id	sid	tid	token	lemma	pos
iajs-1842	1	1	microsoft	microsoft	PROPN
iajs-1842	1	2	word	word	NOUN
iajs-1842	1	3	222	222	NUM
iajs-1842	1	4	-	-	SYM
iajs-1842	1	5	230	230	NUM
iajs-1842	1	6	https://doi.org/10.30526/31.1.1842	https://doi.org/10.30526/31.1.1842	NOUN
iajs-1842	1	7	mathematics	mathematic	NOUN
iajs-1842	1	8	|	|	ADV
iajs-1842	1	9	222	222	NUM
iajs-1842	1	10	2018)عام	2018)عام	NUM
iajs-1842	1	11	1العدد	1العدد	NUM
iajs-1842	1	12	(	(	PUNCT
iajs-1842	1	13	31مجلة	31مجلة	NUM
iajs-1842	1	14	إبن	إبن	VERB
iajs-1842	1	15	الهيثم	الهيثم	ADJ
iajs-1842	1	16	للعلوم	للعلوم	NOUN
iajs-1842	1	17	الصرفة	الصرفة	NOUN
iajs-1842	1	18	والتطبيقية	والتطبيقية	PRON
iajs-1842	1	19	المجلد	المجلد	VERB
iajs-1842	1	20	ibn	ibn	PROPN
iajs-1842	1	21	al	al	PROPN
iajs-1842	1	22	-	-	PUNCT
iajs-1842	1	23	haitham	haitham	PROPN
iajs-1842	1	24	jour	jour	X
iajs-1842	1	25	.	.	PROPN
iajs-1842	2	1	for	for	ADP
iajs-1842	2	2	pure	pure	ADJ
iajs-1842	2	3	&	&	CCONJ
iajs-1842	2	4	appl	appl	PROPN
iajs-1842	2	5	.	.	PUNCT
iajs-1842	3	1	sci	sci	PROPN
iajs-1842	3	2	.	.	PUNCT
iajs-1842	3	3	vol	vol	NOUN
iajs-1842	3	4	.	.	PROPN
iajs-1842	4	1	31	31	NUM
iajs-1842	4	2	(	(	PUNCT
iajs-1842	4	3	1	1	NUM
iajs-1842	4	4	)	)	PUNCT
iajs-1842	4	5	2018	2018	NUM
iajs-1842	4	6	generalized	generalize	VERB
iajs-1842	4	7	spline	spline	NOUN
iajs-1842	4	8	approach	approach	NOUN
iajs-1842	4	9	for	for	ADP
iajs-1842	4	10	solving	solve	VERB
iajs-1842	4	11	system	system	NOUN
iajs-1842	4	12	of	of	ADP
iajs-1842	4	13	linear	linear	PROPN
iajs-1842	4	14	fractional	fractional	PROPN
iajs-1842	4	15	volterra	volterra	PROPN
iajs-1842	4	16	integro	integro	PROPN
iajs-1842	4	17	-	-	PUNCT
iajs-1842	4	18	differential	differential	NOUN
iajs-1842	4	19	equations	equation	NOUN
iajs-1842	4	20	nabaa	nabaa	VERB
iajs-1842	4	21	najdi	najdi	PROPN
iajs-1842	4	22	hasan	hasan	PROPN
iajs-1842	4	23	doaa	doaa	PROPN
iajs-1842	4	24	ahmed	ahmed	PROPN
iajs-1842	4	25	hussien	hussien	PROPN
iajs-1842	4	26	dept	dept	PROPN
iajs-1842	4	27	.	.	PUNCT
iajs-1842	4	28	 	 	SPACE
iajs-1842	4	29	of	of	ADP
iajs-1842	4	30	mathematics/	mathematics/	NUM
iajs-1842	4	31	college	college	NOUN
iajs-1842	4	32	of	of	ADP
iajs-1842	4	33	science/	science/	NUM
iajs-1842	4	34	university	university	PROPN
iajs-1842	4	35	of	of	ADP
iajs-1842	4	36	al	al	PROPN
iajs-1842	4	37	-	-	PUNCT
iajs-1842	4	38	mustansiriyah	mustansiriyah	NOUN
iajs-1842	4	39	doaaa92@yahoo.com	doaaa92@yahoo.com	X
iajs-1842	4	40	alzaer1972@uomustansiriyah.edu.iq	alzaer1972@uomustansiriyah.edu.iq	ADJ
iajs-1842	4	41	received	receive	VERB
iajs-1842	4	42	in	in	ADP
iajs-1842	4	43	:	:	PUNCT
iajs-1842	4	44	20	20	NUM
iajs-1842	4	45	/	/	SYM
iajs-1842	4	46	november/2017	november/2017	NOUN
iajs-1842	4	47	,	,	PUNCT
iajs-1842	4	48	accepted	accept	VERB
iajs-1842	4	49	in:2	in:2	PROPN
iajs-1842	4	50	/	/	SYM
iajs-1842	4	51	january/	january/	NUM
iajs-1842	4	52	2018	2018	NUM
iajs-1842	4	53	abstract	abstract	NOUN
iajs-1842	4	54	in	in	ADP
iajs-1842	4	55	this	this	DET
iajs-1842	4	56	paper	paper	NOUN
iajs-1842	4	57	generalized	generalize	VERB
iajs-1842	4	58	spline	spline	NOUN
iajs-1842	4	59	method	method	NOUN
iajs-1842	4	60	is	be	AUX
iajs-1842	4	61	used	use	VERB
iajs-1842	4	62	for	for	ADP
iajs-1842	4	63	solving	solve	VERB
iajs-1842	4	64	linear	linear	NOUN
iajs-1842	4	65	system	system	NOUN
iajs-1842	4	66	of	of	ADP
iajs-1842	4	67	fractional	fractional	ADJ
iajs-1842	4	68	integro	integro	ADJ
iajs-1842	4	69	-	-	PUNCT
iajs-1842	4	70	differential	differential	NOUN
iajs-1842	4	71	equation	equation	NOUN
iajs-1842	4	72	approximately	approximately	ADV
iajs-1842	4	73	.	.	PUNCT
iajs-1842	5	1	the	the	DET
iajs-1842	5	2	suggested	suggest	VERB
iajs-1842	5	3	method	method	NOUN
iajs-1842	5	4	reduces	reduce	VERB
iajs-1842	5	5	the	the	DET
iajs-1842	5	6	system	system	NOUN
iajs-1842	5	7	to	to	ADP
iajs-1842	5	8	system	system	NOUN
iajs-1842	5	9	of	of	ADP
iajs-1842	5	10	linear	linear	PROPN
iajs-1842	5	11	algebraic	algebraic	ADJ
iajs-1842	5	12	equations	equation	NOUN
iajs-1842	5	13	.	.	PUNCT
iajs-1842	6	1	different	different	ADJ
iajs-1842	6	2	orders	order	NOUN
iajs-1842	6	3	of	of	ADP
iajs-1842	6	4	fractional	fractional	ADJ
iajs-1842	6	5	derivative	derivative	NOUN
iajs-1842	6	6	for	for	ADP
iajs-1842	6	7	test	test	NOUN
iajs-1842	6	8	example	example	NOUN
iajs-1842	6	9	is	be	AUX
iajs-1842	6	10	given	give	VERB
iajs-1842	6	11	in	in	ADP
iajs-1842	6	12	this	this	DET
iajs-1842	6	13	paper	paper	NOUN
iajs-1842	6	14	to	to	PART
iajs-1842	6	15	show	show	VERB
iajs-1842	6	16	the	the	DET
iajs-1842	6	17	accuracy	accuracy	NOUN
iajs-1842	6	18	and	and	CCONJ
iajs-1842	6	19	applicability	applicability	NOUN
iajs-1842	6	20	of	of	ADP
iajs-1842	6	21	the	the	DET
iajs-1842	6	22	presented	present	VERB
iajs-1842	6	23	method	method	NOUN
iajs-1842	6	24	.	.	PUNCT
iajs-1842	7	1	keywords	keyword	NOUN
iajs-1842	7	2	:	:	PUNCT
iajs-1842	7	3	linear	linear	ADJ
iajs-1842	7	4	system	system	NOUN
iajs-1842	7	5	of	of	ADP
iajs-1842	7	6	fractional	fractional	PROPN
iajs-1842	7	7	volterra	volterra	PROPN
iajs-1842	7	8	integro	integro	PROPN
iajs-1842	7	9	-	-	PUNCT
iajs-1842	7	10	differential	differential	NOUN
iajs-1842	7	11	equations	equation	NOUN
iajs-1842	7	12	,	,	PUNCT
iajs-1842	7	13	generalized	generalize	VERB
iajs-1842	7	14	spline	spline	NOUN
iajs-1842	7	15	functions	function	NOUN
iajs-1842	7	16	.	.	PUNCT
iajs-1842	8	1	https://doi.org/10.30526/31.1.1842	https://doi.org/10.30526/31.1.1842	NOUN
iajs-1842	8	2	mathematics	mathematics	PROPN
iajs-1842	8	3	|	|	ADV
iajs-1842	8	4	223	223	NUM
iajs-1842	8	5	2018)عام	2018)عام	NUM
iajs-1842	8	6	1العدد	1العدد	NUM
iajs-1842	8	7	(	(	PUNCT
iajs-1842	8	8	31لمجلد	31لمجلد	NUM
iajs-1842	8	9	ا	ا	INTJ
iajs-1842	8	10	مجلة	مجلة	NOUN
iajs-1842	8	11	إبن	إبن	VERB
iajs-1842	8	12	الهيثم	الهيثم	ADJ
iajs-1842	8	13	للعلوم	للعلوم	NOUN
iajs-1842	8	14	الصرفة	الصرفة	NOUN
iajs-1842	8	15	والتطبيقية	والتطبيقية	VERB
iajs-1842	8	16	ibn	ibn	PROPN
iajs-1842	8	17	al	al	PROPN
iajs-1842	8	18	-	-	PUNCT
iajs-1842	8	19	haitham	haitham	PROPN
iajs-1842	8	20	jour	jour	X
iajs-1842	8	21	.	.	PROPN
iajs-1842	9	1	for	for	ADP
iajs-1842	9	2	pure	pure	ADJ
iajs-1842	9	3	&	&	CCONJ
iajs-1842	9	4	appl	appl	PROPN
iajs-1842	9	5	.	.	PUNCT
iajs-1842	10	1	sci	sci	PROPN
iajs-1842	10	2	.	.	PUNCT
iajs-1842	10	3	vol	vol	NOUN
iajs-1842	10	4	.	.	PROPN
iajs-1842	11	1	31	31	NUM
iajs-1842	11	2	(	(	PUNCT
iajs-1842	11	3	1	1	NUM
iajs-1842	11	4	)	)	SYM
iajs-1842	11	5	2018	2018	NUM
iajs-1842	11	6	introduction	introduction	NOUN
iajs-1842	11	7	the	the	DET
iajs-1842	11	8	concept	concept	NOUN
iajs-1842	11	9	of	of	ADP
iajs-1842	11	10	fractional	fractional	ADJ
iajs-1842	11	11	or	or	CCONJ
iajs-1842	11	12	non	non	ADJ
iajs-1842	11	13	-	-	ADJ
iajs-1842	11	14	integer	integer	ADJ
iajs-1842	11	15	order	order	NOUN
iajs-1842	11	16	derivative	derivative	NOUN
iajs-1842	11	17	and	and	CCONJ
iajs-1842	11	18	integration	integration	NOUN
iajs-1842	11	19	can	can	AUX
iajs-1842	11	20	be	be	AUX
iajs-1842	11	21	traced	trace	VERB
iajs-1842	11	22	back	back	ADV
iajs-1842	11	23	to	to	ADP
iajs-1842	11	24	the	the	DET
iajs-1842	11	25	genesis	genesis	NOUN
iajs-1842	11	26	of	of	ADP
iajs-1842	11	27	integer	integer	NOUN
iajs-1842	11	28	order	order	NOUN
iajs-1842	11	29	calculus	calculus	NOUN
iajs-1842	11	30	itself	itself	PRON
iajs-1842	11	31	.	.	PUNCT
iajs-1842	12	1	almost	almost	ADV
iajs-1842	12	2	every	every	DET
iajs-1842	12	3	mathematical	mathematical	ADJ
iajs-1842	12	4	theory	theory	NOUN
iajs-1842	12	5	applicable	applicable	ADJ
iajs-1842	12	6	to	to	ADP
iajs-1842	12	7	the	the	DET
iajs-1842	12	8	study	study	NOUN
iajs-1842	12	9	of	of	ADP
iajs-1842	12	10	non	non	ADJ
iajs-1842	12	11	-	-	ADJ
iajs-1842	12	12	integer	integer	ADJ
iajs-1842	12	13	order	order	NOUN
iajs-1842	12	14	calculus	calculus	NOUN
iajs-1842	12	15	was	be	AUX
iajs-1842	12	16	developed	develop	VERB
iajs-1842	12	17	through	through	ADP
iajs-1842	12	18	the	the	DET
iajs-1842	12	19	end	end	NOUN
iajs-1842	12	20	of	of	ADP
iajs-1842	12	21	19th	19th	ADJ
iajs-1842	12	22	century	century	NOUN
iajs-1842	12	23	.	.	PUNCT
iajs-1842	13	1	however	however	ADV
iajs-1842	13	2	,	,	PUNCT
iajs-1842	13	3	it	it	PRON
iajs-1842	13	4	is	be	AUX
iajs-1842	13	5	in	in	ADP
iajs-1842	13	6	the	the	DET
iajs-1842	13	7	past	past	ADJ
iajs-1842	13	8	hundred	hundred	NUM
iajs-1842	13	9	year	year	NOUN
iajs-1842	13	10	that	that	PRON
iajs-1842	13	11	the	the	DET
iajs-1842	13	12	most	most	ADV
iajs-1842	13	13	intriguing	intriguing	ADJ
iajs-1842	13	14	leaps	leap	NOUN
iajs-1842	13	15	in	in	ADP
iajs-1842	13	16	engineering	engineering	NOUN
iajs-1842	13	17	and	and	CCONJ
iajs-1842	13	18	scientific	scientific	ADJ
iajs-1842	13	19	application	application	NOUN
iajs-1842	13	20	have	have	AUX
iajs-1842	13	21	been	be	AUX
iajs-1842	13	22	found	find	VERB
iajs-1842	13	23	.	.	PUNCT
iajs-1842	14	1	the	the	DET
iajs-1842	14	2	calculation	calculation	NOUN
iajs-1842	14	3	technique	technique	NOUN
iajs-1842	14	4	has	have	VERB
iajs-1842	14	5	to	to	PART
iajs-1842	14	6	change	change	VERB
iajs-1842	14	7	in	in	ADP
iajs-1842	14	8	order	order	NOUN
iajs-1842	14	9	to	to	PART
iajs-1842	14	10	meet	meet	VERB
iajs-1842	14	11	the	the	DET
iajs-1842	14	12	requirement	requirement	NOUN
iajs-1842	14	13	of	of	ADP
iajs-1842	14	14	physical	physical	ADJ
iajs-1842	14	15	reality	reality	NOUN
iajs-1842	14	16	in	in	ADP
iajs-1842	14	17	some	some	DET
iajs-1842	14	18	cases	case	NOUN
iajs-1842	14	19	[	[	X
iajs-1842	14	20	1	1	NUM
iajs-1842	14	21	]	]	PUNCT
iajs-1842	14	22	.	.	PUNCT
iajs-1842	15	1	the	the	DET
iajs-1842	15	2	use	use	NOUN
iajs-1842	15	3	of	of	ADP
iajs-1842	15	4	fractional	fractional	ADJ
iajs-1842	15	5	differentiation	differentiation	NOUN
iajs-1842	15	6	for	for	ADP
iajs-1842	15	7	the	the	DET
iajs-1842	15	8	mathematical	mathematical	ADJ
iajs-1842	15	9	modeling	modeling	NOUN
iajs-1842	15	10	of	of	ADP
iajs-1842	15	11	real	real	ADJ
iajs-1842	15	12	world	world	NOUN
iajs-1842	15	13	physical	physical	ADJ
iajs-1842	15	14	problems	problem	NOUN
iajs-1842	15	15	has	have	AUX
iajs-1842	15	16	been	be	AUX
iajs-1842	15	17	wide	wide	ADV
iajs-1842	15	18	spread	spread	VERB
iajs-1842	15	19	in	in	ADP
iajs-1842	15	20	recent	recent	ADJ
iajs-1842	15	21	years	year	NOUN
iajs-1842	15	22	,	,	PUNCT
iajs-1842	15	23	e.g.	e.g.	ADV
iajs-1842	15	24	the	the	DET
iajs-1842	15	25	modeling	modeling	NOUN
iajs-1842	15	26	of	of	ADP
iajs-1842	15	27	earthquake	earthquake	NOUN
iajs-1842	15	28	,	,	PUNCT
iajs-1842	15	29	the	the	DET
iajs-1842	15	30	fluid	fluid	ADJ
iajs-1842	15	31	dynamic	dynamic	NOUN
iajs-1842	15	32	of	of	ADP
iajs-1842	15	33	viscoelastic	viscoelastic	ADJ
iajs-1842	15	34	material	material	NOUN
iajs-1842	15	35	properties	property	NOUN
iajs-1842	15	36	,	,	PUNCT
iajs-1842	15	37	etc	etc	X
iajs-1842	15	38	,	,	PUNCT
iajs-1842	15	39	[	[	X
iajs-1842	15	40	2	2	NUM
iajs-1842	15	41	]	]	PUNCT
iajs-1842	15	42	.	.	PUNCT
iajs-1842	16	1	there	there	PRON
iajs-1842	16	2	are	be	VERB
iajs-1842	16	3	several	several	ADJ
iajs-1842	16	4	approaches	approach	NOUN
iajs-1842	16	5	to	to	ADP
iajs-1842	16	6	the	the	DET
iajs-1842	16	7	generalization	generalization	NOUN
iajs-1842	16	8	of	of	ADP
iajs-1842	16	9	the	the	DET
iajs-1842	16	10	notation	notation	NOUN
iajs-1842	16	11	of	of	ADP
iajs-1842	16	12	differentiation	differentiation	NOUN
iajs-1842	16	13	of	of	ADP
iajs-1842	16	14	fractional	fractional	ADJ
iajs-1842	16	15	orders	order	NOUN
iajs-1842	16	16	,	,	PUNCT
iajs-1842	16	17	e.g.	e.g.	ADV
iajs-1842	16	18	riemann	riemann	PROPN
iajs-1842	16	19	-	-	PUNCT
iajs-1842	16	20	liouville	liouville	VERB
iajs-1842	16	21	,	,	PUNCT
iajs-1842	16	22	grunwald	grunwald	NOUN
iajs-1842	16	23	-	-	PUNCT
iajs-1842	16	24	letnikov	letnikov	PROPN
iajs-1842	16	25	,	,	PUNCT
iajs-1842	16	26	caputo	caputo	NOUN
iajs-1842	16	27	and	and	CCONJ
iajs-1842	16	28	generalized	generalized	ADJ
iajs-1842	16	29	functions	function	NOUN
iajs-1842	16	30	approach	approach	NOUN
iajs-1842	16	31	[	[	X
iajs-1842	16	32	3	3	NUM
iajs-1842	16	33	]	]	PUNCT
iajs-1842	16	34	.	.	PUNCT
iajs-1842	17	1	in	in	ADP
iajs-1842	17	2	this	this	DET
iajs-1842	17	3	paper	paper	NOUN
iajs-1842	17	4	,	,	PUNCT
iajs-1842	17	5	we	we	PRON
iajs-1842	17	6	present	present	VERB
iajs-1842	17	7	numerical	numerical	ADJ
iajs-1842	17	8	solution	solution	NOUN
iajs-1842	17	9	of	of	ADP
iajs-1842	17	10	the	the	DET
iajs-1842	17	11	system	system	NOUN
iajs-1842	17	12	of	of	ADP
iajs-1842	17	13	integro	integro	ADJ
iajs-1842	17	14	-	-	PUNCT
iajs-1842	17	15	differential	differential	NOUN
iajs-1842	17	16	equation	equation	NOUN
iajs-1842	17	17	with	with	ADP
iajs-1842	17	18	fractional	fractional	ADJ
iajs-1842	17	19	derivative	derivative	NOUN
iajs-1842	17	20	.	.	PUNCT
iajs-1842	18	1	,	,	PUNCT
iajs-1842	18	2	,	,	PUNCT
iajs-1842	18	3	1,2	1,2	NUM
iajs-1842	18	4	,	,	PUNCT
iajs-1842	18	5	…	…	PUNCT
iajs-1842	18	6	…	…	PUNCT
iajs-1842	18	7	1	1	NUM
iajs-1842	18	8	with	with	ADP
iajs-1842	18	9	initial	initial	ADJ
iajs-1842	18	10	conditions	condition	NOUN
iajs-1842	18	11	:	:	PUNCT
iajs-1842	18	12	0	0	NUM
iajs-1842	18	13	,	,	PUNCT
iajs-1842	18	14	0,1	0,1	NUM
iajs-1842	18	15	,	,	PUNCT
iajs-1842	18	16	…	…	PUNCT
iajs-1842	18	17	,	,	PUNCT
iajs-1842	18	18	1	1	X
iajs-1842	18	19	.	.	X
iajs-1842	18	20	generalized	generalize	VERB
iajs-1842	18	21	spline	spline	NOUN
iajs-1842	18	22	function	function	NOUN
iajs-1842	18	23	:	:	PUNCT
iajs-1842	18	24	consider	consider	VERB
iajs-1842	18	25	the	the	DET
iajs-1842	18	26	linear	linear	ADJ
iajs-1842	18	27	differential	differential	NOUN
iajs-1842	18	28	operator	operator	NOUN
iajs-1842	18	29	,	,	PUNCT
iajs-1842	18	30	[	[	X
iajs-1842	18	31	4	4	NUM
iajs-1842	18	32	]	]	PUNCT
iajs-1842	18	33	:	:	PUNCT
iajs-1842	18	34	⋯	⋯	PROPN
iajs-1842	18	35	.	.	PUNCT
iajs-1842	19	1	where	where	SCONJ
iajs-1842	19	2	∈	∈	PROPN
iajs-1842	19	3	,	,	PUNCT
iajs-1842	19	4	,	,	PUNCT
iajs-1842	19	5	(	(	PUNCT
iajs-1842	19	6	class	class	NOUN
iajs-1842	19	7	of	of	ADP
iajs-1842	19	8	all	all	DET
iajs-1842	19	9	function	function	NOUN
iajs-1842	19	10	which	which	PRON
iajs-1842	19	11	are	be	AUX
iajs-1842	19	12	n	n	PRON
iajs-1842	19	13	continuously	continuously	ADV
iajs-1842	19	14	differentiable	differentiable	ADJ
iajs-1842	19	15	defined	define	VERB
iajs-1842	19	16	on	on	ADP
iajs-1842	19	17	,	,	PUNCT
iajs-1842	19	18	,	,	PUNCT
iajs-1842	19	19	0,1	0,1	NUM
iajs-1842	19	20	,	,	PUNCT
iajs-1842	19	21	…	…	PUNCT
iajs-1842	19	22	,	,	PUNCT
iajs-1842	19	23	0	0	NUM
iajs-1842	19	24	,	,	PUNCT
iajs-1842	19	25	,	,	PUNCT
iajs-1842	19	26	/	/	PUNCT
iajs-1842	19	27	and	and	CCONJ
iajs-1842	19	28	associate	associate	VERB
iajs-1842	19	29	with	with	ADP
iajs-1842	19	30	l	l	NOUN
iajs-1842	19	31	its	its	PRON
iajs-1842	19	32	formula	formula	NOUN
iajs-1842	19	33	adjoint	adjoint	NOUN
iajs-1842	19	34	operator	operator	NOUN
iajs-1842	19	35	∗	∗	NOUN
iajs-1842	19	36	1	1	NUM
iajs-1842	19	37	1	1	NUM
iajs-1842	19	38	⋯	⋯	ADP
iajs-1842	19	39	1	1	NUM
iajs-1842	19	40	(	(	PUNCT
iajs-1842	19	41	1	1	NUM
iajs-1842	19	42	)	)	PUNCT
iajs-1842	19	43	,	,	PUNCT
iajs-1842	20	1	[	[	X
iajs-1842	20	2	5	5	NUM
iajs-1842	20	3	]	]	PUNCT
iajs-1842	20	4	:	:	PUNCT
iajs-1842	20	5	let	let	VERB
iajs-1842	20	6			NOUN
iajs-1842	20	7	:	:	PUNCT
iajs-1842	20	8	a	a	DET
iajs-1842	20	9			PROPN
iajs-1842	20	10	w0	w0	PROPN
iajs-1842	20	11	<	<	X
iajs-1842	20	12	w1	w1	NOUN
iajs-1842	20	13	<	<	X
iajs-1842	20	14	…	…	PUNCT
iajs-1842	20	15	<	<	X
iajs-1842	20	16	wn	wn	PROPN
iajs-1842	20	17			PROPN
iajs-1842	20	18	b	b	PROPN
iajs-1842	20	19	,	,	PUNCT
iajs-1842	20	20	n	n	PROPN
iajs-1842	20	21	be	be	VERB
iajs-1842	20	22	a	a	DET
iajs-1842	20	23	partition	partition	NOUN
iajs-1842	20	24	on	on	ADP
iajs-1842	20	25	[	[	X
iajs-1842	20	26	a	a	DET
iajs-1842	20	27	,	,	PUNCT
iajs-1842	20	28	b	b	NOUN
iajs-1842	20	29	]	]	X
iajs-1842	20	30	.	.	PUNCT
iajs-1842	21	1	a	a	DET
iajs-1842	21	2	real	real	ADJ
iajs-1842	21	3	function	function	NOUN
iajs-1842	21	4	s	s	PROPN
iajs-1842	21	5	,	,	PUNCT
iajs-1842	21	6	defined	define	VERB
iajs-1842	21	7	on	on	ADP
iajs-1842	21	8	[	[	X
iajs-1842	21	9	a	a	DET
iajs-1842	21	10	,	,	PUNCT
iajs-1842	21	11	b	b	NOUN
iajs-1842	21	12	]	]	PUNCT
iajs-1842	21	13	is	be	AUX
iajs-1842	21	14	said	say	VERB
iajs-1842	21	15	to	to	PART
iajs-1842	21	16	be	be	AUX
iajs-1842	21	17	generalized	generalize	VERB
iajs-1842	21	18	spline	spline	NOUN
iajs-1842	21	19	with	with	ADP
iajs-1842	21	20	partition	partition	NOUN
iajs-1842	21	21			PUNCT
iajs-1842	21	22	if	if	SCONJ
iajs-1842	21	23	:	:	PUNCT
iajs-1842	21	24	s	s	VERB
iajs-1842	21	25			NOUN
iajs-1842	21	26	2n	2n	X
iajs-1842	22	1	[	[	X
iajs-1842	22	2	wi-1,wi	wi-1,wi	X
iajs-1842	22	3	]	]	PUNCT
iajs-1842	22	4	;	;	PUNCT
iajs-1842	22	5	i=1,2	i=1,2	ADJ
iajs-1842	22	6	,	,	PUNCT
iajs-1842	22	7	…	…	PUNCT
iajs-1842	22	8	,	,	PUNCT
iajs-1842	22	9	n.	n.	NOUN
iajs-1842	22	10	1‐	1‐	NUM
iajs-1842	22	11	l	l	NOUN
iajs-1842	22	12	*	*	X
iajs-1842	22	13	ls(x	ls(x	X
iajs-1842	22	14	)	)	PUNCT
iajs-1842	22	15	=	=	SYM
iajs-1842	22	16	0	0	NUM
iajs-1842	22	17	;	;	PUNCT
iajs-1842	22	18	∀	∀	X
iajs-1842	22	19	w	w	ADP
iajs-1842	22	20			PROPN
iajs-1842	22	21	[	[	X
iajs-1842	22	22	wi-1,wi	wi-1,wi	X
iajs-1842	22	23	]	]	PUNCT
iajs-1842	22	24	;	;	PUNCT
iajs-1842	22	25	i=1,2	i=1,2	ADJ
iajs-1842	22	26	,	,	PUNCT
iajs-1842	22	27	…	…	PUNCT
iajs-1842	22	28	,	,	PUNCT
iajs-1842	22	29	n.	n.	PROPN
iajs-1842	22	30	2‐	2‐	NUM
iajs-1842	22	31			NOUN
iajs-1842	22	32	,	,	PUNCT
iajs-1842	22	33	where	where	SCONJ
iajs-1842	22	34	2n	2n	NUM
iajs-1842	22	35	[	[	X
iajs-1842	22	36	wi-1,wi	wi-1,wi	X
iajs-1842	22	37	]	]	X
iajs-1842	22	38	class	class	NOUN
iajs-1842	22	39	of	of	ADP
iajs-1842	22	40	all	all	DET
iajs-1842	22	41	functions	function	NOUN
iajs-1842	22	42	defined	define	VERB
iajs-1842	22	43	on	on	ADP
iajs-1842	22	44	[	[	PUNCT
iajs-1842	22	45	wi-1,wi	wi-1,wi	X
iajs-1842	22	46	]	]	PUNCT
iajs-1842	22	47	has	have	VERB
iajs-1842	22	48	derivative	derivative	NOUN
iajs-1842	22	49	of	of	ADP
iajs-1842	22	50	order	order	NOUN
iajs-1842	22	51	2n	2n	NUM
iajs-1842	22	52	.	.	PUNCT
iajs-1842	23	1	definition	definition	NOUN
iajs-1842	23	2	(	(	PUNCT
iajs-1842	23	3	2	2	NUM
iajs-1842	23	4	)	)	PUNCT
iajs-1842	23	5	,	,	PUNCT
iajs-1842	24	1	[	[	X
iajs-1842	24	2	5	5	NUM
iajs-1842	24	3	]	]	PUNCT
iajs-1842	24	4	:	:	PUNCT
iajs-1842	24	5	let	let	VERB
iajs-1842	24	6	:	:	PUNCT
iajs-1842	24	7	,	,	PUNCT
iajs-1842	24	8	→	→	X
iajs-1842	24	9	is	be	AUX
iajs-1842	24	10	an	an	DET
iajs-1842	24	11	interpolating	interpolate	VERB
iajs-1842	24	12	generalized	generalize	VERB
iajs-1842	24	13	spline	spline	NOUN
iajs-1842	24	14	function	function	NOUN
iajs-1842	24	15	of	of	ADP
iajs-1842	24	16	f	f	PROPN
iajs-1842	24	17	associated	associate	VERB
iajs-1842	24	18	with	with	ADP
iajs-1842	24	19	the	the	DET
iajs-1842	24	20	partition	partition	NOUN
iajs-1842	24	21			NOUN
iajs-1842	24	22	and	and	CCONJ
iajs-1842	24	23	the	the	DET
iajs-1842	24	24	operator	operator	NOUN
iajs-1842	24	25	l	l	NOUN
iajs-1842	24	26	,	,	PUNCT
iajs-1842	24	27	if	if	SCONJ
iajs-1842	24	28	in	in	ADP
iajs-1842	24	29	addition	addition	NOUN
iajs-1842	24	30	to	to	ADP
iajs-1842	24	31	the	the	DET
iajs-1842	24	32	conditions	condition	NOUN
iajs-1842	24	33	of	of	ADP
iajs-1842	24	34	definition	definition	NOUN
iajs-1842	24	35	(	(	PUNCT
iajs-1842	24	36	2.1	2.1	NUM
iajs-1842	24	37	)	)	PUNCT
iajs-1842	24	38	,	,	PUNCT
iajs-1842	24	39	on	on	ADP
iajs-1842	24	40			NOUN
iajs-1842	24	41	and	and	CCONJ
iajs-1842	24	42	for	for	ADP
iajs-1842	24	43	i	i	PROPN
iajs-1842	24	44	=	=	NOUN
iajs-1842	24	45	0	0	NUM
iajs-1842	24	46	,	,	PUNCT
iajs-1842	24	47	…	…	PUNCT
iajs-1842	24	48	,	,	PUNCT
iajs-1842	24	49	n	n	NOUN
iajs-1842	24	50	and	and	CCONJ
iajs-1842	24	51	g	g	NOUN
iajs-1842	24	52	=	=	SYM
iajs-1842	24	53	1,2	1,2	NUM
iajs-1842	24	54	,	,	PUNCT
iajs-1842	24	55	…	…	PUNCT
iajs-1842	24	56	,	,	PUNCT
iajs-1842	24	57	n	n	PROPN
iajs-1842	24	58	1	1	NUM
iajs-1842	24	59	.	.	PUNCT
iajs-1842	25	1	definition	definition	NOUN
iajs-1842	25	2	(	(	PUNCT
iajs-1842	25	3	3	3	NUM
iajs-1842	25	4	):	):	PUNCT
iajs-1842	25	5	the	the	DET
iajs-1842	25	6	caputo	caputo	PROPN
iajs-1842	25	7	fractional	fractional	ADJ
iajs-1842	25	8	derivative	derivative	ADJ
iajs-1842	25	9	operator	operator	NOUN
iajs-1842	25	10	of	of	ADP
iajs-1842	25	11	order	order	NOUN
iajs-1842	25	12	v	v	NOUN
iajs-1842	25	13	is	be	AUX
iajs-1842	25	14	defined	define	VERB
iajs-1842	25	15	in	in	ADP
iajs-1842	25	16	the	the	DET
iajs-1842	25	17	following	following	NOUN
iajs-1842	25	18	from	from	ADP
iajs-1842	25	19	:	:	PUNCT
iajs-1842	25	20	https://doi.org/10.30526/31.1.1842	https://doi.org/10.30526/31.1.1842	PROPN
iajs-1842	25	21	mathematics	mathematic	NOUN
iajs-1842	25	22	|	|	ADV
iajs-1842	25	23	224	224	NUM
iajs-1842	25	24	2018)عام	2018)عام	NUM
iajs-1842	25	25	1العدد	1العدد	NUM
iajs-1842	25	26	(	(	PUNCT
iajs-1842	25	27	31لمجلد	31لمجلد	NUM
iajs-1842	25	28	ا	ا	INTJ
iajs-1842	25	29	مجلة	مجلة	NOUN
iajs-1842	25	30	إبن	إبن	VERB
iajs-1842	25	31	الهيثم	الهيثم	ADJ
iajs-1842	25	32	للعلوم	للعلوم	NOUN
iajs-1842	25	33	الصرفة	الصرفة	NOUN
iajs-1842	25	34	والتطبيقية	والتطبيقية	VERB
iajs-1842	25	35	ibn	ibn	PROPN
iajs-1842	25	36	al	al	PROPN
iajs-1842	25	37	-	-	PUNCT
iajs-1842	25	38	haitham	haitham	PROPN
iajs-1842	25	39	jour	jour	X
iajs-1842	25	40	.	.	PROPN
iajs-1842	26	1	for	for	ADP
iajs-1842	26	2	pure	pure	ADJ
iajs-1842	26	3	&	&	CCONJ
iajs-1842	26	4	appl	appl	PROPN
iajs-1842	26	5	.	.	PUNCT
iajs-1842	27	1	sci	sci	PROPN
iajs-1842	27	2	.	.	PUNCT
iajs-1842	27	3	vol	vol	NOUN
iajs-1842	27	4	.	.	PROPN
iajs-1842	28	1	31	31	NUM
iajs-1842	28	2	(	(	PUNCT
iajs-1842	28	3	1	1	NUM
iajs-1842	28	4	)	)	PUNCT
iajs-1842	28	5	2018	2018	NUM
iajs-1842	28	6	∗	∗	NOUN
iajs-1842	28	7	∗	∗	NOUN
iajs-1842	28	8	∗	∗	NOUN
iajs-1842	28	9	,	,	PUNCT
iajs-1842	28	10	0	0	NUM
iajs-1842	28	11	…	…	PUNCT
iajs-1842	28	12	(	(	PUNCT
iajs-1842	28	13	2	2	NUM
iajs-1842	28	14	)	)	PUNCT
iajs-1842	28	15	where	where	SCONJ
iajs-1842	28	16	∗	∗	NOUN
iajs-1842	28	17	1	1	NUM
iajs-1842	28	18	∗	∗	NOUN
iajs-1842	28	19	,	,	PUNCT
iajs-1842	28	20	∗	∗	NOUN
iajs-1842	28	21	∈	∈	PROPN
iajs-1842	28	22	.	.	PUNCT
iajs-1842	29	1	similar	similar	ADJ
iajs-1842	29	2	to	to	ADP
iajs-1842	29	3	integer	integer	NOUN
iajs-1842	29	4	-	-	PUNCT
iajs-1842	29	5	order	order	NOUN
iajs-1842	29	6	differentiation	differentiation	NOUN
iajs-1842	29	7	,	,	PUNCT
iajs-1842	29	8	caputo	caputo	PROPN
iajs-1842	29	9	fractional	fractional	PROPN
iajs-1842	29	10	derivative	derivative	ADJ
iajs-1842	29	11	operator	operator	NOUN
iajs-1842	29	12	is	be	AUX
iajs-1842	29	13	a	a	DET
iajs-1842	29	14	linear	linear	ADJ
iajs-1842	29	15	operatin	operatin	PROPN
iajs-1842	29	16	.	.	PUNCT
iajs-1842	30	1	where	where	SCONJ
iajs-1842	30	2	,	,	PUNCT
iajs-1842	30	3	and	and	CCONJ
iajs-1842	30	4	µ	µ	NOUN
iajs-1842	30	5	are	be	AUX
iajs-1842	30	6	constants	constant	NOUN
iajs-1842	30	7	,	,	PUNCT
iajs-1842	30	8	for	for	ADP
iajs-1842	30	9	the	the	DET
iajs-1842	30	10	caputo	caputo	PROPN
iajs-1842	30	11	's	's	PART
iajs-1842	30	12	derivative	derivative	NOUN
iajs-1842	30	13	we	we	PRON
iajs-1842	30	14	have	have	VERB
iajs-1842	30	15	[	[	X
iajs-1842	30	16	6	6	NUM
iajs-1842	30	17	]	]	SYM
iajs-1842	30	18	:	:	PUNCT
iajs-1842	30	19	0	0	NUM
iajs-1842	30	20	,	,	PUNCT
iajs-1842	30	21	islconstant	islconstant	ADJ
iajs-1842	30	22	.	.	PUNCT
iajs-1842	30	23	0	0	NUM
iajs-1842	31	1	∈	∈	PROPN
iajs-1842	31	2	┌	┌	PROPN
iajs-1842	31	3	┐	┐	PROPN
iajs-1842	31	4	;	;	PUNCT
iajs-1842	31	5	1	1	NUM
iajs-1842	31	6	1	1	NUM
iajs-1842	31	7	∈	∈	PROPN
iajs-1842	31	8	┌	┌	PROPN
iajs-1842	31	9	┐	┐	PROPN
iajs-1842	31	10	…	…	PUNCT
iajs-1842	31	11	3	3	NUM
iajs-1842	31	12	we	we	PRON
iajs-1842	31	13	use	use	VERB
iajs-1842	31	14	the	the	DET
iajs-1842	31	15	ceiling	ceiling	NOUN
iajs-1842	31	16	function	function	NOUN
iajs-1842	31	17	┌	┌	PROPN
iajs-1842	31	18	┐	┐	PROPN
iajs-1842	31	19	to	to	PART
iajs-1842	31	20	denote	denote	VERB
iajs-1842	31	21	the	the	DET
iajs-1842	31	22	smallest	small	ADJ
iajs-1842	31	23	integer	integer	NOUN
iajs-1842	31	24	greater	great	ADJ
iajs-1842	31	25	than	than	ADP
iajs-1842	31	26	or	or	CCONJ
iajs-1842	31	27	equal	equal	ADJ
iajs-1842	31	28	to	to	ADP
iajs-1842	31	29	v	v	NOUN
iajs-1842	31	30	,	,	PUNCT
iajs-1842	31	31	and	and	CCONJ
iajs-1842	31	32	1,2	1,2	NUM
iajs-1842	31	33	,	,	PUNCT
iajs-1842	31	34	…	…	PUNCT
iajs-1842	31	35	.	.	PUNCT
iajs-1842	32	1	recall	recall	VERB
iajs-1842	32	2	that	that	PRON
iajs-1842	32	3	for	for	ADP
iajs-1842	32	4	∈	∈	PROPN
iajs-1842	32	5	,	,	PUNCT
iajs-1842	32	6	the	the	DET
iajs-1842	32	7	caputo	caputo	PROPN
iajs-1842	32	8	differential	differential	PROPN
iajs-1842	32	9	operator	operator	NOUN
iajs-1842	32	10	coincides	coincide	VERB
iajs-1842	32	11	with	with	ADP
iajs-1842	32	12	the	the	DET
iajs-1842	32	13	usual	usual	ADJ
iajs-1842	32	14	differential	differential	ADJ
iajs-1842	32	15	operator	operator	NOUN
iajs-1842	32	16	of	of	ADP
iajs-1842	32	17	linear	linear	ADJ
iajs-1842	32	18	order	order	NOUN
iajs-1842	32	19	.	.	PUNCT
iajs-1842	33	1	2theorem,[7]:let	2theorem,[7]:let	ADJ
iajs-1842	33	2	∈	∈	PROPN
iajs-1842	33	3	,	,	PUNCT
iajs-1842	33	4	1	1	NUM
iajs-1842	33	5	,	,	PUNCT
iajs-1842	33	6	∈	∈	PROPN
iajs-1842	33	7	,	,	PUNCT
iajs-1842	33	8	∈	∈	PROPN
iajs-1842	33	9	.	.	PUNCT
iajs-1842	34	1	then	then	ADV
iajs-1842	34	2	the	the	DET
iajs-1842	34	3	caputo	caputo	PROPN
iajs-1842	34	4	fractional	fractional	PROPN
iajs-1842	34	5	derivative	derivative	NOUN
iajs-1842	34	6	of	of	ADP
iajs-1842	34	7	the	the	DET
iajs-1842	34	8	exponential	exponential	ADJ
iajs-1842	34	9	function	function	NOUN
iajs-1842	34	10	has	have	VERB
iajs-1842	34	11	the	the	DET
iajs-1842	34	12	form	form	NOUN
iajs-1842	34	13	:	:	PUNCT
iajs-1842	34	14	г	г	PROPN
iajs-1842	34	15	1	1	NUM
iajs-1842	34	16	,	,	PUNCT
iajs-1842	34	17	where	where	SCONJ
iajs-1842	34	18	,	,	PUNCT
iajs-1842	34	19	is	be	AUX
iajs-1842	34	20	the	the	DET
iajs-1842	34	21	two	two	NUM
iajs-1842	34	22	-	-	PUNCT
iajs-1842	34	23	parameter	parameter	NOUN
iajs-1842	34	24	function	function	NOUN
iajs-1842	34	25	of	of	ADP
iajs-1842	34	26	mittag	mittag	ADJ
iajs-1842	34	27	-	-	PUNCT
iajs-1842	34	28	leffler	leffler	NOUN
iajs-1842	34	29	type	type	NOUN
iajs-1842	34	30	.	.	PUNCT
iajs-1842	35	1	proof	proof	NOUN
iajs-1842	35	2	:	:	PUNCT
iajs-1842	35	3	to	to	PART
iajs-1842	35	4	prove	prove	VERB
iajs-1842	35	5	the	the	DET
iajs-1842	35	6	theorem	theorem	NOUN
iajs-1842	35	7	,	,	PUNCT
iajs-1842	35	8	the	the	DET
iajs-1842	35	9	relation	relation	NOUN
iajs-1842	35	10	between	between	ADP
iajs-1842	35	11	caputo	caputo	PROPN
iajs-1842	35	12	and	and	CCONJ
iajs-1842	35	13	riemann	riemann	PROPN
iajs-1842	35	14	-	-	PUNCT
iajs-1842	35	15	liouville	liouville	VERB
iajs-1842	35	16	fractional	fractional	ADJ
iajs-1842	35	17	derivative	derivative	NOUN
iajs-1842	35	18	:	:	PUNCT
iajs-1842	35	19	∑	∑	PUNCT
iajs-1842	35	20	г	г	PROPN
iajs-1842	35	21	0	0	NUM
iajs-1842	35	22	as	as	ADV
iajs-1842	35	23	well	well	ADV
iajs-1842	35	24	as	as	ADP
iajs-1842	35	25	the	the	DET
iajs-1842	35	26	well	well	ADV
iajs-1842	35	27	-	-	PUNCT
iajs-1842	35	28	known	know	VERB
iajs-1842	35	29	riemann	riemann	PROPN
iajs-1842	35	30	-	-	PUNCT
iajs-1842	35	31	liouville	liouville	VERB
iajs-1842	35	32	fractional	fractional	ADJ
iajs-1842	35	33	derivative	derivative	NOUN
iajs-1842	35	34	of	of	ADP
iajs-1842	35	35	the	the	DET
iajs-1842	35	36	exponential	exponential	ADJ
iajs-1842	35	37	function	function	NOUN
iajs-1842	35	38	,	,	PUNCT
iajs-1842	35	39	namely	namely	ADV
iajs-1842	35	40	,	,	PUNCT
iajs-1842	35	41	,	,	PUNCT
iajs-1842	35	42	could	could	AUX
iajs-1842	35	43	be	be	AUX
iajs-1842	35	44	used	use	VERB
iajs-1842	35	45	.	.	PUNCT
iajs-1842	36	1	then	then	ADV
iajs-1842	36	2	for	for	ADP
iajs-1842	36	3	the	the	DET
iajs-1842	36	4	caputo	caputo	PROPN
iajs-1842	36	5	fractional	fractional	PROPN
iajs-1842	36	6	derivative	derivative	PROPN
iajs-1842	36	7	holds	hold	VERB
iajs-1842	36	8	г	г	PROPN
iajs-1842	36	9	1	1	NUM
iajs-1842	36	10	0	0	NUM
iajs-1842	36	11	,	,	PUNCT
iajs-1842	36	12	∑	∑	PUNCT
iajs-1842	36	13	г	г	PROPN
iajs-1842	36	14	∑	∑	PROPN
iajs-1842	36	15	г	г	PROPN
iajs-1842	36	16	∑	∑	PROPN
iajs-1842	36	17	г	г	PROPN
iajs-1842	36	18	https://doi.org/10.30526/31.1.1842	https://doi.org/10.30526/31.1.1842	PROPN
iajs-1842	36	19	mathematics	mathematics	PROPN
iajs-1842	36	20	|	|	ADV
iajs-1842	36	21	225	225	NUM
iajs-1842	36	22	2018)عام	2018)عام	NUM
iajs-1842	36	23	1العدد	1العدد	NUM
iajs-1842	36	24	(	(	PUNCT
iajs-1842	36	25	31لمجلد	31لمجلد	NUM
iajs-1842	36	26	ا	ا	INTJ
iajs-1842	36	27	مجلة	مجلة	NOUN
iajs-1842	36	28	إبن	إبن	VERB
iajs-1842	36	29	الهيثم	الهيثم	ADJ
iajs-1842	36	30	للعلوم	للعلوم	NOUN
iajs-1842	36	31	الصرفة	الصرفة	NOUN
iajs-1842	36	32	والتطبيقية	والتطبيقية	VERB
iajs-1842	36	33	ibn	ibn	PROPN
iajs-1842	36	34	al	al	PROPN
iajs-1842	36	35	-	-	PUNCT
iajs-1842	36	36	haitham	haitham	PROPN
iajs-1842	36	37	jour	jour	X
iajs-1842	36	38	.	.	PROPN
iajs-1842	37	1	for	for	ADP
iajs-1842	37	2	pure	pure	ADJ
iajs-1842	37	3	&	&	CCONJ
iajs-1842	37	4	appl	appl	PROPN
iajs-1842	37	5	.	.	PUNCT
iajs-1842	38	1	sci	sci	PROPN
iajs-1842	38	2	.	.	PUNCT
iajs-1842	38	3	vol	vol	NOUN
iajs-1842	38	4	.	.	PROPN
iajs-1842	39	1	31	31	NUM
iajs-1842	39	2	(	(	PUNCT
iajs-1842	39	3	1	1	NUM
iajs-1842	39	4	)	)	PUNCT
iajs-1842	39	5	2018	2018	NUM
iajs-1842	39	6	∑	∑	PUNCT
iajs-1842	39	7	г	г	PROPN
iajs-1842	39	8	∑	∑	PROPN
iajs-1842	39	9	г	г	PROPN
iajs-1842	39	10	,	,	PUNCT
iajs-1842	39	11	.	.	PUNCT
iajs-1842	40	1	solution	solution	NOUN
iajs-1842	40	2	of	of	ADP
iajs-1842	40	3	system	system	NOUN
iajs-1842	40	4	of	of	ADP
iajs-1842	40	5	linear	linear	ADJ
iajs-1842	40	6	fractional	fractional	ADJ
iajs-1842	40	7	integro	integro	ADJ
iajs-1842	40	8	-	-	PUNCT
iajs-1842	40	9	differential	differential	NOUN
iajs-1842	40	10	equation	equation	NOUN
iajs-1842	40	11	in	in	ADP
iajs-1842	40	12	this	this	DET
iajs-1842	40	13	paper	paper	NOUN
iajs-1842	40	14	,	,	PUNCT
iajs-1842	40	15	the	the	DET
iajs-1842	40	16	generalized	generalize	VERB
iajs-1842	40	17	spline	spline	NOUN
iajs-1842	40	18	function	function	NOUN
iajs-1842	40	19	is	be	AUX
iajs-1842	40	20	applied	apply	VERB
iajs-1842	40	21	to	to	PART
iajs-1842	40	22	study	study	VERB
iajs-1842	40	23	the	the	DET
iajs-1842	40	24	approximate	approximate	ADJ
iajs-1842	40	25	solution	solution	NOUN
iajs-1842	40	26	of	of	ADP
iajs-1842	40	27	system	system	NOUN
iajs-1842	40	28	of	of	ADP
iajs-1842	40	29	fractional	fractional	ADJ
iajs-1842	40	30	integro	integro	NOUN
iajs-1842	40	31	-	-	PUNCT
iajs-1842	40	32	differential	differential	NOUN
iajs-1842	40	33	of	of	ADP
iajs-1842	40	34	equations	equation	NOUN
iajs-1842	40	35	are	be	AUX
iajs-1842	40	36	given	give	VERB
iajs-1842	40	37	in	in	ADP
iajs-1842	40	38	equation	equation	NOUN
iajs-1842	40	39	(	(	PUNCT
iajs-1842	40	40	1	1	X
iajs-1842	40	41	)	)	PUNCT
iajs-1842	40	42	let	let	VERB
iajs-1842	40	43	∑	∑	VERB
iajs-1842	40	44	,	,	PUNCT
iajs-1842	40	45	1	1	NUM
iajs-1842	40	46	,	,	PUNCT
iajs-1842	40	47	…	…	PUNCT
iajs-1842	40	48	,	,	PUNCT
iajs-1842	40	49	0	0	NUM
iajs-1842	40	50	1	1	NUM
iajs-1842	40	51	…	…	PUNCT
iajs-1842	40	52	(	(	PUNCT
iajs-1842	40	53	4	4	X
iajs-1842	40	54	)	)	PUNCT
iajs-1842	40	55	be	be	VERB
iajs-1842	40	56	the	the	DET
iajs-1842	40	57	generalized	generalized	ADJ
iajs-1842	40	58	spline	spline	NOUN
iajs-1842	40	59	function	function	NOUN
iajs-1842	40	60	to	to	PART
iajs-1842	40	61	approximate	approximate	VERB
iajs-1842	40	62	the	the	DET
iajs-1842	40	63	solution	solution	NOUN
iajs-1842	40	64	of	of	ADP
iajs-1842	40	65	equation	equation	NOUN
iajs-1842	40	66	(	(	PUNCT
iajs-1842	40	67	1	1	NUM
iajs-1842	40	68	)	)	PUNCT
iajs-1842	40	69	where	where	SCONJ
iajs-1842	40	70	,	,	PUNCT
iajs-1842	40	71	1	1	NUM
iajs-1842	40	72	,	,	PUNCT
iajs-1842	40	73	…	…	PUNCT
iajs-1842	40	74	,	,	PUNCT
iajs-1842	40	75	2	2	NUM
iajs-1842	40	76	be	be	AUX
iajs-1842	40	77	the	the	DET
iajs-1842	40	78	basis	basis	NOUN
iajs-1842	40	79	function	function	NOUN
iajs-1842	40	80	of	of	ADP
iajs-1842	40	81	generalized	generalized	ADJ
iajs-1842	40	82	spline	spline	NOUN
iajs-1842	40	83	and	and	CCONJ
iajs-1842	40	84	2n	2n	NUM
iajs-1842	40	85	is	be	AUX
iajs-1842	40	86	order	order	NOUN
iajs-1842	40	87	of	of	ADP
iajs-1842	40	88	∗	∗	NOUN
iajs-1842	40	89	0	0	PUNCT
iajs-1842	40	90	and	and	CCONJ
iajs-1842	40	91	be	be	AUX
iajs-1842	40	92	the	the	DET
iajs-1842	40	93	coefficients	coefficient	NOUN
iajs-1842	40	94	,	,	PUNCT
iajs-1842	40	95	1	1	NUM
iajs-1842	40	96	,	,	PUNCT
iajs-1842	40	97	…	…	PUNCT
iajs-1842	40	98	,	,	PUNCT
iajs-1842	40	99	,	,	PUNCT
iajs-1842	40	100	∈	∈	PROPN
iajs-1842	40	101	,	,	PUNCT
iajs-1842	40	102	1	1	NUM
iajs-1842	40	103	,	,	PUNCT
iajs-1842	40	104	…	…	PUNCT
iajs-1842	40	105	,	,	PUNCT
iajs-1842	40	106	2	2	NUM
iajs-1842	40	107	.	.	PUNCT
iajs-1842	41	1	now	now	ADV
iajs-1842	41	2	,	,	PUNCT
iajs-1842	41	3	substituting	substitute	VERB
iajs-1842	41	4	equation	equation	NOUN
iajs-1842	41	5	(	(	PUNCT
iajs-1842	41	6	4	4	NUM
iajs-1842	41	7	)	)	PUNCT
iajs-1842	41	8	in	in	ADP
iajs-1842	41	9	equation	equation	NOUN
iajs-1842	41	10	(	(	PUNCT
iajs-1842	41	11	1	1	NUM
iajs-1842	41	12	)	)	PUNCT
iajs-1842	41	13	,	,	PUNCT
iajs-1842	41	14	∑	∑	ADP
iajs-1842	41	15	∑	∑	PROPN
iajs-1842	41	16	∑	∑	INTJ
iajs-1842	41	17	,	,	PUNCT
iajs-1842	41	18	∑	∑	ADP
iajs-1842	41	19	…	…	PUNCT
iajs-1842	41	20	5	5	NUM
iajs-1842	41	21	then	then	ADV
iajs-1842	41	22	∑	∑	ADP
iajs-1842	41	23	∑	∑	PROPN
iajs-1842	41	24	∑	∑	INTJ
iajs-1842	41	25	,	,	PUNCT
iajs-1842	41	26	∑	∑	ADP
iajs-1842	41	27	…	…	PUNCT
iajs-1842	41	28	6	6	NUM
iajs-1842	41	29	,	,	PUNCT
iajs-1842	41	30	let	let	VERB
iajs-1842	41	31	∑	∑	VERB
iajs-1842	41	32	∑	∑	ADV
iajs-1842	41	33	,	,	PUNCT
iajs-1842	41	34	,	,	PUNCT
iajs-1842	41	35	1	1	NUM
iajs-1842	41	36	,	,	PUNCT
iajs-1842	41	37	…	…	PUNCT
iajs-1842	41	38	,	,	PUNCT
iajs-1842	41	39	2	2	NUM
iajs-1842	41	40	adding	add	VERB
iajs-1842	41	41	the	the	DET
iajs-1842	41	42	initial	initial	ADJ
iajs-1842	41	43	conditions	condition	NOUN
iajs-1842	41	44	of	of	ADP
iajs-1842	41	45	equation	equation	NOUN
iajs-1842	41	46	(	(	PUNCT
iajs-1842	41	47	1	1	NUM
iajs-1842	41	48	)	)	PUNCT
iajs-1842	41	49	as	as	ADP
iajs-1842	41	50	a	a	DET
iajs-1842	41	51	new	new	ADJ
iajs-1842	41	52	raw	raw	NOUN
iajs-1842	41	53	in	in	ADP
iajs-1842	41	54	the	the	DET
iajs-1842	41	55	following	follow	VERB
iajs-1842	41	56	matrices	matrix	NOUN
iajs-1842	41	57	:	:	PUNCT
iajs-1842	41	58	https://doi.org/10.30526/31.1.1842	https://doi.org/10.30526/31.1.1842	NOUN
iajs-1842	41	59	mathematics	mathematics	PROPN
iajs-1842	41	60	|	|	ADV
iajs-1842	41	61	226	226	NUM
iajs-1842	41	62	2018)عام	2018)عام	NUM
iajs-1842	41	63	1العدد	1العدد	NUM
iajs-1842	41	64	(	(	PUNCT
iajs-1842	41	65	31لمجلد	31لمجلد	NUM
iajs-1842	41	66	ا	ا	INTJ
iajs-1842	41	67	مجلة	مجلة	NOUN
iajs-1842	41	68	إبن	إبن	VERB
iajs-1842	41	69	الهيثم	الهيثم	ADJ
iajs-1842	41	70	للعلوم	للعلوم	NOUN
iajs-1842	41	71	الصرفة	الصرفة	NOUN
iajs-1842	41	72	والتطبيقية	والتطبيقية	VERB
iajs-1842	41	73	ibn	ibn	PROPN
iajs-1842	41	74	al	al	PROPN
iajs-1842	41	75	-	-	PUNCT
iajs-1842	41	76	haitham	haitham	PROPN
iajs-1842	41	77	jour	jour	X
iajs-1842	41	78	.	.	PROPN
iajs-1842	42	1	for	for	ADP
iajs-1842	42	2	pure	pure	ADJ
iajs-1842	42	3	&	&	CCONJ
iajs-1842	42	4	appl	appl	PROPN
iajs-1842	42	5	.	.	PUNCT
iajs-1842	43	1	sci	sci	PROPN
iajs-1842	43	2	.	.	PUNCT
iajs-1842	43	3	vol	vol	NOUN
iajs-1842	43	4	.	.	PROPN
iajs-1842	44	1	31	31	NUM
iajs-1842	44	2	(	(	PUNCT
iajs-1842	44	3	1	1	NUM
iajs-1842	44	4	)	)	PUNCT
iajs-1842	44	5	2018	2018	NUM
iajs-1842	44	6	⋯	⋯	NOUN
iajs-1842	44	7	⋮	⋮	NOUN
iajs-1842	44	8	⋮	⋮	ADJ
iajs-1842	44	9	⋮	⋮	ADJ
iajs-1842	44	10	⋮	⋮	PROPN
iajs-1842	44	11	⋯	⋯	ADP
iajs-1842	44	12	ˊ	ˊ	PROPN
iajs-1842	44	13	0	0	NUM
iajs-1842	44	14	ˊ	ˊ	PROPN
iajs-1842	44	15	0	0	PUNCT
iajs-1842	44	16	⋯	⋯	ADP
iajs-1842	44	17	ˊ	ˊ	PROPN
iajs-1842	44	18	0	0	NUM
iajs-1842	44	19	⋮	⋮	NOUN
iajs-1842	44	20	⋮	⋮	ADJ
iajs-1842	44	21	⋮	⋮	ADJ
iajs-1842	44	22	⋮	⋮	NOUN
iajs-1842	44	23	0	0	NUM
iajs-1842	44	24	0	0	NUM
iajs-1842	44	25	⋯	⋯	NOUN
iajs-1842	44	26	0	0	NUM
iajs-1842	44	27	,	,	PUNCT
iajs-1842	44	28	⋮	⋮	NOUN
iajs-1842	44	29	⋮	⋮	ADJ
iajs-1842	44	30	⋮	⋮	ADJ
iajs-1842	44	31	⋮	⋮	ADJ
iajs-1842	44	32	⋮	⋮	NOUN
iajs-1842	44	33	,	,	PUNCT
iajs-1842	44	34	⋮	⋮	NOUN
iajs-1842	44	35	⋮	⋮	ADJ
iajs-1842	44	36	⋮	⋮	ADJ
iajs-1842	44	37	⋮	⋮	ADJ
iajs-1842	44	38	⋮	⋮	ADJ
iajs-1842	44	39	⋮	⋮	ADJ
iajs-1842	44	40	⋮	⋮	NOUN
iajs-1842	44	41	…	…	PUNCT
iajs-1842	44	42	(	(	PUNCT
iajs-1842	44	43	7	7	NUM
iajs-1842	44	44	)	)	PUNCT
iajs-1842	44	45	or	or	CCONJ
iajs-1842	44	46	in	in	ADP
iajs-1842	44	47	the	the	DET
iajs-1842	44	48	system	system	NOUN
iajs-1842	44	49	form	form	NOUN
iajs-1842	44	50	:	:	PUNCT
iajs-1842	44	51	…	…	PUNCT
iajs-1842	44	52	(	(	PUNCT
iajs-1842	44	53	8)	8)	NUM
iajs-1842	44	54	and	and	CCONJ
iajs-1842	44	55	f	f	PROPN
iajs-1842	44	56	are	be	AUX
iajs-1842	44	57	constant	constant	ADJ
iajs-1842	44	58	matrices	matrix	NOUN
iajs-1842	44	59	with	with	ADP
iajs-1842	44	60	dimensions	dimension	NOUN
iajs-1842	44	61	(	(	PUNCT
iajs-1842	44	62	n+	n+	NOUN
iajs-1842	44	63	)	)	PUNCT
iajs-1842	44	64	×2n	×2n	PROPN
iajs-1842	44	65	and	and	CCONJ
iajs-1842	44	66	(	(	PUNCT
iajs-1842	44	67	n+	n+	X
iajs-1842	44	68	)	)	PUNCT
iajs-1842	44	69	×1	×1	NOUN
iajs-1842	44	70	respectively	respectively	ADV
iajs-1842	44	71	.	.	PUNCT
iajs-1842	45	1	the	the	DET
iajs-1842	45	2	system	system	NOUN
iajs-1842	45	3	will	will	AUX
iajs-1842	45	4	construct	construct	VERB
iajs-1842	45	5	has	have	AUX
iajs-1842	45	6	n+	n+	ADP
iajs-1842	45	7	equations	equation	NOUN
iajs-1842	45	8	and	and	CCONJ
iajs-1842	45	9	coefficients	coefficient	NOUN
iajs-1842	45	10	where	where	SCONJ
iajs-1842	45	11	1	1	NUM
iajs-1842	45	12	,	,	PUNCT
iajs-1842	45	13	…	…	PUNCT
iajs-1842	45	14	,	,	PUNCT
iajs-1842	45	15	1	1	NUM
iajs-1842	45	16	,	,	PUNCT
iajs-1842	45	17	…	…	PUNCT
iajs-1842	45	18	,	,	PUNCT
iajs-1842	45	19	2	2	NUM
iajs-1842	45	20	.	.	PUNCT
iajs-1842	45	21	by	by	ADP
iajs-1842	45	22	solving	solve	VERB
iajs-1842	45	23	the	the	DET
iajs-1842	45	24	above	above	ADJ
iajs-1842	45	25	system	system	NOUN
iajs-1842	45	26	,	,	PUNCT
iajs-1842	45	27	we	we	PRON
iajs-1842	45	28	obtain	obtain	VERB
iajs-1842	45	29	the	the	DET
iajs-1842	45	30	values	value	NOUN
iajs-1842	45	31	of	of	ADP
iajs-1842	45	32	the	the	DET
iajs-1842	45	33	unknown	unknown	ADJ
iajs-1842	45	34	coefficients	coefficient	NOUN
iajs-1842	45	35	and	and	CCONJ
iajs-1842	45	36	the	the	DET
iajs-1842	45	37	approximate	approximate	ADJ
iajs-1842	45	38	solution	solution	NOUN
iajs-1842	45	39	of	of	ADP
iajs-1842	45	40	equation	equation	NOUN
iajs-1842	45	41	(	(	PUNCT
iajs-1842	45	42	1	1	NUM
iajs-1842	45	43	)	)	PUNCT
iajs-1842	45	44	.	.	PUNCT
iajs-1842	46	1	to	to	PART
iajs-1842	46	2	demonstrate	demonstrate	VERB
iajs-1842	46	3	the	the	DET
iajs-1842	46	4	accuracy	accuracy	NOUN
iajs-1842	46	5	and	and	CCONJ
iajs-1842	46	6	applicability	applicability	NOUN
iajs-1842	46	7	of	of	ADP
iajs-1842	46	8	the	the	DET
iajs-1842	46	9	presented	present	VERB
iajs-1842	46	10	method	method	NOUN
iajs-1842	46	11	illustrative	illustrative	ADJ
iajs-1842	46	12	example	example	NOUN
iajs-1842	46	13	for	for	ADP
iajs-1842	46	14	solving	solve	VERB
iajs-1842	46	15	linear	linear	NOUN
iajs-1842	46	16	system	system	NOUN
iajs-1842	46	17	of	of	ADP
iajs-1842	46	18	fractional	fractional	ADJ
iajs-1842	46	19	integro	integro	ADJ
iajs-1842	46	20	-	-	PUNCT
iajs-1842	46	21	differential	differential	NOUN
iajs-1842	46	22	equations	equation	NOUN
iajs-1842	46	23	with	with	ADP
iajs-1842	46	24	different	different	ADJ
iajs-1842	46	25	values	value	NOUN
iajs-1842	46	26	of	of	ADP
iajs-1842	46	27	fractional	fractional	ADJ
iajs-1842	46	28	derivative	derivative	NOUN
iajs-1842	46	29	is	be	AUX
iajs-1842	46	30	provided	provide	VERB
iajs-1842	46	31	.	.	PUNCT
iajs-1842	47	1	illustrative	illustrative	ADJ
iajs-1842	47	2	example	example	NOUN
iajs-1842	47	3	:	:	PUNCT
iajs-1842	47	4	consider	consider	VERB
iajs-1842	47	5	the	the	DET
iajs-1842	47	6	following	follow	VERB
iajs-1842	47	7	system	system	NOUN
iajs-1842	47	8	of	of	ADP
iajs-1842	47	9	integro	integro	ADJ
iajs-1842	47	10	-	-	PUNCT
iajs-1842	47	11	differential	differential	NOUN
iajs-1842	47	12	equations	equation	NOUN
iajs-1842	47	13	of	of	ADP
iajs-1842	47	14	fractional	fractional	ADJ
iajs-1842	47	15	order	order	NOUN
iajs-1842	47	16	,	,	PUNCT
iajs-1842	47	17	,	,	PUNCT
iajs-1842	47	18	.	.	PUNCT
iajs-1842	48	1	∗	∗	NOUN
iajs-1842	48	2	∗	∗	NOUN
iajs-1842	48	3	sin	sin	NOUN
iajs-1842	48	4	∗	∗	NOUN
iajs-1842	48	5	…	…	PUNCT
iajs-1842	48	6	9	9	NUM
iajs-1842	48	7	.	.	PUNCT
iajs-1842	49	1	∗	∗	NOUN
iajs-1842	49	2	∗	∗	X
iajs-1842	49	3	1	1	NUM
iajs-1842	49	4	,	,	PUNCT
iajs-1842	49	5	∗	∗	NOUN
iajs-1842	49	6	…	…	PUNCT
iajs-1842	49	7	(	(	PUNCT
iajs-1842	49	8	10	10	NUM
iajs-1842	49	9	)	)	PUNCT
iajs-1842	49	10	.	.	PUNCT
iajs-1842	50	1	∗	∗	NOUN
iajs-1842	50	2	∗	∗	NOUN
iajs-1842	50	3	∗	∗	NOUN
iajs-1842	50	4	…	…	PUNCT
iajs-1842	50	5	(	(	PUNCT
iajs-1842	50	6	11	11	NUM
iajs-1842	50	7	)	)	PUNCT
iajs-1842	50	8	the	the	DET
iajs-1842	50	9	exact	exact	ADJ
iajs-1842	50	10	solution	solution	NOUN
iajs-1842	50	11	of	of	ADP
iajs-1842	50	12	this	this	DET
iajs-1842	50	13	system	system	NOUN
iajs-1842	50	14	is	be	AUX
iajs-1842	50	15	,	,	PUNCT
iajs-1842	50	16	[	[	X
iajs-1842	50	17	8	8	NUM
iajs-1842	50	18	]	]	SYM
iajs-1842	50	19	:	:	PUNCT
iajs-1842	50	20	∗	∗	NOUN
iajs-1842	50	21	∗	∗	NOUN
iajs-1842	50	22	,	,	PUNCT
iajs-1842	50	23	∗	∗	NOUN
iajs-1842	50	24	∗	∗	NOUN
iajs-1842	50	25	,	,	PUNCT
iajs-1842	50	26	∗	∗	NOUN
iajs-1842	50	27	∗	∗	NOUN
iajs-1842	50	28	.	.	PUNCT
iajs-1842	51	1	and	and	CCONJ
iajs-1842	51	2	∗	∗	NOUN
iajs-1842	51	3	.	.	PUNCT
iajs-1842	52	1	∗	∗	NOUN
iajs-1842	52	2	/	/	SYM
iajs-1842	52	3	∗	∗	NOUN
iajs-1842	52	4	∗	∗	NOUN
iajs-1842	52	5	∗	∗	NOUN
iajs-1842	52	6	∗	∗	NOUN
iajs-1842	52	7	,	,	PUNCT
iajs-1842	52	8	https://doi.org/10.30526/31.1.1842	https://doi.org/10.30526/31.1.1842	PROPN
iajs-1842	52	9	mathematics	mathematics	PROPN
iajs-1842	52	10	|	|	ADV
iajs-1842	53	1	227	227	NUM
iajs-1842	53	2	2018)عام	2018)عام	NUM
iajs-1842	53	3	1العدد	1العدد	NUM
iajs-1842	53	4	(	(	PUNCT
iajs-1842	53	5	31لمجلد	31لمجلد	NUM
iajs-1842	53	6	ا	ا	INTJ
iajs-1842	53	7	مجلة	مجلة	NOUN
iajs-1842	53	8	إبن	إبن	VERB
iajs-1842	53	9	الهيثم	الهيثم	ADJ
iajs-1842	53	10	للعلوم	للعلوم	NOUN
iajs-1842	53	11	الصرفة	الصرفة	NOUN
iajs-1842	53	12	والتطبيقية	والتطبيقية	VERB
iajs-1842	53	13	ibn	ibn	PROPN
iajs-1842	53	14	al	al	PROPN
iajs-1842	53	15	-	-	PUNCT
iajs-1842	53	16	haitham	haitham	PROPN
iajs-1842	53	17	jour	jour	X
iajs-1842	53	18	.	.	PROPN
iajs-1842	54	1	for	for	ADP
iajs-1842	54	2	pure	pure	ADJ
iajs-1842	54	3	&	&	CCONJ
iajs-1842	54	4	appl	appl	PROPN
iajs-1842	54	5	.	.	PUNCT
iajs-1842	55	1	sci	sci	PROPN
iajs-1842	55	2	.	.	PUNCT
iajs-1842	55	3	vol	vol	NOUN
iajs-1842	55	4	.	.	PROPN
iajs-1842	56	1	31	31	NUM
iajs-1842	56	2	(	(	PUNCT
iajs-1842	56	3	1	1	NUM
iajs-1842	56	4	)	)	PUNCT
iajs-1842	56	5	2018	2018	NUM
iajs-1842	56	6	∗	∗	NOUN
iajs-1842	56	7	.	.	PUNCT
iajs-1842	57	1	∗	∗	NOUN
iajs-1842	57	2	/	/	SYM
iajs-1842	57	3	∗	∗	NOUN
iajs-1842	57	4	∗	∗	NOUN
iajs-1842	57	5	,	,	PUNCT
iajs-1842	57	6	∗	∗	NOUN
iajs-1842	57	7	.	.	PUNCT
iajs-1842	58	1	∗	∗	NOUN
iajs-1842	58	2	/	/	SYM
iajs-1842	58	3	∗	∗	NOUN
iajs-1842	58	4	∗	∗	NOUN
iajs-1842	58	5	∗	∗	NOUN
iajs-1842	58	6	.	.	PUNCT
iajs-1842	59	1	let	let	VERB
iajs-1842	59	2	∆	∆	PROPN
iajs-1842	59	3	be	be	AUX
iajs-1842	59	4	the	the	DET
iajs-1842	59	5	partition	partition	NOUN
iajs-1842	59	6	,	,	PUNCT
iajs-1842	59	7	∆	∆	PROPN
iajs-1842	59	8	0	0	NUM
iajs-1842	60	1	∗	∗	NOUN
iajs-1842	60	2	∗	∗	NOUN
iajs-1842	60	3	∗	∗	NOUN
iajs-1842	60	4	∗	∗	NOUN
iajs-1842	60	5	∗	∗	NOUN
iajs-1842	60	6	∗	∗	NOUN
iajs-1842	60	7	1	1	NUM
iajs-1842	60	8	.	.	PUNCT
iajs-1842	61	1	where	where	SCONJ
iajs-1842	61	2	0.2,then	0.2,then	PRON
iajs-1842	61	3	∗	∗	NOUN
iajs-1842	61	4	0	0	NUM
iajs-1842	61	5	,	,	PUNCT
iajs-1842	61	6	∗	∗	NOUN
iajs-1842	61	7	0.2	0.2	NUM
iajs-1842	61	8	,	,	PUNCT
iajs-1842	61	9	∗	∗	NOUN
iajs-1842	61	10	0.4	0.4	NUM
iajs-1842	61	11	,	,	PUNCT
iajs-1842	61	12	∗	∗	NOUN
iajs-1842	61	13	0.6	0.6	NUM
iajs-1842	61	14	,	,	PUNCT
iajs-1842	61	15	∗	∗	VERB
iajs-1842	61	16	0.8	0.8	NUM
iajs-1842	61	17	,	,	PUNCT
iajs-1842	61	18	∗	∗	NOUN
iajs-1842	61	19	1	1	NUM
iajs-1842	61	20	.	.	PUNCT
iajs-1842	61	21	applying	apply	VERB
iajs-1842	61	22	the	the	DET
iajs-1842	61	23	generalized	generalize	VERB
iajs-1842	61	24	spline	spline	NOUN
iajs-1842	61	25	function	function	NOUN
iajs-1842	61	26	to	to	ADP
iajs-1842	61	27	the	the	DET
iajs-1842	61	28	fractional	fractional	ADJ
iajs-1842	61	29	integro	integro	ADJ
iajs-1842	61	30	-	-	PUNCT
iajs-1842	61	31	differential	differential	NOUN
iajs-1842	61	32	equation	equation	NOUN
iajs-1842	61	33	(	(	PUNCT
iajs-1842	61	34	9	9	NUM
iajs-1842	61	35	)	)	PUNCT
iajs-1842	61	36	,	,	PUNCT
iajs-1842	61	37	(	(	PUNCT
iajs-1842	61	38	10	10	NUM
iajs-1842	61	39	)	)	PUNCT
iajs-1842	61	40	and	and	CCONJ
iajs-1842	61	41	(	(	PUNCT
iajs-1842	61	42	11	11	NUM
iajs-1842	61	43	)	)	PUNCT
iajs-1842	61	44	let	let	VERB
iajs-1842	61	45	∗	∗	NOUN
iajs-1842	61	46	13	13	NUM
iajs-1842	61	47	36	36	NUM
iajs-1842	61	48	,	,	PUNCT
iajs-1842	61	49	with	with	ADP
iajs-1842	61	50	basic	basic	ADJ
iajs-1842	61	51	functions	function	NOUN
iajs-1842	61	52	:	:	PUNCT
iajs-1842	61	53	∗	∗	NOUN
iajs-1842	61	54	∗	∗	NOUN
iajs-1842	61	55	,	,	PUNCT
iajs-1842	61	56	∗	∗	NOUN
iajs-1842	61	57	∗	∗	NOUN
iajs-1842	61	58	,	,	PUNCT
iajs-1842	61	59	∗	∗	NOUN
iajs-1842	61	60	∗	∗	NOUN
iajs-1842	61	61	,	,	PUNCT
iajs-1842	61	62	∗	∗	NOUN
iajs-1842	61	63	∗	∗	NOUN
iajs-1842	61	64	by	by	ADP
iajs-1842	61	65	equation	equation	NOUN
iajs-1842	61	66	(	(	PUNCT
iajs-1842	61	67	4	4	NUM
iajs-1842	61	68	)	)	PUNCT
iajs-1842	61	69	,	,	PUNCT
iajs-1842	61	70	let	let	VERB
iajs-1842	61	71	∗	∗	NOUN
iajs-1842	61	72	will	will	AUX
iajs-1842	61	73	approximate	approximate	VERB
iajs-1842	61	74	by	by	ADP
iajs-1842	61	75	∗	∗	NOUN
iajs-1842	61	76	,	,	PUNCT
iajs-1842	61	77	where	where	SCONJ
iajs-1842	61	78	∗	∗	NOUN
iajs-1842	61	79	∗	∗	NOUN
iajs-1842	61	80	∗	∗	NOUN
iajs-1842	61	81	∗	∗	NOUN
iajs-1842	61	82	∗	∗	NOUN
iajs-1842	61	83	…	…	PUNCT
iajs-1842	61	84	12	12	NUM
iajs-1842	61	85	and	and	CCONJ
iajs-1842	61	86	∗	∗	NOUN
iajs-1842	61	87	will	will	AUX
iajs-1842	61	88	approximate	approximate	VERB
iajs-1842	61	89	by	by	ADP
iajs-1842	61	90	∗	∗	NOUN
iajs-1842	61	91	,	,	PUNCT
iajs-1842	61	92	where	where	SCONJ
iajs-1842	61	93	∗	∗	NOUN
iajs-1842	61	94	∗	∗	NOUN
iajs-1842	61	95	∗	∗	NOUN
iajs-1842	61	96	∗	∗	NOUN
iajs-1842	61	97	∗	∗	NOUN
iajs-1842	61	98	…	…	PUNCT
iajs-1842	61	99	13	13	NUM
iajs-1842	61	100	and	and	CCONJ
iajs-1842	61	101	∗	∗	NOUN
iajs-1842	61	102	will	will	AUX
iajs-1842	61	103	approximate	approximate	VERB
iajs-1842	61	104	by	by	ADP
iajs-1842	61	105	∗	∗	NOUN
iajs-1842	61	106	,	,	PUNCT
iajs-1842	61	107	where	where	SCONJ
iajs-1842	61	108	∗	∗	NOUN
iajs-1842	61	109	∗	∗	NOUN
iajs-1842	61	110	∗	∗	NOUN
iajs-1842	61	111	∗	∗	NOUN
iajs-1842	61	112	∗	∗	NOUN
iajs-1842	61	113	…	…	PUNCT
iajs-1842	61	114	14	14	NUM
iajs-1842	61	115	to	to	PART
iajs-1842	61	116	find	find	VERB
iajs-1842	61	117	the	the	DET
iajs-1842	61	118	unknown	unknown	ADJ
iajs-1842	61	119	coefficients	coefficient	NOUN
iajs-1842	61	120	,	,	PUNCT
iajs-1842	61	121	1,2,3	1,2,3	NUM
iajs-1842	61	122	1,2,3,4	1,2,3,4	NUM
iajs-1842	61	123	twelve	twelve	NUM
iajs-1842	61	124	algebraic	algebraic	ADJ
iajs-1842	61	125	equations	equation	NOUN
iajs-1842	61	126	are	be	AUX
iajs-1842	61	127	needed	need	VERB
iajs-1842	61	128	.	.	PUNCT
iajs-1842	62	1	substituting	substitute	VERB
iajs-1842	62	2	equation	equation	NOUN
iajs-1842	62	3	(	(	PUNCT
iajs-1842	62	4	12	12	NUM
iajs-1842	62	5	)	)	PUNCT
iajs-1842	62	6	,	,	PUNCT
iajs-1842	62	7	(	(	PUNCT
iajs-1842	62	8	13	13	NUM
iajs-1842	62	9	)	)	PUNCT
iajs-1842	62	10	and	and	CCONJ
iajs-1842	62	11	(	(	PUNCT
iajs-1842	62	12	14	14	NUM
iajs-1842	62	13	)	)	PUNCT
iajs-1842	62	14	in	in	ADP
iajs-1842	62	15	the	the	DET
iajs-1842	62	16	initial	initial	ADJ
iajs-1842	62	17	conditions	condition	NOUN
iajs-1842	62	18	0	0	NUM
iajs-1842	62	19	0	0	NUM
iajs-1842	62	20	,	,	PUNCT
iajs-1842	62	21	0	0	NUM
iajs-1842	62	22	0	0	NUM
iajs-1842	62	23	0	0	NUM
iajs-1842	62	24	0	0	NUM
iajs-1842	62	25	,	,	PUNCT
iajs-1842	62	26	respectively	respectively	ADV
iajs-1842	62	27	,	,	PUNCT
iajs-1842	62	28	yield	yield	NOUN
iajs-1842	62	29	:	:	PUNCT
iajs-1842	62	30	0	0	NUM
iajs-1842	62	31	…	…	PUNCT
iajs-1842	62	32	(	(	PUNCT
iajs-1842	62	33	15	15	NUM
iajs-1842	62	34	)	)	PUNCT
iajs-1842	62	35	0	0	NUM
iajs-1842	63	1	…	…	PUNCT
iajs-1842	63	2	(	(	PUNCT
iajs-1842	63	3	16	16	NUM
iajs-1842	63	4	)	)	PUNCT
iajs-1842	63	5	0	0	NUM
iajs-1842	64	1	…	…	PUNCT
iajs-1842	64	2	(	(	PUNCT
iajs-1842	64	3	17	17	NUM
iajs-1842	64	4	)	)	PUNCT
iajs-1842	64	5	now	now	ADV
iajs-1842	64	6	,	,	PUNCT
iajs-1842	64	7	substituting	substitute	VERB
iajs-1842	64	8	equation	equation	NOUN
iajs-1842	64	9	(	(	PUNCT
iajs-1842	64	10	12	12	NUM
iajs-1842	64	11	)	)	PUNCT
iajs-1842	64	12	,	,	PUNCT
iajs-1842	64	13	(	(	PUNCT
iajs-1842	64	14	13	13	NUM
iajs-1842	64	15	)	)	PUNCT
iajs-1842	64	16	and	and	CCONJ
iajs-1842	64	17	(	(	PUNCT
iajs-1842	64	18	14	14	NUM
iajs-1842	64	19	)	)	PUNCT
iajs-1842	64	20	in	in	ADP
iajs-1842	64	21	equation	equation	NOUN
iajs-1842	64	22	(	(	PUNCT
iajs-1842	64	23	9	9	NUM
iajs-1842	64	24	)	)	PUNCT
iajs-1842	64	25	,	,	PUNCT
iajs-1842	64	26	(	(	PUNCT
iajs-1842	64	27	10	10	NUM
iajs-1842	64	28	)	)	PUNCT
iajs-1842	64	29	and	and	CCONJ
iajs-1842	64	30	(	(	PUNCT
iajs-1842	64	31	11	11	NUM
iajs-1842	64	32	)	)	PUNCT
iajs-1842	64	33	respectively	respectively	ADV
iajs-1842	64	34	,	,	PUNCT
iajs-1842	64	35	get	get	VERB
iajs-1842	64	36	:	:	PUNCT
iajs-1842	64	37	.	.	PUNCT
iajs-1842	65	1	∗	∗	NOUN
iajs-1842	65	2	∗	∗	NOUN
iajs-1842	65	3	∗	∗	NOUN
iajs-1842	65	4	∗	∗	NOUN
iajs-1842	65	5	∗	∗	NOUN
iajs-1842	65	6	∗	∗	NOUN
iajs-1842	65	7	…	…	PUNCT
iajs-1842	65	8	18	18	NUM
iajs-1842	65	9	.	.	PUNCT
iajs-1842	66	1	∗	∗	NOUN
iajs-1842	66	2	∗	∗	NOUN
iajs-1842	66	3	∗	∗	NOUN
iajs-1842	66	4	∗	∗	NOUN
iajs-1842	66	5	1	1	NUM
iajs-1842	66	6	3	3	NUM
iajs-1842	66	7	4	4	NUM
iajs-1842	66	8	∗	∗	NOUN
iajs-1842	66	9	∗	∗	NOUN
iajs-1842	66	10	…	…	PUNCT
iajs-1842	66	11	19	19	NUM
iajs-1842	66	12	https://doi.org/10.30526/31.1.1842	https://doi.org/10.30526/31.1.1842	NOUN
iajs-1842	66	13	mathematics	mathematic	NOUN
iajs-1842	66	14	|	|	ADV
iajs-1842	67	1	228	228	NUM
iajs-1842	67	2	2018)عام	2018)عام	NUM
iajs-1842	67	3	1العدد	1العدد	NUM
iajs-1842	67	4	(	(	PUNCT
iajs-1842	67	5	31لمجلد	31لمجلد	NUM
iajs-1842	67	6	ا	ا	INTJ
iajs-1842	67	7	مجلة	مجلة	NOUN
iajs-1842	67	8	إبن	إبن	VERB
iajs-1842	67	9	الهيثم	الهيثم	ADJ
iajs-1842	67	10	للعلوم	للعلوم	NOUN
iajs-1842	67	11	الصرفة	الصرفة	NOUN
iajs-1842	67	12	والتطبيقية	والتطبيقية	VERB
iajs-1842	67	13	ibn	ibn	PROPN
iajs-1842	67	14	al	al	PROPN
iajs-1842	67	15	-	-	PUNCT
iajs-1842	67	16	haitham	haitham	PROPN
iajs-1842	67	17	jour	jour	X
iajs-1842	67	18	.	.	PROPN
iajs-1842	68	1	for	for	ADP
iajs-1842	68	2	pure	pure	ADJ
iajs-1842	68	3	&	&	CCONJ
iajs-1842	68	4	appl	appl	PROPN
iajs-1842	68	5	.	.	PUNCT
iajs-1842	69	1	sci	sci	PROPN
iajs-1842	69	2	.	.	PUNCT
iajs-1842	69	3	vol	vol	NOUN
iajs-1842	69	4	.	.	PROPN
iajs-1842	70	1	31	31	NUM
iajs-1842	70	2	(	(	PUNCT
iajs-1842	70	3	1	1	NUM
iajs-1842	70	4	)	)	PUNCT
iajs-1842	70	5	2018	2018	NUM
iajs-1842	70	6	.	.	PUNCT
iajs-1842	71	1	∗	∗	NOUN
iajs-1842	71	2	∗	∗	NOUN
iajs-1842	71	3	∗	∗	NOUN
iajs-1842	71	4	∗	∗	NOUN
iajs-1842	71	5	∗	∗	NOUN
iajs-1842	71	6	∗	∗	NOUN
iajs-1842	71	7	…	…	PUNCT
iajs-1842	71	8	20	20	NUM
iajs-1842	71	9	where	where	SCONJ
iajs-1842	71	10	∗	∗	NOUN
iajs-1842	71	11	.	.	PUNCT
iajs-1842	72	1	∗	∗	NOUN
iajs-1842	72	2	/	/	SYM
iajs-1842	72	3	∗	∗	NOUN
iajs-1842	72	4	∗	∗	NOUN
iajs-1842	72	5	∗	∗	NOUN
iajs-1842	72	6	∗	∗	NOUN
iajs-1842	72	7	∗	∗	NOUN
iajs-1842	72	8	.	.	PUNCT
iajs-1842	73	1	∗	∗	NOUN
iajs-1842	73	2	/	/	SYM
iajs-1842	73	3	∗	∗	NOUN
iajs-1842	73	4	∗	∗	NOUN
iajs-1842	73	5	∗	∗	NOUN
iajs-1842	73	6	.	.	PUNCT
iajs-1842	74	1	∗	∗	NOUN
iajs-1842	74	2	/	/	SYM
iajs-1842	74	3	∗	∗	NOUN
iajs-1842	74	4	∗	∗	NOUN
iajs-1842	74	5	∗	∗	NOUN
iajs-1842	74	6	.	.	PUNCT
iajs-1842	75	1	then	then	ADV
iajs-1842	75	2	by	by	ADP
iajs-1842	75	3	solving	solve	VERB
iajs-1842	75	4	the	the	DET
iajs-1842	75	5	system	system	NOUN
iajs-1842	75	6	:	:	PUNCT
iajs-1842	75	7	…	…	PUNCT
iajs-1842	75	8	21	21	NUM
iajs-1842	75	9	where	where	SCONJ
iajs-1842	75	10	is	be	AUX
iajs-1842	75	11	constant	constant	ADJ
iajs-1842	75	12	matrix	matrix	NOUN
iajs-1842	75	13	and	and	CCONJ
iajs-1842	75	14	:	:	PUNCT
iajs-1842	75	15	0	0	NUM
iajs-1842	75	16	0	0	NUM
iajs-1842	75	17	0	0	NUM
iajs-1842	75	18	∗	∗	NOUN
iajs-1842	75	19	∗	∗	NOUN
iajs-1842	75	20	∗	∗	NOUN
iajs-1842	75	21	…	…	PUNCT
iajs-1842	75	22	∗	∗	NOUN
iajs-1842	75	23	∗	∗	NOUN
iajs-1842	75	24	∗	∗	NOUN
iajs-1842	75	25	finally	finally	ADV
iajs-1842	75	26	,	,	PUNCT
iajs-1842	75	27	gauss	gauss	ADJ
iajs-1842	75	28	elimination	elimination	NOUN
iajs-1842	75	29	method	method	NOUN
iajs-1842	75	30	may	may	AUX
iajs-1842	75	31	be	be	AUX
iajs-1842	75	32	used	use	VERB
iajs-1842	75	33	to	to	PART
iajs-1842	75	34	solve	solve	VERB
iajs-1842	75	35	system	system	NOUN
iajs-1842	75	36	(	(	PUNCT
iajs-1842	75	37	21	21	NUM
iajs-1842	75	38	)	)	PUNCT
iajs-1842	75	39	to	to	PART
iajs-1842	75	40	find	find	VERB
iajs-1842	75	41	0.067	0.067	NUM
iajs-1842	75	42	,	,	PUNCT
iajs-1842	75	43	0.221	0.221	NUM
iajs-1842	75	44	,	,	PUNCT
iajs-1842	75	45	0.314	0.314	NUM
iajs-1842	75	46	,	,	PUNCT
iajs-1842	75	47	0.023	0.023	NUM
iajs-1842	75	48	,	,	PUNCT
iajs-1842	75	49	0.036	0.036	NUM
iajs-1842	75	50	,	,	PUNCT
iajs-1842	75	51	0.743	0.743	NUM
iajs-1842	75	52	,	,	PUNCT
iajs-1842	75	53	0.205	0.205	NUM
iajs-1842	75	54	,	,	PUNCT
iajs-1842	75	55	0.913	0.913	NUM
iajs-1842	75	56	,	,	PUNCT
iajs-1842	75	57	0.05	0.05	NUM
iajs-1842	75	58	,	,	PUNCT
iajs-1842	75	59	0.952	0.952	NUM
iajs-1842	75	60	,	,	PUNCT
iajs-1842	75	61	0.04	0.04	NUM
iajs-1842	75	62	,	,	PUNCT
iajs-1842	75	63	1.031	1.031	NUM
iajs-1842	75	64	so	so	SCONJ
iajs-1842	75	65	the	the	DET
iajs-1842	75	66	approximate	approximate	ADJ
iajs-1842	75	67	solutions	solution	NOUN
iajs-1842	75	68	:	:	PUNCT
iajs-1842	75	69	∗	∗	NOUN
iajs-1842	75	70	0.067	0.067	NUM
iajs-1842	75	71	∗	∗	NOUN
iajs-1842	75	72	0.221	0.221	NUM
iajs-1842	75	73	∗	∗	NOUN
iajs-1842	76	1	0.314	0.314	NUM
iajs-1842	76	2	∗	∗	NOUN
iajs-1842	76	3	0.023	0.023	NUM
iajs-1842	76	4	∗	∗	NOUN
iajs-1842	76	5	∗	∗	NOUN
iajs-1842	76	6	0.036	0.036	NUM
iajs-1842	76	7	∗	∗	NOUN
iajs-1842	76	8	0.743	0.743	NUM
iajs-1842	76	9	∗	∗	NOUN
iajs-1842	76	10	0.205	0.205	NUM
iajs-1842	76	11	∗	∗	NOUN
iajs-1842	76	12	0.913	0.913	NUM
iajs-1842	76	13	∗	∗	NOUN
iajs-1842	76	14	∗	∗	NOUN
iajs-1842	76	15	0.05	0.05	NUM
iajs-1842	76	16	∗	∗	NOUN
iajs-1842	76	17	0.952	0.952	NUM
iajs-1842	76	18	∗	∗	NOUN
iajs-1842	76	19	0.04	0.04	NUM
iajs-1842	76	20	∗	∗	NOUN
iajs-1842	76	21	1.013	1.013	NUM
iajs-1842	76	22	∗	∗	NOUN
iajs-1842	76	23	.	.	PUNCT
iajs-1842	77	1	table	table	NOUN
iajs-1842	77	2	(	(	PUNCT
iajs-1842	77	3	1	1	NUM
iajs-1842	77	4	)	)	PUNCT
iajs-1842	77	5	,	,	PUNCT
iajs-1842	77	6	presents	present	VERB
iajs-1842	77	7	a	a	DET
iajs-1842	77	8	comparison	comparison	NOUN
iajs-1842	77	9	between	between	ADP
iajs-1842	77	10	the	the	DET
iajs-1842	77	11	exact	exact	ADJ
iajs-1842	77	12	and	and	CCONJ
iajs-1842	77	13	numerical	numerical	ADJ
iajs-1842	77	14	solution	solution	NOUN
iajs-1842	77	15	and	and	CCONJ
iajs-1842	77	16	gives	give	VERB
iajs-1842	77	17	the	the	DET
iajs-1842	77	18	least	least	ADJ
iajs-1842	77	19	square	square	ADJ
iajs-1842	77	20	error	error	NOUN
iajs-1842	77	21	https://doi.org/10.30526/31.1.1842	https://doi.org/10.30526/31.1.1842	NOUN
iajs-1842	77	22	mathematics	mathematic	NOUN
iajs-1842	78	1	|	|	ADV
iajs-1842	78	2	229	229	NUM
iajs-1842	78	3	2018)عام	2018)عام	NUM
iajs-1842	78	4	1العدد	1العدد	NUM
iajs-1842	79	1	(	(	PUNCT
iajs-1842	79	2	31لمجلد	31لمجلد	NUM
iajs-1842	79	3	ا	ا	INTJ
iajs-1842	79	4	مجلة	مجلة	NOUN
iajs-1842	79	5	إبن	إبن	VERB
iajs-1842	79	6	الهيثم	الهيثم	ADJ
iajs-1842	79	7	للعلوم	للعلوم	NOUN
iajs-1842	79	8	الصرفة	الصرفة	NOUN
iajs-1842	79	9	والتطبيقية	والتطبيقية	VERB
iajs-1842	79	10	ibn	ibn	PROPN
iajs-1842	79	11	al	al	PROPN
iajs-1842	79	12	-	-	PUNCT
iajs-1842	79	13	haitham	haitham	PROPN
iajs-1842	79	14	jour	jour	X
iajs-1842	79	15	.	.	PROPN
iajs-1842	80	1	for	for	ADP
iajs-1842	80	2	pure	pure	ADJ
iajs-1842	80	3	&	&	CCONJ
iajs-1842	80	4	appl	appl	PROPN
iajs-1842	80	5	.	.	PUNCT
iajs-1842	81	1	sci	sci	PROPN
iajs-1842	81	2	.	.	PUNCT
iajs-1842	81	3	vol	vol	NOUN
iajs-1842	81	4	.	.	PROPN
iajs-1842	82	1	31	31	NUM
iajs-1842	82	2	(	(	PUNCT
iajs-1842	82	3	1	1	NUM
iajs-1842	82	4	)	)	SYM
iajs-1842	82	5	2018	2018	NUM
iajs-1842	82	6	table	table	NOUN
iajs-1842	82	7	(	(	PUNCT
iajs-1842	82	8	1	1	NUM
iajs-1842	82	9	):	):	PUNCT
iajs-1842	82	10	numerical	numerical	ADJ
iajs-1842	82	11	results	result	NOUN
iajs-1842	82	12	of	of	ADP
iajs-1842	82	13	the	the	DET
iajs-1842	82	14	illustrative	illustrative	ADJ
iajs-1842	82	15	example	example	NOUN
iajs-1842	82	16	above	above	ADP
iajs-1842	82	17	:	:	PUNCT
iajs-1842	82	18	w	w	X
iajs-1842	83	1	|	|	ADV
iajs-1842	83	2	|	|	ADV
iajs-1842	83	3	|	|	INTJ
iajs-1842	84	1	|	|	INTJ
iajs-1842	84	2	|	|	ADV
iajs-1842	85	1	|	|	ADV
iajs-1842	85	2	0	0	NUM
iajs-1842	85	3	3	3	NUM
iajs-1842	85	4	10	10	NUM
iajs-1842	85	5	9	9	NUM
iajs-1842	85	6	10	10	NUM
iajs-1842	85	7	1	1	NUM
iajs-1842	85	8	10	10	NUM
iajs-1842	85	9	0.1	0.1	NUM
iajs-1842	85	10	0.011	0.011	NUM
iajs-1842	85	11	8.218	8.218	NUM
iajs-1842	85	12	10	10	NUM
iajs-1842	85	13	0.037	0.037	NUM
iajs-1842	85	14	0.2	0.2	NUM
iajs-1842	85	15	9.646	9.646	NUM
iajs-1842	85	16	10	10	NUM
iajs-1842	85	17	0.014	0.014	NUM
iajs-1842	85	18	0.044	0.044	NUM
iajs-1842	85	19	0.3	0.3	NUM
iajs-1842	85	20	4.877	4.877	NUM
iajs-1842	85	21	10	10	NUM
iajs-1842	85	22	0.021	0.021	NUM
iajs-1842	85	23	0.035	0.035	NUM
iajs-1842	85	24	0.4	0.4	NUM
iajs-1842	85	25	5.265	5.265	NUM
iajs-1842	85	26	10	10	NUM
iajs-1842	85	27	0.023	0.023	NUM
iajs-1842	85	28	0.019	0.019	NUM
iajs-1842	85	29	0.5	0.5	NUM
iajs-1842	85	30	4.506	4.506	NUM
iajs-1842	85	31	10	10	NUM
iajs-1842	85	32	0.021	0.021	NUM
iajs-1842	85	33	3.865	3.865	NUM
iajs-1842	85	34	10	10	NUM
iajs-1842	85	35	0.6	0.6	NUM
iajs-1842	85	36	6.268	6.268	NUM
iajs-1842	85	37	10	10	NUM
iajs-1842	85	38	0.011	0.011	NUM
iajs-1842	85	39	5.624	5.624	NUM
iajs-1842	85	40	10	10	NUM
iajs-1842	85	41	0.7	0.7	NUM
iajs-1842	85	42	6.535	6.535	NUM
iajs-1842	85	43	10	10	NUM
iajs-1842	85	44	5.162	5.162	NUM
iajs-1842	85	45	10	10	NUM
iajs-1842	85	46	8.192	8.192	NUM
iajs-1842	85	47	10	10	NUM
iajs-1842	85	48	0.8	0.8	NUM
iajs-1842	85	49	7.993	7.993	NUM
iajs-1842	85	50	10	10	NUM
iajs-1842	85	51	0.028	0.028	NUM
iajs-1842	85	52	5.257	5.257	NUM
iajs-1842	85	53	10	10	NUM
iajs-1842	85	54	0.9	0.9	NUM
iajs-1842	85	55	0.016	0.016	NUM
iajs-1842	85	56	0.058	0.058	NUM
iajs-1842	85	57	1.732	1.732	NUM
iajs-1842	85	58	10	10	NUM
iajs-1842	85	59	1	1	NUM
iajs-1842	85	60	0.04	0.04	NUM
iajs-1842	85	61	0.094	0.094	NUM
iajs-1842	85	62	6.85	6.85	NUM
iajs-1842	85	63	10	10	NUM
iajs-1842	85	64	lse	lse	NOUN
iajs-1842	85	65	25	25	NUM
iajs-1842	85	66	10	10	NUM
iajs-1842	85	67	2.665	2.665	NUM
iajs-1842	85	68	10	10	NUM
iajs-1842	85	69	1	1	NUM
iajs-1842	85	70	10	10	NUM
iajs-1842	85	71	to	to	PART
iajs-1842	85	72	show	show	VERB
iajs-1842	85	73	the	the	DET
iajs-1842	85	74	implementation	implementation	NOUN
iajs-1842	85	75	of	of	ADP
iajs-1842	85	76	the	the	DET
iajs-1842	85	77	method	method	ADJ
iajs-1842	85	78	figure	figure	NOUN
iajs-1842	85	79	(	(	PUNCT
iajs-1842	85	80	1	1	NUM
iajs-1842	85	81	)	)	PUNCT
iajs-1842	85	82	is	be	AUX
iajs-1842	85	83	given	give	VERB
iajs-1842	85	84	the	the	DET
iajs-1842	85	85	approximate	approximate	ADJ
iajs-1842	85	86	solution	solution	NOUN
iajs-1842	85	87	of	of	ADP
iajs-1842	85	88	the	the	DET
iajs-1842	85	89	system	system	NOUN
iajs-1842	85	90	of	of	ADP
iajs-1842	85	91	fractional	fractional	ADJ
iajs-1842	85	92	integro	integro	ADJ
iajs-1842	85	93	-	-	PUNCT
iajs-1842	85	94	differential	differential	NOUN
iajs-1842	85	95	equation	equation	NOUN
iajs-1842	85	96	.	.	PUNCT
iajs-1842	86	1	figure	figure	NOUN
iajs-1842	86	2	(	(	PUNCT
iajs-1842	86	3	1	1	NUM
iajs-1842	86	4	):	):	PUNCT
iajs-1842	86	5	exact	exact	ADJ
iajs-1842	86	6	and	and	CCONJ
iajs-1842	86	7	approximate	approximate	ADJ
iajs-1842	86	8	solution	solution	NOUN
iajs-1842	86	9	of	of	ADP
iajs-1842	86	10	the	the	DET
iajs-1842	86	11	illustrative	illustrative	ADJ
iajs-1842	86	12	example	example	NOUN
iajs-1842	86	13	conclusions	conclusion	NOUN
iajs-1842	86	14	in	in	ADP
iajs-1842	86	15	this	this	DET
iajs-1842	86	16	paper	paper	NOUN
iajs-1842	86	17	,	,	PUNCT
iajs-1842	86	18	the	the	DET
iajs-1842	86	19	application	application	NOUN
iajs-1842	86	20	of	of	ADP
iajs-1842	86	21	generalized	generalized	ADJ
iajs-1842	86	22	spline	spline	NOUN
iajs-1842	86	23	functions	function	NOUN
iajs-1842	86	24	investigated	investigate	VERB
iajs-1842	86	25	to	to	PART
iajs-1842	86	26	obtain	obtain	VERB
iajs-1842	86	27	approximate	approximate	ADJ
iajs-1842	86	28	solution	solution	NOUN
iajs-1842	86	29	of	of	ADP
iajs-1842	86	30	system	system	NOUN
iajs-1842	86	31	of	of	ADP
iajs-1842	86	32	linear	linear	ADJ
iajs-1842	86	33	fractional	fractional	ADJ
iajs-1842	86	34	integro	integro	ADJ
iajs-1842	86	35	-	-	PUNCT
iajs-1842	86	36	differential	differential	NOUN
iajs-1842	86	37	equations	equation	NOUN
iajs-1842	86	38	and	and	CCONJ
iajs-1842	86	39	we	we	PRON
iajs-1842	86	40	give	give	VERB
iajs-1842	86	41	illustrative	illustrative	ADJ
iajs-1842	86	42	example	example	NOUN
iajs-1842	86	43	with	with	ADP
iajs-1842	86	44	different	different	ADJ
iajs-1842	86	45	α	α	NOUN
iajs-1842	86	46	to	to	PART
iajs-1842	86	47	show	show	VERB
iajs-1842	86	48	this	this	DET
iajs-1842	86	49	approximation	approximation	NOUN
iajs-1842	86	50	.	.	PUNCT
iajs-1842	87	1	as	as	ADP
iajs-1842	87	2	a	a	DET
iajs-1842	87	3	comparison	comparison	NOUN
iajs-1842	87	4	with	with	ADP
iajs-1842	87	5	the	the	DET
iajs-1842	87	6	exact	exact	ADJ
iajs-1842	87	7	solution	solution	NOUN
iajs-1842	87	8	,	,	PUNCT
iajs-1842	87	9	table	table	NOUN
iajs-1842	87	10	(	(	PUNCT
iajs-1842	87	11	1	1	NUM
iajs-1842	87	12	)	)	PUNCT
iajs-1842	87	13	and	and	CCONJ
iajs-1842	87	14	figure	figure	NOUN
iajs-1842	87	15	(	(	PUNCT
iajs-1842	87	16	1	1	X
iajs-1842	87	17	)	)	PUNCT
iajs-1842	87	18	showed	show	VERB
iajs-1842	87	19	the	the	DET
iajs-1842	87	20	result	result	NOUN
iajs-1842	87	21	.	.	PUNCT
iajs-1842	88	1	0	0	NUM
iajs-1842	88	2	0.1	0.1	NUM
iajs-1842	88	3	0.2	0.2	NUM
iajs-1842	88	4	0.3	0.3	NUM
iajs-1842	88	5	0.4	0.4	NUM
iajs-1842	88	6	0.5	0.5	NUM
iajs-1842	88	7	0.6	0.6	NUM
iajs-1842	88	8	0.7	0.7	NUM
iajs-1842	88	9	0.8	0.8	NUM
iajs-1842	88	10	0.9	0.9	NUM
iajs-1842	88	11	1	1	NUM
iajs-1842	88	12	0	0	NUM
iajs-1842	88	13	0.5	0.5	NUM
iajs-1842	88	14	1	1	NUM
iajs-1842	88	15	s1	s1	PROPN
iajs-1842	88	16	z	z	PROPN
iajs-1842	88	17	(	(	PUNCT
iajs-1842	88	18	)	)	PUNCT
iajs-1842	88	19	y1	y1	NOUN
iajs-1842	88	20	z	z	NOUN
iajs-1842	88	21	(	(	PUNCT
iajs-1842	88	22	)	)	PUNCT
iajs-1842	88	23	s2	s2	PROPN
iajs-1842	88	24	z	z	PROPN
iajs-1842	88	25	(	(	PUNCT
iajs-1842	88	26	)	)	PUNCT
iajs-1842	88	27	y2	y2	PROPN
iajs-1842	89	1	z	z	NOUN
iajs-1842	89	2	(	(	PUNCT
iajs-1842	89	3	)	)	PUNCT
iajs-1842	89	4	s3	s3	PROPN
iajs-1842	89	5	z	z	PROPN
iajs-1842	89	6	(	(	PUNCT
iajs-1842	89	7	)	)	PUNCT
iajs-1842	89	8	y3	y3	PROPN
iajs-1842	89	9	z	z	PROPN
iajs-1842	89	10	(	(	PUNCT
iajs-1842	89	11	)	)	PUNCT
iajs-1842	89	12	z	z	NOUN
iajs-1842	89	13	https://doi.org/10.30526/31.1.1842	https://doi.org/10.30526/31.1.1842	NOUN
iajs-1842	89	14	mathematics	mathematic	NOUN
iajs-1842	89	15	|	|	ADV
iajs-1842	89	16	230	230	NUM
iajs-1842	89	17	2018)عام	2018)عام	NUM
iajs-1842	89	18	1العدد	1العدد	NUM
iajs-1842	89	19	(	(	PUNCT
iajs-1842	89	20	31لمجلد	31لمجلد	NUM
iajs-1842	89	21	ا	ا	INTJ
iajs-1842	89	22	مجلة	مجلة	NOUN
iajs-1842	89	23	إبن	إبن	VERB
iajs-1842	89	24	الهيثم	الهيثم	ADJ
iajs-1842	89	25	للعلوم	للعلوم	NOUN
iajs-1842	89	26	الصرفة	الصرفة	NOUN
iajs-1842	89	27	والتطبيقية	والتطبيقية	VERB
iajs-1842	89	28	ibn	ibn	PROPN
iajs-1842	89	29	al	al	PROPN
iajs-1842	89	30	-	-	PUNCT
iajs-1842	89	31	haitham	haitham	PROPN
iajs-1842	89	32	jour	jour	X
iajs-1842	89	33	.	.	PROPN
iajs-1842	90	1	for	for	ADP
iajs-1842	90	2	pure	pure	ADJ
iajs-1842	90	3	&	&	CCONJ
iajs-1842	90	4	appl	appl	PROPN
iajs-1842	90	5	.	.	PUNCT
iajs-1842	91	1	sci	sci	PROPN
iajs-1842	91	2	.	.	PUNCT
iajs-1842	91	3	vol	vol	NOUN
iajs-1842	91	4	.	.	PROPN
iajs-1842	92	1	31	31	NUM
iajs-1842	92	2	(	(	PUNCT
iajs-1842	92	3	1	1	NUM
iajs-1842	92	4	)	)	SYM
iajs-1842	92	5	2018	2018	NUM
iajs-1842	92	6	references	reference	NOUN
iajs-1842	92	7	[	[	X
iajs-1842	92	8	1	1	NUM
iajs-1842	92	9	]	]	PUNCT
iajs-1842	92	10	.	.	PUNCT
iajs-1842	93	1	jd	jd	PROPN
iajs-1842	93	2	.	.	PUNCT
iajs-1842	93	3	munkhammar,"fractional	munkhammar,"fractional	ADJ
iajs-1842	93	4	calculus	calculus	NOUN
iajs-1842	93	5	and	and	CCONJ
iajs-1842	93	6	the	the	DET
iajs-1842	93	7	taylor	taylor	PROPN
iajs-1842	93	8	-	-	PUNCT
iajs-1842	93	9	riemann	riemann	PROPN
iajs-1842	93	10	series	series	PROPN
iajs-1842	93	11	"	"	PUNCT
iajs-1842	93	12	,	,	PUNCT
iajs-1842	93	13	undergraduate	undergraduate	ADJ
iajs-1842	93	14	math	math	PROPN
iajs-1842	93	15	journal	journal	PROPN
iajs-1842	93	16	,	,	PUNCT
iajs-1842	93	17	2005	2005	NUM
iajs-1842	93	18	.	.	PUNCT
iajs-1842	94	1	[	[	X
iajs-1842	94	2	2	2	NUM
iajs-1842	94	3	]	]	PUNCT
iajs-1842	94	4	.	.	PUNCT
iajs-1842	94	5	a.	a.	PROPN
iajs-1842	94	6	arikoglu	arikoglu	PROPN
iajs-1842	94	7	,	,	PUNCT
iajs-1842	94	8	and	and	CCONJ
iajs-1842	94	9	i.	i.	PROPN
iajs-1842	94	10	ozko,"solution	ozko,"solution	PROPN
iajs-1842	94	11	of	of	ADP
iajs-1842	94	12	fractional	fractional	ADJ
iajs-1842	94	13	integro	integro	ADJ
iajs-1842	94	14	-	-	PUNCT
iajs-1842	94	15	differential	differential	NOUN
iajs-1842	94	16	equation	equation	NOUN
iajs-1842	94	17	by	by	ADP
iajs-1842	94	18	using	use	VERB
iajs-1842	94	19	fractional	fractional	ADJ
iajs-1842	94	20	differential	differential	ADJ
iajs-1842	94	21	transform	transform	NOUN
iajs-1842	94	22	method	method	NOUN
iajs-1842	94	23	"	"	PUNCT
iajs-1842	94	24	,	,	PUNCT
iajs-1842	94	25	choas	choas	NOUN
iajs-1842	94	26	,	,	PUNCT
iajs-1842	94	27	solution	solution	NOUN
iajs-1842	94	28	and	and	CCONJ
iajs-1842	94	29	fractals	fractal	NOUN
iajs-1842	94	30	,	,	PUNCT
iajs-1842	94	31	.5521	.5521	PROPN
iajs-1842	94	32	-	-	PUNCT
iajs-1842	94	33	529	529	NUM
iajs-1842	94	34	,	,	PUNCT
iajs-1842	94	35	2009	2009	NUM
iajs-1842	94	36	.	.	PUNCT
iajs-1842	95	1	[	[	X
iajs-1842	95	2	3	3	NUM
iajs-1842	95	3	]	]	PUNCT
iajs-1842	95	4	.	.	PUNCT
iajs-1842	96	1	i.	i.	PROPN
iajs-1842	96	2	podlobny	podlobny	PROPN
iajs-1842	96	3	,	,	PUNCT
iajs-1842	96	4	"	"	PUNCT
iajs-1842	96	5	fractional	fractional	ADJ
iajs-1842	96	6	differential	differential	ADJ
iajs-1842	96	7	equations	equation	NOUN
iajs-1842	96	8	:	:	PUNCT
iajs-1842	96	9	an	an	DET
iajs-1842	96	10	introduction	introduction	NOUN
iajs-1842	96	11	to	to	ADP
iajs-1842	96	12	fractional	fractional	ADJ
iajs-1842	96	13	derivatives	derivative	NOUN
iajs-1842	96	14	,	,	PUNCT
iajs-1842	96	15	fractional	fractional	ADJ
iajs-1842	96	16	differential	differential	ADJ
iajs-1842	96	17	equations	equation	NOUN
iajs-1842	96	18	,	,	PUNCT
iajs-1842	96	19	to	to	ADP
iajs-1842	96	20	methods	method	NOUN
iajs-1842	96	21	of	of	ADP
iajs-1842	96	22	their	their	PRON
iajs-1842	96	23	solution	solution	NOUN
iajs-1842	96	24	and	and	CCONJ
iajs-1842	96	25	some	some	PRON
iajs-1842	96	26	of	of	ADP
iajs-1842	96	27	their	their	PRON
iajs-1842	96	28	applications	application	NOUN
iajs-1842	96	29	"	"	PUNCT
iajs-1842	96	30	,	,	PUNCT
iajs-1842	96	31	network	network	NOUN
iajs-1842	96	32	;	;	PUNCT
iajs-1842	96	33	academic	academic	ADJ
iajs-1842	96	34	press	press	NOUN
iajs-1842	96	35	;	;	PUNCT
iajs-1842	96	36	1999	1999	NUM
iajs-1842	96	37	.	.	PUNCT
iajs-1842	97	1	[	[	X
iajs-1842	97	2	4	4	NUM
iajs-1842	97	3	]	]	PUNCT
iajs-1842	97	4	.	.	PUNCT
iajs-1842	98	1	j.h	j.h	PROPN
iajs-1842	98	2	.	.	PROPN
iajs-1842	98	3	ahlberge	ahlberge	PROPN
iajs-1842	98	4	;	;	PUNCT
iajs-1842	98	5	e.n	e.n	PROPN
iajs-1842	98	6	.	.	PROPN
iajs-1842	98	7	nilson	nilson	PROPN
iajs-1842	98	8	,	,	PUNCT
iajs-1842	98	9	and	and	CCONJ
iajs-1842	98	10	j.l	j.l	PROPN
iajs-1842	98	11	.	.	PROPN
iajs-1842	98	12	walsh	walsh	PROPN
iajs-1842	98	13	,	,	PUNCT
iajs-1842	98	14	"	"	PUNCT
iajs-1842	98	15	the	the	DET
iajs-1842	98	16	theory	theory	NOUN
iajs-1842	98	17	of	of	ADP
iajs-1842	98	18	splines	spline	NOUN
iajs-1842	98	19	and	and	CCONJ
iajs-1842	98	20	their	their	PRON
iajs-1842	98	21	application	application	NOUN
iajs-1842	98	22	"	"	PUNCT
iajs-1842	98	23	,	,	PUNCT
iajs-1842	98	24	academic	academic	ADJ
iajs-1842	98	25	press	press	NOUN
iajs-1842	98	26	,	,	PUNCT
iajs-1842	98	27	new	new	PROPN
iajs-1842	98	28	york	york	PROPN
iajs-1842	98	29	,	,	PUNCT
iajs-1842	98	30	1967	1967	NUM
iajs-1842	98	31	.	.	PUNCT
iajs-1842	99	1	[	[	X
iajs-1842	99	2	5].fadhel	5].fadhel	NUM
iajs-1842	99	3	,	,	PUNCT
iajs-1842	99	4	s.fadhel;suha.n.al	s.fadhel;suha.n.al	NOUN
iajs-1842	99	5	-	-	PUNCT
iajs-1842	99	6	rawi	rawi	NOUN
iajs-1842	99	7	,	,	PUNCT
iajs-1842	99	8	and	and	CCONJ
iajs-1842	99	9	nabaa	nabaa	PROPN
iajs-1842	99	10	n.hassan	n.hassan	VERB
iajs-1842	99	11	,	,	PUNCT
iajs-1842	99	12	"	"	PUNCT
iajs-1842	99	13	generalized	generalize	VERB
iajs-1842	99	14	spline	spline	NOUN
iajs-1842	99	15	approximation	approximation	NOUN
iajs-1842	99	16	method	method	NOUN
iajs-1842	99	17	for	for	ADP
iajs-1842	99	18	solving	solve	VERB
iajs-1842	99	19	ordinary	ordinary	ADJ
iajs-1842	99	20	and	and	CCONJ
iajs-1842	99	21	partial	partial	ADJ
iajs-1842	99	22	differential	differential	NOUN
iajs-1842	99	23	equations	equation	NOUN
iajs-1842	99	24	"	"	PUNCT
iajs-1842	99	25	,	,	PUNCT
iajs-1842	99	26	eng.&tech	eng.&tech	NOUN
iajs-1842	99	27	.journal	.journal	NOUN
iajs-1842	99	28	,	,	PUNCT
iajs-1842	99	29	2010	2010	NUM
iajs-1842	99	30	.	.	PUNCT
iajs-1842	100	1	[	[	X
iajs-1842	100	2	6	6	NUM
iajs-1842	100	3	]	]	PUNCT
iajs-1842	100	4	.	.	PUNCT
iajs-1842	101	1	i.	i.	PROPN
iajs-1842	101	2	podlubuy	podlubuy	PROPN
iajs-1842	101	3	,	,	PUNCT
iajs-1842	101	4	"	"	PUNCT
iajs-1842	101	5	fractional	fractional	ADJ
iajs-1842	101	6	differential	differential	ADJ
iajs-1842	101	7	equation	equation	NOUN
iajs-1842	101	8	"	"	PUNCT
iajs-1842	101	9	,	,	PUNCT
iajs-1842	101	10	academic	academic	ADJ
iajs-1842	101	11	press	press	NOUN
iajs-1842	101	12	,	,	PUNCT
iajs-1842	101	13	san	san	PROPN
iajs-1842	101	14	diago	diago	PROPN
iajs-1842	101	15	,	,	PUNCT
iajs-1842	101	16	.24	.24	NUM
iajs-1842	101	17	-	-	SYM
iajs-1842	101	18	32	32	NUM
iajs-1842	101	19	,	,	PUNCT
iajs-1842	101	20	1999	1999	NUM
iajs-1842	101	21	.	.	PUNCT
iajs-1842	102	1	[	[	X
iajs-1842	102	2	7].mariya	7].mariya	PROPN
iajs-1842	102	3	kamenova	kamenova	PROPN
iajs-1842	102	4	ishtera	ishtera	NOUN
iajs-1842	102	5	,	,	PUNCT
iajs-1842	102	6	"	"	PUNCT
iajs-1842	102	7	properties	property	NOUN
iajs-1842	102	8	and	and	CCONJ
iajs-1842	102	9	applications	application	NOUN
iajs-1842	102	10	of	of	ADP
iajs-1842	102	11	the	the	DET
iajs-1842	102	12	caputo	caputo	PROPN
iajs-1842	102	13	fractional	fractional	PROPN
iajs-1842	102	14	operator",thesis	operator",thesis	PROPN
iajs-1842	102	15	department	department	PROPN
iajs-1842	102	16	of	of	ADP
iajs-1842	102	17	mathmetics	mathmetics	PROPN
iajs-1842	102	18	unversity	unversity	PROPN
iajs-1842	102	19	karlsruhe(th	karlsruhe(th	PROPN
iajs-1842	102	20	)	)	PUNCT
iajs-1842	102	21	,	,	PUNCT
iajs-1842	102	22	2005	2005	NUM
iajs-1842	102	23	.	.	PUNCT
iajs-1842	103	1	[	[	X
iajs-1842	103	2	8].m.asgari	8].m.asgari	NUM
iajs-1842	103	3	,	,	PUNCT
iajs-1842	103	4	"	"	PUNCT
iajs-1842	103	5	numerical	numerical	ADJ
iajs-1842	103	6	solution	solution	NOUN
iajs-1842	103	7	for	for	ADP
iajs-1842	103	8	solving	solve	VERB
iajs-1842	103	9	a	a	DET
iajs-1842	103	10	system	system	NOUN
iajs-1842	103	11	of	of	ADP
iajs-1842	103	12	fractional	fractional	ADJ
iajs-1842	103	13	integro	integro	ADJ
iajs-1842	103	14	-	-	PUNCT
iajs-1842	103	15	differential	differential	NOUN
iajs-1842	103	16	equations	equation	NOUN
iajs-1842	103	17	"	"	PUNCT
iajs-1842	103	18	,	,	PUNCT
iajs-1842	103	19	iaeng	iaeng	PROPN
iajs-1842	103	20	international	international	PROPN
iajs-1842	103	21	journal	journal	PROPN
iajs-1842	103	22	of	of	ADP
iajs-1842	103	23	applied	apply	VERB
iajs-1842	103	24	mathematics	mathematic	NOUN
iajs-1842	103	25	,	,	PUNCT
iajs-1842	103	26	2015	2015	NUM
iajs-1842	103	27	.	.	PUNCT