id	sid	tid	token	lemma	pos
ejpam-6737	1	1	european	european	PROPN
ejpam-6737	1	2	journal	journal	PROPN
ejpam-6737	1	3	of	of	ADP
ejpam-6737	1	4	pure	pure	ADJ
ejpam-6737	1	5	and	and	CCONJ
ejpam-6737	1	6	applied	applied	ADJ
ejpam-6737	1	7	mathematics	mathematic	NOUN
ejpam-6737	1	8	2025	2025	NUM
ejpam-6737	1	9	,	,	PUNCT
ejpam-6737	1	10	vol	vol	NOUN
ejpam-6737	1	11	.	.	PROPN
ejpam-6737	1	12	18	18	NUM
ejpam-6737	1	13	,	,	PUNCT
ejpam-6737	1	14	issue	issue	NOUN
ejpam-6737	1	15	4	4	NUM
ejpam-6737	1	16	,	,	PUNCT
ejpam-6737	1	17	article	article	NOUN
ejpam-6737	1	18	number	number	NOUN
ejpam-6737	1	19	6737	6737	NUM
ejpam-6737	1	20	issn	issn	VERB
ejpam-6737	1	21	1307	1307	NUM
ejpam-6737	1	22	-	-	SYM
ejpam-6737	1	23	5543	5543	NUM
ejpam-6737	1	24	–	–	PUNCT
ejpam-6737	1	25	ejpam.com	ejpam.com	X
ejpam-6737	1	26	published	publish	VERB
ejpam-6737	1	27	by	by	ADP
ejpam-6737	1	28	new	new	PROPN
ejpam-6737	1	29	york	york	PROPN
ejpam-6737	1	30	business	business	PROPN
ejpam-6737	1	31	global	global	ADJ
ejpam-6737	1	32	fractal	fractal	ADJ
ejpam-6737	1	33	fractional	fractional	ADJ
ejpam-6737	1	34	modelling	modelling	NOUN
ejpam-6737	1	35	of	of	ADP
ejpam-6737	1	36	social	social	ADJ
ejpam-6737	1	37	media	medium	NOUN
ejpam-6737	1	38	addiction	addiction	NOUN
ejpam-6737	1	39	with	with	ADP
ejpam-6737	1	40	mittag	mittag	ADJ
ejpam-6737	1	41	generalized	generalized	ADJ
ejpam-6737	1	42	decay	decay	NOUN
ejpam-6737	1	43	stability	stability	NOUN
ejpam-6737	1	44	and	and	CCONJ
ejpam-6737	1	45	recovery	recovery	NOUN
ejpam-6737	1	46	analysis	analysis	NOUN
ejpam-6737	1	47	s.	s.	PROPN
ejpam-6737	1	48	m.	m.	PROPN
ejpam-6737	1	49	chithra1	chithra1	PROPN
ejpam-6737	1	50	,	,	PUNCT
ejpam-6737	1	51	r.	r.	PROPN
ejpam-6737	1	52	thangathamizh2	thangathamizh2	PROPN
ejpam-6737	1	53	,	,	PUNCT
ejpam-6737	1	54	shivani	shivani	PROPN
ejpam-6737	1	55	gupta3	gupta3	PROPN
ejpam-6737	1	56	,	,	PUNCT
ejpam-6737	1	57	vediyappan	vediyappan	ADJ
ejpam-6737	1	58	govindan4	govindan4	PROPN
ejpam-6737	1	59	,	,	PUNCT
ejpam-6737	1	60	mana	mana	PROPN
ejpam-6737	1	61	donganont5,∗	donganont5,∗	PROPN
ejpam-6737	1	62	1	1	NUM
ejpam-6737	1	63	department	department	NOUN
ejpam-6737	1	64	of	of	ADP
ejpam-6737	1	65	mathematics	mathematics	PROPN
ejpam-6737	1	66	,	,	PUNCT
ejpam-6737	2	1	r.	r.	PROPN
ejpam-6737	2	2	m.	m.	PROPN
ejpam-6737	2	3	k	k	PROPN
ejpam-6737	2	4	college	college	PROPN
ejpam-6737	2	5	of	of	ADP
ejpam-6737	2	6	engineering	engineering	NOUN
ejpam-6737	2	7	and	and	CCONJ
ejpam-6737	2	8	technology	technology	NOUN
ejpam-6737	2	9	,	,	PUNCT
ejpam-6737	2	10	puduvoyal	puduvoyal	ADJ
ejpam-6737	2	11	,	,	PUNCT
ejpam-6737	2	12	tamil	tamil	PROPN
ejpam-6737	2	13	nadu	nadu	PROPN
ejpam-6737	2	14	,	,	PUNCT
ejpam-6737	2	15	india	india	PROPN
ejpam-6737	2	16	2	2	NUM
ejpam-6737	2	17	department	department	NOUN
ejpam-6737	2	18	of	of	ADP
ejpam-6737	2	19	mathematics	mathematic	NOUN
ejpam-6737	2	20	,	,	PUNCT
ejpam-6737	2	21	jeppiaar	jeppiaar	PROPN
ejpam-6737	2	22	institute	institute	PROPN
ejpam-6737	2	23	of	of	ADP
ejpam-6737	2	24	technology	technology	PROPN
ejpam-6737	2	25	,	,	PUNCT
ejpam-6737	2	26	sriperumbudur	sriperumbudur	NOUN
ejpam-6737	2	27	,	,	PUNCT
ejpam-6737	2	28	chennai	chennai	PROPN
ejpam-6737	2	29	,	,	PUNCT
ejpam-6737	2	30	tamil	tamil	PROPN
ejpam-6737	2	31	nadu	nadu	PROPN
ejpam-6737	2	32	,	,	PUNCT
ejpam-6737	2	33	india	india	PROPN
ejpam-6737	2	34	3	3	NUM
ejpam-6737	2	35	school	school	NOUN
ejpam-6737	2	36	of	of	ADP
ejpam-6737	2	37	computer	computer	NOUN
ejpam-6737	2	38	science	science	NOUN
ejpam-6737	2	39	and	and	CCONJ
ejpam-6737	2	40	engineering	engineering	NOUN
ejpam-6737	2	41	,	,	PUNCT
ejpam-6737	2	42	vellore	vellore	PROPN
ejpam-6737	2	43	institute	institute	PROPN
ejpam-6737	2	44	of	of	ADP
ejpam-6737	2	45	technology	technology	PROPN
ejpam-6737	2	46	,	,	PUNCT
ejpam-6737	2	47	chennai	chennai	PROPN
ejpam-6737	2	48	,	,	PUNCT
ejpam-6737	2	49	tamil	tamil	PROPN
ejpam-6737	2	50	nadu	nadu	PROPN
ejpam-6737	2	51	,	,	PUNCT
ejpam-6737	2	52	india	india	PROPN
ejpam-6737	2	53	4	4	NUM
ejpam-6737	2	54	department	department	NOUN
ejpam-6737	2	55	of	of	ADP
ejpam-6737	2	56	mathematics	mathematic	NOUN
ejpam-6737	2	57	,	,	PUNCT
ejpam-6737	2	58	hindustan	hindustan	PROPN
ejpam-6737	2	59	institute	institute	PROPN
ejpam-6737	2	60	of	of	ADP
ejpam-6737	2	61	technology	technology	PROPN
ejpam-6737	2	62	and	and	CCONJ
ejpam-6737	2	63	science	science	NOUN
ejpam-6737	2	64	,	,	PUNCT
ejpam-6737	2	65	chennai	chennai	PROPN
ejpam-6737	2	66	,	,	PUNCT
ejpam-6737	2	67	tamil	tamil	PROPN
ejpam-6737	2	68	nadu	nadu	PROPN
ejpam-6737	2	69	,	,	PUNCT
ejpam-6737	2	70	india	india	PROPN
ejpam-6737	2	71	5	5	NUM
ejpam-6737	2	72	school	school	NOUN
ejpam-6737	2	73	of	of	ADP
ejpam-6737	2	74	science	science	NOUN
ejpam-6737	2	75	,	,	PUNCT
ejpam-6737	2	76	university	university	NOUN
ejpam-6737	2	77	of	of	ADP
ejpam-6737	2	78	phayao	phayao	NOUN
ejpam-6737	2	79	,	,	PUNCT
ejpam-6737	2	80	phayao	phayao	NOUN
ejpam-6737	2	81	56000	56000	NUM
ejpam-6737	2	82	,	,	PUNCT
ejpam-6737	2	83	thailand	thailand	PROPN
ejpam-6737	2	84	abstract	abstract	PROPN
ejpam-6737	2	85	.	.	PUNCT
ejpam-6737	3	1	social	social	ADJ
ejpam-6737	3	2	media	medium	NOUN
ejpam-6737	3	3	addiction	addiction	NOUN
ejpam-6737	3	4	impacts	impact	VERB
ejpam-6737	3	5	mental	mental	ADJ
ejpam-6737	3	6	health	health	NOUN
ejpam-6737	3	7	,	,	PUNCT
ejpam-6737	3	8	social	social	ADJ
ejpam-6737	3	9	interaction	interaction	NOUN
ejpam-6737	3	10	,	,	PUNCT
ejpam-6737	3	11	and	and	CCONJ
ejpam-6737	3	12	productivity	productivity	NOUN
ejpam-6737	3	13	levels	level	NOUN
ejpam-6737	3	14	significantly	significantly	ADV
ejpam-6737	3	15	.	.	PUNCT
ejpam-6737	4	1	the	the	DET
ejpam-6737	4	2	addiction	addiction	NOUN
ejpam-6737	4	3	dynamics	dynamic	NOUN
ejpam-6737	4	4	of	of	ADP
ejpam-6737	4	5	this	this	DET
ejpam-6737	4	6	paper	paper	NOUN
ejpam-6737	4	7	are	be	AUX
ejpam-6737	4	8	modelled	model	VERB
ejpam-6737	4	9	by	by	ADP
ejpam-6737	4	10	stratifying	stratify	VERB
ejpam-6737	4	11	the	the	DET
ejpam-6737	4	12	users	user	NOUN
ejpam-6737	4	13	into	into	ADP
ejpam-6737	4	14	general	general	ADJ
ejpam-6737	4	15	users	user	NOUN
ejpam-6737	4	16	,	,	PUNCT
ejpam-6737	4	17	mildly	mildly	ADV
ejpam-6737	4	18	addicted	addicted	ADJ
ejpam-6737	4	19	,	,	PUNCT
ejpam-6737	4	20	and	and	CCONJ
ejpam-6737	4	21	highly	highly	ADV
ejpam-6737	4	22	addicted	addict	VERB
ejpam-6737	4	23	persons	person	NOUN
ejpam-6737	4	24	in	in	ADP
ejpam-6737	4	25	light	light	NOUN
ejpam-6737	4	26	of	of	ADP
ejpam-6737	4	27	recovery	recovery	NOUN
ejpam-6737	4	28	-	-	PUNCT
ejpam-6737	4	29	based	base	VERB
ejpam-6737	4	30	psychological	psychological	ADJ
ejpam-6737	4	31	treatment	treatment	NOUN
ejpam-6737	4	32	.	.	PUNCT
ejpam-6737	5	1	this	this	DET
ejpam-6737	5	2	paper	paper	NOUN
ejpam-6737	5	3	uses	use	VERB
ejpam-6737	5	4	the	the	DET
ejpam-6737	5	5	fractional	fractional	ADJ
ejpam-6737	5	6	mathematical	mathematical	ADJ
ejpam-6737	5	7	model	model	NOUN
ejpam-6737	5	8	,	,	PUNCT
ejpam-6737	5	9	the	the	DET
ejpam-6737	5	10	fractal	fractal	ADJ
ejpam-6737	5	11	-	-	PUNCT
ejpam-6737	5	12	fractional	fractional	ADJ
ejpam-6737	5	13	operator	operator	NOUN
ejpam-6737	5	14	,	,	PUNCT
ejpam-6737	5	15	and	and	CCONJ
ejpam-6737	5	16	the	the	DET
ejpam-6737	5	17	mittag	mittag	ADJ
ejpam-6737	5	18	-	-	PUNCT
ejpam-6737	5	19	leffler	leffler	NOUN
ejpam-6737	5	20	kernel	kernel	NOUN
ejpam-6737	5	21	to	to	PART
ejpam-6737	5	22	study	study	VERB
ejpam-6737	5	23	addiction	addiction	NOUN
ejpam-6737	5	24	paths	path	NOUN
ejpam-6737	5	25	and	and	CCONJ
ejpam-6737	5	26	recoveries	recovery	NOUN
ejpam-6737	5	27	.	.	PUNCT
ejpam-6737	6	1	reliability	reliability	NOUN
ejpam-6737	6	2	of	of	ADP
ejpam-6737	6	3	the	the	DET
ejpam-6737	6	4	model	model	NOUN
ejpam-6737	6	5	presented	present	VERB
ejpam-6737	6	6	is	be	AUX
ejpam-6737	6	7	established	establish	VERB
ejpam-6737	6	8	through	through	ADP
ejpam-6737	6	9	fixed	fix	VERB
ejpam-6737	6	10	-	-	PUNCT
ejpam-6737	6	11	point	point	NOUN
ejpam-6737	6	12	theory	theory	NOUN
ejpam-6737	6	13	and	and	CCONJ
ejpam-6737	6	14	ulam	ulam	NOUN
ejpam-6737	6	15	–	–	PUNCT
ejpam-6737	6	16	hyers	hyer	NOUN
ejpam-6737	6	17	stability	stability	NOUN
ejpam-6737	6	18	.	.	PUNCT
ejpam-6737	7	1	numerical	numerical	ADJ
ejpam-6737	7	2	simulations	simulation	NOUN
ejpam-6737	7	3	are	be	AUX
ejpam-6737	7	4	conducted	conduct	VERB
ejpam-6737	7	5	to	to	PART
ejpam-6737	7	6	show	show	VERB
ejpam-6737	7	7	the	the	DET
ejpam-6737	7	8	influence	influence	NOUN
ejpam-6737	7	9	of	of	ADP
ejpam-6737	7	10	fractional	fractional	ADJ
ejpam-6737	7	11	-	-	PUNCT
ejpam-6737	7	12	order	order	NOUN
ejpam-6737	7	13	parameters	parameter	NOUN
ejpam-6737	7	14	on	on	ADP
ejpam-6737	7	15	addiction	addiction	NOUN
ejpam-6737	7	16	and	and	CCONJ
ejpam-6737	7	17	recovery	recovery	NOUN
ejpam-6737	7	18	.	.	PUNCT
ejpam-6737	8	1	it	it	PRON
ejpam-6737	8	2	gives	give	VERB
ejpam-6737	8	3	an	an	DET
ejpam-6737	8	4	idea	idea	NOUN
ejpam-6737	8	5	about	about	ADP
ejpam-6737	8	6	how	how	SCONJ
ejpam-6737	8	7	to	to	PART
ejpam-6737	8	8	intervene	intervene	VERB
ejpam-6737	8	9	in	in	ADP
ejpam-6737	8	10	an	an	DET
ejpam-6737	8	11	effective	effective	ADJ
ejpam-6737	8	12	manner	manner	NOUN
ejpam-6737	8	13	.	.	PUNCT
ejpam-6737	9	1	our	our	PRON
ejpam-6737	9	2	findings	finding	NOUN
ejpam-6737	9	3	will	will	AUX
ejpam-6737	9	4	support	support	VERB
ejpam-6737	9	5	the	the	DET
ejpam-6737	9	6	development	development	NOUN
ejpam-6737	9	7	of	of	ADP
ejpam-6737	9	8	targeted	target	VERB
ejpam-6737	9	9	rehabilitation	rehabilitation	NOUN
ejpam-6737	9	10	programs	program	NOUN
ejpam-6737	9	11	and	and	CCONJ
ejpam-6737	9	12	digital	digital	ADJ
ejpam-6737	9	13	wellness	wellness	NOUN
ejpam-6737	9	14	policies	policy	NOUN
ejpam-6737	9	15	.	.	PUNCT
ejpam-6737	10	1	2020	2020	NUM
ejpam-6737	10	2	mathematics	mathematic	NOUN
ejpam-6737	10	3	subject	subject	NOUN
ejpam-6737	10	4	classifications	classification	NOUN
ejpam-6737	10	5	:	:	PUNCT
ejpam-6737	10	6	26a33	26a33	NUM
ejpam-6737	10	7	,	,	PUNCT
ejpam-6737	10	8	34a08	34a08	NUM
ejpam-6737	10	9	,	,	PUNCT
ejpam-6737	10	10	34d20	34d20	NUM
ejpam-6737	10	11	,	,	PUNCT
ejpam-6737	10	12	92d25	92d25	NUM
ejpam-6737	10	13	key	key	ADJ
ejpam-6737	10	14	words	word	NOUN
ejpam-6737	10	15	and	and	CCONJ
ejpam-6737	10	16	phrases	phrase	NOUN
ejpam-6737	10	17	:	:	PUNCT
ejpam-6737	10	18	fractional	fractional	ADJ
ejpam-6737	10	19	-	-	PUNCT
ejpam-6737	10	20	order	order	NOUN
ejpam-6737	10	21	modelling	modelling	NOUN
ejpam-6737	10	22	,	,	PUNCT
ejpam-6737	10	23	fractal	fractal	ADJ
ejpam-6737	10	24	calculus	calculus	NOUN
ejpam-6737	10	25	,	,	PUNCT
ejpam-6737	10	26	unique	unique	ADJ
ejpam-6737	10	27	solvability	solvability	NOUN
ejpam-6737	10	28	,	,	PUNCT
ejpam-6737	10	29	lipschitz	lipschitz	VERB
ejpam-6737	10	30	condition	condition	NOUN
ejpam-6737	10	31	,	,	PUNCT
ejpam-6737	10	32	ulam	ulam	PROPN
ejpam-6737	10	33	–	–	PUNCT
ejpam-6737	10	34	hyers	hyer	NOUN
ejpam-6737	10	35	-	-	PUNCT
ejpam-6737	10	36	type	type	NOUN
ejpam-6737	10	37	stability	stability	NOUN
ejpam-6737	10	38	∗corresponding	∗corresponde	VERB
ejpam-6737	10	39	author	author	NOUN
ejpam-6737	10	40	.	.	PUNCT
ejpam-6737	11	1	doi	doi	NOUN
ejpam-6737	11	2	:	:	PUNCT
ejpam-6737	11	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6737	https://doi.org/10.29020/nybg.ejpam.v18i4.6737	ADJ
ejpam-6737	11	4	email	email	NOUN
ejpam-6737	11	5	addresses	address	NOUN
ejpam-6737	11	6	:	:	PUNCT
ejpam-6737	11	7	chithra.sm@rmkcet.ac.in	chithra.sm@rmkcet.ac.in	X
ejpam-6737	11	8	(	(	PUNCT
ejpam-6737	11	9	s.	s.	PROPN
ejpam-6737	11	10	m.	m.	PROPN
ejpam-6737	11	11	chithra	chithra	PROPN
ejpam-6737	11	12	)	)	PUNCT
ejpam-6737	11	13	,	,	PUNCT
ejpam-6737	11	14	thamizh1418@gmail.com	thamizh1418@gmail.com	X
ejpam-6737	11	15	(	(	PUNCT
ejpam-6737	11	16	r.	r.	PROPN
ejpam-6737	11	17	thangathamizh	thangathamizh	PROPN
ejpam-6737	11	18	)	)	PUNCT
ejpam-6737	11	19	,	,	PUNCT
ejpam-6737	11	20	shivani.gupta@vit.ac.in	shivani.gupta@vit.ac.in	PROPN
ejpam-6737	11	21	(	(	PUNCT
ejpam-6737	11	22	s.	s.	PROPN
ejpam-6737	11	23	gupta	gupta	PROPN
ejpam-6737	11	24	)	)	PUNCT
ejpam-6737	11	25	,	,	PUNCT
ejpam-6737	11	26	vadimalawi@gmail.com	vadimalawi@gmail.com	X
ejpam-6737	11	27	(	(	PUNCT
ejpam-6737	11	28	v.	v.	ADP
ejpam-6737	11	29	govindan	govindan	PROPN
ejpam-6737	11	30	)	)	PUNCT
ejpam-6737	11	31	,	,	PUNCT
ejpam-6737	11	32	mana.do@up.ac.th	mana.do@up.ac.th	PROPN
ejpam-6737	11	33	(	(	PUNCT
ejpam-6737	11	34	m.	m.	NOUN
ejpam-6737	11	35	donganont	donganont	PROPN
ejpam-6737	11	36	)	)	PUNCT
ejpam-6737	11	37	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6737	12	1	1	1	NUM
ejpam-6737	12	2	copyright	copyright	NOUN
ejpam-6737	12	3	:	:	PUNCT
ejpam-6737	12	4	©	©	PROPN
ejpam-6737	12	5	2025	2025	NUM
ejpam-6737	12	6	the	the	DET
ejpam-6737	12	7	author(s	author(s	NOUN
ejpam-6737	12	8	)	)	PUNCT
ejpam-6737	12	9	.	.	PUNCT
ejpam-6737	13	1	(	(	PUNCT
ejpam-6737	13	2	cc	cc	NOUN
ejpam-6737	13	3	by	by	ADP
ejpam-6737	13	4	-	-	PUNCT
ejpam-6737	13	5	nc	nc	PROPN
ejpam-6737	13	6	4.0	4.0	NUM
ejpam-6737	13	7	)	)	PUNCT
ejpam-6737	13	8	s.	s.	PROPN
ejpam-6737	13	9	m.	m.	PROPN
ejpam-6737	13	10	chithra	chithra	PROPN
ejpam-6737	13	11	et	et	PROPN
ejpam-6737	13	12	al	al	PROPN
ejpam-6737	13	13	.	.	PUNCT
ejpam-6737	13	14	/	/	SYM
ejpam-6737	13	15	eur	eur	PROPN
ejpam-6737	13	16	.	.	PUNCT
ejpam-6737	14	1	j.	j.	PROPN
ejpam-6737	14	2	pure	pure	PROPN
ejpam-6737	14	3	appl	appl	PROPN
ejpam-6737	14	4	.	.	PROPN
ejpam-6737	14	5	math	math	PROPN
ejpam-6737	14	6	,	,	PUNCT
ejpam-6737	14	7	18	18	NUM
ejpam-6737	14	8	(	(	PUNCT
ejpam-6737	14	9	4	4	NUM
ejpam-6737	14	10	)	)	PUNCT
ejpam-6737	14	11	(	(	PUNCT
ejpam-6737	14	12	2025	2025	NUM
ejpam-6737	14	13	)	)	PUNCT
ejpam-6737	14	14	,	,	PUNCT
ejpam-6737	14	15	6737	6737	NUM
ejpam-6737	14	16	2	2	NUM
ejpam-6737	14	17	of	of	ADP
ejpam-6737	14	18	23	23	NUM
ejpam-6737	14	19	1	1	NUM
ejpam-6737	14	20	.	.	PUNCT
ejpam-6737	15	1	introduction	introduction	NOUN
ejpam-6737	15	2	social	social	ADJ
ejpam-6737	15	3	media	medium	NOUN
ejpam-6737	15	4	(	(	PUNCT
ejpam-6737	15	5	sm	sm	NOUN
ejpam-6737	15	6	)	)	PUNCT
ejpam-6737	15	7	has	have	AUX
ejpam-6737	15	8	had	have	VERB
ejpam-6737	15	9	a	a	DET
ejpam-6737	15	10	deep	deep	ADJ
ejpam-6737	15	11	impact	impact	NOUN
ejpam-6737	15	12	on	on	ADP
ejpam-6737	15	13	the	the	DET
ejpam-6737	15	14	world	world	NOUN
ejpam-6737	15	15	,	,	PUNCT
ejpam-6737	15	16	with	with	SCONJ
ejpam-6737	15	17	its	its	PRON
ejpam-6737	15	18	effects	effect	NOUN
ejpam-6737	15	19	felt	feel	VERB
ejpam-6737	15	20	in	in	ADP
ejpam-6737	15	21	how	how	SCONJ
ejpam-6737	15	22	people	people	NOUN
ejpam-6737	15	23	and	and	CCONJ
ejpam-6737	15	24	societies	society	NOUN
ejpam-6737	15	25	communicate	communicate	VERB
ejpam-6737	15	26	.	.	PUNCT
ejpam-6737	16	1	services	service	NOUN
ejpam-6737	16	2	such	such	ADJ
ejpam-6737	16	3	as	as	ADP
ejpam-6737	16	4	facebook	facebook	PROPN
ejpam-6737	16	5	,	,	PUNCT
ejpam-6737	16	6	instagram	instagram	PROPN
ejpam-6737	16	7	,	,	PUNCT
ejpam-6737	16	8	tiktok	tiktok	NOUN
ejpam-6737	16	9	,	,	PUNCT
ejpam-6737	16	10	and	and	CCONJ
ejpam-6737	16	11	youtube	youtube	NOUN
ejpam-6737	16	12	have	have	AUX
ejpam-6737	16	13	redefined	redefine	VERB
ejpam-6737	16	14	communication	communication	NOUN
ejpam-6737	16	15	,	,	PUNCT
ejpam-6737	16	16	entertainment	entertainment	NOUN
ejpam-6737	16	17	,	,	PUNCT
ejpam-6737	16	18	and	and	CCONJ
ejpam-6737	16	19	exchange	exchange	NOUN
ejpam-6737	16	20	of	of	ADP
ejpam-6737	16	21	information	information	NOUN
ejpam-6737	16	22	.	.	PUNCT
ejpam-6737	17	1	sm	sm	PROPN
ejpam-6737	17	2	is	be	AUX
ejpam-6737	17	3	utilized	utilize	VERB
ejpam-6737	17	4	for	for	ADP
ejpam-6737	17	5	a	a	DET
ejpam-6737	17	6	wide	wide	ADJ
ejpam-6737	17	7	range	range	NOUN
ejpam-6737	17	8	of	of	ADP
ejpam-6737	17	9	applications	application	NOUN
ejpam-6737	17	10	,	,	PUNCT
ejpam-6737	17	11	including	include	VERB
ejpam-6737	17	12	entertainment	entertainment	NOUN
ejpam-6737	17	13	and	and	CCONJ
ejpam-6737	17	14	business	business	NOUN
ejpam-6737	17	15	,	,	PUNCT
ejpam-6737	17	16	education	education	NOUN
ejpam-6737	17	17	,	,	PUNCT
ejpam-6737	17	18	and	and	CCONJ
ejpam-6737	17	19	socialization	socialization	NOUN
ejpam-6737	17	20	[	[	X
ejpam-6737	17	21	1–4	1–4	NOUN
ejpam-6737	17	22	]	]	X
ejpam-6737	17	23	.	.	PUNCT
ejpam-6737	18	1	for	for	ADP
ejpam-6737	18	2	learners	learner	NOUN
ejpam-6737	18	3	,	,	PUNCT
ejpam-6737	18	4	sm	sm	PROPN
ejpam-6737	18	5	can	can	AUX
ejpam-6737	18	6	be	be	AUX
ejpam-6737	18	7	a	a	DET
ejpam-6737	18	8	means	means	NOUN
ejpam-6737	18	9	of	of	ADP
ejpam-6737	18	10	learning	learning	NOUN
ejpam-6737	18	11	and	and	CCONJ
ejpam-6737	18	12	social	social	ADJ
ejpam-6737	18	13	connection	connection	NOUN
ejpam-6737	18	14	,	,	PUNCT
ejpam-6737	18	15	but	but	CCONJ
ejpam-6737	18	16	excessive	excessive	ADJ
ejpam-6737	18	17	use	use	NOUN
ejpam-6737	18	18	can	can	AUX
ejpam-6737	18	19	have	have	VERB
ejpam-6737	18	20	negative	negative	ADJ
ejpam-6737	18	21	effects	effect	NOUN
ejpam-6737	18	22	,	,	PUNCT
ejpam-6737	18	23	including	include	VERB
ejpam-6737	18	24	compromised	compromise	VERB
ejpam-6737	18	25	academic	academic	ADJ
ejpam-6737	18	26	performance	performance	NOUN
ejpam-6737	18	27	,	,	PUNCT
ejpam-6737	18	28	social	social	ADJ
ejpam-6737	18	29	exclusion	exclusion	NOUN
ejpam-6737	18	30	,	,	PUNCT
ejpam-6737	18	31	and	and	CCONJ
ejpam-6737	18	32	mental	mental	ADJ
ejpam-6737	18	33	health	health	NOUN
ejpam-6737	19	1	[	[	X
ejpam-6737	19	2	5	5	NUM
ejpam-6737	19	3	,	,	PUNCT
ejpam-6737	19	4	6	6	NUM
ejpam-6737	19	5	]	]	PUNCT
ejpam-6737	19	6	.	.	PUNCT
ejpam-6737	20	1	recent	recent	ADJ
ejpam-6737	20	2	reports	report	NOUN
ejpam-6737	20	3	have	have	AUX
ejpam-6737	20	4	pointed	point	VERB
ejpam-6737	20	5	out	out	ADP
ejpam-6737	20	6	that	that	SCONJ
ejpam-6737	20	7	during	during	ADP
ejpam-6737	20	8	the	the	DET
ejpam-6737	20	9	covid-19	covid-19	PROPN
ejpam-6737	20	10	pandemic	pandemic	NOUN
ejpam-6737	20	11	,	,	PUNCT
ejpam-6737	20	12	the	the	DET
ejpam-6737	20	13	increase	increase	NOUN
ejpam-6737	20	14	in	in	ADP
ejpam-6737	20	15	sm	sm	NOUN
ejpam-6737	20	16	usage	usage	NOUN
ejpam-6737	20	17	in	in	ADP
ejpam-6737	20	18	adolescents	adolescent	NOUN
ejpam-6737	20	19	has	have	AUX
ejpam-6737	20	20	been	be	AUX
ejpam-6737	20	21	especially	especially	ADV
ejpam-6737	20	22	concerning	concern	VERB
ejpam-6737	20	23	,	,	PUNCT
ejpam-6737	20	24	with	with	ADP
ejpam-6737	20	25	most	most	ADJ
ejpam-6737	20	26	youths	youth	NOUN
ejpam-6737	20	27	spending	spend	VERB
ejpam-6737	20	28	as	as	ADV
ejpam-6737	20	29	much	much	ADJ
ejpam-6737	20	30	as	as	ADP
ejpam-6737	20	31	9	9	NUM
ejpam-6737	20	32	hours	hour	NOUN
ejpam-6737	20	33	per	per	ADP
ejpam-6737	20	34	day	day	NOUN
ejpam-6737	20	35	on	on	ADP
ejpam-6737	20	36	these	these	DET
ejpam-6737	20	37	sites	site	NOUN
ejpam-6737	20	38	[	[	X
ejpam-6737	20	39	7–9	7–9	X
ejpam-6737	20	40	]	]	PUNCT
ejpam-6737	20	41	.	.	PUNCT
ejpam-6737	21	1	social	social	ADJ
ejpam-6737	21	2	media	medium	NOUN
ejpam-6737	21	3	addiction	addiction	NOUN
ejpam-6737	21	4	(	(	PUNCT
ejpam-6737	21	5	sma	sma	PROPN
ejpam-6737	21	6	)	)	PUNCT
ejpam-6737	21	7	is	be	AUX
ejpam-6737	21	8	presently	presently	ADV
ejpam-6737	21	9	defined	define	VERB
ejpam-6737	21	10	as	as	ADP
ejpam-6737	21	11	a	a	DET
ejpam-6737	21	12	serious	serious	ADJ
ejpam-6737	21	13	phenomenon	phenomenon	NOUN
ejpam-6737	21	14	,	,	PUNCT
ejpam-6737	21	15	simulating	simulate	VERB
ejpam-6737	21	16	other	other	ADJ
ejpam-6737	21	17	types	type	NOUN
ejpam-6737	21	18	of	of	ADP
ejpam-6737	21	19	addiction	addiction	NOUN
ejpam-6737	21	20	like	like	ADP
ejpam-6737	21	21	alcohol	alcohol	NOUN
ejpam-6737	21	22	or	or	CCONJ
ejpam-6737	21	23	drug	drug	NOUN
ejpam-6737	21	24	abuse	abuse	NOUN
ejpam-6737	21	25	.	.	PUNCT
ejpam-6737	22	1	such	such	ADJ
ejpam-6737	22	2	addiction	addiction	NOUN
ejpam-6737	22	3	reflects	reflect	VERB
ejpam-6737	22	4	constant	constant	ADJ
ejpam-6737	22	5	use	use	NOUN
ejpam-6737	22	6	,	,	PUNCT
ejpam-6737	22	7	loss	loss	NOUN
ejpam-6737	22	8	of	of	ADP
ejpam-6737	22	9	control	control	NOUN
ejpam-6737	22	10	,	,	PUNCT
ejpam-6737	22	11	and	and	CCONJ
ejpam-6737	22	12	excess	excess	ADJ
ejpam-6737	22	13	distress	distress	NOUN
ejpam-6737	22	14	experienced	experience	VERB
ejpam-6737	22	15	when	when	SCONJ
ejpam-6737	22	16	people	people	NOUN
ejpam-6737	22	17	can	can	AUX
ejpam-6737	22	18	not	not	PART
ejpam-6737	22	19	access	access	VERB
ejpam-6737	22	20	their	their	PRON
ejpam-6737	22	21	favourite	favourite	ADJ
ejpam-6737	22	22	sites	site	NOUN
ejpam-6737	22	23	.	.	PUNCT
ejpam-6737	23	1	the	the	DET
ejpam-6737	23	2	detrimental	detrimental	ADJ
ejpam-6737	23	3	effects	effect	NOUN
ejpam-6737	23	4	of	of	ADP
ejpam-6737	23	5	sma	sma	NOUN
ejpam-6737	23	6	are	be	AUX
ejpam-6737	23	7	far	far	ADV
ejpam-6737	23	8	-	-	PUNCT
ejpam-6737	23	9	reaching	reach	VERB
ejpam-6737	23	10	and	and	CCONJ
ejpam-6737	23	11	manifest	manifest	VERB
ejpam-6737	23	12	not	not	PART
ejpam-6737	23	13	only	only	ADV
ejpam-6737	23	14	in	in	ADP
ejpam-6737	23	15	the	the	DET
ejpam-6737	23	16	mental	mental	ADJ
ejpam-6737	23	17	health	health	NOUN
ejpam-6737	23	18	of	of	ADP
ejpam-6737	23	19	individuals	individual	NOUN
ejpam-6737	23	20	but	but	CCONJ
ejpam-6737	23	21	also	also	ADV
ejpam-6737	23	22	in	in	ADP
ejpam-6737	23	23	interpersonal	interpersonal	ADJ
ejpam-6737	23	24	relationships	relationship	NOUN
ejpam-6737	23	25	,	,	PUNCT
ejpam-6737	23	26	academic	academic	ADJ
ejpam-6737	23	27	performance	performance	NOUN
ejpam-6737	23	28	,	,	PUNCT
ejpam-6737	23	29	and	and	CCONJ
ejpam-6737	23	30	general	general	ADJ
ejpam-6737	23	31	well	well	ADV
ejpam-6737	23	32	-	-	PUNCT
ejpam-6737	23	33	being	being	NOUN
ejpam-6737	23	34	.	.	PUNCT
ejpam-6737	24	1	this	this	PRON
ejpam-6737	24	2	has	have	AUX
ejpam-6737	24	3	made	make	VERB
ejpam-6737	24	4	sma	sma	NOUN
ejpam-6737	24	5	addressing	address	VERB
ejpam-6737	24	6	imperative	imperative	NOUN
ejpam-6737	24	7	,	,	PUNCT
ejpam-6737	24	8	particularly	particularly	ADV
ejpam-6737	24	9	in	in	ADP
ejpam-6737	24	10	a	a	DET
ejpam-6737	24	11	world	world	NOUN
ejpam-6737	24	12	where	where	SCONJ
ejpam-6737	24	13	digital	digital	ADJ
ejpam-6737	24	14	platforms	platform	NOUN
ejpam-6737	24	15	govern	govern	VERB
ejpam-6737	24	16	day	day	NOUN
ejpam-6737	24	17	-	-	PUNCT
ejpam-6737	24	18	to	to	ADP
ejpam-6737	24	19	-	-	PUNCT
ejpam-6737	24	20	day	day	NOUN
ejpam-6737	24	21	life	life	NOUN
ejpam-6737	24	22	[	[	X
ejpam-6737	24	23	10	10	NUM
ejpam-6737	24	24	,	,	PUNCT
ejpam-6737	24	25	11	11	NUM
ejpam-6737	24	26	]	]	PUNCT
ejpam-6737	24	27	.	.	PUNCT
ejpam-6737	25	1	mathematical	mathematical	ADJ
ejpam-6737	25	2	modelling	modelling	NOUN
ejpam-6737	25	3	has	have	AUX
ejpam-6737	25	4	become	become	VERB
ejpam-6737	25	5	an	an	DET
ejpam-6737	25	6	effective	effective	ADJ
ejpam-6737	25	7	tool	tool	NOUN
ejpam-6737	25	8	for	for	ADP
ejpam-6737	25	9	the	the	DET
ejpam-6737	25	10	analysis	analysis	NOUN
ejpam-6737	25	11	of	of	ADP
ejpam-6737	25	12	intricate	intricate	ADJ
ejpam-6737	25	13	behaviours	behaviour	NOUN
ejpam-6737	25	14	such	such	ADJ
ejpam-6737	25	15	as	as	ADP
ejpam-6737	25	16	addiction	addiction	NOUN
ejpam-6737	25	17	.	.	PUNCT
ejpam-6737	26	1	several	several	ADJ
ejpam-6737	26	2	researchers	researcher	NOUN
ejpam-6737	26	3	have	have	AUX
ejpam-6737	26	4	used	use	VERB
ejpam-6737	26	5	infectious	infectious	ADJ
ejpam-6737	26	6	disease	disease	NOUN
ejpam-6737	26	7	dynamics	dynamic	NOUN
ejpam-6737	26	8	models	model	NOUN
ejpam-6737	26	9	to	to	PART
ejpam-6737	26	10	explore	explore	VERB
ejpam-6737	26	11	different	different	ADJ
ejpam-6737	26	12	forms	form	NOUN
ejpam-6737	26	13	of	of	ADP
ejpam-6737	26	14	addiction	addiction	NOUN
ejpam-6737	26	15	,	,	PUNCT
ejpam-6737	26	16	such	such	ADJ
ejpam-6737	26	17	as	as	ADP
ejpam-6737	26	18	smoking	smoking	NOUN
ejpam-6737	26	19	,	,	PUNCT
ejpam-6737	26	20	alcoholism	alcoholism	NOUN
ejpam-6737	26	21	,	,	PUNCT
ejpam-6737	26	22	drug	drug	NOUN
ejpam-6737	26	23	addiction	addiction	NOUN
ejpam-6737	26	24	,	,	PUNCT
ejpam-6737	26	25	internet	internet	NOUN
ejpam-6737	26	26	gaming	gaming	NOUN
ejpam-6737	26	27	,	,	PUNCT
ejpam-6737	26	28	and	and	CCONJ
ejpam-6737	26	29	social	social	ADJ
ejpam-6737	26	30	media	medium	NOUN
ejpam-6737	26	31	addiction	addiction	NOUN
ejpam-6737	26	32	.	.	PUNCT
ejpam-6737	27	1	prior	prior	ADJ
ejpam-6737	27	2	research	research	NOUN
ejpam-6737	27	3	has	have	AUX
ejpam-6737	27	4	concentrated	concentrate	VERB
ejpam-6737	27	5	on	on	ADP
ejpam-6737	27	6	simulating	simulate	VERB
ejpam-6737	27	7	alcoholism	alcoholism	NOUN
ejpam-6737	27	8	[	[	X
ejpam-6737	27	9	12–16	12–16	NUM
ejpam-6737	27	10	]	]	SYM
ejpam-6737	27	11	,	,	PUNCT
ejpam-6737	27	12	addiction	addiction	NOUN
ejpam-6737	27	13	to	to	ADP
ejpam-6737	27	14	online	online	NOUN
ejpam-6737	27	15	gaming	gaming	NOUN
ejpam-6737	27	16	[	[	X
ejpam-6737	27	17	17	17	NUM
ejpam-6737	27	18	,	,	PUNCT
ejpam-6737	27	19	18	18	NUM
ejpam-6737	27	20	]	]	PUNCT
ejpam-6737	27	21	,	,	PUNCT
ejpam-6737	27	22	and	and	CCONJ
ejpam-6737	27	23	the	the	DET
ejpam-6737	27	24	effect	effect	NOUN
ejpam-6737	27	25	of	of	ADP
ejpam-6737	27	26	social	social	ADJ
ejpam-6737	27	27	media	medium	NOUN
ejpam-6737	27	28	on	on	ADP
ejpam-6737	27	29	academic	academic	ADJ
ejpam-6737	27	30	achievement	achievement	NOUN
ejpam-6737	27	31	[	[	X
ejpam-6737	27	32	19	19	NUM
ejpam-6737	27	33	]	]	PUNCT
ejpam-6737	27	34	.	.	PUNCT
ejpam-6737	28	1	in	in	ADP
ejpam-6737	28	2	addition	addition	NOUN
ejpam-6737	28	3	,	,	PUNCT
ejpam-6737	28	4	optimal	optimal	ADJ
ejpam-6737	28	5	control	control	NOUN
ejpam-6737	28	6	methods	method	NOUN
ejpam-6737	28	7	have	have	AUX
ejpam-6737	28	8	been	be	AUX
ejpam-6737	28	9	utilized	utilize	VERB
ejpam-6737	28	10	to	to	PART
ejpam-6737	28	11	study	study	VERB
ejpam-6737	28	12	control	control	NOUN
ejpam-6737	28	13	and	and	CCONJ
ejpam-6737	28	14	reduction	reduction	NOUN
ejpam-6737	28	15	strategies	strategy	NOUN
ejpam-6737	28	16	of	of	ADP
ejpam-6737	28	17	addiction	addiction	NOUN
ejpam-6737	28	18	with	with	ADP
ejpam-6737	28	19	minimal	minimal	ADJ
ejpam-6737	28	20	implementation	implementation	NOUN
ejpam-6737	28	21	costs	cost	NOUN
ejpam-6737	28	22	[	[	X
ejpam-6737	28	23	20	20	NUM
ejpam-6737	28	24	]	]	PUNCT
ejpam-6737	28	25	.	.	PUNCT
ejpam-6737	29	1	mathematical	mathematical	ADJ
ejpam-6737	29	2	modelling	modelling	NOUN
ejpam-6737	29	3	and	and	CCONJ
ejpam-6737	29	4	optimal	optimal	ADJ
ejpam-6737	29	5	control	control	NOUN
ejpam-6737	29	6	methods	method	NOUN
ejpam-6737	29	7	have	have	AUX
ejpam-6737	29	8	also	also	ADV
ejpam-6737	29	9	recently	recently	ADV
ejpam-6737	29	10	been	be	AUX
ejpam-6737	29	11	studied	study	VERB
ejpam-6737	29	12	in	in	ADP
ejpam-6737	29	13	an	an	DET
ejpam-6737	29	14	effort	effort	NOUN
ejpam-6737	29	15	to	to	PART
ejpam-6737	29	16	better	well	ADV
ejpam-6737	29	17	understand	understand	VERB
ejpam-6737	29	18	and	and	CCONJ
ejpam-6737	29	19	control	control	VERB
ejpam-6737	29	20	social	social	ADJ
ejpam-6737	29	21	media	medium	NOUN
ejpam-6737	29	22	addiction	addiction	NOUN
ejpam-6737	29	23	[	[	X
ejpam-6737	29	24	21	21	NUM
ejpam-6737	29	25	]	]	PUNCT
ejpam-6737	29	26	.	.	PUNCT
ejpam-6737	30	1	fractional	fractional	ADJ
ejpam-6737	30	2	differential	differential	ADJ
ejpam-6737	30	3	equations	equation	NOUN
ejpam-6737	30	4	(	(	PUNCT
ejpam-6737	30	5	fde	fde	PROPN
ejpam-6737	30	6	)	)	PUNCT
ejpam-6737	30	7	has	have	AUX
ejpam-6737	30	8	gained	gain	VERB
ejpam-6737	30	9	much	much	ADJ
ejpam-6737	30	10	attention	attention	NOUN
ejpam-6737	30	11	in	in	ADP
ejpam-6737	30	12	disease	disease	NOUN
ejpam-6737	30	13	modeling	modeling	NOUN
ejpam-6737	30	14	due	due	ADP
ejpam-6737	30	15	to	to	ADP
ejpam-6737	30	16	its	its	PRON
ejpam-6737	30	17	benefits	benefit	NOUN
ejpam-6737	30	18	over	over	ADP
ejpam-6737	30	19	standard	standard	ADJ
ejpam-6737	30	20	integer	integer	NOUN
ejpam-6737	30	21	-	-	PUNCT
ejpam-6737	30	22	order	order	NOUN
ejpam-6737	30	23	models	model	NOUN
ejpam-6737	30	24	as	as	ADV
ejpam-6737	30	25	well	well	ADV
ejpam-6737	30	26	as	as	ADP
ejpam-6737	30	27	the	the	DET
ejpam-6737	30	28	incorporation	incorporation	NOUN
ejpam-6737	30	29	of	of	ADP
ejpam-6737	30	30	memory	memory	NOUN
ejpam-6737	30	31	effects	effect	NOUN
ejpam-6737	30	32	and	and	CCONJ
ejpam-6737	30	33	inherited	inherit	VERB
ejpam-6737	30	34	properties	property	NOUN
ejpam-6737	30	35	,	,	PUNCT
ejpam-6737	30	36	enabling	enable	VERB
ejpam-6737	30	37	more	more	ADV
ejpam-6737	30	38	accurate	accurate	ADJ
ejpam-6737	30	39	representations	representation	NOUN
ejpam-6737	30	40	of	of	ADP
ejpam-6737	30	41	complex	complex	ADJ
ejpam-6737	30	42	temporal	temporal	ADJ
ejpam-6737	30	43	and	and	CCONJ
ejpam-6737	30	44	spatial	spatial	ADJ
ejpam-6737	30	45	dynamics	dynamic	NOUN
ejpam-6737	30	46	.	.	PUNCT
ejpam-6737	31	1	the	the	DET
ejpam-6737	31	2	atangana	atangana	PROPN
ejpam-6737	31	3	-	-	PUNCT
ejpam-6737	31	4	baleanu	baleanu	PROPN
ejpam-6737	31	5	caputo	caputo	PROPN
ejpam-6737	31	6	(	(	PUNCT
ejpam-6737	31	7	abc	abc	PROPN
ejpam-6737	31	8	)	)	PUNCT
ejpam-6737	31	9	operator	operator	NOUN
ejpam-6737	31	10	is	be	AUX
ejpam-6737	31	11	particularly	particularly	ADV
ejpam-6737	31	12	useful	useful	ADJ
ejpam-6737	31	13	due	due	ADP
ejpam-6737	31	14	to	to	ADP
ejpam-6737	31	15	its	its	PRON
ejpam-6737	31	16	non	non	ADJ
ejpam-6737	31	17	-	-	ADJ
ejpam-6737	31	18	singular	singular	ADJ
ejpam-6737	31	19	kernel	kernel	NOUN
ejpam-6737	31	20	,	,	PUNCT
ejpam-6737	31	21	which	which	PRON
ejpam-6737	31	22	removes	remove	VERB
ejpam-6737	31	23	the	the	DET
ejpam-6737	31	24	singularities	singularity	NOUN
ejpam-6737	31	25	inherent	inherent	ADJ
ejpam-6737	31	26	in	in	ADP
ejpam-6737	31	27	other	other	ADJ
ejpam-6737	31	28	fractional	fractional	ADJ
ejpam-6737	31	29	operators	operator	NOUN
ejpam-6737	31	30	like	like	ADP
ejpam-6737	31	31	caputo	caputo	PROPN
ejpam-6737	31	32	and	and	CCONJ
ejpam-6737	31	33	riemann	riemann	PROPN
ejpam-6737	31	34	-	-	PUNCT
ejpam-6737	31	35	liouville	liouville	NOUN
ejpam-6737	31	36	[	[	X
ejpam-6737	31	37	22	22	NUM
ejpam-6737	31	38	,	,	PUNCT
ejpam-6737	31	39	23	23	NUM
ejpam-6737	31	40	]	]	PUNCT
ejpam-6737	31	41	.	.	PUNCT
ejpam-6737	32	1	this	this	PRON
ejpam-6737	32	2	renders	render	VERB
ejpam-6737	32	3	the	the	DET
ejpam-6737	32	4	abc	abc	PROPN
ejpam-6737	32	5	operator	operator	NOUN
ejpam-6737	32	6	more	more	ADV
ejpam-6737	32	7	appropriate	appropriate	ADJ
ejpam-6737	32	8	for	for	ADP
ejpam-6737	32	9	the	the	DET
ejpam-6737	32	10	modeling	modeling	NOUN
ejpam-6737	32	11	of	of	ADP
ejpam-6737	32	12	systems	system	NOUN
ejpam-6737	32	13	with	with	ADP
ejpam-6737	32	14	delayed	delay	VERB
ejpam-6737	32	15	responses	response	NOUN
ejpam-6737	32	16	and	and	CCONJ
ejpam-6737	32	17	anomalous	anomalous	ADJ
ejpam-6737	32	18	diffusion	diffusion	NOUN
ejpam-6737	32	19	,	,	PUNCT
ejpam-6737	32	20	offering	offer	VERB
ejpam-6737	32	21	higher	high	ADJ
ejpam-6737	32	22	flexibility	flexibility	NOUN
ejpam-6737	32	23	and	and	CCONJ
ejpam-6737	32	24	accuracy	accuracy	NOUN
ejpam-6737	32	25	.	.	PUNCT
ejpam-6737	33	1	through	through	ADP
ejpam-6737	33	2	the	the	DET
ejpam-6737	33	3	abc	abc	PROPN
ejpam-6737	33	4	fractional	fractional	PROPN
ejpam-6737	33	5	derivative	derivative	NOUN
ejpam-6737	33	6	,	,	PUNCT
ejpam-6737	33	7	we	we	PRON
ejpam-6737	33	8	can	can	AUX
ejpam-6737	33	9	improve	improve	VERB
ejpam-6737	33	10	our	our	PRON
ejpam-6737	33	11	predictions	prediction	NOUN
ejpam-6737	33	12	of	of	ADP
ejpam-6737	33	13	disease	disease	NOUN
ejpam-6737	33	14	transmission	transmission	NOUN
ejpam-6737	33	15	dynamics	dynamic	NOUN
ejpam-6737	33	16	,	,	PUNCT
ejpam-6737	33	17	enhancing	enhance	VERB
ejpam-6737	33	18	our	our	PRON
ejpam-6737	33	19	knowledge	knowledge	NOUN
ejpam-6737	33	20	and	and	CCONJ
ejpam-6737	33	21	regulation	regulation	NOUN
ejpam-6737	33	22	[	[	X
ejpam-6737	33	23	24	24	NUM
ejpam-6737	33	24	,	,	PUNCT
ejpam-6737	33	25	25	25	NUM
ejpam-6737	33	26	]	]	PUNCT
ejpam-6737	33	27	.	.	PUNCT
ejpam-6737	34	1	current	current	ADJ
ejpam-6737	34	2	research	research	NOUN
ejpam-6737	34	3	[	[	X
ejpam-6737	34	4	26–28	26–28	NOUN
ejpam-6737	34	5	]	]	PUNCT
ejpam-6737	34	6	has	have	AUX
ejpam-6737	34	7	applied	apply	VERB
ejpam-6737	34	8	fractional	fractional	ADJ
ejpam-6737	34	9	calculus	calculus	NOUN
ejpam-6737	34	10	to	to	PART
ejpam-6737	34	11	model	model	VERB
ejpam-6737	34	12	social	social	ADJ
ejpam-6737	34	13	media	medium	NOUN
ejpam-6737	34	14	addiction	addiction	NOUN
ejpam-6737	34	15	(	(	PUNCT
ejpam-6737	34	16	sma	sma	PROPN
ejpam-6737	34	17	)	)	PUNCT
ejpam-6737	34	18	,	,	PUNCT
ejpam-6737	34	19	highlighting	highlight	VERB
ejpam-6737	34	20	its	its	PRON
ejpam-6737	34	21	ability	ability	NOUN
ejpam-6737	34	22	to	to	PART
ejpam-6737	34	23	capture	capture	VERB
ejpam-6737	34	24	long	long	ADJ
ejpam-6737	34	25	-	-	PUNCT
ejpam-6737	34	26	memory	memory	NOUN
ejpam-6737	34	27	effects	effect	NOUN
ejpam-6737	34	28	and	and	CCONJ
ejpam-6737	34	29	complex	complex	ADJ
ejpam-6737	34	30	behaviours	behaviour	NOUN
ejpam-6737	34	31	.	.	PUNCT
ejpam-6737	35	1	studies	study	NOUN
ejpam-6737	35	2	[	[	X
ejpam-6737	35	3	26	26	NUM
ejpam-6737	35	4	]	]	PUNCT
ejpam-6737	35	5	applied	apply	VERB
ejpam-6737	35	6	caputo	caputo	PROPN
ejpam-6737	35	7	(	(	PUNCT
ejpam-6737	35	8	singular	singular	PROPN
ejpam-6737	35	9	)	)	PUNCT
ejpam-6737	35	10	fractional	fractional	ADJ
ejpam-6737	35	11	operators	operator	NOUN
ejpam-6737	35	12	and	and	CCONJ
ejpam-6737	35	13	[	[	X
ejpam-6737	35	14	27	27	NUM
ejpam-6737	35	15	]	]	PUNCT
ejpam-6737	35	16	used	use	VERB
ejpam-6737	35	17	caputo	caputo	PROPN
ejpam-6737	35	18	–	–	PUNCT
ejpam-6737	35	19	fabrizio	fabrizio	PROPN
ejpam-6737	35	20	(	(	PUNCT
ejpam-6737	35	21	non	non	ADJ
ejpam-6737	35	22	-	-	ADJ
ejpam-6737	35	23	singular	singular	ADJ
ejpam-6737	35	24	kernels	kernel	NOUN
ejpam-6737	35	25	)	)	PUNCT
ejpam-6737	35	26	to	to	PART
ejpam-6737	35	27	validate	validate	VERB
ejpam-6737	35	28	the	the	DET
ejpam-6737	35	29	role	role	NOUN
ejpam-6737	35	30	of	of	ADP
ejpam-6737	35	31	memory	memory	NOUN
ejpam-6737	35	32	effects	effect	NOUN
ejpam-6737	35	33	in	in	ADP
ejpam-6737	35	34	sma	sma	NOUN
ejpam-6737	35	35	dynamics	dynamic	NOUN
ejpam-6737	35	36	,	,	PUNCT
ejpam-6737	36	1	while	while	SCONJ
ejpam-6737	36	2	[	[	X
ejpam-6737	36	3	28	28	NUM
ejpam-6737	36	4	]	]	X
ejpam-6737	36	5	s.	s.	PROPN
ejpam-6737	36	6	m.	m.	PROPN
ejpam-6737	36	7	chithra	chithra	PROPN
ejpam-6737	36	8	et	et	PROPN
ejpam-6737	36	9	al	al	PROPN
ejpam-6737	36	10	.	.	PUNCT
ejpam-6737	36	11	/	/	SYM
ejpam-6737	36	12	eur	eur	PROPN
ejpam-6737	36	13	.	.	PUNCT
ejpam-6737	37	1	j.	j.	PROPN
ejpam-6737	37	2	pure	pure	PROPN
ejpam-6737	37	3	appl	appl	PROPN
ejpam-6737	37	4	.	.	PROPN
ejpam-6737	37	5	math	math	PROPN
ejpam-6737	37	6	,	,	PUNCT
ejpam-6737	37	7	18	18	NUM
ejpam-6737	37	8	(	(	PUNCT
ejpam-6737	37	9	4	4	NUM
ejpam-6737	37	10	)	)	PUNCT
ejpam-6737	37	11	(	(	PUNCT
ejpam-6737	37	12	2025	2025	NUM
ejpam-6737	37	13	)	)	PUNCT
ejpam-6737	37	14	,	,	PUNCT
ejpam-6737	37	15	6737	6737	NUM
ejpam-6737	37	16	3	3	NUM
ejpam-6737	37	17	of	of	ADP
ejpam-6737	37	18	23	23	NUM
ejpam-6737	37	19	employed	employ	VERB
ejpam-6737	37	20	fractal	fractal	ADJ
ejpam-6737	37	21	–	–	PUNCT
ejpam-6737	37	22	fractional	fractional	ADJ
ejpam-6737	37	23	operators	operator	NOUN
ejpam-6737	37	24	to	to	PART
ejpam-6737	37	25	improve	improve	VERB
ejpam-6737	37	26	model	model	NOUN
ejpam-6737	37	27	precision	precision	NOUN
ejpam-6737	37	28	through	through	ADP
ejpam-6737	37	29	multi	multi	ADJ
ejpam-6737	37	30	-	-	ADJ
ejpam-6737	37	31	scale	scale	ADJ
ejpam-6737	37	32	behaviour	behaviour	NOUN
ejpam-6737	37	33	.	.	PUNCT
ejpam-6737	38	1	unlike	unlike	ADP
ejpam-6737	38	2	previous	previous	ADJ
ejpam-6737	38	3	works	work	NOUN
ejpam-6737	38	4	,	,	PUNCT
ejpam-6737	38	5	our	our	PRON
ejpam-6737	38	6	study	study	NOUN
ejpam-6737	38	7	introduces	introduce	VERB
ejpam-6737	38	8	a	a	DET
ejpam-6737	38	9	novel	novel	NOUN
ejpam-6737	38	10	sma	sma	NOUN
ejpam-6737	38	11	model	model	NOUN
ejpam-6737	38	12	that	that	PRON
ejpam-6737	38	13	separates	separate	VERB
ejpam-6737	38	14	mildly	mildly	ADV
ejpam-6737	38	15	and	and	CCONJ
ejpam-6737	38	16	severely	severely	ADV
ejpam-6737	38	17	addicted	addicted	ADJ
ejpam-6737	38	18	individuals	individual	NOUN
ejpam-6737	38	19	,	,	PUNCT
ejpam-6737	38	20	with	with	ADP
ejpam-6737	38	21	an	an	DET
ejpam-6737	38	22	additional	additional	ADJ
ejpam-6737	38	23	compartment	compartment	NOUN
ejpam-6737	38	24	for	for	ADP
ejpam-6737	38	25	those	those	PRON
ejpam-6737	38	26	under	under	ADP
ejpam-6737	38	27	psychological	psychological	ADJ
ejpam-6737	38	28	treatment	treatment	NOUN
ejpam-6737	38	29	.	.	PUNCT
ejpam-6737	39	1	this	this	DET
ejpam-6737	39	2	refinement	refinement	NOUN
ejpam-6737	39	3	allows	allow	VERB
ejpam-6737	39	4	a	a	DET
ejpam-6737	39	5	more	more	ADV
ejpam-6737	39	6	realistic	realistic	ADJ
ejpam-6737	39	7	analysis	analysis	NOUN
ejpam-6737	39	8	of	of	ADP
ejpam-6737	39	9	addiction	addiction	NOUN
ejpam-6737	39	10	progression	progression	NOUN
ejpam-6737	39	11	and	and	CCONJ
ejpam-6737	39	12	recovery	recovery	NOUN
ejpam-6737	39	13	,	,	PUNCT
ejpam-6737	39	14	offering	offer	VERB
ejpam-6737	39	15	new	new	ADJ
ejpam-6737	39	16	insights	insight	NOUN
ejpam-6737	39	17	into	into	ADP
ejpam-6737	39	18	effective	effective	ADJ
ejpam-6737	39	19	intervention	intervention	NOUN
ejpam-6737	39	20	strategies	strategy	NOUN
ejpam-6737	39	21	.	.	PUNCT
ejpam-6737	40	1	recent	recent	ADJ
ejpam-6737	40	2	studies	study	NOUN
ejpam-6737	40	3	have	have	AUX
ejpam-6737	40	4	highlighted	highlight	VERB
ejpam-6737	40	5	the	the	DET
ejpam-6737	40	6	growing	grow	VERB
ejpam-6737	40	7	use	use	NOUN
ejpam-6737	40	8	of	of	ADP
ejpam-6737	40	9	fractional	fractional	ADJ
ejpam-6737	40	10	calculus	calculus	NOUN
ejpam-6737	40	11	in	in	ADP
ejpam-6737	40	12	diverse	diverse	ADJ
ejpam-6737	40	13	fields	field	NOUN
ejpam-6737	40	14	.	.	PUNCT
ejpam-6737	41	1	for	for	ADP
ejpam-6737	41	2	instance	instance	NOUN
ejpam-6737	41	3	,	,	PUNCT
ejpam-6737	41	4	[	[	X
ejpam-6737	41	5	29	29	NUM
ejpam-6737	41	6	]	]	PUNCT
ejpam-6737	41	7	explored	explore	VERB
ejpam-6737	41	8	its	its	PRON
ejpam-6737	41	9	role	role	NOUN
ejpam-6737	41	10	in	in	ADP
ejpam-6737	41	11	avoiding	avoid	VERB
ejpam-6737	41	12	divergence	divergence	NOUN
ejpam-6737	41	13	in	in	ADP
ejpam-6737	41	14	newton	newton	PROPN
ejpam-6737	41	15	-	-	PUNCT
ejpam-6737	41	16	like	like	ADJ
ejpam-6737	41	17	solvers	solver	NOUN
ejpam-6737	41	18	for	for	ADP
ejpam-6737	41	19	nonlinear	nonlinear	ADJ
ejpam-6737	41	20	models	model	NOUN
ejpam-6737	41	21	,	,	PUNCT
ejpam-6737	41	22	while	while	SCONJ
ejpam-6737	41	23	[	[	X
ejpam-6737	41	24	30	30	NUM
ejpam-6737	41	25	]	]	PUNCT
ejpam-6737	41	26	proposed	propose	VERB
ejpam-6737	41	27	a	a	DET
ejpam-6737	41	28	modified	modify	VERB
ejpam-6737	41	29	fractional	fractional	PROPN
ejpam-6737	41	30	newton	newton	PROPN
ejpam-6737	41	31	’s	’s	PART
ejpam-6737	41	32	solver	solver	PROPN
ejpam-6737	41	33	to	to	PART
ejpam-6737	41	34	improve	improve	VERB
ejpam-6737	41	35	convergence	convergence	NOUN
ejpam-6737	41	36	and	and	CCONJ
ejpam-6737	41	37	stability	stability	NOUN
ejpam-6737	41	38	.	.	PUNCT
ejpam-6737	42	1	the	the	DET
ejpam-6737	42	2	application	application	NOUN
ejpam-6737	42	3	of	of	ADP
ejpam-6737	42	4	fractional	fractional	ADJ
ejpam-6737	42	5	operators	operator	NOUN
ejpam-6737	42	6	in	in	ADP
ejpam-6737	42	7	epidemiology	epidemiology	NOUN
ejpam-6737	42	8	has	have	AUX
ejpam-6737	42	9	also	also	ADV
ejpam-6737	42	10	been	be	AUX
ejpam-6737	42	11	demonstrated	demonstrate	VERB
ejpam-6737	42	12	,	,	PUNCT
ejpam-6737	42	13	with	with	ADP
ejpam-6737	42	14	[	[	X
ejpam-6737	42	15	31	31	NUM
ejpam-6737	42	16	]	]	PUNCT
ejpam-6737	42	17	analysing	analyse	VERB
ejpam-6737	42	18	bi	bi	ADJ
ejpam-6737	42	19	-	-	ADJ
ejpam-6737	42	20	modal	modal	ADJ
ejpam-6737	42	21	covid-19	covid-19	PROPN
ejpam-6737	42	22	transmission	transmission	NOUN
ejpam-6737	42	23	using	use	VERB
ejpam-6737	42	24	caputo	caputo	PROPN
ejpam-6737	42	25	derivatives	derivative	NOUN
ejpam-6737	42	26	and	and	CCONJ
ejpam-6737	42	27	[	[	X
ejpam-6737	42	28	32	32	NUM
ejpam-6737	42	29	]	]	PUNCT
ejpam-6737	42	30	investigating	investigate	VERB
ejpam-6737	42	31	hiv	hiv	PROPN
ejpam-6737	42	32	/	/	SYM
ejpam-6737	42	33	hcv	hcv	X
ejpam-6737	42	34	co	co	NOUN
ejpam-6737	42	35	-	-	NOUN
ejpam-6737	42	36	infection	infection	NOUN
ejpam-6737	42	37	through	through	ADP
ejpam-6737	42	38	a	a	DET
ejpam-6737	42	39	fractional	fractional	ADJ
ejpam-6737	42	40	epidemic	epidemic	NOUN
ejpam-6737	42	41	model	model	NOUN
ejpam-6737	42	42	.	.	PUNCT
ejpam-6737	43	1	in	in	ADP
ejpam-6737	43	2	addition,[33	addition,[33	PROPN
ejpam-6737	43	3	]	]	PUNCT
ejpam-6737	43	4	examined	examine	VERB
ejpam-6737	43	5	a	a	DET
ejpam-6737	43	6	generalized	generalized	ADJ
ejpam-6737	43	7	tumour	tumour	NOUN
ejpam-6737	43	8	model	model	NOUN
ejpam-6737	43	9	with	with	ADP
ejpam-6737	43	10	caputo	caputo	PROPN
ejpam-6737	43	11	fractional	fractional	ADJ
ejpam-6737	43	12	derivatives	derivative	NOUN
ejpam-6737	43	13	,	,	PUNCT
ejpam-6737	43	14	showing	show	VERB
ejpam-6737	43	15	the	the	DET
ejpam-6737	43	16	effectiveness	effectiveness	NOUN
ejpam-6737	43	17	of	of	ADP
ejpam-6737	43	18	fractional	fractional	ADJ
ejpam-6737	43	19	approaches	approach	NOUN
ejpam-6737	43	20	in	in	ADP
ejpam-6737	43	21	capturing	capture	VERB
ejpam-6737	43	22	complex	complex	ADJ
ejpam-6737	43	23	biological	biological	ADJ
ejpam-6737	43	24	dynamics	dynamic	NOUN
ejpam-6737	43	25	.	.	PUNCT
ejpam-6737	44	1	in	in	ADP
ejpam-6737	44	2	order	order	NOUN
ejpam-6737	44	3	to	to	PART
ejpam-6737	44	4	solve	solve	VERB
ejpam-6737	44	5	the	the	DET
ejpam-6737	44	6	intricacies	intricacy	NOUN
ejpam-6737	44	7	of	of	ADP
ejpam-6737	44	8	sma	sma	PROPN
ejpam-6737	44	9	,	,	PUNCT
ejpam-6737	44	10	mathematical	mathematical	ADJ
ejpam-6737	44	11	models	model	NOUN
ejpam-6737	44	12	with	with	ADP
ejpam-6737	44	13	fractional	fractional	ADJ
ejpam-6737	44	14	order	order	NOUN
ejpam-6737	44	15	have	have	AUX
ejpam-6737	44	16	been	be	AUX
ejpam-6737	44	17	established	establish	VERB
ejpam-6737	44	18	that	that	PRON
ejpam-6737	44	19	combine	combine	VERB
ejpam-6737	44	20	fractal	fractal	ADJ
ejpam-6737	44	21	and	and	CCONJ
ejpam-6737	44	22	fractional	fractional	ADJ
ejpam-6737	44	23	derivatives	derivative	NOUN
ejpam-6737	44	24	.	.	PUNCT
ejpam-6737	45	1	these	these	DET
ejpam-6737	45	2	models	model	NOUN
ejpam-6737	45	3	assist	assist	VERB
ejpam-6737	45	4	in	in	ADP
ejpam-6737	45	5	simulating	simulate	VERB
ejpam-6737	45	6	the	the	DET
ejpam-6737	45	7	memory	memory	NOUN
ejpam-6737	45	8	-	-	PUNCT
ejpam-6737	45	9	dependent	dependent	ADJ
ejpam-6737	45	10	nature	nature	NOUN
ejpam-6737	45	11	of	of	ADP
ejpam-6737	45	12	addiction	addiction	NOUN
ejpam-6737	45	13	and	and	CCONJ
ejpam-6737	45	14	give	give	VERB
ejpam-6737	45	15	insight	insight	NOUN
ejpam-6737	45	16	into	into	ADP
ejpam-6737	45	17	the	the	DET
ejpam-6737	45	18	dynamics	dynamic	NOUN
ejpam-6737	45	19	of	of	ADP
ejpam-6737	45	20	user	user	NOUN
ejpam-6737	45	21	behavior	behavior	NOUN
ejpam-6737	45	22	,	,	PUNCT
ejpam-6737	45	23	the	the	DET
ejpam-6737	45	24	effects	effect	NOUN
ejpam-6737	45	25	of	of	ADP
ejpam-6737	45	26	intervention	intervention	NOUN
ejpam-6737	45	27	,	,	PUNCT
ejpam-6737	45	28	and	and	CCONJ
ejpam-6737	45	29	the	the	DET
ejpam-6737	45	30	efficacy	efficacy	NOUN
ejpam-6737	45	31	of	of	ADP
ejpam-6737	45	32	recovery	recovery	NOUN
ejpam-6737	45	33	approaches	approach	NOUN
ejpam-6737	45	34	.	.	PUNCT
ejpam-6737	46	1	the	the	DET
ejpam-6737	46	2	advent	advent	NOUN
ejpam-6737	46	3	of	of	ADP
ejpam-6737	46	4	atangana	atangana	PROPN
ejpam-6737	46	5	-	-	PUNCT
ejpam-6737	46	6	baleanu	baleanu	ADJ
ejpam-6737	46	7	fractal	fractal	ADJ
ejpam-6737	46	8	-	-	PUNCT
ejpam-6737	46	9	fractional	fractional	ADJ
ejpam-6737	46	10	derivatives	derivative	NOUN
ejpam-6737	46	11	has	have	AUX
ejpam-6737	46	12	heightened	heighten	VERB
ejpam-6737	46	13	classical	classical	ADJ
ejpam-6737	46	14	fractional	fractional	ADJ
ejpam-6737	46	15	models	model	NOUN
ejpam-6737	46	16	to	to	PART
ejpam-6737	46	17	improve	improve	VERB
ejpam-6737	46	18	on	on	ADP
ejpam-6737	46	19	the	the	DET
ejpam-6737	46	20	depiction	depiction	NOUN
ejpam-6737	46	21	of	of	ADP
ejpam-6737	46	22	sma	sma	NOUN
ejpam-6737	46	23	dynamics	dynamic	NOUN
ejpam-6737	46	24	,	,	PUNCT
ejpam-6737	46	25	especially	especially	ADV
ejpam-6737	46	26	in	in	ADP
ejpam-6737	46	27	situations	situation	NOUN
ejpam-6737	46	28	where	where	SCONJ
ejpam-6737	46	29	common	common	ADJ
ejpam-6737	46	30	power	power	NOUN
ejpam-6737	46	31	-	-	PUNCT
ejpam-6737	46	32	law	law	NOUN
ejpam-6737	46	33	or	or	CCONJ
ejpam-6737	46	34	exponential	exponential	ADJ
ejpam-6737	46	35	decay	decay	NOUN
ejpam-6737	46	36	functions	function	NOUN
ejpam-6737	46	37	fail	fail	VERB
ejpam-6737	46	38	.	.	PUNCT
ejpam-6737	47	1	the	the	DET
ejpam-6737	47	2	current	current	ADJ
ejpam-6737	47	3	study	study	NOUN
ejpam-6737	47	4	proposes	propose	VERB
ejpam-6737	47	5	a	a	DET
ejpam-6737	47	6	fractal	fractal	ADJ
ejpam-6737	47	7	-	-	PUNCT
ejpam-6737	47	8	fractional	fractional	ADJ
ejpam-6737	47	9	mathematical	mathematical	ADJ
ejpam-6737	47	10	model	model	NOUN
ejpam-6737	47	11	for	for	ADP
ejpam-6737	47	12	the	the	DET
ejpam-6737	47	13	analysis	analysis	NOUN
ejpam-6737	47	14	and	and	CCONJ
ejpam-6737	47	15	regulation	regulation	NOUN
ejpam-6737	47	16	of	of	ADP
ejpam-6737	47	17	social	social	ADJ
ejpam-6737	47	18	media	medium	NOUN
ejpam-6737	47	19	addiction	addiction	NOUN
ejpam-6737	47	20	,	,	PUNCT
ejpam-6737	47	21	representing	represent	VERB
ejpam-6737	47	22	an	an	DET
ejpam-6737	47	23	innovative	innovative	ADJ
ejpam-6737	47	24	method	method	NOUN
ejpam-6737	47	25	in	in	ADP
ejpam-6737	47	26	this	this	DET
ejpam-6737	47	27	area	area	NOUN
ejpam-6737	47	28	.	.	PUNCT
ejpam-6737	48	1	in	in	ADP
ejpam-6737	48	2	contrast	contrast	NOUN
ejpam-6737	48	3	to	to	ADP
ejpam-6737	48	4	existing	exist	VERB
ejpam-6737	48	5	models	model	NOUN
ejpam-6737	48	6	,	,	PUNCT
ejpam-6737	48	7	the	the	DET
ejpam-6737	48	8	new	new	ADJ
ejpam-6737	48	9	framework	framework	NOUN
ejpam-6737	48	10	models	model	NOUN
ejpam-6737	48	11	memory	memory	NOUN
ejpam-6737	48	12	effects	effect	NOUN
ejpam-6737	48	13	,	,	PUNCT
ejpam-6737	48	14	intricate	intricate	ADJ
ejpam-6737	48	15	behavioral	behavioral	ADJ
ejpam-6737	48	16	processes	process	NOUN
ejpam-6737	48	17	,	,	PUNCT
ejpam-6737	48	18	and	and	CCONJ
ejpam-6737	48	19	nonlinear	nonlinear	ADJ
ejpam-6737	48	20	interactions	interaction	NOUN
ejpam-6737	48	21	,	,	PUNCT
ejpam-6737	48	22	aiming	aim	VERB
ejpam-6737	48	23	at	at	ADP
ejpam-6737	48	24	a	a	DET
ejpam-6737	48	25	more	more	ADV
ejpam-6737	48	26	realistic	realistic	ADJ
ejpam-6737	48	27	and	and	CCONJ
ejpam-6737	48	28	integrated	integrated	ADJ
ejpam-6737	48	29	comprehension	comprehension	NOUN
ejpam-6737	48	30	of	of	ADP
ejpam-6737	48	31	the	the	DET
ejpam-6737	48	32	development	development	NOUN
ejpam-6737	48	33	of	of	ADP
ejpam-6737	48	34	addiction	addiction	NOUN
ejpam-6737	48	35	.	.	PUNCT
ejpam-6737	49	1	the	the	DET
ejpam-6737	49	2	subject	subject	NOUN
ejpam-6737	49	3	of	of	ADP
ejpam-6737	49	4	this	this	DET
ejpam-6737	49	5	study	study	NOUN
ejpam-6737	49	6	includes	include	VERB
ejpam-6737	49	7	the	the	DET
ejpam-6737	49	8	determination	determination	NOUN
ejpam-6737	49	9	of	of	ADP
ejpam-6737	49	10	best	good	ADJ
ejpam-6737	49	11	treatment	treatment	NOUN
ejpam-6737	49	12	approaches	approach	NOUN
ejpam-6737	49	13	that	that	PRON
ejpam-6737	49	14	facilitate	facilitate	VERB
ejpam-6737	49	15	the	the	DET
ejpam-6737	49	16	recovery	recovery	NOUN
ejpam-6737	49	17	of	of	ADP
ejpam-6737	49	18	addicted	addicted	ADJ
ejpam-6737	49	19	persons	person	NOUN
ejpam-6737	49	20	,	,	PUNCT
ejpam-6737	49	21	especially	especially	ADV
ejpam-6737	49	22	students	student	NOUN
ejpam-6737	49	23	,	,	PUNCT
ejpam-6737	49	24	by	by	ADP
ejpam-6737	49	25	integrating	integrate	VERB
ejpam-6737	49	26	psychological	psychological	ADJ
ejpam-6737	49	27	interventions	intervention	NOUN
ejpam-6737	49	28	into	into	ADP
ejpam-6737	49	29	the	the	DET
ejpam-6737	49	30	framework	framework	NOUN
ejpam-6737	49	31	.	.	PUNCT
ejpam-6737	50	1	moreover	moreover	ADV
ejpam-6737	50	2	,	,	PUNCT
ejpam-6737	50	3	through	through	ADP
ejpam-6737	50	4	the	the	DET
ejpam-6737	50	5	application	application	NOUN
ejpam-6737	50	6	of	of	ADP
ejpam-6737	50	7	non	non	ADJ
ejpam-6737	50	8	-	-	ADJ
ejpam-6737	50	9	singular	singular	ADJ
ejpam-6737	50	10	and	and	CCONJ
ejpam-6737	50	11	fractal	fractal	ADJ
ejpam-6737	50	12	-	-	PUNCT
ejpam-6737	50	13	fractional	fractional	ADJ
ejpam-6737	50	14	operators	operator	NOUN
ejpam-6737	50	15	,	,	PUNCT
ejpam-6737	50	16	this	this	DET
ejpam-6737	50	17	study	study	NOUN
ejpam-6737	50	18	enhances	enhance	VERB
ejpam-6737	50	19	precision	precision	NOUN
ejpam-6737	50	20	in	in	ADP
ejpam-6737	50	21	the	the	DET
ejpam-6737	50	22	forecasting	forecasting	NOUN
ejpam-6737	50	23	of	of	ADP
ejpam-6737	50	24	addiction	addiction	NOUN
ejpam-6737	50	25	patterns	pattern	NOUN
ejpam-6737	50	26	and	and	CCONJ
ejpam-6737	50	27	the	the	DET
ejpam-6737	50	28	effectiveness	effectiveness	NOUN
ejpam-6737	50	29	of	of	ADP
ejpam-6737	50	30	interventions	intervention	NOUN
ejpam-6737	50	31	.	.	PUNCT
ejpam-6737	51	1	the	the	DET
ejpam-6737	51	2	research	research	NOUN
ejpam-6737	51	3	outcome	outcome	NOUN
ejpam-6737	51	4	is	be	AUX
ejpam-6737	51	5	useful	useful	ADJ
ejpam-6737	51	6	in	in	ADP
ejpam-6737	51	7	developing	develop	VERB
ejpam-6737	51	8	evidence	evidence	NOUN
ejpam-6737	51	9	-	-	PUNCT
ejpam-6737	51	10	based	base	VERB
ejpam-6737	51	11	policies	policy	NOUN
ejpam-6737	51	12	for	for	ADP
ejpam-6737	51	13	healthier	healthy	ADJ
ejpam-6737	51	14	digital	digital	ADJ
ejpam-6737	51	15	lifestyles	lifestyle	NOUN
ejpam-6737	51	16	and	and	CCONJ
ejpam-6737	51	17	reducing	reduce	VERB
ejpam-6737	51	18	the	the	DET
ejpam-6737	51	19	adverse	adverse	ADJ
ejpam-6737	51	20	effects	effect	NOUN
ejpam-6737	51	21	of	of	ADP
ejpam-6737	51	22	unhealthy	unhealthy	ADJ
ejpam-6737	51	23	social	social	ADJ
ejpam-6737	51	24	media	medium	NOUN
ejpam-6737	51	25	usage	usage	NOUN
ejpam-6737	51	26	.	.	PUNCT
ejpam-6737	52	1	the	the	DET
ejpam-6737	52	2	paper	paper	NOUN
ejpam-6737	52	3	is	be	AUX
ejpam-6737	52	4	divided	divide	VERB
ejpam-6737	52	5	into	into	ADP
ejpam-6737	52	6	clear	clear	ADJ
ejpam-6737	52	7	sections	section	NOUN
ejpam-6737	52	8	:	:	PUNCT
ejpam-6737	52	9	section	section	NOUN
ejpam-6737	52	10	2	2	NUM
ejpam-6737	52	11	brings	bring	VERB
ejpam-6737	52	12	forth	forth	ADV
ejpam-6737	52	13	basic	basic	ADJ
ejpam-6737	52	14	definitions	definition	NOUN
ejpam-6737	52	15	,	,	PUNCT
ejpam-6737	52	16	and	and	CCONJ
ejpam-6737	52	17	model	model	NOUN
ejpam-6737	52	18	formulation	formulation	NOUN
ejpam-6737	52	19	is	be	AUX
ejpam-6737	52	20	presented	present	VERB
ejpam-6737	52	21	in	in	ADP
ejpam-6737	52	22	section	section	NOUN
ejpam-6737	52	23	3	3	NUM
ejpam-6737	52	24	.	.	PUNCT
ejpam-6737	52	25	qualitative	qualitative	ADJ
ejpam-6737	52	26	analysis	analysis	NOUN
ejpam-6737	52	27	is	be	AUX
ejpam-6737	52	28	discussed	discuss	VERB
ejpam-6737	52	29	in	in	ADP
ejpam-6737	52	30	section	section	NOUN
ejpam-6737	52	31	4	4	NUM
ejpam-6737	52	32	,	,	PUNCT
ejpam-6737	52	33	while	while	SCONJ
ejpam-6737	52	34	section	section	NOUN
ejpam-6737	52	35	5	5	NUM
ejpam-6737	52	36	goes	go	VERB
ejpam-6737	52	37	into	into	ADP
ejpam-6737	52	38	studying	study	VERB
ejpam-6737	52	39	the	the	DET
ejpam-6737	52	40	existence	existence	NOUN
ejpam-6737	52	41	and	and	CCONJ
ejpam-6737	52	42	uniqueness	uniqueness	NOUN
ejpam-6737	52	43	of	of	ADP
ejpam-6737	52	44	the	the	DET
ejpam-6737	52	45	suggested	suggest	VERB
ejpam-6737	52	46	model	model	NOUN
ejpam-6737	52	47	.	.	PUNCT
ejpam-6737	53	1	section	section	NOUN
ejpam-6737	53	2	6	6	NUM
ejpam-6737	53	3	contains	contain	VERB
ejpam-6737	53	4	numerical	numerical	ADJ
ejpam-6737	53	5	simulations	simulation	NOUN
ejpam-6737	53	6	,	,	PUNCT
ejpam-6737	53	7	and	and	CCONJ
ejpam-6737	53	8	section	section	NOUN
ejpam-6737	53	9	7	7	NUM
ejpam-6737	53	10	is	be	AUX
ejpam-6737	53	11	reserved	reserve	VERB
ejpam-6737	53	12	for	for	ADP
ejpam-6737	53	13	results	result	NOUN
ejpam-6737	53	14	discussion	discussion	NOUN
ejpam-6737	53	15	.	.	PUNCT
ejpam-6737	54	1	conclusions	conclusion	NOUN
ejpam-6737	54	2	are	be	AUX
ejpam-6737	54	3	then	then	ADV
ejpam-6737	54	4	drawn	draw	VERB
ejpam-6737	54	5	in	in	ADP
ejpam-6737	54	6	section	section	NOUN
ejpam-6737	54	7	8	8	NUM
ejpam-6737	54	8	.	.	PUNCT
ejpam-6737	55	1	s.	s.	PROPN
ejpam-6737	55	2	m.	m.	PROPN
ejpam-6737	55	3	chithra	chithra	PROPN
ejpam-6737	55	4	et	et	PROPN
ejpam-6737	55	5	al	al	PROPN
ejpam-6737	55	6	.	.	PUNCT
ejpam-6737	55	7	/	/	SYM
ejpam-6737	55	8	eur	eur	PROPN
ejpam-6737	55	9	.	.	PUNCT
ejpam-6737	56	1	j.	j.	PROPN
ejpam-6737	56	2	pure	pure	PROPN
ejpam-6737	56	3	appl	appl	PROPN
ejpam-6737	56	4	.	.	PROPN
ejpam-6737	56	5	math	math	PROPN
ejpam-6737	56	6	,	,	PUNCT
ejpam-6737	56	7	18	18	NUM
ejpam-6737	56	8	(	(	PUNCT
ejpam-6737	56	9	4	4	NUM
ejpam-6737	56	10	)	)	PUNCT
ejpam-6737	56	11	(	(	PUNCT
ejpam-6737	56	12	2025	2025	NUM
ejpam-6737	56	13	)	)	PUNCT
ejpam-6737	56	14	,	,	PUNCT
ejpam-6737	56	15	6737	6737	NUM
ejpam-6737	56	16	4	4	NUM
ejpam-6737	56	17	of	of	ADP
ejpam-6737	56	18	23	23	NUM
ejpam-6737	56	19	2	2	NUM
ejpam-6737	56	20	.	.	PUNCT
ejpam-6737	56	21	preliminaries	preliminary	NOUN
ejpam-6737	56	22	some	some	PRON
ejpam-6737	56	23	of	of	ADP
ejpam-6737	56	24	the	the	DET
ejpam-6737	56	25	basic	basic	ADJ
ejpam-6737	56	26	definitions	definition	NOUN
ejpam-6737	56	27	used	use	VERB
ejpam-6737	56	28	in	in	ADP
ejpam-6737	56	29	fractal	fractal	ADJ
ejpam-6737	56	30	-	-	PUNCT
ejpam-6737	56	31	fractional	fractional	ADJ
ejpam-6737	56	32	differential	differential	ADJ
ejpam-6737	56	33	equations	equation	NOUN
ejpam-6737	56	34	are	be	AUX
ejpam-6737	56	35	provided	provide	VERB
ejpam-6737	56	36	in	in	ADP
ejpam-6737	56	37	refs	ref	NOUN
ejpam-6737	56	38	[	[	X
ejpam-6737	56	39	34	34	NUM
ejpam-6737	56	40	,	,	PUNCT
ejpam-6737	56	41	35	35	NUM
ejpam-6737	56	42	]	]	PUNCT
ejpam-6737	56	43	and	and	CCONJ
ejpam-6737	56	44	are	be	AUX
ejpam-6737	56	45	briefly	briefly	ADV
ejpam-6737	56	46	presented	present	VERB
ejpam-6737	56	47	here	here	ADV
ejpam-6737	56	48	for	for	ADP
ejpam-6737	56	49	completeness	completeness	NOUN
ejpam-6737	56	50	.	.	PUNCT
ejpam-6737	57	1	definition	definition	NOUN
ejpam-6737	57	2	1	1	NUM
ejpam-6737	57	3	.	.	PUNCT
ejpam-6737	58	1	let	let	VERB
ejpam-6737	58	2	h	h	NOUN
ejpam-6737	58	3	∈	∈	PROPN
ejpam-6737	58	4	h1(a	h1(a	PROPN
ejpam-6737	58	5	,	,	PUNCT
ejpam-6737	58	6	b	b	NOUN
ejpam-6737	58	7	)	)	PUNCT
ejpam-6737	58	8	,	,	PUNCT
ejpam-6737	58	9	b	b	X
ejpam-6737	58	10	>	>	X
ejpam-6737	58	11	a	a	X
ejpam-6737	58	12	,	,	PUNCT
ejpam-6737	58	13	and	and	CCONJ
ejpam-6737	58	14	η	η	PROPN
ejpam-6737	58	15	∈	∈	PROPN
ejpam-6737	58	16	(	(	PUNCT
ejpam-6737	58	17	0	0	NUM
ejpam-6737	58	18	,	,	PUNCT
ejpam-6737	58	19	1	1	NUM
ejpam-6737	58	20	)	)	PUNCT
ejpam-6737	58	21	.	.	PUNCT
ejpam-6737	59	1	the	the	DET
ejpam-6737	59	2	atangana	atangana	PROPN
ejpam-6737	59	3	–	–	PUNCT
ejpam-6737	59	4	baleanu	baleanu	ADJ
ejpam-6737	59	5	fractional	fractional	ADJ
ejpam-6737	59	6	derivative	derivative	NOUN
ejpam-6737	59	7	in	in	ADP
ejpam-6737	59	8	caputo	caputo	PROPN
ejpam-6737	59	9	sense	sense	NOUN
ejpam-6737	59	10	is	be	AUX
ejpam-6737	59	11	defined	define	VERB
ejpam-6737	59	12	as	as	ADP
ejpam-6737	59	13	abcdη	abcdη	NOUN
ejpam-6737	59	14	0+h(x	0+h(x	NOUN
ejpam-6737	59	15	)	)	PUNCT
ejpam-6737	60	1	=	=	SYM
ejpam-6737	60	2	n	n	PROPN
ejpam-6737	60	3	(	(	PUNCT
ejpam-6737	60	4	η	η	PROPN
ejpam-6737	60	5	)	)	PUNCT
ejpam-6737	60	6	1−	1−	NUM
ejpam-6737	60	7	η	η	PROPN
ejpam-6737	60	8	∫	∫	PROPN
ejpam-6737	60	9	x	x	PROPN
ejpam-6737	60	10	a	a	DET
ejpam-6737	60	11	h′(τ)eη	h′(τ)eη	PROPN
ejpam-6737	60	12	(	(	PUNCT
ejpam-6737	60	13	−	−	PROPN
ejpam-6737	60	14	η	η	PROPN
ejpam-6737	60	15	1−	1−	PROPN
ejpam-6737	60	16	η	η	PROPN
ejpam-6737	60	17	(	(	PUNCT
ejpam-6737	60	18	x−	x−	PROPN
ejpam-6737	60	19	τ)η	τ)η	PUNCT
ejpam-6737	60	20	)	)	PUNCT
ejpam-6737	60	21	dτ	dτ	NOUN
ejpam-6737	60	22	,	,	PUNCT
ejpam-6737	60	23	where	where	SCONJ
ejpam-6737	60	24	n	n	PROPN
ejpam-6737	60	25	(	(	PUNCT
ejpam-6737	60	26	η	η	PROPN
ejpam-6737	60	27	)	)	PUNCT
ejpam-6737	60	28	is	be	AUX
ejpam-6737	60	29	a	a	DET
ejpam-6737	60	30	normalization	normalization	NOUN
ejpam-6737	60	31	function	function	NOUN
ejpam-6737	60	32	satisfying	satisfy	VERB
ejpam-6737	60	33	n	n	CCONJ
ejpam-6737	60	34	(	(	PUNCT
ejpam-6737	60	35	0	0	NUM
ejpam-6737	60	36	)	)	PUNCT
ejpam-6737	60	37	=	=	SYM
ejpam-6737	61	1	n	n	CCONJ
ejpam-6737	61	2	(	(	PUNCT
ejpam-6737	61	3	1	1	NUM
ejpam-6737	61	4	)	)	PUNCT
ejpam-6737	61	5	=	=	SYM
ejpam-6737	61	6	1	1	NUM
ejpam-6737	61	7	,	,	PUNCT
ejpam-6737	61	8	and	and	CCONJ
ejpam-6737	61	9	eη	eη	PROPN
ejpam-6737	61	10	(	(	PUNCT
ejpam-6737	61	11	·	·	PUNCT
ejpam-6737	61	12	)	)	PUNCT
ejpam-6737	61	13	is	be	AUX
ejpam-6737	61	14	the	the	DET
ejpam-6737	61	15	mittag	mittag	ADJ
ejpam-6737	61	16	–	–	PUNCT
ejpam-6737	61	17	leffler	leffler	NOUN
ejpam-6737	61	18	function	function	NOUN
ejpam-6737	61	19	.	.	PUNCT
ejpam-6737	62	1	definition	definition	NOUN
ejpam-6737	62	2	2	2	NUM
ejpam-6737	62	3	.	.	PUNCT
ejpam-6737	63	1	the	the	DET
ejpam-6737	63	2	fractal	fractal	ADJ
ejpam-6737	63	3	-	-	PUNCT
ejpam-6737	63	4	fractional	fractional	ADJ
ejpam-6737	63	5	derivative	derivative	NOUN
ejpam-6737	63	6	with	with	ADP
ejpam-6737	63	7	mittag	mittag	ADJ
ejpam-6737	63	8	–	–	PUNCT
ejpam-6737	63	9	leffler	leffler	ADJ
ejpam-6737	63	10	kernel	kernel	NOUN
ejpam-6737	63	11	(	(	PUNCT
ejpam-6737	63	12	ffm	ffm	NOUN
ejpam-6737	63	13	)	)	PUNCT
ejpam-6737	63	14	of	of	ADP
ejpam-6737	63	15	order	order	NOUN
ejpam-6737	63	16	η	η	PROPN
ejpam-6737	63	17	∈	∈	PROPN
ejpam-6737	63	18	(	(	PUNCT
ejpam-6737	63	19	0	0	NUM
ejpam-6737	63	20	,	,	PUNCT
ejpam-6737	63	21	1	1	NUM
ejpam-6737	63	22	)	)	PUNCT
ejpam-6737	63	23	and	and	CCONJ
ejpam-6737	63	24	fractal	fractal	ADJ
ejpam-6737	63	25	dimension	dimension	NOUN
ejpam-6737	63	26	ϑ	ϑ	X
ejpam-6737	63	27	>	>	X
ejpam-6737	63	28	0	0	NUM
ejpam-6737	63	29	is	be	AUX
ejpam-6737	63	30	given	give	VERB
ejpam-6737	63	31	by	by	ADP
ejpam-6737	63	32	ffmdη,ϑ	ffmdη,ϑ	ADJ
ejpam-6737	63	33	0+u(t	0+u(t	NOUN
ejpam-6737	63	34	)	)	PUNCT
ejpam-6737	63	35	=	=	SYM
ejpam-6737	63	36	n	n	PROPN
ejpam-6737	63	37	(	(	PUNCT
ejpam-6737	63	38	η	η	PROPN
ejpam-6737	63	39	)	)	PUNCT
ejpam-6737	63	40	1−	1−	NUM
ejpam-6737	63	41	η	η	PROPN
ejpam-6737	63	42	d	d	PROPN
ejpam-6737	63	43	dtϑ	dtϑ	ADP
ejpam-6737	64	1	∫	∫	PROPN
ejpam-6737	64	2	t	t	PROPN
ejpam-6737	64	3	0	0	NUM
ejpam-6737	64	4	eη	eη	NOUN
ejpam-6737	64	5	(	(	PUNCT
ejpam-6737	64	6	−	−	PROPN
ejpam-6737	64	7	η	η	PROPN
ejpam-6737	64	8	1−	1−	PROPN
ejpam-6737	64	9	η	η	PROPN
ejpam-6737	64	10	(	(	PUNCT
ejpam-6737	64	11	t−	t−	PROPN
ejpam-6737	64	12	ψ)η	ψ)η	X
ejpam-6737	64	13	)	)	PUNCT
ejpam-6737	64	14	u(ψ)dψ	u(ψ)dψ	NOUN
ejpam-6737	64	15	(	(	PUNCT
ejpam-6737	64	16	1	1	NUM
ejpam-6737	64	17	)	)	PUNCT
ejpam-6737	64	18	with	with	ADP
ejpam-6737	64	19	corresponding	correspond	VERB
ejpam-6737	64	20	integral	integral	ADJ
ejpam-6737	64	21	operator	operator	NOUN
ejpam-6737	64	22	ffmiη,ϑ	ffmiη,ϑ	PROPN
ejpam-6737	64	23	0	0	SYM
ejpam-6737	64	24	+	+	NUM
ejpam-6737	64	25	u(t	u(t	NOUN
ejpam-6737	64	26	)	)	PUNCT
ejpam-6737	64	27	=	=	PUNCT
ejpam-6737	64	28	ϑ(1−	ϑ(1−	PROPN
ejpam-6737	64	29	η)tϑ−1u(t	η)tϑ−1u(t	PROPN
ejpam-6737	64	30	)	)	PUNCT
ejpam-6737	64	31	n	n	PROPN
ejpam-6737	64	32	(	(	PUNCT
ejpam-6737	64	33	η	η	NOUN
ejpam-6737	64	34	)	)	PUNCT
ejpam-6737	64	35	+	+	CCONJ
ejpam-6737	64	36	ηϑ	ηϑ	ADP
ejpam-6737	64	37	n	n	CCONJ
ejpam-6737	64	38	(	(	PUNCT
ejpam-6737	64	39	η)γ(η	η)γ(η	NUM
ejpam-6737	64	40	)	)	PUNCT
ejpam-6737	64	41	∫	∫	PROPN
ejpam-6737	65	1	t	t	NOUN
ejpam-6737	65	2	0	0	X
ejpam-6737	66	1	ψϑ−1(t−	ψϑ−1(t−	PROPN
ejpam-6737	66	2	ψ)η−1u(ψ)dψ	ψ)η−1u(ψ)dψ	NOUN
ejpam-6737	66	3	(	(	PUNCT
ejpam-6737	66	4	2	2	NUM
ejpam-6737	66	5	)	)	PUNCT
ejpam-6737	66	6	where	where	SCONJ
ejpam-6737	66	7	n	n	PROPN
ejpam-6737	66	8	(	(	PUNCT
ejpam-6737	66	9	η	η	PROPN
ejpam-6737	66	10	)	)	PUNCT
ejpam-6737	66	11	=	=	SYM
ejpam-6737	66	12	1−	1−	NUM
ejpam-6737	66	13	η	η	PROPN
ejpam-6737	66	14	+	+	PROPN
ejpam-6737	66	15	η	η	PROPN
ejpam-6737	66	16	γ(η	γ(η	PROPN
ejpam-6737	66	17	)	)	PUNCT
ejpam-6737	66	18	.	.	PUNCT
ejpam-6737	67	1	3	3	X
ejpam-6737	67	2	.	.	X
ejpam-6737	67	3	materials	material	NOUN
ejpam-6737	67	4	and	and	CCONJ
ejpam-6737	67	5	methods	method	NOUN
ejpam-6737	67	6	in	in	ADP
ejpam-6737	67	7	this	this	DET
ejpam-6737	67	8	study	study	NOUN
ejpam-6737	67	9	,	,	PUNCT
ejpam-6737	67	10	the	the	DET
ejpam-6737	67	11	mathematical	mathematical	ADJ
ejpam-6737	67	12	model	model	NOUN
ejpam-6737	67	13	of	of	ADP
ejpam-6737	67	14	social	social	ADJ
ejpam-6737	67	15	media	medium	NOUN
ejpam-6737	67	16	addiction	addiction	NOUN
ejpam-6737	67	17	is	be	AUX
ejpam-6737	67	18	formulated	formulate	VERB
ejpam-6737	67	19	using	use	VERB
ejpam-6737	67	20	a	a	DET
ejpam-6737	67	21	fractal	fractal	ADJ
ejpam-6737	67	22	–	–	PUNCT
ejpam-6737	67	23	fractional	fractional	ADJ
ejpam-6737	67	24	derivative	derivative	NOUN
ejpam-6737	67	25	with	with	ADP
ejpam-6737	67	26	the	the	DET
ejpam-6737	67	27	generalized	generalized	ADJ
ejpam-6737	67	28	mittag	mittag	ADJ
ejpam-6737	67	29	-	-	PUNCT
ejpam-6737	67	30	leffler	leffler	NOUN
ejpam-6737	67	31	kernel	kernel	NOUN
ejpam-6737	67	32	.	.	PUNCT
ejpam-6737	68	1	the	the	DET
ejpam-6737	68	2	mittag	mittag	ADJ
ejpam-6737	68	3	-	-	PUNCT
ejpam-6737	68	4	leffler	leffler	NOUN
ejpam-6737	68	5	kernel	kernel	NOUN
ejpam-6737	68	6	offers	offer	VERB
ejpam-6737	68	7	significant	significant	ADJ
ejpam-6737	68	8	advantages	advantage	NOUN
ejpam-6737	68	9	compared	compare	VERB
ejpam-6737	68	10	to	to	ADP
ejpam-6737	68	11	the	the	DET
ejpam-6737	68	12	classical	classical	ADJ
ejpam-6737	68	13	power	power	NOUN
ejpam-6737	68	14	-	-	PUNCT
ejpam-6737	68	15	law	law	NOUN
ejpam-6737	68	16	and	and	CCONJ
ejpam-6737	68	17	exponential	exponential	ADJ
ejpam-6737	68	18	kernels	kernel	NOUN
ejpam-6737	68	19	:	:	PUNCT
ejpam-6737	68	20	the	the	DET
ejpam-6737	68	21	power	power	NOUN
ejpam-6737	68	22	-	-	PUNCT
ejpam-6737	68	23	law	law	NOUN
ejpam-6737	68	24	kernel	kernel	NOUN
ejpam-6737	68	25	captures	capture	VERB
ejpam-6737	68	26	long	long	ADJ
ejpam-6737	68	27	-	-	PUNCT
ejpam-6737	68	28	term	term	NOUN
ejpam-6737	68	29	memory	memory	NOUN
ejpam-6737	68	30	with	with	ADP
ejpam-6737	68	31	slow	slow	ADJ
ejpam-6737	68	32	decay	decay	NOUN
ejpam-6737	68	33	but	but	CCONJ
ejpam-6737	68	34	may	may	AUX
ejpam-6737	68	35	exaggerate	exaggerate	VERB
ejpam-6737	68	36	past	past	ADJ
ejpam-6737	68	37	influences	influence	NOUN
ejpam-6737	68	38	,	,	PUNCT
ejpam-6737	68	39	while	while	SCONJ
ejpam-6737	68	40	the	the	DET
ejpam-6737	68	41	exponential	exponential	ADJ
ejpam-6737	68	42	kernel	kernel	NOUN
ejpam-6737	68	43	accounts	account	VERB
ejpam-6737	68	44	only	only	ADV
ejpam-6737	68	45	for	for	ADP
ejpam-6737	68	46	short	short	ADJ
ejpam-6737	68	47	-	-	PUNCT
ejpam-6737	68	48	term	term	NOUN
ejpam-6737	68	49	memory	memory	NOUN
ejpam-6737	68	50	with	with	ADP
ejpam-6737	68	51	rapid	rapid	ADJ
ejpam-6737	68	52	decay	decay	NOUN
ejpam-6737	68	53	.	.	PUNCT
ejpam-6737	69	1	in	in	ADP
ejpam-6737	69	2	contrast	contrast	NOUN
ejpam-6737	69	3	,	,	PUNCT
ejpam-6737	69	4	the	the	DET
ejpam-6737	69	5	mittag	mittag	ADJ
ejpam-6737	69	6	-	-	PUNCT
ejpam-6737	69	7	leffler	leffler	NOUN
ejpam-6737	69	8	kernel	kernel	NOUN
ejpam-6737	69	9	provides	provide	VERB
ejpam-6737	69	10	a	a	DET
ejpam-6737	69	11	more	more	ADV
ejpam-6737	69	12	balanced	balanced	ADJ
ejpam-6737	69	13	description	description	NOUN
ejpam-6737	69	14	by	by	ADP
ejpam-6737	69	15	incorporating	incorporate	VERB
ejpam-6737	69	16	both	both	DET
ejpam-6737	69	17	shortand	shortand	NOUN
ejpam-6737	69	18	long	long	ADJ
ejpam-6737	69	19	-	-	PUNCT
ejpam-6737	69	20	range	range	NOUN
ejpam-6737	69	21	memory	memory	NOUN
ejpam-6737	69	22	effects	effect	NOUN
ejpam-6737	69	23	,	,	PUNCT
ejpam-6737	69	24	which	which	PRON
ejpam-6737	69	25	makes	make	VERB
ejpam-6737	69	26	it	it	PRON
ejpam-6737	69	27	particularly	particularly	ADV
ejpam-6737	69	28	suitable	suitable	ADJ
ejpam-6737	69	29	for	for	ADP
ejpam-6737	69	30	modelling	model	VERB
ejpam-6737	69	31	social	social	ADJ
ejpam-6737	69	32	media	medium	NOUN
ejpam-6737	69	33	addiction	addiction	NOUN
ejpam-6737	69	34	where	where	SCONJ
ejpam-6737	69	35	user	user	NOUN
ejpam-6737	69	36	behaviour	behaviour	NOUN
ejpam-6737	69	37	is	be	AUX
ejpam-6737	69	38	influenced	influence	VERB
ejpam-6737	69	39	by	by	ADP
ejpam-6737	69	40	both	both	PRON
ejpam-6737	69	41	recent	recent	ADJ
ejpam-6737	69	42	interactions	interaction	NOUN
ejpam-6737	69	43	and	and	CCONJ
ejpam-6737	69	44	long	long	ADJ
ejpam-6737	69	45	-	-	PUNCT
ejpam-6737	69	46	term	term	NOUN
ejpam-6737	69	47	usage	usage	NOUN
ejpam-6737	69	48	patterns	pattern	NOUN
ejpam-6737	69	49	.	.	PUNCT
ejpam-6737	70	1	furthermore	furthermore	ADV
ejpam-6737	70	2	,	,	PUNCT
ejpam-6737	70	3	the	the	DET
ejpam-6737	70	4	inclusion	inclusion	NOUN
ejpam-6737	70	5	of	of	ADP
ejpam-6737	70	6	the	the	DET
ejpam-6737	70	7	fractal	fractal	ADJ
ejpam-6737	70	8	dimension	dimension	NOUN
ejpam-6737	70	9	(	(	PUNCT
ejpam-6737	70	10	ϑ	ϑ	NOUN
ejpam-6737	70	11	)	)	PUNCT
ejpam-6737	70	12	enables	enable	VERB
ejpam-6737	70	13	the	the	DET
ejpam-6737	70	14	model	model	NOUN
ejpam-6737	70	15	to	to	PART
ejpam-6737	70	16	account	account	VERB
ejpam-6737	70	17	for	for	ADP
ejpam-6737	70	18	complex	complex	ADJ
ejpam-6737	70	19	irregularities	irregularity	NOUN
ejpam-6737	70	20	in	in	ADP
ejpam-6737	70	21	user	user	NOUN
ejpam-6737	70	22	behavior	behavior	NOUN
ejpam-6737	70	23	,	,	PUNCT
ejpam-6737	70	24	while	while	SCONJ
ejpam-6737	70	25	the	the	DET
ejpam-6737	70	26	fractional	fractional	ADJ
ejpam-6737	70	27	-	-	PUNCT
ejpam-6737	70	28	order	order	NOUN
ejpam-6737	70	29	derivative	derivative	NOUN
ejpam-6737	70	30	(	(	PUNCT
ejpam-6737	70	31	0	0	NUM
ejpam-6737	70	32	<	<	X
ejpam-6737	70	33	η	η	X
ejpam-6737	70	34	<	<	X
ejpam-6737	70	35	1	1	NUM
ejpam-6737	70	36	)	)	PUNCT
ejpam-6737	70	37	captures	capture	VERB
ejpam-6737	70	38	the	the	DET
ejpam-6737	70	39	hereditary	hereditary	ADJ
ejpam-6737	70	40	properties	property	NOUN
ejpam-6737	70	41	of	of	ADP
ejpam-6737	70	42	addiction	addiction	NOUN
ejpam-6737	70	43	dynamics	dynamic	NOUN
ejpam-6737	70	44	with	with	ADP
ejpam-6737	70	45	greater	great	ADJ
ejpam-6737	70	46	accuracy	accuracy	NOUN
ejpam-6737	70	47	than	than	ADP
ejpam-6737	70	48	classical	classical	ADJ
ejpam-6737	70	49	integer	integer	NOUN
ejpam-6737	70	50	-	-	PUNCT
ejpam-6737	70	51	order	order	NOUN
ejpam-6737	70	52	models	model	NOUN
ejpam-6737	70	53	.	.	PUNCT
ejpam-6737	71	1	the	the	DET
ejpam-6737	71	2	proposed	propose	VERB
ejpam-6737	71	3	framework	framework	NOUN
ejpam-6737	71	4	divides	divide	VERB
ejpam-6737	71	5	the	the	DET
ejpam-6737	71	6	population	population	NOUN
ejpam-6737	71	7	into	into	ADP
ejpam-6737	71	8	seven	seven	NUM
ejpam-6737	71	9	subpopulations	subpopulation	NOUN
ejpam-6737	71	10	:	:	PUNCT
ejpam-6737	71	11	susceptible	susceptible	ADJ
ejpam-6737	71	12	individuals	individual	NOUN
ejpam-6737	71	13	using	use	VERB
ejpam-6737	71	14	social	social	ADJ
ejpam-6737	71	15	media	medium	NOUN
ejpam-6737	71	16	in	in	ADP
ejpam-6737	71	17	a	a	DET
ejpam-6737	71	18	normal	normal	ADJ
ejpam-6737	71	19	or	or	CCONJ
ejpam-6737	71	20	typical	typical	ADJ
ejpam-6737	71	21	manner	manner	NOUN
ejpam-6737	71	22	(	(	PUNCT
ejpam-6737	71	23	s	s	NOUN
ejpam-6737	71	24	)	)	PUNCT
ejpam-6737	71	25	,	,	PUNCT
ejpam-6737	71	26	exposed	expose	VERB
ejpam-6737	71	27	individuals	individual	NOUN
ejpam-6737	71	28	(	(	PUNCT
ejpam-6737	71	29	e	e	NOUN
ejpam-6737	71	30	)	)	PUNCT
ejpam-6737	71	31	who	who	PRON
ejpam-6737	71	32	spend	spend	VERB
ejpam-6737	71	33	unusually	unusually	ADV
ejpam-6737	71	34	long	long	ADJ
ejpam-6737	71	35	or	or	CCONJ
ejpam-6737	71	36	extended	extended	ADJ
ejpam-6737	71	37	periods	period	NOUN
ejpam-6737	71	38	of	of	ADP
ejpam-6737	71	39	time	time	NOUN
ejpam-6737	71	40	on	on	ADP
ejpam-6737	71	41	social	social	ADJ
ejpam-6737	71	42	media	medium	NOUN
ejpam-6737	71	43	compared	compare	VERB
ejpam-6737	71	44	s.	s.	PROPN
ejpam-6737	71	45	m.	m.	PROPN
ejpam-6737	71	46	chithra	chithra	PROPN
ejpam-6737	71	47	et	et	PROPN
ejpam-6737	71	48	al	al	PROPN
ejpam-6737	71	49	.	.	PUNCT
ejpam-6737	71	50	/	/	SYM
ejpam-6737	71	51	eur	eur	PROPN
ejpam-6737	71	52	.	.	PUNCT
ejpam-6737	72	1	j.	j.	PROPN
ejpam-6737	72	2	pure	pure	PROPN
ejpam-6737	72	3	appl	appl	PROPN
ejpam-6737	72	4	.	.	PROPN
ejpam-6737	72	5	math	math	PROPN
ejpam-6737	72	6	,	,	PUNCT
ejpam-6737	72	7	18	18	NUM
ejpam-6737	72	8	(	(	PUNCT
ejpam-6737	72	9	4	4	NUM
ejpam-6737	72	10	)	)	PUNCT
ejpam-6737	72	11	(	(	PUNCT
ejpam-6737	72	12	2025	2025	NUM
ejpam-6737	72	13	)	)	PUNCT
ejpam-6737	72	14	,	,	PUNCT
ejpam-6737	72	15	6737	6737	NUM
ejpam-6737	72	16	5	5	NUM
ejpam-6737	72	17	of	of	ADP
ejpam-6737	72	18	23	23	NUM
ejpam-6737	72	19	to	to	ADP
ejpam-6737	72	20	typical	typical	ADJ
ejpam-6737	72	21	usage	usage	NOUN
ejpam-6737	72	22	and	and	CCONJ
ejpam-6737	72	23	are	be	AUX
ejpam-6737	72	24	therefore	therefore	ADV
ejpam-6737	72	25	at	at	ADP
ejpam-6737	72	26	higher	high	ADJ
ejpam-6737	72	27	risk	risk	NOUN
ejpam-6737	72	28	of	of	ADP
ejpam-6737	72	29	transitioning	transition	VERB
ejpam-6737	72	30	into	into	ADP
ejpam-6737	72	31	addiction	addiction	NOUN
ejpam-6737	72	32	,	,	PUNCT
ejpam-6737	72	33	mildly	mildly	ADV
ejpam-6737	72	34	addicted	addict	VERB
ejpam-6737	72	35	individuals	individual	NOUN
ejpam-6737	72	36	(	(	PUNCT
ejpam-6737	72	37	a1	a1	NOUN
ejpam-6737	72	38	)	)	PUNCT
ejpam-6737	72	39	,	,	PUNCT
ejpam-6737	72	40	severely	severely	ADV
ejpam-6737	72	41	addicted	addict	VERB
ejpam-6737	72	42	individuals	individual	NOUN
ejpam-6737	72	43	(	(	PUNCT
ejpam-6737	72	44	a2	a2	PROPN
ejpam-6737	72	45	)	)	PUNCT
ejpam-6737	72	46	,	,	PUNCT
ejpam-6737	72	47	individuals	individual	NOUN
ejpam-6737	72	48	undergoing	undergo	VERB
ejpam-6737	72	49	psychological	psychological	ADJ
ejpam-6737	72	50	treatment	treatment	NOUN
ejpam-6737	72	51	(	(	PUNCT
ejpam-6737	72	52	p	p	NOUN
ejpam-6737	72	53	)	)	PUNCT
ejpam-6737	72	54	,	,	PUNCT
ejpam-6737	72	55	recovered	recover	VERB
ejpam-6737	72	56	individuals	individual	NOUN
ejpam-6737	72	57	(	(	PUNCT
ejpam-6737	72	58	r	r	NOUN
ejpam-6737	72	59	)	)	PUNCT
ejpam-6737	72	60	,	,	PUNCT
ejpam-6737	72	61	and	and	CCONJ
ejpam-6737	72	62	non	non	NOUN
ejpam-6737	72	63	-	-	NOUN
ejpam-6737	72	64	users	user	NOUN
ejpam-6737	72	65	(	(	PUNCT
ejpam-6737	72	66	q	q	NOUN
ejpam-6737	72	67	)	)	PUNCT
ejpam-6737	72	68	.	.	PUNCT
ejpam-6737	73	1	the	the	DET
ejpam-6737	73	2	recruitment	recruitment	NOUN
ejpam-6737	73	3	of	of	ADP
ejpam-6737	73	4	new	new	ADJ
ejpam-6737	73	5	susceptible	susceptible	ADJ
ejpam-6737	73	6	individuals	individual	NOUN
ejpam-6737	73	7	is	be	AUX
ejpam-6737	73	8	represented	represent	VERB
ejpam-6737	73	9	by	by	ADP
ejpam-6737	73	10	λ	λ	NOUN
ejpam-6737	73	11	,	,	PUNCT
ejpam-6737	73	12	while	while	SCONJ
ejpam-6737	73	13	natural	natural	ADJ
ejpam-6737	73	14	death	death	NOUN
ejpam-6737	73	15	occurs	occur	VERB
ejpam-6737	73	16	at	at	ADP
ejpam-6737	73	17	rate	rate	NOUN
ejpam-6737	73	18	µ.	µ.	PROPN
ejpam-6737	73	19	the	the	DET
ejpam-6737	73	20	transmission	transmission	NOUN
ejpam-6737	73	21	of	of	ADP
ejpam-6737	73	22	social	social	ADJ
ejpam-6737	73	23	media	medium	NOUN
ejpam-6737	73	24	addiction	addiction	NOUN
ejpam-6737	73	25	is	be	AUX
ejpam-6737	73	26	governed	govern	VERB
ejpam-6737	73	27	by	by	ADP
ejpam-6737	73	28	the	the	DET
ejpam-6737	73	29	parameter	parameter	NOUN
ejpam-6737	73	30	α	α	NOUN
ejpam-6737	73	31	,	,	PUNCT
ejpam-6737	73	32	which	which	PRON
ejpam-6737	73	33	represents	represent	VERB
ejpam-6737	73	34	the	the	DET
ejpam-6737	73	35	rate	rate	NOUN
ejpam-6737	73	36	at	at	ADP
ejpam-6737	73	37	which	which	PRON
ejpam-6737	73	38	susceptible	susceptible	ADJ
ejpam-6737	73	39	individuals	individual	NOUN
ejpam-6737	73	40	become	become	VERB
ejpam-6737	73	41	addicted	addicted	ADJ
ejpam-6737	73	42	due	due	ADP
ejpam-6737	73	43	to	to	ADP
ejpam-6737	73	44	exposure	exposure	NOUN
ejpam-6737	73	45	and	and	CCONJ
ejpam-6737	73	46	peer	peer	NOUN
ejpam-6737	73	47	influence	influence	NOUN
ejpam-6737	73	48	,	,	PUNCT
ejpam-6737	73	49	along	along	ADP
ejpam-6737	73	50	with	with	ADP
ejpam-6737	73	51	the	the	DET
ejpam-6737	73	52	contact	contact	NOUN
ejpam-6737	73	53	rate	rate	NOUN
ejpam-6737	73	54	δ	δ	PROPN
ejpam-6737	73	55	between	between	ADP
ejpam-6737	73	56	susceptible	susceptible	ADJ
ejpam-6737	73	57	and	and	CCONJ
ejpam-6737	73	58	addicted	addicted	ADJ
ejpam-6737	73	59	individuals	individual	NOUN
ejpam-6737	73	60	.	.	PUNCT
ejpam-6737	74	1	susceptible	susceptible	ADJ
ejpam-6737	74	2	individuals	individual	NOUN
ejpam-6737	74	3	may	may	AUX
ejpam-6737	74	4	develop	develop	VERB
ejpam-6737	74	5	mild	mild	ADJ
ejpam-6737	74	6	or	or	CCONJ
ejpam-6737	74	7	severe	severe	ADJ
ejpam-6737	74	8	addiction	addiction	NOUN
ejpam-6737	74	9	at	at	ADP
ejpam-6737	74	10	rates	rate	NOUN
ejpam-6737	74	11	λ1	λ1	ADJ
ejpam-6737	74	12	and	and	CCONJ
ejpam-6737	74	13	λ2	λ2	NOUN
ejpam-6737	74	14	,	,	PUNCT
ejpam-6737	74	15	respectively	respectively	ADV
ejpam-6737	74	16	,	,	PUNCT
ejpam-6737	74	17	while	while	SCONJ
ejpam-6737	74	18	susceptible	susceptible	ADJ
ejpam-6737	74	19	and	and	CCONJ
ejpam-6737	74	20	recovered	recover	VERB
ejpam-6737	74	21	individuals	individual	NOUN
ejpam-6737	74	22	re	re	VERB
ejpam-6737	74	23	-	-	VERB
ejpam-6737	74	24	enter	enter	VERB
ejpam-6737	74	25	the	the	DET
ejpam-6737	74	26	non	non	ADJ
ejpam-6737	74	27	-	-	NOUN
ejpam-6737	74	28	user	user	ADJ
ejpam-6737	74	29	category	category	NOUN
ejpam-6737	74	30	at	at	ADP
ejpam-6737	74	31	rates	rate	NOUN
ejpam-6737	74	32	τ1	τ1	VERB
ejpam-6737	74	33	and	and	CCONJ
ejpam-6737	74	34	τ2	τ2	NOUN
ejpam-6737	74	35	.	.	PUNCT
ejpam-6737	75	1	mildly	mildly	ADV
ejpam-6737	75	2	and	and	CCONJ
ejpam-6737	75	3	severely	severely	ADV
ejpam-6737	75	4	addicted	addict	VERB
ejpam-6737	75	5	individuals	individual	NOUN
ejpam-6737	75	6	may	may	AUX
ejpam-6737	75	7	recover	recover	VERB
ejpam-6737	75	8	naturally	naturally	ADV
ejpam-6737	75	9	,	,	PUNCT
ejpam-6737	75	10	without	without	ADP
ejpam-6737	75	11	clinical	clinical	ADJ
ejpam-6737	75	12	intervention	intervention	NOUN
ejpam-6737	75	13	,	,	PUNCT
ejpam-6737	75	14	at	at	ADP
ejpam-6737	75	15	rates	rate	NOUN
ejpam-6737	75	16	ξ1	ξ1	NOUN
ejpam-6737	75	17	and	and	CCONJ
ejpam-6737	75	18	ξ2	ξ2	ADJ
ejpam-6737	75	19	,	,	PUNCT
ejpam-6737	75	20	reflecting	reflect	VERB
ejpam-6737	75	21	self	self	NOUN
ejpam-6737	75	22	-	-	PUNCT
ejpam-6737	75	23	discipline	discipline	NOUN
ejpam-6737	75	24	,	,	PUNCT
ejpam-6737	75	25	family	family	NOUN
ejpam-6737	75	26	encouragement	encouragement	NOUN
ejpam-6737	75	27	,	,	PUNCT
ejpam-6737	75	28	and	and	CCONJ
ejpam-6737	75	29	awareness	awareness	NOUN
ejpam-6737	75	30	.	.	PUNCT
ejpam-6737	76	1	in	in	ADP
ejpam-6737	76	2	addition	addition	NOUN
ejpam-6737	76	3	,	,	PUNCT
ejpam-6737	76	4	mildly	mildly	ADV
ejpam-6737	76	5	and	and	CCONJ
ejpam-6737	76	6	severely	severely	ADV
ejpam-6737	76	7	addicted	addict	VERB
ejpam-6737	76	8	individuals	individual	NOUN
ejpam-6737	76	9	may	may	AUX
ejpam-6737	76	10	undergo	undergo	VERB
ejpam-6737	76	11	psychological	psychological	ADJ
ejpam-6737	76	12	or	or	CCONJ
ejpam-6737	76	13	behavioural	behavioural	ADJ
ejpam-6737	76	14	treatment	treatment	NOUN
ejpam-6737	76	15	at	at	ADP
ejpam-6737	76	16	rates	rate	NOUN
ejpam-6737	76	17	φ1	φ1	PROPN
ejpam-6737	76	18	and	and	CCONJ
ejpam-6737	76	19	φ2	φ2	PROPN
ejpam-6737	76	20	,	,	PUNCT
ejpam-6737	76	21	respectively	respectively	ADV
ejpam-6737	76	22	,	,	PUNCT
ejpam-6737	76	23	and	and	CCONJ
ejpam-6737	76	24	subsequently	subsequently	ADV
ejpam-6737	76	25	recover	recover	VERB
ejpam-6737	76	26	at	at	ADP
ejpam-6737	76	27	rate	rate	NOUN
ejpam-6737	76	28	ξ3	ξ3	PROPN
ejpam-6737	76	29	.	.	PUNCT
ejpam-6737	77	1	recovered	recover	VERB
ejpam-6737	77	2	individuals	individual	NOUN
ejpam-6737	77	3	may	may	AUX
ejpam-6737	77	4	relapse	relapse	VERB
ejpam-6737	77	5	and	and	CCONJ
ejpam-6737	77	6	return	return	VERB
ejpam-6737	77	7	to	to	ADP
ejpam-6737	77	8	the	the	DET
ejpam-6737	77	9	susceptible	susceptible	ADJ
ejpam-6737	77	10	class	class	NOUN
ejpam-6737	77	11	at	at	ADP
ejpam-6737	77	12	rate	rate	NOUN
ejpam-6737	77	13	γ	γ	PROPN
ejpam-6737	77	14	.	.	PUNCT
ejpam-6737	77	15	finally	finally	ADV
ejpam-6737	77	16	,	,	PUNCT
ejpam-6737	77	17	mildly	mildly	ADV
ejpam-6737	77	18	addicted	addict	VERB
ejpam-6737	77	19	individuals	individual	NOUN
ejpam-6737	77	20	may	may	AUX
ejpam-6737	77	21	progress	progress	VERB
ejpam-6737	77	22	to	to	ADP
ejpam-6737	77	23	severe	severe	ADJ
ejpam-6737	77	24	addiction	addiction	NOUN
ejpam-6737	77	25	at	at	ADP
ejpam-6737	77	26	rate	rate	NOUN
ejpam-6737	77	27	ε	ε	PROPN
ejpam-6737	77	28	.	.	PUNCT
ejpam-6737	78	1	the	the	DET
ejpam-6737	78	2	parameter	parameter	NOUN
ejpam-6737	78	3	transmission	transmission	NOUN
ejpam-6737	78	4	dynamics	dynamic	NOUN
ejpam-6737	78	5	of	of	ADP
ejpam-6737	78	6	the	the	DET
ejpam-6737	78	7	proposed	propose	VERB
ejpam-6737	78	8	model	model	NOUN
ejpam-6737	78	9	are	be	AUX
ejpam-6737	78	10	explained	explain	VERB
ejpam-6737	78	11	in	in	ADP
ejpam-6737	78	12	fig	fig	NOUN
ejpam-6737	78	13	.	.	PUNCT
ejpam-6737	79	1	1	1	X
ejpam-6737	79	2	.	.	X
ejpam-6737	79	3	figure	figure	NOUN
ejpam-6737	79	4	1	1	NUM
ejpam-6737	79	5	:	:	PUNCT
ejpam-6737	79	6	flowchart	flowchart	NOUN
ejpam-6737	79	7	of	of	ADP
ejpam-6737	79	8	the	the	DET
ejpam-6737	79	9	proposed	propose	VERB
ejpam-6737	79	10	fractional	fractional	ADJ
ejpam-6737	79	11	-	-	PUNCT
ejpam-6737	79	12	order	order	NOUN
ejpam-6737	79	13	social	social	ADJ
ejpam-6737	79	14	media	medium	NOUN
ejpam-6737	79	15	addiction	addiction	NOUN
ejpam-6737	79	16	model	model	NOUN
ejpam-6737	79	17	illustrating	illustrate	VERB
ejpam-6737	79	18	the	the	DET
ejpam-6737	79	19	transitions	transition	NOUN
ejpam-6737	79	20	among	among	ADP
ejpam-6737	79	21	susceptible	susceptible	ADJ
ejpam-6737	79	22	,	,	PUNCT
ejpam-6737	79	23	mildly	mildly	ADV
ejpam-6737	79	24	addicted	addicted	ADJ
ejpam-6737	79	25	,	,	PUNCT
ejpam-6737	79	26	severely	severely	ADV
ejpam-6737	79	27	addicted	addict	VERB
ejpam-6737	79	28	,	,	PUNCT
ejpam-6737	79	29	under	under	ADP
ejpam-6737	79	30	psychological	psychological	ADJ
ejpam-6737	79	31	treatment	treatment	NOUN
ejpam-6737	79	32	,	,	PUNCT
ejpam-6737	79	33	and	and	CCONJ
ejpam-6737	79	34	recovered	recover	VERB
ejpam-6737	79	35	compartments	compartment	NOUN
ejpam-6737	79	36	.	.	PUNCT
ejpam-6737	80	1	in	in	ADP
ejpam-6737	80	2	this	this	DET
ejpam-6737	80	3	study	study	NOUN
ejpam-6737	80	4	,	,	PUNCT
ejpam-6737	80	5	the	the	DET
ejpam-6737	80	6	parameters	parameter	NOUN
ejpam-6737	80	7	are	be	AUX
ejpam-6737	80	8	considered	consider	VERB
ejpam-6737	80	9	as	as	ADP
ejpam-6737	80	10	constants	constant	NOUN
ejpam-6737	80	11	,	,	PUNCT
ejpam-6737	80	12	representing	represent	VERB
ejpam-6737	80	13	average	average	ADJ
ejpam-6737	80	14	transition	transition	NOUN
ejpam-6737	80	15	and	and	CCONJ
ejpam-6737	80	16	treatment	treatment	NOUN
ejpam-6737	80	17	rates	rate	NOUN
ejpam-6737	80	18	over	over	ADP
ejpam-6737	80	19	the	the	DET
ejpam-6737	80	20	observation	observation	NOUN
ejpam-6737	80	21	period	period	NOUN
ejpam-6737	80	22	.	.	PUNCT
ejpam-6737	81	1	in	in	ADP
ejpam-6737	81	2	extended	extended	ADJ
ejpam-6737	81	3	formulations	formulation	NOUN
ejpam-6737	81	4	,	,	PUNCT
ejpam-6737	81	5	these	these	DET
ejpam-6737	81	6	parameters	parameter	NOUN
ejpam-6737	81	7	could	could	AUX
ejpam-6737	81	8	alternatively	alternatively	ADV
ejpam-6737	81	9	be	be	AUX
ejpam-6737	81	10	expressed	express	VERB
ejpam-6737	81	11	as	as	ADP
ejpam-6737	81	12	functions	function	NOUN
ejpam-6737	81	13	of	of	ADP
ejpam-6737	81	14	time	time	NOUN
ejpam-6737	81	15	(	(	PUNCT
ejpam-6737	81	16	to	to	PART
ejpam-6737	81	17	capture	capture	VERB
ejpam-6737	81	18	variations	variation	NOUN
ejpam-6737	81	19	due	due	ADP
ejpam-6737	81	20	to	to	ADP
ejpam-6737	81	21	seasonal	seasonal	ADJ
ejpam-6737	81	22	trends	trend	NOUN
ejpam-6737	81	23	or	or	CCONJ
ejpam-6737	81	24	intervention	intervention	NOUN
ejpam-6737	81	25	campaigns	campaign	NOUN
ejpam-6737	81	26	)	)	PUNCT
ejpam-6737	81	27	or	or	CCONJ
ejpam-6737	81	28	as	as	ADP
ejpam-6737	81	29	functions	function	NOUN
ejpam-6737	81	30	of	of	ADP
ejpam-6737	81	31	the	the	DET
ejpam-6737	81	32	system	system	NOUN
ejpam-6737	81	33	state	state	NOUN
ejpam-6737	81	34	(	(	PUNCT
ejpam-6737	81	35	to	to	PART
ejpam-6737	81	36	account	account	VERB
ejpam-6737	81	37	for	for	ADP
ejpam-6737	81	38	behavioral	behavioral	ADJ
ejpam-6737	81	39	saturation	saturation	NOUN
ejpam-6737	81	40	,	,	PUNCT
ejpam-6737	81	41	peer	peer	NOUN
ejpam-6737	81	42	influence	influence	NOUN
ejpam-6737	81	43	,	,	PUNCT
ejpam-6737	81	44	or	or	CCONJ
ejpam-6737	81	45	treatment	treatment	NOUN
ejpam-6737	81	46	capacity	capacity	NOUN
ejpam-6737	81	47	limitations	limitation	NOUN
ejpam-6737	81	48	)	)	PUNCT
ejpam-6737	81	49	.	.	PUNCT
ejpam-6737	82	1	for	for	ADP
ejpam-6737	82	2	analytical	analytical	ADJ
ejpam-6737	82	3	tractability	tractability	NOUN
ejpam-6737	82	4	,	,	PUNCT
ejpam-6737	82	5	the	the	DET
ejpam-6737	82	6	present	present	ADJ
ejpam-6737	82	7	model	model	NOUN
ejpam-6737	82	8	employs	employ	VERB
ejpam-6737	82	9	constant	constant	ADJ
ejpam-6737	82	10	values	value	NOUN
ejpam-6737	82	11	.	.	PUNCT
ejpam-6737	83	1	based	base	VERB
ejpam-6737	83	2	on	on	ADP
ejpam-6737	83	3	the	the	DET
ejpam-6737	83	4	given	give	VERB
ejpam-6737	83	5	parameters	parameter	NOUN
ejpam-6737	83	6	,	,	PUNCT
ejpam-6737	83	7	the	the	DET
ejpam-6737	83	8	mathematical	mathematical	ADJ
ejpam-6737	83	9	model	model	NOUN
ejpam-6737	83	10	is	be	AUX
ejpam-6737	83	11	derived	derive	VERB
ejpam-6737	83	12	that	that	PRON
ejpam-6737	83	13	predicts	predict	VERB
ejpam-6737	83	14	the	the	DET
ejpam-6737	83	15	dynamics	dynamic	NOUN
ejpam-6737	83	16	between	between	ADP
ejpam-6737	83	17	social	social	ADJ
ejpam-6737	83	18	media	medium	NOUN
ejpam-6737	83	19	addiction	addiction	NOUN
ejpam-6737	83	20	and	and	CCONJ
ejpam-6737	83	21	recovery	recovery	NOUN
ejpam-6737	83	22	with	with	ADP
ejpam-6737	83	23	the	the	DET
ejpam-6737	83	24	inclusion	inclusion	NOUN
ejpam-6737	83	25	of	of	ADP
ejpam-6737	83	26	psychological	psychological	ADJ
ejpam-6737	83	27	interventions	intervention	NOUN
ejpam-6737	83	28	aimed	aim	VERB
ejpam-6737	83	29	at	at	ADP
ejpam-6737	83	30	understanding	understand	VERB
ejpam-6737	83	31	their	their	PRON
ejpam-6737	83	32	effects	effect	NOUN
ejpam-6737	83	33	on	on	ADP
ejpam-6737	83	34	controlling	control	VERB
ejpam-6737	83	35	addiction	addiction	NOUN
ejpam-6737	83	36	.	.	PUNCT
ejpam-6737	84	1	these	these	DET
ejpam-6737	84	2	model	model	NOUN
ejpam-6737	84	3	s.	s.	PROPN
ejpam-6737	84	4	m.	m.	PROPN
ejpam-6737	84	5	chithra	chithra	PROPN
ejpam-6737	84	6	et	et	PROPN
ejpam-6737	84	7	al	al	PROPN
ejpam-6737	84	8	.	.	PUNCT
ejpam-6737	84	9	/	/	SYM
ejpam-6737	84	10	eur	eur	PROPN
ejpam-6737	84	11	.	.	PUNCT
ejpam-6737	85	1	j.	j.	PROPN
ejpam-6737	85	2	pure	pure	PROPN
ejpam-6737	85	3	appl	appl	PROPN
ejpam-6737	85	4	.	.	PROPN
ejpam-6737	85	5	math	math	PROPN
ejpam-6737	85	6	,	,	PUNCT
ejpam-6737	85	7	18	18	NUM
ejpam-6737	85	8	(	(	PUNCT
ejpam-6737	85	9	4	4	NUM
ejpam-6737	85	10	)	)	PUNCT
ejpam-6737	85	11	(	(	PUNCT
ejpam-6737	85	12	2025	2025	NUM
ejpam-6737	85	13	)	)	PUNCT
ejpam-6737	85	14	,	,	PUNCT
ejpam-6737	85	15	6737	6737	NUM
ejpam-6737	85	16	6	6	NUM
ejpam-6737	85	17	of	of	ADP
ejpam-6737	85	18	23	23	NUM
ejpam-6737	85	19	equations	equation	NOUN
ejpam-6737	85	20	are	be	AUX
ejpam-6737	85	21	given	give	VERB
ejpam-6737	85	22	below	below	ADP
ejpam-6737	85	23	:	:	PUNCT
ejpam-6737	85	24	ffmdη,ϑ	ffmdη,ϑ	PROPN
ejpam-6737	85	25	0	0	NUM
ejpam-6737	85	26	+	+	NUM
ejpam-6737	85	27	s(t	s(t	NUM
ejpam-6737	85	28	)	)	PUNCT
ejpam-6737	85	29	=	=	PUNCT
ejpam-6737	86	1	λ−	λ−	PROPN
ejpam-6737	86	2	αδs−	αδs−	NUM
ejpam-6737	86	3	(	(	PUNCT
ejpam-6737	86	4	τ1	τ1	NOUN
ejpam-6737	86	5	+	+	CCONJ
ejpam-6737	86	6	µ)s+	µ)s+	NUM
ejpam-6737	86	7	γr	γr	PROPN
ejpam-6737	86	8	,	,	PUNCT
ejpam-6737	86	9	ffmdη,ϑ	ffmdη,ϑ	PROPN
ejpam-6737	86	10	0+e(t	0+e(t	NOUN
ejpam-6737	86	11	)	)	PUNCT
ejpam-6737	86	12	=	=	PUNCT
ejpam-6737	87	1	αδs−	αδs−	VERB
ejpam-6737	87	2	(	(	PUNCT
ejpam-6737	87	3	λ1	λ1	ADJ
ejpam-6737	87	4	+	+	NUM
ejpam-6737	87	5	λ2	λ2	NOUN
ejpam-6737	87	6	+	+	CCONJ
ejpam-6737	87	7	µ)e	µ)e	NOUN
ejpam-6737	87	8	,	,	PUNCT
ejpam-6737	87	9	ffmdη,ϑ	ffmdη,ϑ	ADJ
ejpam-6737	87	10	0+a1(t	0+a1(t	NOUN
ejpam-6737	87	11	)	)	PUNCT
ejpam-6737	88	1	=	=	SYM
ejpam-6737	88	2	λ1e−	λ1e−	PROPN
ejpam-6737	88	3	(	(	PUNCT
ejpam-6737	88	4	ε+	ε+	X
ejpam-6737	88	5	φ1	φ1	NOUN
ejpam-6737	88	6	+	+	CCONJ
ejpam-6737	88	7	ξ1	ξ1	PROPN
ejpam-6737	88	8	+	+	CCONJ
ejpam-6737	88	9	µ)a1	µ)a1	PROPN
ejpam-6737	88	10	,	,	PUNCT
ejpam-6737	88	11	ffmdη,ϑ	ffmdη,ϑ	X
ejpam-6737	88	12	0+a2(t	0+a2(t	NOUN
ejpam-6737	88	13	)	)	PUNCT
ejpam-6737	88	14	=	=	SYM
ejpam-6737	89	1	λ2e+	λ2e+	NOUN
ejpam-6737	89	2	εa1	εa1	NOUN
ejpam-6737	89	3	−	−	PROPN
ejpam-6737	89	4	(	(	PUNCT
ejpam-6737	89	5	φ2	φ2	PROPN
ejpam-6737	89	6	+	+	CCONJ
ejpam-6737	89	7	ξ2	ξ2	NOUN
ejpam-6737	89	8	+	+	CCONJ
ejpam-6737	89	9	µ)a2	µ)a2	PROPN
ejpam-6737	89	10	,	,	PUNCT
ejpam-6737	89	11	ffmdη,ϑ	ffmdη,ϑ	ADJ
ejpam-6737	89	12	0+p(t	0+p(t	NOUN
ejpam-6737	89	13	)	)	PUNCT
ejpam-6737	89	14	=	=	PUNCT
ejpam-6737	90	1	φ1a1	φ1a1	PUNCT
ejpam-6737	90	2	+	+	NUM
ejpam-6737	90	3	φ2a2	φ2a2	NOUN
ejpam-6737	90	4	−	−	PROPN
ejpam-6737	90	5	(	(	PUNCT
ejpam-6737	90	6	ξ3	ξ3	NOUN
ejpam-6737	90	7	+	+	CCONJ
ejpam-6737	90	8	µ)p	µ)p	NOUN
ejpam-6737	90	9	,	,	PUNCT
ejpam-6737	90	10	ffmdη,ϑ	ffmdη,ϑ	ADJ
ejpam-6737	90	11	0+r(t	0+r(t	NOUN
ejpam-6737	90	12	)	)	PUNCT
ejpam-6737	90	13	=	=	SYM
ejpam-6737	91	1	ξ1a1	ξ1a1	X
ejpam-6737	91	2	+	+	SYM
ejpam-6737	91	3	ξ2a2	ξ2a2	NOUN
ejpam-6737	92	1	+	+	CCONJ
ejpam-6737	92	2	ξ3p−	ξ3p−	NUM
ejpam-6737	92	3	(	(	PUNCT
ejpam-6737	92	4	γ	γ	X
ejpam-6737	92	5	+	+	CCONJ
ejpam-6737	92	6	τ2	τ2	NOUN
ejpam-6737	92	7	+	+	CCONJ
ejpam-6737	92	8	µ)r	µ)r	ADJ
ejpam-6737	92	9	,	,	PUNCT
ejpam-6737	92	10	ffmdη,ϑ	ffmdη,ϑ	ADJ
ejpam-6737	92	11	0+q(t	0+q(t	NOUN
ejpam-6737	92	12	)	)	PUNCT
ejpam-6737	92	13	=	=	PUNCT
ejpam-6737	93	1	τ1s+	τ1s+	DET
ejpam-6737	93	2	τ2r−	τ2r−	PROPN
ejpam-6737	93	3	µq	µq	PROPN
ejpam-6737	93	4	.	.	PUNCT
ejpam-6737	94	1	(	(	PUNCT
ejpam-6737	94	2	3	3	X
ejpam-6737	94	3	)	)	PUNCT
ejpam-6737	94	4	these	these	PRON
ejpam-6737	94	5	are	be	AUX
ejpam-6737	94	6	the	the	DET
ejpam-6737	94	7	equations	equation	NOUN
ejpam-6737	94	8	for	for	ADP
ejpam-6737	94	9	the	the	DET
ejpam-6737	94	10	dynamic	dynamic	ADJ
ejpam-6737	94	11	development	development	NOUN
ejpam-6737	94	12	of	of	ADP
ejpam-6737	94	13	variables	variable	NOUN
ejpam-6737	94	14	(	(	PUNCT
ejpam-6737	94	15	s(t	s(t	PROPN
ejpam-6737	94	16	)	)	PUNCT
ejpam-6737	94	17	,	,	PUNCT
ejpam-6737	94	18	e(t	e(t	NOUN
ejpam-6737	94	19	)	)	PUNCT
ejpam-6737	94	20	,	,	PUNCT
ejpam-6737	94	21	a1(t	a1(t	PROPN
ejpam-6737	94	22	)	)	PUNCT
ejpam-6737	94	23	,	,	PUNCT
ejpam-6737	94	24	a2(t	a2(t	PROPN
ejpam-6737	94	25	)	)	PUNCT
ejpam-6737	94	26	,	,	PUNCT
ejpam-6737	94	27	p(t	p(t	NOUN
ejpam-6737	94	28	)	)	PUNCT
ejpam-6737	94	29	,	,	PUNCT
ejpam-6737	94	30	r(t	r(t	NOUN
ejpam-6737	94	31	)	)	PUNCT
ejpam-6737	94	32	,	,	PUNCT
ejpam-6737	94	33	q(t	q(t	PROPN
ejpam-6737	94	34	)	)	PUNCT
ejpam-6737	94	35	)	)	PUNCT
ejpam-6737	94	36	≥	≥	NOUN
ejpam-6737	94	37	0	0	NUM
ejpam-6737	94	38	over	over	ADP
ejpam-6737	94	39	time	time	NOUN
ejpam-6737	94	40	in	in	ADP
ejpam-6737	94	41	the	the	DET
ejpam-6737	94	42	context	context	NOUN
ejpam-6737	94	43	of	of	ADP
ejpam-6737	94	44	the	the	DET
ejpam-6737	94	45	suggested	suggest	VERB
ejpam-6737	94	46	model	model	NOUN
ejpam-6737	94	47	.	.	PUNCT
ejpam-6737	95	1	the	the	DET
ejpam-6737	95	2	adopted	adopt	VERB
ejpam-6737	95	3	framework	framework	NOUN
ejpam-6737	95	4	employs	employ	VERB
ejpam-6737	95	5	caputotype	caputotype	ADJ
ejpam-6737	95	6	concepts	concept	NOUN
ejpam-6737	95	7	,	,	PUNCT
ejpam-6737	95	8	where	where	SCONJ
ejpam-6737	95	9	the	the	DET
ejpam-6737	95	10	fractal	fractal	ADJ
ejpam-6737	95	11	–	–	PUNCT
ejpam-6737	95	12	fractional	fractional	ADJ
ejpam-6737	95	13	derivative	derivative	NOUN
ejpam-6737	95	14	with	with	ADP
ejpam-6737	95	15	a	a	DET
ejpam-6737	95	16	generalized	generalized	ADJ
ejpam-6737	95	17	mittag	mittag	ADJ
ejpam-6737	95	18	-	-	PUNCT
ejpam-6737	95	19	leffler	leffler	NOUN
ejpam-6737	95	20	kernel	kernel	NOUN
ejpam-6737	95	21	(	(	PUNCT
ejpam-6737	95	22	ffm	ffm	NOUN
ejpam-6737	95	23	0	0	NUM
ejpam-6737	95	24	dη,ϑ	dη,ϑ	X
ejpam-6737	95	25	t	t	NOUN
ejpam-6737	95	26	)	)	PUNCT
ejpam-6737	95	27	is	be	AUX
ejpam-6737	95	28	used	use	VERB
ejpam-6737	95	29	,	,	PUNCT
ejpam-6737	95	30	combining	combine	VERB
ejpam-6737	95	31	both	both	DET
ejpam-6737	95	32	the	the	DET
ejpam-6737	95	33	fractional	fractional	ADJ
ejpam-6737	95	34	order	order	NOUN
ejpam-6737	95	35	(	(	PUNCT
ejpam-6737	95	36	η	η	NOUN
ejpam-6737	95	37	)	)	PUNCT
ejpam-6737	95	38	and	and	CCONJ
ejpam-6737	95	39	fractal	fractal	ADJ
ejpam-6737	95	40	dimension	dimension	NOUN
ejpam-6737	95	41	(	(	PUNCT
ejpam-6737	95	42	ϑ	ϑ	NOUN
ejpam-6737	95	43	)	)	PUNCT
ejpam-6737	95	44	to	to	PART
ejpam-6737	95	45	enhance	enhance	VERB
ejpam-6737	95	46	the	the	DET
ejpam-6737	95	47	realism	realism	NOUN
ejpam-6737	95	48	and	and	CCONJ
ejpam-6737	95	49	descriptive	descriptive	ADJ
ejpam-6737	95	50	power	power	NOUN
ejpam-6737	95	51	of	of	ADP
ejpam-6737	95	52	the	the	DET
ejpam-6737	95	53	model	model	NOUN
ejpam-6737	95	54	.	.	PUNCT
ejpam-6737	96	1	4	4	X
ejpam-6737	96	2	.	.	NOUN
ejpam-6737	96	3	qualitative	qualitative	ADJ
ejpam-6737	96	4	analysis	analysis	NOUN
ejpam-6737	96	5	theorem	theorem	VERB
ejpam-6737	96	6	1	1	NUM
ejpam-6737	96	7	.	.	PUNCT
ejpam-6737	97	1	the	the	DET
ejpam-6737	97	2	proposed	propose	VERB
ejpam-6737	97	3	fractional	fractional	ADJ
ejpam-6737	97	4	-	-	PUNCT
ejpam-6737	97	5	order	order	NOUN
ejpam-6737	97	6	system	system	NOUN
ejpam-6737	97	7	(	(	PUNCT
ejpam-6737	97	8	3	3	X
ejpam-6737	97	9	)	)	PUNCT
ejpam-6737	97	10	admits	admit	VERB
ejpam-6737	97	11	a	a	DET
ejpam-6737	97	12	unique	unique	ADJ
ejpam-6737	97	13	,	,	PUNCT
ejpam-6737	97	14	positive	positive	ADJ
ejpam-6737	97	15	,	,	PUNCT
ejpam-6737	97	16	and	and	CCONJ
ejpam-6737	97	17	bounded	bound	VERB
ejpam-6737	97	18	solution	solution	NOUN
ejpam-6737	97	19	in	in	ADP
ejpam-6737	97	20	the	the	DET
ejpam-6737	97	21	region	region	NOUN
ejpam-6737	97	22	r7	r7	PROPN
ejpam-6737	97	23	+	+	PROPN
ejpam-6737	97	24	.	.	PUNCT
ejpam-6737	98	1	proof	proof	NOUN
ejpam-6737	98	2	.	.	PUNCT
ejpam-6737	99	1	to	to	PART
ejpam-6737	99	2	establish	establish	VERB
ejpam-6737	99	3	existence	existence	NOUN
ejpam-6737	99	4	,	,	PUNCT
ejpam-6737	99	5	uniqueness	uniqueness	NOUN
ejpam-6737	99	6	,	,	PUNCT
ejpam-6737	99	7	and	and	CCONJ
ejpam-6737	99	8	positivity	positivity	NOUN
ejpam-6737	99	9	of	of	ADP
ejpam-6737	99	10	the	the	DET
ejpam-6737	99	11	solutions	solution	NOUN
ejpam-6737	99	12	of	of	ADP
ejpam-6737	99	13	system	system	NOUN
ejpam-6737	99	14	(	(	PUNCT
ejpam-6737	99	15	3	3	NUM
ejpam-6737	99	16	)	)	PUNCT
ejpam-6737	99	17	over	over	ADP
ejpam-6737	99	18	the	the	DET
ejpam-6737	99	19	interval	interval	NOUN
ejpam-6737	99	20	(	(	PUNCT
ejpam-6737	99	21	0,∞	0,∞	NUM
ejpam-6737	99	22	)	)	PUNCT
ejpam-6737	99	23	,	,	PUNCT
ejpam-6737	99	24	it	it	PRON
ejpam-6737	99	25	is	be	AUX
ejpam-6737	99	26	sufficient	sufficient	ADJ
ejpam-6737	99	27	to	to	PART
ejpam-6737	99	28	show	show	VERB
ejpam-6737	99	29	that	that	SCONJ
ejpam-6737	99	30	the	the	DET
ejpam-6737	99	31	non	non	ADJ
ejpam-6737	99	32	-	-	ADJ
ejpam-6737	99	33	negative	negative	ADJ
ejpam-6737	99	34	region	region	NOUN
ejpam-6737	99	35	r7	r7	NOUN
ejpam-6737	99	36	+	+	CCONJ
ejpam-6737	99	37	is	be	AUX
ejpam-6737	99	38	invariant	invariant	ADJ
ejpam-6737	99	39	under	under	ADP
ejpam-6737	99	40	the	the	DET
ejpam-6737	99	41	system	system	NOUN
ejpam-6737	99	42	dynamics	dynamic	NOUN
ejpam-6737	99	43	.	.	PUNCT
ejpam-6737	100	1	in	in	ADP
ejpam-6737	100	2	other	other	ADJ
ejpam-6737	100	3	words	word	NOUN
ejpam-6737	100	4	,	,	PUNCT
ejpam-6737	100	5	if	if	SCONJ
ejpam-6737	100	6	the	the	DET
ejpam-6737	100	7	initial	initial	ADJ
ejpam-6737	100	8	conditions	condition	NOUN
ejpam-6737	100	9	are	be	AUX
ejpam-6737	100	10	nonnegative	nonnegative	ADJ
ejpam-6737	100	11	,	,	PUNCT
ejpam-6737	100	12	then	then	ADV
ejpam-6737	100	13	the	the	DET
ejpam-6737	100	14	trajectories	trajectory	NOUN
ejpam-6737	100	15	of	of	ADP
ejpam-6737	100	16	the	the	DET
ejpam-6737	100	17	system	system	NOUN
ejpam-6737	100	18	remain	remain	VERB
ejpam-6737	100	19	in	in	ADP
ejpam-6737	100	20	r7	r7	PROPN
ejpam-6737	100	21	+	+	CCONJ
ejpam-6737	100	22	for	for	ADP
ejpam-6737	100	23	all	all	DET
ejpam-6737	100	24	t	t	NOUN
ejpam-6737	100	25	>	>	X
ejpam-6737	100	26	0	0	X
ejpam-6737	100	27	.	.	PUNCT
ejpam-6737	101	1	furthermore	furthermore	ADV
ejpam-6737	101	2	,	,	PUNCT
ejpam-6737	101	3	by	by	ADP
ejpam-6737	101	4	analysing	analyse	VERB
ejpam-6737	101	5	the	the	DET
ejpam-6737	101	6	governing	govern	VERB
ejpam-6737	101	7	equations	equation	NOUN
ejpam-6737	101	8	,	,	PUNCT
ejpam-6737	101	9	it	it	PRON
ejpam-6737	101	10	can	can	AUX
ejpam-6737	101	11	be	be	AUX
ejpam-6737	101	12	shown	show	VERB
ejpam-6737	101	13	that	that	SCONJ
ejpam-6737	101	14	all	all	DET
ejpam-6737	101	15	state	state	NOUN
ejpam-6737	101	16	variables	variable	NOUN
ejpam-6737	101	17	are	be	AUX
ejpam-6737	101	18	bounded	bound	VERB
ejpam-6737	101	19	above	above	ADV
ejpam-6737	101	20	by	by	ADP
ejpam-6737	101	21	biologically	biologically	ADV
ejpam-6737	101	22	/	/	SYM
ejpam-6737	101	23	socially	socially	ADV
ejpam-6737	101	24	feasible	feasible	ADJ
ejpam-6737	101	25	limits	limit	NOUN
ejpam-6737	101	26	,	,	PUNCT
ejpam-6737	101	27	ensuring	ensure	VERB
ejpam-6737	101	28	that	that	SCONJ
ejpam-6737	101	29	the	the	DET
ejpam-6737	101	30	solutions	solution	NOUN
ejpam-6737	101	31	are	be	AUX
ejpam-6737	101	32	not	not	PART
ejpam-6737	101	33	only	only	ADV
ejpam-6737	101	34	positive	positive	ADJ
ejpam-6737	101	35	but	but	CCONJ
ejpam-6737	101	36	also	also	ADV
ejpam-6737	101	37	uniformly	uniformly	ADV
ejpam-6737	101	38	bounded	bound	VERB
ejpam-6737	101	39	.	.	PUNCT
ejpam-6737	102	1	ffm	ffm	NOUN
ejpam-6737	102	2	0	0	NUM
ejpam-6737	102	3	dη,ϑ	dη,ϑ	PROPN
ejpam-6737	102	4	t	t	PROPN
ejpam-6737	102	5	s(t	s(t	PROPN
ejpam-6737	102	6	)	)	PUNCT
ejpam-6737	103	1	∣∣	∣∣	NUM
ejpam-6737	103	2	s=0	s=0	PROPN
ejpam-6737	104	1	=	=	PUNCT
ejpam-6737	104	2	λ+	λ+	PUNCT
ejpam-6737	104	3	γr	γr	X
ejpam-6737	104	4	≥	≥	NUM
ejpam-6737	104	5	0	0	NUM
ejpam-6737	104	6	,	,	PUNCT
ejpam-6737	104	7	ffm	ffm	NOUN
ejpam-6737	104	8	0	0	NUM
ejpam-6737	104	9	dη,ϑ	dη,ϑ	X
ejpam-6737	104	10	t	t	PROPN
ejpam-6737	104	11	e(t	e(t	PROPN
ejpam-6737	104	12	)	)	PUNCT
ejpam-6737	104	13	∣∣	∣∣	X
ejpam-6737	104	14	e=0	e=0	PUNCT
ejpam-6737	104	15	=	=	SYM
ejpam-6737	104	16	αδs	αδs	ADJ
ejpam-6737	104	17	≥	≥	NOUN
ejpam-6737	104	18	0	0	NUM
ejpam-6737	104	19	,	,	PUNCT
ejpam-6737	104	20	ffm	ffm	NOUN
ejpam-6737	104	21	0	0	NUM
ejpam-6737	104	22	dη,ϑ	dη,ϑ	X
ejpam-6737	104	23	t	t	PROPN
ejpam-6737	104	24	a1(t	a1(t	PROPN
ejpam-6737	104	25	)	)	PUNCT
ejpam-6737	104	26	∣∣	∣∣	NUM
ejpam-6737	105	1	a1=0	a1=0	PROPN
ejpam-6737	105	2	=	=	X
ejpam-6737	105	3	λ1e	λ1e	X
ejpam-6737	105	4	≥	≥	NOUN
ejpam-6737	105	5	0	0	NUM
ejpam-6737	105	6	,	,	PUNCT
ejpam-6737	105	7	ffm	ffm	NOUN
ejpam-6737	105	8	0	0	NUM
ejpam-6737	105	9	dη,ϑ	dη,ϑ	X
ejpam-6737	105	10	t	t	PROPN
ejpam-6737	105	11	a2(t	a2(t	PROPN
ejpam-6737	105	12	)	)	PUNCT
ejpam-6737	105	13	∣∣	∣∣	NUM
ejpam-6737	105	14	a2=0	a2=0	PUNCT
ejpam-6737	105	15	=	=	SYM
ejpam-6737	106	1	λ2e+	λ2e+	PROPN
ejpam-6737	106	2	εa1	εa1	PROPN
ejpam-6737	106	3	≥	≥	NOUN
ejpam-6737	106	4	0	0	NUM
ejpam-6737	106	5	,	,	PUNCT
ejpam-6737	106	6	ffm	ffm	NOUN
ejpam-6737	106	7	0	0	NUM
ejpam-6737	106	8	dη,ϑ	dη,ϑ	NOUN
ejpam-6737	106	9	t	t	NOUN
ejpam-6737	106	10	p(t	p(t	NOUN
ejpam-6737	106	11	)	)	PUNCT
ejpam-6737	106	12	∣∣	∣∣	X
ejpam-6737	107	1	p=0	p=0	X
ejpam-6737	107	2	=	=	PUNCT
ejpam-6737	108	1	φ1a1	φ1a1	PROPN
ejpam-6737	108	2	+	+	NUM
ejpam-6737	108	3	φ2a2	φ2a2	PROPN
ejpam-6737	108	4	≥	≥	NOUN
ejpam-6737	108	5	0	0	NUM
ejpam-6737	108	6	,	,	PUNCT
ejpam-6737	108	7	ffm	ffm	NOUN
ejpam-6737	108	8	0	0	NUM
ejpam-6737	108	9	dη,ϑ	dη,ϑ	X
ejpam-6737	108	10	t	t	NOUN
ejpam-6737	108	11	r(t	r(t	NOUN
ejpam-6737	108	12	)	)	PUNCT
ejpam-6737	108	13	∣∣	∣∣	X
ejpam-6737	109	1	r=0	r=0	X
ejpam-6737	109	2	=	=	PUNCT
ejpam-6737	109	3	ξ1a1	ξ1a1	PROPN
ejpam-6737	109	4	+	+	NUM
ejpam-6737	109	5	ξ2a2	ξ2a2	NOUN
ejpam-6737	109	6	+	+	CCONJ
ejpam-6737	109	7	ξ3p	ξ3p	NUM
ejpam-6737	109	8	≥	≥	NOUN
ejpam-6737	109	9	0	0	NUM
ejpam-6737	109	10	,	,	PUNCT
ejpam-6737	109	11	ffm	ffm	NOUN
ejpam-6737	109	12	0	0	NUM
ejpam-6737	109	13	dη,ϑ	dη,ϑ	X
ejpam-6737	109	14	t	t	PROPN
ejpam-6737	109	15	q(t	q(t	PROPN
ejpam-6737	109	16	)	)	PUNCT
ejpam-6737	109	17	∣∣	∣∣	X
ejpam-6737	109	18	q=0	q=0	NOUN
ejpam-6737	109	19	=	=	PUNCT
ejpam-6737	109	20	τ1s+	τ1s+	PROPN
ejpam-6737	109	21	τ2r	τ2r	ADP
ejpam-6737	109	22	≥	≥	NOUN
ejpam-6737	109	23	0	0	NUM
ejpam-6737	109	24	.	.	PUNCT
ejpam-6737	110	1	(	(	PUNCT
ejpam-6737	110	2	4	4	X
ejpam-6737	110	3	)	)	PUNCT
ejpam-6737	110	4	s.	s.	PROPN
ejpam-6737	110	5	m.	m.	PROPN
ejpam-6737	110	6	chithra	chithra	PROPN
ejpam-6737	110	7	et	et	PROPN
ejpam-6737	110	8	al	al	PROPN
ejpam-6737	110	9	.	.	PUNCT
ejpam-6737	110	10	/	/	SYM
ejpam-6737	110	11	eur	eur	PROPN
ejpam-6737	110	12	.	.	PUNCT
ejpam-6737	111	1	j.	j.	PROPN
ejpam-6737	111	2	pure	pure	PROPN
ejpam-6737	111	3	appl	appl	PROPN
ejpam-6737	111	4	.	.	PROPN
ejpam-6737	111	5	math	math	PROPN
ejpam-6737	111	6	,	,	PUNCT
ejpam-6737	111	7	18	18	NUM
ejpam-6737	111	8	(	(	PUNCT
ejpam-6737	111	9	4	4	NUM
ejpam-6737	111	10	)	)	PUNCT
ejpam-6737	111	11	(	(	PUNCT
ejpam-6737	111	12	2025	2025	NUM
ejpam-6737	111	13	)	)	PUNCT
ejpam-6737	111	14	,	,	PUNCT
ejpam-6737	111	15	6737	6737	NUM
ejpam-6737	111	16	7	7	NUM
ejpam-6737	111	17	of	of	ADP
ejpam-6737	111	18	23	23	NUM
ejpam-6737	111	19	the	the	DET
ejpam-6737	111	20	solution	solution	NOUN
ejpam-6737	111	21	remains	remain	VERB
ejpam-6737	111	22	confined	confine	VERB
ejpam-6737	111	23	within	within	ADP
ejpam-6737	111	24	the	the	DET
ejpam-6737	111	25	hyperplane	hyperplane	NOUN
ejpam-6737	111	26	if	if	SCONJ
ejpam-6737	111	27	the	the	DET
ejpam-6737	111	28	initial	initial	ADJ
ejpam-6737	111	29	values	value	NOUN
ejpam-6737	111	30	are	be	AUX
ejpam-6737	111	31	(	(	PUNCT
ejpam-6737	111	32	sp(0	sp(0	NOUN
ejpam-6737	111	33	)	)	PUNCT
ejpam-6737	111	34	,	,	PUNCT
ejpam-6737	111	35	tp(0	tp(0	NOUN
ejpam-6737	111	36	)	)	PUNCT
ejpam-6737	111	37	,	,	PUNCT
ejpam-6737	111	38	tp(0),kp(0	tp(0),kp(0	PROPN
ejpam-6737	111	39	)	)	PUNCT
ejpam-6737	111	40	,	,	PUNCT
ejpam-6737	111	41	bm(0	bm(0	NOUN
ejpam-6737	111	42	)	)	PUNCT
ejpam-6737	111	43	,	,	PUNCT
ejpam-6737	111	44	sv(0	sv(0	PROPN
ejpam-6737	111	45	)	)	PUNCT
ejpam-6737	111	46	,	,	PUNCT
ejpam-6737	111	47	tv(0	tv(0	NOUN
ejpam-6737	111	48	)	)	PUNCT
ejpam-6737	111	49	)	)	PUNCT
ejpam-6737	112	1	∈	∈	PROPN
ejpam-6737	112	2	r7	r7	PROPN
ejpam-6737	112	3	+	+	ADV
ejpam-6737	112	4	,	,	PUNCT
ejpam-6737	112	5	as	as	SCONJ
ejpam-6737	112	6	specified	specify	VERB
ejpam-6737	112	7	in	in	ADP
ejpam-6737	112	8	equation	equation	NOUN
ejpam-6737	112	9	(	(	PUNCT
ejpam-6737	112	10	4	4	NUM
ejpam-6737	112	11	)	)	PUNCT
ejpam-6737	112	12	.	.	PUNCT
ejpam-6737	113	1	in	in	ADP
ejpam-6737	113	2	addition	addition	NOUN
ejpam-6737	113	3	,	,	PUNCT
ejpam-6737	113	4	the	the	DET
ejpam-6737	113	5	vector	vector	NOUN
ejpam-6737	113	6	field	field	NOUN
ejpam-6737	113	7	always	always	ADV
ejpam-6737	113	8	points	point	VERB
ejpam-6737	113	9	to	to	ADP
ejpam-6737	113	10	the	the	DET
ejpam-6737	113	11	region	region	NOUN
ejpam-6737	113	12	r7	r7	PROPN
ejpam-6737	113	13	+	+	CCONJ
ejpam-6737	113	14	inside	inside	ADP
ejpam-6737	113	15	every	every	DET
ejpam-6737	113	16	hyperplane	hyperplane	NOUN
ejpam-6737	113	17	enclosing	enclose	VERB
ejpam-6737	113	18	the	the	DET
ejpam-6737	113	19	non	non	ADJ
ejpam-6737	113	20	-	-	ADJ
ejpam-6737	113	21	negative	negative	ADJ
ejpam-6737	113	22	space	space	NOUN
ejpam-6737	113	23	.	.	PUNCT
ejpam-6737	114	1	simply	simply	ADV
ejpam-6737	114	2	,	,	PUNCT
ejpam-6737	114	3	the	the	DET
ejpam-6737	114	4	domain	domain	NOUN
ejpam-6737	114	5	r7	r7	NOUN
ejpam-6737	114	6	+	+	CCONJ
ejpam-6737	114	7	as	as	ADP
ejpam-6737	114	8	a	a	DET
ejpam-6737	114	9	whole	whole	ADJ
ejpam-6737	114	10	function	function	NOUN
ejpam-6737	114	11	to	to	PART
ejpam-6737	114	12	be	be	AUX
ejpam-6737	114	13	positively	positively	ADV
ejpam-6737	114	14	invariant	invariant	ADJ
ejpam-6737	114	15	set	set	NOUN
ejpam-6737	114	16	.	.	PUNCT
ejpam-6737	115	1	5	5	X
ejpam-6737	115	2	.	.	X
ejpam-6737	115	3	existence	existence	NOUN
ejpam-6737	115	4	and	and	CCONJ
ejpam-6737	115	5	uniqueness	uniqueness	NOUN
ejpam-6737	115	6	of	of	ADP
ejpam-6737	115	7	suggested	suggested	ADJ
ejpam-6737	115	8	model	model	NOUN
ejpam-6737	115	9	the	the	DET
ejpam-6737	115	10	system	system	NOUN
ejpam-6737	115	11	in	in	ADP
ejpam-6737	115	12	equations	equation	NOUN
ejpam-6737	115	13	(	(	PUNCT
ejpam-6737	115	14	3	3	X
ejpam-6737	115	15	)	)	PUNCT
ejpam-6737	115	16	can	can	AUX
ejpam-6737	115	17	be	be	AUX
ejpam-6737	115	18	reformulated	reformulate	VERB
ejpam-6737	115	19	using	use	VERB
ejpam-6737	115	20	the	the	DET
ejpam-6737	115	21	fractal	fractal	ADJ
ejpam-6737	115	22	–	–	PUNCT
ejpam-6737	115	23	fractional	fractional	ADJ
ejpam-6737	115	24	operator	operator	NOUN
ejpam-6737	115	25	in	in	ADP
ejpam-6737	115	26	the	the	DET
ejpam-6737	115	27	atangana	atangana	PROPN
ejpam-6737	115	28	–	–	PUNCT
ejpam-6737	115	29	baleanu	baleanu	PROPN
ejpam-6737	115	30	caputo	caputo	PROPN
ejpam-6737	115	31	sense	sense	NOUN
ejpam-6737	115	32	.	.	PUNCT
ejpam-6737	116	1	by	by	ADP
ejpam-6737	116	2	applying	apply	VERB
ejpam-6737	116	3	fixed	fix	VERB
ejpam-6737	116	4	-	-	PUNCT
ejpam-6737	116	5	point	point	NOUN
ejpam-6737	116	6	theorems	theorem	NOUN
ejpam-6737	116	7	,	,	PUNCT
ejpam-6737	116	8	we	we	PRON
ejpam-6737	116	9	establish	establish	VERB
ejpam-6737	116	10	the	the	DET
ejpam-6737	116	11	existence	existence	NOUN
ejpam-6737	116	12	and	and	CCONJ
ejpam-6737	116	13	uniqueness	uniqueness	NOUN
ejpam-6737	116	14	of	of	ADP
ejpam-6737	116	15	at	at	ADV
ejpam-6737	116	16	least	least	ADV
ejpam-6737	116	17	one	one	NUM
ejpam-6737	116	18	solution	solution	NOUN
ejpam-6737	116	19	.	.	PUNCT
ejpam-6737	117	1	the	the	DET
ejpam-6737	117	2	model	model	NOUN
ejpam-6737	117	3	is	be	AUX
ejpam-6737	117	4	expressed	express	VERB
ejpam-6737	117	5	as	as	ADP
ejpam-6737	117	6	abc	abc	PROPN
ejpam-6737	117	7	0	0	NUM
ejpam-6737	117	8	dη,ϑ	dη,ϑ	PROPN
ejpam-6737	117	9	t	t	PROPN
ejpam-6737	117	10	s(t	s(t	PROPN
ejpam-6737	117	11	)	)	PUNCT
ejpam-6737	117	12	=	=	PUNCT
ejpam-6737	118	1	ϑtϑ−1g1(t	ϑtϑ−1g1(t	PROPN
ejpam-6737	118	2	,	,	PUNCT
ejpam-6737	118	3	s	s	X
ejpam-6737	118	4	,	,	PUNCT
ejpam-6737	118	5	e	e	NOUN
ejpam-6737	118	6	,	,	PUNCT
ejpam-6737	118	7	a1,a2,p	a1,a2,p	PROPN
ejpam-6737	118	8	,	,	PUNCT
ejpam-6737	118	9	r	r	NOUN
ejpam-6737	118	10	,	,	PUNCT
ejpam-6737	118	11	q	q	NOUN
ejpam-6737	118	12	)	)	PUNCT
ejpam-6737	118	13	,	,	PUNCT
ejpam-6737	118	14	abc	abc	PROPN
ejpam-6737	118	15	0	0	NUM
ejpam-6737	118	16	dη,ϑ	dη,ϑ	PROPN
ejpam-6737	118	17	t	t	PROPN
ejpam-6737	118	18	e(t	e(t	PROPN
ejpam-6737	118	19	)	)	PUNCT
ejpam-6737	118	20	=	=	SYM
ejpam-6737	118	21	ϑtϑ−1g2(t	ϑtϑ−1g2(t	PROPN
ejpam-6737	118	22	,	,	PUNCT
ejpam-6737	118	23	s	s	X
ejpam-6737	118	24	,	,	PUNCT
ejpam-6737	118	25	e	e	NOUN
ejpam-6737	118	26	,	,	PUNCT
ejpam-6737	118	27	a1,a2,p	a1,a2,p	PROPN
ejpam-6737	118	28	,	,	PUNCT
ejpam-6737	118	29	r	r	NOUN
ejpam-6737	118	30	,	,	PUNCT
ejpam-6737	118	31	q	q	NOUN
ejpam-6737	118	32	)	)	PUNCT
ejpam-6737	118	33	,	,	PUNCT
ejpam-6737	118	34	abc	abc	PROPN
ejpam-6737	118	35	0	0	NUM
ejpam-6737	118	36	dη,ϑ	dη,ϑ	X
ejpam-6737	118	37	t	t	PROPN
ejpam-6737	118	38	a1(t	a1(t	PROPN
ejpam-6737	118	39	)	)	PUNCT
ejpam-6737	118	40	=	=	SYM
ejpam-6737	118	41	ϑtϑ−1g3(t	ϑtϑ−1g3(t	PROPN
ejpam-6737	118	42	,	,	PUNCT
ejpam-6737	118	43	s	s	X
ejpam-6737	118	44	,	,	PUNCT
ejpam-6737	118	45	e	e	NOUN
ejpam-6737	118	46	,	,	PUNCT
ejpam-6737	118	47	a1,a2,p	a1,a2,p	PROPN
ejpam-6737	118	48	,	,	PUNCT
ejpam-6737	118	49	r	r	NOUN
ejpam-6737	118	50	,	,	PUNCT
ejpam-6737	118	51	q	q	NOUN
ejpam-6737	118	52	)	)	PUNCT
ejpam-6737	118	53	,	,	PUNCT
ejpam-6737	118	54	abc	abc	PROPN
ejpam-6737	118	55	0	0	NUM
ejpam-6737	118	56	dη,ϑ	dη,ϑ	X
ejpam-6737	118	57	t	t	PROPN
ejpam-6737	118	58	a2(t	a2(t	PROPN
ejpam-6737	118	59	)	)	PUNCT
ejpam-6737	118	60	=	=	SYM
ejpam-6737	119	1	ϑtϑ−1g4(t	ϑtϑ−1g4(t	ADJ
ejpam-6737	119	2	,	,	PUNCT
ejpam-6737	119	3	s	s	X
ejpam-6737	119	4	,	,	PUNCT
ejpam-6737	119	5	e	e	NOUN
ejpam-6737	119	6	,	,	PUNCT
ejpam-6737	119	7	a1,a2,p	a1,a2,p	PROPN
ejpam-6737	119	8	,	,	PUNCT
ejpam-6737	119	9	r	r	NOUN
ejpam-6737	119	10	,	,	PUNCT
ejpam-6737	119	11	q	q	NOUN
ejpam-6737	119	12	)	)	PUNCT
ejpam-6737	119	13	,	,	PUNCT
ejpam-6737	119	14	abc	abc	PROPN
ejpam-6737	119	15	0	0	NUM
ejpam-6737	119	16	dη,ϑ	dη,ϑ	X
ejpam-6737	119	17	t	t	NOUN
ejpam-6737	119	18	p(t	p(t	NOUN
ejpam-6737	119	19	)	)	PUNCT
ejpam-6737	119	20	=	=	SYM
ejpam-6737	120	1	ϑtϑ−1g5(t	ϑtϑ−1g5(t	PROPN
ejpam-6737	120	2	,	,	PUNCT
ejpam-6737	120	3	s	s	X
ejpam-6737	120	4	,	,	PUNCT
ejpam-6737	120	5	e	e	NOUN
ejpam-6737	120	6	,	,	PUNCT
ejpam-6737	120	7	a1,a2,p	a1,a2,p	PROPN
ejpam-6737	120	8	,	,	PUNCT
ejpam-6737	120	9	r	r	NOUN
ejpam-6737	120	10	,	,	PUNCT
ejpam-6737	120	11	q	q	NOUN
ejpam-6737	120	12	)	)	PUNCT
ejpam-6737	120	13	,	,	PUNCT
ejpam-6737	120	14	abc	abc	PROPN
ejpam-6737	120	15	0	0	NUM
ejpam-6737	120	16	dη,ϑ	dη,ϑ	X
ejpam-6737	120	17	t	t	NOUN
ejpam-6737	120	18	r(t	r(t	NOUN
ejpam-6737	120	19	)	)	PUNCT
ejpam-6737	120	20	=	=	SYM
ejpam-6737	120	21	ϑtϑ−1g6(t	ϑtϑ−1g6(t	NOUN
ejpam-6737	120	22	,	,	PUNCT
ejpam-6737	120	23	s	s	X
ejpam-6737	120	24	,	,	PUNCT
ejpam-6737	120	25	e	e	NOUN
ejpam-6737	120	26	,	,	PUNCT
ejpam-6737	120	27	a1,a2,p	a1,a2,p	PROPN
ejpam-6737	120	28	,	,	PUNCT
ejpam-6737	120	29	r	r	NOUN
ejpam-6737	120	30	,	,	PUNCT
ejpam-6737	120	31	q	q	NOUN
ejpam-6737	120	32	)	)	PUNCT
ejpam-6737	120	33	,	,	PUNCT
ejpam-6737	120	34	abc	abc	PROPN
ejpam-6737	120	35	0	0	NUM
ejpam-6737	120	36	dη,ϑ	dη,ϑ	X
ejpam-6737	120	37	t	t	PROPN
ejpam-6737	120	38	q(t	q(t	PROPN
ejpam-6737	120	39	)	)	PUNCT
ejpam-6737	120	40	=	=	SYM
ejpam-6737	120	41	ϑtϑ−1g7(t	ϑtϑ−1g7(t	PROPN
ejpam-6737	120	42	,	,	PUNCT
ejpam-6737	120	43	s	s	X
ejpam-6737	120	44	,	,	PUNCT
ejpam-6737	120	45	e	e	NOUN
ejpam-6737	120	46	,	,	PUNCT
ejpam-6737	120	47	a1,a2,p	a1,a2,p	PROPN
ejpam-6737	120	48	,	,	PUNCT
ejpam-6737	120	49	r	r	NOUN
ejpam-6737	120	50	,	,	PUNCT
ejpam-6737	120	51	q	q	NOUN
ejpam-6737	120	52	)	)	PUNCT
ejpam-6737	120	53	.	.	PUNCT
ejpam-6737	121	1	the	the	DET
ejpam-6737	121	2	system	system	NOUN
ejpam-6737	121	3	can	can	AUX
ejpam-6737	121	4	be	be	AUX
ejpam-6737	121	5	further	far	ADV
ejpam-6737	121	6	written	write	VERB
ejpam-6737	121	7	as	as	ADP
ejpam-6737	121	8	abc	abc	PROPN
ejpam-6737	121	9	0	0	NUM
ejpam-6737	121	10	dη,ϑ	dη,ϑ	X
ejpam-6737	121	11	t	t	PROPN
ejpam-6737	121	12	θ(t	θ(t	PROPN
ejpam-6737	121	13	)	)	PUNCT
ejpam-6737	121	14	=	=	SYM
ejpam-6737	121	15	ϑtϑ−1ω(t	ϑtϑ−1ω(t	NOUN
ejpam-6737	121	16	,	,	PUNCT
ejpam-6737	121	17	θ(t	θ(t	PROPN
ejpam-6737	121	18	)	)	PUNCT
ejpam-6737	121	19	)	)	PUNCT
ejpam-6737	121	20	,	,	PUNCT
ejpam-6737	121	21	θ(0	θ(0	PROPN
ejpam-6737	121	22	)	)	PUNCT
ejpam-6737	121	23	=	=	PUNCT
ejpam-6737	121	24	θ0	θ0	PROPN
ejpam-6737	121	25	.	.	PUNCT
ejpam-6737	122	1	by	by	ADP
ejpam-6737	122	2	applying	apply	VERB
ejpam-6737	122	3	the	the	DET
ejpam-6737	122	4	fractional	fractional	ADJ
ejpam-6737	122	5	integral	integral	ADJ
ejpam-6737	122	6	operator	operator	NOUN
ejpam-6737	122	7	,	,	PUNCT
ejpam-6737	122	8	the	the	DET
ejpam-6737	122	9	system	system	NOUN
ejpam-6737	122	10	can	can	AUX
ejpam-6737	122	11	be	be	AUX
ejpam-6737	122	12	equivalently	equivalently	ADV
ejpam-6737	122	13	represented	represent	VERB
ejpam-6737	122	14	in	in	ADP
ejpam-6737	122	15	its	its	PRON
ejpam-6737	122	16	integral	integral	ADJ
ejpam-6737	122	17	form	form	NOUN
ejpam-6737	122	18	θ(t	θ(t	NOUN
ejpam-6737	122	19	)	)	PUNCT
ejpam-6737	122	20	=	=	SYM
ejpam-6737	122	21	θ(0	θ(0	PROPN
ejpam-6737	122	22	)	)	PUNCT
ejpam-6737	122	23	+	+	CCONJ
ejpam-6737	122	24	ϑtϑ−1(1−	ϑtϑ−1(1−	PROPN
ejpam-6737	122	25	η	η	PROPN
ejpam-6737	122	26	)	)	PUNCT
ejpam-6737	122	27	abc(η	abc(η	PROPN
ejpam-6737	122	28	)	)	PUNCT
ejpam-6737	122	29	ω(t	ω(t	NOUN
ejpam-6737	122	30	,	,	PUNCT
ejpam-6737	122	31	θ(t	θ(t	PROPN
ejpam-6737	122	32	)	)	PUNCT
ejpam-6737	122	33	)	)	PUNCT
ejpam-6737	123	1	+	+	CCONJ
ejpam-6737	123	2	ηϑ	ηϑ	ADP
ejpam-6737	123	3	d(η)abc(η)e	d(η)abc(η)e	PROPN
ejpam-6737	123	4	∫	∫	PROPN
ejpam-6737	123	5	t	t	PROPN
ejpam-6737	123	6	0	0	NUM
ejpam-6737	123	7	mϑ−1(t−m)η−1ω(t	mϑ−1(t−m)η−1ω(t	NOUN
ejpam-6737	123	8	,	,	PUNCT
ejpam-6737	123	9	θ(t	θ(t	PROPN
ejpam-6737	123	10	)	)	PUNCT
ejpam-6737	123	11	)	)	PUNCT
ejpam-6737	124	1	dm	dm	PROPN
ejpam-6737	124	2	.	.	PUNCT
ejpam-6737	125	1	(	(	PUNCT
ejpam-6737	125	2	5	5	NUM
ejpam-6737	125	3	)	)	PUNCT
ejpam-6737	125	4	where	where	SCONJ
ejpam-6737	125	5	θ(t	θ(t	VERB
ejpam-6737	125	6	)	)	PUNCT
ejpam-6737	125	7	=	=	PRON
ejpam-6737	125	8	(	(	PUNCT
ejpam-6737	125	9	s(t),e(t),a1(t),a2(t),p(t),r(t),q(t	s(t),e(t),a1(t),a2(t),p(t),r(t),q(t	PROPN
ejpam-6737	125	10	)	)	PUNCT
ejpam-6737	125	11	)	)	PUNCT
ejpam-6737	125	12	,	,	PUNCT
ejpam-6737	125	13	θ(0	θ(0	PROPN
ejpam-6737	125	14	)	)	PUNCT
ejpam-6737	125	15	=	=	PUNCT
ejpam-6737	125	16	(	(	PUNCT
ejpam-6737	125	17	s(0),e(0),a1(0),a2(0),p(0),r(0),q(0	s(0),e(0),a1(0),a2(0),p(0),r(0),q(0	NOUN
ejpam-6737	125	18	)	)	PUNCT
ejpam-6737	125	19	)	)	PUNCT
ejpam-6737	125	20	.	.	PUNCT
ejpam-6737	126	1	we	we	PRON
ejpam-6737	126	2	let	let	VERB
ejpam-6737	126	3	the	the	DET
ejpam-6737	126	4	banach	banach	NOUN
ejpam-6737	126	5	space	space	NOUN
ejpam-6737	127	1	i	i	NOUN
ejpam-6737	127	2	=	=	SYM
ejpam-6737	127	3	c×c×c×c×c×c×c	c×c×c×c×c×c×c	ADJ
ejpam-6737	127	4	,	,	PUNCT
ejpam-6737	127	5	consist	consist	NOUN
ejpam-6737	127	6	of	of	ADP
ejpam-6737	127	7	component	component	NOUN
ejpam-6737	127	8	functions	function	NOUN
ejpam-6737	127	9	in	in	ADP
ejpam-6737	127	10	c[0,k	c[0,k	PROPN
ejpam-6737	127	11	]	]	PUNCT
ejpam-6737	127	12	equipped	equip	VERB
ejpam-6737	127	13	with	with	ADP
ejpam-6737	127	14	the	the	DET
ejpam-6737	127	15	norm	norm	NOUN
ejpam-6737	127	16	‖θ‖	‖θ‖	PROPN
ejpam-6737	127	17	=	=	SYM
ejpam-6737	127	18	max	max	PROPN
ejpam-6737	127	19	t∈[0,k	t∈[0,k	PROPN
ejpam-6737	127	20	]	]	X
ejpam-6737	127	21	|s(t),e(t),a1(t),a2(t),p(t),r(t),q(t)|	|s(t),e(t),a1(t),a2(t),p(t),r(t),q(t)|	PUNCT
ejpam-6737	127	22	to	to	PART
ejpam-6737	127	23	facilitate	facilitate	VERB
ejpam-6737	127	24	the	the	DET
ejpam-6737	127	25	analysis	analysis	NOUN
ejpam-6737	127	26	of	of	ADP
ejpam-6737	127	27	the	the	DET
ejpam-6737	127	28	existence	existence	NOUN
ejpam-6737	127	29	theory	theory	NOUN
ejpam-6737	127	30	.	.	PUNCT
ejpam-6737	128	1	an	an	DET
ejpam-6737	128	2	operator	operator	NOUN
ejpam-6737	128	3	ψ	ψ	NOUN
ejpam-6737	128	4	:	:	PUNCT
ejpam-6737	128	5	i	i	PRON
ejpam-6737	128	6	→	→	PUNCT
ejpam-6737	128	7	i	i	PRON
ejpam-6737	128	8	is	be	AUX
ejpam-6737	128	9	defined	define	VERB
ejpam-6737	128	10	as	as	SCONJ
ejpam-6737	128	11	follows	follow	VERB
ejpam-6737	128	12	:	:	PUNCT
ejpam-6737	128	13	ψ(θ)(t	ψ(θ)(t	NUM
ejpam-6737	128	14	)	)	PUNCT
ejpam-6737	128	15	=	=	SYM
ejpam-6737	128	16	θ(0	θ(0	PROPN
ejpam-6737	128	17	)	)	PUNCT
ejpam-6737	128	18	+	+	CCONJ
ejpam-6737	128	19	ϑtϑ−1(1−	ϑtϑ−1(1−	PROPN
ejpam-6737	128	20	η	η	PROPN
ejpam-6737	128	21	)	)	PUNCT
ejpam-6737	128	22	abc(η	abc(η	PROPN
ejpam-6737	128	23	)	)	PUNCT
ejpam-6737	128	24	ω(t	ω(t	NOUN
ejpam-6737	128	25	,	,	PUNCT
ejpam-6737	128	26	θ(t	θ(t	PROPN
ejpam-6737	128	27	)	)	PUNCT
ejpam-6737	128	28	)	)	PUNCT
ejpam-6737	129	1	+	+	CCONJ
ejpam-6737	129	2	ηϑ	ηϑ	ADP
ejpam-6737	129	3	d(η)abc(η)e	d(η)abc(η)e	PROPN
ejpam-6737	129	4	∫	∫	PROPN
ejpam-6737	129	5	t	t	PROPN
ejpam-6737	129	6	0	0	NUM
ejpam-6737	129	7	mϑ−1(t−m)η−1ω(t	mϑ−1(t−m)η−1ω(t	NOUN
ejpam-6737	129	8	,	,	PUNCT
ejpam-6737	129	9	θ(t	θ(t	PROPN
ejpam-6737	129	10	)	)	PUNCT
ejpam-6737	129	11	)	)	PUNCT
ejpam-6737	130	1	dm	dm	PROPN
ejpam-6737	130	2	.	.	PUNCT
ejpam-6737	131	1	s.	s.	PROPN
ejpam-6737	131	2	m.	m.	PROPN
ejpam-6737	131	3	chithra	chithra	PROPN
ejpam-6737	131	4	et	et	PROPN
ejpam-6737	131	5	al	al	PROPN
ejpam-6737	131	6	.	.	PUNCT
ejpam-6737	131	7	/	/	SYM
ejpam-6737	131	8	eur	eur	PROPN
ejpam-6737	131	9	.	.	PUNCT
ejpam-6737	132	1	j.	j.	PROPN
ejpam-6737	132	2	pure	pure	PROPN
ejpam-6737	132	3	appl	appl	PROPN
ejpam-6737	132	4	.	.	PROPN
ejpam-6737	132	5	math	math	PROPN
ejpam-6737	132	6	,	,	PUNCT
ejpam-6737	132	7	18	18	NUM
ejpam-6737	132	8	(	(	PUNCT
ejpam-6737	132	9	4	4	NUM
ejpam-6737	132	10	)	)	PUNCT
ejpam-6737	132	11	(	(	PUNCT
ejpam-6737	132	12	2025	2025	NUM
ejpam-6737	132	13	)	)	PUNCT
ejpam-6737	132	14	,	,	PUNCT
ejpam-6737	132	15	6737	6737	NUM
ejpam-6737	132	16	8	8	NUM
ejpam-6737	132	17	of	of	ADP
ejpam-6737	132	18	23	23	NUM
ejpam-6737	132	19	let	let	VERB
ejpam-6737	132	20	ω(t	ω(t	NOUN
ejpam-6737	132	21	,	,	PUNCT
ejpam-6737	132	22	θ(t	θ(t	PROPN
ejpam-6737	132	23	)	)	PUNCT
ejpam-6737	132	24	)	)	PUNCT
ejpam-6737	132	25	be	be	AUX
ejpam-6737	132	26	a	a	DET
ejpam-6737	132	27	nonlinear	nonlinear	ADJ
ejpam-6737	132	28	function	function	NOUN
ejpam-6737	132	29	with	with	ADP
ejpam-6737	132	30	the	the	DET
ejpam-6737	132	31	lipschitz	lipschitz	NOUN
ejpam-6737	132	32	condition	condition	NOUN
ejpam-6737	132	33	and	and	CCONJ
ejpam-6737	132	34	growth	growth	NOUN
ejpam-6737	132	35	restrictions	restriction	NOUN
ejpam-6737	132	36	.	.	PUNCT
ejpam-6737	133	1	then	then	ADV
ejpam-6737	133	2	,	,	PUNCT
ejpam-6737	133	3	for	for	ADP
ejpam-6737	133	4	any	any	DET
ejpam-6737	133	5	θ	θ	PROPN
ejpam-6737	133	6	∈	∈	PROPN
ejpam-6737	134	1	i	i	PRON
ejpam-6737	134	2	,	,	PUNCT
ejpam-6737	134	3	there	there	PRON
ejpam-6737	134	4	are	be	VERB
ejpam-6737	134	5	constants	constant	NOUN
ejpam-6737	134	6	cφ	cφ	NOUN
ejpam-6737	134	7	>	>	X
ejpam-6737	134	8	0	0	PUNCT
ejpam-6737	134	9	and	and	CCONJ
ejpam-6737	134	10	gφ	gφ	X
ejpam-6737	134	11	such	such	ADJ
ejpam-6737	134	12	that	that	SCONJ
ejpam-6737	134	13	|ω(t	|ω(t	NOUN
ejpam-6737	134	14	,	,	PUNCT
ejpam-6737	134	15	θ(t))|	θ(t))|	PROPN
ejpam-6737	134	16	≤	≤	PROPN
ejpam-6737	134	17	cφ|θ(t)|+gφ	cφ|θ(t)|+gφ	VERB
ejpam-6737	134	18	.	.	PUNCT
ejpam-6737	135	1	(	(	PUNCT
ejpam-6737	135	2	6	6	NUM
ejpam-6737	135	3	)	)	PUNCT
ejpam-6737	135	4	in	in	ADP
ejpam-6737	135	5	addition	addition	NOUN
ejpam-6737	135	6	,	,	PUNCT
ejpam-6737	135	7	for	for	ADP
ejpam-6737	135	8	any	any	DET
ejpam-6737	135	9	θ	θ	NOUN
ejpam-6737	135	10	,	,	PUNCT
ejpam-6737	135	11	θ̄	θ̄	PROPN
ejpam-6737	135	12	∈	∈	PROPN
ejpam-6737	136	1	i	i	PRON
ejpam-6737	136	2	,	,	PUNCT
ejpam-6737	136	3	there	there	PRON
ejpam-6737	136	4	is	be	VERB
ejpam-6737	136	5	a	a	DET
ejpam-6737	136	6	constant	constant	ADJ
ejpam-6737	136	7	hφ	hφ	NOUN
ejpam-6737	136	8	>	>	X
ejpam-6737	136	9	0	0	NUM
ejpam-6737	136	10	such	such	ADJ
ejpam-6737	136	11	that	that	SCONJ
ejpam-6737	136	12	|ω(t	|ω(t	NOUN
ejpam-6737	136	13	,	,	PUNCT
ejpam-6737	136	14	θ(t))−	θ(t))−	PROPN
ejpam-6737	136	15	ω(t	ω(t	NOUN
ejpam-6737	136	16	,	,	PUNCT
ejpam-6737	136	17	θ̄(t))|	θ̄(t))|	PROPN
ejpam-6737	136	18	≤	≤	PROPN
ejpam-6737	136	19	hφ|θ(t)−	hφ|θ(t)−	PROPN
ejpam-6737	136	20	θ̄(t)|	θ̄(t)|	PROPN
ejpam-6737	136	21	.	.	PUNCT
ejpam-6737	137	1	(	(	PUNCT
ejpam-6737	137	2	7	7	NUM
ejpam-6737	137	3	)	)	PUNCT
ejpam-6737	137	4	through	through	ADP
ejpam-6737	137	5	this	this	DET
ejpam-6737	137	6	formulation	formulation	NOUN
ejpam-6737	137	7	,	,	PUNCT
ejpam-6737	137	8	we	we	PRON
ejpam-6737	137	9	analyze	analyze	VERB
ejpam-6737	137	10	the	the	DET
ejpam-6737	137	11	uniqueness	uniqueness	NOUN
ejpam-6737	137	12	and	and	CCONJ
ejpam-6737	137	13	stability	stability	NOUN
ejpam-6737	137	14	properties	property	NOUN
ejpam-6737	137	15	of	of	ADP
ejpam-6737	137	16	the	the	DET
ejpam-6737	137	17	proposed	propose	VERB
ejpam-6737	137	18	fractal	fractal	ADJ
ejpam-6737	137	19	–	–	PUNCT
ejpam-6737	137	20	fractional	fractional	ADJ
ejpam-6737	137	21	scheme	scheme	NOUN
ejpam-6737	137	22	under	under	ADP
ejpam-6737	137	23	the	the	DET
ejpam-6737	137	24	atangana	atangana	PROPN
ejpam-6737	137	25	–	–	PUNCT
ejpam-6737	137	26	baleanu	baleanu	ADJ
ejpam-6737	137	27	fractional	fractional	ADJ
ejpam-6737	137	28	operator	operator	NOUN
ejpam-6737	137	29	framework	framework	NOUN
ejpam-6737	137	30	.	.	PUNCT
ejpam-6737	138	1	theorem	theorem	NOUN
ejpam-6737	138	2	2	2	NUM
ejpam-6737	138	3	.	.	PUNCT
ejpam-6737	138	4	assume	assume	VERB
ejpam-6737	138	5	that	that	SCONJ
ejpam-6737	138	6	conditions	condition	NOUN
ejpam-6737	138	7	(	(	PUNCT
ejpam-6737	138	8	4	4	X
ejpam-6737	138	9	)	)	PUNCT
ejpam-6737	138	10	are	be	AUX
ejpam-6737	138	11	fulfilled	fulfil	VERB
ejpam-6737	138	12	.	.	PUNCT
ejpam-6737	139	1	a	a	DET
ejpam-6737	139	2	continuous	continuous	ADJ
ejpam-6737	139	3	function	function	NOUN
ejpam-6737	139	4	ω	ω	NOUN
ejpam-6737	139	5	:	:	PUNCT
ejpam-6737	140	1	[	[	X
ejpam-6737	140	2	0,k]×	0,k]×	X
ejpam-6737	140	3	i	i	PRON
ejpam-6737	140	4	→	→	PUNCT
ejpam-6737	140	5	l	l	NOUN
ejpam-6737	140	6	is	be	AUX
ejpam-6737	140	7	identified	identify	VERB
ejpam-6737	140	8	,	,	PUNCT
ejpam-6737	140	9	ensuring	ensure	VERB
ejpam-6737	140	10	that	that	SCONJ
ejpam-6737	140	11	the	the	DET
ejpam-6737	140	12	proposed	propose	VERB
ejpam-6737	140	13	model	model	NOUN
ejpam-6737	140	14	possesses	possess	VERB
ejpam-6737	140	15	a	a	DET
ejpam-6737	140	16	unique	unique	ADJ
ejpam-6737	140	17	solution	solution	NOUN
ejpam-6737	140	18	.	.	PUNCT
ejpam-6737	141	1	proof	proof	NOUN
ejpam-6737	141	2	.	.	PUNCT
ejpam-6737	142	1	firstly	firstly	ADV
ejpam-6737	142	2	,	,	PUNCT
ejpam-6737	142	3	we	we	PRON
ejpam-6737	142	4	want	want	VERB
ejpam-6737	142	5	to	to	PART
ejpam-6737	142	6	show	show	VERB
ejpam-6737	142	7	the	the	DET
ejpam-6737	142	8	full	full	ADJ
ejpam-6737	142	9	continuity	continuity	NOUN
ejpam-6737	142	10	of	of	ADP
ejpam-6737	142	11	the	the	DET
ejpam-6737	142	12	operator	operator	NOUN
ejpam-6737	142	13	ψ	ψ	NOUN
ejpam-6737	142	14	.	.	PUNCT
ejpam-6737	143	1	with	with	ADP
ejpam-6737	143	2	the	the	DET
ejpam-6737	143	3	constancy	constancy	NOUN
ejpam-6737	143	4	of	of	ADP
ejpam-6737	143	5	ω	ω	PROPN
ejpam-6737	143	6	,	,	PUNCT
ejpam-6737	143	7	the	the	DET
ejpam-6737	143	8	continuity	continuity	NOUN
ejpam-6737	143	9	of	of	ADP
ejpam-6737	143	10	ψ	ψ	NOUN
ejpam-6737	143	11	is	be	AUX
ejpam-6737	143	12	also	also	ADV
ejpam-6737	143	13	guaranteed	guarantee	VERB
ejpam-6737	143	14	.	.	PUNCT
ejpam-6737	144	1	let	let	VERB
ejpam-6737	144	2	φ	φ	PROPN
ejpam-6737	144	3	=	=	SYM
ejpam-6737	144	4	{	{	PUNCT
ejpam-6737	144	5	θ	θ	PROPN
ejpam-6737	144	6	∈	∈	PROPN
ejpam-6737	145	1	i	i	PRON
ejpam-6737	145	2	:	:	PUNCT
ejpam-6737	145	3	‖θ‖	‖θ‖	ADJ
ejpam-6737	145	4	≤	≤	NUM
ejpam-6737	145	5	l	l	NOUN
ejpam-6737	145	6	,	,	PUNCT
ejpam-6737	145	7	l	l	NOUN
ejpam-6737	145	8	>	>	X
ejpam-6737	145	9	0	0	NUM
ejpam-6737	145	10	}	}	PUNCT
ejpam-6737	145	11	.	.	PUNCT
ejpam-6737	146	1	whenever	whenever	SCONJ
ejpam-6737	146	2	θ	θ	PROPN
ejpam-6737	146	3	∈	∈	PROPN
ejpam-6737	146	4	i	i	PRON
ejpam-6737	146	5	,	,	PUNCT
ejpam-6737	146	6	we	we	PRON
ejpam-6737	146	7	obtain	obtain	VERB
ejpam-6737	146	8	|ψ(θ)|	|ψ(θ)|	PROPN
ejpam-6737	146	9	=	=	SYM
ejpam-6737	146	10	max	max	PROPN
ejpam-6737	146	11	t∈[0,k	t∈[0,k	PROPN
ejpam-6737	146	12	]	]	X
ejpam-6737	146	13	∣∣∣∣θ(0	∣∣∣∣θ(0	PROPN
ejpam-6737	146	14	)	)	PUNCT
ejpam-6737	146	15	+	+	CCONJ
ejpam-6737	146	16	ϑtϑ−1(1−	ϑtϑ−1(1−	PROPN
ejpam-6737	146	17	η	η	PROPN
ejpam-6737	146	18	)	)	PUNCT
ejpam-6737	146	19	abc(η	abc(η	PROPN
ejpam-6737	146	20	)	)	PUNCT
ejpam-6737	146	21	ω(t	ω(t	NOUN
ejpam-6737	146	22	,	,	PUNCT
ejpam-6737	146	23	θ(t	θ(t	PROPN
ejpam-6737	146	24	)	)	PUNCT
ejpam-6737	146	25	)	)	PUNCT
ejpam-6737	147	1	+	+	CCONJ
ejpam-6737	147	2	ηϑ	ηϑ	ADP
ejpam-6737	147	3	d(η)abc(η)e	d(η)abc(η)e	PROPN
ejpam-6737	147	4	∫	∫	PROPN
ejpam-6737	147	5	t	t	PROPN
ejpam-6737	147	6	0	0	NUM
ejpam-6737	147	7	mϑ−1(t−m)η−1ω(m	mϑ−1(t−m)η−1ω(m	NOUN
ejpam-6737	147	8	,	,	PUNCT
ejpam-6737	147	9	θ(m	θ(m	NOUN
ejpam-6737	147	10	)	)	PUNCT
ejpam-6737	147	11	)	)	PUNCT
ejpam-6737	147	12	dm	dm	PROPN
ejpam-6737	147	13	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6737	147	14	≤	≤	PROPN
ejpam-6737	147	15	θ(0	θ(0	PROPN
ejpam-6737	147	16	)	)	PUNCT
ejpam-6737	147	17	+	+	CCONJ
ejpam-6737	147	18	ϑkϑ−1(1−	ϑkϑ−1(1−	PROPN
ejpam-6737	147	19	η	η	PROPN
ejpam-6737	147	20	)	)	PUNCT
ejpam-6737	147	21	abc(η	abc(η	PROPN
ejpam-6737	147	22	)	)	PUNCT
ejpam-6737	147	23	(	(	PUNCT
ejpam-6737	147	24	cφ‖θ‖+gφ	cφ‖θ‖+gφ	X
ejpam-6737	147	25	)	)	PUNCT
ejpam-6737	148	1	+	+	CCONJ
ejpam-6737	148	2	max	max	PROPN
ejpam-6737	148	3	t∈[0,k	t∈[0,k	PROPN
ejpam-6737	148	4	]	]	X
ejpam-6737	148	5	ηϑ	ηϑ	NOUN
ejpam-6737	148	6	d(η)abc(η)e	d(η)abc(η)e	PROPN
ejpam-6737	148	7	∫	∫	PROPN
ejpam-6737	149	1	t	t	PROPN
ejpam-6737	149	2	0	0	NUM
ejpam-6737	149	3	mϑ−1(t−m)η−1ω(m	mϑ−1(t−m)η−1ω(m	NOUN
ejpam-6737	149	4	,	,	PUNCT
ejpam-6737	149	5	θ(m	θ(m	NOUN
ejpam-6737	149	6	)	)	PUNCT
ejpam-6737	149	7	)	)	PUNCT
ejpam-6737	150	1	dm	dm	PROPN
ejpam-6737	150	2	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6737	150	3	≤	≤	PROPN
ejpam-6737	150	4	θ(0	θ(0	PROPN
ejpam-6737	150	5	)	)	PUNCT
ejpam-6737	150	6	+	+	CCONJ
ejpam-6737	150	7	ϑkϑ−1(1−	ϑkϑ−1(1−	PROPN
ejpam-6737	150	8	η	η	PROPN
ejpam-6737	150	9	)	)	PUNCT
ejpam-6737	150	10	abc(η	abc(η	PROPN
ejpam-6737	150	11	)	)	PUNCT
ejpam-6737	150	12	(	(	PUNCT
ejpam-6737	150	13	cφ‖θ‖+gφ	cφ‖θ‖+gφ	X
ejpam-6737	150	14	)	)	PUNCT
ejpam-6737	151	1	+	+	CCONJ
ejpam-6737	151	2	ηϑ	ηϑ	X
ejpam-6737	151	3	d(η)abc(η)e	d(η)abc(η)e	PROPN
ejpam-6737	151	4	(	(	PUNCT
ejpam-6737	151	5	cφ‖θ‖+gφ)k	cφ‖θ‖+gφ)k	PROPN
ejpam-6737	151	6	η+ϑ−1φ(η	η+ϑ−1φ(η	PROPN
ejpam-6737	151	7	,	,	PUNCT
ejpam-6737	151	8	ϑ	ϑ	NOUN
ejpam-6737	151	9	)	)	PUNCT
ejpam-6737	151	10	≤	≤	NUM
ejpam-6737	151	11	l	l	NOUN
ejpam-6737	151	12	.	.	PUNCT
ejpam-6737	152	1	(	(	PUNCT
ejpam-6737	152	2	8)	8)	NUM
ejpam-6737	152	3	accordingly	accordingly	ADV
ejpam-6737	152	4	,	,	PUNCT
ejpam-6737	152	5	whenever	whenever	SCONJ
ejpam-6737	152	6	φ(η	φ(η	PROPN
ejpam-6737	152	7	,	,	PUNCT
ejpam-6737	152	8	ϑ	ϑ	NOUN
ejpam-6737	152	9	)	)	PUNCT
ejpam-6737	152	10	represents	represent	VERB
ejpam-6737	152	11	a	a	DET
ejpam-6737	152	12	function	function	NOUN
ejpam-6737	152	13	,	,	PUNCT
ejpam-6737	152	14	the	the	DET
ejpam-6737	152	15	operator	operator	NOUN
ejpam-6737	152	16	ψ	ψ	NOUN
ejpam-6737	152	17	is	be	AUX
ejpam-6737	152	18	restricted	restrict	VERB
ejpam-6737	152	19	by	by	ADP
ejpam-6737	152	20	homogeneity	homogeneity	NOUN
ejpam-6737	152	21	.	.	PUNCT
ejpam-6737	153	1	as	as	ADP
ejpam-6737	153	2	ψ	ψ	PROPN
ejpam-6737	153	3	is	be	AUX
ejpam-6737	153	4	equi	equi	NOUN
ejpam-6737	153	5	-	-	PUNCT
ejpam-6737	153	6	continuous	continuous	ADJ
ejpam-6737	153	7	,	,	PUNCT
ejpam-6737	153	8	suppose	suppose	VERB
ejpam-6737	153	9	that	that	SCONJ
ejpam-6737	153	10	t1	t1	NOUN
ejpam-6737	153	11	,	,	PUNCT
ejpam-6737	153	12	t2	t2	PROPN
ejpam-6737	153	13	≤	≤	PROPN
ejpam-6737	153	14	k.	k.	PROPN
ejpam-6737	153	15	then	then	ADV
ejpam-6737	153	16	consider	consider	VERB
ejpam-6737	153	17	|ψ(θ)(t2)−	|ψ(θ)(t2)−	ADJ
ejpam-6737	153	18	ψ(θ)(t1)|	ψ(θ)(t1)|	NOUN
ejpam-6737	153	19	=	=	SYM
ejpam-6737	153	20	∣∣∣∣ϑtϑ−1	∣∣∣∣ϑtϑ−1	NOUN
ejpam-6737	153	21	2	2	NUM
ejpam-6737	153	22	(	(	PUNCT
ejpam-6737	153	23	1−	1−	NUM
ejpam-6737	153	24	η	η	NOUN
ejpam-6737	153	25	)	)	PUNCT
ejpam-6737	153	26	abc(η	abc(η	PROPN
ejpam-6737	153	27	)	)	PUNCT
ejpam-6737	153	28	ω(t2	ω(t2	NOUN
ejpam-6737	153	29	,	,	PUNCT
ejpam-6737	153	30	θ(t2	θ(t2	NOUN
ejpam-6737	153	31	)	)	PUNCT
ejpam-6737	153	32	)	)	PUNCT
ejpam-6737	154	1	+	+	CCONJ
ejpam-6737	154	2	ηϑ	ηϑ	ADP
ejpam-6737	154	3	d(η)abc(η)e	d(η)abc(η)e	PROPN
ejpam-6737	154	4	∫	∫	PROPN
ejpam-6737	154	5	t2	t2	PROPN
ejpam-6737	154	6	0	0	NUM
ejpam-6737	154	7	mϑ−1(t2	mϑ−1(t2	PROPN
ejpam-6737	154	8	−m)η−1ω(m	−m)η−1ω(m	PROPN
ejpam-6737	154	9	,	,	PUNCT
ejpam-6737	154	10	θ(m	θ(m	NOUN
ejpam-6737	154	11	)	)	PUNCT
ejpam-6737	154	12	)	)	PUNCT
ejpam-6737	155	1	dm	dm	VERB
ejpam-6737	155	2	−	−	PROPN
ejpam-6737	155	3	ϑtϑ−1	ϑtϑ−1	NOUN
ejpam-6737	155	4	1	1	NUM
ejpam-6737	155	5	(	(	PUNCT
ejpam-6737	155	6	1−	1−	NUM
ejpam-6737	155	7	η	η	NOUN
ejpam-6737	155	8	)	)	PUNCT
ejpam-6737	155	9	abc(η	abc(η	PROPN
ejpam-6737	155	10	)	)	PUNCT
ejpam-6737	155	11	ω(t1	ω(t1	NOUN
ejpam-6737	155	12	,	,	PUNCT
ejpam-6737	155	13	θ(t1))−	θ(t1))−	VERB
ejpam-6737	155	14	ηϑ	ηϑ	ADP
ejpam-6737	155	15	d(η)abc(η)e	d(η)abc(η)e	PROPN
ejpam-6737	155	16	∫	∫	PROPN
ejpam-6737	156	1	t1	t1	NOUN
ejpam-6737	156	2	0	0	PUNCT
ejpam-6737	157	1	mϑ−1(t1	mϑ−1(t1	PROPN
ejpam-6737	157	2	−m)η−1ω(m	−m)η−1ω(m	PROPN
ejpam-6737	157	3	,	,	PUNCT
ejpam-6737	157	4	θ(m	θ(m	NOUN
ejpam-6737	157	5	)	)	PUNCT
ejpam-6737	157	6	)	)	PUNCT
ejpam-6737	158	1	dm	dm	VERB
ejpam-6737	158	2	∣∣∣∣.	∣∣∣∣.	PRON
ejpam-6737	158	3	≤	≤	NOUN
ejpam-6737	158	4	∣∣∣∣ϑtϑ−1	∣∣∣∣ϑtϑ−1	NOUN
ejpam-6737	158	5	2	2	NUM
ejpam-6737	158	6	(	(	PUNCT
ejpam-6737	158	7	1−	1−	NUM
ejpam-6737	158	8	η	η	NOUN
ejpam-6737	158	9	)	)	PUNCT
ejpam-6737	158	10	abc(η	abc(η	PROPN
ejpam-6737	158	11	)	)	PUNCT
ejpam-6737	158	12	ω(t2	ω(t2	NOUN
ejpam-6737	158	13	,	,	PUNCT
ejpam-6737	158	14	θ(t2	θ(t2	NOUN
ejpam-6737	158	15	)	)	PUNCT
ejpam-6737	158	16	)	)	PUNCT
ejpam-6737	159	1	+	+	CCONJ
ejpam-6737	159	2	ηϑ	ηϑ	ADP
ejpam-6737	159	3	d(η)abc(η)e	d(η)abc(η)e	PROPN
ejpam-6737	159	4	∫	∫	PROPN
ejpam-6737	159	5	t2	t2	PROPN
ejpam-6737	159	6	0	0	NUM
ejpam-6737	159	7	mϑ−1(t2	mϑ−1(t2	PROPN
ejpam-6737	159	8	−m)η−1ω(m	−m)η−1ω(m	PROPN
ejpam-6737	159	9	,	,	PUNCT
ejpam-6737	159	10	θ(m	θ(m	NOUN
ejpam-6737	159	11	)	)	PUNCT
ejpam-6737	159	12	)	)	PUNCT
ejpam-6737	159	13	dm	dm	PROPN
ejpam-6737	159	14	s.	s.	PROPN
ejpam-6737	159	15	m.	m.	PROPN
ejpam-6737	159	16	chithra	chithra	PROPN
ejpam-6737	159	17	et	et	PROPN
ejpam-6737	159	18	al	al	PROPN
ejpam-6737	159	19	.	.	PUNCT
ejpam-6737	159	20	/	/	SYM
ejpam-6737	159	21	eur	eur	PROPN
ejpam-6737	159	22	.	.	PUNCT
ejpam-6737	160	1	j.	j.	PROPN
ejpam-6737	160	2	pure	pure	PROPN
ejpam-6737	160	3	appl	appl	PROPN
ejpam-6737	160	4	.	.	PROPN
ejpam-6737	160	5	math	math	PROPN
ejpam-6737	160	6	,	,	PUNCT
ejpam-6737	160	7	18	18	NUM
ejpam-6737	160	8	(	(	PUNCT
ejpam-6737	160	9	4	4	NUM
ejpam-6737	160	10	)	)	PUNCT
ejpam-6737	160	11	(	(	PUNCT
ejpam-6737	160	12	2025	2025	NUM
ejpam-6737	160	13	)	)	PUNCT
ejpam-6737	160	14	,	,	PUNCT
ejpam-6737	160	15	6737	6737	NUM
ejpam-6737	160	16	9	9	NUM
ejpam-6737	160	17	of	of	ADP
ejpam-6737	160	18	23	23	NUM
ejpam-6737	160	19	−	−	PROPN
ejpam-6737	160	20	ϑtϑ−1	ϑtϑ−1	NOUN
ejpam-6737	160	21	1	1	NUM
ejpam-6737	160	22	(	(	PUNCT
ejpam-6737	160	23	1−	1−	NUM
ejpam-6737	160	24	η	η	NOUN
ejpam-6737	160	25	)	)	PUNCT
ejpam-6737	160	26	abc(η	abc(η	PROPN
ejpam-6737	160	27	)	)	PUNCT
ejpam-6737	160	28	ω(t1	ω(t1	NOUN
ejpam-6737	160	29	,	,	PUNCT
ejpam-6737	160	30	θ(t1))−	θ(t1))−	VERB
ejpam-6737	160	31	ηϑ	ηϑ	ADP
ejpam-6737	160	32	d(η)abc(η)e	d(η)abc(η)e	PROPN
ejpam-6737	160	33	∫	∫	PROPN
ejpam-6737	161	1	t1	t1	NOUN
ejpam-6737	161	2	0	0	PUNCT
ejpam-6737	162	1	mϑ−1(t1	mϑ−1(t1	PROPN
ejpam-6737	162	2	−m)η−1ω(m	−m)η−1ω(m	PROPN
ejpam-6737	162	3	,	,	PUNCT
ejpam-6737	162	4	θ(m	θ(m	NOUN
ejpam-6737	162	5	)	)	PUNCT
ejpam-6737	162	6	)	)	PUNCT
ejpam-6737	163	1	dm	dm	VERB
ejpam-6737	163	2	∣∣∣∣.	∣∣∣∣.	PRON
ejpam-6737	163	3	when	when	SCONJ
ejpam-6737	163	4	t1	t1	NOUN
ejpam-6737	163	5	,	,	PUNCT
ejpam-6737	163	6	t2	t2	NOUN
ejpam-6737	163	7	then	then	ADV
ejpam-6737	163	8	|ψ(θ)(t2)−ψ(θ)(t1)|	|ψ(θ)(t2)−ψ(θ)(t1)|	PROPN
ejpam-6737	163	9	→	→	SYM
ejpam-6737	163	10	0	0	NUM
ejpam-6737	163	11	.	.	PUNCT
ejpam-6737	164	1	as	as	ADP
ejpam-6737	164	2	a	a	DET
ejpam-6737	164	3	result	result	NOUN
ejpam-6737	164	4	,	,	PUNCT
ejpam-6737	164	5	we	we	PRON
ejpam-6737	164	6	have	have	VERB
ejpam-6737	164	7	‖ψ(θ)(t2)−ψ(θ)(t1)‖	‖ψ(θ)(t2)−ψ(θ)(t1)‖	NOUN
ejpam-6737	164	8	→	→	SYM
ejpam-6737	164	9	0	0	NUM
ejpam-6737	164	10	when	when	SCONJ
ejpam-6737	164	11	t1	t1	NOUN
ejpam-6737	164	12	→	→	SYM
ejpam-6737	164	13	t2	t2	PROPN
ejpam-6737	164	14	.	.	PUNCT
ejpam-6737	165	1	since	since	SCONJ
ejpam-6737	165	2	ψ	ψ	NOUN
ejpam-6737	165	3	is	be	AUX
ejpam-6737	165	4	also	also	ADV
ejpam-6737	165	5	continuous	continuous	ADJ
ejpam-6737	165	6	,	,	PUNCT
ejpam-6737	165	7	the	the	DET
ejpam-6737	165	8	theory	theory	NOUN
ejpam-6737	165	9	of	of	ADP
ejpam-6737	165	10	arzela	arzela	PROPN
ejpam-6737	165	11	-	-	PUNCT
ejpam-6737	165	12	ascoli	ascoli	PROPN
ejpam-6737	165	13	is	be	AUX
ejpam-6737	165	14	also	also	ADV
ejpam-6737	165	15	completely	completely	ADV
ejpam-6737	165	16	continuous	continuous	ADJ
ejpam-6737	165	17	.	.	PUNCT
ejpam-6737	166	1	hence	hence	ADV
ejpam-6737	166	2	,	,	PUNCT
ejpam-6737	166	3	schauder	schauder	PROPN
ejpam-6737	166	4	’s	’s	PART
ejpam-6737	166	5	fixed	fix	VERB
ejpam-6737	166	6	point	point	NOUN
ejpam-6737	166	7	theorem	theorem	NOUN
ejpam-6737	166	8	shows	show	VERB
ejpam-6737	166	9	that	that	SCONJ
ejpam-6737	166	10	the	the	DET
ejpam-6737	166	11	suggested	suggest	VERB
ejpam-6737	166	12	model	model	NOUN
ejpam-6737	166	13	has	have	VERB
ejpam-6737	166	14	at	at	ADV
ejpam-6737	166	15	least	least	ADJ
ejpam-6737	166	16	one	one	NUM
ejpam-6737	166	17	solution	solution	NOUN
ejpam-6737	166	18	.	.	PUNCT
ejpam-6737	167	1	theorem	theorem	NOUN
ejpam-6737	167	2	3	3	NUM
ejpam-6737	167	3	.	.	PUNCT
ejpam-6737	167	4	assume	assume	VERB
ejpam-6737	167	5	that	that	SCONJ
ejpam-6737	167	6	condition	condition	NOUN
ejpam-6737	167	7	(	(	PUNCT
ejpam-6737	167	8	8)	8)	NUM
ejpam-6737	167	9	holds	hold	VERB
ejpam-6737	167	10	with	with	ADP
ejpam-6737	167	11	$	$	SYM
ejpam-6737	167	12	<	<	X
ejpam-6737	167	13	1	1	NUM
ejpam-6737	167	14	,	,	PUNCT
ejpam-6737	167	15	where	where	SCONJ
ejpam-6737	167	16	$	$	SYM
ejpam-6737	167	17	=	=	SYM
ejpam-6737	167	18	(	(	PUNCT
ejpam-6737	167	19	ϑkϑ−1(1−	ϑkϑ−1(1−	X
ejpam-6737	167	20	η	η	NOUN
ejpam-6737	167	21	)	)	PUNCT
ejpam-6737	167	22	abc(η	abc(η	PROPN
ejpam-6737	167	23	)	)	PUNCT
ejpam-6737	167	24	+	+	NUM
ejpam-6737	167	25	ηϑ	ηϑ	ADP
ejpam-6737	167	26	d(η)abc(η)e	d(η)abc(η)e	PROPN
ejpam-6737	167	27	kη+ϑ−1φ(η	kη+ϑ−1φ(η	PROPN
ejpam-6737	167	28	,	,	PUNCT
ejpam-6737	167	29	ϑ	ϑ	NOUN
ejpam-6737	167	30	)	)	PUNCT
ejpam-6737	167	31	)	)	PUNCT
ejpam-6737	168	1	hφ	hφ	VERB
ejpam-6737	168	2	then	then	ADV
ejpam-6737	168	3	,	,	PUNCT
ejpam-6737	168	4	model	model	NOUN
ejpam-6737	168	5	(	(	PUNCT
ejpam-6737	168	6	7	7	X
ejpam-6737	168	7	)	)	PUNCT
ejpam-6737	168	8	gives	give	VERB
ejpam-6737	168	9	a	a	DET
ejpam-6737	168	10	definite	definite	ADJ
ejpam-6737	168	11	answer	answer	NOUN
ejpam-6737	168	12	.	.	PUNCT
ejpam-6737	169	1	proof	proof	NOUN
ejpam-6737	169	2	.	.	PUNCT
ejpam-6737	170	1	let	let	VERB
ejpam-6737	170	2	θ	θ	NOUN
ejpam-6737	170	3	,	,	PUNCT
ejpam-6737	170	4	θ̄	θ̄	PROPN
ejpam-6737	170	5	∈	∈	PROPN
ejpam-6737	171	1	i	i	PRON
ejpam-6737	171	2	,	,	PUNCT
ejpam-6737	171	3	we	we	PRON
ejpam-6737	171	4	have	have	AUX
ejpam-6737	171	5	|ψ(θ)−	|ψ(θ)−	VERB
ejpam-6737	171	6	ψ(θ̄)|	ψ(θ̄)|	X
ejpam-6737	171	7	=	=	SYM
ejpam-6737	171	8	max	max	PROPN
ejpam-6737	171	9	t∈[0,k	t∈[0,k	PROPN
ejpam-6737	171	10	]	]	PUNCT
ejpam-6737	171	11	∣∣∣∣ϑtϑ−1(1−	∣∣∣∣ϑtϑ−1(1−	PROPN
ejpam-6737	171	12	η	η	PROPN
ejpam-6737	171	13	)	)	PUNCT
ejpam-6737	171	14	abc(η	abc(η	PROPN
ejpam-6737	171	15	)	)	PUNCT
ejpam-6737	172	1	[	[	X
ejpam-6737	172	2	ω(t	ω(t	NOUN
ejpam-6737	172	3	,	,	PUNCT
ejpam-6737	172	4	θ(t))−	θ(t))−	PROPN
ejpam-6737	172	5	ω(t	ω(t	NOUN
ejpam-6737	172	6	,	,	PUNCT
ejpam-6737	172	7	θ̄(t	θ̄(t	NOUN
ejpam-6737	172	8	)	)	PUNCT
ejpam-6737	172	9	)	)	PUNCT
ejpam-6737	172	10	]	]	PUNCT
ejpam-6737	173	1	+	+	CCONJ
ejpam-6737	173	2	ηϑ	ηϑ	ADP
ejpam-6737	173	3	d(η)abc(η)e	d(η)abc(η)e	PROPN
ejpam-6737	173	4	∫	∫	PROPN
ejpam-6737	173	5	t	t	PROPN
ejpam-6737	173	6	0	0	NUM
ejpam-6737	173	7	mϑ−1(t−m)η−1[ω(m	mϑ−1(t−m)η−1[ω(m	PROPN
ejpam-6737	173	8	,	,	PUNCT
ejpam-6737	173	9	θ(m))−	θ(m))−	NOUN
ejpam-6737	173	10	ω(m	ω(m	NOUN
ejpam-6737	173	11	,	,	PUNCT
ejpam-6737	173	12	θ̄(m	θ̄(m	NOUN
ejpam-6737	173	13	)	)	PUNCT
ejpam-6737	173	14	)	)	PUNCT
ejpam-6737	173	15	]	]	PUNCT
ejpam-6737	174	1	dm	dm	PROPN
ejpam-6737	174	2	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6737	174	3	≤	≤	NOUN
ejpam-6737	174	4	[	[	PUNCT
ejpam-6737	174	5	ϑkϑ−1(1−	ϑkϑ−1(1−	X
ejpam-6737	174	6	η	η	NOUN
ejpam-6737	174	7	)	)	PUNCT
ejpam-6737	174	8	abc(η	abc(η	PROPN
ejpam-6737	174	9	)	)	PUNCT
ejpam-6737	174	10	+	+	NUM
ejpam-6737	174	11	ηϑ	ηϑ	ADP
ejpam-6737	174	12	d(η)abc(η)e	d(η)abc(η)e	PROPN
ejpam-6737	174	13	kη+ϑ−1φ(η	kη+ϑ−1φ(η	PROPN
ejpam-6737	174	14	,	,	PUNCT
ejpam-6737	174	15	ϑ	ϑ	NOUN
ejpam-6737	174	16	)	)	PUNCT
ejpam-6737	174	17	]	]	PUNCT
ejpam-6737	174	18	‖θ	‖θ	ADV
ejpam-6737	174	19	−	−	PROPN
ejpam-6737	174	20	θ̄‖	θ̄‖	PROPN
ejpam-6737	174	21	≤	≤	NOUN
ejpam-6737	174	22	$	$	SYM
ejpam-6737	174	23	‖θ	‖θ	ADV
ejpam-6737	174	24	−	−	ADP
ejpam-6737	174	25	θ̄‖.	θ̄‖.	NOUN
ejpam-6737	174	26	as	as	ADP
ejpam-6737	174	27	a	a	DET
ejpam-6737	174	28	result	result	NOUN
ejpam-6737	174	29	,	,	PUNCT
ejpam-6737	174	30	ψ	ψ	X
ejpam-6737	174	31	is	be	AUX
ejpam-6737	174	32	a	a	DET
ejpam-6737	174	33	contraction	contraction	NOUN
ejpam-6737	174	34	mapping	mapping	NOUN
ejpam-6737	174	35	,	,	PUNCT
ejpam-6737	174	36	and	and	CCONJ
ejpam-6737	174	37	the	the	DET
ejpam-6737	174	38	proposed	propose	VERB
ejpam-6737	174	39	model	model	NOUN
ejpam-6737	174	40	possesses	possess	VERB
ejpam-6737	174	41	a	a	DET
ejpam-6737	174	42	solution	solution	NOUN
ejpam-6737	174	43	by	by	ADP
ejpam-6737	174	44	virtue	virtue	NOUN
ejpam-6737	174	45	of	of	ADP
ejpam-6737	174	46	the	the	DET
ejpam-6737	174	47	banach	banach	NOUN
ejpam-6737	174	48	contraction	contraction	NOUN
ejpam-6737	174	49	principle	principle	NOUN
ejpam-6737	174	50	.	.	PUNCT
ejpam-6737	175	1	5.1	5.1	NUM
ejpam-6737	175	2	.	.	PUNCT
ejpam-6737	176	1	ulam	ulam	NOUN
ejpam-6737	176	2	-	-	PUNCT
ejpam-6737	176	3	hyers	hyer	NOUN
ejpam-6737	176	4	stability	stability	NOUN
ejpam-6737	176	5	definition	definition	NOUN
ejpam-6737	176	6	:	:	PUNCT
ejpam-6737	176	7	the	the	DET
ejpam-6737	176	8	considered	consider	VERB
ejpam-6737	176	9	model	model	NOUN
ejpam-6737	176	10	is	be	AUX
ejpam-6737	176	11	ulam	ulam	NOUN
ejpam-6737	176	12	-	-	PUNCT
ejpam-6737	176	13	hyers	hyer	NOUN
ejpam-6737	176	14	stable	stable	ADJ
ejpam-6737	176	15	if	if	SCONJ
ejpam-6737	176	16	for	for	ADP
ejpam-6737	176	17	every	every	DET
ejpam-6737	176	18	small	small	ADJ
ejpam-6737	176	19	perturbation	perturbation	NOUN
ejpam-6737	176	20	q(t	q(t	NOUN
ejpam-6737	176	21	)	)	PUNCT
ejpam-6737	176	22	with	with	ADP
ejpam-6737	176	23	|q(t)|	|q(t)|	ADJ
ejpam-6737	176	24	≤	≤	X
ejpam-6737	176	25	ε	ε	PROPN
ejpam-6737	176	26	for	for	ADP
ejpam-6737	176	27	ε	ε	PROPN
ejpam-6737	176	28	>	>	X
ejpam-6737	176	29	0	0	PROPN
ejpam-6737	176	30	,	,	PUNCT
ejpam-6737	176	31	there	there	PRON
ejpam-6737	176	32	is	be	VERB
ejpam-6737	176	33	an	an	DET
ejpam-6737	176	34	exact	exact	ADJ
ejpam-6737	176	35	unique	unique	ADJ
ejpam-6737	176	36	solution	solution	NOUN
ejpam-6737	176	37	p	p	X
ejpam-6737	176	38	(	(	PUNCT
ejpam-6737	176	39	t	t	NOUN
ejpam-6737	176	40	)	)	PUNCT
ejpam-6737	176	41	in	in	ADP
ejpam-6737	176	42	such	such	DET
ejpam-6737	176	43	a	a	DET
ejpam-6737	176	44	way	way	NOUN
ejpam-6737	176	45	that	that	PRON
ejpam-6737	176	46	the	the	DET
ejpam-6737	176	47	perturbed	perturb	VERB
ejpam-6737	176	48	solution	solution	NOUN
ejpam-6737	176	49	θ(t	θ(t	NOUN
ejpam-6737	176	50	)	)	PUNCT
ejpam-6737	176	51	fulfills	fulfill	VERB
ejpam-6737	176	52	the	the	DET
ejpam-6737	176	53	inequality	inequality	NOUN
ejpam-6737	176	54	|θ(t)−	|θ(t)−	PROPN
ejpam-6737	176	55	p	p	X
ejpam-6737	176	56	(	(	PUNCT
ejpam-6737	176	57	t)|	t)|	PROPN
ejpam-6737	176	58	≤	≤	ADJ
ejpam-6737	176	59	ψη,ϑε	ψη,ϑε	ADV
ejpam-6737	176	60	,	,	PUNCT
ejpam-6737	176	61	for	for	ADP
ejpam-6737	176	62	every	every	DET
ejpam-6737	176	63	t	t	NOUN
ejpam-6737	176	64	∈	∈	PROPN
ejpam-6737	177	1	[	[	X
ejpam-6737	177	2	0,k	0,k	X
ejpam-6737	177	3	]	]	PUNCT
ejpam-6737	177	4	where	where	SCONJ
ejpam-6737	177	5	ψη,ϑ	ψη,ϑ	PRON
ejpam-6737	177	6	is	be	AUX
ejpam-6737	177	7	a	a	DET
ejpam-6737	177	8	positive	positive	ADJ
ejpam-6737	177	9	constant	constant	ADJ
ejpam-6737	177	10	depending	depend	VERB
ejpam-6737	177	11	on	on	ADP
ejpam-6737	177	12	the	the	DET
ejpam-6737	177	13	system	system	NOUN
ejpam-6737	177	14	’s	’s	PART
ejpam-6737	177	15	parameters	parameter	NOUN
ejpam-6737	177	16	.	.	PUNCT
ejpam-6737	178	1	according	accord	VERB
ejpam-6737	178	2	to	to	ADP
ejpam-6737	178	3	the	the	DET
ejpam-6737	178	4	above	above	ADJ
ejpam-6737	178	5	definition	definition	NOUN
ejpam-6737	178	6	of	of	ADP
ejpam-6737	178	7	ulam	ulam	NOUN
ejpam-6737	178	8	–	–	PUNCT
ejpam-6737	178	9	hyers	hyer	NOUN
ejpam-6737	178	10	stability	stability	NOUN
ejpam-6737	178	11	,	,	PUNCT
ejpam-6737	178	12	we	we	PRON
ejpam-6737	178	13	now	now	ADV
ejpam-6737	178	14	use	use	VERB
ejpam-6737	178	15	the	the	DET
ejpam-6737	178	16	concept	concept	NOUN
ejpam-6737	178	17	to	to	PART
ejpam-6737	178	18	investigate	investigate	VERB
ejpam-6737	178	19	the	the	DET
ejpam-6737	178	20	behaviour	behaviour	NOUN
ejpam-6737	178	21	of	of	ADP
ejpam-6737	178	22	the	the	DET
ejpam-6737	178	23	provided	provide	VERB
ejpam-6737	178	24	fractional	fractional	ADJ
ejpam-6737	178	25	-	-	PUNCT
ejpam-6737	178	26	order	order	NOUN
ejpam-6737	178	27	system	system	NOUN
ejpam-6737	178	28	:	:	PUNCT
ejpam-6737	178	29	ffm	ffm	NOUN
ejpam-6737	178	30	0	0	NUM
ejpam-6737	178	31	dη,ϑ	dη,ϑ	X
ejpam-6737	178	32	t	t	PROPN
ejpam-6737	178	33	θ(t	θ(t	PROPN
ejpam-6737	178	34	)	)	PUNCT
ejpam-6737	178	35	=	=	SYM
ejpam-6737	178	36	ω(t	ω(t	NOUN
ejpam-6737	178	37	,	,	PUNCT
ejpam-6737	178	38	θ(t	θ(t	PROPN
ejpam-6737	178	39	)	)	PUNCT
ejpam-6737	178	40	)	)	PUNCT
ejpam-6737	179	1	+	+	VERB
ejpam-6737	179	2	q(t	q(t	NOUN
ejpam-6737	179	3	)	)	PUNCT
ejpam-6737	179	4	,	,	PUNCT
ejpam-6737	179	5	θ(0	θ(0	PROPN
ejpam-6737	179	6	)	)	PUNCT
ejpam-6737	179	7	=	=	SYM
ejpam-6737	179	8	θ0	θ0	PROPN
ejpam-6737	179	9	.	.	PUNCT
ejpam-6737	180	1	lemma	lemma	PROPN
ejpam-6737	180	2	1	1	X
ejpam-6737	180	3	.	.	PUNCT
ejpam-6737	181	1	let	let	VERB
ejpam-6737	181	2	p	p	PROPN
ejpam-6737	181	3	(	(	PUNCT
ejpam-6737	181	4	t	t	NOUN
ejpam-6737	181	5	)	)	PUNCT
ejpam-6737	181	6	be	be	AUX
ejpam-6737	181	7	the	the	DET
ejpam-6737	181	8	exact	exact	ADJ
ejpam-6737	181	9	solution	solution	NOUN
ejpam-6737	181	10	of	of	ADP
ejpam-6737	181	11	the	the	DET
ejpam-6737	181	12	unperturbed	unperturbed	ADJ
ejpam-6737	181	13	system	system	NOUN
ejpam-6737	181	14	,	,	PUNCT
ejpam-6737	181	15	and	and	CCONJ
ejpam-6737	181	16	let	let	VERB
ejpam-6737	181	17	θ(t	θ(t	PROPN
ejpam-6737	181	18	)	)	PUNCT
ejpam-6737	181	19	be	be	AUX
ejpam-6737	181	20	the	the	DET
ejpam-6737	181	21	solution	solution	NOUN
ejpam-6737	181	22	of	of	ADP
ejpam-6737	181	23	the	the	DET
ejpam-6737	181	24	perturbed	perturb	VERB
ejpam-6737	181	25	system	system	NOUN
ejpam-6737	181	26	.	.	PUNCT
ejpam-6737	182	1	if	if	SCONJ
ejpam-6737	182	2	|q(t)|	|q(t)|	ADJ
ejpam-6737	182	3	≤	≤	X
ejpam-6737	182	4	ε	ε	PROPN
ejpam-6737	182	5	,	,	PUNCT
ejpam-6737	182	6	then	then	ADV
ejpam-6737	182	7	|θ(t)−	|θ(t)−	VERB
ejpam-6737	182	8	p	p	X
ejpam-6737	182	9	(	(	PUNCT
ejpam-6737	182	10	t)|	t)|	PROPN
ejpam-6737	182	11	≤	≤	NUM
ejpam-6737	182	12	αη,ϑε+$|θ(t)−	αη,ϑε+$|θ(t)−	NUM
ejpam-6737	183	1	p	p	NOUN
ejpam-6737	183	2	(	(	PUNCT
ejpam-6737	183	3	t)|	t)|	NOUN
ejpam-6737	183	4	.	.	PUNCT
ejpam-6737	184	1	s.	s.	PROPN
ejpam-6737	184	2	m.	m.	PROPN
ejpam-6737	184	3	chithra	chithra	PROPN
ejpam-6737	184	4	et	et	PROPN
ejpam-6737	184	5	al	al	PROPN
ejpam-6737	184	6	.	.	PUNCT
ejpam-6737	184	7	/	/	SYM
ejpam-6737	184	8	eur	eur	PROPN
ejpam-6737	184	9	.	.	PUNCT
ejpam-6737	185	1	j.	j.	PROPN
ejpam-6737	185	2	pure	pure	PROPN
ejpam-6737	185	3	appl	appl	PROPN
ejpam-6737	185	4	.	.	PROPN
ejpam-6737	185	5	math	math	PROPN
ejpam-6737	185	6	,	,	PUNCT
ejpam-6737	185	7	18	18	NUM
ejpam-6737	185	8	(	(	PUNCT
ejpam-6737	185	9	4	4	NUM
ejpam-6737	185	10	)	)	PUNCT
ejpam-6737	185	11	(	(	PUNCT
ejpam-6737	185	12	2025	2025	NUM
ejpam-6737	185	13	)	)	PUNCT
ejpam-6737	185	14	,	,	PUNCT
ejpam-6737	185	15	6737	6737	NUM
ejpam-6737	185	16	10	10	NUM
ejpam-6737	185	17	of	of	ADP
ejpam-6737	185	18	23	23	NUM
ejpam-6737	185	19	proof	proof	NOUN
ejpam-6737	185	20	.	.	PUNCT
ejpam-6737	186	1	this	this	PRON
ejpam-6737	186	2	is	be	AUX
ejpam-6737	186	3	a	a	DET
ejpam-6737	186	4	very	very	ADV
ejpam-6737	186	5	basic	basic	ADJ
ejpam-6737	186	6	demonstration	demonstration	NOUN
ejpam-6737	186	7	.	.	PUNCT
ejpam-6737	187	1	it	it	PRON
ejpam-6737	187	2	can	can	AUX
ejpam-6737	187	3	be	be	AUX
ejpam-6737	187	4	illustrated	illustrate	VERB
ejpam-6737	187	5	by	by	ADP
ejpam-6737	187	6	taking	take	VERB
ejpam-6737	187	7	system	system	NOUN
ejpam-6737	187	8	(	(	PUNCT
ejpam-6737	187	9	7	7	NUM
ejpam-6737	187	10	)	)	PUNCT
ejpam-6737	187	11	into	into	ADP
ejpam-6737	187	12	consideration	consideration	NOUN
ejpam-6737	187	13	:	:	PUNCT
ejpam-6737	187	14	ffm	ffm	NOUN
ejpam-6737	187	15	0	0	NUM
ejpam-6737	187	16	dη,ϑ	dη,ϑ	X
ejpam-6737	187	17	t	t	NOUN
ejpam-6737	187	18	(	(	PUNCT
ejpam-6737	187	19	θ(t)−	θ(t)−	PROPN
ejpam-6737	187	20	p	p	PROPN
ejpam-6737	187	21	(	(	PUNCT
ejpam-6737	187	22	t	t	PROPN
ejpam-6737	187	23	)	)	PUNCT
ejpam-6737	187	24	)	)	PUNCT
ejpam-6737	188	1	=	=	SYM
ejpam-6737	188	2	ω(t	ω(t	NOUN
ejpam-6737	188	3	,	,	PUNCT
ejpam-6737	188	4	θ(t	θ(t	PROPN
ejpam-6737	188	5	)	)	PUNCT
ejpam-6737	188	6	)	)	PUNCT
ejpam-6737	189	1	+	+	NOUN
ejpam-6737	189	2	q(t)−	q(t)−	PROPN
ejpam-6737	189	3	p	p	X
ejpam-6737	189	4	(	(	PUNCT
ejpam-6737	189	5	t	t	PROPN
ejpam-6737	189	6	)	)	PUNCT
ejpam-6737	189	7	.	.	PUNCT
ejpam-6737	190	1	using	use	VERB
ejpam-6737	190	2	lipschitz	lipschitz	NOUN
ejpam-6737	190	3	condition	condition	NOUN
ejpam-6737	190	4	for	for	ADP
ejpam-6737	190	5	ω	ω	NOUN
ejpam-6737	190	6	:	:	PUNCT
ejpam-6737	190	7	|ffm	|ffm	NUM
ejpam-6737	190	8	0	0	NUM
ejpam-6737	190	9	dη,ϑ	dη,ϑ	X
ejpam-6737	190	10	t	t	NOUN
ejpam-6737	190	11	(	(	PUNCT
ejpam-6737	190	12	θ(t)−	θ(t)−	PROPN
ejpam-6737	190	13	p	p	X
ejpam-6737	190	14	(	(	PUNCT
ejpam-6737	190	15	t))|	t))|	PROPN
ejpam-6737	190	16	≤	≤	PROPN
ejpam-6737	191	1	l	l	NOUN
ejpam-6737	191	2	|θ(t)−	|θ(t)−	PROPN
ejpam-6737	191	3	p	p	X
ejpam-6737	191	4	(	(	PUNCT
ejpam-6737	191	5	t)|+	t)|+	PRON
ejpam-6737	191	6	|q(t)|	|q(t)|	VERB
ejpam-6737	191	7	,	,	PUNCT
ejpam-6737	191	8	where	where	SCONJ
ejpam-6737	191	9	l	l	NOUN
ejpam-6737	191	10	is	be	AUX
ejpam-6737	191	11	lipschitz	lipschitz	NOUN
ejpam-6737	191	12	condition	condition	NOUN
ejpam-6737	191	13	.	.	PUNCT
ejpam-6737	192	1	the	the	DET
ejpam-6737	192	2	fractional	fractional	ADJ
ejpam-6737	192	3	derivative	derivative	ADJ
ejpam-6737	192	4	expansion	expansion	NOUN
ejpam-6737	192	5	gives	give	VERB
ejpam-6737	192	6	|θ(t)−p	|θ(t)−p	PUNCT
ejpam-6737	192	7	(	(	PUNCT
ejpam-6737	192	8	t)|	t)|	NOUN
ejpam-6737	192	9	=	=	SYM
ejpam-6737	192	10	∣∣∣∣∣θ(t)−	∣∣∣∣∣θ(t)−	X
ejpam-6737	192	11	(	(	PUNCT
ejpam-6737	192	12	p	p	X
ejpam-6737	192	13	(	(	PUNCT
ejpam-6737	192	14	0)+	0)+	NUM
ejpam-6737	192	15	ϑtϑ−1(1−	ϑtϑ−1(1−	PROPN
ejpam-6737	192	16	η	η	PROPN
ejpam-6737	192	17	)	)	PUNCT
ejpam-6737	192	18	abc(η	abc(η	PROPN
ejpam-6737	192	19	)	)	PUNCT
ejpam-6737	192	20	ω(t	ω(t	NOUN
ejpam-6737	192	21	,	,	PUNCT
ejpam-6737	192	22	p	p	X
ejpam-6737	192	23	(	(	PUNCT
ejpam-6737	192	24	t))+	t))+	PROPN
ejpam-6737	192	25	ηϑ	ηϑ	PROPN
ejpam-6737	192	26	d(η)abc(η	d(η)abc(η	PROPN
ejpam-6737	192	27	)	)	PUNCT
ejpam-6737	193	1	∫	∫	PROPN
ejpam-6737	193	2	t	t	PROPN
ejpam-6737	193	3	0	0	NUM
ejpam-6737	194	1	mϑ−1(t−m)η−1ω(m	mϑ−1(t−m)η−1ω(m	NOUN
ejpam-6737	194	2	,	,	PUNCT
ejpam-6737	194	3	p	p	X
ejpam-6737	194	4	(	(	PUNCT
ejpam-6737	194	5	m	m	NOUN
ejpam-6737	194	6	)	)	PUNCT
ejpam-6737	194	7	)	)	PUNCT
ejpam-6737	195	1	dm	dm	NOUN
ejpam-6737	195	2	)	)	PUNCT
ejpam-6737	195	3	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-6737	195	4	≤	≤	PROPN
ejpam-6737	195	5	ϑkϑ−1(1−	ϑkϑ−1(1−	PROPN
ejpam-6737	195	6	η	η	NOUN
ejpam-6737	195	7	)	)	PUNCT
ejpam-6737	195	8	abc(η	abc(η	PROPN
ejpam-6737	195	9	)	)	PUNCT
ejpam-6737	196	1	+	+	NUM
ejpam-6737	196	2	ηϑ	ηϑ	ADP
ejpam-6737	196	3	d(η)abc(η	d(η)abc(η	PROPN
ejpam-6737	196	4	)	)	PUNCT
ejpam-6737	197	1	kη+ϑ−1φ(η	kη+ϑ−1φ(η	PROPN
ejpam-6737	197	2	,	,	PUNCT
ejpam-6737	197	3	ϑ	ϑ	X
ejpam-6737	197	4	)	)	PUNCT
ejpam-6737	197	5	+	+	ADP
ejpam-6737	197	6	$	$	SYM
ejpam-6737	197	7	|θ(t)−	|θ(t)−	PROPN
ejpam-6737	197	8	p	p	X
ejpam-6737	198	1	(	(	PUNCT
ejpam-6737	198	2	t)|	t)|	NOUN
ejpam-6737	198	3	.	.	PUNCT
ejpam-6737	199	1	thus	thus	ADV
ejpam-6737	199	2	,	,	PUNCT
ejpam-6737	199	3	the	the	DET
ejpam-6737	199	4	condition	condition	NOUN
ejpam-6737	199	5	holds	hold	VERB
ejpam-6737	199	6	:	:	PUNCT
ejpam-6737	199	7	|θ(t)−	|θ(t)−	PROPN
ejpam-6737	199	8	p	p	X
ejpam-6737	199	9	(	(	PUNCT
ejpam-6737	199	10	t)|	t)|	PROPN
ejpam-6737	199	11	≤	≤	NUM
ejpam-6737	199	12	αη,ϑε+$|θ(t)−	αη,ϑε+$|θ(t)−	NUM
ejpam-6737	199	13	p	p	NOUN
ejpam-6737	200	1	(	(	PUNCT
ejpam-6737	200	2	t)|	t)|	NOUN
ejpam-6737	200	3	,	,	PUNCT
ejpam-6737	200	4	where	where	SCONJ
ejpam-6737	200	5	αη,ϑε	αη,ϑε	ADJ
ejpam-6737	200	6	=	=	SYM
ejpam-6737	200	7	ϑkϑ−1(1−	ϑkϑ−1(1−	PROPN
ejpam-6737	200	8	η	η	NOUN
ejpam-6737	200	9	)	)	PUNCT
ejpam-6737	200	10	abc(η	abc(η	PROPN
ejpam-6737	200	11	)	)	PUNCT
ejpam-6737	200	12	+	+	NUM
ejpam-6737	200	13	ηϑ	ηϑ	ADP
ejpam-6737	200	14	d(η)abc(η	d(η)abc(η	PROPN
ejpam-6737	200	15	)	)	PUNCT
ejpam-6737	201	1	kη+ϑ−1φ(η	kη+ϑ−1φ(η	PROPN
ejpam-6737	201	2	,	,	PUNCT
ejpam-6737	201	3	ϑ	ϑ	NOUN
ejpam-6737	201	4	)	)	PUNCT
ejpam-6737	201	5	.	.	PUNCT
ejpam-6737	202	1	therefore	therefore	ADV
ejpam-6737	202	2	,	,	PUNCT
ejpam-6737	202	3	the	the	DET
ejpam-6737	202	4	proof	proof	NOUN
ejpam-6737	202	5	is	be	AUX
ejpam-6737	202	6	verified	verify	VERB
ejpam-6737	202	7	.	.	PUNCT
ejpam-6737	203	1	lemma	lemma	PROPN
ejpam-6737	203	2	2	2	X
ejpam-6737	203	3	.	.	PUNCT
ejpam-6737	204	1	if	if	SCONJ
ejpam-6737	204	2	$	$	SYM
ejpam-6737	204	3	<	<	X
ejpam-6737	204	4	1	1	NUM
ejpam-6737	204	5	,	,	PUNCT
ejpam-6737	204	6	the	the	DET
ejpam-6737	204	7	suggested	suggest	VERB
ejpam-6737	204	8	model	model	NOUN
ejpam-6737	204	9	’s	’s	PART
ejpam-6737	204	10	ulam	ulam	PROPN
ejpam-6737	204	11	-	-	PUNCT
ejpam-6737	204	12	hyers	hyer	NOUN
ejpam-6737	204	13	reliable	reliable	ADJ
ejpam-6737	204	14	result	result	NOUN
ejpam-6737	204	15	interacts	interact	VERB
ejpam-6737	204	16	with	with	ADP
ejpam-6737	204	17	lemma	lemma	PROPN
ejpam-6737	204	18	1	1	NUM
ejpam-6737	204	19	.	.	PUNCT
ejpam-6737	205	1	the	the	DET
ejpam-6737	205	2	ulam	ulam	PROPN
ejpam-6737	205	3	-	-	PUNCT
ejpam-6737	205	4	hyers	hyer	NOUN
ejpam-6737	205	5	stability	stability	NOUN
ejpam-6737	205	6	of	of	ADP
ejpam-6737	205	7	the	the	DET
ejpam-6737	205	8	fractional	fractional	ADJ
ejpam-6737	205	9	-	-	PUNCT
ejpam-6737	205	10	order	order	NOUN
ejpam-6737	205	11	system	system	NOUN
ejpam-6737	205	12	is	be	AUX
ejpam-6737	205	13	assured	assure	VERB
ejpam-6737	205	14	if	if	SCONJ
ejpam-6737	205	15	$	$	SYM
ejpam-6737	205	16	<	<	X
ejpam-6737	205	17	1	1	NUM
ejpam-6737	205	18	.	.	PUNCT
ejpam-6737	206	1	under	under	ADP
ejpam-6737	206	2	this	this	DET
ejpam-6737	206	3	condition	condition	NOUN
ejpam-6737	206	4	,	,	PUNCT
ejpam-6737	206	5	the	the	DET
ejpam-6737	206	6	perturbed	perturb	VERB
ejpam-6737	206	7	solution	solution	NOUN
ejpam-6737	206	8	υ(t	υ(t	NOUN
ejpam-6737	206	9	)	)	PUNCT
ejpam-6737	206	10	satisfies	satisfie	NOUN
ejpam-6737	206	11	:	:	PUNCT
ejpam-6737	206	12	|θ(t)−	|θ(t)−	PROPN
ejpam-6737	206	13	p	p	X
ejpam-6737	206	14	(	(	PUNCT
ejpam-6737	206	15	t)|	t)|	ADV
ejpam-6737	206	16	≤	≤	NUM
ejpam-6737	206	17	αη,ϑ	αη,ϑ	NOUN
ejpam-6737	206	18	1−$	1−$	NUM
ejpam-6737	206	19	.	.	PUNCT
ejpam-6737	207	1	proof	proof	NOUN
ejpam-6737	207	2	.	.	PUNCT
ejpam-6737	208	1	from	from	ADP
ejpam-6737	208	2	lemma	lemma	PROPN
ejpam-6737	208	3	1	1	NUM
ejpam-6737	208	4	,	,	PUNCT
ejpam-6737	208	5	|θ(t)−	|θ(t)−	ADV
ejpam-6737	208	6	p	p	X
ejpam-6737	208	7	(	(	PUNCT
ejpam-6737	208	8	t)|	t)|	PROPN
ejpam-6737	208	9	≤	≤	NUM
ejpam-6737	208	10	αη,ϑε+$|θ(t)−	αη,ϑε+$|θ(t)−	NUM
ejpam-6737	209	1	p	p	NOUN
ejpam-6737	209	2	(	(	PUNCT
ejpam-6737	209	3	t)|	t)|	NOUN
ejpam-6737	209	4	.	.	PUNCT
ejpam-6737	210	1	a	a	DET
ejpam-6737	210	2	different	different	ADJ
ejpam-6737	210	3	form	form	NOUN
ejpam-6737	210	4	to	to	PART
ejpam-6737	210	5	write	write	VERB
ejpam-6737	210	6	the	the	DET
ejpam-6737	210	7	above	above	ADJ
ejpam-6737	210	8	relation	relation	NOUN
ejpam-6737	210	9	is	be	AUX
ejpam-6737	210	10	given	give	VERB
ejpam-6737	210	11	as	as	ADP
ejpam-6737	210	12	|θ(t)−	|θ(t)−	PROPN
ejpam-6737	210	13	p	p	X
ejpam-6737	210	14	(	(	PUNCT
ejpam-6737	210	15	t)|	t)|	ADV
ejpam-6737	210	16	≤	≤	NUM
ejpam-6737	210	17	ψη,ϑε	ψη,ϑε	ADV
ejpam-6737	210	18	,	,	PUNCT
ejpam-6737	210	19	where	where	SCONJ
ejpam-6737	210	20	ψη,ϑ	ψη,ϑ	PUNCT
ejpam-6737	210	21	=	=	SYM
ejpam-6737	210	22	αη,ϑ	αη,ϑ	X
ejpam-6737	210	23	1−$	1−$	NUM
ejpam-6737	210	24	.	.	PUNCT
ejpam-6737	211	1	with	with	ADP
ejpam-6737	211	2	the	the	DET
ejpam-6737	211	3	above	above	ADJ
ejpam-6737	211	4	lemmas	lemmas	NOUN
ejpam-6737	211	5	,	,	PUNCT
ejpam-6737	211	6	it	it	PRON
ejpam-6737	211	7	is	be	AUX
ejpam-6737	211	8	established	establish	VERB
ejpam-6737	211	9	that	that	SCONJ
ejpam-6737	211	10	the	the	DET
ejpam-6737	211	11	system	system	NOUN
ejpam-6737	211	12	is	be	AUX
ejpam-6737	211	13	ulam	ulam	NOUN
ejpam-6737	211	14	-	-	PUNCT
ejpam-6737	211	15	hyers	hyer	NOUN
ejpam-6737	211	16	stable	stable	ADJ
ejpam-6737	211	17	.	.	PUNCT
ejpam-6737	212	1	this	this	DET
ejpam-6737	212	2	result	result	NOUN
ejpam-6737	212	3	ensures	ensure	VERB
ejpam-6737	212	4	that	that	SCONJ
ejpam-6737	212	5	any	any	DET
ejpam-6737	212	6	small	small	ADJ
ejpam-6737	212	7	perturbationq(t	perturbationq(t	NOUN
ejpam-6737	212	8	)	)	PUNCT
ejpam-6737	212	9	leads	lead	VERB
ejpam-6737	212	10	to	to	ADP
ejpam-6737	212	11	bounded	bound	VERB
ejpam-6737	212	12	deviations	deviation	NOUN
ejpam-6737	212	13	in	in	ADP
ejpam-6737	212	14	the	the	DET
ejpam-6737	212	15	solution	solution	NOUN
ejpam-6737	212	16	,	,	PUNCT
ejpam-6737	212	17	thereby	thereby	ADV
ejpam-6737	212	18	preserving	preserve	VERB
ejpam-6737	212	19	the	the	DET
ejpam-6737	212	20	stability	stability	NOUN
ejpam-6737	212	21	of	of	ADP
ejpam-6737	212	22	the	the	DET
ejpam-6737	212	23	system	system	NOUN
ejpam-6737	212	24	.	.	PUNCT
ejpam-6737	213	1	s.	s.	PROPN
ejpam-6737	213	2	m.	m.	PROPN
ejpam-6737	213	3	chithra	chithra	PROPN
ejpam-6737	213	4	et	et	PROPN
ejpam-6737	213	5	al	al	PROPN
ejpam-6737	213	6	.	.	PUNCT
ejpam-6737	213	7	/	/	SYM
ejpam-6737	213	8	eur	eur	PROPN
ejpam-6737	213	9	.	.	PUNCT
ejpam-6737	214	1	j.	j.	PROPN
ejpam-6737	214	2	pure	pure	PROPN
ejpam-6737	214	3	appl	appl	PROPN
ejpam-6737	214	4	.	.	PROPN
ejpam-6737	214	5	math	math	PROPN
ejpam-6737	214	6	,	,	PUNCT
ejpam-6737	214	7	18	18	NUM
ejpam-6737	214	8	(	(	PUNCT
ejpam-6737	214	9	4	4	NUM
ejpam-6737	214	10	)	)	PUNCT
ejpam-6737	214	11	(	(	PUNCT
ejpam-6737	214	12	2025	2025	NUM
ejpam-6737	214	13	)	)	PUNCT
ejpam-6737	214	14	,	,	PUNCT
ejpam-6737	214	15	6737	6737	NUM
ejpam-6737	214	16	11	11	NUM
ejpam-6737	214	17	of	of	ADP
ejpam-6737	214	18	23	23	NUM
ejpam-6737	214	19	6	6	NUM
ejpam-6737	214	20	.	.	PUNCT
ejpam-6737	214	21	fractal	fractal	NOUN
ejpam-6737	214	22	-	-	PUNCT
ejpam-6737	214	23	based	base	VERB
ejpam-6737	214	24	numerical	numerical	ADJ
ejpam-6737	214	25	framework	framework	NOUN
ejpam-6737	214	26	–	–	PUNCT
ejpam-6737	214	27	fractional	fractional	ADJ
ejpam-6737	214	28	representation	representation	NOUN
ejpam-6737	214	29	now	now	ADV
ejpam-6737	214	30	,	,	PUNCT
ejpam-6737	214	31	since	since	SCONJ
ejpam-6737	214	32	the	the	DET
ejpam-6737	214	33	numerical	numerical	ADJ
ejpam-6737	214	34	scheme	scheme	NOUN
ejpam-6737	214	35	can	can	AUX
ejpam-6737	214	36	be	be	AUX
ejpam-6737	214	37	obtained	obtain	VERB
ejpam-6737	214	38	in	in	ADP
ejpam-6737	214	39	t	t	PROPN
ejpam-6737	214	40	=	=	SYM
ejpam-6737	214	41	td+1	td+1	PROPN
ejpam-6737	214	42	,	,	PUNCT
ejpam-6737	214	43	we	we	PRON
ejpam-6737	214	44	can	can	AUX
ejpam-6737	214	45	obtain	obtain	VERB
ejpam-6737	214	46	the	the	DET
ejpam-6737	214	47	approximate	approximate	ADJ
ejpam-6737	214	48	solution	solution	NOUN
ejpam-6737	214	49	in	in	ADP
ejpam-6737	214	50	system	system	NOUN
ejpam-6737	214	51	(	(	PUNCT
ejpam-6737	214	52	3	3	X
ejpam-6737	214	53	)	)	PUNCT
ejpam-6737	214	54	using	use	VERB
ejpam-6737	214	55	the	the	DET
ejpam-6737	214	56	caputo	caputo	PROPN
ejpam-6737	214	57	sense	sense	PROPN
ejpam-6737	214	58	atangana	atangana	PROPN
ejpam-6737	214	59	–	–	PUNCT
ejpam-6737	214	60	baleanu	baleanu	ADJ
ejpam-6737	214	61	fractal	fractal	ADJ
ejpam-6737	214	62	–	–	PUNCT
ejpam-6737	214	63	fractional	fractional	ADJ
ejpam-6737	214	64	operators	operator	NOUN
ejpam-6737	214	65	[	[	X
ejpam-6737	214	66	36	36	NUM
ejpam-6737	214	67	,	,	PUNCT
ejpam-6737	214	68	37	37	NUM
ejpam-6737	214	69	]	]	PUNCT
ejpam-6737	214	70	.	.	PUNCT
ejpam-6737	215	1	sd+1	sd+1	PART
ejpam-6737	216	1	=	=	PUNCT
ejpam-6737	216	2	s0p	s0p	VERB
ejpam-6737	216	3	+	+	CCONJ
ejpam-6737	216	4	ϑtϑ−1(1−	ϑtϑ−1(1−	PROPN
ejpam-6737	216	5	η	η	PROPN
ejpam-6737	216	6	)	)	PUNCT
ejpam-6737	216	7	abc(η	abc(η	PROPN
ejpam-6737	216	8	)	)	PUNCT
ejpam-6737	216	9	k1(td	k1(td	PROPN
ejpam-6737	216	10	,	,	PUNCT
ejpam-6737	216	11	sd	sd	NOUN
ejpam-6737	216	12	,	,	PUNCT
ejpam-6737	216	13	ed	ed	NOUN
ejpam-6737	216	14	,	,	PUNCT
ejpam-6737	216	15	ad	ad	NOUN
ejpam-6737	216	16	1,ad	1,ad	NOUN
ejpam-6737	216	17	2,pd	2,pd	NOUN
ejpam-6737	216	18	,	,	PUNCT
ejpam-6737	216	19	rd	rd	NOUN
ejpam-6737	216	20	,	,	PUNCT
ejpam-6737	216	21	qd	qd	PROPN
ejpam-6737	216	22	)	)	PUNCT
ejpam-6737	217	1	+	+	CCONJ
ejpam-6737	217	2	ηϑ	ηϑ	ADP
ejpam-6737	217	3	γ(η)abc(η	γ(η)abc(η	ADJ
ejpam-6737	217	4	)	)	PUNCT
ejpam-6737	217	5	∫	∫	PROPN
ejpam-6737	218	1	t	t	NOUN
ejpam-6737	218	2	0	0	X
ejpam-6737	219	1	sϑ−1(s−	sϑ−1(s−	PROPN
ejpam-6737	219	2	t)η−1k1(t	t)η−1k1(t	PROPN
ejpam-6737	219	3	,	,	PUNCT
ejpam-6737	219	4	s	s	X
ejpam-6737	219	5	,	,	PUNCT
ejpam-6737	219	6	e	e	NOUN
ejpam-6737	219	7	,	,	PUNCT
ejpam-6737	219	8	a1,a2,p	a1,a2,p	PROPN
ejpam-6737	219	9	,	,	PUNCT
ejpam-6737	219	10	r	r	NOUN
ejpam-6737	219	11	,	,	PUNCT
ejpam-6737	219	12	q	q	NOUN
ejpam-6737	219	13	)	)	PUNCT
ejpam-6737	219	14	ds	ds	ADJ
ejpam-6737	219	15	ed+1	ed+1	NOUN
ejpam-6737	219	16	=	=	SYM
ejpam-6737	219	17	i0p	i0p	NOUN
ejpam-6737	219	18	+	+	NUM
ejpam-6737	219	19	ϑtϑ−1(1−	ϑtϑ−1(1−	PROPN
ejpam-6737	219	20	η	η	PROPN
ejpam-6737	219	21	)	)	PUNCT
ejpam-6737	219	22	abc(η	abc(η	PROPN
ejpam-6737	219	23	)	)	PUNCT
ejpam-6737	219	24	k2(td	k2(td	PROPN
ejpam-6737	219	25	,	,	PUNCT
ejpam-6737	219	26	sd	sd	NOUN
ejpam-6737	219	27	,	,	PUNCT
ejpam-6737	219	28	ed	ed	NOUN
ejpam-6737	219	29	,	,	PUNCT
ejpam-6737	219	30	ad	ad	NOUN
ejpam-6737	219	31	1,ad	1,ad	NOUN
ejpam-6737	219	32	2,pd	2,pd	NOUN
ejpam-6737	219	33	,	,	PUNCT
ejpam-6737	219	34	rd	rd	NOUN
ejpam-6737	219	35	,	,	PUNCT
ejpam-6737	219	36	qd	qd	PROPN
ejpam-6737	219	37	)	)	PUNCT
ejpam-6737	220	1	+	+	CCONJ
ejpam-6737	220	2	ηϑ	ηϑ	ADP
ejpam-6737	220	3	γ(η)abc(η	γ(η)abc(η	ADJ
ejpam-6737	220	4	)	)	PUNCT
ejpam-6737	220	5	∫	∫	PROPN
ejpam-6737	221	1	t	t	NOUN
ejpam-6737	221	2	0	0	X
ejpam-6737	222	1	sϑ−1(s−	sϑ−1(s−	PROPN
ejpam-6737	222	2	t)η−1k2(t	t)η−1k2(t	NOUN
ejpam-6737	222	3	,	,	PUNCT
ejpam-6737	222	4	s	s	X
ejpam-6737	222	5	,	,	PUNCT
ejpam-6737	222	6	e	e	NOUN
ejpam-6737	222	7	,	,	PUNCT
ejpam-6737	222	8	a1,a2,p	a1,a2,p	PROPN
ejpam-6737	222	9	,	,	PUNCT
ejpam-6737	222	10	r	r	NOUN
ejpam-6737	222	11	,	,	PUNCT
ejpam-6737	222	12	q	q	NOUN
ejpam-6737	222	13	)	)	PUNCT
ejpam-6737	222	14	ds	ds	NOUN
ejpam-6737	222	15	ad+1	ad+1	NOUN
ejpam-6737	222	16	1	1	NUM
ejpam-6737	222	17	=	=	SYM
ejpam-6737	222	18	t	t	NOUN
ejpam-6737	222	19	0	0	NUM
ejpam-6737	223	1	p	p	X
ejpam-6737	223	2	+	+	PROPN
ejpam-6737	223	3	ϑtϑ−1(1−	ϑtϑ−1(1−	PROPN
ejpam-6737	223	4	η	η	PROPN
ejpam-6737	223	5	)	)	PUNCT
ejpam-6737	223	6	abc(η	abc(η	PROPN
ejpam-6737	223	7	)	)	PUNCT
ejpam-6737	223	8	k3(td	k3(td	PROPN
ejpam-6737	223	9	,	,	PUNCT
ejpam-6737	223	10	sd	sd	NOUN
ejpam-6737	223	11	,	,	PUNCT
ejpam-6737	223	12	ed	ed	NOUN
ejpam-6737	223	13	,	,	PUNCT
ejpam-6737	223	14	ad	ad	NOUN
ejpam-6737	223	15	1,ad	1,ad	NOUN
ejpam-6737	223	16	2,pd	2,pd	NOUN
ejpam-6737	223	17	,	,	PUNCT
ejpam-6737	223	18	rd	rd	NOUN
ejpam-6737	223	19	,	,	PUNCT
ejpam-6737	223	20	qd	qd	PROPN
ejpam-6737	223	21	)	)	PUNCT
ejpam-6737	224	1	+	+	CCONJ
ejpam-6737	224	2	ηϑ	ηϑ	ADP
ejpam-6737	224	3	γ(η)abc(η	γ(η)abc(η	ADJ
ejpam-6737	224	4	)	)	PUNCT
ejpam-6737	224	5	∫	∫	PROPN
ejpam-6737	225	1	t	t	PROPN
ejpam-6737	225	2	0	0	X
ejpam-6737	226	1	sϑ−1(s−	sϑ−1(s−	PROPN
ejpam-6737	226	2	t)η−1k3(t	t)η−1k3(t	VERB
ejpam-6737	226	3	,	,	PUNCT
ejpam-6737	226	4	s	s	X
ejpam-6737	226	5	,	,	PUNCT
ejpam-6737	226	6	e	e	NOUN
ejpam-6737	226	7	,	,	PUNCT
ejpam-6737	226	8	a1,a2,p	a1,a2,p	PROPN
ejpam-6737	226	9	,	,	PUNCT
ejpam-6737	226	10	r	r	NOUN
ejpam-6737	226	11	,	,	PUNCT
ejpam-6737	226	12	q	q	NOUN
ejpam-6737	226	13	)	)	PUNCT
ejpam-6737	226	14	ds	ds	ADJ
ejpam-6737	226	15	,	,	PUNCT
ejpam-6737	226	16	ad+1	ad+1	PROPN
ejpam-6737	226	17	2	2	NUM
ejpam-6737	226	18	=	=	SYM
ejpam-6737	226	19	r0	r0	NOUN
ejpam-6737	226	20	p	p	NOUN
ejpam-6737	226	21	+	+	CCONJ
ejpam-6737	226	22	ϑtϑ−1(1−	ϑtϑ−1(1−	PROPN
ejpam-6737	226	23	η	η	PROPN
ejpam-6737	226	24	)	)	PUNCT
ejpam-6737	226	25	abc(η	abc(η	PROPN
ejpam-6737	226	26	)	)	PUNCT
ejpam-6737	226	27	k4(td	k4(td	NUM
ejpam-6737	226	28	,	,	PUNCT
ejpam-6737	226	29	sd	sd	NOUN
ejpam-6737	226	30	,	,	PUNCT
ejpam-6737	226	31	ed	ed	NOUN
ejpam-6737	226	32	,	,	PUNCT
ejpam-6737	226	33	ad	ad	NOUN
ejpam-6737	226	34	1,ad	1,ad	NOUN
ejpam-6737	226	35	2,pd	2,pd	NOUN
ejpam-6737	226	36	,	,	PUNCT
ejpam-6737	226	37	rd	rd	NOUN
ejpam-6737	226	38	,	,	PUNCT
ejpam-6737	226	39	qd	qd	PROPN
ejpam-6737	226	40	)	)	PUNCT
ejpam-6737	227	1	+	+	CCONJ
ejpam-6737	227	2	ηϑ	ηϑ	ADP
ejpam-6737	227	3	γ(η)abc(η	γ(η)abc(η	ADJ
ejpam-6737	227	4	)	)	PUNCT
ejpam-6737	227	5	∫	∫	PROPN
ejpam-6737	228	1	t	t	PROPN
ejpam-6737	228	2	0	0	X
ejpam-6737	229	1	sϑ−1(s−	sϑ−1(s−	PROPN
ejpam-6737	229	2	t)η−1k4(t	t)η−1k4(t	PROPN
ejpam-6737	229	3	,	,	PUNCT
ejpam-6737	229	4	s	s	X
ejpam-6737	229	5	,	,	PUNCT
ejpam-6737	229	6	e	e	NOUN
ejpam-6737	229	7	,	,	PUNCT
ejpam-6737	229	8	a1,a2,p	a1,a2,p	PROPN
ejpam-6737	229	9	,	,	PUNCT
ejpam-6737	229	10	r	r	NOUN
ejpam-6737	229	11	,	,	PUNCT
ejpam-6737	229	12	q	q	NOUN
ejpam-6737	229	13	)	)	PUNCT
ejpam-6737	229	14	ds	ds	ADJ
ejpam-6737	229	15	pd+1	pd+1	PROPN
ejpam-6737	229	16	=	=	SYM
ejpam-6737	229	17	b0	b0	PROPN
ejpam-6737	229	18	m	m	PROPN
ejpam-6737	229	19	+	+	NUM
ejpam-6737	229	20	ϑtϑ−1(1−	ϑtϑ−1(1−	PROPN
ejpam-6737	229	21	η	η	PROPN
ejpam-6737	229	22	)	)	PUNCT
ejpam-6737	229	23	abc(η	abc(η	PROPN
ejpam-6737	229	24	)	)	PUNCT
ejpam-6737	229	25	k5(td	k5(td	PROPN
ejpam-6737	229	26	,	,	PUNCT
ejpam-6737	229	27	sd	sd	NOUN
ejpam-6737	229	28	,	,	PUNCT
ejpam-6737	229	29	ed	ed	NOUN
ejpam-6737	229	30	,	,	PUNCT
ejpam-6737	229	31	ad	ad	NOUN
ejpam-6737	229	32	1,ad	1,ad	NOUN
ejpam-6737	229	33	2,pd	2,pd	NOUN
ejpam-6737	229	34	,	,	PUNCT
ejpam-6737	229	35	rd	rd	NOUN
ejpam-6737	229	36	,	,	PUNCT
ejpam-6737	229	37	qd	qd	PROPN
ejpam-6737	229	38	)	)	PUNCT
ejpam-6737	230	1	+	+	CCONJ
ejpam-6737	230	2	ηϑ	ηϑ	ADP
ejpam-6737	230	3	γ(η)abc(η	γ(η)abc(η	ADJ
ejpam-6737	230	4	)	)	PUNCT
ejpam-6737	230	5	∫	∫	PROPN
ejpam-6737	231	1	t	t	NOUN
ejpam-6737	231	2	0	0	X
ejpam-6737	232	1	sϑ−1(s−	sϑ−1(s−	PROPN
ejpam-6737	232	2	t)η−1k5(t	t)η−1k5(t	PROPN
ejpam-6737	232	3	,	,	PUNCT
ejpam-6737	232	4	s	s	X
ejpam-6737	232	5	,	,	PUNCT
ejpam-6737	232	6	e	e	NOUN
ejpam-6737	232	7	,	,	PUNCT
ejpam-6737	232	8	a1,a2,p	a1,a2,p	PROPN
ejpam-6737	232	9	,	,	PUNCT
ejpam-6737	232	10	r	r	NOUN
ejpam-6737	232	11	,	,	PUNCT
ejpam-6737	232	12	q	q	NOUN
ejpam-6737	232	13	)	)	PUNCT
ejpam-6737	232	14	ds	ds	ADJ
ejpam-6737	232	15	,	,	PUNCT
ejpam-6737	232	16	r(d+1	r(d+1	NOUN
ejpam-6737	232	17	)	)	PUNCT
ejpam-6737	232	18	=	=	SYM
ejpam-6737	232	19	s0v	s0v	PROPN
ejpam-6737	232	20	+	+	CCONJ
ejpam-6737	232	21	ϑtϑ−1(1−	ϑtϑ−1(1−	PROPN
ejpam-6737	232	22	η	η	PROPN
ejpam-6737	232	23	)	)	PUNCT
ejpam-6737	232	24	abc(η	abc(η	PROPN
ejpam-6737	232	25	)	)	PUNCT
ejpam-6737	232	26	k6(td	k6(td	PROPN
ejpam-6737	232	27	,	,	PUNCT
ejpam-6737	232	28	sd	sd	NOUN
ejpam-6737	232	29	,	,	PUNCT
ejpam-6737	232	30	ed	ed	NOUN
ejpam-6737	232	31	,	,	PUNCT
ejpam-6737	232	32	ad	ad	NOUN
ejpam-6737	232	33	1,ad	1,ad	NOUN
ejpam-6737	232	34	2,pd	2,pd	NOUN
ejpam-6737	232	35	,	,	PUNCT
ejpam-6737	232	36	rd	rd	NOUN
ejpam-6737	232	37	,	,	PUNCT
ejpam-6737	232	38	qd	qd	PROPN
ejpam-6737	232	39	)	)	PUNCT
ejpam-6737	233	1	+	+	CCONJ
ejpam-6737	233	2	ηϑ	ηϑ	ADP
ejpam-6737	233	3	γ(η)abc(η	γ(η)abc(η	ADJ
ejpam-6737	233	4	)	)	PUNCT
ejpam-6737	233	5	∫	∫	PROPN
ejpam-6737	234	1	t	t	NOUN
ejpam-6737	234	2	0	0	X
ejpam-6737	235	1	sϑ−1(s−	sϑ−1(s−	PROPN
ejpam-6737	235	2	t)η−1k6(t	t)η−1k6(t	NOUN
ejpam-6737	235	3	,	,	PUNCT
ejpam-6737	235	4	s	s	X
ejpam-6737	235	5	,	,	PUNCT
ejpam-6737	235	6	e	e	NOUN
ejpam-6737	235	7	,	,	PUNCT
ejpam-6737	235	8	a1,a2,p	a1,a2,p	PROPN
ejpam-6737	235	9	,	,	PUNCT
ejpam-6737	235	10	r	r	NOUN
ejpam-6737	235	11	,	,	PUNCT
ejpam-6737	235	12	q	q	NOUN
ejpam-6737	235	13	)	)	PUNCT
ejpam-6737	235	14	ds	ds	ADJ
ejpam-6737	235	15	,	,	PUNCT
ejpam-6737	235	16	qd+1	qd+1	NOUN
ejpam-6737	235	17	=	=	SYM
ejpam-6737	235	18	i0v	i0v	PROPN
ejpam-6737	235	19	+	+	CCONJ
ejpam-6737	235	20	ϑtϑ−1(1−	ϑtϑ−1(1−	PROPN
ejpam-6737	235	21	η	η	PROPN
ejpam-6737	235	22	)	)	PUNCT
ejpam-6737	235	23	abc(η	abc(η	PROPN
ejpam-6737	235	24	)	)	PUNCT
ejpam-6737	235	25	k7	k7	PROPN
ejpam-6737	235	26	(	(	PUNCT
ejpam-6737	235	27	td	td	NOUN
ejpam-6737	235	28	,	,	PUNCT
ejpam-6737	235	29	sd	sd	NOUN
ejpam-6737	235	30	,	,	PUNCT
ejpam-6737	235	31	ed	ed	NOUN
ejpam-6737	235	32	,	,	PUNCT
ejpam-6737	235	33	ad	ad	NOUN
ejpam-6737	235	34	1,ad	1,ad	NOUN
ejpam-6737	235	35	2,pd	2,pd	NOUN
ejpam-6737	235	36	,	,	PUNCT
ejpam-6737	235	37	rd	rd	PROPN
ejpam-6737	235	38	,	,	PUNCT
ejpam-6737	235	39	qd	qd	NOUN
ejpam-6737	235	40	)	)	PUNCT
ejpam-6737	236	1	+	+	CCONJ
ejpam-6737	236	2	ηϑ	ηϑ	ADP
ejpam-6737	236	3	γ(η)abc(η	γ(η)abc(η	ADJ
ejpam-6737	236	4	)	)	PUNCT
ejpam-6737	236	5	∫	∫	PROPN
ejpam-6737	237	1	t	t	NOUN
ejpam-6737	237	2	0	0	X
ejpam-6737	238	1	sϑ−1(s−	sϑ−1(s−	PROPN
ejpam-6737	238	2	t)η−1k7	t)η−1k7	PROPN
ejpam-6737	238	3	(	(	PUNCT
ejpam-6737	238	4	t	t	PROPN
ejpam-6737	238	5	,	,	PUNCT
ejpam-6737	238	6	s	s	X
ejpam-6737	238	7	,	,	PUNCT
ejpam-6737	238	8	e	e	NOUN
ejpam-6737	238	9	,	,	PUNCT
ejpam-6737	238	10	a1,a2,p	a1,a2,p	PROPN
ejpam-6737	238	11	,	,	PUNCT
ejpam-6737	238	12	r	r	NOUN
ejpam-6737	238	13	,	,	PUNCT
ejpam-6737	238	14	q	q	NOUN
ejpam-6737	238	15	)	)	PUNCT
ejpam-6737	238	16	ds	ds	NOUN
ejpam-6737	238	17	.	.	PUNCT
ejpam-6737	238	18	(	(	PUNCT
ejpam-6737	238	19	9	9	X
ejpam-6737	238	20	)	)	PUNCT
ejpam-6737	238	21	s.	s.	PROPN
ejpam-6737	238	22	m.	m.	PROPN
ejpam-6737	238	23	chithra	chithra	PROPN
ejpam-6737	238	24	et	et	PROPN
ejpam-6737	238	25	al	al	PROPN
ejpam-6737	238	26	.	.	PUNCT
ejpam-6737	238	27	/	/	SYM
ejpam-6737	238	28	eur	eur	PROPN
ejpam-6737	238	29	.	.	PUNCT
ejpam-6737	239	1	j.	j.	PROPN
ejpam-6737	239	2	pure	pure	PROPN
ejpam-6737	239	3	appl	appl	PROPN
ejpam-6737	239	4	.	.	PROPN
ejpam-6737	239	5	math	math	PROPN
ejpam-6737	239	6	,	,	PUNCT
ejpam-6737	239	7	18	18	NUM
ejpam-6737	239	8	(	(	PUNCT
ejpam-6737	239	9	4	4	NUM
ejpam-6737	239	10	)	)	PUNCT
ejpam-6737	239	11	(	(	PUNCT
ejpam-6737	239	12	2025	2025	NUM
ejpam-6737	239	13	)	)	PUNCT
ejpam-6737	239	14	,	,	PUNCT
ejpam-6737	239	15	6737	6737	NUM
ejpam-6737	239	16	12	12	NUM
ejpam-6737	239	17	of	of	ADP
ejpam-6737	239	18	23	23	NUM
ejpam-6737	239	19	applying	apply	VERB
ejpam-6737	239	20	the	the	DET
ejpam-6737	239	21	approximation	approximation	NOUN
ejpam-6737	239	22	of	of	ADP
ejpam-6737	239	23	the	the	DET
ejpam-6737	239	24	integrals	integral	NOUN
ejpam-6737	239	25	from	from	ADP
ejpam-6737	239	26	the	the	DET
ejpam-6737	239	27	right	right	ADJ
ejpam-6737	239	28	-	-	PUNCT
ejpam-6737	239	29	hand	hand	NOUN
ejpam-6737	239	30	side	side	NOUN
ejpam-6737	239	31	of	of	ADP
ejpam-6737	239	32	equation	equation	NOUN
ejpam-6737	239	33	(	(	PUNCT
ejpam-6737	239	34	9	9	NUM
ejpam-6737	239	35	)	)	PUNCT
ejpam-6737	240	1	,	,	PUNCT
ejpam-6737	240	2	we	we	PRON
ejpam-6737	240	3	have	have	VERB
ejpam-6737	240	4	sd+1	sd+1	NOUN
ejpam-6737	240	5	=	=	SYM
ejpam-6737	240	6	s0	s0	PROPN
ejpam-6737	240	7	+	+	CCONJ
ejpam-6737	240	8	ϑtϑ−1	ϑtϑ−1	PROPN
ejpam-6737	240	9	d	d	PROPN
ejpam-6737	240	10	(	(	PUNCT
ejpam-6737	240	11	1−	1−	NUM
ejpam-6737	240	12	η	η	NOUN
ejpam-6737	240	13	)	)	PUNCT
ejpam-6737	240	14	abc(η	abc(η	PROPN
ejpam-6737	240	15	)	)	PUNCT
ejpam-6737	240	16	k1(td	k1(td	PROPN
ejpam-6737	240	17	,	,	PUNCT
ejpam-6737	240	18	sd	sd	NOUN
ejpam-6737	240	19	,	,	PUNCT
ejpam-6737	240	20	ed	ed	NOUN
ejpam-6737	240	21	,	,	PUNCT
ejpam-6737	240	22	ad	ad	NOUN
ejpam-6737	240	23	1,ad	1,ad	NOUN
ejpam-6737	240	24	2,pd	2,pd	NOUN
ejpam-6737	240	25	,	,	PUNCT
ejpam-6737	240	26	rd	rd	NOUN
ejpam-6737	240	27	,	,	PUNCT
ejpam-6737	240	28	qd	qd	PROPN
ejpam-6737	240	29	)	)	PUNCT
ejpam-6737	241	1	+	+	CCONJ
ejpam-6737	241	2	ηϑ	ηϑ	ADP
ejpam-6737	241	3	γ(η)abc(η	γ(η)abc(η	ADJ
ejpam-6737	241	4	)	)	PUNCT
ejpam-6737	241	5	d∑	d∑	PROPN
ejpam-6737	241	6	c=0	c=0	PUNCT
ejpam-6737	241	7	∫	∫	PROPN
ejpam-6737	241	8	tc+1	tc+1	PROPN
ejpam-6737	241	9	tc	tc	NOUN
ejpam-6737	241	10	sϑ−1(td+1	sϑ−1(td+1	NOUN
ejpam-6737	241	11	−	−	PROPN
ejpam-6737	241	12	s)η−1k1(t	s)η−1k1(t	PROPN
ejpam-6737	241	13	,	,	PUNCT
ejpam-6737	241	14	s	s	X
ejpam-6737	241	15	,	,	PUNCT
ejpam-6737	241	16	e	e	NOUN
ejpam-6737	241	17	,	,	PUNCT
ejpam-6737	241	18	a1,a2,p	a1,a2,p	PROPN
ejpam-6737	241	19	,	,	PUNCT
ejpam-6737	241	20	r	r	NOUN
ejpam-6737	241	21	,	,	PUNCT
ejpam-6737	241	22	q	q	NOUN
ejpam-6737	241	23	)	)	PUNCT
ejpam-6737	241	24	ds	ds	ADJ
ejpam-6737	241	25	,	,	PUNCT
ejpam-6737	241	26	ed+1	ed+1	NOUN
ejpam-6737	241	27	=	=	SYM
ejpam-6737	241	28	e0	e0	PROPN
ejpam-6737	241	29	+	+	CCONJ
ejpam-6737	241	30	ϑtϑ−1	ϑtϑ−1	PROPN
ejpam-6737	241	31	d	d	PROPN
ejpam-6737	241	32	(	(	PUNCT
ejpam-6737	241	33	1−	1−	NUM
ejpam-6737	241	34	η	η	NOUN
ejpam-6737	241	35	)	)	PUNCT
ejpam-6737	241	36	abc(η	abc(η	PROPN
ejpam-6737	241	37	)	)	PUNCT
ejpam-6737	241	38	k2(td	k2(td	PROPN
ejpam-6737	241	39	,	,	PUNCT
ejpam-6737	241	40	sd	sd	NOUN
ejpam-6737	241	41	,	,	PUNCT
ejpam-6737	241	42	ed	ed	NOUN
ejpam-6737	241	43	,	,	PUNCT
ejpam-6737	241	44	ad	ad	NOUN
ejpam-6737	241	45	1,ad	1,ad	NOUN
ejpam-6737	241	46	2,pd	2,pd	NOUN
ejpam-6737	241	47	,	,	PUNCT
ejpam-6737	241	48	rd	rd	NOUN
ejpam-6737	241	49	,	,	PUNCT
ejpam-6737	241	50	qd	qd	PROPN
ejpam-6737	241	51	)	)	PUNCT
ejpam-6737	242	1	+	+	CCONJ
ejpam-6737	242	2	ηϑ	ηϑ	ADP
ejpam-6737	242	3	γ(η)abc(η	γ(η)abc(η	ADJ
ejpam-6737	242	4	)	)	PUNCT
ejpam-6737	242	5	d∑	d∑	PROPN
ejpam-6737	242	6	c=0	c=0	PUNCT
ejpam-6737	242	7	∫	∫	PROPN
ejpam-6737	242	8	tc+1	tc+1	PROPN
ejpam-6737	242	9	tc	tc	PROPN
ejpam-6737	242	10	sϑ−1(td+1	sϑ−1(td+1	NOUN
ejpam-6737	242	11	−	−	PROPN
ejpam-6737	242	12	s)η−1k2(t	s)η−1k2(t	NOUN
ejpam-6737	242	13	,	,	PUNCT
ejpam-6737	242	14	s	s	NOUN
ejpam-6737	242	15	,	,	PUNCT
ejpam-6737	242	16	e	e	NOUN
ejpam-6737	242	17	,	,	PUNCT
ejpam-6737	242	18	a1,a2,p	a1,a2,p	PROPN
ejpam-6737	242	19	,	,	PUNCT
ejpam-6737	242	20	r	r	NOUN
ejpam-6737	242	21	,	,	PUNCT
ejpam-6737	242	22	q	q	NOUN
ejpam-6737	242	23	)	)	PUNCT
ejpam-6737	242	24	ds	ds	ADJ
ejpam-6737	242	25	,	,	PUNCT
ejpam-6737	242	26	ad+1	ad+1	PROPN
ejpam-6737	242	27	1	1	NUM
ejpam-6737	242	28	=	=	SYM
ejpam-6737	242	29	a0	a0	NOUN
ejpam-6737	242	30	1	1	NUM
ejpam-6737	242	31	+	+	CCONJ
ejpam-6737	242	32	ϑtϑ−1	ϑtϑ−1	PROPN
ejpam-6737	242	33	d	d	PROPN
ejpam-6737	242	34	(	(	PUNCT
ejpam-6737	242	35	1−	1−	NUM
ejpam-6737	242	36	η	η	NOUN
ejpam-6737	242	37	)	)	PUNCT
ejpam-6737	242	38	abc(η	abc(η	PROPN
ejpam-6737	242	39	)	)	PUNCT
ejpam-6737	242	40	k3(td	k3(td	PROPN
ejpam-6737	242	41	,	,	PUNCT
ejpam-6737	242	42	sd	sd	NOUN
ejpam-6737	242	43	,	,	PUNCT
ejpam-6737	242	44	ed	ed	NOUN
ejpam-6737	242	45	,	,	PUNCT
ejpam-6737	242	46	ad	ad	NOUN
ejpam-6737	242	47	1,ad	1,ad	NOUN
ejpam-6737	242	48	2,pd	2,pd	NOUN
ejpam-6737	242	49	,	,	PUNCT
ejpam-6737	242	50	rd	rd	NOUN
ejpam-6737	242	51	,	,	PUNCT
ejpam-6737	242	52	qd	qd	PROPN
ejpam-6737	242	53	)	)	PUNCT
ejpam-6737	242	54	+	+	CCONJ
ejpam-6737	242	55	ηϑ	ηϑ	ADP
ejpam-6737	242	56	γ(η)abc(η	γ(η)abc(η	ADJ
ejpam-6737	242	57	)	)	PUNCT
ejpam-6737	242	58	d∑	d∑	PROPN
ejpam-6737	243	1	c=0	c=0	PUNCT
ejpam-6737	243	2	∫	∫	PROPN
ejpam-6737	243	3	tc+1	tc+1	PROPN
ejpam-6737	243	4	tc	tc	PROPN
ejpam-6737	243	5	sϑ−1(td+1	sϑ−1(td+1	NOUN
ejpam-6737	243	6	−	−	PROPN
ejpam-6737	243	7	s)η−1k3(t	s)η−1k3(t	VERB
ejpam-6737	243	8	,	,	PUNCT
ejpam-6737	243	9	s	s	X
ejpam-6737	243	10	,	,	PUNCT
ejpam-6737	243	11	e	e	NOUN
ejpam-6737	243	12	,	,	PUNCT
ejpam-6737	243	13	a1,a2,p	a1,a2,p	PROPN
ejpam-6737	243	14	,	,	PUNCT
ejpam-6737	243	15	r	r	NOUN
ejpam-6737	243	16	,	,	PUNCT
ejpam-6737	243	17	q	q	NOUN
ejpam-6737	243	18	)	)	PUNCT
ejpam-6737	243	19	ds	ds	ADJ
ejpam-6737	243	20	,	,	PUNCT
ejpam-6737	243	21	ad+1	ad+1	PROPN
ejpam-6737	243	22	2	2	NUM
ejpam-6737	243	23	=	=	SYM
ejpam-6737	243	24	a0	a0	NOUN
ejpam-6737	243	25	2	2	NUM
ejpam-6737	244	1	+	+	CCONJ
ejpam-6737	244	2	ϑtϑ−1	ϑtϑ−1	PROPN
ejpam-6737	244	3	d	d	PROPN
ejpam-6737	244	4	(	(	PUNCT
ejpam-6737	244	5	1−	1−	NUM
ejpam-6737	244	6	η	η	NOUN
ejpam-6737	244	7	)	)	PUNCT
ejpam-6737	244	8	abc(η	abc(η	PROPN
ejpam-6737	244	9	)	)	PUNCT
ejpam-6737	244	10	k4(td	k4(td	NUM
ejpam-6737	244	11	,	,	PUNCT
ejpam-6737	244	12	sd	sd	NOUN
ejpam-6737	244	13	,	,	PUNCT
ejpam-6737	244	14	ed	ed	NOUN
ejpam-6737	244	15	,	,	PUNCT
ejpam-6737	244	16	ad	ad	NOUN
ejpam-6737	244	17	1,ad	1,ad	NOUN
ejpam-6737	244	18	2,pd	2,pd	NOUN
ejpam-6737	244	19	,	,	PUNCT
ejpam-6737	244	20	rd	rd	NOUN
ejpam-6737	244	21	,	,	PUNCT
ejpam-6737	244	22	qd	qd	PROPN
ejpam-6737	244	23	)	)	PUNCT
ejpam-6737	245	1	+	+	CCONJ
ejpam-6737	245	2	ηϑ	ηϑ	ADP
ejpam-6737	245	3	γ(η)abc(η	γ(η)abc(η	ADJ
ejpam-6737	245	4	)	)	PUNCT
ejpam-6737	245	5	d∑	d∑	PROPN
ejpam-6737	245	6	c=0	c=0	PUNCT
ejpam-6737	245	7	∫	∫	PROPN
ejpam-6737	245	8	tc+1	tc+1	PROPN
ejpam-6737	245	9	tc	tc	PROPN
ejpam-6737	245	10	sϑ−1(td+1	sϑ−1(td+1	NOUN
ejpam-6737	245	11	−	−	PROPN
ejpam-6737	245	12	s)η−1k4(t	s)η−1k4(t	PROPN
ejpam-6737	245	13	,	,	PUNCT
ejpam-6737	245	14	s	s	X
ejpam-6737	245	15	,	,	PUNCT
ejpam-6737	245	16	e	e	NOUN
ejpam-6737	245	17	,	,	PUNCT
ejpam-6737	245	18	a1,a2,p	a1,a2,p	PROPN
ejpam-6737	245	19	,	,	PUNCT
ejpam-6737	245	20	r	r	NOUN
ejpam-6737	245	21	,	,	PUNCT
ejpam-6737	245	22	q	q	NOUN
ejpam-6737	245	23	)	)	PUNCT
ejpam-6737	245	24	ds	ds	PROPN
ejpam-6737	245	25	,	,	PUNCT
ejpam-6737	245	26	pd+1	pd+1	NOUN
ejpam-6737	245	27	=	=	SYM
ejpam-6737	245	28	p0	p0	NOUN
ejpam-6737	246	1	+	+	CCONJ
ejpam-6737	246	2	ϑtϑ−1	ϑtϑ−1	PROPN
ejpam-6737	246	3	d	d	PROPN
ejpam-6737	246	4	(	(	PUNCT
ejpam-6737	246	5	1−	1−	NUM
ejpam-6737	246	6	η	η	NOUN
ejpam-6737	246	7	)	)	PUNCT
ejpam-6737	246	8	abc(η	abc(η	PROPN
ejpam-6737	246	9	)	)	PUNCT
ejpam-6737	246	10	k5(td	k5(td	PROPN
ejpam-6737	246	11	,	,	PUNCT
ejpam-6737	246	12	sd	sd	NOUN
ejpam-6737	246	13	,	,	PUNCT
ejpam-6737	246	14	ed	ed	NOUN
ejpam-6737	246	15	,	,	PUNCT
ejpam-6737	246	16	ad	ad	NOUN
ejpam-6737	246	17	1,ad	1,ad	NOUN
ejpam-6737	246	18	2,pd	2,pd	NOUN
ejpam-6737	246	19	,	,	PUNCT
ejpam-6737	246	20	rd	rd	NOUN
ejpam-6737	246	21	,	,	PUNCT
ejpam-6737	246	22	qd	qd	PROPN
ejpam-6737	246	23	)	)	PUNCT
ejpam-6737	247	1	+	+	CCONJ
ejpam-6737	247	2	ηϑ	ηϑ	ADP
ejpam-6737	247	3	γ(η)abc(η	γ(η)abc(η	ADJ
ejpam-6737	247	4	)	)	PUNCT
ejpam-6737	247	5	d∑	d∑	PROPN
ejpam-6737	247	6	c=0	c=0	PUNCT
ejpam-6737	247	7	∫	∫	PROPN
ejpam-6737	247	8	tc+1	tc+1	NUM
ejpam-6737	247	9	tc	tc	PROPN
ejpam-6737	247	10	sϑ−1(td+1	sϑ−1(td+1	NOUN
ejpam-6737	247	11	−	−	PROPN
ejpam-6737	247	12	s)η−1k5(t	s)η−1k5(t	PROPN
ejpam-6737	247	13	,	,	PUNCT
ejpam-6737	247	14	s	s	X
ejpam-6737	247	15	,	,	PUNCT
ejpam-6737	247	16	e	e	NOUN
ejpam-6737	247	17	,	,	PUNCT
ejpam-6737	247	18	a1,a2,p	a1,a2,p	PROPN
ejpam-6737	247	19	,	,	PUNCT
ejpam-6737	247	20	r	r	NOUN
ejpam-6737	247	21	,	,	PUNCT
ejpam-6737	247	22	q	q	NOUN
ejpam-6737	247	23	)	)	PUNCT
ejpam-6737	247	24	ds	ds	ADJ
ejpam-6737	247	25	,	,	PUNCT
ejpam-6737	247	26	rd	rd	NOUN
ejpam-6737	247	27	=	=	SYM
ejpam-6737	247	28	r0	r0	NOUN
ejpam-6737	247	29	+	+	CCONJ
ejpam-6737	247	30	ϑtϑ−1	ϑtϑ−1	PROPN
ejpam-6737	247	31	d	d	PROPN
ejpam-6737	247	32	(	(	PUNCT
ejpam-6737	247	33	1−	1−	NUM
ejpam-6737	247	34	η	η	NOUN
ejpam-6737	247	35	)	)	PUNCT
ejpam-6737	247	36	abc(η	abc(η	PROPN
ejpam-6737	247	37	)	)	PUNCT
ejpam-6737	247	38	k6(td	k6(td	PROPN
ejpam-6737	247	39	,	,	PUNCT
ejpam-6737	247	40	sd	sd	NOUN
ejpam-6737	247	41	,	,	PUNCT
ejpam-6737	247	42	ed	ed	NOUN
ejpam-6737	247	43	,	,	PUNCT
ejpam-6737	247	44	ad	ad	NOUN
ejpam-6737	247	45	1,ad	1,ad	NOUN
ejpam-6737	247	46	2,pd	2,pd	NOUN
ejpam-6737	247	47	,	,	PUNCT
ejpam-6737	247	48	rd	rd	NOUN
ejpam-6737	247	49	,	,	PUNCT
ejpam-6737	247	50	qd	qd	PROPN
ejpam-6737	247	51	)	)	PUNCT
ejpam-6737	248	1	+	+	CCONJ
ejpam-6737	248	2	ηϑ	ηϑ	ADP
ejpam-6737	248	3	γ(η)abc(η	γ(η)abc(η	ADJ
ejpam-6737	248	4	)	)	PUNCT
ejpam-6737	248	5	d∑	d∑	PROPN
ejpam-6737	248	6	c=0	c=0	PUNCT
ejpam-6737	248	7	∫	∫	PROPN
ejpam-6737	248	8	tc+1	tc+1	NUM
ejpam-6737	248	9	tc	tc	PROPN
ejpam-6737	248	10	sϑ−1(td+1	sϑ−1(td+1	NOUN
ejpam-6737	248	11	−	−	PROPN
ejpam-6737	248	12	s)η−1k6(t	s)η−1k6(t	NOUN
ejpam-6737	248	13	,	,	PUNCT
ejpam-6737	248	14	s	s	X
ejpam-6737	248	15	,	,	PUNCT
ejpam-6737	248	16	e	e	NOUN
ejpam-6737	248	17	,	,	PUNCT
ejpam-6737	248	18	a1,a2,p	a1,a2,p	PROPN
ejpam-6737	248	19	,	,	PUNCT
ejpam-6737	248	20	r	r	NOUN
ejpam-6737	248	21	,	,	PUNCT
ejpam-6737	248	22	q	q	NOUN
ejpam-6737	248	23	)	)	PUNCT
ejpam-6737	248	24	ds	ds	ADJ
ejpam-6737	248	25	,	,	PUNCT
ejpam-6737	248	26	qd	qd	NOUN
ejpam-6737	248	27	=	=	NOUN
ejpam-6737	248	28	q0	q0	PROPN
ejpam-6737	249	1	+	+	CCONJ
ejpam-6737	249	2	ϑtϑ−1	ϑtϑ−1	PROPN
ejpam-6737	249	3	d	d	PROPN
ejpam-6737	249	4	(	(	PUNCT
ejpam-6737	249	5	1−	1−	NUM
ejpam-6737	249	6	η	η	NOUN
ejpam-6737	249	7	)	)	PUNCT
ejpam-6737	249	8	abc(η	abc(η	PROPN
ejpam-6737	249	9	)	)	PUNCT
ejpam-6737	249	10	k7(td	k7(td	NOUN
ejpam-6737	249	11	,	,	PUNCT
ejpam-6737	249	12	sd	sd	NOUN
ejpam-6737	249	13	,	,	PUNCT
ejpam-6737	249	14	ed	ed	NOUN
ejpam-6737	249	15	,	,	PUNCT
ejpam-6737	249	16	ad	ad	NOUN
ejpam-6737	249	17	1,ad	1,ad	NOUN
ejpam-6737	249	18	2,pd	2,pd	NOUN
ejpam-6737	249	19	,	,	PUNCT
ejpam-6737	249	20	rd	rd	NOUN
ejpam-6737	249	21	,	,	PUNCT
ejpam-6737	249	22	qd	qd	PROPN
ejpam-6737	249	23	)	)	PUNCT
ejpam-6737	250	1	+	+	CCONJ
ejpam-6737	250	2	ηϑ	ηϑ	ADP
ejpam-6737	250	3	γ(η)abc(η	γ(η)abc(η	ADJ
ejpam-6737	250	4	)	)	PUNCT
ejpam-6737	250	5	d∑	d∑	PROPN
ejpam-6737	250	6	c=0	c=0	PUNCT
ejpam-6737	250	7	∫	∫	PROPN
ejpam-6737	250	8	tc+1	tc+1	NUM
ejpam-6737	250	9	tc	tc	PROPN
ejpam-6737	250	10	sϑ−1(td+1	sϑ−1(td+1	NOUN
ejpam-6737	250	11	−	−	PROPN
ejpam-6737	250	12	s)η−1k7(t	s)η−1k7(t	NOUN
ejpam-6737	250	13	,	,	PUNCT
ejpam-6737	250	14	s	s	X
ejpam-6737	250	15	,	,	PUNCT
ejpam-6737	250	16	e	e	NOUN
ejpam-6737	250	17	,	,	PUNCT
ejpam-6737	250	18	a1,a2,p	a1,a2,p	PROPN
ejpam-6737	250	19	,	,	PUNCT
ejpam-6737	250	20	r	r	NOUN
ejpam-6737	250	21	,	,	PUNCT
ejpam-6737	250	22	q	q	NOUN
ejpam-6737	250	23	)	)	PUNCT
ejpam-6737	250	24	ds	ds	NOUN
ejpam-6737	250	25	.	.	PUNCT
ejpam-6737	251	1	(	(	PUNCT
ejpam-6737	251	2	10	10	NUM
ejpam-6737	251	3	)	)	PUNCT
ejpam-6737	251	4	s.	s.	PROPN
ejpam-6737	251	5	m.	m.	PROPN
ejpam-6737	251	6	chithra	chithra	PROPN
ejpam-6737	251	7	et	et	PROPN
ejpam-6737	251	8	al	al	PROPN
ejpam-6737	251	9	.	.	PUNCT
ejpam-6737	251	10	/	/	SYM
ejpam-6737	251	11	eur	eur	PROPN
ejpam-6737	251	12	.	.	PUNCT
ejpam-6737	252	1	j.	j.	PROPN
ejpam-6737	252	2	pure	pure	PROPN
ejpam-6737	252	3	appl	appl	PROPN
ejpam-6737	252	4	.	.	PROPN
ejpam-6737	252	5	math	math	PROPN
ejpam-6737	252	6	,	,	PUNCT
ejpam-6737	252	7	18	18	NUM
ejpam-6737	252	8	(	(	PUNCT
ejpam-6737	252	9	4	4	NUM
ejpam-6737	252	10	)	)	PUNCT
ejpam-6737	252	11	(	(	PUNCT
ejpam-6737	252	12	2025	2025	NUM
ejpam-6737	252	13	)	)	PUNCT
ejpam-6737	252	14	,	,	PUNCT
ejpam-6737	252	15	6737	6737	NUM
ejpam-6737	252	16	13	13	NUM
ejpam-6737	252	17	of	of	ADP
ejpam-6737	252	18	23	23	NUM
ejpam-6737	252	19	afterward	afterward	ADV
ejpam-6737	252	20	,	,	PUNCT
ejpam-6737	252	21	we	we	PRON
ejpam-6737	252	22	have	have	AUX
ejpam-6737	252	23	qξ(s	qξ(	NOUN
ejpam-6737	252	24	)	)	PUNCT
ejpam-6737	252	25	=	=	SYM
ejpam-6737	252	26	s−	s−	PROPN
ejpam-6737	252	27	tξ−1	tξ−1	NOUN
ejpam-6737	252	28	tξ	tξ	ADP
ejpam-6737	252	29	−	−	PROPN
ejpam-6737	252	30	tξ−1	tξ−1	PROPN
ejpam-6737	252	31	tϑ−1	tϑ−1	PROPN
ejpam-6737	252	32	ξ	ξ	PROPN
ejpam-6737	252	33	k1(tξ	k1(tξ	PROPN
ejpam-6737	252	34	,	,	PUNCT
ejpam-6737	252	35	sξ	sξ	PROPN
ejpam-6737	252	36	,	,	PUNCT
ejpam-6737	252	37	eξ	eξ	PROPN
ejpam-6737	252	38	,	,	PUNCT
ejpam-6737	252	39	aξ	aξ	VERB
ejpam-6737	252	40	1,a	1,a	NUM
ejpam-6737	253	1	ξ	ξ	PROPN
ejpam-6737	253	2	2,p	2,p	PROPN
ejpam-6737	253	3	ξ	ξ	PROPN
ejpam-6737	253	4	,	,	PUNCT
ejpam-6737	253	5	rξ	rξ	PROPN
ejpam-6737	253	6	,	,	PUNCT
ejpam-6737	253	7	qξ	qξ	NOUN
ejpam-6737	253	8	)	)	PUNCT
ejpam-6737	254	1	−	−	ADP
ejpam-6737	255	1	s−	s−	PROPN
ejpam-6737	255	2	tξ	tξ	PRON
ejpam-6737	255	3	tξ	tξ	ADP
ejpam-6737	255	4	−	−	PROPN
ejpam-6737	255	5	tξ−1	tξ−1	ADJ
ejpam-6737	255	6	tϑ−1	tϑ−1	NOUN
ejpam-6737	255	7	ξ−1k1(tξ−1	ξ−1k1(tξ−1	NOUN
ejpam-6737	255	8	,	,	PUNCT
ejpam-6737	255	9	sξ−1,eξ−1,aξ−1	sξ−1,eξ−1,aξ−1	ADJ
ejpam-6737	255	10	1	1	NUM
ejpam-6737	255	11	,	,	PUNCT
ejpam-6737	255	12	aξ−1	aξ−1	PROPN
ejpam-6737	255	13	2	2	NUM
ejpam-6737	255	14	,	,	PUNCT
ejpam-6737	255	15	pξ−1,rξ−1,qξ−1	pξ−1,rξ−1,qξ−1	NUM
ejpam-6737	255	16	)	)	PUNCT
ejpam-6737	255	17	,	,	PUNCT
ejpam-6737	255	18	uξ(s	uξ(s	X
ejpam-6737	255	19	)	)	PUNCT
ejpam-6737	255	20	=	=	SYM
ejpam-6737	255	21	s−	s−	PROPN
ejpam-6737	255	22	tξ−1	tξ−1	NOUN
ejpam-6737	255	23	tξ	tξ	ADP
ejpam-6737	255	24	−	−	PROPN
ejpam-6737	255	25	tξ−1	tξ−1	PROPN
ejpam-6737	255	26	tϑ−1	tϑ−1	PROPN
ejpam-6737	255	27	ξ	ξ	PROPN
ejpam-6737	255	28	k2(tξ	k2(tξ	PROPN
ejpam-6737	255	29	,	,	PUNCT
ejpam-6737	255	30	sξ	sξ	PROPN
ejpam-6737	255	31	,	,	PUNCT
ejpam-6737	255	32	eξ	eξ	PROPN
ejpam-6737	255	33	,	,	PUNCT
ejpam-6737	255	34	aξ	aξ	VERB
ejpam-6737	255	35	1,a	1,a	NUM
ejpam-6737	255	36	ξ	ξ	PROPN
ejpam-6737	255	37	2,p	2,p	PROPN
ejpam-6737	255	38	ξ	ξ	PROPN
ejpam-6737	255	39	,	,	PUNCT
ejpam-6737	255	40	rξ	rξ	PROPN
ejpam-6737	255	41	,	,	PUNCT
ejpam-6737	255	42	qξ	qξ	NOUN
ejpam-6737	255	43	)	)	PUNCT
ejpam-6737	255	44	−	−	ADP
ejpam-6737	256	1	s−	s−	PROPN
ejpam-6737	256	2	tξ	tξ	PRON
ejpam-6737	256	3	tξ	tξ	ADP
ejpam-6737	256	4	−	−	PROPN
ejpam-6737	256	5	tξ−1	tξ−1	ADJ
ejpam-6737	256	6	tϑ−1	tϑ−1	PROPN
ejpam-6737	256	7	ξ−1k2(tξ−1	ξ−1k2(tξ−1	NOUN
ejpam-6737	256	8	,	,	PUNCT
ejpam-6737	256	9	sξ−1,eξ−1,aξ−1	sξ−1,eξ−1,aξ−1	ADJ
ejpam-6737	256	10	1	1	NUM
ejpam-6737	256	11	,	,	PUNCT
ejpam-6737	256	12	aξ−1	aξ−1	PROPN
ejpam-6737	256	13	2	2	NUM
ejpam-6737	256	14	,	,	PUNCT
ejpam-6737	256	15	pξ−1,rξ−1,qξ−1	pξ−1,rξ−1,qξ−1	PROPN
ejpam-6737	256	16	)	)	PUNCT
ejpam-6737	256	17	,	,	PUNCT
ejpam-6737	256	18	vξ(s	vξ(s	X
ejpam-6737	256	19	)	)	PUNCT
ejpam-6737	256	20	=	=	SYM
ejpam-6737	256	21	s−	s−	PROPN
ejpam-6737	256	22	tξ−1	tξ−1	NOUN
ejpam-6737	256	23	tξ	tξ	ADP
ejpam-6737	256	24	−	−	PROPN
ejpam-6737	256	25	tξ−1	tξ−1	PROPN
ejpam-6737	256	26	tϑ−1	tϑ−1	PROPN
ejpam-6737	256	27	ξ	ξ	PROPN
ejpam-6737	256	28	k3(tξ	k3(tξ	PROPN
ejpam-6737	256	29	,	,	PUNCT
ejpam-6737	256	30	sξ	sξ	PROPN
ejpam-6737	256	31	,	,	PUNCT
ejpam-6737	256	32	eξ	eξ	PROPN
ejpam-6737	256	33	,	,	PUNCT
ejpam-6737	256	34	aξ	aξ	VERB
ejpam-6737	256	35	1,a	1,a	NUM
ejpam-6737	256	36	ξ	ξ	PROPN
ejpam-6737	256	37	2,p	2,p	PROPN
ejpam-6737	256	38	ξ	ξ	PROPN
ejpam-6737	256	39	,	,	PUNCT
ejpam-6737	256	40	rξ	rξ	PROPN
ejpam-6737	256	41	,	,	PUNCT
ejpam-6737	256	42	qξ	qξ	NOUN
ejpam-6737	256	43	)	)	PUNCT
ejpam-6737	256	44	−	−	ADP
ejpam-6737	257	1	s−	s−	PROPN
ejpam-6737	257	2	tξ	tξ	PRON
ejpam-6737	257	3	tξ	tξ	ADP
ejpam-6737	257	4	−	−	PROPN
ejpam-6737	257	5	tξ−1	tξ−1	NOUN
ejpam-6737	257	6	tϑ−1	tϑ−1	NOUN
ejpam-6737	257	7	ξ−1k3(tξ−1,sξ−1,eξ−1,aξ−1	ξ−1k3(tξ−1,sξ−1,eξ−1,aξ−1	PROPN
ejpam-6737	257	8	1	1	NUM
ejpam-6737	257	9	,	,	PUNCT
ejpam-6737	257	10	aξ−1	aξ−1	PROPN
ejpam-6737	257	11	2	2	NUM
ejpam-6737	257	12	,	,	PUNCT
ejpam-6737	257	13	pξ−1,rξ−1,qξ−1	pξ−1,rξ−1,qξ−1	NUM
ejpam-6737	257	14	)	)	PUNCT
ejpam-6737	257	15	,	,	PUNCT
ejpam-6737	257	16	wξ(s	wξ(s	X
ejpam-6737	257	17	)	)	PUNCT
ejpam-6737	257	18	=	=	SYM
ejpam-6737	257	19	s−	s−	PROPN
ejpam-6737	257	20	tξ−1	tξ−1	NOUN
ejpam-6737	257	21	tξ	tξ	ADP
ejpam-6737	257	22	−	−	PROPN
ejpam-6737	257	23	tξ−1	tξ−1	PROPN
ejpam-6737	257	24	tϑ−1	tϑ−1	PROPN
ejpam-6737	257	25	ξ	ξ	PROPN
ejpam-6737	257	26	k4(tξ	k4(tξ	PROPN
ejpam-6737	257	27	,	,	PUNCT
ejpam-6737	257	28	sξ	sξ	PROPN
ejpam-6737	257	29	,	,	PUNCT
ejpam-6737	257	30	eξ	eξ	PROPN
ejpam-6737	257	31	,	,	PUNCT
ejpam-6737	257	32	aξ	aξ	VERB
ejpam-6737	257	33	1,a	1,a	NUM
ejpam-6737	257	34	ξ	ξ	PROPN
ejpam-6737	257	35	2,p	2,p	PROPN
ejpam-6737	257	36	ξ	ξ	PROPN
ejpam-6737	257	37	,	,	PUNCT
ejpam-6737	257	38	rξ	rξ	PROPN
ejpam-6737	257	39	,	,	PUNCT
ejpam-6737	257	40	qξ	qξ	NOUN
ejpam-6737	257	41	)	)	PUNCT
ejpam-6737	257	42	−	−	ADP
ejpam-6737	258	1	s−	s−	PROPN
ejpam-6737	258	2	tξ	tξ	PRON
ejpam-6737	258	3	tξ	tξ	ADP
ejpam-6737	258	4	−	−	PROPN
ejpam-6737	258	5	tξ−1	tξ−1	ADJ
ejpam-6737	258	6	tϑ−1	tϑ−1	PROPN
ejpam-6737	258	7	ξ−1k4(tξ−1,sξ−1,eξ−1,aξ−1	ξ−1k4(tξ−1,sξ−1,eξ−1,aξ−1	PROPN
ejpam-6737	258	8	1	1	NUM
ejpam-6737	258	9	,	,	PUNCT
ejpam-6737	258	10	aξ−1	aξ−1	PROPN
ejpam-6737	258	11	2	2	NUM
ejpam-6737	258	12	,	,	PUNCT
ejpam-6737	258	13	pξ−1,rξ−1,qξ−1	pξ−1,rξ−1,qξ−1	NUM
ejpam-6737	258	14	)	)	PUNCT
ejpam-6737	258	15	,	,	PUNCT
ejpam-6737	258	16	xξ(s	xξ(s	PROPN
ejpam-6737	258	17	)	)	PUNCT
ejpam-6737	258	18	=	=	SYM
ejpam-6737	258	19	s−	s−	PROPN
ejpam-6737	258	20	tξ−1	tξ−1	NOUN
ejpam-6737	258	21	tξ	tξ	ADP
ejpam-6737	258	22	−	−	PROPN
ejpam-6737	258	23	tξ−1	tξ−1	PROPN
ejpam-6737	258	24	tϑ−1	tϑ−1	PROPN
ejpam-6737	258	25	ξ	ξ	PROPN
ejpam-6737	258	26	k5(tξ	k5(tξ	PROPN
ejpam-6737	258	27	,	,	PUNCT
ejpam-6737	258	28	sξ	sξ	PROPN
ejpam-6737	258	29	,	,	PUNCT
ejpam-6737	258	30	eξ	eξ	PROPN
ejpam-6737	258	31	,	,	PUNCT
ejpam-6737	258	32	aξ	aξ	VERB
ejpam-6737	258	33	1,a	1,a	NUM
ejpam-6737	258	34	ξ	ξ	PROPN
ejpam-6737	258	35	2,p	2,p	PROPN
ejpam-6737	258	36	ξ	ξ	PROPN
ejpam-6737	258	37	,	,	PUNCT
ejpam-6737	258	38	rξ	rξ	PROPN
ejpam-6737	258	39	,	,	PUNCT
ejpam-6737	258	40	qξ	qξ	NOUN
ejpam-6737	258	41	)	)	PUNCT
ejpam-6737	258	42	−	−	ADP
ejpam-6737	259	1	s−	s−	PROPN
ejpam-6737	259	2	tξ	tξ	PRON
ejpam-6737	259	3	tξ	tξ	ADP
ejpam-6737	259	4	−	−	PROPN
ejpam-6737	259	5	tξ−1	tξ−1	ADJ
ejpam-6737	259	6	tϑ−1	tϑ−1	NOUN
ejpam-6737	259	7	ξ−1k5(tξ−1,sξ−1,eξ−1,aξ−1	ξ−1k5(tξ−1,sξ−1,eξ−1,aξ−1	PROPN
ejpam-6737	259	8	1	1	NUM
ejpam-6737	259	9	,	,	PUNCT
ejpam-6737	259	10	aξ−1	aξ−1	PROPN
ejpam-6737	259	11	2	2	NUM
ejpam-6737	259	12	,	,	PUNCT
ejpam-6737	259	13	pξ−1,rξ−1,qξ−1	pξ−1,rξ−1,qξ−1	PROPN
ejpam-6737	259	14	)	)	PUNCT
ejpam-6737	259	15	,	,	PUNCT
ejpam-6737	259	16	yξ(s	yξ(s	NUM
ejpam-6737	259	17	)	)	PUNCT
ejpam-6737	259	18	=	=	SYM
ejpam-6737	259	19	s−	s−	PROPN
ejpam-6737	259	20	tξ−1	tξ−1	NOUN
ejpam-6737	259	21	tξ	tξ	ADP
ejpam-6737	259	22	−	−	PROPN
ejpam-6737	259	23	tξ−1	tξ−1	PROPN
ejpam-6737	259	24	tϑ−1	tϑ−1	PROPN
ejpam-6737	259	25	ξ	ξ	PROPN
ejpam-6737	259	26	k6(tξ	k6(tξ	PROPN
ejpam-6737	259	27	,	,	PUNCT
ejpam-6737	259	28	sξ	sξ	PROPN
ejpam-6737	259	29	,	,	PUNCT
ejpam-6737	259	30	eξ	eξ	PROPN
ejpam-6737	259	31	,	,	PUNCT
ejpam-6737	259	32	aξ	aξ	VERB
ejpam-6737	259	33	1,a	1,a	NUM
ejpam-6737	259	34	ξ	ξ	PROPN
ejpam-6737	259	35	2,p	2,p	PROPN
ejpam-6737	259	36	ξ	ξ	PROPN
ejpam-6737	259	37	,	,	PUNCT
ejpam-6737	259	38	rξ	rξ	PROPN
ejpam-6737	259	39	,	,	PUNCT
ejpam-6737	259	40	qξ	qξ	NOUN
ejpam-6737	259	41	)	)	PUNCT
ejpam-6737	259	42	−	−	ADP
ejpam-6737	260	1	s−	s−	PROPN
ejpam-6737	260	2	tξ	tξ	PRON
ejpam-6737	260	3	tξ	tξ	ADP
ejpam-6737	260	4	−	−	PROPN
ejpam-6737	260	5	tξ−1	tξ−1	ADJ
ejpam-6737	260	6	tϑ−1	tϑ−1	NOUN
ejpam-6737	260	7	ξ−1k6(tξ−1,sξ−1,eξ−1,aξ−1	ξ−1k6(tξ−1,sξ−1,eξ−1,aξ−1	PROPN
ejpam-6737	260	8	1	1	NUM
ejpam-6737	260	9	,	,	PUNCT
ejpam-6737	260	10	aξ−1	aξ−1	PROPN
ejpam-6737	260	11	2	2	NUM
ejpam-6737	260	12	,	,	PUNCT
ejpam-6737	260	13	pξ−1,rξ−1,qξ−1	pξ−1,rξ−1,qξ−1	NUM
ejpam-6737	260	14	)	)	PUNCT
ejpam-6737	260	15	,	,	PUNCT
ejpam-6737	260	16	zξ(s	zξ(s	X
ejpam-6737	260	17	)	)	PUNCT
ejpam-6737	260	18	=	=	SYM
ejpam-6737	260	19	(	(	PUNCT
ejpam-6737	260	20	s−	s−	PROPN
ejpam-6737	260	21	tξ−1	tξ−1	PROPN
ejpam-6737	260	22	)	)	PUNCT
ejpam-6737	260	23	(	(	PUNCT
ejpam-6737	260	24	tξ	tξ	ADP
ejpam-6737	260	25	−	−	PROPN
ejpam-6737	260	26	tξ−1	tξ−1	ADJ
ejpam-6737	260	27	)	)	PUNCT
ejpam-6737	260	28	tϑ−1	tϑ−1	NOUN
ejpam-6737	260	29	ξ	ξ	PROPN
ejpam-6737	260	30	k7(tξ	k7(tξ	PROPN
ejpam-6737	260	31	,	,	PUNCT
ejpam-6737	260	32	sξ	sξ	PROPN
ejpam-6737	260	33	,	,	PUNCT
ejpam-6737	260	34	eξ	eξ	PROPN
ejpam-6737	260	35	,	,	PUNCT
ejpam-6737	260	36	aξ	aξ	VERB
ejpam-6737	260	37	1,a	1,a	NUM
ejpam-6737	260	38	ξ	ξ	PROPN
ejpam-6737	260	39	2,p	2,p	PROPN
ejpam-6737	260	40	ξ	ξ	PROPN
ejpam-6737	260	41	,	,	PUNCT
ejpam-6737	260	42	rξ	rξ	PROPN
ejpam-6737	260	43	,	,	PUNCT
ejpam-6737	260	44	qξ	qξ	NOUN
ejpam-6737	260	45	)	)	PUNCT
ejpam-6737	260	46	−	−	PROPN
ejpam-6737	261	1	(	(	PUNCT
ejpam-6737	261	2	s−	s−	PROPN
ejpam-6737	261	3	tξ	tξ	VERB
ejpam-6737	261	4	)	)	PUNCT
ejpam-6737	261	5	(	(	PUNCT
ejpam-6737	261	6	tξ	tξ	AUX
ejpam-6737	261	7	−	−	PROPN
ejpam-6737	261	8	tξ−1	tξ−1	ADJ
ejpam-6737	261	9	)	)	PUNCT
ejpam-6737	261	10	tϑ−1	tϑ−1	NOUN
ejpam-6737	261	11	ξ−1k7(tξ−1,sξ−1,eξ−1,aξ−1	ξ−1k7(tξ−1,sξ−1,eξ−1,aξ−1	PROPN
ejpam-6737	261	12	1	1	NUM
ejpam-6737	261	13	,	,	PUNCT
ejpam-6737	261	14	aξ−1	aξ−1	PROPN
ejpam-6737	261	15	2	2	NUM
ejpam-6737	261	16	,	,	PUNCT
ejpam-6737	261	17	pξ−1,rξ−1,qξ−1	pξ−1,rξ−1,qξ−1	NUM
ejpam-6737	261	18	)	)	PUNCT
ejpam-6737	261	19	.	.	PUNCT
ejpam-6737	262	1	(	(	PUNCT
ejpam-6737	262	2	11	11	X
ejpam-6737	262	3	)	)	PUNCT
ejpam-6737	262	4	s.	s.	PROPN
ejpam-6737	262	5	m.	m.	PROPN
ejpam-6737	262	6	chithra	chithra	PROPN
ejpam-6737	262	7	et	et	PROPN
ejpam-6737	262	8	al	al	PROPN
ejpam-6737	262	9	.	.	PUNCT
ejpam-6737	262	10	/	/	SYM
ejpam-6737	262	11	eur	eur	PROPN
ejpam-6737	262	12	.	.	PUNCT
ejpam-6737	263	1	j.	j.	PROPN
ejpam-6737	263	2	pure	pure	PROPN
ejpam-6737	263	3	appl	appl	PROPN
ejpam-6737	263	4	.	.	PROPN
ejpam-6737	263	5	math	math	PROPN
ejpam-6737	263	6	,	,	PUNCT
ejpam-6737	263	7	18	18	NUM
ejpam-6737	263	8	(	(	PUNCT
ejpam-6737	263	9	4	4	NUM
ejpam-6737	263	10	)	)	PUNCT
ejpam-6737	263	11	(	(	PUNCT
ejpam-6737	263	12	2025	2025	NUM
ejpam-6737	263	13	)	)	PUNCT
ejpam-6737	263	14	,	,	PUNCT
ejpam-6737	263	15	6737	6737	NUM
ejpam-6737	263	16	14	14	NUM
ejpam-6737	263	17	of	of	ADP
ejpam-6737	263	18	23	23	NUM
ejpam-6737	263	19	by	by	ADP
ejpam-6737	263	20	solving	solve	VERB
ejpam-6737	263	21	the	the	DET
ejpam-6737	263	22	lagrangian	lagrangian	ADJ
ejpam-6737	263	23	polynomial	polynomial	NOUN
ejpam-6737	263	24	in	in	ADP
ejpam-6737	263	25	segments	segment	NOUN
ejpam-6737	263	26	in	in	ADP
ejpam-6737	263	27	equation	equation	NOUN
ejpam-6737	263	28	(	(	PUNCT
ejpam-6737	263	29	11	11	NUM
ejpam-6737	263	30	)	)	PUNCT
ejpam-6737	264	1	,	,	PUNCT
ejpam-6737	264	2	we	we	PRON
ejpam-6737	264	3	have	have	VERB
ejpam-6737	264	4	the	the	DET
ejpam-6737	264	5	following	follow	VERB
ejpam-6737	264	6	outcomes	outcome	NOUN
ejpam-6737	264	7	,	,	PUNCT
ejpam-6737	264	8	which	which	PRON
ejpam-6737	264	9	are	be	AUX
ejpam-6737	264	10	the	the	DET
ejpam-6737	264	11	fundation	fundation	NOUN
ejpam-6737	264	12	for	for	ADP
ejpam-6737	264	13	the	the	DET
ejpam-6737	264	14	further	further	ADJ
ejpam-6737	264	15	numerical	numerical	ADJ
ejpam-6737	264	16	analysis	analysis	NOUN
ejpam-6737	264	17	.	.	PUNCT
ejpam-6737	265	1	sd+1	sd+1	PART
ejpam-6737	266	1	=	=	SYM
ejpam-6737	266	2	s0	s0	PROPN
ejpam-6737	266	3	+	+	CCONJ
ejpam-6737	266	4	ϑtϑ−1	ϑtϑ−1	PROPN
ejpam-6737	266	5	d	d	PROPN
ejpam-6737	266	6	(	(	PUNCT
ejpam-6737	266	7	1−	1−	NUM
ejpam-6737	266	8	η	η	NOUN
ejpam-6737	266	9	)	)	PUNCT
ejpam-6737	266	10	abc(η	abc(η	PROPN
ejpam-6737	266	11	)	)	PUNCT
ejpam-6737	266	12	k1(td	k1(td	PROPN
ejpam-6737	266	13	,	,	PUNCT
ejpam-6737	266	14	sd	sd	NOUN
ejpam-6737	266	15	,	,	PUNCT
ejpam-6737	266	16	ed	ed	NOUN
ejpam-6737	266	17	,	,	PUNCT
ejpam-6737	266	18	ad	ad	NOUN
ejpam-6737	266	19	1,ad	1,ad	NOUN
ejpam-6737	266	20	2,pd	2,pd	NOUN
ejpam-6737	266	21	,	,	PUNCT
ejpam-6737	266	22	rd	rd	NOUN
ejpam-6737	266	23	,	,	PUNCT
ejpam-6737	266	24	qd	qd	PROPN
ejpam-6737	266	25	)	)	PUNCT
ejpam-6737	267	1	+	+	NUM
ejpam-6737	267	2	ϑ(δt)η	ϑ(δt)η	NOUN
ejpam-6737	267	3	(	(	PUNCT
ejpam-6737	267	4	η	η	PROPN
ejpam-6737	267	5	+	+	PROPN
ejpam-6737	267	6	2)abc(η	2)abc(η	NUM
ejpam-6737	267	7	)	)	PUNCT
ejpam-6737	267	8	d∑	d∑	X
ejpam-6737	268	1	ξ=0	ξ=0	PROPN
ejpam-6737	269	1	[	[	PUNCT
ejpam-6737	269	2	tϑ−1	tϑ−1	NOUN
ejpam-6737	269	3	ξ	ξ	PROPN
ejpam-6737	269	4	k1(tξ	k1(tξ	PROPN
ejpam-6737	269	5	,	,	PUNCT
ejpam-6737	269	6	sξ	sξ	PROPN
ejpam-6737	269	7	,	,	PUNCT
ejpam-6737	269	8	eξ	eξ	PROPN
ejpam-6737	269	9	,	,	PUNCT
ejpam-6737	269	10	aξ	aξ	VERB
ejpam-6737	269	11	1,a	1,a	NUM
ejpam-6737	269	12	ξ	ξ	PROPN
ejpam-6737	269	13	2,p	2,p	PROPN
ejpam-6737	269	14	ξ	ξ	PROPN
ejpam-6737	269	15	,	,	PUNCT
ejpam-6737	269	16	rξ	rξ	PROPN
ejpam-6737	269	17	,	,	PUNCT
ejpam-6737	269	18	qξ	qξ	NOUN
ejpam-6737	269	19	)	)	PUNCT
ejpam-6737	269	20	×	×	NOUN
ejpam-6737	269	21	(	(	PUNCT
ejpam-6737	269	22	(	(	PUNCT
ejpam-6737	269	23	d+	d+	NOUN
ejpam-6737	269	24	1−	1−	NUM
ejpam-6737	269	25	ξ)η(d−	ξ)η(d−	PROPN
ejpam-6737	269	26	ξ	ξ	PROPN
ejpam-6737	270	1	+	+	CCONJ
ejpam-6737	270	2	2	2	NUM
ejpam-6737	270	3	+	+	CCONJ
ejpam-6737	270	4	η)−	η)−	PROPN
ejpam-6737	270	5	(	(	PUNCT
ejpam-6737	270	6	d−	d−	PROPN
ejpam-6737	270	7	ξ)(2	ξ)(2	NUM
ejpam-6737	270	8	+	+	CCONJ
ejpam-6737	270	9	2η	2η	NUM
ejpam-6737	270	10	+	+	CCONJ
ejpam-6737	270	11	d−	d−	PROPN
ejpam-6737	270	12	ξ	ξ	NUM
ejpam-6737	270	13	)	)	PUNCT
ejpam-6737	270	14	)	)	PUNCT
ejpam-6737	271	1	−	−	PROPN
ejpam-6737	271	2	tϑ−1	tϑ−1	NOUN
ejpam-6737	271	3	ξ−1k1(tξ−1	ξ−1k1(tξ−1	PROPN
ejpam-6737	271	4	,	,	PUNCT
ejpam-6737	271	5	sξ−1,eξ−1,aξ−1	sξ−1,eξ−1,aξ−1	ADJ
ejpam-6737	271	6	1	1	NUM
ejpam-6737	271	7	,	,	PUNCT
ejpam-6737	271	8	aξ−1	aξ−1	PROPN
ejpam-6737	271	9	2	2	NUM
ejpam-6737	271	10	,	,	PUNCT
ejpam-6737	271	11	pξ−1,rξ−1,qξ−1	pξ−1,rξ−1,qξ−1	NUM
ejpam-6737	271	12	)	)	PUNCT
ejpam-6737	271	13	×	×	NOUN
ejpam-6737	271	14	(	(	PUNCT
ejpam-6737	271	15	(	(	PUNCT
ejpam-6737	271	16	d+	d+	X
ejpam-6737	271	17	1−	1−	NUM
ejpam-6737	271	18	ξ)η+1	ξ)η+1	NOUN
ejpam-6737	271	19	−	−	PROPN
ejpam-6737	271	20	(	(	PUNCT
ejpam-6737	271	21	d−	d−	PROPN
ejpam-6737	271	22	ξ)η(1	ξ)η(1	PROPN
ejpam-6737	271	23	+	+	CCONJ
ejpam-6737	271	24	η	η	PROPN
ejpam-6737	271	25	+	+	PROPN
ejpam-6737	271	26	d−	d−	PROPN
ejpam-6737	271	27	ξ	ξ	NUM
ejpam-6737	271	28	)	)	PUNCT
ejpam-6737	271	29	)	)	PUNCT
ejpam-6737	271	30	]	]	PUNCT
ejpam-6737	271	31	.	.	PUNCT
ejpam-6737	272	1	ed+1	ed+1	X
ejpam-6737	272	2	=	=	SYM
ejpam-6737	272	3	e0	e0	PROPN
ejpam-6737	273	1	+	+	CCONJ
ejpam-6737	273	2	ϑtϑ−1	ϑtϑ−1	PROPN
ejpam-6737	273	3	d	d	PROPN
ejpam-6737	273	4	(	(	PUNCT
ejpam-6737	273	5	1−	1−	NUM
ejpam-6737	273	6	η	η	NOUN
ejpam-6737	273	7	)	)	PUNCT
ejpam-6737	273	8	abc(η	abc(η	PROPN
ejpam-6737	273	9	)	)	PUNCT
ejpam-6737	273	10	k2(td	k2(td	PROPN
ejpam-6737	273	11	,	,	PUNCT
ejpam-6737	273	12	sd	sd	NOUN
ejpam-6737	273	13	,	,	PUNCT
ejpam-6737	273	14	ed	ed	NOUN
ejpam-6737	273	15	,	,	PUNCT
ejpam-6737	273	16	ad	ad	NOUN
ejpam-6737	273	17	1,ad	1,ad	NOUN
ejpam-6737	273	18	2,pd	2,pd	NOUN
ejpam-6737	273	19	,	,	PUNCT
ejpam-6737	273	20	rd	rd	NOUN
ejpam-6737	273	21	,	,	PUNCT
ejpam-6737	273	22	qd	qd	PROPN
ejpam-6737	273	23	)	)	PUNCT
ejpam-6737	274	1	+	+	NUM
ejpam-6737	274	2	ϑ(δt)η	ϑ(δt)η	NOUN
ejpam-6737	274	3	(	(	PUNCT
ejpam-6737	274	4	η	η	PROPN
ejpam-6737	274	5	+	+	PROPN
ejpam-6737	274	6	2)abc(η	2)abc(η	NUM
ejpam-6737	274	7	)	)	PUNCT
ejpam-6737	274	8	d∑	d∑	X
ejpam-6737	275	1	ξ=0	ξ=0	PROPN
ejpam-6737	276	1	[	[	PUNCT
ejpam-6737	276	2	tϑ−1	tϑ−1	NOUN
ejpam-6737	276	3	ξ	ξ	PROPN
ejpam-6737	276	4	k2(tξ	k2(tξ	PROPN
ejpam-6737	276	5	,	,	PUNCT
ejpam-6737	276	6	sξ	sξ	PROPN
ejpam-6737	276	7	,	,	PUNCT
ejpam-6737	276	8	eξ	eξ	PROPN
ejpam-6737	276	9	,	,	PUNCT
ejpam-6737	276	10	aξ	aξ	VERB
ejpam-6737	276	11	1,a	1,a	NUM
ejpam-6737	276	12	ξ	ξ	PROPN
ejpam-6737	276	13	2,p	2,p	PROPN
ejpam-6737	276	14	ξ	ξ	PROPN
ejpam-6737	276	15	,	,	PUNCT
ejpam-6737	276	16	rξ	rξ	PROPN
ejpam-6737	276	17	,	,	PUNCT
ejpam-6737	276	18	qξ	qξ	NOUN
ejpam-6737	276	19	)	)	PUNCT
ejpam-6737	276	20	×	×	NOUN
ejpam-6737	276	21	(	(	PUNCT
ejpam-6737	276	22	(	(	PUNCT
ejpam-6737	276	23	d+	d+	NOUN
ejpam-6737	276	24	1−	1−	NUM
ejpam-6737	276	25	ξ)η(d−	ξ)η(d−	PROPN
ejpam-6737	276	26	ξ	ξ	PROPN
ejpam-6737	277	1	+	+	CCONJ
ejpam-6737	277	2	2	2	NUM
ejpam-6737	277	3	+	+	CCONJ
ejpam-6737	277	4	η)−	η)−	PROPN
ejpam-6737	277	5	(	(	PUNCT
ejpam-6737	277	6	d−	d−	PROPN
ejpam-6737	277	7	ξ)(2	ξ)(2	NUM
ejpam-6737	277	8	+	+	CCONJ
ejpam-6737	277	9	2η	2η	NUM
ejpam-6737	277	10	+	+	CCONJ
ejpam-6737	277	11	d−	d−	PROPN
ejpam-6737	277	12	ξ	ξ	NUM
ejpam-6737	277	13	)	)	PUNCT
ejpam-6737	277	14	)	)	PUNCT
ejpam-6737	278	1	−	−	PROPN
ejpam-6737	278	2	tϑ−1	tϑ−1	PROPN
ejpam-6737	278	3	ξ−1k2(tξ−1	ξ−1k2(tξ−1	NOUN
ejpam-6737	278	4	,	,	PUNCT
ejpam-6737	278	5	sξ−1,eξ−1,aξ−1	sξ−1,eξ−1,aξ−1	ADJ
ejpam-6737	278	6	1	1	NUM
ejpam-6737	278	7	,	,	PUNCT
ejpam-6737	278	8	aξ−1	aξ−1	PROPN
ejpam-6737	278	9	2	2	NUM
ejpam-6737	278	10	,	,	PUNCT
ejpam-6737	278	11	pξ−1,rξ−1,qξ−1	pξ−1,rξ−1,qξ−1	NUM
ejpam-6737	278	12	)	)	PUNCT
ejpam-6737	278	13	×	×	NOUN
ejpam-6737	278	14	(	(	PUNCT
ejpam-6737	278	15	(	(	PUNCT
ejpam-6737	278	16	d+	d+	X
ejpam-6737	278	17	1−	1−	NUM
ejpam-6737	278	18	ξ)η+1	ξ)η+1	NOUN
ejpam-6737	279	1	−	−	PROPN
ejpam-6737	280	1	(	(	PUNCT
ejpam-6737	280	2	d−	d−	PROPN
ejpam-6737	280	3	ξ)η(1	ξ)η(1	PROPN
ejpam-6737	280	4	+	+	CCONJ
ejpam-6737	280	5	η	η	PROPN
ejpam-6737	280	6	+	+	PROPN
ejpam-6737	280	7	d−	d−	PROPN
ejpam-6737	280	8	ξ	ξ	NUM
ejpam-6737	280	9	)	)	PUNCT
ejpam-6737	280	10	)	)	PUNCT
ejpam-6737	280	11	]	]	PUNCT
ejpam-6737	280	12	.	.	PUNCT
ejpam-6737	281	1	ad+1	ad+1	PROPN
ejpam-6737	281	2	1	1	NUM
ejpam-6737	281	3	=	=	SYM
ejpam-6737	281	4	a0	a0	NOUN
ejpam-6737	281	5	1	1	NUM
ejpam-6737	282	1	+	+	CCONJ
ejpam-6737	282	2	ϑtϑ−1	ϑtϑ−1	PROPN
ejpam-6737	282	3	d	d	PROPN
ejpam-6737	282	4	(	(	PUNCT
ejpam-6737	282	5	1−	1−	NUM
ejpam-6737	282	6	η	η	NOUN
ejpam-6737	282	7	)	)	PUNCT
ejpam-6737	282	8	abc(η	abc(η	PROPN
ejpam-6737	282	9	)	)	PUNCT
ejpam-6737	282	10	k3(td	k3(td	PROPN
ejpam-6737	282	11	,	,	PUNCT
ejpam-6737	282	12	sd	sd	NOUN
ejpam-6737	282	13	,	,	PUNCT
ejpam-6737	282	14	ed	ed	NOUN
ejpam-6737	282	15	,	,	PUNCT
ejpam-6737	282	16	ad	ad	NOUN
ejpam-6737	282	17	1,ad	1,ad	NOUN
ejpam-6737	282	18	2,pd	2,pd	NOUN
ejpam-6737	282	19	,	,	PUNCT
ejpam-6737	282	20	rd	rd	NOUN
ejpam-6737	282	21	,	,	PUNCT
ejpam-6737	282	22	qd	qd	PROPN
ejpam-6737	282	23	)	)	PUNCT
ejpam-6737	283	1	+	+	NUM
ejpam-6737	283	2	ϑ(δt)η	ϑ(δt)η	NOUN
ejpam-6737	283	3	(	(	PUNCT
ejpam-6737	283	4	η	η	PROPN
ejpam-6737	283	5	+	+	PROPN
ejpam-6737	283	6	2)abc(η	2)abc(η	NUM
ejpam-6737	283	7	)	)	PUNCT
ejpam-6737	283	8	d∑	d∑	X
ejpam-6737	284	1	ξ=0	ξ=0	PROPN
ejpam-6737	285	1	[	[	PUNCT
ejpam-6737	285	2	tϑ−1	tϑ−1	NOUN
ejpam-6737	285	3	ξ	ξ	PROPN
ejpam-6737	285	4	k3(tξ	k3(tξ	PROPN
ejpam-6737	285	5	,	,	PUNCT
ejpam-6737	285	6	sξ	sξ	PROPN
ejpam-6737	285	7	,	,	PUNCT
ejpam-6737	285	8	eξ	eξ	PROPN
ejpam-6737	285	9	,	,	PUNCT
ejpam-6737	285	10	aξ	aξ	VERB
ejpam-6737	285	11	1,a	1,a	NUM
ejpam-6737	285	12	ξ	ξ	PROPN
ejpam-6737	285	13	2,p	2,p	PROPN
ejpam-6737	285	14	ξ	ξ	PROPN
ejpam-6737	285	15	,	,	PUNCT
ejpam-6737	285	16	rξ	rξ	PROPN
ejpam-6737	285	17	,	,	PUNCT
ejpam-6737	285	18	qξ	qξ	NOUN
ejpam-6737	285	19	)	)	PUNCT
ejpam-6737	285	20	×	×	NOUN
ejpam-6737	285	21	(	(	PUNCT
ejpam-6737	285	22	(	(	PUNCT
ejpam-6737	285	23	d+	d+	NOUN
ejpam-6737	285	24	1−	1−	NUM
ejpam-6737	285	25	ξ)η(d−	ξ)η(d−	PROPN
ejpam-6737	285	26	ξ	ξ	PROPN
ejpam-6737	286	1	+	+	CCONJ
ejpam-6737	286	2	2	2	NUM
ejpam-6737	286	3	+	+	CCONJ
ejpam-6737	286	4	η)−	η)−	PROPN
ejpam-6737	286	5	(	(	PUNCT
ejpam-6737	286	6	d−	d−	PROPN
ejpam-6737	286	7	ξ)(2	ξ)(2	NUM
ejpam-6737	286	8	+	+	CCONJ
ejpam-6737	286	9	2η	2η	NUM
ejpam-6737	286	10	+	+	CCONJ
ejpam-6737	286	11	d−	d−	PROPN
ejpam-6737	286	12	ξ	ξ	NUM
ejpam-6737	286	13	)	)	PUNCT
ejpam-6737	286	14	)	)	PUNCT
ejpam-6737	287	1	−	−	PROPN
ejpam-6737	287	2	tϑ−1	tϑ−1	PROPN
ejpam-6737	287	3	ξ−1k3(tξ−1	ξ−1k3(tξ−1	PROPN
ejpam-6737	287	4	,	,	PUNCT
ejpam-6737	287	5	sξ−1,eξ−1,aξ−1	sξ−1,eξ−1,aξ−1	ADJ
ejpam-6737	287	6	1	1	NUM
ejpam-6737	287	7	,	,	PUNCT
ejpam-6737	287	8	aξ−1	aξ−1	PROPN
ejpam-6737	287	9	2	2	NUM
ejpam-6737	287	10	,	,	PUNCT
ejpam-6737	287	11	pξ−1,rξ−1,qξ−1	pξ−1,rξ−1,qξ−1	NUM
ejpam-6737	287	12	)	)	PUNCT
ejpam-6737	287	13	×	×	NOUN
ejpam-6737	287	14	(	(	PUNCT
ejpam-6737	287	15	(	(	PUNCT
ejpam-6737	287	16	d+	d+	X
ejpam-6737	287	17	1−	1−	NUM
ejpam-6737	287	18	ξ)η+1	ξ)η+1	NOUN
ejpam-6737	288	1	−	−	PROPN
ejpam-6737	288	2	(	(	PUNCT
ejpam-6737	288	3	d−	d−	PROPN
ejpam-6737	288	4	ξ)η(1	ξ)η(1	PROPN
ejpam-6737	288	5	+	+	CCONJ
ejpam-6737	288	6	η	η	PROPN
ejpam-6737	288	7	+	+	PROPN
ejpam-6737	288	8	d−	d−	PROPN
ejpam-6737	288	9	ξ	ξ	NUM
ejpam-6737	288	10	)	)	PUNCT
ejpam-6737	288	11	)	)	PUNCT
ejpam-6737	288	12	]	]	PUNCT
ejpam-6737	288	13	.	.	PUNCT
ejpam-6737	289	1	ad+1	ad+1	PROPN
ejpam-6737	289	2	2	2	NUM
ejpam-6737	289	3	=	=	SYM
ejpam-6737	289	4	a0	a0	NOUN
ejpam-6737	289	5	2	2	NUM
ejpam-6737	290	1	+	+	CCONJ
ejpam-6737	290	2	ϑtϑ−1	ϑtϑ−1	PROPN
ejpam-6737	290	3	d	d	PROPN
ejpam-6737	290	4	(	(	PUNCT
ejpam-6737	290	5	1−	1−	NUM
ejpam-6737	290	6	η	η	NOUN
ejpam-6737	290	7	)	)	PUNCT
ejpam-6737	290	8	abc(η	abc(η	PROPN
ejpam-6737	290	9	)	)	PUNCT
ejpam-6737	290	10	k4(td	k4(td	NUM
ejpam-6737	290	11	,	,	PUNCT
ejpam-6737	290	12	sd	sd	NOUN
ejpam-6737	290	13	,	,	PUNCT
ejpam-6737	290	14	ed	ed	NOUN
ejpam-6737	290	15	,	,	PUNCT
ejpam-6737	290	16	ad	ad	NOUN
ejpam-6737	290	17	1,ad	1,ad	NOUN
ejpam-6737	290	18	2,pd	2,pd	NOUN
ejpam-6737	290	19	,	,	PUNCT
ejpam-6737	290	20	rd	rd	NOUN
ejpam-6737	290	21	,	,	PUNCT
ejpam-6737	290	22	qd	qd	PROPN
ejpam-6737	290	23	)	)	PUNCT
ejpam-6737	291	1	+	+	NUM
ejpam-6737	291	2	ϑ(δt)η	ϑ(δt)η	NOUN
ejpam-6737	291	3	(	(	PUNCT
ejpam-6737	291	4	η	η	PROPN
ejpam-6737	291	5	+	+	PROPN
ejpam-6737	291	6	2)abc(η	2)abc(η	NUM
ejpam-6737	291	7	)	)	PUNCT
ejpam-6737	291	8	d∑	d∑	X
ejpam-6737	292	1	ξ=0	ξ=0	PROPN
ejpam-6737	293	1	[	[	PUNCT
ejpam-6737	293	2	tϑ−1	tϑ−1	NOUN
ejpam-6737	293	3	ξ	ξ	X
ejpam-6737	293	4	k4(tξ	k4(tξ	PROPN
ejpam-6737	293	5	,	,	PUNCT
ejpam-6737	293	6	sξ	sξ	PROPN
ejpam-6737	293	7	,	,	PUNCT
ejpam-6737	293	8	eξ	eξ	PROPN
ejpam-6737	293	9	,	,	PUNCT
ejpam-6737	293	10	aξ	aξ	VERB
ejpam-6737	293	11	1,a	1,a	NUM
ejpam-6737	293	12	ξ	ξ	PROPN
ejpam-6737	293	13	2,p	2,p	PROPN
ejpam-6737	293	14	ξ	ξ	PROPN
ejpam-6737	293	15	,	,	PUNCT
ejpam-6737	293	16	rξ	rξ	PROPN
ejpam-6737	293	17	,	,	PUNCT
ejpam-6737	293	18	qξ	qξ	NOUN
ejpam-6737	293	19	)	)	PUNCT
ejpam-6737	293	20	×	×	NOUN
ejpam-6737	293	21	(	(	PUNCT
ejpam-6737	293	22	(	(	PUNCT
ejpam-6737	293	23	d+	d+	NOUN
ejpam-6737	293	24	1−	1−	NUM
ejpam-6737	293	25	ξ)η(d−	ξ)η(d−	PROPN
ejpam-6737	293	26	ξ	ξ	PROPN
ejpam-6737	294	1	+	+	CCONJ
ejpam-6737	294	2	2	2	NUM
ejpam-6737	294	3	+	+	CCONJ
ejpam-6737	294	4	η)−	η)−	PROPN
ejpam-6737	294	5	(	(	PUNCT
ejpam-6737	294	6	d−	d−	PROPN
ejpam-6737	294	7	ξ)(2	ξ)(2	NUM
ejpam-6737	294	8	+	+	CCONJ
ejpam-6737	294	9	2η	2η	NUM
ejpam-6737	294	10	+	+	CCONJ
ejpam-6737	294	11	d−	d−	PROPN
ejpam-6737	294	12	ξ	ξ	NUM
ejpam-6737	294	13	)	)	PUNCT
ejpam-6737	294	14	)	)	PUNCT
ejpam-6737	295	1	−	−	PROPN
ejpam-6737	295	2	tϑ−1	tϑ−1	NOUN
ejpam-6737	295	3	ξ−1k4(tξ−1	ξ−1k4(tξ−1	NOUN
ejpam-6737	295	4	,	,	PUNCT
ejpam-6737	295	5	sξ−1,eξ−1,aξ−1	sξ−1,eξ−1,aξ−1	ADJ
ejpam-6737	295	6	1	1	NUM
ejpam-6737	295	7	,	,	PUNCT
ejpam-6737	295	8	aξ−1	aξ−1	PROPN
ejpam-6737	295	9	2	2	NUM
ejpam-6737	295	10	,	,	PUNCT
ejpam-6737	295	11	pξ−1,rξ−1,qξ−1	pξ−1,rξ−1,qξ−1	NUM
ejpam-6737	295	12	)	)	PUNCT
ejpam-6737	295	13	×	×	NOUN
ejpam-6737	295	14	(	(	PUNCT
ejpam-6737	295	15	(	(	PUNCT
ejpam-6737	295	16	d+	d+	X
ejpam-6737	295	17	1−	1−	NUM
ejpam-6737	295	18	ξ)η+1	ξ)η+1	NOUN
ejpam-6737	295	19	−	−	PROPN
ejpam-6737	295	20	(	(	PUNCT
ejpam-6737	295	21	d−	d−	PROPN
ejpam-6737	295	22	ξ)η(1	ξ)η(1	PROPN
ejpam-6737	295	23	+	+	CCONJ
ejpam-6737	295	24	η	η	PROPN
ejpam-6737	295	25	+	+	PROPN
ejpam-6737	295	26	d−	d−	PROPN
ejpam-6737	295	27	ξ	ξ	NUM
ejpam-6737	295	28	)	)	PUNCT
ejpam-6737	295	29	)	)	PUNCT
ejpam-6737	295	30	]	]	PUNCT
ejpam-6737	295	31	.	.	PUNCT
ejpam-6737	296	1	s.	s.	PROPN
ejpam-6737	296	2	m.	m.	PROPN
ejpam-6737	296	3	chithra	chithra	PROPN
ejpam-6737	296	4	et	et	PROPN
ejpam-6737	296	5	al	al	PROPN
ejpam-6737	296	6	.	.	PUNCT
ejpam-6737	296	7	/	/	SYM
ejpam-6737	296	8	eur	eur	PROPN
ejpam-6737	296	9	.	.	PUNCT
ejpam-6737	297	1	j.	j.	PROPN
ejpam-6737	297	2	pure	pure	PROPN
ejpam-6737	297	3	appl	appl	PROPN
ejpam-6737	297	4	.	.	PROPN
ejpam-6737	297	5	math	math	PROPN
ejpam-6737	297	6	,	,	PUNCT
ejpam-6737	297	7	18	18	NUM
ejpam-6737	297	8	(	(	PUNCT
ejpam-6737	297	9	4	4	NUM
ejpam-6737	297	10	)	)	PUNCT
ejpam-6737	297	11	(	(	PUNCT
ejpam-6737	297	12	2025	2025	NUM
ejpam-6737	297	13	)	)	PUNCT
ejpam-6737	297	14	,	,	PUNCT
ejpam-6737	297	15	6737	6737	NUM
ejpam-6737	297	16	15	15	NUM
ejpam-6737	297	17	of	of	ADP
ejpam-6737	297	18	23	23	NUM
ejpam-6737	297	19	pd+1	pd+1	NOUN
ejpam-6737	297	20	=	=	NOUN
ejpam-6737	297	21	p0	p0	NOUN
ejpam-6737	298	1	+	+	CCONJ
ejpam-6737	298	2	ϑtϑ−1	ϑtϑ−1	PROPN
ejpam-6737	298	3	d	d	PROPN
ejpam-6737	298	4	(	(	PUNCT
ejpam-6737	298	5	1−	1−	NUM
ejpam-6737	298	6	η	η	NOUN
ejpam-6737	298	7	)	)	PUNCT
ejpam-6737	298	8	abc(η	abc(η	PROPN
ejpam-6737	298	9	)	)	PUNCT
ejpam-6737	298	10	k5(td	k5(td	PROPN
ejpam-6737	298	11	,	,	PUNCT
ejpam-6737	298	12	sd	sd	NOUN
ejpam-6737	298	13	,	,	PUNCT
ejpam-6737	298	14	ed	ed	NOUN
ejpam-6737	298	15	,	,	PUNCT
ejpam-6737	298	16	ad	ad	NOUN
ejpam-6737	298	17	1,ad	1,ad	NOUN
ejpam-6737	298	18	2,pd	2,pd	NOUN
ejpam-6737	298	19	,	,	PUNCT
ejpam-6737	298	20	rd	rd	NOUN
ejpam-6737	298	21	,	,	PUNCT
ejpam-6737	298	22	qd	qd	PROPN
ejpam-6737	298	23	)	)	PUNCT
ejpam-6737	299	1	+	+	NUM
ejpam-6737	299	2	ϑ(δt)η	ϑ(δt)η	NOUN
ejpam-6737	299	3	(	(	PUNCT
ejpam-6737	299	4	η	η	PROPN
ejpam-6737	299	5	+	+	PROPN
ejpam-6737	299	6	2)abc(η	2)abc(η	NUM
ejpam-6737	299	7	)	)	PUNCT
ejpam-6737	299	8	d∑	d∑	X
ejpam-6737	300	1	ξ=0	ξ=0	PROPN
ejpam-6737	301	1	[	[	PUNCT
ejpam-6737	301	2	tϑ−1	tϑ−1	NOUN
ejpam-6737	301	3	ξ	ξ	PROPN
ejpam-6737	301	4	k5(tξ	k5(tξ	PROPN
ejpam-6737	301	5	,	,	PUNCT
ejpam-6737	301	6	sξ	sξ	PROPN
ejpam-6737	301	7	,	,	PUNCT
ejpam-6737	301	8	eξ	eξ	PROPN
ejpam-6737	301	9	,	,	PUNCT
ejpam-6737	301	10	aξ	aξ	VERB
ejpam-6737	301	11	1,a	1,a	NUM
ejpam-6737	301	12	ξ	ξ	PROPN
ejpam-6737	301	13	2,p	2,p	PROPN
ejpam-6737	301	14	ξ	ξ	PROPN
ejpam-6737	301	15	,	,	PUNCT
ejpam-6737	301	16	rξ	rξ	PROPN
ejpam-6737	301	17	,	,	PUNCT
ejpam-6737	301	18	qξ	qξ	NOUN
ejpam-6737	301	19	)	)	PUNCT
ejpam-6737	301	20	×	×	NOUN
ejpam-6737	301	21	(	(	PUNCT
ejpam-6737	301	22	(	(	PUNCT
ejpam-6737	301	23	d+	d+	NOUN
ejpam-6737	301	24	1−	1−	NUM
ejpam-6737	301	25	ξ)η(d−	ξ)η(d−	PROPN
ejpam-6737	301	26	ξ	ξ	PROPN
ejpam-6737	302	1	+	+	CCONJ
ejpam-6737	302	2	2	2	NUM
ejpam-6737	302	3	+	+	CCONJ
ejpam-6737	302	4	η)−	η)−	PROPN
ejpam-6737	302	5	(	(	PUNCT
ejpam-6737	302	6	d−	d−	PROPN
ejpam-6737	302	7	ξ)(2	ξ)(2	NUM
ejpam-6737	302	8	+	+	CCONJ
ejpam-6737	302	9	2η	2η	NUM
ejpam-6737	302	10	+	+	CCONJ
ejpam-6737	302	11	d−	d−	PROPN
ejpam-6737	302	12	ξ	ξ	NUM
ejpam-6737	302	13	)	)	PUNCT
ejpam-6737	302	14	)	)	PUNCT
ejpam-6737	303	1	−	−	PROPN
ejpam-6737	303	2	tϑ−1	tϑ−1	PROPN
ejpam-6737	303	3	ξ−1k5(tξ−1	ξ−1k5(tξ−1	PROPN
ejpam-6737	303	4	,	,	PUNCT
ejpam-6737	303	5	sξ−1,eξ−1,aξ−1	sξ−1,eξ−1,aξ−1	ADJ
ejpam-6737	303	6	1	1	NUM
ejpam-6737	303	7	,	,	PUNCT
ejpam-6737	303	8	aξ−1	aξ−1	PROPN
ejpam-6737	303	9	2	2	NUM
ejpam-6737	303	10	,	,	PUNCT
ejpam-6737	303	11	pξ−1,rξ−1,qξ−1	pξ−1,rξ−1,qξ−1	NUM
ejpam-6737	303	12	)	)	PUNCT
ejpam-6737	303	13	×	×	NOUN
ejpam-6737	303	14	(	(	PUNCT
ejpam-6737	303	15	(	(	PUNCT
ejpam-6737	303	16	d+	d+	X
ejpam-6737	303	17	1−	1−	NUM
ejpam-6737	303	18	ξ)η+1	ξ)η+1	NOUN
ejpam-6737	303	19	−	−	PROPN
ejpam-6737	303	20	(	(	PUNCT
ejpam-6737	303	21	d−	d−	PROPN
ejpam-6737	303	22	ξ)η(1	ξ)η(1	PROPN
ejpam-6737	303	23	+	+	CCONJ
ejpam-6737	303	24	η	η	PROPN
ejpam-6737	303	25	+	+	PROPN
ejpam-6737	303	26	d−	d−	PROPN
ejpam-6737	303	27	ξ	ξ	NUM
ejpam-6737	303	28	)	)	PUNCT
ejpam-6737	303	29	)	)	PUNCT
ejpam-6737	303	30	]	]	PUNCT
ejpam-6737	303	31	.	.	PUNCT
ejpam-6737	304	1	rd+1	rd+1	NOUN
ejpam-6737	305	1	=	=	PUNCT
ejpam-6737	305	2	r0	r0	NOUN
ejpam-6737	305	3	+	+	NOUN
ejpam-6737	305	4	ϑtϑ−1	ϑtϑ−1	PROPN
ejpam-6737	305	5	d	d	PROPN
ejpam-6737	305	6	(	(	PUNCT
ejpam-6737	305	7	1−	1−	NUM
ejpam-6737	305	8	η	η	NOUN
ejpam-6737	305	9	)	)	PUNCT
ejpam-6737	305	10	abc(η	abc(η	PROPN
ejpam-6737	305	11	)	)	PUNCT
ejpam-6737	305	12	k6(td	k6(td	PROPN
ejpam-6737	305	13	,	,	PUNCT
ejpam-6737	305	14	sd	sd	NOUN
ejpam-6737	305	15	,	,	PUNCT
ejpam-6737	305	16	ed	ed	NOUN
ejpam-6737	305	17	,	,	PUNCT
ejpam-6737	305	18	ad	ad	NOUN
ejpam-6737	305	19	1,ad	1,ad	NOUN
ejpam-6737	305	20	2,pd	2,pd	NOUN
ejpam-6737	305	21	,	,	PUNCT
ejpam-6737	305	22	rd	rd	NOUN
ejpam-6737	305	23	,	,	PUNCT
ejpam-6737	305	24	qd	qd	PROPN
ejpam-6737	305	25	)	)	PUNCT
ejpam-6737	306	1	+	+	NUM
ejpam-6737	306	2	ϑ(δt)η	ϑ(δt)η	NOUN
ejpam-6737	306	3	(	(	PUNCT
ejpam-6737	306	4	η	η	PROPN
ejpam-6737	306	5	+	+	PROPN
ejpam-6737	306	6	2)abc(η	2)abc(η	NUM
ejpam-6737	306	7	)	)	PUNCT
ejpam-6737	306	8	d∑	d∑	X
ejpam-6737	307	1	ξ=0	ξ=0	PROPN
ejpam-6737	308	1	[	[	PUNCT
ejpam-6737	308	2	tϑ−1	tϑ−1	NOUN
ejpam-6737	308	3	ξ	ξ	PROPN
ejpam-6737	308	4	k6(tξ	k6(tξ	PROPN
ejpam-6737	308	5	,	,	PUNCT
ejpam-6737	308	6	sξ	sξ	PROPN
ejpam-6737	308	7	,	,	PUNCT
ejpam-6737	308	8	eξ	eξ	PROPN
ejpam-6737	308	9	,	,	PUNCT
ejpam-6737	308	10	aξ	aξ	VERB
ejpam-6737	308	11	1,a	1,a	NUM
ejpam-6737	308	12	ξ	ξ	PROPN
ejpam-6737	308	13	2,p	2,p	PROPN
ejpam-6737	308	14	ξ	ξ	PROPN
ejpam-6737	308	15	,	,	PUNCT
ejpam-6737	308	16	rξ	rξ	PROPN
ejpam-6737	308	17	,	,	PUNCT
ejpam-6737	308	18	qξ	qξ	NOUN
ejpam-6737	308	19	)	)	PUNCT
ejpam-6737	308	20	×	×	NOUN
ejpam-6737	308	21	(	(	PUNCT
ejpam-6737	308	22	(	(	PUNCT
ejpam-6737	308	23	d+	d+	NOUN
ejpam-6737	308	24	1−	1−	NUM
ejpam-6737	308	25	ξ)η(d−	ξ)η(d−	PROPN
ejpam-6737	308	26	ξ	ξ	PROPN
ejpam-6737	309	1	+	+	CCONJ
ejpam-6737	309	2	2	2	NUM
ejpam-6737	309	3	+	+	CCONJ
ejpam-6737	309	4	η)−	η)−	PROPN
ejpam-6737	309	5	(	(	PUNCT
ejpam-6737	309	6	d−	d−	PROPN
ejpam-6737	309	7	ξ)(2	ξ)(2	NUM
ejpam-6737	309	8	+	+	CCONJ
ejpam-6737	309	9	2η	2η	NUM
ejpam-6737	309	10	+	+	CCONJ
ejpam-6737	309	11	d−	d−	PROPN
ejpam-6737	309	12	ξ	ξ	NUM
ejpam-6737	309	13	)	)	PUNCT
ejpam-6737	309	14	)	)	PUNCT
ejpam-6737	310	1	−	−	PROPN
ejpam-6737	310	2	tϑ−1	tϑ−1	PROPN
ejpam-6737	310	3	ξ−1k2(tξ−1	ξ−1k2(tξ−1	NOUN
ejpam-6737	310	4	,	,	PUNCT
ejpam-6737	310	5	sξ−1,eξ−1,aξ−1	sξ−1,eξ−1,aξ−1	ADJ
ejpam-6737	310	6	1	1	NUM
ejpam-6737	310	7	,	,	PUNCT
ejpam-6737	310	8	aξ−1	aξ−1	PROPN
ejpam-6737	310	9	2	2	NUM
ejpam-6737	310	10	,	,	PUNCT
ejpam-6737	310	11	pξ−1,rξ−1,qξ−1	pξ−1,rξ−1,qξ−1	NUM
ejpam-6737	310	12	)	)	PUNCT
ejpam-6737	310	13	×	×	NOUN
ejpam-6737	310	14	(	(	PUNCT
ejpam-6737	310	15	(	(	PUNCT
ejpam-6737	310	16	d+	d+	X
ejpam-6737	310	17	1−	1−	NUM
ejpam-6737	310	18	ξ)η+1	ξ)η+1	NOUN
ejpam-6737	311	1	−	−	PROPN
ejpam-6737	312	1	(	(	PUNCT
ejpam-6737	312	2	d−	d−	PROPN
ejpam-6737	312	3	ξ)η(1	ξ)η(1	PROPN
ejpam-6737	312	4	+	+	CCONJ
ejpam-6737	312	5	η	η	PROPN
ejpam-6737	312	6	+	+	PROPN
ejpam-6737	312	7	d−	d−	PROPN
ejpam-6737	312	8	ξ	ξ	NUM
ejpam-6737	312	9	)	)	PUNCT
ejpam-6737	312	10	)	)	PUNCT
ejpam-6737	312	11	]	]	PUNCT
ejpam-6737	312	12	.	.	PUNCT
ejpam-6737	313	1	qd+1	qd+1	X
ejpam-6737	314	1	=	=	NOUN
ejpam-6737	314	2	q0	q0	PROPN
ejpam-6737	315	1	+	+	CCONJ
ejpam-6737	315	2	ϑtϑ−1	ϑtϑ−1	PROPN
ejpam-6737	315	3	d	d	PROPN
ejpam-6737	315	4	(	(	PUNCT
ejpam-6737	315	5	1−	1−	NUM
ejpam-6737	315	6	η	η	NOUN
ejpam-6737	315	7	)	)	PUNCT
ejpam-6737	315	8	abc(η	abc(η	PROPN
ejpam-6737	315	9	)	)	PUNCT
ejpam-6737	315	10	k7(td	k7(td	NOUN
ejpam-6737	315	11	,	,	PUNCT
ejpam-6737	315	12	sd	sd	NOUN
ejpam-6737	315	13	,	,	PUNCT
ejpam-6737	315	14	ed	ed	NOUN
ejpam-6737	315	15	,	,	PUNCT
ejpam-6737	315	16	ad	ad	NOUN
ejpam-6737	315	17	1,ad	1,ad	NOUN
ejpam-6737	315	18	2,pd	2,pd	NOUN
ejpam-6737	315	19	,	,	PUNCT
ejpam-6737	315	20	rd	rd	NOUN
ejpam-6737	315	21	,	,	PUNCT
ejpam-6737	315	22	qd	qd	PROPN
ejpam-6737	315	23	)	)	PUNCT
ejpam-6737	316	1	+	+	NUM
ejpam-6737	316	2	ϑ(δt)η	ϑ(δt)η	NOUN
ejpam-6737	316	3	(	(	PUNCT
ejpam-6737	316	4	η	η	PROPN
ejpam-6737	316	5	+	+	PROPN
ejpam-6737	316	6	2)abc(η	2)abc(η	NUM
ejpam-6737	316	7	)	)	PUNCT
ejpam-6737	316	8	d∑	d∑	X
ejpam-6737	317	1	ξ=0	ξ=0	PROPN
ejpam-6737	318	1	[	[	PUNCT
ejpam-6737	318	2	tϑ−1	tϑ−1	NOUN
ejpam-6737	318	3	ξ	ξ	PROPN
ejpam-6737	318	4	k7(tξ	k7(tξ	PROPN
ejpam-6737	318	5	,	,	PUNCT
ejpam-6737	318	6	sξ	sξ	PROPN
ejpam-6737	318	7	,	,	PUNCT
ejpam-6737	318	8	eξ	eξ	PROPN
ejpam-6737	318	9	,	,	PUNCT
ejpam-6737	318	10	aξ	aξ	VERB
ejpam-6737	318	11	1,a	1,a	NUM
ejpam-6737	318	12	ξ	ξ	PROPN
ejpam-6737	318	13	2,p	2,p	PROPN
ejpam-6737	318	14	ξ	ξ	PROPN
ejpam-6737	318	15	,	,	PUNCT
ejpam-6737	318	16	rξ	rξ	PROPN
ejpam-6737	318	17	,	,	PUNCT
ejpam-6737	318	18	qξ	qξ	NOUN
ejpam-6737	318	19	)	)	PUNCT
ejpam-6737	318	20	×	×	NOUN
ejpam-6737	318	21	(	(	PUNCT
ejpam-6737	318	22	(	(	PUNCT
ejpam-6737	318	23	d+	d+	NOUN
ejpam-6737	318	24	1−	1−	NUM
ejpam-6737	318	25	ξ)η(d−	ξ)η(d−	PROPN
ejpam-6737	318	26	ξ	ξ	PROPN
ejpam-6737	319	1	+	+	CCONJ
ejpam-6737	319	2	2	2	NUM
ejpam-6737	319	3	+	+	CCONJ
ejpam-6737	319	4	η)−	η)−	PROPN
ejpam-6737	319	5	(	(	PUNCT
ejpam-6737	319	6	d−	d−	PROPN
ejpam-6737	319	7	ξ)(2	ξ)(2	NUM
ejpam-6737	319	8	+	+	CCONJ
ejpam-6737	319	9	2η	2η	NUM
ejpam-6737	319	10	+	+	CCONJ
ejpam-6737	319	11	d−	d−	PROPN
ejpam-6737	319	12	ξ	ξ	NUM
ejpam-6737	319	13	)	)	PUNCT
ejpam-6737	319	14	)	)	PUNCT
ejpam-6737	320	1	−	−	PROPN
ejpam-6737	320	2	tϑ−1	tϑ−1	NOUN
ejpam-6737	320	3	ξ−1k7(tξ−1,sξ−1,eξ−1,aξ−1	ξ−1k7(tξ−1,sξ−1,eξ−1,aξ−1	PROPN
ejpam-6737	320	4	1	1	NUM
ejpam-6737	320	5	,	,	PUNCT
ejpam-6737	320	6	aξ−1	aξ−1	PROPN
ejpam-6737	320	7	2	2	NUM
ejpam-6737	320	8	,	,	PUNCT
ejpam-6737	320	9	pξ−1,rξ−1,qξ−1	pξ−1,rξ−1,qξ−1	NUM
ejpam-6737	320	10	)	)	PUNCT
ejpam-6737	320	11	×	×	NOUN
ejpam-6737	320	12	(	(	PUNCT
ejpam-6737	320	13	(	(	PUNCT
ejpam-6737	320	14	d+	d+	X
ejpam-6737	320	15	1−	1−	NUM
ejpam-6737	320	16	ξ)η+1	ξ)η+1	NOUN
ejpam-6737	321	1	−	−	PROPN
ejpam-6737	321	2	(	(	PUNCT
ejpam-6737	321	3	d−	d−	PROPN
ejpam-6737	321	4	ξ)η(1	ξ)η(1	PROPN
ejpam-6737	321	5	+	+	CCONJ
ejpam-6737	321	6	η	η	PROPN
ejpam-6737	321	7	+	+	PROPN
ejpam-6737	321	8	d−	d−	PROPN
ejpam-6737	321	9	ξ	ξ	NUM
ejpam-6737	321	10	)	)	PUNCT
ejpam-6737	321	11	)	)	PUNCT
ejpam-6737	321	12	]	]	PUNCT
ejpam-6737	321	13	.	.	PUNCT
ejpam-6737	322	1	(	(	PUNCT
ejpam-6737	322	2	12	12	NUM
ejpam-6737	322	3	)	)	PUNCT
ejpam-6737	322	4	7	7	NUM
ejpam-6737	322	5	.	.	NOUN
ejpam-6737	322	6	results	result	NOUN
ejpam-6737	322	7	and	and	CCONJ
ejpam-6737	322	8	discussion	discussion	NOUN
ejpam-6737	322	9	this	this	DET
ejpam-6737	322	10	section	section	NOUN
ejpam-6737	322	11	presents	present	VERB
ejpam-6737	322	12	matlab	matlab	PROPN
ejpam-6737	322	13	-	-	PUNCT
ejpam-6737	322	14	based	base	VERB
ejpam-6737	322	15	simulations	simulation	NOUN
ejpam-6737	322	16	for	for	ADP
ejpam-6737	322	17	system	system	NOUN
ejpam-6737	322	18	(	(	PUNCT
ejpam-6737	322	19	12	12	NUM
ejpam-6737	322	20	)	)	PUNCT
ejpam-6737	322	21	using	use	VERB
ejpam-6737	322	22	the	the	DET
ejpam-6737	322	23	fractal	fractal	ADJ
ejpam-6737	322	24	–	–	PUNCT
ejpam-6737	322	25	fractional	fractional	ADJ
ejpam-6737	322	26	derivative	derivative	ADJ
ejpam-6737	322	27	approach	approach	NOUN
ejpam-6737	322	28	and	and	CCONJ
ejpam-6737	322	29	compares	compare	VERB
ejpam-6737	322	30	its	its	PRON
ejpam-6737	322	31	efficiency	efficiency	NOUN
ejpam-6737	322	32	with	with	ADP
ejpam-6737	322	33	existing	exist	VERB
ejpam-6737	322	34	fractional	fractional	ADJ
ejpam-6737	322	35	-	-	PUNCT
ejpam-6737	322	36	order	order	NOUN
ejpam-6737	322	37	operators	operator	NOUN
ejpam-6737	322	38	.	.	PUNCT
ejpam-6737	323	1	the	the	DET
ejpam-6737	323	2	data	datum	NOUN
ejpam-6737	323	3	used	use	VERB
ejpam-6737	323	4	,	,	PUNCT
ejpam-6737	323	5	taken	take	VERB
ejpam-6737	323	6	from	from	ADP
ejpam-6737	323	7	[	[	X
ejpam-6737	323	8	21	21	NUM
ejpam-6737	323	9	]	]	PUNCT
ejpam-6737	323	10	,	,	PUNCT
ejpam-6737	323	11	reflect	reflect	VERB
ejpam-6737	323	12	the	the	DET
ejpam-6737	323	13	social	social	ADJ
ejpam-6737	323	14	media	medium	NOUN
ejpam-6737	323	15	addiction	addiction	NOUN
ejpam-6737	323	16	and	and	CCONJ
ejpam-6737	323	17	recovery	recovery	NOUN
ejpam-6737	323	18	dynamics	dynamic	NOUN
ejpam-6737	323	19	described	describe	VERB
ejpam-6737	323	20	in	in	ADP
ejpam-6737	323	21	table	table	NOUN
ejpam-6737	323	22	1	1	NUM
ejpam-6737	323	23	.	.	PUNCT
ejpam-6737	324	1	the	the	DET
ejpam-6737	324	2	results	result	NOUN
ejpam-6737	324	3	highlight	highlight	VERB
ejpam-6737	324	4	key	key	ADJ
ejpam-6737	324	5	trends	trend	NOUN
ejpam-6737	324	6	and	and	CCONJ
ejpam-6737	324	7	parameter	parameter	NOUN
ejpam-6737	324	8	variations	variation	NOUN
ejpam-6737	324	9	,	,	PUNCT
ejpam-6737	324	10	offering	offer	VERB
ejpam-6737	324	11	insights	insight	NOUN
ejpam-6737	324	12	into	into	ADP
ejpam-6737	324	13	system	system	NOUN
ejpam-6737	324	14	sensitivity	sensitivity	NOUN
ejpam-6737	324	15	and	and	CCONJ
ejpam-6737	324	16	transmission	transmission	NOUN
ejpam-6737	324	17	dynamics	dynamic	NOUN
ejpam-6737	324	18	,	,	PUNCT
ejpam-6737	324	19	consistent	consistent	ADJ
ejpam-6737	324	20	with	with	ADP
ejpam-6737	324	21	earlier	early	ADJ
ejpam-6737	324	22	studies	study	NOUN
ejpam-6737	324	23	[	[	X
ejpam-6737	324	24	26	26	NUM
ejpam-6737	324	25	,	,	PUNCT
ejpam-6737	324	26	27	27	NUM
ejpam-6737	324	27	]	]	PUNCT
ejpam-6737	324	28	.	.	PUNCT
ejpam-6737	325	1	the	the	DET
ejpam-6737	325	2	results	result	NOUN
ejpam-6737	325	3	of	of	ADP
ejpam-6737	325	4	the	the	DET
ejpam-6737	325	5	simulation	simulation	NOUN
ejpam-6737	325	6	show	show	VERB
ejpam-6737	325	7	the	the	DET
ejpam-6737	325	8	social	social	ADJ
ejpam-6737	325	9	media	medium	NOUN
ejpam-6737	325	10	addiction	addiction	NOUN
ejpam-6737	325	11	dynamics	dynamic	NOUN
ejpam-6737	325	12	under	under	ADP
ejpam-6737	325	13	various	various	ADJ
ejpam-6737	325	14	fractional	fractional	ADJ
ejpam-6737	325	15	orders	order	NOUN
ejpam-6737	325	16	,	,	PUNCT
ejpam-6737	325	17	which	which	PRON
ejpam-6737	325	18	provide	provide	VERB
ejpam-6737	325	19	information	information	NOUN
ejpam-6737	325	20	about	about	ADP
ejpam-6737	325	21	the	the	DET
ejpam-6737	325	22	intervention	intervention	NOUN
ejpam-6737	325	23	strategies	strategy	NOUN
ejpam-6737	325	24	’	'	PUNCT
ejpam-6737	325	25	effectiveness	effectiveness	NOUN
ejpam-6737	325	26	.	.	PUNCT
ejpam-6737	326	1	the	the	DET
ejpam-6737	326	2	trends	trend	NOUN
ejpam-6737	326	3	seen	see	VERB
ejpam-6737	326	4	throughout	throughout	ADP
ejpam-6737	326	5	the	the	DET
ejpam-6737	326	6	figures	figure	NOUN
ejpam-6737	326	7	highlight	highlight	VERB
ejpam-6737	326	8	the	the	DET
ejpam-6737	326	9	need	need	NOUN
ejpam-6737	326	10	for	for	ADP
ejpam-6737	326	11	early	early	ADJ
ejpam-6737	326	12	intervention	intervention	NOUN
ejpam-6737	326	13	,	,	PUNCT
ejpam-6737	326	14	s.	s.	PROPN
ejpam-6737	326	15	m.	m.	PROPN
ejpam-6737	326	16	chithra	chithra	PROPN
ejpam-6737	326	17	et	et	PROPN
ejpam-6737	326	18	al	al	PROPN
ejpam-6737	326	19	.	.	PUNCT
ejpam-6737	326	20	/	/	SYM
ejpam-6737	326	21	eur	eur	PROPN
ejpam-6737	326	22	.	.	PUNCT
ejpam-6737	327	1	j.	j.	PROPN
ejpam-6737	327	2	pure	pure	PROPN
ejpam-6737	327	3	appl	appl	PROPN
ejpam-6737	327	4	.	.	PROPN
ejpam-6737	327	5	math	math	PROPN
ejpam-6737	327	6	,	,	PUNCT
ejpam-6737	327	7	18	18	NUM
ejpam-6737	327	8	(	(	PUNCT
ejpam-6737	327	9	4	4	NUM
ejpam-6737	327	10	)	)	PUNCT
ejpam-6737	327	11	(	(	PUNCT
ejpam-6737	327	12	2025	2025	NUM
ejpam-6737	327	13	)	)	PUNCT
ejpam-6737	327	14	,	,	PUNCT
ejpam-6737	327	15	6737	6737	NUM
ejpam-6737	327	16	16	16	NUM
ejpam-6737	327	17	of	of	ADP
ejpam-6737	327	18	23	23	NUM
ejpam-6737	327	19	table	table	NOUN
ejpam-6737	327	20	1	1	NUM
ejpam-6737	327	21	:	:	PUNCT
ejpam-6737	327	22	model	model	NOUN
ejpam-6737	327	23	parameters	parameter	NOUN
ejpam-6737	327	24	for	for	ADP
ejpam-6737	327	25	social	social	ADJ
ejpam-6737	327	26	media	medium	NOUN
ejpam-6737	327	27	addiction	addiction	NOUN
ejpam-6737	327	28	dynamics	dynamic	NOUN
ejpam-6737	327	29	parameter	parameter	NOUN
ejpam-6737	327	30	description	description	NOUN
ejpam-6737	327	31	value	value	NOUN
ejpam-6737	327	32	λ	λ	PROPN
ejpam-6737	327	33	recruitment	recruitment	NOUN
ejpam-6737	327	34	rate	rate	NOUN
ejpam-6737	327	35	into	into	ADP
ejpam-6737	327	36	susceptible	susceptible	ADJ
ejpam-6737	327	37	class	class	NOUN
ejpam-6737	327	38	0.975	0.975	NUM
ejpam-6737	327	39	δ	δ	PROPN
ejpam-6737	327	40	addiction	addiction	NOUN
ejpam-6737	327	41	transmission	transmission	NOUN
ejpam-6737	327	42	rate	rate	NOUN
ejpam-6737	327	43	0.1–0.8	0.1–0.8	NUM
ejpam-6737	327	44	θ	θ	NOUN
ejpam-6737	327	45	contact	contact	NOUN
ejpam-6737	327	46	rate	rate	NOUN
ejpam-6737	327	47	(	(	PUNCT
ejpam-6737	327	48	susceptible	susceptible	ADJ
ejpam-6737	327	49	–	–	PUNCT
ejpam-6737	327	50	addicted	addicted	ADJ
ejpam-6737	327	51	)	)	PUNCT
ejpam-6737	327	52	0.2	0.2	NUM
ejpam-6737	327	53	λ1	λ1	ADJ
ejpam-6737	327	54	transition	transition	NOUN
ejpam-6737	327	55	to	to	ADP
ejpam-6737	327	56	mild	mild	ADJ
ejpam-6737	327	57	addiction	addiction	NOUN
ejpam-6737	327	58	0.5	0.5	NUM
ejpam-6737	327	59	λ2	λ2	NOUN
ejpam-6737	327	60	transition	transition	NOUN
ejpam-6737	327	61	to	to	ADP
ejpam-6737	327	62	severe	severe	ADJ
ejpam-6737	327	63	addiction	addiction	NOUN
ejpam-6737	327	64	0.7	0.7	NUM
ejpam-6737	327	65	µ	µ	PRON
ejpam-6737	327	66	natural	natural	ADJ
ejpam-6737	327	67	exit	exit	NOUN
ejpam-6737	327	68	(	(	PUNCT
ejpam-6737	327	69	death	death	NOUN
ejpam-6737	327	70	)	)	PUNCT
ejpam-6737	327	71	rate	rate	NOUN
ejpam-6737	327	72	0.05	0.05	NUM
ejpam-6737	327	73	τ1	τ1	NOUN
ejpam-6737	327	74	non	non	ADJ
ejpam-6737	327	75	-	-	ADJ
ejpam-6737	327	76	users	user	NOUN
ejpam-6737	327	77	staying	stay	VERB
ejpam-6737	327	78	non	non	NOUN
ejpam-6737	327	79	-	-	NOUN
ejpam-6737	327	80	users	user	NOUN
ejpam-6737	327	81	0.4	0.4	NUM
ejpam-6737	327	82	τ2	τ2	PROPN
ejpam-6737	327	83	recovered	recover	VERB
ejpam-6737	327	84	becoming	become	VERB
ejpam-6737	327	85	non	non	NOUN
ejpam-6737	327	86	-	-	NOUN
ejpam-6737	327	87	users	user	NOUN
ejpam-6737	327	88	0.35	0.35	NUM
ejpam-6737	327	89	ξ1	ξ1	NOUN
ejpam-6737	327	90	recovery	recovery	NOUN
ejpam-6737	327	91	from	from	ADP
ejpam-6737	327	92	mild	mild	ADJ
ejpam-6737	327	93	addiction	addiction	NOUN
ejpam-6737	327	94	0.02	0.02	NUM
ejpam-6737	327	95	ξ2	ξ2	NOUN
ejpam-6737	327	96	recovery	recovery	NOUN
ejpam-6737	327	97	from	from	ADP
ejpam-6737	327	98	severe	severe	ADJ
ejpam-6737	327	99	addiction	addiction	NOUN
ejpam-6737	327	100	0.03	0.03	NUM
ejpam-6737	327	101	ξ3	ξ3	PROPN
ejpam-6737	327	102	recovery	recovery	NOUN
ejpam-6737	327	103	under	under	ADP
ejpam-6737	327	104	treatment	treatment	NOUN
ejpam-6737	327	105	0.25	0.25	NUM
ejpam-6737	327	106	φ1	φ1	NOUN
ejpam-6737	327	107	treatment	treatment	NOUN
ejpam-6737	327	108	rate	rate	NOUN
ejpam-6737	327	109	(	(	PUNCT
ejpam-6737	327	110	mild	mild	ADJ
ejpam-6737	327	111	)	)	PUNCT
ejpam-6737	327	112	0.01	0.01	NUM
ejpam-6737	327	113	φ2	φ2	NOUN
ejpam-6737	327	114	treatment	treatment	NOUN
ejpam-6737	327	115	rate	rate	NOUN
ejpam-6737	327	116	(	(	PUNCT
ejpam-6737	327	117	severe	severe	ADJ
ejpam-6737	327	118	)	)	PUNCT
ejpam-6737	327	119	0.05	0.05	NUM
ejpam-6737	327	120	γ	γ	NOUN
ejpam-6737	327	121	relapse	relapse	NOUN
ejpam-6737	327	122	rate	rate	NOUN
ejpam-6737	327	123	(	(	PUNCT
ejpam-6737	327	124	recovered	recover	VERB
ejpam-6737	327	125	→	→	SYM
ejpam-6737	327	126	susceptible	susceptible	ADJ
ejpam-6737	327	127	)	)	PUNCT
ejpam-6737	327	128	0.01	0.01	NUM
ejpam-6737	327	129	ε	ε	PROPN
ejpam-6737	327	130	progression	progression	NOUN
ejpam-6737	327	131	(	(	PUNCT
ejpam-6737	327	132	mild	mild	ADJ
ejpam-6737	327	133	→	→	SYM
ejpam-6737	327	134	severe	severe	ADJ
ejpam-6737	327	135	addiction	addiction	NOUN
ejpam-6737	327	136	)	)	PUNCT
ejpam-6737	327	137	0.7	0.7	NUM
ejpam-6737	327	138	awareness	awareness	NOUN
ejpam-6737	327	139	campaigns	campaign	NOUN
ejpam-6737	327	140	,	,	PUNCT
ejpam-6737	327	141	and	and	CCONJ
ejpam-6737	327	142	mental	mental	ADJ
ejpam-6737	327	143	support	support	NOUN
ejpam-6737	327	144	in	in	ADP
ejpam-6737	327	145	decreasing	decrease	VERB
ejpam-6737	327	146	the	the	DET
ejpam-6737	327	147	negative	negative	ADJ
ejpam-6737	327	148	effects	effect	NOUN
ejpam-6737	327	149	of	of	ADP
ejpam-6737	327	150	addiction	addiction	NOUN
ejpam-6737	327	151	.	.	PUNCT
ejpam-6737	328	1	figure	figure	NOUN
ejpam-6737	328	2	2	2	NUM
ejpam-6737	328	3	illustrates	illustrate	VERB
ejpam-6737	328	4	a	a	DET
ejpam-6737	328	5	consistent	consistent	ADJ
ejpam-6737	328	6	decrease	decrease	NOUN
ejpam-6737	328	7	in	in	ADP
ejpam-6737	328	8	the	the	DET
ejpam-6737	328	9	susceptible	susceptible	ADJ
ejpam-6737	328	10	population	population	NOUN
ejpam-6737	328	11	for	for	ADP
ejpam-6737	328	12	various	various	ADJ
ejpam-6737	328	13	fractional	fractional	ADJ
ejpam-6737	328	14	orders	order	NOUN
ejpam-6737	328	15	.	.	PUNCT
ejpam-6737	329	1	this	this	DET
ejpam-6737	329	2	behaviour	behaviour	NOUN
ejpam-6737	329	3	indicates	indicate	VERB
ejpam-6737	329	4	that	that	SCONJ
ejpam-6737	329	5	as	as	SCONJ
ejpam-6737	329	6	social	social	ADJ
ejpam-6737	329	7	media	medium	NOUN
ejpam-6737	329	8	influence	influence	NOUN
ejpam-6737	329	9	grows	grow	VERB
ejpam-6737	329	10	,	,	PUNCT
ejpam-6737	329	11	more	more	ADJ
ejpam-6737	329	12	people	people	NOUN
ejpam-6737	329	13	move	move	VERB
ejpam-6737	329	14	from	from	ADP
ejpam-6737	329	15	the	the	DET
ejpam-6737	329	16	susceptible	susceptible	ADJ
ejpam-6737	329	17	class	class	NOUN
ejpam-6737	329	18	into	into	ADP
ejpam-6737	329	19	the	the	DET
ejpam-6737	329	20	exposed	expose	VERB
ejpam-6737	329	21	or	or	CCONJ
ejpam-6737	329	22	addicted	addicted	ADJ
ejpam-6737	329	23	classes	class	NOUN
ejpam-6737	329	24	.	.	PUNCT
ejpam-6737	330	1	the	the	DET
ejpam-6737	330	2	different	different	ADJ
ejpam-6737	330	3	rates	rate	NOUN
ejpam-6737	330	4	of	of	ADP
ejpam-6737	330	5	decrease	decrease	NOUN
ejpam-6737	330	6	for	for	ADP
ejpam-6737	330	7	various	various	ADJ
ejpam-6737	330	8	fractional	fractional	ADJ
ejpam-6737	330	9	orders	order	NOUN
ejpam-6737	330	10	indicate	indicate	VERB
ejpam-6737	330	11	that	that	SCONJ
ejpam-6737	330	12	addiction	addiction	NOUN
ejpam-6737	330	13	propagates	propagate	VERB
ejpam-6737	330	14	with	with	ADP
ejpam-6737	330	15	different	different	ADJ
ejpam-6737	330	16	intensities	intensity	NOUN
ejpam-6737	330	17	based	base	VERB
ejpam-6737	330	18	on	on	ADP
ejpam-6737	330	19	susceptibility	susceptibility	NOUN
ejpam-6737	330	20	and	and	CCONJ
ejpam-6737	330	21	external	external	ADJ
ejpam-6737	330	22	factors	factor	NOUN
ejpam-6737	330	23	like	like	ADP
ejpam-6737	330	24	peer	peer	NOUN
ejpam-6737	330	25	pressure	pressure	NOUN
ejpam-6737	330	26	,	,	PUNCT
ejpam-6737	330	27	online	online	ADJ
ejpam-6737	330	28	activity	activity	NOUN
ejpam-6737	330	29	,	,	PUNCT
ejpam-6737	330	30	and	and	CCONJ
ejpam-6737	330	31	social	social	ADJ
ejpam-6737	330	32	trends	trend	NOUN
ejpam-6737	330	33	.	.	PUNCT
ejpam-6737	331	1	figure	figure	NOUN
ejpam-6737	331	2	3	3	NUM
ejpam-6737	331	3	demonstrates	demonstrate	VERB
ejpam-6737	331	4	a	a	DET
ejpam-6737	331	5	downward	downward	ADJ
ejpam-6737	331	6	trend	trend	NOUN
ejpam-6737	331	7	in	in	ADP
ejpam-6737	331	8	the	the	DET
ejpam-6737	331	9	exposed	expose	VERB
ejpam-6737	331	10	population	population	NOUN
ejpam-6737	331	11	,	,	PUNCT
ejpam-6737	331	12	showing	show	VERB
ejpam-6737	331	13	that	that	SCONJ
ejpam-6737	331	14	people	people	NOUN
ejpam-6737	331	15	either	either	CCONJ
ejpam-6737	331	16	advance	advance	VERB
ejpam-6737	331	17	to	to	ADP
ejpam-6737	331	18	the	the	DET
ejpam-6737	331	19	stage	stage	NOUN
ejpam-6737	331	20	of	of	ADP
ejpam-6737	331	21	addiction	addiction	NOUN
ejpam-6737	331	22	or	or	CCONJ
ejpam-6737	331	23	get	get	AUX
ejpam-6737	331	24	cured	cure	VERB
ejpam-6737	331	25	with	with	ADP
ejpam-6737	331	26	intervention	intervention	NOUN
ejpam-6737	331	27	.	.	PUNCT
ejpam-6737	332	1	the	the	DET
ejpam-6737	332	2	rate	rate	NOUN
ejpam-6737	332	3	of	of	ADP
ejpam-6737	332	4	this	this	DET
ejpam-6737	332	5	change	change	NOUN
ejpam-6737	332	6	depends	depend	VERB
ejpam-6737	332	7	on	on	ADP
ejpam-6737	332	8	psychological	psychological	ADJ
ejpam-6737	332	9	aspects	aspect	NOUN
ejpam-6737	332	10	,	,	PUNCT
ejpam-6737	332	11	efficacy	efficacy	NOUN
ejpam-6737	332	12	of	of	ADP
ejpam-6737	332	13	intervention	intervention	NOUN
ejpam-6737	332	14	,	,	PUNCT
ejpam-6737	332	15	and	and	CCONJ
ejpam-6737	332	16	external	external	ADJ
ejpam-6737	332	17	motivational	motivational	ADJ
ejpam-6737	332	18	forces	force	NOUN
ejpam-6737	332	19	like	like	ADP
ejpam-6737	332	20	social	social	ADJ
ejpam-6737	332	21	awareness	awareness	NOUN
ejpam-6737	332	22	programs	program	NOUN
ejpam-6737	332	23	.	.	PUNCT
ejpam-6737	333	1	the	the	DET
ejpam-6737	333	2	reduction	reduction	NOUN
ejpam-6737	333	3	in	in	ADP
ejpam-6737	333	4	the	the	DET
ejpam-6737	333	5	exposed	expose	VERB
ejpam-6737	333	6	group	group	NOUN
ejpam-6737	333	7	suggests	suggest	VERB
ejpam-6737	333	8	that	that	SCONJ
ejpam-6737	333	9	in	in	ADP
ejpam-6737	333	10	the	the	DET
ejpam-6737	333	11	absence	absence	NOUN
ejpam-6737	333	12	of	of	ADP
ejpam-6737	333	13	early	early	ADJ
ejpam-6737	333	14	intervention	intervention	NOUN
ejpam-6737	333	15	,	,	PUNCT
ejpam-6737	333	16	people	people	NOUN
ejpam-6737	333	17	tend	tend	VERB
ejpam-6737	333	18	to	to	PART
ejpam-6737	333	19	develop	develop	VERB
ejpam-6737	333	20	addiction	addiction	NOUN
ejpam-6737	333	21	to	to	ADP
ejpam-6737	333	22	social	social	ADJ
ejpam-6737	333	23	media	medium	NOUN
ejpam-6737	333	24	,	,	PUNCT
ejpam-6737	333	25	emphasizing	emphasize	VERB
ejpam-6737	333	26	the	the	DET
ejpam-6737	333	27	necessity	necessity	NOUN
ejpam-6737	333	28	for	for	ADP
ejpam-6737	333	29	proactive	proactive	ADJ
ejpam-6737	333	30	psychological	psychological	ADJ
ejpam-6737	333	31	and	and	CCONJ
ejpam-6737	333	32	behavioural	behavioural	ADJ
ejpam-6737	333	33	interventions	intervention	NOUN
ejpam-6737	333	34	.	.	PUNCT
ejpam-6737	334	1	figures	figure	NOUN
ejpam-6737	334	2	4	4	NUM
ejpam-6737	334	3	and	and	CCONJ
ejpam-6737	334	4	5	5	NUM
ejpam-6737	334	5	demonstrate	demonstrate	VERB
ejpam-6737	334	6	the	the	DET
ejpam-6737	334	7	decline	decline	NOUN
ejpam-6737	334	8	in	in	ADP
ejpam-6737	334	9	the	the	DET
ejpam-6737	334	10	mildly	mildly	ADV
ejpam-6737	334	11	and	and	CCONJ
ejpam-6737	334	12	severely	severely	ADV
ejpam-6737	334	13	addicted	addict	VERB
ejpam-6737	334	14	groups	group	NOUN
ejpam-6737	334	15	over	over	ADP
ejpam-6737	334	16	a	a	DET
ejpam-6737	334	17	period	period	NOUN
ejpam-6737	334	18	.	.	PUNCT
ejpam-6737	335	1	the	the	DET
ejpam-6737	335	2	pattern	pattern	NOUN
ejpam-6737	335	3	indicates	indicate	VERB
ejpam-6737	335	4	the	the	DET
ejpam-6737	335	5	successful	successful	ADJ
ejpam-6737	335	6	outcome	outcome	NOUN
ejpam-6737	335	7	of	of	ADP
ejpam-6737	335	8	psychological	psychological	ADJ
ejpam-6737	335	9	therapies	therapy	NOUN
ejpam-6737	335	10	,	,	PUNCT
ejpam-6737	335	11	behavioural	behavioural	ADJ
ejpam-6737	335	12	counselling	counselling	NOUN
ejpam-6737	335	13	,	,	PUNCT
ejpam-6737	335	14	and	and	CCONJ
ejpam-6737	335	15	awareness	awareness	NOUN
ejpam-6737	335	16	campaigns	campaign	NOUN
ejpam-6737	335	17	in	in	ADP
ejpam-6737	335	18	managing	manage	VERB
ejpam-6737	335	19	social	social	ADJ
ejpam-6737	335	20	media	medium	NOUN
ejpam-6737	335	21	addiction	addiction	NOUN
ejpam-6737	335	22	.	.	PUNCT
ejpam-6737	336	1	the	the	DET
ejpam-6737	336	2	decline	decline	NOUN
ejpam-6737	336	3	in	in	ADP
ejpam-6737	336	4	the	the	DET
ejpam-6737	336	5	groups	group	NOUN
ejpam-6737	336	6	indicates	indicate	VERB
ejpam-6737	336	7	that	that	SCONJ
ejpam-6737	336	8	targeted	target	VERB
ejpam-6737	336	9	interventions	intervention	NOUN
ejpam-6737	336	10	are	be	AUX
ejpam-6737	336	11	successful	successful	ADJ
ejpam-6737	336	12	in	in	ADP
ejpam-6737	336	13	reducing	reduce	VERB
ejpam-6737	336	14	addiction	addiction	NOUN
ejpam-6737	336	15	levels	level	NOUN
ejpam-6737	336	16	step	step	VERB
ejpam-6737	336	17	by	by	ADP
ejpam-6737	336	18	step	step	NOUN
ejpam-6737	336	19	,	,	PUNCT
ejpam-6737	336	20	avoiding	avoid	VERB
ejpam-6737	336	21	long	long	ADJ
ejpam-6737	336	22	-	-	PUNCT
ejpam-6737	336	23	term	term	NOUN
ejpam-6737	336	24	dependency	dependency	NOUN
ejpam-6737	336	25	,	,	PUNCT
ejpam-6737	336	26	and	and	CCONJ
ejpam-6737	336	27	promoting	promote	VERB
ejpam-6737	336	28	recovery	recovery	NOUN
ejpam-6737	336	29	.	.	PUNCT
ejpam-6737	337	1	the	the	DET
ejpam-6737	337	2	fractional	fractional	ADJ
ejpam-6737	337	3	-	-	PUNCT
ejpam-6737	337	4	order	order	NOUN
ejpam-6737	337	5	dynamics	dynamic	NOUN
ejpam-6737	337	6	also	also	ADV
ejpam-6737	337	7	suggest	suggest	VERB
ejpam-6737	337	8	memory	memory	NOUN
ejpam-6737	337	9	effects	effect	NOUN
ejpam-6737	337	10	are	be	AUX
ejpam-6737	337	11	important	important	ADJ
ejpam-6737	337	12	in	in	ADP
ejpam-6737	337	13	addiction	addiction	NOUN
ejpam-6737	337	14	behaviour	behaviour	NOUN
ejpam-6737	337	15	since	since	SCONJ
ejpam-6737	337	16	those	those	PRON
ejpam-6737	337	17	with	with	ADP
ejpam-6737	337	18	a	a	DET
ejpam-6737	337	19	history	history	NOUN
ejpam-6737	337	20	of	of	ADP
ejpam-6737	337	21	extensive	extensive	ADJ
ejpam-6737	337	22	social	social	ADJ
ejpam-6737	337	23	media	medium	NOUN
ejpam-6737	337	24	usage	usage	NOUN
ejpam-6737	337	25	take	take	VERB
ejpam-6737	337	26	longer	long	ADV
ejpam-6737	337	27	to	to	PART
ejpam-6737	337	28	recover	recover	VERB
ejpam-6737	337	29	.	.	PUNCT
ejpam-6737	338	1	figures	figure	NOUN
ejpam-6737	338	2	6	6	NUM
ejpam-6737	338	3	to	to	PART
ejpam-6737	338	4	8	8	NUM
ejpam-6737	338	5	show	show	VERB
ejpam-6737	338	6	a	a	DET
ejpam-6737	338	7	significant	significant	ADJ
ejpam-6737	338	8	increase	increase	NOUN
ejpam-6737	338	9	in	in	ADP
ejpam-6737	338	10	the	the	DET
ejpam-6737	338	11	population	population	NOUN
ejpam-6737	338	12	being	be	AUX
ejpam-6737	338	13	treated	treat	VERB
ejpam-6737	338	14	for	for	ADP
ejpam-6737	338	15	psys	psys	NOUN
ejpam-6737	338	16	.	.	PUNCT
ejpam-6737	339	1	m.	m.	PROPN
ejpam-6737	339	2	chithra	chithra	PROPN
ejpam-6737	339	3	et	et	PROPN
ejpam-6737	339	4	al	al	PROPN
ejpam-6737	339	5	.	.	PUNCT
ejpam-6737	339	6	/	/	SYM
ejpam-6737	339	7	eur	eur	PROPN
ejpam-6737	339	8	.	.	PUNCT
ejpam-6737	340	1	j.	j.	PROPN
ejpam-6737	340	2	pure	pure	PROPN
ejpam-6737	340	3	appl	appl	PROPN
ejpam-6737	340	4	.	.	PROPN
ejpam-6737	340	5	math	math	PROPN
ejpam-6737	340	6	,	,	PUNCT
ejpam-6737	340	7	18	18	NUM
ejpam-6737	340	8	(	(	PUNCT
ejpam-6737	340	9	4	4	NUM
ejpam-6737	340	10	)	)	PUNCT
ejpam-6737	340	11	(	(	PUNCT
ejpam-6737	340	12	2025	2025	NUM
ejpam-6737	340	13	)	)	PUNCT
ejpam-6737	340	14	,	,	PUNCT
ejpam-6737	340	15	6737	6737	NUM
ejpam-6737	340	16	17	17	NUM
ejpam-6737	340	17	of	of	ADP
ejpam-6737	340	18	23	23	NUM
ejpam-6737	340	19	figure	figure	NOUN
ejpam-6737	340	20	2	2	NUM
ejpam-6737	340	21	:	:	PUNCT
ejpam-6737	340	22	simulation	simulation	NOUN
ejpam-6737	340	23	of	of	ADP
ejpam-6737	340	24	population	population	NOUN
ejpam-6737	340	25	under	under	ADP
ejpam-6737	340	26	different	different	ADJ
ejpam-6737	340	27	fractional	fractional	ADJ
ejpam-6737	340	28	orders	order	NOUN
ejpam-6737	340	29	for	for	ADP
ejpam-6737	340	30	susceptible	susceptible	ADJ
ejpam-6737	340	31	.	.	PUNCT
ejpam-6737	341	1	figure	figure	NOUN
ejpam-6737	341	2	3	3	NUM
ejpam-6737	341	3	:	:	PUNCT
ejpam-6737	341	4	simulation	simulation	NOUN
ejpam-6737	341	5	of	of	ADP
ejpam-6737	341	6	population	population	NOUN
ejpam-6737	341	7	under	under	ADP
ejpam-6737	341	8	different	different	ADJ
ejpam-6737	341	9	fractional	fractional	ADJ
ejpam-6737	341	10	orders	order	NOUN
ejpam-6737	341	11	for	for	ADP
ejpam-6737	341	12	exposed	expose	VERB
ejpam-6737	341	13	chological	chological	ADJ
ejpam-6737	341	14	issues	issue	NOUN
ejpam-6737	341	15	,	,	PUNCT
ejpam-6737	341	16	recovered	recover	VERB
ejpam-6737	341	17	users	user	NOUN
ejpam-6737	341	18	,	,	PUNCT
ejpam-6737	341	19	and	and	CCONJ
ejpam-6737	341	20	non	non	NOUN
ejpam-6737	341	21	-	-	NOUN
ejpam-6737	341	22	users	user	NOUN
ejpam-6737	341	23	.	.	PUNCT
ejpam-6737	342	1	this	this	DET
ejpam-6737	342	2	increasing	increase	VERB
ejpam-6737	342	3	trend	trend	NOUN
ejpam-6737	342	4	highlights	highlight	VERB
ejpam-6737	342	5	the	the	DET
ejpam-6737	342	6	success	success	NOUN
ejpam-6737	342	7	of	of	ADP
ejpam-6737	342	8	intervention	intervention	NOUN
ejpam-6737	342	9	efforts	effort	NOUN
ejpam-6737	342	10	at	at	ADP
ejpam-6737	342	11	enabling	enable	VERB
ejpam-6737	342	12	recovery	recovery	NOUN
ejpam-6737	342	13	and	and	CCONJ
ejpam-6737	342	14	individuals	individual	NOUN
ejpam-6737	342	15	to	to	PART
ejpam-6737	342	16	have	have	VERB
ejpam-6737	342	17	control	control	NOUN
ejpam-6737	342	18	over	over	ADP
ejpam-6737	342	19	their	their	PRON
ejpam-6737	342	20	social	social	ADJ
ejpam-6737	342	21	media	medium	NOUN
ejpam-6737	342	22	behaviour	behaviour	NOUN
ejpam-6737	342	23	.	.	PUNCT
ejpam-6737	343	1	the	the	DET
ejpam-6737	343	2	rise	rise	NOUN
ejpam-6737	343	3	in	in	ADP
ejpam-6737	343	4	the	the	DET
ejpam-6737	343	5	population	population	NOUN
ejpam-6737	343	6	of	of	ADP
ejpam-6737	343	7	non	non	NOUN
ejpam-6737	343	8	-	-	NOUN
ejpam-6737	343	9	users	user	NOUN
ejpam-6737	343	10	indicates	indicate	VERB
ejpam-6737	343	11	that	that	SCONJ
ejpam-6737	343	12	if	if	SCONJ
ejpam-6737	343	13	the	the	DET
ejpam-6737	343	14	right	right	ADJ
ejpam-6737	343	15	treatment	treatment	NOUN
ejpam-6737	343	16	protocols	protocol	NOUN
ejpam-6737	343	17	are	be	AUX
ejpam-6737	343	18	followed	follow	VERB
ejpam-6737	343	19	,	,	PUNCT
ejpam-6737	343	20	not	not	PART
ejpam-6737	343	21	only	only	ADV
ejpam-6737	343	22	can	can	AUX
ejpam-6737	343	23	people	people	NOUN
ejpam-6737	343	24	recover	recover	VERB
ejpam-6737	343	25	,	,	PUNCT
ejpam-6737	343	26	but	but	CCONJ
ejpam-6737	343	27	they	they	PRON
ejpam-6737	343	28	can	can	AUX
ejpam-6737	343	29	also	also	ADV
ejpam-6737	343	30	give	give	VERB
ejpam-6737	343	31	up	up	ADP
ejpam-6737	343	32	on	on	ADP
ejpam-6737	343	33	excessive	excessive	ADJ
ejpam-6737	343	34	social	social	ADJ
ejpam-6737	343	35	media	medium	NOUN
ejpam-6737	343	36	usage	usage	NOUN
ejpam-6737	343	37	entirely	entirely	ADV
ejpam-6737	343	38	.	.	PUNCT
ejpam-6737	344	1	this	this	DET
ejpam-6737	344	2	trend	trend	NOUN
ejpam-6737	344	3	points	point	VERB
ejpam-6737	344	4	towards	towards	ADP
ejpam-6737	344	5	the	the	DET
ejpam-6737	344	6	importance	importance	NOUN
ejpam-6737	344	7	of	of	ADP
ejpam-6737	344	8	awareness	awareness	NOUN
ejpam-6737	344	9	campaigns	campaign	NOUN
ejpam-6737	344	10	,	,	PUNCT
ejpam-6737	344	11	self	self	NOUN
ejpam-6737	344	12	-	-	PUNCT
ejpam-6737	344	13	regulation	regulation	NOUN
ejpam-6737	344	14	methods	method	NOUN
ejpam-6737	344	15	,	,	PUNCT
ejpam-6737	344	16	and	and	CCONJ
ejpam-6737	344	17	support	support	NOUN
ejpam-6737	344	18	mechanisms	mechanism	NOUN
ejpam-6737	344	19	in	in	ADP
ejpam-6737	344	20	minimizing	minimize	VERB
ejpam-6737	344	21	addiction	addiction	NOUN
ejpam-6737	344	22	relapse	relapse	NOUN
ejpam-6737	344	23	threats	threat	NOUN
ejpam-6737	344	24	.	.	PUNCT
ejpam-6737	345	1	in	in	ADP
ejpam-6737	345	2	addition	addition	NOUN
ejpam-6737	345	3	,	,	PUNCT
ejpam-6737	345	4	initiating	initiate	VERB
ejpam-6737	345	5	treatment	treatment	NOUN
ejpam-6737	345	6	early	early	ADJ
ejpam-6737	345	7	results	result	NOUN
ejpam-6737	345	8	strongly	strongly	ADV
ejpam-6737	345	9	in	in	ADP
ejpam-6737	345	10	enhanced	enhanced	ADJ
ejpam-6737	345	11	recovery	recovery	NOUN
ejpam-6737	345	12	rates	rate	NOUN
ejpam-6737	345	13	,	,	PUNCT
ejpam-6737	345	14	further	far	ADV
ejpam-6737	345	15	justifying	justify	VERB
ejpam-6737	345	16	the	the	DET
ejpam-6737	345	17	importance	importance	NOUN
ejpam-6737	345	18	of	of	ADP
ejpam-6737	345	19	early	early	ADJ
ejpam-6737	345	20	intervention	intervention	NOUN
ejpam-6737	345	21	programs	program	NOUN
ejpam-6737	345	22	.	.	PUNCT
ejpam-6737	346	1	figure	figure	VERB
ejpam-6737	346	2	9	9	NUM
ejpam-6737	346	3	illustrates	illustrate	VERB
ejpam-6737	346	4	the	the	DET
ejpam-6737	346	5	comparison	comparison	NOUN
ejpam-6737	346	6	between	between	ADP
ejpam-6737	346	7	integer	integer	NOUN
ejpam-6737	346	8	-	-	PUNCT
ejpam-6737	346	9	order	order	NOUN
ejpam-6737	346	10	(	(	PUNCT
ejpam-6737	346	11	η	η	X
ejpam-6737	346	12	=	=	PROPN
ejpam-6737	346	13	1	1	NUM
ejpam-6737	346	14	)	)	PUNCT
ejpam-6737	346	15	and	and	CCONJ
ejpam-6737	346	16	fractional	fractional	ADJ
ejpam-6737	346	17	-	-	PUNCT
ejpam-6737	346	18	order	order	NOUN
ejpam-6737	346	19	(	(	PUNCT
ejpam-6737	346	20	0	0	NUM
ejpam-6737	346	21	<	<	X
ejpam-6737	346	22	η	η	X
ejpam-6737	346	23	<	<	X
ejpam-6737	346	24	1	1	NUM
ejpam-6737	346	25	)	)	PUNCT
ejpam-6737	346	26	formulations	formulation	NOUN
ejpam-6737	346	27	of	of	ADP
ejpam-6737	346	28	the	the	DET
ejpam-6737	346	29	social	social	ADJ
ejpam-6737	346	30	media	medium	NOUN
ejpam-6737	346	31	addiction	addiction	NOUN
ejpam-6737	346	32	model	model	NOUN
ejpam-6737	346	33	.	.	PUNCT
ejpam-6737	347	1	the	the	DET
ejpam-6737	347	2	integer	integer	NOUN
ejpam-6737	347	3	-	-	PUNCT
ejpam-6737	347	4	order	order	NOUN
ejpam-6737	347	5	dynamics	dynamic	NOUN
ejpam-6737	347	6	show	show	VERB
ejpam-6737	347	7	sharper	sharp	ADJ
ejpam-6737	347	8	transitions	transition	NOUN
ejpam-6737	347	9	and	and	CCONJ
ejpam-6737	347	10	faster	fast	ADJ
ejpam-6737	347	11	stabilization	stabilization	NOUN
ejpam-6737	347	12	across	across	ADP
ejpam-6737	347	13	compartments	compartment	NOUN
ejpam-6737	347	14	,	,	PUNCT
ejpam-6737	347	15	reflecting	reflect	VERB
ejpam-6737	347	16	only	only	ADV
ejpam-6737	347	17	the	the	DET
ejpam-6737	347	18	present	present	ADJ
ejpam-6737	347	19	state	state	NOUN
ejpam-6737	347	20	.	.	PUNCT
ejpam-6737	348	1	in	in	ADP
ejpam-6737	348	2	contrast	contrast	NOUN
ejpam-6737	348	3	,	,	PUNCT
ejpam-6737	348	4	the	the	DET
ejpam-6737	348	5	fractional	fractional	ADJ
ejpam-6737	348	6	-	-	PUNCT
ejpam-6737	348	7	order	order	NOUN
ejpam-6737	348	8	case	case	NOUN
ejpam-6737	348	9	exhibits	exhibit	VERB
ejpam-6737	348	10	smoother	smooth	ADJ
ejpam-6737	348	11	and	and	CCONJ
ejpam-6737	348	12	slower	slow	ADJ
ejpam-6737	348	13	changes	change	NOUN
ejpam-6737	348	14	,	,	PUNCT
ejpam-6737	348	15	highlighting	highlight	VERB
ejpam-6737	348	16	the	the	DET
ejpam-6737	348	17	role	role	NOUN
ejpam-6737	348	18	of	of	ADP
ejpam-6737	348	19	memory	memory	NOUN
ejpam-6737	348	20	in	in	ADP
ejpam-6737	348	21	addiction	addiction	NOUN
ejpam-6737	348	22	and	and	CCONJ
ejpam-6737	348	23	recovery	recovery	NOUN
ejpam-6737	348	24	processes	process	NOUN
ejpam-6737	348	25	.	.	PUNCT
ejpam-6737	349	1	this	this	PRON
ejpam-6737	349	2	demonstrates	demonstrate	VERB
ejpam-6737	349	3	that	that	SCONJ
ejpam-6737	349	4	fractional	fractional	ADJ
ejpam-6737	349	5	-	-	PUNCT
ejpam-6737	349	6	order	order	NOUN
ejpam-6737	349	7	modelling	modelling	NOUN
ejpam-6737	349	8	provides	provide	VERB
ejpam-6737	349	9	a	a	DET
ejpam-6737	349	10	more	more	ADV
ejpam-6737	349	11	realistic	realistic	ADJ
ejpam-6737	349	12	description	description	NOUN
ejpam-6737	349	13	of	of	ADP
ejpam-6737	349	14	social	social	ADJ
ejpam-6737	349	15	media	medium	NOUN
ejpam-6737	349	16	addics	addic	NOUN
ejpam-6737	349	17	.	.	PUNCT
ejpam-6737	350	1	m.	m.	PROPN
ejpam-6737	350	2	chithra	chithra	PROPN
ejpam-6737	350	3	et	et	PROPN
ejpam-6737	350	4	al	al	PROPN
ejpam-6737	350	5	.	.	PUNCT
ejpam-6737	350	6	/	/	SYM
ejpam-6737	350	7	eur	eur	PROPN
ejpam-6737	350	8	.	.	PUNCT
ejpam-6737	351	1	j.	j.	PROPN
ejpam-6737	351	2	pure	pure	PROPN
ejpam-6737	351	3	appl	appl	PROPN
ejpam-6737	351	4	.	.	PROPN
ejpam-6737	351	5	math	math	PROPN
ejpam-6737	351	6	,	,	PUNCT
ejpam-6737	351	7	18	18	NUM
ejpam-6737	351	8	(	(	PUNCT
ejpam-6737	351	9	4	4	NUM
ejpam-6737	351	10	)	)	PUNCT
ejpam-6737	351	11	(	(	PUNCT
ejpam-6737	351	12	2025	2025	NUM
ejpam-6737	351	13	)	)	PUNCT
ejpam-6737	351	14	,	,	PUNCT
ejpam-6737	351	15	6737	6737	NUM
ejpam-6737	351	16	18	18	NUM
ejpam-6737	351	17	of	of	ADP
ejpam-6737	351	18	23	23	NUM
ejpam-6737	351	19	figure	figure	NOUN
ejpam-6737	351	20	4	4	NUM
ejpam-6737	351	21	:	:	PUNCT
ejpam-6737	351	22	simulation	simulation	NOUN
ejpam-6737	351	23	of	of	ADP
ejpam-6737	351	24	population	population	NOUN
ejpam-6737	351	25	under	under	ADP
ejpam-6737	351	26	different	different	ADJ
ejpam-6737	351	27	fractional	fractional	ADJ
ejpam-6737	351	28	orders	order	NOUN
ejpam-6737	351	29	for	for	ADP
ejpam-6737	351	30	mildly	mildly	ADV
ejpam-6737	351	31	addicted	addict	VERB
ejpam-6737	351	32	figure	figure	NOUN
ejpam-6737	351	33	5	5	NUM
ejpam-6737	351	34	:	:	PUNCT
ejpam-6737	351	35	simulation	simulation	NOUN
ejpam-6737	351	36	of	of	ADP
ejpam-6737	351	37	population	population	NOUN
ejpam-6737	351	38	under	under	ADP
ejpam-6737	351	39	different	different	ADJ
ejpam-6737	351	40	fractional	fractional	ADJ
ejpam-6737	351	41	orders	order	NOUN
ejpam-6737	351	42	for	for	ADP
ejpam-6737	351	43	mildly	mildly	ADV
ejpam-6737	351	44	addicted	addict	VERB
ejpam-6737	351	45	tion	tion	NOUN
ejpam-6737	351	46	dynamics	dynamic	NOUN
ejpam-6737	351	47	than	than	ADP
ejpam-6737	351	48	the	the	DET
ejpam-6737	351	49	classical	classical	ADJ
ejpam-6737	351	50	integer	integer	NOUN
ejpam-6737	351	51	-	-	PUNCT
ejpam-6737	351	52	order	order	NOUN
ejpam-6737	351	53	model	model	NOUN
ejpam-6737	351	54	.	.	PUNCT
ejpam-6737	352	1	generally	generally	ADV
ejpam-6737	352	2	,	,	PUNCT
ejpam-6737	352	3	these	these	PRON
ejpam-6737	352	4	results	result	NOUN
ejpam-6737	352	5	affirm	affirm	VERB
ejpam-6737	352	6	that	that	SCONJ
ejpam-6737	352	7	psychological	psychological	ADJ
ejpam-6737	352	8	interventions	intervention	NOUN
ejpam-6737	352	9	combined	combine	VERB
ejpam-6737	352	10	with	with	ADP
ejpam-6737	352	11	fractionalorder	fractionalorder	NOUN
ejpam-6737	352	12	modelling	modelling	NOUN
ejpam-6737	352	13	offer	offer	VERB
ejpam-6737	352	14	a	a	DET
ejpam-6737	352	15	robust	robust	ADJ
ejpam-6737	352	16	model	model	NOUN
ejpam-6737	352	17	for	for	ADP
ejpam-6737	352	18	grasping	grasp	VERB
ejpam-6737	352	19	and	and	CCONJ
ejpam-6737	352	20	counteracting	counteract	VERB
ejpam-6737	352	21	social	social	ADJ
ejpam-6737	352	22	media	medium	NOUN
ejpam-6737	352	23	addiction	addiction	NOUN
ejpam-6737	352	24	.	.	PUNCT
ejpam-6737	353	1	the	the	DET
ejpam-6737	353	2	findings	finding	NOUN
ejpam-6737	353	3	highlight	highlight	VERB
ejpam-6737	353	4	that	that	SCONJ
ejpam-6737	353	5	early	early	ADJ
ejpam-6737	353	6	intervention	intervention	NOUN
ejpam-6737	353	7	,	,	PUNCT
ejpam-6737	353	8	organized	organize	VERB
ejpam-6737	353	9	treatment	treatment	NOUN
ejpam-6737	353	10	programs	program	NOUN
ejpam-6737	353	11	,	,	PUNCT
ejpam-6737	353	12	and	and	CCONJ
ejpam-6737	353	13	social	social	ADJ
ejpam-6737	353	14	campaigns	campaign	NOUN
ejpam-6737	353	15	are	be	AUX
ejpam-6737	353	16	the	the	DET
ejpam-6737	353	17	most	most	ADV
ejpam-6737	353	18	important	important	ADJ
ejpam-6737	353	19	elements	element	NOUN
ejpam-6737	353	20	in	in	ADP
ejpam-6737	353	21	combating	combat	VERB
ejpam-6737	353	22	and	and	CCONJ
ejpam-6737	353	23	managing	manage	VERB
ejpam-6737	353	24	addiction	addiction	NOUN
ejpam-6737	353	25	dynamics	dynamic	NOUN
ejpam-6737	353	26	.	.	PUNCT
ejpam-6737	354	1	8	8	X
ejpam-6737	354	2	.	.	PUNCT
ejpam-6737	354	3	conclusions	conclusion	NOUN
ejpam-6737	354	4	social	social	ADJ
ejpam-6737	354	5	media	medium	NOUN
ejpam-6737	354	6	addiction	addiction	NOUN
ejpam-6737	354	7	has	have	VERB
ejpam-6737	354	8	a	a	DET
ejpam-6737	354	9	strong	strong	ADJ
ejpam-6737	354	10	impact	impact	NOUN
ejpam-6737	354	11	on	on	ADP
ejpam-6737	354	12	mental	mental	ADJ
ejpam-6737	354	13	well	well	ADV
ejpam-6737	354	14	-	-	PUNCT
ejpam-6737	354	15	being	being	NOUN
ejpam-6737	354	16	,	,	PUNCT
ejpam-6737	354	17	interpersonal	interpersonal	ADJ
ejpam-6737	354	18	relationships	relationship	NOUN
ejpam-6737	354	19	,	,	PUNCT
ejpam-6737	354	20	and	and	CCONJ
ejpam-6737	354	21	productivity	productivity	NOUN
ejpam-6737	354	22	and	and	CCONJ
ejpam-6737	354	23	as	as	ADP
ejpam-6737	354	24	such	such	ADJ
ejpam-6737	354	25	,	,	PUNCT
ejpam-6737	354	26	it	it	PRON
ejpam-6737	354	27	is	be	AUX
ejpam-6737	354	28	crucial	crucial	ADJ
ejpam-6737	354	29	to	to	PART
ejpam-6737	354	30	model	model	VERB
ejpam-6737	354	31	its	its	PRON
ejpam-6737	354	32	dynamics	dynamic	NOUN
ejpam-6737	354	33	for	for	ADP
ejpam-6737	354	34	efficient	efficient	ADJ
ejpam-6737	354	35	intervention	intervention	NOUN
ejpam-6737	354	36	.	.	PUNCT
ejpam-6737	355	1	this	this	DET
ejpam-6737	355	2	research	research	NOUN
ejpam-6737	355	3	utilizes	utilize	VERB
ejpam-6737	355	4	a	a	DET
ejpam-6737	355	5	fractional	fractional	ADJ
ejpam-6737	355	6	mathematical	mathematical	ADJ
ejpam-6737	355	7	model	model	NOUN
ejpam-6737	355	8	based	base	VERB
ejpam-6737	355	9	on	on	ADP
ejpam-6737	355	10	the	the	DET
ejpam-6737	355	11	fractals	fractal	NOUN
ejpam-6737	355	12	.	.	PUNCT
ejpam-6737	356	1	m.	m.	PROPN
ejpam-6737	356	2	chithra	chithra	PROPN
ejpam-6737	356	3	et	et	PROPN
ejpam-6737	356	4	al	al	PROPN
ejpam-6737	356	5	.	.	PUNCT
ejpam-6737	356	6	/	/	SYM
ejpam-6737	356	7	eur	eur	PROPN
ejpam-6737	356	8	.	.	PUNCT
ejpam-6737	357	1	j.	j.	PROPN
ejpam-6737	357	2	pure	pure	PROPN
ejpam-6737	357	3	appl	appl	PROPN
ejpam-6737	357	4	.	.	PROPN
ejpam-6737	357	5	math	math	PROPN
ejpam-6737	357	6	,	,	PUNCT
ejpam-6737	357	7	18	18	NUM
ejpam-6737	357	8	(	(	PUNCT
ejpam-6737	357	9	4	4	NUM
ejpam-6737	357	10	)	)	PUNCT
ejpam-6737	357	11	(	(	PUNCT
ejpam-6737	357	12	2025	2025	NUM
ejpam-6737	357	13	)	)	PUNCT
ejpam-6737	357	14	,	,	PUNCT
ejpam-6737	357	15	6737	6737	NUM
ejpam-6737	357	16	19	19	NUM
ejpam-6737	357	17	of	of	ADP
ejpam-6737	357	18	23	23	NUM
ejpam-6737	357	19	figure	figure	NOUN
ejpam-6737	357	20	6	6	NUM
ejpam-6737	357	21	:	:	PUNCT
ejpam-6737	357	22	simulation	simulation	NOUN
ejpam-6737	357	23	of	of	ADP
ejpam-6737	357	24	population	population	NOUN
ejpam-6737	357	25	under	under	ADP
ejpam-6737	357	26	different	different	ADJ
ejpam-6737	357	27	fractional	fractional	ADJ
ejpam-6737	357	28	orders	order	NOUN
ejpam-6737	357	29	for	for	ADP
ejpam-6737	357	30	psychological	psychological	ADJ
ejpam-6737	357	31	treatment	treatment	NOUN
ejpam-6737	357	32	figure	figure	NOUN
ejpam-6737	357	33	7	7	NUM
ejpam-6737	357	34	:	:	PUNCT
ejpam-6737	357	35	simulation	simulation	NOUN
ejpam-6737	357	36	of	of	ADP
ejpam-6737	357	37	population	population	NOUN
ejpam-6737	357	38	under	under	ADP
ejpam-6737	357	39	different	different	ADJ
ejpam-6737	357	40	fractional	fractional	ADJ
ejpam-6737	357	41	orders	order	NOUN
ejpam-6737	357	42	for	for	ADP
ejpam-6737	357	43	mildly	mildly	ADV
ejpam-6737	357	44	recovered	recover	VERB
ejpam-6737	357	45	fractional	fractional	ADJ
ejpam-6737	357	46	operator	operator	NOUN
ejpam-6737	357	47	and	and	CCONJ
ejpam-6737	357	48	mittag	mittag	ADJ
ejpam-6737	357	49	-	-	PUNCT
ejpam-6737	357	50	leffler	leffler	NOUN
ejpam-6737	357	51	kernel	kernel	NOUN
ejpam-6737	357	52	to	to	PART
ejpam-6737	357	53	study	study	VERB
ejpam-6737	357	54	the	the	DET
ejpam-6737	357	55	evolution	evolution	NOUN
ejpam-6737	357	56	of	of	ADP
ejpam-6737	357	57	addiction	addiction	NOUN
ejpam-6737	357	58	and	and	CCONJ
ejpam-6737	357	59	recovery	recovery	NOUN
ejpam-6737	357	60	.	.	PUNCT
ejpam-6737	358	1	by	by	ADP
ejpam-6737	358	2	dividing	divide	VERB
ejpam-6737	358	3	users	user	NOUN
ejpam-6737	358	4	into	into	ADP
ejpam-6737	358	5	general	general	ADJ
ejpam-6737	358	6	,	,	PUNCT
ejpam-6737	358	7	mildly	mildly	ADV
ejpam-6737	358	8	addicted	addicted	ADJ
ejpam-6737	358	9	,	,	PUNCT
ejpam-6737	358	10	and	and	CCONJ
ejpam-6737	358	11	heavily	heavily	ADV
ejpam-6737	358	12	addicted	addicted	ADJ
ejpam-6737	358	13	classes	class	NOUN
ejpam-6737	358	14	,	,	PUNCT
ejpam-6737	358	15	the	the	DET
ejpam-6737	358	16	model	model	NOUN
ejpam-6737	358	17	successfully	successfully	ADV
ejpam-6737	358	18	exhibits	exhibit	VERB
ejpam-6737	358	19	how	how	SCONJ
ejpam-6737	358	20	psychological	psychological	ADJ
ejpam-6737	358	21	treatment	treatment	NOUN
ejpam-6737	358	22	decreases	decrease	VERB
ejpam-6737	358	23	the	the	DET
ejpam-6737	358	24	severity	severity	NOUN
ejpam-6737	358	25	of	of	ADP
ejpam-6737	358	26	addiction	addiction	NOUN
ejpam-6737	358	27	.	.	PUNCT
ejpam-6737	359	1	the	the	DET
ejpam-6737	359	2	model	model	NOUN
ejpam-6737	359	3	’s	’s	PART
ejpam-6737	359	4	reliability	reliability	NOUN
ejpam-6737	359	5	is	be	AUX
ejpam-6737	359	6	guaranteed	guarantee	VERB
ejpam-6737	359	7	by	by	ADP
ejpam-6737	359	8	fixed	fix	VERB
ejpam-6737	359	9	-	-	PUNCT
ejpam-6737	359	10	point	point	NOUN
ejpam-6737	359	11	theory	theory	NOUN
ejpam-6737	359	12	and	and	CCONJ
ejpam-6737	359	13	ulam	ulam	NOUN
ejpam-6737	359	14	–	–	PUNCT
ejpam-6737	359	15	hyers	hyer	NOUN
ejpam-6737	359	16	stability	stability	NOUN
ejpam-6737	359	17	,	,	PUNCT
ejpam-6737	359	18	ensuring	ensure	VERB
ejpam-6737	359	19	its	its	PRON
ejpam-6737	359	20	validity	validity	NOUN
ejpam-6737	359	21	for	for	ADP
ejpam-6737	359	22	practical	practical	ADJ
ejpam-6737	359	23	applications	application	NOUN
ejpam-6737	359	24	.	.	PUNCT
ejpam-6737	360	1	numerical	numerical	ADJ
ejpam-6737	360	2	analysis	analysis	NOUN
ejpam-6737	360	3	brings	bring	VERB
ejpam-6737	360	4	out	out	ADP
ejpam-6737	360	5	the	the	DET
ejpam-6737	360	6	memory	memory	NOUN
ejpam-6737	360	7	-	-	PUNCT
ejpam-6737	360	8	dependent	dependent	ADJ
ejpam-6737	360	9	character	character	NOUN
ejpam-6737	360	10	of	of	ADP
ejpam-6737	360	11	addiction	addiction	NOUN
ejpam-6737	360	12	and	and	CCONJ
ejpam-6737	360	13	offers	offer	VERB
ejpam-6737	360	14	a	a	DET
ejpam-6737	360	15	versatile	versatile	ADJ
ejpam-6737	360	16	,	,	PUNCT
ejpam-6737	360	17	accurate	accurate	ADJ
ejpam-6737	360	18	framework	framework	NOUN
ejpam-6737	360	19	for	for	ADP
ejpam-6737	360	20	explaining	explain	VERB
ejpam-6737	360	21	long	long	ADJ
ejpam-6737	360	22	-	-	PUNCT
ejpam-6737	360	23	term	term	NOUN
ejpam-6737	360	24	patterns	pattern	NOUN
ejpam-6737	360	25	of	of	ADP
ejpam-6737	360	26	behaviour	behaviour	NOUN
ejpam-6737	360	27	.	.	PUNCT
ejpam-6737	361	1	this	this	DET
ejpam-6737	361	2	method	method	NOUN
ejpam-6737	361	3	increases	increase	VERB
ejpam-6737	361	4	predictive	predictive	ADJ
ejpam-6737	361	5	power	power	NOUN
ejpam-6737	361	6	,	,	PUNCT
ejpam-6737	361	7	enabling	enable	VERB
ejpam-6737	361	8	improved	improved	ADJ
ejpam-6737	361	9	strategies	strategy	NOUN
ejpam-6737	361	10	for	for	ADP
ejpam-6737	361	11	intervention	intervention	NOUN
ejpam-6737	361	12	.	.	PUNCT
ejpam-6737	362	1	the	the	DET
ejpam-6737	362	2	implications	implication	NOUN
ejpam-6737	362	3	conclude	conclude	VERB
ejpam-6737	362	4	that	that	SCONJ
ejpam-6737	362	5	early	early	ADJ
ejpam-6737	362	6	intervention	intervention	NOUN
ejpam-6737	362	7	and	and	CCONJ
ejpam-6737	362	8	structured	structured	ADJ
ejpam-6737	362	9	rehabilitation	rehabilitation	NOUN
ejpam-6737	362	10	programs	program	NOUN
ejpam-6737	362	11	are	be	AUX
ejpam-6737	362	12	significantly	significantly	ADV
ejpam-6737	362	13	important	important	ADJ
ejpam-6737	362	14	in	in	ADP
ejpam-6737	362	15	minimizing	minimize	VERB
ejpam-6737	362	16	addiction	addiction	NOUN
ejpam-6737	362	17	relapse	relapse	NOUN
ejpam-6737	362	18	and	and	CCONJ
ejpam-6737	362	19	enhancing	enhance	VERB
ejpam-6737	362	20	recovery	recovery	NOUN
ejpam-6737	362	21	levels.future	levels.future	NOUN
ejpam-6737	362	22	research	research	NOUN
ejpam-6737	362	23	will	will	AUX
ejpam-6737	362	24	investigate	investigate	VERB
ejpam-6737	362	25	the	the	DET
ejpam-6737	362	26	effect	effect	NOUN
ejpam-6737	362	27	of	of	ADP
ejpam-6737	362	28	social	social	ADJ
ejpam-6737	362	29	habits	habit	NOUN
ejpam-6737	362	30	,	,	PUNCT
ejpam-6737	362	31	digital	digital	ADJ
ejpam-6737	362	32	detox	detox	NOUN
ejpam-6737	362	33	methods	method	NOUN
ejpam-6737	362	34	,	,	PUNCT
ejpam-6737	362	35	and	and	CCONJ
ejpam-6737	362	36	ai	ai	AUX
ejpam-6737	362	37	-	-	PUNCT
ejpam-6737	362	38	driven	drive	VERB
ejpam-6737	362	39	predictions	prediction	NOUN
ejpam-6737	362	40	to	to	PART
ejpam-6737	362	41	develop	develop	VERB
ejpam-6737	362	42	more	more	ADV
ejpam-6737	362	43	effective	effective	ADJ
ejpam-6737	362	44	intervention	intervention	NOUN
ejpam-6737	362	45	strategies	strategy	NOUN
ejpam-6737	362	46	.	.	PUNCT
ejpam-6737	363	1	the	the	DET
ejpam-6737	363	2	social	social	ADJ
ejpam-6737	363	3	implication	implication	NOUN
ejpam-6737	363	4	of	of	ADP
ejpam-6737	363	5	this	this	DET
ejpam-6737	363	6	study	study	NOUN
ejpam-6737	363	7	is	be	AUX
ejpam-6737	363	8	in	in	ADP
ejpam-6737	363	9	informing	inform	VERB
ejpam-6737	363	10	digital	digital	ADJ
ejpam-6737	363	11	wellness	wellness	NOUN
ejpam-6737	363	12	policies	policy	NOUN
ejpam-6737	363	13	and	and	CCONJ
ejpam-6737	363	14	rehabilitation	rehabilitation	NOUN
ejpam-6737	363	15	interventions	intervention	NOUN
ejpam-6737	363	16	,	,	PUNCT
ejpam-6737	364	1	ultimately	ultimately	ADV
ejpam-6737	364	2	s.	s.	PROPN
ejpam-6737	364	3	m.	m.	PROPN
ejpam-6737	364	4	chithra	chithra	PROPN
ejpam-6737	364	5	et	et	PROPN
ejpam-6737	364	6	al	al	PROPN
ejpam-6737	364	7	.	.	PUNCT
ejpam-6737	364	8	/	/	SYM
ejpam-6737	364	9	eur	eur	PROPN
ejpam-6737	364	10	.	.	PUNCT
ejpam-6737	365	1	j.	j.	PROPN
ejpam-6737	365	2	pure	pure	PROPN
ejpam-6737	365	3	appl	appl	PROPN
ejpam-6737	365	4	.	.	PROPN
ejpam-6737	365	5	math	math	PROPN
ejpam-6737	365	6	,	,	PUNCT
ejpam-6737	365	7	18	18	NUM
ejpam-6737	365	8	(	(	PUNCT
ejpam-6737	365	9	4	4	NUM
ejpam-6737	365	10	)	)	PUNCT
ejpam-6737	365	11	(	(	PUNCT
ejpam-6737	365	12	2025	2025	NUM
ejpam-6737	365	13	)	)	PUNCT
ejpam-6737	365	14	,	,	PUNCT
ejpam-6737	365	15	6737	6737	NUM
ejpam-6737	365	16	20	20	NUM
ejpam-6737	365	17	of	of	ADP
ejpam-6737	365	18	23	23	NUM
ejpam-6737	365	19	figure	figure	NOUN
ejpam-6737	365	20	8	8	NUM
ejpam-6737	365	21	:	:	PUNCT
ejpam-6737	365	22	simulation	simulation	NOUN
ejpam-6737	365	23	of	of	ADP
ejpam-6737	365	24	population	population	NOUN
ejpam-6737	365	25	under	under	ADP
ejpam-6737	365	26	different	different	ADJ
ejpam-6737	365	27	fractional	fractional	ADJ
ejpam-6737	365	28	orders	order	NOUN
ejpam-6737	365	29	for	for	ADP
ejpam-6737	365	30	non	non	ADJ
ejpam-6737	365	31	-	-	ADJ
ejpam-6737	365	32	users	user	NOUN
ejpam-6737	365	33	figure	figure	NOUN
ejpam-6737	365	34	9	9	NUM
ejpam-6737	365	35	:	:	PUNCT
ejpam-6737	365	36	comparison	comparison	NOUN
ejpam-6737	365	37	of	of	ADP
ejpam-6737	365	38	integer	integer	NOUN
ejpam-6737	365	39	-	-	PUNCT
ejpam-6737	365	40	order	order	NOUN
ejpam-6737	365	41	(	(	PUNCT
ejpam-6737	365	42	η	η	X
ejpam-6737	365	43	=	=	PROPN
ejpam-6737	365	44	1	1	NUM
ejpam-6737	365	45	)	)	PUNCT
ejpam-6737	365	46	and	and	CCONJ
ejpam-6737	365	47	fractional	fractional	ADJ
ejpam-6737	365	48	-	-	PUNCT
ejpam-6737	365	49	order	order	NOUN
ejpam-6737	365	50	(	(	PUNCT
ejpam-6737	365	51	0	0	NUM
ejpam-6737	365	52	<	<	X
ejpam-6737	365	53	η	η	X
ejpam-6737	365	54	<	<	X
ejpam-6737	365	55	1	1	NUM
ejpam-6737	365	56	)	)	PUNCT
ejpam-6737	365	57	trajectories	trajectory	NOUN
ejpam-6737	365	58	in	in	ADP
ejpam-6737	365	59	the	the	DET
ejpam-6737	365	60	social	social	ADJ
ejpam-6737	365	61	media	medium	NOUN
ejpam-6737	365	62	addiction	addiction	NOUN
ejpam-6737	365	63	model	model	NOUN
ejpam-6737	365	64	,	,	PUNCT
ejpam-6737	365	65	showing	show	VERB
ejpam-6737	365	66	the	the	DET
ejpam-6737	365	67	impact	impact	NOUN
ejpam-6737	365	68	of	of	ADP
ejpam-6737	365	69	memory	memory	NOUN
ejpam-6737	365	70	effects	effect	NOUN
ejpam-6737	365	71	on	on	ADP
ejpam-6737	365	72	addiction	addiction	NOUN
ejpam-6737	365	73	and	and	CCONJ
ejpam-6737	365	74	recovery	recovery	NOUN
ejpam-6737	365	75	dynamics	dynamic	NOUN
ejpam-6737	365	76	leading	lead	VERB
ejpam-6737	365	77	to	to	ADP
ejpam-6737	365	78	healthier	healthy	ADJ
ejpam-6737	365	79	web	web	NOUN
ejpam-6737	365	80	use	use	NOUN
ejpam-6737	365	81	behaviours	behaviour	NOUN
ejpam-6737	365	82	and	and	CCONJ
ejpam-6737	365	83	better	well	ADJ
ejpam-6737	365	84	mental	mental	ADJ
ejpam-6737	365	85	health	health	NOUN
ejpam-6737	365	86	in	in	ADP
ejpam-6737	365	87	the	the	DET
ejpam-6737	365	88	digital	digital	ADJ
ejpam-6737	365	89	age	age	NOUN
ejpam-6737	365	90	.	.	PUNCT
ejpam-6737	366	1	funding	fund	VERB
ejpam-6737	366	2	this	this	DET
ejpam-6737	366	3	research	research	NOUN
ejpam-6737	366	4	was	be	AUX
ejpam-6737	366	5	supported	support	VERB
ejpam-6737	366	6	by	by	ADP
ejpam-6737	366	7	university	university	NOUN
ejpam-6737	366	8	of	of	ADP
ejpam-6737	366	9	phayao	phayao	NOUN
ejpam-6737	366	10	and	and	CCONJ
ejpam-6737	366	11	thailand	thailand	PROPN
ejpam-6737	366	12	science	science	PROPN
ejpam-6737	366	13	research	research	PROPN
ejpam-6737	366	14	and	and	CCONJ
ejpam-6737	366	15	innovation	innovation	NOUN
ejpam-6737	366	16	fund	fund	NOUN
ejpam-6737	366	17	(	(	PUNCT
ejpam-6737	366	18	fundamental	fundamental	ADJ
ejpam-6737	366	19	fund	fund	NOUN
ejpam-6737	366	20	2026	2026	NUM
ejpam-6737	366	21	,	,	PUNCT
ejpam-6737	366	22	grant	grant	VERB
ejpam-6737	366	23	no.xxxx/2568	no.xxxx/2568	ADV
ejpam-6737	366	24	)	)	PUNCT
ejpam-6737	366	25	.	.	PUNCT
ejpam-6737	367	1	author	author	NOUN
ejpam-6737	367	2	contributions	contribution	NOUN
ejpam-6737	367	3	:	:	PUNCT
ejpam-6737	367	4	the	the	DET
ejpam-6737	367	5	authors	author	NOUN
ejpam-6737	367	6	equally	equally	ADV
ejpam-6737	367	7	conceived	conceive	VERB
ejpam-6737	367	8	of	of	ADP
ejpam-6737	367	9	the	the	DET
ejpam-6737	367	10	study	study	NOUN
ejpam-6737	367	11	,	,	PUNCT
ejpam-6737	367	12	participated	participate	VERB
ejpam-6737	367	13	in	in	ADP
ejpam-6737	367	14	its	its	PRON
ejpam-6737	367	15	design	design	NOUN
ejpam-6737	367	16	and	and	CCONJ
ejpam-6737	367	17	coordination	coordination	NOUN
ejpam-6737	367	18	,	,	PUNCT
ejpam-6737	367	19	drafted	draft	VERB
ejpam-6737	367	20	the	the	DET
ejpam-6737	367	21	manuscript	manuscript	NOUN
ejpam-6737	367	22	,	,	PUNCT
ejpam-6737	367	23	participated	participate	VERB
ejpam-6737	367	24	in	in	ADP
ejpam-6737	367	25	the	the	DET
ejpam-6737	367	26	sequence	sequence	NOUN
ejpam-6737	367	27	alignment	alignment	NOUN
ejpam-6737	367	28	,	,	PUNCT
ejpam-6737	367	29	and	and	CCONJ
ejpam-6737	367	30	read	read	VERB
ejpam-6737	367	31	and	and	CCONJ
ejpam-6737	367	32	approved	approve	VERB
ejpam-6737	367	33	the	the	DET
ejpam-6737	367	34	final	final	ADJ
ejpam-6737	367	35	manuscript	manuscript	NOUN
ejpam-6737	367	36	.	.	PUNCT
ejpam-6737	368	1	conflicts	conflict	NOUN
ejpam-6737	368	2	of	of	ADP
ejpam-6737	368	3	interest	interest	NOUN
ejpam-6737	368	4	:	:	PUNCT
ejpam-6737	368	5	the	the	DET
ejpam-6737	368	6	authors	author	NOUN
ejpam-6737	368	7	declare	declare	VERB
ejpam-6737	368	8	that	that	SCONJ
ejpam-6737	368	9	they	they	PRON
ejpam-6737	368	10	have	have	VERB
ejpam-6737	368	11	no	no	DET
ejpam-6737	368	12	competing	compete	VERB
ejpam-6737	368	13	interests	interest	NOUN
ejpam-6737	368	14	.	.	PUNCT
ejpam-6737	369	1	s.	s.	PROPN
ejpam-6737	369	2	m.	m.	PROPN
ejpam-6737	369	3	chithra	chithra	PROPN
ejpam-6737	369	4	et	et	PROPN
ejpam-6737	369	5	al	al	PROPN
ejpam-6737	369	6	.	.	PUNCT
ejpam-6737	369	7	/	/	SYM
ejpam-6737	369	8	eur	eur	PROPN
ejpam-6737	369	9	.	.	PUNCT
ejpam-6737	370	1	j.	j.	PROPN
ejpam-6737	370	2	pure	pure	PROPN
ejpam-6737	370	3	appl	appl	PROPN
ejpam-6737	370	4	.	.	PROPN
ejpam-6737	370	5	math	math	PROPN
ejpam-6737	370	6	,	,	PUNCT
ejpam-6737	370	7	18	18	NUM
ejpam-6737	370	8	(	(	PUNCT
ejpam-6737	370	9	4	4	NUM
ejpam-6737	370	10	)	)	PUNCT
ejpam-6737	370	11	(	(	PUNCT
ejpam-6737	370	12	2025	2025	NUM
ejpam-6737	370	13	)	)	PUNCT
ejpam-6737	370	14	,	,	PUNCT
ejpam-6737	370	15	6737	6737	NUM
ejpam-6737	370	16	21	21	NUM
ejpam-6737	370	17	of	of	ADP
ejpam-6737	370	18	23	23	NUM
ejpam-6737	370	19	references	reference	NOUN
ejpam-6737	370	20	[	[	X
ejpam-6737	370	21	1	1	NUM
ejpam-6737	370	22	]	]	PUNCT
ejpam-6737	370	23	martina	martina	PROPN
ejpam-6737	370	24	drahošová	drahošová	PROPN
ejpam-6737	370	25	and	and	CCONJ
ejpam-6737	370	26	peter	peter	PROPN
ejpam-6737	370	27	balco	balco	PROPN
ejpam-6737	370	28	.	.	PUNCT
ejpam-6737	371	1	the	the	DET
ejpam-6737	371	2	analysis	analysis	NOUN
ejpam-6737	371	3	of	of	ADP
ejpam-6737	371	4	advantages	advantage	NOUN
ejpam-6737	371	5	and	and	CCONJ
ejpam-6737	371	6	disadvantages	disadvantage	NOUN
ejpam-6737	371	7	of	of	ADP
ejpam-6737	371	8	use	use	NOUN
ejpam-6737	371	9	of	of	ADP
ejpam-6737	371	10	social	social	ADJ
ejpam-6737	371	11	media	medium	NOUN
ejpam-6737	371	12	in	in	ADP
ejpam-6737	371	13	european	european	PROPN
ejpam-6737	371	14	union	union	PROPN
ejpam-6737	371	15	.	.	PUNCT
ejpam-6737	372	1	procedia	procedia	PROPN
ejpam-6737	372	2	computer	computer	NOUN
ejpam-6737	372	3	science	science	NOUN
ejpam-6737	372	4	,	,	PUNCT
ejpam-6737	372	5	109:1005–1009	109:1005–1009	NUM
ejpam-6737	372	6	,	,	PUNCT
ejpam-6737	372	7	2017	2017	NUM
ejpam-6737	372	8	.	.	PUNCT
ejpam-6737	373	1	[	[	X
ejpam-6737	373	2	2	2	NUM
ejpam-6737	373	3	]	]	X
ejpam-6737	373	4	rdouan	rdouan	PROPN
ejpam-6737	373	5	faizi	faizi	PROPN
ejpam-6737	373	6	,	,	PUNCT
ejpam-6737	373	7	abdellatif	abdellatif	NOUN
ejpam-6737	373	8	el	el	PROPN
ejpam-6737	373	9	afia	afia	PROPN
ejpam-6737	373	10	,	,	PUNCT
ejpam-6737	373	11	and	and	CCONJ
ejpam-6737	373	12	raddouane	raddouane	PROPN
ejpam-6737	373	13	chiheb	chiheb	NOUN
ejpam-6737	373	14	.	.	PUNCT
ejpam-6737	374	1	exploring	explore	VERB
ejpam-6737	374	2	the	the	DET
ejpam-6737	374	3	potential	potential	ADJ
ejpam-6737	374	4	benefits	benefit	NOUN
ejpam-6737	374	5	of	of	ADP
ejpam-6737	374	6	using	use	VERB
ejpam-6737	374	7	social	social	ADJ
ejpam-6737	374	8	media	medium	NOUN
ejpam-6737	374	9	in	in	ADP
ejpam-6737	374	10	education	education	NOUN
ejpam-6737	374	11	.	.	PUNCT
ejpam-6737	375	1	international	international	ADJ
ejpam-6737	375	2	journal	journal	NOUN
ejpam-6737	375	3	of	of	ADP
ejpam-6737	375	4	engineering	engineering	NOUN
ejpam-6737	375	5	pedagogy	pedagogy	NOUN
ejpam-6737	375	6	(	(	PUNCT
ejpam-6737	375	7	ijep	ijep	PROPN
ejpam-6737	375	8	)	)	PUNCT
ejpam-6737	375	9	,	,	PUNCT
ejpam-6737	375	10	3(4):50–53	3(4):50–53	NUM
ejpam-6737	375	11	,	,	PUNCT
ejpam-6737	375	12	2013	2013	NUM
ejpam-6737	375	13	.	.	PUNCT
ejpam-6737	376	1	[	[	X
ejpam-6737	376	2	3	3	X
ejpam-6737	376	3	]	]	X
ejpam-6737	376	4	dana	dana	PROPN
ejpam-6737	376	5	howard	howard	PROPN
ejpam-6737	376	6	,	,	PUNCT
ejpam-6737	376	7	w	w	PROPN
ejpam-6737	376	8	glynn	glynn	PROPN
ejpam-6737	376	9	mangold	mangold	PROPN
ejpam-6737	376	10	,	,	PUNCT
ejpam-6737	376	11	and	and	CCONJ
ejpam-6737	376	12	tim	tim	PROPN
ejpam-6737	376	13	johnston	johnston	PROPN
ejpam-6737	376	14	.	.	PUNCT
ejpam-6737	377	1	managing	manage	VERB
ejpam-6737	377	2	your	your	PRON
ejpam-6737	377	3	social	social	ADJ
ejpam-6737	377	4	campaign	campaign	NOUN
ejpam-6737	377	5	strategy	strategy	NOUN
ejpam-6737	377	6	using	use	VERB
ejpam-6737	377	7	facebook	facebook	PROPN
ejpam-6737	377	8	,	,	PUNCT
ejpam-6737	377	9	twitter	twitter	NOUN
ejpam-6737	377	10	,	,	PUNCT
ejpam-6737	377	11	instagram	instagram	PROPN
ejpam-6737	377	12	,	,	PUNCT
ejpam-6737	377	13	youtube	youtube	NOUN
ejpam-6737	377	14	&	&	CCONJ
ejpam-6737	377	15	pinterest	pinter	ADJ
ejpam-6737	377	16	:	:	PUNCT
ejpam-6737	377	17	an	an	DET
ejpam-6737	377	18	interview	interview	NOUN
ejpam-6737	377	19	with	with	ADP
ejpam-6737	377	20	dana	dana	PROPN
ejpam-6737	377	21	howard	howard	PROPN
ejpam-6737	377	22	,	,	PUNCT
ejpam-6737	377	23	social	social	ADJ
ejpam-6737	377	24	media	media	NOUN
ejpam-6737	377	25	marketing	marketing	NOUN
ejpam-6737	377	26	manager	manager	NOUN
ejpam-6737	377	27	.	.	PUNCT
ejpam-6737	378	1	business	business	NOUN
ejpam-6737	378	2	horizons	horizon	NOUN
ejpam-6737	378	3	,	,	PUNCT
ejpam-6737	378	4	5(57):657–665	5(57):657–665	NUM
ejpam-6737	378	5	,	,	PUNCT
ejpam-6737	378	6	2014	2014	NUM
ejpam-6737	378	7	.	.	PUNCT
ejpam-6737	379	1	[	[	X
ejpam-6737	379	2	4	4	X
ejpam-6737	379	3	]	]	X
ejpam-6737	379	4	linah	linah	PROPN
ejpam-6737	379	5	aburahmah	aburahmah	PROPN
ejpam-6737	379	6	,	,	PUNCT
ejpam-6737	379	7	hajar	hajar	PROPN
ejpam-6737	379	8	alrawi	alrawi	PROPN
ejpam-6737	379	9	,	,	PUNCT
ejpam-6737	379	10	yamamah	yamamah	NOUN
ejpam-6737	379	11	izz	izz	NOUN
ejpam-6737	379	12	,	,	PUNCT
ejpam-6737	379	13	and	and	CCONJ
ejpam-6737	379	14	liyakathunisa	liyakathunisa	NOUN
ejpam-6737	379	15	syed	sye	VERB
ejpam-6737	379	16	.	.	PUNCT
ejpam-6737	380	1	online	online	ADJ
ejpam-6737	380	2	social	social	ADJ
ejpam-6737	380	3	gaming	gaming	NOUN
ejpam-6737	380	4	and	and	CCONJ
ejpam-6737	380	5	social	social	ADJ
ejpam-6737	380	6	networking	networking	NOUN
ejpam-6737	380	7	sites	site	NOUN
ejpam-6737	380	8	.	.	PUNCT
ejpam-6737	381	1	procedia	procedia	NOUN
ejpam-6737	381	2	computer	computer	NOUN
ejpam-6737	381	3	science	science	NOUN
ejpam-6737	381	4	,	,	PUNCT
ejpam-6737	381	5	82:72–79	82:72–79	NUM
ejpam-6737	381	6	,	,	PUNCT
ejpam-6737	381	7	2016	2016	NUM
ejpam-6737	381	8	.	.	PUNCT
ejpam-6737	382	1	[	[	X
ejpam-6737	382	2	5	5	NUM
ejpam-6737	382	3	]	]	X
ejpam-6737	382	4	hsuan	hsuan	PROPN
ejpam-6737	382	5	-	-	PUNCT
ejpam-6737	382	6	ting	ting	PROPN
ejpam-6737	382	7	chen	chen	PROPN
ejpam-6737	382	8	and	and	CCONJ
ejpam-6737	382	9	xueqing	xueqing	PROPN
ejpam-6737	382	10	li	li	PROPN
ejpam-6737	382	11	.	.	PUNCT
ejpam-6737	383	1	the	the	DET
ejpam-6737	383	2	contribution	contribution	NOUN
ejpam-6737	383	3	of	of	ADP
ejpam-6737	383	4	mobile	mobile	ADJ
ejpam-6737	383	5	social	social	ADJ
ejpam-6737	383	6	media	medium	NOUN
ejpam-6737	383	7	to	to	ADP
ejpam-6737	383	8	social	social	ADJ
ejpam-6737	383	9	capital	capital	NOUN
ejpam-6737	383	10	and	and	CCONJ
ejpam-6737	383	11	psychological	psychological	ADJ
ejpam-6737	383	12	well	well	ADV
ejpam-6737	383	13	-	-	PUNCT
ejpam-6737	383	14	being	being	NOUN
ejpam-6737	383	15	:	:	PUNCT
ejpam-6737	383	16	examining	examine	VERB
ejpam-6737	383	17	the	the	DET
ejpam-6737	383	18	role	role	NOUN
ejpam-6737	383	19	of	of	ADP
ejpam-6737	383	20	communicative	communicative	ADJ
ejpam-6737	383	21	use	use	NOUN
ejpam-6737	383	22	,	,	PUNCT
ejpam-6737	383	23	friending	friende	VERB
ejpam-6737	383	24	and	and	CCONJ
ejpam-6737	383	25	self	self	NOUN
ejpam-6737	383	26	-	-	PUNCT
ejpam-6737	383	27	disclosure	disclosure	NOUN
ejpam-6737	383	28	.	.	PUNCT
ejpam-6737	384	1	computers	computer	NOUN
ejpam-6737	384	2	in	in	ADP
ejpam-6737	384	3	human	human	ADJ
ejpam-6737	384	4	behavior	behavior	NOUN
ejpam-6737	384	5	,	,	PUNCT
ejpam-6737	384	6	75:958–965	75:958–965	PROPN
ejpam-6737	384	7	,	,	PUNCT
ejpam-6737	384	8	2017	2017	NUM
ejpam-6737	384	9	.	.	PUNCT
ejpam-6737	385	1	[	[	X
ejpam-6737	385	2	6	6	NUM
ejpam-6737	385	3	]	]	X
ejpam-6737	385	4	james	james	PROPN
ejpam-6737	385	5	a	a	DET
ejpam-6737	385	6	roberts	roberts	PROPN
ejpam-6737	385	7	and	and	CCONJ
ejpam-6737	385	8	meredith	meredith	PROPN
ejpam-6737	385	9	e	e	PROPN
ejpam-6737	385	10	david	david	PROPN
ejpam-6737	385	11	.	.	PUNCT
ejpam-6737	386	1	the	the	DET
ejpam-6737	386	2	social	social	ADJ
ejpam-6737	386	3	media	medium	NOUN
ejpam-6737	386	4	party	party	NOUN
ejpam-6737	386	5	:	:	PUNCT
ejpam-6737	386	6	fear	fear	NOUN
ejpam-6737	386	7	of	of	ADP
ejpam-6737	386	8	missing	miss	VERB
ejpam-6737	386	9	out	out	ADP
ejpam-6737	386	10	(	(	PUNCT
ejpam-6737	386	11	fomo	fomo	NOUN
ejpam-6737	386	12	)	)	PUNCT
ejpam-6737	386	13	,	,	PUNCT
ejpam-6737	386	14	social	social	ADJ
ejpam-6737	386	15	media	medium	NOUN
ejpam-6737	386	16	intensity	intensity	NOUN
ejpam-6737	386	17	,	,	PUNCT
ejpam-6737	386	18	connection	connection	NOUN
ejpam-6737	386	19	,	,	PUNCT
ejpam-6737	386	20	and	and	CCONJ
ejpam-6737	386	21	well	well	ADV
ejpam-6737	386	22	-	-	PUNCT
ejpam-6737	386	23	being	being	NOUN
ejpam-6737	386	24	.	.	PUNCT
ejpam-6737	387	1	international	international	ADJ
ejpam-6737	387	2	journal	journal	PROPN
ejpam-6737	387	3	of	of	ADP
ejpam-6737	387	4	human	human	ADJ
ejpam-6737	387	5	–	–	PUNCT
ejpam-6737	387	6	computer	computer	NOUN
ejpam-6737	387	7	interaction	interaction	NOUN
ejpam-6737	387	8	,	,	PUNCT
ejpam-6737	387	9	36(4):386–392	36(4):386–392	NUM
ejpam-6737	387	10	,	,	PUNCT
ejpam-6737	387	11	2020	2020	NUM
ejpam-6737	387	12	.	.	PUNCT
ejpam-6737	388	1	[	[	X
ejpam-6737	388	2	7	7	NUM
ejpam-6737	388	3	]	]	PUNCT
ejpam-6737	388	4	davide	davide	PROPN
ejpam-6737	388	5	marengo	marengo	PROPN
ejpam-6737	388	6	,	,	PUNCT
ejpam-6737	388	7	matteo	matteo	PROPN
ejpam-6737	388	8	angelo	angelo	PROPN
ejpam-6737	388	9	fabris	fabris	PROPN
ejpam-6737	388	10	,	,	PUNCT
ejpam-6737	388	11	claudio	claudio	NOUN
ejpam-6737	388	12	longobardi	longobardi	NOUN
ejpam-6737	388	13	,	,	PUNCT
ejpam-6737	388	14	and	and	CCONJ
ejpam-6737	388	15	michele	michele	PROPN
ejpam-6737	388	16	settanni	settanni	PROPN
ejpam-6737	388	17	.	.	PUNCT
ejpam-6737	389	1	smartphone	smartphone	PROPN
ejpam-6737	389	2	and	and	CCONJ
ejpam-6737	389	3	social	social	ADJ
ejpam-6737	389	4	media	medium	NOUN
ejpam-6737	389	5	use	use	NOUN
ejpam-6737	389	6	contributed	contribute	VERB
ejpam-6737	389	7	to	to	ADP
ejpam-6737	389	8	individual	individual	ADJ
ejpam-6737	389	9	tendencies	tendency	NOUN
ejpam-6737	389	10	towards	towards	ADP
ejpam-6737	389	11	social	social	ADJ
ejpam-6737	389	12	media	medium	NOUN
ejpam-6737	389	13	addiction	addiction	NOUN
ejpam-6737	389	14	in	in	ADP
ejpam-6737	389	15	italian	italian	ADJ
ejpam-6737	389	16	adolescents	adolescent	NOUN
ejpam-6737	389	17	during	during	ADP
ejpam-6737	389	18	the	the	DET
ejpam-6737	389	19	covid-19	covid-19	PROPN
ejpam-6737	389	20	pandemic	pandemic	NOUN
ejpam-6737	389	21	.	.	PUNCT
ejpam-6737	390	1	addictive	addictive	ADJ
ejpam-6737	390	2	behaviors	behavior	NOUN
ejpam-6737	390	3	,	,	PUNCT
ejpam-6737	390	4	126:107204	126:107204	NUM
ejpam-6737	390	5	,	,	PUNCT
ejpam-6737	390	6	2022	2022	NUM
ejpam-6737	390	7	.	.	PUNCT
ejpam-6737	391	1	[	[	X
ejpam-6737	391	2	8	8	NUM
ejpam-6737	391	3	]	]	X
ejpam-6737	391	4	sultan	sultan	ADJ
ejpam-6737	391	5	alshamrani	alshamrani	NOUN
ejpam-6737	391	6	,	,	PUNCT
ejpam-6737	391	7	ahmed	ahmed	PROPN
ejpam-6737	391	8	abusnaina	abusnaina	PROPN
ejpam-6737	391	9	,	,	PUNCT
ejpam-6737	391	10	mohammed	mohammed	PROPN
ejpam-6737	391	11	abuhamad	abuhamad	PROPN
ejpam-6737	391	12	,	,	PUNCT
ejpam-6737	391	13	daehun	daehun	PROPN
ejpam-6737	391	14	nyang	nyang	PROPN
ejpam-6737	391	15	,	,	PUNCT
ejpam-6737	391	16	and	and	CCONJ
ejpam-6737	391	17	david	david	PROPN
ejpam-6737	391	18	mohaisen	mohaisen	PROPN
ejpam-6737	391	19	.	.	PUNCT
ejpam-6737	392	1	hate	hate	PROPN
ejpam-6737	392	2	,	,	PUNCT
ejpam-6737	392	3	obscenity	obscenity	NOUN
ejpam-6737	392	4	,	,	PUNCT
ejpam-6737	392	5	and	and	CCONJ
ejpam-6737	392	6	insults	insult	NOUN
ejpam-6737	392	7	:	:	PUNCT
ejpam-6737	392	8	measuring	measure	VERB
ejpam-6737	392	9	the	the	DET
ejpam-6737	392	10	exposure	exposure	NOUN
ejpam-6737	392	11	of	of	ADP
ejpam-6737	392	12	children	child	NOUN
ejpam-6737	392	13	to	to	PART
ejpam-6737	392	14	inappropriate	inappropriate	VERB
ejpam-6737	392	15	comments	comment	NOUN
ejpam-6737	392	16	in	in	ADP
ejpam-6737	392	17	youtube	youtube	NOUN
ejpam-6737	392	18	.	.	PUNCT
ejpam-6737	393	1	in	in	ADP
ejpam-6737	393	2	companion	companion	ADJ
ejpam-6737	393	3	proceedings	proceeding	NOUN
ejpam-6737	393	4	of	of	ADP
ejpam-6737	393	5	the	the	DET
ejpam-6737	393	6	web	web	NOUN
ejpam-6737	393	7	conference	conference	NOUN
ejpam-6737	393	8	2021	2021	NUM
ejpam-6737	393	9	,	,	PUNCT
ejpam-6737	393	10	pages	page	NOUN
ejpam-6737	393	11	508–515	508–515	NUM
ejpam-6737	393	12	,	,	PUNCT
ejpam-6737	393	13	2021	2021	NUM
ejpam-6737	393	14	.	.	PUNCT
ejpam-6737	394	1	[	[	X
ejpam-6737	394	2	9	9	NUM
ejpam-6737	394	3	]	]	X
ejpam-6737	394	4	s	s	VERB
ejpam-6737	394	5	malesev	malesev	NOUN
ejpam-6737	394	6	and	and	CCONJ
ejpam-6737	394	7	m	m	NOUN
ejpam-6737	394	8	cherry	cherry	NOUN
ejpam-6737	394	9	.	.	PUNCT
ejpam-6737	395	1	digital	digital	ADJ
ejpam-6737	395	2	and	and	CCONJ
ejpam-6737	395	3	social	social	ADJ
ejpam-6737	395	4	media	medium	NOUN
ejpam-6737	395	5	marketing	marketing	NOUN
ejpam-6737	395	6	-	-	PUNCT
ejpam-6737	395	7	growing	grow	VERB
ejpam-6737	395	8	market	market	NOUN
ejpam-6737	395	9	share	share	NOUN
ejpam-6737	395	10	for	for	ADP
ejpam-6737	395	11	construction	construction	NOUN
ejpam-6737	395	12	smes	sme	NOUN
ejpam-6737	395	13	.	.	PUNCT
ejpam-6737	396	1	construction	construction	NOUN
ejpam-6737	396	2	economics	economic	NOUN
ejpam-6737	396	3	and	and	CCONJ
ejpam-6737	396	4	building	building	NOUN
ejpam-6737	396	5	,	,	PUNCT
ejpam-6737	396	6	21	21	NUM
ejpam-6737	396	7	(	(	PUNCT
ejpam-6737	396	8	1	1	NUM
ejpam-6737	396	9	)	)	PUNCT
ejpam-6737	396	10	,	,	PUNCT
ejpam-6737	396	11	65–82	65–82	NUM
ejpam-6737	396	12	,	,	PUNCT
ejpam-6737	396	13	2021	2021	NUM
ejpam-6737	396	14	.	.	PUNCT
ejpam-6737	397	1	[	[	X
ejpam-6737	397	2	10	10	NUM
ejpam-6737	397	3	]	]	SYM
ejpam-6737	397	4	farai	farai	NUM
ejpam-6737	397	5	nyabadza	nyabadza	NOUN
ejpam-6737	397	6	,	,	PUNCT
ejpam-6737	397	7	john	john	PROPN
ejpam-6737	397	8	bh	bh	PROPN
ejpam-6737	397	9	njagarah	njagarah	PROPN
ejpam-6737	397	10	,	,	PUNCT
ejpam-6737	397	11	and	and	CCONJ
ejpam-6737	397	12	robert	robert	PROPN
ejpam-6737	397	13	j	j	PROPN
ejpam-6737	397	14	smith	smith	PROPN
ejpam-6737	397	15	.	.	PUNCT
ejpam-6737	398	1	modelling	model	VERB
ejpam-6737	398	2	the	the	DET
ejpam-6737	398	3	dynamics	dynamic	NOUN
ejpam-6737	398	4	of	of	ADP
ejpam-6737	398	5	crystal	crystal	NOUN
ejpam-6737	398	6	meth	meth	NOUN
ejpam-6737	398	7	(	(	PUNCT
ejpam-6737	398	8	‘	'	PUNCT
ejpam-6737	398	9	tik	tik	NOUN
ejpam-6737	398	10	’	'	PUNCT
ejpam-6737	398	11	)	)	PUNCT
ejpam-6737	398	12	abuse	abuse	NOUN
ejpam-6737	398	13	in	in	ADP
ejpam-6737	398	14	the	the	DET
ejpam-6737	398	15	presence	presence	NOUN
ejpam-6737	398	16	of	of	ADP
ejpam-6737	398	17	drug	drug	NOUN
ejpam-6737	398	18	-	-	PUNCT
ejpam-6737	398	19	supply	supply	NOUN
ejpam-6737	398	20	chains	chain	NOUN
ejpam-6737	398	21	in	in	ADP
ejpam-6737	398	22	south	south	PROPN
ejpam-6737	398	23	africa	africa	PROPN
ejpam-6737	398	24	.	.	PUNCT
ejpam-6737	399	1	bulletin	bulletin	NOUN
ejpam-6737	399	2	of	of	ADP
ejpam-6737	399	3	mathematical	mathematical	ADJ
ejpam-6737	399	4	biology	biology	NOUN
ejpam-6737	399	5	,	,	PUNCT
ejpam-6737	399	6	75(1):24–48	75(1):24–48	NUM
ejpam-6737	399	7	,	,	PUNCT
ejpam-6737	399	8	2013	2013	NUM
ejpam-6737	399	9	.	.	PUNCT
ejpam-6737	400	1	[	[	X
ejpam-6737	400	2	11	11	NUM
ejpam-6737	400	3	]	]	X
ejpam-6737	400	4	j	j	PROPN
ejpam-6737	400	5	mushanyu	mushanyu	PROPN
ejpam-6737	400	6	,	,	PUNCT
ejpam-6737	400	7	f	f	PROPN
ejpam-6737	400	8	nyabadza	nyabadza	NOUN
ejpam-6737	400	9	,	,	PUNCT
ejpam-6737	400	10	and	and	CCONJ
ejpam-6737	400	11	agr	agr	PROPN
ejpam-6737	400	12	stewart	stewart	PROPN
ejpam-6737	400	13	.	.	PUNCT
ejpam-6737	401	1	modelling	model	VERB
ejpam-6737	401	2	the	the	DET
ejpam-6737	401	3	trends	trend	NOUN
ejpam-6737	401	4	of	of	ADP
ejpam-6737	401	5	inpatient	inpatient	NOUN
ejpam-6737	401	6	and	and	CCONJ
ejpam-6737	401	7	outpatient	outpatient	NOUN
ejpam-6737	401	8	rehabilitation	rehabilitation	NOUN
ejpam-6737	401	9	for	for	ADP
ejpam-6737	401	10	methamphetamine	methamphetamine	NOUN
ejpam-6737	401	11	in	in	ADP
ejpam-6737	401	12	the	the	DET
ejpam-6737	401	13	western	western	ADJ
ejpam-6737	401	14	cape	cape	NOUN
ejpam-6737	401	15	province	province	NOUN
ejpam-6737	401	16	of	of	ADP
ejpam-6737	401	17	south	south	PROPN
ejpam-6737	401	18	africa	africa	PROPN
ejpam-6737	401	19	.	.	PUNCT
ejpam-6737	402	1	bmc	bmc	PROPN
ejpam-6737	402	2	research	research	NOUN
ejpam-6737	402	3	notes	note	NOUN
ejpam-6737	402	4	,	,	PUNCT
ejpam-6737	402	5	8(1):797	8(1):797	NUM
ejpam-6737	402	6	,	,	PUNCT
ejpam-6737	402	7	2015	2015	NUM
ejpam-6737	402	8	.	.	PUNCT
ejpam-6737	403	1	[	[	X
ejpam-6737	403	2	12	12	NUM
ejpam-6737	403	3	]	]	X
ejpam-6737	403	4	isaac	isaac	PROPN
ejpam-6737	403	5	kwasi	kwasi	PROPN
ejpam-6737	403	6	adu	adu	PROPN
ejpam-6737	403	7	,	,	PUNCT
ejpam-6737	403	8	maren	maren	PROPN
ejpam-6737	403	9	osman	osman	PROPN
ejpam-6737	403	10	,	,	PUNCT
ejpam-6737	403	11	and	and	CCONJ
ejpam-6737	403	12	cuihong	cuihong	PROPN
ejpam-6737	403	13	yang	yang	PROPN
ejpam-6737	403	14	.	.	PUNCT
ejpam-6737	404	1	mathematical	mathematical	ADJ
ejpam-6737	404	2	model	model	NOUN
ejpam-6737	404	3	of	of	ADP
ejpam-6737	404	4	drinking	drinking	NOUN
ejpam-6737	404	5	epidemic	epidemic	NOUN
ejpam-6737	404	6	.	.	PUNCT
ejpam-6737	405	1	br	br	PROPN
ejpam-6737	405	2	.	.	PUNCT
ejpam-6737	406	1	j.	j.	PROPN
ejpam-6737	406	2	math	math	PROPN
ejpam-6737	406	3	.	.	PUNCT
ejpam-6737	407	1	computer	computer	PROPN
ejpam-6737	407	2	sci	sci	PROPN
ejpam-6737	407	3	,	,	PUNCT
ejpam-6737	407	4	22(5):1–10	22(5):1–10	NOUN
ejpam-6737	407	5	,	,	PUNCT
ejpam-6737	407	6	2017	2017	NUM
ejpam-6737	407	7	.	.	PUNCT
ejpam-6737	408	1	[	[	X
ejpam-6737	408	2	13	13	NUM
ejpam-6737	408	3	]	]	SYM
ejpam-6737	408	4	yubo	yubo	PROPN
ejpam-6737	408	5	hou	hou	PROPN
ejpam-6737	408	6	,	,	PUNCT
ejpam-6737	408	7	dan	dan	PROPN
ejpam-6737	408	8	xiong	xiong	PROPN
ejpam-6737	408	9	,	,	PUNCT
ejpam-6737	408	10	tonglin	tonglin	PROPN
ejpam-6737	408	11	jiang	jiang	PROPN
ejpam-6737	408	12	,	,	PUNCT
ejpam-6737	408	13	lily	lily	ADJ
ejpam-6737	408	14	song	song	NOUN
ejpam-6737	408	15	,	,	PUNCT
ejpam-6737	408	16	and	and	CCONJ
ejpam-6737	408	17	qi	qi	PROPN
ejpam-6737	408	18	wang	wang	PROPN
ejpam-6737	408	19	.	.	PUNCT
ejpam-6737	409	1	social	social	ADJ
ejpam-6737	409	2	media	medium	NOUN
ejpam-6737	409	3	addiction	addiction	NOUN
ejpam-6737	409	4	:	:	PUNCT
ejpam-6737	409	5	its	its	PRON
ejpam-6737	409	6	impact	impact	NOUN
ejpam-6737	409	7	,	,	PUNCT
ejpam-6737	409	8	mediation	mediation	NOUN
ejpam-6737	409	9	,	,	PUNCT
ejpam-6737	409	10	and	and	CCONJ
ejpam-6737	409	11	intervention	intervention	NOUN
ejpam-6737	409	12	.	.	PUNCT
ejpam-6737	410	1	cyberpsychology	cyberpsychology	NOUN
ejpam-6737	410	2	:	:	PUNCT
ejpam-6737	410	3	journal	journal	NOUN
ejpam-6737	410	4	of	of	ADP
ejpam-6737	410	5	psychosocial	psychosocial	ADJ
ejpam-6737	410	6	research	research	NOUN
ejpam-6737	410	7	on	on	ADP
ejpam-6737	410	8	cyberspace	cyberspace	NOUN
ejpam-6737	410	9	,	,	PUNCT
ejpam-6737	410	10	13(1	13(1	NUM
ejpam-6737	410	11	)	)	PUNCT
ejpam-6737	410	12	,	,	PUNCT
ejpam-6737	410	13	2019	2019	NUM
ejpam-6737	410	14	.	.	PUNCT
ejpam-6737	411	1	[	[	X
ejpam-6737	411	2	14	14	NUM
ejpam-6737	411	3	]	]	X
ejpam-6737	411	4	bouchaib	bouchaib	PROPN
ejpam-6737	411	5	khajji	khajji	NOUN
ejpam-6737	411	6	,	,	PUNCT
ejpam-6737	411	7	abderrahim	abderrahim	PROPN
ejpam-6737	411	8	labzai	labzai	PROPN
ejpam-6737	411	9	,	,	PUNCT
ejpam-6737	411	10	omar	omar	PROPN
ejpam-6737	411	11	balatif	balatif	PROPN
ejpam-6737	411	12	,	,	PUNCT
ejpam-6737	411	13	and	and	CCONJ
ejpam-6737	411	14	mostafa	mostafa	PROPN
ejpam-6737	411	15	rachik	rachik	PROPN
ejpam-6737	411	16	.	.	PUNCT
ejpam-6737	412	1	mathematical	mathematical	ADJ
ejpam-6737	412	2	modeling	modeling	NOUN
ejpam-6737	412	3	and	and	CCONJ
ejpam-6737	412	4	analysis	analysis	NOUN
ejpam-6737	412	5	of	of	ADP
ejpam-6737	412	6	an	an	DET
ejpam-6737	412	7	alcohol	alcohol	NOUN
ejpam-6737	412	8	drinking	drinking	NOUN
ejpam-6737	412	9	model	model	NOUN
ejpam-6737	412	10	with	with	ADP
ejpam-6737	412	11	the	the	DET
ejpam-6737	412	12	influence	influence	NOUN
ejpam-6737	412	13	of	of	ADP
ejpam-6737	412	14	s.	s.	PROPN
ejpam-6737	412	15	m.	m.	PROPN
ejpam-6737	412	16	chithra	chithra	PROPN
ejpam-6737	412	17	et	et	PROPN
ejpam-6737	412	18	al	al	PROPN
ejpam-6737	412	19	.	.	PUNCT
ejpam-6737	412	20	/	/	SYM
ejpam-6737	412	21	eur	eur	PROPN
ejpam-6737	412	22	.	.	PUNCT
ejpam-6737	413	1	j.	j.	PROPN
ejpam-6737	413	2	pure	pure	PROPN
ejpam-6737	413	3	appl	appl	PROPN
ejpam-6737	413	4	.	.	PROPN
ejpam-6737	413	5	math	math	PROPN
ejpam-6737	413	6	,	,	PUNCT
ejpam-6737	413	7	18	18	NUM
ejpam-6737	413	8	(	(	PUNCT
ejpam-6737	413	9	4	4	NUM
ejpam-6737	413	10	)	)	PUNCT
ejpam-6737	413	11	(	(	PUNCT
ejpam-6737	413	12	2025	2025	NUM
ejpam-6737	413	13	)	)	PUNCT
ejpam-6737	413	14	,	,	PUNCT
ejpam-6737	413	15	6737	6737	NUM
ejpam-6737	413	16	22	22	NUM
ejpam-6737	413	17	of	of	ADP
ejpam-6737	413	18	23	23	NUM
ejpam-6737	413	19	alcohol	alcohol	NOUN
ejpam-6737	413	20	treatment	treatment	NOUN
ejpam-6737	413	21	centers	center	NOUN
ejpam-6737	413	22	.	.	PUNCT
ejpam-6737	414	1	international	international	ADJ
ejpam-6737	414	2	journal	journal	PROPN
ejpam-6737	414	3	of	of	ADP
ejpam-6737	414	4	mathematics	mathematics	PROPN
ejpam-6737	414	5	and	and	CCONJ
ejpam-6737	414	6	mathematical	mathematical	ADJ
ejpam-6737	414	7	sciences	science	NOUN
ejpam-6737	414	8	,	,	PUNCT
ejpam-6737	414	9	2020(1):4903168	2020(1):4903168	NOUN
ejpam-6737	414	10	,	,	PUNCT
ejpam-6737	414	11	2020	2020	NUM
ejpam-6737	414	12	.	.	PUNCT
ejpam-6737	415	1	[	[	X
ejpam-6737	415	2	15	15	NUM
ejpam-6737	415	3	]	]	X
ejpam-6737	415	4	shuang	shuang	PROPN
ejpam-6737	415	5	-	-	PROPN
ejpam-6737	415	6	hong	hong	PROPN
ejpam-6737	415	7	ma	ma	PROPN
ejpam-6737	415	8	,	,	PUNCT
ejpam-6737	415	9	hai	hai	PROPN
ejpam-6737	415	10	-	-	PUNCT
ejpam-6737	415	11	feng	feng	PROPN
ejpam-6737	415	12	huo	huo	PROPN
ejpam-6737	415	13	,	,	PUNCT
ejpam-6737	415	14	and	and	CCONJ
ejpam-6737	415	15	xin	xin	PROPN
ejpam-6737	415	16	-	-	PROPN
ejpam-6737	415	17	you	you	PRON
ejpam-6737	415	18	meng	meng	PROPN
ejpam-6737	415	19	.	.	PUNCT
ejpam-6737	416	1	modelling	model	VERB
ejpam-6737	416	2	alcoholism	alcoholism	NOUN
ejpam-6737	416	3	as	as	ADP
ejpam-6737	416	4	a	a	DET
ejpam-6737	416	5	contagious	contagious	ADJ
ejpam-6737	416	6	disease	disease	NOUN
ejpam-6737	416	7	:	:	PUNCT
ejpam-6737	416	8	a	a	DET
ejpam-6737	416	9	mathematical	mathematical	ADJ
ejpam-6737	416	10	model	model	NOUN
ejpam-6737	416	11	with	with	ADP
ejpam-6737	416	12	awareness	awareness	NOUN
ejpam-6737	416	13	programs	program	NOUN
ejpam-6737	416	14	and	and	CCONJ
ejpam-6737	416	15	time	time	NOUN
ejpam-6737	416	16	delay	delay	NOUN
ejpam-6737	416	17	.	.	PUNCT
ejpam-6737	417	1	discrete	discrete	ADJ
ejpam-6737	417	2	dynamics	dynamic	NOUN
ejpam-6737	417	3	in	in	ADP
ejpam-6737	417	4	nature	nature	NOUN
ejpam-6737	417	5	and	and	CCONJ
ejpam-6737	417	6	society	society	NOUN
ejpam-6737	417	7	,	,	PUNCT
ejpam-6737	417	8	2015(1):260195	2015(1):260195	NUM
ejpam-6737	417	9	,	,	PUNCT
ejpam-6737	417	10	2015	2015	NUM
ejpam-6737	417	11	.	.	PUNCT
ejpam-6737	418	1	[	[	X
ejpam-6737	418	2	16	16	NUM
ejpam-6737	418	3	]	]	SYM
ejpam-6737	418	4	swarnali	swarnali	PROPN
ejpam-6737	418	5	sharma	sharma	PROPN
ejpam-6737	418	6	and	and	CCONJ
ejpam-6737	418	7	gp	gp	PROPN
ejpam-6737	418	8	samanta	samanta	PROPN
ejpam-6737	418	9	.	.	PUNCT
ejpam-6737	419	1	drinking	drink	VERB
ejpam-6737	419	2	as	as	ADP
ejpam-6737	419	3	an	an	DET
ejpam-6737	419	4	epidemic	epidemic	NOUN
ejpam-6737	419	5	:	:	PUNCT
ejpam-6737	419	6	a	a	DET
ejpam-6737	419	7	mathematical	mathematical	ADJ
ejpam-6737	419	8	model	model	NOUN
ejpam-6737	419	9	with	with	ADP
ejpam-6737	419	10	dynamic	dynamic	ADJ
ejpam-6737	419	11	behaviour	behaviour	NOUN
ejpam-6737	419	12	.	.	PUNCT
ejpam-6737	420	1	journal	journal	PROPN
ejpam-6737	420	2	of	of	ADP
ejpam-6737	420	3	applied	apply	VERB
ejpam-6737	420	4	mathematics	mathematics	PROPN
ejpam-6737	420	5	&	&	CCONJ
ejpam-6737	420	6	informatics	informatic	NOUN
ejpam-6737	420	7	,	,	PUNCT
ejpam-6737	420	8	31(1_2):1–25	31(1_2):1–25	NUM
ejpam-6737	420	9	,	,	PUNCT
ejpam-6737	420	10	2013	2013	NUM
ejpam-6737	420	11	.	.	PUNCT
ejpam-6737	421	1	[	[	X
ejpam-6737	421	2	17	17	NUM
ejpam-6737	421	3	]	]	PUNCT
ejpam-6737	421	4	youming	youme	VERB
ejpam-6737	421	5	guo	guo	PROPN
ejpam-6737	421	6	and	and	CCONJ
ejpam-6737	421	7	tingting	tingte	VERB
ejpam-6737	421	8	li	li	PROPN
ejpam-6737	421	9	.	.	PUNCT
ejpam-6737	421	10	optimal	optimal	ADJ
ejpam-6737	421	11	control	control	NOUN
ejpam-6737	421	12	and	and	CCONJ
ejpam-6737	421	13	stability	stability	NOUN
ejpam-6737	421	14	analysis	analysis	NOUN
ejpam-6737	421	15	of	of	ADP
ejpam-6737	421	16	an	an	DET
ejpam-6737	421	17	online	online	ADJ
ejpam-6737	421	18	game	game	NOUN
ejpam-6737	421	19	addiction	addiction	NOUN
ejpam-6737	421	20	model	model	NOUN
ejpam-6737	421	21	with	with	ADP
ejpam-6737	421	22	two	two	NUM
ejpam-6737	421	23	stages	stage	NOUN
ejpam-6737	421	24	.	.	PUNCT
ejpam-6737	422	1	mathematical	mathematical	ADJ
ejpam-6737	422	2	methods	method	NOUN
ejpam-6737	422	3	in	in	ADP
ejpam-6737	422	4	the	the	DET
ejpam-6737	422	5	applied	apply	VERB
ejpam-6737	422	6	sciences	science	NOUN
ejpam-6737	422	7	,	,	PUNCT
ejpam-6737	422	8	43(7):4391–4408	43(7):4391–4408	NUM
ejpam-6737	422	9	,	,	PUNCT
ejpam-6737	422	10	2020	2020	NUM
ejpam-6737	422	11	.	.	PUNCT
ejpam-6737	423	1	[	[	X
ejpam-6737	423	2	18	18	NUM
ejpam-6737	423	3	]	]	PUNCT
ejpam-6737	423	4	tingting	tingte	VERB
ejpam-6737	423	5	li	li	PROPN
ejpam-6737	423	6	and	and	CCONJ
ejpam-6737	423	7	youming	youme	VERB
ejpam-6737	423	8	guo	guo	PROPN
ejpam-6737	423	9	.	.	PUNCT
ejpam-6737	423	10	stability	stability	NOUN
ejpam-6737	423	11	and	and	CCONJ
ejpam-6737	423	12	optimal	optimal	ADJ
ejpam-6737	423	13	control	control	NOUN
ejpam-6737	423	14	in	in	ADP
ejpam-6737	423	15	a	a	DET
ejpam-6737	423	16	mathematical	mathematical	ADJ
ejpam-6737	423	17	model	model	NOUN
ejpam-6737	423	18	of	of	ADP
ejpam-6737	423	19	online	online	ADJ
ejpam-6737	423	20	game	game	NOUN
ejpam-6737	423	21	addiction	addiction	NOUN
ejpam-6737	423	22	.	.	PUNCT
ejpam-6737	424	1	filomat	filomat	NOUN
ejpam-6737	424	2	,	,	PUNCT
ejpam-6737	424	3	33(17):5691–5711	33(17):5691–5711	NUM
ejpam-6737	424	4	,	,	PUNCT
ejpam-6737	424	5	2019	2019	NUM
ejpam-6737	424	6	.	.	PUNCT
ejpam-6737	425	1	[	[	X
ejpam-6737	425	2	19	19	NUM
ejpam-6737	425	3	]	]	PUNCT
ejpam-6737	425	4	adamu	adamu	PROPN
ejpam-6737	425	5	ishaku	ishaku	PROPN
ejpam-6737	425	6	,	,	PUNCT
ejpam-6737	425	7	bashir	bashir	PROPN
ejpam-6737	425	8	saidu	saidu	PROPN
ejpam-6737	425	9	musa	musa	PROPN
ejpam-6737	425	10	,	,	PUNCT
ejpam-6737	425	11	ayuba	ayuba	PROPN
ejpam-6737	425	12	sanda	sanda	NOUN
ejpam-6737	425	13	,	,	PUNCT
ejpam-6737	425	14	and	and	CCONJ
ejpam-6737	425	15	abubakar	abubakar	PROPN
ejpam-6737	425	16	muhammad	muhammad	PROPN
ejpam-6737	425	17	bakoji	bakoji	PROPN
ejpam-6737	425	18	.	.	PUNCT
ejpam-6737	426	1	mathematical	mathematical	ADJ
ejpam-6737	426	2	assessment	assessment	NOUN
ejpam-6737	426	3	of	of	ADP
ejpam-6737	426	4	social	social	ADJ
ejpam-6737	426	5	media	medium	NOUN
ejpam-6737	426	6	impact	impact	NOUN
ejpam-6737	426	7	on	on	ADP
ejpam-6737	426	8	academic	academic	ADJ
ejpam-6737	426	9	performance	performance	NOUN
ejpam-6737	426	10	of	of	ADP
ejpam-6737	426	11	students	student	NOUN
ejpam-6737	426	12	in	in	ADP
ejpam-6737	426	13	higher	high	ADJ
ejpam-6737	426	14	institution	institution	NOUN
ejpam-6737	426	15	.	.	PUNCT
ejpam-6737	427	1	iosr	iosr	PROPN
ejpam-6737	427	2	j.	j.	PROPN
ejpam-6737	427	3	math	math	PROPN
ejpam-6737	427	4	,	,	PUNCT
ejpam-6737	427	5	14(1):72–79	14(1):72–79	NUM
ejpam-6737	427	6	,	,	PUNCT
ejpam-6737	427	7	2018	2018	NUM
ejpam-6737	427	8	.	.	PUNCT
ejpam-6737	428	1	[	[	X
ejpam-6737	428	2	20	20	NUM
ejpam-6737	428	3	]	]	X
ejpam-6737	428	4	xun	xun	PROPN
ejpam-6737	428	5	-	-	PUNCT
ejpam-6737	428	6	yang	yang	PROPN
ejpam-6737	428	7	wang	wang	PROPN
ejpam-6737	428	8	,	,	PUNCT
ejpam-6737	428	9	hai	hai	PROPN
ejpam-6737	428	10	-	-	PUNCT
ejpam-6737	428	11	feng	feng	PROPN
ejpam-6737	428	12	huo	huo	PROPN
ejpam-6737	428	13	,	,	PUNCT
ejpam-6737	428	14	qing	qing	NOUN
ejpam-6737	428	15	-	-	PUNCT
ejpam-6737	428	16	kai	kai	PROPN
ejpam-6737	428	17	kong	kong	PROPN
ejpam-6737	428	18	,	,	PUNCT
ejpam-6737	428	19	and	and	CCONJ
ejpam-6737	428	20	wei	wei	PROPN
ejpam-6737	428	21	-	-	PROPN
ejpam-6737	428	22	xuan	xuan	PROPN
ejpam-6737	428	23	shi	shi	PROPN
ejpam-6737	428	24	.	.	PUNCT
ejpam-6737	429	1	optimal	optimal	ADJ
ejpam-6737	429	2	control	control	NOUN
ejpam-6737	429	3	strategies	strategy	NOUN
ejpam-6737	429	4	in	in	ADP
ejpam-6737	429	5	an	an	DET
ejpam-6737	429	6	alcoholism	alcoholism	NOUN
ejpam-6737	429	7	model	model	NOUN
ejpam-6737	429	8	.	.	PUNCT
ejpam-6737	430	1	in	in	ADP
ejpam-6737	430	2	abstract	abstract	ADJ
ejpam-6737	430	3	and	and	CCONJ
ejpam-6737	430	4	applied	apply	VERB
ejpam-6737	430	5	analysis	analysis	NOUN
ejpam-6737	430	6	,	,	PUNCT
ejpam-6737	430	7	volume	volume	NOUN
ejpam-6737	430	8	2014	2014	NUM
ejpam-6737	430	9	,	,	PUNCT
ejpam-6737	430	10	page	page	NOUN
ejpam-6737	430	11	954069	954069	NUM
ejpam-6737	430	12	.	.	PUNCT
ejpam-6737	431	1	wiley	wiley	PROPN
ejpam-6737	431	2	online	online	PROPN
ejpam-6737	431	3	library	library	PROPN
ejpam-6737	431	4	,	,	PUNCT
ejpam-6737	431	5	2014	2014	NUM
ejpam-6737	431	6	.	.	PUNCT
ejpam-6737	432	1	[	[	X
ejpam-6737	432	2	21	21	NUM
ejpam-6737	432	3	]	]	X
ejpam-6737	432	4	h.	h.	PROPN
ejpam-6737	432	5	t.	t.	PROPN
ejpam-6737	432	6	alemneh	alemneh	PROPN
ejpam-6737	432	7	and	and	CCONJ
ejpam-6737	432	8	n.	n.	PROPN
ejpam-6737	432	9	y.	y.	PROPN
ejpam-6737	432	10	alemu	alemu	PROPN
ejpam-6737	432	11	.	.	PROPN
ejpam-6737	432	12	mathematical	mathematical	ADJ
ejpam-6737	432	13	modeling	modeling	NOUN
ejpam-6737	432	14	with	with	ADP
ejpam-6737	432	15	optimal	optimal	ADJ
ejpam-6737	432	16	control	control	NOUN
ejpam-6737	432	17	analysis	analysis	NOUN
ejpam-6737	432	18	of	of	ADP
ejpam-6737	432	19	social	social	ADJ
ejpam-6737	432	20	media	medium	NOUN
ejpam-6737	432	21	addiction	addiction	NOUN
ejpam-6737	432	22	.	.	PUNCT
ejpam-6737	433	1	infectious	infectious	ADJ
ejpam-6737	433	2	disease	disease	NOUN
ejpam-6737	433	3	modelling	modelling	NOUN
ejpam-6737	433	4	,	,	PUNCT
ejpam-6737	433	5	6:405–419	6:405–419	NOUN
ejpam-6737	433	6	,	,	PUNCT
ejpam-6737	433	7	2021	2021	NUM
ejpam-6737	433	8	.	.	PUNCT
ejpam-6737	434	1	[	[	X
ejpam-6737	434	2	22	22	NUM
ejpam-6737	434	3	]	]	PUNCT
ejpam-6737	434	4	i.	i.	PROPN
ejpam-6737	434	5	slimane	slimane	PROPN
ejpam-6737	434	6	,	,	PUNCT
ejpam-6737	434	7	g.	g.	PROPN
ejpam-6737	434	8	nazir	nazir	PROPN
ejpam-6737	434	9	,	,	PUNCT
ejpam-6737	434	10	j.	j.	PROPN
ejpam-6737	434	11	j.	j.	PROPN
ejpam-6737	434	12	nieto	nieto	PROPN
ejpam-6737	434	13	,	,	PUNCT
ejpam-6737	434	14	and	and	CCONJ
ejpam-6737	434	15	f.	f.	PROPN
ejpam-6737	434	16	yaqoob	yaqoob	PROPN
ejpam-6737	434	17	.	.	PUNCT
ejpam-6737	435	1	mathematical	mathematical	ADJ
ejpam-6737	435	2	analysis	analysis	NOUN
ejpam-6737	435	3	of	of	ADP
ejpam-6737	435	4	hepatitis	hepatitis	PROPN
ejpam-6737	435	5	c	c	PROPN
ejpam-6737	435	6	virus	virus	NOUN
ejpam-6737	435	7	infection	infection	NOUN
ejpam-6737	435	8	model	model	NOUN
ejpam-6737	435	9	in	in	ADP
ejpam-6737	435	10	the	the	DET
ejpam-6737	435	11	framework	framework	NOUN
ejpam-6737	435	12	of	of	ADP
ejpam-6737	435	13	non	non	ADJ
ejpam-6737	435	14	-	-	ADJ
ejpam-6737	435	15	local	local	ADJ
ejpam-6737	435	16	and	and	CCONJ
ejpam-6737	435	17	non	non	ADJ
ejpam-6737	435	18	-	-	ADJ
ejpam-6737	435	19	singular	singular	ADJ
ejpam-6737	435	20	kernel	kernel	PROPN
ejpam-6737	435	21	fractional	fractional	PROPN
ejpam-6737	435	22	derivative	derivative	PROPN
ejpam-6737	435	23	.	.	PUNCT
ejpam-6737	436	1	international	international	ADJ
ejpam-6737	436	2	journal	journal	PROPN
ejpam-6737	436	3	of	of	ADP
ejpam-6737	436	4	biomathematics	biomathematic	NOUN
ejpam-6737	436	5	,	,	PUNCT
ejpam-6737	436	6	16(1):2250064	16(1):2250064	NUM
ejpam-6737	436	7	,	,	PUNCT
ejpam-6737	436	8	2023	2023	NUM
ejpam-6737	436	9	.	.	PUNCT
ejpam-6737	437	1	[	[	X
ejpam-6737	437	2	23	23	NUM
ejpam-6737	437	3	]	]	PUNCT
ejpam-6737	437	4	i.	i.	PROPN
ejpam-6737	437	5	slimane	slimane	PROPN
ejpam-6737	437	6	,	,	PUNCT
ejpam-6737	437	7	j.	j.	PROPN
ejpam-6737	437	8	j.	j.	PROPN
ejpam-6737	437	9	nieto	nieto	PROPN
ejpam-6737	437	10	,	,	PUNCT
ejpam-6737	437	11	and	and	CCONJ
ejpam-6737	437	12	s.	s.	PROPN
ejpam-6737	437	13	ahmad	ahmad	PROPN
ejpam-6737	437	14	.	.	PUNCT
ejpam-6737	438	1	a	a	DET
ejpam-6737	438	2	fractional	fractional	ADJ
ejpam-6737	438	3	-	-	PUNCT
ejpam-6737	438	4	order	order	NOUN
ejpam-6737	438	5	bovine	bovine	NOUN
ejpam-6737	438	6	babesiosis	babesiosis	NOUN
ejpam-6737	438	7	epidemic	epidemic	NOUN
ejpam-6737	438	8	transmission	transmission	NOUN
ejpam-6737	438	9	model	model	NOUN
ejpam-6737	438	10	with	with	ADP
ejpam-6737	438	11	non	non	ADJ
ejpam-6737	438	12	-	-	ADJ
ejpam-6737	438	13	singular	singular	ADJ
ejpam-6737	438	14	mittag	mittag	ADJ
ejpam-6737	438	15	-	-	PUNCT
ejpam-6737	438	16	leffler	leffler	NOUN
ejpam-6737	438	17	law	law	NOUN
ejpam-6737	438	18	.	.	PUNCT
ejpam-6737	439	1	fractals	fractal	NOUN
ejpam-6737	439	2	,	,	PUNCT
ejpam-6737	439	3	31(2):2340033	31(2):2340033	NUM
ejpam-6737	439	4	,	,	PUNCT
ejpam-6737	439	5	2023	2023	NUM
ejpam-6737	439	6	.	.	PUNCT
ejpam-6737	440	1	[	[	X
ejpam-6737	440	2	24	24	NUM
ejpam-6737	440	3	]	]	PUNCT
ejpam-6737	440	4	n.	n.	NOUN
ejpam-6737	440	5	özdemir	özdemir	PROPN
ejpam-6737	440	6	and	and	CCONJ
ejpam-6737	440	7	e.	e.	PROPN
ejpam-6737	440	8	uçar	uçar	PROPN
ejpam-6737	440	9	.	.	PUNCT
ejpam-6737	441	1	investigating	investigate	VERB
ejpam-6737	441	2	of	of	ADP
ejpam-6737	441	3	an	an	DET
ejpam-6737	441	4	immune	immune	ADJ
ejpam-6737	441	5	system	system	NOUN
ejpam-6737	441	6	-	-	PUNCT
ejpam-6737	441	7	cancer	cancer	NOUN
ejpam-6737	441	8	mathematical	mathematical	ADJ
ejpam-6737	441	9	model	model	NOUN
ejpam-6737	441	10	with	with	ADP
ejpam-6737	441	11	mittag	mittag	ADJ
ejpam-6737	441	12	-	-	PUNCT
ejpam-6737	441	13	leffler	leffler	NOUN
ejpam-6737	441	14	kernel	kernel	NOUN
ejpam-6737	441	15	.	.	PUNCT
ejpam-6737	442	1	chaos	chaos	NOUN
ejpam-6737	442	2	,	,	PUNCT
ejpam-6737	442	3	solitons	soliton	NOUN
ejpam-6737	442	4	&	&	CCONJ
ejpam-6737	442	5	fractals	fractal	NOUN
ejpam-6737	442	6	,	,	PUNCT
ejpam-6737	442	7	2020	2020	NUM
ejpam-6737	442	8	.	.	PUNCT
ejpam-6737	443	1	unpublished	unpublished	ADJ
ejpam-6737	443	2	preprint	preprint	NOUN
ejpam-6737	443	3	or	or	CCONJ
ejpam-6737	443	4	conference	conference	NOUN
ejpam-6737	443	5	abstract	abstract	NOUN
ejpam-6737	443	6	;	;	PUNCT
ejpam-6737	443	7	full	full	ADJ
ejpam-6737	443	8	details	detail	NOUN
ejpam-6737	443	9	may	may	AUX
ejpam-6737	443	10	be	be	AUX
ejpam-6737	443	11	incomplete	incomplete	ADJ
ejpam-6737	443	12	.	.	PUNCT
ejpam-6737	444	1	[	[	X
ejpam-6737	444	2	25	25	NUM
ejpam-6737	444	3	]	]	PUNCT
ejpam-6737	444	4	z.	z.	PROPN
ejpam-6737	444	5	ahmad	ahmad	PROPN
ejpam-6737	444	6	,	,	PUNCT
ejpam-6737	444	7	s.	s.	PROPN
ejpam-6737	444	8	a.	a.	PROPN
ejpam-6737	444	9	el	el	PROPN
ejpam-6737	444	10	-	-	PUNCT
ejpam-6737	444	11	kafrawy	kafrawy	PROPN
ejpam-6737	444	12	,	,	PUNCT
ejpam-6737	444	13	t.	t.	PROPN
ejpam-6737	444	14	a.	a.	PROPN
ejpam-6737	444	15	alandijany	alandijany	PROPN
ejpam-6737	444	16	,	,	PUNCT
ejpam-6737	444	17	f.	f.	PROPN
ejpam-6737	444	18	giannino	giannino	PROPN
ejpam-6737	444	19	,	,	PUNCT
ejpam-6737	444	20	a.	a.	NOUN
ejpam-6737	444	21	a.	a.	NOUN
ejpam-6737	444	22	mirza	mirza	PROPN
ejpam-6737	444	23	,	,	PUNCT
ejpam-6737	444	24	m.	m.	NOUN
ejpam-6737	444	25	m.	m.	PROPN
ejpam-6737	444	26	eldaly	eldaly	PROPN
ejpam-6737	444	27	,	,	PUNCT
ejpam-6737	444	28	and	and	CCONJ
ejpam-6737	444	29	e.	e.	PROPN
ejpam-6737	444	30	i.	i.	PROPN
ejpam-6737	444	31	azhar	azhar	PROPN
ejpam-6737	444	32	.	.	PUNCT
ejpam-6737	445	1	a	a	DET
ejpam-6737	445	2	global	global	ADJ
ejpam-6737	445	3	report	report	NOUN
ejpam-6737	445	4	on	on	ADP
ejpam-6737	445	5	the	the	DET
ejpam-6737	445	6	dynamics	dynamic	NOUN
ejpam-6737	445	7	of	of	ADP
ejpam-6737	445	8	covid-19	covid-19	PROPN
ejpam-6737	445	9	with	with	ADP
ejpam-6737	445	10	quarantine	quarantine	NOUN
ejpam-6737	445	11	and	and	CCONJ
ejpam-6737	445	12	hospitalization	hospitalization	NOUN
ejpam-6737	445	13	:	:	PUNCT
ejpam-6737	445	14	a	a	DET
ejpam-6737	445	15	fractional	fractional	ADJ
ejpam-6737	445	16	order	order	NOUN
ejpam-6737	445	17	model	model	NOUN
ejpam-6737	445	18	with	with	ADP
ejpam-6737	445	19	non	non	ADJ
ejpam-6737	445	20	-	-	ADJ
ejpam-6737	445	21	local	local	ADJ
ejpam-6737	445	22	kernel	kernel	NOUN
ejpam-6737	445	23	.	.	PUNCT
ejpam-6737	446	1	computational	computational	ADJ
ejpam-6737	446	2	biology	biology	NOUN
ejpam-6737	446	3	and	and	CCONJ
ejpam-6737	446	4	chemistry	chemistry	NOUN
ejpam-6737	446	5	,	,	PUNCT
ejpam-6737	446	6	98:107645	98:107645	NUM
ejpam-6737	446	7	,	,	PUNCT
ejpam-6737	446	8	2022	2022	NUM
ejpam-6737	446	9	.	.	PUNCT
ejpam-6737	447	1	[	[	X
ejpam-6737	447	2	26	26	NUM
ejpam-6737	447	3	]	]	X
ejpam-6737	447	4	s.	s.	PROPN
ejpam-6737	447	5	momani	momani	PROPN
ejpam-6737	447	6	,	,	PUNCT
ejpam-6737	447	7	r.	r.	PROPN
ejpam-6737	447	8	p.	p.	PROPN
ejpam-6737	447	9	chauhan	chauhan	PROPN
ejpam-6737	447	10	,	,	PUNCT
ejpam-6737	447	11	s.	s.	PROPN
ejpam-6737	447	12	kumar	kumar	PROPN
ejpam-6737	447	13	,	,	PUNCT
ejpam-6737	447	14	and	and	CCONJ
ejpam-6737	447	15	s.	s.	PROPN
ejpam-6737	447	16	hadid	hadid	PROPN
ejpam-6737	447	17	.	.	PUNCT
ejpam-6737	448	1	analysis	analysis	NOUN
ejpam-6737	448	2	of	of	ADP
ejpam-6737	448	3	social	social	ADJ
ejpam-6737	448	4	media	medium	NOUN
ejpam-6737	448	5	addiction	addiction	NOUN
ejpam-6737	448	6	model	model	NOUN
ejpam-6737	448	7	with	with	ADP
ejpam-6737	448	8	singular	singular	ADJ
ejpam-6737	448	9	operator	operator	NOUN
ejpam-6737	448	10	.	.	PUNCT
ejpam-6737	449	1	fractals	fractal	NOUN
ejpam-6737	449	2	,	,	PUNCT
ejpam-6737	449	3	31(10):2340097	31(10):2340097	NUM
ejpam-6737	449	4	,	,	PUNCT
ejpam-6737	449	5	2023	2023	NUM
ejpam-6737	449	6	.	.	PUNCT
ejpam-6737	450	1	[	[	X
ejpam-6737	450	2	27	27	NUM
ejpam-6737	450	3	]	]	PUNCT
ejpam-6737	450	4	m.	m.	NOUN
ejpam-6737	450	5	dasumani	dasumani	PROPN
ejpam-6737	450	6	,	,	PUNCT
ejpam-6737	450	7	b.	b.	PROPN
ejpam-6737	450	8	s.	s.	PROPN
ejpam-6737	450	9	lassong	lassong	PROPN
ejpam-6737	450	10	,	,	PUNCT
ejpam-6737	450	11	i.	i.	PROPN
ejpam-6737	450	12	k.	k.	PROPN
ejpam-6737	450	13	adu	adu	PROPN
ejpam-6737	450	14	,	,	PUNCT
ejpam-6737	450	15	f.	f.	PROPN
ejpam-6737	450	16	a.	a.	PROPN
ejpam-6737	450	17	wireko	wireko	PROPN
ejpam-6737	450	18	,	,	PUNCT
ejpam-6737	450	19	and	and	CCONJ
ejpam-6737	450	20	s.	s.	PROPN
ejpam-6737	450	21	e.	e.	PROPN
ejpam-6737	450	22	moore	moore	PROPN
ejpam-6737	450	23	.	.	PUNCT
ejpam-6737	451	1	fractional	fractional	ADJ
ejpam-6737	451	2	derivative	derivative	ADJ
ejpam-6737	451	3	technique	technique	NOUN
ejpam-6737	451	4	for	for	ADP
ejpam-6737	451	5	modeling	model	VERB
ejpam-6737	451	6	the	the	DET
ejpam-6737	451	7	dynamics	dynamic	NOUN
ejpam-6737	451	8	of	of	ADP
ejpam-6737	451	9	social	social	ADJ
ejpam-6737	451	10	media	medium	NOUN
ejpam-6737	451	11	impacts	impact	NOUN
ejpam-6737	451	12	.	.	PUNCT
ejpam-6737	452	1	discrete	discrete	ADJ
ejpam-6737	452	2	dynamics	dynamic	NOUN
ejpam-6737	452	3	in	in	ADP
ejpam-6737	452	4	nature	nature	NOUN
ejpam-6737	452	5	and	and	CCONJ
ejpam-6737	452	6	society	society	NOUN
ejpam-6737	452	7	,	,	PUNCT
ejpam-6737	452	8	2024	2024	NUM
ejpam-6737	452	9	,	,	PUNCT
ejpam-6737	452	10	2024	2024	NUM
ejpam-6737	452	11	.	.	PUNCT
ejpam-6737	453	1	[	[	X
ejpam-6737	453	2	28	28	NUM
ejpam-6737	453	3	]	]	X
ejpam-6737	453	4	s.	s.	PROPN
ejpam-6737	453	5	rashid	rashid	PROPN
ejpam-6737	453	6	,	,	PUNCT
ejpam-6737	453	7	r.	r.	PROPN
ejpam-6737	453	8	ashraf	ashraf	PROPN
ejpam-6737	453	9	,	,	PUNCT
ejpam-6737	453	10	and	and	CCONJ
ejpam-6737	453	11	e.	e.	PROPN
ejpam-6737	453	12	bonyah	bonyah	PROPN
ejpam-6737	453	13	.	.	PUNCT
ejpam-6737	454	1	nonlinear	nonlinear	ADJ
ejpam-6737	454	2	dynamics	dynamic	NOUN
ejpam-6737	454	3	of	of	ADP
ejpam-6737	454	4	the	the	DET
ejpam-6737	454	5	media	medium	NOUN
ejpam-6737	454	6	addiction	addiction	NOUN
ejpam-6737	454	7	model	model	NOUN
ejpam-6737	454	8	using	use	VERB
ejpam-6737	454	9	the	the	DET
ejpam-6737	454	10	fractal	fractal	ADJ
ejpam-6737	454	11	–	–	PUNCT
ejpam-6737	454	12	fractional	fractional	ADJ
ejpam-6737	454	13	derivative	derivative	ADJ
ejpam-6737	454	14	technique	technique	NOUN
ejpam-6737	454	15	.	.	PUNCT
ejpam-6737	455	1	complexity	complexity	NOUN
ejpam-6737	455	2	,	,	PUNCT
ejpam-6737	455	3	2022	2022	NUM
ejpam-6737	455	4	,	,	PUNCT
ejpam-6737	455	5	2022	2022	NUM
ejpam-6737	455	6	.	.	PUNCT
ejpam-6737	456	1	[	[	X
ejpam-6737	456	2	29	29	NUM
ejpam-6737	456	3	]	]	X
ejpam-6737	456	4	s.	s.	PROPN
ejpam-6737	456	5	qureshi	qureshi	PROPN
ejpam-6737	456	6	,	,	PUNCT
ejpam-6737	456	7	a.	a.	PROPN
ejpam-6737	456	8	soomro	soomro	PROPN
ejpam-6737	456	9	,	,	PUNCT
ejpam-6737	456	10	i.	i.	PROPN
ejpam-6737	456	11	k.	k.	PROPN
ejpam-6737	456	12	argyros	argyros	PROPN
ejpam-6737	456	13	,	,	PUNCT
ejpam-6737	456	14	k.	k.	PROPN
ejpam-6737	456	15	gdawiec	gdawiec	PROPN
ejpam-6737	456	16	,	,	PUNCT
ejpam-6737	456	17	a.	a.	NOUN
ejpam-6737	456	18	akgül	akgül	NOUN
ejpam-6737	456	19	,	,	PUNCT
ejpam-6737	456	20	and	and	CCONJ
ejpam-6737	456	21	m.	m.	NOUN
ejpam-6737	456	22	alquran	alquran	PROPN
ejpam-6737	456	23	.	.	PUNCT
ejpam-6737	457	1	use	use	NOUN
ejpam-6737	457	2	of	of	ADP
ejpam-6737	457	3	fractional	fractional	ADJ
ejpam-6737	457	4	calculus	calculus	NOUN
ejpam-6737	457	5	to	to	PART
ejpam-6737	457	6	avoid	avoid	VERB
ejpam-6737	457	7	divergence	divergence	NOUN
ejpam-6737	457	8	in	in	ADP
ejpam-6737	457	9	newton	newton	PROPN
ejpam-6737	457	10	-	-	PUNCT
ejpam-6737	457	11	like	like	NOUN
ejpam-6737	457	12	solver	solver	NOUN
ejpam-6737	457	13	for	for	ADP
ejpam-6737	457	14	solving	solve	VERB
ejpam-6737	457	15	ones	one	NOUN
ejpam-6737	457	16	.	.	PUNCT
ejpam-6737	458	1	m.	m.	NOUN
ejpam-6737	458	2	chithra	chithra	PROPN
ejpam-6737	458	3	et	et	PROPN
ejpam-6737	458	4	al	al	PROPN
ejpam-6737	458	5	.	.	PUNCT
ejpam-6737	458	6	/	/	SYM
ejpam-6737	458	7	eur	eur	PROPN
ejpam-6737	458	8	.	.	PUNCT
ejpam-6737	459	1	j.	j.	PROPN
ejpam-6737	459	2	pure	pure	PROPN
ejpam-6737	459	3	appl	appl	PROPN
ejpam-6737	459	4	.	.	PROPN
ejpam-6737	459	5	math	math	PROPN
ejpam-6737	459	6	,	,	PUNCT
ejpam-6737	459	7	18	18	NUM
ejpam-6737	459	8	(	(	PUNCT
ejpam-6737	459	9	4	4	NUM
ejpam-6737	459	10	)	)	PUNCT
ejpam-6737	459	11	(	(	PUNCT
ejpam-6737	459	12	2025	2025	NUM
ejpam-6737	459	13	)	)	PUNCT
ejpam-6737	459	14	,	,	PUNCT
ejpam-6737	459	15	6737	6737	NUM
ejpam-6737	459	16	23	23	NUM
ejpam-6737	459	17	of	of	ADP
ejpam-6737	459	18	23	23	NUM
ejpam-6737	459	19	dimensional	dimensional	ADJ
ejpam-6737	459	20	nonlinear	nonlinear	ADJ
ejpam-6737	459	21	polynomial	polynomial	ADJ
ejpam-6737	459	22	-	-	PUNCT
ejpam-6737	459	23	based	base	VERB
ejpam-6737	459	24	models	model	NOUN
ejpam-6737	459	25	.	.	PUNCT
ejpam-6737	460	1	communications	communication	NOUN
ejpam-6737	460	2	in	in	ADP
ejpam-6737	460	3	nonlinear	nonlinear	ADJ
ejpam-6737	460	4	science	science	NOUN
ejpam-6737	460	5	and	and	CCONJ
ejpam-6737	460	6	numerical	numerical	PROPN
ejpam-6737	460	7	simulation	simulation	PROPN
ejpam-6737	460	8	,	,	PUNCT
ejpam-6737	460	9	143:108631	143:108631	NUM
ejpam-6737	460	10	,	,	PUNCT
ejpam-6737	460	11	2025	2025	NUM
ejpam-6737	460	12	.	.	PUNCT
ejpam-6737	461	1	[	[	X
ejpam-6737	461	2	30	30	NUM
ejpam-6737	461	3	]	]	X
ejpam-6737	461	4	c.	c.	PROPN
ejpam-6737	461	5	w.	w.	PROPN
ejpam-6737	461	6	chang	chang	PROPN
ejpam-6737	461	7	,	,	PUNCT
ejpam-6737	461	8	s.	s.	PROPN
ejpam-6737	461	9	qureshi	qureshi	PROPN
ejpam-6737	461	10	,	,	PUNCT
ejpam-6737	461	11	i.	i.	PROPN
ejpam-6737	461	12	k.	k.	PROPN
ejpam-6737	461	13	argyros	argyros	PROPN
ejpam-6737	461	14	,	,	PUNCT
ejpam-6737	461	15	k.	k.	PROPN
ejpam-6737	461	16	m.	m.	PROPN
ejpam-6737	461	17	saraz	saraz	PROPN
ejpam-6737	461	18	,	,	PUNCT
ejpam-6737	461	19	and	and	CCONJ
ejpam-6737	461	20	e.	e.	PROPN
ejpam-6737	461	21	hincal	hincal	PROPN
ejpam-6737	461	22	.	.	PUNCT
ejpam-6737	462	1	a	a	DET
ejpam-6737	462	2	modified	modify	VERB
ejpam-6737	462	3	fractional	fractional	PROPN
ejpam-6737	462	4	newton	newton	PROPN
ejpam-6737	462	5	’s	’s	PART
ejpam-6737	462	6	solver	solver	NOUN
ejpam-6737	462	7	.	.	PUNCT
ejpam-6737	463	1	axioms	axiom	NOUN
ejpam-6737	463	2	,	,	PUNCT
ejpam-6737	463	3	13(10):689	13(10):689	NUM
ejpam-6737	463	4	,	,	PUNCT
ejpam-6737	463	5	2024	2024	NUM
ejpam-6737	463	6	.	.	PUNCT
ejpam-6737	464	1	[	[	X
ejpam-6737	464	2	31	31	NUM
ejpam-6737	464	3	]	]	X
ejpam-6737	464	4	d.	d.	PROPN
ejpam-6737	464	5	baleanu	baleanu	PROPN
ejpam-6737	464	6	,	,	PUNCT
ejpam-6737	464	7	s.	s.	PROPN
ejpam-6737	464	8	qureshi	qureshi	PROPN
ejpam-6737	464	9	,	,	PUNCT
ejpam-6737	464	10	a.	a.	PROPN
ejpam-6737	464	11	yusuf	yusuf	PROPN
ejpam-6737	464	12	,	,	PUNCT
ejpam-6737	464	13	a.	a.	PROPN
ejpam-6737	464	14	soomro	soomro	PROPN
ejpam-6737	464	15	,	,	PUNCT
ejpam-6737	464	16	and	and	CCONJ
ejpam-6737	464	17	m.	m.	PROPN
ejpam-6737	464	18	s.	s.	PROPN
ejpam-6737	464	19	osman	osman	PROPN
ejpam-6737	464	20	.	.	PUNCT
ejpam-6737	465	1	bi	bi	ADJ
ejpam-6737	465	2	-	-	ADJ
ejpam-6737	465	3	modal	modal	ADJ
ejpam-6737	465	4	covid-19	covid-19	PROPN
ejpam-6737	465	5	transmission	transmission	NOUN
ejpam-6737	465	6	with	with	ADP
ejpam-6737	465	7	caputo	caputo	PROPN
ejpam-6737	465	8	fractional	fractional	PROPN
ejpam-6737	465	9	derivative	derivative	ADJ
ejpam-6737	465	10	using	use	VERB
ejpam-6737	465	11	statistical	statistical	ADJ
ejpam-6737	465	12	epidemic	epidemic	NOUN
ejpam-6737	465	13	cases	case	NOUN
ejpam-6737	465	14	.	.	PUNCT
ejpam-6737	466	1	partial	partial	ADJ
ejpam-6737	466	2	differential	differential	ADJ
ejpam-6737	466	3	equations	equation	NOUN
ejpam-6737	466	4	in	in	ADP
ejpam-6737	466	5	applied	applied	ADJ
ejpam-6737	466	6	mathematics	mathematic	NOUN
ejpam-6737	466	7	,	,	PUNCT
ejpam-6737	466	8	10:100732	10:100732	NUM
ejpam-6737	466	9	,	,	PUNCT
ejpam-6737	466	10	2024	2024	NUM
ejpam-6737	466	11	.	.	PUNCT
ejpam-6737	467	1	[	[	X
ejpam-6737	467	2	32	32	NUM
ejpam-6737	467	3	]	]	PUNCT
ejpam-6737	467	4	p.	p.	NOUN
ejpam-6737	467	5	a.	a.	PROPN
ejpam-6737	467	6	naik	naik	PROPN
ejpam-6737	467	7	,	,	PUNCT
ejpam-6737	467	8	b.	b.	PROPN
ejpam-6737	467	9	m.	m.	PROPN
ejpam-6737	467	10	yeolekar	yeolekar	PROPN
ejpam-6737	467	11	,	,	PUNCT
ejpam-6737	467	12	s.	s.	PROPN
ejpam-6737	467	13	qureshi	qureshi	PROPN
ejpam-6737	467	14	,	,	PUNCT
ejpam-6737	467	15	m.	m.	NOUN
ejpam-6737	467	16	yeolekar	yeolekar	PROPN
ejpam-6737	467	17	,	,	PUNCT
ejpam-6737	467	18	and	and	CCONJ
ejpam-6737	467	19	a.	a.	NOUN
ejpam-6737	467	20	madzvamuse	madzvamuse	NOUN
ejpam-6737	467	21	.	.	PUNCT
ejpam-6737	468	1	modeling	modeling	NOUN
ejpam-6737	468	2	and	and	CCONJ
ejpam-6737	468	3	analysis	analysis	NOUN
ejpam-6737	468	4	of	of	ADP
ejpam-6737	468	5	the	the	DET
ejpam-6737	468	6	fractional	fractional	ADJ
ejpam-6737	468	7	-	-	PUNCT
ejpam-6737	468	8	order	order	NOUN
ejpam-6737	468	9	epidemic	epidemic	NOUN
ejpam-6737	468	10	model	model	NOUN
ejpam-6737	468	11	to	to	PART
ejpam-6737	468	12	investigate	investigate	VERB
ejpam-6737	468	13	mutual	mutual	ADJ
ejpam-6737	468	14	influence	influence	NOUN
ejpam-6737	468	15	in	in	ADP
ejpam-6737	468	16	hiv	hiv	PROPN
ejpam-6737	468	17	/	/	SYM
ejpam-6737	468	18	hcv	hcv	X
ejpam-6737	468	19	co	co	NOUN
ejpam-6737	468	20	-	-	NOUN
ejpam-6737	468	21	infection	infection	NOUN
ejpam-6737	468	22	.	.	PUNCT
ejpam-6737	469	1	nonlinear	nonlinear	ADJ
ejpam-6737	469	2	dynamics	dynamic	NOUN
ejpam-6737	469	3	,	,	PUNCT
ejpam-6737	469	4	112(13):11679–11710	112(13):11679–11710	NUM
ejpam-6737	469	5	,	,	PUNCT
ejpam-6737	469	6	2024	2024	NUM
ejpam-6737	469	7	.	.	PUNCT
ejpam-6737	470	1	[	[	X
ejpam-6737	470	2	33	33	NUM
ejpam-6737	470	3	]	]	PUNCT
ejpam-6737	470	4	a.	a.	NOUN
ejpam-6737	470	5	padder	padder	NOUN
ejpam-6737	470	6	,	,	PUNCT
ejpam-6737	470	7	l.	l.	PROPN
ejpam-6737	470	8	almutairi	almutairi	PROPN
ejpam-6737	470	9	,	,	PUNCT
ejpam-6737	470	10	s.	s.	PROPN
ejpam-6737	470	11	qureshi	qureshi	PROPN
ejpam-6737	470	12	,	,	PUNCT
ejpam-6737	470	13	a.	a.	PROPN
ejpam-6737	470	14	soomro	soomro	PROPN
ejpam-6737	470	15	,	,	PUNCT
ejpam-6737	470	16	a.	a.	PROPN
ejpam-6737	470	17	afroz	afroz	PROPN
ejpam-6737	470	18	,	,	PUNCT
ejpam-6737	470	19	e.	e.	PROPN
ejpam-6737	470	20	hincal	hincal	PROPN
ejpam-6737	470	21	,	,	PUNCT
ejpam-6737	470	22	and	and	CCONJ
ejpam-6737	470	23	a.	a.	NOUN
ejpam-6737	470	24	tassaddiq	tassaddiq	NOUN
ejpam-6737	470	25	.	.	PUNCT
ejpam-6737	471	1	dynamical	dynamical	ADJ
ejpam-6737	471	2	analysis	analysis	NOUN
ejpam-6737	471	3	of	of	ADP
ejpam-6737	471	4	generalized	generalized	ADJ
ejpam-6737	471	5	tumor	tumor	NOUN
ejpam-6737	471	6	model	model	NOUN
ejpam-6737	471	7	with	with	ADP
ejpam-6737	471	8	caputo	caputo	PROPN
ejpam-6737	471	9	fractional	fractional	ADJ
ejpam-6737	471	10	-	-	PUNCT
ejpam-6737	471	11	order	order	NOUN
ejpam-6737	471	12	derivative	derivative	NOUN
ejpam-6737	471	13	.	.	PUNCT
ejpam-6737	472	1	fractal	fractal	PROPN
ejpam-6737	472	2	and	and	CCONJ
ejpam-6737	472	3	fractional	fractional	ADJ
ejpam-6737	472	4	,	,	PUNCT
ejpam-6737	472	5	7(3):258	7(3):258	NUM
ejpam-6737	472	6	,	,	PUNCT
ejpam-6737	472	7	2023	2023	NUM
ejpam-6737	472	8	.	.	PUNCT
ejpam-6737	473	1	[	[	X
ejpam-6737	473	2	34	34	NUM
ejpam-6737	473	3	]	]	PUNCT
ejpam-6737	473	4	l.	l.	PROPN
ejpam-6737	473	5	zhang	zhang	PROPN
ejpam-6737	473	6	,	,	PUNCT
ejpam-6737	473	7	e.	e.	PROPN
ejpam-6737	473	8	addai	addai	PROPN
ejpam-6737	473	9	,	,	PUNCT
ejpam-6737	473	10	j.	j.	PROPN
ejpam-6737	473	11	ackora	ackora	PROPN
ejpam-6737	473	12	-	-	PUNCT
ejpam-6737	473	13	prah	prah	PROPN
ejpam-6737	473	14	,	,	PUNCT
ejpam-6737	473	15	y.	y.	PROPN
ejpam-6737	473	16	d.	d.	PROPN
ejpam-6737	473	17	arthur	arthur	PROPN
ejpam-6737	473	18	,	,	PUNCT
ejpam-6737	473	19	and	and	CCONJ
ejpam-6737	473	20	j.	j.	PROPN
ejpam-6737	473	21	k.	k.	PROPN
ejpam-6737	473	22	k.	k.	PROPN
ejpam-6737	473	23	asamoah	asamoah	PROPN
ejpam-6737	473	24	.	.	PUNCT
ejpam-6737	474	1	fractionalorder	fractionalorder	PROPN
ejpam-6737	474	2	ebola	ebola	PROPN
ejpam-6737	474	3	-	-	PUNCT
ejpam-6737	474	4	malaria	malaria	NOUN
ejpam-6737	474	5	coinfection	coinfection	NOUN
ejpam-6737	474	6	model	model	NOUN
ejpam-6737	474	7	with	with	ADP
ejpam-6737	474	8	a	a	DET
ejpam-6737	474	9	focus	focus	NOUN
ejpam-6737	474	10	on	on	ADP
ejpam-6737	474	11	detection	detection	NOUN
ejpam-6737	474	12	and	and	CCONJ
ejpam-6737	474	13	treatment	treatment	NOUN
ejpam-6737	474	14	rate	rate	NOUN
ejpam-6737	474	15	.	.	PUNCT
ejpam-6737	475	1	computational	computational	ADJ
ejpam-6737	475	2	and	and	CCONJ
ejpam-6737	475	3	mathematical	mathematical	ADJ
ejpam-6737	475	4	methods	method	NOUN
ejpam-6737	475	5	in	in	ADP
ejpam-6737	475	6	medicine	medicine	NOUN
ejpam-6737	475	7	,	,	PUNCT
ejpam-6737	475	8	2022	2022	NUM
ejpam-6737	475	9	,	,	PUNCT
ejpam-6737	475	10	2022	2022	NUM
ejpam-6737	475	11	.	.	PUNCT
ejpam-6737	476	1	[	[	X
ejpam-6737	476	2	35	35	NUM
ejpam-6737	476	3	]	]	X
ejpam-6737	476	4	n.	n.	PROPN
ejpam-6737	476	5	zhang	zhang	PROPN
ejpam-6737	476	6	,	,	PUNCT
ejpam-6737	476	7	e.	e.	PROPN
ejpam-6737	476	8	addai	addai	PROPN
ejpam-6737	476	9	,	,	PUNCT
ejpam-6737	476	10	l.	l.	PROPN
ejpam-6737	476	11	zhang	zhang	PROPN
ejpam-6737	476	12	,	,	PUNCT
ejpam-6737	476	13	m.	m.	NOUN
ejpam-6737	476	14	ngungu	ngungu	PROPN
ejpam-6737	476	15	,	,	PUNCT
ejpam-6737	476	16	e.	e.	PROPN
ejpam-6737	476	17	marinda	marinda	PROPN
ejpam-6737	476	18	,	,	PUNCT
ejpam-6737	476	19	and	and	CCONJ
ejpam-6737	476	20	j.	j.	PROPN
ejpam-6737	476	21	k.	k.	PROPN
ejpam-6737	476	22	k.	k.	PROPN
ejpam-6737	476	23	asamoah	asamoah	PROPN
ejpam-6737	476	24	.	.	PUNCT
ejpam-6737	477	1	fractional	fractional	ADJ
ejpam-6737	477	2	modeling	modeling	NOUN
ejpam-6737	477	3	and	and	CCONJ
ejpam-6737	477	4	numerical	numerical	ADJ
ejpam-6737	477	5	simulation	simulation	NOUN
ejpam-6737	477	6	for	for	ADP
ejpam-6737	477	7	unfolding	unfold	VERB
ejpam-6737	477	8	marburg	marburg	PROPN
ejpam-6737	477	9	–	–	PUNCT
ejpam-6737	477	10	monkeypox	monkeypox	PROPN
ejpam-6737	477	11	virus	virus	NOUN
ejpam-6737	477	12	co	co	NOUN
ejpam-6737	477	13	-	-	NOUN
ejpam-6737	477	14	infection	infection	NOUN
ejpam-6737	477	15	transmission	transmission	NOUN
ejpam-6737	477	16	.	.	PUNCT
ejpam-6737	478	1	fractals	fractal	NOUN
ejpam-6737	478	2	,	,	PUNCT
ejpam-6737	478	3	31(7):2350086	31(7):2350086	NUM
ejpam-6737	478	4	,	,	PUNCT
ejpam-6737	478	5	2023	2023	NUM
ejpam-6737	478	6	.	.	PUNCT
ejpam-6737	479	1	[	[	X
ejpam-6737	479	2	36	36	NUM
ejpam-6737	479	3	]	]	PUNCT
ejpam-6737	479	4	a.	a.	NOUN
ejpam-6737	479	5	atangana	atangana	PROPN
ejpam-6737	479	6	.	.	PUNCT
ejpam-6737	480	1	fractal	fractal	ADJ
ejpam-6737	480	2	-	-	PUNCT
ejpam-6737	480	3	fractional	fractional	ADJ
ejpam-6737	480	4	differentiation	differentiation	NOUN
ejpam-6737	480	5	and	and	CCONJ
ejpam-6737	480	6	integration	integration	NOUN
ejpam-6737	480	7	:	:	PUNCT
ejpam-6737	480	8	connecting	connect	VERB
ejpam-6737	480	9	fractal	fractal	ADJ
ejpam-6737	480	10	calculus	calculus	NOUN
ejpam-6737	480	11	and	and	CCONJ
ejpam-6737	480	12	fractional	fractional	ADJ
ejpam-6737	480	13	calculus	calculus	NOUN
ejpam-6737	480	14	to	to	PART
ejpam-6737	480	15	predict	predict	VERB
ejpam-6737	480	16	complex	complex	ADJ
ejpam-6737	480	17	system	system	NOUN
ejpam-6737	480	18	.	.	PUNCT
ejpam-6737	481	1	chaos	chaos	NOUN
ejpam-6737	481	2	,	,	PUNCT
ejpam-6737	481	3	solitons	soliton	NOUN
ejpam-6737	481	4	&	&	CCONJ
ejpam-6737	481	5	fractals	fractal	NOUN
ejpam-6737	481	6	,	,	PUNCT
ejpam-6737	481	7	102:396–406	102:396–406	NUM
ejpam-6737	481	8	,	,	PUNCT
ejpam-6737	481	9	2017	2017	NUM
ejpam-6737	481	10	.	.	PUNCT
ejpam-6737	482	1	[	[	X
ejpam-6737	482	2	37	37	NUM
ejpam-6737	482	3	]	]	PUNCT
ejpam-6737	482	4	s.	s.	PROPN
ejpam-6737	482	5	w.	w.	PROPN
ejpam-6737	482	6	yao	yao	PROPN
ejpam-6737	482	7	,	,	PUNCT
ejpam-6737	482	8	a.	a.	PROPN
ejpam-6737	482	9	ahmad	ahmad	PROPN
ejpam-6737	482	10	,	,	PUNCT
ejpam-6737	482	11	m.	m.	PROPN
ejpam-6737	482	12	inc	inc	PROPN
ejpam-6737	482	13	,	,	PUNCT
ejpam-6737	482	14	m.	m.	PROPN
ejpam-6737	482	15	farman	farman	PROPN
ejpam-6737	482	16	,	,	PUNCT
ejpam-6737	482	17	a.	a.	PROPN
ejpam-6737	482	18	ghaffar	ghaffar	NOUN
ejpam-6737	482	19	,	,	PUNCT
ejpam-6737	482	20	and	and	CCONJ
ejpam-6737	482	21	a.	a.	NOUN
ejpam-6737	482	22	akgul	akgul	NOUN
ejpam-6737	482	23	.	.	PUNCT
ejpam-6737	483	1	analysis	analysis	NOUN
ejpam-6737	483	2	of	of	ADP
ejpam-6737	483	3	fractional	fractional	ADJ
ejpam-6737	483	4	order	order	NOUN
ejpam-6737	483	5	diarrhea	diarrhea	NOUN
ejpam-6737	483	6	model	model	NOUN
ejpam-6737	483	7	using	use	VERB
ejpam-6737	483	8	fractal	fractal	ADJ
ejpam-6737	483	9	fractional	fractional	ADJ
ejpam-6737	483	10	operator	operator	NOUN
ejpam-6737	483	11	.	.	PUNCT
ejpam-6737	484	1	fractals	fractal	NOUN
ejpam-6737	484	2	,	,	PUNCT
ejpam-6737	484	3	30(5):2240173	30(5):2240173	NUM
ejpam-6737	484	4	,	,	PUNCT
ejpam-6737	484	5	2022	2022	NUM
ejpam-6737	484	6	.	.	PUNCT