id	sid	tid	token	lemma	pos
iajs-1442	1	1	conseguences	conseguence	NOUN
iajs-1442	1	2	of	of	ADP
iajs-1442	1	3	soil	soil	NOUN
iajs-1442	1	4	crude	crude	ADJ
iajs-1442	1	5	oil	oil	NOUN
iajs-1442	1	6	pollution	pollution	NOUN
iajs-1442	1	7	on	on	ADP
iajs-1442	1	8	some	some	DET
iajs-1442	1	9	wood	wood	NOUN
iajs-1442	1	10	properties	property	NOUN
iajs-1442	1	11	of	of	ADP
iajs-1442	1	12	olive	olive	NOUN
iajs-1442	1	13	trees	tree	NOUN
iajs-1442	1	14	mathematics	mathematics	PROPN
iajs-1442	1	15	|192	|192	PROPN
iajs-1442	1	16	2102	2102	NUM
iajs-1442	1	17	(	(	PUNCT
iajs-1442	1	18	عام	عام	ADP
iajs-1442	1	19	2	2	NUM
iajs-1442	1	20	(	(	PUNCT
iajs-1442	1	21	العدد	العدد	PROPN
iajs-1442	1	22	)	)	PUNCT
iajs-1442	1	23	30المجلد	30المجلد	NUM
iajs-1442	1	24	)	)	PUNCT
iajs-1442	2	1	مجلة	مجلة	VERB
iajs-1442	2	2	إبن	إبن	NOUN
iajs-1442	2	3	الهيثم	الهيثم	ADJ
iajs-1442	2	4	للعلوم	للعلوم	NOUN
iajs-1442	2	5	الصرفة	الصرفة	NOUN
iajs-1442	2	6	و	و	PRON
iajs-1442	2	7	التطبيقية	التطبيقية	ADJ
iajs-1442	2	8	ibn	ibn	PROPN
iajs-1442	2	9	al	al	PROPN
iajs-1442	2	10	-	-	PUNCT
iajs-1442	2	11	haitham	haitham	PROPN
iajs-1442	2	12	j.	j.	PROPN
iajs-1442	2	13	for	for	ADP
iajs-1442	2	14	pure	pure	PROPN
iajs-1442	2	15	&	&	CCONJ
iajs-1442	2	16	appl	appl	PROPN
iajs-1442	2	17	.	.	PUNCT
iajs-1442	3	1	sci	sci	PROPN
iajs-1442	3	2	.	.	PUNCT
iajs-1442	4	1	vol.03	vol.03	PROPN
iajs-1442	4	2	(	(	PUNCT
iajs-1442	4	3	2	2	NUM
iajs-1442	4	4	)	)	PUNCT
iajs-1442	4	5	2017	2017	NUM
iajs-1442	4	6	algorithm	algorithm	NOUN
iajs-1442	4	7	to	to	PART
iajs-1442	4	8	solve	solve	VERB
iajs-1442	4	9	linear	linear	PROPN
iajs-1442	4	10	volterra	volterra	NOUN
iajs-1442	4	11	fractional	fractional	ADJ
iajs-1442	4	12	integrodifferential	integrodifferential	ADJ
iajs-1442	4	13	equation	equation	NOUN
iajs-1442	4	14	via	via	ADP
iajs-1442	4	15	elzaki	elzaki	NOUN
iajs-1442	4	16	transform	transform	VERB
iajs-1442	4	17	amaal	amaal	NOUN
iajs-1442	4	18	a.	a.	PROPN
iajs-1442	4	19	mohammed	mohammed	PROPN
iajs-1442	4	20	yasmin	yasmin	PROPN
iajs-1442	4	21	h.	h.	PROPN
iajs-1442	4	22	abd	abd	PROPN
iajs-1442	4	23	dept	dept	PROPN
iajs-1442	4	24	.	.	PROPN
iajs-1442	4	25	of	of	ADP
iajs-1442	4	26	ways	way	NOUN
iajs-1442	4	27	&	&	CCONJ
iajs-1442	4	28	transportation	transportation	PROPN
iajs-1442	4	29	/	/	SYM
iajs-1442	4	30	college	college	NOUN
iajs-1442	4	31	of	of	ADP
iajs-1442	4	32	engineering	engineering	PROPN
iajs-1442	4	33	/	/	SYM
iajs-1442	4	34	al	al	PROPN
iajs-1442	4	35	-	-	PUNCT
iajs-1442	4	36	mustansiriya	mustansiriya	PROPN
iajs-1442	4	37	university	university	NOUN
iajs-1442	4	38	received	receive	VERB
iajs-1442	4	39	in	in	ADP
iajs-1442	4	40	:	:	PUNCT
iajs-1442	4	41	28/	28/	NUM
iajs-1442	4	42	june	june	PROPN
iajs-1442	4	43	/2016	/2016	PUNCT
iajs-1442	4	44	,	,	PUNCT
iajs-1442	4	45	accepted	accept	VERB
iajs-1442	4	46	in	in	ADP
iajs-1442	4	47	:	:	PUNCT
iajs-1442	4	48	4	4	NUM
iajs-1442	4	49	/january/	/january/	SYM
iajs-1442	4	50	2017	2017	NUM
iajs-1442	4	51	abstract	abstract	NOUN
iajs-1442	4	52	in	in	ADP
iajs-1442	4	53	this	this	DET
iajs-1442	4	54	work	work	NOUN
iajs-1442	4	55	,	,	PUNCT
iajs-1442	4	56	elzaki	elzaki	NOUN
iajs-1442	4	57	transform	transform	VERB
iajs-1442	4	58	(	(	PUNCT
iajs-1442	4	59	et	et	NOUN
iajs-1442	4	60	)	)	PUNCT
iajs-1442	4	61	introduced	introduce	VERB
iajs-1442	4	62	by	by	ADP
iajs-1442	4	63	tarig	tarig	PROPN
iajs-1442	4	64	elzaki	elzaki	PROPN
iajs-1442	4	65	is	be	AUX
iajs-1442	4	66	applied	apply	VERB
iajs-1442	4	67	to	to	PART
iajs-1442	4	68	solve	solve	VERB
iajs-1442	4	69	linear	linear	PROPN
iajs-1442	4	70	volterra	volterra	PROPN
iajs-1442	4	71	fractional	fractional	PROPN
iajs-1442	4	72	integro	integro	PROPN
iajs-1442	4	73	-	-	PUNCT
iajs-1442	4	74	differential	differential	NOUN
iajs-1442	4	75	equations	equation	NOUN
iajs-1442	4	76	(	(	PUNCT
iajs-1442	4	77	lvfide	lvfide	NOUN
iajs-1442	4	78	)	)	PUNCT
iajs-1442	4	79	.	.	PUNCT
iajs-1442	5	1	the	the	DET
iajs-1442	5	2	fractional	fractional	ADJ
iajs-1442	5	3	derivative	derivative	NOUN
iajs-1442	5	4	is	be	AUX
iajs-1442	5	5	considered	consider	VERB
iajs-1442	5	6	in	in	ADP
iajs-1442	5	7	the	the	DET
iajs-1442	5	8	riemman	riemman	NOUN
iajs-1442	5	9	-	-	PUNCT
iajs-1442	5	10	liouville	liouville	NOUN
iajs-1442	5	11	sense	sense	NOUN
iajs-1442	5	12	.	.	PUNCT
iajs-1442	6	1	the	the	DET
iajs-1442	6	2	procedure	procedure	NOUN
iajs-1442	6	3	is	be	AUX
iajs-1442	6	4	based	base	VERB
iajs-1442	6	5	on	on	ADP
iajs-1442	6	6	the	the	DET
iajs-1442	6	7	application	application	NOUN
iajs-1442	6	8	of	of	ADP
iajs-1442	6	9	(	(	PUNCT
iajs-1442	6	10	et	et	NOUN
iajs-1442	6	11	)	)	PUNCT
iajs-1442	6	12	to	to	ADP
iajs-1442	6	13	(	(	PUNCT
iajs-1442	6	14	lvfide	lvfide	ADV
iajs-1442	6	15	)	)	PUNCT
iajs-1442	6	16	and	and	CCONJ
iajs-1442	6	17	using	use	VERB
iajs-1442	6	18	properties	property	NOUN
iajs-1442	6	19	of	of	ADP
iajs-1442	6	20	(	(	PUNCT
iajs-1442	6	21	et	et	NOUN
iajs-1442	6	22	)	)	PUNCT
iajs-1442	6	23	and	and	CCONJ
iajs-1442	6	24	its	its	PRON
iajs-1442	6	25	inverse	inverse	NOUN
iajs-1442	6	26	.	.	PUNCT
iajs-1442	7	1	finally	finally	ADV
iajs-1442	7	2	,	,	PUNCT
iajs-1442	7	3	some	some	DET
iajs-1442	7	4	examples	example	NOUN
iajs-1442	7	5	are	be	AUX
iajs-1442	7	6	solved	solve	VERB
iajs-1442	7	7	to	to	PART
iajs-1442	7	8	show	show	VERB
iajs-1442	7	9	that	that	SCONJ
iajs-1442	7	10	this	this	PRON
iajs-1442	7	11	is	be	AUX
iajs-1442	7	12	computationally	computationally	ADV
iajs-1442	7	13	efficient	efficient	ADJ
iajs-1442	7	14	and	and	CCONJ
iajs-1442	7	15	accurate	accurate	ADJ
iajs-1442	7	16	.	.	PUNCT
iajs-1442	8	1	key	key	ADJ
iajs-1442	8	2	word	word	NOUN
iajs-1442	8	3	:	:	PUNCT
iajs-1442	8	4	integral	integral	ADJ
iajs-1442	8	5	,	,	PUNCT
iajs-1442	8	6	differential	differential	ADJ
iajs-1442	8	7	,	,	PUNCT
iajs-1442	8	8	volterra	volterra	NOUN
iajs-1442	8	9	,	,	PUNCT
iajs-1442	8	10	fractional	fractional	ADJ
iajs-1442	8	11	,	,	PUNCT
iajs-1442	8	12	elzaki	elzaki	NOUN
iajs-1442	8	13	.	.	PUNCT
iajs-1442	9	1	mathematics	mathematic	NOUN
iajs-1442	9	2	|193	|193	NOUN
iajs-1442	9	3	2102	2102	NUM
iajs-1442	9	4	(	(	PUNCT
iajs-1442	9	5	عام	عام	ADP
iajs-1442	9	6	2	2	NUM
iajs-1442	9	7	(	(	PUNCT
iajs-1442	9	8	العدد	العدد	PROPN
iajs-1442	9	9	)	)	PUNCT
iajs-1442	9	10	30المجلد	30المجلد	NUM
iajs-1442	9	11	)	)	PUNCT
iajs-1442	10	1	مجلة	مجلة	VERB
iajs-1442	10	2	إبن	إبن	NOUN
iajs-1442	10	3	الهيثم	الهيثم	ADJ
iajs-1442	10	4	للعلوم	للعلوم	NOUN
iajs-1442	10	5	الصرفة	الصرفة	NOUN
iajs-1442	10	6	و	و	PRON
iajs-1442	10	7	التطبيقية	التطبيقية	ADJ
iajs-1442	10	8	ibn	ibn	PROPN
iajs-1442	10	9	al	al	PROPN
iajs-1442	10	10	-	-	PUNCT
iajs-1442	10	11	haitham	haitham	PROPN
iajs-1442	10	12	j.	j.	PROPN
iajs-1442	10	13	for	for	ADP
iajs-1442	10	14	pure	pure	PROPN
iajs-1442	10	15	&	&	CCONJ
iajs-1442	10	16	appl	appl	PROPN
iajs-1442	10	17	.	.	PUNCT
iajs-1442	11	1	sci	sci	PROPN
iajs-1442	11	2	.	.	PUNCT
iajs-1442	12	1	vol.03	vol.03	PROPN
iajs-1442	12	2	(	(	PUNCT
iajs-1442	12	3	2	2	NUM
iajs-1442	12	4	)	)	PUNCT
iajs-1442	12	5	2017	2017	NUM
iajs-1442	12	6	introduction	introduction	NOUN
iajs-1442	12	7	many	many	ADJ
iajs-1442	12	8	fields	field	NOUN
iajs-1442	12	9	of	of	ADP
iajs-1442	12	10	science	science	NOUN
iajs-1442	12	11	and	and	CCONJ
iajs-1442	12	12	engineering	engineering	NOUN
iajs-1442	12	13	are	be	AUX
iajs-1442	12	14	described	describe	VERB
iajs-1442	12	15	by	by	ADP
iajs-1442	12	16	integro	integro	ADJ
iajs-1442	12	17	-	-	PUNCT
iajs-1442	12	18	differential	differential	NOUN
iajs-1442	12	19	equation	equation	NOUN
iajs-1442	12	20	of	of	ADP
iajs-1442	12	21	fractional	fractional	ADJ
iajs-1442	12	22	order	order	NOUN
iajs-1442	12	23	such	such	ADJ
iajs-1442	12	24	as	as	ADP
iajs-1442	12	25	,	,	PUNCT
iajs-1442	12	26	fluid	fluid	ADJ
iajs-1442	12	27	mechanics	mechanic	NOUN
iajs-1442	12	28	,	,	PUNCT
iajs-1442	12	29	vis	vis	X
iajs-1442	12	30	co	co	NOUN
iajs-1442	12	31	-	-	NOUN
iajs-1442	12	32	elasticity	elasticity	ADJ
iajs-1442	12	33	,	,	PUNCT
iajs-1442	12	34	diffusion	diffusion	NOUN
iajs-1442	12	35	processes	process	NOUN
iajs-1442	12	36	,	,	PUNCT
iajs-1442	12	37	biology	biology	NOUN
iajs-1442	12	38	and	and	CCONJ
iajs-1442	12	39	so	so	ADV
iajs-1442	12	40	on	on	ADP
iajs-1442	12	41	[	[	PUNCT
iajs-1442	12	42	1	1	NUM
iajs-1442	12	43	-	-	SYM
iajs-1442	12	44	4	4	NUM
iajs-1442	12	45	]	]	PUNCT
iajs-1442	12	46	.	.	PUNCT
iajs-1442	13	1	several	several	ADJ
iajs-1442	13	2	methods	method	NOUN
iajs-1442	13	3	to	to	PART
iajs-1442	13	4	solve	solve	VERB
iajs-1442	13	5	vfides	vfide	NOUN
iajs-1442	13	6	have	have	AUX
iajs-1442	13	7	been	be	AUX
iajs-1442	13	8	proposed	propose	VERB
iajs-1442	13	9	such	such	ADJ
iajs-1442	13	10	as	as	ADP
iajs-1442	13	11	,	,	PUNCT
iajs-1442	13	12	expansion	expansion	NOUN
iajs-1442	13	13	methods	method	NOUN
iajs-1442	13	14	and	and	CCONJ
iajs-1442	13	15	spline	spline	NOUN
iajs-1442	13	16	method	method	NOUN
iajs-1442	13	17	[	[	X
iajs-1442	13	18	5	5	NUM
iajs-1442	13	19	]	]	PUNCT
iajs-1442	13	20	,	,	PUNCT
iajs-1442	13	21	variation	variation	NOUN
iajs-1442	13	22	iteration	iteration	NOUN
iajs-1442	13	23	method	method	NOUN
iajs-1442	13	24	[	[	X
iajs-1442	13	25	6	6	NUM
iajs-1442	13	26	]	]	PUNCT
iajs-1442	13	27	,	,	PUNCT
iajs-1442	13	28	laplace	laplace	NOUN
iajs-1442	13	29	decomposition	decomposition	NOUN
iajs-1442	13	30	method	method	NOUN
iajs-1442	13	31	[	[	X
iajs-1442	13	32	7	7	NUM
iajs-1442	13	33	]	]	PUNCT
iajs-1442	13	34	and	and	CCONJ
iajs-1442	13	35	legender	legender	PROPN
iajs-1442	13	36	pseudo	pseudo	NOUN
iajs-1442	13	37	spectral	spectral	ADJ
iajs-1442	13	38	method	method	NOUN
iajs-1442	13	39	[	[	X
iajs-1442	13	40	8	8	NUM
iajs-1442	13	41	]	]	PUNCT
iajs-1442	13	42	.	.	PUNCT
iajs-1442	14	1	in	in	ADP
iajs-1442	14	2	recent	recent	ADJ
iajs-1442	14	3	years	year	NOUN
iajs-1442	14	4	,	,	PUNCT
iajs-1442	14	5	elzaki	elzaki	NOUN
iajs-1442	14	6	transform	transform	VERB
iajs-1442	14	7	(	(	PUNCT
iajs-1442	14	8	et	et	NOUN
iajs-1442	14	9	)	)	PUNCT
iajs-1442	14	10	was	be	AUX
iajs-1442	14	11	introduced	introduce	VERB
iajs-1442	14	12	by	by	ADP
iajs-1442	14	13	tarig	tarig	PROPN
iajs-1442	14	14	elzaki	elzaki	PROPN
iajs-1442	14	15	(	(	PUNCT
iajs-1442	14	16	2010	2010	NUM
iajs-1442	14	17	)	)	PUNCT
iajs-1442	14	18	has	have	AUX
iajs-1442	14	19	been	be	AUX
iajs-1442	14	20	used	use	VERB
iajs-1442	14	21	to	to	PART
iajs-1442	14	22	find	find	VERB
iajs-1442	14	23	solutions	solution	NOUN
iajs-1442	14	24	of	of	ADP
iajs-1442	14	25	a	a	DET
iajs-1442	14	26	wide	wide	ADJ
iajs-1442	14	27	class	class	NOUN
iajs-1442	14	28	of	of	ADP
iajs-1442	14	29	differential	differential	ADJ
iajs-1442	14	30	,	,	PUNCT
iajs-1442	14	31	integral	integral	ADJ
iajs-1442	14	32	,	,	PUNCT
iajs-1442	14	33	partial	partial	ADJ
iajs-1442	14	34	differential	differential	NOUN
iajs-1442	14	35	and	and	CCONJ
iajs-1442	14	36	the	the	DET
iajs-1442	14	37	integrodifferential	integrodifferential	ADJ
iajs-1442	14	38	equations	equation	NOUN
iajs-1442	14	39	,	,	PUNCT
iajs-1442	14	40	see	see	VERB
iajs-1442	14	41	[	[	X
iajs-1442	14	42	9	9	NUM
iajs-1442	14	43	-	-	SYM
iajs-1442	14	44	12	12	NUM
iajs-1442	14	45	]	]	PUNCT
iajs-1442	14	46	.	.	PUNCT
iajs-1442	15	1	in	in	ADP
iajs-1442	15	2	this	this	DET
iajs-1442	15	3	paper	paper	NOUN
iajs-1442	15	4	,	,	PUNCT
iajs-1442	15	5	et	et	NOUN
iajs-1442	15	6	and	and	CCONJ
iajs-1442	15	7	some	some	PRON
iajs-1442	15	8	of	of	ADP
iajs-1442	15	9	its	its	PRON
iajs-1442	15	10	fundamental	fundamental	ADJ
iajs-1442	15	11	properties	property	NOUN
iajs-1442	15	12	are	be	AUX
iajs-1442	15	13	used	use	VERB
iajs-1442	15	14	to	to	PART
iajs-1442	15	15	solve	solve	VERB
iajs-1442	15	16	lvfides	lvfide	NOUN
iajs-1442	15	17	with	with	ADP
iajs-1442	15	18	initial	initial	ADJ
iajs-1442	15	19	value	value	NOUN
iajs-1442	15	20	problems	problem	NOUN
iajs-1442	15	21	:	:	PUNCT
iajs-1442	16	1			X
iajs-1442	17	1	t	t	PROPN
iajs-1442	17	2	0	0	NUM
iajs-1442	18	1	(	(	PUNCT
iajs-1442	18	2	1)dτ)τ(y)τx,(k)t(g)t(y	1)dτ)τ(y)τx,(k)t(g)t(y	NUM
iajs-1442	18	3	dα	dα	NOUN
iajs-1442	18	4	subject	subject	NOUN
iajs-1442	18	5	to	to	ADP
iajs-1442	18	6	the	the	DET
iajs-1442	18	7	initial	initial	ADJ
iajs-1442	18	8	conditions	condition	NOUN
iajs-1442	18	9	nn	nn	X
iajs-1442	18	10	,	,	PUNCT
iajs-1442	18	11	nα1	nα1	NOUN
iajs-1442	18	12	-	-	PUNCT
iajs-1442	18	13	n	n	CCONJ
iajs-1442	18	14	,	,	PUNCT
iajs-1442	18	15	n	n	CCONJ
iajs-1442	18	16	...	...	PUNCT
iajs-1442	18	17	,2,1,z,)t(yd	,2,1,z,)t(yd	PUNCT
iajs-1442	18	18	zcz	zcz	NOUN
iajs-1442	18	19	-	-	PUNCT
iajs-1442	18	20	α	α	NOUN
iajs-1442	18	21			NOUN
iajs-1442	18	22	where	where	SCONJ
iajs-1442	18	23	zc	zc	NOUN
iajs-1442	18	24	is	be	AUX
iajs-1442	18	25	a	a	DET
iajs-1442	18	26	specified	specify	VERB
iajs-1442	18	27	constant	constant	ADJ
iajs-1442	18	28	,	,	PUNCT
iajs-1442	18	29	α	α	PROPN
iajs-1442	18	30	is	be	AUX
iajs-1442	18	31	a	a	DET
iajs-1442	18	32	parameter	parameter	NOUN
iajs-1442	18	33	describing	describe	VERB
iajs-1442	18	34	the	the	DET
iajs-1442	18	35	order	order	NOUN
iajs-1442	18	36	of	of	ADP
iajs-1442	18	37	the	the	DET
iajs-1442	18	38	time	time	NOUN
iajs-1442	18	39	fractional	fractional	ADJ
iajs-1442	18	40	,	,	PUNCT
iajs-1442	18	41	g	g	PROPN
iajs-1442	18	42	and	and	CCONJ
iajs-1442	18	43	k	k	PROPN
iajs-1442	18	44	are	be	AUX
iajs-1442	18	45	known	know	VERB
iajs-1442	18	46	functions	function	NOUN
iajs-1442	18	47	,	,	PUNCT
iajs-1442	18	48	y(t	y(t	NUM
iajs-1442	18	49	)	)	PUNCT
iajs-1442	18	50	is	be	AUX
iajs-1442	18	51	the	the	DET
iajs-1442	18	52	unknown	unknown	ADJ
iajs-1442	18	53	function	function	NOUN
iajs-1442	18	54	and	and	CCONJ
iajs-1442	18	55	αd	αd	PROPN
iajs-1442	18	56	is	be	AUX
iajs-1442	18	57	the	the	DET
iajs-1442	18	58	fractional	fractional	ADJ
iajs-1442	18	59	differential	differential	NOUN
iajs-1442	18	60	operator	operator	NOUN
iajs-1442	18	61	of	of	ADP
iajs-1442	18	62	order	order	NOUN
iajs-1442	18	63	α	α	NOUN
iajs-1442	18	64	.	.	PUNCT
iajs-1442	19	1	the	the	DET
iajs-1442	19	2	present	present	ADJ
iajs-1442	19	3	paper	paper	NOUN
iajs-1442	19	4	has	have	AUX
iajs-1442	19	5	been	be	AUX
iajs-1442	19	6	organized	organize	VERB
iajs-1442	19	7	as	as	SCONJ
iajs-1442	19	8	follows	follow	VERB
iajs-1442	19	9	.	.	PUNCT
iajs-1442	20	1	in	in	ADP
iajs-1442	20	2	section	section	NOUN
iajs-1442	20	3	2	2	NUM
iajs-1442	20	4	,	,	PUNCT
iajs-1442	20	5	some	some	DET
iajs-1442	20	6	definitions	definition	NOUN
iajs-1442	20	7	,	,	PUNCT
iajs-1442	20	8	theorems	theorem	NOUN
iajs-1442	20	9	and	and	CCONJ
iajs-1442	20	10	properties	property	NOUN
iajs-1442	20	11	of	of	ADP
iajs-1442	20	12	the	the	DET
iajs-1442	20	13	fraction	fraction	NOUN
iajs-1442	20	14	calculus	calculus	NOUN
iajs-1442	20	15	and	and	CCONJ
iajs-1442	20	16	et	et	NOUN
iajs-1442	20	17	are	be	AUX
iajs-1442	20	18	presented	present	VERB
iajs-1442	20	19	.	.	PUNCT
iajs-1442	21	1	in	in	ADP
iajs-1442	21	2	section	section	NOUN
iajs-1442	21	3	3	3	NUM
iajs-1442	21	4	,	,	PUNCT
iajs-1442	21	5	the	the	DET
iajs-1442	21	6	solution	solution	NOUN
iajs-1442	21	7	steps	step	VERB
iajs-1442	21	8	to	to	PART
iajs-1442	21	9	solve	solve	VERB
iajs-1442	21	10	lvfide	lvfide	ADV
iajs-1442	21	11	by	by	ADP
iajs-1442	21	12	using	use	VERB
iajs-1442	21	13	et	et	NOUN
iajs-1442	21	14	are	be	AUX
iajs-1442	21	15	described	describe	VERB
iajs-1442	21	16	.	.	PUNCT
iajs-1442	22	1	finally	finally	ADV
iajs-1442	22	2	,	,	PUNCT
iajs-1442	22	3	in	in	ADP
iajs-1442	22	4	section	section	NOUN
iajs-1442	22	5	4	4	NUM
iajs-1442	22	6	,	,	PUNCT
iajs-1442	22	7	some	some	DET
iajs-1442	22	8	test	test	NOUN
iajs-1442	22	9	examples	example	NOUN
iajs-1442	22	10	are	be	AUX
iajs-1442	22	11	solved	solve	VERB
iajs-1442	22	12	.	.	PUNCT
iajs-1442	23	1	preliminaries	preliminary	NOUN
iajs-1442	23	2	in	in	ADP
iajs-1442	23	3	this	this	DET
iajs-1442	23	4	section	section	NOUN
iajs-1442	23	5	,	,	PUNCT
iajs-1442	23	6	we	we	PRON
iajs-1442	23	7	present	present	VERB
iajs-1442	23	8	some	some	DET
iajs-1442	23	9	basic	basic	ADJ
iajs-1442	23	10	definitions	definition	NOUN
iajs-1442	23	11	,	,	PUNCT
iajs-1442	23	12	some	some	DET
iajs-1442	23	13	theorems	theorem	NOUN
iajs-1442	23	14	and	and	CCONJ
iajs-1442	23	15	useful	useful	ADJ
iajs-1442	23	16	properties	property	NOUN
iajs-1442	23	17	of	of	ADP
iajs-1442	23	18	the	the	DET
iajs-1442	23	19	fractional	fractional	ADJ
iajs-1442	23	20	calculus	calculus	NOUN
iajs-1442	23	21	and	and	CCONJ
iajs-1442	23	22	elzaki	elzaki	NOUN
iajs-1442	23	23	transform	transform	NOUN
iajs-1442	23	24	,	,	PUNCT
iajs-1442	23	25	as	as	ADV
iajs-1442	23	26	well	well	ADV
iajs-1442	23	27	as	as	SCONJ
iajs-1442	23	28	we	we	PRON
iajs-1442	23	29	proved	prove	VERB
iajs-1442	23	30	some	some	DET
iajs-1442	23	31	theorems	theorem	NOUN
iajs-1442	23	32	which	which	PRON
iajs-1442	23	33	are	be	AUX
iajs-1442	23	34	used	use	VERB
iajs-1442	23	35	in	in	ADP
iajs-1442	23	36	this	this	DET
iajs-1442	23	37	work	work	NOUN
iajs-1442	23	38	.	.	PUNCT
iajs-1442	24	1	definition	definition	NOUN
iajs-1442	24	2	(	(	PUNCT
iajs-1442	24	3	1	1	NUM
iajs-1442	24	4	):	):	PUNCT
iajs-1442	24	5	[	[	X
iajs-1442	24	6	1	1	NUM
iajs-1442	24	7	,	,	PUNCT
iajs-1442	24	8	13	13	NUM
iajs-1442	24	9	]	]	PUNCT
iajs-1442	24	10	the	the	DET
iajs-1442	24	11	riemann	riemann	PROPN
iajs-1442	24	12	–	–	PUNCT
iajs-1442	24	13	liouville	liouville	VERB
iajs-1442	24	14	fractional	fractional	ADJ
iajs-1442	24	15	derivative	derivative	NOUN
iajs-1442	24	16	of	of	ADP
iajs-1442	24	17	order	order	NOUN
iajs-1442	24	18	α	α	NOUN
iajs-1442	24	19	,	,	PUNCT
iajs-1442	24	20	is	be	AUX
iajs-1442	24	21	defined	define	VERB
iajs-1442	24	22	to	to	PART
iajs-1442	24	23	be	be	AUX
iajs-1442	24	24	for	for	ADP
iajs-1442	24	25	α	α	X
iajs-1442	24	26	>	>	X
iajs-1442	24	27	0	0	NUM
iajs-1442	25	1	:	:	PUNCT
iajs-1442	25	2	dt)t(ft)(x	dt)t(ft)(x	NOUN
iajs-1442	25	3	dx	dx	PROPN
iajs-1442	25	4	d	d	X
iajs-1442	25	5	α)γ(n	α)γ(n	PROPN
iajs-1442	25	6	1	1	NUM
iajs-1442	25	7	(	(	PUNCT
iajs-1442	25	8	x)fdd(x)fd	x)fdd(x)fd	X
iajs-1442	25	9	x	x	PROPN
iajs-1442	25	10	0	0	NUM
iajs-1442	25	11	1α	1α	NUM
iajs-1442	25	12	n	n	CCONJ
iajs-1442	25	13	n	n	CCONJ
iajs-1442	25	14	n	n	CCONJ
iajs-1442	25	15	n	n	CCONJ
iajs-1442	25	16	-	-	PUNCT
iajs-1442	25	17	αnα	αnα	NOUN
iajs-1442	25	18			PUNCT
iajs-1442	25	19			NOUN
iajs-1442	25	20			NOUN
iajs-1442	25	21			NUM
iajs-1442	25	22	or	or	CCONJ
iajs-1442	25	23	for	for	ADP
iajs-1442	25	24	α	α	PRON
iajs-1442	25	25	<	<	X
iajs-1442	25	26	0	0	NUM
iajs-1442	25	27	:	:	PUNCT
iajs-1442	25	28	dt)t(ft)(x	dt)t(ft)(x	NOUN
iajs-1442	25	29	)	)	PUNCT
iajs-1442	25	30	αγ	αγ	PROPN
iajs-1442	25	31	(	(	PUNCT
iajs-1442	25	32	1	1	NUM
iajs-1442	25	33	(	(	PUNCT
iajs-1442	25	34	x)fd	x)fd	PROPN
iajs-1442	25	35	x	x	SYM
iajs-1442	25	36	0	0	NUM
iajs-1442	25	37	1αα	1αα	NOUN
iajs-1442	25	38			PUNCT
iajs-1442	25	39			PROPN
iajs-1442	25	40			PROPN
iajs-1442	25	41			PROPN
iajs-1442	25	42	where	where	SCONJ
iajs-1442	25	43	n	n	X
iajs-1442	25	44	–	–	PUNCT
iajs-1442	25	45	1	1	NUM
iajs-1442	25	46	<	<	X
iajs-1442	25	47	α	α	PROPN
iajs-1442	25	48	≤	≤	PUNCT
iajs-1442	25	49	n	n	PRON
iajs-1442	25	50	definition	definition	NOUN
iajs-1442	25	51	(	(	PUNCT
iajs-1442	25	52	2	2	NUM
iajs-1442	25	53	):	):	PUNCT
iajs-1442	25	54	[	[	X
iajs-1442	25	55	6	6	NUM
iajs-1442	25	56	,	,	PUNCT
iajs-1442	25	57	13	13	NUM
iajs-1442	25	58	,	,	PUNCT
iajs-1442	25	59	14	14	NUM
iajs-1442	25	60	]	]	PUNCT
iajs-1442	25	61	the	the	DET
iajs-1442	25	62	riemann	riemann	PROPN
iajs-1442	25	63	–	–	PUNCT
iajs-1442	25	64	liouville	liouville	VERB
iajs-1442	25	65	fractional	fractional	ADJ
iajs-1442	25	66	integral	integral	ADJ
iajs-1442	25	67	operator	operator	NOUN
iajs-1442	25	68	of	of	ADP
iajs-1442	25	69	order	order	NOUN
iajs-1442	25	70	α	α	PRON
iajs-1442	25	71	≥	≥	NOUN
iajs-1442	25	72	0	0	NUM
iajs-1442	25	73	,	,	PUNCT
iajs-1442	25	74	of	of	ADP
iajs-1442	25	75	a	a	DET
iajs-1442	25	76	function	function	NOUN
iajs-1442	25	77	1,cf	1,cf	NOUN
iajs-1442	25	78			NOUN
iajs-1442	25	79	μ	μ	PART
iajs-1442	25	80	is	be	AUX
iajs-1442	25	81	defined	define	VERB
iajs-1442	25	82	as	as	ADP
iajs-1442	25	83	:	:	PUNCT
iajs-1442	25	84	dt)t(ft)(x	dt)t(ft)(x	NOUN
iajs-1442	25	85	)	)	PUNCT
iajs-1442	25	86	αγ	αγ	PROPN
iajs-1442	25	87	(	(	PUNCT
iajs-1442	25	88	1	1	NUM
iajs-1442	25	89	(	(	PUNCT
iajs-1442	25	90	x)fj(x)fd	x)fj(x)fd	NOUN
iajs-1442	25	91	x	x	SYM
iajs-1442	25	92	0	0	NUM
iajs-1442	25	93	1ααα	1ααα	NUM
iajs-1442	25	94			PUNCT
iajs-1442	25	95			PUNCT
iajs-1442	25	96			NUM
iajs-1442	25	97	it	it	PRON
iajs-1442	25	98	has	have	VERB
iajs-1442	25	99	the	the	DET
iajs-1442	25	100	following	follow	VERB
iajs-1442	25	101	properties	property	NOUN
iajs-1442	25	102	:	:	PUNCT
iajs-1442	26	1	for	for	ADP
iajs-1442	26	2	0	0	NUM
iajs-1442	26	3	γand0β	γand0β	NOUN
iajs-1442	26	4	,	,	PUNCT
iajs-1442	26	5	α	α	PROPN
iajs-1442	26	6			PROPN
iajs-1442	26	7	mathematics	mathematic	NOUN
iajs-1442	26	8	|194	|194	PROPN
iajs-1442	26	9	2102	2102	NUM
iajs-1442	26	10	(	(	PUNCT
iajs-1442	26	11	عام	عام	ADP
iajs-1442	26	12	2	2	NUM
iajs-1442	26	13	(	(	PUNCT
iajs-1442	26	14	العدد	العدد	PROPN
iajs-1442	26	15	)	)	PUNCT
iajs-1442	26	16	30المجلد	30المجلد	NUM
iajs-1442	26	17	)	)	PUNCT
iajs-1442	26	18	مجلة	مجلة	VERB
iajs-1442	26	19	إبن	إبن	NOUN
iajs-1442	26	20	الهيثم	الهيثم	ADJ
iajs-1442	26	21	للعلوم	للعلوم	NOUN
iajs-1442	26	22	الصرفة	الصرفة	NOUN
iajs-1442	26	23	و	و	PRON
iajs-1442	26	24	التطبيقية	التطبيقية	ADJ
iajs-1442	26	25	ibn	ibn	PROPN
iajs-1442	26	26	al	al	PROPN
iajs-1442	26	27	-	-	PUNCT
iajs-1442	26	28	haitham	haitham	PROPN
iajs-1442	26	29	j.	j.	PROPN
iajs-1442	26	30	for	for	ADP
iajs-1442	26	31	pure	pure	PROPN
iajs-1442	26	32	&	&	CCONJ
iajs-1442	26	33	appl	appl	PROPN
iajs-1442	26	34	.	.	PUNCT
iajs-1442	27	1	sci	sci	PROPN
iajs-1442	27	2	.	.	PUNCT
iajs-1442	28	1	vol.03	vol.03	PROPN
iajs-1442	28	2	(	(	PUNCT
iajs-1442	28	3	2	2	NUM
iajs-1442	28	4	)	)	PUNCT
iajs-1442	28	5	2017	2017	NUM
iajs-1442	28	6	1	1	NUM
iajs-1442	28	7	)	)	PUNCT
iajs-1442	28	8	(	(	PUNCT
iajs-1442	28	9	x)f(x)fj	x)f(x)fj	NOUN
iajs-1442	28	10	0	0	PUNCT
iajs-1442	29	1			NUM
iajs-1442	29	2	2	2	NUM
iajs-1442	29	3	)	)	PUNCT
iajs-1442	29	4	(	(	PUNCT
iajs-1442	29	5	x)fj(x)fjj	x)fj(x)fjj	PROPN
iajs-1442	29	6	βαβα	βαβα	NOUN
iajs-1442	29	7			ADJ
iajs-1442	29	8	3	3	NUM
iajs-1442	29	9	)	)	PUNCT
iajs-1442	29	10	(	(	PUNCT
iajs-1442	29	11	x)fjj(x)fjj	x)fjj(x)fjj	X
iajs-1442	29	12	αββα	αββα	VERB
iajs-1442	29	13			PROPN
iajs-1442	29	14	4	4	NUM
iajs-1442	29	15	)	)	PUNCT
iajs-1442	29	16	0α,(x)f(x)fjd	0α,(x)f(x)fjd	NUM
iajs-1442	30	1	αα	αα	PROPN
iajs-1442	30	2			PROPN
iajs-1442	30	3	5	5	NUM
iajs-1442	30	4	)	)	PUNCT
iajs-1442	30	5	γαγα	γαγα	PROPN
iajs-1442	30	6	x	x	X
iajs-1442	30	7	1)γγ(α	1)γγ(α	NUM
iajs-1442	30	8	1)γγ	1)γγ	PROPN
iajs-1442	30	9	(	(	PUNCT
iajs-1442	30	10	xj	xj	PROPN
iajs-1442	30	11			PROPN
iajs-1442	30	12			PROPN
iajs-1442	30	13			ADJ
iajs-1442	30	14			NUM
iajs-1442	30	15	6	6	NUM
iajs-1442	30	16	)	)	PUNCT
iajs-1442	30	17	...	...	PUNCT
iajs-1442	30	18	,	,	PUNCT
iajs-1442	30	19	10,γ	10,γ	NUM
iajs-1442	30	20	,	,	PUNCT
iajs-1442	30	21	x	x	PROPN
iajs-1442	30	22	1)γαγ(1)γγ	1)γαγ(1)γγ	NUM
iajs-1442	30	23	(	(	PUNCT
iajs-1442	30	24	xd	xd	INTJ
iajs-1442	30	25	γα	γα	NOUN
iajs-1442	30	26	-	-	PUNCT
iajs-1442	30	27	γα	γα	ADP
iajs-1442	30	28			PROPN
iajs-1442	30	29			PROPN
iajs-1442	30	30			ADJ
iajs-1442	30	31			PROPN
iajs-1442	30	32			PROPN
iajs-1442	30	33	k	k	PROPN
iajs-1442	30	34	k	k	X
iajs-1442	30	35	c(0)fdandnα1nwhere	c(0)fdandnα1nwhere	PROPN
iajs-1442	30	36	,	,	PUNCT
iajs-1442	30	37	1)kαγ	1)kαγ	NUM
iajs-1442	30	38	(	(	PUNCT
iajs-1442	30	39	xc	xc	PROPN
iajs-1442	30	40	(	(	PUNCT
iajs-1442	30	41	x)f(x)fdj7	x)f(x)fdj7	PROPN
iajs-1442	30	42	)	)	PUNCT
iajs-1442	31	1	k	k	NOUN
iajs-1442	31	2	-	-	PUNCT
iajs-1442	31	3	α	α	NOUN
iajs-1442	31	4	n	n	NOUN
iajs-1442	31	5	1k	1k	NOUN
iajs-1442	31	6	k	k	X
iajs-1442	31	7	-	-	PUNCT
iajs-1442	31	8	α	α	PROPN
iajs-1442	31	9	αα	αα	NOUN
iajs-1442	31	10			NOUN
iajs-1442	31	11			PROPN
iajs-1442	31	12			X
iajs-1442	31	13			X
iajs-1442	31	14			NUM
iajs-1442	31	15	definition	definition	NOUN
iajs-1442	31	16	(	(	PUNCT
iajs-1442	31	17	3	3	NUM
iajs-1442	31	18	):	):	PUNCT
iajs-1442	31	19	[	[	X
iajs-1442	31	20	11	11	NUM
iajs-1442	31	21	,	,	PUNCT
iajs-1442	31	22	15	15	NUM
iajs-1442	31	23	]	]	PUNCT
iajs-1442	31	24	elzaki	elzaki	NOUN
iajs-1442	31	25	transform	transform	NOUN
iajs-1442	31	26	is	be	AUX
iajs-1442	31	27	defined	define	VERB
iajs-1442	31	28	by	by	ADP
iajs-1442	31	29	:	:	PUNCT
iajs-1442	31	30	)	)	PUNCT
iajs-1442	31	31	,	,	PUNCT
iajs-1442	31	32	(	(	PUNCT
iajs-1442	31	33	u	u	NOUN
iajs-1442	31	34	,	,	PUNCT
iajs-1442	31	35	0	0	NUM
iajs-1442	31	36	t	t	PROPN
iajs-1442	31	37	21	21	NUM
iajs-1442	31	38	2	2	NUM
iajs-1442	31	39	dt)t(ufu(u)t])t(f	dt)t(ufu(u)t])t(f	NOUN
iajs-1442	31	40	[	[	PUNCT
iajs-1442	31	41	e	e	PROPN
iajs-1442	31	42	kke	kke	PROPN
iajs-1442	31	43			PROPN
iajs-1442	31	44			VERB
iajs-1442	31	45			PROPN
iajs-1442	31	46			PROPN
iajs-1442	31	47	where	where	SCONJ
iajs-1442	31	48	the	the	DET
iajs-1442	31	49	function	function	NOUN
iajs-1442	31	50	f	f	X
iajs-1442	31	51	(	(	PUNCT
iajs-1442	31	52	t	t	PROPN
iajs-1442	31	53	)	)	PUNCT
iajs-1442	31	54	in	in	ADP
iajs-1442	31	55	te	te	ADP
iajs-1442	31	56	set	set	VERB
iajs-1442	31	57	a	a	PRON
iajs-1442	31	58	defined	define	VERB
iajs-1442	31	59	by	by	ADP
iajs-1442	31	60	:	:	PUNCT
iajs-1442	31	61			NUM
iajs-1442	31	62			NUM
iajs-1442	31	63			PROPN
iajs-1442	31	64			PROPN
iajs-1442	31	65			NOUN
iajs-1442	31	66			NUM
iajs-1442	31	67			NUM
iajs-1442	31	68			ADP
iajs-1442	31	69			NOUN
iajs-1442	31	70	)	)	PUNCT
iajs-1442	31	71	,	,	PUNCT
iajs-1442	32	1	[	[	X
iajs-1442	32	2	0x1)(tifm)t(f0k	0x1)(tifm)t(f0k	NOUN
iajs-1442	32	3	,	,	PUNCT
iajs-1442	32	4	k	k	PROPN
iajs-1442	32	5	,	,	PUNCT
iajs-1442	32	6	m)t(fa	m)t(fa	PUNCT
iajs-1442	32	7	jj	jj	PROPN
iajs-1442	32	8	kt	kt	PROPN
iajs-1442	32	9	21	21	NUM
iajs-1442	32	10	e	e	NOUN
iajs-1442	32	11	definition	definition	NOUN
iajs-1442	32	12	(	(	PUNCT
iajs-1442	32	13	4	4	NUM
iajs-1442	32	14	):	):	PUNCT
iajs-1442	32	15	[	[	X
iajs-1442	32	16	15	15	NUM
iajs-1442	32	17	,	,	PUNCT
iajs-1442	32	18	12	12	NUM
iajs-1442	32	19	]	]	PUNCT
iajs-1442	32	20	defined	define	VERB
iajs-1442	32	21	for	for	ADP
iajs-1442	32	22	re(s	re(s	ADJ
iajs-1442	32	23	)	)	PUNCT
iajs-1442	32	24	>	>	X
iajs-1442	32	25	0	0	PUNCT
iajs-1442	32	26	,	,	PUNCT
iajs-1442	32	27	the	the	DET
iajs-1442	32	28	laplace	laplace	NOUN
iajs-1442	32	29	transform	transform	NOUN
iajs-1442	32	30	(	(	PUNCT
iajs-1442	32	31	lt	lt	NOUN
iajs-1442	32	32	)	)	PUNCT
iajs-1442	32	33	is	be	AUX
iajs-1442	32	34	given	give	VERB
iajs-1442	32	35	by	by	ADP
iajs-1442	32	36	:	:	PUNCT
iajs-1442	32	37	dt)t(f(s)f})t(f	dt)t(f(s)f})t(f	NOUN
iajs-1442	32	38	{	{	PUNCT
iajs-1442	32	39	0	0	NUM
iajs-1442	32	40	te	te	NOUN
iajs-1442	32	41			VERB
iajs-1442	32	42			NOUN
iajs-1442	32	43			NUM
iajs-1442	32	44	s	s	PART
iajs-1442	32	45	l	l	NOUN
iajs-1442	32	46	some	some	DET
iajs-1442	32	47	properties	property	NOUN
iajs-1442	32	48	of	of	ADP
iajs-1442	32	49	et	et	NOUN
iajs-1442	32	50	are	be	AUX
iajs-1442	32	51	given	give	VERB
iajs-1442	32	52	by	by	ADP
iajs-1442	32	53	following	follow	VERB
iajs-1442	32	54	theorems	theorem	NOUN
iajs-1442	32	55	:	:	PUNCT
iajs-1442	32	56	theorem	theorem	ADJ
iajs-1442	32	57	(	(	PUNCT
iajs-1442	32	58	1	1	NUM
iajs-1442	32	59	):	):	PUNCT
iajs-1442	32	60	[	[	X
iajs-1442	32	61	9	9	NUM
iajs-1442	32	62	,	,	PUNCT
iajs-1442	32	63	15	15	NUM
iajs-1442	32	64	]	]	PUNCT
iajs-1442	32	65	let	let	NOUN
iajs-1442	32	66			NUM
iajs-1442	32	67			NUM
iajs-1442	32	68			PROPN
iajs-1442	32	69			PROPN
iajs-1442	32	70			NOUN
iajs-1442	32	71			NUM
iajs-1442	32	72			NUM
iajs-1442	32	73			NOUN
iajs-1442	32	74			NOUN
iajs-1442	32	75	)	)	PUNCT
iajs-1442	32	76	,	,	PUNCT
iajs-1442	33	1	[	[	X
iajs-1442	33	2	0x1)(tifm)t(f0k	0x1)(tifm)t(f0k	NOUN
iajs-1442	33	3	,	,	PUNCT
iajs-1442	33	4	k	k	PROPN
iajs-1442	33	5	,	,	PUNCT
iajs-1442	33	6	m)t(fa)t(f	m)t(fa)t(f	PROPN
iajs-1442	33	7	jt	jt	PROPN
iajs-1442	33	8	j	j	PROPN
iajs-1442	33	9	k	k	PROPN
iajs-1442	33	10	21	21	NUM
iajs-1442	33	11	e	e	NOUN
iajs-1442	33	12	with	with	ADP
iajs-1442	33	13	lt	lt	PRON
iajs-1442	33	14	,	,	PUNCT
iajs-1442	33	15	f(s	f(s	ADV
iajs-1442	33	16	)	)	PUNCT
iajs-1442	33	17	then	then	ADV
iajs-1442	33	18	the	the	DET
iajs-1442	33	19	et	et	NOUN
iajs-1442	33	20	,	,	PUNCT
iajs-1442	33	21	t(u	t(u	PROPN
iajs-1442	33	22	)	)	PUNCT
iajs-1442	33	23	of	of	ADP
iajs-1442	33	24	f	f	PROPN
iajs-1442	33	25	(	(	PUNCT
iajs-1442	33	26	t	t	PROPN
iajs-1442	33	27	)	)	PUNCT
iajs-1442	33	28	is	be	AUX
iajs-1442	33	29	given	give	VERB
iajs-1442	33	30	by	by	ADP
iajs-1442	33	31	:	:	PUNCT
iajs-1442	33	32	)	)	PUNCT
iajs-1442	33	33	s	s	PART
iajs-1442	33	34	1	1	NUM
iajs-1442	33	35	(	(	PUNCT
iajs-1442	33	36	ts(s)fand	ts(s)fand	NOUN
iajs-1442	33	37	)	)	PUNCT
iajs-1442	33	38	u	u	NOUN
iajs-1442	33	39	1	1	NUM
iajs-1442	33	40	(	(	PUNCT
iajs-1442	33	41	fu(u)t	fu(u)t	X
iajs-1442	33	42			NUM
iajs-1442	33	43	theorem	theorem	NOUN
iajs-1442	33	44	(	(	PUNCT
iajs-1442	33	45	2	2	NUM
iajs-1442	33	46	):	):	PUNCT
iajs-1442	33	47	[	[	X
iajs-1442	33	48	9	9	NUM
iajs-1442	33	49	]	]	PUNCT
iajs-1442	33	50	let	let	VERB
iajs-1442	33	51	t(u	t(u	NUM
iajs-1442	33	52	)	)	PUNCT
iajs-1442	33	53	denote	denote	VERB
iajs-1442	33	54	the	the	DET
iajs-1442	33	55	et	et	NOUN
iajs-1442	33	56	of	of	ADP
iajs-1442	33	57	the	the	DET
iajs-1442	33	58	f(t	f(t	NOUN
iajs-1442	33	59	)	)	PUNCT
iajs-1442	33	60	,	,	PUNCT
iajs-1442	33	61	the	the	DET
iajs-1442	33	62	et	et	NOUN
iajs-1442	33	63	of	of	ADP
iajs-1442	33	64	the	the	DET
iajs-1442	33	65	definite	definite	ADJ
iajs-1442	33	66	integral	integral	NOUN
iajs-1442	33	67	of	of	ADP
iajs-1442	33	68	f(t	f(t	NOUN
iajs-1442	33	69	)	)	PUNCT
iajs-1442	33	70	,	,	PUNCT
iajs-1442	33	71	that	that	PRON
iajs-1442	33	72	is	be	AUX
iajs-1442	33	73	t(u)u)]t(h[ethendτ)τ(f)t(h	t(u)u)]t(h[ethendτ)τ(f)t(h	PROPN
iajs-1442	33	74	t	t	PROPN
iajs-1442	33	75	0	0	NUM
iajs-1442	33	76			NUM
iajs-1442	33	77			PUNCT
iajs-1442	33	78	theorem	theorem	NOUN
iajs-1442	33	79	(	(	PUNCT
iajs-1442	33	80	3	3	NUM
iajs-1442	33	81	):	):	PUNCT
iajs-1442	33	82	[	[	X
iajs-1442	33	83	9	9	NUM
iajs-1442	33	84	,	,	PUNCT
iajs-1442	33	85	11	11	NUM
iajs-1442	33	86	,	,	PUNCT
iajs-1442	33	87	15	15	NUM
iajs-1442	33	88	]	]	PUNCT
iajs-1442	33	89	let	let	VERB
iajs-1442	33	90	the	the	DET
iajs-1442	33	91	et	et	NOUN
iajs-1442	33	92	,	,	PUNCT
iajs-1442	33	93	f(u	f(u	PROPN
iajs-1442	33	94	)	)	PUNCT
iajs-1442	33	95	and	and	CCONJ
iajs-1442	33	96	g(u	g(u	PROPN
iajs-1442	33	97	)	)	PUNCT
iajs-1442	33	98	of	of	ADP
iajs-1442	33	99	the	the	DET
iajs-1442	33	100	functions	function	NOUN
iajs-1442	33	101	f(t	f(t	NOUN
iajs-1442	33	102	)	)	PUNCT
iajs-1442	33	103	and	and	CCONJ
iajs-1442	33	104	g(t	g(t	PROPN
iajs-1442	33	105	)	)	PUNCT
iajs-1442	33	106	respectively	respectively	ADV
iajs-1442	33	107	,	,	PUNCT
iajs-1442	33	108	then	then	ADV
iajs-1442	33	109	the	the	DET
iajs-1442	33	110	et	et	NOUN
iajs-1442	33	111	of	of	ADP
iajs-1442	33	112	the	the	DET
iajs-1442	33	113	convolution	convolution	NOUN
iajs-1442	33	114	of	of	ADP
iajs-1442	33	115	f	f	PROPN
iajs-1442	33	116	and	and	CCONJ
iajs-1442	33	117	g	g	PROPN
iajs-1442	33	118	is	be	AUX
iajs-1442	33	119	:	:	PUNCT
iajs-1442	33	120	g(u)f(u	g(u)f(u	NUM
iajs-1442	33	121	)	)	PUNCT
iajs-1442	33	122	u	u	NOUN
iajs-1442	33	123	1	1	NUM
iajs-1442	33	124	)	)	PUNCT
iajs-1442	33	125	]	]	PUNCT
iajs-1442	33	126	t(g)*[(febygivenisdτ)τ	t(g)*[(febygivenisdτ)τ	NOUN
iajs-1442	33	127	-	-	PUNCT
iajs-1442	33	128	t(g)τ(f)t(g)*(f	t(g)τ(f)t(g)*(f	PROPN
iajs-1442	33	129	t	t	NOUN
iajs-1442	33	130	0	0	NUM
iajs-1442	33	131			NUM
iajs-1442	33	132			PUNCT
iajs-1442	33	133	theorem	theorem	NOUN
iajs-1442	33	134	(	(	PUNCT
iajs-1442	33	135	4	4	NUM
iajs-1442	33	136	):	):	PUNCT
iajs-1442	33	137	[	[	X
iajs-1442	33	138	1	1	NUM
iajs-1442	33	139	,	,	PUNCT
iajs-1442	33	140	5	5	NUM
iajs-1442	33	141	,	,	PUNCT
iajs-1442	33	142	13	13	NUM
iajs-1442	33	143	]	]	PUNCT
iajs-1442	33	144	the	the	DET
iajs-1442	33	145	lt	lt	NOUN
iajs-1442	33	146	of	of	ADP
iajs-1442	33	147	the	the	DET
iajs-1442	33	148	riemann	riemann	PROPN
iajs-1442	33	149	–	–	PUNCT
iajs-1442	33	150	liouville	liouville	NOUN
iajs-1442	33	151	is	be	AUX
iajs-1442	33	152	defined	define	VERB
iajs-1442	33	153	as	as	ADP
iajs-1442	33	154	:	:	PUNCT
iajs-1442	33	155	nn	nn	PROPN
iajs-1442	33	156	,	,	PUNCT
iajs-1442	33	157	nα1nandαallfor	nα1nandαallfor	ADV
iajs-1442	33	158	,	,	PUNCT
iajs-1442	33	159	xd	xd	INTJ
iajs-1442	33	160	f(0)d	f(0)d	ADJ
iajs-1442	33	161	s(s)fs(s)f}(t)fd{l	s(s)fs(s)f}(t)fd{l	SYM
iajs-1442	33	162	1	1	NUM
iajs-1442	33	163	-	-	PUNCT
iajs-1442	33	164	n	n	PRON
iajs-1442	33	165	0k	0k	NOUN
iajs-1442	33	166	1	1	NUM
iajs-1442	33	167	-	-	PUNCT
iajs-1442	33	168	k	k	NOUN
iajs-1442	33	169	-	-	PUNCT
iajs-1442	33	170	α	α	PRON
iajs-1442	33	171	1	1	NUM
iajs-1442	33	172	-	-	PUNCT
iajs-1442	33	173	k	k	NOUN
iajs-1442	33	174	-	-	PUNCT
iajs-1442	33	175	α	α	NOUN
iajs-1442	33	176	kααα	kααα	PROPN
iajs-1442	33	177			PROPN
iajs-1442	33	178			X
iajs-1442	34	1			PRON
iajs-1442	34	2	theorem	theorem	NOUN
iajs-1442	34	3	(	(	PUNCT
iajs-1442	34	4	5	5	NUM
iajs-1442	34	5	):	):	PUNCT
iajs-1442	34	6	if	if	SCONJ
iajs-1442	34	7	f(s	f(	NOUN
iajs-1442	34	8	)	)	PUNCT
iajs-1442	34	9	and	and	CCONJ
iajs-1442	34	10	t(u	t(u	NUM
iajs-1442	34	11	)	)	PUNCT
iajs-1442	34	12	are	be	AUX
iajs-1442	34	13	lt	lt	PRON
iajs-1442	34	14	and	and	CCONJ
iajs-1442	34	15	et	et	NOUN
iajs-1442	34	16	of	of	ADP
iajs-1442	34	17	f(t	f(t	PROPN
iajs-1442	34	18	)	)	PUNCT
iajs-1442	34	19	respectively	respectively	ADV
iajs-1442	34	20	,	,	PUNCT
iajs-1442	34	21	then	then	ADV
iajs-1442	34	22	mathematics	mathematic	NOUN
iajs-1442	34	23	|195	|195	X
iajs-1442	34	24	2102	2102	NUM
iajs-1442	34	25	(	(	PUNCT
iajs-1442	34	26	عام	عام	ADP
iajs-1442	34	27	2	2	NUM
iajs-1442	34	28	(	(	PUNCT
iajs-1442	34	29	العدد	العدد	PROPN
iajs-1442	34	30	)	)	PUNCT
iajs-1442	34	31	30المجلد	30المجلد	NUM
iajs-1442	34	32	)	)	PUNCT
iajs-1442	35	1	مجلة	مجلة	VERB
iajs-1442	35	2	إبن	إبن	NOUN
iajs-1442	35	3	الهيثم	الهيثم	ADJ
iajs-1442	35	4	للعلوم	للعلوم	NOUN
iajs-1442	35	5	الصرفة	الصرفة	NOUN
iajs-1442	35	6	و	و	PRON
iajs-1442	35	7	التطبيقية	التطبيقية	ADJ
iajs-1442	35	8	ibn	ibn	PROPN
iajs-1442	35	9	al	al	PROPN
iajs-1442	35	10	-	-	PUNCT
iajs-1442	35	11	haitham	haitham	PROPN
iajs-1442	35	12	j.	j.	PROPN
iajs-1442	35	13	for	for	ADP
iajs-1442	35	14	pure	pure	PROPN
iajs-1442	35	15	&	&	CCONJ
iajs-1442	35	16	appl	appl	PROPN
iajs-1442	35	17	.	.	PUNCT
iajs-1442	36	1	sci	sci	PROPN
iajs-1442	36	2	.	.	PUNCT
iajs-1442	37	1	vol.03	vol.03	PROPN
iajs-1442	37	2	(	(	PUNCT
iajs-1442	37	3	2	2	NUM
iajs-1442	37	4	)	)	PUNCT
iajs-1442	37	5	2017	2017	NUM
iajs-1442	37	6	}	}	PUNCT
iajs-1442	37	7	(	(	PUNCT
iajs-1442	37	8	t)fd{l(s)fwhere	t)fd{l(s)fwhere	ADV
iajs-1442	37	9	)	)	PUNCT
iajs-1442	37	10	u	u	NOUN
iajs-1442	37	11	1	1	NUM
iajs-1442	37	12	(	(	PUNCT
iajs-1442	37	13	fu(u)t}(t)fd	fu(u)t}(t)fd	PROPN
iajs-1442	37	14	{	{	PUNCT
iajs-1442	37	15	ααααα	ααααα	ADJ
iajs-1442	37	16	e	e	ADJ
iajs-1442	37	17	proof	proof	NOUN
iajs-1442	37	18	:	:	PUNCT
iajs-1442	37	19	from	from	ADP
iajs-1442	37	20	definition(3	definition(3	PROPN
iajs-1442	37	21	)	)	PUNCT
iajs-1442	37	22	we	we	PRON
iajs-1442	37	23	have	have	VERB
iajs-1442	37	24	:	:	PUNCT
iajs-1442	37	25	dt])t(uf[du(u)t])t(fd[e	dt])t(uf[du(u)t])t(fd[e	VERB
iajs-1442	37	26	0	0	NUM
iajs-1442	37	27	tααα	tααα	PROPN
iajs-1442	37	28	e2	e2	PROPN
iajs-1442	37	29			PUNCT
iajs-1442	37	30			VERB
iajs-1442	37	31			PROPN
iajs-1442	37	32			NUM
iajs-1442	37	33	now	now	ADV
iajs-1442	37	34	,	,	PUNCT
iajs-1442	37	35	let	let	VERB
iajs-1442	37	36	w	w	NOUN
iajs-1442	37	37	=	=	PUNCT
iajs-1442	37	38	ut	ut	PROPN
iajs-1442	37	39	then	then	ADV
iajs-1442	37	40	we	we	PRON
iajs-1442	37	41	get	get	VERB
iajs-1442	37	42	:	:	PUNCT
iajs-1442	37	43	)	)	PUNCT
iajs-1442	37	44	u	u	NOUN
iajs-1442	37	45	1	1	NUM
iajs-1442	37	46	(	(	PUNCT
iajs-1442	37	47	fudw])(wf[du(u)t	fudw])(wf[du(u)t	PROPN
iajs-1442	37	48	α	α	NOUN
iajs-1442	37	49	0	0	NUM
iajs-1442	37	50	uwαα	uwαα	ADJ
iajs-1442	37	51	e	e	NOUN
iajs-1442	37	52			NUM
iajs-1442	37	53			PUNCT
iajs-1442	37	54			VERB
iajs-1442	37	55			PROPN
iajs-1442	37	56	theorem	theorem	NOUN
iajs-1442	37	57	(	(	PUNCT
iajs-1442	37	58	6	6	NUM
iajs-1442	37	59	):	):	PUNCT
iajs-1442	37	60	the	the	DET
iajs-1442	37	61	et	et	NOUN
iajs-1442	37	62	of	of	ADP
iajs-1442	37	63	the	the	DET
iajs-1442	37	64	riemann	riemann	PROPN
iajs-1442	37	65	–	–	PUNCT
iajs-1442	37	66	liouville	liouville	VERB
iajs-1442	37	67	fractional	fractional	ADJ
iajs-1442	37	68	derivative	derivative	NOUN
iajs-1442	37	69	is	be	AUX
iajs-1442	37	70	defined	define	VERB
iajs-1442	37	71	:	:	PUNCT
iajs-1442	37	72			X
iajs-1442	37	73			NUM
iajs-1442	37	74			NUM
iajs-1442	37	75	1	1	NUM
iajs-1442	37	76	-	-	PUNCT
iajs-1442	37	77	n	n	NUM
iajs-1442	37	78	0k	0k	NOUN
iajs-1442	37	79	1	1	NUM
iajs-1442	37	80	-	-	PUNCT
iajs-1442	37	81	k	k	NOUN
iajs-1442	37	82	-	-	PUNCT
iajs-1442	37	83	α	α	PRON
iajs-1442	37	84	1	1	NUM
iajs-1442	37	85	-	-	PUNCT
iajs-1442	37	86	k	k	NOUN
iajs-1442	37	87	-	-	PUNCT
iajs-1442	37	88	α	α	NOUN
iajs-1442	37	89	k-1	k-1	PROPN
iajs-1442	37	90	α	α	PROPN
iajs-1442	37	91	αα	αα	VERB
iajs-1442	37	92	xd	xd	INTJ
iajs-1442	38	1	f(0)d	f(0)d	ADJ
iajs-1442	38	2	u	u	X
iajs-1442	38	3	u	u	NOUN
iajs-1442	38	4	(	(	PUNCT
iajs-1442	38	5	u)t	u)t	X
iajs-1442	38	6	(	(	PUNCT
iajs-1442	38	7	u)t}(t)fd{e	u)t}(t)fd{e	NOUN
iajs-1442	38	8	proof	proof	NOUN
iajs-1442	38	9	:	:	PUNCT
iajs-1442	38	10	at	at	ADP
iajs-1442	38	11	first	first	ADV
iajs-1442	38	12	from	from	ADP
iajs-1442	38	13	the	the	DET
iajs-1442	38	14	above	above	ADJ
iajs-1442	38	15	theorem	theorem	NOUN
iajs-1442	38	16	we	we	PRON
iajs-1442	38	17	have	have	VERB
iajs-1442	38	18	:	:	PUNCT
iajs-1442	38	19	)	)	PUNCT
iajs-1442	38	20	u	u	NOUN
iajs-1442	38	21	1	1	NUM
iajs-1442	38	22	(	(	PUNCT
iajs-1442	38	23	fu(u)t])t(fd[e	fu(u)t])t(fd[e	PROPN
iajs-1442	38	24	ααα	ααα	ADV
iajs-1442	38	25			NUM
iajs-1442	38	26	and	and	CCONJ
iajs-1442	38	27	using	use	VERB
iajs-1442	38	28	theorem	theorem	NOUN
iajs-1442	38	29	(	(	PUNCT
iajs-1442	38	30	4	4	NUM
iajs-1442	38	31	)	)	PUNCT
iajs-1442	38	32	with	with	ADP
iajs-1442	38	33	u	u	PROPN
iajs-1442	38	34	1	1	NUM
iajs-1442	38	35	s	s	PART
iajs-1442	38	36			NOUN
iajs-1442	38	37	we	we	PRON
iajs-1442	38	38	obtain	obtain	VERB
iajs-1442	38	39	:	:	PUNCT
iajs-1442	38	40			PROPN
iajs-1442	38	41			PROPN
iajs-1442	38	42			PROPN
iajs-1442	38	43			X
iajs-1442	38	44			NOUN
iajs-1442	38	45			X
iajs-1442	38	46			VERB
iajs-1442	38	47			PROPN
iajs-1442	39	1			NOUN
iajs-1442	39	2			NOUN
iajs-1442	39	3	1	1	NUM
iajs-1442	39	4	-	-	PUNCT
iajs-1442	39	5	n	n	NUM
iajs-1442	39	6	0k	0k	NOUN
iajs-1442	39	7	1	1	NUM
iajs-1442	39	8	-	-	PUNCT
iajs-1442	39	9	k	k	NOUN
iajs-1442	39	10	-	-	PUNCT
iajs-1442	39	11	α	α	DET
iajs-1442	39	12	1	1	NUM
iajs-1442	39	13	-	-	PUNCT
iajs-1442	39	14	k	k	NOUN
iajs-1442	39	15	-	-	PUNCT
iajs-1442	39	16	α	α	NOUN
iajs-1442	39	17	kαα	kαα	NOUN
iajs-1442	39	18	xd	xd	INTJ
iajs-1442	39	19	f(0)d	f(0)d	ADJ
iajs-1442	39	20	)	)	PUNCT
iajs-1442	39	21	u	u	NOUN
iajs-1442	39	22	1	1	NUM
iajs-1442	39	23	(	(	PUNCT
iajs-1442	39	24	)	)	PUNCT
iajs-1442	39	25	u	u	NOUN
iajs-1442	39	26	1	1	NUM
iajs-1442	39	27	f	f	PROPN
iajs-1442	39	28	(	(	PUNCT
iajs-1442	39	29	)	)	PUNCT
iajs-1442	39	30	u	u	NOUN
iajs-1442	39	31	1	1	NUM
iajs-1442	39	32	(	(	PUNCT
iajs-1442	39	33	u(u)t	u(u)t	PROPN
iajs-1442	39	34	then	then	ADV
iajs-1442	39	35	by	by	ADP
iajs-1442	39	36	theorem	theorem	NOUN
iajs-1442	39	37	(	(	PUNCT
iajs-1442	39	38	1	1	NUM
iajs-1442	39	39	)	)	PUNCT
iajs-1442	39	40	,	,	PUNCT
iajs-1442	39	41	we	we	PRON
iajs-1442	39	42	get	get	VERB
iajs-1442	39	43	:	:	PUNCT
iajs-1442	39	44			X
iajs-1442	39	45			NUM
iajs-1442	39	46			ADJ
iajs-1442	39	47	1	1	NUM
iajs-1442	39	48	-	-	PUNCT
iajs-1442	39	49	n	n	NUM
iajs-1442	39	50	0k	0k	NOUN
iajs-1442	39	51	1	1	NUM
iajs-1442	39	52	-	-	PUNCT
iajs-1442	39	53	k	k	NOUN
iajs-1442	39	54	-	-	PUNCT
iajs-1442	39	55	α	α	PRON
iajs-1442	39	56	1	1	NUM
iajs-1442	39	57	-	-	PUNCT
iajs-1442	39	58	k	k	NOUN
iajs-1442	39	59	-	-	PUNCT
iajs-1442	39	60	α	α	NOUN
iajs-1442	39	61	k-1	k-1	PROPN
iajs-1442	39	62	α	α	PROPN
iajs-1442	39	63	α	α	NOUN
iajs-1442	39	64	xd	xd	INTJ
iajs-1442	40	1	f(0)d	f(0)d	ADJ
iajs-1442	40	2	u	u	X
iajs-1442	40	3	u	u	NOUN
iajs-1442	40	4	(	(	PUNCT
iajs-1442	40	5	u)t	u)t	X
iajs-1442	40	6	(	(	PUNCT
iajs-1442	40	7	u)t	u)t	X
iajs-1442	40	8	theorem	theorem	NOUN
iajs-1442	40	9	(	(	PUNCT
iajs-1442	40	10	7	7	NUM
iajs-1442	40	11	):	):	PUNCT
iajs-1442	40	12	let	let	VERB
iajs-1442	40	13	t(u	t(u	NUM
iajs-1442	40	14	)	)	PUNCT
iajs-1442	40	15	be	be	AUX
iajs-1442	40	16	et	et	NOUN
iajs-1442	40	17	of	of	ADP
iajs-1442	40	18	the	the	DET
iajs-1442	40	19	f(x	f(x	PROPN
iajs-1442	40	20	)	)	PUNCT
iajs-1442	40	21	,	,	PUNCT
iajs-1442	40	22	then	then	ADV
iajs-1442	40	23	et	et	VERB
iajs-1442	40	24	for	for	ADP
iajs-1442	40	25	f(x	f(x	PROPN
iajs-1442	40	26	)	)	PUNCT
iajs-1442	40	27	=	=	SYM
iajs-1442	40	28	)	)	PUNCT
iajs-1442	40	29	x(erfxe	x(erfxe	NOUN
iajs-1442	40	30	is	be	AUX
iajs-1442	40	31	given	give	VERB
iajs-1442	40	32	by	by	ADP
iajs-1442	40	33	:	:	PUNCT
iajs-1442	40	34	u-1	u-1	PROPN
iajs-1442	40	35	uu	uu	PROPN
iajs-1442	40	36	t(u	t(u	PROPN
iajs-1442	40	37	)	)	PUNCT
iajs-1442	40	38	2	2	NUM
iajs-1442	40	39			PROPN
iajs-1442	40	40	proof	proof	NOUN
iajs-1442	40	41	:	:	PUNCT
iajs-1442	40	42	the	the	DET
iajs-1442	40	43	proof	proof	NOUN
iajs-1442	40	44	of	of	ADP
iajs-1442	40	45	this	this	DET
iajs-1442	40	46	equation	equation	NOUN
iajs-1442	40	47	is	be	AUX
iajs-1442	40	48	easy	easy	ADJ
iajs-1442	40	49	,	,	PUNCT
iajs-1442	40	50	by	by	ADP
iajs-1442	40	51	using	use	VERB
iajs-1442	40	52	table	table	NOUN
iajs-1442	40	53	of	of	ADP
iajs-1442	40	54	lt	lt	NOUN
iajs-1442	40	55	,	,	PUNCT
iajs-1442	40	56	[	[	X
iajs-1442	40	57	16	16	NUM
iajs-1442	40	58	]	]	PUNCT
iajs-1442	40	59	and	and	CCONJ
iajs-1442	40	60	theorem	theorem	VERB
iajs-1442	40	61	(	(	PUNCT
iajs-1442	40	62	1	1	NUM
iajs-1442	40	63	)	)	PUNCT
iajs-1442	40	64	as	as	SCONJ
iajs-1442	40	65	follows	follow	VERB
iajs-1442	40	66	:	:	PUNCT
iajs-1442	40	67			PROPN
iajs-1442	40	68			PROPN
iajs-1442	40	69	1)(ss	1)(ss	NUM
iajs-1442	40	70	1	1	NUM
iajs-1442	40	71	)	)	PUNCT
iajs-1442	40	72	x(erfel	x(erfel	NOUN
iajs-1442	41	1	x	x	X
iajs-1442	41	2			NOUN
iajs-1442	41	3			NOUN
iajs-1442	41	4	u1	u1	NOUN
iajs-1442	41	5	uu	uu	ADJ
iajs-1442	41	6	1	1	X
iajs-1442	41	7	)	)	PUNCT
iajs-1442	41	8	u	u	NOUN
iajs-1442	41	9	1	1	NUM
iajs-1442	41	10	(	(	PUNCT
iajs-1442	41	11	u	u	NOUN
iajs-1442	41	12	1	1	NUM
iajs-1442	41	13	1	1	NUM
iajs-1442	41	14	u	u	NOUN
iajs-1442	41	15	)	)	PUNCT
iajs-1442	41	16	u	u	NOUN
iajs-1442	41	17	1	1	NUM
iajs-1442	41	18	f(u(u)t	f(u(u)t	NOUN
iajs-1442	41	19	2	2	NUM
iajs-1442	41	20	and	and	CCONJ
iajs-1442	41	21			PROPN
iajs-1442	41	22			PROPN
iajs-1442	41	23			PROPN
iajs-1442	41	24			NUM
iajs-1442	41	25	applications	application	NOUN
iajs-1442	41	26	to	to	ADP
iajs-1442	41	27	(	(	PUNCT
iajs-1442	41	28	lvfide	lvfide	PROPN
iajs-1442	41	29	)	)	PUNCT
iajs-1442	41	30	recall	recall	NOUN
iajs-1442	41	31	equation	equation	NOUN
iajs-1442	41	32	(	(	PUNCT
iajs-1442	41	33	1	1	NUM
iajs-1442	41	34	)	)	PUNCT
iajs-1442	41	35	,	,	PUNCT
iajs-1442	41	36	the	the	DET
iajs-1442	41	37	lvfide	lvfide	NOUN
iajs-1442	41	38	with	with	ADP
iajs-1442	41	39	initial	initial	ADJ
iajs-1442	41	40	value	value	NOUN
iajs-1442	41	41	problems	problem	NOUN
iajs-1442	41	42	:	:	PUNCT
iajs-1442	41	43	mathematics	mathematics	PROPN
iajs-1442	41	44	|196	|196	PROPN
iajs-1442	41	45	2102	2102	NUM
iajs-1442	41	46	(	(	PUNCT
iajs-1442	41	47	عام	عام	ADP
iajs-1442	41	48	2	2	NUM
iajs-1442	41	49	(	(	PUNCT
iajs-1442	41	50	العدد	العدد	PROPN
iajs-1442	41	51	)	)	PUNCT
iajs-1442	41	52	30المجلد	30المجلد	NUM
iajs-1442	41	53	)	)	PUNCT
iajs-1442	41	54	مجلة	مجلة	VERB
iajs-1442	41	55	إبن	إبن	NOUN
iajs-1442	41	56	الهيثم	الهيثم	ADJ
iajs-1442	41	57	للعلوم	للعلوم	NOUN
iajs-1442	41	58	الصرفة	الصرفة	NOUN
iajs-1442	42	1	و	و	PRON
iajs-1442	42	2	التطبيقية	التطبيقية	ADJ
iajs-1442	42	3	ibn	ibn	PROPN
iajs-1442	42	4	al	al	PROPN
iajs-1442	42	5	-	-	PUNCT
iajs-1442	42	6	haitham	haitham	PROPN
iajs-1442	42	7	j.	j.	PROPN
iajs-1442	42	8	for	for	ADP
iajs-1442	42	9	pure	pure	PROPN
iajs-1442	42	10	&	&	CCONJ
iajs-1442	42	11	appl	appl	PROPN
iajs-1442	42	12	.	.	PUNCT
iajs-1442	43	1	sci	sci	PROPN
iajs-1442	43	2	.	.	PUNCT
iajs-1442	44	1	vol.03	vol.03	PROPN
iajs-1442	44	2	(	(	PUNCT
iajs-1442	44	3	2	2	NUM
iajs-1442	44	4	)	)	PUNCT
iajs-1442	44	5	2017	2017	NUM
iajs-1442	44	6			ADV
iajs-1442	44	7	t	t	PROPN
iajs-1442	44	8	0	0	NUM
iajs-1442	45	1	α	α	PRON
iajs-1442	45	2	dτ)τ(y)τx,(k)t(g)t(y	dτ)τ(y)τx,(k)t(g)t(y	PROPN
iajs-1442	46	1	d	d	NOUN
iajs-1442	46	2	subject	subject	ADJ
iajs-1442	46	3	to	to	ADP
iajs-1442	46	4	the	the	DET
iajs-1442	46	5	initial	initial	ADJ
iajs-1442	46	6	conditions	condition	NOUN
iajs-1442	46	7	nn	nn	X
iajs-1442	46	8	,	,	PUNCT
iajs-1442	46	9	nα1	nα1	NOUN
iajs-1442	46	10	-	-	PUNCT
iajs-1442	46	11	n	n	CCONJ
iajs-1442	46	12	,	,	PUNCT
iajs-1442	46	13	n	n	CCONJ
iajs-1442	46	14	...	...	PUNCT
iajs-1442	46	15	,2,1,z,)t(yd	,2,1,z,)t(yd	PUNCT
iajs-1442	46	16	zc	zc	X
iajs-1442	46	17	z	z	X
iajs-1442	46	18	-	-	PUNCT
iajs-1442	46	19	α	α	X
iajs-1442	46	20			NOUN
iajs-1442	46	21	the	the	DET
iajs-1442	46	22	first	first	ADJ
iajs-1442	46	23	step	step	NOUN
iajs-1442	46	24	,	,	PUNCT
iajs-1442	46	25	we	we	PRON
iajs-1442	46	26	apply	apply	VERB
iajs-1442	46	27	et	et	NOUN
iajs-1442	46	28	on	on	ADP
iajs-1442	46	29	both	both	DET
iajs-1442	46	30	sides	side	NOUN
iajs-1442	46	31	we	we	PRON
iajs-1442	46	32	have	have	VERB
iajs-1442	46	33	:	:	PUNCT
iajs-1442	46	34			ADJ
iajs-1442	46	35			NOUN
iajs-1442	46	36			PROPN
iajs-1442	46	37			PROPN
iajs-1442	46	38			X
iajs-1442	46	39			NOUN
iajs-1442	46	40			VERB
iajs-1442	46	41			PROPN
iajs-1442	46	42			ADV
iajs-1442	46	43			NOUN
iajs-1442	46	44			NOUN
iajs-1442	46	45			PROPN
iajs-1442	46	46			PROPN
iajs-1442	46	47	t	t	NOUN
iajs-1442	46	48	0	0	NUM
iajs-1442	47	1	α	α	PRON
iajs-1442	47	2	dτ)τ(y)τx,(k)t(g)t(y	dτ)τ(y)τx,(k)t(g)t(y	PROPN
iajs-1442	47	3	d	d	SYM
iajs-1442	47	4	eee	eee	NOUN
iajs-1442	47	5	can	can	AUX
iajs-1442	47	6	easily	easily	ADV
iajs-1442	47	7	be	be	AUX
iajs-1442	47	8	transformed	transform	VERB
iajs-1442	47	9	into	into	ADP
iajs-1442	47	10	its	its	PRON
iajs-1442	47	11	et	et	NOUN
iajs-1442	47	12	using	use	VERB
iajs-1442	47	13	theorem	theorem	NOUN
iajs-1442	47	14	(	(	PUNCT
iajs-1442	47	15	6	6	NUM
iajs-1442	47	16	)	)	PUNCT
iajs-1442	47	17	,	,	PUNCT
iajs-1442	47	18	equivalent	equivalent	ADJ
iajs-1442	47	19	to	to	ADP
iajs-1442	47	20	:	:	PUNCT
iajs-1442	47	21			PROPN
iajs-1442	47	22			PROPN
iajs-1442	47	23			X
iajs-1442	48	1			NOUN
iajs-1442	48	2			NOUN
iajs-1442	48	3			PROPN
iajs-1442	48	4			NOUN
iajs-1442	48	5	t	t	PROPN
iajs-1442	48	6	0	0	NUM
iajs-1442	49	1	α	α	PRON
iajs-1442	49	2	dτ)τ(y)τx,(k)u(gc	dτ)τ(y)τx,(k)u(gc	PROPN
iajs-1442	49	3	u	u	SYM
iajs-1442	49	4	(	(	PUNCT
iajs-1442	49	5	u)t	u)t	X
iajs-1442	49	6	e	e	NOUN
iajs-1442	49	7	where	where	SCONJ
iajs-1442	49	8			X
iajs-1442	49	9			NUM
iajs-1442	49	10			NUM
iajs-1442	49	11	1	1	NUM
iajs-1442	49	12	-	-	PUNCT
iajs-1442	49	13	n	n	NUM
iajs-1442	49	14	0k	0k	NOUN
iajs-1442	49	15	1	1	NUM
iajs-1442	49	16	-	-	PUNCT
iajs-1442	49	17	k	k	NOUN
iajs-1442	49	18	-	-	PUNCT
iajs-1442	49	19	α	α	PRON
iajs-1442	49	20	1	1	NUM
iajs-1442	49	21	-	-	PUNCT
iajs-1442	49	22	k	k	NOUN
iajs-1442	49	23	-	-	PUNCT
iajs-1442	49	24	α	α	NOUN
iajs-1442	49	25	k-1	k-1	PROPN
iajs-1442	49	26	xd	xd	INTJ
iajs-1442	50	1	y(0)d	y(0)d	PROPN
iajs-1442	50	2	uc	uc	PROPN
iajs-1442	50	3	,	,	PUNCT
iajs-1442	50	4	t(u	t(u	NUM
iajs-1442	50	5	)	)	PUNCT
iajs-1442	50	6	and	and	CCONJ
iajs-1442	50	7	g(u	g(u	PROPN
iajs-1442	50	8	)	)	PUNCT
iajs-1442	50	9	are	be	AUX
iajs-1442	50	10	et	et	NOUN
iajs-1442	50	11	for	for	ADP
iajs-1442	50	12	y(t	y(t	PROPN
iajs-1442	50	13	)	)	PUNCT
iajs-1442	50	14	and	and	CCONJ
iajs-1442	50	15	g(t	g(t	PROPN
iajs-1442	50	16	)	)	PUNCT
iajs-1442	50	17	respectively	respectively	ADV
iajs-1442	50	18	.	.	PUNCT
iajs-1442	51	1	the	the	DET
iajs-1442	51	2	general	general	ADJ
iajs-1442	51	3	elzaki	elzaki	NOUN
iajs-1442	51	4	solution	solution	NOUN
iajs-1442	51	5	is	be	AUX
iajs-1442	51	6	:	:	PUNCT
iajs-1442	51	7	)	)	PUNCT
iajs-1442	51	8	2(dτ)τ(y)τx,(ku)u(gucu(u)t	2(dτ)τ(y)τx,(ku)u(gucu(u)t	NUM
iajs-1442	51	9	t	t	NOUN
iajs-1442	51	10	0	0	NUM
iajs-1442	51	11	ααα	ααα	ADJ
iajs-1442	51	12			PROPN
iajs-1442	51	13			PROPN
iajs-1442	51	14			NOUN
iajs-1442	51	15			NOUN
iajs-1442	51	16			VERB
iajs-1442	51	17			PROPN
iajs-1442	51	18			VERB
iajs-1442	51	19	e	e	AUX
iajs-1442	51	20	the	the	DET
iajs-1442	51	21	second	second	ADJ
iajs-1442	51	22	step	step	NOUN
iajs-1442	51	23	is	be	AUX
iajs-1442	51	24	to	to	PART
iajs-1442	51	25	find	find	VERB
iajs-1442	51	26	et	et	PRON
iajs-1442	51	27	of	of	ADP
iajs-1442	51	28	integral	integral	ADJ
iajs-1442	51	29	in	in	ADP
iajs-1442	51	30	above	above	ADP
iajs-1442	51	31	equation	equation	NOUN
iajs-1442	51	32	which	which	PRON
iajs-1442	51	33	depends	depend	VERB
iajs-1442	51	34	on	on	ADP
iajs-1442	51	35	the	the	DET
iajs-1442	51	36	type	type	NOUN
iajs-1442	51	37	function	function	NOUN
iajs-1442	51	38	)	)	PUNCT
iajs-1442	51	39	τx,(k	τx,(k	PROPN
iajs-1442	52	1	(	(	PUNCT
iajs-1442	52	2	kernel	kernel	NOUN
iajs-1442	52	3	of	of	ADP
iajs-1442	52	4	the	the	DET
iajs-1442	52	5	integral	integral	ADJ
iajs-1442	52	6	equation	equation	NOUN
iajs-1442	52	7	)	)	PUNCT
iajs-1442	52	8	as	as	SCONJ
iajs-1442	52	9	follows	follow	VERB
iajs-1442	52	10	:	:	PUNCT
iajs-1442	52	11	a.	a.	NOUN
iajs-1442	52	12	if	if	SCONJ
iajs-1442	52	13	the	the	DET
iajs-1442	52	14	kernel	kernel	NOUN
iajs-1442	52	15	is	be	AUX
iajs-1442	52	16	constant	constant	ADJ
iajs-1442	52	17	that	that	SCONJ
iajs-1442	52	18	is	be	AUX
iajs-1442	52	19	,	,	PUNCT
iajs-1442	52	20	)	)	PUNCT
iajs-1442	52	21	τ	τ	PROPN
iajs-1442	52	22	,	,	PUNCT
iajs-1442	52	23	x(k	x(k	PROPN
iajs-1442	52	24	=	=	PUNCT
iajs-1442	53	1	r	r	NOUN
iajs-1442	53	2	,	,	PUNCT
iajs-1442	53	3	then	then	ADV
iajs-1442	53	4	by	by	ADP
iajs-1442	53	5	using	use	VERB
iajs-1442	53	6	theorem	theorem	NOUN
iajs-1442	53	7	(	(	PUNCT
iajs-1442	53	8	2	2	NUM
iajs-1442	53	9	)	)	PUNCT
iajs-1442	53	10	we	we	PRON
iajs-1442	53	11	have	have	AUX
iajs-1442	53	12	:	:	PUNCT
iajs-1442	53	13	(	(	PUNCT
iajs-1442	53	14	3)t(u)urdτ)τ(yr	3)t(u)urdτ)τ(yr	NOUN
iajs-1442	53	15	t	t	NOUN
iajs-1442	53	16	0	0	X
iajs-1442	53	17			PROPN
iajs-1442	53	18			PROPN
iajs-1442	53	19			NOUN
iajs-1442	53	20			NOUN
iajs-1442	53	21			VERB
iajs-1442	53	22			PROPN
iajs-1442	53	23	e	e	ADP
iajs-1442	53	24	where	where	SCONJ
iajs-1442	53	25	t(u	t(u	NOUN
iajs-1442	53	26	)	)	PUNCT
iajs-1442	53	27	is	be	AUX
iajs-1442	53	28	the	the	DET
iajs-1442	53	29	et	et	NOUN
iajs-1442	53	30	of	of	ADP
iajs-1442	53	31	y(t	y(t	PROPN
iajs-1442	53	32	)	)	PUNCT
iajs-1442	53	33	.	.	PUNCT
iajs-1442	54	1	b.	b.	PROPN
iajs-1442	55	1	if	if	SCONJ
iajs-1442	55	2	the	the	DET
iajs-1442	55	3	kernel	kernel	NOUN
iajs-1442	55	4	is	be	AUX
iajs-1442	55	5	deference	deference	NOUN
iajs-1442	55	6	that	that	PRON
iajs-1442	55	7	is	be	AUX
iajs-1442	55	8	,	,	PUNCT
iajs-1442	55	9	)	)	PUNCT
iajs-1442	56	1	τx(k)τ	τx(k)τ	PROPN
iajs-1442	56	2	,	,	PUNCT
iajs-1442	56	3	x(k	x(k	PROPN
iajs-1442	56	4			PROPN
iajs-1442	56	5	,	,	PUNCT
iajs-1442	56	6	by	by	ADP
iajs-1442	56	7	theorem	theorem	NOUN
iajs-1442	56	8	(	(	PUNCT
iajs-1442	56	9	3	3	X
iajs-1442	56	10	)	)	PUNCT
iajs-1442	56	11	we	we	PRON
iajs-1442	56	12	get	get	VERB
iajs-1442	56	13	:	:	PUNCT
iajs-1442	56	14	(	(	PUNCT
iajs-1442	56	15	4)t(u)*k(u	4)t(u)*k(u	NOUN
iajs-1442	56	16	)	)	PUNCT
iajs-1442	56	17	u	u	NOUN
iajs-1442	56	18	1	1	NUM
iajs-1442	56	19	dτ)τ(y)τx(k	dτ)τ(y)τx(k	PROPN
iajs-1442	56	20	t	t	PROPN
iajs-1442	56	21	0	0	NUM
iajs-1442	56	22			PROPN
iajs-1442	56	23			PROPN
iajs-1442	56	24			PROPN
iajs-1442	56	25			X
iajs-1442	56	26			NOUN
iajs-1442	56	27			VERB
iajs-1442	56	28			PROPN
iajs-1442	56	29	e	e	ADP
iajs-1442	56	30	where	where	SCONJ
iajs-1442	56	31	k(u	k(u	NOUN
iajs-1442	56	32	)	)	PUNCT
iajs-1442	56	33	and	and	CCONJ
iajs-1442	56	34	t(u	t(u	NUM
iajs-1442	56	35	)	)	PUNCT
iajs-1442	57	1	are	be	AUX
iajs-1442	57	2	et	et	NOUN
iajs-1442	57	3	of	of	ADP
iajs-1442	57	4	the	the	DET
iajs-1442	57	5	functions	function	NOUN
iajs-1442	57	6	k	k	PROPN
iajs-1442	57	7	and	and	CCONJ
iajs-1442	57	8	y	y	PROPN
iajs-1442	57	9	respectively	respectively	ADV
iajs-1442	57	10	.	.	PUNCT
iajs-1442	58	1	c.	c.	NOUN
iajs-1442	58	2	if	if	SCONJ
iajs-1442	58	3	the	the	DET
iajs-1442	58	4	kernel	kernel	NOUN
iajs-1442	58	5	is	be	AUX
iajs-1442	58	6	any	any	DET
iajs-1442	58	7	function	function	NOUN
iajs-1442	58	8	,	,	PUNCT
iajs-1442	58	9	we	we	PRON
iajs-1442	58	10	represent	represent	VERB
iajs-1442	58	11	the	the	DET
iajs-1442	58	12	solution	solution	NOUN
iajs-1442	58	13	as	as	ADP
iajs-1442	58	14	an	an	DET
iajs-1442	58	15	infinite	infinite	ADJ
iajs-1442	58	16	series	series	NOUN
iajs-1442	58	17	,	,	PUNCT
iajs-1442	58	18	that	that	PRON
iajs-1442	58	19	is	be	AUX
iajs-1442	58	20	:	:	PUNCT
iajs-1442	58	21			X
iajs-1442	58	22			VERB
iajs-1442	58	23			PRON
iajs-1442	58	24			PROPN
iajs-1442	58	25	0i	0i	NOUN
iajs-1442	58	26	(	(	PUNCT
iajs-1442	58	27	t)yy(t	t)yy(t	NUM
iajs-1442	58	28	)	)	PUNCT
iajs-1442	58	29	i	i	PRON
iajs-1442	58	30	the	the	DET
iajs-1442	58	31	et	et	NOUN
iajs-1442	58	32	of	of	ADP
iajs-1442	58	33	the	the	DET
iajs-1442	58	34	integral	integral	ADJ
iajs-1442	58	35	is	be	AUX
iajs-1442	58	36	become	become	VERB
iajs-1442	58	37	:	:	PUNCT
iajs-1442	58	38	mathematics	mathematic	NOUN
iajs-1442	58	39	|197	|197	X
iajs-1442	58	40	2102	2102	NUM
iajs-1442	58	41	(	(	PUNCT
iajs-1442	58	42	عام	عام	ADP
iajs-1442	58	43	2	2	NUM
iajs-1442	58	44	(	(	PUNCT
iajs-1442	58	45	العدد	العدد	PROPN
iajs-1442	58	46	)	)	PUNCT
iajs-1442	58	47	30المجلد	30المجلد	NUM
iajs-1442	58	48	)	)	PUNCT
iajs-1442	59	1	مجلة	مجلة	VERB
iajs-1442	59	2	إبن	إبن	NOUN
iajs-1442	59	3	الهيثم	الهيثم	ADJ
iajs-1442	59	4	للعلوم	للعلوم	NOUN
iajs-1442	59	5	الصرفة	الصرفة	NOUN
iajs-1442	59	6	و	و	PRON
iajs-1442	59	7	التطبيقية	التطبيقية	ADJ
iajs-1442	59	8	ibn	ibn	PROPN
iajs-1442	59	9	al	al	PROPN
iajs-1442	59	10	-	-	PUNCT
iajs-1442	59	11	haitham	haitham	PROPN
iajs-1442	59	12	j.	j.	PROPN
iajs-1442	59	13	for	for	ADP
iajs-1442	59	14	pure	pure	PROPN
iajs-1442	59	15	&	&	CCONJ
iajs-1442	59	16	appl	appl	PROPN
iajs-1442	59	17	.	.	PUNCT
iajs-1442	60	1	sci	sci	PROPN
iajs-1442	60	2	.	.	PUNCT
iajs-1442	61	1	vol.03	vol.03	PROPN
iajs-1442	61	2	(	(	PUNCT
iajs-1442	61	3	2	2	NUM
iajs-1442	61	4	)	)	PUNCT
iajs-1442	61	5	2017	2017	NUM
iajs-1442	61	6	)	)	PUNCT
iajs-1442	62	1	5(dτ)τ(y)τx,(kdτ)τ(y)τx,(k	5(dτ)τ(y)τx,(kdτ)τ(y)τx,(k	NOUN
iajs-1442	62	2	t	t	NOUN
iajs-1442	62	3	0	0	NUM
iajs-1442	62	4	0i	0i	NOUN
iajs-1442	63	1	i	i	PRON
iajs-1442	63	2	t	t	VERB
iajs-1442	63	3	0	0	NUM
iajs-1442	64	1			PROPN
iajs-1442	64	2			PROPN
iajs-1442	64	3			X
iajs-1442	64	4			NOUN
iajs-1442	64	5			VERB
iajs-1442	64	6			PROPN
iajs-1442	64	7			ADJ
iajs-1442	64	8			PUNCT
iajs-1442	64	9			PROPN
iajs-1442	64	10			PRON
iajs-1442	64	11			NOUN
iajs-1442	64	12			VERB
iajs-1442	64	13			PROPN
iajs-1442	64	14			NOUN
iajs-1442	64	15			VERB
iajs-1442	64	16			PRON
iajs-1442	64	17			NOUN
iajs-1442	64	18	ee	ee	ADP
iajs-1442	64	19	the	the	DET
iajs-1442	64	20	third	third	ADJ
iajs-1442	64	21	step	step	NOUN
iajs-1442	64	22	,	,	PUNCT
iajs-1442	64	23	we	we	PRON
iajs-1442	64	24	substitute	substitute	VERB
iajs-1442	64	25	either	either	CCONJ
iajs-1442	64	26	eq.(3	eq.(3	NOUN
iajs-1442	64	27	)	)	PUNCT
iajs-1442	64	28	or	or	CCONJ
iajs-1442	64	29	eq.(4	eq.(4	ADJ
iajs-1442	64	30	)	)	PUNCT
iajs-1442	64	31	or	or	CCONJ
iajs-1442	64	32	eq.(5	eq.(5	NOUN
iajs-1442	64	33	)	)	PUNCT
iajs-1442	64	34	into	into	ADP
iajs-1442	64	35	eq.(2	eq.(2	ADJ
iajs-1442	64	36	)	)	PUNCT
iajs-1442	64	37	,	,	PUNCT
iajs-1442	64	38	we	we	PRON
iajs-1442	64	39	will	will	AUX
iajs-1442	64	40	get	get	VERB
iajs-1442	64	41	:	:	PUNCT
iajs-1442	64	42	either	either	ADV
iajs-1442	64	43	,	,	PUNCT
iajs-1442	64	44	t(u)ur)u(uu(u)t	t(u)ur)u(uu(u)t	PROPN
iajs-1442	64	45	1ααα	1ααα	PROPN
iajs-1442	64	46	gc	gc	PROPN
iajs-1442	64	47			VERB
iajs-1442	64	48	then	then	ADV
iajs-1442	64	49	the	the	DET
iajs-1442	64	50	general	general	ADJ
iajs-1442	64	51	elzaki	elzaki	NOUN
iajs-1442	64	52	solution	solution	NOUN
iajs-1442	64	53	:	:	PUNCT
iajs-1442	64	54	)	)	PUNCT
iajs-1442	64	55	6	6	NUM
iajs-1442	64	56	(	(	PUNCT
iajs-1442	64	57	ur1	ur1	NOUN
iajs-1442	64	58	)	)	PUNCT
iajs-1442	64	59	)	)	PUNCT
iajs-1442	65	1	u(g(cu	u(g(cu	INTJ
iajs-1442	65	2	(	(	PUNCT
iajs-1442	65	3	u)t	u)t	ADJ
iajs-1442	65	4	1α	1α	NUM
iajs-1442	65	5	α	α	PROPN
iajs-1442	65	6			PROPN
iajs-1442	65	7			ADV
iajs-1442	65	8			PROPN
iajs-1442	65	9	or	or	CCONJ
iajs-1442	65	10	t(u)*k(u)u))u(g(cu(u)t	t(u)*k(u)u))u(g(cu(u)t	PRON
iajs-1442	65	11	1	1	NUM
iajs-1442	65	12	-	-	PUNCT
iajs-1442	65	13	αα	αα	NOUN
iajs-1442	65	14			PUNCT
iajs-1442	65	15	then	then	ADV
iajs-1442	65	16	)	)	PUNCT
iajs-1442	65	17	7	7	NUM
iajs-1442	65	18	(	(	PUNCT
iajs-1442	65	19	k(u)u1	k(u)u1	NOUN
iajs-1442	65	20	)	)	PUNCT
iajs-1442	65	21	)	)	PUNCT
iajs-1442	66	1	u(g(cu	u(g(cu	X
iajs-1442	66	2	(	(	PUNCT
iajs-1442	66	3	u)t	u)t	ADJ
iajs-1442	66	4	1	1	NUM
iajs-1442	66	5	-	-	PUNCT
iajs-1442	66	6	α	α	PRON
iajs-1442	66	7	α	α	PROPN
iajs-1442	66	8			PROPN
iajs-1442	66	9			ADV
iajs-1442	66	10			NUM
iajs-1442	66	11	or	or	CCONJ
iajs-1442	66	12			PROPN
iajs-1442	66	13			PROPN
iajs-1442	66	14			X
iajs-1442	66	15			NOUN
iajs-1442	66	16			AUX
iajs-1442	66	17			PROPN
iajs-1442	66	18			NOUN
iajs-1442	66	19			ADV
iajs-1442	66	20			VERB
iajs-1442	66	21			PRON
iajs-1442	66	22			NOUN
iajs-1442	66	23			NOUN
iajs-1442	66	24			PUNCT
iajs-1442	66	25			NOUN
iajs-1442	66	26			PROPN
iajs-1442	66	27			PROPN
iajs-1442	66	28			X
iajs-1442	66	29			NOUN
iajs-1442	66	30			X
iajs-1442	66	31			VERB
iajs-1442	66	32			PROPN
iajs-1442	66	33	t	t	NOUN
iajs-1442	66	34	0	0	NUM
iajs-1442	66	35	0i	0i	NOUN
iajs-1442	67	1	i	i	PRON
iajs-1442	67	2	αα	αα	VERB
iajs-1442	67	3	0i	0i	X
iajs-1442	68	1	i	i	PRON
iajs-1442	68	2	dτ)τ(y)τx,(ku))u(g(cu(t)y	dτ)τ(y)τx,(ku))u(g(cu(t)y	VERB
iajs-1442	68	3	ee	ee	INTJ
iajs-1442	68	4	matching	match	VERB
iajs-1442	68	5	both	both	DET
iajs-1442	68	6	sides	side	NOUN
iajs-1442	68	7	of	of	ADP
iajs-1442	68	8	this	this	DET
iajs-1442	68	9	equation	equation	NOUN
iajs-1442	68	10	yields	yield	VERB
iajs-1442	68	11	the	the	DET
iajs-1442	68	12	following	follow	VERB
iajs-1442	68	13	iterative	iterative	NOUN
iajs-1442	68	14	relations	relation	NOUN
iajs-1442	68	15	:	:	PUNCT
iajs-1442	68	16			ADJ
iajs-1442	68	17			NOUN
iajs-1442	68	18	)	)	PUNCT
iajs-1442	68	19	8())u(g(cu(t)y	8())u(g(cu(t)y	NOUN
iajs-1442	69	1	α	α	NOUN
iajs-1442	69	2	0	0	NUM
iajs-1442	69	3	e	e	PRON
iajs-1442	69	4			ADJ
iajs-1442	69	5			NOUN
iajs-1442	69	6			PROPN
iajs-1442	69	7			PROPN
iajs-1442	69	8			X
iajs-1442	69	9			NOUN
iajs-1442	69	10			VERB
iajs-1442	69	11			PROPN
iajs-1442	69	12			NOUN
iajs-1442	69	13	t	t	NOUN
iajs-1442	69	14	0	0	NUM
iajs-1442	70	1	α	α	NOUN
iajs-1442	70	2	dτ)τ(y)τx,(ku(t)y	dτ)τ(y)τx,(ku(t)y	NOUN
iajs-1442	70	3	01	01	NUM
iajs-1442	70	4	ee	ee	ADP
iajs-1442	70	5			PROPN
iajs-1442	70	6			PROPN
iajs-1442	70	7			PROPN
iajs-1442	70	8			PROPN
iajs-1442	70	9			X
iajs-1442	70	10			NOUN
iajs-1442	70	11			VERB
iajs-1442	70	12			PROPN
iajs-1442	70	13			NOUN
iajs-1442	70	14	t	t	NOUN
iajs-1442	70	15	0	0	NUM
iajs-1442	71	1	α	α	NOUN
iajs-1442	71	2	dτ)τ(y)τx,(ku(t)y	dτ)τ(y)τx,(ku(t)y	NOUN
iajs-1442	71	3	12	12	NUM
iajs-1442	71	4	ee	ee	INTJ
iajs-1442	71	5	in	in	ADP
iajs-1442	71	6	general	general	ADJ
iajs-1442	71	7	,	,	PUNCT
iajs-1442	71	8			ADJ
iajs-1442	71	9			NOUN
iajs-1442	71	10	)	)	PUNCT
iajs-1442	71	11	9(	9(	NOUN
iajs-1442	71	12	...	...	PUNCT
iajs-1442	71	13	1,0,i	1,0,i	NUM
iajs-1442	71	14	,	,	PUNCT
iajs-1442	71	15	dτ)τ(y)τx,(ku(t)y	dτ)τ(y)τx,(ku(t)y	NOUN
iajs-1442	71	16	t	t	NOUN
iajs-1442	71	17	0	0	NUM
iajs-1442	72	1	i	i	PRON
iajs-1442	72	2	α	α	NOUN
iajs-1442	72	3	1i	1i	NOUN
iajs-1442	72	4			NUM
iajs-1442	72	5			PROPN
iajs-1442	73	1			PROPN
iajs-1442	73	2			PRON
iajs-1442	73	3			NOUN
iajs-1442	73	4			VERB
iajs-1442	73	5			PROPN
iajs-1442	73	6			NOUN
iajs-1442	73	7	ee	ee	ADP
iajs-1442	73	8	the	the	DET
iajs-1442	73	9	fourth	fourth	ADJ
iajs-1442	73	10	step	step	NOUN
iajs-1442	73	11	,	,	PUNCT
iajs-1442	73	12	we	we	PRON
iajs-1442	73	13	apply	apply	VERB
iajs-1442	73	14	inverse	inverse	NOUN
iajs-1442	73	15	et	et	NOUN
iajs-1442	73	16	of	of	ADP
iajs-1442	73	17	either	either	DET
iajs-1442	73	18	eq.(6	eq.(6	ADJ
iajs-1442	73	19	)	)	PUNCT
iajs-1442	73	20	or	or	CCONJ
iajs-1442	73	21	eq.(7	eq.(7	VERB
iajs-1442	73	22	)	)	PUNCT
iajs-1442	73	23	or	or	CCONJ
iajs-1442	73	24	(	(	PUNCT
iajs-1442	73	25	eq.(8	eq.(8	X
iajs-1442	73	26	)	)	PUNCT
iajs-1442	73	27	and	and	CCONJ
iajs-1442	73	28	eq.(9	eq.(9	ADJ
iajs-1442	73	29	)	)	PUNCT
iajs-1442	73	30	)	)	PUNCT
iajs-1442	73	31	give	give	VERB
iajs-1442	73	32	the	the	DET
iajs-1442	73	33	general	general	ADJ
iajs-1442	73	34	solution	solution	NOUN
iajs-1442	73	35	for	for	ADP
iajs-1442	73	36	(	(	PUNCT
iajs-1442	73	37	lvfide	lvfide	ADV
iajs-1442	73	38	):	):	PUNCT
iajs-1442	73	39	either	either	CCONJ
iajs-1442	73	40	)	)	PUNCT
iajs-1442	73	41	10	10	NUM
iajs-1442	73	42	(	(	PUNCT
iajs-1442	73	43	ur1	ur1	NOUN
iajs-1442	73	44	)	)	PUNCT
iajs-1442	73	45	)	)	PUNCT
iajs-1442	74	1	u(g(cu	u(g(cu	X
iajs-1442	74	2	t(t)y	t(t)y	NOUN
iajs-1442	74	3	1α	1α	NUM
iajs-1442	74	4	α	α	PRON
iajs-1442	74	5	1	1	NUM
iajs-1442	74	6			NOUN
iajs-1442	74	7			PROPN
iajs-1442	74	8			PROPN
iajs-1442	74	9			X
iajs-1442	74	10			NOUN
iajs-1442	74	11			NOUN
iajs-1442	74	12			VERB
iajs-1442	74	13			PROPN
iajs-1442	74	14			PROPN
iajs-1442	74	15			VERB
iajs-1442	74	16			NUM
iajs-1442	74	17			ADJ
iajs-1442	74	18			NOUN
iajs-1442	74	19	or	or	CCONJ
iajs-1442	74	20	)	)	PUNCT
iajs-1442	74	21	11	11	NUM
iajs-1442	74	22	(	(	PUNCT
iajs-1442	74	23	k(u)u1	k(u)u1	NOUN
iajs-1442	74	24	)	)	PUNCT
iajs-1442	74	25	)	)	PUNCT
iajs-1442	75	1	u(g(cu	u(g(cu	X
iajs-1442	75	2	t(t)y	t(t)y	NOUN
iajs-1442	75	3	1	1	NUM
iajs-1442	75	4	-	-	NUM
iajs-1442	75	5	α	α	NOUN
iajs-1442	75	6	α	α	NOUN
iajs-1442	75	7	1	1	NUM
iajs-1442	75	8			NOUN
iajs-1442	75	9			PROPN
iajs-1442	75	10			PROPN
iajs-1442	75	11			X
iajs-1442	75	12			NOUN
iajs-1442	75	13			NOUN
iajs-1442	75	14			VERB
iajs-1442	75	15			PROPN
iajs-1442	75	16			PROPN
iajs-1442	75	17			VERB
iajs-1442	75	18			NUM
iajs-1442	75	19			NOUN
iajs-1442	75	20	or	or	CCONJ
iajs-1442	75	21			ADJ
iajs-1442	75	22			NOUN
iajs-1442	75	23	)	)	PUNCT
iajs-1442	75	24	12(p(t)))u(g(cu(t)y	12(p(t)))u(g(cu(t)y	NUM
iajs-1442	75	25	α1	α1	PROPN
iajs-1442	75	26	0	0	NUM
iajs-1442	75	27			NOUN
iajs-1442	75	28	e	e	NOUN
iajs-1442	75	29	mathematics	mathematics	PROPN
iajs-1442	75	30	|198	|198	PROPN
iajs-1442	75	31	2102	2102	NUM
iajs-1442	75	32	(	(	PUNCT
iajs-1442	75	33	عام	عام	ADP
iajs-1442	75	34	2	2	NUM
iajs-1442	75	35	(	(	PUNCT
iajs-1442	75	36	العدد	العدد	PROPN
iajs-1442	75	37	)	)	PUNCT
iajs-1442	75	38	30المجلد	30المجلد	NUM
iajs-1442	75	39	)	)	PUNCT
iajs-1442	75	40	مجلة	مجلة	VERB
iajs-1442	75	41	إبن	إبن	NOUN
iajs-1442	75	42	الهيثم	الهيثم	ADJ
iajs-1442	75	43	للعلوم	للعلوم	NOUN
iajs-1442	75	44	الصرفة	الصرفة	NOUN
iajs-1442	76	1	و	و	PRON
iajs-1442	76	2	التطبيقية	التطبيقية	ADJ
iajs-1442	76	3	ibn	ibn	PROPN
iajs-1442	76	4	al	al	PROPN
iajs-1442	76	5	-	-	PUNCT
iajs-1442	76	6	haitham	haitham	PROPN
iajs-1442	76	7	j.	j.	PROPN
iajs-1442	76	8	for	for	ADP
iajs-1442	76	9	pure	pure	PROPN
iajs-1442	76	10	&	&	CCONJ
iajs-1442	76	11	appl	appl	PROPN
iajs-1442	76	12	.	.	PUNCT
iajs-1442	77	1	sci	sci	PROPN
iajs-1442	77	2	.	.	PUNCT
iajs-1442	78	1	vol.03	vol.03	PROPN
iajs-1442	78	2	(	(	PUNCT
iajs-1442	78	3	2	2	NUM
iajs-1442	78	4	)	)	PUNCT
iajs-1442	78	5	2017	2017	NUM
iajs-1442	78	6	with	with	ADP
iajs-1442	78	7	)	)	PUNCT
iajs-1442	78	8	13(	13(	NUM
iajs-1442	78	9	...	...	PUNCT
iajs-1442	78	10	1,0,i	1,0,i	NUM
iajs-1442	78	11	,	,	PUNCT
iajs-1442	78	12	dτ)τ(y)τx,(ku(t)y	dτ)τ(y)τx,(ku(t)y	NOUN
iajs-1442	78	13	t	t	NOUN
iajs-1442	78	14	0	0	NUM
iajs-1442	79	1	α	α	NOUN
iajs-1442	80	1	i	i	NOUN
iajs-1442	81	1	1	1	NUM
iajs-1442	82	1	1i	1i	NUM
iajs-1442	82	2			NOUN
iajs-1442	82	3			NOUN
iajs-1442	83	1			PROPN
iajs-1442	83	2			PROPN
iajs-1442	83	3			X
iajs-1442	83	4			NOUN
iajs-1442	83	5			X
iajs-1442	83	6			VERB
iajs-1442	83	7			PROPN
iajs-1442	83	8			NOUN
iajs-1442	83	9			PROPN
iajs-1442	83	10			PROPN
iajs-1442	83	11			X
iajs-1442	83	12			NOUN
iajs-1442	83	13			SYM
iajs-1442	83	14			VERB
iajs-1442	83	15			PROPN
iajs-1442	84	1			NOUN
iajs-1442	84	2			PUNCT
iajs-1442	85	1			PROPN
iajs-1442	85	2			VERB
iajs-1442	85	3	ee	ee	ADP
iajs-1442	85	4	the	the	DET
iajs-1442	85	5	function	function	NOUN
iajs-1442	85	6	p(t	p(t	NOUN
iajs-1442	85	7	)	)	PUNCT
iajs-1442	85	8	defined	define	VERB
iajs-1442	85	9	in	in	ADP
iajs-1442	85	10	eq.(12	eq.(12	NOUN
iajs-1442	85	11	)	)	PUNCT
iajs-1442	85	12	can	can	AUX
iajs-1442	85	13	be	be	AUX
iajs-1442	85	14	decomposed	decompose	VERB
iajs-1442	85	15	into	into	ADP
iajs-1442	85	16	two	two	NUM
iajs-1442	85	17	parts	part	NOUN
iajs-1442	85	18	:	:	PUNCT
iajs-1442	85	19	p(t	p(t	NOUN
iajs-1442	85	20	)	)	PUNCT
iajs-1442	85	21	=	=	SYM
iajs-1442	86	1	p1(t	p1(t	X
iajs-1442	86	2	)	)	PUNCT
iajs-1442	86	3	+	+	CCONJ
iajs-1442	86	4	p2(t	p2(t	NOUN
iajs-1442	86	5	)	)	PUNCT
iajs-1442	86	6	so	so	ADV
iajs-1442	86	7	,	,	PUNCT
iajs-1442	86	8	the	the	DET
iajs-1442	86	9	modified	modify	VERB
iajs-1442	86	10	recursion	recursion	NOUN
iajs-1442	86	11	relation	relation	NOUN
iajs-1442	86	12	is	be	AUX
iajs-1442	86	13	obtained	obtain	VERB
iajs-1442	86	14	)	)	PUNCT
iajs-1442	86	15	14	14	NUM
iajs-1442	86	16	(	(	PUNCT
iajs-1442	86	17	...	...	PUNCT
iajs-1442	86	18	2,1,i	2,1,i	NUM
iajs-1442	86	19	,	,	PUNCT
iajs-1442	86	20	dτ)τ(y)τx,(ku(t)y	dτ)τ(y)τx,(ku(t)y	NOUN
iajs-1442	86	21	dτ)τ(y)τx,(ku(t)p(t)y	dτ)τ(y)τx,(ku(t)p(t)y	NOUN
iajs-1442	87	1	(	(	PUNCT
iajs-1442	87	2	t)p(t)y	t)p(t)y	ADP
iajs-1442	87	3	t	t	PROPN
iajs-1442	87	4	0	0	NUM
iajs-1442	88	1	α	α	NOUN
iajs-1442	88	2	t	t	NOUN
iajs-1442	88	3	0	0	NUM
iajs-1442	89	1	α	α	NOUN
iajs-1442	89	2	i	i	NOUN
iajs-1442	89	3	1	1	NUM
iajs-1442	89	4	1i	1i	NOUN
iajs-1442	89	5	0	0	NUM
iajs-1442	89	6	1	1	NUM
iajs-1442	89	7	21	21	NUM
iajs-1442	89	8	10	10	NUM
iajs-1442	89	9			NUM
iajs-1442	89	10			NUM
iajs-1442	89	11			NUM
iajs-1442	89	12			NUM
iajs-1442	89	13			NUM
iajs-1442	89	14			NUM
iajs-1442	89	15			NUM
iajs-1442	89	16			NUM
iajs-1442	89	17			NUM
iajs-1442	89	18			NUM
iajs-1442	89	19			NUM
iajs-1442	89	20			NOUN
iajs-1442	89	21			PROPN
iajs-1442	90	1			NUM
iajs-1442	90	2			PROPN
iajs-1442	90	3			PROPN
iajs-1442	90	4			PROPN
iajs-1442	90	5			X
iajs-1442	90	6			NOUN
iajs-1442	90	7			X
iajs-1442	90	8			VERB
iajs-1442	90	9			PROPN
iajs-1442	90	10			NOUN
iajs-1442	90	11			PROPN
iajs-1442	90	12			PROPN
iajs-1442	90	13			X
iajs-1442	90	14			NOUN
iajs-1442	90	15			SYM
iajs-1442	90	16			VERB
iajs-1442	90	17			PROPN
iajs-1442	90	18			ADJ
iajs-1442	90	19			PROPN
iajs-1442	90	20			PROPN
iajs-1442	90	21			PROPN
iajs-1442	90	22			X
iajs-1442	90	23			NOUN
iajs-1442	90	24			X
iajs-1442	90	25			VERB
iajs-1442	90	26			PROPN
iajs-1442	90	27			NOUN
iajs-1442	90	28			PROPN
iajs-1442	90	29			PROPN
iajs-1442	90	30			X
iajs-1442	90	31			NOUN
iajs-1442	90	32			SYM
iajs-1442	90	33			VERB
iajs-1442	90	34			PROPN
iajs-1442	90	35			ADJ
iajs-1442	90	36			NOUN
iajs-1442	90	37			PUNCT
iajs-1442	90	38			PUNCT
iajs-1442	91	1			PROPN
iajs-1442	91	2			VERB
iajs-1442	91	3			VERB
iajs-1442	91	4	ee	ee	ADP
iajs-1442	91	5	ee	ee	ADP
iajs-1442	91	6	the	the	DET
iajs-1442	91	7	solution	solution	NOUN
iajs-1442	91	8	depends	depend	VERB
iajs-1442	91	9	on	on	ADP
iajs-1442	91	10	the	the	DET
iajs-1442	91	11	choice	choice	NOUN
iajs-1442	91	12	of	of	ADP
iajs-1442	91	13	p1(t	p1(t	PROPN
iajs-1442	91	14	)	)	PUNCT
iajs-1442	91	15	and	and	CCONJ
iajs-1442	91	16	p2(t	p2(t	PROPN
iajs-1442	91	17	)	)	PUNCT
iajs-1442	91	18	.	.	PUNCT
iajs-1442	92	1	we	we	PRON
iajs-1442	92	2	will	will	AUX
iajs-1442	92	3	show	show	VERB
iajs-1442	92	4	how	how	SCONJ
iajs-1442	92	5	to	to	PART
iajs-1442	92	6	suitably	suitably	ADV
iajs-1442	92	7	choose	choose	VERB
iajs-1442	92	8	p1(t	p1(t	PART
iajs-1442	92	9	)	)	PUNCT
iajs-1442	92	10	and	and	CCONJ
iajs-1442	92	11	p2(t	p2(t	PROPN
iajs-1442	92	12	)	)	PUNCT
iajs-1442	92	13	as	as	ADV
iajs-1442	92	14	well	well	ADV
iajs-1442	92	15	as	as	ADP
iajs-1442	92	16	testing	test	VERB
iajs-1442	92	17	the	the	DET
iajs-1442	92	18	method	method	NOUN
iajs-1442	92	19	by	by	ADP
iajs-1442	92	20	some	some	DET
iajs-1442	92	21	examples	example	NOUN
iajs-1442	92	22	in	in	ADP
iajs-1442	92	23	the	the	DET
iajs-1442	92	24	next	next	ADJ
iajs-1442	92	25	section	section	NOUN
iajs-1442	92	26	.	.	PUNCT
iajs-1442	93	1	test	test	NOUN
iajs-1442	93	2	examples	example	NOUN
iajs-1442	93	3	in	in	ADP
iajs-1442	93	4	this	this	DET
iajs-1442	93	5	section	section	NOUN
iajs-1442	93	6	,	,	PUNCT
iajs-1442	93	7	we	we	PRON
iajs-1442	93	8	present	present	VERB
iajs-1442	93	9	some	some	DET
iajs-1442	93	10	test	test	NOUN
iajs-1442	93	11	examples	example	NOUN
iajs-1442	93	12	to	to	PART
iajs-1442	93	13	show	show	VERB
iajs-1442	93	14	the	the	DET
iajs-1442	93	15	effectiveness	effectiveness	NOUN
iajs-1442	93	16	of	of	ADP
iajs-1442	93	17	the	the	DET
iajs-1442	93	18	et	et	NOUN
iajs-1442	93	19	method	method	NOUN
iajs-1442	93	20	for	for	ADP
iajs-1442	93	21	solving	solve	VERB
iajs-1442	93	22	lvfide	lvfide	NOUN
iajs-1442	93	23	's	's	PART
iajs-1442	93	24	.	.	PUNCT
iajs-1442	94	1	example	example	NOUN
iajs-1442	94	2	(	(	PUNCT
iajs-1442	94	3	1	1	NUM
iajs-1442	94	4	):	):	PUNCT
iajs-1442	94	5	consider	consider	VERB
iajs-1442	94	6	the	the	DET
iajs-1442	94	7	following	follow	VERB
iajs-1442	94	8	linear	linear	PROPN
iajs-1442	94	9	lvfide	lvfide	NOUN
iajs-1442	95	1	[	[	X
iajs-1442	95	2	5	5	NUM
iajs-1442	95	3	]	]	X
iajs-1442	95	4			NOUN
iajs-1442	95	5	x	x	SYM
iajs-1442	95	6	0	0	NUM
iajs-1442	95	7	dt)t(y1)xerf	dt)t(y1)xerf	NOUN
iajs-1442	95	8	(	(	PUNCT
iajs-1442	95	9	xπ	xπ	NOUN
iajs-1442	95	10	1	1	X
iajs-1442	95	11	)	)	PUNCT
iajs-1442	95	12	x(y	x(y	PROPN
iajs-1442	96	1	d	d	PROPN
iajs-1442	96	2	x0.5	x0.5	PROPN
iajs-1442	96	3	eex	eex	NOUN
iajs-1442	96	4	with	with	ADP
iajs-1442	96	5	0)0(yd	0)0(yd	NUM
iajs-1442	96	6	1	1	NUM
iajs-1442	96	7	0.5c	0.5c	NOUN
iajs-1442	96	8			NUM
iajs-1442	96	9	since	since	SCONJ
iajs-1442	96	10	1nthen	1nthen	NUM
iajs-1442	96	11	,	,	PUNCT
iajs-1442	96	12	nα1	nα1	NOUN
iajs-1442	96	13	-	-	PUNCT
iajs-1442	96	14	nand0.5α	nand0.5α	NOUN
iajs-1442	96	15			PROPN
iajs-1442	96	16	applying	apply	VERB
iajs-1442	96	17	(	(	PUNCT
iajs-1442	96	18	et	et	NOUN
iajs-1442	96	19	)	)	PUNCT
iajs-1442	96	20	of	of	ADP
iajs-1442	96	21	the	the	DET
iajs-1442	96	22	above	above	ADJ
iajs-1442	96	23	equation	equation	NOUN
iajs-1442	96	24	and	and	CCONJ
iajs-1442	96	25	since	since	SCONJ
iajs-1442	96	26	k(x	k(x	PROPN
iajs-1442	96	27	,	,	PUNCT
iajs-1442	96	28	t	t	PROPN
iajs-1442	96	29	)	)	PUNCT
iajs-1442	96	30	=	=	SYM
iajs-1442	96	31	1	1	NUM
iajs-1442	96	32	,	,	PUNCT
iajs-1442	96	33	then	then	ADV
iajs-1442	96	34	by	by	ADP
iajs-1442	96	35	using	use	VERB
iajs-1442	96	36	eq.(10	eq.(10	NOUN
iajs-1442	96	37	)	)	PUNCT
iajs-1442	96	38	we	we	PRON
iajs-1442	96	39	have	have	VERB
iajs-1442	96	40	the	the	DET
iajs-1442	96	41	solution	solution	NOUN
iajs-1442	96	42	:	:	PUNCT
iajs-1442	96	43	)	)	PUNCT
iajs-1442	96	44	15	15	NUM
iajs-1442	96	45	(	(	PUNCT
iajs-1442	96	46	u1	u1	NOUN
iajs-1442	96	47	)	)	PUNCT
iajs-1442	96	48	)	)	PUNCT
iajs-1442	97	1	u(g(cu	u(g(cu	X
iajs-1442	97	2	t(x)y	t(x)y	PROPN
iajs-1442	97	3	1.5	1.5	NUM
iajs-1442	97	4	0.5	0.5	NUM
iajs-1442	97	5	1	1	NUM
iajs-1442	97	6			NOUN
iajs-1442	97	7			PROPN
iajs-1442	97	8			PROPN
iajs-1442	97	9			X
iajs-1442	97	10			NOUN
iajs-1442	97	11			NOUN
iajs-1442	97	12			VERB
iajs-1442	97	13			PROPN
iajs-1442	97	14			PROPN
iajs-1442	97	15			VERB
iajs-1442	97	16			PROPN
iajs-1442	97	17			NOUN
iajs-1442	97	18	where	where	SCONJ
iajs-1442	97	19	0)0(yduc	0)0(yduc	NOUN
iajs-1442	97	20	0.5	0.5	PUNCT
iajs-1442	97	21	and	and	CCONJ
iajs-1442	97	22			PROPN
iajs-1442	97	23			PROPN
iajs-1442	97	24			X
iajs-1442	97	25			NOUN
iajs-1442	97	26			VERB
iajs-1442	97	27			PROPN
iajs-1442	97	28			PROPN
iajs-1442	97	29	1)xerf	1)xerf	NUM
iajs-1442	97	30	(	(	PUNCT
iajs-1442	97	31	xπ	xπ	ADP
iajs-1442	97	32	1	1	NUM
iajs-1442	97	33	g(u	g(u	PROPN
iajs-1442	97	34	)	)	PUNCT
iajs-1442	97	35	xx	xx	NUM
iajs-1442	97	36	eee	eee	NOUN
iajs-1442	97	37	from	from	ADP
iajs-1442	97	38	appendix	appendix	NOUN
iajs-1442	97	39	given	give	VERB
iajs-1442	97	40	in	in	ADP
iajs-1442	97	41	[	[	X
iajs-1442	97	42	11	11	NUM
iajs-1442	97	43	]	]	X
iajs-1442	97	44	(	(	PUNCT
iajs-1442	97	45	et	et	NOUN
iajs-1442	97	46	of	of	ADP
iajs-1442	97	47	some	some	DET
iajs-1442	97	48	functions	function	NOUN
iajs-1442	97	49	)	)	PUNCT
iajs-1442	97	50	and	and	CCONJ
iajs-1442	97	51	theorem	theorem	VERB
iajs-1442	97	52	(	(	PUNCT
iajs-1442	97	53	7	7	NUM
iajs-1442	97	54	)	)	PUNCT
iajs-1442	97	55	we	we	PRON
iajs-1442	97	56	have	have	VERB
iajs-1442	97	57	:	:	PUNCT
iajs-1442	97	58	mathematics	mathematic	NOUN
iajs-1442	97	59	|199	|199	X
iajs-1442	97	60	2102	2102	NUM
iajs-1442	97	61	(	(	PUNCT
iajs-1442	97	62	عام	عام	ADP
iajs-1442	97	63	2	2	NUM
iajs-1442	97	64	(	(	PUNCT
iajs-1442	97	65	العدد	العدد	PROPN
iajs-1442	97	66	)	)	PUNCT
iajs-1442	97	67	30المجلد	30المجلد	NUM
iajs-1442	97	68	)	)	PUNCT
iajs-1442	98	1	مجلة	مجلة	VERB
iajs-1442	98	2	إبن	إبن	NOUN
iajs-1442	98	3	الهيثم	الهيثم	ADJ
iajs-1442	98	4	للعلوم	للعلوم	NOUN
iajs-1442	98	5	الصرفة	الصرفة	NOUN
iajs-1442	98	6	و	و	PRON
iajs-1442	98	7	التطبيقية	التطبيقية	ADJ
iajs-1442	98	8	ibn	ibn	PROPN
iajs-1442	98	9	al	al	PROPN
iajs-1442	98	10	-	-	PUNCT
iajs-1442	98	11	haitham	haitham	PROPN
iajs-1442	98	12	j.	j.	PROPN
iajs-1442	98	13	for	for	ADP
iajs-1442	98	14	pure	pure	PROPN
iajs-1442	98	15	&	&	CCONJ
iajs-1442	98	16	appl	appl	PROPN
iajs-1442	98	17	.	.	PUNCT
iajs-1442	99	1	sci	sci	PROPN
iajs-1442	99	2	.	.	PUNCT
iajs-1442	100	1	vol.03	vol.03	PROPN
iajs-1442	100	2	(	(	PUNCT
iajs-1442	100	3	2	2	NUM
iajs-1442	100	4	)	)	PUNCT
iajs-1442	100	5	2017	2017	NUM
iajs-1442	100	6	u1	u1	NOUN
iajs-1442	100	7	uuu	uuu	NOUN
iajs-1442	100	8	u	u	PROPN
iajs-1442	100	9	u1	u1	NOUN
iajs-1442	100	10	u	u	PROPN
iajs-1442	100	11	u1	u1	PROPN
iajs-1442	100	12	uu	uu	PROPN
iajs-1442	100	13	uug(u	uug(u	PROPN
iajs-1442	100	14	)	)	PUNCT
iajs-1442	100	15	3	3	NUM
iajs-1442	100	16	2	2	NUM
iajs-1442	100	17	22	22	NUM
iajs-1442	100	18			PROPN
iajs-1442	100	19			PROPN
iajs-1442	100	20			ADP
iajs-1442	100	21			PROPN
iajs-1442	100	22			PROPN
iajs-1442	100	23			PROPN
iajs-1442	100	24			ADJ
iajs-1442	100	25	substituting	substituting	NOUN
iajs-1442	100	26	in	in	ADP
iajs-1442	100	27	eq.(15	eq.(15	NOUN
iajs-1442	100	28	)	)	PUNCT
iajs-1442	100	29	,	,	PUNCT
iajs-1442	100	30	we	we	PRON
iajs-1442	100	31	obtain	obtain	VERB
iajs-1442	100	32	:	:	PUNCT
iajs-1442	100	33			PROPN
iajs-1442	100	34			PROPN
iajs-1442	100	35			PROPN
iajs-1442	100	36			X
iajs-1442	100	37			NOUN
iajs-1442	100	38			X
iajs-1442	100	39			VERB
iajs-1442	100	40			PROPN
iajs-1442	100	41			NOUN
iajs-1442	100	42			PROPN
iajs-1442	100	43			PROPN
iajs-1442	100	44			X
iajs-1442	100	45			NOUN
iajs-1442	100	46			NOUN
iajs-1442	100	47			VERB
iajs-1442	100	48			PROPN
iajs-1442	100	49			NOUN
iajs-1442	100	50			PRON
iajs-1442	100	51			NOUN
iajs-1442	100	52			NOUN
iajs-1442	100	53			PRON
iajs-1442	100	54			NOUN
iajs-1442	100	55	u1	u1	VERB
iajs-1442	100	56	u	u	NOUN
iajs-1442	100	57	t	t	PROPN
iajs-1442	100	58	)	)	PUNCT
iajs-1442	100	59	uu(1u)(1	uu(1u)(1	PROPN
iajs-1442	100	60	uuu	uuu	PROPN
iajs-1442	100	61	t(x)y	t(x)y	PROPN
iajs-1442	100	62	2	2	NUM
iajs-1442	100	63	1	1	NUM
iajs-1442	100	64	32	32	NUM
iajs-1442	100	65	1	1	NUM
iajs-1442	100	66	again	again	ADV
iajs-1442	100	67	from	from	ADP
iajs-1442	100	68	appendix	appendix	NOUN
iajs-1442	100	69	given	give	VERB
iajs-1442	100	70	in	in	ADP
iajs-1442	100	71	[	[	PUNCT
iajs-1442	100	72	11	11	NUM
iajs-1442	100	73	]	]	PUNCT
iajs-1442	100	74	,	,	PUNCT
iajs-1442	100	75	we	we	PRON
iajs-1442	100	76	get	get	VERB
iajs-1442	100	77	the	the	DET
iajs-1442	100	78	exact	exact	ADJ
iajs-1442	100	79	solution	solution	NOUN
iajs-1442	100	80	:	:	PUNCT
iajs-1442	100	81	y(x	y(x	X
iajs-1442	100	82	)	)	PUNCT
iajs-1442	100	83	=	=	PUNCT
iajs-1442	101	1	e	e	X
iajs-1442	101	2	x	x	PROPN
iajs-1442	101	3	.	.	PUNCT
iajs-1442	102	1	example	example	NOUN
iajs-1442	102	2	(	(	PUNCT
iajs-1442	102	3	2	2	NUM
iajs-1442	102	4	):	):	PUNCT
iajs-1442	102	5	let	let	VERB
iajs-1442	102	6	us	we	PRON
iajs-1442	102	7	consider	consider	VERB
iajs-1442	102	8	the	the	DET
iajs-1442	102	9	following	following	NOUN
iajs-1442	102	10	lvfide	lvfide	ADV
iajs-1442	102	11	with	with	ADP
iajs-1442	102	12	difference	difference	NOUN
iajs-1442	102	13	kernel	kernel	NOUN
iajs-1442	102	14	)	)	PUNCT
iajs-1442	102	15	16(dt)t(y	16(dt)t(y	NUM
iajs-1442	102	16	tx	tx	PROPN
iajs-1442	102	17	)	)	PUNCT
iajs-1442	102	18	x(g)x(y	x(g)x(y	PROPN
iajs-1442	103	1	d	d	X
iajs-1442	103	2	x	x	SYM
iajs-1442	103	3	0	0	NUM
iajs-1442	103	4	e56	e56	PROPN
iajs-1442	103	5			PUNCT
iajs-1442	103	6			PROPN
iajs-1442	103	7			ADV
iajs-1442	103	8	where	where	SCONJ
iajs-1442	103	9	x66x6x3xx	x66x6x3xx	PROPN
iajs-1442	103	10	5)14γ	5)14γ	NUM
iajs-1442	103	11	(	(	PUNCT
iajs-1442	103	12	6	6	NUM
iajs-1442	103	13	g(x	g(x	NOUN
iajs-1442	103	14	)	)	PUNCT
iajs-1442	104	1	e2359	e2359	PROPN
iajs-1442	104	2			VERB
iajs-1442	104	3	with	with	ADP
iajs-1442	104	4	initial	initial	ADJ
iajs-1442	104	5	conditions	condition	NOUN
iajs-1442	104	6	:	:	PUNCT
iajs-1442	104	7	0)0(ydand0)0(yd	0)0(ydand0)0(yd	NUM
iajs-1442	104	8	2	2	NUM
iajs-1442	104	9	54	54	NUM
iajs-1442	104	10	1	1	NUM
iajs-1442	104	11	51	51	NUM
iajs-1442	104	12	cc	cc	NOUN
iajs-1442	104	13			PROPN
iajs-1442	104	14			NOUN
iajs-1442	104	15	take	take	VERB
iajs-1442	104	16	the	the	DET
iajs-1442	104	17	(	(	PUNCT
iajs-1442	104	18	et	et	NOUN
iajs-1442	104	19	)	)	PUNCT
iajs-1442	104	20	of	of	ADP
iajs-1442	104	21	eq.(16	eq.(16	NOUN
iajs-1442	104	22	)	)	PUNCT
iajs-1442	104	23	and	and	CCONJ
iajs-1442	104	24	since	since	SCONJ
iajs-1442	104	25	k(x	k(x	PROPN
iajs-1442	104	26	,	,	PUNCT
iajs-1442	104	27	t	t	PROPN
iajs-1442	104	28	)	)	PUNCT
iajs-1442	104	29	is	be	AUX
iajs-1442	104	30	difference	difference	NOUN
iajs-1442	104	31	kernel	kernel	NOUN
iajs-1442	104	32	,	,	PUNCT
iajs-1442	104	33	so	so	ADV
iajs-1442	104	34	by	by	ADP
iajs-1442	104	35	eq.(11	eq.(11	PROPN
iajs-1442	104	36	)	)	PUNCT
iajs-1442	104	37	yields	yield	VERB
iajs-1442	104	38	:	:	PUNCT
iajs-1442	104	39	)	)	PUNCT
iajs-1442	104	40	17	17	NUM
iajs-1442	104	41	(	(	PUNCT
iajs-1442	104	42	k(u)u1	k(u)u1	NOUN
iajs-1442	104	43	)	)	PUNCT
iajs-1442	104	44	)	)	PUNCT
iajs-1442	105	1	u(g(cu	u(g(cu	X
iajs-1442	105	2	t(x)y	t(x)y	PROPN
iajs-1442	105	3	51	51	NUM
iajs-1442	105	4	56	56	NUM
iajs-1442	105	5	1	1	NUM
iajs-1442	105	6			NOUN
iajs-1442	105	7			PROPN
iajs-1442	105	8			PROPN
iajs-1442	105	9			X
iajs-1442	105	10			NOUN
iajs-1442	105	11			NOUN
iajs-1442	105	12			VERB
iajs-1442	105	13			PROPN
iajs-1442	105	14			PROPN
iajs-1442	105	15			VERB
iajs-1442	105	16			DET
iajs-1442	105	17			NOUN
iajs-1442	105	18	where	where	SCONJ
iajs-1442	105	19	c	c	NOUN
iajs-1442	105	20	=	=	SYM
iajs-1442	105	21	u	u	PROPN
iajs-1442	105	22	c1	c1	PROPN
iajs-1442	105	23	+	+	CCONJ
iajs-1442	105	24	c2	c2	PROPN
iajs-1442	105	25	=	=	SYM
iajs-1442	105	26	0	0	PROPN
iajs-1442	105	27	.	.	PUNCT
iajs-1442	106	1			ADJ
iajs-1442	106	2			PROPN
iajs-1442	106	3			PROPN
iajs-1442	106	4			PROPN
iajs-1442	106	5			PROPN
iajs-1442	106	6			X
iajs-1442	106	7			NOUN
iajs-1442	106	8			NOUN
iajs-1442	106	9			VERB
iajs-1442	106	10			PROPN
iajs-1442	106	11			NOUN
iajs-1442	106	12			NUM
iajs-1442	106	13			NUM
iajs-1442	106	14			NOUN
iajs-1442	106	15			PROPN
iajs-1442	106	16			PROPN
iajs-1442	106	17			X
iajs-1442	106	18			NOUN
iajs-1442	106	19			NOUN
iajs-1442	106	20			VERB
iajs-1442	106	21			PROPN
iajs-1442	106	22			PROPN
iajs-1442	106	23			PROPN
iajs-1442	106	24	u1	u1	NOUN
iajs-1442	106	25	uuu	uuu	NOUN
iajs-1442	106	26	6	6	NUM
iajs-1442	106	27	u1	u1	PROPN
iajs-1442	106	28	u	u	PROPN
iajs-1442	106	29	uuuuu6g(x)g(u	uuuuu6g(x)g(u	PROPN
iajs-1442	106	30	)	)	PUNCT
iajs-1442	106	31	6524519	6524519	NUM
iajs-1442	106	32	2	2	NUM
iajs-1442	106	33	2345519	2345519	NUM
iajs-1442	106	34	e	e	NOUN
iajs-1442	106	35	and	and	CCONJ
iajs-1442	106	36			ADJ
iajs-1442	106	37			NOUN
iajs-1442	106	38	u1	u1	NOUN
iajs-1442	106	39	u	u	NOUN
iajs-1442	106	40	k(u	k(u	NOUN
iajs-1442	106	41	)	)	PUNCT
iajs-1442	106	42	2	2	NUM
iajs-1442	106	43	xe	xe	PROPN
iajs-1442	106	44			NOUN
iajs-1442	106	45			NUM
iajs-1442	106	46	e	e	X
iajs-1442	106	47	now	now	ADV
iajs-1442	106	48	,	,	PUNCT
iajs-1442	106	49	eq.(17	eq.(17	NOUN
iajs-1442	106	50	)	)	PUNCT
iajs-1442	106	51	can	can	AUX
iajs-1442	106	52	be	be	AUX
iajs-1442	106	53	written	write	VERB
iajs-1442	106	54	in	in	ADP
iajs-1442	106	55	the	the	DET
iajs-1442	106	56	form	form	NOUN
iajs-1442	106	57	:	:	PUNCT
iajs-1442	106	58			ADJ
iajs-1442	106	59	51	51	NOUN
iajs-1442	106	60	511	511	NUM
iajs-1442	106	61	53665	53665	NUM
iajs-1442	106	62	1	1	NUM
iajs-1442	106	63	u6	u6	NOUN
iajs-1442	106	64	t	t	NOUN
iajs-1442	106	65	)	)	PUNCT
iajs-1442	106	66	u1	u1	NOUN
iajs-1442	106	67	u	u	PROPN
iajs-1442	106	68	(	(	PUNCT
iajs-1442	106	69	1u)(1	1u)(1	PROPN
iajs-1442	106	70	uuu	uuu	PROPN
iajs-1442	106	71	t6(x)y	t6(x)y	PROPN
iajs-1442	106	72			NUM
iajs-1442	106	73			NUM
iajs-1442	106	74			NOUN
iajs-1442	106	75			NOUN
iajs-1442	106	76			PUNCT
iajs-1442	106	77			NOUN
iajs-1442	107	1			PROPN
iajs-1442	107	2			PROPN
iajs-1442	107	3			X
iajs-1442	107	4			NOUN
iajs-1442	107	5			NOUN
iajs-1442	107	6			NOUN
iajs-1442	107	7			NOUN
iajs-1442	107	8			NOUN
iajs-1442	107	9			VERB
iajs-1442	107	10			PROPN
iajs-1442	107	11			NOUN
iajs-1442	107	12			NUM
iajs-1442	107	13			NUM
iajs-1442	107	14			NUM
iajs-1442	107	15	upon	upon	SCONJ
iajs-1442	107	16	inverting	inverting	NOUN
iajs-1442	107	17	,	,	PUNCT
iajs-1442	107	18	we	we	PRON
iajs-1442	107	19	get	get	VERB
iajs-1442	107	20	the	the	DET
iajs-1442	107	21	exact	exact	ADJ
iajs-1442	107	22	solution	solution	NOUN
iajs-1442	107	23	:	:	PUNCT
iajs-1442	107	24	y(x	y(x	X
iajs-1442	107	25	)	)	PUNCT
iajs-1442	108	1	=	=	PUNCT
iajs-1442	108	2	x	x	SYM
iajs-1442	108	3	3	3	X
iajs-1442	108	4	.	.	PUNCT
iajs-1442	108	5	example	example	NOUN
iajs-1442	108	6	(	(	PUNCT
iajs-1442	108	7	3	3	NUM
iajs-1442	108	8	):	):	PUNCT
iajs-1442	108	9	consider	consider	VERB
iajs-1442	108	10	the	the	DET
iajs-1442	108	11	following	follow	VERB
iajs-1442	108	12	lvfide	lvfide	ADJ
iajs-1442	108	13	mathematics	mathematics	PROPN
iajs-1442	108	14	|200	|200	ADP
iajs-1442	108	15	2102	2102	NUM
iajs-1442	108	16	(	(	PUNCT
iajs-1442	108	17	عام	عام	ADP
iajs-1442	108	18	2	2	NUM
iajs-1442	108	19	(	(	PUNCT
iajs-1442	108	20	العدد	العدد	PROPN
iajs-1442	108	21	)	)	PUNCT
iajs-1442	108	22	30المجلد	30المجلد	NUM
iajs-1442	108	23	)	)	PUNCT
iajs-1442	109	1	مجلة	مجلة	VERB
iajs-1442	109	2	إبن	إبن	NOUN
iajs-1442	109	3	الهيثم	الهيثم	ADJ
iajs-1442	109	4	للعلوم	للعلوم	NOUN
iajs-1442	109	5	الصرفة	الصرفة	NOUN
iajs-1442	109	6	و	و	PRON
iajs-1442	109	7	التطبيقية	التطبيقية	ADJ
iajs-1442	109	8	ibn	ibn	PROPN
iajs-1442	109	9	al	al	PROPN
iajs-1442	109	10	-	-	PUNCT
iajs-1442	109	11	haitham	haitham	PROPN
iajs-1442	109	12	j.	j.	PROPN
iajs-1442	109	13	for	for	ADP
iajs-1442	109	14	pure	pure	PROPN
iajs-1442	109	15	&	&	CCONJ
iajs-1442	109	16	appl	appl	PROPN
iajs-1442	109	17	.	.	PUNCT
iajs-1442	110	1	sci	sci	PROPN
iajs-1442	110	2	.	.	PUNCT
iajs-1442	111	1	vol.03	vol.03	PROPN
iajs-1442	111	2	(	(	PUNCT
iajs-1442	111	3	2	2	NUM
iajs-1442	111	4	)	)	PUNCT
iajs-1442	111	5	2017	2017	NUM
iajs-1442	111	6			PUNCT
iajs-1442	111	7			PUNCT
iajs-1442	111	8			PROPN
iajs-1442	111	9			PROPN
iajs-1442	111	10	t	t	PROPN
iajs-1442	111	11	0	0	NUM
iajs-1442	111	12	dτ)τ(yτ)(t	dτ)τ(yτ)(t	PROPN
iajs-1442	111	13	15	15	NUM
iajs-1442	111	14	65	65	NUM
iajs-1442	111	15	220.5	220.5	NUM
iajs-1442	111	16	tt)t(y	tt)t(y	NUM
iajs-1442	111	17	d	d	NOUN
iajs-1442	111	18	with	with	ADP
iajs-1442	111	19	initial	initial	ADJ
iajs-1442	111	20	conditions	condition	NOUN
iajs-1442	111	21	:	:	PUNCT
iajs-1442	111	22	πc1	πc1	PROPN
iajs-1442	111	23			NOUN
iajs-1442	111	24	.	.	PUNCT
iajs-1442	112	1	applying	apply	VERB
iajs-1442	112	2	the	the	DET
iajs-1442	112	3	et	et	NOUN
iajs-1442	112	4	to	to	ADP
iajs-1442	112	5	both	both	DET
iajs-1442	112	6	sides	side	NOUN
iajs-1442	112	7	of	of	ADP
iajs-1442	112	8	above	above	ADP
iajs-1442	112	9	equation	equation	NOUN
iajs-1442	112	10	as	as	ADV
iajs-1442	112	11	well	well	ADV
iajs-1442	112	12	as	as	ADP
iajs-1442	112	13	using	use	VERB
iajs-1442	112	14	eq.(12	eq.(12	NOUN
iajs-1442	112	15	)	)	PUNCT
iajs-1442	112	16	and	and	CCONJ
iajs-1442	112	17	eq.(13	eq.(13	ADJ
iajs-1442	112	18	)	)	PUNCT
iajs-1442	112	19	give	give	VERB
iajs-1442	112	20	:	:	PUNCT
iajs-1442	112	21			NOUN
iajs-1442	112	22			NOUN
iajs-1442	112	23			PROPN
iajs-1442	112	24			PROPN
iajs-1442	112	25			ADJ
iajs-1442	112	26			NOUN
iajs-1442	112	27	)	)	PUNCT
iajs-1442	112	28	)	)	PUNCT
iajs-1442	113	1	u(g(cu(t)y	u(g(cu(t)y	NOUN
iajs-1442	113	2	0.51	0.51	NUM
iajs-1442	113	3	0	0	NUM
iajs-1442	113	4	e	e	NOUN
iajs-1442	113	5	...	...	PUNCT
iajs-1442	113	6	1,0,i	1,0,i	NUM
iajs-1442	113	7	,	,	PUNCT
iajs-1442	113	8	t	t	PROPN
iajs-1442	113	9	0	0	NUM
iajs-1442	113	10	dτ)τ(y)τt((t)y	dτ)τ(y)τt((t)y	PROPN
iajs-1442	114	1	i	i	PRON
iajs-1442	114	2	20.51	20.51	NUM
iajs-1442	115	1	1i	1i	NUM
iajs-1442	115	2	u	u	NOUN
iajs-1442	115	3			ADJ
iajs-1442	115	4			PROPN
iajs-1442	115	5			PROPN
iajs-1442	116	1			PROPN
iajs-1442	116	2			PROPN
iajs-1442	116	3			X
iajs-1442	116	4			NOUN
iajs-1442	116	5			NOUN
iajs-1442	116	6			NOUN
iajs-1442	116	7			NOUN
iajs-1442	116	8			PROPN
iajs-1442	116	9			ADJ
iajs-1442	116	10			PROPN
iajs-1442	116	11			PROPN
iajs-1442	116	12			PROPN
iajs-1442	116	13			X
iajs-1442	116	14			NOUN
iajs-1442	116	15			SYM
iajs-1442	116	16			VERB
iajs-1442	116	17			PROPN
iajs-1442	116	18			NOUN
iajs-1442	116	19			PUNCT
iajs-1442	116	20			PROPN
iajs-1442	116	21			ADV
iajs-1442	116	22	ee	ee	ADP
iajs-1442	116	23	where	where	SCONJ
iajs-1442	116	24	πucu)0(yduc	πucu)0(yduc	ADV
iajs-1442	116	25	1	1	NUM
iajs-1442	116	26	0.5	0.5	NOUN
iajs-1442	116	27	292	292	NUM
iajs-1442	116	28	u	u	NOUN
iajs-1442	116	29	2)7γ	2)7γ	X
iajs-1442	116	30	(	(	PUNCT
iajs-1442	116	31	ttg(u	ttg(u	PROPN
iajs-1442	116	32	)	)	PUNCT
iajs-1442	116	33	15	15	NUM
iajs-1442	116	34	65	65	NUM
iajs-1442	116	35	15	15	NUM
iajs-1442	116	36	65	65	NUM
iajs-1442	116	37	and	and	CCONJ
iajs-1442	116	38			PROPN
iajs-1442	116	39			PROPN
iajs-1442	116	40			PROPN
iajs-1442	116	41			NOUN
iajs-1442	116	42			NOUN
iajs-1442	116	43			NOUN
iajs-1442	116	44			VERB
iajs-1442	116	45			PROPN
iajs-1442	116	46	e	e	PROPN
iajs-1442	116	47	(	(	PUNCT
iajs-1442	116	48	t)p(t)pp(t	t)p(t)pp(t	PROPN
iajs-1442	116	49	)	)	PUNCT
iajs-1442	116	50	t	t	PROPN
iajs-1442	116	51	1	1	NUM
iajs-1442	116	52	u	u	NOUN
iajs-1442	116	53	15	15	NUM
iajs-1442	116	54	2)7γ(65	2)7γ(65	NUM
iajs-1442	116	55	uπe	uπe	ADJ
iajs-1442	116	56	21	21	NUM
iajs-1442	116	57	5231	5231	NUM
iajs-1442	116	58	0	0	NUM
iajs-1442	116	59	3	3	NUM
iajs-1442	116	60	t	t	PROPN
iajs-1442	116	61	45	45	NUM
iajs-1442	116	62	2)7γ(28	2)7γ(28	NUM
iajs-1442	116	63	(	(	PUNCT
iajs-1442	116	64	t)ythen	t)ythen	ADP
iajs-1442	116	65			NUM
iajs-1442	116	66			ADJ
iajs-1442	116	67			ADJ
iajs-1442	116	68			PROPN
iajs-1442	116	69			PROPN
iajs-1442	116	70			X
iajs-1442	116	71			NOUN
iajs-1442	116	72			NOUN
iajs-1442	116	73			VERB
iajs-1442	116	74	so	so	ADV
iajs-1442	116	75	we	we	PRON
iajs-1442	116	76	have	have	VERB
iajs-1442	116	77	the	the	DET
iajs-1442	116	78	following	follow	VERB
iajs-1442	116	79	relations	relation	NOUN
iajs-1442	116	80	:	:	PUNCT
iajs-1442	116	81	)	)	PUNCT
iajs-1442	116	82	18(u	18(u	NUM
iajs-1442	116	83	t	t	NOUN
iajs-1442	116	84	1	1	NUM
iajs-1442	116	85	t	t	NOUN
iajs-1442	116	86	0	0	NUM
iajs-1442	116	87	dτ)τ(y)τt(t	dτ)τ(y)τt(t	NOUN
iajs-1442	116	88	45	45	NUM
iajs-1442	116	89	2)7γ(82	2)7γ(82	NOUN
iajs-1442	116	90	(	(	PUNCT
iajs-1442	116	91	t)y	t)y	X
iajs-1442	116	92	(	(	PUNCT
iajs-1442	116	93	t)y	t)y	NOUN
iajs-1442	116	94	0	0	NUM
iajs-1442	116	95	20.51	20.51	NUM
iajs-1442	116	96	1	1	NUM
iajs-1442	116	97	0	0	NUM
iajs-1442	116	98	3	3	NUM
iajs-1442	116	99			NOUN
iajs-1442	116	100			PROPN
iajs-1442	116	101			PROPN
iajs-1442	116	102			PROPN
iajs-1442	116	103			X
iajs-1442	116	104			NOUN
iajs-1442	116	105			NOUN
iajs-1442	116	106			NOUN
iajs-1442	116	107			NOUN
iajs-1442	116	108			PROPN
iajs-1442	116	109			ADJ
iajs-1442	116	110			PROPN
iajs-1442	116	111			PROPN
iajs-1442	116	112			PROPN
iajs-1442	116	113			X
iajs-1442	116	114			NOUN
iajs-1442	116	115			X
iajs-1442	116	116			X
iajs-1442	116	117			PROPN
iajs-1442	116	118			NUM
iajs-1442	116	119			NUM
iajs-1442	116	120			PUNCT
iajs-1442	116	121			NOUN
iajs-1442	116	122	ee	ee	INTJ
iajs-1442	116	123	and	and	CCONJ
iajs-1442	116	124	...	...	PUNCT
iajs-1442	116	125	2,1,i	2,1,i	NUM
iajs-1442	116	126	,	,	PUNCT
iajs-1442	116	127	t	t	PROPN
iajs-1442	116	128	0	0	NUM
iajs-1442	116	129	dτ)τ(y)τt((t)y	dτ)τ(y)τt((t)y	PROPN
iajs-1442	117	1	i	i	PRON
iajs-1442	117	2	20.51	20.51	NUM
iajs-1442	118	1	1i	1i	NUM
iajs-1442	118	2	u	u	NOUN
iajs-1442	118	3			ADJ
iajs-1442	118	4			PROPN
iajs-1442	118	5			PROPN
iajs-1442	119	1			PROPN
iajs-1442	119	2			PROPN
iajs-1442	119	3			X
iajs-1442	119	4			NOUN
iajs-1442	119	5			NOUN
iajs-1442	119	6			NOUN
iajs-1442	119	7			NOUN
iajs-1442	119	8			PROPN
iajs-1442	119	9			ADJ
iajs-1442	119	10			PROPN
iajs-1442	119	11			PROPN
iajs-1442	119	12			PROPN
iajs-1442	119	13			X
iajs-1442	119	14			NOUN
iajs-1442	119	15			SYM
iajs-1442	119	16			VERB
iajs-1442	119	17			PROPN
iajs-1442	119	18			NOUN
iajs-1442	119	19			PUNCT
iajs-1442	119	20			PROPN
iajs-1442	119	21			VERB
iajs-1442	119	22	ee	ee	INTJ
iajs-1442	119	23	now	now	ADV
iajs-1442	119	24	,	,	PUNCT
iajs-1442	119	25	we	we	PRON
iajs-1442	119	26	find	find	VERB
iajs-1442	119	27	the	the	DET
iajs-1442	119	28	et	et	NOUN
iajs-1442	119	29	of	of	ADP
iajs-1442	119	30	integral	integral	ADJ
iajs-1442	119	31	in	in	ADP
iajs-1442	119	32	eq.(18	eq.(18	NOUN
iajs-1442	119	33	)	)	PUNCT
iajs-1442	119	34	we	we	PRON
iajs-1442	119	35	have	have	VERB
iajs-1442	119	36	:	:	PUNCT
iajs-1442	119	37	2922	2922	NUM
iajs-1442	119	38	u	u	NOUN
iajs-1442	119	39	65	65	NUM
iajs-1442	119	40	tt	tt	PROPN
iajs-1442	119	41	15	15	NUM
iajs-1442	119	42	2)7γ	2)7γ	NOUN
iajs-1442	119	43	(	(	PUNCT
iajs-1442	119	44	15	15	NUM
iajs-1442	119	45	56	56	NUM
iajs-1442	119	46	t	t	NOUN
iajs-1442	119	47	0	0	NUM
iajs-1442	119	48	dτ	dτ	NOUN
iajs-1442	119	49	τ	τ	PROPN
iajs-1442	119	50	1	1	NUM
iajs-1442	119	51	)	)	PUNCT
iajs-1442	119	52	τt	τt	PROPN
iajs-1442	119	53	(	(	PUNCT
iajs-1442	119	54			PROPN
iajs-1442	119	55			PROPN
iajs-1442	119	56			NOUN
iajs-1442	119	57			NOUN
iajs-1442	119	58			VERB
iajs-1442	119	59			PROPN
iajs-1442	119	60			ADV
iajs-1442	119	61			NOUN
iajs-1442	119	62			PROPN
iajs-1442	119	63			PROPN
iajs-1442	119	64			PROPN
iajs-1442	119	65			X
iajs-1442	119	66			NOUN
iajs-1442	119	67			SYM
iajs-1442	119	68			X
iajs-1442	119	69			PROPN
iajs-1442	119	70			X
iajs-1442	119	71	ee	ee	PROPN
iajs-1442	119	72	then	then	ADV
iajs-1442	119	73			PROPN
iajs-1442	119	74			PROPN
iajs-1442	119	75			X
iajs-1442	119	76			NOUN
iajs-1442	119	77			NOUN
iajs-1442	119	78			VERB
iajs-1442	119	79	51	51	NUM
iajs-1442	119	80	1	1	NUM
iajs-1442	119	81	u	u	NOUN
iajs-1442	119	82	15	15	NUM
iajs-1442	119	83	2)7γ(65	2)7γ(65	NUM
iajs-1442	119	84	t	t	NOUN
iajs-1442	119	85	2)7γ(28	2)7γ(28	NUM
iajs-1442	119	86	(	(	PUNCT
iajs-1442	119	87	t)y	t)y	NOUN
iajs-1442	119	88	3	3	NUM
iajs-1442	119	89	45	45	NUM
iajs-1442	119	90	e	e	NOUN
iajs-1442	119	91	that	that	PRON
iajs-1442	119	92	is	be	AUX
iajs-1442	119	93	...	...	PUNCT
iajs-1442	119	94	2,1,i0and0	2,1,i0and0	NUM
iajs-1442	119	95	(	(	PUNCT
iajs-1442	119	96	t)y(t)y	t)y(t)y	NOUN
iajs-1442	119	97	1i1	1i1	NUM
iajs-1442	119	98			VERB
iajs-1442	119	99			ADV
iajs-1442	119	100	therefore	therefore	ADV
iajs-1442	119	101	,	,	PUNCT
iajs-1442	119	102	the	the	DET
iajs-1442	119	103	solution	solution	NOUN
iajs-1442	119	104	is	be	AUX
iajs-1442	119	105	obtained	obtain	VERB
iajs-1442	119	106	to	to	PART
iajs-1442	119	107	be	be	AUX
iajs-1442	119	108	and	and	CCONJ
iajs-1442	119	109	its	its	PRON
iajs-1442	119	110	exact	exact	ADJ
iajs-1442	119	111	solution	solution	NOUN
iajs-1442	119	112	:	:	PUNCT
iajs-1442	119	113	t	t	PROPN
iajs-1442	119	114	1	1	NUM
iajs-1442	119	115	(	(	PUNCT
iajs-1442	119	116	t)yy(t	t)yy(t	NUM
iajs-1442	119	117	)	)	PUNCT
iajs-1442	119	118	0i	0i	NOUN
iajs-1442	120	1	i	i	PRON
iajs-1442	120	2			NUM
iajs-1442	120	3			X
iajs-1442	120	4			VERB
iajs-1442	120	5			PRON
iajs-1442	120	6	.	.	PUNCT
iajs-1442	121	1	mathematics	mathematic	NOUN
iajs-1442	121	2	|201	|201	VERB
iajs-1442	121	3	2102	2102	NUM
iajs-1442	121	4	(	(	PUNCT
iajs-1442	121	5	عام	عام	ADP
iajs-1442	121	6	2	2	NUM
iajs-1442	121	7	(	(	PUNCT
iajs-1442	121	8	العدد	العدد	PROPN
iajs-1442	121	9	)	)	PUNCT
iajs-1442	121	10	30المجلد	30المجلد	NUM
iajs-1442	121	11	)	)	PUNCT
iajs-1442	122	1	مجلة	مجلة	VERB
iajs-1442	122	2	إبن	إبن	NOUN
iajs-1442	122	3	الهيثم	الهيثم	ADJ
iajs-1442	122	4	للعلوم	للعلوم	NOUN
iajs-1442	122	5	الصرفة	الصرفة	NOUN
iajs-1442	122	6	و	و	PRON
iajs-1442	122	7	التطبيقية	التطبيقية	ADJ
iajs-1442	122	8	ibn	ibn	PROPN
iajs-1442	122	9	al	al	PROPN
iajs-1442	122	10	-	-	PUNCT
iajs-1442	122	11	haitham	haitham	PROPN
iajs-1442	122	12	j.	j.	PROPN
iajs-1442	122	13	for	for	ADP
iajs-1442	122	14	pure	pure	PROPN
iajs-1442	122	15	&	&	CCONJ
iajs-1442	122	16	appl	appl	PROPN
iajs-1442	122	17	.	.	PUNCT
iajs-1442	123	1	sci	sci	PROPN
iajs-1442	123	2	.	.	PUNCT
iajs-1442	124	1	vol.03	vol.03	PROPN
iajs-1442	124	2	(	(	PUNCT
iajs-1442	124	3	2	2	NUM
iajs-1442	124	4	)	)	PUNCT
iajs-1442	124	5	2017	2017	NUM
iajs-1442	124	6	conclusions	conclusion	NOUN
iajs-1442	124	7	the	the	DET
iajs-1442	124	8	properties	property	NOUN
iajs-1442	124	9	of	of	ADP
iajs-1442	124	10	the	the	DET
iajs-1442	124	11	elzaki	elzaki	NOUN
iajs-1442	124	12	transform	transform	NOUN
iajs-1442	124	13	are	be	AUX
iajs-1442	124	14	used	use	VERB
iajs-1442	124	15	to	to	PART
iajs-1442	124	16	solve	solve	VERB
iajs-1442	124	17	and	and	CCONJ
iajs-1442	124	18	to	to	PART
iajs-1442	124	19	get	get	VERB
iajs-1442	124	20	the	the	DET
iajs-1442	124	21	general	general	ADJ
iajs-1442	124	22	solution	solution	NOUN
iajs-1442	124	23	of	of	ADP
iajs-1442	124	24	linear	linear	PROPN
iajs-1442	124	25	volterra	volterra	PROPN
iajs-1442	124	26	fractional	fractional	PROPN
iajs-1442	124	27	integro	integro	PROPN
iajs-1442	124	28	-	-	PUNCT
iajs-1442	124	29	differentioal	differentioal	NOUN
iajs-1442	124	30	equations	equation	NOUN
iajs-1442	124	31	.	.	PUNCT
iajs-1442	125	1	the	the	DET
iajs-1442	125	2	fractional	fractional	ADJ
iajs-1442	125	3	derivative	derivative	NOUN
iajs-1442	125	4	is	be	AUX
iajs-1442	125	5	considered	consider	VERB
iajs-1442	125	6	in	in	ADP
iajs-1442	125	7	the	the	DET
iajs-1442	125	8	riemman	riemman	NOUN
iajs-1442	125	9	-	-	PUNCT
iajs-1442	125	10	liouville	liouville	NOUN
iajs-1442	125	11	sense	sense	NOUN
iajs-1442	125	12	.	.	PUNCT
iajs-1442	126	1	the	the	DET
iajs-1442	126	2	results	result	NOUN
iajs-1442	126	3	of	of	ADP
iajs-1442	126	4	illustrate	illustrate	ADJ
iajs-1442	126	5	examples	example	NOUN
iajs-1442	126	6	as	as	ADV
iajs-1442	126	7	well	well	ADV
iajs-1442	126	8	as	as	ADP
iajs-1442	126	9	the	the	DET
iajs-1442	126	10	simplicity	simplicity	NOUN
iajs-1442	126	11	of	of	ADP
iajs-1442	126	12	the	the	DET
iajs-1442	126	13	algorithm	algorithm	NOUN
iajs-1442	126	14	and	and	CCONJ
iajs-1442	126	15	obtained	obtain	VERB
iajs-1442	126	16	exact	exact	ADJ
iajs-1442	126	17	solution	solution	NOUN
iajs-1442	126	18	show	show	NOUN
iajs-1442	126	19	efficiency	efficiency	NOUN
iajs-1442	126	20	and	and	CCONJ
iajs-1442	126	21	accuracy	accuracy	NOUN
iajs-1442	126	22	of	of	ADP
iajs-1442	126	23	the	the	DET
iajs-1442	126	24	method	method	NOUN
iajs-1442	126	25	also	also	ADV
iajs-1442	126	26	show	show	VERB
iajs-1442	126	27	that	that	SCONJ
iajs-1442	126	28	it	it	PRON
iajs-1442	126	29	is	be	AUX
iajs-1442	126	30	a	a	DET
iajs-1442	126	31	special	special	ADJ
iajs-1442	126	32	case	case	NOUN
iajs-1442	126	33	of	of	ADP
iajs-1442	126	34	the	the	DET
iajs-1442	126	35	analysis	analysis	NOUN
iajs-1442	126	36	methods	method	NOUN
iajs-1442	126	37	.	.	PUNCT
iajs-1442	127	1	finally	finally	ADV
iajs-1442	127	2	,	,	PUNCT
iajs-1442	127	3	the	the	DET
iajs-1442	127	4	proposed	propose	VERB
iajs-1442	127	5	approach	approach	NOUN
iajs-1442	127	6	is	be	AUX
iajs-1442	127	7	very	very	ADV
iajs-1442	127	8	powerful	powerful	ADJ
iajs-1442	127	9	to	to	PART
iajs-1442	127	10	find	find	VERB
iajs-1442	127	11	analytical	analytical	ADJ
iajs-1442	127	12	solution	solution	NOUN
iajs-1442	127	13	of	of	ADP
iajs-1442	127	14	linear	linear	ADJ
iajs-1442	127	15	problems	problem	NOUN
iajs-1442	127	16	in	in	ADP
iajs-1442	127	17	fractional	fractional	ADJ
iajs-1442	127	18	calculus	calculus	NOUN
iajs-1442	127	19	field	field	NOUN
iajs-1442	127	20	.	.	PUNCT
iajs-1442	128	1	references	reference	NOUN
iajs-1442	128	2	1	1	NUM
iajs-1442	128	3	.	.	X
iajs-1442	128	4	oldham	oldham	PROPN
iajs-1442	128	5	,	,	PUNCT
iajs-1442	128	6	k.	k.	PROPN
iajs-1442	128	7	b.	b.	PROPN
iajs-1442	128	8	and	and	CCONJ
iajs-1442	128	9	spanier	spanier	NOUN
iajs-1442	128	10	,	,	PUNCT
iajs-1442	128	11	j.	j.	PROPN
iajs-1442	128	12	(	(	PUNCT
iajs-1442	128	13	1974	1974	NUM
iajs-1442	128	14	)	)	PUNCT
iajs-1442	128	15	the	the	DET
iajs-1442	128	16	fractional	fractional	ADJ
iajs-1442	128	17	calculus	calculus	NOUN
iajs-1442	128	18	,	,	PUNCT
iajs-1442	128	19	london	london	PROPN
iajs-1442	128	20	,	,	PUNCT
iajs-1442	128	21	academic	academic	ADJ
iajs-1442	128	22	press	press	NOUN
iajs-1442	128	23	.	.	PUNCT
iajs-1442	129	1	inc	inc	PROPN
iajs-1442	129	2	.	.	PROPN
iajs-1442	129	3	2	2	NUM
iajs-1442	129	4	.	.	X
iajs-1442	129	5	nishimoto	nishimoto	NOUN
iajs-1442	129	6	,	,	PUNCT
iajs-1442	129	7	k.	k.	PROPN
iajs-1442	129	8	(	(	PUNCT
iajs-1442	129	9	1984	1984	NUM
iajs-1442	129	10	)	)	PUNCT
iajs-1442	129	11	fractional	fractional	ADJ
iajs-1442	129	12	calculus	calculus	NOUN
iajs-1442	129	13	:	:	PUNCT
iajs-1442	129	14	integrations	integration	NOUN
iajs-1442	129	15	and	and	CCONJ
iajs-1442	129	16	differentiations	differentiation	NOUN
iajs-1442	129	17	of	of	ADP
iajs-1442	129	18	arbitrary	arbitrary	ADJ
iajs-1442	129	19	order	order	NOUN
iajs-1442	129	20	,	,	PUNCT
iajs-1442	129	21	descartes	descartes	PROPN
iajs-1442	129	22	press	press	PROPN
iajs-1442	129	23	co.	co.	PROPN
iajs-1442	129	24	koriyama	koriyama	PROPN
iajs-1442	129	25	,	,	PUNCT
iajs-1442	129	26	japan	japan	PROPN
iajs-1442	129	27	.	.	PUNCT
iajs-1442	130	1	3	3	X
iajs-1442	130	2	.	.	X
iajs-1442	130	3	schmidt	schmidt	PROPN
iajs-1442	130	4	,	,	PUNCT
iajs-1442	130	5	a.	a.	NOUN
iajs-1442	130	6	and	and	CCONJ
iajs-1442	130	7	gaul	gaul	PROPN
iajs-1442	130	8	,	,	PUNCT
iajs-1442	130	9	l.	l.	PROPN
iajs-1442	130	10	(	(	PUNCT
iajs-1442	130	11	2000	2000	NUM
iajs-1442	130	12	)	)	PUNCT
iajs-1442	130	13	fe	fe	NOUN
iajs-1442	130	14	implementation	implementation	NOUN
iajs-1442	130	15	of	of	ADP
iajs-1442	130	16	viscoelastic	viscoelastic	ADJ
iajs-1442	130	17	constitutive	constitutive	ADJ
iajs-1442	130	18	stressstrain	stressstrain	NOUN
iajs-1442	130	19	relations	relation	NOUN
iajs-1442	130	20	involving	involve	VERB
iajs-1442	130	21	fractional	fractional	ADJ
iajs-1442	130	22	time	time	NOUN
iajs-1442	130	23	derivatives	derivative	NOUN
iajs-1442	130	24	,	,	PUNCT
iajs-1442	130	25	a	a	DET
iajs-1442	130	26	report	report	NOUN
iajs-1442	130	27	,	,	PUNCT
iajs-1442	130	28	institute	institute	VERB
iajs-1442	130	29	a	a	DET
iajs-1442	130	30	fur	fur	NOUN
iajs-1442	130	31	mechanic	mechanic	NOUN
iajs-1442	130	32	,	,	PUNCT
iajs-1442	130	33	universitat	universitat	PROPN
iajs-1442	130	34	stuttgart	stuttgart	PROPN
iajs-1442	130	35	,	,	PUNCT
iajs-1442	130	36	germany	germany	PROPN
iajs-1442	130	37	.	.	PUNCT
iajs-1442	131	1	4	4	X
iajs-1442	131	2	.	.	X
iajs-1442	131	3	adolfsson	adolfsson	NOUN
iajs-1442	131	4	,	,	PUNCT
iajs-1442	131	5	k.	k.	PROPN
iajs-1442	131	6	and	and	CCONJ
iajs-1442	131	7	enelund	enelund	PROPN
iajs-1442	131	8	,	,	PUNCT
iajs-1442	131	9	m.	m.	NOUN
iajs-1442	131	10	(	(	PUNCT
iajs-1442	131	11	2004	2004	NUM
iajs-1442	131	12	)	)	PUNCT
iajs-1442	131	13	,	,	PUNCT
iajs-1442	131	14	dicretization	dicretization	NOUN
iajs-1442	131	15	of	of	ADP
iajs-1442	131	16	integro	integro	ADJ
iajs-1442	131	17	-	-	PUNCT
iajs-1442	131	18	differential	differential	NOUN
iajs-1442	131	19	equations	equation	NOUN
iajs-1442	131	20	modeling	model	VERB
iajs-1442	131	21	dynamic	dynamic	ADJ
iajs-1442	131	22	fractional	fractional	ADJ
iajs-1442	131	23	order	order	NOUN
iajs-1442	131	24	viscoelasticity	viscoelasticity	NOUN
iajs-1442	131	25	,	,	PUNCT
iajs-1442	131	26	appl	appl	PROPN
iajs-1442	131	27	.	.	PROPN
iajs-1442	131	28	mech	mech	PROPN
iajs-1442	131	29	.	.	PUNCT
iajs-1442	132	1	5	5	X
iajs-1442	132	2	.	.	X
iajs-1442	132	3	al	al	PROPN
iajs-1442	132	4	-	-	PUNCT
iajs-1442	132	5	rahhal	rahhal	NOUN
iajs-1442	132	6	,	,	PUNCT
iajs-1442	132	7	d.	d.	PROPN
iajs-1442	132	8	m.	m.	PROPN
iajs-1442	132	9	(	(	PUNCT
iajs-1442	132	10	2005	2005	NUM
iajs-1442	132	11	)	)	PUNCT
iajs-1442	132	12	numerical	numerical	ADJ
iajs-1442	132	13	solution	solution	NOUN
iajs-1442	132	14	for	for	ADP
iajs-1442	132	15	fractional	fractional	ADJ
iajs-1442	132	16	integro	integro	ADJ
iajs-1442	132	17	-	-	PUNCT
iajs-1442	132	18	differential	differential	NOUN
iajs-1442	132	19	equations	equation	NOUN
iajs-1442	132	20	,	,	PUNCT
iajs-1442	132	21	ph	ph	PROPN
iajs-1442	132	22	.	.	PROPN
iajs-1442	132	23	d.	d.	PROPN
iajs-1442	132	24	thesis	thesis	PROPN
iajs-1442	132	25	,	,	PUNCT
iajs-1442	132	26	university	university	NOUN
iajs-1442	132	27	of	of	ADP
iajs-1442	132	28	baghdad	baghdad	PROPN
iajs-1442	132	29	,	,	PUNCT
iajs-1442	132	30	college	college	NOUN
iajs-1442	132	31	of	of	ADP
iajs-1442	132	32	ibn	ibn	PROPN
iajs-1442	132	33	al	al	PROPN
iajs-1442	132	34	-	-	PUNCT
iajs-1442	132	35	haitham	haitham	PROPN
iajs-1442	132	36	.	.	PROPN
iajs-1442	133	1	6	6	NUM
iajs-1442	133	2	.	.	PUNCT
iajs-1442	133	3	kurulay	kurulay	ADJ
iajs-1442	133	4	,	,	PUNCT
iajs-1442	133	5	m.	m.	NOUN
iajs-1442	133	6	and	and	CCONJ
iajs-1442	133	7	secer	secer	NOUN
iajs-1442	133	8	,	,	PUNCT
iajs-1442	133	9	a.	a.	NOUN
iajs-1442	133	10	(	(	PUNCT
iajs-1442	133	11	2011	2011	NUM
iajs-1442	133	12	)	)	PUNCT
iajs-1442	133	13	,	,	PUNCT
iajs-1442	133	14	variational	variational	ADJ
iajs-1442	133	15	iteration	iteration	NOUN
iajs-1442	133	16	method	method	NOUN
iajs-1442	133	17	for	for	ADP
iajs-1442	133	18	nonlinear	nonlinear	ADJ
iajs-1442	133	19	fractional	fractional	ADJ
iajs-1442	133	20	integro	integro	ADJ
iajs-1442	133	21	-	-	PUNCT
iajs-1442	133	22	differential	differential	NOUN
iajs-1442	133	23	equations	equation	NOUN
iajs-1442	133	24	,	,	PUNCT
iajs-1442	133	25	international	international	ADJ
iajs-1442	133	26	journal	journal	NOUN
iajs-1442	133	27	of	of	ADP
iajs-1442	133	28	computer	computer	NOUN
iajs-1442	133	29	science	science	PROPN
iajs-1442	133	30	&	&	CCONJ
iajs-1442	133	31	emerging	emerge	VERB
iajs-1442	133	32	technologies	technology	NOUN
iajs-1442	133	33	,	,	PUNCT
iajs-1442	133	34	issue	issue	NOUN
iajs-1442	133	35	1	1	NUM
iajs-1442	133	36	,	,	PUNCT
iajs-1442	133	37	2	2	NUM
iajs-1442	133	38	,	,	PUNCT
iajs-1442	133	39	18	18	NUM
iajs-1442	133	40	-	-	SYM
iajs-1442	133	41	20	20	NUM
iajs-1442	133	42	.	.	PUNCT
iajs-1442	134	1	7	7	X
iajs-1442	134	2	.	.	X
iajs-1442	134	3	yang	yang	PROPN
iajs-1442	134	4	,	,	PUNCT
iajs-1442	134	5	c.	c.	PROPN
iajs-1442	134	6	and	and	CCONJ
iajs-1442	134	7	hou	hou	PROPN
iajs-1442	134	8	,	,	PUNCT
iajs-1442	134	9	j.	j.	PROPN
iajs-1442	134	10	(	(	PUNCT
iajs-1442	134	11	2013	2013	NUM
iajs-1442	134	12	)	)	PUNCT
iajs-1442	134	13	,	,	PUNCT
iajs-1442	134	14	''	''	PUNCT
iajs-1442	134	15	numerical	numerical	ADJ
iajs-1442	134	16	solution	solution	NOUN
iajs-1442	134	17	of	of	ADP
iajs-1442	134	18	integro	integro	ADJ
iajs-1442	134	19	-	-	PUNCT
iajs-1442	134	20	differential	differential	NOUN
iajs-1442	134	21	equations	equation	NOUN
iajs-1442	134	22	of	of	ADP
iajs-1442	134	23	fractional	fractional	ADJ
iajs-1442	134	24	order	order	NOUN
iajs-1442	134	25	by	by	ADP
iajs-1442	134	26	laplace	laplace	NOUN
iajs-1442	134	27	decomposition	decomposition	NOUN
iajs-1442	134	28	method	method	NOUN
iajs-1442	134	29	''	''	PUNCT
iajs-1442	134	30	,	,	PUNCT
iajs-1442	134	31	wseas	wseas	VERB
iajs-1442	134	32	transactions	transaction	NOUN
iajs-1442	134	33	on	on	ADP
iajs-1442	134	34	mathematics	mathematic	NOUN
iajs-1442	134	35	,	,	PUNCT
iajs-1442	134	36	issue	issue	NOUN
iajs-1442	134	37	12,12,1173	12,12,1173	NUM
iajs-1442	134	38	-	-	SYM
iajs-1442	134	39	1183	1183	NUM
iajs-1442	134	40	.	.	PUNCT
iajs-1442	135	1	8	8	NUM
iajs-1442	135	2	.	.	PUNCT
iajs-1442	136	1	khader	khader	PROPN
iajs-1442	136	2	,	,	PUNCT
iajs-1442	136	3	m.	m.	NOUN
iajs-1442	136	4	m.	m.	NOUN
iajs-1442	136	5	;	;	PUNCT
iajs-1442	136	6	sweilam	sweilam	PROPN
iajs-1442	136	7	,	,	PUNCT
iajs-1442	136	8	n.	n.	PROPN
iajs-1442	136	9	h.	h.	PROPN
iajs-1442	136	10	and	and	CCONJ
iajs-1442	136	11	assiri	assiri	NOUN
iajs-1442	136	12	,	,	PUNCT
iajs-1442	136	13	t.	t.	NOUN
iajs-1442	136	14	a.	a.	NOUN
iajs-1442	136	15	(	(	PUNCT
iajs-1442	136	16	2013	2013	NUM
iajs-1442	136	17	)	)	PUNCT
iajs-1442	136	18	,	,	PUNCT
iajs-1442	136	19	on	on	ADP
iajs-1442	136	20	the	the	DET
iajs-1442	136	21	numerical	numerical	ADJ
iajs-1442	136	22	solution	solution	NOUN
iajs-1442	136	23	for	for	ADP
iajs-1442	136	24	the	the	DET
iajs-1442	136	25	fractional	fractional	ADJ
iajs-1442	136	26	wave	wave	NOUN
iajs-1442	136	27	equation	equation	NOUN
iajs-1442	136	28	using	use	VERB
iajs-1442	136	29	legender	legender	PROPN
iajs-1442	136	30	pseudo	pseudo	NOUN
iajs-1442	136	31	spectral	spectral	ADJ
iajs-1442	136	32	method	method	NOUN
iajs-1442	136	33	,	,	PUNCT
iajs-1442	136	34	international	international	ADJ
iajs-1442	136	35	journal	journal	NOUN
iajs-1442	136	36	of	of	ADP
iajs-1442	136	37	pure	pure	ADJ
iajs-1442	136	38	and	and	CCONJ
iajs-1442	136	39	applied	applied	ADJ
iajs-1442	136	40	mathematics	mathematic	NOUN
iajs-1442	136	41	,	,	PUNCT
iajs-1442	136	42	84	84	NUM
iajs-1442	136	43	,	,	PUNCT
iajs-1442	136	44	4	4	NUM
iajs-1442	136	45	,	,	PUNCT
iajs-1442	136	46	307	307	NUM
iajs-1442	136	47	-	-	SYM
iajs-1442	136	48	319	319	NUM
iajs-1442	136	49	.	.	PUNCT
iajs-1442	137	1	9	9	NUM
iajs-1442	137	2	.	.	X
iajs-1442	137	3	elzaki	elzaki	PROPN
iajs-1442	137	4	,	,	PUNCT
iajs-1442	137	5	t.	t.	NOUN
iajs-1442	137	6	m.	m.	NOUN
iajs-1442	137	7	and	and	CCONJ
iajs-1442	137	8	elzaki	elzaki	PROPN
iajs-1442	137	9	,	,	PUNCT
iajs-1442	137	10	s.	s.	PROPN
iajs-1442	137	11	m.	m.	PROPN
iajs-1442	137	12	(	(	PUNCT
iajs-1442	137	13	2011	2011	NUM
iajs-1442	137	14	)	)	PUNCT
iajs-1442	137	15	,	,	PUNCT
iajs-1442	137	16	solution	solution	NOUN
iajs-1442	137	17	of	of	ADP
iajs-1442	137	18	integro	integro	ADJ
iajs-1442	137	19	-	-	PUNCT
iajs-1442	137	20	differential	differential	NOUN
iajs-1442	137	21	equations	equation	NOUN
iajs-1442	137	22	by	by	ADP
iajs-1442	137	23	using	use	VERB
iajs-1442	137	24	elzaki	elzaki	NOUN
iajs-1442	137	25	transform	transform	NOUN
iajs-1442	137	26	,	,	PUNCT
iajs-1442	137	27	global	global	ADJ
iajs-1442	137	28	journal	journal	NOUN
iajs-1442	137	29	of	of	ADP
iajs-1442	137	30	mathematical	mathematical	ADJ
iajs-1442	137	31	sciences	science	NOUN
iajs-1442	137	32	:	:	PUNCT
iajs-1442	137	33	theory	theory	NOUN
iajs-1442	137	34	and	and	CCONJ
iajs-1442	137	35	practical	practical	ADJ
iajs-1442	137	36	,	,	PUNCT
iajs-1442	137	37	3	3	NUM
iajs-1442	137	38	,	,	PUNCT
iajs-1442	137	39	1,1	1,1	NUM
iajs-1442	137	40	-	-	SYM
iajs-1442	137	41	11	11	NUM
iajs-1442	137	42	.	.	PUNCT
iajs-1442	138	1	10	10	NUM
iajs-1442	138	2	.	.	PUNCT
iajs-1442	138	3	elzaki	elzaki	PROPN
iajs-1442	138	4	,	,	PUNCT
iajs-1442	138	5	t.	t.	NOUN
iajs-1442	138	6	m.	m.	NOUN
iajs-1442	138	7	and	and	CCONJ
iajs-1442	138	8	elzaki	elzaki	PROPN
iajs-1442	138	9	,	,	PUNCT
iajs-1442	138	10	s.	s.	PROPN
iajs-1442	138	11	m.	m.	PROPN
iajs-1442	138	12	(	(	PUNCT
iajs-1442	138	13	2011	2011	NUM
iajs-1442	138	14	)	)	PUNCT
iajs-1442	138	15	,	,	PUNCT
iajs-1442	138	16	the	the	DET
iajs-1442	138	17	new	new	ADJ
iajs-1442	138	18	integral	integral	ADJ
iajs-1442	138	19	transform	transform	NOUN
iajs-1442	138	20	''	''	PUNCT
iajs-1442	138	21	tarig	tarig	PROPN
iajs-1442	138	22	transform	transform	NOUN
iajs-1442	138	23	''	''	PUNCT
iajs-1442	138	24	properties	property	NOUN
iajs-1442	138	25	and	and	CCONJ
iajs-1442	138	26	applications	application	NOUN
iajs-1442	138	27	to	to	PART
iajs-1442	138	28	differential	differential	VERB
iajs-1442	138	29	equations	equation	NOUN
iajs-1442	138	30	,	,	PUNCT
iajs-1442	138	31	elixir	elixir	NOUN
iajs-1442	138	32	international	international	ADJ
iajs-1442	138	33	journal	journal	NOUN
iajs-1442	138	34	,	,	PUNCT
iajs-1442	138	35	38	38	NUM
iajs-1442	138	36	,	,	PUNCT
iajs-1442	138	37	4239	4239	NUM
iajs-1442	138	38	-	-	SYM
iajs-1442	138	39	4242	4242	NUM
iajs-1442	138	40	.	.	PUNCT
iajs-1442	139	1	11	11	NUM
iajs-1442	139	2	.	.	X
iajs-1442	139	3	elzaki	elzaki	PROPN
iajs-1442	139	4	,	,	PUNCT
iajs-1442	139	5	t.	t.	NOUN
iajs-1442	139	6	m.	m.	NOUN
iajs-1442	139	7	;	;	PUNCT
iajs-1442	139	8	elzaki	elzaki	PROPN
iajs-1442	139	9	,	,	PUNCT
iajs-1442	139	10	s.	s.	PROPN
iajs-1442	139	11	m.	m.	PROPN
iajs-1442	139	12	and	and	CCONJ
iajs-1442	139	13	elnour	elnour	PROPN
iajs-1442	139	14	,	,	PUNCT
iajs-1442	139	15	e.	e.	PROPN
iajs-1442	139	16	a.	a.	PROPN
iajs-1442	139	17	(	(	PUNCT
iajs-1442	139	18	2012	2012	NUM
iajs-1442	139	19	)	)	PUNCT
iajs-1442	139	20	,	,	PUNCT
iajs-1442	139	21	on	on	ADP
iajs-1442	139	22	some	some	DET
iajs-1442	139	23	applications	application	NOUN
iajs-1442	139	24	of	of	ADP
iajs-1442	139	25	new	new	ADJ
iajs-1442	139	26	integral	integral	ADJ
iajs-1442	139	27	transform	transform	NOUN
iajs-1442	139	28	''	''	PUNCT
iajs-1442	139	29	elzaki	elzaki	NOUN
iajs-1442	139	30	transform	transform	NOUN
iajs-1442	139	31	''	''	PUNCT
iajs-1442	139	32	,	,	PUNCT
iajs-1442	139	33	global	global	ADJ
iajs-1442	139	34	journal	journal	NOUN
iajs-1442	139	35	of	of	ADP
iajs-1442	139	36	mathematical	mathematical	ADJ
iajs-1442	139	37	sciences	science	NOUN
iajs-1442	139	38	:	:	PUNCT
iajs-1442	139	39	theory	theory	NOUN
iajs-1442	139	40	and	and	CCONJ
iajs-1442	139	41	practical	practical	ADJ
iajs-1442	139	42	,	,	PUNCT
iajs-1442	139	43	4	4	NUM
iajs-1442	139	44	,	,	PUNCT
iajs-1442	139	45	1,15	1,15	NUM
iajs-1442	139	46	-	-	SYM
iajs-1442	139	47	23	23	NUM
iajs-1442	139	48	.	.	PUNCT
iajs-1442	140	1	12	12	NUM
iajs-1442	140	2	.	.	PUNCT
iajs-1442	140	3	chopade	chopade	NOUN
iajs-1442	140	4	,	,	PUNCT
iajs-1442	140	5	p.	p.	NOUN
iajs-1442	140	6	p.and	p.and	PROPN
iajs-1442	141	1	devi	devi	PROPN
iajs-1442	141	2	,	,	PUNCT
iajs-1442	141	3	s.	s.	PROPN
iajs-1442	141	4	b.	b.	PROPN
iajs-1442	141	5	(	(	PUNCT
iajs-1442	141	6	2015	2015	NUM
iajs-1442	141	7	)	)	PUNCT
iajs-1442	141	8	,	,	PUNCT
iajs-1442	141	9	applications	application	NOUN
iajs-1442	141	10	of	of	ADP
iajs-1442	141	11	elzaki	elzaki	NOUN
iajs-1442	141	12	transform	transform	NOUN
iajs-1442	141	13	to	to	ADP
iajs-1442	141	14	ordinary	ordinary	ADJ
iajs-1442	141	15	differential	differential	ADJ
iajs-1442	141	16	and	and	CCONJ
iajs-1442	141	17	partial	partial	ADJ
iajs-1442	141	18	differential	differential	NOUN
iajs-1442	141	19	equations	equation	NOUN
iajs-1442	141	20	,	,	PUNCT
iajs-1442	141	21	international	international	ADJ
iajs-1442	141	22	journal	journal	NOUN
iajs-1442	141	23	of	of	ADP
iajs-1442	141	24	advanced	advanced	ADJ
iajs-1442	141	25	research	research	NOUN
iajs-1442	141	26	in	in	ADP
iajs-1442	141	27	computer	computer	NOUN
iajs-1442	141	28	science	science	NOUN
iajs-1442	141	29	and	and	CCONJ
iajs-1442	141	30	software	software	NOUN
iajs-1442	141	31	engineering	engineering	NOUN
iajs-1442	141	32	,	,	PUNCT
iajs-1442	141	33	issue	issue	NOUN
iajs-1442	141	34	.	.	PUNCT
iajs-1442	142	1	3	3	NUM
iajs-1442	142	2	,	,	PUNCT
iajs-1442	142	3	5	5	NUM
iajs-1442	142	4	,	,	PUNCT
iajs-1442	142	5	38	38	NUM
iajs-1442	142	6	-	-	SYM
iajs-1442	142	7	41	41	NUM
iajs-1442	142	8	.	.	NOUN
iajs-1442	143	1	13	13	NUM
iajs-1442	143	2	.	.	PUNCT
iajs-1442	144	1	mohammed	mohammed	PROPN
iajs-1442	144	2	,	,	PUNCT
iajs-1442	144	3	a.	a.	NOUN
iajs-1442	144	4	a.	a.	PROPN
iajs-1442	144	5	(	(	PUNCT
iajs-1442	144	6	2006	2006	NUM
iajs-1442	144	7	)	)	PUNCT
iajs-1442	144	8	,	,	PUNCT
iajs-1442	144	9	approximate	approximate	ADJ
iajs-1442	144	10	solutions	solution	NOUN
iajs-1442	144	11	for	for	ADP
iajs-1442	144	12	a	a	DET
iajs-1442	144	13	system	system	NOUN
iajs-1442	144	14	of	of	ADP
iajs-1442	144	15	fractional	fractional	ADJ
iajs-1442	144	16	order	order	NOUN
iajs-1442	144	17	integro	integro	ADJ
iajs-1442	144	18	-	-	PUNCT
iajs-1442	144	19	differential	differential	NOUN
iajs-1442	144	20	equations	equation	NOUN
iajs-1442	144	21	of	of	ADP
iajs-1442	144	22	volterra	volterra	NOUN
iajs-1442	144	23	types	type	NOUN
iajs-1442	144	24	,	,	PUNCT
iajs-1442	144	25	ph	ph	PROPN
iajs-1442	144	26	.	.	PROPN
iajs-1442	144	27	d.	d.	PROPN
iajs-1442	144	28	thesis	thesis	PROPN
iajs-1442	144	29	,	,	PUNCT
iajs-1442	144	30	university	university	NOUN
iajs-1442	144	31	of	of	ADP
iajs-1442	144	32	almustansiriy	almustansiriy	NOUN
iajs-1442	144	33	,	,	PUNCT
iajs-1442	144	34	college	college	NOUN
iajs-1442	144	35	of	of	ADP
iajs-1442	144	36	science	science	NOUN
iajs-1442	144	37	.	.	PUNCT
iajs-1442	145	1	14	14	NUM
iajs-1442	145	2	.	.	X
iajs-1442	145	3	asgari	asgari	PROPN
iajs-1442	145	4	,	,	PUNCT
iajs-1442	145	5	m.	m.	NOUN
iajs-1442	145	6	(	(	PUNCT
iajs-1442	145	7	2015	2015	NUM
iajs-1442	145	8	)	)	PUNCT
iajs-1442	145	9	numerical	numerical	ADJ
iajs-1442	145	10	solution	solution	NOUN
iajs-1442	145	11	for	for	ADP
iajs-1442	145	12	solving	solve	VERB
iajs-1442	145	13	a	a	DET
iajs-1442	145	14	system	system	NOUN
iajs-1442	145	15	of	of	ADP
iajs-1442	145	16	fractional	fractional	ADJ
iajs-1442	145	17	integrodifferential	integrodifferential	ADJ
iajs-1442	145	18	equations	equation	NOUN
iajs-1442	145	19	,	,	PUNCT
iajs-1442	145	20	iaeng	iaeng	PROPN
iajs-1442	145	21	inter	inter	PROPN
iajs-1442	145	22	.	.	PROPN
iajs-1442	145	23	journal	journal	PROPN
iajs-1442	145	24	of	of	ADP
iajs-1442	145	25	applied	apply	VERB
iajs-1442	145	26	mathematics	mathematic	NOUN
iajs-1442	145	27	,	,	PUNCT
iajs-1442	145	28	45	45	NUM
iajs-1442	145	29	,	,	PUNCT
iajs-1442	145	30	2	2	NUM
iajs-1442	145	31	.	.	NOUN
iajs-1442	145	32	15	15	NUM
iajs-1442	145	33	.	.	PUNCT
iajs-1442	146	1	elzaki	elzaki	PROPN
iajs-1442	146	2	,	,	PUNCT
iajs-1442	146	3	t.	t.	NOUN
iajs-1442	146	4	m.	m.	NOUN
iajs-1442	146	5	;	;	PUNCT
iajs-1442	146	6	elzaki	elzaki	PROPN
iajs-1442	146	7	,	,	PUNCT
iajs-1442	146	8	s.	s.	PROPN
iajs-1442	146	9	m.	m.	PROPN
iajs-1442	146	10	and	and	CCONJ
iajs-1442	146	11	elnour	elnour	PROPN
iajs-1442	146	12	,	,	PUNCT
iajs-1442	146	13	e.	e.	PROPN
iajs-1442	146	14	a.	a.	PROPN
iajs-1442	146	15	(	(	PUNCT
iajs-1442	146	16	2012	2012	NUM
iajs-1442	146	17	)	)	PUNCT
iajs-1442	146	18	on	on	ADP
iajs-1442	146	19	the	the	DET
iajs-1442	146	20	new	new	ADJ
iajs-1442	146	21	integral	integral	ADJ
iajs-1442	146	22	transform	transform	NOUN
iajs-1442	146	23	''	''	PUNCT
iajs-1442	146	24	elzaki	elzaki	NOUN
iajs-1442	146	25	transform	transform	NOUN
iajs-1442	146	26	''	''	PUNCT
iajs-1442	146	27	fundamental	fundamental	ADJ
iajs-1442	146	28	properties	property	NOUN
iajs-1442	146	29	investigations	investigation	NOUN
iajs-1442	146	30	and	and	CCONJ
iajs-1442	146	31	applications	application	NOUN
iajs-1442	146	32	,	,	PUNCT
iajs-1442	146	33	global	global	ADJ
iajs-1442	146	34	journal	journal	NOUN
iajs-1442	146	35	of	of	ADP
iajs-1442	146	36	mathematical	mathematical	ADJ
iajs-1442	146	37	sciences	science	NOUN
iajs-1442	146	38	:	:	PUNCT
iajs-1442	146	39	theory	theory	NOUN
iajs-1442	146	40	and	and	CCONJ
iajs-1442	146	41	practical	practical	ADJ
iajs-1442	146	42	,	,	PUNCT
iajs-1442	146	43	4	4	NUM
iajs-1442	146	44	,	,	PUNCT
iajs-1442	146	45	1	1	NUM
iajs-1442	146	46	,	,	PUNCT
iajs-1442	146	47	1	1	NUM
iajs-1442	146	48	-	-	SYM
iajs-1442	146	49	13	13	NUM
iajs-1442	146	50	.	.	PUNCT