id	sid	tid	token	lemma	pos
ejpam-5366	1	1	european	european	PROPN
ejpam-5366	1	2	journal	journal	PROPN
ejpam-5366	1	3	of	of	ADP
ejpam-5366	1	4	pure	pure	ADJ
ejpam-5366	1	5	and	and	CCONJ
ejpam-5366	1	6	applied	apply	VERB
ejpam-5366	1	7	mathematics	mathematic	NOUN
ejpam-5366	1	8	vol	vol	NOUN
ejpam-5366	1	9	.	.	PROPN
ejpam-5366	2	1	17	17	NUM
ejpam-5366	2	2	,	,	PUNCT
ejpam-5366	2	3	no	no	INTJ
ejpam-5366	2	4	.	.	NOUN
ejpam-5366	2	5	4	4	NUM
ejpam-5366	2	6	,	,	PUNCT
ejpam-5366	2	7	2024	2024	NUM
ejpam-5366	2	8	,	,	PUNCT
ejpam-5366	2	9	2676	2676	NUM
ejpam-5366	2	10	-	-	SYM
ejpam-5366	2	11	2691	2691	NUM
ejpam-5366	2	12	issn	issn	VERB
ejpam-5366	2	13	1307	1307	NUM
ejpam-5366	2	14	-	-	SYM
ejpam-5366	2	15	5543	5543	NUM
ejpam-5366	2	16	–	–	PUNCT
ejpam-5366	2	17	ejpam.com	ejpam.com	X
ejpam-5366	2	18	published	publish	VERB
ejpam-5366	2	19	by	by	ADP
ejpam-5366	2	20	new	new	PROPN
ejpam-5366	2	21	york	york	PROPN
ejpam-5366	2	22	business	business	PROPN
ejpam-5366	2	23	global	global	ADJ
ejpam-5366	2	24	using	use	VERB
ejpam-5366	2	25	modified	modify	VERB
ejpam-5366	2	26	fractional	fractional	ADJ
ejpam-5366	2	27	euler	euler	NOUN
ejpam-5366	2	28	formula	formula	NOUN
ejpam-5366	2	29	for	for	ADP
ejpam-5366	2	30	solving	solve	VERB
ejpam-5366	2	31	the	the	DET
ejpam-5366	2	32	fractional	fractional	ADJ
ejpam-5366	2	33	smoking	smoking	NOUN
ejpam-5366	2	34	model	model	NOUN
ejpam-5366	3	1	mohamed	mohamed	PROPN
ejpam-5366	3	2	m.	m.	PROPN
ejpam-5366	4	1	khader1,2	khader1,2	PROPN
ejpam-5366	5	1	1	1	NUM
ejpam-5366	5	2	department	department	NOUN
ejpam-5366	5	3	of	of	ADP
ejpam-5366	5	4	mathematics	mathematic	NOUN
ejpam-5366	5	5	and	and	CCONJ
ejpam-5366	5	6	statistics	statistic	NOUN
ejpam-5366	5	7	,	,	PUNCT
ejpam-5366	5	8	college	college	NOUN
ejpam-5366	5	9	of	of	ADP
ejpam-5366	5	10	science	science	NOUN
ejpam-5366	5	11	,	,	PUNCT
ejpam-5366	5	12	imam	imam	PROPN
ejpam-5366	5	13	mohammad	mohammad	PROPN
ejpam-5366	5	14	ibn	ibn	PROPN
ejpam-5366	5	15	saud	saud	PROPN
ejpam-5366	5	16	islamic	islamic	PROPN
ejpam-5366	5	17	university	university	PROPN
ejpam-5366	5	18	(	(	PUNCT
ejpam-5366	5	19	imsiu	imsiu	PROPN
ejpam-5366	5	20	)	)	PUNCT
ejpam-5366	5	21	,	,	PUNCT
ejpam-5366	5	22	riyadh	riyadh	PROPN
ejpam-5366	5	23	,	,	PUNCT
ejpam-5366	5	24	saudi	saudi	PROPN
ejpam-5366	5	25	arabia	arabia	PROPN
ejpam-5366	5	26	2	2	NUM
ejpam-5366	5	27	department	department	NOUN
ejpam-5366	5	28	of	of	ADP
ejpam-5366	5	29	mathematics	mathematic	NOUN
ejpam-5366	5	30	,	,	PUNCT
ejpam-5366	5	31	faculty	faculty	NOUN
ejpam-5366	5	32	of	of	ADP
ejpam-5366	5	33	science	science	NOUN
ejpam-5366	5	34	,	,	PUNCT
ejpam-5366	5	35	benha	benha	VERB
ejpam-5366	5	36	university	university	NOUN
ejpam-5366	5	37	,	,	PUNCT
ejpam-5366	5	38	benha	benha	NOUN
ejpam-5366	5	39	,	,	PUNCT
ejpam-5366	5	40	egypt	egypt	PROPN
ejpam-5366	5	41	abstract	abstract	PROPN
ejpam-5366	5	42	.	.	PUNCT
ejpam-5366	6	1	worldwide	worldwide	ADV
ejpam-5366	6	2	,	,	PUNCT
ejpam-5366	6	3	smoking	smoking	NOUN
ejpam-5366	6	4	is	be	AUX
ejpam-5366	6	5	a	a	DET
ejpam-5366	6	6	common	common	ADJ
ejpam-5366	6	7	social	social	ADJ
ejpam-5366	6	8	practice	practice	NOUN
ejpam-5366	6	9	,	,	PUNCT
ejpam-5366	6	10	especially	especially	ADV
ejpam-5366	6	11	in	in	ADP
ejpam-5366	6	12	places	place	NOUN
ejpam-5366	6	13	like	like	ADP
ejpam-5366	6	14	schools	school	NOUN
ejpam-5366	6	15	and	and	CCONJ
ejpam-5366	6	16	on	on	ADP
ejpam-5366	6	17	important	important	ADJ
ejpam-5366	6	18	occasions	occasion	NOUN
ejpam-5366	6	19	.	.	PUNCT
ejpam-5366	7	1	world	world	NOUN
ejpam-5366	7	2	health	health	PROPN
ejpam-5366	7	3	organization	organization	NOUN
ejpam-5366	7	4	(	(	PUNCT
ejpam-5366	7	5	who	who	PRON
ejpam-5366	7	6	)	)	PUNCT
ejpam-5366	7	7	states	state	VERB
ejpam-5366	7	8	that	that	SCONJ
ejpam-5366	7	9	smoking	smoking	NOUN
ejpam-5366	7	10	is	be	AUX
ejpam-5366	7	11	the	the	DET
ejpam-5366	7	12	third	third	ADJ
ejpam-5366	7	13	leading	lead	VERB
ejpam-5366	7	14	cause	cause	NOUN
ejpam-5366	7	15	of	of	ADP
ejpam-5366	7	16	death	death	NOUN
ejpam-5366	7	17	worldwide	worldwide	ADV
ejpam-5366	7	18	and	and	CCONJ
ejpam-5366	7	19	the	the	DET
ejpam-5366	7	20	most	most	ADV
ejpam-5366	7	21	significant	significant	ADJ
ejpam-5366	7	22	avoidable	avoidable	ADJ
ejpam-5366	7	23	reason	reason	NOUN
ejpam-5366	7	24	for	for	ADP
ejpam-5366	7	25	disease	disease	NOUN
ejpam-5366	7	26	.	.	PUNCT
ejpam-5366	8	1	so	so	ADV
ejpam-5366	8	2	,	,	PUNCT
ejpam-5366	8	3	this	this	DET
ejpam-5366	8	4	work	work	NOUN
ejpam-5366	8	5	is	be	AUX
ejpam-5366	8	6	devoted	devote	VERB
ejpam-5366	8	7	to	to	ADP
ejpam-5366	8	8	giving	give	VERB
ejpam-5366	8	9	a	a	DET
ejpam-5366	8	10	numerical	numerical	ADJ
ejpam-5366	8	11	simulation	simulation	NOUN
ejpam-5366	8	12	of	of	ADP
ejpam-5366	8	13	the	the	DET
ejpam-5366	8	14	smoking	smoking	NOUN
ejpam-5366	8	15	model	model	NOUN
ejpam-5366	8	16	in	in	ADP
ejpam-5366	8	17	its	its	PRON
ejpam-5366	8	18	fractional	fractional	ADJ
ejpam-5366	8	19	form	form	NOUN
ejpam-5366	8	20	(	(	PUNCT
ejpam-5366	8	21	liouville	liouville	NOUN
ejpam-5366	8	22	-	-	PUNCT
ejpam-5366	8	23	caputo	caputo	PROPN
ejpam-5366	8	24	sense	sense	NOUN
ejpam-5366	8	25	)	)	PUNCT
ejpam-5366	8	26	.	.	PUNCT
ejpam-5366	9	1	the	the	DET
ejpam-5366	9	2	novel	novel	ADJ
ejpam-5366	9	3	numerical	numerical	ADJ
ejpam-5366	9	4	scheme	scheme	NOUN
ejpam-5366	9	5	used	use	VERB
ejpam-5366	9	6	is	be	AUX
ejpam-5366	9	7	the	the	DET
ejpam-5366	9	8	modified	modify	VERB
ejpam-5366	9	9	fractional	fractional	PROPN
ejpam-5366	9	10	euler	euler	NOUN
ejpam-5366	9	11	method	method	NOUN
ejpam-5366	9	12	(	(	PUNCT
ejpam-5366	9	13	mfem	mfem	PROPN
ejpam-5366	9	14	)	)	PUNCT
ejpam-5366	9	15	.	.	PUNCT
ejpam-5366	10	1	we	we	PRON
ejpam-5366	10	2	compare	compare	VERB
ejpam-5366	10	3	the	the	DET
ejpam-5366	10	4	given	give	VERB
ejpam-5366	10	5	technique	technique	NOUN
ejpam-5366	10	6	with	with	ADP
ejpam-5366	10	7	the	the	DET
ejpam-5366	10	8	traditional	traditional	ADJ
ejpam-5366	10	9	fractional	fractional	ADJ
ejpam-5366	10	10	euler	euler	NOUN
ejpam-5366	10	11	method	method	NOUN
ejpam-5366	10	12	.	.	PUNCT
ejpam-5366	11	1	in	in	ADP
ejpam-5366	11	2	the	the	DET
ejpam-5366	11	3	hope	hope	NOUN
ejpam-5366	11	4	of	of	ADP
ejpam-5366	11	5	providing	provide	VERB
ejpam-5366	11	6	some	some	DET
ejpam-5366	11	7	recommendations	recommendation	NOUN
ejpam-5366	11	8	to	to	PART
ejpam-5366	11	9	reduce	reduce	VERB
ejpam-5366	11	10	the	the	DET
ejpam-5366	11	11	risks	risk	NOUN
ejpam-5366	11	12	of	of	ADP
ejpam-5366	11	13	this	this	DET
ejpam-5366	11	14	bad	bad	ADJ
ejpam-5366	11	15	behavior	behavior	NOUN
ejpam-5366	11	16	,	,	PUNCT
ejpam-5366	11	17	the	the	DET
ejpam-5366	11	18	effect	effect	NOUN
ejpam-5366	11	19	of	of	ADP
ejpam-5366	11	20	some	some	DET
ejpam-5366	11	21	parameters	parameter	NOUN
ejpam-5366	11	22	and	and	CCONJ
ejpam-5366	11	23	external	external	ADJ
ejpam-5366	11	24	factors	factor	NOUN
ejpam-5366	11	25	affecting	affect	VERB
ejpam-5366	11	26	the	the	DET
ejpam-5366	11	27	solution	solution	NOUN
ejpam-5366	11	28	behavior	behavior	NOUN
ejpam-5366	11	29	of	of	ADP
ejpam-5366	11	30	this	this	DET
ejpam-5366	11	31	proposed	propose	VERB
ejpam-5366	11	32	mathematical	mathematical	ADJ
ejpam-5366	11	33	model	model	NOUN
ejpam-5366	11	34	was	be	AUX
ejpam-5366	11	35	studied	study	VERB
ejpam-5366	11	36	,	,	PUNCT
ejpam-5366	11	37	including	include	VERB
ejpam-5366	11	38	the	the	DET
ejpam-5366	11	39	recruitment	recruitment	NOUN
ejpam-5366	11	40	rate	rate	NOUN
ejpam-5366	11	41	(	(	PUNCT
ejpam-5366	11	42	due	due	ADP
ejpam-5366	11	43	to	to	ADP
ejpam-5366	11	44	immigration	immigration	NOUN
ejpam-5366	11	45	or	or	CCONJ
ejpam-5366	11	46	birth	birth	NOUN
ejpam-5366	11	47	)	)	PUNCT
ejpam-5366	11	48	and	and	CCONJ
ejpam-5366	11	49	the	the	DET
ejpam-5366	11	50	smoking	smoking	NOUN
ejpam-5366	11	51	cessation	cessation	NOUN
ejpam-5366	11	52	rate	rate	NOUN
ejpam-5366	11	53	.	.	PUNCT
ejpam-5366	12	1	the	the	DET
ejpam-5366	12	2	results	result	NOUN
ejpam-5366	12	3	confirm	confirm	VERB
ejpam-5366	12	4	the	the	DET
ejpam-5366	12	5	implemented	implement	VERB
ejpam-5366	12	6	scheme	scheme	NOUN
ejpam-5366	12	7	is	be	AUX
ejpam-5366	12	8	a	a	DET
ejpam-5366	12	9	straightforward	straightforward	ADJ
ejpam-5366	12	10	and	and	CCONJ
ejpam-5366	12	11	efficient	efficient	ADJ
ejpam-5366	12	12	tool	tool	NOUN
ejpam-5366	12	13	for	for	ADP
ejpam-5366	12	14	obtaining	obtain	VERB
ejpam-5366	12	15	solutions	solution	NOUN
ejpam-5366	12	16	to	to	ADP
ejpam-5366	12	17	these	these	DET
ejpam-5366	12	18	problems	problem	NOUN
ejpam-5366	12	19	.	.	PUNCT
ejpam-5366	13	1	2020	2020	NUM
ejpam-5366	13	2	mathematics	mathematic	NOUN
ejpam-5366	13	3	subject	subject	NOUN
ejpam-5366	13	4	classifications	classification	NOUN
ejpam-5366	13	5	:	:	PUNCT
ejpam-5366	13	6	26a33	26a33	NUM
ejpam-5366	13	7	,	,	PUNCT
ejpam-5366	13	8	34k37	34k37	NUM
ejpam-5366	13	9	,	,	PUNCT
ejpam-5366	13	10	65m60	65m60	NUM
ejpam-5366	13	11	,	,	PUNCT
ejpam-5366	13	12	65n12	65n12	NUM
ejpam-5366	13	13	key	key	ADJ
ejpam-5366	13	14	words	word	NOUN
ejpam-5366	13	15	and	and	CCONJ
ejpam-5366	13	16	phrases	phrase	NOUN
ejpam-5366	13	17	:	:	PUNCT
ejpam-5366	13	18	fractional	fractional	ADJ
ejpam-5366	13	19	smoking	smoking	NOUN
ejpam-5366	13	20	model	model	NOUN
ejpam-5366	13	21	,	,	PUNCT
ejpam-5366	13	22	liouville	liouville	PROPN
ejpam-5366	13	23	-	-	PUNCT
ejpam-5366	13	24	caputo	caputo	PROPN
ejpam-5366	13	25	fractional	fractional	PROPN
ejpam-5366	13	26	derivative	derivative	NOUN
ejpam-5366	13	27	,	,	PUNCT
ejpam-5366	13	28	modified	modify	VERB
ejpam-5366	13	29	fractional	fractional	PROPN
ejpam-5366	13	30	euler	euler	NOUN
ejpam-5366	13	31	method	method	PROPN
ejpam-5366	13	32	1	1	NUM
ejpam-5366	13	33	.	.	PUNCT
ejpam-5366	14	1	introduction	introduction	NOUN
ejpam-5366	14	2	according	accord	VERB
ejpam-5366	14	3	to	to	ADP
ejpam-5366	14	4	a	a	DET
ejpam-5366	14	5	report	report	NOUN
ejpam-5366	14	6	by	by	ADP
ejpam-5366	14	7	the	the	PRON
ejpam-5366	14	8	who	who	PRON
ejpam-5366	14	9	,	,	PUNCT
ejpam-5366	14	10	many	many	ADJ
ejpam-5366	14	11	smokers	smoker	NOUN
ejpam-5366	14	12	pass	pass	VERB
ejpam-5366	14	13	away	away	ADV
ejpam-5366	14	14	in	in	ADP
ejpam-5366	14	15	their	their	PRON
ejpam-5366	14	16	prime	prime	ADJ
ejpam-5366	14	17	years	year	NOUN
ejpam-5366	14	18	.	.	PUNCT
ejpam-5366	15	1	more	more	ADJ
ejpam-5366	15	2	than	than	ADP
ejpam-5366	15	3	5	5	NUM
ejpam-5366	15	4	million	million	NUM
ejpam-5366	15	5	deaths	death	NOUN
ejpam-5366	15	6	globally	globally	ADV
ejpam-5366	15	7	occur	occur	VERB
ejpam-5366	15	8	each	each	DET
ejpam-5366	15	9	year	year	NOUN
ejpam-5366	15	10	as	as	ADP
ejpam-5366	15	11	a	a	DET
ejpam-5366	15	12	result	result	NOUN
ejpam-5366	15	13	of	of	ADP
ejpam-5366	15	14	smoking	smoking	NOUN
ejpam-5366	15	15	’s	’s	PART
ejpam-5366	15	16	effects	effect	NOUN
ejpam-5366	15	17	on	on	ADP
ejpam-5366	15	18	various	various	ADJ
ejpam-5366	15	19	body	body	NOUN
ejpam-5366	15	20	processes	process	NOUN
ejpam-5366	15	21	;	;	PUNCT
ejpam-5366	15	22	by	by	ADP
ejpam-5366	15	23	2030	2030	NUM
ejpam-5366	15	24	,	,	PUNCT
ejpam-5366	15	25	this	this	DET
ejpam-5366	15	26	number	number	NOUN
ejpam-5366	15	27	may	may	AUX
ejpam-5366	15	28	increase	increase	VERB
ejpam-5366	15	29	to	to	ADP
ejpam-5366	15	30	8	8	NUM
ejpam-5366	15	31	million	million	NUM
ejpam-5366	15	32	(	(	PUNCT
ejpam-5366	15	33	[	[	X
ejpam-5366	15	34	14	14	NUM
ejpam-5366	15	35	]	]	PUNCT
ejpam-5366	15	36	,	,	PUNCT
ejpam-5366	15	37	[	[	X
ejpam-5366	15	38	17	17	NUM
ejpam-5366	15	39	]	]	NUM
ejpam-5366	15	40	)	)	PUNCT
ejpam-5366	15	41	.	.	PUNCT
ejpam-5366	16	1	smokers	smoker	NOUN
ejpam-5366	16	2	are	be	AUX
ejpam-5366	16	3	70	70	NUM
ejpam-5366	16	4	%	%	NOUN
ejpam-5366	16	5	more	more	ADV
ejpam-5366	16	6	likely	likely	ADJ
ejpam-5366	16	7	to	to	PART
ejpam-5366	16	8	experience	experience	VERB
ejpam-5366	16	9	a	a	DET
ejpam-5366	16	10	heart	heart	NOUN
ejpam-5366	16	11	attack	attack	NOUN
ejpam-5366	16	12	compared	compare	VERB
ejpam-5366	16	13	to	to	ADP
ejpam-5366	16	14	non	non	NOUN
ejpam-5366	16	15	-	-	NOUN
ejpam-5366	16	16	smokers	smoker	NOUN
ejpam-5366	16	17	.	.	PUNCT
ejpam-5366	17	1	lung	lung	NOUN
ejpam-5366	17	2	cancer	cancer	NOUN
ejpam-5366	17	3	occurs	occur	VERB
ejpam-5366	17	4	10	10	NUM
ejpam-5366	17	5	%	%	NOUN
ejpam-5366	17	6	more	more	ADV
ejpam-5366	17	7	frequently	frequently	ADV
ejpam-5366	17	8	in	in	ADP
ejpam-5366	17	9	smokers	smoker	NOUN
ejpam-5366	17	10	than	than	ADP
ejpam-5366	17	11	in	in	ADP
ejpam-5366	17	12	non	non	ADJ
ejpam-5366	17	13	-	-	NOUN
ejpam-5366	17	14	smokers	smoker	NOUN
ejpam-5366	17	15	.	.	PUNCT
ejpam-5366	18	1	smokers	smoker	NOUN
ejpam-5366	18	2	often	often	ADV
ejpam-5366	18	3	live	live	VERB
ejpam-5366	18	4	10	10	NUM
ejpam-5366	18	5	to	to	PART
ejpam-5366	18	6	13	13	NUM
ejpam-5366	18	7	years	year	NOUN
ejpam-5366	18	8	less	less	ADJ
ejpam-5366	18	9	than	than	SCONJ
ejpam-5366	18	10	others	other	NOUN
ejpam-5366	18	11	do	do	VERB
ejpam-5366	18	12	.	.	PUNCT
ejpam-5366	19	1	researchers	researcher	NOUN
ejpam-5366	19	2	work	work	VERB
ejpam-5366	19	3	to	to	PART
ejpam-5366	19	4	extend	extend	VERB
ejpam-5366	19	5	people	people	NOUN
ejpam-5366	19	6	’s	’s	PART
ejpam-5366	19	7	lives	life	NOUN
ejpam-5366	19	8	to	to	PART
ejpam-5366	19	9	reduce	reduce	VERB
ejpam-5366	19	10	smoking	smoking	NOUN
ejpam-5366	19	11	.	.	PUNCT
ejpam-5366	20	1	many	many	ADJ
ejpam-5366	20	2	researchers	researcher	NOUN
ejpam-5366	20	3	have	have	AUX
ejpam-5366	20	4	attempted	attempt	VERB
ejpam-5366	20	5	to	to	PART
ejpam-5366	20	6	investigate	investigate	VERB
ejpam-5366	20	7	a	a	DET
ejpam-5366	20	8	variety	variety	NOUN
ejpam-5366	20	9	of	of	ADP
ejpam-5366	20	10	efficient	efficient	ADJ
ejpam-5366	20	11	smoking	smoking	NOUN
ejpam-5366	20	12	models	model	NOUN
ejpam-5366	20	13	to	to	PART
ejpam-5366	20	14	give	give	VERB
ejpam-5366	20	15	the	the	DET
ejpam-5366	20	16	finest	fine	ADJ
ejpam-5366	20	17	description	description	NOUN
ejpam-5366	20	18	of	of	ADP
ejpam-5366	20	19	the	the	DET
ejpam-5366	20	20	phenomena	phenomenon	NOUN
ejpam-5366	20	21	of	of	ADP
ejpam-5366	20	22	cigarette	cigarette	NOUN
ejpam-5366	20	23	smoking	smoking	NOUN
ejpam-5366	20	24	.	.	PUNCT
ejpam-5366	21	1	by	by	ADP
ejpam-5366	21	2	categorizing	categorize	VERB
ejpam-5366	21	3	the	the	DET
ejpam-5366	21	4	entire	entire	ADJ
ejpam-5366	21	5	population	population	NOUN
ejpam-5366	21	6	into	into	ADP
ejpam-5366	21	7	three	three	NUM
ejpam-5366	21	8	groups	group	NOUN
ejpam-5366	21	9	-	-	PUNCT
ejpam-5366	21	10	potential	potential	ADJ
ejpam-5366	21	11	smokers	smoker	NOUN
ejpam-5366	21	12	,	,	PUNCT
ejpam-5366	21	13	chain	chain	NOUN
ejpam-5366	21	14	smokers	smoker	NOUN
ejpam-5366	21	15	,	,	PUNCT
ejpam-5366	21	16	and	and	CCONJ
ejpam-5366	21	17	permanently	permanently	ADV
ejpam-5366	21	18	abstinent	abstinent	ADJ
ejpam-5366	21	19	smokers	smoker	NOUN
ejpam-5366	21	20	.	.	PUNCT
ejpam-5366	22	1	the	the	DET
ejpam-5366	22	2	smoking	smoking	NOUN
ejpam-5366	22	3	model	model	NOUN
ejpam-5366	22	4	was	be	AUX
ejpam-5366	22	5	expressed	express	VERB
ejpam-5366	22	6	in	in	ADP
ejpam-5366	22	7	mathematical	mathematical	ADJ
ejpam-5366	22	8	equations	equation	NOUN
ejpam-5366	22	9	and	and	CCONJ
ejpam-5366	22	10	was	be	AUX
ejpam-5366	22	11	doi	doi	ADJ
ejpam-5366	22	12	:	:	PUNCT
ejpam-5366	22	13	https://doi.org/10.29020/nybg.ejpam.v17i4.5366	https://doi.org/10.29020/nybg.ejpam.v17i4.5366	PROPN
ejpam-5366	22	14	email	email	NOUN
ejpam-5366	22	15	address	address	NOUN
ejpam-5366	22	16	:	:	PUNCT
ejpam-5366	22	17	mmkhader@imamu.edu.sa	mmkhader@imamu.edu.sa	PROPN
ejpam-5366	22	18	(	(	PUNCT
ejpam-5366	22	19	m.	m.	NOUN
ejpam-5366	22	20	m.	m.	NOUN
ejpam-5366	22	21	khader	khader	PROPN
ejpam-5366	22	22	)	)	PUNCT
ejpam-5366	22	23	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5366	23	1	2676	2676	NUM
ejpam-5366	23	2	copyright	copyright	NOUN
ejpam-5366	23	3	:	:	PUNCT
ejpam-5366	23	4	©	©	PROPN
ejpam-5366	23	5	2024	2024	NUM
ejpam-5366	23	6	the	the	DET
ejpam-5366	23	7	author(s	author(s	NOUN
ejpam-5366	23	8	)	)	PUNCT
ejpam-5366	23	9	.	.	PUNCT
ejpam-5366	24	1	(	(	PUNCT
ejpam-5366	24	2	cc	cc	NOUN
ejpam-5366	24	3	by	by	ADP
ejpam-5366	24	4	-	-	PUNCT
ejpam-5366	24	5	nc	nc	PROPN
ejpam-5366	24	6	4.0	4.0	NUM
ejpam-5366	24	7	)	)	PUNCT
ejpam-5366	24	8	m.	m.	NOUN
ejpam-5366	24	9	m.	m.	NOUN
ejpam-5366	24	10	khader	khader	PROPN
ejpam-5366	24	11	/	/	SYM
ejpam-5366	24	12	eur	eur	PROPN
ejpam-5366	24	13	.	.	PUNCT
ejpam-5366	25	1	j.	j.	PROPN
ejpam-5366	25	2	pure	pure	PROPN
ejpam-5366	25	3	appl	appl	PROPN
ejpam-5366	25	4	.	.	PROPN
ejpam-5366	25	5	math	math	PROPN
ejpam-5366	25	6	,	,	PUNCT
ejpam-5366	25	7	17	17	NUM
ejpam-5366	25	8	(	(	PUNCT
ejpam-5366	25	9	4	4	NUM
ejpam-5366	25	10	)	)	PUNCT
ejpam-5366	25	11	(	(	PUNCT
ejpam-5366	25	12	2024	2024	NUM
ejpam-5366	25	13	)	)	PUNCT
ejpam-5366	25	14	,	,	PUNCT
ejpam-5366	25	15	2676	2676	NUM
ejpam-5366	25	16	-	-	SYM
ejpam-5366	25	17	2691	2691	NUM
ejpam-5366	25	18	2677	2677	NUM
ejpam-5366	25	19	originally	originally	ADV
ejpam-5366	25	20	developed	develop	VERB
ejpam-5366	25	21	in	in	ADP
ejpam-5366	25	22	1997	1997	NUM
ejpam-5366	25	23	[	[	X
ejpam-5366	25	24	7	7	NUM
ejpam-5366	25	25	]	]	PUNCT
ejpam-5366	25	26	.	.	PUNCT
ejpam-5366	26	1	more	more	ADV
ejpam-5366	26	2	recently	recently	ADV
ejpam-5366	26	3	,	,	PUNCT
ejpam-5366	26	4	in	in	ADP
ejpam-5366	26	5	2007	2007	NUM
ejpam-5366	26	6	,	,	PUNCT
ejpam-5366	26	7	a	a	DET
ejpam-5366	26	8	survey	survey	NOUN
ejpam-5366	26	9	conducted	conduct	VERB
ejpam-5366	26	10	in	in	ADP
ejpam-5366	26	11	korea	korea	PROPN
ejpam-5366	26	12	by	by	ADP
ejpam-5366	26	13	ham	ham	PROPN
ejpam-5366	27	1	[	[	X
ejpam-5366	27	2	8	8	NUM
ejpam-5366	27	3	]	]	PUNCT
ejpam-5366	27	4	recorded	record	VERB
ejpam-5366	27	5	the	the	DET
ejpam-5366	27	6	various	various	ADJ
ejpam-5366	27	7	stages	stage	NOUN
ejpam-5366	27	8	and	and	CCONJ
ejpam-5366	27	9	practices	practice	NOUN
ejpam-5366	27	10	of	of	ADP
ejpam-5366	27	11	smoking	smoke	VERB
ejpam-5366	27	12	among	among	ADP
ejpam-5366	27	13	students	student	NOUN
ejpam-5366	27	14	.	.	PUNCT
ejpam-5366	28	1	in	in	ADP
ejpam-5366	28	2	this	this	DET
ejpam-5366	28	3	work	work	NOUN
ejpam-5366	28	4	,	,	PUNCT
ejpam-5366	28	5	the	the	DET
ejpam-5366	28	6	creation	creation	NOUN
ejpam-5366	28	7	of	of	ADP
ejpam-5366	28	8	an	an	DET
ejpam-5366	28	9	integer	integer	NOUN
ejpam-5366	28	10	-	-	PUNCT
ejpam-5366	28	11	order	order	NOUN
ejpam-5366	28	12	model	model	NOUN
ejpam-5366	28	13	with	with	ADP
ejpam-5366	28	14	a	a	DET
ejpam-5366	28	15	dynamic	dynamic	ADJ
ejpam-5366	28	16	interaction	interaction	NOUN
ejpam-5366	28	17	and	and	CCONJ
ejpam-5366	28	18	a	a	DET
ejpam-5366	28	19	new	new	ADJ
ejpam-5366	28	20	class	class	NOUN
ejpam-5366	28	21	of	of	ADP
ejpam-5366	28	22	infrequent	infrequent	ADJ
ejpam-5366	28	23	smokers	smoker	NOUN
ejpam-5366	28	24	was	be	AUX
ejpam-5366	28	25	described	describe	VERB
ejpam-5366	28	26	as	as	ADP
ejpam-5366	28	27	an	an	DET
ejpam-5366	28	28	expansion	expansion	NOUN
ejpam-5366	28	29	of	of	ADP
ejpam-5366	28	30	the	the	DET
ejpam-5366	28	31	model	model	NOUN
ejpam-5366	28	32	.	.	PUNCT
ejpam-5366	29	1	the	the	DET
ejpam-5366	29	2	smoking	smoking	NOUN
ejpam-5366	29	3	models	model	NOUN
ejpam-5366	29	4	have	have	AUX
ejpam-5366	29	5	also	also	ADV
ejpam-5366	29	6	been	be	AUX
ejpam-5366	29	7	provided	provide	VERB
ejpam-5366	29	8	by	by	ADP
ejpam-5366	29	9	several	several	ADJ
ejpam-5366	29	10	other	other	ADJ
ejpam-5366	29	11	authors	author	NOUN
ejpam-5366	29	12	in	in	ADP
ejpam-5366	29	13	integer	integer	NOUN
ejpam-5366	29	14	and	and	CCONJ
ejpam-5366	29	15	fractional	fractional	ADJ
ejpam-5366	29	16	orders	order	NOUN
ejpam-5366	29	17	(	(	PUNCT
ejpam-5366	29	18	[	[	X
ejpam-5366	29	19	3]-[13	3]-[13	NUM
ejpam-5366	29	20	]	]	PUNCT
ejpam-5366	29	21	)	)	PUNCT
ejpam-5366	29	22	.	.	PUNCT
ejpam-5366	30	1	the	the	DET
ejpam-5366	30	2	numerical	numerical	ADJ
ejpam-5366	30	3	evaluation	evaluation	NOUN
ejpam-5366	30	4	of	of	ADP
ejpam-5366	30	5	fractional	fractional	ADJ
ejpam-5366	30	6	-	-	PUNCT
ejpam-5366	30	7	order	order	NOUN
ejpam-5366	30	8	delay	delay	NOUN
ejpam-5366	30	9	differential	differential	ADJ
ejpam-5366	30	10	equations	equation	NOUN
ejpam-5366	30	11	is	be	AUX
ejpam-5366	30	12	done	do	VERB
ejpam-5366	30	13	using	use	VERB
ejpam-5366	30	14	a	a	DET
ejpam-5366	30	15	spectral	spectral	ADJ
ejpam-5366	30	16	collocation	collocation	NOUN
ejpam-5366	30	17	-	-	PUNCT
ejpam-5366	30	18	based	base	VERB
ejpam-5366	30	19	approximate	approximate	ADJ
ejpam-5366	30	20	technique	technique	NOUN
ejpam-5366	30	21	[	[	X
ejpam-5366	30	22	11	11	NUM
ejpam-5366	30	23	]	]	PUNCT
ejpam-5366	30	24	.	.	PUNCT
ejpam-5366	31	1	the	the	DET
ejpam-5366	31	2	authors	author	NOUN
ejpam-5366	31	3	used	use	VERB
ejpam-5366	31	4	fractional	fractional	ADJ
ejpam-5366	31	5	operators	operator	NOUN
ejpam-5366	31	6	namely	namely	ADV
ejpam-5366	31	7	,	,	PUNCT
ejpam-5366	31	8	caputo	caputo	PROPN
ejpam-5366	31	9	-	-	PUNCT
ejpam-5366	31	10	fabrizio	fabrizio	PROPN
ejpam-5366	31	11	and	and	CCONJ
ejpam-5366	31	12	liouville	liouville	PROPN
ejpam-5366	31	13	-	-	PUNCT
ejpam-5366	31	14	caputo	caputo	NOUN
ejpam-5366	31	15	derivatives	derivative	NOUN
ejpam-5366	31	16	.	.	PUNCT
ejpam-5366	32	1	the	the	DET
ejpam-5366	32	2	collocation	collocation	NOUN
ejpam-5366	32	3	approach	approach	NOUN
ejpam-5366	32	4	uses	use	VERB
ejpam-5366	32	5	narayana	narayana	PROPN
ejpam-5366	32	6	polynomials	polynomial	NOUN
ejpam-5366	32	7	and	and	CCONJ
ejpam-5366	32	8	their	their	PRON
ejpam-5366	32	9	generalization	generalization	NOUN
ejpam-5366	32	10	forms	form	NOUN
ejpam-5366	32	11	.	.	PUNCT
ejpam-5366	33	1	using	use	VERB
ejpam-5366	33	2	convergence	convergence	NOUN
ejpam-5366	33	3	analysis	analysis	NOUN
ejpam-5366	33	4	in	in	ADP
ejpam-5366	33	5	a	a	DET
ejpam-5366	33	6	weighted	weight	VERB
ejpam-5366	33	7	l2	l2	NOUN
ejpam-5366	33	8	norm	norm	NOUN
ejpam-5366	33	9	,	,	PUNCT
ejpam-5366	33	10	they	they	PRON
ejpam-5366	33	11	found	find	VERB
ejpam-5366	33	12	an	an	DET
ejpam-5366	33	13	upper	upper	ADJ
ejpam-5366	33	14	bound	bind	VERB
ejpam-5366	33	15	on	on	ADP
ejpam-5366	33	16	the	the	DET
ejpam-5366	33	17	narayana	narayana	PROPN
ejpam-5366	33	18	polynomials	polynomials	PROPN
ejpam-5366	33	19	’	'	PUNCT
ejpam-5366	33	20	series	series	NOUN
ejpam-5366	33	21	expansion	expansion	NOUN
ejpam-5366	33	22	form	form	NOUN
ejpam-5366	33	23	.	.	PUNCT
ejpam-5366	34	1	the	the	DET
ejpam-5366	34	2	present	present	ADJ
ejpam-5366	34	3	matrix	matrix	NOUN
ejpam-5366	34	4	collocation	collocation	NOUN
ejpam-5366	34	5	solves	solve	VERB
ejpam-5366	34	6	three	three	NUM
ejpam-5366	34	7	fractional	fractional	ADJ
ejpam-5366	34	8	operator	operator	NOUN
ejpam-5366	34	9	and	and	CCONJ
ejpam-5366	34	10	fractional	fractional	ADJ
ejpam-5366	34	11	order	order	NOUN
ejpam-5366	34	12	test	test	NOUN
ejpam-5366	34	13	situations	situation	NOUN
ejpam-5366	34	14	to	to	PART
ejpam-5366	34	15	demonstrate	demonstrate	VERB
ejpam-5366	34	16	its	its	PRON
ejpam-5366	34	17	performance	performance	NOUN
ejpam-5366	34	18	.	.	PUNCT
ejpam-5366	35	1	in	in	ADP
ejpam-5366	35	2	[	[	X
ejpam-5366	35	3	10	10	NUM
ejpam-5366	35	4	]	]	PUNCT
ejpam-5366	35	5	,	,	PUNCT
ejpam-5366	35	6	the	the	DET
ejpam-5366	35	7	authors	author	NOUN
ejpam-5366	35	8	solved	solve	VERB
ejpam-5366	35	9	fractional	fractional	ADJ
ejpam-5366	35	10	-	-	PUNCT
ejpam-5366	35	11	order	order	NOUN
ejpam-5366	35	12	differential	differential	ADJ
ejpam-5366	35	13	equations	equation	NOUN
ejpam-5366	35	14	with	with	ADP
ejpam-5366	35	15	singularity	singularity	NOUN
ejpam-5366	35	16	and	and	CCONJ
ejpam-5366	35	17	strong	strong	ADJ
ejpam-5366	35	18	nonlinearity	nonlinearity	NOUN
ejpam-5366	35	19	for	for	ADP
ejpam-5366	35	20	electro	electro	ADJ
ejpam-5366	35	21	-	-	PUNCT
ejpam-5366	35	22	hydrodynamic	hydrodynamic	ADJ
ejpam-5366	35	23	flow	flow	NOUN
ejpam-5366	35	24	in	in	ADP
ejpam-5366	35	25	a	a	DET
ejpam-5366	35	26	circular	circular	ADJ
ejpam-5366	35	27	cylindrical	cylindrical	ADJ
ejpam-5366	35	28	conduit	conduit	NOUN
ejpam-5366	35	29	numerically	numerically	ADV
ejpam-5366	35	30	.	.	PUNCT
ejpam-5366	36	1	by	by	ADP
ejpam-5366	36	2	using	use	VERB
ejpam-5366	36	3	the	the	DET
ejpam-5366	36	4	quasi	quasi	ADJ
ejpam-5366	36	5	-	-	ADJ
ejpam-5366	36	6	linearization	linearization	NOUN
ejpam-5366	36	7	technique	technique	NOUN
ejpam-5366	36	8	,	,	PUNCT
ejpam-5366	36	9	they	they	PRON
ejpam-5366	36	10	obtained	obtain	VERB
ejpam-5366	36	11	a	a	DET
ejpam-5366	36	12	set	set	NOUN
ejpam-5366	36	13	of	of	ADP
ejpam-5366	36	14	linearized	linearize	VERB
ejpam-5366	36	15	equations	equation	NOUN
ejpam-5366	36	16	from	from	ADP
ejpam-5366	36	17	the	the	DET
ejpam-5366	36	18	nonlinear	nonlinear	ADJ
ejpam-5366	36	19	model	model	NOUN
ejpam-5366	36	20	.	.	PUNCT
ejpam-5366	37	1	using	use	VERB
ejpam-5366	37	2	the	the	DET
ejpam-5366	37	3	generalized	generalize	VERB
ejpam-5366	37	4	shifted	shift	VERB
ejpam-5366	37	5	airfoil	airfoil	NOUN
ejpam-5366	37	6	polynomials	polynomial	NOUN
ejpam-5366	37	7	of	of	ADP
ejpam-5366	37	8	the	the	DET
ejpam-5366	37	9	second	second	ADJ
ejpam-5366	37	10	kind	kind	NOUN
ejpam-5366	37	11	(	(	PUNCT
ejpam-5366	37	12	sapsk	sapsk	NOUN
ejpam-5366	37	13	)	)	PUNCT
ejpam-5366	37	14	and	and	CCONJ
ejpam-5366	37	15	appropriate	appropriate	ADJ
ejpam-5366	37	16	collocation	collocation	NOUN
ejpam-5366	37	17	points	point	NOUN
ejpam-5366	37	18	as	as	ADP
ejpam-5366	37	19	sapsk	sapsk	NOUN
ejpam-5366	37	20	roots	root	NOUN
ejpam-5366	37	21	,	,	PUNCT
ejpam-5366	37	22	they	they	PRON
ejpam-5366	37	23	created	create	VERB
ejpam-5366	37	24	an	an	DET
ejpam-5366	37	25	iterative	iterative	NOUN
ejpam-5366	37	26	algebraic	algebraic	ADJ
ejpam-5366	37	27	system	system	NOUN
ejpam-5366	37	28	of	of	ADP
ejpam-5366	37	29	linear	linear	PROPN
ejpam-5366	37	30	equations	equation	NOUN
ejpam-5366	37	31	.	.	PUNCT
ejpam-5366	38	1	the	the	DET
ejpam-5366	38	2	error	error	NOUN
ejpam-5366	38	3	analysis	analysis	NOUN
ejpam-5366	38	4	and	and	CCONJ
ejpam-5366	38	5	convergence	convergence	NOUN
ejpam-5366	38	6	are	be	AUX
ejpam-5366	38	7	established	establish	VERB
ejpam-5366	38	8	in	in	ADP
ejpam-5366	38	9	l2	l2	NOUN
ejpam-5366	38	10	,	,	PUNCT
ejpam-5366	38	11	and	and	CCONJ
ejpam-5366	38	12	l∞	l∞	NOUN
ejpam-5366	38	13	norms	norm	NOUN
ejpam-5366	38	14	.	.	PUNCT
ejpam-5366	39	1	the	the	DET
ejpam-5366	39	2	novelty	novelty	NOUN
ejpam-5366	39	3	in	in	ADP
ejpam-5366	39	4	the	the	DET
ejpam-5366	39	5	current	current	ADJ
ejpam-5366	39	6	research	research	NOUN
ejpam-5366	39	7	is	be	AUX
ejpam-5366	39	8	the	the	DET
ejpam-5366	39	9	attempt	attempt	NOUN
ejpam-5366	39	10	to	to	PART
ejpam-5366	39	11	reach	reach	VERB
ejpam-5366	39	12	numerical	numerical	ADJ
ejpam-5366	39	13	simulations	simulation	NOUN
ejpam-5366	39	14	(	(	PUNCT
ejpam-5366	39	15	through	through	ADP
ejpam-5366	39	16	a	a	DET
ejpam-5366	39	17	good	good	ADJ
ejpam-5366	39	18	numerical	numerical	ADJ
ejpam-5366	39	19	method	method	NOUN
ejpam-5366	39	20	)	)	PUNCT
ejpam-5366	39	21	to	to	PART
ejpam-5366	39	22	study	study	VERB
ejpam-5366	39	23	the	the	DET
ejpam-5366	39	24	important	important	ADJ
ejpam-5366	39	25	system	system	NOUN
ejpam-5366	39	26	under	under	ADP
ejpam-5366	39	27	consideration	consideration	NOUN
ejpam-5366	39	28	which	which	PRON
ejpam-5366	39	29	is	be	AUX
ejpam-5366	39	30	of	of	ADP
ejpam-5366	39	31	interest	interest	NOUN
ejpam-5366	39	32	to	to	ADP
ejpam-5366	39	33	many	many	ADJ
ejpam-5366	39	34	researchers	researcher	NOUN
ejpam-5366	39	35	,	,	PUNCT
ejpam-5366	39	36	so	so	SCONJ
ejpam-5366	39	37	we	we	PRON
ejpam-5366	39	38	presented	present	VERB
ejpam-5366	39	39	by	by	ADP
ejpam-5366	39	40	shedding	shed	VERB
ejpam-5366	39	41	some	some	DET
ejpam-5366	39	42	light	light	NOUN
ejpam-5366	39	43	on	on	ADP
ejpam-5366	39	44	the	the	DET
ejpam-5366	39	45	convergence	convergence	NOUN
ejpam-5366	39	46	and	and	CCONJ
ejpam-5366	39	47	calculating	calculate	VERB
ejpam-5366	39	48	the	the	DET
ejpam-5366	39	49	resulting	result	VERB
ejpam-5366	39	50	error	error	NOUN
ejpam-5366	39	51	as	as	ADV
ejpam-5366	39	52	well	well	ADV
ejpam-5366	39	53	as	as	ADP
ejpam-5366	39	54	comparisons	comparison	NOUN
ejpam-5366	39	55	with	with	ADP
ejpam-5366	39	56	the	the	DET
ejpam-5366	39	57	same	same	ADJ
ejpam-5366	39	58	method	method	NOUN
ejpam-5366	39	59	but	but	CCONJ
ejpam-5366	39	60	in	in	ADP
ejpam-5366	39	61	a	a	DET
ejpam-5366	39	62	less	less	ADV
ejpam-5366	39	63	accurate	accurate	ADJ
ejpam-5366	39	64	case	case	NOUN
ejpam-5366	39	65	and	and	CCONJ
ejpam-5366	39	66	finally	finally	ADV
ejpam-5366	39	67	the	the	DET
ejpam-5366	39	68	effect	effect	NOUN
ejpam-5366	39	69	of	of	ADP
ejpam-5366	39	70	the	the	DET
ejpam-5366	39	71	parameters	parameter	NOUN
ejpam-5366	39	72	in	in	ADP
ejpam-5366	39	73	the	the	DET
ejpam-5366	39	74	system	system	NOUN
ejpam-5366	39	75	on	on	ADP
ejpam-5366	39	76	the	the	DET
ejpam-5366	39	77	behavior	behavior	NOUN
ejpam-5366	39	78	of	of	ADP
ejpam-5366	39	79	the	the	DET
ejpam-5366	39	80	solution	solution	NOUN
ejpam-5366	39	81	to	to	PART
ejpam-5366	39	82	provide	provide	VERB
ejpam-5366	39	83	recommendations	recommendation	NOUN
ejpam-5366	39	84	that	that	PRON
ejpam-5366	39	85	can	can	AUX
ejpam-5366	39	86	be	be	AUX
ejpam-5366	39	87	used	use	VERB
ejpam-5366	39	88	by	by	ADP
ejpam-5366	39	89	those	those	PRON
ejpam-5366	39	90	interested	interested	ADJ
ejpam-5366	39	91	in	in	ADP
ejpam-5366	39	92	studying	study	VERB
ejpam-5366	39	93	this	this	DET
ejpam-5366	39	94	model	model	NOUN
ejpam-5366	39	95	medically	medically	ADV
ejpam-5366	39	96	or	or	CCONJ
ejpam-5366	39	97	industrially	industrially	ADV
ejpam-5366	39	98	.	.	PUNCT
ejpam-5366	40	1	this	this	DET
ejpam-5366	40	2	work	work	NOUN
ejpam-5366	40	3	is	be	AUX
ejpam-5366	40	4	devoted	devote	VERB
ejpam-5366	40	5	to	to	ADP
ejpam-5366	40	6	giving	give	VERB
ejpam-5366	40	7	a	a	DET
ejpam-5366	40	8	numerical	numerical	ADJ
ejpam-5366	40	9	solution	solution	NOUN
ejpam-5366	40	10	for	for	ADP
ejpam-5366	40	11	the	the	DET
ejpam-5366	40	12	fractional	fractional	ADJ
ejpam-5366	40	13	smoking	smoking	NOUN
ejpam-5366	40	14	model	model	NOUN
ejpam-5366	40	15	.	.	PUNCT
ejpam-5366	41	1	this	this	PRON
ejpam-5366	41	2	is	be	AUX
ejpam-5366	41	3	by	by	ADP
ejpam-5366	41	4	using	use	VERB
ejpam-5366	41	5	the	the	DET
ejpam-5366	41	6	mfem	mfem	NOUN
ejpam-5366	41	7	see	see	VERB
ejpam-5366	41	8	[	[	X
ejpam-5366	41	9	9	9	NUM
ejpam-5366	41	10	]	]	PUNCT
ejpam-5366	41	11	.	.	PUNCT
ejpam-5366	42	1	the	the	DET
ejpam-5366	42	2	outline	outline	NOUN
ejpam-5366	42	3	of	of	ADP
ejpam-5366	42	4	the	the	DET
ejpam-5366	42	5	paper	paper	NOUN
ejpam-5366	42	6	is	be	AUX
ejpam-5366	42	7	given	give	VERB
ejpam-5366	42	8	as	as	SCONJ
ejpam-5366	42	9	follows	follow	VERB
ejpam-5366	42	10	:	:	PUNCT
ejpam-5366	42	11	section	section	NOUN
ejpam-5366	42	12	2	2	NUM
ejpam-5366	42	13	,	,	PUNCT
ejpam-5366	42	14	presents	present	VERB
ejpam-5366	42	15	some	some	DET
ejpam-5366	42	16	basic	basic	ADJ
ejpam-5366	42	17	concepts	concept	NOUN
ejpam-5366	42	18	of	of	ADP
ejpam-5366	42	19	fractional	fractional	ADJ
ejpam-5366	42	20	calculus	calculus	NOUN
ejpam-5366	42	21	.	.	PUNCT
ejpam-5366	43	1	section	section	NOUN
ejpam-5366	43	2	3	3	NUM
ejpam-5366	43	3	,	,	PUNCT
ejpam-5366	43	4	describes	describe	VERB
ejpam-5366	43	5	the	the	DET
ejpam-5366	43	6	smoking	smoking	NOUN
ejpam-5366	43	7	system	system	NOUN
ejpam-5366	43	8	in	in	ADP
ejpam-5366	43	9	its	its	PRON
ejpam-5366	43	10	fractional	fractional	ADJ
ejpam-5366	43	11	form	form	NOUN
ejpam-5366	43	12	.	.	PUNCT
ejpam-5366	44	1	section	section	NOUN
ejpam-5366	44	2	4	4	NUM
ejpam-5366	44	3	,	,	PUNCT
ejpam-5366	44	4	introduces	introduce	VERB
ejpam-5366	44	5	the	the	DET
ejpam-5366	44	6	modified	modify	VERB
ejpam-5366	44	7	fractional	fractional	PROPN
ejpam-5366	44	8	euler	euler	NOUN
ejpam-5366	44	9	method	method	NOUN
ejpam-5366	44	10	.	.	PUNCT
ejpam-5366	45	1	section	section	NOUN
ejpam-5366	45	2	5	5	NUM
ejpam-5366	45	3	,	,	PUNCT
ejpam-5366	45	4	solves	solve	VERB
ejpam-5366	45	5	the	the	DET
ejpam-5366	45	6	fractional	fractional	ADJ
ejpam-5366	45	7	-	-	PUNCT
ejpam-5366	45	8	order	order	NOUN
ejpam-5366	45	9	smoking	smoking	NOUN
ejpam-5366	45	10	model	model	NOUN
ejpam-5366	45	11	.	.	PUNCT
ejpam-5366	46	1	section	section	NOUN
ejpam-5366	46	2	6	6	NUM
ejpam-5366	46	3	,	,	PUNCT
ejpam-5366	46	4	presents	present	VERB
ejpam-5366	46	5	a	a	DET
ejpam-5366	46	6	numerical	numerical	ADJ
ejpam-5366	46	7	simulation	simulation	NOUN
ejpam-5366	46	8	for	for	ADP
ejpam-5366	46	9	the	the	DET
ejpam-5366	46	10	model	model	NOUN
ejpam-5366	46	11	under	under	ADP
ejpam-5366	46	12	study	study	NOUN
ejpam-5366	46	13	.	.	PUNCT
ejpam-5366	47	1	section	section	NOUN
ejpam-5366	47	2	7	7	NUM
ejpam-5366	47	3	,	,	PUNCT
ejpam-5366	47	4	gives	give	VERB
ejpam-5366	47	5	the	the	DET
ejpam-5366	47	6	conclusions	conclusion	NOUN
ejpam-5366	47	7	and	and	CCONJ
ejpam-5366	47	8	discussions	discussion	NOUN
ejpam-5366	47	9	.	.	PUNCT
ejpam-5366	48	1	2	2	X
ejpam-5366	48	2	.	.	NUM
ejpam-5366	48	3	basic	basic	ADJ
ejpam-5366	48	4	concepts	concept	NOUN
ejpam-5366	48	5	of	of	ADP
ejpam-5366	48	6	fractional	fractional	ADJ
ejpam-5366	48	7	calculus	calculus	NOUN
ejpam-5366	48	8	to	to	PART
ejpam-5366	48	9	improve	improve	VERB
ejpam-5366	48	10	the	the	DET
ejpam-5366	48	11	system	system	NOUN
ejpam-5366	48	12	’s	’s	PART
ejpam-5366	48	13	ability	ability	NOUN
ejpam-5366	48	14	to	to	PART
ejpam-5366	48	15	describe	describe	VERB
ejpam-5366	48	16	memory	memory	NOUN
ejpam-5366	48	17	and	and	CCONJ
ejpam-5366	48	18	global	global	ADJ
ejpam-5366	48	19	correlation	correlation	NOUN
ejpam-5366	48	20	,	,	PUNCT
ejpam-5366	48	21	fractional	fractional	ADJ
ejpam-5366	48	22	derivative	derivative	ADJ
ejpam-5366	48	23	models	model	NOUN
ejpam-5366	48	24	have	have	AUX
ejpam-5366	48	25	employed	employ	VERB
ejpam-5366	48	26	power	power	NOUN
ejpam-5366	48	27	-	-	PUNCT
ejpam-5366	48	28	law	law	NOUN
ejpam-5366	48	29	memory	memory	NOUN
ejpam-5366	48	30	kernels	kernel	NOUN
ejpam-5366	48	31	to	to	PART
ejpam-5366	48	32	give	give	VERB
ejpam-5366	48	33	the	the	DET
ejpam-5366	48	34	fractional	fractional	ADJ
ejpam-5366	48	35	derivatives	derivative	NOUN
ejpam-5366	48	36	.	.	PUNCT
ejpam-5366	49	1	the	the	DET
ejpam-5366	49	2	most	most	ADV
ejpam-5366	49	3	important	important	ADJ
ejpam-5366	49	4	definition	definition	NOUN
ejpam-5366	49	5	that	that	PRON
ejpam-5366	49	6	is	be	AUX
ejpam-5366	49	7	utilized	utilize	VERB
ejpam-5366	49	8	in	in	ADP
ejpam-5366	49	9	the	the	DET
ejpam-5366	49	10	creation	creation	NOUN
ejpam-5366	49	11	of	of	ADP
ejpam-5366	49	12	fractional	fractional	ADJ
ejpam-5366	49	13	calculus	calculus	NOUN
ejpam-5366	49	14	theory	theory	NOUN
ejpam-5366	49	15	is	be	AUX
ejpam-5366	49	16	this	this	DET
ejpam-5366	49	17	one	one	NUM
ejpam-5366	49	18	.	.	PUNCT
ejpam-5366	50	1	while	while	SCONJ
ejpam-5366	50	2	modeling	model	VERB
ejpam-5366	50	3	certain	certain	ADJ
ejpam-5366	50	4	real	real	ADJ
ejpam-5366	50	5	-	-	PUNCT
ejpam-5366	50	6	world	world	NOUN
ejpam-5366	50	7	problems	problem	NOUN
ejpam-5366	50	8	,	,	PUNCT
ejpam-5366	50	9	the	the	DET
ejpam-5366	50	10	riemann	riemann	PROPN
ejpam-5366	50	11	-	-	PUNCT
ejpam-5366	50	12	liouville	liouville	VERB
ejpam-5366	50	13	formulation	formulation	NOUN
ejpam-5366	50	14	has	have	VERB
ejpam-5366	50	15	some	some	DET
ejpam-5366	50	16	restrictions	restriction	NOUN
ejpam-5366	50	17	[	[	X
ejpam-5366	50	18	11	11	NUM
ejpam-5366	50	19	]	]	PUNCT
ejpam-5366	50	20	.	.	PUNCT
ejpam-5366	51	1	on	on	ADP
ejpam-5366	51	2	the	the	DET
ejpam-5366	51	3	other	other	ADJ
ejpam-5366	51	4	hand	hand	NOUN
ejpam-5366	51	5	,	,	PUNCT
ejpam-5366	51	6	these	these	DET
ejpam-5366	51	7	issues	issue	NOUN
ejpam-5366	51	8	were	be	AUX
ejpam-5366	51	9	addressed	address	VERB
ejpam-5366	51	10	in	in	ADP
ejpam-5366	51	11	the	the	DET
ejpam-5366	51	12	creation	creation	NOUN
ejpam-5366	51	13	of	of	ADP
ejpam-5366	51	14	the	the	DET
ejpam-5366	51	15	liouville	liouville	PROPN
ejpam-5366	51	16	-	-	PUNCT
ejpam-5366	51	17	caputo	caputo	PROPN
ejpam-5366	51	18	definition	definition	NOUN
ejpam-5366	51	19	.	.	PUNCT
ejpam-5366	52	1	here	here	ADV
ejpam-5366	52	2	,	,	PUNCT
ejpam-5366	52	3	we	we	PRON
ejpam-5366	52	4	will	will	AUX
ejpam-5366	52	5	present	present	VERB
ejpam-5366	52	6	some	some	DET
ejpam-5366	52	7	concepts	concept	NOUN
ejpam-5366	52	8	of	of	ADP
ejpam-5366	52	9	the	the	DET
ejpam-5366	52	10	fractional	fractional	ADJ
ejpam-5366	52	11	calculus	calculus	NOUN
ejpam-5366	52	12	(	(	PUNCT
ejpam-5366	52	13	[	[	X
ejpam-5366	52	14	2]-[12	2]-[12	NUM
ejpam-5366	52	15	]	]	PUNCT
ejpam-5366	52	16	)	)	PUNCT
ejpam-5366	52	17	.	.	PUNCT
ejpam-5366	53	1	definition	definition	NOUN
ejpam-5366	53	2	1	1	NUM
ejpam-5366	53	3	.	.	PUNCT
ejpam-5366	54	1	the	the	DET
ejpam-5366	54	2	fractional	fractional	ADJ
ejpam-5366	54	3	riemann	riemann	PROPN
ejpam-5366	54	4	-	-	PUNCT
ejpam-5366	54	5	liouville	liouville	VERB
ejpam-5366	54	6	integral	integral	ADJ
ejpam-5366	54	7	of	of	ADP
ejpam-5366	54	8	a	a	DET
ejpam-5366	54	9	function	function	NOUN
ejpam-5366	54	10	ψ(τ	ψ(τ	NOUN
ejpam-5366	54	11	)	)	PUNCT
ejpam-5366	54	12	of	of	ADP
ejpam-5366	54	13	order	order	NOUN
ejpam-5366	54	14	β	β	X
ejpam-5366	54	15	∈	∈	PROPN
ejpam-5366	54	16	m.	m.	NOUN
ejpam-5366	54	17	m.	m.	NOUN
ejpam-5366	54	18	khader	khader	PROPN
ejpam-5366	54	19	/	/	SYM
ejpam-5366	54	20	eur	eur	PROPN
ejpam-5366	54	21	.	.	PUNCT
ejpam-5366	55	1	j.	j.	PROPN
ejpam-5366	55	2	pure	pure	PROPN
ejpam-5366	55	3	appl	appl	PROPN
ejpam-5366	55	4	.	.	PROPN
ejpam-5366	55	5	math	math	PROPN
ejpam-5366	55	6	,	,	PUNCT
ejpam-5366	55	7	17	17	NUM
ejpam-5366	55	8	(	(	PUNCT
ejpam-5366	55	9	4	4	NUM
ejpam-5366	55	10	)	)	PUNCT
ejpam-5366	55	11	(	(	PUNCT
ejpam-5366	55	12	2024	2024	NUM
ejpam-5366	55	13	)	)	PUNCT
ejpam-5366	55	14	,	,	PUNCT
ejpam-5366	55	15	2676	2676	NUM
ejpam-5366	55	16	-	-	SYM
ejpam-5366	55	17	2691	2691	NUM
ejpam-5366	55	18	2678	2678	NUM
ejpam-5366	55	19	(	(	PUNCT
ejpam-5366	55	20	0	0	NUM
ejpam-5366	55	21	,	,	PUNCT
ejpam-5366	55	22	1	1	NUM
ejpam-5366	55	23	)	)	PUNCT
ejpam-5366	55	24	is	be	AUX
ejpam-5366	55	25	defined	define	VERB
ejpam-5366	55	26	as	as	ADP
ejpam-5366	55	27	:	:	PUNCT
ejpam-5366	55	28	iβψ(τ	iβψ(τ	NUM
ejpam-5366	55	29	)	)	PUNCT
ejpam-5366	55	30	=	=	SYM
ejpam-5366	55	31	1	1	NUM
ejpam-5366	55	32	γ(β	γ(β	PROPN
ejpam-5366	55	33	)	)	PUNCT
ejpam-5366	55	34	∫	∫	PROPN
ejpam-5366	56	1	τ	τ	PROPN
ejpam-5366	56	2	0	0	PROPN
ejpam-5366	56	3	(	(	PUNCT
ejpam-5366	56	4	τ	τ	PROPN
ejpam-5366	56	5	−	−	PROPN
ejpam-5366	56	6	s)β−1ψ(s)ds	s)β−1ψ(s)ds	PROPN
ejpam-5366	56	7	,	,	PUNCT
ejpam-5366	56	8	t	t	X
ejpam-5366	56	9	>	>	X
ejpam-5366	56	10	0	0	X
ejpam-5366	56	11	.	.	PUNCT
ejpam-5366	56	12	definition	definition	NOUN
ejpam-5366	56	13	2	2	NUM
ejpam-5366	56	14	.	.	PUNCT
ejpam-5366	57	1	the	the	DET
ejpam-5366	57	2	liouville	liouville	PROPN
ejpam-5366	57	3	-	-	PUNCT
ejpam-5366	57	4	caputo	caputo	PROPN
ejpam-5366	57	5	fractional	fractional	PROPN
ejpam-5366	57	6	derivative	derivative	PROPN
ejpam-5366	57	7	dβ	dβ	NOUN
ejpam-5366	57	8	of	of	ADP
ejpam-5366	57	9	a	a	DET
ejpam-5366	57	10	function	function	NOUN
ejpam-5366	57	11	ψ(τ	ψ(τ	NOUN
ejpam-5366	57	12	)	)	PUNCT
ejpam-5366	57	13	of	of	ADP
ejpam-5366	57	14	order	order	NOUN
ejpam-5366	57	15	β	β	X
ejpam-5366	57	16	∈	∈	PROPN
ejpam-5366	57	17	(	(	PUNCT
ejpam-5366	57	18	m−	m−	PROPN
ejpam-5366	57	19	1,m	1,m	PROPN
ejpam-5366	57	20	]	]	PUNCT
ejpam-5366	57	21	,	,	PUNCT
ejpam-5366	57	22	m	m	VERB
ejpam-5366	57	23	∈	∈	NOUN
ejpam-5366	57	24	n	n	PRON
ejpam-5366	57	25	is	be	AUX
ejpam-5366	57	26	formulated	formulate	VERB
ejpam-5366	57	27	by	by	ADP
ejpam-5366	57	28	:	:	PUNCT
ejpam-5366	57	29	dβψ(τ	dβψ(τ	X
ejpam-5366	57	30	)	)	PUNCT
ejpam-5366	57	31	=	=	SYM
ejpam-5366	57	32	1	1	NUM
ejpam-5366	57	33	γ(m−	γ(m−	PROPN
ejpam-5366	57	34	β	β	NOUN
ejpam-5366	57	35	)	)	PUNCT
ejpam-5366	57	36	∫	∫	PROPN
ejpam-5366	58	1	τ	τ	PROPN
ejpam-5366	58	2	0	0	PROPN
ejpam-5366	58	3	(	(	PUNCT
ejpam-5366	58	4	τ	τ	PROPN
ejpam-5366	58	5	−	−	PROPN
ejpam-5366	58	6	s)m−β−1ψ(m)(s)ds	s)m−β−1ψ(m)(s)ds	PROPN
ejpam-5366	58	7	.	.	PUNCT
ejpam-5366	59	1	the	the	DET
ejpam-5366	59	2	relation	relation	NOUN
ejpam-5366	59	3	between	between	ADP
ejpam-5366	59	4	the	the	DET
ejpam-5366	59	5	fractional	fractional	ADJ
ejpam-5366	59	6	derivatives	derivative	NOUN
ejpam-5366	59	7	and	and	CCONJ
ejpam-5366	59	8	fractional	fractional	ADJ
ejpam-5366	59	9	integral	integral	ADJ
ejpam-5366	59	10	for	for	ADP
ejpam-5366	59	11	their	their	PRON
ejpam-5366	59	12	significance	significance	NOUN
ejpam-5366	59	13	is	be	AUX
ejpam-5366	59	14	stated	state	VERB
ejpam-5366	59	15	as	as	ADP
ejpam-5366	59	16	:	:	PUNCT
ejpam-5366	59	17	iβdβψ(t	iβdβψ(t	NOUN
ejpam-5366	59	18	)	)	PUNCT
ejpam-5366	59	19	=	=	SYM
ejpam-5366	59	20	ψ(t)−	ψ(t)−	PROPN
ejpam-5366	59	21	m∑	m∑	VERB
ejpam-5366	59	22	j=1	j=1	PROPN
ejpam-5366	59	23	ψ(j)(0	ψ(j)(0	PROPN
ejpam-5366	60	1	+	+	PROPN
ejpam-5366	60	2	)	)	PUNCT
ejpam-5366	60	3	tj	tj	PROPN
ejpam-5366	60	4	j	j	PROPN
ejpam-5366	60	5	!	!	PROPN
ejpam-5366	60	6	,	,	PUNCT
ejpam-5366	60	7	t	t	X
ejpam-5366	60	8	>	>	X
ejpam-5366	60	9	0	0	PROPN
ejpam-5366	60	10	,	,	PUNCT
ejpam-5366	60	11	β	β	X
ejpam-5366	60	12	∈	∈	PROPN
ejpam-5366	60	13	(	(	PUNCT
ejpam-5366	60	14	m−	m−	PROPN
ejpam-5366	60	15	1,m	1,m	PROPN
ejpam-5366	60	16	]	]	X
ejpam-5366	60	17	.	.	PUNCT
ejpam-5366	61	1	3	3	X
ejpam-5366	61	2	.	.	X
ejpam-5366	61	3	description	description	NOUN
ejpam-5366	61	4	of	of	ADP
ejpam-5366	61	5	the	the	DET
ejpam-5366	61	6	smoking	smoking	NOUN
ejpam-5366	61	7	system	system	NOUN
ejpam-5366	61	8	given	give	VERB
ejpam-5366	61	9	the	the	DET
ejpam-5366	61	10	importance	importance	NOUN
ejpam-5366	61	11	of	of	ADP
ejpam-5366	61	12	mathematical	mathematical	ADJ
ejpam-5366	61	13	modeling	modeling	NOUN
ejpam-5366	61	14	as	as	ADP
ejpam-5366	61	15	a	a	DET
ejpam-5366	61	16	good	good	ADJ
ejpam-5366	61	17	tool	tool	NOUN
ejpam-5366	61	18	for	for	ADP
ejpam-5366	61	19	pandemic	pandemic	ADJ
ejpam-5366	61	20	grasp	grasp	NOUN
ejpam-5366	61	21	in	in	ADP
ejpam-5366	61	22	recent	recent	ADJ
ejpam-5366	61	23	decades	decade	NOUN
ejpam-5366	61	24	,	,	PUNCT
ejpam-5366	61	25	we	we	PRON
ejpam-5366	61	26	may	may	AUX
ejpam-5366	61	27	use	use	VERB
ejpam-5366	61	28	it	it	PRON
ejpam-5366	61	29	to	to	PART
ejpam-5366	61	30	stop	stop	VERB
ejpam-5366	61	31	tobacco	tobacco	NOUN
ejpam-5366	61	32	smoking	smoking	NOUN
ejpam-5366	61	33	from	from	ADP
ejpam-5366	61	34	spreading	spread	VERB
ejpam-5366	61	35	.	.	PUNCT
ejpam-5366	62	1	a	a	DET
ejpam-5366	62	2	generic	generic	ADJ
ejpam-5366	62	3	model	model	NOUN
ejpam-5366	62	4	is	be	AUX
ejpam-5366	62	5	the	the	DET
ejpam-5366	62	6	susceptible	susceptible	ADJ
ejpam-5366	62	7	-	-	PUNCT
ejpam-5366	62	8	exposed	expose	VERB
ejpam-5366	62	9	-	-	PUNCT
ejpam-5366	62	10	infected	infect	VERB
ejpam-5366	62	11	-	-	PUNCT
ejpam-5366	62	12	recovered	recover	VERB
ejpam-5366	62	13	(	(	PUNCT
ejpam-5366	62	14	seir	seir	NOUN
ejpam-5366	62	15	)	)	PUNCT
ejpam-5366	62	16	.	.	PUNCT
ejpam-5366	63	1	in	in	ADP
ejpam-5366	63	2	this	this	DET
ejpam-5366	63	3	section	section	NOUN
ejpam-5366	63	4	,	,	PUNCT
ejpam-5366	63	5	to	to	PART
ejpam-5366	63	6	gain	gain	VERB
ejpam-5366	63	7	a	a	DET
ejpam-5366	63	8	deeper	deep	ADJ
ejpam-5366	63	9	understanding	understanding	NOUN
ejpam-5366	63	10	of	of	ADP
ejpam-5366	63	11	the	the	DET
ejpam-5366	63	12	qualitative	qualitative	ADJ
ejpam-5366	63	13	analysis	analysis	NOUN
ejpam-5366	63	14	and	and	CCONJ
ejpam-5366	63	15	the	the	DET
ejpam-5366	63	16	numerical	numerical	ADJ
ejpam-5366	63	17	iterative	iterative	NOUN
ejpam-5366	63	18	analysis	analysis	NOUN
ejpam-5366	63	19	utilized	utilize	VERB
ejpam-5366	63	20	to	to	PART
ejpam-5366	63	21	solve	solve	VERB
ejpam-5366	63	22	it	it	PRON
ejpam-5366	63	23	,	,	PUNCT
ejpam-5366	63	24	the	the	DET
ejpam-5366	63	25	updated	update	VERB
ejpam-5366	63	26	version	version	NOUN
ejpam-5366	63	27	of	of	ADP
ejpam-5366	63	28	the	the	DET
ejpam-5366	63	29	smoking	smoking	NOUN
ejpam-5366	63	30	model	model	NOUN
ejpam-5366	63	31	will	will	AUX
ejpam-5366	63	32	be	be	AUX
ejpam-5366	63	33	considered	consider	VERB
ejpam-5366	63	34	as	as	SCONJ
ejpam-5366	63	35	follows	follow	VERB
ejpam-5366	63	36	(	(	PUNCT
ejpam-5366	63	37	[	[	X
ejpam-5366	63	38	1	1	NUM
ejpam-5366	63	39	]	]	PUNCT
ejpam-5366	63	40	,	,	PUNCT
ejpam-5366	64	1	[	[	X
ejpam-5366	64	2	4	4	NUM
ejpam-5366	64	3	]	]	PUNCT
ejpam-5366	64	4	):	):	PUNCT
ejpam-5366	64	5	ṡ1(t	ṡ1(t	PROPN
ejpam-5366	64	6	)	)	PUNCT
ejpam-5366	65	1	=	=	PUNCT
ejpam-5366	65	2	κ−	κ−	PROPN
ejpam-5366	65	3	ε1	ε1	VERB
ejpam-5366	65	4	s1(t)s2(t	s1(t)s2(t	PROPN
ejpam-5366	65	5	)	)	PUNCT
ejpam-5366	66	1	+	+	CCONJ
ejpam-5366	66	2	ω	ω	NUM
ejpam-5366	66	3	s4(t)−	s4(t)−	PROPN
ejpam-5366	66	4	µ	µ	X
ejpam-5366	66	5	s1(t	s1(t	X
ejpam-5366	66	6	)	)	PUNCT
ejpam-5366	66	7	,	,	PUNCT
ejpam-5366	66	8	ṡ2(t	ṡ2(t	PROPN
ejpam-5366	66	9	)	)	PUNCT
ejpam-5366	66	10	=	=	PUNCT
ejpam-5366	66	11	ε1	ε1	VERB
ejpam-5366	66	12	s1(t)s2(t)−	s1(t)s2(t)−	PROPN
ejpam-5366	66	13	ε2	ε2	PROPN
ejpam-5366	66	14	s2(t)s3(t)−	s2(t)s3(t)−	PROPN
ejpam-5366	66	15	(	(	PUNCT
ejpam-5366	66	16	κ1	κ1	NOUN
ejpam-5366	66	17	+	+	CCONJ
ejpam-5366	66	18	µ	µ	X
ejpam-5366	66	19	)	)	PUNCT
ejpam-5366	66	20	s2(t	s2(t	PROPN
ejpam-5366	66	21	)	)	PUNCT
ejpam-5366	66	22	,	,	PUNCT
ejpam-5366	66	23	ṡ3(t	ṡ3(t	X
ejpam-5366	66	24	)	)	PUNCT
ejpam-5366	66	25	=	=	SYM
ejpam-5366	66	26	ε2	ε2	ADJ
ejpam-5366	66	27	s2(t)s3(t)−	s2(t)s3(t)−	PROPN
ejpam-5366	66	28	(	(	PUNCT
ejpam-5366	66	29	φ+	φ+	NOUN
ejpam-5366	66	30	κ2	κ2	NOUN
ejpam-5366	66	31	+	+	CCONJ
ejpam-5366	66	32	µ	µ	X
ejpam-5366	66	33	)	)	PUNCT
ejpam-5366	66	34	s3(t	s3(t	NUM
ejpam-5366	66	35	)	)	PUNCT
ejpam-5366	66	36	,	,	PUNCT
ejpam-5366	66	37	ṡ4(t	ṡ4(t	ADJ
ejpam-5366	66	38	)	)	PUNCT
ejpam-5366	66	39	=	=	SYM
ejpam-5366	66	40	φs3(t)−	φs3(t)−	PROPN
ejpam-5366	66	41	(	(	PUNCT
ejpam-5366	66	42	λ+	λ+	X
ejpam-5366	66	43	µ+	µ+	X
ejpam-5366	66	44	ω	ω	NOUN
ejpam-5366	66	45	)	)	PUNCT
ejpam-5366	66	46	s4(t	s4(t	PROPN
ejpam-5366	66	47	)	)	PUNCT
ejpam-5366	66	48	,	,	PUNCT
ejpam-5366	66	49	ṡ5(t	ṡ5(t	NOUN
ejpam-5366	66	50	)	)	PUNCT
ejpam-5366	66	51	=	=	SYM
ejpam-5366	66	52	λs4(t)−	λs4(t)−	PROPN
ejpam-5366	66	53	µs5(t	µs5(t	PROPN
ejpam-5366	66	54	)	)	PUNCT
ejpam-5366	66	55	,	,	PUNCT
ejpam-5366	66	56	(	(	PUNCT
ejpam-5366	66	57	1	1	X
ejpam-5366	66	58	)	)	PUNCT
ejpam-5366	66	59	where	where	SCONJ
ejpam-5366	66	60	ṡi(t	ṡi(t	NOUN
ejpam-5366	66	61	)	)	PUNCT
ejpam-5366	66	62	=	=	SYM
ejpam-5366	66	63	ds	ds	ADJ
ejpam-5366	67	1	dt	dt	X
ejpam-5366	67	2	,	,	PUNCT
ejpam-5366	67	3	i	i	PRON
ejpam-5366	67	4	=	=	NOUN
ejpam-5366	67	5	1	1	NUM
ejpam-5366	67	6	,	,	PUNCT
ejpam-5366	67	7	2	2	NUM
ejpam-5366	67	8	,	,	PUNCT
ejpam-5366	67	9	3	3	NUM
ejpam-5366	67	10	,	,	PUNCT
ejpam-5366	67	11	4	4	NUM
ejpam-5366	67	12	,	,	PUNCT
ejpam-5366	67	13	5	5	NUM
ejpam-5366	67	14	.	.	PUNCT
ejpam-5366	67	15	with	with	ADP
ejpam-5366	67	16	the	the	DET
ejpam-5366	67	17	initial	initial	ADJ
ejpam-5366	67	18	conditions	condition	NOUN
ejpam-5366	67	19	si(0	si(0	NOUN
ejpam-5366	67	20	)	)	PUNCT
ejpam-5366	67	21	=	=	X
ejpam-5366	67	22	s0i	s0i	NOUN
ejpam-5366	67	23	.	.	PUNCT
ejpam-5366	68	1	the	the	DET
ejpam-5366	68	2	whole	whole	ADJ
ejpam-5366	68	3	population	population	NOUN
ejpam-5366	68	4	is	be	AUX
ejpam-5366	68	5	split	split	VERB
ejpam-5366	68	6	into	into	ADP
ejpam-5366	68	7	five	five	NUM
ejpam-5366	68	8	classes	class	NOUN
ejpam-5366	68	9	in	in	ADP
ejpam-5366	68	10	this	this	DET
ejpam-5366	68	11	model	model	NOUN
ejpam-5366	68	12	:	:	PUNCT
ejpam-5366	68	13	at	at	ADP
ejpam-5366	68	14	a	a	DET
ejpam-5366	68	15	time	time	NOUN
ejpam-5366	68	16	t	t	NOUN
ejpam-5366	68	17	,	,	PUNCT
ejpam-5366	68	18	the	the	DET
ejpam-5366	68	19	susceptible	susceptible	ADJ
ejpam-5366	68	20	smokers	smoker	NOUN
ejpam-5366	68	21	(	(	PUNCT
ejpam-5366	68	22	s1	s1	NOUN
ejpam-5366	68	23	,	,	PUNCT
ejpam-5366	68	24	s2	s2	PROPN
ejpam-5366	68	25	,	,	PUNCT
ejpam-5366	68	26	s3	s3	PROPN
ejpam-5366	68	27	,	,	PUNCT
ejpam-5366	68	28	s4	s4	PROPN
ejpam-5366	68	29	,	,	PUNCT
ejpam-5366	68	30	and	and	CCONJ
ejpam-5366	68	31	s5	s5	NOUN
ejpam-5366	68	32	)	)	PUNCT
ejpam-5366	68	33	represent	represent	VERB
ejpam-5366	68	34	respectively	respectively	ADV
ejpam-5366	68	35	,	,	PUNCT
ejpam-5366	68	36	the	the	DET
ejpam-5366	68	37	snuffing	snuff	VERB
ejpam-5366	68	38	class	class	NOUN
ejpam-5366	68	39	,	,	PUNCT
ejpam-5366	68	40	irregular	irregular	ADJ
ejpam-5366	68	41	smokers	smoker	NOUN
ejpam-5366	68	42	,	,	PUNCT
ejpam-5366	68	43	regular	regular	ADJ
ejpam-5366	68	44	smokers	smoker	NOUN
ejpam-5366	68	45	,	,	PUNCT
ejpam-5366	68	46	and	and	CCONJ
ejpam-5366	68	47	quitters	quitter	NOUN
ejpam-5366	68	48	.	.	PUNCT
ejpam-5366	69	1	the	the	DET
ejpam-5366	69	2	parameters	parameter	NOUN
ejpam-5366	69	3	(	(	PUNCT
ejpam-5366	69	4	κ	κ	NOUN
ejpam-5366	69	5	,	,	PUNCT
ejpam-5366	69	6	φ	φ	PROPN
ejpam-5366	69	7	,	,	PUNCT
ejpam-5366	69	8	λ	λ	PROPN
ejpam-5366	69	9	,	,	PUNCT
ejpam-5366	69	10	µ	µ	PRON
ejpam-5366	69	11	,	,	PUNCT
ejpam-5366	69	12	ω	ω	PROPN
ejpam-5366	69	13	,	,	PUNCT
ejpam-5366	69	14	ε1	ε1	PROPN
ejpam-5366	69	15	,	,	PUNCT
ejpam-5366	69	16	ε2	ε2	ADJ
ejpam-5366	69	17	,	,	PUNCT
ejpam-5366	69	18	κ1	κ1	NOUN
ejpam-5366	69	19	,	,	PUNCT
ejpam-5366	69	20	κ2	κ2	PROPN
ejpam-5366	69	21	)	)	PUNCT
ejpam-5366	69	22	utilized	utilize	VERB
ejpam-5366	69	23	in	in	ADP
ejpam-5366	69	24	the	the	DET
ejpam-5366	69	25	system	system	NOUN
ejpam-5366	69	26	(	(	PUNCT
ejpam-5366	69	27	1	1	X
ejpam-5366	69	28	)	)	PUNCT
ejpam-5366	69	29	are	be	AUX
ejpam-5366	69	30	explained	explain	VERB
ejpam-5366	69	31	and	and	CCONJ
ejpam-5366	69	32	defined	define	VERB
ejpam-5366	69	33	as	as	ADP
ejpam-5366	69	34	in	in	ADP
ejpam-5366	69	35	the	the	DET
ejpam-5366	69	36	following	follow	VERB
ejpam-5366	69	37	table	table	NOUN
ejpam-5366	69	38	1	1	NUM
ejpam-5366	69	39	:	:	PUNCT
ejpam-5366	69	40	m.	m.	NOUN
ejpam-5366	69	41	m.	m.	NOUN
ejpam-5366	69	42	khader	khader	PROPN
ejpam-5366	69	43	/	/	SYM
ejpam-5366	69	44	eur	eur	PROPN
ejpam-5366	69	45	.	.	PUNCT
ejpam-5366	70	1	j.	j.	PROPN
ejpam-5366	70	2	pure	pure	PROPN
ejpam-5366	70	3	appl	appl	PROPN
ejpam-5366	70	4	.	.	PROPN
ejpam-5366	70	5	math	math	PROPN
ejpam-5366	70	6	,	,	PUNCT
ejpam-5366	70	7	17	17	NUM
ejpam-5366	70	8	(	(	PUNCT
ejpam-5366	70	9	4	4	NUM
ejpam-5366	70	10	)	)	PUNCT
ejpam-5366	70	11	(	(	PUNCT
ejpam-5366	70	12	2024	2024	NUM
ejpam-5366	70	13	)	)	PUNCT
ejpam-5366	70	14	,	,	PUNCT
ejpam-5366	70	15	2676	2676	NUM
ejpam-5366	70	16	-	-	SYM
ejpam-5366	70	17	2691	2691	NUM
ejpam-5366	70	18	2679	2679	NUM
ejpam-5366	70	19	table	table	NOUN
ejpam-5366	70	20	1	1	NUM
ejpam-5366	70	21	:	:	PUNCT
ejpam-5366	70	22	description	description	NOUN
ejpam-5366	70	23	of	of	ADP
ejpam-5366	70	24	the	the	DET
ejpam-5366	70	25	included	include	VERB
ejpam-5366	70	26	parameters	parameter	NOUN
ejpam-5366	70	27	of	of	ADP
ejpam-5366	70	28	the	the	DET
ejpam-5366	70	29	system	system	NOUN
ejpam-5366	70	30	(	(	PUNCT
ejpam-5366	70	31	1	1	NUM
ejpam-5366	70	32	)	)	PUNCT
ejpam-5366	70	33	.	.	PUNCT
ejpam-5366	71	1	symbol	symbol	NOUN
ejpam-5366	71	2	description	description	NOUN
ejpam-5366	71	3	s1	s1	PROPN
ejpam-5366	71	4	the	the	DET
ejpam-5366	71	5	susceptible	susceptible	ADJ
ejpam-5366	71	6	smokers	smoker	NOUN
ejpam-5366	71	7	s2	s2	VERB
ejpam-5366	71	8	the	the	DET
ejpam-5366	71	9	snuffing	snuffing	NOUN
ejpam-5366	71	10	(	(	PUNCT
ejpam-5366	71	11	ingestion	ingestion	NOUN
ejpam-5366	71	12	)	)	PUNCT
ejpam-5366	71	13	class	class	NOUN
ejpam-5366	71	14	s3	s3	PROPN
ejpam-5366	71	15	the	the	DET
ejpam-5366	71	16	irregular	irregular	ADJ
ejpam-5366	71	17	smokers	smoker	NOUN
ejpam-5366	71	18	s4	s4	VERB
ejpam-5366	71	19	the	the	DET
ejpam-5366	71	20	regular	regular	ADJ
ejpam-5366	71	21	smokers	smoker	NOUN
ejpam-5366	71	22	s5	s5	X
ejpam-5366	71	23	the	the	DET
ejpam-5366	71	24	quit	quit	ADJ
ejpam-5366	71	25	smokers	smoker	NOUN
ejpam-5366	71	26	κ	κ	ADP
ejpam-5366	71	27	the	the	DET
ejpam-5366	71	28	rate	rate	NOUN
ejpam-5366	71	29	of	of	ADP
ejpam-5366	71	30	recruitment	recruitment	NOUN
ejpam-5366	71	31	(	(	PUNCT
ejpam-5366	71	32	due	due	ADP
ejpam-5366	71	33	to	to	ADP
ejpam-5366	71	34	migration	migration	NOUN
ejpam-5366	71	35	or	or	CCONJ
ejpam-5366	71	36	birth	birth	NOUN
ejpam-5366	71	37	)	)	PUNCT
ejpam-5366	72	1	φ	φ	NOUN
ejpam-5366	72	2	the	the	DET
ejpam-5366	72	3	percentage	percentage	NOUN
ejpam-5366	72	4	of	of	ADP
ejpam-5366	72	5	infrequent	infrequent	ADJ
ejpam-5366	72	6	smokers	smoker	NOUN
ejpam-5366	72	7	who	who	PRON
ejpam-5366	72	8	start	start	VERB
ejpam-5366	72	9	smoking	smoke	VERB
ejpam-5366	72	10	regularly	regularly	ADV
ejpam-5366	72	11	λ	λ	PROPN
ejpam-5366	72	12	,	,	PUNCT
ejpam-5366	72	13	µ	µ	NUM
ejpam-5366	72	14	,	,	PUNCT
ejpam-5366	72	15	ω	ω	NUM
ejpam-5366	72	16	the	the	DET
ejpam-5366	72	17	rate	rate	NOUN
ejpam-5366	72	18	of	of	ADP
ejpam-5366	72	19	natural	natural	ADJ
ejpam-5366	72	20	death	death	NOUN
ejpam-5366	72	21	,	,	PUNCT
ejpam-5366	72	22	the	the	DET
ejpam-5366	72	23	rate	rate	NOUN
ejpam-5366	72	24	of	of	ADP
ejpam-5366	72	25	departure	departure	NOUN
ejpam-5366	72	26	,	,	PUNCT
ejpam-5366	72	27	and	and	CCONJ
ejpam-5366	72	28	the	the	DET
ejpam-5366	72	29	pace	pace	NOUN
ejpam-5366	72	30	of	of	ADP
ejpam-5366	72	31	recuperation	recuperation	NOUN
ejpam-5366	72	32	ε1	ε1	VERB
ejpam-5366	72	33	the	the	DET
ejpam-5366	72	34	proportion	proportion	NOUN
ejpam-5366	72	35	of	of	ADP
ejpam-5366	72	36	the	the	DET
ejpam-5366	72	37	population	population	NOUN
ejpam-5366	72	38	that	that	PRON
ejpam-5366	72	39	moves	move	VERB
ejpam-5366	72	40	from	from	ADP
ejpam-5366	72	41	being	be	AUX
ejpam-5366	72	42	vulnerable	vulnerable	ADJ
ejpam-5366	72	43	to	to	ADP
ejpam-5366	72	44	being	be	AUX
ejpam-5366	72	45	snuffers	snuffer	NOUN
ejpam-5366	72	46	ε2	ε2	ADJ
ejpam-5366	72	47	snuffing	snuff	VERB
ejpam-5366	72	48	rates	rate	NOUN
ejpam-5366	72	49	start	start	VERB
ejpam-5366	72	50	to	to	PART
ejpam-5366	72	51	fluctuate	fluctuate	VERB
ejpam-5366	72	52	among	among	ADP
ejpam-5366	72	53	smokers	smoker	NOUN
ejpam-5366	72	54	κ1	κ1	NOUN
ejpam-5366	72	55	the	the	DET
ejpam-5366	72	56	percentage	percentage	NOUN
ejpam-5366	72	57	of	of	ADP
ejpam-5366	72	58	smoking	smoking	NOUN
ejpam-5366	72	59	-	-	PUNCT
ejpam-5366	72	60	related	relate	VERB
ejpam-5366	72	61	deaths	death	NOUN
ejpam-5366	72	62	class	class	NOUN
ejpam-5366	72	63	κ2	κ2	NOUN
ejpam-5366	72	64	the	the	DET
ejpam-5366	72	65	percentage	percentage	NOUN
ejpam-5366	72	66	of	of	ADP
ejpam-5366	72	67	smoking	smoking	NOUN
ejpam-5366	72	68	-	-	PUNCT
ejpam-5366	72	69	related	relate	VERB
ejpam-5366	72	70	deaths	death	NOUN
ejpam-5366	72	71	among	among	ADP
ejpam-5366	72	72	the	the	DET
ejpam-5366	72	73	snuffing	snuff	VERB
ejpam-5366	72	74	class	class	NOUN
ejpam-5366	72	75	3.1	3.1	NUM
ejpam-5366	72	76	.	.	PUNCT
ejpam-5366	72	77	liouville	liouville	PROPN
ejpam-5366	72	78	-	-	PUNCT
ejpam-5366	72	79	caputo	caputo	PROPN
ejpam-5366	72	80	-	-	PUNCT
ejpam-5366	72	81	fractional	fractional	ADJ
ejpam-5366	72	82	smoking	smoking	NOUN
ejpam-5366	72	83	system	system	NOUN
ejpam-5366	72	84	the	the	DET
ejpam-5366	72	85	fractional	fractional	ADJ
ejpam-5366	72	86	derivative	derivative	ADJ
ejpam-5366	72	87	increases	increase	NOUN
ejpam-5366	72	88	the	the	DET
ejpam-5366	72	89	opportunity	opportunity	NOUN
ejpam-5366	72	90	to	to	PART
ejpam-5366	72	91	study	study	VERB
ejpam-5366	72	92	and	and	CCONJ
ejpam-5366	72	93	evaluate	evaluate	VERB
ejpam-5366	72	94	the	the	DET
ejpam-5366	72	95	real	real	ADJ
ejpam-5366	72	96	phenomenon	phenomenon	NOUN
ejpam-5366	72	97	in	in	ADP
ejpam-5366	72	98	terms	term	NOUN
ejpam-5366	72	99	of	of	ADP
ejpam-5366	72	100	fractional	fractional	NOUN
ejpam-5366	72	101	,	,	PUNCT
ejpam-5366	72	102	which	which	PRON
ejpam-5366	72	103	is	be	AUX
ejpam-5366	72	104	why	why	SCONJ
ejpam-5366	72	105	a	a	DET
ejpam-5366	72	106	lot	lot	NOUN
ejpam-5366	72	107	of	of	ADP
ejpam-5366	72	108	academics	academic	NOUN
ejpam-5366	72	109	have	have	AUX
ejpam-5366	72	110	focused	focus	VERB
ejpam-5366	72	111	on	on	ADP
ejpam-5366	72	112	this	this	DET
ejpam-5366	72	113	subject	subject	NOUN
ejpam-5366	72	114	(	(	PUNCT
ejpam-5366	72	115	[	[	X
ejpam-5366	72	116	15	15	NUM
ejpam-5366	72	117	]	]	PUNCT
ejpam-5366	72	118	,	,	PUNCT
ejpam-5366	72	119	[	[	X
ejpam-5366	72	120	16	16	NUM
ejpam-5366	72	121	]	]	PUNCT
ejpam-5366	72	122	)	)	PUNCT
ejpam-5366	72	123	.	.	PUNCT
ejpam-5366	73	1	we	we	PRON
ejpam-5366	73	2	reinterpret	reinterpret	VERB
ejpam-5366	73	3	the	the	DET
ejpam-5366	73	4	smoking	smoking	NOUN
ejpam-5366	73	5	system	system	NOUN
ejpam-5366	73	6	in	in	ADP
ejpam-5366	73	7	terms	term	NOUN
ejpam-5366	73	8	of	of	ADP
ejpam-5366	73	9	fractional	fractional	ADJ
ejpam-5366	73	10	derivatives	derivative	NOUN
ejpam-5366	73	11	of	of	ADP
ejpam-5366	73	12	order	order	NOUN
ejpam-5366	73	13	α	α	X
ejpam-5366	73	14	∈	∈	PROPN
ejpam-5366	73	15	(	(	PUNCT
ejpam-5366	73	16	0	0	NUM
ejpam-5366	73	17	,	,	PUNCT
ejpam-5366	73	18	1	1	NUM
ejpam-5366	73	19	]	]	PUNCT
ejpam-5366	73	20	as	as	SCONJ
ejpam-5366	73	21	follows	follow	VERB
ejpam-5366	73	22	:	:	PUNCT
ejpam-5366	73	23	dαs1(t	dαs1(t	NUM
ejpam-5366	73	24	)	)	PUNCT
ejpam-5366	73	25	=	=	SYM
ejpam-5366	73	26	κ−	κ−	PROPN
ejpam-5366	73	27	ε1	ε1	VERB
ejpam-5366	73	28	s1(t)s2(t	s1(t)s2(t	PROPN
ejpam-5366	73	29	)	)	PUNCT
ejpam-5366	74	1	+	+	CCONJ
ejpam-5366	74	2	ω	ω	NUM
ejpam-5366	74	3	s4(t)−	s4(t)−	PROPN
ejpam-5366	74	4	µ	µ	X
ejpam-5366	74	5	s1(t	s1(t	X
ejpam-5366	74	6	)	)	PUNCT
ejpam-5366	74	7	,	,	PUNCT
ejpam-5366	74	8	dαs2(t	dαs2(t	NOUN
ejpam-5366	74	9	)	)	PUNCT
ejpam-5366	74	10	=	=	PUNCT
ejpam-5366	74	11	ε1	ε1	VERB
ejpam-5366	74	12	s1(t)s2(t)−	s1(t)s2(t)−	PROPN
ejpam-5366	74	13	ε2	ε2	PROPN
ejpam-5366	74	14	s2(t)s3(t)−	s2(t)s3(t)−	PROPN
ejpam-5366	74	15	(	(	PUNCT
ejpam-5366	74	16	κ1	κ1	NOUN
ejpam-5366	74	17	+	+	CCONJ
ejpam-5366	74	18	µ	µ	X
ejpam-5366	74	19	)	)	PUNCT
ejpam-5366	74	20	s2(t	s2(t	PROPN
ejpam-5366	74	21	)	)	PUNCT
ejpam-5366	74	22	,	,	PUNCT
ejpam-5366	74	23	dαs3(t	dαs3(t	VERB
ejpam-5366	74	24	)	)	PUNCT
ejpam-5366	74	25	=	=	SYM
ejpam-5366	74	26	ε2	ε2	ADJ
ejpam-5366	74	27	s2(t)s3(t)−	s2(t)s3(t)−	PROPN
ejpam-5366	74	28	(	(	PUNCT
ejpam-5366	74	29	φ+	φ+	NOUN
ejpam-5366	74	30	κ2	κ2	NOUN
ejpam-5366	74	31	+	+	CCONJ
ejpam-5366	74	32	µ	µ	X
ejpam-5366	74	33	)	)	PUNCT
ejpam-5366	74	34	s3(t	s3(t	NUM
ejpam-5366	74	35	)	)	PUNCT
ejpam-5366	74	36	)	)	PUNCT
ejpam-5366	74	37	,	,	PUNCT
ejpam-5366	74	38	dαs4(t	dαs4(t	NUM
ejpam-5366	74	39	)	)	PUNCT
ejpam-5366	74	40	=	=	SYM
ejpam-5366	74	41	φs3(t)−	φs3(t)−	PROPN
ejpam-5366	74	42	(	(	PUNCT
ejpam-5366	74	43	λ+	λ+	X
ejpam-5366	74	44	µ+	µ+	X
ejpam-5366	74	45	ω	ω	NOUN
ejpam-5366	74	46	)	)	PUNCT
ejpam-5366	74	47	s4(t	s4(t	PROPN
ejpam-5366	74	48	)	)	PUNCT
ejpam-5366	74	49	,	,	PUNCT
ejpam-5366	74	50	dαs5(t	dαs5(t	NUM
ejpam-5366	74	51	)	)	PUNCT
ejpam-5366	74	52	=	=	SYM
ejpam-5366	74	53	λs4(t)−	λs4(t)−	PROPN
ejpam-5366	74	54	µs5(t	µs5(t	PROPN
ejpam-5366	74	55	)	)	PUNCT
ejpam-5366	74	56	)	)	PUNCT
ejpam-5366	74	57	.	.	PUNCT
ejpam-5366	75	1	(	(	PUNCT
ejpam-5366	75	2	2	2	X
ejpam-5366	75	3	)	)	PUNCT
ejpam-5366	75	4	throughout	throughout	ADP
ejpam-5366	75	5	the	the	DET
ejpam-5366	75	6	examination	examination	NOUN
ejpam-5366	75	7	of	of	ADP
ejpam-5366	75	8	the	the	DET
ejpam-5366	75	9	model	model	NOUN
ejpam-5366	75	10	presented	present	VERB
ejpam-5366	75	11	in	in	ADP
ejpam-5366	75	12	(	(	PUNCT
ejpam-5366	75	13	2	2	NUM
ejpam-5366	75	14	)	)	PUNCT
ejpam-5366	75	15	,	,	PUNCT
ejpam-5366	75	16	the	the	DET
ejpam-5366	75	17	subsequent	subsequent	ADJ
ejpam-5366	75	18	approaches	approach	NOUN
ejpam-5366	75	19	will	will	AUX
ejpam-5366	75	20	be	be	AUX
ejpam-5366	75	21	employed	employ	VERB
ejpam-5366	75	22	.	.	PUNCT
ejpam-5366	76	1	we	we	PRON
ejpam-5366	76	2	will	will	AUX
ejpam-5366	76	3	provide	provide	VERB
ejpam-5366	76	4	the	the	DET
ejpam-5366	76	5	necessary	necessary	ADJ
ejpam-5366	76	6	definitions	definition	NOUN
ejpam-5366	76	7	in	in	ADP
ejpam-5366	76	8	the	the	DET
ejpam-5366	76	9	next	next	ADJ
ejpam-5366	76	10	sections	section	NOUN
ejpam-5366	76	11	.	.	PUNCT
ejpam-5366	77	1	the	the	DET
ejpam-5366	77	2	advanced	advanced	ADJ
ejpam-5366	77	3	portions	portion	NOUN
ejpam-5366	77	4	will	will	AUX
ejpam-5366	77	5	then	then	ADV
ejpam-5366	77	6	contain	contain	VERB
ejpam-5366	77	7	numerical	numerical	ADJ
ejpam-5366	77	8	results	result	NOUN
ejpam-5366	77	9	,	,	PUNCT
ejpam-5366	77	10	simulations	simulation	NOUN
ejpam-5366	77	11	,	,	PUNCT
ejpam-5366	77	12	and	and	CCONJ
ejpam-5366	77	13	a	a	DET
ejpam-5366	77	14	conclusion	conclusion	NOUN
ejpam-5366	77	15	.	.	PUNCT
ejpam-5366	78	1	this	this	DET
ejpam-5366	78	2	study	study	NOUN
ejpam-5366	78	3	’s	’s	PART
ejpam-5366	78	4	primary	primary	ADJ
ejpam-5366	78	5	goal	goal	NOUN
ejpam-5366	78	6	is	be	AUX
ejpam-5366	78	7	to	to	PART
ejpam-5366	78	8	examine	examine	VERB
ejpam-5366	78	9	the	the	DET
ejpam-5366	78	10	model	model	NOUN
ejpam-5366	78	11	under	under	ADP
ejpam-5366	78	12	the	the	DET
ejpam-5366	78	13	fractional	fractional	ADJ
ejpam-5366	78	14	derivative	derivative	NOUN
ejpam-5366	78	15	.	.	PUNCT
ejpam-5366	79	1	4	4	X
ejpam-5366	79	2	.	.	NUM
ejpam-5366	79	3	modified	modify	VERB
ejpam-5366	79	4	fractional	fractional	PROPN
ejpam-5366	79	5	euler	euler	NOUN
ejpam-5366	79	6	method	method	NOUN
ejpam-5366	79	7	theorem	theorem	VERB
ejpam-5366	79	8	1	1	NUM
ejpam-5366	79	9	.	.	X
ejpam-5366	79	10	for	for	ADP
ejpam-5366	79	11	the	the	DET
ejpam-5366	79	12	function	function	NOUN
ejpam-5366	79	13	ψ(t	ψ(t	PROPN
ejpam-5366	79	14	)	)	PUNCT
ejpam-5366	79	15	which	which	PRON
ejpam-5366	79	16	satisfies	satisfy	VERB
ejpam-5366	79	17	the	the	DET
ejpam-5366	79	18	condition	condition	NOUN
ejpam-5366	79	19	dkαψ(t	dkαψ(t	PROPN
ejpam-5366	79	20	)	)	PUNCT
ejpam-5366	79	21	∈	∈	PROPN
ejpam-5366	79	22	c(0	c(0	PROPN
ejpam-5366	79	23	,	,	PUNCT
ejpam-5366	79	24	a	a	DET
ejpam-5366	79	25	]	]	X
ejpam-5366	79	26	,	,	PUNCT
ejpam-5366	79	27	for	for	ADP
ejpam-5366	79	28	k	k	PROPN
ejpam-5366	79	29	=	=	SYM
ejpam-5366	79	30	0	0	NUM
ejpam-5366	79	31	,	,	PUNCT
ejpam-5366	79	32	1	1	NUM
ejpam-5366	79	33	,	,	PUNCT
ejpam-5366	79	34	...	...	PUNCT
ejpam-5366	79	35	,	,	PUNCT
ejpam-5366	79	36	n+	n+	PUNCT
ejpam-5366	79	37	1	1	NUM
ejpam-5366	79	38	,	,	PUNCT
ejpam-5366	79	39	where	where	SCONJ
ejpam-5366	79	40	0	0	X
ejpam-5366	79	41	<	<	X
ejpam-5366	79	42	α	α	X
ejpam-5366	79	43	≤	≤	ADJ
ejpam-5366	79	44	1	1	NUM
ejpam-5366	79	45	.	.	PUNCT
ejpam-5366	80	1	then	then	ADV
ejpam-5366	80	2	the	the	DET
ejpam-5366	80	3	generalization	generalization	NOUN
ejpam-5366	80	4	of	of	ADP
ejpam-5366	80	5	taylor	taylor	PROPN
ejpam-5366	80	6	’s	’s	PART
ejpam-5366	80	7	formula	formula	NOUN
ejpam-5366	80	8	that	that	PRON
ejpam-5366	80	9	involves	involve	VERB
ejpam-5366	80	10	liouville	liouville	PROPN
ejpam-5366	80	11	-	-	PUNCT
ejpam-5366	80	12	caputo	caputo	NOUN
ejpam-5366	80	13	fractional	fractional	ADJ
ejpam-5366	80	14	derivatives	derivative	NOUN
ejpam-5366	80	15	can	can	AUX
ejpam-5366	80	16	be	be	AUX
ejpam-5366	80	17	defined	define	VERB
ejpam-5366	80	18	as	as	SCONJ
ejpam-5366	80	19	follows	follow	VERB
ejpam-5366	80	20	[	[	X
ejpam-5366	80	21	18	18	NUM
ejpam-5366	80	22	]	]	PUNCT
ejpam-5366	80	23	:	:	PUNCT
ejpam-5366	80	24	ψ(t	ψ(t	PROPN
ejpam-5366	80	25	)	)	PUNCT
ejpam-5366	81	1	=	=	SYM
ejpam-5366	81	2	n∑	n∑	PROPN
ejpam-5366	81	3	i=0	i=0	PROPN
ejpam-5366	81	4	tiα	tiα	VERB
ejpam-5366	81	5	γ(iα+	γ(iα+	ADJ
ejpam-5366	81	6	1	1	NUM
ejpam-5366	81	7	)	)	PUNCT
ejpam-5366	81	8	diαψ(0	diαψ(0	NOUN
ejpam-5366	81	9	+	+	NOUN
ejpam-5366	81	10	)	)	PUNCT
ejpam-5366	81	11	+	+	CCONJ
ejpam-5366	81	12	d(n+1)αψ(ξ	d(n+1)αψ(ξ	X
ejpam-5366	81	13	)	)	PUNCT
ejpam-5366	81	14	γ((n+	γ((n+	NOUN
ejpam-5366	81	15	1)α+	1)α+	NUM
ejpam-5366	81	16	1	1	NUM
ejpam-5366	81	17	)	)	PUNCT
ejpam-5366	81	18	t(n+1)α	t(n+1)α	VERB
ejpam-5366	81	19	,	,	PUNCT
ejpam-5366	81	20	0	0	NUM
ejpam-5366	81	21	≤	≤	NUM
ejpam-5366	81	22	ξ	ξ	PROPN
ejpam-5366	81	23	≤	≤	PROPN
ejpam-5366	81	24	t	t	PROPN
ejpam-5366	81	25	,	,	PUNCT
ejpam-5366	81	26	∀	∀	X
ejpam-5366	81	27	t	t	NOUN
ejpam-5366	81	28	∈	∈	PROPN
ejpam-5366	81	29	(	(	PUNCT
ejpam-5366	81	30	0	0	NUM
ejpam-5366	81	31	,	,	PUNCT
ejpam-5366	81	32	a	a	PRON
ejpam-5366	81	33	]	]	X
ejpam-5366	81	34	.	.	PUNCT
ejpam-5366	82	1	(	(	PUNCT
ejpam-5366	82	2	3	3	X
ejpam-5366	82	3	)	)	PUNCT
ejpam-5366	82	4	m.	m.	NOUN
ejpam-5366	82	5	m.	m.	NOUN
ejpam-5366	82	6	khader	khader	PROPN
ejpam-5366	82	7	/	/	SYM
ejpam-5366	82	8	eur	eur	PROPN
ejpam-5366	82	9	.	.	PUNCT
ejpam-5366	83	1	j.	j.	PROPN
ejpam-5366	83	2	pure	pure	PROPN
ejpam-5366	83	3	appl	appl	PROPN
ejpam-5366	83	4	.	.	PROPN
ejpam-5366	83	5	math	math	PROPN
ejpam-5366	83	6	,	,	PUNCT
ejpam-5366	83	7	17	17	NUM
ejpam-5366	83	8	(	(	PUNCT
ejpam-5366	83	9	4	4	NUM
ejpam-5366	83	10	)	)	PUNCT
ejpam-5366	83	11	(	(	PUNCT
ejpam-5366	83	12	2024	2024	NUM
ejpam-5366	83	13	)	)	PUNCT
ejpam-5366	83	14	,	,	PUNCT
ejpam-5366	83	15	2676	2676	NUM
ejpam-5366	83	16	-	-	SYM
ejpam-5366	83	17	2691	2691	NUM
ejpam-5366	83	18	2680	2680	NUM
ejpam-5366	83	19	the	the	DET
ejpam-5366	83	20	classical	classical	ADJ
ejpam-5366	83	21	taylor	taylor	PROPN
ejpam-5366	83	22	’s	’s	PART
ejpam-5366	83	23	formula	formula	NOUN
ejpam-5366	84	1	[	[	X
ejpam-5366	84	2	5	5	NUM
ejpam-5366	84	3	]	]	PUNCT
ejpam-5366	84	4	can	can	AUX
ejpam-5366	84	5	be	be	AUX
ejpam-5366	84	6	obtained	obtain	VERB
ejpam-5366	84	7	from	from	ADP
ejpam-5366	84	8	this	this	DET
ejpam-5366	84	9	formula	formula	NOUN
ejpam-5366	84	10	(	(	PUNCT
ejpam-5366	84	11	3	3	NUM
ejpam-5366	84	12	)	)	PUNCT
ejpam-5366	84	13	at	at	ADP
ejpam-5366	84	14	α	α	NOUN
ejpam-5366	84	15	=	=	SYM
ejpam-5366	84	16	1	1	X
ejpam-5366	84	17	.	.	PUNCT
ejpam-5366	85	1	now	now	ADV
ejpam-5366	85	2	,	,	PUNCT
ejpam-5366	85	3	we	we	PRON
ejpam-5366	85	4	introduce	introduce	VERB
ejpam-5366	85	5	the	the	DET
ejpam-5366	85	6	generalized	generalize	VERB
ejpam-5366	85	7	euler	euler	NOUN
ejpam-5366	85	8	’s	’s	PART
ejpam-5366	85	9	method	method	NOUN
ejpam-5366	85	10	(	(	PUNCT
ejpam-5366	85	11	gem	gem	NOUN
ejpam-5366	85	12	)	)	PUNCT
ejpam-5366	85	13	which	which	PRON
ejpam-5366	85	14	was	be	AUX
ejpam-5366	85	15	derived	derive	VERB
ejpam-5366	85	16	by	by	ADP
ejpam-5366	85	17	zaid	zaid	PROPN
ejpam-5366	85	18	and	and	CCONJ
ejpam-5366	85	19	momani	momani	X
ejpam-5366	85	20	[	[	X
ejpam-5366	85	21	18	18	NUM
ejpam-5366	85	22	]	]	PUNCT
ejpam-5366	85	23	.	.	PUNCT
ejpam-5366	86	1	consider	consider	VERB
ejpam-5366	86	2	the	the	DET
ejpam-5366	86	3	following	follow	VERB
ejpam-5366	86	4	general	general	ADJ
ejpam-5366	86	5	form	form	NOUN
ejpam-5366	86	6	of	of	ADP
ejpam-5366	86	7	the	the	DET
ejpam-5366	86	8	initial	initial	ADJ
ejpam-5366	86	9	value	value	NOUN
ejpam-5366	86	10	problem	problem	NOUN
ejpam-5366	86	11	(	(	PUNCT
ejpam-5366	86	12	ivp	ivp	NOUN
ejpam-5366	86	13	)	)	PUNCT
ejpam-5366	86	14	in	in	ADP
ejpam-5366	86	15	the	the	DET
ejpam-5366	86	16	interval	interval	NOUN
ejpam-5366	86	17	[	[	X
ejpam-5366	86	18	0	0	NUM
ejpam-5366	86	19	,	,	PUNCT
ejpam-5366	86	20	t	t	X
ejpam-5366	86	21	]	]	PUNCT
ejpam-5366	86	22	with	with	ADP
ejpam-5366	86	23	liouville	liouville	PROPN
ejpam-5366	86	24	-	-	PUNCT
ejpam-5366	86	25	caputo	caputo	NOUN
ejpam-5366	86	26	derivatives	derivative	NOUN
ejpam-5366	86	27	of	of	ADP
ejpam-5366	86	28	order	order	NOUN
ejpam-5366	86	29	0	0	PUNCT
ejpam-5366	86	30	<	<	X
ejpam-5366	86	31	α	α	PROPN
ejpam-5366	86	32	≤	≤	NUM
ejpam-5366	86	33	1	1	NUM
ejpam-5366	87	1	[	[	X
ejpam-5366	87	2	18	18	NUM
ejpam-5366	87	3	]	]	SYM
ejpam-5366	87	4	:	:	PUNCT
ejpam-5366	87	5	dαz(t	dαz(t	X
ejpam-5366	87	6	)	)	PUNCT
ejpam-5366	87	7	=	=	SYM
ejpam-5366	87	8	g(t	g(t	PROPN
ejpam-5366	87	9	,	,	PUNCT
ejpam-5366	87	10	z(t	z(t	NOUN
ejpam-5366	87	11	)	)	PUNCT
ejpam-5366	87	12	)	)	PUNCT
ejpam-5366	87	13	,	,	PUNCT
ejpam-5366	87	14	z(0	z(0	X
ejpam-5366	87	15	)	)	PUNCT
ejpam-5366	87	16	=	=	SYM
ejpam-5366	87	17	z0	z0	PROPN
ejpam-5366	87	18	.	.	PUNCT
ejpam-5366	88	1	(	(	PUNCT
ejpam-5366	88	2	4	4	NUM
ejpam-5366	88	3	)	)	PUNCT
ejpam-5366	88	4	to	to	PART
ejpam-5366	88	5	get	get	VERB
ejpam-5366	88	6	the	the	DET
ejpam-5366	88	7	required	require	VERB
ejpam-5366	88	8	scheme	scheme	NOUN
ejpam-5366	88	9	of	of	ADP
ejpam-5366	88	10	the	the	DET
ejpam-5366	88	11	gem	gem	NOUN
ejpam-5366	88	12	,	,	PUNCT
ejpam-5366	88	13	we	we	PRON
ejpam-5366	88	14	follow	follow	VERB
ejpam-5366	88	15	the	the	DET
ejpam-5366	88	16	following	follow	VERB
ejpam-5366	88	17	steps	step	NOUN
ejpam-5366	88	18	:	:	PUNCT
ejpam-5366	88	19	(	(	PUNCT
ejpam-5366	88	20	i	i	NOUN
ejpam-5366	88	21	)	)	PUNCT
ejpam-5366	88	22	divide	divide	VERB
ejpam-5366	88	23	the	the	DET
ejpam-5366	88	24	interval	interval	NOUN
ejpam-5366	88	25	[	[	X
ejpam-5366	88	26	0	0	NUM
ejpam-5366	88	27	,	,	PUNCT
ejpam-5366	88	28	t	t	NOUN
ejpam-5366	88	29	]	]	PUNCT
ejpam-5366	88	30	into	into	ADP
ejpam-5366	88	31	n	n	ADP
ejpam-5366	88	32	subintervals	subinterval	NOUN
ejpam-5366	88	33	[	[	X
ejpam-5366	88	34	tj	tj	X
ejpam-5366	88	35	,	,	PUNCT
ejpam-5366	88	36	tj+1	tj+1	PROPN
ejpam-5366	88	37	]	]	PUNCT
ejpam-5366	88	38	of	of	ADP
ejpam-5366	88	39	equal	equal	ADJ
ejpam-5366	88	40	width	width	NOUN
ejpam-5366	88	41	(	(	PUNCT
ejpam-5366	88	42	step	step	NOUN
ejpam-5366	88	43	size	size	NOUN
ejpam-5366	88	44	)	)	PUNCT
ejpam-5366	89	1	h	h	NOUN
ejpam-5366	89	2	=	=	SYM
ejpam-5366	89	3	t	t	PROPN
ejpam-5366	89	4	/	/	SYM
ejpam-5366	89	5	n	n	NOUN
ejpam-5366	89	6	with	with	ADP
ejpam-5366	89	7	nodes	node	NOUN
ejpam-5366	89	8	tj+1	tj+1	ADJ
ejpam-5366	89	9	=	=	SYM
ejpam-5366	89	10	tj	tj	NOUN
ejpam-5366	90	1	+	+	PROPN
ejpam-5366	90	2	h	h	NOUN
ejpam-5366	90	3	,	,	PUNCT
ejpam-5366	90	4	for	for	ADP
ejpam-5366	90	5	j	j	PROPN
ejpam-5366	90	6	=	=	SYM
ejpam-5366	90	7	0	0	PROPN
ejpam-5366	90	8	,	,	PUNCT
ejpam-5366	90	9	1	1	NUM
ejpam-5366	90	10	,	,	PUNCT
ejpam-5366	90	11	...	...	PUNCT
ejpam-5366	90	12	,	,	PUNCT
ejpam-5366	90	13	n.	n.	PROPN
ejpam-5366	90	14	(	(	PUNCT
ejpam-5366	90	15	ii	ii	NOUN
ejpam-5366	90	16	)	)	PUNCT
ejpam-5366	90	17	assume	assume	VERB
ejpam-5366	90	18	that	that	SCONJ
ejpam-5366	90	19	dℓ	dℓ	NOUN
ejpam-5366	90	20	αz(t	αz(t	NOUN
ejpam-5366	90	21	)	)	PUNCT
ejpam-5366	90	22	,	,	PUNCT
ejpam-5366	90	23	ℓ	ℓ	X
ejpam-5366	90	24	=	=	SYM
ejpam-5366	90	25	0	0	NUM
ejpam-5366	90	26	,	,	PUNCT
ejpam-5366	90	27	1	1	NUM
ejpam-5366	90	28	,	,	PUNCT
ejpam-5366	90	29	2	2	NUM
ejpam-5366	90	30	are	be	AUX
ejpam-5366	90	31	continuous	continuous	ADJ
ejpam-5366	90	32	on	on	ADP
ejpam-5366	90	33	[	[	X
ejpam-5366	90	34	0	0	NUM
ejpam-5366	90	35	,	,	PUNCT
ejpam-5366	90	36	t	t	X
ejpam-5366	90	37	]	]	PUNCT
ejpam-5366	90	38	.	.	PUNCT
ejpam-5366	91	1	(	(	PUNCT
ejpam-5366	91	2	iii	iii	X
ejpam-5366	91	3	)	)	PUNCT
ejpam-5366	91	4	use	use	VERB
ejpam-5366	91	5	the	the	DET
ejpam-5366	91	6	generalized	generalized	ADJ
ejpam-5366	91	7	taylor	taylor	PROPN
ejpam-5366	91	8	’s	’s	PART
ejpam-5366	91	9	formula	formula	NOUN
ejpam-5366	91	10	(	(	PUNCT
ejpam-5366	91	11	3	3	NUM
ejpam-5366	91	12	)	)	PUNCT
ejpam-5366	91	13	to	to	PART
ejpam-5366	91	14	expand	expand	VERB
ejpam-5366	91	15	z(t	z(t	NOUN
ejpam-5366	91	16	)	)	PUNCT
ejpam-5366	91	17	about	about	ADP
ejpam-5366	91	18	t	t	NOUN
ejpam-5366	91	19	=	=	SYM
ejpam-5366	91	20	t0	t0	PROPN
ejpam-5366	91	21	=	=	SYM
ejpam-5366	91	22	0	0	PUNCT
ejpam-5366	91	23	as	as	SCONJ
ejpam-5366	91	24	follows	follow	VERB
ejpam-5366	91	25	:	:	PUNCT
ejpam-5366	91	26	z(t	z(t	X
ejpam-5366	91	27	)	)	PUNCT
ejpam-5366	91	28	=	=	SYM
ejpam-5366	91	29	z(t0	z(t0	NOUN
ejpam-5366	91	30	)	)	PUNCT
ejpam-5366	92	1	+	+	CCONJ
ejpam-5366	92	2	dαz(t0	dαz(t0	NOUN
ejpam-5366	92	3	)	)	PUNCT
ejpam-5366	92	4	γ(α+	γ(α+	DET
ejpam-5366	92	5	1	1	NUM
ejpam-5366	92	6	)	)	PUNCT
ejpam-5366	92	7	tα	tα	PROPN
ejpam-5366	92	8	+	+	CCONJ
ejpam-5366	92	9	d2αz(c1	d2αz(c1	PROPN
ejpam-5366	92	10	)	)	PUNCT
ejpam-5366	92	11	γ(2α+	γ(2α+	NOUN
ejpam-5366	92	12	1	1	NUM
ejpam-5366	92	13	)	)	PUNCT
ejpam-5366	92	14	t2α	t2α	NUM
ejpam-5366	92	15	,	,	PUNCT
ejpam-5366	92	16	0	0	NUM
ejpam-5366	92	17	<	<	X
ejpam-5366	92	18	c1	c1	PROPN
ejpam-5366	92	19	<	<	X
ejpam-5366	92	20	t.	t.	PROPN
ejpam-5366	92	21	(	(	PUNCT
ejpam-5366	92	22	5	5	NUM
ejpam-5366	92	23	)	)	PUNCT
ejpam-5366	92	24	(	(	PUNCT
ejpam-5366	92	25	iv	iv	X
ejpam-5366	92	26	)	)	PUNCT
ejpam-5366	92	27	substitute	substitute	NOUN
ejpam-5366	92	28	by	by	ADP
ejpam-5366	92	29	dαz(t0	dαz(t0	NOUN
ejpam-5366	92	30	)	)	PUNCT
ejpam-5366	92	31	=	=	SYM
ejpam-5366	92	32	g(t0	g(t0	NOUN
ejpam-5366	92	33	,	,	PUNCT
ejpam-5366	92	34	z(t0	z(t0	NOUN
ejpam-5366	92	35	)	)	PUNCT
ejpam-5366	92	36	)	)	PUNCT
ejpam-5366	93	1	and	and	CCONJ
ejpam-5366	93	2	h	h	NOUN
ejpam-5366	93	3	=	=	NOUN
ejpam-5366	93	4	t1	t1	NOUN
ejpam-5366	93	5	−	−	PROPN
ejpam-5366	93	6	t0	t0	PROPN
ejpam-5366	93	7	in	in	ADP
ejpam-5366	93	8	equation	equation	NOUN
ejpam-5366	93	9	(	(	PUNCT
ejpam-5366	93	10	5	5	NUM
ejpam-5366	93	11	)	)	PUNCT
ejpam-5366	93	12	,	,	PUNCT
ejpam-5366	93	13	to	to	PART
ejpam-5366	93	14	get	get	VERB
ejpam-5366	93	15	the	the	DET
ejpam-5366	93	16	following	follow	VERB
ejpam-5366	93	17	expression	expression	NOUN
ejpam-5366	93	18	for	for	ADP
ejpam-5366	93	19	z(t1	z(t1	PROPN
ejpam-5366	93	20	):	):	PUNCT
ejpam-5366	93	21	z(t1	z(t1	X
ejpam-5366	93	22	)	)	PUNCT
ejpam-5366	94	1	=	=	SYM
ejpam-5366	94	2	z(t0	z(t0	NOUN
ejpam-5366	94	3	)	)	PUNCT
ejpam-5366	95	1	+	+	CCONJ
ejpam-5366	95	2	g(t0	g(t0	NOUN
ejpam-5366	95	3	,	,	PUNCT
ejpam-5366	95	4	z(t0	z(t0	NOUN
ejpam-5366	95	5	)	)	PUNCT
ejpam-5366	95	6	)	)	PUNCT
ejpam-5366	95	7	hα	hα	ADP
ejpam-5366	95	8	γ(α+	γ(α+	DET
ejpam-5366	95	9	1	1	NUM
ejpam-5366	95	10	)	)	PUNCT
ejpam-5366	95	11	+	+	NOUN
ejpam-5366	95	12	d2αz(c1	d2αz(c1	NOUN
ejpam-5366	95	13	)	)	PUNCT
ejpam-5366	95	14	h2α	h2α	PROPN
ejpam-5366	95	15	γ(2α+	γ(2α+	PROPN
ejpam-5366	95	16	1	1	NUM
ejpam-5366	95	17	)	)	PUNCT
ejpam-5366	95	18	.	.	PUNCT
ejpam-5366	96	1	(	(	PUNCT
ejpam-5366	96	2	v	v	X
ejpam-5366	96	3	)	)	PUNCT
ejpam-5366	96	4	if	if	SCONJ
ejpam-5366	96	5	we	we	PRON
ejpam-5366	96	6	choose	choose	VERB
ejpam-5366	96	7	h	h	NOUN
ejpam-5366	96	8	small	small	ADJ
ejpam-5366	96	9	enough	enough	ADV
ejpam-5366	96	10	,	,	PUNCT
ejpam-5366	96	11	then	then	ADV
ejpam-5366	96	12	we	we	PRON
ejpam-5366	96	13	may	may	AUX
ejpam-5366	96	14	neglect	neglect	VERB
ejpam-5366	96	15	the	the	DET
ejpam-5366	96	16	second	second	ADJ
ejpam-5366	96	17	-	-	PUNCT
ejpam-5366	96	18	order	order	NOUN
ejpam-5366	96	19	term	term	NOUN
ejpam-5366	96	20	(	(	PUNCT
ejpam-5366	96	21	involving	involve	VERB
ejpam-5366	96	22	h2α	h2α	NOUN
ejpam-5366	96	23	)	)	PUNCT
ejpam-5366	96	24	in	in	ADP
ejpam-5366	96	25	the	the	DET
ejpam-5366	96	26	previous	previous	ADJ
ejpam-5366	96	27	expansion	expansion	NOUN
ejpam-5366	96	28	and	and	CCONJ
ejpam-5366	96	29	get	get	VERB
ejpam-5366	96	30	the	the	DET
ejpam-5366	96	31	following	follow	VERB
ejpam-5366	96	32	approximation	approximation	NOUN
ejpam-5366	96	33	:	:	PUNCT
ejpam-5366	96	34	z(t1	z(t1	X
ejpam-5366	96	35	)	)	PUNCT
ejpam-5366	97	1	=	=	SYM
ejpam-5366	97	2	z(t0	z(t0	NOUN
ejpam-5366	97	3	)	)	PUNCT
ejpam-5366	98	1	+	+	CCONJ
ejpam-5366	98	2	g(t0	g(t0	NOUN
ejpam-5366	98	3	,	,	PUNCT
ejpam-5366	98	4	z(t0	z(t0	NOUN
ejpam-5366	98	5	)	)	PUNCT
ejpam-5366	98	6	)	)	PUNCT
ejpam-5366	98	7	hα	hα	ADP
ejpam-5366	98	8	γ(α+	γ(α+	DET
ejpam-5366	98	9	1	1	NUM
ejpam-5366	98	10	)	)	PUNCT
ejpam-5366	98	11	.	.	PUNCT
ejpam-5366	99	1	(	(	PUNCT
ejpam-5366	99	2	vi	vi	X
ejpam-5366	99	3	)	)	PUNCT
ejpam-5366	99	4	repeat	repeat	VERB
ejpam-5366	99	5	the	the	DET
ejpam-5366	99	6	above	above	ADJ
ejpam-5366	99	7	process	process	NOUN
ejpam-5366	99	8	to	to	PART
ejpam-5366	99	9	generate	generate	VERB
ejpam-5366	99	10	a	a	DET
ejpam-5366	99	11	sequence	sequence	NOUN
ejpam-5366	99	12	of	of	ADP
ejpam-5366	99	13	points	point	NOUN
ejpam-5366	99	14	zj	zj	PROPN
ejpam-5366	99	15	=	=	SYM
ejpam-5366	99	16	z(tj	z(tj	NUM
ejpam-5366	99	17	)	)	PUNCT
ejpam-5366	99	18	that	that	PRON
ejpam-5366	99	19	approximates	approximate	VERB
ejpam-5366	99	20	the	the	DET
ejpam-5366	99	21	solution	solution	NOUN
ejpam-5366	99	22	z(t	z(t	NOUN
ejpam-5366	99	23	)	)	PUNCT
ejpam-5366	99	24	at	at	ADP
ejpam-5366	99	25	the	the	DET
ejpam-5366	99	26	nodes	node	NOUN
ejpam-5366	99	27	tj	tj	NOUN
ejpam-5366	99	28	,	,	PUNCT
ejpam-5366	99	29	j	j	PROPN
ejpam-5366	100	1	=	=	SYM
ejpam-5366	100	2	0	0	NUM
ejpam-5366	100	3	,	,	PUNCT
ejpam-5366	100	4	1	1	NUM
ejpam-5366	100	5	,	,	PUNCT
ejpam-5366	100	6	2	2	NUM
ejpam-5366	100	7	,	,	PUNCT
ejpam-5366	100	8	...	...	PUNCT
ejpam-5366	100	9	.	.	PUNCT
ejpam-5366	101	1	the	the	DET
ejpam-5366	101	2	general	general	ADJ
ejpam-5366	101	3	formula	formula	NOUN
ejpam-5366	101	4	for	for	ADP
ejpam-5366	101	5	the	the	DET
ejpam-5366	101	6	gem	gem	NOUN
ejpam-5366	101	7	is	be	AUX
ejpam-5366	101	8	given	give	VERB
ejpam-5366	101	9	as	as	SCONJ
ejpam-5366	101	10	follows	follow	VERB
ejpam-5366	101	11	:	:	PUNCT
ejpam-5366	101	12	z(tj+1	z(tj+1	X
ejpam-5366	101	13	)	)	PUNCT
ejpam-5366	101	14	=	=	SYM
ejpam-5366	101	15	z(tj	z(tj	NUM
ejpam-5366	101	16	)	)	PUNCT
ejpam-5366	102	1	+	+	CCONJ
ejpam-5366	102	2	g(tj	g(tj	PROPN
ejpam-5366	102	3	,	,	PUNCT
ejpam-5366	102	4	z(tj	z(tj	NUM
ejpam-5366	102	5	)	)	PUNCT
ejpam-5366	102	6	)	)	PUNCT
ejpam-5366	103	1	hα	hα	ADP
ejpam-5366	103	2	γ(α+	γ(α+	DET
ejpam-5366	103	3	1	1	NUM
ejpam-5366	103	4	)	)	PUNCT
ejpam-5366	103	5	,	,	PUNCT
ejpam-5366	103	6	j	j	PROPN
ejpam-5366	103	7	=	=	SYM
ejpam-5366	103	8	0	0	NUM
ejpam-5366	103	9	,	,	PUNCT
ejpam-5366	103	10	1	1	NUM
ejpam-5366	103	11	,	,	PUNCT
ejpam-5366	103	12	...	...	PUNCT
ejpam-5366	103	13	,	,	PUNCT
ejpam-5366	103	14	n−	n−	NOUN
ejpam-5366	103	15	1	1	NUM
ejpam-5366	103	16	.	.	PUNCT
ejpam-5366	104	1	(	(	PUNCT
ejpam-5366	104	2	6	6	NUM
ejpam-5366	104	3	)	)	PUNCT
ejpam-5366	104	4	(	(	PUNCT
ejpam-5366	104	5	vii	vii	PROPN
ejpam-5366	104	6	)	)	PUNCT
ejpam-5366	104	7	apply	apply	VERB
ejpam-5366	104	8	the	the	DET
ejpam-5366	104	9	developed	developed	ADJ
ejpam-5366	104	10	a	a	DET
ejpam-5366	104	11	new	new	ADJ
ejpam-5366	104	12	modification	modification	NOUN
ejpam-5366	104	13	in	in	ADP
ejpam-5366	104	14	[	[	X
ejpam-5366	104	15	6	6	NUM
ejpam-5366	104	16	]	]	PUNCT
ejpam-5366	104	17	,	,	PUNCT
ejpam-5366	104	18	to	to	PART
ejpam-5366	104	19	obtain	obtain	VERB
ejpam-5366	104	20	the	the	DET
ejpam-5366	104	21	general	general	ADJ
ejpam-5366	104	22	form	form	NOUN
ejpam-5366	104	23	of	of	ADP
ejpam-5366	104	24	the	the	DET
ejpam-5366	104	25	scheme	scheme	NOUN
ejpam-5366	104	26	of	of	ADP
ejpam-5366	104	27	the	the	DET
ejpam-5366	104	28	mfem	mfem	NOUN
ejpam-5366	104	29	for	for	ADP
ejpam-5366	104	30	solving	solve	VERB
ejpam-5366	104	31	fractional	fractional	ADJ
ejpam-5366	104	32	ivp	ivp	NOUN
ejpam-5366	104	33	(	(	PUNCT
ejpam-5366	104	34	4	4	NUM
ejpam-5366	104	35	)	)	PUNCT
ejpam-5366	104	36	as	as	SCONJ
ejpam-5366	104	37	follows	follow	VERB
ejpam-5366	104	38	:	:	PUNCT
ejpam-5366	104	39	z(tj+1	z(tj+1	X
ejpam-5366	104	40	)	)	PUNCT
ejpam-5366	104	41	=	=	PUNCT
ejpam-5366	105	1	z(tj)+	z(tj)+	PUNCT
ejpam-5366	105	2	hα	hα	ADP
ejpam-5366	105	3	γ(α+	γ(α+	DET
ejpam-5366	105	4	1	1	NUM
ejpam-5366	105	5	)	)	PUNCT
ejpam-5366	105	6	g	g	NOUN
ejpam-5366	105	7	(	(	PUNCT
ejpam-5366	105	8	tj	tj	NOUN
ejpam-5366	105	9	+	+	NOUN
ejpam-5366	105	10	hα	hα	ADP
ejpam-5366	105	11	2γ(α+	2γ(α+	PROPN
ejpam-5366	105	12	1	1	NUM
ejpam-5366	105	13	)	)	PUNCT
ejpam-5366	105	14	,	,	PUNCT
ejpam-5366	105	15	z(tj	z(tj	NUM
ejpam-5366	105	16	)	)	PUNCT
ejpam-5366	105	17	+	+	CCONJ
ejpam-5366	105	18	hα	hα	ADP
ejpam-5366	105	19	2γ(α+	2γ(α+	NUM
ejpam-5366	105	20	1	1	NUM
ejpam-5366	105	21	)	)	PUNCT
ejpam-5366	105	22	g(tj	g(tj	PROPN
ejpam-5366	105	23	,	,	PUNCT
ejpam-5366	105	24	z(tj	z(tj	NUM
ejpam-5366	105	25	)	)	PUNCT
ejpam-5366	105	26	)	)	PUNCT
ejpam-5366	105	27	.	.	PUNCT
ejpam-5366	106	1	j	j	X
ejpam-5366	106	2	=	=	SYM
ejpam-5366	106	3	0	0	PROPN
ejpam-5366	106	4	,	,	PUNCT
ejpam-5366	106	5	1	1	NUM
ejpam-5366	106	6	,	,	PUNCT
ejpam-5366	106	7	...	...	PUNCT
ejpam-5366	106	8	,	,	PUNCT
ejpam-5366	106	9	n−1	n−1	PROPN
ejpam-5366	106	10	.	.	PROPN
ejpam-5366	107	1	(	(	PUNCT
ejpam-5366	107	2	7	7	X
ejpam-5366	107	3	)	)	PUNCT
ejpam-5366	107	4	m.	m.	NOUN
ejpam-5366	107	5	m.	m.	NOUN
ejpam-5366	107	6	khader	khader	PROPN
ejpam-5366	107	7	/	/	SYM
ejpam-5366	107	8	eur	eur	PROPN
ejpam-5366	107	9	.	.	PUNCT
ejpam-5366	108	1	j.	j.	PROPN
ejpam-5366	108	2	pure	pure	PROPN
ejpam-5366	108	3	appl	appl	PROPN
ejpam-5366	108	4	.	.	PROPN
ejpam-5366	108	5	math	math	PROPN
ejpam-5366	108	6	,	,	PUNCT
ejpam-5366	108	7	17	17	NUM
ejpam-5366	108	8	(	(	PUNCT
ejpam-5366	108	9	4	4	NUM
ejpam-5366	108	10	)	)	PUNCT
ejpam-5366	108	11	(	(	PUNCT
ejpam-5366	108	12	2024	2024	NUM
ejpam-5366	108	13	)	)	PUNCT
ejpam-5366	108	14	,	,	PUNCT
ejpam-5366	108	15	2676	2676	NUM
ejpam-5366	108	16	-	-	SYM
ejpam-5366	108	17	2691	2691	NUM
ejpam-5366	108	18	2681	2681	NUM
ejpam-5366	108	19	the	the	DET
ejpam-5366	108	20	upper	upper	ADJ
ejpam-5366	108	21	bound	bind	VERB
ejpam-5366	108	22	of	of	ADP
ejpam-5366	108	23	the	the	DET
ejpam-5366	108	24	error	error	NOUN
ejpam-5366	108	25	generated	generate	VERB
ejpam-5366	108	26	by	by	ADP
ejpam-5366	108	27	the	the	DET
ejpam-5366	108	28	given	give	VERB
ejpam-5366	108	29	numerical	numerical	ADJ
ejpam-5366	108	30	scheme	scheme	NOUN
ejpam-5366	108	31	(	(	PUNCT
ejpam-5366	108	32	7	7	X
ejpam-5366	108	33	)	)	PUNCT
ejpam-5366	108	34	will	will	AUX
ejpam-5366	108	35	be	be	AUX
ejpam-5366	108	36	estimated	estimate	VERB
ejpam-5366	108	37	through	through	ADP
ejpam-5366	108	38	the	the	DET
ejpam-5366	108	39	next	next	ADJ
ejpam-5366	108	40	theorem	theorem	PROPN
ejpam-5366	108	41	.	.	PUNCT
ejpam-5366	108	42	theorem	theorem	NOUN
ejpam-5366	108	43	2	2	NUM
ejpam-5366	108	44	.	.	PUNCT
ejpam-5366	109	1	[	[	X
ejpam-5366	109	2	6	6	NUM
ejpam-5366	109	3	]	]	PUNCT
ejpam-5366	109	4	suppose	suppose	VERB
ejpam-5366	109	5	that	that	SCONJ
ejpam-5366	109	6	g	g	PROPN
ejpam-5366	109	7	is	be	AUX
ejpam-5366	109	8	a	a	DET
ejpam-5366	109	9	continuous	continuous	ADJ
ejpam-5366	109	10	real	real	ADV
ejpam-5366	109	11	-	-	PUNCT
ejpam-5366	109	12	valued	value	VERB
ejpam-5366	109	13	function	function	NOUN
ejpam-5366	109	14	and	and	CCONJ
ejpam-5366	109	15	satisfies	satisfy	VERB
ejpam-5366	109	16	the	the	DET
ejpam-5366	109	17	following	follow	VERB
ejpam-5366	109	18	lipschitz	lipschitz	NOUN
ejpam-5366	109	19	condition	condition	NOUN
ejpam-5366	109	20	:	:	PUNCT
ejpam-5366	109	21	|g(t	|g(t	NOUN
ejpam-5366	109	22	,	,	PUNCT
ejpam-5366	109	23	z1)−	z1)−	PROPN
ejpam-5366	109	24	g(t	g(t	PROPN
ejpam-5366	109	25	,	,	PUNCT
ejpam-5366	109	26	z2)|	z2)|	PROPN
ejpam-5366	109	27	≤	≤	ADV
ejpam-5366	110	1	κ|z1	κ|z1	NUM
ejpam-5366	110	2	−	−	NUM
ejpam-5366	110	3	z2|	z2|	NOUN
ejpam-5366	110	4	,	,	PUNCT
ejpam-5366	110	5	κ	κ	PROPN
ejpam-5366	110	6	∈	∈	PROPN
ejpam-5366	110	7	ω	ω	NOUN
ejpam-5366	110	8	=	=	PUNCT
ejpam-5366	111	1	[	[	X
ejpam-5366	111	2	a	a	PRON
ejpam-5366	111	3	,	,	PUNCT
ejpam-5366	111	4	b]×	b]×	NOUN
ejpam-5366	111	5	r.	r.	PROPN
ejpam-5366	111	6	suppose	suppose	VERB
ejpam-5366	111	7	that	that	SCONJ
ejpam-5366	111	8	a	a	DET
ejpam-5366	111	9	constant	constant	ADJ
ejpam-5366	111	10	δ	δ	NOUN
ejpam-5366	111	11	exists	exist	VERB
ejpam-5366	111	12	with	with	ADP
ejpam-5366	111	13	|dnαz(t)|	|dnαz(t)|	PROPN
ejpam-5366	111	14	≤	≤	PROPN
ejpam-5366	111	15	δ	δ	PROPN
ejpam-5366	111	16	,	,	PUNCT
ejpam-5366	111	17	∀	∀	VERB
ejpam-5366	111	18	a	a	DET
ejpam-5366	111	19	≤	≤	NUM
ejpam-5366	111	20	t	t	PROPN
ejpam-5366	111	21	≤	≤	PROPN
ejpam-5366	111	22	b.	b.	PROPN
ejpam-5366	112	1	then	then	ADV
ejpam-5366	112	2	,	,	PUNCT
ejpam-5366	112	3	we	we	PRON
ejpam-5366	112	4	have	have	VERB
ejpam-5366	112	5	:	:	PUNCT
ejpam-5366	112	6	|z(tk)−	|z(tk)−	ADJ
ejpam-5366	112	7	zk|	zk|	PROPN
ejpam-5366	112	8	≤	≤	NUM
ejpam-5366	112	9	γ	γ	X
ejpam-5366	112	10	(	(	PUNCT
ejpam-5366	112	11	ek	ek	NOUN
ejpam-5366	112	12	θ	θ	PROPN
ejpam-5366	112	13	−	−	PROPN
ejpam-5366	112	14	1	1	NUM
ejpam-5366	112	15	)	)	PUNCT
ejpam-5366	112	16	,	,	PUNCT
ejpam-5366	112	17	k	k	X
ejpam-5366	113	1	=	=	SYM
ejpam-5366	113	2	0	0	NUM
ejpam-5366	113	3	,	,	PUNCT
ejpam-5366	113	4	1	1	NUM
ejpam-5366	113	5	,	,	PUNCT
ejpam-5366	113	6	2	2	NUM
ejpam-5366	113	7	,	,	PUNCT
ejpam-5366	113	8	...	...	PUNCT
ejpam-5366	113	9	,	,	PUNCT
ejpam-5366	113	10	n	n	CCONJ
ejpam-5366	113	11	,	,	PUNCT
ejpam-5366	113	12	(	(	PUNCT
ejpam-5366	113	13	8)	8)	NUM
ejpam-5366	113	14	where	where	SCONJ
ejpam-5366	113	15	γ	γ	PROPN
ejpam-5366	113	16	and	and	CCONJ
ejpam-5366	113	17	θ	θ	PROPN
ejpam-5366	113	18	are	be	AUX
ejpam-5366	113	19	defined	define	VERB
ejpam-5366	113	20	as	as	SCONJ
ejpam-5366	113	21	follows	follow	VERB
ejpam-5366	113	22	:	:	PUNCT
ejpam-5366	113	23	γ	γ	X
ejpam-5366	113	24	=	=	NOUN
ejpam-5366	113	25	2γ2(α+	2γ2(α+	NUM
ejpam-5366	113	26	1)h2α	1)h2α	NUM
ejpam-5366	113	27	δ	δ	PROPN
ejpam-5366	113	28	γ(2α+	γ(2α+	VERB
ejpam-5366	113	29	1)(2γ(α+	1)(2γ(α+	NUM
ejpam-5366	113	30	1)hα	1)hα	NUM
ejpam-5366	113	31	+	+	CCONJ
ejpam-5366	113	32	h2ακ	h2ακ	X
ejpam-5366	113	33	)	)	PUNCT
ejpam-5366	113	34	,	,	PUNCT
ejpam-5366	113	35	θ	θ	X
ejpam-5366	113	36	=	=	PUNCT
ejpam-5366	114	1	2γ(α+	2γ(α+	NUM
ejpam-5366	114	2	1)hα	1)hα	NUM
ejpam-5366	114	3	+	+	CCONJ
ejpam-5366	114	4	h2ακ	h2ακ	X
ejpam-5366	114	5	2γ2(α+	2γ2(α+	NUM
ejpam-5366	114	6	1	1	NUM
ejpam-5366	114	7	)	)	PUNCT
ejpam-5366	114	8	.	.	PUNCT
ejpam-5366	115	1	proof	proof	NOUN
ejpam-5366	115	2	.	.	PUNCT
ejpam-5366	116	1	the	the	DET
ejpam-5366	116	2	detail	detail	NOUN
ejpam-5366	116	3	of	of	ADP
ejpam-5366	116	4	the	the	DET
ejpam-5366	116	5	proof	proof	NOUN
ejpam-5366	116	6	of	of	ADP
ejpam-5366	116	7	this	this	DET
ejpam-5366	116	8	theorem	theorem	NOUN
ejpam-5366	116	9	can	can	AUX
ejpam-5366	116	10	be	be	AUX
ejpam-5366	116	11	found	find	VERB
ejpam-5366	116	12	in	in	ADP
ejpam-5366	116	13	[	[	X
ejpam-5366	116	14	6	6	NUM
ejpam-5366	116	15	]	]	PUNCT
ejpam-5366	116	16	.	.	PUNCT
ejpam-5366	117	1	5	5	X
ejpam-5366	117	2	.	.	X
ejpam-5366	117	3	solving	solve	VERB
ejpam-5366	117	4	fractional	fractional	ADJ
ejpam-5366	117	5	-	-	PUNCT
ejpam-5366	117	6	order	order	NOUN
ejpam-5366	117	7	smoking	smoking	NOUN
ejpam-5366	117	8	model	model	NOUN
ejpam-5366	117	9	in	in	ADP
ejpam-5366	117	10	this	this	DET
ejpam-5366	117	11	section	section	NOUN
ejpam-5366	117	12	,	,	PUNCT
ejpam-5366	117	13	we	we	PRON
ejpam-5366	117	14	obtain	obtain	VERB
ejpam-5366	117	15	numerical	numerical	ADJ
ejpam-5366	117	16	solutions	solution	NOUN
ejpam-5366	117	17	for	for	ADP
ejpam-5366	117	18	the	the	DET
ejpam-5366	117	19	smoking	smoking	NOUN
ejpam-5366	117	20	model	model	NOUN
ejpam-5366	117	21	in	in	ADP
ejpam-5366	117	22	its	its	PRON
ejpam-5366	117	23	fractional	fractional	ADJ
ejpam-5366	117	24	form	form	NOUN
ejpam-5366	117	25	using	use	VERB
ejpam-5366	117	26	the	the	DET
ejpam-5366	117	27	method	method	NOUN
ejpam-5366	117	28	proposed	propose	VERB
ejpam-5366	117	29	in	in	ADP
ejpam-5366	117	30	the	the	DET
ejpam-5366	117	31	previous	previous	ADJ
ejpam-5366	117	32	section	section	NOUN
ejpam-5366	117	33	(	(	PUNCT
ejpam-5366	117	34	mfem	mfem	PROPN
ejpam-5366	117	35	)	)	PUNCT
ejpam-5366	117	36	.	.	PUNCT
ejpam-5366	118	1	for	for	ADP
ejpam-5366	118	2	this	this	DET
ejpam-5366	118	3	purpose	purpose	NOUN
ejpam-5366	118	4	,	,	PUNCT
ejpam-5366	118	5	we	we	PRON
ejpam-5366	118	6	can	can	AUX
ejpam-5366	118	7	revise	revise	VERB
ejpam-5366	118	8	this	this	DET
ejpam-5366	118	9	model	model	NOUN
ejpam-5366	118	10	(	(	PUNCT
ejpam-5366	118	11	2	2	NUM
ejpam-5366	118	12	)	)	PUNCT
ejpam-5366	118	13	again	again	ADV
ejpam-5366	118	14	as	as	SCONJ
ejpam-5366	118	15	follows	follow	VERB
ejpam-5366	118	16	:	:	PUNCT
ejpam-5366	118	17	dαsr(t	dαsr(t	NUM
ejpam-5366	118	18	)	)	PUNCT
ejpam-5366	118	19	=	=	SYM
ejpam-5366	118	20	gr(s1,s2	gr(s1,s2	PROPN
ejpam-5366	118	21	,	,	PUNCT
ejpam-5366	118	22	s3,s4,s5	s3,s4,s5	PROPN
ejpam-5366	118	23	,	,	PUNCT
ejpam-5366	118	24	t	t	PROPN
ejpam-5366	118	25	)	)	PUNCT
ejpam-5366	118	26	,	,	PUNCT
ejpam-5366	118	27	r	r	NOUN
ejpam-5366	118	28	=	=	SYM
ejpam-5366	118	29	1	1	NUM
ejpam-5366	118	30	,	,	PUNCT
ejpam-5366	118	31	2	2	NUM
ejpam-5366	118	32	,	,	PUNCT
ejpam-5366	118	33	3	3	NUM
ejpam-5366	118	34	,	,	PUNCT
ejpam-5366	118	35	4	4	NUM
ejpam-5366	118	36	,	,	PUNCT
ejpam-5366	118	37	5	5	NUM
ejpam-5366	118	38	,	,	PUNCT
ejpam-5366	118	39	(	(	PUNCT
ejpam-5366	118	40	9	9	X
ejpam-5366	118	41	)	)	PUNCT
ejpam-5366	118	42	where	where	SCONJ
ejpam-5366	118	43	g1(s1	g1(s1	NOUN
ejpam-5366	118	44	,	,	PUNCT
ejpam-5366	118	45	s2,s3,s4	s2,s3,s4	NOUN
ejpam-5366	118	46	,	,	PUNCT
ejpam-5366	118	47	s5	s5	PROPN
ejpam-5366	118	48	,	,	PUNCT
ejpam-5366	118	49	t	t	PROPN
ejpam-5366	118	50	)	)	PUNCT
ejpam-5366	119	1	=	=	PUNCT
ejpam-5366	119	2	κ−	κ−	PROPN
ejpam-5366	119	3	ε1	ε1	VERB
ejpam-5366	119	4	s1(t)s2(t	s1(t)s2(t	PROPN
ejpam-5366	119	5	)	)	PUNCT
ejpam-5366	120	1	+	+	NUM
ejpam-5366	120	2	ω	ω	X
ejpam-5366	120	3	s4(t)−	s4(t)−	PROPN
ejpam-5366	120	4	µs1(t	µs1(t	PROPN
ejpam-5366	120	5	)	)	PUNCT
ejpam-5366	120	6	,	,	PUNCT
ejpam-5366	120	7	g2(s1	g2(s1	PROPN
ejpam-5366	120	8	,	,	PUNCT
ejpam-5366	120	9	s2,s3,s4	s2,s3,s4	ADJ
ejpam-5366	120	10	,	,	PUNCT
ejpam-5366	120	11	s5	s5	PROPN
ejpam-5366	120	12	,	,	PUNCT
ejpam-5366	120	13	t	t	PROPN
ejpam-5366	120	14	)	)	PUNCT
ejpam-5366	120	15	=	=	VERB
ejpam-5366	120	16	ε1	ε1	VERB
ejpam-5366	120	17	s1(t)s2(t)−	s1(t)s2(t)−	PROPN
ejpam-5366	120	18	ε2	ε2	PROPN
ejpam-5366	120	19	s2(t)s3(t)−	s2(t)s3(t)−	PROPN
ejpam-5366	120	20	(	(	PUNCT
ejpam-5366	120	21	κ1	κ1	NOUN
ejpam-5366	120	22	+	+	CCONJ
ejpam-5366	120	23	µ	µ	X
ejpam-5366	120	24	)	)	PUNCT
ejpam-5366	120	25	s2(t	s2(t	PROPN
ejpam-5366	120	26	)	)	PUNCT
ejpam-5366	120	27	,	,	PUNCT
ejpam-5366	120	28	g3(s1	g3(s1	PROPN
ejpam-5366	120	29	,	,	PUNCT
ejpam-5366	120	30	s2	s2	PROPN
ejpam-5366	120	31	,	,	PUNCT
ejpam-5366	120	32	s3,s4	s3,s4	PROPN
ejpam-5366	120	33	,	,	PUNCT
ejpam-5366	120	34	s5	s5	PROPN
ejpam-5366	120	35	,	,	PUNCT
ejpam-5366	120	36	t	t	PROPN
ejpam-5366	120	37	)	)	PUNCT
ejpam-5366	121	1	=	=	SYM
ejpam-5366	121	2	ε2	ε2	ADJ
ejpam-5366	121	3	s2(t)s3(t)−	s2(t)s3(t)−	PROPN
ejpam-5366	121	4	(	(	PUNCT
ejpam-5366	121	5	φ+	φ+	NOUN
ejpam-5366	121	6	κ2	κ2	NOUN
ejpam-5366	121	7	+	+	CCONJ
ejpam-5366	121	8	µ)s3(t	µ)s3(t	NOUN
ejpam-5366	121	9	)	)	PUNCT
ejpam-5366	121	10	,	,	PUNCT
ejpam-5366	121	11	g4(s1,s2	g4(s1,s2	PROPN
ejpam-5366	121	12	,	,	PUNCT
ejpam-5366	121	13	s3,s4	s3,s4	PROPN
ejpam-5366	121	14	,	,	PUNCT
ejpam-5366	121	15	s5	s5	PROPN
ejpam-5366	121	16	,	,	PUNCT
ejpam-5366	121	17	t	t	PROPN
ejpam-5366	121	18	)	)	PUNCT
ejpam-5366	121	19	=	=	SYM
ejpam-5366	121	20	φs3(t)−	φs3(t)−	PROPN
ejpam-5366	121	21	(	(	PUNCT
ejpam-5366	121	22	λ+	λ+	X
ejpam-5366	121	23	µ+	µ+	X
ejpam-5366	121	24	ω)s4(t	ω)s4(t	NUM
ejpam-5366	121	25	)	)	PUNCT
ejpam-5366	121	26	,	,	PUNCT
ejpam-5366	121	27	g5(s1,s2	g5(s1,s2	PROPN
ejpam-5366	121	28	,	,	PUNCT
ejpam-5366	121	29	s3,s4,s5	s3,s4,s5	PROPN
ejpam-5366	121	30	,	,	PUNCT
ejpam-5366	121	31	t	t	PROPN
ejpam-5366	121	32	)	)	PUNCT
ejpam-5366	121	33	=	=	PUNCT
ejpam-5366	122	1	λ	λ	X
ejpam-5366	122	2	s4(t)−	s4(t)−	PROPN
ejpam-5366	122	3	µ	µ	X
ejpam-5366	122	4	s5(t	s5(t	NOUN
ejpam-5366	122	5	)	)	PUNCT
ejpam-5366	122	6	.	.	PUNCT
ejpam-5366	123	1	(	(	PUNCT
ejpam-5366	123	2	10	10	NUM
ejpam-5366	123	3	)	)	PUNCT
ejpam-5366	123	4	we	we	PRON
ejpam-5366	123	5	assume	assume	VERB
ejpam-5366	123	6	that	that	SCONJ
ejpam-5366	123	7	dkαsr(t	dkαsr(t	NOUN
ejpam-5366	123	8	)	)	PUNCT
ejpam-5366	123	9	,	,	PUNCT
ejpam-5366	123	10	k	k	X
ejpam-5366	124	1	=	=	SYM
ejpam-5366	124	2	0	0	NUM
ejpam-5366	124	3	,	,	PUNCT
ejpam-5366	124	4	1	1	NUM
ejpam-5366	124	5	,	,	PUNCT
ejpam-5366	124	6	2	2	NUM
ejpam-5366	124	7	are	be	AUX
ejpam-5366	124	8	continuous	continuous	ADJ
ejpam-5366	124	9	on	on	ADP
ejpam-5366	124	10	(	(	PUNCT
ejpam-5366	124	11	0	0	NUM
ejpam-5366	124	12	,	,	PUNCT
ejpam-5366	124	13	t	t	X
ejpam-5366	124	14	]	]	PUNCT
ejpam-5366	124	15	.	.	PUNCT
ejpam-5366	125	1	then	then	ADV
ejpam-5366	125	2	we	we	PRON
ejpam-5366	125	3	can	can	AUX
ejpam-5366	125	4	generate	generate	VERB
ejpam-5366	125	5	the	the	DET
ejpam-5366	125	6	numerical	numerical	ADJ
ejpam-5366	125	7	solution	solution	NOUN
ejpam-5366	125	8	sr(tk	sr(tk	PROPN
ejpam-5366	125	9	)	)	PUNCT
ejpam-5366	125	10	,	,	PUNCT
ejpam-5366	125	11	r	r	NOUN
ejpam-5366	125	12	=	=	SYM
ejpam-5366	125	13	1	1	NUM
ejpam-5366	125	14	,	,	PUNCT
ejpam-5366	125	15	2	2	NUM
ejpam-5366	125	16	,	,	PUNCT
ejpam-5366	125	17	3	3	NUM
ejpam-5366	125	18	,	,	PUNCT
ejpam-5366	125	19	4	4	NUM
ejpam-5366	125	20	,	,	PUNCT
ejpam-5366	125	21	5	5	NUM
ejpam-5366	125	22	of	of	ADP
ejpam-5366	125	23	the	the	DET
ejpam-5366	125	24	system	system	NOUN
ejpam-5366	125	25	(	(	PUNCT
ejpam-5366	125	26	9	9	NUM
ejpam-5366	125	27	)	)	PUNCT
ejpam-5366	125	28	by	by	ADP
ejpam-5366	125	29	applying	apply	VERB
ejpam-5366	125	30	the	the	DET
ejpam-5366	125	31	derived	derive	VERB
ejpam-5366	125	32	numerical	numerical	ADJ
ejpam-5366	125	33	scheme	scheme	NOUN
ejpam-5366	125	34	(	(	PUNCT
ejpam-5366	125	35	7	7	NUM
ejpam-5366	125	36	)	)	PUNCT
ejpam-5366	125	37	with	with	ADP
ejpam-5366	125	38	the	the	DET
ejpam-5366	125	39	following	follow	VERB
ejpam-5366	125	40	iteration	iteration	NOUN
ejpam-5366	125	41	form	form	NOUN
ejpam-5366	125	42	:	:	PUNCT
ejpam-5366	125	43	sr(tj+1	sr(tj+1	ADJ
ejpam-5366	125	44	)	)	PUNCT
ejpam-5366	125	45	=	=	SYM
ejpam-5366	125	46	sr(tj	sr(tj	PROPN
ejpam-5366	125	47	)	)	PUNCT
ejpam-5366	126	1	+	+	CCONJ
ejpam-5366	126	2	hα	hα	ADP
ejpam-5366	126	3	γ(α+	γ(α+	PRON
ejpam-5366	126	4	1	1	NUM
ejpam-5366	126	5	)	)	PUNCT
ejpam-5366	126	6	gr	gr	PROPN
ejpam-5366	126	7	(	(	PUNCT
ejpam-5366	126	8	tj	tj	NOUN
ejpam-5366	126	9	+	+	NOUN
ejpam-5366	126	10	hα	hα	ADP
ejpam-5366	126	11	2γ(α+	2γ(α+	PROPN
ejpam-5366	126	12	1	1	NUM
ejpam-5366	126	13	)	)	PUNCT
ejpam-5366	126	14	,	,	PUNCT
ejpam-5366	126	15	sr(tj	sr(tj	PROPN
ejpam-5366	126	16	)	)	PUNCT
ejpam-5366	126	17	+	+	CCONJ
ejpam-5366	126	18	hα	hα	ADP
ejpam-5366	126	19	2γ(α+	2γ(α+	NUM
ejpam-5366	126	20	1	1	NUM
ejpam-5366	126	21	)	)	PUNCT
ejpam-5366	126	22	.	.	PUNCT
ejpam-5366	127	1	gr(tj	gr(tj	ADJ
ejpam-5366	127	2	,	,	PUNCT
ejpam-5366	127	3	s1(tj),s2(tj),s3(tj),s4(tj	s1(tj),s2(tj),s3(tj),s4(tj	NOUN
ejpam-5366	127	4	)	)	PUNCT
ejpam-5366	127	5	,	,	PUNCT
ejpam-5366	127	6	s5(tj	s5(tj	PROPN
ejpam-5366	127	7	)	)	PUNCT
ejpam-5366	127	8	)	)	PUNCT
ejpam-5366	127	9	)	)	PUNCT
ejpam-5366	128	1	,	,	PUNCT
ejpam-5366	128	2	r	r	NOUN
ejpam-5366	128	3	=	=	SYM
ejpam-5366	128	4	1	1	NUM
ejpam-5366	128	5	,	,	PUNCT
ejpam-5366	128	6	2	2	NUM
ejpam-5366	128	7	,	,	PUNCT
ejpam-5366	128	8	3	3	NUM
ejpam-5366	128	9	,	,	PUNCT
ejpam-5366	128	10	4	4	NUM
ejpam-5366	128	11	,	,	PUNCT
ejpam-5366	128	12	5	5	NUM
ejpam-5366	128	13	,	,	PUNCT
ejpam-5366	128	14	(	(	PUNCT
ejpam-5366	128	15	11	11	NUM
ejpam-5366	128	16	)	)	PUNCT
ejpam-5366	128	17	where	where	SCONJ
ejpam-5366	128	18	gr	gr	NOUN
ejpam-5366	128	19	,	,	PUNCT
ejpam-5366	128	20	r	r	NOUN
ejpam-5366	128	21	=	=	SYM
ejpam-5366	128	22	1	1	NUM
ejpam-5366	128	23	,	,	PUNCT
ejpam-5366	128	24	2	2	NUM
ejpam-5366	128	25	,	,	PUNCT
ejpam-5366	128	26	3	3	NUM
ejpam-5366	128	27	,	,	PUNCT
ejpam-5366	128	28	4	4	NUM
ejpam-5366	128	29	,	,	PUNCT
ejpam-5366	128	30	5	5	NUM
ejpam-5366	128	31	are	be	AUX
ejpam-5366	128	32	defined	define	VERB
ejpam-5366	128	33	in	in	ADP
ejpam-5366	128	34	(	(	PUNCT
ejpam-5366	128	35	10	10	NUM
ejpam-5366	128	36	)	)	PUNCT
ejpam-5366	128	37	.	.	PUNCT
ejpam-5366	129	1	m.	m.	NOUN
ejpam-5366	129	2	m.	m.	NOUN
ejpam-5366	129	3	khader	khader	PROPN
ejpam-5366	129	4	/	/	SYM
ejpam-5366	129	5	eur	eur	PROPN
ejpam-5366	129	6	.	.	PUNCT
ejpam-5366	130	1	j.	j.	PROPN
ejpam-5366	130	2	pure	pure	PROPN
ejpam-5366	130	3	appl	appl	PROPN
ejpam-5366	130	4	.	.	PROPN
ejpam-5366	130	5	math	math	PROPN
ejpam-5366	130	6	,	,	PUNCT
ejpam-5366	130	7	17	17	NUM
ejpam-5366	130	8	(	(	PUNCT
ejpam-5366	130	9	4	4	NUM
ejpam-5366	130	10	)	)	PUNCT
ejpam-5366	130	11	(	(	PUNCT
ejpam-5366	130	12	2024	2024	NUM
ejpam-5366	130	13	)	)	PUNCT
ejpam-5366	130	14	,	,	PUNCT
ejpam-5366	130	15	2676	2676	NUM
ejpam-5366	130	16	-	-	SYM
ejpam-5366	130	17	2691	2691	NUM
ejpam-5366	130	18	2682	2682	NUM
ejpam-5366	130	19	6	6	NUM
ejpam-5366	130	20	.	.	PUNCT
ejpam-5366	131	1	computational	computational	ADJ
ejpam-5366	131	2	results	result	NOUN
ejpam-5366	131	3	in	in	ADP
ejpam-5366	131	4	this	this	DET
ejpam-5366	131	5	section	section	NOUN
ejpam-5366	131	6	,	,	PUNCT
ejpam-5366	131	7	we	we	PRON
ejpam-5366	131	8	give	give	VERB
ejpam-5366	131	9	a	a	DET
ejpam-5366	131	10	numerical	numerical	ADJ
ejpam-5366	131	11	simulation	simulation	NOUN
ejpam-5366	131	12	of	of	ADP
ejpam-5366	131	13	the	the	DET
ejpam-5366	131	14	proposed	propose	VERB
ejpam-5366	131	15	model	model	NOUN
ejpam-5366	131	16	(	(	PUNCT
ejpam-5366	131	17	2	2	NUM
ejpam-5366	131	18	)	)	PUNCT
ejpam-5366	131	19	in	in	ADP
ejpam-5366	131	20	the	the	DET
ejpam-5366	131	21	interval	interval	NOUN
ejpam-5366	131	22	[	[	X
ejpam-5366	131	23	0	0	NUM
ejpam-5366	131	24	,	,	PUNCT
ejpam-5366	131	25	30	30	NUM
ejpam-5366	131	26	]	]	PUNCT
ejpam-5366	131	27	with	with	ADP
ejpam-5366	131	28	varying	vary	VERB
ejpam-5366	131	29	values	value	NOUN
ejpam-5366	131	30	of	of	ADP
ejpam-5366	131	31	the	the	DET
ejpam-5366	131	32	initial	initial	ADJ
ejpam-5366	131	33	solution	solution	NOUN
ejpam-5366	131	34	and	and	CCONJ
ejpam-5366	131	35	fractional	fractional	ADJ
ejpam-5366	131	36	order	order	NOUN
ejpam-5366	131	37	α	α	NOUN
ejpam-5366	131	38	,	,	PUNCT
ejpam-5366	131	39	and	and	CCONJ
ejpam-5366	131	40	the	the	DET
ejpam-5366	131	41	important	important	ADJ
ejpam-5366	131	42	two	two	NUM
ejpam-5366	131	43	parameters	parameter	NOUN
ejpam-5366	131	44	µ	µ	NUM
ejpam-5366	131	45	,	,	PUNCT
ejpam-5366	131	46	κ	κ	X
ejpam-5366	131	47	;	;	PUNCT
ejpam-5366	131	48	with	with	ADP
ejpam-5366	131	49	step	step	NOUN
ejpam-5366	131	50	size	size	NOUN
ejpam-5366	131	51	h	h	NOUN
ejpam-5366	131	52	=	=	NOUN
ejpam-5366	131	53	0.3	0.3	NUM
ejpam-5366	131	54	and	and	CCONJ
ejpam-5366	131	55	we	we	PRON
ejpam-5366	131	56	will	will	AUX
ejpam-5366	131	57	be	be	AUX
ejpam-5366	131	58	able	able	ADJ
ejpam-5366	131	59	to	to	PART
ejpam-5366	131	60	confirm	confirm	VERB
ejpam-5366	131	61	the	the	DET
ejpam-5366	131	62	accuracy	accuracy	NOUN
ejpam-5366	131	63	and	and	CCONJ
ejpam-5366	131	64	persistency	persistency	NOUN
ejpam-5366	131	65	of	of	ADP
ejpam-5366	131	66	the	the	DET
ejpam-5366	131	67	given	give	VERB
ejpam-5366	131	68	technique	technique	NOUN
ejpam-5366	131	69	.	.	PUNCT
ejpam-5366	132	1	however	however	ADV
ejpam-5366	132	2	,	,	PUNCT
ejpam-5366	132	3	we	we	PRON
ejpam-5366	132	4	use	use	VERB
ejpam-5366	132	5	the	the	DET
ejpam-5366	132	6	same	same	ADJ
ejpam-5366	132	7	values	value	NOUN
ejpam-5366	132	8	in	in	ADP
ejpam-5366	132	9	all	all	DET
ejpam-5366	132	10	figures	figure	NOUN
ejpam-5366	132	11	:	:	PUNCT
ejpam-5366	132	12	κ	κ	X
ejpam-5366	132	13	=	=	SYM
ejpam-5366	132	14	0.1	0.1	NUM
ejpam-5366	132	15	,	,	PUNCT
ejpam-5366	132	16	ε1	ε1	PROPN
ejpam-5366	132	17	=	=	SYM
ejpam-5366	132	18	ω	ω	PROPN
ejpam-5366	132	19	=	=	PROPN
ejpam-5366	132	20	κ1	κ1	PROPN
ejpam-5366	132	21	=	=	SYM
ejpam-5366	132	22	κ2	κ2	NOUN
ejpam-5366	132	23	=	=	SYM
ejpam-5366	132	24	0.003	0.003	NUM
ejpam-5366	132	25	,	,	PUNCT
ejpam-5366	132	26	ε2	ε2	NOUN
ejpam-5366	132	27	=	=	SYM
ejpam-5366	132	28	µ	µ	X
ejpam-5366	132	29	=	=	SYM
ejpam-5366	132	30	0.002	0.002	NUM
ejpam-5366	132	31	,	,	PUNCT
ejpam-5366	132	32	φ	φ	NOUN
ejpam-5366	133	1	=	=	SYM
ejpam-5366	133	2	λ	λ	X
ejpam-5366	133	3	=	=	NOUN
ejpam-5366	133	4	0.05	0.05	NUM
ejpam-5366	133	5	.	.	PUNCT
ejpam-5366	134	1	the	the	DET
ejpam-5366	134	2	following	follow	VERB
ejpam-5366	134	3	two	two	NUM
ejpam-5366	134	4	cases	case	NOUN
ejpam-5366	134	5	of	of	ADP
ejpam-5366	134	6	the	the	DET
ejpam-5366	134	7	initial	initial	ADJ
ejpam-5366	134	8	solutions	solution	NOUN
ejpam-5366	134	9	are	be	AUX
ejpam-5366	134	10	considered	consider	VERB
ejpam-5366	134	11	:	:	PUNCT
ejpam-5366	134	12	(	(	PUNCT
ejpam-5366	134	13	i	i	NOUN
ejpam-5366	134	14	)	)	PUNCT
ejpam-5366	134	15	case	case	NOUN
ejpam-5366	134	16	1	1	NUM
ejpam-5366	134	17	:	:	PUNCT
ejpam-5366	134	18	s01	s01	NOUN
ejpam-5366	134	19	=	=	SYM
ejpam-5366	134	20	25	25	NUM
ejpam-5366	134	21	,	,	PUNCT
ejpam-5366	134	22	s02	s02	NOUN
ejpam-5366	134	23	=	=	SYM
ejpam-5366	134	24	20	20	NUM
ejpam-5366	134	25	,	,	PUNCT
ejpam-5366	134	26	s03	s03	NOUN
ejpam-5366	134	27	=	=	SYM
ejpam-5366	134	28	15	15	NUM
ejpam-5366	134	29	,	,	PUNCT
ejpam-5366	134	30	s04	s04	NOUN
ejpam-5366	134	31	=	=	SYM
ejpam-5366	134	32	10	10	NUM
ejpam-5366	134	33	,	,	PUNCT
ejpam-5366	134	34	s05	s05	NOUN
ejpam-5366	134	35	=	=	SYM
ejpam-5366	134	36	5	5	NUM
ejpam-5366	134	37	;	;	PUNCT
ejpam-5366	134	38	(	(	PUNCT
ejpam-5366	134	39	ii	ii	NOUN
ejpam-5366	134	40	)	)	PUNCT
ejpam-5366	134	41	case	case	NOUN
ejpam-5366	134	42	2	2	NUM
ejpam-5366	134	43	:	:	PUNCT
ejpam-5366	134	44	s01	s01	NOUN
ejpam-5366	134	45	=	=	SYM
ejpam-5366	134	46	65	65	NUM
ejpam-5366	134	47	,	,	PUNCT
ejpam-5366	134	48	s02	s02	NOUN
ejpam-5366	134	49	=	=	SYM
ejpam-5366	134	50	55	55	NUM
ejpam-5366	134	51	,	,	PUNCT
ejpam-5366	134	52	s03	s03	NOUN
ejpam-5366	134	53	=	=	SYM
ejpam-5366	134	54	45	45	NUM
ejpam-5366	134	55	,	,	PUNCT
ejpam-5366	134	56	s04	s04	NOUN
ejpam-5366	134	57	=	=	SYM
ejpam-5366	134	58	25	25	NUM
ejpam-5366	134	59	,	,	PUNCT
ejpam-5366	134	60	s05	s05	NOUN
ejpam-5366	134	61	=	=	SYM
ejpam-5366	134	62	15	15	NUM
ejpam-5366	134	63	.	.	PUNCT
ejpam-5366	134	64	to	to	PART
ejpam-5366	134	65	assess	assess	VERB
ejpam-5366	134	66	the	the	DET
ejpam-5366	134	67	accuracy	accuracy	NOUN
ejpam-5366	134	68	and	and	CCONJ
ejpam-5366	134	69	efficiency	efficiency	NOUN
ejpam-5366	134	70	of	of	ADP
ejpam-5366	134	71	the	the	DET
ejpam-5366	134	72	proposed	propose	VERB
ejpam-5366	134	73	scheme	scheme	NOUN
ejpam-5366	134	74	,	,	PUNCT
ejpam-5366	134	75	we	we	PRON
ejpam-5366	134	76	also	also	ADV
ejpam-5366	134	77	provide	provide	VERB
ejpam-5366	134	78	a	a	DET
ejpam-5366	134	79	comparison	comparison	NOUN
ejpam-5366	134	80	between	between	ADP
ejpam-5366	134	81	the	the	DET
ejpam-5366	134	82	results	result	NOUN
ejpam-5366	134	83	produced	produce	VERB
ejpam-5366	134	84	by	by	ADP
ejpam-5366	134	85	the	the	DET
ejpam-5366	134	86	given	give	VERB
ejpam-5366	134	87	scheme	scheme	NOUN
ejpam-5366	134	88	and	and	CCONJ
ejpam-5366	134	89	those	those	PRON
ejpam-5366	134	90	obtained	obtain	VERB
ejpam-5366	134	91	by	by	ADP
ejpam-5366	134	92	applying	apply	VERB
ejpam-5366	134	93	the	the	DET
ejpam-5366	134	94	generalized	generalize	VERB
ejpam-5366	134	95	euler	euler	NOUN
ejpam-5366	134	96	method	method	NOUN
ejpam-5366	134	97	.	.	PUNCT
ejpam-5366	135	1	labels	label	NOUN
ejpam-5366	135	2	of	of	ADP
ejpam-5366	135	3	figures	figure	NOUN
ejpam-5366	135	4	.	.	PUNCT
ejpam-5366	136	1	no	no	INTJ
ejpam-5366	136	2	.	.	PUNCT
ejpam-5366	137	1	description	description	NOUN
ejpam-5366	137	2	used	use	VERB
ejpam-5366	137	3	values	value	NOUN
ejpam-5366	137	4	initial	initial	ADJ
ejpam-5366	137	5	conditions	condition	NOUN
ejpam-5366	137	6	1	1	NUM
ejpam-5366	137	7	numerical	numerical	ADJ
ejpam-5366	137	8	solution	solution	NOUN
ejpam-5366	137	9	α	α	NOUN
ejpam-5366	137	10	=	=	SYM
ejpam-5366	137	11	1.0	1.0	NUM
ejpam-5366	137	12	,	,	PUNCT
ejpam-5366	137	13	0.9	0.9	NUM
ejpam-5366	137	14	,	,	PUNCT
ejpam-5366	137	15	0.8	0.8	NUM
ejpam-5366	137	16	,	,	PUNCT
ejpam-5366	137	17	0.7	0.7	NUM
ejpam-5366	137	18	case	case	NOUN
ejpam-5366	137	19	1	1	NUM
ejpam-5366	137	20	2	2	NUM
ejpam-5366	137	21	numerical	numerical	ADJ
ejpam-5366	137	22	solution	solution	NOUN
ejpam-5366	137	23	α	α	NOUN
ejpam-5366	137	24	=	=	SYM
ejpam-5366	137	25	1.0	1.0	NUM
ejpam-5366	137	26	,	,	PUNCT
ejpam-5366	137	27	0.9	0.9	NUM
ejpam-5366	137	28	,	,	PUNCT
ejpam-5366	137	29	0.8	0.8	NUM
ejpam-5366	137	30	,	,	PUNCT
ejpam-5366	137	31	0.7	0.7	NUM
ejpam-5366	137	32	case	case	NOUN
ejpam-5366	137	33	2	2	NUM
ejpam-5366	137	34	3	3	NUM
ejpam-5366	137	35	comparison	comparison	NOUN
ejpam-5366	137	36	between	between	ADP
ejpam-5366	137	37	the	the	DET
ejpam-5366	137	38	method	method	NOUN
ejpam-5366	137	39	and	and	CCONJ
ejpam-5366	137	40	gem	gem	NOUN
ejpam-5366	137	41	α	α	NOUN
ejpam-5366	137	42	=	=	NOUN
ejpam-5366	137	43	0.95	0.95	NUM
ejpam-5366	137	44	case	case	NOUN
ejpam-5366	137	45	1	1	NUM
ejpam-5366	137	46	4	4	NUM
ejpam-5366	137	47	comparison	comparison	NOUN
ejpam-5366	137	48	between	between	ADP
ejpam-5366	137	49	the	the	DET
ejpam-5366	137	50	method	method	NOUN
ejpam-5366	137	51	and	and	CCONJ
ejpam-5366	137	52	gem	gem	NOUN
ejpam-5366	137	53	α	α	NOUN
ejpam-5366	137	54	=	=	NOUN
ejpam-5366	137	55	0.95	0.95	NUM
ejpam-5366	137	56	case	case	NOUN
ejpam-5366	137	57	2	2	NUM
ejpam-5366	137	58	5	5	NUM
ejpam-5366	137	59	the	the	DET
ejpam-5366	137	60	impact	impact	NOUN
ejpam-5366	137	61	of	of	ADP
ejpam-5366	137	62	the	the	DET
ejpam-5366	137	63	system	system	NOUN
ejpam-5366	137	64	’s	’s	PART
ejpam-5366	137	65	natural	natural	ADJ
ejpam-5366	137	66	death	death	NOUN
ejpam-5366	137	67	rate	rate	NOUN
ejpam-5366	137	68	µ	µ	X
ejpam-5366	137	69	=	=	PUNCT
ejpam-5366	137	70	(	(	PUNCT
ejpam-5366	137	71	3	3	NUM
ejpam-5366	137	72	,	,	PUNCT
ejpam-5366	137	73	4	4	NUM
ejpam-5366	137	74	,	,	PUNCT
ejpam-5366	137	75	11	11	NUM
ejpam-5366	137	76	,	,	PUNCT
ejpam-5366	137	77	14)×	14)×	NUM
ejpam-5366	137	78	10−4	10−4	NUM
ejpam-5366	137	79	case	case	NOUN
ejpam-5366	137	80	1	1	NUM
ejpam-5366	137	81	6	6	NUM
ejpam-5366	137	82	the	the	DET
ejpam-5366	137	83	impact	impact	NOUN
ejpam-5366	137	84	of	of	ADP
ejpam-5366	137	85	the	the	DET
ejpam-5366	137	86	system	system	NOUN
ejpam-5366	137	87	’s	’s	PART
ejpam-5366	137	88	recruitment	recruitment	NOUN
ejpam-5366	137	89	rate	rate	NOUN
ejpam-5366	137	90	κ	κ	X
ejpam-5366	137	91	=	=	NOUN
ejpam-5366	137	92	0.1	0.1	NUM
ejpam-5366	137	93	,	,	PUNCT
ejpam-5366	137	94	0.3	0.3	NUM
ejpam-5366	137	95	,	,	PUNCT
ejpam-5366	137	96	0.5	0.5	NUM
ejpam-5366	137	97	,	,	PUNCT
ejpam-5366	137	98	0.7	0.7	NUM
ejpam-5366	137	99	case	case	NOUN
ejpam-5366	137	100	1	1	NUM
ejpam-5366	137	101	figures	figure	NOUN
ejpam-5366	137	102	1	1	NUM
ejpam-5366	137	103	through	through	ADP
ejpam-5366	137	104	6	6	NUM
ejpam-5366	137	105	present	present	VERB
ejpam-5366	137	106	the	the	DET
ejpam-5366	137	107	numerical	numerical	ADJ
ejpam-5366	137	108	findings	finding	NOUN
ejpam-5366	137	109	for	for	ADP
ejpam-5366	137	110	the	the	DET
ejpam-5366	137	111	model	model	NOUN
ejpam-5366	137	112	under	under	ADP
ejpam-5366	137	113	study	study	NOUN
ejpam-5366	137	114	that	that	PRON
ejpam-5366	137	115	were	be	AUX
ejpam-5366	137	116	produced	produce	VERB
ejpam-5366	137	117	by	by	ADP
ejpam-5366	137	118	using	use	VERB
ejpam-5366	137	119	the	the	DET
ejpam-5366	137	120	suggested	suggest	VERB
ejpam-5366	137	121	technique	technique	NOUN
ejpam-5366	137	122	.	.	PUNCT
ejpam-5366	138	1	based	base	VERB
ejpam-5366	138	2	on	on	ADP
ejpam-5366	138	3	these	these	DET
ejpam-5366	138	4	findings	finding	NOUN
ejpam-5366	138	5	,	,	PUNCT
ejpam-5366	138	6	we	we	PRON
ejpam-5366	138	7	can	can	AUX
ejpam-5366	138	8	conclude	conclude	VERB
ejpam-5366	138	9	that	that	SCONJ
ejpam-5366	138	10	the	the	DET
ejpam-5366	138	11	given	give	VERB
ejpam-5366	138	12	technique	technique	NOUN
ejpam-5366	138	13	is	be	AUX
ejpam-5366	138	14	appropriate	appropriate	ADJ
ejpam-5366	138	15	for	for	ADP
ejpam-5366	138	16	solving	solve	VERB
ejpam-5366	138	17	the	the	DET
ejpam-5366	138	18	current	current	ADJ
ejpam-5366	138	19	model	model	NOUN
ejpam-5366	138	20	in	in	ADP
ejpam-5366	138	21	its	its	PRON
ejpam-5366	138	22	liouville	liouville	NOUN
ejpam-5366	138	23	-	-	PUNCT
ejpam-5366	138	24	caputo	caputo	PROPN
ejpam-5366	138	25	fractional	fractional	ADJ
ejpam-5366	138	26	form	form	NOUN
ejpam-5366	138	27	,	,	PUNCT
ejpam-5366	138	28	as	as	SCONJ
ejpam-5366	138	29	the	the	DET
ejpam-5366	138	30	behavior	behavior	NOUN
ejpam-5366	138	31	of	of	ADP
ejpam-5366	138	32	the	the	DET
ejpam-5366	138	33	numerical	numerical	ADJ
ejpam-5366	138	34	solution	solution	NOUN
ejpam-5366	138	35	obtained	obtain	VERB
ejpam-5366	138	36	by	by	ADP
ejpam-5366	138	37	applying	apply	VERB
ejpam-5366	138	38	the	the	DET
ejpam-5366	138	39	proposed	propose	VERB
ejpam-5366	138	40	method	method	NOUN
ejpam-5366	138	41	depends	depend	VERB
ejpam-5366	138	42	on	on	ADP
ejpam-5366	138	43	the	the	DET
ejpam-5366	138	44	values	value	NOUN
ejpam-5366	138	45	of	of	ADP
ejpam-5366	138	46	α	α	NOUN
ejpam-5366	138	47	,	,	PUNCT
ejpam-5366	138	48	h	h	NOUN
ejpam-5366	138	49	,	,	PUNCT
ejpam-5366	138	50	µ	µ	NOUN
ejpam-5366	138	51	,	,	PUNCT
ejpam-5366	138	52	and	and	CCONJ
ejpam-5366	138	53	κ	κ	NOUN
ejpam-5366	138	54	.	.	PUNCT
ejpam-5366	139	1	furthermore	furthermore	ADV
ejpam-5366	139	2	,	,	PUNCT
ejpam-5366	139	3	the	the	DET
ejpam-5366	139	4	efficiency	efficiency	NOUN
ejpam-5366	139	5	of	of	ADP
ejpam-5366	139	6	the	the	DET
ejpam-5366	139	7	process	process	NOUN
ejpam-5366	139	8	and	and	CCONJ
ejpam-5366	139	9	the	the	DET
ejpam-5366	139	10	outcomes	outcome	NOUN
ejpam-5366	139	11	are	be	AUX
ejpam-5366	139	12	significantly	significantly	ADV
ejpam-5366	139	13	enhanced	enhance	VERB
ejpam-5366	139	14	by	by	ADP
ejpam-5366	139	15	the	the	DET
ejpam-5366	139	16	suggested	suggest	VERB
ejpam-5366	139	17	methodology	methodology	NOUN
ejpam-5366	139	18	.	.	PUNCT
ejpam-5366	140	1	in	in	ADP
ejpam-5366	140	2	figures	figure	NOUN
ejpam-5366	140	3	5	5	NUM
ejpam-5366	140	4	and	and	CCONJ
ejpam-5366	140	5	6	6	NUM
ejpam-5366	140	6	,	,	PUNCT
ejpam-5366	140	7	respectively	respectively	ADV
ejpam-5366	140	8	,	,	PUNCT
ejpam-5366	140	9	the	the	DET
ejpam-5366	140	10	effect	effect	NOUN
ejpam-5366	140	11	of	of	ADP
ejpam-5366	140	12	the	the	DET
ejpam-5366	140	13	recruitment	recruitment	NOUN
ejpam-5366	140	14	rate	rate	NOUN
ejpam-5366	140	15	(	(	PUNCT
ejpam-5366	140	16	due	due	ADP
ejpam-5366	140	17	to	to	ADP
ejpam-5366	140	18	immigration	immigration	NOUN
ejpam-5366	140	19	or	or	CCONJ
ejpam-5366	140	20	birth	birth	NOUN
ejpam-5366	140	21	)	)	PUNCT
ejpam-5366	140	22	,	,	PUNCT
ejpam-5366	140	23	and	and	CCONJ
ejpam-5366	140	24	the	the	DET
ejpam-5366	140	25	smoking	smoking	NOUN
ejpam-5366	140	26	cessation	cessation	NOUN
ejpam-5366	140	27	rate	rate	NOUN
ejpam-5366	140	28	on	on	ADP
ejpam-5366	140	29	the	the	DET
ejpam-5366	140	30	behavior	behavior	NOUN
ejpam-5366	140	31	and	and	CCONJ
ejpam-5366	140	32	dynamics	dynamic	NOUN
ejpam-5366	140	33	of	of	ADP
ejpam-5366	140	34	the	the	DET
ejpam-5366	140	35	solutions	solution	NOUN
ejpam-5366	140	36	was	be	AUX
ejpam-5366	140	37	studied	study	VERB
ejpam-5366	140	38	.	.	PUNCT
ejpam-5366	141	1	from	from	ADP
ejpam-5366	141	2	figure	figure	NOUN
ejpam-5366	141	3	5	5	NUM
ejpam-5366	141	4	,	,	PUNCT
ejpam-5366	141	5	we	we	PRON
ejpam-5366	141	6	find	find	VERB
ejpam-5366	141	7	that	that	SCONJ
ejpam-5366	141	8	indeed	indeed	ADV
ejpam-5366	141	9	,	,	PUNCT
ejpam-5366	141	10	increasing	increase	VERB
ejpam-5366	141	11	the	the	DET
ejpam-5366	141	12	values	value	NOUN
ejpam-5366	141	13	of	of	ADP
ejpam-5366	141	14	the	the	DET
ejpam-5366	141	15	departure	departure	NOUN
ejpam-5366	141	16	rate	rate	NOUN
ejpam-5366	141	17	leads	lead	VERB
ejpam-5366	141	18	to	to	ADP
ejpam-5366	141	19	a	a	DET
ejpam-5366	141	20	decrease	decrease	NOUN
ejpam-5366	141	21	in	in	ADP
ejpam-5366	141	22	the	the	DET
ejpam-5366	141	23	values	value	NOUN
ejpam-5366	141	24	of	of	ADP
ejpam-5366	141	25	each	each	PRON
ejpam-5366	141	26	of	of	ADP
ejpam-5366	141	27	the	the	DET
ejpam-5366	141	28	four	four	NUM
ejpam-5366	141	29	components	component	NOUN
ejpam-5366	141	30	s2(t	s2(t	NOUN
ejpam-5366	141	31	)	)	PUNCT
ejpam-5366	141	32	to	to	ADP
ejpam-5366	141	33	s5(t	s5(t	PRON
ejpam-5366	141	34	)	)	PUNCT
ejpam-5366	141	35	without	without	ADP
ejpam-5366	141	36	affecting	affect	VERB
ejpam-5366	141	37	the	the	DET
ejpam-5366	141	38	component	component	NOUN
ejpam-5366	141	39	s1(t	s1(t	NOUN
ejpam-5366	141	40	)	)	PUNCT
ejpam-5366	141	41	,	,	PUNCT
ejpam-5366	141	42	and	and	CCONJ
ejpam-5366	141	43	this	this	PRON
ejpam-5366	141	44	is	be	AUX
ejpam-5366	141	45	largely	largely	ADV
ejpam-5366	141	46	consistent	consistent	ADJ
ejpam-5366	141	47	with	with	ADP
ejpam-5366	141	48	the	the	DET
ejpam-5366	141	49	natural	natural	ADJ
ejpam-5366	141	50	meaning	meaning	NOUN
ejpam-5366	141	51	of	of	ADP
ejpam-5366	141	52	the	the	DET
ejpam-5366	141	53	model	model	NOUN
ejpam-5366	141	54	under	under	ADP
ejpam-5366	141	55	study	study	NOUN
ejpam-5366	141	56	,	,	PUNCT
ejpam-5366	141	57	especially	especially	ADV
ejpam-5366	141	58	from	from	ADP
ejpam-5366	141	59	a	a	DET
ejpam-5366	141	60	medical	medical	ADJ
ejpam-5366	141	61	and	and	CCONJ
ejpam-5366	141	62	therapeutic	therapeutic	ADJ
ejpam-5366	141	63	perspective	perspective	NOUN
ejpam-5366	141	64	.	.	PUNCT
ejpam-5366	142	1	likewise	likewise	ADV
ejpam-5366	142	2	,	,	PUNCT
ejpam-5366	142	3	from	from	ADP
ejpam-5366	142	4	figure	figure	NOUN
ejpam-5366	142	5	6	6	NUM
ejpam-5366	142	6	we	we	PRON
ejpam-5366	142	7	found	find	VERB
ejpam-5366	142	8	that	that	SCONJ
ejpam-5366	142	9	indeed	indeed	ADV
ejpam-5366	142	10	,	,	PUNCT
ejpam-5366	142	11	increasing	increase	VERB
ejpam-5366	142	12	the	the	DET
ejpam-5366	142	13	values	value	NOUN
ejpam-5366	142	14	of	of	ADP
ejpam-5366	142	15	the	the	DET
ejpam-5366	142	16	recruitment	recruitment	NOUN
ejpam-5366	142	17	rate	rate	NOUN
ejpam-5366	142	18	(	(	PUNCT
ejpam-5366	142	19	due	due	ADP
ejpam-5366	142	20	to	to	ADP
ejpam-5366	142	21	migration	migration	NOUN
ejpam-5366	142	22	or	or	CCONJ
ejpam-5366	142	23	birth	birth	NOUN
ejpam-5366	142	24	)	)	PUNCT
ejpam-5366	142	25	leads	lead	VERB
ejpam-5366	142	26	to	to	ADP
ejpam-5366	142	27	an	an	DET
ejpam-5366	142	28	increase	increase	NOUN
ejpam-5366	142	29	in	in	ADP
ejpam-5366	142	30	the	the	DET
ejpam-5366	142	31	values	value	NOUN
ejpam-5366	142	32	of	of	ADP
ejpam-5366	142	33	each	each	PRON
ejpam-5366	142	34	of	of	ADP
ejpam-5366	142	35	the	the	DET
ejpam-5366	142	36	four	four	NUM
ejpam-5366	142	37	components	component	NOUN
ejpam-5366	142	38	s1(t	s1(t	NOUN
ejpam-5366	142	39	)	)	PUNCT
ejpam-5366	142	40	to	to	ADP
ejpam-5366	142	41	s4(t	s4(t	VERB
ejpam-5366	142	42	)	)	PUNCT
ejpam-5366	142	43	without	without	ADP
ejpam-5366	142	44	affecting	affect	VERB
ejpam-5366	142	45	the	the	DET
ejpam-5366	142	46	component	component	NOUN
ejpam-5366	142	47	s5(t	s5(t	ADP
ejpam-5366	142	48	)	)	PUNCT
ejpam-5366	142	49	,	,	PUNCT
ejpam-5366	142	50	and	and	CCONJ
ejpam-5366	142	51	this	this	PRON
ejpam-5366	142	52	is	be	AUX
ejpam-5366	142	53	largely	largely	ADV
ejpam-5366	142	54	consistent	consistent	ADJ
ejpam-5366	142	55	with	with	ADP
ejpam-5366	142	56	the	the	DET
ejpam-5366	142	57	natural	natural	ADJ
ejpam-5366	142	58	meaning	meaning	NOUN
ejpam-5366	142	59	of	of	ADP
ejpam-5366	142	60	the	the	DET
ejpam-5366	142	61	system	system	NOUN
ejpam-5366	142	62	under	under	ADP
ejpam-5366	142	63	study	study	NOUN
ejpam-5366	142	64	,	,	PUNCT
ejpam-5366	142	65	especially	especially	ADV
ejpam-5366	142	66	from	from	ADP
ejpam-5366	142	67	a	a	DET
ejpam-5366	142	68	medical	medical	ADJ
ejpam-5366	142	69	and	and	CCONJ
ejpam-5366	142	70	therapeutic	therapeutic	ADJ
ejpam-5366	142	71	perspective	perspective	NOUN
ejpam-5366	142	72	.	.	PUNCT
ejpam-5366	143	1	m.	m.	NOUN
ejpam-5366	143	2	m.	m.	NOUN
ejpam-5366	143	3	khader	khader	PROPN
ejpam-5366	143	4	/	/	SYM
ejpam-5366	143	5	eur	eur	PROPN
ejpam-5366	143	6	.	.	PUNCT
ejpam-5366	144	1	j.	j.	PROPN
ejpam-5366	144	2	pure	pure	PROPN
ejpam-5366	144	3	appl	appl	PROPN
ejpam-5366	144	4	.	.	PROPN
ejpam-5366	144	5	math	math	PROPN
ejpam-5366	144	6	,	,	PUNCT
ejpam-5366	144	7	17	17	NUM
ejpam-5366	144	8	(	(	PUNCT
ejpam-5366	144	9	4	4	NUM
ejpam-5366	144	10	)	)	PUNCT
ejpam-5366	144	11	(	(	PUNCT
ejpam-5366	144	12	2024	2024	NUM
ejpam-5366	144	13	)	)	PUNCT
ejpam-5366	144	14	,	,	PUNCT
ejpam-5366	144	15	2676	2676	NUM
ejpam-5366	144	16	-	-	SYM
ejpam-5366	144	17	2691	2691	NUM
ejpam-5366	144	18	2683	2683	NUM
ejpam-5366	144	19	fig	fig	NOUN
ejpam-5366	144	20	.	.	PUNCT
ejpam-5366	145	1	1	1	NUM
ejpam-5366	145	2	:	:	PUNCT
ejpam-5366	145	3	the	the	DET
ejpam-5366	145	4	solution	solution	NOUN
ejpam-5366	145	5	si(t	si(t	VERB
ejpam-5366	145	6	)	)	PUNCT
ejpam-5366	145	7	,	,	PUNCT
ejpam-5366	145	8	i	i	PRON
ejpam-5366	145	9	=	=	NOUN
ejpam-5366	145	10	1	1	NUM
ejpam-5366	145	11	,	,	PUNCT
ejpam-5366	145	12	2	2	NUM
ejpam-5366	145	13	,	,	PUNCT
ejpam-5366	145	14	3	3	NUM
ejpam-5366	145	15	,	,	PUNCT
ejpam-5366	145	16	4	4	NUM
ejpam-5366	145	17	,	,	PUNCT
ejpam-5366	145	18	5	5	NUM
ejpam-5366	145	19	for	for	ADP
ejpam-5366	145	20	some	some	DET
ejpam-5366	145	21	α	α	NOUN
ejpam-5366	145	22	with	with	ADP
ejpam-5366	145	23	small	small	ADJ
ejpam-5366	145	24	initial	initial	ADJ
ejpam-5366	145	25	values	value	NOUN
ejpam-5366	145	26	.	.	PUNCT
ejpam-5366	146	1	m.	m.	NOUN
ejpam-5366	146	2	m.	m.	NOUN
ejpam-5366	146	3	khader	khader	PROPN
ejpam-5366	146	4	/	/	SYM
ejpam-5366	146	5	eur	eur	PROPN
ejpam-5366	146	6	.	.	PUNCT
ejpam-5366	147	1	j.	j.	PROPN
ejpam-5366	147	2	pure	pure	PROPN
ejpam-5366	147	3	appl	appl	PROPN
ejpam-5366	147	4	.	.	PROPN
ejpam-5366	147	5	math	math	PROPN
ejpam-5366	147	6	,	,	PUNCT
ejpam-5366	147	7	17	17	NUM
ejpam-5366	147	8	(	(	PUNCT
ejpam-5366	147	9	4	4	NUM
ejpam-5366	147	10	)	)	PUNCT
ejpam-5366	147	11	(	(	PUNCT
ejpam-5366	147	12	2024	2024	NUM
ejpam-5366	147	13	)	)	PUNCT
ejpam-5366	147	14	,	,	PUNCT
ejpam-5366	147	15	2676	2676	NUM
ejpam-5366	147	16	-	-	SYM
ejpam-5366	147	17	2691	2691	NUM
ejpam-5366	147	18	2684	2684	NUM
ejpam-5366	147	19	fig	fig	NOUN
ejpam-5366	147	20	.	.	PUNCT
ejpam-5366	148	1	2	2	NUM
ejpam-5366	148	2	:	:	PUNCT
ejpam-5366	148	3	the	the	DET
ejpam-5366	148	4	solution	solution	NOUN
ejpam-5366	148	5	si(t	si(t	VERB
ejpam-5366	148	6	)	)	PUNCT
ejpam-5366	148	7	,	,	PUNCT
ejpam-5366	148	8	i	i	PRON
ejpam-5366	148	9	=	=	NOUN
ejpam-5366	148	10	1	1	NUM
ejpam-5366	148	11	,	,	PUNCT
ejpam-5366	148	12	2	2	NUM
ejpam-5366	148	13	,	,	PUNCT
ejpam-5366	148	14	3	3	NUM
ejpam-5366	148	15	,	,	PUNCT
ejpam-5366	148	16	4	4	NUM
ejpam-5366	148	17	,	,	PUNCT
ejpam-5366	148	18	5	5	NUM
ejpam-5366	148	19	for	for	ADP
ejpam-5366	148	20	some	some	DET
ejpam-5366	148	21	α	α	NOUN
ejpam-5366	148	22	with	with	ADP
ejpam-5366	148	23	large	large	ADJ
ejpam-5366	148	24	initial	initial	ADJ
ejpam-5366	148	25	values	value	NOUN
ejpam-5366	148	26	.	.	PUNCT
ejpam-5366	149	1	m.	m.	NOUN
ejpam-5366	149	2	m.	m.	NOUN
ejpam-5366	149	3	khader	khader	PROPN
ejpam-5366	149	4	/	/	SYM
ejpam-5366	149	5	eur	eur	PROPN
ejpam-5366	149	6	.	.	PUNCT
ejpam-5366	150	1	j.	j.	PROPN
ejpam-5366	150	2	pure	pure	PROPN
ejpam-5366	150	3	appl	appl	PROPN
ejpam-5366	150	4	.	.	PROPN
ejpam-5366	150	5	math	math	PROPN
ejpam-5366	150	6	,	,	PUNCT
ejpam-5366	150	7	17	17	NUM
ejpam-5366	150	8	(	(	PUNCT
ejpam-5366	150	9	4	4	NUM
ejpam-5366	150	10	)	)	PUNCT
ejpam-5366	150	11	(	(	PUNCT
ejpam-5366	150	12	2024	2024	NUM
ejpam-5366	150	13	)	)	PUNCT
ejpam-5366	150	14	,	,	PUNCT
ejpam-5366	150	15	2676	2676	NUM
ejpam-5366	150	16	-	-	SYM
ejpam-5366	150	17	2691	2691	NUM
ejpam-5366	150	18	2685	2685	NUM
ejpam-5366	150	19	fig	fig	NOUN
ejpam-5366	150	20	.	.	PUNCT
ejpam-5366	151	1	3	3	NUM
ejpam-5366	151	2	:	:	PUNCT
ejpam-5366	151	3	the	the	DET
ejpam-5366	151	4	si(t	si(t	NOUN
ejpam-5366	151	5	)	)	PUNCT
ejpam-5366	151	6	,	,	PUNCT
ejpam-5366	151	7	i	i	PRON
ejpam-5366	151	8	=	=	NOUN
ejpam-5366	151	9	1	1	NUM
ejpam-5366	151	10	,	,	PUNCT
ejpam-5366	151	11	2	2	NUM
ejpam-5366	151	12	,	,	PUNCT
ejpam-5366	151	13	3	3	NUM
ejpam-5366	151	14	,	,	PUNCT
ejpam-5366	151	15	4	4	NUM
ejpam-5366	151	16	,	,	PUNCT
ejpam-5366	151	17	5	5	NUM
ejpam-5366	151	18	by	by	ADP
ejpam-5366	151	19	the	the	DET
ejpam-5366	151	20	present	present	ADJ
ejpam-5366	151	21	and	and	CCONJ
ejpam-5366	151	22	gem	gem	NOUN
ejpam-5366	151	23	methods	method	NOUN
ejpam-5366	151	24	α	α	NOUN
ejpam-5366	151	25	=	=	NOUN
ejpam-5366	151	26	1	1	NUM
ejpam-5366	151	27	with	with	ADP
ejpam-5366	151	28	small	small	ADJ
ejpam-5366	151	29	initial	initial	ADJ
ejpam-5366	151	30	values	value	NOUN
ejpam-5366	151	31	.	.	PUNCT
ejpam-5366	152	1	in	in	ADP
ejpam-5366	152	2	addition	addition	NOUN
ejpam-5366	152	3	,	,	PUNCT
ejpam-5366	152	4	to	to	PART
ejpam-5366	152	5	strongly	strongly	ADV
ejpam-5366	152	6	prove	prove	VERB
ejpam-5366	152	7	and	and	CCONJ
ejpam-5366	152	8	confirm	confirm	VERB
ejpam-5366	152	9	the	the	DET
ejpam-5366	152	10	effectiveness	effectiveness	NOUN
ejpam-5366	152	11	of	of	ADP
ejpam-5366	152	12	the	the	DET
ejpam-5366	152	13	given	give	VERB
ejpam-5366	152	14	technique	technique	NOUN
ejpam-5366	152	15	,	,	PUNCT
ejpam-5366	152	16	we	we	PRON
ejpam-5366	152	17	present	present	VERB
ejpam-5366	152	18	a	a	DET
ejpam-5366	152	19	comparison	comparison	NOUN
ejpam-5366	152	20	between	between	ADP
ejpam-5366	152	21	the	the	DET
ejpam-5366	152	22	mfem	mfem	NOUN
ejpam-5366	152	23	with	with	ADP
ejpam-5366	152	24	the	the	DET
ejpam-5366	152	25	generalized	generalize	VERB
ejpam-5366	152	26	fractional	fractional	PROPN
ejpam-5366	152	27	euler	euler	NOUN
ejpam-5366	152	28	method	method	NOUN
ejpam-5366	152	29	.	.	PUNCT
ejpam-5366	153	1	this	this	DET
ejpam-5366	153	2	comparison	comparison	NOUN
ejpam-5366	153	3	is	be	AUX
ejpam-5366	153	4	done	do	VERB
ejpam-5366	153	5	through	through	ADP
ejpam-5366	153	6	table	table	NOUN
ejpam-5366	153	7	2	2	NUM
ejpam-5366	153	8	at	at	ADP
ejpam-5366	153	9	some	some	DET
ejpam-5366	153	10	different	different	ADJ
ejpam-5366	153	11	iterations	iteration	NOUN
ejpam-5366	153	12	of	of	ADP
ejpam-5366	153	13	the	the	DET
ejpam-5366	153	14	procedure	procedure	NOUN
ejpam-5366	153	15	with	with	ADP
ejpam-5366	153	16	α	α	NOUN
ejpam-5366	153	17	=	=	NOUN
ejpam-5366	153	18	0.95	0.95	NUM
ejpam-5366	153	19	,	,	PUNCT
ejpam-5366	153	20	and	and	CCONJ
ejpam-5366	153	21	h	h	NOUN
ejpam-5366	153	22	=	=	NOUN
ejpam-5366	153	23	0.15	0.15	NUM
ejpam-5366	153	24	in	in	ADP
ejpam-5366	153	25	each	each	DET
ejpam-5366	153	26	method	method	NOUN
ejpam-5366	153	27	,	,	PUNCT
ejpam-5366	153	28	but	but	CCONJ
ejpam-5366	153	29	with	with	ADP
ejpam-5366	153	30	the	the	DET
ejpam-5366	153	31	same	same	ADJ
ejpam-5366	153	32	initial	initial	ADJ
ejpam-5366	153	33	conditions	condition	NOUN
ejpam-5366	153	34	as	as	ADP
ejpam-5366	153	35	in	in	ADP
ejpam-5366	153	36	case	case	NOUN
ejpam-5366	153	37	2	2	NUM
ejpam-5366	153	38	and	and	CCONJ
ejpam-5366	153	39	the	the	DET
ejpam-5366	153	40	same	same	ADJ
ejpam-5366	153	41	parameters	parameter	NOUN
ejpam-5366	153	42	as	as	ADP
ejpam-5366	153	43	in	in	ADP
ejpam-5366	153	44	figure	figure	NOUN
ejpam-5366	153	45	1	1	NUM
ejpam-5366	153	46	.	.	PUNCT
ejpam-5366	153	47	where	where	SCONJ
ejpam-5366	153	48	for	for	ADP
ejpam-5366	153	49	each	each	DET
ejpam-5366	153	50	method	method	NOUN
ejpam-5366	153	51	,	,	PUNCT
ejpam-5366	153	52	we	we	PRON
ejpam-5366	153	53	computed	compute	VERB
ejpam-5366	153	54	the	the	DET
ejpam-5366	153	55	relative	relative	ADJ
ejpam-5366	153	56	approximate	approximate	ADJ
ejpam-5366	153	57	error	error	NOUN
ejpam-5366	153	58	(	(	PUNCT
ejpam-5366	153	59	rae	rae	PROPN
ejpam-5366	153	60	)	)	PUNCT
ejpam-5366	153	61	which	which	PRON
ejpam-5366	153	62	is	be	AUX
ejpam-5366	153	63	defined	define	VERB
ejpam-5366	153	64	as	as	ADP
ejpam-5366	153	65	below	below	ADV
ejpam-5366	153	66	to	to	PART
ejpam-5366	153	67	show	show	VERB
ejpam-5366	153	68	that	that	SCONJ
ejpam-5366	153	69	our	our	PRON
ejpam-5366	153	70	presented	present	VERB
ejpam-5366	153	71	m.	m.	NOUN
ejpam-5366	153	72	m.	m.	NOUN
ejpam-5366	153	73	khader	khader	PROPN
ejpam-5366	153	74	/	/	SYM
ejpam-5366	153	75	eur	eur	PROPN
ejpam-5366	153	76	.	.	PUNCT
ejpam-5366	154	1	j.	j.	PROPN
ejpam-5366	154	2	pure	pure	PROPN
ejpam-5366	154	3	appl	appl	PROPN
ejpam-5366	154	4	.	.	PROPN
ejpam-5366	154	5	math	math	PROPN
ejpam-5366	154	6	,	,	PUNCT
ejpam-5366	154	7	17	17	NUM
ejpam-5366	154	8	(	(	PUNCT
ejpam-5366	154	9	4	4	NUM
ejpam-5366	154	10	)	)	PUNCT
ejpam-5366	154	11	(	(	PUNCT
ejpam-5366	154	12	2024	2024	NUM
ejpam-5366	154	13	)	)	PUNCT
ejpam-5366	154	14	,	,	PUNCT
ejpam-5366	154	15	2676	2676	NUM
ejpam-5366	154	16	-	-	SYM
ejpam-5366	154	17	2691	2691	NUM
ejpam-5366	154	18	2686	2686	NUM
ejpam-5366	154	19	fig	fig	NOUN
ejpam-5366	154	20	.	.	PUNCT
ejpam-5366	155	1	4	4	NUM
ejpam-5366	155	2	:	:	PUNCT
ejpam-5366	155	3	the	the	DET
ejpam-5366	155	4	solution	solution	NOUN
ejpam-5366	155	5	si(t	si(t	NOUN
ejpam-5366	155	6	)	)	PUNCT
ejpam-5366	155	7	,	,	PUNCT
ejpam-5366	155	8	i	i	PRON
ejpam-5366	155	9	=	=	NOUN
ejpam-5366	155	10	1	1	NUM
ejpam-5366	155	11	,	,	PUNCT
ejpam-5366	155	12	2	2	NUM
ejpam-5366	155	13	,	,	PUNCT
ejpam-5366	155	14	3	3	NUM
ejpam-5366	155	15	,	,	PUNCT
ejpam-5366	155	16	4	4	NUM
ejpam-5366	155	17	,	,	PUNCT
ejpam-5366	155	18	5	5	NUM
ejpam-5366	155	19	by	by	ADP
ejpam-5366	155	20	the	the	DET
ejpam-5366	155	21	present	present	ADJ
ejpam-5366	155	22	and	and	CCONJ
ejpam-5366	155	23	gem	gem	NOUN
ejpam-5366	155	24	methods	method	NOUN
ejpam-5366	155	25	α	α	NOUN
ejpam-5366	155	26	=	=	NOUN
ejpam-5366	155	27	1	1	NUM
ejpam-5366	155	28	with	with	ADP
ejpam-5366	155	29	large	large	ADJ
ejpam-5366	155	30	initial	initial	ADJ
ejpam-5366	155	31	values	value	NOUN
ejpam-5366	155	32	.	.	PUNCT
ejpam-5366	156	1	method	method	NOUN
ejpam-5366	156	2	is	be	AUX
ejpam-5366	156	3	more	more	ADV
ejpam-5366	156	4	accurate	accurate	ADJ
ejpam-5366	156	5	and	and	CCONJ
ejpam-5366	156	6	computationally	computationally	ADV
ejpam-5366	156	7	effective	effective	ADJ
ejpam-5366	156	8	in	in	ADP
ejpam-5366	156	9	solving	solve	VERB
ejpam-5366	156	10	the	the	DET
ejpam-5366	156	11	given	give	VERB
ejpam-5366	156	12	system	system	NOUN
ejpam-5366	156	13	:	:	PUNCT
ejpam-5366	156	14	rae	rae	PROPN
ejpam-5366	156	15	of	of	ADP
ejpam-5366	156	16	sp(tk	sp(tk	PROPN
ejpam-5366	156	17	)	)	PUNCT
ejpam-5366	157	1	=	=	SYM
ejpam-5366	157	2	∣∣∣∣sp(tk+1)−	∣∣∣∣sp(tk+1)−	ADJ
ejpam-5366	157	3	sp(tk	sp(tk	PROPN
ejpam-5366	157	4	)	)	PUNCT
ejpam-5366	157	5	sp(tk+1	sp(tk+1	PROPN
ejpam-5366	157	6	)	)	PUNCT
ejpam-5366	157	7	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5366	157	8	,	,	PUNCT
ejpam-5366	157	9	p	p	NOUN
ejpam-5366	157	10	=	=	NOUN
ejpam-5366	157	11	1	1	NUM
ejpam-5366	157	12	,	,	PUNCT
ejpam-5366	157	13	2	2	NUM
ejpam-5366	157	14	,	,	PUNCT
ejpam-5366	157	15	3	3	NUM
ejpam-5366	157	16	,	,	PUNCT
ejpam-5366	157	17	4	4	NUM
ejpam-5366	157	18	,	,	PUNCT
ejpam-5366	157	19	5	5	NUM
ejpam-5366	157	20	.	.	PUNCT
ejpam-5366	157	21	also	also	ADV
ejpam-5366	157	22	,	,	PUNCT
ejpam-5366	157	23	we	we	PRON
ejpam-5366	157	24	computed	compute	VERB
ejpam-5366	157	25	the	the	DET
ejpam-5366	157	26	allowed	allow	VERB
ejpam-5366	157	27	time	time	NOUN
ejpam-5366	157	28	t̄	t̄	PROPN
ejpam-5366	157	29	for	for	ADP
ejpam-5366	157	30	obtaining	obtain	VERB
ejpam-5366	157	31	these	these	DET
ejpam-5366	157	32	results	result	NOUN
ejpam-5366	157	33	by	by	ADP
ejpam-5366	157	34	applying	apply	VERB
ejpam-5366	157	35	the	the	DET
ejpam-5366	157	36	two	two	NUM
ejpam-5366	157	37	methods	method	NOUN
ejpam-5366	157	38	(	(	PUNCT
ejpam-5366	157	39	t̄=75	t̄=75	PROPN
ejpam-5366	157	40	sec	sec	PROPN
ejpam-5366	157	41	.	.	PROPN
ejpam-5366	157	42	for	for	ADP
ejpam-5366	157	43	mfem	mfem	NOUN
ejpam-5366	157	44	,	,	PUNCT
ejpam-5366	157	45	t̄=160	t̄=160	PROPN
ejpam-5366	157	46	sec	sec	PROPN
ejpam-5366	157	47	.	.	PUNCT
ejpam-5366	158	1	for	for	ADP
ejpam-5366	158	2	gem	gem	NOUN
ejpam-5366	158	3	)	)	PUNCT
ejpam-5366	158	4	.	.	PUNCT
ejpam-5366	159	1	m.	m.	NOUN
ejpam-5366	159	2	m.	m.	NOUN
ejpam-5366	159	3	khader	khader	PROPN
ejpam-5366	159	4	/	/	SYM
ejpam-5366	159	5	eur	eur	PROPN
ejpam-5366	159	6	.	.	PUNCT
ejpam-5366	160	1	j.	j.	PROPN
ejpam-5366	160	2	pure	pure	PROPN
ejpam-5366	160	3	appl	appl	PROPN
ejpam-5366	160	4	.	.	PROPN
ejpam-5366	160	5	math	math	PROPN
ejpam-5366	160	6	,	,	PUNCT
ejpam-5366	160	7	17	17	NUM
ejpam-5366	160	8	(	(	PUNCT
ejpam-5366	160	9	4	4	NUM
ejpam-5366	160	10	)	)	PUNCT
ejpam-5366	160	11	(	(	PUNCT
ejpam-5366	160	12	2024	2024	NUM
ejpam-5366	160	13	)	)	PUNCT
ejpam-5366	160	14	,	,	PUNCT
ejpam-5366	160	15	2676	2676	NUM
ejpam-5366	160	16	-	-	SYM
ejpam-5366	160	17	2691	2691	NUM
ejpam-5366	160	18	2687	2687	NUM
ejpam-5366	160	19	fig	fig	NOUN
ejpam-5366	160	20	.	.	PUNCT
ejpam-5366	161	1	5	5	NUM
ejpam-5366	161	2	:	:	PUNCT
ejpam-5366	161	3	the	the	DET
ejpam-5366	161	4	effect	effect	NOUN
ejpam-5366	161	5	of	of	ADP
ejpam-5366	161	6	µ	µ	NOUN
ejpam-5366	161	7	on	on	ADP
ejpam-5366	161	8	the	the	DET
ejpam-5366	161	9	approximate	approximate	ADJ
ejpam-5366	161	10	solution	solution	NOUN
ejpam-5366	161	11	si(t	si(t	NOUN
ejpam-5366	161	12	)	)	PUNCT
ejpam-5366	161	13	,	,	PUNCT
ejpam-5366	161	14	i	i	PRON
ejpam-5366	161	15	=	=	NOUN
ejpam-5366	161	16	1	1	NUM
ejpam-5366	161	17	,	,	PUNCT
ejpam-5366	161	18	2	2	NUM
ejpam-5366	161	19	,	,	PUNCT
ejpam-5366	161	20	3	3	NUM
ejpam-5366	161	21	,	,	PUNCT
ejpam-5366	161	22	4	4	NUM
ejpam-5366	161	23	,	,	PUNCT
ejpam-5366	161	24	5	5	NUM
ejpam-5366	161	25	.	.	PUNCT
ejpam-5366	161	26	m.	m.	NOUN
ejpam-5366	161	27	m.	m.	NOUN
ejpam-5366	161	28	khader	khader	PROPN
ejpam-5366	161	29	/	/	SYM
ejpam-5366	161	30	eur	eur	PROPN
ejpam-5366	161	31	.	.	PUNCT
ejpam-5366	162	1	j.	j.	PROPN
ejpam-5366	162	2	pure	pure	PROPN
ejpam-5366	162	3	appl	appl	PROPN
ejpam-5366	162	4	.	.	PROPN
ejpam-5366	162	5	math	math	PROPN
ejpam-5366	162	6	,	,	PUNCT
ejpam-5366	162	7	17	17	NUM
ejpam-5366	162	8	(	(	PUNCT
ejpam-5366	162	9	4	4	NUM
ejpam-5366	162	10	)	)	PUNCT
ejpam-5366	162	11	(	(	PUNCT
ejpam-5366	162	12	2024	2024	NUM
ejpam-5366	162	13	)	)	PUNCT
ejpam-5366	162	14	,	,	PUNCT
ejpam-5366	162	15	2676	2676	NUM
ejpam-5366	162	16	-	-	SYM
ejpam-5366	162	17	2691	2691	NUM
ejpam-5366	162	18	2688	2688	NUM
ejpam-5366	162	19	fig	fig	NOUN
ejpam-5366	162	20	.	.	PUNCT
ejpam-5366	163	1	6	6	NUM
ejpam-5366	163	2	:	:	PUNCT
ejpam-5366	163	3	the	the	DET
ejpam-5366	163	4	effect	effect	NOUN
ejpam-5366	163	5	of	of	ADP
ejpam-5366	163	6	κ	κ	PROPN
ejpam-5366	163	7	on	on	ADP
ejpam-5366	163	8	the	the	DET
ejpam-5366	163	9	approximate	approximate	ADJ
ejpam-5366	163	10	solution	solution	NOUN
ejpam-5366	163	11	si(t	si(t	NOUN
ejpam-5366	163	12	)	)	PUNCT
ejpam-5366	163	13	,	,	PUNCT
ejpam-5366	163	14	i	i	PRON
ejpam-5366	163	15	=	=	NOUN
ejpam-5366	163	16	1	1	NUM
ejpam-5366	163	17	,	,	PUNCT
ejpam-5366	163	18	2	2	NUM
ejpam-5366	163	19	,	,	PUNCT
ejpam-5366	163	20	3	3	NUM
ejpam-5366	163	21	,	,	PUNCT
ejpam-5366	163	22	4	4	NUM
ejpam-5366	163	23	,	,	PUNCT
ejpam-5366	163	24	5	5	NUM
ejpam-5366	163	25	.	.	PUNCT
ejpam-5366	163	26	m.	m.	NOUN
ejpam-5366	163	27	m.	m.	NOUN
ejpam-5366	163	28	khader	khader	PROPN
ejpam-5366	163	29	/	/	SYM
ejpam-5366	163	30	eur	eur	PROPN
ejpam-5366	163	31	.	.	PUNCT
ejpam-5366	164	1	j.	j.	PROPN
ejpam-5366	164	2	pure	pure	PROPN
ejpam-5366	164	3	appl	appl	PROPN
ejpam-5366	164	4	.	.	PROPN
ejpam-5366	164	5	math	math	PROPN
ejpam-5366	164	6	,	,	PUNCT
ejpam-5366	164	7	17	17	NUM
ejpam-5366	164	8	(	(	PUNCT
ejpam-5366	164	9	4	4	NUM
ejpam-5366	164	10	)	)	PUNCT
ejpam-5366	164	11	(	(	PUNCT
ejpam-5366	164	12	2024	2024	NUM
ejpam-5366	164	13	)	)	PUNCT
ejpam-5366	164	14	,	,	PUNCT
ejpam-5366	164	15	2676	2676	NUM
ejpam-5366	164	16	-	-	SYM
ejpam-5366	164	17	2691	2691	NUM
ejpam-5366	164	18	2689	2689	NUM
ejpam-5366	164	19	table	table	NOUN
ejpam-5366	164	20	2	2	NUM
ejpam-5366	164	21	:	:	PUNCT
ejpam-5366	164	22	values	value	NOUN
ejpam-5366	164	23	of	of	ADP
ejpam-5366	164	24	the	the	DET
ejpam-5366	164	25	rae	rae	NOUN
ejpam-5366	164	26	for	for	ADP
ejpam-5366	164	27	the	the	DET
ejpam-5366	164	28	present	present	ADJ
ejpam-5366	164	29	method	method	NOUN
ejpam-5366	164	30	(	(	PUNCT
ejpam-5366	164	31	first	first	ADJ
ejpam-5366	164	32	row	row	NOUN
ejpam-5366	164	33	)	)	PUNCT
ejpam-5366	164	34	and	and	CCONJ
ejpam-5366	164	35	gem	gem	NOUN
ejpam-5366	164	36	(	(	PUNCT
ejpam-5366	164	37	second	second	ADJ
ejpam-5366	164	38	row	row	NOUN
ejpam-5366	164	39	)	)	PUNCT
ejpam-5366	164	40	with	with	ADP
ejpam-5366	164	41	α	α	NOUN
ejpam-5366	164	42	=	=	NOUN
ejpam-5366	164	43	0.95	0.95	NUM
ejpam-5366	164	44	.	.	PUNCT
ejpam-5366	165	1	k	k	PROPN
ejpam-5366	165	2	rae	rae	PROPN
ejpam-5366	165	3	−	−	PROPN
ejpam-5366	165	4	s1(tk	s1(tk	PROPN
ejpam-5366	165	5	)	)	PUNCT
ejpam-5366	165	6	rae	rae	PROPN
ejpam-5366	165	7	−	−	PROPN
ejpam-5366	165	8	s2(tk	s2(tk	PROPN
ejpam-5366	165	9	)	)	PUNCT
ejpam-5366	165	10	rae	rae	PROPN
ejpam-5366	165	11	−	−	PROPN
ejpam-5366	165	12	s3(tk	s3(tk	PROPN
ejpam-5366	165	13	)	)	PUNCT
ejpam-5366	165	14	rae	rae	PROPN
ejpam-5366	165	15	−	−	PROPN
ejpam-5366	165	16	s4(tk	s4(tk	PROPN
ejpam-5366	165	17	)	)	PUNCT
ejpam-5366	165	18	rae	rae	PROPN
ejpam-5366	165	19	−	−	PROPN
ejpam-5366	165	20	s5(tk	s5(tk	PROPN
ejpam-5366	165	21	)	)	PUNCT
ejpam-5366	166	1	10	10	NUM
ejpam-5366	166	2	0.2583×	0.2583×	NOUN
ejpam-5366	166	3	10−5	10−5	NUM
ejpam-5366	166	4	5.2660×	5.2660×	NUM
ejpam-5366	166	5	10−4	10−4	NUM
ejpam-5366	166	6	8.2511×	8.2511×	NUM
ejpam-5366	166	7	10−3	10−3	NUM
ejpam-5366	166	8	8.6542×	8.6542×	NUM
ejpam-5366	166	9	10−3	10−3	NUM
ejpam-5366	166	10	6.3508×	6.3508×	NUM
ejpam-5366	166	11	10−4	10−4	NUM
ejpam-5366	166	12	7.5621×	7.5621×	NOUN
ejpam-5366	166	13	10−3	10−3	NUM
ejpam-5366	166	14	6.3255×	6.3255×	NUM
ejpam-5366	166	15	10−2	10−2	NUM
ejpam-5366	166	16	7.5621×	7.5621×	NUM
ejpam-5366	166	17	10−1	10−1	NUM
ejpam-5366	166	18	0.0226×	0.0226×	NUM
ejpam-5366	166	19	10−2	10−2	NUM
ejpam-5366	166	20	9.2145×	9.2145×	NUM
ejpam-5366	166	21	10−3	10−3	NUM
ejpam-5366	166	22	20	20	NUM
ejpam-5366	166	23	4.2154×	4.2154×	NUM
ejpam-5366	166	24	10−4	10−4	NUM
ejpam-5366	166	25	1.9512×	1.9512×	NOUN
ejpam-5366	166	26	10−5	10−5	NUM
ejpam-5366	166	27	7.2584×	7.2584×	NOUN
ejpam-5366	167	1	10−5	10−5	NUM
ejpam-5366	167	2	6.2581×	6.2581×	NOUN
ejpam-5366	168	1	10−5	10−5	NUM
ejpam-5366	168	2	1.2005×	1.2005×	NUM
ejpam-5366	168	3	10−4	10−4	NUM
ejpam-5366	168	4	8.5201×	8.5201×	NUM
ejpam-5366	168	5	10−2	10−2	NUM
ejpam-5366	168	6	8.2509×	8.2509×	NOUN
ejpam-5366	168	7	10−2	10−2	NUM
ejpam-5366	168	8	7.2156×	7.2156×	NUM
ejpam-5366	168	9	10−4	10−4	NUM
ejpam-5366	168	10	9.2812×	9.2812×	NUM
ejpam-5366	168	11	10−3	10−3	NUM
ejpam-5366	168	12	9.2580×	9.2580×	NOUN
ejpam-5366	168	13	10−2	10−2	NUM
ejpam-5366	168	14	30	30	NUM
ejpam-5366	168	15	8.0056×	8.0056×	NUM
ejpam-5366	168	16	10−6	10−6	NUM
ejpam-5366	168	17	9.2258×	9.2258×	NUM
ejpam-5366	168	18	10−5	10−5	NUM
ejpam-5366	168	19	2.0897×	2.0897×	NUM
ejpam-5366	168	20	10−5	10−5	NUM
ejpam-5366	168	21	9.2581×	9.2581×	X
ejpam-5366	169	1	10−6	10−6	NUM
ejpam-5366	169	2	6.2581×	6.2581×	NUM
ejpam-5366	169	3	10−5	10−5	NUM
ejpam-5366	169	4	8.2581×	8.2581×	NUM
ejpam-5366	169	5	10−4	10−4	NUM
ejpam-5366	169	6	9.2581×	9.2581×	NUM
ejpam-5366	169	7	10−3	10−3	NUM
ejpam-5366	169	8	8.2554×	8.2554×	NUM
ejpam-5366	169	9	10−3	10−3	NUM
ejpam-5366	169	10	6.0057×	6.0057×	NUM
ejpam-5366	169	11	10−4	10−4	NUM
ejpam-5366	169	12	6.0257×	6.0257×	NUM
ejpam-5366	169	13	10−4	10−4	NUM
ejpam-5366	169	14	40	40	NUM
ejpam-5366	169	15	6.2014×	6.2014×	NUM
ejpam-5366	169	16	10−5	10−5	NUM
ejpam-5366	169	17	9.8025×	9.8025×	NUM
ejpam-5366	169	18	10−6	10−6	NUM
ejpam-5366	169	19	5.6241×	5.6241×	NUM
ejpam-5366	169	20	10−5	10−5	NUM
ejpam-5366	169	21	8.2943×	8.2943×	NUM
ejpam-5366	169	22	10−5	10−5	NUM
ejpam-5366	169	23	6.2581×	6.2581×	NUM
ejpam-5366	170	1	10−5	10−5	NUM
ejpam-5366	170	2	5.2210×	5.2210×	SYM
ejpam-5366	170	3	10−3	10−3	NUM
ejpam-5366	170	4	4.0579×	4.0579×	NUM
ejpam-5366	170	5	10−4	10−4	NUM
ejpam-5366	170	6	9.3025×	9.3025×	NUM
ejpam-5366	170	7	10−2	10−2	NUM
ejpam-5366	170	8	8.2581×	8.2581×	NUM
ejpam-5366	170	9	10−3	10−3	NUM
ejpam-5366	170	10	9.2508×	9.2508×	NUM
ejpam-5366	170	11	10−3	10−3	NUM
ejpam-5366	170	12	50	50	NUM
ejpam-5366	170	13	8.2030×	8.2030×	NUM
ejpam-5366	170	14	10−7	10−7	NUM
ejpam-5366	170	15	6.0258×	6.0258×	NUM
ejpam-5366	170	16	10−7	10−7	NUM
ejpam-5366	170	17	5.2017×	5.2017×	NUM
ejpam-5366	170	18	10−6	10−6	NUM
ejpam-5366	170	19	8.2589×	8.2589×	NUM
ejpam-5366	170	20	10−6	10−6	NUM
ejpam-5366	170	21	7.5623×	7.5623×	NUM
ejpam-5366	170	22	10−6	10−6	NUM
ejpam-5366	170	23	8.2587×	8.2587×	NUM
ejpam-5366	170	24	10−5	10−5	NUM
ejpam-5366	170	25	4.2587×	4.2587×	NUM
ejpam-5366	170	26	10−5	10−5	NUM
ejpam-5366	170	27	9.3652×	9.3652×	NOUN
ejpam-5366	170	28	10−4	10−4	NUM
ejpam-5366	170	29	8.5214×	8.5214×	NUM
ejpam-5366	170	30	10−5	10−5	NUM
ejpam-5366	170	31	9.0258×	9.0258×	NOUN
ejpam-5366	170	32	10−4	10−4	NUM
ejpam-5366	170	33	60	60	NUM
ejpam-5366	170	34	9.2584×	9.2584×	NUM
ejpam-5366	170	35	10−6	10−6	NUM
ejpam-5366	170	36	5.0254×	5.0254×	NUM
ejpam-5366	170	37	10−7	10−7	NUM
ejpam-5366	170	38	8.2541×	8.2541×	NOUN
ejpam-5366	170	39	10−7	10−7	NUM
ejpam-5366	170	40	6.2587×	6.2587×	NUM
ejpam-5366	170	41	10−7	10−7	NUM
ejpam-5366	170	42	6.0258×	6.0258×	NOUN
ejpam-5366	170	43	10−6	10−6	NUM
ejpam-5366	170	44	7.2564×	7.2564×	NUM
ejpam-5366	170	45	10−4	10−4	NUM
ejpam-5366	170	46	7.5824×	7.5824×	NUM
ejpam-5366	170	47	10−5	10−5	NUM
ejpam-5366	170	48	9.3587×	9.3587×	NUM
ejpam-5366	170	49	10−5	10−5	NUM
ejpam-5366	170	50	9.2587×	9.2587×	NUM
ejpam-5366	170	51	10−4	10−4	NUM
ejpam-5366	170	52	5.3698×	5.3698×	NUM
ejpam-5366	170	53	10−4	10−4	NUM
ejpam-5366	170	54	70	70	NUM
ejpam-5366	170	55	6.2874×	6.2874×	NOUN
ejpam-5366	170	56	10−8	10−8	NUM
ejpam-5366	170	57	9.2580×	9.2580×	NOUN
ejpam-5366	170	58	10−7	10−7	NUM
ejpam-5366	170	59	7.2054×	7.2054×	NOUN
ejpam-5366	170	60	10−7	10−7	NUM
ejpam-5366	170	61	6.3258×	6.3258×	NOUN
ejpam-5366	170	62	10−8	10−8	NUM
ejpam-5366	170	63	7.6250×	7.6250×	NUM
ejpam-5366	170	64	10−8	10−8	NUM
ejpam-5366	170	65	4.6528×	4.6528×	NUM
ejpam-5366	170	66	10−7	10−7	NUM
ejpam-5366	170	67	7.9542×	7.9542×	NUM
ejpam-5366	170	68	10−5	10−5	NUM
ejpam-5366	170	69	0.1593×	0.1593×	NOUN
ejpam-5366	170	70	10−5	10−5	NUM
ejpam-5366	170	71	5.2810×	5.2810×	NOUN
ejpam-5366	170	72	10−7	10−7	NUM
ejpam-5366	170	73	6.2591×	6.2591×	NUM
ejpam-5366	170	74	10−6	10−6	NUM
ejpam-5366	170	75	80	80	NUM
ejpam-5366	170	76	5.2914×	5.2914×	NUM
ejpam-5366	170	77	10−7	10−7	NUM
ejpam-5366	170	78	7.5630×	7.5630×	NOUN
ejpam-5366	170	79	10−8	10−8	NUM
ejpam-5366	170	80	4.6528×	4.6528×	NUM
ejpam-5366	170	81	10−7	10−7	NUM
ejpam-5366	170	82	2.2147×	2.2147×	NOUN
ejpam-5366	170	83	10−8	10−8	NUM
ejpam-5366	170	84	8.9254×	8.9254×	NUM
ejpam-5366	170	85	10−7	10−7	NUM
ejpam-5366	170	86	6.2581×	6.2581×	NUM
ejpam-5366	170	87	10−6	10−6	NUM
ejpam-5366	170	88	7.5829×	7.5829×	NUM
ejpam-5366	170	89	10−7	10−7	NUM
ejpam-5366	170	90	5.2810×	5.2810×	NOUN
ejpam-5366	170	91	10−6	10−6	NUM
ejpam-5366	170	92	5.9190×	5.9190×	NUM
ejpam-5366	170	93	10−7	10−7	NUM
ejpam-5366	170	94	6.2581×	6.2581×	NUM
ejpam-5366	170	95	10−5	10−5	NUM
ejpam-5366	171	1	90	90	NUM
ejpam-5366	171	2	6.2587×	6.2587×	NUM
ejpam-5366	171	3	10−9	10−9	NUM
ejpam-5366	171	4	0.2580×	0.2580×	NOUN
ejpam-5366	171	5	10−8	10−8	NUM
ejpam-5366	171	6	1.2250×	1.2250×	NUM
ejpam-5366	171	7	10−9	10−9	NUM
ejpam-5366	171	8	2.5879×	2.5879×	NUM
ejpam-5366	171	9	10−9	10−9	NUM
ejpam-5366	171	10	6.2415×	6.2415×	NUM
ejpam-5366	171	11	10−8	10−8	NUM
ejpam-5366	171	12	5.2614×	5.2614×	NUM
ejpam-5366	171	13	10−7	10−7	NUM
ejpam-5366	171	14	2.2581×	2.2581×	NUM
ejpam-5366	171	15	10−6	10−6	NUM
ejpam-5366	171	16	3.9650×	3.9650×	NUM
ejpam-5366	171	17	10−7	10−7	NUM
ejpam-5366	171	18	4.2589×	4.2589×	NOUN
ejpam-5366	171	19	10−7	10−7	NUM
ejpam-5366	171	20	3.2590×	3.2590×	NUM
ejpam-5366	171	21	10−6	10−6	NUM
ejpam-5366	171	22	100	100	NUM
ejpam-5366	171	23	5.6280×	5.6280×	NOUN
ejpam-5366	171	24	10−8	10−8	NUM
ejpam-5366	171	25	7.2941×	7.2941×	NUM
ejpam-5366	171	26	10−9	10−9	NUM
ejpam-5366	171	27	1.0236×	1.0236×	NUM
ejpam-5366	171	28	10−9	10−9	NUM
ejpam-5366	171	29	1.5587×	1.5587×	NUM
ejpam-5366	171	30	10−8	10−8	NUM
ejpam-5366	171	31	9.0054×	9.0054×	NOUN
ejpam-5366	171	32	10−8	10−8	NUM
ejpam-5366	171	33	8.2541×	8.2541×	NOUN
ejpam-5366	171	34	10−6	10−6	NUM
ejpam-5366	171	35	5.2913×	5.2913×	NUM
ejpam-5366	171	36	10−7	10−7	NUM
ejpam-5366	171	37	7.2564×	7.2564×	NUM
ejpam-5366	171	38	10−7	10−7	NUM
ejpam-5366	171	39	6.2591×	6.2591×	NUM
ejpam-5366	171	40	10−6	10−6	NUM
ejpam-5366	171	41	2.9514×	2.9514×	NUM
ejpam-5366	171	42	10−7	10−7	NUM
ejpam-5366	171	43	7	7	NUM
ejpam-5366	171	44	.	.	PUNCT
ejpam-5366	171	45	conclusions	conclusion	NOUN
ejpam-5366	171	46	and	and	CCONJ
ejpam-5366	171	47	discussions	discussion	NOUN
ejpam-5366	171	48	in	in	ADP
ejpam-5366	171	49	this	this	DET
ejpam-5366	171	50	research	research	NOUN
ejpam-5366	171	51	work	work	NOUN
ejpam-5366	172	1	,	,	PUNCT
ejpam-5366	172	2	we	we	PRON
ejpam-5366	172	3	applied	apply	VERB
ejpam-5366	172	4	the	the	DET
ejpam-5366	172	5	modified	modify	VERB
ejpam-5366	172	6	fractional	fractional	PROPN
ejpam-5366	172	7	euler	euler	NOUN
ejpam-5366	172	8	method	method	NOUN
ejpam-5366	172	9	to	to	PART
ejpam-5366	172	10	provide	provide	VERB
ejpam-5366	172	11	a	a	DET
ejpam-5366	172	12	numerical	numerical	ADJ
ejpam-5366	172	13	study	study	NOUN
ejpam-5366	172	14	and	and	CCONJ
ejpam-5366	172	15	simulation	simulation	NOUN
ejpam-5366	172	16	of	of	ADP
ejpam-5366	172	17	the	the	DET
ejpam-5366	172	18	smoking	smoking	NOUN
ejpam-5366	172	19	model	model	NOUN
ejpam-5366	172	20	in	in	ADP
ejpam-5366	172	21	its	its	PRON
ejpam-5366	172	22	fractional	fractional	ADJ
ejpam-5366	172	23	form	form	NOUN
ejpam-5366	172	24	,	,	PUNCT
ejpam-5366	172	25	which	which	PRON
ejpam-5366	172	26	is	be	AUX
ejpam-5366	172	27	represented	represent	VERB
ejpam-5366	172	28	by	by	ADP
ejpam-5366	172	29	a	a	DET
ejpam-5366	172	30	system	system	NOUN
ejpam-5366	172	31	of	of	ADP
ejpam-5366	172	32	mathematical	mathematical	ADJ
ejpam-5366	172	33	equations	equation	NOUN
ejpam-5366	172	34	.	.	PUNCT
ejpam-5366	173	1	therefore	therefore	ADV
ejpam-5366	173	2	,	,	PUNCT
ejpam-5366	173	3	we	we	PRON
ejpam-5366	173	4	paid	pay	VERB
ejpam-5366	173	5	attention	attention	NOUN
ejpam-5366	173	6	to	to	ADP
ejpam-5366	173	7	studying	study	VERB
ejpam-5366	173	8	the	the	DET
ejpam-5366	173	9	behavior	behavior	NOUN
ejpam-5366	173	10	of	of	ADP
ejpam-5366	173	11	the	the	DET
ejpam-5366	173	12	numerical	numerical	ADJ
ejpam-5366	173	13	solution	solution	NOUN
ejpam-5366	173	14	of	of	ADP
ejpam-5366	173	15	the	the	DET
ejpam-5366	173	16	problem	problem	NOUN
ejpam-5366	173	17	under	under	ADP
ejpam-5366	173	18	study	study	NOUN
ejpam-5366	173	19	for	for	ADP
ejpam-5366	173	20	different	different	ADJ
ejpam-5366	173	21	fractional	fractional	ADJ
ejpam-5366	173	22	motions	motion	NOUN
ejpam-5366	173	23	as	as	ADV
ejpam-5366	173	24	well	well	ADV
ejpam-5366	173	25	as	as	ADP
ejpam-5366	173	26	for	for	ADP
ejpam-5366	173	27	the	the	DET
ejpam-5366	173	28	standard	standard	ADJ
ejpam-5366	173	29	motion	motion	NOUN
ejpam-5366	173	30	α	α	NOUN
ejpam-5366	173	31	=	=	SYM
ejpam-5366	173	32	1	1	X
ejpam-5366	173	33	.	.	PUNCT
ejpam-5366	174	1	the	the	DET
ejpam-5366	174	2	resulting	result	VERB
ejpam-5366	174	3	numerical	numerical	ADJ
ejpam-5366	174	4	solution	solution	NOUN
ejpam-5366	174	5	was	be	AUX
ejpam-5366	174	6	also	also	ADV
ejpam-5366	174	7	compared	compare	VERB
ejpam-5366	174	8	with	with	ADP
ejpam-5366	174	9	its	its	PRON
ejpam-5366	174	10	counterpart	counterpart	NOUN
ejpam-5366	174	11	and	and	CCONJ
ejpam-5366	174	12	the	the	DET
ejpam-5366	174	13	result	result	NOUN
ejpam-5366	174	14	of	of	ADP
ejpam-5366	174	15	the	the	DET
ejpam-5366	174	16	generalized	generalized	ADJ
ejpam-5366	174	17	fem	fem	NOUN
ejpam-5366	174	18	,	,	PUNCT
ejpam-5366	174	19	and	and	CCONJ
ejpam-5366	174	20	this	this	DET
ejpam-5366	174	21	comparison	comparison	NOUN
ejpam-5366	174	22	helped	help	VERB
ejpam-5366	174	23	us	we	PRON
ejpam-5366	174	24	to	to	PART
ejpam-5366	174	25	fully	fully	ADV
ejpam-5366	174	26	confirm	confirm	VERB
ejpam-5366	174	27	that	that	SCONJ
ejpam-5366	174	28	the	the	DET
ejpam-5366	174	29	numerical	numerical	ADJ
ejpam-5366	174	30	solution	solution	NOUN
ejpam-5366	174	31	resulting	result	VERB
ejpam-5366	174	32	from	from	ADP
ejpam-5366	174	33	this	this	DET
ejpam-5366	174	34	applied	apply	VERB
ejpam-5366	174	35	numerical	numerical	ADJ
ejpam-5366	174	36	method	method	NOUN
ejpam-5366	174	37	agrees	agree	VERB
ejpam-5366	174	38	well	well	ADV
ejpam-5366	174	39	with	with	ADP
ejpam-5366	174	40	the	the	DET
ejpam-5366	174	41	standard	standard	ADJ
ejpam-5366	174	42	case	case	NOUN
ejpam-5366	174	43	of	of	ADP
ejpam-5366	174	44	the	the	DET
ejpam-5366	174	45	same	same	ADJ
ejpam-5366	174	46	method	method	NOUN
ejpam-5366	174	47	.	.	PUNCT
ejpam-5366	175	1	in	in	ADP
ejpam-5366	175	2	addition	addition	NOUN
ejpam-5366	175	3	,	,	PUNCT
ejpam-5366	175	4	through	through	ADP
ejpam-5366	175	5	this	this	DET
ejpam-5366	175	6	study	study	NOUN
ejpam-5366	175	7	,	,	PUNCT
ejpam-5366	175	8	we	we	PRON
ejpam-5366	175	9	found	find	VERB
ejpam-5366	175	10	that	that	SCONJ
ejpam-5366	175	11	this	this	DET
ejpam-5366	175	12	proposed	propose	VERB
ejpam-5366	175	13	approach	approach	NOUN
ejpam-5366	175	14	can	can	AUX
ejpam-5366	175	15	solve	solve	VERB
ejpam-5366	175	16	problems	problem	NOUN
ejpam-5366	175	17	effectively	effectively	ADV
ejpam-5366	175	18	with	with	ADP
ejpam-5366	175	19	high	high	ADJ
ejpam-5366	175	20	accuracy	accuracy	NOUN
ejpam-5366	175	21	.	.	PUNCT
ejpam-5366	176	1	finally	finally	ADV
ejpam-5366	176	2	,	,	PUNCT
ejpam-5366	176	3	the	the	DET
ejpam-5366	176	4	present	present	ADJ
ejpam-5366	176	5	study	study	NOUN
ejpam-5366	176	6	may	may	AUX
ejpam-5366	176	7	contribute	contribute	VERB
ejpam-5366	176	8	to	to	ADP
ejpam-5366	176	9	providing	provide	VERB
ejpam-5366	176	10	more	more	ADV
ejpam-5366	176	11	robust	robust	ADJ
ejpam-5366	176	12	physical	physical	ADJ
ejpam-5366	176	13	explanations	explanation	NOUN
ejpam-5366	176	14	for	for	ADP
ejpam-5366	176	15	future	future	ADJ
ejpam-5366	176	16	theoretical	theoretical	ADJ
ejpam-5366	176	17	and	and	CCONJ
ejpam-5366	176	18	computational	computational	ADJ
ejpam-5366	176	19	studies	study	NOUN
ejpam-5366	176	20	on	on	ADP
ejpam-5366	176	21	the	the	DET
ejpam-5366	176	22	same	same	ADJ
ejpam-5366	176	23	topic	topic	NOUN
ejpam-5366	176	24	.	.	PUNCT
ejpam-5366	177	1	all	all	DET
ejpam-5366	177	2	calculations	calculation	NOUN
ejpam-5366	177	3	in	in	ADP
ejpam-5366	177	4	this	this	DET
ejpam-5366	177	5	research	research	NOUN
ejpam-5366	177	6	work	work	NOUN
ejpam-5366	177	7	were	be	AUX
ejpam-5366	177	8	done	do	VERB
ejpam-5366	177	9	using	use	VERB
ejpam-5366	177	10	mathematica	mathematica	PROPN
ejpam-5366	177	11	8.0	8.0	NUM
ejpam-5366	177	12	.	.	PUNCT
ejpam-5366	178	1	conflict	conflict	NOUN
ejpam-5366	178	2	of	of	ADP
ejpam-5366	178	3	interest	interest	NOUN
ejpam-5366	178	4	:	:	PUNCT
ejpam-5366	178	5	the	the	DET
ejpam-5366	178	6	author	author	NOUN
ejpam-5366	178	7	has	have	VERB
ejpam-5366	178	8	no	no	DET
ejpam-5366	178	9	relevant	relevant	ADJ
ejpam-5366	178	10	financial	financial	ADJ
ejpam-5366	178	11	or	or	CCONJ
ejpam-5366	178	12	non	non	ADJ
ejpam-5366	178	13	-	-	ADJ
ejpam-5366	178	14	financial	financial	ADJ
ejpam-5366	178	15	interests	interest	NOUN
ejpam-5366	178	16	to	to	PART
ejpam-5366	178	17	disclose	disclose	VERB
ejpam-5366	178	18	.	.	PUNCT
ejpam-5366	179	1	data	datum	NOUN
ejpam-5366	179	2	availability	availability	NOUN
ejpam-5366	179	3	:	:	PUNCT
ejpam-5366	179	4	the	the	DET
ejpam-5366	179	5	datasets	dataset	NOUN
ejpam-5366	179	6	generated	generate	VERB
ejpam-5366	179	7	during	during	ADP
ejpam-5366	179	8	the	the	DET
ejpam-5366	179	9	current	current	ADJ
ejpam-5366	179	10	study	study	NOUN
ejpam-5366	179	11	are	be	AUX
ejpam-5366	179	12	available	available	ADJ
ejpam-5366	179	13	from	from	ADP
ejpam-5366	179	14	the	the	DET
ejpam-5366	179	15	corresponding	corresponding	ADJ
ejpam-5366	179	16	author	author	NOUN
ejpam-5366	179	17	upon	upon	SCONJ
ejpam-5366	179	18	reasonable	reasonable	ADJ
ejpam-5366	179	19	request	request	NOUN
ejpam-5366	179	20	.	.	PUNCT
ejpam-5366	180	1	references	reference	NOUN
ejpam-5366	180	2	2690	2690	NUM
ejpam-5366	180	3	references	reference	NOUN
ejpam-5366	180	4	[	[	X
ejpam-5366	180	5	1	1	NUM
ejpam-5366	180	6	]	]	PUNCT
ejpam-5366	180	7	m.	m.	NOUN
ejpam-5366	180	8	adel	adel	PROPN
ejpam-5366	180	9	,	,	PUNCT
ejpam-5366	180	10	m.m	m.m	PROPN
ejpam-5366	180	11	.	.	PROPN
ejpam-5366	180	12	khader	khader	PROPN
ejpam-5366	180	13	,	,	PUNCT
ejpam-5366	180	14	i.	i.	PROPN
ejpam-5366	180	15	alraddadi	alraddadi	PROPN
ejpam-5366	180	16	,	,	PUNCT
ejpam-5366	180	17	n.h	n.h	PROPN
ejpam-5366	180	18	.	.	PROPN
ejpam-5366	180	19	sweilam	sweilam	PROPN
ejpam-5366	180	20	,	,	PUNCT
ejpam-5366	180	21	m.b	m.b	PROPN
ejpam-5366	180	22	.	.	PROPN
ejpam-5366	180	23	riaz	riaz	PROPN
ejpam-5366	180	24	,	,	PUNCT
ejpam-5366	180	25	and	and	CCONJ
ejpam-5366	180	26	h.	h.	PROPN
ejpam-5366	180	27	ahmad	ahmad	PROPN
ejpam-5366	180	28	.	.	PUNCT
ejpam-5366	181	1	effective	effective	ADJ
ejpam-5366	181	2	numerical	numerical	ADJ
ejpam-5366	181	3	method	method	NOUN
ejpam-5366	181	4	for	for	ADP
ejpam-5366	181	5	studying	study	VERB
ejpam-5366	181	6	the	the	DET
ejpam-5366	181	7	fractal	fractal	ADJ
ejpam-5366	181	8	-	-	PUNCT
ejpam-5366	181	9	fractional	fractional	ADJ
ejpam-5366	181	10	smoking	smoking	NOUN
ejpam-5366	181	11	model	model	NOUN
ejpam-5366	181	12	.	.	PUNCT
ejpam-5366	182	1	fractals	fractal	NOUN
ejpam-5366	182	2	,	,	PUNCT
ejpam-5366	182	3	pages	page	NOUN
ejpam-5366	182	4	xx	xx	NUM
ejpam-5366	182	5	–	–	PUNCT
ejpam-5366	182	6	yy	yy	PROPN
ejpam-5366	182	7	,	,	PUNCT
ejpam-5366	182	8	2024	2024	NUM
ejpam-5366	182	9	.	.	PUNCT
ejpam-5366	183	1	[	[	X
ejpam-5366	183	2	2	2	NUM
ejpam-5366	183	3	]	]	PUNCT
ejpam-5366	183	4	m.	m.	NOUN
ejpam-5366	183	5	adel	adel	PROPN
ejpam-5366	183	6	,	,	PUNCT
ejpam-5366	183	7	h.m	h.m	PROPN
ejpam-5366	183	8	.	.	PROPN
ejpam-5366	183	9	srivastava	srivastava	PROPN
ejpam-5366	183	10	,	,	PUNCT
ejpam-5366	183	11	and	and	CCONJ
ejpam-5366	183	12	m.m	m.m	PROPN
ejpam-5366	183	13	.	.	PROPN
ejpam-5366	183	14	khader	khader	PROPN
ejpam-5366	183	15	.	.	PUNCT
ejpam-5366	184	1	implementation	implementation	NOUN
ejpam-5366	184	2	of	of	ADP
ejpam-5366	184	3	an	an	DET
ejpam-5366	184	4	accurate	accurate	ADJ
ejpam-5366	184	5	method	method	NOUN
ejpam-5366	184	6	for	for	ADP
ejpam-5366	184	7	the	the	DET
ejpam-5366	184	8	analysis	analysis	NOUN
ejpam-5366	184	9	and	and	CCONJ
ejpam-5366	184	10	simulation	simulation	NOUN
ejpam-5366	184	11	of	of	ADP
ejpam-5366	184	12	electrical	electrical	ADJ
ejpam-5366	184	13	r	r	NOUN
ejpam-5366	184	14	-	-	PUNCT
ejpam-5366	184	15	l	l	NOUN
ejpam-5366	184	16	circuits	circuit	NOUN
ejpam-5366	184	17	.	.	PUNCT
ejpam-5366	185	1	math	math	NOUN
ejpam-5366	185	2	.	.	PUNCT
ejpam-5366	186	1	meth	meth	NOUN
ejpam-5366	186	2	.	.	PUNCT
ejpam-5366	187	1	appl	appl	PROPN
ejpam-5366	187	2	.	.	PUNCT
ejpam-5366	188	1	sci	sci	PROPN
ejpam-5366	188	2	.	.	PROPN
ejpam-5366	188	3	,	,	PUNCT
ejpam-5366	188	4	46:8362–8371	46:8362–8371	PROPN
ejpam-5366	188	5	,	,	PUNCT
ejpam-5366	188	6	2023	2023	NUM
ejpam-5366	188	7	.	.	PUNCT
ejpam-5366	189	1	[	[	X
ejpam-5366	189	2	3	3	X
ejpam-5366	189	3	]	]	PUNCT
ejpam-5366	189	4	z.	z.	PROPN
ejpam-5366	189	5	alkhudhari	alkhudhari	PROPN
ejpam-5366	189	6	,	,	PUNCT
ejpam-5366	189	7	s.	s.	PROPN
ejpam-5366	189	8	al	al	PROPN
ejpam-5366	189	9	-	-	PUNCT
ejpam-5366	189	10	sheikh	sheikh	PROPN
ejpam-5366	189	11	,	,	PUNCT
ejpam-5366	189	12	and	and	CCONJ
ejpam-5366	189	13	s.	s.	PROPN
ejpam-5366	189	14	al	al	PROPN
ejpam-5366	189	15	-	-	PUNCT
ejpam-5366	189	16	tuwairqi	tuwairqi	PROPN
ejpam-5366	189	17	.	.	PUNCT
ejpam-5366	190	1	global	global	ADJ
ejpam-5366	190	2	dynamics	dynamic	NOUN
ejpam-5366	190	3	of	of	ADP
ejpam-5366	190	4	a	a	DET
ejpam-5366	190	5	mathematical	mathematical	ADJ
ejpam-5366	190	6	model	model	NOUN
ejpam-5366	190	7	on	on	ADP
ejpam-5366	190	8	smoking	smoking	NOUN
ejpam-5366	190	9	.	.	PUNCT
ejpam-5366	191	1	appl	appl	PROPN
ejpam-5366	191	2	.	.	PROPN
ejpam-5366	191	3	math	math	PROPN
ejpam-5366	191	4	.	.	PUNCT
ejpam-5366	192	1	,	,	PUNCT
ejpam-5366	192	2	pages	page	VERB
ejpam-5366	192	3	1–16	1–16	PROPN
ejpam-5366	192	4	,	,	PUNCT
ejpam-5366	192	5	2014	2014	NUM
ejpam-5366	192	6	.	.	PUNCT
ejpam-5366	193	1	[	[	X
ejpam-5366	193	2	4	4	X
ejpam-5366	193	3	]	]	X
ejpam-5366	193	4	y.n	y.n	PROPN
ejpam-5366	193	5	.	.	PROPN
ejpam-5366	193	6	anjam	anjam	PROPN
ejpam-5366	193	7	,	,	PUNCT
ejpam-5366	193	8	r.	r.	PROPN
ejpam-5366	193	9	shafqat	shafqat	PROPN
ejpam-5366	193	10	,	,	PUNCT
ejpam-5366	193	11	i.e.	i.e.	X
ejpam-5366	193	12	sarris	sarris	NOUN
ejpam-5366	193	13	,	,	PUNCT
ejpam-5366	193	14	m.	m.	NOUN
ejpam-5366	193	15	rahma	rahma	PROPN
ejpam-5366	193	16	,	,	PUNCT
ejpam-5366	193	17	s.	s.	PROPN
ejpam-5366	193	18	touseef	touseef	PROPN
ejpam-5366	193	19	,	,	PUNCT
ejpam-5366	193	20	and	and	CCONJ
ejpam-5366	193	21	m.	m.	PROPN
ejpam-5366	193	22	arshad	arshad	PROPN
ejpam-5366	193	23	.	.	PUNCT
ejpam-5366	194	1	a	a	DET
ejpam-5366	194	2	fractional	fractional	ADJ
ejpam-5366	194	3	order	order	NOUN
ejpam-5366	194	4	investigation	investigation	NOUN
ejpam-5366	194	5	of	of	ADP
ejpam-5366	194	6	smoking	smoking	NOUN
ejpam-5366	194	7	model	model	NOUN
ejpam-5366	194	8	using	use	VERB
ejpam-5366	194	9	caputo	caputo	PROPN
ejpam-5366	194	10	-	-	PUNCT
ejpam-5366	194	11	fabrizio	fabrizio	PROPN
ejpam-5366	194	12	differential	differential	NOUN
ejpam-5366	194	13	operator	operator	NOUN
ejpam-5366	194	14	.	.	PUNCT
ejpam-5366	195	1	fractal	fractal	ADJ
ejpam-5366	195	2	fract	fract	PROPN
ejpam-5366	195	3	.	.	PUNCT
ejpam-5366	195	4	,	,	PUNCT
ejpam-5366	195	5	6:1–15	6:1–15	NUM
ejpam-5366	195	6	,	,	PUNCT
ejpam-5366	195	7	2022	2022	NUM
ejpam-5366	195	8	.	.	PUNCT
ejpam-5366	196	1	[	[	X
ejpam-5366	196	2	5	5	NUM
ejpam-5366	196	3	]	]	X
ejpam-5366	196	4	a.a.m	a.a.m	PROPN
ejpam-5366	196	5	.	.	PROPN
ejpam-5366	196	6	arafa	arafa	PROPN
ejpam-5366	196	7	,	,	PUNCT
ejpam-5366	196	8	s.z	s.z	PROPN
ejpam-5366	196	9	.	.	PROPN
ejpam-5366	196	10	rida	rida	PROPN
ejpam-5366	196	11	,	,	PUNCT
ejpam-5366	196	12	and	and	CCONJ
ejpam-5366	196	13	m.	m.	PROPN
ejpam-5366	196	14	khalil	khalil	PROPN
ejpam-5366	196	15	.	.	PUNCT
ejpam-5366	197	1	fractional	fractional	ADJ
ejpam-5366	197	2	modeling	modeling	NOUN
ejpam-5366	197	3	dynamics	dynamic	NOUN
ejpam-5366	197	4	of	of	ADP
ejpam-5366	197	5	hiv	hiv	PROPN
ejpam-5366	197	6	and	and	CCONJ
ejpam-5366	197	7	cd4	cd4	PROPN
ejpam-5366	197	8	+	+	PROPN
ejpam-5366	197	9	t	t	PROPN
ejpam-5366	197	10	-	-	PUNCT
ejpam-5366	197	11	cells	cell	NOUN
ejpam-5366	197	12	during	during	ADP
ejpam-5366	197	13	primary	primary	ADJ
ejpam-5366	197	14	infection	infection	NOUN
ejpam-5366	197	15	.	.	PUNCT
ejpam-5366	198	1	nonl	nonl	PROPN
ejpam-5366	198	2	.	.	PUNCT
ejpam-5366	199	1	bio	bio	PROPN
ejpam-5366	199	2	.	.	PROPN
ejpam-5366	199	3	phy	phy	PROPN
ejpam-5366	199	4	.	.	PROPN
ejpam-5366	199	5	,	,	PUNCT
ejpam-5366	200	1	6:1–7	6:1–7	PROPN
ejpam-5366	200	2	,	,	PUNCT
ejpam-5366	200	3	2012	2012	NUM
ejpam-5366	200	4	.	.	PUNCT
ejpam-5366	201	1	[	[	X
ejpam-5366	201	2	6	6	NUM
ejpam-5366	201	3	]	]	X
ejpam-5366	201	4	i.m	i.m	PROPN
ejpam-5366	201	5	.	.	PROPN
ejpam-5366	201	6	batiha	batiha	PROPN
ejpam-5366	201	7	,	,	PUNCT
ejpam-5366	201	8	a.	a.	NOUN
ejpam-5366	201	9	bataihah	bataihah	PROPN
ejpam-5366	201	10	,	,	PUNCT
ejpam-5366	201	11	abeer	abeer	PROPN
ejpam-5366	201	12	a.	a.	PROPN
ejpam-5366	201	13	al	al	PROPN
ejpam-5366	201	14	-	-	PUNCT
ejpam-5366	201	15	nana	nana	PROPN
ejpam-5366	201	16	,	,	PUNCT
ejpam-5366	201	17	s.	s.	PROPN
ejpam-5366	201	18	alshorm	alshorm	PROPN
ejpam-5366	201	19	,	,	PUNCT
ejpam-5366	201	20	i.h	i.h	PROPN
ejpam-5366	201	21	.	.	PROPN
ejpam-5366	201	22	jebril	jebril	NOUN
ejpam-5366	201	23	,	,	PUNCT
ejpam-5366	201	24	and	and	CCONJ
ejpam-5366	201	25	a.	a.	NOUN
ejpam-5366	201	26	zraiqat	zraiqat	PROPN
ejpam-5366	201	27	.	.	PUNCT
ejpam-5366	202	1	a	a	DET
ejpam-5366	202	2	numerical	numerical	ADJ
ejpam-5366	202	3	scheme	scheme	NOUN
ejpam-5366	202	4	for	for	ADP
ejpam-5366	202	5	dealing	deal	VERB
ejpam-5366	202	6	with	with	ADP
ejpam-5366	202	7	fractional	fractional	ADJ
ejpam-5366	202	8	initial	initial	ADJ
ejpam-5366	202	9	value	value	NOUN
ejpam-5366	202	10	problem	problem	NOUN
ejpam-5366	202	11	.	.	PUNCT
ejpam-5366	203	1	int	int	NOUN
ejpam-5366	203	2	.	.	PUNCT
ejpam-5366	204	1	j.	j.	PROPN
ejpam-5366	204	2	innov	innov	PROPN
ejpam-5366	204	3	.	.	PUNCT
ejpam-5366	205	1	comput	comput	NOUN
ejpam-5366	205	2	.	.	PUNCT
ejpam-5366	206	1	inform	inform	NOUN
ejpam-5366	206	2	.	.	PUNCT
ejpam-5366	207	1	cont	cont	PROPN
ejpam-5366	207	2	.	.	PUNCT
ejpam-5366	207	3	,	,	PUNCT
ejpam-5366	207	4	19:763–774	19:763–774	NUM
ejpam-5366	207	5	,	,	PUNCT
ejpam-5366	207	6	2023	2023	NUM
ejpam-5366	207	7	.	.	PUNCT
ejpam-5366	208	1	[	[	X
ejpam-5366	208	2	7	7	NUM
ejpam-5366	208	3	]	]	X
ejpam-5366	208	4	c.c	c.c	PROPN
ejpam-5366	208	5	.	.	PROPN
ejpam-5366	208	6	garsow	garsow	PROPN
ejpam-5366	208	7	,	,	PUNCT
ejpam-5366	208	8	g.j	g.j	PROPN
ejpam-5366	208	9	.	.	PROPN
ejpam-5366	208	10	salivia	salivia	PROPN
ejpam-5366	208	11	,	,	PUNCT
ejpam-5366	208	12	and	and	CCONJ
ejpam-5366	208	13	a.r	a.r	PROPN
ejpam-5366	208	14	.	.	PROPN
ejpam-5366	208	15	herrera	herrera	PROPN
ejpam-5366	208	16	.	.	PUNCT
ejpam-5366	209	1	mathematical	mathematical	ADJ
ejpam-5366	209	2	models	model	NOUN
ejpam-5366	209	3	for	for	ADP
ejpam-5366	209	4	dynamics	dynamic	NOUN
ejpam-5366	209	5	of	of	ADP
ejpam-5366	209	6	tobacco	tobacco	NOUN
ejpam-5366	209	7	use	use	NOUN
ejpam-5366	209	8	,	,	PUNCT
ejpam-5366	209	9	recovery	recovery	NOUN
ejpam-5366	209	10	and	and	CCONJ
ejpam-5366	209	11	relapse	relapse	NOUN
ejpam-5366	209	12	.	.	PUNCT
ejpam-5366	210	1	technical	technical	ADJ
ejpam-5366	210	2	report	report	PROPN
ejpam-5366	210	3	,	,	PUNCT
ejpam-5366	210	4	cornell	cornell	PROPN
ejpam-5366	210	5	university	university	PROPN
ejpam-5366	210	6	,	,	PUNCT
ejpam-5366	210	7	london	london	PROPN
ejpam-5366	210	8	,	,	PUNCT
ejpam-5366	210	9	uk	uk	PROPN
ejpam-5366	210	10	,	,	PUNCT
ejpam-5366	210	11	2000	2000	NUM
ejpam-5366	210	12	.	.	PUNCT
ejpam-5366	211	1	[	[	X
ejpam-5366	211	2	8	8	NUM
ejpam-5366	211	3	]	]	X
ejpam-5366	211	4	o.k	o.k	PROPN
ejpam-5366	211	5	.	.	PROPN
ejpam-5366	211	6	ham	ham	PROPN
ejpam-5366	211	7	.	.	PUNCT
ejpam-5366	211	8	stages	stage	NOUN
ejpam-5366	211	9	and	and	CCONJ
ejpam-5366	211	10	processes	process	NOUN
ejpam-5366	211	11	of	of	ADP
ejpam-5366	211	12	smoking	smoking	NOUN
ejpam-5366	211	13	cessation	cessation	NOUN
ejpam-5366	211	14	among	among	ADP
ejpam-5366	211	15	adolescents	adolescent	NOUN
ejpam-5366	211	16	.	.	PUNCT
ejpam-5366	212	1	west	west	PROPN
ejpam-5366	212	2	.	.	PUNCT
ejpam-5366	213	1	j.	j.	PROPN
ejpam-5366	213	2	nurs	nurs	PROPN
ejpam-5366	213	3	.	.	PUNCT
ejpam-5366	214	1	res	re	NOUN
ejpam-5366	214	2	.	.	PROPN
ejpam-5366	214	3	,	,	PUNCT
ejpam-5366	214	4	29:301–315	29:301–315	NUM
ejpam-5366	214	5	,	,	PUNCT
ejpam-5366	214	6	2007	2007	NUM
ejpam-5366	214	7	.	.	PUNCT
ejpam-5366	215	1	[	[	X
ejpam-5366	215	2	9	9	NUM
ejpam-5366	215	3	]	]	X
ejpam-5366	215	4	m.a	m.a	PROPN
ejpam-5366	215	5	.	.	PROPN
ejpam-5366	215	6	hammad	hammad	PROPN
ejpam-5366	215	7	,	,	PUNCT
ejpam-5366	215	8	i.h	i.h	PROPN
ejpam-5366	215	9	.	.	PROPN
ejpam-5366	215	10	jebril	jebril	NOUN
ejpam-5366	215	11	,	,	PUNCT
ejpam-5366	215	12	s.	s.	PROPN
ejpam-5366	215	13	alshorm	alshorm	PROPN
ejpam-5366	215	14	,	,	PUNCT
ejpam-5366	215	15	i.m	i.m	PROPN
ejpam-5366	215	16	.	.	PROPN
ejpam-5366	215	17	batiha	batiha	PROPN
ejpam-5366	215	18	,	,	PUNCT
ejpam-5366	215	19	and	and	CCONJ
ejpam-5366	215	20	n.a	n.a	PROPN
ejpam-5366	215	21	.	.	PROPN
ejpam-5366	215	22	hammad	hammad	PROPN
ejpam-5366	215	23	.	.	PROPN
ejpam-5366	215	24	numerical	numerical	ADJ
ejpam-5366	215	25	solution	solution	NOUN
ejpam-5366	215	26	for	for	ADP
ejpam-5366	215	27	fractional	fractional	ADJ
ejpam-5366	215	28	-	-	PUNCT
ejpam-5366	215	29	order	order	NOUN
ejpam-5366	215	30	mathematical	mathematical	ADJ
ejpam-5366	215	31	model	model	NOUN
ejpam-5366	215	32	of	of	ADP
ejpam-5366	215	33	immune	immune	NOUN
ejpam-5366	215	34	-	-	PUNCT
ejpam-5366	215	35	chemotherapeutic	chemotherapeutic	NOUN
ejpam-5366	215	36	treatment	treatment	NOUN
ejpam-5366	215	37	for	for	ADP
ejpam-5366	215	38	breast	breast	NOUN
ejpam-5366	215	39	cancer	cancer	NOUN
ejpam-5366	215	40	using	use	VERB
ejpam-5366	215	41	modified	modify	VERB
ejpam-5366	215	42	fractional	fractional	ADJ
ejpam-5366	215	43	formula	formula	NOUN
ejpam-5366	215	44	.	.	PUNCT
ejpam-5366	216	1	int	int	NOUN
ejpam-5366	216	2	.	.	PUNCT
ejpam-5366	217	1	j.	j.	PROPN
ejpam-5366	217	2	anal	anal	PROPN
ejpam-5366	217	3	.	.	PUNCT
ejpam-5366	218	1	appl	appl	PROPN
ejpam-5366	218	2	.	.	PROPN
ejpam-5366	218	3	,	,	PUNCT
ejpam-5366	218	4	21:1–9	21:1–9	NUM
ejpam-5366	218	5	,	,	PUNCT
ejpam-5366	218	6	2023	2023	NUM
ejpam-5366	218	7	.	.	PUNCT
ejpam-5366	219	1	[	[	X
ejpam-5366	219	2	10	10	NUM
ejpam-5366	219	3	]	]	PUNCT
ejpam-5366	219	4	m.	m.	NOUN
ejpam-5366	219	5	izadi	izadi	NOUN
ejpam-5366	219	6	and	and	CCONJ
ejpam-5366	219	7	h.m	h.m	PROPN
ejpam-5366	219	8	.	.	PROPN
ejpam-5366	219	9	srivastava	srivastava	PROPN
ejpam-5366	219	10	.	.	PUNCT
ejpam-5366	220	1	generalized	generalize	VERB
ejpam-5366	220	2	shifted	shift	VERB
ejpam-5366	220	3	airfoil	airfoil	NOUN
ejpam-5366	220	4	polynomials	polynomial	NOUN
ejpam-5366	220	5	of	of	ADP
ejpam-5366	220	6	the	the	DET
ejpam-5366	220	7	second	second	ADJ
ejpam-5366	220	8	kind	kind	NOUN
ejpam-5366	220	9	to	to	PART
ejpam-5366	220	10	solve	solve	VERB
ejpam-5366	220	11	a	a	DET
ejpam-5366	220	12	class	class	NOUN
ejpam-5366	220	13	of	of	ADP
ejpam-5366	220	14	singular	singular	ADJ
ejpam-5366	220	15	electrohydrodynamic	electrohydrodynamic	ADJ
ejpam-5366	220	16	fluid	fluid	NOUN
ejpam-5366	220	17	model	model	NOUN
ejpam-5366	220	18	of	of	ADP
ejpam-5366	220	19	fractional	fractional	ADJ
ejpam-5366	220	20	order	order	NOUN
ejpam-5366	220	21	.	.	PUNCT
ejpam-5366	221	1	fractal	fractal	ADJ
ejpam-5366	221	2	fract	fract	PROPN
ejpam-5366	221	3	.	.	PUNCT
ejpam-5366	221	4	,	,	PUNCT
ejpam-5366	221	5	7:93–105	7:93–105	NUM
ejpam-5366	221	6	,	,	PUNCT
ejpam-5366	221	7	2023	2023	NUM
ejpam-5366	221	8	.	.	PUNCT
ejpam-5366	222	1	[	[	X
ejpam-5366	222	2	11	11	NUM
ejpam-5366	222	3	]	]	PUNCT
ejpam-5366	222	4	m.	m.	NOUN
ejpam-5366	222	5	izadi	izadi	NOUN
ejpam-5366	222	6	and	and	CCONJ
ejpam-5366	222	7	h.m	h.m	PROPN
ejpam-5366	222	8	.	.	PROPN
ejpam-5366	222	9	srivastava	srivastava	PROPN
ejpam-5366	222	10	.	.	PUNCT
ejpam-5366	223	1	an	an	DET
ejpam-5366	223	2	accurate	accurate	ADJ
ejpam-5366	223	3	numerical	numerical	ADJ
ejpam-5366	223	4	algorithm	algorithm	NOUN
ejpam-5366	223	5	based	base	VERB
ejpam-5366	223	6	on	on	ADP
ejpam-5366	223	7	the	the	DET
ejpam-5366	223	8	generalized	generalize	VERB
ejpam-5366	223	9	narayana	narayana	PROPN
ejpam-5366	223	10	polynomials	polynomial	NOUN
ejpam-5366	223	11	to	to	PART
ejpam-5366	223	12	solve	solve	VERB
ejpam-5366	223	13	a	a	DET
ejpam-5366	223	14	class	class	NOUN
ejpam-5366	223	15	of	of	ADP
ejpam-5366	223	16	caputo	caputo	PROPN
ejpam-5366	223	17	-	-	PUNCT
ejpam-5366	223	18	fabrizio	fabrizio	PROPN
ejpam-5366	223	19	and	and	CCONJ
ejpam-5366	223	20	liouville	liouville	PROPN
ejpam-5366	223	21	-	-	PUNCT
ejpam-5366	223	22	caputo	caputo	NOUN
ejpam-5366	223	23	fractional	fractional	ADJ
ejpam-5366	223	24	-	-	PUNCT
ejpam-5366	223	25	order	order	NOUN
ejpam-5366	223	26	delay	delay	NOUN
ejpam-5366	223	27	differential	differential	ADJ
ejpam-5366	223	28	equations	equation	NOUN
ejpam-5366	223	29	.	.	PUNCT
ejpam-5366	224	1	math	math	NOUN
ejpam-5366	224	2	.	.	PUNCT
ejpam-5366	225	1	commun	commun	PROPN
ejpam-5366	225	2	.	.	PROPN
ejpam-5366	225	3	,	,	PUNCT
ejpam-5366	225	4	29:61–81	29:61–81	NUM
ejpam-5366	225	5	,	,	PUNCT
ejpam-5366	225	6	2024	2024	NUM
ejpam-5366	225	7	.	.	PUNCT
ejpam-5366	226	1	[	[	X
ejpam-5366	226	2	12	12	NUM
ejpam-5366	226	3	]	]	X
ejpam-5366	226	4	m.m	m.m	PROPN
ejpam-5366	226	5	.	.	PROPN
ejpam-5366	226	6	khader	khader	PROPN
ejpam-5366	226	7	and	and	CCONJ
ejpam-5366	226	8	k.m	k.m	PROPN
ejpam-5366	226	9	.	.	PROPN
ejpam-5366	226	10	saad	saad	PROPN
ejpam-5366	226	11	.	.	PUNCT
ejpam-5366	227	1	on	on	ADP
ejpam-5366	227	2	the	the	DET
ejpam-5366	227	3	numerical	numerical	ADJ
ejpam-5366	227	4	evaluation	evaluation	NOUN
ejpam-5366	227	5	for	for	ADP
ejpam-5366	227	6	studying	study	VERB
ejpam-5366	227	7	the	the	DET
ejpam-5366	227	8	fractional	fractional	ADJ
ejpam-5366	227	9	kdv	kdv	NOUN
ejpam-5366	227	10	,	,	PUNCT
ejpam-5366	227	11	kdv	kdv	NOUN
ejpam-5366	227	12	-	-	PUNCT
ejpam-5366	227	13	burger	burger	NOUN
ejpam-5366	227	14	’s	’s	NOUN
ejpam-5366	227	15	,	,	PUNCT
ejpam-5366	227	16	and	and	CCONJ
ejpam-5366	227	17	burger	burger	NOUN
ejpam-5366	227	18	’s	’s	PART
ejpam-5366	227	19	equations	equation	NOUN
ejpam-5366	227	20	.	.	PUNCT
ejpam-5366	228	1	the	the	DET
ejpam-5366	228	2	eur	eur	PROPN
ejpam-5366	228	3	.	.	PUNCT
ejpam-5366	229	1	ph	ph	PROPN
ejpam-5366	229	2	.	.	PROPN
ejpam-5366	229	3	j.	j.	PROPN
ejpam-5366	229	4	plus	plus	PROPN
ejpam-5366	229	5	,	,	PUNCT
ejpam-5366	229	6	33:1–13	33:1–13	NUM
ejpam-5366	229	7	,	,	PUNCT
ejpam-5366	229	8	2018	2018	NUM
ejpam-5366	229	9	.	.	PUNCT
ejpam-5366	230	1	references	reference	NOUN
ejpam-5366	230	2	2691	2691	NUM
ejpam-5366	230	3	[	[	X
ejpam-5366	230	4	13	13	NUM
ejpam-5366	230	5	]	]	PUNCT
ejpam-5366	230	6	t.	t.	PROPN
ejpam-5366	230	7	liu	liu	PROPN
ejpam-5366	230	8	,	,	PUNCT
ejpam-5366	230	9	t.j	t.j	PROPN
ejpam-5366	230	10	.	.	PROPN
ejpam-5366	230	11	deiss	deiss	PROPN
ejpam-5366	230	12	,	,	PUNCT
ejpam-5366	230	13	m.w	m.w	PROPN
ejpam-5366	230	14	.	.	PROPN
ejpam-5366	230	15	lippi	lippi	PROPN
ejpam-5366	230	16	,	,	PUNCT
ejpam-5366	230	17	a.	a.	PROPN
ejpam-5366	230	18	jauregui	jauregui	PROPN
ejpam-5366	230	19	,	,	PUNCT
ejpam-5366	230	20	k.	k.	PROPN
ejpam-5366	230	21	vessel	vessel	PROPN
ejpam-5366	230	22	,	,	PUNCT
ejpam-5366	230	23	s.	s.	PROPN
ejpam-5366	230	24	ke	ke	PROPN
ejpam-5366	230	25	,	,	PUNCT
ejpam-5366	230	26	a.	a.	NOUN
ejpam-5366	230	27	belzer	belzer	PROPN
ejpam-5366	230	28	,	,	PUNCT
ejpam-5366	230	29	h.	h.	PROPN
ejpam-5366	230	30	zhuo	zhuo	PROPN
ejpam-5366	230	31	,	,	PUNCT
ejpam-5366	230	32	k.n	k.n	PROPN
ejpam-5366	230	33	.	.	PROPN
ejpam-5366	230	34	kangelaris	kangelaris	PROPN
ejpam-5366	230	35	,	,	PUNCT
ejpam-5366	230	36	and	and	CCONJ
ejpam-5366	231	1	et	et	PROPN
ejpam-5366	231	2	al	al	PROPN
ejpam-5366	231	3	.	.	PROPN
ejpam-5366	231	4	a.d	a.d	PROPN
ejpam-5366	231	5	.	.	PROPN
ejpam-5366	231	6	gomez	gomez	PROPN
ejpam-5366	231	7	.	.	PUNCT
ejpam-5366	232	1	alternative	alternative	ADJ
ejpam-5366	232	2	tobacco	tobacco	NOUN
ejpam-5366	232	3	product	product	NOUN
ejpam-5366	232	4	use	use	NOUN
ejpam-5366	232	5	in	in	ADP
ejpam-5366	232	6	critically	critically	ADV
ejpam-5366	232	7	ill	ill	ADJ
ejpam-5366	232	8	patients	patient	NOUN
ejpam-5366	232	9	.	.	PUNCT
ejpam-5366	233	1	int	int	NOUN
ejpam-5366	233	2	.	.	PUNCT
ejpam-5366	234	1	j.	j.	PROPN
ejpam-5366	234	2	environ	environ	PROPN
ejpam-5366	234	3	.	.	PUNCT
ejpam-5366	235	1	res	re	NOUN
ejpam-5366	235	2	.	.	PUNCT
ejpam-5366	236	1	public	public	ADJ
ejpam-5366	236	2	health	health	NOUN
ejpam-5366	236	3	,	,	PUNCT
ejpam-5366	236	4	17:1–15	17:1–15	NUM
ejpam-5366	236	5	,	,	PUNCT
ejpam-5366	236	6	2020	2020	NUM
ejpam-5366	236	7	.	.	PUNCT
ejpam-5366	237	1	[	[	X
ejpam-5366	237	2	14	14	NUM
ejpam-5366	237	3	]	]	PUNCT
ejpam-5366	237	4	world	world	NOUN
ejpam-5366	237	5	health	health	NOUN
ejpam-5366	237	6	organisation	organisation	NOUN
ejpam-5366	237	7	.	.	PUNCT
ejpam-5366	238	1	monitoring	monitor	VERB
ejpam-5366	238	2	tobacco	tobacco	NOUN
ejpam-5366	238	3	use	use	NOUN
ejpam-5366	238	4	and	and	CCONJ
ejpam-5366	238	5	prevention	prevention	NOUN
ejpam-5366	238	6	policies	policy	NOUN
ejpam-5366	238	7	.	.	PUNCT
ejpam-5366	239	1	executive	executive	ADJ
ejpam-5366	239	2	summary	summary	NOUN
ejpam-5366	239	3	,	,	PUNCT
ejpam-5366	239	4	2017	2017	NUM
ejpam-5366	239	5	.	.	PUNCT
ejpam-5366	240	1	[	[	X
ejpam-5366	240	2	15	15	NUM
ejpam-5366	240	3	]	]	X
ejpam-5366	240	4	k.m	k.m	PROPN
ejpam-5366	240	5	.	.	PROPN
ejpam-5366	240	6	owolabi	owolabi	PROPN
ejpam-5366	240	7	,	,	PUNCT
ejpam-5366	240	8	a.	a.	PROPN
ejpam-5366	240	9	atangana	atangana	PROPN
ejpam-5366	240	10	,	,	PUNCT
ejpam-5366	240	11	and	and	CCONJ
ejpam-5366	240	12	a.	a.	NOUN
ejpam-5366	240	13	akgul	akgul	NOUN
ejpam-5366	240	14	.	.	PUNCT
ejpam-5366	241	1	modelling	modelling	NOUN
ejpam-5366	241	2	and	and	CCONJ
ejpam-5366	241	3	analysis	analysis	NOUN
ejpam-5366	241	4	of	of	ADP
ejpam-5366	241	5	fractalfractional	fractalfractional	ADJ
ejpam-5366	241	6	partial	partial	ADJ
ejpam-5366	241	7	differential	differential	NOUN
ejpam-5366	241	8	equations	equation	NOUN
ejpam-5366	241	9	:	:	PUNCT
ejpam-5366	241	10	application	application	NOUN
ejpam-5366	241	11	to	to	ADP
ejpam-5366	241	12	reaction	reaction	NOUN
ejpam-5366	241	13	-	-	PUNCT
ejpam-5366	241	14	diffusion	diffusion	NOUN
ejpam-5366	241	15	model	model	NOUN
ejpam-5366	241	16	.	.	PUNCT
ejpam-5366	242	1	alex	alex	PROPN
ejpam-5366	242	2	.	.	PUNCT
ejpam-5366	243	1	eng	eng	PROPN
ejpam-5366	243	2	.	.	PUNCT
ejpam-5366	244	1	j.	j.	PROPN
ejpam-5366	244	2	,	,	PUNCT
ejpam-5366	244	3	59:2477–2490	59:2477–2490	NUM
ejpam-5366	244	4	,	,	PUNCT
ejpam-5366	244	5	2020	2020	NUM
ejpam-5366	244	6	.	.	PUNCT
ejpam-5366	245	1	[	[	X
ejpam-5366	245	2	16	16	NUM
ejpam-5366	245	3	]	]	X
ejpam-5366	245	4	m.p	m.p	PROPN
ejpam-5366	245	5	.	.	PROPN
ejpam-5366	245	6	yadav	yadav	PROPN
ejpam-5366	245	7	and	and	CCONJ
ejpam-5366	245	8	r.	r.	PROPN
ejpam-5366	245	9	agarwal	agarwal	PROPN
ejpam-5366	245	10	.	.	PUNCT
ejpam-5366	246	1	numerical	numerical	PROPN
ejpam-5366	246	2	investigation	investigation	NOUN
ejpam-5366	246	3	of	of	ADP
ejpam-5366	246	4	fractional	fractional	ADJ
ejpam-5366	246	5	-	-	PUNCT
ejpam-5366	246	6	fractal	fractal	ADJ
ejpam-5366	246	7	boussinesq	boussinesq	ADJ
ejpam-5366	246	8	equation	equation	NOUN
ejpam-5366	246	9	.	.	PUNCT
ejpam-5366	247	1	chaos	chaos	NOUN
ejpam-5366	247	2	,	,	PUNCT
ejpam-5366	247	3	29:01–31	29:01–31	PROPN
ejpam-5366	247	4	,	,	PUNCT
ejpam-5366	247	5	2019	2019	NUM
ejpam-5366	247	6	.	.	PUNCT
ejpam-5366	248	1	[	[	X
ejpam-5366	248	2	17	17	NUM
ejpam-5366	248	3	]	]	PUNCT
ejpam-5366	248	4	a.	a.	NOUN
ejpam-5366	248	5	yildirim	yildirim	PROPN
ejpam-5366	248	6	and	and	CCONJ
ejpam-5366	248	7	y.	y.	PROPN
ejpam-5366	248	8	cherruault	cherruault	PROPN
ejpam-5366	248	9	.	.	PUNCT
ejpam-5366	249	1	analytical	analytical	ADJ
ejpam-5366	249	2	approximate	approximate	ADJ
ejpam-5366	249	3	solution	solution	NOUN
ejpam-5366	249	4	of	of	ADP
ejpam-5366	249	5	a	a	DET
ejpam-5366	249	6	sir	sir	NOUN
ejpam-5366	249	7	epidemic	epidemic	NOUN
ejpam-5366	249	8	model	model	NOUN
ejpam-5366	249	9	with	with	ADP
ejpam-5366	249	10	constant	constant	ADJ
ejpam-5366	249	11	vaccination	vaccination	NOUN
ejpam-5366	249	12	strategy	strategy	NOUN
ejpam-5366	249	13	by	by	ADP
ejpam-5366	249	14	homotopy	homotopy	NOUN
ejpam-5366	249	15	perturbation	perturbation	NOUN
ejpam-5366	249	16	method	method	NOUN
ejpam-5366	249	17	.	.	PUNCT
ejpam-5366	250	1	emerald	emerald	NOUN
ejpam-5366	250	2	,	,	PUNCT
ejpam-5366	250	3	38:1566–1581	38:1566–1581	NUM
ejpam-5366	250	4	,	,	PUNCT
ejpam-5366	250	5	2009	2009	NUM
ejpam-5366	250	6	.	.	PUNCT
ejpam-5366	251	1	[	[	X
ejpam-5366	251	2	18	18	NUM
ejpam-5366	251	3	]	]	X
ejpam-5366	251	4	m.o	m.o	PROPN
ejpam-5366	251	5	.	.	PROPN
ejpam-5366	251	6	zaid	zaid	PROPN
ejpam-5366	251	7	and	and	CCONJ
ejpam-5366	251	8	n.t	n.t	PROPN
ejpam-5366	251	9	.	.	PROPN
ejpam-5366	251	10	shawagfeh	shawagfeh	PROPN
ejpam-5366	251	11	.	.	PUNCT
ejpam-5366	252	1	generalized	generalized	PROPN
ejpam-5366	252	2	taylor	taylor	PROPN
ejpam-5366	252	3	’s	’s	PART
ejpam-5366	252	4	formula	formula	NOUN
ejpam-5366	252	5	.	.	PUNCT
ejpam-5366	253	1	app	app	PROPN
ejpam-5366	253	2	.	.	PROPN
ejpam-5366	253	3	math	math	PROPN
ejpam-5366	253	4	.	.	PUNCT
ejpam-5366	254	1	com	com	PROPN
ejpam-5366	254	2	.	.	PROPN
ejpam-5366	254	3	,	,	PUNCT
ejpam-5366	254	4	186:286–293	186:286–293	NUM
ejpam-5366	254	5	,	,	PUNCT
ejpam-5366	254	6	2007	2007	NUM
ejpam-5366	254	7	.	.	PUNCT