id	sid	tid	token	lemma	pos
iajs-3359	1	1	378	378	NUM
iajs-3359	1	2	this	this	DET
iajs-3359	1	3	work	work	NOUN
iajs-3359	1	4	is	be	AUX
iajs-3359	1	5	licensed	license	VERB
iajs-3359	1	6	under	under	ADP
iajs-3359	1	7	a	a	DET
iajs-3359	1	8	creative	creative	ADJ
iajs-3359	1	9	commons	common	NOUN
iajs-3359	1	10	attribution	attribution	NOUN
iajs-3359	1	11	4.0	4.0	NUM
iajs-3359	1	12	international	international	ADJ
iajs-3359	1	13	license	license	NOUN
iajs-3359	1	14	ihjpas.37	ihjpas.37	PROPN
iajs-3359	1	15	(	(	PUNCT
iajs-3359	1	16	2	2	NUM
iajs-3359	1	17	)	)	PUNCT
iajs-3359	1	18	2024	2024	NUM
iajs-3359	1	19	ibn	ibn	PROPN
iajs-3359	1	20	al	al	PROPN
iajs-3359	1	21	-	-	PUNCT
iajs-3359	1	22	haitham	haitham	PROPN
iajs-3359	1	23	journal	journal	PROPN
iajs-3359	1	24	for	for	ADP
iajs-3359	1	25	pure	pure	ADJ
iajs-3359	1	26	and	and	CCONJ
iajs-3359	1	27	applied	applied	ADJ
iajs-3359	1	28	sciences	sciences	PROPN
iajs-3359	1	29	journal	journal	PROPN
iajs-3359	1	30	homepage	homepage	NOUN
iajs-3359	1	31	:	:	PUNCT
iajs-3359	1	32	jih.uobaghdad.edu.iq	jih.uobaghdad.edu.iq	NOUN
iajs-3359	1	33	pissn	pissn	ADJ
iajs-3359	1	34	:	:	PUNCT
iajs-3359	1	35	1609	1609	NUM
iajs-3359	1	36	-	-	SYM
iajs-3359	1	37	4042	4042	NUM
iajs-3359	1	38	,	,	PUNCT
iajs-3359	1	39	eissn	eissn	NOUN
iajs-3359	1	40	:	:	PUNCT
iajs-3359	1	41	2521	2521	NUM
iajs-3359	1	42	-	-	SYM
iajs-3359	1	43	3407	3407	NUM
iajs-3359	1	44	zahraa	zahraa	PROPN
iajs-3359	1	45	k.	k.	PROPN
iajs-3359	1	46	abdulla*1	abdulla*1	PROPN
iajs-3359	1	47	,	,	PUNCT
iajs-3359	1	48	emna	emna	VERB
iajs-3359	1	49	ouhibi	ouhibi	NOUN
iajs-3359	1	50	2	2	NUM
iajs-3359	1	51	and	and	CCONJ
iajs-3359	1	52	saad	saad	PROPN
iajs-3359	1	53	naji	naji	PROPN
iajs-3359	1	54	al	al	PROPN
iajs-3359	1	55	-	-	PROPN
iajs-3359	1	56	azzawi	azzawi	PROPN
iajs-3359	1	57	3	3	NUM
iajs-3359	1	58	1,3department	1,3department	NUM
iajs-3359	1	59	of	of	ADP
iajs-3359	1	60	mathematics	mathematic	NOUN
iajs-3359	1	61	,	,	PUNCT
iajs-3359	1	62	college	college	NOUN
iajs-3359	1	63	of	of	ADP
iajs-3359	1	64	science	science	NOUN
iajs-3359	1	65	for	for	ADP
iajs-3359	1	66	women	woman	NOUN
iajs-3359	1	67	,	,	PUNCT
iajs-3359	1	68	university	university	NOUN
iajs-3359	1	69	of	of	ADP
iajs-3359	1	70	baghdad	baghdad	PROPN
iajs-3359	1	71	,	,	PUNCT
iajs-3359	1	72	baghdad	baghdad	PROPN
iajs-3359	1	73	,	,	PUNCT
iajs-3359	1	74	iraq	iraq	PROPN
iajs-3359	1	75	.	.	PUNCT
iajs-3359	2	1	2université	2université	NUM
iajs-3359	2	2	de	de	X
iajs-3359	2	3	tunis	tunis	PROPN
iajs-3359	2	4	el	el	PROPN
iajs-3359	2	5	manar	manar	PROPN
iajs-3359	2	6	,	,	PUNCT
iajs-3359	2	7	école	école	PROPN
iajs-3359	2	8	nationale	nationale	PROPN
iajs-3359	2	9	d’ingénieurs	d’ingénieurs	PROPN
iajs-3359	2	10	de	de	X
iajs-3359	2	11	tunis	tunis	PROPN
iajs-3359	2	12	,	,	PUNCT
iajs-3359	2	13	lr11es20	lr11es20	X
iajs-3359	2	14	laboratoire	laboratoire	PROPN
iajs-3359	2	15	analyse	analyse	PROPN
iajs-3359	2	16	,	,	PUNCT
iajs-3359	2	17	conception	conception	NOUN
iajs-3359	2	18	et	et	PROPN
iajs-3359	2	19	commande	commande	PROPN
iajs-3359	2	20	des	des	PROPN
iajs-3359	2	21	systèmes	systèmes	PROPN
iajs-3359	2	22	,	,	PUNCT
iajs-3359	2	23	tunis	tunis	NOUN
iajs-3359	2	24	,	,	PUNCT
iajs-3359	2	25	tunisi	tunisi	ADJ
iajs-3359	2	26	.	.	PUNCT
iajs-3359	3	1	*	*	PUNCT
iajs-3359	3	2	corresponding	correspond	VERB
iajs-3359	3	3	author	author	NOUN
iajs-3359	3	4	.	.	PUNCT
iajs-3359	4	1	abstract	abstract	ADJ
iajs-3359	4	2	this	this	DET
iajs-3359	4	3	article	article	NOUN
iajs-3359	4	4	talks	talk	VERB
iajs-3359	4	5	about	about	ADP
iajs-3359	4	6	a	a	DET
iajs-3359	4	7	model	model	NOUN
iajs-3359	4	8	of	of	ADP
iajs-3359	4	9	fractional	fractional	ADJ
iajs-3359	4	10	differential	differential	ADJ
iajs-3359	4	11	equations	equation	NOUN
iajs-3359	4	12	to	to	PART
iajs-3359	4	13	describe	describe	VERB
iajs-3359	4	14	how	how	SCONJ
iajs-3359	4	15	covid-19	covid-19	PROPN
iajs-3359	4	16	is	be	AUX
iajs-3359	4	17	spread	spread	VERB
iajs-3359	4	18	in	in	ADP
iajs-3359	4	19	the	the	DET
iajs-3359	4	20	world	world	NOUN
iajs-3359	4	21	in	in	ADP
iajs-3359	4	22	general	general	ADJ
iajs-3359	4	23	and	and	CCONJ
iajs-3359	4	24	iraq	iraq	PROPN
iajs-3359	4	25	in	in	ADP
iajs-3359	4	26	particular	particular	ADJ
iajs-3359	4	27	.	.	PUNCT
iajs-3359	5	1	the	the	DET
iajs-3359	5	2	model	model	NOUN
iajs-3359	5	3	contains	contain	VERB
iajs-3359	5	4	five	five	NUM
iajs-3359	5	5	fractional	fractional	ADJ
iajs-3359	5	6	differential	differential	ADJ
iajs-3359	5	7	equations	equation	NOUN
iajs-3359	5	8	.	.	PUNCT
iajs-3359	6	1	moreover	moreover	ADV
iajs-3359	6	2	,	,	PUNCT
iajs-3359	6	3	we	we	PRON
iajs-3359	6	4	have	have	AUX
iajs-3359	6	5	proven	prove	VERB
iajs-3359	6	6	the	the	DET
iajs-3359	6	7	existence	existence	NOUN
iajs-3359	6	8	and	and	CCONJ
iajs-3359	6	9	uniqueness	uniqueness	NOUN
iajs-3359	6	10	of	of	ADP
iajs-3359	6	11	the	the	DET
iajs-3359	6	12	solution	solution	NOUN
iajs-3359	6	13	of	of	ADP
iajs-3359	6	14	the	the	DET
iajs-3359	6	15	model	model	NOUN
iajs-3359	6	16	,	,	PUNCT
iajs-3359	6	17	found	find	VERB
iajs-3359	6	18	the	the	DET
iajs-3359	6	19	equilibrium	equilibrium	NOUN
iajs-3359	6	20	points	point	NOUN
iajs-3359	6	21	of	of	ADP
iajs-3359	6	22	the	the	DET
iajs-3359	6	23	model	model	NOUN
iajs-3359	6	24	and	and	CCONJ
iajs-3359	6	25	checked	check	VERB
iajs-3359	6	26	its	its	PRON
iajs-3359	6	27	stability	stability	NOUN
iajs-3359	6	28	.	.	PUNCT
iajs-3359	7	1	then	then	ADV
iajs-3359	7	2	we	we	PRON
iajs-3359	7	3	solved	solve	VERB
iajs-3359	7	4	it	it	PRON
iajs-3359	7	5	using	use	VERB
iajs-3359	7	6	a	a	DET
iajs-3359	7	7	fractional	fractional	ADJ
iajs-3359	7	8	linear	linear	ADJ
iajs-3359	7	9	multi	multi	ADJ
iajs-3359	7	10	-	-	ADJ
iajs-3359	7	11	step	step	ADJ
iajs-3359	7	12	method	method	NOUN
iajs-3359	7	13	.	.	PUNCT
iajs-3359	8	1	when	when	SCONJ
iajs-3359	8	2	we	we	PRON
iajs-3359	8	3	compare	compare	VERB
iajs-3359	8	4	the	the	DET
iajs-3359	8	5	results	result	NOUN
iajs-3359	8	6	with	with	ADP
iajs-3359	8	7	the	the	DET
iajs-3359	8	8	data	datum	NOUN
iajs-3359	8	9	documented	document	VERB
iajs-3359	8	10	by	by	ADP
iajs-3359	8	11	the	the	DET
iajs-3359	8	12	world	world	PROPN
iajs-3359	8	13	health	health	NOUN
iajs-3359	8	14	organisation	organisation	NOUN
iajs-3359	8	15	(	(	PUNCT
iajs-3359	8	16	who	who	PRON
iajs-3359	8	17	)	)	PUNCT
iajs-3359	8	18	,	,	PUNCT
iajs-3359	8	19	we	we	PRON
iajs-3359	8	20	find	find	VERB
iajs-3359	8	21	that	that	SCONJ
iajs-3359	8	22	the	the	DET
iajs-3359	8	23	total	total	ADJ
iajs-3359	8	24	number	number	NOUN
iajs-3359	8	25	of	of	ADP
iajs-3359	8	26	active	active	ADJ
iajs-3359	8	27	cases	case	NOUN
iajs-3359	8	28	in	in	ADP
iajs-3359	8	29	the	the	DET
iajs-3359	8	30	world	world	NOUN
iajs-3359	8	31	are	be	AUX
iajs-3359	8	32	equal	equal	ADJ
iajs-3359	8	33	to	to	ADP
iajs-3359	8	34	584498294	584498294	NUM
iajs-3359	8	35	on	on	ADP
iajs-3359	8	36	3/8/2022	3/8/2022	NUM
iajs-3359	8	37	,	,	PUNCT
iajs-3359	8	38	and	and	CCONJ
iajs-3359	8	39	it	it	PRON
iajs-3359	8	40	is	be	AUX
iajs-3359	8	41	similar	similar	ADJ
iajs-3359	8	42	to	to	ADP
iajs-3359	8	43	what	what	PRON
iajs-3359	8	44	was	be	AUX
iajs-3359	8	45	done	do	VERB
iajs-3359	8	46	with	with	ADP
iajs-3359	8	47	the	the	DET
iajs-3359	8	48	system	system	NOUN
iajs-3359	8	49	.	.	PUNCT
iajs-3359	9	1	the	the	DET
iajs-3359	9	2	number	number	NOUN
iajs-3359	9	3	of	of	ADP
iajs-3359	9	4	those	those	PRON
iajs-3359	9	5	who	who	PRON
iajs-3359	9	6	have	have	AUX
iajs-3359	9	7	recovered	recover	VERB
iajs-3359	9	8	and	and	CCONJ
iajs-3359	9	9	died	die	VERB
iajs-3359	9	10	from	from	ADP
iajs-3359	9	11	the	the	DET
iajs-3359	9	12	disease	disease	NOUN
iajs-3359	9	13	has	have	AUX
iajs-3359	9	14	also	also	ADV
iajs-3359	9	15	been	be	AUX
iajs-3359	9	16	calculated	calculate	VERB
iajs-3359	9	17	.	.	PUNCT
iajs-3359	10	1	for	for	ADP
iajs-3359	10	2	iraq	iraq	PROPN
iajs-3359	10	3	,	,	PUNCT
iajs-3359	10	4	the	the	DET
iajs-3359	10	5	total	total	ADJ
iajs-3359	10	6	number	number	NOUN
iajs-3359	10	7	of	of	ADP
iajs-3359	10	8	active	active	ADJ
iajs-3359	10	9	cases	case	NOUN
iajs-3359	10	10	is	be	AUX
iajs-3359	10	11	2448484	2448484	NUM
iajs-3359	10	12	and	and	CCONJ
iajs-3359	10	13	the	the	DET
iajs-3359	10	14	total	total	ADJ
iajs-3359	10	15	number	number	NOUN
iajs-3359	10	16	of	of	ADP
iajs-3359	10	17	active	active	ADJ
iajs-3359	10	18	cases	case	NOUN
iajs-3359	10	19	calculated	calculate	VERB
iajs-3359	10	20	by	by	ADP
iajs-3359	10	21	the	the	DET
iajs-3359	10	22	model	model	NOUN
iajs-3359	10	23	is	be	AUX
iajs-3359	10	24	2628000	2628000	NUM
iajs-3359	10	25	.	.	PUNCT
iajs-3359	11	1	in	in	ADP
iajs-3359	11	2	comparison	comparison	NOUN
iajs-3359	11	3	,	,	PUNCT
iajs-3359	11	4	the	the	DET
iajs-3359	11	5	calculated	calculate	VERB
iajs-3359	11	6	number	number	NOUN
iajs-3359	11	7	is	be	AUX
iajs-3359	11	8	slightly	slightly	ADV
iajs-3359	11	9	higher	high	ADJ
iajs-3359	11	10	than	than	ADP
iajs-3359	11	11	what	what	PRON
iajs-3359	11	12	is	be	AUX
iajs-3359	11	13	given	give	VERB
iajs-3359	11	14	in	in	ADP
iajs-3359	11	15	the	the	DET
iajs-3359	11	16	data	datum	NOUN
iajs-3359	11	17	.	.	PUNCT
iajs-3359	12	1	this	this	PRON
iajs-3359	12	2	is	be	AUX
iajs-3359	12	3	quite	quite	ADV
iajs-3359	12	4	normal	normal	ADJ
iajs-3359	12	5	because	because	SCONJ
iajs-3359	12	6	not	not	PART
iajs-3359	12	7	all	all	DET
iajs-3359	12	8	infected	infected	ADJ
iajs-3359	12	9	patients	patient	NOUN
iajs-3359	12	10	go	go	VERB
iajs-3359	12	11	to	to	ADP
iajs-3359	12	12	the	the	DET
iajs-3359	12	13	health	health	NOUN
iajs-3359	12	14	centres	centre	NOUN
iajs-3359	12	15	and	and	CCONJ
iajs-3359	12	16	it	it	PRON
iajs-3359	12	17	is	be	AUX
iajs-3359	12	18	difficult	difficult	ADJ
iajs-3359	12	19	to	to	PART
iajs-3359	12	20	record	record	VERB
iajs-3359	12	21	them	they	PRON
iajs-3359	12	22	as	as	ADP
iajs-3359	12	23	active	active	ADJ
iajs-3359	12	24	cases	case	NOUN
iajs-3359	12	25	.	.	PUNCT
iajs-3359	13	1	keywords	keyword	NOUN
iajs-3359	13	2	:	:	PUNCT
iajs-3359	13	3	caputo	caputo	PROPN
iajs-3359	13	4	fractional	fractional	PROPN
iajs-3359	13	5	derivative	derivative	PROPN
iajs-3359	13	6	,	,	PUNCT
iajs-3359	13	7	riemann	riemann	PROPN
iajs-3359	13	8	-	-	PUNCT
iajs-3359	13	9	liouville	liouville	VERB
iajs-3359	13	10	fractional	fractional	ADJ
iajs-3359	13	11	derivative	derivative	ADJ
iajs-3359	13	12	,	,	PUNCT
iajs-3359	13	13	fractional	fractional	ADJ
iajs-3359	13	14	covid-19	covid-19	PROPN
iajs-3359	13	15	model	model	NOUN
iajs-3359	13	16	,	,	PUNCT
iajs-3359	13	17	numerical	numerical	ADJ
iajs-3359	13	18	simulations	simulation	NOUN
iajs-3359	13	19	,	,	PUNCT
iajs-3359	13	20	fractional	fractional	ADJ
iajs-3359	13	21	linear	linear	ADJ
iajs-3359	13	22	multi	multi	ADJ
iajs-3359	13	23	-	-	ADJ
iajs-3359	13	24	step	step	ADJ
iajs-3359	13	25	method	method	NOUN
iajs-3359	13	26	.	.	PUNCT
iajs-3359	14	1	1	1	X
iajs-3359	14	2	.	.	X
iajs-3359	14	3	introduction	introduction	NOUN
iajs-3359	14	4	in	in	ADP
iajs-3359	14	5	2019	2019	NUM
iajs-3359	14	6	,	,	PUNCT
iajs-3359	14	7	a	a	DET
iajs-3359	14	8	new	new	ADJ
iajs-3359	14	9	respiratory	respiratory	ADJ
iajs-3359	14	10	disease	disease	NOUN
iajs-3359	14	11	emerged	emerge	VERB
iajs-3359	14	12	that	that	PRON
iajs-3359	14	13	caused	cause	VERB
iajs-3359	14	14	the	the	DET
iajs-3359	14	15	death	death	NOUN
iajs-3359	14	16	of	of	ADP
iajs-3359	14	17	a	a	DET
iajs-3359	14	18	large	large	ADJ
iajs-3359	14	19	number	number	NOUN
iajs-3359	14	20	of	of	ADP
iajs-3359	14	21	people	people	NOUN
iajs-3359	14	22	around	around	ADP
iajs-3359	14	23	the	the	DET
iajs-3359	14	24	world	world	NOUN
iajs-3359	14	25	,	,	PUNCT
iajs-3359	14	26	starting	start	VERB
iajs-3359	14	27	.	.	PUNCT
iajs-3359	15	1	it	it	PRON
iajs-3359	15	2	started	start	VERB
iajs-3359	15	3	in	in	ADP
iajs-3359	15	4	wuhan	wuhan	PROPN
iajs-3359	15	5	and	and	CCONJ
iajs-3359	15	6	spread	spread	VERB
iajs-3359	15	7	to	to	ADP
iajs-3359	15	8	every	every	DET
iajs-3359	15	9	country	country	NOUN
iajs-3359	15	10	in	in	ADP
iajs-3359	15	11	the	the	DET
iajs-3359	15	12	world	world	NOUN
iajs-3359	16	1	[	[	X
iajs-3359	16	2	1	1	NUM
iajs-3359	16	3	]	]	PUNCT
iajs-3359	16	4	.	.	PUNCT
iajs-3359	17	1	this	this	DET
iajs-3359	17	2	disease	disease	NOUN
iajs-3359	17	3	is	be	AUX
iajs-3359	17	4	caused	cause	VERB
iajs-3359	17	5	by	by	ADP
iajs-3359	17	6	a	a	DET
iajs-3359	17	7	virus	virus	NOUN
iajs-3359	17	8	called	call	VERB
iajs-3359	17	9	coronavirus	coronavirus	NOUN
iajs-3359	17	10	.	.	PUNCT
iajs-3359	18	1	covid-19	covid-19	PROPN
iajs-3359	18	2	attacks	attack	VERB
iajs-3359	18	3	the	the	DET
iajs-3359	18	4	respiratory	respiratory	ADJ
iajs-3359	18	5	system	system	NOUN
iajs-3359	18	6	and	and	CCONJ
iajs-3359	18	7	lowers	lower	VERB
iajs-3359	18	8	oxygen	oxygen	NOUN
iajs-3359	18	9	levels	level	NOUN
iajs-3359	18	10	in	in	ADP
iajs-3359	18	11	the	the	DET
iajs-3359	18	12	blood	blood	NOUN
iajs-3359	18	13	,	,	PUNCT
iajs-3359	18	14	causing	cause	VERB
iajs-3359	18	15	problems	problem	NOUN
iajs-3359	18	16	.	.	PUNCT
iajs-3359	19	1	these	these	DET
iajs-3359	19	2	problems	problem	NOUN
iajs-3359	19	3	vary	vary	VERB
iajs-3359	19	4	from	from	ADP
iajs-3359	19	5	person	person	NOUN
iajs-3359	19	6	to	to	ADP
iajs-3359	19	7	person	person	NOUN
iajs-3359	19	8	.	.	PUNCT
iajs-3359	20	1	who	who	PRON
iajs-3359	20	2	classified	classify	VERB
iajs-3359	20	3	covid-19	covid-19	PROPN
iajs-3359	20	4	as	as	ADP
iajs-3359	20	5	an	an	DET
iajs-3359	20	6	epidemic	epidemic	NOUN
iajs-3359	20	7	on	on	ADP
iajs-3359	20	8	11	11	NUM
iajs-3359	20	9	march	march	NOUN
iajs-3359	20	10	2020	2020	NUM
iajs-3359	20	11	due	due	ADP
iajs-3359	20	12	to	to	ADP
iajs-3359	20	13	its	its	PRON
iajs-3359	20	14	rapid	rapid	ADJ
iajs-3359	20	15	spread	spread	NOUN
iajs-3359	20	16	and	and	CCONJ
iajs-3359	20	17	high	high	ADJ
iajs-3359	20	18	mortality	mortality	NOUN
iajs-3359	20	19	rate	rate	NOUN
iajs-3359	20	20	.	.	PUNCT
iajs-3359	21	1	covid-19	covid-19	PROPN
iajs-3359	21	2	became	become	VERB
iajs-3359	21	3	the	the	DET
iajs-3359	21	4	focus	focus	NOUN
iajs-3359	21	5	of	of	ADP
iajs-3359	21	6	the	the	DET
iajs-3359	21	7	world	world	NOUN
iajs-3359	21	8	,	,	PUNCT
iajs-3359	21	9	especially	especially	ADV
iajs-3359	21	10	researchers	researcher	NOUN
iajs-3359	21	11	,	,	PUNCT
iajs-3359	21	12	including	include	VERB
iajs-3359	21	13	mathematicians	mathematician	NOUN
iajs-3359	21	14	[	[	PUNCT
iajs-3359	21	15	2	2	NUM
iajs-3359	21	16	-	-	SYM
iajs-3359	21	17	4	4	NUM
iajs-3359	21	18	]	]	PUNCT
iajs-3359	21	19	.	.	PUNCT
iajs-3359	22	1	to	to	PART
iajs-3359	22	2	find	find	VERB
iajs-3359	22	3	solutions	solution	NOUN
iajs-3359	22	4	and	and	CCONJ
iajs-3359	22	5	strategies	strategy	NOUN
iajs-3359	22	6	that	that	PRON
iajs-3359	22	7	can	can	AUX
iajs-3359	22	8	help	help	VERB
iajs-3359	22	9	contain	contain	VERB
iajs-3359	22	10	the	the	DET
iajs-3359	22	11	spread	spread	NOUN
iajs-3359	22	12	of	of	ADP
iajs-3359	22	13	this	this	DET
iajs-3359	22	14	virus	virus	NOUN
iajs-3359	22	15	.	.	PUNCT
iajs-3359	23	1	with	with	ADP
iajs-3359	23	2	the	the	DET
iajs-3359	23	3	help	help	NOUN
iajs-3359	23	4	of	of	ADP
iajs-3359	23	5	ordinary	ordinary	ADJ
iajs-3359	23	6	or	or	CCONJ
iajs-3359	23	7	fractional	fractional	ADJ
iajs-3359	23	8	order	order	NOUN
iajs-3359	23	9	system	system	NOUN
iajs-3359	23	10	differential	differential	NOUN
iajs-3359	23	11	equations	equation	NOUN
iajs-3359	23	12	,	,	PUNCT
iajs-3359	23	13	delays	delay	NOUN
iajs-3359	23	14	and	and	CCONJ
iajs-3359	23	15	stochastic	stochastic	ADJ
iajs-3359	23	16	models	model	NOUN
iajs-3359	23	17	.	.	PUNCT
iajs-3359	24	1	many	many	ADJ
iajs-3359	24	2	researchers	researcher	NOUN
iajs-3359	24	3	have	have	AUX
iajs-3359	24	4	been	be	AUX
iajs-3359	24	5	able	able	ADJ
iajs-3359	24	6	to	to	PART
iajs-3359	24	7	construct	construct	VERB
iajs-3359	24	8	and	and	CCONJ
iajs-3359	24	9	develop	develop	VERB
iajs-3359	24	10	mathematical	mathematical	ADJ
iajs-3359	24	11	models	model	NOUN
iajs-3359	24	12	to	to	PART
iajs-3359	24	13	describe	describe	VERB
iajs-3359	24	14	the	the	DET
iajs-3359	24	15	dynamics	dynamic	NOUN
iajs-3359	24	16	of	of	ADP
iajs-3359	24	17	the	the	DET
iajs-3359	24	18	disease	disease	NOUN
iajs-3359	24	19	,	,	PUNCT
iajs-3359	24	20	e.g.	e.g.	ADV
iajs-3359	24	21	sir	sir	NOUN
iajs-3359	24	22	,	,	PUNCT
iajs-3359	24	23	seir	seir	NOUN
iajs-3359	24	24	,	,	PUNCT
iajs-3359	24	25	sis	sis	NOUN
iajs-3359	24	26	,	,	PUNCT
iajs-3359	24	27	seirf	seirf	NOUN
iajs-3359	24	28	…	…	SYM
iajs-3359	24	29	etc	etc	X
iajs-3359	25	1	[	[	X
iajs-3359	25	2	5	5	NUM
iajs-3359	25	3	-	-	SYM
iajs-3359	25	4	8	8	NUM
iajs-3359	25	5	]	]	PUNCT
iajs-3359	25	6	.	.	PUNCT
iajs-3359	26	1	shah	shah	PROPN
iajs-3359	26	2	and	and	CCONJ
iajs-3359	26	3	mittal	mittal	NOUN
iajs-3359	27	1	[	[	X
iajs-3359	27	2	9	9	NUM
iajs-3359	27	3	]	]	PUNCT
iajs-3359	27	4	described	describe	VERB
iajs-3359	27	5	the	the	DET
iajs-3359	27	6	basics	basic	NOUN
iajs-3359	27	7	of	of	ADP
iajs-3359	27	8	epidemiologic	epidemiologic	ADJ
iajs-3359	27	9	compartmental	compartmental	ADJ
iajs-3359	27	10	models	model	NOUN
iajs-3359	27	11	and	and	CCONJ
iajs-3359	27	12	the	the	DET
iajs-3359	27	13	necessary	necessary	ADJ
iajs-3359	27	14	analyses	analysis	NOUN
iajs-3359	27	15	that	that	PRON
iajs-3359	27	16	contains	contain	VERB
iajs-3359	27	17	a	a	DET
iajs-3359	27	18	large	large	ADJ
iajs-3359	27	19	number	number	NOUN
iajs-3359	27	20	of	of	ADP
iajs-3359	27	21	studies	study	NOUN
iajs-3359	27	22	on	on	ADP
iajs-3359	27	23	the	the	DET
iajs-3359	27	24	corona	corona	NOUN
iajs-3359	27	25	epidemic	epidemic	NOUN
iajs-3359	27	26	,	,	PUNCT
iajs-3359	27	27	using	use	VERB
iajs-3359	27	28	various	various	ADJ
iajs-3359	27	29	models	model	NOUN
iajs-3359	27	30	of	of	ADP
iajs-3359	27	31	systems	system	NOUN
iajs-3359	27	32	of	of	ADP
iajs-3359	27	33	ordinary	ordinary	ADJ
iajs-3359	27	34	differential	differential	ADJ
iajs-3359	27	35	equations	equation	NOUN
iajs-3359	27	36	that	that	PRON
iajs-3359	27	37	describe	describe	VERB
iajs-3359	27	38	the	the	DET
iajs-3359	27	39	spread	spread	NOUN
iajs-3359	27	40	of	of	ADP
iajs-3359	27	41	the	the	DET
iajs-3359	27	42	corona	corona	NOUN
iajs-3359	27	43	epidemic	epidemic	NOUN
iajs-3359	27	44	and	and	CCONJ
iajs-3359	27	45	calculate	calculate	VERB
iajs-3359	27	46	the	the	DET
iajs-3359	27	47	received	receive	VERB
iajs-3359	27	48	23	23	NUM
iajs-3359	27	49	march	march	NOUN
iajs-3359	27	50	2023	2023	NUM
iajs-3359	27	51	accepted	accept	VERB
iajs-3359	27	52	22	22	NUM
iajs-3359	27	53	june	june	PROPN
iajs-3359	27	54	2023	2023	NUM
iajs-3359	27	55	published	publish	VERB
iajs-3359	27	56	20	20	NUM
iajs-3359	27	57	april	april	PROPN
iajs-3359	27	58	2024	2024	NUM
iajs-3359	27	59	fractional	fractional	ADJ
iajs-3359	27	60	modelling	modelling	NOUN
iajs-3359	27	61	for	for	ADP
iajs-3359	27	62	covid-19	covid-19	PROPN
iajs-3359	27	63	in	in	ADP
iajs-3359	27	64	the	the	DET
iajs-3359	27	65	world	world	NOUN
iajs-3359	27	66	and	and	CCONJ
iajs-3359	27	67	iraq	iraq	PROPN
iajs-3359	27	68	doi.org/10.30526/37.2.3359	doi.org/10.30526/37.2.3359	VERB
iajs-3359	27	69	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-3359	27	70	https://jih.uobaghdad.edu.iq/index.php/j/index#1609-4042	https://jih.uobaghdad.edu.iq/index.php/j/index#1609-4042	PROPN
iajs-3359	27	71	https://jih.uobaghdad.edu.iq/index.php/j/index#2521-3407	https://jih.uobaghdad.edu.iq/index.php/j/index#2521-3407	VERB
iajs-3359	28	1	https://orcid.org/0000-0003-4092-434x	https://orcid.org/0000-0003-4092-434x	ADP
iajs-3359	28	2	mailto:zahraa.khodair1203a@csw.uobaghdad.edu.iq	mailto:zahraa.khodair1203a@csw.uobaghdad.edu.iq	PROPN
iajs-3359	28	3	https://orcid.org/0000-0002-0632-3455	https://orcid.org/0000-0002-0632-3455	PROPN
iajs-3359	28	4	mailto:emna.ouhibi@enit.utm.tn	mailto:emna.ouhibi@enit.utm.tn	PROPN
iajs-3359	28	5	https://orcid.org/0000-0002-6865-979	https://orcid.org/0000-0002-6865-979	NUM
iajs-3359	28	6	mailto:saadnaji58@gmail.com	mailto:saadnaji58@gmail.com	PROPN
iajs-3359	28	7	ihjpas	ihjpas	PROPN
iajs-3359	28	8	.	.	PUNCT
iajs-3359	29	1	37	37	NUM
iajs-3359	29	2	(	(	PUNCT
iajs-3359	29	3	2	2	NUM
iajs-3359	29	4	)	)	PUNCT
iajs-3359	29	5	2024	2024	NUM
iajs-3359	29	6	379	379	NUM
iajs-3359	29	7	active	active	ADJ
iajs-3359	29	8	case	case	NOUN
iajs-3359	29	9	in	in	ADP
iajs-3359	29	10	different	different	ADJ
iajs-3359	29	11	countries	country	NOUN
iajs-3359	29	12	of	of	ADP
iajs-3359	29	13	the	the	DET
iajs-3359	29	14	world	world	NOUN
iajs-3359	29	15	.	.	PUNCT
iajs-3359	30	1	higazy	higazy	PROPN
iajs-3359	30	2	m	m	PROPN
iajs-3359	30	3	,	,	PUNCT
iajs-3359	30	4	et	et	PROPN
iajs-3359	30	5	al	al	PROPN
iajs-3359	30	6	,	,	PUNCT
iajs-3359	30	7	[	[	X
iajs-3359	30	8	10	10	NUM
iajs-3359	30	9	]	]	PUNCT
iajs-3359	30	10	modified	modify	VERB
iajs-3359	30	11	the	the	DET
iajs-3359	30	12	conventional	conventional	ADJ
iajs-3359	30	13	seir	seir	NOUN
iajs-3359	30	14	model	model	NOUN
iajs-3359	30	15	and	and	CCONJ
iajs-3359	30	16	used	use	VERB
iajs-3359	30	17	a	a	DET
iajs-3359	30	18	fractional	fractional	ADJ
iajs-3359	30	19	differential	differential	ADJ
iajs-3359	30	20	equation	equation	NOUN
iajs-3359	30	21	with	with	ADP
iajs-3359	30	22	caputo	caputo	PROPN
iajs-3359	30	23	derivative	derivative	PROPN
iajs-3359	30	24	to	to	PART
iajs-3359	30	25	represent	represent	VERB
iajs-3359	30	26	the	the	DET
iajs-3359	30	27	dynamics	dynamic	NOUN
iajs-3359	30	28	of	of	ADP
iajs-3359	30	29	covid-19	covid-19	PROPN
iajs-3359	30	30	transmission	transmission	NOUN
iajs-3359	30	31	infected	infect	VERB
iajs-3359	30	32	individual	individual	NOUN
iajs-3359	30	33	’s	’s	PART
iajs-3359	30	34	abo	abo	NOUN
iajs-3359	30	35	blood	blood	NOUN
iajs-3359	30	36	groups	group	NOUN
iajs-3359	30	37	.	.	PUNCT
iajs-3359	31	1	shahram	shahram	PROPN
iajs-3359	31	2	rezapour	rezapour	PROPN
iajs-3359	31	3	,	,	PUNCT
iajs-3359	31	4	et	et	PROPN
iajs-3359	31	5	al	al	PROPN
iajs-3359	31	6	,	,	PUNCT
iajs-3359	31	7	[	[	X
iajs-3359	31	8	11	11	NUM
iajs-3359	31	9	]	]	PUNCT
iajs-3359	31	10	use	use	NOUN
iajs-3359	31	11	the	the	DET
iajs-3359	31	12	caputo	caputo	PROPN
iajs-3359	31	13	fractional	fractional	PROPN
iajs-3359	31	14	derivative	derivative	NOUN
iajs-3359	31	15	to	to	PART
iajs-3359	31	16	build	build	VERB
iajs-3359	31	17	an	an	DET
iajs-3359	31	18	seir	seir	ADJ
iajs-3359	31	19	epidemic	epidemic	NOUN
iajs-3359	31	20	fractional	fractional	ADJ
iajs-3359	31	21	model	model	NOUN
iajs-3359	31	22	of	of	ADP
iajs-3359	31	23	the	the	DET
iajs-3359	31	24	covid-19	covid-19	PROPN
iajs-3359	31	25	spread	spread	NOUN
iajs-3359	31	26	.	.	PUNCT
iajs-3359	32	1	they	they	PRON
iajs-3359	32	2	want	want	VERB
iajs-3359	32	3	an	an	DET
iajs-3359	32	4	approximate	approximate	ADJ
iajs-3359	32	5	solution	solution	NOUN
iajs-3359	32	6	to	to	ADP
iajs-3359	32	7	the	the	DET
iajs-3359	32	8	system	system	NOUN
iajs-3359	32	9	by	by	ADP
iajs-3359	32	10	using	use	VERB
iajs-3359	32	11	the	the	DET
iajs-3359	32	12	fractional	fractional	PROPN
iajs-3359	32	13	euler	euler	NOUN
iajs-3359	32	14	method	method	NOUN
iajs-3359	32	15	.	.	PUNCT
iajs-3359	33	1	they	they	PRON
iajs-3359	33	2	offer	offer	VERB
iajs-3359	33	3	a	a	DET
iajs-3359	33	4	numerical	numerical	ADJ
iajs-3359	33	5	simulation	simulation	NOUN
iajs-3359	33	6	based	base	VERB
iajs-3359	33	7	on	on	ADP
iajs-3359	33	8	actual	actual	ADJ
iajs-3359	33	9	data	datum	NOUN
iajs-3359	33	10	to	to	PART
iajs-3359	33	11	predict	predict	VERB
iajs-3359	33	12	covid19	covid19	NOUN
iajs-3359	33	13	transmission	transmission	NOUN
iajs-3359	33	14	in	in	ADP
iajs-3359	33	15	the	the	DET
iajs-3359	33	16	world	world	NOUN
iajs-3359	33	17	and	and	CCONJ
iajs-3359	33	18	iran	iran	PROPN
iajs-3359	33	19	.	.	PUNCT
iajs-3359	34	1	this	this	DET
iajs-3359	34	2	article	article	NOUN
iajs-3359	34	3	is	be	AUX
iajs-3359	34	4	based	base	VERB
iajs-3359	34	5	on	on	ADP
iajs-3359	34	6	a	a	DET
iajs-3359	34	7	model	model	NOUN
iajs-3359	34	8	of	of	ADP
iajs-3359	34	9	fractional	fractional	ADJ
iajs-3359	34	10	equations	equation	NOUN
iajs-3359	34	11	with	with	ADP
iajs-3359	34	12	caputo	caputo	PROPN
iajs-3359	34	13	derivation	derivation	NOUN
iajs-3359	34	14	.	.	PUNCT
iajs-3359	35	1	he	he	PRON
iajs-3359	35	2	chose	choose	VERB
iajs-3359	35	3	the	the	DET
iajs-3359	35	4	world	world	NOUN
iajs-3359	35	5	and	and	CCONJ
iajs-3359	35	6	iraq	iraq	PROPN
iajs-3359	35	7	as	as	ADP
iajs-3359	35	8	the	the	DET
iajs-3359	35	9	study	study	NOUN
iajs-3359	35	10	areas	area	NOUN
iajs-3359	35	11	and	and	CCONJ
iajs-3359	35	12	used	use	VERB
iajs-3359	35	13	a	a	DET
iajs-3359	35	14	model	model	NOUN
iajs-3359	35	15	that	that	PRON
iajs-3359	35	16	divides	divide	VERB
iajs-3359	35	17	the	the	DET
iajs-3359	35	18	community	community	NOUN
iajs-3359	35	19	into	into	ADP
iajs-3359	35	20	five	five	NUM
iajs-3359	35	21	classes	class	NOUN
iajs-3359	35	22	.	.	PUNCT
iajs-3359	36	1	the	the	DET
iajs-3359	36	2	first	first	ADJ
iajs-3359	36	3	equation	equation	NOUN
iajs-3359	36	4	is	be	AUX
iajs-3359	36	5	the	the	DET
iajs-3359	36	6	disease	disease	NOUN
iajs-3359	36	7	susceptible	susceptible	ADJ
iajs-3359	36	8	class	class	NOUN
iajs-3359	36	9	,	,	PUNCT
iajs-3359	36	10	the	the	DET
iajs-3359	36	11	second	second	ADJ
iajs-3359	36	12	equation	equation	NOUN
iajs-3359	36	13	is	be	AUX
iajs-3359	36	14	the	the	DET
iajs-3359	36	15	exposed	expose	VERB
iajs-3359	36	16	individuals	individual	NOUN
iajs-3359	36	17	,	,	PUNCT
iajs-3359	36	18	the	the	DET
iajs-3359	36	19	third	third	ADJ
iajs-3359	36	20	equation	equation	NOUN
iajs-3359	36	21	is	be	AUX
iajs-3359	36	22	the	the	DET
iajs-3359	36	23	infected	infected	ADJ
iajs-3359	36	24	patients	patient	NOUN
iajs-3359	36	25	,	,	PUNCT
iajs-3359	36	26	the	the	DET
iajs-3359	36	27	fourth	fourth	ADJ
iajs-3359	36	28	is	be	AUX
iajs-3359	36	29	the	the	DET
iajs-3359	36	30	survivors	survivor	NOUN
iajs-3359	36	31	of	of	ADP
iajs-3359	36	32	the	the	DET
iajs-3359	36	33	disease	disease	NOUN
iajs-3359	36	34	and	and	CCONJ
iajs-3359	36	35	the	the	DET
iajs-3359	36	36	fifth	fifth	ADJ
iajs-3359	36	37	equation	equation	NOUN
iajs-3359	36	38	is	be	AUX
iajs-3359	36	39	the	the	DET
iajs-3359	36	40	dead	dead	NOUN
iajs-3359	36	41	of	of	ADP
iajs-3359	36	42	the	the	DET
iajs-3359	36	43	disease	disease	NOUN
iajs-3359	36	44	and	and	CCONJ
iajs-3359	36	45	where	where	SCONJ
iajs-3359	36	46	is	be	AUX
iajs-3359	36	47	the	the	DET
iajs-3359	36	48	population	population	NOUN
iajs-3359	36	49	size	size	NOUN
iajs-3359	36	50	.	.	PUNCT
iajs-3359	37	1	we	we	PRON
iajs-3359	37	2	proved	prove	VERB
iajs-3359	37	3	the	the	DET
iajs-3359	37	4	existence	existence	NOUN
iajs-3359	37	5	and	and	CCONJ
iajs-3359	37	6	uniqueness	uniqueness	NOUN
iajs-3359	37	7	of	of	ADP
iajs-3359	37	8	the	the	DET
iajs-3359	37	9	solution	solution	NOUN
iajs-3359	37	10	of	of	ADP
iajs-3359	37	11	the	the	DET
iajs-3359	37	12	model	model	NOUN
iajs-3359	37	13	and	and	CCONJ
iajs-3359	37	14	found	find	VERB
iajs-3359	37	15	the	the	DET
iajs-3359	37	16	equilibrium	equilibrium	NOUN
iajs-3359	37	17	points	point	NOUN
iajs-3359	37	18	and	and	CCONJ
iajs-3359	37	19	checked	check	VERB
iajs-3359	37	20	their	their	PRON
iajs-3359	37	21	stability	stability	NOUN
iajs-3359	37	22	.	.	PUNCT
iajs-3359	38	1	then	then	ADV
iajs-3359	38	2	find	find	VERB
iajs-3359	38	3	the	the	DET
iajs-3359	38	4	solution	solution	NOUN
iajs-3359	38	5	numerically	numerically	ADV
iajs-3359	38	6	using	use	VERB
iajs-3359	38	7	a	a	DET
iajs-3359	38	8	fractional	fractional	ADJ
iajs-3359	38	9	linear	linear	ADJ
iajs-3359	38	10	multi	multi	ADJ
iajs-3359	38	11	-	-	ADJ
iajs-3359	38	12	step	step	ADJ
iajs-3359	38	13	method	method	NOUN
iajs-3359	38	14	and	and	CCONJ
iajs-3359	38	15	compare	compare	VERB
iajs-3359	38	16	it	it	PRON
iajs-3359	38	17	with	with	ADP
iajs-3359	38	18	the	the	DET
iajs-3359	38	19	data	datum	NOUN
iajs-3359	38	20	given	give	VERB
iajs-3359	38	21	in	in	ADP
iajs-3359	38	22	[	[	X
iajs-3359	38	23	12	12	NUM
iajs-3359	38	24	]	]	PUNCT
iajs-3359	38	25	.	.	PUNCT
iajs-3359	39	1	this	this	DET
iajs-3359	39	2	article	article	NOUN
iajs-3359	39	3	consists	consist	VERB
iajs-3359	39	4	of	of	ADP
iajs-3359	39	5	five	five	NUM
iajs-3359	39	6	sections	section	NOUN
iajs-3359	39	7	:	:	PUNCT
iajs-3359	39	8	the	the	DET
iajs-3359	39	9	first	first	ADJ
iajs-3359	39	10	section	section	NOUN
iajs-3359	39	11	is	be	AUX
iajs-3359	39	12	the	the	DET
iajs-3359	39	13	introduction	introduction	NOUN
iajs-3359	39	14	.	.	PUNCT
iajs-3359	40	1	the	the	DET
iajs-3359	40	2	next	next	ADJ
iajs-3359	40	3	section	section	NOUN
iajs-3359	40	4	contains	contain	VERB
iajs-3359	40	5	the	the	DET
iajs-3359	40	6	basic	basic	ADJ
iajs-3359	40	7	concepts	concept	NOUN
iajs-3359	40	8	used	use	VERB
iajs-3359	40	9	in	in	ADP
iajs-3359	40	10	this	this	DET
iajs-3359	40	11	article	article	NOUN
iajs-3359	40	12	.	.	PUNCT
iajs-3359	41	1	the	the	DET
iajs-3359	41	2	third	third	ADJ
iajs-3359	41	3	section	section	NOUN
iajs-3359	41	4	is	be	AUX
iajs-3359	41	5	about	about	ADP
iajs-3359	41	6	the	the	DET
iajs-3359	41	7	mathematical	mathematical	ADJ
iajs-3359	41	8	model	model	NOUN
iajs-3359	41	9	of	of	ADP
iajs-3359	41	10	covid-19	covid-19	PROPN
iajs-3359	41	11	and	and	CCONJ
iajs-3359	41	12	how	how	SCONJ
iajs-3359	41	13	to	to	PART
iajs-3359	41	14	prove	prove	VERB
iajs-3359	41	15	the	the	DET
iajs-3359	41	16	existence	existence	NOUN
iajs-3359	41	17	and	and	CCONJ
iajs-3359	41	18	uniqueness	uniqueness	NOUN
iajs-3359	41	19	of	of	ADP
iajs-3359	41	20	the	the	DET
iajs-3359	41	21	solution	solution	NOUN
iajs-3359	41	22	of	of	ADP
iajs-3359	41	23	the	the	DET
iajs-3359	41	24	model	model	NOUN
iajs-3359	41	25	and	and	CCONJ
iajs-3359	41	26	determine	determine	VERB
iajs-3359	41	27	the	the	DET
iajs-3359	41	28	equilibrium	equilibrium	NOUN
iajs-3359	41	29	points	point	NOUN
iajs-3359	41	30	.	.	PUNCT
iajs-3359	42	1	in	in	ADP
iajs-3359	42	2	the	the	DET
iajs-3359	42	3	last	last	ADJ
iajs-3359	42	4	part	part	NOUN
iajs-3359	42	5	,	,	PUNCT
iajs-3359	42	6	a	a	DET
iajs-3359	42	7	numerical	numerical	ADJ
iajs-3359	42	8	simulation	simulation	NOUN
iajs-3359	42	9	was	be	AUX
iajs-3359	42	10	carried	carry	VERB
iajs-3359	42	11	out	out	ADP
iajs-3359	42	12	in	in	ADP
iajs-3359	42	13	the	the	DET
iajs-3359	42	14	world	world	NOUN
iajs-3359	42	15	and	and	CCONJ
iajs-3359	42	16	in	in	ADP
iajs-3359	42	17	iraq	iraq	PROPN
iajs-3359	42	18	.	.	PUNCT
iajs-3359	43	1	finally	finally	ADV
iajs-3359	43	2	:	:	PUNCT
iajs-3359	43	3	conclusions	conclusion	NOUN
iajs-3359	43	4	.	.	PUNCT
iajs-3359	44	1	2	2	X
iajs-3359	44	2	.	.	X
iajs-3359	44	3	background	background	NOUN
iajs-3359	44	4	this	this	DET
iajs-3359	44	5	section	section	NOUN
iajs-3359	44	6	introducing	introduce	VERB
iajs-3359	44	7	the	the	DET
iajs-3359	44	8	basic	basic	ADJ
iajs-3359	44	9	concepts	concept	NOUN
iajs-3359	44	10	that	that	PRON
iajs-3359	44	11	is	be	AUX
iajs-3359	44	12	needed	need	VERB
iajs-3359	44	13	in	in	ADP
iajs-3359	44	14	this	this	DET
iajs-3359	44	15	article	article	NOUN
iajs-3359	44	16	.	.	PUNCT
iajs-3359	45	1	2.1	2.1	NUM
iajs-3359	45	2	caputo	caputo	PROPN
iajs-3359	45	3	fractional	fractional	ADJ
iajs-3359	45	4	derivatives	derivative	NOUN
iajs-3359	45	5	[	[	X
iajs-3359	45	6	13,14	13,14	NUM
iajs-3359	45	7	]	]	X
iajs-3359	45	8	it	it	PRON
iajs-3359	45	9	is	be	AUX
iajs-3359	45	10	defined	define	VERB
iajs-3359	45	11	by	by	ADP
iajs-3359	45	12	:	:	PUNCT
iajs-3359	45	13	{	{	PUNCT
iajs-3359	45	14	𝐷∗	𝐷∗	NOUN
iajs-3359	45	15	𝛼𝑓(𝑡	𝛼𝑓(𝑡	NUM
iajs-3359	45	16	)	)	PUNCT
iajs-3359	45	17	=	=	SYM
iajs-3359	45	18	1	1	NUM
iajs-3359	45	19	𝛤(𝜂−𝛼	𝛤(𝜂−𝛼	NOUN
iajs-3359	45	20	)	)	PUNCT
iajs-3359	45	21	∫	∫	PROPN
iajs-3359	45	22	𝑓(𝜂)(𝜏	𝑓(𝜂)(𝜏	X
iajs-3359	45	23	)	)	PUNCT
iajs-3359	45	24	(	(	PUNCT
iajs-3359	45	25	𝑡−𝜏)(𝛼−𝜂+1	𝑡−𝜏)(𝛼−𝜂+1	NOUN
iajs-3359	45	26	)	)	PUNCT
iajs-3359	45	27	𝑡	𝑡	PROPN
iajs-3359	45	28	𝑎	𝑎	DET
iajs-3359	45	29	𝑑𝜏	𝑑𝜏	NOUN
iajs-3359	45	30	,	,	PUNCT
iajs-3359	45	31	𝜂-1<𝛼	𝜂-1<𝛼	X
iajs-3359	45	32	<	<	X
iajs-3359	45	33	𝜂	𝜂	X
iajs-3359	45	34	∈	∈	PROPN
iajs-3359	45	35	𝑁	𝑁	PROPN
iajs-3359	45	36	,	,	PUNCT
iajs-3359	45	37	𝑑𝜂	𝑑𝜂	ADJ
iajs-3359	45	38	𝑑𝑡𝜂	𝑑𝑡𝜂	NOUN
iajs-3359	45	39	𝑓(𝑡	𝑓(𝑡	NOUN
iajs-3359	45	40	)	)	PUNCT
iajs-3359	45	41	𝛼	𝛼	NOUN
iajs-3359	45	42	=	=	SYM
iajs-3359	45	43	𝜂	𝜂	X
iajs-3359	45	44	∈	∈	PROPN
iajs-3359	45	45	𝑁	𝑁	PROPN
iajs-3359	45	46	,	,	PUNCT
iajs-3359	45	47	(	(	PUNCT
iajs-3359	45	48	1	1	X
iajs-3359	45	49	)	)	PUNCT
iajs-3359	45	50	where	where	SCONJ
iajs-3359	45	51	is	be	AUX
iajs-3359	45	52	the	the	DET
iajs-3359	45	53	order	order	NOUN
iajs-3359	45	54	of	of	ADP
iajs-3359	45	55	the	the	DET
iajs-3359	45	56	derivatives	derivative	NOUN
iajs-3359	45	57	,	,	PUNCT
iajs-3359	45	58	𝑡	𝑡	X
iajs-3359	45	59	>	>	X
iajs-3359	45	60	𝑎	𝑎	PROPN
iajs-3359	45	61	,	,	PUNCT
iajs-3359	45	62	𝛼	𝛼	NOUN
iajs-3359	45	63	,	,	PUNCT
iajs-3359	45	64	𝑎	𝑎	PROPN
iajs-3359	45	65	,	,	PUNCT
iajs-3359	45	66	𝑡	𝑡	PROPN
iajs-3359	45	67	∈	∈	PROPN
iajs-3359	45	68	𝑅	𝑅	PROPN
iajs-3359	45	69	,	,	PUNCT
iajs-3359	45	70	and	and	CCONJ
iajs-3359	45	71	η	η	PROPN
iajs-3359	45	72	is	be	AUX
iajs-3359	45	73	the	the	DET
iajs-3359	45	74	smallest	small	ADJ
iajs-3359	45	75	integer	integer	NOUN
iajs-3359	45	76	greater	great	ADJ
iajs-3359	45	77	than	than	ADP
iajs-3359	45	78	α	α	PROPN
iajs-3359	45	79	.	.	PROPN
iajs-3359	45	80	2.2	2.2	NUM
iajs-3359	45	81	riemann	riemann	PROPN
iajs-3359	45	82	-	-	PUNCT
iajs-3359	45	83	liouville	liouville	VERB
iajs-3359	45	84	fractional	fractional	ADJ
iajs-3359	45	85	derivative	derivative	NOUN
iajs-3359	45	86	[	[	X
iajs-3359	45	87	15	15	NUM
iajs-3359	45	88	]	]	X
iajs-3359	45	89	the	the	DET
iajs-3359	45	90	derivative	derivative	NOUN
iajs-3359	45	91	of	of	ADP
iajs-3359	45	92	order	order	NOUN
iajs-3359	45	93	α	α	NOUN
iajs-3359	45	94	is	be	AUX
iajs-3359	45	95	defined	define	VERB
iajs-3359	45	96	as	as	ADP
iajs-3359	45	97	:	:	PUNCT
iajs-3359	45	98	𝑎𝐷𝑡	𝑎𝐷𝑡	NOUN
iajs-3359	45	99	𝛼𝑓(𝑡	𝛼𝑓(𝑡	NUM
iajs-3359	45	100	)	)	PUNCT
iajs-3359	45	101	=	=	SYM
iajs-3359	45	102	𝑑𝑚	𝑑𝑚	NOUN
iajs-3359	45	103	𝑑𝑥𝑚	𝑑𝑥𝑚	PROPN
iajs-3359	45	104	∫	∫	PROPN
iajs-3359	45	105	(	(	PUNCT
iajs-3359	45	106	𝑥−𝑡)𝑚−𝑛−1𝑓(𝑡	𝑥−𝑡)𝑚−𝑛−1𝑓(𝑡	X
iajs-3359	45	107	)	)	PUNCT
iajs-3359	46	1	𝛤(𝑚−𝑛	𝛤(𝑚−𝑛	NOUN
iajs-3359	46	2	)	)	PUNCT
iajs-3359	46	3	𝑥	𝑥	PRON
iajs-3359	47	1	𝑎	𝑎	NOUN
iajs-3359	47	2	𝑑𝑡	𝑑𝑡	ADP
iajs-3359	47	3	,	,	PUNCT
iajs-3359	47	4	(	(	PUNCT
iajs-3359	47	5	2	2	X
iajs-3359	47	6	)	)	PUNCT
iajs-3359	47	7	where	where	SCONJ
iajs-3359	47	8	𝑚	𝑚	PROPN
iajs-3359	47	9	−	−	PROPN
iajs-3359	47	10	1	1	NUM
iajs-3359	47	11	≤	≤	NUM
iajs-3359	47	12	𝑛	𝑛	PRON
iajs-3359	47	13	<	<	X
iajs-3359	47	14	𝑚	𝑚	PROPN
iajs-3359	47	15	,	,	PUNCT
iajs-3359	47	16	𝑚	𝑚	PROPN
iajs-3359	47	17	∈	∈	PROPN
iajs-3359	47	18	𝑁.	𝑁.	PROPN
iajs-3359	47	19	2.3	2.3	NUM
iajs-3359	47	20	relation	relation	NOUN
iajs-3359	47	21	between	between	ADP
iajs-3359	47	22	caputo	caputo	PROPN
iajs-3359	47	23	and	and	CCONJ
iajs-3359	47	24	riemann	riemann	PROPN
iajs-3359	47	25	-	-	PUNCT
iajs-3359	47	26	liouville	liouville	VERB
iajs-3359	47	27	fractional	fractional	ADJ
iajs-3359	47	28	derivative	derivative	NOUN
iajs-3359	47	29	[	[	X
iajs-3359	47	30	16,17	16,17	NUM
iajs-3359	47	31	]	]	PUNCT
iajs-3359	47	32	let	let	VERB
iajs-3359	47	33	𝛼	𝛼	PRON
iajs-3359	47	34	>	>	X
iajs-3359	47	35	0	0	PUNCT
iajs-3359	47	36	be	be	AUX
iajs-3359	47	37	a	a	DET
iajs-3359	47	38	fractional	fractional	ADJ
iajs-3359	47	39	order	order	NOUN
iajs-3359	47	40	derivative	derivative	NOUN
iajs-3359	47	41	of	of	ADP
iajs-3359	47	42	the	the	DET
iajs-3359	47	43	function	function	NOUN
iajs-3359	47	44	f	f	PROPN
iajs-3359	47	45	and	and	CCONJ
iajs-3359	47	46	δ=⌈α⌉	δ=⌈α⌉	PROPN
iajs-3359	47	47	which	which	PRON
iajs-3359	47	48	mean	mean	VERB
iajs-3359	47	49	δ	δ	PROPN
iajs-3359	47	50	is	be	AUX
iajs-3359	47	51	smallest	small	ADJ
iajs-3359	47	52	natural	natural	ADJ
iajs-3359	47	53	number	number	NOUN
iajs-3359	47	54	greater	great	ADJ
iajs-3359	47	55	than	than	ADP
iajs-3359	47	56	α	α	X
iajs-3359	47	57	.	.	PUNCT
iajs-3359	47	58	suppose	suppose	VERB
iajs-3359	47	59	that	that	SCONJ
iajs-3359	47	60	f	f	PROPN
iajs-3359	47	61	is	be	AUX
iajs-3359	47	62	such	such	ADJ
iajs-3359	47	63	that	that	SCONJ
iajs-3359	47	64	both	both	DET
iajs-3359	47	65	𝐷∗𝑎	𝐷∗𝑎	NOUN
iajs-3359	47	66	𝛼	𝛼	PRON
iajs-3359	47	67	𝑓	𝑓	NOUN
iajs-3359	47	68	and	and	CCONJ
iajs-3359	47	69	𝐷𝑎	𝐷𝑎	PROPN
iajs-3359	47	70	𝛼	𝛼	NOUN
iajs-3359	47	71	f	f	NOUN
iajs-3359	47	72	exist	exist	VERB
iajs-3359	47	73	,	,	PUNCT
iajs-3359	47	74	then	then	ADV
iajs-3359	47	75	:	:	PUNCT
iajs-3359	47	76	𝐷∗𝑎	𝐷∗𝑎	NOUN
iajs-3359	47	77	𝛼	𝛼	PRON
iajs-3359	47	78	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3359	47	79	)	)	PUNCT
iajs-3359	48	1	=	=	PUNCT
iajs-3359	48	2	𝐷𝑎	𝐷𝑎	NOUN
iajs-3359	48	3	𝛼𝑓(𝑥	𝛼𝑓(𝑥	NOUN
iajs-3359	48	4	)	)	PUNCT
iajs-3359	48	5	−	−	NUM
iajs-3359	48	6	∑	∑	SYM
iajs-3359	48	7	𝐷𝑘𝑓(𝑎	𝐷𝑘𝑓(𝑎	NOUN
iajs-3359	48	8	)	)	PUNCT
iajs-3359	48	9	𝛤(𝑘−𝛼+1	𝛤(𝑘−𝛼+1	NOUN
iajs-3359	48	10	)	)	PUNCT
iajs-3359	49	1	(	(	PUNCT
iajs-3359	49	2	𝑥	𝑥	X
iajs-3359	49	3	−	−	NOUN
iajs-3359	49	4	𝑎)𝑘−𝛼𝛿−1	𝑎)𝑘−𝛼𝛿−1	NOUN
iajs-3359	49	5	𝑘=0	𝑘=0	VERB
iajs-3359	49	6	,	,	PUNCT
iajs-3359	49	7	(	(	PUNCT
iajs-3359	49	8	3	3	X
iajs-3359	49	9	)	)	PUNCT
iajs-3359	49	10	where	where	SCONJ
iajs-3359	49	11	𝐷∗𝑎	𝐷∗𝑎	PROPN
iajs-3359	49	12	𝛼	𝛼	X
iajs-3359	49	13	is	be	AUX
iajs-3359	49	14	the	the	DET
iajs-3359	49	15	caputo	caputo	PROPN
iajs-3359	49	16	differential	differential	NOUN
iajs-3359	49	17	operator	operator	NOUN
iajs-3359	49	18	of	of	ADP
iajs-3359	49	19	order	order	NOUN
iajs-3359	49	20	α	α	NOUN
iajs-3359	49	21	and	and	CCONJ
iajs-3359	49	22	𝐷𝑎	𝐷𝑎	NOUN
iajs-3359	49	23	𝛼	𝛼	NOUN
iajs-3359	49	24	is	be	AUX
iajs-3359	49	25	the	the	DET
iajs-3359	49	26	riemann	riemann	PROPN
iajs-3359	49	27	-	-	PUNCT
iajs-3359	49	28	liouville	liouville	VERB
iajs-3359	49	29	differential	differential	NOUN
iajs-3359	49	30	operator	operator	NOUN
iajs-3359	49	31	of	of	ADP
iajs-3359	49	32	order	order	NOUN
iajs-3359	49	33	α	α	NOUN
iajs-3359	49	34	.	.	PROPN
iajs-3359	49	35	2.4	2.4	NUM
iajs-3359	49	36	equilibrium	equilibrium	NOUN
iajs-3359	49	37	point	point	NOUN
iajs-3359	49	38	[	[	X
iajs-3359	49	39	18,19	18,19	X
iajs-3359	49	40	]	]	X
iajs-3359	49	41	let	let	VERB
iajs-3359	49	42	�	�	PART
iajs-3359	49	43	̇	̇	VERB
iajs-3359	49	44	�	�	PROPN
iajs-3359	49	45	(𝑡	(𝑡	PROPN
iajs-3359	49	46	)	)	PUNCT
iajs-3359	49	47	=	=	SYM
iajs-3359	49	48	𝐹(𝑋(𝑡	𝐹(𝑋(𝑡	ADJ
iajs-3359	49	49	)	)	PUNCT
iajs-3359	49	50	)	)	PUNCT
iajs-3359	50	1	be	be	AUX
iajs-3359	50	2	a	a	DET
iajs-3359	50	3	dynamical	dynamical	ADJ
iajs-3359	50	4	system	system	NOUN
iajs-3359	50	5	.	.	PUNCT
iajs-3359	51	1	a	a	DET
iajs-3359	51	2	point	point	NOUN
iajs-3359	51	3	𝑋0	𝑋0	NOUN
iajs-3359	51	4	is	be	AUX
iajs-3359	51	5	called	call	VERB
iajs-3359	51	6	an	an	DET
iajs-3359	51	7	equilibrium	equilibrium	NOUN
iajs-3359	51	8	point	point	NOUN
iajs-3359	51	9	if	if	SCONJ
iajs-3359	51	10	𝐹(𝑋0	𝐹(𝑋0	PRON
iajs-3359	51	11	)	)	PUNCT
iajs-3359	52	1	=	=	SYM
iajs-3359	52	2	0	0	X
iajs-3359	52	3	.	.	NUM
iajs-3359	52	4	ihjpas	ihjpas	PROPN
iajs-3359	52	5	.	.	PUNCT
iajs-3359	53	1	37	37	NUM
iajs-3359	53	2	(	(	PUNCT
iajs-3359	53	3	2	2	NUM
iajs-3359	53	4	)	)	PUNCT
iajs-3359	53	5	2024	2024	NUM
iajs-3359	53	6	380	380	NUM
iajs-3359	53	7	2.5	2.5	NUM
iajs-3359	53	8	fractional	fractional	ADJ
iajs-3359	53	9	multi	multi	ADJ
iajs-3359	53	10	-	-	ADJ
iajs-3359	53	11	step	step	ADJ
iajs-3359	53	12	method	method	NOUN
iajs-3359	53	13	[	[	X
iajs-3359	53	14	20,21	20,21	NUM
iajs-3359	53	15	]	]	PUNCT
iajs-3359	53	16	let	let	VERB
iajs-3359	53	17	:	:	PUNCT
iajs-3359	53	18	{	{	PUNCT
iajs-3359	53	19	𝐷𝑡0	𝐷𝑡0	NOUN
iajs-3359	53	20	𝛼	𝛼	X
iajs-3359	53	21	𝑔(𝑡	𝑔(𝑡	PROPN
iajs-3359	53	22	)	)	PUNCT
iajs-3359	53	23	=	=	PUNCT
iajs-3359	54	1	𝑓(𝑡	𝑓(𝑡	NOUN
iajs-3359	54	2	,	,	PUNCT
iajs-3359	54	3	𝑔(𝑡	𝑔(𝑡	PROPN
iajs-3359	54	4	)	)	PUNCT
iajs-3359	54	5	𝑔(𝑡0	𝑔(𝑡0	NOUN
iajs-3359	54	6	)	)	PUNCT
iajs-3359	54	7	=	=	SYM
iajs-3359	54	8	𝑔0	𝑔0	NOUN
iajs-3359	54	9	,	,	PUNCT
iajs-3359	54	10	𝑔	𝑔	PROPN
iajs-3359	54	11	′(𝑡0	′(𝑡0	NOUN
iajs-3359	54	12	)	)	PUNCT
iajs-3359	55	1	=	=	SYM
iajs-3359	55	2	𝑔0	𝑔0	NOUN
iajs-3359	55	3	(	(	PUNCT
iajs-3359	55	4	1	1	NUM
iajs-3359	55	5	)	)	PUNCT
iajs-3359	55	6	,	,	PUNCT
iajs-3359	55	7	.	.	PUNCT
iajs-3359	55	8	.	.	PUNCT
iajs-3359	55	9	.	.	PUNCT
iajs-3359	56	1	,	,	PUNCT
iajs-3359	56	2	𝑔(𝑚−1)(𝑡0	𝑔(𝑚−1)(𝑡0	NOUN
iajs-3359	56	3	)	)	PUNCT
iajs-3359	56	4	=	=	SYM
iajs-3359	56	5	𝑔0	𝑔0	NOUN
iajs-3359	56	6	(	(	PUNCT
iajs-3359	56	7	𝑚−1	𝑚−1	PROPN
iajs-3359	56	8	)	)	PUNCT
iajs-3359	56	9	where	where	SCONJ
iajs-3359	56	10	𝛼	𝛼	NOUN
iajs-3359	56	11	is	be	AUX
iajs-3359	56	12	a	a	DET
iajs-3359	56	13	fractional	fractional	ADJ
iajs-3359	56	14	order	order	NOUN
iajs-3359	56	15	derivative	derivative	NOUN
iajs-3359	56	16	and	and	CCONJ
iajs-3359	56	17	𝑓(𝑡	𝑓(𝑡	NOUN
iajs-3359	56	18	,	,	PUNCT
iajs-3359	56	19	𝑔	𝑔	NOUN
iajs-3359	56	20	)	)	PUNCT
iajs-3359	56	21	is	be	AUX
iajs-3359	56	22	assumed	assume	VERB
iajs-3359	56	23	to	to	PART
iajs-3359	56	24	be	be	AUX
iajs-3359	56	25	continuous	continuous	ADJ
iajs-3359	56	26	and	and	CCONJ
iajs-3359	56	27	𝑔0	𝑔0	NOUN
iajs-3359	56	28	,	,	PUNCT
iajs-3359	56	29	𝑔0	𝑔0	NOUN
iajs-3359	56	30	(	(	PUNCT
iajs-3359	56	31	1	1	NUM
iajs-3359	56	32	)	)	PUNCT
iajs-3359	56	33	,	,	PUNCT
iajs-3359	56	34	.	.	PUNCT
iajs-3359	56	35	.	.	PUNCT
iajs-3359	57	1	.	.	PUNCT
iajs-3359	58	1	,	,	PUNCT
iajs-3359	58	2	𝑔0	𝑔0	NOUN
iajs-3359	58	3	(	(	PUNCT
iajs-3359	58	4	𝑚−1	𝑚−1	NOUN
iajs-3359	58	5	)	)	PUNCT
iajs-3359	58	6	are	be	AUX
iajs-3359	58	7	the	the	DET
iajs-3359	58	8	assigned	assign	VERB
iajs-3359	58	9	values	value	NOUN
iajs-3359	58	10	of	of	ADP
iajs-3359	58	11	the	the	DET
iajs-3359	58	12	derivatives	derivative	NOUN
iajs-3359	58	13	at	at	ADP
iajs-3359	58	14	𝑡0	𝑡0	PROPN
iajs-3359	58	15	.	.	PUNCT
iajs-3359	59	1	therefore	therefore	ADV
iajs-3359	59	2	,	,	PUNCT
iajs-3359	59	3	fractional	fractional	ADJ
iajs-3359	59	4	multi	multi	ADJ
iajs-3359	59	5	-	-	ADJ
iajs-3359	59	6	step	step	ADJ
iajs-3359	59	7	approaches	approach	NOUN
iajs-3359	59	8	are	be	AUX
iajs-3359	59	9	convolution	convolution	NOUN
iajs-3359	59	10	quadrature	quadrature	NOUN
iajs-3359	59	11	formulas	formula	NOUN
iajs-3359	59	12	,	,	PUNCT
iajs-3359	59	13	which	which	PRON
iajs-3359	59	14	may	may	AUX
iajs-3359	59	15	be	be	AUX
iajs-3359	59	16	expressed	express	VERB
iajs-3359	59	17	generally	generally	ADV
iajs-3359	59	18	as	as	SCONJ
iajs-3359	59	19	follows	follow	VERB
iajs-3359	59	20	:	:	PUNCT
iajs-3359	59	21	𝑔𝑛	𝑔𝑛	PROPN
iajs-3359	59	22	=	=	PUNCT
iajs-3359	59	23	𝜙𝑛	𝜙𝑛	PROPN
iajs-3359	60	1	+	+	CCONJ
iajs-3359	60	2	∑	∑	PROPN
iajs-3359	60	3	𝑢𝑛−𝑗𝑓𝑗	𝑢𝑛−𝑗𝑓𝑗	PROPN
iajs-3359	60	4	𝑛	𝑛	PRON
iajs-3359	60	5	𝑗=0	𝑗=0	PROPN
iajs-3359	60	6	,	,	PUNCT
iajs-3359	60	7	𝑓𝑗	𝑓𝑗	ADJ
iajs-3359	60	8	=	=	ADJ
iajs-3359	60	9	𝑓(𝑡𝑗	𝑓(𝑡𝑗	PROPN
iajs-3359	60	10	,	,	PUNCT
iajs-3359	60	11	𝑔𝑛	𝑔𝑛	PROPN
iajs-3359	60	12	)	)	PUNCT
iajs-3359	60	13	.	.	PUNCT
iajs-3359	61	1	where	where	SCONJ
iajs-3359	61	2	𝜙𝑛	𝜙𝑛	NOUN
iajs-3359	61	3	and	and	CCONJ
iajs-3359	61	4	𝑢𝑛−𝑗	𝑢𝑛−𝑗	PROPN
iajs-3359	61	5	are	be	AUX
iajs-3359	61	6	known	know	VERB
iajs-3359	61	7	coefficients	coefficient	NOUN
iajs-3359	61	8	and	and	CCONJ
iajs-3359	61	9	𝑡𝑛	𝑡𝑛	ADJ
iajs-3359	61	10	=	=	SYM
iajs-3359	61	11	𝑡0	𝑡0	NOUN
iajs-3359	61	12	+	+	CCONJ
iajs-3359	61	13	𝑛ℎ	𝑛ℎ	NOUN
iajs-3359	61	14	is	be	AUX
iajs-3359	61	15	an	an	DET
iajs-3359	61	16	assigned	assign	VERB
iajs-3359	61	17	grid	grid	NOUN
iajs-3359	61	18	,	,	PUNCT
iajs-3359	61	19	with	with	ADP
iajs-3359	61	20	the	the	DET
iajs-3359	61	21	constant	constant	ADJ
iajs-3359	61	22	step	step	NOUN
iajs-3359	61	23	-	-	PUNCT
iajs-3359	61	24	size	size	NOUN
iajs-3359	61	25	ℎ	ℎ	PROPN
iajs-3359	61	26	>	>	X
iajs-3359	61	27	0	0	NUM
iajs-3359	61	28	.	.	NOUN
iajs-3359	62	1	3	3	X
iajs-3359	62	2	.	.	X
iajs-3359	62	3	mathematical	mathematical	ADJ
iajs-3359	62	4	model	model	NOUN
iajs-3359	62	5	the	the	DET
iajs-3359	62	6	researchers	researcher	NOUN
iajs-3359	62	7	divided	divide	VERB
iajs-3359	62	8	the	the	DET
iajs-3359	62	9	society	society	NOUN
iajs-3359	62	10	into	into	ADP
iajs-3359	62	11	five	five	NUM
iajs-3359	62	12	categories	category	NOUN
iajs-3359	62	13	.	.	PUNCT
iajs-3359	63	1	the	the	DET
iajs-3359	63	2	first	first	ADJ
iajs-3359	63	3	category	category	NOUN
iajs-3359	63	4	is	be	AUX
iajs-3359	63	5	the	the	DET
iajs-3359	63	6	diseasesensitive	diseasesensitive	ADJ
iajs-3359	63	7	𝑆(𝑡	𝑆(𝑡	NUM
iajs-3359	63	8	)	)	PUNCT
iajs-3359	63	9	,	,	PUNCT
iajs-3359	63	10	the	the	DET
iajs-3359	63	11	next	next	ADJ
iajs-3359	63	12	one	one	NOUN
iajs-3359	63	13	is	be	AUX
iajs-3359	63	14	the	the	DET
iajs-3359	63	15	exposed	expose	VERB
iajs-3359	63	16	individuals	individual	NOUN
iajs-3359	63	17	𝐸(𝑡	𝐸(𝑡	VERB
iajs-3359	63	18	)	)	PUNCT
iajs-3359	63	19	,	,	PUNCT
iajs-3359	63	20	the	the	DET
iajs-3359	63	21	equation	equation	NOUN
iajs-3359	63	22	of	of	ADP
iajs-3359	63	23	the	the	DET
iajs-3359	63	24	infected	infected	ADJ
iajs-3359	63	25	patients	patient	NOUN
iajs-3359	63	26	is	be	AUX
iajs-3359	63	27	given	give	VERB
iajs-3359	63	28	by	by	ADP
iajs-3359	63	29	𝐼(𝑡	𝐼(𝑡	NUM
iajs-3359	63	30	)	)	PUNCT
iajs-3359	63	31	,	,	PUNCT
iajs-3359	63	32	𝑅(𝑡	𝑅(𝑡	NOUN
iajs-3359	63	33	)	)	PUNCT
iajs-3359	63	34	presents	present	VERB
iajs-3359	63	35	the	the	DET
iajs-3359	63	36	disease	disease	NOUN
iajs-3359	63	37	survivors	survivor	NOUN
iajs-3359	63	38	and	and	CCONJ
iajs-3359	63	39	𝐹(𝑡	𝐹(𝑡	NUM
iajs-3359	63	40	)	)	PUNCT
iajs-3359	63	41	gives	give	VERB
iajs-3359	63	42	the	the	DET
iajs-3359	63	43	equation	equation	NOUN
iajs-3359	63	44	of	of	ADP
iajs-3359	63	45	the	the	DET
iajs-3359	63	46	disease	disease	NOUN
iajs-3359	63	47	die	die	VERB
iajs-3359	63	48	.	.	PUNCT
iajs-3359	64	1	in	in	ADP
iajs-3359	64	2	addition	addition	NOUN
iajs-3359	64	3	,	,	PUNCT
iajs-3359	64	4	all	all	DET
iajs-3359	64	5	equations	equation	NOUN
iajs-3359	64	6	respect	respect	VERB
iajs-3359	64	7	time	time	NOUN
iajs-3359	64	8	.	.	PUNCT
iajs-3359	65	1	form	form	VERB
iajs-3359	65	2	this	this	DET
iajs-3359	65	3	standpoint	standpoint	NOUN
iajs-3359	65	4	,	,	PUNCT
iajs-3359	65	5	the	the	DET
iajs-3359	65	6	fractional	fractional	ADJ
iajs-3359	65	7	mathematical	mathematical	ADJ
iajs-3359	65	8	model	model	NOUN
iajs-3359	65	9	can	can	AUX
iajs-3359	65	10	be	be	AUX
iajs-3359	65	11	formulated	formulate	VERB
iajs-3359	65	12	as	as	SCONJ
iajs-3359	65	13	follows	follow	VERB
iajs-3359	65	14	:	:	PUNCT
iajs-3359	65	15	𝐷∗	𝐷∗	PROPN
iajs-3359	65	16	𝛼𝑆(𝑡	𝛼𝑆(𝑡	NUM
iajs-3359	65	17	)	)	PUNCT
iajs-3359	66	1	=	=	SYM
iajs-3359	67	1	−	−	PROPN
iajs-3359	67	2	𝛽	𝛽	NOUN
iajs-3359	67	3	𝑁	𝑁	PROPN
iajs-3359	67	4	𝑆𝐼	𝑆𝐼	PROPN
iajs-3359	67	5	,	,	PUNCT
iajs-3359	67	6	𝐷∗	𝐷∗	PROPN
iajs-3359	67	7	𝛼𝐸(𝑡	𝛼𝐸(𝑡	NUM
iajs-3359	67	8	)	)	PUNCT
iajs-3359	68	1	=	=	SYM
iajs-3359	68	2	𝐵	𝐵	NOUN
iajs-3359	68	3	𝑁	𝑁	NOUN
iajs-3359	68	4	𝑆𝐼	𝑆𝐼	ADV
iajs-3359	68	5	−	−	PROPN
iajs-3359	68	6	𝜔𝐸	𝜔𝐸	NOUN
iajs-3359	68	7	,	,	PUNCT
iajs-3359	68	8	𝐷∗	𝐷∗	PROPN
iajs-3359	68	9	𝛼𝐼(𝑡	𝛼𝐼(𝑡	NUM
iajs-3359	68	10	)	)	PUNCT
iajs-3359	68	11	=	=	SYM
iajs-3359	68	12	𝜔𝜗𝐸	𝜔𝜗𝐸	NOUN
iajs-3359	68	13	−	−	PROPN
iajs-3359	68	14	(	(	PUNCT
iajs-3359	68	15	𝑙	𝑙	PROPN
iajs-3359	69	1	+	+	CCONJ
iajs-3359	69	2	𝜈)𝐼	𝜈)𝐼	ADJ
iajs-3359	69	3	,	,	PUNCT
iajs-3359	69	4	(	(	PUNCT
iajs-3359	69	5	4	4	X
iajs-3359	69	6	)	)	PUNCT
iajs-3359	69	7	𝐷∗	𝐷∗	NOUN
iajs-3359	69	8	𝛼𝑅(𝑡	𝛼𝑅(𝑡	NUM
iajs-3359	69	9	)	)	PUNCT
iajs-3359	69	10	=	=	PUNCT
iajs-3359	70	1	𝑙𝐼	𝑙𝐼	VERB
iajs-3359	70	2	,	,	PUNCT
iajs-3359	70	3	𝐷∗	𝐷∗	PROPN
iajs-3359	70	4	𝛼𝐹(𝑡	𝛼𝐹(𝑡	NUM
iajs-3359	70	5	)	)	PUNCT
iajs-3359	70	6	=	=	PUNCT
iajs-3359	70	7	𝜈𝐼	𝜈𝐼	ADJ
iajs-3359	70	8	.	.	PUNCT
iajs-3359	71	1	the	the	DET
iajs-3359	71	2	coefficients	coefficient	NOUN
iajs-3359	71	3	of	of	ADP
iajs-3359	71	4	the	the	DET
iajs-3359	71	5	model	model	NOUN
iajs-3359	71	6	parameters	parameter	NOUN
iajs-3359	71	7	are	be	AUX
iajs-3359	71	8	given	give	VERB
iajs-3359	71	9	in	in	ADP
iajs-3359	71	10	table	table	NOUN
iajs-3359	71	11	1	1	NUM
iajs-3359	71	12	.	.	PUNCT
iajs-3359	71	13	table	table	NOUN
iajs-3359	71	14	1	1	NUM
iajs-3359	71	15	:	:	PUNCT
iajs-3359	71	16	description	description	NOUN
iajs-3359	71	17	of	of	ADP
iajs-3359	71	18	the	the	DET
iajs-3359	71	19	model	model	NOUN
iajs-3359	71	20	.	.	PUNCT
iajs-3359	72	1	parameters	parameter	NOUN
iajs-3359	72	2	description	description	VERB
iajs-3359	72	3	𝛼	𝛼	PRON
iajs-3359	72	4	fractional	fractional	ADJ
iajs-3359	72	5	order	order	NOUN
iajs-3359	72	6	derivative	derivative	ADJ
iajs-3359	72	7	ℬ	ℬ	NOUN
iajs-3359	72	8	measures	measure	VERB
iajs-3359	72	9	the	the	DET
iajs-3359	72	10	coefficient	coefficient	NOUN
iajs-3359	72	11	of	of	ADP
iajs-3359	72	12	human	human	NOUN
iajs-3359	72	13	-	-	PUNCT
iajs-3359	72	14	to	to	ADP
iajs-3359	72	15	-	-	PUNCT
iajs-3359	72	16	human	human	ADJ
iajs-3359	72	17	transmission	transmission	NOUN
iajs-3359	72	18	per	per	ADP
iajs-3359	72	19	unit	unit	NOUN
iajs-3359	72	20	time	time	NOUN
iajs-3359	72	21	(	(	PUNCT
iajs-3359	72	22	days	day	NOUN
iajs-3359	72	23	)	)	PUNCT
iajs-3359	72	24	per	per	ADP
iajs-3359	72	25	person	person	NOUN
iajs-3359	72	26	.	.	PUNCT
iajs-3359	73	1	𝒩	𝒩	ADJ
iajs-3359	73	2	population	population	NOUN
iajs-3359	73	3	size	size	NOUN
iajs-3359	73	4	.	.	PUNCT
iajs-3359	74	1	𝜔	𝜔	X
iajs-3359	74	2	is	be	AUX
iajs-3359	74	3	the	the	DET
iajs-3359	74	4	rate	rate	NOUN
iajs-3359	74	5	at	at	ADP
iajs-3359	74	6	which	which	PRON
iajs-3359	74	7	a	a	DET
iajs-3359	74	8	person	person	NOUN
iajs-3359	74	9	becomes	become	VERB
iajs-3359	74	10	infectious	infectious	ADJ
iajs-3359	74	11	and	and	CCONJ
iajs-3359	74	12	leaves	leave	VERB
iajs-3359	74	13	the	the	DET
iajs-3359	74	14	exposed	expose	VERB
iajs-3359	74	15	class	class	NOUN
iajs-3359	74	16	.	.	PUNCT
iajs-3359	75	1	𝜗	𝜗	NOUN
iajs-3359	75	2	is	be	AUX
iajs-3359	75	3	the	the	DET
iajs-3359	75	4	percentage	percentage	NOUN
iajs-3359	75	5	of	of	ADP
iajs-3359	75	6	people	people	NOUN
iajs-3359	75	7	who	who	PRON
iajs-3359	75	8	advance	advance	VERB
iajs-3359	75	9	from	from	ADP
iajs-3359	75	10	e	e	NOUN
iajs-3359	75	11	to	to	ADP
iajs-3359	75	12	i.	i.	PROPN
iajs-3359	75	13	𝑙	𝑙	PROPN
iajs-3359	75	14	recovery	recovery	NOUN
iajs-3359	75	15	rate	rate	NOUN
iajs-3359	75	16	.	.	PUNCT
iajs-3359	76	1	𝜈	𝜈	X
iajs-3359	76	2	death	death	NOUN
iajs-3359	76	3	rate	rate	NOUN
iajs-3359	76	4	.	.	PUNCT
iajs-3359	77	1	ihjpas	ihjpas	PROPN
iajs-3359	77	2	.	.	PUNCT
iajs-3359	78	1	37	37	NUM
iajs-3359	78	2	(	(	PUNCT
iajs-3359	78	3	2	2	NUM
iajs-3359	78	4	)	)	PUNCT
iajs-3359	78	5	2024	2024	NUM
iajs-3359	78	6	381	381	NUM
iajs-3359	78	7	3.1	3.1	NUM
iajs-3359	78	8	existence	existence	NOUN
iajs-3359	78	9	and	and	CCONJ
iajs-3359	78	10	uniqueness	uniqueness	ADJ
iajs-3359	78	11	solution	solution	NOUN
iajs-3359	78	12	of	of	ADP
iajs-3359	78	13	the	the	DET
iajs-3359	78	14	model	model	NOUN
iajs-3359	78	15	[	[	X
iajs-3359	78	16	22,23	22,23	NOUN
iajs-3359	78	17	]	]	X
iajs-3359	78	18	we	we	PRON
iajs-3359	78	19	rewrite	rewrite	VERB
iajs-3359	78	20	the	the	DET
iajs-3359	78	21	system	system	NOUN
iajs-3359	78	22	eq.(4	eq.(4	ADV
iajs-3359	78	23	)	)	PUNCT
iajs-3359	78	24	in	in	ADP
iajs-3359	78	25	matrix	matrix	NOUN
iajs-3359	78	26	form	form	NOUN
iajs-3359	78	27	as	as	SCONJ
iajs-3359	78	28	follows	follow	VERB
iajs-3359	78	29	:	:	PUNCT
iajs-3359	78	30	let	let	VERB
iajs-3359	78	31	𝑀	𝑀	PROPN
iajs-3359	78	32	=	=	PUNCT
iajs-3359	79	1	[	[	PUNCT
iajs-3359	79	2	𝑆	𝑆	PROPN
iajs-3359	79	3	𝐸	𝐸	PROPN
iajs-3359	79	4	𝐼	𝐼	PROPN
iajs-3359	79	5	𝑅	𝑅	PROPN
iajs-3359	79	6	𝐹	𝐹	PROPN
iajs-3359	79	7	]	]	PUNCT
iajs-3359	79	8	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
iajs-3359	79	9	𝑀∗	𝑀∗	PROPN
iajs-3359	79	10	𝛼	𝛼	X
iajs-3359	80	1	=	=	X
iajs-3359	80	2	[	[	PUNCT
iajs-3359	80	3	𝐷∗	𝐷∗	X
iajs-3359	80	4	𝛼𝑆(𝑡	𝛼𝑆(𝑡	NUM
iajs-3359	80	5	)	)	PUNCT
iajs-3359	80	6	=	=	SYM
iajs-3359	81	1	−	−	PROPN
iajs-3359	81	2	𝛽	𝛽	NOUN
iajs-3359	81	3	𝑁	𝑁	PROPN
iajs-3359	81	4	𝑆𝐼	𝑆𝐼	ADJ
iajs-3359	81	5	𝐷∗	𝐷∗	NOUN
iajs-3359	81	6	𝛼𝐸(𝑡	𝛼𝐸(𝑡	NUM
iajs-3359	81	7	)	)	PUNCT
iajs-3359	82	1	=	=	SYM
iajs-3359	82	2	𝛽	𝛽	NOUN
iajs-3359	82	3	𝑁	𝑁	NOUN
iajs-3359	82	4	𝑆𝐼	𝑆𝐼	ADJ
iajs-3359	82	5	−	−	PROPN
iajs-3359	82	6	𝜔𝐸	𝜔𝐸	PROPN
iajs-3359	82	7	𝐷∗	𝐷∗	NOUN
iajs-3359	82	8	𝛼𝐼(𝑡	𝛼𝐼(𝑡	NUM
iajs-3359	82	9	)	)	PUNCT
iajs-3359	82	10	=	=	SYM
iajs-3359	82	11	𝜔𝜗𝐸	𝜔𝜗𝐸	NOUN
iajs-3359	82	12	−	−	PROPN
iajs-3359	82	13	(	(	PUNCT
iajs-3359	82	14	𝑙	𝑙	PROPN
iajs-3359	82	15	+	+	CCONJ
iajs-3359	82	16	𝜈)𝐼	𝜈)𝐼	PROPN
iajs-3359	82	17	𝐷∗	𝐷∗	PROPN
iajs-3359	82	18	𝛼𝑅(𝑡	𝛼𝑅(𝑡	NUM
iajs-3359	82	19	)	)	PUNCT
iajs-3359	82	20	=	=	PUNCT
iajs-3359	82	21	𝑙𝐼	𝑙𝐼	VERB
iajs-3359	82	22	𝐷∗	𝐷∗	NOUN
iajs-3359	83	1	𝛼𝐹(𝑡	𝛼𝐹(𝑡	NUM
iajs-3359	83	2	)	)	PUNCT
iajs-3359	83	3	=	=	PUNCT
iajs-3359	84	1	𝜈𝐼	𝜈𝐼	NOUN
iajs-3359	84	2	]	]	PUNCT
iajs-3359	84	3	by	by	ADP
iajs-3359	84	4	using	use	VERB
iajs-3359	84	5	the	the	DET
iajs-3359	84	6	relation	relation	NOUN
iajs-3359	84	7	between	between	ADP
iajs-3359	84	8	caputo	caputo	PROPN
iajs-3359	84	9	derivative	derivative	PROPN
iajs-3359	84	10	and	and	CCONJ
iajs-3359	84	11	riemann	riemann	PROPN
iajs-3359	84	12	derivative	derivative	NOUN
iajs-3359	84	13	to	to	ADP
iajs-3359	84	14	the	the	DET
iajs-3359	84	15	model	model	NOUN
iajs-3359	84	16	:	:	PUNCT
iajs-3359	84	17	𝑀∗	𝑀∗	NOUN
iajs-3359	84	18	𝛼	𝛼	NOUN
iajs-3359	84	19	=	=	PUNCT
iajs-3359	84	20	𝑀𝛼	𝑀𝛼	PROPN
iajs-3359	84	21	−	−	PROPN
iajs-3359	84	22	[	[	PUNCT
iajs-3359	84	23	∑	∑	PROPN
iajs-3359	84	24	𝜏𝑘−𝛼	𝜏𝑘−𝛼	PROPN
iajs-3359	84	25	𝛤(𝑘	𝛤(𝑘	PART
iajs-3359	84	26	−	−	NUM
iajs-3359	84	27	𝛼	𝛼	NOUN
iajs-3359	84	28	+	+	NOUN
iajs-3359	84	29	1	1	NUM
iajs-3359	84	30	)	)	PUNCT
iajs-3359	84	31	𝑛−1	𝑛−1	PROPN
iajs-3359	84	32	𝑘=0	𝑘=0	PROPN
iajs-3359	84	33	𝑆(𝑘)(0	𝑆(𝑘)(0	NOUN
iajs-3359	84	34	)	)	PUNCT
iajs-3359	84	35	∑	∑	PUNCT
iajs-3359	84	36	𝜏𝑘−𝛼	𝜏𝑘−𝛼	PROPN
iajs-3359	84	37	𝛤(𝑘	𝛤(𝑘	PART
iajs-3359	84	38	−	−	NUM
iajs-3359	84	39	𝛼	𝛼	NOUN
iajs-3359	84	40	+	+	NOUN
iajs-3359	84	41	1	1	NUM
iajs-3359	84	42	)	)	PUNCT
iajs-3359	84	43	𝑛−1	𝑛−1	PROPN
iajs-3359	84	44	𝑘=0	𝑘=0	ADP
iajs-3359	84	45	𝐸(𝑘)(0	𝐸(𝑘)(0	PROPN
iajs-3359	84	46	)	)	PUNCT
iajs-3359	84	47	∑	∑	PUNCT
iajs-3359	84	48	𝜏𝑘−𝛼	𝜏𝑘−𝛼	PROPN
iajs-3359	84	49	𝛤(𝑘	𝛤(𝑘	PART
iajs-3359	84	50	−	−	NUM
iajs-3359	84	51	𝛼	𝛼	NOUN
iajs-3359	84	52	+	+	NOUN
iajs-3359	84	53	1	1	NUM
iajs-3359	84	54	)	)	PUNCT
iajs-3359	84	55	𝑛−1	𝑛−1	PROPN
iajs-3359	84	56	𝑘=0	𝑘=0	ADP
iajs-3359	84	57	𝐼(𝑘)(0	𝐼(𝑘)(0	NOUN
iajs-3359	84	58	)	)	PUNCT
iajs-3359	84	59	∑	∑	PROPN
iajs-3359	84	60	𝜏𝑘−𝛼	𝜏𝑘−𝛼	PROPN
iajs-3359	84	61	𝛤(𝑘	𝛤(𝑘	PART
iajs-3359	84	62	−	−	NUM
iajs-3359	84	63	𝛼	𝛼	NOUN
iajs-3359	84	64	+	+	NOUN
iajs-3359	84	65	1	1	NUM
iajs-3359	84	66	)	)	PUNCT
iajs-3359	84	67	𝑛−1	𝑛−1	PROPN
iajs-3359	84	68	𝑘=0	𝑘=0	NUM
iajs-3359	84	69	𝑅(𝑘)(0	𝑅(𝑘)(0	ADJ
iajs-3359	84	70	)	)	PUNCT
iajs-3359	84	71	∑	∑	PROPN
iajs-3359	84	72	𝜏𝑘−𝛼	𝜏𝑘−𝛼	PROPN
iajs-3359	84	73	𝛤(𝑘	𝛤(𝑘	PART
iajs-3359	84	74	−	−	NUM
iajs-3359	84	75	𝛼	𝛼	NOUN
iajs-3359	84	76	+	+	NOUN
iajs-3359	84	77	1	1	NUM
iajs-3359	84	78	)	)	PUNCT
iajs-3359	84	79	𝑛−1	𝑛−1	PROPN
iajs-3359	84	80	𝑘=0	𝑘=0	VERB
iajs-3359	84	81	𝐹	𝐹	PROPN
iajs-3359	84	82	(	(	PUNCT
iajs-3359	84	83	𝑘)(0	𝑘)(0	PROPN
iajs-3359	84	84	)	)	PUNCT
iajs-3359	84	85	]	]	PUNCT
iajs-3359	85	1	𝑀𝛼	𝑀𝛼	PROPN
iajs-3359	85	2	=	=	SYM
iajs-3359	85	3	𝑀∗	𝑀∗	NOUN
iajs-3359	85	4	𝛼	𝛼	NOUN
iajs-3359	86	1	+	+	X
iajs-3359	86	2	[	[	PUNCT
iajs-3359	86	3	∑	∑	PROPN
iajs-3359	86	4	𝜏𝑘−𝛼	𝜏𝑘−𝛼	PROPN
iajs-3359	86	5	𝛤(𝑘	𝛤(𝑘	PART
iajs-3359	86	6	−	−	NUM
iajs-3359	86	7	𝛼	𝛼	NOUN
iajs-3359	86	8	+	+	NOUN
iajs-3359	86	9	1	1	NUM
iajs-3359	86	10	)	)	PUNCT
iajs-3359	86	11	𝑛−1	𝑛−1	PROPN
iajs-3359	86	12	𝑘=0	𝑘=0	PROPN
iajs-3359	86	13	𝑆(𝑘)(0	𝑆(𝑘)(0	NOUN
iajs-3359	86	14	)	)	PUNCT
iajs-3359	86	15	∑	∑	PUNCT
iajs-3359	86	16	𝜏𝑘−𝛼	𝜏𝑘−𝛼	PROPN
iajs-3359	86	17	𝛤(𝑘	𝛤(𝑘	PART
iajs-3359	86	18	−	−	NUM
iajs-3359	86	19	𝛼	𝛼	NOUN
iajs-3359	86	20	+	+	NOUN
iajs-3359	86	21	1	1	NUM
iajs-3359	86	22	)	)	PUNCT
iajs-3359	86	23	𝑛−1	𝑛−1	PROPN
iajs-3359	86	24	𝑘=0	𝑘=0	ADP
iajs-3359	86	25	𝐸(𝑘)(0	𝐸(𝑘)(0	PROPN
iajs-3359	86	26	)	)	PUNCT
iajs-3359	86	27	∑	∑	PUNCT
iajs-3359	86	28	𝜏𝑘−𝛼	𝜏𝑘−𝛼	PROPN
iajs-3359	86	29	𝛤(𝑘	𝛤(𝑘	PART
iajs-3359	86	30	−	−	NUM
iajs-3359	86	31	𝛼	𝛼	NOUN
iajs-3359	86	32	+	+	NOUN
iajs-3359	86	33	1	1	NUM
iajs-3359	86	34	)	)	PUNCT
iajs-3359	86	35	𝑛−1	𝑛−1	PROPN
iajs-3359	86	36	𝑘=0	𝑘=0	ADP
iajs-3359	86	37	𝐼(𝑘)(0	𝐼(𝑘)(0	NOUN
iajs-3359	86	38	)	)	PUNCT
iajs-3359	86	39	∑	∑	PROPN
iajs-3359	86	40	𝜏𝑘−𝛼	𝜏𝑘−𝛼	PROPN
iajs-3359	86	41	𝛤(𝑘	𝛤(𝑘	PART
iajs-3359	86	42	−	−	NUM
iajs-3359	86	43	𝛼	𝛼	NOUN
iajs-3359	86	44	+	+	NOUN
iajs-3359	86	45	1	1	NUM
iajs-3359	86	46	)	)	PUNCT
iajs-3359	86	47	𝑛−1	𝑛−1	PROPN
iajs-3359	86	48	𝑘=0	𝑘=0	NUM
iajs-3359	86	49	𝑅(𝑘)(0	𝑅(𝑘)(0	ADJ
iajs-3359	86	50	)	)	PUNCT
iajs-3359	86	51	∑	∑	PROPN
iajs-3359	86	52	𝜏𝑘−𝛼	𝜏𝑘−𝛼	PROPN
iajs-3359	86	53	𝛤(𝑘	𝛤(𝑘	PART
iajs-3359	86	54	−	−	NUM
iajs-3359	86	55	𝛼	𝛼	NOUN
iajs-3359	86	56	+	+	NOUN
iajs-3359	86	57	1	1	NUM
iajs-3359	86	58	)	)	PUNCT
iajs-3359	86	59	𝑛−1	𝑛−1	PROPN
iajs-3359	86	60	𝑘=0	𝑘=0	VERB
iajs-3359	86	61	𝐹	𝐹	PROPN
iajs-3359	86	62	(	(	PUNCT
iajs-3359	86	63	𝑘)(0	𝑘)(0	PROPN
iajs-3359	86	64	)	)	PUNCT
iajs-3359	86	65	]	]	PUNCT
iajs-3359	87	1	𝑙𝑒𝑡	𝑙𝑒𝑡	PROPN
iajs-3359	87	2	𝐿	𝐿	PROPN
iajs-3359	87	3	=	=	PROPN
iajs-3359	87	4	𝑀∗	𝑀∗	NOUN
iajs-3359	87	5	𝛼	𝛼	NOUN
iajs-3359	87	6	+	+	CCONJ
iajs-3359	87	7	[	[	PUNCT
iajs-3359	87	8	∑	∑	PROPN
iajs-3359	87	9	𝜏𝑘−𝛼	𝜏𝑘−𝛼	PROPN
iajs-3359	87	10	𝛤(𝑘	𝛤(𝑘	PART
iajs-3359	87	11	−	−	NUM
iajs-3359	87	12	𝛼	𝛼	NOUN
iajs-3359	87	13	+	+	NOUN
iajs-3359	87	14	1	1	NUM
iajs-3359	87	15	)	)	PUNCT
iajs-3359	87	16	𝑛−1	𝑛−1	PROPN
iajs-3359	87	17	𝑘=0	𝑘=0	PROPN
iajs-3359	87	18	𝑆(𝑘)(0	𝑆(𝑘)(0	NOUN
iajs-3359	87	19	)	)	PUNCT
iajs-3359	87	20	∑	∑	PUNCT
iajs-3359	87	21	𝜏𝑘−𝛼	𝜏𝑘−𝛼	PROPN
iajs-3359	87	22	𝛤(𝑘	𝛤(𝑘	PART
iajs-3359	87	23	−	−	NUM
iajs-3359	87	24	𝛼	𝛼	NOUN
iajs-3359	87	25	+	+	NOUN
iajs-3359	87	26	1	1	NUM
iajs-3359	87	27	)	)	PUNCT
iajs-3359	87	28	𝑛−1	𝑛−1	PROPN
iajs-3359	87	29	𝑘=0	𝑘=0	ADP
iajs-3359	87	30	𝐸(𝑘)(0	𝐸(𝑘)(0	PROPN
iajs-3359	87	31	)	)	PUNCT
iajs-3359	87	32	∑	∑	PUNCT
iajs-3359	87	33	𝜏𝑘−𝛼	𝜏𝑘−𝛼	PROPN
iajs-3359	87	34	𝛤(𝑘	𝛤(𝑘	PART
iajs-3359	87	35	−	−	NUM
iajs-3359	87	36	𝛼	𝛼	NOUN
iajs-3359	87	37	+	+	NOUN
iajs-3359	87	38	1	1	NUM
iajs-3359	87	39	)	)	PUNCT
iajs-3359	87	40	𝑛−1	𝑛−1	PROPN
iajs-3359	87	41	𝑘=0	𝑘=0	ADP
iajs-3359	87	42	𝐼(𝑘)(0	𝐼(𝑘)(0	NOUN
iajs-3359	87	43	)	)	PUNCT
iajs-3359	87	44	∑	∑	PROPN
iajs-3359	87	45	𝜏𝑘−𝛼	𝜏𝑘−𝛼	PROPN
iajs-3359	87	46	𝛤(𝑘	𝛤(𝑘	PART
iajs-3359	87	47	−	−	NUM
iajs-3359	87	48	𝛼	𝛼	NOUN
iajs-3359	87	49	+	+	NOUN
iajs-3359	87	50	1	1	NUM
iajs-3359	87	51	)	)	PUNCT
iajs-3359	87	52	𝑛−1	𝑛−1	PROPN
iajs-3359	87	53	𝑘=0	𝑘=0	NUM
iajs-3359	87	54	𝑅(𝑘)(0	𝑅(𝑘)(0	ADJ
iajs-3359	87	55	)	)	PUNCT
iajs-3359	87	56	∑	∑	PROPN
iajs-3359	87	57	𝜏𝑘−𝛼	𝜏𝑘−𝛼	PROPN
iajs-3359	87	58	𝛤(𝑘	𝛤(𝑘	PART
iajs-3359	87	59	−	−	NUM
iajs-3359	87	60	𝛼	𝛼	NOUN
iajs-3359	87	61	+	+	NOUN
iajs-3359	87	62	1	1	NUM
iajs-3359	87	63	)	)	PUNCT
iajs-3359	87	64	𝑛−1	𝑛−1	PROPN
iajs-3359	87	65	𝑘=0	𝑘=0	VERB
iajs-3359	87	66	𝐹	𝐹	PROPN
iajs-3359	87	67	(	(	PUNCT
iajs-3359	87	68	𝑘)(0	𝑘)(0	PROPN
iajs-3359	87	69	)	)	PUNCT
iajs-3359	87	70	]	]	PUNCT
iajs-3359	88	1	𝑀𝛼	𝑀𝛼	PROPN
iajs-3359	88	2	=	=	SYM
iajs-3359	88	3	𝐿(𝑆	𝐿(𝑆	PROPN
iajs-3359	88	4	,	,	PUNCT
iajs-3359	88	5	𝐸	𝐸	PROPN
iajs-3359	88	6	,	,	PUNCT
iajs-3359	88	7	𝐼	𝐼	PROPN
iajs-3359	88	8	,	,	PUNCT
iajs-3359	88	9	𝑅	𝑅	PROPN
iajs-3359	88	10	,	,	PUNCT
iajs-3359	88	11	𝐹	𝐹	PROPN
iajs-3359	88	12	)	)	PUNCT
iajs-3359	88	13	and	and	CCONJ
iajs-3359	88	14	𝑀𝛼(𝑡0	𝑀𝛼(𝑡0	PROPN
iajs-3359	88	15	)	)	PUNCT
iajs-3359	89	1	=	=	PRON
iajs-3359	89	2	𝑀0	𝑀0	ADJ
iajs-3359	89	3	is	be	AUX
iajs-3359	89	4	an	an	DET
iajs-3359	89	5	initial	initial	ADJ
iajs-3359	89	6	value	value	NOUN
iajs-3359	89	7	problem	problem	NOUN
iajs-3359	89	8	.	.	PUNCT
iajs-3359	90	1	in	in	ADP
iajs-3359	90	2	addition	addition	NOUN
iajs-3359	90	3	,	,	PUNCT
iajs-3359	90	4	l	l	NOUN
iajs-3359	90	5	is	be	AUX
iajs-3359	90	6	continues	continue	VERB
iajs-3359	90	7	for	for	ADP
iajs-3359	90	8	all	all	DET
iajs-3359	90	9	variables	variable	NOUN
iajs-3359	90	10	and	and	CCONJ
iajs-3359	90	11	t	t	PROPN
iajs-3359	90	12	,	,	PUNCT
iajs-3359	90	13	l	l	PROPN
iajs-3359	90	14	has	have	AUX
iajs-3359	90	15	bounded	bound	VERB
iajs-3359	90	16	partial	partial	ADJ
iajs-3359	90	17	derivatives	derivative	NOUN
iajs-3359	90	18	then	then	ADV
iajs-3359	90	19	according	accord	VERB
iajs-3359	90	20	to	to	ADP
iajs-3359	90	21	the	the	DET
iajs-3359	90	22	existence	existence	NOUN
iajs-3359	90	23	and	and	CCONJ
iajs-3359	90	24	uniqueness	uniqueness	NOUN
iajs-3359	90	25	theorem	theorem	VERB
iajs-3359	90	26	.	.	PUNCT
iajs-3359	91	1	that	that	PRON
iajs-3359	91	2	means	mean	VERB
iajs-3359	91	3	there	there	PRON
iajs-3359	91	4	exist	exist	VERB
iajs-3359	91	5	unique	unique	ADJ
iajs-3359	91	6	solution	solution	NOUN
iajs-3359	91	7	to	to	ADP
iajs-3359	91	8	system	system	NOUN
iajs-3359	91	9	eq.(4	eq.(4	ADJ
iajs-3359	91	10	)	)	PUNCT
iajs-3359	91	11	.	.	PUNCT
iajs-3359	92	1	proof	proof	NOUN
iajs-3359	92	2	:	:	PUNCT
iajs-3359	92	3	let	let	VERB
iajs-3359	92	4	𝑢𝑡	𝑢𝑡	NOUN
iajs-3359	92	5	(	(	PUNCT
iajs-3359	92	6	𝛼)(𝑡	𝛼)(𝑡	X
iajs-3359	92	7	)	)	PUNCT
iajs-3359	92	8	be	be	VERB
iajs-3359	92	9	the	the	DET
iajs-3359	92	10	fractional	fractional	ADJ
iajs-3359	92	11	derivative	derivative	NOUN
iajs-3359	92	12	of	of	ADP
iajs-3359	92	13	𝑢(𝑡	𝑢(𝑡	NOUN
iajs-3359	92	14	)	)	PUNCT
iajs-3359	92	15	of	of	ADP
iajs-3359	92	16	order	order	NOUN
iajs-3359	92	17	α	α	NOUN
iajs-3359	92	18	.	.	PUNCT
iajs-3359	93	1	the	the	DET
iajs-3359	93	2	substitution	substitution	NOUN
iajs-3359	93	3	𝜉(𝑡	𝜉(𝑡	NOUN
iajs-3359	93	4	)	)	PUNCT
iajs-3359	94	1	=	=	PUNCT
iajs-3359	94	2	𝑡𝛼	𝑡𝛼	PROPN
iajs-3359	94	3	𝛤(𝛼+1	𝛤(𝛼+1	NUM
iajs-3359	94	4	)	)	PUNCT
iajs-3359	95	1	+	+	CCONJ
iajs-3359	95	2	𝜉0	𝜉0	NOUN
iajs-3359	95	3	reduce	reduce	VERB
iajs-3359	95	4	𝑢(𝛼)(𝑡)𝑡𝑜	𝑢(𝛼)(𝑡)𝑡𝑜	NOUN
iajs-3359	95	5	𝑢′(𝜉	𝑢′(𝜉	NOUN
iajs-3359	95	6	)	)	PUNCT
iajs-3359	95	7	as	as	SCONJ
iajs-3359	95	8	follows	follow	VERB
iajs-3359	95	9	:	:	PUNCT
iajs-3359	95	10	𝑢𝑡	𝑢𝑡	NOUN
iajs-3359	95	11	(	(	PUNCT
iajs-3359	95	12	𝛼)(𝑡	𝛼)(𝑡	X
iajs-3359	95	13	)	)	PUNCT
iajs-3359	95	14	=	=	SYM
iajs-3359	95	15	𝑢𝑡	𝑢𝑡	NOUN
iajs-3359	95	16	(	(	PUNCT
iajs-3359	95	17	𝛼)(𝜉	𝛼)(𝜉	NOUN
iajs-3359	95	18	)	)	PUNCT
iajs-3359	95	19	=	=	SYM
iajs-3359	95	20	𝑢′(𝜉	𝑢′(𝜉	PROPN
iajs-3359	95	21	)	)	PUNCT
iajs-3359	95	22	𝐷𝑡	𝐷𝑡	PROPN
iajs-3359	95	23	𝛼𝜉	𝛼𝜉	NOUN
iajs-3359	95	24	=	=	SYM
iajs-3359	95	25	𝑢′(𝜉	𝑢′(𝜉	PROPN
iajs-3359	95	26	)	)	PUNCT
iajs-3359	95	27	1	1	NUM
iajs-3359	95	28	𝛤(𝛼+1	𝛤(𝛼+1	NOUN
iajs-3359	95	29	)	)	PUNCT
iajs-3359	95	30	𝛤(𝛼+1	𝛤(𝛼+1	X
iajs-3359	95	31	)	)	PUNCT
iajs-3359	95	32	𝛤(𝛼−𝛼+1	𝛤(𝛼−𝛼+1	ADV
iajs-3359	95	33	)	)	PUNCT
iajs-3359	95	34	𝑡𝛼−𝛼	𝑡𝛼−𝛼	NOUN
iajs-3359	95	35	=	=	SYM
iajs-3359	95	36	𝑢′(𝜉	𝑢′(𝜉	PROPN
iajs-3359	95	37	)	)	PUNCT
iajs-3359	95	38	therefore	therefore	ADV
iajs-3359	95	39	the	the	DET
iajs-3359	95	40	system	system	NOUN
iajs-3359	95	41	eq.(4	eq.(4	VERB
iajs-3359	95	42	)	)	PUNCT
iajs-3359	95	43	𝑀(𝛼)(𝑡	𝑀(𝛼)(𝑡	PROPN
iajs-3359	95	44	)	)	PUNCT
iajs-3359	95	45	=	=	SYM
iajs-3359	95	46	𝑀′(𝜉	𝑀′(𝜉	NOUN
iajs-3359	95	47	)	)	PUNCT
iajs-3359	95	48	,	,	PUNCT
iajs-3359	95	49	ihjpas	ihjpa	VERB
iajs-3359	95	50	.	.	PUNCT
iajs-3359	96	1	37	37	NUM
iajs-3359	96	2	(	(	PUNCT
iajs-3359	96	3	2	2	NUM
iajs-3359	96	4	)	)	PUNCT
iajs-3359	96	5	2024	2024	NUM
iajs-3359	96	6	382	382	NUM
iajs-3359	96	7	𝑀∗	𝑀∗	NOUN
iajs-3359	96	8	(	(	PUNCT
iajs-3359	96	9	𝛼	𝛼	X
iajs-3359	96	10	)	)	PUNCT
iajs-3359	96	11	=	=	PUNCT
iajs-3359	96	12	[	[	PUNCT
iajs-3359	96	13	𝐷∗	𝐷∗	X
iajs-3359	96	14	𝛼𝑆(𝑡	𝛼𝑆(𝑡	NUM
iajs-3359	96	15	)	)	PUNCT
iajs-3359	96	16	=	=	SYM
iajs-3359	97	1	−	−	PROPN
iajs-3359	97	2	𝛽	𝛽	NOUN
iajs-3359	97	3	𝑁	𝑁	PROPN
iajs-3359	97	4	𝑆𝐼	𝑆𝐼	ADJ
iajs-3359	97	5	𝐷∗	𝐷∗	NOUN
iajs-3359	97	6	𝛼𝐸(𝑡	𝛼𝐸(𝑡	NUM
iajs-3359	97	7	)	)	PUNCT
iajs-3359	98	1	=	=	SYM
iajs-3359	98	2	𝛽	𝛽	NOUN
iajs-3359	98	3	𝑁	𝑁	NOUN
iajs-3359	98	4	𝑆𝐼	𝑆𝐼	ADJ
iajs-3359	98	5	−	−	PROPN
iajs-3359	98	6	𝜔𝐸	𝜔𝐸	PROPN
iajs-3359	98	7	𝐷∗	𝐷∗	NOUN
iajs-3359	98	8	𝛼𝐼(𝑡	𝛼𝐼(𝑡	NUM
iajs-3359	98	9	)	)	PUNCT
iajs-3359	98	10	=	=	SYM
iajs-3359	98	11	𝜔𝜗𝐸	𝜔𝜗𝐸	NOUN
iajs-3359	98	12	−	−	PROPN
iajs-3359	98	13	(	(	PUNCT
iajs-3359	98	14	𝑙	𝑙	PROPN
iajs-3359	98	15	+	+	CCONJ
iajs-3359	98	16	𝜈)𝐼	𝜈)𝐼	PROPN
iajs-3359	98	17	𝐷∗	𝐷∗	PROPN
iajs-3359	98	18	𝛼𝑅(𝑡	𝛼𝑅(𝑡	NUM
iajs-3359	98	19	)	)	PUNCT
iajs-3359	98	20	=	=	PUNCT
iajs-3359	98	21	𝑙𝐼	𝑙𝐼	VERB
iajs-3359	98	22	𝐷∗	𝐷∗	NOUN
iajs-3359	99	1	𝛼𝐹(𝑡	𝛼𝐹(𝑡	NUM
iajs-3359	99	2	)	)	PUNCT
iajs-3359	99	3	=	=	PUNCT
iajs-3359	100	1	𝜈𝐼	𝜈𝐼	ADJ
iajs-3359	100	2	]	]	PUNCT
iajs-3359	100	3	𝑀5∗1	𝑀5∗1	NOUN
iajs-3359	100	4	′	′	NUM
iajs-3359	100	5	(	(	PUNCT
iajs-3359	100	6	𝜉	𝜉	NOUN
iajs-3359	100	7	)	)	PUNCT
iajs-3359	100	8	=	=	SYM
iajs-3359	100	9	𝑀∗	𝑀∗	NOUN
iajs-3359	100	10	(	(	PUNCT
iajs-3359	100	11	𝛼	𝛼	NOUN
iajs-3359	100	12	)	)	PUNCT
iajs-3359	100	13	+	+	CCONJ
iajs-3359	100	14	𝐿	𝐿	PROPN
iajs-3359	100	15	≑	≑	PROPN
iajs-3359	100	16	𝑓(𝑡	𝑓(𝑡	PROPN
iajs-3359	100	17	,	,	PUNCT
iajs-3359	100	18	𝑆	𝑆	PROPN
iajs-3359	100	19	,	,	PUNCT
iajs-3359	100	20	𝐸	𝐸	PROPN
iajs-3359	100	21	,	,	PUNCT
iajs-3359	100	22	𝐼	𝐼	PROPN
iajs-3359	100	23	,	,	PUNCT
iajs-3359	100	24	𝑅	𝑅	PROPN
iajs-3359	100	25	,	,	PUNCT
iajs-3359	100	26	𝐹),𝑀(0	𝐹),𝑀(0	ADJ
iajs-3359	100	27	)	)	PUNCT
iajs-3359	101	1	=	=	SYM
iajs-3359	101	2	𝑀0	𝑀0	ADJ
iajs-3359	101	3	and	and	CCONJ
iajs-3359	101	4	according	accord	VERB
iajs-3359	101	5	to	to	ADP
iajs-3359	101	6	the	the	DET
iajs-3359	101	7	theorem	theorem	NOUN
iajs-3359	101	8	1	1	NUM
iajs-3359	101	9	in	in	ADP
iajs-3359	101	10	[	[	X
iajs-3359	101	11	24	24	NUM
iajs-3359	101	12	]	]	PUNCT
iajs-3359	101	13	then	then	ADV
iajs-3359	101	14	there	there	PRON
iajs-3359	101	15	exist	exist	VERB
iajs-3359	101	16	unique	unique	ADJ
iajs-3359	101	17	solution	solution	NOUN
iajs-3359	101	18	of	of	ADP
iajs-3359	101	19	eq.(4	eq.(4	ADJ
iajs-3359	101	20	)	)	PUNCT
iajs-3359	101	21	3.2	3.2	NUM
iajs-3359	101	22	the	the	DET
iajs-3359	101	23	equilibrium	equilibrium	NOUN
iajs-3359	101	24	points	point	NOUN
iajs-3359	101	25	of	of	ADP
iajs-3359	101	26	the	the	DET
iajs-3359	101	27	model	model	NOUN
iajs-3359	102	1	[	[	X
iajs-3359	102	2	25	25	NUM
iajs-3359	102	3	]	]	PUNCT
iajs-3359	102	4	to	to	PART
iajs-3359	102	5	find	find	VERB
iajs-3359	102	6	the	the	DET
iajs-3359	102	7	equilibrium	equilibrium	NOUN
iajs-3359	102	8	points	point	NOUN
iajs-3359	102	9	of	of	ADP
iajs-3359	102	10	the	the	DET
iajs-3359	102	11	model	model	NOUN
iajs-3359	102	12	eq.(4	eq.(4	PROPN
iajs-3359	102	13	)	)	PUNCT
iajs-3359	102	14	,	,	PUNCT
iajs-3359	102	15	equalizing	equalize	VERB
iajs-3359	102	16	the	the	DET
iajs-3359	102	17	equations	equation	NOUN
iajs-3359	102	18	to	to	ADP
iajs-3359	102	19	zero	zero	NUM
iajs-3359	102	20	𝐷∗	𝐷∗	NOUN
iajs-3359	102	21	𝛼𝑆(𝑡	𝛼𝑆(𝑡	NUM
iajs-3359	102	22	)	)	PUNCT
iajs-3359	102	23	=	=	SYM
iajs-3359	102	24	𝐷∗	𝐷∗	NOUN
iajs-3359	102	25	𝛼𝐸(𝑡	𝛼𝐸(𝑡	NUM
iajs-3359	102	26	)	)	PUNCT
iajs-3359	102	27	=	=	SYM
iajs-3359	102	28	𝐷∗	𝐷∗	PROPN
iajs-3359	102	29	𝛼𝐼(𝑡	𝛼𝐼(𝑡	NUM
iajs-3359	102	30	)	)	PUNCT
iajs-3359	103	1	=	=	SYM
iajs-3359	103	2	𝐷∗	𝐷∗	NOUN
iajs-3359	103	3	𝛼𝑅(𝑡	𝛼𝑅(𝑡	NUM
iajs-3359	103	4	)	)	PUNCT
iajs-3359	103	5	=	=	SYM
iajs-3359	103	6	𝐷∗	𝐷∗	NOUN
iajs-3359	103	7	𝛼𝐹(𝑡	𝛼𝐹(𝑡	VERB
iajs-3359	103	8	)	)	PUNCT
iajs-3359	103	9	=	=	SYM
iajs-3359	103	10	0	0	PUNCT
iajs-3359	104	1	(	(	PUNCT
iajs-3359	104	2	5	5	NUM
iajs-3359	104	3	)	)	PUNCT
iajs-3359	104	4	then	then	ADV
iajs-3359	104	5	the	the	DET
iajs-3359	104	6	equilibrium	equilibrium	NOUN
iajs-3359	104	7	point	point	NOUN
iajs-3359	104	8	:	:	PUNCT
iajs-3359	104	9	(	(	PUNCT
iajs-3359	104	10	𝑆	𝑆	PROPN
iajs-3359	104	11	,	,	PUNCT
iajs-3359	104	12	𝐸	𝐸	PROPN
iajs-3359	104	13	,	,	PUNCT
iajs-3359	104	14	𝐼	𝐼	PROPN
iajs-3359	104	15	,	,	PUNCT
iajs-3359	104	16	𝑅	𝑅	PROPN
iajs-3359	104	17	,	,	PUNCT
iajs-3359	104	18	𝐹	𝐹	PROPN
iajs-3359	104	19	)	)	PUNCT
iajs-3359	104	20	=	=	SYM
iajs-3359	105	1	(	(	PUNCT
iajs-3359	105	2	𝑁	𝑁	PROPN
iajs-3359	105	3	,	,	PUNCT
iajs-3359	105	4	0,0,0,0	0,0,0,0	NUM
iajs-3359	105	5	)	)	PUNCT
iajs-3359	105	6	(	(	PUNCT
iajs-3359	105	7	6	6	NUM
iajs-3359	105	8	)	)	PUNCT
iajs-3359	105	9	now	now	ADV
iajs-3359	105	10	to	to	PART
iajs-3359	105	11	find	find	VERB
iajs-3359	105	12	the	the	DET
iajs-3359	105	13	stability	stability	NOUN
iajs-3359	105	14	of	of	ADP
iajs-3359	105	15	the	the	DET
iajs-3359	105	16	equilibrium	equilibrium	NOUN
iajs-3359	105	17	point	point	NOUN
iajs-3359	105	18	𝐷∗	𝐷∗	PROPN
iajs-3359	105	19	𝛼𝑆(𝑡	𝛼𝑆(𝑡	NUM
iajs-3359	105	20	)	)	PUNCT
iajs-3359	105	21	=	=	SYM
iajs-3359	106	1	−	−	PROPN
iajs-3359	106	2	𝛽	𝛽	NOUN
iajs-3359	106	3	𝑁	𝑁	PROPN
iajs-3359	106	4	𝑆𝐼	𝑆𝐼	NOUN
iajs-3359	106	5	=	=	SYM
iajs-3359	106	6	𝑓1	𝑓1	PROPN
iajs-3359	106	7	,	,	PUNCT
iajs-3359	106	8	𝐷∗	𝐷∗	NOUN
iajs-3359	106	9	𝛼𝐸(𝑡	𝛼𝐸(𝑡	NUM
iajs-3359	106	10	)	)	PUNCT
iajs-3359	107	1	=	=	SYM
iajs-3359	107	2	𝛽	𝛽	NOUN
iajs-3359	107	3	𝑁	𝑁	PROPN
iajs-3359	107	4	𝑆𝐼	𝑆𝐼	ADJ
iajs-3359	107	5	−	−	NOUN
iajs-3359	107	6	𝜔𝐸	𝜔𝐸	NOUN
iajs-3359	107	7	=	=	SYM
iajs-3359	107	8	𝑓2	𝑓2	PROPN
iajs-3359	107	9	,	,	PUNCT
iajs-3359	107	10	𝐷∗	𝐷∗	X
iajs-3359	107	11	𝛼𝐼(𝑡	𝛼𝐼(𝑡	NUM
iajs-3359	107	12	)	)	PUNCT
iajs-3359	107	13	=	=	SYM
iajs-3359	107	14	𝜔𝜗𝐸	𝜔𝜗𝐸	NOUN
iajs-3359	107	15	−	−	PROPN
iajs-3359	107	16	(	(	PUNCT
iajs-3359	107	17	𝑙	𝑙	PROPN
iajs-3359	107	18	+	+	CCONJ
iajs-3359	107	19	𝜈)𝐼	𝜈)𝐼	ADJ
iajs-3359	107	20	=	=	PROPN
iajs-3359	107	21	𝑓3	𝑓3	PROPN
iajs-3359	107	22	,	,	PUNCT
iajs-3359	107	23	(	(	PUNCT
iajs-3359	107	24	7	7	X
iajs-3359	107	25	)	)	PUNCT
iajs-3359	107	26	𝐷∗	𝐷∗	NOUN
iajs-3359	107	27	𝛼𝑅(𝑡	𝛼𝑅(𝑡	NUM
iajs-3359	107	28	)	)	PUNCT
iajs-3359	107	29	=	=	SYM
iajs-3359	107	30	𝑙𝐼	𝑙𝐼	NOUN
iajs-3359	108	1	=	=	SYM
iajs-3359	108	2	𝑓4	𝑓4	PROPN
iajs-3359	108	3	,	,	PUNCT
iajs-3359	108	4	𝐷∗	𝐷∗	X
iajs-3359	108	5	𝛼𝐹(𝑡	𝛼𝐹(𝑡	NUM
iajs-3359	108	6	)	)	PUNCT
iajs-3359	108	7	=	=	PUNCT
iajs-3359	109	1	𝜈𝐼	𝜈𝐼	ADJ
iajs-3359	109	2	=	=	NUM
iajs-3359	109	3	𝑓5	𝑓5	NOUN
iajs-3359	109	4	.	.	PUNCT
iajs-3359	110	1	expanding	expand	VERB
iajs-3359	110	2	𝑓1	𝑓1	ADJ
iajs-3359	110	3	,	,	PUNCT
iajs-3359	110	4	𝑓2	𝑓2	ADJ
iajs-3359	110	5	,	,	PUNCT
iajs-3359	110	6	𝑓3	𝑓3	NOUN
iajs-3359	110	7	,	,	PUNCT
iajs-3359	110	8	𝑓4	𝑓4	NOUN
iajs-3359	110	9	,	,	PUNCT
iajs-3359	110	10	𝑓5	𝑓5	NOUN
iajs-3359	110	11	by	by	ADP
iajs-3359	110	12	tayler	tayler	PROPN
iajs-3359	110	13	series	series	PROPN
iajs-3359	110	14	about	about	ADP
iajs-3359	110	15	(	(	PUNCT
iajs-3359	110	16	𝑁	𝑁	PROPN
iajs-3359	110	17	,	,	PUNCT
iajs-3359	110	18	0,0,0,0	0,0,0,0	NOUN
iajs-3359	110	19	)	)	PUNCT
iajs-3359	110	20	.	.	PUNCT
iajs-3359	111	1	𝐷∗	𝐷∗	PROPN
iajs-3359	111	2	𝛼𝑆(𝑡	𝛼𝑆(𝑡	NUM
iajs-3359	111	3	)	)	PUNCT
iajs-3359	111	4	=	=	NOUN
iajs-3359	111	5	𝜕𝑓1	𝜕𝑓1	NOUN
iajs-3359	111	6	𝜕𝑆	𝜕𝑆	NOUN
iajs-3359	111	7	|(𝒩,0,0,0,0)(𝑆	|(𝒩,0,0,0,0)(𝑆	VERB
iajs-3359	111	8	−	−	PROPN
iajs-3359	111	9	𝒩	𝒩	PROPN
iajs-3359	111	10	)	)	PUNCT
iajs-3359	111	11	+	+	NUM
iajs-3359	112	1	𝜕𝑓1	𝜕𝑓1	NOUN
iajs-3359	112	2	𝜕𝐸	𝜕𝐸	NOUN
iajs-3359	112	3	|(𝒩,0,0,0,0)𝐸	|(𝒩,0,0,0,0)𝐸	PUNCT
iajs-3359	112	4	+	+	CCONJ
iajs-3359	112	5	𝜕𝑓1	𝜕𝑓1	NOUN
iajs-3359	112	6	𝜕𝐼	𝜕𝐼	PROPN
iajs-3359	112	7	|(𝒩,0,0,0,0)𝐼	|(𝒩,0,0,0,0)𝐼	PROPN
iajs-3359	112	8	+	+	SYM
iajs-3359	112	9	𝜕𝑓1	𝜕𝑓1	NOUN
iajs-3359	112	10	𝜕𝑅	𝜕𝑅	PROPN
iajs-3359	112	11	|(𝒩,0,0,0,0)𝑅	|(𝒩,0,0,0,0)𝑅	NOUN
iajs-3359	112	12	+	+	SYM
iajs-3359	112	13	𝜕𝑓1	𝜕𝑓1	NOUN
iajs-3359	112	14	𝜕𝐹	𝜕𝐹	PRON
iajs-3359	112	15	|(𝒩,0,0,0,0)𝐹	|(𝒩,0,0,0,0)𝐹	X
iajs-3359	112	16	+	+	X
iajs-3359	112	17	⋯	⋯	VERB
iajs-3359	112	18	𝐷∗	𝐷∗	NOUN
iajs-3359	112	19	𝛼𝐸(𝑡	𝛼𝐸(𝑡	NUM
iajs-3359	112	20	)	)	PUNCT
iajs-3359	113	1	=	=	NOUN
iajs-3359	114	1	𝜕𝑓2	𝜕𝑓2	NOUN
iajs-3359	114	2	𝜕𝑆	𝜕𝑆	INTJ
iajs-3359	114	3	|(𝒩,0,0,0,0)(𝑆	|(𝒩,0,0,0,0)(𝑆	VERB
iajs-3359	114	4	−	−	PROPN
iajs-3359	114	5	𝒩	𝒩	PROPN
iajs-3359	114	6	)	)	PUNCT
iajs-3359	115	1	+	+	NUM
iajs-3359	115	2	𝜕𝑓2	𝜕𝑓2	PROPN
iajs-3359	115	3	𝜕𝐸	𝜕𝐸	X
iajs-3359	115	4	|(𝒩,0,0,0,0)𝐸	|(𝒩,0,0,0,0)𝐸	PUNCT
iajs-3359	115	5	+	+	CCONJ
iajs-3359	115	6	𝜕𝑓2	𝜕𝑓2	PROPN
iajs-3359	115	7	𝜕𝐼	𝜕𝐼	PROPN
iajs-3359	115	8	|(𝒩,0,0,0,0)𝐼	|(𝒩,0,0,0,0)𝐼	PROPN
iajs-3359	115	9	+	+	CCONJ
iajs-3359	115	10	𝜕𝑓2	𝜕𝑓2	PROPN
iajs-3359	115	11	𝜕𝑅	𝜕𝑅	PART
iajs-3359	115	12	|(𝒩,0,0,0,0)𝑅	|(𝒩,0,0,0,0)𝑅	NOUN
iajs-3359	115	13	+	+	CCONJ
iajs-3359	115	14	𝜕𝑓2	𝜕𝑓2	VERB
iajs-3359	115	15	𝜕𝐹	𝜕𝐹	PRON
iajs-3359	115	16	|(𝒩,0,0,0,0)𝐹	|(𝒩,0,0,0,0)𝐹	X
iajs-3359	115	17	+	+	X
iajs-3359	115	18	⋯	⋯	VERB
iajs-3359	115	19	𝐷∗	𝐷∗	NOUN
iajs-3359	115	20	𝛼𝐼(𝑡	𝛼𝐼(𝑡	NUM
iajs-3359	115	21	)	)	PUNCT
iajs-3359	116	1	=	=	NOUN
iajs-3359	116	2	𝜕𝑓3	𝜕𝑓3	X
iajs-3359	116	3	𝜕𝑆	𝜕𝑆	PRON
iajs-3359	116	4	|(𝒩,0,0,0,0)(𝑆	|(𝒩,0,0,0,0)(𝑆	VERB
iajs-3359	116	5	−	−	PROPN
iajs-3359	116	6	𝒩	𝒩	PROPN
iajs-3359	116	7	)	)	PUNCT
iajs-3359	116	8	+	+	NUM
iajs-3359	116	9	𝜕𝑓3	𝜕𝑓3	PROPN
iajs-3359	116	10	𝜕𝐸	𝜕𝐸	PROPN
iajs-3359	116	11	|(𝒩,0,0,0,0)𝐸	|(𝒩,0,0,0,0)𝐸	PUNCT
iajs-3359	116	12	+	+	CCONJ
iajs-3359	116	13	𝜕𝑓3	𝜕𝑓3	PROPN
iajs-3359	116	14	𝜕𝐼	𝜕𝐼	PROPN
iajs-3359	116	15	|(𝒩,0,0,0,0)𝐼	|(𝒩,0,0,0,0)𝐼	PROPN
iajs-3359	116	16	+	+	NUM
iajs-3359	116	17	𝜕𝑓3	𝜕𝑓3	PROPN
iajs-3359	116	18	𝜕𝑅	𝜕𝑅	PROPN
iajs-3359	116	19	|(𝒩,0,0,0,0)𝑅	|(𝒩,0,0,0,0)𝑅	PROPN
iajs-3359	116	20	+	+	NUM
iajs-3359	116	21	𝜕𝑓3	𝜕𝑓3	PROPN
iajs-3359	116	22	𝜕𝐹	𝜕𝐹	PROPN
iajs-3359	116	23	|(𝒩,0,0,0,0)𝐹	|(𝒩,0,0,0,0)𝐹	PROPN
iajs-3359	116	24	+	+	SYM
iajs-3359	116	25	⋯	⋯	PROPN
iajs-3359	116	26	(	(	PUNCT
iajs-3359	116	27	8)	8)	NUM
iajs-3359	116	28	𝐷∗	𝐷∗	NOUN
iajs-3359	116	29	𝛼𝑅(𝑡	𝛼𝑅(𝑡	NUM
iajs-3359	116	30	)	)	PUNCT
iajs-3359	116	31	=	=	PUNCT
iajs-3359	117	1	𝜕𝑓4	𝜕𝑓4	NUM
iajs-3359	117	2	𝜕𝑆	𝜕𝑆	PRON
iajs-3359	117	3	|(𝒩,0,0,0,0)(𝑆	|(𝒩,0,0,0,0)(𝑆	ADJ
iajs-3359	117	4	−	−	PROPN
iajs-3359	117	5	𝒩	𝒩	PROPN
iajs-3359	117	6	)	)	PUNCT
iajs-3359	117	7	+	+	CCONJ
iajs-3359	117	8	𝜕𝑓4	𝜕𝑓4	ADJ
iajs-3359	117	9	𝜕𝐸	𝜕𝐸	ADP
iajs-3359	117	10	|(𝒩,0,0,0,0)𝐸	|(𝒩,0,0,0,0)𝐸	NOUN
iajs-3359	117	11	+	+	CCONJ
iajs-3359	117	12	𝜕𝑓4	𝜕𝑓4	PROPN
iajs-3359	117	13	𝜕𝐼	𝜕𝐼	PROPN
iajs-3359	117	14	|(𝒩,0,0,0,0)𝐼	|(𝒩,0,0,0,0)𝐼	NOUN
iajs-3359	117	15	+	+	CCONJ
iajs-3359	117	16	𝜕𝑓4	𝜕𝑓4	ADJ
iajs-3359	117	17	𝜕𝑅	𝜕𝑅	X
iajs-3359	117	18	|(𝒩,0,0,0,0)𝑅	|(𝒩,0,0,0,0)𝑅	NOUN
iajs-3359	117	19	+	+	CCONJ
iajs-3359	117	20	𝜕𝑓4	𝜕𝑓4	VERB
iajs-3359	117	21	𝜕𝐹	𝜕𝐹	PRON
iajs-3359	117	22	|(𝒩,0,0,0,0)𝐹	|(𝒩,0,0,0,0)𝐹	X
iajs-3359	117	23	+	+	NUM
iajs-3359	117	24	⋯	⋯	VERB
iajs-3359	117	25	𝐷∗	𝐷∗	NOUN
iajs-3359	117	26	𝛼𝐹(𝑡	𝛼𝐹(𝑡	NUM
iajs-3359	117	27	)	)	PUNCT
iajs-3359	117	28	=	=	SYM
iajs-3359	118	1	𝜕𝑓5	𝜕𝑓5	NOUN
iajs-3359	118	2	𝜕𝑆	𝜕𝑆	PRON
iajs-3359	118	3	|(𝒩,0,0,0,0)(𝑆	|(𝒩,0,0,0,0)(𝑆	VERB
iajs-3359	118	4	−	−	PROPN
iajs-3359	118	5	𝒩	𝒩	PROPN
iajs-3359	118	6	)	)	PUNCT
iajs-3359	119	1	+	+	CCONJ
iajs-3359	119	2	𝜕𝑓5	𝜕𝑓5	PROPN
iajs-3359	119	3	𝜕𝐸	𝜕𝐸	PART
iajs-3359	119	4	|(𝒩,0,0,0,0)𝐸	|(𝒩,0,0,0,0)𝐸	PROPN
iajs-3359	119	5	+	+	CCONJ
iajs-3359	119	6	𝜕𝑓5	𝜕𝑓5	PROPN
iajs-3359	119	7	𝜕𝐼	𝜕𝐼	PROPN
iajs-3359	119	8	|(𝒩,0,0,0,0)𝐼	|(𝒩,0,0,0,0)𝐼	PROPN
iajs-3359	119	9	+	+	PROPN
iajs-3359	119	10	𝜕𝑓5	𝜕𝑓5	PROPN
iajs-3359	119	11	𝜕𝑅	𝜕𝑅	PART
iajs-3359	119	12	|(𝒩,0,0,0,0)𝑅	|(𝒩,0,0,0,0)𝑅	NOUN
iajs-3359	120	1	+	+	PUNCT
iajs-3359	120	2	𝜕𝑓5	𝜕𝑓5	PROPN
iajs-3359	120	3	𝜕𝐹	𝜕𝐹	ADJ
iajs-3359	120	4	|(𝒩,0,0,0,0)𝐹	|(𝒩,0,0,0,0)𝐹	X
iajs-3359	121	1	+	+	SYM
iajs-3359	121	2	⋯	⋯	PROPN
iajs-3359	121	3	then	then	ADV
iajs-3359	121	4	the	the	DET
iajs-3359	121	5	coefficients	coefficient	NOUN
iajs-3359	121	6	matrix	matrix	NOUN
iajs-3359	121	7	is	be	AUX
iajs-3359	121	8	:	:	PUNCT
iajs-3359	121	9	[	[	PUNCT
iajs-3359	121	10	0	0	X
iajs-3359	121	11	0	0	NUM
iajs-3359	121	12	−𝛽	−𝛽	NOUN
iajs-3359	121	13	0	0	NUM
iajs-3359	121	14	0	0	NUM
iajs-3359	121	15	0	0	NUM
iajs-3359	122	1	−𝜔	−𝜔	PROPN
iajs-3359	122	2	𝛽	𝛽	NOUN
iajs-3359	122	3	0	0	NUM
iajs-3359	122	4	0	0	NUM
iajs-3359	122	5	0	0	NUM
iajs-3359	122	6	𝜔𝜗	𝜔𝜗	ADP
iajs-3359	122	7	−(𝑙	−(𝑙	NOUN
iajs-3359	122	8	+	+	CCONJ
iajs-3359	122	9	𝑣	𝑣	X
iajs-3359	122	10	)	)	PUNCT
iajs-3359	122	11	0	0	NUM
iajs-3359	122	12	0	0	NUM
iajs-3359	122	13	0	0	NUM
iajs-3359	122	14	0	0	NUM
iajs-3359	122	15	0	0	NUM
iajs-3359	122	16	0	0	NUM
iajs-3359	123	1	𝑙	𝑙	X
iajs-3359	123	2	𝑣	𝑣	ADP
iajs-3359	123	3	0	0	NUM
iajs-3359	123	4	0	0	NUM
iajs-3359	123	5	0	0	NUM
iajs-3359	123	6	0	0	NUM
iajs-3359	123	7	]	]	PUNCT
iajs-3359	123	8	and	and	CCONJ
iajs-3359	123	9	the	the	DET
iajs-3359	123	10	eigenvalues	eigenvalue	NOUN
iajs-3359	123	11	of	of	ADP
iajs-3359	123	12	this	this	DET
iajs-3359	123	13	matrix	matrix	NOUN
iajs-3359	123	14	are	be	AUX
iajs-3359	123	15	:	:	PUNCT
iajs-3359	123	16	𝜆1	𝜆1	VERB
iajs-3359	123	17	=	=	SYM
iajs-3359	123	18	0	0	NUM
iajs-3359	123	19	,	,	PUNCT
iajs-3359	123	20	𝜆2	𝜆2	NOUN
iajs-3359	123	21	=	=	SYM
iajs-3359	123	22	0	0	NUM
iajs-3359	123	23	,	,	PUNCT
iajs-3359	123	24	𝜆3	𝜆3	NOUN
iajs-3359	123	25	=	=	SYM
iajs-3359	123	26	0	0	NUM
iajs-3359	123	27	,	,	PUNCT
iajs-3359	123	28	𝜆4	𝜆4	NOUN
iajs-3359	123	29	=	=	PUNCT
iajs-3359	124	1	−	−	PROPN
iajs-3359	124	2	𝑙	𝑙	SYM
iajs-3359	124	3	2	2	NUM
iajs-3359	124	4	−	−	NOUN
iajs-3359	124	5	𝜈	𝜈	SYM
iajs-3359	124	6	2	2	NUM
iajs-3359	124	7	−	−	NOUN
iajs-3359	124	8	𝜔	𝜔	SYM
iajs-3359	124	9	2	2	NUM
iajs-3359	124	10	+	+	NUM
iajs-3359	124	11	√4𝜔𝜗𝛽	√4𝜔𝜗𝛽	NOUN
iajs-3359	125	1	+	+	CCONJ
iajs-3359	125	2	𝑙2	𝑙2	NOUN
iajs-3359	125	3	+	+	CCONJ
iajs-3359	125	4	2𝑙𝜈	2𝑙𝜈	ADJ
iajs-3359	125	5	−	−	NOUN
iajs-3359	125	6	2𝜔𝑙	2𝜔𝑙	ADJ
iajs-3359	126	1	+	+	CCONJ
iajs-3359	126	2	𝜈2	𝜈2	NOUN
iajs-3359	126	3	−	−	NOUN
iajs-3359	126	4	2𝜔𝜈	2𝜔𝜈	NOUN
iajs-3359	127	1	+	+	CCONJ
iajs-3359	127	2	𝜔2	𝜔2	PROPN
iajs-3359	127	3	2	2	NUM
iajs-3359	127	4	,	,	PUNCT
iajs-3359	127	5	ihjpas	ihjpa	VERB
iajs-3359	127	6	.	.	PUNCT
iajs-3359	128	1	37	37	NUM
iajs-3359	128	2	(	(	PUNCT
iajs-3359	128	3	2	2	NUM
iajs-3359	128	4	)	)	PUNCT
iajs-3359	128	5	2024	2024	NUM
iajs-3359	128	6	383	383	NUM
iajs-3359	128	7	𝜆5	𝜆5	NOUN
iajs-3359	128	8	=	=	PUNCT
iajs-3359	129	1	−	−	PROPN
iajs-3359	129	2	𝑙	𝑙	SYM
iajs-3359	129	3	2	2	NUM
iajs-3359	129	4	−	−	NOUN
iajs-3359	129	5	𝜈	𝜈	SYM
iajs-3359	129	6	2	2	NUM
iajs-3359	129	7	−	−	NOUN
iajs-3359	129	8	𝜔	𝜔	PART
iajs-3359	129	9	2	2	NUM
iajs-3359	129	10	−	−	NOUN
iajs-3359	129	11	√4𝜔𝜗𝛽	√4𝜔𝜗𝛽	NOUN
iajs-3359	130	1	+	+	CCONJ
iajs-3359	130	2	𝑙2	𝑙2	PROPN
iajs-3359	130	3	+	+	CCONJ
iajs-3359	131	1	2𝑙𝜈	2𝑙𝜈	ADJ
iajs-3359	131	2	−	−	NOUN
iajs-3359	131	3	2𝜔𝑙	2𝜔𝑙	ADJ
iajs-3359	131	4	+	+	CCONJ
iajs-3359	131	5	𝜈2	𝜈2	NOUN
iajs-3359	131	6	−	−	NOUN
iajs-3359	131	7	2𝜔𝜈	2𝜔𝜈	NOUN
iajs-3359	132	1	+	+	CCONJ
iajs-3359	132	2	𝜔2	𝜔2	PROPN
iajs-3359	132	3	2	2	NUM
iajs-3359	132	4	.	.	PUNCT
iajs-3359	133	1	and	and	CCONJ
iajs-3359	133	2	when	when	SCONJ
iajs-3359	133	3	substituting	substitute	VERB
iajs-3359	133	4	the	the	DET
iajs-3359	133	5	value	value	NOUN
iajs-3359	133	6	of	of	ADP
iajs-3359	133	7	𝛽	𝛽	NOUN
iajs-3359	133	8	=	=	NOUN
iajs-3359	133	9	1.55	1.55	NUM
iajs-3359	133	10	,	,	PUNCT
iajs-3359	133	11	𝜔	𝜔	NOUN
iajs-3359	133	12	=	=	NOUN
iajs-3359	133	13	0.25	0.25	NUM
iajs-3359	133	14	,	,	PUNCT
iajs-3359	133	15	𝜗	𝜗	NOUN
iajs-3359	133	16	=	=	SYM
iajs-3359	133	17	0.58	0.58	NUM
iajs-3359	133	18	,	,	PUNCT
iajs-3359	133	19	𝑙	𝑙	X
iajs-3359	133	20	=	=	SYM
iajs-3359	133	21	0.27	0.27	NUM
iajs-3359	133	22	,	,	PUNCT
iajs-3359	133	23	𝜈	𝜈	X
iajs-3359	133	24	=	=	SYM
iajs-3359	133	25	0.01	0.01	NUM
iajs-3359	133	26	get	get	VERB
iajs-3359	133	27	:	:	PUNCT
iajs-3359	133	28	𝜆1	𝜆1	VERB
iajs-3359	133	29	=	=	SYM
iajs-3359	133	30	0	0	NUM
iajs-3359	133	31	,	,	PUNCT
iajs-3359	133	32	𝜆2	𝜆2	NOUN
iajs-3359	133	33	=	=	SYM
iajs-3359	133	34	0	0	NUM
iajs-3359	133	35	,	,	PUNCT
iajs-3359	133	36	𝜆3	𝜆3	NOUN
iajs-3359	133	37	=	=	SYM
iajs-3359	133	38	0	0	NUM
iajs-3359	133	39	,	,	PUNCT
iajs-3359	133	40	𝜆4	𝜆4	NOUN
iajs-3359	133	41	=	=	SYM
iajs-3359	133	42	0.2093	0.2093	NUM
iajs-3359	133	43	,	,	PUNCT
iajs-3359	133	44	𝜆5	𝜆5	NOUN
iajs-3359	133	45	=	=	PUNCT
iajs-3359	134	1	−0.7393	−0.7393	NOUN
iajs-3359	134	2	.	.	PUNCT
iajs-3359	135	1	hence	hence	ADV
iajs-3359	135	2	the	the	DET
iajs-3359	135	3	equilibrium	equilibrium	NOUN
iajs-3359	135	4	point	point	NOUN
iajs-3359	135	5	is	be	AUX
iajs-3359	135	6	unstable	unstable	ADJ
iajs-3359	135	7	[	[	X
iajs-3359	135	8	26	26	NUM
iajs-3359	135	9	]	]	PUNCT
iajs-3359	135	10	.	.	PUNCT
iajs-3359	136	1	4	4	X
iajs-3359	136	2	.	.	X
iajs-3359	136	3	simulation	simulation	NOUN
iajs-3359	136	4	results	result	NOUN
iajs-3359	136	5	adopting	adopt	VERB
iajs-3359	136	6	the	the	DET
iajs-3359	136	7	system	system	NOUN
iajs-3359	136	8	equations	equation	NOUN
iajs-3359	136	9	given	give	VERB
iajs-3359	136	10	by	by	ADP
iajs-3359	136	11	eq.(4	eq.(4	ADJ
iajs-3359	136	12	)	)	PUNCT
iajs-3359	136	13	and	and	CCONJ
iajs-3359	136	14	the	the	DET
iajs-3359	136	15	toolbox	toolbox	NOUN
iajs-3359	136	16	of	of	ADP
iajs-3359	136	17	matlab	matlab	PROPN
iajs-3359	137	1	[	[	X
iajs-3359	137	2	27	27	NUM
iajs-3359	137	3	-	-	SYM
iajs-3359	137	4	29	29	NUM
iajs-3359	137	5	]	]	PUNCT
iajs-3359	137	6	“	"	PUNCT
iajs-3359	137	7	flmm	flmm	PROPN
iajs-3359	137	8	”	"	PUNCT
iajs-3359	137	9	allows	allow	VERB
iajs-3359	137	10	us	we	PRON
iajs-3359	137	11	to	to	PART
iajs-3359	137	12	resolve	resolve	VERB
iajs-3359	137	13	fractional	fractional	ADJ
iajs-3359	137	14	linear	linear	ADJ
iajs-3359	137	15	multi	multi	ADJ
iajs-3359	137	16	-	-	ADJ
iajs-3359	137	17	step	step	ADJ
iajs-3359	137	18	method	method	NOUN
iajs-3359	137	19	for	for	ADP
iajs-3359	137	20	the	the	DET
iajs-3359	137	21	numerical	numerical	ADJ
iajs-3359	137	22	solution	solution	NOUN
iajs-3359	137	23	of	of	ADP
iajs-3359	137	24	differential	differential	ADJ
iajs-3359	137	25	equations	equation	NOUN
iajs-3359	137	26	[	[	X
iajs-3359	137	27	30	30	NUM
iajs-3359	137	28	]	]	PUNCT
iajs-3359	137	29	,	,	PUNCT
iajs-3359	137	30	to	to	PART
iajs-3359	137	31	represent	represent	VERB
iajs-3359	137	32	the	the	DET
iajs-3359	137	33	pandemic	pandemic	NOUN
iajs-3359	137	34	in	in	ADP
iajs-3359	137	35	the	the	DET
iajs-3359	137	36	world	world	NOUN
iajs-3359	137	37	and	and	CCONJ
iajs-3359	137	38	iraq	iraq	PROPN
iajs-3359	137	39	.	.	PUNCT
iajs-3359	138	1	and	and	CCONJ
iajs-3359	138	2	the	the	DET
iajs-3359	138	3	number	number	NOUN
iajs-3359	138	4	of	of	ADP
iajs-3359	138	5	parameters	parameter	NOUN
iajs-3359	138	6	in	in	ADP
iajs-3359	138	7	the	the	DET
iajs-3359	138	8	model	model	NOUN
iajs-3359	138	9	is	be	AUX
iajs-3359	138	10	equal	equal	ADJ
iajs-3359	138	11	to	to	ADP
iajs-3359	138	12	:	:	PUNCT
iajs-3359	138	13	𝛽	𝛽	NOUN
iajs-3359	138	14	=	=	SYM
iajs-3359	138	15	1.55,𝜔	1.55,𝜔	NUM
iajs-3359	138	16	=	=	SYM
iajs-3359	138	17	0.25	0.25	NUM
iajs-3359	138	18	,	,	PUNCT
iajs-3359	138	19	𝜗	𝜗	NOUN
iajs-3359	138	20	=	=	SYM
iajs-3359	138	21	0.58	0.58	NUM
iajs-3359	138	22	,	,	PUNCT
iajs-3359	138	23	𝑙	𝑙	X
iajs-3359	139	1	=	=	SYM
iajs-3359	139	2	0.27	0.27	NUM
iajs-3359	139	3	,	,	PUNCT
iajs-3359	139	4	𝜈	𝜈	X
iajs-3359	139	5	=	=	PUNCT
iajs-3359	139	6	0.01	0.01	NUM
iajs-3359	139	7	.	.	PUNCT
iajs-3359	140	1	4.1	4.1	NUM
iajs-3359	140	2	world	world	NOUN
iajs-3359	140	3	model	model	NOUN
iajs-3359	140	4	the	the	DET
iajs-3359	140	5	five	five	NUM
iajs-3359	140	6	classes	class	NOUN
iajs-3359	140	7	𝑆(𝑡	𝑆(𝑡	VERB
iajs-3359	140	8	)	)	PUNCT
iajs-3359	140	9	,	,	PUNCT
iajs-3359	140	10	𝐸(𝑡	𝐸(𝑡	VERB
iajs-3359	140	11	)	)	PUNCT
iajs-3359	140	12	,	,	PUNCT
iajs-3359	140	13	𝐼(𝑡	𝐼(𝑡	NUM
iajs-3359	140	14	)	)	PUNCT
iajs-3359	140	15	,	,	PUNCT
iajs-3359	140	16	𝑅(𝑡	𝑅(𝑡	NOUN
iajs-3359	140	17	)	)	PUNCT
iajs-3359	140	18	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-3359	140	19	𝐹(𝑡	𝐹(𝑡	NUM
iajs-3359	140	20	)	)	PUNCT
iajs-3359	140	21	associated	associate	VERB
iajs-3359	140	22	of	of	ADP
iajs-3359	140	23	the	the	DET
iajs-3359	140	24	world	world	NOUN
iajs-3359	140	25	.	.	PUNCT
iajs-3359	141	1	the	the	DET
iajs-3359	141	2	population	population	NOUN
iajs-3359	141	3	size	size	NOUN
iajs-3359	141	4	of	of	ADP
iajs-3359	141	5	the	the	DET
iajs-3359	141	6	world	world	NOUN
iajs-3359	141	7	is	be	AUX
iajs-3359	141	8	𝑁	𝑁	PROPN
iajs-3359	141	9	=	=	SYM
iajs-3359	141	10	7.753	7.753	NUM
iajs-3359	141	11	∗	∗	NOUN
iajs-3359	141	12	109	109	NUM
iajs-3359	141	13	with	with	ADP
iajs-3359	141	14	an	an	DET
iajs-3359	141	15	initial	initial	ADJ
iajs-3359	141	16	values	value	NOUN
iajs-3359	141	17	[	[	X
iajs-3359	141	18	12	12	NUM
iajs-3359	141	19	]	]	PUNCT
iajs-3359	141	20	𝑆(0	𝑆(0	NUM
iajs-3359	141	21	)	)	PUNCT
iajs-3359	141	22	=	=	PUNCT
iajs-3359	141	23	7.753	7.753	NUM
iajs-3359	141	24	∗	∗	NOUN
iajs-3359	141	25	109	109	NUM
iajs-3359	141	26	−	−	NUM
iajs-3359	141	27	5320948	5320948	NUM
iajs-3359	141	28	,	,	PUNCT
iajs-3359	141	29	𝐸(0	𝐸(0	NUM
iajs-3359	141	30	)	)	PUNCT
iajs-3359	141	31	=	=	SYM
iajs-3359	141	32	0	0	NUM
iajs-3359	141	33	,	,	PUNCT
iajs-3359	141	34	𝐼(0	𝐼(0	X
iajs-3359	141	35	)	)	PUNCT
iajs-3359	141	36	=	=	SYM
iajs-3359	141	37	5320948	5320948	NUM
iajs-3359	141	38	,	,	PUNCT
iajs-3359	141	39	𝑅(0	𝑅(0	NUM
iajs-3359	141	40	)	)	PUNCT
iajs-3359	141	41	=	=	SYM
iajs-3359	141	42	0	0	NUM
iajs-3359	141	43	,	,	PUNCT
iajs-3359	141	44	𝐹(0	𝐹(0	NUM
iajs-3359	141	45	)	)	PUNCT
iajs-3359	141	46	=	=	SYM
iajs-3359	142	1	0	0	X
iajs-3359	142	2	.	.	PUNCT
iajs-3359	143	1	different	different	ADJ
iajs-3359	143	2	values	value	NOUN
iajs-3359	143	3	of	of	ADP
iajs-3359	143	4	α	α	PROPN
iajs-3359	143	5	are	be	AUX
iajs-3359	143	6	shown	show	VERB
iajs-3359	143	7	respectively	respectively	ADV
iajs-3359	143	8	in	in	ADP
iajs-3359	143	9	figure1	figure1	PROPN
iajs-3359	143	10	.	.	PUNCT
iajs-3359	144	1	figure	figure	NOUN
iajs-3359	144	2	1	1	NUM
iajs-3359	144	3	:	:	PUNCT
iajs-3359	144	4	world	world	NOUN
iajs-3359	144	5	model	model	NOUN
iajs-3359	144	6	for	for	ADP
iajs-3359	144	7	different	different	ADJ
iajs-3359	144	8	values	value	NOUN
iajs-3359	144	9	of	of	ADP
iajs-3359	144	10	α	α	PROPN
iajs-3359	144	11	.	.	PUNCT
iajs-3359	144	12	figure	figure	NOUN
iajs-3359	144	13	1	1	NUM
iajs-3359	144	14	shows	show	VERB
iajs-3359	144	15	the	the	DET
iajs-3359	144	16	effect	effect	NOUN
iajs-3359	144	17	of	of	ADP
iajs-3359	144	18	the	the	DET
iajs-3359	144	19	fractional	fractional	ADJ
iajs-3359	144	20	derivative	derivative	NOUN
iajs-3359	144	21	on	on	ADP
iajs-3359	144	22	spread	spread	ADJ
iajs-3359	144	23	dynamics	dynamic	NOUN
iajs-3359	144	24	of	of	ADP
iajs-3359	144	25	coronavirus	coronavirus	NOUN
iajs-3359	144	26	in	in	ADP
iajs-3359	144	27	the	the	DET
iajs-3359	144	28	world	world	NOUN
iajs-3359	144	29	.	.	PUNCT
iajs-3359	145	1	through	through	ADP
iajs-3359	145	2	it	it	PRON
iajs-3359	145	3	,	,	PUNCT
iajs-3359	145	4	we	we	PRON
iajs-3359	145	5	conclude	conclude	VERB
iajs-3359	145	6	that	that	SCONJ
iajs-3359	145	7	the	the	DET
iajs-3359	145	8	beast	beast	NOUN
iajs-3359	145	9	value	value	NOUN
iajs-3359	145	10	of	of	ADP
iajs-3359	145	11	the	the	DET
iajs-3359	145	12	fractional	fractional	ADJ
iajs-3359	145	13	derivative	derivative	NOUN
iajs-3359	145	14	to	to	PART
iajs-3359	145	15	describe	describe	VERB
iajs-3359	145	16	the	the	DET
iajs-3359	145	17	spread	spread	NOUN
iajs-3359	145	18	of	of	ADP
iajs-3359	145	19	the	the	DET
iajs-3359	145	20	virus	virus	NOUN
iajs-3359	145	21	in	in	ADP
iajs-3359	145	22	the	the	DET
iajs-3359	145	23	world	world	NOUN
iajs-3359	145	24	at	at	ADP
iajs-3359	145	25	𝛼	𝛼	NOUN
iajs-3359	145	26	=	=	NOUN
iajs-3359	145	27	0.75	0.75	NUM
iajs-3359	145	28	,	,	PUNCT
iajs-3359	145	29	as	as	SCONJ
iajs-3359	145	30	shown	show	VERB
iajs-3359	145	31	in	in	ADP
iajs-3359	145	32	the	the	DET
iajs-3359	145	33	figure	figure	NOUN
iajs-3359	145	34	:	:	PUNCT
iajs-3359	145	35	ihjpas	ihjpas	PROPN
iajs-3359	145	36	.	.	PUNCT
iajs-3359	146	1	37	37	NUM
iajs-3359	146	2	(	(	PUNCT
iajs-3359	146	3	2	2	NUM
iajs-3359	146	4	)	)	PUNCT
iajs-3359	146	5	2024	2024	NUM
iajs-3359	146	6	384	384	NUM
iajs-3359	146	7	figure	figure	NOUN
iajs-3359	146	8	2	2	NUM
iajs-3359	146	9	:	:	PUNCT
iajs-3359	146	10	the	the	DET
iajs-3359	146	11	infected	infected	ADJ
iajs-3359	146	12	cases	case	NOUN
iajs-3359	146	13	in	in	ADP
iajs-3359	146	14	the	the	DET
iajs-3359	146	15	word	word	NOUN
iajs-3359	146	16	at	at	ADP
iajs-3359	146	17	𝛼	𝛼	NOUN
iajs-3359	146	18	=	=	SYM
iajs-3359	146	19	0.75	0.75	NUM
iajs-3359	146	20	figure	figure	NOUN
iajs-3359	146	21	2	2	NUM
iajs-3359	146	22	shows	show	VERB
iajs-3359	146	23	the	the	DET
iajs-3359	146	24	number	number	NOUN
iajs-3359	146	25	of	of	ADP
iajs-3359	146	26	infected	infected	ADJ
iajs-3359	146	27	cases	case	NOUN
iajs-3359	146	28	in	in	ADP
iajs-3359	146	29	the	the	DET
iajs-3359	146	30	world	world	NOUN
iajs-3359	146	31	.	.	PUNCT
iajs-3359	147	1	it	it	PRON
iajs-3359	147	2	is	be	AUX
iajs-3359	147	3	clear	clear	ADJ
iajs-3359	147	4	that	that	SCONJ
iajs-3359	147	5	the	the	DET
iajs-3359	147	6	disease	disease	NOUN
iajs-3359	147	7	does	do	AUX
iajs-3359	147	8	not	not	PART
iajs-3359	147	9	stop	stop	VERB
iajs-3359	147	10	permanently	permanently	ADV
iajs-3359	147	11	,	,	PUNCT
iajs-3359	147	12	but	but	CCONJ
iajs-3359	147	13	gradually	gradually	ADV
iajs-3359	147	14	declines	decline	VERB
iajs-3359	147	15	and	and	CCONJ
iajs-3359	147	16	levels	level	NOUN
iajs-3359	147	17	off	off	ADP
iajs-3359	147	18	at	at	ADP
iajs-3359	147	19	a	a	DET
iajs-3359	147	20	certain	certain	ADJ
iajs-3359	147	21	limit	limit	NOUN
iajs-3359	147	22	.	.	PUNCT
iajs-3359	148	1	this	this	PRON
iajs-3359	148	2	is	be	AUX
iajs-3359	148	3	the	the	DET
iajs-3359	148	4	result	result	NOUN
iajs-3359	148	5	of	of	ADP
iajs-3359	148	6	the	the	DET
iajs-3359	148	7	discovery	discovery	NOUN
iajs-3359	148	8	of	of	ADP
iajs-3359	148	9	vaccines	vaccine	NOUN
iajs-3359	148	10	,	,	PUNCT
iajs-3359	148	11	adherence	adherence	NOUN
iajs-3359	148	12	to	to	ADP
iajs-3359	148	13	isolation	isolation	NOUN
iajs-3359	148	14	policies	policy	NOUN
iajs-3359	148	15	and	and	CCONJ
iajs-3359	148	16	countries	country	NOUN
iajs-3359	148	17	and	and	CCONJ
iajs-3359	148	18	individuals	individual	NOUN
iajs-3359	148	19	taking	take	VERB
iajs-3359	148	20	the	the	DET
iajs-3359	148	21	necessary	necessary	ADJ
iajs-3359	148	22	measures	measure	NOUN
iajs-3359	148	23	to	to	PART
iajs-3359	148	24	control	control	VERB
iajs-3359	148	25	the	the	DET
iajs-3359	148	26	disease	disease	NOUN
iajs-3359	148	27	.	.	PUNCT
iajs-3359	149	1	4.2	4.2	NUM
iajs-3359	149	2	iraqi	iraqi	ADJ
iajs-3359	149	3	model	model	NOUN
iajs-3359	149	4	now	now	ADV
iajs-3359	149	5	we	we	PRON
iajs-3359	149	6	are	be	AUX
iajs-3359	149	7	going	go	VERB
iajs-3359	149	8	to	to	PART
iajs-3359	149	9	apply	apply	VERB
iajs-3359	149	10	the	the	DET
iajs-3359	149	11	model	model	NOUN
iajs-3359	149	12	eq.(4	eq.(4	NOUN
iajs-3359	149	13	)	)	PUNCT
iajs-3359	149	14	to	to	ADP
iajs-3359	149	15	iraq	iraq	PROPN
iajs-3359	149	16	.	.	PUNCT
iajs-3359	150	1	the	the	DET
iajs-3359	150	2	population	population	NOUN
iajs-3359	150	3	size	size	NOUN
iajs-3359	150	4	of	of	ADP
iajs-3359	150	5	iraq	iraq	PROPN
iajs-3359	150	6	is	be	AUX
iajs-3359	150	7	𝑁	𝑁	PROPN
iajs-3359	150	8	=	=	SYM
iajs-3359	150	9	40	40	NUM
iajs-3359	150	10	∗	∗	NOUN
iajs-3359	150	11	106	106	NUM
iajs-3359	150	12	with	with	ADP
iajs-3359	150	13	an	an	DET
iajs-3359	150	14	initial	initial	ADJ
iajs-3359	150	15	values	value	NOUN
iajs-3359	150	16	[	[	X
iajs-3359	150	17	12	12	NUM
iajs-3359	150	18	]	]	PUNCT
iajs-3359	150	19	𝑆(0	𝑆(0	NUM
iajs-3359	150	20	)	)	PUNCT
iajs-3359	150	21	=	=	SYM
iajs-3359	150	22	40	40	NUM
iajs-3359	150	23	∗	∗	NOUN
iajs-3359	150	24	106	106	NUM
iajs-3359	150	25	−	−	NOUN
iajs-3359	150	26	4520	4520	NUM
iajs-3359	150	27	,	,	PUNCT
iajs-3359	150	28	𝐸(0	𝐸(0	NUM
iajs-3359	150	29	)	)	PUNCT
iajs-3359	150	30	=	=	SYM
iajs-3359	150	31	0	0	NUM
iajs-3359	150	32	,	,	PUNCT
iajs-3359	150	33	𝐼(0	𝐼(0	X
iajs-3359	150	34	)	)	PUNCT
iajs-3359	150	35	=	=	SYM
iajs-3359	150	36	4520	4520	NUM
iajs-3359	150	37	,	,	PUNCT
iajs-3359	150	38	𝑅(0	𝑅(0	NUM
iajs-3359	150	39	)	)	PUNCT
iajs-3359	150	40	=	=	SYM
iajs-3359	150	41	0	0	NUM
iajs-3359	150	42	,	,	PUNCT
iajs-3359	150	43	𝐹(0	𝐹(0	NUM
iajs-3359	150	44	)	)	PUNCT
iajs-3359	150	45	=	=	SYM
iajs-3359	151	1	0	0	X
iajs-3359	151	2	.	.	PUNCT
iajs-3359	151	3	figure	figure	NOUN
iajs-3359	151	4	3	3	NUM
iajs-3359	151	5	shows	show	VERB
iajs-3359	151	6	the	the	DET
iajs-3359	151	7	stability	stability	NOUN
iajs-3359	151	8	of	of	ADP
iajs-3359	151	9	the	the	DET
iajs-3359	151	10	total	total	ADJ
iajs-3359	151	11	number	number	NOUN
iajs-3359	151	12	of	of	ADP
iajs-3359	151	13	infections	infection	NOUN
iajs-3359	151	14	and	and	CCONJ
iajs-3359	151	15	the	the	DET
iajs-3359	151	16	variance	variance	NOUN
iajs-3359	151	17	in	in	ADP
iajs-3359	151	18	convergence	convergence	NOUN
iajs-3359	151	19	speed	speed	NOUN
iajs-3359	151	20	for	for	ADP
iajs-3359	151	21	various	various	ADJ
iajs-3359	151	22	values	value	NOUN
iajs-3359	151	23	of	of	ADP
iajs-3359	151	24	α	α	NOUN
iajs-3359	151	25	.	.	PUNCT
iajs-3359	152	1	in	in	ADP
iajs-3359	152	2	figure	figure	NOUN
iajs-3359	152	3	4	4	NUM
iajs-3359	152	4	,	,	PUNCT
iajs-3359	152	5	we	we	PRON
iajs-3359	152	6	see	see	VERB
iajs-3359	152	7	that	that	SCONJ
iajs-3359	152	8	infected	infected	ADJ
iajs-3359	152	9	populations	population	NOUN
iajs-3359	152	10	decline	decline	VERB
iajs-3359	152	11	and	and	CCONJ
iajs-3359	152	12	eventually	eventually	ADV
iajs-3359	152	13	gravitate	gravitate	VERB
iajs-3359	152	14	to	to	ADP
iajs-3359	152	15	zero	zero	NUM
iajs-3359	152	16	over	over	ADP
iajs-3359	152	17	time	time	NOUN
iajs-3359	152	18	.	.	PUNCT
iajs-3359	153	1	additionally	additionally	ADV
iajs-3359	153	2	,	,	PUNCT
iajs-3359	153	3	the	the	DET
iajs-3359	153	4	convergence	convergence	NOUN
iajs-3359	153	5	to	to	ADP
iajs-3359	153	6	the	the	DET
iajs-3359	153	7	steady	steady	ADJ
iajs-3359	153	8	state	state	NOUN
iajs-3359	153	9	occurs	occur	VERB
iajs-3359	153	10	more	more	ADV
iajs-3359	153	11	slowly	slowly	ADV
iajs-3359	153	12	the	the	PRON
iajs-3359	153	13	lower	low	ADJ
iajs-3359	153	14	the	the	DET
iajs-3359	153	15	level	level	NOUN
iajs-3359	153	16	of	of	ADP
iajs-3359	153	17	differentiation	differentiation	NOUN
iajs-3359	153	18	.	.	PUNCT
iajs-3359	154	1	figure	figure	NOUN
iajs-3359	154	2	3	3	NUM
iajs-3359	154	3	:	:	PUNCT
iajs-3359	154	4	iraqi	iraqi	ADJ
iajs-3359	154	5	model	model	NOUN
iajs-3359	154	6	for	for	ADP
iajs-3359	154	7	different	different	ADJ
iajs-3359	154	8	values	value	NOUN
iajs-3359	154	9	of	of	ADP
iajs-3359	154	10	α	α	NOUN
iajs-3359	154	11	for	for	ADP
iajs-3359	154	12	α=0.6	α=0.6	ADJ
iajs-3359	154	13	,	,	PUNCT
iajs-3359	154	14	we	we	PRON
iajs-3359	154	15	represent	represent	VERB
iajs-3359	154	16	the	the	DET
iajs-3359	154	17	infected	infect	VERB
iajs-3359	154	18	patients	patient	NOUN
iajs-3359	154	19	which	which	PRON
iajs-3359	154	20	are	be	AUX
iajs-3359	154	21	given	give	VERB
iajs-3359	154	22	in	in	ADP
iajs-3359	154	23	figure	figure	NOUN
iajs-3359	154	24	4	4	NUM
iajs-3359	154	25	.	.	PUNCT
iajs-3359	154	26	ihjpas	ihjpas	PROPN
iajs-3359	154	27	.	.	PUNCT
iajs-3359	155	1	37	37	NUM
iajs-3359	155	2	(	(	PUNCT
iajs-3359	155	3	2	2	NUM
iajs-3359	155	4	)	)	PUNCT
iajs-3359	155	5	2024	2024	NUM
iajs-3359	155	6	385	385	NUM
iajs-3359	155	7	figure	figure	NOUN
iajs-3359	155	8	4	4	NUM
iajs-3359	155	9	:	:	PUNCT
iajs-3359	155	10	the	the	DET
iajs-3359	155	11	iraqi	iraqi	ADJ
iajs-3359	155	12	infected	infect	VERB
iajs-3359	155	13	cases	case	NOUN
iajs-3359	155	14	i(t	i(t	NOUN
iajs-3359	155	15	)	)	PUNCT
iajs-3359	155	16	of	of	ADP
iajs-3359	155	17	α=0.6	α=0.6	NOUN
iajs-3359	155	18	.	.	PUNCT
iajs-3359	156	1	5	5	X
iajs-3359	156	2	.	.	X
iajs-3359	156	3	discussions	discussion	NOUN
iajs-3359	156	4	the	the	DET
iajs-3359	156	5	fractional	fractional	ADJ
iajs-3359	156	6	covid-19	covid-19	PROPN
iajs-3359	156	7	model	model	NOUN
iajs-3359	156	8	eq.(4	eq.(4	NOUN
iajs-3359	156	9	)	)	PUNCT
iajs-3359	156	10	was	be	AUX
iajs-3359	156	11	solved	solve	VERB
iajs-3359	156	12	using	use	VERB
iajs-3359	156	13	the	the	DET
iajs-3359	156	14	fractional	fractional	ADJ
iajs-3359	156	15	linear	linear	ADJ
iajs-3359	156	16	multistep	multistep	NOUN
iajs-3359	156	17	method	method	NOUN
iajs-3359	156	18	for	for	ADP
iajs-3359	156	19	the	the	DET
iajs-3359	156	20	numerical	numerical	ADJ
iajs-3359	156	21	solution	solution	NOUN
iajs-3359	156	22	of	of	ADP
iajs-3359	156	23	differential	differential	ADJ
iajs-3359	156	24	equations	equation	NOUN
iajs-3359	156	25	.	.	PUNCT
iajs-3359	157	1	the	the	DET
iajs-3359	157	2	figures	figure	NOUN
iajs-3359	157	3	show	show	VERB
iajs-3359	157	4	the	the	DET
iajs-3359	157	5	effects	effect	NOUN
iajs-3359	157	6	of	of	ADP
iajs-3359	157	7	the	the	DET
iajs-3359	157	8	fractional	fractional	ADJ
iajs-3359	157	9	derivatives	derivative	NOUN
iajs-3359	157	10	on	on	ADP
iajs-3359	157	11	the	the	DET
iajs-3359	157	12	solution	solution	NOUN
iajs-3359	157	13	of	of	ADP
iajs-3359	157	14	the	the	DET
iajs-3359	157	15	model	model	NOUN
iajs-3359	157	16	in	in	ADP
iajs-3359	157	17	a	a	DET
iajs-3359	157	18	more	more	ADV
iajs-3359	157	19	detailed	detailed	ADJ
iajs-3359	157	20	sense	sense	NOUN
iajs-3359	157	21	(	(	PUNCT
iajs-3359	157	22	see	see	VERB
iajs-3359	157	23	figures	figure	NOUN
iajs-3359	157	24	1	1	NUM
iajs-3359	157	25	and	and	CCONJ
iajs-3359	157	26	3	3	NUM
iajs-3359	157	27	)	)	PUNCT
iajs-3359	157	28	.	.	PUNCT
iajs-3359	158	1	6	6	X
iajs-3359	158	2	.	.	X
iajs-3359	158	3	conclusions	conclusion	NOUN
iajs-3359	158	4	in	in	ADP
iajs-3359	158	5	this	this	DET
iajs-3359	158	6	article	article	NOUN
iajs-3359	158	7	,	,	PUNCT
iajs-3359	158	8	the	the	DET
iajs-3359	158	9	detail	detail	NOUN
iajs-3359	158	10	was	be	AUX
iajs-3359	158	11	analyzed	analyze	VERB
iajs-3359	158	12	in	in	ADP
iajs-3359	158	13	a	a	DET
iajs-3359	158	14	fractional	fractional	ADJ
iajs-3359	158	15	-	-	PUNCT
iajs-3359	158	16	order	order	NOUN
iajs-3359	158	17	covid-19	covid-19	PROPN
iajs-3359	158	18	model	model	NOUN
iajs-3359	158	19	.	.	PUNCT
iajs-3359	159	1	the	the	DET
iajs-3359	159	2	model	model	NOUN
iajs-3359	159	3	consists	consist	VERB
iajs-3359	159	4	of	of	ADP
iajs-3359	159	5	five	five	NUM
iajs-3359	159	6	differential	differential	ADJ
iajs-3359	159	7	equations	equation	NOUN
iajs-3359	159	8	of	of	ADP
iajs-3359	159	9	the	the	DET
iajs-3359	159	10	fractional	fractional	ADJ
iajs-3359	159	11	derivative	derivative	NOUN
iajs-3359	159	12	of	of	ADP
iajs-3359	159	13	caputo	caputo	PROPN
iajs-3359	159	14	.	.	PUNCT
iajs-3359	160	1	we	we	PRON
iajs-3359	160	2	proved	prove	VERB
iajs-3359	160	3	the	the	DET
iajs-3359	160	4	existence	existence	NOUN
iajs-3359	160	5	and	and	CCONJ
iajs-3359	160	6	uniqueness	uniqueness	NOUN
iajs-3359	160	7	of	of	ADP
iajs-3359	160	8	the	the	DET
iajs-3359	160	9	solution	solution	NOUN
iajs-3359	160	10	for	for	ADP
iajs-3359	160	11	the	the	DET
iajs-3359	160	12	system	system	NOUN
iajs-3359	160	13	and	and	CCONJ
iajs-3359	160	14	then	then	ADV
iajs-3359	160	15	calculated	calculate	VERB
iajs-3359	160	16	the	the	DET
iajs-3359	160	17	equilibrium	equilibrium	NOUN
iajs-3359	160	18	points	point	NOUN
iajs-3359	160	19	of	of	ADP
iajs-3359	160	20	the	the	DET
iajs-3359	160	21	model	model	NOUN
iajs-3359	160	22	and	and	CCONJ
iajs-3359	160	23	checked	check	VERB
iajs-3359	160	24	their	their	PRON
iajs-3359	160	25	stability	stability	NOUN
iajs-3359	160	26	.	.	PUNCT
iajs-3359	161	1	finally	finally	ADV
iajs-3359	161	2	,	,	PUNCT
iajs-3359	161	3	the	the	DET
iajs-3359	161	4	model	model	NOUN
iajs-3359	161	5	was	be	AUX
iajs-3359	161	6	solved	solve	VERB
iajs-3359	161	7	in	in	ADP
iajs-3359	161	8	the	the	DET
iajs-3359	161	9	fractional	fractional	ADJ
iajs-3359	161	10	linear	linear	ADJ
iajs-3359	161	11	multistep	multistep	ADJ
iajs-3359	161	12	method	method	NOUN
iajs-3359	161	13	.	.	PUNCT
iajs-3359	162	1	acknowledgment	acknowledgment	NOUN
iajs-3359	162	2	our	our	PRON
iajs-3359	162	3	researcher	researcher	NOUN
iajs-3359	162	4	extends	extend	VERB
iajs-3359	162	5	his	his	PRON
iajs-3359	162	6	sincere	sincere	ADJ
iajs-3359	162	7	thanks	thank	NOUN
iajs-3359	162	8	to	to	ADP
iajs-3359	162	9	the	the	DET
iajs-3359	162	10	editor	editor	NOUN
iajs-3359	162	11	and	and	CCONJ
iajs-3359	162	12	members	member	NOUN
iajs-3359	162	13	of	of	ADP
iajs-3359	162	14	the	the	DET
iajs-3359	162	15	preparatory	preparatory	PROPN
iajs-3359	162	16	committee	committee	NOUN
iajs-3359	162	17	of	of	ADP
iajs-3359	162	18	the	the	DET
iajs-3359	162	19	ibn	ibn	PROPN
iajs-3359	162	20	al	al	PROPN
iajs-3359	162	21	-	-	PUNCT
iajs-3359	162	22	haitham	haitham	PROPN
iajs-3359	162	23	journal	journal	PROPN
iajs-3359	162	24	of	of	ADP
iajs-3359	162	25	pure	pure	ADJ
iajs-3359	162	26	and	and	CCONJ
iajs-3359	162	27	applied	applied	ADJ
iajs-3359	162	28	sciences	science	NOUN
iajs-3359	162	29	.	.	PUNCT
iajs-3359	163	1	conflict	conflict	NOUN
iajs-3359	163	2	of	of	ADP
iajs-3359	163	3	interest	interest	NOUN
iajs-3359	163	4	there	there	PRON
iajs-3359	163	5	are	be	VERB
iajs-3359	163	6	no	no	DET
iajs-3359	163	7	conflicts	conflict	NOUN
iajs-3359	163	8	of	of	ADP
iajs-3359	163	9	interest	interest	NOUN
iajs-3359	163	10	.	.	PUNCT
iajs-3359	164	1	funding	funding	NOUN
iajs-3359	164	2	there	there	PRON
iajs-3359	164	3	is	be	VERB
iajs-3359	164	4	no	no	DET
iajs-3359	164	5	funding	funding	NOUN
iajs-3359	164	6	for	for	ADP
iajs-3359	164	7	the	the	DET
iajs-3359	164	8	article	article	NOUN
iajs-3359	164	9	.	.	PUNCT
iajs-3359	165	1	references	reference	NOUN
iajs-3359	165	2	1	1	NUM
iajs-3359	165	3	.	.	PUNCT
iajs-3359	166	1	tuan	tuan	PROPN
iajs-3359	166	2	,	,	PUNCT
iajs-3359	166	3	n.	n.	PROPN
iajs-3359	166	4	h.	h.	PROPN
iajs-3359	166	5	;	;	PUNCT
iajs-3359	166	6	mohammadi	mohammadi	NOUN
iajs-3359	166	7	,	,	PUNCT
iajs-3359	166	8	h.	h.	PROPN
iajs-3359	166	9	;	;	PUNCT
iajs-3359	166	10	rezapour	rezapour	VERB
iajs-3359	166	11	,	,	PUNCT
iajs-3359	166	12	s.	s.	PROPN
iajs-3359	166	13	a	a	DET
iajs-3359	166	14	mathematical	mathematical	ADJ
iajs-3359	166	15	model	model	NOUN
iajs-3359	166	16	for	for	ADP
iajs-3359	166	17	covid-19	covid-19	PROPN
iajs-3359	166	18	transmission	transmission	NOUN
iajs-3359	166	19	by	by	ADP
iajs-3359	166	20	using	use	VERB
iajs-3359	166	21	the	the	DET
iajs-3359	166	22	caputo	caputo	PROPN
iajs-3359	166	23	fractional	fractional	PROPN
iajs-3359	166	24	derivative	derivative	PROPN
iajs-3359	166	25	.	.	PUNCT
iajs-3359	167	1	chaos	chaos	NOUN
iajs-3359	167	2	,	,	PUNCT
iajs-3359	167	3	solitons	soliton	NOUN
iajs-3359	167	4	&	&	CCONJ
iajs-3359	167	5	fractals	fractal	NOUN
iajs-3359	167	6	,	,	PUNCT
iajs-3359	167	7	2020	2020	NUM
iajs-3359	167	8	,	,	PUNCT
iajs-3359	167	9	140	140	NUM
iajs-3359	167	10	,	,	PUNCT
iajs-3359	167	11	110107	110107	NUM
iajs-3359	167	12	.	.	PUNCT
iajs-3359	168	1	https://doi.org/10.1016/j.chaos.2020.110107	https://doi.org/10.1016/j.chaos.2020.110107	NOUN
iajs-3359	168	2	2	2	NUM
iajs-3359	168	3	.	.	PUNCT
iajs-3359	168	4	al	al	PROPN
iajs-3359	168	5	-	-	PUNCT
iajs-3359	168	6	saedi	saedi	PROPN
iajs-3359	168	7	,	,	PUNCT
iajs-3359	168	8	h.	h.	PROPN
iajs-3359	168	9	m.	m.	PROPN
iajs-3359	168	10	,	,	PUNCT
iajs-3359	168	11	;	;	PUNCT
iajs-3359	168	12	hameed	hameed	PROPN
iajs-3359	168	13	,	,	PUNCT
iajs-3359	168	14	h.	h.	PROPN
iajs-3359	168	15	h.	h.	PROPN
iajs-3359	168	16	mathematical	mathematical	PROPN
iajs-3359	168	17	modeling	modeling	NOUN
iajs-3359	168	18	for	for	ADP
iajs-3359	168	19	covid-19	covid-19	PROPN
iajs-3359	168	20	pandemic	pandemic	NOUN
iajs-3359	168	21	in	in	ADP
iajs-3359	168	22	iraq	iraq	PROPN
iajs-3359	168	23	.	.	PUNCT
iajs-3359	169	1	j	j	PROPN
iajs-3359	169	2	interdiscip	interdiscip	PROPN
iajs-3359	169	3	math	math	PROPN
iajs-3359	169	4	.	.	PUNCT
iajs-3359	170	1	2021	2021	NUM
iajs-3359	170	2	,	,	PUNCT
iajs-3359	170	3	24(5	24(5	NUM
iajs-3359	170	4	)	)	PUNCT
iajs-3359	170	5	,	,	PUNCT
iajs-3359	170	6	1407–1427	1407–1427	NUM
iajs-3359	170	7	.	.	PUNCT
iajs-3359	170	8	https://doi.org/10.1080/09720502.2021.1923943	https://doi.org/10.1080/09720502.2021.1923943	PROPN
iajs-3359	170	9	3	3	NUM
iajs-3359	170	10	.	.	PUNCT
iajs-3359	170	11	ndaïrou	ndaïrou	PROPN
iajs-3359	170	12	,	,	PUNCT
iajs-3359	170	13	f.	f.	PROPN
iajs-3359	170	14	;	;	PUNCT
iajs-3359	170	15	area	area	NOUN
iajs-3359	170	16	,	,	PUNCT
iajs-3359	170	17	i.	i.	PROPN
iajs-3359	170	18	;	;	PUNCT
iajs-3359	170	19	nieto	nieto	PROPN
iajs-3359	170	20	,	,	PUNCT
iajs-3359	170	21	j.	j.	PROPN
iajs-3359	170	22	j.	j.	PROPN
iajs-3359	170	23	;	;	PUNCT
iajs-3359	170	24	silva	silva	PROPN
iajs-3359	170	25	,	,	PUNCT
iajs-3359	170	26	c.	c.	PROPN
iajs-3359	170	27	j.	j.	PROPN
iajs-3359	170	28	;	;	PUNCT
iajs-3359	170	29	torres	torre	NOUN
iajs-3359	170	30	,	,	PUNCT
iajs-3359	170	31	d.	d.	PROPN
iajs-3359	170	32	f	f	PROPN
iajs-3359	170	33	fractional	fractional	PROPN
iajs-3359	170	34	model	model	NOUN
iajs-3359	170	35	of	of	ADP
iajs-3359	170	36	covid-19	covid-19	PROPN
iajs-3359	170	37	applied	apply	VERB
iajs-3359	170	38	to	to	ADP
iajs-3359	170	39	galicia	galicia	PROPN
iajs-3359	170	40	,	,	PUNCT
iajs-3359	170	41	spain	spain	PROPN
iajs-3359	170	42	and	and	CCONJ
iajs-3359	170	43	portugal	portugal	PROPN
iajs-3359	170	44	.	.	PUNCT
iajs-3359	171	1	chaos	chaos	PROPN
iajs-3359	171	2	,	,	PUNCT
iajs-3359	171	3	solitons	soliton	NOUN
iajs-3359	171	4	&	&	CCONJ
iajs-3359	171	5	fractals	fractal	NOUN
iajs-3359	171	6	,	,	PUNCT
iajs-3359	171	7	2021	2021	NUM
iajs-3359	171	8	,	,	PUNCT
iajs-3359	171	9	144	144	NUM
iajs-3359	171	10	,	,	PUNCT
iajs-3359	171	11	110652	110652	NUM
iajs-3359	171	12	.	.	PUNCT
iajs-3359	172	1	https://doi.org/10.1016/j.chaos.2021.110652	https://doi.org/10.1016/j.chaos.2021.110652	PROPN
iajs-3359	172	2	4	4	NUM
iajs-3359	172	3	.	.	PUNCT
iajs-3359	172	4	kareem	kareem	PROPN
iajs-3359	172	5	,	,	PUNCT
iajs-3359	172	6	a.	a.	NOUN
iajs-3359	172	7	m.	m.	NOUN
iajs-3359	172	8	;	;	PUNCT
iajs-3359	172	9	al	al	PROPN
iajs-3359	172	10	-	-	PUNCT
iajs-3359	172	11	azzawi	azzawi	PROPN
iajs-3359	172	12	,	,	PUNCT
iajs-3359	172	13	s.	s.	PROPN
iajs-3359	172	14	n.	n.	PROPN
iajs-3359	172	15	comparison	comparison	NOUN
iajs-3359	172	16	between	between	ADP
iajs-3359	172	17	deterministic	deterministic	ADJ
iajs-3359	172	18	and	and	CCONJ
iajs-3359	172	19	stochastic	stochastic	ADJ
iajs-3359	172	20	model	model	NOUN
iajs-3359	172	21	for	for	ADP
iajs-3359	172	22	interaction	interaction	NOUN
iajs-3359	172	23	(	(	PUNCT
iajs-3359	172	24	covid-19	covid-19	PROPN
iajs-3359	172	25	)	)	PUNCT
iajs-3359	172	26	with	with	ADP
iajs-3359	172	27	host	host	NOUN
iajs-3359	172	28	cells	cell	NOUN
iajs-3359	172	29	in	in	ADP
iajs-3359	172	30	humans	human	NOUN
iajs-3359	172	31	.	.	PUNCT
iajs-3359	173	1	baghdad	baghdad	PROPN
iajs-3359	173	2	science	science	PROPN
iajs-3359	173	3	journal	journal	PROPN
iajs-3359	173	4	,	,	PUNCT
iajs-3359	173	5	2022	2022	NUM
iajs-3359	173	6	,	,	PUNCT
iajs-3359	173	7	19(5	19(5	NUM
iajs-3359	173	8	)	)	PUNCT
iajs-3359	173	9	,	,	PUNCT
iajs-3359	173	10	11401140	11401140	NUM
iajs-3359	173	11	.	.	PUNCT
iajs-3359	174	1	https://doi.org/10.21123/bsj.2022.6111	https://doi.org/10.21123/bsj.2022.6111	NOUN
iajs-3359	174	2	https://doi.org/10.1016/j.chaos.2020.110107	https://doi.org/10.1016/j.chaos.2020.110107	ADJ
iajs-3359	174	3	https://doi.org/10.1080/09720502.2021.1923943	https://doi.org/10.1080/09720502.2021.1923943	PROPN
iajs-3359	174	4	https://doi.org/10.1016/j.chaos.2021.110652	https://doi.org/10.1016/j.chaos.2021.110652	PROPN
iajs-3359	174	5	https://doi.org/10.21123/bsj.2022.6111	https://doi.org/10.21123/bsj.2022.6111	PROPN
iajs-3359	174	6	ihjpas	ihjpa	VERB
iajs-3359	174	7	.	.	PUNCT
iajs-3359	175	1	37	37	NUM
iajs-3359	175	2	(	(	PUNCT
iajs-3359	175	3	2	2	NUM
iajs-3359	175	4	)	)	PUNCT
iajs-3359	175	5	2024	2024	NUM
iajs-3359	175	6	386	386	NUM
iajs-3359	175	7	5	5	NUM
iajs-3359	175	8	.	.	PUNCT
iajs-3359	176	1	martcheva	martcheva	PROPN
iajs-3359	176	2	,	,	PUNCT
iajs-3359	176	3	m	m	PROPN
iajs-3359	176	4	..	..	PUNCT
iajs-3359	176	5	an	an	DET
iajs-3359	176	6	introduction	introduction	NOUN
iajs-3359	176	7	to	to	ADP
iajs-3359	176	8	mathematical	mathematical	ADJ
iajs-3359	176	9	epidemiology	epidemiology	NOUN
iajs-3359	176	10	,	,	PUNCT
iajs-3359	176	11	new	new	PROPN
iajs-3359	176	12	york	york	PROPN
iajs-3359	176	13	:	:	PUNCT
iajs-3359	176	14	springer	springer	NOUN
iajs-3359	176	15	.	.	PUNCT
iajs-3359	177	1	2015	2015	NUM
iajs-3359	177	2	,	,	PUNCT
iajs-3359	177	3	61	61	NUM
iajs-3359	177	4	,	,	PUNCT
iajs-3359	177	5	9	9	NUM
iajs-3359	177	6	-	-	SYM
iajs-3359	177	7	31	31	NUM
iajs-3359	177	8	.	.	PUNCT
iajs-3359	178	1	https://doi.org/10.1007/978-1-4899-7612-3	https://doi.org/10.1007/978-1-4899-7612-3	PROPN
iajs-3359	178	2	6	6	NUM
iajs-3359	178	3	.	.	PUNCT
iajs-3359	179	1	yunus	yunus	PROPN
iajs-3359	179	2	,	,	PUNCT
iajs-3359	179	3	a.	a.	PROPN
iajs-3359	179	4	a.	a.	PROPN
iajs-3359	179	5	b.	b.	PROPN
iajs-3359	179	6	m.	m.	PROPN
iajs-3359	179	7	;	;	PUNCT
iajs-3359	179	8	yunus	yunus	PROPN
iajs-3359	179	9	,	,	PUNCT
iajs-3359	179	10	a.	a.	PROPN
iajs-3359	179	11	a.	a.	PROPN
iajs-3359	179	12	b.	b.	PROPN
iajs-3359	179	13	m.	m.	PROPN
iajs-3359	179	14	;	;	PUNCT
iajs-3359	179	15	ibrahim	ibrahim	PROPN
iajs-3359	179	16	,	,	PUNCT
iajs-3359	179	17	m.	m.	PROPN
iajs-3359	179	18	s.	s.	PROPN
iajs-3359	179	19	b.	b.	PROPN
iajs-3359	179	20	,	,	PUNCT
iajs-3359	179	21	;	;	PUNCT
iajs-3359	179	22	ismail	ismail	PROPN
iajs-3359	179	23	,	,	PUNCT
iajs-3359	179	24	s.	s.	PROPN
iajs-3359	179	25	b.	b.	PROPN
iajs-3359	179	26	future	future	PROPN
iajs-3359	179	27	of	of	ADP
iajs-3359	179	28	mathematical	mathematical	ADJ
iajs-3359	179	29	modelling	modelling	NOUN
iajs-3359	179	30	:	:	PUNCT
iajs-3359	179	31	a	a	DET
iajs-3359	179	32	review	review	NOUN
iajs-3359	179	33	of	of	ADP
iajs-3359	179	34	covid-19	covid-19	PROPN
iajs-3359	179	35	infected	infect	VERB
iajs-3359	179	36	cases	case	NOUN
iajs-3359	179	37	using	use	VERB
iajs-3359	179	38	s	s	PART
iajs-3359	179	39	-	-	PUNCT
iajs-3359	179	40	i	i	NOUN
iajs-3359	179	41	-	-	PUNCT
iajs-3359	179	42	r	r	NOUN
iajs-3359	179	43	model	model	NOUN
iajs-3359	179	44	.	.	PUNCT
iajs-3359	180	1	baghdad	baghdad	PROPN
iajs-3359	180	2	science	science	PROPN
iajs-3359	180	3	journal	journal	PROPN
iajs-3359	180	4	.	.	PUNCT
iajs-3359	181	1	2021	2021	NUM
iajs-3359	181	2	,	,	PUNCT
iajs-3359	181	3	18(1	18(1	NUM
iajs-3359	181	4	)	)	PUNCT
iajs-3359	181	5	,	,	PUNCT
iajs-3359	181	6	824–9	824–9	NUM
iajs-3359	181	7	.	.	PUNCT
iajs-3359	182	1	http://dx.doi.org/10.21123/bsj.2021.18.1(suppl.).0824	http://dx.doi.org/10.21123/bsj.2021.18.1(suppl.).0824	PROPN
iajs-3359	182	2	7	7	X
iajs-3359	182	3	.	.	PUNCT
iajs-3359	182	4	krishna	krishna	PROPN
iajs-3359	182	5	,	,	PUNCT
iajs-3359	182	6	m.	m.	NOUN
iajs-3359	182	7	v.	v.	ADP
iajs-3359	182	8	mathematical	mathematical	ADJ
iajs-3359	182	9	modelling	modelling	NOUN
iajs-3359	182	10	on	on	ADP
iajs-3359	182	11	diffusion	diffusion	NOUN
iajs-3359	182	12	and	and	CCONJ
iajs-3359	182	13	control	control	NOUN
iajs-3359	182	14	of	of	ADP
iajs-3359	182	15	covid–19	covid–19	NOUN
iajs-3359	182	16	.	.	PUNCT
iajs-3359	182	17	infectious	infectious	ADJ
iajs-3359	182	18	disease	disease	NOUN
iajs-3359	182	19	modelling	modelling	NOUN
iajs-3359	182	20	.	.	PUNCT
iajs-3359	183	1	2020	2020	NUM
iajs-3359	183	2	,	,	PUNCT
iajs-3359	183	3	5	5	NUM
iajs-3359	183	4	,	,	PUNCT
iajs-3359	183	5	588–597	588–597	NUM
iajs-3359	183	6	https://doi.org/10.1016/j.idm.2020.08.009	https://doi.org/10.1016/j.idm.2020.08.009	PROPN
iajs-3359	183	7	8	8	NUM
iajs-3359	183	8	.	.	PUNCT
iajs-3359	184	1	ndaïrou	ndaïrou	PROPN
iajs-3359	184	2	,	,	PUNCT
iajs-3359	184	3	f.	f.	PROPN
iajs-3359	184	4	;	;	PUNCT
iajs-3359	184	5	area	area	NOUN
iajs-3359	184	6	,	,	PUNCT
iajs-3359	184	7	i.	i.	PROPN
iajs-3359	184	8	;	;	PUNCT
iajs-3359	184	9	nieto	nieto	PROPN
iajs-3359	184	10	,	,	PUNCT
iajs-3359	184	11	j.	j.	PROPN
iajs-3359	184	12	j.	j.	PROPN
iajs-3359	184	13	;	;	PUNCT
iajs-3359	184	14	torres	torre	NOUN
iajs-3359	184	15	,	,	PUNCT
iajs-3359	184	16	d.	d.	PROPN
iajs-3359	184	17	f.	f.	PROPN
iajs-3359	184	18	mathematical	mathematical	PROPN
iajs-3359	185	1	modeling	modeling	NOUN
iajs-3359	185	2	of	of	ADP
iajs-3359	185	3	covid-19	covid-19	PROPN
iajs-3359	185	4	transmission	transmission	NOUN
iajs-3359	185	5	dynamics	dynamic	NOUN
iajs-3359	185	6	with	with	ADP
iajs-3359	185	7	a	a	DET
iajs-3359	185	8	case	case	NOUN
iajs-3359	185	9	study	study	NOUN
iajs-3359	185	10	of	of	ADP
iajs-3359	185	11	wuhan	wuhan	PROPN
iajs-3359	185	12	.	.	PUNCT
iajs-3359	186	1	chaos	chaos	PROPN
iajs-3359	186	2	,	,	PUNCT
iajs-3359	186	3	solitons	soliton	NOUN
iajs-3359	186	4	&	&	CCONJ
iajs-3359	186	5	fractals	fractal	NOUN
iajs-3359	186	6	,	,	PUNCT
iajs-3359	186	7	2020	2020	NUM
iajs-3359	186	8	,	,	PUNCT
iajs-3359	186	9	135	135	NUM
iajs-3359	186	10	,	,	PUNCT
iajs-3359	186	11	109846	109846	NUM
iajs-3359	186	12	.	.	PUNCT
iajs-3359	187	1	https://doi.org/10.1016/j.chaos.2020.109846	https://doi.org/10.1016/j.chaos.2020.109846	ADJ
iajs-3359	187	2	9	9	PROPN
iajs-3359	187	3	.	.	X
iajs-3359	187	4	shah	shah	NOUN
iajs-3359	187	5	,	,	PUNCT
iajs-3359	187	6	n.	n.	PROPN
iajs-3359	187	7	h.	h.	PROPN
iajs-3359	187	8	;	;	PUNCT
iajs-3359	187	9	mittal	mittal	PROPN
iajs-3359	187	10	,	,	PUNCT
iajs-3359	187	11	m.	m.	NOUN
iajs-3359	187	12	(	(	PUNCT
iajs-3359	187	13	eds	ed	NOUN
iajs-3359	187	14	.	.	PUNCT
iajs-3359	187	15	)	)	PUNCT
iajs-3359	187	16	.	.	PUNCT
iajs-3359	188	1	mathematical	mathematical	ADJ
iajs-3359	188	2	analysis	analysis	NOUN
iajs-3359	188	3	for	for	ADP
iajs-3359	188	4	transmission	transmission	NOUN
iajs-3359	188	5	of	of	ADP
iajs-3359	188	6	covid-19.springer	covid-19.springer	NUM
iajs-3359	188	7	singapore	singapore	NOUN
iajs-3359	188	8	,	,	PUNCT
iajs-3359	188	9	2021	2021	NUM
iajs-3359	188	10	.	.	PUNCT
iajs-3359	189	1	10	10	NUM
iajs-3359	189	2	.	.	X
iajs-3359	190	1	higazy	higazy	NOUN
iajs-3359	190	2	,	,	PUNCT
iajs-3359	190	3	m.	m.	NOUN
iajs-3359	190	4	;	;	PUNCT
iajs-3359	190	5	allehiany	allehiany	NOUN
iajs-3359	190	6	,	,	PUNCT
iajs-3359	190	7	f.	f.	PROPN
iajs-3359	190	8	m.	m.	PROPN
iajs-3359	190	9	;	;	PUNCT
iajs-3359	190	10	mahmoud	mahmoud	PROPN
iajs-3359	190	11	,	,	PUNCT
iajs-3359	190	12	e.	e.	PROPN
iajs-3359	190	13	e.	e.	PROPN
iajs-3359	190	14	numerical	numerical	PROPN
iajs-3359	190	15	study	study	PROPN
iajs-3359	190	16	of	of	ADP
iajs-3359	190	17	fractional	fractional	ADJ
iajs-3359	190	18	order	order	NOUN
iajs-3359	190	19	covid-19	covid-19	PROPN
iajs-3359	190	20	pandemic	pandemic	ADJ
iajs-3359	190	21	transmission	transmission	NOUN
iajs-3359	190	22	model	model	NOUN
iajs-3359	190	23	in	in	ADP
iajs-3359	190	24	context	context	NOUN
iajs-3359	190	25	of	of	ADP
iajs-3359	190	26	abo	abo	ADJ
iajs-3359	190	27	blood	blood	NOUN
iajs-3359	190	28	group	group	NOUN
iajs-3359	190	29	.	.	PUNCT
iajs-3359	191	1	results	result	NOUN
iajs-3359	191	2	in	in	ADP
iajs-3359	191	3	physics	physics	NOUN
iajs-3359	191	4	,	,	PUNCT
iajs-3359	191	5	2021	2021	NUM
iajs-3359	191	6	,	,	PUNCT
iajs-3359	191	7	22	22	NUM
iajs-3359	191	8	,	,	PUNCT
iajs-3359	191	9	103852	103852	NUM
iajs-3359	191	10	.	.	PUNCT
iajs-3359	192	1	https://doi.org/10.1016/j.rinp.2021.103852	https://doi.org/10.1016/j.rinp.2021.103852	PROPN
iajs-3359	192	2	11	11	NUM
iajs-3359	192	3	.	.	PUNCT
iajs-3359	193	1	rezapour	rezapour	PROPN
iajs-3359	193	2	,	,	PUNCT
iajs-3359	193	3	s.	s.	PROPN
iajs-3359	193	4	;	;	PUNCT
iajs-3359	193	5	mohammadi	mohammadi	NOUN
iajs-3359	193	6	,	,	PUNCT
iajs-3359	193	7	h.	h.	PROPN
iajs-3359	193	8	;	;	PUNCT
iajs-3359	193	9	samei	samei	PROPN
iajs-3359	193	10	,	,	PUNCT
iajs-3359	193	11	m.	m.	NOUN
iajs-3359	193	12	e.	e.	PROPN
iajs-3359	193	13	seir	seir	PROPN
iajs-3359	193	14	epidemic	epidemic	NOUN
iajs-3359	193	15	model	model	NOUN
iajs-3359	193	16	for	for	ADP
iajs-3359	193	17	covid-19	covid-19	PROPN
iajs-3359	193	18	transmission	transmission	NOUN
iajs-3359	193	19	by	by	ADP
iajs-3359	193	20	caputo	caputo	PROPN
iajs-3359	193	21	derivative	derivative	NOUN
iajs-3359	193	22	of	of	ADP
iajs-3359	193	23	fractional	fractional	ADJ
iajs-3359	193	24	order	order	NOUN
iajs-3359	193	25	.	.	PUNCT
iajs-3359	194	1	advances	advance	NOUN
iajs-3359	194	2	in	in	ADP
iajs-3359	194	3	difference	difference	NOUN
iajs-3359	194	4	equations	equation	NOUN
iajs-3359	194	5	,	,	PUNCT
iajs-3359	194	6	2020	2020	NUM
iajs-3359	194	7	,	,	PUNCT
iajs-3359	194	8	119.https://doi.org/10.1186/s13662-020-02952-y	119.https://doi.org/10.1186/s13662-020-02952-y	NUM
iajs-3359	194	9	12	12	NUM
iajs-3359	194	10	.	.	PUNCT
iajs-3359	195	1	abdulla	abdulla	PROPN
iajs-3359	195	2	,	,	PUNCT
iajs-3359	195	3	z.	z.	PROPN
iajs-3359	195	4	k.	k.	PROPN
iajs-3359	195	5	;	;	PUNCT
iajs-3359	195	6	al	al	PROPN
iajs-3359	195	7	-	-	PUNCT
iajs-3359	195	8	azzawi	azzawi	PROPN
iajs-3359	195	9	,	,	PUNCT
iajs-3359	195	10	s.	s.	PROPN
iajs-3359	195	11	n	n	CCONJ
iajs-3359	195	12	..	..	PUNCT
iajs-3359	195	13	solving	solve	VERB
iajs-3359	195	14	the	the	DET
iajs-3359	195	15	covid-19	covid-19	PROPN
iajs-3359	195	16	fractional	fractional	ADJ
iajs-3359	195	17	model	model	NOUN
iajs-3359	195	18	by	by	ADP
iajs-3359	195	19	using	use	VERB
iajs-3359	195	20	sumudu	sumudu	NOUN
iajs-3359	195	21	transform	transform	NOUN
iajs-3359	195	22	and	and	CCONJ
iajs-3359	195	23	adm	adm	PROPN
iajs-3359	195	24	.	.	PUNCT
iajs-3359	196	1	in	in	ADP
iajs-3359	196	2	aip	aip	PROPN
iajs-3359	196	3	conference	conference	NOUN
iajs-3359	196	4	proceedings	proceeding	NOUN
iajs-3359	196	5	,	,	PUNCT
iajs-3359	196	6	2023	2023	NUM
iajs-3359	196	7	,	,	PUNCT
iajs-3359	196	8	2839(1	2839(1	NUM
iajs-3359	196	9	)	)	PUNCT
iajs-3359	196	10	.	.	PUNCT
iajs-3359	197	1	aip	aip	PROPN
iajs-3359	197	2	publishing	publishing	PROPN
iajs-3359	197	3	.	.	PUNCT
iajs-3359	198	1	https://doi.org/10.1063/5.0167781	https://doi.org/10.1063/5.0167781	X
iajs-3359	198	2	13	13	NUM
iajs-3359	198	3	.	.	PUNCT
iajs-3359	199	1	kai	kai	PROPN
iajs-3359	199	2	,	,	PUNCT
iajs-3359	199	3	d.	d.	PROPN
iajs-3359	199	4	the	the	DET
iajs-3359	199	5	analysis	analysis	NOUN
iajs-3359	199	6	of	of	ADP
iajs-3359	199	7	fractional	fractional	ADJ
iajs-3359	199	8	differential	differential	ADJ
iajs-3359	199	9	equations	equation	NOUN
iajs-3359	199	10	:	:	PUNCT
iajs-3359	199	11	an	an	DET
iajs-3359	199	12	application	application	NOUN
iajs-3359	199	13	-	-	PUNCT
iajs-3359	199	14	oriented	orient	VERB
iajs-3359	199	15	exposition	exposition	NOUN
iajs-3359	199	16	using	use	VERB
iajs-3359	199	17	differential	differential	ADJ
iajs-3359	199	18	operators	operator	NOUN
iajs-3359	199	19	of	of	ADP
iajs-3359	199	20	caputo	caputo	PROPN
iajs-3359	199	21	type	type	NOUN
iajs-3359	199	22	.	.	PUNCT
iajs-3359	200	1	in	in	ADP
iajs-3359	200	2	lecture	lecture	NOUN
iajs-3359	200	3	notes	note	NOUN
iajs-3359	200	4	in	in	ADP
iajs-3359	200	5	mathematics	mathematic	NOUN
iajs-3359	200	6	.	.	PUNCT
iajs-3359	200	7	springer	springer	NOUN
iajs-3359	200	8	.	.	PUNCT
iajs-3359	200	9	2010	2010	NUM
iajs-3359	200	10	.	.	PUNCT
iajs-3359	200	11	http://dx.doi.org/10.1007/978-3-642-14574-2	http://dx.doi.org/10.1007/978-3-642-14574-2	NOUN
iajs-3359	200	12	14	14	NUM
iajs-3359	200	13	.	.	PUNCT
iajs-3359	200	14	ati	ati	PROPN
iajs-3359	200	15	,	,	PUNCT
iajs-3359	200	16	r.	r.	PROPN
iajs-3359	200	17	r.	r.	PROPN
iajs-3359	200	18	;	;	PUNCT
iajs-3359	200	19	al	al	PROPN
iajs-3359	200	20	-	-	PUNCT
iajs-3359	200	21	azzawi	azzawi	PROPN
iajs-3359	200	22	,	,	PUNCT
iajs-3359	200	23	s.	s.	PROPN
iajs-3359	200	24	n.	n.	PROPN
iajs-3359	200	25	fractional	fractional	PROPN
iajs-3359	200	26	order	order	NOUN
iajs-3359	200	27	modification	modification	NOUN
iajs-3359	200	28	of	of	ADP
iajs-3359	200	29	tuckwell	tuckwell	NOUN
iajs-3359	200	30	and	and	CCONJ
iajs-3359	200	31	wan	wan	PROPN
iajs-3359	200	32	medical	medical	ADJ
iajs-3359	200	33	model	model	PROPN
iajs-3359	200	34	.	.	PUNCT
iajs-3359	201	1	in	in	ADP
iajs-3359	201	2	journal	journal	PROPN
iajs-3359	201	3	of	of	ADP
iajs-3359	201	4	physics	physics	PROPN
iajs-3359	201	5	:	:	PUNCT
iajs-3359	201	6	conference	conference	NOUN
iajs-3359	201	7	series	series	NOUN
iajs-3359	201	8	2021	2021	NUM
iajs-3359	201	9	,	,	PUNCT
iajs-3359	201	10	1818(1	1818(1	NUM
iajs-3359	201	11	)	)	PUNCT
iajs-3359	201	12	,	,	PUNCT
iajs-3359	201	13	012028	012028	NUM
iajs-3359	201	14	.	.	PUNCT
iajs-3359	202	1	iop	iop	NOUN
iajs-3359	202	2	publishing	publishing	NOUN
iajs-3359	202	3	.	.	PUNCT
iajs-3359	203	1	http://dx.doi.org/10.1088/1742-6596/1818/1/012028	http://dx.doi.org/10.1088/1742-6596/1818/1/012028	NOUN
iajs-3359	203	2	15	15	NUM
iajs-3359	203	3	.	.	PUNCT
iajs-3359	204	1	mirevski	mirevski	PROPN
iajs-3359	204	2	,	,	PUNCT
iajs-3359	204	3	s.	s.	PROPN
iajs-3359	204	4	p.	p.	PROPN
iajs-3359	204	5	;	;	PUNCT
iajs-3359	204	6	boyadjiev	boyadjiev	PROPN
iajs-3359	204	7	,	,	PUNCT
iajs-3359	204	8	l.	l.	PROPN
iajs-3359	204	9	;	;	PUNCT
iajs-3359	204	10	scherer	scherer	PROPN
iajs-3359	204	11	,	,	PUNCT
iajs-3359	204	12	r.	r.	PROPN
iajs-3359	204	13	on	on	ADP
iajs-3359	204	14	the	the	DET
iajs-3359	204	15	riemann	riemann	PROPN
iajs-3359	204	16	–	–	PUNCT
iajs-3359	204	17	liouville	liouville	VERB
iajs-3359	204	18	fractional	fractional	ADJ
iajs-3359	204	19	calculus	calculus	NOUN
iajs-3359	204	20	,	,	PUNCT
iajs-3359	204	21	g	g	PROPN
iajs-3359	204	22	-	-	PUNCT
iajs-3359	204	23	jacobi	jacobi	NOUN
iajs-3359	204	24	functions	function	NOUN
iajs-3359	204	25	and	and	CCONJ
iajs-3359	204	26	f	f	X
iajs-3359	204	27	-	-	PUNCT
iajs-3359	204	28	gauss	gauss	NOUN
iajs-3359	204	29	functions	function	NOUN
iajs-3359	204	30	.	.	PUNCT
iajs-3359	205	1	applied	apply	VERB
iajs-3359	205	2	mathematics	mathematic	NOUN
iajs-3359	205	3	and	and	CCONJ
iajs-3359	205	4	computation	computation	NOUN
iajs-3359	205	5	,	,	PUNCT
iajs-3359	205	6	2007	2007	NUM
iajs-3359	205	7	,	,	PUNCT
iajs-3359	205	8	187(1	187(1	NUM
iajs-3359	205	9	)	)	PUNCT
iajs-3359	205	10	,	,	PUNCT
iajs-3359	205	11	315	315	NUM
iajs-3359	205	12	-	-	SYM
iajs-3359	205	13	325	325	NUM
iajs-3359	205	14	.	.	PUNCT
iajs-3359	206	1	https://dx.doi.org/10.1016/j.amc.2007.01.035	https://dx.doi.org/10.1016/j.amc.2007.01.035	PROPN
iajs-3359	206	2	16	16	NUM
iajs-3359	206	3	.	.	PUNCT
iajs-3359	207	1	diethelm	diethelm	PROPN
iajs-3359	207	2	,	,	PUNCT
iajs-3359	207	3	k.	k.	PROPN
iajs-3359	207	4	;	;	PUNCT
iajs-3359	207	5	ford	ford	PROPN
iajs-3359	207	6	,	,	PUNCT
iajs-3359	207	7	n.	n.	PROPN
iajs-3359	207	8	j.	j.	PROPN
iajs-3359	207	9	analysis	analysis	NOUN
iajs-3359	207	10	of	of	ADP
iajs-3359	207	11	fractional	fractional	ADJ
iajs-3359	207	12	differential	differential	ADJ
iajs-3359	207	13	equations	equation	NOUN
iajs-3359	207	14	.	.	PUNCT
iajs-3359	208	1	journal	journal	PROPN
iajs-3359	208	2	of	of	ADP
iajs-3359	208	3	mathematical	mathematical	ADJ
iajs-3359	208	4	analysis	analysis	NOUN
iajs-3359	208	5	and	and	CCONJ
iajs-3359	208	6	applications	application	NOUN
iajs-3359	208	7	,	,	PUNCT
iajs-3359	208	8	2002	2002	NUM
iajs-3359	208	9	,	,	PUNCT
iajs-3359	208	10	265(2	265(2	NUM
iajs-3359	208	11	)	)	PUNCT
iajs-3359	208	12	,	,	PUNCT
iajs-3359	208	13	229	229	NUM
iajs-3359	208	14	-	-	SYM
iajs-3359	208	15	248	248	NUM
iajs-3359	208	16	.	.	PUNCT
iajs-3359	209	1	https://doi.org/10.1006/jmaa.2000.7194	https://doi.org/10.1006/jmaa.2000.7194	PROPN
iajs-3359	209	2	17	17	NUM
iajs-3359	209	3	.	.	PUNCT
iajs-3359	209	4	tarasov	tarasov	NOUN
iajs-3359	209	5	,	,	PUNCT
iajs-3359	209	6	v.	v.	PROPN
iajs-3359	209	7	e.	e.	PROPN
iajs-3359	209	8	fractional	fractional	PROPN
iajs-3359	209	9	dynamics	dynamic	NOUN
iajs-3359	209	10	:	:	PUNCT
iajs-3359	209	11	applications	application	NOUN
iajs-3359	209	12	of	of	ADP
iajs-3359	209	13	fractional	fractional	ADJ
iajs-3359	209	14	calculus	calculus	NOUN
iajs-3359	209	15	to	to	ADP
iajs-3359	209	16	dynamics	dynamic	NOUN
iajs-3359	209	17	of	of	ADP
iajs-3359	209	18	particles	particle	NOUN
iajs-3359	209	19	,	,	PUNCT
iajs-3359	209	20	fields	field	NOUN
iajs-3359	209	21	and	and	CCONJ
iajs-3359	209	22	media	medium	NOUN
iajs-3359	209	23	.	.	PUNCT
iajs-3359	210	1	springer	springer	NOUN
iajs-3359	210	2	science	science	PROPN
iajs-3359	210	3	&	&	CCONJ
iajs-3359	210	4	business	business	NOUN
iajs-3359	210	5	media	medium	NOUN
iajs-3359	210	6	.	.	PUNCT
iajs-3359	211	1	2011	2011	NUM
iajs-3359	211	2	.	.	PUNCT
iajs-3359	212	1	18	18	NUM
iajs-3359	212	2	.	.	X
iajs-3359	213	1	zhang	zhang	PROPN
iajs-3359	213	2	,	,	PUNCT
iajs-3359	213	3	w.	w.	PROPN
iajs-3359	213	4	b.	b.	PROPN
iajs-3359	213	5	differential	differential	PROPN
iajs-3359	213	6	equations	equation	NOUN
iajs-3359	213	7	,	,	PUNCT
iajs-3359	213	8	bifurcations	bifurcation	NOUN
iajs-3359	213	9	,	,	PUNCT
iajs-3359	213	10	and	and	CCONJ
iajs-3359	213	11	chaos	chaos	NOUN
iajs-3359	213	12	in	in	ADP
iajs-3359	213	13	economics	economic	NOUN
iajs-3359	213	14	2005	2005	NUM
iajs-3359	213	15	,	,	PUNCT
iajs-3359	213	16	68	68	NUM
iajs-3359	213	17	.	.	PUNCT
iajs-3359	214	1	world	world	NOUN
iajs-3359	214	2	scientific	scientific	ADJ
iajs-3359	214	3	.	.	PUNCT
iajs-3359	215	1	19	19	NUM
iajs-3359	215	2	.	.	X
iajs-3359	215	3	arrowsmith	arrowsmith	PROPN
iajs-3359	215	4	,	,	PUNCT
iajs-3359	215	5	d.	d.	PROPN
iajs-3359	215	6	;	;	PUNCT
iajs-3359	215	7	place	place	NOUN
iajs-3359	215	8	,	,	PUNCT
iajs-3359	215	9	c.	c.	PROPN
iajs-3359	215	10	m.	m.	PROPN
iajs-3359	215	11	dynamical	dynamical	ADJ
iajs-3359	215	12	systems	system	NOUN
iajs-3359	215	13	:	:	PUNCT
iajs-3359	215	14	differential	differential	ADJ
iajs-3359	215	15	equations	equation	NOUN
iajs-3359	215	16	,	,	PUNCT
iajs-3359	215	17	maps	map	NOUN
iajs-3359	215	18	,	,	PUNCT
iajs-3359	215	19	and	and	CCONJ
iajs-3359	215	20	chaotic	chaotic	ADJ
iajs-3359	215	21	behavior	behavior	NOUN
iajs-3359	215	22	.	.	PUNCT
iajs-3359	216	1	1992,5	1992,5	X
iajs-3359	216	2	.	.	PUNCT
iajs-3359	217	1	crc	crc	PROPN
iajs-3359	217	2	press	press	PROPN
iajs-3359	217	3	.	.	PUNCT
iajs-3359	218	1	https://doi.org/10.1201/978131514154	https://doi.org/10.1201/978131514154	NOUN
iajs-3359	219	1	20	20	NUM
iajs-3359	219	2	.	.	PUNCT
iajs-3359	219	3	garrappa	garrappa	PROPN
iajs-3359	219	4	,	,	PUNCT
iajs-3359	219	5	r.	r.	PROPN
iajs-3359	219	6	numerical	numerical	PROPN
iajs-3359	219	7	solution	solution	NOUN
iajs-3359	219	8	of	of	ADP
iajs-3359	219	9	fractional	fractional	ADJ
iajs-3359	219	10	differential	differential	ADJ
iajs-3359	219	11	equations	equation	NOUN
iajs-3359	219	12	:	:	PUNCT
iajs-3359	219	13	a	a	DET
iajs-3359	219	14	survey	survey	NOUN
iajs-3359	219	15	and	and	CCONJ
iajs-3359	219	16	a	a	DET
iajs-3359	219	17	software	software	NOUN
iajs-3359	219	18	tutorial	tutorial	NOUN
iajs-3359	219	19	.	.	PUNCT
iajs-3359	220	1	mathematics	mathematic	NOUN
iajs-3359	220	2	,	,	PUNCT
iajs-3359	220	3	2018	2018	NUM
iajs-3359	220	4	,	,	PUNCT
iajs-3359	220	5	6(2	6(2	NUM
iajs-3359	220	6	)	)	PUNCT
iajs-3359	220	7	,	,	PUNCT
iajs-3359	220	8	16	16	NUM
iajs-3359	220	9	.	.	PUNCT
iajs-3359	221	1	https://doi.org/10.3390/math6020016	https://doi.org/10.3390/math6020016	PROPN
iajs-3359	221	2	21	21	NUM
iajs-3359	221	3	.	.	PUNCT
iajs-3359	222	1	owolabi	owolabi	NOUN
iajs-3359	222	2	,	,	PUNCT
iajs-3359	222	3	k.	k.	PROPN
iajs-3359	222	4	m.	m.	PROPN
iajs-3359	222	5	mathematical	mathematical	ADJ
iajs-3359	222	6	analysis	analysis	NOUN
iajs-3359	222	7	and	and	CCONJ
iajs-3359	222	8	numerical	numerical	PROPN
iajs-3359	222	9	simulation	simulation	NOUN
iajs-3359	222	10	of	of	ADP
iajs-3359	222	11	patterns	pattern	NOUN
iajs-3359	222	12	in	in	ADP
iajs-3359	222	13	fractional	fractional	ADJ
iajs-3359	222	14	and	and	CCONJ
iajs-3359	222	15	classical	classical	ADJ
iajs-3359	222	16	reaction	reaction	NOUN
iajs-3359	222	17	-	-	PUNCT
iajs-3359	222	18	diffusion	diffusion	NOUN
iajs-3359	222	19	systems	system	NOUN
iajs-3359	222	20	.	.	PUNCT
iajs-3359	223	1	chaos	chaos	NOUN
iajs-3359	223	2	,	,	PUNCT
iajs-3359	223	3	solitons	soliton	NOUN
iajs-3359	223	4	&	&	CCONJ
iajs-3359	223	5	fractals	fractal	NOUN
iajs-3359	223	6	,	,	PUNCT
iajs-3359	223	7	2016	2016	NUM
iajs-3359	223	8	,	,	PUNCT
iajs-3359	223	9	93	93	NUM
iajs-3359	223	10	,	,	PUNCT
iajs-3359	223	11	89	89	NUM
iajs-3359	223	12	-	-	SYM
iajs-3359	223	13	98	98	NUM
iajs-3359	223	14	.	.	PUNCT
iajs-3359	224	1	https://doi.org/10.1016/j.chaos.2016.10.005	https://doi.org/10.1016/j.chaos.2016.10.005	NOUN
iajs-3359	224	2	.	.	PUNCT
iajs-3359	225	1	22	22	NUM
iajs-3359	225	2	.	.	PUNCT
iajs-3359	225	3	klages	klage	NOUN
iajs-3359	225	4	,	,	PUNCT
iajs-3359	225	5	r	r	NOUN
iajs-3359	225	6	..	..	PUNCT
iajs-3359	225	7	introduction	introduction	NOUN
iajs-3359	225	8	to	to	ADP
iajs-3359	225	9	dynamical	dynamical	ADJ
iajs-3359	225	10	systems	system	NOUN
iajs-3359	225	11	.	.	PUNCT
iajs-3359	226	1	lecture	lecture	NOUN
iajs-3359	226	2	notes	note	NOUN
iajs-3359	226	3	for	for	ADP
iajs-3359	226	4	mas424	mas424	PROPN
iajs-3359	226	5	/	/	SYM
iajs-3359	226	6	mthm021	mthm021	PROPN
iajs-3359	226	7	.	.	PROPN
iajs-3359	226	8	queen	queen	PROPN
iajs-3359	226	9	mary	mary	PROPN
iajs-3359	226	10	university	university	PROPN
iajs-3359	226	11	of	of	ADP
iajs-3359	226	12	london	london	PROPN
iajs-3359	226	13	,	,	PUNCT
iajs-3359	226	14	2008	2008	NUM
iajs-3359	226	15	,	,	PUNCT
iajs-3359	226	16	24	24	NUM
iajs-3359	226	17	,	,	PUNCT
iajs-3359	226	18	26	26	NUM
iajs-3359	226	19	.	.	NOUN
iajs-3359	226	20	23	23	NUM
iajs-3359	226	21	.	.	PUNCT
iajs-3359	227	1	malley	malley	PROPN
iajs-3359	227	2	jr	jr	PROPN
iajs-3359	227	3	,	,	PUNCT
iajs-3359	227	4	r.	r.	PROPN
iajs-3359	227	5	e.	e.	PROPN
iajs-3359	228	1	the	the	DET
iajs-3359	228	2	theory	theory	NOUN
iajs-3359	228	3	of	of	ADP
iajs-3359	228	4	differential	differential	ADJ
iajs-3359	228	5	equations	equation	NOUN
iajs-3359	228	6	:	:	PUNCT
iajs-3359	228	7	classical	classical	ADJ
iajs-3359	228	8	and	and	CCONJ
iajs-3359	228	9	qualitative	qualitative	NOUN
iajs-3359	228	10	.	.	PUNCT
iajs-3359	229	1	:	:	PUNCT
iajs-3359	230	1	classical	classical	ADJ
iajs-3359	230	2	and	and	CCONJ
iajs-3359	230	3	qualitative	qualitative	NOUN
iajs-3359	230	4	.	.	PUNCT
iajs-3359	231	1	siam	siam	PROPN
iajs-3359	231	2	review	review	PROPN
iajs-3359	231	3	,	,	PUNCT
iajs-3359	231	4	2005	2005	NUM
iajs-3359	231	5	,	,	PUNCT
iajs-3359	231	6	47(1	47(1	NUM
iajs-3359	231	7	)	)	PUNCT
iajs-3359	231	8	,	,	PUNCT
iajs-3359	231	9	185	185	NUM
iajs-3359	231	10	.	.	PUNCT
iajs-3359	232	1	24	24	NUM
iajs-3359	232	2	.	.	PUNCT
iajs-3359	232	3	derrick	derrick	PROPN
iajs-3359	232	4	,	,	PUNCT
iajs-3359	232	5	w.	w.	PROPN
iajs-3359	232	6	r.	r.	PROPN
iajs-3359	232	7	;	;	PUNCT
iajs-3359	232	8	grossman	grossman	PROPN
iajs-3359	232	9	,	,	PUNCT
iajs-3359	232	10	s.	s.	PROPN
iajs-3359	232	11	i.	i.	PROPN
iajs-3359	232	12	elementary	elementary	PROPN
iajs-3359	232	13	differential	differential	PROPN
iajs-3359	232	14	equations	equation	NOUN
iajs-3359	232	15	with	with	ADP
iajs-3359	232	16	applications	application	NOUN
iajs-3359	232	17	.	.	PUNCT
iajs-3359	232	18	1976	1976	NUM
iajs-3359	232	19	.	.	PUNCT
iajs-3359	233	1	https://lccn.loc.gov/80022057	https://lccn.loc.gov/80022057	PROPN
iajs-3359	233	2	https://doi.org/10.1007/978-1-4899-7612-3	https://doi.org/10.1007/978-1-4899-7612-3	PROPN
iajs-3359	233	3	http://dx.doi.org/10.21123/bsj.2021.18.1(suppl.).0824	http://dx.doi.org/10.21123/bsj.2021.18.1(suppl.).0824	PROPN
iajs-3359	233	4	https://doi.org/10.1016/j.idm.2020.08.009	https://doi.org/10.1016/j.idm.2020.08.009	PROPN
iajs-3359	233	5	https://doi.org/10.1016/j.chaos.2020.109846	https://doi.org/10.1016/j.chaos.2020.109846	PROPN
iajs-3359	233	6	https://doi.org/10.1016/j.chaos.2020.109846	https://doi.org/10.1016/j.chaos.2020.109846	PROPN
iajs-3359	233	7	https://doi.org/10.1016/j.rinp.2021.103852	https://doi.org/10.1016/j.rinp.2021.103852	PROPN
iajs-3359	233	8	https://doi.org/10.1186/s13662-020-02952-y	https://doi.org/10.1186/s13662-020-02952-y	PRON
iajs-3359	233	9	https://doi.org/10.1186/s13662-020-02952-y	https://doi.org/10.1186/s13662-020-02952-y	PROPN
iajs-3359	233	10	https://doi.org/10.1063/5.0167781	https://doi.org/10.1063/5.0167781	VERB
iajs-3359	233	11	http://dx.doi.org/10.1007/978-3-642-14574-2	http://dx.doi.org/10.1007/978-3-642-14574-2	PROPN
iajs-3359	233	12	http://dx.doi.org/10.1088/1742-6596/1818/1/012028	http://dx.doi.org/10.1088/1742-6596/1818/1/012028	PROPN
iajs-3359	233	13	https://dx.doi.org/10.1016/j.amc.2007.01.035	https://dx.doi.org/10.1016/j.amc.2007.01.035	PROPN
iajs-3359	233	14	https://doi.org/10.1006/jmaa.2000.7194	https://doi.org/10.1006/jmaa.2000.7194	PROPN
iajs-3359	233	15	https://doi.org/10.1201/978131514154	https://doi.org/10.1201/978131514154	VERB
iajs-3359	234	1	https://doi.org/10.3390/math6020016	https://doi.org/10.3390/math6020016	PROPN
iajs-3359	235	1	https://doi.org/10.1016/j.chaos.2016.10.005	https://doi.org/10.1016/j.chaos.2016.10.005	VERB
iajs-3359	235	2	https://lccn.loc.gov/80022057	https://lccn.loc.gov/80022057	ADV
iajs-3359	235	3	ihjpas	ihjpas	PROPN
iajs-3359	235	4	.	.	PUNCT
iajs-3359	236	1	37	37	NUM
iajs-3359	236	2	(	(	PUNCT
iajs-3359	236	3	2	2	NUM
iajs-3359	236	4	)	)	PUNCT
iajs-3359	236	5	2024	2024	NUM
iajs-3359	236	6	387	387	NUM
iajs-3359	236	7	25	25	NUM
iajs-3359	236	8	.	.	PUNCT
iajs-3359	237	1	ahmad	ahmad	PROPN
iajs-3359	237	2	,	,	PUNCT
iajs-3359	237	3	s.	s.	PROPN
iajs-3359	237	4	;	;	PUNCT
iajs-3359	237	5	ambrosetti	ambrosetti	PROPN
iajs-3359	237	6	,	,	PUNCT
iajs-3359	237	7	a.	a.	NOUN
iajs-3359	237	8	a	a	DET
iajs-3359	237	9	textbook	textbook	NOUN
iajs-3359	237	10	on	on	ADP
iajs-3359	237	11	ordinary	ordinary	ADJ
iajs-3359	237	12	differential	differential	ADJ
iajs-3359	237	13	equations	equation	NOUN
iajs-3359	237	14	.	.	PUNCT
iajs-3359	238	1	2015	2015	NUM
iajs-3359	238	2	,	,	PUNCT
iajs-3359	238	3	88	88	NUM
iajs-3359	238	4	.	.	PUNCT
iajs-3359	238	5	springer	springer	NOUN
iajs-3359	238	6	.	.	PUNCT
iajs-3359	239	1	https://doi.org/10.1007/978-3-319-16408-3	https://doi.org/10.1007/978-3-319-16408-3	PROPN
iajs-3359	239	2	26	26	NUM
iajs-3359	239	3	.	.	PUNCT
iajs-3359	240	1	hirsch	hirsch	PROPN
iajs-3359	240	2	,	,	PUNCT
iajs-3359	240	3	m.	m.	PROPN
iajs-3359	240	4	w.	w.	PROPN
iajs-3359	240	5	;	;	PUNCT
iajs-3359	240	6	smale	smale	PROPN
iajs-3359	240	7	,	,	PUNCT
iajs-3359	240	8	s.	s.	PROPN
iajs-3359	240	9	;	;	PUNCT
iajs-3359	240	10	devaney	devaney	PROPN
iajs-3359	240	11	,	,	PUNCT
iajs-3359	240	12	r.	r.	PROPN
iajs-3359	240	13	l.	l.	PROPN
iajs-3359	240	14	differential	differential	PROPN
iajs-3359	240	15	equations	equation	NOUN
iajs-3359	240	16	,	,	PUNCT
iajs-3359	240	17	dynamical	dynamical	ADJ
iajs-3359	240	18	systems	system	NOUN
iajs-3359	240	19	,	,	PUNCT
iajs-3359	240	20	and	and	CCONJ
iajs-3359	240	21	an	an	DET
iajs-3359	240	22	introduction	introduction	NOUN
iajs-3359	240	23	to	to	PART
iajs-3359	240	24	chaos	chaos	VERB
iajs-3359	240	25	.	.	PUNCT
iajs-3359	241	1	academic	academic	ADJ
iajs-3359	241	2	press	press	NOUN
iajs-3359	241	3	.	.	PUNCT
iajs-3359	242	1	2012	2012	NUM
iajs-3359	242	2	.	.	PUNCT
iajs-3359	243	1	27	27	NUM
iajs-3359	243	2	.	.	PUNCT
iajs-3359	243	3	dukkipati	dukkipati	NOUN
iajs-3359	243	4	,	,	PUNCT
iajs-3359	243	5	r.	r.	PROPN
iajs-3359	243	6	v.	v.	PROPN
iajs-3359	243	7	matlab	matlab	PROPN
iajs-3359	243	8	:	:	PUNCT
iajs-3359	243	9	an	an	DET
iajs-3359	243	10	introduction	introduction	NOUN
iajs-3359	243	11	with	with	ADP
iajs-3359	243	12	applications	application	NOUN
iajs-3359	243	13	.	.	PUNCT
iajs-3359	244	1	new	new	ADJ
iajs-3359	244	2	age	age	NOUN
iajs-3359	244	3	international	international	PROPN
iajs-3359	244	4	.	.	PUNCT
iajs-3359	244	5	2008	2008	NUM
iajs-3359	244	6	.	.	PUNCT
iajs-3359	245	1	28	28	NUM
iajs-3359	245	2	.	.	PUNCT
iajs-3359	246	1	lynch	lynch	PROPN
iajs-3359	246	2	,	,	PUNCT
iajs-3359	246	3	s.	s.	PROPN
iajs-3359	246	4	dynamical	dynamical	ADJ
iajs-3359	246	5	systems	system	NOUN
iajs-3359	246	6	with	with	ADP
iajs-3359	246	7	applications	application	NOUN
iajs-3359	246	8	using	use	VERB
iajs-3359	246	9	matlab	matlab	PROPN
iajs-3359	246	10	.	.	PUNCT
iajs-3359	247	1	boston	boston	PROPN
iajs-3359	247	2	:	:	PUNCT
iajs-3359	248	1	birkhäuser	birkhäuser	PROPN
iajs-3359	248	2	.	.	PUNCT
iajs-3359	249	1	2004	2004	NUM
iajs-3359	249	2	.https://doi.org/10.1007/978-3-319-06820-6	.https://doi.org/10.1007/978-3-319-06820-6	PUNCT
iajs-3359	249	3	.	.	PUNCT
iajs-3359	250	1	29	29	NUM
iajs-3359	250	2	.	.	PUNCT
iajs-3359	250	3	burden	burden	NOUN
iajs-3359	250	4	,	,	PUNCT
iajs-3359	250	5	r.	r.	PROPN
iajs-3359	250	6	l.	l.	PROPN
iajs-3359	250	7	;	;	PUNCT
iajs-3359	250	8	faires	faire	NOUN
iajs-3359	250	9	,	,	PUNCT
iajs-3359	250	10	j.	j.	PROPN
iajs-3359	250	11	d.	d.	PROPN
iajs-3359	250	12	numerical	numerical	PROPN
iajs-3359	250	13	analysis	analysis	PROPN
iajs-3359	250	14	(	(	PUNCT
iajs-3359	250	15	nineth	nineth	PROPN
iajs-3359	250	16	edition	edition	NOUN
iajs-3359	250	17	)	)	PUNCT
iajs-3359	250	18	.	.	PUNCT
iajs-3359	251	1	thomson	thomson	PROPN
iajs-3359	251	2	brooks	brooks	PROPN
iajs-3359	251	3	/	/	SYM
iajs-3359	251	4	cole	cole	PROPN
iajs-3359	251	5	,	,	PUNCT
iajs-3359	251	6	2010	2010	NUM
iajs-3359	251	7	.	.	PUNCT
iajs-3359	252	1	https://doi.org/10.1007/978-3-319-16408-3	https://doi.org/10.1007/978-3-319-16408-3	PROPN
iajs-3359	252	2	https://doi.org/10.1007/978-3-319-06820-6	https://doi.org/10.1007/978-3-319-06820-6	PROPN
iajs-3359	252	3	.	.	PUNCT