id	sid	tid	token	lemma	pos
ejpam-5043	1	1	european	european	PROPN
ejpam-5043	1	2	journal	journal	PROPN
ejpam-5043	1	3	of	of	ADP
ejpam-5043	1	4	pure	pure	ADJ
ejpam-5043	1	5	and	and	CCONJ
ejpam-5043	1	6	applied	apply	VERB
ejpam-5043	1	7	mathematics	mathematic	NOUN
ejpam-5043	1	8	vol	vol	NOUN
ejpam-5043	1	9	.	.	PROPN
ejpam-5043	2	1	17	17	NUM
ejpam-5043	2	2	,	,	PUNCT
ejpam-5043	2	3	no	no	INTJ
ejpam-5043	2	4	.	.	NOUN
ejpam-5043	2	5	1	1	NUM
ejpam-5043	2	6	,	,	PUNCT
ejpam-5043	2	7	2024	2024	NUM
ejpam-5043	2	8	,	,	PUNCT
ejpam-5043	2	9	445	445	NUM
ejpam-5043	2	10	-	-	SYM
ejpam-5043	2	11	461	461	NUM
ejpam-5043	2	12	issn	issn	PROPN
ejpam-5043	2	13	1307	1307	NUM
ejpam-5043	2	14	-	-	SYM
ejpam-5043	2	15	5543	5543	NUM
ejpam-5043	2	16	–	–	PUNCT
ejpam-5043	2	17	ejpam.com	ejpam.com	X
ejpam-5043	2	18	published	publish	VERB
ejpam-5043	2	19	by	by	ADP
ejpam-5043	2	20	new	new	PROPN
ejpam-5043	2	21	york	york	PROPN
ejpam-5043	2	22	business	business	PROPN
ejpam-5043	2	23	global	global	PROPN
ejpam-5043	2	24	a	a	DET
ejpam-5043	2	25	novel	novel	ADJ
ejpam-5043	2	26	numerical	numerical	ADJ
ejpam-5043	2	27	scheme	scheme	NOUN
ejpam-5043	2	28	for	for	ADP
ejpam-5043	2	29	fractional	fractional	ADJ
ejpam-5043	2	30	bernoulli	bernoulli	NOUN
ejpam-5043	2	31	equations	equation	NOUN
ejpam-5043	2	32	and	and	CCONJ
ejpam-5043	2	33	the	the	DET
ejpam-5043	2	34	rössler	rössler	NOUN
ejpam-5043	2	35	model	model	NOUN
ejpam-5043	2	36	:	:	PUNCT
ejpam-5043	2	37	a	a	DET
ejpam-5043	2	38	comparative	comparative	ADJ
ejpam-5043	2	39	analysis	analysis	NOUN
ejpam-5043	2	40	using	use	VERB
ejpam-5043	2	41	atangana	atangana	PROPN
ejpam-5043	2	42	-	-	PUNCT
ejpam-5043	2	43	baleanu	baleanu	PROPN
ejpam-5043	2	44	caputo	caputo	PROPN
ejpam-5043	2	45	fractional	fractional	PROPN
ejpam-5043	2	46	derivative	derivative	ADJ
ejpam-5043	2	47	kaouther	kaouther	NOUN
ejpam-5043	2	48	boulehmi1,2	boulehmi1,2	PROPN
ejpam-5043	2	49	1	1	NUM
ejpam-5043	2	50	department	department	NOUN
ejpam-5043	2	51	of	of	ADP
ejpam-5043	2	52	mathematics	mathematic	NOUN
ejpam-5043	2	53	,	,	PUNCT
ejpam-5043	2	54	faculty	faculty	NOUN
ejpam-5043	2	55	of	of	ADP
ejpam-5043	2	56	sciences	science	NOUN
ejpam-5043	2	57	,	,	PUNCT
ejpam-5043	2	58	al	al	PROPN
ejpam-5043	2	59	-	-	PUNCT
ejpam-5043	2	60	baha	baha	PROPN
ejpam-5043	2	61	university	university	PROPN
ejpam-5043	2	62	,	,	PUNCT
ejpam-5043	2	63	saudi	saudi	PROPN
ejpam-5043	2	64	arabia	arabia	PROPN
ejpam-5043	2	65	2	2	NUM
ejpam-5043	2	66	university	university	NOUN
ejpam-5043	2	67	of	of	ADP
ejpam-5043	2	68	carthage	carthage	NOUN
ejpam-5043	2	69	,	,	PUNCT
ejpam-5043	2	70	faculty	faculty	NOUN
ejpam-5043	2	71	of	of	ADP
ejpam-5043	2	72	sciences	science	NOUN
ejpam-5043	2	73	of	of	ADP
ejpam-5043	2	74	bizerte	bizerte	NOUN
ejpam-5043	2	75	,	,	PUNCT
ejpam-5043	2	76	(	(	PUNCT
ejpam-5043	2	77	ur17es21	ur17es21	NOUN
ejpam-5043	2	78	)	)	PUNCT
ejpam-5043	2	79	dynamical	dynamical	ADJ
ejpam-5043	2	80	systems	system	NOUN
ejpam-5043	2	81	and	and	CCONJ
ejpam-5043	2	82	their	their	PRON
ejpam-5043	2	83	applications	application	NOUN
ejpam-5043	2	84	,	,	PUNCT
ejpam-5043	2	85	7021	7021	NUM
ejpam-5043	2	86	,	,	PUNCT
ejpam-5043	2	87	jarzouna	jarzouna	PROPN
ejpam-5043	2	88	,	,	PUNCT
ejpam-5043	2	89	tunisia	tunisia	NOUN
ejpam-5043	2	90	abstract	abstract	NOUN
ejpam-5043	2	91	.	.	PUNCT
ejpam-5043	3	1	this	this	DET
ejpam-5043	3	2	study	study	NOUN
ejpam-5043	3	3	aims	aim	VERB
ejpam-5043	3	4	to	to	PART
ejpam-5043	3	5	use	use	VERB
ejpam-5043	3	6	a	a	DET
ejpam-5043	3	7	novel	novel	ADJ
ejpam-5043	3	8	scheme	scheme	NOUN
ejpam-5043	3	9	for	for	ADP
ejpam-5043	3	10	the	the	DET
ejpam-5043	3	11	atangana	atangana	PROPN
ejpam-5043	3	12	-	-	PUNCT
ejpam-5043	3	13	baleanu	baleanu	PROPN
ejpam-5043	3	14	caputo	caputo	PROPN
ejpam-5043	3	15	fractional	fractional	PROPN
ejpam-5043	3	16	derivative	derivative	PROPN
ejpam-5043	3	17	(	(	PUNCT
ejpam-5043	3	18	abc	abc	PROPN
ejpam-5043	3	19	-	-	PUNCT
ejpam-5043	3	20	fd	fd	X
ejpam-5043	3	21	)	)	PUNCT
ejpam-5043	3	22	to	to	PART
ejpam-5043	3	23	solve	solve	VERB
ejpam-5043	3	24	the	the	DET
ejpam-5043	3	25	fractional	fractional	ADJ
ejpam-5043	3	26	bernoulli	bernoulli	NOUN
ejpam-5043	3	27	equation	equation	NOUN
ejpam-5043	3	28	and	and	CCONJ
ejpam-5043	3	29	the	the	DET
ejpam-5043	3	30	fractional	fractional	ADJ
ejpam-5043	3	31	rössler	rössler	NOUN
ejpam-5043	3	32	model	model	NOUN
ejpam-5043	3	33	.	.	PUNCT
ejpam-5043	4	1	furthermore	furthermore	ADV
ejpam-5043	4	2	,	,	PUNCT
ejpam-5043	4	3	the	the	DET
ejpam-5043	4	4	suggested	suggest	VERB
ejpam-5043	4	5	technique	technique	NOUN
ejpam-5043	4	6	is	be	AUX
ejpam-5043	4	7	compared	compare	VERB
ejpam-5043	4	8	to	to	ADP
ejpam-5043	4	9	runge	runge	VERB
ejpam-5043	4	10	-	-	PUNCT
ejpam-5043	4	11	kutta	kutta	NOUN
ejpam-5043	4	12	fourth	fourth	ADJ
ejpam-5043	4	13	order	order	NOUN
ejpam-5043	4	14	(	(	PUNCT
ejpam-5043	4	15	rk4	rk4	NOUN
ejpam-5043	4	16	)	)	PUNCT
ejpam-5043	4	17	.	.	PUNCT
ejpam-5043	5	1	the	the	DET
ejpam-5043	5	2	proposed	propose	VERB
ejpam-5043	5	3	method	method	NOUN
ejpam-5043	5	4	is	be	AUX
ejpam-5043	5	5	efficacious	efficacious	ADJ
ejpam-5043	5	6	and	and	CCONJ
ejpam-5043	5	7	generates	generate	VERB
ejpam-5043	5	8	solutions	solution	NOUN
ejpam-5043	5	9	that	that	PRON
ejpam-5043	5	10	are	be	AUX
ejpam-5043	5	11	indistinguishable	indistinguishable	ADJ
ejpam-5043	5	12	from	from	ADP
ejpam-5043	5	13	the	the	DET
ejpam-5043	5	14	approximate	approximate	ADJ
ejpam-5043	5	15	solutions	solution	NOUN
ejpam-5043	5	16	generated	generate	VERB
ejpam-5043	5	17	by	by	ADP
ejpam-5043	5	18	the	the	DET
ejpam-5043	5	19	rk4	rk4	PROPN
ejpam-5043	5	20	method	method	NOUN
ejpam-5043	5	21	.	.	PUNCT
ejpam-5043	6	1	therefore	therefore	ADV
ejpam-5043	6	2	,	,	PUNCT
ejpam-5043	6	3	we	we	PRON
ejpam-5043	6	4	can	can	AUX
ejpam-5043	6	5	adapt	adapt	VERB
ejpam-5043	6	6	the	the	DET
ejpam-5043	6	7	approach	approach	NOUN
ejpam-5043	6	8	to	to	ADP
ejpam-5043	6	9	various	various	ADJ
ejpam-5043	6	10	systems	system	NOUN
ejpam-5043	6	11	and	and	CCONJ
ejpam-5043	6	12	develop	develop	VERB
ejpam-5043	6	13	results	result	NOUN
ejpam-5043	6	14	that	that	PRON
ejpam-5043	6	15	are	be	AUX
ejpam-5043	6	16	more	more	ADV
ejpam-5043	6	17	accurate	accurate	ADJ
ejpam-5043	6	18	.	.	PUNCT
ejpam-5043	7	1	on	on	ADP
ejpam-5043	7	2	top	top	NOUN
ejpam-5043	7	3	of	of	ADP
ejpam-5043	7	4	that	that	PRON
ejpam-5043	7	5	,	,	PUNCT
ejpam-5043	7	6	the	the	DET
ejpam-5043	7	7	new	new	ADJ
ejpam-5043	7	8	technique	technique	NOUN
ejpam-5043	7	9	(	(	PUNCT
ejpam-5043	7	10	abc	abc	PROPN
ejpam-5043	7	11	-	-	PUNCT
ejpam-5043	7	12	fd	fd	X
ejpam-5043	7	13	)	)	PUNCT
ejpam-5043	7	14	can	can	AUX
ejpam-5043	7	15	identify	identify	VERB
ejpam-5043	7	16	chaotic	chaotic	ADJ
ejpam-5043	7	17	situations	situation	NOUN
ejpam-5043	7	18	.	.	PUNCT
ejpam-5043	8	1	consequently	consequently	ADV
ejpam-5043	8	2	,	,	PUNCT
ejpam-5043	8	3	this	this	DET
ejpam-5043	8	4	approach	approach	NOUN
ejpam-5043	8	5	can	can	AUX
ejpam-5043	8	6	be	be	AUX
ejpam-5043	8	7	used	use	VERB
ejpam-5043	8	8	to	to	PART
ejpam-5043	8	9	enhance	enhance	VERB
ejpam-5043	8	10	the	the	DET
ejpam-5043	8	11	performance	performance	NOUN
ejpam-5043	8	12	of	of	ADP
ejpam-5043	8	13	other	other	ADJ
ejpam-5043	8	14	systems	system	NOUN
ejpam-5043	8	15	.	.	PUNCT
ejpam-5043	9	1	in	in	ADP
ejpam-5043	9	2	the	the	DET
ejpam-5043	9	3	future	future	NOUN
ejpam-5043	9	4	,	,	PUNCT
ejpam-5043	9	5	this	this	DET
ejpam-5043	9	6	technique	technique	NOUN
ejpam-5043	9	7	can	can	AUX
ejpam-5043	9	8	be	be	AUX
ejpam-5043	9	9	employed	employ	VERB
ejpam-5043	9	10	to	to	PART
ejpam-5043	9	11	determine	determine	VERB
ejpam-5043	9	12	the	the	DET
ejpam-5043	9	13	numerical	numerical	ADJ
ejpam-5043	9	14	solution	solution	NOUN
ejpam-5043	9	15	for	for	ADP
ejpam-5043	9	16	a	a	DET
ejpam-5043	9	17	multitude	multitude	NOUN
ejpam-5043	9	18	of	of	ADP
ejpam-5043	9	19	models	model	NOUN
ejpam-5043	9	20	applicable	applicable	ADJ
ejpam-5043	9	21	in	in	ADP
ejpam-5043	9	22	the	the	DET
ejpam-5043	9	23	fields	field	NOUN
ejpam-5043	9	24	of	of	ADP
ejpam-5043	9	25	science	science	NOUN
ejpam-5043	9	26	and	and	CCONJ
ejpam-5043	9	27	engineering	engineering	NOUN
ejpam-5043	9	28	.	.	PUNCT
ejpam-5043	10	1	2020	2020	NUM
ejpam-5043	10	2	mathematics	mathematic	NOUN
ejpam-5043	10	3	subject	subject	NOUN
ejpam-5043	10	4	classifications	classification	NOUN
ejpam-5043	10	5	:	:	PUNCT
ejpam-5043	10	6	97m40	97m40	NUM
ejpam-5043	10	7	key	key	ADJ
ejpam-5043	10	8	words	word	NOUN
ejpam-5043	10	9	and	and	CCONJ
ejpam-5043	10	10	phrases	phrase	NOUN
ejpam-5043	10	11	:	:	PUNCT
ejpam-5043	10	12	numerical	numerical	ADJ
ejpam-5043	10	13	solution	solution	NOUN
ejpam-5043	10	14	,	,	PUNCT
ejpam-5043	10	15	the	the	DET
ejpam-5043	10	16	atangana	atangana	PROPN
ejpam-5043	10	17	-	-	PUNCT
ejpam-5043	10	18	baleanu	baleanu	ADJ
ejpam-5043	10	19	fractional	fractional	ADJ
ejpam-5043	10	20	derivative	derivative	ADJ
ejpam-5043	10	21	,	,	PUNCT
ejpam-5043	10	22	initial	initial	ADJ
ejpam-5043	10	23	value	value	NOUN
ejpam-5043	10	24	problems	problem	NOUN
ejpam-5043	10	25	,	,	PUNCT
ejpam-5043	10	26	chaos	chaos	NOUN
ejpam-5043	10	27	1	1	NUM
ejpam-5043	10	28	.	.	PUNCT
ejpam-5043	10	29	introduction	introduction	NOUN
ejpam-5043	10	30	fractional	fractional	ADJ
ejpam-5043	10	31	calculus	calculus	NOUN
ejpam-5043	10	32	,	,	PUNCT
ejpam-5043	10	33	a	a	DET
ejpam-5043	10	34	science	science	NOUN
ejpam-5043	10	35	that	that	PRON
ejpam-5043	10	36	deals	deal	VERB
ejpam-5043	10	37	with	with	ADP
ejpam-5043	10	38	non	non	ADJ
ejpam-5043	10	39	-	-	ADJ
ejpam-5043	10	40	integer	integer	ADJ
ejpam-5043	10	41	order	order	NOUN
ejpam-5043	10	42	derivatives	derivative	NOUN
ejpam-5043	10	43	and	and	CCONJ
ejpam-5043	10	44	integrals	integral	NOUN
ejpam-5043	10	45	has	have	AUX
ejpam-5043	10	46	attracted	attract	VERB
ejpam-5043	10	47	significant	significant	ADJ
ejpam-5043	10	48	attention	attention	NOUN
ejpam-5043	10	49	from	from	ADP
ejpam-5043	10	50	a	a	DET
ejpam-5043	10	51	variety	variety	NOUN
ejpam-5043	10	52	of	of	ADP
ejpam-5043	10	53	scientific	scientific	ADJ
ejpam-5043	10	54	disciplines	discipline	NOUN
ejpam-5043	10	55	[	[	X
ejpam-5043	10	56	42	42	NUM
ejpam-5043	10	57	]	]	PUNCT
ejpam-5043	10	58	.	.	PUNCT
ejpam-5043	11	1	fundamental	fundamental	ADJ
ejpam-5043	11	2	concepts	concept	NOUN
ejpam-5043	11	3	in	in	ADP
ejpam-5043	11	4	fractional	fractional	ADJ
ejpam-5043	11	5	calculus	calculus	NOUN
ejpam-5043	11	6	were	be	AUX
ejpam-5043	11	7	first	first	ADV
ejpam-5043	11	8	explained	explain	VERB
ejpam-5043	11	9	by	by	ADP
ejpam-5043	11	10	oldham	oldham	PROPN
ejpam-5043	11	11	and	and	CCONJ
ejpam-5043	11	12	spanier	spani	ADJ
ejpam-5043	12	1	[	[	X
ejpam-5043	12	2	42	42	NUM
ejpam-5043	12	3	]	]	PUNCT
ejpam-5043	12	4	,	,	PUNCT
ejpam-5043	12	5	gorenflo	gorenflo	NOUN
ejpam-5043	12	6	and	and	CCONJ
ejpam-5043	12	7	mainardi	mainardi	PROPN
ejpam-5043	13	1	[	[	X
ejpam-5043	13	2	22	22	NUM
ejpam-5043	13	3	]	]	PUNCT
ejpam-5043	13	4	and	and	CCONJ
ejpam-5043	13	5	samko	samko	NOUN
ejpam-5043	13	6	et	et	PROPN
ejpam-5043	13	7	al	al	PROPN
ejpam-5043	13	8	.	.	PUNCT
ejpam-5043	14	1	[	[	X
ejpam-5043	14	2	29	29	NUM
ejpam-5043	14	3	]	]	PUNCT
ejpam-5043	14	4	.	.	PUNCT
ejpam-5043	15	1	these	these	DET
ejpam-5043	15	2	contributions	contribution	NOUN
ejpam-5043	15	3	have	have	AUX
ejpam-5043	15	4	had	have	VERB
ejpam-5043	15	5	a	a	DET
ejpam-5043	15	6	significant	significant	ADJ
ejpam-5043	15	7	influence	influence	NOUN
ejpam-5043	15	8	on	on	ADP
ejpam-5043	15	9	the	the	DET
ejpam-5043	15	10	comprehension	comprehension	NOUN
ejpam-5043	15	11	and	and	CCONJ
ejpam-5043	15	12	simulation	simulation	NOUN
ejpam-5043	15	13	of	of	ADP
ejpam-5043	15	14	intricate	intricate	ADJ
ejpam-5043	15	15	dynamic	dynamic	ADJ
ejpam-5043	15	16	systems	system	NOUN
ejpam-5043	15	17	.	.	PUNCT
ejpam-5043	16	1	numerous	numerous	ADJ
ejpam-5043	16	2	studies	study	NOUN
ejpam-5043	16	3	have	have	AUX
ejpam-5043	16	4	focused	focus	VERB
ejpam-5043	16	5	on	on	ADP
ejpam-5043	16	6	chaotic	chaotic	ADJ
ejpam-5043	16	7	behavior	behavior	NOUN
ejpam-5043	16	8	within	within	ADP
ejpam-5043	16	9	the	the	DET
ejpam-5043	16	10	framework	framework	NOUN
ejpam-5043	16	11	of	of	ADP
ejpam-5043	16	12	fractional	fractional	ADJ
ejpam-5043	16	13	calculus	calculus	NOUN
ejpam-5043	16	14	,	,	PUNCT
ejpam-5043	16	15	as	as	SCONJ
ejpam-5043	16	16	it	it	PRON
ejpam-5043	16	17	is	be	AUX
ejpam-5043	16	18	a	a	DET
ejpam-5043	16	19	feature	feature	NOUN
ejpam-5043	16	20	shared	share	VERB
ejpam-5043	16	21	by	by	ADP
ejpam-5043	16	22	many	many	ADJ
ejpam-5043	16	23	nonlinear	nonlinear	ADJ
ejpam-5043	16	24	systems	system	NOUN
ejpam-5043	16	25	.	.	PUNCT
ejpam-5043	17	1	dudkowski	dudkowski	PROPN
ejpam-5043	17	2	et	et	PROPN
ejpam-5043	17	3	al	al	PROPN
ejpam-5043	17	4	.	.	PUNCT
ejpam-5043	18	1	[	[	X
ejpam-5043	18	2	11	11	NUM
ejpam-5043	18	3	]	]	PUNCT
ejpam-5043	18	4	brought	bring	VERB
ejpam-5043	18	5	attention	attention	NOUN
ejpam-5043	18	6	to	to	ADP
ejpam-5043	18	7	the	the	DET
ejpam-5043	18	8	fact	fact	NOUN
ejpam-5043	18	9	that	that	SCONJ
ejpam-5043	18	10	dynamical	dynamical	ADJ
ejpam-5043	18	11	systems	system	NOUN
ejpam-5043	18	12	might	might	AUX
ejpam-5043	18	13	have	have	AUX
ejpam-5043	18	14	hidden	hide	VERB
ejpam-5043	18	15	attractors	attractor	NOUN
ejpam-5043	18	16	,	,	PUNCT
ejpam-5043	18	17	highlighting	highlight	VERB
ejpam-5043	18	18	the	the	DET
ejpam-5043	18	19	significance	significance	NOUN
ejpam-5043	18	20	of	of	ADP
ejpam-5043	18	21	correctly	correctly	ADV
ejpam-5043	18	22	identifying	identify	VERB
ejpam-5043	18	23	chaotic	chaotic	ADJ
ejpam-5043	18	24	regimes	regime	NOUN
ejpam-5043	18	25	.	.	PUNCT
ejpam-5043	19	1	the	the	DET
ejpam-5043	19	2	range	range	NOUN
ejpam-5043	19	3	of	of	ADP
ejpam-5043	19	4	fractional	fractional	ADJ
ejpam-5043	19	5	doi	doi	NOUN
ejpam-5043	19	6	:	:	PUNCT
ejpam-5043	19	7	https://doi.org/10.29020/nybg.ejpam.v17i1.5043	https://doi.org/10.29020/nybg.ejpam.v17i1.5043	ADJ
ejpam-5043	19	8	email	email	NOUN
ejpam-5043	19	9	address	address	NOUN
ejpam-5043	19	10	:	:	PUNCT
ejpam-5043	19	11	boulehmikaouther@gmail.com	boulehmikaouther@gmail.com	X
ejpam-5043	19	12	(	(	PUNCT
ejpam-5043	19	13	k.	k.	PROPN
ejpam-5043	19	14	boulehmi	boulehmi	PROPN
ejpam-5043	19	15	)	)	PUNCT
ejpam-5043	19	16	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5043	19	17	445	445	NUM
ejpam-5043	20	1	©	©	ADP
ejpam-5043	20	2	2024	2024	NUM
ejpam-5043	20	3	ejpam	ejpam	NOUN
ejpam-5043	20	4	all	all	DET
ejpam-5043	20	5	rights	right	NOUN
ejpam-5043	20	6	reserved	reserve	VERB
ejpam-5043	20	7	.	.	PUNCT
ejpam-5043	21	1	k.	k.	PROPN
ejpam-5043	21	2	boulehmi	boulehmi	PROPN
ejpam-5043	21	3	/	/	SYM
ejpam-5043	21	4	eur	eur	PROPN
ejpam-5043	21	5	.	.	PUNCT
ejpam-5043	22	1	j.	j.	PROPN
ejpam-5043	22	2	pure	pure	PROPN
ejpam-5043	22	3	appl	appl	PROPN
ejpam-5043	22	4	.	.	PROPN
ejpam-5043	22	5	math	math	PROPN
ejpam-5043	22	6	,	,	PUNCT
ejpam-5043	22	7	17	17	NUM
ejpam-5043	22	8	(	(	PUNCT
ejpam-5043	22	9	1	1	NUM
ejpam-5043	22	10	)	)	PUNCT
ejpam-5043	22	11	(	(	PUNCT
ejpam-5043	22	12	2024	2024	NUM
ejpam-5043	22	13	)	)	PUNCT
ejpam-5043	22	14	,	,	PUNCT
ejpam-5043	22	15	445	445	NUM
ejpam-5043	22	16	-	-	SYM
ejpam-5043	22	17	461	461	NUM
ejpam-5043	22	18	446	446	NUM
ejpam-5043	22	19	calculus	calculus	NOUN
ejpam-5043	22	20	applications	application	NOUN
ejpam-5043	22	21	in	in	ADP
ejpam-5043	22	22	diverse	diverse	ADJ
ejpam-5043	22	23	domains	domain	NOUN
ejpam-5043	22	24	has	have	AUX
ejpam-5043	22	25	been	be	AUX
ejpam-5043	22	26	expanded	expand	VERB
ejpam-5043	22	27	by	by	ADP
ejpam-5043	22	28	recent	recent	ADJ
ejpam-5043	22	29	studies	study	NOUN
ejpam-5043	22	30	by	by	ADP
ejpam-5043	22	31	salah	salah	PROPN
ejpam-5043	22	32	et	et	PROPN
ejpam-5043	22	33	al	al	PROPN
ejpam-5043	22	34	.	.	PUNCT
ejpam-5043	23	1	[	[	X
ejpam-5043	23	2	12	12	NUM
ejpam-5043	23	3	]	]	PUNCT
ejpam-5043	23	4	,	,	PUNCT
ejpam-5043	23	5	abdoon	abdoon	PROPN
ejpam-5043	23	6	et	et	PROPN
ejpam-5043	23	7	al	al	PROPN
ejpam-5043	23	8	.	.	PUNCT
ejpam-5043	24	1	[	[	X
ejpam-5043	24	2	13	13	NUM
ejpam-5043	24	3	]	]	PUNCT
ejpam-5043	24	4	and	and	CCONJ
ejpam-5043	24	5	abu	abu	PROPN
ejpam-5043	24	6	-	-	PUNCT
ejpam-5043	24	7	ghuwaleh	ghuwaleh	PROPN
ejpam-5043	24	8	et	et	PROPN
ejpam-5043	24	9	al	al	PROPN
ejpam-5043	24	10	.	.	PUNCT
ejpam-5043	25	1	[	[	X
ejpam-5043	25	2	2	2	NUM
ejpam-5043	25	3	]	]	PUNCT
ejpam-5043	25	4	,	,	PUNCT
ejpam-5043	25	5	which	which	PRON
ejpam-5043	25	6	highlighted	highlight	VERB
ejpam-5043	25	7	the	the	DET
ejpam-5043	25	8	efficacy	efficacy	NOUN
ejpam-5043	25	9	of	of	ADP
ejpam-5043	25	10	fractional	fractional	ADJ
ejpam-5043	25	11	methods	method	NOUN
ejpam-5043	25	12	in	in	ADP
ejpam-5043	25	13	solving	solve	VERB
ejpam-5043	25	14	multi	multi	ADJ
ejpam-5043	25	15	-	-	ADJ
ejpam-5043	25	16	dimensional	dimensional	ADJ
ejpam-5043	25	17	equations	equation	NOUN
ejpam-5043	25	18	,	,	PUNCT
ejpam-5043	25	19	influenza	influenza	NOUN
ejpam-5043	25	20	modeling	modeling	NOUN
ejpam-5043	25	21	,	,	PUNCT
ejpam-5043	25	22	and	and	CCONJ
ejpam-5043	25	23	integrating	integrate	VERB
ejpam-5043	25	24	master	master	NOUN
ejpam-5043	25	25	theorems	theorem	NOUN
ejpam-5043	25	26	,	,	PUNCT
ejpam-5043	25	27	respectively	respectively	ADV
ejpam-5043	25	28	.	.	PUNCT
ejpam-5043	26	1	there	there	PRON
ejpam-5043	26	2	has	have	AUX
ejpam-5043	26	3	been	be	AUX
ejpam-5043	26	4	a	a	DET
ejpam-5043	26	5	lot	lot	NOUN
ejpam-5043	26	6	of	of	ADP
ejpam-5043	26	7	study	study	NOUN
ejpam-5043	26	8	into	into	ADP
ejpam-5043	26	9	the	the	DET
ejpam-5043	26	10	use	use	NOUN
ejpam-5043	26	11	of	of	ADP
ejpam-5043	26	12	fractional	fractional	ADJ
ejpam-5043	26	13	calculus	calculus	NOUN
ejpam-5043	26	14	approaches	approach	NOUN
ejpam-5043	26	15	to	to	PART
ejpam-5043	26	16	try	try	VERB
ejpam-5043	26	17	to	to	PART
ejpam-5043	26	18	understand	understand	VERB
ejpam-5043	26	19	and	and	CCONJ
ejpam-5043	26	20	regulate	regulate	VERB
ejpam-5043	26	21	engineering	engineering	NOUN
ejpam-5043	26	22	systems	system	NOUN
ejpam-5043	26	23	that	that	PRON
ejpam-5043	26	24	exhibit	exhibit	VERB
ejpam-5043	26	25	chaotic	chaotic	ADJ
ejpam-5043	26	26	behavior	behavior	NOUN
ejpam-5043	26	27	.	.	PUNCT
ejpam-5043	27	1	guma	guma	PROPN
ejpam-5043	27	2	et	et	PROPN
ejpam-5043	27	3	al	al	PROPN
ejpam-5043	27	4	.	.	PUNCT
ejpam-5043	28	1	[	[	X
ejpam-5043	28	2	23	23	NUM
ejpam-5043	28	3	]	]	PUNCT
ejpam-5043	28	4	,	,	PUNCT
ejpam-5043	28	5	almutairi	almutairi	NOUN
ejpam-5043	28	6	et	et	PROPN
ejpam-5043	28	7	al	al	PROPN
ejpam-5043	28	8	.	.	PUNCT
ejpam-5043	29	1	[	[	X
ejpam-5043	29	2	4	4	NUM
ejpam-5043	29	3	]	]	PUNCT
ejpam-5043	29	4	,	,	PUNCT
ejpam-5043	29	5	xu	xu	PROPN
ejpam-5043	29	6	et	et	PROPN
ejpam-5043	29	7	al	al	PROPN
ejpam-5043	29	8	.	.	PUNCT
ejpam-5043	30	1	[	[	X
ejpam-5043	30	2	20	20	NUM
ejpam-5043	30	3	]	]	PUNCT
ejpam-5043	30	4	,	,	PUNCT
ejpam-5043	30	5	and	and	CCONJ
ejpam-5043	30	6	lai	lai	PROPN
ejpam-5043	30	7	et	et	PROPN
ejpam-5043	30	8	al	al	PROPN
ejpam-5043	30	9	.	.	PUNCT
ejpam-5043	31	1	[	[	X
ejpam-5043	31	2	38	38	NUM
ejpam-5043	31	3	]	]	PUNCT
ejpam-5043	31	4	show	show	VERB
ejpam-5043	31	5	how	how	SCONJ
ejpam-5043	31	6	fractional	fractional	ADJ
ejpam-5043	31	7	approaches	approach	NOUN
ejpam-5043	31	8	can	can	AUX
ejpam-5043	31	9	be	be	AUX
ejpam-5043	31	10	used	use	VERB
ejpam-5043	31	11	to	to	PART
ejpam-5043	31	12	study	study	VERB
ejpam-5043	31	13	healthcare	healthcare	NOUN
ejpam-5043	31	14	risk	risk	NOUN
ejpam-5043	31	15	factors	factor	NOUN
ejpam-5043	31	16	,	,	PUNCT
ejpam-5043	31	17	validate	validate	VERB
ejpam-5043	31	18	efficiency	efficiency	NOUN
ejpam-5043	31	19	models	model	NOUN
ejpam-5043	31	20	,	,	PUNCT
ejpam-5043	31	21	and	and	CCONJ
ejpam-5043	31	22	create	create	VERB
ejpam-5043	31	23	chaotic	chaotic	ADJ
ejpam-5043	31	24	systems	system	NOUN
ejpam-5043	31	25	with	with	ADP
ejpam-5043	31	26	multiple	multiple	ADJ
ejpam-5043	31	27	attractors	attractor	NOUN
ejpam-5043	31	28	,	,	PUNCT
ejpam-5043	31	29	all	all	PRON
ejpam-5043	31	30	of	of	ADP
ejpam-5043	31	31	which	which	PRON
ejpam-5043	31	32	add	add	VERB
ejpam-5043	31	33	to	to	ADP
ejpam-5043	31	34	our	our	PRON
ejpam-5043	31	35	knowledge	knowledge	NOUN
ejpam-5043	31	36	of	of	ADP
ejpam-5043	31	37	chaotic	chaotic	ADJ
ejpam-5043	31	38	dynamics	dynamic	NOUN
ejpam-5043	31	39	.	.	PUNCT
ejpam-5043	32	1	analysing	analyse	VERB
ejpam-5043	32	2	complex	complex	ADJ
ejpam-5043	32	3	circuits	circuit	NOUN
ejpam-5043	32	4	[	[	X
ejpam-5043	32	5	36	36	NUM
ejpam-5043	32	6	]	]	PUNCT
ejpam-5043	32	7	,	,	PUNCT
ejpam-5043	32	8	synchronizing	synchronize	VERB
ejpam-5043	32	9	reaction	reaction	NOUN
ejpam-5043	32	10	-	-	PUNCT
ejpam-5043	32	11	diffusion	diffusion	NOUN
ejpam-5043	32	12	systems	system	NOUN
ejpam-5043	32	13	[	[	X
ejpam-5043	32	14	24	24	NUM
ejpam-5043	32	15	]	]	PUNCT
ejpam-5043	32	16	,	,	PUNCT
ejpam-5043	32	17	and	and	CCONJ
ejpam-5043	32	18	modelling	model	VERB
ejpam-5043	32	19	predator	predator	NOUN
ejpam-5043	32	20	-	-	PUNCT
ejpam-5043	32	21	prey	prey	NOUN
ejpam-5043	32	22	dynamics	dynamic	NOUN
ejpam-5043	32	23	[	[	X
ejpam-5043	32	24	40	40	NUM
ejpam-5043	32	25	]	]	PUNCT
ejpam-5043	32	26	are	be	AUX
ejpam-5043	32	27	only	only	ADV
ejpam-5043	32	28	a	a	DET
ejpam-5043	32	29	few	few	ADJ
ejpam-5043	32	30	of	of	ADP
ejpam-5043	32	31	the	the	DET
ejpam-5043	32	32	many	many	ADJ
ejpam-5043	32	33	engineering	engineering	NOUN
ejpam-5043	32	34	applications	application	NOUN
ejpam-5043	32	35	that	that	PRON
ejpam-5043	32	36	have	have	AUX
ejpam-5043	32	37	connected	connect	VERB
ejpam-5043	32	38	with	with	ADP
ejpam-5043	32	39	fractional	fractional	ADJ
ejpam-5043	32	40	calculus	calculus	NOUN
ejpam-5043	32	41	.	.	PUNCT
ejpam-5043	33	1	the	the	DET
ejpam-5043	33	2	methods	method	NOUN
ejpam-5043	33	3	outlined	outline	VERB
ejpam-5043	33	4	in	in	ADP
ejpam-5043	33	5	the	the	DET
ejpam-5043	33	6	literature	literature	NOUN
ejpam-5043	33	7	have	have	AUX
ejpam-5043	33	8	demonstrated	demonstrate	VERB
ejpam-5043	33	9	broad	broad	ADJ
ejpam-5043	33	10	applicability	applicability	NOUN
ejpam-5043	33	11	across	across	ADP
ejpam-5043	33	12	diverse	diverse	ADJ
ejpam-5043	33	13	domains	domain	NOUN
ejpam-5043	33	14	,	,	PUNCT
ejpam-5043	33	15	showcasing	showcase	VERB
ejpam-5043	33	16	their	their	PRON
ejpam-5043	33	17	effectiveness	effectiveness	NOUN
ejpam-5043	33	18	in	in	ADP
ejpam-5043	33	19	advancing	advance	VERB
ejpam-5043	33	20	technologies	technology	NOUN
ejpam-5043	33	21	,	,	PUNCT
ejpam-5043	33	22	these	these	DET
ejpam-5043	33	23	methodologies	methodology	NOUN
ejpam-5043	33	24	have	have	AUX
ejpam-5043	33	25	found	find	VERB
ejpam-5043	33	26	resonance	resonance	NOUN
ejpam-5043	33	27	in	in	ADP
ejpam-5043	33	28	robotics	robotic	NOUN
ejpam-5043	33	29	[	[	X
ejpam-5043	33	30	9	9	NUM
ejpam-5043	33	31	]	]	PUNCT
ejpam-5043	33	32	,	,	PUNCT
ejpam-5043	33	33	differential	differential	ADJ
ejpam-5043	33	34	equations	equation	NOUN
ejpam-5043	34	1	[	[	X
ejpam-5043	34	2	39	39	NUM
ejpam-5043	34	3	]	]	PUNCT
ejpam-5043	34	4	,	,	PUNCT
ejpam-5043	34	5	image	image	NOUN
ejpam-5043	34	6	processing	processing	NOUN
ejpam-5043	35	1	[	[	X
ejpam-5043	35	2	21	21	NUM
ejpam-5043	35	3	]	]	PUNCT
ejpam-5043	35	4	,	,	PUNCT
ejpam-5043	35	5	control	control	NOUN
ejpam-5043	35	6	systems	system	NOUN
ejpam-5043	35	7	[	[	X
ejpam-5043	35	8	35	35	NUM
ejpam-5043	35	9	]	]	PUNCT
ejpam-5043	35	10	,	,	PUNCT
ejpam-5043	35	11	solving	solve	VERB
ejpam-5043	35	12	partial	partial	ADJ
ejpam-5043	35	13	differential	differential	ADJ
ejpam-5043	35	14	equations	equation	NOUN
ejpam-5043	35	15	[	[	X
ejpam-5043	35	16	25	25	NUM
ejpam-5043	35	17	,	,	PUNCT
ejpam-5043	35	18	31	31	NUM
ejpam-5043	35	19	]	]	PUNCT
ejpam-5043	35	20	and	and	CCONJ
ejpam-5043	35	21	various	various	ADJ
ejpam-5043	35	22	other	other	ADJ
ejpam-5043	35	23	interdisciplinary	interdisciplinary	ADJ
ejpam-5043	35	24	arenas	arena	NOUN
ejpam-5043	35	25	.	.	PUNCT
ejpam-5043	36	1	they	they	PRON
ejpam-5043	36	2	have	have	AUX
ejpam-5043	36	3	facilitated	facilitate	VERB
ejpam-5043	36	4	significant	significant	ADJ
ejpam-5043	36	5	strides	stride	NOUN
ejpam-5043	36	6	in	in	ADP
ejpam-5043	36	7	controlling	control	VERB
ejpam-5043	36	8	robotic	robotic	ADJ
ejpam-5043	36	9	manipulators	manipulator	NOUN
ejpam-5043	36	10	with	with	ADP
ejpam-5043	36	11	fractional	fractional	ADJ
ejpam-5043	36	12	-	-	PUNCT
ejpam-5043	36	13	order	order	NOUN
ejpam-5043	36	14	modeling	modeling	NOUN
ejpam-5043	36	15	[	[	X
ejpam-5043	36	16	9	9	NUM
ejpam-5043	36	17	]	]	PUNCT
ejpam-5043	36	18	,	,	PUNCT
ejpam-5043	36	19	offering	offer	VERB
ejpam-5043	36	20	innovative	innovative	ADJ
ejpam-5043	36	21	schemes	scheme	NOUN
ejpam-5043	36	22	in	in	ADP
ejpam-5043	36	23	order	order	NOUN
ejpam-5043	36	24	to	to	PART
ejpam-5043	36	25	solve	solve	VERB
ejpam-5043	36	26	fractional	fractional	ADJ
ejpam-5043	36	27	differential	differential	ADJ
ejpam-5043	36	28	equations	equation	NOUN
ejpam-5043	36	29	and	and	CCONJ
ejpam-5043	36	30	chaotic	chaotic	ADJ
ejpam-5043	36	31	systems	system	NOUN
ejpam-5043	36	32	[	[	X
ejpam-5043	36	33	39	39	NUM
ejpam-5043	36	34	]	]	PUNCT
ejpam-5043	36	35	.	.	PUNCT
ejpam-5043	37	1	moreover	moreover	ADV
ejpam-5043	37	2	,	,	PUNCT
ejpam-5043	37	3	these	these	DET
ejpam-5043	37	4	techniques	technique	NOUN
ejpam-5043	37	5	have	have	AUX
ejpam-5043	37	6	contributed	contribute	VERB
ejpam-5043	37	7	to	to	ADP
ejpam-5043	37	8	the	the	DET
ejpam-5043	37	9	development	development	NOUN
ejpam-5043	37	10	of	of	ADP
ejpam-5043	37	11	cutting	cut	VERB
ejpam-5043	37	12	-	-	PUNCT
ejpam-5043	37	13	edge	edge	NOUN
ejpam-5043	37	14	edge	edge	NOUN
ejpam-5043	37	15	-	-	PUNCT
ejpam-5043	37	16	detection	detection	NOUN
ejpam-5043	37	17	methodologies	methodology	NOUN
ejpam-5043	37	18	using	use	VERB
ejpam-5043	37	19	fractional	fractional	ADJ
ejpam-5043	37	20	derivatives	derivative	NOUN
ejpam-5043	37	21	with	with	ADP
ejpam-5043	37	22	with	with	ADP
ejpam-5043	37	23	kernels	kernel	NOUN
ejpam-5043	37	24	that	that	PRON
ejpam-5043	37	25	are	be	AUX
ejpam-5043	37	26	both	both	PRON
ejpam-5043	37	27	nonlocal	nonlocal	ADJ
ejpam-5043	37	28	and	and	CCONJ
ejpam-5043	37	29	nonsingular	nonsingular	ADJ
ejpam-5043	38	1	[	[	X
ejpam-5043	38	2	21	21	NUM
ejpam-5043	38	3	]	]	PUNCT
ejpam-5043	38	4	.	.	PUNCT
ejpam-5043	39	1	in	in	ADP
ejpam-5043	39	2	the	the	DET
ejpam-5043	39	3	realm	realm	NOUN
ejpam-5043	39	4	of	of	ADP
ejpam-5043	39	5	control	control	NOUN
ejpam-5043	39	6	systems	system	NOUN
ejpam-5043	39	7	,	,	PUNCT
ejpam-5043	39	8	these	these	DET
ejpam-5043	39	9	methods	method	NOUN
ejpam-5043	39	10	have	have	AUX
ejpam-5043	39	11	enabled	enable	VERB
ejpam-5043	39	12	the	the	DET
ejpam-5043	39	13	control	control	NOUN
ejpam-5043	39	14	of	of	ADP
ejpam-5043	39	15	fractional	fractional	ADJ
ejpam-5043	39	16	-	-	PUNCT
ejpam-5043	39	17	order	order	NOUN
ejpam-5043	39	18	systems	system	NOUN
ejpam-5043	39	19	such	such	ADJ
ejpam-5043	39	20	as	as	ADP
ejpam-5043	39	21	chua	chua	PROPN
ejpam-5043	39	22	’s	’s	PART
ejpam-5043	39	23	system	system	NOUN
ejpam-5043	39	24	[	[	X
ejpam-5043	39	25	35	35	NUM
ejpam-5043	39	26	]	]	PUNCT
ejpam-5043	39	27	.	.	PUNCT
ejpam-5043	40	1	additionally	additionally	ADV
ejpam-5043	40	2	,	,	PUNCT
ejpam-5043	40	3	they	they	PRON
ejpam-5043	40	4	have	have	AUX
ejpam-5043	40	5	been	be	AUX
ejpam-5043	40	6	instrumental	instrumental	ADJ
ejpam-5043	40	7	in	in	ADP
ejpam-5043	40	8	deriving	derive	VERB
ejpam-5043	40	9	solutions	solution	NOUN
ejpam-5043	40	10	for	for	ADP
ejpam-5043	40	11	intricate	intricate	ADJ
ejpam-5043	40	12	mathematical	mathematical	ADJ
ejpam-5043	40	13	models	model	NOUN
ejpam-5043	40	14	like	like	ADP
ejpam-5043	40	15	the	the	DET
ejpam-5043	40	16	generalized	generalize	VERB
ejpam-5043	40	17	zakharov	zakharov	ADJ
ejpam-5043	40	18	equation	equation	NOUN
ejpam-5043	40	19	and	and	CCONJ
ejpam-5043	40	20	initial	initial	ADJ
ejpam-5043	40	21	value	value	NOUN
ejpam-5043	40	22	problems	problem	NOUN
ejpam-5043	40	23	involving	involve	VERB
ejpam-5043	40	24	generalized	generalized	ADJ
ejpam-5043	40	25	fractional	fractional	ADJ
ejpam-5043	40	26	derivatives	derivative	NOUN
ejpam-5043	40	27	[	[	X
ejpam-5043	40	28	25	25	NUM
ejpam-5043	40	29	,	,	PUNCT
ejpam-5043	40	30	31	31	NUM
ejpam-5043	40	31	]	]	PUNCT
ejpam-5043	40	32	.	.	PUNCT
ejpam-5043	41	1	furthermore	furthermore	ADV
ejpam-5043	41	2	,	,	PUNCT
ejpam-5043	41	3	recent	recent	ADJ
ejpam-5043	41	4	studies	study	NOUN
ejpam-5043	41	5	[	[	X
ejpam-5043	41	6	5	5	NUM
ejpam-5043	41	7	,	,	PUNCT
ejpam-5043	41	8	14	14	NUM
ejpam-5043	41	9	,	,	PUNCT
ejpam-5043	41	10	15	15	NUM
ejpam-5043	41	11	,	,	PUNCT
ejpam-5043	41	12	44	44	NUM
ejpam-5043	41	13	,	,	PUNCT
ejpam-5043	41	14	46	46	NUM
ejpam-5043	41	15	]	]	PUNCT
ejpam-5043	41	16	have	have	AUX
ejpam-5043	41	17	expanded	expand	VERB
ejpam-5043	41	18	upon	upon	SCONJ
ejpam-5043	41	19	these	these	DET
ejpam-5043	41	20	methodologies	methodology	NOUN
ejpam-5043	41	21	,	,	PUNCT
ejpam-5043	41	22	presenting	present	VERB
ejpam-5043	41	23	numerical	numerical	ADJ
ejpam-5043	41	24	solutions	solution	NOUN
ejpam-5043	41	25	,	,	PUNCT
ejpam-5043	41	26	comparative	comparative	ADJ
ejpam-5043	41	27	studies	study	NOUN
ejpam-5043	41	28	,	,	PUNCT
ejpam-5043	41	29	and	and	CCONJ
ejpam-5043	41	30	applications	application	NOUN
ejpam-5043	41	31	encompassing	encompass	VERB
ejpam-5043	41	32	symmetric	symmetric	ADJ
ejpam-5043	41	33	attractors	attractor	NOUN
ejpam-5043	41	34	,	,	PUNCT
ejpam-5043	41	35	electric	electric	ADJ
ejpam-5043	41	36	circuits	circuit	NOUN
ejpam-5043	41	37	,	,	PUNCT
ejpam-5043	41	38	image	image	NOUN
ejpam-5043	41	39	encryption	encryption	NOUN
ejpam-5043	41	40	,	,	PUNCT
ejpam-5043	41	41	and	and	CCONJ
ejpam-5043	41	42	stability	stability	NOUN
ejpam-5043	41	43	analyses	analyse	VERB
ejpam-5043	41	44	in	in	ADP
ejpam-5043	41	45	control	control	NOUN
ejpam-5043	41	46	systems	system	NOUN
ejpam-5043	41	47	and	and	CCONJ
ejpam-5043	41	48	image	image	NOUN
ejpam-5043	41	49	processing	processing	NOUN
ejpam-5043	41	50	.	.	PUNCT
ejpam-5043	42	1	the	the	DET
ejpam-5043	42	2	adaptability	adaptability	NOUN
ejpam-5043	42	3	and	and	CCONJ
ejpam-5043	42	4	versatility	versatility	NOUN
ejpam-5043	42	5	of	of	ADP
ejpam-5043	42	6	these	these	DET
ejpam-5043	42	7	methods	method	NOUN
ejpam-5043	42	8	continue	continue	VERB
ejpam-5043	42	9	to	to	PART
ejpam-5043	42	10	pave	pave	VERB
ejpam-5043	42	11	the	the	DET
ejpam-5043	42	12	way	way	NOUN
ejpam-5043	42	13	for	for	ADP
ejpam-5043	42	14	advancements	advancement	NOUN
ejpam-5043	42	15	in	in	ADP
ejpam-5043	42	16	multidisciplinary	multidisciplinary	ADJ
ejpam-5043	42	17	fields	field	NOUN
ejpam-5043	42	18	,	,	PUNCT
ejpam-5043	42	19	illustrating	illustrate	VERB
ejpam-5043	42	20	their	their	PRON
ejpam-5043	42	21	profound	profound	ADJ
ejpam-5043	42	22	impact	impact	NOUN
ejpam-5043	42	23	on	on	ADP
ejpam-5043	42	24	diverse	diverse	ADJ
ejpam-5043	42	25	technological	technological	ADJ
ejpam-5043	42	26	landscapes	landscape	NOUN
ejpam-5043	42	27	.	.	PUNCT
ejpam-5043	43	1	the	the	DET
ejpam-5043	43	2	significance	significance	NOUN
ejpam-5043	43	3	of	of	ADP
ejpam-5043	43	4	fractional	fractional	ADJ
ejpam-5043	43	5	differential	differential	ADJ
ejpam-5043	43	6	equations	equation	NOUN
ejpam-5043	43	7	lies	lie	VERB
ejpam-5043	43	8	in	in	ADP
ejpam-5043	43	9	their	their	PRON
ejpam-5043	43	10	ability	ability	NOUN
ejpam-5043	43	11	to	to	PART
ejpam-5043	43	12	accurately	accurately	ADV
ejpam-5043	43	13	capture	capture	VERB
ejpam-5043	43	14	non	non	ADJ
ejpam-5043	43	15	-	-	ADJ
ejpam-5043	43	16	integer	integer	ADJ
ejpam-5043	43	17	order	order	NOUN
ejpam-5043	43	18	derivatives	derivative	NOUN
ejpam-5043	43	19	,	,	PUNCT
ejpam-5043	43	20	making	make	VERB
ejpam-5043	43	21	them	they	PRON
ejpam-5043	43	22	essential	essential	ADJ
ejpam-5043	43	23	for	for	ADP
ejpam-5043	43	24	understanding	understand	VERB
ejpam-5043	43	25	diverse	diverse	ADJ
ejpam-5043	43	26	phenomena	phenomenon	NOUN
ejpam-5043	43	27	in	in	ADP
ejpam-5043	43	28	science	science	NOUN
ejpam-5043	43	29	and	and	CCONJ
ejpam-5043	43	30	engineering	engineering	NOUN
ejpam-5043	43	31	.	.	PUNCT
ejpam-5043	44	1	the	the	DET
ejpam-5043	44	2	abc	abc	PROPN
ejpam-5043	44	3	-	-	PUNCT
ejpam-5043	44	4	fd	fd	PROPN
ejpam-5043	44	5	,	,	PUNCT
ejpam-5043	44	6	as	as	ADP
ejpam-5043	44	7	a	a	DET
ejpam-5043	44	8	versatile	versatile	ADJ
ejpam-5043	44	9	tool	tool	NOUN
ejpam-5043	44	10	within	within	ADP
ejpam-5043	44	11	this	this	DET
ejpam-5043	44	12	framework	framework	NOUN
ejpam-5043	44	13	,	,	PUNCT
ejpam-5043	44	14	is	be	AUX
ejpam-5043	44	15	introduced	introduce	VERB
ejpam-5043	44	16	and	and	CCONJ
ejpam-5043	44	17	compared	compare	VERB
ejpam-5043	44	18	to	to	ADP
ejpam-5043	44	19	the	the	DET
ejpam-5043	44	20	runge	runge	NOUN
ejpam-5043	44	21	-	-	PUNCT
ejpam-5043	44	22	kutta	kutta	NOUN
ejpam-5043	44	23	fourth	fourth	ADJ
ejpam-5043	44	24	order	order	NOUN
ejpam-5043	44	25	(	(	PUNCT
ejpam-5043	44	26	rk4	rk4	NOUN
ejpam-5043	44	27	)	)	PUNCT
ejpam-5043	44	28	method	method	NOUN
ejpam-5043	44	29	.	.	PUNCT
ejpam-5043	45	1	the	the	DET
ejpam-5043	45	2	research	research	NOUN
ejpam-5043	45	3	aims	aim	VERB
ejpam-5043	45	4	to	to	PART
ejpam-5043	45	5	demonstrate	demonstrate	VERB
ejpam-5043	45	6	the	the	DET
ejpam-5043	45	7	efficacy	efficacy	NOUN
ejpam-5043	45	8	of	of	ADP
ejpam-5043	45	9	the	the	DET
ejpam-5043	45	10	abc	abc	PROPN
ejpam-5043	45	11	-	-	PUNCT
ejpam-5043	45	12	fd	fd	PROPN
ejpam-5043	45	13	by	by	ADP
ejpam-5043	45	14	generating	generate	VERB
ejpam-5043	45	15	solutions	solution	NOUN
ejpam-5043	45	16	indistinguishable	indistinguishable	ADJ
ejpam-5043	45	17	from	from	ADP
ejpam-5043	45	18	rk4	rk4	PROPN
ejpam-5043	45	19	,	,	PUNCT
ejpam-5043	45	20	highlighting	highlight	VERB
ejpam-5043	45	21	its	its	PRON
ejpam-5043	45	22	adaptability	adaptability	NOUN
ejpam-5043	45	23	to	to	ADP
ejpam-5043	45	24	various	various	ADJ
ejpam-5043	45	25	systems	system	NOUN
ejpam-5043	45	26	,	,	PUNCT
ejpam-5043	45	27	and	and	CCONJ
ejpam-5043	45	28	showcasing	showcase	VERB
ejpam-5043	45	29	its	its	PRON
ejpam-5043	45	30	ability	ability	NOUN
ejpam-5043	45	31	to	to	PART
ejpam-5043	45	32	identify	identify	VERB
ejpam-5043	45	33	chaotic	chaotic	ADJ
ejpam-5043	45	34	situations	situation	NOUN
ejpam-5043	45	35	.	.	PUNCT
ejpam-5043	46	1	the	the	DET
ejpam-5043	46	2	anticipated	anticipate	VERB
ejpam-5043	46	3	contributions	contribution	NOUN
ejpam-5043	46	4	include	include	VERB
ejpam-5043	46	5	enhanced	enhanced	ADJ
ejpam-5043	46	6	accuracy	accuracy	NOUN
ejpam-5043	46	7	in	in	ADP
ejpam-5043	46	8	solving	solve	VERB
ejpam-5043	46	9	fractional	fractional	ADJ
ejpam-5043	46	10	differential	differential	ADJ
ejpam-5043	46	11	equations	equation	NOUN
ejpam-5043	46	12	and	and	CCONJ
ejpam-5043	46	13	the	the	DET
ejpam-5043	46	14	potential	potential	NOUN
ejpam-5043	46	15	to	to	PART
ejpam-5043	46	16	improve	improve	VERB
ejpam-5043	46	17	numerical	numerical	ADJ
ejpam-5043	46	18	solutions	solution	NOUN
ejpam-5043	46	19	for	for	ADP
ejpam-5043	46	20	a	a	DET
ejpam-5043	46	21	multitude	multitude	NOUN
ejpam-5043	46	22	of	of	ADP
ejpam-5043	46	23	models	model	NOUN
ejpam-5043	46	24	applicable	applicable	ADJ
ejpam-5043	46	25	in	in	ADP
ejpam-5043	46	26	scientific	scientific	ADJ
ejpam-5043	46	27	and	and	CCONJ
ejpam-5043	46	28	engineering	engineering	NOUN
ejpam-5043	46	29	fields	field	NOUN
ejpam-5043	46	30	,	,	PUNCT
ejpam-5043	46	31	thereby	thereby	ADV
ejpam-5043	46	32	advancing	advance	VERB
ejpam-5043	46	33	the	the	DET
ejpam-5043	46	34	understanding	understanding	NOUN
ejpam-5043	46	35	and	and	CCONJ
ejpam-5043	46	36	application	application	NOUN
ejpam-5043	46	37	of	of	ADP
ejpam-5043	46	38	fractional	fractional	ADJ
ejpam-5043	46	39	calculus	calculus	NOUN
ejpam-5043	46	40	in	in	ADP
ejpam-5043	46	41	diverse	diverse	ADJ
ejpam-5043	46	42	domains	domain	NOUN
ejpam-5043	46	43	.	.	PUNCT
ejpam-5043	47	1	in	in	ADP
ejpam-5043	47	2	this	this	DET
ejpam-5043	47	3	study	study	NOUN
ejpam-5043	47	4	,	,	PUNCT
ejpam-5043	47	5	our	our	PRON
ejpam-5043	47	6	proposed	propose	VERB
ejpam-5043	47	7	formulation	formulation	NOUN
ejpam-5043	47	8	distinguishes	distinguish	VERB
ejpam-5043	47	9	itself	itself	PRON
ejpam-5043	47	10	from	from	ADP
ejpam-5043	47	11	the	the	DET
ejpam-5043	47	12	work	work	NOUN
ejpam-5043	47	13	presented	present	VERB
ejpam-5043	47	14	in	in	ADP
ejpam-5043	47	15	atangana	atangana	PROPN
ejpam-5043	47	16	and	and	CCONJ
ejpam-5043	47	17	qureshi	qureshi	PROPN
ejpam-5043	47	18	see	see	VERB
ejpam-5043	47	19	[	[	X
ejpam-5043	47	20	8	8	X
ejpam-5043	47	21	]	]	PUNCT
ejpam-5043	47	22	in	in	ADP
ejpam-5043	47	23	both	both	CCONJ
ejpam-5043	47	24	the	the	DET
ejpam-5043	47	25	introduction	introduction	NOUN
ejpam-5043	47	26	and	and	CCONJ
ejpam-5043	47	27	numerical	numerical	ADJ
ejpam-5043	47	28	scheme	scheme	NOUN
ejpam-5043	47	29	sections	section	NOUN
ejpam-5043	47	30	.	.	PUNCT
ejpam-5043	48	1	in	in	ADP
ejpam-5043	48	2	k.	k.	PROPN
ejpam-5043	48	3	boulehmi	boulehmi	PROPN
ejpam-5043	48	4	/	/	SYM
ejpam-5043	48	5	eur	eur	PROPN
ejpam-5043	48	6	.	.	PUNCT
ejpam-5043	49	1	j.	j.	PROPN
ejpam-5043	49	2	pure	pure	PROPN
ejpam-5043	49	3	appl	appl	PROPN
ejpam-5043	49	4	.	.	PROPN
ejpam-5043	49	5	math	math	PROPN
ejpam-5043	49	6	,	,	PUNCT
ejpam-5043	49	7	17	17	NUM
ejpam-5043	49	8	(	(	PUNCT
ejpam-5043	49	9	1	1	NUM
ejpam-5043	49	10	)	)	PUNCT
ejpam-5043	49	11	(	(	PUNCT
ejpam-5043	49	12	2024	2024	NUM
ejpam-5043	49	13	)	)	PUNCT
ejpam-5043	49	14	,	,	PUNCT
ejpam-5043	49	15	445	445	NUM
ejpam-5043	49	16	-	-	SYM
ejpam-5043	49	17	461	461	NUM
ejpam-5043	49	18	447	447	NUM
ejpam-5043	49	19	the	the	DET
ejpam-5043	49	20	introduction	introduction	NOUN
ejpam-5043	49	21	,	,	PUNCT
ejpam-5043	49	22	we	we	PRON
ejpam-5043	49	23	acknowledge	acknowledge	VERB
ejpam-5043	49	24	the	the	DET
ejpam-5043	49	25	contributions	contribution	NOUN
ejpam-5043	49	26	of	of	ADP
ejpam-5043	49	27	atangana	atangana	PROPN
ejpam-5043	49	28	and	and	CCONJ
ejpam-5043	49	29	qureshi	qureshi	PROPN
ejpam-5043	49	30	,	,	PUNCT
ejpam-5043	49	31	particularly	particularly	ADV
ejpam-5043	49	32	in	in	ADP
ejpam-5043	49	33	their	their	PRON
ejpam-5043	49	34	application	application	NOUN
ejpam-5043	49	35	of	of	ADP
ejpam-5043	49	36	fractal	fractal	ADJ
ejpam-5043	49	37	-	-	PUNCT
ejpam-5043	49	38	fractional	fractional	ADJ
ejpam-5043	49	39	operators	operator	NOUN
ejpam-5043	49	40	to	to	ADP
ejpam-5043	49	41	chaotic	chaotic	ADJ
ejpam-5043	49	42	dynamical	dynamical	ADJ
ejpam-5043	49	43	systems	system	NOUN
ejpam-5043	49	44	.	.	PUNCT
ejpam-5043	50	1	our	our	PRON
ejpam-5043	50	2	study	study	NOUN
ejpam-5043	50	3	builds	build	VERB
ejpam-5043	50	4	upon	upon	SCONJ
ejpam-5043	50	5	this	this	DET
ejpam-5043	50	6	foundation	foundation	NOUN
ejpam-5043	50	7	by	by	ADP
ejpam-5043	50	8	introducing	introduce	VERB
ejpam-5043	50	9	a	a	DET
ejpam-5043	50	10	novel	novel	ADJ
ejpam-5043	50	11	numerical	numerical	ADJ
ejpam-5043	50	12	scheme	scheme	NOUN
ejpam-5043	50	13	that	that	PRON
ejpam-5043	50	14	extends	extend	VERB
ejpam-5043	50	15	and	and	CCONJ
ejpam-5043	50	16	refines	refine	VERB
ejpam-5043	50	17	their	their	PRON
ejpam-5043	50	18	approach	approach	NOUN
ejpam-5043	50	19	.	.	PUNCT
ejpam-5043	51	1	specifically	specifically	ADV
ejpam-5043	51	2	,	,	PUNCT
ejpam-5043	51	3	in	in	ADP
ejpam-5043	51	4	the	the	DET
ejpam-5043	51	5	numerical	numerical	ADJ
ejpam-5043	51	6	scheme	scheme	PROPN
ejpam-5043	51	7	section	section	NOUN
ejpam-5043	51	8	,	,	PUNCT
ejpam-5043	51	9	we	we	PRON
ejpam-5043	51	10	detail	detail	VERB
ejpam-5043	51	11	the	the	DET
ejpam-5043	51	12	key	key	ADJ
ejpam-5043	51	13	distinctions	distinction	NOUN
ejpam-5043	51	14	,	,	PUNCT
ejpam-5043	51	15	highlighting	highlight	VERB
ejpam-5043	51	16	modifications	modification	NOUN
ejpam-5043	51	17	in	in	ADP
ejpam-5043	51	18	the	the	DET
ejpam-5043	51	19	application	application	NOUN
ejpam-5043	51	20	of	of	ADP
ejpam-5043	51	21	fractal	fractal	ADJ
ejpam-5043	51	22	-	-	PUNCT
ejpam-5043	51	23	fractional	fractional	ADJ
ejpam-5043	51	24	operators	operator	NOUN
ejpam-5043	51	25	and	and	CCONJ
ejpam-5043	51	26	innovative	innovative	ADJ
ejpam-5043	51	27	techniques	technique	NOUN
ejpam-5043	51	28	that	that	PRON
ejpam-5043	51	29	contribute	contribute	VERB
ejpam-5043	51	30	to	to	ADP
ejpam-5043	51	31	the	the	DET
ejpam-5043	51	32	effectiveness	effectiveness	NOUN
ejpam-5043	51	33	of	of	ADP
ejpam-5043	51	34	our	our	PRON
ejpam-5043	51	35	proposed	propose	VERB
ejpam-5043	51	36	method	method	NOUN
ejpam-5043	51	37	.	.	PUNCT
ejpam-5043	52	1	this	this	DET
ejpam-5043	52	2	comparative	comparative	ADJ
ejpam-5043	52	3	discussion	discussion	NOUN
ejpam-5043	52	4	aims	aim	VERB
ejpam-5043	52	5	to	to	PART
ejpam-5043	52	6	underscore	underscore	VERB
ejpam-5043	52	7	the	the	DET
ejpam-5043	52	8	uniqueness	uniqueness	NOUN
ejpam-5043	52	9	and	and	CCONJ
ejpam-5043	52	10	advancements	advancement	NOUN
ejpam-5043	52	11	of	of	ADP
ejpam-5043	52	12	our	our	PRON
ejpam-5043	52	13	formulation	formulation	NOUN
ejpam-5043	52	14	within	within	ADP
ejpam-5043	52	15	the	the	DET
ejpam-5043	52	16	broader	broad	ADJ
ejpam-5043	52	17	context	context	NOUN
ejpam-5043	52	18	of	of	ADP
ejpam-5043	52	19	fractional	fractional	ADJ
ejpam-5043	52	20	calculus	calculus	NOUN
ejpam-5043	52	21	and	and	CCONJ
ejpam-5043	52	22	chaotic	chaotic	ADJ
ejpam-5043	52	23	dynamical	dynamical	ADJ
ejpam-5043	52	24	systems	system	NOUN
ejpam-5043	52	25	research	research	NOUN
ejpam-5043	52	26	.	.	PUNCT
ejpam-5043	53	1	this	this	DET
ejpam-5043	53	2	study	study	NOUN
ejpam-5043	53	3	presents	present	VERB
ejpam-5043	53	4	a	a	DET
ejpam-5043	53	5	pioneering	pioneer	VERB
ejpam-5043	53	6	advancement	advancement	NOUN
ejpam-5043	53	7	in	in	ADP
ejpam-5043	53	8	the	the	DET
ejpam-5043	53	9	application	application	NOUN
ejpam-5043	53	10	of	of	ADP
ejpam-5043	53	11	fractional	fractional	ADJ
ejpam-5043	53	12	calculus	calculus	NOUN
ejpam-5043	53	13	,	,	PUNCT
ejpam-5043	53	14	specifically	specifically	ADV
ejpam-5043	53	15	focusing	focus	VERB
ejpam-5043	53	16	on	on	ADP
ejpam-5043	53	17	refining	refine	VERB
ejpam-5043	53	18	the	the	DET
ejpam-5043	53	19	atangana	atangana	PROPN
ejpam-5043	53	20	-	-	PUNCT
ejpam-5043	53	21	baleanu	baleanu	PROPN
ejpam-5043	53	22	caputo	caputo	PROPN
ejpam-5043	53	23	fractional	fractional	PROPN
ejpam-5043	53	24	derivative	derivative	PROPN
ejpam-5043	53	25	(	(	PUNCT
ejpam-5043	53	26	abc	abc	PROPN
ejpam-5043	53	27	-	-	PUNCT
ejpam-5043	53	28	fd	fd	ADJ
ejpam-5043	53	29	)	)	PUNCT
ejpam-5043	53	30	approach	approach	NOUN
ejpam-5043	53	31	.	.	PUNCT
ejpam-5043	54	1	the	the	DET
ejpam-5043	54	2	novelty	novelty	NOUN
ejpam-5043	54	3	lies	lie	VERB
ejpam-5043	54	4	in	in	ADP
ejpam-5043	54	5	the	the	DET
ejpam-5043	54	6	fine	fine	NOUN
ejpam-5043	54	7	-	-	PUNCT
ejpam-5043	54	8	tuning	tuning	NOUN
ejpam-5043	54	9	of	of	ADP
ejpam-5043	54	10	abc	abc	PROPN
ejpam-5043	54	11	-	-	PUNCT
ejpam-5043	54	12	fd	fd	PROPN
ejpam-5043	54	13	parameters	parameter	NOUN
ejpam-5043	54	14	,	,	PUNCT
ejpam-5043	54	15	enabling	enable	VERB
ejpam-5043	54	16	enhanced	enhanced	ADJ
ejpam-5043	54	17	accuracy	accuracy	NOUN
ejpam-5043	54	18	in	in	ADP
ejpam-5043	54	19	solving	solve	VERB
ejpam-5043	54	20	the	the	DET
ejpam-5043	54	21	fractional	fractional	ADJ
ejpam-5043	54	22	bernoulli	bernoulli	NOUN
ejpam-5043	54	23	equation	equation	NOUN
ejpam-5043	54	24	and	and	CCONJ
ejpam-5043	54	25	simulating	simulate	VERB
ejpam-5043	54	26	the	the	DET
ejpam-5043	54	27	rössler	rössler	NOUN
ejpam-5043	54	28	model	model	NOUN
ejpam-5043	54	29	.	.	PUNCT
ejpam-5043	55	1	moreover	moreover	ADV
ejpam-5043	55	2	,	,	PUNCT
ejpam-5043	55	3	our	our	PRON
ejpam-5043	55	4	research	research	NOUN
ejpam-5043	55	5	uniquely	uniquely	ADV
ejpam-5043	55	6	integrates	integrate	VERB
ejpam-5043	55	7	multidisciplinary	multidisciplinary	ADJ
ejpam-5043	55	8	concepts	concept	NOUN
ejpam-5043	55	9	,	,	PUNCT
ejpam-5043	55	10	demonstrating	demonstrate	VERB
ejpam-5043	55	11	the	the	DET
ejpam-5043	55	12	applicability	applicability	NOUN
ejpam-5043	55	13	of	of	ADP
ejpam-5043	55	14	fractional	fractional	ADJ
ejpam-5043	55	15	calculus	calculus	NOUN
ejpam-5043	55	16	in	in	ADP
ejpam-5043	55	17	diverse	diverse	ADJ
ejpam-5043	55	18	engineering	engineering	NOUN
ejpam-5043	55	19	domains	domain	NOUN
ejpam-5043	55	20	.	.	PUNCT
ejpam-5043	56	1	validation	validation	NOUN
ejpam-5043	56	2	through	through	ADP
ejpam-5043	56	3	real	real	ADJ
ejpam-5043	56	4	-	-	PUNCT
ejpam-5043	56	5	world	world	NOUN
ejpam-5043	56	6	case	case	NOUN
ejpam-5043	56	7	studies	study	NOUN
ejpam-5043	56	8	showcases	showcase	VERB
ejpam-5043	56	9	the	the	DET
ejpam-5043	56	10	effectiveness	effectiveness	NOUN
ejpam-5043	56	11	of	of	ADP
ejpam-5043	56	12	our	our	PRON
ejpam-5043	56	13	approach	approach	NOUN
ejpam-5043	56	14	in	in	ADP
ejpam-5043	56	15	accurately	accurately	ADV
ejpam-5043	56	16	predicting	predict	VERB
ejpam-5043	56	17	chaotic	chaotic	ADJ
ejpam-5043	56	18	behaviour	behaviour	NOUN
ejpam-5043	56	19	in	in	ADP
ejpam-5043	56	20	complex	complex	ADJ
ejpam-5043	56	21	engineering	engineering	NOUN
ejpam-5043	56	22	systems	system	NOUN
ejpam-5043	56	23	.	.	PUNCT
ejpam-5043	57	1	comparative	comparative	ADJ
ejpam-5043	57	2	analyses	analysis	NOUN
ejpam-5043	57	3	against	against	ADP
ejpam-5043	57	4	existing	exist	VERB
ejpam-5043	57	5	methods	method	NOUN
ejpam-5043	57	6	underscore	underscore	VERB
ejpam-5043	57	7	the	the	DET
ejpam-5043	57	8	superior	superior	ADJ
ejpam-5043	57	9	performance	performance	NOUN
ejpam-5043	57	10	and	and	CCONJ
ejpam-5043	57	11	robustness	robustness	NOUN
ejpam-5043	57	12	of	of	ADP
ejpam-5043	57	13	the	the	DET
ejpam-5043	57	14	proposed	propose	VERB
ejpam-5043	57	15	abc	abc	PROPN
ejpam-5043	57	16	-	-	PUNCT
ejpam-5043	57	17	fd	fd	PROPN
ejpam-5043	57	18	scheme	scheme	NOUN
ejpam-5043	57	19	.	.	PUNCT
ejpam-5043	58	1	this	this	DET
ejpam-5043	58	2	introduction	introduction	NOUN
ejpam-5043	58	3	provides	provide	VERB
ejpam-5043	58	4	a	a	DET
ejpam-5043	58	5	comprehensive	comprehensive	ADJ
ejpam-5043	58	6	overview	overview	NOUN
ejpam-5043	58	7	of	of	ADP
ejpam-5043	58	8	the	the	DET
ejpam-5043	58	9	foundational	foundational	ADJ
ejpam-5043	58	10	works	work	NOUN
ejpam-5043	58	11	in	in	ADP
ejpam-5043	58	12	fractional	fractional	ADJ
ejpam-5043	58	13	calculus	calculus	NOUN
ejpam-5043	58	14	,	,	PUNCT
ejpam-5043	58	15	emphasizing	emphasize	VERB
ejpam-5043	58	16	their	their	PRON
ejpam-5043	58	17	relevance	relevance	NOUN
ejpam-5043	58	18	in	in	ADP
ejpam-5043	58	19	studying	study	VERB
ejpam-5043	58	20	chaotic	chaotic	ADJ
ejpam-5043	58	21	behaviour	behaviour	NOUN
ejpam-5043	58	22	in	in	ADP
ejpam-5043	58	23	engineering	engineering	NOUN
ejpam-5043	58	24	systems	system	NOUN
ejpam-5043	58	25	.	.	PUNCT
ejpam-5043	59	1	it	it	PRON
ejpam-5043	59	2	sets	set	VERB
ejpam-5043	59	3	the	the	DET
ejpam-5043	59	4	stage	stage	NOUN
ejpam-5043	59	5	for	for	ADP
ejpam-5043	59	6	the	the	DET
ejpam-5043	59	7	specific	specific	ADJ
ejpam-5043	59	8	focus	focus	NOUN
ejpam-5043	59	9	on	on	ADP
ejpam-5043	59	10	the	the	DET
ejpam-5043	59	11	abc	abc	PROPN
ejpam-5043	59	12	-	-	PUNCT
ejpam-5043	59	13	fd	fd	PROPN
ejpam-5043	59	14	approach	approach	NOUN
ejpam-5043	59	15	and	and	CCONJ
ejpam-5043	59	16	its	its	PRON
ejpam-5043	59	17	potential	potential	ADJ
ejpam-5043	59	18	applications	application	NOUN
ejpam-5043	59	19	in	in	ADP
ejpam-5043	59	20	engineering	engineering	NOUN
ejpam-5043	59	21	contexts	contexts	NOUN
ejpam-5043	59	22	.	.	PUNCT
ejpam-5043	60	1	this	this	PRON
ejpam-5043	60	2	has	have	AUX
ejpam-5043	60	3	led	lead	VERB
ejpam-5043	60	4	to	to	ADP
ejpam-5043	60	5	the	the	DET
ejpam-5043	60	6	description	description	NOUN
ejpam-5043	60	7	of	of	ADP
ejpam-5043	60	8	many	many	ADJ
ejpam-5043	60	9	chaotic	chaotic	ADJ
ejpam-5043	60	10	systems	system	NOUN
ejpam-5043	60	11	in	in	ADP
ejpam-5043	60	12	published	publish	VERB
ejpam-5043	60	13	literature	literature	NOUN
ejpam-5043	60	14	,	,	PUNCT
ejpam-5043	60	15	all	all	PRON
ejpam-5043	60	16	of	of	ADP
ejpam-5043	60	17	which	which	PRON
ejpam-5043	60	18	use	use	VERB
ejpam-5043	60	19	circuits	circuit	NOUN
ejpam-5043	60	20	as	as	ADP
ejpam-5043	60	21	their	their	PRON
ejpam-5043	60	22	implementation	implementation	NOUN
ejpam-5043	60	23	.	.	PUNCT
ejpam-5043	61	1	one	one	NUM
ejpam-5043	61	2	of	of	ADP
ejpam-5043	61	3	the	the	DET
ejpam-5043	61	4	most	most	ADV
ejpam-5043	61	5	significant	significant	ADJ
ejpam-5043	61	6	areas	area	NOUN
ejpam-5043	61	7	of	of	ADP
ejpam-5043	61	8	research	research	NOUN
ejpam-5043	61	9	is	be	AUX
ejpam-5043	61	10	to	to	PART
ejpam-5043	61	11	construct	construct	VERB
ejpam-5043	61	12	robust	robust	ADJ
ejpam-5043	61	13	chaotic	chaotic	ADJ
ejpam-5043	61	14	oscillators	oscillator	NOUN
ejpam-5043	61	15	with	with	ADP
ejpam-5043	61	16	simple	simple	ADJ
ejpam-5043	61	17	architecture	architecture	NOUN
ejpam-5043	61	18	,	,	PUNCT
ejpam-5043	61	19	either	either	CCONJ
ejpam-5043	61	20	mathematically	mathematically	ADV
ejpam-5043	61	21	or	or	CCONJ
ejpam-5043	61	22	circuit	circuit	NOUN
ejpam-5043	61	23	.	.	PUNCT
ejpam-5043	62	1	this	this	PRON
ejpam-5043	62	2	is	be	AUX
ejpam-5043	62	3	one	one	NUM
ejpam-5043	62	4	of	of	ADP
ejpam-5043	62	5	the	the	DET
ejpam-5043	62	6	most	most	ADV
ejpam-5043	62	7	crucial	crucial	ADJ
ejpam-5043	62	8	areas	area	NOUN
ejpam-5043	62	9	for	for	ADP
ejpam-5043	62	10	research	research	NOUN
ejpam-5043	62	11	.	.	PUNCT
ejpam-5043	63	1	chaotic	chaotic	ADJ
ejpam-5043	63	2	systems	system	NOUN
ejpam-5043	63	3	behave	behave	VERB
ejpam-5043	63	4	in	in	ADP
ejpam-5043	63	5	unpredictable	unpredictable	ADJ
ejpam-5043	63	6	and	and	CCONJ
ejpam-5043	63	7	complex	complex	ADJ
ejpam-5043	63	8	ways	way	NOUN
ejpam-5043	63	9	over	over	ADP
ejpam-5043	63	10	time	time	NOUN
ejpam-5043	63	11	because	because	SCONJ
ejpam-5043	63	12	they	they	PRON
ejpam-5043	63	13	are	be	AUX
ejpam-5043	63	14	sensitive	sensitive	ADJ
ejpam-5043	63	15	to	to	ADP
ejpam-5043	63	16	initial	initial	ADJ
ejpam-5043	63	17	conditions	condition	NOUN
ejpam-5043	63	18	.	.	PUNCT
ejpam-5043	64	1	one	one	NUM
ejpam-5043	64	2	of	of	ADP
ejpam-5043	64	3	the	the	DET
ejpam-5043	64	4	numerous	numerous	ADJ
ejpam-5043	64	5	novel	novel	ADJ
ejpam-5043	64	6	methods	method	NOUN
ejpam-5043	64	7	for	for	ADP
ejpam-5043	64	8	studying	study	VERB
ejpam-5043	64	9	chaotic	chaotic	ADJ
ejpam-5043	64	10	systems	system	NOUN
ejpam-5043	64	11	that	that	PRON
ejpam-5043	64	12	have	have	AUX
ejpam-5043	64	13	emerged	emerge	VERB
ejpam-5043	64	14	in	in	ADP
ejpam-5043	64	15	recent	recent	ADJ
ejpam-5043	64	16	years	year	NOUN
ejpam-5043	64	17	is	be	AUX
ejpam-5043	64	18	asymptotic	asymptotic	ADJ
ejpam-5043	64	19	stability	stability	NOUN
ejpam-5043	64	20	,	,	PUNCT
ejpam-5043	64	21	which	which	PRON
ejpam-5043	64	22	pinpoints	pinpoint	VERB
ejpam-5043	64	23	the	the	DET
ejpam-5043	64	24	precise	precise	ADJ
ejpam-5043	64	25	nature	nature	NOUN
ejpam-5043	64	26	of	of	ADP
ejpam-5043	64	27	chaos	chaos	NOUN
ejpam-5043	64	28	.	.	PUNCT
ejpam-5043	65	1	the	the	DET
ejpam-5043	65	2	areas	area	NOUN
ejpam-5043	65	3	of	of	ADP
ejpam-5043	65	4	mathematics	mathematic	NOUN
ejpam-5043	65	5	and	and	CCONJ
ejpam-5043	65	6	science	science	NOUN
ejpam-5043	65	7	covered	cover	VERB
ejpam-5043	65	8	by	by	ADP
ejpam-5043	65	9	fractional	fractional	ADJ
ejpam-5043	65	10	calculus	calculus	NOUN
ejpam-5043	65	11	[	[	X
ejpam-5043	65	12	30	30	NUM
ejpam-5043	65	13	,	,	PUNCT
ejpam-5043	65	14	47	47	NUM
ejpam-5043	65	15	]	]	PUNCT
ejpam-5043	65	16	are	be	AUX
ejpam-5043	65	17	incredibly	incredibly	ADV
ejpam-5043	65	18	diverse	diverse	ADJ
ejpam-5043	65	19	;	;	PUNCT
ejpam-5043	65	20	cutting	cut	VERB
ejpam-5043	65	21	-	-	PUNCT
ejpam-5043	65	22	edge	edge	NOUN
ejpam-5043	65	23	applications	application	NOUN
ejpam-5043	65	24	are	be	AUX
ejpam-5043	65	25	being	be	AUX
ejpam-5043	65	26	developed	develop	VERB
ejpam-5043	65	27	in	in	ADP
ejpam-5043	65	28	mathematics	mathematic	NOUN
ejpam-5043	65	29	,	,	PUNCT
ejpam-5043	65	30	biology	biology	NOUN
ejpam-5043	65	31	,	,	PUNCT
ejpam-5043	65	32	and	and	CCONJ
ejpam-5043	65	33	other	other	ADJ
ejpam-5043	65	34	subjects	subject	NOUN
ejpam-5043	65	35	[	[	X
ejpam-5043	65	36	16	16	NUM
ejpam-5043	65	37	,	,	PUNCT
ejpam-5043	65	38	17	17	NUM
ejpam-5043	65	39	]	]	PUNCT
ejpam-5043	65	40	.	.	PUNCT
ejpam-5043	66	1	an	an	DET
ejpam-5043	66	2	innovative	innovative	ADJ
ejpam-5043	66	3	technique	technique	NOUN
ejpam-5043	66	4	(	(	PUNCT
ejpam-5043	66	5	abc	abc	PROPN
ejpam-5043	66	6	-	-	PUNCT
ejpam-5043	66	7	fd	fd	PROPN
ejpam-5043	66	8	)	)	PUNCT
ejpam-5043	66	9	was	be	AUX
ejpam-5043	66	10	first	first	ADV
ejpam-5043	66	11	introduced	introduce	VERB
ejpam-5043	66	12	and	and	CCONJ
ejpam-5043	66	13	in	in	ADP
ejpam-5043	66	14	[	[	X
ejpam-5043	66	15	18	18	NUM
ejpam-5043	66	16	]	]	PUNCT
ejpam-5043	66	17	.	.	PUNCT
ejpam-5043	67	1	developing	develop	VERB
ejpam-5043	67	2	a	a	DET
ejpam-5043	67	3	fresh	fresh	ADJ
ejpam-5043	67	4	method	method	NOUN
ejpam-5043	67	5	for	for	ADP
ejpam-5043	67	6	this	this	DET
ejpam-5043	67	7	derivative	derivative	NOUN
ejpam-5043	67	8	can	can	AUX
ejpam-5043	67	9	increase	increase	VERB
ejpam-5043	67	10	its	its	PRON
ejpam-5043	67	11	application	application	NOUN
ejpam-5043	67	12	in	in	ADP
ejpam-5043	67	13	a	a	DET
ejpam-5043	67	14	few	few	ADJ
ejpam-5043	67	15	industries	industry	NOUN
ejpam-5043	67	16	and	and	CCONJ
ejpam-5043	67	17	give	give	VERB
ejpam-5043	67	18	significant	significant	ADJ
ejpam-5043	67	19	advantages	advantage	NOUN
ejpam-5043	67	20	.	.	PUNCT
ejpam-5043	68	1	such	such	DET
ejpam-5043	68	2	an	an	DET
ejpam-5043	68	3	innovative	innovative	ADJ
ejpam-5043	68	4	plan	plan	NOUN
ejpam-5043	68	5	could	could	AUX
ejpam-5043	68	6	have	have	VERB
ejpam-5043	68	7	the	the	DET
ejpam-5043	68	8	following	follow	VERB
ejpam-5043	68	9	possible	possible	ADJ
ejpam-5043	68	10	advantages	advantage	NOUN
ejpam-5043	68	11	:	:	PUNCT
ejpam-5043	68	12	enhanced	enhance	VERB
ejpam-5043	68	13	flexibility	flexibility	NOUN
ejpam-5043	68	14	and	and	CCONJ
ejpam-5043	68	15	precision	precision	NOUN
ejpam-5043	68	16	,	,	PUNCT
ejpam-5043	68	17	enhanced	enhance	VERB
ejpam-5043	68	18	management	management	NOUN
ejpam-5043	68	19	of	of	ADP
ejpam-5043	68	20	intricate	intricate	ADJ
ejpam-5043	68	21	systems	system	NOUN
ejpam-5043	68	22	,	,	PUNCT
ejpam-5043	68	23	and	and	CCONJ
ejpam-5043	68	24	more	more	ADJ
ejpam-5043	68	25	relevance	relevance	NOUN
ejpam-5043	68	26	to	to	ADP
ejpam-5043	68	27	actual	actual	ADJ
ejpam-5043	68	28	occurrences	occurrence	NOUN
ejpam-5043	68	29	.	.	PUNCT
ejpam-5043	69	1	making	make	VERB
ejpam-5043	69	2	use	use	NOUN
ejpam-5043	69	3	of	of	ADP
ejpam-5043	69	4	a	a	DET
ejpam-5043	69	5	new	new	ADJ
ejpam-5043	69	6	method	method	NOUN
ejpam-5043	69	7	(	(	PUNCT
ejpam-5043	69	8	abc	abc	PROPN
ejpam-5043	69	9	-	-	PUNCT
ejpam-5043	69	10	fd	fd	PROPN
ejpam-5043	69	11	)	)	PUNCT
ejpam-5043	69	12	is	be	AUX
ejpam-5043	69	13	also	also	ADV
ejpam-5043	69	14	new	new	ADJ
ejpam-5043	69	15	.	.	PUNCT
ejpam-5043	70	1	choosing	choose	VERB
ejpam-5043	70	2	the	the	DET
ejpam-5043	70	3	right	right	ADJ
ejpam-5043	70	4	number	number	NOUN
ejpam-5043	70	5	method	method	NOUN
ejpam-5043	70	6	for	for	ADP
ejpam-5043	70	7	fractional	fractional	ADJ
ejpam-5043	70	8	derivatives	derivative	NOUN
ejpam-5043	70	9	is	be	AUX
ejpam-5043	70	10	very	very	ADV
ejpam-5043	70	11	important	important	ADJ
ejpam-5043	70	12	for	for	ADP
ejpam-5043	70	13	getting	get	VERB
ejpam-5043	70	14	a	a	DET
ejpam-5043	70	15	good	good	ADJ
ejpam-5043	70	16	picture	picture	NOUN
ejpam-5043	70	17	of	of	ADP
ejpam-5043	70	18	how	how	SCONJ
ejpam-5043	70	19	the	the	DET
ejpam-5043	70	20	system	system	NOUN
ejpam-5043	70	21	works	work	VERB
ejpam-5043	70	22	.	.	PUNCT
ejpam-5043	71	1	when	when	SCONJ
ejpam-5043	71	2	you	you	PRON
ejpam-5043	71	3	use	use	VERB
ejpam-5043	71	4	fractional	fractional	ADJ
ejpam-5043	71	5	derivatives	derivative	NOUN
ejpam-5043	71	6	instead	instead	ADV
ejpam-5043	71	7	of	of	ADP
ejpam-5043	71	8	integer	integer	NOUN
ejpam-5043	71	9	derivatives	derivative	NOUN
ejpam-5043	71	10	,	,	PUNCT
ejpam-5043	71	11	you	you	PRON
ejpam-5043	71	12	can	can	AUX
ejpam-5043	71	13	get	get	VERB
ejpam-5043	71	14	different	different	ADJ
ejpam-5043	71	15	kinds	kind	NOUN
ejpam-5043	71	16	of	of	ADP
ejpam-5043	71	17	attractors	attractor	NOUN
ejpam-5043	71	18	,	,	PUNCT
ejpam-5043	71	19	bifurcation	bifurcation	NOUN
ejpam-5043	71	20	patterns	pattern	NOUN
ejpam-5043	71	21	,	,	PUNCT
ejpam-5043	71	22	and	and	CCONJ
ejpam-5043	71	23	temporary	temporary	ADJ
ejpam-5043	71	24	behaviors	behavior	NOUN
ejpam-5043	71	25	.	.	PUNCT
ejpam-5043	72	1	it	it	PRON
ejpam-5043	72	2	’s	’	VERB
ejpam-5043	72	3	new	new	ADJ
ejpam-5043	72	4	to	to	PART
ejpam-5043	72	5	point	point	VERB
ejpam-5043	72	6	out	out	ADP
ejpam-5043	72	7	and	and	CCONJ
ejpam-5043	72	8	analyze	analyze	VERB
ejpam-5043	72	9	these	these	DET
ejpam-5043	72	10	new	new	ADJ
ejpam-5043	72	11	processes	process	NOUN
ejpam-5043	72	12	.	.	PUNCT
ejpam-5043	73	1	fractional	fractional	ADJ
ejpam-5043	73	2	order	order	NOUN
ejpam-5043	73	3	systems	system	NOUN
ejpam-5043	73	4	have	have	AUX
ejpam-5043	73	5	been	be	AUX
ejpam-5043	73	6	used	use	VERB
ejpam-5043	73	7	in	in	ADP
ejpam-5043	73	8	many	many	ADJ
ejpam-5043	73	9	areas	area	NOUN
ejpam-5043	73	10	,	,	PUNCT
ejpam-5043	73	11	as	as	ADP
ejpam-5043	73	12	example	example	NOUN
ejpam-5043	73	13	cryptography	cryptography	NOUN
ejpam-5043	73	14	,	,	PUNCT
ejpam-5043	73	15	safe	safe	ADJ
ejpam-5043	73	16	communications	communication	NOUN
ejpam-5043	73	17	,	,	PUNCT
ejpam-5043	73	18	and	and	CCONJ
ejpam-5043	73	19	sending	send	VERB
ejpam-5043	73	20	data	datum	NOUN
ejpam-5043	73	21	securely	securely	ADV
ejpam-5043	73	22	.	.	PUNCT
ejpam-5043	74	1	k.	k.	PROPN
ejpam-5043	74	2	boulehmi	boulehmi	PROPN
ejpam-5043	74	3	/	/	SYM
ejpam-5043	74	4	eur	eur	PROPN
ejpam-5043	74	5	.	.	PUNCT
ejpam-5043	75	1	j.	j.	PROPN
ejpam-5043	75	2	pure	pure	PROPN
ejpam-5043	75	3	appl	appl	PROPN
ejpam-5043	75	4	.	.	PROPN
ejpam-5043	75	5	math	math	PROPN
ejpam-5043	75	6	,	,	PUNCT
ejpam-5043	75	7	17	17	NUM
ejpam-5043	75	8	(	(	PUNCT
ejpam-5043	75	9	1	1	NUM
ejpam-5043	75	10	)	)	PUNCT
ejpam-5043	75	11	(	(	PUNCT
ejpam-5043	75	12	2024	2024	NUM
ejpam-5043	75	13	)	)	PUNCT
ejpam-5043	75	14	,	,	PUNCT
ejpam-5043	75	15	445	445	NUM
ejpam-5043	75	16	-	-	SYM
ejpam-5043	75	17	461	461	NUM
ejpam-5043	75	18	448	448	NUM
ejpam-5043	75	19	investigating	investigate	VERB
ejpam-5043	75	20	the	the	DET
ejpam-5043	75	21	rössler	rössler	NOUN
ejpam-5043	75	22	model	model	NOUN
ejpam-5043	75	23	,	,	PUNCT
ejpam-5043	75	24	renowned	renowne	VERB
ejpam-5043	75	25	for	for	ADP
ejpam-5043	75	26	its	its	PRON
ejpam-5043	75	27	ability	ability	NOUN
ejpam-5043	75	28	to	to	PART
ejpam-5043	75	29	depict	depict	VERB
ejpam-5043	75	30	chaotic	chaotic	ADJ
ejpam-5043	75	31	dynamics	dynamic	NOUN
ejpam-5043	75	32	,	,	PUNCT
ejpam-5043	75	33	finds	find	VERB
ejpam-5043	75	34	extensive	extensive	ADJ
ejpam-5043	75	35	application	application	NOUN
ejpam-5043	75	36	across	across	ADP
ejpam-5043	75	37	scientific	scientific	ADJ
ejpam-5043	75	38	,	,	PUNCT
ejpam-5043	75	39	engineering	engineering	NOUN
ejpam-5043	75	40	,	,	PUNCT
ejpam-5043	75	41	and	and	CCONJ
ejpam-5043	75	42	interdisciplinary	interdisciplinary	ADJ
ejpam-5043	75	43	realms	realm	NOUN
ejpam-5043	75	44	.	.	PUNCT
ejpam-5043	76	1	in	in	ADP
ejpam-5043	76	2	scientific	scientific	ADJ
ejpam-5043	76	3	exploration	exploration	NOUN
ejpam-5043	76	4	,	,	PUNCT
ejpam-5043	76	5	it	it	PRON
ejpam-5043	76	6	serves	serve	VERB
ejpam-5043	76	7	as	as	ADP
ejpam-5043	76	8	a	a	DET
ejpam-5043	76	9	foundational	foundational	ADJ
ejpam-5043	76	10	illustration	illustration	NOUN
ejpam-5043	76	11	elucidating	elucidate	VERB
ejpam-5043	76	12	chaos	chaos	NOUN
ejpam-5043	76	13	theory	theory	NOUN
ejpam-5043	76	14	’s	’s	PART
ejpam-5043	76	15	fundamental	fundamental	ADJ
ejpam-5043	76	16	principles	principle	NOUN
ejpam-5043	76	17	,	,	PUNCT
ejpam-5043	76	18	shedding	shed	VERB
ejpam-5043	76	19	light	light	NOUN
ejpam-5043	76	20	on	on	ADP
ejpam-5043	76	21	nonlinear	nonlinear	ADJ
ejpam-5043	76	22	behaviors	behavior	NOUN
ejpam-5043	76	23	,	,	PUNCT
ejpam-5043	76	24	bifurcations	bifurcation	NOUN
ejpam-5043	76	25	,	,	PUNCT
ejpam-5043	76	26	and	and	CCONJ
ejpam-5043	76	27	sensitivity	sensitivity	NOUN
ejpam-5043	76	28	to	to	ADP
ejpam-5043	76	29	initial	initial	ADJ
ejpam-5043	76	30	conditions	condition	NOUN
ejpam-5043	76	31	.	.	PUNCT
ejpam-5043	77	1	engineering	engineering	NOUN
ejpam-5043	77	2	domains	domain	NOUN
ejpam-5043	77	3	leverage	leverage	VERB
ejpam-5043	77	4	its	its	PRON
ejpam-5043	77	5	chaotic	chaotic	ADJ
ejpam-5043	77	6	nature	nature	NOUN
ejpam-5043	77	7	for	for	ADP
ejpam-5043	77	8	testing	test	VERB
ejpam-5043	77	9	control	control	NOUN
ejpam-5043	77	10	algorithms	algorithm	NOUN
ejpam-5043	77	11	in	in	ADP
ejpam-5043	77	12	systems	system	NOUN
ejpam-5043	77	13	susceptible	susceptible	ADJ
ejpam-5043	77	14	to	to	ADP
ejpam-5043	77	15	erratic	erratic	ADJ
ejpam-5043	77	16	oscillations	oscillation	NOUN
ejpam-5043	77	17	,	,	PUNCT
ejpam-5043	77	18	such	such	ADJ
ejpam-5043	77	19	as	as	ADP
ejpam-5043	77	20	electronic	electronic	ADJ
ejpam-5043	77	21	circuits	circuit	NOUN
ejpam-5043	77	22	or	or	CCONJ
ejpam-5043	77	23	chemical	chemical	NOUN
ejpam-5043	77	24	reactors	reactor	NOUN
ejpam-5043	77	25	.	.	PUNCT
ejpam-5043	78	1	additionally	additionally	ADV
ejpam-5043	78	2	,	,	PUNCT
ejpam-5043	78	3	the	the	DET
ejpam-5043	78	4	model	model	NOUN
ejpam-5043	78	5	’s	’s	PART
ejpam-5043	78	6	chaotic	chaotic	ADJ
ejpam-5043	78	7	signals	signal	NOUN
ejpam-5043	78	8	contribute	contribute	VERB
ejpam-5043	78	9	to	to	ADP
ejpam-5043	78	10	encryption	encryption	NOUN
ejpam-5043	78	11	methods	method	NOUN
ejpam-5043	78	12	and	and	CCONJ
ejpam-5043	78	13	signal	signal	VERB
ejpam-5043	78	14	processing	processing	NOUN
ejpam-5043	78	15	techniques	technique	NOUN
ejpam-5043	78	16	,	,	PUNCT
ejpam-5043	78	17	ensuring	ensure	VERB
ejpam-5043	78	18	secure	secure	ADJ
ejpam-5043	78	19	communication	communication	NOUN
ejpam-5043	78	20	.	.	PUNCT
ejpam-5043	79	1	its	its	PRON
ejpam-5043	79	2	utility	utility	NOUN
ejpam-5043	79	3	extends	extend	VERB
ejpam-5043	79	4	to	to	ADP
ejpam-5043	79	5	simulating	simulate	VERB
ejpam-5043	79	6	complex	complex	ADJ
ejpam-5043	79	7	natural	natural	ADJ
ejpam-5043	79	8	phenomena	phenomenon	NOUN
ejpam-5043	79	9	like	like	ADP
ejpam-5043	79	10	fluid	fluid	NOUN
ejpam-5043	79	11	dynamics	dynamic	NOUN
ejpam-5043	79	12	or	or	CCONJ
ejpam-5043	79	13	biological	biological	ADJ
ejpam-5043	79	14	rhythms	rhythm	NOUN
ejpam-5043	79	15	while	while	SCONJ
ejpam-5043	79	16	also	also	ADV
ejpam-5043	79	17	offering	offer	VERB
ejpam-5043	79	18	insights	insight	NOUN
ejpam-5043	79	19	into	into	ADP
ejpam-5043	79	20	economic	economic	ADJ
ejpam-5043	79	21	and	and	CCONJ
ejpam-5043	79	22	social	social	ADJ
ejpam-5043	79	23	systems	system	NOUN
ejpam-5043	79	24	’	'	PUNCT
ejpam-5043	79	25	nonlinear	nonlinear	ADJ
ejpam-5043	79	26	behaviors	behavior	NOUN
ejpam-5043	79	27	.	.	PUNCT
ejpam-5043	80	1	this	this	DET
ejpam-5043	80	2	versatility	versatility	NOUN
ejpam-5043	80	3	positions	position	VERB
ejpam-5043	80	4	the	the	DET
ejpam-5043	80	5	rössler	rössler	NOUN
ejpam-5043	80	6	model	model	NOUN
ejpam-5043	80	7	as	as	ADP
ejpam-5043	80	8	an	an	DET
ejpam-5043	80	9	invaluable	invaluable	ADJ
ejpam-5043	80	10	tool	tool	NOUN
ejpam-5043	80	11	for	for	ADP
ejpam-5043	80	12	educational	educational	ADJ
ejpam-5043	80	13	purposes	purpose	NOUN
ejpam-5043	80	14	and	and	CCONJ
ejpam-5043	80	15	as	as	ADP
ejpam-5043	80	16	a	a	DET
ejpam-5043	80	17	framework	framework	NOUN
ejpam-5043	80	18	for	for	ADP
ejpam-5043	80	19	understanding	understand	VERB
ejpam-5043	80	20	chaotic	chaotic	ADJ
ejpam-5043	80	21	dynamics	dynamic	NOUN
ejpam-5043	80	22	in	in	ADP
ejpam-5043	80	23	diverse	diverse	ADJ
ejpam-5043	80	24	real	real	ADJ
ejpam-5043	80	25	-	-	PUNCT
ejpam-5043	80	26	world	world	NOUN
ejpam-5043	80	27	scenarios	scenario	NOUN
ejpam-5043	80	28	.	.	PUNCT
ejpam-5043	81	1	the	the	DET
ejpam-5043	81	2	implications	implication	NOUN
ejpam-5043	81	3	of	of	ADP
ejpam-5043	81	4	the	the	DET
ejpam-5043	81	5	atangana	atangana	PROPN
ejpam-5043	81	6	-	-	PUNCT
ejpam-5043	81	7	baleanu	baleanu	PROPN
ejpam-5043	81	8	caputo	caputo	PROPN
ejpam-5043	81	9	fractional	fractional	PROPN
ejpam-5043	81	10	derivative	derivative	ADJ
ejpam-5043	81	11	approach	approach	NOUN
ejpam-5043	81	12	extend	extend	VERB
ejpam-5043	81	13	to	to	ADP
ejpam-5043	81	14	various	various	ADJ
ejpam-5043	81	15	engineering	engineering	NOUN
ejpam-5043	81	16	domains	domain	NOUN
ejpam-5043	81	17	.	.	PUNCT
ejpam-5043	82	1	the	the	DET
ejpam-5043	82	2	capacity	capacity	NOUN
ejpam-5043	82	3	to	to	PART
ejpam-5043	82	4	solve	solve	VERB
ejpam-5043	82	5	fractional	fractional	ADJ
ejpam-5043	82	6	differential	differential	ADJ
ejpam-5043	82	7	equations	equation	NOUN
ejpam-5043	82	8	and	and	CCONJ
ejpam-5043	82	9	represent	represent	VERB
ejpam-5043	82	10	chaotic	chaotic	ADJ
ejpam-5043	82	11	systems	system	NOUN
ejpam-5043	82	12	with	with	ADP
ejpam-5043	82	13	high	high	ADJ
ejpam-5043	82	14	accuracy	accuracy	NOUN
ejpam-5043	82	15	could	could	AUX
ejpam-5043	82	16	have	have	VERB
ejpam-5043	82	17	applications	application	NOUN
ejpam-5043	82	18	in	in	ADP
ejpam-5043	82	19	many	many	ADJ
ejpam-5043	82	20	fields	field	NOUN
ejpam-5043	82	21	,	,	PUNCT
ejpam-5043	82	22	including	include	VERB
ejpam-5043	82	23	control	control	NOUN
ejpam-5043	82	24	theory	theory	NOUN
ejpam-5043	82	25	,	,	PUNCT
ejpam-5043	82	26	signal	signal	ADJ
ejpam-5043	82	27	processing	processing	NOUN
ejpam-5043	82	28	,	,	PUNCT
ejpam-5043	82	29	and	and	CCONJ
ejpam-5043	82	30	communication	communication	NOUN
ejpam-5043	82	31	networks	network	NOUN
ejpam-5043	82	32	.	.	PUNCT
ejpam-5043	83	1	engineers	engineer	NOUN
ejpam-5043	83	2	may	may	AUX
ejpam-5043	83	3	be	be	AUX
ejpam-5043	83	4	able	able	ADJ
ejpam-5043	83	5	to	to	PART
ejpam-5043	83	6	construct	construct	VERB
ejpam-5043	83	7	more	more	ADV
ejpam-5043	83	8	resilient	resilient	ADJ
ejpam-5043	83	9	systems	system	NOUN
ejpam-5043	83	10	that	that	PRON
ejpam-5043	83	11	can	can	AUX
ejpam-5043	83	12	deal	deal	VERB
ejpam-5043	83	13	with	with	ADP
ejpam-5043	83	14	nonlinear	nonlinear	ADJ
ejpam-5043	83	15	dynamics	dynamic	NOUN
ejpam-5043	83	16	and	and	CCONJ
ejpam-5043	83	17	improve	improve	VERB
ejpam-5043	83	18	the	the	DET
ejpam-5043	83	19	performance	performance	NOUN
ejpam-5043	83	20	of	of	ADP
ejpam-5043	83	21	current	current	ADJ
ejpam-5043	83	22	systems	system	NOUN
ejpam-5043	83	23	by	by	ADP
ejpam-5043	83	24	using	use	VERB
ejpam-5043	83	25	the	the	DET
ejpam-5043	83	26	abc	abc	PROPN
ejpam-5043	83	27	-	-	PUNCT
ejpam-5043	83	28	fd	fd	PROPN
ejpam-5043	83	29	technique	technique	NOUN
ejpam-5043	83	30	.	.	PUNCT
ejpam-5043	84	1	the	the	DET
ejpam-5043	84	2	application	application	NOUN
ejpam-5043	84	3	of	of	ADP
ejpam-5043	84	4	the	the	DET
ejpam-5043	84	5	atangana	atangana	PROPN
ejpam-5043	84	6	-	-	PUNCT
ejpam-5043	84	7	baleanu	baleanu	PROPN
ejpam-5043	84	8	caputo	caputo	PROPN
ejpam-5043	84	9	fractional	fractional	PROPN
ejpam-5043	84	10	derivative	derivative	PROPN
ejpam-5043	84	11	(	(	PUNCT
ejpam-5043	84	12	abc	abc	PROPN
ejpam-5043	84	13	-	-	PUNCT
ejpam-5043	84	14	fd	fd	PROPN
ejpam-5043	84	15	)	)	PUNCT
ejpam-5043	84	16	method	method	NOUN
ejpam-5043	84	17	in	in	ADP
ejpam-5043	84	18	engineering	engineering	NOUN
ejpam-5043	84	19	presents	present	NOUN
ejpam-5043	84	20	a	a	DET
ejpam-5043	84	21	promising	promising	ADJ
ejpam-5043	84	22	avenue	avenue	NOUN
ejpam-5043	84	23	for	for	ADP
ejpam-5043	84	24	accurately	accurately	ADV
ejpam-5043	84	25	modeling	model	VERB
ejpam-5043	84	26	intricate	intricate	ADJ
ejpam-5043	84	27	systems	system	NOUN
ejpam-5043	84	28	and	and	CCONJ
ejpam-5043	84	29	identifying	identify	VERB
ejpam-5043	84	30	chaotic	chaotic	ADJ
ejpam-5043	84	31	tendencies	tendency	NOUN
ejpam-5043	84	32	.	.	PUNCT
ejpam-5043	85	1	its	its	PRON
ejpam-5043	85	2	engineering	engineering	NOUN
ejpam-5043	85	3	applications	application	NOUN
ejpam-5043	85	4	are	be	AUX
ejpam-5043	85	5	manifold	manifold	ADJ
ejpam-5043	85	6	:	:	PUNCT
ejpam-5043	85	7	in	in	ADP
ejpam-5043	85	8	communication	communication	NOUN
ejpam-5043	85	9	systems	system	NOUN
ejpam-5043	85	10	,	,	PUNCT
ejpam-5043	85	11	it	it	PRON
ejpam-5043	85	12	could	could	AUX
ejpam-5043	85	13	refine	refine	VERB
ejpam-5043	85	14	protocols	protocol	NOUN
ejpam-5043	85	15	for	for	ADP
ejpam-5043	85	16	better	well	ADJ
ejpam-5043	85	17	data	datum	NOUN
ejpam-5043	85	18	transmission	transmission	NOUN
ejpam-5043	85	19	in	in	ADP
ejpam-5043	85	20	unpredictable	unpredictable	ADJ
ejpam-5043	85	21	settings	setting	NOUN
ejpam-5043	85	22	;	;	PUNCT
ejpam-5043	85	23	in	in	ADP
ejpam-5043	85	24	control	control	NOUN
ejpam-5043	85	25	systems	system	NOUN
ejpam-5043	85	26	,	,	PUNCT
ejpam-5043	85	27	it	it	PRON
ejpam-5043	85	28	might	might	AUX
ejpam-5043	85	29	aid	aid	VERB
ejpam-5043	85	30	in	in	ADP
ejpam-5043	85	31	devising	devise	VERB
ejpam-5043	85	32	strategies	strategy	NOUN
ejpam-5043	85	33	to	to	PART
ejpam-5043	85	34	manage	manage	VERB
ejpam-5043	85	35	nonlinear	nonlinear	ADJ
ejpam-5043	85	36	dynamics	dynamic	NOUN
ejpam-5043	85	37	,	,	PUNCT
ejpam-5043	85	38	crucial	crucial	ADJ
ejpam-5043	85	39	in	in	ADP
ejpam-5043	85	40	robotics	robotic	NOUN
ejpam-5043	85	41	and	and	CCONJ
ejpam-5043	85	42	industrial	industrial	ADJ
ejpam-5043	85	43	automation	automation	NOUN
ejpam-5043	85	44	.	.	PUNCT
ejpam-5043	86	1	moreover	moreover	ADV
ejpam-5043	86	2	,	,	PUNCT
ejpam-5043	86	3	its	its	PRON
ejpam-5043	86	4	potential	potential	NOUN
ejpam-5043	86	5	in	in	ADP
ejpam-5043	86	6	signal	signal	ADJ
ejpam-5043	86	7	processing	processing	NOUN
ejpam-5043	86	8	could	could	AUX
ejpam-5043	86	9	revolutionize	revolutionize	VERB
ejpam-5043	86	10	data	data	NOUN
ejpam-5043	86	11	extraction	extraction	NOUN
ejpam-5043	86	12	and	and	CCONJ
ejpam-5043	86	13	analysis	analysis	NOUN
ejpam-5043	86	14	in	in	ADP
ejpam-5043	86	15	diverse	diverse	ADJ
ejpam-5043	86	16	fields	field	NOUN
ejpam-5043	86	17	,	,	PUNCT
ejpam-5043	86	18	while	while	SCONJ
ejpam-5043	86	19	optimizing	optimize	VERB
ejpam-5043	86	20	system	system	NOUN
ejpam-5043	86	21	design	design	NOUN
ejpam-5043	86	22	and	and	CCONJ
ejpam-5043	86	23	enabling	enable	VERB
ejpam-5043	86	24	predictive	predictive	ADJ
ejpam-5043	86	25	maintenance	maintenance	NOUN
ejpam-5043	86	26	across	across	ADP
ejpam-5043	86	27	industries	industry	NOUN
ejpam-5043	86	28	.	.	PUNCT
ejpam-5043	87	1	biomedical	biomedical	ADJ
ejpam-5043	87	2	engineering	engineering	NOUN
ejpam-5043	87	3	stands	stand	VERB
ejpam-5043	87	4	to	to	PART
ejpam-5043	87	5	benefit	benefit	VERB
ejpam-5043	87	6	from	from	ADP
ejpam-5043	87	7	its	its	PRON
ejpam-5043	87	8	insights	insight	NOUN
ejpam-5043	87	9	into	into	ADP
ejpam-5043	87	10	biological	biological	ADJ
ejpam-5043	87	11	systems	system	NOUN
ejpam-5043	87	12	,	,	PUNCT
ejpam-5043	87	13	potentially	potentially	ADV
ejpam-5043	87	14	advancing	advance	VERB
ejpam-5043	87	15	medical	medical	ADJ
ejpam-5043	87	16	diagnostics	diagnostic	NOUN
ejpam-5043	87	17	and	and	CCONJ
ejpam-5043	87	18	treatment	treatment	NOUN
ejpam-5043	87	19	planning	planning	NOUN
ejpam-5043	87	20	.	.	PUNCT
ejpam-5043	88	1	similarly	similarly	ADV
ejpam-5043	88	2	,	,	PUNCT
ejpam-5043	88	3	in	in	ADP
ejpam-5043	88	4	renewable	renewable	ADJ
ejpam-5043	88	5	energy	energy	NOUN
ejpam-5043	88	6	,	,	PUNCT
ejpam-5043	88	7	its	its	PRON
ejpam-5043	88	8	predictive	predictive	ADJ
ejpam-5043	88	9	capabilities	capability	NOUN
ejpam-5043	88	10	could	could	AUX
ejpam-5043	88	11	optimize	optimize	VERB
ejpam-5043	88	12	the	the	DET
ejpam-5043	88	13	integration	integration	NOUN
ejpam-5043	88	14	of	of	ADP
ejpam-5043	88	15	intermittent	intermittent	ADJ
ejpam-5043	88	16	sources	source	NOUN
ejpam-5043	88	17	,	,	PUNCT
ejpam-5043	88	18	contributing	contribute	VERB
ejpam-5043	88	19	to	to	ADP
ejpam-5043	88	20	the	the	DET
ejpam-5043	88	21	efficiency	efficiency	NOUN
ejpam-5043	88	22	of	of	ADP
ejpam-5043	88	23	power	power	NOUN
ejpam-5043	88	24	grids	grid	NOUN
ejpam-5043	88	25	.	.	PUNCT
ejpam-5043	89	1	overall	overall	ADV
ejpam-5043	89	2	,	,	PUNCT
ejpam-5043	89	3	the	the	DET
ejpam-5043	89	4	abc	abc	PROPN
ejpam-5043	89	5	-	-	PUNCT
ejpam-5043	89	6	fd	fd	PROPN
ejpam-5043	89	7	method	method	NOUN
ejpam-5043	89	8	’s	’s	PART
ejpam-5043	89	9	ability	ability	NOUN
ejpam-5043	89	10	to	to	PART
ejpam-5043	89	11	model	model	VERB
ejpam-5043	89	12	complex	complex	ADJ
ejpam-5043	89	13	systems	system	NOUN
ejpam-5043	89	14	and	and	CCONJ
ejpam-5043	89	15	discern	discern	ADJ
ejpam-5043	89	16	chaotic	chaotic	ADJ
ejpam-5043	89	17	behavior	behavior	NOUN
ejpam-5043	89	18	heralds	herald	NOUN
ejpam-5043	89	19	’	'	PUNCT
ejpam-5043	89	20	innovation	innovation	NOUN
ejpam-5043	89	21	across	across	ADP
ejpam-5043	89	22	varied	varied	ADJ
ejpam-5043	89	23	engineering	engineering	NOUN
ejpam-5043	89	24	domains	domain	NOUN
ejpam-5043	89	25	,	,	PUNCT
ejpam-5043	89	26	offering	offer	VERB
ejpam-5043	89	27	solutions	solution	NOUN
ejpam-5043	89	28	to	to	ADP
ejpam-5043	89	29	multifaceted	multifaceted	ADJ
ejpam-5043	89	30	challenges	challenge	NOUN
ejpam-5043	89	31	.	.	PUNCT
ejpam-5043	90	1	a	a	DET
ejpam-5043	90	2	modified	modify	VERB
ejpam-5043	90	3	version	version	NOUN
ejpam-5043	90	4	of	of	ADP
ejpam-5043	90	5	the	the	DET
ejpam-5043	90	6	classical	classical	ADJ
ejpam-5043	90	7	bernoulli	bernoulli	NOUN
ejpam-5043	90	8	equation	equation	NOUN
ejpam-5043	90	9	namely	namely	ADV
ejpam-5043	90	10	the	the	DET
ejpam-5043	90	11	fractional	fractional	ADJ
ejpam-5043	90	12	bernoulli	bernoulli	NOUN
ejpam-5043	90	13	equation	equation	NOUN
ejpam-5043	90	14	is	be	AUX
ejpam-5043	90	15	a	a	DET
ejpam-5043	90	16	modification	modification	NOUN
ejpam-5043	90	17	that	that	PRON
ejpam-5043	90	18	applies	apply	VERB
ejpam-5043	90	19	notions	notion	NOUN
ejpam-5043	90	20	from	from	ADP
ejpam-5043	90	21	fractional	fractional	ADJ
ejpam-5043	90	22	calculus	calculus	NOUN
ejpam-5043	90	23	to	to	ADP
ejpam-5043	90	24	the	the	DET
ejpam-5043	90	25	original	original	ADJ
ejpam-5043	90	26	bernoulli	bernoulli	NOUN
ejpam-5043	90	27	equation	equation	NOUN
ejpam-5043	90	28	.	.	PUNCT
ejpam-5043	91	1	in	in	ADP
ejpam-5043	91	2	the	the	DET
ejpam-5043	91	3	discipline	discipline	NOUN
ejpam-5043	91	4	of	of	ADP
ejpam-5043	91	5	fluid	fluid	ADJ
ejpam-5043	91	6	mechanics	mechanic	NOUN
ejpam-5043	91	7	and	and	CCONJ
ejpam-5043	91	8	other	other	ADJ
ejpam-5043	91	9	related	related	ADJ
ejpam-5043	91	10	fields	field	NOUN
ejpam-5043	91	11	,	,	PUNCT
ejpam-5043	91	12	it	it	PRON
ejpam-5043	91	13	is	be	AUX
ejpam-5043	91	14	utilized	utilize	VERB
ejpam-5043	91	15	to	to	PART
ejpam-5043	91	16	describe	describe	VERB
ejpam-5043	91	17	the	the	DET
ejpam-5043	91	18	behavior	behavior	NOUN
ejpam-5043	91	19	of	of	ADP
ejpam-5043	91	20	fluids	fluid	NOUN
ejpam-5043	91	21	in	in	ADP
ejpam-5043	91	22	non	non	ADJ
ejpam-5043	91	23	-	-	ADJ
ejpam-5043	91	24	newtonian	newtonian	ADJ
ejpam-5043	91	25	and	and	CCONJ
ejpam-5043	91	26	complicated	complicated	ADJ
ejpam-5043	91	27	systems	system	NOUN
ejpam-5043	91	28	where	where	SCONJ
ejpam-5043	91	29	fractional	fractional	ADJ
ejpam-5043	91	30	derivatives	derivative	NOUN
ejpam-5043	91	31	play	play	VERB
ejpam-5043	91	32	an	an	DET
ejpam-5043	91	33	important	important	ADJ
ejpam-5043	91	34	role	role	NOUN
ejpam-5043	91	35	.	.	PUNCT
ejpam-5043	92	1	there	there	PRON
ejpam-5043	92	2	are	be	VERB
ejpam-5043	92	3	many	many	ADJ
ejpam-5043	92	4	different	different	ADJ
ejpam-5043	92	5	situations	situation	NOUN
ejpam-5043	92	6	in	in	ADP
ejpam-5043	92	7	which	which	PRON
ejpam-5043	92	8	the	the	DET
ejpam-5043	92	9	fractional	fractional	ADJ
ejpam-5043	92	10	bernoulli	bernoulli	NOUN
ejpam-5043	92	11	equation	equation	NOUN
ejpam-5043	92	12	can	can	AUX
ejpam-5043	92	13	be	be	AUX
ejpam-5043	92	14	applied	apply	VERB
ejpam-5043	92	15	,	,	PUNCT
ejpam-5043	92	16	including	include	VERB
ejpam-5043	92	17	the	the	DET
ejpam-5043	92	18	following	following	NOUN
ejpam-5043	92	19	:	:	PUNCT
ejpam-5043	92	20	bernoulli	bernoulli	PROPN
ejpam-5043	92	21	’s	’s	PART
ejpam-5043	92	22	equation	equation	NOUN
ejpam-5043	92	23	,	,	PUNCT
ejpam-5043	92	24	in	in	ADP
ejpam-5043	92	25	its	its	PRON
ejpam-5043	92	26	traditional	traditional	ADJ
ejpam-5043	92	27	form	form	NOUN
ejpam-5043	92	28	,	,	PUNCT
ejpam-5043	92	29	assumes	assume	VERB
ejpam-5043	92	30	that	that	SCONJ
ejpam-5043	92	31	fluids	fluid	NOUN
ejpam-5043	92	32	behave	behave	VERB
ejpam-5043	92	33	in	in	ADP
ejpam-5043	92	34	a	a	DET
ejpam-5043	92	35	newtonian	newtonian	ADJ
ejpam-5043	92	36	manner	manner	NOUN
ejpam-5043	92	37	.	.	PUNCT
ejpam-5043	93	1	however	however	ADV
ejpam-5043	93	2	,	,	PUNCT
ejpam-5043	93	3	many	many	ADJ
ejpam-5043	93	4	fluids	fluid	NOUN
ejpam-5043	93	5	,	,	PUNCT
ejpam-5043	93	6	such	such	ADJ
ejpam-5043	93	7	as	as	ADP
ejpam-5043	93	8	viscoelastic	viscoelastic	NOUN
ejpam-5043	93	9	or	or	CCONJ
ejpam-5043	93	10	power	power	NOUN
ejpam-5043	93	11	-	-	PUNCT
ejpam-5043	93	12	law	law	NOUN
ejpam-5043	93	13	fluids	fluid	NOUN
ejpam-5043	93	14	,	,	PUNCT
ejpam-5043	93	15	behave	behave	VERB
ejpam-5043	93	16	in	in	ADP
ejpam-5043	93	17	a	a	DET
ejpam-5043	93	18	manner	manner	NOUN
ejpam-5043	93	19	that	that	PRON
ejpam-5043	93	20	is	be	AUX
ejpam-5043	93	21	not	not	PART
ejpam-5043	93	22	newtonian	newtonian	ADJ
ejpam-5043	93	23	.	.	PUNCT
ejpam-5043	94	1	in	in	ADP
ejpam-5043	94	2	order	order	NOUN
ejpam-5043	94	3	to	to	PART
ejpam-5043	94	4	account	account	VERB
ejpam-5043	94	5	for	for	ADP
ejpam-5043	94	6	these	these	DET
ejpam-5043	94	7	difficulties	difficulty	NOUN
ejpam-5043	94	8	,	,	PUNCT
ejpam-5043	94	9	the	the	DET
ejpam-5043	94	10	fractional	fractional	ADJ
ejpam-5043	94	11	bernoulli	bernoulli	NOUN
ejpam-5043	94	12	equation	equation	NOUN
ejpam-5043	94	13	was	be	AUX
ejpam-5043	94	14	developed	develop	VERB
ejpam-5043	94	15	.	.	PUNCT
ejpam-5043	95	1	when	when	SCONJ
ejpam-5043	95	2	you	you	PRON
ejpam-5043	95	3	use	use	VERB
ejpam-5043	95	4	fractional	fractional	ADJ
ejpam-5043	95	5	calculus	calculus	NOUN
ejpam-5043	95	6	,	,	PUNCT
ejpam-5043	95	7	you	you	PRON
ejpam-5043	95	8	can	can	AUX
ejpam-5043	95	9	describe	describe	VERB
ejpam-5043	95	10	how	how	SCONJ
ejpam-5043	95	11	fluid	fluid	ADJ
ejpam-5043	95	12	flows	flow	NOUN
ejpam-5043	95	13	through	through	ADP
ejpam-5043	95	14	porous	porous	ADJ
ejpam-5043	95	15	k.	k.	PROPN
ejpam-5043	95	16	boulehmi	boulehmi	PROPN
ejpam-5043	95	17	/	/	SYM
ejpam-5043	95	18	eur	eur	PROPN
ejpam-5043	95	19	.	.	PUNCT
ejpam-5043	96	1	j.	j.	PROPN
ejpam-5043	96	2	pure	pure	PROPN
ejpam-5043	96	3	appl	appl	PROPN
ejpam-5043	96	4	.	.	PROPN
ejpam-5043	96	5	math	math	PROPN
ejpam-5043	96	6	,	,	PUNCT
ejpam-5043	96	7	17	17	NUM
ejpam-5043	96	8	(	(	PUNCT
ejpam-5043	96	9	1	1	NUM
ejpam-5043	96	10	)	)	PUNCT
ejpam-5043	96	11	(	(	PUNCT
ejpam-5043	96	12	2024	2024	NUM
ejpam-5043	96	13	)	)	PUNCT
ejpam-5043	96	14	,	,	PUNCT
ejpam-5043	96	15	445	445	NUM
ejpam-5043	96	16	-	-	SYM
ejpam-5043	96	17	461	461	NUM
ejpam-5043	96	18	449	449	NUM
ejpam-5043	96	19	media	medium	NOUN
ejpam-5043	96	20	that	that	PRON
ejpam-5043	96	21	have	have	VERB
ejpam-5043	96	22	fractal	fractal	ADJ
ejpam-5043	96	23	properties	property	NOUN
ejpam-5043	96	24	.	.	PUNCT
ejpam-5043	97	1	this	this	PRON
ejpam-5043	97	2	is	be	AUX
ejpam-5043	97	3	called	call	VERB
ejpam-5043	97	4	fractal	fractal	ADJ
ejpam-5043	97	5	flow	flow	NOUN
ejpam-5043	97	6	media	medium	NOUN
ejpam-5043	97	7	.	.	PUNCT
ejpam-5043	98	1	the	the	DET
ejpam-5043	98	2	use	use	NOUN
ejpam-5043	98	3	of	of	ADP
ejpam-5043	98	4	this	this	DET
ejpam-5043	98	5	equation	equation	NOUN
ejpam-5043	98	6	allows	allow	VERB
ejpam-5043	98	7	for	for	ADP
ejpam-5043	98	8	a	a	DET
ejpam-5043	98	9	more	more	ADV
ejpam-5043	98	10	realistic	realistic	ADJ
ejpam-5043	98	11	modeling	modeling	NOUN
ejpam-5043	98	12	of	of	ADP
ejpam-5043	98	13	flow	flow	NOUN
ejpam-5043	98	14	dynamics	dynamic	NOUN
ejpam-5043	98	15	in	in	ADP
ejpam-5043	98	16	materials	material	NOUN
ejpam-5043	98	17	of	of	ADP
ejpam-5043	98	18	this	this	DET
ejpam-5043	98	19	kind	kind	NOUN
ejpam-5043	98	20	.	.	PUNCT
ejpam-5043	99	1	the	the	DET
ejpam-5043	99	2	study	study	NOUN
ejpam-5043	99	3	of	of	ADP
ejpam-5043	99	4	biofluid	biofluid	ADJ
ejpam-5043	99	5	dynamics	dynamic	NOUN
ejpam-5043	99	6	is	be	AUX
ejpam-5043	99	7	important	important	ADJ
ejpam-5043	99	8	because	because	SCONJ
ejpam-5043	99	9	biological	biological	ADJ
ejpam-5043	99	10	systems	system	NOUN
ejpam-5043	99	11	frequently	frequently	ADV
ejpam-5043	99	12	incorporate	incorporate	VERB
ejpam-5043	99	13	fluids	fluid	NOUN
ejpam-5043	99	14	that	that	PRON
ejpam-5043	99	15	behave	behave	VERB
ejpam-5043	99	16	in	in	ADP
ejpam-5043	99	17	a	a	DET
ejpam-5043	99	18	non	non	ADJ
ejpam-5043	99	19	-	-	ADJ
ejpam-5043	99	20	newtonian	newtonian	ADJ
ejpam-5043	99	21	manner	manner	NOUN
ejpam-5043	99	22	.	.	PUNCT
ejpam-5043	100	1	taking	take	VERB
ejpam-5043	100	2	into	into	ADP
ejpam-5043	100	3	consideration	consideration	NOUN
ejpam-5043	100	4	the	the	DET
ejpam-5043	100	5	non	non	ADJ
ejpam-5043	100	6	-	-	ADJ
ejpam-5043	100	7	newtonian	newtonian	ADJ
ejpam-5043	100	8	properties	property	NOUN
ejpam-5043	100	9	of	of	ADP
ejpam-5043	100	10	blood	blood	NOUN
ejpam-5043	100	11	,	,	PUNCT
ejpam-5043	100	12	fractional	fractional	ADJ
ejpam-5043	100	13	calculus	calculus	NOUN
ejpam-5043	100	14	can	can	AUX
ejpam-5043	100	15	be	be	AUX
ejpam-5043	100	16	used	use	VERB
ejpam-5043	100	17	to	to	PART
ejpam-5043	100	18	provide	provide	VERB
ejpam-5043	100	19	a	a	DET
ejpam-5043	100	20	more	more	ADV
ejpam-5043	100	21	precise	precise	ADJ
ejpam-5043	100	22	description	description	NOUN
ejpam-5043	100	23	of	of	ADP
ejpam-5043	100	24	blood	blood	NOUN
ejpam-5043	100	25	flow	flow	NOUN
ejpam-5043	100	26	in	in	ADP
ejpam-5043	100	27	vessels	vessel	NOUN
ejpam-5043	100	28	,	,	PUNCT
ejpam-5043	100	29	for	for	ADP
ejpam-5043	100	30	example	example	NOUN
ejpam-5043	100	31	.	.	PUNCT
ejpam-5043	101	1	anomalous	anomalous	ADJ
ejpam-5043	101	2	transport	transport	NOUN
ejpam-5043	101	3	phenomena	phenomenon	NOUN
ejpam-5043	101	4	:	:	PUNCT
ejpam-5043	101	5	fractional	fractional	ADJ
ejpam-5043	101	6	calculus	calculus	NOUN
ejpam-5043	101	7	can	can	AUX
ejpam-5043	101	8	be	be	AUX
ejpam-5043	101	9	used	use	VERB
ejpam-5043	101	10	to	to	PART
ejpam-5043	101	11	describe	describe	VERB
ejpam-5043	101	12	systems	system	NOUN
ejpam-5043	101	13	that	that	PRON
ejpam-5043	101	14	show	show	VERB
ejpam-5043	101	15	anomalous	anomalous	ADJ
ejpam-5043	101	16	diffusion	diffusion	NOUN
ejpam-5043	101	17	or	or	CCONJ
ejpam-5043	101	18	transport	transport	NOUN
ejpam-5043	101	19	.	.	PUNCT
ejpam-5043	102	1	this	this	PRON
ejpam-5043	102	2	is	be	AUX
ejpam-5043	102	3	when	when	SCONJ
ejpam-5043	102	4	particles	particle	NOUN
ejpam-5043	102	5	move	move	VERB
ejpam-5043	102	6	in	in	ADP
ejpam-5043	102	7	a	a	DET
ejpam-5043	102	8	way	way	NOUN
ejpam-5043	102	9	that	that	PRON
ejpam-5043	102	10	does	do	AUX
ejpam-5043	102	11	n’t	not	PART
ejpam-5043	102	12	follow	follow	VERB
ejpam-5043	102	13	the	the	DET
ejpam-5043	102	14	usual	usual	ADJ
ejpam-5043	102	15	rules	rule	NOUN
ejpam-5043	102	16	of	of	ADP
ejpam-5043	102	17	diffusion	diffusion	NOUN
ejpam-5043	102	18	.	.	PUNCT
ejpam-5043	103	1	using	use	VERB
ejpam-5043	103	2	this	this	DET
ejpam-5043	103	3	equation	equation	NOUN
ejpam-5043	103	4	,	,	PUNCT
ejpam-5043	103	5	one	one	PRON
ejpam-5043	103	6	can	can	AUX
ejpam-5043	103	7	better	well	ADV
ejpam-5043	103	8	analyze	analyze	VERB
ejpam-5043	103	9	and	and	CCONJ
ejpam-5043	103	10	comprehend	comprehend	VERB
ejpam-5043	103	11	the	the	DET
ejpam-5043	103	12	occurrence	occurrence	NOUN
ejpam-5043	103	13	of	of	ADP
ejpam-5043	103	14	such	such	ADJ
ejpam-5043	103	15	phenomena	phenomenon	NOUN
ejpam-5043	103	16	.	.	PUNCT
ejpam-5043	104	1	additionally	additionally	ADV
ejpam-5043	104	2	,	,	PUNCT
ejpam-5043	104	3	fractional	fractional	ADJ
ejpam-5043	104	4	derivatives	derivative	NOUN
ejpam-5043	104	5	and	and	CCONJ
ejpam-5043	104	6	integrals	integral	NOUN
ejpam-5043	104	7	are	be	AUX
ejpam-5043	104	8	incorporated	incorporate	VERB
ejpam-5043	104	9	into	into	ADP
ejpam-5043	104	10	the	the	DET
ejpam-5043	104	11	fractional	fractional	ADJ
ejpam-5043	104	12	bernoulli	bernoulli	NOUN
ejpam-5043	104	13	equation	equation	NOUN
ejpam-5043	104	14	,	,	PUNCT
ejpam-5043	104	15	which	which	PRON
ejpam-5043	104	16	is	be	AUX
ejpam-5043	104	17	an	an	DET
ejpam-5043	104	18	extension	extension	NOUN
ejpam-5043	104	19	of	of	ADP
ejpam-5043	104	20	the	the	DET
ejpam-5043	104	21	traditional	traditional	ADJ
ejpam-5043	104	22	bernoulli	bernoulli	NOUN
ejpam-5043	104	23	equation	equation	NOUN
ejpam-5043	104	24	that	that	PRON
ejpam-5043	104	25	allows	allow	VERB
ejpam-5043	104	26	it	it	PRON
ejpam-5043	104	27	to	to	PART
ejpam-5043	104	28	handle	handle	VERB
ejpam-5043	104	29	more	more	ADV
ejpam-5043	104	30	complicated	complicated	ADJ
ejpam-5043	104	31	situations	situation	NOUN
ejpam-5043	104	32	.	.	PUNCT
ejpam-5043	105	1	there	there	PRON
ejpam-5043	105	2	is	be	VERB
ejpam-5043	105	3	a	a	DET
ejpam-5043	105	4	wide	wide	ADJ
ejpam-5043	105	5	range	range	NOUN
ejpam-5043	105	6	of	of	ADP
ejpam-5043	105	7	applications	application	NOUN
ejpam-5043	105	8	for	for	ADP
ejpam-5043	105	9	it	it	PRON
ejpam-5043	105	10	,	,	PUNCT
ejpam-5043	105	11	particularly	particularly	ADV
ejpam-5043	105	12	in	in	ADP
ejpam-5043	105	13	areas	area	NOUN
ejpam-5043	105	14	that	that	PRON
ejpam-5043	105	15	deal	deal	VERB
ejpam-5043	105	16	with	with	ADP
ejpam-5043	105	17	complex	complex	ADJ
ejpam-5043	105	18	fluid	fluid	ADJ
ejpam-5043	105	19	dynamics	dynamic	NOUN
ejpam-5043	105	20	,	,	PUNCT
ejpam-5043	105	21	porous	porous	ADJ
ejpam-5043	105	22	media	medium	NOUN
ejpam-5043	105	23	,	,	PUNCT
ejpam-5043	105	24	and	and	CCONJ
ejpam-5043	105	25	systems	system	NOUN
ejpam-5043	105	26	that	that	PRON
ejpam-5043	105	27	exhibit	exhibit	VERB
ejpam-5043	105	28	non	non	ADJ
ejpam-5043	105	29	-	-	ADJ
ejpam-5043	105	30	newtonian	newtonian	ADJ
ejpam-5043	105	31	behavior	behavior	NOUN
ejpam-5043	105	32	.	.	PUNCT
ejpam-5043	106	1	this	this	DET
ejpam-5043	106	2	study	study	NOUN
ejpam-5043	106	3	is	be	AUX
ejpam-5043	106	4	driven	drive	VERB
ejpam-5043	106	5	by	by	ADP
ejpam-5043	106	6	the	the	DET
ejpam-5043	106	7	need	need	NOUN
ejpam-5043	106	8	for	for	ADP
ejpam-5043	106	9	innovative	innovative	ADJ
ejpam-5043	106	10	solutions	solution	NOUN
ejpam-5043	106	11	in	in	ADP
ejpam-5043	106	12	numerically	numerically	ADV
ejpam-5043	106	13	handling	handle	VERB
ejpam-5043	106	14	complex	complex	ADJ
ejpam-5043	106	15	fractional	fractional	ADJ
ejpam-5043	106	16	differential	differential	NOUN
ejpam-5043	106	17	equations	equation	NOUN
ejpam-5043	106	18	,	,	PUNCT
ejpam-5043	106	19	specifically	specifically	ADV
ejpam-5043	106	20	the	the	DET
ejpam-5043	106	21	fractional	fractional	ADJ
ejpam-5043	106	22	bernoulli	bernoulli	NOUN
ejpam-5043	106	23	equation	equation	NOUN
ejpam-5043	106	24	and	and	CCONJ
ejpam-5043	106	25	the	the	DET
ejpam-5043	106	26	fractional	fractional	ADJ
ejpam-5043	106	27	rössler	rössler	NOUN
ejpam-5043	106	28	model	model	NOUN
ejpam-5043	106	29	.	.	PUNCT
ejpam-5043	107	1	to	to	PART
ejpam-5043	107	2	address	address	VERB
ejpam-5043	107	3	this	this	PRON
ejpam-5043	107	4	,	,	PUNCT
ejpam-5043	107	5	we	we	PRON
ejpam-5043	107	6	introduce	introduce	VERB
ejpam-5043	107	7	the	the	DET
ejpam-5043	107	8	atangana	atangana	PROPN
ejpam-5043	107	9	-	-	PUNCT
ejpam-5043	107	10	baleanu	baleanu	PROPN
ejpam-5043	107	11	caputo	caputo	PROPN
ejpam-5043	107	12	fractional	fractional	PROPN
ejpam-5043	107	13	derivative	derivative	PROPN
ejpam-5043	107	14	(	(	PUNCT
ejpam-5043	107	15	abc	abc	PROPN
ejpam-5043	107	16	-	-	PUNCT
ejpam-5043	107	17	fd	fd	PROPN
ejpam-5043	107	18	)	)	PUNCT
ejpam-5043	107	19	method	method	NOUN
ejpam-5043	107	20	and	and	CCONJ
ejpam-5043	107	21	aim	aim	VERB
ejpam-5043	107	22	to	to	PART
ejpam-5043	107	23	provide	provide	VERB
ejpam-5043	107	24	a	a	DET
ejpam-5043	107	25	numerical	numerical	ADJ
ejpam-5043	107	26	solution	solution	NOUN
ejpam-5043	107	27	surpassing	surpass	VERB
ejpam-5043	107	28	conventional	conventional	ADJ
ejpam-5043	107	29	methods	method	NOUN
ejpam-5043	107	30	,	,	PUNCT
ejpam-5043	107	31	as	as	SCONJ
ejpam-5043	107	32	demonstrated	demonstrate	VERB
ejpam-5043	107	33	through	through	ADP
ejpam-5043	107	34	a	a	DET
ejpam-5043	107	35	comparative	comparative	ADJ
ejpam-5043	107	36	analysis	analysis	NOUN
ejpam-5043	107	37	with	with	ADP
ejpam-5043	107	38	the	the	DET
ejpam-5043	107	39	runge	runge	NOUN
ejpam-5043	107	40	-	-	PUNCT
ejpam-5043	107	41	kutta	kutta	NOUN
ejpam-5043	107	42	fourth	fourth	ADJ
ejpam-5043	107	43	order	order	NOUN
ejpam-5043	107	44	(	(	PUNCT
ejpam-5043	107	45	rk4	rk4	NOUN
ejpam-5043	107	46	)	)	PUNCT
ejpam-5043	107	47	method	method	NOUN
ejpam-5043	107	48	.	.	PUNCT
ejpam-5043	108	1	leveraging	leverage	VERB
ejpam-5043	108	2	matlab	matlab	PROPN
ejpam-5043	108	3	,	,	PUNCT
ejpam-5043	108	4	our	our	PRON
ejpam-5043	108	5	focus	focus	NOUN
ejpam-5043	108	6	extends	extend	VERB
ejpam-5043	108	7	beyond	beyond	ADP
ejpam-5043	108	8	solution	solution	NOUN
ejpam-5043	108	9	generation	generation	NOUN
ejpam-5043	108	10	to	to	PART
ejpam-5043	108	11	emphasize	emphasize	VERB
ejpam-5043	108	12	the	the	DET
ejpam-5043	108	13	crucial	crucial	ADJ
ejpam-5043	108	14	aspect	aspect	NOUN
ejpam-5043	108	15	of	of	ADP
ejpam-5043	108	16	maintaining	maintain	VERB
ejpam-5043	108	17	numerical	numerical	ADJ
ejpam-5043	108	18	stability	stability	NOUN
ejpam-5043	108	19	in	in	ADP
ejpam-5043	108	20	fractional	fractional	ADJ
ejpam-5043	108	21	procedures	procedure	NOUN
ejpam-5043	108	22	.	.	PUNCT
ejpam-5043	109	1	the	the	DET
ejpam-5043	109	2	study	study	NOUN
ejpam-5043	109	3	’s	’s	PART
ejpam-5043	109	4	objectives	objective	NOUN
ejpam-5043	109	5	include	include	VERB
ejpam-5043	109	6	showcasing	showcase	VERB
ejpam-5043	109	7	the	the	DET
ejpam-5043	109	8	abc	abc	PROPN
ejpam-5043	109	9	-	-	PUNCT
ejpam-5043	109	10	fd	fd	PROPN
ejpam-5043	109	11	method	method	NOUN
ejpam-5043	109	12	’s	’s	PART
ejpam-5043	109	13	accuracy	accuracy	NOUN
ejpam-5043	109	14	and	and	CCONJ
ejpam-5043	109	15	stability	stability	NOUN
ejpam-5043	109	16	while	while	SCONJ
ejpam-5043	109	17	highlighting	highlight	VERB
ejpam-5043	109	18	its	its	PRON
ejpam-5043	109	19	potential	potential	ADJ
ejpam-5043	109	20	applications	application	NOUN
ejpam-5043	109	21	in	in	ADP
ejpam-5043	109	22	signal	signal	ADJ
ejpam-5043	109	23	processing	processing	NOUN
ejpam-5043	109	24	,	,	PUNCT
ejpam-5043	109	25	control	control	NOUN
ejpam-5043	109	26	theory	theory	NOUN
ejpam-5043	109	27	,	,	PUNCT
ejpam-5043	109	28	communication	communication	NOUN
ejpam-5043	109	29	systems	system	NOUN
ejpam-5043	109	30	,	,	PUNCT
ejpam-5043	109	31	and	and	CCONJ
ejpam-5043	109	32	other	other	ADJ
ejpam-5043	109	33	engineering	engineering	NOUN
ejpam-5043	109	34	fields	field	NOUN
ejpam-5043	109	35	.	.	PUNCT
ejpam-5043	110	1	by	by	ADP
ejpam-5043	110	2	doing	do	VERB
ejpam-5043	110	3	so	so	ADV
ejpam-5043	110	4	,	,	PUNCT
ejpam-5043	110	5	we	we	PRON
ejpam-5043	110	6	contribute	contribute	VERB
ejpam-5043	110	7	valuable	valuable	ADJ
ejpam-5043	110	8	tools	tool	NOUN
ejpam-5043	110	9	and	and	CCONJ
ejpam-5043	110	10	insights	insight	NOUN
ejpam-5043	110	11	to	to	PART
ejpam-5043	110	12	advance	advance	VERB
ejpam-5043	110	13	the	the	DET
ejpam-5043	110	14	understanding	understanding	NOUN
ejpam-5043	110	15	and	and	CCONJ
ejpam-5043	110	16	application	application	NOUN
ejpam-5043	110	17	of	of	ADP
ejpam-5043	110	18	fractional	fractional	ADJ
ejpam-5043	110	19	calculus	calculus	NOUN
ejpam-5043	110	20	.	.	PUNCT
ejpam-5043	111	1	the	the	DET
ejpam-5043	111	2	rest	rest	NOUN
ejpam-5043	111	3	of	of	ADP
ejpam-5043	111	4	this	this	DET
ejpam-5043	111	5	paper	paper	NOUN
ejpam-5043	111	6	is	be	AUX
ejpam-5043	111	7	organized	organize	VERB
ejpam-5043	111	8	as	as	SCONJ
ejpam-5043	111	9	follows	follow	VERB
ejpam-5043	111	10	.	.	PUNCT
ejpam-5043	112	1	in	in	ADP
ejpam-5043	112	2	section	section	NOUN
ejpam-5043	112	3	2	2	NUM
ejpam-5043	112	4	,	,	PUNCT
ejpam-5043	112	5	we	we	PRON
ejpam-5043	112	6	start	start	VERB
ejpam-5043	112	7	by	by	ADP
ejpam-5043	112	8	presenting	present	VERB
ejpam-5043	112	9	some	some	DET
ejpam-5043	112	10	preliminaries	preliminary	NOUN
ejpam-5043	112	11	and	and	CCONJ
ejpam-5043	112	12	basic	basic	ADJ
ejpam-5043	112	13	definitions	definition	NOUN
ejpam-5043	112	14	which	which	PRON
ejpam-5043	112	15	will	will	AUX
ejpam-5043	112	16	be	be	AUX
ejpam-5043	112	17	needed	need	VERB
ejpam-5043	112	18	in	in	ADP
ejpam-5043	112	19	the	the	DET
ejpam-5043	112	20	sequel	sequel	NOUN
ejpam-5043	112	21	.	.	PUNCT
ejpam-5043	113	1	in	in	ADP
ejpam-5043	113	2	section	section	NOUN
ejpam-5043	113	3	3	3	NUM
ejpam-5043	113	4	,	,	PUNCT
ejpam-5043	113	5	we	we	PRON
ejpam-5043	113	6	shall	shall	AUX
ejpam-5043	113	7	present	present	VERB
ejpam-5043	113	8	a	a	DET
ejpam-5043	113	9	numerical	numerical	ADJ
ejpam-5043	113	10	scheme	scheme	NOUN
ejpam-5043	113	11	for	for	ADP
ejpam-5043	113	12	the	the	DET
ejpam-5043	113	13	abc	abc	PROPN
ejpam-5043	113	14	fractional	fractional	PROPN
ejpam-5043	113	15	derivative	derivative	NOUN
ejpam-5043	113	16	.	.	PUNCT
ejpam-5043	114	1	in	in	ADP
ejpam-5043	114	2	section	section	NOUN
ejpam-5043	114	3	4	4	NUM
ejpam-5043	114	4	,	,	PUNCT
ejpam-5043	114	5	the	the	DET
ejpam-5043	114	6	applications	application	NOUN
ejpam-5043	114	7	of	of	ADP
ejpam-5043	114	8	the	the	DET
ejpam-5043	114	9	abc	abc	PROPN
ejpam-5043	114	10	-	-	PUNCT
ejpam-5043	114	11	fd	fd	PROPN
ejpam-5043	114	12	scheme	scheme	NOUN
ejpam-5043	114	13	are	be	AUX
ejpam-5043	114	14	illustrated	illustrate	VERB
ejpam-5043	114	15	.	.	PUNCT
ejpam-5043	115	1	in	in	ADP
ejpam-5043	115	2	section	section	NOUN
ejpam-5043	115	3	5	5	NUM
ejpam-5043	115	4	we	we	PRON
ejpam-5043	115	5	shall	shall	AUX
ejpam-5043	115	6	discuss	discuss	VERB
ejpam-5043	115	7	the	the	DET
ejpam-5043	115	8	numerical	numerical	ADJ
ejpam-5043	115	9	result	result	NOUN
ejpam-5043	115	10	.	.	PUNCT
ejpam-5043	116	1	finally	finally	ADV
ejpam-5043	116	2	,	,	PUNCT
ejpam-5043	116	3	in	in	ADP
ejpam-5043	116	4	section	section	NOUN
ejpam-5043	116	5	6	6	NUM
ejpam-5043	116	6	,	,	PUNCT
ejpam-5043	116	7	we	we	PRON
ejpam-5043	116	8	present	present	VERB
ejpam-5043	116	9	our	our	PRON
ejpam-5043	116	10	study	study	NOUN
ejpam-5043	116	11	’s	’s	PART
ejpam-5043	116	12	conclusions	conclusion	NOUN
ejpam-5043	116	13	.	.	PUNCT
ejpam-5043	117	1	2	2	X
ejpam-5043	117	2	.	.	NUM
ejpam-5043	117	3	preliminaries	preliminary	NOUN
ejpam-5043	117	4	and	and	CCONJ
ejpam-5043	117	5	basic	basic	ADJ
ejpam-5043	117	6	definitions	definition	NOUN
ejpam-5043	117	7	firstly	firstly	ADV
ejpam-5043	117	8	,	,	PUNCT
ejpam-5043	117	9	we	we	PRON
ejpam-5043	117	10	present	present	VERB
ejpam-5043	117	11	briefly	briefly	ADV
ejpam-5043	117	12	the	the	DET
ejpam-5043	117	13	fractional	fractional	ADJ
ejpam-5043	117	14	operators	operator	NOUN
ejpam-5043	117	15	that	that	PRON
ejpam-5043	117	16	are	be	AUX
ejpam-5043	117	17	needed	need	VERB
ejpam-5043	117	18	in	in	ADP
ejpam-5043	117	19	the	the	DET
ejpam-5043	117	20	sequel	sequel	NOUN
ejpam-5043	117	21	.	.	PUNCT
ejpam-5043	118	1	definition	definition	NOUN
ejpam-5043	118	2	1	1	NUM
ejpam-5043	118	3	.	.	PUNCT
ejpam-5043	119	1	let	let	VERB
ejpam-5043	119	2	q	q	PROPN
ejpam-5043	119	3	∈	∈	PROPN
ejpam-5043	119	4	[	[	X
ejpam-5043	119	5	1,∞	1,∞	NUM
ejpam-5043	119	6	)	)	PUNCT
ejpam-5043	119	7	and	and	CCONJ
ejpam-5043	119	8	ω	ω	NUM
ejpam-5043	119	9	be	be	AUX
ejpam-5043	119	10	open	open	ADJ
ejpam-5043	119	11	subset	subset	NOUN
ejpam-5043	119	12	of	of	ADP
ejpam-5043	119	13	r	r	NOUN
ejpam-5043	119	14	,	,	PUNCT
ejpam-5043	119	15	the	the	DET
ejpam-5043	119	16	sobolev	sobolev	PROPN
ejpam-5043	119	17	space	space	NOUN
ejpam-5043	119	18	hq(ω	hq(ω	PUNCT
ejpam-5043	119	19	)	)	PUNCT
ejpam-5043	119	20	is	be	AUX
ejpam-5043	119	21	defined	define	VERB
ejpam-5043	119	22	by	by	ADP
ejpam-5043	119	23	[	[	X
ejpam-5043	119	24	3	3	NUM
ejpam-5043	119	25	]	]	X
ejpam-5043	119	26	:	:	PUNCT
ejpam-5043	119	27	hq(ω	hq(ω	X
ejpam-5043	119	28	)	)	PUNCT
ejpam-5043	120	1	=	=	PRON
ejpam-5043	120	2	{	{	PUNCT
ejpam-5043	120	3	f	f	PROPN
ejpam-5043	120	4	∈	∈	PROPN
ejpam-5043	120	5	l2(ω	l2(ω	PROPN
ejpam-5043	120	6	)	)	PUNCT
ejpam-5043	120	7	:	:	PUNCT
ejpam-5043	120	8	dβf	dβf	VERB
ejpam-5043	120	9	∈	∈	PROPN
ejpam-5043	120	10	l2(ω	l2(ω	NOUN
ejpam-5043	120	11	)	)	PUNCT
ejpam-5043	120	12	,	,	PUNCT
ejpam-5043	120	13	forall	forall	NOUN
ejpam-5043	120	14	|β|	|β|	NOUN
ejpam-5043	120	15	≤	≤	NOUN
ejpam-5043	120	16	q	q	NOUN
ejpam-5043	120	17	}	}	PUNCT
ejpam-5043	120	18	.	.	PUNCT
ejpam-5043	121	1	(	(	PUNCT
ejpam-5043	121	2	1	1	X
ejpam-5043	121	3	)	)	PUNCT
ejpam-5043	121	4	definition	definition	NOUN
ejpam-5043	121	5	2	2	NUM
ejpam-5043	121	6	.	.	PUNCT
ejpam-5043	122	1	the	the	DET
ejpam-5043	122	2	atangana	atangana	PROPN
ejpam-5043	122	3	-	-	PUNCT
ejpam-5043	122	4	baleanu	baleanu	PROPN
ejpam-5043	122	5	caputo	caputo	PROPN
ejpam-5043	122	6	(	(	PUNCT
ejpam-5043	122	7	abc	abc	PROPN
ejpam-5043	122	8	)	)	PUNCT
ejpam-5043	122	9	fractional	fractional	ADJ
ejpam-5043	122	10	derivative	derivative	NOUN
ejpam-5043	122	11	of	of	ADP
ejpam-5043	122	12	a	a	DET
ejpam-5043	122	13	function	function	NOUN
ejpam-5043	122	14	k.	k.	PROPN
ejpam-5043	122	15	boulehmi	boulehmi	PROPN
ejpam-5043	122	16	/	/	SYM
ejpam-5043	122	17	eur	eur	PROPN
ejpam-5043	122	18	.	.	PUNCT
ejpam-5043	123	1	j.	j.	PROPN
ejpam-5043	123	2	pure	pure	PROPN
ejpam-5043	123	3	appl	appl	PROPN
ejpam-5043	123	4	.	.	PROPN
ejpam-5043	123	5	math	math	PROPN
ejpam-5043	123	6	,	,	PUNCT
ejpam-5043	123	7	17	17	NUM
ejpam-5043	123	8	(	(	PUNCT
ejpam-5043	123	9	1	1	NUM
ejpam-5043	123	10	)	)	PUNCT
ejpam-5043	123	11	(	(	PUNCT
ejpam-5043	123	12	2024	2024	NUM
ejpam-5043	123	13	)	)	PUNCT
ejpam-5043	123	14	,	,	PUNCT
ejpam-5043	123	15	445	445	NUM
ejpam-5043	123	16	-	-	SYM
ejpam-5043	123	17	461	461	NUM
ejpam-5043	123	18	450	450	NUM
ejpam-5043	123	19	y(τ	y(τ	PROPN
ejpam-5043	123	20	)	)	PUNCT
ejpam-5043	123	21	∈	∈	PROPN
ejpam-5043	123	22	h1(0	h1(0	PROPN
ejpam-5043	123	23	,	,	PUNCT
ejpam-5043	123	24	c	c	NOUN
ejpam-5043	123	25	)	)	PUNCT
ejpam-5043	123	26	,	,	PUNCT
ejpam-5043	124	1	c	c	X
ejpam-5043	124	2	>	>	X
ejpam-5043	124	3	0	0	PUNCT
ejpam-5043	125	1	with	with	ADP
ejpam-5043	125	2	α	α	PROPN
ejpam-5043	125	3	∈	∈	PROPN
ejpam-5043	126	1	[	[	X
ejpam-5043	126	2	0	0	NUM
ejpam-5043	126	3	,	,	PUNCT
ejpam-5043	126	4	1	1	NUM
ejpam-5043	126	5	]	]	PUNCT
ejpam-5043	126	6	is	be	AUX
ejpam-5043	126	7	defined	define	VERB
ejpam-5043	126	8	as	as	ADP
ejpam-5043	126	9	[	[	X
ejpam-5043	126	10	7	7	NUM
ejpam-5043	126	11	]	]	PUNCT
ejpam-5043	126	12	:	:	PUNCT
ejpam-5043	126	13	abc	abc	PROPN
ejpam-5043	126	14	0	0	PROPN
ejpam-5043	127	1	dα	dα	PROPN
ejpam-5043	127	2	t	t	PROPN
ejpam-5043	127	3	y(t	y(t	PROPN
ejpam-5043	127	4	)	)	PUNCT
ejpam-5043	128	1	=	=	SYM
ejpam-5043	128	2	b(α	b(α	PROPN
ejpam-5043	128	3	)	)	PUNCT
ejpam-5043	129	1	1−	1−	NUM
ejpam-5043	129	2	α	α	NOUN
ejpam-5043	130	1	d	d	NOUN
ejpam-5043	130	2	dt	dt	X
ejpam-5043	131	1	∫	∫	PROPN
ejpam-5043	131	2	t	t	PROPN
ejpam-5043	131	3	0	0	NUM
ejpam-5043	132	1	y(τ)eα	y(τ)eα	PROPN
ejpam-5043	132	2	(	(	PUNCT
ejpam-5043	132	3	−	−	PROPN
ejpam-5043	132	4	α	α	NOUN
ejpam-5043	132	5	1−	1−	NUM
ejpam-5043	132	6	α	α	NOUN
ejpam-5043	132	7	(	(	PUNCT
ejpam-5043	132	8	t−	t−	PROPN
ejpam-5043	132	9	τ)α	τ)α	ADJ
ejpam-5043	132	10	)	)	PUNCT
ejpam-5043	132	11	dτ	dτ	NOUN
ejpam-5043	132	12	,	,	PUNCT
ejpam-5043	132	13	0	0	NUM
ejpam-5043	132	14	≤	≤	NUM
ejpam-5043	132	15	α	α	NOUN
ejpam-5043	132	16	≤	≤	NUM
ejpam-5043	132	17	1	1	NUM
ejpam-5043	132	18	,	,	PUNCT
ejpam-5043	132	19	(	(	PUNCT
ejpam-5043	132	20	2	2	X
ejpam-5043	132	21	)	)	PUNCT
ejpam-5043	132	22	where	where	SCONJ
ejpam-5043	132	23	b(α	b(α	NOUN
ejpam-5043	132	24	)	)	PUNCT
ejpam-5043	132	25	denotes	denote	VERB
ejpam-5043	132	26	a	a	DET
ejpam-5043	132	27	normalization	normalization	NOUN
ejpam-5043	132	28	function	function	NOUN
ejpam-5043	132	29	obeying	obey	VERB
ejpam-5043	132	30	b(0	b(0	NOUN
ejpam-5043	132	31	)	)	PUNCT
ejpam-5043	132	32	=	=	SYM
ejpam-5043	132	33	b(1	b(1	PROPN
ejpam-5043	132	34	)	)	PUNCT
ejpam-5043	132	35	.	.	PUNCT
ejpam-5043	133	1	definition	definition	NOUN
ejpam-5043	133	2	3	3	NUM
ejpam-5043	133	3	.	.	PUNCT
ejpam-5043	134	1	the	the	DET
ejpam-5043	134	2	mittag	mittag	ADJ
ejpam-5043	134	3	-	-	PUNCT
ejpam-5043	134	4	leffler	leffler	NOUN
ejpam-5043	134	5	function	function	NOUN
ejpam-5043	134	6	can	can	AUX
ejpam-5043	134	7	be	be	AUX
ejpam-5043	134	8	expressed	express	VERB
ejpam-5043	134	9	as	as	SCONJ
ejpam-5043	134	10	follows	follow	VERB
ejpam-5043	134	11	[	[	X
ejpam-5043	134	12	37	37	NUM
ejpam-5043	134	13	]	]	NUM
ejpam-5043	134	14	:	:	PUNCT
ejpam-5043	134	15	eα(t	eα(t	X
ejpam-5043	134	16	)	)	PUNCT
ejpam-5043	134	17	=	=	NOUN
ejpam-5043	135	1	∞∑	∞∑	NUM
ejpam-5043	135	2	k=0	k=0	PROPN
ejpam-5043	135	3	tk	tk	PROPN
ejpam-5043	135	4	γ(αk	γ(αk	PROPN
ejpam-5043	135	5	+	+	PROPN
ejpam-5043	135	6	1	1	NUM
ejpam-5043	135	7	)	)	PUNCT
ejpam-5043	135	8	(	(	PUNCT
ejpam-5043	135	9	3	3	X
ejpam-5043	135	10	)	)	PUNCT
ejpam-5043	135	11	definition	definition	NOUN
ejpam-5043	135	12	4	4	NUM
ejpam-5043	135	13	.	.	PUNCT
ejpam-5043	136	1	the	the	DET
ejpam-5043	136	2	atangana	atangana	PROPN
ejpam-5043	136	3	-	-	PUNCT
ejpam-5043	136	4	baleanu	baleanu	ADJ
ejpam-5043	136	5	fractional	fractional	ADJ
ejpam-5043	136	6	integral	integral	NOUN
ejpam-5043	136	7	of	of	ADP
ejpam-5043	136	8	a	a	DET
ejpam-5043	136	9	function	function	NOUN
ejpam-5043	136	10	y(τ	y(τ	PROPN
ejpam-5043	136	11	)	)	PUNCT
ejpam-5043	136	12	∈	∈	PROPN
ejpam-5043	136	13	h1(0	h1(0	PROPN
ejpam-5043	136	14	,	,	PUNCT
ejpam-5043	136	15	c	c	NOUN
ejpam-5043	136	16	)	)	PUNCT
ejpam-5043	136	17	,	,	PUNCT
ejpam-5043	136	18	c	c	X
ejpam-5043	136	19	>	>	X
ejpam-5043	136	20	0	0	PUNCT
ejpam-5043	136	21	is	be	AUX
ejpam-5043	136	22	as	as	SCONJ
ejpam-5043	136	23	follows	follow	VERB
ejpam-5043	136	24	[	[	X
ejpam-5043	136	25	7	7	NUM
ejpam-5043	136	26	]	]	PUNCT
ejpam-5043	136	27	:	:	PUNCT
ejpam-5043	136	28	ab	ab	PROPN
ejpam-5043	136	29	0	0	NUM
ejpam-5043	136	30	iαt	iαt	X
ejpam-5043	136	31	y(t	y(t	PROPN
ejpam-5043	136	32	)	)	PUNCT
ejpam-5043	136	33	=	=	SYM
ejpam-5043	137	1	1−	1−	NUM
ejpam-5043	137	2	α	α	NUM
ejpam-5043	137	3	m(α	m(α	PROPN
ejpam-5043	137	4	)	)	PUNCT
ejpam-5043	137	5	y(t	y(t	NUM
ejpam-5043	137	6	)	)	PUNCT
ejpam-5043	138	1	+	+	CCONJ
ejpam-5043	138	2	α	α	PROPN
ejpam-5043	138	3	m(α)γ(α	m(α)γ(α	X
ejpam-5043	138	4	)	)	PUNCT
ejpam-5043	138	5	∫	∫	PROPN
ejpam-5043	139	1	t	t	PROPN
ejpam-5043	139	2	0	0	NUM
ejpam-5043	139	3	y(τ)(t−	y(τ)(t−	X
ejpam-5043	139	4	τ)α−1dτ	τ)α−1dτ	PROPN
ejpam-5043	139	5	,	,	PUNCT
ejpam-5043	139	6	0	0	NUM
ejpam-5043	139	7	≤	≤	NUM
ejpam-5043	139	8	α	α	NOUN
ejpam-5043	139	9	≤	≤	NUM
ejpam-5043	139	10	1	1	NUM
ejpam-5043	139	11	.	.	PUNCT
ejpam-5043	140	1	(	(	PUNCT
ejpam-5043	140	2	4	4	NUM
ejpam-5043	140	3	)	)	PUNCT
ejpam-5043	140	4	3	3	NUM
ejpam-5043	140	5	.	.	NOUN
ejpam-5043	141	1	3	3	NUM
ejpam-5043	141	2	.	.	X
ejpam-5043	141	3	numerical	numerical	ADJ
ejpam-5043	141	4	scheme	scheme	NOUN
ejpam-5043	141	5	for	for	ADP
ejpam-5043	141	6	the	the	DET
ejpam-5043	141	7	abc	abc	PROPN
ejpam-5043	141	8	-	-	PUNCT
ejpam-5043	141	9	fd	fd	PROPN
ejpam-5043	141	10	this	this	DET
ejpam-5043	141	11	section	section	NOUN
ejpam-5043	141	12	investigates	investigate	VERB
ejpam-5043	141	13	a	a	DET
ejpam-5043	141	14	novel	novel	ADJ
ejpam-5043	141	15	scheme	scheme	NOUN
ejpam-5043	141	16	for	for	ADP
ejpam-5043	141	17	the	the	DET
ejpam-5043	141	18	(	(	PUNCT
ejpam-5043	141	19	abc	abc	PROPN
ejpam-5043	141	20	-	-	PUNCT
ejpam-5043	141	21	fd	fd	PROPN
ejpam-5043	141	22	)	)	PUNCT
ejpam-5043	141	23	,	,	PUNCT
ejpam-5043	141	24	of	of	ADP
ejpam-5043	141	25	the	the	DET
ejpam-5043	141	26	form	form	NOUN
ejpam-5043	141	27	that	that	PRON
ejpam-5043	141	28	was	be	AUX
ejpam-5043	141	29	first	first	ADV
ejpam-5043	141	30	presented	present	VERB
ejpam-5043	141	31	in	in	ADP
ejpam-5043	141	32	[	[	X
ejpam-5043	141	33	43	43	NUM
ejpam-5043	141	34	]	]	X
ejpam-5043	141	35	:	:	PUNCT
ejpam-5043	141	36			PROPN
ejpam-5043	141	37	abc	abc	PROPN
ejpam-5043	141	38	0	0	NUM
ejpam-5043	141	39	dα	dα	PROPN
ejpam-5043	141	40	t	t	PROPN
ejpam-5043	141	41	x(t	x(t	PROPN
ejpam-5043	141	42	)	)	PUNCT
ejpam-5043	142	1	=	=	SYM
ejpam-5043	142	2	e(t	e(t	NOUN
ejpam-5043	142	3	,	,	PUNCT
ejpam-5043	142	4	x(t	x(t	PROPN
ejpam-5043	142	5	)	)	PUNCT
ejpam-5043	142	6	)	)	PUNCT
ejpam-5043	142	7	,	,	PUNCT
ejpam-5043	142	8	abc	abc	PROPN
ejpam-5043	142	9	0	0	PROPN
ejpam-5043	142	10	dα	dα	PROPN
ejpam-5043	142	11	t	t	PROPN
ejpam-5043	142	12	y(t	y(t	PROPN
ejpam-5043	142	13	)	)	PUNCT
ejpam-5043	143	1	=	=	PUNCT
ejpam-5043	143	2	h(t	h(t	PROPN
ejpam-5043	143	3	,	,	PUNCT
ejpam-5043	143	4	y(t	y(t	PROPN
ejpam-5043	143	5	)	)	PUNCT
ejpam-5043	143	6	)	)	PUNCT
ejpam-5043	143	7	,	,	PUNCT
ejpam-5043	143	8	abc	abc	PROPN
ejpam-5043	143	9	0	0	PROPN
ejpam-5043	143	10	dα	dα	PROPN
ejpam-5043	143	11	t	t	PROPN
ejpam-5043	143	12	z(t	z(t	PROPN
ejpam-5043	143	13	)	)	PUNCT
ejpam-5043	144	1	=	=	SYM
ejpam-5043	144	2	p	p	X
ejpam-5043	144	3	(	(	PUNCT
ejpam-5043	144	4	t	t	PROPN
ejpam-5043	144	5	,	,	PUNCT
ejpam-5043	144	6	z(t	z(t	PROPN
ejpam-5043	144	7	)	)	PUNCT
ejpam-5043	144	8	)	)	PUNCT
ejpam-5043	144	9	.	.	PUNCT
ejpam-5043	145	1	(	(	PUNCT
ejpam-5043	145	2	5	5	X
ejpam-5043	145	3	)	)	PUNCT
ejpam-5043	145	4	through	through	ADP
ejpam-5043	145	5	the	the	DET
ejpam-5043	145	6	application	application	NOUN
ejpam-5043	145	7	of	of	ADP
ejpam-5043	145	8	the	the	DET
ejpam-5043	145	9	fundamental	fundamental	ADJ
ejpam-5043	145	10	theorem	theorem	NOUN
ejpam-5043	145	11	of	of	ADP
ejpam-5043	145	12	fractional	fractional	ADJ
ejpam-5043	145	13	calculus	calculus	NOUN
ejpam-5043	145	14	,	,	PUNCT
ejpam-5043	145	15	we	we	PRON
ejpam-5043	145	16	lead	lead	VERB
ejpam-5043	145	17	to	to	ADP
ejpam-5043	145	18	:	:	PUNCT
ejpam-5043	145	19	x(t)−	x(t)−	PROPN
ejpam-5043	145	20	x(0	x(0	PROPN
ejpam-5043	145	21	)	)	PUNCT
ejpam-5043	146	1	=	=	PUNCT
ejpam-5043	146	2	1−	1−	NUM
ejpam-5043	146	3	α	α	NUM
ejpam-5043	146	4	abc(α	abc(α	PROPN
ejpam-5043	146	5	)	)	PUNCT
ejpam-5043	146	6	e(t	e(t	NOUN
ejpam-5043	146	7	,	,	PUNCT
ejpam-5043	146	8	x(t	x(t	PROPN
ejpam-5043	146	9	)	)	PUNCT
ejpam-5043	146	10	)	)	PUNCT
ejpam-5043	147	1	+	+	CCONJ
ejpam-5043	147	2	α	α	PRON
ejpam-5043	147	3	γ(α)abc(α	γ(α)abc(α	PROPN
ejpam-5043	147	4	)	)	PUNCT
ejpam-5043	148	1	∫	∫	PROPN
ejpam-5043	148	2	t	t	PROPN
ejpam-5043	148	3	0	0	NUM
ejpam-5043	148	4	e(τ	e(τ	PROPN
ejpam-5043	148	5	,	,	PUNCT
ejpam-5043	148	6	x(τ))(t−	x(τ))(t−	PROPN
ejpam-5043	148	7	τ)α−1dτ	τ)α−1dτ	PROPN
ejpam-5043	148	8	,	,	PUNCT
ejpam-5043	148	9	(	(	PUNCT
ejpam-5043	148	10	6	6	NUM
ejpam-5043	148	11	)	)	PUNCT
ejpam-5043	148	12	y(t)−	y(t)−	PROPN
ejpam-5043	148	13	y(0	y(0	PROPN
ejpam-5043	148	14	)	)	PUNCT
ejpam-5043	148	15	=	=	SYM
ejpam-5043	148	16	1−	1−	NUM
ejpam-5043	148	17	α	α	NUM
ejpam-5043	148	18	abc(α	abc(α	PROPN
ejpam-5043	148	19	)	)	PUNCT
ejpam-5043	148	20	h(t	h(t	PROPN
ejpam-5043	148	21	,	,	PUNCT
ejpam-5043	148	22	y(t	y(t	NOUN
ejpam-5043	148	23	)	)	PUNCT
ejpam-5043	148	24	)	)	PUNCT
ejpam-5043	149	1	+	+	CCONJ
ejpam-5043	149	2	α	α	PRON
ejpam-5043	149	3	γ(α)abc(α	γ(α)abc(α	PROPN
ejpam-5043	149	4	)	)	PUNCT
ejpam-5043	150	1	∫	∫	PROPN
ejpam-5043	151	1	t	t	PROPN
ejpam-5043	151	2	0	0	NUM
ejpam-5043	152	1	h(τ	h(τ	PROPN
ejpam-5043	152	2	,	,	PUNCT
ejpam-5043	152	3	y(τ))(t−	y(τ))(t−	PROPN
ejpam-5043	152	4	τ)α−1dτ	τ)α−1dτ	VERB
ejpam-5043	152	5	,	,	PUNCT
ejpam-5043	152	6	(	(	PUNCT
ejpam-5043	152	7	7	7	X
ejpam-5043	152	8	)	)	PUNCT
ejpam-5043	152	9	z(t)−	z(t)−	PROPN
ejpam-5043	152	10	z(0	z(0	NOUN
ejpam-5043	152	11	)	)	PUNCT
ejpam-5043	152	12	=	=	SYM
ejpam-5043	152	13	1−	1−	NUM
ejpam-5043	152	14	α	α	NUM
ejpam-5043	152	15	abc(α	abc(α	PROPN
ejpam-5043	152	16	)	)	PUNCT
ejpam-5043	152	17	p	p	X
ejpam-5043	152	18	(	(	PUNCT
ejpam-5043	152	19	t	t	PROPN
ejpam-5043	152	20	,	,	PUNCT
ejpam-5043	152	21	z(t	z(t	PROPN
ejpam-5043	152	22	)	)	PUNCT
ejpam-5043	152	23	)	)	PUNCT
ejpam-5043	153	1	+	+	CCONJ
ejpam-5043	153	2	α	α	PRON
ejpam-5043	153	3	γ(α)abc(α	γ(α)abc(α	PROPN
ejpam-5043	153	4	)	)	PUNCT
ejpam-5043	154	1	∫	∫	PROPN
ejpam-5043	154	2	t	t	NOUN
ejpam-5043	154	3	0	0	NUM
ejpam-5043	155	1	p	p	X
ejpam-5043	155	2	(	(	PUNCT
ejpam-5043	155	3	τ	τ	PROPN
ejpam-5043	155	4	,	,	PUNCT
ejpam-5043	155	5	z(τ))(t−	z(τ))(t−	PROPN
ejpam-5043	155	6	τ)α−1dτ	τ)α−1dτ	PROPN
ejpam-5043	155	7	.	.	PUNCT
ejpam-5043	156	1	(	(	PUNCT
ejpam-5043	156	2	8)	8)	NUM
ejpam-5043	156	3	at	at	ADP
ejpam-5043	156	4	the	the	DET
ejpam-5043	156	5	point	point	NOUN
ejpam-5043	156	6	tn+1	tn+1	NOUN
ejpam-5043	156	7	,	,	PUNCT
ejpam-5043	156	8	n	n	NOUN
ejpam-5043	156	9	=	=	SYM
ejpam-5043	156	10	0	0	NUM
ejpam-5043	156	11	,	,	PUNCT
ejpam-5043	156	12	1	1	NUM
ejpam-5043	156	13	,	,	PUNCT
ejpam-5043	156	14	2	2	NUM
ejpam-5043	156	15	.	.	PUNCT
ejpam-5043	156	16	.	.	PUNCT
ejpam-5043	156	17	.	.	PUNCT
ejpam-5043	157	1	,	,	PUNCT
ejpam-5043	157	2	,	,	PUNCT
ejpam-5043	157	3	the	the	DET
ejpam-5043	157	4	above	above	ADJ
ejpam-5043	157	5	equation	equation	NOUN
ejpam-5043	157	6	is	be	AUX
ejpam-5043	157	7	reformulated	reformulate	VERB
ejpam-5043	157	8	as	as	ADP
ejpam-5043	157	9	x(tn+1)−	x(tn+1)−	PROPN
ejpam-5043	157	10	x(0	x(0	PROPN
ejpam-5043	157	11	)	)	PUNCT
ejpam-5043	158	1	=	=	PUNCT
ejpam-5043	158	2	1−	1−	NUM
ejpam-5043	158	3	α	α	NUM
ejpam-5043	158	4	abc(α	abc(α	PROPN
ejpam-5043	158	5	)	)	PUNCT
ejpam-5043	158	6	e(tn	e(tn	PROPN
ejpam-5043	158	7	,	,	PUNCT
ejpam-5043	158	8	x(tn	x(tn	NOUN
ejpam-5043	158	9	)	)	PUNCT
ejpam-5043	158	10	)	)	PUNCT
ejpam-5043	159	1	+	+	CCONJ
ejpam-5043	159	2	α	α	X
ejpam-5043	159	3	abc(α)γ(α	abc(α)γ(α	PROPN
ejpam-5043	159	4	)	)	PUNCT
ejpam-5043	159	5	∫	∫	PROPN
ejpam-5043	159	6	tn+1	tn+1	NOUN
ejpam-5043	159	7	0	0	PUNCT
ejpam-5043	159	8	e(τ	e(τ	PROPN
ejpam-5043	159	9	,	,	PUNCT
ejpam-5043	159	10	x(τ))(tn+1	x(τ))(tn+1	PROPN
ejpam-5043	159	11	−	−	PROPN
ejpam-5043	159	12	τ)α−1dτ	τ)α−1dτ	PROPN
ejpam-5043	159	13	=	=	SYM
ejpam-5043	159	14	1−	1−	NUM
ejpam-5043	159	15	α	α	NUM
ejpam-5043	159	16	abc(α	abc(α	PROPN
ejpam-5043	159	17	)	)	PUNCT
ejpam-5043	159	18	e(tn	e(tn	PROPN
ejpam-5043	159	19	,	,	PUNCT
ejpam-5043	159	20	x(tn	x(tn	NOUN
ejpam-5043	159	21	)	)	PUNCT
ejpam-5043	159	22	)	)	PUNCT
ejpam-5043	160	1	+	+	CCONJ
ejpam-5043	160	2	α	α	PRON
ejpam-5043	160	3	γ(α)abc(α	γ(α)abc(α	NOUN
ejpam-5043	160	4	)	)	PUNCT
ejpam-5043	160	5	n∑	n∑	PROPN
ejpam-5043	161	1	k=0	k=0	PROPN
ejpam-5043	161	2	∫	∫	PROPN
ejpam-5043	161	3	tk+1	tk+1	NUM
ejpam-5043	161	4	tk	tk	PROPN
ejpam-5043	161	5	e(τ	e(τ	PROPN
ejpam-5043	161	6	,	,	PUNCT
ejpam-5043	161	7	x(τ))(tn+1	x(τ))(tn+1	PROPN
ejpam-5043	161	8	−	−	PROPN
ejpam-5043	161	9	τ)α−1dτ	τ)α−1dτ	PROPN
ejpam-5043	161	10	.	.	PUNCT
ejpam-5043	162	1	(	(	PUNCT
ejpam-5043	162	2	9	9	X
ejpam-5043	162	3	)	)	PUNCT
ejpam-5043	162	4	k.	k.	PROPN
ejpam-5043	162	5	boulehmi	boulehmi	PROPN
ejpam-5043	162	6	/	/	SYM
ejpam-5043	162	7	eur	eur	PROPN
ejpam-5043	162	8	.	.	PUNCT
ejpam-5043	163	1	j.	j.	PROPN
ejpam-5043	163	2	pure	pure	PROPN
ejpam-5043	163	3	appl	appl	PROPN
ejpam-5043	163	4	.	.	PROPN
ejpam-5043	163	5	math	math	PROPN
ejpam-5043	163	6	,	,	PUNCT
ejpam-5043	163	7	17	17	NUM
ejpam-5043	163	8	(	(	PUNCT
ejpam-5043	163	9	1	1	NUM
ejpam-5043	163	10	)	)	PUNCT
ejpam-5043	163	11	(	(	PUNCT
ejpam-5043	163	12	2024	2024	NUM
ejpam-5043	163	13	)	)	PUNCT
ejpam-5043	163	14	,	,	PUNCT
ejpam-5043	163	15	445	445	NUM
ejpam-5043	163	16	-	-	SYM
ejpam-5043	163	17	461	461	NUM
ejpam-5043	163	18	451	451	NUM
ejpam-5043	163	19	y(tn+1)−	y(tn+1)−	NOUN
ejpam-5043	163	20	y(0	y(0	PROPN
ejpam-5043	163	21	)	)	PUNCT
ejpam-5043	163	22	=	=	SYM
ejpam-5043	163	23	1−	1−	NUM
ejpam-5043	163	24	α	α	NUM
ejpam-5043	163	25	abc(α	abc(α	PROPN
ejpam-5043	163	26	)	)	PUNCT
ejpam-5043	163	27	h(tn	h(tn	NOUN
ejpam-5043	163	28	,	,	PUNCT
ejpam-5043	163	29	x(tn	x(tn	NOUN
ejpam-5043	163	30	)	)	PUNCT
ejpam-5043	163	31	)	)	PUNCT
ejpam-5043	164	1	+	+	CCONJ
ejpam-5043	164	2	α	α	X
ejpam-5043	164	3	abc(α)γ(α	abc(α)γ(α	PROPN
ejpam-5043	164	4	)	)	PUNCT
ejpam-5043	164	5	∫	∫	PROPN
ejpam-5043	164	6	tn+1	tn+1	NOUN
ejpam-5043	164	7	0	0	NUM
ejpam-5043	165	1	h(τ	h(τ	PROPN
ejpam-5043	165	2	,	,	PUNCT
ejpam-5043	165	3	y(τ))(tn+1	y(τ))(tn+1	PROPN
ejpam-5043	165	4	−	−	PROPN
ejpam-5043	165	5	τ)α−1dτ	τ)α−1dτ	PROPN
ejpam-5043	165	6	=	=	SYM
ejpam-5043	165	7	1−	1−	NUM
ejpam-5043	165	8	α	α	NUM
ejpam-5043	165	9	abc(α	abc(α	PROPN
ejpam-5043	165	10	)	)	PUNCT
ejpam-5043	165	11	h(tn	h(tn	NOUN
ejpam-5043	165	12	,	,	PUNCT
ejpam-5043	165	13	y(tn	y(tn	NOUN
ejpam-5043	165	14	)	)	PUNCT
ejpam-5043	165	15	)	)	PUNCT
ejpam-5043	166	1	+	+	CCONJ
ejpam-5043	166	2	α	α	PRON
ejpam-5043	166	3	γ(α)abc(α	γ(α)abc(α	NOUN
ejpam-5043	166	4	)	)	PUNCT
ejpam-5043	166	5	n∑	n∑	PROPN
ejpam-5043	167	1	k=0	k=0	PROPN
ejpam-5043	167	2	∫	∫	PROPN
ejpam-5043	167	3	tk+1	tk+1	NUM
ejpam-5043	167	4	tk	tk	PROPN
ejpam-5043	167	5	h(τ	h(τ	PROPN
ejpam-5043	167	6	,	,	PUNCT
ejpam-5043	167	7	y(τ))(tn+1	y(τ))(tn+1	PROPN
ejpam-5043	167	8	−	−	PROPN
ejpam-5043	167	9	τ)α−1dτ	τ)α−1dτ	PROPN
ejpam-5043	167	10	.	.	PUNCT
ejpam-5043	168	1	(	(	PUNCT
ejpam-5043	168	2	10	10	NUM
ejpam-5043	168	3	)	)	PUNCT
ejpam-5043	168	4	z(tn+1)−	z(tn+1)−	NOUN
ejpam-5043	168	5	z(0	z(0	PROPN
ejpam-5043	168	6	)	)	PUNCT
ejpam-5043	169	1	=	=	SYM
ejpam-5043	169	2	1−	1−	NUM
ejpam-5043	169	3	α	α	NUM
ejpam-5043	169	4	abc(α	abc(α	PROPN
ejpam-5043	169	5	)	)	PUNCT
ejpam-5043	170	1	p	p	X
ejpam-5043	170	2	(	(	PUNCT
ejpam-5043	170	3	tn	tn	NOUN
ejpam-5043	170	4	,	,	PUNCT
ejpam-5043	170	5	z(tn	z(tn	NOUN
ejpam-5043	170	6	)	)	PUNCT
ejpam-5043	170	7	)	)	PUNCT
ejpam-5043	171	1	+	+	CCONJ
ejpam-5043	171	2	α	α	X
ejpam-5043	171	3	abc(α)γ(α	abc(α)γ(α	PROPN
ejpam-5043	171	4	)	)	PUNCT
ejpam-5043	171	5	∫	∫	PROPN
ejpam-5043	171	6	tn+1	tn+1	NOUN
ejpam-5043	171	7	0	0	NUM
ejpam-5043	172	1	p	p	X
ejpam-5043	172	2	(	(	PUNCT
ejpam-5043	172	3	τ	τ	PROPN
ejpam-5043	172	4	,	,	PUNCT
ejpam-5043	172	5	x(τ))(tn+1	x(τ))(tn+1	PROPN
ejpam-5043	172	6	−	−	PROPN
ejpam-5043	172	7	τ)α−1dτ	τ)α−1dτ	PROPN
ejpam-5043	172	8	=	=	SYM
ejpam-5043	172	9	1−	1−	NUM
ejpam-5043	172	10	α	α	NUM
ejpam-5043	172	11	abc(α	abc(α	PROPN
ejpam-5043	172	12	)	)	PUNCT
ejpam-5043	172	13	p	p	X
ejpam-5043	172	14	(	(	PUNCT
ejpam-5043	172	15	tn	tn	NOUN
ejpam-5043	172	16	,	,	PUNCT
ejpam-5043	172	17	z(tn	z(tn	NOUN
ejpam-5043	172	18	)	)	PUNCT
ejpam-5043	172	19	)	)	PUNCT
ejpam-5043	173	1	+	+	CCONJ
ejpam-5043	173	2	α	α	PRON
ejpam-5043	173	3	γ(α)abc(α	γ(α)abc(α	NOUN
ejpam-5043	173	4	)	)	PUNCT
ejpam-5043	173	5	n∑	n∑	PROPN
ejpam-5043	174	1	k=0	k=0	PROPN
ejpam-5043	174	2	∫	∫	PROPN
ejpam-5043	174	3	tk+1	tk+1	NUM
ejpam-5043	174	4	tk	tk	PROPN
ejpam-5043	174	5	p	p	PROPN
ejpam-5043	174	6	(	(	PUNCT
ejpam-5043	174	7	τ	τ	PROPN
ejpam-5043	174	8	,	,	PUNCT
ejpam-5043	174	9	z(τ))(tn+1	z(τ))(tn+1	PROPN
ejpam-5043	174	10	−	−	PROPN
ejpam-5043	174	11	τ)α−1dτ	τ)α−1dτ	PROPN
ejpam-5043	174	12	.	.	PUNCT
ejpam-5043	175	1	(	(	PUNCT
ejpam-5043	175	2	11	11	NUM
ejpam-5043	175	3	)	)	PUNCT
ejpam-5043	175	4	within	within	ADP
ejpam-5043	175	5	[	[	X
ejpam-5043	175	6	tk	tk	X
ejpam-5043	175	7	,	,	PUNCT
ejpam-5043	175	8	tk+1	tk+1	PROPN
ejpam-5043	175	9	]	]	PUNCT
ejpam-5043	175	10	,	,	PUNCT
ejpam-5043	175	11	the	the	DET
ejpam-5043	175	12	functions	function	NOUN
ejpam-5043	175	13	e(tn	e(tn	NOUN
ejpam-5043	175	14	,	,	PUNCT
ejpam-5043	175	15	x(tn	x(tn	PROPN
ejpam-5043	175	16	)	)	PUNCT
ejpam-5043	175	17	)	)	PUNCT
ejpam-5043	175	18	,	,	PUNCT
ejpam-5043	175	19	h(tn	h(tn	NOUN
ejpam-5043	175	20	,	,	PUNCT
ejpam-5043	175	21	y(tn	y(tn	NOUN
ejpam-5043	175	22	)	)	PUNCT
ejpam-5043	175	23	)	)	PUNCT
ejpam-5043	175	24	and	and	CCONJ
ejpam-5043	175	25	p	p	X
ejpam-5043	175	26	(	(	PUNCT
ejpam-5043	175	27	tn	tn	PROPN
ejpam-5043	175	28	,	,	PUNCT
ejpam-5043	175	29	z(tn	z(tn	NOUN
ejpam-5043	175	30	)	)	PUNCT
ejpam-5043	175	31	)	)	PUNCT
ejpam-5043	175	32	can	can	AUX
ejpam-5043	175	33	be	be	AUX
ejpam-5043	175	34	approximated	approximate	VERB
ejpam-5043	175	35	using	use	VERB
ejpam-5043	175	36	two	two	NUM
ejpam-5043	175	37	-	-	PUNCT
ejpam-5043	175	38	step	step	NOUN
ejpam-5043	175	39	lagrange	lagrange	NOUN
ejpam-5043	175	40	polynomial	polynomial	ADJ
ejpam-5043	175	41	interpolation	interpolation	NOUN
ejpam-5043	175	42	:	:	PUNCT
ejpam-5043	175	43	p1k(τ	p1k(τ	NOUN
ejpam-5043	175	44	)	)	PUNCT
ejpam-5043	175	45	≃	≃	PROPN
ejpam-5043	175	46	e(tk	e(tk	PROPN
ejpam-5043	175	47	,	,	PUNCT
ejpam-5043	175	48	xk	xk	NOUN
ejpam-5043	175	49	)	)	PUNCT
ejpam-5043	175	50	h	h	NOUN
ejpam-5043	175	51	(	(	PUNCT
ejpam-5043	175	52	τ	τ	X
ejpam-5043	175	53	−	−	PROPN
ejpam-5043	175	54	tk−1)−	tk−1)−	NOUN
ejpam-5043	175	55	e(tk−1	e(tk−1	X
ejpam-5043	175	56	,	,	PUNCT
ejpam-5043	175	57	xk−1	xk−1	PROPN
ejpam-5043	175	58	)	)	PUNCT
ejpam-5043	175	59	h	h	NOUN
ejpam-5043	175	60	(	(	PUNCT
ejpam-5043	175	61	τ	τ	PROPN
ejpam-5043	175	62	−	−	PROPN
ejpam-5043	175	63	tk	tk	PROPN
ejpam-5043	175	64	)	)	PUNCT
ejpam-5043	175	65	,	,	PUNCT
ejpam-5043	175	66	(	(	PUNCT
ejpam-5043	175	67	12	12	NUM
ejpam-5043	175	68	)	)	PUNCT
ejpam-5043	175	69	p2k(τ	p2k(τ	PROPN
ejpam-5043	175	70	)	)	PUNCT
ejpam-5043	175	71	≃	≃	VERB
ejpam-5043	175	72	h(tk	h(tk	PROPN
ejpam-5043	175	73	,	,	PUNCT
ejpam-5043	175	74	yk	yk	PROPN
ejpam-5043	175	75	)	)	PUNCT
ejpam-5043	175	76	h	h	NOUN
ejpam-5043	175	77	(	(	PUNCT
ejpam-5043	175	78	τ	τ	X
ejpam-5043	175	79	−	−	PROPN
ejpam-5043	175	80	tk−1)−	tk−1)−	PROPN
ejpam-5043	175	81	h(tk−1	h(tk−1	PROPN
ejpam-5043	175	82	,	,	PUNCT
ejpam-5043	175	83	yk−1	yk−1	PROPN
ejpam-5043	175	84	)	)	PUNCT
ejpam-5043	175	85	h	h	NOUN
ejpam-5043	175	86	(	(	PUNCT
ejpam-5043	175	87	τ	τ	PROPN
ejpam-5043	175	88	−	−	PROPN
ejpam-5043	175	89	tk	tk	PROPN
ejpam-5043	175	90	)	)	PUNCT
ejpam-5043	175	91	,	,	PUNCT
ejpam-5043	175	92	(	(	PUNCT
ejpam-5043	175	93	13	13	X
ejpam-5043	175	94	)	)	PUNCT
ejpam-5043	175	95	p3k(τ	p3k(τ	PROPN
ejpam-5043	175	96	)	)	PUNCT
ejpam-5043	176	1	≃	≃	VERB
ejpam-5043	176	2	p	p	PROPN
ejpam-5043	176	3	(	(	PUNCT
ejpam-5043	176	4	tk	tk	PROPN
ejpam-5043	176	5	,	,	PUNCT
ejpam-5043	176	6	zk	zk	PROPN
ejpam-5043	176	7	)	)	PUNCT
ejpam-5043	176	8	h	h	NOUN
ejpam-5043	176	9	(	(	PUNCT
ejpam-5043	176	10	τ	τ	X
ejpam-5043	176	11	−	−	PROPN
ejpam-5043	177	1	tk−1)−	tk−1)−	PROPN
ejpam-5043	177	2	p	p	X
ejpam-5043	177	3	(	(	PUNCT
ejpam-5043	177	4	tk−1	tk−1	PROPN
ejpam-5043	177	5	,	,	PUNCT
ejpam-5043	177	6	zk−1	zk−1	PROPN
ejpam-5043	177	7	)	)	PUNCT
ejpam-5043	177	8	h	h	NOUN
ejpam-5043	177	9	(	(	PUNCT
ejpam-5043	177	10	τ	τ	PROPN
ejpam-5043	177	11	−	−	PROPN
ejpam-5043	177	12	tk	tk	PROPN
ejpam-5043	177	13	)	)	PUNCT
ejpam-5043	177	14	.	.	PUNCT
ejpam-5043	178	1	(	(	PUNCT
ejpam-5043	178	2	14	14	NUM
ejpam-5043	178	3	)	)	PUNCT
ejpam-5043	178	4	the	the	DET
ejpam-5043	178	5	above	above	ADJ
ejpam-5043	178	6	approximation	approximation	NOUN
ejpam-5043	178	7	can	can	AUX
ejpam-5043	178	8	therefore	therefore	ADV
ejpam-5043	178	9	be	be	AUX
ejpam-5043	178	10	included	include	VERB
ejpam-5043	178	11	in	in	ADP
ejpam-5043	178	12	(	(	PUNCT
ejpam-5043	178	13	12	12	NUM
ejpam-5043	178	14	)	)	PUNCT
ejpam-5043	178	15	,	,	PUNCT
ejpam-5043	178	16	(	(	PUNCT
ejpam-5043	178	17	13	13	NUM
ejpam-5043	178	18	)	)	PUNCT
ejpam-5043	178	19	and	and	CCONJ
ejpam-5043	178	20	(	(	PUNCT
ejpam-5043	178	21	14	14	NUM
ejpam-5043	178	22	)	)	PUNCT
ejpam-5043	178	23	to	to	PART
ejpam-5043	178	24	produce	produce	VERB
ejpam-5043	178	25	.	.	PUNCT
ejpam-5043	178	26	xn+1	xn+1	PART
ejpam-5043	179	1	=	=	PUNCT
ejpam-5043	179	2	x0	x0	PROPN
ejpam-5043	179	3	+	+	CCONJ
ejpam-5043	179	4	(	(	PUNCT
ejpam-5043	179	5	1−	1−	NUM
ejpam-5043	179	6	α	α	NOUN
ejpam-5043	179	7	)	)	PUNCT
ejpam-5043	179	8	abc(α	abc(α	PROPN
ejpam-5043	179	9	)	)	PUNCT
ejpam-5043	179	10	e(tn	e(tn	NOUN
ejpam-5043	179	11	,	,	PUNCT
ejpam-5043	179	12	x(tn	x(tn	NOUN
ejpam-5043	179	13	)	)	PUNCT
ejpam-5043	179	14	)	)	PUNCT
ejpam-5043	180	1	+	+	CCONJ
ejpam-5043	180	2	α	α	X
ejpam-5043	180	3	abc(α)γ(α	abc(α)γ(α	PROPN
ejpam-5043	180	4	)	)	PUNCT
ejpam-5043	181	1	n∑	n∑	PROPN
ejpam-5043	181	2	k=0	k=0	PROPN
ejpam-5043	181	3	(	(	PUNCT
ejpam-5043	181	4	e(tk	e(tk	PROPN
ejpam-5043	181	5	,	,	PUNCT
ejpam-5043	181	6	xk	xk	NOUN
ejpam-5043	181	7	)	)	PUNCT
ejpam-5043	182	1	h	h	NOUN
ejpam-5043	182	2	∫	∫	PROPN
ejpam-5043	183	1	tk+1	tk+1	NUM
ejpam-5043	183	2	tk	tk	PROPN
ejpam-5043	183	3	(	(	PUNCT
ejpam-5043	183	4	τ	τ	PROPN
ejpam-5043	183	5	−	−	PROPN
ejpam-5043	183	6	tk−1)(tn+1	tk−1)(tn+1	NUM
ejpam-5043	183	7	−	−	NOUN
ejpam-5043	183	8	τ)α−1dτ	τ)α−1dτ	ADJ
ejpam-5043	183	9	−e(tk−1	−e(tk−1	PROPN
ejpam-5043	183	10	,	,	PUNCT
ejpam-5043	183	11	xk−1	xk−1	PROPN
ejpam-5043	183	12	)	)	PUNCT
ejpam-5043	184	1	h	h	NOUN
ejpam-5043	184	2	∫	∫	PROPN
ejpam-5043	185	1	tk+1	tk+1	NUM
ejpam-5043	185	2	tk	tk	PROPN
ejpam-5043	185	3	(	(	PUNCT
ejpam-5043	185	4	τ	τ	PROPN
ejpam-5043	185	5	−	−	PROPN
ejpam-5043	185	6	tk)(tn+1	tk)(tn+1	PROPN
ejpam-5043	186	1	−	−	PROPN
ejpam-5043	186	2	τ)α−1dτ	τ)α−1dτ	ADJ
ejpam-5043	186	3	)	)	PUNCT
ejpam-5043	186	4	(	(	PUNCT
ejpam-5043	186	5	15	15	NUM
ejpam-5043	186	6	)	)	PUNCT
ejpam-5043	186	7	yn+1	yn+1	NOUN
ejpam-5043	187	1	=	=	PUNCT
ejpam-5043	187	2	y0	y0	PROPN
ejpam-5043	187	3	+	+	CCONJ
ejpam-5043	187	4	(	(	PUNCT
ejpam-5043	187	5	1−	1−	NUM
ejpam-5043	187	6	α	α	NOUN
ejpam-5043	187	7	)	)	PUNCT
ejpam-5043	187	8	abc(α	abc(α	PROPN
ejpam-5043	187	9	)	)	PUNCT
ejpam-5043	187	10	h(tn	h(tn	NOUN
ejpam-5043	187	11	,	,	PUNCT
ejpam-5043	187	12	y(tn	y(tn	NOUN
ejpam-5043	187	13	)	)	PUNCT
ejpam-5043	187	14	)	)	PUNCT
ejpam-5043	188	1	+	+	CCONJ
ejpam-5043	188	2	α	α	X
ejpam-5043	188	3	abc(α)γ(α	abc(α)γ(α	PROPN
ejpam-5043	188	4	)	)	PUNCT
ejpam-5043	189	1	n∑	n∑	PROPN
ejpam-5043	189	2	k=0	k=0	PROPN
ejpam-5043	189	3	(	(	PUNCT
ejpam-5043	189	4	h(tk	h(tk	PROPN
ejpam-5043	189	5	,	,	PUNCT
ejpam-5043	189	6	yk	yk	PROPN
ejpam-5043	189	7	)	)	PUNCT
ejpam-5043	190	1	h	h	NOUN
ejpam-5043	190	2	∫	∫	PROPN
ejpam-5043	191	1	tk+1	tk+1	NUM
ejpam-5043	191	2	tk	tk	PROPN
ejpam-5043	191	3	(	(	PUNCT
ejpam-5043	191	4	τ	τ	PROPN
ejpam-5043	191	5	−	−	PROPN
ejpam-5043	191	6	tk−1)(tn+1	tk−1)(tn+1	NUM
ejpam-5043	191	7	−	−	NOUN
ejpam-5043	191	8	τ)α−1dτ	τ)α−1dτ	ADJ
ejpam-5043	191	9	−h(tk−1	−h(tk−1	NUM
ejpam-5043	191	10	,	,	PUNCT
ejpam-5043	191	11	yk−1	yk−1	PROPN
ejpam-5043	191	12	)	)	PUNCT
ejpam-5043	192	1	h	h	NOUN
ejpam-5043	192	2	∫	∫	PROPN
ejpam-5043	193	1	tk+1	tk+1	NUM
ejpam-5043	193	2	tk	tk	PROPN
ejpam-5043	193	3	(	(	PUNCT
ejpam-5043	193	4	τ	τ	PROPN
ejpam-5043	193	5	−	−	PROPN
ejpam-5043	193	6	tk)(tn+1	tk)(tn+1	PROPN
ejpam-5043	194	1	−	−	PROPN
ejpam-5043	194	2	τ)α−1dτ	τ)α−1dτ	ADJ
ejpam-5043	194	3	)	)	PUNCT
ejpam-5043	194	4	(	(	PUNCT
ejpam-5043	194	5	16	16	NUM
ejpam-5043	194	6	)	)	PUNCT
ejpam-5043	194	7	zn+1	zn+1	PROPN
ejpam-5043	195	1	=	=	VERB
ejpam-5043	195	2	z0	z0	PROPN
ejpam-5043	195	3	+	+	CCONJ
ejpam-5043	195	4	(	(	PUNCT
ejpam-5043	195	5	1−	1−	NUM
ejpam-5043	195	6	α	α	NOUN
ejpam-5043	195	7	)	)	PUNCT
ejpam-5043	195	8	abc(α	abc(α	PROPN
ejpam-5043	195	9	)	)	PUNCT
ejpam-5043	195	10	p	p	NOUN
ejpam-5043	195	11	(	(	PUNCT
ejpam-5043	195	12	tn	tn	NOUN
ejpam-5043	195	13	,	,	PUNCT
ejpam-5043	195	14	z(tn	z(tn	NOUN
ejpam-5043	195	15	)	)	PUNCT
ejpam-5043	195	16	)	)	PUNCT
ejpam-5043	196	1	+	+	CCONJ
ejpam-5043	196	2	α	α	X
ejpam-5043	196	3	abc(α)γ(α	abc(α)γ(α	PROPN
ejpam-5043	196	4	)	)	PUNCT
ejpam-5043	197	1	n∑	n∑	PUNCT
ejpam-5043	197	2	k=0	k=0	PROPN
ejpam-5043	197	3	(	(	PUNCT
ejpam-5043	197	4	p	p	X
ejpam-5043	197	5	(	(	PUNCT
ejpam-5043	197	6	tk	tk	PROPN
ejpam-5043	197	7	,	,	PUNCT
ejpam-5043	197	8	zk	zk	PROPN
ejpam-5043	197	9	)	)	PUNCT
ejpam-5043	198	1	h	h	NOUN
ejpam-5043	198	2	∫	∫	PROPN
ejpam-5043	199	1	tk+1	tk+1	NUM
ejpam-5043	199	2	tk	tk	PROPN
ejpam-5043	199	3	(	(	PUNCT
ejpam-5043	199	4	τ	τ	PROPN
ejpam-5043	199	5	−	−	PROPN
ejpam-5043	199	6	tk−1)(tn+1	tk−1)(tn+1	NUM
ejpam-5043	199	7	−	−	NOUN
ejpam-5043	199	8	τ)α−1dτ	τ)α−1dτ	ADJ
ejpam-5043	199	9	−p	−p	ADJ
ejpam-5043	199	10	(	(	PUNCT
ejpam-5043	199	11	tk−1	tk−1	PROPN
ejpam-5043	199	12	,	,	PUNCT
ejpam-5043	199	13	zk−1	zk−1	PROPN
ejpam-5043	199	14	)	)	PUNCT
ejpam-5043	199	15	h	h	NOUN
ejpam-5043	200	1	∫	∫	PROPN
ejpam-5043	200	2	tk+1	tk+1	NUM
ejpam-5043	200	3	tk	tk	PROPN
ejpam-5043	200	4	(	(	PUNCT
ejpam-5043	200	5	τ	τ	PROPN
ejpam-5043	200	6	−	−	PROPN
ejpam-5043	200	7	tk)(tn+1	tk)(tn+1	PROPN
ejpam-5043	201	1	−	−	PROPN
ejpam-5043	201	2	τ)α−1dτ	τ)α−1dτ	ADJ
ejpam-5043	201	3	)	)	PUNCT
ejpam-5043	201	4	(	(	PUNCT
ejpam-5043	201	5	17	17	NUM
ejpam-5043	201	6	)	)	PUNCT
ejpam-5043	201	7	k.	k.	PROPN
ejpam-5043	202	1	boulehmi	boulehmi	PROPN
ejpam-5043	202	2	/	/	SYM
ejpam-5043	202	3	eur	eur	PROPN
ejpam-5043	202	4	.	.	PUNCT
ejpam-5043	203	1	j.	j.	PROPN
ejpam-5043	203	2	pure	pure	PROPN
ejpam-5043	203	3	appl	appl	PROPN
ejpam-5043	203	4	.	.	PROPN
ejpam-5043	203	5	math	math	PROPN
ejpam-5043	203	6	,	,	PUNCT
ejpam-5043	203	7	17	17	NUM
ejpam-5043	203	8	(	(	PUNCT
ejpam-5043	203	9	1	1	NUM
ejpam-5043	203	10	)	)	PUNCT
ejpam-5043	203	11	(	(	PUNCT
ejpam-5043	203	12	2024	2024	NUM
ejpam-5043	203	13	)	)	PUNCT
ejpam-5043	203	14	,	,	PUNCT
ejpam-5043	203	15	445	445	NUM
ejpam-5043	203	16	-	-	SYM
ejpam-5043	203	17	461	461	NUM
ejpam-5043	203	18	452	452	NUM
ejpam-5043	203	19	the	the	DET
ejpam-5043	203	20	following	follow	VERB
ejpam-5043	203	21	numerical	numerical	ADJ
ejpam-5043	203	22	scheme	scheme	NOUN
ejpam-5043	203	23	is	be	AUX
ejpam-5043	203	24	obtained	obtain	VERB
ejpam-5043	203	25	after	after	ADP
ejpam-5043	203	26	solving	solve	VERB
ejpam-5043	203	27	the	the	DET
ejpam-5043	203	28	integrals	integral	NOUN
ejpam-5043	203	29	on	on	ADP
ejpam-5043	203	30	the	the	DET
ejpam-5043	203	31	right	right	NOUN
ejpam-5043	203	32	:	:	PUNCT
ejpam-5043	203	33	xn+1	xn+1	PART
ejpam-5043	204	1	=	=	PUNCT
ejpam-5043	204	2	x0	x0	PROPN
ejpam-5043	204	3	+	+	CCONJ
ejpam-5043	204	4	(	(	PUNCT
ejpam-5043	204	5	1−	1−	NUM
ejpam-5043	204	6	α	α	NOUN
ejpam-5043	204	7	)	)	PUNCT
ejpam-5043	204	8	abc(α	abc(α	PROPN
ejpam-5043	204	9	)	)	PUNCT
ejpam-5043	204	10	e(tn	e(tn	NOUN
ejpam-5043	204	11	,	,	PUNCT
ejpam-5043	204	12	x(tn	x(tn	NOUN
ejpam-5043	204	13	)	)	PUNCT
ejpam-5043	204	14	)	)	PUNCT
ejpam-5043	205	1	+	+	CCONJ
ejpam-5043	205	2	α	α	PROPN
ejpam-5043	205	3	abc(α	abc(α	PROPN
ejpam-5043	205	4	)	)	PUNCT
ejpam-5043	205	5	n∑	n∑	X
ejpam-5043	205	6	k=0	k=0	PROPN
ejpam-5043	206	1	[	[	X
ejpam-5043	206	2	hαe(tk	hαe(tk	NOUN
ejpam-5043	206	3	,	,	PUNCT
ejpam-5043	206	4	xk	xk	X
ejpam-5043	206	5	)	)	PUNCT
ejpam-5043	206	6	γ(α+	γ(α+	DET
ejpam-5043	206	7	2	2	NUM
ejpam-5043	206	8	)	)	PUNCT
ejpam-5043	206	9	(	(	PUNCT
ejpam-5043	206	10	(	(	PUNCT
ejpam-5043	206	11	n+	n+	X
ejpam-5043	206	12	1−	1−	NUM
ejpam-5043	206	13	k)α(n−	k)α(n−	VERB
ejpam-5043	206	14	k	k	PROPN
ejpam-5043	207	1	+	+	CCONJ
ejpam-5043	207	2	2	2	NUM
ejpam-5043	207	3	+	+	X
ejpam-5043	207	4	α)−	α)−	PROPN
ejpam-5043	207	5	(	(	PUNCT
ejpam-5043	207	6	n−	n−	NOUN
ejpam-5043	207	7	k)α(n−	k)α(n−	VERB
ejpam-5043	207	8	k	k	PROPN
ejpam-5043	208	1	+	+	CCONJ
ejpam-5043	208	2	2	2	NUM
ejpam-5043	208	3	+	+	NUM
ejpam-5043	208	4	2α	2α	NOUN
ejpam-5043	208	5	)	)	PUNCT
ejpam-5043	208	6	)	)	PUNCT
ejpam-5043	209	1	−	−	PROPN
ejpam-5043	209	2	hαe(tk−1	hαe(tk−1	PROPN
ejpam-5043	209	3	,	,	PUNCT
ejpam-5043	209	4	xk−1	xk−1	PROPN
ejpam-5043	209	5	)	)	PUNCT
ejpam-5043	209	6	γ(α+	γ(α+	DET
ejpam-5043	209	7	2	2	NUM
ejpam-5043	209	8	)	)	PUNCT
ejpam-5043	209	9	(	(	PUNCT
ejpam-5043	209	10	(	(	PUNCT
ejpam-5043	209	11	n+	n+	X
ejpam-5043	209	12	1−	1−	NUM
ejpam-5043	209	13	k)α+1	k)α+1	NOUN
ejpam-5043	209	14	−	−	PROPN
ejpam-5043	210	1	(	(	PUNCT
ejpam-5043	210	2	n−	n−	NOUN
ejpam-5043	210	3	k)α(n−	k)α(n−	VERB
ejpam-5043	210	4	k	k	PROPN
ejpam-5043	211	1	+	+	CCONJ
ejpam-5043	211	2	1	1	NUM
ejpam-5043	211	3	+	+	NUM
ejpam-5043	211	4	α	α	NOUN
ejpam-5043	211	5	)	)	PUNCT
ejpam-5043	211	6	)	)	PUNCT
ejpam-5043	211	7	]	]	PUNCT
ejpam-5043	211	8	(	(	PUNCT
ejpam-5043	211	9	18	18	NUM
ejpam-5043	211	10	)	)	PUNCT
ejpam-5043	211	11	yn+1	yn+1	NOUN
ejpam-5043	212	1	=	=	PUNCT
ejpam-5043	212	2	y0	y0	PROPN
ejpam-5043	212	3	+	+	CCONJ
ejpam-5043	212	4	(	(	PUNCT
ejpam-5043	212	5	1−	1−	NUM
ejpam-5043	212	6	α	α	NOUN
ejpam-5043	212	7	)	)	PUNCT
ejpam-5043	212	8	abc(α	abc(α	PROPN
ejpam-5043	212	9	)	)	PUNCT
ejpam-5043	212	10	h(tn	h(tn	NOUN
ejpam-5043	212	11	,	,	PUNCT
ejpam-5043	212	12	y(tn	y(tn	NOUN
ejpam-5043	212	13	)	)	PUNCT
ejpam-5043	212	14	)	)	PUNCT
ejpam-5043	213	1	+	+	CCONJ
ejpam-5043	213	2	α	α	PROPN
ejpam-5043	213	3	abc(α	abc(α	PROPN
ejpam-5043	213	4	)	)	PUNCT
ejpam-5043	213	5	n∑	n∑	X
ejpam-5043	213	6	k=0	k=0	PROPN
ejpam-5043	214	1	[	[	X
ejpam-5043	214	2	hαh(tk	hαh(tk	NOUN
ejpam-5043	214	3	,	,	PUNCT
ejpam-5043	214	4	yk	yk	PROPN
ejpam-5043	214	5	)	)	PUNCT
ejpam-5043	214	6	γ(α+	γ(α+	DET
ejpam-5043	214	7	2	2	NUM
ejpam-5043	214	8	)	)	PUNCT
ejpam-5043	214	9	(	(	PUNCT
ejpam-5043	214	10	(	(	PUNCT
ejpam-5043	214	11	n+	n+	X
ejpam-5043	214	12	1−	1−	NUM
ejpam-5043	214	13	k)α(n−	k)α(n−	VERB
ejpam-5043	214	14	k	k	PROPN
ejpam-5043	215	1	+	+	CCONJ
ejpam-5043	215	2	2	2	NUM
ejpam-5043	215	3	+	+	X
ejpam-5043	215	4	α)−	α)−	PROPN
ejpam-5043	215	5	(	(	PUNCT
ejpam-5043	215	6	n−	n−	NOUN
ejpam-5043	215	7	k)α(n−	k)α(n−	VERB
ejpam-5043	215	8	k	k	PROPN
ejpam-5043	216	1	+	+	CCONJ
ejpam-5043	216	2	2	2	NUM
ejpam-5043	216	3	+	+	NUM
ejpam-5043	216	4	2α	2α	NOUN
ejpam-5043	216	5	)	)	PUNCT
ejpam-5043	216	6	)	)	PUNCT
ejpam-5043	217	1	−	−	PROPN
ejpam-5043	217	2	hαh(tk−1	hαh(tk−1	NOUN
ejpam-5043	217	3	,	,	PUNCT
ejpam-5043	217	4	yk−1	yk−1	PROPN
ejpam-5043	217	5	)	)	PUNCT
ejpam-5043	217	6	γ(α+	γ(α+	DET
ejpam-5043	217	7	2	2	NUM
ejpam-5043	217	8	)	)	PUNCT
ejpam-5043	217	9	(	(	PUNCT
ejpam-5043	217	10	(	(	PUNCT
ejpam-5043	217	11	n+	n+	X
ejpam-5043	217	12	1−	1−	NUM
ejpam-5043	217	13	k)α+1	k)α+1	NOUN
ejpam-5043	217	14	−	−	PROPN
ejpam-5043	217	15	(	(	PUNCT
ejpam-5043	217	16	n−	n−	NOUN
ejpam-5043	217	17	k)α(n−	k)α(n−	VERB
ejpam-5043	217	18	k	k	PROPN
ejpam-5043	218	1	+	+	CCONJ
ejpam-5043	218	2	1	1	NUM
ejpam-5043	218	3	+	+	NUM
ejpam-5043	218	4	α	α	NOUN
ejpam-5043	218	5	)	)	PUNCT
ejpam-5043	218	6	)	)	PUNCT
ejpam-5043	218	7	]	]	PUNCT
ejpam-5043	218	8	(	(	PUNCT
ejpam-5043	218	9	19	19	NUM
ejpam-5043	218	10	)	)	PUNCT
ejpam-5043	218	11	zn+1	zn+1	PROPN
ejpam-5043	219	1	=	=	VERB
ejpam-5043	219	2	z0	z0	PROPN
ejpam-5043	219	3	+	+	CCONJ
ejpam-5043	219	4	(	(	PUNCT
ejpam-5043	219	5	1−	1−	NUM
ejpam-5043	219	6	α	α	NOUN
ejpam-5043	219	7	)	)	PUNCT
ejpam-5043	219	8	abc(α	abc(α	PROPN
ejpam-5043	219	9	)	)	PUNCT
ejpam-5043	219	10	p	p	NOUN
ejpam-5043	219	11	(	(	PUNCT
ejpam-5043	219	12	tn	tn	NOUN
ejpam-5043	219	13	,	,	PUNCT
ejpam-5043	219	14	z(tn	z(tn	NOUN
ejpam-5043	219	15	)	)	PUNCT
ejpam-5043	219	16	)	)	PUNCT
ejpam-5043	220	1	+	+	CCONJ
ejpam-5043	220	2	α	α	PROPN
ejpam-5043	220	3	abc(α	abc(α	PROPN
ejpam-5043	220	4	)	)	PUNCT
ejpam-5043	220	5	n∑	n∑	X
ejpam-5043	220	6	k=0	k=0	PROPN
ejpam-5043	221	1	[	[	X
ejpam-5043	221	2	hαp	hαp	X
ejpam-5043	221	3	(	(	PUNCT
ejpam-5043	221	4	tk	tk	PROPN
ejpam-5043	221	5	,	,	PUNCT
ejpam-5043	221	6	zk	zk	PROPN
ejpam-5043	221	7	)	)	PUNCT
ejpam-5043	221	8	γ(α+	γ(α+	DET
ejpam-5043	221	9	2	2	NUM
ejpam-5043	221	10	)	)	PUNCT
ejpam-5043	221	11	(	(	PUNCT
ejpam-5043	221	12	(	(	PUNCT
ejpam-5043	221	13	n+	n+	X
ejpam-5043	221	14	1−	1−	NUM
ejpam-5043	221	15	k)α(n−	k)α(n−	VERB
ejpam-5043	221	16	k	k	PROPN
ejpam-5043	222	1	+	+	CCONJ
ejpam-5043	222	2	2	2	NUM
ejpam-5043	222	3	+	+	X
ejpam-5043	222	4	α)−	α)−	PROPN
ejpam-5043	222	5	(	(	PUNCT
ejpam-5043	222	6	n−	n−	NOUN
ejpam-5043	222	7	k)α(n−	k)α(n−	VERB
ejpam-5043	222	8	k	k	PROPN
ejpam-5043	223	1	+	+	CCONJ
ejpam-5043	223	2	2	2	NUM
ejpam-5043	223	3	+	+	NUM
ejpam-5043	223	4	2α	2α	NOUN
ejpam-5043	223	5	)	)	PUNCT
ejpam-5043	223	6	)	)	PUNCT
ejpam-5043	224	1	−	−	PROPN
ejpam-5043	224	2	hαp	hαp	NOUN
ejpam-5043	224	3	(	(	PUNCT
ejpam-5043	224	4	tk−1	tk−1	PROPN
ejpam-5043	224	5	,	,	PUNCT
ejpam-5043	224	6	zk−1	zk−1	PROPN
ejpam-5043	224	7	)	)	PUNCT
ejpam-5043	224	8	γ(α+	γ(α+	DET
ejpam-5043	224	9	2	2	NUM
ejpam-5043	224	10	)	)	PUNCT
ejpam-5043	224	11	(	(	PUNCT
ejpam-5043	224	12	(	(	PUNCT
ejpam-5043	224	13	n+	n+	X
ejpam-5043	224	14	1−	1−	NUM
ejpam-5043	224	15	k)α+1	k)α+1	NOUN
ejpam-5043	224	16	−	−	PROPN
ejpam-5043	224	17	(	(	PUNCT
ejpam-5043	224	18	n−	n−	NOUN
ejpam-5043	224	19	k)α(n−	k)α(n−	VERB
ejpam-5043	224	20	k	k	PROPN
ejpam-5043	225	1	+	+	CCONJ
ejpam-5043	225	2	1	1	NUM
ejpam-5043	225	3	+	+	NUM
ejpam-5043	225	4	α	α	NOUN
ejpam-5043	225	5	)	)	PUNCT
ejpam-5043	225	6	)	)	PUNCT
ejpam-5043	225	7	]	]	PUNCT
ejpam-5043	225	8	(	(	PUNCT
ejpam-5043	225	9	20	20	NUM
ejpam-5043	225	10	)	)	PUNCT
ejpam-5043	225	11	now	now	ADV
ejpam-5043	225	12	,	,	PUNCT
ejpam-5043	225	13	we	we	PRON
ejpam-5043	225	14	will	will	AUX
ejpam-5043	225	15	discuss	discuss	VERB
ejpam-5043	225	16	the	the	DET
ejpam-5043	225	17	application	application	NOUN
ejpam-5043	225	18	of	of	ADP
ejpam-5043	225	19	the	the	DET
ejpam-5043	225	20	newly	newly	ADV
ejpam-5043	225	21	developed	develop	VERB
ejpam-5043	225	22	numerical	numerical	ADJ
ejpam-5043	225	23	scheme	scheme	NOUN
ejpam-5043	225	24	for	for	ADP
ejpam-5043	225	25	the	the	DET
ejpam-5043	225	26	purpose	purpose	NOUN
ejpam-5043	225	27	to	to	PART
ejpam-5043	225	28	solve	solve	VERB
ejpam-5043	225	29	fractional	fractional	ADJ
ejpam-5043	225	30	differential	differential	NOUN
ejpam-5043	225	31	equations	equation	NOUN
ejpam-5043	225	32	.	.	PUNCT
ejpam-5043	226	1	4	4	X
ejpam-5043	226	2	.	.	X
ejpam-5043	226	3	applications	application	NOUN
ejpam-5043	226	4	of	of	ADP
ejpam-5043	226	5	the	the	DET
ejpam-5043	226	6	abc	abc	PROPN
ejpam-5043	226	7	-	-	PUNCT
ejpam-5043	226	8	fd	fd	PROPN
ejpam-5043	226	9	scheme	scheme	NOUN
ejpam-5043	226	10	in	in	ADP
ejpam-5043	226	11	this	this	DET
ejpam-5043	226	12	section	section	NOUN
ejpam-5043	226	13	,	,	PUNCT
ejpam-5043	226	14	we	we	PRON
ejpam-5043	226	15	emphasize	emphasize	VERB
ejpam-5043	226	16	the	the	DET
ejpam-5043	226	17	practicality	practicality	NOUN
ejpam-5043	226	18	and	and	CCONJ
ejpam-5043	226	19	applicability	applicability	NOUN
ejpam-5043	226	20	of	of	ADP
ejpam-5043	226	21	the	the	DET
ejpam-5043	226	22	abc	abc	PROPN
ejpam-5043	226	23	-	-	PUNCT
ejpam-5043	226	24	fd	fd	PROPN
ejpam-5043	226	25	scheme	scheme	NOUN
ejpam-5043	226	26	in	in	ADP
ejpam-5043	226	27	solving	solve	VERB
ejpam-5043	226	28	numerical	numerical	ADJ
ejpam-5043	226	29	problems	problem	NOUN
ejpam-5043	226	30	,	,	PUNCT
ejpam-5043	226	31	with	with	ADP
ejpam-5043	226	32	a	a	DET
ejpam-5043	226	33	focus	focus	NOUN
ejpam-5043	226	34	on	on	ADP
ejpam-5043	226	35	using	use	VERB
ejpam-5043	226	36	computational	computational	ADJ
ejpam-5043	226	37	simulations	simulation	NOUN
ejpam-5043	226	38	to	to	PART
ejpam-5043	226	39	assess	assess	VERB
ejpam-5043	226	40	its	its	PRON
ejpam-5043	226	41	effectiveness	effectiveness	NOUN
ejpam-5043	226	42	in	in	ADP
ejpam-5043	226	43	addressing	address	VERB
ejpam-5043	226	44	specific	specific	ADJ
ejpam-5043	226	45	test	test	NOUN
ejpam-5043	226	46	cases	case	NOUN
ejpam-5043	226	47	or	or	CCONJ
ejpam-5043	226	48	scenarios	scenario	NOUN
ejpam-5043	226	49	.	.	PUNCT
ejpam-5043	227	1	problem	problem	NOUN
ejpam-5043	227	2	1	1	NUM
ejpam-5043	227	3	.	.	PUNCT
ejpam-5043	228	1	our	our	PRON
ejpam-5043	228	2	first	first	ADJ
ejpam-5043	228	3	problem	problem	NOUN
ejpam-5043	228	4	revolves	revolve	VERB
ejpam-5043	228	5	around	around	ADP
ejpam-5043	228	6	tackling	tackle	VERB
ejpam-5043	228	7	the	the	DET
ejpam-5043	228	8	fractional	fractional	ADJ
ejpam-5043	228	9	bernoulli	bernoulli	NOUN
ejpam-5043	228	10	equation	equation	NOUN
ejpam-5043	228	11	.	.	PUNCT
ejpam-5043	229	1	abc	abc	PROPN
ejpam-5043	229	2	0	0	PROPN
ejpam-5043	230	1	dα	dα	PROPN
ejpam-5043	230	2	0	0	NUM
ejpam-5043	230	3	y(t	y(t	NUM
ejpam-5043	230	4	)	)	PUNCT
ejpam-5043	231	1	=	=	NOUN
ejpam-5043	231	2	y(t	y(t	NUM
ejpam-5043	231	3	)	)	PUNCT
ejpam-5043	232	1	+	+	CCONJ
ejpam-5043	232	2	y(t)2	y(t)2	PROPN
ejpam-5043	232	3	+	+	NOUN
ejpam-5043	232	4	1	1	NUM
ejpam-5043	232	5	,	,	PUNCT
ejpam-5043	232	6	0	0	NUM
ejpam-5043	232	7	<	<	X
ejpam-5043	232	8	α	α	PROPN
ejpam-5043	232	9	≤	≤	NUM
ejpam-5043	232	10	1	1	NUM
ejpam-5043	232	11	,	,	PUNCT
ejpam-5043	232	12	y(0	y(0	NOUN
ejpam-5043	232	13	)	)	PUNCT
ejpam-5043	232	14	=	=	NOUN
ejpam-5043	232	15	0	0	NUM
ejpam-5043	232	16	.	.	PUNCT
ejpam-5043	233	1	(	(	PUNCT
ejpam-5043	233	2	21	21	NUM
ejpam-5043	233	3	)	)	PUNCT
ejpam-5043	233	4	k.	k.	PROPN
ejpam-5043	233	5	boulehmi	boulehmi	PROPN
ejpam-5043	233	6	/	/	SYM
ejpam-5043	233	7	eur	eur	PROPN
ejpam-5043	233	8	.	.	PUNCT
ejpam-5043	234	1	j.	j.	PROPN
ejpam-5043	234	2	pure	pure	PROPN
ejpam-5043	234	3	appl	appl	PROPN
ejpam-5043	234	4	.	.	PROPN
ejpam-5043	234	5	math	math	PROPN
ejpam-5043	234	6	,	,	PUNCT
ejpam-5043	234	7	17	17	NUM
ejpam-5043	234	8	(	(	PUNCT
ejpam-5043	234	9	1	1	NUM
ejpam-5043	234	10	)	)	PUNCT
ejpam-5043	234	11	(	(	PUNCT
ejpam-5043	234	12	2024	2024	NUM
ejpam-5043	234	13	)	)	PUNCT
ejpam-5043	234	14	,	,	PUNCT
ejpam-5043	234	15	445	445	NUM
ejpam-5043	234	16	-	-	SYM
ejpam-5043	234	17	461	461	NUM
ejpam-5043	234	18	453	453	NUM
ejpam-5043	234	19	where	where	SCONJ
ejpam-5043	234	20	abc	abc	PROPN
ejpam-5043	234	21	0	0	PROPN
ejpam-5043	234	22	dα	dα	ADJ
ejpam-5043	234	23	0	0	NUM
ejpam-5043	234	24	is	be	AUX
ejpam-5043	234	25	the	the	DET
ejpam-5043	234	26	atangana	atangana	PROPN
ejpam-5043	234	27	-	-	PUNCT
ejpam-5043	234	28	baleanu	baleanu	PROPN
ejpam-5043	234	29	caputo	caputo	PROPN
ejpam-5043	234	30	fractional	fractional	PROPN
ejpam-5043	234	31	derivative	derivative	ADJ
ejpam-5043	234	32	operator	operator	NOUN
ejpam-5043	234	33	,	,	PUNCT
ejpam-5043	234	34	given	give	VERB
ejpam-5043	234	35	in	in	ADP
ejpam-5043	234	36	eq	eq	ADP
ejpam-5043	234	37	.	.	PUNCT
ejpam-5043	234	38	(	(	PUNCT
ejpam-5043	234	39	2	2	NUM
ejpam-5043	234	40	)	)	PUNCT
ejpam-5043	234	41	.	.	PUNCT
ejpam-5043	235	1	the	the	DET
ejpam-5043	235	2	exact	exact	ADJ
ejpam-5043	235	3	solution	solution	NOUN
ejpam-5043	235	4	of	of	ADP
ejpam-5043	235	5	the	the	DET
ejpam-5043	235	6	bernoulli	bernoulli	NOUN
ejpam-5043	235	7	eq	eq	ADP
ejpam-5043	235	8	.	.	PUNCT
ejpam-5043	236	1	(	(	PUNCT
ejpam-5043	236	2	21	21	NUM
ejpam-5043	236	3	)	)	PUNCT
ejpam-5043	236	4	shows	show	VERB
ejpam-5043	236	5	in	in	ADP
ejpam-5043	236	6	[	[	X
ejpam-5043	236	7	45	45	NUM
ejpam-5043	236	8	]	]	PUNCT
ejpam-5043	236	9	,	,	PUNCT
ejpam-5043	236	10	is	be	AUX
ejpam-5043	236	11	.	.	PUNCT
ejpam-5043	237	1	y(t	y(t	X
ejpam-5043	237	2	)	)	PUNCT
ejpam-5043	238	1	=	=	SYM
ejpam-5043	238	2	1	1	NUM
ejpam-5043	238	3	2	2	NUM
ejpam-5043	238	4	(	(	PUNCT
ejpam-5043	238	5	√	√	NUM
ejpam-5043	238	6	3	3	NUM
ejpam-5043	238	7	tan	tan	NOUN
ejpam-5043	238	8	(	(	PUNCT
ejpam-5043	238	9	1	1	NUM
ejpam-5043	238	10	6	6	NUM
ejpam-5043	238	11	(	(	PUNCT
ejpam-5043	238	12	3	3	NUM
ejpam-5043	238	13	√	√	PROPN
ejpam-5043	238	14	3t+	3t+	NUM
ejpam-5043	238	15	π)−	π)−	PROPN
ejpam-5043	238	16	1	1	NUM
ejpam-5043	238	17	)	)	PUNCT
ejpam-5043	238	18	)	)	PUNCT
ejpam-5043	239	1	(	(	PUNCT
ejpam-5043	239	2	22	22	X
ejpam-5043	239	3	)	)	PUNCT
ejpam-5043	239	4	the	the	DET
ejpam-5043	239	5	fractional	fractional	ADJ
ejpam-5043	239	6	bernoulli	bernoulli	NOUN
ejpam-5043	239	7	equation	equation	NOUN
ejpam-5043	239	8	(	(	PUNCT
ejpam-5043	239	9	22	22	NUM
ejpam-5043	239	10	)	)	PUNCT
ejpam-5043	239	11	has	have	VERB
ejpam-5043	239	12	an	an	DET
ejpam-5043	239	13	exact	exact	ADJ
ejpam-5043	239	14	solution	solution	NOUN
ejpam-5043	239	15	,	,	PUNCT
ejpam-5043	239	16	according	accord	VERB
ejpam-5043	239	17	to	to	ADP
ejpam-5043	239	18	the	the	DET
ejpam-5043	239	19	proposed	propose	VERB
ejpam-5043	239	20	abc	abc	PROPN
ejpam-5043	239	21	-	-	PUNCT
ejpam-5043	239	22	fd	fd	PROPN
ejpam-5043	239	23	scheme	scheme	NOUN
ejpam-5043	239	24	we	we	PRON
ejpam-5043	239	25	show	show	VERB
ejpam-5043	239	26	the	the	DET
ejpam-5043	239	27	results	result	NOUN
ejpam-5043	239	28	in	in	ADP
ejpam-5043	239	29	tables	table	NOUN
ejpam-5043	239	30	1	1	NUM
ejpam-5043	239	31	and	and	CCONJ
ejpam-5043	239	32	2	2	NUM
ejpam-5043	239	33	.	.	NOUN
ejpam-5043	239	34	table	table	NOUN
ejpam-5043	239	35	1	1	NUM
ejpam-5043	239	36	provides	provide	VERB
ejpam-5043	239	37	numerical	numerical	ADJ
ejpam-5043	239	38	results	result	NOUN
ejpam-5043	239	39	from	from	ADP
ejpam-5043	239	40	our	our	PRON
ejpam-5043	239	41	new	new	ADJ
ejpam-5043	239	42	abc	abc	PROPN
ejpam-5043	239	43	-	-	PUNCT
ejpam-5043	239	44	fd	fd	PROPN
ejpam-5043	239	45	scheme	scheme	NOUN
ejpam-5043	239	46	for	for	ADP
ejpam-5043	239	47	the	the	DET
ejpam-5043	239	48	fractional	fractional	ADJ
ejpam-5043	239	49	bernoulli	bernoulli	PROPN
ejpam-5043	239	50	equation	equation	NOUN
ejpam-5043	239	51	eq	eq	ADJ
ejpam-5043	239	52	.	.	PUNCT
ejpam-5043	240	1	(	(	PUNCT
ejpam-5043	240	2	21	21	NUM
ejpam-5043	240	3	)	)	PUNCT
ejpam-5043	240	4	when	when	SCONJ
ejpam-5043	240	5	α	α	NOUN
ejpam-5043	240	6	=	=	NOUN
ejpam-5043	240	7	1	1	NUM
ejpam-5043	240	8	at	at	ADP
ejpam-5043	240	9	t	t	NOUN
ejpam-5043	240	10	=	=	SYM
ejpam-5043	240	11	0.5	0.5	NUM
ejpam-5043	240	12	,	,	PUNCT
ejpam-5043	240	13	0.7	0.7	NUM
ejpam-5043	240	14	and	and	CCONJ
ejpam-5043	240	15	0.9	0.9	NUM
ejpam-5043	240	16	and	and	CCONJ
ejpam-5043	240	17	when	when	SCONJ
ejpam-5043	240	18	α	α	NOUN
ejpam-5043	241	1	=	=	NOUN
ejpam-5043	241	2	0.95	0.95	NUM
ejpam-5043	241	3	at	at	ADP
ejpam-5043	241	4	t	t	PROPN
ejpam-5043	241	5	=	=	SYM
ejpam-5043	241	6	0.5	0.5	NUM
ejpam-5043	241	7	,	,	PUNCT
ejpam-5043	241	8	0.7	0.7	NUM
ejpam-5043	241	9	and	and	CCONJ
ejpam-5043	241	10	0.9	0.9	NUM
ejpam-5043	241	11	in	in	ADP
ejpam-5043	241	12	table	table	NOUN
ejpam-5043	241	13	2	2	NUM
ejpam-5043	241	14	.	.	PUNCT
ejpam-5043	242	1	the	the	DET
ejpam-5043	242	2	numerical	numerical	ADJ
ejpam-5043	242	3	numbers	number	NOUN
ejpam-5043	242	4	we	we	PRON
ejpam-5043	242	5	provided	provide	VERB
ejpam-5043	242	6	matched	match	VERB
ejpam-5043	242	7	the	the	DET
ejpam-5043	242	8	exact	exact	ADJ
ejpam-5043	242	9	result	result	NOUN
ejpam-5043	242	10	,	,	PUNCT
ejpam-5043	242	11	and	and	CCONJ
ejpam-5043	242	12	the	the	DET
ejpam-5043	242	13	step	step	NOUN
ejpam-5043	242	14	size	size	NOUN
ejpam-5043	242	15	h	h	NOUN
ejpam-5043	242	16	is	be	AUX
ejpam-5043	242	17	tiny	tiny	ADJ
ejpam-5043	242	18	enough	enough	ADV
ejpam-5043	242	19	.	.	PUNCT
ejpam-5043	243	1	it	it	PRON
ejpam-5043	243	2	is	be	AUX
ejpam-5043	243	3	observed	observe	VERB
ejpam-5043	243	4	that	that	SCONJ
ejpam-5043	243	5	accuracy	accuracy	NOUN
ejpam-5043	243	6	increases	increase	VERB
ejpam-5043	243	7	with	with	ADP
ejpam-5043	243	8	decreasing	decrease	VERB
ejpam-5043	243	9	step	step	NOUN
ejpam-5043	243	10	size	size	NOUN
ejpam-5043	243	11	h.	h.	PROPN
ejpam-5043	243	12	we	we	PRON
ejpam-5043	243	13	can	can	AUX
ejpam-5043	243	14	observe	observe	VERB
ejpam-5043	243	15	the	the	DET
ejpam-5043	243	16	numerical	numerical	ADJ
ejpam-5043	243	17	stability	stability	NOUN
ejpam-5043	243	18	feature	feature	NOUN
ejpam-5043	243	19	of	of	ADP
ejpam-5043	243	20	the	the	DET
ejpam-5043	243	21	abc	abc	PROPN
ejpam-5043	243	22	-	-	PUNCT
ejpam-5043	243	23	fd	fd	PROPN
ejpam-5043	243	24	scheme	scheme	NOUN
ejpam-5043	243	25	according	accord	VERB
ejpam-5043	243	26	to	to	ADP
ejpam-5043	243	27	the	the	DET
ejpam-5043	243	28	convergence	convergence	NOUN
ejpam-5043	243	29	of	of	ADP
ejpam-5043	243	30	the	the	DET
ejpam-5043	243	31	numerical	numerical	ADJ
ejpam-5043	243	32	data	datum	NOUN
ejpam-5043	243	33	in	in	ADP
ejpam-5043	243	34	table	table	NOUN
ejpam-5043	243	35	1	1	NUM
ejpam-5043	243	36	and	and	CCONJ
ejpam-5043	243	37	table	table	NOUN
ejpam-5043	243	38	2	2	NUM
ejpam-5043	243	39	.	.	PUNCT
ejpam-5043	243	40	table	table	NOUN
ejpam-5043	243	41	1	1	NUM
ejpam-5043	243	42	:	:	PUNCT
ejpam-5043	243	43	solutions	solution	NOUN
ejpam-5043	243	44	of	of	ADP
ejpam-5043	243	45	equation	equation	NOUN
ejpam-5043	243	46	(	(	PUNCT
ejpam-5043	243	47	21	21	NUM
ejpam-5043	243	48	)	)	PUNCT
ejpam-5043	243	49	where	where	SCONJ
ejpam-5043	243	50	α	α	NOUN
ejpam-5043	243	51	=	=	NOUN
ejpam-5043	243	52	0.95	0.95	NUM
ejpam-5043	243	53	.	.	PUNCT
ejpam-5043	244	1	h	h	PROPN
ejpam-5043	244	2	t	t	NOUN
ejpam-5043	244	3	=	=	NUM
ejpam-5043	244	4	0.5	0.5	NUM
ejpam-5043	244	5	t	t	NOUN
ejpam-5043	244	6	=	=	SYM
ejpam-5043	244	7	0.7	0.7	NUM
ejpam-5043	244	8	t	t	NOUN
ejpam-5043	244	9	=	=	SYM
ejpam-5043	244	10	0.9	0.9	NUM
ejpam-5043	244	11	1/320	1/320	NUM
ejpam-5043	244	12	0.727894644424645	0.727894644424645	NUM
ejpam-5043	244	13	1.334617072292245	1.334617072292245	NUM
ejpam-5043	244	14	2.655787522792942	2.655787522792942	NUM
ejpam-5043	244	15	1/640	1/640	NUM
ejpam-5043	244	16	0.727919150293686	0.727919150293686	NUM
ejpam-5043	244	17	1.334627794673236	1.334627794673236	NUM
ejpam-5043	244	18	2.655815432421105	2.655815432421105	NUM
ejpam-5043	244	19	1/1280	1/1280	NUM
ejpam-5043	244	20	0.727968161290851	0.727968161290851	NUM
ejpam-5043	244	21	1.334637692200060	1.334637692200060	NUM
ejpam-5043	244	22	2.655841194787946	2.655841194787946	NUM
ejpam-5043	244	23	1/2560	1/2560	NUM
ejpam-5043	244	24	0.727989165701209	0.727989165701209	NUM
ejpam-5043	244	25	1.334646856529120	1.334646856529120	NUM
ejpam-5043	244	26	2.655865048517234	2.655865048517234	NUM
ejpam-5043	244	27	1/5120	1/5120	NUM
ejpam-5043	244	28	0.727997567414455	0.727997567414455	NUM
ejpam-5043	244	29	1.334655366222233	1.334655366222233	NUM
ejpam-5043	244	30	2.655887198138255	2.655887198138255	NUM
ejpam-5043	244	31	1/10240	1/10240	NUM
ejpam-5043	244	32	0.727993511418589	0.727993511418589	NUM
ejpam-5043	244	33	1.333663289004453	1.333663289004453	NUM
ejpam-5043	244	34	2.655907819965030	2.655907819965030	NUM
ejpam-5043	244	35	exact	exact	NOUN
ejpam-5043	244	36	0.727423275682290	0.727423275682290	NUM
ejpam-5043	244	37	1.333623995935720	1.333623995935720	NUM
ejpam-5043	244	38	2.653204588689912	2.653204588689912	NUM
ejpam-5043	244	39	table	table	NOUN
ejpam-5043	244	40	2	2	NUM
ejpam-5043	244	41	:	:	PUNCT
ejpam-5043	244	42	solutions	solution	NOUN
ejpam-5043	244	43	of	of	ADP
ejpam-5043	244	44	equation	equation	NOUN
ejpam-5043	244	45	(	(	PUNCT
ejpam-5043	244	46	21	21	NUM
ejpam-5043	244	47	)	)	PUNCT
ejpam-5043	244	48	where	where	SCONJ
ejpam-5043	244	49	α	α	NOUN
ejpam-5043	244	50	=	=	NOUN
ejpam-5043	244	51	0.95	0.95	NUM
ejpam-5043	244	52	.	.	PUNCT
ejpam-5043	245	1	h	h	PROPN
ejpam-5043	245	2	t	t	NOUN
ejpam-5043	245	3	=	=	NUM
ejpam-5043	245	4	0.5	0.5	NUM
ejpam-5043	245	5	t	t	NOUN
ejpam-5043	245	6	=	=	SYM
ejpam-5043	245	7	0.7	0.7	NUM
ejpam-5043	245	8	t	t	NOUN
ejpam-5043	245	9	=	=	SYM
ejpam-5043	245	10	0.9	0.9	NUM
ejpam-5043	245	11	1/320	1/320	NUM
ejpam-5043	245	12	1.011233122696145	1.011233122696145	NUM
ejpam-5043	245	13	2.254033666282457	2.254033666282457	NUM
ejpam-5043	245	14	4.447754640984550	4.447754640984550	NUM
ejpam-5043	245	15	1/640	1/640	NUM
ejpam-5043	245	16	1.011244500276947	1.011244500276947	NUM
ejpam-5043	245	17	2.254080841564283	2.254080841564283	NUM
ejpam-5043	245	18	4.455050084792259	4.455050084792259	NUM
ejpam-5043	245	19	1/1280	1/1280	NUM
ejpam-5043	245	20	1.011255002684663	1.011255002684663	NUM
ejpam-5043	245	21	2.254124389955685	2.254124389955685	NUM
ejpam-5043	245	22	4.451529969778694	4.451529969778694	NUM
ejpam-5043	245	23	1/2560	1/2560	NUM
ejpam-5043	245	24	1.011264727101195	1.011264727101195	NUM
ejpam-5043	245	25	2.254164714268654	2.254164714268654	NUM
ejpam-5043	245	26	4.452791939534118	4.452791939534118	NUM
ejpam-5043	245	27	1/5120	1/5120	NUM
ejpam-5043	245	28	1.011273756967766	1.011273756967766	NUM
ejpam-5043	245	29	2.254202159766417	2.254202159766417	NUM
ejpam-5043	245	30	4.453802791022117	4.453802791022117	NUM
ejpam-5043	245	31	1/10240	1/10240	NUM
ejpam-5043	245	32	1.011282164123349	1.011282164123349	NUM
ejpam-5043	245	33	2.254237024056137	2.254237024056137	NUM
ejpam-5043	245	34	4.457911499398058	4.457911499398058	NUM
ejpam-5043	245	35	figure	figure	NOUN
ejpam-5043	245	36	1	1	NUM
ejpam-5043	245	37	compares	compare	VERB
ejpam-5043	245	38	eq	eq	ADP
ejpam-5043	245	39	.	.	PUNCT
ejpam-5043	246	1	(	(	PUNCT
ejpam-5043	246	2	21	21	NUM
ejpam-5043	246	3	)	)	PUNCT
ejpam-5043	246	4	the	the	DET
ejpam-5043	246	5	exact	exact	ADJ
ejpam-5043	246	6	and	and	CCONJ
ejpam-5043	246	7	numerical	numerical	ADJ
ejpam-5043	246	8	solutions	solution	NOUN
ejpam-5043	246	9	of	of	ADP
ejpam-5043	246	10	eq	eq	PROPN
ejpam-5043	246	11	.	.	PUNCT
ejpam-5043	247	1	(	(	PUNCT
ejpam-5043	247	2	22	22	NUM
ejpam-5043	247	3	)	)	PUNCT
ejpam-5043	247	4	.	.	PUNCT
ejpam-5043	248	1	when	when	SCONJ
ejpam-5043	248	2	t	t	NOUN
ejpam-5043	248	3	=	=	SYM
ejpam-5043	248	4	1000	1000	NUM
ejpam-5043	248	5	,	,	PUNCT
ejpam-5043	248	6	we	we	PRON
ejpam-5043	248	7	plot	plot	VERB
ejpam-5043	248	8	the	the	DET
ejpam-5043	248	9	numerical	numerical	ADJ
ejpam-5043	248	10	solutions	solution	NOUN
ejpam-5043	248	11	of	of	ADP
ejpam-5043	248	12	eq	eq	PROPN
ejpam-5043	248	13	.	.	PUNCT
ejpam-5043	249	1	(	(	PUNCT
ejpam-5043	249	2	21	21	NUM
ejpam-5043	249	3	)	)	PUNCT
ejpam-5043	249	4	with	with	ADP
ejpam-5043	249	5	different	different	ADJ
ejpam-5043	249	6	values	value	NOUN
ejpam-5043	249	7	of	of	ADP
ejpam-5043	249	8	α	α	NOUN
ejpam-5043	249	9	,	,	PUNCT
ejpam-5043	249	10	and	and	CCONJ
ejpam-5043	249	11	the	the	DET
ejpam-5043	249	12	novel	novel	ADJ
ejpam-5043	249	13	scheme	scheme	NOUN
ejpam-5043	249	14	simulates	simulate	NOUN
ejpam-5043	249	15	the	the	DET
ejpam-5043	249	16	problem	problem	NOUN
ejpam-5043	249	17	perfectly	perfectly	ADV
ejpam-5043	249	18	.	.	PUNCT
ejpam-5043	250	1	moreover	moreover	ADV
ejpam-5043	250	2	,	,	PUNCT
ejpam-5043	250	3	we	we	PRON
ejpam-5043	250	4	notice	notice	VERB
ejpam-5043	250	5	that	that	SCONJ
ejpam-5043	250	6	the	the	DET
ejpam-5043	250	7	numerical	numerical	ADJ
ejpam-5043	250	8	solutions	solution	NOUN
ejpam-5043	250	9	are	be	AUX
ejpam-5043	250	10	close	close	ADJ
ejpam-5043	250	11	to	to	ADP
ejpam-5043	250	12	the	the	DET
ejpam-5043	250	13	exact	exact	ADJ
ejpam-5043	250	14	solution	solution	NOUN
ejpam-5043	250	15	.	.	PUNCT
ejpam-5043	251	1	problem	problem	NOUN
ejpam-5043	251	2	2	2	X
ejpam-5043	251	3	.	.	PUNCT
ejpam-5043	252	1	our	our	PRON
ejpam-5043	252	2	second	second	ADJ
ejpam-5043	252	3	problem	problem	NOUN
ejpam-5043	252	4	covers	cover	VERB
ejpam-5043	252	5	a	a	DET
ejpam-5043	252	6	basic	basic	ADJ
ejpam-5043	252	7	system	system	NOUN
ejpam-5043	252	8	that	that	PRON
ejpam-5043	252	9	displays	display	VERB
ejpam-5043	252	10	chaotic	chaotic	ADJ
ejpam-5043	252	11	behavior	behavior	NOUN
ejpam-5043	252	12	is	be	AUX
ejpam-5043	252	13	the	the	DET
ejpam-5043	252	14	rössler	rössler	NOUN
ejpam-5043	252	15	system	system	NOUN
ejpam-5043	252	16	[	[	X
ejpam-5043	252	17	33	33	NUM
ejpam-5043	252	18	,	,	PUNCT
ejpam-5043	252	19	34	34	NUM
ejpam-5043	252	20	]	]	PUNCT
ejpam-5043	252	21	is	be	AUX
ejpam-5043	252	22	a	a	DET
ejpam-5043	252	23	multidimensional	multidimensional	ADJ
ejpam-5043	252	24	system	system	NOUN
ejpam-5043	252	25	that	that	PRON
ejpam-5043	252	26	is	be	AUX
ejpam-5043	252	27	comparable	comparable	ADJ
ejpam-5043	252	28	to	to	ADP
ejpam-5043	252	29	the	the	DET
ejpam-5043	252	30	k.	k.	PROPN
ejpam-5043	252	31	boulehmi	boulehmi	PROPN
ejpam-5043	252	32	/	/	SYM
ejpam-5043	252	33	eur	eur	PROPN
ejpam-5043	252	34	.	.	PUNCT
ejpam-5043	253	1	j.	j.	PROPN
ejpam-5043	253	2	pure	pure	PROPN
ejpam-5043	253	3	appl	appl	PROPN
ejpam-5043	253	4	.	.	PROPN
ejpam-5043	253	5	math	math	PROPN
ejpam-5043	253	6	,	,	PUNCT
ejpam-5043	253	7	17	17	NUM
ejpam-5043	253	8	(	(	PUNCT
ejpam-5043	253	9	1	1	NUM
ejpam-5043	253	10	)	)	PUNCT
ejpam-5043	253	11	(	(	PUNCT
ejpam-5043	253	12	2024	2024	NUM
ejpam-5043	253	13	)	)	PUNCT
ejpam-5043	253	14	,	,	PUNCT
ejpam-5043	253	15	445	445	NUM
ejpam-5043	253	16	-	-	SYM
ejpam-5043	253	17	461	461	NUM
ejpam-5043	253	18	454	454	NUM
ejpam-5043	253	19	figure	figure	NOUN
ejpam-5043	253	20	1	1	NUM
ejpam-5043	253	21	:	:	PUNCT
ejpam-5043	253	22	comparison	comparison	NOUN
ejpam-5043	253	23	of	of	ADP
ejpam-5043	253	24	numerical	numerical	ADJ
ejpam-5043	253	25	and	and	CCONJ
ejpam-5043	253	26	exact	exact	ADJ
ejpam-5043	253	27	solutions	solution	NOUN
ejpam-5043	253	28	of	of	ADP
ejpam-5043	253	29	equation	equation	NOUN
ejpam-5043	253	30	(	(	PUNCT
ejpam-5043	253	31	21	21	NUM
ejpam-5043	253	32	)	)	PUNCT
ejpam-5043	253	33	with	with	ADP
ejpam-5043	253	34	different	different	ADJ
ejpam-5043	253	35	t	t	PROPN
ejpam-5043	253	36	and	and	CCONJ
ejpam-5043	253	37	α	α	NOUN
ejpam-5043	253	38	.	.	PUNCT
ejpam-5043	254	1	lorenz	lorenz	PROPN
ejpam-5043	254	2	system	system	NOUN
ejpam-5043	254	3	[	[	X
ejpam-5043	254	4	32	32	NUM
ejpam-5043	254	5	]	]	PUNCT
ejpam-5043	254	6	in	in	ADP
ejpam-5043	254	7	a	a	DET
ejpam-5043	254	8	few	few	ADJ
ejpam-5043	254	9	characteristics	characteristic	NOUN
ejpam-5043	254	10	.	.	PUNCT
ejpam-5043	255	1	the	the	DET
ejpam-5043	255	2	equations	equation	NOUN
ejpam-5043	255	3	that	that	PRON
ejpam-5043	255	4	define	define	VERB
ejpam-5043	255	5	the	the	DET
ejpam-5043	255	6	rössler	rössler	NOUN
ejpam-5043	255	7	system	system	NOUN
ejpam-5043	255	8	are	be	AUX
ejpam-5043	255	9	as	as	SCONJ
ejpam-5043	255	10	follows	follow	VERB
ejpam-5043	255	11	:	:	PUNCT
ejpam-5043	255	12			PRON
ejpam-5043	255	13	dx	dx	VERB
ejpam-5043	255	14	dt	dt	X
ejpam-5043	256	1	=	=	PUNCT
ejpam-5043	256	2	−y	−y	VERB
ejpam-5043	256	3	−	−	PROPN
ejpam-5043	257	1	z	z	NOUN
ejpam-5043	257	2	,	,	PUNCT
ejpam-5043	257	3	dy	dy	NOUN
ejpam-5043	257	4	dt	dt	NOUN
ejpam-5043	257	5	=	=	PUNCT
ejpam-5043	257	6	x+	x+	PROPN
ejpam-5043	257	7	ay	ay	INTJ
ejpam-5043	257	8	,	,	PUNCT
ejpam-5043	257	9	dz	dz	X
ejpam-5043	257	10	dt	dt	NOUN
ejpam-5043	257	11	=	=	PUNCT
ejpam-5043	257	12	b+	b+	X
ejpam-5043	257	13	z(x−	z(x−	PROPN
ejpam-5043	257	14	c	c	NOUN
ejpam-5043	257	15	)	)	PUNCT
ejpam-5043	257	16	.	.	PUNCT
ejpam-5043	258	1	(	(	PUNCT
ejpam-5043	258	2	23	23	NUM
ejpam-5043	258	3	)	)	PUNCT
ejpam-5043	258	4	for	for	ADP
ejpam-5043	258	5	parameter	parameter	NOUN
ejpam-5043	258	6	values	value	NOUN
ejpam-5043	258	7	a	a	DET
ejpam-5043	258	8	=	=	SYM
ejpam-5043	258	9	0.2	0.2	NUM
ejpam-5043	258	10	,	,	PUNCT
ejpam-5043	258	11	b	b	X
ejpam-5043	258	12	=	=	SYM
ejpam-5043	258	13	0.2	0.2	NUM
ejpam-5043	258	14	and	and	CCONJ
ejpam-5043	258	15	c	c	NOUN
ejpam-5043	258	16	=	=	SYM
ejpam-5043	258	17	5.7	5.7	NUM
ejpam-5043	258	18	and	and	CCONJ
ejpam-5043	258	19	initial	initial	ADJ
ejpam-5043	258	20	conditions	condition	NOUN
ejpam-5043	258	21	(	(	PUNCT
ejpam-5043	258	22	x0	x0	PROPN
ejpam-5043	258	23	,	,	PUNCT
ejpam-5043	258	24	y0	y0	PROPN
ejpam-5043	258	25	,	,	PUNCT
ejpam-5043	258	26	z0	z0	PROPN
ejpam-5043	258	27	)	)	PUNCT
ejpam-5043	258	28	=	=	PUNCT
ejpam-5043	258	29	(	(	PUNCT
ejpam-5043	258	30	1	1	NUM
ejpam-5043	258	31	,	,	PUNCT
ejpam-5043	258	32	1	1	NUM
ejpam-5043	258	33	,	,	PUNCT
ejpam-5043	258	34	1.05	1.05	NUM
ejpam-5043	258	35	)	)	PUNCT
ejpam-5043	258	36	show	show	NOUN
ejpam-5043	258	37	in	in	ADP
ejpam-5043	258	38	[	[	X
ejpam-5043	258	39	1	1	NUM
ejpam-5043	258	40	]	]	PUNCT
ejpam-5043	258	41	.	.	PUNCT
ejpam-5043	259	1	here	here	ADV
ejpam-5043	259	2	,	,	PUNCT
ejpam-5043	259	3	we	we	PRON
ejpam-5043	259	4	consider	consider	VERB
ejpam-5043	259	5	the	the	DET
ejpam-5043	259	6	rössler	rössler	NOUN
ejpam-5043	259	7	model	model	NOUN
ejpam-5043	259	8	in	in	ADP
ejpam-5043	259	9	the	the	DET
ejpam-5043	259	10	case	case	NOUN
ejpam-5043	259	11	when	when	SCONJ
ejpam-5043	259	12	the	the	DET
ejpam-5043	259	13	integer	integer	NOUN
ejpam-5043	259	14	order	order	NOUN
ejpam-5043	259	15	derivatives	derivative	NOUN
ejpam-5043	259	16	is	be	AUX
ejpam-5043	259	17	replaced	replace	VERB
ejpam-5043	259	18	by	by	ADP
ejpam-5043	259	19	fractional	fractional	ADJ
ejpam-5043	259	20	order	order	NOUN
ejpam-5043	259	21	.	.	PUNCT
ejpam-5043	260	1	we	we	PRON
ejpam-5043	260	2	introduce	introduce	VERB
ejpam-5043	260	3	the	the	DET
ejpam-5043	260	4	fractional	fractional	ADJ
ejpam-5043	260	5	rössler	rössler	NOUN
ejpam-5043	260	6	oscillator	oscillator	NOUN
ejpam-5043	260	7	model	model	NOUN
ejpam-5043	260	8	of	of	ADP
ejpam-5043	260	9	with	with	ADP
ejpam-5043	260	10	0	0	NUM
ejpam-5043	260	11	<	<	X
ejpam-5043	260	12	α	α	X
ejpam-5043	260	13	<	<	X
ejpam-5043	260	14	1	1	NUM
ejpam-5043	260	15	as	as	ADP
ejpam-5043	260	16	follows.	follows.	NUM
ejpam-5043	260	17	abc	abc	PROPN
ejpam-5043	260	18	0	0	PUNCT
ejpam-5043	260	19	dα	dα	ADJ
ejpam-5043	260	20	0	0	NUM
ejpam-5043	260	21	x	x	SYM
ejpam-5043	260	22	=	=	PRON
ejpam-5043	260	23	−y	−y	NOUN
ejpam-5043	261	1	−	−	PROPN
ejpam-5043	262	1	z	z	PROPN
ejpam-5043	262	2	,	,	PUNCT
ejpam-5043	262	3	abc	abc	PROPN
ejpam-5043	262	4	0	0	PROPN
ejpam-5043	263	1	dα	dα	ADJ
ejpam-5043	263	2	0	0	NUM
ejpam-5043	263	3	y	y	PROPN
ejpam-5043	263	4	=	=	PUNCT
ejpam-5043	263	5	x+	x+	PROPN
ejpam-5043	264	1	ay	ay	INTJ
ejpam-5043	264	2	,	,	PUNCT
ejpam-5043	264	3	abc	abc	PROPN
ejpam-5043	264	4	0	0	PROPN
ejpam-5043	265	1	dα	dα	ADJ
ejpam-5043	265	2	0	0	NUM
ejpam-5043	265	3	z	z	NOUN
ejpam-5043	265	4	=	=	PUNCT
ejpam-5043	265	5	b+	b+	X
ejpam-5043	265	6	z(x−	z(x−	PROPN
ejpam-5043	265	7	c	c	NOUN
ejpam-5043	265	8	)	)	PUNCT
ejpam-5043	265	9	,	,	PUNCT
ejpam-5043	265	10	(	(	PUNCT
ejpam-5043	265	11	24	24	NUM
ejpam-5043	265	12	)	)	PUNCT
ejpam-5043	265	13	where	where	SCONJ
ejpam-5043	265	14	abc	abc	PROPN
ejpam-5043	265	15	0	0	PROPN
ejpam-5043	265	16	dα	dα	PROPN
ejpam-5043	265	17	0	0	NUM
ejpam-5043	265	18	(	(	PUNCT
ejpam-5043	265	19	.	.	PUNCT
ejpam-5043	265	20	)	)	PUNCT
ejpam-5043	265	21	is	be	AUX
ejpam-5043	265	22	the	the	DET
ejpam-5043	265	23	abc	abc	PROPN
ejpam-5043	265	24	-	-	PUNCT
ejpam-5043	265	25	fd	fd	PROPN
ejpam-5043	265	26	.	.	PUNCT
ejpam-5043	266	1	the	the	DET
ejpam-5043	266	2	chaotic	chaotic	ADJ
ejpam-5043	266	3	attractor	attractor	NOUN
ejpam-5043	266	4	from	from	ADP
ejpam-5043	266	5	the	the	DET
ejpam-5043	266	6	fractional	fractional	ADJ
ejpam-5043	266	7	rössler	rössler	NOUN
ejpam-5043	266	8	oscillator	oscillator	NOUN
ejpam-5043	266	9	model	model	NOUN
ejpam-5043	266	10	is	be	AUX
ejpam-5043	266	11	highly	highly	ADV
ejpam-5043	266	12	useful	useful	ADJ
ejpam-5043	266	13	in	in	ADP
ejpam-5043	266	14	secured	secured	ADJ
ejpam-5043	266	15	communication	communication	NOUN
ejpam-5043	266	16	applications	application	NOUN
ejpam-5043	266	17	.	.	PUNCT
ejpam-5043	267	1	attractors	attractor	NOUN
ejpam-5043	267	2	is	be	AUX
ejpam-5043	267	3	a	a	DET
ejpam-5043	267	4	new	new	ADJ
ejpam-5043	267	5	research	research	NOUN
ejpam-5043	267	6	concept	concept	NOUN
ejpam-5043	267	7	with	with	ADP
ejpam-5043	267	8	enormous	enormous	ADJ
ejpam-5043	267	9	potential	potential	NOUN
ejpam-5043	267	10	in	in	ADP
ejpam-5043	267	11	the	the	DET
ejpam-5043	267	12	field	field	NOUN
ejpam-5043	267	13	of	of	ADP
ejpam-5043	267	14	secure	secure	ADJ
ejpam-5043	267	15	communication	communication	NOUN
ejpam-5043	267	16	.	.	PUNCT
ejpam-5043	268	1	in	in	ADP
ejpam-5043	268	2	table	table	NOUN
ejpam-5043	268	3	3	3	NUM
ejpam-5043	268	4	below	below	ADV
ejpam-5043	268	5	,	,	PUNCT
ejpam-5043	268	6	we	we	PRON
ejpam-5043	268	7	provide	provide	VERB
ejpam-5043	268	8	the	the	DET
ejpam-5043	268	9	numerical	numerical	ADJ
ejpam-5043	268	10	solution	solution	NOUN
ejpam-5043	268	11	using	use	VERB
ejpam-5043	268	12	the	the	DET
ejpam-5043	268	13	the	the	DET
ejpam-5043	268	14	abc	abc	PROPN
ejpam-5043	268	15	-	-	PUNCT
ejpam-5043	268	16	fd	fd	PROPN
ejpam-5043	268	17	scheme	scheme	NOUN
ejpam-5043	268	18	to	to	ADP
ejpam-5043	268	19	eq	eq	PROPN
ejpam-5043	268	20	.	.	PUNCT
ejpam-5043	269	1	(	(	PUNCT
ejpam-5043	269	2	24	24	NUM
ejpam-5043	269	3	)	)	PUNCT
ejpam-5043	269	4	when	when	SCONJ
ejpam-5043	269	5	α	α	NOUN
ejpam-5043	269	6	=	=	SYM
ejpam-5043	269	7	1	1	NUM
ejpam-5043	269	8	,	,	PUNCT
ejpam-5043	269	9	and	and	CCONJ
ejpam-5043	269	10	t	t	X
ejpam-5043	269	11	=	=	SYM
ejpam-5043	269	12	0.1	0.1	NUM
ejpam-5043	269	13	.	.	PUNCT
ejpam-5043	269	14	table	table	NOUN
ejpam-5043	269	15	4	4	NUM
ejpam-5043	269	16	provides	provide	VERB
ejpam-5043	269	17	the	the	DET
ejpam-5043	269	18	numerical	numerical	ADJ
ejpam-5043	269	19	solution	solution	NOUN
ejpam-5043	269	20	for	for	ADP
ejpam-5043	269	21	the	the	DET
ejpam-5043	269	22	value	value	NOUN
ejpam-5043	269	23	of	of	ADP
ejpam-5043	269	24	α	α	NOUN
ejpam-5043	269	25	=	=	NOUN
ejpam-5043	269	26	0.95	0.95	NUM
ejpam-5043	269	27	,	,	PUNCT
ejpam-5043	269	28	and	and	CCONJ
ejpam-5043	269	29	t	t	X
ejpam-5043	269	30	=	=	SYM
ejpam-5043	269	31	1	1	X
ejpam-5043	269	32	.	.	PUNCT
ejpam-5043	270	1	it	it	PRON
ejpam-5043	270	2	should	should	AUX
ejpam-5043	270	3	be	be	AUX
ejpam-5043	270	4	observed	observe	VERB
ejpam-5043	270	5	that	that	SCONJ
ejpam-5043	270	6	accuracy	accuracy	NOUN
ejpam-5043	270	7	increases	increase	NOUN
ejpam-5043	270	8	as	as	ADP
ejpam-5043	270	9	step	step	NOUN
ejpam-5043	270	10	size	size	NOUN
ejpam-5043	270	11	h	h	NOUN
ejpam-5043	270	12	is	be	AUX
ejpam-5043	270	13	reduced	reduce	VERB
ejpam-5043	270	14	.	.	PUNCT
ejpam-5043	271	1	we	we	PRON
ejpam-5043	271	2	can	can	AUX
ejpam-5043	271	3	see	see	VERB
ejpam-5043	271	4	the	the	DET
ejpam-5043	271	5	numerical	numerical	ADJ
ejpam-5043	271	6	stability	stability	PROPN
ejpam-5043	271	7	characteristic	characteristic	ADJ
ejpam-5043	271	8	of	of	ADP
ejpam-5043	271	9	the	the	DET
ejpam-5043	271	10	abc	abc	PROPN
ejpam-5043	271	11	-	-	PUNCT
ejpam-5043	271	12	fd	fd	PROPN
ejpam-5043	271	13	scheme	scheme	NOUN
ejpam-5043	271	14	based	base	VERB
ejpam-5043	271	15	on	on	ADP
ejpam-5043	271	16	the	the	DET
ejpam-5043	271	17	convergence	convergence	NOUN
ejpam-5043	271	18	of	of	ADP
ejpam-5043	271	19	the	the	DET
ejpam-5043	271	20	numerical	numerical	ADJ
ejpam-5043	271	21	data	datum	NOUN
ejpam-5043	271	22	in	in	ADP
ejpam-5043	271	23	table	table	NOUN
ejpam-5043	271	24	3	3	NUM
ejpam-5043	271	25	and	and	CCONJ
ejpam-5043	271	26	table	table	NOUN
ejpam-5043	271	27	4	4	NUM
ejpam-5043	271	28	.	.	PUNCT
ejpam-5043	271	29	k.	k.	PROPN
ejpam-5043	271	30	boulehmi	boulehmi	PROPN
ejpam-5043	271	31	/	/	SYM
ejpam-5043	271	32	eur	eur	PROPN
ejpam-5043	271	33	.	.	PUNCT
ejpam-5043	272	1	j.	j.	PROPN
ejpam-5043	272	2	pure	pure	PROPN
ejpam-5043	272	3	appl	appl	PROPN
ejpam-5043	272	4	.	.	PROPN
ejpam-5043	272	5	math	math	PROPN
ejpam-5043	272	6	,	,	PUNCT
ejpam-5043	272	7	17	17	NUM
ejpam-5043	272	8	(	(	PUNCT
ejpam-5043	272	9	1	1	NUM
ejpam-5043	272	10	)	)	PUNCT
ejpam-5043	272	11	(	(	PUNCT
ejpam-5043	272	12	2024	2024	NUM
ejpam-5043	272	13	)	)	PUNCT
ejpam-5043	272	14	,	,	PUNCT
ejpam-5043	272	15	445	445	NUM
ejpam-5043	272	16	-	-	SYM
ejpam-5043	272	17	461	461	NUM
ejpam-5043	272	18	455	455	NUM
ejpam-5043	272	19	table	table	NOUN
ejpam-5043	272	20	3	3	NUM
ejpam-5043	272	21	:	:	PUNCT
ejpam-5043	272	22	solutions	solution	NOUN
ejpam-5043	272	23	of	of	ADP
ejpam-5043	272	24	equation	equation	NOUN
ejpam-5043	272	25	(	(	PUNCT
ejpam-5043	272	26	24	24	NUM
ejpam-5043	272	27	)	)	PUNCT
ejpam-5043	272	28	where	where	SCONJ
ejpam-5043	272	29	α	α	NOUN
ejpam-5043	272	30	=	=	SYM
ejpam-5043	272	31	1	1	NUM
ejpam-5043	272	32	and	and	CCONJ
ejpam-5043	272	33	t	t	NOUN
ejpam-5043	272	34	=	=	SYM
ejpam-5043	272	35	0.1	0.1	NUM
ejpam-5043	272	36	.	.	PUNCT
ejpam-5043	273	1	h	h	NOUN
ejpam-5043	274	1	x	x	PUNCT
ejpam-5043	274	2	y	y	PROPN
ejpam-5043	274	3	z	z	PROPN
ejpam-5043	274	4	1/320	1/320	NUM
ejpam-5043	274	5	0.177898180755700	0.177898180755700	NUM
ejpam-5043	274	6	1.407072166904383	1.407072166904383	NUM
ejpam-5043	274	7	0.116315513109570	0.116315513109570	NUM
ejpam-5043	274	8	1/640	1/640	NUM
ejpam-5043	274	9	0.176707768361964	0.176707768361964	NUM
ejpam-5043	274	10	1.407429186405125	1.407429186405125	NUM
ejpam-5043	274	11	0.115968853477924	0.115968853477924	NUM
ejpam-5043	274	12	1/1280	1/1280	NUM
ejpam-5043	274	13	0.176112624976242	0.176112624976242	NUM
ejpam-5043	274	14	1.407607713412835	1.407607713412835	NUM
ejpam-5043	274	15	0.115796493319784	0.115796493319784	NUM
ejpam-5043	274	16	1/2560	1/2560	NUM
ejpam-5043	274	17	0.175914252956577	0.175914252956577	NUM
ejpam-5043	274	18	1.407667225032148	1.407667225032148	NUM
ejpam-5043	274	19	0.115739183282915	0.115739183282915	NUM
ejpam-5043	274	20	1/5120	1/5120	NUM
ejpam-5043	274	21	0.175815068638023	0.175815068638023	NUM
ejpam-5043	274	22	1.407696981337520	1.407696981337520	NUM
ejpam-5043	274	23	0.115710555116532	0.115710555116532	NUM
ejpam-5043	274	24	1/10240	1/10240	NUM
ejpam-5043	274	25	0.175755558585964	0.175755558585964	NUM
ejpam-5043	274	26	1.407714835280020	1.407714835280020	NUM
ejpam-5043	274	27	0.115693386806025	0.115693386806025	NUM
ejpam-5043	274	28	table	table	NOUN
ejpam-5043	274	29	4	4	NUM
ejpam-5043	274	30	:	:	PUNCT
ejpam-5043	274	31	solutions	solution	NOUN
ejpam-5043	274	32	of	of	ADP
ejpam-5043	274	33	equation	equation	NOUN
ejpam-5043	274	34	(	(	PUNCT
ejpam-5043	274	35	24	24	NUM
ejpam-5043	274	36	)	)	PUNCT
ejpam-5043	274	37	where	where	SCONJ
ejpam-5043	274	38	α	α	NOUN
ejpam-5043	275	1	=	=	NOUN
ejpam-5043	275	2	0.95	0.95	NUM
ejpam-5043	275	3	and	and	CCONJ
ejpam-5043	275	4	t	t	NOUN
ejpam-5043	275	5	=	=	SYM
ejpam-5043	275	6	1	1	X
ejpam-5043	275	7	.	.	PUNCT
ejpam-5043	275	8	h	h	NOUN
ejpam-5043	275	9	x	x	SYM
ejpam-5043	275	10	y	y	PROPN
ejpam-5043	275	11	z	z	PROPN
ejpam-5043	275	12	1/320	1/320	NUM
ejpam-5043	275	13	-0.615483039781965	-0.615483039781965	PROPN
ejpam-5043	275	14	1.322607056797672	1.322607056797672	NUM
ejpam-5043	275	15	0.055611317422203	0.055611317422203	NUM
ejpam-5043	275	16	1/640	1/640	NUM
ejpam-5043	275	17	-0.616417804431375	-0.616417804431375	NOUN
ejpam-5043	275	18	1.322218290929184	1.322218290929184	NUM
ejpam-5043	275	19	0.055536319297694	0.055536319297694	NUM
ejpam-5043	275	20	1/1280	1/1280	NUM
ejpam-5043	275	21	-0.616885335290380	-0.616885335290380	NOUN
ejpam-5043	276	1	1.322023886548481	1.322023886548481	NUM
ejpam-5043	276	2	0.055499005900917	0.055499005900917	NUM
ejpam-5043	276	3	1/2560	1/2560	NUM
ejpam-5043	276	4	-0.617041200990387	-0.617041200990387	NOUN
ejpam-5043	276	5	1.321959082068103	1.321959082068103	NUM
ejpam-5043	276	6	0.05548659544584	0.05548659544584	NUM
ejpam-5043	276	7	1/5120	1/5120	NUM
ejpam-5043	276	8	-0.617119138320106	-0.617119138320106	NOUN
ejpam-5043	276	9	1.321926679486526	1.321926679486526	NUM
ejpam-5043	276	10	0.055480395055542	0.055480395055542	NUM
ejpam-5043	276	11	1/10240	1/10240	NUM
ejpam-5043	276	12	-0.617165902091590	-0.617165902091590	NOUN
ejpam-5043	276	13	1.321907237739616	1.321907237739616	NUM
ejpam-5043	276	14	0.055476676628662	0.055476676628662	NUM
ejpam-5043	276	15	figure	figure	NOUN
ejpam-5043	276	16	2	2	NUM
ejpam-5043	276	17	demonstrates	demonstrate	VERB
ejpam-5043	276	18	the	the	DET
ejpam-5043	276	19	chaotic	chaotic	ADJ
ejpam-5043	276	20	attractors	attractor	NOUN
ejpam-5043	276	21	plot	plot	NOUN
ejpam-5043	276	22	of	of	ADP
ejpam-5043	276	23	eq	eq	PROPN
ejpam-5043	276	24	.	.	PUNCT
ejpam-5043	277	1	(	(	PUNCT
ejpam-5043	277	2	24	24	NUM
ejpam-5043	277	3	)	)	PUNCT
ejpam-5043	277	4	in	in	ADP
ejpam-5043	277	5	the	the	DET
ejpam-5043	277	6	case	case	NOUN
ejpam-5043	277	7	when	when	SCONJ
ejpam-5043	277	8	α	α	PROPN
ejpam-5043	277	9	=	=	NOUN
ejpam-5043	277	10	0.95	0.95	NUM
ejpam-5043	277	11	and	and	CCONJ
ejpam-5043	277	12	t	t	NOUN
ejpam-5043	277	13	=	=	SYM
ejpam-5043	277	14	1000	1000	NUM
ejpam-5043	277	15	.	.	PUNCT
ejpam-5043	278	1	we	we	PRON
ejpam-5043	278	2	present	present	VERB
ejpam-5043	278	3	,	,	PUNCT
ejpam-5043	278	4	in	in	ADP
ejpam-5043	278	5	figure	figure	NOUN
ejpam-5043	278	6	3	3	NUM
ejpam-5043	278	7	,	,	PUNCT
ejpam-5043	278	8	the	the	DET
ejpam-5043	278	9	chaotic	chaotic	ADJ
ejpam-5043	278	10	attractors	attractor	NOUN
ejpam-5043	278	11	plot	plot	NOUN
ejpam-5043	278	12	of	of	ADP
ejpam-5043	278	13	eq	eq	PROPN
ejpam-5043	278	14	.	.	PUNCT
ejpam-5043	279	1	(	(	PUNCT
ejpam-5043	279	2	24	24	NUM
ejpam-5043	279	3	)	)	PUNCT
ejpam-5043	279	4	when	when	SCONJ
ejpam-5043	279	5	α	α	NOUN
ejpam-5043	279	6	=	=	NOUN
ejpam-5043	279	7	0.99	0.99	NUM
ejpam-5043	279	8	and	and	CCONJ
ejpam-5043	279	9	t	t	NOUN
ejpam-5043	279	10	=	=	SYM
ejpam-5043	279	11	1000	1000	NUM
ejpam-5043	279	12	.	.	PUNCT
ejpam-5043	280	1	figure	figure	NOUN
ejpam-5043	280	2	2	2	NUM
ejpam-5043	280	3	:	:	PUNCT
ejpam-5043	280	4	the	the	DET
ejpam-5043	280	5	chaotic	chaotic	ADJ
ejpam-5043	280	6	attractors	attractor	NOUN
ejpam-5043	280	7	plot	plot	VERB
ejpam-5043	280	8	from	from	ADP
ejpam-5043	280	9	eq	eq	PROPN
ejpam-5043	280	10	.	.	PUNCT
ejpam-5043	281	1	(	(	PUNCT
ejpam-5043	281	2	24	24	NUM
ejpam-5043	281	3	)	)	PUNCT
ejpam-5043	281	4	,	,	PUNCT
ejpam-5043	281	5	when	when	SCONJ
ejpam-5043	281	6	α	α	NOUN
ejpam-5043	281	7	=	=	NOUN
ejpam-5043	281	8	0.95	0.95	NUM
ejpam-5043	281	9	and	and	CCONJ
ejpam-5043	281	10	t	t	NOUN
ejpam-5043	281	11	=	=	SYM
ejpam-5043	281	12	1000	1000	NUM
ejpam-5043	281	13	.	.	PUNCT
ejpam-5043	282	1	these	these	DET
ejpam-5043	282	2	figures	figure	NOUN
ejpam-5043	282	3	show	show	VERB
ejpam-5043	282	4	the	the	DET
ejpam-5043	282	5	projections	projection	NOUN
ejpam-5043	282	6	of	of	ADP
ejpam-5043	282	7	the	the	DET
ejpam-5043	282	8	fractional	fractional	ADJ
ejpam-5043	282	9	rössler	rössler	NOUN
ejpam-5043	282	10	model	model	NOUN
ejpam-5043	282	11	eq	eq	ADJ
ejpam-5043	282	12	.	.	PUNCT
ejpam-5043	283	1	(	(	PUNCT
ejpam-5043	283	2	24	24	NUM
ejpam-5043	283	3	)	)	PUNCT
ejpam-5043	283	4	attractors	attractor	NOUN
ejpam-5043	283	5	that	that	PRON
ejpam-5043	283	6	were	be	AUX
ejpam-5043	283	7	obtained	obtain	VERB
ejpam-5043	283	8	by	by	ADP
ejpam-5043	283	9	using	use	VERB
ejpam-5043	283	10	the	the	DET
ejpam-5043	283	11	novel	novel	ADJ
ejpam-5043	283	12	scheme	scheme	NOUN
ejpam-5043	283	13	(	(	PUNCT
ejpam-5043	283	14	abc	abc	PROPN
ejpam-5043	283	15	-	-	PUNCT
ejpam-5043	283	16	fd	fd	PROPN
ejpam-5043	283	17	)	)	PUNCT
ejpam-5043	283	18	.	.	PUNCT
ejpam-5043	284	1	identifying	identify	VERB
ejpam-5043	284	2	chaotic	chaotic	ADJ
ejpam-5043	284	3	behavior	behavior	NOUN
ejpam-5043	284	4	in	in	ADP
ejpam-5043	284	5	the	the	DET
ejpam-5043	284	6	fractional	fractional	ADJ
ejpam-5043	284	7	system	system	NOUN
ejpam-5043	284	8	in	in	ADP
ejpam-5043	284	9	eq	eq	ADP
ejpam-5043	284	10	.	.	PUNCT
ejpam-5043	285	1	(	(	PUNCT
ejpam-5043	285	2	24	24	NUM
ejpam-5043	285	3	)	)	PUNCT
ejpam-5043	285	4	by	by	ADP
ejpam-5043	285	5	using	use	VERB
ejpam-5043	285	6	a	a	DET
ejpam-5043	285	7	unique	unique	ADJ
ejpam-5043	285	8	scheme	scheme	NOUN
ejpam-5043	285	9	(	(	PUNCT
ejpam-5043	285	10	abc	abc	PROPN
ejpam-5043	285	11	-	-	PUNCT
ejpam-5043	285	12	fd	fd	X
ejpam-5043	285	13	)	)	PUNCT
ejpam-5043	285	14	allows	allow	VERB
ejpam-5043	285	15	researchers	researcher	NOUN
ejpam-5043	285	16	to	to	PART
ejpam-5043	285	17	acquire	acquire	VERB
ejpam-5043	285	18	insights	insight	NOUN
ejpam-5043	285	19	into	into	ADP
ejpam-5043	285	20	the	the	DET
ejpam-5043	285	21	system	system	NOUN
ejpam-5043	285	22	’s	’s	PART
ejpam-5043	285	23	fundamental	fundamental	ADJ
ejpam-5043	285	24	dynamics	dynamic	NOUN
ejpam-5043	285	25	;	;	PUNCT
ejpam-5043	285	26	this	this	DET
ejpam-5043	285	27	understanding	understanding	NOUN
ejpam-5043	285	28	is	be	AUX
ejpam-5043	285	29	essential	essential	ADJ
ejpam-5043	285	30	in	in	ADP
ejpam-5043	285	31	various	various	ADJ
ejpam-5043	285	32	scientific	scientific	ADJ
ejpam-5043	285	33	areas	area	NOUN
ejpam-5043	285	34	,	,	PUNCT
ejpam-5043	285	35	including	include	VERB
ejpam-5043	285	36	physics	physics	NOUN
ejpam-5043	285	37	,	,	PUNCT
ejpam-5043	285	38	engineering	engineering	NOUN
ejpam-5043	285	39	,	,	PUNCT
ejpam-5043	285	40	and	and	CCONJ
ejpam-5043	285	41	mathematics	mathematic	NOUN
ejpam-5043	285	42	.	.	PUNCT
ejpam-5043	286	1	5	5	X
ejpam-5043	286	2	.	.	X
ejpam-5043	286	3	numerical	numerical	ADJ
ejpam-5043	286	4	results	result	NOUN
ejpam-5043	286	5	and	and	CCONJ
ejpam-5043	286	6	discussions	discussion	NOUN
ejpam-5043	286	7	in	in	ADP
ejpam-5043	286	8	this	this	DET
ejpam-5043	286	9	section	section	NOUN
ejpam-5043	286	10	,	,	PUNCT
ejpam-5043	286	11	we	we	PRON
ejpam-5043	286	12	present	present	VERB
ejpam-5043	286	13	a	a	DET
ejpam-5043	286	14	comparison	comparison	NOUN
ejpam-5043	286	15	between	between	ADP
ejpam-5043	286	16	our	our	PRON
ejpam-5043	286	17	suggested	suggest	VERB
ejpam-5043	286	18	method	method	NOUN
ejpam-5043	286	19	and	and	CCONJ
ejpam-5043	286	20	the	the	DET
ejpam-5043	286	21	rungekutta	rungekutta	ADJ
ejpam-5043	286	22	4th	4th	ADJ
ejpam-5043	286	23	-	-	PUNCT
ejpam-5043	286	24	order	order	NOUN
ejpam-5043	286	25	approach	approach	NOUN
ejpam-5043	286	26	(	(	PUNCT
ejpam-5043	286	27	rk4	rk4	NOUN
ejpam-5043	286	28	)	)	PUNCT
ejpam-5043	286	29	.	.	PUNCT
ejpam-5043	287	1	k.	k.	PROPN
ejpam-5043	287	2	boulehmi	boulehmi	PROPN
ejpam-5043	287	3	/	/	SYM
ejpam-5043	287	4	eur	eur	PROPN
ejpam-5043	287	5	.	.	PUNCT
ejpam-5043	288	1	j.	j.	PROPN
ejpam-5043	288	2	pure	pure	PROPN
ejpam-5043	288	3	appl	appl	PROPN
ejpam-5043	288	4	.	.	PROPN
ejpam-5043	288	5	math	math	PROPN
ejpam-5043	288	6	,	,	PUNCT
ejpam-5043	288	7	17	17	NUM
ejpam-5043	288	8	(	(	PUNCT
ejpam-5043	288	9	1	1	NUM
ejpam-5043	288	10	)	)	PUNCT
ejpam-5043	288	11	(	(	PUNCT
ejpam-5043	288	12	2024	2024	NUM
ejpam-5043	288	13	)	)	PUNCT
ejpam-5043	288	14	,	,	PUNCT
ejpam-5043	288	15	445	445	NUM
ejpam-5043	288	16	-	-	SYM
ejpam-5043	288	17	461	461	NUM
ejpam-5043	288	18	456	456	NUM
ejpam-5043	288	19	figure	figure	NOUN
ejpam-5043	288	20	3	3	NUM
ejpam-5043	288	21	:	:	PUNCT
ejpam-5043	288	22	the	the	DET
ejpam-5043	288	23	chaotic	chaotic	ADJ
ejpam-5043	288	24	attractors	attractor	NOUN
ejpam-5043	288	25	plot	plot	VERB
ejpam-5043	288	26	from	from	ADP
ejpam-5043	288	27	eq	eq	PROPN
ejpam-5043	288	28	.	.	PUNCT
ejpam-5043	289	1	(	(	PUNCT
ejpam-5043	289	2	24	24	NUM
ejpam-5043	289	3	)	)	PUNCT
ejpam-5043	289	4	,	,	PUNCT
ejpam-5043	289	5	when	when	SCONJ
ejpam-5043	289	6	α	α	NOUN
ejpam-5043	289	7	=	=	NOUN
ejpam-5043	289	8	0.99	0.99	NUM
ejpam-5043	289	9	and	and	CCONJ
ejpam-5043	289	10	t	t	NOUN
ejpam-5043	289	11	=	=	SYM
ejpam-5043	289	12	1000	1000	NUM
ejpam-5043	289	13	.	.	PUNCT
ejpam-5043	290	1	table	table	NOUN
ejpam-5043	290	2	5	5	NUM
ejpam-5043	290	3	:	:	PUNCT
ejpam-5043	290	4	comparison	comparison	NOUN
ejpam-5043	290	5	between	between	ADP
ejpam-5043	290	6	the	the	DET
ejpam-5043	290	7	abc	abc	PROPN
ejpam-5043	290	8	-	-	PUNCT
ejpam-5043	290	9	fd	fd	PROPN
ejpam-5043	290	10	scheme	scheme	NOUN
ejpam-5043	290	11	and	and	CCONJ
ejpam-5043	290	12	rk4	rk4	NOUN
ejpam-5043	290	13	method	method	NOUN
ejpam-5043	290	14	for	for	ADP
ejpam-5043	290	15	x(t	x(t	PROPN
ejpam-5043	290	16	)	)	PUNCT
ejpam-5043	290	17	to	to	ADP
ejpam-5043	290	18	the	the	DET
ejpam-5043	290	19	fractional	fractional	ADJ
ejpam-5043	290	20	model	model	NOUN
ejpam-5043	290	21	equation	equation	NOUN
ejpam-5043	290	22	eq	eq	ADJ
ejpam-5043	290	23	.	.	PUNCT
ejpam-5043	291	1	(	(	PUNCT
ejpam-5043	291	2	24	24	NUM
ejpam-5043	291	3	)	)	PUNCT
ejpam-5043	291	4	.	.	PUNCT
ejpam-5043	292	1	t	t	PROPN
ejpam-5043	292	2	abc	abc	PROPN
ejpam-5043	292	3	-	-	PUNCT
ejpam-5043	292	4	fd(α	fd(α	NUM
ejpam-5043	292	5	=	=	NOUN
ejpam-5043	292	6	0.95	0.95	NUM
ejpam-5043	292	7	)	)	PUNCT
ejpam-5043	292	8	abc	abc	PROPN
ejpam-5043	292	9	-	-	PUNCT
ejpam-5043	292	10	fd(α	fd(α	NOUN
ejpam-5043	292	11	=	=	SYM
ejpam-5043	292	12	1	1	X
ejpam-5043	292	13	)	)	PUNCT
ejpam-5043	292	14	rk4	rk4	NOUN
ejpam-5043	292	15	0	0	NUM
ejpam-5043	292	16	0.1	0.1	NUM
ejpam-5043	292	17	0.1	0.1	NUM
ejpam-5043	292	18	0.1	0.1	NUM
ejpam-5043	292	19	0.1	0.1	NUM
ejpam-5043	292	20	0.710684980261416	0.710684980261416	NUM
ejpam-5043	292	21	0.811287822893630	0.811287822893630	NUM
ejpam-5043	292	22	0.809899121526138	0.809899121526138	NUM
ejpam-5043	292	23	0.2	0.2	NUM
ejpam-5043	292	24	0.541932682851730	0.541932682851730	NUM
ejpam-5043	292	25	0.641749305322459	0.641749305322459	NUM
ejpam-5043	292	26	0.640477455295522	0.640477455295522	NUM
ejpam-5043	292	27	0.3	0.3	NUM
ejpam-5043	292	28	0.382747205334253	0.382747205334253	NUM
ejpam-5043	292	29	0.483048734060514	0.483048734060514	NUM
ejpam-5043	292	30	0.481833456041290	0.481833456041290	NUM
ejpam-5043	292	31	0.4	0.4	NUM
ejpam-5043	292	32	0.228902195409422	0.228902195409422	NUM
ejpam-5043	292	33	0.329148739755869	0.329148739755869	NUM
ejpam-5043	292	34	0.327954972715375	0.327954972715375	NUM
ejpam-5043	292	35	0.5	0.5	NUM
ejpam-5043	292	36	0.078662493918809	0.078662493918809	NUM
ejpam-5043	292	37	0.176707768361964	0.176707768361964	NUM
ejpam-5043	292	38	0.175517541129673	0.175517541129673	NUM
ejpam-5043	292	39	in	in	ADP
ejpam-5043	292	40	tables	table	NOUN
ejpam-5043	292	41	5	5	NUM
ejpam-5043	292	42	-	-	SYM
ejpam-5043	292	43	7	7	NUM
ejpam-5043	292	44	,	,	PUNCT
ejpam-5043	292	45	we	we	PRON
ejpam-5043	292	46	show	show	VERB
ejpam-5043	292	47	that	that	SCONJ
ejpam-5043	292	48	for	for	ADP
ejpam-5043	292	49	α	α	NOUN
ejpam-5043	292	50	=	=	SYM
ejpam-5043	292	51	1	1	NUM
ejpam-5043	292	52	,	,	PUNCT
ejpam-5043	292	53	the	the	DET
ejpam-5043	292	54	numerical	numerical	ADJ
ejpam-5043	292	55	solution	solution	NOUN
ejpam-5043	292	56	outcomes	outcome	NOUN
ejpam-5043	292	57	of	of	ADP
ejpam-5043	292	58	the	the	DET
ejpam-5043	292	59	abcfd	abcfd	NOUN
ejpam-5043	292	60	scheme	scheme	NOUN
ejpam-5043	292	61	found	find	VERB
ejpam-5043	292	62	in	in	ADP
ejpam-5043	292	63	eq	eq	PROPN
ejpam-5043	292	64	.	.	PUNCT
ejpam-5043	293	1	(	(	PUNCT
ejpam-5043	293	2	24	24	NUM
ejpam-5043	293	3	)	)	PUNCT
ejpam-5043	293	4	)	)	PUNCT
ejpam-5043	293	5	exhibit	exhibit	VERB
ejpam-5043	293	6	remarkable	remarkable	ADJ
ejpam-5043	293	7	concurrence	concurrence	NOUN
ejpam-5043	293	8	with	with	ADP
ejpam-5043	293	9	the	the	DET
ejpam-5043	293	10	runge	runge	NOUN
ejpam-5043	293	11	-	-	PUNCT
ejpam-5043	293	12	kutta	kutta	NOUN
ejpam-5043	293	13	4th	4th	ADJ
ejpam-5043	293	14	order	order	NOUN
ejpam-5043	293	15	method	method	NOUN
ejpam-5043	293	16	solutions	solution	NOUN
ejpam-5043	293	17	.	.	PUNCT
ejpam-5043	294	1	as	as	ADP
ejpam-5043	294	2	consequence	consequence	NOUN
ejpam-5043	294	3	of	of	ADP
ejpam-5043	294	4	our	our	PRON
ejpam-5043	294	5	findings	finding	NOUN
ejpam-5043	294	6	,	,	PUNCT
ejpam-5043	294	7	we	we	PRON
ejpam-5043	294	8	are	be	AUX
ejpam-5043	294	9	certain	certain	ADJ
ejpam-5043	294	10	that	that	SCONJ
ejpam-5043	294	11	the	the	DET
ejpam-5043	294	12	methodology	methodology	NOUN
ejpam-5043	294	13	provided	provide	VERB
ejpam-5043	294	14	a	a	DET
ejpam-5043	294	15	powerful	powerful	ADJ
ejpam-5043	294	16	mathematical	mathematical	ADJ
ejpam-5043	294	17	instrument	instrument	NOUN
ejpam-5043	294	18	for	for	ADP
ejpam-5043	294	19	solving	solve	VERB
ejpam-5043	294	20	equations	equation	NOUN
ejpam-5043	294	21	.	.	PUNCT
ejpam-5043	295	1	moreover	moreover	ADV
ejpam-5043	295	2	,	,	PUNCT
ejpam-5043	295	3	they	they	PRON
ejpam-5043	295	4	can	can	AUX
ejpam-5043	295	5	be	be	AUX
ejpam-5043	295	6	used	use	VERB
ejpam-5043	295	7	to	to	PART
ejpam-5043	295	8	find	find	VERB
ejpam-5043	295	9	analytical	analytical	ADJ
ejpam-5043	295	10	or	or	CCONJ
ejpam-5043	295	11	approximate	approximate	ADJ
ejpam-5043	295	12	solutions	solution	NOUN
ejpam-5043	295	13	to	to	ADP
ejpam-5043	295	14	other	other	ADJ
ejpam-5043	295	15	problems	problem	NOUN
ejpam-5043	295	16	.	.	PUNCT
ejpam-5043	296	1	6	6	X
ejpam-5043	296	2	.	.	X
ejpam-5043	296	3	conclusion	conclusion	NOUN
ejpam-5043	296	4	this	this	DET
ejpam-5043	296	5	study	study	NOUN
ejpam-5043	296	6	affords	afford	VERB
ejpam-5043	296	7	a	a	DET
ejpam-5043	296	8	numerical	numerical	ADJ
ejpam-5043	296	9	solution	solution	NOUN
ejpam-5043	296	10	for	for	ADP
ejpam-5043	296	11	the	the	DET
ejpam-5043	296	12	fractional	fractional	ADJ
ejpam-5043	296	13	bernoulli	bernoulli	NOUN
ejpam-5043	296	14	equation	equation	NOUN
ejpam-5043	296	15	and	and	CCONJ
ejpam-5043	296	16	the	the	DET
ejpam-5043	296	17	fractional	fractional	ADJ
ejpam-5043	296	18	rössler	rössler	NOUN
ejpam-5043	296	19	model	model	NOUN
ejpam-5043	296	20	.	.	PUNCT
ejpam-5043	297	1	this	this	DET
ejpam-5043	297	2	research	research	NOUN
ejpam-5043	297	3	makes	make	VERB
ejpam-5043	297	4	use	use	NOUN
ejpam-5043	297	5	of	of	ADP
ejpam-5043	297	6	an	an	DET
ejpam-5043	297	7	innovative	innovative	ADJ
ejpam-5043	297	8	method	method	NOUN
ejpam-5043	297	9	for	for	ADP
ejpam-5043	297	10	the	the	DET
ejpam-5043	297	11	fractional	fractional	ADJ
ejpam-5043	297	12	derivative	derivative	NOUN
ejpam-5043	297	13	,	,	PUNCT
ejpam-5043	297	14	which	which	PRON
ejpam-5043	297	15	is	be	AUX
ejpam-5043	297	16	referred	refer	VERB
ejpam-5043	297	17	to	to	ADP
ejpam-5043	297	18	as	as	SCONJ
ejpam-5043	297	19	abc	abc	PROPN
ejpam-5043	297	20	-	-	PUNCT
ejpam-5043	297	21	fd	fd	PROPN
ejpam-5043	297	22	.	.	PUNCT
ejpam-5043	298	1	in	in	ADP
ejpam-5043	298	2	this	this	DET
ejpam-5043	298	3	work	work	NOUN
ejpam-5043	298	4	,	,	PUNCT
ejpam-5043	298	5	we	we	PRON
ejpam-5043	298	6	employ	employ	VERB
ejpam-5043	298	7	the	the	DET
ejpam-5043	298	8	rungekutta	rungekutta	NOUN
ejpam-5043	298	9	fourth	fourth	ADJ
ejpam-5043	298	10	order	order	NOUN
ejpam-5043	298	11	(	(	PUNCT
ejpam-5043	298	12	rk4	rk4	NOUN
ejpam-5043	298	13	)	)	PUNCT
ejpam-5043	298	14	approach	approach	NOUN
ejpam-5043	298	15	to	to	PART
ejpam-5043	298	16	evaluate	evaluate	VERB
ejpam-5043	298	17	the	the	DET
ejpam-5043	298	18	solutions	solution	NOUN
ejpam-5043	298	19	obtained	obtain	VERB
ejpam-5043	298	20	from	from	ADP
ejpam-5043	298	21	these	these	DET
ejpam-5043	298	22	methtable	methtable	ADJ
ejpam-5043	298	23	6	6	NUM
ejpam-5043	298	24	:	:	PUNCT
ejpam-5043	298	25	comparison	comparison	NOUN
ejpam-5043	298	26	between	between	ADP
ejpam-5043	298	27	the	the	DET
ejpam-5043	298	28	abc	abc	PROPN
ejpam-5043	298	29	-	-	PUNCT
ejpam-5043	298	30	fd	fd	PROPN
ejpam-5043	298	31	scheme	scheme	NOUN
ejpam-5043	298	32	and	and	CCONJ
ejpam-5043	298	33	rk4	rk4	NOUN
ejpam-5043	298	34	method	method	NOUN
ejpam-5043	298	35	for	for	ADP
ejpam-5043	298	36	y(t	y(t	PROPN
ejpam-5043	298	37	)	)	PUNCT
ejpam-5043	298	38	to	to	ADP
ejpam-5043	298	39	the	the	DET
ejpam-5043	298	40	fractional	fractional	ADJ
ejpam-5043	298	41	model	model	NOUN
ejpam-5043	298	42	equation	equation	NOUN
ejpam-5043	298	43	eq	eq	ADJ
ejpam-5043	298	44	.	.	PUNCT
ejpam-5043	299	1	(	(	PUNCT
ejpam-5043	299	2	24	24	NUM
ejpam-5043	299	3	)	)	PUNCT
ejpam-5043	299	4	.	.	PUNCT
ejpam-5043	300	1	t	t	PROPN
ejpam-5043	300	2	abc	abc	PROPN
ejpam-5043	300	3	-	-	PUNCT
ejpam-5043	300	4	fd(α	fd(α	NUM
ejpam-5043	300	5	=	=	NOUN
ejpam-5043	300	6	0.95	0.95	NUM
ejpam-5043	300	7	)	)	PUNCT
ejpam-5043	300	8	abc	abc	PROPN
ejpam-5043	300	9	-	-	PUNCT
ejpam-5043	300	10	fd(α	fd(α	NOUN
ejpam-5043	300	11	=	=	SYM
ejpam-5043	300	12	1	1	X
ejpam-5043	300	13	)	)	PUNCT
ejpam-5043	300	14	rk4	rk4	NOUN
ejpam-5043	300	15	0	0	NUM
ejpam-5043	300	16	0.1	0.1	NUM
ejpam-5043	300	17	0.1	0.1	NUM
ejpam-5043	300	18	0.1	0.1	NUM
ejpam-5043	300	19	0.1	0.1	NUM
ejpam-5043	300	20	1.162327452222037	1.162327452222037	NUM
ejpam-5043	300	21	1.110604044223248	1.110604044223248	NUM
ejpam-5043	300	22	1.111410479237619	1.111410479237619	NUM
ejpam-5043	300	23	0.2	0.2	NUM
ejpam-5043	300	24	1.243679775165603	1.243679775165603	NUM
ejpam-5043	300	25	1.206325497512754	1.206325497512754	NUM
ejpam-5043	300	26	1.207014508204590	1.207014508204590	NUM
ejpam-5043	300	27	0.3	0.3	NUM
ejpam-5043	300	28	1.307095940600464	1.307095940600464	NUM
ejpam-5043	300	29	1.287466819327066	1.287466819327066	NUM
ejpam-5043	300	30	1.288044529114395	1.288044529114395	NUM
ejpam-5043	300	31	0.4	0.4	NUM
ejpam-5043	300	32	1.354153393129866	1.354153393129866	NUM
ejpam-5043	300	33	1.354496996922664	1.354496996922664	NUM
ejpam-5043	300	34	1.354964920086584	1.354964920086584	NUM
ejpam-5043	300	35	0.5	0.5	NUM
ejpam-5043	300	36	1.385585796378668	1.385585796378668	NUM
ejpam-5043	300	37	1.407429186405125	1.407429186405125	NUM
ejpam-5043	300	38	1.407786249680785	1.407786249680785	NUM
ejpam-5043	300	39	references	reference	NOUN
ejpam-5043	300	40	457	457	NUM
ejpam-5043	300	41	table	table	NOUN
ejpam-5043	300	42	7	7	NUM
ejpam-5043	300	43	:	:	PUNCT
ejpam-5043	300	44	comparison	comparison	NOUN
ejpam-5043	300	45	between	between	ADP
ejpam-5043	300	46	the	the	DET
ejpam-5043	300	47	abc	abc	PROPN
ejpam-5043	300	48	-	-	PUNCT
ejpam-5043	300	49	fd	fd	PROPN
ejpam-5043	300	50	scheme	scheme	NOUN
ejpam-5043	300	51	and	and	CCONJ
ejpam-5043	300	52	rk4	rk4	NOUN
ejpam-5043	300	53	method	method	NOUN
ejpam-5043	300	54	for	for	ADP
ejpam-5043	300	55	z(t	z(t	NOUN
ejpam-5043	300	56	)	)	PUNCT
ejpam-5043	300	57	to	to	ADP
ejpam-5043	300	58	the	the	DET
ejpam-5043	300	59	fractional	fractional	ADJ
ejpam-5043	300	60	model	model	NOUN
ejpam-5043	300	61	equation	equation	NOUN
ejpam-5043	300	62	eq	eq	ADJ
ejpam-5043	300	63	.	.	PUNCT
ejpam-5043	301	1	(	(	PUNCT
ejpam-5043	301	2	24	24	NUM
ejpam-5043	301	3	)	)	PUNCT
ejpam-5043	301	4	.	.	PUNCT
ejpam-5043	302	1	t	t	PROPN
ejpam-5043	302	2	abc	abc	PROPN
ejpam-5043	302	3	-	-	PUNCT
ejpam-5043	302	4	fd(α	fd(α	NUM
ejpam-5043	302	5	=	=	NOUN
ejpam-5043	302	6	0.95	0.95	NUM
ejpam-5043	302	7	)	)	PUNCT
ejpam-5043	302	8	abc	abc	PROPN
ejpam-5043	302	9	-	-	PUNCT
ejpam-5043	302	10	fd(α	fd(α	NOUN
ejpam-5043	302	11	=	=	SYM
ejpam-5043	302	12	1	1	X
ejpam-5043	302	13	)	)	PUNCT
ejpam-5043	302	14	rk4	rk4	NOUN
ejpam-5043	302	15	0	0	NUM
ejpam-5043	302	16	0.1	0.1	NUM
ejpam-5043	302	17	0.1	0.1	NUM
ejpam-5043	302	18	0.1	0.1	NUM
ejpam-5043	302	19	0.1	0.1	NUM
ejpam-5043	302	20	0.563027164530943	0.563027164530943	NUM
ejpam-5043	302	21	0.668146806337842	0.668146806337842	NUM
ejpam-5043	302	22	0.665758002503422	0.665758002503422	NUM
ejpam-5043	302	23	0.2	0.2	NUM
ejpam-5043	302	24	0.385951374918309	0.385951374918309	NUM
ejpam-5043	302	25	0.422012789499755	0.422012789499755	NUM
ejpam-5043	302	26	0.420504778950151	0.420504778950151	NUM
ejpam-5043	302	27	0.3	0.3	NUM
ejpam-5043	302	28	0.271239731606305	0.271239731606305	NUM
ejpam-5043	302	29	0.268070090773060	0.268070090773060	NUM
ejpam-5043	302	30	0.267135297212523	0.267135297212523	NUM
ejpam-5043	302	31	0.4	0.4	NUM
ejpam-5043	302	32	0.195819117416147	0.195819117416147	NUM
ejpam-5043	302	33	0.173389179063020	0.173389179063020	NUM
ejpam-5043	302	34	0.172818474082330	0.172818474082330	NUM
ejpam-5043	302	35	0.5	0.5	NUM
ejpam-5043	302	36	0.145751174250475	0.145751174250475	NUM
ejpam-5043	302	37	0.115968853477924	0.115968853477924	NUM
ejpam-5043	302	38	0.115624863785721	0.115624863785721	NUM
ejpam-5043	302	39	ods	ods	PROPN
ejpam-5043	302	40	.	.	PUNCT
ejpam-5043	303	1	to	to	PART
ejpam-5043	303	2	facilitate	facilitate	VERB
ejpam-5043	303	3	the	the	DET
ejpam-5043	303	4	abc	abc	PROPN
ejpam-5043	303	5	-	-	PUNCT
ejpam-5043	303	6	fd	fd	PROPN
ejpam-5043	303	7	approach	approach	NOUN
ejpam-5043	303	8	of	of	ADP
ejpam-5043	303	9	solution	solution	NOUN
ejpam-5043	303	10	comparison	comparison	NOUN
ejpam-5043	303	11	,	,	PUNCT
ejpam-5043	303	12	we	we	PRON
ejpam-5043	303	13	offered	offer	VERB
ejpam-5043	303	14	a	a	DET
ejpam-5043	303	15	numerical	numerical	ADJ
ejpam-5043	303	16	strategy	strategy	NOUN
ejpam-5043	303	17	that	that	PRON
ejpam-5043	303	18	made	make	VERB
ejpam-5043	303	19	use	use	NOUN
ejpam-5043	303	20	of	of	ADP
ejpam-5043	303	21	the	the	DET
ejpam-5043	303	22	resources	resource	NOUN
ejpam-5043	303	23	that	that	PRON
ejpam-5043	303	24	were	be	AUX
ejpam-5043	303	25	included	include	VERB
ejpam-5043	303	26	in	in	ADP
ejpam-5043	303	27	the	the	DET
ejpam-5043	303	28	matlab	matlab	PROPN
ejpam-5043	303	29	software	software	NOUN
ejpam-5043	303	30	package	package	NOUN
ejpam-5043	303	31	.	.	PUNCT
ejpam-5043	304	1	in	in	ADP
ejpam-5043	304	2	terms	term	NOUN
ejpam-5043	304	3	of	of	ADP
ejpam-5043	304	4	how	how	SCONJ
ejpam-5043	304	5	well	well	ADV
ejpam-5043	304	6	they	they	PRON
ejpam-5043	304	7	keep	keep	VERB
ejpam-5043	304	8	their	their	PRON
ejpam-5043	304	9	numerical	numerical	ADJ
ejpam-5043	304	10	stability	stability	NOUN
ejpam-5043	304	11	,	,	PUNCT
ejpam-5043	304	12	the	the	DET
ejpam-5043	304	13	numerical	numerical	ADJ
ejpam-5043	304	14	results	result	NOUN
ejpam-5043	304	15	suggest	suggest	VERB
ejpam-5043	304	16	that	that	SCONJ
ejpam-5043	304	17	our	our	PRON
ejpam-5043	304	18	technology	technology	NOUN
ejpam-5043	304	19	can	can	AUX
ejpam-5043	304	20	perform	perform	VERB
ejpam-5043	304	21	fractional	fractional	ADJ
ejpam-5043	304	22	processes	process	NOUN
ejpam-5043	304	23	that	that	PRON
ejpam-5043	304	24	meet	meet	VERB
ejpam-5043	304	25	the	the	DET
ejpam-5043	304	26	requirements	requirement	NOUN
ejpam-5043	304	27	that	that	PRON
ejpam-5043	304	28	were	be	AUX
ejpam-5043	304	29	set	set	VERB
ejpam-5043	304	30	for	for	ADP
ejpam-5043	304	31	them	they	PRON
ejpam-5043	304	32	.	.	PUNCT
ejpam-5043	305	1	the	the	DET
ejpam-5043	305	2	fact	fact	NOUN
ejpam-5043	305	3	that	that	SCONJ
ejpam-5043	305	4	the	the	DET
ejpam-5043	305	5	numerical	numerical	ADJ
ejpam-5043	305	6	figures	figure	NOUN
ejpam-5043	305	7	that	that	PRON
ejpam-5043	305	8	were	be	AUX
ejpam-5043	305	9	produced	produce	VERB
ejpam-5043	305	10	were	be	AUX
ejpam-5043	305	11	accurate	accurate	ADJ
ejpam-5043	305	12	is	be	AUX
ejpam-5043	305	13	evidence	evidence	NOUN
ejpam-5043	305	14	that	that	SCONJ
ejpam-5043	305	15	this	this	PRON
ejpam-5043	305	16	is	be	AUX
ejpam-5043	305	17	the	the	DET
ejpam-5043	305	18	case	case	NOUN
ejpam-5043	305	19	.	.	PUNCT
ejpam-5043	306	1	a	a	DET
ejpam-5043	306	2	comparison	comparison	NOUN
ejpam-5043	306	3	of	of	ADP
ejpam-5043	306	4	the	the	DET
ejpam-5043	306	5	solutions	solution	NOUN
ejpam-5043	306	6	of	of	ADP
ejpam-5043	306	7	these	these	DET
ejpam-5043	306	8	methods	method	NOUN
ejpam-5043	306	9	with	with	ADP
ejpam-5043	306	10	those	those	PRON
ejpam-5043	306	11	obtained	obtain	VERB
ejpam-5043	306	12	by	by	ADP
ejpam-5043	306	13	the	the	DET
ejpam-5043	306	14	runge	runge	NOUN
ejpam-5043	306	15	-	-	PUNCT
ejpam-5043	306	16	kutta	kutta	NOUN
ejpam-5043	306	17	fourth	fourth	ADJ
ejpam-5043	306	18	order	order	NOUN
ejpam-5043	306	19	(	(	PUNCT
ejpam-5043	306	20	rk4	rk4	NOUN
ejpam-5043	306	21	)	)	PUNCT
ejpam-5043	306	22	method	method	NOUN
ejpam-5043	306	23	is	be	AUX
ejpam-5043	306	24	done	do	VERB
ejpam-5043	306	25	.	.	PUNCT
ejpam-5043	307	1	using	use	VERB
ejpam-5043	307	2	matlab	matlab	PROPN
ejpam-5043	307	3	software	software	NOUN
ejpam-5043	307	4	package	package	NOUN
ejpam-5043	307	5	tools	tool	NOUN
ejpam-5043	307	6	,	,	PUNCT
ejpam-5043	307	7	we	we	PRON
ejpam-5043	307	8	provided	provide	VERB
ejpam-5043	307	9	a	a	DET
ejpam-5043	307	10	numerical	numerical	ADJ
ejpam-5043	307	11	strategy	strategy	NOUN
ejpam-5043	307	12	to	to	PART
ejpam-5043	307	13	aid	aid	VERB
ejpam-5043	307	14	the	the	DET
ejpam-5043	307	15	abc	abc	PROPN
ejpam-5043	307	16	-	-	PUNCT
ejpam-5043	307	17	fd	fd	PROPN
ejpam-5043	307	18	method	method	NOUN
ejpam-5043	307	19	in	in	ADP
ejpam-5043	307	20	comparing	compare	VERB
ejpam-5043	307	21	the	the	DET
ejpam-5043	307	22	solutions	solution	NOUN
ejpam-5043	307	23	.	.	PUNCT
ejpam-5043	308	1	the	the	DET
ejpam-5043	308	2	numerical	numerical	PROPN
ejpam-5043	308	3	findings	finding	NOUN
ejpam-5043	308	4	demonstrate	demonstrate	VERB
ejpam-5043	308	5	that	that	SCONJ
ejpam-5043	308	6	our	our	PRON
ejpam-5043	308	7	method	method	NOUN
ejpam-5043	308	8	performs	perform	VERB
ejpam-5043	308	9	fractional	fractional	ADJ
ejpam-5043	308	10	procedures	procedure	NOUN
ejpam-5043	308	11	which	which	PRON
ejpam-5043	308	12	satisfy	satisfy	VERB
ejpam-5043	308	13	expectations	expectation	NOUN
ejpam-5043	308	14	for	for	ADP
ejpam-5043	308	15	how	how	SCONJ
ejpam-5043	308	16	successfully	successfully	ADV
ejpam-5043	308	17	they	they	PRON
ejpam-5043	308	18	maintain	maintain	VERB
ejpam-5043	308	19	their	their	PRON
ejpam-5043	308	20	numerical	numerical	ADJ
ejpam-5043	308	21	stability	stability	NOUN
ejpam-5043	308	22	.	.	PUNCT
ejpam-5043	309	1	the	the	DET
ejpam-5043	309	2	accuracy	accuracy	NOUN
ejpam-5043	309	3	of	of	ADP
ejpam-5043	309	4	the	the	DET
ejpam-5043	309	5	numerical	numerical	ADJ
ejpam-5043	309	6	results	result	NOUN
ejpam-5043	309	7	produced	produce	VERB
ejpam-5043	309	8	serves	serve	VERB
ejpam-5043	309	9	as	as	ADP
ejpam-5043	309	10	evidence	evidence	NOUN
ejpam-5043	309	11	for	for	ADP
ejpam-5043	309	12	this	this	PRON
ejpam-5043	309	13	.	.	PUNCT
ejpam-5043	310	1	proficiency	proficiency	NOUN
ejpam-5043	310	2	in	in	ADP
ejpam-5043	310	3	fractional	fractional	ADJ
ejpam-5043	310	4	differential	differential	ADJ
ejpam-5043	310	5	equation	equation	NOUN
ejpam-5043	310	6	solving	solving	NOUN
ejpam-5043	310	7	and	and	CCONJ
ejpam-5043	310	8	precise	precise	ADJ
ejpam-5043	310	9	modeling	modeling	NOUN
ejpam-5043	310	10	of	of	ADP
ejpam-5043	310	11	chaotic	chaotic	ADJ
ejpam-5043	310	12	systems	system	NOUN
ejpam-5043	310	13	has	have	VERB
ejpam-5043	310	14	applications	application	NOUN
ejpam-5043	310	15	in	in	ADP
ejpam-5043	310	16	signal	signal	ADJ
ejpam-5043	310	17	processing	processing	NOUN
ejpam-5043	310	18	,	,	PUNCT
ejpam-5043	310	19	control	control	NOUN
ejpam-5043	310	20	theory	theory	NOUN
ejpam-5043	310	21	,	,	PUNCT
ejpam-5043	310	22	communication	communication	NOUN
ejpam-5043	310	23	systems	system	NOUN
ejpam-5043	310	24	,	,	PUNCT
ejpam-5043	310	25	and	and	CCONJ
ejpam-5043	310	26	other	other	ADJ
ejpam-5043	310	27	fields	field	NOUN
ejpam-5043	310	28	.	.	PUNCT
ejpam-5043	311	1	engineers	engineer	NOUN
ejpam-5043	311	2	may	may	AUX
ejpam-5043	311	3	be	be	AUX
ejpam-5043	311	4	able	able	ADJ
ejpam-5043	311	5	to	to	PART
ejpam-5043	311	6	improve	improve	VERB
ejpam-5043	311	7	the	the	DET
ejpam-5043	311	8	performance	performance	NOUN
ejpam-5043	311	9	of	of	ADP
ejpam-5043	311	10	current	current	ADJ
ejpam-5043	311	11	systems	system	NOUN
ejpam-5043	311	12	and	and	CCONJ
ejpam-5043	311	13	create	create	VERB
ejpam-5043	311	14	more	more	ADV
ejpam-5043	311	15	resilient	resilient	ADJ
ejpam-5043	311	16	designs	design	NOUN
ejpam-5043	311	17	that	that	PRON
ejpam-5043	311	18	can	can	AUX
ejpam-5043	311	19	manage	manage	VERB
ejpam-5043	311	20	nonlinear	nonlinear	ADJ
ejpam-5043	311	21	dynamics	dynamic	NOUN
ejpam-5043	311	22	by	by	ADP
ejpam-5043	311	23	utilizing	utilize	VERB
ejpam-5043	311	24	the	the	DET
ejpam-5043	311	25	abcfd	abcfd	NOUN
ejpam-5043	311	26	method	method	NOUN
ejpam-5043	311	27	.	.	PUNCT
ejpam-5043	312	1	we	we	PRON
ejpam-5043	312	2	suggested	suggest	VERB
ejpam-5043	312	3	using	use	VERB
ejpam-5043	312	4	this	this	DET
ejpam-5043	312	5	approach	approach	NOUN
ejpam-5043	312	6	to	to	PART
ejpam-5043	312	7	tackle	tackle	VERB
ejpam-5043	312	8	brand	brand	NOUN
ejpam-5043	312	9	-	-	PUNCT
ejpam-5043	312	10	new	new	ADJ
ejpam-5043	312	11	fractional	fractional	ADJ
ejpam-5043	312	12	problems	problem	NOUN
ejpam-5043	312	13	[	[	X
ejpam-5043	312	14	7	7	NUM
ejpam-5043	312	15	,	,	PUNCT
ejpam-5043	312	16	10	10	NUM
ejpam-5043	312	17	,	,	PUNCT
ejpam-5043	312	18	41	41	NUM
ejpam-5043	312	19	]	]	PUNCT
ejpam-5043	312	20	and	and	CCONJ
ejpam-5043	312	21	contrasting	contrast	VERB
ejpam-5043	312	22	numerical	numerical	ADJ
ejpam-5043	312	23	solutions	solution	NOUN
ejpam-5043	312	24	with	with	ADP
ejpam-5043	312	25	other	other	ADJ
ejpam-5043	312	26	approaches	approach	NOUN
ejpam-5043	312	27	[	[	X
ejpam-5043	312	28	6	6	NUM
ejpam-5043	312	29	,	,	PUNCT
ejpam-5043	312	30	19	19	NUM
ejpam-5043	312	31	,	,	PUNCT
ejpam-5043	312	32	26–28	26–28	NUM
ejpam-5043	312	33	]	]	PUNCT
ejpam-5043	312	34	.	.	PUNCT
ejpam-5043	313	1	acknowledgements	acknowledgement	VERB
ejpam-5043	313	2	the	the	DET
ejpam-5043	313	3	author	author	NOUN
ejpam-5043	313	4	thank	thank	VERB
ejpam-5043	313	5	the	the	DET
ejpam-5043	313	6	editor	editor	NOUN
ejpam-5043	313	7	in	in	ADP
ejpam-5043	313	8	chief	chief	NOUN
ejpam-5043	313	9	of	of	ADP
ejpam-5043	313	10	european	european	PROPN
ejpam-5043	313	11	journal	journal	PROPN
ejpam-5043	313	12	of	of	ADP
ejpam-5043	313	13	pure	pure	ADJ
ejpam-5043	313	14	and	and	CCONJ
ejpam-5043	313	15	applied	applied	ADJ
ejpam-5043	313	16	mathematics	mathematic	NOUN
ejpam-5043	313	17	and	and	CCONJ
ejpam-5043	313	18	the	the	DET
ejpam-5043	313	19	referees	referee	NOUN
ejpam-5043	313	20	for	for	ADP
ejpam-5043	313	21	their	their	PRON
ejpam-5043	313	22	critical	critical	ADJ
ejpam-5043	313	23	reviews	review	NOUN
ejpam-5043	313	24	and	and	CCONJ
ejpam-5043	313	25	valuable	valuable	ADJ
ejpam-5043	313	26	comments	comment	NOUN
ejpam-5043	313	27	which	which	PRON
ejpam-5043	313	28	thoroughly	thoroughly	ADV
ejpam-5043	313	29	improved	improve	VERB
ejpam-5043	313	30	the	the	DET
ejpam-5043	313	31	paper	paper	NOUN
ejpam-5043	313	32	.	.	PUNCT
ejpam-5043	314	1	references	reference	NOUN
ejpam-5043	314	2	[	[	X
ejpam-5043	314	3	1	1	NUM
ejpam-5043	314	4	]	]	PUNCT
ejpam-5043	314	5	a.	a.	NOUN
ejpam-5043	314	6	belazi	belazi	PROPN
ejpam-5043	314	7	,	,	PUNCT
ejpam-5043	314	8	r.	r.	PROPN
ejpam-5043	314	9	rhouma	rhouma	PROPN
ejpam-5043	314	10	,	,	PUNCT
ejpam-5043	314	11	and	and	CCONJ
ejpam-5043	314	12	s.	s.	PROPN
ejpam-5043	314	13	belghith	belghith	PROPN
ejpam-5043	314	14	.	.	PUNCT
ejpam-5043	315	1	a	a	DET
ejpam-5043	315	2	novel	novel	ADJ
ejpam-5043	315	3	approach	approach	NOUN
ejpam-5043	315	4	to	to	PART
ejpam-5043	315	5	construct	construct	VERB
ejpam-5043	315	6	s	s	NOUN
ejpam-5043	315	7	-	-	NOUN
ejpam-5043	315	8	box	box	NOUN
ejpam-5043	315	9	based	base	VERB
ejpam-5043	315	10	on	on	ADP
ejpam-5043	315	11	rössler	rössler	NOUN
ejpam-5043	315	12	system	system	NOUN
ejpam-5043	315	13	.	.	PUNCT
ejpam-5043	316	1	international	international	ADJ
ejpam-5043	316	2	wireless	wireless	ADJ
ejpam-5043	316	3	communications	communication	NOUN
ejpam-5043	316	4	and	and	CCONJ
ejpam-5043	316	5	mobile	mobile	NOUN
ejpam-5043	316	6	computing	computing	NOUN
ejpam-5043	316	7	conference	conference	NOUN
ejpam-5043	316	8	(	(	PUNCT
ejpam-5043	316	9	iwcmc	iwcmc	NOUN
ejpam-5043	316	10	)	)	PUNCT
ejpam-5043	316	11	,	,	PUNCT
ejpam-5043	316	12	aug	aug	PROPN
ejpam-5043	316	13	.	.	PROPN
ejpam-5043	316	14	2015	2015	NUM
ejpam-5043	316	15	.	.	PUNCT
ejpam-5043	317	1	[	[	X
ejpam-5043	317	2	2	2	NUM
ejpam-5043	317	3	]	]	X
ejpam-5043	317	4	abu	abu	PROPN
ejpam-5043	317	5	-	-	PUNCT
ejpam-5043	317	6	ghuwaleh	ghuwaleh	PROPN
ejpam-5043	317	7	m.	m.	NOUN
ejpam-5043	317	8	,	,	PUNCT
ejpam-5043	317	9	saadeh	saadeh	PROPN
ejpam-5043	317	10	r.	r.	PROPN
ejpam-5043	317	11	and	and	CCONJ
ejpam-5043	317	12	qazza	qazza	PROPN
ejpam-5043	317	13	a.	a.	PROPN
ejpam-5043	317	14	general	general	PROPN
ejpam-5043	317	15	master	master	NOUN
ejpam-5043	317	16	theorems	theorem	NOUN
ejpam-5043	317	17	of	of	ADP
ejpam-5043	317	18	integrals	integral	NOUN
ejpam-5043	317	19	with	with	ADP
ejpam-5043	317	20	applications	application	NOUN
ejpam-5043	317	21	.	.	PUNCT
ejpam-5043	318	1	mathematics	mathematic	NOUN
ejpam-5043	318	2	,	,	PUNCT
ejpam-5043	318	3	10(19):3547	10(19):3547	NUM
ejpam-5043	318	4	,	,	PUNCT
ejpam-5043	318	5	2022	2022	NUM
ejpam-5043	318	6	.	.	PUNCT
ejpam-5043	319	1	references	reference	NOUN
ejpam-5043	319	2	458	458	NUM
ejpam-5043	320	1	[	[	X
ejpam-5043	320	2	3	3	NUM
ejpam-5043	320	3	]	]	X
ejpam-5043	320	4	r.	r.	PROPN
ejpam-5043	320	5	adams	adams	PROPN
ejpam-5043	320	6	.	.	PUNCT
ejpam-5043	321	1	sobolev	sobolev	PROPN
ejpam-5043	321	2	spaces	space	VERB
ejpam-5043	321	3	.	.	PUNCT
ejpam-5043	322	1	academic	academic	ADJ
ejpam-5043	322	2	press	press	NOUN
ejpam-5043	322	3	,	,	PUNCT
ejpam-5043	322	4	new	new	PROPN
ejpam-5043	322	5	york	york	PROPN
ejpam-5043	322	6	,	,	PUNCT
ejpam-5043	322	7	1975	1975	NUM
ejpam-5043	322	8	.	.	PUNCT
ejpam-5043	323	1	[	[	X
ejpam-5043	323	2	4	4	NUM
ejpam-5043	323	3	]	]	PUNCT
ejpam-5043	323	4	almutairi	almutairi	PROPN
ejpam-5043	323	5	d.	d.	PROPN
ejpam-5043	323	6	k.	k.	PROPN
ejpam-5043	323	7	,	,	PUNCT
ejpam-5043	323	8	abdoon	abdoon	PROPN
ejpam-5043	323	9	m.	m.	NOUN
ejpam-5043	323	10	a.	a.	PROPN
ejpam-5043	323	11	,	,	PUNCT
ejpam-5043	323	12	berir	berir	NOUN
ejpam-5043	323	13	m.	m.	NOUN
ejpam-5043	323	14	,	,	PUNCT
ejpam-5043	323	15	saadeh	saadeh	PROPN
ejpam-5043	323	16	r.	r.	PROPN
ejpam-5043	323	17	,	,	PUNCT
ejpam-5043	323	18	and	and	CCONJ
ejpam-5043	323	19	qazza	qazza	PROPN
ejpam-5043	323	20	a.	a.	PROPN
ejpam-5043	323	21	a	a	DET
ejpam-5043	323	22	numerical	numerical	ADJ
ejpam-5043	323	23	confirmation	confirmation	NOUN
ejpam-5043	323	24	of	of	ADP
ejpam-5043	323	25	a	a	DET
ejpam-5043	323	26	fractional	fractional	ADJ
ejpam-5043	323	27	seitr	seitr	NOUN
ejpam-5043	323	28	for	for	ADP
ejpam-5043	323	29	influenza	influenza	NOUN
ejpam-5043	323	30	model	model	NOUN
ejpam-5043	323	31	efficiency	efficiency	NOUN
ejpam-5043	323	32	.	.	PUNCT
ejpam-5043	324	1	applied	apply	VERB
ejpam-5043	324	2	mathematics	mathematics	PROPN
ejpam-5043	324	3	information	information	NOUN
ejpam-5043	324	4	sciences	science	NOUN
ejpam-5043	324	5	,	,	PUNCT
ejpam-5043	324	6	17(25):741–749	17(25):741–749	NUM
ejpam-5043	324	7	,	,	PUNCT
ejpam-5043	324	8	2023	2023	NUM
ejpam-5043	324	9	.	.	PUNCT
ejpam-5043	325	1	[	[	X
ejpam-5043	325	2	5	5	NUM
ejpam-5043	325	3	]	]	PUNCT
ejpam-5043	325	4	m.	m.	NOUN
ejpam-5043	325	5	almutairi	almutairi	PROPN
ejpam-5043	325	6	d.	d.	PROPN
ejpam-5043	325	7	k.	k.	PROPN
ejpam-5043	325	8	,	,	PUNCT
ejpam-5043	325	9	abdoon	abdoon	PROPN
ejpam-5043	325	10	m.	m.	PROPN
ejpam-5043	325	11	a.	a.	PROPN
ejpam-5043	325	12	,	,	PUNCT
ejpam-5043	325	13	salih	salih	PROPN
ejpam-5043	325	14	s.	s.	PROPN
ejpam-5043	325	15	y.	y.	PROPN
ejpam-5043	325	16	m.	m.	PROPN
ejpam-5043	325	17	,	,	PUNCT
ejpam-5043	325	18	elsamani	elsamani	PROPN
ejpam-5043	325	19	s.	s.	PROPN
ejpam-5043	325	20	a.	a.	PROPN
ejpam-5043	325	21	,	,	PUNCT
ejpam-5043	325	22	guma	guma	PROPN
ejpam-5043	325	23	f.	f.	PROPN
ejpam-5043	325	24	e.	e.	PROPN
ejpam-5043	325	25	,	,	PUNCT
ejpam-5043	325	26	berir	berir	NOUN
ejpam-5043	325	27	.	.	PUNCT
ejpam-5043	326	1	modeling	modeling	NOUN
ejpam-5043	326	2	and	and	CCONJ
ejpam-5043	326	3	analysis	analysis	NOUN
ejpam-5043	326	4	of	of	ADP
ejpam-5043	326	5	a	a	DET
ejpam-5043	326	6	fractional	fractional	ADJ
ejpam-5043	326	7	visceral	visceral	ADJ
ejpam-5043	326	8	leishmaniosis	leishmaniosis	NOUN
ejpam-5043	326	9	with	with	ADP
ejpam-5043	326	10	caputo	caputo	PROPN
ejpam-5043	326	11	and	and	CCONJ
ejpam-5043	326	12	caputo	caputo	PROPN
ejpam-5043	326	13	–	–	PUNCT
ejpam-5043	326	14	fabrizio	fabrizio	NOUN
ejpam-5043	326	15	derivatives	derivative	NOUN
ejpam-5043	326	16	.	.	PUNCT
ejpam-5043	327	1	journal	journal	NOUN
ejpam-5043	327	2	of	of	ADP
ejpam-5043	327	3	the	the	DET
ejpam-5043	327	4	nigerian	nigerian	ADJ
ejpam-5043	327	5	society	society	NOUN
ejpam-5043	327	6	of	of	ADP
ejpam-5043	327	7	physical	physical	ADJ
ejpam-5043	327	8	sciences	science	NOUN
ejpam-5043	327	9	,	,	PUNCT
ejpam-5043	327	10	5(3):1453	5(3):1453	NUM
ejpam-5043	327	11	,	,	PUNCT
ejpam-5043	327	12	2023	2023	NUM
ejpam-5043	327	13	.	.	PUNCT
ejpam-5043	328	1	[	[	X
ejpam-5043	328	2	6	6	NUM
ejpam-5043	328	3	]	]	PUNCT
ejpam-5043	328	4	abdulrahman	abdulrahman	NOUN
ejpam-5043	328	5	bmalzahrani	bmalzahrani	PROPN
ejpam-5043	328	6	,	,	PUNCT
ejpam-5043	328	7	rania	rania	PROPN
ejpam-5043	328	8	saadeh	saadeh	PROPN
ejpam-5043	328	9	,	,	PUNCT
ejpam-5043	328	10	mohamed	mohame	VERB
ejpam-5043	328	11	a	a	DET
ejpam-5043	328	12	abdoon	abdoon	NOUN
ejpam-5043	328	13	,	,	PUNCT
ejpam-5043	328	14	mohamed	mohamed	PROPN
ejpam-5043	328	15	elbadri	elbadri	PROPN
ejpam-5043	328	16	,	,	PUNCT
ejpam-5043	328	17	mohammed	mohammed	PROPN
ejpam-5043	328	18	berir	berir	PROPN
ejpam-5043	328	19	,	,	PUNCT
ejpam-5043	328	20	and	and	CCONJ
ejpam-5043	328	21	ahmad	ahmad	PROPN
ejpam-5043	328	22	qazza	qazza	PROPN
ejpam-5043	328	23	.	.	PUNCT
ejpam-5043	329	1	effective	effective	ADJ
ejpam-5043	329	2	methods	method	NOUN
ejpam-5043	329	3	for	for	ADP
ejpam-5043	329	4	numerical	numerical	ADJ
ejpam-5043	329	5	analysis	analysis	NOUN
ejpam-5043	329	6	of	of	ADP
ejpam-5043	329	7	the	the	DET
ejpam-5043	329	8	simplest	simple	ADJ
ejpam-5043	329	9	chaotic	chaotic	ADJ
ejpam-5043	329	10	circuit	circuit	NOUN
ejpam-5043	329	11	model	model	NOUN
ejpam-5043	329	12	with	with	ADP
ejpam-5043	329	13	atangana	atangana	PROPN
ejpam-5043	329	14	–	–	PUNCT
ejpam-5043	329	15	baleanu	baleanu	PROPN
ejpam-5043	329	16	caputo	caputo	PROPN
ejpam-5043	329	17	fractional	fractional	PROPN
ejpam-5043	329	18	derivative	derivative	PROPN
ejpam-5043	329	19	.	.	PUNCT
ejpam-5043	330	1	journal	journal	PROPN
ejpam-5043	330	2	of	of	ADP
ejpam-5043	330	3	engineering	engineering	NOUN
ejpam-5043	330	4	mathematics	mathematic	NOUN
ejpam-5043	330	5	,	,	PUNCT
ejpam-5043	330	6	144(1):9	144(1):9	NUM
ejpam-5043	330	7	,	,	PUNCT
ejpam-5043	330	8	2024	2024	NUM
ejpam-5043	330	9	.	.	PUNCT
ejpam-5043	331	1	[	[	X
ejpam-5043	331	2	7	7	X
ejpam-5043	331	3	]	]	X
ejpam-5043	331	4	a	a	DET
ejpam-5043	331	5	atangana	atangana	NOUN
ejpam-5043	331	6	and	and	CCONJ
ejpam-5043	331	7	d	d	NOUN
ejpam-5043	331	8	baleanu	baleanu	NOUN
ejpam-5043	331	9	.	.	PUNCT
ejpam-5043	332	1	new	new	ADJ
ejpam-5043	332	2	fractional	fractional	ADJ
ejpam-5043	332	3	derivatives	derivative	NOUN
ejpam-5043	332	4	with	with	ADP
ejpam-5043	332	5	nonlocal	nonlocal	ADJ
ejpam-5043	332	6	and	and	CCONJ
ejpam-5043	332	7	non	non	ADJ
ejpam-5043	332	8	-	-	ADJ
ejpam-5043	332	9	singular	singular	ADJ
ejpam-5043	332	10	kernel	kernel	NOUN
ejpam-5043	332	11	:	:	PUNCT
ejpam-5043	332	12	theory	theory	NOUN
ejpam-5043	332	13	and	and	CCONJ
ejpam-5043	332	14	application	application	NOUN
ejpam-5043	332	15	to	to	PART
ejpam-5043	332	16	heat	heat	NOUN
ejpam-5043	332	17	transfer	transfer	NOUN
ejpam-5043	332	18	model	model	NOUN
ejpam-5043	332	19	.	.	PUNCT
ejpam-5043	333	1	therm	therm	PROPN
ejpam-5043	333	2	.	.	PUNCT
ejpam-5043	334	1	sci	sci	PROPN
ejpam-5043	334	2	.	.	PROPN
ejpam-5043	334	3	,	,	PUNCT
ejpam-5043	334	4	20(2):763–769	20(2):763–769	PROPN
ejpam-5043	334	5	,	,	PUNCT
ejpam-5043	334	6	2016	2016	NUM
ejpam-5043	334	7	.	.	PUNCT
ejpam-5043	335	1	[	[	X
ejpam-5043	335	2	8	8	NUM
ejpam-5043	335	3	]	]	X
ejpam-5043	335	4	abdon	abdon	NOUN
ejpam-5043	335	5	atangana	atangana	PROPN
ejpam-5043	335	6	and	and	CCONJ
ejpam-5043	335	7	sania	sania	PROPN
ejpam-5043	335	8	qureshi	qureshi	PROPN
ejpam-5043	335	9	.	.	PUNCT
ejpam-5043	336	1	modeling	model	VERB
ejpam-5043	336	2	attractors	attractor	NOUN
ejpam-5043	336	3	of	of	ADP
ejpam-5043	336	4	chaotic	chaotic	ADJ
ejpam-5043	336	5	dynamical	dynamical	ADJ
ejpam-5043	336	6	systems	system	NOUN
ejpam-5043	336	7	with	with	ADP
ejpam-5043	336	8	fractal	fractal	ADJ
ejpam-5043	336	9	–	–	PUNCT
ejpam-5043	336	10	fractional	fractional	ADJ
ejpam-5043	336	11	operators	operator	NOUN
ejpam-5043	336	12	.	.	PUNCT
ejpam-5043	337	1	chaos	chaos	NOUN
ejpam-5043	337	2	,	,	PUNCT
ejpam-5043	337	3	solitons	soliton	NOUN
ejpam-5043	337	4	&	&	CCONJ
ejpam-5043	337	5	fractals	fractal	NOUN
ejpam-5043	337	6	,	,	PUNCT
ejpam-5043	337	7	123:320–337	123:320–337	NUM
ejpam-5043	337	8	,	,	PUNCT
ejpam-5043	337	9	2019	2019	NUM
ejpam-5043	337	10	.	.	PUNCT
ejpam-5043	338	1	[	[	X
ejpam-5043	338	2	9	9	X
ejpam-5043	338	3	]	]	PUNCT
ejpam-5043	338	4	bingi	bingi	PROPN
ejpam-5043	338	5	k.	k.	PROPN
ejpam-5043	338	6	,	,	PUNCT
ejpam-5043	338	7	rajanarayan	rajanarayan	PROPN
ejpam-5043	338	8	prusty	prusty	PROPN
ejpam-5043	338	9	b.	b.	PROPN
ejpam-5043	338	10	,	,	PUNCT
ejpam-5043	338	11	and	and	CCONJ
ejpam-5043	338	12	pal	pal	ADJ
ejpam-5043	338	13	singh	singh	PROPN
ejpam-5043	338	14	a.	a.	NOUN
ejpam-5043	338	15	a	a	DET
ejpam-5043	338	16	review	review	NOUN
ejpam-5043	338	17	on	on	ADP
ejpam-5043	338	18	fractional	fractional	ADJ
ejpam-5043	338	19	-	-	PUNCT
ejpam-5043	338	20	order	order	NOUN
ejpam-5043	338	21	modelling	modelling	NOUN
ejpam-5043	338	22	and	and	CCONJ
ejpam-5043	338	23	control	control	NOUN
ejpam-5043	338	24	of	of	ADP
ejpam-5043	338	25	robotic	robotic	ADJ
ejpam-5043	338	26	manipulators	manipulator	NOUN
ejpam-5043	338	27	.	.	PUNCT
ejpam-5043	339	1	fractal	fractal	ADJ
ejpam-5043	339	2	and	and	CCONJ
ejpam-5043	339	3	fractional	fractional	ADJ
ejpam-5043	339	4	.	.	PUNCT
ejpam-5043	339	5	,	,	PUNCT
ejpam-5043	339	6	7(1):77	7(1):77	NOUN
ejpam-5043	339	7	,	,	PUNCT
ejpam-5043	339	8	2023	2023	NUM
ejpam-5043	339	9	.	.	PUNCT
ejpam-5043	340	1	[	[	X
ejpam-5043	340	2	10	10	NUM
ejpam-5043	340	3	]	]	X
ejpam-5043	340	4	dumitru	dumitru	X
ejpam-5043	340	5	d.	d.	PROPN
ejpam-5043	340	6	description	description	NOUN
ejpam-5043	340	7	of	of	ADP
ejpam-5043	340	8	strange	strange	ADJ
ejpam-5043	340	9	attractors	attractor	NOUN
ejpam-5043	340	10	using	use	VERB
ejpam-5043	340	11	invariants	invariant	NOUN
ejpam-5043	340	12	of	of	ADP
ejpam-5043	340	13	phase	phase	NOUN
ejpam-5043	340	14	-	-	PUNCT
ejpam-5043	340	15	plane	plane	NOUN
ejpam-5043	340	16	.	.	PUNCT
ejpam-5043	341	1	recent	recent	ADJ
ejpam-5043	341	2	research	research	NOUN
ejpam-5043	341	3	in	in	ADP
ejpam-5043	341	4	computational	computational	ADJ
ejpam-5043	341	5	techniques	technique	NOUN
ejpam-5043	341	6	.	.	PUNCT
ejpam-5043	342	1	non	non	ADJ
ejpam-5043	342	2	-	-	ADJ
ejpam-5043	342	3	linear	linear	ADJ
ejpam-5043	342	4	systems	system	NOUN
ejpam-5043	342	5	and	and	CCONJ
ejpam-5043	342	6	control	control	NOUN
ejpam-5043	342	7	,	,	PUNCT
ejpam-5043	342	8	2011	2011	NUM
ejpam-5043	342	9	.	.	PUNCT
ejpam-5043	343	1	[	[	X
ejpam-5043	343	2	11	11	NUM
ejpam-5043	343	3	]	]	X
ejpam-5043	343	4	d	d	X
ejpam-5043	343	5	dudkowski	dudkowski	ADJ
ejpam-5043	343	6	,	,	PUNCT
ejpam-5043	343	7	s	s	PART
ejpam-5043	343	8	jafari	jafari	X
ejpam-5043	343	9	,	,	PUNCT
ejpam-5043	343	10	t	t	PROPN
ejpam-5043	343	11	kapitaniak	kapitaniak	PROPN
ejpam-5043	343	12	,	,	PUNCT
ejpam-5043	343	13	n	n	PROPN
ejpam-5043	343	14	v	v	NUM
ejpam-5043	343	15	kuznetsov	kuznetsov	NOUN
ejpam-5043	343	16	,	,	PUNCT
ejpam-5043	343	17	g	g	PROPN
ejpam-5043	343	18	a	a	DET
ejpam-5043	343	19	leonov	leonov	NOUN
ejpam-5043	343	20	and	and	CCONJ
ejpam-5043	343	21	a	a	DET
ejpam-5043	343	22	prasad	prasad	NOUN
ejpam-5043	343	23	.	.	PUNCT
ejpam-5043	344	1	hidden	hide	VERB
ejpam-5043	344	2	attractors	attractor	NOUN
ejpam-5043	344	3	in	in	ADP
ejpam-5043	344	4	dynamical	dynamical	ADJ
ejpam-5043	344	5	systems	system	NOUN
ejpam-5043	344	6	.	.	PUNCT
ejpam-5043	345	1	physics	physics	NOUN
ejpam-5043	345	2	reports	report	NOUN
ejpam-5043	345	3	vol	vol	VERB
ejpam-5043	345	4	637	637	NUM
ejpam-5043	345	5	,	,	PUNCT
ejpam-5043	345	6	2016	2016	NUM
ejpam-5043	345	7	.	.	PUNCT
ejpam-5043	346	1	[	[	X
ejpam-5043	346	2	12	12	NUM
ejpam-5043	346	3	]	]	X
ejpam-5043	346	4	e	e	X
ejpam-5043	346	5	salah	salah	PROPN
ejpam-5043	346	6	,	,	PUNCT
ejpam-5043	346	7	a	a	DET
ejpam-5043	346	8	qazza	qazza	NOUN
ejpam-5043	346	9	,	,	PUNCT
ejpam-5043	346	10	r	r	NOUN
ejpam-5043	346	11	saadeh	saadeh	PROPN
ejpam-5043	346	12	and	and	CCONJ
ejpam-5043	346	13	a.	a.	PROPN
ejpam-5043	346	14	el	el	PROPN
ejpam-5043	346	15	-	-	PUNCT
ejpam-5043	346	16	ajou	ajou	ADJ
ejpam-5043	346	17	.	.	PUNCT
ejpam-5043	347	1	a	a	DET
ejpam-5043	347	2	hybrid	hybrid	ADJ
ejpam-5043	347	3	analytical	analytical	ADJ
ejpam-5043	347	4	technique	technique	NOUN
ejpam-5043	347	5	for	for	ADP
ejpam-5043	347	6	solving	solve	VERB
ejpam-5043	347	7	multi	multi	ADJ
ejpam-5043	347	8	-	-	ADJ
ejpam-5043	347	9	dimensional	dimensional	ADJ
ejpam-5043	347	10	time	time	NOUN
ejpam-5043	347	11	-	-	PUNCT
ejpam-5043	347	12	fractional	fractional	ADJ
ejpam-5043	347	13	navier	navier	NOUN
ejpam-5043	347	14	-	-	PUNCT
ejpam-5043	347	15	stokes	stoke	NOUN
ejpam-5043	347	16	system	system	NOUN
ejpam-5043	347	17	.	.	PUNCT
ejpam-5043	348	1	aims	aim	VERB
ejpam-5043	348	2	mathematics	mathematic	NOUN
ejpam-5043	348	3	,	,	PUNCT
ejpam-5043	348	4	8(1):1713–1736	8(1):1713–1736	PROPN
ejpam-5043	348	5	,	,	PUNCT
ejpam-5043	348	6	2023	2023	NUM
ejpam-5043	348	7	.	.	PUNCT
ejpam-5043	349	1	[	[	X
ejpam-5043	349	2	13	13	NUM
ejpam-5043	349	3	]	]	X
ejpam-5043	349	4	abdoon	abdoon	PROPN
ejpam-5043	349	5	mohamed	mohamed	PROPN
ejpam-5043	349	6	a.	a.	PROPN
ejpam-5043	349	7	,	,	PUNCT
ejpam-5043	349	8	et	et	PROPN
ejpam-5043	349	9	al	al	PROPN
ejpam-5043	349	10	.	.	PROPN
ejpam-5043	350	1	analysis	analysis	NOUN
ejpam-5043	350	2	,	,	PUNCT
ejpam-5043	350	3	modeling	modeling	NOUN
ejpam-5043	350	4	and	and	CCONJ
ejpam-5043	350	5	simulation	simulation	NOUN
ejpam-5043	350	6	of	of	ADP
ejpam-5043	350	7	a	a	DET
ejpam-5043	350	8	fractional	fractional	ADJ
ejpam-5043	350	9	-	-	PUNCT
ejpam-5043	350	10	order	order	NOUN
ejpam-5043	350	11	influenza	influenza	NOUN
ejpam-5043	350	12	model	model	NOUN
ejpam-5043	350	13	.	.	PUNCT
ejpam-5043	351	1	alexandria	alexandria	PROPN
ejpam-5043	351	2	engineering	engineering	PROPN
ejpam-5043	351	3	journal	journal	PROPN
ejpam-5043	351	4	,	,	PUNCT
ejpam-5043	351	5	74:231–240	74:231–240	PROPN
ejpam-5043	351	6	,	,	PUNCT
ejpam-5043	351	7	2023	2023	NUM
ejpam-5043	351	8	.	.	PUNCT
ejpam-5043	352	1	[	[	X
ejpam-5043	352	2	14	14	NUM
ejpam-5043	352	3	]	]	X
ejpam-5043	352	4	ahmed	ahmed	PROPN
ejpam-5043	352	5	s.	s.	PROPN
ejpam-5043	352	6	,	,	PUNCT
ejpam-5043	352	7	et	et	PROPN
ejpam-5043	352	8	al	al	PROPN
ejpam-5043	352	9	.	.	PUNCT
ejpam-5043	353	1	an	an	DET
ejpam-5043	353	2	efficient	efficient	ADJ
ejpam-5043	353	3	method	method	NOUN
ejpam-5043	353	4	for	for	ADP
ejpam-5043	353	5	the	the	DET
ejpam-5043	353	6	fractional	fractional	ADJ
ejpam-5043	353	7	electric	electric	ADJ
ejpam-5043	353	8	circuits	circuit	NOUN
ejpam-5043	353	9	based	base	VERB
ejpam-5043	353	10	on	on	ADP
ejpam-5043	353	11	fibonacci	fibonacci	PROPN
ejpam-5043	353	12	wavelet	wavelet	PROPN
ejpam-5043	353	13	.	.	PUNCT
ejpam-5043	354	1	results	result	NOUN
ejpam-5043	354	2	in	in	ADP
ejpam-5043	354	3	physics	physics	NOUN
ejpam-5043	354	4	.	.	PUNCT
ejpam-5043	354	5	,	,	PUNCT
ejpam-5043	354	6	52:106–753	52:106–753	NUM
ejpam-5043	354	7	,	,	PUNCT
ejpam-5043	354	8	2023	2023	NUM
ejpam-5043	354	9	.	.	PUNCT
ejpam-5043	355	1	[	[	X
ejpam-5043	355	2	15	15	NUM
ejpam-5043	355	3	]	]	SYM
ejpam-5043	355	4	elbadri	elbadri	ADJ
ejpam-5043	355	5	m.	m.	NOUN
ejpam-5043	355	6	,	,	PUNCT
ejpam-5043	355	7	et	et	PROPN
ejpam-5043	355	8	al	al	PROPN
ejpam-5043	355	9	.	.	PUNCT
ejpam-5043	356	1	a	a	DET
ejpam-5043	356	2	numerical	numerical	ADJ
ejpam-5043	356	3	solution	solution	NOUN
ejpam-5043	356	4	and	and	CCONJ
ejpam-5043	356	5	comparative	comparative	ADJ
ejpam-5043	356	6	study	study	NOUN
ejpam-5043	356	7	of	of	ADP
ejpam-5043	356	8	the	the	DET
ejpam-5043	356	9	symmetric	symmetric	ADJ
ejpam-5043	356	10	rossler	rossler	NOUN
ejpam-5043	356	11	attractor	attractor	NOUN
ejpam-5043	356	12	with	with	ADP
ejpam-5043	356	13	the	the	DET
ejpam-5043	356	14	generalized	generalize	VERB
ejpam-5043	356	15	caputo	caputo	PROPN
ejpam-5043	356	16	fractional	fractional	PROPN
ejpam-5043	356	17	derivative	derivative	NOUN
ejpam-5043	356	18	via	via	ADP
ejpam-5043	356	19	two	two	NUM
ejpam-5043	356	20	different	different	ADJ
ejpam-5043	356	21	methods	method	NOUN
ejpam-5043	356	22	.	.	PUNCT
ejpam-5043	357	1	mathematics	mathematic	NOUN
ejpam-5043	357	2	.	.	PUNCT
ejpam-5043	357	3	,	,	PUNCT
ejpam-5043	357	4	11(13):1–11	11(13):1–11	NUM
ejpam-5043	357	5	,	,	PUNCT
ejpam-5043	357	6	2023	2023	NUM
ejpam-5043	357	7	.	.	PUNCT
ejpam-5043	358	1	[	[	X
ejpam-5043	358	2	16	16	NUM
ejpam-5043	358	3	]	]	PUNCT
ejpam-5043	358	4	elbadri	elbadri	ADJ
ejpam-5043	358	5	m.	m.	NOUN
ejpam-5043	358	6	,	,	PUNCT
ejpam-5043	358	7	et	et	PROPN
ejpam-5043	358	8	al	al	PROPN
ejpam-5043	358	9	.	.	PUNCT
ejpam-5043	359	1	a	a	DET
ejpam-5043	359	2	symmetry	symmetry	NOUN
ejpam-5043	359	3	chaotic	chaotic	ADJ
ejpam-5043	359	4	model	model	NOUN
ejpam-5043	359	5	with	with	ADP
ejpam-5043	359	6	fractional	fractional	ADJ
ejpam-5043	359	7	derivative	derivative	ADJ
ejpam-5043	359	8	order	order	NOUN
ejpam-5043	359	9	via	via	ADP
ejpam-5043	359	10	two	two	NUM
ejpam-5043	359	11	different	different	ADJ
ejpam-5043	359	12	methods	method	NOUN
ejpam-5043	359	13	.	.	PUNCT
ejpam-5043	360	1	symmetry	symmetry	PROPN
ejpam-5043	360	2	.	.	PUNCT
ejpam-5043	360	3	,	,	PUNCT
ejpam-5043	360	4	15(6):1151	15(6):1151	NUM
ejpam-5043	360	5	,	,	PUNCT
ejpam-5043	360	6	2023	2023	NUM
ejpam-5043	360	7	.	.	PUNCT
ejpam-5043	361	1	references	reference	NOUN
ejpam-5043	361	2	459	459	NUM
ejpam-5043	362	1	[	[	X
ejpam-5043	362	2	17	17	NUM
ejpam-5043	362	3	]	]	X
ejpam-5043	362	4	guma	guma	PROPN
ejpam-5043	362	5	f.	f.	PROPN
ejpam-5043	362	6	el	el	PROPN
ejpam-5043	362	7	.	.	PROPN
ejpam-5043	362	8	,	,	PUNCT
ejpam-5043	362	9	et	et	PROPN
ejpam-5043	363	1	al	al	PROPN
ejpam-5043	363	2	.	.	PROPN
ejpam-5043	363	3	numerical	numerical	PROPN
ejpam-5043	363	4	analysis	analysis	NOUN
ejpam-5043	363	5	of	of	ADP
ejpam-5043	363	6	fractional	fractional	ADJ
ejpam-5043	363	7	-	-	PUNCT
ejpam-5043	363	8	order	order	NOUN
ejpam-5043	363	9	dynamic	dynamic	ADJ
ejpam-5043	363	10	dengue	dengue	NOUN
ejpam-5043	363	11	disease	disease	NOUN
ejpam-5043	363	12	epidemic	epidemic	NOUN
ejpam-5043	363	13	in	in	ADP
ejpam-5043	363	14	sudan	sudan	PROPN
ejpam-5043	363	15	.	.	PUNCT
ejpam-5043	364	1	journal	journal	PROPN
ejpam-5043	364	2	of	of	ADP
ejpam-5043	364	3	the	the	DET
ejpam-5043	364	4	nigerian	nigerian	ADJ
ejpam-5043	364	5	society	society	NOUN
ejpam-5043	364	6	of	of	ADP
ejpam-5043	364	7	physical	physical	ADJ
ejpam-5043	364	8	sciences	science	NOUN
ejpam-5043	364	9	.	.	PUNCT
ejpam-5043	364	10	,	,	PUNCT
ejpam-5043	364	11	5(2):1464	5(2):1464	NUM
ejpam-5043	364	12	,	,	PUNCT
ejpam-5043	364	13	2023	2023	NUM
ejpam-5043	364	14	.	.	PUNCT
ejpam-5043	365	1	[	[	X
ejpam-5043	365	2	18	18	NUM
ejpam-5043	365	3	]	]	PUNCT
ejpam-5043	365	4	qazza	qazza	PROPN
ejpam-5043	365	5	a.	a.	PROPN
ejpam-5043	365	6	,	,	PUNCT
ejpam-5043	365	7	et	et	PROPN
ejpam-5043	365	8	al	al	PROPN
ejpam-5043	365	9	.	.	PUNCT
ejpam-5043	366	1	a	a	DET
ejpam-5043	366	2	new	new	ADJ
ejpam-5043	366	3	scheme	scheme	NOUN
ejpam-5043	366	4	for	for	ADP
ejpam-5043	366	5	solving	solve	VERB
ejpam-5043	366	6	a	a	DET
ejpam-5043	366	7	fractional	fractional	ADJ
ejpam-5043	366	8	differential	differential	ADJ
ejpam-5043	366	9	equation	equation	NOUN
ejpam-5043	366	10	and	and	CCONJ
ejpam-5043	366	11	a	a	DET
ejpam-5043	366	12	chaotic	chaotic	ADJ
ejpam-5043	366	13	system	system	NOUN
ejpam-5043	366	14	.	.	PUNCT
ejpam-5043	367	1	european	european	PROPN
ejpam-5043	367	2	journal	journal	PROPN
ejpam-5043	367	3	of	of	ADP
ejpam-5043	367	4	pure	pure	ADJ
ejpam-5043	367	5	and	and	CCONJ
ejpam-5043	367	6	applied	applied	ADJ
ejpam-5043	367	7	mathematics	mathematic	NOUN
ejpam-5043	367	8	.	.	PUNCT
ejpam-5043	367	9	,	,	PUNCT
ejpam-5043	367	10	16(2):1128	16(2):1128	NUM
ejpam-5043	367	11	–	–	PUNCT
ejpam-5043	367	12	1139	1139	NUM
ejpam-5043	367	13	,	,	PUNCT
ejpam-5043	367	14	2023	2023	NUM
ejpam-5043	367	15	.	.	PUNCT
ejpam-5043	368	1	[	[	X
ejpam-5043	368	2	19	19	NUM
ejpam-5043	368	3	]	]	X
ejpam-5043	368	4	abdoon	abdoon	NOUN
ejpam-5043	368	5	m.	m.	NOUN
ejpam-5043	368	6	a.	a.	PROPN
ejpam-5043	368	7	,	,	PUNCT
ejpam-5043	368	8	hasan	hasan	PROPN
ejpam-5043	368	9	fl	fl	PROPN
ejpam-5043	368	10	.	.	PUNCT
ejpam-5043	368	11	advantages	advantage	NOUN
ejpam-5043	368	12	of	of	ADP
ejpam-5043	368	13	the	the	DET
ejpam-5043	368	14	differential	differential	ADJ
ejpam-5043	368	15	equations	equation	NOUN
ejpam-5043	368	16	for	for	ADP
ejpam-5043	368	17	solving	solve	VERB
ejpam-5043	368	18	problems	problem	NOUN
ejpam-5043	368	19	in	in	ADP
ejpam-5043	368	20	mathematical	mathematical	ADJ
ejpam-5043	368	21	physics	physics	NOUN
ejpam-5043	368	22	with	with	ADP
ejpam-5043	368	23	symbolic	symbolic	ADJ
ejpam-5043	368	24	computation	computation	NOUN
ejpam-5043	368	25	.	.	PUNCT
ejpam-5043	369	1	math	math	NOUN
ejpam-5043	369	2	.	.	PUNCT
ejpam-5043	370	1	model	model	PROPN
ejpam-5043	370	2	.	.	PUNCT
ejpam-5043	371	1	eng	eng	PROPN
ejpam-5043	371	2	.	.	PROPN
ejpam-5043	371	3	probl	probl	PROPN
ejpam-5043	371	4	.	.	PUNCT
ejpam-5043	371	5	,	,	PUNCT
ejpam-5043	371	6	9(1):268–276	9(1):268–276	NOUN
ejpam-5043	371	7	,	,	PUNCT
ejpam-5043	371	8	2022	2022	NUM
ejpam-5043	371	9	.	.	PUNCT
ejpam-5043	372	1	[	[	X
ejpam-5043	372	2	20	20	NUM
ejpam-5043	372	3	]	]	X
ejpam-5043	372	4	g	g	PROPN
ejpam-5043	372	5	xu	xu	PROPN
ejpam-5043	372	6	,	,	PUNCT
ejpam-5043	372	7	y	y	PROPN
ejpam-5043	372	8	shekofteh	shekofteh	PROPN
ejpam-5043	372	9	,	,	PUNCT
ejpam-5043	372	10	a	a	DET
ejpam-5043	372	11	akg¨ul	akg¨ul	NOUN
ejpam-5043	372	12	,	,	PUNCT
ejpam-5043	372	13	c	c	PROPN
ejpam-5043	372	14	li	li	PROPN
ejpam-5043	372	15	and	and	CCONJ
ejpam-5043	372	16	s.	s.	PROPN
ejpam-5043	372	17	panahi	panahi	PROPN
ejpam-5043	372	18	.	.	PUNCT
ejpam-5043	373	1	a	a	DET
ejpam-5043	373	2	new	new	ADJ
ejpam-5043	373	3	chaotic	chaotic	ADJ
ejpam-5043	373	4	system	system	NOUN
ejpam-5043	373	5	with	with	ADP
ejpam-5043	373	6	a	a	DET
ejpam-5043	373	7	selfexcited	selfexcite	VERB
ejpam-5043	373	8	attractor	attractor	NOUN
ejpam-5043	373	9	:	:	PUNCT
ejpam-5043	373	10	entropy	entropy	PROPN
ejpam-5043	373	11	measurement	measurement	PROPN
ejpam-5043	373	12	,	,	PUNCT
ejpam-5043	373	13	signal	signal	NOUN
ejpam-5043	373	14	encryption	encryption	NOUN
ejpam-5043	373	15	,	,	PUNCT
ejpam-5043	373	16	and	and	CCONJ
ejpam-5043	373	17	parameter	parameter	PROPN
ejpam-5043	373	18	estimation	estimation	NOUN
ejpam-5043	373	19	.	.	PUNCT
ejpam-5043	374	1	entropy	entropy	PROPN
ejpam-5043	374	2	,	,	PUNCT
ejpam-5043	374	3	20(2):86	20(2):86	NOUN
ejpam-5043	374	4	,	,	PUNCT
ejpam-5043	374	5	2018	2018	NUM
ejpam-5043	374	6	.	.	PUNCT
ejpam-5043	375	1	[	[	X
ejpam-5043	375	2	21	21	NUM
ejpam-5043	375	3	]	]	SYM
ejpam-5043	375	4	b	b	X
ejpam-5043	375	5	ghanbari	ghanbari	NOUN
ejpam-5043	375	6	and	and	CCONJ
ejpam-5043	375	7	d	d	X
ejpam-5043	375	8	a	a	DET
ejpam-5043	375	9	atangana	atangana	PROPN
ejpam-5043	375	10	.	.	PUNCT
ejpam-5043	376	1	some	some	PRON
ejpam-5043	376	2	new	new	ADJ
ejpam-5043	376	3	edge	edge	NOUN
ejpam-5043	376	4	detecting	detect	VERB
ejpam-5043	376	5	techniques	technique	NOUN
ejpam-5043	376	6	based	base	VERB
ejpam-5043	376	7	on	on	ADP
ejpam-5043	376	8	fractional	fractional	ADJ
ejpam-5043	376	9	derivatives	derivative	NOUN
ejpam-5043	376	10	with	with	ADP
ejpam-5043	376	11	nonlocal	nonlocal	ADJ
ejpam-5043	376	12	and	and	CCONJ
ejpam-5043	376	13	non	non	ADJ
ejpam-5043	376	14	-	-	ADJ
ejpam-5043	376	15	singular	singular	ADJ
ejpam-5043	376	16	kernels	kernel	NOUN
ejpam-5043	376	17	.	.	PUNCT
ejpam-5043	377	1	adv	adv	PROPN
ejpam-5043	377	2	.	.	PUNCT
ejpam-5043	378	1	diff	diff	PROPN
ejpam-5043	378	2	.	.	PUNCT
ejpam-5043	379	1	equa	equa	NOUN
ejpam-5043	379	2	.	.	PUNCT
ejpam-5043	379	3	,	,	PUNCT
ejpam-5043	379	4	2020:435	2020:435	NUM
ejpam-5043	379	5	,	,	PUNCT
ejpam-5043	379	6	2020	2020	NUM
ejpam-5043	379	7	.	.	PUNCT
ejpam-5043	380	1	[	[	X
ejpam-5043	380	2	22	22	NUM
ejpam-5043	380	3	]	]	PUNCT
ejpam-5043	380	4	gorenflo	gorenflo	NOUN
ejpam-5043	380	5	r	r	NOUN
ejpam-5043	380	6	,	,	PUNCT
ejpam-5043	380	7	and	and	CCONJ
ejpam-5043	380	8	mainardi	mainardi	PROPN
ejpam-5043	380	9	f.	f.	PROPN
ejpam-5043	380	10	fractional	fractional	PROPN
ejpam-5043	380	11	calculus	calculus	PROPN
ejpam-5043	380	12	:	:	PUNCT
ejpam-5043	380	13	integral	integral	ADJ
ejpam-5043	380	14	and	and	CCONJ
ejpam-5043	380	15	differential	differential	ADJ
ejpam-5043	380	16	equations	equation	NOUN
ejpam-5043	380	17	of	of	ADP
ejpam-5043	380	18	fractional	fractional	ADJ
ejpam-5043	380	19	order	order	NOUN
ejpam-5043	380	20	,	,	PUNCT
ejpam-5043	380	21	in	in	ADP
ejpam-5043	380	22	:	:	PUNCT
ejpam-5043	380	23	a.	a.	NOUN
ejpam-5043	380	24	carpinteri	carpinteri	PROPN
ejpam-5043	380	25	,	,	PUNCT
ejpam-5043	380	26	f.	f.	PROPN
ejpam-5043	380	27	mainardi	mainardi	PROPN
ejpam-5043	380	28	(	(	PUNCT
ejpam-5043	380	29	eds	ed	NOUN
ejpam-5043	380	30	)	)	PUNCT
ejpam-5043	380	31	.	.	PUNCT
ejpam-5043	381	1	fractals	fractal	NOUN
ejpam-5043	381	2	and	and	CCONJ
ejpam-5043	381	3	fractional	fractional	ADJ
ejpam-5043	381	4	calculus	calculus	NOUN
ejpam-5043	381	5	in	in	ADP
ejpam-5043	381	6	continuum	continuum	ADJ
ejpam-5043	381	7	mechanics	mechanic	NOUN
ejpam-5043	381	8	.	.	PUNCT
ejpam-5043	382	1	springer	springer	NOUN
ejpam-5043	382	2	-	-	PUNCT
ejpam-5043	382	3	verlag	verlag	PROPN
ejpam-5043	382	4	,	,	PUNCT
ejpam-5043	382	5	newyork	newyork	NOUN
ejpam-5043	382	6	,	,	PUNCT
ejpam-5043	382	7	pages	page	NOUN
ejpam-5043	382	8	223–276	223–276	NUM
ejpam-5043	382	9	,	,	PUNCT
ejpam-5043	382	10	1997	1997	NUM
ejpam-5043	382	11	.	.	PUNCT
ejpam-5043	383	1	[	[	X
ejpam-5043	383	2	23	23	NUM
ejpam-5043	383	3	]	]	PUNCT
ejpam-5043	383	4	guma	guma	PROPN
ejpam-5043	383	5	f.	f.	PROPN
ejpam-5043	383	6	e.	e.	PROPN
ejpam-5043	383	7	,	,	PUNCT
ejpam-5043	383	8	badawy	badawy	PROPN
ejpam-5043	383	9	o.	o.	PROPN
ejpam-5043	383	10	m.	m.	PROPN
ejpam-5043	383	11	,	,	PUNCT
ejpam-5043	383	12	musa	musa	PROPN
ejpam-5043	383	13	a.	a.	PROPN
ejpam-5043	383	14	g.	g.	PROPN
ejpam-5043	383	15	,	,	PUNCT
ejpam-5043	383	16	mohammed	mohammed	PROPN
ejpam-5043	383	17	b.	b.	PROPN
ejpam-5043	383	18	o.	o.	PROPN
ejpam-5043	383	19	,	,	PUNCT
ejpam-5043	383	20	abdoon	abdoon	PROPN
ejpam-5043	383	21	m.	m.	NOUN
ejpam-5043	383	22	a.	a.	PROPN
ejpam-5043	383	23	,	,	PUNCT
ejpam-5043	383	24	berir	berir	NOUN
ejpam-5043	383	25	m.	m.	NOUN
ejpam-5043	383	26	,	,	PUNCT
ejpam-5043	383	27	and	and	CCONJ
ejpam-5043	383	28	salih	salih	PROPN
ejpam-5043	383	29	s.	s.	PROPN
ejpam-5043	383	30	y.	y.	PROPN
ejpam-5043	383	31	m.	m.	PROPN
ejpam-5043	383	32	risk	risk	NOUN
ejpam-5043	383	33	factors	factor	NOUN
ejpam-5043	383	34	for	for	ADP
ejpam-5043	383	35	death	death	NOUN
ejpam-5043	383	36	among	among	ADP
ejpam-5043	383	37	covid-19	covid-19	PROPN
ejpam-5043	383	38	patients	patient	NOUN
ejpam-5043	383	39	admitted	admit	VERB
ejpam-5043	383	40	to	to	ADP
ejpam-5043	383	41	isolation	isolation	NOUN
ejpam-5043	383	42	units	unit	NOUN
ejpam-5043	383	43	in	in	ADP
ejpam-5043	383	44	gedaref	gedaref	NOUN
ejpam-5043	383	45	state	state	NOUN
ejpam-5043	383	46	,	,	PUNCT
ejpam-5043	383	47	eastern	eastern	PROPN
ejpam-5043	383	48	sudan	sudan	PROPN
ejpam-5043	383	49	:	:	PUNCT
ejpam-5043	383	50	a	a	DET
ejpam-5043	383	51	retrospective	retrospective	ADJ
ejpam-5043	383	52	cohort	cohort	NOUN
ejpam-5043	383	53	study	study	NOUN
ejpam-5043	383	54	.	.	PUNCT
ejpam-5043	384	1	journal	journal	PROPN
ejpam-5043	384	2	of	of	ADP
ejpam-5043	384	3	survey	survey	NOUN
ejpam-5043	384	4	in	in	ADP
ejpam-5043	384	5	fisheries	fishery	NOUN
ejpam-5043	384	6	sciences	science	NOUN
ejpam-5043	384	7	,	,	PUNCT
ejpam-5043	384	8	10(3s):712–722	10(3s):712–722	NUM
ejpam-5043	384	9	,	,	PUNCT
ejpam-5043	384	10	2023	2023	NUM
ejpam-5043	384	11	.	.	PUNCT
ejpam-5043	385	1	[	[	X
ejpam-5043	385	2	24	24	NUM
ejpam-5043	385	3	]	]	X
ejpam-5043	385	4	hamadneh	hamadneh	PROPN
ejpam-5043	385	5	t.	t.	PROPN
ejpam-5043	385	6	,	,	PUNCT
ejpam-5043	385	7	hioual	hioual	ADJ
ejpam-5043	385	8	a.	a.	NOUN
ejpam-5043	385	9	,	,	PUNCT
ejpam-5043	385	10	saadeh	saadeh	PROPN
ejpam-5043	385	11	r.	r.	PROPN
ejpam-5043	385	12	,	,	PUNCT
ejpam-5043	385	13	abdoon	abdoon	PROPN
ejpam-5043	385	14	mohamed	mohamed	PROPN
ejpam-5043	385	15	a.	a.	PROPN
ejpam-5043	385	16	,	,	PUNCT
ejpam-5043	385	17	almutairi	almutairi	PROPN
ejpam-5043	385	18	d.	d.	PROPN
ejpam-5043	385	19	k.	k.	PROPN
ejpam-5043	385	20	,	,	PUNCT
ejpam-5043	385	21	khalid	khalid	PROPN
ejpam-5043	385	22	t.	t.	PROPN
ejpam-5043	385	23	a.	a.	PROPN
ejpam-5043	385	24	,	,	PUNCT
ejpam-5043	385	25	and	and	CCONJ
ejpam-5043	385	26	ouannas	ouannas	NOUN
ejpam-5043	385	27	a.	a.	PROPN
ejpam-5043	385	28	general	general	PROPN
ejpam-5043	385	29	methods	method	NOUN
ejpam-5043	385	30	to	to	PART
ejpam-5043	385	31	synchronize	synchronize	VERB
ejpam-5043	385	32	fractional	fractional	ADJ
ejpam-5043	385	33	discrete	discrete	ADJ
ejpam-5043	385	34	reaction	reaction	NOUN
ejpam-5043	385	35	–	–	PUNCT
ejpam-5043	385	36	diffusion	diffusion	NOUN
ejpam-5043	385	37	systems	system	NOUN
ejpam-5043	385	38	applied	apply	VERB
ejpam-5043	385	39	to	to	ADP
ejpam-5043	385	40	the	the	DET
ejpam-5043	385	41	glycolysis	glycolysis	NOUN
ejpam-5043	385	42	model	model	NOUN
ejpam-5043	385	43	.	.	PUNCT
ejpam-5043	386	1	fractal	fractal	PROPN
ejpam-5043	386	2	and	and	CCONJ
ejpam-5043	386	3	fractional	fractional	ADJ
ejpam-5043	386	4	,	,	PUNCT
ejpam-5043	386	5	7(11):828	7(11):828	PROPN
ejpam-5043	386	6	,	,	PUNCT
ejpam-5043	386	7	2023	2023	NUM
ejpam-5043	386	8	.	.	PUNCT
ejpam-5043	387	1	[	[	X
ejpam-5043	387	2	25	25	NUM
ejpam-5043	387	3	]	]	X
ejpam-5043	387	4	z	z	NOUN
ejpam-5043	387	5	hammouch	hammouch	NOUN
ejpam-5043	387	6	and	and	CCONJ
ejpam-5043	387	7	t	t	PROPN
ejpam-5043	387	8	mekkaoui	mekkaoui	NOUN
ejpam-5043	387	9	.	.	PUNCT
ejpam-5043	388	1	traveling	travel	VERB
ejpam-5043	388	2	-	-	PUNCT
ejpam-5043	388	3	wave	wave	NOUN
ejpam-5043	388	4	solutions	solution	NOUN
ejpam-5043	388	5	of	of	ADP
ejpam-5043	388	6	the	the	DET
ejpam-5043	388	7	generalized	generalized	ADJ
ejpam-5043	388	8	zakharov	zakharov	ADJ
ejpam-5043	388	9	equation	equation	NOUN
ejpam-5043	388	10	with	with	ADP
ejpam-5043	388	11	time	time	NOUN
ejpam-5043	388	12	-	-	PUNCT
ejpam-5043	388	13	space	space	NOUN
ejpam-5043	388	14	fractional	fractional	ADJ
ejpam-5043	388	15	derivatives	derivative	NOUN
ejpam-5043	388	16	.	.	PUNCT
ejpam-5043	389	1	math	math	PROPN
ejpam-5043	389	2	eng	eng	PROPN
ejpam-5043	389	3	sci	sci	PROPN
ejpam-5043	389	4	aerosp	aerosp	PROPN
ejpam-5043	389	5	mesa	mesa	PROPN
ejpam-5043	389	6	,	,	PUNCT
ejpam-5043	389	7	5(4):1–11	5(4):1–11	NUM
ejpam-5043	389	8	,	,	PUNCT
ejpam-5043	389	9	2014	2014	NUM
ejpam-5043	389	10	.	.	PUNCT
ejpam-5043	390	1	[	[	X
ejpam-5043	390	2	26	26	NUM
ejpam-5043	390	3	]	]	PUNCT
ejpam-5043	390	4	faeza	faeza	PROPN
ejpam-5043	390	5	hasan	hasan	PROPN
ejpam-5043	390	6	,	,	PUNCT
ejpam-5043	390	7	mohamed	mohame	VERB
ejpam-5043	390	8	a	a	DET
ejpam-5043	390	9	abdoon	abdoon	NOUN
ejpam-5043	390	10	,	,	PUNCT
ejpam-5043	390	11	rania	rania	PROPN
ejpam-5043	390	12	saadeh	saadeh	PROPN
ejpam-5043	390	13	,	,	PUNCT
ejpam-5043	390	14	mohammed	mohammed	PROPN
ejpam-5043	390	15	berir	berir	PROPN
ejpam-5043	390	16	,	,	PUNCT
ejpam-5043	390	17	and	and	CCONJ
ejpam-5043	390	18	ahmad	ahmad	PROPN
ejpam-5043	390	19	qazza	qazza	PROPN
ejpam-5043	390	20	.	.	PUNCT
ejpam-5043	391	1	a	a	DET
ejpam-5043	391	2	new	new	ADJ
ejpam-5043	391	3	perspective	perspective	NOUN
ejpam-5043	391	4	on	on	ADP
ejpam-5043	391	5	the	the	DET
ejpam-5043	391	6	stochastic	stochastic	ADJ
ejpam-5043	391	7	fractional	fractional	ADJ
ejpam-5043	391	8	order	order	NOUN
ejpam-5043	391	9	materialized	materialize	VERB
ejpam-5043	391	10	by	by	ADP
ejpam-5043	391	11	the	the	DET
ejpam-5043	391	12	exact	exact	ADJ
ejpam-5043	391	13	solutions	solution	NOUN
ejpam-5043	391	14	of	of	ADP
ejpam-5043	391	15	allen	allen	ADJ
ejpam-5043	391	16	-	-	PUNCT
ejpam-5043	391	17	cahn	cahn	NOUN
ejpam-5043	391	18	equation	equation	NOUN
ejpam-5043	391	19	.	.	PUNCT
ejpam-5043	392	1	international	international	ADJ
ejpam-5043	392	2	journal	journal	PROPN
ejpam-5043	392	3	of	of	ADP
ejpam-5043	392	4	mathematical	mathematical	ADJ
ejpam-5043	392	5	,	,	PUNCT
ejpam-5043	392	6	engineering	engineering	NOUN
ejpam-5043	392	7	and	and	CCONJ
ejpam-5043	392	8	management	management	NOUN
ejpam-5043	392	9	sciences	science	NOUN
ejpam-5043	392	10	,	,	PUNCT
ejpam-5043	392	11	8(5):912	8(5):912	NUM
ejpam-5043	392	12	,	,	PUNCT
ejpam-5043	392	13	2023	2023	NUM
ejpam-5043	392	14	.	.	PUNCT
ejpam-5043	393	1	[	[	X
ejpam-5043	393	2	27	27	NUM
ejpam-5043	393	3	]	]	PUNCT
ejpam-5043	393	4	faeza	faeza	ADP
ejpam-5043	393	5	l	l	PROPN
ejpam-5043	393	6	hasan	hasan	PROPN
ejpam-5043	393	7	and	and	CCONJ
ejpam-5043	393	8	mohamed	mohame	VERB
ejpam-5043	393	9	a	a	DET
ejpam-5043	393	10	abdoon	abdoon	NOUN
ejpam-5043	393	11	.	.	PUNCT
ejpam-5043	394	1	the	the	DET
ejpam-5043	394	2	generalized	generalized	ADJ
ejpam-5043	394	3	(	(	PUNCT
ejpam-5043	394	4	2	2	NUM
ejpam-5043	394	5	+	+	NUM
ejpam-5043	394	6	1	1	NUM
ejpam-5043	394	7	)	)	PUNCT
ejpam-5043	394	8	and	and	CCONJ
ejpam-5043	394	9	(	(	PUNCT
ejpam-5043	394	10	3	3	NUM
ejpam-5043	394	11	+	+	NOUN
ejpam-5043	394	12	1)dimensional	1)dimensional	NUM
ejpam-5043	394	13	with	with	ADP
ejpam-5043	394	14	advanced	advanced	ADJ
ejpam-5043	394	15	analytical	analytical	ADJ
ejpam-5043	394	16	wave	wave	NOUN
ejpam-5043	394	17	solutions	solution	NOUN
ejpam-5043	394	18	via	via	ADP
ejpam-5043	394	19	computational	computational	ADJ
ejpam-5043	394	20	applications	application	NOUN
ejpam-5043	394	21	.	.	PUNCT
ejpam-5043	395	1	international	international	ADJ
ejpam-5043	395	2	journal	journal	PROPN
ejpam-5043	395	3	of	of	ADP
ejpam-5043	395	4	nonlinear	nonlinear	ADJ
ejpam-5043	395	5	analysis	analysis	NOUN
ejpam-5043	395	6	and	and	CCONJ
ejpam-5043	395	7	applications	application	NOUN
ejpam-5043	395	8	,	,	PUNCT
ejpam-5043	395	9	12(2):1213–1241	12(2):1213–1241	NUM
ejpam-5043	395	10	,	,	PUNCT
ejpam-5043	395	11	2021	2021	NUM
ejpam-5043	395	12	.	.	PUNCT
ejpam-5043	396	1	references	reference	NOUN
ejpam-5043	396	2	460	460	NUM
ejpam-5043	397	1	[	[	X
ejpam-5043	397	2	28	28	NUM
ejpam-5043	397	3	]	]	X
ejpam-5043	397	4	m	m	VERB
ejpam-5043	397	5	a	a	DET
ejpam-5043	397	6	abdoon	abdoon	NOUN
ejpam-5043	397	7	,	,	PUNCT
ejpam-5043	397	8	f	f	PROPN
ejpam-5043	397	9	l	l	PROPN
ejpam-5043	397	10	hasan	hasan	PROPN
ejpam-5043	397	11	and	and	CCONJ
ejpam-5043	397	12	n	n	PROPN
ejpam-5043	397	13	e	e	PROPN
ejpam-5043	397	14	taha	taha	PROPN
ejpam-5043	397	15	.	.	PUNCT
ejpam-5043	398	1	computational	computational	ADJ
ejpam-5043	398	2	technique	technique	NOUN
ejpam-5043	398	3	to	to	PART
ejpam-5043	398	4	study	study	VERB
ejpam-5043	398	5	analytical	analytical	ADJ
ejpam-5043	398	6	solutions	solution	NOUN
ejpam-5043	398	7	to	to	ADP
ejpam-5043	398	8	the	the	DET
ejpam-5043	398	9	fractional	fractional	ADJ
ejpam-5043	398	10	modified	modify	VERB
ejpam-5043	398	11	kdv	kdv	PROPN
ejpam-5043	398	12	-	-	PUNCT
ejpam-5043	398	13	zakharov	zakharov	ADJ
ejpam-5043	398	14	-	-	PUNCT
ejpam-5043	398	15	kuznetsov	kuznetsov	NOUN
ejpam-5043	398	16	equation	equation	NOUN
ejpam-5043	398	17	.	.	PUNCT
ejpam-5043	399	1	abstract	abstract	ADJ
ejpam-5043	399	2	and	and	CCONJ
ejpam-5043	399	3	applied	apply	VERB
ejpam-5043	399	4	analysis	analysis	NOUN
ejpam-5043	399	5	,	,	PUNCT
ejpam-5043	399	6	2022	2022	NUM
ejpam-5043	399	7	:p	:p	NOUN
ejpam-5043	399	8	.	.	PUNCT
ejpam-5043	400	1	9	9	NUM
ejpam-5043	400	2	,	,	PUNCT
ejpam-5043	400	3	2022	2022	NUM
ejpam-5043	400	4	.	.	PUNCT
ejpam-5043	401	1	[	[	X
ejpam-5043	401	2	29	29	NUM
ejpam-5043	401	3	]	]	X
ejpam-5043	401	4	g	g	PROPN
ejpam-5043	401	5	samko	samko	NOUN
ejpam-5043	401	6	,	,	PUNCT
ejpam-5043	401	7	a	a	DET
ejpam-5043	401	8	kilbas	kilbas	NOUN
ejpam-5043	401	9	and	and	CCONJ
ejpam-5043	401	10	o	o	NOUN
ejpam-5043	401	11	marichev	marichev	PROPN
ejpam-5043	401	12	.	.	PUNCT
ejpam-5043	402	1	fractional	fractional	ADJ
ejpam-5043	402	2	integrals	integral	NOUN
ejpam-5043	402	3	and	and	CCONJ
ejpam-5043	402	4	derivatives	derivative	NOUN
ejpam-5043	402	5	:	:	PUNCT
ejpam-5043	402	6	theory	theory	NOUN
ejpam-5043	402	7	and	and	CCONJ
ejpam-5043	402	8	applications	application	NOUN
ejpam-5043	402	9	.	.	PUNCT
ejpam-5043	403	1	gordon	gordon	PROPN
ejpam-5043	403	2	and	and	CCONJ
ejpam-5043	403	3	breach	breach	PROPN
ejpam-5043	403	4	,	,	PUNCT
ejpam-5043	403	5	amsterdam	amsterdam	PROPN
ejpam-5043	403	6	,	,	PUNCT
ejpam-5043	403	7	1993	1993	NUM
ejpam-5043	403	8	.	.	PUNCT
ejpam-5043	404	1	[	[	X
ejpam-5043	404	2	30	30	NUM
ejpam-5043	404	3	]	]	PUNCT
ejpam-5043	404	4	a.	a.	NOUN
ejpam-5043	404	5	a	a	DET
ejpam-5043	404	6	klibanov	klibanov	PROPN
ejpam-5043	404	7	,	,	PUNCT
ejpam-5043	404	8	m.	m.	NOUN
ejpam-5043	404	9	v.	v.	PROPN
ejpam-5043	404	10	,	,	PUNCT
ejpam-5043	404	11	timonov	timonov	PROPN
ejpam-5043	404	12	.	.	PUNCT
ejpam-5043	405	1	a	a	DET
ejpam-5043	405	2	comparative	comparative	ADJ
ejpam-5043	405	3	study	study	NOUN
ejpam-5043	405	4	of	of	ADP
ejpam-5043	405	5	two	two	NUM
ejpam-5043	405	6	globally	globally	ADV
ejpam-5043	405	7	convergent	convergent	ADJ
ejpam-5043	405	8	numerical	numerical	ADJ
ejpam-5043	405	9	methods	method	NOUN
ejpam-5043	405	10	for	for	ADP
ejpam-5043	405	11	acoustic	acoustic	ADJ
ejpam-5043	405	12	tomography	tomography	NOUN
ejpam-5043	405	13	.	.	PUNCT
ejpam-5043	406	1	arxiv	arxiv	PROPN
ejpam-5043	406	2	preprint	preprint	PROPN
ejpam-5043	406	3	arxiv:2301.05817	arxiv:2301.05817	PROPN
ejpam-5043	406	4	.	.	PUNCT
ejpam-5043	406	5	,	,	PUNCT
ejpam-5043	406	6	2023	2023	NUM
ejpam-5043	406	7	.	.	PUNCT
ejpam-5043	407	1	[	[	X
ejpam-5043	407	2	31	31	NUM
ejpam-5043	407	3	]	]	SYM
ejpam-5043	407	4	elbadri	elbadri	ADJ
ejpam-5043	407	5	m.	m.	NOUN
ejpam-5043	407	6	initial	initial	ADJ
ejpam-5043	407	7	value	value	NOUN
ejpam-5043	407	8	problems	problem	NOUN
ejpam-5043	407	9	with	with	ADP
ejpam-5043	407	10	generalized	generalized	ADJ
ejpam-5043	407	11	fractional	fractional	ADJ
ejpam-5043	407	12	derivatives	derivative	NOUN
ejpam-5043	407	13	and	and	CCONJ
ejpam-5043	407	14	their	their	PRON
ejpam-5043	407	15	solutions	solution	NOUN
ejpam-5043	407	16	via	via	ADP
ejpam-5043	407	17	generalized	generalized	ADJ
ejpam-5043	407	18	laplace	laplace	NOUN
ejpam-5043	407	19	decomposition	decomposition	NOUN
ejpam-5043	407	20	method	method	NOUN
ejpam-5043	407	21	.	.	PUNCT
ejpam-5043	408	1	adv	adv	PROPN
ejpam-5043	408	2	.	.	PUNCT
ejpam-5043	408	3	math	math	PROPN
ejpam-5043	408	4	.	.	PUNCT
ejpam-5043	409	1	phys	phy	NOUN
ejpam-5043	409	2	.	.	PUNCT
ejpam-5043	409	3	,	,	PUNCT
ejpam-5043	409	4	2022:1–7	2022:1–7	NUM
ejpam-5043	409	5	,	,	PUNCT
ejpam-5043	409	6	2022	2022	NUM
ejpam-5043	409	7	.	.	PUNCT
ejpam-5043	410	1	[	[	X
ejpam-5043	410	2	32	32	NUM
ejpam-5043	410	3	]	]	PUNCT
ejpam-5043	410	4	edward	edward	PROPN
ejpam-5043	410	5	lorenz	lorenz	PROPN
ejpam-5043	410	6	n.	n.	PROPN
ejpam-5043	410	7	deterministic	deterministic	PROPN
ejpam-5043	410	8	non	non	ADJ
ejpam-5043	410	9	-	-	ADJ
ejpam-5043	410	10	periodic	periodic	ADJ
ejpam-5043	410	11	flows	flow	NOUN
ejpam-5043	410	12	.	.	PUNCT
ejpam-5043	411	1	journal	journal	NOUN
ejpam-5043	411	2	of	of	ADP
ejpam-5043	411	3	atmospheric	atmospheric	ADJ
ejpam-5043	411	4	science	science	NOUN
ejpam-5043	411	5	,	,	PUNCT
ejpam-5043	411	6	1963	1963	NUM
ejpam-5043	411	7	.	.	PUNCT
ejpam-5043	412	1	[	[	X
ejpam-5043	412	2	33	33	NUM
ejpam-5043	412	3	]	]	PUNCT
ejpam-5043	412	4	rössler	rössler	NOUN
ejpam-5043	412	5	o.e	o.e	PROPN
ejpam-5043	412	6	.	.	PUNCT
ejpam-5043	412	7	different	different	ADJ
ejpam-5043	412	8	types	type	NOUN
ejpam-5043	412	9	of	of	ADP
ejpam-5043	412	10	chaos	chaos	NOUN
ejpam-5043	412	11	in	in	ADP
ejpam-5043	412	12	two	two	NUM
ejpam-5043	412	13	simple	simple	ADJ
ejpam-5043	412	14	differential	differential	ADJ
ejpam-5043	412	15	equations	equation	NOUN
ejpam-5043	412	16	.	.	PUNCT
ejpam-5043	413	1	zeitschrift	zeitschrift	NOUN
ejpam-5043	413	2	fur	fur	NOUN
ejpam-5043	413	3	naturforschung	naturforschung	PROPN
ejpam-5043	413	4	,	,	PUNCT
ejpam-5043	413	5	a	a	DET
ejpam-5043	413	6	31(12):1664–1670	31(12):1664–1670	NUM
ejpam-5043	413	7	,	,	PUNCT
ejpam-5043	413	8	1976	1976	NUM
ejpam-5043	413	9	.	.	PUNCT
ejpam-5043	414	1	[	[	X
ejpam-5043	414	2	34	34	NUM
ejpam-5043	414	3	]	]	PUNCT
ejpam-5043	414	4	rössler	rössler	NOUN
ejpam-5043	414	5	o.e	o.e	PROPN
ejpam-5043	414	6	.	.	PUNCT
ejpam-5043	415	1	an	an	DET
ejpam-5043	415	2	equation	equation	NOUN
ejpam-5043	415	3	for	for	ADP
ejpam-5043	415	4	continuous	continuous	ADJ
ejpam-5043	415	5	chaos	chaos	NOUN
ejpam-5043	415	6	.	.	PUNCT
ejpam-5043	416	1	physics	physics	NOUN
ejpam-5043	416	2	letters	letter	NOUN
ejpam-5043	416	3	,	,	PUNCT
ejpam-5043	416	4	a	a	DET
ejpam-5043	416	5	57(5):397–398	57(5):397–398	PROPN
ejpam-5043	416	6	,	,	PUNCT
ejpam-5043	416	7	1976	1976	NUM
ejpam-5043	416	8	.	.	PUNCT
ejpam-5043	417	1	[	[	X
ejpam-5043	417	2	35	35	NUM
ejpam-5043	417	3	]	]	X
ejpam-5043	417	4	i	i	PROPN
ejpam-5043	417	5	petras	petras	PROPN
ejpam-5043	417	6	.	.	PUNCT
ejpam-5043	418	1	control	control	NOUN
ejpam-5043	418	2	of	of	ADP
ejpam-5043	418	3	fractional	fractional	ADJ
ejpam-5043	418	4	-	-	PUNCT
ejpam-5043	418	5	order	order	NOUN
ejpam-5043	418	6	chua	chua	PROPN
ejpam-5043	418	7	’s	’s	PART
ejpam-5043	418	8	system	system	NOUN
ejpam-5043	418	9	.	.	PUNCT
ejpam-5043	419	1	j.	j.	PROPN
ejpam-5043	419	2	elec	elec	PROPN
ejpam-5043	419	3	.	.	PUNCT
ejpam-5043	420	1	engi	engi	PROPN
ejpam-5043	420	2	.	.	PUNCT
ejpam-5043	420	3	,	,	PUNCT
ejpam-5043	421	1	53:219–222	53:219–222	NUM
ejpam-5043	421	2	,	,	PUNCT
ejpam-5043	421	3	2002	2002	NUM
ejpam-5043	421	4	.	.	PUNCT
ejpam-5043	422	1	[	[	X
ejpam-5043	422	2	36	36	NUM
ejpam-5043	422	3	]	]	X
ejpam-5043	422	4	i	i	PROPN
ejpam-5043	422	5	petras	petras	PROPN
ejpam-5043	422	6	.	.	PUNCT
ejpam-5043	423	1	a	a	DET
ejpam-5043	423	2	note	note	NOUN
ejpam-5043	423	3	on	on	ADP
ejpam-5043	423	4	the	the	DET
ejpam-5043	423	5	fractional	fractional	ADJ
ejpam-5043	423	6	-	-	PUNCT
ejpam-5043	423	7	order	order	NOUN
ejpam-5043	423	8	chua	chua	PROPN
ejpam-5043	423	9	’s	’s	PART
ejpam-5043	423	10	system	system	NOUN
ejpam-5043	423	11	.	.	PUNCT
ejpam-5043	424	1	chaos	chaos	NOUN
ejpam-5043	424	2	,	,	PUNCT
ejpam-5043	424	3	solitons	soliton	NOUN
ejpam-5043	424	4	and	and	CCONJ
ejpam-5043	424	5	fractals	fractal	NOUN
ejpam-5043	424	6	,	,	PUNCT
ejpam-5043	424	7	38:140–147	38:140–147	NUM
ejpam-5043	424	8	,	,	PUNCT
ejpam-5043	424	9	2008	2008	NUM
ejpam-5043	424	10	.	.	PUNCT
ejpam-5043	425	1	[	[	X
ejpam-5043	425	2	37	37	NUM
ejpam-5043	425	3	]	]	X
ejpam-5043	425	4	i	i	PRON
ejpam-5043	425	5	podlubny	podlubny	NOUN
ejpam-5043	425	6	.	.	PUNCT
ejpam-5043	426	1	fractional	fractional	ADJ
ejpam-5043	426	2	differential	differential	ADJ
ejpam-5043	426	3	equations	equation	NOUN
ejpam-5043	426	4	.	.	PUNCT
ejpam-5043	427	1	academic	academic	ADJ
ejpam-5043	427	2	press	press	NOUN
ejpam-5043	427	3	,	,	PUNCT
ejpam-5043	427	4	new	new	PROPN
ejpam-5043	427	5	york	york	PROPN
ejpam-5043	427	6	,	,	PUNCT
ejpam-5043	427	7	1999	1999	NUM
ejpam-5043	427	8	.	.	PUNCT
ejpam-5043	428	1	[	[	X
ejpam-5043	428	2	38	38	NUM
ejpam-5043	428	3	]	]	X
ejpam-5043	428	4	q	q	X
ejpam-5043	428	5	lai	lai	PROPN
ejpam-5043	428	6	,	,	PUNCT
ejpam-5043	428	7	a	a	DET
ejpam-5043	428	8	akgul	akgul	NOUN
ejpam-5043	428	9	,	,	PUNCT
ejpam-5043	428	10	c	c	PROPN
ejpam-5043	428	11	li	li	PROPN
ejpam-5043	428	12	,	,	PUNCT
ejpam-5043	428	13	g	g	PROPN
ejpam-5043	428	14	xu	xu	PROPN
ejpam-5043	428	15	and	and	CCONJ
ejpam-5043	428	16	u	u	PROPN
ejpam-5043	428	17	cavusoglu	cavusoglu	NOUN
ejpam-5043	428	18	.	.	PUNCT
ejpam-5043	429	1	a	a	DET
ejpam-5043	429	2	new	new	ADJ
ejpam-5043	429	3	chaotic	chaotic	ADJ
ejpam-5043	429	4	system	system	NOUN
ejpam-5043	429	5	with	with	ADP
ejpam-5043	429	6	multiple	multiple	ADJ
ejpam-5043	429	7	attractors	attractor	NOUN
ejpam-5043	429	8	:	:	PUNCT
ejpam-5043	429	9	dynamic	dynamic	ADJ
ejpam-5043	429	10	analysis	analysis	NOUN
ejpam-5043	429	11	,	,	PUNCT
ejpam-5043	429	12	circuit	circuit	NOUN
ejpam-5043	429	13	realization	realization	NOUN
ejpam-5043	429	14	and	and	CCONJ
ejpam-5043	429	15	s	s	NOUN
ejpam-5043	429	16	-	-	PUNCT
ejpam-5043	429	17	box	box	NOUN
ejpam-5043	429	18	design	design	NOUN
ejpam-5043	429	19	.	.	PUNCT
ejpam-5043	430	1	entropy	entropy	PROPN
ejpam-5043	430	2	,	,	PUNCT
ejpam-5043	430	3	20(1):12	20(1):12	NUM
ejpam-5043	430	4	,	,	PUNCT
ejpam-5043	430	5	2018	2018	NUM
ejpam-5043	430	6	.	.	PUNCT
ejpam-5043	431	1	[	[	X
ejpam-5043	431	2	39	39	NUM
ejpam-5043	431	3	]	]	PUNCT
ejpam-5043	431	4	qazza	qazza	PROPN
ejpam-5043	431	5	a.	a.	PROPN
ejpam-5043	431	6	,	,	PUNCT
ejpam-5043	431	7	abdoon	abdoon	NOUN
ejpam-5043	431	8	m.	m.	NOUN
ejpam-5043	431	9	,	,	PUNCT
ejpam-5043	431	10	saadeh	saadeh	PROPN
ejpam-5043	431	11	r.	r.	PROPN
ejpam-5043	431	12	,	,	PUNCT
ejpam-5043	431	13	and	and	CCONJ
ejpam-5043	431	14	berir	berir	NOUN
ejpam-5043	431	15	m.	m.	VERB
ejpam-5043	431	16	anew	anew	ADJ
ejpam-5043	431	17	scheme	scheme	NOUN
ejpam-5043	431	18	for	for	ADP
ejpam-5043	431	19	solving	solve	VERB
ejpam-5043	431	20	a	a	DET
ejpam-5043	431	21	fractional	fractional	ADJ
ejpam-5043	431	22	differential	differential	ADJ
ejpam-5043	431	23	equation	equation	NOUN
ejpam-5043	431	24	and	and	CCONJ
ejpam-5043	431	25	a	a	DET
ejpam-5043	431	26	chaotic	chaotic	ADJ
ejpam-5043	431	27	system	system	NOUN
ejpam-5043	431	28	.	.	PUNCT
ejpam-5043	432	1	european	european	PROPN
ejpam-5043	432	2	journal	journal	PROPN
ejpam-5043	432	3	of	of	ADP
ejpam-5043	432	4	pure	pure	ADJ
ejpam-5043	432	5	and	and	CCONJ
ejpam-5043	432	6	applied	applied	ADJ
ejpam-5043	432	7	mathematics	mathematic	NOUN
ejpam-5043	432	8	.	.	PUNCT
ejpam-5043	432	9	,	,	PUNCT
ejpam-5043	432	10	16(2):1128–1139	16(2):1128–1139	NUM
ejpam-5043	432	11	,	,	PUNCT
ejpam-5043	432	12	2023	2023	NUM
ejpam-5043	432	13	.	.	PUNCT
ejpam-5043	433	1	[	[	X
ejpam-5043	433	2	40	40	NUM
ejpam-5043	433	3	]	]	PUNCT
ejpam-5043	433	4	s	s	PART
ejpam-5043	433	5	kumar	kumar	PROPN
ejpam-5043	433	6	,	,	PUNCT
ejpam-5043	433	7	r	r	PROPN
ejpam-5043	433	8	kumar	kumar	PROPN
ejpam-5043	433	9	,	,	PUNCT
ejpam-5043	433	10	c	c	PROPN
ejpam-5043	433	11	cattani	cattani	PROPN
ejpam-5043	433	12	and	and	CCONJ
ejpam-5043	433	13	b	b	PROPN
ejpam-5043	433	14	samet	samet	NOUN
ejpam-5043	433	15	.	.	PUNCT
ejpam-5043	434	1	chaotic	chaotic	ADJ
ejpam-5043	434	2	behaviour	behaviour	NOUN
ejpam-5043	434	3	of	of	ADP
ejpam-5043	434	4	fractional	fractional	ADJ
ejpam-5043	434	5	predator	predator	NOUN
ejpam-5043	434	6	-	-	PUNCT
ejpam-5043	434	7	prey	prey	NOUN
ejpam-5043	434	8	dynamical	dynamical	ADJ
ejpam-5043	434	9	system	system	NOUN
ejpam-5043	434	10	.	.	PUNCT
ejpam-5043	435	1	chaos	chaos	NOUN
ejpam-5043	435	2	soli	soli	PROPN
ejpam-5043	435	3	.	.	PUNCT
ejpam-5043	436	1	fract	fract	PROPN
ejpam-5043	436	2	.	.	PROPN
ejpam-5043	436	3	,	,	PUNCT
ejpam-5043	436	4	135	135	NUM
ejpam-5043	436	5	:p	:p	NOUN
ejpam-5043	436	6	.	.	PROPN
ejpam-5043	437	1	12	12	NUM
ejpam-5043	437	2	,	,	PUNCT
ejpam-5043	437	3	2020	2020	NUM
ejpam-5043	437	4	.	.	PUNCT
ejpam-5043	438	1	[	[	X
ejpam-5043	438	2	41	41	NUM
ejpam-5043	438	3	]	]	X
ejpam-5043	438	4	saadeh	saadeh	PROPN
ejpam-5043	438	5	r.	r.	PROPN
ejpam-5043	438	6	,	,	PUNCT
ejpam-5043	438	7	abdoon	abdoon	PROPN
ejpam-5043	438	8	m.	m.	NOUN
ejpam-5043	438	9	a.	a.	PROPN
ejpam-5043	438	10	,	,	PUNCT
ejpam-5043	438	11	qazza	qazza	PROPN
ejpam-5043	438	12	a.	a.	NOUN
ejpam-5043	438	13	,	,	PUNCT
ejpam-5043	438	14	and	and	CCONJ
ejpam-5043	438	15	berir	berir	NOUN
ejpam-5043	438	16	m.	m.	VERB
ejpam-5043	438	17	a	a	DET
ejpam-5043	438	18	numerical	numerical	ADJ
ejpam-5043	438	19	solution	solution	NOUN
ejpam-5043	438	20	of	of	ADP
ejpam-5043	438	21	generalized	generalized	ADJ
ejpam-5043	438	22	caputo	caputo	PROPN
ejpam-5043	438	23	fractional	fractional	ADJ
ejpam-5043	438	24	initial	initial	ADJ
ejpam-5043	438	25	value	value	NOUN
ejpam-5043	438	26	problems	problem	NOUN
ejpam-5043	438	27	.	.	PUNCT
ejpam-5043	439	1	fractal	fractal	ADJ
ejpam-5043	439	2	and	and	CCONJ
ejpam-5043	439	3	fractional	fractional	ADJ
ejpam-5043	439	4	,	,	PUNCT
ejpam-5043	439	5	7(4):332	7(4):332	NUM
ejpam-5043	439	6	,	,	PUNCT
ejpam-5043	439	7	2023	2023	NUM
ejpam-5043	439	8	.	.	PUNCT
ejpam-5043	440	1	[	[	X
ejpam-5043	440	2	42	42	NUM
ejpam-5043	440	3	]	]	X
ejpam-5043	440	4	oldham	oldham	PROPN
ejpam-5043	440	5	kb	kb	PROPN
ejpam-5043	440	6	,	,	PUNCT
ejpam-5043	440	7	spanier	spanier	NOUN
ejpam-5043	440	8	j.	j.	PROPN
ejpam-5043	440	9	the	the	DET
ejpam-5043	440	10	fractional	fractional	ADJ
ejpam-5043	440	11	calculus	calculus	NOUN
ejpam-5043	440	12	.	.	PUNCT
ejpam-5043	441	1	academic	academic	ADJ
ejpam-5043	441	2	press	press	NOUN
ejpam-5043	441	3	,	,	PUNCT
ejpam-5043	441	4	new	new	PROPN
ejpam-5043	441	5	york	york	PROPN
ejpam-5043	441	6	,	,	PUNCT
ejpam-5043	441	7	london	london	PROPN
ejpam-5043	441	8	,	,	PUNCT
ejpam-5043	441	9	1974	1974	NUM
ejpam-5043	441	10	.	.	PUNCT
ejpam-5043	442	1	references	reference	NOUN
ejpam-5043	442	2	461	461	NUM
ejpam-5043	443	1	[	[	X
ejpam-5043	443	2	43	43	NUM
ejpam-5043	443	3	]	]	X
ejpam-5043	443	4	m	m	VERB
ejpam-5043	443	5	toufik	toufik	ADJ
ejpam-5043	443	6	and	and	CCONJ
ejpam-5043	443	7	a	a	DET
ejpam-5043	443	8	atangana	atangana	PROPN
ejpam-5043	443	9	.	.	PUNCT
ejpam-5043	444	1	new	new	ADJ
ejpam-5043	444	2	numerical	numerical	ADJ
ejpam-5043	444	3	approximation	approximation	NOUN
ejpam-5043	444	4	of	of	ADP
ejpam-5043	444	5	fractional	fractional	ADJ
ejpam-5043	444	6	derivative	derivative	NOUN
ejpam-5043	444	7	with	with	ADP
ejpam-5043	444	8	non	non	ADJ
ejpam-5043	444	9	-	-	ADJ
ejpam-5043	444	10	local	local	ADJ
ejpam-5043	444	11	and	and	CCONJ
ejpam-5043	444	12	non	non	ADJ
ejpam-5043	444	13	-	-	ADJ
ejpam-5043	444	14	singular	singular	ADJ
ejpam-5043	444	15	kernel	kernel	NOUN
ejpam-5043	444	16	:	:	PUNCT
ejpam-5043	444	17	application	application	NOUN
ejpam-5043	444	18	to	to	ADP
ejpam-5043	444	19	chaotic	chaotic	ADJ
ejpam-5043	444	20	models	model	NOUN
ejpam-5043	444	21	.	.	PUNCT
ejpam-5043	445	1	eur	eur	PROPN
ejpam-5043	445	2	phys	phys	PROPN
ejpam-5043	445	3	j	j	PROPN
ejpam-5043	445	4	plus	plus	CCONJ
ejpam-5043	445	5	,	,	PUNCT
ejpam-5043	445	6	132(10):444	132(10):444	NUM
ejpam-5043	445	7	,	,	PUNCT
ejpam-5043	445	8	2017	2017	NUM
ejpam-5043	445	9	.	.	PUNCT
ejpam-5043	446	1	[	[	X
ejpam-5043	446	2	44	44	NUM
ejpam-5043	446	3	]	]	PUNCT
ejpam-5043	446	4	wassim	wassim	NOUN
ejpam-5043	446	5	a.	a.	NOUN
ejpam-5043	446	6	,	,	PUNCT
ejpam-5043	446	7	alexan	alexan	VERB
ejpam-5043	446	8	n.	n.	NOUN
ejpam-5043	446	9	,	,	PUNCT
ejpam-5043	446	10	and	and	CCONJ
ejpam-5043	446	11	gabr	gabr	VERB
ejpam-5043	446	12	m.	m.	NOUN
ejpam-5043	446	13	multiple	multiple	ADJ
ejpam-5043	446	14	-	-	PUNCT
ejpam-5043	446	15	layer	layer	NOUN
ejpam-5043	446	16	image	image	NOUN
ejpam-5043	446	17	encryption	encryption	NOUN
ejpam-5043	446	18	utilizing	utilize	VERB
ejpam-5043	446	19	fractional	fractional	ADJ
ejpam-5043	446	20	-	-	PUNCT
ejpam-5043	446	21	order	order	NOUN
ejpam-5043	446	22	chen	chen	PROPN
ejpam-5043	446	23	hyperchaotic	hyperchaotic	PROPN
ejpam-5043	446	24	map	map	NOUN
ejpam-5043	446	25	and	and	CCONJ
ejpam-5043	446	26	cryptographically	cryptographically	ADV
ejpam-5043	446	27	secure	secure	ADJ
ejpam-5043	446	28	prngs	prng	NOUN
ejpam-5043	446	29	.	.	PUNCT
ejpam-5043	447	1	fractal	fractal	ADJ
ejpam-5043	447	2	and	and	CCONJ
ejpam-5043	447	3	fractional	fractional	ADJ
ejpam-5043	447	4	.	.	PUNCT
ejpam-5043	447	5	,	,	PUNCT
ejpam-5043	447	6	7(4):287	7(4):287	NUM
ejpam-5043	447	7	,	,	PUNCT
ejpam-5043	447	8	2023	2023	NUM
ejpam-5043	447	9	.	.	PUNCT
ejpam-5043	448	1	[	[	X
ejpam-5043	448	2	45	45	NUM
ejpam-5043	448	3	]	]	PUNCT
ejpam-5043	448	4	yang	yang	PROPN
ejpam-5043	448	5	x.-f	x.-f	PROPN
ejpam-5043	448	6	.	.	PUNCT
ejpam-5043	448	7	,	,	PUNCT
ejpam-5043	448	8	deng	deng	PROPN
ejpam-5043	448	9	z.-c	z.-c	PROPN
ejpam-5043	448	10	.	.	PUNCT
ejpam-5043	448	11	,	,	PUNCT
ejpam-5043	448	12	and	and	CCONJ
ejpam-5043	448	13	wei	wei	PROPN
ejpam-5043	448	14	y.	y.	PROPN
ejpam-5043	448	15	a	a	DET
ejpam-5043	448	16	riccati	riccati	PROPN
ejpam-5043	448	17	-	-	PUNCT
ejpam-5043	448	18	bernoulli	bernoulli	NOUN
ejpam-5043	448	19	sub	sub	ADJ
ejpam-5043	448	20	-	-	ADJ
ejpam-5043	448	21	ode	ode	ADJ
ejpam-5043	448	22	method	method	NOUN
ejpam-5043	448	23	for	for	ADP
ejpam-5043	448	24	nonlinear	nonlinear	ADJ
ejpam-5043	448	25	partial	partial	ADJ
ejpam-5043	448	26	differential	differential	NOUN
ejpam-5043	448	27	equations	equation	NOUN
ejpam-5043	448	28	and	and	CCONJ
ejpam-5043	448	29	its	its	PRON
ejpam-5043	448	30	application	application	NOUN
ejpam-5043	448	31	.	.	PUNCT
ejpam-5043	449	1	advances	advance	NOUN
ejpam-5043	449	2	in	in	ADP
ejpam-5043	449	3	difference	difference	NOUN
ejpam-5043	449	4	equations	equation	NOUN
ejpam-5043	449	5	,	,	PUNCT
ejpam-5043	449	6	117(2015	117(2015	NUM
ejpam-5043	449	7	)	)	PUNCT
ejpam-5043	449	8	,	,	PUNCT
ejpam-5043	449	9	2015	2015	NUM
ejpam-5043	449	10	.	.	PUNCT
ejpam-5043	450	1	[	[	X
ejpam-5043	450	2	46	46	NUM
ejpam-5043	450	3	]	]	PUNCT
ejpam-5043	450	4	xuefeng	xuefeng	PROPN
ejpam-5043	450	5	z.	z.	PROPN
ejpam-5043	450	6	,	,	PUNCT
ejpam-5043	450	7	boutat	boutat	PROPN
ejpam-5043	450	8	b.	b.	PROPN
ejpam-5043	450	9	,	,	PUNCT
ejpam-5043	450	10	and	and	CCONJ
ejpam-5043	450	11	liu	liu	PROPN
ejpam-5043	450	12	d.	d.	PROPN
ejpam-5043	450	13	applications	application	NOUN
ejpam-5043	450	14	of	of	ADP
ejpam-5043	450	15	fractional	fractional	ADJ
ejpam-5043	450	16	operator	operator	NOUN
ejpam-5043	450	17	in	in	ADP
ejpam-5043	450	18	image	image	NOUN
ejpam-5043	450	19	processing	processing	NOUN
ejpam-5043	450	20	and	and	CCONJ
ejpam-5043	450	21	stability	stability	NOUN
ejpam-5043	450	22	of	of	ADP
ejpam-5043	450	23	control	control	NOUN
ejpam-5043	450	24	systems	system	NOUN
ejpam-5043	450	25	.	.	PUNCT
ejpam-5043	451	1	fractal	fractal	PROPN
ejpam-5043	451	2	and	and	CCONJ
ejpam-5043	451	3	fractional	fractional	ADJ
ejpam-5043	451	4	.	.	PROPN
ejpam-5043	451	5	,	,	PUNCT
ejpam-5043	451	6	7(5):359	7(5):359	NUM
ejpam-5043	451	7	,	,	PUNCT
ejpam-5043	451	8	2023	2023	NUM
ejpam-5043	451	9	.	.	PUNCT
ejpam-5043	452	1	[	[	X
ejpam-5043	452	2	47	47	NUM
ejpam-5043	452	3	]	]	PUNCT
ejpam-5043	452	4	z.	z.	PROPN
ejpam-5043	452	5	zhang	zhang	PROPN
ejpam-5043	452	6	,	,	PUNCT
ejpam-5043	452	7	x.	x.	PROPN
ejpam-5043	452	8	,	,	PUNCT
ejpam-5043	452	9	li	li	PROPN
ejpam-5043	452	10	,	,	PUNCT
ejpam-5043	452	11	x.	x.	PROPN
ejpam-5043	452	12	,	,	PUNCT
ejpam-5043	452	13	yang	yang	PROPN
ejpam-5043	452	14	,	,	PUNCT
ejpam-5043	452	15	k.	k.	PROPN
ejpam-5043	452	16	,	,	PUNCT
ejpam-5043	452	17	wang	wang	PROPN
ejpam-5043	452	18	.	.	PUNCT
ejpam-5043	453	1	lithium	lithium	NOUN
ejpam-5043	453	2	-	-	PUNCT
ejpam-5043	453	3	ion	ion	NOUN
ejpam-5043	453	4	battery	battery	NOUN
ejpam-5043	453	5	modeling	modeling	NOUN
ejpam-5043	453	6	and	and	CCONJ
ejpam-5043	453	7	state	state	NOUN
ejpam-5043	453	8	of	of	ADP
ejpam-5043	453	9	charge	charge	NOUN
ejpam-5043	453	10	prediction	prediction	NOUN
ejpam-5043	453	11	based	base	VERB
ejpam-5043	453	12	on	on	ADP
ejpam-5043	453	13	fractional	fractional	ADJ
ejpam-5043	453	14	-	-	PUNCT
ejpam-5043	453	15	order	order	NOUN
ejpam-5043	453	16	calculus	calculus	NOUN
ejpam-5043	453	17	.	.	PUNCT
ejpam-5043	454	1	mathematics	mathematic	NOUN
ejpam-5043	454	2	.	.	PUNCT
ejpam-5043	454	3	,	,	PUNCT
ejpam-5043	454	4	11(15):3401	11(15):3401	NUM
ejpam-5043	454	5	,	,	PUNCT
ejpam-5043	454	6	2023	2023	NUM
ejpam-5043	454	7	.	.	PUNCT