id	sid	tid	token	lemma	pos
bibechana-53971	1	1	bibechana	bibechana	PROPN
bibechana-53971	1	2	vol	vol	NOUN
bibechana-53971	1	3	.	.	PROPN
bibechana-53971	2	1	20	20	NUM
bibechana-53971	2	2	,	,	PUNCT
bibechana-53971	2	3	no	no	INTJ
bibechana-53971	2	4	.	.	NOUN
bibechana-53971	2	5	2	2	NUM
bibechana-53971	2	6	,	,	PUNCT
bibechana-53971	2	7	august	august	PROPN
bibechana-53971	2	8	2023	2023	NUM
bibechana-53971	2	9	,	,	PUNCT
bibechana-53971	2	10	126	126	NUM
bibechana-53971	2	11	-	-	SYM
bibechana-53971	2	12	133	133	NUM
bibechana-53971	2	13	issn	issn	PROPN
bibechana-53971	2	14	2091	2091	NUM
bibechana-53971	2	15	-	-	SYM
bibechana-53971	2	16	0762	0762	NUM
bibechana-53971	2	17	(	(	PUNCT
bibechana-53971	2	18	print	print	NOUN
bibechana-53971	2	19	)	)	PUNCT
bibechana-53971	2	20	,	,	PUNCT
bibechana-53971	2	21	2382	2382	NUM
bibechana-53971	2	22	-	-	SYM
bibechana-53971	2	23	5340	5340	NUM
bibechana-53971	2	24	(	(	PUNCT
bibechana-53971	2	25	online	online	ADJ
bibechana-53971	2	26	)	)	PUNCT
bibechana-53971	2	27	journal	journal	NOUN
bibechana-53971	2	28	homepage	homepage	NOUN
bibechana-53971	2	29	:	:	PUNCT
bibechana-53971	2	30	http://nepjol.info/index.php/bibechana	http://nepjol.info/index.php/bibechana	PROPN
bibechana-53971	2	31	publisher	publisher	NOUN
bibechana-53971	2	32	:	:	PUNCT
bibechana-53971	2	33	dept	dept	NOUN
bibechana-53971	2	34	.	.	PROPN
bibechana-53971	2	35	of	of	ADP
bibechana-53971	2	36	phys	phy	NOUN
bibechana-53971	2	37	.	.	PUNCT
bibechana-53971	2	38	,	,	PUNCT
bibechana-53971	3	1	mahendra	mahendra	PROPN
bibechana-53971	3	2	morang	morang	PROPN
bibechana-53971	3	3	a.	a.	PROPN
bibechana-53971	3	4	m.	m.	PROPN
bibechana-53971	3	5	campus	campus	PROPN
bibechana-53971	3	6	(	(	PUNCT
bibechana-53971	3	7	tribhuvan	tribhuvan	NOUN
bibechana-53971	3	8	university)biratnagar	university)biratnagar	NUM
bibechana-53971	4	1	caputo	caputo	PROPN
bibechana-53971	4	2	-	-	PUNCT
bibechana-53971	4	3	fabrizio	fabrizio	PROPN
bibechana-53971	4	4	approach	approach	NOUN
bibechana-53971	4	5	to	to	ADP
bibechana-53971	4	6	numerical	numerical	ADJ
bibechana-53971	4	7	fractional	fractional	ADJ
bibechana-53971	4	8	derivatives	derivative	NOUN
bibechana-53971	4	9	shankar	shankar	PROPN
bibechana-53971	4	10	pariyar1,2	pariyar1,2	PROPN
bibechana-53971	4	11	,	,	PUNCT
bibechana-53971	4	12	jeevan	jeevan	NOUN
bibechana-53971	4	13	kafle2∗	kafle2∗	PROPN
bibechana-53971	4	14	1tri	1tri	PROPN
bibechana-53971	4	15	-	-	PUNCT
bibechana-53971	4	16	chandra	chandra	PROPN
bibechana-53971	4	17	multiple	multiple	ADJ
bibechana-53971	4	18	campus	campus	NOUN
bibechana-53971	4	19	,	,	PUNCT
bibechana-53971	4	20	ghantaghar	ghantaghar	NOUN
bibechana-53971	4	21	,	,	PUNCT
bibechana-53971	4	22	kathmandu	kathmandu	NOUN
bibechana-53971	4	23	,	,	PUNCT
bibechana-53971	4	24	nepal	nepal	ADJ
bibechana-53971	4	25	,	,	PUNCT
bibechana-53971	4	26	2central	2central	NUM
bibechana-53971	4	27	department	department	NOUN
bibechana-53971	4	28	of	of	ADP
bibechana-53971	4	29	mathematics	mathematics	PROPN
bibechana-53971	4	30	,	,	PUNCT
bibechana-53971	4	31	tribhuvan	tribhuvan	PROPN
bibechana-53971	4	32	university	university	PROPN
bibechana-53971	4	33	,	,	PUNCT
bibechana-53971	4	34	kathmandu	kathmandu	NOUN
bibechana-53971	4	35	,	,	PUNCT
bibechana-53971	4	36	nepal	nepal	NOUN
bibechana-53971	4	37	∗corresponding	∗corresponde	VERB
bibechana-53971	4	38	author.jeevan	author.jeevan	PROPN
bibechana-53971	4	39	kafle	kafle	NOUN
bibechana-53971	4	40	,	,	PUNCT
bibechana-53971	4	41	:	:	PUNCT
bibechana-53971	4	42	jeevan.kafle@cdmath.tu.edu.np	jeevan.kafle@cdmath.tu.edu.np	ADJ
bibechana-53971	4	43	abstract	abstract	ADJ
bibechana-53971	4	44	fractional	fractional	ADJ
bibechana-53971	4	45	calculus	calculus	NOUN
bibechana-53971	4	46	is	be	AUX
bibechana-53971	4	47	an	an	DET
bibechana-53971	4	48	essential	essential	ADJ
bibechana-53971	4	49	tool	tool	NOUN
bibechana-53971	4	50	in	in	ADP
bibechana-53971	4	51	every	every	DET
bibechana-53971	4	52	area	area	NOUN
bibechana-53971	4	53	of	of	ADP
bibechana-53971	4	54	science	science	NOUN
bibechana-53971	4	55	today	today	NOUN
bibechana-53971	4	56	.	.	PUNCT
bibechana-53971	5	1	this	this	DET
bibechana-53971	5	2	work	work	NOUN
bibechana-53971	5	3	gives	give	VERB
bibechana-53971	5	4	the	the	DET
bibechana-53971	5	5	quadratic	quadratic	ADJ
bibechana-53971	5	6	interpolation	interpolation	NOUN
bibechana-53971	5	7	-	-	PUNCT
bibechana-53971	5	8	based	base	VERB
bibechana-53971	5	9	l1	l1	PROPN
bibechana-53971	5	10	-	-	PUNCT
bibechana-53971	5	11	2	2	NUM
bibechana-53971	5	12	formula	formula	NOUN
bibechana-53971	5	13	for	for	ADP
bibechana-53971	5	14	the	the	DET
bibechana-53971	5	15	caputo	caputo	PROPN
bibechana-53971	5	16	-	-	PUNCT
bibechana-53971	5	17	fabrizio	fabrizio	PROPN
bibechana-53971	5	18	derivative	derivative	NOUN
bibechana-53971	5	19	,	,	PUNCT
bibechana-53971	5	20	a	a	DET
bibechana-53971	5	21	numerical	numerical	ADJ
bibechana-53971	5	22	technique	technique	NOUN
bibechana-53971	5	23	for	for	ADP
bibechana-53971	5	24	approximating	approximate	VERB
bibechana-53971	5	25	the	the	DET
bibechana-53971	5	26	fractional	fractional	ADJ
bibechana-53971	5	27	derivative	derivative	NOUN
bibechana-53971	5	28	.	.	PUNCT
bibechana-53971	6	1	to	to	PART
bibechana-53971	6	2	get	get	VERB
bibechana-53971	6	3	quadratic	quadratic	ADJ
bibechana-53971	6	4	and	and	CCONJ
bibechana-53971	6	5	cubic	cubic	ADJ
bibechana-53971	6	6	convergence	convergence	NOUN
bibechana-53971	6	7	rates	rate	NOUN
bibechana-53971	6	8	,	,	PUNCT
bibechana-53971	6	9	respectively	respectively	ADV
bibechana-53971	6	10	,	,	PUNCT
bibechana-53971	6	11	we	we	PRON
bibechana-53971	6	12	study	study	VERB
bibechana-53971	6	13	the	the	DET
bibechana-53971	6	14	use	use	NOUN
bibechana-53971	6	15	of	of	ADP
bibechana-53971	6	16	lagrange	lagrange	NOUN
bibechana-53971	6	17	interpolation	interpolation	NOUN
bibechana-53971	6	18	in	in	ADP
bibechana-53971	6	19	the	the	DET
bibechana-53971	6	20	l1	l1	PROPN
bibechana-53971	6	21	and	and	CCONJ
bibechana-53971	6	22	l1	l1	PROPN
bibechana-53971	6	23	-	-	PUNCT
bibechana-53971	6	24	2	2	NUM
bibechana-53971	6	25	formulations	formulation	NOUN
bibechana-53971	6	26	.	.	PUNCT
bibechana-53971	7	1	our	our	PRON
bibechana-53971	7	2	numerical	numerical	ADJ
bibechana-53971	7	3	analysis	analysis	NOUN
bibechana-53971	7	4	shows	show	VERB
bibechana-53971	7	5	the	the	DET
bibechana-53971	7	6	accuracy	accuracy	NOUN
bibechana-53971	7	7	of	of	ADP
bibechana-53971	7	8	the	the	DET
bibechana-53971	7	9	theory	theory	NOUN
bibechana-53971	7	10	’s	’s	PART
bibechana-53971	7	11	predicted	predict	VERB
bibechana-53971	7	12	convergence	convergence	NOUN
bibechana-53971	7	13	rates	rate	NOUN
bibechana-53971	7	14	.	.	PUNCT
bibechana-53971	8	1	the	the	DET
bibechana-53971	8	2	l1	l1	PROPN
bibechana-53971	8	3	-	-	PUNCT
bibechana-53971	8	4	2	2	NUM
bibechana-53971	8	5	formula	formula	NOUN
bibechana-53971	8	6	aims	aim	VERB
bibechana-53971	8	7	to	to	PART
bibechana-53971	8	8	enhance	enhance	VERB
bibechana-53971	8	9	the	the	DET
bibechana-53971	8	10	accuracy	accuracy	NOUN
bibechana-53971	8	11	and	and	CCONJ
bibechana-53971	8	12	usability	usability	NOUN
bibechana-53971	8	13	of	of	ADP
bibechana-53971	8	14	a	a	DET
bibechana-53971	8	15	flexible	flexible	ADJ
bibechana-53971	8	16	tool	tool	NOUN
bibechana-53971	8	17	for	for	ADP
bibechana-53971	8	18	many	many	ADJ
bibechana-53971	8	19	applications	application	NOUN
bibechana-53971	8	20	in	in	ADP
bibechana-53971	8	21	science	science	NOUN
bibechana-53971	8	22	and	and	CCONJ
bibechana-53971	8	23	mathematics	mathematic	NOUN
bibechana-53971	8	24	.	.	PUNCT
bibechana-53971	9	1	we	we	PRON
bibechana-53971	9	2	demonstrate	demonstrate	VERB
bibechana-53971	9	3	the	the	DET
bibechana-53971	9	4	validity	validity	NOUN
bibechana-53971	9	5	of	of	ADP
bibechana-53971	9	6	the	the	DET
bibechana-53971	9	7	theory	theory	NOUN
bibechana-53971	9	8	’s	’s	PART
bibechana-53971	9	9	predicted	predict	VERB
bibechana-53971	9	10	convergence	convergence	NOUN
bibechana-53971	9	11	rates	rate	NOUN
bibechana-53971	9	12	using	use	VERB
bibechana-53971	9	13	numerical	numerical	ADJ
bibechana-53971	9	14	analysis	analysis	NOUN
bibechana-53971	9	15	.	.	PUNCT
bibechana-53971	10	1	several	several	ADJ
bibechana-53971	10	2	numerical	numerical	ADJ
bibechana-53971	10	3	examples	example	NOUN
bibechana-53971	10	4	are	be	AUX
bibechana-53971	10	5	also	also	ADV
bibechana-53971	10	6	given	give	VERB
bibechana-53971	10	7	to	to	PART
bibechana-53971	10	8	show	show	VERB
bibechana-53971	10	9	how	how	SCONJ
bibechana-53971	10	10	the	the	DET
bibechana-53971	10	11	suggested	suggested	ADJ
bibechana-53971	10	12	approaches	approach	NOUN
bibechana-53971	10	13	may	may	AUX
bibechana-53971	10	14	be	be	AUX
bibechana-53971	10	15	utilized	utilize	VERB
bibechana-53971	10	16	to	to	PART
bibechana-53971	10	17	determine	determine	VERB
bibechana-53971	10	18	the	the	DET
bibechana-53971	10	19	caputo	caputo	PROPN
bibechana-53971	10	20	-	-	PUNCT
bibechana-53971	10	21	fabrizio	fabrizio	PROPN
bibechana-53971	10	22	derivative	derivative	NOUN
bibechana-53971	10	23	of	of	ADP
bibechana-53971	10	24	well	well	ADV
bibechana-53971	10	25	-	-	PUNCT
bibechana-53971	10	26	known	know	VERB
bibechana-53971	10	27	functions	function	NOUN
bibechana-53971	10	28	.	.	PUNCT
bibechana-53971	11	1	lagrange	lagrange	NOUN
bibechana-53971	11	2	interpolation	interpolation	NOUN
bibechana-53971	11	3	is	be	AUX
bibechana-53971	11	4	used	use	VERB
bibechana-53971	11	5	in	in	ADP
bibechana-53971	11	6	the	the	DET
bibechana-53971	11	7	l1	l1	PROPN
bibechana-53971	11	8	and	and	CCONJ
bibechana-53971	11	9	l1	l1	PROPN
bibechana-53971	11	10	-	-	PUNCT
bibechana-53971	11	11	2	2	NUM
bibechana-53971	11	12	procedures	procedure	NOUN
bibechana-53971	11	13	to	to	PART
bibechana-53971	11	14	obtain	obtain	VERB
bibechana-53971	11	15	quadratic	quadratic	ADJ
bibechana-53971	11	16	and	and	CCONJ
bibechana-53971	11	17	cubic	cubic	ADJ
bibechana-53971	11	18	convergence	convergence	NOUN
bibechana-53971	11	19	rates	rate	NOUN
bibechana-53971	11	20	,	,	PUNCT
bibechana-53971	11	21	respectively	respectively	ADV
bibechana-53971	11	22	.	.	PUNCT
bibechana-53971	12	1	the	the	DET
bibechana-53971	12	2	numerical	numerical	PROPN
bibechana-53971	12	3	study	study	NOUN
bibechana-53971	12	4	demonstrates	demonstrate	VERB
bibechana-53971	12	5	that	that	SCONJ
bibechana-53971	12	6	the	the	DET
bibechana-53971	12	7	l1	l1	PROPN
bibechana-53971	12	8	-	-	PUNCT
bibechana-53971	12	9	2	2	NUM
bibechana-53971	12	10	formula	formula	NOUN
bibechana-53971	12	11	offers	offer	VERB
bibechana-53971	12	12	greater	great	ADJ
bibechana-53971	12	13	accuracy	accuracy	NOUN
bibechana-53971	12	14	when	when	SCONJ
bibechana-53971	12	15	compared	compare	VERB
bibechana-53971	12	16	to	to	ADP
bibechana-53971	12	17	current	current	ADJ
bibechana-53971	12	18	approaches	approach	NOUN
bibechana-53971	12	19	.	.	PUNCT
bibechana-53971	13	1	in	in	ADP
bibechana-53971	13	2	addition	addition	NOUN
bibechana-53971	13	3	,	,	PUNCT
bibechana-53971	13	4	it	it	PRON
bibechana-53971	13	5	is	be	AUX
bibechana-53971	13	6	a	a	DET
bibechana-53971	13	7	better	well	ADJ
bibechana-53971	13	8	apparatus	apparatus	NOUN
bibechana-53971	13	9	for	for	ADP
bibechana-53971	13	10	several	several	ADJ
bibechana-53971	13	11	applications	application	NOUN
bibechana-53971	13	12	in	in	ADP
bibechana-53971	13	13	science	science	NOUN
bibechana-53971	13	14	and	and	CCONJ
bibechana-53971	13	15	mathematics	mathematic	NOUN
bibechana-53971	13	16	.	.	PUNCT
bibechana-53971	14	1	due	due	ADP
bibechana-53971	14	2	to	to	ADP
bibechana-53971	14	3	its	its	PRON
bibechana-53971	14	4	higher	high	ADJ
bibechana-53971	14	5	convergence	convergence	NOUN
bibechana-53971	14	6	rate	rate	NOUN
bibechana-53971	14	7	,	,	PUNCT
bibechana-53971	14	8	the	the	DET
bibechana-53971	14	9	l1	l1	PROPN
bibechana-53971	14	10	-	-	PUNCT
bibechana-53971	14	11	2	2	NUM
bibechana-53971	14	12	formula	formula	NOUN
bibechana-53971	14	13	outperforms	outperform	VERB
bibechana-53971	14	14	other	other	ADJ
bibechana-53971	14	15	available	available	ADJ
bibechana-53971	14	16	numerical	numerical	ADJ
bibechana-53971	14	17	methods	method	NOUN
bibechana-53971	14	18	for	for	ADP
bibechana-53971	14	19	scientific	scientific	ADJ
bibechana-53971	14	20	computations	computation	NOUN
bibechana-53971	14	21	.	.	PUNCT
bibechana-53971	15	1	the	the	DET
bibechana-53971	15	2	l1	l1	PROPN
bibechana-53971	15	3	-	-	PUNCT
bibechana-53971	15	4	2	2	NUM
bibechana-53971	15	5	formula	formula	NOUN
bibechana-53971	15	6	,	,	PUNCT
bibechana-53971	15	7	a	a	DET
bibechana-53971	15	8	novel	novel	ADJ
bibechana-53971	15	9	numerical	numerical	ADJ
bibechana-53971	15	10	method	method	NOUN
bibechana-53971	15	11	for	for	ADP
bibechana-53971	15	12	the	the	DET
bibechana-53971	15	13	caputofabrizio	caputofabrizio	PROPN
bibechana-53971	15	14	derivative	derivative	NOUN
bibechana-53971	15	15	that	that	PRON
bibechana-53971	15	16	makes	make	VERB
bibechana-53971	15	17	use	use	NOUN
bibechana-53971	15	18	of	of	ADP
bibechana-53971	15	19	quadratic	quadratic	ADJ
bibechana-53971	15	20	interpolation	interpolation	NOUN
bibechana-53971	15	21	,	,	PUNCT
bibechana-53971	15	22	is	be	AUX
bibechana-53971	15	23	introduced	introduce	VERB
bibechana-53971	15	24	in	in	ADP
bibechana-53971	15	25	this	this	DET
bibechana-53971	15	26	study	study	NOUN
bibechana-53971	15	27	as	as	ADP
bibechana-53971	15	28	a	a	DET
bibechana-53971	15	29	conclusion	conclusion	NOUN
bibechana-53971	15	30	.	.	PUNCT
bibechana-53971	16	1	keywords	keyword	VERB
bibechana-53971	16	2	caputo	caputo	PROPN
bibechana-53971	16	3	fractional	fractional	ADJ
bibechana-53971	16	4	derivatives	derivative	NOUN
bibechana-53971	16	5	,	,	PUNCT
bibechana-53971	16	6	numerical	numerical	ADJ
bibechana-53971	16	7	solution	solution	NOUN
bibechana-53971	16	8	,	,	PUNCT
bibechana-53971	16	9	lagrange	lagrange	NOUN
bibechana-53971	16	10	interpolation	interpolation	NOUN
bibechana-53971	16	11	,	,	PUNCT
bibechana-53971	16	12	l1	l1	PROPN
bibechana-53971	16	13	formula	formula	NOUN
bibechana-53971	16	14	,	,	PUNCT
bibechana-53971	16	15	l1	l1	PROPN
bibechana-53971	16	16	-	-	PUNCT
bibechana-53971	16	17	2	2	NUM
bibechana-53971	16	18	formula	formula	NOUN
bibechana-53971	16	19	.	.	PUNCT
bibechana-53971	17	1	article	article	NOUN
bibechana-53971	17	2	information	information	PROPN
bibechana-53971	17	3	manuscript	manuscript	PROPN
bibechana-53971	17	4	received	receive	VERB
bibechana-53971	17	5	:	:	PUNCT
bibechana-53971	17	6	april	april	PROPN
bibechana-53971	17	7	7	7	NUM
bibechana-53971	17	8	,	,	PUNCT
bibechana-53971	17	9	2023	2023	NUM
bibechana-53971	17	10	;	;	PUNCT
bibechana-53971	17	11	accepted	accept	VERB
bibechana-53971	17	12	:	:	PUNCT
bibechana-53971	17	13	april	april	PROPN
bibechana-53971	17	14	25	25	NUM
bibechana-53971	17	15	,	,	PUNCT
bibechana-53971	17	16	2023	2023	NUM
bibechana-53971	17	17	doi	doi	NOUN
bibechana-53971	17	18	https://doi.org/10.3126/bibechana.v20i2.53971	https://doi.org/10.3126/bibechana.v20i2.53971	PUNCT
bibechana-53971	17	19	this	this	DET
bibechana-53971	17	20	work	work	NOUN
bibechana-53971	17	21	is	be	AUX
bibechana-53971	17	22	licensed	license	VERB
bibechana-53971	17	23	under	under	ADP
bibechana-53971	17	24	the	the	DET
bibechana-53971	17	25	creative	creative	ADJ
bibechana-53971	17	26	commons	common	NOUN
bibechana-53971	17	27	cc	cc	ADP
bibechana-53971	17	28	by	by	ADP
bibechana-53971	17	29	-	-	PUNCT
bibechana-53971	17	30	nc	nc	NOUN
bibechana-53971	17	31	license	license	NOUN
bibechana-53971	17	32	.	.	PUNCT
bibechana-53971	18	1	https://creativecommons	https://creativecommon	NOUN
bibechana-53971	18	2	.	.	PUNCT
bibechana-53971	18	3	org	org	ADJ
bibechana-53971	18	4	/	/	SYM
bibechana-53971	18	5	licenses	license	NOUN
bibechana-53971	18	6	/	/	SYM
bibechana-53971	18	7	by	by	ADP
bibechana-53971	18	8	-	-	PUNCT
bibechana-53971	18	9	nc/4.0/	nc/4.0/	NOUN
bibechana-53971	18	10	1	1	NUM
bibechana-53971	18	11	introduction	introduction	NOUN
bibechana-53971	18	12	a	a	DET
bibechana-53971	18	13	branch	branch	NOUN
bibechana-53971	18	14	of	of	ADP
bibechana-53971	18	15	mathematics	mathematic	NOUN
bibechana-53971	18	16	known	know	VERB
bibechana-53971	18	17	as	as	ADP
bibechana-53971	18	18	numerical	numerical	ADJ
bibechana-53971	18	19	analysis	analysis	NOUN
bibechana-53971	18	20	for	for	ADP
bibechana-53971	18	21	fractional	fractional	ADJ
bibechana-53971	18	22	calculus	calculus	NOUN
bibechana-53971	18	23	is	be	AUX
bibechana-53971	18	24	concerned	concern	VERB
bibechana-53971	18	25	with	with	ADP
bibechana-53971	18	26	the	the	DET
bibechana-53971	18	27	creation	creation	NOUN
bibechana-53971	18	28	and	and	CCONJ
bibechana-53971	18	29	use	use	NOUN
bibechana-53971	18	30	of	of	ADP
bibechana-53971	18	31	numerical	numerical	ADJ
bibechana-53971	18	32	techniques	technique	NOUN
bibechana-53971	18	33	for	for	ADP
bibechana-53971	18	34	the	the	DET
bibechana-53971	18	35	solution	solution	NOUN
bibechana-53971	18	36	of	of	ADP
bibechana-53971	18	37	fractional	fractional	ADJ
bibechana-53971	18	38	calculus	calculus	NOUN
bibechana-53971	18	39	-	-	PUNCT
bibechana-53971	18	40	related	relate	VERB
bibechana-53971	18	41	issues	issue	NOUN
bibechana-53971	18	42	[	[	X
bibechana-53971	18	43	1	1	NUM
bibechana-53971	18	44	]	]	PUNCT
bibechana-53971	18	45	.	.	PUNCT
bibechana-53971	19	1	the	the	DET
bibechana-53971	19	2	study	study	NOUN
bibechana-53971	19	3	of	of	ADP
bibechana-53971	19	4	fractional	fractional	ADJ
bibechana-53971	19	5	calculus	calculus	NOUN
bibechana-53971	19	6	is	be	AUX
bibechana-53971	19	7	still	still	ADV
bibechana-53971	19	8	in	in	ADP
bibechana-53971	19	9	its	its	PRON
bibechana-53971	19	10	infancy	infancy	NOUN
bibechana-53971	19	11	and	and	CCONJ
bibechana-53971	19	12	is	be	AUX
bibechana-53971	19	13	continually	continually	ADV
bibechana-53971	19	14	changing	change	VERB
bibechana-53971	19	15	.	.	PUNCT
bibechana-53971	20	1	integrating	integrate	VERB
bibechana-53971	20	2	and	and	CCONJ
bibechana-53971	20	3	differentiating	differentiate	VERB
bibechana-53971	20	4	non	non	ADJ
bibechana-53971	20	5	-	-	ADJ
bibechana-53971	20	6	integer	integer	ADJ
bibechana-53971	20	7	categories	category	NOUN
bibechana-53971	20	8	is	be	AUX
bibechana-53971	20	9	the	the	DET
bibechana-53971	20	10	main	main	ADJ
bibechana-53971	20	11	concept	concept	NOUN
bibechana-53971	20	12	behind	behind	ADP
bibechana-53971	20	13	it	it	PRON
bibechana-53971	20	14	.	.	PUNCT
bibechana-53971	21	1	it	it	PRON
bibechana-53971	21	2	is	be	AUX
bibechana-53971	21	3	extensively	extensively	ADV
bibechana-53971	21	4	employed	employ	VERB
bibechana-53971	21	5	across	across	ADP
bibechana-53971	21	6	a	a	DET
bibechana-53971	21	7	range	range	NOUN
bibechana-53971	21	8	of	of	ADP
bibechana-53971	21	9	scientific	scientific	ADJ
bibechana-53971	21	10	and	and	CCONJ
bibechana-53971	21	11	technological	technological	ADJ
bibechana-53971	21	12	fields	field	NOUN
bibechana-53971	21	13	of	of	ADP
bibechana-53971	21	14	study	study	NOUN
bibechana-53971	21	15	,	,	PUNCT
bibechana-53971	21	16	including	include	VERB
bibechana-53971	21	17	the	the	DET
bibechana-53971	21	18	sciences	science	NOUN
bibechana-53971	21	19	of	of	ADP
bibechana-53971	21	20	physics	physics	PROPN
bibechana-53971	21	21	,	,	PUNCT
bibechana-53971	21	22	engineering	engineering	NOUN
bibechana-53971	21	23	,	,	PUNCT
bibechana-53971	21	24	biology	biology	NOUN
bibechana-53971	21	25	,	,	PUNCT
bibechana-53971	21	26	eco126	eco126	NOUN
bibechana-53971	21	27	http://nepjol.info/index.php/bibechana	http://nepjol.info/index.php/bibechana	PROPN
bibechana-53971	21	28	jeevan.kafle@cdmath.tu.edu.np	jeevan.kafle@cdmath.tu.edu.np	PROPN
bibechana-53971	21	29	https://doi.org/10.3126/bibechana.v20i2.53971	https://doi.org/10.3126/bibechana.v20i2.53971	NUM
bibechana-53971	21	30	https://creativecommons.org/licenses/by-nc/4.0/	https://creativecommons.org/licenses/by-nc/4.0/	PROPN
bibechana-53971	21	31	https://creativecommons.org/licenses/by-nc/4.0/	https://creativecommons.org/licenses/by-nc/4.0/	PROPN
bibechana-53971	21	32	shankar	shankar	PROPN
bibechana-53971	21	33	pariyar	pariyar	PROPN
bibechana-53971	21	34	and	and	CCONJ
bibechana-53971	21	35	jeevan	jeevan	PROPN
bibechana-53971	21	36	kafle	kafle	PROPN
bibechana-53971	21	37	/	/	PUNCT
bibechana-53971	21	38	bibechana	bibechana	PROPN
bibechana-53971	21	39	20	20	NUM
bibechana-53971	21	40	(	(	PUNCT
bibechana-53971	21	41	2023	2023	NUM
bibechana-53971	21	42	)	)	PUNCT
bibechana-53971	21	43	126	126	NUM
bibechana-53971	21	44	-	-	SYM
bibechana-53971	21	45	133	133	NUM
bibechana-53971	21	46	127	127	NUM
bibechana-53971	21	47	nomics	nomic	NOUN
bibechana-53971	21	48	,	,	PUNCT
bibechana-53971	21	49	and	and	CCONJ
bibechana-53971	21	50	others	other	NOUN
bibechana-53971	22	1	[	[	X
bibechana-53971	22	2	1	1	NUM
bibechana-53971	22	3	]	]	PUNCT
bibechana-53971	22	4	.	.	PUNCT
bibechana-53971	23	1	in	in	ADP
bibechana-53971	23	2	contrast	contrast	NOUN
bibechana-53971	23	3	to	to	ADP
bibechana-53971	23	4	fractional	fractional	ADJ
bibechana-53971	23	5	integral	integral	ADJ
bibechana-53971	23	6	equations	equation	NOUN
bibechana-53971	23	7	,	,	PUNCT
bibechana-53971	23	8	which	which	PRON
bibechana-53971	23	9	involve	involve	VERB
bibechana-53971	23	10	fractional	fractional	ADJ
bibechana-53971	23	11	integrals	integral	NOUN
bibechana-53971	23	12	,	,	PUNCT
bibechana-53971	23	13	fractional	fractional	ADJ
bibechana-53971	23	14	differential	differential	ADJ
bibechana-53971	23	15	equations	equation	NOUN
bibechana-53971	23	16	are	be	AUX
bibechana-53971	23	17	defined	define	VERB
bibechana-53971	23	18	by	by	ADP
bibechana-53971	23	19	the	the	DET
bibechana-53971	23	20	presence	presence	NOUN
bibechana-53971	23	21	of	of	ADP
bibechana-53971	23	22	fractional	fractional	ADJ
bibechana-53971	23	23	derivatives	derivative	NOUN
bibechana-53971	23	24	.	.	PUNCT
bibechana-53971	24	1	a	a	DET
bibechana-53971	24	2	system	system	NOUN
bibechana-53971	24	3	is	be	AUX
bibechana-53971	24	4	said	say	VERB
bibechana-53971	24	5	to	to	PART
bibechana-53971	24	6	have	have	VERB
bibechana-53971	24	7	a	a	DET
bibechana-53971	24	8	differential	differential	ADJ
bibechana-53971	24	9	order	order	NOUN
bibechana-53971	24	10	if	if	SCONJ
bibechana-53971	24	11	its	its	PRON
bibechana-53971	24	12	behavior	behavior	NOUN
bibechana-53971	24	13	can	can	AUX
bibechana-53971	24	14	be	be	AUX
bibechana-53971	24	15	correctly	correctly	ADV
bibechana-53971	24	16	predicted	predict	VERB
bibechana-53971	24	17	by	by	ADP
bibechana-53971	24	18	one	one	NUM
bibechana-53971	24	19	of	of	ADP
bibechana-53971	24	20	these	these	DET
bibechana-53971	24	21	equations	equation	NOUN
bibechana-53971	24	22	,	,	PUNCT
bibechana-53971	24	23	both	both	PRON
bibechana-53971	24	24	of	of	ADP
bibechana-53971	24	25	them	they	PRON
bibechana-53971	24	26	,	,	PUNCT
bibechana-53971	24	27	or	or	CCONJ
bibechana-53971	25	1	both	both	PRON
bibechana-53971	25	2	together	together	ADV
bibechana-53971	26	1	[	[	X
bibechana-53971	26	2	2	2	NUM
bibechana-53971	26	3	]	]	PUNCT
bibechana-53971	26	4	.	.	PUNCT
bibechana-53971	27	1	models	model	NOUN
bibechana-53971	27	2	based	base	VERB
bibechana-53971	27	3	on	on	ADP
bibechana-53971	27	4	fractionalorder	fractionalorder	PROPN
bibechana-53971	27	5	differential	differential	ADJ
bibechana-53971	27	6	equations	equation	NOUN
bibechana-53971	27	7	have	have	AUX
bibechana-53971	27	8	been	be	AUX
bibechana-53971	27	9	developed	develop	VERB
bibechana-53971	27	10	to	to	PART
bibechana-53971	27	11	describe	describe	VERB
bibechana-53971	27	12	complex	complex	ADJ
bibechana-53971	27	13	dynamical	dynamical	ADJ
bibechana-53971	27	14	systems	system	NOUN
bibechana-53971	27	15	and	and	CCONJ
bibechana-53971	27	16	physical	physical	ADJ
bibechana-53971	27	17	phenomena	phenomenon	NOUN
bibechana-53971	27	18	.	.	PUNCT
bibechana-53971	28	1	to	to	PART
bibechana-53971	28	2	advance	advance	VERB
bibechana-53971	28	3	the	the	DET
bibechana-53971	28	4	theory	theory	NOUN
bibechana-53971	28	5	and	and	CCONJ
bibechana-53971	28	6	application	application	NOUN
bibechana-53971	28	7	of	of	ADP
bibechana-53971	28	8	fractional	fractional	ADJ
bibechana-53971	28	9	order	order	NOUN
bibechana-53971	28	10	differentials	differential	NOUN
bibechana-53971	28	11	,	,	PUNCT
bibechana-53971	28	12	committed	committed	ADJ
bibechana-53971	28	13	researchers	researcher	NOUN
bibechana-53971	28	14	have	have	AUX
bibechana-53971	28	15	made	make	VERB
bibechana-53971	28	16	substantial	substantial	ADJ
bibechana-53971	28	17	efforts	effort	NOUN
bibechana-53971	28	18	.	.	PUNCT
bibechana-53971	29	1	the	the	DET
bibechana-53971	29	2	fractional	fractional	ADJ
bibechana-53971	29	3	derivatives	derivative	NOUN
bibechana-53971	29	4	rule	rule	NOUN
bibechana-53971	29	5	is	be	AUX
bibechana-53971	29	6	not	not	PART
bibechana-53971	29	7	a	a	DET
bibechana-53971	29	8	collection	collection	NOUN
bibechana-53971	29	9	of	of	ADP
bibechana-53971	29	10	rules	rule	NOUN
bibechana-53971	29	11	that	that	PRON
bibechana-53971	29	12	can	can	AUX
bibechana-53971	29	13	be	be	AUX
bibechana-53971	29	14	applied	apply	VERB
bibechana-53971	29	15	in	in	ADP
bibechana-53971	29	16	every	every	DET
bibechana-53971	29	17	situation	situation	NOUN
bibechana-53971	29	18	,	,	PUNCT
bibechana-53971	29	19	although	although	SCONJ
bibechana-53971	29	20	the	the	DET
bibechana-53971	29	21	terms	term	NOUN
bibechana-53971	29	22	fractional	fractional	ADJ
bibechana-53971	29	23	differentiation	differentiation	NOUN
bibechana-53971	29	24	and	and	CCONJ
bibechana-53971	29	25	integration	integration	NOUN
bibechana-53971	29	26	have	have	AUX
bibechana-53971	29	27	been	be	AUX
bibechana-53971	29	28	defined	define	VERB
bibechana-53971	29	29	differently	differently	ADV
bibechana-53971	29	30	by	by	ADP
bibechana-53971	29	31	various	various	ADJ
bibechana-53971	29	32	mathematicians	mathematician	NOUN
bibechana-53971	29	33	[	[	X
bibechana-53971	29	34	3	3	NUM
bibechana-53971	29	35	]	]	PUNCT
bibechana-53971	29	36	.	.	PUNCT
bibechana-53971	30	1	because	because	SCONJ
bibechana-53971	30	2	riemann	riemann	PROPN
bibechana-53971	30	3	-	-	PUNCT
bibechana-53971	30	4	liouville	liouville	NOUN
bibechana-53971	30	5	(	(	PUNCT
bibechana-53971	30	6	r	r	NOUN
bibechana-53971	30	7	-	-	PUNCT
bibechana-53971	30	8	l	l	NOUN
bibechana-53971	30	9	)	)	PUNCT
bibechana-53971	30	10	shows	show	VERB
bibechana-53971	30	11	that	that	SCONJ
bibechana-53971	30	12	the	the	DET
bibechana-53971	30	13	derivative	derivative	NOUN
bibechana-53971	30	14	of	of	ADP
bibechana-53971	30	15	a	a	DET
bibechana-53971	30	16	constant	constant	ADJ
bibechana-53971	30	17	component	component	NOUN
bibechana-53971	30	18	is	be	AUX
bibechana-53971	30	19	not	not	PART
bibechana-53971	30	20	zero	zero	NUM
bibechana-53971	30	21	,	,	PUNCT
bibechana-53971	30	22	it	it	PRON
bibechana-53971	30	23	has	have	AUX
bibechana-53971	30	24	been	be	AUX
bibechana-53971	30	25	demonstrated	demonstrate	VERB
bibechana-53971	30	26	that	that	SCONJ
bibechana-53971	30	27	it	it	PRON
bibechana-53971	30	28	can	can	AUX
bibechana-53971	30	29	be	be	AUX
bibechana-53971	30	30	difficult	difficult	ADJ
bibechana-53971	30	31	to	to	PART
bibechana-53971	30	32	calculate	calculate	VERB
bibechana-53971	30	33	fractional	fractional	ADJ
bibechana-53971	30	34	derivatives	derivative	NOUN
bibechana-53971	30	35	using	use	VERB
bibechana-53971	30	36	regular	regular	ADJ
bibechana-53971	30	37	calculus	calculus	NOUN
bibechana-53971	30	38	.	.	PUNCT
bibechana-53971	31	1	the	the	DET
bibechana-53971	31	2	r	r	NOUN
bibechana-53971	31	3	-	-	PUNCT
bibechana-53971	31	4	l	l	NOUN
bibechana-53971	31	5	fractional	fractional	ADJ
bibechana-53971	31	6	derivative	derivative	NOUN
bibechana-53971	31	7	is	be	AUX
bibechana-53971	31	8	the	the	DET
bibechana-53971	31	9	meaning	meaning	NOUN
bibechana-53971	31	10	of	of	ADP
bibechana-53971	31	11	these	these	PRON
bibechana-53971	31	12	that	that	PRON
bibechana-53971	31	13	is	be	AUX
bibechana-53971	31	14	most	most	ADV
bibechana-53971	31	15	widely	widely	ADV
bibechana-53971	31	16	used	use	VERB
bibechana-53971	31	17	.	.	PUNCT
bibechana-53971	32	1	constant	constant	ADJ
bibechana-53971	32	2	terms	term	NOUN
bibechana-53971	32	3	have	have	VERB
bibechana-53971	32	4	non	non	ADJ
bibechana-53971	32	5	-	-	ADJ
bibechana-53971	32	6	zero	zero	NUM
bibechana-53971	32	7	derivatives	derivative	NOUN
bibechana-53971	32	8	,	,	PUNCT
bibechana-53971	32	9	as	as	SCONJ
bibechana-53971	32	10	demonstrated	demonstrate	VERB
bibechana-53971	32	11	by	by	ADP
bibechana-53971	32	12	the	the	DET
bibechana-53971	32	13	r	r	NOUN
bibechana-53971	32	14	-	-	PUNCT
bibechana-53971	32	15	l	l	NOUN
bibechana-53971	32	16	discovery	discovery	NOUN
bibechana-53971	32	17	,	,	PUNCT
bibechana-53971	32	18	which	which	PRON
bibechana-53971	32	19	demonstrates	demonstrate	VERB
bibechana-53971	32	20	that	that	SCONJ
bibechana-53971	32	21	the	the	DET
bibechana-53971	32	22	derivative	derivative	NOUN
bibechana-53971	32	23	of	of	ADP
bibechana-53971	32	24	a	a	DET
bibechana-53971	32	25	constant	constant	ADJ
bibechana-53971	32	26	term	term	NOUN
bibechana-53971	32	27	is	be	AUX
bibechana-53971	32	28	not	not	PART
bibechana-53971	32	29	zero	zero	NUM
bibechana-53971	32	30	,	,	PUNCT
bibechana-53971	32	31	in	in	ADP
bibechana-53971	32	32	the	the	DET
bibechana-53971	32	33	framework	framework	NOUN
bibechana-53971	32	34	of	of	ADP
bibechana-53971	32	35	classical	classical	ADJ
bibechana-53971	32	36	calculus	calculus	NOUN
bibechana-53971	32	37	,	,	PUNCT
bibechana-53971	32	38	it	it	PRON
bibechana-53971	32	39	is	be	AUX
bibechana-53971	32	40	difficult	difficult	ADJ
bibechana-53971	32	41	to	to	PART
bibechana-53971	32	42	analyze	analyze	VERB
bibechana-53971	32	43	fractional	fractional	ADJ
bibechana-53971	32	44	derivatives	derivative	NOUN
bibechana-53971	32	45	[	[	X
bibechana-53971	32	46	4	4	NUM
bibechana-53971	32	47	,	,	PUNCT
bibechana-53971	32	48	5	5	NUM
bibechana-53971	32	49	]	]	PUNCT
bibechana-53971	32	50	.	.	PUNCT
bibechana-53971	33	1	jumarie	jumarie	PROPN
bibechana-53971	33	2	expertly	expertly	ADV
bibechana-53971	33	3	overcame	overcome	VERB
bibechana-53971	33	4	this	this	DET
bibechana-53971	33	5	difficulty	difficulty	NOUN
bibechana-53971	33	6	in	in	ADP
bibechana-53971	33	7	the	the	DET
bibechana-53971	33	8	most	most	ADV
bibechana-53971	33	9	recent	recent	ADJ
bibechana-53971	33	10	version	version	NOUN
bibechana-53971	33	11	by	by	ADP
bibechana-53971	33	12	modernizing	modernize	VERB
bibechana-53971	33	13	the	the	DET
bibechana-53971	33	14	idea	idea	NOUN
bibechana-53971	33	15	of	of	ADP
bibechana-53971	33	16	f.d	f.d	PROPN
bibechana-53971	33	17	.	.	PROPN
bibechana-53971	33	18	of	of	ADP
bibechana-53971	33	19	the	the	DET
bibechana-53971	33	20	r	r	NOUN
bibechana-53971	33	21	-	-	PUNCT
bibechana-53971	33	22	l	l	NOUN
bibechana-53971	33	23	category	category	NOUN
bibechana-53971	33	24	.	.	PUNCT
bibechana-53971	34	1	the	the	DET
bibechana-53971	34	2	fractional	fractional	ADJ
bibechana-53971	34	3	derivative	derivative	ADJ
bibechana-53971	34	4	versions	version	NOUN
bibechana-53971	34	5	of	of	ADP
bibechana-53971	34	6	caputo	caputo	PROPN
bibechana-53971	34	7	,	,	PUNCT
bibechana-53971	34	8	grunwald	grunwald	NOUN
bibechana-53971	34	9	-	-	PUNCT
bibechana-53971	34	10	letinikov	letinikov	PROPN
bibechana-53971	34	11	(	(	PUNCT
bibechana-53971	34	12	g	g	NOUN
bibechana-53971	34	13	-	-	PUNCT
bibechana-53971	34	14	l	l	NOUN
bibechana-53971	34	15	)	)	PUNCT
bibechana-53971	34	16	,	,	PUNCT
bibechana-53971	34	17	and	and	CCONJ
bibechana-53971	34	18	jumarie	jumarie	PROPN
bibechana-53971	34	19	’s	’s	PART
bibechana-53971	34	20	modified	modify	VERB
bibechana-53971	34	21	r	r	NOUN
bibechana-53971	34	22	-	-	PUNCT
bibechana-53971	34	23	l	l	NOUN
bibechana-53971	34	24	are	be	AUX
bibechana-53971	34	25	the	the	DET
bibechana-53971	34	26	most	most	ADV
bibechana-53971	34	27	successful	successful	ADJ
bibechana-53971	34	28	in	in	ADP
bibechana-53971	34	29	avoiding	avoid	VERB
bibechana-53971	34	30	the	the	DET
bibechana-53971	34	31	problem	problem	NOUN
bibechana-53971	34	32	of	of	ADP
bibechana-53971	34	33	non	non	ADJ
bibechana-53971	34	34	-	-	ADJ
bibechana-53971	34	35	zero	zero	NUM
bibechana-53971	34	36	derivatives	derivative	NOUN
bibechana-53971	34	37	resulting	result	VERB
bibechana-53971	34	38	from	from	ADP
bibechana-53971	34	39	a	a	DET
bibechana-53971	34	40	constant	constant	ADJ
bibechana-53971	34	41	function	function	NOUN
bibechana-53971	34	42	[	[	X
bibechana-53971	34	43	2	2	NUM
bibechana-53971	34	44	]	]	PUNCT
bibechana-53971	34	45	.	.	PUNCT
bibechana-53971	35	1	while	while	SCONJ
bibechana-53971	35	2	the	the	DET
bibechana-53971	35	3	grunwald	grunwald	NOUN
bibechana-53971	35	4	-	-	PUNCT
bibechana-53971	35	5	letinikov	letinikov	PROPN
bibechana-53971	35	6	(	(	PUNCT
bibechana-53971	35	7	g	g	NOUN
bibechana-53971	35	8	-	-	PUNCT
bibechana-53971	35	9	l	l	NOUN
bibechana-53971	35	10	)	)	PUNCT
bibechana-53971	35	11	term	term	NOUN
bibechana-53971	35	12	is	be	AUX
bibechana-53971	35	13	useful	useful	ADJ
bibechana-53971	35	14	for	for	ADP
bibechana-53971	35	15	numerical	numerical	ADJ
bibechana-53971	35	16	applications	application	NOUN
bibechana-53971	35	17	,	,	PUNCT
bibechana-53971	35	18	when	when	SCONJ
bibechana-53971	35	19	it	it	PRON
bibechana-53971	35	20	comes	come	VERB
bibechana-53971	35	21	to	to	ADP
bibechana-53971	35	22	analytical	analytical	ADJ
bibechana-53971	35	23	techniques	technique	NOUN
bibechana-53971	35	24	,	,	PUNCT
bibechana-53971	35	25	the	the	DET
bibechana-53971	35	26	concepts	concept	NOUN
bibechana-53971	35	27	of	of	ADP
bibechana-53971	35	28	r	r	NOUN
bibechana-53971	35	29	-	-	PUNCT
bibechana-53971	35	30	l	l	NOUN
bibechana-53971	35	31	and	and	CCONJ
bibechana-53971	35	32	caputo	caputo	PROPN
bibechana-53971	35	33	are	be	AUX
bibechana-53971	35	34	especially	especially	ADV
bibechana-53971	35	35	useful	useful	ADJ
bibechana-53971	35	36	.	.	PUNCT
bibechana-53971	36	1	no	no	DET
bibechana-53971	36	2	one	one	NUM
bibechana-53971	36	3	technique	technique	NOUN
bibechana-53971	36	4	can	can	AUX
bibechana-53971	36	5	be	be	AUX
bibechana-53971	36	6	used	use	VERB
bibechana-53971	36	7	to	to	PART
bibechana-53971	36	8	solve	solve	VERB
bibechana-53971	36	9	the	the	DET
bibechana-53971	36	10	linear	linear	ADJ
bibechana-53971	36	11	fractional	fractional	ADJ
bibechana-53971	36	12	differential	differential	ADJ
bibechana-53971	36	13	equations	equation	NOUN
bibechana-53971	36	14	.	.	PUNCT
bibechana-53971	37	1	the	the	DET
bibechana-53971	37	2	derivative	derivative	NOUN
bibechana-53971	37	3	of	of	ADP
bibechana-53971	37	4	the	the	DET
bibechana-53971	37	5	mittag	mittag	ADJ
bibechana-53971	37	6	-	-	PUNCT
bibechana-53971	37	7	leffler	leffler	NOUN
bibechana-53971	37	8	function	function	NOUN
bibechana-53971	37	9	(	(	PUNCT
bibechana-53971	37	10	mlf	mlf	NOUN
bibechana-53971	37	11	)	)	PUNCT
bibechana-53971	38	1	[	[	X
bibechana-53971	38	2	6	6	NUM
bibechana-53971	38	3	]	]	PUNCT
bibechana-53971	38	4	can	can	AUX
bibechana-53971	38	5	be	be	AUX
bibechana-53971	38	6	calculated	calculate	VERB
bibechana-53971	38	7	using	use	VERB
bibechana-53971	38	8	the	the	DET
bibechana-53971	38	9	fractional	fractional	ADJ
bibechana-53971	38	10	derivative	derivative	NOUN
bibechana-53971	38	11	with	with	ADP
bibechana-53971	38	12	the	the	DET
bibechana-53971	38	13	jumarie	jumarie	PROPN
bibechana-53971	38	14	modification	modification	NOUN
bibechana-53971	38	15	.	.	PUNCT
bibechana-53971	39	1	swedish	swedish	ADJ
bibechana-53971	39	2	scientist	scientist	NOUN
bibechana-53971	39	3	ml	ml	PROPN
bibechana-53971	39	4	developed	develop	VERB
bibechana-53971	39	5	the	the	DET
bibechana-53971	39	6	mlf	mlf	NOUN
bibechana-53971	39	7	for	for	ADP
bibechana-53971	39	8	averaging	average	VERB
bibechana-53971	39	9	divergent	divergent	ADJ
bibechana-53971	39	10	series	series	NOUN
bibechana-53971	39	11	at	at	ADP
bibechana-53971	39	12	the	the	DET
bibechana-53971	39	13	beginning	beginning	NOUN
bibechana-53971	39	14	of	of	ADP
bibechana-53971	39	15	the	the	DET
bibechana-53971	39	16	20th	20th	ADJ
bibechana-53971	39	17	century	century	NOUN
bibechana-53971	39	18	.	.	PUNCT
bibechana-53971	40	1	given	give	VERB
bibechana-53971	40	2	its	its	PRON
bibechana-53971	40	3	crucial	crucial	ADJ
bibechana-53971	40	4	part	part	NOUN
bibechana-53971	40	5	in	in	ADP
bibechana-53971	40	6	supplying	supply	VERB
bibechana-53971	40	7	solutions	solution	NOUN
bibechana-53971	40	8	with	with	ADP
bibechana-53971	40	9	integral	integral	ADJ
bibechana-53971	40	10	and	and	CCONJ
bibechana-53971	40	11	derivatives	derivative	NOUN
bibechana-53971	40	12	of	of	ADP
bibechana-53971	40	13	fractional	fractional	ADJ
bibechana-53971	40	14	order	order	NOUN
bibechana-53971	40	15	,	,	PUNCT
bibechana-53971	40	16	mlf	mlf	NOUN
bibechana-53971	40	17	is	be	AUX
bibechana-53971	40	18	a	a	DET
bibechana-53971	40	19	special	special	ADJ
bibechana-53971	40	20	transcendental	transcendental	ADJ
bibechana-53971	40	21	function	function	NOUN
bibechana-53971	40	22	.	.	PUNCT
bibechana-53971	41	1	the	the	DET
bibechana-53971	41	2	fractional	fractional	ADJ
bibechana-53971	41	3	order	order	NOUN
bibechana-53971	41	4	derivatives	derivative	NOUN
bibechana-53971	41	5	or	or	CCONJ
bibechana-53971	41	6	integrations	integration	NOUN
bibechana-53971	41	7	of	of	ADP
bibechana-53971	41	8	the	the	DET
bibechana-53971	41	9	superdiffusively	superdiffusively	ADJ
bibechana-53971	41	10	transport	transport	NOUN
bibechana-53971	41	11	,	,	PUNCT
bibechana-53971	41	12	random	random	ADJ
bibechana-53971	41	13	walk	walk	NOUN
bibechana-53971	41	14	,	,	PUNCT
bibechana-53971	41	15	kinetic	kinetic	ADJ
bibechana-53971	41	16	equation	equation	NOUN
bibechana-53971	41	17	,	,	PUNCT
bibechana-53971	41	18	and	and	CCONJ
bibechana-53971	41	19	complex	complex	ADJ
bibechana-53971	41	20	systems	system	NOUN
bibechana-53971	41	21	are	be	AUX
bibechana-53971	41	22	readily	readily	ADV
bibechana-53971	41	23	solved	solve	VERB
bibechana-53971	41	24	by	by	ADP
bibechana-53971	41	25	the	the	DET
bibechana-53971	41	26	mlf	mlf	NOUN
bibechana-53971	42	1	[	[	X
bibechana-53971	42	2	4,7	4,7	NUM
bibechana-53971	42	3	]	]	PUNCT
bibechana-53971	42	4	.	.	PUNCT
bibechana-53971	43	1	both	both	CCONJ
bibechana-53971	43	2	the	the	DET
bibechana-53971	43	3	standard	standard	ADJ
bibechana-53971	43	4	and	and	CCONJ
bibechana-53971	43	5	extended	extended	ADJ
bibechana-53971	43	6	mlf	mlf	NOUN
bibechana-53971	43	7	interpolate	interpolate	NOUN
bibechana-53971	43	8	phenomena	phenomenon	NOUN
bibechana-53971	43	9	are	be	AUX
bibechana-53971	43	10	governed	govern	VERB
bibechana-53971	43	11	by	by	ADP
bibechana-53971	43	12	shared	share	VERB
bibechana-53971	43	13	kinetic	kinetic	ADJ
bibechana-53971	43	14	equations	equation	NOUN
bibechana-53971	43	15	and	and	CCONJ
bibechana-53971	43	16	their	their	PRON
bibechana-53971	43	17	fractional	fractional	ADJ
bibechana-53971	43	18	analogs	analog	NOUN
bibechana-53971	43	19	between	between	ADP
bibechana-53971	43	20	an	an	DET
bibechana-53971	43	21	exponential	exponential	ADJ
bibechana-53971	43	22	law	law	NOUN
bibechana-53971	43	23	and	and	CCONJ
bibechana-53971	43	24	a	a	DET
bibechana-53971	43	25	power	power	NOUN
bibechana-53971	43	26	law	law	NOUN
bibechana-53971	43	27	[	[	X
bibechana-53971	43	28	8	8	NUM
bibechana-53971	43	29	,	,	PUNCT
bibechana-53971	43	30	9	9	NUM
bibechana-53971	43	31	]	]	PUNCT
bibechana-53971	43	32	.	.	PUNCT
bibechana-53971	44	1	in	in	ADP
bibechana-53971	44	2	contrast	contrast	NOUN
bibechana-53971	44	3	to	to	ADP
bibechana-53971	44	4	linear	linear	PROPN
bibechana-53971	44	5	fracti	fracti	ADJ
bibechana-53971	44	6	,	,	PUNCT
bibechana-53971	44	7	onal	onal	ADJ
bibechana-53971	44	8	differential	differential	NOUN
bibechana-53971	44	9	equations	equation	NOUN
bibechana-53971	44	10	,	,	PUNCT
bibechana-53971	44	11	which	which	PRON
bibechana-53971	44	12	can	can	AUX
bibechana-53971	44	13	not	not	PART
bibechana-53971	44	14	be	be	AUX
bibechana-53971	44	15	solved	solve	VERB
bibechana-53971	44	16	by	by	ADP
bibechana-53971	44	17	a	a	DET
bibechana-53971	44	18	single	single	ADJ
bibechana-53971	44	19	technique	technique	NOUN
bibechana-53971	44	20	,	,	PUNCT
bibechana-53971	44	21	the	the	DET
bibechana-53971	44	22	fd	fd	PROPN
bibechana-53971	44	23	of	of	ADP
bibechana-53971	44	24	the	the	DET
bibechana-53971	44	25	mlf	mlf	NOUN
bibechana-53971	44	26	function	function	NOUN
bibechana-53971	44	27	can	can	AUX
bibechana-53971	44	28	be	be	AUX
bibechana-53971	44	29	derived	derive	VERB
bibechana-53971	44	30	by	by	ADP
bibechana-53971	44	31	using	use	VERB
bibechana-53971	44	32	the	the	DET
bibechana-53971	44	33	updated	update	VERB
bibechana-53971	44	34	definition	definition	NOUN
bibechana-53971	44	35	of	of	ADP
bibechana-53971	44	36	the	the	DET
bibechana-53971	44	37	fd	fd	PROPN
bibechana-53971	44	38	proposed	propose	VERB
bibechana-53971	44	39	by	by	ADP
bibechana-53971	44	40	jumarie	jumarie	PROPN
bibechana-53971	44	41	.	.	PUNCT
bibechana-53971	45	1	the	the	DET
bibechana-53971	45	2	exponential	exponential	ADJ
bibechana-53971	45	3	function	function	NOUN
bibechana-53971	45	4	ez	ez	PROPN
bibechana-53971	45	5	is	be	AUX
bibechana-53971	45	6	essential	essential	ADJ
bibechana-53971	45	7	for	for	ADP
bibechana-53971	45	8	integer	integer	NOUN
bibechana-53971	45	9	-	-	PUNCT
bibechana-53971	45	10	order	order	NOUN
bibechana-53971	45	11	differential	differential	ADJ
bibechana-53971	45	12	equations	equation	NOUN
bibechana-53971	45	13	,	,	PUNCT
bibechana-53971	45	14	according	accord	VERB
bibechana-53971	45	15	to	to	ADP
bibechana-53971	45	16	theory	theory	NOUN
bibechana-53971	45	17	.	.	PUNCT
bibechana-53971	46	1	g.m	g.m	PROPN
bibechana-53971	46	2	.	.	PROPN
bibechana-53971	46	3	mittag	mittag	ADJ
bibechana-53971	46	4	-	-	PUNCT
bibechana-53971	46	5	leffler	leffler	NOUN
bibechana-53971	46	6	was	be	AUX
bibechana-53971	46	7	the	the	DET
bibechana-53971	46	8	first	first	ADJ
bibechana-53971	46	9	to	to	PART
bibechana-53971	46	10	refer	refer	VERB
bibechana-53971	46	11	to	to	ADP
bibechana-53971	46	12	the	the	DET
bibechana-53971	46	13	function	function	NOUN
bibechana-53971	46	14	that	that	PRON
bibechana-53971	46	15	is	be	AUX
bibechana-53971	46	16	now	now	ADV
bibechana-53971	46	17	denoted	denote	VERB
bibechana-53971	46	18	by	by	ADP
bibechana-53971	46	19	,	,	PUNCT
bibechana-53971	46	20	with	with	ADP
bibechana-53971	46	21	its	its	PRON
bibechana-53971	46	22	one	one	NUM
bibechana-53971	46	23	parameter	parameter	NOUN
bibechana-53971	46	24	generalization	generalization	NOUN
bibechana-53971	46	25	[	[	X
bibechana-53971	46	26	10	10	NUM
bibechana-53971	46	27	]	]	PUNCT
bibechana-53971	46	28	,	,	PUNCT
bibechana-53971	46	29	was	be	AUX
bibechana-53971	46	30	cited	cite	VERB
bibechana-53971	46	31	by	by	ADP
bibechana-53971	46	32	g.m	g.m	PROPN
bibechana-53971	46	33	.	.	PROPN
bibechana-53971	46	34	mittag	mittag	ADJ
bibechana-53971	46	35	-	-	PUNCT
bibechana-53971	46	36	leffler	leffler	NOUN
bibechana-53971	46	37	as	as	ADP
bibechana-53971	46	38	the	the	DET
bibechana-53971	46	39	source	source	NOUN
bibechana-53971	46	40	first	first	ADV
bibechana-53971	46	41	[	[	X
bibechana-53971	46	42	7	7	NUM
bibechana-53971	46	43	]	]	PUNCT
bibechana-53971	46	44	.	.	PUNCT
bibechana-53971	47	1	fractional	fractional	ADJ
bibechana-53971	47	2	calculus	calculus	NOUN
bibechana-53971	47	3	can	can	AUX
bibechana-53971	47	4	be	be	AUX
bibechana-53971	47	5	used	use	VERB
bibechana-53971	47	6	to	to	PART
bibechana-53971	47	7	solve	solve	VERB
bibechana-53971	47	8	fractional	fractional	ADJ
bibechana-53971	47	9	differential	differential	ADJ
bibechana-53971	47	10	equations	equation	NOUN
bibechana-53971	47	11	and	and	CCONJ
bibechana-53971	47	12	explain	explain	VERB
bibechana-53971	47	13	odd	odd	ADJ
bibechana-53971	47	14	phenomena	phenomenon	NOUN
bibechana-53971	47	15	.	.	PUNCT
bibechana-53971	48	1	it	it	PRON
bibechana-53971	48	2	is	be	AUX
bibechana-53971	48	3	closely	closely	ADV
bibechana-53971	48	4	linked	link	VERB
bibechana-53971	48	5	to	to	ADP
bibechana-53971	48	6	mlf	mlf	NOUN
bibechana-53971	48	7	and	and	CCONJ
bibechana-53971	48	8	its	its	PRON
bibechana-53971	48	9	expansions	expansion	NOUN
bibechana-53971	48	10	.	.	PUNCT
bibechana-53971	49	1	the	the	DET
bibechana-53971	49	2	two	two	NUM
bibechana-53971	49	3	-	-	PUNCT
bibechana-53971	49	4	parameter	parameter	NOUN
bibechana-53971	49	5	mlf	mlf	NOUN
bibechana-53971	49	6	,	,	PUNCT
bibechana-53971	49	7	r(β	r(β	PROPN
bibechana-53971	49	8	)	)	PUNCT
bibechana-53971	49	9	>	>	X
bibechana-53971	49	10	0	0	NUM
bibechana-53971	49	11	,	,	PUNCT
bibechana-53971	49	12	was	be	AUX
bibechana-53971	49	13	established	establish	VERB
bibechana-53971	49	14	by	by	ADP
bibechana-53971	49	15	goreflo	goreflo	PROPN
bibechana-53971	49	16	et	et	PROPN
bibechana-53971	49	17	al	al	PROPN
bibechana-53971	49	18	and	and	CCONJ
bibechana-53971	49	19	agarwal	agarwal	PROPN
bibechana-53971	50	1	[	[	X
bibechana-53971	50	2	11	11	NUM
bibechana-53971	50	3	]	]	PUNCT
bibechana-53971	50	4	immediately	immediately	ADV
bibechana-53971	50	5	after	after	ADP
bibechana-53971	50	6	the	the	DET
bibechana-53971	50	7	introduction	introduction	NOUN
bibechana-53971	50	8	of	of	ADP
bibechana-53971	50	9	this	this	DET
bibechana-53971	50	10	version	version	NOUN
bibechana-53971	50	11	with	with	ADP
bibechana-53971	50	12	a	a	DET
bibechana-53971	50	13	second	second	ADJ
bibechana-53971	50	14	complex	complex	ADJ
bibechana-53971	50	15	parameter	parameter	NOUN
bibechana-53971	50	16	.	.	PUNCT
bibechana-53971	51	1	leibniz	leibniz	PROPN
bibechana-53971	51	2	asked	ask	VERB
bibechana-53971	51	3	l	l	NOUN
bibechana-53971	51	4	’	'	PUNCT
bibechana-53971	51	5	hospital	hospital	NOUN
bibechana-53971	52	1	[	[	X
bibechana-53971	52	2	12	12	NUM
bibechana-53971	52	3	]	]	PUNCT
bibechana-53971	52	4	about	about	ADP
bibechana-53971	52	5	the	the	DET
bibechana-53971	52	6	consequences	consequence	NOUN
bibechana-53971	52	7	of	of	ADP
bibechana-53971	52	8	n	n	NOUN
bibechana-53971	52	9	=	=	SYM
bibechana-53971	52	10	1	1	NUM
bibechana-53971	52	11	2	2	NUM
bibechana-53971	52	12	and	and	CCONJ
bibechana-53971	52	13	the	the	DET
bibechana-53971	52	14	nth	nth	NOUN
bibechana-53971	52	15	derivative	derivative	NOUN
bibechana-53971	52	16	of	of	ADP
bibechana-53971	52	17	the	the	DET
bibechana-53971	52	18	f(t	f(t	NOUN
bibechana-53971	52	19	)	)	PUNCT
bibechana-53971	52	20	=	=	SYM
bibechana-53971	52	21	t	t	PROPN
bibechana-53971	52	22	linear	linear	PROPN
bibechana-53971	52	23	model	model	NOUN
bibechana-53971	52	24	.	.	PUNCT
bibechana-53971	53	1	fc	fc	PROPN
bibechana-53971	53	2	was	be	AUX
bibechana-53971	53	3	developed	develop	VERB
bibechana-53971	53	4	in	in	ADP
bibechana-53971	53	5	response	response	NOUN
bibechana-53971	53	6	to	to	ADP
bibechana-53971	53	7	this	this	DET
bibechana-53971	53	8	query	query	NOUN
bibechana-53971	53	9	.	.	PUNCT
bibechana-53971	54	1	leibniz	leibniz	PROPN
bibechana-53971	54	2	discovered	discover	VERB
bibechana-53971	54	3	a	a	DET
bibechana-53971	54	4	paradox	paradox	NOUN
bibechana-53971	54	5	that	that	PRON
bibechana-53971	54	6	had	have	VERB
bibechana-53971	54	7	human	human	ADJ
bibechana-53971	54	8	consequences	consequence	NOUN
bibechana-53971	54	9	,	,	PUNCT
bibechana-53971	54	10	but	but	CCONJ
bibechana-53971	54	11	he	he	PRON
bibechana-53971	54	12	also	also	ADV
bibechana-53971	54	13	noted	note	VERB
bibechana-53971	54	14	the	the	DET
bibechana-53971	54	15	creation	creation	NOUN
bibechana-53971	54	16	of	of	ADP
bibechana-53971	54	17	fc	fc	PROPN
bibechana-53971	54	18	on	on	ADP
bibechana-53971	54	19	september	september	PROPN
bibechana-53971	54	20	30	30	NUM
bibechana-53971	54	21	,	,	PUNCT
bibechana-53971	54	22	1695	1695	NUM
bibechana-53971	54	23	.	.	PUNCT
bibechana-53971	55	1	a	a	DET
bibechana-53971	55	2	34	34	NUM
bibechana-53971	55	3	-	-	PUNCT
bibechana-53971	55	4	year	year	NOUN
bibechana-53971	55	5	delay	delay	NOUN
bibechana-53971	55	6	later	later	ADV
bibechana-53971	55	7	,	,	PUNCT
bibechana-53971	55	8	in	in	ADP
bibechana-53971	55	9	1849	1849	NUM
bibechana-53971	55	10	,	,	PUNCT
bibechana-53971	55	11	he	he	PRON
bibechana-53971	55	12	added	add	VERB
bibechana-53971	55	13	the	the	DET
bibechana-53971	55	14	beta	beta	NOUN
bibechana-53971	55	15	and	and	CCONJ
bibechana-53971	55	16	gamma	gamma	NOUN
bibechana-53971	55	17	functions	function	NOUN
bibechana-53971	55	18	to	to	ADP
bibechana-53971	55	19	it	it	PRON
bibechana-53971	55	20	and	and	CCONJ
bibechana-53971	55	21	referenced	reference	VERB
bibechana-53971	55	22	to	to	ADP
bibechana-53971	55	23	g.h	g.h	PROPN
bibechana-53971	55	24	.	.	PROPN
bibechana-53971	55	25	1849	1849	NUM
bibechana-53971	56	1	[	[	X
bibechana-53971	56	2	13	13	NUM
bibechana-53971	56	3	]	]	PUNCT
bibechana-53971	56	4	.	.	PUNCT
bibechana-53971	57	1	lagrange	lagrange	PROPN
bibechana-53971	58	1	[	[	X
bibechana-53971	58	2	14	14	NUM
bibechana-53971	58	3	]	]	PUNCT
bibechana-53971	58	4	developed	develop	VERB
bibechana-53971	58	5	and	and	CCONJ
bibechana-53971	58	6	published	publish	VERB
bibechana-53971	58	7	the	the	DET
bibechana-53971	58	8	exponent	exponent	ADJ
bibechana-53971	58	9	principle	principle	NOUN
bibechana-53971	58	10	for	for	ADP
bibechana-53971	58	11	integer	integer	NOUN
bibechana-53971	58	12	-	-	PUNCT
bibechana-53971	58	13	order	order	NOUN
bibechana-53971	58	14	differential	differential	NOUN
bibechana-53971	58	15	operators	operator	NOUN
bibechana-53971	58	16	in	in	ADP
bibechana-53971	58	17	1772	1772	NUM
bibechana-53971	58	18	.	.	PUNCT
bibechana-53971	59	1	some	some	PRON
bibechana-53971	59	2	of	of	ADP
bibechana-53971	59	3	the	the	DET
bibechana-53971	59	4	most	most	ADV
bibechana-53971	59	5	significant	significant	ADJ
bibechana-53971	59	6	definitions	definition	NOUN
bibechana-53971	59	7	of	of	ADP
bibechana-53971	59	8	fc	fc	PROPN
bibechana-53971	59	9	from	from	ADP
bibechana-53971	59	10	several	several	ADJ
bibechana-53971	59	11	eminent	eminent	ADJ
bibechana-53971	59	12	mathematicians	mathematician	NOUN
bibechana-53971	59	13	are	be	AUX
bibechana-53971	59	14	given	give	VERB
bibechana-53971	59	15	by	by	ADP
bibechana-53971	59	16	us	we	PRON
bibechana-53971	59	17	.	.	PUNCT
bibechana-53971	60	1	numerous	numerous	ADJ
bibechana-53971	60	2	mathematicians	mathematician	NOUN
bibechana-53971	60	3	,	,	PUNCT
bibechana-53971	60	4	including	include	VERB
bibechana-53971	60	5	fourier	fourier	NOUN
bibechana-53971	60	6	,	,	PUNCT
bibechana-53971	60	7	lacroix	lacroix	PROPN
bibechana-53971	60	8	,	,	PUNCT
bibechana-53971	60	9	riemann	riemann	PROPN
bibechana-53971	60	10	,	,	PUNCT
bibechana-53971	60	11	liouville	liouville	PROPN
bibechana-53971	60	12	,	,	PUNCT
bibechana-53971	60	13	caputo	caputo	PROPN
bibechana-53971	60	14	,	,	PUNCT
bibechana-53971	60	15	euler	euler	NOUN
bibechana-53971	60	16	,	,	PUNCT
bibechana-53971	60	17	and	and	CCONJ
bibechana-53971	60	18	gl	gl	NOUN
bibechana-53971	61	1	[	[	X
bibechana-53971	61	2	15	15	NUM
bibechana-53971	61	3	]	]	PUNCT
bibechana-53971	61	4	,	,	PUNCT
bibechana-53971	61	5	were	be	AUX
bibechana-53971	61	6	inspired	inspire	VERB
bibechana-53971	61	7	by	by	ADP
bibechana-53971	61	8	romero	romero	PROPN
bibechana-53971	61	9	’s	’s	PART
bibechana-53971	61	10	work	work	NOUN
bibechana-53971	61	11	and	and	CCONJ
bibechana-53971	61	12	his	his	PRON
bibechana-53971	61	13	citation	citation	NOUN
bibechana-53971	61	14	by	by	ADP
bibechana-53971	61	15	laplace	laplace	NOUN
bibechana-53971	61	16	[	[	X
bibechana-53971	61	17	16	16	NUM
bibechana-53971	61	18	]	]	PUNCT
bibechana-53971	61	19	in	in	ADP
bibechana-53971	61	20	1812	1812	NUM
bibechana-53971	61	21	to	to	PART
bibechana-53971	61	22	advance	advance	VERB
bibechana-53971	61	23	the	the	DET
bibechana-53971	61	24	subject	subject	NOUN
bibechana-53971	61	25	of	of	ADP
bibechana-53971	61	26	fractional	fractional	ADJ
bibechana-53971	61	27	calculus	calculus	NOUN
bibechana-53971	61	28	.	.	PUNCT
bibechana-53971	62	1	they	they	PRON
bibechana-53971	62	2	also	also	ADV
bibechana-53971	62	3	made	make	VERB
bibechana-53971	62	4	use	use	NOUN
bibechana-53971	62	5	of	of	ADP
bibechana-53971	62	6	legendre	legendre	PROPN
bibechana-53971	62	7	’s	’s	PART
bibechana-53971	62	8	extended	extend	VERB
bibechana-53971	62	9	factorial	factorial	NOUN
bibechana-53971	62	10	notation	notation	NOUN
bibechana-53971	62	11	and	and	CCONJ
bibechana-53971	62	12	lacroix	lacroix	NOUN
bibechana-53971	62	13	’s	’s	PART
bibechana-53971	62	14	simple	simple	ADJ
bibechana-53971	62	15	nth	nth	NOUN
bibechana-53971	62	16	-	-	PUNCT
bibechana-53971	62	17	order	order	NOUN
bibechana-53971	62	18	derivative	derivative	NOUN
bibechana-53971	63	1	[	[	X
bibechana-53971	63	2	11	11	NUM
bibechana-53971	63	3	]	]	PUNCT
bibechana-53971	63	4	.	.	PUNCT
bibechana-53971	64	1	by	by	ADP
bibechana-53971	64	2	using	use	VERB
bibechana-53971	64	3	the	the	DET
bibechana-53971	64	4	laplace	laplace	NOUN
bibechana-53971	64	5	transform	transform	NOUN
bibechana-53971	64	6	approach	approach	NOUN
bibechana-53971	64	7	,	,	PUNCT
bibechana-53971	64	8	humbert	humbert	PROPN
bibechana-53971	64	9	and	and	CCONJ
bibechana-53971	64	10	agarwal	agarwal	PROPN
bibechana-53971	64	11	[	[	X
bibechana-53971	64	12	15	15	NUM
bibechana-53971	64	13	]	]	PUNCT
bibechana-53971	64	14	created	create	VERB
bibechana-53971	64	15	a	a	DET
bibechana-53971	64	16	number	number	NOUN
bibechana-53971	64	17	of	of	ADP
bibechana-53971	64	18	connections	connection	NOUN
bibechana-53971	64	19	for	for	ADP
bibechana-53971	64	20	this	this	DET
bibechana-53971	64	21	study	study	NOUN
bibechana-53971	64	22	.	.	PUNCT
bibechana-53971	65	1	solving	solve	VERB
bibechana-53971	65	2	oscillation	oscillation	NOUN
bibechana-53971	65	3	and	and	CCONJ
bibechana-53971	65	4	relaxation	relaxation	NOUN
bibechana-53971	65	5	equations	equation	NOUN
bibechana-53971	65	6	is	be	AUX
bibechana-53971	65	7	governed	govern	VERB
bibechana-53971	65	8	by	by	ADP
bibechana-53971	65	9	first	first	ADJ
bibechana-53971	65	10	and	and	CCONJ
bibechana-53971	65	11	second	second	ADJ
bibechana-53971	65	12	orders	order	NOUN
bibechana-53971	65	13	of	of	ADP
bibechana-53971	65	14	linear	linear	PROPN
bibechana-53971	65	15	differential	differential	ADJ
bibechana-53971	65	16	equations	equation	NOUN
bibechana-53971	66	1	[	[	X
bibechana-53971	66	2	17,18	17,18	NUM
bibechana-53971	66	3	]	]	PUNCT
bibechana-53971	66	4	.	.	PUNCT
bibechana-53971	67	1	caputo	caputo	PROPN
bibechana-53971	67	2	and	and	CCONJ
bibechana-53971	67	3	fabrizio	fabrizio	PROPN
bibechana-53971	67	4	[	[	X
bibechana-53971	67	5	19	19	NUM
bibechana-53971	67	6	]	]	PUNCT
bibechana-53971	67	7	in	in	ADP
bibechana-53971	67	8	2015	2015	NUM
bibechana-53971	67	9	have	have	AUX
bibechana-53971	67	10	introduced	introduce	VERB
bibechana-53971	67	11	a	a	DET
bibechana-53971	67	12	new	new	ADJ
bibechana-53971	67	13	type	type	NOUN
bibechana-53971	67	14	of	of	ADP
bibechana-53971	67	15	fractional	fractional	ADJ
bibechana-53971	67	16	derivative	derivative	NOUN
bibechana-53971	67	17	called	call	VERB
bibechana-53971	67	18	cfd	cfd	NOUN
bibechana-53971	67	19	to	to	PART
bibechana-53971	67	20	remove	remove	VERB
bibechana-53971	67	21	the	the	DET
bibechana-53971	67	22	singular	singular	ADJ
bibechana-53971	67	23	kernel	kernel	NOUN
bibechana-53971	67	24	.	.	PUNCT
bibechana-53971	68	1	using	use	VERB
bibechana-53971	68	2	both	both	PRON
bibechana-53971	68	3	caputo	caputo	PROPN
bibechana-53971	68	4	-	-	PUNCT
bibechana-53971	68	5	fabrizio	fabrizio	PROPN
bibechana-53971	68	6	and	and	CCONJ
bibechana-53971	68	7	atangana	atangana	PROPN
bibechana-53971	68	8	-	-	PUNCT
bibechana-53971	68	9	baleanu	baleanu	ADJ
bibechana-53971	68	10	derivatives	derivative	NOUN
bibechana-53971	68	11	,	,	PUNCT
bibechana-53971	68	12	algahtani	algahtani	ADJ
bibechana-53971	68	13	[	[	X
bibechana-53971	68	14	20	20	NUM
bibechana-53971	68	15	]	]	PUNCT
bibechana-53971	68	16	(	(	PUNCT
bibechana-53971	68	17	2016	2016	NUM
bibechana-53971	68	18	)	)	PUNCT
bibechana-53971	68	19	carried	carry	VERB
bibechana-53971	68	20	out	out	ADP
bibechana-53971	68	21	a	a	DET
bibechana-53971	68	22	numerical	numerical	ADJ
bibechana-53971	68	23	comparison	comparison	NOUN
bibechana-53971	68	24	of	of	ADP
bibechana-53971	68	25	the	the	DET
bibechana-53971	68	26	allen	allen	ADJ
bibechana-53971	68	27	-	-	PUNCT
bibechana-53971	68	28	cahn	cahn	NOUN
bibechana-53971	68	29	equation	equation	NOUN
bibechana-53971	68	30	gao	gao	PROPN
bibechana-53971	68	31	et	et	PROPN
bibechana-53971	68	32	al	al	PROPN
bibechana-53971	68	33	.	.	PUNCT
bibechana-53971	69	1	[	[	X
bibechana-53971	69	2	13	13	NUM
bibechana-53971	69	3	]	]	PUNCT
bibechana-53971	69	4	in	in	ADP
bibechana-53971	69	5	(	(	PUNCT
bibechana-53971	69	6	2014	2014	NUM
bibechana-53971	69	7	)	)	PUNCT
bibechana-53971	69	8	introduced	introduce	VERB
bibechana-53971	69	9	a	a	DET
bibechana-53971	69	10	novel	novel	ADJ
bibechana-53971	69	11	fractional	fractional	ADJ
bibechana-53971	69	12	numerical	numerical	ADJ
bibechana-53971	69	13	technique	technique	NOUN
bibechana-53971	69	14	,	,	PUNCT
bibechana-53971	69	15	the	the	DET
bibechana-53971	69	16	l1	l1	PROPN
bibechana-53971	69	17	-	-	PUNCT
bibechana-53971	69	18	2	2	NUM
bibechana-53971	69	19	formula	formula	NOUN
bibechana-53971	69	20	,	,	PUNCT
bibechana-53971	69	21	for	for	ADP
bibechana-53971	69	22	the	the	DET
bibechana-53971	69	23	caputo	caputo	PROPN
bibechana-53971	69	24	fractional	fractional	PROPN
bibechana-53971	69	25	derivative	derivative	NOUN
bibechana-53971	69	26	,	,	PUNCT
bibechana-53971	69	27	which	which	PRON
bibechana-53971	69	28	improved	improve	VERB
bibechana-53971	69	29	the	the	DET
bibechana-53971	69	30	accuracy	accuracy	NOUN
bibechana-53971	69	31	of	of	ADP
bibechana-53971	69	32	numerical	numerical	ADJ
bibechana-53971	69	33	solutions	solution	NOUN
bibechana-53971	69	34	from	from	ADP
bibechana-53971	69	35	δt2−α	δt2−α	ADV
bibechana-53971	69	36	to	to	ADP
bibechana-53971	69	37	δt3−α	δt3−α	PROPN
bibechana-53971	69	38	via	via	ADP
bibechana-53971	69	39	quadratic	quadratic	ADJ
bibechana-53971	69	40	interpolation	interpolation	NOUN
bibechana-53971	69	41	.	.	PUNCT
bibechana-53971	70	1	the	the	DET
bibechana-53971	70	2	aforementioned	aforementioned	ADJ
bibechana-53971	70	3	research	research	NOUN
bibechana-53971	70	4	served	serve	VERB
bibechana-53971	70	5	as	as	ADP
bibechana-53971	70	6	an	an	DET
bibechana-53971	70	7	inspiration	inspiration	NOUN
bibechana-53971	70	8	for	for	ADP
bibechana-53971	70	9	the	the	DET
bibechana-53971	70	10	creation	creation	NOUN
bibechana-53971	70	11	of	of	ADP
bibechana-53971	70	12	a	a	DET
bibechana-53971	70	13	new	new	ADJ
bibechana-53971	70	14	quadratic	quadratic	ADJ
bibechana-53971	70	15	lagrange	lagrange	NOUN
bibechana-53971	70	16	interpolation	interpolation	NOUN
bibechana-53971	70	17	l1	l1	PROPN
bibechana-53971	70	18	-	-	PUNCT
bibechana-53971	70	19	2	2	NUM
bibechana-53971	70	20	formula	formula	NOUN
bibechana-53971	70	21	.	.	PUNCT
bibechana-53971	71	1	the	the	DET
bibechana-53971	71	2	accuracy	accuracy	NOUN
bibechana-53971	71	3	of	of	ADP
bibechana-53971	71	4	the	the	DET
bibechana-53971	71	5	caputo	caputo	PROPN
bibechana-53971	71	6	-	-	PUNCT
bibechana-53971	71	7	fabrizio	fabrizio	PROPN
bibechana-53971	71	8	derivative	derivative	NOUN
bibechana-53971	71	9	(	(	PUNCT
bibechana-53971	71	10	cfd	cfd	NOUN
bibechana-53971	71	11	)	)	PUNCT
bibechana-53971	71	12	was	be	AUX
bibechana-53971	71	13	shown	show	VERB
bibechana-53971	71	14	to	to	PART
bibechana-53971	71	15	be	be	AUX
bibechana-53971	71	16	able	able	ADJ
bibechana-53971	71	17	to	to	PART
bibechana-53971	71	18	be	be	AUX
bibechana-53971	71	19	increased	increase	VERB
bibechana-53971	71	20	from	from	ADP
bibechana-53971	71	21	quadratic	quadratic	ADJ
bibechana-53971	71	22	convergence	convergence	NOUN
bibechana-53971	71	23	to	to	ADP
bibechana-53971	71	24	cubic	cubic	ADJ
bibechana-53971	71	25	.	.	PUNCT
bibechana-53971	72	1	to	to	ADP
bibechana-53971	72	2	the	the	DET
bibechana-53971	72	3	best	good	ADJ
bibechana-53971	72	4	of	of	ADP
bibechana-53971	72	5	our	our	PRON
bibechana-53971	72	6	knowledge	knowledge	NOUN
bibechana-53971	72	7	,	,	PUNCT
bibechana-53971	72	8	no	no	DET
bibechana-53971	72	9	previous	previous	ADJ
bibechana-53971	72	10	l1	l1	PROPN
bibechana-53971	72	11	-	-	PUNCT
bibechana-53971	72	12	2	2	NUM
bibechana-53971	72	13	differentiation	differentiation	NOUN
bibechana-53971	72	14	formula	formula	NOUN
bibechana-53971	72	15	for	for	ADP
bibechana-53971	72	16	the	the	DET
bibechana-53971	72	17	caputo	caputo	PROPN
bibechana-53971	72	18	-	-	PUNCT
bibechana-53971	72	19	fabrizio	fabrizio	PROPN
bibechana-53971	72	20	derivative	derivative	NOUN
bibechana-53971	72	21	(	(	PUNCT
bibechana-53971	72	22	cfd	cfd	NOUN
bibechana-53971	72	23	)	)	PUNCT
bibechana-53971	72	24	has	have	AUX
bibechana-53971	72	25	been	be	AUX
bibechana-53971	72	26	presented	present	VERB
bibechana-53971	72	27	before	before	ADP
bibechana-53971	72	28	this	this	DET
bibechana-53971	72	29	study	study	NOUN
bibechana-53971	72	30	.	.	PUNCT
bibechana-53971	73	1	additionally	additionally	ADV
bibechana-53971	73	2	,	,	PUNCT
bibechana-53971	73	3	this	this	DET
bibechana-53971	73	4	formula	formula	NOUN
bibechana-53971	73	5	’s	’s	PART
bibechana-53971	73	6	convergence	convergence	NOUN
bibechana-53971	73	7	rate	rate	NOUN
bibechana-53971	73	8	shankar	shankar	PROPN
bibechana-53971	73	9	pariyar	pariyar	PROPN
bibechana-53971	73	10	and	and	CCONJ
bibechana-53971	73	11	jeevan	jeevan	PROPN
bibechana-53971	73	12	kafle	kafle	PROPN
bibechana-53971	73	13	/	/	PUNCT
bibechana-53971	73	14	bibechana	bibechana	PROPN
bibechana-53971	73	15	20	20	NUM
bibechana-53971	73	16	(	(	PUNCT
bibechana-53971	73	17	2023	2023	NUM
bibechana-53971	73	18	)	)	PUNCT
bibechana-53971	73	19	126	126	NUM
bibechana-53971	73	20	-	-	SYM
bibechana-53971	73	21	133	133	NUM
bibechana-53971	73	22	128	128	NUM
bibechana-53971	73	23	has	have	AUX
bibechana-53971	73	24	been	be	AUX
bibechana-53971	73	25	developed	develop	VERB
bibechana-53971	73	26	.	.	PUNCT
bibechana-53971	74	1	even	even	ADV
bibechana-53971	74	2	though	though	SCONJ
bibechana-53971	74	3	caputo	caputo	PROPN
bibechana-53971	74	4	fabrizio	fabrizio	PROPN
bibechana-53971	74	5	’s	’s	PART
bibechana-53971	74	6	numerical	numerical	PROPN
bibechana-53971	74	7	solution	solution	NOUN
bibechana-53971	74	8	,	,	PUNCT
bibechana-53971	74	9	which	which	PRON
bibechana-53971	74	10	makes	make	VERB
bibechana-53971	74	11	use	use	NOUN
bibechana-53971	74	12	of	of	ADP
bibechana-53971	74	13	the	the	DET
bibechana-53971	74	14	l1	l1	PROPN
bibechana-53971	74	15	and	and	CCONJ
bibechana-53971	74	16	l2	l2	PROPN
bibechana-53971	74	17	numerical	numerical	PROPN
bibechana-53971	74	18	formulae	formulae	PROPN
bibechana-53971	74	19	,	,	PUNCT
bibechana-53971	74	20	is	be	AUX
bibechana-53971	74	21	the	the	DET
bibechana-53971	74	22	main	main	ADJ
bibechana-53971	74	23	emphasis	emphasis	NOUN
bibechana-53971	74	24	of	of	ADP
bibechana-53971	74	25	this	this	DET
bibechana-53971	74	26	paper	paper	NOUN
bibechana-53971	74	27	,	,	PUNCT
bibechana-53971	74	28	there	there	PRON
bibechana-53971	74	29	are	be	VERB
bibechana-53971	74	30	other	other	ADJ
bibechana-53971	74	31	numerical	numerical	ADJ
bibechana-53971	74	32	solutions	solution	NOUN
bibechana-53971	74	33	to	to	ADP
bibechana-53971	74	34	some	some	DET
bibechana-53971	74	35	specific	specific	ADJ
bibechana-53971	74	36	fractional	fractional	ADJ
bibechana-53971	74	37	calculus	calculus	NOUN
bibechana-53971	74	38	functions	function	NOUN
bibechana-53971	74	39	.	.	PUNCT
bibechana-53971	75	1	gao	gao	PROPN
bibechana-53971	75	2	et	et	PROPN
bibechana-53971	75	3	al	al	PROPN
bibechana-53971	75	4	.	.	PUNCT
bibechana-53971	76	1	[	[	X
bibechana-53971	76	2	13	13	NUM
bibechana-53971	76	3	]	]	PUNCT
bibechana-53971	76	4	,	,	PUNCT
bibechana-53971	76	5	introduced	introduce	VERB
bibechana-53971	76	6	an	an	DET
bibechana-53971	76	7	innovative	innovative	ADJ
bibechana-53971	76	8	fractional	fractional	ADJ
bibechana-53971	76	9	numerical	numerical	ADJ
bibechana-53971	76	10	method	method	NOUN
bibechana-53971	76	11	,	,	PUNCT
bibechana-53971	76	12	the	the	DET
bibechana-53971	76	13	l1	l1	PROPN
bibechana-53971	76	14	−	−	PROPN
bibechana-53971	76	15	2	2	NUM
bibechana-53971	76	16	formula	formula	NOUN
bibechana-53971	76	17	,	,	PUNCT
bibechana-53971	76	18	for	for	ADP
bibechana-53971	76	19	the	the	DET
bibechana-53971	76	20	cfd	cfd	NOUN
bibechana-53971	76	21	and	and	CCONJ
bibechana-53971	76	22	used	use	VERB
bibechana-53971	76	23	nonlinear	nonlinear	ADJ
bibechana-53971	76	24	interpolation	interpolation	NOUN
bibechana-53971	76	25	to	to	PART
bibechana-53971	76	26	increase	increase	VERB
bibechana-53971	76	27	the	the	DET
bibechana-53971	76	28	precision	precision	NOUN
bibechana-53971	76	29	of	of	ADP
bibechana-53971	76	30	the	the	DET
bibechana-53971	76	31	numerical	numerical	ADJ
bibechana-53971	76	32	calculation	calculation	NOUN
bibechana-53971	76	33	at	at	ADP
bibechana-53971	76	34	different	different	ADJ
bibechana-53971	76	35	steps	step	NOUN
bibechana-53971	76	36	.	.	PUNCT
bibechana-53971	77	1	our	our	PRON
bibechana-53971	77	2	sounds	sound	NOUN
bibechana-53971	77	3	show	show	VERB
bibechana-53971	77	4	how	how	SCONJ
bibechana-53971	77	5	the	the	DET
bibechana-53971	77	6	quadratic	quadratic	ADJ
bibechana-53971	77	7	rate	rate	NOUN
bibechana-53971	77	8	of	of	ADP
bibechana-53971	77	9	convergence	convergence	NOUN
bibechana-53971	77	10	can	can	AUX
bibechana-53971	77	11	be	be	AUX
bibechana-53971	77	12	transformed	transform	VERB
bibechana-53971	77	13	into	into	ADP
bibechana-53971	77	14	a	a	DET
bibechana-53971	77	15	cubic	cubic	ADJ
bibechana-53971	77	16	,	,	PUNCT
bibechana-53971	77	17	even	even	ADV
bibechana-53971	77	18	fourth	fourth	ADJ
bibechana-53971	77	19	-	-	PUNCT
bibechana-53971	77	20	order	order	NOUN
bibechana-53971	77	21	,	,	PUNCT
bibechana-53971	77	22	cfd	cfd	NOUN
bibechana-53971	77	23	.	.	PUNCT
bibechana-53971	78	1	this	this	DET
bibechana-53971	78	2	study	study	NOUN
bibechana-53971	78	3	,	,	PUNCT
bibechana-53971	78	4	in	in	ADP
bibechana-53971	78	5	our	our	PRON
bibechana-53971	78	6	opinion	opinion	NOUN
bibechana-53971	78	7	,	,	PUNCT
bibechana-53971	78	8	is	be	AUX
bibechana-53971	78	9	the	the	DET
bibechana-53971	78	10	first	first	ADJ
bibechana-53971	78	11	to	to	PART
bibechana-53971	78	12	support	support	VERB
bibechana-53971	78	13	the	the	DET
bibechana-53971	78	14	convergence	convergence	NOUN
bibechana-53971	78	15	of	of	ADP
bibechana-53971	78	16	the	the	DET
bibechana-53971	78	17	method	method	NOUN
bibechana-53971	78	18	and	and	CCONJ
bibechana-53971	78	19	to	to	PART
bibechana-53971	78	20	give	give	VERB
bibechana-53971	78	21	a	a	DET
bibechana-53971	78	22	new	new	ADJ
bibechana-53971	78	23	l1−2	l1−2	NOUN
bibechana-53971	78	24	differentiation	differentiation	NOUN
bibechana-53971	78	25	formula	formula	NOUN
bibechana-53971	78	26	for	for	ADP
bibechana-53971	78	27	cfd	cfd	NOUN
bibechana-53971	78	28	.	.	PUNCT
bibechana-53971	79	1	in	in	ADP
bibechana-53971	79	2	addition	addition	NOUN
bibechana-53971	79	3	to	to	ADP
bibechana-53971	79	4	studying	study	VERB
bibechana-53971	79	5	straightforward	straightforward	ADJ
bibechana-53971	79	6	fractional	fractional	ADJ
bibechana-53971	79	7	relaxation	relaxation	NOUN
bibechana-53971	79	8	and	and	CCONJ
bibechana-53971	79	9	vibration	vibration	NOUN
bibechana-53971	79	10	equations	equation	NOUN
bibechana-53971	79	11	,	,	PUNCT
bibechana-53971	79	12	gerenflo	gerenflo	NOUN
bibechana-53971	79	13	and	and	CCONJ
bibechana-53971	79	14	mainardi	mainardi	PROPN
bibechana-53971	79	15	[	[	X
bibechana-53971	79	16	11	11	NUM
bibechana-53971	79	17	]	]	PUNCT
bibechana-53971	79	18	also	also	ADV
bibechana-53971	79	19	investigated	investigate	VERB
bibechana-53971	79	20	fractional	fractional	ADJ
bibechana-53971	79	21	derivatives	derivative	NOUN
bibechana-53971	79	22	.	.	PUNCT
bibechana-53971	80	1	from	from	ADP
bibechana-53971	80	2	1695	1695	NUM
bibechana-53971	80	3	to	to	ADP
bibechana-53971	80	4	1697	1697	NUM
bibechana-53971	80	5	,	,	PUNCT
bibechana-53971	80	6	leibniz	leibniz	PROPN
bibechana-53971	80	7	wrote	write	VERB
bibechana-53971	80	8	correspondence	correspondence	NOUN
bibechana-53971	80	9	to	to	ADP
bibechana-53971	80	10	j.	j.	PROPN
bibechana-53971	80	11	wallis	wallis	PROPN
bibechana-53971	80	12	and	and	CCONJ
bibechana-53971	80	13	j.	j.	PROPN
bibechana-53971	80	14	bernoulli	bernoulli	PROPN
bibechana-53971	81	1	[	[	X
bibechana-53971	81	2	17,18	17,18	X
bibechana-53971	81	3	]	]	PUNCT
bibechana-53971	81	4	in	in	ADP
bibechana-53971	81	5	which	which	PRON
bibechana-53971	81	6	he	he	PRON
bibechana-53971	81	7	offered	offer	VERB
bibechana-53971	81	8	a	a	DET
bibechana-53971	81	9	potential	potential	ADJ
bibechana-53971	81	10	method	method	NOUN
bibechana-53971	81	11	for	for	ADP
bibechana-53971	81	12	differentiating	differentiate	VERB
bibechana-53971	81	13	fractional	fractional	ADJ
bibechana-53971	81	14	orders	order	NOUN
bibechana-53971	81	15	[	[	X
bibechana-53971	81	16	6	6	NUM
bibechana-53971	81	17	]	]	PUNCT
bibechana-53971	81	18	.	.	PUNCT
bibechana-53971	82	1	2	2	NUM
bibechana-53971	82	2	preliminaries	preliminary	NOUN
bibechana-53971	82	3	some	some	PRON
bibechana-53971	82	4	of	of	ADP
bibechana-53971	82	5	the	the	DET
bibechana-53971	82	6	priliminaries	priliminarie	NOUN
bibechana-53971	82	7	which	which	PRON
bibechana-53971	82	8	are	be	AUX
bibechana-53971	82	9	needed	need	VERB
bibechana-53971	82	10	for	for	ADP
bibechana-53971	82	11	the	the	DET
bibechana-53971	82	12	work	work	NOUN
bibechana-53971	82	13	are	be	AUX
bibechana-53971	82	14	given	give	VERB
bibechana-53971	82	15	below	below	ADP
bibechana-53971	82	16	:	:	PUNCT
bibechana-53971	82	17	definition	definition	NOUN
bibechana-53971	82	18	1	1	NUM
bibechana-53971	82	19	the	the	DET
bibechana-53971	82	20	formula	formula	NOUN
bibechana-53971	82	21	below	below	ADV
bibechana-53971	82	22	represents	represent	VERB
bibechana-53971	82	23	the	the	DET
bibechana-53971	82	24	gamma	gamma	PROPN
bibechana-53971	82	25	function	function	PROPN
bibechana-53971	82	26	’s	’s	PART
bibechana-53971	82	27	integral	integral	ADJ
bibechana-53971	82	28	γ(p	γ(p	PROPN
bibechana-53971	82	29	)	)	PUNCT
bibechana-53971	83	1	=	=	PUNCT
bibechana-53971	83	2	∫∞	∫∞	NOUN
bibechana-53971	83	3	0	0	NUM
bibechana-53971	84	1	e−xx(p−1)dx	e−xx(p−1)dx	NOUN
bibechana-53971	84	2	,	,	PUNCT
bibechana-53971	84	3	p	p	X
bibechana-53971	84	4	>	>	X
bibechana-53971	84	5	0	0	NUM
bibechana-53971	84	6	.	.	PUNCT
bibechana-53971	85	1	because	because	SCONJ
bibechana-53971	85	2	only	only	ADV
bibechana-53971	85	3	when	when	SCONJ
bibechana-53971	85	4	p	p	PROPN
bibechana-53971	85	5	>	>	X
bibechana-53971	85	6	0	0	NUM
bibechana-53971	85	7	does	do	VERB
bibechana-53971	85	8	the	the	DET
bibechana-53971	85	9	aforementioned	aforementioned	ADJ
bibechana-53971	85	10	integral	integral	ADJ
bibechana-53971	85	11	converge	converge	NOUN
bibechana-53971	85	12	.	.	PUNCT
bibechana-53971	86	1	the	the	DET
bibechana-53971	86	2	factorial	factorial	ADJ
bibechana-53971	86	3	function	function	NOUN
bibechana-53971	86	4	is	be	AUX
bibechana-53971	86	5	also	also	ADV
bibechana-53971	86	6	generalized	generalize	VERB
bibechana-53971	86	7	by	by	ADP
bibechana-53971	86	8	the	the	DET
bibechana-53971	86	9	gamma	gamma	PROPN
bibechana-53971	86	10	function	function	NOUN
bibechana-53971	86	11	,	,	PUNCT
bibechana-53971	86	12	as	as	ADP
bibechana-53971	86	13	for	for	ADP
bibechana-53971	86	14	any	any	DET
bibechana-53971	86	15	positive	positive	ADJ
bibechana-53971	86	16	integer	integer	NOUN
bibechana-53971	86	17	p	p	NOUN
bibechana-53971	86	18	,	,	PUNCT
bibechana-53971	86	19	γ(p	γ(p	ADJ
bibechana-53971	86	20	)	)	PUNCT
bibechana-53971	87	1	=	=	PUNCT
bibechana-53971	87	2	∫∞	∫∞	NOUN
bibechana-53971	87	3	0	0	NUM
bibechana-53971	87	4	e−xx(p−1)dx	e−xx(p−1)dx	VERB
bibechana-53971	87	5	=	=	PUNCT
bibechana-53971	87	6	(	(	PUNCT
bibechana-53971	87	7	p−	p−	NOUN
bibechana-53971	87	8	1	1	NUM
bibechana-53971	87	9	)	)	PUNCT
bibechana-53971	87	10	!	!	PUNCT
bibechana-53971	88	1	[	[	X
bibechana-53971	88	2	21	21	NUM
bibechana-53971	88	3	]	]	PUNCT
bibechana-53971	88	4	.	.	PUNCT
bibechana-53971	89	1	definition	definition	NOUN
bibechana-53971	89	2	2	2	NUM
bibechana-53971	89	3	the	the	DET
bibechana-53971	89	4	beta	beta	ADJ
bibechana-53971	89	5	function	function	NOUN
bibechana-53971	89	6	,	,	PUNCT
bibechana-53971	89	7	denoted	denote	VERB
bibechana-53971	89	8	as	as	ADP
bibechana-53971	89	9	β(p	β(p	PROPN
bibechana-53971	89	10	,	,	PUNCT
bibechana-53971	89	11	q	q	X
bibechana-53971	89	12	)	)	PUNCT
bibechana-53971	89	13	with	with	ADP
bibechana-53971	89	14	p	p	NOUN
bibechana-53971	89	15	,	,	PUNCT
bibechana-53971	89	16	q	q	ADJ
bibechana-53971	89	17	>	>	X
bibechana-53971	89	18	0	0	NUM
bibechana-53971	89	19	,	,	PUNCT
bibechana-53971	89	20	is	be	AUX
bibechana-53971	89	21	defined	define	VERB
bibechana-53971	89	22	as	as	ADP
bibechana-53971	89	23	the	the	DET
bibechana-53971	89	24	integral	integral	NOUN
bibechana-53971	89	25	of	of	ADP
bibechana-53971	89	26	xp−1(1−	xp−1(1−	PROPN
bibechana-53971	89	27	x)q−1	x)q−1	PROPN
bibechana-53971	89	28	from	from	ADP
bibechana-53971	89	29	0	0	NUM
bibechana-53971	89	30	to	to	ADP
bibechana-53971	89	31	1	1	NUM
bibechana-53971	89	32	.	.	PUNCT
bibechana-53971	90	1	it	it	PRON
bibechana-53971	90	2	is	be	AUX
bibechana-53971	90	3	related	relate	VERB
bibechana-53971	90	4	to	to	ADP
bibechana-53971	90	5	the	the	DET
bibechana-53971	90	6	gamma	gamma	NOUN
bibechana-53971	90	7	function	function	NOUN
bibechana-53971	90	8	through	through	ADP
bibechana-53971	90	9	the	the	DET
bibechana-53971	90	10	formula	formula	NOUN
bibechana-53971	90	11	β(p	β(p	PROPN
bibechana-53971	90	12	,	,	PUNCT
bibechana-53971	90	13	q	q	NOUN
bibechana-53971	90	14	)	)	PUNCT
bibechana-53971	90	15	=	=	SYM
bibechana-53971	90	16	γ(p)γ(q	γ(p)γ(q	NOUN
bibechana-53971	90	17	)	)	PUNCT
bibechana-53971	90	18	γ(p+q	γ(p+q	NUM
bibechana-53971	90	19	)	)	PUNCT
bibechana-53971	91	1	[	[	X
bibechana-53971	91	2	22	22	NUM
bibechana-53971	91	3	]	]	PUNCT
bibechana-53971	91	4	.	.	PUNCT
bibechana-53971	92	1	definition	definition	NOUN
bibechana-53971	92	2	3	3	NUM
bibechana-53971	92	3	according	accord	VERB
bibechana-53971	92	4	to	to	ADP
bibechana-53971	92	5	gl	gl	PROPN
bibechana-53971	92	6	,	,	PUNCT
bibechana-53971	92	7	the	the	DET
bibechana-53971	92	8	function	function	NOUN
bibechana-53971	92	9	m(x	m(x	PROPN
bibechana-53971	92	10	)	)	PUNCT
bibechana-53971	92	11	of	of	ADP
bibechana-53971	92	12	nth	nth	NOUN
bibechana-53971	92	13	order	order	NOUN
bibechana-53971	92	14	fd	fd	VERB
bibechana-53971	92	15	with	with	ADP
bibechana-53971	92	16	respect	respect	NOUN
bibechana-53971	92	17	to	to	ADP
bibechana-53971	92	18	x	x	PUNCT
bibechana-53971	92	19	is	be	AUX
bibechana-53971	92	20	defined	define	VERB
bibechana-53971	92	21	by	by	ADP
bibechana-53971	92	22	gl	gl	PROPN
bibechana-53971	92	23	if	if	SCONJ
bibechana-53971	92	24	α	α	PRON
bibechana-53971	92	25	is	be	AUX
bibechana-53971	92	26	a	a	DET
bibechana-53971	92	27	non	non	ADJ
bibechana-53971	92	28	-	-	ADJ
bibechana-53971	92	29	negative	negative	ADJ
bibechana-53971	92	30	real	real	ADJ
bibechana-53971	92	31	number	number	NOUN
bibechana-53971	92	32	[	[	X
bibechana-53971	92	33	2	2	NUM
bibechana-53971	92	34	]	]	PUNCT
bibechana-53971	92	35	.	.	PUNCT
bibechana-53971	93	1	gl	gl	PROPN
bibechana-53971	93	2	left	left	PROPN
bibechana-53971	93	3	sided	side	VERB
bibechana-53971	93	4	fd	fd	ADJ
bibechana-53971	93	5	:	:	PUNCT
bibechana-53971	93	6	gldα	gldα	ADJ
bibechana-53971	93	7	a+	a+	PUNCT
bibechana-53971	93	8	[	[	X
bibechana-53971	93	9	m(x	m(x	NOUN
bibechana-53971	93	10	)	)	PUNCT
bibechana-53971	93	11	]	]	PUNCT
bibechana-53971	94	1	=	=	SYM
bibechana-53971	94	2	lim	lim	PROPN
bibechana-53971	94	3	n→	n→	ADV
bibechana-53971	94	4	0	0	NUM
bibechana-53971	94	5	1	1	NUM
bibechana-53971	94	6	hα	hα	ADP
bibechana-53971	94	7	n∑	n∑	PROPN
bibechana-53971	94	8	k=0	k=0	PROPN
bibechana-53971	94	9	(	(	PUNCT
bibechana-53971	94	10	−1)k	−1)k	PROPN
bibechana-53971	94	11	γ(α+	γ(α+	PRON
bibechana-53971	94	12	1)m(x−	1)m(x−	NUM
bibechana-53971	94	13	kh	kh	NOUN
bibechana-53971	94	14	)	)	PUNCT
bibechana-53971	94	15	γ(k	γ(k	PROPN
bibechana-53971	94	16	+	+	CCONJ
bibechana-53971	94	17	1)γ(α−	1)γ(α−	NUM
bibechana-53971	94	18	k	k	X
bibechana-53971	95	1	+	+	PROPN
bibechana-53971	95	2	1	1	NUM
bibechana-53971	95	3	)	)	PUNCT
bibechana-53971	95	4	,	,	PUNCT
bibechana-53971	95	5	nh	nh	PROPN
bibechana-53971	95	6	=	=	SYM
bibechana-53971	95	7	(	(	PUNCT
bibechana-53971	95	8	x−	x−	PROPN
bibechana-53971	95	9	a	a	PRON
bibechana-53971	95	10	)	)	PUNCT
bibechana-53971	95	11	.	.	PUNCT
bibechana-53971	95	12	.	.	PUNCT
bibechana-53971	96	1	gl	gl	PROPN
bibechana-53971	96	2	right	right	PROPN
bibechana-53971	96	3	sided	side	VERB
bibechana-53971	96	4	fd	fd	ADJ
bibechana-53971	96	5	:	:	PUNCT
bibechana-53971	96	6	gldα	gldα	ADJ
bibechana-53971	96	7	b−	b−	PROPN
bibechana-53971	96	8	[	[	X
bibechana-53971	96	9	m(x	m(x	PROPN
bibechana-53971	96	10	)	)	PUNCT
bibechana-53971	96	11	]	]	PUNCT
bibechana-53971	97	1	=	=	SYM
bibechana-53971	97	2	lim	lim	PROPN
bibechana-53971	97	3	n→	n→	ADV
bibechana-53971	97	4	0	0	NUM
bibechana-53971	97	5	1	1	NUM
bibechana-53971	97	6	hα	hα	ADP
bibechana-53971	97	7	n∑	n∑	PROPN
bibechana-53971	97	8	k=0	k=0	PROPN
bibechana-53971	97	9	(	(	PUNCT
bibechana-53971	97	10	−1)k	−1)k	NOUN
bibechana-53971	97	11	γ(α+	γ(α+	NUM
bibechana-53971	97	12	1)m(x+	1)m(x+	PROPN
bibechana-53971	97	13	kh	kh	PROPN
bibechana-53971	97	14	)	)	PUNCT
bibechana-53971	97	15	γ(k	γ(k	PROPN
bibechana-53971	97	16	+	+	CCONJ
bibechana-53971	97	17	1)γ(α−	1)γ(α−	NUM
bibechana-53971	97	18	k	k	X
bibechana-53971	97	19	+	+	PROPN
bibechana-53971	97	20	1	1	NUM
bibechana-53971	97	21	)	)	PUNCT
bibechana-53971	97	22	,	,	PUNCT
bibechana-53971	97	23	nh	nh	PROPN
bibechana-53971	97	24	=	=	SYM
bibechana-53971	97	25	(	(	PUNCT
bibechana-53971	97	26	b−	b−	NOUN
bibechana-53971	97	27	x	x	PROPN
bibechana-53971	97	28	)	)	PUNCT
bibechana-53971	97	29	.	.	PUNCT
bibechana-53971	98	1	definition	definition	NOUN
bibechana-53971	98	2	4	4	NUM
bibechana-53971	98	3	the	the	DET
bibechana-53971	98	4	r	r	NOUN
bibechana-53971	98	5	-	-	PUNCT
bibechana-53971	98	6	l	l	NOUN
bibechana-53971	98	7	fractional	fractional	ADJ
bibechana-53971	98	8	integral	integral	ADJ
bibechana-53971	98	9	,	,	PUNCT
bibechana-53971	98	10	aixα(m(x	aixα(m(x	NUM
bibechana-53971	98	11	)	)	PUNCT
bibechana-53971	98	12	)	)	PUNCT
bibechana-53971	99	1	=	=	SYM
bibechana-53971	99	2	1	1	NUM
bibechana-53971	99	3	γ(α	γ(α	NOUN
bibechana-53971	99	4	)	)	PUNCT
bibechana-53971	99	5	∫	∫	PROPN
bibechana-53971	100	1	x	x	X
bibechana-53971	100	2	a	a	DET
bibechana-53971	100	3	(	(	PUNCT
bibechana-53971	100	4	x−	x−	PROPN
bibechana-53971	100	5	z)α−1m(t)dt	z)α−1m(t)dt	PROPN
bibechana-53971	100	6	;	;	PUNCT
bibechana-53971	100	7	x	x	X
bibechana-53971	100	8	>	>	X
bibechana-53971	100	9	a.	a.	NOUN
bibechana-53971	100	10	xiaα(m(x	xiaα(m(x	PUNCT
bibechana-53971	100	11	)	)	PUNCT
bibechana-53971	100	12	)	)	PUNCT
bibechana-53971	101	1	=	=	SYM
bibechana-53971	101	2	1	1	NUM
bibechana-53971	101	3	γ(α	γ(α	NOUN
bibechana-53971	101	4	)	)	PUNCT
bibechana-53971	101	5	∫	∫	PROPN
bibechana-53971	102	1	a	a	DET
bibechana-53971	102	2	x	x	X
bibechana-53971	102	3	(	(	PUNCT
bibechana-53971	102	4	x−	x−	PROPN
bibechana-53971	102	5	z)α−1m(t)dt	z)α−1m(t)dt	PROPN
bibechana-53971	102	6	;	;	PUNCT
bibechana-53971	102	7	a	a	DET
bibechana-53971	102	8	>	>	X
bibechana-53971	102	9	x.	x.	NOUN
bibechana-53971	102	10	properties	property	NOUN
bibechana-53971	102	11	p1	p1	PROPN
bibechana-53971	102	12	:	:	PUNCT
bibechana-53971	102	13	ai	ai	VERB
bibechana-53971	102	14	α	α	X
bibechana-53971	102	15	x	x	X
bibechana-53971	102	16	(	(	PUNCT
bibechana-53971	102	17	k(t	k(t	X
bibechana-53971	102	18	(	(	PUNCT
bibechana-53971	102	19	x	x	NOUN
bibechana-53971	102	20	)	)	PUNCT
bibechana-53971	102	21	)	)	PUNCT
bibechana-53971	102	22	)	)	PUNCT
bibechana-53971	103	1	=	=	SYM
bibechana-53971	104	1	k	k	X
bibechana-53971	104	2	·	·	PUNCT
bibechana-53971	104	3	a	a	DET
bibechana-53971	104	4	iαx	iαx	NOUN
bibechana-53971	104	5	(	(	PUNCT
bibechana-53971	104	6	t	t	PROPN
bibechana-53971	104	7	(	(	PUNCT
bibechana-53971	104	8	x	x	NOUN
bibechana-53971	104	9	)	)	PUNCT
bibechana-53971	104	10	)	)	PUNCT
bibechana-53971	104	11	.	.	PUNCT
bibechana-53971	105	1	p2	p2	PROPN
bibechana-53971	105	2	:	:	PUNCT
bibechana-53971	105	3	ai	ai	VERB
bibechana-53971	105	4	α	α	X
bibechana-53971	105	5	x	x	X
bibechana-53971	105	6	(	(	PUNCT
bibechana-53971	105	7	p	p	X
bibechana-53971	105	8	(	(	PUNCT
bibechana-53971	105	9	x)±q(x	x)±q(x	PROPN
bibechana-53971	105	10	)	)	PUNCT
bibechana-53971	105	11	)	)	PUNCT
bibechana-53971	105	12	)	)	PUNCT
bibechana-53971	106	1	=	=	NOUN
bibechana-53971	106	2	a	a	DET
bibechana-53971	106	3	iαx	iαx	NOUN
bibechana-53971	106	4	(	(	PUNCT
bibechana-53971	106	5	p	p	X
bibechana-53971	106	6	(	(	PUNCT
bibechana-53971	106	7	x))±a	x))±a	X
bibechana-53971	107	1	i	i	PRON
bibechana-53971	107	2	α	α	INTJ
bibechana-53971	107	3	x	x	INTJ
bibechana-53971	107	4	(	(	PUNCT
bibechana-53971	107	5	q(x	q(x	PROPN
bibechana-53971	107	6	)	)	PUNCT
bibechana-53971	107	7	)	)	PUNCT
bibechana-53971	107	8	.	.	PUNCT
bibechana-53971	108	1	p3	p3	PROPN
bibechana-53971	108	2	:	:	PUNCT
bibechana-53971	108	3	ai	ai	VERB
bibechana-53971	108	4	α	α	X
bibechana-53971	108	5	x	x	PROPN
bibechana-53971	108	6	(	(	PUNCT
bibechana-53971	108	7	n(x)±m(x	n(x)±m(x	NOUN
bibechana-53971	108	8	)	)	PUNCT
bibechana-53971	108	9	)	)	PUNCT
bibechana-53971	109	1	=	=	NOUN
bibechana-53971	109	2	a	a	DET
bibechana-53971	109	3	iαx	iαx	NOUN
bibechana-53971	109	4	(	(	PUNCT
bibechana-53971	109	5	n(x))±a	n(x))±a	NOUN
bibechana-53971	109	6	i	i	NOUN
bibechana-53971	109	7	α	α	NOUN
bibechana-53971	109	8	x	x	X
bibechana-53971	109	9	(	(	PUNCT
bibechana-53971	109	10	m(x	m(x	PROPN
bibechana-53971	109	11	)	)	PUNCT
bibechana-53971	109	12	)	)	PUNCT
bibechana-53971	109	13	.	.	PUNCT
bibechana-53971	110	1	definition	definition	NOUN
bibechana-53971	110	2	5	5	NUM
bibechana-53971	110	3	under	under	ADP
bibechana-53971	110	4	riemann	riemann	PROPN
bibechana-53971	110	5	-	-	PUNCT
bibechana-53971	110	6	liouville	liouville	NOUN
bibechana-53971	110	7	,	,	PUNCT
bibechana-53971	110	8	in	in	ADP
bibechana-53971	110	9	most	most	ADJ
bibechana-53971	110	10	cases	case	NOUN
bibechana-53971	110	11	,	,	PUNCT
bibechana-53971	110	12	the	the	DET
bibechana-53971	110	13	riemann	riemann	PROPN
bibechana-53971	110	14	-	-	PUNCT
bibechana-53971	110	15	liouville	liouville	VERB
bibechana-53971	110	16	formula	formula	NOUN
bibechana-53971	110	17	defines	define	VERB
bibechana-53971	110	18	a	a	DET
bibechana-53971	110	19	fractional	fractional	ADJ
bibechana-53971	110	20	derivative	derivative	NOUN
bibechana-53971	110	21	[	[	X
bibechana-53971	110	22	23	23	NUM
bibechana-53971	110	23	]	]	PUNCT
bibechana-53971	110	24	.	.	PUNCT
bibechana-53971	111	1	bd	bd	PROPN
bibechana-53971	111	2	q	q	PROPN
bibechana-53971	111	3	t	t	PROPN
bibechana-53971	111	4	(	(	PUNCT
bibechana-53971	111	5	v(x	v(x	PROPN
bibechana-53971	111	6	)	)	PUNCT
bibechana-53971	111	7	)	)	PUNCT
bibechana-53971	112	1	=	=	PUNCT
bibechana-53971	112	2			NOUN
bibechana-53971	112	3	1	1	NUM
bibechana-53971	112	4	γ(ν−γ	γ(ν−γ	NOUN
bibechana-53971	112	5	)	)	PUNCT
bibechana-53971	112	6	(	(	PUNCT
bibechana-53971	112	7	d	d	NOUN
bibechana-53971	112	8	dx	dx	PROPN
bibechana-53971	112	9	)	)	PUNCT
bibechana-53971	112	10	t	t	PROPN
bibechana-53971	112	11	∫	∫	PROPN
bibechana-53971	113	1	q	q	PROPN
bibechana-53971	113	2	b	b	PROPN
bibechana-53971	113	3	(	(	PUNCT
bibechana-53971	113	4	q	q	PROPN
bibechana-53971	113	5	−	−	PROPN
bibechana-53971	113	6	t)t−γ−1v(t).dt	t)t−γ−1v(t).dt	SYM
bibechana-53971	113	7	;	;	PUNCT
bibechana-53971	113	8	(	(	PUNCT
bibechana-53971	113	9	t−	t−	PROPN
bibechana-53971	113	10	1	1	NUM
bibechana-53971	113	11	)	)	PUNCT
bibechana-53971	113	12	<	<	X
bibechana-53971	113	13	β	β	X
bibechana-53971	113	14	<	<	X
bibechana-53971	113	15	t	t	X
bibechana-53971	113	16	dt	dt	X
bibechana-53971	113	17	dxt	dxt	PROPN
bibechana-53971	113	18	v(x	v(x	PROPN
bibechana-53971	113	19	)	)	PUNCT
bibechana-53971	113	20	,	,	PUNCT
bibechana-53971	113	21	β	β	X
bibechana-53971	113	22	=	=	SYM
bibechana-53971	113	23	t	t	PROPN
bibechana-53971	113	24	definition	definition	NOUN
bibechana-53971	113	25	6	6	NUM
bibechana-53971	113	26	the	the	DET
bibechana-53971	113	27	caputo	caputo	PROPN
bibechana-53971	113	28	fractional	fractional	PROPN
bibechana-53971	113	29	derivative	derivative	NOUN
bibechana-53971	113	30	is	be	AUX
bibechana-53971	113	31	commonly	commonly	ADV
bibechana-53971	113	32	used	use	VERB
bibechana-53971	113	33	[	[	PUNCT
bibechana-53971	113	34	13	13	NUM
bibechana-53971	113	35	]	]	PUNCT
bibechana-53971	113	36	.	.	PUNCT
bibechana-53971	114	1	adα	adα	PROPN
bibechana-53971	114	2	x(m(x	x(m(x	PROPN
bibechana-53971	114	3	)	)	PUNCT
bibechana-53971	114	4	)	)	PUNCT
bibechana-53971	115	1	=	=	PUNCT
bibechana-53971	115	2			PROPN
bibechana-53971	115	3	1	1	NUM
bibechana-53971	115	4	γ(n−α	γ(n−α	NOUN
bibechana-53971	115	5	)	)	PUNCT
bibechana-53971	115	6	∫	∫	NOUN
bibechana-53971	115	7	x	x	X
bibechana-53971	115	8	a	a	PRON
bibechana-53971	115	9	(	(	PUNCT
bibechana-53971	115	10	x−	x−	PROPN
bibechana-53971	115	11	t)n−α−1	t)n−α−1	PROPN
bibechana-53971	115	12	(	(	PUNCT
bibechana-53971	115	13	d	d	NOUN
bibechana-53971	115	14	dx	dx	PROPN
bibechana-53971	115	15	)	)	PUNCT
bibechana-53971	115	16	n	n	PRON
bibechana-53971	115	17	m(t).dt	m(t).dt	NOUN
bibechana-53971	115	18	,	,	PUNCT
bibechana-53971	115	19	(	(	PUNCT
bibechana-53971	115	20	n−	n−	NOUN
bibechana-53971	115	21	1	1	NUM
bibechana-53971	115	22	)	)	PUNCT
bibechana-53971	115	23	<	<	X
bibechana-53971	115	24	α	α	X
bibechana-53971	115	25	<	<	X
bibechana-53971	115	26	n	n	X
bibechana-53971	115	27	dn	dn	PROPN
bibechana-53971	115	28	dxn	dxn	PROPN
bibechana-53971	115	29	·	·	PUNCT
bibechana-53971	115	30	m(x	m(x	PROPN
bibechana-53971	115	31	)	)	PUNCT
bibechana-53971	115	32	;	;	PUNCT
bibechana-53971	115	33	α	α	X
bibechana-53971	115	34	=	=	SYM
bibechana-53971	115	35	n	n	PROPN
bibechana-53971	115	36	(	(	PUNCT
bibechana-53971	115	37	1	1	NUM
bibechana-53971	115	38	)	)	PUNCT
bibechana-53971	115	39	definition	definition	NOUN
bibechana-53971	115	40	7	7	NUM
bibechana-53971	115	41	mittag	mittag	ADJ
bibechana-53971	115	42	leffler	leffl	ADJ
bibechana-53971	115	43	function	function	NOUN
bibechana-53971	115	44	(	(	PUNCT
bibechana-53971	115	45	mlf	mlf	NOUN
bibechana-53971	115	46	)	)	PUNCT
bibechana-53971	115	47	of	of	ADP
bibechana-53971	115	48	one	one	NUM
bibechana-53971	115	49	parameter	parameter	NOUN
bibechana-53971	115	50	[	[	X
bibechana-53971	115	51	10	10	NUM
bibechana-53971	115	52	]	]	PUNCT
bibechana-53971	115	53	,	,	PUNCT
bibechana-53971	115	54	eα(z	eα(z	PUNCT
bibechana-53971	115	55	)	)	PUNCT
bibechana-53971	115	56	=	=	PUNCT
bibechana-53971	116	1	∞∑	∞∑	NUM
bibechana-53971	116	2	n=0	n=0	NUM
bibechana-53971	116	3	zn	zn	NUM
bibechana-53971	116	4	γ(αk	γ(αk	PROPN
bibechana-53971	116	5	+	+	CCONJ
bibechana-53971	116	6	1	1	NUM
bibechana-53971	116	7	)	)	PUNCT
bibechana-53971	116	8	(	(	PUNCT
bibechana-53971	116	9	2	2	X
bibechana-53971	116	10	)	)	PUNCT
bibechana-53971	116	11	two	two	NUM
bibechana-53971	116	12	-	-	PUNCT
bibechana-53971	116	13	parameters	parameter	NOUN
bibechana-53971	116	14	mlf	mlf	VERB
bibechana-53971	116	15	β	β	X
bibechana-53971	116	16	,	,	PUNCT
bibechana-53971	116	17	r(β	r(β	PROPN
bibechana-53971	116	18	)	)	PUNCT
bibechana-53971	116	19	>	>	X
bibechana-53971	116	20	0	0	PUNCT
bibechana-53971	117	1	[	[	X
bibechana-53971	117	2	11	11	NUM
bibechana-53971	117	3	]	]	PUNCT
bibechana-53971	117	4	and	and	CCONJ
bibechana-53971	117	5	agarwal	agarwal	PROPN
bibechana-53971	118	1	[	[	X
bibechana-53971	118	2	24	24	NUM
bibechana-53971	118	3	]	]	SYM
bibechana-53971	118	4	β	β	NOUN
bibechana-53971	118	5	,	,	PUNCT
bibechana-53971	118	6	r(β	r(β	PROPN
bibechana-53971	118	7	)	)	PUNCT
bibechana-53971	118	8	>	>	X
bibechana-53971	118	9	0	0	NUM
bibechana-53971	118	10	eα	eα	PROPN
bibechana-53971	118	11	,	,	PUNCT
bibechana-53971	118	12	β(z	β(z	PROPN
bibechana-53971	118	13	)	)	PUNCT
bibechana-53971	118	14	=	=	PUNCT
bibechana-53971	119	1	∞∑	∞∑	NUM
bibechana-53971	119	2	n=0	n=0	NUM
bibechana-53971	119	3	zn	zn	NUM
bibechana-53971	119	4	γ(α	γ(α	PROPN
bibechana-53971	119	5	·	·	PUNCT
bibechana-53971	120	1	k	k	X
bibechana-53971	120	2	+	+	PUNCT
bibechana-53971	120	3	β	β	X
bibechana-53971	120	4	)	)	PUNCT
bibechana-53971	120	5	(	(	PUNCT
bibechana-53971	120	6	z	z	X
bibechana-53971	120	7	,	,	PUNCT
bibechana-53971	120	8	α	α	PROPN
bibechana-53971	120	9	,	,	PUNCT
bibechana-53971	120	10	β	β	X
bibechana-53971	120	11	∈	∈	PROPN
bibechana-53971	120	12	c	c	X
bibechana-53971	120	13	)	)	PUNCT
bibechana-53971	120	14	(	(	PUNCT
bibechana-53971	120	15	3	3	X
bibechana-53971	120	16	)	)	PUNCT
bibechana-53971	120	17	the	the	DET
bibechana-53971	120	18	generation	generation	NOUN
bibechana-53971	120	19	of	of	ADP
bibechana-53971	120	20	3	3	NUM
bibechana-53971	120	21	in	in	ADP
bibechana-53971	120	22	terms	term	NOUN
bibechana-53971	120	23	of	of	ADP
bibechana-53971	120	24	series	series	NOUN
bibechana-53971	120	25	representation	representation	NOUN
bibechana-53971	120	26	was	be	AUX
bibechana-53971	120	27	introduced	introduce	VERB
bibechana-53971	120	28	by	by	ADP
bibechana-53971	120	29	prabhakar	prabhakar	NOUN
bibechana-53971	120	30	.	.	PUNCT
bibechana-53971	121	1	eγ	eγ	ADP
bibechana-53971	121	2	α	α	PROPN
bibechana-53971	121	3	,	,	PUNCT
bibechana-53971	121	4	β(z	β(z	PROPN
bibechana-53971	121	5	)	)	PUNCT
bibechana-53971	121	6	=	=	PUNCT
bibechana-53971	122	1	∞∑	∞∑	NUM
bibechana-53971	122	2	k=0	k=0	PROPN
bibechana-53971	122	3	(	(	PUNCT
bibechana-53971	122	4	γ)nz	γ)nz	PROPN
bibechana-53971	122	5	k	k	PROPN
bibechana-53971	122	6	γ(α	γ(α	PROPN
bibechana-53971	122	7	·	·	PUNCT
bibechana-53971	123	1	k	k	X
bibechana-53971	123	2	+	+	PUNCT
bibechana-53971	123	3	β	β	X
bibechana-53971	123	4	)	)	PUNCT
bibechana-53971	123	5	·	·	PUNCT
bibechana-53971	123	6	n	n	X
bibechana-53971	123	7	!	!	PUNCT
bibechana-53971	124	1	(	(	PUNCT
bibechana-53971	124	2	4	4	X
bibechana-53971	124	3	)	)	PUNCT
bibechana-53971	124	4	where	where	SCONJ
bibechana-53971	124	5	(	(	PUNCT
bibechana-53971	124	6	γ)n	γ)n	X
bibechana-53971	124	7	is	be	AUX
bibechana-53971	124	8	pochhammer	pochhammer	NOUN
bibechana-53971	124	9	’s	’s	PART
bibechana-53971	124	10	symbol	symbol	NOUN
bibechana-53971	124	11	.	.	PUNCT
bibechana-53971	125	1	with	with	ADP
bibechana-53971	125	2	the	the	DET
bibechana-53971	125	3	aforementioned	aforementioned	ADJ
bibechana-53971	125	4	considerations	consideration	NOUN
bibechana-53971	125	5	in	in	ADP
bibechana-53971	125	6	mind	mind	NOUN
bibechana-53971	125	7	,	,	PUNCT
bibechana-53971	125	8	we	we	PRON
bibechana-53971	125	9	discuss	discuss	VERB
bibechana-53971	125	10	the	the	DET
bibechana-53971	125	11	fractional	fractional	ADJ
bibechana-53971	125	12	operators	operator	NOUN
bibechana-53971	125	13	with	with	ADP
bibechana-53971	125	14	three	three	NUM
bibechana-53971	125	15	-	-	PUNCT
bibechana-53971	125	16	parameter	parameter	NOUN
bibechana-53971	125	17	generalized	generalize	VERB
bibechana-53971	125	18	mittag	mittag	ADJ
bibechana-53971	125	19	-	-	PUNCT
bibechana-53971	125	20	leffler	leffler	NOUN
bibechana-53971	125	21	kernels	kernel	NOUN
bibechana-53971	125	22	in	in	ADP
bibechana-53971	125	23	our	our	PRON
bibechana-53971	125	24	work	work	NOUN
bibechana-53971	125	25	.	.	PUNCT
bibechana-53971	126	1	definition	definition	NOUN
bibechana-53971	126	2	8	8	NUM
bibechana-53971	126	3	a	a	DET
bibechana-53971	126	4	novel	novel	ADJ
bibechana-53971	126	5	fractional	fractional	ADJ
bibechana-53971	126	6	derivative	derivative	NOUN
bibechana-53971	126	7	with	with	ADP
bibechana-53971	126	8	no	no	DET
bibechana-53971	126	9	singularities	singularity	NOUN
bibechana-53971	126	10	in	in	ADP
bibechana-53971	126	11	its	its	PRON
bibechana-53971	126	12	kernel	kernel	NOUN
bibechana-53971	126	13	was	be	AUX
bibechana-53971	126	14	suggested	suggest	VERB
bibechana-53971	126	15	by	by	ADP
bibechana-53971	126	16	caputo	caputo	PROPN
bibechana-53971	126	17	and	and	CCONJ
bibechana-53971	126	18	fabrizio	fabrizio	PROPN
bibechana-53971	126	19	in	in	ADP
bibechana-53971	126	20	their	their	PRON
bibechana-53971	126	21	[	[	X
bibechana-53971	126	22	17	17	NUM
bibechana-53971	126	23	]	]	PUNCT
bibechana-53971	126	24	.	.	PUNCT
bibechana-53971	127	1	the	the	DET
bibechana-53971	127	2	first	first	ADJ
bibechana-53971	127	3	fractional	fractional	ADJ
bibechana-53971	127	4	derivative	derivative	NOUN
bibechana-53971	127	5	has	have	VERB
bibechana-53971	127	6	an	an	DET
bibechana-53971	127	7	exponential	exponential	ADJ
bibechana-53971	127	8	kernel	kernel	NOUN
bibechana-53971	127	9	,	,	PUNCT
bibechana-53971	127	10	which	which	PRON
bibechana-53971	127	11	is	be	AUX
bibechana-53971	127	12	similar	similar	ADJ
bibechana-53971	127	13	to	to	ADP
bibechana-53971	127	14	an	an	DET
bibechana-53971	127	15	exponential	exponential	ADJ
bibechana-53971	127	16	function	function	NOUN
bibechana-53971	127	17	.	.	PUNCT
bibechana-53971	128	1	cf	cf	VERB
bibechana-53971	128	2	a	a	DET
bibechana-53971	128	3	dx(f(x	dx(f(x	NOUN
bibechana-53971	128	4	)	)	PUNCT
bibechana-53971	128	5	)	)	PUNCT
bibechana-53971	129	1	=	=	SYM
bibechana-53971	129	2	m(α	m(α	PROPN
bibechana-53971	129	3	)	)	PUNCT
bibechana-53971	129	4	(	(	PUNCT
bibechana-53971	129	5	1−α	1−α	NUM
bibechana-53971	129	6	)	)	PUNCT
bibechana-53971	129	7	∫	∫	PROPN
bibechana-53971	129	8	x	x	X
bibechana-53971	129	9	a	a	DET
bibechana-53971	129	10	e−	e−	PROPN
bibechana-53971	129	11	α(x−t	α(x−t	PROPN
bibechana-53971	129	12	)	)	PUNCT
bibechana-53971	129	13	(	(	PUNCT
bibechana-53971	129	14	1−α	1−α	NUM
bibechana-53971	129	15	)	)	PUNCT
bibechana-53971	129	16	·	·	PUNCT
bibechana-53971	130	1	f	f	X
bibechana-53971	130	2	′(t	′(t	PROPN
bibechana-53971	130	3	)	)	PUNCT
bibechana-53971	130	4	·	·	PUNCT
bibechana-53971	131	1	dt	dt	X
bibechana-53971	131	2	;	;	PUNCT
bibechana-53971	131	3	m(0	m(0	PROPN
bibechana-53971	131	4	)	)	PUNCT
bibechana-53971	131	5	=	=	SYM
bibechana-53971	131	6	m(1	m(1	NOUN
bibechana-53971	131	7	)	)	PUNCT
bibechana-53971	131	8	=	=	SYM
bibechana-53971	131	9	1	1	NUM
bibechana-53971	131	10	shankar	shankar	NOUN
bibechana-53971	131	11	pariyar	pariyar	PROPN
bibechana-53971	131	12	and	and	CCONJ
bibechana-53971	131	13	jeevan	jeevan	PROPN
bibechana-53971	131	14	kafle	kafle	PROPN
bibechana-53971	131	15	/	/	PUNCT
bibechana-53971	131	16	bibechana	bibechana	PROPN
bibechana-53971	131	17	20	20	NUM
bibechana-53971	131	18	(	(	PUNCT
bibechana-53971	131	19	2023	2023	NUM
bibechana-53971	131	20	)	)	PUNCT
bibechana-53971	131	21	126	126	NUM
bibechana-53971	131	22	-	-	SYM
bibechana-53971	131	23	133	133	NUM
bibechana-53971	131	24	129	129	NUM
bibechana-53971	131	25	definition	definition	NOUN
bibechana-53971	131	26	9	9	NUM
bibechana-53971	131	27	interpolation	interpolation	NOUN
bibechana-53971	131	28	:	:	PUNCT
bibechana-53971	131	29	the	the	DET
bibechana-53971	131	30	process	process	NOUN
bibechana-53971	131	31	of	of	ADP
bibechana-53971	131	32	figuring	figure	VERB
bibechana-53971	131	33	out	out	ADP
bibechana-53971	131	34	the	the	DET
bibechana-53971	131	35	values	value	NOUN
bibechana-53971	131	36	of	of	ADP
bibechana-53971	131	37	the	the	DET
bibechana-53971	131	38	functions	function	NOUN
bibechana-53971	131	39	at	at	ADP
bibechana-53971	131	40	any	any	DET
bibechana-53971	131	41	intermediate	intermediate	ADJ
bibechana-53971	131	42	point	point	NOUN
bibechana-53971	131	43	when	when	SCONJ
bibechana-53971	131	44	the	the	DET
bibechana-53971	131	45	values	value	NOUN
bibechana-53971	131	46	of	of	ADP
bibechana-53971	131	47	the	the	DET
bibechana-53971	131	48	first	first	ADJ
bibechana-53971	131	49	two	two	NUM
bibechana-53971	131	50	points	point	NOUN
bibechana-53971	131	51	are	be	AUX
bibechana-53971	131	52	known	know	VERB
bibechana-53971	131	53	is	be	AUX
bibechana-53971	131	54	known	know	VERB
bibechana-53971	131	55	as	as	ADP
bibechana-53971	131	56	interpolation	interpolation	NOUN
bibechana-53971	131	57	.	.	PUNCT
bibechana-53971	132	1	definition	definition	NOUN
bibechana-53971	132	2	10	10	NUM
bibechana-53971	132	3	linear	linear	ADJ
bibechana-53971	132	4	interpolation	interpolation	NOUN
bibechana-53971	132	5	[	[	X
bibechana-53971	132	6	25	25	NUM
bibechana-53971	132	7	]	]	X
bibechana-53971	132	8	:	:	PUNCT
bibechana-53971	132	9	the	the	DET
bibechana-53971	132	10	linear	linear	ADJ
bibechana-53971	132	11	polynomial	polynomial	NOUN
bibechana-53971	132	12	that	that	PRON
bibechana-53971	132	13	passes	pass	VERB
bibechana-53971	132	14	through	through	ADP
bibechana-53971	132	15	the	the	DET
bibechana-53971	132	16	specified	specified	ADJ
bibechana-53971	132	17	coordinates	coordinate	NOUN
bibechana-53971	132	18	(	(	PUNCT
bibechana-53971	132	19	a0	a0	NOUN
bibechana-53971	132	20	,	,	PUNCT
bibechana-53971	132	21	b0	b0	NOUN
bibechana-53971	132	22	)	)	PUNCT
bibechana-53971	132	23	and	and	CCONJ
bibechana-53971	132	24	(	(	PUNCT
bibechana-53971	132	25	a1	a1	NOUN
bibechana-53971	132	26	,	,	PUNCT
bibechana-53971	132	27	b1	b1	NOUN
bibechana-53971	132	28	)	)	PUNCT
bibechana-53971	132	29	.	.	PUNCT
bibechana-53971	133	1	one	one	NUM
bibechana-53971	133	2	method	method	NOUN
bibechana-53971	133	3	to	to	PART
bibechana-53971	133	4	express	express	VERB
bibechana-53971	133	5	its	its	PRON
bibechana-53971	133	6	formula	formula	NOUN
bibechana-53971	133	7	is	be	AUX
bibechana-53971	133	8	as	as	SCONJ
bibechana-53971	133	9	follows	follow	VERB
bibechana-53971	133	10	:	:	PUNCT
bibechana-53971	133	11	p1(x	p1(x	NOUN
bibechana-53971	133	12	)	)	PUNCT
bibechana-53971	133	13	=	=	SYM
bibechana-53971	133	14	b0	b0	NOUN
bibechana-53971	133	15	a1−x	a1−x	PROPN
bibechana-53971	133	16	a1−a0	a1−a0	NOUN
bibechana-53971	133	17	+	+	CCONJ
bibechana-53971	133	18	b1	b1	NOUN
bibechana-53971	133	19	x−a0	x−a0	ADP
bibechana-53971	133	20	a1−a0	a1−a0	NOUN
bibechana-53971	133	21	definition	definition	NOUN
bibechana-53971	133	22	11	11	NUM
bibechana-53971	133	23	quadratic	quadratic	ADJ
bibechana-53971	133	24	interpolation	interpolation	NOUN
bibechana-53971	133	25	[	[	X
bibechana-53971	133	26	25	25	NUM
bibechana-53971	133	27	]	]	X
bibechana-53971	133	28	:	:	PUNCT
bibechana-53971	133	29	the	the	DET
bibechana-53971	133	30	quadratic	quadratic	ADJ
bibechana-53971	133	31	polynomial	polynomial	NOUN
bibechana-53971	133	32	that	that	PRON
bibechana-53971	133	33	passes	pass	VERB
bibechana-53971	133	34	through	through	ADP
bibechana-53971	133	35	the	the	DET
bibechana-53971	133	36	specified	specified	ADJ
bibechana-53971	133	37	coordinates	coordinate	NOUN
bibechana-53971	133	38	(	(	PUNCT
bibechana-53971	133	39	a0	a0	NOUN
bibechana-53971	133	40	,	,	PUNCT
bibechana-53971	133	41	b0	b0	NOUN
bibechana-53971	133	42	)	)	PUNCT
bibechana-53971	133	43	,	,	PUNCT
bibechana-53971	133	44	(	(	PUNCT
bibechana-53971	133	45	a1	a1	NOUN
bibechana-53971	133	46	,	,	PUNCT
bibechana-53971	133	47	b1	b1	NOUN
bibechana-53971	133	48	)	)	PUNCT
bibechana-53971	133	49	,	,	PUNCT
bibechana-53971	133	50	and	and	CCONJ
bibechana-53971	133	51	(	(	PUNCT
bibechana-53971	133	52	a2	a2	PROPN
bibechana-53971	133	53	,	,	PUNCT
bibechana-53971	133	54	b2	b2	NOUN
bibechana-53971	133	55	)	)	PUNCT
bibechana-53971	133	56	may	may	AUX
bibechana-53971	133	57	be	be	AUX
bibechana-53971	133	58	written	write	VERB
bibechana-53971	133	59	as	as	ADP
bibechana-53971	133	60	p2(x	p2(x	NOUN
bibechana-53971	133	61	)	)	PUNCT
bibechana-53971	133	62	=	=	SYM
bibechana-53971	133	63	b0m0(x	b0m0(x	NOUN
bibechana-53971	133	64	)	)	PUNCT
bibechana-53971	133	65	+	+	NOUN
bibechana-53971	133	66	b1m1(x	b1m1(x	NOUN
bibechana-53971	133	67	)	)	PUNCT
bibechana-53971	133	68	+	+	CCONJ
bibechana-53971	133	69	b2m2(x	b2m2(x	NOUN
bibechana-53971	133	70	)	)	PUNCT
bibechana-53971	133	71	,	,	PUNCT
bibechana-53971	133	72	m0(x	m0(x	NOUN
bibechana-53971	133	73	)	)	PUNCT
bibechana-53971	133	74	=	=	SYM
bibechana-53971	133	75	(	(	PUNCT
bibechana-53971	133	76	x−	x−	PROPN
bibechana-53971	133	77	a1)(x−	a1)(x−	PROPN
bibechana-53971	133	78	a2	a2	PROPN
bibechana-53971	133	79	)	)	PUNCT
bibechana-53971	133	80	(	(	PUNCT
bibechana-53971	133	81	a0	a0	NOUN
bibechana-53971	133	82	−	−	PROPN
bibechana-53971	133	83	a1)(a0	a1)(a0	NOUN
bibechana-53971	133	84	−	−	PROPN
bibechana-53971	133	85	a2	a2	PROPN
bibechana-53971	133	86	)	)	PUNCT
bibechana-53971	133	87	,	,	PUNCT
bibechana-53971	133	88	m1(x	m1(x	NOUN
bibechana-53971	133	89	)	)	PUNCT
bibechana-53971	134	1	=	=	SYM
bibechana-53971	134	2	(	(	PUNCT
bibechana-53971	134	3	x−	x−	PROPN
bibechana-53971	134	4	a0)(x−	a0)(x−	PROPN
bibechana-53971	134	5	a2	a2	PROPN
bibechana-53971	134	6	)	)	PUNCT
bibechana-53971	134	7	(	(	PUNCT
bibechana-53971	134	8	a1	a1	NOUN
bibechana-53971	134	9	−	−	PROPN
bibechana-53971	134	10	a0)(a1	a0)(a1	NOUN
bibechana-53971	134	11	−	−	PROPN
bibechana-53971	134	12	a2	a2	PROPN
bibechana-53971	134	13	)	)	PUNCT
bibechana-53971	134	14	m2(x	m2(x	PROPN
bibechana-53971	134	15	)	)	PUNCT
bibechana-53971	134	16	=	=	SYM
bibechana-53971	134	17	(	(	PUNCT
bibechana-53971	134	18	x−	x−	PROPN
bibechana-53971	134	19	a0)(x−	a0)(x−	PROPN
bibechana-53971	134	20	a1	a1	PROPN
bibechana-53971	134	21	)	)	PUNCT
bibechana-53971	134	22	(	(	PUNCT
bibechana-53971	134	23	a2	a2	PROPN
bibechana-53971	134	24	−	−	PROPN
bibechana-53971	134	25	a0)(a2	a0)(a2	NOUN
bibechana-53971	134	26	−	−	PROPN
bibechana-53971	134	27	a1	a1	NOUN
bibechana-53971	134	28	)	)	PUNCT
bibechana-53971	134	29	in	in	ADP
bibechana-53971	134	30	the	the	DET
bibechana-53971	134	31	formula	formula	NOUN
bibechana-53971	134	32	above	above	ADV
bibechana-53971	134	33	,	,	PUNCT
bibechana-53971	134	34	the	the	DET
bibechana-53971	134	35	polynomial	polynomial	ADJ
bibechana-53971	134	36	p	p	X
bibechana-53971	134	37	(	(	PUNCT
bibechana-53971	134	38	x	x	X
bibechana-53971	134	39	)	)	PUNCT
bibechana-53971	134	40	is	be	AUX
bibechana-53971	134	41	known	know	VERB
bibechana-53971	134	42	as	as	ADP
bibechana-53971	134	43	the	the	DET
bibechana-53971	134	44	lagrange	lagrange	NOUN
bibechana-53971	134	45	’s	’s	PART
bibechana-53971	134	46	interpolating	interpolate	VERB
bibechana-53971	134	47	polynomial	polynomial	ADJ
bibechana-53971	134	48	,	,	PUNCT
bibechana-53971	134	49	and	and	CCONJ
bibechana-53971	134	50	m0	m0	NOUN
bibechana-53971	134	51	,	,	PUNCT
bibechana-53971	134	52	m1	m1	NOUN
bibechana-53971	134	53	,	,	PUNCT
bibechana-53971	134	54	and	and	CCONJ
bibechana-53971	134	55	m2	m2	PROPN
bibechana-53971	134	56	are	be	AUX
bibechana-53971	134	57	the	the	DET
bibechana-53971	134	58	lagrange	lagrange	NOUN
bibechana-53971	134	59	’s	’s	PART
bibechana-53971	134	60	interpolating	interpolate	VERB
bibechana-53971	134	61	basis	basis	NOUN
bibechana-53971	134	62	functions	function	NOUN
bibechana-53971	134	63	.	.	PUNCT
bibechana-53971	135	1	3	3	NUM
bibechana-53971	135	2	mathematical	mathematical	ADJ
bibechana-53971	135	3	and	and	CCONJ
bibechana-53971	135	4	numerical	numerical	ADJ
bibechana-53971	135	5	methods	method	NOUN
bibechana-53971	135	6	in	in	ADP
bibechana-53971	135	7	caputo	caputo	PROPN
bibechana-53971	135	8	-	-	PUNCT
bibechana-53971	135	9	fabrizio	fabrizio	PROPN
bibechana-53971	135	10	sense	sense	NOUN
bibechana-53971	135	11	3.1	3.1	NUM
bibechana-53971	135	12	l1	l1	PROPN
bibechana-53971	135	13	method	method	NOUN
bibechana-53971	135	14	for	for	ADP
bibechana-53971	135	15	the	the	DET
bibechana-53971	135	16	caputo	caputo	PROPN
bibechana-53971	135	17	fractional	fractional	PROPN
bibechana-53971	135	18	derivative	derivative	PROPN
bibechana-53971	135	19	left	leave	VERB
bibechana-53971	135	20	caputo	caputo	PROPN
bibechana-53971	135	21	fractional	fractional	ADJ
bibechana-53971	135	22	derivatives	derivative	NOUN
bibechana-53971	135	23	are	be	AUX
bibechana-53971	135	24	those	those	DET
bibechana-53971	135	25	fractional	fractional	ADJ
bibechana-53971	135	26	derivatives	derivative	NOUN
bibechana-53971	135	27	of	of	ADP
bibechana-53971	135	28	a	a	DET
bibechana-53971	135	29	function	function	NOUN
bibechana-53971	135	30	that	that	PRON
bibechana-53971	135	31	characterize	characterize	VERB
bibechana-53971	135	32	its	its	PRON
bibechana-53971	135	33	left	left	ADJ
bibechana-53971	135	34	-	-	PUNCT
bibechana-53971	135	35	sided	sided	ADJ
bibechana-53971	135	36	behavior	behavior	NOUN
bibechana-53971	135	37	,	,	PUNCT
bibechana-53971	135	38	and	and	CCONJ
bibechana-53971	135	39	the	the	DET
bibechana-53971	135	40	exact	exact	ADJ
bibechana-53971	135	41	numerical	numerical	ADJ
bibechana-53971	135	42	method	method	NOUN
bibechana-53971	135	43	used	use	VERB
bibechana-53971	135	44	to	to	PART
bibechana-53971	135	45	approximate	approximate	VERB
bibechana-53971	135	46	them	they	PRON
bibechana-53971	135	47	is	be	AUX
bibechana-53971	135	48	called	call	VERB
bibechana-53971	135	49	l1	l1	PROPN
bibechana-53971	135	50	for	for	ADP
bibechana-53971	135	51	0	0	NUM
bibechana-53971	135	52	<	<	X
bibechana-53971	135	53	α	α	X
bibechana-53971	135	54	<	<	X
bibechana-53971	135	55	1	1	NUM
bibechana-53971	135	56	c	c	NOUN
bibechana-53971	135	57	0	0	NUM
bibechana-53971	135	58	dα	dα	PROPN
bibechana-53971	135	59	t	t	PROPN
bibechana-53971	135	60	f(x	f(x	PROPN
bibechana-53971	135	61	)	)	PUNCT
bibechana-53971	136	1	≈	≈	PROPN
bibechana-53971	136	2	1	1	NUM
bibechana-53971	136	3	γ(1−	γ(1−	NOUN
bibechana-53971	136	4	α	α	NUM
bibechana-53971	136	5	)	)	PUNCT
bibechana-53971	136	6	∫	∫	PROPN
bibechana-53971	136	7	x	x	X
bibechana-53971	136	8	0	0	PUNCT
bibechana-53971	136	9	(	(	PUNCT
bibechana-53971	136	10	x−	x−	PROPN
bibechana-53971	136	11	s)−αf	s)−αf	PROPN
bibechana-53971	137	1	′(s)ds	′(s)ds	PROPN
bibechana-53971	137	2	(	(	PUNCT
bibechana-53971	137	3	5	5	NUM
bibechana-53971	137	4	)	)	PUNCT
bibechana-53971	137	5	c	c	NOUN
bibechana-53971	137	6	0	0	NUM
bibechana-53971	138	1	dα	dα	PROPN
bibechana-53971	138	2	t	t	PROPN
bibechana-53971	138	3	f(xn	f(xn	PROPN
bibechana-53971	138	4	)	)	PUNCT
bibechana-53971	139	1	≈	≈	PROPN
bibechana-53971	139	2	1	1	NUM
bibechana-53971	139	3	γ(1−	γ(1−	NOUN
bibechana-53971	139	4	α	α	NUM
bibechana-53971	139	5	)	)	PUNCT
bibechana-53971	139	6	∫	∫	PROPN
bibechana-53971	139	7	xn	xn	PROPN
bibechana-53971	139	8	0	0	NUM
bibechana-53971	140	1	(	(	PUNCT
bibechana-53971	140	2	xn	xn	PROPN
bibechana-53971	140	3	−	−	PROPN
bibechana-53971	140	4	s)−αf	s)−αf	PROPN
bibechana-53971	141	1	′(s)ds	′(s)ds	PROPN
bibechana-53971	141	2	(	(	PUNCT
bibechana-53971	141	3	6	6	NUM
bibechana-53971	141	4	)	)	PUNCT
bibechana-53971	141	5	c	c	NOUN
bibechana-53971	141	6	0	0	NUM
bibechana-53971	142	1	dα	dα	PROPN
bibechana-53971	142	2	t	t	PROPN
bibechana-53971	142	3	f(xn	f(xn	PROPN
bibechana-53971	142	4	)	)	PUNCT
bibechana-53971	143	1	≈	≈	PROPN
bibechana-53971	143	2	1	1	NUM
bibechana-53971	143	3	γ(1−	γ(1−	NOUN
bibechana-53971	143	4	α	α	NUM
bibechana-53971	143	5	)	)	PUNCT
bibechana-53971	143	6	n−1∑	n−1∑	PROPN
bibechana-53971	143	7	k=0	k=0	PROPN
bibechana-53971	143	8	∫	∫	PROPN
bibechana-53971	143	9	xk+1	xk+1	PROPN
bibechana-53971	143	10	xk	xk	PROPN
bibechana-53971	144	1	(	(	PUNCT
bibechana-53971	144	2	xn	xn	PROPN
bibechana-53971	144	3	−	−	PROPN
bibechana-53971	144	4	s)−αf	s)−αf	PROPN
bibechana-53971	145	1	′(s)ds	′(s)ds	PROPN
bibechana-53971	145	2	now	now	ADV
bibechana-53971	145	3	we	we	PRON
bibechana-53971	145	4	replace	replace	VERB
bibechana-53971	145	5	first	first	ADJ
bibechana-53971	145	6	-	-	PUNCT
bibechana-53971	145	7	order	order	NOUN
bibechana-53971	145	8	derivative	derivative	NOUN
bibechana-53971	145	9	in	in	ADP
bibechana-53971	145	10	6	6	NUM
bibechana-53971	145	11	by	by	ADP
bibechana-53971	145	12	forward	forward	ADJ
bibechana-53971	145	13	difference	difference	NOUN
bibechana-53971	145	14	quotient	quotient	NOUN
bibechana-53971	145	15	as	as	SCONJ
bibechana-53971	145	16	follows	follow	VERB
bibechana-53971	145	17	:	:	PUNCT
bibechana-53971	145	18	c	c	NOUN
bibechana-53971	145	19	0	0	PUNCT
bibechana-53971	145	20	dα	dα	PROPN
bibechana-53971	145	21	t	t	PROPN
bibechana-53971	145	22	f(xn	f(xn	PROPN
bibechana-53971	145	23	)	)	PUNCT
bibechana-53971	146	1	≈	≈	PROPN
bibechana-53971	146	2	1	1	NUM
bibechana-53971	146	3	hγ(1−	hγ(1−	PROPN
bibechana-53971	146	4	α	α	NOUN
bibechana-53971	146	5	)	)	PUNCT
bibechana-53971	146	6	n−1∑	n−1∑	PROPN
bibechana-53971	146	7	k=0	k=0	PUNCT
bibechana-53971	147	1	[	[	X
bibechana-53971	147	2	f(xk+1	f(xk+1	VERB
bibechana-53971	147	3	−	−	PRON
bibechana-53971	147	4	f(xk	f(xk	NOUN
bibechana-53971	147	5	)	)	PUNCT
bibechana-53971	147	6	]	]	PUNCT
bibechana-53971	148	1	c	c	X
bibechana-53971	148	2	0	0	PUNCT
bibechana-53971	148	3	dα	dα	PROPN
bibechana-53971	148	4	t	t	PROPN
bibechana-53971	148	5	f(xn	f(xn	PROPN
bibechana-53971	148	6	)	)	PUNCT
bibechana-53971	149	1	≈	≈	PROPN
bibechana-53971	149	2	hα	hα	ADP
bibechana-53971	149	3	γ(2−	γ(2−	PROPN
bibechana-53971	149	4	α	α	NOUN
bibechana-53971	149	5	)	)	PUNCT
bibechana-53971	149	6	n−1∑	n−1∑	PROPN
bibechana-53971	149	7	k=0	k=0	PUNCT
bibechana-53971	150	1	[	[	X
bibechana-53971	150	2	f(xk+1)−	f(xk+1)−	NOUN
bibechana-53971	150	3	f(xk	f(xk	NOUN
bibechana-53971	150	4	)	)	PUNCT
bibechana-53971	150	5	]	]	PUNCT
bibechana-53971	151	1	[	[	X
bibechana-53971	151	2	(	(	PUNCT
bibechana-53971	151	3	n−	n−	NOUN
bibechana-53971	151	4	k)(1−α	k)(1−α	NOUN
bibechana-53971	151	5	)	)	PUNCT
bibechana-53971	151	6	−	−	PROPN
bibechana-53971	152	1	(	(	PUNCT
bibechana-53971	152	2	n−	n−	NOUN
bibechana-53971	152	3	k	k	NOUN
bibechana-53971	152	4	−	−	PROPN
bibechana-53971	152	5	1)(1−α	1)(1−α	NUM
bibechana-53971	152	6	)	)	PUNCT
bibechana-53971	152	7	]	]	PUNCT
bibechana-53971	152	8	is	be	AUX
bibechana-53971	152	9	known	know	VERB
bibechana-53971	152	10	as	as	ADP
bibechana-53971	152	11	the	the	DET
bibechana-53971	152	12	l1	l1	PROPN
bibechana-53971	152	13	approach	approach	NOUN
bibechana-53971	152	14	for	for	ADP
bibechana-53971	152	15	caputo	caputo	PROPN
bibechana-53971	152	16	fractional	fractional	PROPN
bibechana-53971	152	17	derivative	derivative	PROPN
bibechana-53971	152	18	.	.	PUNCT
bibechana-53971	153	1	this	this	DET
bibechana-53971	153	2	method	method	NOUN
bibechana-53971	153	3	is	be	AUX
bibechana-53971	153	4	the	the	DET
bibechana-53971	153	5	most	most	ADV
bibechana-53971	153	6	popular	popular	ADJ
bibechana-53971	153	7	way	way	NOUN
bibechana-53971	153	8	to	to	PART
bibechana-53971	153	9	approximate	approximate	VERB
bibechana-53971	153	10	the	the	DET
bibechana-53971	153	11	caputo	caputo	PROPN
bibechana-53971	153	12	fractional	fractional	ADJ
bibechana-53971	153	13	derivatives	derivative	NOUN
bibechana-53971	153	14	of	of	ADP
bibechana-53971	153	15	a	a	DET
bibechana-53971	153	16	function	function	NOUN
bibechana-53971	153	17	.	.	PUNCT
bibechana-53971	154	1	using	use	VERB
bibechana-53971	154	2	computer	computer	NOUN
bibechana-53971	154	3	tools	tool	NOUN
bibechana-53971	154	4	,	,	PUNCT
bibechana-53971	154	5	we	we	PRON
bibechana-53971	154	6	have	have	AUX
bibechana-53971	154	7	since	since	SCONJ
bibechana-53971	154	8	conducted	conduct	VERB
bibechana-53971	154	9	a	a	DET
bibechana-53971	154	10	more	more	ADV
bibechana-53971	154	11	thorough	thorough	ADJ
bibechana-53971	154	12	analysis	analysis	NOUN
bibechana-53971	154	13	of	of	ADP
bibechana-53971	154	14	the	the	DET
bibechana-53971	154	15	numerical	numerical	ADJ
bibechana-53971	154	16	method	method	NOUN
bibechana-53971	154	17	and	and	CCONJ
bibechana-53971	154	18	compare	compare	VERB
bibechana-53971	154	19	it	it	PRON
bibechana-53971	154	20	to	to	ADP
bibechana-53971	154	21	the	the	DET
bibechana-53971	154	22	precise	precise	ADJ
bibechana-53971	154	23	solution	solution	NOUN
bibechana-53971	154	24	.	.	PUNCT
bibechana-53971	155	1	3.2	3.2	NUM
bibechana-53971	155	2	l2	l2	NOUN
bibechana-53971	155	3	method	method	NOUN
bibechana-53971	155	4	for	for	ADP
bibechana-53971	155	5	the	the	DET
bibechana-53971	155	6	caputo	caputo	PROPN
bibechana-53971	155	7	fractional	fractional	PROPN
bibechana-53971	155	8	derivative	derivative	PROPN
bibechana-53971	155	9	the	the	DET
bibechana-53971	155	10	left	left	ADJ
bibechana-53971	155	11	caputo	caputo	PROPN
bibechana-53971	155	12	fractional	fractional	PROPN
bibechana-53971	155	13	derivative	derivative	NOUN
bibechana-53971	155	14	can	can	AUX
bibechana-53971	155	15	be	be	AUX
bibechana-53971	155	16	approximated	approximate	VERB
bibechana-53971	155	17	via	via	ADP
bibechana-53971	155	18	the	the	DET
bibechana-53971	155	19	l2	l2	NOUN
bibechana-53971	155	20	approach	approach	NOUN
bibechana-53971	155	21	c	c	NOUN
bibechana-53971	155	22	0	0	NUM
bibechana-53971	156	1	dα	dα	NOUN
bibechana-53971	156	2	xf(x	xf(x	PUNCT
bibechana-53971	156	3	)	)	PUNCT
bibechana-53971	157	1	≈	≈	PROPN
bibechana-53971	157	2	1	1	NUM
bibechana-53971	157	3	γ(2−	γ(2−	PROPN
bibechana-53971	157	4	α	α	NOUN
bibechana-53971	157	5	)	)	PUNCT
bibechana-53971	157	6	∫	∫	PROPN
bibechana-53971	157	7	x	x	X
bibechana-53971	157	8	0	0	PUNCT
bibechana-53971	157	9	(	(	PUNCT
bibechana-53971	157	10	x−	x−	PROPN
bibechana-53971	157	11	s)1−αf	s)1−αf	PROPN
bibechana-53971	157	12	′′(s	′′(s	PROPN
bibechana-53971	157	13	)	)	PUNCT
bibechana-53971	157	14	·	·	PUNCT
bibechana-53971	158	1	ds	ds	ADJ
bibechana-53971	158	2	,	,	PUNCT
bibechana-53971	158	3	(	(	PUNCT
bibechana-53971	158	4	1	1	NUM
bibechana-53971	158	5	<	<	X
bibechana-53971	158	6	α	α	X
bibechana-53971	158	7	<	<	X
bibechana-53971	158	8	2	2	NUM
bibechana-53971	158	9	)	)	PUNCT
bibechana-53971	158	10	(	(	PUNCT
bibechana-53971	158	11	7)∫	7)∫	NOUN
bibechana-53971	158	12	a	a	DET
bibechana-53971	158	13	0	0	NUM
bibechana-53971	158	14	f(x)dx	f(x)dx	NUM
bibechana-53971	158	15	=	=	SYM
bibechana-53971	158	16	∫	∫	PROPN
bibechana-53971	158	17	a	a	DET
bibechana-53971	158	18	0	0	NUM
bibechana-53971	158	19	f(a−	f(a−	PROPN
bibechana-53971	158	20	x)dx	x)dx	PROPN
bibechana-53971	158	21	(	(	PUNCT
bibechana-53971	158	22	8)	8)	NUM
bibechana-53971	158	23	from	from	ADP
bibechana-53971	158	24	(	(	PUNCT
bibechana-53971	158	25	7	7	NUM
bibechana-53971	158	26	)	)	PUNCT
bibechana-53971	158	27	and	and	CCONJ
bibechana-53971	158	28	(	(	PUNCT
bibechana-53971	158	29	8)	8)	NUM
bibechana-53971	158	30	as	as	SCONJ
bibechana-53971	158	31	follows	follow	VERB
bibechana-53971	158	32	,	,	PUNCT
bibechana-53971	158	33	c	c	PROPN
bibechana-53971	158	34	0	0	NUM
bibechana-53971	158	35	dα	dα	ADJ
bibechana-53971	158	36	xf(x	xf(x	PUNCT
bibechana-53971	158	37	)	)	PUNCT
bibechana-53971	159	1	≈	≈	PROPN
bibechana-53971	159	2	1	1	NUM
bibechana-53971	159	3	γ(2−	γ(2−	PROPN
bibechana-53971	159	4	α	α	NOUN
bibechana-53971	159	5	)	)	PUNCT
bibechana-53971	159	6	∫	∫	PROPN
bibechana-53971	159	7	xn	xn	PROPN
bibechana-53971	159	8	0	0	NUM
bibechana-53971	160	1	(	(	PUNCT
bibechana-53971	160	2	s)1−αf	s)1−αf	X
bibechana-53971	160	3	′′(xn	′′(xn	PUNCT
bibechana-53971	160	4	−	−	PROPN
bibechana-53971	160	5	s)ds	s)ds	PROPN
bibechana-53971	160	6	,	,	PUNCT
bibechana-53971	160	7	c	c	PROPN
bibechana-53971	160	8	0	0	NUM
bibechana-53971	160	9	dα	dα	PROPN
bibechana-53971	160	10	xf(xn	xf(xn	PROPN
bibechana-53971	160	11	)	)	PUNCT
bibechana-53971	161	1	≈	≈	PROPN
bibechana-53971	161	2	1	1	NUM
bibechana-53971	161	3	h2(2−	h2(2−	NOUN
bibechana-53971	161	4	α)γ(2−	α)γ(2−	PROPN
bibechana-53971	161	5	α	α	NOUN
bibechana-53971	161	6	)	)	PUNCT
bibechana-53971	161	7	(	(	PUNCT
bibechana-53971	161	8	s)1−α	s)1−α	ADJ
bibechana-53971	161	9	n−1∑	n−1∑	PROPN
bibechana-53971	161	10	k=0	k=0	PUNCT
bibechana-53971	162	1	[	[	X
bibechana-53971	162	2	f(xn	f(xn	ADP
bibechana-53971	162	3	−	−	ADP
bibechana-53971	162	4	xk+1)−	xk+1)−	PROPN
bibechana-53971	162	5	2f(xn	2f(xn	NUM
bibechana-53971	162	6	−	−	NUM
bibechana-53971	162	7	xk	xk	PROPN
bibechana-53971	162	8	)	)	PUNCT
bibechana-53971	162	9	+	+	CCONJ
bibechana-53971	162	10	f(xn	f(xn	PROPN
bibechana-53971	162	11	−	−	PROPN
bibechana-53971	162	12	xk−1	xk−1	PROPN
bibechana-53971	162	13	)	)	PUNCT
bibechana-53971	162	14	]	]	PUNCT
bibechana-53971	163	1	[	[	X
bibechana-53971	163	2	(	(	PUNCT
bibechana-53971	163	3	xk+1	xk+1	NUM
bibechana-53971	163	4	)	)	PUNCT
bibechana-53971	163	5	(	(	PUNCT
bibechana-53971	163	6	2−α	2−α	NUM
bibechana-53971	163	7	)	)	PUNCT
bibechana-53971	163	8	−	−	PROPN
bibechana-53971	163	9	(	(	PUNCT
bibechana-53971	163	10	xk	xk	PROPN
bibechana-53971	163	11	)	)	PUNCT
bibechana-53971	163	12	(	(	PUNCT
bibechana-53971	163	13	2−α	2−α	NUM
bibechana-53971	163	14	)	)	PUNCT
bibechana-53971	163	15	]	]	PUNCT
bibechana-53971	163	16	l2	l2	NOUN
bibechana-53971	163	17	method	method	NOUN
bibechana-53971	163	18	for	for	ADP
bibechana-53971	163	19	obtaining	obtain	VERB
bibechana-53971	163	20	caputo	caputo	PROPN
bibechana-53971	163	21	fractional	fractional	ADJ
bibechana-53971	163	22	derivatives	derivative	NOUN
bibechana-53971	163	23	is	be	AUX
bibechana-53971	163	24	,	,	PUNCT
bibechana-53971	163	25	c	c	PROPN
bibechana-53971	163	26	0	0	PUNCT
bibechana-53971	163	27	dα	dα	PROPN
bibechana-53971	163	28	xf(xn	xf(xn	PROPN
bibechana-53971	163	29	)	)	PUNCT
bibechana-53971	164	1	≈	≈	PROPN
bibechana-53971	164	2	n−1∑	n−1∑	PROPN
bibechana-53971	164	3	k=0	k=0	PROPN
bibechana-53971	164	4	wkf(xn−k	wkf(xn−k	PROPN
bibechana-53971	164	5	)	)	PUNCT
bibechana-53971	164	6	(	(	PUNCT
bibechana-53971	164	7	9	9	X
bibechana-53971	164	8	)	)	PUNCT
bibechana-53971	164	9	such	such	ADJ
bibechana-53971	164	10	that	that	SCONJ
bibechana-53971	164	11	where	where	SCONJ
bibechana-53971	164	12	wk	wk	PRON
bibechana-53971	164	13	is	be	AUX
bibechana-53971	164	14	the	the	DET
bibechana-53971	164	15	normalizing	normalizing	ADJ
bibechana-53971	164	16	factor	factor	NOUN
bibechana-53971	164	17	and	and	CCONJ
bibechana-53971	164	18	k	k	PROPN
bibechana-53971	164	19	has	have	VERB
bibechana-53971	164	20	a	a	DET
bibechana-53971	164	21	range	range	NOUN
bibechana-53971	164	22	of	of	ADP
bibechana-53971	164	23	values	value	NOUN
bibechana-53971	164	24	between	between	ADP
bibechana-53971	164	25	−1	−1	NOUN
bibechana-53971	164	26	and	and	CCONJ
bibechana-53971	164	27	n.	n.	NOUN
bibechana-53971	164	28	it	it	PRON
bibechana-53971	164	29	is	be	AUX
bibechana-53971	164	30	generally	generally	ADV
bibechana-53971	164	31	acknowledged	acknowledge	VERB
bibechana-53971	164	32	that	that	SCONJ
bibechana-53971	164	33	the	the	DET
bibechana-53971	164	34	l2	l2	NOUN
bibechana-53971	164	35	approach	approach	NOUN
bibechana-53971	164	36	for	for	ADP
bibechana-53971	164	37	caputo	caputo	PROPN
bibechana-53971	164	38	fractional	fractional	PROPN
bibechana-53971	164	39	derivative	derivative	PROPN
bibechana-53971	164	40	is	be	AUX
bibechana-53971	164	41	the	the	DET
bibechana-53971	164	42	preferred	preferred	ADJ
bibechana-53971	164	43	method	method	NOUN
bibechana-53971	164	44	for	for	ADP
bibechana-53971	164	45	approximating	approximate	VERB
bibechana-53971	164	46	fractional	fractional	ADJ
bibechana-53971	164	47	caputo	caputo	PROPN
bibechana-53971	164	48	derivatives	derivative	NOUN
bibechana-53971	164	49	of	of	ADP
bibechana-53971	164	50	functions	function	NOUN
bibechana-53971	164	51	.	.	PUNCT
bibechana-53971	165	1	recently	recently	ADV
bibechana-53971	165	2	,	,	PUNCT
bibechana-53971	165	3	a	a	DET
bibechana-53971	165	4	more	more	ADV
bibechana-53971	165	5	thorough	thorough	ADJ
bibechana-53971	165	6	analysis	analysis	NOUN
bibechana-53971	165	7	of	of	ADP
bibechana-53971	165	8	this	this	DET
bibechana-53971	165	9	numerical	numerical	ADJ
bibechana-53971	165	10	method	method	NOUN
bibechana-53971	165	11	was	be	AUX
bibechana-53971	165	12	done	do	VERB
bibechana-53971	165	13	,	,	PUNCT
bibechana-53971	165	14	and	and	CCONJ
bibechana-53971	165	15	the	the	DET
bibechana-53971	165	16	results	result	NOUN
bibechana-53971	165	17	were	be	AUX
bibechana-53971	165	18	compared	compare	VERB
bibechana-53971	165	19	to	to	ADP
bibechana-53971	165	20	the	the	DET
bibechana-53971	165	21	exact	exact	ADJ
bibechana-53971	165	22	ones	one	NOUN
bibechana-53971	165	23	.	.	PUNCT
bibechana-53971	166	1	3.3	3.3	NUM
bibechana-53971	166	2	l1	l1	PROPN
bibechana-53971	166	3	method	method	NOUN
bibechana-53971	166	4	for	for	ADP
bibechana-53971	166	5	the	the	DET
bibechana-53971	166	6	caputo	caputo	PROPN
bibechana-53971	166	7	fabrizio	fabrizio	PROPN
bibechana-53971	166	8	derivative	derivative	PROPN
bibechana-53971	166	9	the	the	DET
bibechana-53971	166	10	caputo	caputo	PROPN
bibechana-53971	166	11	fabrizio	fabrizio	PROPN
bibechana-53971	166	12	differential	differential	NOUN
bibechana-53971	166	13	operator	operator	NOUN
bibechana-53971	166	14	is	be	AUX
bibechana-53971	166	15	defined	define	VERB
bibechana-53971	166	16	below	below	ADP
bibechana-53971	166	17	for	for	ADP
bibechana-53971	166	18	0	0	NUM
bibechana-53971	166	19	<	<	X
bibechana-53971	166	20	α	α	X
bibechana-53971	166	21	<	<	X
bibechana-53971	166	22	1	1	NUM
bibechana-53971	166	23	cf	cf	NOUN
bibechana-53971	166	24	0	0	NUM
bibechana-53971	166	25	dα	dα	NOUN
bibechana-53971	166	26	xf(x	xf(x	PUNCT
bibechana-53971	166	27	)	)	PUNCT
bibechana-53971	167	1	≈	≈	PROPN
bibechana-53971	167	2	m(α	m(α	PROPN
bibechana-53971	167	3	)	)	PUNCT
bibechana-53971	167	4	(	(	PUNCT
bibechana-53971	167	5	1−	1−	NUM
bibechana-53971	167	6	α	α	NOUN
bibechana-53971	167	7	)	)	PUNCT
bibechana-53971	167	8	∫	∫	PROPN
bibechana-53971	167	9	x	x	SYM
bibechana-53971	167	10	0	0	NUM
bibechana-53971	167	11	f	f	PROPN
bibechana-53971	167	12	′(s)exp[λ(x−	′(s)exp[λ(x−	PROPN
bibechana-53971	167	13	s)]ds	s)]ds	NOUN
bibechana-53971	167	14	,	,	PUNCT
bibechana-53971	167	15	λ	λ	PROPN
bibechana-53971	167	16	=	=	SYM
bibechana-53971	167	17	−α	−α	PROPN
bibechana-53971	167	18	(	(	PUNCT
bibechana-53971	167	19	1−	1−	NUM
bibechana-53971	167	20	α	α	NOUN
bibechana-53971	167	21	)	)	PUNCT
bibechana-53971	167	22	,	,	PUNCT
bibechana-53971	167	23	(	(	PUNCT
bibechana-53971	167	24	10	10	NUM
bibechana-53971	167	25	)	)	PUNCT
bibechana-53971	167	26	cf	cf	NOUN
bibechana-53971	167	27	0	0	NUM
bibechana-53971	167	28	dα	dα	ADJ
bibechana-53971	167	29	xf(xn	xf(xn	PROPN
bibechana-53971	167	30	)	)	PUNCT
bibechana-53971	168	1	≈	≈	PROPN
bibechana-53971	168	2	m(α	m(α	PROPN
bibechana-53971	168	3	)	)	PUNCT
bibechana-53971	168	4	(	(	PUNCT
bibechana-53971	168	5	1−	1−	NUM
bibechana-53971	168	6	α	α	NOUN
bibechana-53971	168	7	)	)	PUNCT
bibechana-53971	168	8	∫	∫	PROPN
bibechana-53971	168	9	xn	xn	PROPN
bibechana-53971	168	10	0	0	NUM
bibechana-53971	169	1	f	f	PROPN
bibechana-53971	169	2	′(s)exp[λ(xn	′(s)exp[λ(xn	NOUN
bibechana-53971	169	3	−	−	PROPN
bibechana-53971	169	4	s)]ds	s)]ds	NOUN
bibechana-53971	169	5	,	,	PUNCT
bibechana-53971	169	6	(	(	PUNCT
bibechana-53971	169	7	11	11	NUM
bibechana-53971	169	8	)	)	PUNCT
bibechana-53971	169	9	shankar	shankar	PROPN
bibechana-53971	169	10	pariyar	pariyar	PROPN
bibechana-53971	169	11	and	and	CCONJ
bibechana-53971	169	12	jeevan	jeevan	PROPN
bibechana-53971	169	13	kafle	kafle	PROPN
bibechana-53971	169	14	/	/	PUNCT
bibechana-53971	169	15	bibechana	bibechana	PROPN
bibechana-53971	169	16	20	20	NUM
bibechana-53971	169	17	(	(	PUNCT
bibechana-53971	169	18	2023	2023	NUM
bibechana-53971	169	19	)	)	PUNCT
bibechana-53971	169	20	126	126	NUM
bibechana-53971	169	21	-	-	SYM
bibechana-53971	169	22	133	133	NUM
bibechana-53971	169	23	130	130	NUM
bibechana-53971	169	24	cf	cf	NOUN
bibechana-53971	169	25	0	0	NUM
bibechana-53971	169	26	dα	dα	NOUN
bibechana-53971	169	27	xf(xn	xf(xn	PROPN
bibechana-53971	169	28	)	)	PUNCT
bibechana-53971	170	1	≈	≈	PROPN
bibechana-53971	170	2	m(α	m(α	PROPN
bibechana-53971	170	3	)	)	PUNCT
bibechana-53971	170	4	(	(	PUNCT
bibechana-53971	170	5	1−	1−	NUM
bibechana-53971	170	6	α	α	NOUN
bibechana-53971	170	7	)	)	PUNCT
bibechana-53971	170	8	n∑	n∑	NOUN
bibechana-53971	171	1	k=1	k=1	PROPN
bibechana-53971	172	1	∫	∫	PROPN
bibechana-53971	172	2	xk	xk	PROPN
bibechana-53971	173	1	xk−1	xk−1	PROPN
bibechana-53971	173	2	f	f	PROPN
bibechana-53971	173	3	′(s)exp[λ(xn	′(s)exp[λ(xn	NOUN
bibechana-53971	173	4	−	−	PROPN
bibechana-53971	173	5	s)]ds	s)]ds	NOUN
bibechana-53971	173	6	(	(	PUNCT
bibechana-53971	173	7	12	12	NUM
bibechana-53971	173	8	)	)	PUNCT
bibechana-53971	173	9	now	now	ADV
bibechana-53971	173	10	,	,	PUNCT
bibechana-53971	173	11	we	we	PRON
bibechana-53971	173	12	replace	replace	VERB
bibechana-53971	173	13	first	first	ADJ
bibechana-53971	173	14	-	-	PUNCT
bibechana-53971	173	15	order	order	NOUN
bibechana-53971	173	16	derivative	derivative	NOUN
bibechana-53971	173	17	in	in	ADP
bibechana-53971	173	18	(	(	PUNCT
bibechana-53971	173	19	13	13	NUM
bibechana-53971	173	20	)	)	PUNCT
bibechana-53971	173	21	by	by	ADP
bibechana-53971	173	22	the	the	DET
bibechana-53971	173	23	forward	forward	ADJ
bibechana-53971	173	24	difference	difference	NOUN
bibechana-53971	173	25	quotient	quotient	NOUN
bibechana-53971	173	26	as	as	SCONJ
bibechana-53971	173	27	follows	follow	VERB
bibechana-53971	173	28	:	:	PUNCT
bibechana-53971	174	1	cf	cf	NOUN
bibechana-53971	174	2	0	0	NUM
bibechana-53971	174	3	dα	dα	ADJ
bibechana-53971	174	4	xf(xn	xf(xn	PROPN
bibechana-53971	174	5	)	)	PUNCT
bibechana-53971	175	1	≈	≈	PROPN
bibechana-53971	175	2	m(α	m(α	PROPN
bibechana-53971	175	3	)	)	PUNCT
bibechana-53971	175	4	(	(	PUNCT
bibechana-53971	175	5	1−	1−	NUM
bibechana-53971	175	6	α	α	NOUN
bibechana-53971	175	7	)	)	PUNCT
bibechana-53971	175	8	n∑	n∑	NOUN
bibechana-53971	176	1	k=1	k=1	PROPN
bibechana-53971	177	1	∫	∫	PROPN
bibechana-53971	177	2	xk	xk	PROPN
bibechana-53971	177	3	xk−1	xk−1	PROPN
bibechana-53971	177	4	exp[λ(xn	exp[λ(xn	PROPN
bibechana-53971	177	5	−	−	PROPN
bibechana-53971	177	6	s	s	NOUN
bibechana-53971	177	7	)	)	PUNCT
bibechana-53971	177	8	]	]	PUNCT
bibechana-53971	177	9	[	[	PUNCT
bibechana-53971	177	10	f(xk)−	f(xk)−	NOUN
bibechana-53971	177	11	f(xk−1	f(xk−1	PROPN
bibechana-53971	177	12	)	)	PUNCT
bibechana-53971	177	13	h	h	NOUN
bibechana-53971	177	14	]	]	X
bibechana-53971	177	15	ds	ds	X
bibechana-53971	177	16	(	(	PUNCT
bibechana-53971	177	17	13	13	NUM
bibechana-53971	177	18	)	)	PUNCT
bibechana-53971	177	19	cf	cf	NOUN
bibechana-53971	177	20	0	0	NUM
bibechana-53971	177	21	dα	dα	ADJ
bibechana-53971	177	22	xf(xn	xf(xn	PROPN
bibechana-53971	177	23	)	)	PUNCT
bibechana-53971	178	1	=	=	SYM
bibechana-53971	178	2	m(α	m(α	PROPN
bibechana-53971	178	3	)	)	PUNCT
bibechana-53971	178	4	αh	αh	ADP
bibechana-53971	178	5	∑n	∑n	PROPN
bibechana-53971	178	6	k=1[f(kh	k=1[f(kh	PROPN
bibechana-53971	178	7	)	)	PUNCT
bibechana-53971	178	8	−	−	PROPN
bibechana-53971	179	1	f(k	f(k	PUNCT
bibechana-53971	179	2	−	−	PROPN
bibechana-53971	179	3	1)h	1)h	NUM
bibechana-53971	179	4	]	]	X
bibechana-53971	180	1	[	[	X
bibechana-53971	180	2	exp[λh(n−	exp[λh(n−	X
bibechana-53971	180	3	k)]−	k)]−	PROPN
bibechana-53971	180	4	exp[λh(n−	exp[λh(n−	PROPN
bibechana-53971	181	1	k	k	PROPN
bibechana-53971	182	1	+	+	PROPN
bibechana-53971	182	2	1	1	NUM
bibechana-53971	182	3	)	)	PUNCT
bibechana-53971	182	4	]	]	PUNCT
bibechana-53971	182	5	which	which	PRON
bibechana-53971	182	6	is	be	AUX
bibechana-53971	182	7	a	a	DET
bibechana-53971	182	8	derivative	derivative	NOUN
bibechana-53971	182	9	of	of	ADP
bibechana-53971	182	10	the	the	DET
bibechana-53971	182	11	caputo	caputo	PROPN
bibechana-53971	182	12	fabrizio	fabrizio	PROPN
bibechana-53971	182	13	equation	equation	NOUN
bibechana-53971	182	14	using	use	VERB
bibechana-53971	182	15	the	the	DET
bibechana-53971	182	16	l1	l1	PROPN
bibechana-53971	182	17	method	method	NOUN
bibechana-53971	182	18	.	.	PUNCT
bibechana-53971	183	1	we	we	PRON
bibechana-53971	183	2	demonstrate	demonstrate	VERB
bibechana-53971	183	3	how	how	SCONJ
bibechana-53971	183	4	the	the	DET
bibechana-53971	183	5	three	three	NUM
bibechana-53971	183	6	-	-	PUNCT
bibechana-53971	183	7	point	point	NOUN
bibechana-53971	183	8	backward	backward	ADJ
bibechana-53971	183	9	estimate	estimate	NOUN
bibechana-53971	183	10	method	method	NOUN
bibechana-53971	183	11	,	,	PUNCT
bibechana-53971	183	12	which	which	PRON
bibechana-53971	183	13	we	we	PRON
bibechana-53971	183	14	derive	derive	VERB
bibechana-53971	183	15	from	from	ADP
bibechana-53971	183	16	the	the	DET
bibechana-53971	183	17	linear	linear	PROPN
bibechana-53971	183	18	lagrange	lagrange	PROPN
bibechana-53971	183	19	method	method	NOUN
bibechana-53971	183	20	,	,	PUNCT
bibechana-53971	183	21	was	be	AUX
bibechana-53971	183	22	used	use	VERB
bibechana-53971	183	23	to	to	PART
bibechana-53971	183	24	approximate	approximate	VERB
bibechana-53971	183	25	the	the	DET
bibechana-53971	183	26	caputo	caputo	PROPN
bibechana-53971	183	27	fabrizio	fabrizio	PROPN
bibechana-53971	183	28	derivative	derivative	NOUN
bibechana-53971	183	29	.	.	PUNCT
bibechana-53971	184	1	the	the	DET
bibechana-53971	184	2	cubic	cubic	ADJ
bibechana-53971	184	3	lagrange	lagrange	PROPN
bibechana-53971	184	4	interpolation	interpolation	NOUN
bibechana-53971	184	5	can	can	AUX
bibechana-53971	184	6	be	be	AUX
bibechana-53971	184	7	represented	represent	VERB
bibechana-53971	184	8	with	with	ADP
bibechana-53971	184	9	α	α	NOUN
bibechana-53971	184	10	range	range	NOUN
bibechana-53971	184	11	of	of	ADP
bibechana-53971	184	12	1	1	NUM
bibechana-53971	184	13	<	<	X
bibechana-53971	184	14	α	α	X
bibechana-53971	184	15	<	<	X
bibechana-53971	184	16	2	2	NUM
bibechana-53971	184	17	.	.	NOUN
bibechana-53971	184	18	3.4	3.4	NUM
bibechana-53971	184	19	l1	l1	PROPN
bibechana-53971	184	20	-	-	PUNCT
bibechana-53971	184	21	2	2	NUM
bibechana-53971	184	22	method	method	NOUN
bibechana-53971	184	23	for	for	ADP
bibechana-53971	184	24	caputo	caputo	PROPN
bibechana-53971	184	25	fractional	fractional	PROPN
bibechana-53971	184	26	derivative	derivative	PROPN
bibechana-53971	184	27	the	the	DET
bibechana-53971	184	28	cfd	cfd	NOUN
bibechana-53971	184	29	operator	operator	NOUN
bibechana-53971	184	30	is	be	AUX
bibechana-53971	184	31	defined	define	VERB
bibechana-53971	184	32	below	below	ADP
bibechana-53971	184	33	cf	cf	NOUN
bibechana-53971	184	34	0	0	NUM
bibechana-53971	185	1	dα	dα	PROPN
bibechana-53971	185	2	y	y	PROPN
bibechana-53971	185	3	g(y	g(y	PROPN
bibechana-53971	185	4	)	)	PUNCT
bibechana-53971	186	1	=	=	SYM
bibechana-53971	186	2	m(α	m(α	PROPN
bibechana-53971	186	3	)	)	PUNCT
bibechana-53971	186	4	(	(	PUNCT
bibechana-53971	186	5	1−α	1−α	NUM
bibechana-53971	186	6	)	)	PUNCT
bibechana-53971	186	7	∫	∫	PROPN
bibechana-53971	187	1	y	y	PROPN
bibechana-53971	187	2	0	0	PROPN
bibechana-53971	188	1	g′(u)exp[λ(y−u)]du	g′(u)exp[λ(y−u)]du	NOUN
bibechana-53971	188	2	,	,	PUNCT
bibechana-53971	188	3	λ	λ	PROPN
bibechana-53971	188	4	=	=	VERB
bibechana-53971	188	5	−α	−α	PROPN
bibechana-53971	188	6	(	(	PUNCT
bibechana-53971	188	7	1−α	1−α	NUM
bibechana-53971	188	8	)	)	PUNCT
bibechana-53971	188	9	,	,	PUNCT
bibechana-53971	188	10	α	α	PROPN
bibechana-53971	188	11	∈	∈	PROPN
bibechana-53971	188	12	(	(	PUNCT
bibechana-53971	188	13	0	0	NUM
bibechana-53971	188	14	,	,	PUNCT
bibechana-53971	188	15	1	1	NUM
bibechana-53971	188	16	)	)	PUNCT
bibechana-53971	188	17	.	.	PUNCT
bibechana-53971	189	1	cf	cf	NOUN
bibechana-53971	189	2	0	0	NUM
bibechana-53971	190	1	dα	dα	PROPN
bibechana-53971	190	2	y	y	PROPN
bibechana-53971	190	3	f(yk	f(yk	PROPN
bibechana-53971	190	4	)	)	PUNCT
bibechana-53971	190	5	=	=	SYM
bibechana-53971	190	6	m(α	m(α	PROPN
bibechana-53971	190	7	)	)	PUNCT
bibechana-53971	190	8	(	(	PUNCT
bibechana-53971	190	9	1−α	1−α	NUM
bibechana-53971	190	10	)	)	PUNCT
bibechana-53971	190	11	[	[	PUNCT
bibechana-53971	190	12	∫	∫	PROPN
bibechana-53971	190	13	y1	y1	NOUN
bibechana-53971	190	14	y0	y0	PROPN
bibechana-53971	190	15	g′(u)exp[λ(yk	g′(u)exp[λ(yk	PUNCT
bibechana-53971	191	1	−	−	ADP
bibechana-53971	192	1	u)]du	u)]du	NOUN
bibechana-53971	192	2	+	+	CCONJ
bibechana-53971	192	3	∫	∫	ADJ
bibechana-53971	192	4	y2	y2	NOUN
bibechana-53971	192	5	y1	y1	PROPN
bibechana-53971	192	6	g′(u)exp[λ(yk	g′(u)exp[λ(yk	PUNCT
bibechana-53971	192	7	−	−	ADP
bibechana-53971	192	8	u)]du	u)]du	ADJ
bibechana-53971	192	9	+	+	X
bibechana-53971	192	10	·	·	PUNCT
bibechana-53971	192	11	·	·	PUNCT
bibechana-53971	192	12	·	·	PUNCT
bibechana-53971	193	1	+	+	NUM
bibechana-53971	193	2	∫	∫	X
bibechana-53971	193	3	yk	yk	PROPN
bibechana-53971	193	4	yk−1	yk−1	PROPN
bibechana-53971	193	5	g′(u)exp[λ(yk	g′(u)exp[λ(yk	PUNCT
bibechana-53971	194	1	−	−	ADP
bibechana-53971	195	1	u)]du	u)]du	NOUN
bibechana-53971	195	2	]	]	PUNCT
bibechana-53971	195	3	,	,	PUNCT
bibechana-53971	195	4	using	use	VERB
bibechana-53971	195	5	the	the	DET
bibechana-53971	195	6	quadratic	quadratic	ADJ
bibechana-53971	195	7	lagrange	lagrange	NOUN
bibechana-53971	195	8	interpolation	interpolation	NOUN
bibechana-53971	195	9	with	with	ADP
bibechana-53971	195	10	the	the	DET
bibechana-53971	195	11	points	point	NOUN
bibechana-53971	195	12	(	(	PUNCT
bibechana-53971	195	13	yj−2	yj−2	PROPN
bibechana-53971	195	14	,	,	PUNCT
bibechana-53971	195	15	gj−2	gj−2	PROPN
bibechana-53971	195	16	)	)	PUNCT
bibechana-53971	195	17	,	,	PUNCT
bibechana-53971	195	18	(	(	PUNCT
bibechana-53971	195	19	yj−1	yj−1	PROPN
bibechana-53971	195	20	,	,	PUNCT
bibechana-53971	195	21	gj−1	gj−1	PROPN
bibechana-53971	195	22	)	)	PUNCT
bibechana-53971	195	23	,	,	PUNCT
bibechana-53971	195	24	(	(	PUNCT
bibechana-53971	195	25	yj	yj	PROPN
bibechana-53971	195	26	,	,	PUNCT
bibechana-53971	195	27	gj	gj	PROPN
bibechana-53971	195	28	)	)	PUNCT
bibechana-53971	195	29	for	for	ADP
bibechana-53971	195	30	the	the	DET
bibechana-53971	195	31	backward	backward	ADJ
bibechana-53971	195	32	approximation	approximation	NOUN
bibechana-53971	195	33	first	first	ADJ
bibechana-53971	195	34	order	order	NOUN
bibechana-53971	195	35	derivative	derivative	NOUN
bibechana-53971	195	36	as	as	SCONJ
bibechana-53971	195	37	follows	follow	VERB
bibechana-53971	195	38	,	,	PUNCT
bibechana-53971	195	39	π2,jg(y	π2,jg(y	X
bibechana-53971	195	40	)	)	PUNCT
bibechana-53971	196	1	=	=	NOUN
bibechana-53971	196	2	gj−2	gj−2	X
bibechana-53971	196	3	(	(	PUNCT
bibechana-53971	196	4	y	y	PROPN
bibechana-53971	196	5	−	−	PROPN
bibechana-53971	196	6	yj−1)(y	yj−1)(y	PROPN
bibechana-53971	196	7	−	−	PROPN
bibechana-53971	196	8	yj	yj	PROPN
bibechana-53971	196	9	)	)	PUNCT
bibechana-53971	196	10	(	(	PUNCT
bibechana-53971	196	11	yj−2	yj−2	PROPN
bibechana-53971	196	12	−	−	PROPN
bibechana-53971	196	13	yj−1)(yj−2	yj−1)(yj−2	PROPN
bibechana-53971	196	14	−	−	PROPN
bibechana-53971	196	15	yj	yj	PROPN
bibechana-53971	196	16	)	)	PUNCT
bibechana-53971	196	17	+	+	NUM
bibechana-53971	196	18	gj−1	gj−1	NOUN
bibechana-53971	196	19	(	(	PUNCT
bibechana-53971	196	20	y	y	PROPN
bibechana-53971	196	21	−	−	PROPN
bibechana-53971	196	22	yj−2)(y	yj−2)(y	PROPN
bibechana-53971	196	23	−	−	PROPN
bibechana-53971	196	24	yj	yj	PROPN
bibechana-53971	196	25	)	)	PUNCT
bibechana-53971	196	26	(	(	PUNCT
bibechana-53971	196	27	yj−1	yj−1	PROPN
bibechana-53971	196	28	−	−	PROPN
bibechana-53971	196	29	yj−2)(yj−1	yj−2)(yj−1	PROPN
bibechana-53971	196	30	−	−	PROPN
bibechana-53971	196	31	yj	yj	PROPN
bibechana-53971	196	32	)	)	PUNCT
bibechana-53971	197	1	+	+	NUM
bibechana-53971	197	2	gj	gj	NOUN
bibechana-53971	197	3	(	(	PUNCT
bibechana-53971	197	4	y	y	PROPN
bibechana-53971	197	5	−	−	PROPN
bibechana-53971	197	6	yj−2)(y	yj−2)(y	PROPN
bibechana-53971	197	7	−	−	PROPN
bibechana-53971	197	8	yj−1	yj−1	PROPN
bibechana-53971	197	9	)	)	PUNCT
bibechana-53971	197	10	(	(	PUNCT
bibechana-53971	197	11	yj	yj	PROPN
bibechana-53971	197	12	−	−	PROPN
bibechana-53971	197	13	yj−2)(yj	yj−2)(yj	PROPN
bibechana-53971	197	14	−	−	PROPN
bibechana-53971	197	15	yj−1	yj−1	PROPN
bibechana-53971	197	16	)	)	PUNCT
bibechana-53971	197	17	where	where	SCONJ
bibechana-53971	197	18	t	t	PROPN
bibechana-53971	197	19	∈	∈	PROPN
bibechana-53971	197	20	[	[	X
bibechana-53971	197	21	tj−1	tj−1	PROPN
bibechana-53971	197	22	,	,	PUNCT
bibechana-53971	197	23	tj	tj	NOUN
bibechana-53971	197	24	]	]	PUNCT
bibechana-53971	197	25	for	for	ADP
bibechana-53971	197	26	2	2	NUM
bibechana-53971	197	27	≤	≤	NUM
bibechana-53971	197	28	j	j	PROPN
bibechana-53971	197	29	≤	≤	PROPN
bibechana-53971	197	30	k	k	PROPN
bibechana-53971	197	31	and	and	CCONJ
bibechana-53971	197	32	yj	yj	PROPN
bibechana-53971	197	33	=	=	PROPN
bibechana-53971	197	34	jh	jh	PROPN
bibechana-53971	197	35	,	,	PUNCT
bibechana-53971	197	36	yj−1	yj−1	PROPN
bibechana-53971	197	37	=	=	SYM
bibechana-53971	197	38	(	(	PUNCT
bibechana-53971	197	39	j	j	PROPN
bibechana-53971	197	40	−	−	PROPN
bibechana-53971	197	41	1)h	1)h	PROPN
bibechana-53971	197	42	.	.	PUNCT
bibechana-53971	197	43	π2,j(g(y	π2,j(g(y	NUM
bibechana-53971	197	44	)	)	PUNCT
bibechana-53971	197	45	)	)	PUNCT
bibechana-53971	198	1	=	=	PUNCT
bibechana-53971	198	2	gj−2	gj−2	NOUN
bibechana-53971	198	3	2h2	2h2	NUM
bibechana-53971	199	1	[	[	X
bibechana-53971	199	2	(	(	PUNCT
bibechana-53971	199	3	y	y	PROPN
bibechana-53971	199	4	−	−	PROPN
bibechana-53971	199	5	yj−1)(y	yj−1)(y	PROPN
bibechana-53971	199	6	−	−	PROPN
bibechana-53971	199	7	yj)]+	yj)]+	PROPN
bibechana-53971	199	8	fj−1	fj−1	PROPN
bibechana-53971	199	9	h	h	PROPN
bibechana-53971	200	1	[	[	X
bibechana-53971	200	2	(	(	PUNCT
bibechana-53971	200	3	x−	x−	PROPN
bibechana-53971	200	4	xj−2)(xj	xj−2)(xj	PROPN
bibechana-53971	201	1	−	−	PUNCT
bibechana-53971	202	1	x	x	X
bibechana-53971	202	2	)	)	PUNCT
bibechana-53971	202	3	+	+	CCONJ
bibechana-53971	202	4	gj	gj	NOUN
bibechana-53971	202	5	2h2	2h2	NUM
bibechana-53971	203	1	[	[	X
bibechana-53971	203	2	(	(	PUNCT
bibechana-53971	203	3	y	y	PROPN
bibechana-53971	203	4	−	−	PROPN
bibechana-53971	203	5	yj−2)(y	yj−2)(y	PROPN
bibechana-53971	203	6	−	−	PROPN
bibechana-53971	203	7	yj−1	yj−1	PROPN
bibechana-53971	203	8	)	)	PUNCT
bibechana-53971	203	9	]	]	PUNCT
bibechana-53971	203	10	π′	π′	NUM
bibechana-53971	203	11	2j(g(y	2j(g(y	NUM
bibechana-53971	203	12	)	)	PUNCT
bibechana-53971	203	13	)	)	PUNCT
bibechana-53971	204	1	=	=	PUNCT
bibechana-53971	204	2	gj−2	gj−2	NOUN
bibechana-53971	204	3	2h2	2h2	NUM
bibechana-53971	205	1	[	[	X
bibechana-53971	205	2	(	(	PUNCT
bibechana-53971	205	3	2y	2y	PROPN
bibechana-53971	205	4	−	−	PROPN
bibechana-53971	205	5	yj−1	yj−1	PROPN
bibechana-53971	205	6	−	−	PROPN
bibechana-53971	205	7	yj	yj	PROPN
bibechana-53971	205	8	)	)	PUNCT
bibechana-53971	205	9	]	]	PUNCT
bibechana-53971	206	1	+	+	CCONJ
bibechana-53971	206	2	gj−1	gj−1	NOUN
bibechana-53971	206	3	h	h	NOUN
bibechana-53971	207	1	[	[	X
bibechana-53971	207	2	−2y	−2y	PROPN
bibechana-53971	207	3	−	−	PROPN
bibechana-53971	207	4	yj−2	yj−2	PROPN
bibechana-53971	207	5	+	+	CCONJ
bibechana-53971	207	6	yj	yj	PROPN
bibechana-53971	207	7	]	]	PUNCT
bibechana-53971	208	1	+	+	CCONJ
bibechana-53971	208	2	fj	fj	NUM
bibechana-53971	208	3	2h2	2h2	NUM
bibechana-53971	209	1	[	[	X
bibechana-53971	209	2	2y	2y	NUM
bibechana-53971	209	3	−	−	PROPN
bibechana-53971	209	4	yj−2	yj−2	PROPN
bibechana-53971	209	5	−	−	PROPN
bibechana-53971	209	6	yj−1	yj−1	PROPN
bibechana-53971	209	7	]	]	PUNCT
bibechana-53971	209	8	cf	cf	NOUN
bibechana-53971	209	9	0	0	NUM
bibechana-53971	209	10	dα	dα	PROPN
bibechana-53971	209	11	y	y	PROPN
bibechana-53971	209	12	g(yk	g(yk	PROPN
bibechana-53971	209	13	)	)	PUNCT
bibechana-53971	210	1	≈	≈	PROPN
bibechana-53971	210	2	(	(	PUNCT
bibechana-53971	210	3	g1	g1	PROPN
bibechana-53971	210	4	−	−	PROPN
bibechana-53971	210	5	g0	g0	PROPN
bibechana-53971	210	6	)	)	PUNCT
bibechana-53971	210	7	αh	αh	NOUN
bibechana-53971	210	8	(	(	PUNCT
bibechana-53971	210	9	δ1,k	δ1,k	PROPN
bibechana-53971	210	10	−	−	PROPN
bibechana-53971	210	11	δ0,k	δ0,k	PROPN
bibechana-53971	210	12	)	)	PUNCT
bibechana-53971	211	1	+	+	CCONJ
bibechana-53971	211	2	1	1	NUM
bibechana-53971	211	3	α	α	NOUN
bibechana-53971	211	4	k∑	k∑	NOUN
bibechana-53971	211	5	j=2	j=2	PROPN
bibechana-53971	211	6	[	[	PUNCT
bibechana-53971	211	7	gj−2	gj−2	PROPN
bibechana-53971	211	8	2h	2h	NUM
bibechana-53971	211	9	(	(	PUNCT
bibechana-53971	211	10	1−	1−	NUM
bibechana-53971	211	11	2j	2j	NUM
bibechana-53971	211	12	)	)	PUNCT
bibechana-53971	211	13	+	+	CCONJ
bibechana-53971	211	14	gj−1	gj−1	NOUN
bibechana-53971	211	15	h	h	NOUN
bibechana-53971	211	16	(	(	PUNCT
bibechana-53971	211	17	2j	2j	NUM
bibechana-53971	211	18	−	−	NOUN
bibechana-53971	211	19	2	2	NUM
bibechana-53971	211	20	)	)	PUNCT
bibechana-53971	211	21	+	+	NUM
bibechana-53971	211	22	gj	gj	PROPN
bibechana-53971	211	23	2h	2h	NUM
bibechana-53971	211	24	(	(	PUNCT
bibechana-53971	211	25	3−	3−	PROPN
bibechana-53971	211	26	2j)(δj	2j)(δj	NUM
bibechana-53971	211	27	,	,	PUNCT
bibechana-53971	211	28	k	k	PROPN
bibechana-53971	211	29	−	−	PROPN
bibechana-53971	211	30	δj−1,k)+	δj−1,k)+	PROPN
bibechana-53971	211	31	gj−2	gj−2	PROPN
bibechana-53971	211	32	−	−	PROPN
bibechana-53971	211	33	2gj−1	2gj−1	PROPN
bibechana-53971	211	34	+	+	CCONJ
bibechana-53971	211	35	gj	gj	NOUN
bibechana-53971	211	36	)	)	PUNCT
bibechana-53971	211	37	h2	h2	NOUN
bibechana-53971	211	38	(	(	PUNCT
bibechana-53971	211	39	yjδj	yjδj	NOUN
bibechana-53971	211	40	,	,	PUNCT
bibechana-53971	211	41	k)−	k)−	PROPN
bibechana-53971	211	42	(	(	PUNCT
bibechana-53971	211	43	1−	1−	NUM
bibechana-53971	211	44	α	α	NOUN
bibechana-53971	211	45	)	)	PUNCT
bibechana-53971	211	46	α	α	PROPN
bibechana-53971	211	47	δj	δj	NOUN
bibechana-53971	211	48	,	,	PUNCT
bibechana-53971	211	49	k	k	PROPN
bibechana-53971	211	50	−	−	PROPN
bibechana-53971	211	51	yj−1δj−1,k	yj−1δj−1,k	PROPN
bibechana-53971	211	52	+	+	CCONJ
bibechana-53971	211	53	1−	1−	NUM
bibechana-53971	211	54	α	α	NUM
bibechana-53971	211	55	α	α	PROPN
bibechana-53971	211	56	(	(	PUNCT
bibechana-53971	211	57	δj−1,k	δj−1,k	PROPN
bibechana-53971	211	58	)	)	PUNCT
bibechana-53971	211	59	]	]	PUNCT
bibechana-53971	211	60	4	4	NUM
bibechana-53971	211	61	test	test	NOUN
bibechana-53971	211	62	examples	example	NOUN
bibechana-53971	211	63	,	,	PUNCT
bibechana-53971	211	64	relation	relation	NOUN
bibechana-53971	211	65	between	between	ADP
bibechana-53971	211	66	the	the	DET
bibechana-53971	211	67	function	function	NOUN
bibechana-53971	211	68	f(x	f(x	PROPN
bibechana-53971	211	69	)	)	PUNCT
bibechana-53971	212	1	=	=	SYM
bibechana-53971	212	2	e−x	e−x	NOUN
bibechana-53971	212	3	and	and	CCONJ
bibechana-53971	212	4	its	its	PRON
bibechana-53971	212	5	l1	l1	PROPN
bibechana-53971	212	6	fractional	fractional	PROPN
bibechana-53971	212	7	derivative	derivative	PROPN
bibechana-53971	212	8	d0.5f(x	d0.5f(x	NOUN
bibechana-53971	212	9	)	)	PUNCT
bibechana-53971	212	10	figure	figure	NOUN
bibechana-53971	212	11	1	1	NUM
bibechana-53971	212	12	:	:	PUNCT
bibechana-53971	212	13	l1	l1	PROPN
bibechana-53971	212	14	fractional	fractional	PROPN
bibechana-53971	212	15	derivative	derivative	NOUN
bibechana-53971	212	16	,	,	PUNCT
bibechana-53971	212	17	d0.5f(x	d0.5f(x	PROPN
bibechana-53971	212	18	)	)	PUNCT
bibechana-53971	212	19	a	a	DET
bibechana-53971	212	20	continuous	continuous	ADJ
bibechana-53971	212	21	blue	blue	ADJ
bibechana-53971	212	22	curve	curve	NOUN
bibechana-53971	212	23	for	for	ADP
bibechana-53971	212	24	the	the	DET
bibechana-53971	212	25	function	function	NOUN
bibechana-53971	212	26	f(x	f(x	PROPN
bibechana-53971	212	27	)	)	PUNCT
bibechana-53971	213	1	=	=	SYM
bibechana-53971	213	2	e−x	e−x	NOUN
bibechana-53971	213	3	and	and	CCONJ
bibechana-53971	213	4	a	a	DET
bibechana-53971	213	5	dashed	dash	VERB
bibechana-53971	213	6	red	red	ADJ
bibechana-53971	213	7	curve	curve	NOUN
bibechana-53971	213	8	for	for	ADP
bibechana-53971	213	9	d0.5f(x	d0.5f(x	NOUN
bibechana-53971	213	10	)	)	PUNCT
bibechana-53971	213	11	will	will	AUX
bibechana-53971	213	12	be	be	AUX
bibechana-53971	213	13	displayed	display	VERB
bibechana-53971	213	14	on	on	ADP
bibechana-53971	213	15	the	the	DET
bibechana-53971	213	16	same	same	ADJ
bibechana-53971	213	17	plot	plot	NOUN
bibechana-53971	213	18	in	in	ADP
bibechana-53971	213	19	the	the	DET
bibechana-53971	213	20	two	two	NUM
bibechana-53971	213	21	pictures	picture	NOUN
bibechana-53971	213	22	.	.	PUNCT
bibechana-53971	214	1	the	the	DET
bibechana-53971	214	2	function	function	NOUN
bibechana-53971	214	3	used	use	VERB
bibechana-53971	214	4	in	in	ADP
bibechana-53971	214	5	the	the	DET
bibechana-53971	214	6	instance	instance	NOUN
bibechana-53971	214	7	,	,	PUNCT
bibechana-53971	214	8	f(x	f(x	PROPN
bibechana-53971	214	9	)	)	PUNCT
bibechana-53971	215	1	=	=	SYM
bibechana-53971	215	2	e−x	e−x	NOUN
bibechana-53971	215	3	,	,	PUNCT
bibechana-53971	215	4	displays	display	VERB
bibechana-53971	215	5	an	an	DET
bibechana-53971	215	6	exponential	exponential	ADJ
bibechana-53971	215	7	decline	decline	NOUN
bibechana-53971	215	8	.	.	PUNCT
bibechana-53971	216	1	the	the	DET
bibechana-53971	216	2	shape	shape	NOUN
bibechana-53971	216	3	of	of	ADP
bibechana-53971	216	4	f(x	f(x	PROPN
bibechana-53971	216	5	)	)	PUNCT
bibechana-53971	216	6	is	be	AUX
bibechana-53971	216	7	determined	determine	VERB
bibechana-53971	216	8	by	by	ADP
bibechana-53971	216	9	the	the	DET
bibechana-53971	216	10	selected	select	VERB
bibechana-53971	216	11	function	function	NOUN
bibechana-53971	216	12	,	,	PUNCT
bibechana-53971	216	13	f(x	f(x	PROPN
bibechana-53971	216	14	)	)	PUNCT
bibechana-53971	217	1	=	=	SYM
bibechana-53971	217	2	e−x	e−x	NOUN
bibechana-53971	217	3	.	.	PUNCT
bibechana-53971	218	1	the	the	DET
bibechana-53971	218	2	first	first	ADJ
bibechana-53971	218	3	derivative	derivative	NOUN
bibechana-53971	218	4	of	of	ADP
bibechana-53971	218	5	the	the	DET
bibechana-53971	218	6	l1	l1	PROPN
bibechana-53971	218	7	fd	fd	PROPN
bibechana-53971	218	8	,	,	PUNCT
bibechana-53971	218	9	which	which	PRON
bibechana-53971	218	10	determines	determine	VERB
bibechana-53971	218	11	the	the	DET
bibechana-53971	218	12	rate	rate	NOUN
bibechana-53971	218	13	of	of	ADP
bibechana-53971	218	14	change	change	NOUN
bibechana-53971	218	15	,	,	PUNCT
bibechana-53971	218	16	is	be	AUX
bibechana-53971	218	17	standardized	standardize	VERB
bibechana-53971	218	18	.	.	PUNCT
bibechana-53971	219	1	because	because	SCONJ
bibechana-53971	219	2	the	the	DET
bibechana-53971	219	3	fact	fact	NOUN
bibechana-53971	219	4	that	that	SCONJ
bibechana-53971	219	5	the	the	DET
bibechana-53971	219	6	l1	l1	PROPN
bibechana-53971	219	7	fd	fd	PROPN
bibechana-53971	219	8	shape	shape	NOUN
bibechana-53971	219	9	uses	use	VERB
bibechana-53971	219	10	the	the	DET
bibechana-53971	219	11	complete	complete	ADJ
bibechana-53971	219	12	history	history	NOUN
bibechana-53971	219	13	of	of	ADP
bibechana-53971	219	14	the	the	DET
bibechana-53971	219	15	function	function	NOUN
bibechana-53971	219	16	and	and	CCONJ
bibechana-53971	219	17	is	be	AUX
bibechana-53971	219	18	a	a	DET
bibechana-53971	219	19	non	non	ADJ
bibechana-53971	219	20	-	-	ADJ
bibechana-53971	219	21	local	local	ADJ
bibechana-53971	219	22	operator	operator	NOUN
bibechana-53971	219	23	,	,	PUNCT
bibechana-53971	219	24	it	it	PRON
bibechana-53971	219	25	is	be	AUX
bibechana-53971	219	26	typically	typically	ADV
bibechana-53971	219	27	smoother	smooth	ADJ
bibechana-53971	219	28	and	and	CCONJ
bibechana-53971	219	29	less	less	ADV
bibechana-53971	219	30	noisy	noisy	ADJ
bibechana-53971	219	31	than	than	ADP
bibechana-53971	219	32	the	the	DET
bibechana-53971	219	33	first	first	ADJ
bibechana-53971	219	34	derivative	derivative	NOUN
bibechana-53971	219	35	.	.	PUNCT
bibechana-53971	220	1	the	the	DET
bibechana-53971	220	2	l1	l1	PROPN
bibechana-53971	220	3	fd	fd	PROPN
bibechana-53971	220	4	is	be	AUX
bibechana-53971	220	5	thought	think	VERB
bibechana-53971	220	6	to	to	PART
bibechana-53971	220	7	be	be	AUX
bibechana-53971	220	8	less	less	ADJ
bibechana-53971	220	9	that	that	PRON
bibechana-53971	220	10	are	be	AUX
bibechana-53971	220	11	susceptible	susceptible	ADJ
bibechana-53971	220	12	to	to	ADP
bibechana-53971	220	13	outliers	outlier	NOUN
bibechana-53971	220	14	and	and	CCONJ
bibechana-53971	220	15	data	datum	NOUN
bibechana-53971	220	16	noise	noise	NOUN
bibechana-53971	220	17	than	than	ADP
bibechana-53971	220	18	other	other	ADJ
bibechana-53971	220	19	varieties	variety	NOUN
bibechana-53971	220	20	of	of	ADP
bibechana-53971	220	21	fd	fd	PROPN
bibechana-53971	220	22	.	.	PUNCT
bibechana-53971	220	23	example	example	NOUN
bibechana-53971	220	24	1	1	NUM
bibechana-53971	220	25	using	use	VERB
bibechana-53971	220	26	the	the	DET
bibechana-53971	220	27	l1	l1	PROPN
bibechana-53971	220	28	formula	formula	NOUN
bibechana-53971	220	29	and	and	CCONJ
bibechana-53971	220	30	the	the	DET
bibechana-53971	220	31	equation	equation	NOUN
bibechana-53971	220	32	f(x	f(x	PROPN
bibechana-53971	220	33	)	)	PUNCT
bibechana-53971	221	1	=	=	SYM
bibechana-53971	221	2	sin(x	sin(x	PROPN
bibechana-53971	221	3	)	)	PUNCT
bibechana-53971	221	4	over	over	ADP
bibechana-53971	221	5	[	[	X
bibechana-53971	221	6	0	0	NUM
bibechana-53971	221	7	,	,	PUNCT
bibechana-53971	221	8	1	1	NUM
bibechana-53971	221	9	]	]	PUNCT
bibechana-53971	221	10	at	at	ADP
bibechana-53971	221	11	α	α	NOUN
bibechana-53971	221	12	=	=	SYM
bibechana-53971	221	13	0.5	0.5	NUM
bibechana-53971	221	14	,	,	PUNCT
bibechana-53971	221	15	the	the	DET
bibechana-53971	221	16	numerical	numerical	ADJ
bibechana-53971	221	17	results	result	NOUN
bibechana-53971	221	18	are	be	AUX
bibechana-53971	221	19	shown	show	VERB
bibechana-53971	221	20	in	in	ADP
bibechana-53971	221	21	the	the	DET
bibechana-53971	221	22	table	table	NOUN
bibechana-53971	221	23	below	below	ADV
bibechana-53971	221	24	.	.	PUNCT
bibechana-53971	222	1	table	table	NOUN
bibechana-53971	222	2	1	1	NUM
bibechana-53971	222	3	:	:	PUNCT
bibechana-53971	222	4	l1	l1	PROPN
bibechana-53971	222	5	formula	formula	NOUN
bibechana-53971	222	6	of	of	ADP
bibechana-53971	222	7	f(x	f(x	PROPN
bibechana-53971	222	8	)	)	PUNCT
bibechana-53971	223	1	=	=	SYM
bibechana-53971	223	2	sin(x	sin(x	PROPN
bibechana-53971	223	3	)	)	PUNCT
bibechana-53971	223	4	at	at	ADP
bibechana-53971	223	5	α	α	NOUN
bibechana-53971	223	6	=	=	SYM
bibechana-53971	223	7	0.5	0.5	NUM
bibechana-53971	223	8	.	.	PUNCT
bibechana-53971	224	1	l1cd	l1cd	NOUN
bibechana-53971	224	2	*	*	PUNCT
bibechana-53971	224	3	exact	exact	ADJ
bibechana-53971	224	4	error	error	NOUN
bibechana-53971	224	5	step	step	NOUN
bibechana-53971	224	6	sizes	size	VERB
bibechana-53971	224	7	0.8559	0.8559	NUM
bibechana-53971	224	8	0.8461	0.8461	NUM
bibechana-53971	224	9	0.0099	0.0099	NUM
bibechana-53971	224	10	h=0.1	h=0.1	NOUN
bibechana-53971	224	11	0.8472	0.8472	NUM
bibechana-53971	224	12	0.8461	0.8461	NUM
bibechana-53971	224	13	0.0012	0.0012	NUM
bibechana-53971	224	14	h=0.01	h=0.01	ADP
bibechana-53971	224	15	0.8462	0.8462	NUM
bibechana-53971	224	16	0.8461	0.8461	NUM
bibechana-53971	224	17	0.000111	0.000111	NUM
bibechana-53971	224	18	h=0.001	h=0.001	X
bibechana-53971	224	19	0.8461	0.8461	NUM
bibechana-53971	224	20	0.8461	0.8461	NUM
bibechana-53971	224	21	0.00001074	0.00001074	NUM
bibechana-53971	224	22	h=0.0001	h=0.0001	NOUN
bibechana-53971	224	23	0.8461	0.8461	NUM
bibechana-53971	224	24	0.8461	0.8461	NUM
bibechana-53971	224	25	0.0000010611	0.0000010611	NUM
bibechana-53971	224	26	h=0.00001	h=0.00001	NOUN
bibechana-53971	224	27	shankar	shankar	ADJ
bibechana-53971	224	28	pariyar	pariyar	PROPN
bibechana-53971	224	29	and	and	CCONJ
bibechana-53971	224	30	jeevan	jeevan	PROPN
bibechana-53971	224	31	kafle	kafle	PROPN
bibechana-53971	224	32	/	/	PUNCT
bibechana-53971	224	33	bibechana	bibechana	PROPN
bibechana-53971	224	34	20	20	NUM
bibechana-53971	224	35	(	(	PUNCT
bibechana-53971	224	36	2023	2023	NUM
bibechana-53971	224	37	)	)	PUNCT
bibechana-53971	224	38	126	126	NUM
bibechana-53971	224	39	-	-	SYM
bibechana-53971	224	40	133	133	NUM
bibechana-53971	224	41	131	131	NUM
bibechana-53971	224	42	*	*	NOUN
bibechana-53971	224	43	l1cd	l1cd	NOUN
bibechana-53971	224	44	represents	represent	VERB
bibechana-53971	224	45	l1	l1	PROPN
bibechana-53971	224	46	-	-	PUNCT
bibechana-53971	224	47	caputo	caputo	PROPN
bibechana-53971	224	48	-	-	PUNCT
bibechana-53971	224	49	derivative	derivative	ADJ
bibechana-53971	224	50	.	.	PUNCT
bibechana-53971	225	1	table	table	NOUN
bibechana-53971	225	2	1	1	NUM
bibechana-53971	225	3	displays	display	VERB
bibechana-53971	225	4	the	the	DET
bibechana-53971	225	5	numerical	numerical	ADJ
bibechana-53971	225	6	outcomes	outcome	NOUN
bibechana-53971	225	7	under	under	ADP
bibechana-53971	225	8	schemes	scheme	NOUN
bibechana-53971	225	9	5	5	NUM
bibechana-53971	225	10	for	for	ADP
bibechana-53971	225	11	the	the	DET
bibechana-53971	225	12	function	function	NOUN
bibechana-53971	225	13	f(x	f(x	PROPN
bibechana-53971	225	14	)	)	PUNCT
bibechana-53971	225	15	=	=	SYM
bibechana-53971	225	16	sin(x	sin(x	PROPN
bibechana-53971	225	17	)	)	PUNCT
bibechana-53971	225	18	over	over	ADP
bibechana-53971	225	19	the	the	DET
bibechana-53971	225	20	range	range	NOUN
bibechana-53971	225	21	[	[	X
bibechana-53971	225	22	0	0	NUM
bibechana-53971	225	23	,	,	PUNCT
bibechana-53971	225	24	1	1	NUM
bibechana-53971	225	25	]	]	PUNCT
bibechana-53971	225	26	using	use	VERB
bibechana-53971	225	27	the	the	DET
bibechana-53971	225	28	l1	l1	PROPN
bibechana-53971	225	29	-	-	PUNCT
bibechana-53971	225	30	caputo	caputo	PROPN
bibechana-53971	225	31	-	-	PUNCT
bibechana-53971	225	32	der	der	NOUN
bibechana-53971	225	33	formula	formula	NOUN
bibechana-53971	225	34	.	.	PUNCT
bibechana-53971	226	1	there	there	PRON
bibechana-53971	226	2	are	be	VERB
bibechana-53971	226	3	four	four	NUM
bibechana-53971	226	4	columns	column	NOUN
bibechana-53971	226	5	in	in	ADP
bibechana-53971	226	6	the	the	DET
bibechana-53971	226	7	table	table	NOUN
bibechana-53971	226	8	•	•	ADP
bibechana-53971	226	9	l1	l1	PROPN
bibechana-53971	226	10	-	-	PUNCT
bibechana-53971	226	11	cap	cap	NOUN
bibechana-53971	226	12	-	-	PUNCT
bibechana-53971	226	13	der	der	NOUN
bibechana-53971	226	14	:	:	PUNCT
bibechana-53971	226	15	using	use	VERB
bibechana-53971	226	16	the	the	DET
bibechana-53971	226	17	l1	l1	PROPN
bibechana-53971	226	18	-	-	PUNCT
bibechana-53971	226	19	caputo	caputo	PROPN
bibechana-53971	226	20	-	-	PUNCT
bibechana-53971	226	21	der	der	NOUN
bibechana-53971	226	22	formula	formula	NOUN
bibechana-53971	226	23	,	,	PUNCT
bibechana-53971	226	24	this	this	DET
bibechana-53971	226	25	column	column	NOUN
bibechana-53971	226	26	represents	represent	VERB
bibechana-53971	226	27	a	a	DET
bibechana-53971	226	28	numerical	numerical	ADJ
bibechana-53971	226	29	approximation	approximation	NOUN
bibechana-53971	226	30	of	of	ADP
bibechana-53971	226	31	the	the	DET
bibechana-53971	226	32	integral	integral	NOUN
bibechana-53971	226	33	of	of	ADP
bibechana-53971	226	34	the	the	DET
bibechana-53971	226	35	function	function	NOUN
bibechana-53971	226	36	f(x	f(x	PROPN
bibechana-53971	226	37	)	)	PUNCT
bibechana-53971	226	38	.	.	PUNCT
bibechana-53971	227	1	•	•	NUM
bibechana-53971	227	2	exact	exact	ADJ
bibechana-53971	227	3	:	:	PUNCT
bibechana-53971	227	4	the	the	DET
bibechana-53971	227	5	value	value	NOUN
bibechana-53971	227	6	0.8461	0.8461	NUM
bibechana-53971	227	7	is	be	AUX
bibechana-53971	227	8	shown	show	VERB
bibechana-53971	227	9	in	in	ADP
bibechana-53971	227	10	this	this	DET
bibechana-53971	227	11	column	column	NOUN
bibechana-53971	227	12	as	as	ADP
bibechana-53971	227	13	the	the	DET
bibechana-53971	227	14	integral	integral	NOUN
bibechana-53971	227	15	of	of	ADP
bibechana-53971	227	16	the	the	DET
bibechana-53971	227	17	function	function	NOUN
bibechana-53971	227	18	f(x	f(x	PROPN
bibechana-53971	227	19	)	)	PUNCT
bibechana-53971	227	20	over	over	ADP
bibechana-53971	227	21	[	[	X
bibechana-53971	227	22	0	0	NUM
bibechana-53971	227	23	,	,	PUNCT
bibechana-53971	227	24	1	1	NUM
bibechana-53971	227	25	]	]	PUNCT
bibechana-53971	227	26	.	.	PUNCT
bibechana-53971	228	1	•	•	NUM
bibechana-53971	228	2	inaccuracy	inaccuracy	NOUN
bibechana-53971	228	3	:	:	PUNCT
bibechana-53971	228	4	the	the	DET
bibechana-53971	228	5	absolute	absolute	ADJ
bibechana-53971	228	6	inaccuracy	inaccuracy	NOUN
bibechana-53971	228	7	between	between	ADP
bibechana-53971	228	8	the	the	DET
bibechana-53971	228	9	numerical	numerical	ADJ
bibechana-53971	228	10	approximation	approximation	NOUN
bibechana-53971	228	11	and	and	CCONJ
bibechana-53971	228	12	the	the	DET
bibechana-53971	228	13	l1	l1	PROPN
bibechana-53971	228	14	-	-	PUNCT
bibechana-53971	228	15	caputo	caputo	PROPN
bibechana-53971	228	16	-	-	PUNCT
bibechana-53971	228	17	der	der	ADJ
bibechana-53971	228	18	formula	formula	NOUN
bibechana-53971	228	19	is	be	AUX
bibechana-53971	228	20	shown	show	VERB
bibechana-53971	228	21	in	in	ADP
bibechana-53971	228	22	this	this	DET
bibechana-53971	228	23	column	column	NOUN
bibechana-53971	228	24	.	.	PUNCT
bibechana-53971	229	1	•	•	NUM
bibechana-53971	229	2	step	step	NOUN
bibechana-53971	229	3	sizes	size	NOUN
bibechana-53971	229	4	:	:	PUNCT
bibechana-53971	229	5	the	the	DET
bibechana-53971	229	6	fourth	fourth	ADJ
bibechana-53971	229	7	column	column	NOUN
bibechana-53971	229	8	labeled	label	VERB
bibechana-53971	229	9	"	"	PUNCT
bibechana-53971	229	10	step	step	NOUN
bibechana-53971	229	11	sizes	size	NOUN
bibechana-53971	229	12	"	"	PUNCT
bibechana-53971	229	13	shows	show	VERB
bibechana-53971	229	14	the	the	DET
bibechana-53971	229	15	step	step	NOUN
bibechana-53971	229	16	size	size	NOUN
bibechana-53971	229	17	used	use	VERB
bibechana-53971	229	18	for	for	ADP
bibechana-53971	229	19	each	each	DET
bibechana-53971	229	20	numerical	numerical	ADJ
bibechana-53971	229	21	result	result	NOUN
bibechana-53971	229	22	.	.	PUNCT
bibechana-53971	230	1	from	from	ADP
bibechana-53971	230	2	the	the	DET
bibechana-53971	230	3	table	table	NOUN
bibechana-53971	230	4	,	,	PUNCT
bibechana-53971	230	5	we	we	PRON
bibechana-53971	230	6	can	can	AUX
bibechana-53971	230	7	see	see	VERB
bibechana-53971	230	8	that	that	SCONJ
bibechana-53971	230	9	as	as	SCONJ
bibechana-53971	230	10	the	the	DET
bibechana-53971	230	11	step	step	NOUN
bibechana-53971	230	12	size	size	NOUN
bibechana-53971	230	13	decreases	decrease	VERB
bibechana-53971	230	14	,	,	PUNCT
bibechana-53971	230	15	the	the	DET
bibechana-53971	230	16	numerical	numerical	ADJ
bibechana-53971	230	17	result	result	NOUN
bibechana-53971	230	18	obtained	obtain	VERB
bibechana-53971	230	19	using	use	VERB
bibechana-53971	230	20	the	the	DET
bibechana-53971	230	21	l1caputo	l1caputo	NOUN
bibechana-53971	230	22	-	-	PUNCT
bibechana-53971	230	23	der	der	NOUN
bibechana-53971	230	24	formula	formula	NOUN
bibechana-53971	230	25	gets	get	VERB
bibechana-53971	230	26	closer	close	ADJ
bibechana-53971	230	27	to	to	ADP
bibechana-53971	230	28	the	the	DET
bibechana-53971	230	29	exact	exact	ADJ
bibechana-53971	230	30	value	value	NOUN
bibechana-53971	230	31	of	of	ADP
bibechana-53971	230	32	the	the	DET
bibechana-53971	230	33	integral	integral	NOUN
bibechana-53971	230	34	.	.	PUNCT
bibechana-53971	231	1	the	the	DET
bibechana-53971	231	2	error	error	NOUN
bibechana-53971	231	3	decreases	decrease	VERB
bibechana-53971	231	4	as	as	SCONJ
bibechana-53971	231	5	the	the	DET
bibechana-53971	231	6	step	step	NOUN
bibechana-53971	231	7	size	size	NOUN
bibechana-53971	231	8	decreases	decrease	VERB
bibechana-53971	231	9	,	,	PUNCT
bibechana-53971	231	10	indicating	indicate	VERB
bibechana-53971	231	11	that	that	SCONJ
bibechana-53971	231	12	the	the	DET
bibechana-53971	231	13	numerical	numerical	ADJ
bibechana-53971	231	14	approximation	approximation	NOUN
bibechana-53971	231	15	is	be	AUX
bibechana-53971	231	16	becoming	become	VERB
bibechana-53971	231	17	more	more	ADV
bibechana-53971	231	18	accurate	accurate	ADJ
bibechana-53971	231	19	.	.	PUNCT
bibechana-53971	232	1	at	at	ADP
bibechana-53971	232	2	h=0.0001	h=0.0001	PROPN
bibechana-53971	232	3	,	,	PUNCT
bibechana-53971	232	4	the	the	DET
bibechana-53971	232	5	error	error	NOUN
bibechana-53971	232	6	is	be	AUX
bibechana-53971	232	7	less	less	ADJ
bibechana-53971	232	8	than	than	ADP
bibechana-53971	232	9	0.00001	0.00001	NUM
bibechana-53971	232	10	,	,	PUNCT
bibechana-53971	232	11	which	which	PRON
bibechana-53971	232	12	is	be	AUX
bibechana-53971	232	13	a	a	DET
bibechana-53971	232	14	very	very	ADV
bibechana-53971	232	15	small	small	ADJ
bibechana-53971	232	16	error	error	NOUN
bibechana-53971	232	17	,	,	PUNCT
bibechana-53971	232	18	indicating	indicate	VERB
bibechana-53971	232	19	a	a	DET
bibechana-53971	232	20	highly	highly	ADV
bibechana-53971	232	21	accurate	accurate	ADJ
bibechana-53971	232	22	numerical	numerical	ADJ
bibechana-53971	232	23	approximation	approximation	NOUN
bibechana-53971	232	24	.	.	PUNCT
bibechana-53971	233	1	example	example	NOUN
bibechana-53971	233	2	2	2	NUM
bibechana-53971	233	3	using	use	VERB
bibechana-53971	233	4	the	the	DET
bibechana-53971	233	5	l2	l2	NOUN
bibechana-53971	233	6	formula	formula	NOUN
bibechana-53971	233	7	and	and	CCONJ
bibechana-53971	233	8	the	the	DET
bibechana-53971	233	9	equation	equation	NOUN
bibechana-53971	233	10	f(x	f(x	PROPN
bibechana-53971	233	11	)	)	PUNCT
bibechana-53971	234	1	=	=	SYM
bibechana-53971	234	2	sin(x	sin(x	PROPN
bibechana-53971	234	3	)	)	PUNCT
bibechana-53971	234	4	over	over	ADP
bibechana-53971	234	5	[	[	X
bibechana-53971	234	6	0	0	NUM
bibechana-53971	234	7	,	,	PUNCT
bibechana-53971	234	8	1	1	NUM
bibechana-53971	234	9	]	]	PUNCT
bibechana-53971	234	10	at	at	ADP
bibechana-53971	234	11	α	α	NOUN
bibechana-53971	234	12	=	=	SYM
bibechana-53971	234	13	1.5	1.5	NUM
bibechana-53971	234	14	,	,	PUNCT
bibechana-53971	234	15	the	the	DET
bibechana-53971	234	16	numerical	numerical	ADJ
bibechana-53971	234	17	results	result	NOUN
bibechana-53971	234	18	are	be	AUX
bibechana-53971	234	19	shown	show	VERB
bibechana-53971	234	20	in	in	ADP
bibechana-53971	234	21	the	the	DET
bibechana-53971	234	22	table	table	NOUN
bibechana-53971	234	23	below	below	ADV
bibechana-53971	234	24	.	.	PUNCT
bibechana-53971	235	1	table	table	NOUN
bibechana-53971	235	2	2	2	NUM
bibechana-53971	235	3	:	:	PUNCT
bibechana-53971	235	4	l2	l2	NOUN
bibechana-53971	235	5	formula	formula	NOUN
bibechana-53971	235	6	of	of	ADP
bibechana-53971	235	7	f(x	f(x	NOUN
bibechana-53971	235	8	)	)	PUNCT
bibechana-53971	236	1	=	=	SYM
bibechana-53971	236	2	sin(x	sin(x	PROPN
bibechana-53971	236	3	)	)	PUNCT
bibechana-53971	236	4	at	at	ADP
bibechana-53971	236	5	α	α	NOUN
bibechana-53971	236	6	=	=	SYM
bibechana-53971	236	7	1.5	1.5	NUM
bibechana-53971	236	8	l2	l2	NOUN
bibechana-53971	236	9	-	-	PUNCT
bibechana-53971	236	10	cd	cd	NOUN
bibechana-53971	236	11	*	*	SYM
bibechana-53971	236	12	exact	exact	ADJ
bibechana-53971	236	13	error	error	NOUN
bibechana-53971	236	14	step	step	NOUN
bibechana-53971	236	15	sizes	size	NOUN
bibechana-53971	236	16	-0.6219	-0.6219	NOUN
bibechana-53971	236	17	-0.6697	-0.6697	ADV
bibechana-53971	236	18	0.0478	0.0478	NUM
bibechana-53971	236	19	h=0.1	h=0.1	NOUN
bibechana-53971	236	20	-0.6653	-0.6653	NOUN
bibechana-53971	236	21	-0.6697	-0.6697	PROPN
bibechana-53971	237	1	0.0044	0.0044	NUM
bibechana-53971	237	2	h=0.01	h=0.01	DET
bibechana-53971	237	3	-0.6693	-0.6693	NOUN
bibechana-53971	237	4	-0.6697	-0.6697	PUNCT
bibechana-53971	238	1	0.00042716	0.00042716	NUM
bibechana-53971	238	2	h=0.001	h=0.001	X
bibechana-53971	238	3	-0.6696	-0.6696	NOUN
bibechana-53971	238	4	-0.6697	-0.6697	X
bibechana-53971	239	1	0.000042431	0.000042431	NUM
bibechana-53971	239	2	h=0.0001	h=0.0001	NOUN
bibechana-53971	239	3	-0.6697	-0.6697	NOUN
bibechana-53971	239	4	-0.6697	-0.6697	PUNCT
bibechana-53971	240	1	0.0000042307	0.0000042307	NUM
bibechana-53971	240	2	h=0.00001	h=0.00001	NOUN
bibechana-53971	240	3	l2	l2	NOUN
bibechana-53971	240	4	-	-	PUNCT
bibechana-53971	240	5	cd	cd	NOUN
bibechana-53971	240	6	*	*	NOUN
bibechana-53971	240	7	represents	represent	VERB
bibechana-53971	240	8	l2	l2	NOUN
bibechana-53971	240	9	-	-	PUNCT
bibechana-53971	240	10	caputo	caputo	PROPN
bibechana-53971	240	11	derivative	derivative	NOUN
bibechana-53971	240	12	.	.	PUNCT
bibechana-53971	241	1	table	table	NOUN
bibechana-53971	241	2	2	2	NUM
bibechana-53971	241	3	indicates	indicate	VERB
bibechana-53971	241	4	that	that	SCONJ
bibechana-53971	241	5	for	for	SCONJ
bibechana-53971	241	6	the	the	DET
bibechana-53971	241	7	different	different	ADJ
bibechana-53971	241	8	step	step	NOUN
bibechana-53971	241	9	sizes	size	NOUN
bibechana-53971	241	10	to	to	PART
bibechana-53971	241	11	approximate	approximate	VERB
bibechana-53971	241	12	the	the	DET
bibechana-53971	241	13	function	function	NOUN
bibechana-53971	241	14	f(x	f(x	PROPN
bibechana-53971	241	15	)	)	PUNCT
bibechana-53971	242	1	=	=	SYM
bibechana-53971	242	2	sin(x	sin(x	PROPN
bibechana-53971	242	3	)	)	PUNCT
bibechana-53971	242	4	using	use	VERB
bibechana-53971	242	5	the	the	DET
bibechana-53971	242	6	l2caputo	l2caputo	NOUN
bibechana-53971	242	7	-	-	PUNCT
bibechana-53971	242	8	derivative	derivative	NOUN
bibechana-53971	242	9	,	,	PUNCT
bibechana-53971	242	10	using	use	VERB
bibechana-53971	242	11	the	the	DET
bibechana-53971	242	12	scheme	scheme	NOUN
bibechana-53971	242	13	9	9	NUM
bibechana-53971	242	14	over	over	ADP
bibechana-53971	242	15	the	the	DET
bibechana-53971	242	16	range	range	NOUN
bibechana-53971	243	1	[	[	X
bibechana-53971	243	2	0	0	NUM
bibechana-53971	243	3	,	,	PUNCT
bibechana-53971	243	4	1	1	NUM
bibechana-53971	243	5	]	]	PUNCT
bibechana-53971	243	6	,	,	PUNCT
bibechana-53971	243	7	α	α	X
bibechana-53971	243	8	=	=	SYM
bibechana-53971	243	9	1.5	1.5	NUM
bibechana-53971	243	10	is	be	AUX
bibechana-53971	243	11	the	the	DET
bibechana-53971	243	12	value	value	NOUN
bibechana-53971	243	13	that	that	PRON
bibechana-53971	243	14	was	be	AUX
bibechana-53971	243	15	utilized	utilize	VERB
bibechana-53971	243	16	in	in	ADP
bibechana-53971	243	17	the	the	DET
bibechana-53971	243	18	approximation	approximation	NOUN
bibechana-53971	243	19	.	.	PUNCT
bibechana-53971	244	1	the	the	DET
bibechana-53971	244	2	step	step	NOUN
bibechana-53971	244	3	size	size	NOUN
bibechana-53971	244	4	has	have	VERB
bibechana-53971	244	5	an	an	DET
bibechana-53971	244	6	impact	impact	NOUN
bibechana-53971	244	7	on	on	ADP
bibechana-53971	244	8	the	the	DET
bibechana-53971	244	9	numerical	numerical	ADJ
bibechana-53971	244	10	precision	precision	NOUN
bibechana-53971	244	11	.	.	PUNCT
bibechana-53971	245	1	a	a	DET
bibechana-53971	245	2	smaller	small	ADJ
bibechana-53971	245	3	step	step	NOUN
bibechana-53971	245	4	size	size	NOUN
bibechana-53971	245	5	often	often	ADV
bibechana-53971	245	6	results	result	VERB
bibechana-53971	245	7	in	in	ADP
bibechana-53971	245	8	a	a	DET
bibechana-53971	245	9	more	more	ADV
bibechana-53971	245	10	precise	precise	ADJ
bibechana-53971	245	11	estimate	estimate	NOUN
bibechana-53971	245	12	,	,	PUNCT
bibechana-53971	245	13	even	even	ADV
bibechana-53971	245	14	though	though	SCONJ
bibechana-53971	245	15	it	it	PRON
bibechana-53971	245	16	takes	take	VERB
bibechana-53971	245	17	longer	long	ADV
bibechana-53971	245	18	to	to	PART
bibechana-53971	245	19	calculate	calculate	VERB
bibechana-53971	245	20	.	.	PUNCT
bibechana-53971	246	1	a	a	DET
bibechana-53971	246	2	larger	large	ADJ
bibechana-53971	246	3	step	step	NOUN
bibechana-53971	246	4	size	size	NOUN
bibechana-53971	246	5	results	result	VERB
bibechana-53971	246	6	in	in	ADP
bibechana-53971	246	7	a	a	DET
bibechana-53971	246	8	less	less	ADV
bibechana-53971	246	9	accurate	accurate	ADJ
bibechana-53971	246	10	approximation	approximation	NOUN
bibechana-53971	246	11	even	even	ADV
bibechana-53971	246	12	though	though	SCONJ
bibechana-53971	246	13	it	it	PRON
bibechana-53971	246	14	takes	take	VERB
bibechana-53971	246	15	less	less	ADJ
bibechana-53971	246	16	time	time	NOUN
bibechana-53971	246	17	to	to	PART
bibechana-53971	246	18	compute	compute	VERB
bibechana-53971	246	19	.	.	PUNCT
bibechana-53971	247	1	as	as	ADP
bibechana-53971	247	2	a	a	DET
bibechana-53971	247	3	result	result	NOUN
bibechana-53971	247	4	,	,	PUNCT
bibechana-53971	247	5	while	while	SCONJ
bibechana-53971	247	6	choosing	choose	VERB
bibechana-53971	247	7	a	a	DET
bibechana-53971	247	8	step	step	NOUN
bibechana-53971	247	9	size	size	NOUN
bibechana-53971	247	10	,	,	PUNCT
bibechana-53971	247	11	accuracy	accuracy	NOUN
bibechana-53971	247	12	and	and	CCONJ
bibechana-53971	247	13	computation	computation	NOUN
bibechana-53971	247	14	effectiveness	effectiveness	NOUN
bibechana-53971	247	15	must	must	AUX
bibechana-53971	247	16	be	be	AUX
bibechana-53971	247	17	compromised	compromise	VERB
bibechana-53971	247	18	.	.	PUNCT
bibechana-53971	248	1	example	example	NOUN
bibechana-53971	248	2	3	3	NUM
bibechana-53971	248	3	the	the	DET
bibechana-53971	248	4	equation	equation	NOUN
bibechana-53971	248	5	f(x)=cos(4x	f(x)=cos(4x	NOUN
bibechana-53971	248	6	)	)	PUNCT
bibechana-53971	248	7	over	over	ADP
bibechana-53971	248	8	the	the	DET
bibechana-53971	248	9	interval	interval	NOUN
bibechana-53971	249	1	[	[	X
bibechana-53971	249	2	0,2	0,2	NUM
bibechana-53971	249	3	]	]	PUNCT
bibechana-53971	249	4	,	,	PUNCT
bibechana-53971	249	5	with	with	ADP
bibechana-53971	249	6	alpha=0.1	alpha=0.1	NOUN
bibechana-53971	249	7	and	and	CCONJ
bibechana-53971	249	8	different	different	ADJ
bibechana-53971	249	9	step	step	NOUN
bibechana-53971	249	10	sizes	size	NOUN
bibechana-53971	249	11	,	,	PUNCT
bibechana-53971	249	12	can	can	AUX
bibechana-53971	249	13	be	be	AUX
bibechana-53971	249	14	solved	solve	VERB
bibechana-53971	249	15	using	use	VERB
bibechana-53971	249	16	the	the	DET
bibechana-53971	249	17	l1	l1	NOUN
bibechana-53971	249	18	-	-	PUNCT
bibechana-53971	249	19	formula	formula	NOUN
bibechana-53971	249	20	in	in	ADP
bibechana-53971	249	21	the	the	DET
bibechana-53971	249	22	caputo	caputo	PROPN
bibechana-53971	249	23	fabrizio	fabrizio	PROPN
bibechana-53971	249	24	sense	sense	NOUN
bibechana-53971	249	25	.	.	PUNCT
bibechana-53971	250	1	table	table	NOUN
bibechana-53971	250	2	3	3	NUM
bibechana-53971	250	3	:	:	PUNCT
bibechana-53971	250	4	l1	l1	PROPN
bibechana-53971	250	5	for	for	ADP
bibechana-53971	250	6	cfd	cfd	NOUN
bibechana-53971	250	7	at	at	ADP
bibechana-53971	250	8	f(x	f(x	PROPN
bibechana-53971	250	9	)	)	PUNCT
bibechana-53971	251	1	=	=	SYM
bibechana-53971	251	2	cos(4x	cos(4x	NOUN
bibechana-53971	251	3	)	)	PUNCT
bibechana-53971	251	4	at	at	ADP
bibechana-53971	251	5	α	α	NOUN
bibechana-53971	251	6	=	=	SYM
bibechana-53971	251	7	0.1	0.1	NUM
bibechana-53971	251	8	st	st	PROPN
bibechana-53971	251	9	*	*	PROPN
bibechana-53971	251	10	.	.	PUNCT
bibechana-53971	252	1	s.s	s.s	PROPN
bibechana-53971	252	2	*	*	PROPN
bibechana-53971	252	3	.	.	PUNCT
bibechana-53971	253	1	ex	ex	X
bibechana-53971	253	2	*	*	PUNCT
bibechana-53971	253	3	ax	ax	NOUN
bibechana-53971	253	4	*	*	PUNCT
bibechana-53971	253	5	er	er	INTJ
bibechana-53971	253	6	*	*	NUM
bibechana-53971	253	7	20×101	20×101	NUM
bibechana-53971	253	8	10−1	10−1	NUM
bibechana-53971	253	9	-1.0811	-1.0811	NOUN
bibechana-53971	253	10	-1.0807	-1.0807	VERB
bibechana-53971	253	11	3.9720×	3.9720×	NUM
bibechana-53971	253	12	10−4	10−4	NUM
bibechana-53971	253	13	20×102	20×102	NUM
bibechana-53971	253	14	10−2	10−2	NUM
bibechana-53971	253	15	-1.0811	-1.0811	NOUN
bibechana-53971	253	16	-1.0811	-1.0811	VERB
bibechana-53971	254	1	3.9720×	3.9720×	NOUN
bibechana-53971	254	2	10−6	10−6	NUM
bibechana-53971	254	3	20×103	20×103	NUM
bibechana-53971	254	4	10−3	10−3	NUM
bibechana-53971	254	5	-1.0811	-1.0811	NOUN
bibechana-53971	254	6	-1.0811	-1.0811	NOUN
bibechana-53971	255	1	3.9720×	3.9720×	NUM
bibechana-53971	255	2	10−8	10−8	NUM
bibechana-53971	255	3	20×104	20×104	SYM
bibechana-53971	255	4	10−4	10−4	NUM
bibechana-53971	255	5	-1.0811	-1.0811	NOUN
bibechana-53971	255	6	-1.0811	-1.0811	VERB
bibechana-53971	255	7	3.9720×	3.9720×	NUM
bibechana-53971	255	8	10−10	10−10	NUM
bibechana-53971	255	9	acronyms	acronym	NOUN
bibechana-53971	255	10	:	:	PUNCT
bibechana-53971	255	11	st	st	PROPN
bibechana-53971	255	12	*	*	SYM
bibechana-53971	255	13	=	=	NOUN
bibechana-53971	255	14	steps	step	NOUN
bibechana-53971	255	15	,	,	PUNCT
bibechana-53971	255	16	s.s	s.s	PROPN
bibechana-53971	255	17	*	*	SYM
bibechana-53971	255	18	=	=	NOUN
bibechana-53971	255	19	steps	step	NOUN
bibechana-53971	255	20	sizes	size	NOUN
bibechana-53971	255	21	,	,	PUNCT
bibechana-53971	255	22	ex	ex	NOUN
bibechana-53971	255	23	*	*	NOUN
bibechana-53971	255	24	=	=	SYM
bibechana-53971	255	25	exact	exact	ADJ
bibechana-53971	255	26	,	,	PUNCT
bibechana-53971	255	27	ax	ax	NOUN
bibechana-53971	255	28	*	*	PUNCT
bibechana-53971	255	29	=	=	SYM
bibechana-53971	255	30	approximate	approximate	ADJ
bibechana-53971	255	31	,	,	PUNCT
bibechana-53971	255	32	er*=error	er*=error	NOUN
bibechana-53971	255	33	.	.	PUNCT
bibechana-53971	256	1	if	if	SCONJ
bibechana-53971	256	2	we	we	PRON
bibechana-53971	256	3	observe	observe	VERB
bibechana-53971	256	4	an	an	DET
bibechana-53971	256	5	absolute	absolute	ADJ
bibechana-53971	256	6	error	error	NOUN
bibechana-53971	256	7	reduction	reduction	NOUN
bibechana-53971	256	8	of	of	ADP
bibechana-53971	256	9	two	two	NUM
bibechana-53971	256	10	orders	order	NOUN
bibechana-53971	256	11	of	of	ADP
bibechana-53971	256	12	magnitude	magnitude	NOUN
bibechana-53971	256	13	while	while	SCONJ
bibechana-53971	256	14	simultaneously	simultaneously	ADV
bibechana-53971	256	15	reducing	reduce	VERB
bibechana-53971	256	16	the	the	DET
bibechana-53971	256	17	step	step	NOUN
bibechana-53971	256	18	size	size	NOUN
bibechana-53971	256	19	by	by	ADP
bibechana-53971	256	20	one	one	NUM
bibechana-53971	256	21	order	order	NOUN
bibechana-53971	256	22	of	of	ADP
bibechana-53971	256	23	magnitude	magnitude	NOUN
bibechana-53971	256	24	,	,	PUNCT
bibechana-53971	256	25	this	this	PRON
bibechana-53971	256	26	suggests	suggest	VERB
bibechana-53971	256	27	a	a	DET
bibechana-53971	256	28	quadratic	quadratic	ADJ
bibechana-53971	256	29	rate	rate	NOUN
bibechana-53971	256	30	of	of	ADP
bibechana-53971	256	31	convergence	convergence	NOUN
bibechana-53971	256	32	at	at	ADP
bibechana-53971	256	33	the	the	DET
bibechana-53971	256	34	second	second	ADJ
bibechana-53971	256	35	order	order	NOUN
bibechana-53971	256	36	.	.	PUNCT
bibechana-53971	257	1	in	in	ADP
bibechana-53971	257	2	other	other	ADJ
bibechana-53971	257	3	words	word	NOUN
bibechana-53971	257	4	,	,	PUNCT
bibechana-53971	257	5	not	not	PART
bibechana-53971	257	6	only	only	ADV
bibechana-53971	257	7	is	be	AUX
bibechana-53971	257	8	our	our	PRON
bibechana-53971	257	9	progress	progress	NOUN
bibechana-53971	257	10	significant	significant	ADJ
bibechana-53971	257	11	but	but	CCONJ
bibechana-53971	257	12	it	it	PRON
bibechana-53971	257	13	is	be	AUX
bibechana-53971	257	14	also	also	ADV
bibechana-53971	257	15	happening	happen	VERB
bibechana-53971	257	16	quite	quite	ADV
bibechana-53971	257	17	rapidly	rapidly	ADV
bibechana-53971	257	18	.	.	PUNCT
bibechana-53971	258	1	example	example	NOUN
bibechana-53971	258	2	4	4	NUM
bibechana-53971	258	3	the	the	DET
bibechana-53971	258	4	equation	equation	NOUN
bibechana-53971	258	5	f(x	f(x	PROPN
bibechana-53971	258	6	)	)	PUNCT
bibechana-53971	259	1	=	=	SYM
bibechana-53971	259	2	cos(4x	cos(4x	PROPN
bibechana-53971	259	3	)	)	PUNCT
bibechana-53971	259	4	over	over	ADP
bibechana-53971	259	5	the	the	DET
bibechana-53971	259	6	interval	interval	NOUN
bibechana-53971	259	7	[	[	X
bibechana-53971	259	8	0	0	NUM
bibechana-53971	259	9	,	,	PUNCT
bibechana-53971	259	10	2	2	NUM
bibechana-53971	259	11	]	]	PUNCT
bibechana-53971	259	12	,	,	PUNCT
bibechana-53971	259	13	with	with	ADP
bibechana-53971	259	14	α	α	NOUN
bibechana-53971	259	15	=	=	SYM
bibechana-53971	259	16	0.1	0.1	NUM
bibechana-53971	259	17	and	and	CCONJ
bibechana-53971	259	18	different	different	ADJ
bibechana-53971	259	19	step	step	NOUN
bibechana-53971	259	20	sizes	size	NOUN
bibechana-53971	259	21	,	,	PUNCT
bibechana-53971	259	22	can	can	AUX
bibechana-53971	259	23	be	be	AUX
bibechana-53971	259	24	solved	solve	VERB
bibechana-53971	259	25	using	use	VERB
bibechana-53971	259	26	the	the	DET
bibechana-53971	259	27	l1	l1	PROPN
bibechana-53971	259	28	−	−	PROPN
bibechana-53971	260	1	2(backward	2(backward	PROPN
bibechana-53971	260	2	approximation	approximation	NOUN
bibechana-53971	260	3	)	)	PUNCT
bibechana-53971	260	4	for	for	ADP
bibechana-53971	260	5	caputo	caputo	PROPN
bibechana-53971	260	6	-	-	PUNCT
bibechana-53971	260	7	fractional	fractional	ADJ
bibechana-53971	260	8	derivativeformula	derivativeformula	NOUN
bibechana-53971	260	9	in	in	ADP
bibechana-53971	260	10	the	the	DET
bibechana-53971	260	11	caputo	caputo	PROPN
bibechana-53971	260	12	fabrizio	fabrizio	PROPN
bibechana-53971	260	13	sense	sense	NOUN
bibechana-53971	260	14	.	.	PUNCT
bibechana-53971	261	1	table	table	NOUN
bibechana-53971	261	2	4	4	NUM
bibechana-53971	261	3	:	:	PUNCT
bibechana-53971	261	4	l1	l1	PROPN
bibechana-53971	261	5	-	-	PUNCT
bibechana-53971	261	6	2	2	NUM
bibechana-53971	261	7	for	for	ADP
bibechana-53971	261	8	cfd	cfd	NOUN
bibechana-53971	261	9	at	at	ADP
bibechana-53971	261	10	f(x	f(x	PROPN
bibechana-53971	261	11	)	)	PUNCT
bibechana-53971	261	12	=	=	SYM
bibechana-53971	262	1	cos(4x	cos(4x	NOUN
bibechana-53971	262	2	)	)	PUNCT
bibechana-53971	262	3	at	at	ADP
bibechana-53971	262	4	α	α	NOUN
bibechana-53971	262	5	=	=	SYM
bibechana-53971	262	6	0.1	0.1	NUM
bibechana-53971	262	7	st	st	PROPN
bibechana-53971	262	8	*	*	PROPN
bibechana-53971	262	9	.	.	PUNCT
bibechana-53971	263	1	s.s	s.s	PROPN
bibechana-53971	263	2	*	*	PUNCT
bibechana-53971	263	3	ex	ex	PROPN
bibechana-53971	263	4	*	*	NOUN
bibechana-53971	263	5	ax	ax	NOUN
bibechana-53971	263	6	*	*	PUNCT
bibechana-53971	263	7	er	er	INTJ
bibechana-53971	263	8	*	*	NOUN
bibechana-53971	263	9	.	.	PUNCT
bibechana-53971	264	1	2×101	2×101	NUM
bibechana-53971	264	2	1×	1×	NUM
bibechana-53971	264	3	10−1	10−1	PROPN
bibechana-53971	264	4	-1.0811	-1.0811	PROPN
bibechana-53971	264	5	-1.0811	-1.0811	PROPN
bibechana-53971	265	1	2.9514×	2.9514×	NUM
bibechana-53971	265	2	10−7	10−7	NUM
bibechana-53971	265	3	2×102	2×102	NUM
bibechana-53971	265	4	1×	1×	NUM
bibechana-53971	265	5	10−2	10−2	NUM
bibechana-53971	265	6	-1.0811	-1.0811	NOUN
bibechana-53971	265	7	-1.0811	-1.0811	NOUN
bibechana-53971	265	8	2.9090×	2.9090×	NUM
bibechana-53971	265	9	10−11	10−11	NUM
bibechana-53971	265	10	4×101	4×101	NUM
bibechana-53971	265	11	0.05	0.05	NUM
bibechana-53971	265	12	-1.0811	-1.0811	PROPN
bibechana-53971	265	13	-1.0811	-1.0811	PROPN
bibechana-53971	265	14	1.8377×	1.8377×	X
bibechana-53971	265	15	10−8	10−8	NUM
bibechana-53971	265	16	if	if	SCONJ
bibechana-53971	265	17	we	we	PRON
bibechana-53971	265	18	observe	observe	VERB
bibechana-53971	265	19	an	an	DET
bibechana-53971	265	20	absolute	absolute	ADJ
bibechana-53971	265	21	error	error	NOUN
bibechana-53971	265	22	reduction	reduction	NOUN
bibechana-53971	265	23	of	of	ADP
bibechana-53971	265	24	three	three	NUM
bibechana-53971	265	25	orders	order	NOUN
bibechana-53971	265	26	of	of	ADP
bibechana-53971	265	27	magnitude	magnitude	NOUN
bibechana-53971	265	28	while	while	SCONJ
bibechana-53971	265	29	simultaneously	simultaneously	ADV
bibechana-53971	265	30	reducing	reduce	VERB
bibechana-53971	265	31	the	the	DET
bibechana-53971	265	32	step	step	NOUN
bibechana-53971	265	33	size	size	NOUN
bibechana-53971	265	34	by	by	ADP
bibechana-53971	265	35	one	one	NUM
bibechana-53971	265	36	order	order	NOUN
bibechana-53971	265	37	of	of	ADP
bibechana-53971	265	38	magnitude	magnitude	NOUN
bibechana-53971	265	39	,	,	PUNCT
bibechana-53971	265	40	this	this	PRON
bibechana-53971	265	41	suggests	suggest	VERB
bibechana-53971	265	42	a	a	DET
bibechana-53971	265	43	cubic	cubic	ADJ
bibechana-53971	265	44	rate	rate	NOUN
bibechana-53971	265	45	of	of	ADP
bibechana-53971	265	46	convergence	convergence	NOUN
bibechana-53971	265	47	at	at	ADP
bibechana-53971	265	48	the	the	DET
bibechana-53971	265	49	third	third	ADJ
bibechana-53971	265	50	order	order	NOUN
bibechana-53971	265	51	.	.	PUNCT
bibechana-53971	266	1	in	in	ADP
bibechana-53971	266	2	other	other	ADJ
bibechana-53971	266	3	words	word	NOUN
bibechana-53971	266	4	,	,	PUNCT
bibechana-53971	266	5	not	not	PART
bibechana-53971	266	6	only	only	ADV
bibechana-53971	266	7	is	be	AUX
bibechana-53971	266	8	our	our	PRON
bibechana-53971	266	9	progress	progress	NOUN
bibechana-53971	266	10	significant	significant	ADJ
bibechana-53971	266	11	but	but	CCONJ
bibechana-53971	266	12	it	it	PRON
bibechana-53971	266	13	is	be	AUX
bibechana-53971	266	14	also	also	ADV
bibechana-53971	266	15	happening	happen	VERB
bibechana-53971	266	16	quite	quite	ADV
bibechana-53971	266	17	rapidly	rapidly	ADV
bibechana-53971	266	18	compared	compare	VERB
bibechana-53971	266	19	to	to	ADP
bibechana-53971	266	20	l1	l1	NOUN
bibechana-53971	266	21	-	-	PUNCT
bibechana-53971	266	22	formula	formula	NOUN
bibechana-53971	266	23	in	in	ADP
bibechana-53971	266	24	the	the	DET
bibechana-53971	266	25	caputo	caputo	PROPN
bibechana-53971	266	26	-	-	PUNCT
bibechana-53971	266	27	farbrizio	farbrizio	PROPN
bibechana-53971	266	28	sense	sense	NOUN
bibechana-53971	266	29	.	.	PUNCT
bibechana-53971	267	1	figure	figure	VERB
bibechana-53971	267	2	2	2	NUM
bibechana-53971	267	3	:	:	PUNCT
bibechana-53971	267	4	your	your	PRON
bibechana-53971	267	5	figure	figure	NOUN
bibechana-53971	267	6	caption	caption	NOUN
bibechana-53971	267	7	here	here	ADV
bibechana-53971	267	8	.	.	PUNCT
bibechana-53971	268	1	when	when	SCONJ
bibechana-53971	268	2	step	step	NOUN
bibechana-53971	268	3	sizes	size	VERB
bibechana-53971	268	4	h1	h1	VERB
bibechana-53971	268	5	=	=	NOUN
bibechana-53971	268	6	0.1	0.1	NUM
bibechana-53971	268	7	,	,	PUNCT
bibechana-53971	268	8	h2=	h2=	NOUN
bibechana-53971	268	9	0.05	0.05	NUM
bibechana-53971	268	10	,	,	PUNCT
bibechana-53971	268	11	and	and	CCONJ
bibechana-53971	268	12	h	h	NOUN
bibechana-53971	268	13	=	=	NOUN
bibechana-53971	268	14	0.01	0.01	NUM
bibechana-53971	268	15	are	be	AUX
bibechana-53971	268	16	taken	take	VERB
bibechana-53971	268	17	in	in	ADP
bibechana-53971	268	18	the	the	DET
bibechana-53971	268	19	interval	interval	NOUN
bibechana-53971	268	20	[	[	X
bibechana-53971	268	21	0	0	NUM
bibechana-53971	268	22	,	,	PUNCT
bibechana-53971	268	23	2	2	NUM
bibechana-53971	268	24	]	]	PUNCT
bibechana-53971	268	25	,	,	PUNCT
bibechana-53971	268	26	an	an	DET
bibechana-53971	268	27	initial	initial	ADJ
bibechana-53971	268	28	function	function	NOUN
bibechana-53971	268	29	f(x	f(x	PROPN
bibechana-53971	268	30	)	)	PUNCT
bibechana-53971	269	1	=	=	SYM
bibechana-53971	269	2	cos(4x	cos(4x	NOUN
bibechana-53971	269	3	)	)	PUNCT
bibechana-53971	269	4	is	be	AUX
bibechana-53971	269	5	specified	specify	VERB
bibechana-53971	269	6	,	,	PUNCT
bibechana-53971	269	7	with	with	ADP
bibechana-53971	269	8	a	a	DET
bibechana-53971	269	9	curve	curve	NOUN
bibechana-53971	269	10	to	to	ADP
bibechana-53971	269	11	the	the	DET
bibechana-53971	269	12	shankar	shankar	PROPN
bibechana-53971	269	13	pariyar	pariyar	PROPN
bibechana-53971	269	14	and	and	CCONJ
bibechana-53971	269	15	jeevan	jeevan	PROPN
bibechana-53971	269	16	kafle	kafle	PROPN
bibechana-53971	269	17	/	/	PUNCT
bibechana-53971	269	18	bibechana	bibechana	PROPN
bibechana-53971	269	19	20	20	NUM
bibechana-53971	269	20	(	(	PUNCT
bibechana-53971	269	21	2023	2023	NUM
bibechana-53971	269	22	)	)	PUNCT
bibechana-53971	269	23	126	126	NUM
bibechana-53971	269	24	-	-	SYM
bibechana-53971	269	25	133	133	NUM
bibechana-53971	269	26	132	132	NUM
bibechana-53971	269	27	function	function	NOUN
bibechana-53971	269	28	at	at	ADP
bibechana-53971	269	29	each	each	DET
bibechana-53971	269	30	step	step	NOUN
bibechana-53971	269	31	size	size	NOUN
bibechana-53971	269	32	.	.	PUNCT
bibechana-53971	270	1	the	the	DET
bibechana-53971	270	2	figure	figure	NOUN
bibechana-53971	270	3	illustrates	illustrate	VERB
bibechana-53971	270	4	how	how	SCONJ
bibechana-53971	270	5	,	,	PUNCT
bibechana-53971	270	6	as	as	ADP
bibechana-53971	270	7	step	step	NOUN
bibechana-53971	270	8	size	size	NOUN
bibechana-53971	270	9	h	h	NOUN
bibechana-53971	270	10	is	be	AUX
bibechana-53971	270	11	reduced	reduce	VERB
bibechana-53971	270	12	,	,	PUNCT
bibechana-53971	270	13	the	the	DET
bibechana-53971	270	14	approximate	approximate	ADJ
bibechana-53971	270	15	solutions	solution	NOUN
bibechana-53971	270	16	found	find	VERB
bibechana-53971	270	17	using	use	VERB
bibechana-53971	270	18	the	the	DET
bibechana-53971	270	19	l1−	l1−	NOUN
bibechana-53971	270	20	2	2	NUM
bibechana-53971	270	21	backwards	backwards	ADV
bibechana-53971	270	22	approximate	approximate	ADJ
bibechana-53971	270	23	method	method	NOUN
bibechana-53971	270	24	approach	approach	VERB
bibechana-53971	270	25	the	the	DET
bibechana-53971	270	26	exact	exact	ADJ
bibechana-53971	270	27	solution	solution	NOUN
bibechana-53971	270	28	of	of	ADP
bibechana-53971	270	29	the	the	DET
bibechana-53971	270	30	equation	equation	NOUN
bibechana-53971	270	31	f(x	f(x	PROPN
bibechana-53971	270	32	)	)	PUNCT
bibechana-53971	271	1	=	=	PRON
bibechana-53971	271	2	cos(4x).this	cos(4x).this	PROPN
bibechana-53971	271	3	is	be	AUX
bibechana-53971	271	4	so	so	SCONJ
bibechana-53971	271	5	that	that	SCONJ
bibechana-53971	271	6	the	the	DET
bibechana-53971	271	7	function	function	NOUN
bibechana-53971	271	8	’s	’s	PART
bibechana-53971	271	9	derivatives	derivative	NOUN
bibechana-53971	271	10	can	can	AUX
bibechana-53971	271	11	be	be	AUX
bibechana-53971	271	12	approximated	approximate	VERB
bibechana-53971	271	13	with	with	ADP
bibechana-53971	271	14	greater	great	ADJ
bibechana-53971	271	15	accuracy	accuracy	NOUN
bibechana-53971	271	16	using	use	VERB
bibechana-53971	271	17	lower	low	ADJ
bibechana-53971	271	18	step	step	NOUN
bibechana-53971	271	19	sizes	size	NOUN
bibechana-53971	271	20	.	.	PUNCT
bibechana-53971	272	1	5	5	NUM
bibechana-53971	272	2	comparative	comparative	ADJ
bibechana-53971	272	3	analysis	analysis	NOUN
bibechana-53971	272	4	of	of	ADP
bibechana-53971	272	5	a	a	DET
bibechana-53971	272	6	fractional	fractional	ADJ
bibechana-53971	272	7	derivatives	derivative	NOUN
bibechana-53971	272	8	the	the	DET
bibechana-53971	272	9	grunwald	grunwald	NOUN
bibechana-53971	272	10	-	-	PUNCT
bibechana-53971	272	11	letnikov	letnikov	NOUN
bibechana-53971	272	12	,	,	PUNCT
bibechana-53971	272	13	riemann	riemann	PROPN
bibechana-53971	272	14	-	-	PUNCT
bibechana-53971	272	15	liouville	liouville	PROPN
bibechana-53971	272	16	,	,	PUNCT
bibechana-53971	272	17	caputo	caputo	PROPN
bibechana-53971	272	18	,	,	PUNCT
bibechana-53971	272	19	and	and	CCONJ
bibechana-53971	272	20	l1	l1	PROPN
bibechana-53971	272	21	-	-	PUNCT
bibechana-53971	272	22	2	2	NUM
bibechana-53971	272	23	methods	method	NOUN
bibechana-53971	272	24	are	be	AUX
bibechana-53971	272	25	examples	example	NOUN
bibechana-53971	272	26	of	of	ADP
bibechana-53971	272	27	numerical	numerical	ADJ
bibechana-53971	272	28	methods	method	NOUN
bibechana-53971	272	29	for	for	ADP
bibechana-53971	272	30	approximating	approximate	VERB
bibechana-53971	272	31	fractional	fractional	ADJ
bibechana-53971	272	32	derivatives	derivative	NOUN
bibechana-53971	272	33	.	.	PUNCT
bibechana-53971	273	1	below	below	ADV
bibechana-53971	273	2	is	be	AUX
bibechana-53971	273	3	a	a	DET
bibechana-53971	273	4	brief	brief	ADJ
bibechana-53971	273	5	comparison	comparison	NOUN
bibechana-53971	273	6	of	of	ADP
bibechana-53971	273	7	these	these	DET
bibechana-53971	273	8	two	two	NUM
bibechana-53971	273	9	methods	method	NOUN
bibechana-53971	273	10	:	:	PUNCT
bibechana-53971	273	11	accuracy	accuracy	NOUN
bibechana-53971	273	12	:	:	PUNCT
bibechana-53971	273	13	when	when	SCONJ
bibechana-53971	273	14	the	the	DET
bibechana-53971	273	15	fractional	fractional	ADJ
bibechana-53971	273	16	derivative	derivative	NOUN
bibechana-53971	273	17	’s	’s	PART
bibechana-53971	273	18	order	order	NOUN
bibechana-53971	273	19	is	be	AUX
bibechana-53971	273	20	f	f	PROPN
bibechana-53971	273	21	and	and	CCONJ
bibechana-53971	273	22	the	the	DET
bibechana-53971	273	23	step	step	NOUN
bibechana-53971	273	24	size	size	NOUN
bibechana-53971	273	25	is	be	AUX
bibechana-53971	273	26	h	h	NOUN
bibechana-53971	273	27	the	the	DET
bibechana-53971	273	28	convergence	convergence	NOUN
bibechana-53971	273	29	rate	rate	NOUN
bibechana-53971	273	30	of	of	ADP
bibechana-53971	273	31	the	the	DET
bibechana-53971	273	32	grunwald	grunwald	NOUN
bibechana-53971	273	33	-	-	PUNCT
bibechana-53971	273	34	letnikov	letnikov	NOUN
bibechana-53971	273	35	method	method	NOUN
bibechana-53971	273	36	is	be	AUX
bibechana-53971	273	37	o(hα	o(hα	NUM
bibechana-53971	273	38	)	)	PUNCT
bibechana-53971	273	39	.	.	PUNCT
bibechana-53971	274	1	the	the	DET
bibechana-53971	274	2	rate	rate	NOUN
bibechana-53971	274	3	of	of	ADP
bibechana-53971	274	4	convergence	convergence	NOUN
bibechana-53971	274	5	is	be	AUX
bibechana-53971	274	6	not	not	PART
bibechana-53971	274	7	as	as	ADV
bibechana-53971	274	8	rapid	rapid	ADJ
bibechana-53971	274	9	as	as	ADP
bibechana-53971	274	10	other	other	ADJ
bibechana-53971	274	11	methods	method	NOUN
bibechana-53971	274	12	.	.	PUNCT
bibechana-53971	275	1	•	•	NUM
bibechana-53971	275	2	generally	generally	ADV
bibechana-53971	275	3	speaking	speak	VERB
bibechana-53971	275	4	,	,	PUNCT
bibechana-53971	275	5	the	the	DET
bibechana-53971	275	6	riemann	riemann	PROPN
bibechana-53971	275	7	-	-	PUNCT
bibechana-53971	275	8	liouville	liouville	NOUN
bibechana-53971	275	9	technique	technique	NOUN
bibechana-53971	275	10	,	,	PUNCT
bibechana-53971	275	11	which	which	PRON
bibechana-53971	275	12	has	have	VERB
bibechana-53971	275	13	a	a	DET
bibechana-53971	275	14	convergence	convergence	NOUN
bibechana-53971	275	15	rate	rate	NOUN
bibechana-53971	275	16	of	of	ADP
bibechana-53971	275	17	o(h2	o(h2	NOUN
bibechana-53971	275	18	)	)	PUNCT
bibechana-53971	275	19	,	,	PUNCT
bibechana-53971	275	20	is	be	AUX
bibechana-53971	275	21	more	more	ADV
bibechana-53971	275	22	accurate	accurate	ADJ
bibechana-53971	275	23	than	than	ADP
bibechana-53971	275	24	the	the	DET
bibechana-53971	275	25	grunwald	grunwald	NOUN
bibechana-53971	275	26	-	-	PUNCT
bibechana-53971	275	27	letnikov	letnikov	NOUN
bibechana-53971	275	28	method	method	NOUN
bibechana-53971	275	29	.	.	PUNCT
bibechana-53971	276	1	•	•	NUM
bibechana-53971	276	2	the	the	DET
bibechana-53971	276	3	caputo	caputo	PROPN
bibechana-53971	276	4	-	-	PUNCT
bibechana-53971	276	5	fabrizio	fabrizio	PROPN
bibechana-53971	276	6	technique	technique	NOUN
bibechana-53971	276	7	is	be	AUX
bibechana-53971	276	8	quicker	quick	ADJ
bibechana-53971	276	9	than	than	ADP
bibechana-53971	276	10	the	the	DET
bibechana-53971	276	11	grunwald	grunwald	NOUN
bibechana-53971	276	12	-	-	PUNCT
bibechana-53971	276	13	letnikov	letnikov	PROPN
bibechana-53971	276	14	and	and	CCONJ
bibechana-53971	276	15	riemann	riemann	PROPN
bibechana-53971	276	16	-	-	PUNCT
bibechana-53971	276	17	liouville	liouville	VERB
bibechana-53971	276	18	methods	method	NOUN
bibechana-53971	276	19	,	,	PUNCT
bibechana-53971	276	20	with	with	ADP
bibechana-53971	276	21	a	a	DET
bibechana-53971	276	22	convergence	convergence	NOUN
bibechana-53971	276	23	rate	rate	NOUN
bibechana-53971	276	24	of	of	ADP
bibechana-53971	276	25	o(h2	o(h2	NOUN
bibechana-53971	276	26	)	)	PUNCT
bibechana-53971	276	27	.	.	PUNCT
bibechana-53971	277	1	•	•	NUM
bibechana-53971	277	2	the	the	DET
bibechana-53971	277	3	quickest	quick	ADJ
bibechana-53971	277	4	of	of	ADP
bibechana-53971	277	5	all	all	DET
bibechana-53971	277	6	the	the	DET
bibechana-53971	277	7	approaches	approach	NOUN
bibechana-53971	277	8	,	,	PUNCT
bibechana-53971	277	9	the	the	DET
bibechana-53971	277	10	l1	l1	PROPN
bibechana-53971	277	11	-	-	PUNCT
bibechana-53971	277	12	2	2	NUM
bibechana-53971	277	13	caputo	caputo	NOUN
bibechana-53971	277	14	method	method	NOUN
bibechana-53971	277	15	converges	converge	VERB
bibechana-53971	277	16	at	at	ADP
bibechana-53971	277	17	a	a	DET
bibechana-53971	277	18	rate	rate	NOUN
bibechana-53971	277	19	of	of	ADP
bibechana-53971	277	20	o(h3	o(h3	NOUN
bibechana-53971	277	21	)	)	PUNCT
bibechana-53971	277	22	.	.	PUNCT
bibechana-53971	278	1	efficiency	efficiency	NOUN
bibechana-53971	278	2	:	:	PUNCT
bibechana-53971	278	3	•	•	ADP
bibechana-53971	278	4	the	the	DET
bibechana-53971	278	5	grunwald	grunwald	NOUN
bibechana-53971	278	6	-	-	PUNCT
bibechana-53971	278	7	letnikov	letnikov	NOUN
bibechana-53971	278	8	approach	approach	NOUN
bibechana-53971	278	9	only	only	ADV
bibechana-53971	278	10	needs	need	VERB
bibechana-53971	278	11	to	to	PART
bibechana-53971	278	12	evaluate	evaluate	VERB
bibechana-53971	278	13	a	a	DET
bibechana-53971	278	14	discrete	discrete	ADJ
bibechana-53971	278	15	convolution	convolution	NOUN
bibechana-53971	278	16	,	,	PUNCT
bibechana-53971	278	17	hence	hence	ADV
bibechana-53971	278	18	it	it	PRON
bibechana-53971	278	19	is	be	AUX
bibechana-53971	278	20	computationally	computationally	ADV
bibechana-53971	278	21	efficient	efficient	ADJ
bibechana-53971	278	22	.	.	PUNCT
bibechana-53971	279	1	•	•	CCONJ
bibechana-53971	279	2	the	the	DET
bibechana-53971	279	3	riemann	riemann	PROPN
bibechana-53971	279	4	-	-	PUNCT
bibechana-53971	279	5	liouville	liouville	VERB
bibechana-53971	279	6	approach	approach	NOUN
bibechana-53971	279	7	can	can	AUX
bibechana-53971	279	8	be	be	AUX
bibechana-53971	279	9	computationally	computationally	ADV
bibechana-53971	279	10	demanding	demand	VERB
bibechana-53971	279	11	since	since	SCONJ
bibechana-53971	279	12	it	it	PRON
bibechana-53971	279	13	uses	use	VERB
bibechana-53971	279	14	numerous	numerous	ADJ
bibechana-53971	279	15	integrals	integral	NOUN
bibechana-53971	279	16	.	.	PUNCT
bibechana-53971	280	1	•	•	NOUN
bibechana-53971	280	2	utilizing	utilize	VERB
bibechana-53971	280	3	a	a	DET
bibechana-53971	280	4	finite	finite	ADJ
bibechana-53971	280	5	difference	difference	NOUN
bibechana-53971	280	6	formula	formula	NOUN
bibechana-53971	280	7	,	,	PUNCT
bibechana-53971	280	8	the	the	DET
bibechana-53971	280	9	caputofabrizio	caputofabrizio	NOUN
bibechana-53971	280	10	technique	technique	NOUN
bibechana-53971	280	11	is	be	AUX
bibechana-53971	280	12	computationally	computationally	ADV
bibechana-53971	280	13	effective	effective	ADJ
bibechana-53971	280	14	.	.	PUNCT
bibechana-53971	281	1	•	•	ADP
bibechana-53971	281	2	to	to	PART
bibechana-53971	281	3	employ	employ	VERB
bibechana-53971	281	4	the	the	DET
bibechana-53971	281	5	computationally	computationally	ADV
bibechana-53971	281	6	effective	effective	ADJ
bibechana-53971	281	7	l1	l1	PROPN
bibechana-53971	281	8	-	-	PUNCT
bibechana-53971	281	9	2	2	NUM
bibechana-53971	281	10	caputo	caputo	NOUN
bibechana-53971	281	11	approach	approach	NOUN
bibechana-53971	281	12	,	,	PUNCT
bibechana-53971	281	13	the	the	DET
bibechana-53971	281	14	quadratic	quadratic	ADJ
bibechana-53971	281	15	interpolation	interpolation	NOUN
bibechana-53971	281	16	formula	formula	NOUN
bibechana-53971	281	17	must	must	AUX
bibechana-53971	281	18	be	be	AUX
bibechana-53971	281	19	assessed	assess	VERB
bibechana-53971	281	20	.	.	PUNCT
bibechana-53971	282	1	stability	stability	NOUN
bibechana-53971	282	2	:	:	PUNCT
bibechana-53971	282	3	•	•	ADP
bibechana-53971	282	4	the	the	DET
bibechana-53971	282	5	grunwald	grunwald	NOUN
bibechana-53971	282	6	-	-	PUNCT
bibechana-53971	282	7	letnikov	letnikov	NOUN
bibechana-53971	282	8	method	method	NOUN
bibechana-53971	282	9	could	could	AUX
bibechana-53971	282	10	be	be	AUX
bibechana-53971	282	11	numerically	numerically	ADV
bibechana-53971	282	12	unstable	unstable	ADJ
bibechana-53971	282	13	depending	depend	VERB
bibechana-53971	282	14	on	on	ADP
bibechana-53971	282	15	the	the	DET
bibechana-53971	282	16	values	value	NOUN
bibechana-53971	282	17	of	of	ADP
bibechana-53971	282	18	the	the	DET
bibechana-53971	282	19	fractional	fractional	ADJ
bibechana-53971	282	20	derivative	derivative	ADJ
bibechana-53971	282	21	order	order	NOUN
bibechana-53971	282	22	and	and	CCONJ
bibechana-53971	282	23	step	step	NOUN
bibechana-53971	282	24	size	size	NOUN
bibechana-53971	282	25	.	.	PUNCT
bibechana-53971	283	1	•	•	NUM
bibechana-53971	283	2	the	the	DET
bibechana-53971	283	3	riemann	riemann	PROPN
bibechana-53971	283	4	-	-	PUNCT
bibechana-53971	283	5	liouville	liouville	NOUN
bibechana-53971	283	6	method	method	NOUN
bibechana-53971	283	7	could	could	AUX
bibechana-53971	283	8	be	be	AUX
bibechana-53971	283	9	numerically	numerically	ADV
bibechana-53971	283	10	unstable	unstable	ADJ
bibechana-53971	283	11	for	for	ADP
bibechana-53971	283	12	particular	particular	ADJ
bibechana-53971	283	13	values	value	NOUN
bibechana-53971	283	14	of	of	ADP
bibechana-53971	283	15	the	the	DET
bibechana-53971	283	16	fractional	fractional	ADJ
bibechana-53971	283	17	derivative	derivative	ADJ
bibechana-53971	283	18	order	order	NOUN
bibechana-53971	283	19	and	and	CCONJ
bibechana-53971	283	20	integration	integration	NOUN
bibechana-53971	283	21	limitations	limitation	NOUN
bibechana-53971	283	22	.	.	PUNCT
bibechana-53971	284	1	•	•	NUM
bibechana-53971	284	2	the	the	DET
bibechana-53971	284	3	caputo	caputo	PROPN
bibechana-53971	284	4	-	-	PUNCT
bibechana-53971	284	5	fabrizio	fabrizio	PROPN
bibechana-53971	284	6	approach	approach	NOUN
bibechana-53971	284	7	is	be	AUX
bibechana-53971	284	8	often	often	ADV
bibechana-53971	284	9	stable	stable	ADJ
bibechana-53971	284	10	,	,	PUNCT
bibechana-53971	284	11	however	however	ADV
bibechana-53971	284	12	it	it	PRON
bibechana-53971	284	13	can	can	AUX
bibechana-53971	284	14	be	be	AUX
bibechana-53971	284	15	sensitive	sensitive	ADJ
bibechana-53971	284	16	to	to	ADP
bibechana-53971	284	17	the	the	DET
bibechana-53971	284	18	selection	selection	NOUN
bibechana-53971	284	19	of	of	ADP
bibechana-53971	284	20	step	step	NOUN
bibechana-53971	284	21	size	size	NOUN
bibechana-53971	284	22	.	.	PUNCT
bibechana-53971	285	1	•	•	NOUN
bibechana-53971	285	2	generally	generally	ADV
bibechana-53971	285	3	consistent	consistent	ADJ
bibechana-53971	285	4	and	and	CCONJ
bibechana-53971	285	5	accurate	accurate	ADJ
bibechana-53971	285	6	with	with	ADP
bibechana-53971	285	7	the	the	DET
bibechana-53971	285	8	l1	l1	PROPN
bibechana-53971	285	9	-	-	PUNCT
bibechana-53971	285	10	2	2	NUM
bibechana-53971	285	11	caputo	caputo	NOUN
bibechana-53971	285	12	approach	approach	NOUN
bibechana-53971	285	13	.	.	PUNCT
bibechana-53971	286	1	robustness	robustness	NOUN
bibechana-53971	286	2	:	:	PUNCT
bibechana-53971	286	3	•	•	ADP
bibechana-53971	286	4	the	the	DET
bibechana-53971	286	5	grunwald	grunwald	NOUN
bibechana-53971	286	6	-	-	PUNCT
bibechana-53971	286	7	letnikov	letnikov	NOUN
bibechana-53971	286	8	method	method	NOUN
bibechana-53971	286	9	is	be	AUX
bibechana-53971	286	10	a	a	DET
bibechana-53971	286	11	usually	usually	ADV
bibechana-53971	286	12	reliable	reliable	ADJ
bibechana-53971	286	13	technique	technique	NOUN
bibechana-53971	286	14	that	that	PRON
bibechana-53971	286	15	can	can	AUX
bibechana-53971	286	16	be	be	AUX
bibechana-53971	286	17	used	use	VERB
bibechana-53971	286	18	to	to	PART
bibechana-53971	286	19	calculate	calculate	VERB
bibechana-53971	286	20	fractional	fractional	ADJ
bibechana-53971	286	21	derivatives	derivative	NOUN
bibechana-53971	286	22	for	for	ADP
bibechana-53971	286	23	a	a	DET
bibechana-53971	286	24	variety	variety	NOUN
bibechana-53971	286	25	of	of	ADP
bibechana-53971	286	26	functions	function	NOUN
bibechana-53971	286	27	.	.	PUNCT
bibechana-53971	287	1	•	•	NUM
bibechana-53971	287	2	the	the	DET
bibechana-53971	287	3	riemann	riemann	PROPN
bibechana-53971	287	4	-	-	PUNCT
bibechana-53971	287	5	liouville	liouville	VERB
bibechana-53971	287	6	approach	approach	NOUN
bibechana-53971	287	7	is	be	AUX
bibechana-53971	287	8	susceptible	susceptible	ADJ
bibechana-53971	287	9	to	to	ADP
bibechana-53971	287	10	the	the	DET
bibechana-53971	287	11	characteristics	characteristic	NOUN
bibechana-53971	287	12	of	of	ADP
bibechana-53971	287	13	the	the	DET
bibechana-53971	287	14	function	function	NOUN
bibechana-53971	287	15	being	be	AUX
bibechana-53971	287	16	differentiated	differentiate	VERB
bibechana-53971	287	17	and	and	CCONJ
bibechana-53971	287	18	can	can	AUX
bibechana-53971	287	19	be	be	AUX
bibechana-53971	287	20	constrained	constrain	VERB
bibechana-53971	287	21	by	by	ADP
bibechana-53971	287	22	the	the	DET
bibechana-53971	287	23	selection	selection	NOUN
bibechana-53971	287	24	of	of	ADP
bibechana-53971	287	25	integration	integration	NOUN
bibechana-53971	287	26	limits	limit	NOUN
bibechana-53971	287	27	.	.	PUNCT
bibechana-53971	288	1	•	•	NUM
bibechana-53971	288	2	the	the	DET
bibechana-53971	288	3	caputo	caputo	PROPN
bibechana-53971	288	4	-	-	PUNCT
bibechana-53971	288	5	fabrizio	fabrizio	PROPN
bibechana-53971	288	6	method	method	NOUN
bibechana-53971	288	7	can	can	AUX
bibechana-53971	288	8	compute	compute	VERB
bibechana-53971	288	9	fractional	fractional	ADJ
bibechana-53971	288	10	derivatives	derivative	NOUN
bibechana-53971	288	11	for	for	ADP
bibechana-53971	288	12	a	a	DET
bibechana-53971	288	13	variety	variety	NOUN
bibechana-53971	288	14	of	of	ADP
bibechana-53971	288	15	functions	function	NOUN
bibechana-53971	288	16	and	and	CCONJ
bibechana-53971	288	17	is	be	AUX
bibechana-53971	288	18	generally	generally	ADV
bibechana-53971	288	19	reliable	reliable	ADJ
bibechana-53971	288	20	.	.	PUNCT
bibechana-53971	289	1	•	•	ADP
bibechana-53971	289	2	the	the	DET
bibechana-53971	289	3	l1	l1	PROPN
bibechana-53971	289	4	-	-	PUNCT
bibechana-53971	289	5	2	2	NUM
bibechana-53971	289	6	caputo	caputo	NOUN
bibechana-53971	289	7	method	method	NOUN
bibechana-53971	289	8	is	be	AUX
bibechana-53971	289	9	a	a	DET
bibechana-53971	289	10	usually	usually	ADV
bibechana-53971	289	11	reliable	reliable	ADJ
bibechana-53971	289	12	technique	technique	NOUN
bibechana-53971	289	13	that	that	PRON
bibechana-53971	289	14	can	can	AUX
bibechana-53971	289	15	be	be	AUX
bibechana-53971	289	16	used	use	VERB
bibechana-53971	289	17	to	to	PART
bibechana-53971	289	18	calculate	calculate	VERB
bibechana-53971	289	19	fractional	fractional	ADJ
bibechana-53971	289	20	derivatives	derivative	NOUN
bibechana-53971	289	21	for	for	ADP
bibechana-53971	289	22	a	a	DET
bibechana-53971	289	23	variety	variety	NOUN
bibechana-53971	289	24	of	of	ADP
bibechana-53971	289	25	functions	function	NOUN
bibechana-53971	289	26	.	.	PUNCT
bibechana-53971	290	1	the	the	DET
bibechana-53971	290	2	l1	l1	PROPN
bibechana-53971	290	3	-	-	PUNCT
bibechana-53971	290	4	2	2	NUM
bibechana-53971	290	5	caputo	caputo	NOUN
bibechana-53971	290	6	approach	approach	NOUN
bibechana-53971	290	7	is	be	AUX
bibechana-53971	290	8	the	the	DET
bibechana-53971	290	9	most	most	ADV
bibechana-53971	290	10	precise	precise	ADJ
bibechana-53971	290	11	,	,	PUNCT
bibechana-53971	290	12	effective	effective	ADJ
bibechana-53971	290	13	,	,	PUNCT
bibechana-53971	290	14	stable	stable	ADJ
bibechana-53971	290	15	,	,	PUNCT
bibechana-53971	290	16	and	and	CCONJ
bibechana-53971	290	17	reliable	reliable	ADJ
bibechana-53971	290	18	of	of	ADP
bibechana-53971	290	19	the	the	DET
bibechana-53971	290	20	four	four	NUM
bibechana-53971	290	21	ways	way	NOUN
bibechana-53971	290	22	,	,	PUNCT
bibechana-53971	290	23	to	to	PART
bibechana-53971	290	24	put	put	VERB
bibechana-53971	290	25	it	it	PRON
bibechana-53971	290	26	briefly	briefly	ADV
bibechana-53971	290	27	.	.	PUNCT
bibechana-53971	291	1	although	although	SCONJ
bibechana-53971	291	2	less	less	ADV
bibechana-53971	291	3	precise	precise	ADJ
bibechana-53971	291	4	and	and	CCONJ
bibechana-53971	291	5	effective	effective	ADJ
bibechana-53971	291	6	than	than	ADP
bibechana-53971	291	7	the	the	DET
bibechana-53971	291	8	l1	l1	PROPN
bibechana-53971	291	9	-	-	PUNCT
bibechana-53971	291	10	2	2	NUM
bibechana-53971	291	11	caputo	caputo	NOUN
bibechana-53971	291	12	method	method	NOUN
bibechana-53971	291	13	,	,	PUNCT
bibechana-53971	291	14	the	the	DET
bibechana-53971	291	15	caputo	caputo	PROPN
bibechana-53971	291	16	-	-	PUNCT
bibechana-53971	291	17	fabrizio	fabrizio	PROPN
bibechana-53971	291	18	approach	approach	NOUN
bibechana-53971	291	19	is	be	AUX
bibechana-53971	291	20	nevertheless	nevertheless	ADV
bibechana-53971	291	21	a	a	DET
bibechana-53971	291	22	viable	viable	ADJ
bibechana-53971	291	23	alternative	alternative	NOUN
bibechana-53971	291	24	.	.	PUNCT
bibechana-53971	292	1	compared	compare	VERB
bibechana-53971	292	2	to	to	ADP
bibechana-53971	292	3	caputo	caputo	PROPN
bibechana-53971	292	4	-	-	PUNCT
bibechana-53971	292	5	based	base	VERB
bibechana-53971	292	6	approaches	approach	NOUN
bibechana-53971	292	7	,	,	PUNCT
bibechana-53971	292	8	the	the	DET
bibechana-53971	292	9	grunwald	grunwald	NOUN
bibechana-53971	292	10	-	-	PUNCT
bibechana-53971	292	11	letnikov	letnikov	PROPN
bibechana-53971	292	12	and	and	CCONJ
bibechana-53971	292	13	riemann	riemann	PROPN
bibechana-53971	292	14	-	-	PUNCT
bibechana-53971	292	15	liouville	liouville	VERB
bibechana-53971	292	16	methods	method	NOUN
bibechana-53971	292	17	are	be	AUX
bibechana-53971	292	18	typically	typically	ADV
bibechana-53971	292	19	less	less	ADV
bibechana-53971	292	20	precise	precise	ADJ
bibechana-53971	292	21	,	,	PUNCT
bibechana-53971	292	22	less	less	ADV
bibechana-53971	292	23	effective	effective	ADJ
bibechana-53971	292	24	,	,	PUNCT
bibechana-53971	292	25	and	and	CCONJ
bibechana-53971	292	26	can	can	AUX
bibechana-53971	292	27	be	be	AUX
bibechana-53971	292	28	vulnerable	vulnerable	ADJ
bibechana-53971	292	29	to	to	ADP
bibechana-53971	292	30	numerical	numerical	ADJ
bibechana-53971	292	31	instabilities	instability	NOUN
bibechana-53971	292	32	.	.	PUNCT
bibechana-53971	293	1	6	6	NUM
bibechana-53971	293	2	conclusion	conclusion	NOUN
bibechana-53971	293	3	our	our	PRON
bibechana-53971	293	4	approach	approach	NOUN
bibechana-53971	293	5	is	be	AUX
bibechana-53971	293	6	different	different	ADJ
bibechana-53971	293	7	from	from	ADP
bibechana-53971	293	8	most	most	ADJ
bibechana-53971	293	9	other	other	ADJ
bibechana-53971	293	10	domains	domain	NOUN
bibechana-53971	293	11	.	.	PUNCT
bibechana-53971	294	1	a	a	DET
bibechana-53971	294	2	unique	unique	ADJ
bibechana-53971	294	3	numerical	numerical	ADJ
bibechana-53971	294	4	approach	approach	NOUN
bibechana-53971	294	5	called	call	VERB
bibechana-53971	294	6	as	as	ADP
bibechana-53971	294	7	l1	l1	PROPN
bibechana-53971	294	8	,	,	PUNCT
bibechana-53971	294	9	l2	l2	NOUN
bibechana-53971	294	10	,	,	PUNCT
bibechana-53971	294	11	l1	l1	PROPN
bibechana-53971	294	12	has	have	AUX
bibechana-53971	294	13	been	be	AUX
bibechana-53971	294	14	devised	devise	VERB
bibechana-53971	294	15	using	use	VERB
bibechana-53971	294	16	the	the	DET
bibechana-53971	294	17	linear	linear	ADJ
bibechana-53971	294	18	and	and	CCONJ
bibechana-53971	294	19	cubic	cubic	ADJ
bibechana-53971	294	20	interpolations	interpolation	NOUN
bibechana-53971	294	21	for	for	ADP
bibechana-53971	294	22	the	the	DET
bibechana-53971	294	23	numerical	numerical	ADJ
bibechana-53971	294	24	solution	solution	NOUN
bibechana-53971	294	25	of	of	ADP
bibechana-53971	294	26	the	the	DET
bibechana-53971	294	27	cfd	cfd	NOUN
bibechana-53971	294	28	.	.	PUNCT
bibechana-53971	295	1	it	it	PRON
bibechana-53971	295	2	uses	use	VERB
bibechana-53971	295	3	the	the	DET
bibechana-53971	295	4	caputofabrizio	caputofabrizio	NOUN
bibechana-53971	295	5	sense	sense	NOUN
bibechana-53971	295	6	and	and	CCONJ
bibechana-53971	295	7	l1	l1	PROPN
bibechana-53971	295	8	-	-	PUNCT
bibechana-53971	295	9	2	2	NUM
bibechana-53971	295	10	formula	formula	NOUN
bibechana-53971	295	11	.	.	PUNCT
bibechana-53971	296	1	for	for	ADP
bibechana-53971	296	2	backward	backward	ADV
bibechana-53971	296	3	/	/	SYM
bibechana-53971	296	4	forward	forward	ADJ
bibechana-53971	296	5	approximations	approximation	NOUN
bibechana-53971	296	6	,	,	PUNCT
bibechana-53971	296	7	the	the	DET
bibechana-53971	296	8	fourth	fourth	ADJ
bibechana-53971	296	9	-	-	PUNCT
bibechana-53971	296	10	order	order	NOUN
bibechana-53971	296	11	convergence	convergence	NOUN
bibechana-53971	296	12	rate	rate	NOUN
bibechana-53971	296	13	is	be	AUX
bibechana-53971	296	14	found	find	VERB
bibechana-53971	296	15	for	for	ADP
bibechana-53971	296	16	backward	backward	ADJ
bibechana-53971	296	17	approximations	approximation	NOUN
bibechana-53971	296	18	,	,	PUNCT
bibechana-53971	296	19	while	while	SCONJ
bibechana-53971	296	20	the	the	DET
bibechana-53971	296	21	l1	l1	PROPN
bibechana-53971	296	22	and	and	CCONJ
bibechana-53971	296	23	l1	l1	PROPN
bibechana-53971	296	24	-	-	PUNCT
bibechana-53971	296	25	2	2	NUM
bibechana-53971	296	26	equations	equation	NOUN
bibechana-53971	296	27	provide	provide	VERB
bibechana-53971	296	28	quadratic	quadratic	ADJ
bibechana-53971	296	29	and	and	CCONJ
bibechana-53971	296	30	cubic	cubic	ADJ
bibechana-53971	296	31	convergence	convergence	NOUN
bibechana-53971	296	32	rates	rate	NOUN
bibechana-53971	296	33	.	.	PUNCT
bibechana-53971	297	1	the	the	DET
bibechana-53971	297	2	numerical	numerical	ADJ
bibechana-53971	297	3	outcomes	outcome	NOUN
bibechana-53971	297	4	were	be	AUX
bibechana-53971	297	5	consistent	consistent	ADJ
bibechana-53971	297	6	with	with	ADP
bibechana-53971	297	7	a	a	DET
bibechana-53971	297	8	well	well	ADV
bibechana-53971	297	9	-	-	PUNCT
bibechana-53971	297	10	known	know	VERB
bibechana-53971	297	11	functions	function	NOUN
bibechana-53971	297	12	for	for	ADP
bibechana-53971	297	13	different	different	ADJ
bibechana-53971	297	14	orders	order	NOUN
bibechana-53971	297	15	and	and	CCONJ
bibechana-53971	297	16	varied	varied	ADJ
bibechana-53971	297	17	step	step	NOUN
bibechana-53971	297	18	sizes	size	NOUN
bibechana-53971	297	19	.	.	PUNCT
bibechana-53971	298	1	every	every	DET
bibechana-53971	298	2	one	one	NUM
bibechana-53971	298	3	of	of	ADP
bibechana-53971	298	4	these	these	DET
bibechana-53971	298	5	approaches	approach	NOUN
bibechana-53971	298	6	has	have	VERB
bibechana-53971	298	7	advantages	advantage	NOUN
bibechana-53971	298	8	and	and	CCONJ
bibechana-53971	298	9	disadvantages	disadvantage	NOUN
bibechana-53971	298	10	.	.	PUNCT
bibechana-53971	299	1	in	in	ADP
bibechana-53971	299	2	contrast	contrast	NOUN
bibechana-53971	299	3	to	to	ADP
bibechana-53971	299	4	the	the	DET
bibechana-53971	299	5	riemannliouville	riemannliouville	NOUN
bibechana-53971	299	6	technique	technique	NOUN
bibechana-53971	299	7	,	,	PUNCT
bibechana-53971	299	8	which	which	PRON
bibechana-53971	299	9	can	can	AUX
bibechana-53971	299	10	be	be	AUX
bibechana-53971	299	11	challenging	challenge	VERB
bibechana-53971	299	12	to	to	PART
bibechana-53971	299	13	compute	compute	VERB
bibechana-53971	299	14	because	because	SCONJ
bibechana-53971	299	15	of	of	ADP
bibechana-53971	299	16	singularities	singularity	NOUN
bibechana-53971	299	17	,	,	PUNCT
bibechana-53971	299	18	the	the	DET
bibechana-53971	299	19	grünwald	grünwald	NOUN
bibechana-53971	299	20	-	-	PUNCT
bibechana-53971	299	21	letnikov	letnikov	NOUN
bibechana-53971	299	22	approach	approach	NOUN
bibechana-53971	299	23	is	be	AUX
bibechana-53971	299	24	simple	simple	ADJ
bibechana-53971	299	25	to	to	PART
bibechana-53971	299	26	construct	construct	VERB
bibechana-53971	299	27	but	but	CCONJ
bibechana-53971	299	28	can	can	AUX
bibechana-53971	299	29	be	be	AUX
bibechana-53971	299	30	slow	slow	ADJ
bibechana-53971	299	31	.	.	PUNCT
bibechana-53971	300	1	the	the	DET
bibechana-53971	300	2	l1	l1	PROPN
bibechana-53971	300	3	-	-	PUNCT
bibechana-53971	300	4	2	2	NUM
bibechana-53971	300	5	method	method	NOUN
bibechana-53971	300	6	is	be	AUX
bibechana-53971	300	7	a	a	DET
bibechana-53971	300	8	promising	promising	ADJ
bibechana-53971	300	9	new	new	ADJ
bibechana-53971	300	10	approach	approach	NOUN
bibechana-53971	300	11	with	with	ADP
bibechana-53971	300	12	a	a	DET
bibechana-53971	300	13	greater	great	ADJ
bibechana-53971	300	14	convergence	convergence	NOUN
bibechana-53971	300	15	rate	rate	NOUN
bibechana-53971	300	16	,	,	PUNCT
bibechana-53971	300	17	in	in	ADP
bibechana-53971	300	18	contrast	contrast	NOUN
bibechana-53971	300	19	to	to	ADP
bibechana-53971	300	20	the	the	DET
bibechana-53971	300	21	widely	widely	ADV
bibechana-53971	300	22	used	use	VERB
bibechana-53971	300	23	caputo	caputo	PROPN
bibechana-53971	300	24	method	method	PROPN
bibechana-53971	300	25	,	,	PUNCT
bibechana-53971	300	26	which	which	PRON
bibechana-53971	300	27	can	can	AUX
bibechana-53971	300	28	have	have	VERB
bibechana-53971	300	29	accuracy	accuracy	NOUN
bibechana-53971	300	30	problems	problem	NOUN
bibechana-53971	300	31	.	.	PUNCT
bibechana-53971	301	1	the	the	DET
bibechana-53971	301	2	particular	particular	ADJ
bibechana-53971	301	3	application	application	NOUN
bibechana-53971	301	4	and	and	CCONJ
bibechana-53971	301	5	the	the	DET
bibechana-53971	301	6	trade	trade	NOUN
bibechana-53971	301	7	-	-	PUNCT
bibechana-53971	301	8	offs	off	NOUN
bibechana-53971	301	9	between	between	ADP
bibechana-53971	301	10	precision	precision	NOUN
bibechana-53971	301	11	,	,	PUNCT
bibechana-53971	301	12	effectiveness	effectiveness	NOUN
bibechana-53971	301	13	,	,	PUNCT
bibechana-53971	301	14	and	and	CCONJ
bibechana-53971	301	15	simplicity	simplicity	NOUN
bibechana-53971	301	16	will	will	AUX
bibechana-53971	301	17	determine	determine	VERB
bibechana-53971	301	18	the	the	DET
bibechana-53971	301	19	strategy	strategy	NOUN
bibechana-53971	301	20	to	to	PART
bibechana-53971	301	21	choose	choose	VERB
bibechana-53971	301	22	.	.	PUNCT
bibechana-53971	302	1	investigating	investigate	VERB
bibechana-53971	302	2	the	the	DET
bibechana-53971	302	3	l1	l1	PROPN
bibechana-53971	302	4	-	-	PUNCT
bibechana-53971	302	5	2	2	NUM
bibechana-53971	302	6	formula	formula	NOUN
bibechana-53971	302	7	’s	’s	PART
bibechana-53971	302	8	stability	stability	NOUN
bibechana-53971	302	9	and	and	CCONJ
bibechana-53971	302	10	resilience	resilience	NOUN
bibechana-53971	302	11	in	in	ADP
bibechana-53971	302	12	the	the	DET
bibechana-53971	302	13	presence	presence	NOUN
bibechana-53971	302	14	of	of	ADP
bibechana-53971	302	15	noise	noise	NOUN
bibechana-53971	302	16	or	or	CCONJ
bibechana-53971	302	17	other	other	ADJ
bibechana-53971	302	18	error	error	NOUN
bibechana-53971	302	19	sources	source	NOUN
bibechana-53971	302	20	might	might	AUX
bibechana-53971	302	21	be	be	AUX
bibechana-53971	302	22	beneficial	beneficial	ADJ
bibechana-53971	302	23	.	.	PUNCT
bibechana-53971	303	1	this	this	PRON
bibechana-53971	303	2	can	can	AUX
bibechana-53971	303	3	entail	entail	VERB
bibechana-53971	303	4	evaluating	evaluate	VERB
bibechana-53971	303	5	the	the	DET
bibechana-53971	303	6	formula	formula	NOUN
bibechana-53971	303	7	’s	’s	PART
bibechana-53971	303	8	response	response	NOUN
bibechana-53971	303	9	to	to	ADP
bibechana-53971	303	10	various	various	ADJ
bibechana-53971	303	11	noise	noise	NOUN
bibechana-53971	303	12	or	or	CCONJ
bibechana-53971	303	13	disturbance	disturbance	NOUN
bibechana-53971	303	14	levels	level	NOUN
bibechana-53971	303	15	and	and	CCONJ
bibechana-53971	303	16	contrasting	contrast	VERB
bibechana-53971	303	17	its	its	PRON
bibechana-53971	303	18	effectiveness	effectiveness	NOUN
bibechana-53971	303	19	with	with	ADP
bibechana-53971	303	20	that	that	PRON
bibechana-53971	303	21	of	of	ADP
bibechana-53971	303	22	alternative	alternative	ADJ
bibechana-53971	303	23	numerical	numerical	ADJ
bibechana-53971	303	24	techniques	technique	NOUN
bibechana-53971	303	25	.	.	PUNCT
bibechana-53971	304	1	references	reference	NOUN
bibechana-53971	304	2	[	[	X
bibechana-53971	304	3	1	1	X
bibechana-53971	304	4	]	]	PUNCT
bibechana-53971	304	5	s.	s.	PROPN
bibechana-53971	304	6	pariyar	pariyar	PROPN
bibechana-53971	304	7	and	and	CCONJ
bibechana-53971	304	8	j.	j.	PROPN
bibechana-53971	304	9	kafle	kafle	PROPN
bibechana-53971	304	10	.	.	PUNCT
bibechana-53971	305	1	approximation	approximation	NOUN
bibechana-53971	305	2	solutions	solution	NOUN
bibechana-53971	305	3	for	for	ADP
bibechana-53971	305	4	solving	solve	VERB
bibechana-53971	305	5	some	some	DET
bibechana-53971	305	6	special	special	ADJ
bibechana-53971	305	7	functions	function	NOUN
bibechana-53971	305	8	of	of	ADP
bibechana-53971	305	9	fractional	fractional	ADJ
bibechana-53971	305	10	calculus	calculus	NOUN
bibechana-53971	305	11	via	via	ADP
bibechana-53971	305	12	caputo	caputo	PROPN
bibechana-53971	305	13	-	-	PUNCT
bibechana-53971	305	14	fabrizio	fabrizio	PROPN
bibechana-53971	305	15	sense	sense	NOUN
bibechana-53971	305	16	.	.	PUNCT
bibechana-53971	306	1	nepal	nepal	PROPN
bibechana-53971	306	2	journal	journal	PROPN
bibechana-53971	306	3	of	of	ADP
bibechana-53971	306	4	mathematical	mathematical	ADJ
bibechana-53971	306	5	sciences	sciences	PROPN
bibechana-53971	306	6	(	(	PUNCT
bibechana-53971	306	7	njms	njms	NOUN
bibechana-53971	306	8	)	)	PUNCT
bibechana-53971	306	9	,	,	PUNCT
bibechana-53971	306	10	3(2):71–80	3(2):71–80	NUM
bibechana-53971	306	11	,	,	PUNCT
bibechana-53971	306	12	2022	2022	NUM
bibechana-53971	306	13	.	.	PUNCT
bibechana-53971	307	1	[	[	X
bibechana-53971	307	2	2	2	NUM
bibechana-53971	307	3	]	]	X
bibechana-53971	307	4	h.t	h.t	PROPN
bibechana-53971	307	5	.	.	PROPN
bibechana-53971	307	6	davis	davis	PROPN
bibechana-53971	307	7	.	.	PUNCT
bibechana-53971	308	1	the	the	DET
bibechana-53971	308	2	theory	theory	NOUN
bibechana-53971	308	3	of	of	ADP
bibechana-53971	308	4	linear	linear	PROPN
bibechana-53971	308	5	operators	operator	NOUN
bibechana-53971	308	6	.	.	PUNCT
bibechana-53971	309	1	myers	myers	PROPN
bibechana-53971	309	2	press	press	PROPN
bibechana-53971	309	3	,	,	PUNCT
bibechana-53971	309	4	bloomington	bloomington	PROPN
bibechana-53971	309	5	,	,	PUNCT
bibechana-53971	309	6	usa	usa	PROPN
bibechana-53971	309	7	,	,	PUNCT
bibechana-53971	309	8	1985	1985	NUM
bibechana-53971	309	9	.	.	PUNCT
bibechana-53971	310	1	shankar	shankar	PROPN
bibechana-53971	310	2	pariyar	pariyar	PROPN
bibechana-53971	310	3	and	and	CCONJ
bibechana-53971	310	4	jeevan	jeevan	PROPN
bibechana-53971	310	5	kafle	kafle	PROPN
bibechana-53971	310	6	/	/	PUNCT
bibechana-53971	310	7	bibechana	bibechana	PROPN
bibechana-53971	310	8	20	20	NUM
bibechana-53971	310	9	(	(	PUNCT
bibechana-53971	310	10	2023	2023	NUM
bibechana-53971	310	11	)	)	PUNCT
bibechana-53971	310	12	126	126	NUM
bibechana-53971	310	13	-	-	SYM
bibechana-53971	310	14	133	133	NUM
bibechana-53971	310	15	133	133	NUM
bibechana-53971	310	16	[	[	X
bibechana-53971	310	17	3	3	X
bibechana-53971	310	18	]	]	X
bibechana-53971	310	19	t.v	t.v	PROPN
bibechana-53971	310	20	.	.	PROPN
bibechana-53971	310	21	aleroev	aleroev	PROPN
bibechana-53971	310	22	and	and	CCONJ
bibechana-53971	310	23	s.v	s.v	PROPN
bibechana-53971	310	24	.	.	PROPN
bibechana-53971	310	25	eronkhin	eronkhin	PROPN
bibechana-53971	310	26	.	.	PUNCT
bibechana-53971	311	1	parameteric	parameteric	ADJ
bibechana-53971	311	2	identification	identification	NOUN
bibechana-53971	311	3	of	of	ADP
bibechana-53971	311	4	the	the	DET
bibechana-53971	311	5	fractional	fractional	ADJ
bibechana-53971	311	6	-	-	PUNCT
bibechana-53971	311	7	derivative	derivative	ADJ
bibechana-53971	311	8	order	order	NOUN
bibechana-53971	311	9	in	in	ADP
bibechana-53971	311	10	the	the	DET
bibechana-53971	311	11	bagley	bagley	NOUN
bibechana-53971	311	12	-	-	PUNCT
bibechana-53971	311	13	torvik	torvik	NOUN
bibechana-53971	311	14	model	model	NOUN
bibechana-53971	311	15	.	.	PUNCT
bibechana-53971	312	1	math	math	NOUN
bibechana-53971	312	2	.	.	PUNCT
bibechana-53971	313	1	models	model	NOUN
bibechana-53971	313	2	comp	comp	PROPN
bibechana-53971	313	3	.	.	PUNCT
bibechana-53971	314	1	simul	simul	PROPN
bibechana-53971	314	2	.	.	PROPN
bibechana-53971	314	3	,	,	PUNCT
bibechana-53971	314	4	2:219–225	2:219–225	NUM
bibechana-53971	314	5	,	,	PUNCT
bibechana-53971	314	6	2019	2019	NUM
bibechana-53971	314	7	.	.	PUNCT
bibechana-53971	315	1	[	[	X
bibechana-53971	315	2	4	4	X
bibechana-53971	315	3	]	]	PUNCT
bibechana-53971	315	4	s.	s.	PROPN
bibechana-53971	315	5	das	das	PROPN
bibechana-53971	315	6	.	.	PUNCT
bibechana-53971	315	7	functional	functional	ADJ
bibechana-53971	315	8	fractional	fractional	ADJ
bibechana-53971	315	9	calculus	calculus	NOUN
bibechana-53971	315	10	.	.	PUNCT
bibechana-53971	315	11	springerverlag	springerverlag	PROPN
bibechana-53971	315	12	.	.	PUNCT
bibechana-53971	315	13	,	,	PUNCT
bibechana-53971	315	14	2nd	2nd	PROPN
bibechana-53971	315	15	edition	edition	NOUN
bibechana-53971	315	16	,	,	PUNCT
bibechana-53971	315	17	2011	2011	NUM
bibechana-53971	315	18	.	.	PUNCT
bibechana-53971	316	1	[	[	X
bibechana-53971	316	2	5	5	X
bibechana-53971	316	3	]	]	X
bibechana-53971	316	4	y.	y.	PROPN
bibechana-53971	316	5	luchko	luchko	VERB
bibechana-53971	316	6	.	.	PUNCT
bibechana-53971	317	1	general	general	ADJ
bibechana-53971	317	2	fractional	fractional	ADJ
bibechana-53971	317	3	integrals	integral	NOUN
bibechana-53971	317	4	and	and	CCONJ
bibechana-53971	317	5	derivatives	derivative	NOUN
bibechana-53971	317	6	of	of	ADP
bibechana-53971	317	7	arbitrary	arbitrary	ADJ
bibechana-53971	317	8	order	order	NOUN
bibechana-53971	317	9	.	.	PUNCT
bibechana-53971	318	1	symmetry	symmetry	NOUN
bibechana-53971	318	2	,	,	PUNCT
bibechana-53971	318	3	13(5):755	13(5):755	NUM
bibechana-53971	318	4	,	,	PUNCT
bibechana-53971	318	5	2021	2021	NUM
bibechana-53971	318	6	.	.	PUNCT
bibechana-53971	319	1	[	[	X
bibechana-53971	319	2	6	6	NUM
bibechana-53971	319	3	]	]	PUNCT
bibechana-53971	319	4	g.	g.	PROPN
bibechana-53971	319	5	jumarie	jumarie	PROPN
bibechana-53971	319	6	.	.	PUNCT
bibechana-53971	320	1	on	on	ADP
bibechana-53971	320	2	the	the	DET
bibechana-53971	320	3	solution	solution	NOUN
bibechana-53971	320	4	of	of	ADP
bibechana-53971	320	5	the	the	DET
bibechana-53971	320	6	stochastic	stochastic	ADJ
bibechana-53971	320	7	differential	differential	ADJ
bibechana-53971	320	8	equation	equation	NOUN
bibechana-53971	320	9	of	of	ADP
bibechana-53971	320	10	exponential	exponential	ADJ
bibechana-53971	320	11	growth	growth	NOUN
bibechana-53971	320	12	driven	drive	VERB
bibechana-53971	320	13	by	by	ADP
bibechana-53971	320	14	fractional	fractional	ADJ
bibechana-53971	320	15	brownian	brownian	ADJ
bibechana-53971	320	16	motion	motion	NOUN
bibechana-53971	320	17	.	.	PUNCT
bibechana-53971	321	1	applied	apply	VERB
bibechana-53971	321	2	mathematics	mathematics	NOUN
bibechana-53971	321	3	letters	letter	NOUN
bibechana-53971	321	4	,	,	PUNCT
bibechana-53971	321	5	18(7):817–826	18(7):817–826	PROPN
bibechana-53971	321	6	,	,	PUNCT
bibechana-53971	321	7	2005	2005	NUM
bibechana-53971	321	8	.	.	PUNCT
bibechana-53971	322	1	[	[	X
bibechana-53971	322	2	7	7	X
bibechana-53971	322	3	]	]	X
bibechana-53971	322	4	g	g	NOUN
bibechana-53971	322	5	mittag	mittag	ADJ
bibechana-53971	322	6	-	-	PUNCT
bibechana-53971	322	7	leffler	leffler	NOUN
bibechana-53971	322	8	.	.	PUNCT
bibechana-53971	323	1	sur	sur	PROPN
bibechana-53971	323	2	la	la	PROPN
bibechana-53971	323	3	nouvelle	nouvelle	PROPN
bibechana-53971	323	4	fonction	fonction	PROPN
bibechana-53971	323	5	eα	eα	X
bibechana-53971	323	6	(	(	PUNCT
bibechana-53971	323	7	x	x	NOUN
bibechana-53971	323	8	)	)	PUNCT
bibechana-53971	323	9	.	.	PUNCT
bibechana-53971	324	1	comptes	compte	VERB
bibechana-53971	324	2	rendus	rendus	PROPN
bibechana-53971	324	3	de	de	PROPN
bibechana-53971	324	4	l’academie	l’academie	VERB
bibechana-53971	324	5	des	des	PROPN
bibechana-53971	324	6	sciences	sciences	PROPN
bibechana-53971	324	7	paris	paris	PROPN
bibechana-53971	324	8	,	,	PUNCT
bibechana-53971	324	9	137:554–558	137:554–558	NUM
bibechana-53971	324	10	,	,	PUNCT
bibechana-53971	324	11	1903	1903	NUM
bibechana-53971	324	12	.	.	PUNCT
bibechana-53971	325	1	[	[	X
bibechana-53971	325	2	8	8	X
bibechana-53971	325	3	]	]	X
bibechana-53971	325	4	j.	j.	PROPN
bibechana-53971	325	5	kafle	kafle	PROPN
bibechana-53971	325	6	,	,	PUNCT
bibechana-53971	325	7	thakur	thakur	PROPN
bibechana-53971	325	8	b.k	b.k	PROPN
bibechana-53971	325	9	.	.	PROPN
bibechana-53971	325	10	,	,	PUNCT
bibechana-53971	325	11	and	and	CCONJ
bibechana-53971	325	12	i.	i.	PROPN
bibechana-53971	325	13	b.	b.	PROPN
bibechana-53971	325	14	bhandari	bhandari	PROPN
bibechana-53971	325	15	.	.	PUNCT
bibechana-53971	326	1	iterative	iterative	NOUN
bibechana-53971	326	2	methods	method	NOUN
bibechana-53971	326	3	for	for	ADP
bibechana-53971	326	4	transient	transient	ADJ
bibechana-53971	326	5	analysis	analysis	NOUN
bibechana-53971	326	6	of	of	ADP
bibechana-53971	326	7	series	series	PROPN
bibechana-53971	326	8	rlc	rlc	PROPN
bibechana-53971	326	9	circuit	circuit	PROPN
bibechana-53971	326	10	.	.	PUNCT
bibechana-53971	327	1	bibechana	bibechana	PROPN
bibechana-53971	327	2	,	,	PUNCT
bibechana-53971	327	3	17(1):68–76	17(1):68–76	NUM
bibechana-53971	327	4	,	,	PUNCT
bibechana-53971	327	5	2020	2020	NUM
bibechana-53971	327	6	.	.	PUNCT
bibechana-53971	328	1	[	[	X
bibechana-53971	328	2	9	9	NUM
bibechana-53971	328	3	]	]	X
bibechana-53971	328	4	r.p	r.p	PROPN
bibechana-53971	328	5	.	.	PROPN
bibechana-53971	328	6	agarwal	agarwal	PROPN
bibechana-53971	328	7	.	.	PUNCT
bibechana-53971	329	1	a	a	DET
bibechana-53971	329	2	propos	propos	PROPN
bibechana-53971	329	3	d’une	d’une	PROPN
bibechana-53971	329	4	note	note	VERB
bibechana-53971	329	5	de	de	X
bibechana-53971	329	6	m.pierre	m.pierre	X
bibechana-53971	329	7	humbert	humbert	NOUN
bibechana-53971	329	8	.	.	PUNCT
bibechana-53971	330	1	séances	séances	PROPN
bibechana-53971	330	2	acad	acad	PROPN
bibechana-53971	330	3	.	.	PUNCT
bibechana-53971	331	1	sci	sci	PROPN
bibechana-53971	331	2	.	.	PROPN
bibechana-53971	331	3	,	,	PUNCT
bibechana-53971	331	4	236(21):2031–2032	236(21):2031–2032	NUM
bibechana-53971	331	5	,	,	PUNCT
bibechana-53971	331	6	1953	1953	NUM
bibechana-53971	331	7	.	.	PUNCT
bibechana-53971	332	1	[	[	X
bibechana-53971	332	2	10	10	NUM
bibechana-53971	332	3	]	]	PUNCT
bibechana-53971	332	4	a.	a.	NOUN
bibechana-53971	332	5	fenander	fenander	PROPN
bibechana-53971	332	6	.	.	PUNCT
bibechana-53971	333	1	higher	high	ADJ
bibechana-53971	333	2	transcendental	transcendental	ADJ
bibechana-53971	333	3	functions	function	NOUN
bibechana-53971	333	4	.	.	PUNCT
bibechana-53971	334	1	mcgraw	mcgraw	PROPN
bibechana-53971	334	2	-	-	PUNCT
bibechana-53971	334	3	hill	hill	PROPN
bibechana-53971	334	4	,	,	PUNCT
bibechana-53971	334	5	new	new	PROPN
bibechana-53971	334	6	york	york	PROPN
bibechana-53971	334	7	,	,	PUNCT
bibechana-53971	334	8	1955	1955	NUM
bibechana-53971	334	9	.	.	PUNCT
bibechana-53971	335	1	[	[	X
bibechana-53971	335	2	11	11	NUM
bibechana-53971	335	3	]	]	X
bibechana-53971	335	4	r.	r.	PROPN
bibechana-53971	335	5	gorenflo	gorenflo	PROPN
bibechana-53971	335	6	and	and	CCONJ
bibechana-53971	335	7	f.	f.	PROPN
bibechana-53971	335	8	mainardi	mainardi	PROPN
bibechana-53971	335	9	.	.	PUNCT
bibechana-53971	336	1	fractional	fractional	ADJ
bibechana-53971	336	2	calculus	calculus	NOUN
bibechana-53971	336	3	:	:	PUNCT
bibechana-53971	336	4	integral	integral	ADJ
bibechana-53971	336	5	and	and	CCONJ
bibechana-53971	336	6	differential	differential	ADJ
bibechana-53971	336	7	equations	equation	NOUN
bibechana-53971	336	8	of	of	ADP
bibechana-53971	336	9	fractional	fractional	ADJ
bibechana-53971	336	10	order	order	NOUN
bibechana-53971	336	11	.	.	PUNCT
bibechana-53971	337	1	springer	springer	NOUN
bibechana-53971	337	2	verlag	verlag	PROPN
bibechana-53971	337	3	wien	wien	PROPN
bibechana-53971	337	4	and	and	CCONJ
bibechana-53971	337	5	new	new	PROPN
bibechana-53971	337	6	york	york	PROPN
bibechana-53971	337	7	,	,	PUNCT
bibechana-53971	337	8	1997	1997	NUM
bibechana-53971	337	9	.	.	PUNCT
bibechana-53971	338	1	[	[	X
bibechana-53971	338	2	12	12	NUM
bibechana-53971	338	3	]	]	PUNCT
bibechana-53971	338	4	r.	r.	NOUN
bibechana-53971	338	5	hilfer	hilfer	PROPN
bibechana-53971	338	6	.	.	PUNCT
bibechana-53971	339	1	applications	application	NOUN
bibechana-53971	339	2	of	of	ADP
bibechana-53971	339	3	fractional	fractional	ADJ
bibechana-53971	339	4	calculus	calculus	NOUN
bibechana-53971	339	5	in	in	ADP
bibechana-53971	339	6	physics	physics	PROPN
bibechana-53971	339	7	.	.	PUNCT
bibechana-53971	340	1	world	world	NOUN
bibechana-53971	340	2	scientific	scientific	ADJ
bibechana-53971	340	3	publishing	publishing	NOUN
bibechana-53971	340	4	company	company	NOUN
bibechana-53971	340	5	,	,	PUNCT
bibechana-53971	340	6	singapore	singapore	PROPN
bibechana-53971	340	7	,	,	PUNCT
bibechana-53971	340	8	2000	2000	NUM
bibechana-53971	340	9	.	.	PUNCT
bibechana-53971	341	1	[	[	X
bibechana-53971	341	2	13	13	NUM
bibechana-53971	341	3	]	]	X
bibechana-53971	341	4	g.h	g.h	PROPN
bibechana-53971	341	5	.	.	PROPN
bibechana-53971	341	6	gao	gao	PROPN
bibechana-53971	341	7	,	,	PUNCT
bibechana-53971	341	8	z.z	z.z	PROPN
bibechana-53971	341	9	.	.	PROPN
bibechana-53971	341	10	sun	sun	PROPN
bibechana-53971	341	11	,	,	PUNCT
bibechana-53971	341	12	and	and	CCONJ
bibechana-53971	341	13	h.w	h.w	PROPN
bibechana-53971	341	14	.	.	PROPN
bibechana-53971	341	15	zhang	zhang	PROPN
bibechana-53971	341	16	.	.	PUNCT
bibechana-53971	342	1	a	a	DET
bibechana-53971	342	2	new	new	ADJ
bibechana-53971	342	3	fractional	fractional	ADJ
bibechana-53971	342	4	numerical	numerical	ADJ
bibechana-53971	342	5	differentiation	differentiation	NOUN
bibechana-53971	342	6	formula	formula	NOUN
bibechana-53971	342	7	to	to	PART
bibechana-53971	342	8	approximate	approximate	VERB
bibechana-53971	342	9	the	the	DET
bibechana-53971	342	10	caputo	caputo	PROPN
bibechana-53971	342	11	fractional	fractional	PROPN
bibechana-53971	342	12	derivative	derivative	PROPN
bibechana-53971	342	13	and	and	CCONJ
bibechana-53971	342	14	its	its	PRON
bibechana-53971	342	15	applications	application	NOUN
bibechana-53971	342	16	.	.	PUNCT
bibechana-53971	343	1	journal	journal	NOUN
bibechana-53971	343	2	of	of	ADP
bibechana-53971	343	3	computational	computational	ADJ
bibechana-53971	343	4	physics	physics	NOUN
bibechana-53971	343	5	,	,	PUNCT
bibechana-53971	343	6	259:33–50	259:33–50	NUM
bibechana-53971	343	7	,	,	PUNCT
bibechana-53971	343	8	2014	2014	NUM
bibechana-53971	343	9	.	.	PUNCT
bibechana-53971	344	1	[	[	X
bibechana-53971	344	2	14	14	NUM
bibechana-53971	344	3	]	]	X
bibechana-53971	344	4	j.	j.	PROPN
bibechana-53971	344	5	l.	l.	PROPN
bibechana-53971	344	6	lavoi	lavoi	PROPN
bibechana-53971	344	7	,	,	PUNCT
bibechana-53971	344	8	thomas	thomas	PROPN
bibechana-53971	344	9	j.	j.	PROPN
bibechana-53971	344	10	osler	osler	PROPN
bibechana-53971	344	11	,	,	PUNCT
bibechana-53971	344	12	and	and	CCONJ
bibechana-53971	344	13	r.	r.	PROPN
bibechana-53971	344	14	tremblay	tremblay	PROPN
bibechana-53971	344	15	.	.	PUNCT
bibechana-53971	345	1	fractional	fractional	ADJ
bibechana-53971	345	2	derivatives	derivative	NOUN
bibechana-53971	345	3	and	and	CCONJ
bibechana-53971	345	4	special	special	ADJ
bibechana-53971	345	5	functions	function	NOUN
bibechana-53971	345	6	.	.	PUNCT
bibechana-53971	346	1	siam	siam	PROPN
bibechana-53971	346	2	review	review	PROPN
bibechana-53971	346	3	,	,	PUNCT
bibechana-53971	346	4	18(2):240–268	18(2):240–268	PROPN
bibechana-53971	346	5	,	,	PUNCT
bibechana-53971	346	6	1976	1976	NUM
bibechana-53971	346	7	.	.	PUNCT
bibechana-53971	347	1	[	[	X
bibechana-53971	347	2	15	15	NUM
bibechana-53971	347	3	]	]	PUNCT
bibechana-53971	347	4	a.	a.	NOUN
bibechana-53971	347	5	erdelyi	erdelyi	NOUN
bibechana-53971	347	6	.	.	PUNCT
bibechana-53971	348	1	tables	table	NOUN
bibechana-53971	348	2	of	of	ADP
bibechana-53971	348	3	integral	integral	ADJ
bibechana-53971	348	4	transforms	transform	NOUN
bibechana-53971	348	5	.	.	PUNCT
bibechana-53971	349	1	mcgraw	mcgraw	PROPN
bibechana-53971	349	2	-	-	PUNCT
bibechana-53971	349	3	hill	hill	PROPN
bibechana-53971	349	4	,	,	PUNCT
bibechana-53971	349	5	new	new	PROPN
bibechana-53971	349	6	york	york	PROPN
bibechana-53971	349	7	,	,	PUNCT
bibechana-53971	349	8	1954	1954	NUM
bibechana-53971	349	9	.	.	PUNCT
bibechana-53971	350	1	[	[	X
bibechana-53971	350	2	16	16	NUM
bibechana-53971	350	3	]	]	X
bibechana-53971	350	4	l.	l.	PROPN
bibechana-53971	350	5	g.	g.	PROPN
bibechana-53971	350	6	romero	romero	PROPN
bibechana-53971	350	7	,	,	PUNCT
bibechana-53971	350	8	g.	g.	PROPN
bibechana-53971	350	9	d.	d.	PROPN
bibechana-53971	350	10	medina	medina	PROPN
bibechana-53971	350	11	,	,	PUNCT
bibechana-53971	350	12	n.	n.	PROPN
bibechana-53971	350	13	r.	r.	PROPN
bibechana-53971	350	14	ojeda	ojeda	PROPN
bibechana-53971	350	15	,	,	PUNCT
bibechana-53971	350	16	and	and	CCONJ
bibechana-53971	350	17	j.	j.	PROPN
bibechana-53971	350	18	h.	h.	PROPN
bibechana-53971	350	19	pereira	pereira	PROPN
bibechana-53971	350	20	.	.	PUNCT
bibechana-53971	351	1	a	a	DET
bibechana-53971	351	2	new	new	ADJ
bibechana-53971	351	3	alfa	alfa	NOUN
bibechana-53971	351	4	-	-	PUNCT
bibechana-53971	351	5	integral	integral	ADJ
bibechana-53971	351	6	laplace	laplace	NOUN
bibechana-53971	351	7	transform	transform	NOUN
bibechana-53971	351	8	.	.	PUNCT
bibechana-53971	352	1	asian	asian	ADJ
bibechana-53971	352	2	journal	journal	NOUN
bibechana-53971	352	3	of	of	ADP
bibechana-53971	352	4	current	current	ADJ
bibechana-53971	352	5	engineering	engineering	NOUN
bibechana-53971	352	6	and	and	CCONJ
bibechana-53971	352	7	maths	math	NOUN
bibechana-53971	352	8	,	,	PUNCT
bibechana-53971	352	9	pages	page	NOUN
bibechana-53971	352	10	59–62	59–62	NUM
bibechana-53971	352	11	,	,	PUNCT
bibechana-53971	352	12	2016	2016	NUM
bibechana-53971	352	13	.	.	PUNCT
bibechana-53971	353	1	[	[	X
bibechana-53971	353	2	17	17	NUM
bibechana-53971	353	3	]	]	PUNCT
bibechana-53971	353	4	m.	m.	PROPN
bibechana-53971	353	5	caputo	caputo	PROPN
bibechana-53971	353	6	.	.	PROPN
bibechana-53971	354	1	distributed	distribute	VERB
bibechana-53971	354	2	order	order	NOUN
bibechana-53971	354	3	differential	differential	ADJ
bibechana-53971	354	4	equations	equation	NOUN
bibechana-53971	354	5	modelling	modelling	NOUN
bibechana-53971	354	6	,	,	PUNCT
bibechana-53971	354	7	dielectric	dielectric	ADJ
bibechana-53971	354	8	induction	induction	NOUN
bibechana-53971	354	9	and	and	CCONJ
bibechana-53971	354	10	diffusion	diffusion	NOUN
bibechana-53971	354	11	.	.	PUNCT
bibechana-53971	355	1	frac	frac	PROPN
bibechana-53971	355	2	.	.	PUNCT
bibechana-53971	356	1	calc	calc	PROPN
bibechana-53971	356	2	.	.	PUNCT
bibechana-53971	357	1	appl	appl	PROPN
bibechana-53971	357	2	.	.	PUNCT
bibechana-53971	358	1	anal	anal	PROPN
bibechana-53971	358	2	.	.	PROPN
bibechana-53971	358	3	,	,	PUNCT
bibechana-53971	358	4	4:421–442	4:421–442	NUM
bibechana-53971	358	5	,	,	PUNCT
bibechana-53971	358	6	2001	2001	NUM
bibechana-53971	358	7	.	.	PUNCT
bibechana-53971	359	1	[	[	X
bibechana-53971	359	2	18	18	NUM
bibechana-53971	359	3	]	]	PUNCT
bibechana-53971	359	4	a.	a.	NOUN
bibechana-53971	359	5	olagunju	olagunju	PROPN
bibechana-53971	359	6	and	and	CCONJ
bibechana-53971	359	7	l.	l.	PROPN
bibechana-53971	359	8	joseph	joseph	PROPN
bibechana-53971	359	9	.	.	PUNCT
bibechana-53971	360	1	construction	construction	NOUN
bibechana-53971	360	2	of	of	ADP
bibechana-53971	360	3	functions	function	NOUN
bibechana-53971	360	4	for	for	ADP
bibechana-53971	360	5	fractional	fractional	ADJ
bibechana-53971	360	6	derivatives	derivative	NOUN
bibechana-53971	360	7	using	use	VERB
bibechana-53971	360	8	matlab	matlab	PROPN
bibechana-53971	360	9	.	.	PUNCT
bibechana-53971	360	10	journal	journal	PROPN
bibechana-53971	360	11	of	of	ADP
bibechana-53971	360	12	advances	advance	NOUN
bibechana-53971	360	13	in	in	ADP
bibechana-53971	360	14	mathematics	mathematic	NOUN
bibechana-53971	360	15	and	and	CCONJ
bibechana-53971	360	16	computer	computer	NOUN
bibechana-53971	360	17	science	science	NOUN
bibechana-53971	360	18	,	,	PUNCT
bibechana-53971	360	19	36(6):1–10	36(6):1–10	NOUN
bibechana-53971	360	20	,	,	PUNCT
bibechana-53971	360	21	2021	2021	NUM
bibechana-53971	360	22	.	.	PUNCT
bibechana-53971	361	1	[	[	X
bibechana-53971	361	2	19	19	NUM
bibechana-53971	361	3	]	]	PUNCT
bibechana-53971	361	4	m.	m.	NOUN
bibechana-53971	361	5	caputo	caputo	PROPN
bibechana-53971	361	6	and	and	CCONJ
bibechana-53971	361	7	m.	m.	PROPN
bibechana-53971	361	8	fabrizio	fabrizio	PROPN
bibechana-53971	361	9	.	.	PUNCT
bibechana-53971	362	1	a	a	DET
bibechana-53971	362	2	new	new	ADJ
bibechana-53971	362	3	definition	definition	NOUN
bibechana-53971	362	4	of	of	ADP
bibechana-53971	362	5	fractional	fractional	ADJ
bibechana-53971	362	6	derivative	derivative	NOUN
bibechana-53971	362	7	without	without	ADP
bibechana-53971	362	8	singular	singular	ADJ
bibechana-53971	362	9	kernel	kernel	PROPN
bibechana-53971	362	10	.	.	PUNCT
bibechana-53971	363	1	progress	progress	NOUN
bibechana-53971	363	2	in	in	ADP
bibechana-53971	363	3	fracture	fracture	NOUN
bibechana-53971	363	4	and	and	CCONJ
bibechana-53971	363	5	damage	damage	NOUN
bibechana-53971	363	6	mechanics	mechanic	NOUN
bibechana-53971	363	7	:	:	PUNCT
bibechana-53971	363	8	special	special	ADJ
bibechana-53971	363	9	issue	issue	NOUN
bibechana-53971	363	10	on	on	ADP
bibechana-53971	363	11	fractional	fractional	ADJ
bibechana-53971	363	12	differential	differential	ADJ
bibechana-53971	363	13	equations	equation	NOUN
bibechana-53971	363	14	and	and	CCONJ
bibechana-53971	363	15	their	their	PRON
bibechana-53971	363	16	applications	application	NOUN
bibechana-53971	363	17	,	,	PUNCT
bibechana-53971	363	18	1(2):1–13	1(2):1–13	NUM
bibechana-53971	363	19	,	,	PUNCT
bibechana-53971	363	20	2015	2015	NUM
bibechana-53971	363	21	.	.	PUNCT
bibechana-53971	364	1	[	[	X
bibechana-53971	364	2	20	20	NUM
bibechana-53971	364	3	]	]	SYM
bibechana-53971	364	4	o.j.j	o.j.j	PROPN
bibechana-53971	364	5	.	.	PROPN
bibechana-53971	364	6	algahtani	algahtani	PROPN
bibechana-53971	364	7	.	.	PUNCT
bibechana-53971	365	1	comparing	compare	VERB
bibechana-53971	365	2	the	the	DET
bibechana-53971	365	3	atangana	atangana	PROPN
bibechana-53971	365	4	–	–	PUNCT
bibechana-53971	365	5	baleanu	baleanu	PROPN
bibechana-53971	365	6	and	and	CCONJ
bibechana-53971	365	7	caputo	caputo	PROPN
bibechana-53971	365	8	–	–	PUNCT
bibechana-53971	365	9	fabrizio	fabrizio	PROPN
bibechana-53971	365	10	derivative	derivative	NOUN
bibechana-53971	365	11	with	with	ADP
bibechana-53971	365	12	fractional	fractional	ADJ
bibechana-53971	365	13	order	order	NOUN
bibechana-53971	365	14	:	:	PUNCT
bibechana-53971	365	15	allen	allen	PROPN
bibechana-53971	365	16	cahn	cahn	PROPN
bibechana-53971	365	17	model	model	PROPN
bibechana-53971	365	18	.	.	PUNCT
bibechana-53971	366	1	chaos	chaos	NOUN
bibechana-53971	366	2	,	,	PUNCT
bibechana-53971	366	3	solitons	soliton	NOUN
bibechana-53971	366	4	and	and	CCONJ
bibechana-53971	366	5	fractals	fractal	NOUN
bibechana-53971	366	6	,	,	PUNCT
bibechana-53971	366	7	89:552–559	89:552–559	NUM
bibechana-53971	366	8	,	,	PUNCT
bibechana-53971	366	9	2016	2016	NUM
bibechana-53971	366	10	.	.	PUNCT
bibechana-53971	367	1	[	[	X
bibechana-53971	367	2	21	21	NUM
bibechana-53971	367	3	]	]	X
bibechana-53971	367	4	s.	s.	PROPN
bibechana-53971	367	5	abdullah	abdullah	PROPN
bibechana-53971	367	6	.	.	PUNCT
bibechana-53971	368	1	exact	exact	ADJ
bibechana-53971	368	2	solutions	solution	NOUN
bibechana-53971	368	3	for	for	ADP
bibechana-53971	368	4	some	some	DET
bibechana-53971	368	5	fractional	fractional	ADJ
bibechana-53971	368	6	differential	differential	ADJ
bibechana-53971	368	7	equations	equation	NOUN
bibechana-53971	368	8	.	.	PUNCT
bibechana-53971	369	1	advances	advance	NOUN
bibechana-53971	369	2	in	in	ADP
bibechana-53971	369	3	mathematical	mathematical	ADJ
bibechana-53971	369	4	physics	physics	NOUN
bibechana-53971	369	5	,	,	PUNCT
bibechana-53971	369	6	2015:567842	2015:567842	NUM
bibechana-53971	369	7	,	,	PUNCT
bibechana-53971	369	8	2015	2015	NUM
bibechana-53971	369	9	.	.	PUNCT
bibechana-53971	370	1	[	[	X
bibechana-53971	370	2	22	22	NUM
bibechana-53971	370	3	]	]	PUNCT
bibechana-53971	370	4	a.	a.	NOUN
bibechana-53971	370	5	carpinteri	carpinteri	NOUN
bibechana-53971	370	6	.	.	PUNCT
bibechana-53971	371	1	fractals	fractal	NOUN
bibechana-53971	371	2	and	and	CCONJ
bibechana-53971	371	3	fractional	fractional	ADJ
bibechana-53971	371	4	calculus	calculus	NOUN
bibechana-53971	371	5	in	in	ADP
bibechana-53971	371	6	continuum	continuum	ADJ
bibechana-53971	371	7	mechanics	mechanic	NOUN
bibechana-53971	371	8	.	.	PUNCT
bibechana-53971	371	9	springer	springer	PROPN
bibechana-53971	371	10	,	,	PUNCT
bibechana-53971	371	11	wien	wien	NOUN
bibechana-53971	371	12	,	,	PUNCT
bibechana-53971	371	13	1997	1997	NUM
bibechana-53971	371	14	.	.	PUNCT
bibechana-53971	372	1	[	[	X
bibechana-53971	372	2	23	23	NUM
bibechana-53971	372	3	]	]	X
bibechana-53971	372	4	h.	h.	PROPN
bibechana-53971	372	5	bulut	bulut	PROPN
bibechana-53971	372	6	,	,	PUNCT
bibechana-53971	372	7	h.m	h.m	PROPN
bibechana-53971	372	8	.	.	PROPN
bibechana-53971	372	9	baskonus	baskonus	PROPN
bibechana-53971	372	10	,	,	PUNCT
bibechana-53971	372	11	and	and	CCONJ
bibechana-53971	372	12	f.b.m	f.b.m	VERB
bibechana-53971	372	13	.	.	PUNCT
bibechana-53971	372	14	belgacem	belgacem	NOUN
bibechana-53971	372	15	.	.	PUNCT
bibechana-53971	373	1	the	the	DET
bibechana-53971	373	2	analytical	analytical	ADJ
bibechana-53971	373	3	solution	solution	NOUN
bibechana-53971	373	4	of	of	ADP
bibechana-53971	373	5	some	some	DET
bibechana-53971	373	6	fractional	fractional	ADJ
bibechana-53971	373	7	ordinary	ordinary	ADJ
bibechana-53971	373	8	differential	differential	ADJ
bibechana-53971	373	9	equations	equation	NOUN
bibechana-53971	373	10	by	by	ADP
bibechana-53971	373	11	the	the	DET
bibechana-53971	373	12	sumudu	sumudu	NOUN
bibechana-53971	373	13	transform	transform	NOUN
bibechana-53971	373	14	method	method	NOUN
bibechana-53971	373	15	.	.	PUNCT
bibechana-53971	374	1	abstr	abstr	PROPN
bibechana-53971	374	2	.	.	PUNCT
bibechana-53971	374	3	appl	appl	PROPN
bibechana-53971	374	4	.	.	PUNCT
bibechana-53971	375	1	anal	anal	PROPN
bibechana-53971	375	2	.	.	PROPN
bibechana-53971	375	3	,	,	PUNCT
bibechana-53971	375	4	pages	page	NOUN
bibechana-53971	375	5	1–6	1–6	NUM
bibechana-53971	375	6	,	,	PUNCT
bibechana-53971	375	7	2013	2013	NUM
bibechana-53971	375	8	.	.	PUNCT
bibechana-53971	376	1	[	[	X
bibechana-53971	376	2	24	24	NUM
bibechana-53971	376	3	]	]	X
bibechana-53971	376	4	p.	p.	NOUN
bibechana-53971	376	5	agarwal	agarwal	PROPN
bibechana-53971	376	6	and	and	CCONJ
bibechana-53971	376	7	h.	h.	PROPN
bibechana-53971	376	8	irmak	irmak	PROPN
bibechana-53971	376	9	.	.	PUNCT
bibechana-53971	377	1	some	some	DET
bibechana-53971	377	2	comprehensive	comprehensive	ADJ
bibechana-53971	377	3	inequalities	inequality	NOUN
bibechana-53971	377	4	consisting	consist	VERB
bibechana-53971	377	5	of	of	ADP
bibechana-53971	377	6	mittag	mittag	ADJ
bibechana-53971	377	7	-	-	PUNCT
bibechana-53971	377	8	leffler	leffler	NOUN
bibechana-53971	377	9	type	type	NOUN
bibechana-53971	377	10	functions	function	NOUN
bibechana-53971	377	11	in	in	ADP
bibechana-53971	377	12	the	the	DET
bibechana-53971	377	13	complex	complex	ADJ
bibechana-53971	377	14	plane	plane	NOUN
bibechana-53971	377	15	.	.	PUNCT
bibechana-53971	378	1	mathematical	mathematical	ADJ
bibechana-53971	378	2	modelling	modelling	NOUN
bibechana-53971	378	3	and	and	CCONJ
bibechana-53971	378	4	natural	natural	ADJ
bibechana-53971	378	5	phenomena	phenomenon	NOUN
bibechana-53971	378	6	,	,	PUNCT
bibechana-53971	378	7	12	12	NUM
bibechana-53971	378	8	,	,	PUNCT
bibechana-53971	378	9	2017	2017	NUM
bibechana-53971	378	10	.	.	PUNCT
bibechana-53971	379	1	[	[	X
bibechana-53971	379	2	25	25	NUM
bibechana-53971	379	3	]	]	PUNCT
bibechana-53971	379	4	h.	h.	PROPN
bibechana-53971	379	5	s.	s.	PROPN
bibechana-53971	379	6	malvar	malvar	PROPN
bibechana-53971	379	7	,	,	PUNCT
bibechana-53971	379	8	li	li	PROPN
bibechana-53971	379	9	-	-	PUNCT
bibechana-53971	379	10	wei	wei	PROPN
bibechana-53971	379	11	he	he	PRON
bibechana-53971	379	12	,	,	PUNCT
bibechana-53971	379	13	and	and	CCONJ
bibechana-53971	379	14	r.	r.	PROPN
bibechana-53971	379	15	cutler	cutler	PROPN
bibechana-53971	379	16	.	.	PUNCT
bibechana-53971	380	1	highquality	highquality	NOUN
bibechana-53971	380	2	linear	linear	ADJ
bibechana-53971	380	3	interpolation	interpolation	NOUN
bibechana-53971	380	4	for	for	ADP
bibechana-53971	380	5	demosaicing	demosaicing	NOUN
bibechana-53971	380	6	of	of	ADP
bibechana-53971	380	7	bayer	bayer	NOUN
bibechana-53971	380	8	-	-	PUNCT
bibechana-53971	380	9	patterned	pattern	VERB
bibechana-53971	380	10	color	color	NOUN
bibechana-53971	380	11	images	image	NOUN
bibechana-53971	380	12	.	.	PUNCT
bibechana-53971	381	1	in	in	ADP
bibechana-53971	381	2	2004	2004	NUM
bibechana-53971	381	3	ieee	ieee	PROPN
bibechana-53971	381	4	international	international	ADJ
bibechana-53971	381	5	conference	conference	NOUN
bibechana-53971	381	6	on	on	ADP
bibechana-53971	381	7	acoustics	acoustic	NOUN
bibechana-53971	381	8	,	,	PUNCT
bibechana-53971	381	9	speech	speech	NOUN
bibechana-53971	381	10	,	,	PUNCT
bibechana-53971	381	11	and	and	CCONJ
bibechana-53971	381	12	signal	signal	NOUN
bibechana-53971	381	13	processing	processing	NOUN
bibechana-53971	381	14	,	,	PUNCT
bibechana-53971	381	15	volume	volume	NOUN
bibechana-53971	381	16	3	3	NUM
bibechana-53971	381	17	,	,	PUNCT
bibechana-53971	381	18	pages	page	NOUN
bibechana-53971	381	19	iii–485	iii–485	PROPN
bibechana-53971	381	20	.	.	PROPN
bibechana-53971	381	21	ieee	ieee	PROPN
bibechana-53971	381	22	,	,	PUNCT
bibechana-53971	381	23	2004	2004	NUM
bibechana-53971	381	24	.	.	PUNCT
bibechana-53971	382	1	introduction	introduction	NOUN
bibechana-53971	382	2	preliminaries	preliminary	NOUN
bibechana-53971	382	3	mathematical	mathematical	ADJ
bibechana-53971	382	4	and	and	CCONJ
bibechana-53971	382	5	numerical	numerical	ADJ
bibechana-53971	382	6	methods	method	NOUN
bibechana-53971	382	7	in	in	ADP
bibechana-53971	382	8	caputo	caputo	PROPN
bibechana-53971	382	9	-	-	PUNCT
bibechana-53971	382	10	fabrizio	fabrizio	PROPN
bibechana-53971	382	11	sense	sense	NOUN
bibechana-53971	382	12	l1	l1	PROPN
bibechana-53971	382	13	method	method	NOUN
bibechana-53971	382	14	for	for	ADP
bibechana-53971	382	15	the	the	DET
bibechana-53971	382	16	caputo	caputo	PROPN
bibechana-53971	382	17	fractional	fractional	PROPN
bibechana-53971	382	18	derivative	derivative	ADJ
bibechana-53971	382	19	l2	l2	NOUN
bibechana-53971	382	20	method	method	NOUN
bibechana-53971	382	21	for	for	ADP
bibechana-53971	382	22	the	the	DET
bibechana-53971	382	23	caputo	caputo	PROPN
bibechana-53971	382	24	fractional	fractional	PROPN
bibechana-53971	382	25	derivative	derivative	ADJ
bibechana-53971	382	26	l1	l1	PROPN
bibechana-53971	382	27	method	method	NOUN
bibechana-53971	382	28	for	for	ADP
bibechana-53971	382	29	the	the	DET
bibechana-53971	382	30	caputo	caputo	PROPN
bibechana-53971	382	31	fabrizio	fabrizio	PROPN
bibechana-53971	382	32	derivative	derivative	PROPN
bibechana-53971	382	33	l1	l1	PROPN
bibechana-53971	382	34	-	-	PUNCT
bibechana-53971	382	35	2	2	NUM
bibechana-53971	382	36	method	method	NOUN
bibechana-53971	382	37	for	for	ADP
bibechana-53971	382	38	caputo	caputo	PROPN
bibechana-53971	382	39	fractional	fractional	PROPN
bibechana-53971	382	40	derivative	derivative	ADJ
bibechana-53971	382	41	test	test	NOUN
bibechana-53971	382	42	examples	example	NOUN
bibechana-53971	382	43	,	,	PUNCT
bibechana-53971	382	44	comparative	comparative	ADJ
bibechana-53971	382	45	analysis	analysis	NOUN
bibechana-53971	382	46	of	of	ADP
bibechana-53971	382	47	a	a	DET
bibechana-53971	382	48	fractional	fractional	ADJ
bibechana-53971	382	49	derivatives	derivative	NOUN
bibechana-53971	382	50	conclusion	conclusion	NOUN