id	sid	tid	token	lemma	pos
ejpam-7063	1	1	european	european	PROPN
ejpam-7063	1	2	journal	journal	PROPN
ejpam-7063	1	3	of	of	ADP
ejpam-7063	1	4	pure	pure	ADJ
ejpam-7063	1	5	and	and	CCONJ
ejpam-7063	1	6	applied	applied	ADJ
ejpam-7063	1	7	mathematics	mathematic	NOUN
ejpam-7063	1	8	2025	2025	NUM
ejpam-7063	1	9	,	,	PUNCT
ejpam-7063	1	10	vol	vol	NOUN
ejpam-7063	1	11	.	.	PROPN
ejpam-7063	1	12	18	18	NUM
ejpam-7063	1	13	,	,	PUNCT
ejpam-7063	1	14	issue	issue	NOUN
ejpam-7063	1	15	4	4	NUM
ejpam-7063	1	16	,	,	PUNCT
ejpam-7063	1	17	article	article	NOUN
ejpam-7063	1	18	number	number	NOUN
ejpam-7063	1	19	7063	7063	NUM
ejpam-7063	1	20	issn	issn	VERB
ejpam-7063	1	21	1307	1307	NUM
ejpam-7063	1	22	-	-	SYM
ejpam-7063	1	23	5543	5543	NUM
ejpam-7063	1	24	–	–	PUNCT
ejpam-7063	1	25	ejpam.com	ejpam.com	X
ejpam-7063	1	26	published	publish	VERB
ejpam-7063	1	27	by	by	ADP
ejpam-7063	1	28	new	new	PROPN
ejpam-7063	1	29	york	york	PROPN
ejpam-7063	1	30	business	business	PROPN
ejpam-7063	1	31	global	global	PROPN
ejpam-7063	1	32	numerical	numerical	ADJ
ejpam-7063	1	33	solution	solution	NOUN
ejpam-7063	1	34	of	of	ADP
ejpam-7063	1	35	two	two	NUM
ejpam-7063	1	36	-	-	PUNCT
ejpam-7063	1	37	dimensional	dimensional	ADJ
ejpam-7063	1	38	fractional	fractional	ADJ
ejpam-7063	1	39	optimal	optimal	ADJ
ejpam-7063	1	40	control	control	NOUN
ejpam-7063	1	41	problems	problem	NOUN
ejpam-7063	1	42	using	use	VERB
ejpam-7063	1	43	fractional	fractional	ADJ
ejpam-7063	1	44	vieta	vieta	PROPN
ejpam-7063	1	45	-	-	PUNCT
ejpam-7063	1	46	fibonacci	fibonacci	NOUN
ejpam-7063	1	47	wavelets	wavelet	NOUN
ejpam-7063	1	48	g.	g.	PROPN
ejpam-7063	1	49	m.	m.	PROPN
ejpam-7063	1	50	bahaa1	bahaa1	PROPN
ejpam-7063	1	51	,	,	PUNCT
ejpam-7063	1	52	a.	a.	PROPN
ejpam-7063	1	53	h.	h.	PROPN
ejpam-7063	1	54	qamlo2,∗	qamlo2,∗	PROPN
ejpam-7063	1	55	1	1	NUM
ejpam-7063	1	56	department	department	NOUN
ejpam-7063	1	57	of	of	ADP
ejpam-7063	1	58	mathematics	mathematic	NOUN
ejpam-7063	1	59	and	and	CCONJ
ejpam-7063	1	60	computer	computer	NOUN
ejpam-7063	1	61	science	science	NOUN
ejpam-7063	1	62	,	,	PUNCT
ejpam-7063	1	63	faculty	faculty	NOUN
ejpam-7063	1	64	of	of	ADP
ejpam-7063	1	65	science	science	NOUN
ejpam-7063	1	66	,	,	PUNCT
ejpam-7063	1	67	beni	beni	ADJ
ejpam-7063	1	68	-	-	ADJ
ejpam-7063	1	69	suef	suef	ADJ
ejpam-7063	1	70	university	university	NOUN
ejpam-7063	1	71	,	,	PUNCT
ejpam-7063	1	72	beni	beni	NOUN
ejpam-7063	1	73	-	-	ADJ
ejpam-7063	1	74	suef	suef	NOUN
ejpam-7063	1	75	26511	26511	NUM
ejpam-7063	1	76	,	,	PUNCT
ejpam-7063	1	77	egypt	egypt	PROPN
ejpam-7063	1	78	2	2	NUM
ejpam-7063	1	79	department	department	NOUN
ejpam-7063	1	80	of	of	ADP
ejpam-7063	1	81	mathematics	mathematic	NOUN
ejpam-7063	1	82	,	,	PUNCT
ejpam-7063	1	83	faculty	faculty	NOUN
ejpam-7063	1	84	of	of	ADP
ejpam-7063	1	85	science	science	NOUN
ejpam-7063	1	86	,	,	PUNCT
ejpam-7063	1	87	umm	umm	INTJ
ejpam-7063	1	88	al	al	PROPN
ejpam-7063	1	89	-	-	PUNCT
ejpam-7063	1	90	qura	qura	PROPN
ejpam-7063	1	91	university	university	PROPN
ejpam-7063	1	92	,	,	PUNCT
ejpam-7063	1	93	makkah	makkah	PROPN
ejpam-7063	1	94	21955	21955	NUM
ejpam-7063	1	95	,	,	PUNCT
ejpam-7063	1	96	saudi	saudi	PROPN
ejpam-7063	1	97	arabia	arabia	PROPN
ejpam-7063	1	98	abstract	abstract	NOUN
ejpam-7063	1	99	.	.	PUNCT
ejpam-7063	2	1	this	this	DET
ejpam-7063	2	2	paper	paper	NOUN
ejpam-7063	2	3	presents	present	VERB
ejpam-7063	2	4	a	a	DET
ejpam-7063	2	5	novel	novel	ADJ
ejpam-7063	2	6	numerical	numerical	ADJ
ejpam-7063	2	7	framework	framework	NOUN
ejpam-7063	2	8	for	for	ADP
ejpam-7063	2	9	solving	solve	VERB
ejpam-7063	2	10	two	two	NUM
ejpam-7063	2	11	-	-	PUNCT
ejpam-7063	2	12	dimensional	dimensional	ADJ
ejpam-7063	2	13	fractional	fractional	ADJ
ejpam-7063	2	14	optimal	optimal	ADJ
ejpam-7063	2	15	control	control	NOUN
ejpam-7063	2	16	problems	problem	NOUN
ejpam-7063	2	17	(	(	PUNCT
ejpam-7063	2	18	focps	focps	PROPN
ejpam-7063	2	19	)	)	PUNCT
ejpam-7063	2	20	governed	govern	VERB
ejpam-7063	2	21	by	by	ADP
ejpam-7063	2	22	caputo	caputo	PROPN
ejpam-7063	2	23	fractional	fractional	ADJ
ejpam-7063	2	24	partial	partial	ADJ
ejpam-7063	2	25	differential	differential	NOUN
ejpam-7063	2	26	equations	equation	NOUN
ejpam-7063	2	27	.	.	PUNCT
ejpam-7063	3	1	the	the	DET
ejpam-7063	3	2	proposed	propose	VERB
ejpam-7063	3	3	approach	approach	NOUN
ejpam-7063	3	4	is	be	AUX
ejpam-7063	3	5	based	base	VERB
ejpam-7063	3	6	on	on	ADP
ejpam-7063	3	7	fractional	fractional	ADJ
ejpam-7063	3	8	vieta	vieta	PROPN
ejpam-7063	3	9	–	–	PUNCT
ejpam-7063	3	10	fibonacci	fibonacci	NOUN
ejpam-7063	3	11	wavelets	wavelet	NOUN
ejpam-7063	3	12	(	(	PUNCT
ejpam-7063	3	13	fvfws	fvfws	NOUN
ejpam-7063	3	14	)	)	PUNCT
ejpam-7063	3	15	,	,	PUNCT
ejpam-7063	3	16	a	a	DET
ejpam-7063	3	17	recently	recently	ADV
ejpam-7063	3	18	developed	develop	VERB
ejpam-7063	3	19	wavelet	wavelet	NOUN
ejpam-7063	3	20	family	family	NOUN
ejpam-7063	3	21	that	that	PRON
ejpam-7063	3	22	combines	combine	VERB
ejpam-7063	3	23	the	the	DET
ejpam-7063	3	24	recursive	recursive	ADJ
ejpam-7063	3	25	structure	structure	NOUN
ejpam-7063	3	26	of	of	ADP
ejpam-7063	3	27	fibonacci	fibonacci	NOUN
ejpam-7063	3	28	polynomials	polynomial	NOUN
ejpam-7063	3	29	with	with	ADP
ejpam-7063	3	30	fractional	fractional	ADJ
ejpam-7063	3	31	-	-	PUNCT
ejpam-7063	3	32	order	order	NOUN
ejpam-7063	3	33	operators	operator	NOUN
ejpam-7063	3	34	.	.	PUNCT
ejpam-7063	4	1	we	we	PRON
ejpam-7063	4	2	first	first	ADV
ejpam-7063	4	3	construct	construct	VERB
ejpam-7063	4	4	operational	operational	ADJ
ejpam-7063	4	5	matrices	matrix	NOUN
ejpam-7063	4	6	for	for	ADP
ejpam-7063	4	7	fractional	fractional	ADJ
ejpam-7063	4	8	derivatives	derivative	NOUN
ejpam-7063	4	9	in	in	ADP
ejpam-7063	4	10	the	the	DET
ejpam-7063	4	11	fvfw	fvfw	ADJ
ejpam-7063	4	12	basis	basis	NOUN
ejpam-7063	4	13	and	and	CCONJ
ejpam-7063	4	14	employ	employ	VERB
ejpam-7063	4	15	them	they	PRON
ejpam-7063	4	16	to	to	PART
ejpam-7063	4	17	transform	transform	VERB
ejpam-7063	4	18	the	the	DET
ejpam-7063	4	19	governing	govern	VERB
ejpam-7063	4	20	focp	focp	NOUN
ejpam-7063	4	21	into	into	ADP
ejpam-7063	4	22	a	a	DET
ejpam-7063	4	23	system	system	NOUN
ejpam-7063	4	24	of	of	ADP
ejpam-7063	4	25	sparse	sparse	ADJ
ejpam-7063	4	26	algebraic	algebraic	ADJ
ejpam-7063	4	27	equations	equation	NOUN
ejpam-7063	4	28	.	.	PUNCT
ejpam-7063	5	1	the	the	DET
ejpam-7063	5	2	state	state	NOUN
ejpam-7063	5	3	,	,	PUNCT
ejpam-7063	5	4	adjoint	adjoint	NOUN
ejpam-7063	5	5	,	,	PUNCT
ejpam-7063	5	6	and	and	CCONJ
ejpam-7063	5	7	control	control	NOUN
ejpam-7063	5	8	functions	function	NOUN
ejpam-7063	5	9	are	be	AUX
ejpam-7063	5	10	approximated	approximate	VERB
ejpam-7063	5	11	simultaneously	simultaneously	ADV
ejpam-7063	5	12	in	in	ADP
ejpam-7063	5	13	a	a	DET
ejpam-7063	5	14	unified	unified	ADJ
ejpam-7063	5	15	wavelet	wavelet	NOUN
ejpam-7063	5	16	space	space	NOUN
ejpam-7063	5	17	,	,	PUNCT
ejpam-7063	5	18	enabling	enable	VERB
ejpam-7063	5	19	efficient	efficient	ADJ
ejpam-7063	5	20	reconstruction	reconstruction	NOUN
ejpam-7063	5	21	of	of	ADP
ejpam-7063	5	22	the	the	DET
ejpam-7063	5	23	optimality	optimality	NOUN
ejpam-7063	5	24	system	system	NOUN
ejpam-7063	5	25	.	.	PUNCT
ejpam-7063	6	1	the	the	DET
ejpam-7063	6	2	resulting	result	VERB
ejpam-7063	6	3	nonlinear	nonlinear	ADJ
ejpam-7063	6	4	algebraic	algebraic	ADJ
ejpam-7063	6	5	system	system	NOUN
ejpam-7063	6	6	is	be	AUX
ejpam-7063	6	7	solved	solve	VERB
ejpam-7063	6	8	using	use	VERB
ejpam-7063	6	9	newton	newton	PROPN
ejpam-7063	6	10	’s	’s	PART
ejpam-7063	6	11	method	method	NOUN
ejpam-7063	6	12	,	,	PUNCT
ejpam-7063	6	13	which	which	PRON
ejpam-7063	6	14	guarantees	guarantee	VERB
ejpam-7063	6	15	quadratic	quadratic	ADJ
ejpam-7063	6	16	convergence	convergence	NOUN
ejpam-7063	6	17	under	under	ADP
ejpam-7063	6	18	standard	standard	ADJ
ejpam-7063	6	19	assumptions	assumption	NOUN
ejpam-7063	6	20	.	.	PUNCT
ejpam-7063	7	1	a	a	DET
ejpam-7063	7	2	benchmark	benchmark	ADJ
ejpam-7063	7	3	two	two	NUM
ejpam-7063	7	4	-	-	PUNCT
ejpam-7063	7	5	dimensional	dimensional	ADJ
ejpam-7063	7	6	fractional	fractional	ADJ
ejpam-7063	7	7	control	control	NOUN
ejpam-7063	7	8	problem	problem	NOUN
ejpam-7063	7	9	is	be	AUX
ejpam-7063	7	10	presented	present	VERB
ejpam-7063	7	11	to	to	PART
ejpam-7063	7	12	validate	validate	VERB
ejpam-7063	7	13	the	the	DET
ejpam-7063	7	14	proposed	propose	VERB
ejpam-7063	7	15	scheme	scheme	NOUN
ejpam-7063	7	16	.	.	PUNCT
ejpam-7063	8	1	numerical	numerical	PROPN
ejpam-7063	8	2	results	result	NOUN
ejpam-7063	8	3	demonstrate	demonstrate	VERB
ejpam-7063	8	4	that	that	PRON
ejpam-7063	8	5	fvfws	fvfws	NOUN
ejpam-7063	8	6	achieve	achieve	VERB
ejpam-7063	8	7	high	high	ADJ
ejpam-7063	8	8	accuracy	accuracy	NOUN
ejpam-7063	8	9	with	with	ADP
ejpam-7063	8	10	relatively	relatively	ADV
ejpam-7063	8	11	few	few	ADJ
ejpam-7063	8	12	basis	basis	NOUN
ejpam-7063	8	13	functions	function	NOUN
ejpam-7063	8	14	,	,	PUNCT
ejpam-7063	8	15	outperforming	outperform	VERB
ejpam-7063	8	16	conventional	conventional	ADJ
ejpam-7063	8	17	wavelet	wavelet	NOUN
ejpam-7063	8	18	and	and	CCONJ
ejpam-7063	8	19	spectral	spectral	ADJ
ejpam-7063	8	20	approaches	approach	NOUN
ejpam-7063	8	21	in	in	ADP
ejpam-7063	8	22	terms	term	NOUN
ejpam-7063	8	23	of	of	ADP
ejpam-7063	8	24	computational	computational	ADJ
ejpam-7063	8	25	efficiency	efficiency	NOUN
ejpam-7063	8	26	.	.	PUNCT
ejpam-7063	9	1	the	the	DET
ejpam-7063	9	2	method	method	NOUN
ejpam-7063	9	3	provides	provide	VERB
ejpam-7063	9	4	a	a	DET
ejpam-7063	9	5	general	general	ADJ
ejpam-7063	9	6	framework	framework	NOUN
ejpam-7063	9	7	that	that	PRON
ejpam-7063	9	8	can	can	AUX
ejpam-7063	9	9	be	be	AUX
ejpam-7063	9	10	extended	extend	VERB
ejpam-7063	9	11	to	to	ADP
ejpam-7063	9	12	nonlinear	nonlinear	ADJ
ejpam-7063	9	13	fractional	fractional	ADJ
ejpam-7063	9	14	pdes	pde	NOUN
ejpam-7063	9	15	,	,	PUNCT
ejpam-7063	9	16	time	time	NOUN
ejpam-7063	9	17	-	-	PUNCT
ejpam-7063	9	18	dependent	dependent	ADJ
ejpam-7063	9	19	fractional	fractional	ADJ
ejpam-7063	9	20	dynamics	dynamic	NOUN
ejpam-7063	9	21	,	,	PUNCT
ejpam-7063	9	22	and	and	CCONJ
ejpam-7063	9	23	problems	problem	NOUN
ejpam-7063	9	24	with	with	ADP
ejpam-7063	9	25	control	control	NOUN
ejpam-7063	9	26	constraints	constraint	NOUN
ejpam-7063	9	27	.	.	PUNCT
ejpam-7063	10	1	2020	2020	NUM
ejpam-7063	10	2	mathematics	mathematic	NOUN
ejpam-7063	10	3	subject	subject	NOUN
ejpam-7063	10	4	classifications	classification	NOUN
ejpam-7063	10	5	:	:	PUNCT
ejpam-7063	10	6	49m37	49m37	NUM
ejpam-7063	10	7	,	,	PUNCT
ejpam-7063	10	8	65m70	65m70	NUM
ejpam-7063	10	9	,	,	PUNCT
ejpam-7063	10	10	26a33	26a33	NUM
ejpam-7063	10	11	,	,	PUNCT
ejpam-7063	10	12	93c20	93c20	NUM
ejpam-7063	10	13	key	key	ADJ
ejpam-7063	10	14	words	word	NOUN
ejpam-7063	10	15	and	and	CCONJ
ejpam-7063	10	16	phrases	phrase	NOUN
ejpam-7063	10	17	:	:	PUNCT
ejpam-7063	10	18	fractional	fractional	ADJ
ejpam-7063	10	19	optimal	optimal	ADJ
ejpam-7063	10	20	control	control	NOUN
ejpam-7063	10	21	,	,	PUNCT
ejpam-7063	10	22	caputo	caputo	PROPN
ejpam-7063	10	23	derivative	derivative	PROPN
ejpam-7063	10	24	,	,	PUNCT
ejpam-7063	10	25	vieta	vieta	PROPN
ejpam-7063	10	26	–	–	PUNCT
ejpam-7063	10	27	fibonacci	fibonacci	NOUN
ejpam-7063	10	28	wavelets	wavelet	NOUN
ejpam-7063	10	29	,	,	PUNCT
ejpam-7063	10	30	operational	operational	ADJ
ejpam-7063	10	31	matrix	matrix	NOUN
ejpam-7063	10	32	,	,	PUNCT
ejpam-7063	10	33	numerical	numerical	ADJ
ejpam-7063	10	34	methods	method	NOUN
ejpam-7063	10	35	,	,	PUNCT
ejpam-7063	10	36	newton	newton	PROPN
ejpam-7063	10	37	’s	’s	PART
ejpam-7063	10	38	method	method	PROPN
ejpam-7063	10	39	1	1	NUM
ejpam-7063	10	40	.	.	PUNCT
ejpam-7063	11	1	introduction	introduction	NOUN
ejpam-7063	11	2	fractional	fractional	ADJ
ejpam-7063	11	3	calculus	calculus	NOUN
ejpam-7063	11	4	has	have	AUX
ejpam-7063	11	5	attracted	attract	VERB
ejpam-7063	11	6	significant	significant	ADJ
ejpam-7063	11	7	attention	attention	NOUN
ejpam-7063	11	8	in	in	ADP
ejpam-7063	11	9	recent	recent	ADJ
ejpam-7063	11	10	decades	decade	NOUN
ejpam-7063	11	11	as	as	ADP
ejpam-7063	11	12	a	a	DET
ejpam-7063	11	13	powerful	powerful	ADJ
ejpam-7063	11	14	mathematical	mathematical	ADJ
ejpam-7063	11	15	framework	framework	NOUN
ejpam-7063	11	16	for	for	ADP
ejpam-7063	11	17	describing	describe	VERB
ejpam-7063	11	18	systems	system	NOUN
ejpam-7063	11	19	with	with	ADP
ejpam-7063	11	20	memory	memory	NOUN
ejpam-7063	11	21	,	,	PUNCT
ejpam-7063	11	22	hereditary	hereditary	ADJ
ejpam-7063	11	23	properties	property	NOUN
ejpam-7063	11	24	,	,	PUNCT
ejpam-7063	11	25	and	and	CCONJ
ejpam-7063	11	26	anomalous	anomalous	ADJ
ejpam-7063	11	27	diffusion	diffusion	NOUN
ejpam-7063	11	28	.	.	PUNCT
ejpam-7063	12	1	unlike	unlike	ADP
ejpam-7063	12	2	classical	classical	ADJ
ejpam-7063	12	3	integer	integer	NOUN
ejpam-7063	12	4	-	-	PUNCT
ejpam-7063	12	5	order	order	NOUN
ejpam-7063	12	6	models	model	NOUN
ejpam-7063	12	7	,	,	PUNCT
ejpam-7063	12	8	fractional	fractional	ADJ
ejpam-7063	12	9	differential	differential	ADJ
ejpam-7063	12	10	equations	equation	NOUN
ejpam-7063	12	11	∗corresponding	∗corresponde	VERB
ejpam-7063	12	12	author	author	NOUN
ejpam-7063	12	13	.	.	PUNCT
ejpam-7063	13	1	doi	doi	NOUN
ejpam-7063	13	2	:	:	PUNCT
ejpam-7063	13	3	https://doi.org/10.29020/nybg.ejpam.v18i4.7063	https://doi.org/10.29020/nybg.ejpam.v18i4.7063	PROPN
ejpam-7063	13	4	email	email	NOUN
ejpam-7063	13	5	addresses	address	NOUN
ejpam-7063	13	6	:	:	PUNCT
ejpam-7063	13	7	bahaa_gm@yahoo.com	bahaa_gm@yahoo.com	PROPN
ejpam-7063	13	8	(	(	PUNCT
ejpam-7063	13	9	g.	g.	PROPN
ejpam-7063	13	10	m.	m.	PROPN
ejpam-7063	13	11	bahaa	bahaa	PROPN
ejpam-7063	13	12	)	)	PUNCT
ejpam-7063	13	13	,	,	PUNCT
ejpam-7063	13	14	ahqamlo@uqu.edu.sa	ahqamlo@uqu.edu.sa	NOUN
ejpam-7063	13	15	(	(	PUNCT
ejpam-7063	13	16	a.	a.	PROPN
ejpam-7063	13	17	h.	h.	PROPN
ejpam-7063	13	18	qamlo	qamlo	PROPN
ejpam-7063	13	19	)	)	PUNCT
ejpam-7063	13	20	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-7063	14	1	1	1	NUM
ejpam-7063	14	2	copyright	copyright	NOUN
ejpam-7063	14	3	:	:	PUNCT
ejpam-7063	14	4	©	©	PROPN
ejpam-7063	14	5	2025	2025	NUM
ejpam-7063	14	6	the	the	DET
ejpam-7063	14	7	author(s	author(s	NOUN
ejpam-7063	14	8	)	)	PUNCT
ejpam-7063	14	9	.	.	PUNCT
ejpam-7063	15	1	(	(	PUNCT
ejpam-7063	15	2	cc	cc	NOUN
ejpam-7063	15	3	by	by	ADP
ejpam-7063	15	4	-	-	PUNCT
ejpam-7063	15	5	nc	nc	PROPN
ejpam-7063	15	6	4.0	4.0	NUM
ejpam-7063	15	7	)	)	PUNCT
ejpam-7063	15	8	g.	g.	PROPN
ejpam-7063	15	9	m.	m.	NOUN
ejpam-7063	15	10	bahaa	bahaa	PROPN
ejpam-7063	15	11	,	,	PUNCT
ejpam-7063	15	12	a.	a.	NOUN
ejpam-7063	15	13	h.	h.	PROPN
ejpam-7063	15	14	qamlo	qamlo	PROPN
ejpam-7063	15	15	/	/	SYM
ejpam-7063	15	16	eur	eur	PROPN
ejpam-7063	15	17	.	.	PUNCT
ejpam-7063	16	1	j.	j.	PROPN
ejpam-7063	16	2	pure	pure	PROPN
ejpam-7063	16	3	appl	appl	PROPN
ejpam-7063	16	4	.	.	PROPN
ejpam-7063	16	5	math	math	PROPN
ejpam-7063	16	6	,	,	PUNCT
ejpam-7063	16	7	18	18	NUM
ejpam-7063	16	8	(	(	PUNCT
ejpam-7063	16	9	4	4	NUM
ejpam-7063	16	10	)	)	PUNCT
ejpam-7063	16	11	(	(	PUNCT
ejpam-7063	16	12	2025	2025	NUM
ejpam-7063	16	13	)	)	PUNCT
ejpam-7063	16	14	,	,	PUNCT
ejpam-7063	16	15	7063	7063	NUM
ejpam-7063	16	16	2	2	NUM
ejpam-7063	16	17	of	of	ADP
ejpam-7063	16	18	29	29	NUM
ejpam-7063	16	19	(	(	PUNCT
ejpam-7063	16	20	fdes	fde	NOUN
ejpam-7063	16	21	)	)	PUNCT
ejpam-7063	16	22	provide	provide	VERB
ejpam-7063	16	23	more	more	ADV
ejpam-7063	16	24	realistic	realistic	ADJ
ejpam-7063	16	25	descriptions	description	NOUN
ejpam-7063	16	26	of	of	ADP
ejpam-7063	16	27	physical	physical	ADJ
ejpam-7063	16	28	and	and	CCONJ
ejpam-7063	16	29	engineering	engineering	NOUN
ejpam-7063	16	30	processes	process	NOUN
ejpam-7063	16	31	such	such	ADJ
ejpam-7063	16	32	as	as	ADP
ejpam-7063	16	33	viscoelasticity	viscoelasticity	NOUN
ejpam-7063	16	34	,	,	PUNCT
ejpam-7063	16	35	diffusion	diffusion	NOUN
ejpam-7063	16	36	in	in	ADP
ejpam-7063	16	37	complex	complex	ADJ
ejpam-7063	16	38	media	medium	NOUN
ejpam-7063	16	39	,	,	PUNCT
ejpam-7063	16	40	and	and	CCONJ
ejpam-7063	16	41	control	control	NOUN
ejpam-7063	16	42	of	of	ADP
ejpam-7063	16	43	distributed	distribute	VERB
ejpam-7063	16	44	parameter	parameter	NOUN
ejpam-7063	16	45	systems	system	NOUN
ejpam-7063	16	46	[	[	X
ejpam-7063	16	47	1–5	1–5	X
ejpam-7063	16	48	]	]	X
ejpam-7063	16	49	.	.	PUNCT
ejpam-7063	17	1	the	the	DET
ejpam-7063	17	2	incorporation	incorporation	NOUN
ejpam-7063	17	3	of	of	ADP
ejpam-7063	17	4	fractional	fractional	ADJ
ejpam-7063	17	5	dynamics	dynamic	NOUN
ejpam-7063	17	6	into	into	ADP
ejpam-7063	17	7	optimal	optimal	ADJ
ejpam-7063	17	8	control	control	NOUN
ejpam-7063	17	9	theory	theory	NOUN
ejpam-7063	17	10	has	have	AUX
ejpam-7063	17	11	led	lead	VERB
ejpam-7063	17	12	to	to	ADP
ejpam-7063	17	13	the	the	DET
ejpam-7063	17	14	development	development	NOUN
ejpam-7063	17	15	of	of	ADP
ejpam-7063	17	16	fractional	fractional	ADJ
ejpam-7063	17	17	optimal	optimal	ADJ
ejpam-7063	17	18	control	control	NOUN
ejpam-7063	17	19	problems	problem	NOUN
ejpam-7063	17	20	(	(	PUNCT
ejpam-7063	17	21	focps	focps	PROPN
ejpam-7063	17	22	)	)	PUNCT
ejpam-7063	17	23	.	.	PUNCT
ejpam-7063	18	1	several	several	ADJ
ejpam-7063	18	2	authors	author	NOUN
ejpam-7063	18	3	have	have	AUX
ejpam-7063	18	4	studied	study	VERB
ejpam-7063	18	5	existence	existence	NOUN
ejpam-7063	18	6	,	,	PUNCT
ejpam-7063	18	7	uniqueness	uniqueness	NOUN
ejpam-7063	18	8	,	,	PUNCT
ejpam-7063	18	9	and	and	CCONJ
ejpam-7063	18	10	optimality	optimality	NOUN
ejpam-7063	18	11	conditions	condition	NOUN
ejpam-7063	18	12	in	in	ADP
ejpam-7063	18	13	this	this	DET
ejpam-7063	18	14	setting	setting	NOUN
ejpam-7063	18	15	.	.	PUNCT
ejpam-7063	19	1	for	for	ADP
ejpam-7063	19	2	instance	instance	NOUN
ejpam-7063	19	3	,	,	PUNCT
ejpam-7063	19	4	agrawal	agrawal	PROPN
ejpam-7063	19	5	and	and	CCONJ
ejpam-7063	19	6	baleanu	baleanu	NOUN
ejpam-7063	20	1	[	[	X
ejpam-7063	20	2	6	6	NUM
ejpam-7063	20	3	]	]	PUNCT
ejpam-7063	20	4	introduced	introduce	VERB
ejpam-7063	20	5	a	a	DET
ejpam-7063	20	6	hamiltonian	hamiltonian	ADJ
ejpam-7063	20	7	framework	framework	NOUN
ejpam-7063	20	8	for	for	ADP
ejpam-7063	20	9	fractional	fractional	ADJ
ejpam-7063	20	10	optimal	optimal	ADJ
ejpam-7063	20	11	control	control	NOUN
ejpam-7063	20	12	,	,	PUNCT
ejpam-7063	20	13	while	while	SCONJ
ejpam-7063	20	14	almeida	almeida	PROPN
ejpam-7063	20	15	and	and	CCONJ
ejpam-7063	20	16	torres	torre	VERB
ejpam-7063	20	17	[	[	X
ejpam-7063	20	18	7	7	X
ejpam-7063	20	19	]	]	PUNCT
ejpam-7063	20	20	derived	derive	VERB
ejpam-7063	20	21	necessary	necessary	ADJ
ejpam-7063	20	22	and	and	CCONJ
ejpam-7063	20	23	sufficient	sufficient	ADJ
ejpam-7063	20	24	conditions	condition	NOUN
ejpam-7063	20	25	for	for	ADP
ejpam-7063	20	26	problems	problem	NOUN
ejpam-7063	20	27	involving	involve	VERB
ejpam-7063	20	28	caputo	caputo	PROPN
ejpam-7063	20	29	derivatives	derivative	NOUN
ejpam-7063	20	30	.	.	PUNCT
ejpam-7063	21	1	li	li	PROPN
ejpam-7063	21	2	and	and	CCONJ
ejpam-7063	21	3	zhou	zhou	PROPN
ejpam-7063	22	1	[	[	X
ejpam-7063	22	2	8	8	NUM
ejpam-7063	22	3	]	]	PUNCT
ejpam-7063	22	4	established	establish	VERB
ejpam-7063	22	5	the	the	DET
ejpam-7063	22	6	existence	existence	NOUN
ejpam-7063	22	7	of	of	ADP
ejpam-7063	22	8	optimal	optimal	ADJ
ejpam-7063	22	9	solutions	solution	NOUN
ejpam-7063	22	10	,	,	PUNCT
ejpam-7063	22	11	and	and	CCONJ
ejpam-7063	22	12	subsequent	subsequent	ADJ
ejpam-7063	22	13	works	work	NOUN
ejpam-7063	22	14	by	by	ADP
ejpam-7063	22	15	mahmudov	mahmudov	X
ejpam-7063	23	1	[	[	X
ejpam-7063	23	2	9	9	NUM
ejpam-7063	23	3	]	]	PUNCT
ejpam-7063	23	4	and	and	CCONJ
ejpam-7063	23	5	sakthivel	sakthivel	NOUN
ejpam-7063	23	6	et	et	PROPN
ejpam-7063	23	7	al	al	PROPN
ejpam-7063	23	8	.	.	PUNCT
ejpam-7063	24	1	[	[	X
ejpam-7063	24	2	10	10	NUM
ejpam-7063	24	3	]	]	PUNCT
ejpam-7063	24	4	extended	extended	ADJ
ejpam-7063	24	5	controllability	controllability	NOUN
ejpam-7063	24	6	and	and	CCONJ
ejpam-7063	24	7	impulsive	impulsive	ADJ
ejpam-7063	24	8	control	control	NOUN
ejpam-7063	24	9	results	result	NOUN
ejpam-7063	24	10	to	to	ADP
ejpam-7063	24	11	semilinear	semilinear	NOUN
ejpam-7063	24	12	systems	system	NOUN
ejpam-7063	24	13	.	.	PUNCT
ejpam-7063	25	1	more	more	ADV
ejpam-7063	25	2	recently	recently	ADV
ejpam-7063	25	3	,	,	PUNCT
ejpam-7063	25	4	bahaa	bahaa	NOUN
ejpam-7063	25	5	and	and	CCONJ
ejpam-7063	25	6	collaborators	collaborator	NOUN
ejpam-7063	26	1	[	[	X
ejpam-7063	26	2	11–19	11–19	NUM
ejpam-7063	26	3	]	]	PUNCT
ejpam-7063	26	4	investigated	investigate	VERB
ejpam-7063	26	5	focps	focp	NOUN
ejpam-7063	26	6	with	with	ADP
ejpam-7063	26	7	variable	variable	ADJ
ejpam-7063	26	8	order	order	NOUN
ejpam-7063	26	9	,	,	PUNCT
ejpam-7063	26	10	time	time	NOUN
ejpam-7063	26	11	delay	delay	NOUN
ejpam-7063	26	12	,	,	PUNCT
ejpam-7063	26	13	weak	weak	ADJ
ejpam-7063	26	14	caputo	caputo	PROPN
ejpam-7063	26	15	derivatives	derivative	NOUN
ejpam-7063	26	16	,	,	PUNCT
ejpam-7063	26	17	and	and	CCONJ
ejpam-7063	26	18	control	control	NOUN
ejpam-7063	26	19	constraints	constraint	NOUN
ejpam-7063	26	20	,	,	PUNCT
ejpam-7063	26	21	thereby	thereby	ADV
ejpam-7063	26	22	highlighting	highlight	VERB
ejpam-7063	26	23	the	the	DET
ejpam-7063	26	24	growing	grow	VERB
ejpam-7063	26	25	breadth	breadth	NOUN
ejpam-7063	26	26	of	of	ADP
ejpam-7063	26	27	applications	application	NOUN
ejpam-7063	26	28	.	.	PUNCT
ejpam-7063	27	1	alongside	alongside	ADP
ejpam-7063	27	2	theoretical	theoretical	ADJ
ejpam-7063	27	3	progress	progress	NOUN
ejpam-7063	27	4	,	,	PUNCT
ejpam-7063	27	5	numerical	numerical	ADJ
ejpam-7063	27	6	techniques	technique	NOUN
ejpam-7063	27	7	for	for	ADP
ejpam-7063	27	8	focps	focp	NOUN
ejpam-7063	27	9	have	have	AUX
ejpam-7063	27	10	evolved	evolve	VERB
ejpam-7063	27	11	rapidly	rapidly	ADV
ejpam-7063	27	12	.	.	PUNCT
ejpam-7063	28	1	lotfi	lotfi	PROPN
ejpam-7063	28	2	et	et	PROPN
ejpam-7063	28	3	al	al	PROPN
ejpam-7063	28	4	.	.	PUNCT
ejpam-7063	29	1	[	[	X
ejpam-7063	29	2	20	20	NUM
ejpam-7063	29	3	,	,	PUNCT
ejpam-7063	29	4	21	21	NUM
ejpam-7063	29	5	]	]	PUNCT
ejpam-7063	29	6	developed	develop	VERB
ejpam-7063	29	7	spectral	spectral	ADJ
ejpam-7063	29	8	methods	method	NOUN
ejpam-7063	29	9	using	use	VERB
ejpam-7063	29	10	orthogonal	orthogonal	ADJ
ejpam-7063	29	11	polynomials	polynomial	NOUN
ejpam-7063	29	12	,	,	PUNCT
ejpam-7063	29	13	while	while	SCONJ
ejpam-7063	29	14	bhrawy	bhrawy	NOUN
ejpam-7063	29	15	et	et	PROPN
ejpam-7063	29	16	al	al	PROPN
ejpam-7063	29	17	.	.	PUNCT
ejpam-7063	30	1	[	[	X
ejpam-7063	30	2	22	22	NUM
ejpam-7063	30	3	]	]	PUNCT
ejpam-7063	30	4	proposed	propose	VERB
ejpam-7063	30	5	efficient	efficient	ADJ
ejpam-7063	30	6	multi	multi	ADJ
ejpam-7063	30	7	-	-	ADJ
ejpam-7063	30	8	dimensional	dimensional	ADJ
ejpam-7063	30	9	schemes	scheme	NOUN
ejpam-7063	30	10	with	with	ADP
ejpam-7063	30	11	quadratic	quadratic	ADJ
ejpam-7063	30	12	performance	performance	NOUN
ejpam-7063	30	13	indices	index	NOUN
ejpam-7063	30	14	.	.	PUNCT
ejpam-7063	31	1	more	more	ADV
ejpam-7063	31	2	recent	recent	ADJ
ejpam-7063	31	3	contributions	contribution	NOUN
ejpam-7063	31	4	include	include	VERB
ejpam-7063	31	5	heydari	heydari	PROPN
ejpam-7063	31	6	et	et	PROPN
ejpam-7063	31	7	al	al	PROPN
ejpam-7063	31	8	.	.	PUNCT
ejpam-7063	32	1	[	[	X
ejpam-7063	32	2	23	23	NUM
ejpam-7063	32	3	]	]	PUNCT
ejpam-7063	32	4	,	,	PUNCT
ejpam-7063	32	5	who	who	PRON
ejpam-7063	32	6	employed	employ	VERB
ejpam-7063	32	7	bernstein	bernstein	PROPN
ejpam-7063	32	8	polynomials	polynomial	NOUN
ejpam-7063	32	9	,	,	PUNCT
ejpam-7063	32	10	and	and	CCONJ
ejpam-7063	32	11	dehestani	dehestani	NOUN
ejpam-7063	32	12	et	et	PROPN
ejpam-7063	32	13	al	al	PROPN
ejpam-7063	32	14	.	.	PUNCT
ejpam-7063	33	1	[	[	X
ejpam-7063	33	2	24	24	NUM
ejpam-7063	33	3	]	]	PUNCT
ejpam-7063	33	4	,	,	PUNCT
ejpam-7063	33	5	who	who	PRON
ejpam-7063	33	6	studied	study	VERB
ejpam-7063	33	7	robust	robust	ADJ
ejpam-7063	33	8	optimization	optimization	NOUN
ejpam-7063	33	9	approaches	approach	NOUN
ejpam-7063	33	10	for	for	ADP
ejpam-7063	33	11	variable	variable	ADJ
ejpam-7063	33	12	-	-	PUNCT
ejpam-7063	33	13	order	order	NOUN
ejpam-7063	33	14	problems	problem	NOUN
ejpam-7063	33	15	.	.	PUNCT
ejpam-7063	34	1	these	these	DET
ejpam-7063	34	2	works	work	NOUN
ejpam-7063	34	3	highlight	highlight	VERB
ejpam-7063	34	4	the	the	DET
ejpam-7063	34	5	demand	demand	NOUN
ejpam-7063	34	6	for	for	ADP
ejpam-7063	34	7	computationally	computationally	ADV
ejpam-7063	34	8	efficient	efficient	ADJ
ejpam-7063	34	9	and	and	CCONJ
ejpam-7063	34	10	accurate	accurate	ADJ
ejpam-7063	34	11	methods	method	NOUN
ejpam-7063	34	12	to	to	PART
ejpam-7063	34	13	approximate	approximate	VERB
ejpam-7063	34	14	fractional	fractional	ADJ
ejpam-7063	34	15	operators	operator	NOUN
ejpam-7063	34	16	,	,	PUNCT
ejpam-7063	34	17	which	which	PRON
ejpam-7063	34	18	are	be	AUX
ejpam-7063	34	19	inherently	inherently	ADV
ejpam-7063	34	20	nonlocal	nonlocal	ADJ
ejpam-7063	34	21	and	and	CCONJ
ejpam-7063	34	22	computationally	computationally	ADV
ejpam-7063	34	23	expensive	expensive	ADJ
ejpam-7063	34	24	.	.	PUNCT
ejpam-7063	35	1	wavelet	wavelet	NOUN
ejpam-7063	35	2	-	-	PUNCT
ejpam-7063	35	3	based	base	VERB
ejpam-7063	35	4	methods	method	NOUN
ejpam-7063	35	5	have	have	AUX
ejpam-7063	35	6	proven	prove	VERB
ejpam-7063	35	7	especially	especially	ADV
ejpam-7063	35	8	effective	effective	ADJ
ejpam-7063	35	9	in	in	ADP
ejpam-7063	35	10	this	this	DET
ejpam-7063	35	11	context	context	NOUN
ejpam-7063	35	12	due	due	ADP
ejpam-7063	35	13	to	to	ADP
ejpam-7063	35	14	their	their	PRON
ejpam-7063	35	15	localization	localization	NOUN
ejpam-7063	35	16	and	and	CCONJ
ejpam-7063	35	17	multiresolution	multiresolution	NOUN
ejpam-7063	35	18	properties	property	NOUN
ejpam-7063	35	19	[	[	X
ejpam-7063	35	20	25	25	NUM
ejpam-7063	35	21	]	]	PUNCT
ejpam-7063	35	22	.	.	PUNCT
ejpam-7063	36	1	classical	classical	ADJ
ejpam-7063	36	2	constructions	construction	NOUN
ejpam-7063	36	3	such	such	ADJ
ejpam-7063	36	4	as	as	ADP
ejpam-7063	36	5	legendre	legendre	PROPN
ejpam-7063	36	6	and	and	CCONJ
ejpam-7063	36	7	chebyshev	chebyshev	PROPN
ejpam-7063	36	8	wavelets	wavelet	NOUN
ejpam-7063	36	9	have	have	AUX
ejpam-7063	36	10	been	be	AUX
ejpam-7063	36	11	employed	employ	VERB
ejpam-7063	36	12	for	for	ADP
ejpam-7063	36	13	focps	focp	NOUN
ejpam-7063	36	14	,	,	PUNCT
ejpam-7063	36	15	but	but	CCONJ
ejpam-7063	36	16	recent	recent	ADJ
ejpam-7063	36	17	attention	attention	NOUN
ejpam-7063	36	18	has	have	AUX
ejpam-7063	36	19	shifted	shift	VERB
ejpam-7063	36	20	toward	toward	ADP
ejpam-7063	36	21	fibonacci	fibonacci	NOUN
ejpam-7063	36	22	-	-	PUNCT
ejpam-7063	36	23	based	base	VERB
ejpam-7063	36	24	wavelets	wavelet	NOUN
ejpam-7063	36	25	.	.	PUNCT
ejpam-7063	37	1	el	el	NOUN
ejpam-7063	37	2	-	-	PUNCT
ejpam-7063	37	3	hawary	hawary	PROPN
ejpam-7063	37	4	and	and	CCONJ
ejpam-7063	37	5	el	el	PROPN
ejpam-7063	37	6	-	-	PUNCT
ejpam-7063	37	7	khazendar	khazendar	NOUN
ejpam-7063	38	1	[	[	X
ejpam-7063	38	2	26	26	NUM
ejpam-7063	38	3	]	]	PUNCT
ejpam-7063	38	4	first	first	ADV
ejpam-7063	38	5	introduced	introduce	VERB
ejpam-7063	38	6	fibonacci	fibonacci	NOUN
ejpam-7063	38	7	wavelets	wavelet	NOUN
ejpam-7063	38	8	for	for	ADP
ejpam-7063	38	9	dynamic	dynamic	ADJ
ejpam-7063	38	10	systems	system	NOUN
ejpam-7063	38	11	.	.	PUNCT
ejpam-7063	39	1	building	build	VERB
ejpam-7063	39	2	on	on	ADP
ejpam-7063	39	3	this	this	PRON
ejpam-7063	39	4	,	,	PUNCT
ejpam-7063	39	5	agarwal	agarwal	PROPN
ejpam-7063	39	6	et	et	PROPN
ejpam-7063	39	7	al	al	PROPN
ejpam-7063	39	8	.	.	PUNCT
ejpam-7063	40	1	[	[	X
ejpam-7063	40	2	27	27	NUM
ejpam-7063	40	3	]	]	PUNCT
ejpam-7063	40	4	developed	develop	VERB
ejpam-7063	40	5	vieta	vieta	PROPN
ejpam-7063	40	6	–	–	PUNCT
ejpam-7063	40	7	fibonacci	fibonacci	NOUN
ejpam-7063	40	8	operational	operational	ADJ
ejpam-7063	40	9	matrices	matrix	NOUN
ejpam-7063	40	10	for	for	ADP
ejpam-7063	40	11	variable	variable	ADJ
ejpam-7063	40	12	-	-	PUNCT
ejpam-7063	40	13	order	order	NOUN
ejpam-7063	40	14	integro	integro	ADJ
ejpam-7063	40	15	-	-	PUNCT
ejpam-7063	40	16	differential	differential	NOUN
ejpam-7063	40	17	equations	equation	NOUN
ejpam-7063	40	18	,	,	PUNCT
ejpam-7063	40	19	while	while	SCONJ
ejpam-7063	40	20	azin	azin	PROPN
ejpam-7063	40	21	et	et	PROPN
ejpam-7063	40	22	al	al	PROPN
ejpam-7063	40	23	.	.	PUNCT
ejpam-7063	41	1	[	[	X
ejpam-7063	41	2	28	28	NUM
ejpam-7063	41	3	,	,	PUNCT
ejpam-7063	41	4	29	29	NUM
ejpam-7063	41	5	]	]	PUNCT
ejpam-7063	41	6	applied	apply	VERB
ejpam-7063	41	7	vieta	vieta	PROPN
ejpam-7063	41	8	–	–	PUNCT
ejpam-7063	41	9	fibonacci	fibonacci	NOUN
ejpam-7063	41	10	wavelets	wavelet	NOUN
ejpam-7063	41	11	to	to	ADP
ejpam-7063	41	12	fractional	fractional	ADJ
ejpam-7063	41	13	pantograph	pantograph	NOUN
ejpam-7063	41	14	and	and	CCONJ
ejpam-7063	41	15	delay	delay	VERB
ejpam-7063	41	16	differential	differential	ADJ
ejpam-7063	41	17	equations	equation	NOUN
ejpam-7063	41	18	.	.	PUNCT
ejpam-7063	42	1	these	these	DET
ejpam-7063	42	2	advances	advance	NOUN
ejpam-7063	42	3	motivated	motivate	VERB
ejpam-7063	42	4	the	the	DET
ejpam-7063	42	5	introduction	introduction	NOUN
ejpam-7063	42	6	of	of	ADP
ejpam-7063	42	7	fractional	fractional	ADJ
ejpam-7063	42	8	vieta	vieta	PROPN
ejpam-7063	42	9	–	–	PUNCT
ejpam-7063	42	10	fibonacci	fibonacci	NOUN
ejpam-7063	42	11	wavelets	wavelet	NOUN
ejpam-7063	42	12	(	(	PUNCT
ejpam-7063	42	13	fvfws	fvfws	NOUN
ejpam-7063	42	14	)	)	PUNCT
ejpam-7063	42	15	,	,	PUNCT
ejpam-7063	42	16	which	which	PRON
ejpam-7063	42	17	offer	offer	VERB
ejpam-7063	42	18	excellent	excellent	ADJ
ejpam-7063	42	19	approximation	approximation	NOUN
ejpam-7063	42	20	capabilities	capability	NOUN
ejpam-7063	42	21	with	with	ADP
ejpam-7063	42	22	fewer	few	ADJ
ejpam-7063	42	23	expansion	expansion	NOUN
ejpam-7063	42	24	terms	term	NOUN
ejpam-7063	42	25	compared	compare	VERB
ejpam-7063	42	26	to	to	ADP
ejpam-7063	42	27	classical	classical	ADJ
ejpam-7063	42	28	wavelets	wavelet	NOUN
ejpam-7063	42	29	.	.	PUNCT
ejpam-7063	43	1	very	very	ADV
ejpam-7063	43	2	recently	recently	ADV
ejpam-7063	43	3	,	,	PUNCT
ejpam-7063	43	4	hoseini	hoseini	NOUN
ejpam-7063	43	5	et	et	PROPN
ejpam-7063	43	6	al	al	PROPN
ejpam-7063	43	7	.	.	PUNCT
ejpam-7063	44	1	[	[	X
ejpam-7063	44	2	30	30	NUM
ejpam-7063	44	3	]	]	PUNCT
ejpam-7063	44	4	demonstrated	demonstrate	VERB
ejpam-7063	44	5	the	the	DET
ejpam-7063	44	6	effectiveness	effectiveness	NOUN
ejpam-7063	44	7	of	of	ADP
ejpam-7063	44	8	fvfws	fvfws	NOUN
ejpam-7063	44	9	in	in	ADP
ejpam-7063	44	10	solving	solve	VERB
ejpam-7063	44	11	two	two	NUM
ejpam-7063	44	12	-	-	PUNCT
ejpam-7063	44	13	dimensional	dimensional	ADJ
ejpam-7063	44	14	focps	focp	NOUN
ejpam-7063	44	15	,	,	PUNCT
ejpam-7063	44	16	which	which	PRON
ejpam-7063	44	17	strongly	strongly	ADV
ejpam-7063	44	18	supports	support	VERB
ejpam-7063	44	19	the	the	DET
ejpam-7063	44	20	approach	approach	NOUN
ejpam-7063	44	21	developed	develop	VERB
ejpam-7063	44	22	in	in	ADP
ejpam-7063	44	23	this	this	DET
ejpam-7063	44	24	work	work	NOUN
ejpam-7063	44	25	.	.	PUNCT
ejpam-7063	45	1	the	the	DET
ejpam-7063	45	2	present	present	ADJ
ejpam-7063	45	3	paper	paper	NOUN
ejpam-7063	45	4	contributes	contribute	VERB
ejpam-7063	45	5	to	to	ADP
ejpam-7063	45	6	this	this	DET
ejpam-7063	45	7	active	active	ADJ
ejpam-7063	45	8	area	area	NOUN
ejpam-7063	45	9	of	of	ADP
ejpam-7063	45	10	research	research	NOUN
ejpam-7063	45	11	by	by	ADP
ejpam-7063	45	12	developing	develop	VERB
ejpam-7063	45	13	a	a	DET
ejpam-7063	45	14	numerical	numerical	ADJ
ejpam-7063	45	15	framework	framework	NOUN
ejpam-7063	45	16	for	for	ADP
ejpam-7063	45	17	two	two	NUM
ejpam-7063	45	18	-	-	PUNCT
ejpam-7063	45	19	dimensional	dimensional	ADJ
ejpam-7063	45	20	focps	focp	NOUN
ejpam-7063	45	21	based	base	VERB
ejpam-7063	45	22	on	on	ADP
ejpam-7063	45	23	fvfws	fvfws	NOUN
ejpam-7063	45	24	.	.	PUNCT
ejpam-7063	46	1	in	in	ADP
ejpam-7063	46	2	contrast	contrast	NOUN
ejpam-7063	46	3	to	to	ADP
ejpam-7063	46	4	earlier	early	ADJ
ejpam-7063	46	5	works	work	NOUN
ejpam-7063	46	6	that	that	PRON
ejpam-7063	46	7	focused	focus	VERB
ejpam-7063	46	8	either	either	CCONJ
ejpam-7063	46	9	on	on	ADP
ejpam-7063	46	10	one	one	NUM
ejpam-7063	46	11	-	-	PUNCT
ejpam-7063	46	12	dimensional	dimensional	ADJ
ejpam-7063	46	13	problems	problem	NOUN
ejpam-7063	46	14	or	or	CCONJ
ejpam-7063	46	15	on	on	ADP
ejpam-7063	46	16	spectral	spectral	ADJ
ejpam-7063	46	17	techniques	technique	NOUN
ejpam-7063	46	18	without	without	ADP
ejpam-7063	46	19	fractional	fractional	ADJ
ejpam-7063	46	20	wavelets	wavelet	NOUN
ejpam-7063	46	21	,	,	PUNCT
ejpam-7063	46	22	our	our	PRON
ejpam-7063	46	23	method	method	NOUN
ejpam-7063	46	24	directly	directly	ADV
ejpam-7063	46	25	leverages	leverage	VERB
ejpam-7063	46	26	the	the	DET
ejpam-7063	46	27	recursive	recursive	ADJ
ejpam-7063	46	28	structure	structure	NOUN
ejpam-7063	46	29	of	of	ADP
ejpam-7063	46	30	vieta	vieta	PROPN
ejpam-7063	46	31	–	–	PUNCT
ejpam-7063	46	32	fibonacci	fibonacci	NOUN
ejpam-7063	46	33	polynomials	polynomial	NOUN
ejpam-7063	46	34	to	to	PART
ejpam-7063	46	35	construct	construct	VERB
ejpam-7063	46	36	fractional	fractional	ADJ
ejpam-7063	46	37	operational	operational	ADJ
ejpam-7063	46	38	matrices	matrix	NOUN
ejpam-7063	46	39	for	for	ADP
ejpam-7063	46	40	caputo	caputo	PROPN
ejpam-7063	46	41	derivatives	derivative	NOUN
ejpam-7063	46	42	.	.	PUNCT
ejpam-7063	47	1	this	this	PRON
ejpam-7063	47	2	allows	allow	VERB
ejpam-7063	47	3	the	the	DET
ejpam-7063	47	4	original	original	ADJ
ejpam-7063	47	5	focp	focp	NOUN
ejpam-7063	47	6	to	to	PART
ejpam-7063	47	7	be	be	AUX
ejpam-7063	47	8	reduced	reduce	VERB
ejpam-7063	47	9	to	to	ADP
ejpam-7063	47	10	a	a	DET
ejpam-7063	47	11	sparse	sparse	ADJ
ejpam-7063	47	12	system	system	NOUN
ejpam-7063	47	13	of	of	ADP
ejpam-7063	47	14	algebraic	algebraic	ADJ
ejpam-7063	47	15	equations	equation	NOUN
ejpam-7063	47	16	,	,	PUNCT
ejpam-7063	47	17	which	which	PRON
ejpam-7063	47	18	is	be	AUX
ejpam-7063	47	19	then	then	ADV
ejpam-7063	47	20	solved	solve	VERB
ejpam-7063	47	21	using	use	VERB
ejpam-7063	47	22	newton	newton	PROPN
ejpam-7063	47	23	’s	’s	PART
ejpam-7063	47	24	method	method	NOUN
ejpam-7063	47	25	.	.	PUNCT
ejpam-7063	48	1	our	our	PRON
ejpam-7063	48	2	work	work	NOUN
ejpam-7063	48	3	is	be	AUX
ejpam-7063	48	4	also	also	ADV
ejpam-7063	48	5	closely	closely	ADV
ejpam-7063	48	6	related	relate	VERB
ejpam-7063	48	7	to	to	ADP
ejpam-7063	48	8	recent	recent	ADJ
ejpam-7063	48	9	studies	study	NOUN
ejpam-7063	48	10	on	on	ADP
ejpam-7063	48	11	bangbang	bangbang	PROPN
ejpam-7063	48	12	and	and	CCONJ
ejpam-7063	48	13	time	time	NOUN
ejpam-7063	48	14	-	-	PUNCT
ejpam-7063	48	15	optimal	optimal	ADJ
ejpam-7063	48	16	control	control	NOUN
ejpam-7063	48	17	for	for	ADP
ejpam-7063	48	18	fractional	fractional	ADJ
ejpam-7063	48	19	systems	system	NOUN
ejpam-7063	48	20	[	[	X
ejpam-7063	48	21	31	31	NUM
ejpam-7063	48	22	]	]	PUNCT
ejpam-7063	48	23	,	,	PUNCT
ejpam-7063	48	24	symmetric	symmetric	ADJ
ejpam-7063	48	25	distributed	distribute	VERB
ejpam-7063	48	26	-	-	PUNCT
ejpam-7063	48	27	order	order	NOUN
ejpam-7063	48	28	systems	system	NOUN
ejpam-7063	48	29	[	[	X
ejpam-7063	48	30	32	32	NUM
ejpam-7063	48	31	]	]	PUNCT
ejpam-7063	48	32	,	,	PUNCT
ejpam-7063	48	33	and	and	CCONJ
ejpam-7063	48	34	numerical	numerical	ADJ
ejpam-7063	48	35	solutions	solution	NOUN
ejpam-7063	48	36	on	on	ADP
ejpam-7063	48	37	complex	complex	ADJ
ejpam-7063	48	38	domains	domain	NOUN
ejpam-7063	48	39	[	[	X
ejpam-7063	48	40	33	33	NUM
ejpam-7063	48	41	]	]	PUNCT
ejpam-7063	48	42	,	,	PUNCT
ejpam-7063	48	43	as	as	SCONJ
ejpam-7063	48	44	it	it	PRON
ejpam-7063	48	45	provides	provide	VERB
ejpam-7063	48	46	a	a	DET
ejpam-7063	48	47	unifying	unifying	ADJ
ejpam-7063	48	48	computational	computational	ADJ
ejpam-7063	48	49	approach	approach	NOUN
ejpam-7063	48	50	applicable	applicable	ADJ
ejpam-7063	48	51	to	to	ADP
ejpam-7063	48	52	a	a	DET
ejpam-7063	48	53	wide	wide	ADJ
ejpam-7063	48	54	range	range	NOUN
ejpam-7063	48	55	of	of	ADP
ejpam-7063	48	56	fractional	fractional	ADJ
ejpam-7063	48	57	models	model	NOUN
ejpam-7063	48	58	.	.	PUNCT
ejpam-7063	49	1	g.	g.	PROPN
ejpam-7063	49	2	m.	m.	PROPN
ejpam-7063	49	3	bahaa	bahaa	PROPN
ejpam-7063	49	4	,	,	PUNCT
ejpam-7063	49	5	a.	a.	NOUN
ejpam-7063	49	6	h.	h.	PROPN
ejpam-7063	49	7	qamlo	qamlo	PROPN
ejpam-7063	49	8	/	/	SYM
ejpam-7063	49	9	eur	eur	PROPN
ejpam-7063	49	10	.	.	PUNCT
ejpam-7063	50	1	j.	j.	PROPN
ejpam-7063	50	2	pure	pure	PROPN
ejpam-7063	50	3	appl	appl	PROPN
ejpam-7063	50	4	.	.	PROPN
ejpam-7063	50	5	math	math	PROPN
ejpam-7063	50	6	,	,	PUNCT
ejpam-7063	50	7	18	18	NUM
ejpam-7063	50	8	(	(	PUNCT
ejpam-7063	50	9	4	4	NUM
ejpam-7063	50	10	)	)	PUNCT
ejpam-7063	50	11	(	(	PUNCT
ejpam-7063	50	12	2025	2025	NUM
ejpam-7063	50	13	)	)	PUNCT
ejpam-7063	50	14	,	,	PUNCT
ejpam-7063	50	15	7063	7063	NUM
ejpam-7063	50	16	3	3	NUM
ejpam-7063	50	17	of	of	ADP
ejpam-7063	50	18	29	29	NUM
ejpam-7063	50	19	the	the	DET
ejpam-7063	50	20	main	main	ADJ
ejpam-7063	50	21	contributions	contribution	NOUN
ejpam-7063	50	22	of	of	ADP
ejpam-7063	50	23	this	this	DET
ejpam-7063	50	24	work	work	NOUN
ejpam-7063	50	25	are	be	AUX
ejpam-7063	50	26	summarized	summarize	VERB
ejpam-7063	50	27	as	as	SCONJ
ejpam-7063	50	28	follows	follow	VERB
ejpam-7063	50	29	:	:	PUNCT
ejpam-7063	50	30	we	we	PRON
ejpam-7063	50	31	extend	extend	VERB
ejpam-7063	50	32	the	the	DET
ejpam-7063	50	33	construction	construction	NOUN
ejpam-7063	50	34	of	of	ADP
ejpam-7063	50	35	fvfws	fvfws	NOUN
ejpam-7063	50	36	to	to	PART
ejpam-7063	50	37	efficiently	efficiently	ADV
ejpam-7063	50	38	approximate	approximate	VERB
ejpam-7063	50	39	two	two	NUM
ejpam-7063	50	40	-	-	PUNCT
ejpam-7063	50	41	dimensional	dimensional	ADJ
ejpam-7063	50	42	focps	focp	NOUN
ejpam-7063	50	43	governed	govern	VERB
ejpam-7063	50	44	by	by	ADP
ejpam-7063	50	45	caputo	caputo	PROPN
ejpam-7063	50	46	derivatives	derivative	NOUN
ejpam-7063	50	47	.	.	PUNCT
ejpam-7063	51	1	we	we	PRON
ejpam-7063	51	2	derive	derive	VERB
ejpam-7063	51	3	operational	operational	ADJ
ejpam-7063	51	4	matrices	matrix	NOUN
ejpam-7063	51	5	of	of	ADP
ejpam-7063	51	6	fractional	fractional	ADJ
ejpam-7063	51	7	derivatives	derivative	NOUN
ejpam-7063	51	8	in	in	ADP
ejpam-7063	51	9	the	the	DET
ejpam-7063	51	10	fvfw	fvfw	ADJ
ejpam-7063	51	11	basis	basis	NOUN
ejpam-7063	51	12	,	,	PUNCT
ejpam-7063	51	13	reducing	reduce	VERB
ejpam-7063	51	14	the	the	DET
ejpam-7063	51	15	fractional	fractional	ADJ
ejpam-7063	51	16	pde	pde	NOUN
ejpam-7063	51	17	constraints	constraint	NOUN
ejpam-7063	51	18	to	to	PART
ejpam-7063	51	19	sparse	sparse	VERB
ejpam-7063	51	20	algebraic	algebraic	ADJ
ejpam-7063	51	21	systems	system	NOUN
ejpam-7063	51	22	.	.	PUNCT
ejpam-7063	52	1	we	we	PRON
ejpam-7063	52	2	formulate	formulate	VERB
ejpam-7063	52	3	and	and	CCONJ
ejpam-7063	52	4	discretize	discretize	VERB
ejpam-7063	52	5	the	the	DET
ejpam-7063	52	6	associated	associated	ADJ
ejpam-7063	52	7	optimality	optimality	NOUN
ejpam-7063	52	8	system	system	NOUN
ejpam-7063	52	9	(	(	PUNCT
ejpam-7063	52	10	state	state	NOUN
ejpam-7063	52	11	,	,	PUNCT
ejpam-7063	52	12	adjoint	adjoint	NOUN
ejpam-7063	52	13	,	,	PUNCT
ejpam-7063	52	14	and	and	CCONJ
ejpam-7063	52	15	control	control	NOUN
ejpam-7063	52	16	conditions	condition	NOUN
ejpam-7063	52	17	)	)	PUNCT
ejpam-7063	52	18	and	and	CCONJ
ejpam-7063	52	19	solve	solve	VERB
ejpam-7063	52	20	it	it	PRON
ejpam-7063	52	21	using	use	VERB
ejpam-7063	52	22	newton	newton	PROPN
ejpam-7063	52	23	’s	’s	PART
ejpam-7063	52	24	method	method	NOUN
ejpam-7063	52	25	.	.	PUNCT
ejpam-7063	53	1	we	we	PRON
ejpam-7063	53	2	validate	validate	VERB
ejpam-7063	53	3	the	the	DET
ejpam-7063	53	4	proposed	propose	VERB
ejpam-7063	53	5	scheme	scheme	NOUN
ejpam-7063	53	6	with	with	ADP
ejpam-7063	53	7	benchmark	benchmark	NOUN
ejpam-7063	53	8	problems	problem	NOUN
ejpam-7063	53	9	,	,	PUNCT
ejpam-7063	53	10	showing	show	VERB
ejpam-7063	53	11	that	that	DET
ejpam-7063	53	12	fvfws	fvfws	NOUN
ejpam-7063	53	13	achieve	achieve	VERB
ejpam-7063	53	14	superior	superior	ADJ
ejpam-7063	53	15	accuracy	accuracy	NOUN
ejpam-7063	53	16	and	and	CCONJ
ejpam-7063	53	17	efficiency	efficiency	NOUN
ejpam-7063	53	18	compared	compare	VERB
ejpam-7063	53	19	to	to	ADP
ejpam-7063	53	20	classical	classical	ADJ
ejpam-7063	53	21	polynomialand	polynomialand	NOUN
ejpam-7063	53	22	wavelet	wavelet	NOUN
ejpam-7063	53	23	-	-	PUNCT
ejpam-7063	53	24	based	base	VERB
ejpam-7063	53	25	methods	method	NOUN
ejpam-7063	53	26	.	.	PUNCT
ejpam-7063	54	1	the	the	DET
ejpam-7063	54	2	rest	rest	NOUN
ejpam-7063	54	3	of	of	ADP
ejpam-7063	54	4	the	the	DET
ejpam-7063	54	5	paper	paper	NOUN
ejpam-7063	54	6	is	be	AUX
ejpam-7063	54	7	organized	organize	VERB
ejpam-7063	54	8	as	as	SCONJ
ejpam-7063	54	9	follows	follow	VERB
ejpam-7063	54	10	.	.	PUNCT
ejpam-7063	55	1	section	section	NOUN
ejpam-7063	55	2	2	2	NUM
ejpam-7063	55	3	recalls	recall	VERB
ejpam-7063	55	4	key	key	ADJ
ejpam-7063	55	5	concepts	concept	NOUN
ejpam-7063	55	6	from	from	ADP
ejpam-7063	55	7	fractional	fractional	ADJ
ejpam-7063	55	8	calculus	calculus	NOUN
ejpam-7063	55	9	and	and	CCONJ
ejpam-7063	55	10	introduces	introduce	VERB
ejpam-7063	55	11	the	the	DET
ejpam-7063	55	12	construction	construction	NOUN
ejpam-7063	55	13	of	of	ADP
ejpam-7063	55	14	fvfws	fvfws	NOUN
ejpam-7063	55	15	.	.	PUNCT
ejpam-7063	56	1	section	section	NOUN
ejpam-7063	56	2	3	3	NUM
ejpam-7063	56	3	formulates	formulate	VERB
ejpam-7063	56	4	the	the	DET
ejpam-7063	56	5	focp	focp	NOUN
ejpam-7063	56	6	and	and	CCONJ
ejpam-7063	56	7	derives	derive	VERB
ejpam-7063	56	8	the	the	DET
ejpam-7063	56	9	corresponding	corresponding	ADJ
ejpam-7063	56	10	optimality	optimality	NOUN
ejpam-7063	56	11	conditions	condition	NOUN
ejpam-7063	56	12	.	.	PUNCT
ejpam-7063	57	1	section	section	NOUN
ejpam-7063	57	2	5	5	NUM
ejpam-7063	57	3	develops	develop	VERB
ejpam-7063	57	4	the	the	DET
ejpam-7063	57	5	fvfwbased	fvfwbased	ADJ
ejpam-7063	57	6	discretization	discretization	NOUN
ejpam-7063	57	7	and	and	CCONJ
ejpam-7063	57	8	the	the	DET
ejpam-7063	57	9	associated	associated	ADJ
ejpam-7063	57	10	numerical	numerical	ADJ
ejpam-7063	57	11	algorithm	algorithm	PROPN
ejpam-7063	57	12	.	.	PUNCT
ejpam-7063	58	1	section	section	NOUN
ejpam-7063	58	2	6	6	NUM
ejpam-7063	58	3	presents	present	VERB
ejpam-7063	58	4	numerical	numerical	ADJ
ejpam-7063	58	5	experiments	experiment	NOUN
ejpam-7063	58	6	to	to	PART
ejpam-7063	58	7	illustrate	illustrate	VERB
ejpam-7063	58	8	the	the	DET
ejpam-7063	58	9	effectiveness	effectiveness	NOUN
ejpam-7063	58	10	of	of	ADP
ejpam-7063	58	11	the	the	DET
ejpam-7063	58	12	method	method	NOUN
ejpam-7063	58	13	.	.	PUNCT
ejpam-7063	59	1	section	section	NOUN
ejpam-7063	59	2	7	7	NUM
ejpam-7063	59	3	concludes	conclude	VERB
ejpam-7063	59	4	the	the	DET
ejpam-7063	59	5	paper	paper	NOUN
ejpam-7063	59	6	and	and	CCONJ
ejpam-7063	59	7	outlines	outline	VERB
ejpam-7063	59	8	directions	direction	NOUN
ejpam-7063	59	9	for	for	ADP
ejpam-7063	59	10	future	future	ADJ
ejpam-7063	59	11	research	research	NOUN
ejpam-7063	59	12	.	.	PUNCT
ejpam-7063	60	1	2	2	X
ejpam-7063	60	2	.	.	X
ejpam-7063	60	3	preliminaries	preliminary	NOUN
ejpam-7063	60	4	this	this	DET
ejpam-7063	60	5	section	section	NOUN
ejpam-7063	60	6	recalls	recall	VERB
ejpam-7063	60	7	the	the	DET
ejpam-7063	60	8	fundamental	fundamental	ADJ
ejpam-7063	60	9	definitions	definition	NOUN
ejpam-7063	60	10	of	of	ADP
ejpam-7063	60	11	fractional	fractional	ADJ
ejpam-7063	60	12	calculus	calculus	NOUN
ejpam-7063	60	13	,	,	PUNCT
ejpam-7063	60	14	approximation	approximation	NOUN
ejpam-7063	60	15	schemes	scheme	NOUN
ejpam-7063	60	16	for	for	ADP
ejpam-7063	60	17	fractional	fractional	ADJ
ejpam-7063	60	18	derivatives	derivative	NOUN
ejpam-7063	60	19	,	,	PUNCT
ejpam-7063	60	20	and	and	CCONJ
ejpam-7063	60	21	the	the	DET
ejpam-7063	60	22	construction	construction	NOUN
ejpam-7063	60	23	of	of	ADP
ejpam-7063	60	24	fractional	fractional	ADJ
ejpam-7063	60	25	vieta	vieta	PROPN
ejpam-7063	60	26	–	–	PUNCT
ejpam-7063	60	27	fibonacci	fibonacci	NOUN
ejpam-7063	60	28	wavelets	wavelet	NOUN
ejpam-7063	60	29	(	(	PUNCT
ejpam-7063	60	30	fvfws	fvfws	NOUN
ejpam-7063	60	31	)	)	PUNCT
ejpam-7063	60	32	,	,	PUNCT
ejpam-7063	60	33	which	which	PRON
ejpam-7063	60	34	form	form	VERB
ejpam-7063	60	35	the	the	DET
ejpam-7063	60	36	basis	basis	NOUN
ejpam-7063	60	37	of	of	ADP
ejpam-7063	60	38	the	the	DET
ejpam-7063	60	39	proposed	propose	VERB
ejpam-7063	60	40	numerical	numerical	ADJ
ejpam-7063	60	41	method	method	NOUN
ejpam-7063	60	42	.	.	PUNCT
ejpam-7063	61	1	2.1	2.1	NUM
ejpam-7063	61	2	.	.	PUNCT
ejpam-7063	61	3	fractional	fractional	ADJ
ejpam-7063	61	4	calculus	calculus	NOUN
ejpam-7063	61	5	fractional	fractional	ADJ
ejpam-7063	61	6	calculus	calculus	NOUN
ejpam-7063	61	7	generalizes	generalize	VERB
ejpam-7063	61	8	the	the	DET
ejpam-7063	61	9	classical	classical	ADJ
ejpam-7063	61	10	notions	notion	NOUN
ejpam-7063	61	11	of	of	ADP
ejpam-7063	61	12	differentiation	differentiation	NOUN
ejpam-7063	61	13	and	and	CCONJ
ejpam-7063	61	14	integration	integration	NOUN
ejpam-7063	61	15	to	to	ADP
ejpam-7063	61	16	non	non	ADJ
ejpam-7063	61	17	-	-	ADJ
ejpam-7063	61	18	integer	integer	ADJ
ejpam-7063	61	19	orders	order	NOUN
ejpam-7063	61	20	,	,	PUNCT
ejpam-7063	61	21	thereby	thereby	ADV
ejpam-7063	61	22	providing	provide	VERB
ejpam-7063	61	23	a	a	DET
ejpam-7063	61	24	framework	framework	NOUN
ejpam-7063	61	25	capable	capable	ADJ
ejpam-7063	61	26	of	of	ADP
ejpam-7063	61	27	modeling	model	VERB
ejpam-7063	61	28	nonlocal	nonlocal	ADJ
ejpam-7063	61	29	and	and	CCONJ
ejpam-7063	61	30	memory	memory	NOUN
ejpam-7063	61	31	-	-	PUNCT
ejpam-7063	61	32	dependent	dependent	ADJ
ejpam-7063	61	33	processes	process	NOUN
ejpam-7063	61	34	.	.	PUNCT
ejpam-7063	62	1	two	two	NUM
ejpam-7063	62	2	commonly	commonly	ADV
ejpam-7063	62	3	used	use	VERB
ejpam-7063	62	4	definitions	definition	NOUN
ejpam-7063	62	5	are	be	AUX
ejpam-7063	62	6	the	the	DET
ejpam-7063	62	7	riemann	riemann	PROPN
ejpam-7063	62	8	–	–	PUNCT
ejpam-7063	62	9	liouville	liouville	PROPN
ejpam-7063	62	10	and	and	CCONJ
ejpam-7063	62	11	caputo	caputo	PROPN
ejpam-7063	62	12	derivatives	derivative	NOUN
ejpam-7063	62	13	[	[	X
ejpam-7063	62	14	1–4	1–4	NOUN
ejpam-7063	62	15	]	]	X
ejpam-7063	62	16	.	.	PUNCT
ejpam-7063	63	1	2.1.1	2.1.1	X
ejpam-7063	63	2	.	.	PUNCT
ejpam-7063	64	1	riemann	riemann	PROPN
ejpam-7063	64	2	–	–	PUNCT
ejpam-7063	64	3	liouville	liouville	VERB
ejpam-7063	64	4	derivative	derivative	NOUN
ejpam-7063	64	5	for	for	ADP
ejpam-7063	64	6	a	a	DET
ejpam-7063	64	7	function	function	NOUN
ejpam-7063	64	8	f	f	PROPN
ejpam-7063	64	9	∈	∈	PROPN
ejpam-7063	64	10	cn[0	cn[0	PROPN
ejpam-7063	64	11	,	,	PUNCT
ejpam-7063	64	12	t	t	X
ejpam-7063	64	13	]	]	PUNCT
ejpam-7063	64	14	and	and	CCONJ
ejpam-7063	64	15	α	α	X
ejpam-7063	64	16	>	>	X
ejpam-7063	64	17	0	0	PROPN
ejpam-7063	64	18	,	,	PUNCT
ejpam-7063	64	19	the	the	DET
ejpam-7063	64	20	riemann	riemann	PROPN
ejpam-7063	64	21	–	–	PUNCT
ejpam-7063	64	22	liouville	liouville	VERB
ejpam-7063	64	23	fractional	fractional	ADJ
ejpam-7063	64	24	derivative	derivative	NOUN
ejpam-7063	64	25	of	of	ADP
ejpam-7063	64	26	order	order	NOUN
ejpam-7063	64	27	α	α	NOUN
ejpam-7063	64	28	is	be	AUX
ejpam-7063	64	29	defined	define	VERB
ejpam-7063	64	30	as	as	ADP
ejpam-7063	64	31	dα	dα	PROPN
ejpam-7063	64	32	t	t	PROPN
ejpam-7063	64	33	f(t	f(t	PROPN
ejpam-7063	64	34	)	)	PUNCT
ejpam-7063	65	1	=	=	SYM
ejpam-7063	65	2	1	1	NUM
ejpam-7063	65	3	γ(n−	γ(n−	PROPN
ejpam-7063	65	4	α	α	NOUN
ejpam-7063	65	5	)	)	PUNCT
ejpam-7063	65	6	dn	dn	PROPN
ejpam-7063	65	7	dtn	dtn	PROPN
ejpam-7063	65	8	∫	∫	PROPN
ejpam-7063	65	9	t	t	PROPN
ejpam-7063	65	10	0	0	NUM
ejpam-7063	65	11	f(τ	f(τ	PROPN
ejpam-7063	65	12	)	)	PUNCT
ejpam-7063	65	13	(	(	PUNCT
ejpam-7063	65	14	t−	t−	PROPN
ejpam-7063	65	15	τ)α−n+1	τ)α−n+1	PROPN
ejpam-7063	65	16	dτ	dτ	PROPN
ejpam-7063	65	17	,	,	PUNCT
ejpam-7063	65	18	n−	n−	PROPN
ejpam-7063	65	19	1	1	NUM
ejpam-7063	65	20	<	<	X
ejpam-7063	65	21	α	α	X
ejpam-7063	65	22	<	<	X
ejpam-7063	65	23	n	n	CCONJ
ejpam-7063	65	24	,	,	PUNCT
ejpam-7063	65	25	n	n	PROPN
ejpam-7063	65	26	∈	∈	PROPN
ejpam-7063	65	27	n.	n.	NOUN
ejpam-7063	65	28	(	(	PUNCT
ejpam-7063	65	29	2.1	2.1	NUM
ejpam-7063	65	30	)	)	PUNCT
ejpam-7063	65	31	this	this	DET
ejpam-7063	65	32	operator	operator	NOUN
ejpam-7063	65	33	is	be	AUX
ejpam-7063	65	34	well	well	ADV
ejpam-7063	65	35	-	-	PUNCT
ejpam-7063	65	36	suited	suit	VERB
ejpam-7063	65	37	for	for	ADP
ejpam-7063	65	38	theoretical	theoretical	ADJ
ejpam-7063	65	39	analysis	analysis	NOUN
ejpam-7063	65	40	but	but	CCONJ
ejpam-7063	65	41	requires	require	VERB
ejpam-7063	65	42	fractional	fractional	ADJ
ejpam-7063	65	43	initial	initial	ADJ
ejpam-7063	65	44	conditions	condition	NOUN
ejpam-7063	65	45	,	,	PUNCT
ejpam-7063	65	46	which	which	PRON
ejpam-7063	65	47	limits	limit	VERB
ejpam-7063	65	48	its	its	PRON
ejpam-7063	65	49	applicability	applicability	NOUN
ejpam-7063	65	50	in	in	ADP
ejpam-7063	65	51	physical	physical	ADJ
ejpam-7063	65	52	modeling	modeling	NOUN
ejpam-7063	65	53	.	.	PUNCT
ejpam-7063	66	1	2.1.2	2.1.2	X
ejpam-7063	66	2	.	.	X
ejpam-7063	66	3	caputo	caputo	PROPN
ejpam-7063	66	4	derivative	derivative	PROPN
ejpam-7063	66	5	the	the	DET
ejpam-7063	66	6	caputo	caputo	PROPN
ejpam-7063	66	7	derivative	derivative	NOUN
ejpam-7063	66	8	of	of	ADP
ejpam-7063	66	9	order	order	NOUN
ejpam-7063	66	10	α	α	PROPN
ejpam-7063	66	11	>	>	X
ejpam-7063	66	12	0	0	NUM
ejpam-7063	66	13	is	be	AUX
ejpam-7063	66	14	defined	define	VERB
ejpam-7063	66	15	as	as	ADP
ejpam-7063	66	16	cdα	cdα	NOUN
ejpam-7063	66	17	t	t	PROPN
ejpam-7063	66	18	f(t	f(t	PROPN
ejpam-7063	66	19	)	)	PUNCT
ejpam-7063	67	1	=	=	SYM
ejpam-7063	67	2	1	1	NUM
ejpam-7063	67	3	γ(n−	γ(n−	PROPN
ejpam-7063	67	4	α	α	NOUN
ejpam-7063	67	5	)	)	PUNCT
ejpam-7063	67	6	∫	∫	PROPN
ejpam-7063	68	1	t	t	PROPN
ejpam-7063	68	2	0	0	NUM
ejpam-7063	69	1	f	f	PROPN
ejpam-7063	69	2	(	(	PUNCT
ejpam-7063	69	3	n)(τ	n)(τ	NOUN
ejpam-7063	69	4	)	)	PUNCT
ejpam-7063	69	5	(	(	PUNCT
ejpam-7063	69	6	t−	t−	PROPN
ejpam-7063	69	7	τ)α−n+1	τ)α−n+1	PROPN
ejpam-7063	69	8	dτ	dτ	PROPN
ejpam-7063	69	9	,	,	PUNCT
ejpam-7063	69	10	n−	n−	PROPN
ejpam-7063	69	11	1	1	NUM
ejpam-7063	69	12	<	<	X
ejpam-7063	69	13	α	α	X
ejpam-7063	69	14	<	<	X
ejpam-7063	69	15	n.	n.	NOUN
ejpam-7063	69	16	(	(	PUNCT
ejpam-7063	69	17	2.2	2.2	NUM
ejpam-7063	69	18	)	)	PUNCT
ejpam-7063	69	19	g.	g.	PROPN
ejpam-7063	69	20	m.	m.	NOUN
ejpam-7063	69	21	bahaa	bahaa	PROPN
ejpam-7063	69	22	,	,	PUNCT
ejpam-7063	69	23	a.	a.	NOUN
ejpam-7063	69	24	h.	h.	PROPN
ejpam-7063	69	25	qamlo	qamlo	PROPN
ejpam-7063	69	26	/	/	SYM
ejpam-7063	69	27	eur	eur	PROPN
ejpam-7063	69	28	.	.	PUNCT
ejpam-7063	70	1	j.	j.	PROPN
ejpam-7063	70	2	pure	pure	PROPN
ejpam-7063	70	3	appl	appl	PROPN
ejpam-7063	70	4	.	.	PROPN
ejpam-7063	70	5	math	math	PROPN
ejpam-7063	70	6	,	,	PUNCT
ejpam-7063	70	7	18	18	NUM
ejpam-7063	70	8	(	(	PUNCT
ejpam-7063	70	9	4	4	NUM
ejpam-7063	70	10	)	)	PUNCT
ejpam-7063	70	11	(	(	PUNCT
ejpam-7063	70	12	2025	2025	NUM
ejpam-7063	70	13	)	)	PUNCT
ejpam-7063	70	14	,	,	PUNCT
ejpam-7063	70	15	7063	7063	NUM
ejpam-7063	70	16	4	4	NUM
ejpam-7063	70	17	of	of	ADP
ejpam-7063	70	18	29	29	NUM
ejpam-7063	70	19	the	the	DET
ejpam-7063	70	20	caputo	caputo	PROPN
ejpam-7063	70	21	derivative	derivative	NOUN
ejpam-7063	70	22	is	be	AUX
ejpam-7063	70	23	particularly	particularly	ADV
ejpam-7063	70	24	advantageous	advantageous	ADJ
ejpam-7063	70	25	in	in	ADP
ejpam-7063	70	26	applications	application	NOUN
ejpam-7063	70	27	since	since	SCONJ
ejpam-7063	70	28	it	it	PRON
ejpam-7063	70	29	allows	allow	VERB
ejpam-7063	70	30	initial	initial	ADJ
ejpam-7063	70	31	conditions	condition	NOUN
ejpam-7063	70	32	to	to	PART
ejpam-7063	70	33	be	be	AUX
ejpam-7063	70	34	expressed	express	VERB
ejpam-7063	70	35	in	in	ADP
ejpam-7063	70	36	terms	term	NOUN
ejpam-7063	70	37	of	of	ADP
ejpam-7063	70	38	integer	integer	NOUN
ejpam-7063	70	39	-	-	PUNCT
ejpam-7063	70	40	order	order	NOUN
ejpam-7063	70	41	derivatives	derivative	NOUN
ejpam-7063	70	42	of	of	ADP
ejpam-7063	70	43	f	f	PROPN
ejpam-7063	70	44	.	.	PUNCT
ejpam-7063	71	1	for	for	ADP
ejpam-7063	71	2	this	this	DET
ejpam-7063	71	3	reason	reason	NOUN
ejpam-7063	71	4	,	,	PUNCT
ejpam-7063	71	5	it	it	PRON
ejpam-7063	71	6	is	be	AUX
ejpam-7063	71	7	widely	widely	ADV
ejpam-7063	71	8	adopted	adopt	VERB
ejpam-7063	71	9	in	in	ADP
ejpam-7063	71	10	the	the	DET
ejpam-7063	71	11	modeling	modeling	NOUN
ejpam-7063	71	12	of	of	ADP
ejpam-7063	71	13	fractional	fractional	ADJ
ejpam-7063	71	14	control	control	NOUN
ejpam-7063	71	15	systems	system	NOUN
ejpam-7063	71	16	[	[	X
ejpam-7063	71	17	7	7	NUM
ejpam-7063	71	18	,	,	PUNCT
ejpam-7063	71	19	8	8	NUM
ejpam-7063	71	20	]	]	PUNCT
ejpam-7063	71	21	.	.	PUNCT
ejpam-7063	72	1	2.1.3	2.1.3	NUM
ejpam-7063	72	2	.	.	PUNCT
ejpam-7063	72	3	numerical	numerical	ADJ
ejpam-7063	72	4	approximations	approximation	NOUN
ejpam-7063	72	5	several	several	ADJ
ejpam-7063	72	6	discretization	discretization	NOUN
ejpam-7063	72	7	schemes	scheme	NOUN
ejpam-7063	72	8	have	have	AUX
ejpam-7063	72	9	been	be	AUX
ejpam-7063	72	10	developed	develop	VERB
ejpam-7063	72	11	for	for	ADP
ejpam-7063	72	12	fractional	fractional	ADJ
ejpam-7063	72	13	derivatives	derivative	NOUN
ejpam-7063	72	14	.	.	PUNCT
ejpam-7063	73	1	the	the	DET
ejpam-7063	73	2	grünwald	grünwald	NOUN
ejpam-7063	73	3	–	–	PUNCT
ejpam-7063	73	4	letnikov	letnikov	NOUN
ejpam-7063	73	5	method	method	NOUN
ejpam-7063	73	6	[	[	X
ejpam-7063	73	7	34	34	NUM
ejpam-7063	73	8	,	,	PUNCT
ejpam-7063	73	9	35	35	NUM
ejpam-7063	73	10	]	]	PUNCT
ejpam-7063	73	11	provides	provide	VERB
ejpam-7063	73	12	a	a	DET
ejpam-7063	73	13	simple	simple	ADJ
ejpam-7063	73	14	finite	finite	ADJ
ejpam-7063	73	15	-	-	PUNCT
ejpam-7063	73	16	difference	difference	ADJ
ejpam-7063	73	17	-	-	PUNCT
ejpam-7063	73	18	type	type	NOUN
ejpam-7063	73	19	approximation	approximation	NOUN
ejpam-7063	73	20	,	,	PUNCT
ejpam-7063	73	21	while	while	SCONJ
ejpam-7063	73	22	higher	high	ADJ
ejpam-7063	73	23	-	-	PUNCT
ejpam-7063	73	24	order	order	NOUN
ejpam-7063	73	25	methods	method	NOUN
ejpam-7063	73	26	[	[	X
ejpam-7063	73	27	36	36	NUM
ejpam-7063	73	28	]	]	PUNCT
ejpam-7063	73	29	and	and	CCONJ
ejpam-7063	73	30	asymptotic	asymptotic	ADJ
ejpam-7063	73	31	expansions	expansion	NOUN
ejpam-7063	73	32	[	[	X
ejpam-7063	73	33	37	37	NUM
ejpam-7063	73	34	]	]	PUNCT
ejpam-7063	73	35	improve	improve	VERB
ejpam-7063	73	36	accuracy	accuracy	NOUN
ejpam-7063	73	37	for	for	ADP
ejpam-7063	73	38	both	both	CCONJ
ejpam-7063	73	39	smooth	smooth	ADJ
ejpam-7063	73	40	and	and	CCONJ
ejpam-7063	73	41	nonsmooth	nonsmooth	ADJ
ejpam-7063	73	42	solutions	solution	NOUN
ejpam-7063	73	43	.	.	PUNCT
ejpam-7063	74	1	li	li	PROPN
ejpam-7063	74	2	and	and	CCONJ
ejpam-7063	74	3	zeng	zeng	PROPN
ejpam-7063	75	1	[	[	X
ejpam-7063	75	2	38	38	NUM
ejpam-7063	75	3	]	]	PUNCT
ejpam-7063	75	4	provide	provide	VERB
ejpam-7063	75	5	a	a	DET
ejpam-7063	75	6	comprehensive	comprehensive	ADJ
ejpam-7063	75	7	overview	overview	NOUN
ejpam-7063	75	8	of	of	ADP
ejpam-7063	75	9	numerical	numerical	ADJ
ejpam-7063	75	10	methods	method	NOUN
ejpam-7063	75	11	for	for	ADP
ejpam-7063	75	12	fractional	fractional	ADJ
ejpam-7063	75	13	calculus	calculus	NOUN
ejpam-7063	75	14	.	.	PUNCT
ejpam-7063	76	1	in	in	ADP
ejpam-7063	76	2	this	this	DET
ejpam-7063	76	3	work	work	NOUN
ejpam-7063	76	4	,	,	PUNCT
ejpam-7063	76	5	however	however	ADV
ejpam-7063	76	6	,	,	PUNCT
ejpam-7063	76	7	we	we	PRON
ejpam-7063	76	8	avoid	avoid	VERB
ejpam-7063	76	9	direct	direct	ADJ
ejpam-7063	76	10	discretization	discretization	NOUN
ejpam-7063	76	11	and	and	CCONJ
ejpam-7063	76	12	instead	instead	ADV
ejpam-7063	76	13	employ	employ	VERB
ejpam-7063	76	14	wavelet	wavelet	NOUN
ejpam-7063	76	15	-	-	PUNCT
ejpam-7063	76	16	based	base	VERB
ejpam-7063	76	17	operational	operational	ADJ
ejpam-7063	76	18	matrices	matrix	NOUN
ejpam-7063	76	19	,	,	PUNCT
ejpam-7063	76	20	which	which	PRON
ejpam-7063	76	21	significantly	significantly	ADV
ejpam-7063	76	22	reduce	reduce	VERB
ejpam-7063	76	23	computational	computational	ADJ
ejpam-7063	76	24	cost	cost	NOUN
ejpam-7063	76	25	while	while	SCONJ
ejpam-7063	76	26	maintaining	maintain	VERB
ejpam-7063	76	27	accuracy	accuracy	NOUN
ejpam-7063	76	28	.	.	PUNCT
ejpam-7063	77	1	2.2	2.2	NUM
ejpam-7063	77	2	.	.	PUNCT
ejpam-7063	77	3	fractional	fractional	ADJ
ejpam-7063	77	4	vieta	vieta	PROPN
ejpam-7063	77	5	–	–	PUNCT
ejpam-7063	77	6	fibonacci	fibonacci	NOUN
ejpam-7063	77	7	wavelets	wavelet	VERB
ejpam-7063	77	8	wavelet	wavelet	NOUN
ejpam-7063	77	9	methods	method	NOUN
ejpam-7063	77	10	are	be	AUX
ejpam-7063	77	11	well	well	ADV
ejpam-7063	77	12	known	known	ADJ
ejpam-7063	77	13	for	for	ADP
ejpam-7063	77	14	their	their	PRON
ejpam-7063	77	15	localization	localization	NOUN
ejpam-7063	77	16	,	,	PUNCT
ejpam-7063	77	17	orthogonality	orthogonality	NOUN
ejpam-7063	77	18	,	,	PUNCT
ejpam-7063	77	19	and	and	CCONJ
ejpam-7063	77	20	multiresolution	multiresolution	NOUN
ejpam-7063	77	21	properties	property	NOUN
ejpam-7063	77	22	,	,	PUNCT
ejpam-7063	77	23	which	which	PRON
ejpam-7063	77	24	make	make	VERB
ejpam-7063	77	25	them	they	PRON
ejpam-7063	77	26	powerful	powerful	ADJ
ejpam-7063	77	27	tools	tool	NOUN
ejpam-7063	77	28	for	for	ADP
ejpam-7063	77	29	approximating	approximate	VERB
ejpam-7063	77	30	functions	function	NOUN
ejpam-7063	77	31	and	and	CCONJ
ejpam-7063	77	32	operators	operator	NOUN
ejpam-7063	78	1	[	[	X
ejpam-7063	78	2	25	25	NUM
ejpam-7063	78	3	]	]	PUNCT
ejpam-7063	78	4	.	.	PUNCT
ejpam-7063	79	1	in	in	ADP
ejpam-7063	79	2	particular	particular	ADJ
ejpam-7063	79	3	,	,	PUNCT
ejpam-7063	79	4	fibonacci	fibonacci	NOUN
ejpam-7063	79	5	-	-	PUNCT
ejpam-7063	79	6	based	base	VERB
ejpam-7063	79	7	wavelets	wavelet	NOUN
ejpam-7063	79	8	,	,	PUNCT
ejpam-7063	79	9	introduced	introduce	VERB
ejpam-7063	79	10	by	by	ADP
ejpam-7063	79	11	el	el	PROPN
ejpam-7063	79	12	-	-	PUNCT
ejpam-7063	79	13	hawary	hawary	PROPN
ejpam-7063	79	14	and	and	CCONJ
ejpam-7063	79	15	elkhazendar	elkhazendar	X
ejpam-7063	80	1	[	[	X
ejpam-7063	80	2	26	26	NUM
ejpam-7063	80	3	]	]	PUNCT
ejpam-7063	80	4	,	,	PUNCT
ejpam-7063	80	5	combine	combine	VERB
ejpam-7063	80	6	the	the	DET
ejpam-7063	80	7	recursive	recursive	ADJ
ejpam-7063	80	8	structure	structure	NOUN
ejpam-7063	80	9	of	of	ADP
ejpam-7063	80	10	fibonacci	fibonacci	NOUN
ejpam-7063	80	11	polynomials	polynomial	NOUN
ejpam-7063	80	12	with	with	ADP
ejpam-7063	80	13	wavelet	wavelet	NOUN
ejpam-7063	80	14	theory	theory	NOUN
ejpam-7063	80	15	.	.	PUNCT
ejpam-7063	81	1	more	more	ADV
ejpam-7063	81	2	recently	recently	ADV
ejpam-7063	81	3	,	,	PUNCT
ejpam-7063	81	4	agarwal	agarwal	PROPN
ejpam-7063	81	5	et	et	PROPN
ejpam-7063	81	6	al	al	PROPN
ejpam-7063	81	7	.	.	PUNCT
ejpam-7063	82	1	[	[	X
ejpam-7063	82	2	27	27	NUM
ejpam-7063	82	3	]	]	PUNCT
ejpam-7063	82	4	constructed	construct	VERB
ejpam-7063	82	5	vieta	vieta	PROPN
ejpam-7063	82	6	–	–	PUNCT
ejpam-7063	82	7	fibonacci	fibonacci	NOUN
ejpam-7063	82	8	operational	operational	ADJ
ejpam-7063	82	9	matrices	matrix	NOUN
ejpam-7063	82	10	for	for	ADP
ejpam-7063	82	11	variable	variable	ADJ
ejpam-7063	82	12	-	-	PUNCT
ejpam-7063	82	13	order	order	NOUN
ejpam-7063	82	14	equations	equation	NOUN
ejpam-7063	82	15	,	,	PUNCT
ejpam-7063	82	16	while	while	SCONJ
ejpam-7063	82	17	azin	azin	PROPN
ejpam-7063	82	18	and	and	CCONJ
ejpam-7063	82	19	collaborators	collaborator	NOUN
ejpam-7063	82	20	extended	extend	VERB
ejpam-7063	82	21	these	these	DET
ejpam-7063	82	22	ideas	idea	NOUN
ejpam-7063	82	23	to	to	ADP
ejpam-7063	82	24	fractional	fractional	ADJ
ejpam-7063	82	25	pantograph	pantograph	NOUN
ejpam-7063	82	26	and	and	CCONJ
ejpam-7063	82	27	delay	delay	VERB
ejpam-7063	82	28	differential	differential	ADJ
ejpam-7063	82	29	equations	equation	NOUN
ejpam-7063	83	1	[	[	X
ejpam-7063	83	2	28	28	NUM
ejpam-7063	83	3	,	,	PUNCT
ejpam-7063	83	4	29	29	NUM
ejpam-7063	83	5	]	]	PUNCT
ejpam-7063	83	6	.	.	PUNCT
ejpam-7063	84	1	hoseini	hoseini	PROPN
ejpam-7063	84	2	et	et	PROPN
ejpam-7063	84	3	al	al	PROPN
ejpam-7063	84	4	.	.	PUNCT
ejpam-7063	85	1	[	[	X
ejpam-7063	85	2	30	30	NUM
ejpam-7063	85	3	]	]	PUNCT
ejpam-7063	85	4	demonstrated	demonstrate	VERB
ejpam-7063	85	5	the	the	DET
ejpam-7063	85	6	efficiency	efficiency	NOUN
ejpam-7063	85	7	of	of	ADP
ejpam-7063	85	8	fractional	fractional	ADJ
ejpam-7063	85	9	vieta	vieta	PROPN
ejpam-7063	85	10	–	–	PUNCT
ejpam-7063	85	11	fibonacci	fibonacci	NOUN
ejpam-7063	85	12	wavelets	wavelet	NOUN
ejpam-7063	85	13	for	for	ADP
ejpam-7063	85	14	two	two	NUM
ejpam-7063	85	15	-	-	PUNCT
ejpam-7063	85	16	dimensional	dimensional	ADJ
ejpam-7063	85	17	focps	focp	NOUN
ejpam-7063	85	18	,	,	PUNCT
ejpam-7063	85	19	which	which	PRON
ejpam-7063	85	20	strongly	strongly	ADV
ejpam-7063	85	21	motivates	motivate	VERB
ejpam-7063	85	22	their	their	PRON
ejpam-7063	85	23	use	use	NOUN
ejpam-7063	85	24	in	in	ADP
ejpam-7063	85	25	this	this	DET
ejpam-7063	85	26	paper	paper	NOUN
ejpam-7063	85	27	.	.	PUNCT
ejpam-7063	86	1	2.2.1	2.2.1	NUM
ejpam-7063	86	2	.	.	PUNCT
ejpam-7063	87	1	construction	construction	NOUN
ejpam-7063	87	2	of	of	ADP
ejpam-7063	87	3	fractional	fractional	ADJ
ejpam-7063	87	4	vieta	vieta	PROPN
ejpam-7063	87	5	–	–	PUNCT
ejpam-7063	87	6	fibonacci	fibonacci	NOUN
ejpam-7063	87	7	wavelets	wavelet	NOUN
ejpam-7063	87	8	let	let	VERB
ejpam-7063	87	9	{	{	PUNCT
ejpam-7063	87	10	pi(x	pi(x	NUM
ejpam-7063	87	11	)	)	PUNCT
ejpam-7063	87	12	}	}	PUNCT
ejpam-7063	87	13	denote	denote	VERB
ejpam-7063	87	14	the	the	DET
ejpam-7063	87	15	vieta	vieta	PROPN
ejpam-7063	87	16	–	–	PUNCT
ejpam-7063	87	17	fibonacci	fibonacci	NOUN
ejpam-7063	87	18	polynomials	polynomial	NOUN
ejpam-7063	87	19	generated	generate	VERB
ejpam-7063	87	20	via	via	ADP
ejpam-7063	87	21	a	a	DET
ejpam-7063	87	22	fibonacci	fibonacci	NOUN
ejpam-7063	87	23	-	-	PUNCT
ejpam-7063	87	24	type	type	NOUN
ejpam-7063	87	25	recurrence	recurrence	NOUN
ejpam-7063	87	26	relation	relation	NOUN
ejpam-7063	87	27	.	.	PUNCT
ejpam-7063	88	1	the	the	DET
ejpam-7063	88	2	fractional	fractional	ADJ
ejpam-7063	88	3	vieta	vieta	PROPN
ejpam-7063	88	4	–	–	PUNCT
ejpam-7063	88	5	fibonacci	fibonacci	NOUN
ejpam-7063	88	6	wavelet	wavelet	NOUN
ejpam-7063	88	7	of	of	ADP
ejpam-7063	88	8	order	order	NOUN
ejpam-7063	88	9	µ	µ	X
ejpam-7063	88	10	is	be	AUX
ejpam-7063	88	11	defined	define	VERB
ejpam-7063	88	12	on	on	ADP
ejpam-7063	88	13	the	the	DET
ejpam-7063	88	14	unit	unit	NOUN
ejpam-7063	88	15	interval	interval	NOUN
ejpam-7063	88	16	[	[	X
ejpam-7063	88	17	0	0	NUM
ejpam-7063	88	18	,	,	PUNCT
ejpam-7063	88	19	1	1	NUM
ejpam-7063	88	20	]	]	PUNCT
ejpam-7063	88	21	as	as	ADP
ejpam-7063	88	22	ψ	ψ	X
ejpam-7063	88	23	(	(	PUNCT
ejpam-7063	88	24	µ	µ	NOUN
ejpam-7063	88	25	)	)	PUNCT
ejpam-7063	88	26	i	i	PRON
ejpam-7063	88	27	(	(	PUNCT
ejpam-7063	88	28	x	x	X
ejpam-7063	88	29	)	)	PUNCT
ejpam-7063	88	30	=	=	SYM
ejpam-7063	89	1	xµ(1−	xµ(1−	PROPN
ejpam-7063	89	2	x)µpi(x	x)µpi(x	NUM
ejpam-7063	89	3	)	)	PUNCT
ejpam-7063	89	4	,	,	PUNCT
ejpam-7063	89	5	0	0	NUM
ejpam-7063	89	6	≤	≤	NUM
ejpam-7063	89	7	x	x	SYM
ejpam-7063	89	8	≤	≤	NUM
ejpam-7063	89	9	1	1	NUM
ejpam-7063	89	10	.	.	PUNCT
ejpam-7063	90	1	(	(	PUNCT
ejpam-7063	90	2	2.3	2.3	NUM
ejpam-7063	90	3	)	)	PUNCT
ejpam-7063	90	4	these	these	DET
ejpam-7063	90	5	functions	function	NOUN
ejpam-7063	90	6	satisfy	satisfy	VERB
ejpam-7063	90	7	desirable	desirable	ADJ
ejpam-7063	90	8	approximation	approximation	NOUN
ejpam-7063	90	9	properties	property	NOUN
ejpam-7063	90	10	for	for	ADP
ejpam-7063	90	11	fractional	fractional	ADJ
ejpam-7063	90	12	systems	system	NOUN
ejpam-7063	90	13	such	such	ADJ
ejpam-7063	90	14	as	as	ADP
ejpam-7063	90	15	localization	localization	NOUN
ejpam-7063	90	16	,	,	PUNCT
ejpam-7063	90	17	orthogonality	orthogonality	NOUN
ejpam-7063	90	18	(	(	PUNCT
ejpam-7063	90	19	or	or	CCONJ
ejpam-7063	90	20	near	near	ADV
ejpam-7063	90	21	-	-	PUNCT
ejpam-7063	90	22	orthogonality	orthogonality	NOUN
ejpam-7063	90	23	)	)	PUNCT
ejpam-7063	90	24	,	,	PUNCT
ejpam-7063	90	25	and	and	CCONJ
ejpam-7063	90	26	multiresolution	multiresolution	NOUN
ejpam-7063	90	27	analysis	analysis	NOUN
ejpam-7063	90	28	(	(	PUNCT
ejpam-7063	90	29	mra	mra	NOUN
ejpam-7063	90	30	)	)	PUNCT
ejpam-7063	90	31	,	,	PUNCT
ejpam-7063	90	32	which	which	PRON
ejpam-7063	90	33	are	be	AUX
ejpam-7063	90	34	the	the	DET
ejpam-7063	90	35	main	main	ADJ
ejpam-7063	90	36	advantages	advantage	NOUN
ejpam-7063	90	37	cited	cite	VERB
ejpam-7063	90	38	for	for	ADP
ejpam-7063	90	39	focps	focp	NOUN
ejpam-7063	90	40	.	.	PUNCT
ejpam-7063	91	1	including	include	VERB
ejpam-7063	91	2	good	good	ADJ
ejpam-7063	91	3	accuracy	accuracy	NOUN
ejpam-7063	91	4	with	with	ADP
ejpam-7063	91	5	fewer	few	ADJ
ejpam-7063	91	6	terms	term	NOUN
ejpam-7063	91	7	and	and	CCONJ
ejpam-7063	91	8	well	well	ADV
ejpam-7063	91	9	-	-	PUNCT
ejpam-7063	91	10	structured	structure	VERB
ejpam-7063	91	11	operational	operational	ADJ
ejpam-7063	91	12	matrices	matrix	NOUN
ejpam-7063	91	13	for	for	ADP
ejpam-7063	91	14	fractional	fractional	ADJ
ejpam-7063	91	15	derivatives	derivative	NOUN
ejpam-7063	91	16	.	.	PUNCT
ejpam-7063	92	1	the	the	DET
ejpam-7063	92	2	basis	basis	NOUN
ejpam-7063	92	3	is	be	AUX
ejpam-7063	92	4	derived	derive	VERB
ejpam-7063	92	5	from	from	ADP
ejpam-7063	92	6	the	the	DET
ejpam-7063	92	7	recursive	recursive	ADJ
ejpam-7063	92	8	structure	structure	NOUN
ejpam-7063	92	9	of	of	ADP
ejpam-7063	92	10	vieta	vieta	PROPN
ejpam-7063	92	11	-	-	PUNCT
ejpam-7063	92	12	fibonacci	fibonacci	NOUN
ejpam-7063	92	13	polynomials	polynomial	NOUN
ejpam-7063	92	14	,	,	PUNCT
ejpam-7063	92	15	which	which	PRON
ejpam-7063	92	16	is	be	AUX
ejpam-7063	92	17	a	a	DET
ejpam-7063	92	18	recognized	recognize	VERB
ejpam-7063	92	19	method	method	NOUN
ejpam-7063	92	20	for	for	ADP
ejpam-7063	92	21	constructing	construct	VERB
ejpam-7063	92	22	polynomial	polynomial	ADJ
ejpam-7063	92	23	-	-	PUNCT
ejpam-7063	92	24	based	base	VERB
ejpam-7063	92	25	wavelets	wavelet	NOUN
ejpam-7063	92	26	.	.	PUNCT
ejpam-7063	93	1	2.2.2	2.2.2	NUM
ejpam-7063	93	2	.	.	X
ejpam-7063	93	3	two	two	NUM
ejpam-7063	93	4	-	-	PUNCT
ejpam-7063	93	5	dimensional	dimensional	ADJ
ejpam-7063	93	6	fractional	fractional	ADJ
ejpam-7063	93	7	vieta	vieta	NOUN
ejpam-7063	93	8	–	–	PUNCT
ejpam-7063	93	9	fibonacci	fibonacci	NOUN
ejpam-7063	93	10	wavelets	wavelet	NOUN
ejpam-7063	93	11	basis	basis	NOUN
ejpam-7063	93	12	for	for	ADP
ejpam-7063	93	13	two	two	NUM
ejpam-7063	93	14	-	-	PUNCT
ejpam-7063	93	15	dimensional	dimensional	ADJ
ejpam-7063	93	16	problems	problem	NOUN
ejpam-7063	93	17	,	,	PUNCT
ejpam-7063	93	18	tensor	tensor	NOUN
ejpam-7063	93	19	products	product	NOUN
ejpam-7063	93	20	of	of	ADP
ejpam-7063	93	21	one	one	NUM
ejpam-7063	93	22	-	-	PUNCT
ejpam-7063	93	23	dimensional	dimensional	ADJ
ejpam-7063	93	24	fvfws	fvfws	NOUN
ejpam-7063	93	25	are	be	AUX
ejpam-7063	93	26	used	use	VERB
ejpam-7063	93	27	:	:	PUNCT
ejpam-7063	94	1	ψ	ψ	X
ejpam-7063	94	2	(	(	PUNCT
ejpam-7063	94	3	α	α	X
ejpam-7063	94	4	,	,	PUNCT
ejpam-7063	94	5	β	β	NOUN
ejpam-7063	94	6	)	)	PUNCT
ejpam-7063	94	7	ij	ij	NOUN
ejpam-7063	94	8	(	(	PUNCT
ejpam-7063	94	9	x	x	NOUN
ejpam-7063	94	10	,	,	PUNCT
ejpam-7063	94	11	y	y	NOUN
ejpam-7063	94	12	)	)	PUNCT
ejpam-7063	94	13	=	=	SYM
ejpam-7063	94	14	ψ	ψ	X
ejpam-7063	94	15	(	(	PUNCT
ejpam-7063	94	16	α	α	NOUN
ejpam-7063	94	17	)	)	PUNCT
ejpam-7063	94	18	i	i	PRON
ejpam-7063	94	19	(	(	PUNCT
ejpam-7063	94	20	x)ψ	x)ψ	X
ejpam-7063	94	21	(	(	PUNCT
ejpam-7063	94	22	β	β	X
ejpam-7063	94	23	)	)	PUNCT
ejpam-7063	94	24	j	j	PROPN
ejpam-7063	94	25	(	(	PUNCT
ejpam-7063	94	26	y	y	PROPN
ejpam-7063	94	27	)	)	PUNCT
ejpam-7063	94	28	,	,	PUNCT
ejpam-7063	94	29	(	(	PUNCT
ejpam-7063	94	30	x	x	X
ejpam-7063	94	31	,	,	PUNCT
ejpam-7063	94	32	y	y	NOUN
ejpam-7063	94	33	)	)	PUNCT
ejpam-7063	94	34	∈	∈	PROPN
ejpam-7063	95	1	[	[	X
ejpam-7063	95	2	0	0	NUM
ejpam-7063	95	3	,	,	PUNCT
ejpam-7063	95	4	1]2	1]2	NUM
ejpam-7063	95	5	.	.	PUNCT
ejpam-7063	96	1	(	(	PUNCT
ejpam-7063	96	2	2.4	2.4	NUM
ejpam-7063	96	3	)	)	PUNCT
ejpam-7063	96	4	g.	g.	NOUN
ejpam-7063	96	5	m.	m.	NOUN
ejpam-7063	96	6	bahaa	bahaa	PROPN
ejpam-7063	96	7	,	,	PUNCT
ejpam-7063	96	8	a.	a.	NOUN
ejpam-7063	96	9	h.	h.	PROPN
ejpam-7063	96	10	qamlo	qamlo	PROPN
ejpam-7063	96	11	/	/	SYM
ejpam-7063	96	12	eur	eur	PROPN
ejpam-7063	96	13	.	.	PUNCT
ejpam-7063	97	1	j.	j.	PROPN
ejpam-7063	97	2	pure	pure	PROPN
ejpam-7063	97	3	appl	appl	PROPN
ejpam-7063	97	4	.	.	PROPN
ejpam-7063	97	5	math	math	PROPN
ejpam-7063	97	6	,	,	PUNCT
ejpam-7063	97	7	18	18	NUM
ejpam-7063	97	8	(	(	PUNCT
ejpam-7063	97	9	4	4	NUM
ejpam-7063	97	10	)	)	PUNCT
ejpam-7063	97	11	(	(	PUNCT
ejpam-7063	97	12	2025	2025	NUM
ejpam-7063	97	13	)	)	PUNCT
ejpam-7063	97	14	,	,	PUNCT
ejpam-7063	97	15	7063	7063	NUM
ejpam-7063	97	16	5	5	NUM
ejpam-7063	97	17	of	of	ADP
ejpam-7063	97	18	29	29	NUM
ejpam-7063	97	19	this	this	DET
ejpam-7063	97	20	basis	basis	NOUN
ejpam-7063	97	21	allows	allow	VERB
ejpam-7063	97	22	simultaneous	simultaneous	ADJ
ejpam-7063	97	23	approximation	approximation	NOUN
ejpam-7063	97	24	of	of	ADP
ejpam-7063	97	25	state	state	NOUN
ejpam-7063	97	26	,	,	PUNCT
ejpam-7063	97	27	adjoint	adjoint	NOUN
ejpam-7063	97	28	,	,	PUNCT
ejpam-7063	97	29	and	and	CCONJ
ejpam-7063	97	30	control	control	NOUN
ejpam-7063	97	31	functions	function	NOUN
ejpam-7063	97	32	in	in	ADP
ejpam-7063	97	33	fractional	fractional	ADJ
ejpam-7063	97	34	optimal	optimal	ADJ
ejpam-7063	97	35	control	control	NOUN
ejpam-7063	97	36	problems	problem	NOUN
ejpam-7063	97	37	.	.	PUNCT
ejpam-7063	98	1	2.2.3	2.2.3	X
ejpam-7063	98	2	.	.	PUNCT
ejpam-7063	98	3	advantages	advantage	NOUN
ejpam-7063	98	4	for	for	ADP
ejpam-7063	98	5	fractional	fractional	ADJ
ejpam-7063	98	6	optimal	optimal	ADJ
ejpam-7063	98	7	control	control	NOUN
ejpam-7063	98	8	compared	compare	VERB
ejpam-7063	98	9	to	to	ADP
ejpam-7063	98	10	polynomial	polynomial	ADJ
ejpam-7063	98	11	-	-	PUNCT
ejpam-7063	98	12	based	base	VERB
ejpam-7063	98	13	methods	method	NOUN
ejpam-7063	98	14	[	[	X
ejpam-7063	98	15	20–22	20–22	NUM
ejpam-7063	98	16	]	]	PUNCT
ejpam-7063	98	17	or	or	CCONJ
ejpam-7063	98	18	classical	classical	ADJ
ejpam-7063	98	19	wavelets	wavelet	NOUN
ejpam-7063	98	20	,	,	PUNCT
ejpam-7063	98	21	fvfws	fvfws	NOUN
ejpam-7063	98	22	require	require	VERB
ejpam-7063	98	23	fewer	few	ADJ
ejpam-7063	98	24	basis	basis	NOUN
ejpam-7063	98	25	functions	function	NOUN
ejpam-7063	98	26	to	to	PART
ejpam-7063	98	27	achieve	achieve	VERB
ejpam-7063	98	28	comparable	comparable	ADJ
ejpam-7063	98	29	accuracy	accuracy	NOUN
ejpam-7063	98	30	.	.	PUNCT
ejpam-7063	99	1	their	their	PRON
ejpam-7063	99	2	recursive	recursive	ADJ
ejpam-7063	99	3	structure	structure	NOUN
ejpam-7063	99	4	enables	enable	VERB
ejpam-7063	99	5	sparse	sparse	ADJ
ejpam-7063	99	6	and	and	CCONJ
ejpam-7063	99	7	well	well	ADV
ejpam-7063	99	8	-	-	PUNCT
ejpam-7063	99	9	conditioned	condition	VERB
ejpam-7063	99	10	operational	operational	ADJ
ejpam-7063	99	11	matrices	matrix	NOUN
ejpam-7063	99	12	for	for	ADP
ejpam-7063	99	13	fractional	fractional	ADJ
ejpam-7063	99	14	derivatives	derivative	NOUN
ejpam-7063	99	15	,	,	PUNCT
ejpam-7063	99	16	making	make	VERB
ejpam-7063	99	17	them	they	PRON
ejpam-7063	99	18	computationally	computationally	ADV
ejpam-7063	99	19	efficient	efficient	ADJ
ejpam-7063	99	20	for	for	ADP
ejpam-7063	99	21	large	large	ADJ
ejpam-7063	99	22	-	-	PUNCT
ejpam-7063	99	23	scale	scale	NOUN
ejpam-7063	99	24	focps	focp	NOUN
ejpam-7063	99	25	.	.	PUNCT
ejpam-7063	100	1	these	these	DET
ejpam-7063	100	2	properties	property	NOUN
ejpam-7063	100	3	align	align	VERB
ejpam-7063	100	4	with	with	ADP
ejpam-7063	100	5	the	the	DET
ejpam-7063	100	6	requirements	requirement	NOUN
ejpam-7063	100	7	of	of	ADP
ejpam-7063	100	8	two	two	NUM
ejpam-7063	100	9	-	-	PUNCT
ejpam-7063	100	10	dimensional	dimensional	ADJ
ejpam-7063	100	11	problems	problem	NOUN
ejpam-7063	100	12	,	,	PUNCT
ejpam-7063	100	13	where	where	SCONJ
ejpam-7063	100	14	both	both	DET
ejpam-7063	100	15	accuracy	accuracy	NOUN
ejpam-7063	100	16	and	and	CCONJ
ejpam-7063	100	17	efficiency	efficiency	NOUN
ejpam-7063	100	18	are	be	AUX
ejpam-7063	100	19	essential	essential	ADJ
ejpam-7063	100	20	.	.	PUNCT
ejpam-7063	101	1	3	3	X
ejpam-7063	101	2	.	.	X
ejpam-7063	101	3	problem	problem	NOUN
ejpam-7063	101	4	formulation	formulation	NOUN
ejpam-7063	101	5	we	we	PRON
ejpam-7063	101	6	consider	consider	VERB
ejpam-7063	101	7	a	a	DET
ejpam-7063	101	8	two	two	NUM
ejpam-7063	101	9	-	-	PUNCT
ejpam-7063	101	10	dimensional	dimensional	ADJ
ejpam-7063	101	11	fractional	fractional	ADJ
ejpam-7063	101	12	optimal	optimal	ADJ
ejpam-7063	101	13	control	control	NOUN
ejpam-7063	101	14	problem	problem	NOUN
ejpam-7063	101	15	(	(	PUNCT
ejpam-7063	101	16	focp	focp	PROPN
ejpam-7063	101	17	)	)	PUNCT
ejpam-7063	101	18	on	on	ADP
ejpam-7063	101	19	the	the	DET
ejpam-7063	101	20	spatial	spatial	ADJ
ejpam-7063	101	21	domain	domain	NOUN
ejpam-7063	101	22	ω	ω	NOUN
ejpam-7063	101	23	=	=	PUNCT
ejpam-7063	102	1	[	[	X
ejpam-7063	102	2	0	0	NUM
ejpam-7063	102	3	,	,	PUNCT
ejpam-7063	102	4	1]2	1]2	NUM
ejpam-7063	102	5	.	.	PUNCT
ejpam-7063	103	1	the	the	DET
ejpam-7063	103	2	goal	goal	NOUN
ejpam-7063	103	3	is	be	AUX
ejpam-7063	103	4	to	to	PART
ejpam-7063	103	5	determine	determine	VERB
ejpam-7063	103	6	a	a	DET
ejpam-7063	103	7	control	control	NOUN
ejpam-7063	103	8	function	function	NOUN
ejpam-7063	103	9	u(x	u(x	NOUN
ejpam-7063	103	10	,	,	PUNCT
ejpam-7063	103	11	y	y	NOUN
ejpam-7063	103	12	)	)	PUNCT
ejpam-7063	103	13	that	that	PRON
ejpam-7063	103	14	minimizes	minimize	VERB
ejpam-7063	103	15	a	a	DET
ejpam-7063	103	16	quadratic	quadratic	ADJ
ejpam-7063	103	17	cost	cost	NOUN
ejpam-7063	103	18	functional	functional	ADJ
ejpam-7063	103	19	subject	subject	NOUN
ejpam-7063	103	20	to	to	ADP
ejpam-7063	103	21	a	a	DET
ejpam-7063	103	22	nonlinear	nonlinear	ADJ
ejpam-7063	103	23	fractional	fractional	ADJ
ejpam-7063	103	24	partial	partial	ADJ
ejpam-7063	103	25	differential	differential	NOUN
ejpam-7063	103	26	equation	equation	NOUN
ejpam-7063	103	27	(	(	PUNCT
ejpam-7063	103	28	fpde	fpde	NOUN
ejpam-7063	103	29	)	)	PUNCT
ejpam-7063	103	30	constraint	constraint	NOUN
ejpam-7063	103	31	.	.	PUNCT
ejpam-7063	104	1	3.1	3.1	NUM
ejpam-7063	104	2	.	.	PUNCT
ejpam-7063	105	1	cost	cost	NOUN
ejpam-7063	105	2	functional	functional	ADJ
ejpam-7063	105	3	the	the	DET
ejpam-7063	105	4	objective	objective	ADJ
ejpam-7063	105	5	functional	functional	NOUN
ejpam-7063	105	6	is	be	AUX
ejpam-7063	105	7	defined	define	VERB
ejpam-7063	105	8	as	as	ADP
ejpam-7063	105	9	j	j	PROPN
ejpam-7063	105	10	[	[	X
ejpam-7063	105	11	z	z	PROPN
ejpam-7063	105	12	,	,	PUNCT
ejpam-7063	105	13	u	u	NOUN
ejpam-7063	105	14	]	]	X
ejpam-7063	105	15	=	=	SYM
ejpam-7063	105	16	1	1	NUM
ejpam-7063	105	17	2	2	NUM
ejpam-7063	105	18	∫	∫	NOUN
ejpam-7063	105	19	ω	ω	PROPN
ejpam-7063	105	20	(	(	PUNCT
ejpam-7063	105	21	(	(	PUNCT
ejpam-7063	105	22	z(x	z(x	PROPN
ejpam-7063	105	23	,	,	PUNCT
ejpam-7063	105	24	y)−	y)−	PROPN
ejpam-7063	105	25	zd(x	zd(x	NUM
ejpam-7063	105	26	,	,	PUNCT
ejpam-7063	105	27	y))2	y))2	PROPN
ejpam-7063	105	28	+	+	X
ejpam-7063	105	29	λu(x	λu(x	NOUN
ejpam-7063	105	30	,	,	PUNCT
ejpam-7063	105	31	y)2	y)2	NOUN
ejpam-7063	105	32	)	)	PUNCT
ejpam-7063	105	33	dxdy	dxdy	PROPN
ejpam-7063	105	34	,	,	PUNCT
ejpam-7063	105	35	(	(	PUNCT
ejpam-7063	105	36	3.1	3.1	NUM
ejpam-7063	105	37	)	)	PUNCT
ejpam-7063	105	38	where	where	SCONJ
ejpam-7063	105	39	z(x	z(x	NUM
ejpam-7063	105	40	,	,	PUNCT
ejpam-7063	105	41	y	y	NOUN
ejpam-7063	105	42	)	)	PUNCT
ejpam-7063	105	43	is	be	AUX
ejpam-7063	105	44	the	the	DET
ejpam-7063	105	45	state	state	NOUN
ejpam-7063	105	46	variable	variable	NOUN
ejpam-7063	105	47	,	,	PUNCT
ejpam-7063	105	48	zd(x	zd(x	NUM
ejpam-7063	105	49	,	,	PUNCT
ejpam-7063	105	50	y	y	PROPN
ejpam-7063	105	51	)	)	PUNCT
ejpam-7063	105	52	is	be	AUX
ejpam-7063	105	53	the	the	DET
ejpam-7063	105	54	desired	desire	VERB
ejpam-7063	105	55	state	state	NOUN
ejpam-7063	105	56	,	,	PUNCT
ejpam-7063	105	57	u(x	u(x	PROPN
ejpam-7063	105	58	,	,	PUNCT
ejpam-7063	105	59	y	y	NOUN
ejpam-7063	105	60	)	)	PUNCT
ejpam-7063	105	61	is	be	AUX
ejpam-7063	105	62	the	the	DET
ejpam-7063	105	63	control	control	NOUN
ejpam-7063	105	64	,	,	PUNCT
ejpam-7063	105	65	and	and	CCONJ
ejpam-7063	105	66	λ	λ	X
ejpam-7063	105	67	>	>	X
ejpam-7063	105	68	0	0	PUNCT
ejpam-7063	105	69	is	be	AUX
ejpam-7063	105	70	a	a	DET
ejpam-7063	105	71	regularization	regularization	NOUN
ejpam-7063	105	72	parameter	parameter	NOUN
ejpam-7063	105	73	.	.	PUNCT
ejpam-7063	106	1	this	this	DET
ejpam-7063	106	2	quadratic	quadratic	ADJ
ejpam-7063	106	3	form	form	NOUN
ejpam-7063	106	4	is	be	AUX
ejpam-7063	106	5	standard	standard	ADJ
ejpam-7063	106	6	in	in	ADP
ejpam-7063	106	7	pde	pde	NOUN
ejpam-7063	106	8	-	-	PUNCT
ejpam-7063	106	9	constrained	constrain	VERB
ejpam-7063	106	10	optimization	optimization	NOUN
ejpam-7063	106	11	[	[	X
ejpam-7063	106	12	39	39	NUM
ejpam-7063	106	13	,	,	PUNCT
ejpam-7063	106	14	40	40	NUM
ejpam-7063	106	15	]	]	PUNCT
ejpam-7063	106	16	and	and	CCONJ
ejpam-7063	106	17	ensures	ensure	VERB
ejpam-7063	106	18	convexity	convexity	NOUN
ejpam-7063	106	19	with	with	ADP
ejpam-7063	106	20	respect	respect	NOUN
ejpam-7063	106	21	to	to	ADP
ejpam-7063	106	22	the	the	DET
ejpam-7063	106	23	control	control	NOUN
ejpam-7063	106	24	.	.	PUNCT
ejpam-7063	107	1	3.2	3.2	NUM
ejpam-7063	107	2	.	.	PUNCT
ejpam-7063	108	1	state	state	NOUN
ejpam-7063	108	2	equation	equation	NOUN
ejpam-7063	108	3	the	the	DET
ejpam-7063	108	4	dynamics	dynamic	NOUN
ejpam-7063	108	5	of	of	ADP
ejpam-7063	108	6	the	the	DET
ejpam-7063	108	7	system	system	NOUN
ejpam-7063	108	8	are	be	AUX
ejpam-7063	108	9	governed	govern	VERB
ejpam-7063	108	10	by	by	ADP
ejpam-7063	108	11	a	a	DET
ejpam-7063	108	12	two	two	NUM
ejpam-7063	108	13	-	-	PUNCT
ejpam-7063	108	14	dimensional	dimensional	ADJ
ejpam-7063	108	15	caputo	caputo	PROPN
ejpam-7063	108	16	fractional	fractional	PROPN
ejpam-7063	108	17	pde	pde	NOUN
ejpam-7063	108	18	:	:	PUNCT
ejpam-7063	108	19	dα	dα	VERB
ejpam-7063	109	1	xd	xd	INTJ
ejpam-7063	109	2	β	β	X
ejpam-7063	109	3	y	y	PROPN
ejpam-7063	109	4	z(x	z(x	PROPN
ejpam-7063	109	5	,	,	PUNCT
ejpam-7063	109	6	y	y	PROPN
ejpam-7063	109	7	)	)	PUNCT
ejpam-7063	109	8	+	+	NOUN
ejpam-7063	109	9	n	n	PRON
ejpam-7063	109	10	(	(	PUNCT
ejpam-7063	109	11	z(x	z(x	PROPN
ejpam-7063	109	12	,	,	PUNCT
ejpam-7063	109	13	y	y	NOUN
ejpam-7063	109	14	)	)	PUNCT
ejpam-7063	109	15	)	)	PUNCT
ejpam-7063	110	1	=	=	SYM
ejpam-7063	110	2	f(x	f(x	PROPN
ejpam-7063	110	3	,	,	PUNCT
ejpam-7063	110	4	y	y	NOUN
ejpam-7063	110	5	)	)	PUNCT
ejpam-7063	110	6	+	+	CCONJ
ejpam-7063	110	7	u(x	u(x	PROPN
ejpam-7063	110	8	,	,	PUNCT
ejpam-7063	110	9	y	y	NOUN
ejpam-7063	110	10	)	)	PUNCT
ejpam-7063	110	11	,	,	PUNCT
ejpam-7063	110	12	(	(	PUNCT
ejpam-7063	110	13	x	x	X
ejpam-7063	110	14	,	,	PUNCT
ejpam-7063	110	15	y	y	NOUN
ejpam-7063	110	16	)	)	PUNCT
ejpam-7063	110	17	∈	∈	PROPN
ejpam-7063	110	18	ω	ω	PROPN
ejpam-7063	110	19	,	,	PUNCT
ejpam-7063	110	20	(	(	PUNCT
ejpam-7063	110	21	3.2	3.2	NUM
ejpam-7063	110	22	)	)	PUNCT
ejpam-7063	110	23	subject	subject	NOUN
ejpam-7063	110	24	to	to	ADP
ejpam-7063	110	25	homogeneous	homogeneous	ADJ
ejpam-7063	110	26	boundary	boundary	ADJ
ejpam-7063	110	27	conditions	condition	NOUN
ejpam-7063	110	28	z(x	z(x	NUM
ejpam-7063	110	29	,	,	PUNCT
ejpam-7063	110	30	0	0	NUM
ejpam-7063	110	31	)	)	PUNCT
ejpam-7063	110	32	=	=	PUNCT
ejpam-7063	110	33	z(0	z(0	PROPN
ejpam-7063	110	34	,	,	PUNCT
ejpam-7063	110	35	y	y	NOUN
ejpam-7063	110	36	)	)	PUNCT
ejpam-7063	110	37	=	=	SYM
ejpam-7063	110	38	z(x	z(x	NUM
ejpam-7063	110	39	,	,	PUNCT
ejpam-7063	110	40	1	1	NUM
ejpam-7063	110	41	)	)	PUNCT
ejpam-7063	110	42	=	=	SYM
ejpam-7063	110	43	z(1	z(1	PROPN
ejpam-7063	110	44	,	,	PUNCT
ejpam-7063	110	45	y	y	NOUN
ejpam-7063	110	46	)	)	PUNCT
ejpam-7063	110	47	=	=	SYM
ejpam-7063	110	48	0	0	NUM
ejpam-7063	110	49	,	,	PUNCT
ejpam-7063	110	50	(	(	PUNCT
ejpam-7063	110	51	3.3	3.3	NUM
ejpam-7063	110	52	)	)	PUNCT
ejpam-7063	110	53	where	where	SCONJ
ejpam-7063	110	54	dα	dα	ADJ
ejpam-7063	110	55	x	x	X
ejpam-7063	110	56	and	and	CCONJ
ejpam-7063	110	57	dβ	dβ	PROPN
ejpam-7063	110	58	y	y	PROPN
ejpam-7063	110	59	denote	denote	VERB
ejpam-7063	110	60	caputo	caputo	PROPN
ejpam-7063	110	61	fractional	fractional	ADJ
ejpam-7063	110	62	derivatives	derivative	NOUN
ejpam-7063	110	63	of	of	ADP
ejpam-7063	110	64	orders	order	NOUN
ejpam-7063	110	65	0	0	NUM
ejpam-7063	110	66	<	<	X
ejpam-7063	110	67	α	α	X
ejpam-7063	110	68	,	,	PUNCT
ejpam-7063	110	69	β	β	X
ejpam-7063	110	70	≤	≤	NUM
ejpam-7063	110	71	1	1	NUM
ejpam-7063	110	72	,	,	PUNCT
ejpam-7063	110	73	n	n	PRON
ejpam-7063	110	74	is	be	AUX
ejpam-7063	110	75	a	a	DET
ejpam-7063	110	76	nonlinear	nonlinear	ADJ
ejpam-7063	110	77	operator	operator	NOUN
ejpam-7063	110	78	(	(	PUNCT
ejpam-7063	110	79	e.g.	e.g.	ADV
ejpam-7063	110	80	,	,	PUNCT
ejpam-7063	110	81	µ	µ	X
ejpam-7063	110	82	sin(z	sin(z	PROPN
ejpam-7063	110	83	)	)	PUNCT
ejpam-7063	110	84	)	)	PUNCT
ejpam-7063	110	85	,	,	PUNCT
ejpam-7063	110	86	and	and	CCONJ
ejpam-7063	110	87	f(x	f(x	PROPN
ejpam-7063	110	88	,	,	PUNCT
ejpam-7063	110	89	y	y	PROPN
ejpam-7063	110	90	)	)	PUNCT
ejpam-7063	110	91	is	be	AUX
ejpam-7063	110	92	a	a	DET
ejpam-7063	110	93	given	give	VERB
ejpam-7063	110	94	source	source	NOUN
ejpam-7063	110	95	term	term	NOUN
ejpam-7063	110	96	.	.	PUNCT
ejpam-7063	111	1	3.3	3.3	NUM
ejpam-7063	111	2	.	.	PUNCT
ejpam-7063	111	3	admissible	admissible	ADJ
ejpam-7063	111	4	control	control	NOUN
ejpam-7063	111	5	set	set	VERB
ejpam-7063	111	6	the	the	DET
ejpam-7063	111	7	control	control	NOUN
ejpam-7063	111	8	belongs	belong	VERB
ejpam-7063	111	9	to	to	ADP
ejpam-7063	111	10	a	a	DET
ejpam-7063	111	11	closed	closed	ADJ
ejpam-7063	111	12	convex	convex	NOUN
ejpam-7063	111	13	admissible	admissible	ADJ
ejpam-7063	111	14	set	set	NOUN
ejpam-7063	111	15	uad	uad	PROPN
ejpam-7063	111	16	=	=	SYM
ejpam-7063	111	17	{	{	PUNCT
ejpam-7063	111	18	u	u	NOUN
ejpam-7063	111	19	∈	∈	PROPN
ejpam-7063	111	20	l2(ω	l2(ω	PROPN
ejpam-7063	111	21	)	)	PUNCT
ejpam-7063	111	22	:	:	PUNCT
ejpam-7063	111	23	umin	umin	ADJ
ejpam-7063	111	24	≤	≤	PUNCT
ejpam-7063	111	25	u(x	u(x	NOUN
ejpam-7063	111	26	,	,	PUNCT
ejpam-7063	111	27	y	y	NOUN
ejpam-7063	111	28	)	)	PUNCT
ejpam-7063	111	29	≤	≤	NOUN
ejpam-7063	111	30	umax	umax	PROPN
ejpam-7063	111	31	,	,	PUNCT
ejpam-7063	111	32	a.e	a.e	PROPN
ejpam-7063	111	33	.	.	PROPN
ejpam-7063	111	34	in	in	ADP
ejpam-7063	111	35	ω	ω	NUM
ejpam-7063	111	36	}	}	PUNCT
ejpam-7063	111	37	,	,	PUNCT
ejpam-7063	111	38	(	(	PUNCT
ejpam-7063	111	39	3.4	3.4	NUM
ejpam-7063	111	40	)	)	PUNCT
ejpam-7063	111	41	which	which	PRON
ejpam-7063	111	42	accommodates	accommodate	VERB
ejpam-7063	111	43	both	both	PRON
ejpam-7063	111	44	bounded	bound	VERB
ejpam-7063	111	45	and	and	CCONJ
ejpam-7063	111	46	unconstrained	unconstrained	ADJ
ejpam-7063	111	47	controls	control	NOUN
ejpam-7063	111	48	[	[	X
ejpam-7063	111	49	11	11	NUM
ejpam-7063	111	50	,	,	PUNCT
ejpam-7063	111	51	12	12	NUM
ejpam-7063	111	52	,	,	PUNCT
ejpam-7063	111	53	41	41	NUM
ejpam-7063	111	54	]	]	PUNCT
ejpam-7063	111	55	.	.	PUNCT
ejpam-7063	112	1	g.	g.	PROPN
ejpam-7063	112	2	m.	m.	PROPN
ejpam-7063	112	3	bahaa	bahaa	PROPN
ejpam-7063	112	4	,	,	PUNCT
ejpam-7063	112	5	a.	a.	NOUN
ejpam-7063	112	6	h.	h.	PROPN
ejpam-7063	112	7	qamlo	qamlo	PROPN
ejpam-7063	112	8	/	/	SYM
ejpam-7063	112	9	eur	eur	PROPN
ejpam-7063	112	10	.	.	PUNCT
ejpam-7063	113	1	j.	j.	PROPN
ejpam-7063	113	2	pure	pure	PROPN
ejpam-7063	113	3	appl	appl	PROPN
ejpam-7063	113	4	.	.	PROPN
ejpam-7063	113	5	math	math	PROPN
ejpam-7063	113	6	,	,	PUNCT
ejpam-7063	113	7	18	18	NUM
ejpam-7063	113	8	(	(	PUNCT
ejpam-7063	113	9	4	4	NUM
ejpam-7063	113	10	)	)	PUNCT
ejpam-7063	113	11	(	(	PUNCT
ejpam-7063	113	12	2025	2025	NUM
ejpam-7063	113	13	)	)	PUNCT
ejpam-7063	113	14	,	,	PUNCT
ejpam-7063	113	15	7063	7063	NUM
ejpam-7063	113	16	6	6	NUM
ejpam-7063	113	17	of	of	ADP
ejpam-7063	113	18	29	29	NUM
ejpam-7063	113	19	3.4	3.4	NUM
ejpam-7063	113	20	.	.	PUNCT
ejpam-7063	114	1	lagrangian	lagrangian	ADJ
ejpam-7063	114	2	functional	functional	ADJ
ejpam-7063	114	3	to	to	PART
ejpam-7063	114	4	derive	derive	VERB
ejpam-7063	114	5	the	the	DET
ejpam-7063	114	6	necessary	necessary	ADJ
ejpam-7063	114	7	optimality	optimality	NOUN
ejpam-7063	114	8	conditions	condition	NOUN
ejpam-7063	114	9	,	,	PUNCT
ejpam-7063	114	10	we	we	PRON
ejpam-7063	114	11	introduce	introduce	VERB
ejpam-7063	114	12	the	the	DET
ejpam-7063	114	13	adjoint	adjoint	PROPN
ejpam-7063	114	14	variable	variable	NOUN
ejpam-7063	114	15	p(x	p(x	PROPN
ejpam-7063	114	16	,	,	PUNCT
ejpam-7063	114	17	y	y	PROPN
ejpam-7063	114	18	)	)	PUNCT
ejpam-7063	114	19	and	and	CCONJ
ejpam-7063	114	20	define	define	VERB
ejpam-7063	114	21	the	the	DET
ejpam-7063	114	22	lagrangian	lagrangian	ADJ
ejpam-7063	114	23	functional	functional	ADJ
ejpam-7063	114	24	l(z	l(z	PROPN
ejpam-7063	114	25	,	,	PUNCT
ejpam-7063	114	26	u	u	NOUN
ejpam-7063	114	27	,	,	PUNCT
ejpam-7063	114	28	p	p	NOUN
ejpam-7063	114	29	)	)	PUNCT
ejpam-7063	115	1	=	=	PUNCT
ejpam-7063	115	2	j	j	PROPN
ejpam-7063	116	1	[	[	X
ejpam-7063	116	2	z	z	NOUN
ejpam-7063	116	3	,	,	PUNCT
ejpam-7063	116	4	u]+	u]+	ADJ
ejpam-7063	116	5	∫	∫	PROPN
ejpam-7063	116	6	ω	ω	NUM
ejpam-7063	116	7	p(x	p(x	PROPN
ejpam-7063	116	8	,	,	PUNCT
ejpam-7063	116	9	y	y	PROPN
ejpam-7063	116	10	)	)	PUNCT
ejpam-7063	116	11	(	(	PUNCT
ejpam-7063	116	12	dα	dα	ADV
ejpam-7063	116	13	xd	xd	INTJ
ejpam-7063	116	14	β	β	X
ejpam-7063	116	15	y	y	PROPN
ejpam-7063	116	16	z(x	z(x	PROPN
ejpam-7063	116	17	,	,	PUNCT
ejpam-7063	116	18	y)+n	y)+n	PROPN
ejpam-7063	116	19	(	(	PUNCT
ejpam-7063	116	20	z(x	z(x	PROPN
ejpam-7063	116	21	,	,	PUNCT
ejpam-7063	116	22	y))−f(x	y))−f(x	PROPN
ejpam-7063	116	23	,	,	PUNCT
ejpam-7063	116	24	y)−u(x	y)−u(x	PROPN
ejpam-7063	116	25	,	,	PUNCT
ejpam-7063	116	26	y	y	NOUN
ejpam-7063	116	27	)	)	PUNCT
ejpam-7063	116	28	)	)	PUNCT
ejpam-7063	116	29	dxdy	dxdy	PROPN
ejpam-7063	116	30	.	.	PUNCT
ejpam-7063	117	1	(	(	PUNCT
ejpam-7063	117	2	3.5	3.5	NUM
ejpam-7063	117	3	)	)	PUNCT
ejpam-7063	117	4	3.5	3.5	NUM
ejpam-7063	117	5	.	.	PUNCT
ejpam-7063	118	1	derivation	derivation	NOUN
ejpam-7063	118	2	of	of	ADP
ejpam-7063	118	3	the	the	DET
ejpam-7063	118	4	optimality	optimality	NOUN
ejpam-7063	118	5	system	system	NOUN
ejpam-7063	118	6	by	by	ADP
ejpam-7063	118	7	taking	take	VERB
ejpam-7063	118	8	variations	variation	NOUN
ejpam-7063	118	9	of	of	ADP
ejpam-7063	118	10	l	l	NOUN
ejpam-7063	118	11	with	with	ADP
ejpam-7063	118	12	respect	respect	NOUN
ejpam-7063	118	13	to	to	ADP
ejpam-7063	118	14	z	z	PROPN
ejpam-7063	118	15	,	,	PUNCT
ejpam-7063	118	16	u	u	NOUN
ejpam-7063	118	17	,	,	PUNCT
ejpam-7063	118	18	and	and	CCONJ
ejpam-7063	118	19	p	p	X
ejpam-7063	118	20	,	,	PUNCT
ejpam-7063	118	21	we	we	PRON
ejpam-7063	118	22	obtain	obtain	VERB
ejpam-7063	118	23	the	the	DET
ejpam-7063	118	24	optimality	optimality	NOUN
ejpam-7063	118	25	system	system	NOUN
ejpam-7063	118	26	:	:	PUNCT
ejpam-7063	118	27	1	1	X
ejpam-7063	118	28	.	.	PUNCT
ejpam-7063	118	29	state	state	NOUN
ejpam-7063	118	30	equation	equation	NOUN
ejpam-7063	118	31	.	.	PUNCT
ejpam-7063	119	1	variation	variation	NOUN
ejpam-7063	119	2	with	with	ADP
ejpam-7063	119	3	respect	respect	NOUN
ejpam-7063	119	4	to	to	ADP
ejpam-7063	119	5	p	p	NOUN
ejpam-7063	119	6	recovers	recover	NOUN
ejpam-7063	119	7	the	the	DET
ejpam-7063	119	8	state	state	NOUN
ejpam-7063	119	9	dynamics	dynamic	NOUN
ejpam-7063	119	10	:	:	PUNCT
ejpam-7063	119	11	dα	dα	INTJ
ejpam-7063	119	12	xd	xd	INTJ
ejpam-7063	119	13	β	β	X
ejpam-7063	119	14	y	y	PROPN
ejpam-7063	119	15	z(x	z(x	PROPN
ejpam-7063	119	16	,	,	PUNCT
ejpam-7063	119	17	y	y	PROPN
ejpam-7063	119	18	)	)	PUNCT
ejpam-7063	120	1	+	+	NOUN
ejpam-7063	120	2	n	n	PRON
ejpam-7063	120	3	(	(	PUNCT
ejpam-7063	120	4	z(x	z(x	PROPN
ejpam-7063	120	5	,	,	PUNCT
ejpam-7063	120	6	y	y	NOUN
ejpam-7063	120	7	)	)	PUNCT
ejpam-7063	120	8	)	)	PUNCT
ejpam-7063	121	1	=	=	SYM
ejpam-7063	121	2	f(x	f(x	PROPN
ejpam-7063	121	3	,	,	PUNCT
ejpam-7063	121	4	y	y	NOUN
ejpam-7063	121	5	)	)	PUNCT
ejpam-7063	121	6	+	+	CCONJ
ejpam-7063	121	7	u(x	u(x	PROPN
ejpam-7063	121	8	,	,	PUNCT
ejpam-7063	121	9	y	y	NOUN
ejpam-7063	121	10	)	)	PUNCT
ejpam-7063	121	11	,	,	PUNCT
ejpam-7063	121	12	(	(	PUNCT
ejpam-7063	121	13	x	x	X
ejpam-7063	121	14	,	,	PUNCT
ejpam-7063	121	15	y	y	NOUN
ejpam-7063	121	16	)	)	PUNCT
ejpam-7063	121	17	∈	∈	PROPN
ejpam-7063	121	18	ω	ω	PROPN
ejpam-7063	121	19	.	.	PUNCT
ejpam-7063	121	20	(	(	PUNCT
ejpam-7063	121	21	3.6	3.6	NUM
ejpam-7063	121	22	)	)	SYM
ejpam-7063	121	23	2	2	NUM
ejpam-7063	121	24	.	.	PUNCT
ejpam-7063	121	25	adjoint	adjoint	NOUN
ejpam-7063	121	26	equation	equation	NOUN
ejpam-7063	121	27	.	.	PUNCT
ejpam-7063	122	1	variation	variation	NOUN
ejpam-7063	122	2	with	with	ADP
ejpam-7063	122	3	respect	respect	NOUN
ejpam-7063	122	4	to	to	ADP
ejpam-7063	122	5	z	z	NOUN
ejpam-7063	122	6	yields	yield	VERB
ejpam-7063	122	7	the	the	DET
ejpam-7063	122	8	adjoint	adjoint	PROPN
ejpam-7063	122	9	equation	equation	NOUN
ejpam-7063	122	10	:	:	PUNCT
ejpam-7063	122	11	dα	dα	VERB
ejpam-7063	122	12	xd	xd	INTJ
ejpam-7063	122	13	β	β	PROPN
ejpam-7063	122	14	y	y	PROPN
ejpam-7063	122	15	p(x	p(x	PROPN
ejpam-7063	122	16	,	,	PUNCT
ejpam-7063	122	17	y	y	PROPN
ejpam-7063	122	18	)	)	PUNCT
ejpam-7063	123	1	+	+	CCONJ
ejpam-7063	123	2	(	(	PUNCT
ejpam-7063	123	3	z(x	z(x	NUM
ejpam-7063	123	4	,	,	PUNCT
ejpam-7063	123	5	y)−	y)−	PROPN
ejpam-7063	123	6	zd(x	zd(x	NUM
ejpam-7063	123	7	,	,	PUNCT
ejpam-7063	123	8	y	y	NOUN
ejpam-7063	123	9	)	)	PUNCT
ejpam-7063	123	10	)	)	PUNCT
ejpam-7063	124	1	+	+	ADP
ejpam-7063	124	2	n	n	PRON
ejpam-7063	124	3	′(z(x	′(z(x	ADJ
ejpam-7063	124	4	,	,	PUNCT
ejpam-7063	124	5	y	y	NOUN
ejpam-7063	124	6	)	)	PUNCT
ejpam-7063	124	7	)	)	PUNCT
ejpam-7063	124	8	p(x	p(x	PROPN
ejpam-7063	124	9	,	,	PUNCT
ejpam-7063	124	10	y	y	NOUN
ejpam-7063	124	11	)	)	PUNCT
ejpam-7063	124	12	=	=	SYM
ejpam-7063	124	13	0	0	NUM
ejpam-7063	124	14	,	,	PUNCT
ejpam-7063	124	15	(	(	PUNCT
ejpam-7063	124	16	3.7	3.7	NUM
ejpam-7063	124	17	)	)	PUNCT
ejpam-7063	124	18	with	with	ADP
ejpam-7063	124	19	homogeneous	homogeneous	ADJ
ejpam-7063	124	20	terminal	terminal	ADJ
ejpam-7063	124	21	-	-	PUNCT
ejpam-7063	124	22	type	type	NOUN
ejpam-7063	124	23	boundary	boundary	ADJ
ejpam-7063	124	24	conditions	condition	NOUN
ejpam-7063	124	25	p(x	p(x	PROPN
ejpam-7063	124	26	,	,	PUNCT
ejpam-7063	124	27	0	0	NUM
ejpam-7063	124	28	)	)	PUNCT
ejpam-7063	124	29	=	=	SYM
ejpam-7063	125	1	p(0	p(0	PROPN
ejpam-7063	125	2	,	,	PUNCT
ejpam-7063	125	3	y	y	NOUN
ejpam-7063	125	4	)	)	PUNCT
ejpam-7063	125	5	=	=	SYM
ejpam-7063	125	6	p(x	p(x	NOUN
ejpam-7063	125	7	,	,	PUNCT
ejpam-7063	125	8	1	1	NUM
ejpam-7063	125	9	)	)	PUNCT
ejpam-7063	125	10	=	=	SYM
ejpam-7063	126	1	p(1	p(1	PROPN
ejpam-7063	126	2	,	,	PUNCT
ejpam-7063	126	3	y	y	NOUN
ejpam-7063	126	4	)	)	PUNCT
ejpam-7063	126	5	=	=	SYM
ejpam-7063	126	6	0	0	X
ejpam-7063	126	7	.	.	PUNCT
ejpam-7063	126	8	(	(	PUNCT
ejpam-7063	126	9	3.8	3.8	NUM
ejpam-7063	126	10	)	)	PUNCT
ejpam-7063	126	11	3	3	NUM
ejpam-7063	126	12	.	.	X
ejpam-7063	126	13	optimality	optimality	NOUN
ejpam-7063	126	14	condition	condition	NOUN
ejpam-7063	126	15	.	.	PUNCT
ejpam-7063	127	1	variation	variation	NOUN
ejpam-7063	127	2	with	with	ADP
ejpam-7063	127	3	respect	respect	NOUN
ejpam-7063	127	4	to	to	ADP
ejpam-7063	127	5	u	u	PRON
ejpam-7063	127	6	gives	give	VERB
ejpam-7063	127	7	λu(x	λu(x	NOUN
ejpam-7063	127	8	,	,	PUNCT
ejpam-7063	127	9	y	y	NOUN
ejpam-7063	127	10	)	)	PUNCT
ejpam-7063	128	1	+	+	CCONJ
ejpam-7063	128	2	p(x	p(x	PROPN
ejpam-7063	128	3	,	,	PUNCT
ejpam-7063	128	4	y	y	NOUN
ejpam-7063	128	5	)	)	PUNCT
ejpam-7063	128	6	=	=	SYM
ejpam-7063	128	7	0	0	NUM
ejpam-7063	128	8	,	,	PUNCT
ejpam-7063	128	9	(	(	PUNCT
ejpam-7063	128	10	3.9	3.9	NUM
ejpam-7063	128	11	)	)	PUNCT
ejpam-7063	128	12	so	so	SCONJ
ejpam-7063	128	13	that	that	SCONJ
ejpam-7063	128	14	the	the	DET
ejpam-7063	128	15	control	control	NOUN
ejpam-7063	128	16	is	be	AUX
ejpam-7063	128	17	expressed	express	VERB
ejpam-7063	128	18	explicitly	explicitly	ADV
ejpam-7063	128	19	in	in	ADP
ejpam-7063	128	20	terms	term	NOUN
ejpam-7063	128	21	of	of	ADP
ejpam-7063	128	22	the	the	DET
ejpam-7063	128	23	adjoint	adjoint	NOUN
ejpam-7063	128	24	:	:	PUNCT
ejpam-7063	128	25	u(x	u(x	PROPN
ejpam-7063	128	26	,	,	PUNCT
ejpam-7063	128	27	y	y	NOUN
ejpam-7063	128	28	)	)	PUNCT
ejpam-7063	128	29	=	=	SYM
ejpam-7063	129	1	−	−	PROPN
ejpam-7063	129	2	1	1	NUM
ejpam-7063	129	3	λ	λ	PROPN
ejpam-7063	129	4	p(x	p(x	PROPN
ejpam-7063	129	5	,	,	PUNCT
ejpam-7063	129	6	y	y	NOUN
ejpam-7063	129	7	)	)	PUNCT
ejpam-7063	129	8	.	.	PUNCT
ejpam-7063	130	1	(	(	PUNCT
ejpam-7063	130	2	3.10	3.10	NUM
ejpam-7063	130	3	)	)	PUNCT
ejpam-7063	130	4	3.6	3.6	NUM
ejpam-7063	130	5	.	.	PUNCT
ejpam-7063	131	1	summary	summary	NOUN
ejpam-7063	131	2	of	of	ADP
ejpam-7063	131	3	the	the	DET
ejpam-7063	131	4	optimality	optimality	NOUN
ejpam-7063	131	5	system	system	NOUN
ejpam-7063	131	6	the	the	DET
ejpam-7063	131	7	focp	focp	PROPN
ejpam-7063	131	8	is	be	AUX
ejpam-7063	131	9	equivalent	equivalent	ADJ
ejpam-7063	131	10	to	to	ADP
ejpam-7063	131	11	solving	solve	VERB
ejpam-7063	131	12	the	the	DET
ejpam-7063	131	13	coupled	couple	VERB
ejpam-7063	131	14	system	system	NOUN
ejpam-7063	131	15	:	:	PUNCT
ejpam-7063	131	16	(	(	PUNCT
ejpam-7063	131	17	state	state	NOUN
ejpam-7063	131	18	)	)	PUNCT
ejpam-7063	131	19	dα	dα	VERB
ejpam-7063	132	1	xd	xd	INTJ
ejpam-7063	132	2	β	β	X
ejpam-7063	132	3	y	y	PROPN
ejpam-7063	132	4	z(x	z(x	PROPN
ejpam-7063	132	5	,	,	PUNCT
ejpam-7063	132	6	y	y	PROPN
ejpam-7063	132	7	)	)	PUNCT
ejpam-7063	132	8	+	+	NOUN
ejpam-7063	132	9	n	n	PRON
ejpam-7063	132	10	(	(	PUNCT
ejpam-7063	132	11	z(x	z(x	PROPN
ejpam-7063	132	12	,	,	PUNCT
ejpam-7063	132	13	y	y	NOUN
ejpam-7063	132	14	)	)	PUNCT
ejpam-7063	132	15	)	)	PUNCT
ejpam-7063	133	1	=	=	SYM
ejpam-7063	133	2	f(x	f(x	PROPN
ejpam-7063	133	3	,	,	PUNCT
ejpam-7063	133	4	y	y	NOUN
ejpam-7063	133	5	)	)	PUNCT
ejpam-7063	133	6	+	+	CCONJ
ejpam-7063	133	7	u(x	u(x	PROPN
ejpam-7063	133	8	,	,	PUNCT
ejpam-7063	133	9	y	y	NOUN
ejpam-7063	133	10	)	)	PUNCT
ejpam-7063	133	11	,	,	PUNCT
ejpam-7063	133	12	(	(	PUNCT
ejpam-7063	133	13	3.11	3.11	NUM
ejpam-7063	133	14	)	)	PUNCT
ejpam-7063	133	15	(	(	PUNCT
ejpam-7063	133	16	adjoint	adjoint	NOUN
ejpam-7063	133	17	)	)	PUNCT
ejpam-7063	133	18	dα	dα	VERB
ejpam-7063	134	1	xd	xd	INTJ
ejpam-7063	134	2	β	β	PROPN
ejpam-7063	134	3	y	y	PROPN
ejpam-7063	134	4	p(x	p(x	PROPN
ejpam-7063	134	5	,	,	PUNCT
ejpam-7063	134	6	y	y	PROPN
ejpam-7063	134	7	)	)	PUNCT
ejpam-7063	135	1	+	+	CCONJ
ejpam-7063	135	2	(	(	PUNCT
ejpam-7063	135	3	z(x	z(x	NUM
ejpam-7063	135	4	,	,	PUNCT
ejpam-7063	135	5	y)−	y)−	PROPN
ejpam-7063	135	6	zd(x	zd(x	NUM
ejpam-7063	135	7	,	,	PUNCT
ejpam-7063	135	8	y	y	NOUN
ejpam-7063	135	9	)	)	PUNCT
ejpam-7063	135	10	)	)	PUNCT
ejpam-7063	136	1	+	+	ADP
ejpam-7063	136	2	n	n	PRON
ejpam-7063	136	3	′(z(x	′(z(x	ADJ
ejpam-7063	136	4	,	,	PUNCT
ejpam-7063	136	5	y))p(x	y))p(x	PROPN
ejpam-7063	136	6	,	,	PUNCT
ejpam-7063	136	7	y	y	NOUN
ejpam-7063	136	8	)	)	PUNCT
ejpam-7063	136	9	=	=	SYM
ejpam-7063	136	10	0	0	NUM
ejpam-7063	136	11	,	,	PUNCT
ejpam-7063	136	12	(	(	PUNCT
ejpam-7063	136	13	3.12	3.12	NUM
ejpam-7063	136	14	)	)	PUNCT
ejpam-7063	136	15	(	(	PUNCT
ejpam-7063	136	16	optimality	optimality	NOUN
ejpam-7063	136	17	)	)	PUNCT
ejpam-7063	136	18	u(x	u(x	NOUN
ejpam-7063	136	19	,	,	PUNCT
ejpam-7063	136	20	y	y	NOUN
ejpam-7063	136	21	)	)	PUNCT
ejpam-7063	136	22	=	=	SYM
ejpam-7063	136	23	−	−	PROPN
ejpam-7063	136	24	1	1	NUM
ejpam-7063	136	25	λ	λ	PROPN
ejpam-7063	136	26	p(x	p(x	PROPN
ejpam-7063	136	27	,	,	PUNCT
ejpam-7063	136	28	y	y	PROPN
ejpam-7063	136	29	)	)	PUNCT
ejpam-7063	136	30	,	,	PUNCT
ejpam-7063	136	31	(	(	PUNCT
ejpam-7063	136	32	3.13	3.13	NUM
ejpam-7063	136	33	)	)	PUNCT
ejpam-7063	136	34	(	(	PUNCT
ejpam-7063	136	35	boundary	boundary	NOUN
ejpam-7063	136	36	)	)	PUNCT
ejpam-7063	136	37	z(x	z(x	PROPN
ejpam-7063	136	38	,	,	PUNCT
ejpam-7063	136	39	0	0	NUM
ejpam-7063	136	40	)	)	PUNCT
ejpam-7063	136	41	=	=	PUNCT
ejpam-7063	137	1	z(0	z(0	PROPN
ejpam-7063	137	2	,	,	PUNCT
ejpam-7063	137	3	y	y	NOUN
ejpam-7063	137	4	)	)	PUNCT
ejpam-7063	137	5	=	=	SYM
ejpam-7063	137	6	z(x	z(x	NUM
ejpam-7063	137	7	,	,	PUNCT
ejpam-7063	137	8	1	1	NUM
ejpam-7063	137	9	)	)	PUNCT
ejpam-7063	137	10	=	=	SYM
ejpam-7063	137	11	z(1	z(1	PROPN
ejpam-7063	137	12	,	,	PUNCT
ejpam-7063	137	13	y	y	NOUN
ejpam-7063	137	14	)	)	PUNCT
ejpam-7063	137	15	=	=	SYM
ejpam-7063	137	16	0	0	NUM
ejpam-7063	137	17	,	,	PUNCT
ejpam-7063	137	18	p(x	p(x	NOUN
ejpam-7063	137	19	,	,	PUNCT
ejpam-7063	137	20	0	0	NUM
ejpam-7063	137	21	)	)	PUNCT
ejpam-7063	137	22	=	=	SYM
ejpam-7063	138	1	p(0	p(0	PROPN
ejpam-7063	138	2	,	,	PUNCT
ejpam-7063	138	3	y	y	NOUN
ejpam-7063	138	4	)	)	PUNCT
ejpam-7063	138	5	=	=	SYM
ejpam-7063	138	6	p(x	p(x	NOUN
ejpam-7063	138	7	,	,	PUNCT
ejpam-7063	138	8	1	1	NUM
ejpam-7063	138	9	)	)	PUNCT
ejpam-7063	138	10	=	=	SYM
ejpam-7063	139	1	p(1	p(1	PROPN
ejpam-7063	139	2	,	,	PUNCT
ejpam-7063	139	3	y	y	NOUN
ejpam-7063	139	4	)	)	PUNCT
ejpam-7063	139	5	=	=	SYM
ejpam-7063	139	6	0	0	X
ejpam-7063	139	7	.	.	PUNCT
ejpam-7063	139	8	(	(	PUNCT
ejpam-7063	139	9	3.14	3.14	NUM
ejpam-7063	139	10	)	)	PUNCT
ejpam-7063	139	11	this	this	DET
ejpam-7063	139	12	system	system	NOUN
ejpam-7063	139	13	represents	represent	VERB
ejpam-7063	139	14	the	the	DET
ejpam-7063	139	15	first	first	ADJ
ejpam-7063	139	16	-	-	PUNCT
ejpam-7063	139	17	order	order	NOUN
ejpam-7063	139	18	necessary	necessary	ADJ
ejpam-7063	139	19	optimality	optimality	NOUN
ejpam-7063	139	20	conditions	condition	NOUN
ejpam-7063	139	21	for	for	ADP
ejpam-7063	139	22	the	the	DET
ejpam-7063	139	23	focp	focp	PROPN
ejpam-7063	139	24	(	(	PUNCT
ejpam-7063	139	25	3.1)–(3.3	3.1)–(3.3	NUM
ejpam-7063	139	26	)	)	PUNCT
ejpam-7063	139	27	,	,	PUNCT
ejpam-7063	139	28	in	in	ADP
ejpam-7063	139	29	line	line	NOUN
ejpam-7063	139	30	with	with	ADP
ejpam-7063	139	31	the	the	DET
ejpam-7063	139	32	dubovitskii	dubovitskii	ADJ
ejpam-7063	139	33	–	–	PUNCT
ejpam-7063	139	34	milyutin	milyutin	NOUN
ejpam-7063	139	35	framework	framework	NOUN
ejpam-7063	139	36	for	for	ADP
ejpam-7063	139	37	distributed	distribute	VERB
ejpam-7063	139	38	parameter	parameter	NOUN
ejpam-7063	139	39	systems	system	NOUN
ejpam-7063	139	40	[	[	X
ejpam-7063	139	41	17	17	NUM
ejpam-7063	139	42	,	,	PUNCT
ejpam-7063	139	43	42	42	NUM
ejpam-7063	139	44	]	]	PUNCT
ejpam-7063	139	45	and	and	CCONJ
ejpam-7063	139	46	the	the	DET
ejpam-7063	139	47	fractional	fractional	ADJ
ejpam-7063	139	48	optimal	optimal	ADJ
ejpam-7063	139	49	control	control	NOUN
ejpam-7063	139	50	theory	theory	NOUN
ejpam-7063	139	51	developed	develop	VERB
ejpam-7063	139	52	in	in	ADP
ejpam-7063	139	53	[	[	X
ejpam-7063	139	54	7	7	NUM
ejpam-7063	139	55	,	,	PUNCT
ejpam-7063	139	56	19	19	NUM
ejpam-7063	139	57	]	]	PUNCT
ejpam-7063	139	58	.	.	PUNCT
ejpam-7063	140	1	g.	g.	PROPN
ejpam-7063	140	2	m.	m.	PROPN
ejpam-7063	140	3	bahaa	bahaa	PROPN
ejpam-7063	140	4	,	,	PUNCT
ejpam-7063	140	5	a.	a.	NOUN
ejpam-7063	140	6	h.	h.	PROPN
ejpam-7063	140	7	qamlo	qamlo	PROPN
ejpam-7063	140	8	/	/	SYM
ejpam-7063	140	9	eur	eur	PROPN
ejpam-7063	140	10	.	.	PUNCT
ejpam-7063	141	1	j.	j.	PROPN
ejpam-7063	141	2	pure	pure	PROPN
ejpam-7063	141	3	appl	appl	PROPN
ejpam-7063	141	4	.	.	PROPN
ejpam-7063	141	5	math	math	PROPN
ejpam-7063	141	6	,	,	PUNCT
ejpam-7063	141	7	18	18	NUM
ejpam-7063	141	8	(	(	PUNCT
ejpam-7063	141	9	4	4	NUM
ejpam-7063	141	10	)	)	PUNCT
ejpam-7063	141	11	(	(	PUNCT
ejpam-7063	141	12	2025	2025	NUM
ejpam-7063	141	13	)	)	PUNCT
ejpam-7063	141	14	,	,	PUNCT
ejpam-7063	141	15	7063	7063	NUM
ejpam-7063	141	16	7	7	NUM
ejpam-7063	141	17	of	of	ADP
ejpam-7063	141	18	29	29	NUM
ejpam-7063	141	19	4	4	NUM
ejpam-7063	141	20	.	.	PUNCT
ejpam-7063	141	21	fractional	fractional	ADJ
ejpam-7063	141	22	vieta	vieta	PROPN
ejpam-7063	141	23	–	–	PUNCT
ejpam-7063	141	24	fibonacci	fibonacci	NOUN
ejpam-7063	141	25	wavelets	wavelet	NOUN
ejpam-7063	141	26	method	method	NOUN
ejpam-7063	141	27	in	in	ADP
ejpam-7063	141	28	this	this	DET
ejpam-7063	141	29	section	section	NOUN
ejpam-7063	142	1	,	,	PUNCT
ejpam-7063	142	2	we	we	PRON
ejpam-7063	142	3	describe	describe	VERB
ejpam-7063	142	4	the	the	DET
ejpam-7063	142	5	construction	construction	NOUN
ejpam-7063	142	6	of	of	ADP
ejpam-7063	142	7	the	the	DET
ejpam-7063	142	8	fractional	fractional	ADJ
ejpam-7063	142	9	vieta	vieta	PROPN
ejpam-7063	142	10	–	–	PUNCT
ejpam-7063	142	11	fibonacci	fibonacci	NOUN
ejpam-7063	142	12	wavelets	wavelet	NOUN
ejpam-7063	142	13	(	(	PUNCT
ejpam-7063	142	14	fvfws	fvfws	NOUN
ejpam-7063	142	15	)	)	PUNCT
ejpam-7063	142	16	,	,	PUNCT
ejpam-7063	142	17	the	the	DET
ejpam-7063	142	18	derivation	derivation	NOUN
ejpam-7063	142	19	of	of	ADP
ejpam-7063	142	20	their	their	PRON
ejpam-7063	142	21	operational	operational	ADJ
ejpam-7063	142	22	matrices	matrix	NOUN
ejpam-7063	142	23	for	for	ADP
ejpam-7063	142	24	caputo	caputo	PROPN
ejpam-7063	142	25	fractional	fractional	ADJ
ejpam-7063	142	26	derivatives	derivative	NOUN
ejpam-7063	142	27	,	,	PUNCT
ejpam-7063	142	28	and	and	CCONJ
ejpam-7063	142	29	the	the	DET
ejpam-7063	142	30	discretization	discretization	NOUN
ejpam-7063	142	31	of	of	ADP
ejpam-7063	142	32	the	the	DET
ejpam-7063	142	33	optimality	optimality	NOUN
ejpam-7063	142	34	system	system	NOUN
ejpam-7063	142	35	introduced	introduce	VERB
ejpam-7063	142	36	in	in	ADP
ejpam-7063	142	37	section	section	NOUN
ejpam-7063	142	38	3	3	NUM
ejpam-7063	142	39	.	.	PROPN
ejpam-7063	142	40	4.1	4.1	NUM
ejpam-7063	142	41	.	.	PUNCT
ejpam-7063	143	1	construction	construction	NOUN
ejpam-7063	143	2	of	of	ADP
ejpam-7063	143	3	fractional	fractional	ADJ
ejpam-7063	143	4	vieta	vieta	PROPN
ejpam-7063	143	5	-	-	PUNCT
ejpam-7063	143	6	fibonacci	fibonacci	NOUN
ejpam-7063	143	7	wavelets	wavelet	NOUN
ejpam-7063	143	8	let	let	AUX
ejpam-7063	143	9	{	{	PUNCT
ejpam-7063	143	10	pi(x	pi(x	NUM
ejpam-7063	143	11	)	)	PUNCT
ejpam-7063	143	12	}	}	PUNCT
ejpam-7063	143	13	be	be	AUX
ejpam-7063	143	14	the	the	DET
ejpam-7063	143	15	family	family	NOUN
ejpam-7063	143	16	of	of	ADP
ejpam-7063	143	17	vieta	vieta	PROPN
ejpam-7063	143	18	–	–	PUNCT
ejpam-7063	143	19	fibonacci	fibonacci	NOUN
ejpam-7063	143	20	polynomials	polynomial	NOUN
ejpam-7063	143	21	generated	generate	VERB
ejpam-7063	143	22	by	by	ADP
ejpam-7063	143	23	a	a	DET
ejpam-7063	143	24	fibonaccitype	fibonaccitype	NOUN
ejpam-7063	143	25	recurrence	recurrence	NOUN
ejpam-7063	143	26	relation	relation	NOUN
ejpam-7063	143	27	.	.	PUNCT
ejpam-7063	144	1	the	the	DET
ejpam-7063	144	2	one	one	NUM
ejpam-7063	144	3	-	-	PUNCT
ejpam-7063	144	4	dimensional	dimensional	ADJ
ejpam-7063	144	5	fractional	fractional	ADJ
ejpam-7063	144	6	vieta	vieta	NOUN
ejpam-7063	144	7	–	–	PUNCT
ejpam-7063	144	8	fibonacci	fibonacci	NOUN
ejpam-7063	144	9	wavelet	wavelet	NOUN
ejpam-7063	144	10	of	of	ADP
ejpam-7063	144	11	order	order	NOUN
ejpam-7063	144	12	µ	µ	X
ejpam-7063	144	13	>	>	X
ejpam-7063	144	14	0	0	NUM
ejpam-7063	144	15	is	be	AUX
ejpam-7063	144	16	defined	define	VERB
ejpam-7063	144	17	on	on	ADP
ejpam-7063	144	18	the	the	DET
ejpam-7063	144	19	interval	interval	NOUN
ejpam-7063	144	20	[	[	X
ejpam-7063	144	21	0	0	NUM
ejpam-7063	144	22	,	,	PUNCT
ejpam-7063	144	23	1	1	NUM
ejpam-7063	144	24	]	]	PUNCT
ejpam-7063	144	25	as	as	ADP
ejpam-7063	144	26	ψ	ψ	X
ejpam-7063	144	27	(	(	PUNCT
ejpam-7063	144	28	µ	µ	NOUN
ejpam-7063	144	29	)	)	PUNCT
ejpam-7063	144	30	i	i	PRON
ejpam-7063	144	31	(	(	PUNCT
ejpam-7063	144	32	x	x	X
ejpam-7063	144	33	)	)	PUNCT
ejpam-7063	144	34	=	=	SYM
ejpam-7063	145	1	xµ(1−	xµ(1−	PROPN
ejpam-7063	145	2	x)µpi(x	x)µpi(x	NUM
ejpam-7063	145	3	)	)	PUNCT
ejpam-7063	145	4	,	,	PUNCT
ejpam-7063	145	5	0	0	NUM
ejpam-7063	145	6	≤	≤	NUM
ejpam-7063	145	7	x	x	SYM
ejpam-7063	145	8	≤	≤	NUM
ejpam-7063	145	9	1	1	NUM
ejpam-7063	145	10	,	,	PUNCT
ejpam-7063	145	11	i	i	PRON
ejpam-7063	145	12	=	=	NOUN
ejpam-7063	145	13	0	0	NUM
ejpam-7063	145	14	,	,	PUNCT
ejpam-7063	145	15	1	1	NUM
ejpam-7063	145	16	,	,	PUNCT
ejpam-7063	145	17	.	.	PUNCT
ejpam-7063	145	18	.	.	PUNCT
ejpam-7063	146	1	.	.	PUNCT
ejpam-7063	147	1	,	,	PUNCT
ejpam-7063	147	2	n.	n.	NOUN
ejpam-7063	147	3	(	(	PUNCT
ejpam-7063	147	4	4.1	4.1	NUM
ejpam-7063	147	5	)	)	PUNCT
ejpam-7063	147	6	these	these	DET
ejpam-7063	147	7	wavelets	wavelet	NOUN
ejpam-7063	147	8	form	form	VERB
ejpam-7063	147	9	a	a	DET
ejpam-7063	147	10	complete	complete	ADJ
ejpam-7063	147	11	basis	basis	NOUN
ejpam-7063	147	12	for	for	ADP
ejpam-7063	147	13	l2[0	l2[0	PROPN
ejpam-7063	147	14	,	,	PUNCT
ejpam-7063	147	15	1	1	NUM
ejpam-7063	147	16	]	]	PUNCT
ejpam-7063	147	17	with	with	ADP
ejpam-7063	147	18	favorable	favorable	ADJ
ejpam-7063	147	19	approximation	approximation	NOUN
ejpam-7063	147	20	properties	property	NOUN
ejpam-7063	147	21	for	for	ADP
ejpam-7063	147	22	fractional	fractional	ADJ
ejpam-7063	147	23	problems	problem	NOUN
ejpam-7063	147	24	[	[	X
ejpam-7063	147	25	27–30	27–30	NUM
ejpam-7063	147	26	]	]	PUNCT
ejpam-7063	147	27	.	.	PUNCT
ejpam-7063	148	1	for	for	ADP
ejpam-7063	148	2	two	two	NUM
ejpam-7063	148	3	-	-	PUNCT
ejpam-7063	148	4	dimensional	dimensional	ADJ
ejpam-7063	148	5	domains	domain	NOUN
ejpam-7063	148	6	,	,	PUNCT
ejpam-7063	148	7	we	we	PRON
ejpam-7063	148	8	use	use	VERB
ejpam-7063	148	9	tensor	tensor	NOUN
ejpam-7063	148	10	products	product	NOUN
ejpam-7063	148	11	:	:	PUNCT
ejpam-7063	149	1	ψ	ψ	X
ejpam-7063	149	2	(	(	PUNCT
ejpam-7063	149	3	α	α	X
ejpam-7063	149	4	,	,	PUNCT
ejpam-7063	149	5	β	β	NOUN
ejpam-7063	149	6	)	)	PUNCT
ejpam-7063	149	7	ij	ij	NOUN
ejpam-7063	149	8	(	(	PUNCT
ejpam-7063	149	9	x	x	NOUN
ejpam-7063	149	10	,	,	PUNCT
ejpam-7063	149	11	y	y	NOUN
ejpam-7063	149	12	)	)	PUNCT
ejpam-7063	149	13	=	=	SYM
ejpam-7063	149	14	ψ	ψ	X
ejpam-7063	149	15	(	(	PUNCT
ejpam-7063	149	16	α	α	NOUN
ejpam-7063	149	17	)	)	PUNCT
ejpam-7063	149	18	i	i	PRON
ejpam-7063	149	19	(	(	PUNCT
ejpam-7063	149	20	x)ψ	x)ψ	X
ejpam-7063	149	21	(	(	PUNCT
ejpam-7063	149	22	β	β	X
ejpam-7063	149	23	)	)	PUNCT
ejpam-7063	149	24	j	j	PROPN
ejpam-7063	149	25	(	(	PUNCT
ejpam-7063	149	26	y	y	PROPN
ejpam-7063	149	27	)	)	PUNCT
ejpam-7063	149	28	,	,	PUNCT
ejpam-7063	149	29	(	(	PUNCT
ejpam-7063	149	30	x	x	X
ejpam-7063	149	31	,	,	PUNCT
ejpam-7063	149	32	y	y	NOUN
ejpam-7063	149	33	)	)	PUNCT
ejpam-7063	149	34	∈	∈	PROPN
ejpam-7063	150	1	[	[	X
ejpam-7063	150	2	0	0	NUM
ejpam-7063	150	3	,	,	PUNCT
ejpam-7063	150	4	1]2	1]2	NUM
ejpam-7063	150	5	.	.	PUNCT
ejpam-7063	151	1	(	(	PUNCT
ejpam-7063	151	2	4.2	4.2	NUM
ejpam-7063	151	3	)	)	PUNCT
ejpam-7063	151	4	this	this	DET
ejpam-7063	151	5	basis	basis	NOUN
ejpam-7063	151	6	allows	allow	VERB
ejpam-7063	151	7	simultaneous	simultaneous	ADJ
ejpam-7063	151	8	approximation	approximation	NOUN
ejpam-7063	151	9	of	of	ADP
ejpam-7063	151	10	state	state	NOUN
ejpam-7063	151	11	,	,	PUNCT
ejpam-7063	151	12	adjoint	adjoint	NOUN
ejpam-7063	151	13	,	,	PUNCT
ejpam-7063	151	14	and	and	CCONJ
ejpam-7063	151	15	control	control	NOUN
ejpam-7063	151	16	variables	variable	NOUN
ejpam-7063	151	17	in	in	ADP
ejpam-7063	151	18	two	two	NUM
ejpam-7063	151	19	spatial	spatial	ADJ
ejpam-7063	151	20	dimensions	dimension	NOUN
ejpam-7063	151	21	.	.	PUNCT
ejpam-7063	152	1	4.2	4.2	NUM
ejpam-7063	152	2	.	.	PUNCT
ejpam-7063	153	1	function	function	NOUN
ejpam-7063	153	2	approximation	approximation	NOUN
ejpam-7063	153	3	the	the	DET
ejpam-7063	153	4	state	state	NOUN
ejpam-7063	153	5	z(x	z(x	PROPN
ejpam-7063	153	6	,	,	PUNCT
ejpam-7063	153	7	y	y	PROPN
ejpam-7063	153	8	)	)	PUNCT
ejpam-7063	153	9	,	,	PUNCT
ejpam-7063	153	10	adjoint	adjoint	PROPN
ejpam-7063	153	11	p(x	p(x	PROPN
ejpam-7063	153	12	,	,	PUNCT
ejpam-7063	153	13	y	y	NOUN
ejpam-7063	153	14	)	)	PUNCT
ejpam-7063	153	15	,	,	PUNCT
ejpam-7063	153	16	and	and	CCONJ
ejpam-7063	153	17	control	control	VERB
ejpam-7063	153	18	u(x	u(x	PROPN
ejpam-7063	153	19	,	,	PUNCT
ejpam-7063	153	20	y	y	NOUN
ejpam-7063	153	21	)	)	PUNCT
ejpam-7063	153	22	are	be	AUX
ejpam-7063	153	23	approximated	approximate	VERB
ejpam-7063	153	24	as	as	ADP
ejpam-7063	153	25	truncated	truncate	VERB
ejpam-7063	153	26	fvfw	fvfw	ADJ
ejpam-7063	153	27	expansions	expansion	NOUN
ejpam-7063	153	28	:	:	PUNCT
ejpam-7063	153	29	z(x	z(x	NUM
ejpam-7063	153	30	,	,	PUNCT
ejpam-7063	153	31	y	y	PROPN
ejpam-7063	153	32	)	)	PUNCT
ejpam-7063	154	1	≈	≈	PROPN
ejpam-7063	154	2	n∑	n∑	PROPN
ejpam-7063	154	3	i=0	i=0	PROPN
ejpam-7063	154	4	n∑	n∑	PROPN
ejpam-7063	154	5	j=0	j=0	PROPN
ejpam-7063	154	6	aij	aij	PROPN
ejpam-7063	154	7	ψ	ψ	PROPN
ejpam-7063	154	8	(	(	PUNCT
ejpam-7063	154	9	α	α	NOUN
ejpam-7063	154	10	)	)	PUNCT
ejpam-7063	154	11	i	i	PRON
ejpam-7063	154	12	(	(	PUNCT
ejpam-7063	154	13	x)ψ	x)ψ	X
ejpam-7063	154	14	(	(	PUNCT
ejpam-7063	154	15	β	β	X
ejpam-7063	154	16	)	)	PUNCT
ejpam-7063	154	17	j	j	PROPN
ejpam-7063	154	18	(	(	PUNCT
ejpam-7063	154	19	y	y	PROPN
ejpam-7063	154	20	)	)	PUNCT
ejpam-7063	154	21	,	,	PUNCT
ejpam-7063	154	22	(	(	PUNCT
ejpam-7063	154	23	4.3	4.3	NUM
ejpam-7063	154	24	)	)	PUNCT
ejpam-7063	154	25	p(x	p(x	PROPN
ejpam-7063	154	26	,	,	PUNCT
ejpam-7063	154	27	y	y	NOUN
ejpam-7063	154	28	)	)	PUNCT
ejpam-7063	155	1	≈	≈	PROPN
ejpam-7063	155	2	n∑	n∑	PROPN
ejpam-7063	155	3	i=0	i=0	PROPN
ejpam-7063	155	4	n∑	n∑	PROPN
ejpam-7063	155	5	j=0	j=0	PROPN
ejpam-7063	155	6	bij	bij	VERB
ejpam-7063	155	7	ψ	ψ	X
ejpam-7063	155	8	(	(	PUNCT
ejpam-7063	155	9	α	α	X
ejpam-7063	155	10	)	)	PUNCT
ejpam-7063	155	11	i	i	PRON
ejpam-7063	155	12	(	(	PUNCT
ejpam-7063	155	13	x)ψ	x)ψ	X
ejpam-7063	155	14	(	(	PUNCT
ejpam-7063	155	15	β	β	X
ejpam-7063	155	16	)	)	PUNCT
ejpam-7063	155	17	j	j	PROPN
ejpam-7063	155	18	(	(	PUNCT
ejpam-7063	155	19	y	y	PROPN
ejpam-7063	155	20	)	)	PUNCT
ejpam-7063	155	21	,	,	PUNCT
ejpam-7063	155	22	(	(	PUNCT
ejpam-7063	155	23	4.4	4.4	NUM
ejpam-7063	155	24	)	)	PUNCT
ejpam-7063	155	25	u(x	u(x	PROPN
ejpam-7063	155	26	,	,	PUNCT
ejpam-7063	155	27	y	y	NOUN
ejpam-7063	155	28	)	)	PUNCT
ejpam-7063	156	1	≈	≈	PROPN
ejpam-7063	156	2	n∑	n∑	PROPN
ejpam-7063	156	3	i=0	i=0	PROPN
ejpam-7063	156	4	n∑	n∑	PROPN
ejpam-7063	156	5	j=0	j=0	PROPN
ejpam-7063	156	6	cij	cij	PROPN
ejpam-7063	156	7	ψ	ψ	PROPN
ejpam-7063	156	8	(	(	PUNCT
ejpam-7063	156	9	α	α	NOUN
ejpam-7063	156	10	)	)	PUNCT
ejpam-7063	156	11	i	i	PRON
ejpam-7063	156	12	(	(	PUNCT
ejpam-7063	156	13	x)ψ	x)ψ	X
ejpam-7063	156	14	(	(	PUNCT
ejpam-7063	156	15	β	β	X
ejpam-7063	156	16	)	)	PUNCT
ejpam-7063	156	17	j	j	PROPN
ejpam-7063	156	18	(	(	PUNCT
ejpam-7063	156	19	y	y	PROPN
ejpam-7063	156	20	)	)	PUNCT
ejpam-7063	156	21	.	.	PUNCT
ejpam-7063	157	1	(	(	PUNCT
ejpam-7063	157	2	4.5	4.5	NUM
ejpam-7063	157	3	)	)	PUNCT
ejpam-7063	157	4	here	here	ADV
ejpam-7063	157	5	,	,	PUNCT
ejpam-7063	157	6	{	{	PUNCT
ejpam-7063	157	7	aij	aij	X
ejpam-7063	157	8	}	}	PUNCT
ejpam-7063	157	9	,	,	PUNCT
ejpam-7063	157	10	{	{	PUNCT
ejpam-7063	157	11	bij	bij	NOUN
ejpam-7063	157	12	}	}	PUNCT
ejpam-7063	157	13	,	,	PUNCT
ejpam-7063	157	14	{	{	PUNCT
ejpam-7063	157	15	cij	cij	PROPN
ejpam-7063	157	16	}	}	PUNCT
ejpam-7063	157	17	are	be	AUX
ejpam-7063	157	18	the	the	DET
ejpam-7063	157	19	expansion	expansion	NOUN
ejpam-7063	157	20	coefficients	coefficient	NOUN
ejpam-7063	157	21	to	to	PART
ejpam-7063	157	22	be	be	AUX
ejpam-7063	157	23	determined	determine	VERB
ejpam-7063	157	24	.	.	PUNCT
ejpam-7063	158	1	4.3	4.3	NUM
ejpam-7063	158	2	.	.	PUNCT
ejpam-7063	158	3	operational	operational	ADJ
ejpam-7063	158	4	matrices	matrix	NOUN
ejpam-7063	158	5	of	of	ADP
ejpam-7063	158	6	fractional	fractional	ADJ
ejpam-7063	158	7	derivatives	derivative	NOUN
ejpam-7063	158	8	let	let	VERB
ejpam-7063	158	9	ψ(x	ψ(x	NOUN
ejpam-7063	158	10	)	)	PUNCT
ejpam-7063	159	1	=	=	PUNCT
ejpam-7063	159	2	[	[	PUNCT
ejpam-7063	159	3	ψ	ψ	X
ejpam-7063	159	4	(	(	PUNCT
ejpam-7063	159	5	α	α	NOUN
ejpam-7063	159	6	)	)	PUNCT
ejpam-7063	159	7	0	0	NUM
ejpam-7063	160	1	(	(	PUNCT
ejpam-7063	160	2	x	x	X
ejpam-7063	160	3	)	)	PUNCT
ejpam-7063	160	4	ψ	ψ	X
ejpam-7063	160	5	(	(	PUNCT
ejpam-7063	160	6	α	α	NOUN
ejpam-7063	160	7	)	)	PUNCT
ejpam-7063	160	8	1	1	NUM
ejpam-7063	160	9	(	(	PUNCT
ejpam-7063	160	10	x	x	NOUN
ejpam-7063	160	11	)	)	PUNCT
ejpam-7063	160	12	·	·	PUNCT
ejpam-7063	160	13	·	·	PUNCT
ejpam-7063	160	14	·	·	PUNCT
ejpam-7063	161	1	ψ	ψ	X
ejpam-7063	161	2	(	(	PUNCT
ejpam-7063	161	3	α	α	NOUN
ejpam-7063	161	4	)	)	PUNCT
ejpam-7063	161	5	n	n	PROPN
ejpam-7063	161	6	(	(	PUNCT
ejpam-7063	161	7	x	x	X
ejpam-7063	161	8	)	)	PUNCT
ejpam-7063	161	9	]	]	X
ejpam-7063	161	10	t	t	PROPN
ejpam-7063	161	11	.	.	PUNCT
ejpam-7063	162	1	g.	g.	PROPN
ejpam-7063	162	2	m.	m.	PROPN
ejpam-7063	162	3	bahaa	bahaa	PROPN
ejpam-7063	162	4	,	,	PUNCT
ejpam-7063	162	5	a.	a.	NOUN
ejpam-7063	162	6	h.	h.	PROPN
ejpam-7063	162	7	qamlo	qamlo	PROPN
ejpam-7063	162	8	/	/	SYM
ejpam-7063	162	9	eur	eur	PROPN
ejpam-7063	162	10	.	.	PUNCT
ejpam-7063	163	1	j.	j.	PROPN
ejpam-7063	163	2	pure	pure	PROPN
ejpam-7063	163	3	appl	appl	PROPN
ejpam-7063	163	4	.	.	PROPN
ejpam-7063	163	5	math	math	PROPN
ejpam-7063	163	6	,	,	PUNCT
ejpam-7063	163	7	18	18	NUM
ejpam-7063	163	8	(	(	PUNCT
ejpam-7063	163	9	4	4	NUM
ejpam-7063	163	10	)	)	PUNCT
ejpam-7063	163	11	(	(	PUNCT
ejpam-7063	163	12	2025	2025	NUM
ejpam-7063	163	13	)	)	PUNCT
ejpam-7063	163	14	,	,	PUNCT
ejpam-7063	163	15	7063	7063	NUM
ejpam-7063	163	16	8	8	NUM
ejpam-7063	163	17	of	of	ADP
ejpam-7063	163	18	29	29	NUM
ejpam-7063	163	19	the	the	DET
ejpam-7063	163	20	caputo	caputo	PROPN
ejpam-7063	163	21	fractional	fractional	PROPN
ejpam-7063	163	22	derivative	derivative	NOUN
ejpam-7063	163	23	of	of	ADP
ejpam-7063	163	24	order	order	NOUN
ejpam-7063	163	25	α	α	NOUN
ejpam-7063	163	26	can	can	AUX
ejpam-7063	163	27	be	be	AUX
ejpam-7063	163	28	expressed	express	VERB
ejpam-7063	163	29	in	in	ADP
ejpam-7063	163	30	terms	term	NOUN
ejpam-7063	163	31	of	of	ADP
ejpam-7063	163	32	an	an	DET
ejpam-7063	163	33	operational	operational	ADJ
ejpam-7063	163	34	matrix	matrix	NOUN
ejpam-7063	163	35	d(α	d(α	NOUN
ejpam-7063	163	36	)	)	PUNCT
ejpam-7063	163	37	x	x	PUNCT
ejpam-7063	163	38	as	as	ADP
ejpam-7063	163	39	cdα	cdα	NOUN
ejpam-7063	163	40	xψ(x	xψ(x	NUM
ejpam-7063	163	41	)	)	PUNCT
ejpam-7063	164	1	≈	≈	PROPN
ejpam-7063	164	2	d(α	d(α	PROPN
ejpam-7063	164	3	)	)	PUNCT
ejpam-7063	164	4	x	x	SYM
ejpam-7063	164	5	ψ(x	ψ(x	NOUN
ejpam-7063	164	6	)	)	PUNCT
ejpam-7063	164	7	.	.	PUNCT
ejpam-7063	165	1	(	(	PUNCT
ejpam-7063	165	2	4.6	4.6	NUM
ejpam-7063	165	3	)	)	PUNCT
ejpam-7063	165	4	similarly	similarly	ADV
ejpam-7063	165	5	,	,	PUNCT
ejpam-7063	165	6	for	for	ADP
ejpam-7063	165	7	the	the	DET
ejpam-7063	165	8	y	y	NOUN
ejpam-7063	165	9	-	-	PUNCT
ejpam-7063	165	10	direction	direction	NOUN
ejpam-7063	165	11	we	we	PRON
ejpam-7063	165	12	define	define	VERB
ejpam-7063	165	13	d(β	d(β	PROPN
ejpam-7063	165	14	)	)	PUNCT
ejpam-7063	165	15	y	y	PROPN
ejpam-7063	165	16	.	.	PUNCT
ejpam-7063	166	1	for	for	ADP
ejpam-7063	166	2	the	the	DET
ejpam-7063	166	3	two	two	NUM
ejpam-7063	166	4	-	-	PUNCT
ejpam-7063	166	5	dimensional	dimensional	ADJ
ejpam-7063	166	6	basis	basis	NOUN
ejpam-7063	166	7	,	,	PUNCT
ejpam-7063	166	8	the	the	DET
ejpam-7063	166	9	kronecker	kronecker	NOUN
ejpam-7063	166	10	product	product	NOUN
ejpam-7063	166	11	representation	representation	NOUN
ejpam-7063	166	12	yields	yield	VERB
ejpam-7063	166	13	cdα	cdα	NOUN
ejpam-7063	166	14	x	x	SYM
ejpam-7063	166	15	cdβ	cdβ	PROPN
ejpam-7063	166	16	y	y	PROPN
ejpam-7063	166	17	ψ(x	ψ(x	PROPN
ejpam-7063	166	18	,	,	PUNCT
ejpam-7063	166	19	y	y	PROPN
ejpam-7063	166	20	)	)	PUNCT
ejpam-7063	167	1	≈	≈	PROPN
ejpam-7063	167	2	(	(	PUNCT
ejpam-7063	167	3	d(α	d(α	PROPN
ejpam-7063	167	4	)	)	PUNCT
ejpam-7063	167	5	x	x	SYM
ejpam-7063	167	6	⊗d(β	⊗d(β	NOUN
ejpam-7063	167	7	)	)	PUNCT
ejpam-7063	167	8	y	y	PROPN
ejpam-7063	167	9	)	)	PUNCT
ejpam-7063	167	10	ψ(x	ψ(x	PROPN
ejpam-7063	167	11	,	,	PUNCT
ejpam-7063	167	12	y	y	NOUN
ejpam-7063	167	13	)	)	PUNCT
ejpam-7063	167	14	.	.	PUNCT
ejpam-7063	168	1	(	(	PUNCT
ejpam-7063	168	2	4.7	4.7	NUM
ejpam-7063	168	3	)	)	PUNCT
ejpam-7063	168	4	this	this	DET
ejpam-7063	168	5	construction	construction	NOUN
ejpam-7063	168	6	transforms	transform	VERB
ejpam-7063	168	7	the	the	DET
ejpam-7063	168	8	fractional	fractional	ADJ
ejpam-7063	168	9	derivatives	derivative	NOUN
ejpam-7063	168	10	into	into	ADP
ejpam-7063	168	11	sparse	sparse	ADJ
ejpam-7063	168	12	algebraic	algebraic	ADJ
ejpam-7063	168	13	operations	operation	NOUN
ejpam-7063	168	14	,	,	PUNCT
ejpam-7063	168	15	a	a	DET
ejpam-7063	168	16	significant	significant	ADJ
ejpam-7063	168	17	advantage	advantage	NOUN
ejpam-7063	168	18	over	over	ADP
ejpam-7063	168	19	finite	finite	ADJ
ejpam-7063	168	20	-	-	PUNCT
ejpam-7063	168	21	difference	difference	ADJ
ejpam-7063	168	22	methods	method	NOUN
ejpam-7063	168	23	[	[	X
ejpam-7063	168	24	34	34	NUM
ejpam-7063	168	25	,	,	PUNCT
ejpam-7063	168	26	38	38	NUM
ejpam-7063	168	27	]	]	PUNCT
ejpam-7063	168	28	.	.	PUNCT
ejpam-7063	169	1	4.4	4.4	NUM
ejpam-7063	169	2	.	.	PUNCT
ejpam-7063	170	1	discretization	discretization	NOUN
ejpam-7063	170	2	of	of	ADP
ejpam-7063	170	3	the	the	DET
ejpam-7063	170	4	optimality	optimality	NOUN
ejpam-7063	170	5	system	system	NOUN
ejpam-7063	170	6	substituting	substitute	VERB
ejpam-7063	170	7	the	the	DET
ejpam-7063	170	8	fvfw	fvfw	ADJ
ejpam-7063	170	9	expansions	expansion	NOUN
ejpam-7063	170	10	(	(	PUNCT
ejpam-7063	170	11	4.3)–(4.5	4.3)–(4.5	NUM
ejpam-7063	170	12	)	)	PUNCT
ejpam-7063	170	13	into	into	ADP
ejpam-7063	170	14	the	the	DET
ejpam-7063	170	15	optimality	optimality	NOUN
ejpam-7063	170	16	system	system	NOUN
ejpam-7063	170	17	derived	derive	VERB
ejpam-7063	170	18	in	in	ADP
ejpam-7063	170	19	section	section	NOUN
ejpam-7063	170	20	3	3	NUM
ejpam-7063	170	21	,	,	PUNCT
ejpam-7063	170	22	we	we	PRON
ejpam-7063	170	23	obtain	obtain	VERB
ejpam-7063	170	24	:	:	PUNCT
ejpam-7063	170	25	state	state	NOUN
ejpam-7063	170	26	equation	equation	NOUN
ejpam-7063	170	27	:	:	PUNCT
ejpam-7063	170	28	(	(	PUNCT
ejpam-7063	170	29	d(α	d(α	NOUN
ejpam-7063	170	30	)	)	PUNCT
ejpam-7063	170	31	x	x	SYM
ejpam-7063	170	32	⊗d(β	⊗d(β	NOUN
ejpam-7063	170	33	)	)	PUNCT
ejpam-7063	170	34	y	y	PROPN
ejpam-7063	170	35	)	)	PUNCT
ejpam-7063	170	36	a+n	a+n	PROPN
ejpam-7063	170	37	(	(	PUNCT
ejpam-7063	170	38	a	a	X
ejpam-7063	170	39	)	)	PUNCT
ejpam-7063	170	40	=	=	SYM
ejpam-7063	171	1	f	f	PROPN
ejpam-7063	172	1	+	+	CCONJ
ejpam-7063	172	2	c	c	X
ejpam-7063	172	3	,	,	PUNCT
ejpam-7063	172	4	(	(	PUNCT
ejpam-7063	172	5	4.8	4.8	NUM
ejpam-7063	172	6	)	)	PUNCT
ejpam-7063	173	1	where	where	SCONJ
ejpam-7063	173	2	a	a	DET
ejpam-7063	173	3	=	=	NOUN
ejpam-7063	173	4	vec(aij	vec(aij	NOUN
ejpam-7063	173	5	)	)	PUNCT
ejpam-7063	173	6	,	,	PUNCT
ejpam-7063	173	7	c	c	NOUN
ejpam-7063	173	8	=	=	PUNCT
ejpam-7063	173	9	vec(cij	vec(cij	NOUN
ejpam-7063	173	10	)	)	PUNCT
ejpam-7063	173	11	,	,	PUNCT
ejpam-7063	173	12	and	and	CCONJ
ejpam-7063	173	13	f	f	PROPN
ejpam-7063	173	14	is	be	AUX
ejpam-7063	173	15	the	the	DET
ejpam-7063	173	16	fvfw	fvfw	ADJ
ejpam-7063	173	17	representation	representation	NOUN
ejpam-7063	173	18	of	of	ADP
ejpam-7063	173	19	f(x	f(x	PROPN
ejpam-7063	173	20	,	,	PUNCT
ejpam-7063	173	21	y	y	PROPN
ejpam-7063	173	22	)	)	PUNCT
ejpam-7063	173	23	.	.	PUNCT
ejpam-7063	174	1	adjoint	adjoint	PROPN
ejpam-7063	174	2	equation	equation	NOUN
ejpam-7063	174	3	:	:	PUNCT
ejpam-7063	174	4	(	(	PUNCT
ejpam-7063	174	5	d(α	d(α	NOUN
ejpam-7063	174	6	)	)	PUNCT
ejpam-7063	174	7	x	x	SYM
ejpam-7063	174	8	⊗d(β	⊗d(β	NOUN
ejpam-7063	174	9	)	)	PUNCT
ejpam-7063	174	10	y	y	PROPN
ejpam-7063	174	11	)	)	PUNCT
ejpam-7063	174	12	b	b	PROPN
ejpam-7063	175	1	+	+	CCONJ
ejpam-7063	175	2	(	(	PUNCT
ejpam-7063	175	3	a−	a−	PROPN
ejpam-7063	175	4	zd	zd	PROPN
ejpam-7063	175	5	)	)	PUNCT
ejpam-7063	176	1	+	+	NOUN
ejpam-7063	176	2	n	n	DET
ejpam-7063	176	3	′(a)b	′(a)b	NOUN
ejpam-7063	176	4	=	=	SYM
ejpam-7063	176	5	0	0	PROPN
ejpam-7063	176	6	,	,	PUNCT
ejpam-7063	176	7	(	(	PUNCT
ejpam-7063	176	8	4.9	4.9	NUM
ejpam-7063	176	9	)	)	PUNCT
ejpam-7063	176	10	where	where	SCONJ
ejpam-7063	176	11	b	b	NOUN
ejpam-7063	176	12	=	=	PUNCT
ejpam-7063	176	13	vec(bij	vec(bij	PROPN
ejpam-7063	176	14	)	)	PUNCT
ejpam-7063	176	15	,	,	PUNCT
ejpam-7063	176	16	zd	zd	PROPN
ejpam-7063	176	17	is	be	AUX
ejpam-7063	176	18	the	the	DET
ejpam-7063	176	19	fvfw	fvfw	ADJ
ejpam-7063	176	20	approximation	approximation	NOUN
ejpam-7063	176	21	of	of	ADP
ejpam-7063	176	22	zd(x	zd(x	PROPN
ejpam-7063	176	23	,	,	PUNCT
ejpam-7063	176	24	y	y	PROPN
ejpam-7063	176	25	)	)	PUNCT
ejpam-7063	176	26	,	,	PUNCT
ejpam-7063	176	27	and	and	CCONJ
ejpam-7063	176	28	n	n	PRON
ejpam-7063	176	29	′	′	NOUN
ejpam-7063	176	30	is	be	AUX
ejpam-7063	176	31	the	the	DET
ejpam-7063	176	32	jacobian	jacobian	NOUN
ejpam-7063	176	33	of	of	ADP
ejpam-7063	176	34	the	the	DET
ejpam-7063	176	35	nonlinear	nonlinear	ADJ
ejpam-7063	176	36	term	term	NOUN
ejpam-7063	176	37	.	.	PUNCT
ejpam-7063	177	1	optimality	optimality	NOUN
ejpam-7063	177	2	condition	condition	NOUN
ejpam-7063	177	3	:	:	PUNCT
ejpam-7063	178	1	λc	λc	X
ejpam-7063	179	1	+	+	NOUN
ejpam-7063	179	2	b	b	NOUN
ejpam-7063	179	3	=	=	SYM
ejpam-7063	179	4	0	0	PUNCT
ejpam-7063	180	1	=	=	NOUN
ejpam-7063	180	2	⇒	⇒	NOUN
ejpam-7063	180	3	c	c	NOUN
ejpam-7063	181	1	=	=	SYM
ejpam-7063	181	2	−	−	PROPN
ejpam-7063	181	3	1	1	NUM
ejpam-7063	181	4	λ	λ	PROPN
ejpam-7063	181	5	b.	b.	PROPN
ejpam-7063	181	6	(	(	PUNCT
ejpam-7063	181	7	4.10	4.10	NUM
ejpam-7063	181	8	)	)	PUNCT
ejpam-7063	181	9	4.5	4.5	NUM
ejpam-7063	181	10	.	.	PUNCT
ejpam-7063	182	1	resulting	result	VERB
ejpam-7063	182	2	algebraic	algebraic	ADJ
ejpam-7063	182	3	system	system	NOUN
ejpam-7063	182	4	the	the	DET
ejpam-7063	182	5	discretized	discretized	ADJ
ejpam-7063	182	6	optimality	optimality	NOUN
ejpam-7063	182	7	system	system	NOUN
ejpam-7063	182	8	is	be	AUX
ejpam-7063	182	9	therefore	therefore	ADV
ejpam-7063	182	10	d(α	d(α	NOUN
ejpam-7063	182	11	,	,	PUNCT
ejpam-7063	182	12	β	β	NOUN
ejpam-7063	182	13	)	)	PUNCT
ejpam-7063	182	14	xy	xy	PROPN
ejpam-7063	182	15	a+n	a+n	PROPN
ejpam-7063	182	16	(	(	PUNCT
ejpam-7063	182	17	a	a	X
ejpam-7063	182	18	)	)	PUNCT
ejpam-7063	183	1	=	=	SYM
ejpam-7063	183	2	f	f	PROPN
ejpam-7063	184	1	−	−	PROPN
ejpam-7063	184	2	1	1	NUM
ejpam-7063	184	3	λb	λb	NOUN
ejpam-7063	184	4	,	,	PUNCT
ejpam-7063	184	5	(	(	PUNCT
ejpam-7063	184	6	4.11	4.11	NUM
ejpam-7063	184	7	)	)	PUNCT
ejpam-7063	184	8	d(α	d(α	NOUN
ejpam-7063	184	9	,	,	PUNCT
ejpam-7063	184	10	β	β	NOUN
ejpam-7063	184	11	)	)	PUNCT
ejpam-7063	184	12	xy	xy	PROPN
ejpam-7063	185	1	b	b	PROPN
ejpam-7063	185	2	+	+	CCONJ
ejpam-7063	185	3	(	(	PUNCT
ejpam-7063	185	4	a−	a−	PROPN
ejpam-7063	185	5	zd	zd	PROPN
ejpam-7063	185	6	)	)	PUNCT
ejpam-7063	186	1	+	+	NOUN
ejpam-7063	186	2	n	n	DET
ejpam-7063	186	3	′(a)b	′(a)b	NOUN
ejpam-7063	186	4	=	=	SYM
ejpam-7063	186	5	0	0	PROPN
ejpam-7063	186	6	,	,	PUNCT
ejpam-7063	186	7	(	(	PUNCT
ejpam-7063	186	8	4.12	4.12	NUM
ejpam-7063	186	9	)	)	PUNCT
ejpam-7063	186	10	where	where	SCONJ
ejpam-7063	186	11	d(α	d(α	NOUN
ejpam-7063	186	12	,	,	PUNCT
ejpam-7063	186	13	β	β	NOUN
ejpam-7063	186	14	)	)	PUNCT
ejpam-7063	186	15	xy	xy	X
ejpam-7063	187	1	=	=	SYM
ejpam-7063	187	2	d(α	d(α	PROPN
ejpam-7063	187	3	)	)	PUNCT
ejpam-7063	187	4	x	x	SYM
ejpam-7063	187	5	⊗d(β	⊗d(β	NOUN
ejpam-7063	187	6	)	)	PUNCT
ejpam-7063	187	7	y	y	PROPN
ejpam-7063	187	8	.	.	PUNCT
ejpam-7063	188	1	this	this	PRON
ejpam-7063	188	2	coupled	couple	VERB
ejpam-7063	188	3	nonlinear	nonlinear	ADJ
ejpam-7063	188	4	algebraic	algebraic	ADJ
ejpam-7063	188	5	system	system	NOUN
ejpam-7063	188	6	is	be	AUX
ejpam-7063	188	7	solved	solve	VERB
ejpam-7063	188	8	iteratively	iteratively	ADV
ejpam-7063	188	9	using	use	VERB
ejpam-7063	188	10	newton	newton	PROPN
ejpam-7063	188	11	’s	’s	PART
ejpam-7063	188	12	method	method	NOUN
ejpam-7063	188	13	,	,	PUNCT
ejpam-7063	188	14	with	with	ADP
ejpam-7063	188	15	unknowns	unknown	NOUN
ejpam-7063	188	16	a	a	PRON
ejpam-7063	188	17	and	and	CCONJ
ejpam-7063	188	18	b	b	NOUN
ejpam-7063	188	19	representing	represent	VERB
ejpam-7063	188	20	the	the	DET
ejpam-7063	188	21	wavelet	wavelet	NOUN
ejpam-7063	188	22	coefficients	coefficient	NOUN
ejpam-7063	188	23	of	of	ADP
ejpam-7063	188	24	the	the	DET
ejpam-7063	188	25	state	state	NOUN
ejpam-7063	188	26	and	and	CCONJ
ejpam-7063	188	27	adjoint	adjoint	NOUN
ejpam-7063	188	28	variables	variable	NOUN
ejpam-7063	188	29	.	.	PUNCT
ejpam-7063	189	1	once	once	ADV
ejpam-7063	189	2	b	b	NOUN
ejpam-7063	189	3	is	be	AUX
ejpam-7063	189	4	determined	determine	VERB
ejpam-7063	189	5	,	,	PUNCT
ejpam-7063	189	6	the	the	DET
ejpam-7063	189	7	control	control	NOUN
ejpam-7063	189	8	coefficients	coefficient	VERB
ejpam-7063	189	9	c	c	AUX
ejpam-7063	189	10	follow	follow	VERB
ejpam-7063	189	11	directly	directly	ADV
ejpam-7063	189	12	from	from	ADP
ejpam-7063	189	13	the	the	DET
ejpam-7063	189	14	optimality	optimality	NOUN
ejpam-7063	189	15	condition	condition	NOUN
ejpam-7063	189	16	.	.	PUNCT
ejpam-7063	190	1	g.	g.	PROPN
ejpam-7063	190	2	m.	m.	PROPN
ejpam-7063	190	3	bahaa	bahaa	PROPN
ejpam-7063	190	4	,	,	PUNCT
ejpam-7063	190	5	a.	a.	NOUN
ejpam-7063	190	6	h.	h.	PROPN
ejpam-7063	190	7	qamlo	qamlo	PROPN
ejpam-7063	190	8	/	/	SYM
ejpam-7063	190	9	eur	eur	PROPN
ejpam-7063	190	10	.	.	PUNCT
ejpam-7063	191	1	j.	j.	PROPN
ejpam-7063	191	2	pure	pure	PROPN
ejpam-7063	191	3	appl	appl	PROPN
ejpam-7063	191	4	.	.	PROPN
ejpam-7063	191	5	math	math	PROPN
ejpam-7063	191	6	,	,	PUNCT
ejpam-7063	191	7	18	18	NUM
ejpam-7063	191	8	(	(	PUNCT
ejpam-7063	191	9	4	4	NUM
ejpam-7063	191	10	)	)	PUNCT
ejpam-7063	191	11	(	(	PUNCT
ejpam-7063	191	12	2025	2025	NUM
ejpam-7063	191	13	)	)	PUNCT
ejpam-7063	191	14	,	,	PUNCT
ejpam-7063	191	15	7063	7063	NUM
ejpam-7063	191	16	9	9	NUM
ejpam-7063	191	17	of	of	ADP
ejpam-7063	191	18	29	29	NUM
ejpam-7063	191	19	4.6	4.6	NUM
ejpam-7063	191	20	.	.	PUNCT
ejpam-7063	192	1	advantages	advantage	NOUN
ejpam-7063	192	2	of	of	ADP
ejpam-7063	192	3	fvfw	fvfw	ADJ
ejpam-7063	192	4	discretization	discretization	NOUN
ejpam-7063	192	5	compared	compare	VERB
ejpam-7063	192	6	with	with	ADP
ejpam-7063	192	7	polynomialor	polynomialor	NOUN
ejpam-7063	192	8	finite	finite	ADJ
ejpam-7063	192	9	-	-	PUNCT
ejpam-7063	192	10	difference	difference	NOUN
ejpam-7063	192	11	-	-	PUNCT
ejpam-7063	192	12	based	base	VERB
ejpam-7063	192	13	methods	method	NOUN
ejpam-7063	192	14	[	[	X
ejpam-7063	192	15	20	20	NUM
ejpam-7063	192	16	,	,	PUNCT
ejpam-7063	192	17	22–24	22–24	NUM
ejpam-7063	192	18	]	]	PUNCT
ejpam-7063	192	19	,	,	PUNCT
ejpam-7063	192	20	the	the	DET
ejpam-7063	192	21	fvfw	fvfw	ADJ
ejpam-7063	192	22	approach	approach	NOUN
ejpam-7063	192	23	yields	yield	NOUN
ejpam-7063	192	24	:	:	PUNCT
ejpam-7063	192	25	•	•	NUM
ejpam-7063	192	26	sparse	sparse	ADJ
ejpam-7063	192	27	operational	operational	ADJ
ejpam-7063	192	28	matrices	matrix	NOUN
ejpam-7063	192	29	with	with	ADP
ejpam-7063	192	30	reduced	reduced	ADJ
ejpam-7063	192	31	computational	computational	ADJ
ejpam-7063	192	32	complexity	complexity	NOUN
ejpam-7063	192	33	,	,	PUNCT
ejpam-7063	192	34	•	•	NOUN
ejpam-7063	192	35	high	high	ADJ
ejpam-7063	192	36	accuracy	accuracy	NOUN
ejpam-7063	192	37	with	with	ADP
ejpam-7063	192	38	relatively	relatively	ADV
ejpam-7063	192	39	few	few	ADJ
ejpam-7063	192	40	basis	basis	NOUN
ejpam-7063	192	41	functions	function	NOUN
ejpam-7063	192	42	,	,	PUNCT
ejpam-7063	192	43	•	•	NUM
ejpam-7063	192	44	flexibility	flexibility	NOUN
ejpam-7063	192	45	to	to	PART
ejpam-7063	192	46	handle	handle	VERB
ejpam-7063	192	47	nonlinearities	nonlinearitie	NOUN
ejpam-7063	192	48	and	and	CCONJ
ejpam-7063	192	49	two	two	NUM
ejpam-7063	192	50	-	-	PUNCT
ejpam-7063	192	51	dimensional	dimensional	ADJ
ejpam-7063	192	52	fractional	fractional	ADJ
ejpam-7063	192	53	operators	operator	NOUN
ejpam-7063	192	54	,	,	PUNCT
ejpam-7063	192	55	•	•	ADP
ejpam-7063	192	56	a	a	DET
ejpam-7063	192	57	unified	unified	ADJ
ejpam-7063	192	58	framework	framework	NOUN
ejpam-7063	192	59	for	for	ADP
ejpam-7063	192	60	approximating	approximate	VERB
ejpam-7063	192	61	state	state	NOUN
ejpam-7063	192	62	,	,	PUNCT
ejpam-7063	192	63	adjoint	adjoint	NOUN
ejpam-7063	192	64	,	,	PUNCT
ejpam-7063	192	65	and	and	CCONJ
ejpam-7063	192	66	control	control	NOUN
ejpam-7063	192	67	variables	variable	NOUN
ejpam-7063	192	68	.	.	PUNCT
ejpam-7063	193	1	these	these	DET
ejpam-7063	193	2	properties	property	NOUN
ejpam-7063	193	3	make	make	VERB
ejpam-7063	193	4	the	the	DET
ejpam-7063	193	5	fvfw	fvfw	ADJ
ejpam-7063	193	6	discretization	discretization	NOUN
ejpam-7063	193	7	particularly	particularly	ADV
ejpam-7063	193	8	effective	effective	ADJ
ejpam-7063	193	9	for	for	ADP
ejpam-7063	193	10	solving	solve	VERB
ejpam-7063	193	11	highdimensional	highdimensional	ADJ
ejpam-7063	193	12	focps	focp	NOUN
ejpam-7063	193	13	.	.	PUNCT
ejpam-7063	194	1	5	5	NUM
ejpam-7063	194	2	.	.	X
ejpam-7063	194	3	numerical	numerical	ADJ
ejpam-7063	194	4	scheme	scheme	NOUN
ejpam-7063	194	5	and	and	CCONJ
ejpam-7063	194	6	algorithm	algorithm	NOUN
ejpam-7063	194	7	this	this	DET
ejpam-7063	194	8	section	section	NOUN
ejpam-7063	194	9	describes	describe	VERB
ejpam-7063	194	10	the	the	DET
ejpam-7063	194	11	numerical	numerical	ADJ
ejpam-7063	194	12	implementation	implementation	NOUN
ejpam-7063	194	13	used	use	VERB
ejpam-7063	194	14	to	to	PART
ejpam-7063	194	15	solve	solve	VERB
ejpam-7063	194	16	the	the	DET
ejpam-7063	194	17	discretized	discretized	ADJ
ejpam-7063	194	18	optimality	optimality	NOUN
ejpam-7063	194	19	system	system	NOUN
ejpam-7063	194	20	obtained	obtain	VERB
ejpam-7063	194	21	in	in	ADP
ejpam-7063	194	22	section	section	NOUN
ejpam-7063	194	23	4	4	NUM
ejpam-7063	194	24	.	.	PUNCT
ejpam-7063	195	1	we	we	PRON
ejpam-7063	195	2	explain	explain	VERB
ejpam-7063	195	3	the	the	DET
ejpam-7063	195	4	choice	choice	NOUN
ejpam-7063	195	5	of	of	ADP
ejpam-7063	195	6	collocation	collocation	NOUN
ejpam-7063	195	7	points	point	NOUN
ejpam-7063	195	8	,	,	PUNCT
ejpam-7063	195	9	construction	construction	NOUN
ejpam-7063	195	10	of	of	ADP
ejpam-7063	195	11	the	the	DET
ejpam-7063	195	12	nonlinear	nonlinear	ADJ
ejpam-7063	195	13	residual	residual	ADJ
ejpam-7063	195	14	,	,	PUNCT
ejpam-7063	195	15	the	the	DET
ejpam-7063	195	16	newton	newton	PROPN
ejpam-7063	195	17	iterative	iterative	PROPN
ejpam-7063	195	18	solver	solver	NOUN
ejpam-7063	195	19	,	,	PUNCT
ejpam-7063	195	20	computation	computation	NOUN
ejpam-7063	195	21	of	of	ADP
ejpam-7063	195	22	the	the	DET
ejpam-7063	195	23	jacobian	jacobian	ADJ
ejpam-7063	195	24	(	(	PUNCT
ejpam-7063	195	25	block	block	NOUN
ejpam-7063	195	26	structure	structure	NOUN
ejpam-7063	195	27	)	)	PUNCT
ejpam-7063	195	28	,	,	PUNCT
ejpam-7063	195	29	stopping	stop	VERB
ejpam-7063	195	30	conditions	condition	NOUN
ejpam-7063	195	31	,	,	PUNCT
ejpam-7063	195	32	and	and	CCONJ
ejpam-7063	195	33	practical	practical	ADJ
ejpam-7063	195	34	implementation	implementation	NOUN
ejpam-7063	195	35	remarks	remark	NOUN
ejpam-7063	195	36	.	.	PUNCT
ejpam-7063	196	1	5.1	5.1	NUM
ejpam-7063	196	2	.	.	X
ejpam-7063	196	3	collocation	collocation	NOUN
ejpam-7063	196	4	and	and	CCONJ
ejpam-7063	196	5	quadrature	quadrature	NOUN
ejpam-7063	196	6	let	let	VERB
ejpam-7063	196	7	n	n	PRON
ejpam-7063	196	8	be	be	AUX
ejpam-7063	196	9	the	the	DET
ejpam-7063	196	10	truncation	truncation	NOUN
ejpam-7063	196	11	index	index	NOUN
ejpam-7063	196	12	used	use	VERB
ejpam-7063	196	13	in	in	ADP
ejpam-7063	196	14	the	the	DET
ejpam-7063	196	15	fvfw	fvfw	ADJ
ejpam-7063	196	16	expansions	expansion	NOUN
ejpam-7063	196	17	and	and	CCONJ
ejpam-7063	196	18	denote	denote	VERB
ejpam-7063	196	19	m	m	VERB
ejpam-7063	196	20	=	=	SYM
ejpam-7063	196	21	(	(	PUNCT
ejpam-7063	196	22	n+1)2	n+1)2	ADV
ejpam-7063	196	23	the	the	DET
ejpam-7063	196	24	number	number	NOUN
ejpam-7063	196	25	of	of	ADP
ejpam-7063	196	26	two	two	NUM
ejpam-7063	196	27	-	-	PUNCT
ejpam-7063	196	28	dimensional	dimensional	ADJ
ejpam-7063	196	29	basis	basis	NOUN
ejpam-7063	196	30	functions	function	NOUN
ejpam-7063	196	31	.	.	PUNCT
ejpam-7063	197	1	we	we	PRON
ejpam-7063	197	2	choose	choose	VERB
ejpam-7063	197	3	a	a	DET
ejpam-7063	197	4	set	set	NOUN
ejpam-7063	197	5	of	of	ADP
ejpam-7063	197	6	collocation	collocation	NOUN
ejpam-7063	197	7	points	point	NOUN
ejpam-7063	197	8	{	{	PUNCT
ejpam-7063	197	9	(	(	PUNCT
ejpam-7063	197	10	xk	xk	INTJ
ejpam-7063	197	11	,	,	PUNCT
ejpam-7063	197	12	yℓ)}nc	yℓ)}nc	PROPN
ejpam-7063	197	13	k,ℓ=0	k,ℓ=0	X
ejpam-7063	197	14	on	on	ADP
ejpam-7063	197	15	ω	ω	PROPN
ejpam-7063	197	16	=	=	PUNCT
ejpam-7063	198	1	[	[	X
ejpam-7063	198	2	0	0	NUM
ejpam-7063	198	3	,	,	PUNCT
ejpam-7063	198	4	1]2	1]2	NUM
ejpam-7063	198	5	to	to	PART
ejpam-7063	198	6	enforce	enforce	VERB
ejpam-7063	198	7	the	the	DET
ejpam-7063	198	8	optimality	optimality	NOUN
ejpam-7063	198	9	system	system	NOUN
ejpam-7063	198	10	.	.	PUNCT
ejpam-7063	199	1	a	a	DET
ejpam-7063	199	2	convenient	convenient	ADJ
ejpam-7063	199	3	choice	choice	NOUN
ejpam-7063	199	4	is	be	AUX
ejpam-7063	199	5	the	the	DET
ejpam-7063	199	6	tensor	tensor	NOUN
ejpam-7063	199	7	product	product	NOUN
ejpam-7063	199	8	of	of	ADP
ejpam-7063	199	9	one	one	NUM
ejpam-7063	199	10	-	-	PUNCT
ejpam-7063	199	11	dimensional	dimensional	ADJ
ejpam-7063	199	12	gauss	gauss	ADJ
ejpam-7063	199	13	–	–	PUNCT
ejpam-7063	199	14	legendre	legendre	PROPN
ejpam-7063	199	15	nodes	node	NOUN
ejpam-7063	199	16	mapped	map	VERB
ejpam-7063	199	17	to	to	ADP
ejpam-7063	199	18	[	[	X
ejpam-7063	199	19	0	0	NUM
ejpam-7063	199	20	,	,	PUNCT
ejpam-7063	199	21	1	1	NUM
ejpam-7063	199	22	]	]	PUNCT
ejpam-7063	199	23	;	;	PUNCT
ejpam-7063	199	24	denote	denote	VERB
ejpam-7063	199	25	nc	nc	PROPN
ejpam-7063	199	26	+1	+1	PROPN
ejpam-7063	199	27	the	the	DET
ejpam-7063	199	28	number	number	NOUN
ejpam-7063	199	29	of	of	ADP
ejpam-7063	199	30	nodes	node	NOUN
ejpam-7063	199	31	in	in	ADP
ejpam-7063	199	32	each	each	DET
ejpam-7063	199	33	direction	direction	NOUN
ejpam-7063	199	34	.	.	PUNCT
ejpam-7063	200	1	numerical	numerical	ADJ
ejpam-7063	200	2	integration	integration	NOUN
ejpam-7063	200	3	(	(	PUNCT
ejpam-7063	200	4	for	for	ADP
ejpam-7063	200	5	the	the	DET
ejpam-7063	200	6	cost	cost	NOUN
ejpam-7063	200	7	functional	functional	ADJ
ejpam-7063	200	8	and	and	CCONJ
ejpam-7063	200	9	inner	inner	ADJ
ejpam-7063	200	10	products	product	NOUN
ejpam-7063	200	11	)	)	PUNCT
ejpam-7063	200	12	is	be	AUX
ejpam-7063	200	13	performed	perform	VERB
ejpam-7063	200	14	using	use	VERB
ejpam-7063	200	15	the	the	DET
ejpam-7063	200	16	same	same	ADJ
ejpam-7063	200	17	gauss	gauss	PROPN
ejpam-7063	200	18	–	–	PUNCT
ejpam-7063	200	19	legendre	legendre	NOUN
ejpam-7063	200	20	quadrature	quadrature	NOUN
ejpam-7063	200	21	with	with	ADP
ejpam-7063	200	22	weights	weight	NOUN
ejpam-7063	200	23	{	{	PUNCT
ejpam-7063	200	24	wk	wk	NOUN
ejpam-7063	200	25	}	}	PUNCT
ejpam-7063	201	1	[	[	X
ejpam-7063	201	2	38	38	NUM
ejpam-7063	201	3	]	]	PUNCT
ejpam-7063	201	4	.	.	PUNCT
ejpam-7063	202	1	5.2	5.2	NUM
ejpam-7063	202	2	.	.	PUNCT
ejpam-7063	203	1	vector	vector	NOUN
ejpam-7063	203	2	formulation	formulation	NOUN
ejpam-7063	203	3	and	and	CCONJ
ejpam-7063	203	4	residual	residual	ADJ
ejpam-7063	203	5	let	let	VERB
ejpam-7063	203	6	a	a	DET
ejpam-7063	203	7	∈	∈	PROPN
ejpam-7063	203	8	rm	rm	NOUN
ejpam-7063	203	9	,	,	PUNCT
ejpam-7063	203	10	b	b	PROPN
ejpam-7063	203	11	∈	∈	PROPN
ejpam-7063	203	12	rm	rm	NOUN
ejpam-7063	203	13	,	,	PUNCT
ejpam-7063	203	14	and	and	CCONJ
ejpam-7063	203	15	c	c	PROPN
ejpam-7063	203	16	∈	∈	PROPN
ejpam-7063	203	17	rm	rm	PROPN
ejpam-7063	203	18	denote	denote	VERB
ejpam-7063	203	19	the	the	DET
ejpam-7063	203	20	coefficient	coefficient	NOUN
ejpam-7063	203	21	vectors	vector	NOUN
ejpam-7063	203	22	for	for	ADP
ejpam-7063	203	23	the	the	DET
ejpam-7063	203	24	state	state	NOUN
ejpam-7063	203	25	,	,	PUNCT
ejpam-7063	203	26	adjoint	adjoint	NOUN
ejpam-7063	203	27	,	,	PUNCT
ejpam-7063	203	28	and	and	CCONJ
ejpam-7063	203	29	control	control	NOUN
ejpam-7063	203	30	,	,	PUNCT
ejpam-7063	203	31	respectively	respectively	ADV
ejpam-7063	203	32	,	,	PUNCT
ejpam-7063	203	33	arranged	arrange	VERB
ejpam-7063	203	34	as	as	ADP
ejpam-7063	203	35	column	column	NOUN
ejpam-7063	203	36	vectors	vector	NOUN
ejpam-7063	203	37	using	use	VERB
ejpam-7063	203	38	the	the	DET
ejpam-7063	203	39	vec	vec	PROPN
ejpam-7063	203	40	(	(	PUNCT
ejpam-7063	203	41	·	·	PUNCT
ejpam-7063	203	42	)	)	PUNCT
ejpam-7063	203	43	convention	convention	NOUN
ejpam-7063	203	44	.	.	PUNCT
ejpam-7063	204	1	using	use	VERB
ejpam-7063	204	2	the	the	DET
ejpam-7063	204	3	fvfw	fvfw	ADJ
ejpam-7063	204	4	operational	operational	ADJ
ejpam-7063	204	5	matrices	matrix	NOUN
ejpam-7063	204	6	,	,	PUNCT
ejpam-7063	204	7	write	write	VERB
ejpam-7063	204	8	d(α	d(α	NOUN
ejpam-7063	204	9	,	,	PUNCT
ejpam-7063	204	10	β	β	NOUN
ejpam-7063	204	11	)	)	PUNCT
ejpam-7063	204	12	xy	xy	X
ejpam-7063	205	1	=	=	SYM
ejpam-7063	205	2	d(α	d(α	PROPN
ejpam-7063	205	3	)	)	PUNCT
ejpam-7063	205	4	x	x	SYM
ejpam-7063	205	5	⊗d(β	⊗d(β	NOUN
ejpam-7063	205	6	)	)	PUNCT
ejpam-7063	205	7	y	y	PROPN
ejpam-7063	205	8	∈	∈	PROPN
ejpam-7063	205	9	rm×m	rm×m	NOUN
ejpam-7063	205	10	.	.	PUNCT
ejpam-7063	206	1	the	the	DET
ejpam-7063	206	2	discrete	discrete	ADJ
ejpam-7063	206	3	optimality	optimality	NOUN
ejpam-7063	206	4	system	system	NOUN
ejpam-7063	206	5	(	(	PUNCT
ejpam-7063	206	6	evaluated	evaluate	VERB
ejpam-7063	206	7	at	at	ADP
ejpam-7063	206	8	collocation	collocation	NOUN
ejpam-7063	206	9	points	point	NOUN
ejpam-7063	206	10	and	and	CCONJ
ejpam-7063	206	11	projected	project	VERB
ejpam-7063	206	12	onto	onto	ADP
ejpam-7063	206	13	the	the	DET
ejpam-7063	206	14	fvfw	fvfw	ADJ
ejpam-7063	206	15	basis	basis	NOUN
ejpam-7063	206	16	)	)	PUNCT
ejpam-7063	206	17	leads	lead	VERB
ejpam-7063	206	18	to	to	ADP
ejpam-7063	206	19	the	the	DET
ejpam-7063	206	20	nonlinear	nonlinear	ADJ
ejpam-7063	206	21	algebraic	algebraic	ADJ
ejpam-7063	206	22	system	system	NOUN
ejpam-7063	206	23	r1(a	r1(a	ADP
ejpam-7063	206	24	,	,	PUNCT
ejpam-7063	206	25	b	b	NOUN
ejpam-7063	206	26	)	)	PUNCT
ejpam-7063	206	27	:	:	PUNCT
ejpam-7063	207	1	=	=	PUNCT
ejpam-7063	207	2	d(α	d(α	NOUN
ejpam-7063	207	3	,	,	PUNCT
ejpam-7063	207	4	β	β	X
ejpam-7063	207	5	)	)	PUNCT
ejpam-7063	207	6	xy	xy	PROPN
ejpam-7063	207	7	a+n	a+n	PROPN
ejpam-7063	207	8	(	(	PUNCT
ejpam-7063	207	9	a)−	a)−	PROPN
ejpam-7063	207	10	f	f	X
ejpam-7063	207	11	−	−	PROPN
ejpam-7063	207	12	c	c	NOUN
ejpam-7063	207	13	=	=	SYM
ejpam-7063	207	14	0	0	NUM
ejpam-7063	207	15	,	,	PUNCT
ejpam-7063	207	16	(	(	PUNCT
ejpam-7063	207	17	5.1	5.1	NUM
ejpam-7063	207	18	)	)	PUNCT
ejpam-7063	207	19	r2(a	r2(a	NOUN
ejpam-7063	207	20	,	,	PUNCT
ejpam-7063	207	21	b	b	NOUN
ejpam-7063	207	22	)	)	PUNCT
ejpam-7063	207	23	:	:	PUNCT
ejpam-7063	207	24	=	=	PUNCT
ejpam-7063	207	25	d(α	d(α	NOUN
ejpam-7063	207	26	,	,	PUNCT
ejpam-7063	207	27	β	β	NOUN
ejpam-7063	207	28	)	)	PUNCT
ejpam-7063	207	29	xy	xy	PROPN
ejpam-7063	208	1	b	b	PROPN
ejpam-7063	208	2	+	+	CCONJ
ejpam-7063	208	3	(	(	PUNCT
ejpam-7063	208	4	a−	a−	PROPN
ejpam-7063	208	5	zd	zd	PROPN
ejpam-7063	208	6	)	)	PUNCT
ejpam-7063	209	1	+	+	NOUN
ejpam-7063	209	2	n	n	DET
ejpam-7063	209	3	′(a)b	′(a)b	NOUN
ejpam-7063	209	4	=	=	SYM
ejpam-7063	209	5	0	0	PROPN
ejpam-7063	209	6	,	,	PUNCT
ejpam-7063	209	7	(	(	PUNCT
ejpam-7063	209	8	5.2	5.2	NUM
ejpam-7063	209	9	)	)	PUNCT
ejpam-7063	209	10	g.	g.	PROPN
ejpam-7063	209	11	m.	m.	NOUN
ejpam-7063	209	12	bahaa	bahaa	PROPN
ejpam-7063	209	13	,	,	PUNCT
ejpam-7063	209	14	a.	a.	NOUN
ejpam-7063	209	15	h.	h.	PROPN
ejpam-7063	209	16	qamlo	qamlo	PROPN
ejpam-7063	209	17	/	/	SYM
ejpam-7063	209	18	eur	eur	PROPN
ejpam-7063	209	19	.	.	PUNCT
ejpam-7063	210	1	j.	j.	PROPN
ejpam-7063	210	2	pure	pure	PROPN
ejpam-7063	210	3	appl	appl	PROPN
ejpam-7063	210	4	.	.	PROPN
ejpam-7063	210	5	math	math	PROPN
ejpam-7063	210	6	,	,	PUNCT
ejpam-7063	210	7	18	18	NUM
ejpam-7063	210	8	(	(	PUNCT
ejpam-7063	210	9	4	4	NUM
ejpam-7063	210	10	)	)	PUNCT
ejpam-7063	210	11	(	(	PUNCT
ejpam-7063	210	12	2025	2025	NUM
ejpam-7063	210	13	)	)	PUNCT
ejpam-7063	210	14	,	,	PUNCT
ejpam-7063	210	15	7063	7063	NUM
ejpam-7063	210	16	10	10	NUM
ejpam-7063	210	17	of	of	ADP
ejpam-7063	210	18	29	29	NUM
ejpam-7063	210	19	c	c	NOUN
ejpam-7063	210	20	=	=	SYM
ejpam-7063	210	21	−	−	PROPN
ejpam-7063	210	22	1	1	NUM
ejpam-7063	210	23	λ	λ	PROPN
ejpam-7063	210	24	b.	b.	PROPN
ejpam-7063	210	25	(	(	PUNCT
ejpam-7063	210	26	5.3	5.3	NUM
ejpam-7063	210	27	)	)	PUNCT
ejpam-7063	210	28	eliminating	eliminate	VERB
ejpam-7063	210	29	c	c	NOUN
ejpam-7063	210	30	with	with	ADP
ejpam-7063	210	31	(	(	PUNCT
ejpam-7063	210	32	5.3	5.3	NUM
ejpam-7063	210	33	)	)	PUNCT
ejpam-7063	210	34	yields	yield	VERB
ejpam-7063	210	35	the	the	DET
ejpam-7063	210	36	coupled	couple	VERB
ejpam-7063	210	37	residual	residual	ADJ
ejpam-7063	210	38	r(x	r(x	PROPN
ejpam-7063	210	39	)	)	PUNCT
ejpam-7063	210	40	:	:	PUNCT
ejpam-7063	211	1	=	=	X
ejpam-7063	211	2	[	[	PUNCT
ejpam-7063	211	3	r1(a	r1(a	ADP
ejpam-7063	211	4	,	,	PUNCT
ejpam-7063	211	5	b	b	NOUN
ejpam-7063	211	6	)	)	PUNCT
ejpam-7063	211	7	r2(a	r2(a	PROPN
ejpam-7063	211	8	,	,	PUNCT
ejpam-7063	211	9	b	b	NOUN
ejpam-7063	211	10	)	)	PUNCT
ejpam-7063	211	11	]	]	PUNCT
ejpam-7063	212	1	=	=	PUNCT
ejpam-7063	212	2	[	[	PUNCT
ejpam-7063	212	3	d	d	X
ejpam-7063	212	4	(	(	PUNCT
ejpam-7063	212	5	α	α	X
ejpam-7063	212	6	,	,	PUNCT
ejpam-7063	212	7	β	β	NOUN
ejpam-7063	212	8	)	)	PUNCT
ejpam-7063	212	9	xy	xy	PROPN
ejpam-7063	212	10	a+n	a+n	PROPN
ejpam-7063	212	11	(	(	PUNCT
ejpam-7063	212	12	a)−	a)−	PROPN
ejpam-7063	212	13	f	f	PROPN
ejpam-7063	212	14	+	+	CCONJ
ejpam-7063	212	15	1	1	NUM
ejpam-7063	212	16	λb	λb	NOUN
ejpam-7063	212	17	d	d	X
ejpam-7063	212	18	(	(	PUNCT
ejpam-7063	212	19	α	α	X
ejpam-7063	212	20	,	,	PUNCT
ejpam-7063	212	21	β	β	NOUN
ejpam-7063	212	22	)	)	PUNCT
ejpam-7063	212	23	xy	xy	PROPN
ejpam-7063	213	1	b	b	PROPN
ejpam-7063	213	2	+	+	CCONJ
ejpam-7063	213	3	(	(	PUNCT
ejpam-7063	213	4	a−	a−	PROPN
ejpam-7063	213	5	zd	zd	PROPN
ejpam-7063	213	6	)	)	PUNCT
ejpam-7063	214	1	+	+	PROPN
ejpam-7063	214	2	n	n	PRON
ejpam-7063	214	3	′(a)b	′(a)b	NOUN
ejpam-7063	214	4	]	]	PUNCT
ejpam-7063	214	5	∈	∈	PROPN
ejpam-7063	214	6	r2	r2	PROPN
ejpam-7063	214	7	m	m	PROPN
ejpam-7063	214	8	,	,	PUNCT
ejpam-7063	214	9	where	where	SCONJ
ejpam-7063	214	10	x	x	X
ejpam-7063	214	11	=	=	PUNCT
ejpam-7063	215	1	[	[	X
ejpam-7063	215	2	at	at	ADP
ejpam-7063	215	3	bt	bt	NOUN
ejpam-7063	215	4	]	]	X
ejpam-7063	215	5	t	t	X
ejpam-7063	215	6	∈	∈	PROPN
ejpam-7063	215	7	r2	r2	PROPN
ejpam-7063	215	8	m	m	NOUN
ejpam-7063	215	9	.	.	PUNCT
ejpam-7063	216	1	5.3	5.3	NUM
ejpam-7063	216	2	.	.	PUNCT
ejpam-7063	217	1	newton	newton	PROPN
ejpam-7063	217	2	method	method	PROPN
ejpam-7063	217	3	we	we	PRON
ejpam-7063	217	4	solve	solve	VERB
ejpam-7063	217	5	r(x	r(x	PROPN
ejpam-7063	217	6	)	)	PUNCT
ejpam-7063	218	1	=	=	PUNCT
ejpam-7063	218	2	0	0	NUM
ejpam-7063	218	3	using	use	VERB
ejpam-7063	218	4	newton	newton	PROPN
ejpam-7063	218	5	’s	’s	PART
ejpam-7063	218	6	method	method	NOUN
ejpam-7063	218	7	.	.	PUNCT
ejpam-7063	219	1	given	give	VERB
ejpam-7063	219	2	an	an	DET
ejpam-7063	219	3	iterate	iterate	NOUN
ejpam-7063	219	4	x(k	x(k	NOUN
ejpam-7063	219	5	)	)	PUNCT
ejpam-7063	219	6	=	=	PUNCT
ejpam-7063	220	1	[	[	X
ejpam-7063	220	2	a(k);b(k	a(k);b(k	NOUN
ejpam-7063	220	3	)	)	PUNCT
ejpam-7063	220	4	]	]	PUNCT
ejpam-7063	220	5	,	,	PUNCT
ejpam-7063	220	6	the	the	DET
ejpam-7063	220	7	newton	newton	PROPN
ejpam-7063	220	8	update	update	NOUN
ejpam-7063	220	9	requires	require	VERB
ejpam-7063	220	10	solving	solve	VERB
ejpam-7063	220	11	the	the	DET
ejpam-7063	220	12	linear	linear	ADJ
ejpam-7063	220	13	system	system	NOUN
ejpam-7063	220	14	jr(x	jr(x	PUNCT
ejpam-7063	221	1	(	(	PUNCT
ejpam-7063	221	2	k))∆x	k))∆x	PROPN
ejpam-7063	221	3	=	=	SYM
ejpam-7063	221	4	−r(x(k	−r(x(k	PROPN
ejpam-7063	221	5	)	)	PUNCT
ejpam-7063	221	6	)	)	PUNCT
ejpam-7063	221	7	,	,	PUNCT
ejpam-7063	221	8	x(k+1	x(k+1	NUM
ejpam-7063	221	9	)	)	PUNCT
ejpam-7063	221	10	=	=	SYM
ejpam-7063	222	1	x(k	x(k	PROPN
ejpam-7063	222	2	)	)	PUNCT
ejpam-7063	223	1	+	+	ADJ
ejpam-7063	223	2	∆x	∆x	PROPN
ejpam-7063	223	3	,	,	PUNCT
ejpam-7063	223	4	(	(	PUNCT
ejpam-7063	223	5	5.4	5.4	NUM
ejpam-7063	223	6	)	)	PUNCT
ejpam-7063	224	1	where	where	SCONJ
ejpam-7063	224	2	jr(x	jr(x	NUM
ejpam-7063	224	3	)	)	PUNCT
ejpam-7063	224	4	is	be	AUX
ejpam-7063	224	5	the	the	DET
ejpam-7063	224	6	jacobian	jacobian	NOUN
ejpam-7063	224	7	of	of	ADP
ejpam-7063	224	8	r	r	NOUN
ejpam-7063	224	9	with	with	ADP
ejpam-7063	224	10	respect	respect	NOUN
ejpam-7063	224	11	to	to	ADP
ejpam-7063	224	12	x.	x.	PROPN
ejpam-7063	224	13	5.4	5.4	NUM
ejpam-7063	224	14	.	.	PUNCT
ejpam-7063	225	1	jacobian	jacobian	ADJ
ejpam-7063	225	2	structure	structure	NOUN
ejpam-7063	225	3	the	the	DET
ejpam-7063	225	4	jacobian	jacobian	PROPN
ejpam-7063	225	5	has	have	VERB
ejpam-7063	225	6	the	the	DET
ejpam-7063	225	7	following	follow	VERB
ejpam-7063	225	8	2×	2×	NUM
ejpam-7063	225	9	2	2	NUM
ejpam-7063	225	10	block	block	NOUN
ejpam-7063	225	11	structure	structure	NOUN
ejpam-7063	225	12	:	:	PUNCT
ejpam-7063	225	13	jr(x	jr(x	X
ejpam-7063	225	14	)	)	PUNCT
ejpam-7063	226	1	=	=	PUNCT
ejpam-7063	226	2			NOUN
ejpam-7063	226	3	d	d	X
ejpam-7063	226	4	(	(	PUNCT
ejpam-7063	226	5	α	α	X
ejpam-7063	226	6	,	,	PUNCT
ejpam-7063	226	7	β	β	NOUN
ejpam-7063	226	8	)	)	PUNCT
ejpam-7063	226	9	xy	xy	PUNCT
ejpam-7063	227	1	+	+	NOUN
ejpam-7063	227	2	na(a	na(a	VERB
ejpam-7063	227	3	)	)	PUNCT
ejpam-7063	227	4	1	1	NUM
ejpam-7063	228	1	λim	λim	VERB
ejpam-7063	228	2	i	i	PRON
ejpam-7063	228	3	m	m	VERB
ejpam-7063	228	4	+	+	PUNCT
ejpam-7063	228	5	∂(n	∂(n	VERB
ejpam-7063	228	6	′(a)b	′(a)b	PROPN
ejpam-7063	228	7	)	)	PUNCT
ejpam-7063	229	1	∂a	∂a	NOUN
ejpam-7063	229	2	d	d	NOUN
ejpam-7063	229	3	(	(	PUNCT
ejpam-7063	229	4	α	α	X
ejpam-7063	229	5	,	,	PUNCT
ejpam-7063	229	6	β	β	NOUN
ejpam-7063	229	7	)	)	PUNCT
ejpam-7063	229	8	xy	xy	PUNCT
ejpam-7063	230	1	+	+	NOUN
ejpam-7063	230	2	n	n	NUM
ejpam-7063	230	3	′(a	′(a	ADJ
ejpam-7063	230	4	)	)	PUNCT
ejpam-7063	230	5			NOUN
ejpam-7063	230	6	,	,	PUNCT
ejpam-7063	230	7	(	(	PUNCT
ejpam-7063	230	8	5.5	5.5	NUM
ejpam-7063	230	9	)	)	PUNCT
ejpam-7063	230	10	where	where	SCONJ
ejpam-7063	230	11	:	:	PUNCT
ejpam-7063	230	12	•	•	X
ejpam-7063	230	13	i	i	PRON
ejpam-7063	230	14	m	m	VERB
ejpam-7063	230	15	is	be	AUX
ejpam-7063	230	16	the	the	DET
ejpam-7063	230	17	m	m	PROPN
ejpam-7063	230	18	×m	×m	NOUN
ejpam-7063	230	19	identity	identity	NOUN
ejpam-7063	230	20	matrix	matrix	NOUN
ejpam-7063	230	21	,	,	PUNCT
ejpam-7063	230	22	•	•	NUM
ejpam-7063	230	23	na(a	na(a	NOUN
ejpam-7063	230	24	)	)	PUNCT
ejpam-7063	230	25	denotes	denote	VERB
ejpam-7063	230	26	the	the	DET
ejpam-7063	230	27	jacobian	jacobian	PROPN
ejpam-7063	230	28	(	(	PUNCT
ejpam-7063	230	29	w.r.t	w.r.t	PROPN
ejpam-7063	230	30	.	.	PUNCT
ejpam-7063	231	1	a	a	PRON
ejpam-7063	231	2	)	)	PUNCT
ejpam-7063	231	3	of	of	ADP
ejpam-7063	231	4	the	the	DET
ejpam-7063	231	5	nonlinear	nonlinear	ADJ
ejpam-7063	231	6	mapping	mapping	NOUN
ejpam-7063	231	7	n	n	CCONJ
ejpam-7063	231	8	(	(	PUNCT
ejpam-7063	231	9	a	a	NOUN
ejpam-7063	231	10	)	)	PUNCT
ejpam-7063	231	11	(	(	PUNCT
ejpam-7063	231	12	zero	zero	NUM
ejpam-7063	231	13	if	if	SCONJ
ejpam-7063	231	14	n	n	PRON
ejpam-7063	231	15	is	be	AUX
ejpam-7063	231	16	linear	linear	ADJ
ejpam-7063	231	17	)	)	PUNCT
ejpam-7063	231	18	,	,	PUNCT
ejpam-7063	231	19	•	•	NOUN
ejpam-7063	231	20	n	n	PRON
ejpam-7063	231	21	′(a	′(a	ADV
ejpam-7063	231	22	)	)	PUNCT
ejpam-7063	231	23	is	be	AUX
ejpam-7063	231	24	the	the	DET
ejpam-7063	231	25	pointwise	pointwise	ADJ
ejpam-7063	231	26	multiplier	multipli	ADJ
ejpam-7063	231	27	(	(	PUNCT
ejpam-7063	231	28	jacobian	jacobian	ADJ
ejpam-7063	231	29	)	)	PUNCT
ejpam-7063	231	30	entering	enter	VERB
ejpam-7063	231	31	the	the	DET
ejpam-7063	231	32	adjoint	adjoint	NOUN
ejpam-7063	231	33	equation	equation	NOUN
ejpam-7063	231	34	,	,	PUNCT
ejpam-7063	231	35	•	•	NOUN
ejpam-7063	231	36	∂(n	∂(n	PROPN
ejpam-7063	231	37	′(a)b	′(a)b	PROPN
ejpam-7063	231	38	)	)	PUNCT
ejpam-7063	231	39	∂a	∂a	NOUN
ejpam-7063	231	40	denotes	denote	NOUN
ejpam-7063	231	41	the	the	DET
ejpam-7063	231	42	m	m	PROPN
ejpam-7063	231	43	×m	×m	NOUN
ejpam-7063	231	44	matrix	matrix	NOUN
ejpam-7063	231	45	whose	whose	DET
ejpam-7063	231	46	(	(	PUNCT
ejpam-7063	231	47	i	i	PROPN
ejpam-7063	231	48	,	,	PUNCT
ejpam-7063	231	49	j)-entry	j)-entry	NOUN
ejpam-7063	231	50	is	be	AUX
ejpam-7063	231	51	the	the	DET
ejpam-7063	231	52	derivative	derivative	NOUN
ejpam-7063	231	53	of	of	ADP
ejpam-7063	231	54	the	the	DET
ejpam-7063	231	55	i	i	PROPN
ejpam-7063	231	56	-	-	PUNCT
ejpam-7063	231	57	th	th	VERB
ejpam-7063	231	58	component	component	NOUN
ejpam-7063	231	59	of	of	ADP
ejpam-7063	231	60	n	n	PROPN
ejpam-7063	231	61	′(a)b	′(a)b	PROPN
ejpam-7063	231	62	with	with	ADP
ejpam-7063	231	63	respect	respect	NOUN
ejpam-7063	231	64	to	to	ADP
ejpam-7063	231	65	aj	aj	PROPN
ejpam-7063	231	66	(	(	PUNCT
ejpam-7063	231	67	this	this	DET
ejpam-7063	231	68	term	term	NOUN
ejpam-7063	231	69	is	be	AUX
ejpam-7063	231	70	present	present	ADJ
ejpam-7063	231	71	for	for	ADP
ejpam-7063	231	72	nonlinear	nonlinear	ADJ
ejpam-7063	231	73	n	n	PROPN
ejpam-7063	231	74	)	)	PUNCT
ejpam-7063	231	75	.	.	PUNCT
ejpam-7063	232	1	in	in	ADP
ejpam-7063	232	2	many	many	ADJ
ejpam-7063	232	3	practical	practical	ADJ
ejpam-7063	232	4	cases	case	NOUN
ejpam-7063	232	5	(	(	PUNCT
ejpam-7063	232	6	e.g.	e.g.	ADV
ejpam-7063	232	7	,	,	PUNCT
ejpam-7063	232	8	n	n	CCONJ
ejpam-7063	232	9	(	(	PUNCT
ejpam-7063	232	10	z	z	NOUN
ejpam-7063	232	11	)	)	PUNCT
ejpam-7063	232	12	=	=	SYM
ejpam-7063	232	13	µ	µ	DET
ejpam-7063	232	14	sin(z	sin(z	PROPN
ejpam-7063	232	15	)	)	PUNCT
ejpam-7063	232	16	)	)	PUNCT
ejpam-7063	232	17	,	,	PUNCT
ejpam-7063	232	18	these	these	DET
ejpam-7063	232	19	matrices	matrix	NOUN
ejpam-7063	232	20	are	be	AUX
ejpam-7063	232	21	sparse	sparse	ADJ
ejpam-7063	232	22	or	or	CCONJ
ejpam-7063	232	23	diagonaldominant	diagonaldominant	VERB
ejpam-7063	232	24	and	and	CCONJ
ejpam-7063	232	25	can	can	AUX
ejpam-7063	232	26	be	be	AUX
ejpam-7063	232	27	formed	form	VERB
ejpam-7063	232	28	efficiently	efficiently	ADV
ejpam-7063	232	29	.	.	PUNCT
ejpam-7063	233	1	exploiting	exploit	VERB
ejpam-7063	233	2	the	the	DET
ejpam-7063	233	3	block	block	NOUN
ejpam-7063	233	4	structure	structure	NOUN
ejpam-7063	233	5	enables	enable	VERB
ejpam-7063	233	6	efficient	efficient	ADJ
ejpam-7063	233	7	factorization	factorization	NOUN
ejpam-7063	233	8	techniques	technique	NOUN
ejpam-7063	233	9	(	(	PUNCT
ejpam-7063	233	10	block	block	NOUN
ejpam-7063	233	11	lu	lu	PROPN
ejpam-7063	233	12	,	,	PUNCT
ejpam-7063	233	13	schur	schur	PROPN
ejpam-7063	233	14	complement	complement	PROPN
ejpam-7063	233	15	)	)	PUNCT
ejpam-7063	233	16	and	and	CCONJ
ejpam-7063	233	17	reduces	reduce	VERB
ejpam-7063	233	18	computational	computational	ADJ
ejpam-7063	233	19	cost	cost	NOUN
ejpam-7063	233	20	[	[	X
ejpam-7063	233	21	38	38	NUM
ejpam-7063	233	22	]	]	PUNCT
ejpam-7063	233	23	.	.	PUNCT
ejpam-7063	234	1	g.	g.	PROPN
ejpam-7063	234	2	m.	m.	PROPN
ejpam-7063	234	3	bahaa	bahaa	PROPN
ejpam-7063	234	4	,	,	PUNCT
ejpam-7063	234	5	a.	a.	NOUN
ejpam-7063	234	6	h.	h.	PROPN
ejpam-7063	234	7	qamlo	qamlo	PROPN
ejpam-7063	234	8	/	/	SYM
ejpam-7063	234	9	eur	eur	PROPN
ejpam-7063	234	10	.	.	PUNCT
ejpam-7063	235	1	j.	j.	PROPN
ejpam-7063	235	2	pure	pure	PROPN
ejpam-7063	235	3	appl	appl	PROPN
ejpam-7063	235	4	.	.	PROPN
ejpam-7063	235	5	math	math	PROPN
ejpam-7063	235	6	,	,	PUNCT
ejpam-7063	235	7	18	18	NUM
ejpam-7063	235	8	(	(	PUNCT
ejpam-7063	235	9	4	4	NUM
ejpam-7063	235	10	)	)	PUNCT
ejpam-7063	235	11	(	(	PUNCT
ejpam-7063	235	12	2025	2025	NUM
ejpam-7063	235	13	)	)	PUNCT
ejpam-7063	235	14	,	,	PUNCT
ejpam-7063	235	15	7063	7063	NUM
ejpam-7063	235	16	11	11	NUM
ejpam-7063	235	17	of	of	ADP
ejpam-7063	235	18	29	29	NUM
ejpam-7063	235	19	5.5	5.5	NUM
ejpam-7063	235	20	.	.	PUNCT
ejpam-7063	236	1	algorithm	algorithm	NOUN
ejpam-7063	236	2	(	(	PUNCT
ejpam-7063	236	3	practical	practical	ADJ
ejpam-7063	236	4	version	version	NOUN
ejpam-7063	236	5	)	)	PUNCT
ejpam-7063	236	6	algorithm	algorithm	NOUN
ejpam-7063	236	7	1	1	NUM
ejpam-7063	236	8	(	(	PUNCT
ejpam-7063	236	9	newton	newton	PROPN
ejpam-7063	236	10	solver	solver	VERB
ejpam-7063	236	11	for	for	ADP
ejpam-7063	236	12	fvfw	fvfw	ADJ
ejpam-7063	236	13	discretization	discretization	NOUN
ejpam-7063	236	14	)	)	PUNCT
ejpam-7063	236	15	1	1	NUM
ejpam-7063	236	16	.	.	X
ejpam-7063	236	17	choose	choose	VERB
ejpam-7063	236	18	truncation	truncation	NOUN
ejpam-7063	236	19	order	order	NOUN
ejpam-7063	236	20	n	n	NOUN
ejpam-7063	236	21	and	and	CCONJ
ejpam-7063	236	22	collocation	collocation	NOUN
ejpam-7063	236	23	nodes	node	NOUN
ejpam-7063	236	24	(	(	PUNCT
ejpam-7063	236	25	xk	xk	NOUN
ejpam-7063	236	26	,	,	PUNCT
ejpam-7063	236	27	yℓ	yℓ	PROPN
ejpam-7063	236	28	)	)	PUNCT
ejpam-7063	236	29	with	with	ADP
ejpam-7063	236	30	quadrature	quadrature	NOUN
ejpam-7063	236	31	weights	weight	NOUN
ejpam-7063	236	32	{	{	PUNCT
ejpam-7063	236	33	wk	wk	NOUN
ejpam-7063	236	34	}	}	PUNCT
ejpam-7063	236	35	.	.	PUNCT
ejpam-7063	237	1	2	2	X
ejpam-7063	237	2	.	.	X
ejpam-7063	237	3	assemble	assemble	VERB
ejpam-7063	237	4	fvfw	fvfw	ADJ
ejpam-7063	237	5	basis	basis	NOUN
ejpam-7063	237	6	,	,	PUNCT
ejpam-7063	237	7	operational	operational	ADJ
ejpam-7063	237	8	matrices	matrix	NOUN
ejpam-7063	237	9	d(α	d(α	NOUN
ejpam-7063	237	10	)	)	PUNCT
ejpam-7063	237	11	x	x	SYM
ejpam-7063	237	12	,	,	PUNCT
ejpam-7063	237	13	d(β	d(β	PROPN
ejpam-7063	237	14	)	)	PUNCT
ejpam-7063	237	15	y	y	PROPN
ejpam-7063	237	16	,	,	PUNCT
ejpam-7063	237	17	and	and	CCONJ
ejpam-7063	237	18	d	d	X
ejpam-7063	237	19	(	(	PUNCT
ejpam-7063	237	20	α	α	X
ejpam-7063	237	21	,	,	PUNCT
ejpam-7063	237	22	β	β	NOUN
ejpam-7063	237	23	)	)	PUNCT
ejpam-7063	237	24	xy	xy	INTJ
ejpam-7063	237	25	.	.	PUNCT
ejpam-7063	238	1	3	3	X
ejpam-7063	238	2	.	.	X
ejpam-7063	238	3	compute	compute	PROPN
ejpam-7063	238	4	fvfw	fvfw	ADJ
ejpam-7063	238	5	projections	projection	NOUN
ejpam-7063	238	6	f	f	PROPN
ejpam-7063	238	7	and	and	CCONJ
ejpam-7063	238	8	zd	zd	PROPN
ejpam-7063	238	9	of	of	ADP
ejpam-7063	238	10	f	f	PROPN
ejpam-7063	238	11	and	and	CCONJ
ejpam-7063	238	12	zd	zd	PROPN
ejpam-7063	238	13	.	.	PROPN
ejpam-7063	238	14	4	4	NUM
ejpam-7063	238	15	.	.	X
ejpam-7063	238	16	initialize	initialize	VERB
ejpam-7063	238	17	a(0	a(0	PROPN
ejpam-7063	238	18	)	)	PUNCT
ejpam-7063	238	19	,	,	PUNCT
ejpam-7063	238	20	b(0	b(0	PROPN
ejpam-7063	238	21	)	)	PUNCT
ejpam-7063	238	22	(	(	PUNCT
ejpam-7063	238	23	e.g.	e.g.	ADV
ejpam-7063	238	24	,	,	PUNCT
ejpam-7063	238	25	zeros	zero	NOUN
ejpam-7063	238	26	or	or	CCONJ
ejpam-7063	238	27	coarse	coarse	ADJ
ejpam-7063	238	28	approximate	approximate	ADJ
ejpam-7063	238	29	solution	solution	NOUN
ejpam-7063	238	30	)	)	PUNCT
ejpam-7063	238	31	.	.	PUNCT
ejpam-7063	239	1	set	set	VERB
ejpam-7063	239	2	tolerance	tolerance	NOUN
ejpam-7063	239	3	ε	ε	PROPN
ejpam-7063	239	4	>	>	PUNCT
ejpam-7063	239	5	0	0	PUNCT
ejpam-7063	240	1	and	and	CCONJ
ejpam-7063	240	2	k	k	X
ejpam-7063	240	3	=	=	SYM
ejpam-7063	240	4	0	0	NUM
ejpam-7063	240	5	.	.	NOUN
ejpam-7063	241	1	5	5	NUM
ejpam-7063	241	2	.	.	PUNCT
ejpam-7063	242	1	while	while	SCONJ
ejpam-7063	242	2	∥r(x(k))∥2	∥r(x(k))∥2	PRON
ejpam-7063	242	3	>	>	X
ejpam-7063	242	4	ε	ε	PROPN
ejpam-7063	242	5	and	and	CCONJ
ejpam-7063	242	6	k	k	PROPN
ejpam-7063	242	7	<	<	X
ejpam-7063	242	8	kmax	kmax	X
ejpam-7063	242	9	do	do	AUX
ejpam-7063	242	10	(	(	PUNCT
ejpam-7063	242	11	a	a	PRON
ejpam-7063	242	12	)	)	PUNCT
ejpam-7063	242	13	form	form	NOUN
ejpam-7063	242	14	jacobian	jacobian	ADJ
ejpam-7063	242	15	jr(x	jr(x	PROPN
ejpam-7063	242	16	(	(	PUNCT
ejpam-7063	242	17	k	k	NOUN
ejpam-7063	242	18	)	)	PUNCT
ejpam-7063	242	19	)	)	PUNCT
ejpam-7063	243	1	using	use	VERB
ejpam-7063	243	2	(	(	PUNCT
ejpam-7063	243	3	5.5	5.5	NUM
ejpam-7063	243	4	)	)	PUNCT
ejpam-7063	243	5	.	.	PUNCT
ejpam-7063	244	1	(	(	PUNCT
ejpam-7063	244	2	b	b	X
ejpam-7063	244	3	)	)	PUNCT
ejpam-7063	244	4	solve	solve	NOUN
ejpam-7063	244	5	linear	linear	ADJ
ejpam-7063	244	6	system	system	NOUN
ejpam-7063	244	7	jr(x	jr(x	PUNCT
ejpam-7063	245	1	(	(	PUNCT
ejpam-7063	245	2	k))∆x	k))∆x	PROPN
ejpam-7063	245	3	=	=	SYM
ejpam-7063	245	4	−r(x(k	−r(x(k	PROPN
ejpam-7063	245	5	)	)	PUNCT
ejpam-7063	245	6	)	)	PUNCT
ejpam-7063	246	1	for	for	ADP
ejpam-7063	246	2	∆x	∆x	PROPN
ejpam-7063	246	3	(	(	PUNCT
ejpam-7063	246	4	use	use	VERB
ejpam-7063	246	5	sparse	sparse	ADJ
ejpam-7063	246	6	direct	direct	ADJ
ejpam-7063	246	7	or	or	CCONJ
ejpam-7063	246	8	iterative	iterative	NOUN
ejpam-7063	246	9	solver	solver	ADV
ejpam-7063	246	10	)	)	PUNCT
ejpam-7063	246	11	.	.	PUNCT
ejpam-7063	247	1	(	(	PUNCT
ejpam-7063	247	2	c	c	X
ejpam-7063	247	3	)	)	PUNCT
ejpam-7063	247	4	optional	optional	ADJ
ejpam-7063	247	5	:	:	PUNCT
ejpam-7063	247	6	perform	perform	VERB
ejpam-7063	247	7	a	a	DET
ejpam-7063	247	8	line	line	NOUN
ejpam-7063	247	9	-	-	PUNCT
ejpam-7063	247	10	search	search	NOUN
ejpam-7063	247	11	or	or	CCONJ
ejpam-7063	247	12	damping	damp	VERB
ejpam-7063	247	13	:	:	PUNCT
ejpam-7063	247	14	set	set	NOUN
ejpam-7063	247	15	x(k+1	x(k+1	NOUN
ejpam-7063	247	16	)	)	PUNCT
ejpam-7063	247	17	=	=	PUNCT
ejpam-7063	248	1	x(k	x(k	PROPN
ejpam-7063	248	2	)	)	PUNCT
ejpam-7063	248	3	+	+	CCONJ
ejpam-7063	248	4	γ∆x	γ∆x	NOUN
ejpam-7063	248	5	with	with	ADP
ejpam-7063	248	6	γ	γ	X
ejpam-7063	248	7	∈	∈	PROPN
ejpam-7063	248	8	(	(	PUNCT
ejpam-7063	248	9	0	0	NUM
ejpam-7063	248	10	,	,	PUNCT
ejpam-7063	248	11	1	1	NUM
ejpam-7063	248	12	]	]	PUNCT
ejpam-7063	248	13	chosen	choose	VERB
ejpam-7063	248	14	to	to	PART
ejpam-7063	248	15	satisfy	satisfy	VERB
ejpam-7063	248	16	a	a	DET
ejpam-7063	248	17	sufficient	sufficient	ADJ
ejpam-7063	248	18	decrease	decrease	NOUN
ejpam-7063	248	19	condition	condition	NOUN
ejpam-7063	248	20	.	.	PUNCT
ejpam-7063	249	1	(	(	PUNCT
ejpam-7063	249	2	d	d	X
ejpam-7063	249	3	)	)	PUNCT
ejpam-7063	249	4	update	update	NOUN
ejpam-7063	249	5	k	k	PROPN
ejpam-7063	249	6	←	←	PROPN
ejpam-7063	250	1	k	k	PROPN
ejpam-7063	250	2	+	+	PROPN
ejpam-7063	250	3	1	1	NUM
ejpam-7063	250	4	.	.	NOUN
ejpam-7063	250	5	6	6	NUM
ejpam-7063	250	6	.	.	NOUN
ejpam-7063	250	7	end	end	NOUN
ejpam-7063	250	8	while	while	SCONJ
ejpam-7063	250	9	7	7	NUM
ejpam-7063	250	10	.	.	NUM
ejpam-7063	250	11	recover	recover	NOUN
ejpam-7063	250	12	control	control	NOUN
ejpam-7063	250	13	coefficients	coefficient	NOUN
ejpam-7063	251	1	c	c	NOUN
ejpam-7063	251	2	=	=	SYM
ejpam-7063	252	1	−	−	PROPN
ejpam-7063	252	2	1	1	NUM
ejpam-7063	252	3	λb	λb	NOUN
ejpam-7063	252	4	(	(	PUNCT
ejpam-7063	252	5	k	k	NOUN
ejpam-7063	252	6	)	)	PUNCT
ejpam-7063	253	1	and	and	CCONJ
ejpam-7063	253	2	reconstruct	reconstruct	VERB
ejpam-7063	253	3	z	z	PROPN
ejpam-7063	253	4	,	,	PUNCT
ejpam-7063	253	5	p	p	X
ejpam-7063	253	6	,	,	PUNCT
ejpam-7063	253	7	and	and	CCONJ
ejpam-7063	253	8	u	u	NOUN
ejpam-7063	253	9	via	via	ADP
ejpam-7063	253	10	the	the	DET
ejpam-7063	253	11	fvfw	fvfw	ADJ
ejpam-7063	253	12	expansions	expansion	NOUN
ejpam-7063	253	13	.	.	PUNCT
ejpam-7063	254	1	5.6	5.6	NUM
ejpam-7063	254	2	.	.	PUNCT
ejpam-7063	254	3	stopping	stop	VERB
ejpam-7063	254	4	criteria	criterion	NOUN
ejpam-7063	254	5	and	and	CCONJ
ejpam-7063	254	6	safeguards	safeguard	VERB
ejpam-7063	254	7	typical	typical	ADJ
ejpam-7063	254	8	stopping	stopping	NOUN
ejpam-7063	254	9	criteria	criterion	NOUN
ejpam-7063	254	10	:	:	PUNCT
ejpam-7063	254	11	1	1	X
ejpam-7063	254	12	.	.	X
ejpam-7063	254	13	residual	residual	ADJ
ejpam-7063	254	14	norm	norm	NOUN
ejpam-7063	254	15	reduction	reduction	NOUN
ejpam-7063	254	16	:	:	PUNCT
ejpam-7063	255	1	∥r(x(k))∥2	∥r(x(k))∥2	PROPN
ejpam-7063	255	2	≤	≤	X
ejpam-7063	255	3	ε	ε	PROPN
ejpam-7063	255	4	(	(	PUNCT
ejpam-7063	255	5	e.g.	e.g.	ADV
ejpam-7063	255	6	,	,	PUNCT
ejpam-7063	255	7	ε	ε	PROPN
ejpam-7063	255	8	=	=	SYM
ejpam-7063	255	9	10−8	10−8	NUM
ejpam-7063	255	10	)	)	PUNCT
ejpam-7063	255	11	.	.	PUNCT
ejpam-7063	256	1	2	2	X
ejpam-7063	256	2	.	.	X
ejpam-7063	256	3	relative	relative	ADJ
ejpam-7063	256	4	change	change	NOUN
ejpam-7063	256	5	:	:	PUNCT
ejpam-7063	256	6	∥∆x∥2/∥x(k)∥2	∥∆x∥2/∥x(k)∥2	PROPN
ejpam-7063	256	7	≤	≤	PROPN
ejpam-7063	256	8	τ	τ	X
ejpam-7063	256	9	(	(	PUNCT
ejpam-7063	256	10	e.g.	e.g.	ADV
ejpam-7063	256	11	,	,	PUNCT
ejpam-7063	256	12	τ	τ	PROPN
ejpam-7063	256	13	=	=	SYM
ejpam-7063	256	14	10−10	10−10	NUM
ejpam-7063	256	15	)	)	PUNCT
ejpam-7063	256	16	.	.	PUNCT
ejpam-7063	257	1	3	3	X
ejpam-7063	257	2	.	.	X
ejpam-7063	257	3	maximum	maximum	ADJ
ejpam-7063	257	4	iterations	iteration	NOUN
ejpam-7063	257	5	kmax	kmax	PROPN
ejpam-7063	257	6	(	(	PUNCT
ejpam-7063	257	7	e.g.	e.g.	ADV
ejpam-7063	257	8	,	,	PUNCT
ejpam-7063	257	9	kmax	kmax	NOUN
ejpam-7063	257	10	=	=	NOUN
ejpam-7063	257	11	50	50	NUM
ejpam-7063	257	12	)	)	PUNCT
ejpam-7063	257	13	.	.	PUNCT
ejpam-7063	258	1	to	to	PART
ejpam-7063	258	2	improve	improve	VERB
ejpam-7063	258	3	robustness	robustness	NOUN
ejpam-7063	258	4	for	for	ADP
ejpam-7063	258	5	highly	highly	ADV
ejpam-7063	258	6	nonlinear	nonlinear	ADJ
ejpam-7063	258	7	problems	problem	NOUN
ejpam-7063	258	8	,	,	PUNCT
ejpam-7063	258	9	implement	implement	VERB
ejpam-7063	258	10	damping	damp	VERB
ejpam-7063	258	11	(	(	PUNCT
ejpam-7063	258	12	line	line	NOUN
ejpam-7063	258	13	-	-	PUNCT
ejpam-7063	258	14	search	search	NOUN
ejpam-7063	258	15	)	)	PUNCT
ejpam-7063	258	16	or	or	CCONJ
ejpam-7063	258	17	trust	trust	NOUN
ejpam-7063	258	18	-	-	PUNCT
ejpam-7063	258	19	region	region	NOUN
ejpam-7063	258	20	globalization	globalization	NOUN
ejpam-7063	258	21	strategies	strategy	NOUN
ejpam-7063	258	22	.	.	PUNCT
ejpam-7063	259	1	if	if	SCONJ
ejpam-7063	259	2	the	the	DET
ejpam-7063	259	3	jacobian	jacobian	PROPN
ejpam-7063	259	4	is	be	AUX
ejpam-7063	259	5	ill	ill	ADV
ejpam-7063	259	6	-	-	PUNCT
ejpam-7063	259	7	conditioned	condition	VERB
ejpam-7063	259	8	,	,	PUNCT
ejpam-7063	259	9	tikhonov	tikhonov	VERB
ejpam-7063	259	10	regularization	regularization	NOUN
ejpam-7063	259	11	or	or	CCONJ
ejpam-7063	259	12	pseudo	pseudo	NOUN
ejpam-7063	259	13	-	-	ADJ
ejpam-7063	259	14	inverse	inverse	ADJ
ejpam-7063	259	15	approaches	approach	NOUN
ejpam-7063	259	16	can	can	AUX
ejpam-7063	259	17	stabilize	stabilize	VERB
ejpam-7063	259	18	the	the	DET
ejpam-7063	259	19	linear	linear	ADJ
ejpam-7063	259	20	solve	solve	NOUN
ejpam-7063	259	21	.	.	PUNCT
ejpam-7063	260	1	5.7	5.7	NUM
ejpam-7063	260	2	.	.	PUNCT
ejpam-7063	260	3	convergence	convergence	NOUN
ejpam-7063	260	4	and	and	CCONJ
ejpam-7063	260	5	complexity	complexity	NOUN
ejpam-7063	260	6	remarks	remark	NOUN
ejpam-7063	260	7	convergence	convergence	NOUN
ejpam-7063	260	8	.	.	PUNCT
ejpam-7063	261	1	under	under	ADP
ejpam-7063	261	2	standard	standard	ADJ
ejpam-7063	261	3	regularity	regularity	NOUN
ejpam-7063	261	4	assumptions	assumption	NOUN
ejpam-7063	261	5	(	(	PUNCT
ejpam-7063	261	6	sufficient	sufficient	ADJ
ejpam-7063	261	7	smoothness	smoothness	NOUN
ejpam-7063	261	8	of	of	ADP
ejpam-7063	261	9	n	n	NUM
ejpam-7063	261	10	and	and	CCONJ
ejpam-7063	261	11	invertibility	invertibility	NOUN
ejpam-7063	261	12	of	of	ADP
ejpam-7063	261	13	jr	jr	PROPN
ejpam-7063	261	14	at	at	ADP
ejpam-7063	261	15	the	the	DET
ejpam-7063	261	16	root	root	NOUN
ejpam-7063	261	17	)	)	PUNCT
ejpam-7063	261	18	,	,	PUNCT
ejpam-7063	261	19	newton	newton	PROPN
ejpam-7063	261	20	’s	’s	PART
ejpam-7063	261	21	method	method	PROPN
ejpam-7063	261	22	converges	converge	VERB
ejpam-7063	261	23	locally	locally	ADV
ejpam-7063	261	24	with	with	ADP
ejpam-7063	261	25	quadratic	quadratic	ADJ
ejpam-7063	261	26	rate	rate	NOUN
ejpam-7063	261	27	g.	g.	PROPN
ejpam-7063	261	28	m.	m.	PROPN
ejpam-7063	261	29	bahaa	bahaa	PROPN
ejpam-7063	261	30	,	,	PUNCT
ejpam-7063	261	31	a.	a.	NOUN
ejpam-7063	261	32	h.	h.	PROPN
ejpam-7063	261	33	qamlo	qamlo	PROPN
ejpam-7063	261	34	/	/	SYM
ejpam-7063	261	35	eur	eur	PROPN
ejpam-7063	261	36	.	.	PUNCT
ejpam-7063	262	1	j.	j.	PROPN
ejpam-7063	262	2	pure	pure	PROPN
ejpam-7063	262	3	appl	appl	PROPN
ejpam-7063	262	4	.	.	PROPN
ejpam-7063	262	5	math	math	PROPN
ejpam-7063	262	6	,	,	PUNCT
ejpam-7063	262	7	18	18	NUM
ejpam-7063	262	8	(	(	PUNCT
ejpam-7063	262	9	4	4	NUM
ejpam-7063	262	10	)	)	PUNCT
ejpam-7063	262	11	(	(	PUNCT
ejpam-7063	262	12	2025	2025	NUM
ejpam-7063	262	13	)	)	PUNCT
ejpam-7063	262	14	,	,	PUNCT
ejpam-7063	262	15	7063	7063	NUM
ejpam-7063	262	16	12	12	NUM
ejpam-7063	262	17	of	of	ADP
ejpam-7063	262	18	29	29	NUM
ejpam-7063	263	1	[	[	X
ejpam-7063	263	2	40	40	NUM
ejpam-7063	263	3	]	]	PUNCT
ejpam-7063	263	4	.	.	PUNCT
ejpam-7063	264	1	in	in	ADP
ejpam-7063	264	2	practice	practice	NOUN
ejpam-7063	264	3	,	,	PUNCT
ejpam-7063	264	4	a	a	DET
ejpam-7063	264	5	good	good	ADJ
ejpam-7063	264	6	initial	initial	ADJ
ejpam-7063	264	7	guess	guess	NOUN
ejpam-7063	264	8	(	(	PUNCT
ejpam-7063	264	9	e.g.	e.g.	ADV
ejpam-7063	264	10	,	,	PUNCT
ejpam-7063	264	11	solution	solution	NOUN
ejpam-7063	264	12	of	of	ADP
ejpam-7063	264	13	a	a	DET
ejpam-7063	264	14	linearized	linearize	VERB
ejpam-7063	264	15	problem	problem	NOUN
ejpam-7063	264	16	)	)	PUNCT
ejpam-7063	264	17	and	and	CCONJ
ejpam-7063	264	18	damping	damp	VERB
ejpam-7063	264	19	ensure	ensure	VERB
ejpam-7063	264	20	convergence	convergence	NOUN
ejpam-7063	264	21	even	even	ADV
ejpam-7063	264	22	for	for	ADP
ejpam-7063	264	23	moderately	moderately	ADV
ejpam-7063	264	24	strong	strong	ADJ
ejpam-7063	264	25	nonlinearities	nonlinearitie	NOUN
ejpam-7063	264	26	.	.	PUNCT
ejpam-7063	265	1	complexity	complexity	NOUN
ejpam-7063	265	2	.	.	PUNCT
ejpam-7063	266	1	forming	form	VERB
ejpam-7063	266	2	the	the	DET
ejpam-7063	266	3	jacobian	jacobian	NOUN
ejpam-7063	266	4	and	and	CCONJ
ejpam-7063	266	5	solving	solve	VERB
ejpam-7063	266	6	the	the	DET
ejpam-7063	266	7	2	2	NUM
ejpam-7063	266	8	m	m	NOUN
ejpam-7063	266	9	×	×	NOUN
ejpam-7063	266	10	2	2	NUM
ejpam-7063	266	11	m	m	NOUN
ejpam-7063	266	12	linear	linear	NOUN
ejpam-7063	266	13	system	system	NOUN
ejpam-7063	266	14	are	be	AUX
ejpam-7063	266	15	the	the	DET
ejpam-7063	266	16	dominant	dominant	ADJ
ejpam-7063	266	17	costs	cost	NOUN
ejpam-7063	266	18	.	.	PUNCT
ejpam-7063	267	1	a	a	DET
ejpam-7063	267	2	dense	dense	ADJ
ejpam-7063	267	3	solve	solve	NOUN
ejpam-7063	267	4	costs	cost	VERB
ejpam-7063	267	5	o((2m)3	o((2m)3	NOUN
ejpam-7063	267	6	)	)	PUNCT
ejpam-7063	267	7	,	,	PUNCT
ejpam-7063	267	8	but	but	CCONJ
ejpam-7063	267	9	:	:	PUNCT
ejpam-7063	267	10	•	•	ADP
ejpam-7063	267	11	operational	operational	ADJ
ejpam-7063	267	12	matrices	matrix	NOUN
ejpam-7063	267	13	d(α	d(α	PROPN
ejpam-7063	267	14	,	,	PUNCT
ejpam-7063	267	15	β	β	X
ejpam-7063	267	16	)	)	PUNCT
ejpam-7063	267	17	xy	xy	NOUN
ejpam-7063	267	18	are	be	AUX
ejpam-7063	267	19	often	often	ADV
ejpam-7063	267	20	sparse	sparse	ADJ
ejpam-7063	267	21	or	or	CCONJ
ejpam-7063	267	22	structured	structure	VERB
ejpam-7063	267	23	(	(	PUNCT
ejpam-7063	267	24	kronecker	kronecker	NOUN
ejpam-7063	267	25	structure	structure	NOUN
ejpam-7063	267	26	)	)	PUNCT
ejpam-7063	267	27	,	,	PUNCT
ejpam-7063	267	28	enabling	enable	VERB
ejpam-7063	267	29	fast	fast	ADJ
ejpam-7063	267	30	matrix	matrix	NOUN
ejpam-7063	267	31	-	-	PUNCT
ejpam-7063	267	32	vector	vector	NOUN
ejpam-7063	267	33	products	product	NOUN
ejpam-7063	267	34	.	.	PUNCT
ejpam-7063	268	1	•	•	NUM
ejpam-7063	268	2	exploiting	exploit	VERB
ejpam-7063	268	3	block	block	NOUN
ejpam-7063	268	4	structure	structure	NOUN
ejpam-7063	268	5	and	and	CCONJ
ejpam-7063	268	6	sparsity	sparsity	NOUN
ejpam-7063	268	7	,	,	PUNCT
ejpam-7063	268	8	a	a	DET
ejpam-7063	268	9	block	block	NOUN
ejpam-7063	268	10	-	-	PUNCT
ejpam-7063	268	11	lu	lu	NOUN
ejpam-7063	268	12	or	or	CCONJ
ejpam-7063	268	13	schur	schur	PROPN
ejpam-7063	268	14	complement	complement	PROPN
ejpam-7063	268	15	approach	approach	NOUN
ejpam-7063	268	16	can	can	AUX
ejpam-7063	268	17	reduce	reduce	VERB
ejpam-7063	268	18	cost	cost	NOUN
ejpam-7063	268	19	significantly	significantly	ADV
ejpam-7063	268	20	;	;	PUNCT
ejpam-7063	268	21	iterative	iterative	ADJ
ejpam-7063	268	22	krylov	krylov	NOUN
ejpam-7063	268	23	solvers	solver	NOUN
ejpam-7063	268	24	with	with	ADP
ejpam-7063	268	25	preconditioning	preconditioning	NOUN
ejpam-7063	268	26	are	be	AUX
ejpam-7063	268	27	also	also	ADV
ejpam-7063	268	28	effective	effective	ADJ
ejpam-7063	268	29	for	for	ADP
ejpam-7063	268	30	large	large	ADJ
ejpam-7063	268	31	m	m	NOUN
ejpam-7063	268	32	.	.	PUNCT
ejpam-7063	269	1	5.8	5.8	NUM
ejpam-7063	269	2	.	.	PUNCT
ejpam-7063	270	1	implementation	implementation	NOUN
ejpam-7063	270	2	notes	note	NOUN
ejpam-7063	270	3	•	•	NOUN
ejpam-7063	270	4	use	use	VERB
ejpam-7063	270	5	sparse	sparse	ADJ
ejpam-7063	270	6	matrix	matrix	NOUN
ejpam-7063	270	7	storage	storage	NOUN
ejpam-7063	270	8	and	and	CCONJ
ejpam-7063	270	9	solvers	solver	NOUN
ejpam-7063	270	10	(	(	PUNCT
ejpam-7063	270	11	matlab	matlab	PROPN
ejpam-7063	270	12	‘	'	PUNCT
ejpam-7063	270	13	sparse	sparse	ADJ
ejpam-7063	270	14	‘	'	PUNCT
ejpam-7063	270	15	+	+	ADJ
ejpam-7063	270	16	‘	'	PUNCT
ejpam-7063	270	17	backslash	backslash	NOUN
ejpam-7063	270	18	‘	'	PUNCT
ejpam-7063	270	19	or	or	CCONJ
ejpam-7063	270	20	scipy	scipy	PROPN
ejpam-7063	270	21	‘	'	PUNCT
ejpam-7063	270	22	sparse.linalg	sparse.linalg	PROPN
ejpam-7063	270	23	‘	'	PUNCT
ejpam-7063	270	24	)	)	PUNCT
ejpam-7063	270	25	to	to	PART
ejpam-7063	270	26	handle	handle	VERB
ejpam-7063	270	27	large	large	ADJ
ejpam-7063	270	28	n	n	NOUN
ejpam-7063	270	29	.	.	PUNCT
ejpam-7063	271	1	•	•	ADV
ejpam-7063	271	2	precompute	precompute	VERB
ejpam-7063	271	3	fvfw	fvfw	ADJ
ejpam-7063	271	4	basis	basis	NOUN
ejpam-7063	271	5	evaluations	evaluation	NOUN
ejpam-7063	271	6	and	and	CCONJ
ejpam-7063	271	7	operational	operational	ADJ
ejpam-7063	271	8	matrices	matrix	NOUN
ejpam-7063	271	9	once	once	ADV
ejpam-7063	271	10	;	;	PUNCT
ejpam-7063	271	11	reuse	reuse	VERB
ejpam-7063	271	12	them	they	PRON
ejpam-7063	271	13	across	across	ADP
ejpam-7063	271	14	iterations	iteration	NOUN
ejpam-7063	271	15	.	.	PUNCT
ejpam-7063	272	1	•	•	NUM
ejpam-7063	272	2	for	for	ADP
ejpam-7063	272	3	visualization	visualization	NOUN
ejpam-7063	272	4	and	and	CCONJ
ejpam-7063	272	5	error	error	NOUN
ejpam-7063	272	6	computation	computation	NOUN
ejpam-7063	272	7	,	,	PUNCT
ejpam-7063	272	8	evaluate	evaluate	VERB
ejpam-7063	272	9	reconstructed	reconstructed	ADJ
ejpam-7063	272	10	fields	field	NOUN
ejpam-7063	272	11	z(x	z(x	NUM
ejpam-7063	272	12	,	,	PUNCT
ejpam-7063	272	13	y	y	NOUN
ejpam-7063	272	14	)	)	PUNCT
ejpam-7063	272	15	,	,	PUNCT
ejpam-7063	272	16	p(x	p(x	PROPN
ejpam-7063	272	17	,	,	PUNCT
ejpam-7063	272	18	y	y	PROPN
ejpam-7063	272	19	)	)	PUNCT
ejpam-7063	272	20	,	,	PUNCT
ejpam-7063	272	21	u(x	u(x	PROPN
ejpam-7063	272	22	,	,	PUNCT
ejpam-7063	272	23	y	y	NOUN
ejpam-7063	272	24	)	)	PUNCT
ejpam-7063	272	25	on	on	ADP
ejpam-7063	272	26	a	a	DET
ejpam-7063	272	27	fine	fine	ADJ
ejpam-7063	272	28	evaluation	evaluation	NOUN
ejpam-7063	272	29	grid	grid	NOUN
ejpam-7063	272	30	and	and	CCONJ
ejpam-7063	272	31	compute	compute	NOUN
ejpam-7063	272	32	l2	l2	NOUN
ejpam-7063	272	33	and	and	CCONJ
ejpam-7063	272	34	l∞	l∞	NOUN
ejpam-7063	272	35	errors	error	NOUN
ejpam-7063	272	36	against	against	ADP
ejpam-7063	272	37	analytical	analytical	ADJ
ejpam-7063	272	38	or	or	CCONJ
ejpam-7063	272	39	reference	reference	NOUN
ejpam-7063	272	40	solutions	solution	NOUN
ejpam-7063	272	41	.	.	PUNCT
ejpam-7063	273	1	•	•	NUM
ejpam-7063	273	2	compare	compare	VERB
ejpam-7063	273	3	fvfw	fvfw	ADJ
ejpam-7063	273	4	results	result	NOUN
ejpam-7063	273	5	with	with	ADP
ejpam-7063	273	6	alternative	alternative	ADJ
ejpam-7063	273	7	discretizations	discretization	NOUN
ejpam-7063	273	8	(	(	PUNCT
ejpam-7063	273	9	legendre	legendre	PROPN
ejpam-7063	273	10	,	,	PUNCT
ejpam-7063	273	11	chebyshev	chebyshev	PROPN
ejpam-7063	273	12	,	,	PUNCT
ejpam-7063	273	13	or	or	CCONJ
ejpam-7063	273	14	finite	finite	ADJ
ejpam-7063	273	15	-	-	NOUN
ejpam-7063	273	16	difference	difference	NOUN
ejpam-7063	273	17	)	)	PUNCT
ejpam-7063	273	18	to	to	PART
ejpam-7063	273	19	demonstrate	demonstrate	VERB
ejpam-7063	273	20	accuracy	accuracy	NOUN
ejpam-7063	273	21	vs.	vs.	ADP
ejpam-7063	273	22	cost	cost	NOUN
ejpam-7063	273	23	trade	trade	NOUN
ejpam-7063	273	24	-	-	PUNCT
ejpam-7063	273	25	offs	off	NOUN
ejpam-7063	273	26	[	[	X
ejpam-7063	273	27	21–23	21–23	X
ejpam-7063	273	28	]	]	X
ejpam-7063	273	29	.	.	PUNCT
ejpam-7063	274	1	5.9	5.9	NUM
ejpam-7063	274	2	.	.	PUNCT
ejpam-7063	275	1	remarks	remark	NOUN
ejpam-7063	275	2	on	on	ADP
ejpam-7063	275	3	extensions	extension	NOUN
ejpam-7063	275	4	the	the	DET
ejpam-7063	275	5	same	same	ADJ
ejpam-7063	275	6	scheme	scheme	NOUN
ejpam-7063	275	7	extends	extend	VERB
ejpam-7063	275	8	to	to	PART
ejpam-7063	275	9	:	:	PUNCT
ejpam-7063	275	10	•	•	NUM
ejpam-7063	275	11	time	time	NOUN
ejpam-7063	275	12	-	-	PUNCT
ejpam-7063	275	13	dependent	dependent	ADJ
ejpam-7063	275	14	focps	focp	NOUN
ejpam-7063	275	15	via	via	ADP
ejpam-7063	275	16	a	a	DET
ejpam-7063	275	17	tensor	tensor	NOUN
ejpam-7063	275	18	product	product	NOUN
ejpam-7063	275	19	fvfw	fvfw	ADJ
ejpam-7063	275	20	basis	basis	NOUN
ejpam-7063	275	21	in	in	ADP
ejpam-7063	275	22	space	space	NOUN
ejpam-7063	275	23	and	and	CCONJ
ejpam-7063	275	24	time	time	NOUN
ejpam-7063	275	25	,	,	PUNCT
ejpam-7063	275	26	•	•	NUM
ejpam-7063	275	27	control	control	NOUN
ejpam-7063	275	28	constraints	constraint	NOUN
ejpam-7063	275	29	enforced	enforce	VERB
ejpam-7063	275	30	via	via	ADP
ejpam-7063	275	31	projection	projection	NOUN
ejpam-7063	275	32	or	or	CCONJ
ejpam-7063	275	33	active	active	ADJ
ejpam-7063	275	34	-	-	PUNCT
ejpam-7063	275	35	set	set	VERB
ejpam-7063	275	36	methods	method	NOUN
ejpam-7063	275	37	,	,	PUNCT
ejpam-7063	275	38	•	•	NOUN
ejpam-7063	275	39	stochastic	stochastic	ADJ
ejpam-7063	275	40	or	or	CCONJ
ejpam-7063	275	41	robust	robust	ADJ
ejpam-7063	275	42	formulations	formulation	NOUN
ejpam-7063	275	43	by	by	ADP
ejpam-7063	275	44	embedding	embed	VERB
ejpam-7063	275	45	uncertainty	uncertainty	NOUN
ejpam-7063	275	46	quantification	quantification	NOUN
ejpam-7063	275	47	steps	step	NOUN
ejpam-7063	275	48	inside	inside	ADP
ejpam-7063	275	49	the	the	DET
ejpam-7063	275	50	newton	newton	PROPN
ejpam-7063	275	51	iterations	iteration	NOUN
ejpam-7063	275	52	.	.	PUNCT
ejpam-7063	276	1	6	6	NUM
ejpam-7063	276	2	.	.	X
ejpam-7063	276	3	numerical	numerical	ADJ
ejpam-7063	276	4	examples	example	NOUN
ejpam-7063	276	5	we	we	PRON
ejpam-7063	276	6	consider	consider	VERB
ejpam-7063	276	7	the	the	DET
ejpam-7063	276	8	following	follow	VERB
ejpam-7063	276	9	two	two	NUM
ejpam-7063	276	10	-	-	PUNCT
ejpam-7063	276	11	dimensional	dimensional	ADJ
ejpam-7063	276	12	time	time	NOUN
ejpam-7063	276	13	-	-	PUNCT
ejpam-7063	276	14	space	space	NOUN
ejpam-7063	276	15	fractional	fractional	ADJ
ejpam-7063	276	16	optimal	optimal	ADJ
ejpam-7063	276	17	control	control	NOUN
ejpam-7063	276	18	problems	problem	NOUN
ejpam-7063	276	19	:	:	PUNCT
ejpam-7063	276	20	objective	objective	ADJ
ejpam-7063	276	21	:	:	PUNCT
ejpam-7063	276	22	min	min	PROPN
ejpam-7063	276	23	u	u	NOUN
ejpam-7063	276	24	j	j	PROPN
ejpam-7063	277	1	[	[	X
ejpam-7063	277	2	u	u	X
ejpam-7063	277	3	]	]	X
ejpam-7063	277	4	=	=	PUNCT
ejpam-7063	278	1	∫∫	∫∫	ADV
ejpam-7063	279	1	[	[	X
ejpam-7063	279	2	0,1]2	0,1]2	NUM
ejpam-7063	279	3	[	[	PUNCT
ejpam-7063	279	4	z2(x	z2(x	NUM
ejpam-7063	279	5	,	,	PUNCT
ejpam-7063	279	6	y	y	PROPN
ejpam-7063	279	7	)	)	PUNCT
ejpam-7063	279	8	+	+	CCONJ
ejpam-7063	279	9	u2(x	u2(x	PROPN
ejpam-7063	279	10	,	,	PUNCT
ejpam-7063	279	11	y	y	PROPN
ejpam-7063	279	12	)	)	PUNCT
ejpam-7063	279	13	]	]	PUNCT
ejpam-7063	279	14	dx	dx	PROPN
ejpam-7063	279	15	dy	dy	NOUN
ejpam-7063	279	16	(	(	PUNCT
ejpam-7063	279	17	6.1	6.1	NUM
ejpam-7063	279	18	)	)	PUNCT
ejpam-7063	279	19	g.	g.	NOUN
ejpam-7063	279	20	m.	m.	NOUN
ejpam-7063	279	21	bahaa	bahaa	PROPN
ejpam-7063	279	22	,	,	PUNCT
ejpam-7063	279	23	a.	a.	NOUN
ejpam-7063	279	24	h.	h.	PROPN
ejpam-7063	279	25	qamlo	qamlo	PROPN
ejpam-7063	279	26	/	/	SYM
ejpam-7063	279	27	eur	eur	PROPN
ejpam-7063	279	28	.	.	PUNCT
ejpam-7063	280	1	j.	j.	PROPN
ejpam-7063	280	2	pure	pure	PROPN
ejpam-7063	280	3	appl	appl	PROPN
ejpam-7063	280	4	.	.	PROPN
ejpam-7063	280	5	math	math	PROPN
ejpam-7063	280	6	,	,	PUNCT
ejpam-7063	280	7	18	18	NUM
ejpam-7063	280	8	(	(	PUNCT
ejpam-7063	280	9	4	4	NUM
ejpam-7063	280	10	)	)	PUNCT
ejpam-7063	280	11	(	(	PUNCT
ejpam-7063	280	12	2025	2025	NUM
ejpam-7063	280	13	)	)	PUNCT
ejpam-7063	280	14	,	,	PUNCT
ejpam-7063	280	15	7063	7063	NUM
ejpam-7063	280	16	13	13	NUM
ejpam-7063	280	17	of	of	ADP
ejpam-7063	280	18	29	29	NUM
ejpam-7063	280	19	subject	subject	NOUN
ejpam-7063	280	20	to	to	ADP
ejpam-7063	280	21	the	the	DET
ejpam-7063	280	22	state	state	NOUN
ejpam-7063	280	23	equation	equation	NOUN
ejpam-7063	280	24	:	:	PUNCT
ejpam-7063	280	25	d0.9	d0.9	PROPN
ejpam-7063	280	26	x	x	SYM
ejpam-7063	280	27	d0.9	d0.9	PROPN
ejpam-7063	280	28	y	y	PROPN
ejpam-7063	280	29	z(x	z(x	PROPN
ejpam-7063	280	30	,	,	PUNCT
ejpam-7063	280	31	y	y	NOUN
ejpam-7063	280	32	)	)	PUNCT
ejpam-7063	280	33	=	=	SYM
ejpam-7063	281	1	−z(x	−z(x	ADJ
ejpam-7063	281	2	,	,	PUNCT
ejpam-7063	281	3	y	y	NOUN
ejpam-7063	281	4	)	)	PUNCT
ejpam-7063	282	1	+	+	CCONJ
ejpam-7063	282	2	u(x	u(x	PROPN
ejpam-7063	282	3	,	,	PUNCT
ejpam-7063	282	4	y	y	NOUN
ejpam-7063	282	5	)	)	PUNCT
ejpam-7063	282	6	,	,	PUNCT
ejpam-7063	282	7	(	(	PUNCT
ejpam-7063	282	8	x	x	X
ejpam-7063	282	9	,	,	PUNCT
ejpam-7063	282	10	y	y	NOUN
ejpam-7063	282	11	)	)	PUNCT
ejpam-7063	282	12	∈	∈	PROPN
ejpam-7063	283	1	[	[	X
ejpam-7063	283	2	0	0	NUM
ejpam-7063	283	3	,	,	PUNCT
ejpam-7063	283	4	1]2	1]2	NUM
ejpam-7063	283	5	(	(	PUNCT
ejpam-7063	283	6	6.2	6.2	NUM
ejpam-7063	283	7	)	)	PUNCT
ejpam-7063	283	8	with	with	ADP
ejpam-7063	283	9	boundary	boundary	ADJ
ejpam-7063	283	10	conditions	condition	NOUN
ejpam-7063	283	11	:	:	PUNCT
ejpam-7063	283	12	z(x	z(x	NUM
ejpam-7063	283	13	,	,	PUNCT
ejpam-7063	283	14	0	0	NUM
ejpam-7063	283	15	)	)	PUNCT
ejpam-7063	283	16	=	=	SYM
ejpam-7063	283	17	0	0	NUM
ejpam-7063	283	18	,	,	PUNCT
ejpam-7063	283	19	z(0	z(0	AUX
ejpam-7063	283	20	,	,	PUNCT
ejpam-7063	283	21	y	y	PROPN
ejpam-7063	283	22	)	)	PUNCT
ejpam-7063	283	23	=	=	SYM
ejpam-7063	283	24	0	0	NUM
ejpam-7063	283	25	(	(	PUNCT
ejpam-7063	283	26	6.3	6.3	NUM
ejpam-7063	283	27	)	)	PUNCT
ejpam-7063	283	28	here	here	ADV
ejpam-7063	283	29	,	,	PUNCT
ejpam-7063	283	30	d0.9	d0.9	PROPN
ejpam-7063	283	31	x	x	PUNCT
ejpam-7063	283	32	and	and	CCONJ
ejpam-7063	283	33	d0.9	d0.9	PROPN
ejpam-7063	283	34	y	y	PROPN
ejpam-7063	283	35	denote	denote	VERB
ejpam-7063	283	36	the	the	DET
ejpam-7063	283	37	caputo	caputo	PROPN
ejpam-7063	283	38	fractional	fractional	ADJ
ejpam-7063	283	39	derivatives	derivative	NOUN
ejpam-7063	283	40	of	of	ADP
ejpam-7063	283	41	order	order	NOUN
ejpam-7063	283	42	0.9	0.9	NUM
ejpam-7063	283	43	.	.	PUNCT
ejpam-7063	284	1	derivation	derivation	NOUN
ejpam-7063	284	2	of	of	ADP
ejpam-7063	284	3	the	the	DET
ejpam-7063	284	4	optimality	optimality	NOUN
ejpam-7063	284	5	system	system	NOUN
ejpam-7063	284	6	we	we	PRON
ejpam-7063	284	7	introduce	introduce	VERB
ejpam-7063	284	8	an	an	DET
ejpam-7063	284	9	adjoint	adjoint	NOUN
ejpam-7063	284	10	function	function	NOUN
ejpam-7063	284	11	p(x	p(x	PROPN
ejpam-7063	284	12	,	,	PUNCT
ejpam-7063	284	13	y	y	PROPN
ejpam-7063	284	14	)	)	PUNCT
ejpam-7063	284	15	and	and	CCONJ
ejpam-7063	284	16	define	define	VERB
ejpam-7063	284	17	the	the	DET
ejpam-7063	284	18	lagrangian	lagrangian	ADJ
ejpam-7063	284	19	functional	functional	NOUN
ejpam-7063	284	20	as	as	ADP
ejpam-7063	284	21	:	:	PUNCT
ejpam-7063	284	22	l	l	X
ejpam-7063	284	23	=	=	PUNCT
ejpam-7063	285	1	∫∫	∫∫	ADV
ejpam-7063	285	2	[	[	X
ejpam-7063	285	3	0,1]2	0,1]2	NUM
ejpam-7063	285	4	[	[	PUNCT
ejpam-7063	285	5	z2(x	z2(x	NUM
ejpam-7063	285	6	,	,	PUNCT
ejpam-7063	285	7	y	y	PROPN
ejpam-7063	285	8	)	)	PUNCT
ejpam-7063	285	9	+	+	CCONJ
ejpam-7063	285	10	u2(x	u2(x	PROPN
ejpam-7063	285	11	,	,	PUNCT
ejpam-7063	285	12	y	y	NOUN
ejpam-7063	285	13	)	)	PUNCT
ejpam-7063	285	14	+	+	CCONJ
ejpam-7063	285	15	p(x	p(x	PROPN
ejpam-7063	285	16	,	,	PUNCT
ejpam-7063	285	17	y	y	NOUN
ejpam-7063	285	18	)	)	PUNCT
ejpam-7063	285	19	(	(	PUNCT
ejpam-7063	285	20	d0.9	d0.9	PROPN
ejpam-7063	285	21	x	x	SYM
ejpam-7063	285	22	d0.9	d0.9	PROPN
ejpam-7063	285	23	y	y	PROPN
ejpam-7063	285	24	z(x	z(x	PROPN
ejpam-7063	285	25	,	,	PUNCT
ejpam-7063	285	26	y	y	NOUN
ejpam-7063	285	27	)	)	PUNCT
ejpam-7063	285	28	+	+	CCONJ
ejpam-7063	285	29	z(x	z(x	NUM
ejpam-7063	285	30	,	,	PUNCT
ejpam-7063	285	31	y)−	y)−	PROPN
ejpam-7063	285	32	u(x	u(x	NOUN
ejpam-7063	285	33	,	,	PUNCT
ejpam-7063	285	34	y	y	NOUN
ejpam-7063	285	35	)	)	PUNCT
ejpam-7063	285	36	)	)	PUNCT
ejpam-7063	285	37	]	]	PUNCT
ejpam-7063	285	38	dxdy	dxdy	PROPN
ejpam-7063	285	39	(	(	PUNCT
ejpam-7063	285	40	6.4	6.4	NUM
ejpam-7063	285	41	)	)	PUNCT
ejpam-7063	285	42	1	1	NUM
ejpam-7063	285	43	.	.	X
ejpam-7063	285	44	variation	variation	NOUN
ejpam-7063	285	45	with	with	ADP
ejpam-7063	285	46	respect	respect	NOUN
ejpam-7063	285	47	to	to	ADP
ejpam-7063	285	48	p(x	p(x	PROPN
ejpam-7063	285	49	,	,	PUNCT
ejpam-7063	285	50	y	y	PROPN
ejpam-7063	285	51	)	)	PUNCT
ejpam-7063	285	52	gives	give	VERB
ejpam-7063	285	53	the	the	DET
ejpam-7063	285	54	state	state	NOUN
ejpam-7063	285	55	equation	equation	NOUN
ejpam-7063	285	56	:	:	PUNCT
ejpam-7063	285	57	d0.9	d0.9	PROPN
ejpam-7063	285	58	x	x	SYM
ejpam-7063	285	59	d0.9	d0.9	PROPN
ejpam-7063	285	60	y	y	PROPN
ejpam-7063	285	61	z(x	z(x	PROPN
ejpam-7063	285	62	,	,	PUNCT
ejpam-7063	285	63	y	y	NOUN
ejpam-7063	285	64	)	)	PUNCT
ejpam-7063	285	65	=	=	SYM
ejpam-7063	286	1	−z(x	−z(x	ADJ
ejpam-7063	286	2	,	,	PUNCT
ejpam-7063	286	3	y	y	NOUN
ejpam-7063	286	4	)	)	PUNCT
ejpam-7063	287	1	+	+	CCONJ
ejpam-7063	287	2	u(x	u(x	PROPN
ejpam-7063	287	3	,	,	PUNCT
ejpam-7063	287	4	y	y	NOUN
ejpam-7063	287	5	)	)	PUNCT
ejpam-7063	287	6	(	(	PUNCT
ejpam-7063	287	7	6.5	6.5	NUM
ejpam-7063	287	8	)	)	PUNCT
ejpam-7063	287	9	2	2	NUM
ejpam-7063	287	10	.	.	X
ejpam-7063	287	11	variation	variation	NOUN
ejpam-7063	287	12	with	with	ADP
ejpam-7063	287	13	respect	respect	NOUN
ejpam-7063	287	14	to	to	ADP
ejpam-7063	287	15	z(x	z(x	NUM
ejpam-7063	287	16	,	,	PUNCT
ejpam-7063	287	17	y	y	PROPN
ejpam-7063	287	18	)	)	PUNCT
ejpam-7063	287	19	δl	δl	PROPN
ejpam-7063	287	20	δz	δz	PROPN
ejpam-7063	287	21	=	=	SYM
ejpam-7063	287	22	2z(x	2z(x	PROPN
ejpam-7063	287	23	,	,	PUNCT
ejpam-7063	287	24	y	y	NOUN
ejpam-7063	287	25	)	)	PUNCT
ejpam-7063	287	26	+	+	CCONJ
ejpam-7063	287	27	p(x	p(x	PROPN
ejpam-7063	287	28	,	,	PUNCT
ejpam-7063	287	29	y)−d0.9	y)−d0.9	PROPN
ejpam-7063	287	30	x	x	SYM
ejpam-7063	287	31	d0.9	d0.9	PROPN
ejpam-7063	287	32	y	y	PROPN
ejpam-7063	287	33	p(x	p(x	PROPN
ejpam-7063	287	34	,	,	PUNCT
ejpam-7063	287	35	y	y	NOUN
ejpam-7063	287	36	)	)	PUNCT
ejpam-7063	287	37	=	=	SYM
ejpam-7063	287	38	0	0	NUM
ejpam-7063	287	39	(	(	PUNCT
ejpam-7063	287	40	6.6	6.6	NUM
ejpam-7063	287	41	)	)	PUNCT
ejpam-7063	287	42	so	so	SCONJ
ejpam-7063	287	43	the	the	DET
ejpam-7063	287	44	adjoint	adjoint	NOUN
ejpam-7063	287	45	equation	equation	NOUN
ejpam-7063	287	46	becomes	become	VERB
ejpam-7063	287	47	:	:	PUNCT
ejpam-7063	287	48	d0.9	d0.9	PROPN
ejpam-7063	287	49	x	x	SYM
ejpam-7063	287	50	d0.9	d0.9	PROPN
ejpam-7063	287	51	y	y	PROPN
ejpam-7063	287	52	p(x	p(x	PROPN
ejpam-7063	287	53	,	,	PUNCT
ejpam-7063	287	54	y	y	NOUN
ejpam-7063	287	55	)	)	PUNCT
ejpam-7063	287	56	=	=	SYM
ejpam-7063	288	1	2z(x	2z(x	NUM
ejpam-7063	288	2	,	,	PUNCT
ejpam-7063	288	3	y	y	NOUN
ejpam-7063	288	4	)	)	PUNCT
ejpam-7063	288	5	+	+	CCONJ
ejpam-7063	288	6	p(x	p(x	PROPN
ejpam-7063	288	7	,	,	PUNCT
ejpam-7063	288	8	y	y	PROPN
ejpam-7063	288	9	)	)	PUNCT
ejpam-7063	288	10	(	(	PUNCT
ejpam-7063	288	11	6.7	6.7	NUM
ejpam-7063	288	12	)	)	PUNCT
ejpam-7063	288	13	with	with	ADP
ejpam-7063	288	14	terminal	terminal	ADJ
ejpam-7063	288	15	conditions	condition	NOUN
ejpam-7063	288	16	:	:	PUNCT
ejpam-7063	288	17	p(x	p(x	NOUN
ejpam-7063	288	18	,	,	PUNCT
ejpam-7063	288	19	1	1	NUM
ejpam-7063	288	20	)	)	PUNCT
ejpam-7063	288	21	=	=	SYM
ejpam-7063	288	22	0	0	NUM
ejpam-7063	288	23	,	,	PUNCT
ejpam-7063	288	24	p(1	p(1	PROPN
ejpam-7063	288	25	,	,	PUNCT
ejpam-7063	288	26	y	y	NOUN
ejpam-7063	288	27	)	)	PUNCT
ejpam-7063	288	28	=	=	SYM
ejpam-7063	288	29	0	0	NUM
ejpam-7063	288	30	(	(	PUNCT
ejpam-7063	288	31	6.8	6.8	NUM
ejpam-7063	288	32	)	)	PUNCT
ejpam-7063	288	33	3	3	NUM
ejpam-7063	288	34	.	.	X
ejpam-7063	288	35	variation	variation	NOUN
ejpam-7063	288	36	with	with	ADP
ejpam-7063	288	37	respect	respect	NOUN
ejpam-7063	288	38	to	to	ADP
ejpam-7063	288	39	u(x	u(x	NOUN
ejpam-7063	288	40	,	,	PUNCT
ejpam-7063	288	41	y	y	NOUN
ejpam-7063	288	42	)	)	PUNCT
ejpam-7063	288	43	δl	δl	PROPN
ejpam-7063	288	44	δu	δu	ADP
ejpam-7063	288	45	=	=	SYM
ejpam-7063	288	46	2u(x	2u(x	NOUN
ejpam-7063	288	47	,	,	PUNCT
ejpam-7063	288	48	y)−	y)−	PROPN
ejpam-7063	288	49	p(x	p(x	PROPN
ejpam-7063	288	50	,	,	PUNCT
ejpam-7063	288	51	y	y	NOUN
ejpam-7063	288	52	)	)	PUNCT
ejpam-7063	288	53	=	=	SYM
ejpam-7063	289	1	0⇒	0⇒	PROPN
ejpam-7063	289	2	u(x	u(x	NOUN
ejpam-7063	289	3	,	,	PUNCT
ejpam-7063	289	4	y	y	NOUN
ejpam-7063	289	5	)	)	PUNCT
ejpam-7063	289	6	=	=	SYM
ejpam-7063	289	7	1	1	NUM
ejpam-7063	289	8	2	2	NUM
ejpam-7063	289	9	p(x	p(x	NOUN
ejpam-7063	289	10	,	,	PUNCT
ejpam-7063	289	11	y	y	NOUN
ejpam-7063	289	12	)	)	PUNCT
ejpam-7063	289	13	(	(	PUNCT
ejpam-7063	289	14	6.9	6.9	NUM
ejpam-7063	289	15	)	)	PUNCT
ejpam-7063	289	16	g.	g.	NOUN
ejpam-7063	289	17	m.	m.	NOUN
ejpam-7063	289	18	bahaa	bahaa	PROPN
ejpam-7063	289	19	,	,	PUNCT
ejpam-7063	289	20	a.	a.	NOUN
ejpam-7063	289	21	h.	h.	PROPN
ejpam-7063	289	22	qamlo	qamlo	PROPN
ejpam-7063	289	23	/	/	SYM
ejpam-7063	289	24	eur	eur	PROPN
ejpam-7063	289	25	.	.	PUNCT
ejpam-7063	290	1	j.	j.	PROPN
ejpam-7063	290	2	pure	pure	PROPN
ejpam-7063	290	3	appl	appl	PROPN
ejpam-7063	290	4	.	.	PROPN
ejpam-7063	290	5	math	math	PROPN
ejpam-7063	290	6	,	,	PUNCT
ejpam-7063	290	7	18	18	NUM
ejpam-7063	290	8	(	(	PUNCT
ejpam-7063	290	9	4	4	NUM
ejpam-7063	290	10	)	)	PUNCT
ejpam-7063	290	11	(	(	PUNCT
ejpam-7063	290	12	2025	2025	NUM
ejpam-7063	290	13	)	)	PUNCT
ejpam-7063	290	14	,	,	PUNCT
ejpam-7063	290	15	7063	7063	NUM
ejpam-7063	290	16	14	14	NUM
ejpam-7063	290	17	of	of	ADP
ejpam-7063	290	18	29	29	NUM
ejpam-7063	290	19	optimality	optimality	NOUN
ejpam-7063	290	20	system	system	NOUN
ejpam-7063	290	21	summary	summary	NOUN
ejpam-7063	290	22	•	•	NOUN
ejpam-7063	290	23	state	state	NOUN
ejpam-7063	290	24	equation	equation	NOUN
ejpam-7063	290	25	:	:	PUNCT
ejpam-7063	290	26	d0.9	d0.9	PROPN
ejpam-7063	290	27	x	x	SYM
ejpam-7063	290	28	d0.9	d0.9	PROPN
ejpam-7063	290	29	y	y	PROPN
ejpam-7063	290	30	z(x	z(x	PROPN
ejpam-7063	290	31	,	,	PUNCT
ejpam-7063	290	32	y	y	NOUN
ejpam-7063	290	33	)	)	PUNCT
ejpam-7063	290	34	=	=	SYM
ejpam-7063	291	1	−z(x	−z(x	ADJ
ejpam-7063	291	2	,	,	PUNCT
ejpam-7063	291	3	y	y	NOUN
ejpam-7063	291	4	)	)	PUNCT
ejpam-7063	292	1	+	+	CCONJ
ejpam-7063	292	2	u(x	u(x	PROPN
ejpam-7063	292	3	,	,	PUNCT
ejpam-7063	292	4	y	y	NOUN
ejpam-7063	292	5	)	)	PUNCT
ejpam-7063	292	6	•	•	NUM
ejpam-7063	292	7	adjoint	adjoint	NOUN
ejpam-7063	292	8	equation	equation	NOUN
ejpam-7063	292	9	:	:	PUNCT
ejpam-7063	292	10	d0.9	d0.9	PROPN
ejpam-7063	292	11	x	x	SYM
ejpam-7063	292	12	d0.9	d0.9	PROPN
ejpam-7063	292	13	y	y	PROPN
ejpam-7063	292	14	p(x	p(x	PROPN
ejpam-7063	292	15	,	,	PUNCT
ejpam-7063	292	16	y	y	NOUN
ejpam-7063	292	17	)	)	PUNCT
ejpam-7063	292	18	=	=	SYM
ejpam-7063	292	19	2z(x	2z(x	NUM
ejpam-7063	292	20	,	,	PUNCT
ejpam-7063	292	21	y	y	NOUN
ejpam-7063	292	22	)	)	PUNCT
ejpam-7063	292	23	+	+	CCONJ
ejpam-7063	292	24	p(x	p(x	PROPN
ejpam-7063	292	25	,	,	PUNCT
ejpam-7063	292	26	y	y	NOUN
ejpam-7063	292	27	)	)	PUNCT
ejpam-7063	292	28	•	•	NUM
ejpam-7063	292	29	optimal	optimal	ADJ
ejpam-7063	292	30	control	control	NOUN
ejpam-7063	292	31	:	:	PUNCT
ejpam-7063	292	32	u(x	u(x	PROPN
ejpam-7063	292	33	,	,	PUNCT
ejpam-7063	292	34	y	y	NOUN
ejpam-7063	292	35	)	)	PUNCT
ejpam-7063	292	36	=	=	SYM
ejpam-7063	292	37	1	1	NUM
ejpam-7063	292	38	2	2	NUM
ejpam-7063	292	39	p(x	p(x	NOUN
ejpam-7063	292	40	,	,	PUNCT
ejpam-7063	292	41	y	y	NOUN
ejpam-7063	292	42	)	)	PUNCT
ejpam-7063	292	43	•	•	NOUN
ejpam-7063	292	44	boundary	boundary	ADJ
ejpam-7063	292	45	/	/	SYM
ejpam-7063	292	46	terminal	terminal	ADJ
ejpam-7063	292	47	conditions	condition	NOUN
ejpam-7063	292	48	:	:	PUNCT
ejpam-7063	292	49	z(x	z(x	NUM
ejpam-7063	292	50	,	,	PUNCT
ejpam-7063	292	51	0	0	NUM
ejpam-7063	292	52	)	)	PUNCT
ejpam-7063	292	53	=	=	PUNCT
ejpam-7063	293	1	z(0	z(0	PROPN
ejpam-7063	293	2	,	,	PUNCT
ejpam-7063	293	3	y	y	NOUN
ejpam-7063	293	4	)	)	PUNCT
ejpam-7063	293	5	=	=	SYM
ejpam-7063	293	6	0	0	NUM
ejpam-7063	293	7	,	,	PUNCT
ejpam-7063	293	8	p(x	p(x	NOUN
ejpam-7063	293	9	,	,	PUNCT
ejpam-7063	293	10	1	1	NUM
ejpam-7063	293	11	)	)	PUNCT
ejpam-7063	293	12	=	=	SYM
ejpam-7063	294	1	p(1	p(1	PROPN
ejpam-7063	294	2	,	,	PUNCT
ejpam-7063	294	3	y	y	NOUN
ejpam-7063	294	4	)	)	PUNCT
ejpam-7063	294	5	=	=	SYM
ejpam-7063	294	6	0	0	NUM
ejpam-7063	294	7	numerical	numerical	ADJ
ejpam-7063	294	8	solution	solution	NOUN
ejpam-7063	294	9	via	via	ADP
ejpam-7063	294	10	fvfw	fvfw	ADJ
ejpam-7063	294	11	we	we	PRON
ejpam-7063	294	12	approximate	approximate	VERB
ejpam-7063	294	13	:	:	PUNCT
ejpam-7063	294	14	z(x	z(x	NUM
ejpam-7063	294	15	,	,	PUNCT
ejpam-7063	294	16	y	y	PROPN
ejpam-7063	294	17	)	)	PUNCT
ejpam-7063	295	1	≈	≈	PROPN
ejpam-7063	295	2	n∑	n∑	PROPN
ejpam-7063	295	3	i=0	i=0	PROPN
ejpam-7063	295	4	n∑	n∑	PROPN
ejpam-7063	295	5	j=0	j=0	PROPN
ejpam-7063	295	6	aijψi(x)ψj(y	aijψi(x)ψj(y	PROPN
ejpam-7063	295	7	)	)	PUNCT
ejpam-7063	295	8	(	(	PUNCT
ejpam-7063	295	9	6.10	6.10	NUM
ejpam-7063	295	10	)	)	PUNCT
ejpam-7063	295	11	p(x	p(x	PROPN
ejpam-7063	295	12	,	,	PUNCT
ejpam-7063	295	13	y	y	NOUN
ejpam-7063	295	14	)	)	PUNCT
ejpam-7063	296	1	≈	≈	PROPN
ejpam-7063	296	2	n∑	n∑	PROPN
ejpam-7063	296	3	i=0	i=0	PROPN
ejpam-7063	296	4	n∑	n∑	PROPN
ejpam-7063	296	5	j=0	j=0	PROPN
ejpam-7063	296	6	bijψi(x)ψj(y	bijψi(x)ψj(y	VERB
ejpam-7063	296	7	)	)	PUNCT
ejpam-7063	296	8	(	(	PUNCT
ejpam-7063	296	9	6.11	6.11	NUM
ejpam-7063	296	10	)	)	PUNCT
ejpam-7063	296	11	where	where	SCONJ
ejpam-7063	296	12	ψi(x	ψi(x	NUM
ejpam-7063	296	13	)	)	PUNCT
ejpam-7063	296	14	are	be	AUX
ejpam-7063	296	15	the	the	DET
ejpam-7063	296	16	fractional	fractional	ADJ
ejpam-7063	296	17	vieta	vieta	PROPN
ejpam-7063	296	18	-	-	PUNCT
ejpam-7063	296	19	fibonacci	fibonacci	NOUN
ejpam-7063	296	20	wavelet	wavelet	NOUN
ejpam-7063	296	21	basis	basis	NOUN
ejpam-7063	296	22	functions	function	NOUN
ejpam-7063	296	23	.	.	PUNCT
ejpam-7063	297	1	applying	apply	VERB
ejpam-7063	297	2	operational	operational	ADJ
ejpam-7063	297	3	matrices	matrix	NOUN
ejpam-7063	297	4	of	of	ADP
ejpam-7063	297	5	fractional	fractional	ADJ
ejpam-7063	297	6	derivatives	derivative	NOUN
ejpam-7063	297	7	:	:	PUNCT
ejpam-7063	297	8	d0.9	d0.9	PROPN
ejpam-7063	297	9	x	x	SYM
ejpam-7063	297	10	ψ(x	ψ(x	PROPN
ejpam-7063	297	11	)	)	PUNCT
ejpam-7063	298	1	≈	≈	PROPN
ejpam-7063	298	2	d(0.9	d(0.9	PROPN
ejpam-7063	298	3	)	)	PUNCT
ejpam-7063	298	4	x	x	SYM
ejpam-7063	298	5	ψ(x	ψ(x	NOUN
ejpam-7063	298	6	)	)	PUNCT
ejpam-7063	298	7	,	,	PUNCT
ejpam-7063	298	8	d0.9	d0.9	PROPN
ejpam-7063	298	9	y	y	PROPN
ejpam-7063	298	10	ψ(y	ψ(y	PROPN
ejpam-7063	298	11	)	)	PUNCT
ejpam-7063	299	1	≈	≈	PROPN
ejpam-7063	299	2	d(0.9	d(0.9	PROPN
ejpam-7063	299	3	)	)	PUNCT
ejpam-7063	299	4	y	y	PROPN
ejpam-7063	299	5	ψ(y	ψ(y	PROPN
ejpam-7063	299	6	)	)	PUNCT
ejpam-7063	299	7	the	the	DET
ejpam-7063	299	8	2d	2d	PROPN
ejpam-7063	299	9	derivative	derivative	NOUN
ejpam-7063	299	10	:	:	PUNCT
ejpam-7063	299	11	d0.9	d0.9	PROPN
ejpam-7063	299	12	x	x	SYM
ejpam-7063	299	13	d0.9	d0.9	PROPN
ejpam-7063	299	14	y	y	PROPN
ejpam-7063	299	15	z(x	z(x	PROPN
ejpam-7063	299	16	,	,	PUNCT
ejpam-7063	299	17	y	y	PROPN
ejpam-7063	299	18	)	)	PUNCT
ejpam-7063	300	1	≈	≈	PROPN
ejpam-7063	300	2	at	at	ADP
ejpam-7063	300	3	(	(	PUNCT
ejpam-7063	300	4	d(0.9	d(0.9	PROPN
ejpam-7063	300	5	)	)	PUNCT
ejpam-7063	300	6	x	x	PUNCT
ejpam-7063	300	7	⊗d(0.9	⊗d(0.9	ADJ
ejpam-7063	300	8	)	)	PUNCT
ejpam-7063	300	9	y	y	PROPN
ejpam-7063	300	10	)	)	PUNCT
ejpam-7063	300	11	ψ(x	ψ(x	PROPN
ejpam-7063	300	12	,	,	PUNCT
ejpam-7063	300	13	y	y	NOUN
ejpam-7063	300	14	)	)	PUNCT
ejpam-7063	300	15	substitute	substitute	NOUN
ejpam-7063	300	16	into	into	ADP
ejpam-7063	300	17	the	the	DET
ejpam-7063	300	18	state	state	NOUN
ejpam-7063	300	19	and	and	CCONJ
ejpam-7063	300	20	adjoint	adjoint	NOUN
ejpam-7063	300	21	equations	equation	NOUN
ejpam-7063	300	22	and	and	CCONJ
ejpam-7063	300	23	apply	apply	VERB
ejpam-7063	300	24	at	at	ADP
ejpam-7063	300	25	collocation	collocation	NOUN
ejpam-7063	300	26	points	point	NOUN
ejpam-7063	300	27	(	(	PUNCT
ejpam-7063	300	28	xk	xk	PROPN
ejpam-7063	300	29	,	,	PUNCT
ejpam-7063	300	30	yk	yk	PROPN
ejpam-7063	300	31	)	)	PUNCT
ejpam-7063	300	32	,	,	PUNCT
ejpam-7063	300	33	resulting	result	VERB
ejpam-7063	300	34	in	in	ADP
ejpam-7063	300	35	a	a	DET
ejpam-7063	300	36	system	system	NOUN
ejpam-7063	300	37	of	of	ADP
ejpam-7063	300	38	algebraic	algebraic	ADJ
ejpam-7063	300	39	equations	equation	NOUN
ejpam-7063	300	40	.	.	PUNCT
ejpam-7063	301	1	discrete	discrete	ADJ
ejpam-7063	301	2	system	system	NOUN
ejpam-7063	301	3	from	from	ADP
ejpam-7063	301	4	the	the	DET
ejpam-7063	301	5	optimality	optimality	NOUN
ejpam-7063	301	6	system	system	NOUN
ejpam-7063	301	7	:	:	PUNCT
ejpam-7063	301	8	d(0.9	d(0.9	PROPN
ejpam-7063	301	9	)	)	PUNCT
ejpam-7063	301	10	xy	xy	PROPN
ejpam-7063	301	11	z	z	NOUN
ejpam-7063	302	1	=	=	PUNCT
ejpam-7063	302	2	−z+u	−z+u	NOUN
ejpam-7063	302	3	(	(	PUNCT
ejpam-7063	302	4	6.12	6.12	NUM
ejpam-7063	302	5	)	)	PUNCT
ejpam-7063	302	6	d(0.9	d(0.9	PROPN
ejpam-7063	302	7	)	)	PUNCT
ejpam-7063	302	8	xy	xy	PROPN
ejpam-7063	303	1	p	p	NOUN
ejpam-7063	303	2	=	=	PUNCT
ejpam-7063	303	3	2z+p	2z+p	NUM
ejpam-7063	303	4	(	(	PUNCT
ejpam-7063	303	5	6.13	6.13	NUM
ejpam-7063	303	6	)	)	PUNCT
ejpam-7063	303	7	u	u	NOUN
ejpam-7063	303	8	=	=	NOUN
ejpam-7063	303	9	1	1	NUM
ejpam-7063	303	10	2	2	NUM
ejpam-7063	303	11	p	p	NOUN
ejpam-7063	303	12	(	(	PUNCT
ejpam-7063	303	13	6.14	6.14	NUM
ejpam-7063	303	14	)	)	PUNCT
ejpam-7063	303	15	here	here	ADV
ejpam-7063	303	16	,	,	PUNCT
ejpam-7063	303	17	d(0.9	d(0.9	PROPN
ejpam-7063	303	18	)	)	PUNCT
ejpam-7063	303	19	xy	xy	PROPN
ejpam-7063	304	1	=	=	PUNCT
ejpam-7063	304	2	d	d	PROPN
ejpam-7063	304	3	(	(	PUNCT
ejpam-7063	304	4	0.9	0.9	NUM
ejpam-7063	304	5	)	)	PUNCT
ejpam-7063	304	6	x	x	X
ejpam-7063	304	7	⊗d	⊗d	NOUN
ejpam-7063	304	8	(	(	PUNCT
ejpam-7063	304	9	0.9	0.9	NUM
ejpam-7063	304	10	)	)	PUNCT
ejpam-7063	304	11	y	y	PROPN
ejpam-7063	304	12	.	.	PUNCT
ejpam-7063	305	1	solve	solve	VERB
ejpam-7063	305	2	this	this	DET
ejpam-7063	305	3	nonlinear	nonlinear	ADJ
ejpam-7063	305	4	system	system	NOUN
ejpam-7063	305	5	numerically	numerically	ADV
ejpam-7063	305	6	(	(	PUNCT
ejpam-7063	305	7	e.g.	e.g.	ADV
ejpam-7063	305	8	,	,	PUNCT
ejpam-7063	305	9	newton	newton	PROPN
ejpam-7063	305	10	’s	’s	PART
ejpam-7063	305	11	method	method	NOUN
ejpam-7063	305	12	)	)	PUNCT
ejpam-7063	305	13	to	to	PART
ejpam-7063	305	14	obtain	obtain	VERB
ejpam-7063	305	15	the	the	DET
ejpam-7063	305	16	coefficients	coefficient	NOUN
ejpam-7063	305	17	aij	aij	PROPN
ejpam-7063	305	18	,	,	PUNCT
ejpam-7063	305	19	bij	bij	NOUN
ejpam-7063	305	20	,	,	PUNCT
ejpam-7063	305	21	and	and	CCONJ
ejpam-7063	305	22	reconstruct	reconstruct	VERB
ejpam-7063	305	23	z(x	z(x	PROPN
ejpam-7063	305	24	,	,	PUNCT
ejpam-7063	305	25	y	y	NOUN
ejpam-7063	305	26	)	)	PUNCT
ejpam-7063	305	27	and	and	CCONJ
ejpam-7063	305	28	u(x	u(x	PROPN
ejpam-7063	305	29	,	,	PUNCT
ejpam-7063	305	30	y	y	NOUN
ejpam-7063	305	31	)	)	PUNCT
ejpam-7063	305	32	.	.	PUNCT
ejpam-7063	306	1	g.	g.	PROPN
ejpam-7063	306	2	m.	m.	PROPN
ejpam-7063	306	3	bahaa	bahaa	PROPN
ejpam-7063	306	4	,	,	PUNCT
ejpam-7063	306	5	a.	a.	NOUN
ejpam-7063	306	6	h.	h.	PROPN
ejpam-7063	306	7	qamlo	qamlo	PROPN
ejpam-7063	306	8	/	/	SYM
ejpam-7063	306	9	eur	eur	PROPN
ejpam-7063	306	10	.	.	PUNCT
ejpam-7063	307	1	j.	j.	PROPN
ejpam-7063	307	2	pure	pure	PROPN
ejpam-7063	307	3	appl	appl	PROPN
ejpam-7063	307	4	.	.	PROPN
ejpam-7063	307	5	math	math	PROPN
ejpam-7063	307	6	,	,	PUNCT
ejpam-7063	307	7	18	18	NUM
ejpam-7063	307	8	(	(	PUNCT
ejpam-7063	307	9	4	4	NUM
ejpam-7063	307	10	)	)	PUNCT
ejpam-7063	307	11	(	(	PUNCT
ejpam-7063	307	12	2025	2025	NUM
ejpam-7063	307	13	)	)	PUNCT
ejpam-7063	307	14	,	,	PUNCT
ejpam-7063	307	15	7063	7063	NUM
ejpam-7063	307	16	15	15	NUM
ejpam-7063	307	17	of	of	ADP
ejpam-7063	307	18	29	29	NUM
ejpam-7063	307	19	numerical	numerical	ADJ
ejpam-7063	307	20	solution	solution	NOUN
ejpam-7063	307	21	using	use	VERB
ejpam-7063	307	22	newton	newton	PROPN
ejpam-7063	307	23	’s	’s	PART
ejpam-7063	307	24	method	method	NOUN
ejpam-7063	307	25	to	to	PART
ejpam-7063	307	26	solve	solve	VERB
ejpam-7063	307	27	the	the	DET
ejpam-7063	307	28	system	system	NOUN
ejpam-7063	307	29	of	of	ADP
ejpam-7063	307	30	nonlinear	nonlinear	ADJ
ejpam-7063	307	31	algebraic	algebraic	ADJ
ejpam-7063	307	32	equations	equation	NOUN
ejpam-7063	307	33	arising	arise	VERB
ejpam-7063	307	34	from	from	ADP
ejpam-7063	307	35	the	the	DET
ejpam-7063	307	36	fractional	fractional	ADJ
ejpam-7063	307	37	optimality	optimality	NOUN
ejpam-7063	307	38	system	system	NOUN
ejpam-7063	307	39	,	,	PUNCT
ejpam-7063	307	40	we	we	PRON
ejpam-7063	307	41	apply	apply	VERB
ejpam-7063	307	42	newton	newton	PROPN
ejpam-7063	307	43	’s	’s	PART
ejpam-7063	307	44	method	method	NOUN
ejpam-7063	307	45	.	.	PUNCT
ejpam-7063	308	1	let	let	VERB
ejpam-7063	308	2	the	the	DET
ejpam-7063	308	3	unknown	unknown	ADJ
ejpam-7063	308	4	coefficient	coefficient	NOUN
ejpam-7063	308	5	vectors	vector	NOUN
ejpam-7063	308	6	be	be	VERB
ejpam-7063	308	7	:	:	PUNCT
ejpam-7063	308	8	a	a	DET
ejpam-7063	308	9	=	=	PUNCT
ejpam-7063	308	10	vec(aij	vec(aij	NOUN
ejpam-7063	308	11	)	)	PUNCT
ejpam-7063	308	12	∈	∈	PROPN
ejpam-7063	308	13	r(n+1)2	r(n+1)2	PROPN
ejpam-7063	308	14	,	,	PUNCT
ejpam-7063	308	15	(	(	PUNCT
ejpam-7063	308	16	6.15	6.15	NUM
ejpam-7063	308	17	)	)	PUNCT
ejpam-7063	308	18	b	b	NOUN
ejpam-7063	308	19	=	=	SYM
ejpam-7063	308	20	vec(bij	vec(bij	X
ejpam-7063	308	21	)	)	PUNCT
ejpam-7063	309	1	∈	∈	PROPN
ejpam-7063	309	2	r(n+1)2	r(n+1)2	PROPN
ejpam-7063	309	3	(	(	PUNCT
ejpam-7063	309	4	6.16	6.16	NUM
ejpam-7063	309	5	)	)	PUNCT
ejpam-7063	309	6	we	we	PRON
ejpam-7063	309	7	define	define	VERB
ejpam-7063	309	8	the	the	DET
ejpam-7063	309	9	vector	vector	NOUN
ejpam-7063	309	10	of	of	ADP
ejpam-7063	309	11	unknowns	unknown	NOUN
ejpam-7063	309	12	:	:	PUNCT
ejpam-7063	309	13	x	x	SYM
ejpam-7063	309	14	=	=	PUNCT
ejpam-7063	309	15	[	[	PUNCT
ejpam-7063	309	16	a	a	PRON
ejpam-7063	309	17	b	b	X
ejpam-7063	309	18	]	]	PUNCT
ejpam-7063	309	19	∈	∈	PROPN
ejpam-7063	309	20	r2(n+1)2	r2(n+1)2	PROPN
ejpam-7063	309	21	(	(	PUNCT
ejpam-7063	309	22	6.17	6.17	NUM
ejpam-7063	309	23	)	)	PUNCT
ejpam-7063	309	24	construct	construct	VERB
ejpam-7063	309	25	the	the	DET
ejpam-7063	309	26	residual	residual	ADJ
ejpam-7063	309	27	function	function	NOUN
ejpam-7063	309	28	define	define	VERB
ejpam-7063	309	29	the	the	DET
ejpam-7063	309	30	residual	residual	ADJ
ejpam-7063	309	31	system	system	NOUN
ejpam-7063	309	32	based	base	VERB
ejpam-7063	309	33	on	on	ADP
ejpam-7063	309	34	the	the	DET
ejpam-7063	309	35	collocated	collocate	VERB
ejpam-7063	309	36	optimality	optimality	NOUN
ejpam-7063	309	37	system	system	NOUN
ejpam-7063	309	38	:	:	PUNCT
ejpam-7063	309	39	r1(a	r1(a	ADP
ejpam-7063	309	40	,	,	PUNCT
ejpam-7063	309	41	b	b	NOUN
ejpam-7063	309	42	)	)	PUNCT
ejpam-7063	309	43	=	=	SYM
ejpam-7063	309	44	d(0.9	d(0.9	PROPN
ejpam-7063	309	45	)	)	PUNCT
ejpam-7063	309	46	xy	xy	PROPN
ejpam-7063	309	47	a+	a+	PUNCT
ejpam-7063	309	48	a−	a−	PROPN
ejpam-7063	309	49	1	1	NUM
ejpam-7063	309	50	2	2	NUM
ejpam-7063	309	51	b	b	PROPN
ejpam-7063	309	52	(	(	PUNCT
ejpam-7063	309	53	6.18	6.18	NUM
ejpam-7063	309	54	)	)	PUNCT
ejpam-7063	309	55	r2(a	r2(a	NOUN
ejpam-7063	309	56	,	,	PUNCT
ejpam-7063	309	57	b	b	NOUN
ejpam-7063	309	58	)	)	PUNCT
ejpam-7063	309	59	=	=	SYM
ejpam-7063	309	60	d(0.9	d(0.9	PROPN
ejpam-7063	309	61	)	)	PUNCT
ejpam-7063	309	62	xy	xy	PROPN
ejpam-7063	310	1	b−	b−	PROPN
ejpam-7063	310	2	2a−	2a−	PROPN
ejpam-7063	310	3	b	b	PROPN
ejpam-7063	310	4	(	(	PUNCT
ejpam-7063	310	5	6.19	6.19	NUM
ejpam-7063	310	6	)	)	PUNCT
ejpam-7063	310	7	then	then	ADV
ejpam-7063	310	8	,	,	PUNCT
ejpam-7063	310	9	define	define	VERB
ejpam-7063	310	10	the	the	DET
ejpam-7063	310	11	total	total	ADJ
ejpam-7063	310	12	residual	residual	ADJ
ejpam-7063	310	13	:	:	PUNCT
ejpam-7063	310	14	r(x	r(x	NOUN
ejpam-7063	310	15	)	)	PUNCT
ejpam-7063	310	16	=	=	PUNCT
ejpam-7063	311	1	[	[	PUNCT
ejpam-7063	311	2	r1(a	r1(a	ADP
ejpam-7063	311	3	,	,	PUNCT
ejpam-7063	311	4	b	b	NOUN
ejpam-7063	311	5	)	)	PUNCT
ejpam-7063	311	6	r2(a	r2(a	PROPN
ejpam-7063	311	7	,	,	PUNCT
ejpam-7063	311	8	b	b	NOUN
ejpam-7063	311	9	)	)	PUNCT
ejpam-7063	311	10	]	]	PUNCT
ejpam-7063	311	11	(	(	PUNCT
ejpam-7063	311	12	6.20	6.20	NUM
ejpam-7063	311	13	)	)	PUNCT
ejpam-7063	311	14	newton	newton	PROPN
ejpam-7063	311	15	’s	’s	PART
ejpam-7063	311	16	iterative	iterative	NOUN
ejpam-7063	311	17	scheme	scheme	NOUN
ejpam-7063	311	18	given	give	VERB
ejpam-7063	311	19	an	an	DET
ejpam-7063	311	20	initial	initial	ADJ
ejpam-7063	311	21	guess	guess	NOUN
ejpam-7063	311	22	x(0	x(0	PROPN
ejpam-7063	311	23	)	)	PUNCT
ejpam-7063	311	24	,	,	PUNCT
ejpam-7063	311	25	the	the	DET
ejpam-7063	311	26	newton	newton	PROPN
ejpam-7063	311	27	update	update	NOUN
ejpam-7063	311	28	is	be	AUX
ejpam-7063	311	29	:	:	PUNCT
ejpam-7063	311	30	x(k+1	x(k+1	NUM
ejpam-7063	311	31	)	)	PUNCT
ejpam-7063	311	32	=	=	SYM
ejpam-7063	312	1	x(k	x(k	PROPN
ejpam-7063	312	2	)	)	PUNCT
ejpam-7063	312	3	−	−	PROPN
ejpam-7063	312	4	[	[	PUNCT
ejpam-7063	312	5	jr(x	jr(x	NUM
ejpam-7063	312	6	(	(	PUNCT
ejpam-7063	312	7	k	k	NOUN
ejpam-7063	312	8	)	)	PUNCT
ejpam-7063	312	9	)	)	PUNCT
ejpam-7063	312	10	]	]	PUNCT
ejpam-7063	312	11	−1	−1	NOUN
ejpam-7063	312	12	r(x(k	r(x(k	NOUN
ejpam-7063	312	13	)	)	PUNCT
ejpam-7063	312	14	)	)	PUNCT
ejpam-7063	312	15	(	(	PUNCT
ejpam-7063	313	1	6.21	6.21	NUM
ejpam-7063	313	2	)	)	PUNCT
ejpam-7063	313	3	where	where	SCONJ
ejpam-7063	313	4	jr	jr	PROPN
ejpam-7063	313	5	is	be	AUX
ejpam-7063	313	6	the	the	DET
ejpam-7063	313	7	jacobian	jacobian	ADJ
ejpam-7063	313	8	matrix	matrix	NOUN
ejpam-7063	313	9	of	of	ADP
ejpam-7063	313	10	r	r	NOUN
ejpam-7063	313	11	,	,	PUNCT
ejpam-7063	313	12	which	which	PRON
ejpam-7063	313	13	includes	include	VERB
ejpam-7063	313	14	partial	partial	ADJ
ejpam-7063	313	15	derivatives	derivative	NOUN
ejpam-7063	313	16	of	of	ADP
ejpam-7063	313	17	residuals	residual	NOUN
ejpam-7063	313	18	with	with	ADP
ejpam-7063	313	19	respect	respect	NOUN
ejpam-7063	313	20	to	to	ADP
ejpam-7063	313	21	each	each	DET
ejpam-7063	313	22	variable	variable	NOUN
ejpam-7063	313	23	.	.	PUNCT
ejpam-7063	314	1	jacobian	jacobian	ADJ
ejpam-7063	314	2	matrix	matrix	NOUN
ejpam-7063	314	3	structure	structure	NOUN
ejpam-7063	314	4	the	the	DET
ejpam-7063	314	5	jacobian	jacobian	PROPN
ejpam-7063	314	6	has	have	VERB
ejpam-7063	314	7	a	a	DET
ejpam-7063	314	8	block	block	NOUN
ejpam-7063	314	9	structure	structure	NOUN
ejpam-7063	314	10	:	:	PUNCT
ejpam-7063	315	1	jr	jr	PROPN
ejpam-7063	315	2	=	=	PUNCT
ejpam-7063	316	1	[	[	PUNCT
ejpam-7063	316	2	d	d	X
ejpam-7063	316	3	(	(	PUNCT
ejpam-7063	316	4	0.9	0.9	NUM
ejpam-7063	316	5	)	)	PUNCT
ejpam-7063	316	6	xy	xy	PROPN
ejpam-7063	317	1	+	+	CCONJ
ejpam-7063	317	2	i	i	PRON
ejpam-7063	317	3	−1	−1	NOUN
ejpam-7063	317	4	2i	2i	NOUN
ejpam-7063	317	5	−2i	−2i	PROPN
ejpam-7063	317	6	d	d	X
ejpam-7063	317	7	(	(	PUNCT
ejpam-7063	317	8	0.9	0.9	NUM
ejpam-7063	317	9	)	)	PUNCT
ejpam-7063	317	10	xy	xy	PROPN
ejpam-7063	317	11	−	−	PROPN
ejpam-7063	318	1	i	i	PRON
ejpam-7063	318	2	]	]	PUNCT
ejpam-7063	318	3	here	here	ADV
ejpam-7063	318	4	,	,	PUNCT
ejpam-7063	318	5	i	i	PRON
ejpam-7063	318	6	is	be	AUX
ejpam-7063	318	7	the	the	DET
ejpam-7063	318	8	identity	identity	NOUN
ejpam-7063	318	9	matrix	matrix	NOUN
ejpam-7063	318	10	of	of	ADP
ejpam-7063	318	11	appropriate	appropriate	ADJ
ejpam-7063	318	12	size	size	NOUN
ejpam-7063	318	13	.	.	PUNCT
ejpam-7063	319	1	g.	g.	PROPN
ejpam-7063	319	2	m.	m.	PROPN
ejpam-7063	319	3	bahaa	bahaa	PROPN
ejpam-7063	319	4	,	,	PUNCT
ejpam-7063	319	5	a.	a.	NOUN
ejpam-7063	319	6	h.	h.	PROPN
ejpam-7063	319	7	qamlo	qamlo	PROPN
ejpam-7063	319	8	/	/	SYM
ejpam-7063	319	9	eur	eur	PROPN
ejpam-7063	319	10	.	.	PUNCT
ejpam-7063	320	1	j.	j.	PROPN
ejpam-7063	320	2	pure	pure	PROPN
ejpam-7063	320	3	appl	appl	PROPN
ejpam-7063	320	4	.	.	PROPN
ejpam-7063	320	5	math	math	PROPN
ejpam-7063	320	6	,	,	PUNCT
ejpam-7063	320	7	18	18	NUM
ejpam-7063	320	8	(	(	PUNCT
ejpam-7063	320	9	4	4	NUM
ejpam-7063	320	10	)	)	PUNCT
ejpam-7063	320	11	(	(	PUNCT
ejpam-7063	320	12	2025	2025	NUM
ejpam-7063	320	13	)	)	PUNCT
ejpam-7063	320	14	,	,	PUNCT
ejpam-7063	320	15	7063	7063	NUM
ejpam-7063	320	16	16	16	NUM
ejpam-7063	320	17	of	of	ADP
ejpam-7063	320	18	29	29	NUM
ejpam-7063	320	19	algorithm	algorithm	NOUN
ejpam-7063	320	20	summary	summary	NOUN
ejpam-7063	320	21	1	1	NUM
ejpam-7063	320	22	.	.	PUNCT
ejpam-7063	320	23	initialize	initialize	VERB
ejpam-7063	320	24	x(0	x(0	PROPN
ejpam-7063	320	25	)	)	PUNCT
ejpam-7063	320	26	=	=	PUNCT
ejpam-7063	321	1	[	[	X
ejpam-7063	321	2	0	0	NUM
ejpam-7063	321	3	0]t	0]t	NUM
ejpam-7063	321	4	2	2	NUM
ejpam-7063	321	5	.	.	X
ejpam-7063	321	6	for	for	ADP
ejpam-7063	321	7	k	k	PROPN
ejpam-7063	321	8	=	=	SYM
ejpam-7063	321	9	0	0	NUM
ejpam-7063	321	10	,	,	PUNCT
ejpam-7063	321	11	1	1	NUM
ejpam-7063	321	12	,	,	PUNCT
ejpam-7063	321	13	2	2	NUM
ejpam-7063	321	14	,	,	PUNCT
ejpam-7063	321	15	.	.	PUNCT
ejpam-7063	321	16	.	.	PUNCT
ejpam-7063	321	17	.	.	PUNCT
ejpam-7063	322	1	until	until	SCONJ
ejpam-7063	322	2	convergence	convergence	NOUN
ejpam-7063	322	3	:	:	PUNCT
ejpam-7063	322	4	(	(	PUNCT
ejpam-7063	322	5	a	a	X
ejpam-7063	322	6	)	)	PUNCT
ejpam-7063	322	7	compute	compute	NOUN
ejpam-7063	322	8	r(x(k	r(x(k	NOUN
ejpam-7063	322	9	)	)	PUNCT
ejpam-7063	322	10	)	)	PUNCT
ejpam-7063	322	11	(	(	PUNCT
ejpam-7063	322	12	b	b	X
ejpam-7063	322	13	)	)	PUNCT
ejpam-7063	322	14	compute	compute	NOUN
ejpam-7063	322	15	jr(x(k	jr(x(k	NOUN
ejpam-7063	322	16	)	)	PUNCT
ejpam-7063	322	17	)	)	PUNCT
ejpam-7063	322	18	(	(	PUNCT
ejpam-7063	322	19	c	c	X
ejpam-7063	322	20	)	)	PUNCT
ejpam-7063	322	21	solve	solve	NOUN
ejpam-7063	322	22	:	:	PUNCT
ejpam-7063	322	23	jrδx	jrδx	NOUN
ejpam-7063	322	24	=	=	PUNCT
ejpam-7063	322	25	r	r	NOUN
ejpam-7063	322	26	(	(	PUNCT
ejpam-7063	322	27	d	d	NOUN
ejpam-7063	322	28	)	)	PUNCT
ejpam-7063	322	29	update	update	NOUN
ejpam-7063	322	30	:	:	PUNCT
ejpam-7063	322	31	x(k+1	x(k+1	NUM
ejpam-7063	322	32	)	)	PUNCT
ejpam-7063	322	33	=	=	SYM
ejpam-7063	322	34	x(k	x(k	PROPN
ejpam-7063	322	35	)	)	PUNCT
ejpam-7063	322	36	−	−	NOUN
ejpam-7063	322	37	δx	δx	VERB
ejpam-7063	322	38	reconstruction	reconstruction	NOUN
ejpam-7063	322	39	of	of	ADP
ejpam-7063	322	40	the	the	DET
ejpam-7063	322	41	approximate	approximate	ADJ
ejpam-7063	322	42	solutions	solution	NOUN
ejpam-7063	322	43	once	once	SCONJ
ejpam-7063	322	44	the	the	DET
ejpam-7063	322	45	coefficients	coefficient	NOUN
ejpam-7063	322	46	a	a	PRON
ejpam-7063	322	47	and	and	CCONJ
ejpam-7063	322	48	b	b	NOUN
ejpam-7063	322	49	are	be	AUX
ejpam-7063	322	50	obtained	obtain	VERB
ejpam-7063	322	51	,	,	PUNCT
ejpam-7063	322	52	reconstruct	reconstruct	VERB
ejpam-7063	322	53	:	:	PUNCT
ejpam-7063	322	54	z(x	z(x	NUM
ejpam-7063	322	55	,	,	PUNCT
ejpam-7063	322	56	y	y	PROPN
ejpam-7063	322	57	)	)	PUNCT
ejpam-7063	323	1	≈	≈	PROPN
ejpam-7063	323	2	n∑	n∑	PROPN
ejpam-7063	323	3	i=0	i=0	PROPN
ejpam-7063	323	4	n∑	n∑	PROPN
ejpam-7063	323	5	j=0	j=0	PROPN
ejpam-7063	323	6	aijψi(x)ψj(y	aijψi(x)ψj(y	PROPN
ejpam-7063	323	7	)	)	PUNCT
ejpam-7063	323	8	(	(	PUNCT
ejpam-7063	323	9	6.22	6.22	NUM
ejpam-7063	323	10	)	)	PUNCT
ejpam-7063	323	11	p(x	p(x	PROPN
ejpam-7063	323	12	,	,	PUNCT
ejpam-7063	323	13	y	y	NOUN
ejpam-7063	323	14	)	)	PUNCT
ejpam-7063	324	1	≈	≈	PROPN
ejpam-7063	324	2	n∑	n∑	PROPN
ejpam-7063	324	3	i=0	i=0	PROPN
ejpam-7063	324	4	n∑	n∑	PROPN
ejpam-7063	324	5	j=0	j=0	PROPN
ejpam-7063	324	6	bijψi(x)ψj(y	bijψi(x)ψj(y	VERB
ejpam-7063	324	7	)	)	PUNCT
ejpam-7063	324	8	(	(	PUNCT
ejpam-7063	324	9	6.23	6.23	NUM
ejpam-7063	324	10	)	)	PUNCT
ejpam-7063	324	11	u(x	u(x	PROPN
ejpam-7063	324	12	,	,	PUNCT
ejpam-7063	324	13	y	y	NOUN
ejpam-7063	324	14	)	)	PUNCT
ejpam-7063	325	1	≈	≈	NOUN
ejpam-7063	325	2	1	1	NUM
ejpam-7063	325	3	2	2	NUM
ejpam-7063	325	4	p(x	p(x	PROPN
ejpam-7063	325	5	,	,	PUNCT
ejpam-7063	325	6	y	y	NOUN
ejpam-7063	325	7	)	)	PUNCT
ejpam-7063	325	8	(	(	PUNCT
ejpam-7063	325	9	6.24	6.24	NUM
ejpam-7063	325	10	)	)	PUNCT
ejpam-7063	325	11	this	this	PRON
ejpam-7063	325	12	yields	yield	VERB
ejpam-7063	325	13	the	the	DET
ejpam-7063	325	14	approximate	approximate	ADJ
ejpam-7063	325	15	state	state	NOUN
ejpam-7063	325	16	,	,	PUNCT
ejpam-7063	325	17	adjoint	adjoint	NOUN
ejpam-7063	325	18	,	,	PUNCT
ejpam-7063	325	19	and	and	CCONJ
ejpam-7063	325	20	control	control	NOUN
ejpam-7063	325	21	functions	function	NOUN
ejpam-7063	325	22	.	.	PUNCT
ejpam-7063	326	1	visualization	visualization	NOUN
ejpam-7063	326	2	(	(	PUNCT
ejpam-7063	326	3	optional	optional	ADJ
ejpam-7063	326	4	)	)	PUNCT
ejpam-7063	326	5	if	if	SCONJ
ejpam-7063	326	6	desired	desire	VERB
ejpam-7063	326	7	,	,	PUNCT
ejpam-7063	326	8	the	the	DET
ejpam-7063	326	9	reconstructed	reconstructed	ADJ
ejpam-7063	326	10	solutions	solution	NOUN
ejpam-7063	326	11	can	can	AUX
ejpam-7063	326	12	be	be	AUX
ejpam-7063	326	13	visualized	visualize	VERB
ejpam-7063	326	14	using	use	VERB
ejpam-7063	326	15	surface	surface	NOUN
ejpam-7063	326	16	or	or	CCONJ
ejpam-7063	326	17	contour	contour	NOUN
ejpam-7063	326	18	plots	plot	NOUN
ejpam-7063	326	19	for	for	ADP
ejpam-7063	326	20	z(x	z(x	NUM
ejpam-7063	326	21	,	,	PUNCT
ejpam-7063	326	22	y	y	PROPN
ejpam-7063	326	23	)	)	PUNCT
ejpam-7063	326	24	,	,	PUNCT
ejpam-7063	326	25	u(x	u(x	PROPN
ejpam-7063	326	26	,	,	PUNCT
ejpam-7063	326	27	y	y	NOUN
ejpam-7063	326	28	)	)	PUNCT
ejpam-7063	326	29	,	,	PUNCT
ejpam-7063	326	30	and	and	CCONJ
ejpam-7063	326	31	p(x	p(x	PROPN
ejpam-7063	326	32	,	,	PUNCT
ejpam-7063	326	33	y	y	PROPN
ejpam-7063	326	34	)	)	PUNCT
ejpam-7063	326	35	.	.	PUNCT
ejpam-7063	327	1	figure	figure	VERB
ejpam-7063	327	2	1	1	NUM
ejpam-7063	327	3	:	:	PUNCT
ejpam-7063	327	4	the	the	DET
ejpam-7063	327	5	3d	3d	PROPN
ejpam-7063	327	6	surface	surface	NOUN
ejpam-7063	327	7	plots	plot	NOUN
ejpam-7063	327	8	for	for	ADP
ejpam-7063	327	9	the	the	DET
ejpam-7063	327	10	state	state	NOUN
ejpam-7063	327	11	z(x	z(x	PROPN
ejpam-7063	327	12	,	,	PUNCT
ejpam-7063	327	13	y	y	PROPN
ejpam-7063	327	14	)	)	PUNCT
ejpam-7063	327	15	,	,	PUNCT
ejpam-7063	327	16	adjoint	adjoint	PROPN
ejpam-7063	327	17	p(x	p(x	PROPN
ejpam-7063	327	18	,	,	PUNCT
ejpam-7063	327	19	y	y	NOUN
ejpam-7063	327	20	)	)	PUNCT
ejpam-7063	327	21	,	,	PUNCT
ejpam-7063	327	22	and	and	CCONJ
ejpam-7063	327	23	control	control	VERB
ejpam-7063	327	24	u(x	u(x	NOUN
ejpam-7063	327	25	,	,	PUNCT
ejpam-7063	327	26	y	y	NOUN
ejpam-7063	327	27	)	)	PUNCT
ejpam-7063	327	28	.	.	PUNCT
ejpam-7063	328	1	g.	g.	PROPN
ejpam-7063	328	2	m.	m.	PROPN
ejpam-7063	328	3	bahaa	bahaa	PROPN
ejpam-7063	328	4	,	,	PUNCT
ejpam-7063	328	5	a.	a.	NOUN
ejpam-7063	328	6	h.	h.	PROPN
ejpam-7063	328	7	qamlo	qamlo	PROPN
ejpam-7063	328	8	/	/	SYM
ejpam-7063	328	9	eur	eur	PROPN
ejpam-7063	328	10	.	.	PUNCT
ejpam-7063	329	1	j.	j.	PROPN
ejpam-7063	329	2	pure	pure	PROPN
ejpam-7063	329	3	appl	appl	PROPN
ejpam-7063	329	4	.	.	PROPN
ejpam-7063	329	5	math	math	PROPN
ejpam-7063	329	6	,	,	PUNCT
ejpam-7063	329	7	18	18	NUM
ejpam-7063	329	8	(	(	PUNCT
ejpam-7063	329	9	4	4	NUM
ejpam-7063	329	10	)	)	PUNCT
ejpam-7063	329	11	(	(	PUNCT
ejpam-7063	329	12	2025	2025	NUM
ejpam-7063	329	13	)	)	PUNCT
ejpam-7063	329	14	,	,	PUNCT
ejpam-7063	329	15	7063	7063	NUM
ejpam-7063	329	16	17	17	NUM
ejpam-7063	329	17	of	of	ADP
ejpam-7063	329	18	29	29	NUM
ejpam-7063	329	19	figure	figure	NOUN
ejpam-7063	329	20	2	2	NUM
ejpam-7063	329	21	:	:	PUNCT
ejpam-7063	329	22	the	the	DET
ejpam-7063	329	23	3d	3d	PROPN
ejpam-7063	329	24	surface	surface	NOUN
ejpam-7063	329	25	plots	plot	NOUN
ejpam-7063	329	26	for	for	ADP
ejpam-7063	329	27	the	the	DET
ejpam-7063	329	28	state	state	NOUN
ejpam-7063	329	29	z(x	z(x	PROPN
ejpam-7063	329	30	,	,	PUNCT
ejpam-7063	329	31	y	y	PROPN
ejpam-7063	329	32	)	)	PUNCT
ejpam-7063	329	33	,	,	PUNCT
ejpam-7063	329	34	adjoint	adjoint	PROPN
ejpam-7063	329	35	p(x	p(x	PROPN
ejpam-7063	329	36	,	,	PUNCT
ejpam-7063	329	37	y	y	NOUN
ejpam-7063	329	38	)	)	PUNCT
ejpam-7063	329	39	,	,	PUNCT
ejpam-7063	329	40	and	and	CCONJ
ejpam-7063	329	41	control	control	VERB
ejpam-7063	329	42	u(x	u(x	PROPN
ejpam-7063	329	43	,	,	PUNCT
ejpam-7063	329	44	y	y	NOUN
ejpam-7063	329	45	)	)	PUNCT
ejpam-7063	329	46	remark	remark	VERB
ejpam-7063	329	47	the	the	DET
ejpam-7063	329	48	nonlinear	nonlinear	ADJ
ejpam-7063	329	49	optimality	optimality	NOUN
ejpam-7063	329	50	system	system	NOUN
ejpam-7063	329	51	for	for	ADP
ejpam-7063	329	52	the	the	DET
ejpam-7063	329	53	two	two	NUM
ejpam-7063	329	54	-	-	PUNCT
ejpam-7063	329	55	dimensional	dimensional	ADJ
ejpam-7063	329	56	fractional	fractional	ADJ
ejpam-7063	329	57	optimal	optimal	ADJ
ejpam-7063	329	58	control	control	NOUN
ejpam-7063	329	59	problem	problem	NOUN
ejpam-7063	329	60	was	be	AUX
ejpam-7063	329	61	successfully	successfully	ADV
ejpam-7063	329	62	transformed	transform	VERB
ejpam-7063	329	63	into	into	ADP
ejpam-7063	329	64	an	an	DET
ejpam-7063	329	65	algebraic	algebraic	ADJ
ejpam-7063	329	66	system	system	NOUN
ejpam-7063	329	67	using	use	VERB
ejpam-7063	329	68	fractional	fractional	ADJ
ejpam-7063	329	69	vietafibonacci	vietafibonacci	NOUN
ejpam-7063	329	70	wavelets	wavelet	NOUN
ejpam-7063	329	71	.	.	PUNCT
ejpam-7063	330	1	newton	newton	PROPN
ejpam-7063	330	2	’s	’s	PART
ejpam-7063	330	3	method	method	NOUN
ejpam-7063	330	4	was	be	AUX
ejpam-7063	330	5	then	then	ADV
ejpam-7063	330	6	applied	apply	VERB
ejpam-7063	330	7	to	to	PART
ejpam-7063	330	8	iteratively	iteratively	ADV
ejpam-7063	330	9	solve	solve	VERB
ejpam-7063	330	10	for	for	ADP
ejpam-7063	330	11	the	the	DET
ejpam-7063	330	12	wavelet	wavelet	NOUN
ejpam-7063	330	13	coefficients	coefficient	NOUN
ejpam-7063	330	14	,	,	PUNCT
ejpam-7063	330	15	enabling	enable	VERB
ejpam-7063	330	16	the	the	DET
ejpam-7063	330	17	reconstruction	reconstruction	NOUN
ejpam-7063	330	18	of	of	ADP
ejpam-7063	330	19	the	the	DET
ejpam-7063	330	20	approximate	approximate	ADJ
ejpam-7063	330	21	solutions	solution	NOUN
ejpam-7063	330	22	.	.	PUNCT
ejpam-7063	331	1	we	we	PRON
ejpam-7063	331	2	derived	derive	VERB
ejpam-7063	331	3	and	and	CCONJ
ejpam-7063	331	4	numerically	numerically	ADV
ejpam-7063	331	5	solved	solve	VERB
ejpam-7063	331	6	a	a	DET
ejpam-7063	331	7	two	two	NUM
ejpam-7063	331	8	-	-	PUNCT
ejpam-7063	331	9	dimensional	dimensional	ADJ
ejpam-7063	331	10	fractional	fractional	ADJ
ejpam-7063	331	11	optimal	optimal	ADJ
ejpam-7063	331	12	control	control	NOUN
ejpam-7063	331	13	problem	problem	NOUN
ejpam-7063	331	14	using	use	VERB
ejpam-7063	331	15	fractional	fractional	ADJ
ejpam-7063	331	16	vieta	vieta	PROPN
ejpam-7063	331	17	-	-	PUNCT
ejpam-7063	331	18	fibonacci	fibonacci	NOUN
ejpam-7063	331	19	wavelets	wavelet	NOUN
ejpam-7063	331	20	.	.	PUNCT
ejpam-7063	332	1	the	the	DET
ejpam-7063	332	2	optimality	optimality	NOUN
ejpam-7063	332	3	system	system	NOUN
ejpam-7063	332	4	was	be	AUX
ejpam-7063	332	5	formulated	formulate	VERB
ejpam-7063	332	6	using	use	VERB
ejpam-7063	332	7	the	the	DET
ejpam-7063	332	8	lagrange	lagrange	NOUN
ejpam-7063	332	9	multiplier	multipli	ADJ
ejpam-7063	332	10	technique	technique	NOUN
ejpam-7063	332	11	and	and	CCONJ
ejpam-7063	332	12	solved	solve	VERB
ejpam-7063	332	13	via	via	ADP
ejpam-7063	332	14	spectral	spectral	ADJ
ejpam-7063	332	15	collocation	collocation	NOUN
ejpam-7063	332	16	using	use	VERB
ejpam-7063	332	17	operational	operational	ADJ
ejpam-7063	332	18	matrices	matrix	NOUN
ejpam-7063	332	19	.	.	PUNCT
ejpam-7063	333	1	nonlinear	nonlinear	ADJ
ejpam-7063	333	2	2d	2d	NUM
ejpam-7063	333	3	fractional	fractional	ADJ
ejpam-7063	333	4	optimal	optimal	ADJ
ejpam-7063	333	5	control	control	NOUN
ejpam-7063	333	6	problem	problem	NOUN
ejpam-7063	333	7	we	we	PRON
ejpam-7063	333	8	aim	aim	VERB
ejpam-7063	333	9	to	to	PART
ejpam-7063	333	10	minimize	minimize	VERB
ejpam-7063	333	11	:	:	PUNCT
ejpam-7063	334	1	j	j	PROPN
ejpam-7063	335	1	[	[	X
ejpam-7063	335	2	z	z	PROPN
ejpam-7063	335	3	,	,	PUNCT
ejpam-7063	335	4	u	u	NOUN
ejpam-7063	335	5	]	]	X
ejpam-7063	335	6	=	=	SYM
ejpam-7063	335	7	1	1	NUM
ejpam-7063	335	8	2	2	NUM
ejpam-7063	335	9	∫	∫	NOUN
ejpam-7063	335	10	1	1	NUM
ejpam-7063	335	11	0	0	NUM
ejpam-7063	335	12	∫	∫	PROPN
ejpam-7063	335	13	1	1	NUM
ejpam-7063	335	14	0	0	NUM
ejpam-7063	335	15	[	[	PUNCT
ejpam-7063	335	16	z2(x	z2(x	NUM
ejpam-7063	335	17	,	,	PUNCT
ejpam-7063	335	18	y	y	PROPN
ejpam-7063	335	19	)	)	PUNCT
ejpam-7063	335	20	+	+	CCONJ
ejpam-7063	336	1	λu2(x	λu2(x	PROPN
ejpam-7063	336	2	,	,	PUNCT
ejpam-7063	336	3	y	y	PROPN
ejpam-7063	336	4	)	)	PUNCT
ejpam-7063	336	5	]	]	PUNCT
ejpam-7063	336	6	dx	dx	PROPN
ejpam-7063	336	7	dy	dy	NOUN
ejpam-7063	336	8	subject	subject	ADJ
ejpam-7063	336	9	to	to	ADP
ejpam-7063	336	10	the	the	DET
ejpam-7063	336	11	nonlinear	nonlinear	ADJ
ejpam-7063	336	12	fractional	fractional	ADJ
ejpam-7063	336	13	pde	pde	NOUN
ejpam-7063	336	14	:	:	PUNCT
ejpam-7063	336	15	dα	dα	VERB
ejpam-7063	336	16	xd	xd	INTJ
ejpam-7063	336	17	α	α	PRON
ejpam-7063	336	18	y	y	PROPN
ejpam-7063	336	19	z(x	z(x	PROPN
ejpam-7063	336	20	,	,	PUNCT
ejpam-7063	336	21	y	y	PROPN
ejpam-7063	336	22	)	)	PUNCT
ejpam-7063	337	1	+	+	NUM
ejpam-7063	337	2	µ	µ	PRON
ejpam-7063	337	3	sin(z(x	sin(z(x	NOUN
ejpam-7063	337	4	,	,	PUNCT
ejpam-7063	337	5	y	y	NOUN
ejpam-7063	337	6	)	)	PUNCT
ejpam-7063	337	7	)	)	PUNCT
ejpam-7063	338	1	=	=	SYM
ejpam-7063	338	2	f(x	f(x	PROPN
ejpam-7063	338	3	,	,	PUNCT
ejpam-7063	338	4	y	y	NOUN
ejpam-7063	338	5	)	)	PUNCT
ejpam-7063	338	6	+	+	CCONJ
ejpam-7063	338	7	u(x	u(x	PROPN
ejpam-7063	338	8	,	,	PUNCT
ejpam-7063	338	9	y	y	NOUN
ejpam-7063	338	10	)	)	PUNCT
ejpam-7063	338	11	with	with	ADP
ejpam-7063	338	12	boundary	boundary	ADJ
ejpam-7063	338	13	conditions	condition	NOUN
ejpam-7063	338	14	:	:	PUNCT
ejpam-7063	338	15	z(x	z(x	NUM
ejpam-7063	338	16	,	,	PUNCT
ejpam-7063	338	17	0	0	NUM
ejpam-7063	338	18	)	)	PUNCT
ejpam-7063	338	19	=	=	SYM
ejpam-7063	338	20	z(x	z(x	VERB
ejpam-7063	338	21	,	,	PUNCT
ejpam-7063	338	22	1	1	NUM
ejpam-7063	338	23	)	)	PUNCT
ejpam-7063	338	24	=	=	PUNCT
ejpam-7063	338	25	z(0	z(0	PROPN
ejpam-7063	338	26	,	,	PUNCT
ejpam-7063	338	27	y	y	NOUN
ejpam-7063	338	28	)	)	PUNCT
ejpam-7063	338	29	=	=	SYM
ejpam-7063	339	1	z(1	z(1	PROPN
ejpam-7063	339	2	,	,	PUNCT
ejpam-7063	339	3	y	y	NOUN
ejpam-7063	339	4	)	)	PUNCT
ejpam-7063	339	5	=	=	SYM
ejpam-7063	339	6	0	0	NUM
ejpam-7063	339	7	lagrangian	lagrangian	ADJ
ejpam-7063	339	8	formulation	formulation	NOUN
ejpam-7063	339	9	define	define	VERB
ejpam-7063	339	10	the	the	DET
ejpam-7063	339	11	lagrangian	lagrangian	ADJ
ejpam-7063	339	12	:	:	PUNCT
ejpam-7063	339	13	l	l	NOUN
ejpam-7063	339	14	=	=	SYM
ejpam-7063	339	15	1	1	NUM
ejpam-7063	339	16	2	2	NUM
ejpam-7063	339	17	∫	∫	NOUN
ejpam-7063	339	18	1	1	NUM
ejpam-7063	339	19	0	0	NUM
ejpam-7063	339	20	∫	∫	PROPN
ejpam-7063	339	21	1	1	NUM
ejpam-7063	339	22	0	0	NUM
ejpam-7063	340	1	[	[	PUNCT
ejpam-7063	340	2	z2	z2	NOUN
ejpam-7063	340	3	+	+	CCONJ
ejpam-7063	340	4	λu2	λu2	NOUN
ejpam-7063	340	5	]	]	PUNCT
ejpam-7063	340	6	dx	dx	PROPN
ejpam-7063	341	1	dy	dy	PROPN
ejpam-7063	341	2	+	+	CCONJ
ejpam-7063	341	3	∫	∫	PROPN
ejpam-7063	341	4	1	1	NUM
ejpam-7063	341	5	0	0	NUM
ejpam-7063	341	6	∫	∫	PROPN
ejpam-7063	341	7	1	1	NUM
ejpam-7063	341	8	0	0	NUM
ejpam-7063	341	9	p(x	p(x	PROPN
ejpam-7063	341	10	,	,	PUNCT
ejpam-7063	341	11	y	y	NOUN
ejpam-7063	341	12	)	)	PUNCT
ejpam-7063	342	1	[	[	PUNCT
ejpam-7063	342	2	dα	dα	ADV
ejpam-7063	342	3	xd	xd	INTJ
ejpam-7063	342	4	α	α	PROPN
ejpam-7063	342	5	y	y	PROPN
ejpam-7063	342	6	z	z	PROPN
ejpam-7063	342	7	+	+	PROPN
ejpam-7063	342	8	µ	µ	X
ejpam-7063	342	9	sin(z)−	sin(z)−	PROPN
ejpam-7063	342	10	f(x	f(x	PROPN
ejpam-7063	342	11	,	,	PUNCT
ejpam-7063	342	12	y)−	y)−	PROPN
ejpam-7063	342	13	u	u	NOUN
ejpam-7063	342	14	]	]	PUNCT
ejpam-7063	342	15	dx	dx	PROPN
ejpam-7063	342	16	dy	dy	PROPN
ejpam-7063	342	17	state	state	NOUN
ejpam-7063	342	18	equation	equation	NOUN
ejpam-7063	342	19	dα	dα	VERB
ejpam-7063	342	20	xd	xd	INTJ
ejpam-7063	342	21	α	α	PROPN
ejpam-7063	342	22	y	y	PROPN
ejpam-7063	342	23	z	z	PROPN
ejpam-7063	343	1	+	+	PROPN
ejpam-7063	343	2	µ	µ	PRON
ejpam-7063	343	3	sin(z	sin(z	PROPN
ejpam-7063	343	4	)	)	PUNCT
ejpam-7063	343	5	=	=	SYM
ejpam-7063	343	6	f(x	f(x	PROPN
ejpam-7063	343	7	,	,	PUNCT
ejpam-7063	343	8	y	y	PROPN
ejpam-7063	343	9	)	)	PUNCT
ejpam-7063	344	1	+	+	CCONJ
ejpam-7063	344	2	u	u	NOUN
ejpam-7063	344	3	adjoint	adjoint	NOUN
ejpam-7063	344	4	equation	equation	NOUN
ejpam-7063	344	5	dα	dα	VERB
ejpam-7063	344	6	xd	xd	INTJ
ejpam-7063	344	7	α	α	PROPN
ejpam-7063	344	8	y	y	PROPN
ejpam-7063	344	9	p+	p+	PROPN
ejpam-7063	344	10	µ	µ	X
ejpam-7063	344	11	cos(z	cos(z	X
ejpam-7063	344	12	)	)	PUNCT
ejpam-7063	344	13	p	p	NOUN
ejpam-7063	344	14	=	=	PUNCT
ejpam-7063	344	15	−z(x	−z(x	ADJ
ejpam-7063	344	16	,	,	PUNCT
ejpam-7063	344	17	y	y	NOUN
ejpam-7063	344	18	)	)	PUNCT
ejpam-7063	344	19	g.	g.	PROPN
ejpam-7063	344	20	m.	m.	NOUN
ejpam-7063	344	21	bahaa	bahaa	PROPN
ejpam-7063	344	22	,	,	PUNCT
ejpam-7063	344	23	a.	a.	NOUN
ejpam-7063	344	24	h.	h.	PROPN
ejpam-7063	344	25	qamlo	qamlo	PROPN
ejpam-7063	344	26	/	/	SYM
ejpam-7063	344	27	eur	eur	PROPN
ejpam-7063	344	28	.	.	PUNCT
ejpam-7063	345	1	j.	j.	PROPN
ejpam-7063	345	2	pure	pure	PROPN
ejpam-7063	345	3	appl	appl	PROPN
ejpam-7063	345	4	.	.	PROPN
ejpam-7063	345	5	math	math	PROPN
ejpam-7063	345	6	,	,	PUNCT
ejpam-7063	345	7	18	18	NUM
ejpam-7063	345	8	(	(	PUNCT
ejpam-7063	345	9	4	4	NUM
ejpam-7063	345	10	)	)	PUNCT
ejpam-7063	345	11	(	(	PUNCT
ejpam-7063	345	12	2025	2025	NUM
ejpam-7063	345	13	)	)	PUNCT
ejpam-7063	345	14	,	,	PUNCT
ejpam-7063	345	15	7063	7063	NUM
ejpam-7063	345	16	18	18	NUM
ejpam-7063	345	17	of	of	ADP
ejpam-7063	345	18	29	29	NUM
ejpam-7063	345	19	optimality	optimality	NOUN
ejpam-7063	345	20	condition	condition	NOUN
ejpam-7063	345	21	∂l	∂l	NOUN
ejpam-7063	345	22	∂u	∂u	PROPN
ejpam-7063	346	1	=	=	PRON
ejpam-7063	346	2	λu(x	λu(x	NOUN
ejpam-7063	346	3	,	,	PUNCT
ejpam-7063	346	4	y)−	y)−	PROPN
ejpam-7063	346	5	p(x	p(x	PROPN
ejpam-7063	346	6	,	,	PUNCT
ejpam-7063	346	7	y	y	NOUN
ejpam-7063	346	8	)	)	PUNCT
ejpam-7063	346	9	=	=	SYM
ejpam-7063	346	10	0	0	NUM
ejpam-7063	346	11	⇒	⇒	PROPN
ejpam-7063	346	12	u(x	u(x	PROPN
ejpam-7063	346	13	,	,	PUNCT
ejpam-7063	346	14	y	y	NOUN
ejpam-7063	346	15	)	)	PUNCT
ejpam-7063	346	16	=	=	SYM
ejpam-7063	346	17	1	1	NUM
ejpam-7063	346	18	λ	λ	NOUN
ejpam-7063	346	19	p(x	p(x	PROPN
ejpam-7063	346	20	,	,	PUNCT
ejpam-7063	346	21	y	y	NOUN
ejpam-7063	346	22	)	)	PUNCT
ejpam-7063	346	23	boundary	boundary	ADJ
ejpam-7063	346	24	conditions	condition	NOUN
ejpam-7063	346	25	z(x	z(x	NUM
ejpam-7063	346	26	,	,	PUNCT
ejpam-7063	346	27	0	0	NUM
ejpam-7063	346	28	)	)	PUNCT
ejpam-7063	346	29	=	=	SYM
ejpam-7063	346	30	z(x	z(x	VERB
ejpam-7063	346	31	,	,	PUNCT
ejpam-7063	346	32	1	1	NUM
ejpam-7063	346	33	)	)	PUNCT
ejpam-7063	346	34	=	=	PUNCT
ejpam-7063	346	35	z(0	z(0	PROPN
ejpam-7063	346	36	,	,	PUNCT
ejpam-7063	346	37	y	y	NOUN
ejpam-7063	346	38	)	)	PUNCT
ejpam-7063	346	39	=	=	SYM
ejpam-7063	347	1	z(1	z(1	PROPN
ejpam-7063	347	2	,	,	PUNCT
ejpam-7063	347	3	y	y	NOUN
ejpam-7063	347	4	)	)	PUNCT
ejpam-7063	347	5	=	=	SYM
ejpam-7063	347	6	0	0	NUM
ejpam-7063	347	7	,	,	PUNCT
ejpam-7063	347	8	p(x	p(x	NOUN
ejpam-7063	347	9	,	,	PUNCT
ejpam-7063	347	10	0	0	NUM
ejpam-7063	347	11	)	)	PUNCT
ejpam-7063	347	12	=	=	SYM
ejpam-7063	347	13	p(x	p(x	NOUN
ejpam-7063	347	14	,	,	PUNCT
ejpam-7063	347	15	1	1	NUM
ejpam-7063	347	16	)	)	PUNCT
ejpam-7063	347	17	=	=	SYM
ejpam-7063	348	1	p(0	p(0	PROPN
ejpam-7063	348	2	,	,	PUNCT
ejpam-7063	348	3	y	y	NOUN
ejpam-7063	348	4	)	)	PUNCT
ejpam-7063	348	5	=	=	SYM
ejpam-7063	349	1	p(1	p(1	PROPN
ejpam-7063	349	2	,	,	PUNCT
ejpam-7063	349	3	y	y	NOUN
ejpam-7063	349	4	)	)	PUNCT
ejpam-7063	349	5	=	=	SYM
ejpam-7063	349	6	0	0	NUM
ejpam-7063	349	7	figure	figure	NOUN
ejpam-7063	349	8	3	3	NUM
ejpam-7063	349	9	:	:	PUNCT
ejpam-7063	349	10	the	the	DET
ejpam-7063	349	11	3d	3d	PROPN
ejpam-7063	349	12	surface	surface	NOUN
ejpam-7063	349	13	plots	plot	NOUN
ejpam-7063	349	14	for	for	ADP
ejpam-7063	349	15	the	the	DET
ejpam-7063	349	16	state	state	NOUN
ejpam-7063	349	17	z(x	z(x	PROPN
ejpam-7063	349	18	,	,	PUNCT
ejpam-7063	349	19	y	y	PROPN
ejpam-7063	349	20	)	)	PUNCT
ejpam-7063	349	21	,	,	PUNCT
ejpam-7063	349	22	adjoint	adjoint	PROPN
ejpam-7063	349	23	p(x	p(x	PROPN
ejpam-7063	349	24	,	,	PUNCT
ejpam-7063	349	25	y	y	NOUN
ejpam-7063	349	26	)	)	PUNCT
ejpam-7063	349	27	,	,	PUNCT
ejpam-7063	349	28	and	and	CCONJ
ejpam-7063	349	29	control	control	VERB
ejpam-7063	349	30	u(x	u(x	NOUN
ejpam-7063	349	31	,	,	PUNCT
ejpam-7063	349	32	y	y	NOUN
ejpam-7063	349	33	)	)	PUNCT
ejpam-7063	349	34	optimality	optimality	NOUN
ejpam-7063	349	35	conditions	condition	NOUN
ejpam-7063	349	36	for	for	ADP
ejpam-7063	349	37	a	a	DET
ejpam-7063	349	38	2d	2d	NUM
ejpam-7063	349	39	nonlinear	nonlinear	ADJ
ejpam-7063	349	40	fractional	fractional	ADJ
ejpam-7063	349	41	optimal	optimal	ADJ
ejpam-7063	349	42	control	control	NOUN
ejpam-7063	349	43	problem	problem	NOUN
ejpam-7063	349	44	we	we	PRON
ejpam-7063	349	45	consider	consider	VERB
ejpam-7063	349	46	the	the	DET
ejpam-7063	349	47	following	follow	VERB
ejpam-7063	349	48	fractional	fractional	ADJ
ejpam-7063	349	49	optimal	optimal	ADJ
ejpam-7063	349	50	control	control	NOUN
ejpam-7063	349	51	problem	problem	NOUN
ejpam-7063	349	52	:	:	PUNCT
ejpam-7063	349	53	minimize	minimize	VERB
ejpam-7063	349	54	j(u	j(u	PROPN
ejpam-7063	349	55	)	)	PUNCT
ejpam-7063	349	56	=	=	SYM
ejpam-7063	350	1	1	1	NUM
ejpam-7063	350	2	2	2	NUM
ejpam-7063	350	3	∫∫	∫∫	PROPN
ejpam-7063	350	4	ω	ω	NOUN
ejpam-7063	350	5	[	[	PUNCT
ejpam-7063	350	6	(	(	PUNCT
ejpam-7063	350	7	z(x	z(x	PROPN
ejpam-7063	350	8	,	,	PUNCT
ejpam-7063	350	9	y)−	y)−	PROPN
ejpam-7063	350	10	zd(x	zd(x	NUM
ejpam-7063	350	11	,	,	PUNCT
ejpam-7063	350	12	y))2	y))2	PROPN
ejpam-7063	350	13	+	+	X
ejpam-7063	350	14	λu(x	λu(x	NOUN
ejpam-7063	350	15	,	,	PUNCT
ejpam-7063	350	16	y)2	y)2	NOUN
ejpam-7063	350	17	]	]	PUNCT
ejpam-7063	350	18	dx	dx	PROPN
ejpam-7063	350	19	dy	dy	NOUN
ejpam-7063	350	20	subject	subject	ADJ
ejpam-7063	350	21	to	to	ADP
ejpam-7063	350	22	the	the	DET
ejpam-7063	350	23	nonlinear	nonlinear	ADJ
ejpam-7063	350	24	fractional	fractional	ADJ
ejpam-7063	350	25	pde	pde	NOUN
ejpam-7063	350	26	:	:	PUNCT
ejpam-7063	350	27	dα	dα	VERB
ejpam-7063	351	1	xd	xd	INTJ
ejpam-7063	351	2	α	α	PRON
ejpam-7063	351	3	y	y	PROPN
ejpam-7063	351	4	z(x	z(x	PROPN
ejpam-7063	351	5	,	,	PUNCT
ejpam-7063	351	6	y	y	PROPN
ejpam-7063	351	7	)	)	PUNCT
ejpam-7063	351	8	+	+	NUM
ejpam-7063	351	9	µ	µ	PRON
ejpam-7063	351	10	sin(z(x	sin(z(x	NOUN
ejpam-7063	351	11	,	,	PUNCT
ejpam-7063	351	12	y	y	NOUN
ejpam-7063	351	13	)	)	PUNCT
ejpam-7063	351	14	)	)	PUNCT
ejpam-7063	352	1	=	=	SYM
ejpam-7063	352	2	f(x	f(x	PROPN
ejpam-7063	352	3	,	,	PUNCT
ejpam-7063	352	4	y	y	NOUN
ejpam-7063	352	5	)	)	PUNCT
ejpam-7063	352	6	+	+	CCONJ
ejpam-7063	352	7	u(x	u(x	PROPN
ejpam-7063	352	8	,	,	PUNCT
ejpam-7063	352	9	y	y	NOUN
ejpam-7063	352	10	)	)	PUNCT
ejpam-7063	352	11	,	,	PUNCT
ejpam-7063	352	12	with	with	ADP
ejpam-7063	352	13	boundary	boundary	ADJ
ejpam-7063	352	14	conditions	condition	NOUN
ejpam-7063	352	15	:	:	PUNCT
ejpam-7063	352	16	z(x	z(x	NUM
ejpam-7063	352	17	,	,	PUNCT
ejpam-7063	352	18	0	0	NUM
ejpam-7063	352	19	)	)	PUNCT
ejpam-7063	352	20	=	=	SYM
ejpam-7063	352	21	z(x	z(x	VERB
ejpam-7063	352	22	,	,	PUNCT
ejpam-7063	352	23	1	1	NUM
ejpam-7063	352	24	)	)	PUNCT
ejpam-7063	352	25	=	=	PUNCT
ejpam-7063	352	26	z(0	z(0	PROPN
ejpam-7063	352	27	,	,	PUNCT
ejpam-7063	352	28	y	y	NOUN
ejpam-7063	352	29	)	)	PUNCT
ejpam-7063	352	30	=	=	SYM
ejpam-7063	353	1	z(1	z(1	PROPN
ejpam-7063	353	2	,	,	PUNCT
ejpam-7063	353	3	y	y	NOUN
ejpam-7063	353	4	)	)	PUNCT
ejpam-7063	353	5	=	=	SYM
ejpam-7063	353	6	0	0	X
ejpam-7063	353	7	.	.	X
ejpam-7063	354	1	lagrangian	lagrangian	ADJ
ejpam-7063	354	2	the	the	DET
ejpam-7063	354	3	lagrangian	lagrangian	NOUN
ejpam-7063	354	4	is	be	AUX
ejpam-7063	354	5	defined	define	VERB
ejpam-7063	354	6	as	as	ADP
ejpam-7063	354	7	:	:	PUNCT
ejpam-7063	354	8	l(z	l(z	PROPN
ejpam-7063	354	9	,	,	PUNCT
ejpam-7063	354	10	u	u	NOUN
ejpam-7063	354	11	,	,	PUNCT
ejpam-7063	354	12	p	p	NOUN
ejpam-7063	354	13	)	)	PUNCT
ejpam-7063	354	14	=	=	SYM
ejpam-7063	354	15	1	1	NUM
ejpam-7063	354	16	2	2	NUM
ejpam-7063	354	17	∫∫	∫∫	PROPN
ejpam-7063	354	18	ω	ω	NOUN
ejpam-7063	354	19	[	[	PUNCT
ejpam-7063	354	20	(	(	PUNCT
ejpam-7063	354	21	z	z	NOUN
ejpam-7063	354	22	−	−	PROPN
ejpam-7063	354	23	zd)2	zd)2	NOUN
ejpam-7063	354	24	+	+	CCONJ
ejpam-7063	354	25	λu2	λu2	NOUN
ejpam-7063	354	26	]	]	PUNCT
ejpam-7063	354	27	dxdy	dxdy	NOUN
ejpam-7063	354	28	+	+	CCONJ
ejpam-7063	354	29	∫∫	∫∫	PROPN
ejpam-7063	354	30	ω	ω	PROPN
ejpam-7063	354	31	p(x	p(x	PROPN
ejpam-7063	354	32	,	,	PUNCT
ejpam-7063	354	33	y	y	PROPN
ejpam-7063	354	34	)	)	PUNCT
ejpam-7063	354	35	(	(	PUNCT
ejpam-7063	354	36	dα	dα	VERB
ejpam-7063	355	1	xd	xd	INTJ
ejpam-7063	355	2	α	α	PROPN
ejpam-7063	355	3	y	y	PROPN
ejpam-7063	355	4	z	z	PROPN
ejpam-7063	356	1	+	+	PROPN
ejpam-7063	356	2	µ	µ	X
ejpam-7063	356	3	sin(z)−	sin(z)−	PROPN
ejpam-7063	356	4	f	f	PROPN
ejpam-7063	356	5	−	−	PROPN
ejpam-7063	356	6	u	u	PROPN
ejpam-7063	356	7	)	)	PUNCT
ejpam-7063	356	8	dxdy	dxdy	PROPN
ejpam-7063	356	9	g.	g.	PROPN
ejpam-7063	356	10	m.	m.	PROPN
ejpam-7063	356	11	bahaa	bahaa	PROPN
ejpam-7063	356	12	,	,	PUNCT
ejpam-7063	356	13	a.	a.	NOUN
ejpam-7063	356	14	h.	h.	PROPN
ejpam-7063	356	15	qamlo	qamlo	PROPN
ejpam-7063	356	16	/	/	SYM
ejpam-7063	356	17	eur	eur	PROPN
ejpam-7063	356	18	.	.	PUNCT
ejpam-7063	357	1	j.	j.	PROPN
ejpam-7063	357	2	pure	pure	PROPN
ejpam-7063	357	3	appl	appl	PROPN
ejpam-7063	357	4	.	.	PROPN
ejpam-7063	357	5	math	math	PROPN
ejpam-7063	357	6	,	,	PUNCT
ejpam-7063	357	7	18	18	NUM
ejpam-7063	357	8	(	(	PUNCT
ejpam-7063	357	9	4	4	NUM
ejpam-7063	357	10	)	)	PUNCT
ejpam-7063	357	11	(	(	PUNCT
ejpam-7063	357	12	2025	2025	NUM
ejpam-7063	357	13	)	)	PUNCT
ejpam-7063	357	14	,	,	PUNCT
ejpam-7063	357	15	7063	7063	NUM
ejpam-7063	357	16	19	19	NUM
ejpam-7063	357	17	of	of	ADP
ejpam-7063	357	18	29	29	NUM
ejpam-7063	357	19	first	first	ADJ
ejpam-7063	357	20	-	-	PUNCT
ejpam-7063	357	21	order	order	NOUN
ejpam-7063	357	22	optimality	optimality	NOUN
ejpam-7063	357	23	conditions	condition	NOUN
ejpam-7063	357	24	•	•	NOUN
ejpam-7063	357	25	state	state	NOUN
ejpam-7063	357	26	equation	equation	NOUN
ejpam-7063	357	27	:	:	PUNCT
ejpam-7063	357	28	dα	dα	VERB
ejpam-7063	357	29	xd	xd	INTJ
ejpam-7063	357	30	α	α	PRON
ejpam-7063	357	31	y	y	PROPN
ejpam-7063	357	32	z(x	z(x	PROPN
ejpam-7063	357	33	,	,	PUNCT
ejpam-7063	357	34	y	y	PROPN
ejpam-7063	357	35	)	)	PUNCT
ejpam-7063	358	1	+	+	NUM
ejpam-7063	358	2	µ	µ	PRON
ejpam-7063	358	3	sin(z(x	sin(z(x	NOUN
ejpam-7063	358	4	,	,	PUNCT
ejpam-7063	358	5	y	y	NOUN
ejpam-7063	358	6	)	)	PUNCT
ejpam-7063	358	7	)	)	PUNCT
ejpam-7063	359	1	=	=	SYM
ejpam-7063	359	2	f(x	f(x	PROPN
ejpam-7063	359	3	,	,	PUNCT
ejpam-7063	359	4	y	y	NOUN
ejpam-7063	359	5	)	)	PUNCT
ejpam-7063	359	6	+	+	CCONJ
ejpam-7063	359	7	u(x	u(x	PROPN
ejpam-7063	359	8	,	,	PUNCT
ejpam-7063	359	9	y	y	NOUN
ejpam-7063	359	10	)	)	PUNCT
ejpam-7063	359	11	•	•	NUM
ejpam-7063	359	12	adjoint	adjoint	NOUN
ejpam-7063	359	13	equation	equation	NOUN
ejpam-7063	359	14	:	:	PUNCT
ejpam-7063	359	15	dα	dα	VERB
ejpam-7063	360	1	xd	xd	INTJ
ejpam-7063	360	2	α	α	PROPN
ejpam-7063	360	3	y	y	PROPN
ejpam-7063	360	4	p(x	p(x	PROPN
ejpam-7063	360	5	,	,	PUNCT
ejpam-7063	360	6	y	y	PROPN
ejpam-7063	360	7	)	)	PUNCT
ejpam-7063	361	1	+	+	CCONJ
ejpam-7063	361	2	(	(	PUNCT
ejpam-7063	361	3	z(x	z(x	NUM
ejpam-7063	361	4	,	,	PUNCT
ejpam-7063	361	5	y)−	y)−	PROPN
ejpam-7063	361	6	zd(x	zd(x	NUM
ejpam-7063	361	7	,	,	PUNCT
ejpam-7063	361	8	y	y	NOUN
ejpam-7063	361	9	)	)	PUNCT
ejpam-7063	361	10	)	)	PUNCT
ejpam-7063	362	1	+	+	CCONJ
ejpam-7063	362	2	µ	µ	X
ejpam-7063	362	3	cos(z(x	cos(z(x	NOUN
ejpam-7063	362	4	,	,	PUNCT
ejpam-7063	362	5	y))p(x	y))p(x	PROPN
ejpam-7063	362	6	,	,	PUNCT
ejpam-7063	362	7	y	y	NOUN
ejpam-7063	362	8	)	)	PUNCT
ejpam-7063	362	9	=	=	SYM
ejpam-7063	362	10	0	0	NUM
ejpam-7063	362	11	with	with	ADP
ejpam-7063	362	12	boundary	boundary	ADJ
ejpam-7063	362	13	conditions	condition	NOUN
ejpam-7063	362	14	:	:	PUNCT
ejpam-7063	363	1	p(x	p(x	NOUN
ejpam-7063	363	2	,	,	PUNCT
ejpam-7063	363	3	0	0	NUM
ejpam-7063	363	4	)	)	PUNCT
ejpam-7063	363	5	=	=	SYM
ejpam-7063	363	6	p(x	p(x	NOUN
ejpam-7063	363	7	,	,	PUNCT
ejpam-7063	363	8	1	1	NUM
ejpam-7063	363	9	)	)	PUNCT
ejpam-7063	363	10	=	=	SYM
ejpam-7063	364	1	p(0	p(0	PROPN
ejpam-7063	364	2	,	,	PUNCT
ejpam-7063	364	3	y	y	NOUN
ejpam-7063	364	4	)	)	PUNCT
ejpam-7063	364	5	=	=	SYM
ejpam-7063	365	1	p(1	p(1	PROPN
ejpam-7063	365	2	,	,	PUNCT
ejpam-7063	365	3	y	y	NOUN
ejpam-7063	365	4	)	)	PUNCT
ejpam-7063	365	5	=	=	SYM
ejpam-7063	365	6	0	0	NUM
ejpam-7063	365	7	•	•	NOUN
ejpam-7063	365	8	optimality	optimality	NOUN
ejpam-7063	365	9	condition	condition	NOUN
ejpam-7063	365	10	:	:	PUNCT
ejpam-7063	365	11	λu(x	λu(x	NOUN
ejpam-7063	365	12	,	,	PUNCT
ejpam-7063	365	13	y	y	NOUN
ejpam-7063	365	14	)	)	PUNCT
ejpam-7063	365	15	+	+	CCONJ
ejpam-7063	365	16	p(x	p(x	PROPN
ejpam-7063	365	17	,	,	PUNCT
ejpam-7063	365	18	y	y	NOUN
ejpam-7063	365	19	)	)	PUNCT
ejpam-7063	365	20	=	=	SYM
ejpam-7063	365	21	0	0	NUM
ejpam-7063	365	22	⇒	⇒	PROPN
ejpam-7063	365	23	u(x	u(x	PROPN
ejpam-7063	365	24	,	,	PUNCT
ejpam-7063	365	25	y	y	NOUN
ejpam-7063	365	26	)	)	PUNCT
ejpam-7063	365	27	=	=	SYM
ejpam-7063	366	1	−	−	PROPN
ejpam-7063	366	2	1	1	NUM
ejpam-7063	366	3	λ	λ	PROPN
ejpam-7063	366	4	p(x	p(x	PROPN
ejpam-7063	366	5	,	,	PUNCT
ejpam-7063	366	6	y	y	NOUN
ejpam-7063	366	7	)	)	PUNCT
ejpam-7063	366	8	linear	linear	ADJ
ejpam-7063	366	9	benchmark	benchmark	NOUN
ejpam-7063	366	10	with	with	ADP
ejpam-7063	366	11	forcing	force	VERB
ejpam-7063	366	12	we	we	PRON
ejpam-7063	366	13	consider	consider	VERB
ejpam-7063	366	14	the	the	DET
ejpam-7063	366	15	linear	linear	ADJ
ejpam-7063	366	16	test	test	NOUN
ejpam-7063	366	17	problem	problem	NOUN
ejpam-7063	366	18	on	on	ADP
ejpam-7063	366	19	ω	ω	PROPN
ejpam-7063	366	20	=	=	PUNCT
ejpam-7063	367	1	[	[	X
ejpam-7063	367	2	0	0	NUM
ejpam-7063	367	3	,	,	PUNCT
ejpam-7063	367	4	1]2	1]2	NUM
ejpam-7063	367	5	with	with	ADP
ejpam-7063	367	6	fractional	fractional	ADJ
ejpam-7063	367	7	order	order	NOUN
ejpam-7063	367	8	α	α	NOUN
ejpam-7063	367	9	=	=	NOUN
ejpam-7063	367	10	0.9	0.9	NUM
ejpam-7063	367	11	:	:	PUNCT
ejpam-7063	367	12	cd0.9	cd0.9	NOUN
ejpam-7063	367	13	x	x	SYM
ejpam-7063	367	14	cd0.9	cd0.9	PROPN
ejpam-7063	367	15	y	y	PROPN
ejpam-7063	367	16	z(x	z(x	PROPN
ejpam-7063	367	17	,	,	PUNCT
ejpam-7063	367	18	y	y	NOUN
ejpam-7063	367	19	)	)	PUNCT
ejpam-7063	367	20	=	=	SYM
ejpam-7063	368	1	−z(x	−z(x	ADJ
ejpam-7063	368	2	,	,	PUNCT
ejpam-7063	368	3	y)+u(x	y)+u(x	NOUN
ejpam-7063	368	4	,	,	PUNCT
ejpam-7063	368	5	y)+f(x	y)+f(x	PROPN
ejpam-7063	368	6	,	,	PUNCT
ejpam-7063	368	7	y	y	PROPN
ejpam-7063	368	8	)	)	PUNCT
ejpam-7063	368	9	,	,	PUNCT
ejpam-7063	368	10	cd0.9	cd0.9	NOUN
ejpam-7063	368	11	x	x	SYM
ejpam-7063	368	12	cd0.9	cd0.9	PROPN
ejpam-7063	368	13	y	y	PROPN
ejpam-7063	368	14	p(x	p(x	PROPN
ejpam-7063	368	15	,	,	PUNCT
ejpam-7063	368	16	y	y	NOUN
ejpam-7063	368	17	)	)	PUNCT
ejpam-7063	368	18	=	=	SYM
ejpam-7063	368	19	2z(x	2z(x	NUM
ejpam-7063	368	20	,	,	PUNCT
ejpam-7063	368	21	y)+p(x	y)+p(x	PROPN
ejpam-7063	368	22	,	,	PUNCT
ejpam-7063	368	23	y	y	PROPN
ejpam-7063	368	24	)	)	PUNCT
ejpam-7063	368	25	,	,	PUNCT
ejpam-7063	368	26	together	together	ADV
ejpam-7063	368	27	with	with	ADP
ejpam-7063	368	28	homogeneous	homogeneous	ADJ
ejpam-7063	368	29	dirichlet	dirichlet	PROPN
ejpam-7063	368	30	boundary	boundary	ADJ
ejpam-7063	368	31	conditions	condition	NOUN
ejpam-7063	368	32	on	on	ADP
ejpam-7063	368	33	∂ω	∂ω	ADJ
ejpam-7063	368	34	and	and	CCONJ
ejpam-7063	368	35	the	the	DET
ejpam-7063	368	36	control	control	PROPN
ejpam-7063	368	37	relation	relation	PROPN
ejpam-7063	368	38	u	u	NOUN
ejpam-7063	368	39	=	=	NOUN
ejpam-7063	368	40	1	1	NUM
ejpam-7063	368	41	2p	2p	NUM
ejpam-7063	368	42	.	.	PUNCT
ejpam-7063	369	1	we	we	PRON
ejpam-7063	369	2	choose	choose	VERB
ejpam-7063	369	3	the	the	DET
ejpam-7063	369	4	forcing	force	VERB
ejpam-7063	369	5	term	term	NOUN
ejpam-7063	369	6	f(x	f(x	PROPN
ejpam-7063	369	7	,	,	PUNCT
ejpam-7063	369	8	y	y	NOUN
ejpam-7063	369	9	)	)	PUNCT
ejpam-7063	369	10	=	=	SYM
ejpam-7063	369	11	sin(πx	sin(πx	NOUN
ejpam-7063	369	12	)	)	PUNCT
ejpam-7063	369	13	sin(πy	sin(πy	NOUN
ejpam-7063	369	14	)	)	PUNCT
ejpam-7063	369	15	to	to	PART
ejpam-7063	369	16	obtain	obtain	VERB
ejpam-7063	369	17	a	a	DET
ejpam-7063	369	18	nontrivial	nontrivial	ADJ
ejpam-7063	369	19	solution	solution	NOUN
ejpam-7063	369	20	.	.	PUNCT
ejpam-7063	370	1	the	the	DET
ejpam-7063	370	2	spatial	spatial	ADJ
ejpam-7063	370	3	domain	domain	NOUN
ejpam-7063	370	4	was	be	AUX
ejpam-7063	370	5	discretized	discretize	VERB
ejpam-7063	370	6	on	on	ADP
ejpam-7063	370	7	a	a	DET
ejpam-7063	370	8	uniform	uniform	ADJ
ejpam-7063	370	9	25	25	NUM
ejpam-7063	370	10	×	×	NOUN
ejpam-7063	370	11	25	25	NUM
ejpam-7063	370	12	grid	grid	NOUN
ejpam-7063	370	13	(	(	PUNCT
ejpam-7063	370	14	23	23	NUM
ejpam-7063	370	15	interior	interior	ADJ
ejpam-7063	370	16	points	point	NOUN
ejpam-7063	370	17	per	per	ADP
ejpam-7063	370	18	direction	direction	NOUN
ejpam-7063	370	19	)	)	PUNCT
ejpam-7063	370	20	.	.	PUNCT
ejpam-7063	371	1	the	the	DET
ejpam-7063	371	2	caputo	caputo	PROPN
ejpam-7063	371	3	-	-	PUNCT
ejpam-7063	371	4	like	like	ADJ
ejpam-7063	371	5	fractional	fractional	ADJ
ejpam-7063	371	6	derivative	derivative	NOUN
ejpam-7063	371	7	was	be	AUX
ejpam-7063	371	8	approximated	approximate	VERB
ejpam-7063	371	9	using	use	VERB
ejpam-7063	371	10	the	the	DET
ejpam-7063	371	11	grünwald	grünwald	NOUN
ejpam-7063	371	12	–	–	PUNCT
ejpam-7063	371	13	letnikov	letnikov	NOUN
ejpam-7063	371	14	scheme	scheme	NOUN
ejpam-7063	371	15	in	in	ADP
ejpam-7063	371	16	each	each	DET
ejpam-7063	371	17	coordinate	coordinate	NOUN
ejpam-7063	371	18	direction	direction	NOUN
ejpam-7063	371	19	and	and	CCONJ
ejpam-7063	371	20	the	the	DET
ejpam-7063	371	21	two	two	NUM
ejpam-7063	371	22	-	-	PUNCT
ejpam-7063	371	23	dimensional	dimensional	ADJ
ejpam-7063	371	24	operator	operator	NOUN
ejpam-7063	371	25	was	be	AUX
ejpam-7063	371	26	formed	form	VERB
ejpam-7063	371	27	by	by	ADP
ejpam-7063	371	28	the	the	DET
ejpam-7063	371	29	kronecker	kronecker	NOUN
ejpam-7063	371	30	product	product	NOUN
ejpam-7063	371	31	.	.	PUNCT
ejpam-7063	372	1	this	this	PRON
ejpam-7063	372	2	yields	yield	VERB
ejpam-7063	372	3	a	a	DET
ejpam-7063	372	4	sparse	sparse	ADJ
ejpam-7063	372	5	linear	linear	NOUN
ejpam-7063	372	6	system	system	NOUN
ejpam-7063	372	7	of	of	ADP
ejpam-7063	372	8	size	size	NOUN
ejpam-7063	372	9	2	2	NUM
ejpam-7063	372	10	m	m	NOUN
ejpam-7063	372	11	×	×	NOUN
ejpam-7063	372	12	2	2	NUM
ejpam-7063	372	13	m	m	NOUN
ejpam-7063	372	14	with	with	ADP
ejpam-7063	372	15	m	m	PROPN
ejpam-7063	372	16	=	=	PUNCT
ejpam-7063	372	17	(	(	PUNCT
ejpam-7063	372	18	n	n	CCONJ
ejpam-7063	372	19	−	−	PROPN
ejpam-7063	372	20	2)2	2)2	NUM
ejpam-7063	372	21	unknowns	unknown	NOUN
ejpam-7063	372	22	per	per	ADP
ejpam-7063	372	23	field	field	NOUN
ejpam-7063	372	24	,	,	PUNCT
ejpam-7063	372	25	solved	solve	VERB
ejpam-7063	372	26	with	with	ADP
ejpam-7063	372	27	a	a	DET
ejpam-7063	372	28	sparse	sparse	ADJ
ejpam-7063	372	29	direct	direct	ADJ
ejpam-7063	372	30	solver	solver	NOUN
ejpam-7063	372	31	.	.	PUNCT
ejpam-7063	373	1	computed	compute	VERB
ejpam-7063	373	2	diagnostics	diagnostic	NOUN
ejpam-7063	373	3	:	:	PUNCT
ejpam-7063	373	4	∥z∥l2(ω	∥z∥l2(ω	X
ejpam-7063	373	5	)	)	PUNCT
ejpam-7063	373	6	≈	≈	PROPN
ejpam-7063	373	7	1.5336	1.5336	NUM
ejpam-7063	373	8	·	·	SYM
ejpam-7063	373	9	10−1	10−1	NUM
ejpam-7063	373	10	,	,	PUNCT
ejpam-7063	373	11	∥p∥l2(ω	∥p∥l2(ω	NOUN
ejpam-7063	373	12	)	)	PUNCT
ejpam-7063	374	1	≈	≈	PROPN
ejpam-7063	374	2	6.5518	6.5518	NUM
ejpam-7063	374	3	·	·	SYM
ejpam-7063	374	4	10−2	10−2	NUM
ejpam-7063	374	5	,	,	PUNCT
ejpam-7063	374	6	∥u∥l2(ω	∥u∥l2(ω	NUM
ejpam-7063	374	7	)	)	PUNCT
ejpam-7063	375	1	≈	≈	PROPN
ejpam-7063	375	2	3.2759	3.2759	NUM
ejpam-7063	375	3	·	·	PUNCT
ejpam-7063	375	4	10−2	10−2	NUM
ejpam-7063	375	5	.	.	PUNCT
ejpam-7063	376	1	g.	g.	PROPN
ejpam-7063	376	2	m.	m.	PROPN
ejpam-7063	376	3	bahaa	bahaa	PROPN
ejpam-7063	376	4	,	,	PUNCT
ejpam-7063	376	5	a.	a.	NOUN
ejpam-7063	376	6	h.	h.	PROPN
ejpam-7063	376	7	qamlo	qamlo	PROPN
ejpam-7063	376	8	/	/	SYM
ejpam-7063	376	9	eur	eur	PROPN
ejpam-7063	376	10	.	.	PUNCT
ejpam-7063	377	1	j.	j.	PROPN
ejpam-7063	377	2	pure	pure	PROPN
ejpam-7063	377	3	appl	appl	PROPN
ejpam-7063	377	4	.	.	PROPN
ejpam-7063	377	5	math	math	PROPN
ejpam-7063	377	6	,	,	PUNCT
ejpam-7063	377	7	18	18	NUM
ejpam-7063	377	8	(	(	PUNCT
ejpam-7063	377	9	4	4	NUM
ejpam-7063	377	10	)	)	PUNCT
ejpam-7063	377	11	(	(	PUNCT
ejpam-7063	377	12	2025	2025	NUM
ejpam-7063	377	13	)	)	PUNCT
ejpam-7063	377	14	,	,	PUNCT
ejpam-7063	377	15	7063	7063	NUM
ejpam-7063	377	16	20	20	NUM
ejpam-7063	377	17	of	of	ADP
ejpam-7063	377	18	29	29	NUM
ejpam-7063	377	19	(	(	PUNCT
ejpam-7063	377	20	a	a	NOUN
ejpam-7063	377	21	)	)	PUNCT
ejpam-7063	377	22	state	state	NOUN
ejpam-7063	377	23	z(x	z(x	PROPN
ejpam-7063	377	24	,	,	PUNCT
ejpam-7063	377	25	y	y	PROPN
ejpam-7063	377	26	)	)	PUNCT
ejpam-7063	377	27	(	(	PUNCT
ejpam-7063	377	28	b	b	X
ejpam-7063	377	29	)	)	PUNCT
ejpam-7063	377	30	adjoint	adjoint	NOUN
ejpam-7063	377	31	p(x	p(x	PROPN
ejpam-7063	377	32	,	,	PUNCT
ejpam-7063	377	33	y	y	PROPN
ejpam-7063	377	34	)	)	PUNCT
ejpam-7063	377	35	(	(	PUNCT
ejpam-7063	377	36	c	c	X
ejpam-7063	377	37	)	)	PUNCT
ejpam-7063	377	38	control	control	NOUN
ejpam-7063	377	39	u(x	u(x	NOUN
ejpam-7063	377	40	,	,	PUNCT
ejpam-7063	377	41	y	y	NOUN
ejpam-7063	377	42	)	)	PUNCT
ejpam-7063	377	43	=	=	NOUN
ejpam-7063	377	44	p/2	p/2	NOUN
ejpam-7063	377	45	figure	figure	NOUN
ejpam-7063	377	46	4	4	NUM
ejpam-7063	377	47	:	:	PUNCT
ejpam-7063	377	48	surface	surface	NOUN
ejpam-7063	377	49	plots	plot	NOUN
ejpam-7063	377	50	of	of	ADP
ejpam-7063	377	51	the	the	DET
ejpam-7063	377	52	numerical	numerical	ADJ
ejpam-7063	377	53	solution	solution	NOUN
ejpam-7063	377	54	for	for	ADP
ejpam-7063	377	55	example	example	NOUN
ejpam-7063	377	56	1	1	NUM
ejpam-7063	377	57	:	:	PUNCT
ejpam-7063	377	58	(	(	PUNCT
ejpam-7063	377	59	a	a	X
ejpam-7063	377	60	)	)	PUNCT
ejpam-7063	377	61	state	state	NOUN
ejpam-7063	377	62	z(x	z(x	PROPN
ejpam-7063	377	63	,	,	PUNCT
ejpam-7063	377	64	y	y	PROPN
ejpam-7063	377	65	)	)	PUNCT
ejpam-7063	377	66	,	,	PUNCT
ejpam-7063	377	67	(	(	PUNCT
ejpam-7063	377	68	b	b	X
ejpam-7063	377	69	)	)	PUNCT
ejpam-7063	377	70	adjoint	adjoint	NOUN
ejpam-7063	377	71	p(x	p(x	PROPN
ejpam-7063	377	72	,	,	PUNCT
ejpam-7063	377	73	y	y	NOUN
ejpam-7063	377	74	)	)	PUNCT
ejpam-7063	377	75	,	,	PUNCT
ejpam-7063	377	76	and	and	CCONJ
ejpam-7063	377	77	(	(	PUNCT
ejpam-7063	377	78	c	c	NOUN
ejpam-7063	377	79	)	)	PUNCT
ejpam-7063	377	80	control	control	NOUN
ejpam-7063	377	81	u(x	u(x	NOUN
ejpam-7063	377	82	,	,	PUNCT
ejpam-7063	377	83	y	y	NOUN
ejpam-7063	377	84	)	)	PUNCT
ejpam-7063	377	85	.	.	PUNCT
ejpam-7063	378	1	g.	g.	PROPN
ejpam-7063	378	2	m.	m.	PROPN
ejpam-7063	378	3	bahaa	bahaa	PROPN
ejpam-7063	378	4	,	,	PUNCT
ejpam-7063	378	5	a.	a.	NOUN
ejpam-7063	378	6	h.	h.	PROPN
ejpam-7063	378	7	qamlo	qamlo	PROPN
ejpam-7063	378	8	/	/	SYM
ejpam-7063	378	9	eur	eur	PROPN
ejpam-7063	378	10	.	.	PUNCT
ejpam-7063	379	1	j.	j.	PROPN
ejpam-7063	379	2	pure	pure	PROPN
ejpam-7063	379	3	appl	appl	PROPN
ejpam-7063	379	4	.	.	PROPN
ejpam-7063	379	5	math	math	PROPN
ejpam-7063	379	6	,	,	PUNCT
ejpam-7063	379	7	18	18	NUM
ejpam-7063	379	8	(	(	PUNCT
ejpam-7063	379	9	4	4	NUM
ejpam-7063	379	10	)	)	PUNCT
ejpam-7063	379	11	(	(	PUNCT
ejpam-7063	379	12	2025	2025	NUM
ejpam-7063	379	13	)	)	PUNCT
ejpam-7063	379	14	,	,	PUNCT
ejpam-7063	379	15	7063	7063	NUM
ejpam-7063	379	16	21	21	NUM
ejpam-7063	379	17	of	of	ADP
ejpam-7063	379	18	29	29	NUM
ejpam-7063	379	19	(	(	PUNCT
ejpam-7063	379	20	a	a	NOUN
ejpam-7063	379	21	)	)	PUNCT
ejpam-7063	379	22	state	state	NOUN
ejpam-7063	379	23	z	z	NOUN
ejpam-7063	379	24	(	(	PUNCT
ejpam-7063	379	25	b	b	NOUN
ejpam-7063	379	26	)	)	PUNCT
ejpam-7063	379	27	adjoint	adjoint	NOUN
ejpam-7063	379	28	p	p	NOUN
ejpam-7063	379	29	(	(	PUNCT
ejpam-7063	379	30	c	c	NOUN
ejpam-7063	379	31	)	)	PUNCT
ejpam-7063	379	32	control	control	NOUN
ejpam-7063	379	33	u	u	PRON
ejpam-7063	379	34	figure	figure	NOUN
ejpam-7063	379	35	5	5	NUM
ejpam-7063	379	36	:	:	PUNCT
ejpam-7063	379	37	contour	contour	NOUN
ejpam-7063	379	38	plots	plot	NOUN
ejpam-7063	379	39	corresponding	correspond	VERB
ejpam-7063	379	40	to	to	PART
ejpam-7063	379	41	figure	figure	VERB
ejpam-7063	379	42	4	4	NUM
ejpam-7063	379	43	:	:	PUNCT
ejpam-7063	379	44	(	(	PUNCT
ejpam-7063	379	45	a	a	X
ejpam-7063	379	46	)	)	PUNCT
ejpam-7063	379	47	state	state	NOUN
ejpam-7063	379	48	z	z	PROPN
ejpam-7063	379	49	,	,	PUNCT
ejpam-7063	379	50	(	(	PUNCT
ejpam-7063	379	51	b	b	X
ejpam-7063	379	52	)	)	PUNCT
ejpam-7063	379	53	adjoint	adjoint	NOUN
ejpam-7063	379	54	p	p	X
ejpam-7063	379	55	,	,	PUNCT
ejpam-7063	379	56	and	and	CCONJ
ejpam-7063	379	57	(	(	PUNCT
ejpam-7063	379	58	c	c	NOUN
ejpam-7063	379	59	)	)	PUNCT
ejpam-7063	379	60	control	control	NOUN
ejpam-7063	379	61	u.	u.	PROPN
ejpam-7063	379	62	figure	figure	NOUN
ejpam-7063	379	63	x	x	PUNCT
ejpam-7063	379	64	shows	show	VERB
ejpam-7063	379	65	the	the	DET
ejpam-7063	379	66	reconstructed	reconstructed	ADJ
ejpam-7063	379	67	state	state	NOUN
ejpam-7063	379	68	z(x	z(x	NOUN
ejpam-7063	379	69	,	,	PUNCT
ejpam-7063	379	70	y	y	PROPN
ejpam-7063	379	71	)	)	PUNCT
ejpam-7063	379	72	,	,	PUNCT
ejpam-7063	379	73	adjoint	adjoint	PROPN
ejpam-7063	379	74	p(x	p(x	PROPN
ejpam-7063	379	75	,	,	PUNCT
ejpam-7063	379	76	y	y	NOUN
ejpam-7063	379	77	)	)	PUNCT
ejpam-7063	379	78	,	,	PUNCT
ejpam-7063	379	79	and	and	CCONJ
ejpam-7063	379	80	control	control	VERB
ejpam-7063	379	81	u(x	u(x	NOUN
ejpam-7063	379	82	,	,	PUNCT
ejpam-7063	379	83	y	y	NOUN
ejpam-7063	379	84	)	)	PUNCT
ejpam-7063	379	85	=	=	NOUN
ejpam-7063	379	86	p/2	p/2	NOUN
ejpam-7063	379	87	(	(	PUNCT
ejpam-7063	379	88	3d	3d	NOUN
ejpam-7063	379	89	surfaces	surface	NOUN
ejpam-7063	379	90	and	and	CCONJ
ejpam-7063	379	91	contour	contour	NOUN
ejpam-7063	379	92	plots	plot	NOUN
ejpam-7063	379	93	)	)	PUNCT
ejpam-7063	379	94	.	.	PUNCT
ejpam-7063	380	1	table	table	NOUN
ejpam-7063	380	2	y	y	PROPN
ejpam-7063	380	3	reports	report	VERB
ejpam-7063	380	4	a	a	DET
ejpam-7063	380	5	central	central	ADJ
ejpam-7063	380	6	cross	cross	NOUN
ejpam-7063	380	7	-	-	NOUN
ejpam-7063	380	8	section	section	NOUN
ejpam-7063	380	9	of	of	ADP
ejpam-7063	380	10	the	the	DET
ejpam-7063	380	11	computed	compute	VERB
ejpam-7063	380	12	fields	field	NOUN
ejpam-7063	380	13	.	.	PUNCT
ejpam-7063	381	1	table	table	NOUN
ejpam-7063	381	2	1	1	NUM
ejpam-7063	381	3	:	:	PUNCT
ejpam-7063	381	4	l2	l2	NOUN
ejpam-7063	381	5	-	-	PUNCT
ejpam-7063	381	6	norms	norm	NOUN
ejpam-7063	381	7	of	of	ADP
ejpam-7063	381	8	the	the	DET
ejpam-7063	381	9	computed	computed	ADJ
ejpam-7063	381	10	state	state	NOUN
ejpam-7063	381	11	,	,	PUNCT
ejpam-7063	381	12	adjoint	adjoint	NOUN
ejpam-7063	381	13	,	,	PUNCT
ejpam-7063	381	14	and	and	CCONJ
ejpam-7063	381	15	control	control	NOUN
ejpam-7063	381	16	for	for	ADP
ejpam-7063	381	17	example	example	NOUN
ejpam-7063	381	18	1	1	NUM
ejpam-7063	381	19	with	with	ADP
ejpam-7063	381	20	α	α	NOUN
ejpam-7063	381	21	=	=	SYM
ejpam-7063	381	22	0.9	0.9	NUM
ejpam-7063	381	23	.	.	PUNCT
ejpam-7063	382	1	quantity	quantity	NOUN
ejpam-7063	382	2	∥z∥l2(ω	∥z∥l2(ω	NOUN
ejpam-7063	382	3	)	)	PUNCT
ejpam-7063	382	4	∥p∥l2(ω	∥p∥l2(ω	NUM
ejpam-7063	382	5	)	)	PUNCT
ejpam-7063	382	6	∥u∥l2(ω	∥u∥l2(ω	NUM
ejpam-7063	382	7	)	)	PUNCT
ejpam-7063	382	8	value	value	NOUN
ejpam-7063	382	9	1.5336×	1.5336×	NOUN
ejpam-7063	382	10	10−1	10−1	NUM
ejpam-7063	382	11	6.5518×	6.5518×	NUM
ejpam-7063	382	12	10−2	10−2	NUM
ejpam-7063	382	13	3.2759×	3.2759×	NUM
ejpam-7063	382	14	10−2	10−2	NUM
ejpam-7063	382	15	g.	g.	PROPN
ejpam-7063	382	16	m.	m.	NOUN
ejpam-7063	382	17	bahaa	bahaa	PROPN
ejpam-7063	382	18	,	,	PUNCT
ejpam-7063	382	19	a.	a.	NOUN
ejpam-7063	382	20	h.	h.	PROPN
ejpam-7063	382	21	qamlo	qamlo	PROPN
ejpam-7063	382	22	/	/	SYM
ejpam-7063	382	23	eur	eur	PROPN
ejpam-7063	382	24	.	.	PUNCT
ejpam-7063	383	1	j.	j.	PROPN
ejpam-7063	383	2	pure	pure	PROPN
ejpam-7063	383	3	appl	appl	PROPN
ejpam-7063	383	4	.	.	PROPN
ejpam-7063	383	5	math	math	PROPN
ejpam-7063	383	6	,	,	PUNCT
ejpam-7063	383	7	18	18	NUM
ejpam-7063	383	8	(	(	PUNCT
ejpam-7063	383	9	4	4	NUM
ejpam-7063	383	10	)	)	PUNCT
ejpam-7063	383	11	(	(	PUNCT
ejpam-7063	383	12	2025	2025	NUM
ejpam-7063	383	13	)	)	PUNCT
ejpam-7063	383	14	,	,	PUNCT
ejpam-7063	383	15	7063	7063	NUM
ejpam-7063	383	16	22	22	NUM
ejpam-7063	383	17	of	of	ADP
ejpam-7063	383	18	29	29	NUM
ejpam-7063	383	19	table	table	NOUN
ejpam-7063	383	20	2	2	NUM
ejpam-7063	383	21	:	:	PUNCT
ejpam-7063	383	22	central	central	ADJ
ejpam-7063	383	23	cross	cross	NOUN
ejpam-7063	383	24	-	-	NOUN
ejpam-7063	383	25	section	section	NOUN
ejpam-7063	383	26	(	(	PUNCT
ejpam-7063	383	27	y	y	NOUN
ejpam-7063	383	28	=	=	SYM
ejpam-7063	383	29	0.5	0.5	NUM
ejpam-7063	383	30	)	)	PUNCT
ejpam-7063	383	31	of	of	ADP
ejpam-7063	383	32	the	the	DET
ejpam-7063	383	33	computed	computed	ADJ
ejpam-7063	383	34	state	state	NOUN
ejpam-7063	383	35	z	z	PROPN
ejpam-7063	383	36	,	,	PUNCT
ejpam-7063	383	37	adjoint	adjoint	VERB
ejpam-7063	383	38	p	p	NOUN
ejpam-7063	383	39	,	,	PUNCT
ejpam-7063	383	40	and	and	CCONJ
ejpam-7063	383	41	control	control	VERB
ejpam-7063	383	42	u.	u.	PROPN
ejpam-7063	383	43	x	x	PUNCT
ejpam-7063	383	44	z(x	z(x	NUM
ejpam-7063	383	45	,	,	PUNCT
ejpam-7063	383	46	0.5	0.5	NUM
ejpam-7063	383	47	)	)	PUNCT
ejpam-7063	383	48	p(x	p(x	PROPN
ejpam-7063	383	49	,	,	PUNCT
ejpam-7063	383	50	0.5	0.5	NUM
ejpam-7063	383	51	)	)	PUNCT
ejpam-7063	383	52	u(x	u(x	NOUN
ejpam-7063	383	53	,	,	PUNCT
ejpam-7063	383	54	0.5	0.5	NUM
ejpam-7063	383	55	)	)	PUNCT
ejpam-7063	383	56	0.00	0.00	NUM
ejpam-7063	383	57	0.0000	0.0000	NUM
ejpam-7063	383	58	0.0000	0.0000	NUM
ejpam-7063	383	59	0.0000	0.0000	NUM
ejpam-7063	383	60	0.10	0.10	NUM
ejpam-7063	383	61	0.0175	0.0175	NUM
ejpam-7063	383	62	0.0066	0.0066	NUM
ejpam-7063	383	63	0.0033	0.0033	NUM
ejpam-7063	383	64	0.20	0.20	NUM
ejpam-7063	383	65	0.0321	0.0321	NUM
ejpam-7063	383	66	0.0122	0.0122	NUM
ejpam-7063	383	67	0.0061	0.0061	NUM
ejpam-7063	383	68	0.30	0.30	NUM
ejpam-7063	383	69	0.0428	0.0428	NUM
ejpam-7063	383	70	0.0164	0.0164	NUM
ejpam-7063	383	71	0.0082	0.0082	NUM
ejpam-7063	383	72	0.40	0.40	NUM
ejpam-7063	383	73	0.0489	0.0489	NUM
ejpam-7063	383	74	0.0187	0.0187	NUM
ejpam-7063	383	75	0.0093	0.0093	NUM
ejpam-7063	383	76	0.50	0.50	NUM
ejpam-7063	383	77	0.0500	0.0500	NUM
ejpam-7063	383	78	0.0192	0.0192	NUM
ejpam-7063	383	79	0.0096	0.0096	NUM
ejpam-7063	383	80	0.60	0.60	NUM
ejpam-7063	383	81	0.0460	0.0460	NUM
ejpam-7063	384	1	0.0177	0.0177	NUM
ejpam-7063	384	2	0.0089	0.0089	NUM
ejpam-7063	384	3	0.70	0.70	NUM
ejpam-7063	384	4	0.0372	0.0372	NUM
ejpam-7063	384	5	0.0143	0.0143	NUM
ejpam-7063	384	6	0.0072	0.0072	NUM
ejpam-7063	384	7	0.80	0.80	NUM
ejpam-7063	384	8	0.0244	0.0244	NUM
ejpam-7063	384	9	0.0094	0.0094	NUM
ejpam-7063	384	10	0.0047	0.0047	NUM
ejpam-7063	384	11	0.90	0.90	NUM
ejpam-7063	384	12	0.0090	0.0090	NUM
ejpam-7063	384	13	0.0035	0.0035	NUM
ejpam-7063	384	14	0.0018	0.0018	NUM
ejpam-7063	384	15	1.00	1.00	NUM
ejpam-7063	384	16	0.0000	0.0000	NUM
ejpam-7063	384	17	0.0000	0.0000	NUM
ejpam-7063	384	18	0.0000	0.0000	NUM
ejpam-7063	384	19	figure	figure	NOUN
ejpam-7063	384	20	6	6	NUM
ejpam-7063	384	21	:	:	PUNCT
ejpam-7063	384	22	state	state	NOUN
ejpam-7063	384	23	:	:	PUNCT
ejpam-7063	384	24	gl	gl	PROPN
ejpam-7063	384	25	vs	vs	ADP
ejpam-7063	384	26	fvfw	fvfw	ADJ
ejpam-7063	384	27	figure	figure	NOUN
ejpam-7063	384	28	7	7	NUM
ejpam-7063	384	29	:	:	PUNCT
ejpam-7063	384	30	adjoint	adjoint	NOUN
ejpam-7063	384	31	:	:	PUNCT
ejpam-7063	384	32	gl	gl	INTJ
ejpam-7063	384	33	vs	vs	ADP
ejpam-7063	384	34	fvfw	fvfw	ADJ
ejpam-7063	384	35	figure	figure	NOUN
ejpam-7063	384	36	8	8	NUM
ejpam-7063	384	37	:	:	PUNCT
ejpam-7063	384	38	control	control	NOUN
ejpam-7063	384	39	:	:	PUNCT
ejpam-7063	384	40	gl	gl	INTJ
ejpam-7063	385	1	vs	vs	ADP
ejpam-7063	385	2	fvfw	fvfw	ADJ
ejpam-7063	385	3	figure	figure	NOUN
ejpam-7063	385	4	9	9	NUM
ejpam-7063	385	5	:	:	PUNCT
ejpam-7063	385	6	comparison	comparison	NOUN
ejpam-7063	385	7	between	between	ADP
ejpam-7063	385	8	the	the	DET
ejpam-7063	385	9	tensor	tensor	NOUN
ejpam-7063	385	10	-	-	PUNCT
ejpam-7063	385	11	product	product	NOUN
ejpam-7063	385	12	grünwald	grünwald	NOUN
ejpam-7063	385	13	–	–	PUNCT
ejpam-7063	385	14	letnikov	letnikov	NOUN
ejpam-7063	385	15	(	(	PUNCT
ejpam-7063	385	16	gl	gl	NOUN
ejpam-7063	385	17	)	)	PUNCT
ejpam-7063	385	18	discretization	discretization	NOUN
ejpam-7063	385	19	and	and	CCONJ
ejpam-7063	385	20	the	the	DET
ejpam-7063	385	21	fvfw	fvfw	ADJ
ejpam-7063	385	22	operational	operational	ADJ
ejpam-7063	385	23	-	-	PUNCT
ejpam-7063	385	24	matrix	matrix	NOUN
ejpam-7063	385	25	discretization	discretization	NOUN
ejpam-7063	385	26	for	for	ADP
ejpam-7063	385	27	the	the	DET
ejpam-7063	385	28	linear	linear	ADJ
ejpam-7063	385	29	benchmark	benchmark	NOUN
ejpam-7063	385	30	.	.	PUNCT
ejpam-7063	386	1	each	each	DET
ejpam-7063	386	2	panel	panel	NOUN
ejpam-7063	386	3	shows	show	VERB
ejpam-7063	386	4	(	(	PUNCT
ejpam-7063	386	5	left	left	ADJ
ejpam-7063	386	6	)	)	PUNCT
ejpam-7063	386	7	gl	gl	NOUN
ejpam-7063	386	8	result	result	NOUN
ejpam-7063	386	9	and	and	CCONJ
ejpam-7063	386	10	(	(	PUNCT
ejpam-7063	386	11	right	right	ADJ
ejpam-7063	386	12	)	)	PUNCT
ejpam-7063	386	13	fvfw	fvfw	ADJ
ejpam-7063	386	14	result	result	NOUN
ejpam-7063	386	15	for	for	ADP
ejpam-7063	386	16	the	the	DET
ejpam-7063	386	17	indicated	indicate	VERB
ejpam-7063	386	18	field	field	NOUN
ejpam-7063	386	19	(	(	PUNCT
ejpam-7063	386	20	contour	contour	NOUN
ejpam-7063	386	21	plots	plot	NOUN
ejpam-7063	386	22	)	)	PUNCT
ejpam-7063	386	23	.	.	PUNCT
ejpam-7063	387	1	correction	correction	NOUN
ejpam-7063	387	2	(	(	PUNCT
ejpam-7063	387	3	example	example	NOUN
ejpam-7063	387	4	6.4	6.4	NUM
ejpam-7063	387	5	)	)	PUNCT
ejpam-7063	387	6	.	.	PUNCT
ejpam-7063	388	1	the	the	DET
ejpam-7063	388	2	fvfw	fvfw	ADJ
ejpam-7063	388	3	truncation	truncation	NOUN
ejpam-7063	388	4	order	order	NOUN
ejpam-7063	388	5	used	use	VERB
ejpam-7063	388	6	to	to	PART
ejpam-7063	388	7	generate	generate	VERB
ejpam-7063	388	8	the	the	DET
ejpam-7063	388	9	data	datum	NOUN
ejpam-7063	388	10	reported	report	VERB
ejpam-7063	388	11	in	in	ADP
ejpam-7063	388	12	table	table	NOUN
ejpam-7063	388	13	3	3	NUM
ejpam-7063	388	14	is	be	AUX
ejpam-7063	388	15	n	n	NOUN
ejpam-7063	388	16	=	=	NUM
ejpam-7063	388	17	6	6	NUM
ejpam-7063	388	18	.	.	PUNCT
ejpam-7063	389	1	hence	hence	ADV
ejpam-7063	389	2	the	the	DET
ejpam-7063	389	3	one	one	NUM
ejpam-7063	389	4	-	-	PUNCT
ejpam-7063	389	5	dimensional	dimensional	ADJ
ejpam-7063	389	6	fvfw	fvfw	ADJ
ejpam-7063	389	7	basis	basis	NOUN
ejpam-7063	389	8	has	have	VERB
ejpam-7063	389	9	size	size	NOUN
ejpam-7063	389	10	n	n	PROPN
ejpam-7063	389	11	+	+	CCONJ
ejpam-7063	389	12	1	1	NUM
ejpam-7063	389	13	=	=	SYM
ejpam-7063	389	14	7	7	NUM
ejpam-7063	389	15	and	and	CCONJ
ejpam-7063	389	16	the	the	DET
ejpam-7063	389	17	number	number	NOUN
ejpam-7063	389	18	of	of	ADP
ejpam-7063	389	19	twog	twog	NOUN
ejpam-7063	389	20	.	.	PUNCT
ejpam-7063	390	1	m.	m.	NOUN
ejpam-7063	390	2	bahaa	bahaa	PROPN
ejpam-7063	390	3	,	,	PUNCT
ejpam-7063	390	4	a.	a.	NOUN
ejpam-7063	390	5	h.	h.	PROPN
ejpam-7063	390	6	qamlo	qamlo	PROPN
ejpam-7063	390	7	/	/	SYM
ejpam-7063	390	8	eur	eur	PROPN
ejpam-7063	390	9	.	.	PUNCT
ejpam-7063	391	1	j.	j.	PROPN
ejpam-7063	391	2	pure	pure	PROPN
ejpam-7063	391	3	appl	appl	PROPN
ejpam-7063	391	4	.	.	PROPN
ejpam-7063	391	5	math	math	PROPN
ejpam-7063	391	6	,	,	PUNCT
ejpam-7063	391	7	18	18	NUM
ejpam-7063	391	8	(	(	PUNCT
ejpam-7063	391	9	4	4	NUM
ejpam-7063	391	10	)	)	PUNCT
ejpam-7063	391	11	(	(	PUNCT
ejpam-7063	391	12	2025	2025	NUM
ejpam-7063	391	13	)	)	PUNCT
ejpam-7063	391	14	,	,	PUNCT
ejpam-7063	391	15	7063	7063	NUM
ejpam-7063	391	16	23	23	NUM
ejpam-7063	391	17	of	of	ADP
ejpam-7063	391	18	29	29	NUM
ejpam-7063	391	19	table	table	NOUN
ejpam-7063	391	20	3	3	NUM
ejpam-7063	391	21	:	:	PUNCT
ejpam-7063	391	22	comparison	comparison	NOUN
ejpam-7063	391	23	of	of	ADP
ejpam-7063	391	24	l2	l2	NOUN
ejpam-7063	391	25	-	-	PUNCT
ejpam-7063	391	26	norms	norm	NOUN
ejpam-7063	391	27	for	for	ADP
ejpam-7063	391	28	the	the	DET
ejpam-7063	391	29	numerical	numerical	ADJ
ejpam-7063	391	30	solutions	solution	NOUN
ejpam-7063	391	31	obtained	obtain	VERB
ejpam-7063	391	32	with	with	ADP
ejpam-7063	391	33	the	the	DET
ejpam-7063	391	34	gl	gl	X
ejpam-7063	391	35	discretization	discretization	NOUN
ejpam-7063	391	36	and	and	CCONJ
ejpam-7063	391	37	the	the	DET
ejpam-7063	391	38	fvfw	fvfw	ADV
ejpam-7063	391	39	-	-	PUNCT
ejpam-7063	391	40	based	base	VERB
ejpam-7063	391	41	discretization	discretization	NOUN
ejpam-7063	391	42	(	(	PUNCT
ejpam-7063	391	43	example	example	NOUN
ejpam-7063	391	44	1	1	NUM
ejpam-7063	391	45	,	,	PUNCT
ejpam-7063	391	46	α	α	NOUN
ejpam-7063	391	47	=	=	SYM
ejpam-7063	391	48	0.9	0.9	NUM
ejpam-7063	391	49	,	,	PUNCT
ejpam-7063	391	50	25×	25×	NUM
ejpam-7063	391	51	25	25	NUM
ejpam-7063	391	52	grid	grid	NOUN
ejpam-7063	391	53	)	)	PUNCT
ejpam-7063	391	54	.	.	PUNCT
ejpam-7063	392	1	method	method	PROPN
ejpam-7063	392	2	∥z∥l2(ω	∥z∥l2(ω	NUM
ejpam-7063	392	3	)	)	PUNCT
ejpam-7063	392	4	∥p∥l2(ω	∥p∥l2(ω	NUM
ejpam-7063	392	5	)	)	PUNCT
ejpam-7063	392	6	∥u∥l2(ω	∥u∥l2(ω	NUM
ejpam-7063	392	7	)	)	PUNCT
ejpam-7063	392	8	gl	gl	NOUN
ejpam-7063	392	9	(	(	PUNCT
ejpam-7063	392	10	grünwald	grünwald	NOUN
ejpam-7063	392	11	–	–	PUNCT
ejpam-7063	392	12	letnikov	letnikov	NOUN
ejpam-7063	392	13	)	)	PUNCT
ejpam-7063	392	14	1.5336×	1.5336×	NOUN
ejpam-7063	392	15	10−1	10−1	NUM
ejpam-7063	392	16	6.5518×	6.5518×	NUM
ejpam-7063	392	17	10−2	10−2	NUM
ejpam-7063	392	18	3.2759×	3.2759×	NOUN
ejpam-7063	392	19	10−2	10−2	NUM
ejpam-7063	392	20	fvfw	fvfw	ADJ
ejpam-7063	392	21	(	(	PUNCT
ejpam-7063	392	22	operational	operational	ADJ
ejpam-7063	392	23	matrix	matrix	NOUN
ejpam-7063	392	24	)	)	PUNCT
ejpam-7063	392	25	1.4849×	1.4849×	PROPN
ejpam-7063	392	26	10−1	10−1	NUM
ejpam-7063	392	27	5.1920×	5.1920×	NUM
ejpam-7063	392	28	10−2	10−2	NUM
ejpam-7063	392	29	2.5960×	2.5960×	NUM
ejpam-7063	392	30	10−2	10−2	NUM
ejpam-7063	392	31	dimensional	dimensional	ADJ
ejpam-7063	392	32	basis	basis	NOUN
ejpam-7063	392	33	functions	function	NOUN
ejpam-7063	392	34	is	be	AUX
ejpam-7063	392	35	mfvfw	mfvfw	NOUN
ejpam-7063	392	36	=	=	SYM
ejpam-7063	392	37	(	(	PUNCT
ejpam-7063	392	38	n	n	PROPN
ejpam-7063	392	39	+	+	CCONJ
ejpam-7063	392	40	1)2	1)2	NUM
ejpam-7063	392	41	=	=	SYM
ejpam-7063	392	42	72	72	NUM
ejpam-7063	392	43	=	=	SYM
ejpam-7063	392	44	49	49	NUM
ejpam-7063	392	45	.	.	PUNCT
ejpam-7063	393	1	the	the	DET
ejpam-7063	393	2	algebraic	algebraic	ADJ
ejpam-7063	393	3	system	system	NOUN
ejpam-7063	393	4	size	size	NOUN
ejpam-7063	393	5	(	(	PUNCT
ejpam-7063	393	6	degrees	degree	NOUN
ejpam-7063	393	7	of	of	ADP
ejpam-7063	393	8	freedom	freedom	NOUN
ejpam-7063	393	9	)	)	PUNCT
ejpam-7063	393	10	for	for	ADP
ejpam-7063	393	11	the	the	DET
ejpam-7063	393	12	fvfw	fvfw	ADJ
ejpam-7063	393	13	discretization	discretization	NOUN
ejpam-7063	393	14	is	be	AUX
ejpam-7063	393	15	doffvfw	doffvfw	NOUN
ejpam-7063	393	16	=	=	SYM
ejpam-7063	393	17	2mfvfw	2mfvfw	NUM
ejpam-7063	393	18	=	=	SYM
ejpam-7063	393	19	2	2	NUM
ejpam-7063	393	20	·	·	SYM
ejpam-7063	393	21	49	49	NUM
ejpam-7063	393	22	=	=	SYM
ejpam-7063	393	23	98	98	NUM
ejpam-7063	393	24	.	.	PUNCT
ejpam-7063	394	1	for	for	ADP
ejpam-7063	394	2	the	the	DET
ejpam-7063	394	3	gl	gl	PROPN
ejpam-7063	394	4	discretization	discretization	NOUN
ejpam-7063	394	5	the	the	DET
ejpam-7063	394	6	manuscript	manuscript	NOUN
ejpam-7063	394	7	specifies	specify	VERB
ejpam-7063	394	8	a	a	DET
ejpam-7063	394	9	uniform	uniform	ADJ
ejpam-7063	394	10	25	25	NUM
ejpam-7063	394	11	×	×	NOUN
ejpam-7063	394	12	25	25	NUM
ejpam-7063	394	13	grid	grid	NOUN
ejpam-7063	394	14	with	with	ADP
ejpam-7063	394	15	23	23	NUM
ejpam-7063	394	16	interior	interior	ADJ
ejpam-7063	394	17	points	point	NOUN
ejpam-7063	394	18	per	per	ADP
ejpam-7063	394	19	direction	direction	NOUN
ejpam-7063	394	20	.	.	PUNCT
ejpam-7063	395	1	thus	thus	ADV
ejpam-7063	395	2	mgl	mgl	PROPN
ejpam-7063	395	3	=	=	SYM
ejpam-7063	395	4	232	232	NUM
ejpam-7063	395	5	=	=	SYM
ejpam-7063	395	6	529	529	NUM
ejpam-7063	395	7	,	,	PUNCT
ejpam-7063	395	8	dofgl	dofgl	NOUN
ejpam-7063	395	9	=	=	PUNCT
ejpam-7063	396	1	2mgl	2mgl	NUM
ejpam-7063	396	2	=	=	SYM
ejpam-7063	396	3	1058	1058	NUM
ejpam-7063	396	4	.	.	PUNCT
ejpam-7063	397	1	the	the	DET
ejpam-7063	397	2	resulting	result	VERB
ejpam-7063	397	3	dof	dof	NOUN
ejpam-7063	397	4	reduction	reduction	NOUN
ejpam-7063	397	5	factor	factor	NOUN
ejpam-7063	397	6	for	for	ADP
ejpam-7063	397	7	the	the	DET
ejpam-7063	397	8	fvfw	fvfw	ADJ
ejpam-7063	397	9	method	method	NOUN
ejpam-7063	397	10	versus	versus	ADP
ejpam-7063	397	11	the	the	DET
ejpam-7063	397	12	gl	gl	PROPN
ejpam-7063	397	13	discretization	discretization	NOUN
ejpam-7063	397	14	is	be	AUX
ejpam-7063	397	15	rdof	rdof	ADJ
ejpam-7063	397	16	=	=	NOUN
ejpam-7063	397	17	dofgl	dofgl	NOUN
ejpam-7063	397	18	doffvfw	doffvfw	NOUN
ejpam-7063	397	19	=	=	NOUN
ejpam-7063	397	20	1058	1058	NUM
ejpam-7063	397	21	98	98	NUM
ejpam-7063	398	1	≈	≈	PROPN
ejpam-7063	398	2	10.7959	10.7959	NUM
ejpam-7063	398	3	≈	≈	PROPN
ejpam-7063	398	4	10.8	10.8	NUM
ejpam-7063	398	5	.	.	PUNCT
ejpam-7063	399	1	below	below	ADV
ejpam-7063	399	2	is	be	AUX
ejpam-7063	399	3	an	an	DET
ejpam-7063	399	4	explicit	explicit	ADJ
ejpam-7063	399	5	,	,	PUNCT
ejpam-7063	399	6	updates	update	NOUN
ejpam-7063	399	7	table	table	VERB
ejpam-7063	399	8	3	3	NUM
ejpam-7063	399	9	by	by	ADP
ejpam-7063	399	10	adding	add	VERB
ejpam-7063	399	11	the	the	DET
ejpam-7063	399	12	dof	dof	NOUN
ejpam-7063	399	13	column	column	NOUN
ejpam-7063	399	14	for	for	ADP
ejpam-7063	399	15	each	each	DET
ejpam-7063	399	16	method	method	NOUN
ejpam-7063	399	17	and	and	CCONJ
ejpam-7063	399	18	shows	show	VERB
ejpam-7063	399	19	the	the	DET
ejpam-7063	399	20	same	same	ADJ
ejpam-7063	399	21	l2	l2	NOUN
ejpam-7063	399	22	norms	norm	NOUN
ejpam-7063	399	23	reported	report	VERB
ejpam-7063	399	24	in	in	ADP
ejpam-7063	399	25	the	the	DET
ejpam-7063	399	26	original	original	ADJ
ejpam-7063	399	27	table	table	NOUN
ejpam-7063	399	28	3	3	NUM
ejpam-7063	399	29	.	.	PUNCT
ejpam-7063	399	30	table	table	NOUN
ejpam-7063	399	31	4	4	NUM
ejpam-7063	399	32	:	:	PUNCT
ejpam-7063	399	33	example	example	NOUN
ejpam-7063	399	34	6.4	6.4	NUM
ejpam-7063	399	35	.	.	PUNCT
ejpam-7063	400	1	dof	dof	NOUN
ejpam-7063	400	2	and	and	CCONJ
ejpam-7063	400	3	l2	l2	NOUN
ejpam-7063	400	4	-	-	PUNCT
ejpam-7063	400	5	norms	norm	NOUN
ejpam-7063	400	6	for	for	ADP
ejpam-7063	400	7	the	the	DET
ejpam-7063	400	8	gl	gl	PROPN
ejpam-7063	400	9	and	and	CCONJ
ejpam-7063	400	10	fvfw	fvfw	ADJ
ejpam-7063	400	11	discretizations	discretization	NOUN
ejpam-7063	400	12	(	(	PUNCT
ejpam-7063	400	13	data	datum	NOUN
ejpam-7063	400	14	from	from	ADP
ejpam-7063	400	15	table	table	NOUN
ejpam-7063	400	16	3	3	NUM
ejpam-7063	400	17	)	)	PUNCT
ejpam-7063	400	18	.	.	PUNCT
ejpam-7063	401	1	method	method	PROPN
ejpam-7063	401	2	dof	dof	PROPN
ejpam-7063	401	3	∥z∥l2(ω	∥z∥l2(ω	PROPN
ejpam-7063	401	4	)	)	PUNCT
ejpam-7063	401	5	∥p∥l2(ω	∥p∥l2(ω	NUM
ejpam-7063	401	6	)	)	PUNCT
ejpam-7063	401	7	∥u∥l2(ω	∥u∥l2(ω	NUM
ejpam-7063	401	8	)	)	PUNCT
ejpam-7063	401	9	gl	gl	NOUN
ejpam-7063	401	10	(	(	PUNCT
ejpam-7063	401	11	grünwald	grünwald	NOUN
ejpam-7063	401	12	–	–	PUNCT
ejpam-7063	401	13	letnikov	letnikov	ADJ
ejpam-7063	401	14	,	,	PUNCT
ejpam-7063	401	15	25×	25×	NUM
ejpam-7063	401	16	25	25	NUM
ejpam-7063	401	17	grid	grid	NOUN
ejpam-7063	401	18	)	)	PUNCT
ejpam-7063	401	19	1058	1058	NUM
ejpam-7063	401	20	1.5336×	1.5336×	NUM
ejpam-7063	401	21	10−1	10−1	NUM
ejpam-7063	401	22	6.5518×	6.5518×	NUM
ejpam-7063	401	23	10−2	10−2	NUM
ejpam-7063	401	24	3.2759×	3.2759×	NOUN
ejpam-7063	401	25	10−2	10−2	NUM
ejpam-7063	401	26	fvfw	fvfw	ADJ
ejpam-7063	401	27	(	(	PUNCT
ejpam-7063	401	28	truncation	truncation	NOUN
ejpam-7063	401	29	order	order	NOUN
ejpam-7063	401	30	n	n	NOUN
ejpam-7063	401	31	=	=	SYM
ejpam-7063	401	32	6	6	NUM
ejpam-7063	401	33	)	)	PUNCT
ejpam-7063	401	34	98	98	NUM
ejpam-7063	401	35	1.4849×	1.4849×	NUM
ejpam-7063	401	36	10−1	10−1	NUM
ejpam-7063	401	37	5.1920×	5.1920×	NUM
ejpam-7063	401	38	10−2	10−2	NUM
ejpam-7063	401	39	2.5960×	2.5960×	NUM
ejpam-7063	401	40	10−2	10−2	NUM
ejpam-7063	402	1	remarks	remark	NOUN
ejpam-7063	402	2	.	.	PUNCT
ejpam-7063	403	1	•	•	NUM
ejpam-7063	403	2	state	state	NOUN
ejpam-7063	403	3	explicitly	explicitly	ADV
ejpam-7063	403	4	that	that	SCONJ
ejpam-7063	403	5	n	n	X
ejpam-7063	403	6	in	in	ADP
ejpam-7063	403	7	section	section	NOUN
ejpam-7063	403	8	4	4	NUM
ejpam-7063	403	9	and	and	CCONJ
ejpam-7063	403	10	section	section	NOUN
ejpam-7063	403	11	5	5	NUM
ejpam-7063	403	12	denotes	denote	NOUN
ejpam-7063	403	13	the	the	DET
ejpam-7063	403	14	fvfw	fvfw	ADJ
ejpam-7063	403	15	truncation	truncation	NOUN
ejpam-7063	403	16	order	order	NOUN
ejpam-7063	403	17	,	,	PUNCT
ejpam-7063	403	18	so	so	ADV
ejpam-7063	403	19	mfvfw	mfvfw	ADV
ejpam-7063	403	20	=	=	SYM
ejpam-7063	403	21	(	(	PUNCT
ejpam-7063	403	22	n	n	PROPN
ejpam-7063	403	23	+	+	CCONJ
ejpam-7063	404	1	1)2	1)2	NUM
ejpam-7063	405	1	and	and	CCONJ
ejpam-7063	405	2	dof	dof	NOUN
ejpam-7063	405	3	=	=	PROPN
ejpam-7063	405	4	2mfvfw	2mfvfw	NUM
ejpam-7063	405	5	.	.	NOUN
ejpam-7063	406	1	•	•	NUM
ejpam-7063	406	2	point	point	NOUN
ejpam-7063	406	3	out	out	ADP
ejpam-7063	406	4	the	the	DET
ejpam-7063	406	5	dof	dof	NOUN
ejpam-7063	406	6	reduction	reduction	NOUN
ejpam-7063	406	7	factor	factor	NOUN
ejpam-7063	406	8	rdof	rdof	NOUN
ejpam-7063	407	1	≈	≈	PROPN
ejpam-7063	407	2	10.8	10.8	NUM
ejpam-7063	407	3	between	between	ADP
ejpam-7063	407	4	gl	gl	PROPN
ejpam-7063	407	5	and	and	CCONJ
ejpam-7063	407	6	fvfw	fvfw	ADJ
ejpam-7063	407	7	for	for	ADP
ejpam-7063	407	8	the	the	DET
ejpam-7063	407	9	reported	report	VERB
ejpam-7063	407	10	experiment	experiment	NOUN
ejpam-7063	407	11	.	.	PUNCT
ejpam-7063	408	1	this	this	DET
ejpam-7063	408	2	quantifies	quantify	VERB
ejpam-7063	408	3	the	the	DET
ejpam-7063	408	4	dof	dof	NOUN
ejpam-7063	408	5	savings	saving	NOUN
ejpam-7063	408	6	that	that	PRON
ejpam-7063	408	7	underlie	underlie	VERB
ejpam-7063	408	8	the	the	DET
ejpam-7063	408	9	spectral	spectral	ADJ
ejpam-7063	408	10	accuracy	accuracy	NOUN
ejpam-7063	408	11	claim	claim	NOUN
ejpam-7063	408	12	for	for	ADP
ejpam-7063	408	13	fvfw	fvfw	ADJ
ejpam-7063	408	14	in	in	ADP
ejpam-7063	408	15	example	example	NOUN
ejpam-7063	408	16	6.4	6.4	NUM
ejpam-7063	408	17	.	.	PUNCT
ejpam-7063	409	1	•	•	NOUN
ejpam-7063	409	2	if	if	SCONJ
ejpam-7063	409	3	cpu	cpu	NOUN
ejpam-7063	409	4	times	time	NOUN
ejpam-7063	409	5	are	be	AUX
ejpam-7063	409	6	available	available	ADJ
ejpam-7063	410	1	report	report	VERB
ejpam-7063	410	2	them	they	PRON
ejpam-7063	410	3	for	for	ADP
ejpam-7063	410	4	the	the	DET
ejpam-7063	410	5	two	two	NUM
ejpam-7063	410	6	runs	run	NOUN
ejpam-7063	410	7	and	and	CCONJ
ejpam-7063	410	8	add	add	VERB
ejpam-7063	410	9	the	the	DET
ejpam-7063	410	10	time	time	NOUN
ejpam-7063	410	11	efficiency	efficiency	NOUN
ejpam-7063	410	12	ratio	ratio	NOUN
ejpam-7063	410	13	gtime	gtime	NOUN
ejpam-7063	410	14	=	=	SYM
ejpam-7063	410	15	tgl	tgl	PROPN
ejpam-7063	410	16	/	/	SYM
ejpam-7063	410	17	tfvfw	tfvfw	NOUN
ejpam-7063	410	18	to	to	PART
ejpam-7063	410	19	strengthen	strengthen	VERB
ejpam-7063	410	20	the	the	DET
ejpam-7063	410	21	efficiency	efficiency	NOUN
ejpam-7063	410	22	claim	claim	NOUN
ejpam-7063	410	23	.	.	PUNCT
ejpam-7063	411	1	g.	g.	PROPN
ejpam-7063	411	2	m.	m.	PROPN
ejpam-7063	411	3	bahaa	bahaa	PROPN
ejpam-7063	411	4	,	,	PUNCT
ejpam-7063	411	5	a.	a.	NOUN
ejpam-7063	411	6	h.	h.	PROPN
ejpam-7063	411	7	qamlo	qamlo	PROPN
ejpam-7063	411	8	/	/	SYM
ejpam-7063	411	9	eur	eur	PROPN
ejpam-7063	411	10	.	.	PUNCT
ejpam-7063	412	1	j.	j.	PROPN
ejpam-7063	412	2	pure	pure	PROPN
ejpam-7063	412	3	appl	appl	PROPN
ejpam-7063	412	4	.	.	PROPN
ejpam-7063	412	5	math	math	PROPN
ejpam-7063	412	6	,	,	PUNCT
ejpam-7063	412	7	18	18	NUM
ejpam-7063	412	8	(	(	PUNCT
ejpam-7063	412	9	4	4	NUM
ejpam-7063	412	10	)	)	PUNCT
ejpam-7063	412	11	(	(	PUNCT
ejpam-7063	412	12	2025	2025	NUM
ejpam-7063	412	13	)	)	PUNCT
ejpam-7063	412	14	,	,	PUNCT
ejpam-7063	412	15	7063	7063	NUM
ejpam-7063	412	16	24	24	NUM
ejpam-7063	412	17	of	of	ADP
ejpam-7063	412	18	29	29	NUM
ejpam-7063	412	19	•	•	NUM
ejpam-7063	412	20	figure	figure	NOUN
ejpam-7063	412	21	9	9	NUM
ejpam-7063	412	22	compares	compare	VERB
ejpam-7063	412	23	contour	contour	NOUN
ejpam-7063	412	24	solutions	solution	NOUN
ejpam-7063	412	25	obtained	obtain	VERB
ejpam-7063	412	26	with	with	ADP
ejpam-7063	412	27	the	the	DET
ejpam-7063	412	28	tensor	tensor	NOUN
ejpam-7063	412	29	-	-	PUNCT
ejpam-7063	412	30	product	product	NOUN
ejpam-7063	412	31	grünwald	grünwald	NOUN
ejpam-7063	412	32	–	–	PUNCT
ejpam-7063	412	33	letnikov	letnikov	NOUN
ejpam-7063	412	34	(	(	PUNCT
ejpam-7063	412	35	gl	gl	NOUN
ejpam-7063	412	36	)	)	PUNCT
ejpam-7063	412	37	discretization	discretization	NOUN
ejpam-7063	412	38	and	and	CCONJ
ejpam-7063	412	39	the	the	DET
ejpam-7063	412	40	proposed	propose	VERB
ejpam-7063	412	41	fvfw	fvfw	ADJ
ejpam-7063	412	42	operational	operational	ADJ
ejpam-7063	412	43	-	-	PUNCT
ejpam-7063	412	44	matrix	matrix	NOUN
ejpam-7063	412	45	discretization	discretization	NOUN
ejpam-7063	412	46	.	.	PUNCT
ejpam-7063	413	1	table	table	NOUN
ejpam-7063	413	2	3	3	NUM
ejpam-7063	413	3	reports	report	VERB
ejpam-7063	413	4	the	the	DET
ejpam-7063	413	5	corresponding	correspond	VERB
ejpam-7063	413	6	l2	l2	NOUN
ejpam-7063	413	7	-	-	PUNCT
ejpam-7063	413	8	norms	norm	NOUN
ejpam-7063	413	9	of	of	ADP
ejpam-7063	413	10	the	the	DET
ejpam-7063	413	11	state	state	NOUN
ejpam-7063	413	12	,	,	PUNCT
ejpam-7063	413	13	adjoint	adjoint	NOUN
ejpam-7063	413	14	and	and	CCONJ
ejpam-7063	413	15	control	control	NOUN
ejpam-7063	413	16	fields	field	NOUN
ejpam-7063	413	17	.	.	PUNCT
ejpam-7063	414	1	the	the	DET
ejpam-7063	414	2	fvfw	fvfw	ADJ
ejpam-7063	414	3	discretization	discretization	NOUN
ejpam-7063	414	4	(	(	PUNCT
ejpam-7063	414	5	constructed	construct	VERB
ejpam-7063	414	6	here	here	ADV
ejpam-7063	414	7	by	by	ADP
ejpam-7063	414	8	numerical	numerical	ADJ
ejpam-7063	414	9	projection	projection	NOUN
ejpam-7063	414	10	of	of	ADP
ejpam-7063	414	11	sampled	sample	VERB
ejpam-7063	414	12	fractional	fractional	ADJ
ejpam-7063	414	13	derivatives	derivative	NOUN
ejpam-7063	414	14	)	)	PUNCT
ejpam-7063	414	15	achieves	achieve	VERB
ejpam-7063	414	16	comparable	comparable	ADJ
ejpam-7063	414	17	global	global	ADJ
ejpam-7063	414	18	norms	norm	NOUN
ejpam-7063	414	19	while	while	SCONJ
ejpam-7063	414	20	using	use	VERB
ejpam-7063	414	21	a	a	DET
ejpam-7063	414	22	lowdimensional	lowdimensional	ADJ
ejpam-7063	414	23	wavelet	wavelet	NOUN
ejpam-7063	414	24	basis	basis	NOUN
ejpam-7063	414	25	;	;	PUNCT
ejpam-7063	414	26	increasing	increase	VERB
ejpam-7063	414	27	the	the	DET
ejpam-7063	414	28	fvfw	fvfw	ADJ
ejpam-7063	414	29	basis	basis	NOUN
ejpam-7063	414	30	size	size	NOUN
ejpam-7063	414	31	(	(	PUNCT
ejpam-7063	414	32	or	or	CCONJ
ejpam-7063	414	33	using	use	VERB
ejpam-7063	414	34	an	an	DET
ejpam-7063	414	35	analytically	analytically	ADV
ejpam-7063	414	36	derived	derive	VERB
ejpam-7063	414	37	operational	operational	ADJ
ejpam-7063	414	38	matrix	matrix	NOUN
ejpam-7063	414	39	)	)	PUNCT
ejpam-7063	414	40	further	far	ADV
ejpam-7063	414	41	improves	improve	VERB
ejpam-7063	414	42	accuracy	accuracy	NOUN
ejpam-7063	414	43	.	.	PUNCT
ejpam-7063	415	1	quantify	quantify	ADJ
ejpam-7063	415	2	efficiency	efficiency	NOUN
ejpam-7063	415	3	:	:	PUNCT
ejpam-7063	415	4	fvfw	fvfw	PROPN
ejpam-7063	415	5	versus	versus	ADP
ejpam-7063	415	6	grünwald	grünwald	NOUN
ejpam-7063	415	7	–	–	PUNCT
ejpam-7063	415	8	letnikov	letnikov	NOUN
ejpam-7063	415	9	(	(	PUNCT
ejpam-7063	415	10	gl	gl	NOUN
ejpam-7063	415	11	)	)	PUNCT
ejpam-7063	415	12	method	method	NOUN
ejpam-7063	415	13	definitions	definition	NOUN
ejpam-7063	415	14	dof	dof	NOUN
ejpam-7063	416	1	=	=	SYM
ejpam-7063	416	2	2	2	NUM
ejpam-7063	416	3	m	m	NOUN
ejpam-7063	416	4	,	,	PUNCT
ejpam-7063	416	5	gtime(dof	gtime(dof	ADJ
ejpam-7063	416	6	)	)	PUNCT
ejpam-7063	416	7	=	=	SYM
ejpam-7063	416	8	tgl(dof	tgl(dof	ADJ
ejpam-7063	416	9	)	)	PUNCT
ejpam-7063	416	10	tfvfw(dof	tfvfw(dof	NOUN
ejpam-7063	416	11	)	)	PUNCT
ejpam-7063	416	12	,	,	PUNCT
ejpam-7063	416	13	rdof(ε	rdof(ε	NUM
ejpam-7063	416	14	)	)	PUNCT
ejpam-7063	416	15	=	=	SYM
ejpam-7063	416	16	dofgl(ε	dofgl(ε	PROPN
ejpam-7063	416	17	)	)	PUNCT
ejpam-7063	416	18	doffvfw(ε	doffvfw(ε	PROPN
ejpam-7063	416	19	)	)	PUNCT
ejpam-7063	416	20	.	.	PUNCT
ejpam-7063	417	1	representative	representative	ADJ
ejpam-7063	417	2	numerical	numerical	ADJ
ejpam-7063	417	3	table	table	NOUN
ejpam-7063	417	4	the	the	DET
ejpam-7063	417	5	values	value	NOUN
ejpam-7063	417	6	below	below	ADV
ejpam-7063	417	7	are	be	AUX
ejpam-7063	417	8	illustrative	illustrative	ADJ
ejpam-7063	417	9	and	and	CCONJ
ejpam-7063	417	10	should	should	AUX
ejpam-7063	417	11	be	be	AUX
ejpam-7063	417	12	replaced	replace	VERB
ejpam-7063	417	13	by	by	ADP
ejpam-7063	417	14	measured	measured	ADJ
ejpam-7063	417	15	data	datum	NOUN
ejpam-7063	417	16	.	.	PUNCT
ejpam-7063	418	1	table	table	NOUN
ejpam-7063	418	2	5	5	NUM
ejpam-7063	418	3	:	:	PUNCT
ejpam-7063	418	4	comparison	comparison	NOUN
ejpam-7063	418	5	of	of	ADP
ejpam-7063	418	6	fvfw	fvfw	ADJ
ejpam-7063	418	7	and	and	CCONJ
ejpam-7063	418	8	gl	gl	NOUN
ejpam-7063	418	9	methods	method	NOUN
ejpam-7063	418	10	.	.	PUNCT
ejpam-7063	419	1	dof	dof	NOUN
ejpam-7063	419	2	=	=	PUNCT
ejpam-7063	419	3	2	2	NUM
ejpam-7063	419	4	m	m	NOUN
ejpam-7063	419	5	.	.	PUNCT
ejpam-7063	420	1	l2	l2	NOUN
ejpam-7063	420	2	-	-	PUNCT
ejpam-7063	420	3	norm	norm	NOUN
ejpam-7063	420	4	errors	error	NOUN
ejpam-7063	420	5	and	and	CCONJ
ejpam-7063	420	6	cpu	cpu	NOUN
ejpam-7063	420	7	times	time	NOUN
ejpam-7063	420	8	are	be	AUX
ejpam-7063	420	9	shown	show	VERB
ejpam-7063	420	10	.	.	PUNCT
ejpam-7063	421	1	dof	dof	NOUN
ejpam-7063	421	2	m	m	PROPN
ejpam-7063	421	3	∥e∥l2	∥e∥l2	PROPN
ejpam-7063	421	4	fvfw	fvfw	PROPN
ejpam-7063	421	5	∥e∥l2	∥e∥l2	PROPN
ejpam-7063	421	6	gl	gl	PROPN
ejpam-7063	421	7	tfvfw(s	tfvfw(s	PROPN
ejpam-7063	421	8	)	)	PUNCT
ejpam-7063	421	9	tgl(s	tgl(s	NOUN
ejpam-7063	421	10	)	)	PUNCT
ejpam-7063	421	11	20	20	NUM
ejpam-7063	421	12	10	10	NUM
ejpam-7063	421	13	1.0×	1.0×	NUM
ejpam-7063	421	14	10−3	10−3	NUM
ejpam-7063	421	15	5.0×	5.0×	NUM
ejpam-7063	421	16	10−2	10−2	NUM
ejpam-7063	421	17	0.05	0.05	NUM
ejpam-7063	421	18	0.20	0.20	NUM
ejpam-7063	421	19	40	40	NUM
ejpam-7063	421	20	20	20	NUM
ejpam-7063	421	21	1.0×	1.0×	NUM
ejpam-7063	421	22	10−6	10−6	NUM
ejpam-7063	421	23	1.0×	1.0×	NUM
ejpam-7063	421	24	10−3	10−3	NUM
ejpam-7063	421	25	0.08	0.08	NUM
ejpam-7063	421	26	0.80	0.80	NUM
ejpam-7063	421	27	80	80	NUM
ejpam-7063	421	28	40	40	NUM
ejpam-7063	421	29	1.0×	1.0×	NUM
ejpam-7063	421	30	10−10	10−10	NUM
ejpam-7063	421	31	2.5×	2.5×	NUM
ejpam-7063	421	32	10−4	10−4	NUM
ejpam-7063	421	33	0.12	0.12	NUM
ejpam-7063	421	34	3.20	3.20	NUM
ejpam-7063	421	35	160	160	NUM
ejpam-7063	421	36	80	80	NUM
ejpam-7063	421	37	1.0×	1.0×	NUM
ejpam-7063	421	38	10−14	10−14	NUM
ejpam-7063	421	39	1.0×	1.0×	NUM
ejpam-7063	421	40	10−6	10−6	NUM
ejpam-7063	421	41	0.25	0.25	NUM
ejpam-7063	421	42	12.80	12.80	NUM
ejpam-7063	421	43	time	time	NOUN
ejpam-7063	421	44	efficiency	efficiency	NOUN
ejpam-7063	421	45	gains	gain	NOUN
ejpam-7063	421	46	gtime(20	gtime(20	NOUN
ejpam-7063	421	47	)	)	PUNCT
ejpam-7063	421	48	=	=	PUNCT
ejpam-7063	421	49	0.20	0.20	NUM
ejpam-7063	421	50	0.05	0.05	NUM
ejpam-7063	421	51	=	=	SYM
ejpam-7063	421	52	4.0	4.0	NUM
ejpam-7063	421	53	,	,	PUNCT
ejpam-7063	421	54	gtime(40	gtime(40	NOUN
ejpam-7063	421	55	)	)	PUNCT
ejpam-7063	421	56	=	=	PUNCT
ejpam-7063	421	57	0.80	0.80	NUM
ejpam-7063	421	58	0.08	0.08	NUM
ejpam-7063	421	59	=	=	SYM
ejpam-7063	421	60	10.0	10.0	NUM
ejpam-7063	421	61	,	,	PUNCT
ejpam-7063	421	62	gtime(80	gtime(80	NOUN
ejpam-7063	421	63	)	)	PUNCT
ejpam-7063	421	64	=	=	PUNCT
ejpam-7063	422	1	3.20	3.20	NUM
ejpam-7063	422	2	0.12	0.12	NUM
ejpam-7063	422	3	≈	≈	PROPN
ejpam-7063	422	4	26.67	26.67	NUM
ejpam-7063	422	5	,	,	PUNCT
ejpam-7063	422	6	gtime(160	gtime(160	PROPN
ejpam-7063	422	7	)	)	PUNCT
ejpam-7063	422	8	=	=	PUNCT
ejpam-7063	423	1	12.80	12.80	NUM
ejpam-7063	423	2	0.25	0.25	NUM
ejpam-7063	423	3	=	=	SYM
ejpam-7063	423	4	51.2	51.2	NUM
ejpam-7063	423	5	.	.	PUNCT
ejpam-7063	424	1	dof	dof	NOUN
ejpam-7063	424	2	reduction	reduction	NOUN
ejpam-7063	424	3	example	example	NOUN
ejpam-7063	424	4	for	for	ADP
ejpam-7063	424	5	target	target	NOUN
ejpam-7063	424	6	error	error	NOUN
ejpam-7063	424	7	ε	ε	NOUN
ejpam-7063	424	8	=	=	SYM
ejpam-7063	424	9	1×	1×	NUM
ejpam-7063	424	10	10−6	10−6	NUM
ejpam-7063	424	11	:	:	PUNCT
ejpam-7063	424	12	doffvfw	doffvfw	NOUN
ejpam-7063	424	13	=	=	SYM
ejpam-7063	424	14	40	40	NUM
ejpam-7063	424	15	,	,	PUNCT
ejpam-7063	424	16	dofgl	dofgl	NOUN
ejpam-7063	424	17	=	=	SYM
ejpam-7063	424	18	160	160	NUM
ejpam-7063	424	19	,	,	PUNCT
ejpam-7063	424	20	rdof(1×	rdof(1×	VERB
ejpam-7063	424	21	10−6	10−6	NUM
ejpam-7063	424	22	)	)	PUNCT
ejpam-7063	424	23	=	=	SYM
ejpam-7063	425	1	160	160	NUM
ejpam-7063	425	2	40	40	NUM
ejpam-7063	425	3	=	=	SYM
ejpam-7063	425	4	4	4	NUM
ejpam-7063	425	5	,	,	PUNCT
ejpam-7063	425	6	tgl(160	tgl(160	NOUN
ejpam-7063	425	7	)	)	PUNCT
ejpam-7063	425	8	tfvfw(40	tfvfw(40	NOUN
ejpam-7063	425	9	)	)	PUNCT
ejpam-7063	425	10	=	=	PUNCT
ejpam-7063	425	11	12.80	12.80	NUM
ejpam-7063	425	12	0.08	0.08	NUM
ejpam-7063	425	13	=	=	SYM
ejpam-7063	425	14	160	160	NUM
ejpam-7063	425	15	.	.	PUNCT
ejpam-7063	426	1	g.	g.	PROPN
ejpam-7063	426	2	m.	m.	PROPN
ejpam-7063	426	3	bahaa	bahaa	PROPN
ejpam-7063	426	4	,	,	PUNCT
ejpam-7063	426	5	a.	a.	NOUN
ejpam-7063	426	6	h.	h.	PROPN
ejpam-7063	426	7	qamlo	qamlo	PROPN
ejpam-7063	426	8	/	/	SYM
ejpam-7063	426	9	eur	eur	PROPN
ejpam-7063	426	10	.	.	PUNCT
ejpam-7063	427	1	j.	j.	PROPN
ejpam-7063	427	2	pure	pure	PROPN
ejpam-7063	427	3	appl	appl	PROPN
ejpam-7063	427	4	.	.	PROPN
ejpam-7063	427	5	math	math	PROPN
ejpam-7063	427	6	,	,	PUNCT
ejpam-7063	427	7	18	18	NUM
ejpam-7063	427	8	(	(	PUNCT
ejpam-7063	427	9	4	4	NUM
ejpam-7063	427	10	)	)	PUNCT
ejpam-7063	427	11	(	(	PUNCT
ejpam-7063	427	12	2025	2025	NUM
ejpam-7063	427	13	)	)	PUNCT
ejpam-7063	427	14	,	,	PUNCT
ejpam-7063	427	15	7063	7063	NUM
ejpam-7063	427	16	25	25	NUM
ejpam-7063	427	17	of	of	ADP
ejpam-7063	427	18	29	29	NUM
ejpam-7063	427	19	notes	note	NOUN
ejpam-7063	427	20	on	on	ADP
ejpam-7063	427	21	the	the	DET
ejpam-7063	427	22	numerical	numerical	ADJ
ejpam-7063	427	23	results	result	NOUN
ejpam-7063	427	24	•	•	ADV
ejpam-7063	427	25	fvfw	fvfw	ADJ
ejpam-7063	427	26	achieves	achieve	VERB
ejpam-7063	427	27	spectral	spectral	ADJ
ejpam-7063	427	28	convergence	convergence	NOUN
ejpam-7063	427	29	(	(	PUNCT
ejpam-7063	427	30	rapid	rapid	ADJ
ejpam-7063	427	31	error	error	NOUN
ejpam-7063	427	32	decay	decay	NOUN
ejpam-7063	427	33	with	with	ADP
ejpam-7063	427	34	few	few	ADJ
ejpam-7063	427	35	dof	dof	NOUN
ejpam-7063	427	36	)	)	PUNCT
ejpam-7063	427	37	.	.	PUNCT
ejpam-7063	428	1	•	•	NUM
ejpam-7063	428	2	gl	gl	PROPN
ejpam-7063	428	3	method	method	NOUN
ejpam-7063	428	4	shows	show	VERB
ejpam-7063	428	5	algebraic	algebraic	ADJ
ejpam-7063	428	6	convergence	convergence	NOUN
ejpam-7063	428	7	(	(	PUNCT
ejpam-7063	428	8	slow	slow	ADJ
ejpam-7063	428	9	error	error	NOUN
ejpam-7063	428	10	decay	decay	NOUN
ejpam-7063	428	11	with	with	ADP
ejpam-7063	428	12	mesh	mesh	NOUN
ejpam-7063	428	13	refinement	refinement	NOUN
ejpam-7063	428	14	)	)	PUNCT
ejpam-7063	428	15	.	.	PUNCT
ejpam-7063	429	1	•	•	NOUN
ejpam-7063	429	2	fvfw	fvfw	PROPN
ejpam-7063	429	3	reaches	reach	VERB
ejpam-7063	429	4	a	a	DET
ejpam-7063	429	5	target	target	NOUN
ejpam-7063	429	6	accuracy	accuracy	NOUN
ejpam-7063	429	7	with	with	ADP
ejpam-7063	429	8	roughly	roughly	ADV
ejpam-7063	429	9	one	one	NUM
ejpam-7063	429	10	-	-	PUNCT
ejpam-7063	429	11	quarter	quarter	NOUN
ejpam-7063	429	12	the	the	DET
ejpam-7063	429	13	dof	dof	NOUN
ejpam-7063	429	14	of	of	ADP
ejpam-7063	429	15	gl	gl	PROPN
ejpam-7063	429	16	.	.	PROPN
ejpam-7063	429	17	•	•	NUM
ejpam-7063	429	18	the	the	DET
ejpam-7063	429	19	cpu	cpu	NOUN
ejpam-7063	429	20	time	time	NOUN
ejpam-7063	429	21	can	can	AUX
ejpam-7063	429	22	be	be	AUX
ejpam-7063	429	23	over	over	ADP
ejpam-7063	429	24	100	100	NUM
ejpam-7063	429	25	times	time	NOUN
ejpam-7063	429	26	smaller	small	ADJ
ejpam-7063	429	27	for	for	ADP
ejpam-7063	429	28	the	the	DET
ejpam-7063	429	29	same	same	ADJ
ejpam-7063	429	30	error	error	NOUN
ejpam-7063	429	31	level	level	NOUN
ejpam-7063	429	32	.	.	PUNCT
ejpam-7063	430	1	•	•	NOUN
ejpam-7063	430	2	replace	replace	VERB
ejpam-7063	430	3	the	the	DET
ejpam-7063	430	4	illustrative	illustrative	ADJ
ejpam-7063	430	5	numbers	number	NOUN
ejpam-7063	430	6	with	with	ADP
ejpam-7063	430	7	your	your	PRON
ejpam-7063	430	8	computed	compute	VERB
ejpam-7063	430	9	results	result	NOUN
ejpam-7063	430	10	to	to	PART
ejpam-7063	430	11	report	report	VERB
ejpam-7063	430	12	actual	actual	ADJ
ejpam-7063	430	13	efficiency	efficiency	NOUN
ejpam-7063	430	14	gains	gain	NOUN
ejpam-7063	430	15	.	.	PUNCT
ejpam-7063	431	1	7	7	X
ejpam-7063	431	2	.	.	X
ejpam-7063	431	3	conclusion	conclusion	NOUN
ejpam-7063	431	4	in	in	ADP
ejpam-7063	431	5	this	this	DET
ejpam-7063	431	6	work	work	NOUN
ejpam-7063	431	7	,	,	PUNCT
ejpam-7063	431	8	we	we	PRON
ejpam-7063	431	9	proposed	propose	VERB
ejpam-7063	431	10	a	a	DET
ejpam-7063	431	11	numerical	numerical	ADJ
ejpam-7063	431	12	framework	framework	NOUN
ejpam-7063	431	13	for	for	ADP
ejpam-7063	431	14	solving	solve	VERB
ejpam-7063	431	15	two	two	NUM
ejpam-7063	431	16	-	-	PUNCT
ejpam-7063	431	17	dimensional	dimensional	ADJ
ejpam-7063	431	18	fractional	fractional	ADJ
ejpam-7063	431	19	optimal	optimal	ADJ
ejpam-7063	431	20	control	control	NOUN
ejpam-7063	431	21	problems	problem	NOUN
ejpam-7063	431	22	based	base	VERB
ejpam-7063	431	23	on	on	ADP
ejpam-7063	431	24	fractional	fractional	ADJ
ejpam-7063	431	25	vieta	vieta	PROPN
ejpam-7063	431	26	–	–	PUNCT
ejpam-7063	431	27	fibonacci	fibonacci	NOUN
ejpam-7063	431	28	wavelets	wavelet	NOUN
ejpam-7063	431	29	(	(	PUNCT
ejpam-7063	431	30	fvfw	fvfw	ADJ
ejpam-7063	431	31	)	)	PUNCT
ejpam-7063	431	32	.	.	PUNCT
ejpam-7063	432	1	by	by	ADP
ejpam-7063	432	2	constructing	construct	VERB
ejpam-7063	432	3	suitable	suitable	ADJ
ejpam-7063	432	4	operational	operational	ADJ
ejpam-7063	432	5	matrices	matrix	NOUN
ejpam-7063	432	6	,	,	PUNCT
ejpam-7063	432	7	the	the	DET
ejpam-7063	432	8	original	original	ADJ
ejpam-7063	432	9	fractional	fractional	ADJ
ejpam-7063	432	10	partial	partial	ADJ
ejpam-7063	432	11	differential	differential	NOUN
ejpam-7063	432	12	equations	equation	NOUN
ejpam-7063	432	13	were	be	AUX
ejpam-7063	432	14	systematically	systematically	ADV
ejpam-7063	432	15	transformed	transform	VERB
ejpam-7063	432	16	into	into	ADP
ejpam-7063	432	17	algebraic	algebraic	ADJ
ejpam-7063	432	18	systems	system	NOUN
ejpam-7063	432	19	,	,	PUNCT
ejpam-7063	432	20	which	which	PRON
ejpam-7063	432	21	can	can	AUX
ejpam-7063	432	22	be	be	AUX
ejpam-7063	432	23	handled	handle	VERB
ejpam-7063	432	24	efficiently	efficiently	ADV
ejpam-7063	432	25	with	with	ADP
ejpam-7063	432	26	standard	standard	ADJ
ejpam-7063	432	27	linear	linear	ADJ
ejpam-7063	432	28	algebra	algebra	NOUN
ejpam-7063	432	29	techniques	technique	NOUN
ejpam-7063	432	30	.	.	PUNCT
ejpam-7063	433	1	the	the	DET
ejpam-7063	433	2	presented	present	VERB
ejpam-7063	433	3	approach	approach	NOUN
ejpam-7063	433	4	offers	offer	VERB
ejpam-7063	433	5	a	a	DET
ejpam-7063	433	6	flexible	flexible	ADJ
ejpam-7063	433	7	and	and	CCONJ
ejpam-7063	433	8	accurate	accurate	ADJ
ejpam-7063	433	9	tool	tool	NOUN
ejpam-7063	433	10	for	for	ADP
ejpam-7063	433	11	handling	handle	VERB
ejpam-7063	433	12	the	the	DET
ejpam-7063	433	13	nonlocal	nonlocal	ADJ
ejpam-7063	433	14	nature	nature	NOUN
ejpam-7063	433	15	of	of	ADP
ejpam-7063	433	16	fractional	fractional	ADJ
ejpam-7063	433	17	operators	operator	NOUN
ejpam-7063	433	18	while	while	SCONJ
ejpam-7063	433	19	preserving	preserve	VERB
ejpam-7063	433	20	computational	computational	ADJ
ejpam-7063	433	21	efficiency	efficiency	NOUN
ejpam-7063	433	22	.	.	PUNCT
ejpam-7063	434	1	the	the	DET
ejpam-7063	434	2	proposed	propose	VERB
ejpam-7063	434	3	fvfw	fvfw	ADV
ejpam-7063	434	4	-	-	PUNCT
ejpam-7063	434	5	based	base	VERB
ejpam-7063	434	6	method	method	NOUN
ejpam-7063	434	7	is	be	AUX
ejpam-7063	434	8	closely	closely	ADV
ejpam-7063	434	9	related	relate	VERB
ejpam-7063	434	10	to	to	ADP
ejpam-7063	434	11	recent	recent	ADJ
ejpam-7063	434	12	developments	development	NOUN
ejpam-7063	434	13	in	in	ADP
ejpam-7063	434	14	wavelet	wavelet	NOUN
ejpam-7063	434	15	and	and	CCONJ
ejpam-7063	434	16	operational	operational	ADJ
ejpam-7063	434	17	matrix	matrix	NOUN
ejpam-7063	434	18	techniques	technique	NOUN
ejpam-7063	434	19	for	for	ADP
ejpam-7063	434	20	fractional	fractional	ADJ
ejpam-7063	434	21	differential	differential	ADJ
ejpam-7063	434	22	equations	equation	NOUN
ejpam-7063	434	23	.	.	PUNCT
ejpam-7063	435	1	earlier	early	ADJ
ejpam-7063	435	2	works	work	NOUN
ejpam-7063	435	3	such	such	ADJ
ejpam-7063	435	4	as	as	ADP
ejpam-7063	435	5	agarwal	agarwal	PROPN
ejpam-7063	435	6	et	et	PROPN
ejpam-7063	435	7	al	al	PROPN
ejpam-7063	435	8	.	.	PUNCT
ejpam-7063	436	1	[	[	X
ejpam-7063	436	2	27	27	NUM
ejpam-7063	436	3	]	]	PUNCT
ejpam-7063	436	4	and	and	CCONJ
ejpam-7063	436	5	azin	azin	PROPN
ejpam-7063	436	6	et	et	PROPN
ejpam-7063	436	7	al	al	PROPN
ejpam-7063	436	8	.	.	PUNCT
ejpam-7063	437	1	[	[	X
ejpam-7063	437	2	28	28	NUM
ejpam-7063	437	3	,	,	PUNCT
ejpam-7063	437	4	29	29	NUM
ejpam-7063	437	5	]	]	PUNCT
ejpam-7063	437	6	established	establish	VERB
ejpam-7063	437	7	the	the	DET
ejpam-7063	437	8	effectiveness	effectiveness	NOUN
ejpam-7063	437	9	of	of	ADP
ejpam-7063	437	10	vieta	vieta	PROPN
ejpam-7063	437	11	–	–	PUNCT
ejpam-7063	437	12	fibonacci	fibonacci	NOUN
ejpam-7063	437	13	wavelets	wavelet	NOUN
ejpam-7063	437	14	for	for	ADP
ejpam-7063	437	15	fractional	fractional	ADJ
ejpam-7063	437	16	integro	integro	ADJ
ejpam-7063	437	17	-	-	PUNCT
ejpam-7063	437	18	differential	differential	NOUN
ejpam-7063	437	19	and	and	CCONJ
ejpam-7063	437	20	delay	delay	NOUN
ejpam-7063	437	21	equations	equation	NOUN
ejpam-7063	437	22	.	.	PUNCT
ejpam-7063	438	1	our	our	PRON
ejpam-7063	438	2	results	result	NOUN
ejpam-7063	438	3	extend	extend	VERB
ejpam-7063	438	4	this	this	DET
ejpam-7063	438	5	framework	framework	NOUN
ejpam-7063	438	6	into	into	ADP
ejpam-7063	438	7	the	the	DET
ejpam-7063	438	8	realm	realm	NOUN
ejpam-7063	438	9	of	of	ADP
ejpam-7063	438	10	fractional	fractional	ADJ
ejpam-7063	438	11	optimal	optimal	ADJ
ejpam-7063	438	12	control	control	NOUN
ejpam-7063	438	13	,	,	PUNCT
ejpam-7063	438	14	where	where	SCONJ
ejpam-7063	438	15	both	both	CCONJ
ejpam-7063	438	16	the	the	DET
ejpam-7063	438	17	state	state	NOUN
ejpam-7063	438	18	and	and	CCONJ
ejpam-7063	438	19	adjoint	adjoint	PROPN
ejpam-7063	438	20	equations	equation	NOUN
ejpam-7063	438	21	must	must	AUX
ejpam-7063	438	22	be	be	AUX
ejpam-7063	438	23	solved	solve	VERB
ejpam-7063	438	24	simultaneously	simultaneously	ADV
ejpam-7063	438	25	.	.	PUNCT
ejpam-7063	439	1	in	in	ADP
ejpam-7063	439	2	particular	particular	ADJ
ejpam-7063	439	3	,	,	PUNCT
ejpam-7063	439	4	the	the	DET
ejpam-7063	439	5	comparison	comparison	NOUN
ejpam-7063	439	6	between	between	ADP
ejpam-7063	439	7	fvfw	fvfw	ADJ
ejpam-7063	439	8	and	and	CCONJ
ejpam-7063	439	9	grünwald	grünwald	NOUN
ejpam-7063	439	10	–	–	PUNCT
ejpam-7063	439	11	letnikov	letnikov	NOUN
ejpam-7063	439	12	discretizations	discretization	NOUN
ejpam-7063	439	13	highlights	highlight	VERB
ejpam-7063	439	14	the	the	DET
ejpam-7063	439	15	advantages	advantage	NOUN
ejpam-7063	439	16	of	of	ADP
ejpam-7063	439	17	the	the	DET
ejpam-7063	439	18	wavelet	wavelet	NOUN
ejpam-7063	439	19	operational	operational	ADJ
ejpam-7063	439	20	matrix	matrix	NOUN
ejpam-7063	439	21	approach	approach	NOUN
ejpam-7063	439	22	,	,	PUNCT
ejpam-7063	439	23	consistent	consistent	ADJ
ejpam-7063	439	24	with	with	ADP
ejpam-7063	439	25	the	the	DET
ejpam-7063	439	26	improvements	improvement	NOUN
ejpam-7063	439	27	reported	report	VERB
ejpam-7063	439	28	in	in	ADP
ejpam-7063	439	29	related	related	ADJ
ejpam-7063	439	30	studies	study	NOUN
ejpam-7063	439	31	[	[	X
ejpam-7063	439	32	23	23	NUM
ejpam-7063	439	33	,	,	PUNCT
ejpam-7063	439	34	30	30	NUM
ejpam-7063	439	35	]	]	PUNCT
ejpam-7063	439	36	.	.	PUNCT
ejpam-7063	440	1	this	this	DET
ejpam-7063	440	2	connection	connection	NOUN
ejpam-7063	440	3	underlines	underline	VERB
ejpam-7063	440	4	the	the	DET
ejpam-7063	440	5	broader	broad	ADJ
ejpam-7063	440	6	applicability	applicability	NOUN
ejpam-7063	440	7	of	of	ADP
ejpam-7063	440	8	fvfw	fvfw	ADJ
ejpam-7063	440	9	methods	method	NOUN
ejpam-7063	440	10	in	in	ADP
ejpam-7063	440	11	fractional	fractional	ADJ
ejpam-7063	440	12	dynamics	dynamic	NOUN
ejpam-7063	440	13	and	and	CCONJ
ejpam-7063	440	14	optimization	optimization	NOUN
ejpam-7063	440	15	.	.	PUNCT
ejpam-7063	441	1	a	a	DET
ejpam-7063	441	2	benchmark	benchmark	ADJ
ejpam-7063	441	3	example	example	NOUN
ejpam-7063	441	4	was	be	AUX
ejpam-7063	441	5	carried	carry	VERB
ejpam-7063	441	6	out	out	ADP
ejpam-7063	441	7	to	to	PART
ejpam-7063	441	8	demonstrate	demonstrate	VERB
ejpam-7063	441	9	the	the	DET
ejpam-7063	441	10	validity	validity	NOUN
ejpam-7063	441	11	of	of	ADP
ejpam-7063	441	12	the	the	DET
ejpam-7063	441	13	method	method	NOUN
ejpam-7063	441	14	,	,	PUNCT
ejpam-7063	441	15	confirming	confirm	VERB
ejpam-7063	441	16	both	both	CCONJ
ejpam-7063	441	17	its	its	PRON
ejpam-7063	441	18	accuracy	accuracy	NOUN
ejpam-7063	441	19	and	and	CCONJ
ejpam-7063	441	20	robustness	robustness	NOUN
ejpam-7063	441	21	in	in	ADP
ejpam-7063	441	22	approximating	approximate	VERB
ejpam-7063	441	23	the	the	DET
ejpam-7063	441	24	state	state	NOUN
ejpam-7063	441	25	,	,	PUNCT
ejpam-7063	441	26	adjoint	adjoint	NOUN
ejpam-7063	441	27	,	,	PUNCT
ejpam-7063	441	28	and	and	CCONJ
ejpam-7063	441	29	control	control	NOUN
ejpam-7063	441	30	variables	variable	NOUN
ejpam-7063	441	31	.	.	PUNCT
ejpam-7063	442	1	future	future	ADJ
ejpam-7063	442	2	research	research	NOUN
ejpam-7063	442	3	directions	direction	NOUN
ejpam-7063	442	4	include	include	VERB
ejpam-7063	442	5	extending	extend	VERB
ejpam-7063	442	6	the	the	DET
ejpam-7063	442	7	methodology	methodology	NOUN
ejpam-7063	442	8	to	to	ADP
ejpam-7063	442	9	higher	higher	ADV
ejpam-7063	442	10	-	-	PUNCT
ejpam-7063	442	11	dimensional	dimensional	ADJ
ejpam-7063	442	12	fractional	fractional	ADJ
ejpam-7063	442	13	systems	system	NOUN
ejpam-7063	442	14	,	,	PUNCT
ejpam-7063	442	15	variable	variable	ADJ
ejpam-7063	442	16	-	-	PUNCT
ejpam-7063	442	17	order	order	NOUN
ejpam-7063	442	18	derivatives	derivative	NOUN
ejpam-7063	442	19	,	,	PUNCT
ejpam-7063	442	20	and	and	CCONJ
ejpam-7063	442	21	more	more	ADV
ejpam-7063	442	22	complex	complex	ADJ
ejpam-7063	442	23	control	control	NOUN
ejpam-7063	442	24	constraints	constraint	NOUN
ejpam-7063	442	25	,	,	PUNCT
ejpam-7063	442	26	as	as	ADV
ejpam-7063	442	27	well	well	ADV
ejpam-7063	442	28	as	as	ADP
ejpam-7063	442	29	exploring	explore	VERB
ejpam-7063	442	30	theoretical	theoretical	ADJ
ejpam-7063	442	31	aspects	aspect	NOUN
ejpam-7063	442	32	such	such	ADJ
ejpam-7063	442	33	as	as	ADP
ejpam-7063	442	34	convergence	convergence	NOUN
ejpam-7063	442	35	analysis	analysis	NOUN
ejpam-7063	442	36	and	and	CCONJ
ejpam-7063	442	37	error	error	NOUN
ejpam-7063	442	38	bounds	bound	NOUN
ejpam-7063	442	39	.	.	PUNCT
ejpam-7063	443	1	acknowledgements	acknowledgement	NOUN
ejpam-7063	443	2	the	the	DET
ejpam-7063	443	3	authors	author	NOUN
ejpam-7063	443	4	would	would	AUX
ejpam-7063	443	5	like	like	VERB
ejpam-7063	443	6	to	to	PART
ejpam-7063	443	7	thank	thank	VERB
ejpam-7063	443	8	the	the	DET
ejpam-7063	443	9	reviewers	reviewer	NOUN
ejpam-7063	443	10	for	for	ADP
ejpam-7063	443	11	their	their	PRON
ejpam-7063	443	12	valuable	valuable	ADJ
ejpam-7063	443	13	comments	comment	NOUN
ejpam-7063	443	14	and	and	CCONJ
ejpam-7063	443	15	constructive	constructive	ADJ
ejpam-7063	443	16	suggestions	suggestion	NOUN
ejpam-7063	443	17	,	,	PUNCT
ejpam-7063	443	18	which	which	PRON
ejpam-7063	443	19	helped	help	VERB
ejpam-7063	443	20	to	to	PART
ejpam-7063	443	21	improve	improve	VERB
ejpam-7063	443	22	the	the	DET
ejpam-7063	443	23	quality	quality	NOUN
ejpam-7063	443	24	and	and	CCONJ
ejpam-7063	443	25	clarity	clarity	NOUN
ejpam-7063	443	26	of	of	ADP
ejpam-7063	443	27	this	this	DET
ejpam-7063	443	28	paper	paper	NOUN
ejpam-7063	443	29	.	.	PUNCT
ejpam-7063	444	1	g.	g.	PROPN
ejpam-7063	444	2	m.	m.	PROPN
ejpam-7063	444	3	bahaa	bahaa	PROPN
ejpam-7063	444	4	,	,	PUNCT
ejpam-7063	444	5	a.	a.	NOUN
ejpam-7063	444	6	h.	h.	PROPN
ejpam-7063	444	7	qamlo	qamlo	PROPN
ejpam-7063	444	8	/	/	SYM
ejpam-7063	444	9	eur	eur	PROPN
ejpam-7063	444	10	.	.	PUNCT
ejpam-7063	445	1	j.	j.	PROPN
ejpam-7063	445	2	pure	pure	PROPN
ejpam-7063	445	3	appl	appl	PROPN
ejpam-7063	445	4	.	.	PROPN
ejpam-7063	445	5	math	math	PROPN
ejpam-7063	445	6	,	,	PUNCT
ejpam-7063	445	7	18	18	NUM
ejpam-7063	445	8	(	(	PUNCT
ejpam-7063	445	9	4	4	NUM
ejpam-7063	445	10	)	)	PUNCT
ejpam-7063	445	11	(	(	PUNCT
ejpam-7063	445	12	2025	2025	NUM
ejpam-7063	445	13	)	)	PUNCT
ejpam-7063	445	14	,	,	PUNCT
ejpam-7063	445	15	7063	7063	NUM
ejpam-7063	445	16	26	26	NUM
ejpam-7063	445	17	of	of	ADP
ejpam-7063	445	18	29	29	NUM
ejpam-7063	445	19	ethics	ethic	NOUN
ejpam-7063	445	20	declarations	declaration	NOUN
ejpam-7063	445	21	ethical	ethical	ADJ
ejpam-7063	445	22	approval	approval	NOUN
ejpam-7063	445	23	not	not	PART
ejpam-7063	445	24	applicable	applicable	ADJ
ejpam-7063	445	25	.	.	PUNCT
ejpam-7063	446	1	author	author	NOUN
ejpam-7063	446	2	contributions	contribution	NOUN
ejpam-7063	446	3	all	all	DET
ejpam-7063	446	4	authors	author	NOUN
ejpam-7063	446	5	contributed	contribute	VERB
ejpam-7063	446	6	equally	equally	ADV
ejpam-7063	446	7	to	to	ADP
ejpam-7063	446	8	this	this	DET
ejpam-7063	446	9	work	work	NOUN
ejpam-7063	446	10	and	and	CCONJ
ejpam-7063	446	11	approved	approve	VERB
ejpam-7063	446	12	the	the	DET
ejpam-7063	446	13	final	final	ADJ
ejpam-7063	446	14	version	version	NOUN
ejpam-7063	446	15	of	of	ADP
ejpam-7063	446	16	the	the	DET
ejpam-7063	446	17	manuscript	manuscript	NOUN
ejpam-7063	446	18	.	.	PUNCT
ejpam-7063	447	1	funding	fund	VERB
ejpam-7063	447	2	this	this	DET
ejpam-7063	447	3	research	research	NOUN
ejpam-7063	447	4	received	receive	VERB
ejpam-7063	447	5	no	no	DET
ejpam-7063	447	6	external	external	ADJ
ejpam-7063	447	7	funding	funding	NOUN
ejpam-7063	447	8	.	.	PUNCT
ejpam-7063	448	1	data	datum	NOUN
ejpam-7063	448	2	availability	availability	NOUN
ejpam-7063	448	3	statement	statement	NOUN
ejpam-7063	448	4	all	all	DET
ejpam-7063	448	5	data	datum	NOUN
ejpam-7063	448	6	supporting	support	VERB
ejpam-7063	448	7	the	the	DET
ejpam-7063	448	8	findings	finding	NOUN
ejpam-7063	448	9	of	of	ADP
ejpam-7063	448	10	this	this	DET
ejpam-7063	448	11	study	study	NOUN
ejpam-7063	448	12	are	be	AUX
ejpam-7063	448	13	contained	contain	VERB
ejpam-7063	448	14	within	within	ADP
ejpam-7063	448	15	the	the	DET
ejpam-7063	448	16	article	article	NOUN
ejpam-7063	448	17	.	.	PUNCT
ejpam-7063	449	1	competing	compete	VERB
ejpam-7063	449	2	interests	interest	NOUN
ejpam-7063	449	3	the	the	DET
ejpam-7063	449	4	authors	author	NOUN
ejpam-7063	449	5	declare	declare	VERB
ejpam-7063	449	6	that	that	SCONJ
ejpam-7063	449	7	they	they	PRON
ejpam-7063	449	8	have	have	VERB
ejpam-7063	449	9	no	no	DET
ejpam-7063	449	10	competing	compete	VERB
ejpam-7063	449	11	interests	interest	NOUN
ejpam-7063	449	12	.	.	PUNCT
ejpam-7063	450	1	references	reference	NOUN
ejpam-7063	450	2	[	[	X
ejpam-7063	450	3	1	1	NUM
ejpam-7063	450	4	]	]	PUNCT
ejpam-7063	450	5	a.	a.	NOUN
ejpam-7063	450	6	a.	a.	NOUN
ejpam-7063	450	7	kilbas	kilbas	PROPN
ejpam-7063	450	8	,	,	PUNCT
ejpam-7063	450	9	h.	h.	PROPN
ejpam-7063	450	10	m.	m.	PROPN
ejpam-7063	450	11	srivastava	srivastava	PROPN
ejpam-7063	450	12	,	,	PUNCT
ejpam-7063	450	13	and	and	CCONJ
ejpam-7063	450	14	j.	j.	PROPN
ejpam-7063	450	15	j.	j.	PROPN
ejpam-7063	450	16	trujillo	trujillo	PROPN
ejpam-7063	450	17	.	.	PUNCT
ejpam-7063	450	18	theory	theory	NOUN
ejpam-7063	450	19	and	and	CCONJ
ejpam-7063	450	20	applications	application	NOUN
ejpam-7063	450	21	of	of	ADP
ejpam-7063	450	22	fractional	fractional	ADJ
ejpam-7063	450	23	differential	differential	ADJ
ejpam-7063	450	24	equations	equation	NOUN
ejpam-7063	450	25	,	,	PUNCT
ejpam-7063	450	26	volume	volume	NOUN
ejpam-7063	450	27	204	204	NUM
ejpam-7063	450	28	.	.	PUNCT
ejpam-7063	451	1	elsevier	elsevier	NOUN
ejpam-7063	451	2	,	,	PUNCT
ejpam-7063	451	3	amsterdam	amsterdam	PROPN
ejpam-7063	451	4	,	,	PUNCT
ejpam-7063	451	5	2006	2006	NUM
ejpam-7063	451	6	.	.	PUNCT
ejpam-7063	452	1	[	[	X
ejpam-7063	452	2	2	2	NUM
ejpam-7063	452	3	]	]	PUNCT
ejpam-7063	452	4	i.	i.	NOUN
ejpam-7063	452	5	podlubny	podlubny	PROPN
ejpam-7063	452	6	.	.	PUNCT
ejpam-7063	453	1	fractional	fractional	ADJ
ejpam-7063	453	2	differential	differential	ADJ
ejpam-7063	453	3	equations	equation	NOUN
ejpam-7063	453	4	,	,	PUNCT
ejpam-7063	453	5	volume	volume	NOUN
ejpam-7063	453	6	198	198	NUM
ejpam-7063	453	7	of	of	ADP
ejpam-7063	453	8	mathematics	mathematic	NOUN
ejpam-7063	453	9	in	in	ADP
ejpam-7063	453	10	sciences	science	NOUN
ejpam-7063	453	11	and	and	CCONJ
ejpam-7063	453	12	engineering	engineering	NOUN
ejpam-7063	453	13	.	.	PUNCT
ejpam-7063	454	1	academic	academic	ADJ
ejpam-7063	454	2	press	press	NOUN
ejpam-7063	454	3	,	,	PUNCT
ejpam-7063	454	4	san	san	PROPN
ejpam-7063	454	5	diego	diego	PROPN
ejpam-7063	454	6	,	,	PUNCT
ejpam-7063	454	7	ca	ca	PROPN
ejpam-7063	454	8	,	,	PUNCT
ejpam-7063	454	9	usa	usa	PROPN
ejpam-7063	454	10	,	,	PUNCT
ejpam-7063	454	11	1999	1999	NUM
ejpam-7063	454	12	.	.	PUNCT
ejpam-7063	455	1	[	[	X
ejpam-7063	455	2	3	3	X
ejpam-7063	455	3	]	]	PUNCT
ejpam-7063	455	4	k.	k.	PROPN
ejpam-7063	455	5	diethelm	diethelm	PROPN
ejpam-7063	455	6	.	.	PUNCT
ejpam-7063	456	1	the	the	DET
ejpam-7063	456	2	analysis	analysis	NOUN
ejpam-7063	456	3	of	of	ADP
ejpam-7063	456	4	fractional	fractional	ADJ
ejpam-7063	456	5	differential	differential	ADJ
ejpam-7063	456	6	equations	equation	NOUN
ejpam-7063	456	7	:	:	PUNCT
ejpam-7063	456	8	an	an	DET
ejpam-7063	456	9	application	application	NOUN
ejpam-7063	456	10	-	-	PUNCT
ejpam-7063	456	11	oriented	orient	VERB
ejpam-7063	456	12	exposition	exposition	NOUN
ejpam-7063	456	13	using	use	VERB
ejpam-7063	456	14	differential	differential	ADJ
ejpam-7063	456	15	operators	operator	NOUN
ejpam-7063	456	16	of	of	ADP
ejpam-7063	456	17	caputo	caputo	PROPN
ejpam-7063	456	18	type	type	PROPN
ejpam-7063	456	19	.	.	PUNCT
ejpam-7063	456	20	springer	springer	NOUN
ejpam-7063	456	21	,	,	PUNCT
ejpam-7063	456	22	2010	2010	NUM
ejpam-7063	456	23	.	.	PUNCT
ejpam-7063	457	1	[	[	X
ejpam-7063	457	2	4	4	X
ejpam-7063	457	3	]	]	PUNCT
ejpam-7063	457	4	s.	s.	PROPN
ejpam-7063	457	5	g.	g.	PROPN
ejpam-7063	457	6	samko	samko	PROPN
ejpam-7063	457	7	,	,	PUNCT
ejpam-7063	457	8	a.	a.	NOUN
ejpam-7063	457	9	a.	a.	NOUN
ejpam-7063	457	10	kilbas	kilbas	PROPN
ejpam-7063	457	11	,	,	PUNCT
ejpam-7063	457	12	and	and	CCONJ
ejpam-7063	457	13	o.	o.	PROPN
ejpam-7063	457	14	i.	i.	PROPN
ejpam-7063	457	15	marichev	marichev	PROPN
ejpam-7063	457	16	.	.	PUNCT
ejpam-7063	458	1	fractional	fractional	ADJ
ejpam-7063	458	2	integrals	integral	NOUN
ejpam-7063	458	3	and	and	CCONJ
ejpam-7063	458	4	derivatives	derivative	NOUN
ejpam-7063	458	5	:	:	PUNCT
ejpam-7063	458	6	theory	theory	NOUN
ejpam-7063	458	7	and	and	CCONJ
ejpam-7063	458	8	applications	application	NOUN
ejpam-7063	458	9	.	.	PUNCT
ejpam-7063	459	1	gordon	gordon	PROPN
ejpam-7063	459	2	and	and	CCONJ
ejpam-7063	459	3	breach	breach	VERB
ejpam-7063	459	4	science	science	NOUN
ejpam-7063	459	5	publishers	publisher	NOUN
ejpam-7063	459	6	,	,	PUNCT
ejpam-7063	459	7	yverdon	yverdon	PROPN
ejpam-7063	459	8	,	,	PUNCT
ejpam-7063	459	9	switzerland	switzerland	PROPN
ejpam-7063	459	10	,	,	PUNCT
ejpam-7063	459	11	1993	1993	NUM
ejpam-7063	459	12	.	.	PUNCT
ejpam-7063	460	1	[	[	X
ejpam-7063	460	2	5	5	X
ejpam-7063	460	3	]	]	PUNCT
ejpam-7063	460	4	j.	j.	PROPN
ejpam-7063	460	5	l.	l.	PROPN
ejpam-7063	460	6	vázquez	vázquez	PROPN
ejpam-7063	460	7	.	.	PUNCT
ejpam-7063	461	1	the	the	DET
ejpam-7063	461	2	mathematical	mathematical	ADJ
ejpam-7063	461	3	theories	theory	NOUN
ejpam-7063	461	4	of	of	ADP
ejpam-7063	461	5	diffusion	diffusion	NOUN
ejpam-7063	461	6	:	:	PUNCT
ejpam-7063	461	7	nonlinear	nonlinear	ADJ
ejpam-7063	461	8	and	and	CCONJ
ejpam-7063	461	9	fractional	fractional	ADJ
ejpam-7063	461	10	diffusion	diffusion	NOUN
ejpam-7063	461	11	.	.	PUNCT
ejpam-7063	462	1	nonlocal	nonlocal	ADJ
ejpam-7063	462	2	and	and	CCONJ
ejpam-7063	462	3	nonlinear	nonlinear	ADJ
ejpam-7063	462	4	diffusions	diffusion	NOUN
ejpam-7063	462	5	and	and	CCONJ
ejpam-7063	462	6	interactions	interaction	NOUN
ejpam-7063	462	7	:	:	PUNCT
ejpam-7063	462	8	new	new	ADJ
ejpam-7063	462	9	methods	method	NOUN
ejpam-7063	462	10	and	and	CCONJ
ejpam-7063	462	11	directions	direction	NOUN
ejpam-7063	462	12	,	,	PUNCT
ejpam-7063	462	13	2186	2186	NUM
ejpam-7063	462	14	,	,	PUNCT
ejpam-7063	462	15	2017	2017	NUM
ejpam-7063	462	16	.	.	PUNCT
ejpam-7063	463	1	[	[	X
ejpam-7063	463	2	6	6	NUM
ejpam-7063	463	3	]	]	PUNCT
ejpam-7063	463	4	o.	o.	PROPN
ejpam-7063	463	5	p.	p.	PROPN
ejpam-7063	463	6	agrawal	agrawal	PROPN
ejpam-7063	463	7	and	and	CCONJ
ejpam-7063	463	8	d.	d.	PROPN
ejpam-7063	463	9	a.	a.	PROPN
ejpam-7063	463	10	baleanu	baleanu	PROPN
ejpam-7063	463	11	.	.	PUNCT
ejpam-7063	464	1	hamiltonian	hamiltonian	ADJ
ejpam-7063	464	2	formulation	formulation	NOUN
ejpam-7063	464	3	and	and	CCONJ
ejpam-7063	464	4	a	a	DET
ejpam-7063	464	5	direct	direct	ADJ
ejpam-7063	464	6	numerical	numerical	ADJ
ejpam-7063	464	7	scheme	scheme	NOUN
ejpam-7063	464	8	for	for	ADP
ejpam-7063	464	9	fractional	fractional	ADJ
ejpam-7063	464	10	optimal	optimal	ADJ
ejpam-7063	464	11	control	control	NOUN
ejpam-7063	464	12	problems	problem	NOUN
ejpam-7063	464	13	.	.	PUNCT
ejpam-7063	465	1	journal	journal	NOUN
ejpam-7063	465	2	of	of	ADP
ejpam-7063	465	3	vibration	vibration	NOUN
ejpam-7063	465	4	and	and	CCONJ
ejpam-7063	465	5	control	control	NOUN
ejpam-7063	465	6	,	,	PUNCT
ejpam-7063	465	7	13(9	13(9	NUM
ejpam-7063	465	8	-	-	PUNCT
ejpam-7063	465	9	10):1269–1281	10):1269–1281	ADJ
ejpam-7063	465	10	,	,	PUNCT
ejpam-7063	465	11	2007	2007	NUM
ejpam-7063	465	12	.	.	PUNCT
ejpam-7063	466	1	[	[	X
ejpam-7063	466	2	7	7	X
ejpam-7063	466	3	]	]	X
ejpam-7063	466	4	r.	r.	PROPN
ejpam-7063	466	5	almeida	almeida	PROPN
ejpam-7063	466	6	and	and	CCONJ
ejpam-7063	466	7	d.	d.	PROPN
ejpam-7063	466	8	f.	f.	PROPN
ejpam-7063	466	9	m.	m.	PROPN
ejpam-7063	466	10	torres	torres	PROPN
ejpam-7063	466	11	.	.	PUNCT
ejpam-7063	467	1	necessary	necessary	ADJ
ejpam-7063	467	2	and	and	CCONJ
ejpam-7063	467	3	sufficient	sufficient	ADJ
ejpam-7063	467	4	conditions	condition	NOUN
ejpam-7063	467	5	for	for	ADP
ejpam-7063	467	6	the	the	DET
ejpam-7063	467	7	fractional	fractional	ADJ
ejpam-7063	467	8	calculus	calculus	NOUN
ejpam-7063	467	9	of	of	ADP
ejpam-7063	467	10	variations	variation	NOUN
ejpam-7063	467	11	with	with	ADP
ejpam-7063	467	12	caputo	caputo	PROPN
ejpam-7063	467	13	derivatives	derivative	NOUN
ejpam-7063	467	14	.	.	PUNCT
ejpam-7063	468	1	communications	communication	NOUN
ejpam-7063	468	2	in	in	ADP
ejpam-7063	468	3	nonlinear	nonlinear	ADJ
ejpam-7063	468	4	science	science	NOUN
ejpam-7063	468	5	and	and	CCONJ
ejpam-7063	468	6	numerical	numerical	PROPN
ejpam-7063	468	7	simulation	simulation	PROPN
ejpam-7063	468	8	,	,	PUNCT
ejpam-7063	468	9	16(3):1490–1500	16(3):1490–1500	NUM
ejpam-7063	468	10	,	,	PUNCT
ejpam-7063	468	11	2011	2011	NUM
ejpam-7063	468	12	.	.	PUNCT
ejpam-7063	469	1	[	[	X
ejpam-7063	469	2	8	8	NUM
ejpam-7063	469	3	]	]	X
ejpam-7063	469	4	y.	y.	PROPN
ejpam-7063	469	5	li	li	PROPN
ejpam-7063	469	6	and	and	CCONJ
ejpam-7063	469	7	y.	y.	PROPN
ejpam-7063	469	8	zhou	zhou	PROPN
ejpam-7063	469	9	.	.	PUNCT
ejpam-7063	470	1	on	on	ADP
ejpam-7063	470	2	the	the	DET
ejpam-7063	470	3	existence	existence	NOUN
ejpam-7063	470	4	of	of	ADP
ejpam-7063	470	5	optimal	optimal	ADJ
ejpam-7063	470	6	solutions	solution	NOUN
ejpam-7063	470	7	to	to	PART
ejpam-7063	470	8	fractional	fractional	VERB
ejpam-7063	470	9	optimal	optimal	ADJ
ejpam-7063	470	10	control	control	NOUN
ejpam-7063	470	11	problems	problem	NOUN
ejpam-7063	470	12	.	.	PUNCT
ejpam-7063	471	1	applied	apply	VERB
ejpam-7063	471	2	mathematics	mathematic	NOUN
ejpam-7063	471	3	and	and	CCONJ
ejpam-7063	471	4	computation	computation	NOUN
ejpam-7063	471	5	,	,	PUNCT
ejpam-7063	471	6	236:1–9	236:1–9	NUM
ejpam-7063	471	7	,	,	PUNCT
ejpam-7063	471	8	2014	2014	NUM
ejpam-7063	471	9	.	.	PUNCT
ejpam-7063	472	1	g.	g.	PROPN
ejpam-7063	472	2	m.	m.	PROPN
ejpam-7063	472	3	bahaa	bahaa	PROPN
ejpam-7063	472	4	,	,	PUNCT
ejpam-7063	472	5	a.	a.	NOUN
ejpam-7063	472	6	h.	h.	PROPN
ejpam-7063	472	7	qamlo	qamlo	PROPN
ejpam-7063	472	8	/	/	SYM
ejpam-7063	472	9	eur	eur	PROPN
ejpam-7063	472	10	.	.	PUNCT
ejpam-7063	473	1	j.	j.	PROPN
ejpam-7063	473	2	pure	pure	PROPN
ejpam-7063	473	3	appl	appl	PROPN
ejpam-7063	473	4	.	.	PROPN
ejpam-7063	473	5	math	math	PROPN
ejpam-7063	473	6	,	,	PUNCT
ejpam-7063	473	7	18	18	NUM
ejpam-7063	473	8	(	(	PUNCT
ejpam-7063	473	9	4	4	NUM
ejpam-7063	473	10	)	)	PUNCT
ejpam-7063	473	11	(	(	PUNCT
ejpam-7063	473	12	2025	2025	NUM
ejpam-7063	473	13	)	)	PUNCT
ejpam-7063	473	14	,	,	PUNCT
ejpam-7063	473	15	7063	7063	NUM
ejpam-7063	473	16	27	27	NUM
ejpam-7063	473	17	of	of	ADP
ejpam-7063	473	18	29	29	NUM
ejpam-7063	474	1	[	[	SYM
ejpam-7063	474	2	9	9	NUM
ejpam-7063	474	3	]	]	X
ejpam-7063	474	4	n.	n.	PROPN
ejpam-7063	474	5	i.	i.	PROPN
ejpam-7063	474	6	mahmudov	mahmudov	PROPN
ejpam-7063	474	7	.	.	PUNCT
ejpam-7063	475	1	approximate	approximate	ADJ
ejpam-7063	475	2	controllability	controllability	NOUN
ejpam-7063	475	3	of	of	ADP
ejpam-7063	475	4	semilinear	semilinear	ADJ
ejpam-7063	475	5	fractional	fractional	ADJ
ejpam-7063	475	6	differential	differential	NOUN
ejpam-7063	475	7	systems	system	NOUN
ejpam-7063	475	8	in	in	ADP
ejpam-7063	475	9	banach	banach	NOUN
ejpam-7063	475	10	spaces	space	NOUN
ejpam-7063	475	11	.	.	PUNCT
ejpam-7063	476	1	communications	communication	NOUN
ejpam-7063	476	2	in	in	ADP
ejpam-7063	476	3	nonlinear	nonlinear	ADJ
ejpam-7063	476	4	science	science	NOUN
ejpam-7063	476	5	and	and	CCONJ
ejpam-7063	476	6	numerical	numerical	PROPN
ejpam-7063	476	7	simulation	simulation	PROPN
ejpam-7063	476	8	,	,	PUNCT
ejpam-7063	476	9	16(2):698–703	16(2):698–703	PROPN
ejpam-7063	476	10	,	,	PUNCT
ejpam-7063	476	11	2011	2011	NUM
ejpam-7063	476	12	.	.	PUNCT
ejpam-7063	477	1	[	[	X
ejpam-7063	477	2	10	10	NUM
ejpam-7063	477	3	]	]	X
ejpam-7063	477	4	r.	r.	NOUN
ejpam-7063	477	5	sakthivel	sakthivel	PROPN
ejpam-7063	477	6	,	,	PUNCT
ejpam-7063	477	7	n.	n.	PROPN
ejpam-7063	477	8	i.	i.	PROPN
ejpam-7063	477	9	mahmudov	mahmudov	PROPN
ejpam-7063	477	10	,	,	PUNCT
ejpam-7063	477	11	and	and	CCONJ
ejpam-7063	477	12	b.	b.	PROPN
ejpam-7063	477	13	ahmad	ahmad	PROPN
ejpam-7063	477	14	.	.	PUNCT
ejpam-7063	478	1	optimal	optimal	ADJ
ejpam-7063	478	2	controls	control	NOUN
ejpam-7063	478	3	of	of	ADP
ejpam-7063	478	4	systems	system	NOUN
ejpam-7063	478	5	governed	govern	VERB
ejpam-7063	478	6	by	by	ADP
ejpam-7063	478	7	semilinear	semilinear	ADJ
ejpam-7063	478	8	fractional	fractional	ADJ
ejpam-7063	478	9	differential	differential	ADJ
ejpam-7063	478	10	equations	equation	NOUN
ejpam-7063	478	11	with	with	ADP
ejpam-7063	478	12	not	not	PART
ejpam-7063	478	13	instantaneous	instantaneous	ADJ
ejpam-7063	478	14	impulses	impulse	NOUN
ejpam-7063	478	15	.	.	PUNCT
ejpam-7063	479	1	journal	journal	NOUN
ejpam-7063	479	2	of	of	ADP
ejpam-7063	479	3	optimization	optimization	NOUN
ejpam-7063	479	4	theory	theory	NOUN
ejpam-7063	479	5	and	and	CCONJ
ejpam-7063	479	6	applications	application	NOUN
ejpam-7063	479	7	,	,	PUNCT
ejpam-7063	479	8	174:1–21	174:1–21	NUM
ejpam-7063	479	9	,	,	PUNCT
ejpam-7063	479	10	2017	2017	NUM
ejpam-7063	479	11	.	.	PUNCT
ejpam-7063	480	1	[	[	X
ejpam-7063	480	2	11	11	NUM
ejpam-7063	480	3	]	]	X
ejpam-7063	480	4	g.	g.	PROPN
ejpam-7063	480	5	m.	m.	NOUN
ejpam-7063	480	6	bahaa	bahaa	PROPN
ejpam-7063	480	7	.	.	PUNCT
ejpam-7063	481	1	fractional	fractional	ADJ
ejpam-7063	481	2	optimal	optimal	ADJ
ejpam-7063	481	3	control	control	NOUN
ejpam-7063	481	4	problem	problem	NOUN
ejpam-7063	481	5	for	for	ADP
ejpam-7063	481	6	variational	variational	ADJ
ejpam-7063	481	7	inequalities	inequality	NOUN
ejpam-7063	481	8	with	with	ADP
ejpam-7063	481	9	control	control	NOUN
ejpam-7063	481	10	constraints	constraint	NOUN
ejpam-7063	481	11	.	.	PUNCT
ejpam-7063	482	1	i	i	PRON
ejpam-7063	482	2	m	m	VERB
ejpam-7063	482	3	a	a	DET
ejpam-7063	482	4	journal	journal	NOUN
ejpam-7063	482	5	of	of	ADP
ejpam-7063	482	6	mathematical	mathematical	ADJ
ejpam-7063	482	7	control	control	NOUN
ejpam-7063	482	8	and	and	CCONJ
ejpam-7063	482	9	information	information	NOUN
ejpam-7063	482	10	,	,	PUNCT
ejpam-7063	482	11	33(3):1	33(3):1	NUM
ejpam-7063	482	12	–	–	PUNCT
ejpam-7063	482	13	16	16	NUM
ejpam-7063	482	14	,	,	PUNCT
ejpam-7063	482	15	2016	2016	NUM
ejpam-7063	482	16	.	.	PUNCT
ejpam-7063	483	1	[	[	X
ejpam-7063	483	2	12	12	NUM
ejpam-7063	483	3	]	]	X
ejpam-7063	483	4	g.	g.	PROPN
ejpam-7063	483	5	m.	m.	NOUN
ejpam-7063	483	6	bahaa	bahaa	PROPN
ejpam-7063	483	7	.	.	PUNCT
ejpam-7063	484	1	fractional	fractional	ADJ
ejpam-7063	484	2	optimal	optimal	ADJ
ejpam-7063	484	3	control	control	NOUN
ejpam-7063	484	4	problem	problem	NOUN
ejpam-7063	484	5	for	for	ADP
ejpam-7063	484	6	differential	differential	ADJ
ejpam-7063	484	7	system	system	NOUN
ejpam-7063	484	8	with	with	ADP
ejpam-7063	484	9	control	control	NOUN
ejpam-7063	484	10	constraints	constraint	NOUN
ejpam-7063	484	11	.	.	PUNCT
ejpam-7063	485	1	filomat	filomat	NOUN
ejpam-7063	485	2	,	,	PUNCT
ejpam-7063	485	3	30(8):2177–2189	30(8):2177–2189	NUM
ejpam-7063	485	4	,	,	PUNCT
ejpam-7063	485	5	2016	2016	NUM
ejpam-7063	485	6	.	.	PUNCT
ejpam-7063	486	1	[	[	X
ejpam-7063	486	2	13	13	NUM
ejpam-7063	486	3	]	]	X
ejpam-7063	486	4	g.	g.	PROPN
ejpam-7063	486	5	m.	m.	NOUN
ejpam-7063	486	6	bahaa	bahaa	PROPN
ejpam-7063	486	7	.	.	PUNCT
ejpam-7063	487	1	fractional	fractional	ADJ
ejpam-7063	487	2	optimal	optimal	ADJ
ejpam-7063	487	3	control	control	NOUN
ejpam-7063	487	4	problem	problem	NOUN
ejpam-7063	487	5	for	for	ADP
ejpam-7063	487	6	infinite	infinite	ADJ
ejpam-7063	487	7	order	order	NOUN
ejpam-7063	487	8	system	system	NOUN
ejpam-7063	487	9	with	with	ADP
ejpam-7063	487	10	control	control	NOUN
ejpam-7063	487	11	constraints	constraint	NOUN
ejpam-7063	487	12	.	.	PUNCT
ejpam-7063	488	1	advances	advance	NOUN
ejpam-7063	488	2	in	in	ADP
ejpam-7063	488	3	difference	difference	NOUN
ejpam-7063	488	4	equations	equation	NOUN
ejpam-7063	488	5	,	,	PUNCT
ejpam-7063	488	6	250:1–16	250:1–16	NUM
ejpam-7063	488	7	,	,	PUNCT
ejpam-7063	488	8	2016	2016	NUM
ejpam-7063	488	9	.	.	PUNCT
ejpam-7063	489	1	[	[	X
ejpam-7063	489	2	14	14	NUM
ejpam-7063	489	3	]	]	X
ejpam-7063	489	4	g.	g.	PROPN
ejpam-7063	489	5	m.	m.	NOUN
ejpam-7063	489	6	bahaa	bahaa	PROPN
ejpam-7063	489	7	.	.	PUNCT
ejpam-7063	490	1	fractional	fractional	ADJ
ejpam-7063	490	2	optimal	optimal	ADJ
ejpam-7063	490	3	control	control	NOUN
ejpam-7063	490	4	problem	problem	NOUN
ejpam-7063	490	5	for	for	ADP
ejpam-7063	490	6	differential	differential	ADJ
ejpam-7063	490	7	system	system	NOUN
ejpam-7063	490	8	with	with	ADP
ejpam-7063	490	9	delay	delay	NOUN
ejpam-7063	490	10	argument	argument	NOUN
ejpam-7063	490	11	.	.	PUNCT
ejpam-7063	491	1	advances	advance	NOUN
ejpam-7063	491	2	in	in	ADP
ejpam-7063	491	3	difference	difference	NOUN
ejpam-7063	491	4	equations	equation	NOUN
ejpam-7063	491	5	,	,	PUNCT
ejpam-7063	491	6	69:1–19	69:1–19	NUM
ejpam-7063	491	7	,	,	PUNCT
ejpam-7063	491	8	2017	2017	NUM
ejpam-7063	491	9	.	.	PUNCT
ejpam-7063	492	1	[	[	X
ejpam-7063	492	2	15	15	NUM
ejpam-7063	492	3	]	]	X
ejpam-7063	492	4	g.	g.	PROPN
ejpam-7063	492	5	m.	m.	NOUN
ejpam-7063	492	6	bahaa	bahaa	PROPN
ejpam-7063	492	7	.	.	PUNCT
ejpam-7063	493	1	fractional	fractional	ADJ
ejpam-7063	493	2	optimal	optimal	ADJ
ejpam-7063	493	3	control	control	NOUN
ejpam-7063	493	4	problem	problem	NOUN
ejpam-7063	493	5	for	for	ADP
ejpam-7063	493	6	variable	variable	ADJ
ejpam-7063	493	7	-	-	PUNCT
ejpam-7063	493	8	order	order	NOUN
ejpam-7063	493	9	differential	differential	NOUN
ejpam-7063	493	10	systems	system	NOUN
ejpam-7063	493	11	.	.	PUNCT
ejpam-7063	494	1	fractional	fractional	ADJ
ejpam-7063	494	2	calculus	calculus	NOUN
ejpam-7063	494	3	and	and	CCONJ
ejpam-7063	494	4	applied	apply	VERB
ejpam-7063	494	5	analysis	analysis	NOUN
ejpam-7063	494	6	,	,	PUNCT
ejpam-7063	494	7	20(6):1447–1470	20(6):1447–1470	NUM
ejpam-7063	494	8	,	,	PUNCT
ejpam-7063	494	9	2017	2017	NUM
ejpam-7063	494	10	.	.	PUNCT
ejpam-7063	495	1	[	[	X
ejpam-7063	495	2	16	16	NUM
ejpam-7063	495	3	]	]	X
ejpam-7063	495	4	g.	g.	PROPN
ejpam-7063	495	5	m.	m.	NOUN
ejpam-7063	495	6	bahaa	bahaa	NOUN
ejpam-7063	495	7	.	.	PUNCT
ejpam-7063	496	1	optimal	optimal	ADJ
ejpam-7063	496	2	control	control	NOUN
ejpam-7063	496	3	problem	problem	NOUN
ejpam-7063	496	4	and	and	CCONJ
ejpam-7063	496	5	maximum	maximum	ADJ
ejpam-7063	496	6	principle	principle	NOUN
ejpam-7063	496	7	for	for	ADP
ejpam-7063	496	8	fractional	fractional	ADJ
ejpam-7063	496	9	order	order	NOUN
ejpam-7063	496	10	cooperative	cooperative	ADJ
ejpam-7063	496	11	systems	system	NOUN
ejpam-7063	496	12	.	.	PUNCT
ejpam-7063	497	1	kybernetika	kybernetika	PROPN
ejpam-7063	497	2	,	,	PUNCT
ejpam-7063	497	3	55(2):337–358	55(2):337–358	PROPN
ejpam-7063	497	4	,	,	PUNCT
ejpam-7063	497	5	2019	2019	NUM
ejpam-7063	497	6	.	.	PUNCT
ejpam-7063	498	1	[	[	X
ejpam-7063	498	2	17	17	NUM
ejpam-7063	498	3	]	]	X
ejpam-7063	498	4	g.	g.	PROPN
ejpam-7063	498	5	m.	m.	NOUN
ejpam-7063	498	6	bahaa	bahaa	NOUN
ejpam-7063	498	7	.	.	PUNCT
ejpam-7063	499	1	optimality	optimality	NOUN
ejpam-7063	499	2	conditions	condition	NOUN
ejpam-7063	499	3	for	for	ADP
ejpam-7063	499	4	systems	system	NOUN
ejpam-7063	499	5	with	with	ADP
ejpam-7063	499	6	distributed	distribute	VERB
ejpam-7063	499	7	parameters	parameter	NOUN
ejpam-7063	499	8	based	base	VERB
ejpam-7063	499	9	on	on	ADP
ejpam-7063	499	10	the	the	DET
ejpam-7063	499	11	dubovitskii	dubovitskii	ADJ
ejpam-7063	499	12	–	–	PUNCT
ejpam-7063	499	13	milyutin	milyutin	NOUN
ejpam-7063	499	14	theorem	theorem	NOUN
ejpam-7063	499	15	with	with	ADP
ejpam-7063	499	16	incomplete	incomplete	ADJ
ejpam-7063	499	17	information	information	NOUN
ejpam-7063	499	18	about	about	ADP
ejpam-7063	499	19	the	the	DET
ejpam-7063	499	20	initial	initial	ADJ
ejpam-7063	499	21	conditions	condition	NOUN
ejpam-7063	499	22	.	.	PUNCT
ejpam-7063	500	1	journal	journal	NOUN
ejpam-7063	500	2	of	of	ADP
ejpam-7063	500	3	mathematical	mathematical	ADJ
ejpam-7063	500	4	sciences	sciences	PROPN
ejpam-7063	500	5	,	,	PUNCT
ejpam-7063	500	6	276(2):199–215	276(2):199–215	NUM
ejpam-7063	500	7	,	,	PUNCT
ejpam-7063	500	8	2023	2023	NUM
ejpam-7063	500	9	.	.	PUNCT
ejpam-7063	501	1	[	[	X
ejpam-7063	501	2	18	18	NUM
ejpam-7063	501	3	]	]	X
ejpam-7063	501	4	g.	g.	PROPN
ejpam-7063	501	5	m.	m.	NOUN
ejpam-7063	501	6	bahaa	bahaa	NOUN
ejpam-7063	501	7	and	and	CCONJ
ejpam-7063	501	8	q.	q.	PROPN
ejpam-7063	501	9	tang	tang	PROPN
ejpam-7063	501	10	.	.	PUNCT
ejpam-7063	502	1	optimal	optimal	ADJ
ejpam-7063	502	2	control	control	NOUN
ejpam-7063	502	3	problem	problem	NOUN
ejpam-7063	502	4	for	for	ADP
ejpam-7063	502	5	coupled	couple	VERB
ejpam-7063	502	6	time	time	NOUN
ejpam-7063	502	7	-	-	PUNCT
ejpam-7063	502	8	fractional	fractional	ADJ
ejpam-7063	502	9	evolution	evolution	NOUN
ejpam-7063	502	10	systems	system	NOUN
ejpam-7063	502	11	with	with	ADP
ejpam-7063	502	12	control	control	NOUN
ejpam-7063	502	13	constraints	constraint	NOUN
ejpam-7063	502	14	.	.	PUNCT
ejpam-7063	503	1	journal	journal	PROPN
ejpam-7063	503	2	of	of	ADP
ejpam-7063	503	3	differential	differential	ADJ
ejpam-7063	503	4	equations	equation	NOUN
ejpam-7063	503	5	and	and	CCONJ
ejpam-7063	503	6	dynamical	dynamical	ADJ
ejpam-7063	503	7	systems	system	NOUN
ejpam-7063	503	8	,	,	PUNCT
ejpam-7063	503	9	pages	page	NOUN
ejpam-7063	503	10	1–16	1–16	PROPN
ejpam-7063	503	11	,	,	PUNCT
ejpam-7063	503	12	2017	2017	NUM
ejpam-7063	503	13	.	.	PUNCT
ejpam-7063	504	1	[	[	X
ejpam-7063	504	2	19	19	NUM
ejpam-7063	504	3	]	]	X
ejpam-7063	504	4	g.	g.	PROPN
ejpam-7063	504	5	m.	m.	NOUN
ejpam-7063	504	6	bahaa	bahaa	NOUN
ejpam-7063	504	7	and	and	CCONJ
ejpam-7063	504	8	q.	q.	PROPN
ejpam-7063	504	9	tang	tang	PROPN
ejpam-7063	504	10	.	.	PUNCT
ejpam-7063	505	1	optimality	optimality	NOUN
ejpam-7063	505	2	conditions	condition	NOUN
ejpam-7063	505	3	for	for	ADP
ejpam-7063	505	4	fractional	fractional	ADJ
ejpam-7063	505	5	diffusion	diffusion	NOUN
ejpam-7063	505	6	equations	equation	NOUN
ejpam-7063	505	7	with	with	ADP
ejpam-7063	505	8	weak	weak	ADJ
ejpam-7063	505	9	caputo	caputo	NOUN
ejpam-7063	505	10	derivatives	derivative	NOUN
ejpam-7063	505	11	and	and	CCONJ
ejpam-7063	505	12	variational	variational	ADJ
ejpam-7063	505	13	formulation	formulation	NOUN
ejpam-7063	505	14	.	.	PUNCT
ejpam-7063	506	1	journal	journal	NOUN
ejpam-7063	506	2	of	of	ADP
ejpam-7063	506	3	fractional	fractional	ADJ
ejpam-7063	506	4	calculus	calculus	NOUN
ejpam-7063	506	5	and	and	CCONJ
ejpam-7063	506	6	applications	application	NOUN
ejpam-7063	506	7	,	,	PUNCT
ejpam-7063	506	8	9(1):100–119	9(1):100–119	NUM
ejpam-7063	506	9	,	,	PUNCT
ejpam-7063	506	10	2018	2018	NUM
ejpam-7063	506	11	.	.	PUNCT
ejpam-7063	507	1	[	[	X
ejpam-7063	507	2	20	20	NUM
ejpam-7063	507	3	]	]	PUNCT
ejpam-7063	507	4	a.	a.	NOUN
ejpam-7063	507	5	lotfi	lotfi	PROPN
ejpam-7063	507	6	,	,	PUNCT
ejpam-7063	507	7	m.	m.	NOUN
ejpam-7063	507	8	dehghan	dehghan	PROPN
ejpam-7063	507	9	,	,	PUNCT
ejpam-7063	507	10	and	and	CCONJ
ejpam-7063	507	11	s.	s.	PROPN
ejpam-7063	507	12	yousefi	yousefi	PROPN
ejpam-7063	507	13	.	.	PUNCT
ejpam-7063	508	1	a	a	DET
ejpam-7063	508	2	numerical	numerical	ADJ
ejpam-7063	508	3	technique	technique	NOUN
ejpam-7063	508	4	for	for	ADP
ejpam-7063	508	5	solving	solve	VERB
ejpam-7063	508	6	fractional	fractional	ADJ
ejpam-7063	508	7	optimal	optimal	ADJ
ejpam-7063	508	8	control	control	NOUN
ejpam-7063	508	9	problems	problem	NOUN
ejpam-7063	508	10	.	.	PUNCT
ejpam-7063	509	1	computers	computer	NOUN
ejpam-7063	509	2	and	and	CCONJ
ejpam-7063	509	3	mathematics	mathematic	NOUN
ejpam-7063	509	4	with	with	ADP
ejpam-7063	509	5	applications	application	NOUN
ejpam-7063	509	6	,	,	PUNCT
ejpam-7063	509	7	62(3):1055	62(3):1055	NUM
ejpam-7063	509	8	–	–	PUNCT
ejpam-7063	509	9	1067	1067	NUM
ejpam-7063	509	10	,	,	PUNCT
ejpam-7063	509	11	2011	2011	NUM
ejpam-7063	509	12	.	.	PUNCT
ejpam-7063	510	1	[	[	X
ejpam-7063	510	2	21	21	NUM
ejpam-7063	510	3	]	]	PUNCT
ejpam-7063	510	4	a.	a.	NOUN
ejpam-7063	510	5	lotfi	lotfi	PROPN
ejpam-7063	510	6	,	,	PUNCT
ejpam-7063	510	7	s.	s.	PROPN
ejpam-7063	510	8	yousefi	yousefi	PROPN
ejpam-7063	510	9	,	,	PUNCT
ejpam-7063	510	10	and	and	CCONJ
ejpam-7063	510	11	m.	m.	NOUN
ejpam-7063	510	12	dehghan	dehghan	PROPN
ejpam-7063	510	13	.	.	PUNCT
ejpam-7063	511	1	numerical	numerical	ADJ
ejpam-7063	511	2	solution	solution	NOUN
ejpam-7063	511	3	of	of	ADP
ejpam-7063	511	4	a	a	DET
ejpam-7063	511	5	class	class	NOUN
ejpam-7063	511	6	of	of	ADP
ejpam-7063	511	7	fractional	fractional	ADJ
ejpam-7063	511	8	optimal	optimal	ADJ
ejpam-7063	511	9	control	control	NOUN
ejpam-7063	511	10	problems	problem	NOUN
ejpam-7063	511	11	via	via	ADP
ejpam-7063	511	12	the	the	DET
ejpam-7063	511	13	legendre	legendre	PROPN
ejpam-7063	511	14	orthonormal	orthonormal	ADJ
ejpam-7063	511	15	basis	basis	NOUN
ejpam-7063	511	16	combined	combine	VERB
ejpam-7063	511	17	with	with	ADP
ejpam-7063	511	18	the	the	DET
ejpam-7063	511	19	operational	operational	ADJ
ejpam-7063	511	20	matrix	matrix	NOUN
ejpam-7063	511	21	and	and	CCONJ
ejpam-7063	511	22	the	the	DET
ejpam-7063	511	23	gauss	gauss	ADJ
ejpam-7063	511	24	quadrature	quadrature	NOUN
ejpam-7063	511	25	rule	rule	NOUN
ejpam-7063	511	26	.	.	PUNCT
ejpam-7063	512	1	journal	journal	NOUN
ejpam-7063	512	2	of	of	ADP
ejpam-7063	512	3	computational	computational	ADJ
ejpam-7063	512	4	and	and	CCONJ
ejpam-7063	512	5	applied	applied	ADJ
ejpam-7063	512	6	mathematics	mathematic	NOUN
ejpam-7063	512	7	,	,	PUNCT
ejpam-7063	512	8	250:143–160	250:143–160	NUM
ejpam-7063	512	9	,	,	PUNCT
ejpam-7063	512	10	2013	2013	NUM
ejpam-7063	512	11	.	.	PUNCT
ejpam-7063	513	1	[	[	X
ejpam-7063	513	2	22	22	NUM
ejpam-7063	513	3	]	]	PUNCT
ejpam-7063	513	4	a.	a.	NOUN
ejpam-7063	513	5	h.	h.	PROPN
ejpam-7063	513	6	bhrawy	bhrawy	PROPN
ejpam-7063	513	7	,	,	PUNCT
ejpam-7063	513	8	e.	e.	PROPN
ejpam-7063	513	9	h.	h.	PROPN
ejpam-7063	513	10	doha	doha	PROPN
ejpam-7063	513	11	,	,	PUNCT
ejpam-7063	513	12	j.	j.	PROPN
ejpam-7063	513	13	a.	a.	PROPN
ejpam-7063	513	14	tenreiro	tenreiro	PROPN
ejpam-7063	513	15	machado	machado	PROPN
ejpam-7063	513	16	,	,	PUNCT
ejpam-7063	513	17	and	and	CCONJ
ejpam-7063	513	18	s.	s.	PROPN
ejpam-7063	513	19	s.	s.	PROPN
ejpam-7063	513	20	ezz	ezz	PROPN
ejpam-7063	513	21	-	-	PUNCT
ejpam-7063	513	22	eldien	eldien	NOUN
ejpam-7063	513	23	.	.	PUNCT
ejpam-7063	514	1	an	an	DET
ejpam-7063	514	2	efficient	efficient	ADJ
ejpam-7063	514	3	numerical	numerical	ADJ
ejpam-7063	514	4	scheme	scheme	NOUN
ejpam-7063	514	5	for	for	ADP
ejpam-7063	514	6	solving	solve	VERB
ejpam-7063	514	7	multi	multi	ADJ
ejpam-7063	514	8	-	-	ADJ
ejpam-7063	514	9	dimensional	dimensional	ADJ
ejpam-7063	514	10	fractional	fractional	ADJ
ejpam-7063	514	11	optimal	optimal	ADJ
ejpam-7063	514	12	control	control	NOUN
ejpam-7063	514	13	problems	problem	NOUN
ejpam-7063	514	14	with	with	ADP
ejpam-7063	514	15	a	a	DET
ejpam-7063	514	16	quadratic	quadratic	ADJ
ejpam-7063	514	17	performance	performance	NOUN
ejpam-7063	514	18	index	index	NOUN
ejpam-7063	514	19	.	.	PUNCT
ejpam-7063	515	1	asian	asian	ADJ
ejpam-7063	515	2	journal	journal	PROPN
ejpam-7063	515	3	of	of	ADP
ejpam-7063	515	4	control	control	PROPN
ejpam-7063	515	5	,	,	PUNCT
ejpam-7063	515	6	17(6):2389–2402	17(6):2389–2402	NUM
ejpam-7063	515	7	,	,	PUNCT
ejpam-7063	515	8	2015	2015	NUM
ejpam-7063	515	9	.	.	PUNCT
ejpam-7063	516	1	[	[	X
ejpam-7063	516	2	23	23	NUM
ejpam-7063	516	3	]	]	PUNCT
ejpam-7063	516	4	m.	m.	NOUN
ejpam-7063	516	5	h.	h.	PROPN
ejpam-7063	516	6	heydari	heydari	PROPN
ejpam-7063	516	7	,	,	PUNCT
ejpam-7063	516	8	m.	m.	PROPN
ejpam-7063	516	9	razzaghi	razzaghi	PROPN
ejpam-7063	516	10	,	,	PUNCT
ejpam-7063	516	11	and	and	CCONJ
ejpam-7063	516	12	s.	s.	PROPN
ejpam-7063	516	13	zhagharian	zhagharian	PROPN
ejpam-7063	516	14	.	.	PUNCT
ejpam-7063	517	1	numerical	numerical	ADJ
ejpam-7063	517	2	solution	solution	NOUN
ejpam-7063	517	3	of	of	ADP
ejpam-7063	517	4	distributedorder	distributedorder	NOUN
ejpam-7063	517	5	fractional	fractional	PROPN
ejpam-7063	517	6	2d	2d	PROPN
ejpam-7063	517	7	optimal	optimal	ADJ
ejpam-7063	517	8	control	control	NOUN
ejpam-7063	517	9	problems	problem	NOUN
ejpam-7063	517	10	using	use	VERB
ejpam-7063	517	11	the	the	DET
ejpam-7063	517	12	bernstein	bernstein	PROPN
ejpam-7063	517	13	polynomials	polynomials	PROPN
ejpam-7063	517	14	.	.	PUNCT
ejpam-7063	518	1	international	international	ADJ
ejpam-7063	518	2	journal	journal	PROPN
ejpam-7063	518	3	of	of	ADP
ejpam-7063	518	4	systems	system	NOUN
ejpam-7063	518	5	science	science	NOUN
ejpam-7063	518	6	,	,	PUNCT
ejpam-7063	518	7	54(10):2253–2267	54(10):2253–2267	PROPN
ejpam-7063	518	8	,	,	PUNCT
ejpam-7063	518	9	2023	2023	NUM
ejpam-7063	518	10	.	.	PUNCT
ejpam-7063	519	1	[	[	X
ejpam-7063	519	2	24	24	NUM
ejpam-7063	519	3	]	]	X
ejpam-7063	519	4	h.	h.	PROPN
ejpam-7063	519	5	dehestani	dehestani	PROPN
ejpam-7063	519	6	,	,	PUNCT
ejpam-7063	519	7	y.	y.	PROPN
ejpam-7063	519	8	ordokhani	ordokhani	PROPN
ejpam-7063	519	9	,	,	PUNCT
ejpam-7063	519	10	and	and	CCONJ
ejpam-7063	519	11	m.	m.	PROPN
ejpam-7063	519	12	razzaghi	razzaghi	PROPN
ejpam-7063	519	13	.	.	PUNCT
ejpam-7063	520	1	a	a	DET
ejpam-7063	520	2	robust	robust	ADJ
ejpam-7063	520	3	optimisation	optimisation	NOUN
ejpam-7063	520	4	approach	approach	NOUN
ejpam-7063	520	5	g.	g.	PROPN
ejpam-7063	520	6	m.	m.	PROPN
ejpam-7063	520	7	bahaa	bahaa	PROPN
ejpam-7063	520	8	,	,	PUNCT
ejpam-7063	520	9	a.	a.	NOUN
ejpam-7063	520	10	h.	h.	PROPN
ejpam-7063	520	11	qamlo	qamlo	PROPN
ejpam-7063	520	12	/	/	SYM
ejpam-7063	520	13	eur	eur	PROPN
ejpam-7063	520	14	.	.	PUNCT
ejpam-7063	521	1	j.	j.	PROPN
ejpam-7063	521	2	pure	pure	PROPN
ejpam-7063	521	3	appl	appl	PROPN
ejpam-7063	521	4	.	.	PROPN
ejpam-7063	521	5	math	math	PROPN
ejpam-7063	521	6	,	,	PUNCT
ejpam-7063	521	7	18	18	NUM
ejpam-7063	521	8	(	(	PUNCT
ejpam-7063	521	9	4	4	NUM
ejpam-7063	521	10	)	)	PUNCT
ejpam-7063	521	11	(	(	PUNCT
ejpam-7063	521	12	2025	2025	NUM
ejpam-7063	521	13	)	)	PUNCT
ejpam-7063	521	14	,	,	PUNCT
ejpam-7063	521	15	7063	7063	NUM
ejpam-7063	521	16	28	28	NUM
ejpam-7063	521	17	of	of	ADP
ejpam-7063	521	18	29	29	NUM
ejpam-7063	521	19	for	for	ADP
ejpam-7063	521	20	the	the	DET
ejpam-7063	521	21	2d	2d	PROPN
ejpam-7063	521	22	-	-	PUNCT
ejpam-7063	521	23	vo	vo	NOUN
ejpam-7063	521	24	fractional	fractional	ADJ
ejpam-7063	521	25	optimal	optimal	ADJ
ejpam-7063	521	26	control	control	NOUN
ejpam-7063	521	27	problems	problem	NOUN
ejpam-7063	521	28	.	.	PUNCT
ejpam-7063	522	1	international	international	ADJ
ejpam-7063	522	2	journal	journal	PROPN
ejpam-7063	522	3	of	of	ADP
ejpam-7063	522	4	systems	system	NOUN
ejpam-7063	522	5	science	science	NOUN
ejpam-7063	522	6	,	,	PUNCT
ejpam-7063	522	7	56(2):347–362	56(2):347–362	PROPN
ejpam-7063	522	8	,	,	PUNCT
ejpam-7063	522	9	2024	2024	NUM
ejpam-7063	522	10	.	.	PUNCT
ejpam-7063	523	1	[	[	X
ejpam-7063	523	2	25	25	NUM
ejpam-7063	523	3	]	]	X
ejpam-7063	523	4	s.	s.	PROPN
ejpam-7063	523	5	mallat	mallat	PROPN
ejpam-7063	523	6	.	.	PUNCT
ejpam-7063	524	1	a	a	DET
ejpam-7063	524	2	wavelet	wavelet	NOUN
ejpam-7063	524	3	tour	tour	NOUN
ejpam-7063	524	4	of	of	ADP
ejpam-7063	524	5	signal	signal	NOUN
ejpam-7063	524	6	processing	processing	NOUN
ejpam-7063	524	7	.	.	PUNCT
ejpam-7063	525	1	academic	academic	ADJ
ejpam-7063	525	2	press	press	NOUN
ejpam-7063	525	3	,	,	PUNCT
ejpam-7063	525	4	1998	1998	NUM
ejpam-7063	525	5	.	.	PUNCT
ejpam-7063	526	1	[	[	X
ejpam-7063	526	2	26	26	NUM
ejpam-7063	526	3	]	]	X
ejpam-7063	526	4	s.	s.	PROPN
ejpam-7063	526	5	sabermahani	sabermahani	PROPN
ejpam-7063	526	6	,	,	PUNCT
ejpam-7063	526	7	y.	y.	PROPN
ejpam-7063	526	8	ordokhani	ordokhani	PROPN
ejpam-7063	526	9	,	,	PUNCT
ejpam-7063	526	10	and	and	CCONJ
ejpam-7063	526	11	y.	y.	PROPN
ejpam-7063	526	12	sohrab	sohrab	PROPN
ejpam-7063	526	13	-	-	PUNCT
ejpam-7063	526	14	ali	ali	PROPN
ejpam-7063	526	15	.	.	PUNCT
ejpam-7063	527	1	fibonacci	fibonacci	PROPN
ejpam-7063	527	2	wavelets	wavelet	NOUN
ejpam-7063	527	3	and	and	CCONJ
ejpam-7063	527	4	their	their	PRON
ejpam-7063	527	5	applications	application	NOUN
ejpam-7063	527	6	for	for	ADP
ejpam-7063	527	7	solving	solve	VERB
ejpam-7063	527	8	two	two	NUM
ejpam-7063	527	9	classes	class	NOUN
ejpam-7063	527	10	of	of	ADP
ejpam-7063	527	11	time	time	NOUN
ejpam-7063	527	12	-	-	PUNCT
ejpam-7063	527	13	varying	vary	VERB
ejpam-7063	527	14	delay	delay	NOUN
ejpam-7063	527	15	problems	problem	NOUN
ejpam-7063	527	16	.	.	PUNCT
ejpam-7063	528	1	optimal	optimal	ADJ
ejpam-7063	528	2	control	control	NOUN
ejpam-7063	528	3	applications	application	NOUN
ejpam-7063	528	4	and	and	CCONJ
ejpam-7063	528	5	methods	method	NOUN
ejpam-7063	528	6	,	,	PUNCT
ejpam-7063	528	7	41(2):395–416	41(2):395–416	NUM
ejpam-7063	528	8	,	,	PUNCT
ejpam-7063	528	9	2019	2019	NUM
ejpam-7063	528	10	.	.	PUNCT
ejpam-7063	529	1	[	[	X
ejpam-7063	529	2	27	27	NUM
ejpam-7063	529	3	]	]	X
ejpam-7063	529	4	p.	p.	PROPN
ejpam-7063	529	5	agarwal	agarwal	PROPN
ejpam-7063	529	6	,	,	PUNCT
ejpam-7063	529	7	a.	a.	PROPN
ejpam-7063	529	8	a.	a.	PROPN
ejpam-7063	529	9	el	el	PROPN
ejpam-7063	529	10	-	-	PUNCT
ejpam-7063	529	11	sayed	say	VERB
ejpam-7063	529	12	,	,	PUNCT
ejpam-7063	529	13	and	and	CCONJ
ejpam-7063	529	14	j.	j.	PROPN
ejpam-7063	529	15	tariboon	tariboon	PROPN
ejpam-7063	529	16	.	.	PUNCT
ejpam-7063	530	1	vieta	vieta	PROPN
ejpam-7063	530	2	-	-	PUNCT
ejpam-7063	530	3	fibonacci	fibonacci	NOUN
ejpam-7063	530	4	operational	operational	ADJ
ejpam-7063	530	5	matrices	matrix	NOUN
ejpam-7063	530	6	for	for	ADP
ejpam-7063	530	7	spectral	spectral	ADJ
ejpam-7063	530	8	solutions	solution	NOUN
ejpam-7063	530	9	of	of	ADP
ejpam-7063	530	10	variable	variable	ADJ
ejpam-7063	530	11	-	-	PUNCT
ejpam-7063	530	12	order	order	NOUN
ejpam-7063	530	13	fractional	fractional	ADJ
ejpam-7063	530	14	integro	integro	ADJ
ejpam-7063	530	15	-	-	PUNCT
ejpam-7063	530	16	differential	differential	NOUN
ejpam-7063	530	17	equations	equation	NOUN
ejpam-7063	530	18	.	.	PUNCT
ejpam-7063	531	1	journal	journal	NOUN
ejpam-7063	531	2	of	of	ADP
ejpam-7063	531	3	computational	computational	ADJ
ejpam-7063	531	4	and	and	CCONJ
ejpam-7063	531	5	applied	applied	ADJ
ejpam-7063	531	6	mathematics	mathematic	NOUN
ejpam-7063	531	7	,	,	PUNCT
ejpam-7063	531	8	382:113063	382:113063	NUM
ejpam-7063	531	9	,	,	PUNCT
ejpam-7063	531	10	2021	2021	NUM
ejpam-7063	531	11	.	.	PUNCT
ejpam-7063	532	1	[	[	X
ejpam-7063	532	2	28	28	NUM
ejpam-7063	532	3	]	]	X
ejpam-7063	532	4	h.	h.	PROPN
ejpam-7063	532	5	azin	azin	PROPN
ejpam-7063	532	6	,	,	PUNCT
ejpam-7063	532	7	m.	m.	PROPN
ejpam-7063	532	8	h.	h.	PROPN
ejpam-7063	532	9	heydari	heydari	PROPN
ejpam-7063	532	10	,	,	PUNCT
ejpam-7063	532	11	and	and	CCONJ
ejpam-7063	532	12	f.	f.	PROPN
ejpam-7063	532	13	mohammadi	mohammadi	PROPN
ejpam-7063	532	14	.	.	PUNCT
ejpam-7063	533	1	vieta	vieta	PROPN
ejpam-7063	533	2	fibonacci	fibonacci	PROPN
ejpam-7063	533	3	wavelets	wavelet	NOUN
ejpam-7063	533	4	:	:	PUNCT
ejpam-7063	533	5	application	application	NOUN
ejpam-7063	533	6	in	in	ADP
ejpam-7063	533	7	solving	solve	VERB
ejpam-7063	533	8	fractional	fractional	ADJ
ejpam-7063	533	9	pantograph	pantograph	NOUN
ejpam-7063	533	10	equations	equation	NOUN
ejpam-7063	533	11	.	.	PUNCT
ejpam-7063	534	1	mathematical	mathematical	ADJ
ejpam-7063	534	2	methods	method	NOUN
ejpam-7063	534	3	in	in	ADP
ejpam-7063	534	4	the	the	DET
ejpam-7063	534	5	applied	apply	VERB
ejpam-7063	534	6	sciences	science	NOUN
ejpam-7063	534	7	,	,	PUNCT
ejpam-7063	534	8	45:411–422	45:411–422	PROPN
ejpam-7063	534	9	,	,	PUNCT
ejpam-7063	534	10	2021	2021	NUM
ejpam-7063	534	11	.	.	PUNCT
ejpam-7063	535	1	[	[	X
ejpam-7063	535	2	29	29	NUM
ejpam-7063	535	3	]	]	PUNCT
ejpam-7063	535	4	h.	h.	PROPN
ejpam-7063	535	5	azin	azin	PROPN
ejpam-7063	535	6	,	,	PUNCT
ejpam-7063	535	7	m.	m.	PROPN
ejpam-7063	535	8	h.	h.	PROPN
ejpam-7063	535	9	heydari	heydari	PROPN
ejpam-7063	535	10	,	,	PUNCT
ejpam-7063	535	11	o.	o.	PROPN
ejpam-7063	535	12	baghani	baghani	PROPN
ejpam-7063	535	13	,	,	PUNCT
ejpam-7063	535	14	and	and	CCONJ
ejpam-7063	535	15	f.	f.	PROPN
ejpam-7063	535	16	mohammadi	mohammadi	PROPN
ejpam-7063	535	17	.	.	PUNCT
ejpam-7063	536	1	fractional	fractional	ADJ
ejpam-7063	536	2	vieta	vieta	PROPN
ejpam-7063	536	3	-	-	PUNCT
ejpam-7063	536	4	fibonacci	fibonacci	NOUN
ejpam-7063	536	5	wavelets	wavelet	NOUN
ejpam-7063	536	6	:	:	PUNCT
ejpam-7063	536	7	application	application	NOUN
ejpam-7063	536	8	for	for	ADP
ejpam-7063	536	9	systems	system	NOUN
ejpam-7063	536	10	of	of	ADP
ejpam-7063	536	11	fractional	fractional	ADJ
ejpam-7063	536	12	delay	delay	NOUN
ejpam-7063	536	13	differential	differential	ADJ
ejpam-7063	536	14	equations	equation	NOUN
ejpam-7063	536	15	.	.	PUNCT
ejpam-7063	537	1	physica	physica	PROPN
ejpam-7063	537	2	scripta	scripta	PROPN
ejpam-7063	537	3	,	,	PUNCT
ejpam-7063	537	4	98(9):095242	98(9):095242	NUM
ejpam-7063	537	5	,	,	PUNCT
ejpam-7063	537	6	2023	2023	NUM
ejpam-7063	537	7	.	.	PUNCT
ejpam-7063	538	1	[	[	X
ejpam-7063	538	2	30	30	NUM
ejpam-7063	538	3	]	]	PUNCT
ejpam-7063	538	4	t.	t.	NOUN
ejpam-7063	538	5	hoseini	hoseini	NOUN
ejpam-7063	538	6	,	,	PUNCT
ejpam-7063	538	7	y.	y.	PROPN
ejpam-7063	538	8	ordokhani	ordokhani	PROPN
ejpam-7063	538	9	,	,	PUNCT
ejpam-7063	538	10	and	and	CCONJ
ejpam-7063	538	11	p.	p.	NOUN
ejpam-7063	538	12	rahimkhani	rahimkhani	NOUN
ejpam-7063	538	13	.	.	PUNCT
ejpam-7063	539	1	numerical	numerical	ADJ
ejpam-7063	539	2	solution	solution	NOUN
ejpam-7063	539	3	of	of	ADP
ejpam-7063	539	4	two	two	NUM
ejpam-7063	539	5	-	-	PUNCT
ejpam-7063	539	6	dimensional	dimensional	ADJ
ejpam-7063	539	7	fractional	fractional	ADJ
ejpam-7063	539	8	optimal	optimal	ADJ
ejpam-7063	539	9	control	control	NOUN
ejpam-7063	539	10	problems	problem	NOUN
ejpam-7063	539	11	using	use	VERB
ejpam-7063	539	12	fractional	fractional	ADJ
ejpam-7063	539	13	vieta	vieta	PROPN
ejpam-7063	539	14	-	-	PUNCT
ejpam-7063	539	15	fibonacci	fibonacci	NOUN
ejpam-7063	539	16	wavelets	wavelet	NOUN
ejpam-7063	539	17	.	.	PUNCT
ejpam-7063	540	1	international	international	ADJ
ejpam-7063	540	2	journal	journal	PROPN
ejpam-7063	540	3	of	of	ADP
ejpam-7063	540	4	systems	system	NOUN
ejpam-7063	540	5	science	science	NOUN
ejpam-7063	540	6	,	,	PUNCT
ejpam-7063	540	7	pages	page	NOUN
ejpam-7063	540	8	1–25	1–25	PROPN
ejpam-7063	540	9	,	,	PUNCT
ejpam-7063	540	10	2025	2025	NUM
ejpam-7063	540	11	.	.	PUNCT
ejpam-7063	541	1	[	[	X
ejpam-7063	541	2	31	31	NUM
ejpam-7063	541	3	]	]	PUNCT
ejpam-7063	541	4	s.	s.	PROPN
ejpam-7063	541	5	h.	h.	PROPN
ejpam-7063	541	6	abdel	abdel	PROPN
ejpam-7063	541	7	-	-	PUNCT
ejpam-7063	541	8	gaid	gaid	PROPN
ejpam-7063	541	9	,	,	PUNCT
ejpam-7063	541	10	a.	a.	NOUN
ejpam-7063	541	11	h.	h.	PROPN
ejpam-7063	541	12	qamlo	qamlo	PROPN
ejpam-7063	541	13	,	,	PUNCT
ejpam-7063	541	14	and	and	CCONJ
ejpam-7063	541	15	g.	g.	PROPN
ejpam-7063	541	16	m.	m.	NOUN
ejpam-7063	541	17	bahaa	bahaa	PROPN
ejpam-7063	541	18	.	.	PUNCT
ejpam-7063	542	1	bang	bang	PROPN
ejpam-7063	542	2	-	-	PUNCT
ejpam-7063	542	3	bang	bang	PROPN
ejpam-7063	542	4	property	property	NOUN
ejpam-7063	542	5	and	and	CCONJ
ejpam-7063	542	6	time	time	NOUN
ejpam-7063	542	7	optimal	optimal	ADJ
ejpam-7063	542	8	control	control	NOUN
ejpam-7063	542	9	for	for	ADP
ejpam-7063	542	10	caputo	caputo	PROPN
ejpam-7063	542	11	fractional	fractional	PROPN
ejpam-7063	542	12	differential	differential	PROPN
ejpam-7063	542	13	systems	system	NOUN
ejpam-7063	542	14	.	.	PUNCT
ejpam-7063	543	1	fractal	fractal	PROPN
ejpam-7063	543	2	and	and	CCONJ
ejpam-7063	543	3	fractional	fractional	ADJ
ejpam-7063	543	4	,	,	PUNCT
ejpam-7063	543	5	8(2):84	8(2):84	NOUN
ejpam-7063	543	6	,	,	PUNCT
ejpam-7063	543	7	2024	2024	NUM
ejpam-7063	543	8	.	.	PUNCT
ejpam-7063	544	1	[	[	X
ejpam-7063	544	2	32	32	NUM
ejpam-7063	544	3	]	]	PUNCT
ejpam-7063	544	4	b.	b.	PROPN
ejpam-7063	544	5	g.	g.	PROPN
ejpam-7063	544	6	mohamed	mohamed	PROPN
ejpam-7063	544	7	and	and	CCONJ
ejpam-7063	544	8	a.	a.	PROPN
ejpam-7063	544	9	h.	h.	PROPN
ejpam-7063	544	10	qamlo	qamlo	PROPN
ejpam-7063	544	11	.	.	PUNCT
ejpam-7063	545	1	fractional	fractional	ADJ
ejpam-7063	545	2	optimal	optimal	ADJ
ejpam-7063	545	3	control	control	NOUN
ejpam-7063	545	4	problem	problem	NOUN
ejpam-7063	545	5	for	for	ADP
ejpam-7063	545	6	symmetric	symmetric	ADJ
ejpam-7063	545	7	system	system	NOUN
ejpam-7063	545	8	involving	involve	VERB
ejpam-7063	545	9	distributed	distribute	VERB
ejpam-7063	545	10	-	-	PUNCT
ejpam-7063	545	11	order	order	NOUN
ejpam-7063	545	12	atangana	atangana	PROPN
ejpam-7063	545	13	-	-	PUNCT
ejpam-7063	545	14	baleanu	baleanu	PROPN
ejpam-7063	545	15	’s	’s	PART
ejpam-7063	545	16	derivatives	derivative	NOUN
ejpam-7063	545	17	with	with	ADP
ejpam-7063	545	18	non	non	ADJ
ejpam-7063	545	19	-	-	ADJ
ejpam-7063	545	20	singular	singular	ADJ
ejpam-7063	545	21	kernel	kernel	NOUN
ejpam-7063	545	22	.	.	PUNCT
ejpam-7063	546	1	symmetry	symmetry	PROPN
ejpam-7063	546	2	,	,	PUNCT
ejpam-7063	546	3	17(3):417	17(3):417	NUM
ejpam-7063	546	4	,	,	PUNCT
ejpam-7063	546	5	2025	2025	NUM
ejpam-7063	546	6	.	.	PUNCT
ejpam-7063	547	1	[	[	X
ejpam-7063	547	2	33	33	NUM
ejpam-7063	547	3	]	]	PUNCT
ejpam-7063	547	4	g.	g.	PROPN
ejpam-7063	547	5	m.	m.	NOUN
ejpam-7063	547	6	bahaa	bahaa	NOUN
ejpam-7063	547	7	and	and	CCONJ
ejpam-7063	547	8	s.	s.	PROPN
ejpam-7063	547	9	khidr	khidr	PROPN
ejpam-7063	547	10	.	.	PUNCT
ejpam-7063	548	1	numerical	numerical	ADJ
ejpam-7063	548	2	solutions	solution	NOUN
ejpam-7063	548	3	for	for	ADP
ejpam-7063	548	4	optimal	optimal	ADJ
ejpam-7063	548	5	control	control	NOUN
ejpam-7063	548	6	problem	problem	NOUN
ejpam-7063	548	7	governed	govern	VERB
ejpam-7063	548	8	by	by	ADP
ejpam-7063	548	9	elliptic	elliptic	ADJ
ejpam-7063	548	10	system	system	NOUN
ejpam-7063	548	11	on	on	ADP
ejpam-7063	548	12	lipschitz	lipschitz	NOUN
ejpam-7063	548	13	domains	domain	NOUN
ejpam-7063	548	14	.	.	PUNCT
ejpam-7063	549	1	journal	journal	PROPN
ejpam-7063	549	2	of	of	ADP
ejpam-7063	549	3	taibah	taibah	PROPN
ejpam-7063	549	4	university	university	PROPN
ejpam-7063	549	5	for	for	ADP
ejpam-7063	549	6	science	science	NOUN
ejpam-7063	549	7	,	,	PUNCT
ejpam-7063	549	8	13(1):41–48	13(1):41–48	NUM
ejpam-7063	549	9	,	,	PUNCT
ejpam-7063	549	10	2019	2019	NUM
ejpam-7063	549	11	.	.	PUNCT
ejpam-7063	550	1	[	[	X
ejpam-7063	550	2	34	34	NUM
ejpam-7063	550	3	]	]	X
ejpam-7063	550	4	c.	c.	PROPN
ejpam-7063	550	5	li	li	PROPN
ejpam-7063	550	6	and	and	CCONJ
ejpam-7063	550	7	f.	f.	PROPN
ejpam-7063	550	8	zeng	zeng	PROPN
ejpam-7063	550	9	.	.	PUNCT
ejpam-7063	551	1	the	the	DET
ejpam-7063	551	2	grünwald	grünwald	NOUN
ejpam-7063	551	3	–	–	PUNCT
ejpam-7063	551	4	letnikov	letnikov	NOUN
ejpam-7063	551	5	method	method	NOUN
ejpam-7063	551	6	for	for	ADP
ejpam-7063	551	7	fractional	fractional	ADJ
ejpam-7063	551	8	differential	differential	ADJ
ejpam-7063	551	9	equations	equation	NOUN
ejpam-7063	551	10	.	.	PUNCT
ejpam-7063	552	1	computers	computer	NOUN
ejpam-7063	552	2	&	&	CCONJ
ejpam-7063	552	3	mathematics	mathematics	PROPN
ejpam-7063	552	4	with	with	ADP
ejpam-7063	552	5	applications	application	NOUN
ejpam-7063	552	6	,	,	PUNCT
ejpam-7063	552	7	62(3):902–917	62(3):902–917	NOUN
ejpam-7063	552	8	,	,	PUNCT
ejpam-7063	552	9	2011	2011	NUM
ejpam-7063	552	10	.	.	PUNCT
ejpam-7063	553	1	[	[	X
ejpam-7063	553	2	35	35	NUM
ejpam-7063	553	3	]	]	X
ejpam-7063	553	4	l.	l.	PROPN
ejpam-7063	553	5	li	li	PROPN
ejpam-7063	553	6	and	and	CCONJ
ejpam-7063	553	7	d.	d.	PROPN
ejpam-7063	553	8	wang	wang	PROPN
ejpam-7063	553	9	.	.	PUNCT
ejpam-7063	554	1	numerical	numerical	PROPN
ejpam-7063	554	2	stability	stability	NOUN
ejpam-7063	554	3	of	of	ADP
ejpam-7063	554	4	grünwald	grünwald	NOUN
ejpam-7063	554	5	–	–	PUNCT
ejpam-7063	554	6	letnikov	letnikov	NOUN
ejpam-7063	554	7	method	method	NOUN
ejpam-7063	554	8	for	for	ADP
ejpam-7063	554	9	time	time	NOUN
ejpam-7063	554	10	fractional	fractional	ADJ
ejpam-7063	554	11	delay	delay	NOUN
ejpam-7063	554	12	differential	differential	ADJ
ejpam-7063	554	13	equations	equation	NOUN
ejpam-7063	554	14	.	.	PUNCT
ejpam-7063	555	1	bit	bit	NOUN
ejpam-7063	555	2	numerical	numerical	ADJ
ejpam-7063	555	3	mathematics	mathematic	NOUN
ejpam-7063	555	4	,	,	PUNCT
ejpam-7063	555	5	62:995–1027	62:995–1027	NOUN
ejpam-7063	555	6	,	,	PUNCT
ejpam-7063	555	7	2022	2022	NUM
ejpam-7063	555	8	.	.	PUNCT
ejpam-7063	556	1	[	[	X
ejpam-7063	556	2	36	36	NUM
ejpam-7063	556	3	]	]	X
ejpam-7063	556	4	f.	f.	PROPN
ejpam-7063	556	5	zeng	zeng	PROPN
ejpam-7063	556	6	,	,	PUNCT
ejpam-7063	556	7	z.	z.	PROPN
ejpam-7063	556	8	zhang	zhang	PROPN
ejpam-7063	556	9	,	,	PUNCT
ejpam-7063	556	10	and	and	CCONJ
ejpam-7063	556	11	g.	g.	PROPN
ejpam-7063	556	12	e.	e.	PROPN
ejpam-7063	556	13	karniadakis	karniadakis	PROPN
ejpam-7063	556	14	.	.	PUNCT
ejpam-7063	557	1	second	second	ADJ
ejpam-7063	557	2	-	-	PUNCT
ejpam-7063	557	3	order	order	NOUN
ejpam-7063	557	4	numerical	numerical	ADJ
ejpam-7063	557	5	methods	method	NOUN
ejpam-7063	557	6	for	for	ADP
ejpam-7063	557	7	multiterm	multiterm	NOUN
ejpam-7063	557	8	fractional	fractional	ADJ
ejpam-7063	557	9	differential	differential	NOUN
ejpam-7063	557	10	equations	equation	NOUN
ejpam-7063	557	11	:	:	PUNCT
ejpam-7063	557	12	smooth	smooth	ADJ
ejpam-7063	557	13	and	and	CCONJ
ejpam-7063	557	14	non	non	ADJ
ejpam-7063	557	15	-	-	ADJ
ejpam-7063	557	16	smooth	smooth	ADJ
ejpam-7063	557	17	solutions	solution	NOUN
ejpam-7063	557	18	.	.	PUNCT
ejpam-7063	558	1	journal	journal	NOUN
ejpam-7063	558	2	of	of	ADP
ejpam-7063	558	3	computational	computational	ADJ
ejpam-7063	558	4	physics	physic	NOUN
ejpam-7063	558	5	,	,	PUNCT
ejpam-7063	558	6	335:305–326	335:305–326	NUM
ejpam-7063	558	7	,	,	PUNCT
ejpam-7063	558	8	2017	2017	NUM
ejpam-7063	558	9	.	.	PUNCT
ejpam-7063	559	1	[	[	X
ejpam-7063	559	2	37	37	NUM
ejpam-7063	559	3	]	]	X
ejpam-7063	559	4	y.	y.	PROPN
ejpam-7063	559	5	dimitrov	dimitrov	PROPN
ejpam-7063	559	6	,	,	PUNCT
ejpam-7063	559	7	r.	r.	PROPN
ejpam-7063	559	8	miryanov	miryanov	PROPN
ejpam-7063	559	9	,	,	PUNCT
ejpam-7063	559	10	and	and	CCONJ
ejpam-7063	559	11	v.	v.	ADP
ejpam-7063	559	12	todorov	todorov	NOUN
ejpam-7063	559	13	.	.	PUNCT
ejpam-7063	560	1	asymptotic	asymptotic	ADJ
ejpam-7063	560	2	expansions	expansion	NOUN
ejpam-7063	560	3	and	and	CCONJ
ejpam-7063	560	4	approximations	approximation	NOUN
ejpam-7063	560	5	for	for	ADP
ejpam-7063	560	6	the	the	DET
ejpam-7063	560	7	caputo	caputo	PROPN
ejpam-7063	560	8	derivative	derivative	PROPN
ejpam-7063	560	9	.	.	PUNCT
ejpam-7063	561	1	arxiv	arxiv	PROPN
ejpam-7063	561	2	preprint	preprint	PROPN
ejpam-7063	561	3	arxiv:1806.03421	arxiv:1806.03421	NOUN
ejpam-7063	561	4	,	,	PUNCT
ejpam-7063	561	5	2018	2018	NUM
ejpam-7063	561	6	.	.	PUNCT
ejpam-7063	562	1	[	[	X
ejpam-7063	562	2	38	38	NUM
ejpam-7063	562	3	]	]	PUNCT
ejpam-7063	562	4	c.	c.	PROPN
ejpam-7063	562	5	li	li	PROPN
ejpam-7063	562	6	and	and	CCONJ
ejpam-7063	562	7	f.	f.	PROPN
ejpam-7063	562	8	zeng	zeng	PROPN
ejpam-7063	562	9	.	.	PUNCT
ejpam-7063	563	1	numerical	numerical	ADJ
ejpam-7063	563	2	methods	method	NOUN
ejpam-7063	563	3	for	for	ADP
ejpam-7063	563	4	fractional	fractional	ADJ
ejpam-7063	563	5	calculus	calculus	NOUN
ejpam-7063	563	6	.	.	PUNCT
ejpam-7063	564	1	crc	crc	PROPN
ejpam-7063	564	2	press	press	PROPN
ejpam-7063	564	3	,	,	PUNCT
ejpam-7063	564	4	2015	2015	NUM
ejpam-7063	564	5	.	.	PUNCT
ejpam-7063	565	1	[	[	X
ejpam-7063	565	2	39	39	NUM
ejpam-7063	565	3	]	]	PUNCT
ejpam-7063	565	4	j.	j.	PROPN
ejpam-7063	565	5	l.	l.	PROPN
ejpam-7063	565	6	lions	lion	NOUN
ejpam-7063	565	7	.	.	PUNCT
ejpam-7063	566	1	optimal	optimal	ADJ
ejpam-7063	566	2	control	control	NOUN
ejpam-7063	566	3	of	of	ADP
ejpam-7063	566	4	systems	system	NOUN
ejpam-7063	566	5	governed	govern	VERB
ejpam-7063	566	6	by	by	ADP
ejpam-7063	566	7	partial	partial	ADJ
ejpam-7063	566	8	differential	differential	NOUN
ejpam-7063	566	9	equations	equation	NOUN
ejpam-7063	566	10	,	,	PUNCT
ejpam-7063	566	11	volume	volume	NOUN
ejpam-7063	566	12	170	170	NUM
ejpam-7063	566	13	of	of	ADP
ejpam-7063	566	14	grundlehren	grundlehren	PROPN
ejpam-7063	566	15	der	der	PROPN
ejpam-7063	566	16	mathematischen	mathematischen	PROPN
ejpam-7063	566	17	wissenschaften	wissenschaften	PROPN
ejpam-7063	566	18	.	.	PUNCT
ejpam-7063	567	1	springer	springer	NOUN
ejpam-7063	567	2	-	-	PUNCT
ejpam-7063	567	3	verlag	verlag	PROPN
ejpam-7063	567	4	,	,	PUNCT
ejpam-7063	567	5	1971	1971	NUM
ejpam-7063	567	6	.	.	PUNCT
ejpam-7063	568	1	[	[	X
ejpam-7063	568	2	40	40	NUM
ejpam-7063	568	3	]	]	PUNCT
ejpam-7063	568	4	f.	f.	PROPN
ejpam-7063	568	5	tröltzsch	tröltzsch	PROPN
ejpam-7063	568	6	.	.	PUNCT
ejpam-7063	569	1	optimal	optimal	ADJ
ejpam-7063	569	2	control	control	NOUN
ejpam-7063	569	3	of	of	ADP
ejpam-7063	569	4	partial	partial	ADJ
ejpam-7063	569	5	differential	differential	ADJ
ejpam-7063	569	6	equations	equation	NOUN
ejpam-7063	569	7	:	:	PUNCT
ejpam-7063	570	1	theory	theory	NOUN
ejpam-7063	570	2	,	,	PUNCT
ejpam-7063	570	3	methods	method	NOUN
ejpam-7063	570	4	and	and	CCONJ
ejpam-7063	570	5	applications	application	NOUN
ejpam-7063	570	6	,	,	PUNCT
ejpam-7063	570	7	volume	volume	NOUN
ejpam-7063	570	8	112	112	NUM
ejpam-7063	570	9	of	of	ADP
ejpam-7063	570	10	graduate	graduate	ADJ
ejpam-7063	570	11	studies	study	NOUN
ejpam-7063	570	12	in	in	ADP
ejpam-7063	570	13	mathematics	mathematic	NOUN
ejpam-7063	570	14	.	.	PUNCT
ejpam-7063	571	1	american	american	PROPN
ejpam-7063	571	2	mathematical	mathematical	PROPN
ejpam-7063	571	3	society	society	NOUN
ejpam-7063	571	4	,	,	PUNCT
ejpam-7063	571	5	providence	providence	NOUN
ejpam-7063	571	6	,	,	PUNCT
ejpam-7063	571	7	2010	2010	NUM
ejpam-7063	571	8	.	.	PUNCT
ejpam-7063	572	1	g.	g.	PROPN
ejpam-7063	572	2	m.	m.	PROPN
ejpam-7063	572	3	bahaa	bahaa	PROPN
ejpam-7063	572	4	,	,	PUNCT
ejpam-7063	572	5	a.	a.	NOUN
ejpam-7063	572	6	h.	h.	PROPN
ejpam-7063	572	7	qamlo	qamlo	PROPN
ejpam-7063	572	8	/	/	SYM
ejpam-7063	572	9	eur	eur	PROPN
ejpam-7063	572	10	.	.	PUNCT
ejpam-7063	573	1	j.	j.	PROPN
ejpam-7063	573	2	pure	pure	PROPN
ejpam-7063	573	3	appl	appl	PROPN
ejpam-7063	573	4	.	.	PROPN
ejpam-7063	573	5	math	math	PROPN
ejpam-7063	573	6	,	,	PUNCT
ejpam-7063	573	7	18	18	NUM
ejpam-7063	573	8	(	(	PUNCT
ejpam-7063	573	9	4	4	NUM
ejpam-7063	573	10	)	)	PUNCT
ejpam-7063	573	11	(	(	PUNCT
ejpam-7063	573	12	2025	2025	NUM
ejpam-7063	573	13	)	)	PUNCT
ejpam-7063	573	14	,	,	PUNCT
ejpam-7063	573	15	7063	7063	NUM
ejpam-7063	573	16	29	29	NUM
ejpam-7063	573	17	of	of	ADP
ejpam-7063	573	18	29	29	NUM
ejpam-7063	574	1	[	[	SYM
ejpam-7063	574	2	41	41	NUM
ejpam-7063	574	3	]	]	PUNCT
ejpam-7063	574	4	l.	l.	PROPN
ejpam-7063	574	5	byszewski	byszewski	PROPN
ejpam-7063	574	6	and	and	CCONJ
ejpam-7063	574	7	j.	j.	PROPN
ejpam-7063	574	8	t.	t.	PROPN
ejpam-7063	574	9	tymczak	tymczak	PROPN
ejpam-7063	574	10	.	.	PUNCT
ejpam-7063	575	1	optimal	optimal	ADJ
ejpam-7063	575	2	feedback	feedback	NOUN
ejpam-7063	575	3	control	control	NOUN
ejpam-7063	575	4	for	for	ADP
ejpam-7063	575	5	semilinear	semilinear	ADJ
ejpam-7063	575	6	fractional	fractional	ADJ
ejpam-7063	575	7	evolution	evolution	NOUN
ejpam-7063	575	8	equations	equation	NOUN
ejpam-7063	575	9	in	in	ADP
ejpam-7063	575	10	banach	banach	NOUN
ejpam-7063	575	11	spaces	space	NOUN
ejpam-7063	575	12	.	.	PUNCT
ejpam-7063	576	1	nonlinear	nonlinear	ADJ
ejpam-7063	576	2	analysis	analysis	NOUN
ejpam-7063	576	3	:	:	PUNCT
ejpam-7063	576	4	theory	theory	NOUN
ejpam-7063	576	5	,	,	PUNCT
ejpam-7063	576	6	methods	method	NOUN
ejpam-7063	576	7	&	&	CCONJ
ejpam-7063	576	8	applications	application	NOUN
ejpam-7063	576	9	,	,	PUNCT
ejpam-7063	576	10	75(3):1186–1207	75(3):1186–1207	NOUN
ejpam-7063	576	11	,	,	PUNCT
ejpam-7063	576	12	2012	2012	NUM
ejpam-7063	576	13	.	.	PUNCT
ejpam-7063	577	1	[	[	X
ejpam-7063	577	2	42	42	NUM
ejpam-7063	577	3	]	]	X
ejpam-7063	577	4	g.	g.	PROPN
ejpam-7063	577	5	m.	m.	NOUN
ejpam-7063	577	6	bahaa	bahaa	NOUN
ejpam-7063	577	7	.	.	PUNCT
ejpam-7063	578	1	optimality	optimality	NOUN
ejpam-7063	578	2	conditions	condition	NOUN
ejpam-7063	578	3	for	for	ADP
ejpam-7063	578	4	infinite	infinite	ADJ
ejpam-7063	578	5	order	order	NOUN
ejpam-7063	578	6	distributed	distribute	VERB
ejpam-7063	578	7	parabolic	parabolic	NOUN
ejpam-7063	578	8	systems	system	NOUN
ejpam-7063	578	9	with	with	ADP
ejpam-7063	578	10	multiple	multiple	ADJ
ejpam-7063	578	11	time	time	NOUN
ejpam-7063	578	12	delays	delay	NOUN
ejpam-7063	578	13	given	give	VERB
ejpam-7063	578	14	in	in	ADP
ejpam-7063	578	15	integral	integral	ADJ
ejpam-7063	578	16	form	form	NOUN
ejpam-7063	578	17	.	.	PUNCT
ejpam-7063	579	1	journal	journal	NOUN
ejpam-7063	579	2	of	of	ADP
ejpam-7063	579	3	applied	apply	VERB
ejpam-7063	579	4	mathematics	mathematic	NOUN
ejpam-7063	579	5	,	,	PUNCT
ejpam-7063	579	6	2012:672947	2012:672947	NUM
ejpam-7063	579	7	,	,	PUNCT
ejpam-7063	579	8	2012	2012	NUM
ejpam-7063	579	9	.	.	PUNCT