	τ	τ	PROPN
ejpam-6411	45	23	)	)	PUNCT
ejpam-6411	45	24	,	,	PUNCT
ejpam-6411	45	25	ω	ω	PROPN
ejpam-6411	45	26	(	(	PUNCT
ejpam-6411	45	27	t	t	PROPN
ejpam-6411	45	28	)	)	PUNCT
ejpam-6411	45	29	)	)	PUNCT
ejpam-6411	45	30	,	,	PUNCT
ejpam-6411	45	31	τ	τ	PROPN
ejpam-6411	45	32	∈	∈	PROPN
ejpam-6411	46	1	[	[	X
ejpam-6411	46	2	0,h	0,h	X
ejpam-6411	46	3	]	]	X
ejpam-6411	46	4	,	,	PUNCT
ejpam-6411	46	5	1	1	NUM
ejpam-6411	46	6	<	<	X
ejpam-6411	46	7	β	β	X
ejpam-6411	46	8	≤	≤	NOUN
ejpam-6411	46	9	2	2	NUM
ejpam-6411	46	10	,	,	PUNCT
ejpam-6411	46	11	(	(	PUNCT
ejpam-6411	46	12	1	1	X
ejpam-6411	46	13	)	)	PUNCT
ejpam-6411	46	14	where	where	SCONJ
ejpam-6411	46	15	h	h	NOUN
ejpam-6411	46	16	>	>	X
ejpam-6411	46	17	0	0	PUNCT
ejpam-6411	46	18	,	,	PUNCT
ejpam-6411	46	19	enhanced	enhance	VERB
ejpam-6411	46	20	with	with	ADP
ejpam-6411	46	21	integral	integral	ADJ
ejpam-6411	46	22	bcs	bc	NOUN
ejpam-6411	46	23	in	in	ADP
ejpam-6411	46	24	the	the	DET
ejpam-6411	46	25	following	follow	VERB
ejpam-6411	46	26	form	form	NOUN
ejpam-6411	46	27	:	:	PUNCT
ejpam-6411	46	28	{	{	PUNCT
ejpam-6411	46	29	∫	∫	PROPN
ejpam-6411	46	30	h	h	NOUN
ejpam-6411	46	31	0	0	PUNCT
ejpam-6411	47	1	υ	υ	PRON
ejpam-6411	47	2	′(t)dt	′(t)dt	PROPN
ejpam-6411	47	3	=	=	PUNCT
ejpam-6411	47	4	ζω	ζω	NOUN
ejpam-6411	47	5	′(µ	′(µ	PROPN
ejpam-6411	47	6	)	)	PUNCT
ejpam-6411	47	7	,	,	PUNCT
ejpam-6411	47	8	∫	∫	PROPN
ejpam-6411	47	9	h	h	PROPN
ejpam-6411	47	10	0	0	PROPN
ejpam-6411	47	11	ω′	ω′	PROPN
ejpam-6411	47	12	(	(	PUNCT
ejpam-6411	47	13	t	t	NOUN
ejpam-6411	47	14	)	)	PUNCT
ejpam-6411	47	15	dt	dt	NOUN
ejpam-6411	48	1	=	=	SYM
ejpam-6411	48	2	ηυ′	ηυ′	X
ejpam-6411	48	3	(	(	PUNCT
ejpam-6411	48	4	ρ	ρ	PROPN
ejpam-6411	48	5	)	)	PUNCT
ejpam-6411	48	6	,	,	PUNCT
ejpam-6411	48	7	µ	µ	NOUN
ejpam-6411	48	8	,	,	PUNCT
ejpam-6411	48	9	ρ	ρ	PROPN
ejpam-6411	48	10	∈	∈	PROPN
ejpam-6411	48	11	[	[	X
ejpam-6411	48	12	0,h	0,h	X
ejpam-6411	48	13	]	]	X
ejpam-6411	48	14	υ	υ	X
ejpam-6411	48	15	(	(	PUNCT
ejpam-6411	48	16	0	0	NUM
ejpam-6411	48	17	)	)	PUNCT
ejpam-6411	48	18	=	=	SYM
ejpam-6411	48	19	0	0	NUM
ejpam-6411	48	20	,	,	PUNCT
ejpam-6411	48	21	ω	ω	X
ejpam-6411	48	22	(	(	PUNCT
ejpam-6411	48	23	0	0	NUM
ejpam-6411	48	24	)	)	PUNCT
ejpam-6411	48	25	=	=	SYM
ejpam-6411	48	26	0	0	NUM
ejpam-6411	48	27	,	,	PUNCT
ejpam-6411	48	28	(	(	PUNCT
ejpam-6411	48	29	2	2	X
ejpam-6411	48	30	)	)	PUNCT
ejpam-6411	48	31	where	where	SCONJ
ejpam-6411	48	32	cdi	cdi	PROPN
ejpam-6411	48	33	represents	represent	VERB
ejpam-6411	48	34	the	the	DET
ejpam-6411	48	35	caputo	caputo	PROPN
ejpam-6411	48	36	fractional	fractional	ADJ
ejpam-6411	48	37	derivatives	derivative	NOUN
ejpam-6411	48	38	of	of	ADP
ejpam-6411	48	39	order	order	NOUN
ejpam-6411	49	1	i	i	PRON
ejpam-6411	49	2	,	,	PUNCT
ejpam-6411	49	3	i	i	PROPN
ejpam-6411	49	4	=	=	NOUN
ejpam-6411	49	5	α	α	PROPN
ejpam-6411	49	6	,	,	PUNCT
ejpam-6411	49	7	β	β	NOUN
ejpam-6411	49	8	,	,	PUNCT
ejpam-6411	49	9	and	and	CCONJ
ejpam-6411	49	10	u	u	NOUN
ejpam-6411	49	11	,	,	PUNCT
ejpam-6411	49	12	h∈c([0,h]×r2,r	h∈c([0,h]×r2,r	NOUN
ejpam-6411	49	13	)	)	PUNCT
ejpam-6411	49	14	are	be	AUX
ejpam-6411	49	15	continuous	continuous	ADJ
ejpam-6411	49	16	functions	function	NOUN
ejpam-6411	49	17	,	,	PUNCT
ejpam-6411	49	18	and	and	CCONJ
ejpam-6411	49	19	ζ	ζ	NOUN
ejpam-6411	49	20	,	,	PUNCT
ejpam-6411	49	21	η	η	PROPN
ejpam-6411	49	22	are	be	AUX
ejpam-6411	49	23	real	real	ADJ
ejpam-6411	49	24	constants	constant	NOUN
ejpam-6411	49	25	.	.	PUNCT
ejpam-6411	50	1	the	the	DET
ejpam-6411	50	2	model	model	NOUN
ejpam-6411	50	3	in	in	ADP
ejpam-6411	50	4	equations	equation	NOUN
ejpam-6411	50	5	:	:	PUNCT
ejpam-6411	50	6	e.	e.	PROPN
ejpam-6411	50	7	(	(	PUNCT
ejpam-6411	50	8	1	1	NUM
ejpam-6411	50	9	)	)	PUNCT
ejpam-6411	50	10	and	and	CCONJ
ejpam-6411	50	11	e.	e.	PROPN
ejpam-6411	50	12	(	(	PUNCT
ejpam-6411	50	13	2	2	X
ejpam-6411	50	14	)	)	PUNCT
ejpam-6411	50	15	can	can	AUX
ejpam-6411	50	16	describe	describe	VERB
ejpam-6411	50	17	real	real	ADJ
ejpam-6411	50	18	-	-	PUNCT
ejpam-6411	50	19	life	life	NOUN
ejpam-6411	50	20	systems	system	NOUN
ejpam-6411	50	21	where	where	SCONJ
ejpam-6411	50	22	the	the	DET
ejpam-6411	50	23	current	current	ADJ
ejpam-6411	50	24	state	state	NOUN
ejpam-6411	50	25	depends	depend	VERB
ejpam-6411	50	26	on	on	ADP
ejpam-6411	50	27	past	past	ADJ
ejpam-6411	50	28	behavior	behavior	NOUN
ejpam-6411	50	29	,	,	PUNCT
ejpam-6411	50	30	like	like	ADP
ejpam-6411	50	31	stretchy	stretchy	ADJ
ejpam-6411	50	32	materials	material	NOUN
ejpam-6411	50	33	,	,	PUNCT
ejpam-6411	50	34	spreading	spread	VERB
ejpam-6411	50	35	substances	substance	NOUN
ejpam-6411	50	36	,	,	PUNCT
ejpam-6411	50	37	or	or	CCONJ
ejpam-6411	50	38	controlling	control	VERB
ejpam-6411	50	39	machines	machine	NOUN
ejpam-6411	50	40	.	.	PUNCT
ejpam-6411	51	1	it	it	PRON
ejpam-6411	51	2	’s	’	VERB
ejpam-6411	51	3	useful	useful	ADJ
ejpam-6411	51	4	for	for	ADP
ejpam-6411	51	5	accurately	accurately	ADV
ejpam-6411	51	6	capturing	capture	VERB
ejpam-6411	51	7	how	how	SCONJ
ejpam-6411	51	8	these	these	DET
ejpam-6411	51	9	systems	system	NOUN
ejpam-6411	51	10	behave	behave	VERB
ejpam-6411	51	11	over	over	ADP
ejpam-6411	51	12	time	time	NOUN
ejpam-6411	51	13	.	.	PUNCT
ejpam-6411	52	1	2	2	X
ejpam-6411	52	2	.	.	NUM
ejpam-6411	52	3	preliminaries	preliminary	NOUN
ejpam-6411	52	4	in	in	ADP
ejpam-6411	52	5	this	this	DET
ejpam-6411	52	6	section	section	NOUN
ejpam-6411	52	7	,	,	PUNCT
ejpam-6411	52	8	we	we	PRON
ejpam-6411	52	9	go	go	VERB
ejpam-6411	52	10	over	over	ADP
ejpam-6411	52	11	the	the	DET
ejpam-6411	52	12	meanings	meaning	NOUN
ejpam-6411	52	13	of	of	ADP
ejpam-6411	52	14	fractional	fractional	ADJ
ejpam-6411	52	15	derivatives	derivative	NOUN
ejpam-6411	52	16	and	and	CCONJ
ejpam-6411	52	17	integrals	integral	NOUN
ejpam-6411	52	18	from	from	ADP
ejpam-6411	52	19	[	[	X
ejpam-6411	52	20	25	25	NUM
ejpam-6411	52	21	,	,	PUNCT
ejpam-6411	52	22	26	26	NUM
ejpam-6411	52	23	]	]	PUNCT
ejpam-6411	52	24	.	.	PUNCT
ejpam-6411	53	1	definition	definition	NOUN
ejpam-6411	53	2	2.1	2.1	NUM
ejpam-6411	53	3	:	:	PUNCT
ejpam-6411	53	4	the	the	DET
ejpam-6411	53	5	riemann	riemann	PROPN
ejpam-6411	53	6	-	-	PUNCT
ejpam-6411	53	7	liouville	liouville	VERB
ejpam-6411	53	8	fractional	fractional	ADJ
ejpam-6411	53	9	integral	integral	ADJ
ejpam-6411	53	10	of	of	ADP
ejpam-6411	53	11	order	order	NOUN
ejpam-6411	53	12	p	p	NOUN
ejpam-6411	53	13	for	for	ADP
ejpam-6411	53	14	a	a	DET
ejpam-6411	53	15	continuous	continuous	ADJ
ejpam-6411	53	16	function	function	NOUN
ejpam-6411	53	17	h	h	NOUN
ejpam-6411	53	18	is	be	AUX
ejpam-6411	53	19	defined	define	VERB
ejpam-6411	53	20	as	as	ADP
ejpam-6411	53	21	iph	iph	NOUN
ejpam-6411	53	22	(	(	PUNCT
ejpam-6411	53	23	t	t	NOUN
ejpam-6411	53	24	)	)	PUNCT
ejpam-6411	53	25	=	=	SYM
ejpam-6411	53	26	1	1	NUM
ejpam-6411	53	27	γ	γ	X
ejpam-6411	53	28	(	(	PUNCT
ejpam-6411	53	29	p	p	NOUN
ejpam-6411	53	30	)	)	PUNCT
ejpam-6411	53	31	∫	∫	PROPN
ejpam-6411	54	1	t	t	PROPN
ejpam-6411	54	2	0	0	NUM
ejpam-6411	54	3	h	h	PROPN
ejpam-6411	54	4	(	(	PUNCT
ejpam-6411	54	5	s	s	NOUN
ejpam-6411	54	6	)	)	PUNCT
ejpam-6411	54	7	(	(	PUNCT
ejpam-6411	54	8	t−	t−	PROPN
ejpam-6411	54	9	s)1−pds	s)1−pds	PROPN
ejpam-6411	54	10	,	,	PUNCT
ejpam-6411	54	11	p	p	X
ejpam-6411	54	12	>	>	X
ejpam-6411	54	13	0	0	X
ejpam-6411	54	14	.	.	PUNCT
ejpam-6411	55	1	definition	definition	NOUN
ejpam-6411	55	2	2.2	2.2	NUM
ejpam-6411	55	3	:	:	PUNCT
ejpam-6411	55	4	the	the	DET
ejpam-6411	55	5	caputo	caputo	PROPN
ejpam-6411	55	6	fractional	fractional	ADJ
ejpam-6411	55	7	derivatives	derivative	NOUN
ejpam-6411	55	8	of	of	ADP
ejpam-6411	55	9	order	order	NOUN
ejpam-6411	55	10	p	p	NOUN
ejpam-6411	55	11	for	for	ADP
ejpam-6411	55	12	a	a	DET
ejpam-6411	55	13	continuous	continuous	ADJ
ejpam-6411	55	14	function	function	NOUN
ejpam-6411	55	15	h	h	NOUN
ejpam-6411	55	16	:	:	PUNCT
ejpam-6411	56	1	[	[	X
ejpam-6411	56	2	0,∞)→r	0,∞)→r	X
ejpam-6411	56	3	is	be	AUX
ejpam-6411	56	4	given	give	VERB
ejpam-6411	56	5	as	as	SCONJ
ejpam-6411	56	6	follows	follow	VERB
ejpam-6411	56	7	cdph	cdph	NOUN
ejpam-6411	56	8	(	(	PUNCT
ejpam-6411	56	9	t	t	NOUN
ejpam-6411	56	10	)	)	PUNCT
ejpam-6411	56	11	=	=	SYM
ejpam-6411	56	12	1	1	NUM
ejpam-6411	56	13	γ	γ	X
ejpam-6411	56	14	(	(	PUNCT
ejpam-6411	56	15	k	k	PROPN
ejpam-6411	56	16	−	−	PROPN
ejpam-6411	56	17	p	p	X
ejpam-6411	56	18	)	)	PUNCT
ejpam-6411	56	19	∫	∫	PROPN
ejpam-6411	56	20	t	t	PROPN
ejpam-6411	56	21	0	0	NUM
ejpam-6411	56	22	(	(	PUNCT
ejpam-6411	56	23	t−	t−	PROPN
ejpam-6411	56	24	s)k−p−1h(k	s)k−p−1h(k	NUM
ejpam-6411	56	25	)	)	PUNCT
ejpam-6411	56	26	(	(	PUNCT
ejpam-6411	56	27	s	s	X
ejpam-6411	56	28	)	)	PUNCT
ejpam-6411	56	29	ds	ds	PROPN
ejpam-6411	56	30	,	,	PUNCT
ejpam-6411	56	31	k	k	PROPN
ejpam-6411	56	32	−	−	PROPN
ejpam-6411	56	33	1	1	NUM
ejpam-6411	56	34	<	<	X
ejpam-6411	56	35	p	p	X
ejpam-6411	56	36	<	<	X
ejpam-6411	56	37	k	k	PROPN
ejpam-6411	56	38	,	,	PUNCT
ejpam-6411	56	39	k	k	X
ejpam-6411	57	1	=	=	PUNCT
ejpam-6411	58	1	[	[	X
ejpam-6411	58	2	p	p	X
ejpam-6411	58	3	]	]	X
ejpam-6411	58	4	+	+	NOUN
ejpam-6411	58	5	1	1	X
ejpam-6411	58	6	.	.	X
ejpam-6411	58	7	we	we	PRON
ejpam-6411	58	8	prove	prove	VERB
ejpam-6411	58	9	the	the	DET
ejpam-6411	58	10	following	follow	VERB
ejpam-6411	58	11	auxiliary	auxiliary	NOUN
ejpam-6411	58	12	lemma	lemma	PROPN
ejpam-6411	58	13	in	in	ADP
ejpam-6411	58	14	order	order	NOUN
ejpam-6411	58	15	to	to	PART
ejpam-6411	58	16	specify	specify	VERB
ejpam-6411	58	17	the	the	DET
ejpam-6411	58	18	solution	solution	NOUN
ejpam-6411	58	19	for	for	ADP
ejpam-6411	58	20	the	the	DET
ejpam-6411	58	21	problem	problem	NOUN
ejpam-6411	58	22	in	in	ADP
ejpam-6411	58	23	e.	e.	PROPN
ejpam-6411	58	24	(	(	PUNCT
ejpam-6411	58	25	1	1	NUM
ejpam-6411	58	26	)	)	PUNCT
ejpam-6411	58	27	and	and	CCONJ
ejpam-6411	58	28	e.	e.	PROPN
ejpam-6411	58	29	(	(	PUNCT
ejpam-6411	58	30	2	2	NUM
ejpam-6411	58	31	)	)	PUNCT
ejpam-6411	58	32	.	.	PUNCT
ejpam-6411	59	1	lemma	lemma	PROPN
ejpam-6411	59	2	2.3	2.3	NUM
ejpam-6411	59	3	:	:	PUNCT
ejpam-6411	59	4	let	let	VERB
ejpam-6411	59	5	x	x	PRON
ejpam-6411	59	6	,	,	PUNCT
ejpam-6411	59	7	y∈c([0,h],r	y∈c([0,h],r	PROPN
ejpam-6411	60	1	then	then	ADV
ejpam-6411	60	2	the	the	DET
ejpam-6411	60	3	unique	unique	ADJ
ejpam-6411	60	4	solution	solution	NOUN
ejpam-6411	60	5	for	for	ADP
ejpam-6411	60	6	the	the	DET
ejpam-6411	60	7	problem	problem	NOUN
ejpam-6411	60	8	for	for	ADP
ejpam-6411	60	9	h	h	NOUN
ejpam-6411	60	10	>	>	X
ejpam-6411	60	11	0	0	NUM
ejpam-6411	60	12	cdαυ	cdαυ	NOUN
ejpam-6411	60	13	(	(	PUNCT
ejpam-6411	60	14	τ	τ	X
ejpam-6411	60	15	)	)	PUNCT
ejpam-6411	60	16	=	=	SYM
ejpam-6411	61	1	x	x	X
ejpam-6411	61	2	(	(	PUNCT
ejpam-6411	61	3	τ	τ	X
ejpam-6411	61	4	)	)	PUNCT
ejpam-6411	61	5	,	,	PUNCT
ejpam-6411	61	6	τ	τ	PROPN
ejpam-6411	61	7	∈	∈	PROPN
ejpam-6411	62	1	[	[	X
ejpam-6411	62	2	0,h	0,h	X
ejpam-6411	62	3	]	]	X
ejpam-6411	62	4	,	,	PUNCT
ejpam-6411	62	5	1	1	NUM
ejpam-6411	62	6	<	<	X
ejpam-6411	62	7	α	α	PROPN
ejpam-6411	62	8	≤	≤	ADJ
ejpam-6411	62	9	2	2	NUM
ejpam-6411	62	10	,	,	PUNCT
ejpam-6411	62	11	cdβω	cdβω	NOUN
ejpam-6411	62	12	(	(	PUNCT
ejpam-6411	62	13	τ	τ	X
ejpam-6411	62	14	)	)	PUNCT
ejpam-6411	62	15	=	=	SYM
ejpam-6411	62	16	y	y	PROPN
ejpam-6411	62	17	(	(	PUNCT
ejpam-6411	62	18	τ	τ	PROPN
ejpam-6411	62	19	)	)	PUNCT
ejpam-6411	62	20	,	,	PUNCT
ejpam-6411	62	21	τ	τ	PROPN
ejpam-6411	62	22	∈	∈	PROPN
ejpam-6411	63	1	[	[	X
ejpam-6411	63	2	0,h	0,h	X
ejpam-6411	63	3	]	]	X
ejpam-6411	63	4	,	,	PUNCT
ejpam-6411	63	5	1	1	NUM
ejpam-6411	63	6	<	<	X
ejpam-6411	63	7	β	β	X
ejpam-6411	63	8	≤	≤	NUM
ejpam-6411	63	9	2,∫	2,∫	NUM
ejpam-6411	63	10	h	h	NOUN
ejpam-6411	63	11	0	0	PUNCT
ejpam-6411	64	1	υ′	υ′	PRON
ejpam-6411	64	2	(	(	PUNCT
ejpam-6411	64	3	t	t	NOUN
ejpam-6411	64	4	)	)	PUNCT
ejpam-6411	64	5	dt	dt	NOUN
ejpam-6411	65	1	=	=	PUNCT
ejpam-6411	65	2	ζω′	ζω′	X
ejpam-6411	65	3	(	(	PUNCT
ejpam-6411	65	4	µ	µ	NOUN
ejpam-6411	65	5	)	)	PUNCT
ejpam-6411	65	6	,	,	PUNCT
ejpam-6411	65	7	∫	∫	PROPN
ejpam-6411	65	8	h	h	PROPN
ejpam-6411	65	9	0	0	PROPN
ejpam-6411	65	10	ω′	ω′	PROPN
ejpam-6411	65	11	(	(	PUNCT
ejpam-6411	65	12	t	t	NOUN
ejpam-6411	65	13	)	)	PUNCT
ejpam-6411	65	14	dt	dt	NOUN
ejpam-6411	66	1	=	=	SYM
ejpam-6411	66	2	ηυ′	ηυ′	X
ejpam-6411	66	3	(	(	PUNCT
ejpam-6411	66	4	ρ	ρ	PROPN
ejpam-6411	66	5	)	)	PUNCT
ejpam-6411	66	6	,	,	PUNCT
ejpam-6411	66	7	υ	υ	PROPN
ejpam-6411	66	8	(	(	PUNCT
ejpam-6411	66	9	0	0	NUM
ejpam-6411	66	10	)	)	PUNCT
ejpam-6411	66	11	=	=	SYM
ejpam-6411	66	12	0	0	NUM
ejpam-6411	66	13	,	,	PUNCT
ejpam-6411	66	14	ω	ω	X
ejpam-6411	66	15	(	(	PUNCT
ejpam-6411	66	16	0	0	NUM
ejpam-6411	66	17	)	)	PUNCT
ejpam-6411	66	18	=	=	SYM
ejpam-6411	66	19	0	0	NUM
ejpam-6411	66	20	,	,	PUNCT
ejpam-6411	66	21	µ	µ	NOUN
ejpam-6411	66	22	,	,	PUNCT
ejpam-6411	66	23	ρ	ρ	PROPN
ejpam-6411	66	24	∈	∈	PROPN
ejpam-6411	67	1	[	[	X
ejpam-6411	67	2	0,h	0,h	X
ejpam-6411	67	3	]	]	X
ejpam-6411	67	4	(	(	PUNCT
ejpam-6411	67	5	3	3	X
ejpam-6411	67	6	)	)	PUNCT
ejpam-6411	68	1	s.	s.	PROPN
ejpam-6411	68	2	momani	momani	PROPN
ejpam-6411	68	3	et	et	PROPN
ejpam-6411	68	4	al	al	PROPN
ejpam-6411	68	5	.	.	PUNCT
ejpam-6411	68	6	/	/	SYM
ejpam-6411	68	7	eur	eur	PROPN
ejpam-6411	68	8	.	.	PUNCT
ejpam-6411	69	1	j.	j.	PROPN
ejpam-6411	69	2	pure	pure	PROPN
ejpam-6411	69	3	appl	appl	PROPN
ejpam-6411	69	4	.	.	PROPN
ejpam-6411	69	5	math	math	PROPN
ejpam-6411	69	6	,	,	PUNCT
ejpam-6411	69	7	18	18	NUM
ejpam-6411	69	8	(	(	PUNCT
ejpam-6411	69	9	4	4	NUM
ejpam-6411	69	10	)	)	PUNCT
ejpam-6411	69	11	(	(	PUNCT
ejpam-6411	69	12	2025	2025	NUM
ejpam-6411	69	13	)	)	PUNCT
ejpam-6411	69	14	,	,	PUNCT
ejpam-6411	69	15	6411	6411	NUM
ejpam-6411	69	16	4	4	NUM
ejpam-6411	69	17	of	of	ADP
ejpam-6411	69	18	16	16	NUM
ejpam-6411	69	19	is	be	AUX
ejpam-6411	69	20	υ(τ	υ(τ	PRON
ejpam-6411	69	21	)	)	PUNCT
ejpam-6411	69	22	=	=	PUNCT
ejpam-6411	70	1	τ	τ	X
ejpam-6411	70	2	λ	λ	X
ejpam-6411	70	3	(	(	PUNCT
ejpam-6411	70	4	ζh	ζh	PROPN
ejpam-6411	70	5	∫	∫	PROPN
ejpam-6411	70	6	µ	µ	X
ejpam-6411	70	7	0	0	NUM
ejpam-6411	70	8	(	(	PUNCT
ejpam-6411	70	9	µ−	µ−	PROPN
ejpam-6411	70	10	s)β−2	s)β−2	VERB
ejpam-6411	70	11	γ(β	γ(β	PROPN
ejpam-6411	70	12	−	−	PROPN
ejpam-6411	70	13	1	1	NUM
ejpam-6411	70	14	)	)	PUNCT
ejpam-6411	70	15	y(s	y(s	PROPN
ejpam-6411	70	16	)	)	PUNCT
ejpam-6411	71	1	ds−h	ds−h	NOUN
ejpam-6411	71	2	∫	∫	PROPN
ejpam-6411	72	1	h	h	NOUN
ejpam-6411	72	2	0	0	NUM
ejpam-6411	72	3	∫	∫	PROPN
ejpam-6411	72	4	s	s	PART
ejpam-6411	72	5	0	0	NUM
ejpam-6411	72	6	(	(	PUNCT
ejpam-6411	72	7	s−	s−	PROPN
ejpam-6411	72	8	t)α−2	t)α−2	NOUN
ejpam-6411	72	9	γ(α−	γ(α−	NOUN
ejpam-6411	72	10	1	1	NUM
ejpam-6411	72	11	)	)	PUNCT
ejpam-6411	72	12	x(t	x(t	PROPN
ejpam-6411	72	13	)	)	PUNCT
ejpam-6411	73	1	dt	dt	X
ejpam-6411	74	1	ds	ds	PROPN
ejpam-6411	74	2	+	+	CCONJ
ejpam-6411	74	3	ζη	ζη	ADJ
ejpam-6411	74	4	∫	∫	PROPN
ejpam-6411	74	5	ρ	ρ	PROPN
ejpam-6411	74	6	0	0	PUNCT
ejpam-6411	75	1	(	(	PUNCT
ejpam-6411	75	2	ρ−	ρ−	NOUN
ejpam-6411	75	3	s)α−2	s)α−2	VERB
ejpam-6411	75	4	γ(α−	γ(α−	NOUN
ejpam-6411	75	5	1	1	NUM
ejpam-6411	75	6	)	)	PUNCT
ejpam-6411	75	7	x(s	x(s	PROPN
ejpam-6411	75	8	)	)	PUNCT
ejpam-6411	76	1	ds−	ds−	PROPN
ejpam-6411	76	2	ζ	ζ	NOUN
ejpam-6411	76	3	∫	∫	PROPN
ejpam-6411	76	4	h	h	NOUN
ejpam-6411	76	5	0	0	NUM
ejpam-6411	76	6	∫	∫	PROPN
ejpam-6411	76	7	s	s	PART
ejpam-6411	76	8	0	0	NUM
ejpam-6411	76	9	(	(	PUNCT
ejpam-6411	76	10	s−	s−	PROPN
ejpam-6411	76	11	t)β−2	t)β−2	VERB
ejpam-6411	76	12	γ(β	γ(β	PROPN
ejpam-6411	76	13	−	−	PROPN
ejpam-6411	76	14	1	1	NUM
ejpam-6411	76	15	)	)	PUNCT
ejpam-6411	76	16	y(t	y(t	NUM
ejpam-6411	76	17	)	)	PUNCT
ejpam-6411	77	1	dt	dt	NOUN
ejpam-6411	78	1	ds	ds	X
ejpam-6411	78	2	)	)	PUNCT
ejpam-6411	79	1	+	+	CCONJ
ejpam-6411	79	2	∫	∫	PROPN
ejpam-6411	79	3	τ	τ	X
ejpam-6411	79	4	0	0	NUM
ejpam-6411	79	5	(	(	PUNCT
ejpam-6411	79	6	τ	τ	PROPN
ejpam-6411	79	7	−	−	PROPN
ejpam-6411	79	8	s)α−1	s)α−1	NOUN
ejpam-6411	79	9	γ(α	γ(α	NOUN
ejpam-6411	79	10	)	)	PUNCT
ejpam-6411	79	11	x(s	x(s	PROPN
ejpam-6411	79	12	)	)	PUNCT
ejpam-6411	79	13	ds	ds	PROPN
ejpam-6411	79	14	.	.	PUNCT
ejpam-6411	79	15	(	(	PUNCT
ejpam-6411	79	16	4	4	NUM
ejpam-6411	79	17	)	)	PUNCT
ejpam-6411	79	18	and	and	CCONJ
ejpam-6411	79	19	ω(τ	ω(τ	NOUN
ejpam-6411	79	20	)	)	PUNCT
ejpam-6411	79	21	=	=	PUNCT
ejpam-6411	80	1	τ	τ	X
ejpam-6411	80	2	λ	λ	X
ejpam-6411	80	3	(	(	PUNCT
ejpam-6411	80	4	ζη	ζη	INTJ
ejpam-6411	80	5	∫	∫	PROPN
ejpam-6411	80	6	µ	µ	X
ejpam-6411	80	7	0	0	NUM
ejpam-6411	80	8	(	(	PUNCT
ejpam-6411	80	9	µ−	µ−	PROPN
ejpam-6411	80	10	s)β−2	s)β−2	VERB
ejpam-6411	80	11	γ(β	γ(β	PROPN
ejpam-6411	80	12	−	−	PROPN
ejpam-6411	80	13	1	1	NUM
ejpam-6411	80	14	)	)	PUNCT
ejpam-6411	80	15	y(s	y(s	PROPN
ejpam-6411	80	16	)	)	PUNCT
ejpam-6411	80	17	ds−	ds−	PROPN
ejpam-6411	80	18	η	η	PROPN
ejpam-6411	80	19	∫	∫	PROPN
ejpam-6411	80	20	h	h	PROPN
ejpam-6411	80	21	0	0	NUM
ejpam-6411	80	22	∫	∫	PROPN
ejpam-6411	80	23	s	s	PART
ejpam-6411	80	24	0	0	NUM
ejpam-6411	80	25	(	(	PUNCT
ejpam-6411	80	26	s−	s−	PROPN
ejpam-6411	80	27	t)α−2	t)α−2	NOUN
ejpam-6411	80	28	γ(α−	γ(α−	NOUN
ejpam-6411	80	29	1	1	NUM
ejpam-6411	80	30	)	)	PUNCT
ejpam-6411	80	31	x(t	x(t	PROPN
ejpam-6411	80	32	)	)	PUNCT
ejpam-6411	80	33	dt	dt	X
ejpam-6411	81	1	ds	ds	PROPN
ejpam-6411	81	2	+	+	ADV
ejpam-6411	81	3	hη	hη	PROPN
ejpam-6411	81	4	∫	∫	PROPN
ejpam-6411	81	5	ρ	ρ	PROPN
ejpam-6411	81	6	0	0	PROPN
ejpam-6411	82	1	(	(	PUNCT
ejpam-6411	82	2	ρ−	ρ−	NOUN
ejpam-6411	82	3	s)α−2	s)α−2	VERB
ejpam-6411	82	4	γ(α−	γ(α−	NOUN
ejpam-6411	82	5	1	1	NUM
ejpam-6411	82	6	)	)	PUNCT
ejpam-6411	82	7	x(s	x(s	PROPN
ejpam-6411	82	8	)	)	PUNCT
ejpam-6411	83	1	ds−h	ds−h	NOUN
ejpam-6411	83	2	∫	∫	PROPN
ejpam-6411	84	1	h	h	NOUN
ejpam-6411	84	2	0	0	NUM
ejpam-6411	84	3	∫	∫	PROPN
ejpam-6411	84	4	s	s	PART
ejpam-6411	84	5	0	0	NUM
ejpam-6411	84	6	(	(	PUNCT
ejpam-6411	84	7	s−	s−	PROPN
ejpam-6411	84	8	t)β−2	t)β−2	VERB
ejpam-6411	84	9	γ(β	γ(β	PROPN
ejpam-6411	84	10	−	−	PROPN
ejpam-6411	84	11	1	1	NUM
ejpam-6411	84	12	)	)	PUNCT
ejpam-6411	84	13	y(t	y(t	NUM
ejpam-6411	84	14	)	)	PUNCT
ejpam-6411	85	1	dt	dt	NOUN
ejpam-6411	85	2	ds	ds	X
ejpam-6411	85	3	)	)	PUNCT
ejpam-6411	86	1	+	+	CCONJ
ejpam-6411	86	2	∫	∫	PROPN
ejpam-6411	86	3	τ	τ	X
ejpam-6411	86	4	0	0	NUM
ejpam-6411	86	5	(	(	PUNCT
ejpam-6411	86	6	τ	τ	X
ejpam-6411	86	7	−	−	PROPN
ejpam-6411	86	8	s)β−1	s)β−1	AUX
ejpam-6411	86	9	γ(β	γ(β	PROPN
ejpam-6411	86	10	)	)	PUNCT
ejpam-6411	86	11	y(s	y(s	PROPN
ejpam-6411	86	12	)	)	PUNCT
ejpam-6411	86	13	ds	ds	PROPN
ejpam-6411	86	14	.	.	PUNCT
ejpam-6411	86	15	(	(	PUNCT
ejpam-6411	86	16	5	5	NUM
ejpam-6411	86	17	)	)	PUNCT
ejpam-6411	87	1	where	where	SCONJ
ejpam-6411	87	2	λ	λ	NOUN
ejpam-6411	87	3	=	=	NOUN
ejpam-6411	87	4	h2−ζη	h2−ζη	PRON
ejpam-6411	87	5	̸=0	̸=0	NOUN
ejpam-6411	87	6	.	.	PUNCT
ejpam-6411	88	1	proof	proof	NOUN
ejpam-6411	88	2	:	:	PUNCT
ejpam-6411	88	3	the	the	DET
ejpam-6411	88	4	general	general	ADJ
ejpam-6411	88	5	solution	solution	NOUN
ejpam-6411	88	6	of	of	ADP
ejpam-6411	88	7	the	the	DET
ejpam-6411	88	8	coupled	couple	VERB
ejpam-6411	88	9	system	system	NOUN
ejpam-6411	88	10	in	in	ADP
ejpam-6411	88	11	e.	e.	PROPN
ejpam-6411	88	12	(	(	PUNCT
ejpam-6411	88	13	3	3	X
ejpam-6411	88	14	)	)	PUNCT
ejpam-6411	88	15	are	be	AUX
ejpam-6411	88	16	referred	refer	VERB
ejpam-6411	88	17	to	to	ADP
ejpam-6411	88	18	as	as	SCONJ
ejpam-6411	88	19	follows	follow	VERB
ejpam-6411	88	20	[	[	X
ejpam-6411	88	21	26	26	NUM
ejpam-6411	88	22	]	]	X
ejpam-6411	88	23	υ	υ	PROPN
ejpam-6411	88	24	(	(	PUNCT
ejpam-6411	88	25	τ	τ	NOUN
ejpam-6411	88	26	)	)	PUNCT
ejpam-6411	88	27	=	=	PUNCT
ejpam-6411	88	28	a0τ	a0τ	NOUN
ejpam-6411	88	29	+	+	CCONJ
ejpam-6411	88	30	a1	a1	VERB
ejpam-6411	88	31	+	+	CCONJ
ejpam-6411	88	32	1	1	NUM
ejpam-6411	88	33	γ	γ	X
ejpam-6411	88	34	(	(	PUNCT
ejpam-6411	88	35	α	α	NOUN
ejpam-6411	88	36	)	)	PUNCT
ejpam-6411	88	37	∫	∫	PROPN
ejpam-6411	88	38	τ	τ	PROPN
ejpam-6411	88	39	0	0	NUM
ejpam-6411	89	1	(	(	PUNCT
ejpam-6411	89	2	τ	τ	X
ejpam-6411	89	3	−	−	PROPN
ejpam-6411	89	4	s)α−1x	s)α−1x	NOUN
ejpam-6411	89	5	(	(	PUNCT
ejpam-6411	89	6	s	s	NOUN
ejpam-6411	89	7	)	)	PUNCT
ejpam-6411	89	8	ds	ds	ADJ
ejpam-6411	89	9	,	,	PUNCT
ejpam-6411	89	10	(	(	PUNCT
ejpam-6411	89	11	6	6	NUM
ejpam-6411	89	12	)	)	PUNCT
ejpam-6411	89	13	ω	ω	NOUN
ejpam-6411	89	14	(	(	PUNCT
ejpam-6411	89	15	τ	τ	X
ejpam-6411	89	16	)	)	PUNCT
ejpam-6411	89	17	=	=	PUNCT
ejpam-6411	90	1	b0τ	b0τ	NOUN
ejpam-6411	90	2	+	+	CCONJ
ejpam-6411	90	3	b1	b1	NOUN
ejpam-6411	90	4	+	+	CCONJ
ejpam-6411	90	5	1	1	NUM
ejpam-6411	90	6	γ	γ	X
ejpam-6411	90	7	(	(	PUNCT
ejpam-6411	90	8	β	β	NOUN
ejpam-6411	90	9	)	)	PUNCT
ejpam-6411	90	10	∫	∫	PROPN
ejpam-6411	90	11	τ	τ	PROPN
ejpam-6411	90	12	0	0	PROPN
ejpam-6411	91	1	(	(	PUNCT
ejpam-6411	91	2	τ	τ	PROPN
ejpam-6411	91	3	−	−	PROPN
ejpam-6411	91	4	s)β−1y	s)β−1y	PROPN
ejpam-6411	91	5	(	(	PUNCT
ejpam-6411	91	6	s	s	NOUN
ejpam-6411	91	7	)	)	PUNCT
ejpam-6411	91	8	ds	ds	ADJ
ejpam-6411	91	9	,	,	PUNCT
ejpam-6411	91	10	(	(	PUNCT
ejpam-6411	91	11	7	7	X
ejpam-6411	91	12	)	)	PUNCT
ejpam-6411	91	13	where	where	SCONJ
ejpam-6411	91	14	a0	a0	PROPN
ejpam-6411	91	15	,	,	PUNCT
ejpam-6411	91	16	a1	a1	PROPN
ejpam-6411	91	17	,	,	PUNCT
ejpam-6411	91	18	b0	b0	NOUN
ejpam-6411	91	19	,	,	PUNCT
ejpam-6411	91	20	b1	b1	NOUN
ejpam-6411	91	21	are	be	AUX
ejpam-6411	91	22	arbitrary	arbitrary	ADJ
ejpam-6411	91	23	constants	constant	NOUN
ejpam-6411	91	24	.	.	PUNCT
ejpam-6411	92	1	by	by	ADP
ejpam-6411	92	2	applying	apply	VERB
ejpam-6411	92	3	the	the	DET
ejpam-6411	92	4	conditions	condition	NOUN
ejpam-6411	92	5	υ	υ	X
ejpam-6411	92	6	(	(	PUNCT
ejpam-6411	92	7	0)=	0)=	NOUN
ejpam-6411	92	8	0	0	NUM
ejpam-6411	92	9	and	and	CCONJ
ejpam-6411	92	10	ω	ω	NUM
ejpam-6411	92	11	(	(	PUNCT
ejpam-6411	92	12	0)=	0)=	NOUN
ejpam-6411	92	13	0	0	NUM
ejpam-6411	92	14	,	,	PUNCT
ejpam-6411	92	15	we	we	PRON
ejpam-6411	92	16	obtain	obtain	VERB
ejpam-6411	92	17	a1	a1	NOUN
ejpam-6411	92	18	=	=	NOUN
ejpam-6411	92	19	b1=	b1=	NOUN
ejpam-6411	92	20	0	0	NUM
ejpam-6411	92	21	.	.	PUNCT
ejpam-6411	93	1	here	here	ADV
ejpam-6411	93	2	,	,	PUNCT
ejpam-6411	93	3	we	we	PRON
ejpam-6411	93	4	have	have	VERB
ejpam-6411	93	5	υ′	υ′	PRON
ejpam-6411	93	6	(	(	PUNCT
ejpam-6411	93	7	τ	τ	NOUN
ejpam-6411	93	8	)	)	PUNCT
ejpam-6411	93	9	=	=	SYM
ejpam-6411	93	10	a0	a0	PROPN
ejpam-6411	93	11	+	+	CCONJ
ejpam-6411	93	12	1	1	NUM
ejpam-6411	93	13	γ	γ	X
ejpam-6411	93	14	(	(	PUNCT
ejpam-6411	93	15	α−	α−	ADP
ejpam-6411	93	16	1	1	NUM
ejpam-6411	93	17	)	)	PUNCT
ejpam-6411	93	18	∫	∫	PROPN
ejpam-6411	93	19	τ	τ	PROPN
ejpam-6411	93	20	0	0	PROPN
ejpam-6411	94	1	(	(	PUNCT
ejpam-6411	94	2	τ	τ	PROPN
ejpam-6411	94	3	−	−	PROPN
ejpam-6411	94	4	s)α−2x	s)α−2x	NOUN
ejpam-6411	94	5	(	(	PUNCT
ejpam-6411	94	6	s	s	NOUN
ejpam-6411	94	7	)	)	PUNCT
ejpam-6411	94	8	ds	ds	PROPN
ejpam-6411	94	9	,	,	PUNCT
ejpam-6411	94	10	ω′	ω′	PROPN
ejpam-6411	94	11	(	(	PUNCT
ejpam-6411	94	12	τ	τ	X
ejpam-6411	94	13	)	)	PUNCT
ejpam-6411	94	14	=	=	SYM
ejpam-6411	94	15	b0	b0	NOUN
ejpam-6411	94	16	+	+	CCONJ
ejpam-6411	94	17	1	1	NUM
ejpam-6411	94	18	γ	γ	NOUN
ejpam-6411	94	19	(	(	PUNCT
ejpam-6411	94	20	β	β	NOUN
ejpam-6411	94	21	−	−	NOUN
ejpam-6411	94	22	1	1	NUM
ejpam-6411	94	23	)	)	PUNCT
ejpam-6411	94	24	∫	∫	PROPN
ejpam-6411	94	25	τ	τ	PROPN
ejpam-6411	94	26	0	0	PROPN
ejpam-6411	95	1	(	(	PUNCT
ejpam-6411	95	2	τ	τ	X
ejpam-6411	95	3	−	−	PROPN
ejpam-6411	95	4	s)β−2y	s)β−2y	PROPN
ejpam-6411	95	5	(	(	PUNCT
ejpam-6411	95	6	s	s	NOUN
ejpam-6411	95	7	)	)	PUNCT
ejpam-6411	95	8	ds	ds	NOUN
ejpam-6411	95	9	.	.	PROPN
ejpam-6411	95	10	therefore	therefore	ADV
ejpam-6411	95	11	,	,	PUNCT
ejpam-6411	95	12	in	in	ADP
ejpam-6411	95	13	view	view	NOUN
ejpam-6411	95	14	of	of	ADP
ejpam-6411	95	15	the	the	DET
ejpam-6411	95	16	conditions∫	conditions∫	NOUN
ejpam-6411	95	17	h	h	NOUN
ejpam-6411	95	18	0	0	PUNCT
ejpam-6411	96	1	υ′(s)ds	υ′(s)ds	PROPN
ejpam-6411	96	2	=	=	SYM
ejpam-6411	96	3	ζω′	ζω′	X
ejpam-6411	96	4	(	(	PUNCT
ejpam-6411	96	5	µ	µ	NOUN
ejpam-6411	96	6	)	)	PUNCT
ejpam-6411	96	7	,	,	PUNCT
ejpam-6411	97	1	∫	∫	PROPN
ejpam-6411	97	2	h	h	PROPN
ejpam-6411	97	3	0	0	PROPN
ejpam-6411	97	4	ω′	ω′	PROPN
ejpam-6411	97	5	(	(	PUNCT
ejpam-6411	97	6	s	s	NOUN
ejpam-6411	97	7	)	)	PUNCT
ejpam-6411	97	8	ds	ds	NOUN
ejpam-6411	97	9	=	=	SYM
ejpam-6411	97	10	ηυ′	ηυ′	X
ejpam-6411	97	11	(	(	PUNCT
ejpam-6411	97	12	ρ	ρ	PROPN
ejpam-6411	97	13	)	)	PUNCT
ejpam-6411	97	14	,	,	PUNCT
ejpam-6411	97	15	we	we	PRON
ejpam-6411	97	16	get	get	VERB
ejpam-6411	97	17	a0h+	a0h+	NOUN
ejpam-6411	97	18	∫	∫	PROPN
ejpam-6411	97	19	h	h	PROPN
ejpam-6411	97	20	0	0	NUM
ejpam-6411	98	1	∫	∫	PROPN
ejpam-6411	98	2	s	s	PART
ejpam-6411	98	3	0	0	NUM
ejpam-6411	98	4	(	(	PUNCT
ejpam-6411	98	5	s−	s−	PROPN
ejpam-6411	98	6	t)α−2	t)α−2	VERB
ejpam-6411	98	7	γ	γ	X
ejpam-6411	98	8	(	(	PUNCT
ejpam-6411	98	9	α−	α−	PROPN
ejpam-6411	98	10	1	1	NUM
ejpam-6411	98	11	)	)	PUNCT
ejpam-6411	98	12	x	x	SYM
ejpam-6411	98	13	(	(	PUNCT
ejpam-6411	98	14	t)dtds	t)dtds	ADJ
ejpam-6411	98	15	=	=	SYM
ejpam-6411	98	16	ζb0	ζb0	NOUN
ejpam-6411	98	17	+	+	CCONJ
ejpam-6411	98	18	ζ	ζ	NOUN
ejpam-6411	98	19	∫	∫	PROPN
ejpam-6411	98	20	µ	µ	X
ejpam-6411	98	21	0	0	NUM
ejpam-6411	98	22	(	(	PUNCT
ejpam-6411	98	23	µ−	µ−	PROPN
ejpam-6411	98	24	s)β−2	s)β−2	VERB
ejpam-6411	98	25	γ	γ	X
ejpam-6411	98	26	(	(	PUNCT
ejpam-6411	98	27	β	β	NOUN
ejpam-6411	98	28	−	−	NOUN
ejpam-6411	98	29	1	1	X
ejpam-6411	98	30	)	)	PUNCT
ejpam-6411	98	31	y	y	PROPN
ejpam-6411	98	32	(	(	PUNCT
ejpam-6411	98	33	s	s	NOUN
ejpam-6411	98	34	)	)	PUNCT
ejpam-6411	98	35	ds	ds	ADJ
ejpam-6411	98	36	,	,	PUNCT
ejpam-6411	98	37	and	and	CCONJ
ejpam-6411	98	38	b0h+	b0h+	PROPN
ejpam-6411	98	39	∫	∫	PROPN
ejpam-6411	98	40	h	h	PROPN
ejpam-6411	98	41	0	0	NUM
ejpam-6411	99	1	∫	∫	PROPN
ejpam-6411	99	2	s	s	PART
ejpam-6411	99	3	0	0	NUM
ejpam-6411	99	4	(	(	PUNCT
ejpam-6411	99	5	s−	s−	PROPN
ejpam-6411	99	6	t)β−2	t)β−2	VERB
ejpam-6411	99	7	γ	γ	X
ejpam-6411	99	8	(	(	PUNCT
ejpam-6411	99	9	β	β	NOUN
ejpam-6411	99	10	−	−	NOUN
ejpam-6411	99	11	1	1	X
ejpam-6411	99	12	)	)	PUNCT
ejpam-6411	99	13	y	y	NOUN
ejpam-6411	99	14	(	(	PUNCT
ejpam-6411	99	15	t)dtds	t)dtds	PROPN
ejpam-6411	99	16	=	=	SYM
ejpam-6411	99	17	a0η	a0η	PROPN
ejpam-6411	99	18	+	+	PROPN
ejpam-6411	99	19	η	η	PROPN
ejpam-6411	99	20	∫	∫	PROPN
ejpam-6411	99	21	ρ	ρ	PROPN
ejpam-6411	99	22	0	0	PUNCT
ejpam-6411	100	1	(	(	PUNCT
ejpam-6411	100	2	ρ−	ρ−	NOUN
ejpam-6411	100	3	s)α−2	s)α−2	VERB
ejpam-6411	100	4	γ	γ	X
ejpam-6411	100	5	(	(	PUNCT
ejpam-6411	100	6	α−	α−	PROPN
ejpam-6411	100	7	1	1	NUM
ejpam-6411	100	8	)	)	PUNCT
ejpam-6411	100	9	x	x	X
ejpam-6411	100	10	(	(	PUNCT
ejpam-6411	100	11	s	s	NOUN
ejpam-6411	100	12	)	)	PUNCT
ejpam-6411	100	13	ds	ds	PROPN
ejpam-6411	100	14	,	,	PUNCT
ejpam-6411	101	1	s.	s.	PROPN
ejpam-6411	101	2	momani	momani	PROPN
ejpam-6411	101	3	et	et	PROPN
ejpam-6411	101	4	al	al	PROPN
ejpam-6411	101	5	.	.	PUNCT
ejpam-6411	101	6	/	/	SYM
ejpam-6411	101	7	eur	eur	PROPN
ejpam-6411	101	8	.	.	PUNCT
ejpam-6411	102	1	j.	j.	PROPN
ejpam-6411	102	2	pure	pure	PROPN
ejpam-6411	102	3	appl	appl	PROPN
ejpam-6411	102	4	.	.	PROPN
ejpam-6411	102	5	math	math	PROPN
ejpam-6411	102	6	,	,	PUNCT
ejpam-6411	102	7	18	18	NUM
ejpam-6411	102	8	(	(	PUNCT
ejpam-6411	102	9	4	4	NUM
ejpam-6411	102	10	)	)	PUNCT
ejpam-6411	102	11	(	(	PUNCT
ejpam-6411	102	12	2025	2025	NUM
ejpam-6411	102	13	)	)	PUNCT
ejpam-6411	102	14	,	,	PUNCT
ejpam-6411	102	15	6411	6411	NUM
ejpam-6411	102	16	5	5	NUM
ejpam-6411	102	17	of	of	ADP
ejpam-6411	102	18	16	16	NUM
ejpam-6411	102	19	provided	provide	VERB
ejpam-6411	102	20	that	that	DET
ejpam-6411	102	21	a0	a0	NOUN
ejpam-6411	102	22	=	=	SYM
ejpam-6411	102	23	1	1	NUM
ejpam-6411	102	24	h	h	NOUN
ejpam-6411	102	25	(	(	PUNCT
ejpam-6411	102	26	ζb0	ζb0	NOUN
ejpam-6411	102	27	+	+	CCONJ
ejpam-6411	102	28	ζ	ζ	PRON
ejpam-6411	102	29	∫	∫	PROPN
ejpam-6411	102	30	µ	µ	X
ejpam-6411	102	31	0	0	NUM
ejpam-6411	102	32	(	(	PUNCT
ejpam-6411	102	33	µ−	µ−	PROPN
ejpam-6411	102	34	s)β−2	s)β−2	VERB
ejpam-6411	102	35	γ	γ	X
ejpam-6411	102	36	(	(	PUNCT
ejpam-6411	102	37	β	β	NOUN
ejpam-6411	102	38	−	−	NOUN
ejpam-6411	102	39	1	1	X
ejpam-6411	102	40	)	)	PUNCT
ejpam-6411	102	41	y	y	PROPN
ejpam-6411	102	42	(	(	PUNCT
ejpam-6411	102	43	s	s	NOUN
ejpam-6411	102	44	)	)	PUNCT
ejpam-6411	102	45	ds−	ds−	PROPN
ejpam-6411	102	46	∫	∫	PROPN
ejpam-6411	102	47	h	h	NOUN
ejpam-6411	102	48	0	0	NUM
ejpam-6411	102	49	∫	∫	PROPN
ejpam-6411	102	50	s	s	PART
ejpam-6411	102	51	0	0	NUM
ejpam-6411	102	52	(	(	PUNCT
ejpam-6411	102	53	s−	s−	PROPN
ejpam-6411	102	54	t)α−2	t)α−2	VERB
ejpam-6411	102	55	γ	γ	X
ejpam-6411	102	56	(	(	PUNCT
ejpam-6411	102	57	α−	α−	PROPN
ejpam-6411	102	58	1	1	NUM
ejpam-6411	102	59	)	)	PUNCT
ejpam-6411	102	60	x	x	SYM
ejpam-6411	102	61	(	(	PUNCT
ejpam-6411	102	62	t)dtds	t)dtds	ADV
ejpam-6411	102	63	)	)	PUNCT
ejpam-6411	102	64	,	,	PUNCT
ejpam-6411	102	65	and	and	CCONJ
ejpam-6411	102	66	b0	b0	NOUN
ejpam-6411	102	67	=	=	SYM
ejpam-6411	102	68	1	1	NUM
ejpam-6411	102	69	h	h	NOUN
ejpam-6411	102	70	(	(	PUNCT
ejpam-6411	102	71	a0η	a0η	PROPN
ejpam-6411	102	72	+	+	PROPN
ejpam-6411	102	73	η	η	PROPN
ejpam-6411	102	74	∫	∫	PROPN
ejpam-6411	102	75	ρ	ρ	PROPN
ejpam-6411	102	76	0	0	PUNCT
ejpam-6411	103	1	(	(	PUNCT
ejpam-6411	103	2	ρ−	ρ−	NOUN
ejpam-6411	103	3	s)α−2	s)α−2	VERB
ejpam-6411	103	4	γ	γ	X
ejpam-6411	103	5	(	(	PUNCT
ejpam-6411	103	6	α−	α−	PROPN
ejpam-6411	103	7	1	1	NUM
ejpam-6411	103	8	)	)	PUNCT
ejpam-6411	103	9	x	x	X
ejpam-6411	104	1	(	(	PUNCT
ejpam-6411	104	2	s	s	X
ejpam-6411	104	3	)	)	PUNCT
ejpam-6411	104	4	ds−	ds−	PROPN
ejpam-6411	104	5	∫	∫	PROPN
ejpam-6411	105	1	h	h	NOUN
ejpam-6411	105	2	0	0	NUM
ejpam-6411	105	3	∫	∫	PROPN
ejpam-6411	105	4	s	s	PART
ejpam-6411	105	5	0	0	NUM
ejpam-6411	105	6	(	(	PUNCT
ejpam-6411	105	7	s−	s−	PROPN
ejpam-6411	105	8	t)β−2	t)β−2	VERB
ejpam-6411	105	9	γ	γ	X
ejpam-6411	105	10	(	(	PUNCT
ejpam-6411	105	11	β	β	NOUN
ejpam-6411	105	12	−	−	NOUN
ejpam-6411	105	13	1	1	X
ejpam-6411	105	14	)	)	PUNCT
ejpam-6411	105	15	y	y	PROPN
ejpam-6411	105	16	(	(	PUNCT
ejpam-6411	105	17	t)dtds	t)dtds	ADV
ejpam-6411	105	18	)	)	PUNCT
ejpam-6411	105	19	.	.	PUNCT
ejpam-6411	106	1	after	after	ADP
ejpam-6411	106	2	substituting	substitute	VERB
ejpam-6411	106	3	the	the	DET
ejpam-6411	106	4	value	value	NOUN
ejpam-6411	106	5	of	of	ADP
ejpam-6411	106	6	a0	a0	PROPN
ejpam-6411	106	7	into	into	ADP
ejpam-6411	106	8	b0	b0	NOUN
ejpam-6411	106	9	,	,	PUNCT
ejpam-6411	106	10	we	we	PRON
ejpam-6411	106	11	derive	derive	VERB
ejpam-6411	106	12	the	the	DET
ejpam-6411	106	13	final	final	ADJ
ejpam-6411	106	14	result	result	NOUN
ejpam-6411	106	15	for	for	ADP
ejpam-6411	106	16	such	such	ADJ
ejpam-6411	106	17	constants	constant	NOUN
ejpam-6411	106	18	in	in	ADP
ejpam-6411	106	19	the	the	DET
ejpam-6411	106	20	form	form	NOUN
ejpam-6411	106	21	b0	b0	NOUN
ejpam-6411	106	22	=	=	SYM
ejpam-6411	106	23	1	1	NUM
ejpam-6411	106	24	λ	λ	X
ejpam-6411	106	25	(	(	PUNCT
ejpam-6411	106	26	ζη	ζη	INTJ
ejpam-6411	106	27	∫	∫	PROPN
ejpam-6411	106	28	µ	µ	X
ejpam-6411	106	29	0	0	NUM
ejpam-6411	106	30	(	(	PUNCT
ejpam-6411	106	31	µ−	µ−	PROPN
ejpam-6411	106	32	s)β−2	s)β−2	VERB
ejpam-6411	106	33	γ(β	γ(β	PROPN
ejpam-6411	106	34	−	−	PROPN
ejpam-6411	106	35	1	1	NUM
ejpam-6411	106	36	)	)	PUNCT
ejpam-6411	106	37	y(s	y(s	PROPN
ejpam-6411	106	38	)	)	PUNCT
ejpam-6411	107	1	ds−	ds−	PROPN
ejpam-6411	107	2	η	η	PROPN
ejpam-6411	107	3	∫	∫	PROPN
ejpam-6411	107	4	h	h	PROPN
ejpam-6411	107	5	0	0	NUM
ejpam-6411	107	6	∫	∫	PROPN
ejpam-6411	107	7	s	s	PART
ejpam-6411	107	8	0	0	NUM
ejpam-6411	107	9	(	(	PUNCT
ejpam-6411	107	10	s−	s−	PROPN
ejpam-6411	107	11	t)α−2	t)α−2	NOUN
ejpam-6411	107	12	γ(α−	γ(α−	NOUN
ejpam-6411	107	13	1	1	NUM
ejpam-6411	107	14	)	)	PUNCT
ejpam-6411	107	15	x(t	x(t	PROPN
ejpam-6411	107	16	)	)	PUNCT
ejpam-6411	108	1	dt	dt	X
ejpam-6411	109	1	ds	ds	PROPN
ejpam-6411	109	2	+	+	ADV
ejpam-6411	109	3	hη	hη	PROPN
ejpam-6411	109	4	∫	∫	PROPN
ejpam-6411	109	5	ρ	ρ	PROPN
ejpam-6411	109	6	0	0	PROPN
ejpam-6411	110	1	(	(	PUNCT
ejpam-6411	110	2	ρ−	ρ−	NOUN
ejpam-6411	110	3	s)α−2	s)α−2	VERB
ejpam-6411	110	4	γ(α−	γ(α−	NOUN
ejpam-6411	110	5	1	1	NUM
ejpam-6411	110	6	)	)	PUNCT
ejpam-6411	110	7	x(s	x(s	PROPN
ejpam-6411	110	8	)	)	PUNCT
ejpam-6411	111	1	ds−h	ds−h	NOUN
ejpam-6411	111	2	∫	∫	PROPN
ejpam-6411	112	1	t	t	PROPN
ejpam-6411	112	2	0	0	NUM
ejpam-6411	112	3	∫	∫	PROPN
ejpam-6411	112	4	s	s	PART
ejpam-6411	112	5	0	0	NUM
ejpam-6411	112	6	(	(	PUNCT
ejpam-6411	112	7	s−	s−	PROPN
ejpam-6411	112	8	t)β−2	t)β−2	VERB
ejpam-6411	112	9	γ(β	γ(β	PROPN
ejpam-6411	112	10	−	−	PROPN
ejpam-6411	112	11	1	1	NUM
ejpam-6411	112	12	)	)	PUNCT
ejpam-6411	112	13	y(t	y(t	NUM
ejpam-6411	112	14	)	)	PUNCT
ejpam-6411	113	1	dt	dt	NOUN
ejpam-6411	113	2	ds	ds	ADJ
ejpam-6411	113	3	)	)	PUNCT
ejpam-6411	113	4	.	.	PUNCT
ejpam-6411	114	1	(	(	PUNCT
ejpam-6411	114	2	8)	8)	NUM
ejpam-6411	114	3	and	and	CCONJ
ejpam-6411	114	4	a0	a0	NOUN
ejpam-6411	114	5	=	=	SYM
ejpam-6411	114	6	1	1	NUM
ejpam-6411	114	7	λ	λ	NOUN
ejpam-6411	114	8	(	(	PUNCT
ejpam-6411	114	9	ζh	ζh	PROPN
ejpam-6411	114	10	∫	∫	PROPN
ejpam-6411	114	11	µ	µ	X
ejpam-6411	114	12	0	0	NUM
ejpam-6411	114	13	(	(	PUNCT
ejpam-6411	114	14	µ−	µ−	PROPN
ejpam-6411	114	15	s)β−2	s)β−2	VERB
ejpam-6411	114	16	γ(β	γ(β	PROPN
ejpam-6411	114	17	−	−	PROPN
ejpam-6411	114	18	1	1	NUM
ejpam-6411	114	19	)	)	PUNCT
ejpam-6411	114	20	y(s	y(s	PROPN
ejpam-6411	114	21	)	)	PUNCT
ejpam-6411	114	22	ds−h	ds−h	NOUN
ejpam-6411	114	23	∫	∫	PROPN
ejpam-6411	115	1	t	t	PROPN
ejpam-6411	115	2	0	0	NUM
ejpam-6411	115	3	∫	∫	PROPN
ejpam-6411	115	4	s	s	PART
ejpam-6411	115	5	0	0	NUM
ejpam-6411	115	6	(	(	PUNCT
ejpam-6411	115	7	s−	s−	PROPN
ejpam-6411	115	8	t)α−2	t)α−2	NOUN
ejpam-6411	115	9	γ(α−	γ(α−	NOUN
ejpam-6411	115	10	1	1	NUM
ejpam-6411	115	11	)	)	PUNCT
ejpam-6411	115	12	x(t	x(t	PROPN
ejpam-6411	115	13	)	)	PUNCT
ejpam-6411	115	14	dt	dt	X
ejpam-6411	116	1	ds	ds	PROPN
ejpam-6411	116	2	+	+	CCONJ
ejpam-6411	116	3	ζη	ζη	ADJ
ejpam-6411	116	4	∫	∫	PROPN
ejpam-6411	116	5	ρ	ρ	PROPN
ejpam-6411	116	6	0	0	PUNCT
ejpam-6411	117	1	(	(	PUNCT
ejpam-6411	117	2	ρ−	ρ−	NOUN
ejpam-6411	117	3	s)α−2	s)α−2	VERB
ejpam-6411	117	4	γ(α−	γ(α−	NOUN
ejpam-6411	117	5	1	1	NUM
ejpam-6411	117	6	)	)	PUNCT
ejpam-6411	117	7	x(s	x(s	PROPN
ejpam-6411	117	8	)	)	PUNCT
ejpam-6411	118	1	ds−	ds−	PROPN
ejpam-6411	118	2	ζ	ζ	NOUN
ejpam-6411	118	3	∫	∫	NOUN
ejpam-6411	118	4	t	t	PROPN
ejpam-6411	118	5	0	0	NUM
ejpam-6411	119	1	∫	∫	PROPN
ejpam-6411	119	2	s	s	PART
ejpam-6411	119	3	0	0	NUM
ejpam-6411	119	4	(	(	PUNCT
ejpam-6411	119	5	s−	s−	PROPN
ejpam-6411	119	6	t)β−2	t)β−2	VERB
ejpam-6411	119	7	γ(β	γ(β	PROPN
ejpam-6411	119	8	−	−	PROPN
ejpam-6411	119	9	1	1	NUM
ejpam-6411	119	10	)	)	PUNCT
ejpam-6411	119	11	y(t	y(t	NUM
ejpam-6411	119	12	)	)	PUNCT
ejpam-6411	119	13	dt	dt	NOUN
ejpam-6411	119	14	ds	ds	ADJ
ejpam-6411	119	15	)	)	PUNCT
ejpam-6411	119	16	.	.	PUNCT
ejpam-6411	120	1	(	(	PUNCT
ejpam-6411	120	2	9	9	X
ejpam-6411	120	3	)	)	PUNCT
ejpam-6411	120	4	hence	hence	ADV
ejpam-6411	120	5	,	,	PUNCT
ejpam-6411	120	6	substituting	substitute	VERB
ejpam-6411	120	7	the	the	DET
ejpam-6411	120	8	values	value	NOUN
ejpam-6411	120	9	of	of	ADP
ejpam-6411	120	10	a0	a0	PROPN
ejpam-6411	120	11	,	,	PUNCT
ejpam-6411	120	12	a1	a1	PROPN
ejpam-6411	120	13	,	,	PUNCT
ejpam-6411	120	14	b0	b0	NOUN
ejpam-6411	120	15	,	,	PUNCT
ejpam-6411	120	16	b1	b1	NOUN
ejpam-6411	120	17	in	in	ADP
ejpam-6411	120	18	e.	e.	PROPN
ejpam-6411	120	19	(	(	PUNCT
ejpam-6411	120	20	6	6	NUM
ejpam-6411	120	21	)	)	PUNCT
ejpam-6411	120	22	and	and	CCONJ
ejpam-6411	120	23	e.	e.	PROPN
ejpam-6411	120	24	(	(	PUNCT
ejpam-6411	120	25	7	7	NUM
ejpam-6411	120	26	)	)	PUNCT
ejpam-6411	120	27	,	,	PUNCT
ejpam-6411	120	28	gives	give	VERB
ejpam-6411	120	29	e.	e.	PROPN
ejpam-6411	120	30	(	(	PUNCT
ejpam-6411	120	31	4	4	NUM
ejpam-6411	120	32	)	)	PUNCT
ejpam-6411	120	33	and	and	CCONJ
ejpam-6411	120	34	e.	e.	PROPN
ejpam-6411	120	35	(	(	PUNCT
ejpam-6411	120	36	5	5	NUM
ejpam-6411	120	37	)	)	PUNCT
ejpam-6411	120	38	.	.	PUNCT
ejpam-6411	121	1	the	the	DET
ejpam-6411	121	2	converse	converse	NOUN
ejpam-6411	121	3	can	can	AUX
ejpam-6411	121	4	be	be	AUX
ejpam-6411	121	5	established	establish	VERB
ejpam-6411	121	6	after	after	ADP
ejpam-6411	121	7	a	a	DET
ejpam-6411	121	8	straightforward	straightforward	ADJ
ejpam-6411	121	9	computation	computation	NOUN
ejpam-6411	121	10	.	.	PUNCT
ejpam-6411	122	1	thus	thus	ADV
ejpam-6411	122	2	,	,	PUNCT
ejpam-6411	122	3	the	the	DET
ejpam-6411	122	4	proof	proof	NOUN
ejpam-6411	122	5	is	be	AUX
ejpam-6411	122	6	therefore	therefore	ADV
ejpam-6411	122	7	completed	complete	VERB
ejpam-6411	122	8	.	.	PUNCT
ejpam-6411	123	1	■	■	PUNCT
ejpam-6411	123	2	in	in	ADP
ejpam-6411	123	3	summary	summary	NOUN
ejpam-6411	123	4	,	,	PUNCT
ejpam-6411	123	5	the	the	DET
ejpam-6411	123	6	unique	unique	ADJ
ejpam-6411	123	7	solution	solution	NOUN
ejpam-6411	123	8	for	for	ADP
ejpam-6411	123	9	the	the	DET
ejpam-6411	123	10	coupled	couple	VERB
ejpam-6411	123	11	fractional	fractional	ADJ
ejpam-6411	123	12	system	system	NOUN
ejpam-6411	123	13	defined	define	VERB
ejpam-6411	123	14	in	in	ADP
ejpam-6411	123	15	e.	e.	PROPN
ejpam-6411	123	16	(	(	PUNCT
ejpam-6411	123	17	3	3	X
ejpam-6411	123	18	)	)	PUNCT
ejpam-6411	123	19	is	be	AUX
ejpam-6411	123	20	obtained	obtain	VERB
ejpam-6411	123	21	by	by	ADP
ejpam-6411	123	22	proving	prove	VERB
ejpam-6411	123	23	lemma	lemma	PROPN
ejpam-6411	123	24	2.3	2.3	NUM
ejpam-6411	123	25	,	,	PUNCT
ejpam-6411	123	26	where	where	SCONJ
ejpam-6411	123	27	the	the	DET
ejpam-6411	123	28	solution	solution	NOUN
ejpam-6411	123	29	is	be	AUX
ejpam-6411	123	30	presented	present	VERB
ejpam-6411	123	31	in	in	ADP
ejpam-6411	123	32	e.	e.	PROPN
ejpam-6411	123	33	(	(	PUNCT
ejpam-6411	123	34	4	4	NUM
ejpam-6411	123	35	)	)	PUNCT
ejpam-6411	123	36	and	and	CCONJ
ejpam-6411	123	37	e.	e.	PROPN
ejpam-6411	123	38	(	(	PUNCT
ejpam-6411	123	39	5	5	NUM
ejpam-6411	123	40	)	)	PUNCT
ejpam-6411	123	41	.	.	PUNCT
ejpam-6411	124	1	3	3	X
ejpam-6411	124	2	.	.	X
ejpam-6411	124	3	existence	existence	NOUN
ejpam-6411	124	4	and	and	CCONJ
ejpam-6411	124	5	uniqueness	uniqueness	VERB
ejpam-6411	124	6	this	this	DET
ejpam-6411	124	7	section	section	NOUN
ejpam-6411	124	8	covers	cover	VERB
ejpam-6411	124	9	uniqueness	uniqueness	NOUN
ejpam-6411	124	10	and	and	CCONJ
ejpam-6411	124	11	existence	existence	NOUN
ejpam-6411	124	12	of	of	ADP
ejpam-6411	124	13	the	the	DET
ejpam-6411	124	14	connected	connect	VERB
ejpam-6411	124	15	fractional	fractional	ADJ
ejpam-6411	124	16	system	system	NOUN
ejpam-6411	124	17	defined	define	VERB
ejpam-6411	124	18	by	by	ADP
ejpam-6411	124	19	equations	equation	NOUN
ejpam-6411	124	20	e.	e.	PROPN
ejpam-6411	125	1	(	(	PUNCT
ejpam-6411	125	2	1	1	NUM
ejpam-6411	125	3	)	)	PUNCT
ejpam-6411	125	4	and	and	CCONJ
ejpam-6411	125	5	(	(	PUNCT
ejpam-6411	125	6	2	2	NUM
ejpam-6411	125	7	)	)	PUNCT
ejpam-6411	125	8	.	.	PUNCT
ejpam-6411	126	1	let	let	VERB
ejpam-6411	126	2	’s	’s	PRON
ejpam-6411	126	3	define	define	VERB
ejpam-6411	126	4	the	the	DET
ejpam-6411	126	5	space	space	NOUN
ejpam-6411	126	6	g	g	NOUN
ejpam-6411	126	7	=	=	PUNCT
ejpam-6411	126	8	{	{	PUNCT
ejpam-6411	126	9	υ	υ	X
ejpam-6411	126	10	(	(	PUNCT
ejpam-6411	126	11	τ	τ	PROPN
ejpam-6411	126	12	)	)	PUNCT
ejpam-6411	126	13	,	,	PUNCT
ejpam-6411	126	14	υ	υ	PROPN
ejpam-6411	126	15	(	(	PUNCT
ejpam-6411	126	16	τ	τ	NOUN
ejpam-6411	126	17	)	)	PUNCT
ejpam-6411	126	18	∈	∈	PROPN
ejpam-6411	126	19	c([0,h	c([0,h	NOUN
ejpam-6411	126	20	]	]	X
ejpam-6411	126	21	}	}	PUNCT
ejpam-6411	126	22	,	,	PUNCT
ejpam-6411	126	23	z	z	NOUN
ejpam-6411	126	24	=	=	SYM
ejpam-6411	126	25	{	{	PUNCT
ejpam-6411	126	26	ω	ω	PROPN
ejpam-6411	126	27	(	(	PUNCT
ejpam-6411	126	28	τ	τ	PROPN
ejpam-6411	126	29	)	)	PUNCT
ejpam-6411	126	30	,	,	PUNCT
ejpam-6411	126	31	ω	ω	PROPN
ejpam-6411	126	32	(	(	PUNCT
ejpam-6411	126	33	τ	τ	PROPN
ejpam-6411	126	34	)	)	PUNCT
ejpam-6411	126	35	∈	∈	PROPN
ejpam-6411	126	36	c([0,h	c([0,h	NOUN
ejpam-6411	126	37	]	]	X
ejpam-6411	126	38	}	}	PUNCT
ejpam-6411	126	39	,	,	PUNCT
ejpam-6411	126	40	with	with	ADP
ejpam-6411	126	41	the	the	DET
ejpam-6411	126	42	norm	norm	NOUN
ejpam-6411	126	43	∥υ∥=	∥υ∥=	PROPN
ejpam-6411	126	44	sup	sup	NOUN
ejpam-6411	126	45	0≤τ≤h	0≤τ≤h	NUM
ejpam-6411	126	46	|υ	|υ	NOUN
ejpam-6411	126	47	(	(	PUNCT
ejpam-6411	126	48	τ)|	τ)|	NOUN
ejpam-6411	126	49	and∥ω∥=	and∥ω∥=	PROPN
ejpam-6411	126	50	sup	sup	NOUN
ejpam-6411	126	51	0≤τ≤h	0≤τ≤h	NUM
ejpam-6411	126	52	|ω	|ω	NOUN
ejpam-6411	126	53	(	(	PUNCT
ejpam-6411	126	54	τ)|	τ)|	PROPN
ejpam-6411	126	55	,	,	PUNCT
ejpam-6411	126	56	respectively	respectively	ADV
ejpam-6411	126	57	.	.	PUNCT
ejpam-6411	127	1	it	it	PRON
ejpam-6411	127	2	is	be	AUX
ejpam-6411	127	3	obvious	obvious	ADJ
ejpam-6411	127	4	that	that	SCONJ
ejpam-6411	127	5	both	both	PRON
ejpam-6411	127	6	(	(	PUNCT
ejpam-6411	127	7	g	g	NOUN
ejpam-6411	127	8	,	,	PUNCT
ejpam-6411	127	9	∥	∥	PUNCT
ejpam-6411	127	10	.∥	.∥	PUNCT
ejpam-6411	127	11	)	)	PUNCT
ejpam-6411	127	12	and	and	CCONJ
ejpam-6411	127	13	(	(	PUNCT
ejpam-6411	127	14	z	z	NOUN
ejpam-6411	127	15	,	,	PUNCT
ejpam-6411	127	16	∥	∥	PROPN
ejpam-6411	127	17	.∥	.∥	PUNCT
ejpam-6411	127	18	)	)	PUNCT
ejpam-6411	127	19	are	be	AUX
ejpam-6411	127	20	considered	consider	VERB
ejpam-6411	127	21	as	as	ADP
ejpam-6411	127	22	banach	banach	NOUN
ejpam-6411	127	23	spaces	space	NOUN
ejpam-6411	127	24	.	.	PUNCT
ejpam-6411	128	1	therefore	therefore	ADV
ejpam-6411	128	2	,	,	PUNCT
ejpam-6411	128	3	the	the	DET
ejpam-6411	128	4	product	product	NOUN
ejpam-6411	128	5	space	space	NOUN
ejpam-6411	128	6	(	(	PUNCT
ejpam-6411	128	7	g×z	g×z	PROPN
ejpam-6411	128	8	,	,	PUNCT
ejpam-6411	128	9	∥(υ	∥(υ	NOUN
ejpam-6411	128	10	,	,	PUNCT
ejpam-6411	128	11	ω)∥	ω)∥	PUNCT
ejpam-6411	128	12	)	)	PUNCT
ejpam-6411	128	13	is	be	AUX
ejpam-6411	128	14	also	also	ADV
ejpam-6411	128	15	a	a	DET
ejpam-6411	128	16	banach	banach	NOUN
ejpam-6411	128	17	space	space	NOUN
ejpam-6411	128	18	as	as	ADV
ejpam-6411	128	19	well	well	ADV
ejpam-6411	128	20	as	as	ADP
ejpam-6411	128	21	∥(υ	∥(υ	NOUN
ejpam-6411	128	22	,	,	PUNCT
ejpam-6411	128	23	ω)∥=	ω)∥=	AUX
ejpam-6411	128	24	∥υ∥+	∥υ∥+	VERB
ejpam-6411	128	25	∥ω∥.	∥ω∥.	ADV
ejpam-6411	128	26	but	but	CCONJ
ejpam-6411	128	27	by	by	ADP
ejpam-6411	128	28	considering	consider	VERB
ejpam-6411	128	29	lemma	lemma	PROPN
ejpam-6411	128	30	(	(	PUNCT
ejpam-6411	128	31	?	?	PUNCT
ejpam-6411	128	32	?	?	PUNCT
ejpam-6411	128	33	)	)	PUNCT
ejpam-6411	128	34	,	,	PUNCT
ejpam-6411	128	35	we	we	PRON
ejpam-6411	128	36	establish	establish	VERB
ejpam-6411	128	37	the	the	DET
ejpam-6411	128	38	operator	operator	NOUN
ejpam-6411	128	39	q	q	NOUN
ejpam-6411	128	40	:	:	PUNCT
ejpam-6411	128	41	g×z→g×z	g×z→g×z	PROPN
ejpam-6411	128	42	s.	s.	PROPN
ejpam-6411	128	43	momani	momani	PROPN
ejpam-6411	128	44	et	et	PROPN
ejpam-6411	128	45	al	al	PROPN
ejpam-6411	128	46	.	.	PUNCT
ejpam-6411	128	47	/	/	SYM
ejpam-6411	128	48	eur	eur	PROPN
ejpam-6411	128	49	.	.	PUNCT
ejpam-6411	129	1	j.	j.	PROPN
ejpam-6411	129	2	pure	pure	PROPN
ejpam-6411	129	3	appl	appl	PROPN
ejpam-6411	129	4	.	.	PROPN
ejpam-6411	129	5	math	math	PROPN
ejpam-6411	129	6	,	,	PUNCT
ejpam-6411	129	7	18	18	NUM
ejpam-6411	129	8	(	(	PUNCT
ejpam-6411	129	9	4	4	NUM
ejpam-6411	129	10	)	)	PUNCT
ejpam-6411	129	11	(	(	PUNCT
ejpam-6411	129	12	2025	2025	NUM
ejpam-6411	129	13	)	)	PUNCT
ejpam-6411	129	14	,	,	PUNCT
ejpam-6411	129	15	6411	6411	NUM
ejpam-6411	129	16	6	6	NUM
ejpam-6411	129	17	of	of	ADP
ejpam-6411	129	18	16	16	NUM
ejpam-6411	129	19	q	q	NOUN
ejpam-6411	129	20	(	(	PUNCT
ejpam-6411	129	21	υ	υ	PROPN
ejpam-6411	129	22	,	,	PUNCT
ejpam-6411	129	23	ω	ω	NOUN
ejpam-6411	129	24	)	)	PUNCT
ejpam-6411	129	25	(	(	PUNCT
ejpam-6411	129	26	τ	τ	X
ejpam-6411	129	27	)	)	PUNCT
ejpam-6411	129	28	=	=	SYM
ejpam-6411	129	29	(	(	PUNCT
ejpam-6411	129	30	q1	q1	PROPN
ejpam-6411	129	31	(	(	PUNCT
ejpam-6411	129	32	υ	υ	PROPN
ejpam-6411	129	33	,	,	PUNCT
ejpam-6411	129	34	ω	ω	NOUN
ejpam-6411	129	35	)	)	PUNCT
ejpam-6411	129	36	(	(	PUNCT
ejpam-6411	129	37	τ	τ	X
ejpam-6411	129	38	)	)	PUNCT
ejpam-6411	129	39	,	,	PUNCT
ejpam-6411	129	40	q2	q2	NOUN
ejpam-6411	129	41	(	(	PUNCT
ejpam-6411	129	42	υ	υ	PROPN
ejpam-6411	129	43	,	,	PUNCT
ejpam-6411	129	44	ω	ω	NOUN
ejpam-6411	129	45	)	)	PUNCT
ejpam-6411	129	46	(	(	PUNCT
ejpam-6411	129	47	τ	τ	PROPN
ejpam-6411	129	48	)	)	PUNCT
ejpam-6411	129	49	)	)	PUNCT
ejpam-6411	129	50	,	,	PUNCT
ejpam-6411	129	51	where	where	SCONJ
ejpam-6411	129	52	q1(υ	q1(υ	ADP
ejpam-6411	129	53	,	,	PUNCT
ejpam-6411	129	54	ω)(τ	ω)(τ	PUNCT
ejpam-6411	129	55	)	)	PUNCT
ejpam-6411	130	1	=	=	PUNCT
ejpam-6411	130	2	τ	τ	X
ejpam-6411	130	3	λ	λ	X
ejpam-6411	130	4	(	(	PUNCT
ejpam-6411	130	5	ζh	ζh	PROPN
ejpam-6411	130	6	∫	∫	PROPN
ejpam-6411	130	7	µ	µ	X
ejpam-6411	130	8	0	0	NUM
ejpam-6411	130	9	(	(	PUNCT
ejpam-6411	130	10	µ−	µ−	PROPN
ejpam-6411	130	11	s)β−2	s)β−2	VERB
ejpam-6411	130	12	γ(β	γ(β	PROPN
ejpam-6411	130	13	−	−	PROPN
ejpam-6411	130	14	1	1	NUM
ejpam-6411	130	15	)	)	PUNCT
ejpam-6411	130	16	h(s	h(s	PROPN
ejpam-6411	130	17	,	,	PUNCT
ejpam-6411	130	18	υ(s	υ(s	PROPN
ejpam-6411	130	19	)	)	PUNCT
ejpam-6411	130	20	,	,	PUNCT
ejpam-6411	130	21	ω(s	ω(s	NOUN
ejpam-6411	130	22	)	)	PUNCT
ejpam-6411	130	23	)	)	PUNCT
ejpam-6411	131	1	ds	ds	PROPN
ejpam-6411	131	2	−h	−h	ADJ
ejpam-6411	131	3	∫	∫	PROPN
ejpam-6411	131	4	h	h	NOUN
ejpam-6411	131	5	0	0	NUM
ejpam-6411	131	6	∫	∫	PROPN
ejpam-6411	131	7	s	s	PART
ejpam-6411	131	8	0	0	NUM
ejpam-6411	131	9	(	(	PUNCT
ejpam-6411	131	10	s−	s−	PROPN
ejpam-6411	131	11	t)α−2	t)α−2	NOUN
ejpam-6411	131	12	γ(α−	γ(α−	VERB
ejpam-6411	131	13	1	1	NUM
ejpam-6411	131	14	)	)	PUNCT
ejpam-6411	131	15	u(t	u(t	NOUN
ejpam-6411	131	16	,	,	PUNCT
ejpam-6411	131	17	υ(t	υ(t	NOUN
ejpam-6411	131	18	)	)	PUNCT
ejpam-6411	131	19	,	,	PUNCT
ejpam-6411	131	20	ω(t	ω(t	NOUN
ejpam-6411	131	21	)	)	PUNCT
ejpam-6411	131	22	)	)	PUNCT
ejpam-6411	132	1	dt	dt	X
ejpam-6411	133	1	ds	ds	PROPN
ejpam-6411	133	2	+	+	CCONJ
ejpam-6411	133	3	ζη	ζη	ADJ
ejpam-6411	133	4	∫	∫	PROPN
ejpam-6411	133	5	ρ	ρ	PROPN
ejpam-6411	133	6	0	0	PUNCT
ejpam-6411	134	1	(	(	PUNCT
ejpam-6411	134	2	ρ−	ρ−	NOUN
ejpam-6411	134	3	s)α−2	s)α−2	VERB
ejpam-6411	134	4	γ(α−	γ(α−	NOUN
ejpam-6411	134	5	1	1	NUM
ejpam-6411	134	6	)	)	PUNCT
ejpam-6411	134	7	u(s	u(s	PROPN
ejpam-6411	134	8	,	,	PUNCT
ejpam-6411	134	9	υ(s	υ(s	PROPN
ejpam-6411	134	10	)	)	PUNCT
ejpam-6411	134	11	,	,	PUNCT
ejpam-6411	134	12	ω(s	ω(s	NOUN
ejpam-6411	134	13	)	)	PUNCT
ejpam-6411	134	14	)	)	PUNCT
ejpam-6411	135	1	ds	ds	ADP
ejpam-6411	135	2	−	−	NOUN
ejpam-6411	135	3	ζ	ζ	NOUN
ejpam-6411	135	4	∫	∫	PROPN
ejpam-6411	135	5	h	h	NOUN
ejpam-6411	135	6	0	0	NUM
ejpam-6411	136	1	∫	∫	PROPN
ejpam-6411	136	2	s	s	PART
ejpam-6411	136	3	0	0	NUM
ejpam-6411	136	4	(	(	PUNCT
ejpam-6411	136	5	s−	s−	PROPN
ejpam-6411	136	6	t)β−2	t)β−2	VERB
ejpam-6411	136	7	γ(β	γ(β	PROPN
ejpam-6411	136	8	−	−	PROPN
ejpam-6411	136	9	1	1	NUM
ejpam-6411	136	10	)	)	PUNCT
ejpam-6411	136	11	h(t	h(t	PROPN
ejpam-6411	136	12	,	,	PUNCT
ejpam-6411	136	13	υ(t	υ(t	PROPN
ejpam-6411	136	14	)	)	PUNCT
ejpam-6411	136	15	,	,	PUNCT
ejpam-6411	136	16	ω(t	ω(t	NOUN
ejpam-6411	136	17	)	)	PUNCT
ejpam-6411	136	18	)	)	PUNCT
ejpam-6411	137	1	dt	dt	X
ejpam-6411	137	2	ds	ds	PROPN
ejpam-6411	137	3	)	)	PUNCT
ejpam-6411	138	1	+	+	CCONJ
ejpam-6411	138	2	∫	∫	PROPN
ejpam-6411	138	3	τ	τ	X
ejpam-6411	138	4	0	0	NUM
ejpam-6411	138	5	(	(	PUNCT
ejpam-6411	138	6	τ	τ	PROPN
ejpam-6411	138	7	−	−	PROPN
ejpam-6411	138	8	s)α−1	s)α−1	NOUN
ejpam-6411	138	9	γ(α	γ(α	NOUN
ejpam-6411	138	10	)	)	PUNCT
ejpam-6411	138	11	u(s	u(s	PROPN
ejpam-6411	138	12	,	,	PUNCT
ejpam-6411	138	13	υ(s	υ(s	PROPN
ejpam-6411	138	14	)	)	PUNCT
ejpam-6411	138	15	,	,	PUNCT
ejpam-6411	138	16	ω(s	ω(s	NOUN
ejpam-6411	138	17	)	)	PUNCT
ejpam-6411	138	18	)	)	PUNCT
ejpam-6411	138	19	ds	ds	PROPN
ejpam-6411	138	20	.	.	PUNCT
ejpam-6411	138	21	(	(	PUNCT
ejpam-6411	138	22	10	10	NUM
ejpam-6411	138	23	)	)	PUNCT
ejpam-6411	138	24	and	and	CCONJ
ejpam-6411	138	25	q2(υ	q2(υ	PROPN
ejpam-6411	138	26	,	,	PUNCT
ejpam-6411	138	27	ω)(τ	ω)(τ	PUNCT
ejpam-6411	138	28	)	)	PUNCT
ejpam-6411	138	29	=	=	PUNCT
ejpam-6411	139	1	τ	τ	X
ejpam-6411	139	2	λ	λ	X
ejpam-6411	139	3	(	(	PUNCT
ejpam-6411	139	4	ζη	ζη	INTJ
ejpam-6411	139	5	∫	∫	PROPN
ejpam-6411	139	6	µ	µ	X
ejpam-6411	139	7	0	0	NUM
ejpam-6411	139	8	(	(	PUNCT
ejpam-6411	139	9	µ−	µ−	PROPN
ejpam-6411	139	10	s)β−2	s)β−2	VERB
ejpam-6411	139	11	γ(β	γ(β	PROPN
ejpam-6411	139	12	−	−	PROPN
ejpam-6411	139	13	1	1	NUM
ejpam-6411	139	14	)	)	PUNCT
ejpam-6411	139	15	h(s	h(s	PROPN
ejpam-6411	139	16	,	,	PUNCT
ejpam-6411	139	17	υ(s	υ(s	PROPN
ejpam-6411	139	18	)	)	PUNCT
ejpam-6411	139	19	,	,	PUNCT
ejpam-6411	139	20	ω(s	ω(s	NOUN
ejpam-6411	139	21	)	)	PUNCT
ejpam-6411	139	22	)	)	PUNCT
ejpam-6411	140	1	ds	ds	ADP
ejpam-6411	140	2	−	−	PROPN
ejpam-6411	140	3	η	η	PROPN
ejpam-6411	140	4	∫	∫	PROPN
ejpam-6411	140	5	h	h	PROPN
ejpam-6411	140	6	0	0	NUM
ejpam-6411	140	7	∫	∫	PROPN
ejpam-6411	140	8	s	s	PART
ejpam-6411	140	9	0	0	NUM
ejpam-6411	140	10	(	(	PUNCT
ejpam-6411	140	11	s−	s−	PROPN
ejpam-6411	140	12	t)α−2	t)α−2	NOUN
ejpam-6411	140	13	γ(α−	γ(α−	VERB
ejpam-6411	140	14	1	1	NUM
ejpam-6411	140	15	)	)	PUNCT
ejpam-6411	140	16	u(t	u(t	NOUN
ejpam-6411	140	17	,	,	PUNCT
ejpam-6411	140	18	υ(t	υ(t	NOUN
ejpam-6411	140	19	)	)	PUNCT
ejpam-6411	140	20	,	,	PUNCT
ejpam-6411	140	21	ω(t	ω(t	NOUN
ejpam-6411	140	22	)	)	PUNCT
ejpam-6411	140	23	)	)	PUNCT
ejpam-6411	140	24	dt	dt	X
ejpam-6411	141	1	ds	ds	PROPN
ejpam-6411	141	2	+	+	ADV
ejpam-6411	141	3	hη	hη	PROPN
ejpam-6411	141	4	∫	∫	PROPN
ejpam-6411	141	5	ρ	ρ	PROPN
ejpam-6411	141	6	0	0	PROPN
ejpam-6411	142	1	(	(	PUNCT
ejpam-6411	142	2	ρ−	ρ−	NOUN
ejpam-6411	142	3	s)α−2	s)α−2	VERB
ejpam-6411	142	4	γ(α−	γ(α−	NOUN
ejpam-6411	142	5	1	1	NUM
ejpam-6411	142	6	)	)	PUNCT
ejpam-6411	142	7	u(s	u(s	PROPN
ejpam-6411	142	8	,	,	PUNCT
ejpam-6411	142	9	υ(s	υ(s	PROPN
ejpam-6411	142	10	)	)	PUNCT
ejpam-6411	142	11	,	,	PUNCT
ejpam-6411	142	12	ω(s	ω(s	NOUN
ejpam-6411	142	13	)	)	PUNCT
ejpam-6411	142	14	)	)	PUNCT
ejpam-6411	143	1	ds	ds	PROPN
ejpam-6411	143	2	−h	−h	ADJ
ejpam-6411	143	3	∫	∫	PROPN
ejpam-6411	143	4	h	h	NOUN
ejpam-6411	143	5	0	0	NUM
ejpam-6411	143	6	∫	∫	PROPN
ejpam-6411	143	7	s	s	PART
ejpam-6411	143	8	0	0	NUM
ejpam-6411	143	9	(	(	PUNCT
ejpam-6411	143	10	s−	s−	PROPN
ejpam-6411	143	11	t)β−2	t)β−2	VERB
ejpam-6411	143	12	γ(β	γ(β	PROPN
ejpam-6411	143	13	−	−	PROPN
ejpam-6411	143	14	1	1	NUM
ejpam-6411	143	15	)	)	PUNCT
ejpam-6411	143	16	h(t	h(t	PROPN
ejpam-6411	143	17	,	,	PUNCT
ejpam-6411	143	18	υ(t	υ(t	PROPN
ejpam-6411	143	19	)	)	PUNCT
ejpam-6411	143	20	,	,	PUNCT
ejpam-6411	143	21	ω(t	ω(t	NOUN
ejpam-6411	143	22	)	)	PUNCT
ejpam-6411	143	23	)	)	PUNCT
ejpam-6411	144	1	dt	dt	X
ejpam-6411	144	2	ds	ds	PROPN
ejpam-6411	144	3	)	)	PUNCT
ejpam-6411	145	1	+	+	CCONJ
ejpam-6411	145	2	∫	∫	PROPN
ejpam-6411	145	3	τ	τ	X
ejpam-6411	145	4	0	0	NUM
ejpam-6411	145	5	(	(	PUNCT
ejpam-6411	145	6	τ	τ	X
ejpam-6411	145	7	−	−	PROPN
ejpam-6411	145	8	s)β−1	s)β−1	AUX
ejpam-6411	145	9	γ(β	γ(β	PROPN
ejpam-6411	145	10	)	)	PUNCT
ejpam-6411	145	11	h(s	h(s	PROPN
ejpam-6411	145	12	,	,	PUNCT
ejpam-6411	145	13	υ(s	υ(s	PROPN
ejpam-6411	145	14	)	)	PUNCT
ejpam-6411	145	15	,	,	PUNCT
ejpam-6411	145	16	ω(s	ω(s	NOUN
ejpam-6411	145	17	)	)	PUNCT
ejpam-6411	145	18	)	)	PUNCT
ejpam-6411	145	19	ds	ds	PROPN
ejpam-6411	145	20	.	.	PUNCT
ejpam-6411	146	1	(	(	PUNCT
ejpam-6411	146	2	11	11	NUM
ejpam-6411	146	3	)	)	PUNCT
ejpam-6411	146	4	indeed	indeed	ADV
ejpam-6411	146	5	,	,	PUNCT
ejpam-6411	146	6	properties	property	NOUN
ejpam-6411	146	7	of	of	ADP
ejpam-6411	146	8	existence	existence	NOUN
ejpam-6411	146	9	and	and	CCONJ
ejpam-6411	146	10	uniqueness	uniqueness	NOUN
ejpam-6411	146	11	of	of	ADP
ejpam-6411	146	12	the	the	DET
ejpam-6411	146	13	solutions	solution	NOUN
ejpam-6411	146	14	of	of	ADP
ejpam-6411	146	15	e.	e.	PROPN
ejpam-6411	146	16	(	(	PUNCT
ejpam-6411	146	17	1	1	NUM
ejpam-6411	146	18	)	)	PUNCT
ejpam-6411	146	19	and	and	CCONJ
ejpam-6411	146	20	e.	e.	PROPN
ejpam-6411	146	21	(	(	PUNCT
ejpam-6411	146	22	2	2	X
ejpam-6411	146	23	)	)	PUNCT
ejpam-6411	146	24	may	may	AUX
ejpam-6411	146	25	be	be	AUX
ejpam-6411	146	26	established	establish	VERB
ejpam-6411	146	27	by	by	ADP
ejpam-6411	146	28	applying	apply	VERB
ejpam-6411	146	29	the	the	DET
ejpam-6411	146	30	banach	banach	NOUN
ejpam-6411	146	31	’s	’s	PART
ejpam-6411	146	32	contraction	contraction	NOUN
ejpam-6411	146	33	mapping	mapping	NOUN
ejpam-6411	146	34	theory	theory	NOUN
ejpam-6411	146	35	.	.	PUNCT
ejpam-6411	147	1	theorem	theorem	VERB
ejpam-6411	147	2	3.1	3.1	NUM
ejpam-6411	147	3	:	:	PUNCT
ejpam-6411	147	4	let	let	VERB
ejpam-6411	147	5	u	u	NOUN
ejpam-6411	147	6	,	,	PUNCT
ejpam-6411	147	7	h	h	NOUN
ejpam-6411	147	8	:	:	PUNCT
ejpam-6411	148	1	[	[	X
ejpam-6411	148	2	0,h]×r2→r	0,h]×r2→r	NUM
ejpam-6411	148	3	be	be	AUX
ejpam-6411	148	4	jointly	jointly	ADV
ejpam-6411	148	5	continuous	continuous	ADJ
ejpam-6411	148	6	functions	function	NOUN
ejpam-6411	148	7	.	.	PUNCT
ejpam-6411	149	1	assume	assume	VERB
ejpam-6411	149	2	that	that	SCONJ
ejpam-6411	149	3	(	(	PUNCT
ejpam-6411	149	4	i	i	NOUN
ejpam-6411	149	5	)	)	PUNCT
ejpam-6411	149	6	there	there	PRON
ejpam-6411	149	7	exist	exist	VERB
ejpam-6411	149	8	constants	constant	NOUN
ejpam-6411	149	9	θ,ϖ∈r	θ,ϖ∈r	ADV
ejpam-6411	149	10	such	such	ADJ
ejpam-6411	149	11	that	that	SCONJ
ejpam-6411	149	12	∀	∀	NOUN
ejpam-6411	149	13	z1	z1	VERB
ejpam-6411	149	14	,	,	PUNCT
ejpam-6411	149	15	z2	z2	PROPN
ejpam-6411	149	16	,	,	PUNCT
ejpam-6411	149	17	k1	k1	NOUN
ejpam-6411	149	18	,	,	PUNCT
ejpam-6411	149	19	k2∈r,∈	k2∈r,∈	PUNCT
ejpam-6411	150	1	[	[	X
ejpam-6411	150	2	0,h	0,h	X
ejpam-6411	150	3	]	]	X
ejpam-6411	150	4	,	,	PUNCT
ejpam-6411	150	5	we	we	PRON
ejpam-6411	150	6	have	have	VERB
ejpam-6411	150	7	|u	|u	ADJ
ejpam-6411	150	8	(	(	PUNCT
ejpam-6411	150	9	,	,	PUNCT
ejpam-6411	150	10	z1	z1	PROPN
ejpam-6411	150	11	,	,	PUNCT
ejpam-6411	150	12	z2)−u	z2)−u	PROPN
ejpam-6411	150	13	(	(	PUNCT
ejpam-6411	150	14	,	,	PUNCT
ejpam-6411	150	15	k1	k1	PROPN
ejpam-6411	150	16	,	,	PUNCT
ejpam-6411	150	17	k2)|	k2)|	PROPN
ejpam-6411	150	18	≤θ(|z2	≤θ(|z2	CCONJ
ejpam-6411	150	19	−	−	PROPN
ejpam-6411	150	20	z1|+	z1|+	PROPN
ejpam-6411	150	21	|k2	|k2	NOUN
ejpam-6411	150	22	−	−	PROPN
ejpam-6411	150	23	k1|	k1|	NOUN
ejpam-6411	150	24	)	)	PUNCT
ejpam-6411	150	25	,	,	PUNCT
ejpam-6411	150	26	and	and	CCONJ
ejpam-6411	150	27	|h	|h	X
ejpam-6411	150	28	(	(	PUNCT
ejpam-6411	150	29	τ	τ	PROPN
ejpam-6411	150	30	,	,	PUNCT
ejpam-6411	150	31	z1	z1	PROPN
ejpam-6411	150	32	,	,	PUNCT
ejpam-6411	150	33	z2)−	z2)−	PROPN
ejpam-6411	150	34	h	h	NOUN
ejpam-6411	150	35	(	(	PUNCT
ejpam-6411	150	36	τ	τ	PROPN
ejpam-6411	150	37	,	,	PUNCT
ejpam-6411	150	38	k1	k1	PROPN
ejpam-6411	150	39	,	,	PUNCT
ejpam-6411	150	40	k2)|	k2)|	PROPN
ejpam-6411	150	41	≤	≤	PROPN
ejpam-6411	150	42	ϖ	ϖ	X
ejpam-6411	150	43	(	(	PUNCT
ejpam-6411	150	44	|z2	|z2	ADJ
ejpam-6411	150	45	−	−	PROPN
ejpam-6411	150	46	z1|+	z1|+	PROPN
ejpam-6411	150	47	|k2	|k2	NOUN
ejpam-6411	150	48	−	−	PROPN
ejpam-6411	150	49	k1|	k1|	NOUN
ejpam-6411	150	50	)	)	PUNCT
ejpam-6411	150	51	.	.	PUNCT
ejpam-6411	151	1	(	(	PUNCT
ejpam-6411	151	2	i	i	NOUN
ejpam-6411	151	3	)	)	PUNCT
ejpam-6411	151	4	θ(n1	θ(n1	PROPN
ejpam-6411	152	1	+	+	SYM
ejpam-6411	152	2	n3	n3	NOUN
ejpam-6411	152	3	)	)	PUNCT
ejpam-6411	153	1	+	+	PROPN
ejpam-6411	153	2	ϖ	ϖ	PROPN
ejpam-6411	153	3	(	(	PUNCT
ejpam-6411	153	4	n2	n2	PROPN
ejpam-6411	153	5	+	+	PROPN
ejpam-6411	153	6	n4	n4	PROPN
ejpam-6411	153	7	)	)	PUNCT
ejpam-6411	153	8	<	<	X
ejpam-6411	154	1	1	1	X
ejpam-6411	154	2	.	.	PUNCT
ejpam-6411	154	3	then	then	ADV
ejpam-6411	154	4	the	the	DET
ejpam-6411	154	5	coupled	couple	VERB
ejpam-6411	154	6	fractional	fractional	ADJ
ejpam-6411	154	7	system	system	NOUN
ejpam-6411	154	8	in	in	ADP
ejpam-6411	154	9	the	the	DET
ejpam-6411	154	10	e.	e.	PROPN
ejpam-6411	154	11	(	(	PUNCT
ejpam-6411	154	12	1	1	NUM
ejpam-6411	154	13	)	)	PUNCT
ejpam-6411	154	14	and	and	CCONJ
ejpam-6411	154	15	e.	e.	PROPN
ejpam-6411	154	16	(	(	PUNCT
ejpam-6411	154	17	2	2	NUM
ejpam-6411	154	18	)	)	PUNCT
ejpam-6411	154	19	has	have	VERB
ejpam-6411	154	20	a	a	DET
ejpam-6411	154	21	unique	unique	ADJ
ejpam-6411	154	22	solution	solution	NOUN
ejpam-6411	154	23	on	on	ADP
ejpam-6411	154	24	[	[	X
ejpam-6411	154	25	0,h	0,h	X
ejpam-6411	154	26	]	]	X
ejpam-6411	154	27	,	,	PUNCT
ejpam-6411	154	28	where	where	SCONJ
ejpam-6411	154	29	n1	n1	PROPN
ejpam-6411	154	30	=	=	SYM
ejpam-6411	154	31	h	h	PROPN
ejpam-6411	154	32	|λ|	|λ|	PROPN
ejpam-6411	154	33	(	(	PUNCT
ejpam-6411	154	34	hα+1	hα+1	NOUN
ejpam-6411	154	35	γ	γ	X
ejpam-6411	154	36	(	(	PUNCT
ejpam-6411	154	37	α+	α+	PROPN
ejpam-6411	154	38	1	1	NUM
ejpam-6411	154	39	)	)	PUNCT
ejpam-6411	154	40	+	+	CCONJ
ejpam-6411	154	41	|ζη|	|ζη|	PRON
ejpam-6411	154	42	ρα−1	ρα−1	ADJ
ejpam-6411	154	43	γ	γ	X
ejpam-6411	154	44	(	(	PUNCT
ejpam-6411	154	45	α	α	NOUN
ejpam-6411	154	46	)	)	PUNCT
ejpam-6411	154	47	)	)	PUNCT
ejpam-6411	155	1	+	+	CCONJ
ejpam-6411	155	2	hα	hα	ADP
ejpam-6411	155	3	γ	γ	X
ejpam-6411	155	4	(	(	PUNCT
ejpam-6411	155	5	α+	α+	PROPN
ejpam-6411	155	6	1	1	NUM
ejpam-6411	155	7	)	)	PUNCT
ejpam-6411	155	8	,	,	PUNCT
ejpam-6411	155	9	s.	s.	PROPN
ejpam-6411	155	10	momani	momani	PROPN
ejpam-6411	155	11	et	et	PROPN
ejpam-6411	155	12	al	al	PROPN
ejpam-6411	155	13	.	.	PUNCT
ejpam-6411	155	14	/	/	SYM
ejpam-6411	155	15	eur	eur	PROPN
ejpam-6411	155	16	.	.	PUNCT
ejpam-6411	156	1	j.	j.	PROPN
ejpam-6411	156	2	pure	pure	PROPN
ejpam-6411	156	3	appl	appl	PROPN
ejpam-6411	156	4	.	.	PROPN
ejpam-6411	156	5	math	math	PROPN
ejpam-6411	156	6	,	,	PUNCT
ejpam-6411	156	7	18	18	NUM
ejpam-6411	156	8	(	(	PUNCT
ejpam-6411	156	9	4	4	NUM
ejpam-6411	156	10	)	)	PUNCT
ejpam-6411	156	11	(	(	PUNCT
ejpam-6411	156	12	2025	2025	NUM
ejpam-6411	156	13	)	)	PUNCT
ejpam-6411	156	14	,	,	PUNCT
ejpam-6411	156	15	6411	6411	NUM
ejpam-6411	156	16	7	7	NUM
ejpam-6411	156	17	of	of	ADP
ejpam-6411	156	18	16	16	NUM
ejpam-6411	156	19	n2	n2	NOUN
ejpam-6411	156	20	=	=	PUNCT
ejpam-6411	156	21	h	h	PROPN
ejpam-6411	156	22	|λ|	|λ|	NOUN
ejpam-6411	156	23	(	(	PUNCT
ejpam-6411	156	24	|ζ|hµβ−1	|ζ|hµβ−1	PUNCT
ejpam-6411	156	25	γ	γ	X
ejpam-6411	156	26	(	(	PUNCT
ejpam-6411	156	27	β	β	NOUN
ejpam-6411	156	28	)	)	PUNCT
ejpam-6411	157	1	+	+	CCONJ
ejpam-6411	157	2	|ζ|hβ	|ζ|hβ	PROPN
ejpam-6411	157	3	γ	γ	X
ejpam-6411	157	4	(	(	PUNCT
ejpam-6411	157	5	β	β	X
ejpam-6411	157	6	+	+	NOUN
ejpam-6411	157	7	1	1	NUM
ejpam-6411	157	8	)	)	PUNCT
ejpam-6411	157	9	)	)	PUNCT
ejpam-6411	157	10	,	,	PUNCT
ejpam-6411	157	11	n3	n3	NOUN
ejpam-6411	157	12	=	=	PROPN
ejpam-6411	157	13	h	h	PROPN
ejpam-6411	157	14	|λ|	|λ|	PROPN
ejpam-6411	157	15	(	(	PUNCT
ejpam-6411	157	16	|η|hα	|η|hα	PROPN
ejpam-6411	157	17	γ	γ	X
ejpam-6411	157	18	(	(	PUNCT
ejpam-6411	157	19	α+	α+	NOUN
ejpam-6411	157	20	1	1	NUM
ejpam-6411	157	21	)	)	PUNCT
ejpam-6411	157	22	+	+	NUM
ejpam-6411	157	23	h	h	NOUN
ejpam-6411	157	24	|η|	|η|	PROPN
ejpam-6411	157	25	ρα−1	ρα−1	PROPN
ejpam-6411	157	26	γ	γ	X
ejpam-6411	157	27	(	(	PUNCT
ejpam-6411	157	28	α	α	NOUN
ejpam-6411	157	29	)	)	PUNCT
ejpam-6411	157	30	)	)	PUNCT
ejpam-6411	157	31	,	,	PUNCT
ejpam-6411	157	32	n4	n4	PROPN
ejpam-6411	157	33	=	=	PROPN
ejpam-6411	157	34	h	h	PROPN
ejpam-6411	157	35	|λ|	|λ|	PROPN
ejpam-6411	157	36	(	(	PUNCT
ejpam-6411	157	37	|ζη|µβ−1	|ζη|µβ−1	NUM
ejpam-6411	157	38	γ	γ	X
ejpam-6411	157	39	(	(	PUNCT
ejpam-6411	157	40	β	β	NOUN
ejpam-6411	157	41	)	)	PUNCT
ejpam-6411	158	1	+	+	CCONJ
ejpam-6411	158	2	hβ+1	hβ+1	ADJ
ejpam-6411	158	3	γ	γ	X
ejpam-6411	158	4	(	(	PUNCT
ejpam-6411	158	5	β	β	X
ejpam-6411	158	6	+	+	NOUN
ejpam-6411	158	7	1	1	NUM
ejpam-6411	158	8	)	)	PUNCT
ejpam-6411	158	9	)	)	PUNCT
ejpam-6411	159	1	+	+	CCONJ
ejpam-6411	159	2	hβ	hβ	PROPN
ejpam-6411	159	3	γ	γ	X
ejpam-6411	159	4	(	(	PUNCT
ejpam-6411	159	5	β	β	X
ejpam-6411	159	6	+	+	NOUN
ejpam-6411	159	7	1	1	NUM
ejpam-6411	159	8	)	)	PUNCT
ejpam-6411	159	9	.	.	PUNCT
ejpam-6411	160	1	proof	proof	NOUN
ejpam-6411	160	2	:	:	PUNCT
ejpam-6411	160	3	let	let	VERB
ejpam-6411	160	4	us	we	PRON
ejpam-6411	160	5	define	define	VERB
ejpam-6411	160	6	sup0≤τ≤hu	sup0≤τ≤hu	PROPN
ejpam-6411	160	7	(	(	PUNCT
ejpam-6411	160	8	τ	τ	PROPN
ejpam-6411	160	9	,	,	PUNCT
ejpam-6411	160	10	0	0	NUM
ejpam-6411	160	11	,	,	PUNCT
ejpam-6411	160	12	0)=u0<∞	0)=u0<∞	NOUN
ejpam-6411	160	13	,	,	PUNCT
ejpam-6411	160	14	sup0≤τ≤hh	sup0≤τ≤hh	X
ejpam-6411	160	15	(	(	PUNCT
ejpam-6411	160	16	τ	τ	PROPN
ejpam-6411	160	17	,	,	PUNCT
ejpam-6411	160	18	0	0	NUM
ejpam-6411	160	19	,	,	PUNCT
ejpam-6411	160	20	0)=h0<∞	0)=h0<∞	PROPN
ejpam-6411	160	21	and	and	CCONJ
ejpam-6411	160	22	ψr=	ψr=	PROPN
ejpam-6411	160	23	{	{	PUNCT
ejpam-6411	160	24	(	(	PUNCT
ejpam-6411	160	25	υ	υ	INTJ
ejpam-6411	160	26	,	,	PUNCT
ejpam-6411	160	27	ω)∈g×z	ω)∈g×z	NUM
ejpam-6411	160	28	:	:	PUNCT
ejpam-6411	160	29	∥(υ	∥(υ	NOUN
ejpam-6411	160	30	,	,	PUNCT
ejpam-6411	160	31	ω)∥≤r	ω)∥≤r	NOUN
ejpam-6411	160	32	}	}	PUNCT
ejpam-6411	160	33	,	,	PUNCT
ejpam-6411	160	34	and	and	CCONJ
ejpam-6411	160	35	r	r	X
ejpam-6411	160	36	>	>	X
ejpam-6411	160	37	0	0	NUM
ejpam-6411	160	38	,	,	PUNCT
ejpam-6411	160	39	such	such	ADJ
ejpam-6411	160	40	that	that	SCONJ
ejpam-6411	160	41	r	r	NOUN
ejpam-6411	160	42	≥	≥	NUM
ejpam-6411	160	43	(	(	PUNCT
ejpam-6411	160	44	n1	n1	NOUN
ejpam-6411	160	45	+	+	NOUN
ejpam-6411	160	46	n3)u0	n3)u0	ADV
ejpam-6411	160	47	+	+	CCONJ
ejpam-6411	160	48	(	(	PUNCT
ejpam-6411	160	49	n2	n2	ADJ
ejpam-6411	160	50	+	+	PROPN
ejpam-6411	160	51	n4)h0	n4)h0	PROPN
ejpam-6411	160	52	1−	1−	NUM
ejpam-6411	161	1	[	[	X
ejpam-6411	161	2	θ	θ	X
ejpam-6411	161	3	(	(	PUNCT
ejpam-6411	161	4	n1	n1	PROPN
ejpam-6411	161	5	+	+	SYM
ejpam-6411	161	6	n3	n3	ADJ
ejpam-6411	161	7	)	)	PUNCT
ejpam-6411	161	8	+	+	PROPN
ejpam-6411	161	9	ϖ	ϖ	PROPN
ejpam-6411	161	10	(	(	PUNCT
ejpam-6411	161	11	n2	n2	PROPN
ejpam-6411	161	12	+	+	PROPN
ejpam-6411	161	13	n4	n4	PROPN
ejpam-6411	161	14	)	)	PUNCT
ejpam-6411	161	15	]	]	PUNCT
ejpam-6411	161	16	.	.	PUNCT
ejpam-6411	162	1	hence	hence	ADV
ejpam-6411	162	2	,	,	PUNCT
ejpam-6411	162	3	we	we	PRON
ejpam-6411	162	4	first	first	ADV
ejpam-6411	162	5	show	show	VERB
ejpam-6411	162	6	that	that	SCONJ
ejpam-6411	162	7	qψr⊆ψr	qψr⊆ψr	NOUN
ejpam-6411	162	8	.	.	PUNCT
ejpam-6411	162	9	by	by	ADP
ejpam-6411	162	10	our	our	PRON
ejpam-6411	162	11	assumption	assumption	NOUN
ejpam-6411	162	12	,	,	PUNCT
ejpam-6411	162	13	(	(	PUNCT
ejpam-6411	162	14	υ	υ	NOUN
ejpam-6411	162	15	,	,	PUNCT
ejpam-6411	162	16	ω)∈ψr	ω)∈ψr	PROPN
ejpam-6411	162	17	,	,	PUNCT
ejpam-6411	162	18	τ∈	τ∈	PUNCT
ejpam-6411	163	1	[	[	X
ejpam-6411	163	2	0,h	0,h	X
ejpam-6411	163	3	]	]	X
ejpam-6411	163	4	,	,	PUNCT
ejpam-6411	163	5	we	we	PRON
ejpam-6411	163	6	have	have	VERB
ejpam-6411	163	7	|u	|u	ADJ
ejpam-6411	163	8	(	(	PUNCT
ejpam-6411	163	9	τ	τ	PROPN
ejpam-6411	163	10	,	,	PUNCT
ejpam-6411	163	11	υ	υ	PROPN
ejpam-6411	163	12	(	(	PUNCT
ejpam-6411	163	13	τ	τ	PROPN
ejpam-6411	163	14	)	)	PUNCT
ejpam-6411	163	15	,	,	PUNCT
ejpam-6411	164	1	ω	ω	PROPN
ejpam-6411	164	2	(	(	PUNCT
ejpam-6411	164	3	τ))|	τ))|	PROPN
ejpam-6411	164	4	≤	≤	PROPN
ejpam-6411	164	5	|u	|u	ADJ
ejpam-6411	164	6	(	(	PUNCT
ejpam-6411	164	7	τ	τ	PROPN
ejpam-6411	164	8	,	,	PUNCT
ejpam-6411	164	9	υ	υ	PROPN
ejpam-6411	164	10	(	(	PUNCT
ejpam-6411	164	11	τ	τ	PROPN
ejpam-6411	164	12	)	)	PUNCT
ejpam-6411	164	13	,	,	PUNCT
ejpam-6411	164	14	ω	ω	PROPN
ejpam-6411	164	15	(	(	PUNCT
ejpam-6411	164	16	τ))−	τ))−	PROPN
ejpam-6411	164	17	u	u	NOUN
ejpam-6411	164	18	(	(	PUNCT
ejpam-6411	164	19	τ	τ	PROPN
ejpam-6411	164	20	,	,	PUNCT
ejpam-6411	164	21	0	0	NUM
ejpam-6411	164	22	,	,	PUNCT
ejpam-6411	164	23	0)|+	0)|+	X
ejpam-6411	164	24	|u	|u	ADJ
ejpam-6411	164	25	(	(	PUNCT
ejpam-6411	164	26	τ	τ	PROPN
ejpam-6411	164	27	,	,	PUNCT
ejpam-6411	164	28	0	0	NUM
ejpam-6411	164	29	,	,	PUNCT
ejpam-6411	164	30	0)|	0)|	NOUN
ejpam-6411	164	31	,	,	PUNCT
ejpam-6411	164	32	≤	≤	ADJ
ejpam-6411	164	33	θ(|υ	θ(|υ	PROPN
ejpam-6411	164	34	(	(	PUNCT
ejpam-6411	164	35	τ)|+	τ)|+	NOUN
ejpam-6411	164	36	|ω	|ω	X
ejpam-6411	164	37	(	(	PUNCT
ejpam-6411	164	38	τ)|	τ)|	PROPN
ejpam-6411	164	39	)	)	PUNCT
ejpam-6411	164	40	+	+	CCONJ
ejpam-6411	164	41	u0	u0	ADJ
ejpam-6411	164	42	≤	≤	X
ejpam-6411	164	43	θ(∥υ∥+	θ(∥υ∥+	ADJ
ejpam-6411	164	44	∥ω∥	∥ω∥	NUM
ejpam-6411	164	45	)	)	PUNCT
ejpam-6411	165	1	+	+	NUM
ejpam-6411	165	2	u	u	NOUN
ejpam-6411	165	3	≤	≤	NOUN
ejpam-6411	165	4	θr	θr	NOUN
ejpam-6411	165	5	+	+	CCONJ
ejpam-6411	165	6	u0	u0	ADJ
ejpam-6411	165	7	,	,	PUNCT
ejpam-6411	165	8	and	and	CCONJ
ejpam-6411	165	9	|h	|h	X
ejpam-6411	165	10	(	(	PUNCT
ejpam-6411	165	11	τ	τ	PROPN
ejpam-6411	165	12	,	,	PUNCT
ejpam-6411	165	13	υ	υ	PROPN
ejpam-6411	165	14	(	(	PUNCT
ejpam-6411	165	15	τ	τ	PROPN
ejpam-6411	165	16	)	)	PUNCT
ejpam-6411	165	17	,	,	PUNCT
ejpam-6411	165	18	ω	ω	PROPN
ejpam-6411	165	19	(	(	PUNCT
ejpam-6411	165	20	τ))|	τ))|	PROPN
ejpam-6411	165	21	≤	≤	PROPN
ejpam-6411	165	22	ϖ	ϖ	X
ejpam-6411	165	23	(	(	PUNCT
ejpam-6411	165	24	|υ	|υ	NOUN
ejpam-6411	165	25	(	(	PUNCT
ejpam-6411	165	26	τ)|+	τ)|+	NOUN
ejpam-6411	165	27	|ω	|ω	X
ejpam-6411	165	28	(	(	PUNCT
ejpam-6411	165	29	τ)|	τ)|	PROPN
ejpam-6411	165	30	)	)	PUNCT
ejpam-6411	165	31	+	+	CCONJ
ejpam-6411	165	32	h0	h0	NOUN
ejpam-6411	165	33	≤	≤	PROPN
ejpam-6411	165	34	ϖ	ϖ	PROPN
ejpam-6411	165	35	(	(	PUNCT
ejpam-6411	165	36	∥υ∥+	∥υ∥+	NOUN
ejpam-6411	165	37	∥ω∥	∥ω∥	NUM
ejpam-6411	165	38	)	)	PUNCT
ejpam-6411	165	39	+	+	CCONJ
ejpam-6411	165	40	h0	h0	NOUN
ejpam-6411	165	41	≤	≤	PROPN
ejpam-6411	165	42	ϖr	ϖr	PROPN
ejpam-6411	165	43	+	+	NUM
ejpam-6411	165	44	h0	h0	PROPN
ejpam-6411	165	45	,	,	PUNCT
ejpam-6411	165	46	which	which	PRON
ejpam-6411	165	47	lead	lead	VERB
ejpam-6411	165	48	to	to	ADP
ejpam-6411	165	49	|q1(υ	|q1(υ	PROPN
ejpam-6411	165	50	,	,	PUNCT
ejpam-6411	165	51	ω)(τ)|	ω)(τ)|	PROPN
ejpam-6411	165	52	≤	≤	NUM
ejpam-6411	165	53	h	h	NOUN
ejpam-6411	165	54	|λ|	|λ|	PROPN
ejpam-6411	165	55	(	(	PUNCT
ejpam-6411	165	56	|ζ|h	|ζ|h	VERB
ejpam-6411	165	57	∫	∫	PROPN
ejpam-6411	165	58	µ	µ	X
ejpam-6411	165	59	0	0	NUM
ejpam-6411	165	60	(	(	PUNCT
ejpam-6411	165	61	µ−	µ−	PROPN
ejpam-6411	165	62	s)β−2	s)β−2	VERB
ejpam-6411	165	63	γ(β	γ(β	PROPN
ejpam-6411	165	64	−	−	PROPN
ejpam-6411	165	65	1	1	X
ejpam-6411	165	66	)	)	PUNCT
ejpam-6411	165	67	ds	ds	NOUN
ejpam-6411	165	68	(	(	PUNCT
ejpam-6411	165	69	ϖ(∥υ∥+	ϖ(∥υ∥+	NOUN
ejpam-6411	165	70	∥ω∥	∥ω∥	NUM
ejpam-6411	165	71	)	)	PUNCT
ejpam-6411	165	72	+	+	NUM
ejpam-6411	165	73	h0	h0	NOUN
ejpam-6411	165	74	)	)	PUNCT
ejpam-6411	166	1	+	+	NOUN
ejpam-6411	167	1	h	h	NOUN
ejpam-6411	167	2	∫	∫	PROPN
ejpam-6411	167	3	h	h	PROPN
ejpam-6411	167	4	0	0	NUM
ejpam-6411	167	5	∫	∫	PROPN
ejpam-6411	167	6	s	s	PART
ejpam-6411	167	7	0	0	NUM
ejpam-6411	167	8	(	(	PUNCT
ejpam-6411	167	9	s−	s−	PROPN
ejpam-6411	167	10	t)α−2	t)α−2	NOUN
ejpam-6411	167	11	γ(α−	γ(α−	NOUN
ejpam-6411	167	12	1	1	NUM
ejpam-6411	167	13	)	)	PUNCT
ejpam-6411	167	14	dt	dt	NOUN
ejpam-6411	167	15	ds	ds	PROPN
ejpam-6411	167	16	(	(	PUNCT
ejpam-6411	167	17	θ(∥υ∥+	θ(∥υ∥+	NOUN
ejpam-6411	167	18	∥ω∥	∥ω∥	NUM
ejpam-6411	167	19	)	)	PUNCT
ejpam-6411	167	20	+	+	CCONJ
ejpam-6411	167	21	u0	u0	ADJ
ejpam-6411	167	22	)	)	PUNCT
ejpam-6411	168	1	+	+	CCONJ
ejpam-6411	168	2	|ζη|	|ζη|	NUM
ejpam-6411	168	3	∫	∫	PROPN
ejpam-6411	168	4	ρ	ρ	PROPN
ejpam-6411	168	5	0	0	PUNCT
ejpam-6411	168	6	(	(	PUNCT
ejpam-6411	168	7	ρ−	ρ−	NOUN
ejpam-6411	168	8	s)α−2	s)α−2	VERB
ejpam-6411	168	9	γ(α−	γ(α−	VERB
ejpam-6411	168	10	1	1	X
ejpam-6411	168	11	)	)	PUNCT
ejpam-6411	168	12	ds	ds	NOUN
ejpam-6411	168	13	(	(	PUNCT
ejpam-6411	168	14	θ(∥υ∥+	θ(∥υ∥+	NOUN
ejpam-6411	168	15	∥ω∥	∥ω∥	NUM
ejpam-6411	168	16	)	)	PUNCT
ejpam-6411	168	17	+	+	CCONJ
ejpam-6411	168	18	u0	u0	ADJ
ejpam-6411	168	19	)	)	PUNCT
ejpam-6411	169	1	+	+	CCONJ
ejpam-6411	169	2	|ζ|	|ζ|	NUM
ejpam-6411	170	1	∫	∫	PROPN
ejpam-6411	170	2	h	h	NOUN
ejpam-6411	170	3	0	0	NUM
ejpam-6411	170	4	∫	∫	PROPN
ejpam-6411	170	5	s	s	PART
ejpam-6411	170	6	0	0	NUM
ejpam-6411	170	7	(	(	PUNCT
ejpam-6411	170	8	s−	s−	PROPN
ejpam-6411	170	9	t)β−2	t)β−2	VERB
ejpam-6411	170	10	γ(β	γ(β	PROPN
ejpam-6411	170	11	−	−	PROPN
ejpam-6411	170	12	1	1	NUM
ejpam-6411	170	13	)	)	PUNCT
ejpam-6411	171	1	dt	dt	NOUN
ejpam-6411	171	2	ds	ds	INTJ
ejpam-6411	171	3	(	(	PUNCT
ejpam-6411	171	4	ϖ(∥υ∥+	ϖ(∥υ∥+	NOUN
ejpam-6411	171	5	∥ω∥	∥ω∥	NUM
ejpam-6411	171	6	)	)	PUNCT
ejpam-6411	171	7	+	+	NUM
ejpam-6411	171	8	h0	h0	NOUN
ejpam-6411	171	9	)	)	PUNCT
ejpam-6411	171	10	)	)	PUNCT
ejpam-6411	172	1	+	+	CCONJ
ejpam-6411	172	2	sup	sup	NOUN
ejpam-6411	172	3	0≤τ≤h	0≤τ≤h	NUM
ejpam-6411	172	4	∫	∫	PROPN
ejpam-6411	172	5	τ	τ	X
ejpam-6411	172	6	0	0	NUM
ejpam-6411	173	1	(	(	PUNCT
ejpam-6411	173	2	τ	τ	PROPN
ejpam-6411	173	3	−	−	PROPN
ejpam-6411	173	4	s)α−1	s)α−1	NOUN
ejpam-6411	173	5	γ(α	γ(α	NOUN
ejpam-6411	173	6	)	)	PUNCT
ejpam-6411	174	1	ds	ds	PROPN
ejpam-6411	174	2	(	(	PUNCT
ejpam-6411	174	3	θ(∥υ∥+	θ(∥υ∥+	NOUN
ejpam-6411	174	4	∥ω∥	∥ω∥	NUM
ejpam-6411	174	5	)	)	PUNCT
ejpam-6411	174	6	+	+	CCONJ
ejpam-6411	174	7	u0	u0	ADJ
ejpam-6411	174	8	)	)	PUNCT
ejpam-6411	174	9	≤	≤	NOUN
ejpam-6411	174	10	(	(	PUNCT
ejpam-6411	174	11	θ(∥υ∥+	θ(∥υ∥+	NOUN
ejpam-6411	174	12	∥ω∥	∥ω∥	NUM
ejpam-6411	174	13	)	)	PUNCT
ejpam-6411	174	14	+	+	CCONJ
ejpam-6411	174	15	u0	u0	ADJ
ejpam-6411	174	16	)	)	PUNCT
ejpam-6411	175	1	[	[	X
ejpam-6411	175	2	h	h	X
ejpam-6411	175	3	λ	λ	X
ejpam-6411	175	4	(	(	PUNCT
ejpam-6411	175	5	hα+1	hα+1	NOUN
ejpam-6411	175	6	γ(α+	γ(α+	DET
ejpam-6411	175	7	1	1	NUM
ejpam-6411	175	8	)	)	PUNCT
ejpam-6411	175	9	+	+	NUM
ejpam-6411	175	10	|ζη|ρα−1	|ζη|ρα−1	NUM
ejpam-6411	175	11	γ(α	γ(α	NOUN
ejpam-6411	175	12	)	)	PUNCT
ejpam-6411	175	13	)	)	PUNCT
ejpam-6411	176	1	+	+	CCONJ
ejpam-6411	176	2	hα	hα	ADP
ejpam-6411	176	3	γ(α+	γ(α+	DET
ejpam-6411	176	4	1	1	NUM
ejpam-6411	176	5	)	)	PUNCT
ejpam-6411	176	6	]	]	PUNCT
ejpam-6411	177	1	+	+	CCONJ
ejpam-6411	177	2	(	(	PUNCT
ejpam-6411	177	3	ϖ(∥υ∥+	ϖ(∥υ∥+	NOUN
ejpam-6411	177	4	∥ω∥	∥ω∥	NUM
ejpam-6411	177	5	)	)	PUNCT
ejpam-6411	177	6	+	+	NUM
ejpam-6411	177	7	h0	h0	NOUN
ejpam-6411	177	8	)	)	PUNCT
ejpam-6411	178	1	[	[	X
ejpam-6411	178	2	h	h	X
ejpam-6411	178	3	λ	λ	X
ejpam-6411	178	4	(	(	PUNCT
ejpam-6411	178	5	|ζ|hµβ−1	|ζ|hµβ−1	PUNCT
ejpam-6411	178	6	γ(β	γ(β	PROPN
ejpam-6411	178	7	)	)	PUNCT
ejpam-6411	179	1	+	+	CCONJ
ejpam-6411	179	2	|ζ|hβ	|ζ|hβ	PROPN
ejpam-6411	179	3	γ(β	γ(β	PROPN
ejpam-6411	179	4	+	+	PROPN
ejpam-6411	179	5	1	1	NUM
ejpam-6411	179	6	)	)	PUNCT
ejpam-6411	179	7	)	)	PUNCT
ejpam-6411	179	8	]	]	PUNCT
ejpam-6411	180	1	≤	≤	NUM
ejpam-6411	180	2	(	(	PUNCT
ejpam-6411	180	3	θ(∥υ∥+	θ(∥υ∥+	NOUN
ejpam-6411	180	4	∥ω∥	∥ω∥	NUM
ejpam-6411	180	5	)	)	PUNCT
ejpam-6411	180	6	+	+	CCONJ
ejpam-6411	180	7	u0	u0	ADJ
ejpam-6411	180	8	)	)	PUNCT
ejpam-6411	180	9	n1	n1	NOUN
ejpam-6411	180	10	+	+	CCONJ
ejpam-6411	180	11	(	(	PUNCT
ejpam-6411	180	12	ϖ(∥υ∥+	ϖ(∥υ∥+	NOUN
ejpam-6411	180	13	∥ω∥	∥ω∥	NUM
ejpam-6411	180	14	)	)	PUNCT
ejpam-6411	180	15	+	+	CCONJ
ejpam-6411	180	16	h0	h0	NOUN
ejpam-6411	180	17	)	)	PUNCT
ejpam-6411	180	18	n2	n2	ADJ
ejpam-6411	180	19	≤	≤	NOUN
ejpam-6411	180	20	(	(	PUNCT
ejpam-6411	180	21	θr	θr	NOUN
ejpam-6411	180	22	+	+	CCONJ
ejpam-6411	180	23	u0)n1	u0)n1	NOUN
ejpam-6411	180	24	+	+	CCONJ
ejpam-6411	180	25	(	(	PUNCT
ejpam-6411	180	26	ϖr	ϖr	X
ejpam-6411	180	27	+	+	X
ejpam-6411	180	28	h0)n2	h0)n2	ADJ
ejpam-6411	180	29	.	.	PUNCT
ejpam-6411	181	1	(	(	PUNCT
ejpam-6411	181	2	12	12	NUM
ejpam-6411	181	3	)	)	PUNCT
ejpam-6411	181	4	in	in	ADP
ejpam-6411	181	5	alike	alike	ADJ
ejpam-6411	181	6	manner	manner	NOUN
ejpam-6411	181	7	s.	s.	PROPN
ejpam-6411	181	8	momani	momani	PROPN
ejpam-6411	181	9	et	et	PROPN
ejpam-6411	181	10	al	al	PROPN
ejpam-6411	181	11	.	.	PUNCT
ejpam-6411	181	12	/	/	SYM
ejpam-6411	181	13	eur	eur	PROPN
ejpam-6411	181	14	.	.	PUNCT
ejpam-6411	182	1	j.	j.	PROPN
ejpam-6411	182	2	pure	pure	PROPN
ejpam-6411	182	3	appl	appl	PROPN
ejpam-6411	182	4	.	.	PROPN
ejpam-6411	182	5	math	math	PROPN
ejpam-6411	182	6	,	,	PUNCT
ejpam-6411	182	7	18	18	NUM
ejpam-6411	182	8	(	(	PUNCT
ejpam-6411	182	9	4	4	NUM
ejpam-6411	182	10	)	)	PUNCT
ejpam-6411	182	11	(	(	PUNCT
ejpam-6411	182	12	2025	2025	NUM
ejpam-6411	182	13	)	)	PUNCT
ejpam-6411	182	14	,	,	PUNCT
ejpam-6411	182	15	6411	6411	NUM
ejpam-6411	182	16	8	8	NUM
ejpam-6411	182	17	of	of	ADP
ejpam-6411	182	18	16	16	NUM
ejpam-6411	182	19	|q2	|q2	VERB
ejpam-6411	182	20	(	(	PUNCT
ejpam-6411	182	21	υ	υ	PROPN
ejpam-6411	182	22	,	,	PUNCT
ejpam-6411	182	23	ω	ω	NOUN
ejpam-6411	182	24	)	)	PUNCT
ejpam-6411	182	25	(	(	PUNCT
ejpam-6411	182	26	τ)|	τ)|	NOUN
ejpam-6411	182	27	≤	≤	NOUN
ejpam-6411	182	28	(	(	PUNCT
ejpam-6411	182	29	θ	θ	X
ejpam-6411	182	30	(	(	PUNCT
ejpam-6411	182	31	∥υ∥+	∥υ∥+	NOUN
ejpam-6411	182	32	∥ω∥	∥ω∥	NUM
ejpam-6411	182	33	)	)	PUNCT
ejpam-6411	183	1	+	+	NUM
ejpam-6411	183	2	u0)n3+(ϖ	u0)n3+(ϖ	X
ejpam-6411	183	3	(	(	PUNCT
ejpam-6411	183	4	∥υ∥+	∥υ∥+	NOUN
ejpam-6411	183	5	∥ω∥	∥ω∥	NUM
ejpam-6411	183	6	)	)	PUNCT
ejpam-6411	183	7	+	+	NUM
ejpam-6411	183	8	h0)n4	h0)n4	NOUN
ejpam-6411	183	9	≤	≤	NOUN
ejpam-6411	183	10	(	(	PUNCT
ejpam-6411	183	11	θr	θr	NOUN
ejpam-6411	183	12	+	+	CCONJ
ejpam-6411	183	13	u0)n3+(ϖr	u0)n3+(ϖr	NOUN
ejpam-6411	183	14	+	+	NUM
ejpam-6411	183	15	h0)n4	h0)n4	NOUN
ejpam-6411	183	16	.	.	PUNCT
ejpam-6411	184	1	hence	hence	ADV
ejpam-6411	184	2	,	,	PUNCT
ejpam-6411	184	3	we	we	PRON
ejpam-6411	184	4	derive	derive	VERB
ejpam-6411	184	5	∥q1	∥q1	NOUN
ejpam-6411	184	6	(	(	PUNCT
ejpam-6411	184	7	υ	υ	NOUN
ejpam-6411	184	8	,	,	PUNCT
ejpam-6411	184	9	ω)∥	ω)∥	PUNCT
ejpam-6411	184	10	≤	≤	NUM
ejpam-6411	184	11	(	(	PUNCT
ejpam-6411	184	12	θr	θr	NOUN
ejpam-6411	184	13	+	+	CCONJ
ejpam-6411	184	14	u0)n1	u0)n1	NOUN
ejpam-6411	184	15	+	+	CCONJ
ejpam-6411	184	16	(	(	PUNCT
ejpam-6411	184	17	ϖr	ϖr	X
ejpam-6411	184	18	+	+	X
ejpam-6411	184	19	h0)n2	h0)n2	ADJ
ejpam-6411	184	20	,	,	PUNCT
ejpam-6411	184	21	and	and	CCONJ
ejpam-6411	184	22	∥q2	∥q2	NOUN
ejpam-6411	184	23	(	(	PUNCT
ejpam-6411	184	24	υ	υ	NOUN
ejpam-6411	184	25	,	,	PUNCT
ejpam-6411	184	26	ω)∥	ω)∥	PUNCT
ejpam-6411	184	27	≤	≤	NUM
ejpam-6411	184	28	(	(	PUNCT
ejpam-6411	184	29	θr	θr	NOUN
ejpam-6411	184	30	+	+	CCONJ
ejpam-6411	185	1	u0)n3	u0)n3	NOUN
ejpam-6411	186	1	+	+	CCONJ
ejpam-6411	187	1	(	(	PUNCT
ejpam-6411	187	2	ϖr	ϖr	X
ejpam-6411	187	3	+	+	NUM
ejpam-6411	187	4	h0)n4	h0)n4	NOUN
ejpam-6411	187	5	.	.	PUNCT
ejpam-6411	188	1	consequently	consequently	ADV
ejpam-6411	188	2	,	,	PUNCT
ejpam-6411	188	3	we	we	PRON
ejpam-6411	188	4	get	get	VERB
ejpam-6411	188	5	∥q	∥q	ADJ
ejpam-6411	188	6	(	(	PUNCT
ejpam-6411	188	7	υ	υ	NOUN
ejpam-6411	188	8	,	,	PUNCT
ejpam-6411	188	9	ω)∥	ω)∥	PUNCT
ejpam-6411	188	10	≤	≤	NUM
ejpam-6411	189	1	(	(	PUNCT
ejpam-6411	189	2	θr	θr	NOUN
ejpam-6411	189	3	+	+	CCONJ
ejpam-6411	189	4	u0	u0	ADJ
ejpam-6411	189	5	)	)	PUNCT
ejpam-6411	189	6	(	(	PUNCT
ejpam-6411	189	7	n1	n1	PROPN
ejpam-6411	189	8	+	+	SYM
ejpam-6411	189	9	n3	n3	ADJ
ejpam-6411	189	10	)	)	PUNCT
ejpam-6411	190	1	+	+	CCONJ
ejpam-6411	190	2	(	(	PUNCT
ejpam-6411	190	3	ϖr	ϖr	PROPN
ejpam-6411	190	4	+	+	NUM
ejpam-6411	190	5	h0	h0	PROPN
ejpam-6411	190	6	)	)	PUNCT
ejpam-6411	190	7	(	(	PUNCT
ejpam-6411	190	8	n2	n2	PROPN
ejpam-6411	190	9	+	+	PROPN
ejpam-6411	190	10	n4	n4	PROPN
ejpam-6411	190	11	)	)	PUNCT
ejpam-6411	190	12	≤	≤	NOUN
ejpam-6411	190	13	r	r	NOUN
ejpam-6411	190	14	.	.	PUNCT
ejpam-6411	191	1	therefore	therefore	ADV
ejpam-6411	191	2	,	,	PUNCT
ejpam-6411	191	3	it	it	PRON
ejpam-6411	191	4	follows	follow	VERB
ejpam-6411	191	5	∥q	∥q	PROPN
ejpam-6411	191	6	(	(	PUNCT
ejpam-6411	191	7	υ	υ	NOUN
ejpam-6411	191	8	,	,	PUNCT
ejpam-6411	191	9	ω)∥≤r	ω)∥≤r	ADJ
ejpam-6411	191	10	,	,	PUNCT
ejpam-6411	191	11	i.e.	i.e.	X
ejpam-6411	191	12	,	,	PUNCT
ejpam-6411	191	13	qψr⊆ψr	qψr⊆ψr	ADJ
ejpam-6411	191	14	.	.	PUNCT
ejpam-6411	192	1	now	now	ADV
ejpam-6411	192	2	,	,	PUNCT
ejpam-6411	192	3	let	let	VERB
ejpam-6411	192	4	(	(	PUNCT
ejpam-6411	192	5	υ1	υ1	PROPN
ejpam-6411	192	6	,	,	PUNCT
ejpam-6411	192	7	ω1	ω1	PROPN
ejpam-6411	192	8	)	)	PUNCT
ejpam-6411	192	9	,	,	PUNCT
ejpam-6411	192	10	(	(	PUNCT
ejpam-6411	192	11	υ2	υ2	NOUN
ejpam-6411	192	12	,	,	PUNCT
ejpam-6411	192	13	ω2)∈g×z,∀τ∈	ω2)∈g×z,∀τ∈	PUNCT
ejpam-6411	192	14	[	[	X
ejpam-6411	192	15	0,h	0,h	X
ejpam-6411	192	16	]	]	X
ejpam-6411	192	17	,	,	PUNCT
ejpam-6411	192	18	υ	υ	PROPN
ejpam-6411	192	19	,	,	PUNCT
ejpam-6411	192	20	ω	ω	PROPN
ejpam-6411	192	21	ϵr	ϵr	NOUN
ejpam-6411	192	22	.	.	PUNCT
ejpam-6411	193	1	then	then	ADV
ejpam-6411	193	2	,	,	PUNCT
ejpam-6411	193	3	we	we	PRON
ejpam-6411	193	4	get	get	VERB
ejpam-6411	193	5	|q1(υ1	|q1(υ1	PROPN
ejpam-6411	193	6	,	,	PUNCT
ejpam-6411	193	7	ω1)(τ)−q1(υ2	ω1)(τ)−q1(υ2	NUM
ejpam-6411	193	8	,	,	PUNCT
ejpam-6411	193	9	ω2)(τ)|	ω2)(τ)|	NUM
ejpam-6411	193	10	≤	≤	NUM
ejpam-6411	193	11	h	h	NOUN
ejpam-6411	193	12	|λ|	|λ|	PROPN
ejpam-6411	193	13	(	(	PUNCT
ejpam-6411	193	14	|ζ|h	|ζ|h	VERB
ejpam-6411	193	15	∫	∫	PROPN
ejpam-6411	193	16	µ	µ	X
ejpam-6411	193	17	0	0	NUM
ejpam-6411	193	18	(	(	PUNCT
ejpam-6411	193	19	µ−	µ−	PROPN
ejpam-6411	193	20	s)β−2	s)β−2	VERB
ejpam-6411	193	21	γ(β	γ(β	PROPN
ejpam-6411	193	22	−	−	PROPN
ejpam-6411	193	23	1	1	X
ejpam-6411	193	24	)	)	PUNCT
ejpam-6411	193	25	ds	ds	PRON
ejpam-6411	193	26	ϖ	ϖ	INTJ
ejpam-6411	193	27	(	(	PUNCT
ejpam-6411	193	28	∥υ2	∥υ2	NOUN
ejpam-6411	193	29	−	−	PROPN
ejpam-6411	193	30	υ1∥+	υ1∥+	PROPN
ejpam-6411	193	31	∥ω2	∥ω2	PROPN
ejpam-6411	193	32	−	−	PROPN
ejpam-6411	193	33	ω1∥	ω1∥	PROPN
ejpam-6411	193	34	)	)	PUNCT
ejpam-6411	194	1	+	+	PUNCT
ejpam-6411	194	2	h	h	NOUN
ejpam-6411	194	3	∫	∫	PROPN
ejpam-6411	194	4	h	h	PROPN
ejpam-6411	194	5	0	0	NUM
ejpam-6411	194	6	∫	∫	PROPN
ejpam-6411	194	7	s	s	PART
ejpam-6411	194	8	0	0	NUM
ejpam-6411	194	9	(	(	PUNCT
ejpam-6411	194	10	s−	s−	PROPN
ejpam-6411	194	11	t)α−2	t)α−2	NOUN
ejpam-6411	194	12	γ(α−	γ(α−	NOUN
ejpam-6411	194	13	1	1	NUM
ejpam-6411	194	14	)	)	PUNCT
ejpam-6411	194	15	dt	dt	NOUN
ejpam-6411	194	16	ds	ds	PROPN
ejpam-6411	194	17	θ	θ	PROPN
ejpam-6411	194	18	(	(	PUNCT
ejpam-6411	194	19	∥υ2	∥υ2	X
ejpam-6411	194	20	−	−	PROPN
ejpam-6411	194	21	υ1∥+	υ1∥+	PROPN
ejpam-6411	194	22	∥ω2	∥ω2	PROPN
ejpam-6411	194	23	−	−	PROPN
ejpam-6411	194	24	ω1∥	ω1∥	PROPN
ejpam-6411	194	25	)	)	PUNCT
ejpam-6411	194	26	+	+	CCONJ
ejpam-6411	194	27	|ζη|	|ζη|	NUM
ejpam-6411	194	28	∫	∫	PROPN
ejpam-6411	194	29	ρ	ρ	PROPN
ejpam-6411	194	30	0	0	PUNCT
ejpam-6411	195	1	(	(	PUNCT
ejpam-6411	195	2	ρ−	ρ−	NOUN
ejpam-6411	195	3	s)α−2	s)α−2	VERB
ejpam-6411	195	4	γ(α−	γ(α−	VERB
ejpam-6411	195	5	1	1	X
ejpam-6411	195	6	)	)	PUNCT
ejpam-6411	195	7	ds	ds	ADJ
ejpam-6411	195	8	θ	θ	NOUN
ejpam-6411	195	9	(	(	PUNCT
ejpam-6411	195	10	∥υ2	∥υ2	X
ejpam-6411	195	11	−	−	PROPN
ejpam-6411	195	12	υ1∥+	υ1∥+	PROPN
ejpam-6411	195	13	∥ω2	∥ω2	PROPN
ejpam-6411	195	14	−	−	PROPN
ejpam-6411	195	15	ω1∥	ω1∥	PROPN
ejpam-6411	195	16	)	)	PUNCT
ejpam-6411	196	1	+	+	CCONJ
ejpam-6411	197	1	|ζ|	|ζ|	NUM
ejpam-6411	197	2	∫	∫	PROPN
ejpam-6411	197	3	h	h	NOUN
ejpam-6411	197	4	0	0	NUM
ejpam-6411	198	1	∫	∫	PROPN
ejpam-6411	198	2	s	s	PART
ejpam-6411	198	3	0	0	NUM
ejpam-6411	198	4	(	(	PUNCT
ejpam-6411	198	5	s−	s−	PROPN
ejpam-6411	198	6	t)β−2	t)β−2	VERB
ejpam-6411	198	7	γ(β	γ(β	PROPN
ejpam-6411	198	8	−	−	PROPN
ejpam-6411	198	9	1	1	NUM
ejpam-6411	198	10	)	)	PUNCT
ejpam-6411	199	1	dt	dt	NOUN
ejpam-6411	199	2	ds	ds	INTJ
ejpam-6411	199	3	ϖ	ϖ	INTJ
ejpam-6411	199	4	(	(	PUNCT
ejpam-6411	199	5	∥υ2	∥υ2	NOUN
ejpam-6411	199	6	−	−	PROPN
ejpam-6411	199	7	υ1∥+	υ1∥+	PROPN
ejpam-6411	199	8	∥ω2	∥ω2	PROPN
ejpam-6411	199	9	−	−	PROPN
ejpam-6411	199	10	ω1∥	ω1∥	PROPN
ejpam-6411	199	11	)	)	PUNCT
ejpam-6411	199	12	)	)	PUNCT
ejpam-6411	200	1	+	+	CCONJ
ejpam-6411	200	2	sup	sup	NOUN
ejpam-6411	200	3	0≤τ≤h	0≤τ≤h	NUM
ejpam-6411	200	4	∫	∫	PROPN
ejpam-6411	200	5	τ	τ	X
ejpam-6411	200	6	0	0	NUM
ejpam-6411	201	1	(	(	PUNCT
ejpam-6411	201	2	τ	τ	PROPN
ejpam-6411	201	3	−	−	PROPN
ejpam-6411	201	4	s)α−1	s)α−1	NOUN
ejpam-6411	201	5	γ(α	γ(α	NOUN
ejpam-6411	201	6	)	)	PUNCT
ejpam-6411	201	7	ds	ds	PROPN
ejpam-6411	201	8	θ	θ	NOUN
ejpam-6411	201	9	(	(	PUNCT
ejpam-6411	201	10	∥υ2	∥υ2	X
ejpam-6411	201	11	−	−	PROPN
ejpam-6411	201	12	υ1∥+	υ1∥+	PROPN
ejpam-6411	201	13	∥ω2	∥ω2	PROPN
ejpam-6411	201	14	−	−	PROPN
ejpam-6411	201	15	ω1∥	ω1∥	PROPN
ejpam-6411	201	16	)	)	PUNCT
ejpam-6411	201	17	.	.	PUNCT
ejpam-6411	202	1	(	(	PUNCT
ejpam-6411	202	2	13	13	NUM
ejpam-6411	202	3	)	)	PUNCT
ejpam-6411	202	4	that	that	PRON
ejpam-6411	202	5	is	be	AUX
ejpam-6411	202	6	,	,	PUNCT
ejpam-6411	202	7	∥q1	∥q1	NOUN
ejpam-6411	202	8	(	(	PUNCT
ejpam-6411	202	9	υ1	υ1	PROPN
ejpam-6411	202	10	,	,	PUNCT
ejpam-6411	202	11	ω1)−q1	ω1)−q1	PROPN
ejpam-6411	202	12	(	(	PUNCT
ejpam-6411	202	13	υ2	υ2	NOUN
ejpam-6411	202	14	,	,	PUNCT
ejpam-6411	202	15	ω2)∥	ω2)∥	PROPN
ejpam-6411	202	16	≤	≤	NOUN
ejpam-6411	202	17	n1θ(∥υ2	n1θ(∥υ2	NUM
ejpam-6411	202	18	−	−	PROPN
ejpam-6411	202	19	υ1∥+	υ1∥+	NOUN
ejpam-6411	202	20	∥ω2	∥ω2	NOUN
ejpam-6411	203	1	−	−	PROPN
ejpam-6411	203	2	ω1∥)+n2ϖ	ω1∥)+n2ϖ	NUM
ejpam-6411	203	3	(	(	PUNCT
ejpam-6411	203	4	∥υ2	∥υ2	NOUN
ejpam-6411	203	5	−	−	PROPN
ejpam-6411	203	6	υ1∥+	υ1∥+	PROPN
ejpam-6411	203	7	∥ω2	∥ω2	NOUN
ejpam-6411	203	8	−	−	PROPN
ejpam-6411	203	9	ω1∥	ω1∥	PROPN
ejpam-6411	203	10	)	)	PUNCT
ejpam-6411	203	11	.	.	PUNCT
ejpam-6411	204	1	(	(	PUNCT
ejpam-6411	204	2	14	14	NUM
ejpam-6411	204	3	)	)	PUNCT
ejpam-6411	204	4	similarly	similarly	ADV
ejpam-6411	204	5	,	,	PUNCT
ejpam-6411	204	6	it	it	PRON
ejpam-6411	204	7	follows	follow	VERB
ejpam-6411	204	8	∥q2	∥q2	NOUN
ejpam-6411	205	1	(	(	PUNCT
ejpam-6411	205	2	υ1	υ1	PROPN
ejpam-6411	205	3	,	,	PUNCT
ejpam-6411	205	4	ω1)−q2	ω1)−q2	PROPN
ejpam-6411	205	5	(	(	PUNCT
ejpam-6411	205	6	υ2	υ2	PROPN
ejpam-6411	205	7	,	,	PUNCT
ejpam-6411	205	8	ω2)∥	ω2)∥	PROPN
ejpam-6411	205	9	≤	≤	NUM
ejpam-6411	205	10	n3θ(∥υ2	n3θ(∥υ2	NUM
ejpam-6411	206	1	−	−	PROPN
ejpam-6411	206	2	υ1∥+	υ1∥+	PROPN
ejpam-6411	206	3	∥ω2	∥ω2	NOUN
ejpam-6411	206	4	−	−	PROPN
ejpam-6411	206	5	ω1∥)+n4ϖ	ω1∥)+n4ϖ	NOUN
ejpam-6411	206	6	(	(	PUNCT
ejpam-6411	206	7	∥υ2	∥υ2	X
ejpam-6411	206	8	−	−	PROPN
ejpam-6411	206	9	υ1∥+	υ1∥+	PROPN
ejpam-6411	206	10	∥ω2	∥ω2	NOUN
ejpam-6411	206	11	−	−	PROPN
ejpam-6411	206	12	ω1∥	ω1∥	PROPN
ejpam-6411	206	13	)	)	PUNCT
ejpam-6411	206	14	.	.	PUNCT
ejpam-6411	207	1	(	(	PUNCT
ejpam-6411	207	2	15	15	NUM
ejpam-6411	207	3	)	)	PUNCT
ejpam-6411	207	4	for	for	ADP
ejpam-6411	207	5	υ	υ	PROPN
ejpam-6411	207	6	,	,	PUNCT
ejpam-6411	207	7	ω	ω	PROPN
ejpam-6411	207	8	ϵr	ϵr	X
ejpam-6411	208	1	we	we	PRON
ejpam-6411	208	2	,	,	PUNCT
ejpam-6411	208	3	from	from	ADP
ejpam-6411	208	4	(	(	PUNCT
ejpam-6411	208	5	14	14	NUM
ejpam-6411	208	6	)	)	PUNCT
ejpam-6411	208	7	and	and	CCONJ
ejpam-6411	208	8	(	(	PUNCT
ejpam-6411	208	9	15	15	NUM
ejpam-6411	208	10	)	)	PUNCT
ejpam-6411	208	11	,	,	PUNCT
ejpam-6411	208	12	deduced	deduce	VERB
ejpam-6411	208	13	that	that	SCONJ
ejpam-6411	208	14	∥q	∥q	PROPN
ejpam-6411	208	15	(	(	PUNCT
ejpam-6411	208	16	υ1	υ1	PROPN
ejpam-6411	208	17	,	,	PUNCT
ejpam-6411	208	18	ω1)−q	ω1)−q	PROPN
ejpam-6411	208	19	(	(	PUNCT
ejpam-6411	208	20	υ2	υ2	PROPN
ejpam-6411	208	21	,	,	PUNCT
ejpam-6411	208	22	ω2)∥	ω2)∥	X
ejpam-6411	208	23	≤	≤	NOUN
ejpam-6411	208	24	(	(	PUNCT
ejpam-6411	208	25	θ	θ	NOUN
ejpam-6411	208	26	(	(	PUNCT
ejpam-6411	208	27	n1	n1	PROPN
ejpam-6411	208	28	+	+	SYM
ejpam-6411	208	29	n3	n3	ADJ
ejpam-6411	208	30	)	)	PUNCT
ejpam-6411	208	31	+	+	PROPN
ejpam-6411	208	32	ϖ	ϖ	PROPN
ejpam-6411	208	33	(	(	PUNCT
ejpam-6411	208	34	n2	n2	PROPN
ejpam-6411	208	35	+	+	PROPN
ejpam-6411	208	36	n4	n4	PROPN
ejpam-6411	208	37	)	)	PUNCT
ejpam-6411	208	38	)	)	PUNCT
ejpam-6411	208	39	(	(	PUNCT
ejpam-6411	208	40	∥υ2	∥υ2	X
ejpam-6411	208	41	−	−	PROPN
ejpam-6411	208	42	υ1∥+	υ1∥+	PROPN
ejpam-6411	208	43	∥ω2	∥ω2	PROPN
ejpam-6411	208	44	−	−	PROPN
ejpam-6411	208	45	ω1∥	ω1∥	PROPN
ejpam-6411	208	46	)	)	PUNCT
ejpam-6411	208	47	,	,	PUNCT
ejpam-6411	208	48	as	as	SCONJ
ejpam-6411	208	49	θ(n1	θ(n1	PROPN
ejpam-6411	208	50	+	+	PROPN
ejpam-6411	208	51	n3)+ϖ	n3)+ϖ	PROPN
ejpam-6411	208	52	(	(	PUNCT
ejpam-6411	208	53	n2	n2	PROPN
ejpam-6411	208	54	+	+	PROPN
ejpam-6411	208	55	n4	n4	PROPN
ejpam-6411	208	56	)	)	PUNCT
ejpam-6411	208	57	<	<	X
ejpam-6411	208	58	1	1	X
ejpam-6411	208	59	.	.	PUNCT
ejpam-6411	208	60	further	far	ADV
ejpam-6411	208	61	,	,	PUNCT
ejpam-6411	208	62	as	as	SCONJ
ejpam-6411	208	63	the	the	DET
ejpam-6411	208	64	operator	operator	NOUN
ejpam-6411	208	65	q	q	PUNCT
ejpam-6411	208	66	is	be	AUX
ejpam-6411	208	67	a	a	DET
ejpam-6411	208	68	contraction	contraction	NOUN
ejpam-6411	208	69	operator	operator	NOUN
ejpam-6411	208	70	,	,	PUNCT
ejpam-6411	208	71	the	the	DET
ejpam-6411	208	72	operator	operator	NOUN
ejpam-6411	209	1	q	q	PROPN
ejpam-6411	209	2	possesses	possess	VERB
ejpam-6411	209	3	a	a	DET
ejpam-6411	209	4	unique	unique	ADJ
ejpam-6411	209	5	fixed	fix	VERB
ejpam-6411	209	6	point	point	NOUN
ejpam-6411	209	7	according	accord	VERB
ejpam-6411	209	8	to	to	ADP
ejpam-6411	209	9	the	the	DET
ejpam-6411	209	10	banach	banach	NOUN
ejpam-6411	209	11	’s	’s	PART
ejpam-6411	209	12	fixed	fix	VERB
ejpam-6411	209	13	-	-	PUNCT
ejpam-6411	209	14	point	point	NOUN
ejpam-6411	209	15	theorem	theorem	NOUN
ejpam-6411	209	16	.	.	PUNCT
ejpam-6411	210	1	this	this	PRON
ejpam-6411	210	2	,	,	PUNCT
ejpam-6411	210	3	indeed	indeed	ADV
ejpam-6411	210	4	,	,	PUNCT
ejpam-6411	210	5	equates	equate	VERB
ejpam-6411	210	6	to	to	ADP
ejpam-6411	210	7	the	the	DET
ejpam-6411	210	8	unique	unique	ADJ
ejpam-6411	210	9	solution	solution	NOUN
ejpam-6411	210	10	of	of	ADP
ejpam-6411	210	11	eqs	eqs	PROPN
ejpam-6411	210	12	.	.	PUNCT
ejpam-6411	211	1	(	(	PUNCT
ejpam-6411	211	2	1	1	X
ejpam-6411	211	3	)	)	PUNCT
ejpam-6411	211	4	and	and	CCONJ
ejpam-6411	211	5	(	(	PUNCT
ejpam-6411	211	6	2	2	NUM
ejpam-6411	211	7	)	)	PUNCT
ejpam-6411	211	8	.	.	PUNCT
ejpam-6411	212	1	the	the	DET
ejpam-6411	212	2	proof	proof	NOUN
ejpam-6411	212	3	is	be	AUX
ejpam-6411	212	4	now	now	ADV
ejpam-6411	212	5	complete	complete	ADJ
ejpam-6411	212	6	.	.	PUNCT
ejpam-6411	213	1	■	■	PUNCT
ejpam-6411	213	2	the	the	DET
ejpam-6411	213	3	following	follow	VERB
ejpam-6411	213	4	outcome	outcome	NOUN
ejpam-6411	213	5	relies	rely	VERB
ejpam-6411	213	6	on	on	ADP
ejpam-6411	213	7	the	the	DET
ejpam-6411	213	8	leray	leray	ADJ
ejpam-6411	213	9	-	-	PUNCT
ejpam-6411	213	10	schauder	schauder	NOUN
ejpam-6411	213	11	alternative	alternative	NOUN
ejpam-6411	213	12	.	.	PUNCT
ejpam-6411	214	1	lemma	lemma	PROPN
ejpam-6411	214	2	3.2	3.2	NUM
ejpam-6411	214	3	:	:	PUNCT
ejpam-6411	214	4	(	(	PUNCT
ejpam-6411	214	5	leray	leray	ADJ
ejpam-6411	214	6	-	-	PUNCT
ejpam-6411	214	7	schauder	schauder	NOUN
ejpam-6411	214	8	alternative	alternative	NOUN
ejpam-6411	214	9	)	)	PUNCT
ejpam-6411	215	1	[	[	X
ejpam-6411	215	2	27	27	NUM
ejpam-6411	215	3	]	]	PUNCT
ejpam-6411	215	4	:	:	PUNCT
ejpam-6411	215	5	let	let	VERB
ejpam-6411	215	6	f	f	PRON
ejpam-6411	215	7	:	:	PUNCT
ejpam-6411	215	8	e	e	X
ejpam-6411	215	9	→	→	PUNCT
ejpam-6411	215	10	e	e	AUX
ejpam-6411	215	11	be	be	AUX
ejpam-6411	215	12	a	a	DET
ejpam-6411	215	13	completely	completely	ADV
ejpam-6411	215	14	continuous	continuous	ADJ
ejpam-6411	215	15	operator	operator	NOUN
ejpam-6411	215	16	and	and	CCONJ
ejpam-6411	215	17	assume	assume	VERB
ejpam-6411	215	18	e	e	X
ejpam-6411	215	19	(	(	PUNCT
ejpam-6411	215	20	f	f	PROPN
ejpam-6411	215	21	)	)	PUNCT
ejpam-6411	215	22	=	=	PRON
ejpam-6411	216	1	{	{	PUNCT
ejpam-6411	216	2	x	x	PUNCT
ejpam-6411	216	3	∈	∈	PROPN
ejpam-6411	216	4	e	e	NOUN
ejpam-6411	216	5	:	:	PUNCT
ejpam-6411	216	6	x	x	SYM
ejpam-6411	216	7	=	=	SYM
ejpam-6411	216	8	λf	λf	X
ejpam-6411	216	9	(	(	PUNCT
ejpam-6411	216	10	x	x	NOUN
ejpam-6411	216	11	)	)	PUNCT
ejpam-6411	216	12	for	for	ADP
ejpam-6411	216	13	some	some	PRON
ejpam-6411	216	14	0	0	NUM
ejpam-6411	216	15	<	<	X
ejpam-6411	216	16	λ	λ	X
ejpam-6411	216	17	<	<	X
ejpam-6411	216	18	1	1	NUM
ejpam-6411	216	19	}	}	PUNCT
ejpam-6411	216	20	.	.	PUNCT
ejpam-6411	217	1	then	then	ADV
ejpam-6411	217	2	,	,	PUNCT
ejpam-6411	217	3	either	either	CCONJ
ejpam-6411	217	4	the	the	DET
ejpam-6411	217	5	set	set	NOUN
ejpam-6411	217	6	e	e	X
ejpam-6411	217	7	(	(	PUNCT
ejpam-6411	217	8	f	f	PROPN
ejpam-6411	217	9	)	)	PUNCT
ejpam-6411	217	10	is	be	AUX
ejpam-6411	217	11	unbounded	unbounded	ADJ
ejpam-6411	217	12	or	or	CCONJ
ejpam-6411	217	13	f	f	PROPN
ejpam-6411	217	14	has	have	VERB
ejpam-6411	217	15	at	at	ADV
ejpam-6411	217	16	least	least	ADV
ejpam-6411	217	17	one	one	NUM
ejpam-6411	217	18	fixed	fix	VERB
ejpam-6411	217	19	point	point	NOUN
ejpam-6411	217	20	.	.	PUNCT
ejpam-6411	218	1	s.	s.	PROPN
ejpam-6411	218	2	momani	momani	PROPN
ejpam-6411	218	3	et	et	PROPN
ejpam-6411	218	4	al	al	PROPN
ejpam-6411	218	5	.	.	PUNCT
ejpam-6411	218	6	/	/	SYM
ejpam-6411	218	7	eur	eur	PROPN
ejpam-6411	218	8	.	.	PUNCT
ejpam-6411	219	1	j.	j.	PROPN
ejpam-6411	219	2	pure	pure	PROPN
ejpam-6411	219	3	appl	appl	PROPN
ejpam-6411	219	4	.	.	PROPN
ejpam-6411	219	5	math	math	PROPN
ejpam-6411	219	6	,	,	PUNCT
ejpam-6411	219	7	18	18	NUM
ejpam-6411	219	8	(	(	PUNCT
ejpam-6411	219	9	4	4	NUM
ejpam-6411	219	10	)	)	PUNCT
ejpam-6411	219	11	(	(	PUNCT
ejpam-6411	219	12	2025	2025	NUM
ejpam-6411	219	13	)	)	PUNCT
ejpam-6411	219	14	,	,	PUNCT
ejpam-6411	219	15	6411	6411	NUM
ejpam-6411	219	16	9	9	NUM
ejpam-6411	219	17	of	of	ADP
ejpam-6411	219	18	16	16	NUM
ejpam-6411	219	19	theorem	theorem	VERB
ejpam-6411	219	20	3.3	3.3	NUM
ejpam-6411	219	21	:	:	PUNCT
ejpam-6411	219	22	let	let	VERB
ejpam-6411	219	23	u	u	NOUN
ejpam-6411	219	24	,	,	PUNCT
ejpam-6411	219	25	h	h	NOUN
ejpam-6411	219	26	:	:	PUNCT
ejpam-6411	220	1	[	[	X
ejpam-6411	220	2	0,h]×r2	0,h]×r2	X
ejpam-6411	220	3	→	→	SYM
ejpam-6411	220	4	r	r	NOUN
ejpam-6411	220	5	be	be	AUX
ejpam-6411	220	6	a	a	DET
ejpam-6411	220	7	continuous	continuous	ADJ
ejpam-6411	220	8	function	function	NOUN
ejpam-6411	220	9	.	.	PUNCT
ejpam-6411	221	1	assume	assume	VERB
ejpam-6411	221	2	the	the	DET
ejpam-6411	221	3	following	follow	VERB
ejpam-6411	221	4	hold	hold	VERB
ejpam-6411	221	5	true	true	ADJ
ejpam-6411	221	6	(	(	PUNCT
ejpam-6411	221	7	i	i	NOUN
ejpam-6411	221	8	)	)	PUNCT
ejpam-6411	221	9	there	there	PRON
ejpam-6411	221	10	exist	exist	VERB
ejpam-6411	221	11	1	1	NUM
ejpam-6411	221	12	,	,	PUNCT
ejpam-6411	221	13	2,ϕ1	2,ϕ1	NUM
ejpam-6411	221	14	,	,	PUNCT
ejpam-6411	221	15	ϕ2≥0	ϕ2≥0	PROPN
ejpam-6411	221	16	where	where	SCONJ
ejpam-6411	221	17	1	1	NUM
ejpam-6411	221	18	,	,	PUNCT
ejpam-6411	221	19	2,ϕ1	2,ϕ1	NUM
ejpam-6411	221	20	,	,	PUNCT
ejpam-6411	221	21	ϕ2	ϕ2	ADV
ejpam-6411	221	22	are	be	AUX
ejpam-6411	221	23	real	real	ADJ
ejpam-6411	221	24	constants	constant	NOUN
ejpam-6411	221	25	and	and	CCONJ
ejpam-6411	221	26	0	0	NUM
ejpam-6411	221	27	,	,	PUNCT
ejpam-6411	221	28	ϕ0	ϕ0	NOUN
ejpam-6411	221	29	>	>	X
ejpam-6411	221	30	0	0	NUM
ejpam-6411	222	1	such	such	ADJ
ejpam-6411	222	2	that	that	SCONJ
ejpam-6411	222	3	∀i	∀i	NOUN
ejpam-6411	222	4	,	,	PUNCT
ejpam-6411	222	5	i∈r	i∈r	NOUN
ejpam-6411	222	6	,	,	PUNCT
ejpam-6411	222	7	(	(	PUNCT
ejpam-6411	222	8	i	i	NOUN
ejpam-6411	222	9	=	=	NOUN
ejpam-6411	222	10	1	1	NUM
ejpam-6411	222	11	,	,	PUNCT
ejpam-6411	222	12	2	2	NUM
ejpam-6411	222	13	)	)	PUNCT
ejpam-6411	222	14	,	,	PUNCT
ejpam-6411	222	15	|u	|u	ADJ
ejpam-6411	222	16	(	(	PUNCT
ejpam-6411	222	17	τ	τ	PROPN
ejpam-6411	222	18	,	,	PUNCT
ejpam-6411	222	19	υ1	υ1	PROPN
ejpam-6411	222	20	,	,	PUNCT
ejpam-6411	222	21	υ2)|	υ2)|	PROPN
ejpam-6411	222	22	≤	≤	PUNCT
ejpam-6411	222	23	ψ0	ψ0	ADV
ejpam-6411	222	24	+	+	CCONJ
ejpam-6411	222	25	ψ1	ψ1	ADJ
ejpam-6411	222	26	|υ1|+	|υ1|+	NOUN
ejpam-6411	222	27	ψ2	ψ2	NOUN
ejpam-6411	222	28	|υ2|	|υ2|	NOUN
ejpam-6411	222	29	,	,	PUNCT
ejpam-6411	222	30	and	and	CCONJ
ejpam-6411	222	31	|h	|h	X
ejpam-6411	222	32	(	(	PUNCT
ejpam-6411	222	33	τ	τ	PROPN
ejpam-6411	222	34	,	,	PUNCT
ejpam-6411	222	35	υ1	υ1	PROPN
ejpam-6411	222	36	,	,	PUNCT
ejpam-6411	222	37	υ2)|	υ2)|	PROPN
ejpam-6411	222	38	≤	≤	PROPN
ejpam-6411	222	39	ϕ0	ϕ0	NOUN
ejpam-6411	222	40	+	+	CCONJ
ejpam-6411	222	41	ϕ1	ϕ1	NOUN
ejpam-6411	222	42	|υ1|+	|υ1|+	NOUN
ejpam-6411	222	43	ϕ2	ϕ2	ADV
ejpam-6411	222	44	|υ2|	|υ2|	VERB
ejpam-6411	222	45	.	.	PUNCT
ejpam-6411	223	1	(	(	PUNCT
ejpam-6411	223	2	i	i	NOUN
ejpam-6411	223	3	)	)	PUNCT
ejpam-6411	223	4	(	(	PUNCT
ejpam-6411	223	5	n1	n1	PROPN
ejpam-6411	223	6	+	+	PROPN
ejpam-6411	223	7	n3)ψ1	n3)ψ1	PROPN
ejpam-6411	223	8	+	+	X
ejpam-6411	223	9	(	(	PUNCT
ejpam-6411	223	10	n2	n2	ADJ
ejpam-6411	224	1	+	+	ADP
ejpam-6411	224	2	n4)ϕ1	n4)ϕ1	ADJ
ejpam-6411	224	3	<	<	X
ejpam-6411	224	4	1	1	NUM
ejpam-6411	224	5	,	,	PUNCT
ejpam-6411	224	6	and	and	CCONJ
ejpam-6411	224	7	(	(	PUNCT
ejpam-6411	224	8	n1	n1	X
ejpam-6411	224	9	+	+	NOUN
ejpam-6411	224	10	n3)ψ2	n3)ψ2	ADV
ejpam-6411	224	11	+	+	CCONJ
ejpam-6411	224	12	(	(	PUNCT
ejpam-6411	224	13	n2	n2	ADJ
ejpam-6411	224	14	+	+	NOUN
ejpam-6411	224	15	n4)ϕ2	n4)ϕ2	ADV
ejpam-6411	224	16	<	<	X
ejpam-6411	224	17	1	1	NUM
ejpam-6411	224	18	,	,	PUNCT
ejpam-6411	224	19	where	where	SCONJ
ejpam-6411	224	20	ni	ni	PROPN
ejpam-6411	224	21	,	,	PUNCT
ejpam-6411	224	22	i=	i=	PROPN
ejpam-6411	224	23	1	1	NUM
ejpam-6411	224	24	,	,	PUNCT
ejpam-6411	224	25	2	2	NUM
ejpam-6411	224	26	,	,	PUNCT
ejpam-6411	224	27	3	3	NUM
ejpam-6411	224	28	,	,	PUNCT
ejpam-6411	224	29	4	4	NUM
ejpam-6411	224	30	are	be	AUX
ejpam-6411	224	31	defined	define	VERB
ejpam-6411	224	32	in	in	ADP
ejpam-6411	224	33	theorem	theorem	NOUN
ejpam-6411	224	34	3.1	3.1	NUM
ejpam-6411	224	35	.	.	PUNCT
ejpam-6411	225	1	then	then	ADV
ejpam-6411	225	2	,	,	PUNCT
ejpam-6411	225	3	there	there	PRON
ejpam-6411	225	4	exists	exist	VERB
ejpam-6411	225	5	at	at	ADP
ejpam-6411	225	6	least	least	ADV
ejpam-6411	225	7	one	one	NUM
ejpam-6411	225	8	solution	solution	NOUN
ejpam-6411	225	9	for	for	ADP
ejpam-6411	225	10	the	the	DET
ejpam-6411	225	11	coupled	couple	VERB
ejpam-6411	225	12	fractional	fractional	ADJ
ejpam-6411	225	13	system	system	NOUN
ejpam-6411	225	14	in	in	ADP
ejpam-6411	225	15	e.	e.	PROPN
ejpam-6411	225	16	(	(	PUNCT
ejpam-6411	225	17	1	1	NUM
ejpam-6411	225	18	)	)	PUNCT
ejpam-6411	225	19	and	and	CCONJ
ejpam-6411	225	20	e.	e.	PROPN
ejpam-6411	225	21	(	(	PUNCT
ejpam-6411	225	22	2	2	NUM
ejpam-6411	225	23	)	)	PUNCT
ejpam-6411	225	24	.	.	PUNCT
ejpam-6411	226	1	proof	proof	NOUN
ejpam-6411	226	2	:	:	PUNCT
ejpam-6411	226	3	the	the	DET
ejpam-6411	226	4	proof	proof	NOUN
ejpam-6411	226	5	of	of	ADP
ejpam-6411	226	6	this	this	DET
ejpam-6411	226	7	theorem	theorem	NOUN
ejpam-6411	226	8	is	be	AUX
ejpam-6411	226	9	divided	divide	VERB
ejpam-6411	226	10	into	into	ADP
ejpam-6411	226	11	two	two	NUM
ejpam-6411	226	12	parts	part	NOUN
ejpam-6411	226	13	:	:	PUNCT
ejpam-6411	226	14	first	first	ADJ
ejpam-6411	226	15	step	step	NOUN
ejpam-6411	226	16	:	:	PUNCT
ejpam-6411	226	17	show	show	VERB
ejpam-6411	226	18	that	that	SCONJ
ejpam-6411	226	19	q	q	X
ejpam-6411	226	20	:	:	PUNCT
ejpam-6411	226	21	g×z→g×z	g×z→g×z	PROPN
ejpam-6411	226	22	is	be	AUX
ejpam-6411	226	23	completely	completely	ADV
ejpam-6411	226	24	continuous	continuous	ADJ
ejpam-6411	226	25	,	,	PUNCT
ejpam-6411	226	26	where	where	SCONJ
ejpam-6411	226	27	the	the	DET
ejpam-6411	226	28	continuity	continuity	NOUN
ejpam-6411	226	29	of	of	ADP
ejpam-6411	226	30	the	the	DET
ejpam-6411	226	31	operator	operator	NOUN
ejpam-6411	226	32	q	q	NOUN
ejpam-6411	226	33	holds	hold	VERB
ejpam-6411	226	34	by	by	ADP
ejpam-6411	226	35	the	the	DET
ejpam-6411	226	36	continuity	continuity	NOUN
ejpam-6411	226	37	of	of	ADP
ejpam-6411	226	38	the	the	DET
ejpam-6411	226	39	functions	function	NOUN
ejpam-6411	226	40	u	u	NOUN
ejpam-6411	226	41	,	,	PUNCT
ejpam-6411	226	42	h.	h.	PROPN
ejpam-6411	226	43	let	let	VERB
ejpam-6411	226	44	r⊆g×z	r⊆g×z	NOUN
ejpam-6411	226	45	be	be	AUX
ejpam-6411	226	46	bounded	bound	VERB
ejpam-6411	226	47	.	.	PUNCT
ejpam-6411	227	1	then	then	ADV
ejpam-6411	227	2	,	,	PUNCT
ejpam-6411	227	3	there	there	PRON
ejpam-6411	227	4	exist	exist	VERB
ejpam-6411	227	5	positive	positive	ADJ
ejpam-6411	227	6	constants	constant	NOUN
ejpam-6411	227	7	λ1	λ1	ADJ
ejpam-6411	227	8	,	,	PUNCT
ejpam-6411	227	9	λ2	λ2	NOUN
ejpam-6411	227	10	such	such	ADJ
ejpam-6411	227	11	that	that	SCONJ
ejpam-6411	227	12	|u	|u	ADJ
ejpam-6411	227	13	(	(	PUNCT
ejpam-6411	227	14	τ	τ	PROPN
ejpam-6411	227	15	,	,	PUNCT
ejpam-6411	227	16	υ	υ	PROPN
ejpam-6411	227	17	(	(	PUNCT
ejpam-6411	227	18	τ	τ	PROPN
ejpam-6411	227	19	)	)	PUNCT
ejpam-6411	227	20	,	,	PUNCT
ejpam-6411	227	21	ω	ω	PROPN
ejpam-6411	227	22	(	(	PUNCT
ejpam-6411	227	23	τ))|	τ))|	PROPN
ejpam-6411	227	24	≤	≤	PROPN
ejpam-6411	227	25	λ1	λ1	PROPN
ejpam-6411	227	26	,	,	PUNCT
ejpam-6411	227	27	|h	|h	X
ejpam-6411	227	28	(	(	PUNCT
ejpam-6411	227	29	τ	τ	PROPN
ejpam-6411	227	30	,	,	PUNCT
ejpam-6411	227	31	υ	υ	PROPN
ejpam-6411	227	32	(	(	PUNCT
ejpam-6411	227	33	τ	τ	PROPN
ejpam-6411	227	34	)	)	PUNCT
ejpam-6411	227	35	,	,	PUNCT
ejpam-6411	227	36	ω	ω	PROPN
ejpam-6411	227	37	(	(	PUNCT
ejpam-6411	227	38	τ))|	τ))|	PROPN
ejpam-6411	227	39	≤	≤	PROPN
ejpam-6411	227	40	λ2	λ2	PROPN
ejpam-6411	227	41	,	,	PUNCT
ejpam-6411	227	42	∀τ	∀τ	SYM
ejpam-6411	227	43	∈	∈	PROPN
ejpam-6411	228	1	[	[	X
ejpam-6411	228	2	0,h	0,h	X
ejpam-6411	228	3	]	]	X
ejpam-6411	228	4	.	.	PUNCT
ejpam-6411	229	1	therefore	therefore	ADV
ejpam-6411	229	2	,	,	PUNCT
ejpam-6411	229	3	∀	∀	X
ejpam-6411	229	4	(	(	PUNCT
ejpam-6411	229	5	υ	υ	NOUN
ejpam-6411	229	6	,	,	PUNCT
ejpam-6411	229	7	ω)∈r	ω)∈r	NUM
ejpam-6411	229	8	,	,	PUNCT
ejpam-6411	229	9	we	we	PRON
ejpam-6411	229	10	have	have	VERB
ejpam-6411	229	11	|q1	|q1	NOUN
ejpam-6411	229	12	(	(	PUNCT
ejpam-6411	229	13	υ	υ	NOUN
ejpam-6411	229	14	,	,	PUNCT
ejpam-6411	229	15	ω	ω	NOUN
ejpam-6411	229	16	)	)	PUNCT
ejpam-6411	229	17	(	(	PUNCT
ejpam-6411	229	18	τ)|	τ)|	NOUN
ejpam-6411	229	19	≤	≤	PUNCT
ejpam-6411	230	1	n1λ1	n1λ1	NUM
ejpam-6411	230	2	+	+	SYM
ejpam-6411	230	3	n2λ2	n2λ2	NOUN
ejpam-6411	230	4	.	.	PUNCT
ejpam-6411	231	1	this	this	PRON
ejpam-6411	231	2	implies	imply	VERB
ejpam-6411	231	3	that	that	SCONJ
ejpam-6411	231	4	∥q1	∥q1	VERB
ejpam-6411	231	5	(	(	PUNCT
ejpam-6411	231	6	υ	υ	NOUN
ejpam-6411	231	7	,	,	PUNCT
ejpam-6411	231	8	ω)∥	ω)∥	PUNCT
ejpam-6411	231	9	≤	≤	NUM
ejpam-6411	231	10	n1λ1	n1λ1	NUM
ejpam-6411	231	11	+	+	ADJ
ejpam-6411	231	12	n2λ2	n2λ2	NOUN
ejpam-6411	231	13	.	.	PUNCT
ejpam-6411	231	14	similarly	similarly	ADV
ejpam-6411	231	15	,	,	PUNCT
ejpam-6411	231	16	we	we	PRON
ejpam-6411	231	17	get	get	VERB
ejpam-6411	231	18	∥q2	∥q2	NOUN
ejpam-6411	231	19	(	(	PUNCT
ejpam-6411	231	20	υ	υ	NOUN
ejpam-6411	231	21	,	,	PUNCT
ejpam-6411	231	22	ω)∥	ω)∥	PUNCT
ejpam-6411	231	23	≤	≤	NUM
ejpam-6411	231	24	n3λ1	n3λ1	PUNCT
ejpam-6411	232	1	+	+	NOUN
ejpam-6411	232	2	n4λ2	n4λ2	NOUN
ejpam-6411	232	3	.	.	PUNCT
ejpam-6411	232	4	therefore	therefore	ADV
ejpam-6411	232	5	,	,	PUNCT
ejpam-6411	232	6	based	base	VERB
ejpam-6411	232	7	on	on	ADP
ejpam-6411	232	8	the	the	DET
ejpam-6411	232	9	inequalities	inequality	NOUN
ejpam-6411	232	10	stated	state	VERB
ejpam-6411	232	11	earlier	early	ADV
ejpam-6411	232	12	,	,	PUNCT
ejpam-6411	232	13	it	it	PRON
ejpam-6411	232	14	can	can	AUX
ejpam-6411	232	15	be	be	AUX
ejpam-6411	232	16	concluded	conclude	VERB
ejpam-6411	232	17	that	that	SCONJ
ejpam-6411	232	18	the	the	DET
ejpam-6411	232	19	operator	operator	NOUN
ejpam-6411	232	20	q	q	PUNCT
ejpam-6411	232	21	is	be	AUX
ejpam-6411	232	22	uniformly	uniformly	ADV
ejpam-6411	232	23	bounded	bound	VERB
ejpam-6411	232	24	because∥q	because∥q	PROPN
ejpam-6411	232	25	(	(	PUNCT
ejpam-6411	232	26	υ	υ	NOUN
ejpam-6411	232	27	,	,	PUNCT
ejpam-6411	232	28	ω)∥	ω)∥	NUM
ejpam-6411	232	29	≤	≤	NUM
ejpam-6411	232	30	(	(	PUNCT
ejpam-6411	232	31	n1	n1	NOUN
ejpam-6411	232	32	+	+	ADJ
ejpam-6411	232	33	n3)λ1	n3)λ1	ADJ
ejpam-6411	232	34	+	+	X
ejpam-6411	232	35	(	(	PUNCT
ejpam-6411	232	36	n2	n2	ADJ
ejpam-6411	232	37	+	+	X
ejpam-6411	232	38	n4)λ2	n4)λ2	ADJ
ejpam-6411	232	39	.	.	PUNCT
ejpam-6411	233	1	furthermore	furthermore	ADV
ejpam-6411	233	2	,	,	PUNCT
ejpam-6411	233	3	we	we	PRON
ejpam-6411	233	4	prove	prove	VERB
ejpam-6411	233	5	that	that	SCONJ
ejpam-6411	233	6	the	the	DET
ejpam-6411	233	7	operator	operator	NOUN
ejpam-6411	233	8	q	q	NOUN
ejpam-6411	233	9	is	be	AUX
ejpam-6411	233	10	equicontinuous	equicontinuous	ADJ
ejpam-6411	233	11	.	.	PUNCT
ejpam-6411	234	1	for	for	ADP
ejpam-6411	234	2	,	,	PUNCT
ejpam-6411	234	3	assume	assume	VERB
ejpam-6411	234	4	k1	k1	NOUN
ejpam-6411	234	5	,	,	PUNCT
ejpam-6411	234	6	k2∈	k2∈	PROPN
ejpam-6411	235	1	[	[	X
ejpam-6411	235	2	0,h	0,h	X
ejpam-6411	235	3	]	]	X
ejpam-6411	235	4	with	with	ADP
ejpam-6411	235	5	k1	k1	NOUN
ejpam-6411	235	6	<	<	X
ejpam-6411	235	7	k2	k2	PROPN
ejpam-6411	235	8	.	.	PUNCT
ejpam-6411	236	1	this	this	DET
ejpam-6411	236	2	yields	yield	NOUN
ejpam-6411	236	3	|q1(υ	|q1(υ	PROPN
ejpam-6411	236	4	,	,	PUNCT
ejpam-6411	236	5	ω)(k2)−q1(υ	ω)(k2)−q1(υ	PROPN
ejpam-6411	236	6	,	,	PUNCT
ejpam-6411	236	7	ω)(k1)|	ω)(k1)|	PROPN
ejpam-6411	236	8	≤	≤	ADJ
ejpam-6411	236	9	k2	k2	PROPN
ejpam-6411	236	10	−	−	PROPN
ejpam-6411	236	11	k1	k1	PROPN
ejpam-6411	236	12	|λ|	|λ|	PROPN
ejpam-6411	236	13	[	[	PUNCT
ejpam-6411	236	14	|ζ|h	|ζ|h	PROPN
ejpam-6411	236	15	∫	∫	PROPN
ejpam-6411	236	16	µ	µ	X
ejpam-6411	236	17	0	0	NUM
ejpam-6411	236	18	(	(	PUNCT
ejpam-6411	236	19	µ−	µ−	PROPN
ejpam-6411	236	20	s)β−2	s)β−2	VERB
ejpam-6411	236	21	γ(β	γ(β	PROPN
ejpam-6411	236	22	−	−	PROPN
ejpam-6411	236	23	1	1	X
ejpam-6411	236	24	)	)	PUNCT
ejpam-6411	236	25	∣∣h(s	∣∣h(s	PROPN
ejpam-6411	236	26	,	,	PUNCT
ejpam-6411	236	27	υ(s	υ(s	PROPN
ejpam-6411	236	28	)	)	PUNCT
ejpam-6411	236	29	,	,	PUNCT
ejpam-6411	236	30	ω(s))∣∣	ω(s))∣∣	PROPN
ejpam-6411	237	1	ds	ds	PRON
ejpam-6411	237	2	+	+	NOUN
ejpam-6411	237	3	h	h	NOUN
ejpam-6411	237	4	∫	∫	PROPN
ejpam-6411	237	5	h	h	PROPN
ejpam-6411	237	6	0	0	NUM
ejpam-6411	237	7	∫	∫	PROPN
ejpam-6411	237	8	s	s	PART
ejpam-6411	237	9	0	0	NUM
ejpam-6411	237	10	(	(	PUNCT
ejpam-6411	237	11	s−	s−	PROPN
ejpam-6411	237	12	t)α−2	t)α−2	NOUN
ejpam-6411	237	13	γ(α−	γ(α−	NOUN
ejpam-6411	237	14	1	1	NUM
ejpam-6411	237	15	)	)	PUNCT
ejpam-6411	237	16	∣∣u(t	∣∣u(t	PROPN
ejpam-6411	237	17	,	,	PUNCT
ejpam-6411	237	18	υ(t	υ(t	PROPN
ejpam-6411	237	19	)	)	PUNCT
ejpam-6411	237	20	,	,	PUNCT
ejpam-6411	237	21	ω(t))∣∣	ω(t))∣∣	PROPN
ejpam-6411	237	22	dt	dt	X
ejpam-6411	237	23	ds	ds	PROPN
ejpam-6411	237	24	+	+	CCONJ
ejpam-6411	237	25	|ζη|	|ζη|	NUM
ejpam-6411	237	26	∫	∫	PROPN
ejpam-6411	237	27	ρ	ρ	PROPN
ejpam-6411	237	28	0	0	PUNCT
ejpam-6411	238	1	(	(	PUNCT
ejpam-6411	238	2	ρ−	ρ−	NOUN
ejpam-6411	238	3	s)α−2	s)α−2	VERB
ejpam-6411	238	4	γ(α−	γ(α−	VERB
ejpam-6411	238	5	1	1	NUM
ejpam-6411	238	6	)	)	PUNCT
ejpam-6411	238	7	∣∣u(s	∣∣u(s	PROPN
ejpam-6411	238	8	,	,	PUNCT
ejpam-6411	238	9	υ(s	υ(s	PROPN
ejpam-6411	238	10	)	)	PUNCT
ejpam-6411	238	11	,	,	PUNCT
ejpam-6411	238	12	ω(s))∣∣	ω(s))∣∣	PROPN
ejpam-6411	238	13	ds	ds	X
ejpam-6411	238	14	+	+	CCONJ
ejpam-6411	238	15	|ζ|	|ζ|	PROPN
ejpam-6411	238	16	∫	∫	PROPN
ejpam-6411	238	17	h	h	NOUN
ejpam-6411	238	18	0	0	NUM
ejpam-6411	239	1	∫	∫	PROPN
ejpam-6411	239	2	s	s	PART
ejpam-6411	239	3	0	0	NUM
ejpam-6411	239	4	(	(	PUNCT
ejpam-6411	239	5	s−	s−	PROPN
ejpam-6411	239	6	t)β−2	t)β−2	VERB
ejpam-6411	239	7	γ(β	γ(β	PROPN
ejpam-6411	239	8	−	−	PROPN
ejpam-6411	239	9	1	1	X
ejpam-6411	239	10	)	)	PUNCT
ejpam-6411	239	11	∣∣h(t	∣∣h(t	PROPN
ejpam-6411	239	12	,	,	PUNCT
ejpam-6411	239	13	υ(t	υ(t	PROPN
ejpam-6411	239	14	)	)	PUNCT
ejpam-6411	239	15	,	,	PUNCT
ejpam-6411	239	16	ω(t))∣∣	ω(t))∣∣	PROPN
ejpam-6411	239	17	dt	dt	X
ejpam-6411	239	18	ds	ds	PROPN
ejpam-6411	239	19	]	]	PUNCT
ejpam-6411	239	20	.	.	PUNCT
ejpam-6411	240	1	(	(	PUNCT
ejpam-6411	240	2	16	16	NUM
ejpam-6411	240	3	)	)	PUNCT
ejpam-6411	240	4	s.	s.	PROPN
ejpam-6411	240	5	momani	momani	PROPN
ejpam-6411	240	6	et	et	PROPN
ejpam-6411	240	7	al	al	PROPN
ejpam-6411	240	8	.	.	PUNCT
ejpam-6411	240	9	/	/	SYM
ejpam-6411	240	10	eur	eur	PROPN
ejpam-6411	240	11	.	.	PUNCT
ejpam-6411	241	1	j.	j.	PROPN
ejpam-6411	241	2	pure	pure	PROPN
ejpam-6411	241	3	appl	appl	PROPN
ejpam-6411	241	4	.	.	PROPN
ejpam-6411	241	5	math	math	PROPN
ejpam-6411	241	6	,	,	PUNCT
ejpam-6411	241	7	18	18	NUM
ejpam-6411	241	8	(	(	PUNCT
ejpam-6411	241	9	4	4	NUM
ejpam-6411	241	10	)	)	PUNCT
ejpam-6411	241	11	(	(	PUNCT
ejpam-6411	241	12	2025	2025	NUM
ejpam-6411	241	13	)	)	PUNCT
ejpam-6411	241	14	,	,	PUNCT
ejpam-6411	241	15	6411	6411	NUM
ejpam-6411	241	16	10	10	NUM
ejpam-6411	241	17	of	of	ADP
ejpam-6411	241	18	16	16	NUM
ejpam-6411	241	19	|q1(υ	|q1(υ	PROPN
ejpam-6411	241	20	,	,	PUNCT
ejpam-6411	241	21	ω)(k2)−q1(υ	ω)(k2)−q1(υ	PROPN
ejpam-6411	241	22	,	,	PUNCT
ejpam-6411	241	23	ω)(k1)|	ω)(k1)|	PROPN
ejpam-6411	241	24	≤	≤	ADJ
ejpam-6411	241	25	k2	k2	PROPN
ejpam-6411	241	26	−	−	PROPN
ejpam-6411	241	27	k1	k1	PROPN
ejpam-6411	241	28	|λ|	|λ|	PROPN
ejpam-6411	241	29	(	(	PUNCT
ejpam-6411	241	30	|ζ|hλ2	|ζ|hλ2	PROPN
ejpam-6411	241	31	∫	∫	PROPN
ejpam-6411	241	32	µ	µ	PROPN
ejpam-6411	241	33	0	0	NUM
ejpam-6411	241	34	(	(	PUNCT
ejpam-6411	241	35	µ−	µ−	PROPN
ejpam-6411	241	36	s)β−2	s)β−2	VERB
ejpam-6411	241	37	γ(β	γ(β	PROPN
ejpam-6411	241	38	−	−	PROPN
ejpam-6411	241	39	1	1	X
ejpam-6411	241	40	)	)	PUNCT
ejpam-6411	241	41	ds+hλ1	ds+hλ1	PROPN
ejpam-6411	242	1	∫	∫	PROPN
ejpam-6411	242	2	h	h	PROPN
ejpam-6411	242	3	0	0	NUM
ejpam-6411	242	4	∫	∫	PROPN
ejpam-6411	242	5	s	s	PART
ejpam-6411	242	6	0	0	NUM
ejpam-6411	242	7	(	(	PUNCT
ejpam-6411	242	8	s−	s−	PROPN
ejpam-6411	242	9	t)α−2	t)α−2	NOUN
ejpam-6411	242	10	γ(α−	γ(α−	NOUN
ejpam-6411	242	11	1	1	NUM
ejpam-6411	242	12	)	)	PUNCT
ejpam-6411	242	13	dt	dt	NOUN
ejpam-6411	243	1	ds	ds	NOUN
ejpam-6411	243	2	+	+	ADJ
ejpam-6411	243	3	|ζη|λ1	|ζη|λ1	PROPN
ejpam-6411	243	4	∫	∫	PROPN
ejpam-6411	243	5	ρ	ρ	PROPN
ejpam-6411	243	6	0	0	PUNCT
ejpam-6411	244	1	(	(	PUNCT
ejpam-6411	244	2	ρ−	ρ−	NOUN
ejpam-6411	244	3	s)α−2	s)α−2	VERB
ejpam-6411	244	4	γ(α−	γ(α−	VERB
ejpam-6411	244	5	1	1	NUM
ejpam-6411	244	6	)	)	PUNCT
ejpam-6411	244	7	ds+	ds+	ADJ
ejpam-6411	244	8	|ζ|λ2	|ζ|λ2	NOUN
ejpam-6411	244	9	∫	∫	PROPN
ejpam-6411	245	1	h	h	PROPN
ejpam-6411	245	2	0	0	NUM
ejpam-6411	245	3	∫	∫	PROPN
ejpam-6411	245	4	s	s	PART
ejpam-6411	245	5	0	0	NUM
ejpam-6411	245	6	(	(	PUNCT
ejpam-6411	245	7	s−	s−	PROPN
ejpam-6411	245	8	t)β−2	t)β−2	VERB
ejpam-6411	245	9	γ(β	γ(β	PROPN
ejpam-6411	245	10	−	−	PROPN
ejpam-6411	245	11	1	1	NUM
ejpam-6411	245	12	)	)	PUNCT
ejpam-6411	246	1	dt	dt	NOUN
ejpam-6411	246	2	ds	ds	X
ejpam-6411	246	3	)	)	PUNCT
ejpam-6411	247	1	+	+	CCONJ
ejpam-6411	247	2	λ1	λ1	ADJ
ejpam-6411	247	3	(	(	PUNCT
ejpam-6411	247	4	∫	∫	PROPN
ejpam-6411	247	5	τ2	τ2	PROPN
ejpam-6411	247	6	0	0	NUM
ejpam-6411	247	7	|τ2	|τ2	PROPN
ejpam-6411	247	8	−	−	PROPN
ejpam-6411	247	9	s|α−1	s|α−1	PROPN
ejpam-6411	247	10	γ(α	γ(α	PROPN
ejpam-6411	247	11	)	)	PUNCT
ejpam-6411	247	12	ds+	ds+	PROPN
ejpam-6411	248	1	∫	∫	PROPN
ejpam-6411	248	2	τ1	τ1	PROPN
ejpam-6411	248	3	0	0	NUM
ejpam-6411	248	4	|τ1	|τ1	ADJ
ejpam-6411	248	5	−	−	PROPN
ejpam-6411	248	6	s|α−1	s|α−1	ADP
ejpam-6411	248	7	γ(α	γ(α	NOUN
ejpam-6411	248	8	)	)	PUNCT
ejpam-6411	248	9	ds	ds	PROPN
ejpam-6411	248	10	)	)	PUNCT
ejpam-6411	248	11	≤	≤	NOUN
ejpam-6411	248	12	k2	k2	PROPN
ejpam-6411	248	13	−	−	PROPN
ejpam-6411	248	14	k1	k1	PROPN
ejpam-6411	248	15	|∆|	|∆|	PROPN
ejpam-6411	248	16	(	(	PUNCT
ejpam-6411	248	17	λ2|ζ|hµβ−1	λ2|ζ|hµβ−1	PUNCT
ejpam-6411	248	18	γ(β	γ(β	PROPN
ejpam-6411	248	19	)	)	PUNCT
ejpam-6411	249	1	+	+	CCONJ
ejpam-6411	250	1	λ1h	λ1h	X
ejpam-6411	251	1	α+1	α+1	NUM
ejpam-6411	251	2	γ(α+	γ(α+	DET
ejpam-6411	251	3	1	1	NUM
ejpam-6411	251	4	)	)	PUNCT
ejpam-6411	251	5	+	+	CCONJ
ejpam-6411	251	6	λ1|ζη|ρα−1	λ1|ζη|ρα−1	PROPN
ejpam-6411	251	7	γ(α	γ(α	NOUN
ejpam-6411	251	8	)	)	PUNCT
ejpam-6411	252	1	+	+	CCONJ
ejpam-6411	252	2	λ2|ζ|hβ	λ2|ζ|hβ	PROPN
ejpam-6411	252	3	γ(β	γ(β	PROPN
ejpam-6411	253	1	+	+	CCONJ
ejpam-6411	253	2	1	1	NUM
ejpam-6411	253	3	)	)	PUNCT
ejpam-6411	253	4	)	)	PUNCT
ejpam-6411	254	1	+	+	CCONJ
ejpam-6411	254	2	λ1	λ1	PROPN
ejpam-6411	254	3	γ(α	γ(α	NOUN
ejpam-6411	254	4	)	)	PUNCT
ejpam-6411	254	5	(	(	PUNCT
ejpam-6411	254	6	∫	∫	PROPN
ejpam-6411	254	7	k1	k1	PROPN
ejpam-6411	254	8	0	0	NUM
ejpam-6411	254	9	∣∣(k2	∣∣(k2	PROPN
ejpam-6411	254	10	−	−	PROPN
ejpam-6411	254	11	s)α−1	s)α−1	NOUN
ejpam-6411	254	12	−	−	PROPN
ejpam-6411	254	13	(	(	PUNCT
ejpam-6411	254	14	k1	k1	NOUN
ejpam-6411	254	15	−	−	PROPN
ejpam-6411	254	16	s)α−1	s)α−1	NOUN
ejpam-6411	254	17	∣∣	∣∣	PUNCT
ejpam-6411	254	18	ds+	ds+	PROPN
ejpam-6411	254	19	∫	∫	PROPN
ejpam-6411	254	20	k2	k2	PROPN
ejpam-6411	254	21	k1	k1	PROPN
ejpam-6411	254	22	|k2	|k2	PROPN
ejpam-6411	254	23	−	−	PROPN
ejpam-6411	254	24	s|α−1ds	s|α−1ds	PROPN
ejpam-6411	254	25	)	)	PUNCT
ejpam-6411	254	26	.	.	PUNCT
ejpam-6411	255	1	(	(	PUNCT
ejpam-6411	255	2	17	17	NUM
ejpam-6411	255	3	)	)	PUNCT
ejpam-6411	255	4	now	now	ADV
ejpam-6411	255	5	,	,	PUNCT
ejpam-6411	255	6	we	we	PRON
ejpam-6411	255	7	can	can	AUX
ejpam-6411	255	8	obtain	obtain	VERB
ejpam-6411	255	9	|q1(υ	|q1(υ	PROPN
ejpam-6411	255	10	,	,	PUNCT
ejpam-6411	255	11	ω)(k2)−q1(υ	ω)(k2)−q1(υ	PROPN
ejpam-6411	255	12	,	,	PUNCT
ejpam-6411	255	13	ω)(k1)|	ω)(k1)|	PROPN
ejpam-6411	255	14	≤	≤	ADJ
ejpam-6411	255	15	k2	k2	PROPN
ejpam-6411	255	16	−	−	PROPN
ejpam-6411	255	17	k1	k1	PROPN
ejpam-6411	255	18	|λ|	|λ|	PROPN
ejpam-6411	255	19	(	(	PUNCT
ejpam-6411	255	20	λ2|ζ|h	λ2|ζ|h	X
ejpam-6411	255	21	µβ−1	µβ−1	NOUN
ejpam-6411	255	22	γ(β	γ(β	PROPN
ejpam-6411	255	23	)	)	PUNCT
ejpam-6411	256	1	+	+	CCONJ
ejpam-6411	257	1	λ1h	λ1h	X
ejpam-6411	258	1	α+1	α+1	NUM
ejpam-6411	258	2	γ(α+	γ(α+	DET
ejpam-6411	258	3	1	1	NUM
ejpam-6411	258	4	)	)	PUNCT
ejpam-6411	258	5	+	+	CCONJ
ejpam-6411	258	6	λ1|ζη|ρα−1	λ1|ζη|ρα−1	PROPN
ejpam-6411	258	7	γ(α	γ(α	NOUN
ejpam-6411	258	8	)	)	PUNCT
ejpam-6411	259	1	+	+	CCONJ
ejpam-6411	259	2	λ2|ζ|hβ	λ2|ζ|hβ	PROPN
ejpam-6411	259	3	γ(β	γ(β	PROPN
ejpam-6411	260	1	+	+	CCONJ
ejpam-6411	260	2	1	1	NUM
ejpam-6411	260	3	)	)	PUNCT
ejpam-6411	260	4	)	)	PUNCT
ejpam-6411	261	1	+	+	CCONJ
ejpam-6411	262	1	λ1	λ1	ADJ
ejpam-6411	262	2	γ(α+	γ(α+	DET
ejpam-6411	262	3	1	1	NUM
ejpam-6411	262	4	)	)	PUNCT
ejpam-6411	262	5	(	(	PUNCT
ejpam-6411	262	6	∣∣(k2	∣∣(k2	NOUN
ejpam-6411	262	7	−	−	PROPN
ejpam-6411	262	8	k1	k1	PROPN
ejpam-6411	262	9	)	)	PUNCT
ejpam-6411	262	10	α	α	PROPN
ejpam-6411	262	11	−	−	PROPN
ejpam-6411	262	12	kα2	kα2	PROPN
ejpam-6411	262	13	∣∣+	∣∣+	PROPN
ejpam-6411	263	1	kα1	kα1	PROPN
ejpam-6411	263	2	+	+	PROPN
ejpam-6411	263	3	|k2	|k2	NOUN
ejpam-6411	263	4	−	−	PROPN
ejpam-6411	263	5	k1|α	k1|α	PROPN
ejpam-6411	263	6	)	)	PUNCT
ejpam-6411	263	7	.	.	PUNCT
ejpam-6411	264	1	(	(	PUNCT
ejpam-6411	264	2	18	18	NUM
ejpam-6411	264	3	)	)	PUNCT
ejpam-6411	264	4	hence	hence	ADV
ejpam-6411	264	5	,	,	PUNCT
ejpam-6411	264	6	we	we	PRON
ejpam-6411	264	7	have	have	VERB
ejpam-6411	264	8	∥q1	∥q1	NOUN
ejpam-6411	264	9	(	(	PUNCT
ejpam-6411	264	10	υ	υ	PROPN
ejpam-6411	264	11	,	,	PUNCT
ejpam-6411	264	12	ω	ω	NOUN
ejpam-6411	264	13	)	)	PUNCT
ejpam-6411	264	14	(	(	PUNCT
ejpam-6411	264	15	k2)−q1	k2)−q1	NOUN
ejpam-6411	264	16	(	(	PUNCT
ejpam-6411	264	17	υ	υ	PROPN
ejpam-6411	264	18	,	,	PUNCT
ejpam-6411	264	19	ω	ω	NOUN
ejpam-6411	264	20	)	)	PUNCT
ejpam-6411	264	21	(	(	PUNCT
ejpam-6411	264	22	k1)∥→0	k1)∥→0	NOUN
ejpam-6411	264	23	which	which	PRON
ejpam-6411	264	24	is	be	AUX
ejpam-6411	264	25	independent	independent	ADJ
ejpam-6411	264	26	of	of	ADP
ejpam-6411	264	27	υ	υ	PROPN
ejpam-6411	264	28	and	and	CCONJ
ejpam-6411	264	29	ω	ω	NOUN
ejpam-6411	264	30	as	as	ADP
ejpam-6411	264	31	k2→k1	k2→k1	PROPN
ejpam-6411	264	32	.	.	PUNCT
ejpam-6411	265	1	also	also	ADV
ejpam-6411	265	2	,	,	PUNCT
ejpam-6411	265	3	we	we	PRON
ejpam-6411	265	4	can	can	AUX
ejpam-6411	265	5	obtain	obtain	VERB
ejpam-6411	265	6	|q2(υ	|q2(υ	NUM
ejpam-6411	265	7	,	,	PUNCT
ejpam-6411	265	8	ω)(k2)−q2(υ	ω)(k2)−q2(υ	PROPN
ejpam-6411	265	9	,	,	PUNCT
ejpam-6411	265	10	ω)(k1)|	ω)(k1)|	PROPN
ejpam-6411	265	11	≤	≤	PROPN
ejpam-6411	265	12	k2	k2	PROPN
ejpam-6411	265	13	−	−	PROPN
ejpam-6411	265	14	k1	k1	PROPN
ejpam-6411	265	15	|λ|	|λ|	NOUN
ejpam-6411	265	16	(	(	PUNCT
ejpam-6411	265	17	λ2|ζη|µβ−1	λ2|ζη|µβ−1	X
ejpam-6411	265	18	γ(β	γ(β	PROPN
ejpam-6411	265	19	)	)	PUNCT
ejpam-6411	265	20	+	+	CCONJ
ejpam-6411	265	21	λ1|η|hα	λ1|η|hα	VERB
ejpam-6411	265	22	γ(α+	γ(α+	DET
ejpam-6411	265	23	1	1	NUM
ejpam-6411	265	24	)	)	PUNCT
ejpam-6411	265	25	+	+	NUM
ejpam-6411	265	26	λ1h|η|ρα−1	λ1h|η|ρα−1	X
ejpam-6411	265	27	γ(α	γ(α	NOUN
ejpam-6411	265	28	)	)	PUNCT
ejpam-6411	266	1	+	+	CCONJ
ejpam-6411	266	2	λ2h	λ2h	NOUN
ejpam-6411	266	3	β+1	β+1	NUM
ejpam-6411	266	4	γ(β	γ(β	X
ejpam-6411	266	5	+	+	CCONJ
ejpam-6411	266	6	1	1	NUM
ejpam-6411	266	7	)	)	PUNCT
ejpam-6411	266	8	)	)	PUNCT
ejpam-6411	267	1	+	+	PUNCT
ejpam-6411	267	2	λ2	λ2	NOUN
ejpam-6411	267	3	γ(β	γ(β	PROPN
ejpam-6411	267	4	+	+	CCONJ
ejpam-6411	267	5	1	1	NUM
ejpam-6411	267	6	)	)	PUNCT
ejpam-6411	267	7	(	(	PUNCT
ejpam-6411	267	8	∣∣∣(k2	∣∣∣(k2	PROPN
ejpam-6411	267	9	−	−	PROPN
ejpam-6411	267	10	k1	k1	NOUN
ejpam-6411	267	11	)	)	PUNCT
ejpam-6411	267	12	β	β	NOUN
ejpam-6411	267	13	−	−	PROPN
ejpam-6411	267	14	kβ2	kβ2	NOUN
ejpam-6411	267	15	∣∣∣+	∣∣∣+	PROPN
ejpam-6411	267	16	kβ1	kβ1	NOUN
ejpam-6411	267	17	+	+	NUM
ejpam-6411	267	18	|k2	|k2	NOUN
ejpam-6411	267	19	−	−	PROPN
ejpam-6411	267	20	k1|β	k1|β	PROPN
ejpam-6411	267	21	)	)	PUNCT
ejpam-6411	267	22	.	.	PUNCT
ejpam-6411	268	1	(	(	PUNCT
ejpam-6411	268	2	19	19	NUM
ejpam-6411	268	3	)	)	PUNCT
ejpam-6411	268	4	which	which	PRON
ejpam-6411	268	5	implies	imply	VERB
ejpam-6411	268	6	that	that	DET
ejpam-6411	268	7	∥q2	∥q2	NOUN
ejpam-6411	268	8	(	(	PUNCT
ejpam-6411	268	9	υ	υ	PROPN
ejpam-6411	268	10	,	,	PUNCT
ejpam-6411	268	11	ω	ω	NOUN
ejpam-6411	268	12	)	)	PUNCT
ejpam-6411	268	13	(	(	PUNCT
ejpam-6411	268	14	k2)−q2	k2)−q2	X
ejpam-6411	268	15	(	(	PUNCT
ejpam-6411	268	16	υ	υ	PROPN
ejpam-6411	268	17	,	,	PUNCT
ejpam-6411	268	18	ω	ω	NOUN
ejpam-6411	268	19	)	)	PUNCT
ejpam-6411	268	20	(	(	PUNCT
ejpam-6411	268	21	k1)∥→0	k1)∥→0	NOUN
ejpam-6411	268	22	which	which	PRON
ejpam-6411	268	23	is	be	AUX
ejpam-6411	268	24	independent	independent	ADJ
ejpam-6411	268	25	of	of	ADP
ejpam-6411	268	26	υ	υ	PROPN
ejpam-6411	268	27	and	and	CCONJ
ejpam-6411	268	28	ω	ω	NOUN
ejpam-6411	268	29	as	as	ADP
ejpam-6411	268	30	k2→k1	k2→k1	PROPN
ejpam-6411	268	31	.	.	PUNCT
ejpam-6411	269	1	so	so	ADV
ejpam-6411	269	2	,	,	PUNCT
ejpam-6411	269	3	the	the	DET
ejpam-6411	269	4	operator	operator	NOUN
ejpam-6411	269	5	q	q	PROPN
ejpam-6411	269	6	(	(	PUNCT
ejpam-6411	269	7	υ	υ	PROPN
ejpam-6411	269	8	,	,	PUNCT
ejpam-6411	269	9	ω	ω	NOUN
ejpam-6411	269	10	)	)	PUNCT
ejpam-6411	269	11	is	be	AUX
ejpam-6411	269	12	equicontinuous	equicontinuous	ADJ
ejpam-6411	269	13	,	,	PUNCT
ejpam-6411	269	14	and	and	CCONJ
ejpam-6411	269	15	,	,	PUNCT
ejpam-6411	269	16	thus	thus	ADV
ejpam-6411	269	17	,	,	PUNCT
ejpam-6411	269	18	the	the	DET
ejpam-6411	269	19	operator	operator	NOUN
ejpam-6411	269	20	q	q	PROPN
ejpam-6411	269	21	(	(	PUNCT
ejpam-6411	269	22	υ	υ	PROPN
ejpam-6411	269	23	,	,	PUNCT
ejpam-6411	269	24	ω	ω	NOUN
ejpam-6411	269	25	)	)	PUNCT
ejpam-6411	269	26	is	be	AUX
ejpam-6411	269	27	also	also	ADV
ejpam-6411	269	28	completely	completely	ADV
ejpam-6411	269	29	continuous	continuous	ADJ
ejpam-6411	269	30	.	.	PUNCT
ejpam-6411	270	1	second	second	ADJ
ejpam-6411	270	2	step	step	NOUN
ejpam-6411	270	3	:	:	PUNCT
ejpam-6411	270	4	(	(	PUNCT
ejpam-6411	270	5	boundedness	boundedness	NOUN
ejpam-6411	270	6	of	of	ADP
ejpam-6411	270	7	operator	operator	NOUN
ejpam-6411	270	8	)	)	PUNCT
ejpam-6411	270	9	finally	finally	ADV
ejpam-6411	270	10	,	,	PUNCT
ejpam-6411	270	11	we	we	PRON
ejpam-6411	270	12	show	show	VERB
ejpam-6411	270	13	that	that	SCONJ
ejpam-6411	270	14	b=	b=	NOUN
ejpam-6411	270	15	{	{	PUNCT
ejpam-6411	270	16	(	(	PUNCT
ejpam-6411	270	17	υ	υ	INTJ
ejpam-6411	270	18	,	,	PUNCT
ejpam-6411	270	19	ω)∈g×z	ω)∈g×z	NUM
ejpam-6411	270	20	:	:	PUNCT
ejpam-6411	270	21	(	(	PUNCT
ejpam-6411	270	22	υ	υ	NOUN
ejpam-6411	270	23	,	,	PUNCT
ejpam-6411	270	24	ω)=λq	ω)=λq	X
ejpam-6411	270	25	(	(	PUNCT
ejpam-6411	270	26	υ	υ	PROPN
ejpam-6411	270	27	,	,	PUNCT
ejpam-6411	270	28	ω	ω	NOUN
ejpam-6411	270	29	)	)	PUNCT
ejpam-6411	270	30	,	,	PUNCT
ejpam-6411	270	31	λ∈	λ∈	NOUN
ejpam-6411	270	32	[	[	X
ejpam-6411	270	33	0	0	NUM
ejpam-6411	270	34	,	,	PUNCT
ejpam-6411	270	35	1	1	NUM
ejpam-6411	270	36	]	]	PUNCT
ejpam-6411	270	37	}	}	PUNCT
ejpam-6411	270	38	is	be	AUX
ejpam-6411	270	39	bounded	bound	VERB
ejpam-6411	270	40	.	.	PUNCT
ejpam-6411	271	1	let	let	VERB
ejpam-6411	271	2	(	(	PUNCT
ejpam-6411	271	3	υ	υ	NOUN
ejpam-6411	271	4	,	,	PUNCT
ejpam-6411	271	5	ω)∈r	ω)∈r	NUM
ejpam-6411	271	6	,	,	PUNCT
ejpam-6411	271	7	where	where	SCONJ
ejpam-6411	271	8	(	(	PUNCT
ejpam-6411	271	9	υ	υ	NOUN
ejpam-6411	271	10	,	,	PUNCT
ejpam-6411	271	11	ω)=λq	ω)=λq	X
ejpam-6411	271	12	(	(	PUNCT
ejpam-6411	271	13	υ	υ	PROPN
ejpam-6411	271	14	,	,	PUNCT
ejpam-6411	271	15	ω	ω	NOUN
ejpam-6411	271	16	)	)	PUNCT
ejpam-6411	271	17	for	for	ADP
ejpam-6411	271	18	any	any	PRON
ejpam-6411	271	19	τ∈	τ∈	PUNCT
ejpam-6411	272	1	[	[	X
ejpam-6411	272	2	0,h	0,h	X
ejpam-6411	272	3	]	]	X
ejpam-6411	272	4	,	,	PUNCT
ejpam-6411	272	5	and	and	CCONJ
ejpam-6411	272	6	υ	υ	PROPN
ejpam-6411	272	7	(	(	PUNCT
ejpam-6411	272	8	τ	τ	X
ejpam-6411	272	9	)	)	PUNCT
ejpam-6411	272	10	=	=	SYM
ejpam-6411	272	11	λq1	λq1	NOUN
ejpam-6411	272	12	(	(	PUNCT
ejpam-6411	272	13	υ	υ	PROPN
ejpam-6411	272	14	,	,	PUNCT
ejpam-6411	272	15	ω	ω	NOUN
ejpam-6411	272	16	)	)	PUNCT
ejpam-6411	272	17	(	(	PUNCT
ejpam-6411	272	18	τ	τ	X
ejpam-6411	272	19	)	)	PUNCT
ejpam-6411	272	20	and	and	CCONJ
ejpam-6411	272	21	ω	ω	NUM
ejpam-6411	272	22	(	(	PUNCT
ejpam-6411	272	23	τ	τ	X
ejpam-6411	272	24	)	)	PUNCT
ejpam-6411	272	25	=	=	SYM
ejpam-6411	272	26	λq2	λq2	NOUN
ejpam-6411	272	27	(	(	PUNCT
ejpam-6411	272	28	υ	υ	PROPN
ejpam-6411	272	29	,	,	PUNCT
ejpam-6411	272	30	ω	ω	NOUN
ejpam-6411	272	31	)	)	PUNCT
ejpam-6411	272	32	(	(	PUNCT
ejpam-6411	272	33	τ	τ	X
ejpam-6411	272	34	)	)	PUNCT
ejpam-6411	272	35	.	.	PUNCT
ejpam-6411	273	1	therefore	therefore	ADV
ejpam-6411	273	2	,	,	PUNCT
ejpam-6411	273	3	|υ	|υ	NOUN
ejpam-6411	273	4	(	(	PUNCT
ejpam-6411	273	5	τ)|	τ)|	PROPN
ejpam-6411	273	6	≤	≤	NUM
ejpam-6411	273	7	n1	n1	NOUN
ejpam-6411	273	8	(	(	PUNCT
ejpam-6411	273	9	ψ0	ψ0	ADJ
ejpam-6411	273	10	+	+	CCONJ
ejpam-6411	273	11	ψ1	ψ1	ADJ
ejpam-6411	273	12	|υ|+	|υ|+	PROPN
ejpam-6411	273	13	ψ2	ψ2	NOUN
ejpam-6411	273	14	|ω|	|ω|	NOUN
ejpam-6411	273	15	)	)	PUNCT
ejpam-6411	273	16	+	+	NOUN
ejpam-6411	273	17	n2	n2	ADJ
ejpam-6411	273	18	(	(	PUNCT
ejpam-6411	273	19	ϕ0	ϕ0	NOUN
ejpam-6411	273	20	+	+	CCONJ
ejpam-6411	273	21	ϕ1	ϕ1	NOUN
ejpam-6411	273	22	|υ|+	|υ|+	PROPN
ejpam-6411	273	23	ϕ2	ϕ2	ADV
ejpam-6411	273	24	|ω|	|ω|	NOUN
ejpam-6411	273	25	)	)	PUNCT
ejpam-6411	273	26	,	,	PUNCT
ejpam-6411	273	27	s.	s.	PROPN
ejpam-6411	273	28	momani	momani	PROPN
ejpam-6411	273	29	et	et	PROPN
ejpam-6411	273	30	al	al	PROPN
ejpam-6411	273	31	.	.	PUNCT
ejpam-6411	273	32	/	/	SYM
ejpam-6411	273	33	eur	eur	PROPN
ejpam-6411	273	34	.	.	PUNCT
ejpam-6411	274	1	j.	j.	PROPN
ejpam-6411	274	2	pure	pure	PROPN
ejpam-6411	274	3	appl	appl	PROPN
ejpam-6411	274	4	.	.	PROPN
ejpam-6411	274	5	math	math	PROPN
ejpam-6411	274	6	,	,	PUNCT
ejpam-6411	274	7	18	18	NUM
ejpam-6411	274	8	(	(	PUNCT
ejpam-6411	274	9	4	4	NUM
ejpam-6411	274	10	)	)	PUNCT
ejpam-6411	274	11	(	(	PUNCT
ejpam-6411	274	12	2025	2025	NUM
ejpam-6411	274	13	)	)	PUNCT
ejpam-6411	274	14	,	,	PUNCT
ejpam-6411	274	15	6411	6411	NUM
ejpam-6411	274	16	11	11	NUM
ejpam-6411	274	17	of	of	ADP
ejpam-6411	274	18	16	16	NUM
ejpam-6411	274	19	and	and	CCONJ
ejpam-6411	274	20	|ω	|ω	NOUN
ejpam-6411	274	21	(	(	PUNCT
ejpam-6411	274	22	τ)|	τ)|	PROPN
ejpam-6411	274	23	≤	≤	PROPN
ejpam-6411	274	24	n3	n3	NOUN
ejpam-6411	274	25	(	(	PUNCT
ejpam-6411	274	26	ψ0	ψ0	ADJ
ejpam-6411	274	27	+	+	CCONJ
ejpam-6411	274	28	ψ1	ψ1	ADJ
ejpam-6411	274	29	|υ|+	|υ|+	PROPN
ejpam-6411	274	30	ψ2	ψ2	NOUN
ejpam-6411	274	31	|ω|	|ω|	NOUN
ejpam-6411	274	32	)	)	PUNCT
ejpam-6411	274	33	+	+	PROPN
ejpam-6411	274	34	n4	n4	PROPN
ejpam-6411	274	35	(	(	PUNCT
ejpam-6411	274	36	ϕ0	ϕ0	NOUN
ejpam-6411	274	37	+	+	CCONJ
ejpam-6411	274	38	ϕ1	ϕ1	NOUN
ejpam-6411	274	39	|υ|+	|υ|+	PROPN
ejpam-6411	274	40	ϕ2	ϕ2	ADV
ejpam-6411	274	41	|ω|	|ω|	NOUN
ejpam-6411	274	42	)	)	PUNCT
ejpam-6411	274	43	.	.	PUNCT
ejpam-6411	275	1	thus	thus	ADV
ejpam-6411	275	2	,	,	PUNCT
ejpam-6411	275	3	we	we	PRON
ejpam-6411	275	4	get	get	VERB
ejpam-6411	275	5	∥υ∥	∥υ∥	ADJ
ejpam-6411	275	6	≤	≤	NUM
ejpam-6411	275	7	n1	n1	NOUN
ejpam-6411	275	8	(	(	PUNCT
ejpam-6411	275	9	ψ0	ψ0	ADJ
ejpam-6411	275	10	+	+	CCONJ
ejpam-6411	275	11	ψ1	ψ1	ADJ
ejpam-6411	275	12	∥υ∥+	∥υ∥+	NOUN
ejpam-6411	275	13	ψ2	ψ2	NOUN
ejpam-6411	275	14	∥ω∥	∥ω∥	NOUN
ejpam-6411	275	15	)	)	PUNCT
ejpam-6411	275	16	+	+	NOUN
ejpam-6411	275	17	n2	n2	NOUN
ejpam-6411	275	18	(	(	PUNCT
ejpam-6411	275	19	ϕ0	ϕ0	NOUN
ejpam-6411	275	20	+	+	NUM
ejpam-6411	275	21	ϕ1	ϕ1	NOUN
ejpam-6411	275	22	∥υ∥+	∥υ∥+	VERB
ejpam-6411	275	23	ϕ2	ϕ2	ADV
ejpam-6411	275	24	∥ω∥	∥ω∥	NOUN
ejpam-6411	275	25	)	)	PUNCT
ejpam-6411	275	26	,	,	PUNCT
ejpam-6411	275	27	and	and	CCONJ
ejpam-6411	275	28	∥ω∥	∥ω∥	VERB
ejpam-6411	275	29	≤	≤	ADJ
ejpam-6411	275	30	n3	n3	NOUN
ejpam-6411	275	31	(	(	PUNCT
ejpam-6411	275	32	ψ0	ψ0	ADJ
ejpam-6411	275	33	+	+	CCONJ
ejpam-6411	275	34	ψ1	ψ1	ADJ
ejpam-6411	275	35	∥υ∥+	∥υ∥+	NOUN
ejpam-6411	275	36	ψ2	ψ2	NOUN
ejpam-6411	275	37	∥ω∥	∥ω∥	NOUN
ejpam-6411	275	38	)	)	PUNCT
ejpam-6411	276	1	+	+	PROPN
ejpam-6411	276	2	n4	n4	PROPN
ejpam-6411	276	3	(	(	PUNCT
ejpam-6411	276	4	ϕ0	ϕ0	NOUN
ejpam-6411	276	5	+	+	CCONJ
ejpam-6411	276	6	ϕ1	ϕ1	NOUN
ejpam-6411	276	7	∥υ∥+	∥υ∥+	VERB
ejpam-6411	276	8	ϕ2	ϕ2	ADV
ejpam-6411	276	9	∥ω∥	∥ω∥	NOUN
ejpam-6411	276	10	)	)	PUNCT
ejpam-6411	276	11	.	.	PUNCT
ejpam-6411	277	1	this	this	PRON
ejpam-6411	277	2	leads	lead	VERB
ejpam-6411	277	3	to	to	ADP
ejpam-6411	277	4	the	the	DET
ejpam-6411	277	5	conclusion	conclusion	NOUN
ejpam-6411	277	6	that	that	SCONJ
ejpam-6411	277	7	∥υ∥+	∥υ∥+	NOUN
ejpam-6411	277	8	∥ω∥	∥ω∥	VERB
ejpam-6411	277	9	≤	≤	NOUN
ejpam-6411	277	10	(	(	PUNCT
ejpam-6411	277	11	n1	n1	PROPN
ejpam-6411	277	12	+	+	PROPN
ejpam-6411	277	13	n3)ψ0	n3)ψ0	PROPN
ejpam-6411	277	14	+	+	CCONJ
ejpam-6411	277	15	(	(	PUNCT
ejpam-6411	277	16	n2	n2	ADJ
ejpam-6411	277	17	+	+	PROPN
ejpam-6411	277	18	n4)ϕ0	n4)ϕ0	ADJ
ejpam-6411	277	19	+	+	X
ejpam-6411	277	20	(	(	PUNCT
ejpam-6411	277	21	(	(	PUNCT
ejpam-6411	277	22	n1	n1	PROPN
ejpam-6411	277	23	+	+	NOUN
ejpam-6411	277	24	n3)ψ1	n3)ψ1	PROPN
ejpam-6411	277	25	+	+	X
ejpam-6411	277	26	(	(	PUNCT
ejpam-6411	277	27	n2	n2	ADJ
ejpam-6411	277	28	+	+	NOUN
ejpam-6411	277	29	n4)ϕ1	n4)ϕ1	ADJ
ejpam-6411	277	30	)	)	PUNCT
ejpam-6411	277	31	∥υ∥	∥υ∥	X
ejpam-6411	278	1	+	+	PUNCT
ejpam-6411	278	2	(	(	PUNCT
ejpam-6411	278	3	(	(	PUNCT
ejpam-6411	278	4	n1	n1	X
ejpam-6411	278	5	+	+	NOUN
ejpam-6411	278	6	n3)ψ2	n3)ψ2	ADV
ejpam-6411	278	7	+	+	CCONJ
ejpam-6411	278	8	(	(	PUNCT
ejpam-6411	278	9	n2	n2	ADJ
ejpam-6411	278	10	+	+	NOUN
ejpam-6411	278	11	n4)ϕ2	n4)ϕ2	ADV
ejpam-6411	278	12	)	)	PUNCT
ejpam-6411	278	13	∥ω∥	∥ω∥	NOUN
ejpam-6411	278	14	.	.	PUNCT
ejpam-6411	279	1	therefore	therefore	ADV
ejpam-6411	279	2	,	,	PUNCT
ejpam-6411	279	3	∥(υ	∥(υ	NOUN
ejpam-6411	279	4	,	,	PUNCT
ejpam-6411	279	5	ω)∥	ω)∥	PUNCT
ejpam-6411	279	6	≤	≤	NUM
ejpam-6411	279	7	(	(	PUNCT
ejpam-6411	279	8	n1	n1	PROPN
ejpam-6411	279	9	+	+	PROPN
ejpam-6411	279	10	n3)ψ0	n3)ψ0	PROPN
ejpam-6411	279	11	+	+	CCONJ
ejpam-6411	279	12	(	(	PUNCT
ejpam-6411	279	13	n2	n2	ADJ
ejpam-6411	279	14	+	+	PROPN
ejpam-6411	279	15	n4)ϕ0	n4)ϕ0	PROPN
ejpam-6411	279	16	n0	n0	NOUN
ejpam-6411	279	17	,	,	PUNCT
ejpam-6411	279	18	where	where	SCONJ
ejpam-6411	279	19	n0	n0	PROPN
ejpam-6411	279	20	=	=	NOUN
ejpam-6411	279	21	min	min	X
ejpam-6411	279	22	{	{	PUNCT
ejpam-6411	279	23	1−	1−	NUM
ejpam-6411	279	24	(	(	PUNCT
ejpam-6411	279	25	n1	n1	PROPN
ejpam-6411	279	26	+	+	X
ejpam-6411	279	27	n3)ψ1−	n3)ψ1−	ADJ
ejpam-6411	279	28	(	(	PUNCT
ejpam-6411	279	29	n2	n2	NOUN
ejpam-6411	279	30	+	+	PROPN
ejpam-6411	279	31	n4)ϕ1	n4)ϕ1	ADJ
ejpam-6411	279	32	,	,	PUNCT
ejpam-6411	279	33	1−	1−	NUM
ejpam-6411	279	34	(	(	PUNCT
ejpam-6411	279	35	n1	n1	PROPN
ejpam-6411	279	36	+	+	NOUN
ejpam-6411	279	37	n3)ψ2−	n3)ψ2−	NOUN
ejpam-6411	279	38	(	(	PUNCT
ejpam-6411	279	39	n2	n2	NOUN
ejpam-6411	279	40	+	+	PROPN
ejpam-6411	279	41	n4)ϕ2	n4)ϕ2	ADV
ejpam-6411	279	42	}	}	PUNCT
ejpam-6411	279	43	.	.	PUNCT
ejpam-6411	280	1	thus	thus	ADV
ejpam-6411	280	2	,	,	PUNCT
ejpam-6411	280	3	this	this	PRON
ejpam-6411	280	4	demonstrates	demonstrate	VERB
ejpam-6411	280	5	that	that	SCONJ
ejpam-6411	280	6	b	b	NOUN
ejpam-6411	280	7	is	be	AUX
ejpam-6411	280	8	bounded	bound	VERB
ejpam-6411	280	9	and	and	CCONJ
ejpam-6411	280	10	that	that	SCONJ
ejpam-6411	280	11	the	the	DET
ejpam-6411	280	12	operator	operator	NOUN
ejpam-6411	280	13	g	g	NOUN
ejpam-6411	280	14	has	have	VERB
ejpam-6411	280	15	at	at	ADV
ejpam-6411	280	16	least	least	ADV
ejpam-6411	280	17	one	one	NUM
ejpam-6411	280	18	fixed	fix	VERB
ejpam-6411	280	19	point	point	NOUN
ejpam-6411	280	20	in	in	ADP
ejpam-6411	280	21	accordance	accordance	NOUN
ejpam-6411	280	22	to	to	ADP
ejpam-6411	280	23	the	the	DET
ejpam-6411	280	24	leray	leray	ADJ
ejpam-6411	280	25	-	-	PUNCT
ejpam-6411	280	26	schauder	schauder	NOUN
ejpam-6411	280	27	theorem	theorem	PROPN
ejpam-6411	280	28	.	.	PUNCT
ejpam-6411	281	1	therefore	therefore	ADV
ejpam-6411	281	2	,	,	PUNCT
ejpam-6411	281	3	there	there	PRON
ejpam-6411	281	4	is	be	VERB
ejpam-6411	281	5	at	at	ADV
ejpam-6411	281	6	least	least	ADJ
ejpam-6411	281	7	one	one	NUM
ejpam-6411	281	8	solution	solution	NOUN
ejpam-6411	281	9	to	to	ADP
ejpam-6411	281	10	both	both	DET
ejpam-6411	281	11	eqs	eqs	X
ejpam-6411	281	12	.	.	PUNCT
ejpam-6411	282	1	(	(	PUNCT
ejpam-6411	282	2	1	1	X
ejpam-6411	282	3	)	)	PUNCT
ejpam-6411	282	4	and	and	CCONJ
ejpam-6411	282	5	(	(	PUNCT
ejpam-6411	282	6	2	2	X
ejpam-6411	282	7	)	)	PUNCT
ejpam-6411	282	8	on	on	ADP
ejpam-6411	282	9	[	[	X
ejpam-6411	282	10	0,h	0,h	X
ejpam-6411	282	11	]	]	X
ejpam-6411	282	12	.	.	PUNCT
ejpam-6411	283	1	the	the	DET
ejpam-6411	283	2	proof	proof	NOUN
ejpam-6411	283	3	is	be	AUX
ejpam-6411	283	4	complete	complete	ADJ
ejpam-6411	283	5	.	.	PUNCT
ejpam-6411	284	1	■	■	PUNCT
ejpam-6411	284	2	in	in	ADP
ejpam-6411	284	3	summary	summary	NOUN
ejpam-6411	284	4	,	,	PUNCT
ejpam-6411	284	5	this	this	DET
ejpam-6411	284	6	section	section	NOUN
ejpam-6411	284	7	discusses	discuss	VERB
ejpam-6411	284	8	and	and	CCONJ
ejpam-6411	284	9	proves	prove	VERB
ejpam-6411	284	10	the	the	DET
ejpam-6411	284	11	uniqueness	uniqueness	NOUN
ejpam-6411	284	12	of	of	ADP
ejpam-6411	284	13	our	our	PRON
ejpam-6411	284	14	proposed	propose	VERB
ejpam-6411	284	15	fractional	fractional	ADJ
ejpam-6411	284	16	coupled	couple	VERB
ejpam-6411	284	17	system	system	NOUN
ejpam-6411	284	18	in	in	ADP
ejpam-6411	284	19	theorem	theorem	NOUN
ejpam-6411	284	20	3.1	3.1	NUM
ejpam-6411	284	21	.	.	PUNCT
ejpam-6411	285	1	following	follow	VERB
ejpam-6411	285	2	this	this	PRON
ejpam-6411	285	3	,	,	PUNCT
ejpam-6411	285	4	by	by	ADP
ejpam-6411	285	5	applying	apply	VERB
ejpam-6411	285	6	the	the	DET
ejpam-6411	285	7	leray	leray	ADJ
ejpam-6411	285	8	-	-	PUNCT
ejpam-6411	285	9	schauder	schauder	NOUN
ejpam-6411	285	10	alternative	alternative	NOUN
ejpam-6411	285	11	described	describe	VERB
ejpam-6411	285	12	in	in	ADP
ejpam-6411	285	13	lemma	lemma	PROPN
ejpam-6411	285	14	3.2	3.2	NUM
ejpam-6411	285	15	and	and	CCONJ
ejpam-6411	285	16	proving	prove	VERB
ejpam-6411	285	17	theorem	theorem	ADJ
ejpam-6411	285	18	3.3	3.3	NUM
ejpam-6411	285	19	,	,	PUNCT
ejpam-6411	285	20	we	we	PRON
ejpam-6411	285	21	demonstrate	demonstrate	VERB
ejpam-6411	285	22	that	that	SCONJ
ejpam-6411	285	23	our	our	PRON
ejpam-6411	285	24	proposed	propose	VERB
ejpam-6411	285	25	fractional	fractional	ADJ
ejpam-6411	285	26	coupled	couple	VERB
ejpam-6411	285	27	system	system	NOUN
ejpam-6411	285	28	has	have	VERB
ejpam-6411	285	29	at	at	ADV
ejpam-6411	285	30	least	least	ADJ
ejpam-6411	285	31	one	one	NUM
ejpam-6411	285	32	solution	solution	NOUN
ejpam-6411	285	33	.	.	PUNCT
ejpam-6411	286	1	4	4	X
ejpam-6411	286	2	.	.	X
ejpam-6411	286	3	hyers	hyer	NOUN
ejpam-6411	286	4	-	-	PUNCT
ejpam-6411	286	5	ulam	ulam	PROPN
ejpam-6411	286	6	stability	stability	NOUN
ejpam-6411	286	7	this	this	DET
ejpam-6411	286	8	section	section	NOUN
ejpam-6411	286	9	discusses	discuss	VERB
ejpam-6411	286	10	the	the	DET
ejpam-6411	286	11	hyers	hyers	PROPN
ejpam-6411	286	12	-	-	PUNCT
ejpam-6411	286	13	ulam	ulam	PROPN
ejpam-6411	286	14	stability	stability	NOUN
ejpam-6411	286	15	for	for	ADP
ejpam-6411	286	16	the	the	DET
ejpam-6411	286	17	boundary	boundary	ADJ
ejpam-6411	286	18	value	value	NOUN
ejpam-6411	286	19	issues	issue	NOUN
ejpam-6411	286	20	in	in	ADP
ejpam-6411	286	21	equations	equation	NOUN
ejpam-6411	286	22	(	(	PUNCT
ejpam-6411	286	23	1	1	NUM
ejpam-6411	286	24	)	)	PUNCT
ejpam-6411	286	25	and	and	CCONJ
ejpam-6411	286	26	(	(	PUNCT
ejpam-6411	286	27	2	2	X
ejpam-6411	286	28	)	)	PUNCT
ejpam-6411	286	29	using	use	VERB
ejpam-6411	286	30	an	an	DET
ejpam-6411	286	31	integral	integral	ADJ
ejpam-6411	286	32	form	form	NOUN
ejpam-6411	286	33	of	of	ADP
ejpam-6411	286	34	the	the	DET
ejpam-6411	286	35	general	general	ADJ
ejpam-6411	286	36	solution	solution	NOUN
ejpam-6411	286	37	,	,	PUNCT
ejpam-6411	286	38	described	describe	VERB
ejpam-6411	286	39	by	by	ADP
ejpam-6411	286	40	υ	υ	PROPN
ejpam-6411	286	41	(	(	PUNCT
ejpam-6411	286	42	τ)=q1	τ)=q1	X
ejpam-6411	286	43	(	(	PUNCT
ejpam-6411	286	44	υ	υ	PROPN
ejpam-6411	286	45	,	,	PUNCT
ejpam-6411	286	46	ω	ω	NOUN
ejpam-6411	286	47	)	)	PUNCT
ejpam-6411	286	48	(	(	PUNCT
ejpam-6411	286	49	τ	τ	X
ejpam-6411	286	50	)	)	PUNCT
ejpam-6411	286	51	,	,	PUNCT
ejpam-6411	286	52	ω	ω	PROPN
ejpam-6411	286	53	(	(	PUNCT
ejpam-6411	286	54	τ)=q2	τ)=q2	X
ejpam-6411	286	55	(	(	PUNCT
ejpam-6411	286	56	υ	υ	PROPN
ejpam-6411	286	57	,	,	PUNCT
ejpam-6411	286	58	ω	ω	NOUN
ejpam-6411	286	59	)	)	PUNCT
ejpam-6411	286	60	(	(	PUNCT
ejpam-6411	286	61	τ	τ	X
ejpam-6411	286	62	)	)	PUNCT
ejpam-6411	286	63	,	,	PUNCT
ejpam-6411	286	64	where	where	SCONJ
ejpam-6411	286	65	q1and	q1and	NOUN
ejpam-6411	286	66	q2	q2	NOUN
ejpam-6411	286	67	are	be	AUX
ejpam-6411	286	68	expressed	express	VERB
ejpam-6411	286	69	in	in	ADP
ejpam-6411	286	70	eq.(8	eq.(8	ADJ
ejpam-6411	286	71	)	)	PUNCT
ejpam-6411	286	72	and	and	CCONJ
ejpam-6411	286	73	eq.(9	eq.(9	ADJ
ejpam-6411	286	74	)	)	PUNCT
ejpam-6411	286	75	.	.	PUNCT
ejpam-6411	287	1	define	define	VERB
ejpam-6411	287	2	the	the	DET
ejpam-6411	287	3	following	follow	VERB
ejpam-6411	287	4	nonlinear	nonlinear	ADJ
ejpam-6411	287	5	operators	operator	NOUN
ejpam-6411	287	6	m1,m2∈c	m1,m2∈c	PROPN
ejpam-6411	287	7	(	(	PUNCT
ejpam-6411	287	8	[	[	X
ejpam-6411	287	9	0,h	0,h	X
ejpam-6411	287	10	]	]	X
ejpam-6411	287	11	,	,	PUNCT
ejpam-6411	287	12	r)×c	r)×c	NOUN
ejpam-6411	287	13	(	(	PUNCT
ejpam-6411	287	14	[	[	X
ejpam-6411	287	15	0,h	0,h	X
ejpam-6411	287	16	]	]	X
ejpam-6411	287	17	,	,	PUNCT
ejpam-6411	287	18	r)→c	r)→c	PROPN
ejpam-6411	287	19	(	(	PUNCT
ejpam-6411	287	20	[	[	X
ejpam-6411	287	21	0,h	0,h	X
ejpam-6411	287	22	]	]	PUNCT
ejpam-6411	287	23	,	,	PUNCT
ejpam-6411	287	24	r	r	NOUN
ejpam-6411	287	25	)	)	PUNCT
ejpam-6411	287	26	;	;	PUNCT
ejpam-6411	287	27	cdαυ	cdαυ	NOUN
ejpam-6411	287	28	(	(	PUNCT
ejpam-6411	287	29	τ)−u	τ)−u	X
ejpam-6411	287	30	(	(	PUNCT
ejpam-6411	287	31	τ	τ	PROPN
ejpam-6411	287	32	,	,	PUNCT
ejpam-6411	287	33	υ	υ	PROPN
ejpam-6411	287	34	(	(	PUNCT
ejpam-6411	287	35	τ	τ	PROPN
ejpam-6411	287	36	)	)	PUNCT
ejpam-6411	287	37	,	,	PUNCT
ejpam-6411	287	38	ω	ω	PROPN
ejpam-6411	287	39	(	(	PUNCT
ejpam-6411	287	40	τ))=m1	τ))=m1	PROPN
ejpam-6411	287	41	(	(	PUNCT
ejpam-6411	287	42	υ	υ	PROPN
ejpam-6411	287	43	,	,	PUNCT
ejpam-6411	287	44	ω	ω	NOUN
ejpam-6411	287	45	)	)	PUNCT
ejpam-6411	287	46	(	(	PUNCT
ejpam-6411	287	47	τ	τ	X
ejpam-6411	287	48	)	)	PUNCT
ejpam-6411	287	49	,	,	PUNCT
ejpam-6411	287	50	τ∈	τ∈	PROPN
ejpam-6411	288	1	[	[	X
ejpam-6411	288	2	0,h	0,h	X
ejpam-6411	288	3	]	]	PUNCT
ejpam-6411	288	4	,	,	PUNCT
ejpam-6411	288	5	cdβω	cdβω	NOUN
ejpam-6411	288	6	(	(	PUNCT
ejpam-6411	288	7	τ)−h	τ)−h	X
ejpam-6411	288	8	(	(	PUNCT
ejpam-6411	288	9	τ	τ	PROPN
ejpam-6411	288	10	,	,	PUNCT
ejpam-6411	288	11	υ	υ	PROPN
ejpam-6411	288	12	(	(	PUNCT
ejpam-6411	288	13	τ	τ	PROPN
ejpam-6411	288	14	)	)	PUNCT
ejpam-6411	288	15	,	,	PUNCT
ejpam-6411	288	16	ω	ω	PROPN
ejpam-6411	288	17	(	(	PUNCT
ejpam-6411	288	18	τ))=m2	τ))=m2	X
ejpam-6411	288	19	(	(	PUNCT
ejpam-6411	288	20	υ	υ	PROPN
ejpam-6411	288	21	,	,	PUNCT
ejpam-6411	288	22	ω	ω	NOUN
ejpam-6411	288	23	)	)	PUNCT
ejpam-6411	288	24	(	(	PUNCT
ejpam-6411	288	25	τ	τ	X
ejpam-6411	288	26	)	)	PUNCT
ejpam-6411	288	27	,	,	PUNCT
ejpam-6411	288	28	τ∈	τ∈	PROPN
ejpam-6411	289	1	[	[	X
ejpam-6411	289	2	0,h	0,h	X
ejpam-6411	289	3	]	]	PUNCT
ejpam-6411	289	4	.	.	PUNCT
ejpam-6411	290	1	for	for	ADP
ejpam-6411	290	2	some	some	DET
ejpam-6411	290	3	r1	r1	NOUN
ejpam-6411	290	4	,	,	PUNCT
ejpam-6411	290	5	r2	r2	PROPN
ejpam-6411	290	6	>	>	X
ejpam-6411	290	7	0	0	NUM
ejpam-6411	290	8	,	,	PUNCT
ejpam-6411	290	9	we	we	PRON
ejpam-6411	290	10	consider	consider	VERB
ejpam-6411	290	11	the	the	DET
ejpam-6411	290	12	following	follow	VERB
ejpam-6411	290	13	inequality	inequality	NOUN
ejpam-6411	290	14	∥m1	∥m1	ADP
ejpam-6411	290	15	(	(	PUNCT
ejpam-6411	290	16	υ	υ	NOUN
ejpam-6411	290	17	,	,	PUNCT
ejpam-6411	290	18	ω)∥≤r1	ω)∥≤r1	NOUN
ejpam-6411	290	19	and	and	CCONJ
ejpam-6411	290	20	∥m2	∥m2	NOUN
ejpam-6411	290	21	(	(	PUNCT
ejpam-6411	290	22	υ	υ	NOUN
ejpam-6411	290	23	,	,	PUNCT
ejpam-6411	290	24	ω)∥≤r2	ω)∥≤r2	NOUN
ejpam-6411	290	25	.	.	PUNCT
ejpam-6411	291	1	(	(	PUNCT
ejpam-6411	291	2	20	20	NUM
ejpam-6411	291	3	)	)	PUNCT
ejpam-6411	291	4	s.	s.	PROPN
ejpam-6411	291	5	momani	momani	PROPN
ejpam-6411	291	6	et	et	PROPN
ejpam-6411	291	7	al	al	PROPN
ejpam-6411	291	8	.	.	PUNCT
ejpam-6411	291	9	/	/	SYM
ejpam-6411	291	10	eur	eur	PROPN
ejpam-6411	291	11	.	.	PUNCT
ejpam-6411	292	1	j.	j.	PROPN
ejpam-6411	292	2	pure	pure	PROPN
ejpam-6411	292	3	appl	appl	PROPN
ejpam-6411	292	4	.	.	PROPN
ejpam-6411	292	5	math	math	PROPN
ejpam-6411	292	6	,	,	PUNCT
ejpam-6411	292	7	18	18	NUM
ejpam-6411	292	8	(	(	PUNCT
ejpam-6411	292	9	4	4	NUM
ejpam-6411	292	10	)	)	PUNCT
ejpam-6411	292	11	(	(	PUNCT
ejpam-6411	292	12	2025	2025	NUM
ejpam-6411	292	13	)	)	PUNCT
ejpam-6411	292	14	,	,	PUNCT
ejpam-6411	292	15	6411	6411	NUM
ejpam-6411	292	16	12	12	NUM
ejpam-6411	292	17	of	of	ADP
ejpam-6411	292	18	16	16	NUM
ejpam-6411	292	19	definition	definition	NOUN
ejpam-6411	292	20	4.1	4.1	NUM
ejpam-6411	292	21	:	:	PUNCT
ejpam-6411	293	1	[	[	X
ejpam-6411	293	2	27	27	NUM
ejpam-6411	293	3	,	,	PUNCT
ejpam-6411	293	4	28	28	NUM
ejpam-6411	293	5	]	]	PUNCT
ejpam-6411	293	6	the	the	DET
ejpam-6411	293	7	coupled	couple	VERB
ejpam-6411	293	8	fractional	fractional	ADJ
ejpam-6411	293	9	system	system	NOUN
ejpam-6411	293	10	in	in	ADP
ejpam-6411	293	11	e.(1	e.(1	PROPN
ejpam-6411	293	12	)	)	PUNCT
ejpam-6411	293	13	and	and	CCONJ
ejpam-6411	293	14	e.(2	e.(2	NUM
ejpam-6411	293	15	)	)	PUNCT
ejpam-6411	293	16	is	be	AUX
ejpam-6411	293	17	said	say	VERB
ejpam-6411	293	18	to	to	PART
ejpam-6411	293	19	be	be	AUX
ejpam-6411	293	20	hyers	hyer	NOUN
ejpam-6411	293	21	-	-	PUNCT
ejpam-6411	293	22	ulam	ulam	X
ejpam-6411	293	23	stable	stable	ADJ
ejpam-6411	293	24	,	,	PUNCT
ejpam-6411	293	25	if	if	SCONJ
ejpam-6411	293	26	there	there	PRON
ejpam-6411	293	27	exist	exist	VERB
ejpam-6411	293	28	eq1	eq1	PROPN
ejpam-6411	293	29	,	,	PUNCT
ejpam-6411	293	30	eq2	eq2	PROPN
ejpam-6411	293	31	>	>	X
ejpam-6411	293	32	0	0	NUM
ejpam-6411	293	33	,	,	PUNCT
ejpam-6411	293	34	such	such	ADJ
ejpam-6411	293	35	that	that	PRON
ejpam-6411	293	36	for	for	ADP
ejpam-6411	293	37	every	every	DET
ejpam-6411	293	38	solution	solution	NOUN
ejpam-6411	293	39	(	(	PUNCT
ejpam-6411	293	40	υ∗	υ∗	NOUN
ejpam-6411	293	41	,	,	PUNCT
ejpam-6411	293	42	ω∗)∈c	ω∗)∈c	NOUN
ejpam-6411	293	43	(	(	PUNCT
ejpam-6411	293	44	[	[	X
ejpam-6411	293	45	0,h	0,h	X
ejpam-6411	293	46	]	]	X
ejpam-6411	293	47	,	,	PUNCT
ejpam-6411	293	48	r)×c	r)×c	NOUN
ejpam-6411	293	49	(	(	PUNCT
ejpam-6411	293	50	[	[	X
ejpam-6411	293	51	0,h	0,h	X
ejpam-6411	293	52	]	]	PUNCT
ejpam-6411	293	53	,	,	PUNCT
ejpam-6411	293	54	r	r	NOUN
ejpam-6411	293	55	)	)	PUNCT
ejpam-6411	293	56	as	as	SCONJ
ejpam-6411	293	57	given	give	VERB
ejpam-6411	293	58	in	in	ADP
ejpam-6411	293	59	eq.(12	eq.(12	PROPN
ejpam-6411	293	60	)	)	PUNCT
ejpam-6411	293	61	,	,	PUNCT
ejpam-6411	293	62	there	there	PRON
ejpam-6411	293	63	exists	exist	VERB
ejpam-6411	293	64	a	a	DET
ejpam-6411	293	65	unique	unique	ADJ
ejpam-6411	293	66	solution	solution	NOUN
ejpam-6411	293	67	(	(	PUNCT
ejpam-6411	293	68	υ	υ	NOUN
ejpam-6411	293	69	,	,	PUNCT
ejpam-6411	293	70	ω)∈c([0,h],r)×c([0,h],r	ω)∈c([0,h],r)×c([0,h],r	NUM
ejpam-6411	293	71	)	)	PUNCT
ejpam-6411	293	72	of	of	ADP
ejpam-6411	293	73	the	the	DET
ejpam-6411	293	74	system	system	NOUN
ejpam-6411	293	75	presented	present	VERB
ejpam-6411	293	76	in	in	ADP
ejpam-6411	293	77	eq.(1	eq.(1	ADJ
ejpam-6411	293	78	)	)	PUNCT
ejpam-6411	293	79	and	and	CCONJ
ejpam-6411	293	80	eq.(2	eq.(2	ADJ
ejpam-6411	293	81	)	)	PUNCT
ejpam-6411	293	82	such	such	ADJ
ejpam-6411	293	83	that	that	DET
ejpam-6411	293	84	∥(υ	∥(υ	NOUN
ejpam-6411	293	85	,	,	PUNCT
ejpam-6411	293	86	ω)−	ω)−	PROPN
ejpam-6411	293	87	(	(	PUNCT
ejpam-6411	293	88	υ∗	υ∗	PROPN
ejpam-6411	293	89	,	,	PUNCT
ejpam-6411	293	90	ω∗)∥≤eq1r1+eq1r2	ω∗)∥≤eq1r1+eq1r2	NOUN
ejpam-6411	293	91	.	.	PUNCT
ejpam-6411	294	1	theorem	theorem	VERB
ejpam-6411	294	2	4.2	4.2	NUM
ejpam-6411	294	3	:	:	PUNCT
ejpam-6411	294	4	let	let	VERB
ejpam-6411	294	5	the	the	DET
ejpam-6411	294	6	assumptions	assumption	NOUN
ejpam-6411	294	7	of	of	ADP
ejpam-6411	294	8	theorem	theorem	ADJ
ejpam-6411	294	9	3.1	3.1	NUM
ejpam-6411	294	10	hold	hold	NOUN
ejpam-6411	294	11	.	.	PUNCT
ejpam-6411	295	1	then	then	ADV
ejpam-6411	295	2	,	,	PUNCT
ejpam-6411	295	3	the	the	DET
ejpam-6411	295	4	coupled	couple	VERB
ejpam-6411	295	5	system	system	NOUN
ejpam-6411	295	6	in	in	ADP
ejpam-6411	295	7	e.(1	e.(1	PROPN
ejpam-6411	295	8	)	)	PUNCT
ejpam-6411	295	9	and	and	CCONJ
ejpam-6411	295	10	e.(2	e.(2	NUM
ejpam-6411	295	11	)	)	PUNCT
ejpam-6411	295	12	is	be	AUX
ejpam-6411	295	13	hyers	hyer	NOUN
ejpam-6411	295	14	-	-	PUNCT
ejpam-6411	295	15	ulam	ulam	X
ejpam-6411	295	16	stable	stable	ADJ
ejpam-6411	295	17	.	.	PUNCT
ejpam-6411	296	1	proof	proof	NOUN
ejpam-6411	296	2	.	.	PUNCT
ejpam-6411	297	1	let	let	AUX
ejpam-6411	297	2	(	(	PUNCT
ejpam-6411	297	3	υ	υ	NOUN
ejpam-6411	297	4	,	,	PUNCT
ejpam-6411	297	5	ω)∈c([0,h],r)×c([0,h],r	ω)∈c([0,h],r)×c([0,h],r	NUM
ejpam-6411	297	6	)	)	PUNCT
ejpam-6411	297	7	be	be	VERB
ejpam-6411	297	8	the	the	DET
ejpam-6411	297	9	solution	solution	NOUN
ejpam-6411	297	10	of	of	ADP
ejpam-6411	297	11	the	the	DET
ejpam-6411	297	12	problems	problem	NOUN
ejpam-6411	297	13	in	in	ADP
ejpam-6411	297	14	e.(1	e.(1	PROPN
ejpam-6411	297	15	)	)	PUNCT
ejpam-6411	297	16	and	and	CCONJ
ejpam-6411	297	17	e.(2	e.(2	NUM
ejpam-6411	297	18	)	)	PUNCT
ejpam-6411	297	19	satisfying	satisfy	VERB
ejpam-6411	297	20	eq.(8	eq.(8	NOUN
ejpam-6411	297	21	)	)	PUNCT
ejpam-6411	297	22	and	and	CCONJ
ejpam-6411	297	23	eq.(9	eq.(9	ADJ
ejpam-6411	297	24	)	)	PUNCT
ejpam-6411	297	25	and	and	CCONJ
ejpam-6411	297	26	(	(	PUNCT
ejpam-6411	297	27	υ∗	υ∗	NOUN
ejpam-6411	297	28	,	,	PUNCT
ejpam-6411	297	29	ω∗	ω∗	NOUN
ejpam-6411	297	30	)	)	PUNCT
ejpam-6411	297	31	be	be	VERB
ejpam-6411	297	32	any	any	DET
ejpam-6411	297	33	solution	solution	NOUN
ejpam-6411	297	34	satisfying	satisfy	VERB
ejpam-6411	297	35	e.(20	e.(20	ADV
ejpam-6411	297	36	):	):	PUNCT
ejpam-6411	297	37	cdαυ∗	cdαυ∗	X
ejpam-6411	297	38	(	(	PUNCT
ejpam-6411	297	39	τ)=u	τ)=u	X
ejpam-6411	297	40	(	(	PUNCT
ejpam-6411	297	41	τ	τ	X
ejpam-6411	297	42	,	,	PUNCT
ejpam-6411	297	43	υ∗	υ∗	NOUN
ejpam-6411	297	44	(	(	PUNCT
ejpam-6411	297	45	τ	τ	PROPN
ejpam-6411	297	46	)	)	PUNCT
ejpam-6411	297	47	,	,	PUNCT
ejpam-6411	297	48	ω∗	ω∗	NOUN
ejpam-6411	297	49	(	(	PUNCT
ejpam-6411	297	50	τ))+m1	τ))+m1	PROPN
ejpam-6411	297	51	(	(	PUNCT
ejpam-6411	297	52	υ	υ	NOUN
ejpam-6411	297	53	∗	∗	NOUN
ejpam-6411	297	54	,	,	PUNCT
ejpam-6411	297	55	ω∗	ω∗	NOUN
ejpam-6411	297	56	)	)	PUNCT
ejpam-6411	297	57	(	(	PUNCT
ejpam-6411	297	58	τ	τ	X
ejpam-6411	297	59	)	)	PUNCT
ejpam-6411	297	60	,	,	PUNCT
ejpam-6411	297	61	τ∈	τ∈	PROPN
ejpam-6411	298	1	[	[	X
ejpam-6411	298	2	0,h	0,h	X
ejpam-6411	298	3	]	]	X
ejpam-6411	298	4	,	,	PUNCT
ejpam-6411	298	5	cdβω∗	cdβω∗	X
ejpam-6411	298	6	(	(	PUNCT
ejpam-6411	298	7	τ)=h	τ)=h	PUNCT
ejpam-6411	298	8	(	(	PUNCT
ejpam-6411	298	9	τ	τ	NOUN
ejpam-6411	298	10	,	,	PUNCT
ejpam-6411	298	11	υ∗	υ∗	NOUN
ejpam-6411	298	12	(	(	PUNCT
ejpam-6411	298	13	τ	τ	PROPN
ejpam-6411	298	14	)	)	PUNCT
ejpam-6411	298	15	,	,	PUNCT
ejpam-6411	298	16	ω∗	ω∗	NOUN
ejpam-6411	298	17	(	(	PUNCT
ejpam-6411	298	18	τ))+m2	τ))+m2	X
ejpam-6411	298	19	(	(	PUNCT
ejpam-6411	298	20	υ	υ	NOUN
ejpam-6411	298	21	∗	∗	NOUN
ejpam-6411	298	22	,	,	PUNCT
ejpam-6411	298	23	ω∗	ω∗	NOUN
ejpam-6411	298	24	)	)	PUNCT
ejpam-6411	298	25	(	(	PUNCT
ejpam-6411	298	26	τ	τ	X
ejpam-6411	298	27	)	)	PUNCT
ejpam-6411	298	28	,	,	PUNCT
ejpam-6411	298	29	τ∈	τ∈	PROPN
ejpam-6411	299	1	[	[	X
ejpam-6411	299	2	0,h	0,h	X
ejpam-6411	299	3	]	]	PUNCT
ejpam-6411	299	4	.	.	PUNCT
ejpam-6411	300	1	then	then	ADV
ejpam-6411	300	2	,	,	PUNCT
ejpam-6411	300	3	we	we	PRON
ejpam-6411	300	4	have	have	VERB
ejpam-6411	300	5	υ∗(τ	υ∗(τ	NOUN
ejpam-6411	300	6	)	)	PUNCT
ejpam-6411	300	7	=	=	VERB
ejpam-6411	301	1	q1(υ	q1(υ	NUM
ejpam-6411	301	2	∗	∗	NOUN
ejpam-6411	301	3	,	,	PUNCT
ejpam-6411	301	4	ω∗)(τ	ω∗)(τ	NOUN
ejpam-6411	301	5	)	)	PUNCT
ejpam-6411	302	1	+	+	CCONJ
ejpam-6411	302	2	τ	τ	X
ejpam-6411	302	3	λ	λ	X
ejpam-6411	302	4	[	[	PUNCT
ejpam-6411	302	5	ζh	ζh	PROPN
ejpam-6411	302	6	∫	∫	PROPN
ejpam-6411	302	7	µ	µ	X
ejpam-6411	302	8	0	0	NUM
ejpam-6411	302	9	(	(	PUNCT
ejpam-6411	302	10	µ−	µ−	PROPN
ejpam-6411	302	11	s)β−2	s)β−2	VERB
ejpam-6411	302	12	γ(β	γ(β	PROPN
ejpam-6411	302	13	−	−	PROPN
ejpam-6411	302	14	1	1	X
ejpam-6411	302	15	)	)	PUNCT
ejpam-6411	302	16	m2(υ	m2(υ	PROPN
ejpam-6411	302	17	∗	∗	NOUN
ejpam-6411	302	18	,	,	PUNCT
ejpam-6411	302	19	ω∗)(s	ω∗)(s	NOUN
ejpam-6411	302	20	)	)	PUNCT
ejpam-6411	303	1	ds	ds	PROPN
ejpam-6411	303	2	−h	−h	ADJ
ejpam-6411	303	3	∫	∫	PROPN
ejpam-6411	303	4	h	h	NOUN
ejpam-6411	303	5	0	0	NUM
ejpam-6411	303	6	∫	∫	PROPN
ejpam-6411	303	7	s	s	PART
ejpam-6411	303	8	0	0	NUM
ejpam-6411	303	9	(	(	PUNCT
ejpam-6411	303	10	s−	s−	PROPN
ejpam-6411	303	11	t)α−2	t)α−2	NOUN
ejpam-6411	303	12	γ(α−	γ(α−	NOUN
ejpam-6411	303	13	1	1	NUM
ejpam-6411	303	14	)	)	PUNCT
ejpam-6411	303	15	m1(υ	m1(υ	VERB
ejpam-6411	303	16	∗	∗	NOUN
ejpam-6411	303	17	,	,	PUNCT
ejpam-6411	303	18	ω∗)(t	ω∗)(t	PROPN
ejpam-6411	303	19	)	)	PUNCT
ejpam-6411	303	20	dt	dt	NOUN
ejpam-6411	304	1	ds	ds	PROPN
ejpam-6411	304	2	+	+	CCONJ
ejpam-6411	304	3	ζη	ζη	ADJ
ejpam-6411	304	4	∫	∫	PROPN
ejpam-6411	304	5	ρ	ρ	PROPN
ejpam-6411	304	6	0	0	PUNCT
ejpam-6411	305	1	(	(	PUNCT
ejpam-6411	305	2	ρ−	ρ−	NOUN
ejpam-6411	305	3	s)α−2	s)α−2	VERB
ejpam-6411	305	4	γ(α−	γ(α−	NOUN
ejpam-6411	305	5	1	1	NUM
ejpam-6411	305	6	)	)	PUNCT
ejpam-6411	305	7	m1(υ	m1(υ	VERB
ejpam-6411	305	8	∗	∗	NOUN
ejpam-6411	305	9	,	,	PUNCT
ejpam-6411	305	10	ω∗)(s	ω∗)(s	NOUN
ejpam-6411	305	11	)	)	PUNCT
ejpam-6411	305	12	ds	ds	ADJ
ejpam-6411	305	13	−	−	NOUN
ejpam-6411	305	14	ζ	ζ	NOUN
ejpam-6411	305	15	∫	∫	PROPN
ejpam-6411	305	16	h	h	NOUN
ejpam-6411	305	17	0	0	NUM
ejpam-6411	306	1	∫	∫	PROPN
ejpam-6411	306	2	s	s	PART
ejpam-6411	306	3	0	0	NUM
ejpam-6411	306	4	(	(	PUNCT
ejpam-6411	306	5	s−	s−	PROPN
ejpam-6411	306	6	t)β−2	t)β−2	VERB
ejpam-6411	306	7	γ(β	γ(β	PROPN
ejpam-6411	306	8	−	−	PROPN
ejpam-6411	306	9	1	1	X
ejpam-6411	306	10	)	)	PUNCT
ejpam-6411	306	11	m2(υ	m2(υ	PROPN
ejpam-6411	306	12	∗	∗	NOUN
ejpam-6411	306	13	,	,	PUNCT
ejpam-6411	306	14	ω∗)(t	ω∗)(t	PROPN
ejpam-6411	306	15	)	)	PUNCT
ejpam-6411	307	1	dt	dt	NOUN
ejpam-6411	307	2	ds	ds	X
ejpam-6411	307	3	]	]	PUNCT
ejpam-6411	308	1	+	+	CCONJ
ejpam-6411	308	2	∫	∫	PROPN
ejpam-6411	308	3	τ	τ	X
ejpam-6411	308	4	0	0	NUM
ejpam-6411	308	5	(	(	PUNCT
ejpam-6411	308	6	τ	τ	PROPN
ejpam-6411	308	7	−	−	PROPN
ejpam-6411	308	8	s)α−1	s)α−1	NOUN
ejpam-6411	308	9	γ(α	γ(α	NOUN
ejpam-6411	308	10	)	)	PUNCT
ejpam-6411	308	11	m1(υ	m1(υ	PROPN
ejpam-6411	308	12	∗	∗	NOUN
ejpam-6411	308	13	,	,	PUNCT
ejpam-6411	308	14	ω∗)(s	ω∗)(s	NOUN
ejpam-6411	308	15	)	)	PUNCT
ejpam-6411	308	16	ds	ds	PROPN
ejpam-6411	308	17	.	.	PUNCT
ejpam-6411	309	1	(	(	PUNCT
ejpam-6411	309	2	21	21	NUM
ejpam-6411	309	3	)	)	PUNCT
ejpam-6411	309	4	it	it	PRON
ejpam-6411	309	5	hence	hence	ADV
ejpam-6411	309	6	follows	follow	VERB
ejpam-6411	309	7	that	that	SCONJ
ejpam-6411	309	8	|q1(υ	|q1(υ	PROPN
ejpam-6411	309	9	∗	∗	NOUN
ejpam-6411	309	10	,	,	PUNCT
ejpam-6411	309	11	ω∗)(τ)−	ω∗)(τ)−	NOUN
ejpam-6411	309	12	υ∗(τ)|	υ∗(τ)|	PROPN
ejpam-6411	309	13	≤	≤	PROPN
ejpam-6411	309	14	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6411	309	15	τλ	τλ	X
ejpam-6411	309	16	(	(	PUNCT
ejpam-6411	309	17	ζη	ζη	INTJ
ejpam-6411	309	18	∫	∫	PROPN
ejpam-6411	309	19	µ	µ	X
ejpam-6411	309	20	0	0	NUM
ejpam-6411	309	21	(	(	PUNCT
ejpam-6411	309	22	µ−	µ−	PROPN
ejpam-6411	309	23	s)β−2	s)β−2	VERB
ejpam-6411	309	24	γ(β	γ(β	PROPN
ejpam-6411	309	25	−	−	PROPN
ejpam-6411	309	26	1	1	X
ejpam-6411	309	27	)	)	PUNCT
ejpam-6411	309	28	r2(s	r2(s	NOUN
ejpam-6411	309	29	)	)	PUNCT
ejpam-6411	309	30	ds−	ds−	PROPN
ejpam-6411	309	31	η	η	PROPN
ejpam-6411	309	32	∫	∫	PROPN
ejpam-6411	309	33	h	h	PROPN
ejpam-6411	309	34	0	0	NUM
ejpam-6411	309	35	∫	∫	PROPN
ejpam-6411	309	36	s	s	PART
ejpam-6411	309	37	0	0	NUM
ejpam-6411	310	1	(	(	PUNCT
ejpam-6411	310	2	s−	s−	PROPN
ejpam-6411	310	3	t)α−2	t)α−2	NOUN
ejpam-6411	310	4	γ(α−	γ(α−	VERB
ejpam-6411	310	5	1	1	NUM
ejpam-6411	310	6	)	)	PUNCT
ejpam-6411	310	7	r1(t	r1(t	PROPN
ejpam-6411	310	8	)	)	PUNCT
ejpam-6411	310	9	dt	dt	NOUN
ejpam-6411	310	10	ds	ds	PROPN
ejpam-6411	310	11	+	+	ADV
ejpam-6411	310	12	hη	hη	PROPN
ejpam-6411	310	13	∫	∫	PROPN
ejpam-6411	310	14	ρ	ρ	PROPN
ejpam-6411	310	15	0	0	PROPN
ejpam-6411	311	1	(	(	PUNCT
ejpam-6411	311	2	ρ−	ρ−	NOUN
ejpam-6411	311	3	s)α−2	s)α−2	VERB
ejpam-6411	311	4	γ(α−	γ(α−	VERB
ejpam-6411	311	5	1	1	NUM
ejpam-6411	311	6	)	)	PUNCT
ejpam-6411	311	7	r1(s	r1(s	NOUN
ejpam-6411	311	8	)	)	PUNCT
ejpam-6411	311	9	ds−h	ds−h	NOUN
ejpam-6411	311	10	∫	∫	PROPN
ejpam-6411	311	11	h	h	NOUN
ejpam-6411	311	12	0	0	NUM
ejpam-6411	311	13	∫	∫	PROPN
ejpam-6411	311	14	s	s	PART
ejpam-6411	311	15	0	0	NUM
ejpam-6411	311	16	(	(	PUNCT
ejpam-6411	311	17	s−	s−	PROPN
ejpam-6411	311	18	t)β−2	t)β−2	VERB
ejpam-6411	311	19	γ(β	γ(β	PROPN
ejpam-6411	311	20	−	−	PROPN
ejpam-6411	311	21	1	1	NUM
ejpam-6411	311	22	)	)	PUNCT
ejpam-6411	311	23	r2(t	r2(t	NOUN
ejpam-6411	311	24	)	)	PUNCT
ejpam-6411	311	25	dt	dt	X
ejpam-6411	312	1	ds	ds	X
ejpam-6411	312	2	)	)	PUNCT
ejpam-6411	313	1	+	+	CCONJ
ejpam-6411	313	2	∫	∫	PROPN
ejpam-6411	313	3	τ	τ	X
ejpam-6411	313	4	0	0	NUM
ejpam-6411	313	5	(	(	PUNCT
ejpam-6411	313	6	τ	τ	X
ejpam-6411	313	7	−	−	PROPN
ejpam-6411	313	8	s)β−1	s)β−1	AUX
ejpam-6411	313	9	γ(β	γ(β	PROPN
ejpam-6411	313	10	)	)	PUNCT
ejpam-6411	313	11	r2(s	r2(s	NOUN
ejpam-6411	313	12	)	)	PUNCT
ejpam-6411	313	13	ds	ds	ADJ
ejpam-6411	313	14	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6411	313	15	≤	≤	NOUN
ejpam-6411	313	16	(	(	PUNCT
ejpam-6411	313	17	h	h	NOUN
ejpam-6411	313	18	λ	λ	X
ejpam-6411	313	19	(	(	PUNCT
ejpam-6411	313	20	hα+1	hα+1	NOUN
ejpam-6411	313	21	γ(α+	γ(α+	DET
ejpam-6411	313	22	1	1	NUM
ejpam-6411	313	23	)	)	PUNCT
ejpam-6411	313	24	+	+	NUM
ejpam-6411	313	25	|ζη|ρα−1	|ζη|ρα−1	NUM
ejpam-6411	313	26	γ(α	γ(α	NOUN
ejpam-6411	313	27	)	)	PUNCT
ejpam-6411	313	28	)	)	PUNCT
ejpam-6411	314	1	+	+	CCONJ
ejpam-6411	314	2	hα	hα	ADP
ejpam-6411	314	3	γ(α+	γ(α+	DET
ejpam-6411	314	4	1	1	NUM
ejpam-6411	314	5	)	)	PUNCT
ejpam-6411	314	6	)	)	PUNCT
ejpam-6411	314	7	r1	r1	PROPN
ejpam-6411	314	8	+	+	CCONJ
ejpam-6411	314	9	(	(	PUNCT
ejpam-6411	314	10	h	h	NOUN
ejpam-6411	314	11	λ	λ	PROPN
ejpam-6411	314	12	(	(	PUNCT
ejpam-6411	314	13	|ζ|hµβ−1	|ζ|hµβ−1	PUNCT
ejpam-6411	314	14	γ(β	γ(β	PROPN
ejpam-6411	314	15	)	)	PUNCT
ejpam-6411	315	1	+	+	CCONJ
ejpam-6411	315	2	|ζ|hβ	|ζ|hβ	PROPN
ejpam-6411	315	3	γ(β	γ(β	PROPN
ejpam-6411	315	4	+	+	PROPN
ejpam-6411	315	5	1	1	NUM
ejpam-6411	315	6	)	)	PUNCT
ejpam-6411	315	7	)	)	PUNCT
ejpam-6411	315	8	)	)	PUNCT
ejpam-6411	316	1	r2	r2	PROPN
ejpam-6411	316	2	≤	≤	NUM
ejpam-6411	316	3	n1r1	n1r1	PROPN
ejpam-6411	316	4	+	+	SYM
ejpam-6411	316	5	n2r2	n2r2	NOUN
ejpam-6411	316	6	.	.	PUNCT
ejpam-6411	316	7	s.	s.	PROPN
ejpam-6411	316	8	momani	momani	PROPN
ejpam-6411	316	9	et	et	PROPN
ejpam-6411	316	10	al	al	PROPN
ejpam-6411	316	11	.	.	PUNCT
ejpam-6411	316	12	/	/	SYM
ejpam-6411	316	13	eur	eur	PROPN
ejpam-6411	316	14	.	.	PUNCT
ejpam-6411	317	1	j.	j.	PROPN
ejpam-6411	317	2	pure	pure	PROPN
ejpam-6411	317	3	appl	appl	PROPN
ejpam-6411	317	4	.	.	PROPN
ejpam-6411	317	5	math	math	PROPN
ejpam-6411	317	6	,	,	PUNCT
ejpam-6411	317	7	18	18	NUM
ejpam-6411	317	8	(	(	PUNCT
ejpam-6411	317	9	4	4	NUM
ejpam-6411	317	10	)	)	PUNCT
ejpam-6411	317	11	(	(	PUNCT
ejpam-6411	317	12	2025	2025	NUM
ejpam-6411	317	13	)	)	PUNCT
ejpam-6411	317	14	,	,	PUNCT
ejpam-6411	317	15	6411	6411	NUM
ejpam-6411	317	16	13	13	NUM
ejpam-6411	317	17	of	of	ADP
ejpam-6411	317	18	16	16	NUM
ejpam-6411	317	19	similarly	similarly	ADV
ejpam-6411	317	20	,	,	PUNCT
ejpam-6411	317	21	|q2	|q2	NOUN
ejpam-6411	317	22	(	(	PUNCT
ejpam-6411	317	23	υ	υ	NOUN
ejpam-6411	317	24	∗	∗	NOUN
ejpam-6411	317	25	,	,	PUNCT
ejpam-6411	317	26	ω∗	ω∗	NOUN
ejpam-6411	317	27	)	)	PUNCT
ejpam-6411	317	28	(	(	PUNCT
ejpam-6411	317	29	τ)−ω∗	τ)−ω∗	X
ejpam-6411	317	30	(	(	PUNCT
ejpam-6411	317	31	τ)|	τ)|	PROPN
ejpam-6411	317	32	≤n3r1+n4r2	≤n3r1+n4r2	VERB
ejpam-6411	317	33	.	.	PUNCT
ejpam-6411	318	1	we	we	PRON
ejpam-6411	318	2	therefore	therefore	ADV
ejpam-6411	318	3	arrive	arrive	VERB
ejpam-6411	318	4	to	to	ADP
ejpam-6411	318	5	the	the	DET
ejpam-6411	318	6	following	follow	VERB
ejpam-6411	318	7	conclusion	conclusion	NOUN
ejpam-6411	318	8	based	base	VERB
ejpam-6411	318	9	on	on	ADP
ejpam-6411	318	10	using	use	VERB
ejpam-6411	318	11	the	the	DET
ejpam-6411	318	12	operator	operator	NOUN
ejpam-6411	318	13	q	q	PROPN
ejpam-6411	318	14	’s	’s	ADV
ejpam-6411	318	15	fixed	fix	VERB
ejpam-6411	318	16	-	-	PUNCT
ejpam-6411	318	17	point	point	NOUN
ejpam-6411	318	18	property	property	NOUN
ejpam-6411	318	19	,	,	PUNCT
ejpam-6411	318	20	given	give	VERB
ejpam-6411	318	21	by	by	ADP
ejpam-6411	318	22	eqs	eqs	PROPN
ejpam-6411	318	23	.	.	PUNCT
ejpam-6411	319	1	(	(	PUNCT
ejpam-6411	319	2	10	10	NUM
ejpam-6411	319	3	)	)	PUNCT
ejpam-6411	319	4	and	and	CCONJ
ejpam-6411	319	5	(	(	PUNCT
ejpam-6411	319	6	11	11	NUM
ejpam-6411	319	7	)	)	PUNCT
ejpam-6411	319	8	,	,	PUNCT
ejpam-6411	319	9	as	as	SCONJ
ejpam-6411	319	10	follows	follow	VERB
ejpam-6411	319	11	|υ(τ)−	|υ(τ)−	PROPN
ejpam-6411	319	12	υ∗	υ∗	NOUN
ejpam-6411	319	13	(	(	PUNCT
ejpam-6411	319	14	τ)|	τ)|	NOUN
ejpam-6411	319	15	=	=	PUNCT
ejpam-6411	319	16	|υ	|υ	NOUN
ejpam-6411	319	17	(	(	PUNCT
ejpam-6411	319	18	τ)−q1	τ)−q1	PROPN
ejpam-6411	319	19	(	(	PUNCT
ejpam-6411	319	20	υ	υ	NOUN
ejpam-6411	319	21	∗	∗	NOUN
ejpam-6411	319	22	,	,	PUNCT
ejpam-6411	319	23	ω∗	ω∗	NOUN
ejpam-6411	319	24	)	)	PUNCT
ejpam-6411	319	25	(	(	PUNCT
ejpam-6411	319	26	τ	τ	X
ejpam-6411	319	27	)	)	PUNCT
ejpam-6411	320	1	+	+	NUM
ejpam-6411	320	2	q1	q1	PROPN
ejpam-6411	320	3	(	(	PUNCT
ejpam-6411	320	4	υ	υ	NOUN
ejpam-6411	320	5	∗	∗	NOUN
ejpam-6411	320	6	,	,	PUNCT
ejpam-6411	320	7	ω∗	ω∗	NOUN
ejpam-6411	320	8	)	)	PUNCT
ejpam-6411	320	9	(	(	PUNCT
ejpam-6411	320	10	τ)−	τ)−	PROPN
ejpam-6411	320	11	υ∗	υ∗	NOUN
ejpam-6411	320	12	(	(	PUNCT
ejpam-6411	320	13	τ)|	τ)|	NOUN
ejpam-6411	320	14	≤	≤	ADJ
ejpam-6411	320	15	|q1	|q1	NOUN
ejpam-6411	320	16	(	(	PUNCT
ejpam-6411	320	17	υ	υ	PROPN
ejpam-6411	320	18	,	,	PUNCT
ejpam-6411	320	19	ω	ω	NOUN
ejpam-6411	320	20	)	)	PUNCT
ejpam-6411	320	21	(	(	PUNCT
ejpam-6411	320	22	τ)−q1	τ)−q1	PROPN
ejpam-6411	320	23	(	(	PUNCT
ejpam-6411	320	24	υ	υ	NOUN
ejpam-6411	320	25	∗	∗	NOUN
ejpam-6411	320	26	,	,	PUNCT
ejpam-6411	320	27	ω∗	ω∗	NOUN
ejpam-6411	320	28	)	)	PUNCT
ejpam-6411	320	29	(	(	PUNCT
ejpam-6411	320	30	τ)|+	τ)|+	NOUN
ejpam-6411	320	31	|m1	|m1	NOUN
ejpam-6411	320	32	(	(	PUNCT
ejpam-6411	320	33	υ	υ	NOUN
ejpam-6411	320	34	∗	∗	NOUN
ejpam-6411	320	35	,	,	PUNCT
ejpam-6411	320	36	ω∗	ω∗	NOUN
ejpam-6411	320	37	)	)	PUNCT
ejpam-6411	320	38	(	(	PUNCT
ejpam-6411	320	39	τ)−υ∗	τ)−υ∗	NOUN
ejpam-6411	320	40	(	(	PUNCT
ejpam-6411	320	41	τ)|	τ)|	NOUN
ejpam-6411	320	42	≤	≤	PROPN
ejpam-6411	320	43	(	(	PUNCT
ejpam-6411	320	44	n1θ+n2ϖ	n1θ+n2ϖ	PROPN
ejpam-6411	320	45	)	)	PUNCT
ejpam-6411	320	46	∥(υ	∥(υ	NOUN
ejpam-6411	320	47	,	,	PUNCT
ejpam-6411	320	48	ω)−	ω)−	PROPN
ejpam-6411	320	49	(	(	PUNCT
ejpam-6411	320	50	υ∗	υ∗	NOUN
ejpam-6411	320	51	,	,	PUNCT
ejpam-6411	320	52	ω∗)∥+n1r1+n2r2	ω∗)∥+n1r1+n2r2	NUM
ejpam-6411	320	53	.	.	PUNCT
ejpam-6411	321	1	(	(	PUNCT
ejpam-6411	321	2	22	22	NUM
ejpam-6411	321	3	)	)	PUNCT
ejpam-6411	321	4	similarly	similarly	ADV
ejpam-6411	321	5	|υ(τ)−	|υ(τ)−	NOUN
ejpam-6411	321	6	υ∗	υ∗	NOUN
ejpam-6411	321	7	(	(	PUNCT
ejpam-6411	321	8	τ)|	τ)|	NOUN
ejpam-6411	321	9	=	=	PUNCT
ejpam-6411	321	10	|υ	|υ	NOUN
ejpam-6411	321	11	(	(	PUNCT
ejpam-6411	321	12	τ)−q2	τ)−q2	X
ejpam-6411	321	13	(	(	PUNCT
ejpam-6411	321	14	υ	υ	NOUN
ejpam-6411	321	15	∗	∗	NOUN
ejpam-6411	321	16	,	,	PUNCT
ejpam-6411	321	17	ω∗	ω∗	NOUN
ejpam-6411	321	18	)	)	PUNCT
ejpam-6411	321	19	(	(	PUNCT
ejpam-6411	321	20	τ	τ	X
ejpam-6411	321	21	)	)	PUNCT
ejpam-6411	322	1	+	+	NUM
ejpam-6411	322	2	q2	q2	NOUN
ejpam-6411	322	3	(	(	PUNCT
ejpam-6411	322	4	υ	υ	NOUN
ejpam-6411	322	5	∗	∗	NOUN
ejpam-6411	322	6	,	,	PUNCT
ejpam-6411	322	7	ω∗	ω∗	NOUN
ejpam-6411	322	8	)	)	PUNCT
ejpam-6411	322	9	(	(	PUNCT
ejpam-6411	322	10	τ)−	τ)−	PROPN
ejpam-6411	322	11	υ∗	υ∗	NOUN
ejpam-6411	322	12	(	(	PUNCT
ejpam-6411	322	13	τ)|	τ)|	PROPN
ejpam-6411	322	14	≤	≤	PROPN
ejpam-6411	322	15	|q2	|q2	VERB
ejpam-6411	322	16	(	(	PUNCT
ejpam-6411	322	17	υ	υ	PROPN
ejpam-6411	322	18	,	,	PUNCT
ejpam-6411	322	19	ω	ω	NOUN
ejpam-6411	322	20	)	)	PUNCT
ejpam-6411	322	21	(	(	PUNCT
ejpam-6411	322	22	τ)−q2	τ)−q2	X
ejpam-6411	322	23	(	(	PUNCT
ejpam-6411	322	24	υ	υ	NOUN
ejpam-6411	322	25	∗	∗	NOUN
ejpam-6411	322	26	,	,	PUNCT
ejpam-6411	322	27	ω∗	ω∗	NOUN
ejpam-6411	322	28	)	)	PUNCT
ejpam-6411	322	29	(	(	PUNCT
ejpam-6411	322	30	τ)|+	τ)|+	NOUN
ejpam-6411	322	31	|m2	|m2	NOUN
ejpam-6411	322	32	(	(	PUNCT
ejpam-6411	322	33	υ	υ	NOUN
ejpam-6411	322	34	∗	∗	NOUN
ejpam-6411	322	35	,	,	PUNCT
ejpam-6411	322	36	ω∗	ω∗	NOUN
ejpam-6411	322	37	)	)	PUNCT
ejpam-6411	322	38	(	(	PUNCT
ejpam-6411	322	39	τ)−υ∗	τ)−υ∗	NOUN
ejpam-6411	322	40	(	(	PUNCT
ejpam-6411	322	41	τ)|	τ)|	NOUN
ejpam-6411	322	42	≤	≤	PROPN
ejpam-6411	322	43	(	(	PUNCT
ejpam-6411	322	44	n3θ+n4ϖ	n3θ+n4ϖ	PROPN
ejpam-6411	322	45	)	)	PUNCT
ejpam-6411	322	46	∥(υ	∥(υ	NOUN
ejpam-6411	322	47	,	,	PUNCT
ejpam-6411	322	48	ω)−	ω)−	PROPN
ejpam-6411	322	49	(	(	PUNCT
ejpam-6411	322	50	υ∗	υ∗	PROPN
ejpam-6411	322	51	,	,	PUNCT
ejpam-6411	322	52	ω∗)∥+n3r1+n4r2	ω∗)∥+n3r1+n4r2	PROPN
ejpam-6411	322	53	,	,	PUNCT
ejpam-6411	322	54	.	.	PUNCT
ejpam-6411	323	1	(	(	PUNCT
ejpam-6411	323	2	?	?	PUNCT
ejpam-6411	323	3	?	?	PUNCT
ejpam-6411	323	4	)	)	PUNCT
ejpam-6411	323	5	from	from	ADP
ejpam-6411	323	6	e.(22	e.(22	NOUN
ejpam-6411	323	7	)	)	PUNCT
ejpam-6411	323	8	and	and	CCONJ
ejpam-6411	323	9	e.	e.	PROPN
ejpam-6411	323	10	(	(	PUNCT
ejpam-6411	323	11	?	?	PUNCT
ejpam-6411	323	12	?	?	PUNCT
ejpam-6411	323	13	)	)	PUNCT
ejpam-6411	324	1	it	it	PRON
ejpam-6411	324	2	follows	follow	VERB
ejpam-6411	324	3	that	that	SCONJ
ejpam-6411	324	4	∥(υ	∥(υ	NOUN
ejpam-6411	324	5	,	,	PUNCT
ejpam-6411	324	6	ω)−	ω)−	PROPN
ejpam-6411	324	7	(	(	PUNCT
ejpam-6411	324	8	υ∗	υ∗	PROPN
ejpam-6411	324	9	,	,	PUNCT
ejpam-6411	324	10	ω∗)∥≤	ω∗)∥≤	NUM
ejpam-6411	324	11	(	(	PUNCT
ejpam-6411	324	12	n1θ+n2ϖ+n3θ+n4ϖ	n1θ+n2ϖ+n3θ+n4ϖ	PROPN
ejpam-6411	324	13	)	)	PUNCT
ejpam-6411	324	14	∥(υ	∥(υ	NOUN
ejpam-6411	324	15	,	,	PUNCT
ejpam-6411	324	16	ω)−	ω)−	PROPN
ejpam-6411	324	17	(	(	PUNCT
ejpam-6411	324	18	υ∗	υ∗	NOUN
ejpam-6411	324	19	,	,	PUNCT
ejpam-6411	324	20	ω∗)∥+(n1+n3	ω∗)∥+(n1+n3	NUM
ejpam-6411	324	21	)	)	PUNCT
ejpam-6411	324	22	r1+(n2+n4	r1+(n2+n4	NOUN
ejpam-6411	324	23	)	)	PUNCT
ejpam-6411	324	24	r2	r2	NOUN
ejpam-6411	324	25	,	,	PUNCT
ejpam-6411	324	26	∥(υ	∥(υ	NOUN
ejpam-6411	324	27	,	,	PUNCT
ejpam-6411	324	28	ω)−	ω)−	PROPN
ejpam-6411	324	29	(	(	PUNCT
ejpam-6411	324	30	υ∗	υ∗	PROPN
ejpam-6411	324	31	,	,	PUNCT
ejpam-6411	324	32	ω∗)∥≤	ω∗)∥≤	NUM
ejpam-6411	324	33	(	(	PUNCT
ejpam-6411	324	34	n1+n3	n1+n3	NOUN
ejpam-6411	324	35	)	)	PUNCT
ejpam-6411	324	36	r1+(n2+n4	r1+(n2+n4	NOUN
ejpam-6411	324	37	)	)	PUNCT
ejpam-6411	324	38	r2	r2	PROPN
ejpam-6411	324	39	1−	1−	NUM
ejpam-6411	324	40	(	(	PUNCT
ejpam-6411	324	41	(	(	PUNCT
ejpam-6411	324	42	n1+n3)θ+	n1+n3)θ+	PROPN
ejpam-6411	324	43	(	(	PUNCT
ejpam-6411	324	44	n2+n4)ϖ	n2+n4)ϖ	PROPN
ejpam-6411	324	45	)	)	PUNCT
ejpam-6411	324	46	,	,	PUNCT
ejpam-6411	324	47	where	where	SCONJ
ejpam-6411	324	48	eq1=	eq1=	NOUN
ejpam-6411	324	49	(	(	PUNCT
ejpam-6411	324	50	n1+n3	n1+n3	ADV
ejpam-6411	324	51	)	)	PUNCT
ejpam-6411	324	52	1−((n1+n3)θ+(n2+n4)ϖ	1−((n1+n3)θ+(n2+n4)ϖ	NUM
ejpam-6411	324	53	)	)	PUNCT
ejpam-6411	324	54	,	,	PUNCT
ejpam-6411	324	55	and	and	CCONJ
ejpam-6411	324	56	eq2=	eq2=	PROPN
ejpam-6411	324	57	(	(	PUNCT
ejpam-6411	324	58	n2+n4	n2+n4	NOUN
ejpam-6411	324	59	)	)	PUNCT
ejpam-6411	324	60	1−((n1+n3)θ+(n2+n4)ϖ	1−((n1+n3)θ+(n2+n4)ϖ	NUM
ejpam-6411	324	61	)	)	PUNCT
ejpam-6411	324	62	.	.	PUNCT
ejpam-6411	325	1	thus	thus	ADV
ejpam-6411	325	2	we	we	PRON
ejpam-6411	325	3	obtain	obtain	VERB
ejpam-6411	325	4	the	the	DET
ejpam-6411	325	5	hyers	hyers	PROPN
ejpam-6411	325	6	-	-	PUNCT
ejpam-6411	325	7	ulam	ulam	ADJ
ejpam-6411	325	8	stability	stability	NOUN
ejpam-6411	325	9	condition	condition	NOUN
ejpam-6411	325	10	.	.	PUNCT
ejpam-6411	326	1	in	in	ADP
ejpam-6411	326	2	summary	summary	NOUN
ejpam-6411	326	3	,	,	PUNCT
ejpam-6411	326	4	the	the	DET
ejpam-6411	326	5	hyers	hyers	PROPN
ejpam-6411	326	6	-	-	PUNCT
ejpam-6411	326	7	ulam	ulam	PROPN
ejpam-6411	326	8	stability	stability	NOUN
ejpam-6411	326	9	condition	condition	NOUN
ejpam-6411	326	10	for	for	ADP
ejpam-6411	326	11	the	the	DET
ejpam-6411	326	12	coupled	couple	VERB
ejpam-6411	326	13	fractional	fractional	ADJ
ejpam-6411	326	14	system	system	NOUN
ejpam-6411	326	15	defined	define	VERB
ejpam-6411	326	16	in	in	ADP
ejpam-6411	326	17	e.(1	e.(1	PROPN
ejpam-6411	326	18	)	)	PUNCT
ejpam-6411	326	19	is	be	AUX
ejpam-6411	326	20	obtained	obtain	VERB
ejpam-6411	326	21	by	by	ADP
ejpam-6411	326	22	proving	prove	VERB
ejpam-6411	326	23	lemma	lemma	PROPN
ejpam-6411	326	24	4.2	4.2	NUM
ejpam-6411	326	25	5	5	NUM
ejpam-6411	326	26	.	.	PUNCT
ejpam-6411	327	1	numerical	numerical	PROPN
ejpam-6411	327	2	examples	example	NOUN
ejpam-6411	327	3	example	example	NOUN
ejpam-6411	327	4	1	1	NUM
ejpam-6411	327	5	:	:	PUNCT
ejpam-6411	327	6	examine	examine	VERB
ejpam-6411	327	7	the	the	DET
ejpam-6411	327	8	following	following	ADJ
ejpam-6411	327	9	coupled	couple	VERB
ejpam-6411	327	10	system	system	NOUN
ejpam-6411	327	11	of	of	ADP
ejpam-6411	327	12	fdes	fde	NOUN
ejpam-6411	327	13	given	give	VERB
ejpam-6411	327	14	as	as	PUNCT
ejpam-6411	327	15	cd3/2υ	cd3/2υ	PROPN
ejpam-6411	327	16	(	(	PUNCT
ejpam-6411	327	17	τ	τ	NOUN
ejpam-6411	327	18	)	)	PUNCT
ejpam-6411	327	19	=	=	SYM
ejpam-6411	327	20	1	1	NUM
ejpam-6411	327	21	6π	6π	NOUN
ejpam-6411	327	22	√	√	NOUN
ejpam-6411	327	23	81+τ2	81+τ2	NUM
ejpam-6411	327	24	(	(	PUNCT
ejpam-6411	327	25	|υ(τ)|	|υ(τ)|	PROPN
ejpam-6411	327	26	3+|υ(τ)|	3+|υ(τ)|	NUM
ejpam-6411	327	27	+	+	CCONJ
ejpam-6411	328	1	|ω(τ)|	|ω(τ)|	PROPN
ejpam-6411	328	2	5+|υ(τ)|	5+|υ(τ)|	NUM
ejpam-6411	328	3	)	)	PUNCT
ejpam-6411	328	4	,	,	PUNCT
ejpam-6411	328	5	cd7/4ω	cd7/4ω	NOUN
ejpam-6411	328	6	(	(	PUNCT
ejpam-6411	328	7	τ	τ	X
ejpam-6411	328	8	)	)	PUNCT
ejpam-6411	328	9	=	=	SYM
ejpam-6411	328	10	1	1	NUM
ejpam-6411	328	11	12π	12π	NOUN
ejpam-6411	328	12	√	√	PROPN
ejpam-6411	328	13	64+τ2	64+τ2	PROPN
ejpam-6411	328	14	(	(	PUNCT
ejpam-6411	328	15	sin	sin	NOUN
ejpam-6411	328	16	(	(	PUNCT
ejpam-6411	328	17	υ	υ	NOUN
ejpam-6411	328	18	(	(	PUNCT
ejpam-6411	328	19	τ	τ	PROPN
ejpam-6411	328	20	)	)	PUNCT
ejpam-6411	328	21	)	)	PUNCT
ejpam-6411	329	1	+	+	CCONJ
ejpam-6411	329	2	sin	sin	NOUN
ejpam-6411	329	3	(	(	PUNCT
ejpam-6411	329	4	ω	ω	PROPN
ejpam-6411	329	5	(	(	PUNCT
ejpam-6411	329	6	τ	τ	PROPN
ejpam-6411	329	7	)	)	PUNCT
ejpam-6411	329	8	)	)	PUNCT
ejpam-6411	329	9	)	)	PUNCT
ejpam-6411	329	10	,	,	PUNCT
ejpam-6411	329	11	∫	∫	PROPN
ejpam-6411	329	12	1	1	NUM
ejpam-6411	329	13	0	0	NUM
ejpam-6411	329	14	υ	υ	NOUN
ejpam-6411	329	15	′	′	NUM
ejpam-6411	329	16	(	(	PUNCT
ejpam-6411	329	17	s	s	X
ejpam-6411	329	18	)	)	PUNCT
ejpam-6411	329	19	ds	ds	NOUN
ejpam-6411	329	20	=	=	SYM
ejpam-6411	329	21	2ω′	2ω′	NUM
ejpam-6411	329	22	(	(	PUNCT
ejpam-6411	329	23	1	1	NUM
ejpam-6411	329	24	)	)	PUNCT
ejpam-6411	329	25	,	,	PUNCT
ejpam-6411	329	26	∫	∫	PROPN
ejpam-6411	329	27	1	1	NUM
ejpam-6411	329	28	0	0	NUM
ejpam-6411	329	29	ω	ω	NUM
ejpam-6411	329	30	′(s)ds	′(s)ds	NOUN
ejpam-6411	329	31	=	=	SYM
ejpam-6411	329	32	−υ′	−υ′	PROPN
ejpam-6411	329	33	(	(	PUNCT
ejpam-6411	329	34	1/2	1/2	NUM
ejpam-6411	329	35	)	)	PUNCT
ejpam-6411	329	36	,	,	PUNCT
ejpam-6411	329	37	υ	υ	PROPN
ejpam-6411	329	38	(	(	PUNCT
ejpam-6411	329	39	0	0	NUM
ejpam-6411	329	40	)	)	PUNCT
ejpam-6411	329	41	=	=	SYM
ejpam-6411	329	42	0	0	NUM
ejpam-6411	329	43	,	,	PUNCT
ejpam-6411	329	44	ω	ω	X
ejpam-6411	329	45	(	(	PUNCT
ejpam-6411	329	46	0	0	NUM
ejpam-6411	329	47	)	)	PUNCT
ejpam-6411	329	48	=	=	SYM
ejpam-6411	329	49	0	0	NUM
ejpam-6411	329	50	,	,	PUNCT
ejpam-6411	329	51	(	(	PUNCT
ejpam-6411	329	52	23	23	NUM
ejpam-6411	329	53	)	)	PUNCT
ejpam-6411	329	54	where	where	SCONJ
ejpam-6411	329	55	α	α	NOUN
ejpam-6411	329	56	=	=	NOUN
ejpam-6411	329	57	3	3	NUM
ejpam-6411	329	58	2	2	NUM
ejpam-6411	329	59	,	,	PUNCT
ejpam-6411	329	60	β	β	X
ejpam-6411	329	61	=	=	NOUN
ejpam-6411	329	62	7	7	NUM
ejpam-6411	329	63	4	4	NUM
ejpam-6411	329	64	,	,	PUNCT
ejpam-6411	329	65	h	h	NOUN
ejpam-6411	329	66	=	=	SYM
ejpam-6411	329	67	1	1	NUM
ejpam-6411	329	68	,	,	PUNCT
ejpam-6411	329	69	ζ	ζ	NOUN
ejpam-6411	329	70	=	=	SYM
ejpam-6411	329	71	2	2	NUM
ejpam-6411	329	72	,	,	PUNCT
ejpam-6411	329	73	η	η	NOUN
ejpam-6411	329	74	=	=	SYM
ejpam-6411	329	75	−1	−1	PROPN
ejpam-6411	329	76	,	,	PUNCT
ejpam-6411	329	77	ρ	ρ	PROPN
ejpam-6411	329	78	=	=	SYM
ejpam-6411	329	79	1	1	NUM
ejpam-6411	329	80	2	2	NUM
ejpam-6411	329	81	,	,	PUNCT
ejpam-6411	329	82	µ	µ	NOUN
ejpam-6411	329	83	=	=	SYM
ejpam-6411	329	84	1	1	NUM
ejpam-6411	329	85	.	.	PUNCT
ejpam-6411	329	86	using	use	VERB
ejpam-6411	329	87	the	the	DET
ejpam-6411	329	88	given	give	VERB
ejpam-6411	329	89	data	datum	NOUN
ejpam-6411	329	90	,	,	PUNCT
ejpam-6411	329	91	we	we	PRON
ejpam-6411	329	92	find	find	VERB
ejpam-6411	329	93	that	that	SCONJ
ejpam-6411	329	94	λ=	λ=	VERB
ejpam-6411	329	95	3,n1=	3,n1=	NUM
ejpam-6411	329	96	1.269,n2=	1.269,n2=	NUM
ejpam-6411	329	97	1.1398,n3=	1.1398,n3=	NUM
ejpam-6411	329	98	0.5167,n4=	0.5167,n4=	NOUN
ejpam-6411	330	1	1.554,θ=	1.554,θ=	NUM
ejpam-6411	330	2	1	1	NUM
ejpam-6411	330	3	54π	54π	NOUN
ejpam-6411	330	4	,	,	PUNCT
ejpam-6411	330	5	ϖ=	ϖ=	NOUN
ejpam-6411	330	6	1	1	NUM
ejpam-6411	330	7	48π	48π	X
ejpam-6411	330	8	.	.	PUNCT
ejpam-6411	331	1	it	it	PRON
ejpam-6411	331	2	’s	’	VERB
ejpam-6411	331	3	clear	clear	ADJ
ejpam-6411	331	4	that	that	SCONJ
ejpam-6411	331	5	u	u	NOUN
ejpam-6411	331	6	,	,	PUNCT
ejpam-6411	331	7	h	h	PROPN
ejpam-6411	331	8	are	be	AUX
ejpam-6411	331	9	jointly	jointly	ADV
ejpam-6411	331	10	continuous	continuous	ADJ
ejpam-6411	331	11	functions	function	NOUN
ejpam-6411	331	12	and	and	CCONJ
ejpam-6411	331	13	θ(n1+n3)+ϖ	θ(n1+n3)+ϖ	NOUN
ejpam-6411	331	14	(	(	PUNCT
ejpam-6411	331	15	n2+n4	n2+n4	NOUN
ejpam-6411	331	16	)	)	PUNCT
ejpam-6411	331	17	<	<	X
ejpam-6411	331	18	1	1	NUM
ejpam-6411	331	19	,	,	PUNCT
ejpam-6411	331	20	such	such	ADJ
ejpam-6411	331	21	that	that	SCONJ
ejpam-6411	331	22	1	1	NUM
ejpam-6411	331	23	54π	54π	NOUN
ejpam-6411	331	24	(	(	PUNCT
ejpam-6411	331	25	1.269	1.269	NUM
ejpam-6411	331	26	+	+	NUM
ejpam-6411	331	27	0.5167)+	0.5167)+	NOUN
ejpam-6411	331	28	1	1	NUM
ejpam-6411	331	29	48π	48π	X
ejpam-6411	331	30	(	(	PUNCT
ejpam-6411	331	31	1.1398	1.1398	NUM
ejpam-6411	331	32	+	+	SYM
ejpam-6411	331	33	1.554)=	1.554)=	NUM
ejpam-6411	331	34	0.0283	0.0283	NUM
ejpam-6411	331	35	<	<	X
ejpam-6411	331	36	1	1	NUM
ejpam-6411	331	37	.	.	PUNCT
ejpam-6411	332	1	s.	s.	PROPN
ejpam-6411	332	2	momani	momani	PROPN
ejpam-6411	332	3	et	et	PROPN
ejpam-6411	332	4	al	al	PROPN
ejpam-6411	332	5	.	.	PUNCT
ejpam-6411	332	6	/	/	SYM
ejpam-6411	332	7	eur	eur	PROPN
ejpam-6411	332	8	.	.	PUNCT
ejpam-6411	333	1	j.	j.	PROPN
ejpam-6411	333	2	pure	pure	PROPN
ejpam-6411	333	3	appl	appl	PROPN
ejpam-6411	333	4	.	.	PROPN
ejpam-6411	333	5	math	math	PROPN
ejpam-6411	333	6	,	,	PUNCT
ejpam-6411	333	7	18	18	NUM
ejpam-6411	333	8	(	(	PUNCT
ejpam-6411	333	9	4	4	NUM
ejpam-6411	333	10	)	)	PUNCT
ejpam-6411	333	11	(	(	PUNCT
ejpam-6411	333	12	2025	2025	NUM
ejpam-6411	333	13	)	)	PUNCT
ejpam-6411	333	14	,	,	PUNCT
ejpam-6411	333	15	6411	6411	NUM
ejpam-6411	333	16	14	14	NUM
ejpam-6411	333	17	of	of	ADP
ejpam-6411	333	18	16	16	NUM
ejpam-6411	333	19	therefore	therefore	ADV
ejpam-6411	333	20	,	,	PUNCT
ejpam-6411	333	21	all	all	DET
ejpam-6411	333	22	conditions	condition	NOUN
ejpam-6411	333	23	of	of	ADP
ejpam-6411	333	24	theorem	theorem	ADJ
ejpam-6411	333	25	3.1	3.1	NUM
ejpam-6411	333	26	are	be	AUX
ejpam-6411	333	27	met	meet	VERB
ejpam-6411	333	28	,	,	PUNCT
ejpam-6411	333	29	and	and	CCONJ
ejpam-6411	333	30	as	as	ADP
ejpam-6411	333	31	a	a	DET
ejpam-6411	333	32	result	result	NOUN
ejpam-6411	333	33	of	of	ADP
ejpam-6411	333	34	e.(23	e.(23	NOUN
ejpam-6411	333	35	)	)	PUNCT
ejpam-6411	333	36	it	it	PRON
ejpam-6411	333	37	has	have	VERB
ejpam-6411	333	38	a	a	DET
ejpam-6411	333	39	unique	unique	ADJ
ejpam-6411	333	40	solution	solution	NOUN
ejpam-6411	333	41	is	be	AUX
ejpam-6411	333	42	in	in	ADP
ejpam-6411	333	43	the	the	DET
ejpam-6411	333	44	interval	interval	NOUN
ejpam-6411	333	45	[	[	X
ejpam-6411	333	46	0,1	0,1	NUM
ejpam-6411	333	47	]	]	PUNCT
ejpam-6411	333	48	.	.	PUNCT
ejpam-6411	334	1	example	example	NOUN
ejpam-6411	334	2	2	2	NUM
ejpam-6411	334	3	:	:	PUNCT
ejpam-6411	334	4	consider	consider	VERB
ejpam-6411	334	5	the	the	DET
ejpam-6411	334	6	following	follow	VERB
ejpam-6411	334	7	coupled	couple	VERB
ejpam-6411	334	8	system	system	NOUN
ejpam-6411	334	9	of	of	ADP
ejpam-6411	334	10	fractional	fractional	ADJ
ejpam-6411	334	11	des	des	PROPN
ejpam-6411	334	12	cd5/3υ	cd5/3υ	PROPN
ejpam-6411	334	13	(	(	PUNCT
ejpam-6411	334	14	τ	τ	X
ejpam-6411	334	15	)	)	PUNCT
ejpam-6411	334	16	=	=	SYM
ejpam-6411	334	17	1	1	NUM
ejpam-6411	334	18	80+τ4	80+τ4	NUM
ejpam-6411	334	19	+	+	NUM
ejpam-6411	334	20	|υ(τ)|	|υ(τ)|	PROPN
ejpam-6411	334	21	120(1+ω2(τ	120(1+ω2(τ	NUM
ejpam-6411	334	22	)	)	PUNCT
ejpam-6411	334	23	)	)	PUNCT
ejpam-6411	335	1	+	+	CCONJ
ejpam-6411	335	2	1	1	NUM
ejpam-6411	335	3	4	4	NUM
ejpam-6411	335	4	√	√	NUM
ejpam-6411	335	5	2500+τ2	2500+τ2	NUM
ejpam-6411	335	6	e−3τcos	e−3τcos	X
ejpam-6411	335	7	(	(	PUNCT
ejpam-6411	335	8	ω	ω	PROPN
ejpam-6411	335	9	(	(	PUNCT
ejpam-6411	335	10	τ	τ	PROPN
ejpam-6411	335	11	)	)	PUNCT
ejpam-6411	335	12	)	)	PUNCT
ejpam-6411	335	13	,	,	PUNCT
ejpam-6411	335	14	τ	τ	PROPN
ejpam-6411	335	15	∈	∈	PROPN
ejpam-6411	336	1	[	[	X
ejpam-6411	336	2	0	0	NUM
ejpam-6411	336	3	,	,	PUNCT
ejpam-6411	336	4	1	1	NUM
ejpam-6411	336	5	]	]	PUNCT
ejpam-6411	336	6	cd	cd	NOUN
ejpam-6411	336	7	6	6	NUM
ejpam-6411	336	8	5ω	5ω	NOUN
ejpam-6411	336	9	(	(	PUNCT
ejpam-6411	336	10	τ	τ	X
ejpam-6411	336	11	)	)	PUNCT
ejpam-6411	336	12	=	=	SYM
ejpam-6411	336	13	1√	1√	PROPN
ejpam-6411	336	14	16+τ2	16+τ2	NUM
ejpam-6411	336	15	cosτ	cosτ	NOUN
ejpam-6411	336	16	+	+	CCONJ
ejpam-6411	336	17	1	1	NUM
ejpam-6411	336	18	150e	150e	PROPN
ejpam-6411	336	19	−3τsin	−3τsin	NOUN
ejpam-6411	336	20	(	(	PUNCT
ejpam-6411	336	21	ω	ω	PROPN
ejpam-6411	336	22	(	(	PUNCT
ejpam-6411	336	23	τ	τ	PROPN
ejpam-6411	336	24	)	)	PUNCT
ejpam-6411	336	25	)	)	PUNCT
ejpam-6411	337	1	+	+	CCONJ
ejpam-6411	337	2	1	1	NUM
ejpam-6411	337	3	180υ	180υ	NOUN
ejpam-6411	337	4	(	(	PUNCT
ejpam-6411	337	5	τ	τ	X
ejpam-6411	337	6	)	)	PUNCT
ejpam-6411	337	7	,	,	PUNCT
ejpam-6411	337	8	τ	τ	PROPN
ejpam-6411	337	9	∈	∈	PROPN
ejpam-6411	338	1	[	[	X
ejpam-6411	338	2	0	0	NUM
ejpam-6411	338	3	,	,	PUNCT
ejpam-6411	338	4	1]∫	1]∫	NOUN
ejpam-6411	338	5	1	1	NUM
ejpam-6411	338	6	0	0	NUM
ejpam-6411	338	7	υ	υ	DET
ejpam-6411	338	8	′(s)ds	′(s)ds	PROPN
ejpam-6411	338	9	=	=	SYM
ejpam-6411	338	10	−3ω′	−3ω′	PROPN
ejpam-6411	338	11	(	(	PUNCT
ejpam-6411	338	12	1/3	1/3	NUM
ejpam-6411	338	13	)	)	PUNCT
ejpam-6411	338	14	,	,	PUNCT
ejpam-6411	338	15	∫	∫	PROPN
ejpam-6411	338	16	1	1	NUM
ejpam-6411	338	17	0	0	NUM
ejpam-6411	338	18	ω	ω	NUM
ejpam-6411	338	19	′(s)ds	′(s)ds	NOUN
ejpam-6411	338	20	=	=	PUNCT
ejpam-6411	338	21	υ′	υ′	X
ejpam-6411	338	22	(	(	PUNCT
ejpam-6411	338	23	1	1	NUM
ejpam-6411	338	24	)	)	PUNCT
ejpam-6411	338	25	,	,	PUNCT
ejpam-6411	338	26	υ	υ	PROPN
ejpam-6411	338	27	(	(	PUNCT
ejpam-6411	338	28	0	0	NUM
ejpam-6411	338	29	)	)	PUNCT
ejpam-6411	338	30	=	=	SYM
ejpam-6411	338	31	0	0	NUM
ejpam-6411	338	32	,	,	PUNCT
ejpam-6411	338	33	ω	ω	X
ejpam-6411	338	34	(	(	PUNCT
ejpam-6411	338	35	0	0	NUM
ejpam-6411	338	36	)	)	PUNCT
ejpam-6411	338	37	=	=	SYM
ejpam-6411	338	38	0	0	NUM
ejpam-6411	338	39	,	,	PUNCT
ejpam-6411	338	40	(	(	PUNCT
ejpam-6411	338	41	24	24	NUM
ejpam-6411	338	42	)	)	PUNCT
ejpam-6411	338	43	where	where	SCONJ
ejpam-6411	338	44	α	α	NOUN
ejpam-6411	338	45	=	=	SYM
ejpam-6411	338	46	5	5	NUM
ejpam-6411	338	47	3	3	NUM
ejpam-6411	338	48	,	,	PUNCT
ejpam-6411	338	49	β	β	X
ejpam-6411	338	50	=	=	NOUN
ejpam-6411	338	51	6	6	NUM
ejpam-6411	338	52	5	5	NUM
ejpam-6411	338	53	,	,	PUNCT
ejpam-6411	338	54	h	h	NOUN
ejpam-6411	338	55	=	=	SYM
ejpam-6411	338	56	1	1	NUM
ejpam-6411	338	57	,	,	PUNCT
ejpam-6411	338	58	ζ	ζ	NOUN
ejpam-6411	338	59	=	=	SYM
ejpam-6411	338	60	−3	−3	PROPN
ejpam-6411	338	61	,	,	PUNCT
ejpam-6411	338	62	η	η	PROPN
ejpam-6411	338	63	=	=	PROPN
ejpam-6411	338	64	1	1	NUM
ejpam-6411	338	65	,	,	PUNCT
ejpam-6411	338	66	ρ	ρ	NOUN
ejpam-6411	338	67	=	=	SYM
ejpam-6411	338	68	1	1	NUM
ejpam-6411	338	69	,	,	PUNCT
ejpam-6411	338	70	µ	µ	X
ejpam-6411	338	71	=	=	SYM
ejpam-6411	338	72	1/3	1/3	NUM
ejpam-6411	338	73	.	.	PUNCT
ejpam-6411	339	1	using	use	VERB
ejpam-6411	339	2	the	the	DET
ejpam-6411	339	3	given	give	VERB
ejpam-6411	339	4	data	datum	NOUN
ejpam-6411	339	5	,	,	PUNCT
ejpam-6411	339	6	we	we	PRON
ejpam-6411	339	7	find	find	VERB
ejpam-6411	339	8	that	that	SCONJ
ejpam-6411	339	9	λ=	λ=	VERB
ejpam-6411	339	10	3,n1=	3,n1=	NUM
ejpam-6411	339	11	1.269,n2=	1.269,n2=	NUM
ejpam-6411	339	12	1.1398,n3=	1.1398,n3=	NUM
ejpam-6411	339	13	0.5167,n4=	0.5167,n4=	NOUN
ejpam-6411	340	1	1.554,θ=	1.554,θ=	NUM
ejpam-6411	340	2	1	1	NUM
ejpam-6411	340	3	54π	54π	NOUN
ejpam-6411	340	4	,	,	PUNCT
ejpam-6411	340	5	ϖ=	ϖ=	NOUN
ejpam-6411	340	6	1	1	NUM
ejpam-6411	340	7	48π	48π	X
ejpam-6411	340	8	.	.	PUNCT
ejpam-6411	341	1	it	it	PRON
ejpam-6411	341	2	is	be	AUX
ejpam-6411	341	3	clear	clear	ADJ
ejpam-6411	341	4	that	that	SCONJ
ejpam-6411	341	5	|u	|u	ADJ
ejpam-6411	341	6	(	(	PUNCT
ejpam-6411	341	7	τ	τ	PROPN
ejpam-6411	341	8	,	,	PUNCT
ejpam-6411	341	9	υ1	υ1	PROPN
ejpam-6411	341	10	,	,	PUNCT
ejpam-6411	341	11	υ2)|	υ2)|	PROPN
ejpam-6411	341	12	≤	≤	PROPN
ejpam-6411	341	13	1	1	NUM
ejpam-6411	341	14	80	80	NUM
ejpam-6411	341	15	+	+	NUM
ejpam-6411	341	16	1	1	NUM
ejpam-6411	341	17	120	120	NUM
ejpam-6411	341	18	∥υ∥+	∥υ∥+	NOUN
ejpam-6411	341	19	1	1	NUM
ejpam-6411	341	20	200	200	NUM
ejpam-6411	341	21	∥ω∥	∥ω∥	NUM
ejpam-6411	341	22	,	,	PUNCT
ejpam-6411	341	23	and	and	CCONJ
ejpam-6411	341	24	|h	|h	X
ejpam-6411	341	25	(	(	PUNCT
ejpam-6411	341	26	τ	τ	PROPN
ejpam-6411	341	27	,	,	PUNCT
ejpam-6411	341	28	υ1	υ1	PROPN
ejpam-6411	341	29	,	,	PUNCT
ejpam-6411	341	30	υ2)|	υ2)|	PROPN
ejpam-6411	341	31	≤	≤	ADJ
ejpam-6411	341	32	1	1	NUM
ejpam-6411	341	33	4	4	NUM
ejpam-6411	341	34	+	+	SYM
ejpam-6411	341	35	1	1	NUM
ejpam-6411	341	36	180	180	NUM
ejpam-6411	341	37	∥υ∥+	∥υ∥+	NOUN
ejpam-6411	341	38	1	1	NUM
ejpam-6411	341	39	150	150	NUM
ejpam-6411	341	40	∥ω∥	∥ω∥	NOUN
ejpam-6411	341	41	.	.	PUNCT
ejpam-6411	342	1	thus	thus	ADV
ejpam-6411	342	2	,	,	PUNCT
ejpam-6411	342	3	ψ0	ψ0	NOUN
ejpam-6411	342	4	=	=	SYM
ejpam-6411	342	5	1	1	NUM
ejpam-6411	342	6	80	80	NUM
ejpam-6411	342	7	,	,	PUNCT
ejpam-6411	342	8	ψ1	ψ1	NOUN
ejpam-6411	342	9	=	=	SYM
ejpam-6411	342	10	1	1	NUM
ejpam-6411	342	11	120	120	NUM
ejpam-6411	342	12	,	,	PUNCT
ejpam-6411	342	13	ψ2	ψ2	NOUN
ejpam-6411	342	14	=	=	SYM
ejpam-6411	342	15	1	1	NUM
ejpam-6411	342	16	200	200	NUM
ejpam-6411	342	17	,	,	PUNCT
ejpam-6411	342	18	ϕ0	ϕ0	NOUN
ejpam-6411	342	19	=	=	NOUN
ejpam-6411	342	20	1	1	NUM
ejpam-6411	342	21	4	4	NUM
ejpam-6411	342	22	,	,	PUNCT
ejpam-6411	342	23	ϕ1	ϕ1	NOUN
ejpam-6411	342	24	=	=	SYM
ejpam-6411	342	25	1	1	NUM
ejpam-6411	342	26	180	180	NUM
ejpam-6411	342	27	,	,	PUNCT
ejpam-6411	342	28	ϕ2	ϕ2	ADV
ejpam-6411	342	29	=	=	SYM
ejpam-6411	342	30	1	1	NUM
ejpam-6411	342	31	150	150	NUM
ejpam-6411	342	32	.	.	PUNCT
ejpam-6411	343	1	we	we	PRON
ejpam-6411	343	2	find	find	VERB
ejpam-6411	343	3	(	(	PUNCT
ejpam-6411	343	4	n1+n3)ψ1+(n2+n4)ϕ1=	n1+n3)ψ1+(n2+n4)ϕ1=	PROPN
ejpam-6411	343	5	0.0298	0.0298	NUM
ejpam-6411	343	6	<	<	X
ejpam-6411	343	7	1	1	NUM
ejpam-6411	343	8	and	and	CCONJ
ejpam-6411	343	9	(	(	PUNCT
ejpam-6411	343	10	n1+n3)ψ2+(n2+n4)ϕ2=	n1+n3)ψ2+(n2+n4)ϕ2=	NOUN
ejpam-6411	343	11	0.0269	0.0269	X
ejpam-6411	343	12	<	<	X
ejpam-6411	343	13	1	1	NUM
ejpam-6411	343	14	.	.	PUNCT
ejpam-6411	343	15	therefore	therefore	ADV
ejpam-6411	343	16	,	,	PUNCT
ejpam-6411	343	17	according	accord	VERB
ejpam-6411	343	18	to	to	ADP
ejpam-6411	343	19	theorem	theorem	ADJ
ejpam-6411	343	20	3.3	3.3	NUM
ejpam-6411	343	21	,	,	PUNCT
ejpam-6411	343	22	e.(24	e.(24	PROPN
ejpam-6411	343	23	)	)	PUNCT
ejpam-6411	343	24	has	have	VERB
ejpam-6411	343	25	at	at	ADV
ejpam-6411	343	26	least	least	ADV
ejpam-6411	343	27	one	one	NUM
ejpam-6411	343	28	solution	solution	NOUN
ejpam-6411	343	29	in	in	ADP
ejpam-6411	343	30	the	the	DET
ejpam-6411	343	31	interval	interval	NOUN
ejpam-6411	343	32	[	[	X
ejpam-6411	343	33	0	0	NUM
ejpam-6411	343	34	,	,	PUNCT
ejpam-6411	343	35	1	1	NUM
ejpam-6411	343	36	]	]	PUNCT
ejpam-6411	343	37	.	.	PUNCT
ejpam-6411	344	1	6	6	X
ejpam-6411	344	2	.	.	X
ejpam-6411	344	3	conclusion	conclusion	NOUN
ejpam-6411	344	4	this	this	DET
ejpam-6411	344	5	article	article	NOUN
ejpam-6411	344	6	discussed	discuss	VERB
ejpam-6411	344	7	existence	existence	NOUN
ejpam-6411	344	8	,	,	PUNCT
ejpam-6411	344	9	uniqueness	uniqueness	NOUN
ejpam-6411	344	10	,	,	PUNCT
ejpam-6411	344	11	and	and	CCONJ
ejpam-6411	344	12	stability	stability	NOUN
ejpam-6411	344	13	of	of	ADP
ejpam-6411	344	14	a	a	DET
ejpam-6411	344	15	coupled	couple	VERB
ejpam-6411	344	16	system	system	NOUN
ejpam-6411	344	17	of	of	ADP
ejpam-6411	344	18	fdes	fde	NOUN
ejpam-6411	344	19	with	with	ADP
ejpam-6411	344	20	bcs	bc	NOUN
ejpam-6411	344	21	that	that	PRON
ejpam-6411	344	22	are	be	AUX
ejpam-6411	344	23	two	two	NUM
ejpam-6411	344	24	point	point	NOUN
ejpam-6411	344	25	integral	integral	ADJ
ejpam-6411	344	26	coupled	couple	VERB
ejpam-6411	344	27	.	.	PUNCT
ejpam-6411	345	1	the	the	DET
ejpam-6411	345	2	fixed	fix	VERB
ejpam-6411	345	3	-	-	PUNCT
ejpam-6411	345	4	point	point	NOUN
ejpam-6411	345	5	principle	principle	NOUN
ejpam-6411	345	6	is	be	AUX
ejpam-6411	345	7	used	use	VERB
ejpam-6411	345	8	to	to	PART
ejpam-6411	345	9	examine	examine	VERB
ejpam-6411	345	10	the	the	DET
ejpam-6411	345	11	uniqueness	uniqueness	NOUN
ejpam-6411	345	12	of	of	ADP
ejpam-6411	345	13	the	the	DET
ejpam-6411	345	14	solutions	solution	NOUN
ejpam-6411	345	15	of	of	ADP
ejpam-6411	345	16	the	the	DET
ejpam-6411	345	17	given	give	VERB
ejpam-6411	345	18	problem	problem	NOUN
ejpam-6411	345	19	.	.	PUNCT
ejpam-6411	346	1	then	then	ADV
ejpam-6411	346	2	,	,	PUNCT
ejpam-6411	346	3	the	the	DET
ejpam-6411	346	4	existence	existence	NOUN
ejpam-6411	346	5	of	of	ADP
ejpam-6411	346	6	solutions	solution	NOUN
ejpam-6411	346	7	for	for	ADP
ejpam-6411	346	8	the	the	DET
ejpam-6411	346	9	given	give	VERB
ejpam-6411	346	10	coupled	couple	VERB
ejpam-6411	346	11	system	system	NOUN
ejpam-6411	346	12	is	be	AUX
ejpam-6411	346	13	also	also	ADV
ejpam-6411	346	14	verified	verify	VERB
ejpam-6411	346	15	by	by	ADP
ejpam-6411	346	16	using	use	VERB
ejpam-6411	346	17	the	the	DET
ejpam-6411	346	18	leray	leray	ADJ
ejpam-6411	346	19	-	-	PUNCT
ejpam-6411	346	20	schauder	schauder	NOUN
ejpam-6411	346	21	’s	’s	PART
ejpam-6411	346	22	alternative	alternative	NOUN
ejpam-6411	346	23	.	.	PUNCT
ejpam-6411	347	1	moreover	moreover	ADV
ejpam-6411	347	2	,	,	PUNCT
ejpam-6411	347	3	the	the	DET
ejpam-6411	347	4	hyers	hyers	PROPN
ejpam-6411	347	5	-	-	PUNCT
ejpam-6411	347	6	ulam	ulam	PROPN
ejpam-6411	347	7	stability	stability	NOUN
ejpam-6411	347	8	has	have	AUX
ejpam-6411	347	9	been	be	AUX
ejpam-6411	347	10	employed	employ	VERB
ejpam-6411	347	11	to	to	PART
ejpam-6411	347	12	discuss	discuss	VERB
ejpam-6411	347	13	the	the	DET
ejpam-6411	347	14	proposed	propose	VERB
ejpam-6411	347	15	fractional	fractional	ADJ
ejpam-6411	347	16	coupled	couple	VERB
ejpam-6411	347	17	system	system	NOUN
ejpam-6411	347	18	’s	’s	PART
ejpam-6411	347	19	stability	stability	NOUN
ejpam-6411	347	20	.	.	PUNCT
ejpam-6411	348	1	furthermore	furthermore	ADV
ejpam-6411	348	2	,	,	PUNCT
ejpam-6411	348	3	two	two	NUM
ejpam-6411	348	4	numerical	numerical	ADJ
ejpam-6411	348	5	examples	example	NOUN
ejpam-6411	348	6	are	be	AUX
ejpam-6411	348	7	provided	provide	VERB
ejpam-6411	348	8	to	to	PART
ejpam-6411	348	9	demonstrate	demonstrate	VERB
ejpam-6411	348	10	our	our	PRON
ejpam-6411	348	11	results	result	NOUN
ejpam-6411	348	12	.	.	PUNCT
ejpam-6411	349	1	such	such	DET
ejpam-6411	349	2	an	an	DET
ejpam-6411	349	3	alternative	alternative	ADJ
ejpam-6411	349	4	stability	stability	NOUN
ejpam-6411	349	5	theories	theory	NOUN
ejpam-6411	349	6	and	and	CCONJ
ejpam-6411	349	7	availability	availability	NOUN
ejpam-6411	349	8	of	of	ADP
ejpam-6411	349	9	solutions	solution	NOUN
ejpam-6411	349	10	for	for	ADP
ejpam-6411	349	11	a	a	DET
ejpam-6411	349	12	nonlinear	nonlinear	ADJ
ejpam-6411	349	13	coupled	couple	VERB
ejpam-6411	349	14	system	system	NOUN
ejpam-6411	349	15	of	of	ADP
ejpam-6411	349	16	three	three	NUM
ejpam-6411	349	17	fdes	fde	NOUN
ejpam-6411	349	18	with	with	ADP
ejpam-6411	349	19	nonlocal	nonlocal	ADJ
ejpam-6411	349	20	coupled	couple	VERB
ejpam-6411	349	21	bcs	bc	NOUN
ejpam-6411	349	22	and	and	CCONJ
ejpam-6411	349	23	non	non	ADJ
ejpam-6411	349	24	-	-	ADJ
ejpam-6411	349	25	separated	separated	ADJ
ejpam-6411	349	26	bcs	bc	NOUN
ejpam-6411	349	27	will	will	AUX
ejpam-6411	349	28	be	be	AUX
ejpam-6411	349	29	our	our	PRON
ejpam-6411	349	30	further	further	ADJ
ejpam-6411	349	31	research	research	NOUN
ejpam-6411	349	32	.	.	PUNCT
ejpam-6411	350	1	author	author	NOUN
ejpam-6411	350	2	contributions	contribution	NOUN
ejpam-6411	350	3	:	:	PUNCT
ejpam-6411	350	4	conceptualization	conceptualization	NOUN
ejpam-6411	350	5	,	,	PUNCT
ejpam-6411	350	6	s.	s.	PROPN
ejpam-6411	350	7	momani	momani	PROPN
ejpam-6411	350	8	;	;	PUNCT
ejpam-6411	350	9	methodology	methodology	NOUN
ejpam-6411	350	10	,	,	PUNCT
ejpam-6411	350	11	s.	s.	PROPN
ejpam-6411	350	12	al	al	PROPN
ejpam-6411	350	13	-	-	PUNCT
ejpam-6411	350	14	omari	omari	PROPN
ejpam-6411	350	15	.	.	PUNCT
ejpam-6411	350	16	;	;	PUNCT
ejpam-6411	351	1	software	software	NOUN
ejpam-6411	351	2	,	,	PUNCT
ejpam-6411	351	3	m.	m.	NOUN
ejpam-6411	351	4	khandaqji	khandaqji	PROPN
ejpam-6411	351	5	,	,	PUNCT
ejpam-6411	351	6	validation	validation	NOUN
ejpam-6411	351	7	,	,	PUNCT
ejpam-6411	351	8	s.	s.	PROPN
ejpam-6411	351	9	al	al	PROPN
ejpam-6411	351	10	-	-	PUNCT
ejpam-6411	351	11	omari	omari	PROPN
ejpam-6411	351	12	,	,	PUNCT
ejpam-6411	351	13	m.	m.	NOUN
ejpam-6411	351	14	al	al	PROPN
ejpam-6411	351	15	-	-	PUNCT
ejpam-6411	351	16	smadi	smadi	NOUN
ejpam-6411	351	17	;	;	PUNCT
ejpam-6411	351	18	formal	formal	ADJ
ejpam-6411	351	19	analysis	analysis	NOUN
ejpam-6411	351	20	,	,	PUNCT
ejpam-6411	351	21	h.	h.	PROPN
ejpam-6411	351	22	zureigat	zureigat	PROPN
ejpam-6411	351	23	;	;	PUNCT
ejpam-6411	351	24	investigation	investigation	NOUN
ejpam-6411	351	25	,	,	PUNCT
ejpam-6411	351	26	h.	h.	PROPN
ejpam-6411	351	27	zureigat	zureigat	PROPN
ejpam-6411	351	28	;	;	PUNCT
ejpam-6411	351	29	writing	write	VERB
ejpam-6411	351	30	-	-	PUNCT
ejpam-6411	351	31	original	original	ADJ
ejpam-6411	351	32	draft	draft	NOUN
ejpam-6411	351	33	preparation	preparation	NOUN
ejpam-6411	351	34	,	,	PUNCT
ejpam-6411	351	35	m.	m.	NOUN
ejpam-6411	351	36	al	al	PROPN
ejpam-6411	351	37	-	-	PUNCT
ejpam-6411	351	38	smadi	smadi	NOUN
ejpam-6411	351	39	;	;	PUNCT
ejpam-6411	351	40	writing	write	VERB
ejpam-6411	351	41	-	-	PUNCT
ejpam-6411	351	42	review	review	NOUN
ejpam-6411	351	43	and	and	CCONJ
ejpam-6411	351	44	editing	editing	NOUN
ejpam-6411	351	45	,	,	PUNCT
ejpam-6411	351	46	m.	m.	NOUN
ejpam-6411	351	47	khandaqji	khandaqji	PROPN
ejpam-6411	351	48	;	;	PUNCT
ejpam-6411	351	49	visualization	visualization	NOUN
ejpam-6411	351	50	;	;	PUNCT
ejpam-6411	351	51	supervision	supervision	NOUN
ejpam-6411	351	52	,	,	PUNCT
ejpam-6411	351	53	s.	s.	PROPN
ejpam-6411	351	54	al	al	PROPN
ejpam-6411	351	55	-	-	PUNCT
ejpam-6411	351	56	omari	omari	PROPN
ejpam-6411	351	57	.	.	PUNCT
ejpam-6411	351	58	;	;	PUNCT
ejpam-6411	351	59	project	project	NOUN
ejpam-6411	351	60	administration	administration	NOUN
ejpam-6411	351	61	,	,	PUNCT
ejpam-6411	351	62	h.	h.	PROPN
ejpam-6411	351	63	zureigat	zureigat	PROPN
ejpam-6411	351	64	;	;	PUNCT
ejpam-6411	351	65	funding	funding	NOUN
ejpam-6411	351	66	acquisition	acquisition	NOUN
ejpam-6411	351	67	,	,	PUNCT
ejpam-6411	351	68	s.	s.	PROPN
ejpam-6411	351	69	momani	momani	PROPN
ejpam-6411	351	70	.	.	PUNCT
ejpam-6411	352	1	all	all	DET
ejpam-6411	352	2	authors	author	NOUN
ejpam-6411	352	3	have	have	AUX
ejpam-6411	352	4	read	read	VERB
ejpam-6411	352	5	and	and	CCONJ
ejpam-6411	352	6	agreed	agree	VERB
ejpam-6411	352	7	to	to	ADP
ejpam-6411	352	8	the	the	DET
ejpam-6411	352	9	published	publish	VERB
ejpam-6411	352	10	version	version	NOUN
ejpam-6411	352	11	of	of	ADP
ejpam-6411	352	12	the	the	DET
ejpam-6411	352	13	manuscript	manuscript	NOUN
ejpam-6411	352	14	.	.	PUNCT
ejpam-6411	353	1	data	datum	NOUN
ejpam-6411	353	2	availability	availability	NOUN
ejpam-6411	353	3	statement	statement	NOUN
ejpam-6411	353	4	:	:	PUNCT
ejpam-6411	353	5	data	datum	NOUN
ejpam-6411	353	6	sharing	sharing	NOUN
ejpam-6411	353	7	is	be	AUX
ejpam-6411	353	8	not	not	PART
ejpam-6411	353	9	applicable	applicable	ADJ
ejpam-6411	353	10	to	to	ADP
ejpam-6411	353	11	this	this	DET
ejpam-6411	353	12	article	article	NOUN
ejpam-6411	353	13	as	as	SCONJ
ejpam-6411	353	14	no	no	DET
ejpam-6411	353	15	new	new	ADJ
ejpam-6411	353	16	data	datum	NOUN
ejpam-6411	353	17	were	be	AUX
ejpam-6411	353	18	created	create	VERB
ejpam-6411	353	19	or	or	CCONJ
ejpam-6411	353	20	analyzed	analyze	VERB
ejpam-6411	353	21	in	in	ADP
ejpam-6411	353	22	this	this	DET
ejpam-6411	353	23	study	study	NOUN
ejpam-6411	353	24	.	.	PUNCT
ejpam-6411	354	1	conflicts	conflict	NOUN
ejpam-6411	354	2	of	of	ADP
ejpam-6411	354	3	interest	interest	NOUN
ejpam-6411	354	4	:	:	PUNCT
ejpam-6411	354	5	the	the	DET
ejpam-6411	354	6	authors	author	NOUN
ejpam-6411	354	7	declare	declare	VERB
ejpam-6411	354	8	that	that	SCONJ
ejpam-6411	354	9	they	they	PRON
ejpam-6411	354	10	have	have	VERB
ejpam-6411	354	11	no	no	DET
ejpam-6411	354	12	conflict	conflict	NOUN
ejpam-6411	354	13	of	of	ADP
ejpam-6411	354	14	interest	interest	NOUN
ejpam-6411	354	15	.	.	PUNCT
ejpam-6411	355	1	references	reference	NOUN
ejpam-6411	355	2	s.	s.	PROPN
ejpam-6411	355	3	momani	momani	PROPN
ejpam-6411	355	4	et	et	PROPN
ejpam-6411	355	5	al	al	PROPN
ejpam-6411	355	6	.	.	PUNCT
ejpam-6411	355	7	/	/	SYM
ejpam-6411	355	8	eur	eur	PROPN
ejpam-6411	355	9	.	.	PUNCT
ejpam-6411	356	1	j.	j.	PROPN
ejpam-6411	356	2	pure	pure	PROPN
ejpam-6411	356	3	appl	appl	PROPN
ejpam-6411	356	4	.	.	PROPN
ejpam-6411	356	5	math	math	PROPN
ejpam-6411	356	6	,	,	PUNCT
ejpam-6411	356	7	18	18	NUM
ejpam-6411	356	8	(	(	PUNCT
ejpam-6411	356	9	4	4	NUM
ejpam-6411	356	10	)	)	PUNCT
ejpam-6411	356	11	(	(	PUNCT
ejpam-6411	356	12	2025	2025	NUM
ejpam-6411	356	13	)	)	PUNCT
ejpam-6411	356	14	,	,	PUNCT
ejpam-6411	356	15	6411	6411	NUM
ejpam-6411	356	16	15	15	NUM
ejpam-6411	356	17	of	of	ADP
ejpam-6411	356	18	16	16	NUM
ejpam-6411	356	19	references	reference	NOUN
ejpam-6411	356	20	[	[	X
ejpam-6411	356	21	1	1	NUM
ejpam-6411	356	22	]	]	PUNCT
ejpam-6411	356	23	h.	h.	PROPN
ejpam-6411	356	24	sun	sun	PROPN
ejpam-6411	356	25	,	,	PUNCT
ejpam-6411	356	26	y.	y.	PROPN
ejpam-6411	356	27	zhang	zhang	PROPN
ejpam-6411	356	28	,	,	PUNCT
ejpam-6411	356	29	d.	d.	PROPN
ejpam-6411	356	30	baleanu	baleanu	PROPN
ejpam-6411	356	31	,	,	PUNCT
ejpam-6411	356	32	w.	w.	PROPN
ejpam-6411	356	33	chen	chen	PROPN
ejpam-6411	356	34	,	,	PUNCT
ejpam-6411	356	35	and	and	CCONJ
ejpam-6411	356	36	y.	y.	PROPN
ejpam-6411	356	37	chen	chen	PROPN
ejpam-6411	356	38	.	.	PUNCT
ejpam-6411	357	1	a	a	DET
ejpam-6411	357	2	new	new	ADJ
ejpam-6411	357	3	collection	collection	NOUN
ejpam-6411	357	4	of	of	ADP
ejpam-6411	357	5	real	real	ADJ
ejpam-6411	357	6	world	world	NOUN
ejpam-6411	357	7	applications	application	NOUN
ejpam-6411	357	8	of	of	ADP
ejpam-6411	357	9	fractional	fractional	ADJ
ejpam-6411	357	10	calculus	calculus	NOUN
ejpam-6411	357	11	in	in	ADP
ejpam-6411	357	12	science	science	NOUN
ejpam-6411	357	13	and	and	CCONJ
ejpam-6411	357	14	engineering	engineering	NOUN
ejpam-6411	357	15	.	.	PUNCT
ejpam-6411	358	1	communications	communication	NOUN
ejpam-6411	358	2	in	in	ADP
ejpam-6411	358	3	nonlinear	nonlinear	ADJ
ejpam-6411	358	4	science	science	NOUN
ejpam-6411	358	5	and	and	CCONJ
ejpam-6411	358	6	numerical	numerical	PROPN
ejpam-6411	358	7	simulation	simulation	PROPN
ejpam-6411	358	8	,	,	PUNCT
ejpam-6411	358	9	64:213–231	64:213–231	NUM
ejpam-6411	358	10	,	,	PUNCT
ejpam-6411	358	11	2018	2018	NUM
ejpam-6411	358	12	.	.	PUNCT
ejpam-6411	359	1	[	[	X
ejpam-6411	359	2	2	2	NUM
ejpam-6411	359	3	]	]	PUNCT
ejpam-6411	359	4	x.	x.	NOUN
ejpam-6411	359	5	zhang	zhang	PROPN
ejpam-6411	359	6	,	,	PUNCT
ejpam-6411	359	7	d.	d.	PROPN
ejpam-6411	359	8	boutat	boutat	PROPN
ejpam-6411	359	9	,	,	PUNCT
ejpam-6411	359	10	and	and	CCONJ
ejpam-6411	359	11	d.	d.	PROPN
ejpam-6411	359	12	liu	liu	PROPN
ejpam-6411	359	13	.	.	PUNCT
ejpam-6411	360	1	applications	application	NOUN
ejpam-6411	360	2	of	of	ADP
ejpam-6411	360	3	fractional	fractional	ADJ
ejpam-6411	360	4	operator	operator	NOUN
ejpam-6411	360	5	in	in	ADP
ejpam-6411	360	6	image	image	NOUN
ejpam-6411	360	7	processing	processing	NOUN
ejpam-6411	360	8	and	and	CCONJ
ejpam-6411	360	9	stability	stability	NOUN
ejpam-6411	360	10	of	of	ADP
ejpam-6411	360	11	control	control	NOUN
ejpam-6411	360	12	systems	system	NOUN
ejpam-6411	360	13	.	.	PUNCT
ejpam-6411	361	1	fractal	fractal	PROPN
ejpam-6411	361	2	and	and	CCONJ
ejpam-6411	361	3	fractional	fractional	ADJ
ejpam-6411	361	4	,	,	PUNCT
ejpam-6411	361	5	7(5):359	7(5):359	NUM
ejpam-6411	361	6	,	,	PUNCT
ejpam-6411	361	7	2023	2023	NUM
ejpam-6411	361	8	.	.	PUNCT
ejpam-6411	362	1	[	[	X
ejpam-6411	362	2	3	3	X
ejpam-6411	362	3	]	]	X
ejpam-6411	362	4	h.	h.	PROPN
ejpam-6411	362	5	khan	khan	PROPN
ejpam-6411	362	6	,	,	PUNCT
ejpam-6411	362	7	j.	j.	PROPN
ejpam-6411	362	8	alzabut	alzabut	PROPN
ejpam-6411	362	9	,	,	PUNCT
ejpam-6411	362	10	h.	h.	PROPN
ejpam-6411	362	11	gulzar	gulzar	PROPN
ejpam-6411	362	12	,	,	PUNCT
ejpam-6411	362	13	o.	o.	PROPN
ejpam-6411	362	14	tunç	tunç	PROPN
ejpam-6411	362	15	,	,	PUNCT
ejpam-6411	362	16	and	and	CCONJ
ejpam-6411	362	17	s.	s.	PROPN
ejpam-6411	362	18	pinelas	pinelas	PROPN
ejpam-6411	362	19	.	.	PUNCT
ejpam-6411	363	1	on	on	ADP
ejpam-6411	363	2	system	system	NOUN
ejpam-6411	363	3	of	of	ADP
ejpam-6411	363	4	variable	variable	ADJ
ejpam-6411	363	5	order	order	NOUN
ejpam-6411	363	6	nonlinear	nonlinear	ADJ
ejpam-6411	363	7	p	p	PROPN
ejpam-6411	363	8	-	-	PUNCT
ejpam-6411	363	9	laplacian	laplacian	ADJ
ejpam-6411	363	10	fdes	fde	NOUN
ejpam-6411	363	11	with	with	ADP
ejpam-6411	363	12	biological	biological	ADJ
ejpam-6411	363	13	application	application	NOUN
ejpam-6411	363	14	.	.	PUNCT
ejpam-6411	364	1	mathematics	mathematic	NOUN
ejpam-6411	364	2	,	,	PUNCT
ejpam-6411	364	3	11(8):1913	11(8):1913	NUM
ejpam-6411	364	4	,	,	PUNCT
ejpam-6411	364	5	2023	2023	NUM
ejpam-6411	364	6	.	.	PUNCT
ejpam-6411	365	1	[	[	X
ejpam-6411	365	2	4	4	X
ejpam-6411	365	3	]	]	PUNCT
ejpam-6411	365	4	k.	k.	PROPN
ejpam-6411	365	5	hattaf	hattaf	PROPN
ejpam-6411	365	6	.	.	PUNCT
ejpam-6411	366	1	a	a	DET
ejpam-6411	366	2	new	new	ADJ
ejpam-6411	366	3	mixed	mixed	ADJ
ejpam-6411	366	4	fractional	fractional	ADJ
ejpam-6411	366	5	derivative	derivative	NOUN
ejpam-6411	366	6	with	with	ADP
ejpam-6411	366	7	applications	application	NOUN
ejpam-6411	366	8	in	in	ADP
ejpam-6411	366	9	computational	computational	ADJ
ejpam-6411	366	10	biology	biology	NOUN
ejpam-6411	366	11	.	.	PUNCT
ejpam-6411	367	1	computation	computation	NOUN
ejpam-6411	367	2	,	,	PUNCT
ejpam-6411	367	3	12(1):7	12(1):7	PROPN
ejpam-6411	367	4	,	,	PUNCT
ejpam-6411	367	5	2024	2024	NUM
ejpam-6411	367	6	.	.	PUNCT
ejpam-6411	368	1	[	[	X
ejpam-6411	368	2	5	5	NUM
ejpam-6411	368	3	]	]	PUNCT
ejpam-6411	368	4	a.	a.	NOUN
ejpam-6411	368	5	a.	a.	NOUN
ejpam-6411	368	6	kilbas	kilbas	PROPN
ejpam-6411	368	7	,	,	PUNCT
ejpam-6411	368	8	h.	h.	PROPN
ejpam-6411	368	9	m.	m.	PROPN
ejpam-6411	368	10	srivastava	srivastava	PROPN
ejpam-6411	368	11	,	,	PUNCT
ejpam-6411	368	12	and	and	CCONJ
ejpam-6411	368	13	j.	j.	PROPN
ejpam-6411	368	14	j.	j.	PROPN
ejpam-6411	368	15	trujillo	trujillo	PROPN
ejpam-6411	368	16	.	.	PUNCT
ejpam-6411	368	17	theory	theory	NOUN
ejpam-6411	368	18	and	and	CCONJ
ejpam-6411	368	19	applications	application	NOUN
ejpam-6411	368	20	of	of	ADP
ejpam-6411	368	21	fdes	fde	NOUN
ejpam-6411	368	22	,	,	PUNCT
ejpam-6411	368	23	volume	volume	NOUN
ejpam-6411	368	24	204	204	NUM
ejpam-6411	368	25	.	.	PUNCT
ejpam-6411	369	1	elsevier	elsevier	NOUN
ejpam-6411	369	2	,	,	PUNCT
ejpam-6411	369	3	2006	2006	NUM
ejpam-6411	369	4	.	.	PUNCT
ejpam-6411	370	1	[	[	X
ejpam-6411	370	2	6	6	NUM
ejpam-6411	370	3	]	]	PUNCT
ejpam-6411	370	4	h.	h.	PROPN
ejpam-6411	370	5	zureigat	zureigat	PROPN
ejpam-6411	370	6	,	,	PUNCT
ejpam-6411	370	7	m.	m.	NOUN
ejpam-6411	370	8	al	al	PROPN
ejpam-6411	370	9	-	-	PUNCT
ejpam-6411	370	10	smadi	smadi	NOUN
ejpam-6411	370	11	,	,	PUNCT
ejpam-6411	370	12	a.	a.	PROPN
ejpam-6411	370	13	al	al	PROPN
ejpam-6411	370	14	-	-	PUNCT
ejpam-6411	370	15	khateeb	khateeb	PROPN
ejpam-6411	370	16	,	,	PUNCT
ejpam-6411	370	17	s.	s.	PROPN
ejpam-6411	370	18	al	al	PROPN
ejpam-6411	370	19	-	-	PUNCT
ejpam-6411	370	20	omari	omari	PROPN
ejpam-6411	370	21	,	,	PUNCT
ejpam-6411	370	22	and	and	CCONJ
ejpam-6411	370	23	s.	s.	PROPN
ejpam-6411	370	24	alhazmi	alhazmi	PROPN
ejpam-6411	370	25	.	.	PUNCT
ejpam-6411	371	1	numerical	numerical	ADJ
ejpam-6411	371	2	solution	solution	NOUN
ejpam-6411	371	3	for	for	ADP
ejpam-6411	371	4	fuzzy	fuzzy	ADJ
ejpam-6411	371	5	time	time	NOUN
ejpam-6411	371	6	-	-	PUNCT
ejpam-6411	371	7	fractional	fractional	ADJ
ejpam-6411	371	8	cancer	cancer	NOUN
ejpam-6411	371	9	tumor	tumor	NOUN
ejpam-6411	371	10	model	model	NOUN
ejpam-6411	371	11	with	with	ADP
ejpam-6411	371	12	a	a	DET
ejpam-6411	371	13	time	time	NOUN
ejpam-6411	371	14	-	-	PUNCT
ejpam-6411	371	15	dependent	dependent	ADJ
ejpam-6411	371	16	net	net	ADJ
ejpam-6411	371	17	killing	killing	NOUN
ejpam-6411	371	18	rate	rate	NOUN
ejpam-6411	371	19	of	of	ADP
ejpam-6411	371	20	cancer	cancer	NOUN
ejpam-6411	371	21	cells	cell	NOUN
ejpam-6411	371	22	.	.	PUNCT
ejpam-6411	372	1	international	international	ADJ
ejpam-6411	372	2	journal	journal	PROPN
ejpam-6411	372	3	of	of	ADP
ejpam-6411	372	4	environmental	environmental	ADJ
ejpam-6411	372	5	research	research	NOUN
ejpam-6411	372	6	and	and	CCONJ
ejpam-6411	372	7	public	public	ADJ
ejpam-6411	372	8	health	health	NOUN
ejpam-6411	372	9	,	,	PUNCT
ejpam-6411	372	10	20(4):3766	20(4):3766	NUM
ejpam-6411	372	11	,	,	PUNCT
ejpam-6411	372	12	2023	2023	NUM
ejpam-6411	372	13	.	.	PUNCT
ejpam-6411	373	1	[	[	X
ejpam-6411	373	2	7	7	NUM
ejpam-6411	373	3	]	]	X
ejpam-6411	373	4	i.	i.	NOUN
ejpam-6411	373	5	podlubny	podlubny	PROPN
ejpam-6411	373	6	.	.	PUNCT
ejpam-6411	374	1	fractional	fractional	PROPN
ejpam-6411	374	2	des	des	PROPN
ejpam-6411	374	3	:	:	PUNCT
ejpam-6411	374	4	an	an	DET
ejpam-6411	374	5	introduction	introduction	NOUN
ejpam-6411	374	6	to	to	ADP
ejpam-6411	374	7	fractional	fractional	ADJ
ejpam-6411	374	8	derivatives	derivative	NOUN
ejpam-6411	374	9	,	,	PUNCT
ejpam-6411	374	10	fractional	fractional	ADJ
ejpam-6411	374	11	des	des	PROPN
ejpam-6411	374	12	,	,	PUNCT
ejpam-6411	374	13	to	to	ADP
ejpam-6411	374	14	methods	method	NOUN
ejpam-6411	374	15	of	of	ADP
ejpam-6411	374	16	their	their	PRON
ejpam-6411	374	17	solution	solution	NOUN
ejpam-6411	374	18	and	and	CCONJ
ejpam-6411	374	19	some	some	PRON
ejpam-6411	374	20	of	of	ADP
ejpam-6411	374	21	their	their	PRON
ejpam-6411	374	22	applications	application	NOUN
ejpam-6411	374	23	.	.	PUNCT
ejpam-6411	375	1	elsevier	elsevier	NOUN
ejpam-6411	375	2	,	,	PUNCT
ejpam-6411	375	3	1998	1998	NUM
ejpam-6411	375	4	.	.	PUNCT
ejpam-6411	376	1	[	[	X
ejpam-6411	376	2	8	8	NUM
ejpam-6411	376	3	]	]	X
ejpam-6411	376	4	d.	d.	PROPN
ejpam-6411	376	5	jawad	jawad	PROPN
ejpam-6411	376	6	hashim	hashim	PROPN
ejpam-6411	376	7	,	,	PUNCT
ejpam-6411	376	8	n.	n.	PROPN
ejpam-6411	376	9	r.	r.	PROPN
ejpam-6411	376	10	anakira	anakira	PROPN
ejpam-6411	376	11	,	,	PUNCT
ejpam-6411	376	12	a.	a.	PROPN
ejpam-6411	376	13	fareed	fareed	PROPN
ejpam-6411	376	14	jameel	jameel	PROPN
ejpam-6411	376	15	,	,	PUNCT
ejpam-6411	376	16	a.	a.	PROPN
ejpam-6411	376	17	k.	k.	PROPN
ejpam-6411	376	18	alomari	alomari	PROPN
ejpam-6411	376	19	,	,	PUNCT
ejpam-6411	376	20	h.	h.	PROPN
ejpam-6411	376	21	zureigat	zureigat	PROPN
ejpam-6411	376	22	,	,	PUNCT
ejpam-6411	376	23	m.	m.	NOUN
ejpam-6411	376	24	w.	w.	PROPN
ejpam-6411	376	25	alomari	alomari	PROPN
ejpam-6411	376	26	,	,	PUNCT
ejpam-6411	376	27	and	and	CCONJ
ejpam-6411	376	28	t.	t.	PROPN
ejpam-6411	376	29	y.	y.	PROPN
ejpam-6411	376	30	ying	ying	PROPN
ejpam-6411	376	31	.	.	PUNCT
ejpam-6411	377	1	new	new	ADJ
ejpam-6411	377	2	series	series	NOUN
ejpam-6411	377	3	approach	approach	NOUN
ejpam-6411	377	4	implementation	implementation	NOUN
ejpam-6411	377	5	for	for	ADP
ejpam-6411	377	6	solving	solve	VERB
ejpam-6411	377	7	fuzzy	fuzzy	ADJ
ejpam-6411	377	8	fractional	fractional	ADJ
ejpam-6411	377	9	two‐point	two‐point	NOUN
ejpam-6411	377	10	boundary	boundary	ADJ
ejpam-6411	377	11	value	value	NOUN
ejpam-6411	377	12	problems	problem	NOUN
ejpam-6411	377	13	applications	application	NOUN
ejpam-6411	377	14	.	.	PUNCT
ejpam-6411	378	1	mathematical	mathematical	ADJ
ejpam-6411	378	2	problems	problem	NOUN
ejpam-6411	378	3	in	in	ADP
ejpam-6411	378	4	engineering	engineering	NOUN
ejpam-6411	378	5	,	,	PUNCT
ejpam-6411	378	6	2022(1):7666571	2022(1):7666571	PROPN
ejpam-6411	378	7	,	,	PUNCT
ejpam-6411	378	8	2022	2022	NUM
ejpam-6411	378	9	.	.	PUNCT
ejpam-6411	379	1	[	[	X
ejpam-6411	379	2	9	9	NUM
ejpam-6411	379	3	]	]	PUNCT
ejpam-6411	379	4	d.	d.	NOUN
ejpam-6411	379	5	chalishajar	chalishajar	PROPN
ejpam-6411	379	6	,	,	PUNCT
ejpam-6411	379	7	d.	d.	PROPN
ejpam-6411	379	8	s.	s.	PROPN
ejpam-6411	379	9	raja	raja	PROPN
ejpam-6411	379	10	,	,	PUNCT
ejpam-6411	379	11	k.	k.	PROPN
ejpam-6411	379	12	karthikeyan	karthikeyan	PROPN
ejpam-6411	379	13	,	,	PUNCT
ejpam-6411	379	14	and	and	CCONJ
ejpam-6411	379	15	p.	p.	PROPN
ejpam-6411	379	16	sundararajan	sundararajan	NOUN
ejpam-6411	379	17	.	.	PUNCT
ejpam-6411	380	1	existence	existence	NOUN
ejpam-6411	380	2	results	result	VERB
ejpam-6411	380	3	for	for	ADP
ejpam-6411	380	4	nonautonomous	nonautonomous	ADJ
ejpam-6411	380	5	impulsive	impulsive	ADJ
ejpam-6411	380	6	fractional	fractional	ADJ
ejpam-6411	380	7	evolution	evolution	NOUN
ejpam-6411	380	8	equations	equation	NOUN
ejpam-6411	380	9	.	.	PUNCT
ejpam-6411	381	1	results	result	NOUN
ejpam-6411	381	2	in	in	ADP
ejpam-6411	381	3	nonlinear	nonlinear	ADJ
ejpam-6411	381	4	analysis	analysis	NOUN
ejpam-6411	381	5	,	,	PUNCT
ejpam-6411	381	6	1(3):133–147	1(3):133–147	NUM
ejpam-6411	381	7	,	,	PUNCT
ejpam-6411	381	8	2018	2018	NUM
ejpam-6411	381	9	.	.	PUNCT
ejpam-6411	382	1	[	[	X
ejpam-6411	382	2	10	10	NUM
ejpam-6411	382	3	]	]	X
ejpam-6411	382	4	d.	d.	NOUN
ejpam-6411	382	5	chalishajar	chalishajar	PROPN
ejpam-6411	382	6	and	and	CCONJ
ejpam-6411	382	7	a.	a.	NOUN
ejpam-6411	382	8	kumar	kumar	PROPN
ejpam-6411	382	9	.	.	PUNCT
ejpam-6411	383	1	existence	existence	PROPN
ejpam-6411	383	2	,	,	PUNCT
ejpam-6411	383	3	uniqueness	uniqueness	NOUN
ejpam-6411	383	4	and	and	CCONJ
ejpam-6411	383	5	ulam	ulam	PROPN
ejpam-6411	383	6	’s	’s	PART
ejpam-6411	383	7	stability	stability	NOUN
ejpam-6411	383	8	of	of	ADP
ejpam-6411	383	9	solutions	solution	NOUN
ejpam-6411	383	10	for	for	ADP
ejpam-6411	383	11	a	a	DET
ejpam-6411	383	12	coupled	couple	VERB
ejpam-6411	383	13	system	system	NOUN
ejpam-6411	383	14	of	of	ADP
ejpam-6411	383	15	fdes	fde	NOUN
ejpam-6411	383	16	with	with	ADP
ejpam-6411	383	17	integral	integral	ADJ
ejpam-6411	383	18	boundary	boundary	ADJ
ejpam-6411	383	19	conditions	condition	NOUN
ejpam-6411	383	20	.	.	PUNCT
ejpam-6411	384	1	mathematics	mathematic	NOUN
ejpam-6411	384	2	,	,	PUNCT
ejpam-6411	384	3	6(6):96	6(6):96	PROPN
ejpam-6411	384	4	,	,	PUNCT
ejpam-6411	384	5	2018	2018	NUM
ejpam-6411	384	6	.	.	PUNCT
ejpam-6411	385	1	[	[	X
ejpam-6411	385	2	11	11	NUM
ejpam-6411	385	3	]	]	X
ejpam-6411	385	4	c.	c.	PROPN
ejpam-6411	385	5	zhai	zhai	PROPN
ejpam-6411	385	6	and	and	CCONJ
ejpam-6411	385	7	l.	l.	PROPN
ejpam-6411	385	8	xu	xu	PROPN
ejpam-6411	385	9	.	.	PUNCT
ejpam-6411	386	1	properties	property	NOUN
ejpam-6411	386	2	of	of	ADP
ejpam-6411	386	3	positive	positive	ADJ
ejpam-6411	386	4	solutions	solution	NOUN
ejpam-6411	386	5	to	to	ADP
ejpam-6411	386	6	a	a	DET
ejpam-6411	386	7	class	class	NOUN
ejpam-6411	386	8	of	of	ADP
ejpam-6411	386	9	four	four	NUM
ejpam-6411	386	10	-	-	PUNCT
ejpam-6411	386	11	point	point	NOUN
ejpam-6411	386	12	boundary	boundary	ADJ
ejpam-6411	386	13	value	value	NOUN
ejpam-6411	386	14	problem	problem	NOUN
ejpam-6411	386	15	of	of	ADP
ejpam-6411	386	16	caputo	caputo	PROPN
ejpam-6411	386	17	fdes	fde	NOUN
ejpam-6411	386	18	with	with	ADP
ejpam-6411	386	19	a	a	DET
ejpam-6411	386	20	parameter	parameter	NOUN
ejpam-6411	386	21	.	.	PUNCT
ejpam-6411	387	1	communications	communication	NOUN
ejpam-6411	387	2	in	in	ADP
ejpam-6411	387	3	nonlinear	nonlinear	ADJ
ejpam-6411	387	4	science	science	NOUN
ejpam-6411	387	5	and	and	CCONJ
ejpam-6411	387	6	numerical	numerical	PROPN
ejpam-6411	387	7	simulation	simulation	PROPN
ejpam-6411	387	8	,	,	PUNCT
ejpam-6411	387	9	19(8):2820–2827	19(8):2820–2827	NUM
ejpam-6411	387	10	,	,	PUNCT
ejpam-6411	387	11	2014	2014	NUM
ejpam-6411	387	12	.	.	PUNCT
ejpam-6411	388	1	[	[	X
ejpam-6411	388	2	12	12	NUM
ejpam-6411	388	3	]	]	PUNCT
ejpam-6411	388	4	a.	a.	PROPN
ejpam-6411	388	5	al	al	PROPN
ejpam-6411	388	6	-	-	PUNCT
ejpam-6411	388	7	khateeb	khateeb	PROPN
ejpam-6411	388	8	,	,	PUNCT
ejpam-6411	388	9	h.	h.	PROPN
ejpam-6411	388	10	zureigat	zureigat	PROPN
ejpam-6411	388	11	,	,	PUNCT
ejpam-6411	388	12	o.	o.	PROPN
ejpam-6411	388	13	ala’yed	ala’yed	PROPN
ejpam-6411	388	14	,	,	PUNCT
ejpam-6411	388	15	and	and	CCONJ
ejpam-6411	388	16	s.	s.	PROPN
ejpam-6411	388	17	bawaneh	bawaneh	PROPN
ejpam-6411	388	18	.	.	PUNCT
ejpam-6411	389	1	ulam	ulam	PROPN
ejpam-6411	389	2	–	–	PUNCT
ejpam-6411	389	3	hyers	hyer	NOUN
ejpam-6411	389	4	stability	stability	NOUN
ejpam-6411	389	5	and	and	CCONJ
ejpam-6411	389	6	uniqueness	uniqueness	NOUN
ejpam-6411	389	7	for	for	ADP
ejpam-6411	389	8	nonlinear	nonlinear	ADJ
ejpam-6411	389	9	sequential	sequential	ADJ
ejpam-6411	389	10	fdes	fde	NOUN
ejpam-6411	389	11	involving	involve	VERB
ejpam-6411	389	12	integral	integral	ADJ
ejpam-6411	389	13	boundary	boundary	ADJ
ejpam-6411	389	14	conditions	condition	NOUN
ejpam-6411	389	15	.	.	PUNCT
ejpam-6411	390	1	fractal	fractal	ADJ
ejpam-6411	390	2	and	and	CCONJ
ejpam-6411	390	3	fractional	fractional	ADJ
ejpam-6411	390	4	,	,	PUNCT
ejpam-6411	390	5	5(4):235	5(4):235	NUM
ejpam-6411	390	6	,	,	PUNCT
ejpam-6411	390	7	2021	2021	NUM
ejpam-6411	390	8	.	.	PUNCT
ejpam-6411	391	1	[	[	X
ejpam-6411	391	2	13	13	NUM
ejpam-6411	391	3	]	]	X
ejpam-6411	391	4	n.	n.	PROPN
ejpam-6411	391	5	i.	i.	PROPN
ejpam-6411	391	6	mahmudov	mahmudov	PROPN
ejpam-6411	391	7	and	and	CCONJ
ejpam-6411	391	8	a.	a.	PROPN
ejpam-6411	391	9	al	al	PROPN
ejpam-6411	391	10	-	-	PUNCT
ejpam-6411	391	11	khateeb	khateeb	PROPN
ejpam-6411	391	12	.	.	PUNCT
ejpam-6411	392	1	existence	existence	PROPN
ejpam-6411	392	2	and	and	CCONJ
ejpam-6411	392	3	ulam	ulam	NOUN
ejpam-6411	392	4	–	–	PUNCT
ejpam-6411	392	5	hyers	hyer	NOUN
ejpam-6411	392	6	stability	stability	NOUN
ejpam-6411	392	7	of	of	ADP
ejpam-6411	392	8	coupled	couple	VERB
ejpam-6411	392	9	sequential	sequential	ADJ
ejpam-6411	392	10	fdes	fde	NOUN
ejpam-6411	392	11	with	with	ADP
ejpam-6411	392	12	integral	integral	ADJ
ejpam-6411	392	13	boundary	boundary	ADJ
ejpam-6411	392	14	conditions	condition	NOUN
ejpam-6411	392	15	.	.	PUNCT
ejpam-6411	393	1	journal	journal	NOUN
ejpam-6411	393	2	of	of	ADP
ejpam-6411	393	3	inequalities	inequality	NOUN
ejpam-6411	393	4	and	and	CCONJ
ejpam-6411	393	5	applications	application	NOUN
ejpam-6411	393	6	,	,	PUNCT
ejpam-6411	393	7	2019:1–15	2019:1–15	NUM
ejpam-6411	393	8	,	,	PUNCT
ejpam-6411	393	9	2019	2019	NUM
ejpam-6411	393	10	.	.	PUNCT
ejpam-6411	394	1	[	[	X
ejpam-6411	394	2	14	14	NUM
ejpam-6411	394	3	]	]	X
ejpam-6411	394	4	b.	b.	PROPN
ejpam-6411	394	5	ahmad	ahmad	PROPN
ejpam-6411	394	6	and	and	CCONJ
ejpam-6411	394	7	s.	s.	PROPN
ejpam-6411	394	8	k.	k.	PROPN
ejpam-6411	394	9	ntouyas	ntouyas	PROPN
ejpam-6411	394	10	.	.	PUNCT
ejpam-6411	395	1	existence	existence	NOUN
ejpam-6411	395	2	results	result	VERB
ejpam-6411	395	3	for	for	ADP
ejpam-6411	395	4	a	a	DET
ejpam-6411	395	5	coupled	couple	VERB
ejpam-6411	395	6	system	system	NOUN
ejpam-6411	395	7	of	of	ADP
ejpam-6411	395	8	caputo	caputo	PROPN
ejpam-6411	395	9	type	type	NOUN
ejpam-6411	395	10	sequential	sequential	ADJ
ejpam-6411	395	11	fdes	fde	NOUN
ejpam-6411	395	12	with	with	ADP
ejpam-6411	395	13	nonlocal	nonlocal	ADJ
ejpam-6411	395	14	integral	integral	ADJ
ejpam-6411	395	15	boundary	boundary	ADJ
ejpam-6411	395	16	conditions	condition	NOUN
ejpam-6411	395	17	.	.	PUNCT
ejpam-6411	396	1	applied	apply	VERB
ejpam-6411	396	2	mathematics	mathematic	NOUN
ejpam-6411	396	3	and	and	CCONJ
ejpam-6411	396	4	computation	computation	NOUN
ejpam-6411	396	5	,	,	PUNCT
ejpam-6411	396	6	266:615–622	266:615–622	NUM
ejpam-6411	396	7	,	,	PUNCT
ejpam-6411	396	8	2015	2015	NUM
ejpam-6411	396	9	.	.	PUNCT
ejpam-6411	397	1	[	[	X
ejpam-6411	397	2	15	15	NUM
ejpam-6411	397	3	]	]	X
ejpam-6411	397	4	n.	n.	PROPN
ejpam-6411	397	5	i.	i.	PROPN
ejpam-6411	397	6	mahmudov	mahmudov	PROPN
ejpam-6411	397	7	,	,	PUNCT
ejpam-6411	397	8	s.	s.	PROPN
ejpam-6411	397	9	bawaneh	bawaneh	PROPN
ejpam-6411	397	10	,	,	PUNCT
ejpam-6411	397	11	and	and	CCONJ
ejpam-6411	397	12	a.	a.	PROPN
ejpam-6411	397	13	al	al	PROPN
ejpam-6411	397	14	-	-	PUNCT
ejpam-6411	397	15	khateeb	khateeb	PROPN
ejpam-6411	397	16	.	.	PUNCT
ejpam-6411	398	1	on	on	ADP
ejpam-6411	398	2	a	a	DET
ejpam-6411	398	3	coupled	couple	VERB
ejpam-6411	398	4	system	system	NOUN
ejpam-6411	398	5	of	of	ADP
ejpam-6411	398	6	fdes	fde	NOUN
ejpam-6411	398	7	with	with	ADP
ejpam-6411	398	8	four	four	NUM
ejpam-6411	398	9	point	point	NOUN
ejpam-6411	398	10	integral	integral	ADJ
ejpam-6411	398	11	boundary	boundary	ADJ
ejpam-6411	398	12	conditions	condition	NOUN
ejpam-6411	398	13	.	.	PUNCT
ejpam-6411	399	1	mathematics	mathematic	NOUN
ejpam-6411	399	2	,	,	PUNCT
ejpam-6411	399	3	7(3):279	7(3):279	NUM
ejpam-6411	399	4	,	,	PUNCT
ejpam-6411	399	5	2019	2019	NUM
ejpam-6411	399	6	.	.	PUNCT
ejpam-6411	400	1	s.	s.	PROPN
ejpam-6411	400	2	momani	momani	PROPN
ejpam-6411	400	3	et	et	PROPN
ejpam-6411	400	4	al	al	PROPN
ejpam-6411	400	5	.	.	PUNCT
ejpam-6411	400	6	/	/	SYM
ejpam-6411	400	7	eur	eur	PROPN
ejpam-6411	400	8	.	.	PUNCT
ejpam-6411	401	1	j.	j.	PROPN
ejpam-6411	401	2	pure	pure	PROPN
ejpam-6411	401	3	appl	appl	PROPN
ejpam-6411	401	4	.	.	PROPN
ejpam-6411	401	5	math	math	PROPN
ejpam-6411	401	6	,	,	PUNCT
ejpam-6411	401	7	18	18	NUM
ejpam-6411	401	8	(	(	PUNCT
ejpam-6411	401	9	4	4	NUM
ejpam-6411	401	10	)	)	PUNCT
ejpam-6411	401	11	(	(	PUNCT
ejpam-6411	401	12	2025	2025	NUM
ejpam-6411	401	13	)	)	PUNCT
ejpam-6411	401	14	,	,	PUNCT
ejpam-6411	401	15	6411	6411	NUM
ejpam-6411	401	16	16	16	NUM
ejpam-6411	401	17	of	of	ADP
ejpam-6411	401	18	16	16	NUM
ejpam-6411	401	19	[	[	X
ejpam-6411	401	20	16	16	NUM
ejpam-6411	401	21	]	]	PUNCT
ejpam-6411	401	22	b.	b.	PROPN
ejpam-6411	401	23	d.	d.	PROPN
ejpam-6411	401	24	reddy	reddy	PROPN
ejpam-6411	401	25	.	.	PUNCT
ejpam-6411	402	1	introductory	introductory	ADJ
ejpam-6411	402	2	functional	functional	ADJ
ejpam-6411	402	3	analysis	analysis	NOUN
ejpam-6411	402	4	:	:	PUNCT
ejpam-6411	402	5	with	with	ADP
ejpam-6411	402	6	applications	application	NOUN
ejpam-6411	402	7	to	to	ADP
ejpam-6411	402	8	boundary	boundary	ADJ
ejpam-6411	402	9	value	value	NOUN
ejpam-6411	402	10	problems	problem	NOUN
ejpam-6411	402	11	and	and	CCONJ
ejpam-6411	402	12	finite	finite	ADJ
ejpam-6411	402	13	elements	element	NOUN
ejpam-6411	402	14	.	.	PUNCT
ejpam-6411	403	1	number	number	NOUN
ejpam-6411	403	2	27	27	NUM
ejpam-6411	403	3	.	.	PUNCT
ejpam-6411	404	1	springer	springer	NOUN
ejpam-6411	404	2	science	science	PROPN
ejpam-6411	404	3	business	business	NOUN
ejpam-6411	404	4	media	medium	NOUN
ejpam-6411	404	5	,	,	PUNCT
ejpam-6411	404	6	1998	1998	NUM
ejpam-6411	404	7	.	.	PUNCT
ejpam-6411	405	1	[	[	X
ejpam-6411	405	2	17	17	NUM
ejpam-6411	405	3	]	]	PUNCT
ejpam-6411	405	4	a.	a.	PROPN
ejpam-6411	405	5	al	al	PROPN
ejpam-6411	405	6	-	-	PUNCT
ejpam-6411	405	7	khateeb	khateeb	PROPN
ejpam-6411	405	8	,	,	PUNCT
ejpam-6411	405	9	a.	a.	NOUN
ejpam-6411	405	10	hazaymeh	hazaymeh	NOUN
ejpam-6411	405	11	,	,	PUNCT
ejpam-6411	405	12	r.	r.	PROPN
ejpam-6411	405	13	hatamleh	hatamleh	PROPN
ejpam-6411	405	14	,	,	PUNCT
ejpam-6411	405	15	and	and	CCONJ
ejpam-6411	405	16	n.	n.	PROPN
ejpam-6411	405	17	al	al	PROPN
ejpam-6411	405	18	odat	odat	PROPN
ejpam-6411	405	19	.	.	PUNCT
ejpam-6411	406	1	uniqueness	uniqueness	NOUN
ejpam-6411	406	2	and	and	CCONJ
ejpam-6411	406	3	stability	stability	NOUN
ejpam-6411	406	4	of	of	ADP
ejpam-6411	406	5	coupled	couple	VERB
ejpam-6411	406	6	sequential	sequential	ADJ
ejpam-6411	406	7	fdes	fde	NOUN
ejpam-6411	406	8	with	with	ADP
ejpam-6411	406	9	boundary	boundary	ADJ
ejpam-6411	406	10	conditions	condition	NOUN
ejpam-6411	406	11	.	.	PUNCT
ejpam-6411	407	1	rocky	rocky	ADJ
ejpam-6411	407	2	mountain	mountain	PROPN
ejpam-6411	407	3	journal	journal	NOUN
ejpam-6411	407	4	of	of	ADP
ejpam-6411	407	5	mathematics	mathematic	NOUN
ejpam-6411	407	6	,	,	PUNCT
ejpam-6411	407	7	52(4):1227–1236	52(4):1227–1236	NUM
ejpam-6411	407	8	,	,	PUNCT
ejpam-6411	407	9	2022	2022	NUM
ejpam-6411	407	10	.	.	PUNCT
ejpam-6411	408	1	[	[	X
ejpam-6411	408	2	18	18	NUM
ejpam-6411	408	3	]	]	X
ejpam-6411	408	4	h.	h.	PROPN
ejpam-6411	408	5	zureigat	zureigat	PROPN
ejpam-6411	408	6	,	,	PUNCT
ejpam-6411	408	7	m.	m.	NOUN
ejpam-6411	408	8	a.	a.	NOUN
ejpam-6411	408	9	tashtoush	tashtoush	PROPN
ejpam-6411	408	10	,	,	PUNCT
ejpam-6411	408	11	a.	a.	PROPN
ejpam-6411	408	12	f.	f.	PROPN
ejpam-6411	408	13	a.	a.	PROPN
ejpam-6411	408	14	jassar	jassar	PROPN
ejpam-6411	408	15	,	,	PUNCT
ejpam-6411	408	16	e.	e.	PROPN
ejpam-6411	408	17	a.	a.	PROPN
ejpam-6411	408	18	az	az	PROPN
ejpam-6411	408	19	-	-	PROPN
ejpam-6411	408	20	zo’bi	zo’bi	PROPN
ejpam-6411	408	21	,	,	PUNCT
ejpam-6411	408	22	and	and	CCONJ
ejpam-6411	408	23	m.	m.	PROPN
ejpam-6411	408	24	w.	w.	PROPN
ejpam-6411	408	25	alomari	alomari	PROPN
ejpam-6411	408	26	.	.	PUNCT
ejpam-6411	409	1	a	a	DET
ejpam-6411	409	2	solution	solution	NOUN
ejpam-6411	409	3	of	of	ADP
ejpam-6411	409	4	the	the	DET
ejpam-6411	409	5	complex	complex	ADJ
ejpam-6411	409	6	fuzzy	fuzzy	ADJ
ejpam-6411	409	7	heat	heat	NOUN
ejpam-6411	409	8	equation	equation	NOUN
ejpam-6411	409	9	in	in	ADP
ejpam-6411	409	10	terms	term	NOUN
ejpam-6411	409	11	of	of	ADP
ejpam-6411	409	12	complex	complex	ADJ
ejpam-6411	409	13	dirichlet	dirichlet	NOUN
ejpam-6411	409	14	conditions	condition	NOUN
ejpam-6411	409	15	using	use	VERB
ejpam-6411	409	16	a	a	DET
ejpam-6411	409	17	modified	modified	ADJ
ejpam-6411	409	18	crank	crank	NOUN
ejpam-6411	409	19	–	–	PUNCT
ejpam-6411	409	20	nicolson	nicolson	PROPN
ejpam-6411	409	21	method	method	PROPN
ejpam-6411	409	22	.	.	PUNCT
ejpam-6411	410	1	advances	advance	NOUN
ejpam-6411	410	2	in	in	ADP
ejpam-6411	410	3	mathematical	mathematical	ADJ
ejpam-6411	410	4	physics	physics	NOUN
ejpam-6411	410	5	,	,	PUNCT
ejpam-6411	410	6	2023(1):6505227	2023(1):6505227	PROPN
ejpam-6411	410	7	,	,	PUNCT
ejpam-6411	410	8	2023	2023	NUM
ejpam-6411	410	9	.	.	PUNCT
ejpam-6411	411	1	[	[	X
ejpam-6411	411	2	19	19	NUM
ejpam-6411	411	3	]	]	PUNCT
ejpam-6411	411	4	s.	s.	PROPN
ejpam-6411	411	5	k.	k.	PROPN
ejpam-6411	411	6	ntouyas	ntouyas	PROPN
ejpam-6411	411	7	and	and	CCONJ
ejpam-6411	411	8	m.	m.	PROPN
ejpam-6411	411	9	obaid	obaid	PROPN
ejpam-6411	411	10	.	.	PUNCT
ejpam-6411	412	1	a	a	DET
ejpam-6411	412	2	coupled	couple	VERB
ejpam-6411	412	3	system	system	NOUN
ejpam-6411	412	4	of	of	ADP
ejpam-6411	412	5	fdes	fde	NOUN
ejpam-6411	412	6	with	with	ADP
ejpam-6411	412	7	nonlocal	nonlocal	ADJ
ejpam-6411	412	8	integral	integral	ADJ
ejpam-6411	412	9	boundary	boundary	ADJ
ejpam-6411	412	10	conditions	condition	NOUN
ejpam-6411	412	11	.	.	PUNCT
ejpam-6411	413	1	advances	advance	NOUN
ejpam-6411	413	2	in	in	ADP
ejpam-6411	413	3	difference	difference	NOUN
ejpam-6411	413	4	equations	equation	NOUN
ejpam-6411	413	5	,	,	PUNCT
ejpam-6411	413	6	2012:1–8	2012:1–8	NUM
ejpam-6411	413	7	,	,	PUNCT
ejpam-6411	413	8	2012	2012	NUM
ejpam-6411	413	9	.	.	PUNCT
ejpam-6411	414	1	[	[	X
ejpam-6411	414	2	20	20	NUM
ejpam-6411	414	3	]	]	PUNCT
ejpam-6411	414	4	b.	b.	PROPN
ejpam-6411	414	5	ahmad	ahmad	PROPN
ejpam-6411	414	6	and	and	CCONJ
ejpam-6411	414	7	s.	s.	PROPN
ejpam-6411	414	8	ntouyas	ntouyas	PROPN
ejpam-6411	414	9	.	.	PUNCT
ejpam-6411	415	1	a	a	DET
ejpam-6411	415	2	coupled	couple	VERB
ejpam-6411	415	3	system	system	NOUN
ejpam-6411	415	4	of	of	ADP
ejpam-6411	415	5	nonlocal	nonlocal	ADJ
ejpam-6411	415	6	fdes	fde	NOUN
ejpam-6411	415	7	with	with	ADP
ejpam-6411	415	8	coupled	couple	VERB
ejpam-6411	415	9	and	and	CCONJ
ejpam-6411	415	10	uncoupled	uncoupled	ADJ
ejpam-6411	415	11	slit	slit	NOUN
ejpam-6411	415	12	-	-	PUNCT
ejpam-6411	415	13	strips	strip	NOUN
ejpam-6411	415	14	-	-	PUNCT
ejpam-6411	415	15	type	type	NOUN
ejpam-6411	415	16	integral	integral	ADJ
ejpam-6411	415	17	boundary	boundary	ADJ
ejpam-6411	415	18	conditions	condition	NOUN
ejpam-6411	415	19	.	.	PUNCT
ejpam-6411	416	1	journal	journal	NOUN
ejpam-6411	416	2	of	of	ADP
ejpam-6411	416	3	mathematical	mathematical	ADJ
ejpam-6411	416	4	sciences	science	NOUN
ejpam-6411	416	5	,	,	PUNCT
ejpam-6411	416	6	226(3	226(3	NUM
ejpam-6411	416	7	)	)	PUNCT
ejpam-6411	416	8	,	,	PUNCT
ejpam-6411	416	9	2017	2017	NUM
ejpam-6411	416	10	.	.	PUNCT
ejpam-6411	417	1	[	[	X
ejpam-6411	417	2	21	21	NUM
ejpam-6411	417	3	]	]	PUNCT
ejpam-6411	417	4	m.	m.	NOUN
ejpam-6411	417	5	tahir	tahir	PROPN
ejpam-6411	417	6	,	,	PUNCT
ejpam-6411	417	7	m.	m.	NOUN
ejpam-6411	417	8	a.	a.	PROPN
ejpam-6411	417	9	imran	imran	PROPN
ejpam-6411	417	10	,	,	PUNCT
ejpam-6411	417	11	n.	n.	PROPN
ejpam-6411	417	12	raza	raza	PROPN
ejpam-6411	417	13	,	,	PUNCT
ejpam-6411	417	14	m.	m.	NOUN
ejpam-6411	417	15	abdullah	abdullah	PROPN
ejpam-6411	417	16	,	,	PUNCT
ejpam-6411	417	17	and	and	CCONJ
ejpam-6411	417	18	m.	m.	NOUN
ejpam-6411	417	19	aleem	aleem	PROPN
ejpam-6411	417	20	.	.	PUNCT
ejpam-6411	418	1	wall	wall	PROPN
ejpam-6411	418	2	slip	slip	NOUN
ejpam-6411	418	3	and	and	CCONJ
ejpam-6411	418	4	noninteger	noninteger	NOUN
ejpam-6411	418	5	order	order	VERB
ejpam-6411	418	6	derivative	derivative	ADJ
ejpam-6411	418	7	effects	effect	NOUN
ejpam-6411	418	8	on	on	ADP
ejpam-6411	418	9	the	the	DET
ejpam-6411	418	10	heat	heat	NOUN
ejpam-6411	418	11	transfer	transfer	NOUN
ejpam-6411	418	12	flow	flow	NOUN
ejpam-6411	418	13	of	of	ADP
ejpam-6411	418	14	maxwell	maxwell	PROPN
ejpam-6411	418	15	fluid	fluid	NOUN
ejpam-6411	418	16	over	over	ADP
ejpam-6411	418	17	an	an	DET
ejpam-6411	418	18	oscillating	oscillate	VERB
ejpam-6411	418	19	vertical	vertical	ADJ
ejpam-6411	418	20	plate	plate	NOUN
ejpam-6411	418	21	with	with	ADP
ejpam-6411	418	22	new	new	ADJ
ejpam-6411	418	23	definition	definition	NOUN
ejpam-6411	418	24	of	of	ADP
ejpam-6411	418	25	fractional	fractional	PROPN
ejpam-6411	418	26	caputo	caputo	PROPN
ejpam-6411	418	27	-	-	PUNCT
ejpam-6411	418	28	fabrizio	fabrizio	PROPN
ejpam-6411	418	29	derivatives	derivative	NOUN
ejpam-6411	418	30	.	.	PUNCT
ejpam-6411	419	1	results	result	NOUN
ejpam-6411	419	2	in	in	ADP
ejpam-6411	419	3	physics	physics	NOUN
ejpam-6411	419	4	,	,	PUNCT
ejpam-6411	419	5	7:1887–1898	7:1887–1898	NUM
ejpam-6411	419	6	,	,	PUNCT
ejpam-6411	419	7	2017	2017	NUM
ejpam-6411	419	8	.	.	PUNCT
ejpam-6411	420	1	[	[	X
ejpam-6411	420	2	22	22	NUM
ejpam-6411	420	3	]	]	PUNCT
ejpam-6411	420	4	m.	m.	NOUN
ejpam-6411	420	5	javaid	javaid	PROPN
ejpam-6411	420	6	,	,	PUNCT
ejpam-6411	420	7	m.	m.	PROPN
ejpam-6411	420	8	tahir	tahir	PROPN
ejpam-6411	420	9	,	,	PUNCT
ejpam-6411	420	10	m.	m.	NOUN
ejpam-6411	420	11	imran	imran	PROPN
ejpam-6411	420	12	,	,	PUNCT
ejpam-6411	420	13	d.	d.	PROPN
ejpam-6411	420	14	baleanu	baleanu	PROPN
ejpam-6411	420	15	,	,	PUNCT
ejpam-6411	420	16	a.	a.	NOUN
ejpam-6411	420	17	akgül	akgül	NOUN
ejpam-6411	420	18	,	,	PUNCT
ejpam-6411	420	19	and	and	CCONJ
ejpam-6411	420	20	m.	m.	NOUN
ejpam-6411	420	21	a.	a.	NOUN
ejpam-6411	420	22	imran	imran	PROPN
ejpam-6411	420	23	.	.	PUNCT
ejpam-6411	421	1	unsteady	unsteady	ADJ
ejpam-6411	421	2	flow	flow	NOUN
ejpam-6411	421	3	of	of	ADP
ejpam-6411	421	4	fractional	fractional	ADJ
ejpam-6411	421	5	burgers	burger	NOUN
ejpam-6411	421	6	’	'	PUNCT
ejpam-6411	421	7	fluid	fluid	NOUN
ejpam-6411	421	8	in	in	ADP
ejpam-6411	421	9	a	a	DET
ejpam-6411	421	10	rotating	rotate	VERB
ejpam-6411	421	11	annulus	annulus	NOUN
ejpam-6411	421	12	region	region	NOUN
ejpam-6411	421	13	with	with	ADP
ejpam-6411	421	14	power	power	NOUN
ejpam-6411	421	15	law	law	NOUN
ejpam-6411	421	16	kernel	kernel	NOUN
ejpam-6411	421	17	.	.	PUNCT
ejpam-6411	422	1	alexandria	alexandria	PROPN
ejpam-6411	422	2	engineering	engineering	PROPN
ejpam-6411	422	3	journal	journal	PROPN
ejpam-6411	422	4	,	,	PUNCT
ejpam-6411	422	5	61(1):17–27	61(1):17–27	NUM
ejpam-6411	422	6	,	,	PUNCT
ejpam-6411	422	7	2022	2022	NUM
ejpam-6411	422	8	.	.	PUNCT
ejpam-6411	423	1	[	[	X
ejpam-6411	423	2	23	23	NUM
ejpam-6411	423	3	]	]	X
ejpam-6411	423	4	b.	b.	PROPN
ejpam-6411	423	5	o.	o.	PROPN
ejpam-6411	423	6	wang	wang	PROPN
ejpam-6411	423	7	,	,	PUNCT
ejpam-6411	423	8	m.	m.	PROPN
ejpam-6411	423	9	tahir	tahir	PROPN
ejpam-6411	423	10	,	,	PUNCT
ejpam-6411	423	11	m.	m.	NOUN
ejpam-6411	423	12	imran	imran	PROPN
ejpam-6411	423	13	,	,	PUNCT
ejpam-6411	423	14	m.	m.	NOUN
ejpam-6411	423	15	javaid	javaid	PROPN
ejpam-6411	423	16	,	,	PUNCT
ejpam-6411	423	17	and	and	CCONJ
ejpam-6411	423	18	c.	c.	PROPN
ejpam-6411	423	19	y.	y.	PROPN
ejpam-6411	423	20	jung	jung	PROPN
ejpam-6411	423	21	.	.	PUNCT
ejpam-6411	424	1	semi	semi	ADJ
ejpam-6411	424	2	analytical	analytical	ADJ
ejpam-6411	424	3	solutions	solution	NOUN
ejpam-6411	424	4	for	for	ADP
ejpam-6411	424	5	fractional	fractional	ADJ
ejpam-6411	424	6	oldroyd	oldroyd	VERB
ejpam-6411	424	7	-	-	PUNCT
ejpam-6411	424	8	b	b	NOUN
ejpam-6411	424	9	fluid	fluid	NOUN
ejpam-6411	424	10	through	through	ADP
ejpam-6411	424	11	rotating	rotate	VERB
ejpam-6411	424	12	annulus	annulus	NOUN
ejpam-6411	424	13	.	.	PUNCT
ejpam-6411	425	1	ieee	ieee	NOUN
ejpam-6411	425	2	access	access	NOUN
ejpam-6411	425	3	,	,	PUNCT
ejpam-6411	425	4	7:72482–72491	7:72482–72491	NUM
ejpam-6411	425	5	,	,	PUNCT
ejpam-6411	425	6	2019	2019	NUM
ejpam-6411	425	7	.	.	PUNCT
ejpam-6411	426	1	[	[	X
ejpam-6411	426	2	24	24	NUM
ejpam-6411	426	3	]	]	PUNCT
ejpam-6411	426	4	m.	m.	NOUN
ejpam-6411	426	5	tahir	tahir	PROPN
ejpam-6411	426	6	,	,	PUNCT
ejpam-6411	426	7	m.	m.	PROPN
ejpam-6411	426	8	n.	n.	PROPN
ejpam-6411	426	9	naeem	naeem	PROPN
ejpam-6411	426	10	,	,	PUNCT
ejpam-6411	426	11	m.	m.	PROPN
ejpam-6411	426	12	javaid	javaid	PROPN
ejpam-6411	426	13	,	,	PUNCT
ejpam-6411	426	14	m.	m.	NOUN
ejpam-6411	426	15	younas	youna	NOUN
ejpam-6411	426	16	,	,	PUNCT
ejpam-6411	426	17	m.	m.	NOUN
ejpam-6411	426	18	imran	imran	PROPN
ejpam-6411	426	19	,	,	PUNCT
ejpam-6411	426	20	n.	n.	PROPN
ejpam-6411	426	21	sadiq	sadiq	PROPN
ejpam-6411	426	22	,	,	PUNCT
ejpam-6411	426	23	and	and	CCONJ
ejpam-6411	426	24	r.	r.	PROPN
ejpam-6411	426	25	safdar	safdar	PROPN
ejpam-6411	426	26	.	.	PUNCT
ejpam-6411	427	1	unsteady	unsteady	ADJ
ejpam-6411	427	2	flow	flow	NOUN
ejpam-6411	427	3	of	of	ADP
ejpam-6411	427	4	fractional	fractional	ADJ
ejpam-6411	427	5	oldroyd	oldroyd	VERB
ejpam-6411	427	6	-	-	PUNCT
ejpam-6411	427	7	b	b	NOUN
ejpam-6411	427	8	fluids	fluid	NOUN
ejpam-6411	427	9	through	through	ADP
ejpam-6411	427	10	rotating	rotate	VERB
ejpam-6411	427	11	annulus	annulus	NOUN
ejpam-6411	427	12	.	.	PUNCT
ejpam-6411	428	1	open	open	ADJ
ejpam-6411	428	2	physics	physics	PROPN
ejpam-6411	428	3	,	,	PUNCT
ejpam-6411	428	4	16(1):193–200	16(1):193–200	PROPN
ejpam-6411	428	5	,	,	PUNCT
ejpam-6411	428	6	2018	2018	NUM
ejpam-6411	428	7	.	.	PUNCT
ejpam-6411	429	1	[	[	X
ejpam-6411	429	2	25	25	NUM
ejpam-6411	429	3	]	]	X
ejpam-6411	429	4	h.	h.	PROPN
ejpam-6411	429	5	h.	h.	PROPN
ejpam-6411	429	6	alsulami	alsulami	PROPN
ejpam-6411	429	7	,	,	PUNCT
ejpam-6411	429	8	s.	s.	PROPN
ejpam-6411	429	9	k.	k.	PROPN
ejpam-6411	429	10	ntouyas	ntouyas	PROPN
ejpam-6411	429	11	,	,	PUNCT
ejpam-6411	429	12	r.	r.	PROPN
ejpam-6411	429	13	p.	p.	PROPN
ejpam-6411	429	14	agarwal	agarwal	PROPN
ejpam-6411	429	15	,	,	PUNCT
ejpam-6411	429	16	b.	b.	PROPN
ejpam-6411	429	17	ahmad	ahmad	PROPN
ejpam-6411	429	18	,	,	PUNCT
ejpam-6411	429	19	and	and	CCONJ
ejpam-6411	429	20	a.	a.	NOUN
ejpam-6411	429	21	alsaedi	alsaedi	PROPN
ejpam-6411	429	22	.	.	PUNCT
ejpam-6411	430	1	a	a	DET
ejpam-6411	430	2	study	study	NOUN
ejpam-6411	430	3	of	of	ADP
ejpam-6411	430	4	fractional	fractional	ADJ
ejpam-6411	430	5	-	-	PUNCT
ejpam-6411	430	6	order	order	NOUN
ejpam-6411	430	7	coupled	couple	VERB
ejpam-6411	430	8	systems	system	NOUN
ejpam-6411	430	9	with	with	ADP
ejpam-6411	430	10	a	a	DET
ejpam-6411	430	11	new	new	ADJ
ejpam-6411	430	12	concept	concept	NOUN
ejpam-6411	430	13	of	of	ADP
ejpam-6411	430	14	coupled	couple	VERB
ejpam-6411	430	15	non	non	ADJ
ejpam-6411	430	16	-	-	ADJ
ejpam-6411	430	17	separated	separate	VERB
ejpam-6411	430	18	boundary	boundary	ADJ
ejpam-6411	430	19	conditions	condition	NOUN
ejpam-6411	430	20	.	.	PUNCT
ejpam-6411	431	1	boundary	boundary	ADJ
ejpam-6411	431	2	value	value	NOUN
ejpam-6411	431	3	problems	problem	NOUN
ejpam-6411	431	4	,	,	PUNCT
ejpam-6411	431	5	2017:1–11	2017:1–11	NUM
ejpam-6411	431	6	,	,	PUNCT
ejpam-6411	431	7	2017	2017	NUM
ejpam-6411	431	8	.	.	PUNCT
ejpam-6411	432	1	[	[	X
ejpam-6411	432	2	26	26	NUM
ejpam-6411	432	3	]	]	X
ejpam-6411	432	4	y.	y.	PROPN
ejpam-6411	432	5	zhang	zhang	PROPN
ejpam-6411	432	6	,	,	PUNCT
ejpam-6411	432	7	z.	z.	PROPN
ejpam-6411	432	8	bai	bai	PROPN
ejpam-6411	432	9	,	,	PUNCT
ejpam-6411	432	10	and	and	CCONJ
ejpam-6411	432	11	t.	t.	PROPN
ejpam-6411	432	12	feng	feng	PROPN
ejpam-6411	432	13	.	.	PUNCT
ejpam-6411	433	1	existence	existence	NOUN
ejpam-6411	433	2	results	result	VERB
ejpam-6411	433	3	for	for	ADP
ejpam-6411	433	4	a	a	DET
ejpam-6411	433	5	coupled	couple	VERB
ejpam-6411	433	6	system	system	NOUN
ejpam-6411	433	7	of	of	ADP
ejpam-6411	433	8	nonlinear	nonlinear	ADJ
ejpam-6411	433	9	fractional	fractional	ADJ
ejpam-6411	433	10	three	three	NUM
ejpam-6411	433	11	-	-	PUNCT
ejpam-6411	433	12	point	point	NOUN
ejpam-6411	433	13	boundary	boundary	ADJ
ejpam-6411	433	14	value	value	NOUN
ejpam-6411	433	15	problems	problem	NOUN
ejpam-6411	433	16	at	at	ADP
ejpam-6411	433	17	resonance	resonance	NOUN
ejpam-6411	433	18	.	.	PUNCT
ejpam-6411	434	1	computers	computer	NOUN
ejpam-6411	434	2	&	&	CCONJ
ejpam-6411	434	3	mathematics	mathematics	PROPN
ejpam-6411	434	4	with	with	ADP
ejpam-6411	434	5	applications	application	NOUN
ejpam-6411	434	6	,	,	PUNCT
ejpam-6411	434	7	61(4):1032–1047	61(4):1032–1047	NUM
ejpam-6411	434	8	,	,	PUNCT
ejpam-6411	434	9	2011	2011	NUM
ejpam-6411	434	10	.	.	PUNCT
ejpam-6411	435	1	[	[	X
ejpam-6411	435	2	27	27	NUM
ejpam-6411	435	3	]	]	PUNCT
ejpam-6411	435	4	m.	m.	NOUN
ejpam-6411	435	5	subramanian	subramanian	PROPN
ejpam-6411	435	6	and	and	CCONJ
ejpam-6411	435	7	d.	d.	PROPN
ejpam-6411	435	8	baleanu	baleanu	PROPN
ejpam-6411	435	9	.	.	PUNCT
ejpam-6411	436	1	stability	stability	NOUN
ejpam-6411	436	2	and	and	CCONJ
ejpam-6411	436	3	existence	existence	NOUN
ejpam-6411	436	4	analysis	analysis	NOUN
ejpam-6411	436	5	to	to	ADP
ejpam-6411	436	6	a	a	DET
ejpam-6411	436	7	coupled	couple	VERB
ejpam-6411	436	8	system	system	NOUN
ejpam-6411	436	9	of	of	ADP
ejpam-6411	436	10	caputo	caputo	PROPN
ejpam-6411	436	11	type	type	NOUN
ejpam-6411	436	12	fdes	fde	NOUN
ejpam-6411	436	13	with	with	ADP
ejpam-6411	436	14	erdelyi	erdelyi	NOUN
ejpam-6411	436	15	-	-	PUNCT
ejpam-6411	436	16	kober	kober	NOUN
ejpam-6411	436	17	integral	integral	ADJ
ejpam-6411	436	18	boundary	boundary	ADJ
ejpam-6411	436	19	conditions	condition	NOUN
ejpam-6411	436	20	.	.	PUNCT
ejpam-6411	437	1	applied	apply	VERB
ejpam-6411	437	2	mathematics	mathematics	PROPN
ejpam-6411	437	3	&	&	CCONJ
ejpam-6411	437	4	information	information	NOUN
ejpam-6411	437	5	sciences	sciences	PROPN
ejpam-6411	437	6	,	,	PUNCT
ejpam-6411	437	7	14(3):415–424	14(3):415–424	NUM
ejpam-6411	437	8	,	,	PUNCT
ejpam-6411	437	9	2020	2020	NUM
ejpam-6411	437	10	.	.	PUNCT
ejpam-6411	438	1	[	[	X
ejpam-6411	438	2	28	28	NUM
ejpam-6411	438	3	]	]	X
ejpam-6411	438	4	n.	n.	PROPN
ejpam-6411	438	5	i.	i.	PROPN
ejpam-6411	438	6	mahmudov	mahmudov	PROPN
ejpam-6411	438	7	and	and	CCONJ
ejpam-6411	438	8	a.	a.	PROPN
ejpam-6411	438	9	al	al	PROPN
ejpam-6411	438	10	-	-	PUNCT
ejpam-6411	438	11	khateeb	khateeb	PROPN
ejpam-6411	438	12	.	.	PUNCT
ejpam-6411	439	1	stability	stability	NOUN
ejpam-6411	439	2	,	,	PUNCT
ejpam-6411	439	3	existence	existence	NOUN
ejpam-6411	439	4	and	and	CCONJ
ejpam-6411	439	5	uniqueness	uniqueness	NOUN
ejpam-6411	439	6	of	of	ADP
ejpam-6411	439	7	boundary	boundary	ADJ
ejpam-6411	439	8	value	value	NOUN
ejpam-6411	439	9	problems	problem	NOUN
ejpam-6411	439	10	for	for	ADP
ejpam-6411	439	11	a	a	DET
ejpam-6411	439	12	coupled	couple	VERB
ejpam-6411	439	13	system	system	NOUN
ejpam-6411	439	14	of	of	ADP
ejpam-6411	439	15	fractional	fractional	PROPN
ejpam-6411	439	16	des	des	PROPN
ejpam-6411	439	17	.	.	PROPN
ejpam-6411	439	18	mathematics	mathematic	NOUN
ejpam-6411	439	19	,	,	PUNCT
ejpam-6411	439	20	7(4):354	7(4):354	NUM
ejpam-6411	439	21	,	,	PUNCT
ejpam-6411	439	22	2019	2019	NUM
ejpam-6411	439	23	.	.	PUNCT