id	sid	tid	token	lemma	pos
ejpam-6631	1	1	european	european	PROPN
ejpam-6631	1	2	journal	journal	PROPN
ejpam-6631	1	3	of	of	ADP
ejpam-6631	1	4	pure	pure	ADJ
ejpam-6631	1	5	and	and	CCONJ
ejpam-6631	1	6	applied	applied	ADJ
ejpam-6631	1	7	mathematics	mathematic	NOUN
ejpam-6631	1	8	2025	2025	NUM
ejpam-6631	1	9	,	,	PUNCT
ejpam-6631	1	10	vol	vol	NOUN
ejpam-6631	1	11	.	.	PROPN
ejpam-6631	1	12	18	18	NUM
ejpam-6631	1	13	,	,	PUNCT
ejpam-6631	1	14	issue	issue	NOUN
ejpam-6631	1	15	4	4	NUM
ejpam-6631	1	16	,	,	PUNCT
ejpam-6631	1	17	article	article	NOUN
ejpam-6631	1	18	number	number	NOUN
ejpam-6631	1	19	6631	6631	NUM
ejpam-6631	1	20	issn	issn	PROPN
ejpam-6631	1	21	1307	1307	NUM
ejpam-6631	1	22	-	-	SYM
ejpam-6631	1	23	5543	5543	NUM
ejpam-6631	1	24	–	–	PUNCT
ejpam-6631	1	25	ejpam.com	ejpam.com	X
ejpam-6631	1	26	published	publish	VERB
ejpam-6631	1	27	by	by	ADP
ejpam-6631	1	28	new	new	PROPN
ejpam-6631	1	29	york	york	PROPN
ejpam-6631	1	30	business	business	PROPN
ejpam-6631	1	31	global	global	PROPN
ejpam-6631	1	32	a	a	DET
ejpam-6631	1	33	new	new	ADJ
ejpam-6631	1	34	numerical	numerical	ADJ
ejpam-6631	1	35	solution	solution	NOUN
ejpam-6631	1	36	for	for	ADP
ejpam-6631	1	37	prabhakar	prabhakar	NOUN
ejpam-6631	1	38	fractional	fractional	ADJ
ejpam-6631	1	39	differential	differential	NOUN
ejpam-6631	1	40	equations	equation	NOUN
ejpam-6631	1	41	using	use	VERB
ejpam-6631	1	42	the	the	DET
ejpam-6631	1	43	explicit	explicit	ADJ
ejpam-6631	1	44	fractional	fractional	ADJ
ejpam-6631	1	45	adams	adam	NOUN
ejpam-6631	1	46	method	method	PROPN
ejpam-6631	1	47	mohammad	mohammad	PROPN
ejpam-6631	1	48	abdel	abdel	PROPN
ejpam-6631	1	49	aal1,∗	aal1,∗	PROPN
ejpam-6631	1	50	,	,	PUNCT
ejpam-6631	1	51	mohammad	mohammad	PROPN
ejpam-6631	1	52	s.	s.	PROPN
ejpam-6631	1	53	ghatasheh2	ghatasheh2	PROPN
ejpam-6631	1	54	,	,	PUNCT
ejpam-6631	1	55	hussien	hussien	PROPN
ejpam-6631	1	56	albadawi1	albadawi1	PROPN
ejpam-6631	1	57	,	,	PUNCT
ejpam-6631	1	58	shaher	shaher	ADJ
ejpam-6631	1	59	momani3	momani3	PROPN
ejpam-6631	1	60	1	1	NUM
ejpam-6631	1	61	department	department	NOUN
ejpam-6631	1	62	of	of	ADP
ejpam-6631	1	63	mathematics	mathematic	NOUN
ejpam-6631	1	64	,	,	PUNCT
ejpam-6631	1	65	faculty	faculty	NOUN
ejpam-6631	1	66	of	of	ADP
ejpam-6631	1	67	arts	art	NOUN
ejpam-6631	1	68	and	and	CCONJ
ejpam-6631	1	69	sciences	science	NOUN
ejpam-6631	1	70	,	,	PUNCT
ejpam-6631	1	71	the	the	DET
ejpam-6631	1	72	world	world	NOUN
ejpam-6631	1	73	islamic	islamic	PROPN
ejpam-6631	1	74	sciences	sciences	PROPN
ejpam-6631	1	75	&	&	CCONJ
ejpam-6631	1	76	education	education	PROPN
ejpam-6631	1	77	university	university	PROPN
ejpam-6631	1	78	(	(	PUNCT
ejpam-6631	1	79	w.i.s.e	w.i.s.e	PROPN
ejpam-6631	1	80	)	)	PUNCT
ejpam-6631	1	81	,	,	PUNCT
ejpam-6631	1	82	amman	amman	PROPN
ejpam-6631	1	83	,	,	PUNCT
ejpam-6631	1	84	jordan	jordan	PROPN
ejpam-6631	1	85	2	2	NUM
ejpam-6631	1	86	department	department	NOUN
ejpam-6631	1	87	of	of	ADP
ejpam-6631	1	88	basic	basic	ADJ
ejpam-6631	1	89	sciences	science	NOUN
ejpam-6631	1	90	,	,	PUNCT
ejpam-6631	1	91	faculty	faculty	NOUN
ejpam-6631	1	92	of	of	ADP
ejpam-6631	1	93	arts	art	NOUN
ejpam-6631	1	94	and	and	CCONJ
ejpam-6631	1	95	educational	educational	ADJ
ejpam-6631	1	96	sciences	science	NOUN
ejpam-6631	1	97	,	,	PUNCT
ejpam-6631	1	98	middle	middle	PROPN
ejpam-6631	1	99	east	east	PROPN
ejpam-6631	1	100	university	university	PROPN
ejpam-6631	1	101	,	,	PUNCT
ejpam-6631	1	102	amman	amman	PROPN
ejpam-6631	1	103	,	,	PUNCT
ejpam-6631	1	104	jordan	jordan	PROPN
ejpam-6631	1	105	3	3	NUM
ejpam-6631	1	106	department	department	PROPN
ejpam-6631	1	107	of	of	ADP
ejpam-6631	1	108	mathematics	mathematic	NOUN
ejpam-6631	1	109	,	,	PUNCT
ejpam-6631	1	110	faculty	faculty	NOUN
ejpam-6631	1	111	of	of	ADP
ejpam-6631	1	112	sciences	science	NOUN
ejpam-6631	1	113	,	,	PUNCT
ejpam-6631	1	114	the	the	DET
ejpam-6631	1	115	university	university	PROPN
ejpam-6631	1	116	of	of	ADP
ejpam-6631	1	117	jordan	jordan	PROPN
ejpam-6631	1	118	,	,	PUNCT
ejpam-6631	1	119	amman	amman	PROPN
ejpam-6631	1	120	,	,	PUNCT
ejpam-6631	1	121	jordan	jordan	PROPN
ejpam-6631	1	122	abstract	abstract	PROPN
ejpam-6631	1	123	.	.	PUNCT
ejpam-6631	2	1	this	this	DET
ejpam-6631	2	2	paper	paper	NOUN
ejpam-6631	2	3	introduces	introduce	VERB
ejpam-6631	2	4	a	a	DET
ejpam-6631	2	5	new	new	ADJ
ejpam-6631	2	6	way	way	NOUN
ejpam-6631	2	7	to	to	PART
ejpam-6631	2	8	solve	solve	VERB
ejpam-6631	2	9	prabhakar	prabhakar	NOUN
ejpam-6631	2	10	fractional	fractional	ADJ
ejpam-6631	2	11	differential	differential	NOUN
ejpam-6631	2	12	equations	equation	NOUN
ejpam-6631	2	13	using	use	VERB
ejpam-6631	2	14	an	an	DET
ejpam-6631	2	15	explicit	explicit	ADJ
ejpam-6631	2	16	fractional	fractional	ADJ
ejpam-6631	2	17	adams	adam	NOUN
ejpam-6631	2	18	method	method	NOUN
ejpam-6631	2	19	.	.	PUNCT
ejpam-6631	3	1	these	these	DET
ejpam-6631	3	2	equations	equation	NOUN
ejpam-6631	3	3	are	be	AUX
ejpam-6631	3	4	difficult	difficult	ADJ
ejpam-6631	3	5	to	to	PART
ejpam-6631	3	6	work	work	VERB
ejpam-6631	3	7	with	with	ADP
ejpam-6631	3	8	because	because	SCONJ
ejpam-6631	3	9	they	they	PRON
ejpam-6631	3	10	have	have	VERB
ejpam-6631	3	11	several	several	ADJ
ejpam-6631	3	12	parameters	parameter	NOUN
ejpam-6631	3	13	.	.	PUNCT
ejpam-6631	4	1	the	the	DET
ejpam-6631	4	2	new	new	ADJ
ejpam-6631	4	3	method	method	NOUN
ejpam-6631	4	4	,	,	PUNCT
ejpam-6631	4	5	which	which	PRON
ejpam-6631	4	6	combines	combine	VERB
ejpam-6631	4	7	the	the	DET
ejpam-6631	4	8	explicit	explicit	ADJ
ejpam-6631	4	9	fractional	fractional	ADJ
ejpam-6631	4	10	adams	adam	NOUN
ejpam-6631	4	11	method	method	NOUN
ejpam-6631	4	12	with	with	ADP
ejpam-6631	4	13	lagrange	lagrange	NOUN
ejpam-6631	4	14	interpolation	interpolation	NOUN
ejpam-6631	4	15	,	,	PUNCT
ejpam-6631	4	16	effectively	effectively	ADV
ejpam-6631	4	17	tackles	tackle	VERB
ejpam-6631	4	18	these	these	DET
ejpam-6631	4	19	difficulties	difficulty	NOUN
ejpam-6631	4	20	.	.	PUNCT
ejpam-6631	5	1	the	the	DET
ejpam-6631	5	2	paper	paper	NOUN
ejpam-6631	5	3	also	also	ADV
ejpam-6631	5	4	includes	include	VERB
ejpam-6631	5	5	an	an	DET
ejpam-6631	5	6	analysis	analysis	NOUN
ejpam-6631	5	7	to	to	PART
ejpam-6631	5	8	show	show	VERB
ejpam-6631	5	9	how	how	SCONJ
ejpam-6631	5	10	well	well	ADV
ejpam-6631	5	11	the	the	DET
ejpam-6631	5	12	method	method	NOUN
ejpam-6631	5	13	works	work	VERB
ejpam-6631	5	14	.	.	PUNCT
ejpam-6631	6	1	it	it	PRON
ejpam-6631	6	2	provides	provide	VERB
ejpam-6631	6	3	several	several	ADJ
ejpam-6631	6	4	examples	example	NOUN
ejpam-6631	6	5	to	to	PART
ejpam-6631	6	6	demonstrate	demonstrate	VERB
ejpam-6631	6	7	the	the	DET
ejpam-6631	6	8	method	method	NOUN
ejpam-6631	6	9	’s	’s	PART
ejpam-6631	6	10	effectiveness	effectiveness	NOUN
ejpam-6631	6	11	and	and	CCONJ
ejpam-6631	6	12	compares	compare	VERB
ejpam-6631	6	13	it	it	PRON
ejpam-6631	6	14	with	with	ADP
ejpam-6631	6	15	other	other	ADJ
ejpam-6631	6	16	existing	exist	VERB
ejpam-6631	6	17	methods	method	NOUN
ejpam-6631	6	18	.	.	PUNCT
ejpam-6631	7	1	the	the	DET
ejpam-6631	7	2	results	result	NOUN
ejpam-6631	7	3	show	show	VERB
ejpam-6631	7	4	that	that	SCONJ
ejpam-6631	7	5	the	the	DET
ejpam-6631	7	6	proposed	propose	VERB
ejpam-6631	7	7	method	method	NOUN
ejpam-6631	7	8	is	be	AUX
ejpam-6631	7	9	efficient	efficient	ADJ
ejpam-6631	7	10	and	and	CCONJ
ejpam-6631	7	11	easy	easy	ADJ
ejpam-6631	7	12	to	to	PART
ejpam-6631	7	13	use	use	VERB
ejpam-6631	7	14	.	.	PUNCT
ejpam-6631	8	1	2020	2020	NUM
ejpam-6631	8	2	mathematics	mathematic	NOUN
ejpam-6631	8	3	subject	subject	NOUN
ejpam-6631	8	4	classifications	classification	NOUN
ejpam-6631	8	5	:	:	PUNCT
ejpam-6631	8	6	26a33	26a33	NUM
ejpam-6631	8	7	,	,	PUNCT
ejpam-6631	8	8	33c45	33c45	NUM
ejpam-6631	8	9	,	,	PUNCT
ejpam-6631	8	10	34a08	34a08	NUM
ejpam-6631	8	11	,	,	PUNCT
ejpam-6631	8	12	65l60	65l60	NUM
ejpam-6631	8	13	,	,	PUNCT
ejpam-6631	8	14	65r10	65r10	NUM
ejpam-6631	8	15	key	key	ADJ
ejpam-6631	8	16	words	word	NOUN
ejpam-6631	8	17	and	and	CCONJ
ejpam-6631	8	18	phrases	phrase	NOUN
ejpam-6631	8	19	:	:	PUNCT
ejpam-6631	8	20	lagrange	lagrange	NOUN
ejpam-6631	8	21	interpolation	interpolation	NOUN
ejpam-6631	8	22	,	,	PUNCT
ejpam-6631	8	23	prabhakar	prabhakar	NOUN
ejpam-6631	8	24	fractional	fractional	NOUN
ejpam-6631	8	25	,	,	PUNCT
ejpam-6631	8	26	fractional	fractional	ADJ
ejpam-6631	8	27	differential	differential	ADJ
ejpam-6631	8	28	equations	equation	NOUN
ejpam-6631	8	29	,	,	PUNCT
ejpam-6631	8	30	adams	adams	PROPN
ejpam-6631	8	31	method	method	PROPN
ejpam-6631	8	32	1	1	NUM
ejpam-6631	8	33	.	.	PUNCT
ejpam-6631	9	1	introduction	introduction	NOUN
ejpam-6631	9	2	fractional	fractional	ADJ
ejpam-6631	9	3	calculus	calculus	NOUN
ejpam-6631	9	4	is	be	AUX
ejpam-6631	9	5	an	an	DET
ejpam-6631	9	6	extension	extension	NOUN
ejpam-6631	9	7	of	of	ADP
ejpam-6631	9	8	traditional	traditional	ADJ
ejpam-6631	9	9	calculus	calculus	NOUN
ejpam-6631	9	10	that	that	PRON
ejpam-6631	9	11	broadens	broaden	VERB
ejpam-6631	9	12	the	the	DET
ejpam-6631	9	13	scope	scope	NOUN
ejpam-6631	9	14	of	of	ADP
ejpam-6631	9	15	calculus	calculus	NOUN
ejpam-6631	9	16	operations	operation	NOUN
ejpam-6631	9	17	by	by	ADP
ejpam-6631	9	18	enabling	enable	VERB
ejpam-6631	9	19	the	the	DET
ejpam-6631	9	20	differentiation	differentiation	NOUN
ejpam-6631	9	21	and	and	CCONJ
ejpam-6631	9	22	integration	integration	NOUN
ejpam-6631	9	23	of	of	ADP
ejpam-6631	9	24	functions	function	NOUN
ejpam-6631	9	25	to	to	ADP
ejpam-6631	9	26	arbitrary	arbitrary	ADJ
ejpam-6631	9	27	,	,	PUNCT
ejpam-6631	9	28	non	non	ADJ
ejpam-6631	9	29	-	-	ADJ
ejpam-6631	9	30	integer	integer	ADJ
ejpam-6631	9	31	orders	order	NOUN
ejpam-6631	9	32	[	[	X
ejpam-6631	9	33	1	1	NUM
ejpam-6631	9	34	]	]	PUNCT
ejpam-6631	9	35	.	.	PUNCT
ejpam-6631	10	1	this	this	DET
ejpam-6631	10	2	concept	concept	NOUN
ejpam-6631	10	3	has	have	AUX
ejpam-6631	10	4	gained	gain	VERB
ejpam-6631	10	5	significant	significant	ADJ
ejpam-6631	10	6	traction	traction	NOUN
ejpam-6631	10	7	in	in	ADP
ejpam-6631	10	8	various	various	ADJ
ejpam-6631	10	9	scientific	scientific	ADJ
ejpam-6631	10	10	and	and	CCONJ
ejpam-6631	10	11	engineering	engineering	NOUN
ejpam-6631	10	12	disciplines	discipline	NOUN
ejpam-6631	10	13	because	because	SCONJ
ejpam-6631	10	14	it	it	PRON
ejpam-6631	10	15	often	often	ADV
ejpam-6631	10	16	provides	provide	VERB
ejpam-6631	10	17	a	a	DET
ejpam-6631	10	18	more	more	ADV
ejpam-6631	10	19	accurate	accurate	ADJ
ejpam-6631	10	20	representation	representation	NOUN
ejpam-6631	10	21	of	of	ADP
ejpam-6631	10	22	realworld	realworld	PROPN
ejpam-6631	10	23	systems	system	NOUN
ejpam-6631	10	24	than	than	ADP
ejpam-6631	10	25	classical	classical	ADJ
ejpam-6631	10	26	integer	integer	NOUN
ejpam-6631	10	27	-	-	PUNCT
ejpam-6631	10	28	order	order	NOUN
ejpam-6631	10	29	calculus	calculus	NOUN
ejpam-6631	11	1	[	[	X
ejpam-6631	11	2	2	2	NUM
ejpam-6631	11	3	]	]	PUNCT
ejpam-6631	11	4	.	.	PUNCT
ejpam-6631	12	1	in	in	ADP
ejpam-6631	12	2	particular	particular	ADJ
ejpam-6631	12	3	,	,	PUNCT
ejpam-6631	12	4	fractional	fractional	ADJ
ejpam-6631	12	5	calculus	calculus	NOUN
ejpam-6631	12	6	has	have	AUX
ejpam-6631	12	7	demonstrated	demonstrate	VERB
ejpam-6631	12	8	its	its	PRON
ejpam-6631	12	9	utility	utility	NOUN
ejpam-6631	12	10	in	in	ADP
ejpam-6631	12	11	mathematical	mathematical	ADJ
ejpam-6631	12	12	modelling	modelling	NOUN
ejpam-6631	12	13	across	across	ADP
ejpam-6631	12	14	diverse	diverse	ADJ
ejpam-6631	12	15	fields	field	NOUN
ejpam-6631	12	16	,	,	PUNCT
ejpam-6631	12	17	including	include	VERB
ejpam-6631	12	18	∗corresponding	∗corresponde	VERB
ejpam-6631	12	19	author	author	NOUN
ejpam-6631	12	20	.	.	PUNCT
ejpam-6631	13	1	doi	doi	NOUN
ejpam-6631	13	2	:	:	PUNCT
ejpam-6631	13	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6631	https://doi.org/10.29020/nybg.ejpam.v18i4.6631	PROPN
ejpam-6631	13	4	email	email	NOUN
ejpam-6631	13	5	addresses	address	VERB
ejpam-6631	13	6	:	:	PUNCT
ejpam-6631	13	7	mohammad.abdelaal@wise.edu.jo	mohammad.abdelaal@wise.edu.jo	X
ejpam-6631	13	8	(	(	PUNCT
ejpam-6631	13	9	m.	m.	NOUN
ejpam-6631	13	10	abdel	abdel	PROPN
ejpam-6631	13	11	aal	aal	PROPN
ejpam-6631	13	12	)	)	PUNCT
ejpam-6631	13	13	,	,	PUNCT
ejpam-6631	13	14	mghatasheh@meu.edu.jo	mghatasheh@meu.edu.jo	PROPN
ejpam-6631	13	15	(	(	PUNCT
ejpam-6631	13	16	m.	m.	NOUN
ejpam-6631	13	17	s.	s.	PROPN
ejpam-6631	13	18	ghatasheh	ghatasheh	PROPN
ejpam-6631	13	19	)	)	PUNCT
ejpam-6631	13	20	,	,	PUNCT
ejpam-6631	13	21	hussien.albadawi@wise.edu.jo	hussien.albadawi@wise.edu.jo	PROPN
ejpam-6631	13	22	(	(	PUNCT
ejpam-6631	13	23	h.	h.	PROPN
ejpam-6631	13	24	albadawi	albadawi	PROPN
ejpam-6631	13	25	)	)	PUNCT
ejpam-6631	13	26	,	,	PUNCT
ejpam-6631	13	27	s.momani@ju.edu.jo	s.momani@ju.edu.jo	PROPN
ejpam-6631	13	28	(	(	PUNCT
ejpam-6631	13	29	s.	s.	PROPN
ejpam-6631	13	30	momani	momani	PROPN
ejpam-6631	13	31	)	)	PUNCT
ejpam-6631	13	32	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6631	14	1	1	1	NUM
ejpam-6631	14	2	copyright	copyright	NOUN
ejpam-6631	14	3	:	:	PUNCT
ejpam-6631	14	4	©	©	PROPN
ejpam-6631	14	5	2025	2025	NUM
ejpam-6631	14	6	the	the	DET
ejpam-6631	14	7	author(s	author(s	NOUN
ejpam-6631	14	8	)	)	PUNCT
ejpam-6631	14	9	.	.	PUNCT
ejpam-6631	15	1	(	(	PUNCT
ejpam-6631	15	2	cc	cc	NOUN
ejpam-6631	15	3	by	by	ADP
ejpam-6631	15	4	-	-	PUNCT
ejpam-6631	15	5	nc	nc	PROPN
ejpam-6631	15	6	4.0	4.0	NUM
ejpam-6631	15	7	)	)	PUNCT
ejpam-6631	15	8	m.	m.	NOUN
ejpam-6631	15	9	abdel	abdel	PROPN
ejpam-6631	15	10	aal	aal	PROPN
ejpam-6631	15	11	et	et	PROPN
ejpam-6631	15	12	al	al	PROPN
ejpam-6631	15	13	.	.	PUNCT
ejpam-6631	15	14	/	/	SYM
ejpam-6631	15	15	eur	eur	PROPN
ejpam-6631	15	16	.	.	PUNCT
ejpam-6631	16	1	j.	j.	PROPN
ejpam-6631	16	2	pure	pure	PROPN
ejpam-6631	16	3	appl	appl	PROPN
ejpam-6631	16	4	.	.	PROPN
ejpam-6631	16	5	math	math	PROPN
ejpam-6631	16	6	,	,	PUNCT
ejpam-6631	16	7	18	18	NUM
ejpam-6631	16	8	(	(	PUNCT
ejpam-6631	16	9	4	4	NUM
ejpam-6631	16	10	)	)	PUNCT
ejpam-6631	16	11	(	(	PUNCT
ejpam-6631	16	12	2025	2025	NUM
ejpam-6631	16	13	)	)	PUNCT
ejpam-6631	16	14	,	,	PUNCT
ejpam-6631	16	15	6631	6631	NUM
ejpam-6631	16	16	2	2	NUM
ejpam-6631	16	17	of	of	ADP
ejpam-6631	16	18	20	20	NUM
ejpam-6631	16	19	science	science	NOUN
ejpam-6631	16	20	,	,	PUNCT
ejpam-6631	16	21	physics	physic	NOUN
ejpam-6631	17	1	[	[	X
ejpam-6631	17	2	3	3	NUM
ejpam-6631	17	3	]	]	PUNCT
ejpam-6631	17	4	,	,	PUNCT
ejpam-6631	17	5	engineering	engineer	VERB
ejpam-6631	17	6	[	[	X
ejpam-6631	17	7	4	4	NUM
ejpam-6631	17	8	]	]	PUNCT
ejpam-6631	17	9	,	,	PUNCT
ejpam-6631	17	10	and	and	CCONJ
ejpam-6631	17	11	finance	finance	NOUN
ejpam-6631	17	12	[	[	X
ejpam-6631	17	13	5	5	NUM
ejpam-6631	17	14	]	]	PUNCT
ejpam-6631	17	15	.	.	PUNCT
ejpam-6631	18	1	its	its	PRON
ejpam-6631	18	2	ability	ability	NOUN
ejpam-6631	18	3	to	to	PART
ejpam-6631	18	4	capture	capture	VERB
ejpam-6631	18	5	memory	memory	NOUN
ejpam-6631	18	6	and	and	CCONJ
ejpam-6631	18	7	hereditary	hereditary	ADJ
ejpam-6631	18	8	properties	property	NOUN
ejpam-6631	18	9	of	of	ADP
ejpam-6631	18	10	materials	material	NOUN
ejpam-6631	18	11	and	and	CCONJ
ejpam-6631	18	12	processes	process	NOUN
ejpam-6631	18	13	makes	make	VERB
ejpam-6631	18	14	it	it	PRON
ejpam-6631	18	15	especially	especially	ADV
ejpam-6631	18	16	valuable	valuable	ADJ
ejpam-6631	18	17	for	for	ADP
ejpam-6631	18	18	modelling	model	VERB
ejpam-6631	18	19	complex	complex	ADJ
ejpam-6631	18	20	systems	system	NOUN
ejpam-6631	18	21	that	that	PRON
ejpam-6631	18	22	exhibit	exhibit	VERB
ejpam-6631	18	23	non	non	ADJ
ejpam-6631	18	24	-	-	ADJ
ejpam-6631	18	25	local	local	ADJ
ejpam-6631	18	26	behaviors	behavior	NOUN
ejpam-6631	18	27	.	.	PUNCT
ejpam-6631	19	1	recent	recent	ADJ
ejpam-6631	19	2	studies	study	NOUN
ejpam-6631	19	3	,	,	PUNCT
ejpam-6631	19	4	such	such	ADJ
ejpam-6631	19	5	as	as	ADP
ejpam-6631	19	6	the	the	DET
ejpam-6631	19	7	work	work	NOUN
ejpam-6631	19	8	on	on	ADP
ejpam-6631	19	9	new	new	ADJ
ejpam-6631	19	10	properties	property	NOUN
ejpam-6631	19	11	of	of	ADP
ejpam-6631	19	12	differential	differential	ADJ
ejpam-6631	19	13	transform	transform	NOUN
ejpam-6631	19	14	via	via	ADP
ejpam-6631	19	15	difference	difference	NOUN
ejpam-6631	19	16	equations	equation	NOUN
ejpam-6631	19	17	,	,	PUNCT
ejpam-6631	19	18	further	far	ADV
ejpam-6631	19	19	illustrate	illustrate	VERB
ejpam-6631	19	20	the	the	DET
ejpam-6631	19	21	expanding	expand	VERB
ejpam-6631	19	22	toolkit	toolkit	NOUN
ejpam-6631	19	23	and	and	CCONJ
ejpam-6631	19	24	applications	application	NOUN
ejpam-6631	19	25	of	of	ADP
ejpam-6631	19	26	fractional	fractional	ADJ
ejpam-6631	19	27	calculus	calculus	NOUN
ejpam-6631	19	28	in	in	ADP
ejpam-6631	19	29	discrete	discrete	ADJ
ejpam-6631	19	30	and	and	CCONJ
ejpam-6631	19	31	hybrid	hybrid	ADJ
ejpam-6631	19	32	systems	system	NOUN
ejpam-6631	19	33	[	[	X
ejpam-6631	19	34	6	6	NUM
ejpam-6631	19	35	]	]	PUNCT
ejpam-6631	19	36	.	.	PUNCT
ejpam-6631	20	1	the	the	DET
ejpam-6631	20	2	practical	practical	ADJ
ejpam-6631	20	3	application	application	NOUN
ejpam-6631	20	4	of	of	ADP
ejpam-6631	20	5	fractional	fractional	ADJ
ejpam-6631	20	6	derivatives	derivative	NOUN
ejpam-6631	20	7	and	and	CCONJ
ejpam-6631	20	8	integrals	integral	NOUN
ejpam-6631	20	9	usually	usually	ADV
ejpam-6631	20	10	relies	rely	VERB
ejpam-6631	20	11	on	on	ADP
ejpam-6631	20	12	wellestablished	wellestablished	ADJ
ejpam-6631	20	13	definitions	definition	NOUN
ejpam-6631	20	14	,	,	PUNCT
ejpam-6631	20	15	such	such	ADJ
ejpam-6631	20	16	as	as	ADP
ejpam-6631	20	17	the	the	DET
ejpam-6631	20	18	riemann	riemann	PROPN
ejpam-6631	20	19	–	–	PUNCT
ejpam-6631	20	20	louville	louville	NOUN
ejpam-6631	20	21	[	[	X
ejpam-6631	20	22	7	7	NUM
ejpam-6631	20	23	]	]	PUNCT
ejpam-6631	20	24	and	and	CCONJ
ejpam-6631	20	25	caputo	caputo	PROPN
ejpam-6631	20	26	approaches	approach	VERB
ejpam-6631	20	27	[	[	X
ejpam-6631	20	28	8	8	NUM
ejpam-6631	20	29	,	,	PUNCT
ejpam-6631	20	30	9	9	NUM
ejpam-6631	20	31	]	]	PUNCT
ejpam-6631	20	32	.	.	PUNCT
ejpam-6631	21	1	these	these	DET
ejpam-6631	21	2	classical	classical	ADJ
ejpam-6631	21	3	methods	method	NOUN
ejpam-6631	21	4	have	have	AUX
ejpam-6631	21	5	successfully	successfully	ADV
ejpam-6631	21	6	addressed	address	VERB
ejpam-6631	21	7	a	a	DET
ejpam-6631	21	8	range	range	NOUN
ejpam-6631	21	9	of	of	ADP
ejpam-6631	21	10	challenges	challenge	NOUN
ejpam-6631	21	11	in	in	ADP
ejpam-6631	21	12	dynamic	dynamic	ADJ
ejpam-6631	21	13	systems	system	NOUN
ejpam-6631	21	14	,	,	PUNCT
ejpam-6631	21	15	such	such	ADJ
ejpam-6631	21	16	as	as	ADP
ejpam-6631	21	17	the	the	DET
ejpam-6631	21	18	well	well	ADV
ejpam-6631	21	19	-	-	PUNCT
ejpam-6631	21	20	studied	study	VERB
ejpam-6631	21	21	rössler	rössler	NOUN
ejpam-6631	21	22	system	system	NOUN
ejpam-6631	21	23	,	,	PUNCT
ejpam-6631	21	24	and	and	CCONJ
ejpam-6631	21	25	have	have	AUX
ejpam-6631	21	26	been	be	AUX
ejpam-6631	21	27	utilized	utilize	VERB
ejpam-6631	21	28	in	in	ADP
ejpam-6631	21	29	scenarios	scenario	NOUN
ejpam-6631	21	30	involving	involve	VERB
ejpam-6631	21	31	tempered	temper	VERB
ejpam-6631	21	32	fractional	fractional	ADJ
ejpam-6631	21	33	calculus	calculus	NOUN
ejpam-6631	21	34	[	[	X
ejpam-6631	21	35	10	10	NUM
ejpam-6631	21	36	]	]	PUNCT
ejpam-6631	21	37	.	.	PUNCT
ejpam-6631	22	1	however	however	ADV
ejpam-6631	22	2	,	,	PUNCT
ejpam-6631	22	3	these	these	DET
ejpam-6631	22	4	traditional	traditional	ADJ
ejpam-6631	22	5	techniques	technique	NOUN
ejpam-6631	22	6	primarily	primarily	ADV
ejpam-6631	22	7	emphasize	emphasize	VERB
ejpam-6631	22	8	fractional	fractional	ADJ
ejpam-6631	22	9	orders	order	NOUN
ejpam-6631	22	10	and	and	CCONJ
ejpam-6631	22	11	may	may	AUX
ejpam-6631	22	12	not	not	PART
ejpam-6631	22	13	adequately	adequately	ADV
ejpam-6631	22	14	address	address	VERB
ejpam-6631	22	15	the	the	DET
ejpam-6631	22	16	complexities	complexity	NOUN
ejpam-6631	22	17	that	that	PRON
ejpam-6631	22	18	arise	arise	VERB
ejpam-6631	22	19	in	in	ADP
ejpam-6631	22	20	certain	certain	ADJ
ejpam-6631	22	21	equations	equation	NOUN
ejpam-6631	23	1	[	[	X
ejpam-6631	23	2	11	11	NUM
ejpam-6631	23	3	]	]	PUNCT
ejpam-6631	23	4	.	.	PUNCT
ejpam-6631	24	1	given	give	VERB
ejpam-6631	24	2	the	the	DET
ejpam-6631	24	3	inherent	inherent	ADJ
ejpam-6631	24	4	complexity	complexity	NOUN
ejpam-6631	24	5	and	and	CCONJ
ejpam-6631	24	6	non	non	ADJ
ejpam-6631	24	7	-	-	ADJ
ejpam-6631	24	8	local	local	ADJ
ejpam-6631	24	9	nature	nature	NOUN
ejpam-6631	24	10	of	of	ADP
ejpam-6631	24	11	fractional	fractional	ADJ
ejpam-6631	24	12	differential	differential	ADJ
ejpam-6631	24	13	equations	equation	NOUN
ejpam-6631	24	14	(	(	PUNCT
ejpam-6631	24	15	fdes	fde	NOUN
ejpam-6631	24	16	)	)	PUNCT
ejpam-6631	24	17	,	,	PUNCT
ejpam-6631	24	18	numerical	numerical	ADJ
ejpam-6631	24	19	methods	method	NOUN
ejpam-6631	24	20	are	be	AUX
ejpam-6631	24	21	indispensable	indispensable	ADJ
ejpam-6631	24	22	.	.	PUNCT
ejpam-6631	25	1	advanced	advanced	ADJ
ejpam-6631	25	2	approaches	approach	NOUN
ejpam-6631	25	3	such	such	ADJ
ejpam-6631	25	4	as	as	ADP
ejpam-6631	25	5	the	the	DET
ejpam-6631	25	6	hyperbolic	hyperbolic	ADJ
ejpam-6631	25	7	,	,	PUNCT
ejpam-6631	25	8	rational	rational	ADJ
ejpam-6631	25	9	,	,	PUNCT
ejpam-6631	25	10	fractional	fractional	ADJ
ejpam-6631	25	11	,	,	PUNCT
ejpam-6631	25	12	and	and	CCONJ
ejpam-6631	25	13	logarithmic	logarithmic	ADJ
ejpam-6631	25	14	non	non	ADJ
ejpam-6631	25	15	-	-	ADJ
ejpam-6631	25	16	polynomial	polynomial	ADJ
ejpam-6631	25	17	spline	spline	NOUN
ejpam-6631	25	18	methods	method	NOUN
ejpam-6631	25	19	have	have	AUX
ejpam-6631	25	20	been	be	AUX
ejpam-6631	25	21	developed	develop	VERB
ejpam-6631	25	22	to	to	PART
ejpam-6631	25	23	improve	improve	VERB
ejpam-6631	25	24	accuracy	accuracy	NOUN
ejpam-6631	25	25	,	,	PUNCT
ejpam-6631	25	26	efficiency	efficiency	NOUN
ejpam-6631	25	27	,	,	PUNCT
ejpam-6631	25	28	and	and	CCONJ
ejpam-6631	25	29	convergence	convergence	NOUN
ejpam-6631	25	30	.	.	PUNCT
ejpam-6631	26	1	similarly	similarly	ADV
ejpam-6631	26	2	,	,	PUNCT
ejpam-6631	26	3	α	α	NOUN
ejpam-6631	26	4	-	-	PUNCT
ejpam-6631	26	5	fractional	fractional	ADJ
ejpam-6631	26	6	and	and	CCONJ
ejpam-6631	26	7	βfractional	βfractional	ADJ
ejpam-6631	26	8	finite	finite	ADJ
ejpam-6631	26	9	difference	difference	NOUN
ejpam-6631	26	10	methods	method	NOUN
ejpam-6631	26	11	extend	extend	VERB
ejpam-6631	26	12	the	the	DET
ejpam-6631	26	13	classical	classical	ADJ
ejpam-6631	26	14	fdm	fdm	NOUN
ejpam-6631	26	15	by	by	ADP
ejpam-6631	26	16	incorporating	incorporate	VERB
ejpam-6631	26	17	fractionalorder	fractionalorder	PROPN
ejpam-6631	26	18	operators	operator	NOUN
ejpam-6631	26	19	to	to	PART
ejpam-6631	26	20	capture	capture	VERB
ejpam-6631	26	21	memory	memory	NOUN
ejpam-6631	26	22	effects	effect	NOUN
ejpam-6631	26	23	.	.	PUNCT
ejpam-6631	27	1	analytical	analytical	ADJ
ejpam-6631	27	2	–	–	PUNCT
ejpam-6631	27	3	numerical	numerical	ADJ
ejpam-6631	27	4	approaches	approach	NOUN
ejpam-6631	27	5	,	,	PUNCT
ejpam-6631	27	6	such	such	ADJ
ejpam-6631	27	7	as	as	ADP
ejpam-6631	27	8	the	the	DET
ejpam-6631	27	9	homotopy	homotopy	NOUN
ejpam-6631	27	10	perturbation	perturbation	NOUN
ejpam-6631	27	11	method	method	NOUN
ejpam-6631	27	12	,	,	PUNCT
ejpam-6631	27	13	have	have	AUX
ejpam-6631	27	14	been	be	AUX
ejpam-6631	27	15	successfully	successfully	ADV
ejpam-6631	27	16	applied	apply	VERB
ejpam-6631	27	17	to	to	ADP
ejpam-6631	27	18	various	various	ADJ
ejpam-6631	27	19	functional	functional	ADJ
ejpam-6631	27	20	equations	equation	NOUN
ejpam-6631	27	21	,	,	PUNCT
ejpam-6631	27	22	including	include	VERB
ejpam-6631	27	23	fuzzy	fuzzy	ADJ
ejpam-6631	27	24	pantograph	pantograph	NOUN
ejpam-6631	27	25	problems	problem	NOUN
ejpam-6631	27	26	[	[	X
ejpam-6631	27	27	13	13	NUM
ejpam-6631	27	28	]	]	PUNCT
ejpam-6631	27	29	.	.	PUNCT
ejpam-6631	28	1	moreover	moreover	ADV
ejpam-6631	28	2	,	,	PUNCT
ejpam-6631	28	3	fixed	fixed	ADJ
ejpam-6631	28	4	point	point	NOUN
ejpam-6631	28	5	theory	theory	NOUN
ejpam-6631	28	6	provides	provide	VERB
ejpam-6631	28	7	a	a	DET
ejpam-6631	28	8	rigorous	rigorous	ADJ
ejpam-6631	28	9	framework	framework	NOUN
ejpam-6631	28	10	for	for	ADP
ejpam-6631	28	11	proving	prove	VERB
ejpam-6631	28	12	the	the	DET
ejpam-6631	28	13	existence	existence	NOUN
ejpam-6631	28	14	and	and	CCONJ
ejpam-6631	28	15	uniqueness	uniqueness	NOUN
ejpam-6631	28	16	of	of	ADP
ejpam-6631	28	17	solutions	solution	NOUN
ejpam-6631	28	18	to	to	PART
ejpam-6631	28	19	fractional	fractional	ADJ
ejpam-6631	28	20	and	and	CCONJ
ejpam-6631	28	21	multidimensional	multidimensional	ADJ
ejpam-6631	28	22	systems	system	NOUN
ejpam-6631	28	23	[	[	X
ejpam-6631	28	24	12	12	NUM
ejpam-6631	28	25	,	,	PUNCT
ejpam-6631	28	26	14	14	NUM
ejpam-6631	28	27	]	]	PUNCT
ejpam-6631	28	28	,	,	PUNCT
ejpam-6631	28	29	further	far	ADV
ejpam-6631	28	30	strengthening	strengthen	VERB
ejpam-6631	28	31	the	the	DET
ejpam-6631	28	32	mathematical	mathematical	ADJ
ejpam-6631	28	33	foundation	foundation	NOUN
ejpam-6631	28	34	of	of	ADP
ejpam-6631	28	35	these	these	DET
ejpam-6631	28	36	techniques	technique	NOUN
ejpam-6631	28	37	.	.	PUNCT
ejpam-6631	29	1	one	one	NUM
ejpam-6631	29	2	area	area	NOUN
ejpam-6631	29	3	of	of	ADP
ejpam-6631	29	4	increasing	increase	VERB
ejpam-6631	29	5	interest	interest	NOUN
ejpam-6631	29	6	is	be	AUX
ejpam-6631	29	7	the	the	DET
ejpam-6631	29	8	prabhakar	prabhakar	NOUN
ejpam-6631	29	9	fractional	fractional	PROPN
ejpam-6631	29	10	differential	differential	NOUN
ejpam-6631	29	11	equations	equation	NOUN
ejpam-6631	29	12	,	,	PUNCT
ejpam-6631	29	13	which	which	PRON
ejpam-6631	29	14	incorporate	incorporate	VERB
ejpam-6631	29	15	multiple	multiple	ADJ
ejpam-6631	29	16	parameters	parameter	NOUN
ejpam-6631	29	17	that	that	PRON
ejpam-6631	29	18	introduce	introduce	VERB
ejpam-6631	29	19	additional	additional	ADJ
ejpam-6631	29	20	layers	layer	NOUN
ejpam-6631	29	21	of	of	ADP
ejpam-6631	29	22	complexity	complexity	NOUN
ejpam-6631	29	23	.	.	PUNCT
ejpam-6631	30	1	the	the	DET
ejpam-6631	30	2	challenges	challenge	NOUN
ejpam-6631	30	3	often	often	ADV
ejpam-6631	30	4	arise	arise	VERB
ejpam-6631	30	5	from	from	ADP
ejpam-6631	30	6	their	their	PRON
ejpam-6631	30	7	non	non	ADJ
ejpam-6631	30	8	-	-	ADJ
ejpam-6631	30	9	local	local	ADJ
ejpam-6631	30	10	character	character	NOUN
ejpam-6631	30	11	and	and	CCONJ
ejpam-6631	30	12	the	the	DET
ejpam-6631	30	13	intricate	intricate	ADJ
ejpam-6631	30	14	interplay	interplay	NOUN
ejpam-6631	30	15	between	between	ADP
ejpam-6631	30	16	parameters	parameter	NOUN
ejpam-6631	30	17	,	,	PUNCT
ejpam-6631	30	18	making	make	VERB
ejpam-6631	30	19	them	they	PRON
ejpam-6631	30	20	difficult	difficult	ADJ
ejpam-6631	30	21	to	to	PART
ejpam-6631	30	22	solve	solve	VERB
ejpam-6631	30	23	with	with	ADP
ejpam-6631	30	24	standard	standard	ADJ
ejpam-6631	30	25	techniques	technique	NOUN
ejpam-6631	30	26	.	.	PUNCT
ejpam-6631	31	1	prabhakar	prabhakar	NOUN
ejpam-6631	31	2	derivatives	derivative	NOUN
ejpam-6631	31	3	were	be	AUX
ejpam-6631	31	4	addressed	address	VERB
ejpam-6631	31	5	in	in	ADP
ejpam-6631	31	6	[	[	X
ejpam-6631	31	7	15	15	NUM
ejpam-6631	31	8	]	]	PUNCT
ejpam-6631	31	9	using	use	VERB
ejpam-6631	31	10	the	the	DET
ejpam-6631	31	11	fractional	fractional	ADJ
ejpam-6631	31	12	fourier	fourier	NOUN
ejpam-6631	31	13	transform	transform	NOUN
ejpam-6631	31	14	,	,	PUNCT
ejpam-6631	31	15	demonstrating	demonstrate	VERB
ejpam-6631	31	16	mittagleffler	mittagleffler	NOUN
ejpam-6631	31	17	-	-	PUNCT
ejpam-6631	31	18	hyers	hyer	NOUN
ejpam-6631	31	19	-	-	PUNCT
ejpam-6631	31	20	ulam	ulam	ADJ
ejpam-6631	31	21	stability	stability	NOUN
ejpam-6631	31	22	.	.	PUNCT
ejpam-6631	32	1	in	in	ADP
ejpam-6631	32	2	ref	ref	NOUN
ejpam-6631	32	3	.	.	PUNCT
ejpam-6631	33	1	[	[	X
ejpam-6631	33	2	17	17	NUM
ejpam-6631	33	3	]	]	PUNCT
ejpam-6631	33	4	,	,	PUNCT
ejpam-6631	33	5	the	the	DET
ejpam-6631	33	6	invariant	invariant	ADJ
ejpam-6631	33	7	subspace	subspace	NOUN
ejpam-6631	33	8	method	method	NOUN
ejpam-6631	33	9	was	be	AUX
ejpam-6631	33	10	employed	employ	VERB
ejpam-6631	33	11	to	to	PART
ejpam-6631	33	12	obtain	obtain	VERB
ejpam-6631	33	13	exact	exact	ADJ
ejpam-6631	33	14	solutions	solution	NOUN
ejpam-6631	33	15	for	for	ADP
ejpam-6631	33	16	time	time	NOUN
ejpam-6631	33	17	-	-	PUNCT
ejpam-6631	33	18	fractional	fractional	ADJ
ejpam-6631	33	19	nonlinear	nonlinear	ADJ
ejpam-6631	33	20	differential	differential	ADJ
ejpam-6631	33	21	equations	equation	NOUN
ejpam-6631	33	22	involving	involve	VERB
ejpam-6631	33	23	the	the	DET
ejpam-6631	33	24	regularized	regularize	VERB
ejpam-6631	33	25	prabhakar	prabhakar	NOUN
ejpam-6631	33	26	derivative	derivative	NOUN
ejpam-6631	33	27	.	.	PUNCT
ejpam-6631	34	1	for	for	ADP
ejpam-6631	34	2	commensurate	commensurate	ADJ
ejpam-6631	34	3	systems	system	NOUN
ejpam-6631	34	4	,	,	PUNCT
ejpam-6631	34	5	[	[	X
ejpam-6631	34	6	18	18	NUM
ejpam-6631	34	7	]	]	PUNCT
ejpam-6631	34	8	presented	present	VERB
ejpam-6631	34	9	closed	closed	ADJ
ejpam-6631	34	10	-	-	PUNCT
ejpam-6631	34	11	form	form	NOUN
ejpam-6631	34	12	solutions	solution	NOUN
ejpam-6631	34	13	using	use	VERB
ejpam-6631	34	14	eigenvectors	eigenvector	NOUN
ejpam-6631	34	15	and	and	CCONJ
ejpam-6631	34	16	eigenvalues	eigenvalue	NOUN
ejpam-6631	34	17	,	,	PUNCT
ejpam-6631	34	18	while	while	SCONJ
ejpam-6631	34	19	[	[	X
ejpam-6631	34	20	19	19	NUM
ejpam-6631	34	21	]	]	PUNCT
ejpam-6631	34	22	applied	applied	ADJ
ejpam-6631	34	23	separation	separation	NOUN
ejpam-6631	34	24	of	of	ADP
ejpam-6631	34	25	variables	variable	NOUN
ejpam-6631	34	26	to	to	PART
ejpam-6631	34	27	reduce	reduce	VERB
ejpam-6631	34	28	the	the	DET
ejpam-6631	34	29	problem	problem	NOUN
ejpam-6631	34	30	to	to	ADP
ejpam-6631	34	31	a	a	DET
ejpam-6631	34	32	cauchy	cauchy	NOUN
ejpam-6631	34	33	-	-	PUNCT
ejpam-6631	34	34	type	type	NOUN
ejpam-6631	34	35	fractional	fractional	ADJ
ejpam-6631	34	36	equation	equation	NOUN
ejpam-6631	34	37	,	,	PUNCT
ejpam-6631	34	38	expressible	expressible	ADJ
ejpam-6631	34	39	via	via	ADP
ejpam-6631	34	40	a	a	DET
ejpam-6631	34	41	two	two	NUM
ejpam-6631	34	42	-	-	PUNCT
ejpam-6631	34	43	variable	variable	NOUN
ejpam-6631	34	44	mittag	mittag	ADJ
ejpam-6631	34	45	-	-	PUNCT
ejpam-6631	34	46	leffler	leffler	NOUN
ejpam-6631	34	47	function	function	NOUN
ejpam-6631	34	48	.	.	PUNCT
ejpam-6631	35	1	the	the	DET
ejpam-6631	35	2	study	study	NOUN
ejpam-6631	35	3	in	in	ADP
ejpam-6631	35	4	[	[	X
ejpam-6631	35	5	16	16	NUM
ejpam-6631	35	6	]	]	PUNCT
ejpam-6631	35	7	explored	explore	VERB
ejpam-6631	35	8	the	the	DET
ejpam-6631	35	9	explicit	explicit	ADJ
ejpam-6631	35	10	euler	euler	NOUN
ejpam-6631	35	11	method	method	NOUN
ejpam-6631	35	12	for	for	ADP
ejpam-6631	35	13	a	a	DET
ejpam-6631	35	14	nonlinear	nonlinear	ADJ
ejpam-6631	35	15	fractional	fractional	ADJ
ejpam-6631	35	16	oscillation	oscillation	NOUN
ejpam-6631	35	17	equation	equation	NOUN
ejpam-6631	35	18	using	use	VERB
ejpam-6631	35	19	finite	finite	ADJ
ejpam-6631	35	20	-	-	PUNCT
ejpam-6631	35	21	difference	difference	NOUN
ejpam-6631	35	22	schemes	scheme	NOUN
ejpam-6631	35	23	.	.	PUNCT
ejpam-6631	36	1	in	in	ADP
ejpam-6631	36	2	this	this	DET
ejpam-6631	36	3	paper	paper	NOUN
ejpam-6631	36	4	,	,	PUNCT
ejpam-6631	36	5	we	we	PRON
ejpam-6631	36	6	propose	propose	VERB
ejpam-6631	36	7	a	a	DET
ejpam-6631	36	8	novel	novel	ADJ
ejpam-6631	36	9	application	application	NOUN
ejpam-6631	36	10	of	of	ADP
ejpam-6631	36	11	the	the	DET
ejpam-6631	36	12	explicit	explicit	ADJ
ejpam-6631	36	13	fractional	fractional	ADJ
ejpam-6631	36	14	adams	adam	NOUN
ejpam-6631	36	15	method	method	NOUN
ejpam-6631	36	16	to	to	PART
ejpam-6631	36	17	solve	solve	VERB
ejpam-6631	36	18	prabhakar	prabhakar	NOUN
ejpam-6631	36	19	fractional	fractional	ADJ
ejpam-6631	36	20	differential	differential	NOUN
ejpam-6631	36	21	equations	equation	NOUN
ejpam-6631	36	22	,	,	PUNCT
ejpam-6631	36	23	known	know	VERB
ejpam-6631	36	24	for	for	ADP
ejpam-6631	36	25	their	their	PRON
ejpam-6631	36	26	complexity	complexity	NOUN
ejpam-6631	36	27	due	due	ADP
ejpam-6631	36	28	to	to	ADP
ejpam-6631	36	29	multiple	multiple	ADJ
ejpam-6631	36	30	parameters	parameter	NOUN
ejpam-6631	36	31	.	.	PUNCT
ejpam-6631	37	1	by	by	ADP
ejpam-6631	37	2	integrating	integrate	VERB
ejpam-6631	37	3	lagrange	lagrange	NOUN
ejpam-6631	37	4	interpolation	interpolation	NOUN
ejpam-6631	37	5	,	,	PUNCT
ejpam-6631	37	6	the	the	DET
ejpam-6631	37	7	proposed	propose	VERB
ejpam-6631	37	8	method	method	NOUN
ejpam-6631	37	9	achieves	achieve	VERB
ejpam-6631	37	10	high	high	ADJ
ejpam-6631	37	11	accuracy	accuracy	NOUN
ejpam-6631	37	12	and	and	CCONJ
ejpam-6631	37	13	computational	computational	ADJ
ejpam-6631	37	14	efficiency	efficiency	NOUN
ejpam-6631	37	15	,	,	PUNCT
ejpam-6631	37	16	outperforming	outperform	VERB
ejpam-6631	37	17	existing	exist	VERB
ejpam-6631	37	18	techniques	technique	NOUN
ejpam-6631	37	19	such	such	ADJ
ejpam-6631	37	20	as	as	ADP
ejpam-6631	37	21	hptm	hptm	NOUN
ejpam-6631	37	22	and	and	CCONJ
ejpam-6631	37	23	fhptm	fhptm	NOUN
ejpam-6631	37	24	.	.	PUNCT
ejpam-6631	38	1	a	a	DET
ejpam-6631	38	2	detailed	detailed	ADJ
ejpam-6631	38	3	convergence	convergence	NOUN
ejpam-6631	38	4	analysis	analysis	NOUN
ejpam-6631	38	5	and	and	CCONJ
ejpam-6631	38	6	multiple	multiple	ADJ
ejpam-6631	38	7	numerical	numerical	ADJ
ejpam-6631	38	8	examples	example	NOUN
ejpam-6631	38	9	confirm	confirm	VERB
ejpam-6631	38	10	the	the	DET
ejpam-6631	38	11	method	method	NOUN
ejpam-6631	38	12	’s	’s	PART
ejpam-6631	38	13	m.	m.	NOUN
ejpam-6631	38	14	abdel	abdel	PROPN
ejpam-6631	38	15	aal	aal	PROPN
ejpam-6631	38	16	et	et	PROPN
ejpam-6631	38	17	al	al	PROPN
ejpam-6631	38	18	.	.	PUNCT
ejpam-6631	38	19	/	/	SYM
ejpam-6631	38	20	eur	eur	PROPN
ejpam-6631	38	21	.	.	PUNCT
ejpam-6631	39	1	j.	j.	PROPN
ejpam-6631	39	2	pure	pure	PROPN
ejpam-6631	39	3	appl	appl	PROPN
ejpam-6631	39	4	.	.	PROPN
ejpam-6631	39	5	math	math	PROPN
ejpam-6631	39	6	,	,	PUNCT
ejpam-6631	39	7	18	18	NUM
ejpam-6631	39	8	(	(	PUNCT
ejpam-6631	39	9	4	4	NUM
ejpam-6631	39	10	)	)	PUNCT
ejpam-6631	39	11	(	(	PUNCT
ejpam-6631	39	12	2025	2025	NUM
ejpam-6631	39	13	)	)	PUNCT
ejpam-6631	39	14	,	,	PUNCT
ejpam-6631	39	15	6631	6631	NUM
ejpam-6631	39	16	3	3	NUM
ejpam-6631	39	17	of	of	ADP
ejpam-6631	39	18	20	20	NUM
ejpam-6631	39	19	robustness	robustness	NOUN
ejpam-6631	39	20	,	,	PUNCT
ejpam-6631	39	21	with	with	ADP
ejpam-6631	39	22	potential	potential	ADJ
ejpam-6631	39	23	extensions	extension	NOUN
ejpam-6631	39	24	using	use	VERB
ejpam-6631	39	25	shifted	shift	VERB
ejpam-6631	39	26	legendre	legendre	PROPN
ejpam-6631	39	27	polynomials	polynomial	NOUN
ejpam-6631	39	28	.	.	PUNCT
ejpam-6631	40	1	this	this	DET
ejpam-6631	40	2	outline	outline	NOUN
ejpam-6631	40	3	is	be	AUX
ejpam-6631	40	4	organized	organize	VERB
ejpam-6631	40	5	as	as	SCONJ
ejpam-6631	40	6	follows	follow	VERB
ejpam-6631	40	7	:	:	PUNCT
ejpam-6631	40	8	in	in	ADP
ejpam-6631	40	9	section	section	NOUN
ejpam-6631	40	10	2	2	NUM
ejpam-6631	40	11	,	,	PUNCT
ejpam-6631	40	12	we	we	PRON
ejpam-6631	40	13	discuss	discuss	VERB
ejpam-6631	40	14	basic	basic	ADJ
ejpam-6631	40	15	definitions	definition	NOUN
ejpam-6631	40	16	and	and	CCONJ
ejpam-6631	40	17	important	important	ADJ
ejpam-6631	40	18	properties	property	NOUN
ejpam-6631	40	19	related	relate	VERB
ejpam-6631	40	20	to	to	ADP
ejpam-6631	40	21	prabhakar	prabhakar	PROPN
ejpam-6631	40	22	’s	’s	PART
ejpam-6631	40	23	fractional	fractional	ADJ
ejpam-6631	40	24	integral	integral	ADJ
ejpam-6631	40	25	.	.	PUNCT
ejpam-6631	41	1	we	we	PRON
ejpam-6631	41	2	focus	focus	VERB
ejpam-6631	41	3	on	on	ADP
ejpam-6631	41	4	the	the	DET
ejpam-6631	41	5	basic	basic	ADJ
ejpam-6631	41	6	definitions	definition	NOUN
ejpam-6631	41	7	and	and	CCONJ
ejpam-6631	41	8	key	key	ADJ
ejpam-6631	41	9	properties	property	NOUN
ejpam-6631	41	10	of	of	ADP
ejpam-6631	41	11	prabhakar	prabhakar	NOUN
ejpam-6631	41	12	’s	’s	PART
ejpam-6631	41	13	fractional	fractional	ADJ
ejpam-6631	41	14	integral	integral	ADJ
ejpam-6631	41	15	.	.	PUNCT
ejpam-6631	42	1	it	it	PRON
ejpam-6631	42	2	also	also	ADV
ejpam-6631	42	3	explain	explain	VERB
ejpam-6631	42	4	how	how	SCONJ
ejpam-6631	42	5	it	it	PRON
ejpam-6631	42	6	relates	relate	VERB
ejpam-6631	42	7	to	to	ADP
ejpam-6631	42	8	other	other	ADJ
ejpam-6631	42	9	fractional	fractional	ADJ
ejpam-6631	42	10	integrals	integral	NOUN
ejpam-6631	42	11	.	.	PUNCT
ejpam-6631	43	1	section	section	NOUN
ejpam-6631	43	2	3	3	NUM
ejpam-6631	43	3	looks	look	VERB
ejpam-6631	43	4	at	at	ADP
ejpam-6631	43	5	the	the	DET
ejpam-6631	43	6	concept	concept	NOUN
ejpam-6631	43	7	of	of	ADP
ejpam-6631	43	8	the	the	DET
ejpam-6631	43	9	explicit	explicit	ADJ
ejpam-6631	43	10	fractional	fractional	ADJ
ejpam-6631	43	11	adams	adam	NOUN
ejpam-6631	43	12	method	method	NOUN
ejpam-6631	43	13	for	for	ADP
ejpam-6631	43	14	solving	solve	VERB
ejpam-6631	43	15	prabhakar	prabhakar	NOUN
ejpam-6631	43	16	fractional	fractional	ADJ
ejpam-6631	43	17	differential	differential	NOUN
ejpam-6631	43	18	equations	equation	NOUN
ejpam-6631	43	19	.	.	PUNCT
ejpam-6631	44	1	this	this	DET
ejpam-6631	44	2	method	method	NOUN
ejpam-6631	44	3	relates	relate	VERB
ejpam-6631	44	4	to	to	ADP
ejpam-6631	44	5	the	the	DET
ejpam-6631	44	6	volterra	volterra	NOUN
ejpam-6631	44	7	integral	integral	ADJ
ejpam-6631	44	8	equation	equation	NOUN
ejpam-6631	44	9	and	and	CCONJ
ejpam-6631	44	10	addresses	address	VERB
ejpam-6631	44	11	the	the	DET
ejpam-6631	44	12	initial	initial	ADJ
ejpam-6631	44	13	value	value	NOUN
ejpam-6631	44	14	problem	problem	NOUN
ejpam-6631	44	15	.	.	PUNCT
ejpam-6631	45	1	section	section	NOUN
ejpam-6631	45	2	5	5	NUM
ejpam-6631	45	3	provides	provide	VERB
ejpam-6631	45	4	examples	example	NOUN
ejpam-6631	45	5	to	to	PART
ejpam-6631	45	6	show	show	VERB
ejpam-6631	45	7	how	how	SCONJ
ejpam-6631	45	8	the	the	DET
ejpam-6631	45	9	new	new	ADJ
ejpam-6631	45	10	explicit	explicit	ADJ
ejpam-6631	45	11	fractional	fractional	ADJ
ejpam-6631	45	12	adams	adam	NOUN
ejpam-6631	45	13	method	method	NOUN
ejpam-6631	45	14	for	for	ADP
ejpam-6631	45	15	the	the	DET
ejpam-6631	45	16	prabhakar	prabhakar	PROPN
ejpam-6631	45	17	derivative	derivative	NOUN
ejpam-6631	45	18	works	work	NOUN
ejpam-6631	45	19	and	and	CCONJ
ejpam-6631	45	20	how	how	SCONJ
ejpam-6631	45	21	accurate	accurate	ADJ
ejpam-6631	45	22	it	it	PRON
ejpam-6631	45	23	is	be	AUX
ejpam-6631	45	24	.	.	PUNCT
ejpam-6631	46	1	we	we	PRON
ejpam-6631	46	2	completed	complete	VERB
ejpam-6631	46	3	all	all	DET
ejpam-6631	46	4	calculations	calculation	NOUN
ejpam-6631	46	5	using	use	VERB
ejpam-6631	46	6	the	the	DET
ejpam-6631	46	7	software	software	NOUN
ejpam-6631	46	8	maple	maple	NOUN
ejpam-6631	46	9	18	18	NUM
ejpam-6631	46	10	.	.	PUNCT
ejpam-6631	47	1	finally	finally	ADV
ejpam-6631	47	2	,	,	PUNCT
ejpam-6631	47	3	section	section	NOUN
ejpam-6631	47	4	6	6	NUM
ejpam-6631	47	5	provides	provide	VERB
ejpam-6631	47	6	the	the	DET
ejpam-6631	47	7	conclusion	conclusion	NOUN
ejpam-6631	47	8	.	.	PUNCT
ejpam-6631	48	1	2	2	X
ejpam-6631	48	2	.	.	X
ejpam-6631	48	3	basic	basic	ADJ
ejpam-6631	48	4	definitions	definition	NOUN
ejpam-6631	48	5	and	and	CCONJ
ejpam-6631	48	6	important	important	ADJ
ejpam-6631	48	7	properties	property	NOUN
ejpam-6631	48	8	related	relate	VERB
ejpam-6631	48	9	to	to	ADP
ejpam-6631	48	10	prabhakar	prabhakar	PROPN
ejpam-6631	48	11	’s	’s	PART
ejpam-6631	48	12	fractional	fractional	ADJ
ejpam-6631	48	13	integral	integral	ADJ
ejpam-6631	48	14	this	this	DET
ejpam-6631	48	15	section	section	NOUN
ejpam-6631	48	16	provides	provide	VERB
ejpam-6631	48	17	basic	basic	ADJ
ejpam-6631	48	18	definitions	definition	NOUN
ejpam-6631	48	19	and	and	CCONJ
ejpam-6631	48	20	important	important	ADJ
ejpam-6631	48	21	properties	property	NOUN
ejpam-6631	48	22	related	relate	VERB
ejpam-6631	48	23	to	to	ADP
ejpam-6631	48	24	prabhakar	prabhakar	PROPN
ejpam-6631	48	25	’s	’s	PART
ejpam-6631	48	26	fractional	fractional	ADJ
ejpam-6631	48	27	integral	integral	ADJ
ejpam-6631	48	28	.	.	PUNCT
ejpam-6631	49	1	this	this	PRON
ejpam-6631	49	2	will	will	AUX
ejpam-6631	49	3	help	help	VERB
ejpam-6631	49	4	readers	reader	NOUN
ejpam-6631	49	5	understand	understand	VERB
ejpam-6631	49	6	its	its	PRON
ejpam-6631	49	7	significance	significance	NOUN
ejpam-6631	49	8	in	in	ADP
ejpam-6631	49	9	studying	study	VERB
ejpam-6631	49	10	complex	complex	ADJ
ejpam-6631	49	11	problems	problem	NOUN
ejpam-6631	49	12	.	.	PUNCT
ejpam-6631	50	1	2.1	2.1	NUM
ejpam-6631	50	2	.	.	PUNCT
ejpam-6631	51	1	some	some	DET
ejpam-6631	51	2	preliminaries	preliminary	NOUN
ejpam-6631	51	3	definition	definition	NOUN
ejpam-6631	51	4	relating	relate	VERB
ejpam-6631	51	5	to	to	ADP
ejpam-6631	51	6	prabhakar	prabhakar	NOUN
ejpam-6631	51	7	fractional	fractional	ADJ
ejpam-6631	51	8	integral	integral	ADJ
ejpam-6631	51	9	definition	definition	NOUN
ejpam-6631	51	10	1	1	NUM
ejpam-6631	51	11	.	.	PUNCT
ejpam-6631	52	1	the	the	PRON
ejpam-6631	52	2	one	one	NUM
ejpam-6631	52	3	-	-	PUNCT
ejpam-6631	52	4	parameter	parameter	NOUN
ejpam-6631	52	5	,	,	PUNCT
ejpam-6631	52	6	three	three	NUM
ejpam-6631	52	7	-	-	PUNCT
ejpam-6631	52	8	parameter	parameter	NOUN
ejpam-6631	52	9	,	,	PUNCT
ejpam-6631	52	10	and	and	CCONJ
ejpam-6631	52	11	five	five	NUM
ejpam-6631	52	12	-	-	PUNCT
ejpam-6631	52	13	parameter	parameter	NOUN
ejpam-6631	52	14	mittag	mittag	ADJ
ejpam-6631	52	15	-	-	PUNCT
ejpam-6631	52	16	leffler	leffler	NOUN
ejpam-6631	52	17	functions	function	NOUN
ejpam-6631	52	18	are	be	AUX
ejpam-6631	52	19	defined	define	VERB
ejpam-6631	52	20	as	as	SCONJ
ejpam-6631	52	21	follows	follow	VERB
ejpam-6631	52	22	:	:	PUNCT
ejpam-6631	52	23	mα(ϕ	mα(ϕ	PUNCT
ejpam-6631	52	24	)	)	PUNCT
ejpam-6631	52	25	=	=	PUNCT
ejpam-6631	53	1	∞∑	∞∑	PROPN
ejpam-6631	53	2	n=0	n=0	PROPN
ejpam-6631	53	3	ϕn	ϕn	ADP
ejpam-6631	53	4	γ(αn+	γ(αn+	ADP
ejpam-6631	53	5	1	1	NUM
ejpam-6631	53	6	)	)	PUNCT
ejpam-6631	53	7	,	,	PUNCT
ejpam-6631	53	8	re(α	re(α	NOUN
ejpam-6631	53	9	)	)	PUNCT
ejpam-6631	53	10	>	>	X
ejpam-6631	53	11	0	0	NUM
ejpam-6631	53	12	,	,	PUNCT
ejpam-6631	53	13	mγ	mγ	PROPN
ejpam-6631	53	14	α	α	NOUN
ejpam-6631	53	15	,	,	PUNCT
ejpam-6631	53	16	β(ϕ	β(ϕ	NUM
ejpam-6631	53	17	)	)	PUNCT
ejpam-6631	54	1	=	=	PUNCT
ejpam-6631	55	1	∞∑	∞∑	NUM
ejpam-6631	55	2	n=0	n=0	NUM
ejpam-6631	55	3	γ(γ	γ(γ	NOUN
ejpam-6631	55	4	+	+	CCONJ
ejpam-6631	55	5	n)ϕn	n)ϕn	PROPN
ejpam-6631	55	6	γ(γ)γ(αn+	γ(γ)γ(αn+	X
ejpam-6631	55	7	β)n	β)n	PUNCT
ejpam-6631	55	8	!	!	PROPN
ejpam-6631	55	9	,	,	PUNCT
ejpam-6631	55	10	re(α	re(α	PROPN
ejpam-6631	55	11	)	)	PUNCT
ejpam-6631	55	12	>	>	X
ejpam-6631	55	13	0	0	NUM
ejpam-6631	55	14	,	,	PUNCT
ejpam-6631	55	15	mγ	mγ	PROPN
ejpam-6631	55	16	α1,α2,β1,β2	α1,α2,β1,β2	PROPN
ejpam-6631	55	17	(	(	PUNCT
ejpam-6631	55	18	ϕ	ϕ	NOUN
ejpam-6631	55	19	)	)	PUNCT
ejpam-6631	55	20	=	=	SYM
ejpam-6631	56	1	∞∑	∞∑	NUM
ejpam-6631	56	2	n=0	n=0	NUM
ejpam-6631	56	3	γ(γ	γ(γ	NOUN
ejpam-6631	56	4	+	+	CCONJ
ejpam-6631	56	5	n)ϕn	n)ϕn	PROPN
ejpam-6631	56	6	γ(γ)γ(α1n+	γ(γ)γ(α1n+	PROPN
ejpam-6631	56	7	β1)γ(α2n+	β1)γ(α2n+	PUNCT
ejpam-6631	56	8	β2)n	β2)n	PROPN
ejpam-6631	56	9	!	!	PUNCT
ejpam-6631	56	10	,	,	PUNCT
ejpam-6631	56	11	re(α	re(α	PROPN
ejpam-6631	56	12	)	)	PUNCT
ejpam-6631	56	13	>	>	X
ejpam-6631	56	14	0	0	NUM
ejpam-6631	56	15	,	,	PUNCT
ejpam-6631	56	16	(	(	PUNCT
ejpam-6631	56	17	1	1	X
ejpam-6631	56	18	)	)	PUNCT
ejpam-6631	56	19	definition	definition	NOUN
ejpam-6631	56	20	2	2	NUM
ejpam-6631	56	21	.	.	PUNCT
ejpam-6631	56	22	for	for	ADP
ejpam-6631	56	23	f	f	PROPN
ejpam-6631	56	24	∈	∈	PROPN
ejpam-6631	56	25	l1(a	l1(a	PROPN
ejpam-6631	56	26	,	,	PUNCT
ejpam-6631	56	27	b	b	NOUN
ejpam-6631	56	28	)	)	PUNCT
ejpam-6631	56	29	,	,	PUNCT
ejpam-6631	56	30	the	the	DET
ejpam-6631	56	31	prabhakar	prabhakar	NOUN
ejpam-6631	56	32	fractional	fractional	ADJ
ejpam-6631	56	33	integral	integral	ADJ
ejpam-6631	56	34	is	be	AUX
ejpam-6631	56	35	defined	define	VERB
ejpam-6631	56	36	using	use	VERB
ejpam-6631	56	37	a	a	DET
ejpam-6631	56	38	three	three	NUM
ejpam-6631	56	39	-	-	PUNCT
ejpam-6631	56	40	parameter	parameter	NOUN
ejpam-6631	56	41	mittag	mittag	ADJ
ejpam-6631	56	42	-	-	PUNCT
ejpam-6631	56	43	leffler	leffler	NOUN
ejpam-6631	56	44	function	function	NOUN
ejpam-6631	56	45	as	as	SCONJ
ejpam-6631	56	46	follows	follow	VERB
ejpam-6631	56	47	:	:	PUNCT
ejpam-6631	56	48	iγα	iγα	ADJ
ejpam-6631	56	49	,	,	PUNCT
ejpam-6631	56	50	β	β	PROPN
ejpam-6631	56	51	,	,	PUNCT
ejpam-6631	56	52	τ	τ	PROPN
ejpam-6631	56	53	,	,	PUNCT
ejpam-6631	56	54	a	a	DET
ejpam-6631	56	55	+	+	X
ejpam-6631	56	56	p(x	p(x	NOUN
ejpam-6631	56	57	)	)	PUNCT
ejpam-6631	56	58	=	=	SYM
ejpam-6631	57	1	∫	∫	PROPN
ejpam-6631	57	2	x	x	X
ejpam-6631	57	3	a	a	DET
ejpam-6631	57	4	(	(	PUNCT
ejpam-6631	57	5	x−	x−	PROPN
ejpam-6631	57	6	w)β−1mγ	w)β−1mγ	PROPN
ejpam-6631	57	7	α	α	PROPN
ejpam-6631	57	8	,	,	PUNCT
ejpam-6631	57	9	β(τ(x−	β(τ(x−	SYM
ejpam-6631	57	10	w)α)p(x)dw	w)α)p(x)dw	NOUN
ejpam-6631	57	11	(	(	PUNCT
ejpam-6631	57	12	2	2	NUM
ejpam-6631	57	13	)	)	PUNCT
ejpam-6631	57	14	such	such	ADJ
ejpam-6631	57	15	that	that	PRON
ejpam-6631	57	16	re(β	re(β	X
ejpam-6631	57	17	)	)	PUNCT
ejpam-6631	57	18	>	>	X
ejpam-6631	57	19	0	0	NUM
ejpam-6631	57	20	,	,	PUNCT
ejpam-6631	57	21	re(α	re(α	PROPN
ejpam-6631	57	22	)	)	PUNCT
ejpam-6631	57	23	>	>	X
ejpam-6631	57	24	0	0	PUNCT
ejpam-6631	57	25	and	and	CCONJ
ejpam-6631	57	26	γ	γ	PROPN
ejpam-6631	57	27	,	,	PUNCT
ejpam-6631	57	28	α	α	PROPN
ejpam-6631	57	29	,	,	PUNCT
ejpam-6631	57	30	β	β	PROPN
ejpam-6631	57	31	,	,	PUNCT
ejpam-6631	57	32	τ	τ	PROPN
ejpam-6631	57	33	∈	∈	PROPN
ejpam-6631	57	34	c	c	NOUN
ejpam-6631	57	35	is	be	AUX
ejpam-6631	57	36	integer	integer	ADJ
ejpam-6631	57	37	part	part	NOUN
ejpam-6631	57	38	of	of	ADP
ejpam-6631	57	39	α	α	NOUN
ejpam-6631	57	40	.	.	PUNCT
ejpam-6631	58	1	the	the	DET
ejpam-6631	58	2	definition	definition	NOUN
ejpam-6631	58	3	in	in	ADP
ejpam-6631	58	4	(	(	PUNCT
ejpam-6631	58	5	1	1	X
ejpam-6631	58	6	)	)	PUNCT
ejpam-6631	58	7	can	can	AUX
ejpam-6631	58	8	typically	typically	ADV
ejpam-6631	58	9	be	be	AUX
ejpam-6631	58	10	expressed	express	VERB
ejpam-6631	58	11	as	as	ADP
ejpam-6631	58	12	iγα	iγα	NOUN
ejpam-6631	58	13	,	,	PUNCT
ejpam-6631	58	14	β	β	PROPN
ejpam-6631	58	15	,	,	PUNCT
ejpam-6631	58	16	τ	τ	PROPN
ejpam-6631	58	17	,	,	PUNCT
ejpam-6631	58	18	a	a	DET
ejpam-6631	58	19	+	+	X
ejpam-6631	58	20	p(x	p(x	NOUN
ejpam-6631	58	21	)	)	PUNCT
ejpam-6631	58	22	=	=	SYM
ejpam-6631	59	1	∫	∫	PROPN
ejpam-6631	59	2	x	x	X
ejpam-6631	60	1	a	a	PRON
ejpam-6631	60	2	mγ	mγ	NOUN
ejpam-6631	60	3	α	α	NOUN
ejpam-6631	60	4	,	,	PUNCT
ejpam-6631	60	5	β(x−	β(x−	PROPN
ejpam-6631	60	6	w	w	NOUN
ejpam-6631	60	7	)	)	PUNCT
ejpam-6631	60	8	;	;	PUNCT
ejpam-6631	60	9	τ)p(x)dw	τ)p(x)dw	NOUN
ejpam-6631	60	10	,	,	PUNCT
ejpam-6631	60	11	(	(	PUNCT
ejpam-6631	60	12	3	3	X
ejpam-6631	60	13	)	)	PUNCT
ejpam-6631	60	14	m.	m.	NOUN
ejpam-6631	60	15	abdel	abdel	PROPN
ejpam-6631	60	16	aal	aal	PROPN
ejpam-6631	60	17	et	et	PROPN
ejpam-6631	60	18	al	al	PROPN
ejpam-6631	60	19	.	.	PUNCT
ejpam-6631	60	20	/	/	SYM
ejpam-6631	60	21	eur	eur	PROPN
ejpam-6631	60	22	.	.	PUNCT
ejpam-6631	61	1	j.	j.	PROPN
ejpam-6631	61	2	pure	pure	PROPN
ejpam-6631	61	3	appl	appl	PROPN
ejpam-6631	61	4	.	.	PROPN
ejpam-6631	61	5	math	math	PROPN
ejpam-6631	61	6	,	,	PUNCT
ejpam-6631	61	7	18	18	NUM
ejpam-6631	61	8	(	(	PUNCT
ejpam-6631	61	9	4	4	NUM
ejpam-6631	61	10	)	)	PUNCT
ejpam-6631	61	11	(	(	PUNCT
ejpam-6631	61	12	2025	2025	NUM
ejpam-6631	61	13	)	)	PUNCT
ejpam-6631	61	14	,	,	PUNCT
ejpam-6631	61	15	6631	6631	NUM
ejpam-6631	61	16	4	4	NUM
ejpam-6631	61	17	of	of	ADP
ejpam-6631	61	18	20	20	NUM
ejpam-6631	61	19	such	such	ADJ
ejpam-6631	61	20	that	that	SCONJ
ejpam-6631	61	21	mγ	mγ	PROPN
ejpam-6631	61	22	α	α	NOUN
ejpam-6631	61	23	,	,	PUNCT
ejpam-6631	61	24	β(x	β(x	PROPN
ejpam-6631	61	25	;	;	PUNCT
ejpam-6631	61	26	τ	τ	X
ejpam-6631	61	27	)	)	PUNCT
ejpam-6631	61	28	=	=	PUNCT
ejpam-6631	62	1	xβ−1mγ	xβ−1mγ	NUM
ejpam-6631	62	2	α	α	PROPN
ejpam-6631	62	3	,	,	PUNCT
ejpam-6631	62	4	β(τx	β(τx	ADJ
ejpam-6631	62	5	α	α	NOUN
ejpam-6631	62	6	)	)	PUNCT
ejpam-6631	62	7	.	.	PUNCT
ejpam-6631	63	1	(	(	PUNCT
ejpam-6631	63	2	4	4	X
ejpam-6631	63	3	)	)	PUNCT
ejpam-6631	63	4	employing	employ	VERB
ejpam-6631	63	5	equation	equation	NOUN
ejpam-6631	63	6	(	(	PUNCT
ejpam-6631	63	7	1	1	NUM
ejpam-6631	63	8	)	)	PUNCT
ejpam-6631	63	9	,	,	PUNCT
ejpam-6631	63	10	we	we	PRON
ejpam-6631	63	11	can	can	AUX
ejpam-6631	63	12	explain	explain	VERB
ejpam-6631	63	13	the	the	DET
ejpam-6631	63	14	prabhakar	prabhakar	NOUN
ejpam-6631	63	15	fractional	fractional	PROPN
ejpam-6631	63	16	derivative	derivative	NOUN
ejpam-6631	63	17	and	and	CCONJ
ejpam-6631	63	18	the	the	DET
ejpam-6631	63	19	regularized	regularize	VERB
ejpam-6631	63	20	prabhakar	prabhakar	NOUN
ejpam-6631	63	21	derivative	derivative	ADJ
ejpam-6631	63	22	definition	definition	NOUN
ejpam-6631	63	23	3	3	NUM
ejpam-6631	63	24	.	.	PUNCT
ejpam-6631	64	1	for	for	ADP
ejpam-6631	64	2	values	value	NOUN
ejpam-6631	64	3	of	of	ADP
ejpam-6631	64	4	β	β	PRON
ejpam-6631	64	5	between	between	ADP
ejpam-6631	64	6	0	0	NUM
ejpam-6631	64	7	and	and	CCONJ
ejpam-6631	64	8	1	1	NUM
ejpam-6631	64	9	,	,	PUNCT
ejpam-6631	64	10	(	(	PUNCT
ejpam-6631	64	11	0	0	X
ejpam-6631	64	12	<	<	X
ejpam-6631	64	13	β	β	X
ejpam-6631	64	14	<	<	X
ejpam-6631	64	15	1	1	NUM
ejpam-6631	64	16	)	)	PUNCT
ejpam-6631	64	17	,	,	PUNCT
ejpam-6631	64	18	if	if	SCONJ
ejpam-6631	64	19	f(x	f(x	PROPN
ejpam-6631	64	20	)	)	PUNCT
ejpam-6631	64	21	∈	∈	PROPN
ejpam-6631	64	22	m1[a	m1[a	PROPN
ejpam-6631	64	23	,	,	PUNCT
ejpam-6631	64	24	b	b	AUX
ejpam-6631	64	25	]	]	X
ejpam-6631	64	26	is	be	AUX
ejpam-6631	64	27	a	a	DET
ejpam-6631	64	28	function	function	NOUN
ejpam-6631	64	29	defined	define	VERB
ejpam-6631	64	30	on	on	ADP
ejpam-6631	64	31	the	the	DET
ejpam-6631	64	32	interval	interval	NOUN
ejpam-6631	64	33	[	[	X
ejpam-6631	64	34	a	a	X
ejpam-6631	64	35	,	,	PUNCT
ejpam-6631	64	36	b	b	NOUN
ejpam-6631	64	37	]	]	X
ejpam-6631	64	38	,	,	PUNCT
ejpam-6631	64	39	we	we	PRON
ejpam-6631	64	40	define	define	VERB
ejpam-6631	64	41	the	the	DET
ejpam-6631	64	42	prabhakar	prabhakar	NOUN
ejpam-6631	64	43	fractional	fractional	ADJ
ejpam-6631	64	44	derivative	derivative	NOUN
ejpam-6631	64	45	using	use	VERB
ejpam-6631	64	46	the	the	DET
ejpam-6631	64	47	riemann	riemann	PROPN
ejpam-6631	64	48	-	-	PUNCT
ejpam-6631	64	49	liouville	liouville	NOUN
ejpam-6631	64	50	method	method	NOUN
ejpam-6631	64	51	in	in	ADP
ejpam-6631	64	52	the	the	DET
ejpam-6631	64	53	following	following	ADJ
ejpam-6631	64	54	way	way	NOUN
ejpam-6631	64	55	:	:	PUNCT
ejpam-6631	64	56	rdγ	rdγ	NOUN
ejpam-6631	64	57	α	α	NOUN
ejpam-6631	64	58	,	,	PUNCT
ejpam-6631	64	59	β	β	PROPN
ejpam-6631	64	60	,	,	PUNCT
ejpam-6631	64	61	τ	τ	PROPN
ejpam-6631	64	62	,	,	PUNCT
ejpam-6631	64	63	a	a	DET
ejpam-6631	64	64	+	+	X
ejpam-6631	64	65	p(x	p(x	NOUN
ejpam-6631	64	66	)	)	PUNCT
ejpam-6631	64	67	=	=	VERB
ejpam-6631	64	68	dν	dν	ADJ
ejpam-6631	64	69	dxν	dxν	PROPN
ejpam-6631	64	70	∫	∫	PROPN
ejpam-6631	64	71	x	x	X
ejpam-6631	65	1	a	a	PRON
ejpam-6631	65	2	mγ	mγ	NOUN
ejpam-6631	65	3	α	α	NOUN
ejpam-6631	65	4	,	,	PUNCT
ejpam-6631	65	5	β(x−	β(x−	PROPN
ejpam-6631	65	6	w	w	NOUN
ejpam-6631	65	7	)	)	PUNCT
ejpam-6631	65	8	;	;	PUNCT
ejpam-6631	65	9	τ)p(x)dw	τ)p(x)dw	NOUN
ejpam-6631	65	10	,	,	PUNCT
ejpam-6631	65	11	(	(	PUNCT
ejpam-6631	65	12	5	5	NUM
ejpam-6631	65	13	)	)	PUNCT
ejpam-6631	65	14	where	where	SCONJ
ejpam-6631	65	15	re(α	re(α	NOUN
ejpam-6631	65	16	)	)	PUNCT
ejpam-6631	65	17	>	>	X
ejpam-6631	65	18	0	0	NUM
ejpam-6631	65	19	,	,	PUNCT
ejpam-6631	65	20	re(β	re(β	X
ejpam-6631	65	21	)	)	PUNCT
ejpam-6631	65	22	>	>	X
ejpam-6631	65	23	0	0	PUNCT
ejpam-6631	65	24	and	and	CCONJ
ejpam-6631	65	25	γ	γ	PROPN
ejpam-6631	65	26	,	,	PUNCT
ejpam-6631	65	27	α	α	PROPN
ejpam-6631	65	28	,	,	PUNCT
ejpam-6631	65	29	β	β	PROPN
ejpam-6631	65	30	,	,	PUNCT
ejpam-6631	65	31	τ	τ	PROPN
ejpam-6631	65	32	∈	∈	PROPN
ejpam-6631	65	33	c	c	NOUN
ejpam-6631	65	34	is	be	AUX
ejpam-6631	65	35	integer	integer	ADJ
ejpam-6631	65	36	part	part	NOUN
ejpam-6631	65	37	of	of	ADP
ejpam-6631	65	38	α	α	PROPN
ejpam-6631	65	39	.	.	PUNCT
ejpam-6631	66	1	definition	definition	NOUN
ejpam-6631	66	2	4	4	NUM
ejpam-6631	66	3	.	.	PUNCT
ejpam-6631	67	1	if	if	SCONJ
ejpam-6631	67	2	p(x	p(x	PROPN
ejpam-6631	67	3	)	)	PUNCT
ejpam-6631	67	4	is	be	AUX
ejpam-6631	67	5	a	a	DET
ejpam-6631	67	6	function	function	NOUN
ejpam-6631	67	7	that	that	PRON
ejpam-6631	67	8	belongs	belong	VERB
ejpam-6631	67	9	to	to	ADP
ejpam-6631	67	10	the	the	DET
ejpam-6631	67	11	class	class	NOUN
ejpam-6631	67	12	acν(a	acν(a	PROPN
ejpam-6631	67	13	,	,	PUNCT
ejpam-6631	67	14	b	b	NOUN
ejpam-6631	67	15	)	)	PUNCT
ejpam-6631	67	16	,	,	PUNCT
ejpam-6631	67	17	and	and	CCONJ
ejpam-6631	67	18	if	if	SCONJ
ejpam-6631	67	19	a	a	PRON
ejpam-6631	67	20	and	and	CCONJ
ejpam-6631	67	21	b	b	NOUN
ejpam-6631	67	22	are	be	AUX
ejpam-6631	67	23	numbers	number	NOUN
ejpam-6631	67	24	such	such	ADJ
ejpam-6631	67	25	that	that	SCONJ
ejpam-6631	67	26	0	0	NUM
ejpam-6631	67	27	≤	≤	NOUN
ejpam-6631	67	28	a	a	DET
ejpam-6631	67	29	<	<	X
ejpam-6631	67	30	x	x	X
ejpam-6631	67	31	<	<	X
ejpam-6631	67	32	b	b	X
ejpam-6631	67	33	≤	≤	NUM
ejpam-6631	67	34	∞	∞	PROPN
ejpam-6631	67	35	,	,	PUNCT
ejpam-6631	67	36	then	then	ADV
ejpam-6631	67	37	the	the	DET
ejpam-6631	67	38	regularized	regularized	ADJ
ejpam-6631	67	39	prabhakar	prabhakar	NOUN
ejpam-6631	67	40	derivative	derivative	NOUN
ejpam-6631	67	41	,	,	PUNCT
ejpam-6631	67	42	using	use	VERB
ejpam-6631	67	43	the	the	DET
ejpam-6631	67	44	caputo	caputo	PROPN
ejpam-6631	67	45	definition	definition	NOUN
ejpam-6631	67	46	,	,	PUNCT
ejpam-6631	67	47	is	be	AUX
ejpam-6631	67	48	defined	define	VERB
ejpam-6631	67	49	as	as	SCONJ
ejpam-6631	67	50	follows	follow	VERB
ejpam-6631	67	51	:	:	PUNCT
ejpam-6631	67	52	rcγ	rcγ	PROPN
ejpam-6631	67	53	α	α	NOUN
ejpam-6631	67	54	,	,	PUNCT
ejpam-6631	67	55	β	β	PROPN
ejpam-6631	67	56	,	,	PUNCT
ejpam-6631	67	57	τ	τ	PROPN
ejpam-6631	67	58	,	,	PUNCT
ejpam-6631	67	59	a	a	DET
ejpam-6631	67	60	+	+	X
ejpam-6631	67	61	p(x	p(x	NOUN
ejpam-6631	67	62	)	)	PUNCT
ejpam-6631	67	63	=	=	SYM
ejpam-6631	68	1	∫	∫	PROPN
ejpam-6631	68	2	x	x	X
ejpam-6631	69	1	a	a	PRON
ejpam-6631	69	2	mγ	mγ	NOUN
ejpam-6631	69	3	α	α	NOUN
ejpam-6631	69	4	,	,	PUNCT
ejpam-6631	69	5	β(x−	β(x−	PROPN
ejpam-6631	69	6	w	w	NOUN
ejpam-6631	69	7	)	)	PUNCT
ejpam-6631	69	8	;	;	PUNCT
ejpam-6631	69	9	τ	τ	X
ejpam-6631	69	10	)	)	PUNCT
ejpam-6631	69	11	dνp(x	dνp(x	PROPN
ejpam-6631	69	12	)	)	PUNCT
ejpam-6631	69	13	dxν	dxν	NOUN
ejpam-6631	69	14	dw	dw	PROPN
ejpam-6631	69	15	,	,	PUNCT
ejpam-6631	69	16	(	(	PUNCT
ejpam-6631	69	17	6	6	NUM
ejpam-6631	69	18	)	)	PUNCT
ejpam-6631	69	19	where	where	SCONJ
ejpam-6631	69	20	re(α	re(α	NOUN
ejpam-6631	69	21	)	)	PUNCT
ejpam-6631	69	22	>	>	X
ejpam-6631	69	23	0	0	NUM
ejpam-6631	69	24	,	,	PUNCT
ejpam-6631	69	25	re(β	re(β	X
ejpam-6631	69	26	)	)	PUNCT
ejpam-6631	69	27	>	>	X
ejpam-6631	69	28	0	0	PUNCT
ejpam-6631	69	29	and	and	CCONJ
ejpam-6631	69	30	γ	γ	PROPN
ejpam-6631	69	31	,	,	PUNCT
ejpam-6631	69	32	α	α	PROPN
ejpam-6631	69	33	,	,	PUNCT
ejpam-6631	69	34	β	β	PROPN
ejpam-6631	69	35	,	,	PUNCT
ejpam-6631	69	36	τ	τ	PROPN
ejpam-6631	69	37	∈	∈	PROPN
ejpam-6631	69	38	c	c	NOUN
ejpam-6631	69	39	is	be	AUX
ejpam-6631	69	40	integer	integer	ADJ
ejpam-6631	69	41	part	part	NOUN
ejpam-6631	69	42	of	of	ADP
ejpam-6631	69	43	α	α	PRON
ejpam-6631	69	44	,	,	PUNCT
ejpam-6631	69	45	β	β	NOUN
ejpam-6631	69	46	.	.	PUNCT
ejpam-6631	70	1	definition	definition	NOUN
ejpam-6631	70	2	5	5	NUM
ejpam-6631	70	3	.	.	PUNCT
ejpam-6631	71	1	this	this	DET
ejpam-6631	71	2	research	research	NOUN
ejpam-6631	71	3	paper	paper	NOUN
ejpam-6631	71	4	defines	define	VERB
ejpam-6631	71	5	prabhakar	prabhakar	NOUN
ejpam-6631	71	6	fractional	fractional	ADJ
ejpam-6631	71	7	differential	differential	ADJ
ejpam-6631	71	8	equations	equation	NOUN
ejpam-6631	71	9	as	as	SCONJ
ejpam-6631	71	10	follows	follow	VERB
ejpam-6631	71	11	:	:	PUNCT
ejpam-6631	71	12	rcγ	rcγ	PROPN
ejpam-6631	71	13	α	α	NOUN
ejpam-6631	71	14	,	,	PUNCT
ejpam-6631	71	15	β	β	PROPN
ejpam-6631	71	16	,	,	PUNCT
ejpam-6631	71	17	τ	τ	PROPN
ejpam-6631	71	18	,	,	PUNCT
ejpam-6631	71	19	a	a	DET
ejpam-6631	71	20	+	+	X
ejpam-6631	71	21	p(x	p(x	NOUN
ejpam-6631	71	22	)	)	PUNCT
ejpam-6631	71	23	=	=	SYM
ejpam-6631	72	1	∫	∫	PROPN
ejpam-6631	72	2	x	x	X
ejpam-6631	72	3	a+	a+	PUNCT
ejpam-6631	72	4	mγ	mγ	PROPN
ejpam-6631	72	5	α	α	NOUN
ejpam-6631	72	6	,	,	PUNCT
ejpam-6631	72	7	β(x−	β(x−	PROPN
ejpam-6631	72	8	w	w	NOUN
ejpam-6631	72	9	)	)	PUNCT
ejpam-6631	72	10	;	;	PUNCT
ejpam-6631	72	11	τ	τ	X
ejpam-6631	72	12	)	)	PUNCT
ejpam-6631	72	13	dνp(x	dνp(x	PROPN
ejpam-6631	72	14	)	)	PUNCT
ejpam-6631	72	15	dxν	dxν	NOUN
ejpam-6631	72	16	dw	dw	PROPN
ejpam-6631	72	17	,	,	PUNCT
ejpam-6631	72	18	(	(	PUNCT
ejpam-6631	72	19	7	7	X
ejpam-6631	72	20	)	)	PUNCT
ejpam-6631	72	21	where	where	SCONJ
ejpam-6631	72	22	re(α	re(α	NOUN
ejpam-6631	72	23	)	)	PUNCT
ejpam-6631	72	24	>	>	X
ejpam-6631	72	25	0	0	NUM
ejpam-6631	72	26	,	,	PUNCT
ejpam-6631	72	27	re(β	re(β	X
ejpam-6631	72	28	)	)	PUNCT
ejpam-6631	72	29	>	>	X
ejpam-6631	72	30	0	0	PUNCT
ejpam-6631	72	31	and	and	CCONJ
ejpam-6631	72	32	γ	γ	PROPN
ejpam-6631	72	33	,	,	PUNCT
ejpam-6631	72	34	α	α	PROPN
ejpam-6631	72	35	,	,	PUNCT
ejpam-6631	72	36	β	β	PROPN
ejpam-6631	72	37	,	,	PUNCT
ejpam-6631	72	38	τ	τ	PROPN
ejpam-6631	72	39	∈	∈	PROPN
ejpam-6631	72	40	c	c	NOUN
ejpam-6631	72	41	is	be	AUX
ejpam-6631	72	42	integer	integer	ADJ
ejpam-6631	72	43	part	part	NOUN
ejpam-6631	72	44	of	of	ADP
ejpam-6631	72	45	α	α	PRON
ejpam-6631	72	46	,	,	PUNCT
ejpam-6631	72	47	β	β	NOUN
ejpam-6631	72	48	.	.	PROPN
ejpam-6631	72	49	2.2	2.2	NUM
ejpam-6631	72	50	.	.	PUNCT
ejpam-6631	73	1	prabhakar	prabhakar	NOUN
ejpam-6631	73	2	fractional	fractional	ADJ
ejpam-6631	73	3	integral	integral	ADJ
ejpam-6631	73	4	key	key	ADJ
ejpam-6631	73	5	properties	property	NOUN
ejpam-6631	73	6	and	and	CCONJ
ejpam-6631	73	7	relationships	relationship	NOUN
ejpam-6631	73	8	with	with	ADP
ejpam-6631	73	9	other	other	ADJ
ejpam-6631	73	10	functions	function	NOUN
ejpam-6631	73	11	the	the	DET
ejpam-6631	73	12	prabhakar	prabhakar	NOUN
ejpam-6631	73	13	function	function	NOUN
ejpam-6631	73	14	is	be	AUX
ejpam-6631	73	15	closely	closely	ADV
ejpam-6631	73	16	related	relate	VERB
ejpam-6631	73	17	to	to	ADP
ejpam-6631	73	18	the	the	DET
ejpam-6631	73	19	standard	standard	ADJ
ejpam-6631	73	20	mittag	mittag	ADJ
ejpam-6631	73	21	-	-	PUNCT
ejpam-6631	73	22	leffler	leffler	NOUN
ejpam-6631	73	23	function	function	NOUN
ejpam-6631	73	24	and	and	CCONJ
ejpam-6631	73	25	its	its	PRON
ejpam-6631	73	26	two	two	NUM
ejpam-6631	73	27	-	-	PUNCT
ejpam-6631	73	28	parameter	parameter	NOUN
ejpam-6631	73	29	version	version	NOUN
ejpam-6631	73	30	,	,	PUNCT
ejpam-6631	73	31	as	as	ADV
ejpam-6631	73	32	well	well	ADV
ejpam-6631	73	33	as	as	ADP
ejpam-6631	73	34	other	other	ADJ
ejpam-6631	73	35	special	special	ADJ
ejpam-6631	73	36	functions	function	NOUN
ejpam-6631	73	37	.	.	PUNCT
ejpam-6631	74	1	for	for	ADP
ejpam-6631	74	2	values	value	NOUN
ejpam-6631	74	3	of	of	ADP
ejpam-6631	74	4	n	n	PRON
ejpam-6631	74	5	≥	≥	NOUN
ejpam-6631	74	6	,	,	PUNCT
ejpam-6631	74	7	the	the	DET
ejpam-6631	74	8	following	follow	VERB
ejpam-6631	74	9	applies	applie	NOUN
ejpam-6631	74	10	:	:	PUNCT
ejpam-6631	75	1	φn	φn	NOUN
ejpam-6631	75	2	=	=	PUNCT
ejpam-6631	75	3	γ(φ+	γ(φ+	NOUN
ejpam-6631	75	4	n	n	CCONJ
ejpam-6631	75	5	)	)	PUNCT
ejpam-6631	75	6	γ(φ	γ(φ	NOUN
ejpam-6631	75	7	)	)	PUNCT
ejpam-6631	75	8	=	=	SYM
ejpam-6631	75	9	φ(φ+	φ(φ+	NOUN
ejpam-6631	75	10	1)	1)	NUM
ejpam-6631	75	11	....	....	PUNCT
ejpam-6631	75	12	(φ+	(φ+	PROPN
ejpam-6631	75	13	n−	n−	NOUN
ejpam-6631	75	14	1	1	NUM
ejpam-6631	75	15	)	)	PUNCT
ejpam-6631	75	16	(	(	PUNCT
ejpam-6631	75	17	8)	8)	NUM
ejpam-6631	75	18	when	when	SCONJ
ejpam-6631	75	19	φ	φ	PROPN
ejpam-6631	75	20	=	=	SYM
ejpam-6631	75	21	1	1	NUM
ejpam-6631	75	22	,	,	PUNCT
ejpam-6631	75	23	the	the	DET
ejpam-6631	75	24	equation	equation	NOUN
ejpam-6631	75	25	m0	m0	PROPN
ejpam-6631	75	26	α	α	PROPN
ejpam-6631	75	27	,	,	PUNCT
ejpam-6631	75	28	β	β	X
ejpam-6631	75	29	=	=	SYM
ejpam-6631	75	30	1	1	NUM
ejpam-6631	75	31	γ(β	γ(β	PROPN
ejpam-6631	75	32	)	)	PUNCT
ejpam-6631	75	33	.	.	PUNCT
ejpam-6631	76	1	(	(	PUNCT
ejpam-6631	76	2	9	9	X
ejpam-6631	76	3	)	)	PUNCT
ejpam-6631	76	4	equation	equation	NOUN
ejpam-6631	76	5	(	(	PUNCT
ejpam-6631	76	6	9	9	NUM
ejpam-6631	76	7	)	)	PUNCT
ejpam-6631	76	8	holds	hold	VERB
ejpam-6631	76	9	true	true	ADJ
ejpam-6631	76	10	.	.	PUNCT
ejpam-6631	77	1	when	when	SCONJ
ejpam-6631	77	2	α	α	X
ejpam-6631	77	3	=	=	X
ejpam-6631	77	4	β	β	X
ejpam-6631	77	5	=	=	PUNCT
ejpam-6631	77	6	φ	φ	PROPN
ejpam-6631	77	7	=	=	SYM
ejpam-6631	77	8	1	1	NUM
ejpam-6631	77	9	,	,	PUNCT
ejpam-6631	77	10	we	we	PRON
ejpam-6631	77	11	get	get	VERB
ejpam-6631	77	12	the	the	DET
ejpam-6631	77	13	well	well	ADV
ejpam-6631	77	14	-	-	PUNCT
ejpam-6631	77	15	known	know	VERB
ejpam-6631	77	16	two	two	NUM
ejpam-6631	77	17	-	-	PUNCT
ejpam-6631	77	18	parameter	parameter	NOUN
ejpam-6631	77	19	maximum	maximum	ADJ
ejpam-6631	77	20	likelihood	likelihood	NOUN
ejpam-6631	77	21	function	function	NOUN
ejpam-6631	77	22	,	,	PUNCT
ejpam-6631	77	23	written	write	VERB
ejpam-6631	77	24	as	as	ADP
ejpam-6631	77	25	;	;	PUNCT
ejpam-6631	77	26	m1	m1	PROPN
ejpam-6631	77	27	α	α	NUM
ejpam-6631	77	28	,	,	PUNCT
ejpam-6631	77	29	β(ϕ	β(ϕ	NUM
ejpam-6631	77	30	)	)	PUNCT
ejpam-6631	77	31	=	=	SYM
ejpam-6631	77	32	mα	mα	PROPN
ejpam-6631	77	33	,	,	PUNCT
ejpam-6631	77	34	β(ϕ	β(ϕ	NUM
ejpam-6631	77	35	)	)	PUNCT
ejpam-6631	78	1	=	=	PUNCT
ejpam-6631	79	1	∞∑	∞∑	PROPN
ejpam-6631	79	2	n=0	n=0	PROPN
ejpam-6631	79	3	ϕn	ϕn	ADP
ejpam-6631	79	4	γ(αn+	γ(αn+	ADJ
ejpam-6631	79	5	β	β	NOUN
ejpam-6631	79	6	)	)	PUNCT
ejpam-6631	79	7	.	.	PUNCT
ejpam-6631	80	1	(	(	PUNCT
ejpam-6631	80	2	10	10	NUM
ejpam-6631	80	3	)	)	PUNCT
ejpam-6631	80	4	m.	m.	NOUN
ejpam-6631	80	5	abdel	abdel	PROPN
ejpam-6631	80	6	aal	aal	PROPN
ejpam-6631	80	7	et	et	PROPN
ejpam-6631	80	8	al	al	PROPN
ejpam-6631	80	9	.	.	PUNCT
ejpam-6631	80	10	/	/	SYM
ejpam-6631	80	11	eur	eur	PROPN
ejpam-6631	80	12	.	.	PUNCT
ejpam-6631	81	1	j.	j.	PROPN
ejpam-6631	81	2	pure	pure	PROPN
ejpam-6631	81	3	appl	appl	PROPN
ejpam-6631	81	4	.	.	PROPN
ejpam-6631	81	5	math	math	PROPN
ejpam-6631	81	6	,	,	PUNCT
ejpam-6631	81	7	18	18	NUM
ejpam-6631	81	8	(	(	PUNCT
ejpam-6631	81	9	4	4	NUM
ejpam-6631	81	10	)	)	PUNCT
ejpam-6631	81	11	(	(	PUNCT
ejpam-6631	81	12	2025	2025	NUM
ejpam-6631	81	13	)	)	PUNCT
ejpam-6631	81	14	,	,	PUNCT
ejpam-6631	81	15	6631	6631	NUM
ejpam-6631	81	16	5	5	NUM
ejpam-6631	81	17	of	of	ADP
ejpam-6631	81	18	20	20	NUM
ejpam-6631	81	19	we	we	PRON
ejpam-6631	81	20	then	then	ADV
ejpam-6631	81	21	obtain	obtain	VERB
ejpam-6631	81	22	the	the	DET
ejpam-6631	81	23	classic	classic	ADJ
ejpam-6631	81	24	exponential	exponential	ADJ
ejpam-6631	81	25	function	function	NOUN
ejpam-6631	81	26	,	,	PUNCT
ejpam-6631	82	1	m1	m1	PROPN
ejpam-6631	82	2	1,1	1,1	NUM
ejpam-6631	82	3	=	=	SYM
ejpam-6631	82	4	eτ	eτ	NOUN
ejpam-6631	82	5	.	.	PUNCT
ejpam-6631	83	1	(	(	PUNCT
ejpam-6631	83	2	11	11	NUM
ejpam-6631	83	3	)	)	PUNCT
ejpam-6631	83	4	the	the	DET
ejpam-6631	83	5	prabhakar	prabhakar	NOUN
ejpam-6631	83	6	function	function	NOUN
ejpam-6631	83	7	is	be	AUX
ejpam-6631	83	8	different	different	ADJ
ejpam-6631	83	9	from	from	ADP
ejpam-6631	83	10	the	the	DET
ejpam-6631	83	11	two	two	NUM
ejpam-6631	83	12	-	-	PUNCT
ejpam-6631	83	13	parameter	parameter	NOUN
ejpam-6631	83	14	mittag	mittag	ADJ
ejpam-6631	83	15	-	-	PUNCT
ejpam-6631	83	16	leffler	leffler	NOUN
ejpam-6631	83	17	function	function	NOUN
ejpam-6631	83	18	because	because	SCONJ
ejpam-6631	83	19	it	it	PRON
ejpam-6631	83	20	has	have	VERB
ejpam-6631	83	21	a	a	DET
ejpam-6631	83	22	third	third	ADJ
ejpam-6631	83	23	parameter	parameter	NOUN
ejpam-6631	83	24	,	,	PUNCT
ejpam-6631	83	25	ϕ.	ϕ.	NOUN
ejpam-6631	83	26	this	this	DET
ejpam-6631	83	27	difference	difference	NOUN
ejpam-6631	83	28	means	mean	VERB
ejpam-6631	83	29	we	we	PRON
ejpam-6631	83	30	need	need	VERB
ejpam-6631	83	31	to	to	PART
ejpam-6631	83	32	examine	examine	VERB
ejpam-6631	83	33	the	the	DET
ejpam-6631	83	34	properties	property	NOUN
ejpam-6631	83	35	related	relate	VERB
ejpam-6631	83	36	to	to	ADP
ejpam-6631	83	37	this	this	DET
ejpam-6631	83	38	additional	additional	ADJ
ejpam-6631	83	39	parameter	parameter	NOUN
ejpam-6631	83	40	.	.	PUNCT
ejpam-6631	84	1	an	an	DET
ejpam-6631	84	2	important	important	ADJ
ejpam-6631	84	3	formula	formula	NOUN
ejpam-6631	84	4	from	from	ADP
ejpam-6631	84	5	prabhakar	prabhakar	NOUN
ejpam-6631	84	6	’s	’s	PART
ejpam-6631	84	7	original	original	ADJ
ejpam-6631	84	8	work	work	NOUN
ejpam-6631	84	9	in	in	ADP
ejpam-6631	84	10	ref	ref	NOUN
ejpam-6631	84	11	.	.	PUNCT
ejpam-6631	85	1	[	[	X
ejpam-6631	85	2	23	23	NUM
ejpam-6631	85	3	]	]	PUNCT
ejpam-6631	85	4	allows	allow	VERB
ejpam-6631	85	5	for	for	ADP
ejpam-6631	85	6	simplifying	simplify	VERB
ejpam-6631	85	7	the	the	DET
ejpam-6631	85	8	third	third	ADJ
ejpam-6631	85	9	parameter	parameter	NOUN
ejpam-6631	85	10	.	.	PUNCT
ejpam-6631	86	1	it	it	PRON
ejpam-6631	86	2	is	be	AUX
ejpam-6631	86	3	written	write	VERB
ejpam-6631	86	4	as	as	ADP
ejpam-6631	86	5	;	;	PUNCT
ejpam-6631	86	6	mφ+1	mφ+1	NUM
ejpam-6631	86	7	α	α	NOUN
ejpam-6631	86	8	,	,	PUNCT
ejpam-6631	86	9	β	β	X
ejpam-6631	86	10	(	(	PUNCT
ejpam-6631	86	11	ϕ	ϕ	NOUN
ejpam-6631	86	12	)	)	PUNCT
ejpam-6631	86	13	=	=	SYM
ejpam-6631	86	14	mα	mα	PROPN
ejpam-6631	86	15	,	,	PUNCT
ejpam-6631	86	16	β−1(ϕ	β−1(ϕ	PROPN
ejpam-6631	86	17	)	)	PUNCT
ejpam-6631	87	1	+	+	CCONJ
ejpam-6631	87	2	(	(	PUNCT
ejpam-6631	87	3	1−	1−	NUM
ejpam-6631	87	4	β	β	X
ejpam-6631	87	5	+	+	X
ejpam-6631	87	6	αφ)mα	αφ)mα	NUM
ejpam-6631	87	7	,	,	PUNCT
ejpam-6631	87	8	β(ϕ	β(ϕ	NUM
ejpam-6631	87	9	)	)	PUNCT
ejpam-6631	87	10	αφ	αφ	PROPN
ejpam-6631	87	11	,	,	PUNCT
ejpam-6631	87	12	(	(	PUNCT
ejpam-6631	87	13	12	12	NUM
ejpam-6631	87	14	)	)	PUNCT
ejpam-6631	87	15	additionally	additionally	ADV
ejpam-6631	87	16	,	,	PUNCT
ejpam-6631	87	17	another	another	DET
ejpam-6631	87	18	simplification	simplification	NOUN
ejpam-6631	87	19	formula	formula	NOUN
ejpam-6631	87	20	was	be	AUX
ejpam-6631	87	21	derived	derive	VERB
ejpam-6631	87	22	later	later	ADV
ejpam-6631	87	23	in	in	ADP
ejpam-6631	87	24	[	[	X
ejpam-6631	87	25	32	32	NUM
ejpam-6631	87	26	]	]	PUNCT
ejpam-6631	87	27	and	and	CCONJ
ejpam-6631	87	28	appears	appear	VERB
ejpam-6631	87	29	as	as	ADP
ejpam-6631	87	30	mφ+1	mφ+1	PROPN
ejpam-6631	87	31	α	α	NOUN
ejpam-6631	87	32	,	,	PUNCT
ejpam-6631	87	33	β	β	X
ejpam-6631	87	34	(	(	PUNCT
ejpam-6631	87	35	ϕ	ϕ	NOUN
ejpam-6631	87	36	)	)	PUNCT
ejpam-6631	87	37	=	=	SYM
ejpam-6631	87	38	mα	mα	PROPN
ejpam-6631	87	39	,	,	PUNCT
ejpam-6631	87	40	β−1(ϕ	β−1(ϕ	PROPN
ejpam-6631	87	41	)	)	PUNCT
ejpam-6631	88	1	+	+	CCONJ
ejpam-6631	88	2	(	(	PUNCT
ejpam-6631	88	3	1−	1−	NUM
ejpam-6631	88	4	β	β	X
ejpam-6631	88	5	+	+	X
ejpam-6631	88	6	αφ)mα	αφ)mα	NUM
ejpam-6631	88	7	,	,	PUNCT
ejpam-6631	88	8	β(ϕ	β(ϕ	NUM
ejpam-6631	88	9	)	)	PUNCT
ejpam-6631	88	10	αϕφ	αϕφ	NOUN
ejpam-6631	88	11	,	,	PUNCT
ejpam-6631	88	12	(	(	PUNCT
ejpam-6631	88	13	13	13	NUM
ejpam-6631	88	14	)	)	PUNCT
ejpam-6631	88	15	where	where	SCONJ
ejpam-6631	88	16	φ	φ	PROPN
ejpam-6631	88	17	̸=	̸=	PROPN
ejpam-6631	88	18	0	0	NUM
ejpam-6631	88	19	.	.	PUNCT
ejpam-6631	89	1	we	we	PRON
ejpam-6631	89	2	can	can	AUX
ejpam-6631	89	3	then	then	ADV
ejpam-6631	89	4	utilize	utilize	VERB
ejpam-6631	89	5	both	both	DET
ejpam-6631	89	6	formulas	formula	NOUN
ejpam-6631	89	7	to	to	PART
ejpam-6631	89	8	simplify	simplify	VERB
ejpam-6631	89	9	the	the	DET
ejpam-6631	89	10	value	value	NOUN
ejpam-6631	89	11	of	of	ADP
ejpam-6631	89	12	an	an	DET
ejpam-6631	89	13	additional	additional	ADJ
ejpam-6631	89	14	parameter	parameter	NOUN
ejpam-6631	89	15	.	.	PUNCT
ejpam-6631	90	1	these	these	DET
ejpam-6631	90	2	results	result	NOUN
ejpam-6631	90	3	become	become	VERB
ejpam-6631	90	4	clearer	clear	ADJ
ejpam-6631	90	5	when	when	SCONJ
ejpam-6631	90	6	φ	φ	PROPN
ejpam-6631	90	7	is	be	AUX
ejpam-6631	90	8	an	an	DET
ejpam-6631	90	9	integer	integer	NOUN
ejpam-6631	90	10	.	.	PUNCT
ejpam-6631	91	1	for	for	ADP
ejpam-6631	91	2	instance	instance	NOUN
ejpam-6631	91	3	,	,	PUNCT
ejpam-6631	91	4	let	let	VERB
ejpam-6631	91	5	φ	φ	PROPN
ejpam-6631	91	6	=	=	SYM
ejpam-6631	91	7	n	n	SYM
ejpam-6631	91	8	∈	∈	PROPN
ejpam-6631	91	9	n	n	CCONJ
ejpam-6631	91	10	,	,	PUNCT
ejpam-6631	91	11	where	where	SCONJ
ejpam-6631	91	12	n	n	PRON
ejpam-6631	91	13	is	be	AUX
ejpam-6631	91	14	a	a	DET
ejpam-6631	91	15	natural	natural	ADJ
ejpam-6631	91	16	number	number	NOUN
ejpam-6631	91	17	.	.	PUNCT
ejpam-6631	92	1	in	in	ADP
ejpam-6631	92	2	this	this	DET
ejpam-6631	92	3	scenario	scenario	NOUN
ejpam-6631	92	4	,	,	PUNCT
ejpam-6631	92	5	we	we	PRON
ejpam-6631	92	6	have	have	VERB
ejpam-6631	92	7	mn+1	mn+1	PROPN
ejpam-6631	92	8	α	α	PROPN
ejpam-6631	92	9	,	,	PUNCT
ejpam-6631	92	10	β	β	X
ejpam-6631	92	11	(	(	PUNCT
ejpam-6631	92	12	ϕ	ϕ	NOUN
ejpam-6631	92	13	)	)	PUNCT
ejpam-6631	92	14	=	=	SYM
ejpam-6631	92	15	1	1	NUM
ejpam-6631	92	16	αnn	αnn	NOUN
ejpam-6631	92	17	!	!	PUNCT
ejpam-6631	93	1	n∑	n∑	PROPN
ejpam-6631	94	1	i=0	i=0	PROPN
ejpam-6631	94	2	a	a	DET
ejpam-6631	94	3	(	(	PUNCT
ejpam-6631	94	4	n	n	CCONJ
ejpam-6631	94	5	)	)	PUNCT
ejpam-6631	94	6	i	i	PRON
ejpam-6631	94	7	mα	mα	PROPN
ejpam-6631	94	8	,	,	PUNCT
ejpam-6631	94	9	β−i(ϕ	β−i(ϕ	PROPN
ejpam-6631	94	10	)	)	PUNCT
ejpam-6631	94	11	,	,	PUNCT
ejpam-6631	94	12	(	(	PUNCT
ejpam-6631	94	13	14	14	NUM
ejpam-6631	94	14	)	)	PUNCT
ejpam-6631	94	15	and	and	CCONJ
ejpam-6631	94	16	mn+1	mn+1	PROPN
ejpam-6631	94	17	α	α	PROPN
ejpam-6631	94	18	,	,	PUNCT
ejpam-6631	94	19	β	β	X
ejpam-6631	94	20	(	(	PUNCT
ejpam-6631	94	21	ϕ	ϕ	NOUN
ejpam-6631	94	22	)	)	PUNCT
ejpam-6631	94	23	=	=	SYM
ejpam-6631	94	24	1	1	NUM
ejpam-6631	94	25	αnϕnn	αnϕnn	NOUN
ejpam-6631	94	26	!	!	PUNCT
ejpam-6631	95	1	n∑	n∑	PROPN
ejpam-6631	96	1	i=0	i=0	PROPN
ejpam-6631	96	2	a	a	PRON
ejpam-6631	96	3	(	(	PUNCT
ejpam-6631	96	4	n	n	CCONJ
ejpam-6631	96	5	)	)	PUNCT
ejpam-6631	96	6	i	i	PRON
ejpam-6631	96	7	mα	mα	PROPN
ejpam-6631	96	8	,	,	PUNCT
ejpam-6631	96	9	β−αn−i(ϕ	β−αn−i(ϕ	NUM
ejpam-6631	96	10	)	)	PUNCT
ejpam-6631	96	11	,	,	PUNCT
ejpam-6631	96	12	(	(	PUNCT
ejpam-6631	96	13	15	15	NUM
ejpam-6631	96	14	)	)	PUNCT
ejpam-6631	97	1	where	where	SCONJ
ejpam-6631	97	2	φ	φ	PROPN
ejpam-6631	97	3	̸=	̸=	PROPN
ejpam-6631	97	4	0	0	NUM
ejpam-6631	97	5	.	.	PUNCT
ejpam-6631	98	1	this	this	PRON
ejpam-6631	98	2	implies	imply	VERB
ejpam-6631	98	3	that	that	SCONJ
ejpam-6631	98	4	mn+1	mn+1	PROPN
ejpam-6631	98	5	α	α	PROPN
ejpam-6631	98	6	,	,	PUNCT
ejpam-6631	98	7	β	β	NOUN
ejpam-6631	98	8	from	from	ADP
ejpam-6631	98	9	the	the	DET
ejpam-6631	98	10	right	right	ADJ
ejpam-6631	98	11	-	-	PUNCT
ejpam-6631	98	12	side	side	NOUN
ejpam-6631	98	13	of	of	ADP
ejpam-6631	98	14	(	(	PUNCT
ejpam-6631	98	15	15	15	NUM
ejpam-6631	98	16	)	)	PUNCT
ejpam-6631	98	17	can	can	AUX
ejpam-6631	98	18	be	be	AUX
ejpam-6631	98	19	expressed	express	VERB
ejpam-6631	98	20	as	as	ADP
ejpam-6631	98	21	a	a	DET
ejpam-6631	98	22	combination	combination	NOUN
ejpam-6631	98	23	of	of	ADP
ejpam-6631	98	24	two	two	NUM
ejpam-6631	98	25	-	-	PUNCT
ejpam-6631	98	26	parameter	parameter	NOUN
ejpam-6631	98	27	ml	ml	NOUN
ejpam-6631	98	28	functions	function	NOUN
ejpam-6631	98	29	.	.	PUNCT
ejpam-6631	99	1	the	the	DET
ejpam-6631	99	2	coefficients	coefficient	NOUN
ejpam-6631	99	3	a	a	DET
ejpam-6631	99	4	(	(	PUNCT
ejpam-6631	99	5	n	n	CCONJ
ejpam-6631	99	6	)	)	PUNCT
ejpam-6631	99	7	i	i	PRON
ejpam-6631	99	8	in	in	ADP
ejpam-6631	99	9	equations	equation	NOUN
ejpam-6631	99	10	(	(	PUNCT
ejpam-6631	99	11	15	15	NUM
ejpam-6631	99	12	)	)	PUNCT
ejpam-6631	99	13	and	and	CCONJ
ejpam-6631	99	14	(	(	PUNCT
ejpam-6631	99	15	(	(	PUNCT
ejpam-6631	99	16	15	15	NUM
ejpam-6631	99	17	)	)	PUNCT
ejpam-6631	99	18	are	be	AUX
ejpam-6631	99	19	derived	derive	VERB
ejpam-6631	99	20	from	from	ADP
ejpam-6631	99	21	the	the	DET
ejpam-6631	99	22	recursive	recursive	ADJ
ejpam-6631	99	23	formula	formula	NOUN
ejpam-6631	99	24	:	:	PUNCT
ejpam-6631	99	25	a	a	PRON
ejpam-6631	99	26	(	(	PUNCT
ejpam-6631	99	27	n	n	CCONJ
ejpam-6631	99	28	)	)	PUNCT
ejpam-6631	99	29	i	i	PRON
ejpam-6631	99	30	=	=	SYM
ejpam-6631	100	1			PROPN
ejpam-6631	100	2	(	(	PUNCT
ejpam-6631	100	3	1	1	NUM
ejpam-6631	100	4	+	+	CCONJ
ejpam-6631	100	5	α−	α−	ADP
ejpam-6631	100	6	β)a	β)a	X
ejpam-6631	100	7	(	(	PUNCT
ejpam-6631	100	8	n−1	n−1	PROPN
ejpam-6631	100	9	)	)	PUNCT
ejpam-6631	100	10	0	0	NUM
ejpam-6631	101	1	for	for	ADP
ejpam-6631	101	2	i	i	PRON
ejpam-6631	101	3	=	=	NOUN
ejpam-6631	101	4	0	0	X
ejpam-6631	101	5	a	a	PRON
ejpam-6631	101	6	(	(	PUNCT
ejpam-6631	101	7	n	n	CCONJ
ejpam-6631	101	8	)	)	PUNCT
ejpam-6631	101	9	i	i	PRON
ejpam-6631	101	10	+	+	PUNCT
ejpam-6631	101	11	(	(	PUNCT
ejpam-6631	101	12	1	1	NUM
ejpam-6631	101	13	+	+	CCONJ
ejpam-6631	101	14	α−	α−	ADP
ejpam-6631	101	15	β	β	X
ejpam-6631	101	16	+	+	X
ejpam-6631	101	17	i)a	i)a	X
ejpam-6631	101	18	(	(	PUNCT
ejpam-6631	101	19	n−1	n−1	PROPN
ejpam-6631	101	20	)	)	PUNCT
ejpam-6631	101	21	i	i	PRON
ejpam-6631	101	22	for	for	ADP
ejpam-6631	101	23	i	i	PRON
ejpam-6631	101	24	=	=	NOUN
ejpam-6631	101	25	1	1	NUM
ejpam-6631	101	26	,	,	PUNCT
ejpam-6631	101	27	...	...	PUNCT
ejpam-6631	101	28	,	,	PUNCT
ejpam-6631	101	29	n−	n−	NOUN
ejpam-6631	101	30	1	1	NUM
ejpam-6631	101	31	,	,	PUNCT
ejpam-6631	101	32	1	1	NUM
ejpam-6631	101	33	for	for	ADP
ejpam-6631	101	34	i	i	PRON
ejpam-6631	101	35	=	=	PUNCT
ejpam-6631	101	36	n.	n.	NOUN
ejpam-6631	101	37	(	(	PUNCT
ejpam-6631	101	38	16	16	NUM
ejpam-6631	101	39	)	)	PUNCT
ejpam-6631	101	40	3	3	NUM
ejpam-6631	101	41	.	.	PUNCT
ejpam-6631	102	1	the	the	DET
ejpam-6631	102	2	concept	concept	NOUN
ejpam-6631	102	3	of	of	ADP
ejpam-6631	102	4	the	the	DET
ejpam-6631	102	5	explicit	explicit	ADJ
ejpam-6631	102	6	fractional	fractional	ADJ
ejpam-6631	102	7	adams	adam	NOUN
ejpam-6631	102	8	method	method	NOUN
ejpam-6631	102	9	for	for	ADP
ejpam-6631	102	10	solving	solve	VERB
ejpam-6631	102	11	prabhakar	prabhakar	NOUN
ejpam-6631	102	12	fractional	fractional	ADJ
ejpam-6631	102	13	differential	differential	ADJ
ejpam-6631	102	14	equations	equation	NOUN
ejpam-6631	102	15	in	in	ADP
ejpam-6631	102	16	this	this	DET
ejpam-6631	102	17	section	section	NOUN
ejpam-6631	102	18	,	,	PUNCT
ejpam-6631	102	19	we	we	PRON
ejpam-6631	102	20	discuss	discuss	VERB
ejpam-6631	102	21	the	the	DET
ejpam-6631	102	22	explicit	explicit	ADJ
ejpam-6631	102	23	fractional	fractional	ADJ
ejpam-6631	102	24	adams	adam	NOUN
ejpam-6631	102	25	method	method	NOUN
ejpam-6631	102	26	.	.	PUNCT
ejpam-6631	103	1	this	this	DET
ejpam-6631	103	2	method	method	NOUN
ejpam-6631	103	3	relates	relate	VERB
ejpam-6631	103	4	to	to	ADP
ejpam-6631	103	5	the	the	DET
ejpam-6631	103	6	volterra	volterra	NOUN
ejpam-6631	103	7	integral	integral	ADJ
ejpam-6631	103	8	equation	equation	NOUN
ejpam-6631	103	9	and	and	CCONJ
ejpam-6631	103	10	addresses	address	VERB
ejpam-6631	103	11	the	the	DET
ejpam-6631	103	12	initial	initial	ADJ
ejpam-6631	103	13	value	value	NOUN
ejpam-6631	103	14	problem	problem	NOUN
ejpam-6631	103	15	.	.	PUNCT
ejpam-6631	104	1	m.	m.	NOUN
ejpam-6631	104	2	abdel	abdel	PROPN
ejpam-6631	104	3	aal	aal	PROPN
ejpam-6631	104	4	et	et	PROPN
ejpam-6631	104	5	al	al	PROPN
ejpam-6631	104	6	.	.	PUNCT
ejpam-6631	104	7	/	/	SYM
ejpam-6631	104	8	eur	eur	PROPN
ejpam-6631	104	9	.	.	PUNCT
ejpam-6631	105	1	j.	j.	PROPN
ejpam-6631	105	2	pure	pure	PROPN
ejpam-6631	105	3	appl	appl	PROPN
ejpam-6631	105	4	.	.	PROPN
ejpam-6631	105	5	math	math	PROPN
ejpam-6631	105	6	,	,	PUNCT
ejpam-6631	105	7	18	18	NUM
ejpam-6631	105	8	(	(	PUNCT
ejpam-6631	105	9	4	4	NUM
ejpam-6631	105	10	)	)	PUNCT
ejpam-6631	105	11	(	(	PUNCT
ejpam-6631	105	12	2025	2025	NUM
ejpam-6631	105	13	)	)	PUNCT
ejpam-6631	105	14	,	,	PUNCT
ejpam-6631	105	15	6631	6631	NUM
ejpam-6631	105	16	6	6	NUM
ejpam-6631	105	17	of	of	ADP
ejpam-6631	105	18	20	20	NUM
ejpam-6631	105	19	3.1	3.1	NUM
ejpam-6631	105	20	.	.	PUNCT
ejpam-6631	106	1	the	the	DET
ejpam-6631	106	2	explicit	explicit	ADJ
ejpam-6631	106	3	fractional	fractional	ADJ
ejpam-6631	106	4	adams	adam	NOUN
ejpam-6631	106	5	method	method	PROPN
ejpam-6631	106	6	the	the	DET
ejpam-6631	106	7	volterra	volterra	NOUN
ejpam-6631	106	8	integral	integral	ADJ
ejpam-6631	106	9	equation	equation	NOUN
ejpam-6631	106	10	connects	connect	VERB
ejpam-6631	106	11	to	to	ADP
ejpam-6631	106	12	the	the	DET
ejpam-6631	106	13	initial	initial	ADJ
ejpam-6631	106	14	value	value	NOUN
ejpam-6631	106	15	problem	problem	NOUN
ejpam-6631	106	16	as	as	SCONJ
ejpam-6631	106	17	follows	follow	VERB
ejpam-6631	106	18	:	:	PUNCT
ejpam-6631	106	19	definition	definition	NOUN
ejpam-6631	106	20	5	5	NUM
ejpam-6631	106	21	.	.	PUNCT
ejpam-6631	107	1	the	the	DET
ejpam-6631	107	2	explicit	explicit	ADJ
ejpam-6631	107	3	fractional	fractional	ADJ
ejpam-6631	107	4	adams	adam	NOUN
ejpam-6631	107	5	method	method	NOUN
ejpam-6631	107	6	that	that	PRON
ejpam-6631	107	7	is	be	AUX
ejpam-6631	107	8	related	relate	VERB
ejpam-6631	107	9	to	to	ADP
ejpam-6631	107	10	the	the	DET
ejpam-6631	107	11	volterra	volterra	NOUN
ejpam-6631	107	12	integral	integral	ADJ
ejpam-6631	107	13	equation	equation	NOUN
ejpam-6631	107	14	and	and	CCONJ
ejpam-6631	107	15	addresses	address	VERB
ejpam-6631	107	16	the	the	DET
ejpam-6631	107	17	initial	initial	ADJ
ejpam-6631	107	18	value	value	NOUN
ejpam-6631	107	19	problem	problem	NOUN
ejpam-6631	107	20	is	be	AUX
ejpam-6631	107	21	define	define	VERB
ejpam-6631	107	22	here	here	ADV
ejpam-6631	107	23	as	as	ADP
ejpam-6631	107	24	:	:	PUNCT
ejpam-6631	107	25	p(x	p(x	NOUN
ejpam-6631	107	26	)	)	PUNCT
ejpam-6631	107	27	=	=	SYM
ejpam-6631	108	1	p0	p0	NOUN
ejpam-6631	109	1	+	+	CCONJ
ejpam-6631	109	2	∫	∫	PROPN
ejpam-6631	109	3	x	x	SYM
ejpam-6631	109	4	0	0	NUM
ejpam-6631	109	5	(	(	PUNCT
ejpam-6631	109	6	x−	x−	PROPN
ejpam-6631	109	7	w)β−1mγ	w)β−1mγ	PROPN
ejpam-6631	109	8	α	α	PROPN
ejpam-6631	109	9	,	,	PUNCT
ejpam-6631	109	10	β(τ(x−	β(τ(x−	PUNCT
ejpam-6631	109	11	w)α)µ(v	w)α)µ(v	VERB
ejpam-6631	109	12	;	;	PUNCT
ejpam-6631	109	13	p(x))dw	p(x))dw	NOUN
ejpam-6631	109	14	.	.	PUNCT
ejpam-6631	110	1	(	(	PUNCT
ejpam-6631	110	2	17	17	NUM
ejpam-6631	110	3	)	)	PUNCT
ejpam-6631	110	4	then	then	ADV
ejpam-6631	110	5	,	,	PUNCT
ejpam-6631	110	6	further	far	ADV
ejpam-6631	110	7	break	break	VERB
ejpam-6631	110	8	down	down	ADP
ejpam-6631	110	9	the	the	DET
ejpam-6631	110	10	integral	integral	ADJ
ejpam-6631	110	11	from	from	ADP
ejpam-6631	110	12	equation	equation	NOUN
ejpam-6631	110	13	(	(	PUNCT
ejpam-6631	110	14	17	17	NUM
ejpam-6631	110	15	)	)	PUNCT
ejpam-6631	110	16	as	as	SCONJ
ejpam-6631	110	17	follows	follow	VERB
ejpam-6631	110	18	:	:	PUNCT
ejpam-6631	110	19	p(xk+1	p(xk+1	X
ejpam-6631	110	20	)	)	PUNCT
ejpam-6631	110	21	=	=	SYM
ejpam-6631	111	1	p(xk	p(xk	X
ejpam-6631	111	2	)	)	PUNCT
ejpam-6631	112	1	+	+	CCONJ
ejpam-6631	112	2	∫	∫	PROPN
ejpam-6631	112	3	xk+1	xk+1	PROPN
ejpam-6631	112	4	0	0	NUM
ejpam-6631	113	1	(	(	PUNCT
ejpam-6631	113	2	xk+1	xk+1	NUM
ejpam-6631	113	3	−	−	PROPN
ejpam-6631	113	4	w)β−1mγ	w)β−1mγ	PROPN
ejpam-6631	113	5	α	α	PRON
ejpam-6631	113	6	,	,	PUNCT
ejpam-6631	113	7	β(τ(xk+1	β(τ(xk+1	VERB
ejpam-6631	113	8	−	−	PUNCT
ejpam-6631	113	9	w)α)µ(v	w)α)µ(v	NOUN
ejpam-6631	113	10	;	;	PUNCT
ejpam-6631	113	11	p(x))dw	p(x))dw	NOUN
ejpam-6631	113	12	−	−	PROPN
ejpam-6631	113	13	∫	∫	PROPN
ejpam-6631	113	14	xk	xk	PROPN
ejpam-6631	113	15	0	0	PROPN
ejpam-6631	114	1	(	(	PUNCT
ejpam-6631	114	2	xk	xk	PROPN
ejpam-6631	114	3	−	−	PROPN
ejpam-6631	114	4	w)β−1mγ	w)β−1mγ	PROPN
ejpam-6631	114	5	α	α	PROPN
ejpam-6631	114	6	,	,	PUNCT
ejpam-6631	114	7	β(τ(xk	β(τ(xk	NUM
ejpam-6631	114	8	−	−	NOUN
ejpam-6631	114	9	w)α)µ(v	w)α)µ(v	PROPN
ejpam-6631	114	10	;	;	PUNCT
ejpam-6631	114	11	p(x))dw	p(x))dw	NOUN
ejpam-6631	114	12	(	(	PUNCT
ejpam-6631	114	13	18	18	NUM
ejpam-6631	114	14	)	)	PUNCT
ejpam-6631	114	15	using	use	VERB
ejpam-6631	114	16	three	three	NUM
ejpam-6631	114	17	-	-	PUNCT
ejpam-6631	114	18	point	point	NOUN
ejpam-6631	114	19	lagrange	lagrange	NOUN
ejpam-6631	114	20	interpolation	interpolation	NOUN
ejpam-6631	114	21	,	,	PUNCT
ejpam-6631	114	22	equation	equation	NOUN
ejpam-6631	114	23	(	(	PUNCT
ejpam-6631	114	24	18	18	NUM
ejpam-6631	114	25	)	)	PUNCT
ejpam-6631	114	26	can	can	AUX
ejpam-6631	114	27	be	be	AUX
ejpam-6631	114	28	expressed	express	VERB
ejpam-6631	114	29	in	in	ADP
ejpam-6631	114	30	a	a	DET
ejpam-6631	114	31	different	different	ADJ
ejpam-6631	114	32	form	form	NOUN
ejpam-6631	114	33	.	.	PUNCT
ejpam-6631	115	1	p(xk+1	p(xk+1	X
ejpam-6631	115	2	)	)	PUNCT
ejpam-6631	115	3	=	=	SYM
ejpam-6631	116	1	p(xk	p(xk	X
ejpam-6631	116	2	)	)	PUNCT
ejpam-6631	117	1	+	+	CCONJ
ejpam-6631	117	2	∫	∫	PROPN
ejpam-6631	117	3	xk+1	xk+1	PROPN
ejpam-6631	117	4	0	0	NUM
ejpam-6631	118	1	(	(	PUNCT
ejpam-6631	118	2	xk+1	xk+1	NUM
ejpam-6631	118	3	−	−	PROPN
ejpam-6631	118	4	w)β−1mγ	w)β−1mγ	PROPN
ejpam-6631	118	5	α	α	PRON
ejpam-6631	118	6	,	,	PUNCT
ejpam-6631	118	7	β(τ(xk+1	β(τ(xk+1	VERB
ejpam-6631	118	8	−	−	PRON
ejpam-6631	118	9	w)α	w)α	SCONJ
ejpam-6631	118	10	)	)	PUNCT
ejpam-6631	118	11	[	[	PUNCT
ejpam-6631	118	12	(	(	PUNCT
ejpam-6631	118	13	x−	x−	PROPN
ejpam-6631	118	14	xk−1)(x−	xk−1)(x−	PROPN
ejpam-6631	118	15	xk−2	xk−2	PROPN
ejpam-6631	118	16	)	)	PUNCT
ejpam-6631	118	17	(	(	PUNCT
ejpam-6631	118	18	xk	xk	PROPN
ejpam-6631	118	19	−	−	PROPN
ejpam-6631	118	20	xk−1)(xk	xk−1)(xk	PROPN
ejpam-6631	119	1	−	−	PROPN
ejpam-6631	119	2	xk−2	xk−2	PROPN
ejpam-6631	119	3	)	)	PUNCT
ejpam-6631	119	4	gk	gk	PROPN
ejpam-6631	119	5	+	+	CCONJ
ejpam-6631	119	6	(	(	PUNCT
ejpam-6631	119	7	x−	x−	PROPN
ejpam-6631	119	8	xk)(x−	xk)(x−	PROPN
ejpam-6631	119	9	xk−2	xk−2	PROPN
ejpam-6631	119	10	)	)	PUNCT
ejpam-6631	119	11	(	(	PUNCT
ejpam-6631	119	12	xk−1	xk−1	PROPN
ejpam-6631	119	13	−	−	PROPN
ejpam-6631	120	1	xk)(xk−1	xk)(xk−1	PROPN
ejpam-6631	120	2	−	−	PROPN
ejpam-6631	120	3	xk−2	xk−2	PROPN
ejpam-6631	120	4	)	)	PUNCT
ejpam-6631	120	5	gk−1	gk−1	PROPN
ejpam-6631	120	6	+	+	CCONJ
ejpam-6631	120	7	(	(	PUNCT
ejpam-6631	120	8	x−	x−	PROPN
ejpam-6631	120	9	xk−1)(x−	xk−1)(x−	PROPN
ejpam-6631	120	10	xk−1	xk−1	PROPN
ejpam-6631	120	11	)	)	PUNCT
ejpam-6631	120	12	(	(	PUNCT
ejpam-6631	120	13	xk−2	xk−2	PROPN
ejpam-6631	120	14	−	−	PROPN
ejpam-6631	120	15	xk)(xk−2	xk)(xk−2	PROPN
ejpam-6631	120	16	−	−	PROPN
ejpam-6631	120	17	xk−1	xk−1	PROPN
ejpam-6631	120	18	)	)	PUNCT
ejpam-6631	120	19	gk−2	gk−2	PROPN
ejpam-6631	120	20	]	]	PUNCT
ejpam-6631	120	21	dx	dx	PROPN
ejpam-6631	121	1	−	−	PROPN
ejpam-6631	121	2	∫	∫	PROPN
ejpam-6631	121	3	xk	xk	PROPN
ejpam-6631	121	4	0	0	PROPN
ejpam-6631	122	1	(	(	PUNCT
ejpam-6631	122	2	xk	xk	PROPN
ejpam-6631	122	3	−	−	PROPN
ejpam-6631	122	4	w)β−1mγ	w)β−1mγ	PROPN
ejpam-6631	122	5	α	α	PROPN
ejpam-6631	122	6	,	,	PUNCT
ejpam-6631	122	7	β(τ(xk	β(τ(xk	INTJ
ejpam-6631	122	8	−	−	NOUN
ejpam-6631	122	9	w)α	w)α	SCONJ
ejpam-6631	122	10	)	)	PUNCT
ejpam-6631	122	11	[	[	PUNCT
ejpam-6631	122	12	(	(	PUNCT
ejpam-6631	122	13	x−	x−	PROPN
ejpam-6631	122	14	xk−1)(x−	xk−1)(x−	PROPN
ejpam-6631	122	15	xk−2	xk−2	PROPN
ejpam-6631	122	16	)	)	PUNCT
ejpam-6631	122	17	(	(	PUNCT
ejpam-6631	122	18	xk	xk	PROPN
ejpam-6631	122	19	−	−	PROPN
ejpam-6631	122	20	xk−1)(xk	xk−1)(xk	PROPN
ejpam-6631	123	1	−	−	PROPN
ejpam-6631	123	2	xk−2	xk−2	PROPN
ejpam-6631	123	3	)	)	PUNCT
ejpam-6631	123	4	gk	gk	PROPN
ejpam-6631	123	5	+	+	CCONJ
ejpam-6631	123	6	(	(	PUNCT
ejpam-6631	123	7	x−	x−	PROPN
ejpam-6631	123	8	xk)(x−	xk)(x−	PROPN
ejpam-6631	123	9	xk−2	xk−2	PROPN
ejpam-6631	123	10	)	)	PUNCT
ejpam-6631	123	11	(	(	PUNCT
ejpam-6631	123	12	xk−1	xk−1	PROPN
ejpam-6631	123	13	−	−	PROPN
ejpam-6631	124	1	xk)(xk−1	xk)(xk−1	PROPN
ejpam-6631	124	2	−	−	PROPN
ejpam-6631	124	3	xk−2	xk−2	PROPN
ejpam-6631	124	4	)	)	PUNCT
ejpam-6631	124	5	gk−1	gk−1	PROPN
ejpam-6631	124	6	+	+	CCONJ
ejpam-6631	124	7	(	(	PUNCT
ejpam-6631	124	8	x−	x−	PROPN
ejpam-6631	124	9	xk−1)(x−	xk−1)(x−	PROPN
ejpam-6631	124	10	xk−1	xk−1	PROPN
ejpam-6631	124	11	)	)	PUNCT
ejpam-6631	124	12	(	(	PUNCT
ejpam-6631	124	13	xk−2	xk−2	PROPN
ejpam-6631	124	14	−	−	PROPN
ejpam-6631	124	15	xk)(xk−2	xk)(xk−2	PROPN
ejpam-6631	124	16	−	−	PROPN
ejpam-6631	124	17	xk−1	xk−1	PROPN
ejpam-6631	124	18	)	)	PUNCT
ejpam-6631	124	19	gk−2	gk−2	PROPN
ejpam-6631	124	20	]	]	PUNCT
ejpam-6631	124	21	dx	dx	PROPN
ejpam-6631	124	22	.	.	PUNCT
ejpam-6631	125	1	(	(	PUNCT
ejpam-6631	125	2	19	19	NUM
ejpam-6631	125	3	)	)	PUNCT
ejpam-6631	125	4	the	the	DET
ejpam-6631	125	5	first	first	ADJ
ejpam-6631	125	6	integral	integral	NOUN
ejpam-6631	125	7	presented	present	VERB
ejpam-6631	125	8	in	in	ADP
ejpam-6631	125	9	equation	equation	NOUN
ejpam-6631	125	10	(	(	PUNCT
ejpam-6631	125	11	18	18	NUM
ejpam-6631	125	12	)	)	PUNCT
ejpam-6631	125	13	can	can	AUX
ejpam-6631	125	14	be	be	AUX
ejpam-6631	125	15	expressed	express	VERB
ejpam-6631	125	16	in	in	ADP
ejpam-6631	125	17	a	a	DET
ejpam-6631	125	18	more	more	ADV
ejpam-6631	125	19	concise	concise	ADJ
ejpam-6631	125	20	form	form	NOUN
ejpam-6631	125	21	as	as	SCONJ
ejpam-6631	125	22	follows	follow	VERB
ejpam-6631	125	23	:	:	PUNCT
ejpam-6631	126	1	m.	m.	NOUN
ejpam-6631	126	2	abdel	abdel	PROPN
ejpam-6631	126	3	aal	aal	PROPN
ejpam-6631	126	4	et	et	PROPN
ejpam-6631	126	5	al	al	PROPN
ejpam-6631	126	6	.	.	PUNCT
ejpam-6631	126	7	/	/	SYM
ejpam-6631	126	8	eur	eur	PROPN
ejpam-6631	126	9	.	.	PUNCT
ejpam-6631	127	1	j.	j.	PROPN
ejpam-6631	127	2	pure	pure	PROPN
ejpam-6631	127	3	appl	appl	PROPN
ejpam-6631	127	4	.	.	PROPN
ejpam-6631	127	5	math	math	PROPN
ejpam-6631	127	6	,	,	PUNCT
ejpam-6631	127	7	18	18	NUM
ejpam-6631	127	8	(	(	PUNCT
ejpam-6631	127	9	4	4	NUM
ejpam-6631	127	10	)	)	PUNCT
ejpam-6631	127	11	(	(	PUNCT
ejpam-6631	127	12	2025	2025	NUM
ejpam-6631	127	13	)	)	PUNCT
ejpam-6631	127	14	,	,	PUNCT
ejpam-6631	127	15	6631	6631	NUM
ejpam-6631	127	16	7	7	NUM
ejpam-6631	127	17	of	of	ADP
ejpam-6631	127	18	20	20	NUM
ejpam-6631	127	19	∫	∫	NOUN
ejpam-6631	127	20	xk+1	xk+1	PROPN
ejpam-6631	127	21	0	0	NUM
ejpam-6631	128	1	(	(	PUNCT
ejpam-6631	128	2	xk+1	xk+1	NUM
ejpam-6631	128	3	−	−	PROPN
ejpam-6631	128	4	w)β−1mγ	w)β−1mγ	PROPN
ejpam-6631	128	5	α	α	PRON
ejpam-6631	128	6	,	,	PUNCT
ejpam-6631	128	7	β(τ(xk+1	β(τ(xk+1	VERB
ejpam-6631	128	8	−	−	PRON
ejpam-6631	128	9	w)α	w)α	SCONJ
ejpam-6631	128	10	)	)	PUNCT
ejpam-6631	128	11	[	[	PUNCT
ejpam-6631	128	12	(	(	PUNCT
ejpam-6631	128	13	x−	x−	PROPN
ejpam-6631	128	14	xk−1)(x−	xk−1)(x−	PROPN
ejpam-6631	128	15	xk−2	xk−2	PROPN
ejpam-6631	128	16	)	)	PUNCT
ejpam-6631	128	17	(	(	PUNCT
ejpam-6631	128	18	xk	xk	PROPN
ejpam-6631	128	19	−	−	PROPN
ejpam-6631	128	20	xk−1)(xk	xk−1)(xk	PROPN
ejpam-6631	129	1	−	−	PROPN
ejpam-6631	129	2	xk−2	xk−2	PROPN
ejpam-6631	129	3	)	)	PUNCT
ejpam-6631	129	4	gk	gk	PROPN
ejpam-6631	129	5	+	+	CCONJ
ejpam-6631	129	6	(	(	PUNCT
ejpam-6631	129	7	x−	x−	PROPN
ejpam-6631	129	8	xk)(x−	xk)(x−	PROPN
ejpam-6631	129	9	xk−2	xk−2	PROPN
ejpam-6631	129	10	)	)	PUNCT
ejpam-6631	129	11	(	(	PUNCT
ejpam-6631	129	12	xk−1	xk−1	PROPN
ejpam-6631	129	13	−	−	PROPN
ejpam-6631	130	1	xk)(xk−1	xk)(xk−1	PROPN
ejpam-6631	130	2	−	−	PROPN
ejpam-6631	130	3	xk−2	xk−2	PROPN
ejpam-6631	130	4	)	)	PUNCT
ejpam-6631	130	5	gk−1	gk−1	PROPN
ejpam-6631	130	6	+	+	CCONJ
ejpam-6631	130	7	(	(	PUNCT
ejpam-6631	130	8	x−	x−	PROPN
ejpam-6631	130	9	xk−1)(x−	xk−1)(x−	PROPN
ejpam-6631	130	10	xk−1	xk−1	PROPN
ejpam-6631	130	11	)	)	PUNCT
ejpam-6631	130	12	(	(	PUNCT
ejpam-6631	130	13	xk−2	xk−2	PROPN
ejpam-6631	130	14	−	−	PROPN
ejpam-6631	130	15	xk)(xk−2	xk)(xk−2	PROPN
ejpam-6631	130	16	−	−	PROPN
ejpam-6631	130	17	xk−1	xk−1	PROPN
ejpam-6631	130	18	)	)	PUNCT
ejpam-6631	130	19	gk−2	gk−2	PROPN
ejpam-6631	130	20	]	]	PUNCT
ejpam-6631	130	21	dx	dx	PROPN
ejpam-6631	131	1	=	=	PUNCT
ejpam-6631	131	2	[	[	PUNCT
ejpam-6631	131	3	gk	gk	NOUN
ejpam-6631	131	4	2h2	2h2	NUM
ejpam-6631	131	5	∫	∫	PROPN
ejpam-6631	131	6	xk+1	xk+1	PROPN
ejpam-6631	131	7	0	0	NUM
ejpam-6631	132	1	(	(	PUNCT
ejpam-6631	132	2	xk+1	xk+1	NUM
ejpam-6631	132	3	−	−	PROPN
ejpam-6631	132	4	w)β−1mγ	w)β−1mγ	PROPN
ejpam-6631	132	5	α	α	PRON
ejpam-6631	132	6	,	,	PUNCT
ejpam-6631	132	7	β(τ(xk+1	β(τ(xk+1	VERB
ejpam-6631	132	8	−	−	X
ejpam-6631	132	9	w)α)(x−	w)α)(x−	X
ejpam-6631	132	10	xk−1)(x−	xk−1)(x−	NUM
ejpam-6631	133	1	xk−2)dx	xk−2)dx	NUM
ejpam-6631	133	2	−	−	NUM
ejpam-6631	133	3	gk−1	gk−1	PROPN
ejpam-6631	133	4	h2	h2	PROPN
ejpam-6631	133	5	∫	∫	PROPN
ejpam-6631	133	6	xk+1	xk+1	PROPN
ejpam-6631	133	7	0	0	NUM
ejpam-6631	133	8	(	(	PUNCT
ejpam-6631	133	9	xk+1	xk+1	NUM
ejpam-6631	133	10	−	−	PROPN
ejpam-6631	133	11	w)β−1mγ	w)β−1mγ	PROPN
ejpam-6631	133	12	α	α	PRON
ejpam-6631	133	13	,	,	PUNCT
ejpam-6631	133	14	β(τ(xk+1	β(τ(xk+1	VERB
ejpam-6631	133	15	−	−	X
ejpam-6631	133	16	w)α)(x−	w)α)(x−	X
ejpam-6631	133	17	xk−1)(x−	xk−1)(x−	NUM
ejpam-6631	134	1	xk−2)dx	xk−2)dx	PROPN
ejpam-6631	135	1	+	+	CCONJ
ejpam-6631	135	2	gk−1	gk−1	PROPN
ejpam-6631	135	3	h2	h2	NOUN
ejpam-6631	135	4	∫	∫	NOUN
ejpam-6631	135	5	xk+1	xk+1	PROPN
ejpam-6631	135	6	0	0	NUM
ejpam-6631	136	1	(	(	PUNCT
ejpam-6631	136	2	xk+1	xk+1	NUM
ejpam-6631	136	3	−	−	PROPN
ejpam-6631	136	4	w)β−1mγ	w)β−1mγ	PROPN
ejpam-6631	136	5	α	α	PRON
ejpam-6631	136	6	,	,	PUNCT
ejpam-6631	136	7	β(τ(xk+1	β(τ(xk+1	VERB
ejpam-6631	136	8	−	−	PUNCT
ejpam-6631	136	9	w)α)(x−	w)α)(x−	X
ejpam-6631	136	10	xk−1)(x−	xk−1)(x−	PRON
ejpam-6631	136	11	xk−1	xk−1	PROPN
ejpam-6631	136	12	)	)	PUNCT
ejpam-6631	136	13	]	]	PUNCT
ejpam-6631	136	14	dx	dx	PROPN
ejpam-6631	136	15	=	=	SYM
ejpam-6631	136	16	gx	gx	PROPN
ejpam-6631	136	17	2h2	2h2	NUM
ejpam-6631	136	18	b1	b1	PROPN
ejpam-6631	136	19	−	−	PROPN
ejpam-6631	136	20	gx	gx	PROPN
ejpam-6631	136	21	h2	h2	PROPN
ejpam-6631	136	22	b2	b2	NOUN
ejpam-6631	136	23	+	+	CCONJ
ejpam-6631	136	24	gx−2	gx−2	PROPN
ejpam-6631	136	25	2h2	2h2	NUM
ejpam-6631	136	26	b3	b3	NOUN
ejpam-6631	136	27	.	.	PUNCT
ejpam-6631	137	1	(	(	PUNCT
ejpam-6631	137	2	20	20	X
ejpam-6631	137	3	)	)	PUNCT
ejpam-6631	137	4	setting	set	VERB
ejpam-6631	137	5	∫	∫	PROPN
ejpam-6631	137	6	x	x	SYM
ejpam-6631	137	7	0	0	NUM
ejpam-6631	137	8	(	(	PUNCT
ejpam-6631	137	9	x−	x−	PROPN
ejpam-6631	137	10	w)β−1mγ	w)β−1mγ	PROPN
ejpam-6631	137	11	α	α	PROPN
ejpam-6631	137	12	,	,	PUNCT
ejpam-6631	137	13	β(τ(x−	β(τ(x−	NUM
ejpam-6631	137	14	w)α)pu−1dp	w)α)pu−1dp	NOUN
ejpam-6631	137	15	=	=	PUNCT
ejpam-6631	137	16	γ(u)xβ+u−1mγ	γ(u)xβ+u−1mγ	PROPN
ejpam-6631	137	17	α	α	X
ejpam-6631	137	18	,	,	PUNCT
ejpam-6631	137	19	β(τ(x−	β(τ(x−	NUM
ejpam-6631	137	20	w)α	w)α	NOUN
ejpam-6631	137	21	)	)	PUNCT
ejpam-6631	137	22	,	,	PUNCT
ejpam-6631	137	23	so	so	SCONJ
ejpam-6631	137	24	that	that	SCONJ
ejpam-6631	137	25	the	the	DET
ejpam-6631	137	26	specific	specific	ADJ
ejpam-6631	137	27	formula	formula	NOUN
ejpam-6631	137	28	is	be	AUX
ejpam-6631	137	29	:	:	PUNCT
ejpam-6631	137	30	z1	z1	PROPN
ejpam-6631	137	31	=	=	SYM
ejpam-6631	137	32	∫	∫	PROPN
ejpam-6631	137	33	xk+1	xk+1	PROPN
ejpam-6631	137	34	0	0	NUM
ejpam-6631	138	1	(	(	PUNCT
ejpam-6631	138	2	xk+1	xk+1	NUM
ejpam-6631	138	3	−	−	PROPN
ejpam-6631	138	4	w)β−1mγ	w)β−1mγ	PROPN
ejpam-6631	138	5	α	α	PRON
ejpam-6631	138	6	,	,	PUNCT
ejpam-6631	138	7	β(τ(xk+1	β(τ(xk+1	VERB
ejpam-6631	138	8	−	−	X
ejpam-6631	138	9	w)α)(x−	w)α)(x−	X
ejpam-6631	138	10	xk−1)(x−	xk−1)(x−	NUM
ejpam-6631	138	11	xx−2)dx	xx−2)dx	PUNCT
ejpam-6631	139	1	=	=	PUNCT
ejpam-6631	139	2	γ(3)(xk+1	γ(3)(xk+1	VERB
ejpam-6631	139	3	−	−	NOUN
ejpam-6631	139	4	w)β+2mγ	w)β+2mγ	NOUN
ejpam-6631	139	5	α	α	X
ejpam-6631	139	6	,	,	PUNCT
ejpam-6631	139	7	β+3(τ(xk+1	β+3(τ(xk+1	NOUN
ejpam-6631	139	8	−	−	NOUN
ejpam-6631	139	9	w)α)−	w)α)−	VERB
ejpam-6631	139	10	(	(	PUNCT
ejpam-6631	139	11	xk−2	xk−2	PROPN
ejpam-6631	139	12	+	+	PROPN
ejpam-6631	139	13	xk−1)γ(2)(xk+1	xk−1)γ(2)(xk+1	NOUN
ejpam-6631	139	14	)	)	PUNCT
ejpam-6631	139	15	β+1mγ	β+1mγ	PART
ejpam-6631	139	16	α	α	NOUN
ejpam-6631	139	17	,	,	PUNCT
ejpam-6631	139	18	β(τ(xk+1	β(τ(xk+1	VERB
ejpam-6631	139	19	−	−	PRON
ejpam-6631	139	20	w)α	w)α	SCONJ
ejpam-6631	139	21	)	)	PUNCT
ejpam-6631	140	1	+	+	CCONJ
ejpam-6631	140	2	xk−1xk−2γ(1)(xk+1	xk−1xk−2γ(1)(xk+1	PROPN
ejpam-6631	140	3	)	)	PUNCT
ejpam-6631	140	4	βmγ	βmγ	NOUN
ejpam-6631	141	1	α	α	NOUN
ejpam-6631	141	2	,	,	PUNCT
ejpam-6631	141	3	β(τ(xk+1	β(τ(xk+1	VERB
ejpam-6631	141	4	−	−	PRON
ejpam-6631	141	5	w)α	w)α	SCONJ
ejpam-6631	141	6	)	)	PUNCT
ejpam-6631	141	7	=	=	SYM
ejpam-6631	142	1	(	(	PUNCT
ejpam-6631	142	2	k	k	PROPN
ejpam-6631	142	3	+	+	CCONJ
ejpam-6631	142	4	1)βhβ+2	1)βhβ+2	PROPN
ejpam-6631	142	5	[	[	PUNCT
ejpam-6631	142	6	2(k	2(k	NUM
ejpam-6631	142	7	+	+	CCONJ
ejpam-6631	142	8	1)2mγ	1)2mγ	NUM
ejpam-6631	142	9	α	α	NOUN
ejpam-6631	142	10	,	,	PUNCT
ejpam-6631	142	11	β+3(τ(xh+	β+3(τ(xh+	PROPN
ejpam-6631	142	12	h)α)−	h)α)−	X
ejpam-6631	142	13	(	(	PUNCT
ejpam-6631	142	14	2k	2k	NOUN
ejpam-6631	142	15	−	−	PROPN
ejpam-6631	142	16	3)(k	3)(k	NUM
ejpam-6631	143	1	+	+	NUM
ejpam-6631	143	2	1)mγ	1)mγ	NUM
ejpam-6631	143	3	α	α	NOUN
ejpam-6631	143	4	,	,	PUNCT
ejpam-6631	143	5	β+2(τ(xh+	β+2(τ(xh+	PROPN
ejpam-6631	143	6	h)α	h)α	NOUN
ejpam-6631	143	7	)	)	PUNCT
ejpam-6631	144	1	+	+	CCONJ
ejpam-6631	144	2	(	(	PUNCT
ejpam-6631	144	3	k	k	X
ejpam-6631	144	4	−	−	PROPN
ejpam-6631	144	5	2)(k	2)(k	NUM
ejpam-6631	145	1	−	−	PROPN
ejpam-6631	146	1	1)mγ	1)mγ	NUM
ejpam-6631	146	2	α	α	PROPN
ejpam-6631	146	3	,	,	PUNCT
ejpam-6631	146	4	β+1(τ(xh+	β+1(τ(xh+	PROPN
ejpam-6631	146	5	h)α	h)α	NOUN
ejpam-6631	146	6	]	]	PUNCT
ejpam-6631	146	7	.	.	PUNCT
ejpam-6631	147	1	(	(	PUNCT
ejpam-6631	147	2	21	21	NUM
ejpam-6631	147	3	)	)	PUNCT
ejpam-6631	147	4	by	by	ADP
ejpam-6631	147	5	employing	employ	VERB
ejpam-6631	147	6	the	the	DET
ejpam-6631	147	7	same	same	ADJ
ejpam-6631	147	8	established	establish	VERB
ejpam-6631	147	9	procedure	procedure	NOUN
ejpam-6631	147	10	,	,	PUNCT
ejpam-6631	147	11	we	we	PRON
ejpam-6631	147	12	successfully	successfully	ADV
ejpam-6631	147	13	obtained	obtain	VERB
ejpam-6631	147	14	.	.	PUNCT
ejpam-6631	148	1	z2	z2	PROPN
ejpam-6631	148	2	=	=	SYM
ejpam-6631	148	3	(	(	PUNCT
ejpam-6631	148	4	k	k	PROPN
ejpam-6631	148	5	+	+	CCONJ
ejpam-6631	148	6	1)βhβ+2	1)βhβ+2	PROPN
ejpam-6631	148	7	[	[	PUNCT
ejpam-6631	148	8	2(k	2(k	NUM
ejpam-6631	149	1	+	+	CCONJ
ejpam-6631	149	2	1)2mγ	1)2mγ	NUM
ejpam-6631	149	3	α	α	NOUN
ejpam-6631	149	4	,	,	PUNCT
ejpam-6631	149	5	β+3(τ(xh+	β+3(τ(xh+	PROPN
ejpam-6631	149	6	h)α)−	h)α)−	X
ejpam-6631	149	7	(	(	PUNCT
ejpam-6631	149	8	2k	2k	NOUN
ejpam-6631	149	9	−	−	PROPN
ejpam-6631	149	10	2)(k	2)(k	NUM
ejpam-6631	150	1	+	+	CCONJ
ejpam-6631	150	2	1)mγ	1)mγ	NUM
ejpam-6631	150	3	α	α	NOUN
ejpam-6631	150	4	,	,	PUNCT
ejpam-6631	150	5	β+2(τ(xh+	β+2(τ(xh+	PROPN
ejpam-6631	150	6	h)α	h)α	NOUN
ejpam-6631	150	7	)	)	PUNCT
ejpam-6631	151	1	+	+	CCONJ
ejpam-6631	151	2	(	(	PUNCT
ejpam-6631	151	3	k	k	X
ejpam-6631	151	4	−	−	PROPN
ejpam-6631	151	5	2)(k	2)(k	NUM
ejpam-6631	152	1	−	−	PROPN
ejpam-6631	153	1	1)mγ	1)mγ	NUM
ejpam-6631	153	2	α	α	PROPN
ejpam-6631	153	3	,	,	PUNCT
ejpam-6631	153	4	β+1(τ(xh+	β+1(τ(xh+	PROPN
ejpam-6631	153	5	h)α	h)α	NOUN
ejpam-6631	153	6	]	]	PUNCT
ejpam-6631	153	7	.	.	PUNCT
ejpam-6631	154	1	(	(	PUNCT
ejpam-6631	154	2	22	22	NUM
ejpam-6631	154	3	)	)	PUNCT
ejpam-6631	154	4	and	and	CCONJ
ejpam-6631	154	5	ditto	ditto	NOUN
ejpam-6631	154	6	to	to	ADP
ejpam-6631	154	7	;	;	PUNCT
ejpam-6631	154	8	m.	m.	NOUN
ejpam-6631	154	9	abdel	abdel	PROPN
ejpam-6631	154	10	aal	aal	PROPN
ejpam-6631	154	11	et	et	PROPN
ejpam-6631	154	12	al	al	PROPN
ejpam-6631	154	13	.	.	PUNCT
ejpam-6631	154	14	/	/	SYM
ejpam-6631	154	15	eur	eur	PROPN
ejpam-6631	154	16	.	.	PUNCT
ejpam-6631	155	1	j.	j.	PROPN
ejpam-6631	155	2	pure	pure	PROPN
ejpam-6631	155	3	appl	appl	PROPN
ejpam-6631	155	4	.	.	PROPN
ejpam-6631	155	5	math	math	PROPN
ejpam-6631	155	6	,	,	PUNCT
ejpam-6631	155	7	18	18	NUM
ejpam-6631	155	8	(	(	PUNCT
ejpam-6631	155	9	4	4	NUM
ejpam-6631	155	10	)	)	PUNCT
ejpam-6631	155	11	(	(	PUNCT
ejpam-6631	155	12	2025	2025	NUM
ejpam-6631	155	13	)	)	PUNCT
ejpam-6631	155	14	,	,	PUNCT
ejpam-6631	155	15	6631	6631	NUM
ejpam-6631	155	16	8	8	NUM
ejpam-6631	155	17	of	of	ADP
ejpam-6631	155	18	20	20	NUM
ejpam-6631	155	19	z3	z3	NOUN
ejpam-6631	155	20	=	=	PUNCT
ejpam-6631	155	21	(	(	PUNCT
ejpam-6631	155	22	k	k	PROPN
ejpam-6631	155	23	+	+	CCONJ
ejpam-6631	155	24	1)βhβ+2	1)βhβ+2	PROPN
ejpam-6631	155	25	[	[	PUNCT
ejpam-6631	155	26	2(k	2(k	NUM
ejpam-6631	156	1	+	+	CCONJ
ejpam-6631	156	2	1)2mγ	1)2mγ	NUM
ejpam-6631	156	3	α	α	NOUN
ejpam-6631	156	4	,	,	PUNCT
ejpam-6631	156	5	β+3(τ(xh+	β+3(τ(xh+	PROPN
ejpam-6631	156	6	h)α)−	h)α)−	X
ejpam-6631	156	7	(	(	PUNCT
ejpam-6631	156	8	2k	2k	NOUN
ejpam-6631	156	9	−	−	PROPN
ejpam-6631	156	10	1)(k	1)(k	NUM
ejpam-6631	157	1	+	+	CCONJ
ejpam-6631	157	2	1)mγ	1)mγ	NUM
ejpam-6631	157	3	α	α	NOUN
ejpam-6631	157	4	,	,	PUNCT
ejpam-6631	157	5	β+2(τ(xh+	β+2(τ(xh+	PROPN
ejpam-6631	157	6	h)α	h)α	NOUN
ejpam-6631	157	7	)	)	PUNCT
ejpam-6631	158	1	+	+	CCONJ
ejpam-6631	158	2	(	(	PUNCT
ejpam-6631	158	3	k	k	X
ejpam-6631	158	4	−	−	PROPN
ejpam-6631	158	5	2)(k	2)(k	NUM
ejpam-6631	159	1	−	−	PROPN
ejpam-6631	160	1	1)mγ	1)mγ	NUM
ejpam-6631	160	2	α	α	PROPN
ejpam-6631	160	3	,	,	PUNCT
ejpam-6631	160	4	β+1(τ(xh+	β+1(τ(xh+	PROPN
ejpam-6631	160	5	h)α	h)α	NOUN
ejpam-6631	160	6	]	]	PUNCT
ejpam-6631	160	7	.	.	PUNCT
ejpam-6631	161	1	(	(	PUNCT
ejpam-6631	161	2	23	23	NUM
ejpam-6631	161	3	)	)	PUNCT
ejpam-6631	161	4	using	use	VERB
ejpam-6631	161	5	the	the	DET
ejpam-6631	161	6	established	establish	VERB
ejpam-6631	161	7	procedure	procedure	NOUN
ejpam-6631	161	8	,	,	PUNCT
ejpam-6631	161	9	we	we	PRON
ejpam-6631	161	10	successfully	successfully	ADV
ejpam-6631	161	11	obtained	obtain	VERB
ejpam-6631	161	12	the	the	DET
ejpam-6631	161	13	second	second	ADJ
ejpam-6631	161	14	integral	integral	ADJ
ejpam-6631	161	15	in	in	ADP
ejpam-6631	161	16	equation	equation	NOUN
ejpam-6631	161	17	(	(	PUNCT
ejpam-6631	161	18	18	18	NUM
ejpam-6631	161	19	)	)	PUNCT
ejpam-6631	161	20	,	,	PUNCT
ejpam-6631	161	21	which	which	PRON
ejpam-6631	161	22	can	can	AUX
ejpam-6631	161	23	be	be	AUX
ejpam-6631	161	24	rewritten	rewrite	VERB
ejpam-6631	161	25	as	as	ADP
ejpam-6631	161	26	:	:	PUNCT
ejpam-6631	161	27	∫	∫	PROPN
ejpam-6631	161	28	xk+1	xk+1	PROPN
ejpam-6631	161	29	0	0	NUM
ejpam-6631	162	1	(	(	PUNCT
ejpam-6631	162	2	xk+1	xk+1	NUM
ejpam-6631	162	3	−	−	PROPN
ejpam-6631	162	4	w)β−1mγ	w)β−1mγ	PROPN
ejpam-6631	162	5	α	α	PRON
ejpam-6631	162	6	,	,	PUNCT
ejpam-6631	162	7	β(τ(xk+1	β(τ(xk+1	VERB
ejpam-6631	162	8	−	−	PRON
ejpam-6631	162	9	w)α	w)α	SCONJ
ejpam-6631	162	10	)	)	PUNCT
ejpam-6631	162	11	[	[	PUNCT
ejpam-6631	162	12	(	(	PUNCT
ejpam-6631	162	13	x−	x−	PROPN
ejpam-6631	162	14	xk−1)(x−	xk−1)(x−	PROPN
ejpam-6631	162	15	xk−2	xk−2	PROPN
ejpam-6631	162	16	)	)	PUNCT
ejpam-6631	162	17	(	(	PUNCT
ejpam-6631	162	18	xk	xk	PROPN
ejpam-6631	162	19	−	−	PROPN
ejpam-6631	162	20	xk−1)(xk	xk−1)(xk	PROPN
ejpam-6631	163	1	−	−	PROPN
ejpam-6631	163	2	xk−2	xk−2	PROPN
ejpam-6631	163	3	)	)	PUNCT
ejpam-6631	163	4	gk	gk	PROPN
ejpam-6631	163	5	+	+	CCONJ
ejpam-6631	163	6	(	(	PUNCT
ejpam-6631	163	7	x−	x−	PROPN
ejpam-6631	163	8	xk)(x−	xk)(x−	PROPN
ejpam-6631	163	9	xk−2	xk−2	PROPN
ejpam-6631	163	10	)	)	PUNCT
ejpam-6631	163	11	(	(	PUNCT
ejpam-6631	163	12	xk−1	xk−1	PROPN
ejpam-6631	163	13	−	−	PROPN
ejpam-6631	164	1	xk)(xk−1	xk)(xk−1	PROPN
ejpam-6631	164	2	−	−	PROPN
ejpam-6631	164	3	xk−2	xk−2	PROPN
ejpam-6631	164	4	)	)	PUNCT
ejpam-6631	164	5	gk−1	gk−1	PROPN
ejpam-6631	164	6	+	+	CCONJ
ejpam-6631	164	7	(	(	PUNCT
ejpam-6631	164	8	x−	x−	PROPN
ejpam-6631	164	9	xk)(x−	xk)(x−	PROPN
ejpam-6631	164	10	xk−1	xk−1	PROPN
ejpam-6631	164	11	)	)	PUNCT
ejpam-6631	164	12	(	(	PUNCT
ejpam-6631	164	13	xk−2	xk−2	PROPN
ejpam-6631	164	14	−	−	PROPN
ejpam-6631	164	15	xk)(xk−2	xk)(xk−2	PROPN
ejpam-6631	164	16	−	−	PROPN
ejpam-6631	164	17	xk−1	xk−1	PROPN
ejpam-6631	164	18	)	)	PUNCT
ejpam-6631	164	19	gk−2	gk−2	PROPN
ejpam-6631	164	20	]	]	PUNCT
ejpam-6631	164	21	dx	dx	PROPN
ejpam-6631	165	1	=	=	PUNCT
ejpam-6631	165	2	[	[	PUNCT
ejpam-6631	165	3	gk	gk	NOUN
ejpam-6631	165	4	2h2	2h2	NUM
ejpam-6631	165	5	∫	∫	PROPN
ejpam-6631	165	6	xk+1	xk+1	PROPN
ejpam-6631	165	7	0	0	NUM
ejpam-6631	165	8	(	(	PUNCT
ejpam-6631	165	9	xk+1	xk+1	PROPN
ejpam-6631	165	10	−	−	PROPN
ejpam-6631	165	11	x)β−1mγ	x)β−1mγ	PROPN
ejpam-6631	165	12	α	α	PROPN
ejpam-6631	165	13	,	,	PUNCT
ejpam-6631	165	14	β(τ(xk+1	β(τ(xk+1	VERB
ejpam-6631	165	15	−	−	PROPN
ejpam-6631	165	16	w)α)(x−	w)α)(x−	X
ejpam-6631	165	17	xk−1)(x−	xk−1)(x−	NUM
ejpam-6631	165	18	xk−2)dx	xk−2)dx	NUM
ejpam-6631	165	19	−	−	NUM
ejpam-6631	165	20	gk−1	gk−1	PROPN
ejpam-6631	165	21	h2	h2	PROPN
ejpam-6631	165	22	∫	∫	PROPN
ejpam-6631	165	23	xk+1	xk+1	PROPN
ejpam-6631	165	24	0	0	NUM
ejpam-6631	166	1	(	(	PUNCT
ejpam-6631	166	2	xk+1	xk+1	PROPN
ejpam-6631	166	3	−	−	PROPN
ejpam-6631	166	4	x)β−1mγ	x)β−1mγ	PROPN
ejpam-6631	166	5	α	α	PROPN
ejpam-6631	166	6	,	,	PUNCT
ejpam-6631	166	7	β(τ(xk+1	β(τ(xk+1	VERB
ejpam-6631	166	8	−	−	X
ejpam-6631	166	9	w)α)(x−	w)α)(x−	X
ejpam-6631	166	10	xk−1)(x−	xk−1)(x−	NUM
ejpam-6631	166	11	xk−2)dx	xk−2)dx	PROPN
ejpam-6631	167	1	+	+	CCONJ
ejpam-6631	167	2	gk−1	gk−1	PROPN
ejpam-6631	167	3	2h2	2h2	NUM
ejpam-6631	167	4	∫	∫	PROPN
ejpam-6631	167	5	xk+1	xk+1	PROPN
ejpam-6631	167	6	0	0	NUM
ejpam-6631	168	1	(	(	PUNCT
ejpam-6631	168	2	xk+1	xk+1	PROPN
ejpam-6631	168	3	−	−	PROPN
ejpam-6631	168	4	x)β−1mγ	x)β−1mγ	PROPN
ejpam-6631	168	5	α	α	PROPN
ejpam-6631	168	6	,	,	PUNCT
ejpam-6631	168	7	β(τ(xk+1	β(τ(xk+1	VERB
ejpam-6631	168	8	−	−	PROPN
ejpam-6631	168	9	w)α)(x−	w)α)(x−	X
ejpam-6631	168	10	xk−1)(x−	xk−1)(x−	PRON
ejpam-6631	168	11	xk−1	xk−1	PROPN
ejpam-6631	168	12	)	)	PUNCT
ejpam-6631	168	13	]	]	PUNCT
ejpam-6631	169	1	dx	dx	PROPN
ejpam-6631	169	2	=	=	SYM
ejpam-6631	169	3	gx	gx	PROPN
ejpam-6631	169	4	2h2	2h2	NUM
ejpam-6631	169	5	b1	b1	PROPN
ejpam-6631	169	6	−	−	PROPN
ejpam-6631	169	7	gx	gx	PROPN
ejpam-6631	169	8	h2	h2	PROPN
ejpam-6631	169	9	b2	b2	NOUN
ejpam-6631	169	10	+	+	CCONJ
ejpam-6631	169	11	gx−2	gx−2	PROPN
ejpam-6631	169	12	2h2	2h2	NUM
ejpam-6631	169	13	b3	b3	NOUN
ejpam-6631	169	14	.	.	PUNCT
ejpam-6631	170	1	(	(	PUNCT
ejpam-6631	170	2	24	24	NUM
ejpam-6631	170	3	)	)	PUNCT
ejpam-6631	170	4	z4	z4	PROPN
ejpam-6631	170	5	=	=	SYM
ejpam-6631	170	6	(	(	PUNCT
ejpam-6631	170	7	k)βhβ+2	k)βhβ+2	PROPN
ejpam-6631	170	8	[	[	PUNCT
ejpam-6631	170	9	2k2mγ	2k2mγ	NUM
ejpam-6631	170	10	α	α	NUM
ejpam-6631	170	11	,	,	PUNCT
ejpam-6631	170	12	β+3(τ(xh	β+3(τ(xh	ADJ
ejpam-6631	170	13	)	)	PUNCT
ejpam-6631	170	14	α)−	α)−	PROPN
ejpam-6631	170	15	(	(	PUNCT
ejpam-6631	170	16	2k	2k	NOUN
ejpam-6631	170	17	−	−	PROPN
ejpam-6631	170	18	3)kmγ	3)kmγ	NUM
ejpam-6631	170	19	α	α	NOUN
ejpam-6631	170	20	,	,	PUNCT
ejpam-6631	170	21	β+2(τ(xh	β+2(τ(xh	PROPN
ejpam-6631	170	22	)	)	PUNCT
ejpam-6631	170	23	α	α	NOUN
ejpam-6631	170	24	)	)	PUNCT
ejpam-6631	170	25	+	+	CCONJ
ejpam-6631	170	26	(	(	PUNCT
ejpam-6631	170	27	k	k	X
ejpam-6631	170	28	−	−	PROPN
ejpam-6631	170	29	2)(k	2)(k	NUM
ejpam-6631	170	30	−	−	PROPN
ejpam-6631	171	1	1)mγ	1)mγ	NUM
ejpam-6631	171	2	α	α	NOUN
ejpam-6631	171	3	,	,	PUNCT
ejpam-6631	171	4	β+1(τ(xh	β+1(τ(xh	ADJ
ejpam-6631	171	5	)	)	PUNCT
ejpam-6631	171	6	α	α	NOUN
ejpam-6631	171	7	]	]	PUNCT
ejpam-6631	171	8	.	.	PUNCT
ejpam-6631	172	1	(	(	PUNCT
ejpam-6631	172	2	25	25	NUM
ejpam-6631	172	3	)	)	PUNCT
ejpam-6631	172	4	z5	z5	NOUN
ejpam-6631	172	5	=	=	SYM
ejpam-6631	172	6	(	(	PUNCT
ejpam-6631	172	7	k)βhβ+2	k)βhβ+2	PROPN
ejpam-6631	172	8	[	[	PUNCT
ejpam-6631	172	9	2k2mγ	2k2mγ	NUM
ejpam-6631	172	10	α	α	NUM
ejpam-6631	172	11	,	,	PUNCT
ejpam-6631	172	12	β+3(τ(xh	β+3(τ(xh	ADJ
ejpam-6631	172	13	)	)	PUNCT
ejpam-6631	172	14	α)−	α)−	PROPN
ejpam-6631	172	15	(	(	PUNCT
ejpam-6631	172	16	2k	2k	NOUN
ejpam-6631	172	17	−	−	PROPN
ejpam-6631	172	18	2)kmγ	2)kmγ	NUM
ejpam-6631	172	19	α	α	NOUN
ejpam-6631	172	20	,	,	PUNCT
ejpam-6631	172	21	β+2(τ(xh	β+2(τ(xh	PROPN
ejpam-6631	172	22	)	)	PUNCT
ejpam-6631	172	23	α	α	NOUN
ejpam-6631	172	24	)	)	PUNCT
ejpam-6631	173	1	+	+	CCONJ
ejpam-6631	173	2	(	(	PUNCT
ejpam-6631	173	3	k	k	X
ejpam-6631	173	4	−	−	PROPN
ejpam-6631	173	5	2)(k	2)(k	NUM
ejpam-6631	174	1	−	−	PROPN
ejpam-6631	175	1	1)mγ	1)mγ	NUM
ejpam-6631	175	2	α	α	NOUN
ejpam-6631	175	3	,	,	PUNCT
ejpam-6631	175	4	β+1(τ(xh	β+1(τ(xh	ADJ
ejpam-6631	175	5	)	)	PUNCT
ejpam-6631	175	6	α	α	NOUN
ejpam-6631	175	7	]	]	PUNCT
ejpam-6631	175	8	.	.	PUNCT
ejpam-6631	176	1	(	(	PUNCT
ejpam-6631	176	2	26	26	NUM
ejpam-6631	176	3	)	)	PUNCT
ejpam-6631	176	4	and	and	CCONJ
ejpam-6631	176	5	ditto	ditto	NOUN
ejpam-6631	176	6	to	to	ADP
ejpam-6631	176	7	;	;	PUNCT
ejpam-6631	176	8	z6	z6	PROPN
ejpam-6631	176	9	=	=	SYM
ejpam-6631	176	10	(	(	PUNCT
ejpam-6631	176	11	k)βhβ+2	k)βhβ+2	PROPN
ejpam-6631	176	12	[	[	PUNCT
ejpam-6631	176	13	2k2mγ	2k2mγ	NUM
ejpam-6631	176	14	α	α	NUM
ejpam-6631	176	15	,	,	PUNCT
ejpam-6631	176	16	β+3(τ(xh	β+3(τ(xh	ADJ
ejpam-6631	176	17	)	)	PUNCT
ejpam-6631	176	18	α)−	α)−	PROPN
ejpam-6631	176	19	(	(	PUNCT
ejpam-6631	176	20	2k	2k	NOUN
ejpam-6631	176	21	−	−	PROPN
ejpam-6631	176	22	2)kmγ	2)kmγ	NUM
ejpam-6631	176	23	α	α	NOUN
ejpam-6631	176	24	,	,	PUNCT
ejpam-6631	176	25	β+2(τ(xh	β+2(τ(xh	PROPN
ejpam-6631	176	26	)	)	PUNCT
ejpam-6631	176	27	α	α	NOUN
ejpam-6631	176	28	)	)	PUNCT
ejpam-6631	176	29	+	+	CCONJ
ejpam-6631	176	30	(	(	PUNCT
ejpam-6631	176	31	k	k	PROPN
ejpam-6631	176	32	−	−	PROPN
ejpam-6631	176	33	1)(k	1)(k	NUM
ejpam-6631	176	34	−	−	PROPN
ejpam-6631	176	35	1)mγ	1)mγ	NUM
ejpam-6631	176	36	α	α	NOUN
ejpam-6631	176	37	,	,	PUNCT
ejpam-6631	176	38	β+1(τ(xh	β+1(τ(xh	ADJ
ejpam-6631	176	39	)	)	PUNCT
ejpam-6631	176	40	α	α	NOUN
ejpam-6631	176	41	]	]	PUNCT
ejpam-6631	176	42	.	.	PUNCT
ejpam-6631	177	1	(	(	PUNCT
ejpam-6631	177	2	27	27	NUM
ejpam-6631	177	3	)	)	PUNCT
ejpam-6631	177	4	m.	m.	NOUN
ejpam-6631	177	5	abdel	abdel	PROPN
ejpam-6631	177	6	aal	aal	PROPN
ejpam-6631	177	7	et	et	PROPN
ejpam-6631	177	8	al	al	PROPN
ejpam-6631	177	9	.	.	PUNCT
ejpam-6631	177	10	/	/	SYM
ejpam-6631	177	11	eur	eur	PROPN
ejpam-6631	177	12	.	.	PUNCT
ejpam-6631	178	1	j.	j.	PROPN
ejpam-6631	178	2	pure	pure	PROPN
ejpam-6631	178	3	appl	appl	PROPN
ejpam-6631	178	4	.	.	PROPN
ejpam-6631	178	5	math	math	PROPN
ejpam-6631	178	6	,	,	PUNCT
ejpam-6631	178	7	18	18	NUM
ejpam-6631	178	8	(	(	PUNCT
ejpam-6631	178	9	4	4	NUM
ejpam-6631	178	10	)	)	PUNCT
ejpam-6631	178	11	(	(	PUNCT
ejpam-6631	178	12	2025	2025	NUM
ejpam-6631	178	13	)	)	PUNCT
ejpam-6631	178	14	,	,	PUNCT
ejpam-6631	178	15	6631	6631	NUM
ejpam-6631	178	16	9	9	NUM
ejpam-6631	178	17	of	of	ADP
ejpam-6631	178	18	20	20	NUM
ejpam-6631	178	19	a	a	DET
ejpam-6631	178	20	new	new	ADJ
ejpam-6631	178	21	method	method	NOUN
ejpam-6631	178	22	for	for	ADP
ejpam-6631	178	23	solving	solve	VERB
ejpam-6631	178	24	the	the	DET
ejpam-6631	178	25	prabhakar	prabhakar	NOUN
ejpam-6631	178	26	fractional	fractional	ADJ
ejpam-6631	178	27	differential	differential	NOUN
ejpam-6631	178	28	equation	equation	NOUN
ejpam-6631	178	29	is	be	AUX
ejpam-6631	178	30	presented	present	VERB
ejpam-6631	178	31	below	below	ADP
ejpam-6631	178	32	:	:	PUNCT
ejpam-6631	178	33	p(xk+1	p(xk+1	X
ejpam-6631	178	34	)	)	PUNCT
ejpam-6631	178	35	=	=	SYM
ejpam-6631	178	36	p(xk	p(xk	X
ejpam-6631	178	37	)	)	PUNCT
ejpam-6631	178	38	+	+	CCONJ
ejpam-6631	178	39	gx	gx	PROPN
ejpam-6631	178	40	2h2	2h2	NUM
ejpam-6631	178	41	b1	b1	PROPN
ejpam-6631	178	42	−	−	PROPN
ejpam-6631	178	43	gx	gx	PROPN
ejpam-6631	178	44	h2	h2	PROPN
ejpam-6631	178	45	b2	b2	NOUN
ejpam-6631	178	46	+	+	CCONJ
ejpam-6631	178	47	gx−2	gx−2	PROPN
ejpam-6631	178	48	2h2	2h2	NUM
ejpam-6631	178	49	b3	b3	NOUN
ejpam-6631	178	50	−	−	PROPN
ejpam-6631	178	51	gx−2	gx−2	PROPN
ejpam-6631	178	52	2h2	2h2	NUM
ejpam-6631	178	53	b4	b4	NOUN
ejpam-6631	178	54	+	+	CCONJ
ejpam-6631	178	55	gx−2	gx−2	PROPN
ejpam-6631	178	56	h2	h2	PROPN
ejpam-6631	178	57	b5	b5	PROPN
ejpam-6631	178	58	−	−	PROPN
ejpam-6631	179	1	gx−2	gx−2	VERB
ejpam-6631	179	2	2h2	2h2	NUM
ejpam-6631	179	3	b6	b6	NOUN
ejpam-6631	179	4	.	.	PUNCT
ejpam-6631	180	1	(	(	PUNCT
ejpam-6631	180	2	28	28	NUM
ejpam-6631	180	3	)	)	PUNCT
ejpam-6631	180	4	in	in	ADP
ejpam-6631	180	5	this	this	DET
ejpam-6631	180	6	paper	paper	NOUN
ejpam-6631	180	7	,	,	PUNCT
ejpam-6631	180	8	we	we	PRON
ejpam-6631	180	9	seek	seek	VERB
ejpam-6631	180	10	to	to	PART
ejpam-6631	180	11	address	address	VERB
ejpam-6631	180	12	the	the	DET
ejpam-6631	180	13	prabhakar	prabhakar	NOUN
ejpam-6631	180	14	fractional	fractional	ADJ
ejpam-6631	180	15	differential	differential	NOUN
ejpam-6631	180	16	equation	equation	NOUN
ejpam-6631	180	17	,	,	PUNCT
ejpam-6631	180	18	which	which	PRON
ejpam-6631	180	19	is	be	AUX
ejpam-6631	180	20	defined	define	VERB
ejpam-6631	180	21	as	as	SCONJ
ejpam-6631	180	22	follows	follow	VERB
ejpam-6631	180	23	:	:	PUNCT
ejpam-6631	180	24	dγ	dγ	ADP
ejpam-6631	180	25	α	α	X
ejpam-6631	180	26	,	,	PUNCT
ejpam-6631	180	27	β	β	X
ejpam-6631	180	28	,	,	PUNCT
ejpam-6631	180	29	τp(x	τp(x	NUM
ejpam-6631	180	30	)	)	PUNCT
ejpam-6631	180	31	=	=	SYM
ejpam-6631	180	32	f(x	f(x	PROPN
ejpam-6631	180	33	,	,	PUNCT
ejpam-6631	180	34	p(x	p(x	PROPN
ejpam-6631	180	35	)	)	PUNCT
ejpam-6631	180	36	)	)	PUNCT
ejpam-6631	180	37	,	,	PUNCT
ejpam-6631	180	38	(	(	PUNCT
ejpam-6631	180	39	29	29	NUM
ejpam-6631	180	40	)	)	PUNCT
ejpam-6631	180	41	subject	subject	NOUN
ejpam-6631	180	42	to	to	ADP
ejpam-6631	180	43	the	the	DET
ejpam-6631	180	44	initial	initial	ADJ
ejpam-6631	180	45	condition	condition	NOUN
ejpam-6631	180	46	p(0	p(0	NOUN
ejpam-6631	180	47	)	)	PUNCT
ejpam-6631	180	48	=	=	SYM
ejpam-6631	180	49	p0	p0	NOUN
ejpam-6631	180	50	,	,	PUNCT
ejpam-6631	180	51	where	where	SCONJ
ejpam-6631	180	52	τ	τ	PROPN
ejpam-6631	180	53	∈	∈	PROPN
ejpam-6631	180	54	r	r	NOUN
ejpam-6631	180	55	and	and	CCONJ
ejpam-6631	180	56	α	α	NOUN
ejpam-6631	180	57	,	,	PUNCT
ejpam-6631	180	58	β	β	X
ejpam-6631	180	59	,	,	PUNCT
ejpam-6631	180	60	γ	γ	PROPN
ejpam-6631	180	61	∈	∈	PROPN
ejpam-6631	180	62	(	(	PUNCT
ejpam-6631	180	63	0	0	NUM
ejpam-6631	180	64	,	,	PUNCT
ejpam-6631	180	65	1	1	NUM
ejpam-6631	180	66	)	)	PUNCT
ejpam-6631	180	67	.	.	PUNCT
ejpam-6631	181	1	4	4	X
ejpam-6631	181	2	.	.	X
ejpam-6631	181	3	convergence	convergence	NOUN
ejpam-6631	181	4	analysis	analysis	NOUN
ejpam-6631	181	5	in	in	ADP
ejpam-6631	181	6	this	this	DET
ejpam-6631	181	7	subsection	subsection	NOUN
ejpam-6631	181	8	,	,	PUNCT
ejpam-6631	181	9	we	we	PRON
ejpam-6631	181	10	present	present	VERB
ejpam-6631	181	11	the	the	DET
ejpam-6631	181	12	convergence	convergence	NOUN
ejpam-6631	181	13	analysis	analysis	NOUN
ejpam-6631	181	14	for	for	ADP
ejpam-6631	181	15	the	the	DET
ejpam-6631	181	16	proposed	propose	VERB
ejpam-6631	181	17	numerical	numerical	ADJ
ejpam-6631	181	18	methods	method	NOUN
ejpam-6631	181	19	addressing	address	VERB
ejpam-6631	181	20	the	the	DET
ejpam-6631	181	21	prabhakar	prabhakar	NOUN
ejpam-6631	181	22	fractional	fractional	ADJ
ejpam-6631	181	23	differential	differential	NOUN
ejpam-6631	181	24	equation	equation	NOUN
ejpam-6631	181	25	.	.	PUNCT
ejpam-6631	182	1	the	the	DET
ejpam-6631	182	2	following	follow	VERB
ejpam-6631	182	3	theorem	theorem	ADJ
ejpam-6631	182	4	summarizes	summarize	NOUN
ejpam-6631	182	5	our	our	PRON
ejpam-6631	182	6	findings	finding	NOUN
ejpam-6631	182	7	.	.	PUNCT
ejpam-6631	183	1	theorem	theorem	NOUN
ejpam-6631	183	2	1	1	NUM
ejpam-6631	183	3	.	.	PUNCT
ejpam-6631	184	1	let	let	VERB
ejpam-6631	184	2	p(x	p(x	PROPN
ejpam-6631	184	3	)	)	PUNCT
ejpam-6631	184	4	represent	represent	VERB
ejpam-6631	184	5	the	the	DET
ejpam-6631	184	6	solution	solution	NOUN
ejpam-6631	184	7	to	to	ADP
ejpam-6631	184	8	the	the	DET
ejpam-6631	184	9	initial	initial	ADJ
ejpam-6631	184	10	value	value	NOUN
ejpam-6631	184	11	problem	problem	NOUN
ejpam-6631	184	12	outlined	outline	VERB
ejpam-6631	184	13	in	in	ADP
ejpam-6631	184	14	equation	equation	NOUN
ejpam-6631	184	15	(	(	PUNCT
ejpam-6631	184	16	29	29	NUM
ejpam-6631	184	17	)	)	PUNCT
ejpam-6631	184	18	.	.	PUNCT
ejpam-6631	185	1	the	the	DET
ejpam-6631	185	2	error	error	NOUN
ejpam-6631	185	3	function	function	NOUN
ejpam-6631	185	4	associated	associate	VERB
ejpam-6631	185	5	with	with	ADP
ejpam-6631	185	6	this	this	DET
ejpam-6631	185	7	solution	solution	NOUN
ejpam-6631	185	8	is	be	AUX
ejpam-6631	185	9	denoted	denote	VERB
ejpam-6631	185	10	as	as	ADP
ejpam-6631	185	11	ℜ(t	ℜ(t	X
ejpam-6631	185	12	,	,	PUNCT
ejpam-6631	185	13	β	β	X
ejpam-6631	185	14	,	,	PUNCT
ejpam-6631	185	15	k	k	NOUN
ejpam-6631	185	16	)	)	PUNCT
ejpam-6631	185	17	.	.	PUNCT
ejpam-6631	186	1	using	use	VERB
ejpam-6631	186	2	the	the	DET
ejpam-6631	186	3	explicit	explicit	ADJ
ejpam-6631	186	4	fractional	fractional	ADJ
ejpam-6631	186	5	adams	adam	NOUN
ejpam-6631	186	6	method	method	NOUN
ejpam-6631	186	7	,	,	PUNCT
ejpam-6631	186	8	we	we	PRON
ejpam-6631	186	9	can	can	AUX
ejpam-6631	186	10	calculate	calculate	VERB
ejpam-6631	186	11	the	the	DET
ejpam-6631	186	12	numerical	numerical	ADJ
ejpam-6631	186	13	solution	solution	NOUN
ejpam-6631	186	14	for	for	ADP
ejpam-6631	186	15	the	the	DET
ejpam-6631	186	16	problem	problem	NOUN
ejpam-6631	186	17	described	describe	VERB
ejpam-6631	186	18	in	in	ADP
ejpam-6631	186	19	(	(	PUNCT
ejpam-6631	186	20	29	29	NUM
ejpam-6631	186	21	)	)	PUNCT
ejpam-6631	186	22	)	)	PUNCT
ejpam-6631	186	23	.	.	PUNCT
ejpam-6631	187	1	this	this	DET
ejpam-6631	187	2	approach	approach	NOUN
ejpam-6631	187	3	involves	involve	VERB
ejpam-6631	187	4	approximating	approximate	VERB
ejpam-6631	187	5	p(x	p(x	NOUN
ejpam-6631	187	6	)	)	PUNCT
ejpam-6631	187	7	based	base	VERB
ejpam-6631	187	8	on	on	ADP
ejpam-6631	187	9	previous	previous	ADJ
ejpam-6631	187	10	values	value	NOUN
ejpam-6631	187	11	and	and	CCONJ
ejpam-6631	187	12	using	use	VERB
ejpam-6631	187	13	the	the	DET
ejpam-6631	187	14	error	error	NOUN
ejpam-6631	187	15	function	function	NOUN
ejpam-6631	187	16	to	to	PART
ejpam-6631	187	17	assess	assess	VERB
ejpam-6631	187	18	the	the	DET
ejpam-6631	187	19	accuracy	accuracy	NOUN
ejpam-6631	187	20	of	of	ADP
ejpam-6631	187	21	the	the	DET
ejpam-6631	187	22	solution	solution	NOUN
ejpam-6631	187	23	.	.	PUNCT
ejpam-6631	188	1	p(xk+1	p(xk+1	X
ejpam-6631	188	2	)	)	PUNCT
ejpam-6631	188	3	=	=	SYM
ejpam-6631	189	1	p(xk	p(xk	X
ejpam-6631	189	2	)	)	PUNCT
ejpam-6631	190	1	+	+	CCONJ
ejpam-6631	190	2	∫	∫	PROPN
ejpam-6631	190	3	xk+1	xk+1	PROPN
ejpam-6631	190	4	0	0	NUM
ejpam-6631	191	1	(	(	PUNCT
ejpam-6631	191	2	xk+1	xk+1	NUM
ejpam-6631	191	3	−	−	PROPN
ejpam-6631	191	4	w)β−1mγ	w)β−1mγ	PROPN
ejpam-6631	191	5	α	α	PRON
ejpam-6631	191	6	,	,	PUNCT
ejpam-6631	191	7	β(τ(xk+1	β(τ(xk+1	VERB
ejpam-6631	191	8	−	−	PRON
ejpam-6631	191	9	w)α	w)α	SCONJ
ejpam-6631	191	10	)	)	PUNCT
ejpam-6631	191	11	[	[	PUNCT
ejpam-6631	191	12	(	(	PUNCT
ejpam-6631	191	13	x−	x−	PROPN
ejpam-6631	191	14	xk−1)(x−	xk−1)(x−	PROPN
ejpam-6631	191	15	xk−2	xk−2	PROPN
ejpam-6631	191	16	)	)	PUNCT
ejpam-6631	191	17	(	(	PUNCT
ejpam-6631	191	18	xk	xk	PROPN
ejpam-6631	191	19	−	−	PROPN
ejpam-6631	191	20	xk−1)(xk	xk−1)(xk	PROPN
ejpam-6631	192	1	−	−	PROPN
ejpam-6631	192	2	xk−2	xk−2	PROPN
ejpam-6631	192	3	)	)	PUNCT
ejpam-6631	192	4	gk	gk	PROPN
ejpam-6631	192	5	+	+	CCONJ
ejpam-6631	192	6	(	(	PUNCT
ejpam-6631	192	7	x−	x−	PROPN
ejpam-6631	192	8	xk)(x−	xk)(x−	PROPN
ejpam-6631	192	9	xk−2	xk−2	PROPN
ejpam-6631	192	10	)	)	PUNCT
ejpam-6631	192	11	(	(	PUNCT
ejpam-6631	192	12	xk−1	xk−1	PROPN
ejpam-6631	192	13	−	−	PROPN
ejpam-6631	193	1	xk)(xk−1	xk)(xk−1	PROPN
ejpam-6631	193	2	−	−	PROPN
ejpam-6631	193	3	xk−2	xk−2	PROPN
ejpam-6631	193	4	)	)	PUNCT
ejpam-6631	193	5	gk−1	gk−1	PROPN
ejpam-6631	193	6	+	+	CCONJ
ejpam-6631	193	7	(	(	PUNCT
ejpam-6631	193	8	x−	x−	PROPN
ejpam-6631	193	9	xk−1)(x−	xk−1)(x−	PROPN
ejpam-6631	193	10	xk−1	xk−1	PROPN
ejpam-6631	193	11	)	)	PUNCT
ejpam-6631	193	12	(	(	PUNCT
ejpam-6631	193	13	xk−2	xk−2	PROPN
ejpam-6631	193	14	−	−	PROPN
ejpam-6631	193	15	xk)(xk−2	xk)(xk−2	PROPN
ejpam-6631	193	16	−	−	PROPN
ejpam-6631	193	17	xk−1	xk−1	PROPN
ejpam-6631	193	18	)	)	PUNCT
ejpam-6631	193	19	gk−2	gk−2	PROPN
ejpam-6631	193	20	]	]	PUNCT
ejpam-6631	193	21	dx	dx	PROPN
ejpam-6631	194	1	−	−	PROPN
ejpam-6631	194	2	∫	∫	PROPN
ejpam-6631	194	3	xk	xk	PROPN
ejpam-6631	194	4	0	0	PROPN
ejpam-6631	195	1	(	(	PUNCT
ejpam-6631	195	2	xk	xk	PROPN
ejpam-6631	195	3	−	−	PROPN
ejpam-6631	195	4	w)β−1mγ	w)β−1mγ	PROPN
ejpam-6631	195	5	α	α	PROPN
ejpam-6631	195	6	,	,	PUNCT
ejpam-6631	195	7	β(τ(xk	β(τ(xk	INTJ
ejpam-6631	195	8	−	−	NOUN
ejpam-6631	195	9	w)α	w)α	SCONJ
ejpam-6631	195	10	)	)	PUNCT
ejpam-6631	195	11	[	[	PUNCT
ejpam-6631	195	12	(	(	PUNCT
ejpam-6631	195	13	x−	x−	PROPN
ejpam-6631	195	14	xk−1)(x−	xk−1)(x−	PROPN
ejpam-6631	195	15	xk−2	xk−2	PROPN
ejpam-6631	195	16	)	)	PUNCT
ejpam-6631	195	17	(	(	PUNCT
ejpam-6631	195	18	xk	xk	PROPN
ejpam-6631	195	19	−	−	PROPN
ejpam-6631	195	20	xk−1)(xk	xk−1)(xk	PROPN
ejpam-6631	196	1	−	−	PROPN
ejpam-6631	196	2	xk−2	xk−2	PROPN
ejpam-6631	196	3	)	)	PUNCT
ejpam-6631	196	4	gk	gk	PROPN
ejpam-6631	196	5	+	+	CCONJ
ejpam-6631	196	6	(	(	PUNCT
ejpam-6631	196	7	x−	x−	PROPN
ejpam-6631	196	8	xk)(x−	xk)(x−	PROPN
ejpam-6631	196	9	xk−2	xk−2	PROPN
ejpam-6631	196	10	)	)	PUNCT
ejpam-6631	196	11	(	(	PUNCT
ejpam-6631	196	12	xk−1	xk−1	PROPN
ejpam-6631	196	13	−	−	PROPN
ejpam-6631	197	1	xk)(xk−1	xk)(xk−1	PROPN
ejpam-6631	197	2	−	−	PROPN
ejpam-6631	197	3	xk−2	xk−2	PROPN
ejpam-6631	197	4	)	)	PUNCT
ejpam-6631	197	5	gk−1	gk−1	PROPN
ejpam-6631	197	6	+	+	CCONJ
ejpam-6631	197	7	(	(	PUNCT
ejpam-6631	197	8	x−	x−	PROPN
ejpam-6631	197	9	xk−1)(x−	xk−1)(x−	PROPN
ejpam-6631	197	10	xk−1	xk−1	PROPN
ejpam-6631	197	11	)	)	PUNCT
ejpam-6631	197	12	(	(	PUNCT
ejpam-6631	197	13	xk−2	xk−2	PROPN
ejpam-6631	197	14	−	−	PROPN
ejpam-6631	197	15	xk)(xk−2	xk)(xk−2	PROPN
ejpam-6631	197	16	−	−	PROPN
ejpam-6631	197	17	xk−1	xk−1	PROPN
ejpam-6631	197	18	)	)	PUNCT
ejpam-6631	197	19	gk−2	gk−2	NOUN
ejpam-6631	197	20	]	]	PUNCT
ejpam-6631	197	21	dx+	dx+	PROPN
ejpam-6631	197	22	ℜ(t	ℜ(t	PROPN
ejpam-6631	197	23	,	,	PUNCT
ejpam-6631	197	24	β	β	X
ejpam-6631	197	25	,	,	PUNCT
ejpam-6631	197	26	k	k	NOUN
ejpam-6631	197	27	)	)	PUNCT
ejpam-6631	197	28	,	,	PUNCT
ejpam-6631	197	29	(	(	PUNCT
ejpam-6631	197	30	30	30	NUM
ejpam-6631	197	31	)	)	PUNCT
ejpam-6631	197	32	such	such	ADJ
ejpam-6631	197	33	that	that	DET
ejpam-6631	197	34	||ℜ(t	||ℜ(t	NOUN
ejpam-6631	197	35	,	,	PUNCT
ejpam-6631	197	36	β	β	X
ejpam-6631	197	37	,	,	PUNCT
ejpam-6631	197	38	k)||∞	k)||∞	VERB
ejpam-6631	197	39	<	<	X
ejpam-6631	197	40	ν	ν	X
ejpam-6631	197	41	.	.	PUNCT
ejpam-6631	197	42	proof	proof	NOUN
ejpam-6631	197	43	.	.	PUNCT
ejpam-6631	198	1	based	base	VERB
ejpam-6631	198	2	on	on	ADP
ejpam-6631	198	3	the	the	DET
ejpam-6631	198	4	(	(	PUNCT
ejpam-6631	198	5	18	18	NUM
ejpam-6631	198	6	)	)	PUNCT
ejpam-6631	198	7	and	and	CCONJ
ejpam-6631	198	8	(	(	PUNCT
ejpam-6631	198	9	19	19	NUM
ejpam-6631	198	10	)	)	PUNCT
ejpam-6631	198	11	,	,	PUNCT
ejpam-6631	198	12	we	we	PRON
ejpam-6631	198	13	arrived	arrive	VERB
ejpam-6631	198	14	at	at	ADP
ejpam-6631	198	15	;	;	PUNCT
ejpam-6631	199	1	m.	m.	NOUN
ejpam-6631	199	2	abdel	abdel	PROPN
ejpam-6631	199	3	aal	aal	PROPN
ejpam-6631	199	4	et	et	PROPN
ejpam-6631	199	5	al	al	PROPN
ejpam-6631	199	6	.	.	PUNCT
ejpam-6631	199	7	/	/	SYM
ejpam-6631	199	8	eur	eur	PROPN
ejpam-6631	199	9	.	.	PUNCT
ejpam-6631	200	1	j.	j.	PROPN
ejpam-6631	200	2	pure	pure	PROPN
ejpam-6631	200	3	appl	appl	PROPN
ejpam-6631	200	4	.	.	PROPN
ejpam-6631	200	5	math	math	PROPN
ejpam-6631	200	6	,	,	PUNCT
ejpam-6631	200	7	18	18	NUM
ejpam-6631	200	8	(	(	PUNCT
ejpam-6631	200	9	4	4	NUM
ejpam-6631	200	10	)	)	PUNCT
ejpam-6631	200	11	(	(	PUNCT
ejpam-6631	200	12	2025	2025	NUM
ejpam-6631	200	13	)	)	PUNCT
ejpam-6631	200	14	,	,	PUNCT
ejpam-6631	200	15	6631	6631	NUM
ejpam-6631	200	16	10	10	NUM
ejpam-6631	200	17	of	of	ADP
ejpam-6631	200	18	20	20	NUM
ejpam-6631	200	19	p(xk+1	p(xk+1	NOUN
ejpam-6631	200	20	)	)	PUNCT
ejpam-6631	200	21	=	=	SYM
ejpam-6631	200	22	p(xk	p(xk	X
ejpam-6631	200	23	)	)	PUNCT
ejpam-6631	201	1	+	+	CCONJ
ejpam-6631	201	2	∫	∫	PROPN
ejpam-6631	201	3	xk+1	xk+1	PROPN
ejpam-6631	201	4	0	0	NUM
ejpam-6631	202	1	(	(	PUNCT
ejpam-6631	202	2	xk+1	xk+1	NUM
ejpam-6631	202	3	−	−	PROPN
ejpam-6631	202	4	w)β−1mγ	w)β−1mγ	PROPN
ejpam-6631	202	5	α	α	PRON
ejpam-6631	202	6	,	,	PUNCT
ejpam-6631	202	7	β(τ(xk+1	β(τ(xk+1	VERB
ejpam-6631	202	8	−	−	PUNCT
ejpam-6631	202	9	w)α)µ(v	w)α)µ(v	NOUN
ejpam-6631	202	10	;	;	PUNCT
ejpam-6631	202	11	p(x))dw	p(x))dw	NOUN
ejpam-6631	202	12	−	−	PROPN
ejpam-6631	202	13	∫	∫	PROPN
ejpam-6631	202	14	xk	xk	PROPN
ejpam-6631	202	15	0	0	PROPN
ejpam-6631	203	1	(	(	PUNCT
ejpam-6631	203	2	xk	xk	PROPN
ejpam-6631	203	3	−	−	PROPN
ejpam-6631	203	4	w)β−1mγ	w)β−1mγ	PROPN
ejpam-6631	203	5	α	α	PROPN
ejpam-6631	203	6	,	,	PUNCT
ejpam-6631	203	7	β(τ(xk	β(τ(xk	NUM
ejpam-6631	203	8	−	−	NOUN
ejpam-6631	203	9	w)α)µ(v	w)α)µ(v	PROPN
ejpam-6631	203	10	;	;	PUNCT
ejpam-6631	203	11	p(x))dw	p(x))dw	NOUN
ejpam-6631	203	12	=	=	SYM
ejpam-6631	203	13	p(xk	p(xk	ADJ
ejpam-6631	203	14	)	)	PUNCT
ejpam-6631	204	1	+	+	CCONJ
ejpam-6631	204	2	∫	∫	PROPN
ejpam-6631	204	3	xk+1	xk+1	PROPN
ejpam-6631	204	4	0	0	NUM
ejpam-6631	205	1	(	(	PUNCT
ejpam-6631	205	2	xk+1	xk+1	NUM
ejpam-6631	205	3	−	−	PROPN
ejpam-6631	205	4	w)β−1mγ	w)β−1mγ	PROPN
ejpam-6631	205	5	α	α	PRON
ejpam-6631	205	6	,	,	PUNCT
ejpam-6631	205	7	β(τ(xk+1	β(τ(xk+1	VERB
ejpam-6631	205	8	−	−	PRON
ejpam-6631	205	9	w)α	w)α	SCONJ
ejpam-6631	205	10	)	)	PUNCT
ejpam-6631	205	11	[	[	PUNCT
ejpam-6631	205	12	(	(	PUNCT
ejpam-6631	205	13	x−	x−	PROPN
ejpam-6631	205	14	xk−1)(x−	xk−1)(x−	PROPN
ejpam-6631	205	15	xk−2	xk−2	PROPN
ejpam-6631	205	16	)	)	PUNCT
ejpam-6631	205	17	(	(	PUNCT
ejpam-6631	205	18	xk	xk	PROPN
ejpam-6631	205	19	−	−	PROPN
ejpam-6631	205	20	xk−1)(xk	xk−1)(xk	PROPN
ejpam-6631	206	1	−	−	PROPN
ejpam-6631	206	2	xk−2	xk−2	PROPN
ejpam-6631	206	3	)	)	PUNCT
ejpam-6631	206	4	gk	gk	PROPN
ejpam-6631	206	5	+	+	CCONJ
ejpam-6631	206	6	(	(	PUNCT
ejpam-6631	206	7	x−	x−	PROPN
ejpam-6631	206	8	xk)(x−	xk)(x−	PROPN
ejpam-6631	206	9	xk−2	xk−2	PROPN
ejpam-6631	206	10	)	)	PUNCT
ejpam-6631	206	11	(	(	PUNCT
ejpam-6631	206	12	xk−1	xk−1	PROPN
ejpam-6631	206	13	−	−	PROPN
ejpam-6631	207	1	xk)(xk−1	xk)(xk−1	PROPN
ejpam-6631	207	2	−	−	PROPN
ejpam-6631	207	3	xk−2	xk−2	PROPN
ejpam-6631	207	4	)	)	PUNCT
ejpam-6631	207	5	gk−1	gk−1	PROPN
ejpam-6631	207	6	+	+	CCONJ
ejpam-6631	207	7	(	(	PUNCT
ejpam-6631	207	8	x−	x−	PROPN
ejpam-6631	207	9	xk−1)(x−	xk−1)(x−	PROPN
ejpam-6631	207	10	xk−1	xk−1	PROPN
ejpam-6631	207	11	)	)	PUNCT
ejpam-6631	207	12	(	(	PUNCT
ejpam-6631	207	13	xk−2	xk−2	PROPN
ejpam-6631	207	14	−	−	PROPN
ejpam-6631	207	15	xk)(xk−2	xk)(xk−2	PROPN
ejpam-6631	207	16	−	−	PROPN
ejpam-6631	207	17	xk−1	xk−1	PROPN
ejpam-6631	207	18	)	)	PUNCT
ejpam-6631	207	19	gk−2	gk−2	PROPN
ejpam-6631	207	20	+	+	NUM
ejpam-6631	207	21	g(k+1)(x	g(k+1)(x	PROPN
ejpam-6631	207	22	)	)	PUNCT
ejpam-6631	208	1	(	(	PUNCT
ejpam-6631	208	2	k	k	X
ejpam-6631	208	3	+	+	PROPN
ejpam-6631	208	4	1	1	NUM
ejpam-6631	208	5	)	)	PUNCT
ejpam-6631	208	6	!	!	PUNCT
ejpam-6631	209	1	k∏	k∏	PROPN
ejpam-6631	209	2	i=1	i=1	PROPN
ejpam-6631	210	1	(	(	PUNCT
ejpam-6631	210	2	x−	x−	PROPN
ejpam-6631	210	3	xi)dx	xi)dx	PUNCT
ejpam-6631	210	4	]	]	PUNCT
ejpam-6631	211	1	−	−	NUM
ejpam-6631	211	2	∫	∫	INTJ
ejpam-6631	211	3	xk	xk	PROPN
ejpam-6631	211	4	0	0	PROPN
ejpam-6631	212	1	(	(	PUNCT
ejpam-6631	212	2	xk	xk	PROPN
ejpam-6631	212	3	−	−	PROPN
ejpam-6631	212	4	w)β−1mγ	w)β−1mγ	PROPN
ejpam-6631	212	5	α	α	PROPN
ejpam-6631	212	6	,	,	PUNCT
ejpam-6631	212	7	β(τ(xk	β(τ(xk	INTJ
ejpam-6631	212	8	−	−	NOUN
ejpam-6631	212	9	w)α	w)α	SCONJ
ejpam-6631	212	10	)	)	PUNCT
ejpam-6631	212	11	[	[	PUNCT
ejpam-6631	212	12	(	(	PUNCT
ejpam-6631	212	13	x−	x−	PROPN
ejpam-6631	212	14	xk−1)(x−	xk−1)(x−	PROPN
ejpam-6631	212	15	xk−2	xk−2	PROPN
ejpam-6631	212	16	)	)	PUNCT
ejpam-6631	212	17	(	(	PUNCT
ejpam-6631	212	18	xk	xk	PROPN
ejpam-6631	212	19	−	−	PROPN
ejpam-6631	212	20	xk−1)(xk	xk−1)(xk	PROPN
ejpam-6631	213	1	−	−	PROPN
ejpam-6631	213	2	xk−2	xk−2	PROPN
ejpam-6631	213	3	)	)	PUNCT
ejpam-6631	213	4	gk	gk	PROPN
ejpam-6631	213	5	+	+	CCONJ
ejpam-6631	213	6	(	(	PUNCT
ejpam-6631	213	7	x−	x−	PROPN
ejpam-6631	213	8	xk)(x−	xk)(x−	PROPN
ejpam-6631	213	9	xk−2	xk−2	PROPN
ejpam-6631	213	10	)	)	PUNCT
ejpam-6631	213	11	(	(	PUNCT
ejpam-6631	213	12	xk−1	xk−1	PROPN
ejpam-6631	213	13	−	−	PROPN
ejpam-6631	214	1	xk)(xk−1	xk)(xk−1	PROPN
ejpam-6631	214	2	−	−	PROPN
ejpam-6631	214	3	xk−2	xk−2	PROPN
ejpam-6631	214	4	)	)	PUNCT
ejpam-6631	214	5	gk−1	gk−1	PROPN
ejpam-6631	214	6	+	+	CCONJ
ejpam-6631	214	7	(	(	PUNCT
ejpam-6631	214	8	x−	x−	PROPN
ejpam-6631	214	9	xk−1)(x−	xk−1)(x−	PROPN
ejpam-6631	214	10	xk−1	xk−1	PROPN
ejpam-6631	214	11	)	)	PUNCT
ejpam-6631	214	12	(	(	PUNCT
ejpam-6631	214	13	xk−2	xk−2	PROPN
ejpam-6631	214	14	−	−	PROPN
ejpam-6631	214	15	xk)(xk−2	xk)(xk−2	PROPN
ejpam-6631	214	16	−	−	PROPN
ejpam-6631	214	17	xk−1	xk−1	PROPN
ejpam-6631	214	18	)	)	PUNCT
ejpam-6631	214	19	gk−2	gk−2	PROPN
ejpam-6631	214	20	+	+	NUM
ejpam-6631	214	21	g(k+1)(x	g(k+1)(x	PROPN
ejpam-6631	214	22	)	)	PUNCT
ejpam-6631	215	1	(	(	PUNCT
ejpam-6631	215	2	k	k	X
ejpam-6631	215	3	+	+	PROPN
ejpam-6631	215	4	1	1	NUM
ejpam-6631	215	5	)	)	PUNCT
ejpam-6631	215	6	!	!	PUNCT
ejpam-6631	216	1	k−1∏	k−1∏	PROPN
ejpam-6631	216	2	i=1	i=1	PROPN
ejpam-6631	217	1	(	(	PUNCT
ejpam-6631	217	2	x−	x−	PROPN
ejpam-6631	217	3	xi)dx	xi)dx	X
ejpam-6631	217	4	]	]	PUNCT
ejpam-6631	218	1	=	=	PUNCT
ejpam-6631	218	2	x(xk	x(xk	X
ejpam-6631	218	3	)	)	PUNCT
ejpam-6631	219	1	+	+	CCONJ
ejpam-6631	219	2	l(x	l(x	PROPN
ejpam-6631	219	3	,	,	PUNCT
ejpam-6631	219	4	β	β	NOUN
ejpam-6631	219	5	,	,	PUNCT
ejpam-6631	219	6	x	x	X
ejpam-6631	219	7	)	)	PUNCT
ejpam-6631	219	8	+	+	CCONJ
ejpam-6631	219	9	ℜ(x	ℜ(x	NUM
ejpam-6631	219	10	,	,	PUNCT
ejpam-6631	219	11	β	β	X
ejpam-6631	219	12	,	,	PUNCT
ejpam-6631	219	13	x	x	NOUN
ejpam-6631	219	14	)	)	PUNCT
ejpam-6631	219	15	.	.	PUNCT
ejpam-6631	220	1	(	(	PUNCT
ejpam-6631	220	2	31	31	NUM
ejpam-6631	220	3	)	)	PUNCT
ejpam-6631	220	4	the	the	DET
ejpam-6631	220	5	functions	function	NOUN
ejpam-6631	220	6	l(x	l(x	PROPN
ejpam-6631	220	7	,	,	PUNCT
ejpam-6631	220	8	β	β	NOUN
ejpam-6631	220	9	,	,	PUNCT
ejpam-6631	220	10	x	x	NOUN
ejpam-6631	220	11	)	)	PUNCT
ejpam-6631	220	12	and	and	CCONJ
ejpam-6631	220	13	ℜ(x	ℜ(x	PROPN
ejpam-6631	220	14	,	,	PUNCT
ejpam-6631	220	15	β	β	X
ejpam-6631	220	16	,	,	PUNCT
ejpam-6631	220	17	x	x	X
ejpam-6631	220	18	)	)	PUNCT
ejpam-6631	220	19	are	be	AUX
ejpam-6631	220	20	defined	define	VERB
ejpam-6631	220	21	as	as	SCONJ
ejpam-6631	220	22	follows	follow	VERB
ejpam-6631	220	23	:	:	PUNCT
ejpam-6631	220	24	l(x	l(x	PROPN
ejpam-6631	220	25	,	,	PUNCT
ejpam-6631	220	26	β	β	X
ejpam-6631	220	27	,	,	PUNCT
ejpam-6631	220	28	x	x	X
ejpam-6631	220	29	)	)	PUNCT
ejpam-6631	221	1	=	=	SYM
ejpam-6631	221	2	∫	∫	PROPN
ejpam-6631	221	3	xk+1	xk+1	PROPN
ejpam-6631	221	4	0	0	NUM
ejpam-6631	222	1	(	(	PUNCT
ejpam-6631	222	2	xk+1	xk+1	NUM
ejpam-6631	222	3	−	−	PROPN
ejpam-6631	222	4	w)β−1mγ	w)β−1mγ	PROPN
ejpam-6631	222	5	α	α	PRON
ejpam-6631	222	6	,	,	PUNCT
ejpam-6631	222	7	β(τ(xk+1	β(τ(xk+1	VERB
ejpam-6631	222	8	−	−	PRON
ejpam-6631	222	9	w)α	w)α	SCONJ
ejpam-6631	222	10	)	)	PUNCT
ejpam-6631	222	11	[	[	PUNCT
ejpam-6631	222	12	(	(	PUNCT
ejpam-6631	222	13	x−	x−	PROPN
ejpam-6631	222	14	xk−1)(x−	xk−1)(x−	PROPN
ejpam-6631	222	15	xk−2	xk−2	PROPN
ejpam-6631	222	16	)	)	PUNCT
ejpam-6631	222	17	(	(	PUNCT
ejpam-6631	222	18	xk	xk	PROPN
ejpam-6631	222	19	−	−	PROPN
ejpam-6631	222	20	xk−1)(xk	xk−1)(xk	PROPN
ejpam-6631	223	1	−	−	PROPN
ejpam-6631	223	2	xk−2	xk−2	PROPN
ejpam-6631	223	3	)	)	PUNCT
ejpam-6631	223	4	gk	gk	PROPN
ejpam-6631	223	5	+	+	CCONJ
ejpam-6631	223	6	(	(	PUNCT
ejpam-6631	223	7	x−	x−	PROPN
ejpam-6631	223	8	xk)(x−	xk)(x−	PROPN
ejpam-6631	223	9	xk−2	xk−2	PROPN
ejpam-6631	223	10	)	)	PUNCT
ejpam-6631	223	11	(	(	PUNCT
ejpam-6631	223	12	xk−1	xk−1	PROPN
ejpam-6631	223	13	−	−	PROPN
ejpam-6631	224	1	xk)(xk−1	xk)(xk−1	PROPN
ejpam-6631	224	2	−	−	PROPN
ejpam-6631	224	3	xk−2	xk−2	PROPN
ejpam-6631	224	4	)	)	PUNCT
ejpam-6631	224	5	gk−1	gk−1	PROPN
ejpam-6631	224	6	+	+	CCONJ
ejpam-6631	224	7	(	(	PUNCT
ejpam-6631	224	8	x−	x−	PROPN
ejpam-6631	224	9	xk−1)(x−	xk−1)(x−	PROPN
ejpam-6631	224	10	xk−1	xk−1	PROPN
ejpam-6631	224	11	)	)	PUNCT
ejpam-6631	224	12	(	(	PUNCT
ejpam-6631	224	13	xk−2	xk−2	PROPN
ejpam-6631	224	14	−	−	PROPN
ejpam-6631	224	15	xk)(xk−2	xk)(xk−2	PROPN
ejpam-6631	224	16	−	−	PROPN
ejpam-6631	224	17	xk−1	xk−1	PROPN
ejpam-6631	224	18	)	)	PUNCT
ejpam-6631	224	19	gk−2	gk−2	PROPN
ejpam-6631	224	20	]	]	PUNCT
ejpam-6631	224	21	dx	dx	PROPN
ejpam-6631	225	1	−	−	PROPN
ejpam-6631	225	2	∫	∫	PROPN
ejpam-6631	225	3	xk	xk	PROPN
ejpam-6631	225	4	0	0	PROPN
ejpam-6631	226	1	(	(	PUNCT
ejpam-6631	226	2	xk	xk	PROPN
ejpam-6631	226	3	−	−	PROPN
ejpam-6631	226	4	w)β−1mγ	w)β−1mγ	PROPN
ejpam-6631	226	5	α	α	PROPN
ejpam-6631	226	6	,	,	PUNCT
ejpam-6631	226	7	β(τ(xk	β(τ(xk	INTJ
ejpam-6631	226	8	−	−	NOUN
ejpam-6631	226	9	w)α	w)α	SCONJ
ejpam-6631	226	10	)	)	PUNCT
ejpam-6631	226	11	[	[	PUNCT
ejpam-6631	226	12	(	(	PUNCT
ejpam-6631	226	13	x−	x−	PROPN
ejpam-6631	226	14	xk−1)(x−	xk−1)(x−	PROPN
ejpam-6631	226	15	xk−2	xk−2	PROPN
ejpam-6631	226	16	)	)	PUNCT
ejpam-6631	226	17	(	(	PUNCT
ejpam-6631	226	18	xk	xk	PROPN
ejpam-6631	226	19	−	−	PROPN
ejpam-6631	226	20	xk−1)(xk	xk−1)(xk	PROPN
ejpam-6631	227	1	−	−	PROPN
ejpam-6631	227	2	xk−2	xk−2	PROPN
ejpam-6631	227	3	)	)	PUNCT
ejpam-6631	227	4	gk	gk	PROPN
ejpam-6631	227	5	+	+	CCONJ
ejpam-6631	227	6	(	(	PUNCT
ejpam-6631	227	7	x−	x−	PROPN
ejpam-6631	227	8	xk)(x−	xk)(x−	PROPN
ejpam-6631	227	9	xk−2	xk−2	PROPN
ejpam-6631	227	10	)	)	PUNCT
ejpam-6631	227	11	(	(	PUNCT
ejpam-6631	227	12	xk−1	xk−1	PROPN
ejpam-6631	227	13	−	−	PROPN
ejpam-6631	228	1	xk)(xk−1	xk)(xk−1	PROPN
ejpam-6631	228	2	−	−	PROPN
ejpam-6631	228	3	xk−2	xk−2	PROPN
ejpam-6631	228	4	)	)	PUNCT
ejpam-6631	228	5	gk−1	gk−1	PROPN
ejpam-6631	228	6	+	+	CCONJ
ejpam-6631	228	7	(	(	PUNCT
ejpam-6631	228	8	x−	x−	PROPN
ejpam-6631	228	9	xk−1)(x−	xk−1)(x−	PROPN
ejpam-6631	228	10	xk−1	xk−1	PROPN
ejpam-6631	228	11	)	)	PUNCT
ejpam-6631	228	12	(	(	PUNCT
ejpam-6631	228	13	xk−2	xk−2	PROPN
ejpam-6631	228	14	−	−	PROPN
ejpam-6631	228	15	xk)(xk−2	xk)(xk−2	PROPN
ejpam-6631	228	16	−	−	PROPN
ejpam-6631	228	17	xk−1	xk−1	PROPN
ejpam-6631	228	18	)	)	PUNCT
ejpam-6631	228	19	gk−2	gk−2	PROPN
ejpam-6631	228	20	]	]	PUNCT
ejpam-6631	228	21	dx	dx	PROPN
ejpam-6631	228	22	,	,	PUNCT
ejpam-6631	228	23	(	(	PUNCT
ejpam-6631	228	24	32	32	NUM
ejpam-6631	228	25	)	)	PUNCT
ejpam-6631	228	26	and	and	CCONJ
ejpam-6631	228	27	ℜ(x	ℜ(x	NOUN
ejpam-6631	228	28	,	,	PUNCT
ejpam-6631	228	29	β	β	NOUN
ejpam-6631	228	30	,	,	PUNCT
ejpam-6631	228	31	x	x	X
ejpam-6631	228	32	)	)	PUNCT
ejpam-6631	228	33	=	=	SYM
ejpam-6631	229	1	∫	∫	PROPN
ejpam-6631	229	2	xk+1	xk+1	PROPN
ejpam-6631	229	3	0	0	NUM
ejpam-6631	230	1	(	(	PUNCT
ejpam-6631	230	2	xk+1	xk+1	NUM
ejpam-6631	230	3	−	−	PROPN
ejpam-6631	230	4	w)β−1mγ	w)β−1mγ	PROPN
ejpam-6631	230	5	α	α	PRON
ejpam-6631	230	6	,	,	PUNCT
ejpam-6631	230	7	β(τ(xk+1	β(τ(xk+1	VERB
ejpam-6631	230	8	−	−	PRON
ejpam-6631	230	9	w)α	w)α	ADJ
ejpam-6631	230	10	)	)	PUNCT
ejpam-6631	230	11	[	[	PUNCT
ejpam-6631	230	12	g(k+1)(x	g(k+1)(x	NOUN
ejpam-6631	230	13	)	)	PUNCT
ejpam-6631	230	14	(	(	PUNCT
ejpam-6631	230	15	k	k	X
ejpam-6631	230	16	+	+	PROPN
ejpam-6631	230	17	1	1	NUM
ejpam-6631	230	18	)	)	PUNCT
ejpam-6631	230	19	!	!	PUNCT
ejpam-6631	231	1	k∏	k∏	PROPN
ejpam-6631	231	2	i=1	i=1	PROPN
ejpam-6631	232	1	(	(	PUNCT
ejpam-6631	232	2	x−	x−	PROPN
ejpam-6631	232	3	xi	xi	PROPN
ejpam-6631	232	4	)	)	PUNCT
ejpam-6631	232	5	]	]	PUNCT
ejpam-6631	233	1	dx	dx	PROPN
ejpam-6631	233	2	−	−	PROPN
ejpam-6631	233	3	∫	∫	PROPN
ejpam-6631	233	4	xk+1	xk+1	PROPN
ejpam-6631	233	5	0	0	NUM
ejpam-6631	234	1	(	(	PUNCT
ejpam-6631	234	2	xk+1	xk+1	NUM
ejpam-6631	234	3	−	−	PROPN
ejpam-6631	234	4	w)β−1mγ	w)β−1mγ	PROPN
ejpam-6631	234	5	α	α	PRON
ejpam-6631	234	6	,	,	PUNCT
ejpam-6631	234	7	β(τ(xk+1	β(τ(xk+1	VERB
ejpam-6631	234	8	−	−	PRON
ejpam-6631	234	9	w)α	w)α	ADJ
ejpam-6631	234	10	)	)	PUNCT
ejpam-6631	234	11	[	[	PUNCT
ejpam-6631	234	12	g(k+1)(x	g(k+1)(x	NOUN
ejpam-6631	234	13	)	)	PUNCT
ejpam-6631	234	14	(	(	PUNCT
ejpam-6631	234	15	k	k	X
ejpam-6631	234	16	+	+	PROPN
ejpam-6631	234	17	1	1	NUM
ejpam-6631	234	18	)	)	PUNCT
ejpam-6631	234	19	!	!	PUNCT
ejpam-6631	235	1	k−1∏	k−1∏	PROPN
ejpam-6631	235	2	i=1	i=1	PROPN
ejpam-6631	236	1	(	(	PUNCT
ejpam-6631	236	2	x−	x−	PROPN
ejpam-6631	236	3	xi	xi	PROPN
ejpam-6631	236	4	)	)	PUNCT
ejpam-6631	236	5	]	]	PUNCT
ejpam-6631	237	1	dx	dx	PROPN
ejpam-6631	237	2	.	.	PUNCT
ejpam-6631	238	1	(	(	PUNCT
ejpam-6631	238	2	33	33	NUM
ejpam-6631	238	3	)	)	PUNCT
ejpam-6631	238	4	it	it	PRON
ejpam-6631	238	5	now	now	ADV
ejpam-6631	238	6	remains	remain	VERB
ejpam-6631	238	7	for	for	SCONJ
ejpam-6631	238	8	us	we	PRON
ejpam-6631	238	9	to	to	PART
ejpam-6631	238	10	show	show	VERB
ejpam-6631	238	11	that	that	SCONJ
ejpam-6631	238	12	the	the	DET
ejpam-6631	238	13	proposed	propose	VERB
ejpam-6631	238	14	scheme	scheme	NOUN
ejpam-6631	238	15	is	be	AUX
ejpam-6631	238	16	convergent	convergent	ADJ
ejpam-6631	238	17	.	.	PUNCT
ejpam-6631	239	1	we	we	PRON
ejpam-6631	239	2	do	do	VERB
ejpam-6631	239	3	this	this	PRON
ejpam-6631	239	4	by	by	ADP
ejpam-6631	239	5	ensuring	ensure	VERB
ejpam-6631	239	6	that	that	SCONJ
ejpam-6631	239	7	||ℜ(t	||ℜ(t	NOUN
ejpam-6631	239	8	,	,	PUNCT
ejpam-6631	239	9	β	β	X
ejpam-6631	239	10	,	,	PUNCT
ejpam-6631	239	11	k)||∞	k)||∞	VERB
ejpam-6631	239	12	<	<	X
ejpam-6631	239	13	ν	ν	PROPN
ejpam-6631	239	14	.	.	PROPN
ejpam-6631	239	15	m.	m.	PROPN
ejpam-6631	239	16	abdel	abdel	PROPN
ejpam-6631	239	17	aal	aal	PROPN
ejpam-6631	239	18	et	et	PROPN
ejpam-6631	239	19	al	al	PROPN
ejpam-6631	239	20	.	.	PUNCT
ejpam-6631	239	21	/	/	SYM
ejpam-6631	239	22	eur	eur	PROPN
ejpam-6631	239	23	.	.	PUNCT
ejpam-6631	240	1	j.	j.	PROPN
ejpam-6631	240	2	pure	pure	PROPN
ejpam-6631	240	3	appl	appl	PROPN
ejpam-6631	240	4	.	.	PROPN
ejpam-6631	240	5	math	math	PROPN
ejpam-6631	240	6	,	,	PUNCT
ejpam-6631	240	7	18	18	NUM
ejpam-6631	240	8	(	(	PUNCT
ejpam-6631	240	9	4	4	NUM
ejpam-6631	240	10	)	)	PUNCT
ejpam-6631	240	11	(	(	PUNCT
ejpam-6631	240	12	2025	2025	NUM
ejpam-6631	240	13	)	)	PUNCT
ejpam-6631	240	14	,	,	PUNCT
ejpam-6631	240	15	6631	6631	NUM
ejpam-6631	240	16	11	11	NUM
ejpam-6631	240	17	of	of	ADP
ejpam-6631	240	18	20	20	NUM
ejpam-6631	240	19	||ℜ(t	||ℜ(t	NOUN
ejpam-6631	240	20	,	,	PUNCT
ejpam-6631	240	21	β	β	X
ejpam-6631	240	22	,	,	PUNCT
ejpam-6631	240	23	k)||∞	k)||∞	X
ejpam-6631	240	24	=	=	PUNCT
ejpam-6631	240	25	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6631	241	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6631	241	2	∫	∫	PROPN
ejpam-6631	241	3	xk+1	xk+1	PROPN
ejpam-6631	241	4	0	0	NUM
ejpam-6631	242	1	(	(	PUNCT
ejpam-6631	242	2	xk+1	xk+1	NUM
ejpam-6631	242	3	−	−	PROPN
ejpam-6631	242	4	w)β−1mγ	w)β−1mγ	PROPN
ejpam-6631	242	5	α	α	PRON
ejpam-6631	242	6	,	,	PUNCT
ejpam-6631	242	7	β(τ(xk+1	β(τ(xk+1	VERB
ejpam-6631	242	8	−	−	PRON
ejpam-6631	242	9	w)α	w)α	ADJ
ejpam-6631	242	10	)	)	PUNCT
ejpam-6631	242	11	[	[	PUNCT
ejpam-6631	242	12	g(k+1)(x	g(k+1)(x	NOUN
ejpam-6631	242	13	)	)	PUNCT
ejpam-6631	242	14	(	(	PUNCT
ejpam-6631	242	15	k	k	X
ejpam-6631	242	16	+	+	PROPN
ejpam-6631	242	17	1	1	NUM
ejpam-6631	242	18	)	)	PUNCT
ejpam-6631	242	19	!	!	PUNCT
ejpam-6631	243	1	k∏	k∏	PROPN
ejpam-6631	243	2	i=1	i=1	PROPN
ejpam-6631	244	1	(	(	PUNCT
ejpam-6631	244	2	x−	x−	PROPN
ejpam-6631	244	3	xi	xi	PROPN
ejpam-6631	244	4	)	)	PUNCT
ejpam-6631	244	5	]	]	PUNCT
ejpam-6631	245	1	dx	dx	PROPN
ejpam-6631	245	2	−	−	PROPN
ejpam-6631	245	3	∫	∫	PROPN
ejpam-6631	245	4	xk+1	xk+1	PROPN
ejpam-6631	245	5	0	0	NUM
ejpam-6631	246	1	(	(	PUNCT
ejpam-6631	246	2	xk+1	xk+1	NUM
ejpam-6631	246	3	−	−	PROPN
ejpam-6631	246	4	w)β−1mγ	w)β−1mγ	PROPN
ejpam-6631	246	5	α	α	PRON
ejpam-6631	246	6	,	,	PUNCT
ejpam-6631	246	7	β(τ(xk+1	β(τ(xk+1	VERB
ejpam-6631	246	8	−	−	PRON
ejpam-6631	246	9	w)α	w)α	ADJ
ejpam-6631	246	10	)	)	PUNCT
ejpam-6631	246	11	[	[	PUNCT
ejpam-6631	246	12	g(k+1)(x	g(k+1)(x	NOUN
ejpam-6631	246	13	)	)	PUNCT
ejpam-6631	246	14	(	(	PUNCT
ejpam-6631	246	15	k	k	X
ejpam-6631	246	16	+	+	PROPN
ejpam-6631	246	17	1	1	NUM
ejpam-6631	246	18	)	)	PUNCT
ejpam-6631	246	19	!	!	PUNCT
ejpam-6631	247	1	k−1∏	k−1∏	PROPN
ejpam-6631	247	2	i=1	i=1	PROPN
ejpam-6631	248	1	(	(	PUNCT
ejpam-6631	248	2	x−	x−	PROPN
ejpam-6631	248	3	xi	xi	PROPN
ejpam-6631	248	4	)	)	PUNCT
ejpam-6631	248	5	]	]	PUNCT
ejpam-6631	248	6	dx	dx	PROPN
ejpam-6631	248	7	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6631	249	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6631	249	2	∞	∞	PROPN
ejpam-6631	249	3	<	<	X
ejpam-6631	249	4	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6631	250	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6631	250	2	∫	∫	PROPN
ejpam-6631	250	3	xk+1	xk+1	PROPN
ejpam-6631	250	4	0	0	NUM
ejpam-6631	251	1	(	(	PUNCT
ejpam-6631	251	2	xk+1	xk+1	NUM
ejpam-6631	251	3	−	−	PROPN
ejpam-6631	251	4	w)β−1mγ	w)β−1mγ	PROPN
ejpam-6631	251	5	α	α	PRON
ejpam-6631	251	6	,	,	PUNCT
ejpam-6631	251	7	β(τ(xk+1	β(τ(xk+1	VERB
ejpam-6631	251	8	−	−	PRON
ejpam-6631	251	9	w)α	w)α	ADJ
ejpam-6631	251	10	)	)	PUNCT
ejpam-6631	251	11	[	[	PUNCT
ejpam-6631	251	12	g(k+1)(x	g(k+1)(x	NOUN
ejpam-6631	251	13	)	)	PUNCT
ejpam-6631	251	14	(	(	PUNCT
ejpam-6631	251	15	k	k	X
ejpam-6631	251	16	+	+	PROPN
ejpam-6631	251	17	1	1	NUM
ejpam-6631	251	18	)	)	PUNCT
ejpam-6631	251	19	!	!	PUNCT
ejpam-6631	252	1	k∏	k∏	PROPN
ejpam-6631	252	2	i=1	i=1	PROPN
ejpam-6631	253	1	(	(	PUNCT
ejpam-6631	253	2	x−	x−	PROPN
ejpam-6631	253	3	xi	xi	PROPN
ejpam-6631	253	4	)	)	PUNCT
ejpam-6631	253	5	]	]	PUNCT
ejpam-6631	253	6	dx	dx	PROPN
ejpam-6631	253	7	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6631	254	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6631	254	2	∞	∞	PROPN
ejpam-6631	255	1	+	+	CCONJ
ejpam-6631	255	2	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6631	256	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6631	256	2	∫	∫	PROPN
ejpam-6631	256	3	xk	xk	PROPN
ejpam-6631	256	4	0	0	PROPN
ejpam-6631	257	1	(	(	PUNCT
ejpam-6631	257	2	xk	xk	PROPN
ejpam-6631	257	3	−	−	PROPN
ejpam-6631	257	4	w)β−1mγ	w)β−1mγ	PROPN
ejpam-6631	257	5	α	α	PROPN
ejpam-6631	257	6	,	,	PUNCT
ejpam-6631	257	7	β(τ(xk	β(τ(xk	INTJ
ejpam-6631	257	8	−	−	NOUN
ejpam-6631	257	9	w)α	w)α	SCONJ
ejpam-6631	257	10	)	)	PUNCT
ejpam-6631	257	11	[	[	PUNCT
ejpam-6631	257	12	g(k)(x	g(k)(x	NOUN
ejpam-6631	257	13	)	)	PUNCT
ejpam-6631	257	14	(	(	PUNCT
ejpam-6631	257	15	k	k	NOUN
ejpam-6631	257	16	)	)	PUNCT
ejpam-6631	257	17	!	!	PUNCT
ejpam-6631	258	1	k−1∏	k−1∏	PROPN
ejpam-6631	258	2	i=1	i=1	PROPN
ejpam-6631	259	1	(	(	PUNCT
ejpam-6631	259	2	x−	x−	PROPN
ejpam-6631	259	3	xi	xi	PROPN
ejpam-6631	259	4	)	)	PUNCT
ejpam-6631	259	5	]	]	PUNCT
ejpam-6631	259	6	dx	dx	PROPN
ejpam-6631	259	7	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6631	260	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6631	260	2	∞	∞	PROPN
ejpam-6631	260	3	<	<	X
ejpam-6631	260	4	max	max	PROPN
ejpam-6631	260	5	x∈[0,xk	x∈[0,xk	NOUN
ejpam-6631	260	6	]	]	X
ejpam-6631	260	7	|g(k+1)(x)|	|g(k+1)(x)|	PUNCT
ejpam-6631	260	8	(	(	PUNCT
ejpam-6631	260	9	k	k	X
ejpam-6631	260	10	+	+	PROPN
ejpam-6631	260	11	1	1	NUM
ejpam-6631	260	12	)	)	PUNCT
ejpam-6631	260	13	!	!	PUNCT
ejpam-6631	261	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6631	262	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6631	262	2	k∏	k∏	PROPN
ejpam-6631	262	3	i=1	i=1	PROPN
ejpam-6631	262	4	(	(	PUNCT
ejpam-6631	262	5	x−	x−	PROPN
ejpam-6631	262	6	xi	xi	PROPN
ejpam-6631	262	7	)	)	PUNCT
ejpam-6631	262	8	∣∣∣∣∣	∣∣∣∣∣	PUNCT
ejpam-6631	263	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6631	263	2	∞	∞	NUM
ejpam-6631	263	3	∫	∫	PROPN
ejpam-6631	263	4	xk+1	xk+1	PROPN
ejpam-6631	263	5	0	0	NUM
ejpam-6631	264	1	(	(	PUNCT
ejpam-6631	264	2	xk+1	xk+1	NUM
ejpam-6631	264	3	−	−	PROPN
ejpam-6631	264	4	w)β−1mγ	w)β−1mγ	PROPN
ejpam-6631	264	5	α	α	PRON
ejpam-6631	264	6	,	,	PUNCT
ejpam-6631	264	7	β(τ(xk+1	β(τ(xk+1	VERB
ejpam-6631	264	8	−	−	PRON
ejpam-6631	264	9	w)α)dx	w)α)dx	NOUN
ejpam-6631	264	10	+	+	CCONJ
ejpam-6631	264	11	max	max	PROPN
ejpam-6631	264	12	x∈[0,xk	x∈[0,xk	NOUN
ejpam-6631	264	13	]	]	X
ejpam-6631	264	14	|g(k)(x)|	|g(k)(x)|	NOUN
ejpam-6631	264	15	k	k	X
ejpam-6631	264	16	!	!	PUNCT
ejpam-6631	264	17	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6631	265	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6631	265	2	k∏	k∏	PROPN
ejpam-6631	265	3	i=1	i=1	PROPN
ejpam-6631	265	4	(	(	PUNCT
ejpam-6631	265	5	x−	x−	PROPN
ejpam-6631	265	6	xi	xi	PROPN
ejpam-6631	265	7	)	)	PUNCT
ejpam-6631	265	8	∣∣∣∣∣	∣∣∣∣∣	PUNCT
ejpam-6631	266	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6631	266	2	∞	∞	NUM
ejpam-6631	266	3	∫	∫	PROPN
ejpam-6631	266	4	xk	xk	PROPN
ejpam-6631	266	5	0	0	PROPN
ejpam-6631	267	1	(	(	PUNCT
ejpam-6631	267	2	xk	xk	PROPN
ejpam-6631	267	3	−	−	PROPN
ejpam-6631	267	4	w)β−1mγ	w)β−1mγ	PROPN
ejpam-6631	267	5	α	α	PROPN
ejpam-6631	267	6	,	,	PUNCT
ejpam-6631	267	7	β(τ(xk	β(τ(xk	NUM
ejpam-6631	267	8	−	−	NOUN
ejpam-6631	267	9	w)α)dx	w)α)dx	NOUN
ejpam-6631	267	10	=	=	PUNCT
ejpam-6631	267	11	max	max	PROPN
ejpam-6631	267	12	x∈[0,xk	x∈[0,xk	NOUN
ejpam-6631	267	13	]	]	X
ejpam-6631	267	14	|g(k+1)(x)|	|g(k+1)(x)|	PUNCT
ejpam-6631	267	15	(	(	PUNCT
ejpam-6631	267	16	k	k	X
ejpam-6631	267	17	+	+	PROPN
ejpam-6631	267	18	1	1	NUM
ejpam-6631	267	19	)	)	PUNCT
ejpam-6631	267	20	!	!	PUNCT
ejpam-6631	268	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6631	269	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6631	269	2	k∏	k∏	PROPN
ejpam-6631	269	3	i=1	i=1	PROPN
ejpam-6631	269	4	(	(	PUNCT
ejpam-6631	269	5	x−	x−	PROPN
ejpam-6631	269	6	xi	xi	PROPN
ejpam-6631	269	7	)	)	PUNCT
ejpam-6631	269	8	∣∣∣∣∣	∣∣∣∣∣	PUNCT
ejpam-6631	270	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6631	270	2	∞	∞	PROPN
ejpam-6631	270	3	x	x	X
ejpam-6631	270	4	β	β	X
ejpam-6631	270	5	k+1	k+1	PROPN
ejpam-6631	270	6	m	m	PROPN
ejpam-6631	270	7	γ	γ	NOUN
ejpam-6631	270	8	α	α	PROPN
ejpam-6631	270	9	,	,	PUNCT
ejpam-6631	270	10	β(τ(x	β(τ(x	ADP
ejpam-6631	270	11	k+1	k+1	X
ejpam-6631	270	12	β	β	X
ejpam-6631	270	13	)	)	PUNCT
ejpam-6631	270	14	)	)	PUNCT
ejpam-6631	271	1	+	+	CCONJ
ejpam-6631	271	2	max	max	PROPN
ejpam-6631	271	3	x∈[0,xk	x∈[0,xk	NOUN
ejpam-6631	271	4	]	]	X
ejpam-6631	271	5	|g(k)(x)|	|g(k)(x)|	NOUN
ejpam-6631	271	6	(	(	PUNCT
ejpam-6631	271	7	k	k	NOUN
ejpam-6631	271	8	)	)	PUNCT
ejpam-6631	271	9	!	!	PUNCT
ejpam-6631	272	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6631	273	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6631	273	2	k∏	k∏	PROPN
ejpam-6631	273	3	i=1	i=1	PROPN
ejpam-6631	273	4	(	(	PUNCT
ejpam-6631	273	5	x−	x−	PROPN
ejpam-6631	273	6	xi	xi	PROPN
ejpam-6631	273	7	)	)	PUNCT
ejpam-6631	273	8	∣∣∣∣∣	∣∣∣∣∣	PUNCT
ejpam-6631	274	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6631	274	2	∞	∞	PROPN
ejpam-6631	274	3	x	x	SYM
ejpam-6631	274	4	β	β	X
ejpam-6631	274	5	km	km	X
ejpam-6631	274	6	γ	γ	PROPN
ejpam-6631	274	7	α	α	PROPN
ejpam-6631	274	8	,	,	PUNCT
ejpam-6631	274	9	β(τ(x	β(τ(x	ADP
ejpam-6631	274	10	k	k	PROPN
ejpam-6631	274	11	β	β	X
ejpam-6631	274	12	)	)	PUNCT
ejpam-6631	274	13	)	)	PUNCT
ejpam-6631	275	1	<	<	X
ejpam-6631	275	2	sup	sup	NOUN
ejpam-6631	275	3	x∈[0,xk+1	x∈[0,xk+1	PUNCT
ejpam-6631	275	4	]	]	PUNCT
ejpam-6631	276	1	(	(	PUNCT
ejpam-6631	276	2	max	max	PROPN
ejpam-6631	276	3	x∈[0,xk	x∈[0,xk	NOUN
ejpam-6631	276	4	]	]	X
ejpam-6631	276	5	|g(k+1)(x)|	|g(k+1)(x)|	PUNCT
ejpam-6631	276	6	(	(	PUNCT
ejpam-6631	276	7	k	k	X
ejpam-6631	276	8	+	+	PROPN
ejpam-6631	276	9	1	1	NUM
ejpam-6631	276	10	)	)	PUNCT
ejpam-6631	276	11	!	!	PUNCT
ejpam-6631	277	1	,	,	PUNCT
ejpam-6631	277	2	max	max	PROPN
ejpam-6631	277	3	x∈[0,xk+1	x∈[0,xk+1	PUNCT
ejpam-6631	277	4	]	]	PUNCT
ejpam-6631	277	5	|g(k)(x)|	|g(k)(x)|	NOUN
ejpam-6631	277	6	(	(	PUNCT
ejpam-6631	277	7	k	k	NOUN
ejpam-6631	277	8	)	)	PUNCT
ejpam-6631	277	9	!	!	PUNCT
ejpam-6631	277	10	)	)	PUNCT
ejpam-6631	278	1	×	×	NOUN
ejpam-6631	278	2	[	[	PUNCT
ejpam-6631	278	3	k!hk+1	k!hk+1	NUM
ejpam-6631	278	4	4	4	NUM
ejpam-6631	278	5	x	x	SYM
ejpam-6631	278	6	β	β	X
ejpam-6631	278	7	k+1	k+1	X
ejpam-6631	278	8	m	m	PROPN
ejpam-6631	278	9	γ	γ	NOUN
ejpam-6631	278	10	α	α	NOUN
ejpam-6631	278	11	,	,	PUNCT
ejpam-6631	278	12	β+1(τ(x	β+1(τ(x	VERB
ejpam-6631	278	13	α	α	PRON
ejpam-6631	278	14	k+1	k+1	NOUN
ejpam-6631	278	15	)	)	PUNCT
ejpam-6631	278	16	)	)	PUNCT
ejpam-6631	279	1	+	+	CCONJ
ejpam-6631	279	2	(	(	PUNCT
ejpam-6631	279	3	k	k	NOUN
ejpam-6631	279	4	−	−	PROPN
ejpam-6631	279	5	1)!hk	1)!hk	NUM
ejpam-6631	279	6	4	4	NUM
ejpam-6631	279	7	x	x	SYM
ejpam-6631	279	8	β	β	X
ejpam-6631	279	9	km	km	NOUN
ejpam-6631	279	10	γ	γ	X
ejpam-6631	279	11	α	α	PROPN
ejpam-6631	279	12	,	,	PUNCT
ejpam-6631	279	13	β+1(τ(x	β+1(τ(x	VERB
ejpam-6631	279	14	α	α	PROPN
ejpam-6631	279	15	k	k	NOUN
ejpam-6631	279	16	)	)	PUNCT
ejpam-6631	279	17	)	)	PUNCT
ejpam-6631	279	18	]	]	PUNCT
ejpam-6631	280	1	<	<	X
ejpam-6631	280	2	ν	ν	X
ejpam-6631	280	3	.	.	PUNCT
ejpam-6631	280	4	(	(	PUNCT
ejpam-6631	280	5	34	34	NUM
ejpam-6631	280	6	)	)	PUNCT
ejpam-6631	280	7	5	5	NUM
ejpam-6631	280	8	.	.	PUNCT
ejpam-6631	280	9	numerical	numerical	ADJ
ejpam-6631	280	10	application	application	NOUN
ejpam-6631	280	11	of	of	ADP
ejpam-6631	280	12	tempered	temper	VERB
ejpam-6631	280	13	fractional	fractional	ADJ
ejpam-6631	280	14	differential	differential	ADJ
ejpam-6631	280	15	equations	equation	NOUN
ejpam-6631	280	16	with	with	ADP
ejpam-6631	280	17	respect	respect	NOUN
ejpam-6631	280	18	to	to	ADP
ejpam-6631	280	19	another	another	DET
ejpam-6631	280	20	function	function	NOUN
ejpam-6631	280	21	this	this	DET
ejpam-6631	280	22	section	section	NOUN
ejpam-6631	280	23	provides	provide	VERB
ejpam-6631	280	24	examples	example	NOUN
ejpam-6631	280	25	to	to	PART
ejpam-6631	280	26	show	show	VERB
ejpam-6631	280	27	how	how	SCONJ
ejpam-6631	280	28	the	the	DET
ejpam-6631	280	29	new	new	ADJ
ejpam-6631	280	30	explicit	explicit	ADJ
ejpam-6631	280	31	fractional	fractional	ADJ
ejpam-6631	280	32	adams	adam	NOUN
ejpam-6631	280	33	method	method	NOUN
ejpam-6631	280	34	for	for	ADP
ejpam-6631	280	35	the	the	DET
ejpam-6631	280	36	prabhakar	prabhakar	PROPN
ejpam-6631	280	37	derivative	derivative	NOUN
ejpam-6631	280	38	works	work	NOUN
ejpam-6631	280	39	and	and	CCONJ
ejpam-6631	280	40	how	how	SCONJ
ejpam-6631	280	41	accurate	accurate	ADJ
ejpam-6631	280	42	it	it	PRON
ejpam-6631	280	43	is	be	AUX
ejpam-6631	280	44	.	.	PUNCT
ejpam-6631	281	1	we	we	PRON
ejpam-6631	281	2	completed	complete	VERB
ejpam-6631	281	3	all	all	DET
ejpam-6631	281	4	calculations	calculation	NOUN
ejpam-6631	281	5	using	use	VERB
ejpam-6631	281	6	the	the	DET
ejpam-6631	281	7	software	software	NOUN
ejpam-6631	281	8	maple	maple	NOUN
ejpam-6631	281	9	18	18	NUM
ejpam-6631	281	10	.	.	PUNCT
ejpam-6631	281	11	example	example	NOUN
ejpam-6631	282	1	1	1	NUM
ejpam-6631	282	2	.	.	X
ejpam-6631	282	3	we	we	PRON
ejpam-6631	282	4	look	look	VERB
ejpam-6631	282	5	at	at	ADP
ejpam-6631	282	6	the	the	DET
ejpam-6631	282	7	simple	simple	ADJ
ejpam-6631	282	8	nonlinear	nonlinear	ADJ
ejpam-6631	282	9	fractional	fractional	ADJ
ejpam-6631	282	10	differential	differential	NOUN
ejpam-6631	282	11	equation	equation	NOUN
ejpam-6631	282	12	defined	define	VERB
ejpam-6631	282	13	using	use	VERB
ejpam-6631	282	14	the	the	DET
ejpam-6631	282	15	prabhakar	prabhakar	NOUN
ejpam-6631	282	16	derivative	derivative	NOUN
ejpam-6631	283	1	[	[	X
ejpam-6631	283	2	22	22	NUM
ejpam-6631	283	3	]	]	X
ejpam-6631	283	4	:	:	PUNCT
ejpam-6631	283	5	rdγ	rdγ	NOUN
ejpam-6631	283	6	α	α	NOUN
ejpam-6631	283	7	,	,	PUNCT
ejpam-6631	283	8	β	β	PROPN
ejpam-6631	283	9	,	,	PUNCT
ejpam-6631	283	10	τ	τ	PROPN
ejpam-6631	283	11	,	,	PUNCT
ejpam-6631	283	12	a	a	DET
ejpam-6631	283	13	+	+	X
ejpam-6631	283	14	p(x	p(x	NOUN
ejpam-6631	283	15	)	)	PUNCT
ejpam-6631	283	16	=	=	PUNCT
ejpam-6631	283	17	g(x)−	g(x)−	PROPN
ejpam-6631	283	18	u2(x	u2(x	PROPN
ejpam-6631	283	19	)	)	PUNCT
ejpam-6631	283	20	.	.	PUNCT
ejpam-6631	284	1	(	(	PUNCT
ejpam-6631	284	2	35	35	NUM
ejpam-6631	284	3	)	)	PUNCT
ejpam-6631	284	4	given	give	VERB
ejpam-6631	284	5	the	the	DET
ejpam-6631	284	6	initial	initial	ADJ
ejpam-6631	284	7	condition	condition	NOUN
ejpam-6631	285	1	that	that	SCONJ
ejpam-6631	285	2	m.	m.	NOUN
ejpam-6631	285	3	abdel	abdel	PROPN
ejpam-6631	285	4	aal	aal	PROPN
ejpam-6631	285	5	et	et	PROPN
ejpam-6631	285	6	al	al	PROPN
ejpam-6631	285	7	.	.	PUNCT
ejpam-6631	285	8	/	/	SYM
ejpam-6631	285	9	eur	eur	PROPN
ejpam-6631	285	10	.	.	PUNCT
ejpam-6631	286	1	j.	j.	PROPN
ejpam-6631	286	2	pure	pure	PROPN
ejpam-6631	286	3	appl	appl	PROPN
ejpam-6631	286	4	.	.	PROPN
ejpam-6631	286	5	math	math	PROPN
ejpam-6631	286	6	,	,	PUNCT
ejpam-6631	286	7	18	18	NUM
ejpam-6631	286	8	(	(	PUNCT
ejpam-6631	286	9	4	4	NUM
ejpam-6631	286	10	)	)	PUNCT
ejpam-6631	286	11	(	(	PUNCT
ejpam-6631	286	12	2025	2025	NUM
ejpam-6631	286	13	)	)	PUNCT
ejpam-6631	286	14	,	,	PUNCT
ejpam-6631	286	15	6631	6631	NUM
ejpam-6631	286	16	12	12	NUM
ejpam-6631	286	17	of	of	ADP
ejpam-6631	286	18	20	20	NUM
ejpam-6631	286	19	p(0	p(0	NOUN
ejpam-6631	286	20	)	)	PUNCT
ejpam-6631	286	21	=	=	SYM
ejpam-6631	286	22	0	0	NUM
ejpam-6631	286	23	,	,	PUNCT
ejpam-6631	286	24	(	(	PUNCT
ejpam-6631	286	25	36	36	NUM
ejpam-6631	286	26	)	)	PUNCT
ejpam-6631	287	1	so	so	SCONJ
ejpam-6631	287	2	that	that	SCONJ
ejpam-6631	287	3	g(t	g(t	PROPN
ejpam-6631	287	4	)	)	PUNCT
ejpam-6631	287	5	=	=	SYM
ejpam-6631	287	6	2	2	NUM
ejpam-6631	287	7	t−	t−	PROPN
ejpam-6631	287	8	3	3	NUM
ejpam-6631	287	9	t2	t2	NOUN
ejpam-6631	287	10	−	−	PROPN
ejpam-6631	287	11	t3	t3	NOUN
ejpam-6631	287	12	+	+	CCONJ
ejpam-6631	287	13	(	(	PUNCT
ejpam-6631	287	14	2	2	NUM
ejpam-6631	287	15	t	t	NOUN
ejpam-6631	287	16	(	(	PUNCT
ejpam-6631	287	17	1−	1−	NUM
ejpam-6631	287	18	β	β	X
ejpam-6631	287	19	+	+	X
ejpam-6631	287	20	β	β	X
ejpam-6631	287	21	tβ	tβ	PROPN
ejpam-6631	287	22	γ	γ	X
ejpam-6631	287	23	(	(	PUNCT
ejpam-6631	287	24	β	β	X
ejpam-6631	287	25	+	+	NOUN
ejpam-6631	287	26	2	2	NUM
ejpam-6631	287	27	)	)	PUNCT
ejpam-6631	287	28	)	)	PUNCT
ejpam-6631	287	29	−	−	PROPN
ejpam-6631	287	30	3	3	NUM
ejpam-6631	287	31	t2	t2	NOUN
ejpam-6631	287	32	(	(	PUNCT
ejpam-6631	287	33	2	2	NUM
ejpam-6631	287	34	t	t	NOUN
ejpam-6631	287	35	(	(	PUNCT
ejpam-6631	287	36	1−	1−	NUM
ejpam-6631	287	37	β	β	X
ejpam-6631	287	38	+	+	CCONJ
ejpam-6631	287	39	2	2	NUM
ejpam-6631	287	40	β	β	NOUN
ejpam-6631	287	41	tβ	tβ	PROPN
ejpam-6631	287	42	γ	γ	X
ejpam-6631	287	43	(	(	PUNCT
ejpam-6631	287	44	β	β	X
ejpam-6631	287	45	+	+	NOUN
ejpam-6631	287	46	3	3	NUM
ejpam-6631	287	47	)	)	PUNCT
ejpam-6631	287	48	)	)	PUNCT
ejpam-6631	288	1	+	+	CCONJ
ejpam-6631	288	2	t3	t3	NOUN
ejpam-6631	288	3	(	(	PUNCT
ejpam-6631	288	4	1−	1−	NUM
ejpam-6631	288	5	β	β	X
ejpam-6631	288	6	+	+	CCONJ
ejpam-6631	288	7	6	6	NUM
ejpam-6631	288	8	β	β	NOUN
ejpam-6631	288	9	tβ	tβ	PROPN
ejpam-6631	288	10	γ	γ	X
ejpam-6631	288	11	(	(	PUNCT
ejpam-6631	288	12	β	β	X
ejpam-6631	288	13	+	+	NOUN
ejpam-6631	288	14	4	4	NUM
ejpam-6631	288	15	)	)	PUNCT
ejpam-6631	288	16	)	)	PUNCT
ejpam-6631	288	17	)	)	PUNCT
ejpam-6631	288	18	)	)	PUNCT
ejpam-6631	288	19	2	2	NUM
ejpam-6631	288	20	,	,	PUNCT
ejpam-6631	288	21	(	(	PUNCT
ejpam-6631	288	22	37	37	NUM
ejpam-6631	288	23	)	)	PUNCT
ejpam-6631	288	24	the	the	DET
ejpam-6631	288	25	exact	exact	ADJ
ejpam-6631	288	26	solution	solution	NOUN
ejpam-6631	288	27	is	be	AUX
ejpam-6631	288	28	;	;	PUNCT
ejpam-6631	288	29	p(t	p(t	NOUN
ejpam-6631	288	30	)	)	PUNCT
ejpam-6631	288	31	=	=	PUNCT
ejpam-6631	288	32	(	(	PUNCT
ejpam-6631	288	33	2	2	NUM
ejpam-6631	288	34	t	t	NOUN
ejpam-6631	288	35	(	(	PUNCT
ejpam-6631	288	36	1−	1−	NUM
ejpam-6631	288	37	β	β	X
ejpam-6631	289	1	+	+	X
ejpam-6631	289	2	β	β	X
ejpam-6631	289	3	tβ	tβ	PROPN
ejpam-6631	289	4	γ	γ	X
ejpam-6631	289	5	(	(	PUNCT
ejpam-6631	289	6	β	β	X
ejpam-6631	289	7	+	+	NOUN
ejpam-6631	289	8	2	2	NUM
ejpam-6631	289	9	)	)	PUNCT
ejpam-6631	289	10	)	)	PUNCT
ejpam-6631	290	1	−	−	PROPN
ejpam-6631	290	2	6	6	NUM
ejpam-6631	290	3	t3	t3	NOUN
ejpam-6631	290	4	(	(	PUNCT
ejpam-6631	290	5	1−	1−	NUM
ejpam-6631	290	6	β	β	X
ejpam-6631	291	1	+	+	CCONJ
ejpam-6631	291	2	2	2	NUM
ejpam-6631	291	3	β	β	NOUN
ejpam-6631	291	4	tβ	tβ	PROPN
ejpam-6631	291	5	γ	γ	X
ejpam-6631	291	6	(	(	PUNCT
ejpam-6631	291	7	β	β	X
ejpam-6631	291	8	+	+	NOUN
ejpam-6631	291	9	3	3	NUM
ejpam-6631	291	10	)	)	PUNCT
ejpam-6631	291	11	)	)	PUNCT
ejpam-6631	292	1	+	+	CCONJ
ejpam-6631	292	2	t3	t3	NOUN
ejpam-6631	292	3	(	(	PUNCT
ejpam-6631	292	4	1−	1−	NUM
ejpam-6631	292	5	β	β	X
ejpam-6631	292	6	+	+	CCONJ
ejpam-6631	292	7	6	6	NUM
ejpam-6631	292	8	β	β	NOUN
ejpam-6631	292	9	tβ	tβ	PROPN
ejpam-6631	292	10	γ	γ	X
ejpam-6631	292	11	(	(	PUNCT
ejpam-6631	292	12	β	β	X
ejpam-6631	292	13	+	+	NOUN
ejpam-6631	292	14	4	4	NUM
ejpam-6631	292	15	)	)	PUNCT
ejpam-6631	292	16	)	)	PUNCT
ejpam-6631	292	17	)	)	PUNCT
ejpam-6631	292	18	2	2	X
ejpam-6631	292	19	.	.	PUNCT
ejpam-6631	293	1	(	(	PUNCT
ejpam-6631	293	2	38	38	NUM
ejpam-6631	293	3	)	)	PUNCT
ejpam-6631	293	4	solution	solution	NOUN
ejpam-6631	293	5	:	:	PUNCT
ejpam-6631	293	6	to	to	PART
ejpam-6631	293	7	check	check	VERB
ejpam-6631	293	8	how	how	SCONJ
ejpam-6631	293	9	accurate	accurate	ADJ
ejpam-6631	293	10	the	the	DET
ejpam-6631	293	11	explicit	explicit	ADJ
ejpam-6631	293	12	fractional	fractional	ADJ
ejpam-6631	293	13	adams	adam	NOUN
ejpam-6631	293	14	method	method	NOUN
ejpam-6631	293	15	from	from	ADP
ejpam-6631	293	16	theorem	theorem	ADJ
ejpam-6631	293	17	1	1	NUM
ejpam-6631	293	18	is	be	AUX
ejpam-6631	293	19	,	,	PUNCT
ejpam-6631	293	20	we	we	PRON
ejpam-6631	293	21	use	use	VERB
ejpam-6631	293	22	it	it	PRON
ejpam-6631	293	23	to	to	PART
ejpam-6631	293	24	estimate	estimate	VERB
ejpam-6631	293	25	the	the	DET
ejpam-6631	293	26	prabhakar	prabhakar	NOUN
ejpam-6631	293	27	derivative	derivative	NOUN
ejpam-6631	293	28	derivative	derivative	NOUN
ejpam-6631	293	29	for	for	ADP
ejpam-6631	293	30	example	example	NOUN
ejpam-6631	293	31	1	1	X
ejpam-6631	293	32	.	.	PUNCT
ejpam-6631	294	1	we	we	PRON
ejpam-6631	294	2	applied	apply	VERB
ejpam-6631	294	3	the	the	DET
ejpam-6631	294	4	five	five	NUM
ejpam-6631	294	5	-	-	PUNCT
ejpam-6631	294	6	parameter	parameter	NOUN
ejpam-6631	294	7	mittag	mittag	ADJ
ejpam-6631	294	8	-	-	PUNCT
ejpam-6631	294	9	leffler	leffler	NOUN
ejpam-6631	294	10	functions	function	NOUN
ejpam-6631	294	11	as	as	SCONJ
ejpam-6631	294	12	defined	define	VERB
ejpam-6631	294	13	:	:	PUNCT
ejpam-6631	294	14	for	for	ADP
ejpam-6631	294	15	rdγ	rdγ	PROPN
ejpam-6631	294	16	α	α	PROPN
ejpam-6631	294	17	,	,	PUNCT
ejpam-6631	294	18	β	β	PROPN
ejpam-6631	294	19	,	,	PUNCT
ejpam-6631	294	20	τ	τ	PROPN
ejpam-6631	294	21	,	,	PUNCT
ejpam-6631	294	22	a	a	DET
ejpam-6631	294	23	+	+	NOUN
ejpam-6631	294	24	p(t	p(t	NOUN
ejpam-6631	294	25	)	)	PUNCT
ejpam-6631	294	26	=	=	NOUN
ejpam-6631	295	1	∞∑	∞∑	PRON
ejpam-6631	295	2	k=0	k=0	PROPN
ejpam-6631	295	3	γ	γ	X
ejpam-6631	295	4	(	(	PUNCT
ejpam-6631	295	5	−r	−r	PROPN
ejpam-6631	295	6	+	+	X
ejpam-6631	295	7	k)wkγ	k)wkγ	PROPN
ejpam-6631	295	8	(	(	PUNCT
ejpam-6631	295	9	p+	p+	NOUN
ejpam-6631	295	10	1	1	NUM
ejpam-6631	295	11	)	)	PUNCT
ejpam-6631	295	12	tαk−β+p	tαk−β+p	NOUN
ejpam-6631	295	13	γ	γ	X
ejpam-6631	295	14	(	(	PUNCT
ejpam-6631	295	15	αk	αk	ADP
ejpam-6631	295	16	−	−	PROPN
ejpam-6631	295	17	β	β	X
ejpam-6631	295	18	+	+	PROPN
ejpam-6631	295	19	p+	p+	PROPN
ejpam-6631	295	20	1)γ	1)γ	PROPN
ejpam-6631	295	21	(	(	PUNCT
ejpam-6631	295	22	−r	−r	ADJ
ejpam-6631	295	23	)	)	PUNCT
ejpam-6631	295	24	γ	γ	PROPN
ejpam-6631	295	25	(	(	PUNCT
ejpam-6631	295	26	k	k	NOUN
ejpam-6631	295	27	)	)	PUNCT
ejpam-6631	295	28	k	k	NOUN
ejpam-6631	295	29	(	(	PUNCT
ejpam-6631	295	30	39	39	NUM
ejpam-6631	295	31	)	)	PUNCT
ejpam-6631	295	32	where	where	SCONJ
ejpam-6631	295	33	β	β	X
ejpam-6631	295	34	=	=	NOUN
ejpam-6631	295	35	0.99	0.99	NUM
ejpam-6631	295	36	,	,	PUNCT
ejpam-6631	295	37	α	α	NOUN
ejpam-6631	295	38	=	=	SYM
ejpam-6631	295	39	1	1	NUM
ejpam-6631	295	40	,	,	PUNCT
ejpam-6631	295	41	w	w	NOUN
ejpam-6631	295	42	=	=	SYM
ejpam-6631	295	43	1	1	NUM
ejpam-6631	295	44	,	,	PUNCT
ejpam-6631	295	45	r	r	NOUN
ejpam-6631	295	46	=	=	SYM
ejpam-6631	295	47	1	1	NUM
ejpam-6631	295	48	so	so	SCONJ
ejpam-6631	295	49	that	that	SCONJ
ejpam-6631	295	50	,	,	PUNCT
ejpam-6631	295	51	rdγ	rdγ	NOUN
ejpam-6631	295	52	α	α	NOUN
ejpam-6631	295	53	,	,	PUNCT
ejpam-6631	295	54	β	β	PROPN
ejpam-6631	295	55	,	,	PUNCT
ejpam-6631	295	56	τ	τ	PROPN
ejpam-6631	295	57	,	,	PUNCT
ejpam-6631	295	58	a+p(x	a+p(x	NOUN
ejpam-6631	295	59	)	)	PUNCT
ejpam-6631	295	60	=	=	PUNCT
ejpam-6631	295	61	−	−	PROPN
ejpam-6631	295	62	32	32	NUM
ejpam-6631	295	63	t	t	NOUN
ejpam-6631	295	64	7	7	NUM
ejpam-6631	295	65	4	4	NUM
ejpam-6631	295	66	315γ	315γ	NOUN
ejpam-6631	295	67	(	(	PUNCT
ejpam-6631	295	68	3	3	NUM
ejpam-6631	295	69	4	4	NUM
ejpam-6631	295	70	)	)	PUNCT
ejpam-6631	295	71	π	π	PROPN
ejpam-6631	295	72	(	(	PUNCT
ejpam-6631	295	73	7	7	NUM
ejpam-6631	295	74	√	√	NOUN
ejpam-6631	295	75	t	t	NOUN
ejpam-6631	295	76	√	√	NOUN
ejpam-6631	295	77	2	2	NUM
ejpam-6631	295	78	(	(	PUNCT
ejpam-6631	295	79	γ	γ	X
ejpam-6631	295	80	(	(	PUNCT
ejpam-6631	295	81	3	3	NUM
ejpam-6631	295	82	4	4	NUM
ejpam-6631	295	83	)	)	PUNCT
ejpam-6631	295	84	)	)	PUNCT
ejpam-6631	295	85	2	2	NUM
ejpam-6631	295	86	2f2	2f2	NUM
ejpam-6631	295	87	(	(	PUNCT
ejpam-6631	295	88	1	1	NUM
ejpam-6631	295	89	4	4	NUM
ejpam-6631	295	90	,	,	PUNCT
ejpam-6631	295	91	3	3	NUM
ejpam-6631	295	92	4	4	NUM
ejpam-6631	295	93	;	;	PUNCT
ejpam-6631	295	94	3	3	NUM
ejpam-6631	295	95	2	2	NUM
ejpam-6631	295	96	,	,	PUNCT
ejpam-6631	295	97	13	13	NUM
ejpam-6631	295	98	4	4	NUM
ejpam-6631	295	99	;	;	PUNCT
ejpam-6631	295	100	t)−	t)−	PROPN
ejpam-6631	295	101	15	15	NUM
ejpam-6631	295	102	2f2(−	2f2(−	NUM
ejpam-6631	295	103	1	1	NUM
ejpam-6631	295	104	4	4	NUM
ejpam-6631	295	105	,	,	PUNCT
ejpam-6631	295	106	1	1	NUM
ejpam-6631	295	107	4	4	NUM
ejpam-6631	295	108	;	;	PUNCT
ejpam-6631	295	109	1	1	NUM
ejpam-6631	295	110	2	2	NUM
ejpam-6631	295	111	,	,	PUNCT
ejpam-6631	295	112	11	11	NUM
ejpam-6631	295	113	4	4	NUM
ejpam-6631	295	114	;	;	PUNCT
ejpam-6631	295	115	t)π	t)π	X
ejpam-6631	295	116	)	)	PUNCT
ejpam-6631	295	117	(	(	PUNCT
ejpam-6631	295	118	40	40	NUM
ejpam-6631	295	119	)	)	PUNCT
ejpam-6631	295	120	table	table	NOUN
ejpam-6631	295	121	1	1	NUM
ejpam-6631	295	122	:	:	PUNCT
ejpam-6631	295	123	the	the	DET
ejpam-6631	295	124	comparison	comparison	NOUN
ejpam-6631	295	125	between	between	ADP
ejpam-6631	295	126	the	the	DET
ejpam-6631	295	127	homotopy	homotopy	NOUN
ejpam-6631	295	128	perturbation	perturbation	NOUN
ejpam-6631	295	129	transform	transform	NOUN
ejpam-6631	295	130	method	method	NOUN
ejpam-6631	295	131	(	(	PUNCT
ejpam-6631	295	132	hptm	hptm	NOUN
ejpam-6631	295	133	)	)	PUNCT
ejpam-6631	295	134	and	and	CCONJ
ejpam-6631	295	135	proposed	propose	VERB
ejpam-6631	295	136	solutions	solution	NOUN
ejpam-6631	295	137	at	at	ADP
ejpam-6631	295	138	when	when	SCONJ
ejpam-6631	295	139	β	β	X
ejpam-6631	295	140	=	=	SYM
ejpam-6631	295	141	0.99	0.99	NUM
ejpam-6631	295	142	t	t	NOUN
ejpam-6631	295	143	exact	exact	ADJ
ejpam-6631	295	144	hptm	hptm	NOUN
ejpam-6631	295	145	solutions	solution	NOUN
ejpam-6631	295	146	absolute	absolute	ADJ
ejpam-6631	295	147	error	error	NOUN
ejpam-6631	295	148	0.01	0.01	NUM
ejpam-6631	295	149	0.0001	0.0001	NUM
ejpam-6631	295	150	0.0003	0.0003	NUM
ejpam-6631	295	151	0.0000	0.0000	NUM
ejpam-6631	295	152	0.00000e+00	0.00000e+00	NUM
ejpam-6631	295	153	0.02	0.02	NUM
ejpam-6631	295	154	0.0004	0.0004	NUM
ejpam-6631	295	155	0.0008	0.0008	NUM
ejpam-6631	295	156	0.0005	0.0005	NUM
ejpam-6631	295	157	1.69000e-01	1.69000e-01	NUM
ejpam-6631	295	158	0.03	0.03	NUM
ejpam-6631	295	159	0.0009	0.0009	NUM
ejpam-6631	295	160	0.0015	0.0015	NUM
ejpam-6631	295	161	0.0012	0.0012	NUM
ejpam-6631	295	162	2.72000e-01	2.72000e-01	NUM
ejpam-6631	295	163	0.04	0.04	NUM
ejpam-6631	295	164	0.0015	0.0015	NUM
ejpam-6631	295	165	0.0023	0.0023	NUM
ejpam-6631	295	166	0.0021	0.0021	NUM
ejpam-6631	295	167	3.03000e-01	3.03000e-01	NUM
ejpam-6631	295	168	0.05	0.05	NUM
ejpam-6631	295	169	0.0024	0.0024	NUM
ejpam-6631	295	170	0.0034	0.0034	NUM
ejpam-6631	295	171	0.0031	0.0031	NUM
ejpam-6631	295	172	2.56000e-01	2.56000e-01	NUM
ejpam-6631	295	173	0.06	0.06	NUM
ejpam-6631	295	174	0.0034	0.0034	NUM
ejpam-6631	295	175	0.0046	0.0046	NUM
ejpam-6631	295	176	0.0044	0.0044	NUM
ejpam-6631	295	177	1.25000e-01	1.25000e-01	NUM
ejpam-6631	295	178	0.07	0.07	NUM
ejpam-6631	295	179	0.0046	0.0046	NUM
ejpam-6631	295	180	0.0059	0.0059	NUM
ejpam-6631	295	181	0.0058	0.0058	NUM
ejpam-6631	295	182	9.60000e-0	9.60000e-0	NUM
ejpam-6631	295	183	0.08	0.08	NUM
ejpam-6631	295	184	0.0059	0.0059	NUM
ejpam-6631	295	185	0.0075	0.0075	NUM
ejpam-6631	295	186	0.0073	0.0073	NUM
ejpam-6631	295	187	4.13000e-01	4.13000e-01	NUM
ejpam-6631	295	188	0.09	0.09	NUM
ejpam-6631	295	189	0.0074	0.0074	NUM
ejpam-6631	295	190	0.0091	0.0091	NUM
ejpam-6631	295	191	0.0090	0.0090	NUM
ejpam-6631	295	192	8.32000e-01	8.32000e-01	NUM
ejpam-6631	295	193	m.	m.	NOUN
ejpam-6631	295	194	abdel	abdel	PROPN
ejpam-6631	295	195	aal	aal	PROPN
ejpam-6631	295	196	et	et	PROPN
ejpam-6631	295	197	al	al	PROPN
ejpam-6631	295	198	.	.	PUNCT
ejpam-6631	295	199	/	/	SYM
ejpam-6631	295	200	eur	eur	PROPN
ejpam-6631	295	201	.	.	PUNCT
ejpam-6631	296	1	j.	j.	PROPN
ejpam-6631	296	2	pure	pure	PROPN
ejpam-6631	296	3	appl	appl	PROPN
ejpam-6631	296	4	.	.	PROPN
ejpam-6631	296	5	math	math	PROPN
ejpam-6631	296	6	,	,	PUNCT
ejpam-6631	296	7	18	18	NUM
ejpam-6631	296	8	(	(	PUNCT
ejpam-6631	296	9	4	4	NUM
ejpam-6631	296	10	)	)	PUNCT
ejpam-6631	296	11	(	(	PUNCT
ejpam-6631	296	12	2025	2025	NUM
ejpam-6631	296	13	)	)	PUNCT
ejpam-6631	296	14	,	,	PUNCT
ejpam-6631	296	15	6631	6631	NUM
ejpam-6631	296	16	13	13	NUM
ejpam-6631	296	17	of	of	ADP
ejpam-6631	296	18	20	20	NUM
ejpam-6631	296	19	we	we	PRON
ejpam-6631	296	20	used	use	VERB
ejpam-6631	296	21	the	the	DET
ejpam-6631	296	22	proposed	propose	VERB
ejpam-6631	296	23	method	method	NOUN
ejpam-6631	296	24	to	to	PART
ejpam-6631	296	25	get	get	VERB
ejpam-6631	296	26	the	the	DET
ejpam-6631	296	27	results	result	NOUN
ejpam-6631	296	28	shown	show	VERB
ejpam-6631	296	29	in	in	ADP
ejpam-6631	296	30	table	table	NOUN
ejpam-6631	296	31	1	1	NUM
ejpam-6631	296	32	.	.	PUNCT
ejpam-6631	297	1	this	this	DET
ejpam-6631	297	2	table	table	NOUN
ejpam-6631	297	3	compares	compare	VERB
ejpam-6631	297	4	our	our	PRON
ejpam-6631	297	5	results	result	NOUN
ejpam-6631	297	6	with	with	ADP
ejpam-6631	297	7	the	the	DET
ejpam-6631	297	8	iteration	iteration	NOUN
ejpam-6631	297	9	method	method	NOUN
ejpam-6631	297	10	(	(	PUNCT
ejpam-6631	297	11	hptm	hptm	NOUN
ejpam-6631	297	12	)	)	PUNCT
ejpam-6631	297	13	in	in	ADP
ejpam-6631	297	14	ref	ref	NOUN
ejpam-6631	297	15	.	.	PUNCT
ejpam-6631	298	1	[	[	X
ejpam-6631	298	2	22	22	NUM
ejpam-6631	298	3	]	]	PUNCT
ejpam-6631	298	4	,	,	PUNCT
ejpam-6631	298	5	using	use	VERB
ejpam-6631	298	6	a	a	DET
ejpam-6631	298	7	step	step	NOUN
ejpam-6631	298	8	size	size	NOUN
ejpam-6631	298	9	of	of	ADP
ejpam-6631	298	10	h	h	NOUN
ejpam-6631	298	11	=	=	NOUN
ejpam-6631	298	12	0.01	0.01	NUM
ejpam-6631	298	13	.	.	PUNCT
ejpam-6631	299	1	our	our	PRON
ejpam-6631	299	2	numerical	numerical	ADJ
ejpam-6631	299	3	results	result	NOUN
ejpam-6631	299	4	show	show	VERB
ejpam-6631	299	5	that	that	SCONJ
ejpam-6631	299	6	even	even	ADV
ejpam-6631	299	7	with	with	ADP
ejpam-6631	299	8	just	just	ADV
ejpam-6631	299	9	a	a	DET
ejpam-6631	299	10	few	few	ADJ
ejpam-6631	299	11	terms	term	NOUN
ejpam-6631	299	12	(	(	PUNCT
ejpam-6631	299	13	n	n	NOUN
ejpam-6631	299	14	=	=	SYM
ejpam-6631	299	15	2	2	NUM
ejpam-6631	299	16	)	)	PUNCT
ejpam-6631	299	17	,	,	PUNCT
ejpam-6631	299	18	we	we	PRON
ejpam-6631	299	19	achieved	achieve	VERB
ejpam-6631	299	20	good	good	ADJ
ejpam-6631	299	21	results	result	NOUN
ejpam-6631	299	22	compared	compare	VERB
ejpam-6631	299	23	to	to	ADP
ejpam-6631	299	24	the	the	DET
ejpam-6631	299	25	method	method	NOUN
ejpam-6631	299	26	in	in	ADP
ejpam-6631	299	27	ref	ref	NOUN
ejpam-6631	299	28	.	.	PUNCT
ejpam-6631	300	1	[	[	X
ejpam-6631	300	2	22	22	NUM
ejpam-6631	300	3	]	]	PUNCT
ejpam-6631	300	4	.	.	PUNCT
ejpam-6631	301	1	figure	figure	NOUN
ejpam-6631	301	2	1	1	NUM
ejpam-6631	301	3	shows	show	VERB
ejpam-6631	301	4	a	a	DET
ejpam-6631	301	5	comparison	comparison	NOUN
ejpam-6631	301	6	between	between	ADP
ejpam-6631	301	7	the	the	DET
ejpam-6631	301	8	exact	exact	ADJ
ejpam-6631	301	9	equation	equation	NOUN
ejpam-6631	301	10	and	and	CCONJ
ejpam-6631	301	11	the	the	DET
ejpam-6631	301	12	approximate	approximate	ADJ
ejpam-6631	301	13	solution	solution	NOUN
ejpam-6631	301	14	.	.	PUNCT
ejpam-6631	302	1	this	this	DET
ejpam-6631	302	2	comparison	comparison	NOUN
ejpam-6631	302	3	demonstrates	demonstrate	VERB
ejpam-6631	302	4	that	that	SCONJ
ejpam-6631	302	5	the	the	DET
ejpam-6631	302	6	proposed	propose	VERB
ejpam-6631	302	7	method	method	NOUN
ejpam-6631	302	8	is	be	AUX
ejpam-6631	302	9	accurate	accurate	ADJ
ejpam-6631	302	10	,	,	PUNCT
ejpam-6631	302	11	as	as	SCONJ
ejpam-6631	302	12	the	the	DET
ejpam-6631	302	13	approximate	approximate	ADJ
ejpam-6631	302	14	solution	solution	NOUN
ejpam-6631	302	15	closely	closely	ADV
ejpam-6631	302	16	matches	match	VERB
ejpam-6631	302	17	the	the	DET
ejpam-6631	302	18	exact	exact	ADJ
ejpam-6631	302	19	values	value	NOUN
ejpam-6631	302	20	.	.	PUNCT
ejpam-6631	303	1	also	also	ADV
ejpam-6631	303	2	,	,	PUNCT
ejpam-6631	303	3	figure	figure	VERB
ejpam-6631	303	4	1	1	NUM
ejpam-6631	303	5	shows	show	VERB
ejpam-6631	303	6	the	the	DET
ejpam-6631	303	7	results	result	NOUN
ejpam-6631	303	8	for	for	ADP
ejpam-6631	303	9	different	different	ADJ
ejpam-6631	303	10	values	value	NOUN
ejpam-6631	303	11	of	of	ADP
ejpam-6631	303	12	the	the	DET
ejpam-6631	303	13	parameter	parameter	NOUN
ejpam-6631	303	14	β	β	NOUN
ejpam-6631	303	15	:	:	PUNCT
ejpam-6631	303	16	0.95	0.95	NUM
ejpam-6631	303	17	,	,	PUNCT
ejpam-6631	303	18	0.75	0.75	NUM
ejpam-6631	303	19	,	,	PUNCT
ejpam-6631	303	20	and	and	CCONJ
ejpam-6631	303	21	0.55	0.55	NUM
ejpam-6631	303	22	,	,	PUNCT
ejpam-6631	303	23	as	as	SCONJ
ejpam-6631	303	24	explained	explain	VERB
ejpam-6631	303	25	in	in	ADP
ejpam-6631	303	26	example	example	NOUN
ejpam-6631	303	27	1	1	NUM
ejpam-6631	303	28	.	.	X
ejpam-6631	303	29	changing	change	VERB
ejpam-6631	303	30	the	the	DET
ejpam-6631	303	31	value	value	NOUN
ejpam-6631	303	32	of	of	ADP
ejpam-6631	303	33	β	β	PROPN
ejpam-6631	303	34	has	have	VERB
ejpam-6631	303	35	a	a	DET
ejpam-6631	303	36	significant	significant	ADJ
ejpam-6631	303	37	effect	effect	NOUN
ejpam-6631	303	38	on	on	ADP
ejpam-6631	303	39	the	the	DET
ejpam-6631	303	40	process	process	NOUN
ejpam-6631	303	41	.	.	PUNCT
ejpam-6631	304	1	this	this	PRON
ejpam-6631	304	2	demonstrates	demonstrate	VERB
ejpam-6631	304	3	how	how	SCONJ
ejpam-6631	304	4	adjustments	adjustment	NOUN
ejpam-6631	304	5	in	in	ADP
ejpam-6631	304	6	this	this	DET
ejpam-6631	304	7	parameter	parameter	NOUN
ejpam-6631	304	8	can	can	AUX
ejpam-6631	304	9	influence	influence	VERB
ejpam-6631	304	10	the	the	DET
ejpam-6631	304	11	results	result	NOUN
ejpam-6631	304	12	and	and	CCONJ
ejpam-6631	304	13	confirms	confirm	VERB
ejpam-6631	304	14	that	that	SCONJ
ejpam-6631	304	15	the	the	DET
ejpam-6631	304	16	proposed	propose	VERB
ejpam-6631	304	17	method	method	NOUN
ejpam-6631	304	18	is	be	AUX
ejpam-6631	304	19	strong	strong	ADJ
ejpam-6631	304	20	enough	enough	ADV
ejpam-6631	304	21	to	to	PART
ejpam-6631	304	22	work	work	VERB
ejpam-6631	304	23	in	in	ADP
ejpam-6631	304	24	various	various	ADJ
ejpam-6631	304	25	situations	situation	NOUN
ejpam-6631	304	26	.	.	PUNCT
ejpam-6631	305	1	figure	figure	NOUN
ejpam-6631	305	2	1	1	NUM
ejpam-6631	305	3	:	:	PUNCT
ejpam-6631	305	4	the	the	DET
ejpam-6631	305	5	results	result	NOUN
ejpam-6631	305	6	of	of	ADP
ejpam-6631	305	7	the	the	DET
ejpam-6631	305	8	comparison	comparison	NOUN
ejpam-6631	305	9	between	between	ADP
ejpam-6631	305	10	the	the	DET
ejpam-6631	305	11	approximate	approximate	ADJ
ejpam-6631	305	12	and	and	CCONJ
ejpam-6631	305	13	exact	exact	ADJ
ejpam-6631	305	14	solutions	solution	NOUN
ejpam-6631	305	15	for	for	ADP
ejpam-6631	305	16	example	example	NOUN
ejpam-6631	305	17	1	1	NUM
ejpam-6631	305	18	table	table	NOUN
ejpam-6631	305	19	2	2	NUM
ejpam-6631	305	20	compares	compare	VERB
ejpam-6631	305	21	our	our	PRON
ejpam-6631	305	22	results	result	NOUN
ejpam-6631	305	23	with	with	ADP
ejpam-6631	305	24	those	those	PRON
ejpam-6631	305	25	obtained	obtain	VERB
ejpam-6631	305	26	from	from	ADP
ejpam-6631	305	27	the	the	DET
ejpam-6631	305	28	fractional	fractional	PROPN
ejpam-6631	305	29	homotopy	homotopy	NOUN
ejpam-6631	305	30	perturbation	perturbation	NOUN
ejpam-6631	305	31	transform	transform	NOUN
ejpam-6631	305	32	method	method	NOUN
ejpam-6631	305	33	(	(	PUNCT
ejpam-6631	305	34	fhptm	fhptm	NOUN
ejpam-6631	305	35	)	)	PUNCT
ejpam-6631	305	36	when	when	SCONJ
ejpam-6631	305	37	β	β	X
ejpam-6631	305	38	=	=	NOUN
ejpam-6631	305	39	0.95	0.95	NUM
ejpam-6631	305	40	.	.	PUNCT
ejpam-6631	306	1	our	our	PRON
ejpam-6631	306	2	findings	finding	NOUN
ejpam-6631	306	3	indicate	indicate	VERB
ejpam-6631	306	4	that	that	SCONJ
ejpam-6631	306	5	we	we	PRON
ejpam-6631	306	6	achieved	achieve	VERB
ejpam-6631	306	7	favourable	favourable	ADJ
ejpam-6631	306	8	results	result	NOUN
ejpam-6631	306	9	compared	compare	VERB
ejpam-6631	306	10	to	to	ADP
ejpam-6631	306	11	the	the	DET
ejpam-6631	306	12	method	method	NOUN
ejpam-6631	306	13	described	describe	VERB
ejpam-6631	306	14	in	in	ADP
ejpam-6631	306	15	ref	ref	NOUN
ejpam-6631	306	16	.	.	PUNCT
ejpam-6631	307	1	[	[	X
ejpam-6631	307	2	22	22	NUM
ejpam-6631	307	3	]	]	PUNCT
ejpam-6631	307	4	.	.	PUNCT
ejpam-6631	308	1	the	the	DET
ejpam-6631	308	2	numerical	numerical	ADJ
ejpam-6631	308	3	results	result	NOUN
ejpam-6631	308	4	demonstrate	demonstrate	VERB
ejpam-6631	308	5	that	that	SCONJ
ejpam-6631	308	6	our	our	PRON
ejpam-6631	308	7	proposed	propose	VERB
ejpam-6631	308	8	method	method	NOUN
ejpam-6631	308	9	is	be	AUX
ejpam-6631	308	10	an	an	DET
ejpam-6631	308	11	efficient	efficient	ADJ
ejpam-6631	308	12	algorithm	algorithm	NOUN
ejpam-6631	308	13	when	when	SCONJ
ejpam-6631	308	14	compared	compare	VERB
ejpam-6631	308	15	to	to	ADP
ejpam-6631	308	16	the	the	DET
ejpam-6631	308	17	hptm	hptm	NOUN
ejpam-6631	308	18	and	and	CCONJ
ejpam-6631	308	19	fhptm	fhptm	ADJ
ejpam-6631	308	20	methods	method	NOUN
ejpam-6631	308	21	discussed	discuss	VERB
ejpam-6631	308	22	in	in	ADP
ejpam-6631	308	23	ref	ref	NOUN
ejpam-6631	308	24	.	.	PUNCT
ejpam-6631	309	1	[	[	X
ejpam-6631	309	2	22	22	NUM
ejpam-6631	309	3	]	]	PUNCT
ejpam-6631	309	4	.	.	PUNCT
ejpam-6631	309	5	example	example	NOUN
ejpam-6631	309	6	2	2	NUM
ejpam-6631	309	7	.	.	X
ejpam-6631	309	8	we	we	PRON
ejpam-6631	309	9	look	look	VERB
ejpam-6631	309	10	at	at	ADP
ejpam-6631	309	11	nonlinear	nonlinear	ADJ
ejpam-6631	309	12	fractional	fractional	ADJ
ejpam-6631	309	13	differential	differential	NOUN
ejpam-6631	309	14	equation	equation	NOUN
ejpam-6631	309	15	defined	define	VERB
ejpam-6631	309	16	using	use	VERB
ejpam-6631	309	17	the	the	DET
ejpam-6631	309	18	prabhakar	prabhakar	NOUN
ejpam-6631	309	19	derivative	derivative	NOUN
ejpam-6631	309	20	;	;	PUNCT
ejpam-6631	309	21	rdγ	rdγ	NOUN
ejpam-6631	309	22	α	α	NOUN
ejpam-6631	309	23	,	,	PUNCT
ejpam-6631	309	24	β	β	PROPN
ejpam-6631	309	25	,	,	PUNCT
ejpam-6631	309	26	τ	τ	PROPN
ejpam-6631	309	27	,	,	PUNCT
ejpam-6631	309	28	a	a	DET
ejpam-6631	309	29	+	+	X
ejpam-6631	309	30	p(x	p(x	NOUN
ejpam-6631	309	31	)	)	PUNCT
ejpam-6631	309	32	=	=	PUNCT
ejpam-6631	309	33	g(x)−	g(x)−	PROPN
ejpam-6631	309	34	u2(x	u2(x	PROPN
ejpam-6631	309	35	)	)	PUNCT
ejpam-6631	309	36	.	.	PUNCT
ejpam-6631	310	1	(	(	PUNCT
ejpam-6631	310	2	41	41	NUM
ejpam-6631	310	3	)	)	PUNCT
ejpam-6631	310	4	given	give	VERB
ejpam-6631	310	5	the	the	DET
ejpam-6631	310	6	initial	initial	ADJ
ejpam-6631	310	7	condition	condition	NOUN
ejpam-6631	311	1	that	that	SCONJ
ejpam-6631	311	2	m.	m.	NOUN
ejpam-6631	311	3	abdel	abdel	PROPN
ejpam-6631	311	4	aal	aal	PROPN
ejpam-6631	311	5	et	et	PROPN
ejpam-6631	311	6	al	al	PROPN
ejpam-6631	311	7	.	.	PUNCT
ejpam-6631	311	8	/	/	SYM
ejpam-6631	311	9	eur	eur	PROPN
ejpam-6631	311	10	.	.	PUNCT
ejpam-6631	312	1	j.	j.	PROPN
ejpam-6631	312	2	pure	pure	PROPN
ejpam-6631	312	3	appl	appl	PROPN
ejpam-6631	312	4	.	.	PROPN
ejpam-6631	312	5	math	math	PROPN
ejpam-6631	312	6	,	,	PUNCT
ejpam-6631	312	7	18	18	NUM
ejpam-6631	312	8	(	(	PUNCT
ejpam-6631	312	9	4	4	NUM
ejpam-6631	312	10	)	)	PUNCT
ejpam-6631	312	11	(	(	PUNCT
ejpam-6631	312	12	2025	2025	NUM
ejpam-6631	312	13	)	)	PUNCT
ejpam-6631	312	14	,	,	PUNCT
ejpam-6631	312	15	6631	6631	NUM
ejpam-6631	312	16	14	14	NUM
ejpam-6631	312	17	of	of	ADP
ejpam-6631	312	18	20	20	NUM
ejpam-6631	312	19	figure	figure	NOUN
ejpam-6631	312	20	2	2	NUM
ejpam-6631	312	21	:	:	PUNCT
ejpam-6631	312	22	the	the	DET
ejpam-6631	312	23	results	result	NOUN
ejpam-6631	312	24	of	of	ADP
ejpam-6631	312	25	the	the	DET
ejpam-6631	312	26	comparison	comparison	NOUN
ejpam-6631	312	27	between	between	ADP
ejpam-6631	312	28	the	the	DET
ejpam-6631	312	29	approximate	approximate	ADJ
ejpam-6631	312	30	and	and	CCONJ
ejpam-6631	312	31	exact	exact	ADJ
ejpam-6631	312	32	solutions	solution	NOUN
ejpam-6631	312	33	for	for	ADP
ejpam-6631	312	34	example	example	NOUN
ejpam-6631	312	35	1	1	NUM
ejpam-6631	312	36	table	table	NOUN
ejpam-6631	312	37	2	2	NUM
ejpam-6631	312	38	:	:	PUNCT
ejpam-6631	312	39	the	the	DET
ejpam-6631	312	40	comparison	comparison	NOUN
ejpam-6631	312	41	between	between	ADP
ejpam-6631	312	42	the	the	DET
ejpam-6631	312	43	homotopy	homotopy	NOUN
ejpam-6631	312	44	perturbation	perturbation	NOUN
ejpam-6631	312	45	transform	transform	NOUN
ejpam-6631	312	46	method	method	NOUN
ejpam-6631	312	47	(	(	PUNCT
ejpam-6631	312	48	hptm	hptm	NOUN
ejpam-6631	312	49	)	)	PUNCT
ejpam-6631	312	50	,	,	PUNCT
ejpam-6631	312	51	fractional	fractional	PROPN
ejpam-6631	312	52	homotopy	homotopy	NOUN
ejpam-6631	312	53	perturbation	perturbation	NOUN
ejpam-6631	312	54	transform	transform	NOUN
ejpam-6631	312	55	method	method	NOUN
ejpam-6631	312	56	(	(	PUNCT
ejpam-6631	312	57	fhptm	fhptm	NOUN
ejpam-6631	312	58	)	)	PUNCT
ejpam-6631	312	59	and	and	CCONJ
ejpam-6631	312	60	proposed	propose	VERB
ejpam-6631	312	61	solutions	solution	NOUN
ejpam-6631	312	62	at	at	ADP
ejpam-6631	312	63	when	when	SCONJ
ejpam-6631	312	64	β	β	X
ejpam-6631	312	65	=	=	NOUN
ejpam-6631	312	66	0.95	0.95	NUM
ejpam-6631	312	67	t	t	PROPN
ejpam-6631	312	68	exact	exact	ADJ
ejpam-6631	312	69	hptm	hptm	NOUN
ejpam-6631	312	70	fhptm	fhptm	ADJ
ejpam-6631	312	71	approximate	approximate	ADJ
ejpam-6631	312	72	solution	solution	NOUN
ejpam-6631	312	73	absolute	absolute	ADJ
ejpam-6631	312	74	error	error	NOUN
ejpam-6631	312	75	0.01	0.01	NUM
ejpam-6631	312	76	0.0001	0.0001	NUM
ejpam-6631	312	77	0.0011	0.0011	NUM
ejpam-6631	312	78	0.0008	0.0008	NUM
ejpam-6631	312	79	0.000001	0.000001	NUM
ejpam-6631	312	80	1.33339e+00	1.33339e+00	NUM
ejpam-6631	312	81	0.02	0.02	NUM
ejpam-6631	312	82	0.0004	0.0004	NUM
ejpam-6631	312	83	0.0024	0.0024	NUM
ejpam-6631	312	84	0.0017	0.0017	NUM
ejpam-6631	312	85	0.000006	0.000006	NUM
ejpam-6631	312	86	9.18072e-01	9.18072e-01	NUM
ejpam-6631	312	87	0.03	0.03	NUM
ejpam-6631	312	88	0.0009	0.0009	NUM
ejpam-6631	312	89	0.0039	0.0039	NUM
ejpam-6631	312	90	0.0027	0.0027	NUM
ejpam-6631	312	91	0.000016	0.000016	NUM
ejpam-6631	312	92	5.18988e-01	5.18988e-01	NUM
ejpam-6631	312	93	0.04	0.04	NUM
ejpam-6631	312	94	0.0015	0.0015	NUM
ejpam-6631	312	95	0.0056	0.0056	NUM
ejpam-6631	312	96	0.0039	0.0039	NUM
ejpam-6631	312	97	0.000034	0.000034	NUM
ejpam-6631	312	98	1.57268e-01	1.57268e-01	NUM
ejpam-6631	312	99	0.05	0.05	NUM
ejpam-6631	312	100	0.0024	0.0024	NUM
ejpam-6631	312	101	0.0074	0.0074	NUM
ejpam-6631	312	102	0.0052	0.0052	NUM
ejpam-6631	312	103	0.000062	0.000062	NUM
ejpam-6631	312	104	1.59033e-01	1.59033e-01	NUM
ejpam-6631	312	105	0.06	0.06	NUM
ejpam-6631	312	106	0.0034	0.0034	NUM
ejpam-6631	312	107	0.0093	0.0093	NUM
ejpam-6631	312	108	0.0065	0.0065	NUM
ejpam-6631	312	109	0.000101	0.000101	NUM
ejpam-6631	312	110	4.25645e-01	4.25645e-01	NUM
ejpam-6631	312	111	0.07	0.07	NUM
ejpam-6631	312	112	0.0046	0.0046	NUM
ejpam-6631	312	113	0.0115	0.0115	NUM
ejpam-6631	312	114	0.0080	0.0080	NUM
ejpam-6631	312	115	0.000155	0.000155	NUM
ejpam-6631	312	116	6.39892e-01	6.39892e-01	NUM
ejpam-6631	312	117	0.08	0.08	NUM
ejpam-6631	312	118	0.0059	0.0059	NUM
ejpam-6631	312	119	0.0137	0.0137	NUM
ejpam-6631	312	120	0.0096	0.0096	NUM
ejpam-6631	312	121	0.000225	0.000225	NUM
ejpam-6631	313	1	7.99914e-01	7.99914e-01	NUM
ejpam-6631	313	2	0.09	0.09	NUM
ejpam-6631	313	3	0.0074	0.0074	NUM
ejpam-6631	313	4	0.0161	0.0161	NUM
ejpam-6631	313	5	0.0113	0.0113	NUM
ejpam-6631	313	6	0.000316	0.000316	NUM
ejpam-6631	313	7	9.04328e-01	9.04328e-01	NUM
ejpam-6631	313	8	p(0	p(0	NOUN
ejpam-6631	313	9	)	)	PUNCT
ejpam-6631	313	10	=	=	SYM
ejpam-6631	313	11	0	0	PUNCT
ejpam-6631	313	12	(	(	PUNCT
ejpam-6631	313	13	42	42	NUM
ejpam-6631	313	14	)	)	PUNCT
ejpam-6631	313	15	so	so	SCONJ
ejpam-6631	313	16	that	that	SCONJ
ejpam-6631	313	17	g(x	g(x	NOUN
ejpam-6631	313	18	)	)	PUNCT
ejpam-6631	314	1	=	=	SYM
ejpam-6631	314	2	(	(	PUNCT
ejpam-6631	314	3	2t−	2t−	ADP
ejpam-6631	314	4	3t2	3t2	NUM
ejpam-6631	314	5	+	+	CCONJ
ejpam-6631	314	6	t3)2	t3)2	NUM
ejpam-6631	314	7	+	+	NUM
ejpam-6631	314	8	2t1−β	2t1−β	NUM
ejpam-6631	314	9	γ(2−	γ(2−	NUM
ejpam-6631	314	10	β	β	NOUN
ejpam-6631	314	11	)	)	PUNCT
ejpam-6631	314	12	−	−	PROPN
ejpam-6631	315	1	6t2−β	6t2−β	NUM
ejpam-6631	315	2	γ(3−	γ(3−	ADP
ejpam-6631	315	3	β	β	X
ejpam-6631	315	4	)	)	PUNCT
ejpam-6631	316	1	+	+	CCONJ
ejpam-6631	317	1	6t3−β	6t3−β	NUM
ejpam-6631	317	2	γ(4−	γ(4−	NOUN
ejpam-6631	317	3	β	β	NOUN
ejpam-6631	317	4	)	)	PUNCT
ejpam-6631	317	5	.	.	PUNCT
ejpam-6631	318	1	(	(	PUNCT
ejpam-6631	318	2	43	43	NUM
ejpam-6631	318	3	)	)	PUNCT
ejpam-6631	318	4	the	the	DET
ejpam-6631	318	5	exact	exact	ADJ
ejpam-6631	318	6	solution	solution	NOUN
ejpam-6631	318	7	is	be	AUX
ejpam-6631	318	8	;	;	PUNCT
ejpam-6631	319	1	m.	m.	NOUN
ejpam-6631	319	2	abdel	abdel	PROPN
ejpam-6631	319	3	aal	aal	PROPN
ejpam-6631	319	4	et	et	PROPN
ejpam-6631	319	5	al	al	PROPN
ejpam-6631	319	6	.	.	PUNCT
ejpam-6631	319	7	/	/	SYM
ejpam-6631	319	8	eur	eur	PROPN
ejpam-6631	319	9	.	.	PUNCT
ejpam-6631	320	1	j.	j.	PROPN
ejpam-6631	320	2	pure	pure	PROPN
ejpam-6631	320	3	appl	appl	PROPN
ejpam-6631	320	4	.	.	PROPN
ejpam-6631	320	5	math	math	PROPN
ejpam-6631	320	6	,	,	PUNCT
ejpam-6631	320	7	18	18	NUM
ejpam-6631	320	8	(	(	PUNCT
ejpam-6631	320	9	4	4	NUM
ejpam-6631	320	10	)	)	PUNCT
ejpam-6631	320	11	(	(	PUNCT
ejpam-6631	320	12	2025	2025	NUM
ejpam-6631	320	13	)	)	PUNCT
ejpam-6631	320	14	,	,	PUNCT
ejpam-6631	320	15	6631	6631	NUM
ejpam-6631	320	16	15	15	NUM
ejpam-6631	320	17	of	of	ADP
ejpam-6631	320	18	20	20	NUM
ejpam-6631	320	19	p(t	p(t	NOUN
ejpam-6631	320	20	)	)	PUNCT
ejpam-6631	320	21	=	=	PUNCT
ejpam-6631	321	1	(	(	PUNCT
ejpam-6631	321	2	−t3	−t3	PROPN
ejpam-6631	321	3	−	−	PROPN
ejpam-6631	321	4	3t2	3t2	NUM
ejpam-6631	321	5	+	+	CCONJ
ejpam-6631	321	6	2t)2	2t)2	NUM
ejpam-6631	321	7	.	.	PUNCT
ejpam-6631	322	1	(	(	PUNCT
ejpam-6631	322	2	44	44	NUM
ejpam-6631	322	3	)	)	PUNCT
ejpam-6631	322	4	solution	solution	NOUN
ejpam-6631	322	5	:	:	PUNCT
ejpam-6631	322	6	to	to	PART
ejpam-6631	322	7	check	check	VERB
ejpam-6631	322	8	how	how	SCONJ
ejpam-6631	322	9	accurate	accurate	ADJ
ejpam-6631	322	10	the	the	DET
ejpam-6631	322	11	explicit	explicit	ADJ
ejpam-6631	322	12	fractional	fractional	ADJ
ejpam-6631	322	13	adams	adam	NOUN
ejpam-6631	322	14	method	method	NOUN
ejpam-6631	322	15	from	from	ADP
ejpam-6631	322	16	theorem	theorem	ADJ
ejpam-6631	322	17	1	1	NUM
ejpam-6631	322	18	is	be	AUX
ejpam-6631	322	19	,	,	PUNCT
ejpam-6631	322	20	we	we	PRON
ejpam-6631	322	21	use	use	VERB
ejpam-6631	322	22	it	it	PRON
ejpam-6631	322	23	to	to	PART
ejpam-6631	322	24	estimate	estimate	VERB
ejpam-6631	322	25	the	the	DET
ejpam-6631	322	26	prabhakar	prabhakar	NOUN
ejpam-6631	322	27	derivative	derivative	NOUN
ejpam-6631	322	28	derivative	derivative	NOUN
ejpam-6631	322	29	for	for	ADP
ejpam-6631	322	30	example	example	NOUN
ejpam-6631	322	31	2	2	X
ejpam-6631	322	32	.	.	PUNCT
ejpam-6631	323	1	we	we	PRON
ejpam-6631	323	2	applied	apply	VERB
ejpam-6631	323	3	the	the	DET
ejpam-6631	323	4	five	five	NUM
ejpam-6631	323	5	-	-	PUNCT
ejpam-6631	323	6	parameter	parameter	NOUN
ejpam-6631	323	7	mittag	mittag	ADJ
ejpam-6631	323	8	-	-	PUNCT
ejpam-6631	323	9	leffler	leffler	NOUN
ejpam-6631	323	10	functions	function	NOUN
ejpam-6631	323	11	as	as	SCONJ
ejpam-6631	323	12	defined	define	VERB
ejpam-6631	323	13	,	,	PUNCT
ejpam-6631	323	14	where	where	SCONJ
ejpam-6631	323	15	β	β	X
ejpam-6631	323	16	=	=	NOUN
ejpam-6631	323	17	0.95	0.95	NUM
ejpam-6631	323	18	,	,	PUNCT
ejpam-6631	323	19	α	α	NOUN
ejpam-6631	323	20	=	=	SYM
ejpam-6631	323	21	1	1	NUM
ejpam-6631	323	22	,	,	PUNCT
ejpam-6631	323	23	w	w	NOUN
ejpam-6631	323	24	=	=	SYM
ejpam-6631	323	25	1	1	NUM
ejpam-6631	323	26	,	,	PUNCT
ejpam-6631	323	27	r	r	NOUN
ejpam-6631	323	28	=	=	SYM
ejpam-6631	323	29	1	1	NUM
ejpam-6631	323	30	so	so	SCONJ
ejpam-6631	323	31	that	that	SCONJ
ejpam-6631	323	32	,	,	PUNCT
ejpam-6631	323	33	rdγ	rdγ	NOUN
ejpam-6631	323	34	α	α	NOUN
ejpam-6631	323	35	,	,	PUNCT
ejpam-6631	323	36	β	β	PROPN
ejpam-6631	323	37	,	,	PUNCT
ejpam-6631	323	38	τ	τ	PROPN
ejpam-6631	323	39	,	,	PUNCT
ejpam-6631	323	40	a+p(x	a+p(x	NOUN
ejpam-6631	323	41	)	)	PUNCT
ejpam-6631	323	42	=	=	PUNCT
ejpam-6631	324	1	(	(	PUNCT
ejpam-6631	324	2	−t3	−t3	NOUN
ejpam-6631	324	3	−	−	PROPN
ejpam-6631	324	4	3	3	NUM
ejpam-6631	324	5	t2	t2	NOUN
ejpam-6631	324	6	+	+	CCONJ
ejpam-6631	324	7	2	2	NUM
ejpam-6631	324	8	t	t	NOUN
ejpam-6631	324	9	)	)	PUNCT
ejpam-6631	324	10	2	2	NUM
ejpam-6631	324	11	+2.054433730	+2.054433730	NUM
ejpam-6631	324	12	t0.05−5.869810658	t0.05−5.869810658	DET
ejpam-6631	324	13	t1.05	t1.05	PROPN
ejpam-6631	324	14	+	+	PROPN
ejpam-6631	324	15	2.863322272	2.863322272	NUM
ejpam-6631	324	16	t2.05	t2.05	NOUN
ejpam-6631	324	17	(	(	PUNCT
ejpam-6631	324	18	45	45	NUM
ejpam-6631	324	19	)	)	PUNCT
ejpam-6631	324	20	figure	figure	NOUN
ejpam-6631	324	21	3	3	NUM
ejpam-6631	324	22	:	:	PUNCT
ejpam-6631	324	23	the	the	DET
ejpam-6631	324	24	results	result	NOUN
ejpam-6631	324	25	of	of	ADP
ejpam-6631	324	26	the	the	DET
ejpam-6631	324	27	comparison	comparison	NOUN
ejpam-6631	324	28	between	between	ADP
ejpam-6631	324	29	the	the	DET
ejpam-6631	324	30	approximate	approximate	ADJ
ejpam-6631	324	31	and	and	CCONJ
ejpam-6631	324	32	exact	exact	ADJ
ejpam-6631	324	33	solutions	solution	NOUN
ejpam-6631	324	34	for	for	ADP
ejpam-6631	324	35	example	example	NOUN
ejpam-6631	324	36	2	2	NUM
ejpam-6631	324	37	figure	figure	NOUN
ejpam-6631	324	38	3	3	NUM
ejpam-6631	324	39	presents	present	VERB
ejpam-6631	324	40	a	a	DET
ejpam-6631	324	41	comparison	comparison	NOUN
ejpam-6631	324	42	between	between	ADP
ejpam-6631	324	43	the	the	DET
ejpam-6631	324	44	exact	exact	ADJ
ejpam-6631	324	45	equation	equation	NOUN
ejpam-6631	324	46	and	and	CCONJ
ejpam-6631	324	47	the	the	DET
ejpam-6631	324	48	approximate	approximate	ADJ
ejpam-6631	324	49	solution	solution	NOUN
ejpam-6631	324	50	.	.	PUNCT
ejpam-6631	325	1	this	this	DET
ejpam-6631	325	2	analysis	analysis	NOUN
ejpam-6631	325	3	demonstrates	demonstrate	VERB
ejpam-6631	325	4	the	the	DET
ejpam-6631	325	5	accuracy	accuracy	NOUN
ejpam-6631	325	6	of	of	ADP
ejpam-6631	325	7	the	the	DET
ejpam-6631	325	8	proposed	propose	VERB
ejpam-6631	325	9	method	method	NOUN
ejpam-6631	325	10	,	,	PUNCT
ejpam-6631	325	11	as	as	SCONJ
ejpam-6631	325	12	the	the	DET
ejpam-6631	325	13	approximate	approximate	ADJ
ejpam-6631	325	14	solution	solution	NOUN
ejpam-6631	325	15	shows	show	VERB
ejpam-6631	325	16	a	a	DET
ejpam-6631	325	17	close	close	ADJ
ejpam-6631	325	18	alignment	alignment	NOUN
ejpam-6631	325	19	with	with	ADP
ejpam-6631	325	20	the	the	DET
ejpam-6631	325	21	exact	exact	ADJ
ejpam-6631	325	22	values	value	NOUN
ejpam-6631	325	23	.	.	PUNCT
ejpam-6631	326	1	table	table	NOUN
ejpam-6631	326	2	4	4	NUM
ejpam-6631	326	3	presents	present	VERB
ejpam-6631	326	4	a	a	DET
ejpam-6631	326	5	comprehensive	comprehensive	ADJ
ejpam-6631	326	6	comparison	comparison	NOUN
ejpam-6631	326	7	between	between	ADP
ejpam-6631	326	8	the	the	DET
ejpam-6631	326	9	approximate	approximate	ADJ
ejpam-6631	326	10	and	and	CCONJ
ejpam-6631	326	11	exact	exact	ADJ
ejpam-6631	326	12	solutions	solution	NOUN
ejpam-6631	326	13	,	,	PUNCT
ejpam-6631	326	14	with	with	ADP
ejpam-6631	326	15	particular	particular	ADJ
ejpam-6631	326	16	emphasis	emphasis	NOUN
ejpam-6631	326	17	on	on	ADP
ejpam-6631	326	18	the	the	DET
ejpam-6631	326	19	associated	associate	VERB
ejpam-6631	326	20	error	error	NOUN
ejpam-6631	326	21	rates	rate	NOUN
ejpam-6631	326	22	.	.	PUNCT
ejpam-6631	327	1	a	a	DET
ejpam-6631	327	2	thorough	thorough	ADJ
ejpam-6631	327	3	analysis	analysis	NOUN
ejpam-6631	327	4	,	,	PUNCT
ejpam-6631	327	5	alongside	alongside	ADP
ejpam-6631	327	6	established	establish	VERB
ejpam-6631	327	7	methodologies	methodology	NOUN
ejpam-6631	327	8	in	in	ADP
ejpam-6631	327	9	the	the	DET
ejpam-6631	327	10	field	field	NOUN
ejpam-6631	327	11	,	,	PUNCT
ejpam-6631	327	12	reveals	reveal	VERB
ejpam-6631	327	13	that	that	SCONJ
ejpam-6631	327	14	the	the	DET
ejpam-6631	327	15	proposed	propose	VERB
ejpam-6631	327	16	approach	approach	NOUN
ejpam-6631	327	17	not	not	PART
ejpam-6631	327	18	only	only	ADV
ejpam-6631	327	19	markedly	markedly	ADV
ejpam-6631	327	20	reduces	reduce	VERB
ejpam-6631	327	21	computational	computational	ADJ
ejpam-6631	327	22	costs	cost	NOUN
ejpam-6631	327	23	but	but	CCONJ
ejpam-6631	327	24	also	also	ADV
ejpam-6631	327	25	delivers	deliver	VERB
ejpam-6631	327	26	improved	improved	ADJ
ejpam-6631	327	27	efficiency	efficiency	NOUN
ejpam-6631	327	28	when	when	SCONJ
ejpam-6631	327	29	compared	compare	VERB
ejpam-6631	327	30	to	to	ADP
ejpam-6631	327	31	solutions	solution	NOUN
ejpam-6631	327	32	within	within	ADP
ejpam-6631	327	33	both	both	CCONJ
ejpam-6631	327	34	the	the	DET
ejpam-6631	327	35	approximate	approximate	ADJ
ejpam-6631	327	36	and	and	CCONJ
ejpam-6631	327	37	exact	exact	ADJ
ejpam-6631	327	38	frameworks	framework	NOUN
ejpam-6631	327	39	.	.	PUNCT
ejpam-6631	328	1	this	this	DET
ejpam-6631	328	2	reduction	reduction	NOUN
ejpam-6631	328	3	in	in	ADP
ejpam-6631	328	4	computational	computational	ADJ
ejpam-6631	328	5	expense	expense	NOUN
ejpam-6631	328	6	is	be	AUX
ejpam-6631	328	7	vital	vital	ADJ
ejpam-6631	328	8	for	for	ADP
ejpam-6631	328	9	applications	application	NOUN
ejpam-6631	328	10	where	where	SCONJ
ejpam-6631	328	11	resources	resource	NOUN
ejpam-6631	328	12	and	and	CCONJ
ejpam-6631	328	13	time	time	NOUN
ejpam-6631	328	14	are	be	AUX
ejpam-6631	328	15	constrained	constrain	VERB
ejpam-6631	328	16	.	.	PUNCT
ejpam-6631	328	17	example	example	NOUN
ejpam-6631	329	1	3	3	X
ejpam-6631	329	2	.	.	X
ejpam-6631	329	3	we	we	PRON
ejpam-6631	329	4	look	look	VERB
ejpam-6631	329	5	at	at	ADP
ejpam-6631	329	6	nonlinear	nonlinear	ADJ
ejpam-6631	329	7	fractional	fractional	ADJ
ejpam-6631	329	8	differential	differential	NOUN
ejpam-6631	329	9	equation	equation	NOUN
ejpam-6631	329	10	defined	define	VERB
ejpam-6631	329	11	using	use	VERB
ejpam-6631	329	12	the	the	DET
ejpam-6631	329	13	m.	m.	NOUN
ejpam-6631	329	14	abdel	abdel	PROPN
ejpam-6631	329	15	aal	aal	PROPN
ejpam-6631	329	16	et	et	PROPN
ejpam-6631	329	17	al	al	PROPN
ejpam-6631	329	18	.	.	PUNCT
ejpam-6631	329	19	/	/	SYM
ejpam-6631	329	20	eur	eur	PROPN
ejpam-6631	329	21	.	.	PUNCT
ejpam-6631	330	1	j.	j.	PROPN
ejpam-6631	330	2	pure	pure	PROPN
ejpam-6631	330	3	appl	appl	PROPN
ejpam-6631	330	4	.	.	PROPN
ejpam-6631	330	5	math	math	PROPN
ejpam-6631	330	6	,	,	PUNCT
ejpam-6631	330	7	18	18	NUM
ejpam-6631	330	8	(	(	PUNCT
ejpam-6631	330	9	4	4	NUM
ejpam-6631	330	10	)	)	PUNCT
ejpam-6631	330	11	(	(	PUNCT
ejpam-6631	330	12	2025	2025	NUM
ejpam-6631	330	13	)	)	PUNCT
ejpam-6631	330	14	,	,	PUNCT
ejpam-6631	330	15	6631	6631	NUM
ejpam-6631	330	16	16	16	NUM
ejpam-6631	330	17	of	of	ADP
ejpam-6631	330	18	20	20	NUM
ejpam-6631	330	19	table	table	NOUN
ejpam-6631	330	20	3	3	NUM
ejpam-6631	330	21	:	:	PUNCT
ejpam-6631	330	22	the	the	DET
ejpam-6631	330	23	comparison	comparison	NOUN
ejpam-6631	330	24	between	between	ADP
ejpam-6631	330	25	the	the	DET
ejpam-6631	330	26	exact	exact	ADJ
ejpam-6631	330	27	solutions	solution	NOUN
ejpam-6631	330	28	and	and	CCONJ
ejpam-6631	330	29	the	the	DET
ejpam-6631	330	30	absolute	absolute	ADJ
ejpam-6631	330	31	error	error	NOUN
ejpam-6631	330	32	for	for	ADP
ejpam-6631	330	33	example	example	NOUN
ejpam-6631	330	34	2	2	NUM
ejpam-6631	330	35	t	t	NOUN
ejpam-6631	330	36	exact	exact	ADJ
ejpam-6631	330	37	solutions	solution	NOUN
ejpam-6631	330	38	absolute	absolute	ADJ
ejpam-6631	330	39	error	error	NOUN
ejpam-6631	330	40	absolute	absolute	ADJ
ejpam-6631	330	41	error	error	NOUN
ejpam-6631	330	42	0.1	0.1	NUM
ejpam-6631	330	43	1.3619489510	1.3619489510	NUM
ejpam-6631	330	44	0.0285610000	0.0285610000	NUM
ejpam-6631	331	1	1.33339e+00	1.33339e+00	NUM
ejpam-6631	331	2	0.2	0.2	NUM
ejpam-6631	331	3	0.9920555733	0.9920555733	NUM
ejpam-6631	331	4	0.0739840000	0.0739840000	NUM
ejpam-6631	331	5	9.18072e-01	9.18072e-01	NUM
ejpam-6631	331	6	0.3	0.3	NUM
ejpam-6631	331	7	0.6107966552	0.6107966552	NUM
ejpam-6631	331	8	0.0918090000	0.0918090000	NUM
ejpam-6631	331	9	5.18988e-01	5.18988e-01	NUM
ejpam-6631	331	10	0.4	0.4	NUM
ejpam-6631	331	11	0.2228042575	0.2228042575	NUM
ejpam-6631	331	12	0.0655360000	0.0655360000	NUM
ejpam-6631	331	13	1.57268e-01	1.57268e-01	NUM
ejpam-6631	331	14	0.5	0.5	NUM
ejpam-6631	331	15	-0.1434077531	-0.1434077531	NOUN
ejpam-6631	331	16	0.0156250000	0.0156250000	NUM
ejpam-6631	331	17	1.59033e-01	1.59033e-01	NUM
ejpam-6631	331	18	0.6	0.6	NUM
ejpam-6631	331	19	-0.4164291000	-0.4164291000	NOUN
ejpam-6631	331	20	0.0092160000	0.0092160000	NUM
ejpam-6631	331	21	4.25645e-01	4.25645e-01	NUM
ejpam-6631	331	22	0.7	0.7	NUM
ejpam-6631	331	23	-0.4693227850	-0.4693227850	NOUN
ejpam-6631	331	24	0.1705690000	0.1705690000	NUM
ejpam-6631	331	25	6.39892e-01	6.39892e-01	NUM
ejpam-6631	331	26	0.8	0.8	NUM
ejpam-6631	331	27	-0.1076897890	-0.1076897890	NOUN
ejpam-6631	331	28	0.6922240000	0.6922240000	NUM
ejpam-6631	331	29	7.99914e-01	7.99914e-01	NUM
ejpam-6631	331	30	0.9	0.9	NUM
ejpam-6631	331	31	0.9425527730	0.9425527730	NUM
ejpam-6631	331	32	1.8468810000	1.8468810000	NUM
ejpam-6631	331	33	9.04328e-01	9.04328e-01	NUM
ejpam-6631	331	34	1.0	1.0	NUM
ejpam-6631	331	35	3.0479453440	3.0479453440	NUM
ejpam-6631	331	36	4.0000000000	4.0000000000	NUM
ejpam-6631	331	37	9.52055e-01	9.52055e-01	NUM
ejpam-6631	331	38	prabhakar	prabhakar	NOUN
ejpam-6631	331	39	derivative	derivative	NOUN
ejpam-6631	331	40	in	in	ADP
ejpam-6631	331	41	ref	ref	NOUN
ejpam-6631	331	42	.	.	PUNCT
ejpam-6631	332	1	[	[	X
ejpam-6631	332	2	25	25	NUM
ejpam-6631	332	3	]	]	PUNCT
ejpam-6631	332	4	;	;	PUNCT
ejpam-6631	332	5	rdγ	rdγ	NOUN
ejpam-6631	332	6	α	α	NOUN
ejpam-6631	332	7	,	,	PUNCT
ejpam-6631	332	8	β	β	PROPN
ejpam-6631	332	9	,	,	PUNCT
ejpam-6631	332	10	τ	τ	PROPN
ejpam-6631	332	11	,	,	PUNCT
ejpam-6631	332	12	a	a	DET
ejpam-6631	332	13	+	+	X
ejpam-6631	332	14	p(x	p(x	NOUN
ejpam-6631	332	15	)	)	PUNCT
ejpam-6631	332	16	=	=	PUNCT
ejpam-6631	332	17	g(x)−	g(x)−	PROPN
ejpam-6631	332	18	u2(x	u2(x	PROPN
ejpam-6631	332	19	)	)	PUNCT
ejpam-6631	332	20	.	.	PUNCT
ejpam-6631	333	1	(	(	PUNCT
ejpam-6631	333	2	46	46	NUM
ejpam-6631	333	3	)	)	PUNCT
ejpam-6631	333	4	given	give	VERB
ejpam-6631	333	5	the	the	DET
ejpam-6631	333	6	initial	initial	ADJ
ejpam-6631	333	7	condition	condition	NOUN
ejpam-6631	333	8	that	that	SCONJ
ejpam-6631	333	9	p(0	p(0	NOUN
ejpam-6631	333	10	)	)	PUNCT
ejpam-6631	333	11	=	=	SYM
ejpam-6631	333	12	0	0	PUNCT
ejpam-6631	333	13	(	(	PUNCT
ejpam-6631	333	14	47	47	NUM
ejpam-6631	333	15	)	)	PUNCT
ejpam-6631	333	16	so	so	SCONJ
ejpam-6631	333	17	that	that	SCONJ
ejpam-6631	333	18	g(x	g(x	NOUN
ejpam-6631	333	19	)	)	PUNCT
ejpam-6631	334	1	=	=	PUNCT
ejpam-6631	335	1	2t2−β	2t2−β	NUM
ejpam-6631	335	2	γ(3−	γ(3−	ADP
ejpam-6631	335	3	β	β	X
ejpam-6631	335	4	)	)	PUNCT
ejpam-6631	335	5	+	+	CCONJ
ejpam-6631	335	6	t2	t2	NOUN
ejpam-6631	335	7	.	.	PUNCT
ejpam-6631	336	1	(	(	PUNCT
ejpam-6631	336	2	48	48	NUM
ejpam-6631	336	3	)	)	PUNCT
ejpam-6631	336	4	the	the	DET
ejpam-6631	336	5	exact	exact	ADJ
ejpam-6631	336	6	solution	solution	NOUN
ejpam-6631	336	7	is	be	AUX
ejpam-6631	336	8	;	;	PUNCT
ejpam-6631	336	9	p(t	p(t	NOUN
ejpam-6631	336	10	)	)	PUNCT
ejpam-6631	336	11	=	=	SYM
ejpam-6631	336	12	t2	t2	NOUN
ejpam-6631	336	13	.	.	PUNCT
ejpam-6631	337	1	(	(	PUNCT
ejpam-6631	337	2	49	49	NUM
ejpam-6631	337	3	)	)	PUNCT
ejpam-6631	337	4	solution	solution	NOUN
ejpam-6631	337	5	:	:	PUNCT
ejpam-6631	337	6	(	(	PUNCT
ejpam-6631	337	7	48	48	NUM
ejpam-6631	337	8	)	)	PUNCT
ejpam-6631	337	9	is	be	AUX
ejpam-6631	337	10	solved	solve	VERB
ejpam-6631	337	11	to	to	PART
ejpam-6631	337	12	be	be	AUX
ejpam-6631	337	13	;	;	PUNCT
ejpam-6631	337	14	1.956603553t1.05	1.956603553t1.05	NUM
ejpam-6631	337	15	+	+	CCONJ
ejpam-6631	337	16	t2	t2	NOUN
ejpam-6631	337	17	.	.	PUNCT
ejpam-6631	338	1	(	(	PUNCT
ejpam-6631	338	2	50	50	NUM
ejpam-6631	338	3	)	)	PUNCT
ejpam-6631	338	4	figure	figure	NOUN
ejpam-6631	338	5	4	4	NUM
ejpam-6631	338	6	illustrates	illustrate	VERB
ejpam-6631	338	7	a	a	DET
ejpam-6631	338	8	comparative	comparative	ADJ
ejpam-6631	338	9	analysis	analysis	NOUN
ejpam-6631	338	10	between	between	ADP
ejpam-6631	338	11	the	the	DET
ejpam-6631	338	12	exact	exact	ADJ
ejpam-6631	338	13	equation	equation	NOUN
ejpam-6631	338	14	and	and	CCONJ
ejpam-6631	338	15	the	the	DET
ejpam-6631	338	16	approximate	approximate	ADJ
ejpam-6631	338	17	solution	solution	NOUN
ejpam-6631	338	18	derived	derive	VERB
ejpam-6631	338	19	through	through	ADP
ejpam-6631	338	20	the	the	DET
ejpam-6631	338	21	proposed	propose	VERB
ejpam-6631	338	22	method	method	NOUN
ejpam-6631	338	23	.	.	PUNCT
ejpam-6631	339	1	this	this	DET
ejpam-6631	339	2	analysis	analysis	NOUN
ejpam-6631	339	3	demonstrates	demonstrate	VERB
ejpam-6631	339	4	the	the	DET
ejpam-6631	339	5	accuracy	accuracy	NOUN
ejpam-6631	339	6	of	of	ADP
ejpam-6631	339	7	the	the	DET
ejpam-6631	339	8	method	method	NOUN
ejpam-6631	339	9	,	,	PUNCT
ejpam-6631	339	10	as	as	SCONJ
ejpam-6631	339	11	there	there	PRON
ejpam-6631	339	12	is	be	VERB
ejpam-6631	339	13	a	a	DET
ejpam-6631	339	14	strikingly	strikingly	ADV
ejpam-6631	339	15	close	close	ADJ
ejpam-6631	339	16	alignment	alignment	NOUN
ejpam-6631	339	17	between	between	ADP
ejpam-6631	339	18	the	the	DET
ejpam-6631	339	19	approximate	approximate	ADJ
ejpam-6631	339	20	solutions	solution	NOUN
ejpam-6631	339	21	and	and	CCONJ
ejpam-6631	339	22	the	the	DET
ejpam-6631	339	23	exact	exact	ADJ
ejpam-6631	339	24	values	value	NOUN
ejpam-6631	339	25	,	,	PUNCT
ejpam-6631	339	26	indicating	indicate	VERB
ejpam-6631	339	27	that	that	SCONJ
ejpam-6631	339	28	the	the	DET
ejpam-6631	339	29	approach	approach	NOUN
ejpam-6631	339	30	effectively	effectively	ADV
ejpam-6631	339	31	captures	capture	VERB
ejpam-6631	339	32	the	the	DET
ejpam-6631	339	33	underlying	underlying	ADJ
ejpam-6631	339	34	mathematical	mathematical	ADJ
ejpam-6631	339	35	behaviour	behaviour	NOUN
ejpam-6631	339	36	.	.	PUNCT
ejpam-6631	340	1	in	in	ADP
ejpam-6631	340	2	addition	addition	NOUN
ejpam-6631	340	3	,	,	PUNCT
ejpam-6631	340	4	figure	figure	NOUN
ejpam-6631	340	5	5	5	NUM
ejpam-6631	340	6	showcases	showcase	NOUN
ejpam-6631	340	7	the	the	DET
ejpam-6631	340	8	results	result	NOUN
ejpam-6631	340	9	obtained	obtain	VERB
ejpam-6631	340	10	for	for	ADP
ejpam-6631	340	11	varying	vary	VERB
ejpam-6631	340	12	values	value	NOUN
ejpam-6631	340	13	of	of	ADP
ejpam-6631	340	14	the	the	DET
ejpam-6631	340	15	parameter	parameter	NOUN
ejpam-6631	340	16	β	β	NOUN
ejpam-6631	340	17	,	,	PUNCT
ejpam-6631	340	18	specifically	specifically	ADV
ejpam-6631	340	19	0.95	0.95	NUM
ejpam-6631	340	20	,	,	PUNCT
ejpam-6631	340	21	0.75	0.75	NUM
ejpam-6631	340	22	,	,	PUNCT
ejpam-6631	340	23	and	and	CCONJ
ejpam-6631	340	24	0.55	0.55	NUM
ejpam-6631	340	25	,	,	PUNCT
ejpam-6631	340	26	as	as	SCONJ
ejpam-6631	340	27	detailed	detailed	ADJ
ejpam-6631	340	28	in	in	ADP
ejpam-6631	340	29	example	example	NOUN
ejpam-6631	341	1	3	3	X
ejpam-6631	341	2	.	.	PUNCT
ejpam-6631	342	1	the	the	DET
ejpam-6631	342	2	variations	variation	NOUN
ejpam-6631	342	3	in	in	ADP
ejpam-6631	342	4	β	β	X
ejpam-6631	342	5	significantly	significantly	ADV
ejpam-6631	342	6	influence	influence	VERB
ejpam-6631	342	7	the	the	DET
ejpam-6631	342	8	overall	overall	ADJ
ejpam-6631	342	9	process	process	NOUN
ejpam-6631	342	10	,	,	PUNCT
ejpam-6631	342	11	revealing	reveal	VERB
ejpam-6631	342	12	how	how	SCONJ
ejpam-6631	342	13	changes	change	NOUN
ejpam-6631	342	14	in	in	ADP
ejpam-6631	342	15	this	this	DET
ejpam-6631	342	16	parameter	parameter	NOUN
ejpam-6631	342	17	can	can	AUX
ejpam-6631	342	18	impact	impact	VERB
ejpam-6631	342	19	the	the	DET
ejpam-6631	342	20	outcome	outcome	NOUN
ejpam-6631	342	21	and	and	CCONJ
ejpam-6631	342	22	further	far	ADV
ejpam-6631	342	23	validating	validate	VERB
ejpam-6631	342	24	the	the	DET
ejpam-6631	342	25	robustness	robustness	NOUN
ejpam-6631	342	26	of	of	ADP
ejpam-6631	342	27	the	the	DET
ejpam-6631	342	28	proposed	propose	VERB
ejpam-6631	342	29	method	method	NOUN
ejpam-6631	342	30	in	in	ADP
ejpam-6631	342	31	accommodating	accommodate	VERB
ejpam-6631	342	32	different	different	ADJ
ejpam-6631	342	33	scenarios	scenario	NOUN
ejpam-6631	342	34	.	.	PUNCT
ejpam-6631	343	1	m.	m.	NOUN
ejpam-6631	343	2	abdel	abdel	PROPN
ejpam-6631	343	3	aal	aal	PROPN
ejpam-6631	343	4	et	et	PROPN
ejpam-6631	343	5	al	al	PROPN
ejpam-6631	343	6	.	.	PUNCT
ejpam-6631	343	7	/	/	SYM
ejpam-6631	343	8	eur	eur	PROPN
ejpam-6631	343	9	.	.	PUNCT
ejpam-6631	344	1	j.	j.	PROPN
ejpam-6631	344	2	pure	pure	PROPN
ejpam-6631	344	3	appl	appl	PROPN
ejpam-6631	344	4	.	.	PROPN
ejpam-6631	344	5	math	math	PROPN
ejpam-6631	344	6	,	,	PUNCT
ejpam-6631	344	7	18	18	NUM
ejpam-6631	344	8	(	(	PUNCT
ejpam-6631	344	9	4	4	NUM
ejpam-6631	344	10	)	)	PUNCT
ejpam-6631	344	11	(	(	PUNCT
ejpam-6631	344	12	2025	2025	NUM
ejpam-6631	344	13	)	)	PUNCT
ejpam-6631	344	14	,	,	PUNCT
ejpam-6631	344	15	6631	6631	NUM
ejpam-6631	344	16	17	17	NUM
ejpam-6631	344	17	of	of	ADP
ejpam-6631	344	18	20	20	NUM
ejpam-6631	344	19	6	6	NUM
ejpam-6631	344	20	.	.	PUNCT
ejpam-6631	345	1	conclusion	conclusion	NOUN
ejpam-6631	345	2	in	in	ADP
ejpam-6631	345	3	our	our	PRON
ejpam-6631	345	4	study	study	NOUN
ejpam-6631	345	5	,	,	PUNCT
ejpam-6631	345	6	we	we	PRON
ejpam-6631	345	7	present	present	VERB
ejpam-6631	345	8	an	an	DET
ejpam-6631	345	9	approach	approach	NOUN
ejpam-6631	345	10	to	to	PART
ejpam-6631	345	11	solve	solve	VERB
ejpam-6631	345	12	prabhakar	prabhakar	NOUN
ejpam-6631	345	13	fractional	fractional	ADJ
ejpam-6631	345	14	differential	differential	ADJ
ejpam-6631	345	15	equations	equation	NOUN
ejpam-6631	345	16	through	through	ADP
ejpam-6631	345	17	the	the	DET
ejpam-6631	345	18	explicit	explicit	ADJ
ejpam-6631	345	19	fractional	fractional	ADJ
ejpam-6631	345	20	adams	adam	NOUN
ejpam-6631	345	21	method	method	NOUN
ejpam-6631	345	22	.	.	PUNCT
ejpam-6631	346	1	the	the	DET
ejpam-6631	346	2	inherent	inherent	ADJ
ejpam-6631	346	3	complexity	complexity	NOUN
ejpam-6631	346	4	of	of	ADP
ejpam-6631	346	5	these	these	DET
ejpam-6631	346	6	equations	equation	NOUN
ejpam-6631	346	7	,	,	PUNCT
ejpam-6631	346	8	due	due	ADP
ejpam-6631	346	9	to	to	ADP
ejpam-6631	346	10	the	the	DET
ejpam-6631	346	11	multitude	multitude	NOUN
ejpam-6631	346	12	of	of	ADP
ejpam-6631	346	13	parameters	parameter	NOUN
ejpam-6631	346	14	involved	involve	VERB
ejpam-6631	346	15	,	,	PUNCT
ejpam-6631	346	16	poses	pose	VERB
ejpam-6631	346	17	significant	significant	ADJ
ejpam-6631	346	18	challenges	challenge	NOUN
ejpam-6631	346	19	.	.	PUNCT
ejpam-6631	347	1	however	however	ADV
ejpam-6631	347	2	,	,	PUNCT
ejpam-6631	347	3	our	our	PRON
ejpam-6631	347	4	innovative	innovative	ADJ
ejpam-6631	347	5	numerical	numerical	ADJ
ejpam-6631	347	6	scheme	scheme	NOUN
ejpam-6631	347	7	effectively	effectively	ADV
ejpam-6631	347	8	addresses	address	VERB
ejpam-6631	347	9	these	these	DET
ejpam-6631	347	10	issues	issue	NOUN
ejpam-6631	347	11	by	by	ADP
ejpam-6631	347	12	utilizing	utilize	VERB
ejpam-6631	347	13	lagrange	lagrange	NOUN
ejpam-6631	347	14	interpolation	interpolation	NOUN
ejpam-6631	347	15	within	within	ADP
ejpam-6631	347	16	the	the	DET
ejpam-6631	347	17	explicit	explicit	ADJ
ejpam-6631	347	18	fractional	fractional	ADJ
ejpam-6631	347	19	adams	adam	NOUN
ejpam-6631	347	20	method	method	NOUN
ejpam-6631	347	21	.	.	PUNCT
ejpam-6631	348	1	we	we	PRON
ejpam-6631	348	2	provide	provide	VERB
ejpam-6631	348	3	a	a	DET
ejpam-6631	348	4	convergence	convergence	NOUN
ejpam-6631	348	5	analysis	analysis	NOUN
ejpam-6631	348	6	of	of	ADP
ejpam-6631	348	7	our	our	PRON
ejpam-6631	348	8	newly	newly	ADV
ejpam-6631	348	9	developed	develop	VERB
ejpam-6631	348	10	scheme	scheme	NOUN
ejpam-6631	348	11	,	,	PUNCT
ejpam-6631	348	12	supported	support	VERB
ejpam-6631	348	13	by	by	ADP
ejpam-6631	348	14	several	several	ADJ
ejpam-6631	348	15	illustrative	illustrative	ADJ
ejpam-6631	348	16	examples	example	NOUN
ejpam-6631	348	17	that	that	PRON
ejpam-6631	348	18	clearly	clearly	ADV
ejpam-6631	348	19	demonstrate	demonstrate	VERB
ejpam-6631	348	20	its	its	PRON
ejpam-6631	348	21	superior	superior	ADJ
ejpam-6631	348	22	effectiveness	effectiveness	NOUN
ejpam-6631	348	23	compared	compare	VERB
ejpam-6631	348	24	to	to	ADP
ejpam-6631	348	25	existing	exist	VERB
ejpam-6631	348	26	solutions	solution	NOUN
ejpam-6631	348	27	.	.	PUNCT
ejpam-6631	349	1	our	our	PRON
ejpam-6631	349	2	findings	finding	NOUN
ejpam-6631	349	3	confirm	confirm	VERB
ejpam-6631	349	4	that	that	SCONJ
ejpam-6631	349	5	this	this	DET
ejpam-6631	349	6	method	method	NOUN
ejpam-6631	349	7	is	be	AUX
ejpam-6631	349	8	not	not	PART
ejpam-6631	349	9	only	only	ADV
ejpam-6631	349	10	highly	highly	ADV
ejpam-6631	349	11	efficient	efficient	ADJ
ejpam-6631	349	12	but	but	CCONJ
ejpam-6631	349	13	also	also	ADV
ejpam-6631	349	14	remarkably	remarkably	ADV
ejpam-6631	349	15	straightforward	straightforward	ADJ
ejpam-6631	349	16	to	to	PART
ejpam-6631	349	17	implement	implement	VERB
ejpam-6631	349	18	,	,	PUNCT
ejpam-6631	349	19	revealing	reveal	VERB
ejpam-6631	349	20	its	its	PRON
ejpam-6631	349	21	considerable	considerable	ADJ
ejpam-6631	349	22	potential	potential	NOUN
ejpam-6631	349	23	for	for	ADP
ejpam-6631	349	24	practical	practical	ADJ
ejpam-6631	349	25	applications	application	NOUN
ejpam-6631	349	26	.	.	PUNCT
ejpam-6631	350	1	furthermore	furthermore	ADV
ejpam-6631	350	2	,	,	PUNCT
ejpam-6631	350	3	we	we	PRON
ejpam-6631	350	4	strongly	strongly	ADV
ejpam-6631	350	5	advocate	advocate	VERB
ejpam-6631	350	6	for	for	ADP
ejpam-6631	350	7	further	further	ADJ
ejpam-6631	350	8	research	research	NOUN
ejpam-6631	350	9	to	to	PART
ejpam-6631	350	10	explore	explore	VERB
ejpam-6631	350	11	additional	additional	ADJ
ejpam-6631	350	12	enhancements	enhancement	NOUN
ejpam-6631	350	13	to	to	PART
ejpam-6631	350	14	figure	figure	VERB
ejpam-6631	350	15	4	4	NUM
ejpam-6631	350	16	:	:	PUNCT
ejpam-6631	350	17	the	the	DET
ejpam-6631	350	18	results	result	NOUN
ejpam-6631	350	19	of	of	ADP
ejpam-6631	350	20	the	the	DET
ejpam-6631	350	21	comparison	comparison	NOUN
ejpam-6631	350	22	between	between	ADP
ejpam-6631	350	23	the	the	DET
ejpam-6631	350	24	approximate	approximate	ADJ
ejpam-6631	350	25	and	and	CCONJ
ejpam-6631	350	26	exact	exact	ADJ
ejpam-6631	350	27	solutions	solution	NOUN
ejpam-6631	350	28	for	for	ADP
ejpam-6631	350	29	example	example	NOUN
ejpam-6631	350	30	3	3	NUM
ejpam-6631	350	31	figure	figure	NOUN
ejpam-6631	350	32	5	5	NUM
ejpam-6631	350	33	:	:	PUNCT
ejpam-6631	350	34	the	the	DET
ejpam-6631	350	35	results	result	NOUN
ejpam-6631	350	36	of	of	ADP
ejpam-6631	350	37	the	the	DET
ejpam-6631	350	38	comparison	comparison	NOUN
ejpam-6631	350	39	for	for	ADP
ejpam-6631	350	40	different	different	ADJ
ejpam-6631	350	41	value	value	NOUN
ejpam-6631	350	42	of	of	ADP
ejpam-6631	350	43	β	β	PROPN
ejpam-6631	350	44	for	for	ADP
ejpam-6631	350	45	example	example	NOUN
ejpam-6631	350	46	3	3	NUM
ejpam-6631	350	47	m.	m.	NOUN
ejpam-6631	350	48	abdel	abdel	PROPN
ejpam-6631	350	49	aal	aal	PROPN
ejpam-6631	350	50	et	et	PROPN
ejpam-6631	350	51	al	al	PROPN
ejpam-6631	350	52	.	.	PUNCT
ejpam-6631	350	53	/	/	SYM
ejpam-6631	350	54	eur	eur	PROPN
ejpam-6631	350	55	.	.	PUNCT
ejpam-6631	351	1	j.	j.	PROPN
ejpam-6631	351	2	pure	pure	PROPN
ejpam-6631	351	3	appl	appl	PROPN
ejpam-6631	351	4	.	.	PROPN
ejpam-6631	351	5	math	math	PROPN
ejpam-6631	351	6	,	,	PUNCT
ejpam-6631	351	7	18	18	NUM
ejpam-6631	351	8	(	(	PUNCT
ejpam-6631	351	9	4	4	NUM
ejpam-6631	351	10	)	)	PUNCT
ejpam-6631	351	11	(	(	PUNCT
ejpam-6631	351	12	2025	2025	NUM
ejpam-6631	351	13	)	)	PUNCT
ejpam-6631	351	14	,	,	PUNCT
ejpam-6631	351	15	6631	6631	NUM
ejpam-6631	351	16	18	18	NUM
ejpam-6631	351	17	of	of	ADP
ejpam-6631	351	18	20	20	NUM
ejpam-6631	351	19	table	table	NOUN
ejpam-6631	351	20	4	4	NUM
ejpam-6631	351	21	:	:	PUNCT
ejpam-6631	351	22	the	the	DET
ejpam-6631	351	23	comparison	comparison	NOUN
ejpam-6631	351	24	between	between	ADP
ejpam-6631	351	25	the	the	DET
ejpam-6631	351	26	exact	exact	ADJ
ejpam-6631	351	27	solutions	solution	NOUN
ejpam-6631	351	28	and	and	CCONJ
ejpam-6631	351	29	the	the	DET
ejpam-6631	351	30	absolute	absolute	ADJ
ejpam-6631	351	31	error	error	NOUN
ejpam-6631	351	32	for	for	ADP
ejpam-6631	351	33	example	example	NOUN
ejpam-6631	351	34	3	3	NUM
ejpam-6631	351	35	t	t	NOUN
ejpam-6631	351	36	exact	exact	ADJ
ejpam-6631	351	37	solutions	solution	NOUN
ejpam-6631	351	38	absolute	absolute	ADJ
ejpam-6631	351	39	error	error	NOUN
ejpam-6631	351	40	absolute	absolute	ADJ
ejpam-6631	351	41	error	error	NOUN
ejpam-6631	351	42	0.1	0.1	NUM
ejpam-6631	351	43	0.210	0.210	NUM
ejpam-6631	351	44	0.010	0.010	NUM
ejpam-6631	351	45	2.000e-01	2.000e-01	NUM
ejpam-6631	351	46	0.2	0.2	NUM
ejpam-6631	351	47	0.440	0.440	NUM
ejpam-6631	351	48	0.040	0.040	NUM
ejpam-6631	351	49	4.000e-01	4.000e-01	NUM
ejpam-6631	351	50	0.3	0.3	NUM
ejpam-6631	351	51	0.690	0.690	NUM
ejpam-6631	351	52	0.090	0.090	NUM
ejpam-6631	351	53	6.000e-01	6.000e-01	NUM
ejpam-6631	351	54	0.4	0.4	NUM
ejpam-6631	351	55	0.960	0.960	NUM
ejpam-6631	351	56	0.160	0.160	NUM
ejpam-6631	351	57	8.000e-01	8.000e-01	NUM
ejpam-6631	351	58	0.5	0.5	NUM
ejpam-6631	351	59	1.250	1.250	NUM
ejpam-6631	351	60	0.250	0.250	NUM
ejpam-6631	351	61	1.000e+00	1.000e+00	NUM
ejpam-6631	351	62	0.6	0.6	NUM
ejpam-6631	351	63	1.560	1.560	NUM
ejpam-6631	351	64	0.360	0.360	NUM
ejpam-6631	351	65	1.200e+00	1.200e+00	NUM
ejpam-6631	351	66	0.7	0.7	NUM
ejpam-6631	351	67	1.890	1.890	NUM
ejpam-6631	351	68	0.490	0.490	NUM
ejpam-6631	351	69	1.400e+00	1.400e+00	NUM
ejpam-6631	351	70	0.8	0.8	NUM
ejpam-6631	351	71	2.240	2.240	NUM
ejpam-6631	351	72	0.640	0.640	NUM
ejpam-6631	351	73	1.600e+00	1.600e+00	NUM
ejpam-6631	351	74	0.9	0.9	NUM
ejpam-6631	351	75	2.610	2.610	NUM
ejpam-6631	351	76	0.810	0.810	NUM
ejpam-6631	351	77	1.800e+00	1.800e+00	NUM
ejpam-6631	351	78	1.0	1.0	NUM
ejpam-6631	351	79	3.000	3.000	NUM
ejpam-6631	351	80	1.000	1.000	NUM
ejpam-6631	351	81	2.000e+00	2.000e+00	NUM
ejpam-6631	351	82	this	this	DET
ejpam-6631	351	83	method	method	NOUN
ejpam-6631	351	84	,	,	PUNCT
ejpam-6631	351	85	particularly	particularly	ADV
ejpam-6631	351	86	in	in	ADP
ejpam-6631	351	87	conjunction	conjunction	NOUN
ejpam-6631	351	88	with	with	ADP
ejpam-6631	351	89	the	the	DET
ejpam-6631	351	90	shifted	shift	VERB
ejpam-6631	351	91	legendre	legendre	PROPN
ejpam-6631	351	92	polynomials	polynomial	NOUN
ejpam-6631	351	93	technique	technique	NOUN
ejpam-6631	351	94	.	.	PUNCT
ejpam-6631	352	1	such	such	ADJ
ejpam-6631	352	2	advancements	advancement	NOUN
ejpam-6631	352	3	will	will	AUX
ejpam-6631	352	4	undoubtedly	undoubtedly	ADV
ejpam-6631	352	5	lead	lead	VERB
ejpam-6631	352	6	to	to	ADP
ejpam-6631	352	7	a	a	DET
ejpam-6631	352	8	more	more	ADV
ejpam-6631	352	9	robust	robust	ADJ
ejpam-6631	352	10	and	and	CCONJ
ejpam-6631	352	11	comprehensive	comprehensive	ADJ
ejpam-6631	352	12	solution	solution	NOUN
ejpam-6631	352	13	for	for	ADP
ejpam-6631	352	14	the	the	DET
ejpam-6631	352	15	tempered	temper	VERB
ejpam-6631	352	16	fractional	fractional	ADJ
ejpam-6631	352	17	problem	problem	NOUN
ejpam-6631	352	18	,	,	PUNCT
ejpam-6631	352	19	with	with	ADP
ejpam-6631	352	20	far	far	ADV
ejpam-6631	352	21	-	-	PUNCT
ejpam-6631	352	22	reaching	reach	VERB
ejpam-6631	352	23	implications	implication	NOUN
ejpam-6631	352	24	across	across	ADP
ejpam-6631	352	25	diverse	diverse	ADJ
ejpam-6631	352	26	fields	field	NOUN
ejpam-6631	352	27	such	such	ADJ
ejpam-6631	352	28	as	as	ADP
ejpam-6631	352	29	physics	physics	NOUN
ejpam-6631	352	30	,	,	PUNCT
ejpam-6631	352	31	engineering	engineering	NOUN
ejpam-6631	352	32	,	,	PUNCT
ejpam-6631	352	33	and	and	CCONJ
ejpam-6631	352	34	finance	finance	NOUN
ejpam-6631	352	35	.	.	PUNCT
ejpam-6631	353	1	acknowledgements	acknowledgement	NOUN
ejpam-6631	353	2	the	the	DET
ejpam-6631	353	3	authors	author	NOUN
ejpam-6631	353	4	are	be	AUX
ejpam-6631	353	5	grateful	grateful	ADJ
ejpam-6631	353	6	to	to	ADP
ejpam-6631	353	7	the	the	DET
ejpam-6631	353	8	middle	middle	PROPN
ejpam-6631	353	9	east	east	PROPN
ejpam-6631	353	10	university	university	PROPN
ejpam-6631	353	11	,	,	PUNCT
ejpam-6631	353	12	amman	amman	PROPN
ejpam-6631	353	13	,	,	PUNCT
ejpam-6631	353	14	jordan	jordan	PROPN
ejpam-6631	353	15	,	,	PUNCT
ejpam-6631	353	16	for	for	ADP
ejpam-6631	353	17	financial	financial	ADJ
ejpam-6631	353	18	support	support	NOUN
ejpam-6631	353	19	granted	grant	VERB
ejpam-6631	353	20	to	to	PART
ejpam-6631	353	21	cover	cover	VERB
ejpam-6631	353	22	the	the	DET
ejpam-6631	353	23	publication	publication	NOUN
ejpam-6631	353	24	fees	fee	NOUN
ejpam-6631	353	25	of	of	ADP
ejpam-6631	353	26	this	this	DET
ejpam-6631	353	27	research	research	NOUN
ejpam-6631	353	28	article	article	NOUN
ejpam-6631	353	29	.	.	PUNCT
ejpam-6631	354	1	references	reference	NOUN
ejpam-6631	354	2	[	[	X
ejpam-6631	354	3	1	1	NUM
ejpam-6631	354	4	]	]	PUNCT
ejpam-6631	354	5	p.	p.	NOUN
ejpam-6631	354	6	cambeses	cambese	NOUN
ejpam-6631	354	7	-	-	PUNCT
ejpam-6631	354	8	franco	franco	PROPN
ejpam-6631	354	9	,	,	PUNCT
ejpam-6631	354	10	r.	r.	NOUN
ejpam-6631	354	11	rial	rial	NOUN
ejpam-6631	354	12	,	,	PUNCT
ejpam-6631	354	13	&	&	CCONJ
ejpam-6631	354	14	j.	j.	PROPN
ejpam-6631	354	15	m.	m.	PROPN
ejpam-6631	354	16	ruso	ruso	PROPN
ejpam-6631	354	17	,	,	PUNCT
ejpam-6631	354	18	integrating	integrate	VERB
ejpam-6631	354	19	classical	classical	ADJ
ejpam-6631	354	20	and	and	CCONJ
ejpam-6631	354	21	fractional	fractional	ADJ
ejpam-6631	354	22	calculus	calculus	NOUN
ejpam-6631	354	23	rheological	rheological	ADJ
ejpam-6631	354	24	models	model	NOUN
ejpam-6631	354	25	in	in	ADP
ejpam-6631	354	26	developing	develop	VERB
ejpam-6631	354	27	hydroxyapatite	hydroxyapatite	NOUN
ejpam-6631	354	28	-	-	PUNCT
ejpam-6631	354	29	enhanced	enhance	VERB
ejpam-6631	354	30	hydrogels	hydrogel	NOUN
ejpam-6631	354	31	,	,	PUNCT
ejpam-6631	354	32	physics	physics	NOUN
ejpam-6631	354	33	of	of	ADP
ejpam-6631	354	34	fluids	fluid	NOUN
ejpam-6631	354	35	,	,	PUNCT
ejpam-6631	354	36	(	(	PUNCT
ejpam-6631	354	37	2024	2024	NUM
ejpam-6631	354	38	)	)	PUNCT
ejpam-6631	354	39	36(7	36(7	NUM
ejpam-6631	354	40	)	)	PUNCT
ejpam-6631	354	41	.	.	PUNCT
ejpam-6631	355	1	https://doi.org/10.1063/5.0213561	https://doi.org/10.1063/5.0213561	PROPN
ejpam-6631	355	2	.	.	PUNCT
ejpam-6631	356	1	[	[	X
ejpam-6631	356	2	2	2	X
ejpam-6631	356	3	]	]	X
ejpam-6631	356	4	d.	d.	PROPN
ejpam-6631	356	5	xue	xue	PROPN
ejpam-6631	356	6	&	&	CCONJ
ejpam-6631	356	7	i.	i.	PROPN
ejpam-6631	356	8	bai	bai	PROPN
ejpam-6631	356	9	,	,	PUNCT
ejpam-6631	356	10	introduction	introduction	NOUN
ejpam-6631	356	11	to	to	ADP
ejpam-6631	356	12	fractional	fractional	ADJ
ejpam-6631	356	13	calculus	calculus	NOUN
ejpam-6631	356	14	.	.	PUNCT
ejpam-6631	357	1	in	in	ADP
ejpam-6631	357	2	fractional	fractional	ADJ
ejpam-6631	357	3	calculus	calculus	NOUN
ejpam-6631	357	4	:	:	PUNCT
ejpam-6631	357	5	highprecision	highprecision	NOUN
ejpam-6631	357	6	algorithms	algorithm	NOUN
ejpam-6631	357	7	and	and	CCONJ
ejpam-6631	357	8	numerical	numerical	PROPN
ejpam-6631	357	9	implementations	implementation	NOUN
ejpam-6631	357	10	singapore	singapore	PROPN
ejpam-6631	357	11	:	:	PUNCT
ejpam-6631	357	12	springer	springer	NOUN
ejpam-6631	357	13	nature	nature	PROPN
ejpam-6631	357	14	singapore	singapore	PROPN
ejpam-6631	357	15	,	,	PUNCT
ejpam-6631	357	16	(	(	PUNCT
ejpam-6631	357	17	2024	2024	NUM
ejpam-6631	357	18	)	)	PUNCT
ejpam-6631	357	19	(	(	PUNCT
ejpam-6631	357	20	pp	pp	X
ejpam-6631	357	21	.	.	PUNCT
ejpam-6631	357	22	1	1	NUM
ejpam-6631	357	23	-	-	SYM
ejpam-6631	357	24	17	17	NUM
ejpam-6631	357	25	)	)	PUNCT
ejpam-6631	357	26	.	.	PUNCT
ejpam-6631	358	1	https	https	NOUN
ejpam-6631	358	2	:	:	PUNCT
ejpam-6631	358	3	//doi.org/10.1007/978−	//doi.org/10.1007/978−	X
ejpam-6631	358	4	981−	981−	ADJ
ejpam-6631	358	5	99−	99−	NUM
ejpam-6631	358	6	2070−	2070−	NUM
ejpam-6631	358	7	91	91	NUM
ejpam-6631	358	8	.	.	PUNCT
ejpam-6631	359	1	[	[	X
ejpam-6631	359	2	3	3	X
ejpam-6631	359	3	]	]	X
ejpam-6631	359	4	g.	g.	PROPN
ejpam-6631	359	5	barbero	barbero	PROPN
ejpam-6631	359	6	,	,	PUNCT
ejpam-6631	359	7	l.	l.	PROPN
ejpam-6631	359	8	r.	r.	PROPN
ejpam-6631	359	9	evangelista	evangelista	PROPN
ejpam-6631	359	10	,	,	PUNCT
ejpam-6631	359	11	r.	r.	PROPN
ejpam-6631	359	12	s.	s.	PROPN
ejpam-6631	359	13	zola	zola	PROPN
ejpam-6631	359	14	,	,	PUNCT
ejpam-6631	359	15	e.	e.	PROPN
ejpam-6631	359	16	k.lenzi	k.lenzi	PROPN
ejpam-6631	359	17	,	,	PUNCT
ejpam-6631	359	18	&	&	CCONJ
ejpam-6631	359	19	a.	a.	PROPN
ejpam-6631	359	20	m.	m.	PROPN
ejpam-6631	359	21	scarfone	scarfone	PROPN
ejpam-6631	359	22	,	,	PUNCT
ejpam-6631	359	23	a	a	DET
ejpam-6631	359	24	brief	brief	ADJ
ejpam-6631	359	25	review	review	NOUN
ejpam-6631	359	26	of	of	ADP
ejpam-6631	359	27	fractional	fractional	ADJ
ejpam-6631	359	28	calculus	calculus	NOUN
ejpam-6631	359	29	as	as	ADP
ejpam-6631	359	30	a	a	DET
ejpam-6631	359	31	tool	tool	NOUN
ejpam-6631	359	32	for	for	ADP
ejpam-6631	359	33	applications	application	NOUN
ejpam-6631	359	34	in	in	ADP
ejpam-6631	359	35	physics	physics	NOUN
ejpam-6631	359	36	:	:	PUNCT
ejpam-6631	359	37	adsorption	adsorption	NOUN
ejpam-6631	359	38	phenomena	phenomenon	NOUN
ejpam-6631	359	39	and	and	CCONJ
ejpam-6631	359	40	electrical	electrical	ADJ
ejpam-6631	359	41	impedance	impedance	NOUN
ejpam-6631	359	42	in	in	ADP
ejpam-6631	359	43	complex	complex	ADJ
ejpam-6631	359	44	fluids	fluid	NOUN
ejpam-6631	359	45	,	,	PUNCT
ejpam-6631	359	46	fractal	fractal	ADJ
ejpam-6631	359	47	and	and	CCONJ
ejpam-6631	359	48	fractional	fractional	ADJ
ejpam-6631	359	49	,	,	PUNCT
ejpam-6631	359	50	(	(	PUNCT
ejpam-6631	359	51	2024	2024	NUM
ejpam-6631	359	52	)	)	PUNCT
ejpam-6631	359	53	,	,	PUNCT
ejpam-6631	359	54	8(7	8(7	NUM
ejpam-6631	359	55	)	)	PUNCT
ejpam-6631	359	56	,	,	PUNCT
ejpam-6631	359	57	369	369	NUM
ejpam-6631	359	58	.	.	PUNCT
ejpam-6631	359	59	https://doi.org/10.3390/fractalfract8070369	https://doi.org/10.3390/fractalfract8070369	PROPN
ejpam-6631	359	60	.	.	PUNCT
ejpam-6631	360	1	[	[	X
ejpam-6631	360	2	4	4	X
ejpam-6631	360	3	]	]	PUNCT
ejpam-6631	360	4	s.	s.	PROPN
ejpam-6631	360	5	a.	a.	PROPN
ejpam-6631	360	6	elsamani	elsamani	PROPN
ejpam-6631	360	7	,	,	PUNCT
ejpam-6631	360	8	a.	a.	NOUN
ejpam-6631	360	9	a.	a.	NOUN
ejpam-6631	360	10	mohmmed	mohmme	VERB
ejpam-6631	360	11	,	,	PUNCT
ejpam-6631	360	12	k.	k.	PROPN
ejpam-6631	360	13	m.	m.	PROPN
ejpam-6631	360	14	kogan	kogan	PROPN
ejpam-6631	360	15	,	,	PUNCT
ejpam-6631	360	16	s.	s.	PROPN
ejpam-6631	360	17	y.	y.	PROPN
ejpam-6631	360	18	m.	m.	PROPN
ejpam-6631	360	19	salih	salih	PROPN
ejpam-6631	360	20	,	,	PUNCT
ejpam-6631	360	21	&	&	CCONJ
ejpam-6631	360	22	i.	i.	PROPN
ejpam-6631	360	23	a.	a.	PROPN
ejpam-6631	360	24	ahmed	ahmed	PROPN
ejpam-6631	360	25	,	,	PUNCT
ejpam-6631	360	26	fractional	fractional	ADJ
ejpam-6631	360	27	calculus	calculus	NOUN
ejpam-6631	360	28	applications	application	NOUN
ejpam-6631	360	29	in	in	ADP
ejpam-6631	360	30	engineering	engineering	NOUN
ejpam-6631	360	31	insights	insight	NOUN
ejpam-6631	360	32	into	into	ADP
ejpam-6631	360	33	four	four	NUM
ejpam-6631	360	34	-	-	PUNCT
ejpam-6631	360	35	dimensional	dimensional	ADJ
ejpam-6631	360	36	chaotic	chaotic	ADJ
ejpam-6631	360	37	systems	system	NOUN
ejpam-6631	360	38	.	.	PUNCT
ejpam-6631	361	1	journal	journal	PROPN
ejpam-6631	361	2	of	of	ADP
ejpam-6631	361	3	theory	theory	NOUN
ejpam-6631	361	4	,	,	PUNCT
ejpam-6631	361	5	mathematics	mathematics	PROPN
ejpam-6631	361	6	and	and	CCONJ
ejpam-6631	361	7	physics	physic	NOUN
ejpam-6631	361	8	,	,	PUNCT
ejpam-6631	361	9	(	(	PUNCT
ejpam-6631	361	10	2024	2024	NUM
ejpam-6631	361	11	)	)	PUNCT
ejpam-6631	361	12	,	,	PUNCT
ejpam-6631	361	13	3(5	3(5	NUM
ejpam-6631	361	14	)	)	PUNCT
ejpam-6631	361	15	,	,	PUNCT
ejpam-6631	361	16	75	75	NUM
ejpam-6631	361	17	-	-	SYM
ejpam-6631	361	18	84	84	NUM
ejpam-6631	361	19	:	:	PUNCT
ejpam-6631	361	20	available	available	ADJ
ejpam-6631	361	21	online	online	ADV
ejpam-6631	361	22	:	:	PUNCT
ejpam-6631	361	23	https://jtmp.innovascience.uz/index.php/journal/article/view/147	https://jtmp.innovascience.uz/index.php/journal/article/view/147	NUM
ejpam-6631	361	24	.	.	PUNCT
ejpam-6631	362	1	[	[	X
ejpam-6631	362	2	5	5	NUM
ejpam-6631	362	3	]	]	PUNCT
ejpam-6631	362	4	m.	m.	NOUN
ejpam-6631	362	5	d.	d.	PROPN
ejpam-6631	362	6	johansyah	johansyah	PROPN
ejpam-6631	362	7	,	,	PUNCT
ejpam-6631	362	8	a.	a.	NOUN
ejpam-6631	362	9	sambas	sambas	PROPN
ejpam-6631	362	10	,	,	PUNCT
ejpam-6631	362	11	s.	s.	PROPN
ejpam-6631	362	12	qureshi	qureshi	PROPN
ejpam-6631	362	13	,	,	PUNCT
ejpam-6631	362	14	s.	s.	PROPN
ejpam-6631	362	15	zheng	zheng	PROPN
ejpam-6631	362	16	,	,	PUNCT
ejpam-6631	362	17	t.	t.	PROPN
ejpam-6631	362	18	m.	m.	NOUN
ejpam-6631	362	19	abed	abe	VERB
ejpam-6631	362	20	-	-	PUNCT
ejpam-6631	362	21	elhameed	elhameed	PROPN
ejpam-6631	362	22	,	,	PUNCT
ejpam-6631	362	23	s.	s.	PROPN
ejpam-6631	362	24	vaidyanathan	vaidyanathan	PROPN
ejpam-6631	362	25	,	,	PUNCT
ejpam-6631	362	26	&	&	CCONJ
ejpam-6631	362	27	i.	i.	PROPN
ejpam-6631	362	28	m.	m.	PROPN
ejpam-6631	362	29	sulaiman	sulaiman	PROPN
ejpam-6631	362	30	,	,	PUNCT
ejpam-6631	362	31	investigation	investigation	NOUN
ejpam-6631	362	32	of	of	ADP
ejpam-6631	362	33	the	the	DET
ejpam-6631	362	34	hyperchaos	hyperchaos	PROPN
ejpam-6631	362	35	and	and	CCONJ
ejpam-6631	362	36	control	control	NOUN
ejpam-6631	362	37	in	in	ADP
ejpam-6631	362	38	the	the	DET
ejpam-6631	362	39	m.	m.	NOUN
ejpam-6631	362	40	abdel	abdel	PROPN
ejpam-6631	362	41	aal	aal	PROPN
ejpam-6631	362	42	et	et	PROPN
ejpam-6631	362	43	al	al	PROPN
ejpam-6631	362	44	.	.	PUNCT
ejpam-6631	362	45	/	/	SYM
ejpam-6631	362	46	eur	eur	PROPN
ejpam-6631	362	47	.	.	PUNCT
ejpam-6631	363	1	j.	j.	PROPN
ejpam-6631	363	2	pure	pure	PROPN
ejpam-6631	363	3	appl	appl	PROPN
ejpam-6631	363	4	.	.	PROPN
ejpam-6631	363	5	math	math	PROPN
ejpam-6631	363	6	,	,	PUNCT
ejpam-6631	363	7	18	18	NUM
ejpam-6631	363	8	(	(	PUNCT
ejpam-6631	363	9	4	4	NUM
ejpam-6631	363	10	)	)	PUNCT
ejpam-6631	363	11	(	(	PUNCT
ejpam-6631	363	12	2025	2025	NUM
ejpam-6631	363	13	)	)	PUNCT
ejpam-6631	363	14	,	,	PUNCT
ejpam-6631	363	15	6631	6631	NUM
ejpam-6631	363	16	19	19	NUM
ejpam-6631	363	17	of	of	ADP
ejpam-6631	363	18	20	20	NUM
ejpam-6631	363	19	fractional	fractional	ADJ
ejpam-6631	363	20	order	order	NOUN
ejpam-6631	363	21	financial	financial	ADJ
ejpam-6631	363	22	system	system	NOUN
ejpam-6631	363	23	with	with	ADP
ejpam-6631	363	24	profit	profit	NOUN
ejpam-6631	363	25	margin	margin	NOUN
ejpam-6631	363	26	,	,	PUNCT
ejpam-6631	363	27	partial	partial	ADJ
ejpam-6631	363	28	differential	differential	ADJ
ejpam-6631	363	29	equations	equation	NOUN
ejpam-6631	363	30	in	in	ADP
ejpam-6631	363	31	applied	applied	ADJ
ejpam-6631	363	32	mathematics	mathematic	NOUN
ejpam-6631	363	33	,	,	PUNCT
ejpam-6631	363	34	(	(	PUNCT
ejpam-6631	363	35	2024	2024	NUM
ejpam-6631	363	36	)	)	PUNCT
ejpam-6631	363	37	,	,	PUNCT
ejpam-6631	363	38	9	9	NUM
ejpam-6631	363	39	,	,	PUNCT
ejpam-6631	363	40	100612	100612	NUM
ejpam-6631	363	41	.	.	PUNCT
ejpam-6631	364	1	https://doi.org/10.1016/j.padiff.2023.100612	https://doi.org/10.1016/j.padiff.2023.100612	NOUN
ejpam-6631	364	2	.	.	PUNCT
ejpam-6631	365	1	[	[	X
ejpam-6631	365	2	6	6	NUM
ejpam-6631	365	3	]	]	X
ejpam-6631	365	4	al	al	PROPN
ejpam-6631	365	5	-	-	PUNCT
ejpam-6631	365	6	ahmad	ahmad	PROPN
ejpam-6631	365	7	,	,	PUNCT
ejpam-6631	365	8	s.	s.	PROPN
ejpam-6631	365	9	,	,	PUNCT
ejpam-6631	365	10	mamat	mamat	NOUN
ejpam-6631	365	11	,	,	PUNCT
ejpam-6631	365	12	m.	m.	NOUN
ejpam-6631	365	13	,	,	PUNCT
ejpam-6631	365	14	alahmad	alahmad	ADJ
ejpam-6631	365	15	,	,	PUNCT
ejpam-6631	365	16	r.	r.	PROPN
ejpam-6631	365	17	,	,	PUNCT
ejpam-6631	365	18	sulaiman	sulaiman	PROPN
ejpam-6631	365	19	,	,	PUNCT
ejpam-6631	365	20	i.	i.	PROPN
ejpam-6631	365	21	m.	m.	PROPN
ejpam-6631	365	22	,	,	PUNCT
ejpam-6631	365	23	ghazali	ghazali	PROPN
ejpam-6631	365	24	,	,	PUNCT
ejpam-6631	365	25	p.	p.	PROPN
ejpam-6631	365	26	l.	l.	PROPN
ejpam-6631	365	27	,	,	PUNCT
ejpam-6631	365	28	&	&	CCONJ
ejpam-6631	365	29	mohamed	mohamed	PROPN
ejpam-6631	365	30	,	,	PUNCT
ejpam-6631	365	31	m.	m.	NOUN
ejpam-6631	365	32	a.	a.	NOUN
ejpam-6631	365	33	on	on	ADP
ejpam-6631	365	34	new	new	ADJ
ejpam-6631	365	35	properties	property	NOUN
ejpam-6631	365	36	of	of	ADP
ejpam-6631	365	37	differential	differential	ADJ
ejpam-6631	365	38	transform	transform	NOUN
ejpam-6631	365	39	via	via	ADP
ejpam-6631	365	40	difference	difference	NOUN
ejpam-6631	365	41	equations	equation	NOUN
ejpam-6631	365	42	.	.	PUNCT
ejpam-6631	366	1	international	international	ADJ
ejpam-6631	366	2	journal	journal	PROPN
ejpam-6631	366	3	of	of	ADP
ejpam-6631	366	4	engineering	engineering	PROPN
ejpam-6631	366	5	&	&	CCONJ
ejpam-6631	366	6	technology	technology	PROPN
ejpam-6631	366	7	,	,	PUNCT
ejpam-6631	366	8	(	(	PUNCT
ejpam-6631	366	9	2018	2018	NUM
ejpam-6631	366	10	)	)	PUNCT
ejpam-6631	366	11	,	,	PUNCT
ejpam-6631	366	12	7(3.28	7(3.28	NUM
ejpam-6631	366	13	)	)	PUNCT
ejpam-6631	366	14	,	,	PUNCT
ejpam-6631	366	15	321	321	NUM
ejpam-6631	366	16	-	-	SYM
ejpam-6631	366	17	324	324	NUM
ejpam-6631	366	18	.	.	PUNCT
ejpam-6631	367	1	[	[	X
ejpam-6631	367	2	7	7	X
ejpam-6631	367	3	]	]	X
ejpam-6631	367	4	h.	h.	PROPN
ejpam-6631	367	5	m.	m.	PROPN
ejpam-6631	367	6	fahad	fahad	PROPN
ejpam-6631	367	7	&	&	CCONJ
ejpam-6631	367	8	a.	a.	PROPN
ejpam-6631	367	9	fernandez	fernandez	PROPN
ejpam-6631	367	10	,	,	PUNCT
ejpam-6631	367	11	operational	operational	ADJ
ejpam-6631	367	12	calculus	calculus	NOUN
ejpam-6631	367	13	for	for	ADP
ejpam-6631	367	14	the	the	DET
ejpam-6631	367	15	riemann	riemann	PROPN
ejpam-6631	367	16	–	–	PUNCT
ejpam-6631	367	17	liouville	liouville	VERB
ejpam-6631	367	18	fractional	fractional	ADJ
ejpam-6631	367	19	derivative	derivative	NOUN
ejpam-6631	367	20	with	with	ADP
ejpam-6631	367	21	respect	respect	NOUN
ejpam-6631	367	22	to	to	ADP
ejpam-6631	367	23	a	a	DET
ejpam-6631	367	24	function	function	NOUN
ejpam-6631	367	25	and	and	CCONJ
ejpam-6631	367	26	its	its	PRON
ejpam-6631	367	27	applications	application	NOUN
ejpam-6631	367	28	,	,	PUNCT
ejpam-6631	367	29	fractional	fractional	ADJ
ejpam-6631	367	30	calculus	calculus	NOUN
ejpam-6631	367	31	and	and	CCONJ
ejpam-6631	367	32	applied	apply	VERB
ejpam-6631	367	33	analysis	analysis	NOUN
ejpam-6631	367	34	,	,	PUNCT
ejpam-6631	367	35	(	(	PUNCT
ejpam-6631	367	36	2021	2021	NUM
ejpam-6631	367	37	)	)	PUNCT
ejpam-6631	367	38	,	,	PUNCT
ejpam-6631	367	39	24(2	24(2	NUM
ejpam-6631	367	40	)	)	PUNCT
ejpam-6631	367	41	,	,	PUNCT
ejpam-6631	367	42	518	518	NUM
ejpam-6631	367	43	-	-	SYM
ejpam-6631	367	44	540	540	NUM
ejpam-6631	367	45	.	.	PUNCT
ejpam-6631	368	1	doi	doi	NOUN
ejpam-6631	368	2	:	:	PUNCT
ejpam-6631	368	3	doi.org/10.1515/fca-2021-0023	doi.org/10.1515/fca-2021-0023	NOUN
ejpam-6631	368	4	.	.	PUNCT
ejpam-6631	369	1	[	[	X
ejpam-6631	369	2	8	8	NUM
ejpam-6631	369	3	]	]	X
ejpam-6631	369	4	h.	h.	PROPN
ejpam-6631	369	5	m.	m.	PROPN
ejpam-6631	369	6	fahad	fahad	PROPN
ejpam-6631	369	7	&	&	CCONJ
ejpam-6631	369	8	a.fernandez	a.fernandez	PROPN
ejpam-6631	369	9	,	,	PUNCT
ejpam-6631	369	10	operational	operational	ADJ
ejpam-6631	369	11	calculus	calculus	NOUN
ejpam-6631	369	12	for	for	ADP
ejpam-6631	369	13	caputo	caputo	PROPN
ejpam-6631	369	14	fractional	fractional	PROPN
ejpam-6631	369	15	calculus	calculus	NOUN
ejpam-6631	369	16	with	with	ADP
ejpam-6631	369	17	respect	respect	NOUN
ejpam-6631	369	18	to	to	ADP
ejpam-6631	369	19	functions	function	NOUN
ejpam-6631	369	20	and	and	CCONJ
ejpam-6631	369	21	the	the	DET
ejpam-6631	369	22	associated	associated	ADJ
ejpam-6631	369	23	fractional	fractional	ADJ
ejpam-6631	369	24	differential	differential	NOUN
ejpam-6631	369	25	equations	equation	NOUN
ejpam-6631	369	26	,	,	PUNCT
ejpam-6631	369	27	applied	apply	VERB
ejpam-6631	369	28	mathematics	mathematic	NOUN
ejpam-6631	369	29	and	and	CCONJ
ejpam-6631	369	30	computation	computation	NOUN
ejpam-6631	369	31	,	,	PUNCT
ejpam-6631	369	32	(	(	PUNCT
ejpam-6631	369	33	2021	2021	NUM
ejpam-6631	369	34	)	)	PUNCT
ejpam-6631	369	35	,	,	PUNCT
ejpam-6631	369	36	409	409	NUM
ejpam-6631	369	37	,	,	PUNCT
ejpam-6631	369	38	126400	126400	NUM
ejpam-6631	369	39	.	.	PUNCT
ejpam-6631	370	1	https://doi.org/10.1016/j.amc.2021.126400	https://doi.org/10.1016/j.amc.2021.126400	PUNCT
ejpam-6631	370	2	.	.	PUNCT
ejpam-6631	371	1	[	[	X
ejpam-6631	371	2	9	9	NUM
ejpam-6631	371	3	]	]	PUNCT
ejpam-6631	371	4	a.	a.	PROPN
ejpam-6631	371	5	e.	e.	PROPN
ejpam-6631	371	6	owoyemi	owoyemi	PROPN
ejpam-6631	371	7	,	,	PUNCT
ejpam-6631	371	8	i.	i.	PROPN
ejpam-6631	371	9	m.	m.	PROPN
ejpam-6631	371	10	sulaiman	sulaiman	PROPN
ejpam-6631	371	11	,	,	PUNCT
ejpam-6631	371	12	p.	p.	PROPN
ejpam-6631	371	13	kumar	kumar	PROPN
ejpam-6631	371	14	,	,	PUNCT
ejpam-6631	371	15	v.	v.	ADP
ejpam-6631	371	16	govindaraj	govindaraj	PROPN
ejpam-6631	371	17	&	&	CCONJ
ejpam-6631	371	18	m.	m.	PROPN
ejpam-6631	371	19	mamat	mamat	PROPN
ejpam-6631	371	20	,	,	PUNCT
ejpam-6631	371	21	some	some	DET
ejpam-6631	371	22	novel	novel	ADJ
ejpam-6631	371	23	mathematical	mathematical	ADJ
ejpam-6631	371	24	analysis	analysis	NOUN
ejpam-6631	371	25	on	on	ADP
ejpam-6631	371	26	the	the	DET
ejpam-6631	371	27	fractional	fractional	ADJ
ejpam-6631	371	28	-	-	PUNCT
ejpam-6631	371	29	order	order	NOUN
ejpam-6631	371	30	2019	2019	NUM
ejpam-6631	371	31	-	-	PUNCT
ejpam-6631	371	32	ncov	ncov	ADV
ejpam-6631	371	33	dynamical	dynamical	ADJ
ejpam-6631	371	34	model	model	NOUN
ejpam-6631	371	35	,	,	PUNCT
ejpam-6631	371	36	mathematical	mathematical	ADJ
ejpam-6631	371	37	methods	method	NOUN
ejpam-6631	371	38	in	in	ADP
ejpam-6631	371	39	the	the	DET
ejpam-6631	371	40	applied	apply	VERB
ejpam-6631	371	41	sciences	science	NOUN
ejpam-6631	371	42	,	,	PUNCT
ejpam-6631	371	43	(	(	PUNCT
ejpam-6631	371	44	2023	2023	NUM
ejpam-6631	371	45	)	)	PUNCT
ejpam-6631	371	46	.	.	PUNCT
ejpam-6631	372	1	46(4	46(4	NOUN
ejpam-6631	372	2	)	)	PUNCT
ejpam-6631	372	3	,	,	PUNCT
ejpam-6631	372	4	4466	4466	NUM
ejpam-6631	372	5	-	-	SYM
ejpam-6631	372	6	4474	4474	NUM
ejpam-6631	372	7	.	.	PUNCT
ejpam-6631	373	1	https://doi.org/10.1002/mma.8772	https://doi.org/10.1002/mma.8772	PROPN
ejpam-6631	373	2	.	.	PUNCT
ejpam-6631	374	1	[	[	X
ejpam-6631	374	2	10	10	NUM
ejpam-6631	374	3	]	]	X
ejpam-6631	374	4	i.	i.	PROPN
ejpam-6631	374	5	m.	m.	PROPN
ejpam-6631	374	6	sulaiman	sulaiman	PROPN
ejpam-6631	374	7	,	,	PUNCT
ejpam-6631	374	8	a.	a.	PROPN
ejpam-6631	374	9	e.	e.	PROPN
ejpam-6631	374	10	owoyemi	owoyemi	PROPN
ejpam-6631	374	11	,	,	PUNCT
ejpam-6631	374	12	m.	m.	NOUN
ejpam-6631	374	13	a.	a.	PROPN
ejpam-6631	374	14	a	a	PRON
ejpam-6631	374	15	nawi	nawi	PROPN
ejpam-6631	374	16	,	,	PUNCT
ejpam-6631	374	17	s.	s.	PROPN
ejpam-6631	374	18	s.	s.	PROPN
ejpam-6631	374	19	muhammad	muhammad	PROPN
ejpam-6631	374	20	,	,	PUNCT
ejpam-6631	374	21	u.	u.	PROPN
ejpam-6631	374	22	r.	r.	PROPN
ejpam-6631	374	23	muhammad	muhammad	PROPN
ejpam-6631	374	24	,	,	PUNCT
ejpam-6631	374	25	a.	a.	PROPN
ejpam-6631	374	26	f.	f.	PROPN
ejpam-6631	374	27	jameel	jameel	PROPN
ejpam-6631	374	28	&	&	CCONJ
ejpam-6631	374	29	nawawi	nawawi	PROPN
ejpam-6631	374	30	,	,	PUNCT
ejpam-6631	374	31	m.	m.	PROPN
ejpam-6631	374	32	k.	k.	PROPN
ejpam-6631	374	33	m.	m.	PROPN
ejpam-6631	374	34	,	,	PUNCT
ejpam-6631	374	35	stability	stability	NOUN
ejpam-6631	374	36	and	and	CCONJ
ejpam-6631	374	37	bifurcation	bifurcation	NOUN
ejpam-6631	374	38	analysis	analysis	NOUN
ejpam-6631	374	39	of	of	ADP
ejpam-6631	374	40	rössler	rössler	NOUN
ejpam-6631	374	41	system	system	NOUN
ejpam-6631	374	42	in	in	ADP
ejpam-6631	374	43	fractional	fractional	ADJ
ejpam-6631	374	44	order	order	NOUN
ejpam-6631	374	45	,	,	PUNCT
ejpam-6631	374	46	in	in	ADP
ejpam-6631	374	47	advances	advance	NOUN
ejpam-6631	374	48	in	in	ADP
ejpam-6631	374	49	intelligent	intelligent	ADJ
ejpam-6631	374	50	manufacturing	manufacturing	NOUN
ejpam-6631	374	51	and	and	CCONJ
ejpam-6631	374	52	mechatronics	mechatronic	NOUN
ejpam-6631	374	53	:	:	PUNCT
ejpam-6631	374	54	selected	select	VERB
ejpam-6631	374	55	articles	article	NOUN
ejpam-6631	374	56	from	from	ADP
ejpam-6631	374	57	the	the	DET
ejpam-6631	374	58	innovative	innovative	ADJ
ejpam-6631	374	59	manufacturing	manufacturing	NOUN
ejpam-6631	374	60	,	,	PUNCT
ejpam-6631	374	61	mechatronics	mechatronic	NOUN
ejpam-6631	374	62	and	and	CCONJ
ejpam-6631	374	63	materials	material	NOUN
ejpam-6631	374	64	forum	forum	NOUN
ejpam-6631	374	65	(	(	PUNCT
ejpam-6631	374	66	im3f	im3f	PROPN
ejpam-6631	374	67	2022	2022	NUM
ejpam-6631	374	68	)	)	PUNCT
ejpam-6631	374	69	,	,	PUNCT
ejpam-6631	374	70	pahang	pahang	PROPN
ejpam-6631	374	71	,	,	PUNCT
ejpam-6631	374	72	malaysia	malaysia	PROPN
ejpam-6631	374	73	(	(	PUNCT
ejpam-6631	374	74	pp	pp	ADJ
ejpam-6631	374	75	.	.	PUNCT
ejpam-6631	375	1	239	239	NUM
ejpam-6631	375	2	-	-	SYM
ejpam-6631	375	3	250	250	NUM
ejpam-6631	375	4	)	)	PUNCT
ejpam-6631	375	5	.	.	PUNCT
ejpam-6631	376	1	singapore	singapore	PROPN
ejpam-6631	376	2	:	:	PUNCT
ejpam-6631	376	3	springer	springer	NOUN
ejpam-6631	376	4	nature	nature	PROPN
ejpam-6631	376	5	singapore	singapore	PROPN
ejpam-6631	376	6	.	.	PUNCT
ejpam-6631	377	1	https	https	NOUN
ejpam-6631	377	2	:	:	PUNCT
ejpam-6631	377	3	//doi.org/10.1007/978−	//doi.org/10.1007/978−	PROPN
ejpam-6631	377	4	981−	981−	PROPN
ejpam-6631	377	5	19−	19−	NUM
ejpam-6631	377	6	8703−	8703−	NUM
ejpam-6631	377	7	820	820	NUM
ejpam-6631	377	8	.	.	PUNCT
ejpam-6631	378	1	[	[	X
ejpam-6631	378	2	11	11	NUM
ejpam-6631	378	3	]	]	X
ejpam-6631	378	4	aal	aal	PROPN
ejpam-6631	378	5	,	,	PUNCT
ejpam-6631	378	6	m.	m.	NOUN
ejpam-6631	378	7	a.	a.	PROPN
ejpam-6631	378	8	&	&	CCONJ
ejpam-6631	378	9	arafah	arafah	PROPN
ejpam-6631	378	10	,	,	PUNCT
ejpam-6631	378	11	a.	a.	NOUN
ejpam-6631	378	12	(	(	PUNCT
ejpam-6631	378	13	2025	2025	NUM
ejpam-6631	378	14	)	)	PUNCT
ejpam-6631	378	15	.	.	PUNCT
ejpam-6631	379	1	an	an	DET
ejpam-6631	379	2	efficient	efficient	ADJ
ejpam-6631	379	3	symmetric	symmetric	ADJ
ejpam-6631	379	4	operational	operational	ADJ
ejpam-6631	379	5	matrix	matrix	NOUN
ejpam-6631	379	6	method	method	NOUN
ejpam-6631	379	7	for	for	ADP
ejpam-6631	379	8	solving	solve	VERB
ejpam-6631	379	9	tempered	temper	VERB
ejpam-6631	379	10	fractional	fractional	ADJ
ejpam-6631	379	11	differential	differential	ADJ
ejpam-6631	379	12	equations	equation	NOUN
ejpam-6631	379	13	with	with	ADP
ejpam-6631	379	14	respect	respect	NOUN
ejpam-6631	379	15	to	to	ADP
ejpam-6631	379	16	another	another	DET
ejpam-6631	379	17	function	function	NOUN
ejpam-6631	379	18	.	.	PUNCT
ejpam-6631	380	1	international	international	ADJ
ejpam-6631	380	2	journal	journal	PROPN
ejpam-6631	380	3	of	of	ADP
ejpam-6631	380	4	neutrosophic	neutrosophic	ADJ
ejpam-6631	380	5	science	science	NOUN
ejpam-6631	380	6	(	(	PUNCT
ejpam-6631	380	7	ijns	ijns	PROPN
ejpam-6631	380	8	)	)	PUNCT
ejpam-6631	380	9	,	,	PUNCT
ejpam-6631	380	10	26(1	26(1	NUM
ejpam-6631	380	11	)	)	PUNCT
ejpam-6631	380	12	.	.	PUNCT
ejpam-6631	381	1	[	[	X
ejpam-6631	381	2	12	12	NUM
ejpam-6631	381	3	]	]	X
ejpam-6631	381	4	lsamir	lsamir	PROPN
ejpam-6631	381	5	,	,	PUNCT
ejpam-6631	381	6	h.	h.	PROPN
ejpam-6631	381	7	,	,	PUNCT
ejpam-6631	381	8	noorani	noorani	PROPN
ejpam-6631	381	9	,	,	PUNCT
ejpam-6631	381	10	m.	m.	NOUN
ejpam-6631	381	11	s.	s.	PROPN
ejpam-6631	381	12	,	,	PUNCT
ejpam-6631	381	13	shatanawi	shatanawi	PROPN
ejpam-6631	381	14	,	,	PUNCT
ejpam-6631	381	15	w.	w.	PROPN
ejpam-6631	381	16	,	,	PUNCT
ejpam-6631	381	17	aydi	aydi	VERB
ejpam-6631	381	18	,	,	PUNCT
ejpam-6631	381	19	h.	h.	NOUN
ejpam-6631	381	20	,	,	PUNCT
ejpam-6631	381	21	akhadkulov	akhadkulov	VERB
ejpam-6631	381	22	,	,	PUNCT
ejpam-6631	381	23	h.	h.	PROPN
ejpam-6631	381	24	,	,	PUNCT
ejpam-6631	381	25	qawaqneh	qawaqneh	PROPN
ejpam-6631	381	26	,	,	PUNCT
ejpam-6631	381	27	h.	h.	PROPN
ejpam-6631	381	28	,	,	PUNCT
ejpam-6631	381	29	&	&	CCONJ
ejpam-6631	381	30	alanazi	alanazi	PROPN
ejpam-6631	381	31	,	,	PUNCT
ejpam-6631	381	32	k.	k.	PROPN
ejpam-6631	381	33	(	(	PUNCT
ejpam-6631	381	34	2019	2019	NUM
ejpam-6631	381	35	)	)	PUNCT
ejpam-6631	381	36	.	.	PUNCT
ejpam-6631	382	1	fixed	fix	VERB
ejpam-6631	382	2	point	point	NOUN
ejpam-6631	382	3	results	result	NOUN
ejpam-6631	382	4	in	in	ADP
ejpam-6631	382	5	metric	metric	ADJ
ejpam-6631	382	6	-	-	PUNCT
ejpam-6631	382	7	like	like	ADJ
ejpam-6631	382	8	spaces	space	NOUN
ejpam-6631	382	9	via	via	ADP
ejpam-6631	382	10	sigma	sigma	PROPN
ejpam-6631	382	11	-	-	PUNCT
ejpam-6631	382	12	simulation	simulation	NOUN
ejpam-6631	382	13	functions	function	NOUN
ejpam-6631	382	14	.	.	PUNCT
ejpam-6631	383	1	european	european	ADJ
ejpam-6631	383	2	journal	journal	PROPN
ejpam-6631	383	3	of	of	ADP
ejpam-6631	383	4	pure	pure	ADJ
ejpam-6631	383	5	and	and	CCONJ
ejpam-6631	383	6	applied	applied	ADJ
ejpam-6631	383	7	mathematics	mathematic	NOUN
ejpam-6631	383	8	,	,	PUNCT
ejpam-6631	383	9	12(1	12(1	NUM
ejpam-6631	383	10	)	)	PUNCT
ejpam-6631	383	11	,	,	PUNCT
ejpam-6631	383	12	88	88	NUM
ejpam-6631	383	13	-	-	SYM
ejpam-6631	383	14	100	100	NUM
ejpam-6631	383	15	.	.	PUNCT
ejpam-6631	384	1	[	[	X
ejpam-6631	384	2	13	13	NUM
ejpam-6631	384	3	]	]	SYM
ejpam-6631	384	4	jameel	jameel	PROPN
ejpam-6631	384	5	,	,	PUNCT
ejpam-6631	384	6	a.	a.	PROPN
ejpam-6631	384	7	f.	f.	PROPN
ejpam-6631	384	8	,	,	PUNCT
ejpam-6631	384	9	saaban	saaban	PROPN
ejpam-6631	384	10	,	,	PUNCT
ejpam-6631	384	11	a.	a.	NOUN
ejpam-6631	384	12	,	,	PUNCT
ejpam-6631	384	13	ahadkulov	ahadkulov	PROPN
ejpam-6631	384	14	,	,	PUNCT
ejpam-6631	384	15	h.	h.	PROPN
ejpam-6631	384	16	,	,	PUNCT
ejpam-6631	384	17	&	&	CCONJ
ejpam-6631	384	18	alipiah	alipiah	PROPN
ejpam-6631	384	19	,	,	PUNCT
ejpam-6631	384	20	f.	f.	PROPN
ejpam-6631	384	21	m.	m.	PROPN
ejpam-6631	384	22	(	(	PUNCT
ejpam-6631	384	23	2017	2017	NUM
ejpam-6631	384	24	,	,	PUNCT
ejpam-6631	384	25	september	september	PROPN
ejpam-6631	384	26	)	)	PUNCT
ejpam-6631	384	27	.	.	PUNCT
ejpam-6631	385	1	approximate	approximate	ADJ
ejpam-6631	385	2	solution	solution	NOUN
ejpam-6631	385	3	fuzzy	fuzzy	ADJ
ejpam-6631	385	4	pantograph	pantograph	NOUN
ejpam-6631	385	5	equation	equation	NOUN
ejpam-6631	385	6	by	by	ADP
ejpam-6631	385	7	using	use	VERB
ejpam-6631	385	8	homotopy	homotopy	NOUN
ejpam-6631	385	9	perturbation	perturbation	NOUN
ejpam-6631	385	10	method	method	NOUN
ejpam-6631	385	11	.	.	PUNCT
ejpam-6631	386	1	in	in	ADP
ejpam-6631	386	2	journal	journal	PROPN
ejpam-6631	386	3	of	of	ADP
ejpam-6631	386	4	physics	physics	PROPN
ejpam-6631	386	5	:	:	PUNCT
ejpam-6631	386	6	conference	conference	NOUN
ejpam-6631	386	7	series	series	NOUN
ejpam-6631	386	8	(	(	PUNCT
ejpam-6631	386	9	vol	vol	NOUN
ejpam-6631	386	10	.	.	PROPN
ejpam-6631	386	11	890	890	NUM
ejpam-6631	386	12	,	,	PUNCT
ejpam-6631	386	13	no	no	INTJ
ejpam-6631	386	14	.	.	NOUN
ejpam-6631	386	15	1	1	NUM
ejpam-6631	386	16	,	,	PUNCT
ejpam-6631	386	17	p.	p.	NOUN
ejpam-6631	386	18	012023	012023	NUM
ejpam-6631	386	19	)	)	PUNCT
ejpam-6631	386	20	.	.	PUNCT
ejpam-6631	387	1	iop	iop	NOUN
ejpam-6631	387	2	publishing	publishing	NOUN
ejpam-6631	387	3	.	.	PUNCT
ejpam-6631	388	1	[	[	X
ejpam-6631	388	2	14	14	NUM
ejpam-6631	388	3	]	]	PUNCT
ejpam-6631	388	4	akhadkulov	akhadkulov	PROPN
ejpam-6631	388	5	,	,	PUNCT
ejpam-6631	388	6	h.	h.	PROPN
ejpam-6631	388	7	,	,	PUNCT
ejpam-6631	388	8	saaban	saaban	PROPN
ejpam-6631	388	9	,	,	PUNCT
ejpam-6631	388	10	a.	a.	PROPN
ejpam-6631	388	11	b.	b.	PROPN
ejpam-6631	388	12	,	,	PUNCT
ejpam-6631	388	13	alipiah	alipiah	ADV
ejpam-6631	388	14	,	,	PUNCT
ejpam-6631	388	15	m.	m.	PROPN
ejpam-6631	388	16	f.	f.	PROPN
ejpam-6631	388	17	,	,	PUNCT
ejpam-6631	388	18	&	&	CCONJ
ejpam-6631	388	19	jameel	jameel	PROPN
ejpam-6631	388	20	,	,	PUNCT
ejpam-6631	388	21	a.	a.	PROPN
ejpam-6631	388	22	f.	f.	PROPN
ejpam-6631	388	23	(	(	PUNCT
ejpam-6631	388	24	2018	2018	NUM
ejpam-6631	388	25	)	)	PUNCT
ejpam-6631	388	26	.	.	PUNCT
ejpam-6631	389	1	on	on	ADP
ejpam-6631	389	2	applications	application	NOUN
ejpam-6631	389	3	of	of	ADP
ejpam-6631	389	4	multidimensional	multidimensional	ADJ
ejpam-6631	389	5	fixed	fix	VERB
ejpam-6631	389	6	point	point	NOUN
ejpam-6631	389	7	theorems	theorem	NOUN
ejpam-6631	389	8	.	.	PUNCT
ejpam-6631	390	1	nonlinear	nonlinear	ADJ
ejpam-6631	390	2	functional	functional	ADJ
ejpam-6631	390	3	analysis	analysis	NOUN
ejpam-6631	390	4	and	and	CCONJ
ejpam-6631	390	5	applications	application	NOUN
ejpam-6631	390	6	,	,	PUNCT
ejpam-6631	390	7	585	585	NUM
ejpam-6631	390	8	-	-	SYM
ejpam-6631	390	9	593	593	NUM
ejpam-6631	390	10	.	.	PUNCT
ejpam-6631	391	1	[	[	X
ejpam-6631	391	2	15	15	NUM
ejpam-6631	391	3	]	]	X
ejpam-6631	391	4	s.	s.	PROPN
ejpam-6631	391	5	deepa	deepa	PROPN
ejpam-6631	391	6	,	,	PUNCT
ejpam-6631	391	7	a.	a.	NOUN
ejpam-6631	391	8	ganesh	ganesh	PROPN
ejpam-6631	391	9	,	,	PUNCT
ejpam-6631	391	10	v.	v.	ADP
ejpam-6631	391	11	ibrahimov	ibrahimov	ADJ
ejpam-6631	391	12	,	,	PUNCT
ejpam-6631	391	13	s.	s.	PROPN
ejpam-6631	391	14	s.	s.	PROPN
ejpam-6631	391	15	santra	santra	PROPN
ejpam-6631	391	16	,	,	PUNCT
ejpam-6631	391	17	v.	v.	ADP
ejpam-6631	391	18	govindan	govindan	PROPN
ejpam-6631	391	19	,	,	PUNCT
ejpam-6631	391	20	k.	k.	PROPN
ejpam-6631	391	21	m.khedher	m.khedher	PROPN
ejpam-6631	391	22	&	&	CCONJ
ejpam-6631	391	23	s.	s.	PROPN
ejpam-6631	391	24	noeiaghdam	noeiaghdam	PROPN
ejpam-6631	391	25	,	,	PUNCT
ejpam-6631	391	26	fractional	fractional	ADJ
ejpam-6631	391	27	fourier	fourier	NOUN
ejpam-6631	391	28	transform	transform	NOUN
ejpam-6631	391	29	to	to	AUX
ejpam-6631	391	30	stability	stability	NOUN
ejpam-6631	391	31	analysis	analysis	NOUN
ejpam-6631	391	32	of	of	ADP
ejpam-6631	391	33	fractional	fractional	ADJ
ejpam-6631	391	34	differential	differential	ADJ
ejpam-6631	391	35	equations	equation	NOUN
ejpam-6631	391	36	with	with	ADP
ejpam-6631	391	37	prabhakar	prabhakar	NOUN
ejpam-6631	391	38	derivatives	derivative	NOUN
ejpam-6631	391	39	,	,	PUNCT
ejpam-6631	391	40	azerbaijan	azerbaijan	PROPN
ejpam-6631	391	41	journal	journal	PROPN
ejpam-6631	391	42	of	of	ADP
ejpam-6631	391	43	mathematics	mathematic	NOUN
ejpam-6631	391	44	,	,	PUNCT
ejpam-6631	391	45	(	(	PUNCT
ejpam-6631	391	46	2022	2022	NUM
ejpam-6631	391	47	)	)	PUNCT
ejpam-6631	391	48	,	,	PUNCT
ejpam-6631	391	49	12(2	12(2	NUM
ejpam-6631	391	50	)	)	PUNCT
ejpam-6631	391	51	,	,	PUNCT
ejpam-6631	391	52	1	1	NUM
ejpam-6631	391	53	-	-	SYM
ejpam-6631	391	54	23	23	NUM
ejpam-6631	391	55	:	:	PUNCT
ejpam-6631	391	56	available	available	ADJ
ejpam-6631	391	57	online	online	ADV
ejpam-6631	391	58	:	:	PUNCT
ejpam-6631	392	1	https://www.azjm.org/.	https://www.azjm.org/.	PROPN
ejpam-6631	393	1	[	[	X
ejpam-6631	393	2	16	16	NUM
ejpam-6631	393	3	]	]	X
ejpam-6631	393	4	v.	v.	ADP
ejpam-6631	393	5	a.	a.	PROPN
ejpam-6631	393	6	kim	kim	PROPN
ejpam-6631	393	7	&	&	CCONJ
ejpam-6631	393	8	r.	r.	PROPN
ejpam-6631	393	9	i.	i.	PROPN
ejpam-6631	393	10	parovik	parovik	PROPN
ejpam-6631	393	11	,	,	PUNCT
ejpam-6631	393	12	application	application	NOUN
ejpam-6631	393	13	of	of	ADP
ejpam-6631	393	14	the	the	DET
ejpam-6631	393	15	explicit	explicit	ADJ
ejpam-6631	393	16	euler	euler	NOUN
ejpam-6631	393	17	method	method	NOUN
ejpam-6631	393	18	for	for	ADP
ejpam-6631	393	19	numerical	numerical	ADJ
ejpam-6631	393	20	analysis	analysis	NOUN
ejpam-6631	393	21	of	of	ADP
ejpam-6631	393	22	a	a	DET
ejpam-6631	393	23	nonlinear	nonlinear	ADJ
ejpam-6631	393	24	fractional	fractional	ADJ
ejpam-6631	393	25	oscillation	oscillation	NOUN
ejpam-6631	393	26	equation	equation	NOUN
ejpam-6631	393	27	,	,	PUNCT
ejpam-6631	393	28	fractal	fractal	ADJ
ejpam-6631	393	29	and	and	CCONJ
ejpam-6631	393	30	fractional	fractional	ADJ
ejpam-6631	393	31	,	,	PUNCT
ejpam-6631	393	32	(	(	PUNCT
ejpam-6631	393	33	2022	2022	NUM
ejpam-6631	393	34	)	)	PUNCT
ejpam-6631	393	35	6(5	6(5	NUM
ejpam-6631	393	36	)	)	PUNCT
ejpam-6631	393	37	,	,	PUNCT
ejpam-6631	393	38	274	274	NUM
ejpam-6631	393	39	.	.	PUNCT
ejpam-6631	393	40	https://doi.org/10.3390/fractalfract6050274	https://doi.org/10.3390/fractalfract6050274	PROPN
ejpam-6631	393	41	.	.	PUNCT
ejpam-6631	394	1	[	[	X
ejpam-6631	394	2	17	17	NUM
ejpam-6631	394	3	]	]	X
ejpam-6631	394	4	y.	y.	PROPN
ejpam-6631	394	5	m.	m.	PROPN
ejpam-6631	394	6	chu	chu	PROPN
ejpam-6631	394	7	,	,	PUNCT
ejpam-6631	394	8	m.	m.	PROPN
ejpam-6631	394	9	inc	inc	PROPN
ejpam-6631	394	10	,	,	PUNCT
ejpam-6631	394	11	m.	m.	PROPN
ejpam-6631	394	12	s.	s.	PROPN
ejpam-6631	394	13	hashemi	hashemi	PROPN
ejpam-6631	394	14	&	&	CCONJ
ejpam-6631	394	15	s.	s.	PROPN
ejpam-6631	394	16	eshaghi	eshaghi	PROPN
ejpam-6631	394	17	,	,	PUNCT
ejpam-6631	394	18	analytical	analytical	ADJ
ejpam-6631	394	19	treatment	treatment	NOUN
ejpam-6631	394	20	of	of	ADP
ejpam-6631	394	21	regularized	regularize	VERB
ejpam-6631	394	22	m.	m.	NOUN
ejpam-6631	394	23	abdel	abdel	PROPN
ejpam-6631	394	24	aal	aal	PROPN
ejpam-6631	394	25	et	et	PROPN
ejpam-6631	394	26	al	al	PROPN
ejpam-6631	394	27	.	.	PUNCT
ejpam-6631	394	28	/	/	SYM
ejpam-6631	394	29	eur	eur	PROPN
ejpam-6631	394	30	.	.	PUNCT
ejpam-6631	395	1	j.	j.	PROPN
ejpam-6631	395	2	pure	pure	PROPN
ejpam-6631	395	3	appl	appl	PROPN
ejpam-6631	395	4	.	.	PROPN
ejpam-6631	395	5	math	math	PROPN
ejpam-6631	395	6	,	,	PUNCT
ejpam-6631	395	7	18	18	NUM
ejpam-6631	395	8	(	(	PUNCT
ejpam-6631	395	9	4	4	NUM
ejpam-6631	395	10	)	)	PUNCT
ejpam-6631	395	11	(	(	PUNCT
ejpam-6631	395	12	2025	2025	NUM
ejpam-6631	395	13	)	)	PUNCT
ejpam-6631	395	14	,	,	PUNCT
ejpam-6631	395	15	6631	6631	NUM
ejpam-6631	395	16	20	20	NUM
ejpam-6631	395	17	of	of	ADP
ejpam-6631	395	18	20	20	NUM
ejpam-6631	395	19	prabhakar	prabhakar	NOUN
ejpam-6631	395	20	fractional	fractional	ADJ
ejpam-6631	395	21	differential	differential	NOUN
ejpam-6631	395	22	equations	equation	NOUN
ejpam-6631	395	23	by	by	ADP
ejpam-6631	395	24	invariant	invariant	ADJ
ejpam-6631	395	25	subspaces	subspace	NOUN
ejpam-6631	395	26	.	.	PUNCT
ejpam-6631	395	27	,	,	PUNCT
ejpam-6631	395	28	computational	computational	ADJ
ejpam-6631	395	29	and	and	CCONJ
ejpam-6631	395	30	applied	applied	ADJ
ejpam-6631	395	31	mathematics	mathematic	NOUN
ejpam-6631	395	32	,	,	PUNCT
ejpam-6631	395	33	(	(	PUNCT
ejpam-6631	395	34	2022	2022	NUM
ejpam-6631	395	35	)	)	PUNCT
ejpam-6631	395	36	,	,	PUNCT
ejpam-6631	395	37	41(6	41(6	NOUN
ejpam-6631	395	38	)	)	PUNCT
ejpam-6631	395	39	,	,	PUNCT
ejpam-6631	395	40	271	271	NUM
ejpam-6631	395	41	.	.	PUNCT
ejpam-6631	396	1	https://doi.org/10.1007/s40314-022-019771	https://doi.org/10.1007/s40314-022-019771	NOUN
ejpam-6631	396	2	.	.	PUNCT
ejpam-6631	397	1	[	[	X
ejpam-6631	397	2	18	18	NUM
ejpam-6631	397	3	]	]	PUNCT
ejpam-6631	397	4	t.	t.	PROPN
ejpam-6631	397	5	e.	e.	PROPN
ejpam-6631	397	6	namarneh	namarneh	PROPN
ejpam-6631	397	7	&	&	CCONJ
ejpam-6631	397	8	m.	m.	PROPN
ejpam-6631	397	9	al	al	PROPN
ejpam-6631	397	10	-	-	PUNCT
ejpam-6631	397	11	refai	refai	PROPN
ejpam-6631	397	12	,	,	PUNCT
ejpam-6631	397	13	analytical	analytical	ADJ
ejpam-6631	397	14	study	study	NOUN
ejpam-6631	397	15	to	to	ADP
ejpam-6631	397	16	systems	system	NOUN
ejpam-6631	397	17	of	of	ADP
ejpam-6631	397	18	fractional	fractional	ADJ
ejpam-6631	397	19	differential	differential	ADJ
ejpam-6631	397	20	equations	equation	NOUN
ejpam-6631	397	21	with	with	ADP
ejpam-6631	397	22	prabhakar	prabhakar	PROPN
ejpam-6631	397	23	derivative	derivative	NOUN
ejpam-6631	397	24	,	,	PUNCT
ejpam-6631	397	25	ifac	ifac	NOUN
ejpam-6631	397	26	-	-	PUNCT
ejpam-6631	397	27	papersonline	papersonline	NOUN
ejpam-6631	397	28	,	,	PUNCT
ejpam-6631	397	29	(	(	PUNCT
ejpam-6631	397	30	2024	2024	NUM
ejpam-6631	397	31	)	)	PUNCT
ejpam-6631	397	32	,	,	PUNCT
ejpam-6631	397	33	58(12	58(12	NUM
ejpam-6631	397	34	)	)	PUNCT
ejpam-6631	397	35	,	,	PUNCT
ejpam-6631	397	36	155	155	NUM
ejpam-6631	397	37	-	-	SYM
ejpam-6631	397	38	160	160	NUM
ejpam-6631	397	39	.	.	PUNCT
ejpam-6631	398	1	https://doi.org/10.1016/j.ifacol.2024.08.182	https://doi.org/10.1016/j.ifacol.2024.08.182	NOUN
ejpam-6631	398	2	.	.	PUNCT
ejpam-6631	399	1	[	[	X
ejpam-6631	399	2	19	19	NUM
ejpam-6631	399	3	]	]	X
ejpam-6631	399	4	e.	e.	PROPN
ejpam-6631	399	5	t.	t.	PROPN
ejpam-6631	399	6	karimov	karimov	PROPN
ejpam-6631	399	7	&	&	CCONJ
ejpam-6631	399	8	a.	a.	PROPN
ejpam-6631	399	9	hasanov	hasanov	PROPN
ejpam-6631	399	10	,	,	PUNCT
ejpam-6631	399	11	on	on	ADP
ejpam-6631	399	12	a	a	DET
ejpam-6631	399	13	boundary	boundary	ADJ
ejpam-6631	399	14	-	-	PUNCT
ejpam-6631	399	15	value	value	NOUN
ejpam-6631	399	16	problem	problem	NOUN
ejpam-6631	399	17	in	in	ADP
ejpam-6631	399	18	a	a	DET
ejpam-6631	399	19	bounded	bounded	ADJ
ejpam-6631	399	20	domain	domain	NOUN
ejpam-6631	399	21	for	for	ADP
ejpam-6631	399	22	a	a	DET
ejpam-6631	399	23	time	time	NOUN
ejpam-6631	399	24	-	-	PUNCT
ejpam-6631	399	25	fractional	fractional	ADJ
ejpam-6631	399	26	diffusion	diffusion	NOUN
ejpam-6631	399	27	equation	equation	NOUN
ejpam-6631	399	28	with	with	ADP
ejpam-6631	399	29	the	the	DET
ejpam-6631	399	30	prabhakar	prabhakar	PROPN
ejpam-6631	399	31	fractional	fractional	PROPN
ejpam-6631	399	32	derivative	derivative	ADJ
ejpam-6631	399	33	,	,	PUNCT
ejpam-6631	399	34	bulletin	bulletin	NOUN
ejpam-6631	399	35	of	of	ADP
ejpam-6631	399	36	the	the	DET
ejpam-6631	399	37	karaganda	karaganda	PROPN
ejpam-6631	399	38	university	university	PROPN
ejpam-6631	399	39	.	.	PUNCT
ejpam-6631	400	1	mathematics	mathematic	NOUN
ejpam-6631	400	2	series	series	PROPN
ejpam-6631	400	3	,	,	PUNCT
ejpam-6631	400	4	(	(	PUNCT
ejpam-6631	400	5	2023	2023	NUM
ejpam-6631	400	6	)	)	PUNCT
ejpam-6631	400	7	,	,	PUNCT
ejpam-6631	400	8	111(3	111(3	NUM
ejpam-6631	400	9	)	)	PUNCT
ejpam-6631	400	10	,	,	PUNCT
ejpam-6631	400	11	39	39	NUM
ejpam-6631	400	12	-	-	SYM
ejpam-6631	400	13	46	46	NUM
ejpam-6631	400	14	,	,	PUNCT
ejpam-6631	400	15	https://doi.org/10.31489/2023m3/39-46	https://doi.org/10.31489/2023m3/39-46	PROPN
ejpam-6631	400	16	.	.	PUNCT
ejpam-6631	401	1	[	[	X
ejpam-6631	401	2	20	20	NUM
ejpam-6631	401	3	]	]	PUNCT
ejpam-6631	401	4	f.	f.	PROPN
ejpam-6631	401	5	laxmi	laxmi	PROPN
ejpam-6631	401	6	,	,	PUNCT
ejpam-6631	401	7	s.	s.	PROPN
ejpam-6631	401	8	jain	jain	PROPN
ejpam-6631	401	9	,	,	PUNCT
ejpam-6631	401	10	p.	p.	PROPN
ejpam-6631	401	11	agarwal	agarwal	PROPN
ejpam-6631	401	12	&	&	CCONJ
ejpam-6631	401	13	g.	g.	PROPN
ejpam-6631	401	14	v.	v.	PROPN
ejpam-6631	401	15	milovanović	milovanović	PROPN
ejpam-6631	401	16	,	,	PUNCT
ejpam-6631	401	17	numerical	numerical	ADJ
ejpam-6631	401	18	calculation	calculation	NOUN
ejpam-6631	401	19	of	of	ADP
ejpam-6631	401	20	the	the	DET
ejpam-6631	401	21	extension	extension	NOUN
ejpam-6631	401	22	of	of	ADP
ejpam-6631	401	23	k	k	ADJ
ejpam-6631	401	24	-	-	ADJ
ejpam-6631	401	25	beta	beta	ADJ
ejpam-6631	401	26	function	function	NOUN
ejpam-6631	401	27	and	and	CCONJ
ejpam-6631	401	28	some	some	DET
ejpam-6631	401	29	new	new	ADJ
ejpam-6631	401	30	extensions	extension	NOUN
ejpam-6631	401	31	by	by	ADP
ejpam-6631	401	32	using	use	VERB
ejpam-6631	401	33	two	two	NUM
ejpam-6631	401	34	parameter	parameter	NOUN
ejpam-6631	401	35	kmittag	kmittag	NOUN
ejpam-6631	401	36	-	-	PUNCT
ejpam-6631	401	37	leffler	leffler	NOUN
ejpam-6631	401	38	function	function	NOUN
ejpam-6631	401	39	,	,	PUNCT
ejpam-6631	401	40	applied	apply	VERB
ejpam-6631	401	41	mathematics	mathematic	NOUN
ejpam-6631	401	42	and	and	CCONJ
ejpam-6631	401	43	computation	computation	NOUN
ejpam-6631	401	44	,	,	PUNCT
ejpam-6631	401	45	(	(	PUNCT
ejpam-6631	401	46	2024	2024	NUM
ejpam-6631	401	47	)	)	PUNCT
ejpam-6631	401	48	,	,	PUNCT
ejpam-6631	401	49	479	479	NUM
ejpam-6631	401	50	,	,	PUNCT
ejpam-6631	401	51	128857	128857	NUM
ejpam-6631	401	52	.	.	PUNCT
ejpam-6631	402	1	https://doi.org/10.1016/j.amc.2024.128857	https://doi.org/10.1016/j.amc.2024.128857	PUNCT
ejpam-6631	402	2	.	.	PUNCT
ejpam-6631	403	1	[	[	X
ejpam-6631	403	2	21	21	NUM
ejpam-6631	403	3	]	]	PUNCT
ejpam-6631	403	4	m.	m.	NOUN
ejpam-6631	403	5	a.	a.	PROPN
ejpam-6631	403	6	özarslan	özarslan	PROPN
ejpam-6631	403	7	,	,	PUNCT
ejpam-6631	403	8	&	&	CCONJ
ejpam-6631	403	9	a.	a.	NOUN
ejpam-6631	403	10	fernandez	fernandez	PROPN
ejpam-6631	403	11	,	,	PUNCT
ejpam-6631	403	12	on	on	ADP
ejpam-6631	403	13	a	a	DET
ejpam-6631	403	14	five	five	NUM
ejpam-6631	403	15	-	-	PUNCT
ejpam-6631	403	16	parameter	parameter	NOUN
ejpam-6631	403	17	mittag	mittag	ADJ
ejpam-6631	403	18	-	-	PUNCT
ejpam-6631	403	19	leffler	leffler	NOUN
ejpam-6631	403	20	function	function	NOUN
ejpam-6631	403	21	and	and	CCONJ
ejpam-6631	403	22	the	the	DET
ejpam-6631	403	23	corresponding	corresponding	ADJ
ejpam-6631	403	24	bivariate	bivariate	ADJ
ejpam-6631	403	25	fractional	fractional	ADJ
ejpam-6631	403	26	operators	operator	NOUN
ejpam-6631	403	27	fractal	fractal	ADJ
ejpam-6631	403	28	and	and	CCONJ
ejpam-6631	403	29	fractional	fractional	ADJ
ejpam-6631	403	30	,	,	PUNCT
ejpam-6631	403	31	(	(	PUNCT
ejpam-6631	403	32	2021	2021	NUM
ejpam-6631	403	33	)	)	PUNCT
ejpam-6631	403	34	,	,	PUNCT
ejpam-6631	403	35	5(2	5(2	NUM
ejpam-6631	403	36	)	)	PUNCT
ejpam-6631	403	37	,	,	PUNCT
ejpam-6631	403	38	45	45	NUM
ejpam-6631	403	39	.	.	PUNCT
ejpam-6631	403	40	https://doi.org/10.3390/fractalfract5020045	https://doi.org/10.3390/fractalfract5020045	ADJ
ejpam-6631	403	41	.	.	PUNCT
ejpam-6631	404	1	[	[	X
ejpam-6631	404	2	22	22	NUM
ejpam-6631	404	3	]	]	PUNCT
ejpam-6631	404	4	m.	m.	NOUN
ejpam-6631	404	5	h.	h.	PROPN
ejpam-6631	404	6	derakhshan	derakhshan	PROPN
ejpam-6631	404	7	&	&	CCONJ
ejpam-6631	404	8	a.	a.	PROPN
ejpam-6631	404	9	aminataei	aminataei	PROPN
ejpam-6631	404	10	,	,	PUNCT
ejpam-6631	404	11	comparison	comparison	NOUN
ejpam-6631	404	12	of	of	ADP
ejpam-6631	404	13	homotopy	homotopy	NOUN
ejpam-6631	404	14	perturbation	perturbation	NOUN
ejpam-6631	404	15	transform	transform	NOUN
ejpam-6631	404	16	method	method	NOUN
ejpam-6631	404	17	and	and	CCONJ
ejpam-6631	404	18	fractional	fractional	ADJ
ejpam-6631	404	19	adams	adam	NOUN
ejpam-6631	404	20	–	–	PUNCT
ejpam-6631	404	21	bashforth	bashforth	NOUN
ejpam-6631	404	22	method	method	NOUN
ejpam-6631	404	23	for	for	ADP
ejpam-6631	404	24	the	the	DET
ejpam-6631	404	25	caputo	caputo	PROPN
ejpam-6631	404	26	–	–	PUNCT
ejpam-6631	404	27	prabhakar	prabhakar	PROPN
ejpam-6631	404	28	nonlinear	nonlinear	ADJ
ejpam-6631	404	29	fractional	fractional	ADJ
ejpam-6631	404	30	differential	differential	NOUN
ejpam-6631	404	31	equations	equation	NOUN
ejpam-6631	404	32	,	,	PUNCT
ejpam-6631	404	33	iranian	iranian	ADJ
ejpam-6631	404	34	journal	journal	PROPN
ejpam-6631	404	35	of	of	ADP
ejpam-6631	404	36	numerical	numerical	ADJ
ejpam-6631	404	37	analysis	analysis	NOUN
ejpam-6631	404	38	and	and	CCONJ
ejpam-6631	404	39	optimization	optimization	NOUN
ejpam-6631	404	40	,	,	PUNCT
ejpam-6631	404	41	(	(	PUNCT
ejpam-6631	404	42	2020	2020	NUM
ejpam-6631	404	43	)	)	PUNCT
ejpam-6631	404	44	,	,	PUNCT
ejpam-6631	404	45	10(2	10(2	NUM
ejpam-6631	404	46	)	)	PUNCT
ejpam-6631	404	47	,	,	PUNCT
ejpam-6631	404	48	63	63	NUM
ejpam-6631	404	49	-	-	SYM
ejpam-6631	404	50	85	85	NUM
ejpam-6631	404	51	:	:	PUNCT
ejpam-6631	404	52	available	available	ADJ
ejpam-6631	404	53	online	online	ADJ
ejpam-6631	404	54	:	:	PUNCT
ejpam-6631	404	55	https	https	NOUN
ejpam-6631	404	56	:	:	PUNCT
ejpam-6631	404	57	//ijnao.um.ac.ir	//ijnao.um.ac.ir	PUNCT
ejpam-6631	404	58	/	/	SYM
ejpam-6631	404	59	article25399.html	article25399.html	X
ejpam-6631	404	60	.	.	PUNCT
ejpam-6631	405	1	[	[	X
ejpam-6631	405	2	23	23	NUM
ejpam-6631	405	3	]	]	X
ejpam-6631	405	4	r.	r.	PROPN
ejpam-6631	405	5	garra	garra	PROPN
ejpam-6631	405	6	&	&	CCONJ
ejpam-6631	405	7	r.	r.	PROPN
ejpam-6631	405	8	garrappa	garrappa	PROPN
ejpam-6631	405	9	,	,	PUNCT
ejpam-6631	405	10	the	the	DET
ejpam-6631	405	11	prabhakar	prabhakar	NOUN
ejpam-6631	405	12	or	or	CCONJ
ejpam-6631	405	13	three	three	NUM
ejpam-6631	405	14	parameter	parameter	NOUN
ejpam-6631	405	15	mittag	mittag	ADJ
ejpam-6631	405	16	–	–	PUNCT
ejpam-6631	405	17	leffler	leffler	NOUN
ejpam-6631	405	18	function	function	NOUN
ejpam-6631	405	19	:	:	PUNCT
ejpam-6631	405	20	theory	theory	NOUN
ejpam-6631	405	21	and	and	CCONJ
ejpam-6631	405	22	application	application	NOUN
ejpam-6631	405	23	,	,	PUNCT
ejpam-6631	405	24	communications	communication	NOUN
ejpam-6631	405	25	in	in	ADP
ejpam-6631	405	26	nonlinear	nonlinear	ADJ
ejpam-6631	405	27	science	science	NOUN
ejpam-6631	405	28	and	and	CCONJ
ejpam-6631	405	29	numerical	numerical	PROPN
ejpam-6631	405	30	simulation	simulation	PROPN
ejpam-6631	405	31	,	,	PUNCT
ejpam-6631	405	32	(	(	PUNCT
ejpam-6631	405	33	2018	2018	NUM
ejpam-6631	405	34	)	)	PUNCT
ejpam-6631	405	35	,	,	PUNCT
ejpam-6631	405	36	56	56	NUM
ejpam-6631	405	37	,	,	PUNCT
ejpam-6631	405	38	314	314	NUM
ejpam-6631	405	39	-	-	SYM
ejpam-6631	405	40	329	329	NUM
ejpam-6631	405	41	.	.	PUNCT
ejpam-6631	406	1	https://doi.org/10.1016/j.cnsns.2017.08.018	https://doi.org/10.1016/j.cnsns.2017.08.018	NOUN
ejpam-6631	406	2	.	.	PUNCT
ejpam-6631	407	1	[	[	X
ejpam-6631	407	2	24	24	NUM
ejpam-6631	407	3	]	]	PUNCT
ejpam-6631	407	4	a.	a.	NOUN
ejpam-6631	407	5	saadatmandi	saadatmandi	PROPN
ejpam-6631	407	6	&	&	CCONJ
ejpam-6631	407	7	m.	m.	PROPN
ejpam-6631	407	8	dehghan	dehghan	PROPN
ejpam-6631	407	9	,	,	PUNCT
ejpam-6631	407	10	a	a	DET
ejpam-6631	407	11	new	new	ADJ
ejpam-6631	407	12	operational	operational	ADJ
ejpam-6631	407	13	matrix	matrix	NOUN
ejpam-6631	407	14	for	for	ADP
ejpam-6631	407	15	solving	solve	VERB
ejpam-6631	407	16	fractional	fractional	ADJ
ejpam-6631	407	17	-	-	PUNCT
ejpam-6631	407	18	order	order	NOUN
ejpam-6631	407	19	differential	differential	ADJ
ejpam-6631	407	20	equations	equation	NOUN
ejpam-6631	407	21	,	,	PUNCT
ejpam-6631	407	22	computers	computer	NOUN
ejpam-6631	407	23	and	and	CCONJ
ejpam-6631	407	24	mathematics	mathematic	NOUN
ejpam-6631	407	25	with	with	ADP
ejpam-6631	407	26	applications,(2010	applications,(2010	NOUN
ejpam-6631	407	27	)	)	PUNCT
ejpam-6631	407	28	,	,	PUNCT
ejpam-6631	407	29	59(3	59(3	NUM
ejpam-6631	407	30	)	)	PUNCT
ejpam-6631	407	31	,	,	PUNCT
ejpam-6631	407	32	1326	1326	NUM
ejpam-6631	407	33	-	-	SYM
ejpam-6631	407	34	1336	1336	NUM
ejpam-6631	407	35	,	,	PUNCT
ejpam-6631	407	36	https://doi.org/10.1016/j.camwa.2009.07.006	https://doi.org/10.1016/j.camwa.2009.07.006	PROPN
ejpam-6631	407	37	.	.	PUNCT
ejpam-6631	408	1	[	[	X
ejpam-6631	408	2	25	25	NUM
ejpam-6631	408	3	]	]	X
ejpam-6631	408	4	s.	s.	PROPN
ejpam-6631	408	5	qureshi	qureshi	PROPN
ejpam-6631	408	6	&	&	CCONJ
ejpam-6631	408	7	p.	p.	PROPN
ejpam-6631	408	8	kumar	kumar	PROPN
ejpam-6631	408	9	,	,	PUNCT
ejpam-6631	408	10	using	use	VERB
ejpam-6631	408	11	shehu	shehu	NOUN
ejpam-6631	408	12	integral	integral	ADJ
ejpam-6631	408	13	transform	transform	NOUN
ejpam-6631	408	14	to	to	PART
ejpam-6631	408	15	solve	solve	VERB
ejpam-6631	408	16	fractional	fractional	ADJ
ejpam-6631	408	17	order	order	NOUN
ejpam-6631	408	18	caputo	caputo	PROPN
ejpam-6631	408	19	type	type	NOUN
ejpam-6631	408	20	initial	initial	ADJ
ejpam-6631	408	21	value	value	NOUN
ejpam-6631	408	22	problems	problem	NOUN
ejpam-6631	408	23	,	,	PUNCT
ejpam-6631	408	24	journal	journal	NOUN
ejpam-6631	408	25	of	of	ADP
ejpam-6631	408	26	applied	apply	VERB
ejpam-6631	408	27	mathematics	mathematic	NOUN
ejpam-6631	408	28	and	and	CCONJ
ejpam-6631	408	29	computational	computational	ADJ
ejpam-6631	408	30	mechanics	mechanic	NOUN
ejpam-6631	408	31	,	,	PUNCT
ejpam-6631	408	32	(	(	PUNCT
ejpam-6631	408	33	2019	2019	NUM
ejpam-6631	408	34	)	)	PUNCT
ejpam-6631	408	35	,	,	PUNCT
ejpam-6631	408	36	18(2	18(2	NUM
ejpam-6631	408	37	)	)	PUNCT
ejpam-6631	408	38	,	,	PUNCT
ejpam-6631	408	39	75	75	NUM
ejpam-6631	408	40	-	-	SYM
ejpam-6631	408	41	83	83	NUM
ejpam-6631	408	42	.	.	PUNCT
ejpam-6631	409	1	doi	doi	NOUN
ejpam-6631	409	2	:	:	PUNCT
ejpam-6631	409	3	10.17512	10.17512	NUM
ejpam-6631	409	4	/	/	SYM
ejpam-6631	409	5	jamcm.2019.2.07	jamcm.2019.2.07	PROPN
ejpam-6631	409	6	.	.	PUNCT