id	sid	tid	token	lemma	pos
iajs-2485	1	1	microsoft	microsoft	PROPN
iajs-2485	1	2	word	word	NOUN
iajs-2485	1	3	127	127	NUM
iajs-2485	1	4	-	-	SYM
iajs-2485	1	5	139	139	NUM
iajs-2485	1	6	  	  	SPACE
iajs-2485	1	7	127	127	NUM
iajs-2485	1	8	  	  	SPACE
iajs-2485	1	9	ibn	ibn	PROPN
iajs-2485	1	10	al	al	PROPN
iajs-2485	1	11	-	-	PUNCT
iajs-2485	1	12	haitham	haitham	PROPN
iajs-2485	1	13	jour	jour	X
iajs-2485	1	14	.	.	PROPN
iajs-2485	2	1	for	for	ADP
iajs-2485	2	2	pure	pure	ADJ
iajs-2485	2	3	&	&	CCONJ
iajs-2485	2	4	appl	appl	PROPN
iajs-2485	2	5	.	.	PUNCT
iajs-2485	3	1	sci	sci	PROPN
iajs-2485	3	2	.	.	PROPN
iajs-2485	4	1	33	33	NUM
iajs-2485	4	2	(	(	PUNCT
iajs-2485	4	3	3	3	NUM
iajs-2485	4	4	)	)	PUNCT
iajs-2485	4	5	2020	2020	NUM
iajs-2485	4	6	      	      	SPACE
iajs-2485	4	7	solving	solve	VERB
iajs-2485	4	8	some	some	DET
iajs-2485	4	9	fractional	fractional	ADJ
iajs-2485	4	10	partial	partial	ADJ
iajs-2485	4	11	differential	differential	NOUN
iajs-2485	4	12	equations	equation	NOUN
iajs-2485	4	13	by	by	ADP
iajs-2485	4	14	invariant	invariant	ADJ
iajs-2485	4	15	subspace	subspace	NOUN
iajs-2485	4	16	and	and	CCONJ
iajs-2485	4	17	double	double	ADJ
iajs-2485	4	18	sumudu	sumudu	NOUN
iajs-2485	4	19	transform	transform	NOUN
iajs-2485	4	20	methods	method	NOUN
iajs-2485	4	21	abstract	abstract	ADJ
iajs-2485	4	22	in	in	ADP
iajs-2485	4	23	this	this	DET
iajs-2485	4	24	paper	paper	NOUN
iajs-2485	5	1	,	,	PUNCT
iajs-2485	5	2	several	several	ADJ
iajs-2485	5	3	types	type	NOUN
iajs-2485	5	4	of	of	ADP
iajs-2485	5	5	space	space	NOUN
iajs-2485	5	6	-	-	PUNCT
iajs-2485	5	7	time	time	NOUN
iajs-2485	5	8	fractional	fractional	ADJ
iajs-2485	5	9	partial	partial	ADJ
iajs-2485	5	10	differential	differential	NOUN
iajs-2485	5	11	equations	equation	NOUN
iajs-2485	5	12	has	have	AUX
iajs-2485	5	13	been	be	AUX
iajs-2485	5	14	solved	solve	VERB
iajs-2485	5	15	by	by	ADP
iajs-2485	5	16	using	use	VERB
iajs-2485	5	17	most	most	ADJ
iajs-2485	5	18	of	of	ADP
iajs-2485	5	19	special	special	ADJ
iajs-2485	5	20	double	double	ADJ
iajs-2485	5	21	linear	linear	ADJ
iajs-2485	5	22	integral	integral	ADJ
iajs-2485	5	23	transform	transform	NOUN
iajs-2485	5	24	”	"	PUNCT
iajs-2485	5	25	double	double	ADJ
iajs-2485	5	26	sumudu	sumudu	NOUN
iajs-2485	5	27	”	"	PUNCT
iajs-2485	5	28	.	.	PUNCT
iajs-2485	6	1	also	also	ADV
iajs-2485	6	2	,	,	PUNCT
iajs-2485	6	3	we	we	PRON
iajs-2485	6	4	are	be	AUX
iajs-2485	6	5	going	go	VERB
iajs-2485	6	6	to	to	PART
iajs-2485	6	7	argue	argue	VERB
iajs-2485	6	8	the	the	DET
iajs-2485	6	9	truth	truth	NOUN
iajs-2485	6	10	of	of	ADP
iajs-2485	6	11	these	these	DET
iajs-2485	6	12	solutions	solution	NOUN
iajs-2485	6	13	by	by	ADP
iajs-2485	6	14	another	another	DET
iajs-2485	6	15	analytically	analytically	ADV
iajs-2485	6	16	method	method	NOUN
iajs-2485	6	17	“	"	PUNCT
iajs-2485	6	18	invariant	invariant	ADJ
iajs-2485	6	19	subspace	subspace	NOUN
iajs-2485	6	20	method	method	NOUN
iajs-2485	6	21	”	"	PUNCT
iajs-2485	6	22	.	.	PUNCT
iajs-2485	7	1	all	all	DET
iajs-2485	7	2	results	result	NOUN
iajs-2485	7	3	are	be	AUX
iajs-2485	7	4	illustrative	illustrative	ADJ
iajs-2485	7	5	numerically	numerically	ADV
iajs-2485	7	6	and	and	CCONJ
iajs-2485	7	7	graphically	graphically	ADV
iajs-2485	7	8	.	.	PUNCT
iajs-2485	8	1	key	key	ADJ
iajs-2485	8	2	words	word	NOUN
iajs-2485	8	3	fractional	fractional	ADJ
iajs-2485	8	4	calculus	calculus	NOUN
iajs-2485	8	5	,	,	PUNCT
iajs-2485	8	6	fractional	fractional	ADJ
iajs-2485	8	7	partial	partial	ADJ
iajs-2485	8	8	differential	differential	NOUN
iajs-2485	8	9	equation	equation	NOUN
iajs-2485	8	10	,	,	PUNCT
iajs-2485	8	11	sumudu	sumudu	NOUN
iajs-2485	8	12	transform	transform	NOUN
iajs-2485	8	13	,	,	PUNCT
iajs-2485	8	14	invariant	invariant	ADJ
iajs-2485	8	15	subspace	subspace	NOUN
iajs-2485	8	16	.	.	PUNCT
iajs-2485	9	1	1	1	X
iajs-2485	9	2	.	.	X
iajs-2485	9	3	introduction	introduction	NOUN
iajs-2485	9	4	as	as	ADP
iajs-2485	9	5	known	know	VERB
iajs-2485	9	6	,	,	PUNCT
iajs-2485	9	7	linear	linear	ADJ
iajs-2485	9	8	integral	integral	ADJ
iajs-2485	9	9	transformation	transformation	NOUN
iajs-2485	9	10	is	be	AUX
iajs-2485	9	11	used	use	VERB
iajs-2485	9	12	to	to	PART
iajs-2485	9	13	solve	solve	VERB
iajs-2485	9	14	differential	differential	ADJ
iajs-2485	9	15	equations	equation	NOUN
iajs-2485	9	16	,	,	PUNCT
iajs-2485	9	17	by	by	ADP
iajs-2485	9	18	convert	convert	VERB
iajs-2485	9	19	the	the	DET
iajs-2485	9	20	linear	linear	ADJ
iajs-2485	9	21	partial	partial	ADJ
iajs-2485	9	22	differential	differential	NOUN
iajs-2485	9	23	equation	equation	NOUN
iajs-2485	9	24	into	into	ADP
iajs-2485	9	25	algebraic	algebraic	ADJ
iajs-2485	9	26	equation	equation	NOUN
iajs-2485	9	27	which	which	PRON
iajs-2485	9	28	can	can	AUX
iajs-2485	9	29	be	be	AUX
iajs-2485	9	30	solved	solve	VERB
iajs-2485	9	31	easily	easily	ADV
iajs-2485	9	32	.	.	PUNCT
iajs-2485	10	1	so	so	ADV
iajs-2485	10	2	,	,	PUNCT
iajs-2485	10	3	the	the	DET
iajs-2485	10	4	integral	integral	ADJ
iajs-2485	10	5	transforms	transform	VERB
iajs-2485	10	6	such	such	ADJ
iajs-2485	10	7	as	as	ADP
iajs-2485	10	8	mellin	mellin	PROPN
iajs-2485	10	9	,	,	PUNCT
iajs-2485	10	10	laplace	laplace	NOUN
iajs-2485	10	11	,	,	PUNCT
iajs-2485	10	12	fourier	fourier	NOUN
iajs-2485	10	13	and	and	CCONJ
iajs-2485	10	14	sumudu	sumudu	NOUN
iajs-2485	10	15	were	be	AUX
iajs-2485	10	16	vastly	vastly	ADV
iajs-2485	10	17	applied	apply	VERB
iajs-2485	10	18	to	to	PART
iajs-2485	10	19	obtain	obtain	VERB
iajs-2485	10	20	the	the	DET
iajs-2485	10	21	solution	solution	NOUN
iajs-2485	10	22	of	of	ADP
iajs-2485	10	23	differential	differential	ADJ
iajs-2485	10	24	equations	equation	NOUN
iajs-2485	10	25	,	,	PUNCT
iajs-2485	10	26	which	which	PRON
iajs-2485	10	27	are	be	AUX
iajs-2485	10	28	used	use	VERB
iajs-2485	10	29	in	in	ADP
iajs-2485	10	30	astronomy	astronomy	NOUN
iajs-2485	10	31	,	,	PUNCT
iajs-2485	10	32	physics	physics	NOUN
iajs-2485	10	33	and	and	CCONJ
iajs-2485	10	34	also	also	ADV
iajs-2485	10	35	in	in	ADP
iajs-2485	10	36	engineering	engineering	NOUN
iajs-2485	10	37	.	.	PUNCT
iajs-2485	11	1	partial	partial	ADJ
iajs-2485	11	2	differential	differential	ADJ
iajs-2485	11	3	equations	equation	NOUN
iajs-2485	11	4	are	be	AUX
iajs-2485	11	5	considered	consider	VERB
iajs-2485	11	6	one	one	NUM
iajs-2485	11	7	of	of	ADP
iajs-2485	11	8	the	the	DET
iajs-2485	11	9	most	most	ADV
iajs-2485	11	10	significant	significant	ADJ
iajs-2485	11	11	topics	topic	NOUN
iajs-2485	11	12	in	in	ADP
iajs-2485	11	13	mathematics	mathematic	NOUN
iajs-2485	11	14	and	and	CCONJ
iajs-2485	11	15	others	other	NOUN
iajs-2485	11	16	.	.	PUNCT
iajs-2485	12	1	motivated	motivate	VERB
iajs-2485	12	2	by	by	ADP
iajs-2485	12	3	no	no	DET
iajs-2485	12	4	general	general	ADJ
iajs-2485	12	5	methods	method	NOUN
iajs-2485	12	6	for	for	AUX
iajs-2485	12	7	solve	solve	VERB
iajs-2485	12	8	these	these	DET
iajs-2485	12	9	equations	equation	NOUN
iajs-2485	12	10	,	,	PUNCT
iajs-2485	12	11	integral	integral	ADJ
iajs-2485	12	12	transform	transform	NOUN
iajs-2485	12	13	method	method	NOUN
iajs-2485	12	14	is	be	AUX
iajs-2485	12	15	one	one	NUM
iajs-2485	12	16	of	of	ADP
iajs-2485	12	17	the	the	DET
iajs-2485	12	18	most	most	ADV
iajs-2485	12	19	familiar	familiar	ADJ
iajs-2485	12	20	method	method	NOUN
iajs-2485	12	21	in	in	ADP
iajs-2485	12	22	order	order	NOUN
iajs-2485	12	23	to	to	PART
iajs-2485	12	24	get	get	VERB
iajs-2485	12	25	the	the	DET
iajs-2485	12	26	solution	solution	NOUN
iajs-2485	12	27	of	of	ADP
iajs-2485	12	28	such	such	ADJ
iajs-2485	12	29	equations	equation	NOUN
iajs-2485	12	30	[	[	X
iajs-2485	12	31	1	1	NUM
iajs-2485	12	32	-	-	SYM
iajs-2485	12	33	3	3	NUM
iajs-2485	12	34	]	]	PUNCT
iajs-2485	12	35	.	.	PUNCT
iajs-2485	13	1	double	double	ADJ
iajs-2485	13	2	laplace	laplace	NOUN
iajs-2485	13	3	transform	transform	NOUN
iajs-2485	13	4	method	method	NOUN
iajs-2485	13	5	and	and	CCONJ
iajs-2485	13	6	double	double	ADJ
iajs-2485	13	7	sumudu	sumudu	NOUN
iajs-2485	13	8	transform	transform	NOUN
iajs-2485	13	9	method	method	NOUN
iajs-2485	13	10	(	(	PUNCT
iajs-2485	13	11	dstm	dstm	PROPN
iajs-2485	13	12	)	)	PUNCT
iajs-2485	13	13	were	be	AUX
iajs-2485	13	14	used	use	VERB
iajs-2485	13	15	to	to	PART
iajs-2485	13	16	solve	solve	VERB
iajs-2485	13	17	wave	wave	NOUN
iajs-2485	13	18	and	and	CCONJ
iajs-2485	13	19	poisson	poisson	PROPN
iajs-2485	13	20	equations	equation	NOUN
iajs-2485	14	1	[	[	X
iajs-2485	14	2	4	4	NUM
iajs-2485	14	3	,	,	PUNCT
iajs-2485	14	4	5	5	NUM
iajs-2485	14	5	]	]	PUNCT
iajs-2485	14	6	.	.	PUNCT
iajs-2485	15	1	moreover	moreover	ADV
iajs-2485	15	2	,	,	PUNCT
iajs-2485	15	3	the	the	DET
iajs-2485	15	4	relation	relation	NOUN
iajs-2485	15	5	between	between	ADP
iajs-2485	15	6	these	these	DET
iajs-2485	15	7	linear	linear	ADJ
iajs-2485	15	8	integral	integral	ADJ
iajs-2485	15	9	transformations	transformation	NOUN
iajs-2485	15	10	and	and	CCONJ
iajs-2485	15	11	their	their	PRON
iajs-2485	15	12	applications	application	NOUN
iajs-2485	15	13	to	to	PART
iajs-2485	15	14	differential	differential	VERB
iajs-2485	15	15	equations	equation	NOUN
iajs-2485	15	16	have	have	AUX
iajs-2485	15	17	been	be	AUX
iajs-2485	15	18	determined	determine	VERB
iajs-2485	15	19	and	and	CCONJ
iajs-2485	15	20	studied	study	VERB
iajs-2485	15	21	by	by	ADP
iajs-2485	15	22	[	[	X
iajs-2485	15	23	6	6	NUM
iajs-2485	15	24	]	]	PUNCT
iajs-2485	15	25	.	.	PUNCT
iajs-2485	16	1	in	in	ADP
iajs-2485	16	2	this	this	DET
iajs-2485	16	3	study	study	NOUN
iajs-2485	16	4	we	we	PRON
iajs-2485	16	5	focus	focus	VERB
iajs-2485	16	6	on	on	ADP
iajs-2485	16	7	double	double	ADJ
iajs-2485	16	8	sumudu	sumudu	NOUN
iajs-2485	16	9	integral	integral	ADJ
iajs-2485	16	10	transform	transform	NOUN
iajs-2485	16	11	in	in	ADP
iajs-2485	16	12	addition	addition	NOUN
iajs-2485	16	13	to	to	ADP
iajs-2485	16	14	using	use	VERB
iajs-2485	16	15	analyses	analysis	NOUN
iajs-2485	16	16	method	method	NOUN
iajs-2485	16	17	[	[	X
iajs-2485	16	18	7	7	NUM
iajs-2485	16	19	]	]	PUNCT
iajs-2485	16	20	.	.	PUNCT
iajs-2485	17	1	invariant	invariant	ADJ
iajs-2485	17	2	subspace	subspace	NOUN
iajs-2485	17	3	method	method	NOUN
iajs-2485	17	4	(	(	PUNCT
iajs-2485	17	5	ism	ism	NOUN
iajs-2485	17	6	)	)	PUNCT
iajs-2485	17	7	”	"	PUNCT
iajs-2485	17	8	to	to	PART
iajs-2485	17	9	solve	solve	VERB
iajs-2485	17	10	some	some	PRON
iajs-2485	17	11	of	of	ADP
iajs-2485	17	12	important	important	ADJ
iajs-2485	17	13	time	time	NOUN
iajs-2485	17	14	-	-	PUNCT
iajs-2485	17	15	space	space	NOUN
iajs-2485	17	16	and	and	CCONJ
iajs-2485	17	17	mixed	mixed	ADJ
iajs-2485	17	18	fractional	fractional	ADJ
iajs-2485	17	19	partial	partial	ADJ
iajs-2485	17	20	differential	differential	NOUN
iajs-2485	17	21	equations	equation	NOUN
iajs-2485	17	22	,	,	PUNCT
iajs-2485	17	23	and	and	CCONJ
iajs-2485	17	24	we	we	PRON
iajs-2485	17	25	are	be	AUX
iajs-2485	17	26	going	go	VERB
iajs-2485	17	27	to	to	PART
iajs-2485	17	28	argue	argue	VERB
iajs-2485	17	29	the	the	DET
iajs-2485	17	30	results	result	NOUN
iajs-2485	17	31	solution	solution	NOUN
iajs-2485	17	32	in	in	ADP
iajs-2485	17	33	these	these	DET
iajs-2485	17	34	two	two	NUM
iajs-2485	17	35	methods	method	NOUN
iajs-2485	17	36	graphically	graphically	ADV
iajs-2485	17	37	and	and	CCONJ
iajs-2485	17	38	numerically	numerically	ADV
iajs-2485	17	39	.	.	PUNCT
iajs-2485	18	1	ibn	ibn	PROPN
iajs-2485	18	2	al	al	PROPN
iajs-2485	18	3	haitham	haitham	PROPN
iajs-2485	18	4	journal	journal	PROPN
iajs-2485	18	5	for	for	ADP
iajs-2485	18	6	pure	pure	ADJ
iajs-2485	18	7	and	and	CCONJ
iajs-2485	18	8	applied	apply	VERB
iajs-2485	18	9	science	science	NOUN
iajs-2485	18	10	journal	journal	PROPN
iajs-2485	18	11	homepage	homepage	NOUN
iajs-2485	18	12	:	:	PUNCT
iajs-2485	18	13	http://jih.uobaghdad.edu.iq/index.php/j/index	http://jih.uobaghdad.edu.iq/index.php/j/index	PROPN
iajs-2485	18	14	10.30526/33.3.2485	10.30526/33.3.2485	PROPN
iajs-2485	18	15	doi	doi	NOUN
iajs-2485	18	16	:	:	PUNCT
iajs-2485	18	17	article	article	NOUN
iajs-2485	18	18	history	history	NOUN
iajs-2485	18	19	:	:	PUNCT
iajs-2485	18	20	received	receive	VERB
iajs-2485	18	21	24	24	NUM
iajs-2485	18	22	september	september	PROPN
iajs-2485	18	23	2019	2019	NUM
iajs-2485	18	24	,	,	PUNCT
iajs-2485	18	25	accepted	accept	VERB
iajs-2485	18	26	15	15	NUM
iajs-2485	18	27	december2019	december2019	PROPN
iajs-2485	18	28	,	,	PUNCT
iajs-2485	18	29	published	publish	VERB
iajs-2485	18	30	in	in	ADP
iajs-2485	18	31	july	july	PROPN
iajs-2485	18	32	2020	2020	NUM
iajs-2485	18	33	.	.	PUNCT
iajs-2485	19	1	hasan	hasan	PROPN
iajs-2485	19	2	shather	shather	PROPN
iajs-2485	19	3	kadhem	kadhem	PROPN
iajs-2485	19	4	sameer	sameer	PROPN
iajs-2485	19	5	qasim	qasim	PROPN
iajs-2485	19	6	hasan	hasan	PROPN
iajs-2485	19	7	department	department	PROPN
iajs-2485	19	8	of	of	ADP
iajs-2485	19	9	mathematics	mathematics	PROPN
iajs-2485	19	10	,	,	PUNCT
iajs-2485	19	11	college	college	NOUN
iajs-2485	19	12	of	of	ADP
iajs-2485	19	13	education	education	NOUN
iajs-2485	19	14	for	for	ADP
iajs-2485	19	15	pure	pure	ADJ
iajs-2485	19	16	sciences	science	NOUN
iajs-2485	19	17	(	(	PUNCT
iajs-2485	19	18	ibn	ibn	PROPN
iajs-2485	19	19	al	al	PROPN
iajs-2485	19	20	–	–	PUNCT
iajs-2485	19	21	haitham	haitham	PROPN
iajs-2485	19	22	)	)	PUNCT
iajs-2485	19	23	,	,	PUNCT
iajs-2485	19	24	university	university	NOUN
iajs-2485	19	25	of	of	ADP
iajs-2485	19	26	baghdad	baghdad	PROPN
iajs-2485	19	27	department	department	PROPN
iajs-2485	19	28	of	of	ADP
iajs-2485	19	29	mathematics	mathematics	PROPN
iajs-2485	19	30	,	,	PUNCT
iajs-2485	19	31	college	college	NOUN
iajs-2485	19	32	of	of	ADP
iajs-2485	19	33	science	science	NOUN
iajs-2485	19	34	,	,	PUNCT
iajs-2485	19	35	university	university	NOUN
iajs-2485	19	36	of	of	ADP
iajs-2485	19	37	mustansiriyah	mustansiriyah	NOUN
iajs-2485	19	38	,	,	PUNCT
iajs-2485	19	39	baghdad	baghdad	PROPN
iajs-2485	19	40	,	,	PUNCT
iajs-2485	19	41	iraq	iraq	PROPN
iajs-2485	19	42	.	.	PUNCT
iajs-2485	20	1	hasanshather1968@gmail.com	hasanshather1968@gmail.com	X
iajs-2485	20	2	    	    	SPACE
iajs-2485	20	3	128	128	NUM
iajs-2485	20	4	  	  	SPACE
iajs-2485	20	5	ibn	ibn	PROPN
iajs-2485	20	6	al	al	PROPN
iajs-2485	20	7	-	-	PUNCT
iajs-2485	20	8	haitham	haitham	PROPN
iajs-2485	20	9	jour	jour	X
iajs-2485	20	10	.	.	PROPN
iajs-2485	21	1	for	for	ADP
iajs-2485	21	2	pure	pure	ADJ
iajs-2485	21	3	&	&	CCONJ
iajs-2485	21	4	appl	appl	PROPN
iajs-2485	21	5	.	.	PUNCT
iajs-2485	22	1	sci	sci	PROPN
iajs-2485	22	2	.	.	PROPN
iajs-2485	23	1	33	33	NUM
iajs-2485	23	2	(	(	PUNCT
iajs-2485	23	3	3	3	NUM
iajs-2485	23	4	)	)	PUNCT
iajs-2485	23	5	2020	2020	NUM
iajs-2485	23	6	2	2	NUM
iajs-2485	23	7	.	.	PUNCT
iajs-2485	24	1	some	some	DET
iajs-2485	24	2	basic	basic	ADJ
iajs-2485	24	3	concepts	concept	NOUN
iajs-2485	24	4	1	1	NUM
iajs-2485	24	5	.	.	PUNCT
iajs-2485	24	6	important	important	ADJ
iajs-2485	24	7	facts	fact	NOUN
iajs-2485	24	8	of	of	ADP
iajs-2485	24	9	the	the	DET
iajs-2485	24	10	fractional	fractional	ADJ
iajs-2485	24	11	calculus	calculus	NOUN
iajs-2485	24	12	[	[	X
iajs-2485	24	13	8	8	NUM
iajs-2485	24	14	,	,	PUNCT
iajs-2485	24	15	9	9	NUM
iajs-2485	24	16	]	]	PUNCT
iajs-2485	24	17	.	.	PUNCT
iajs-2485	25	1	in	in	ADP
iajs-2485	25	2	this	this	DET
iajs-2485	25	3	section	section	NOUN
iajs-2485	25	4	,	,	PUNCT
iajs-2485	25	5	we	we	PRON
iajs-2485	25	6	give	give	VERB
iajs-2485	25	7	some	some	DET
iajs-2485	25	8	important	important	ADJ
iajs-2485	25	9	definitions	definition	NOUN
iajs-2485	25	10	and	and	CCONJ
iajs-2485	25	11	notation	notation	NOUN
iajs-2485	25	12	which	which	PRON
iajs-2485	25	13	are	be	AUX
iajs-2485	25	14	needed	need	VERB
iajs-2485	25	15	in	in	ADP
iajs-2485	25	16	our	our	PRON
iajs-2485	25	17	work	work	NOUN
iajs-2485	25	18	.	.	PUNCT
iajs-2485	26	1	definition	definition	NOUN
iajs-2485	26	2	1	1	NUM
iajs-2485	26	3	:	:	PUNCT
iajs-2485	26	4	[	[	X
iajs-2485	26	5	8	8	NUM
iajs-2485	26	6	]	]	PUNCT
iajs-2485	26	7	.	.	PUNCT
iajs-2485	27	1	the	the	DET
iajs-2485	27	2	riemann	riemann	PROPN
iajs-2485	27	3	–	–	PUNCT
iajs-2485	27	4	liouville	liouville	VERB
iajs-2485	27	5	fractional	fractional	ADJ
iajs-2485	27	6	integral	integral	ADJ
iajs-2485	27	7	of	of	ADP
iajs-2485	27	8	order	order	NOUN
iajs-2485	27	9	α	α	NOUN
iajs-2485	27	10	for	for	ADP
iajs-2485	27	11	a	a	DET
iajs-2485	27	12	function	function	NOUN
iajs-2485	27	13	f	f	PROPN
iajs-2485	27	14	is	be	AUX
iajs-2485	27	15	defined	define	VERB
iajs-2485	27	16	as	as	ADP
iajs-2485	27	17	:	:	PUNCT
iajs-2485	27	18	𝐽	𝐽	PROPN
iajs-2485	27	19	𝑓	𝑓	PROPN
iajs-2485	27	20	𝑡	𝑡	PROPN
iajs-2485	27	21	1	1	NUM
iajs-2485	27	22	γ	γ	X
iajs-2485	27	23	𝛼	𝛼	NOUN
iajs-2485	27	24	𝑡	𝑡	VERB
iajs-2485	27	25	𝑥	𝑥	PROPN
iajs-2485	27	26	𝑓	𝑓	PRON
iajs-2485	27	27	𝑥	𝑥	NOUN
iajs-2485	27	28	𝑑𝑥	𝑑𝑥	NOUN
iajs-2485	27	29	𝛼	𝛼	NOUN
iajs-2485	27	30	,	,	PUNCT
iajs-2485	27	31	𝑡	𝑡	PROPN
iajs-2485	27	32	0	0	PUNCT
iajs-2485	27	33	the	the	DET
iajs-2485	27	34	r	r	NOUN
iajs-2485	27	35	-	-	PUNCT
iajs-2485	27	36	l	l	NOUN
iajs-2485	27	37	fractional	fractional	ADJ
iajs-2485	27	38	integral	integral	ADJ
iajs-2485	27	39	operator	operator	NOUN
iajs-2485	27	40	has	have	VERB
iajs-2485	27	41	the	the	DET
iajs-2485	27	42	following	follow	VERB
iajs-2485	27	43	properties	property	NOUN
iajs-2485	27	44	:	:	PUNCT
iajs-2485	28	1	1	1	X
iajs-2485	28	2	.	.	X
iajs-2485	28	3	j	j	PROPN
iajs-2485	28	4	is	be	AUX
iajs-2485	28	5	linear	linear	ADJ
iajs-2485	28	6	2	2	NUM
iajs-2485	28	7	.	.	PUNCT
iajs-2485	29	1	j	j	PROPN
iajs-2485	29	2	i	i	PRON
iajs-2485	29	3	3	3	X
iajs-2485	29	4	.	.	PUNCT
iajs-2485	30	1	lim	lim	PROPN
iajs-2485	30	2	→	→	SYM
iajs-2485	30	3	𝐽	𝐽	PROPN
iajs-2485	30	4	j	j	PROPN
iajs-2485	30	5	definition	definition	NOUN
iajs-2485	30	6	2	2	NUM
iajs-2485	30	7	:	:	PUNCT
iajs-2485	30	8	[	[	X
iajs-2485	30	9	8	8	NUM
iajs-2485	30	10	]	]	PUNCT
iajs-2485	30	11	.	.	PUNCT
iajs-2485	31	1	the	the	DET
iajs-2485	31	2	caputo	caputo	PROPN
iajs-2485	31	3	fractional	fractional	PROPN
iajs-2485	31	4	derivative	derivative	NOUN
iajs-2485	31	5	of	of	ADP
iajs-2485	31	6	positive	positive	ADJ
iajs-2485	31	7	order	order	NOUN
iajs-2485	31	8	𝛼	𝛼	VERB
iajs-2485	31	9	for	for	ADP
iajs-2485	31	10	a	a	DET
iajs-2485	31	11	function	function	NOUN
iajs-2485	31	12	f	f	PROPN
iajs-2485	31	13	is	be	AUX
iajs-2485	31	14	defined	define	VERB
iajs-2485	31	15	as	as	ADP
iajs-2485	31	16	:	:	PUNCT
iajs-2485	31	17	𝐷	𝐷	PROPN
iajs-2485	31	18	𝑓	𝑓	PRON
iajs-2485	31	19	𝑡	𝑡	PROPN
iajs-2485	31	20	𝐽	𝐽	PROPN
iajs-2485	31	21	𝐷	𝐷	NOUN
iajs-2485	31	22	𝑓	𝑓	PRON
iajs-2485	31	23	𝑡	𝑡	PROPN
iajs-2485	31	24	𝑑𝑥	𝑑𝑥	VERB
iajs-2485	31	25	𝑛	𝑛	PROPN
iajs-2485	31	26	𝛼	𝛼	NOUN
iajs-2485	31	27	,	,	PUNCT
iajs-2485	31	28	𝑛	𝑛	PRON
iajs-2485	31	29	∈	∈	PROPN
iajs-2485	31	30	n	n	CCONJ
iajs-2485	31	31	𝑓	𝑓	ADV
iajs-2485	31	32	𝑥	𝑥	X
iajs-2485	31	33	𝑛	𝑛	VERB
iajs-2485	31	34	𝛼	𝛼	NOUN
iajs-2485	31	35	some	some	DET
iajs-2485	31	36	properties	property	NOUN
iajs-2485	31	37	of	of	ADP
iajs-2485	31	38	fractional	fractional	PROPN
iajs-2485	31	39	caputo	caputo	PROPN
iajs-2485	31	40	derivative	derivative	PROPN
iajs-2485	31	41	and	and	CCONJ
iajs-2485	31	42	fractional	fractional	ADJ
iajs-2485	31	43	r	r	NOUN
iajs-2485	31	44	-	-	PUNCT
iajs-2485	31	45	l	l	NOUN
iajs-2485	31	46	integral	integral	ADJ
iajs-2485	31	47	are	be	AUX
iajs-2485	31	48	:	:	PUNCT
iajs-2485	31	49	1	1	X
iajs-2485	31	50	.	.	X
iajs-2485	31	51	𝐽	𝐽	PROPN
iajs-2485	32	1	𝑡	𝑡	PROPN
iajs-2485	32	2	𝑡	𝑡	PROPN
iajs-2485	32	3	𝛼	𝛼	PROPN
iajs-2485	32	4	0	0	NUM
iajs-2485	32	5	,	,	PUNCT
iajs-2485	32	6	𝛽	𝛽	PROPN
iajs-2485	32	7	1	1	NUM
iajs-2485	32	8	,	,	PUNCT
iajs-2485	32	9	𝑡	𝑡	PROPN
iajs-2485	32	10	0	0	NUM
iajs-2485	32	11	2	2	NUM
iajs-2485	32	12	.	.	PUNCT
iajs-2485	32	13	t	t	PROPN
iajs-2485	32	14	t	t	PROPN
iajs-2485	32	15	n	n	PROPN
iajs-2485	32	16	1	1	NUM
iajs-2485	32	17	α	α	NOUN
iajs-2485	32	18	n	n	CCONJ
iajs-2485	32	19	,	,	PUNCT
iajs-2485	32	20	β	β	PROPN
iajs-2485	32	21	n	n	PRON
iajs-2485	32	22	1	1	NUM
iajs-2485	32	23	,	,	PUNCT
iajs-2485	32	24	β	β	X
iajs-2485	32	25	∈	∈	NOUN
iajs-2485	32	26	r	r	NOUN
iajs-2485	32	27	0	0	NUM
iajs-2485	32	28	n	n	CCONJ
iajs-2485	32	29	1	1	NUM
iajs-2485	32	30	α	α	NOUN
iajs-2485	32	31	n	n	CCONJ
iajs-2485	32	32	,	,	PUNCT
iajs-2485	32	33	β	β	PROPN
iajs-2485	32	34	n	n	PRON
iajs-2485	32	35	1	1	NUM
iajs-2485	32	36	,	,	PUNCT
iajs-2485	32	37	β	β	X
iajs-2485	32	38	∈	∈	PROPN
iajs-2485	32	39	n	n	PRON
iajs-2485	32	40	3	3	NUM
iajs-2485	32	41	.	.	PUNCT
iajs-2485	33	1	j	j	PROPN
iajs-2485	33	2	i	i	PRON
iajs-2485	33	3	4	4	NUM
iajs-2485	33	4	.	.	PUNCT
iajs-2485	34	1	j	j	PROPN
iajs-2485	34	2	f	f	PROPN
iajs-2485	34	3	t	t	PROPN
iajs-2485	34	4	f	f	PROPN
iajs-2485	34	5	t	t	PROPN
iajs-2485	34	6	∑	∑	PUNCT
iajs-2485	34	7	!	!	PUNCT
iajs-2485	35	1	f	f	PROPN
iajs-2485	35	2	0	0	NUM
iajs-2485	35	3	5	5	NUM
iajs-2485	35	4	.	.	PUNCT
iajs-2485	36	1	𝑓	𝑓	DET
iajs-2485	36	2	𝑡	𝑡	PROPN
iajs-2485	36	3	𝑓	𝑓	PROPN
iajs-2485	36	4	𝑡	𝑡	PROPN
iajs-2485	36	5	𝑓	𝑓	PRON
iajs-2485	36	6	𝑡	𝑡	X
iajs-2485	36	7	𝑝𝑟𝑜𝑣𝑖𝑑𝑒𝑑	𝑝𝑟𝑜𝑣𝑖𝑑𝑒𝑑	PROPN
iajs-2485	36	8	𝑡ℎ𝑎𝑡	𝑡ℎ𝑎𝑡	ADJ
iajs-2485	37	1	𝑓	𝑓	PRON
iajs-2485	37	2	0	0	NUM
iajs-2485	37	3	,	,	PUNCT
iajs-2485	37	4	𝑖	𝑖	NOUN
iajs-2485	37	5	0,1	0,1	NUM
iajs-2485	37	6	,	,	PUNCT
iajs-2485	37	7	…	…	PUNCT
iajs-2485	37	8	,	,	PUNCT
iajs-2485	37	9	𝑛	𝑛	PROPN
iajs-2485	37	10	1	1	NUM
iajs-2485	37	11	,	,	PUNCT
iajs-2485	37	12	𝛼	𝛼	PROPN
iajs-2485	37	13	𝛽	𝛽	NOUN
iajs-2485	37	14	𝑛	𝑛	PROPN
iajs-2485	37	15	,	,	PUNCT
iajs-2485	37	16	𝑛	𝑛	PRON
iajs-2485	37	17	∈	∈	NOUN
iajs-2485	37	18	𝑁	𝑁	ADJ
iajs-2485	37	19	definition	definition	NOUN
iajs-2485	37	20	3	3	NUM
iajs-2485	37	21	:	:	PUNCT
iajs-2485	37	22	[	[	X
iajs-2485	37	23	8,9	8,9	NUM
iajs-2485	37	24	]	]	PUNCT
iajs-2485	37	25	.	.	PUNCT
iajs-2485	38	1	a	a	DET
iajs-2485	38	2	two	two	NUM
iajs-2485	38	3	parameters	parameter	NOUN
iajs-2485	38	4	mittag	mittag	ADJ
iajs-2485	38	5	-	-	PUNCT
iajs-2485	38	6	leffler	leffler	NOUN
iajs-2485	38	7	function	function	NOUN
iajs-2485	38	8	is	be	AUX
iajs-2485	38	9	defined	define	VERB
iajs-2485	38	10	as	as	ADP
iajs-2485	38	11	:	:	PUNCT
iajs-2485	38	12	𝐸	𝐸	PROPN
iajs-2485	38	13	,	,	PUNCT
iajs-2485	38	14	𝑥	𝑥	PROPN
iajs-2485	38	15	𝑥	𝑥	X
iajs-2485	38	16	γ	γ	X
iajs-2485	38	17	𝛼𝑘	𝛼𝑘	ADP
iajs-2485	38	18	𝛽	𝛽	NOUN
iajs-2485	38	19	𝛼	𝛼	NOUN
iajs-2485	38	20	,	,	PUNCT
iajs-2485	38	21	𝛽	𝛽	PROPN
iajs-2485	38	22	∈	∈	PROPN
iajs-2485	38	23	𝐶	𝐶	PROPN
iajs-2485	38	24	,	,	PUNCT
iajs-2485	38	25	𝑅	𝑅	PROPN
iajs-2485	38	26	𝛼	𝛼	PROPN
iajs-2485	38	27	,	,	PUNCT
iajs-2485	38	28	𝑅	𝑅	PROPN
iajs-2485	38	29	𝛽	𝛽	PROPN
iajs-2485	38	30	0	0	PUNCT
iajs-2485	38	31	lemma	lemma	PROPN
iajs-2485	38	32	1	1	NUM
iajs-2485	38	33	:	:	PUNCT
iajs-2485	38	34	[	[	X
iajs-2485	38	35	8,9	8,9	NUM
iajs-2485	38	36	]	]	PUNCT
iajs-2485	38	37	.	.	PUNCT
iajs-2485	39	1	a	a	DET
iajs-2485	39	2	mittag	mittag	ADJ
iajs-2485	39	3	-	-	PUNCT
iajs-2485	39	4	leffler	leffler	NOUN
iajs-2485	39	5	function	function	NOUN
iajs-2485	39	6	has	have	VERB
iajs-2485	39	7	an	an	DET
iajs-2485	39	8	interesting	interesting	ADJ
iajs-2485	39	9	properties	property	NOUN
iajs-2485	39	10	:	:	PUNCT
iajs-2485	39	11	1	1	X
iajs-2485	39	12	.	.	X
iajs-2485	39	13	𝐸	𝐸	PROPN
iajs-2485	39	14	,	,	PUNCT
iajs-2485	39	15	𝑥	𝑥	PROPN
iajs-2485	39	16	𝐸	𝐸	ADV
iajs-2485	39	17	𝑥	𝑥	PRON
iajs-2485	39	18	3	3	X
iajs-2485	39	19	.	.	X
iajs-2485	39	20	𝐸	𝐸	PROPN
iajs-2485	39	21	,	,	PUNCT
iajs-2485	39	22	𝑥	𝑥	PRON
iajs-2485	39	23	𝑐𝑜𝑠ℎ	𝑐𝑜𝑠ℎ	NOUN
iajs-2485	39	24	𝑥	𝑥	NOUN
iajs-2485	39	25	5	5	NUM
iajs-2485	39	26	.	.	X
iajs-2485	39	27	𝐸	𝐸	PROPN
iajs-2485	39	28	,	,	PUNCT
iajs-2485	40	1	𝑥	𝑥	PROPN
iajs-2485	40	2	𝑐𝑜𝑠	𝑐𝑜𝑠	ADV
iajs-2485	41	1	𝑥	𝑥	X
iajs-2485	41	2	  	  	SPACE
iajs-2485	41	3	129	129	NUM
iajs-2485	41	4	  	  	SPACE
iajs-2485	41	5	ibn	ibn	PROPN
iajs-2485	41	6	al	al	PROPN
iajs-2485	41	7	-	-	PUNCT
iajs-2485	41	8	haitham	haitham	PROPN
iajs-2485	41	9	jour	jour	X
iajs-2485	41	10	.	.	PROPN
iajs-2485	42	1	for	for	ADP
iajs-2485	42	2	pure	pure	ADJ
iajs-2485	42	3	&	&	CCONJ
iajs-2485	42	4	appl	appl	PROPN
iajs-2485	42	5	.	.	PUNCT
iajs-2485	43	1	sci	sci	PROPN
iajs-2485	43	2	.	.	PROPN
iajs-2485	44	1	33	33	NUM
iajs-2485	44	2	(	(	PUNCT
iajs-2485	44	3	3	3	NUM
iajs-2485	44	4	)	)	PUNCT
iajs-2485	44	5	2020	2020	NUM
iajs-2485	44	6	2	2	NUM
iajs-2485	44	7	.	.	X
iajs-2485	44	8	𝐸	𝐸	PROPN
iajs-2485	44	9	,	,	PUNCT
iajs-2485	44	10	𝑥	𝑥	X
iajs-2485	44	11	𝑒	𝑒	PROPN
iajs-2485	44	12	  	  	SPACE
iajs-2485	44	13	4	4	NUM
iajs-2485	44	14	.	.	PUNCT
iajs-2485	44	15	𝑥𝐸	𝑥𝐸	ADJ
iajs-2485	44	16	,	,	PUNCT
iajs-2485	44	17	𝑥	𝑥	PRON
iajs-2485	44	18	𝑠𝑖𝑛ℎ	𝑠𝑖𝑛ℎ	VERB
iajs-2485	44	19	𝑥	𝑥	NOUN
iajs-2485	44	20	6	6	NUM
iajs-2485	44	21	.	.	PUNCT
iajs-2485	45	1	𝑥𝐸	𝑥𝐸	ADJ
iajs-2485	45	2	,	,	PUNCT
iajs-2485	45	3	𝑥	𝑥	PROPN
iajs-2485	45	4	𝑠𝑖𝑛	𝑠𝑖𝑛	NOUN
iajs-2485	45	5	𝑥	𝑥	X
iajs-2485	45	6	lemma	lemma	PROPN
iajs-2485	45	7	2	2	NUM
iajs-2485	45	8	:	:	PUNCT
iajs-2485	45	9	[	[	X
iajs-2485	45	10	9	9	NUM
iajs-2485	45	11	]	]	PUNCT
iajs-2485	45	12	.	.	PUNCT
iajs-2485	46	1	the	the	DET
iajs-2485	46	2	caputo	caputo	PROPN
iajs-2485	46	3	derivatives	derivative	NOUN
iajs-2485	46	4	of	of	ADP
iajs-2485	46	5	mittag	mittag	ADJ
iajs-2485	46	6	-	-	PUNCT
iajs-2485	46	7	leffler	leffler	NOUN
iajs-2485	46	8	are	be	AUX
iajs-2485	46	9	given	give	VERB
iajs-2485	46	10	as	as	ADP
iajs-2485	46	11	:	:	PUNCT
iajs-2485	46	12	1	1	NUM
iajs-2485	46	13	.	.	X
iajs-2485	46	14	𝐸	𝐸	PROPN
iajs-2485	46	15	,	,	PUNCT
iajs-2485	46	16	𝑥	𝑥	INTJ
iajs-2485	46	17	∑	∑	PUNCT
iajs-2485	46	18	!	!	PUNCT
iajs-2485	46	19	!	!	PUNCT
iajs-2485	47	1	𝑛	𝑛	PRON
iajs-2485	47	2	∈	∈	NOUN
iajs-2485	47	3	𝑁	𝑁	PROPN
iajs-2485	47	4	2	2	NUM
iajs-2485	47	5	.	.	PUNCT
iajs-2485	47	6	𝐸	𝐸	PROPN
iajs-2485	47	7	𝑎𝑡	𝑎𝑡	ADP
iajs-2485	47	8	𝑎𝐸	𝑎𝐸	PROPN
iajs-2485	47	9	𝑎𝑡	𝑎𝑡	ADP
iajs-2485	47	10	𝛼	𝛼	NOUN
iajs-2485	47	11	0	0	NUM
iajs-2485	47	12	,	,	PUNCT
iajs-2485	47	13	𝑎	𝑎	PROPN
iajs-2485	47	14	∈	∈	PROPN
iajs-2485	47	15	𝑅	𝑅	PROPN
iajs-2485	47	16	3	3	PROPN
iajs-2485	47	17	.	.	PUNCT
iajs-2485	48	1	𝑡	𝑡	PROPN
iajs-2485	48	2	𝐸	𝐸	PROPN
iajs-2485	48	3	,	,	PUNCT
iajs-2485	48	4	𝑎𝑡	𝑎𝑡	ADP
iajs-2485	48	5	𝑡	𝑡	PROPN
iajs-2485	48	6	𝐸	𝐸	PROPN
iajs-2485	48	7	,	,	PUNCT
iajs-2485	48	8	𝑎𝑡	𝑎𝑡	ADP
iajs-2485	48	9	𝛾	𝛾	NOUN
iajs-2485	48	10	0	0	NUM
iajs-2485	48	11	1	1	NUM
iajs-2485	48	12	.	.	PUNCT
iajs-2485	49	1	on	on	ADP
iajs-2485	49	2	the	the	DET
iajs-2485	49	3	single	single	ADJ
iajs-2485	49	4	and	and	CCONJ
iajs-2485	49	5	double	double	ADJ
iajs-2485	49	6	sumudu	sumudu	NOUN
iajs-2485	49	7	transform	transform	NOUN
iajs-2485	49	8	  	  	SPACE
iajs-2485	49	9	the	the	DET
iajs-2485	49	10	sumudu	sumudu	NOUN
iajs-2485	49	11	transform	transform	NOUN
iajs-2485	49	12	introduced	introduce	VERB
iajs-2485	49	13	firstly	firstly	ADV
iajs-2485	49	14	by	by	ADP
iajs-2485	49	15	the	the	DET
iajs-2485	49	16	watugala	watugala	NOUN
iajs-2485	50	1	[	[	X
iajs-2485	50	2	1,2	1,2	NUM
iajs-2485	50	3	]	]	PUNCT
iajs-2485	50	4	.	.	PUNCT
iajs-2485	51	1	which	which	PRON
iajs-2485	51	2	can	can	AUX
iajs-2485	51	3	be	be	AUX
iajs-2485	51	4	used	use	VERB
iajs-2485	51	5	to	to	PART
iajs-2485	51	6	solve	solve	VERB
iajs-2485	51	7	the	the	DET
iajs-2485	51	8	ordinary	ordinary	ADJ
iajs-2485	51	9	and	and	CCONJ
iajs-2485	51	10	partial	partial	ADJ
iajs-2485	51	11	differential	differential	ADJ
iajs-2485	51	12	equations	equation	NOUN
iajs-2485	51	13	with	with	ADP
iajs-2485	51	14	ordinary	ordinary	ADJ
iajs-2485	51	15	and	and	CCONJ
iajs-2485	51	16	fractional	fractional	ADJ
iajs-2485	51	17	order	order	NOUN
iajs-2485	51	18	.	.	PUNCT
iajs-2485	52	1	the	the	DET
iajs-2485	52	2	following	follow	VERB
iajs-2485	52	3	definitions	definition	NOUN
iajs-2485	52	4	and	and	CCONJ
iajs-2485	52	5	properties	property	NOUN
iajs-2485	52	6	of	of	ADP
iajs-2485	52	7	single	single	ADJ
iajs-2485	52	8	and	and	CCONJ
iajs-2485	52	9	double	double	ADJ
iajs-2485	52	10	sumudu	sumudu	NOUN
iajs-2485	52	11	transform	transform	NOUN
iajs-2485	52	12	are	be	AUX
iajs-2485	52	13	necessary	necessary	ADJ
iajs-2485	52	14	for	for	ADP
iajs-2485	52	15	our	our	PRON
iajs-2485	52	16	work	work	NOUN
iajs-2485	52	17	.	.	PUNCT
iajs-2485	53	1	for	for	ADP
iajs-2485	53	2	all	all	PRON
iajs-2485	53	3	,	,	PUNCT
iajs-2485	53	4	we	we	PRON
iajs-2485	53	5	consider	consider	VERB
iajs-2485	53	6	sumudu	sumudu	NOUN
iajs-2485	53	7	transform	transform	NOUN
iajs-2485	53	8	of	of	ADP
iajs-2485	53	9	a	a	DET
iajs-2485	53	10	function	function	NOUN
iajs-2485	53	11	and	and	CCONJ
iajs-2485	53	12	its	its	PRON
iajs-2485	53	13	inverse	inverse	NOUN
iajs-2485	53	14	is	be	AUX
iajs-2485	53	15	exist	exist	NOUN
iajs-2485	53	16	,	,	PUNCT
iajs-2485	53	17	i.	i.	PROPN
iajs-2485	53	18	e.	e.	PROPN
iajs-2485	53	19	,	,	PUNCT
iajs-2485	53	20	the	the	DET
iajs-2485	53	21	considered	consider	VERB
iajs-2485	53	22	function	function	NOUN
iajs-2485	53	23	is	be	AUX
iajs-2485	53	24	of	of	ADP
iajs-2485	53	25	exponent	exponent	ADJ
iajs-2485	53	26	order	order	NOUN
iajs-2485	53	27	.	.	PUNCT
iajs-2485	54	1	definition	definition	NOUN
iajs-2485	54	2	4	4	NUM
iajs-2485	54	3	:	:	PUNCT
iajs-2485	54	4	[	[	X
iajs-2485	54	5	10	10	NUM
iajs-2485	54	6	]	]	PUNCT
iajs-2485	54	7	.	.	PUNCT
iajs-2485	55	1	a	a	DET
iajs-2485	55	2	function	function	NOUN
iajs-2485	55	3	𝑓	𝑓	PRON
iajs-2485	55	4	𝑥	𝑥	PROPN
iajs-2485	55	5	is	be	AUX
iajs-2485	55	6	said	say	VERB
iajs-2485	55	7	to	to	PART
iajs-2485	55	8	be	be	AUX
iajs-2485	55	9	of	of	ADP
iajs-2485	55	10	exponent	exponent	ADJ
iajs-2485	55	11	order	order	NOUN
iajs-2485	55	12	𝛼	𝛼	NOUN
iajs-2485	55	13	0	0	PUNCT
iajs-2485	55	14	if	if	SCONJ
iajs-2485	55	15	there	there	PRON
iajs-2485	55	16	exist	exist	VERB
iajs-2485	55	17	nonnegative	nonnegative	ADJ
iajs-2485	55	18	constants	constant	NOUN
iajs-2485	55	19	𝑀	𝑀	PROPN
iajs-2485	55	20	,	,	PUNCT
iajs-2485	55	21	𝛼	𝛼	NOUN
iajs-2485	55	22	and	and	CCONJ
iajs-2485	55	23	𝑇	𝑇	PROPN
iajs-2485	55	24	such	such	ADJ
iajs-2485	55	25	that	that	SCONJ
iajs-2485	55	26	|𝑓	|𝑓	NOUN
iajs-2485	55	27	𝑥	𝑥	PROPN
iajs-2485	55	28	|	|	ADV
iajs-2485	55	29	𝑀𝑒	𝑀𝑒	VERB
iajs-2485	55	30	𝑥	𝑥	DET
iajs-2485	55	31	𝑇.	𝑇.	PROPN
iajs-2485	55	32	for	for	ADP
iajs-2485	55	33	example	example	NOUN
iajs-2485	55	34	,	,	PUNCT
iajs-2485	55	35	all	all	PRON
iajs-2485	55	36	polynomials	polynomial	VERB
iajs-2485	55	37	𝑒	𝑒	VERB
iajs-2485	55	38	where	where	SCONJ
iajs-2485	55	39	𝑎	𝑎	NOUN
iajs-2485	55	40	is	be	AUX
iajs-2485	55	41	a	a	DET
iajs-2485	55	42	constant	constant	ADJ
iajs-2485	55	43	,	,	PUNCT
iajs-2485	55	44	sine	sine	ADJ
iajs-2485	55	45	and	and	CCONJ
iajs-2485	55	46	cosine	cosine	NOUN
iajs-2485	55	47	functions	function	NOUN
iajs-2485	55	48	and	and	CCONJ
iajs-2485	55	49	products	product	NOUN
iajs-2485	55	50	of	of	ADP
iajs-2485	55	51	these	these	DET
iajs-2485	55	52	functions	function	NOUN
iajs-2485	55	53	are	be	AUX
iajs-2485	55	54	of	of	ADP
iajs-2485	55	55	exponential	exponential	ADJ
iajs-2485	55	56	order	order	NOUN
iajs-2485	55	57	.	.	PUNCT
iajs-2485	56	1	an	an	DET
iajs-2485	56	2	example	example	NOUN
iajs-2485	56	3	of	of	ADP
iajs-2485	56	4	a	a	DET
iajs-2485	56	5	function	function	NOUN
iajs-2485	56	6	not	not	PART
iajs-2485	56	7	of	of	ADP
iajs-2485	56	8	exponential	exponential	ADJ
iajs-2485	56	9	order	order	NOUN
iajs-2485	56	10	is	be	AUX
iajs-2485	56	11	𝑒	𝑒	PROPN
iajs-2485	56	12	.	.	PUNCT
iajs-2485	57	1	this	this	DET
iajs-2485	57	2	function	function	NOUN
iajs-2485	57	3	grows	grow	VERB
iajs-2485	57	4	too	too	ADV
iajs-2485	57	5	rapidly	rapidly	ADV
iajs-2485	57	6	.	.	PUNCT
iajs-2485	58	1	definition	definition	NOUN
iajs-2485	58	2	5	5	NUM
iajs-2485	58	3	:	:	PUNCT
iajs-2485	58	4	[	[	X
iajs-2485	58	5	3	3	NUM
iajs-2485	58	6	]	]	PUNCT
iajs-2485	58	7	.	.	PUNCT
iajs-2485	59	1	the	the	DET
iajs-2485	59	2	sumudu	sumudu	NOUN
iajs-2485	59	3	transform	transform	VERB
iajs-2485	59	4	for	for	ADP
iajs-2485	59	5	the	the	DET
iajs-2485	59	6	exponent	exponent	NOUN
iajs-2485	59	7	order	order	NOUN
iajs-2485	59	8	function	function	VERB
iajs-2485	59	9	𝑓	𝑓	PRON
iajs-2485	59	10	𝑥	𝑥	PROPN
iajs-2485	59	11	is	be	AUX
iajs-2485	59	12	given	give	VERB
iajs-2485	59	13	by	by	ADP
iajs-2485	59	14	s	s	PROPN
iajs-2485	59	15	f	f	X
iajs-2485	59	16	x	x	SYM
iajs-2485	59	17	t	t	PROPN
iajs-2485	59	18	u	u	NOUN
iajs-2485	59	19	and	and	CCONJ
iajs-2485	59	20	the	the	DET
iajs-2485	59	21	inverse	inverse	NOUN
iajs-2485	59	22	sumudu	sumudu	NOUN
iajs-2485	59	23	transform	transform	NOUN
iajs-2485	59	24	of	of	ADP
iajs-2485	59	25	t(u	t(u	NUM
iajs-2485	59	26	)	)	PUNCT
iajs-2485	59	27	is	be	AUX
iajs-2485	59	28	defined	define	VERB
iajs-2485	59	29	by	by	ADP
iajs-2485	59	30	:	:	PUNCT
iajs-2485	59	31	𝑆	𝑆	PROPN
iajs-2485	59	32	𝑇	𝑇	PROPN
iajs-2485	59	33	𝑢	𝑢	PROPN
iajs-2485	59	34	𝑓	𝑓	PRON
iajs-2485	59	35	𝑥	𝑥	X
iajs-2485	59	36	the	the	DET
iajs-2485	59	37	sumudu	sumudu	NOUN
iajs-2485	59	38	transform	transform	NOUN
iajs-2485	59	39	of	of	ADP
iajs-2485	59	40	the	the	DET
iajs-2485	59	41	important	important	ADJ
iajs-2485	59	42	function	function	NOUN
iajs-2485	59	43	”	"	PUNCT
iajs-2485	59	44	mittag	mittag	ADJ
iajs-2485	59	45	-	-	PUNCT
iajs-2485	59	46	leffler	leffler	NOUN
iajs-2485	59	47	function	function	NOUN
iajs-2485	59	48	”	"	PUNCT
iajs-2485	59	49	is	be	AUX
iajs-2485	59	50	given	give	VERB
iajs-2485	59	51	by	by	ADP
iajs-2485	59	52	s	s	PROPN
iajs-2485	59	53	t	t	PROPN
iajs-2485	59	54	e	e	NOUN
iajs-2485	59	55	,	,	PUNCT
iajs-2485	59	56	λt	λt	ADP
iajs-2485	59	57	u	u	PROPN
iajs-2485	59	58	1	1	NUM
iajs-2485	59	59	λu	λu	ADP
iajs-2485	59	60	sumudu	sumudu	NOUN
iajs-2485	59	61	transform	transform	NOUN
iajs-2485	59	62	for	for	SCONJ
iajs-2485	59	63	some	some	DET
iajs-2485	59	64	famous	famous	ADJ
iajs-2485	59	65	functions	function	NOUN
iajs-2485	59	66	are	be	AUX
iajs-2485	59	67	included	include	VERB
iajs-2485	59	68	in	in	ADP
iajs-2485	59	69	the	the	DET
iajs-2485	59	70	following	follow	VERB
iajs-2485	59	71	table	table	NOUN
iajs-2485	59	72	.	.	PUNCT
iajs-2485	60	1	table	table	NOUN
iajs-2485	60	2	1	1	NUM
iajs-2485	60	3	.	.	PUNCT
iajs-2485	60	4	sumudu	sumudu	NOUN
iajs-2485	60	5	transform	transform	NOUN
iajs-2485	60	6	for	for	ADP
iajs-2485	60	7	some	some	DET
iajs-2485	60	8	special	special	ADJ
iajs-2485	60	9	functions	function	NOUN
iajs-2485	60	10	.	.	PUNCT
iajs-2485	61	1	𝒇	𝒇	X
iajs-2485	61	2	𝒙	𝒙	PROPN
iajs-2485	61	3	𝑺	𝑺	PROPN
iajs-2485	61	4	𝒇	𝒇	PUNCT
iajs-2485	61	5	𝒙	𝒙	NUM
iajs-2485	61	6	𝑻	𝑻	NOUN
iajs-2485	61	7	𝒖	𝒖	NOUN
iajs-2485	61	8	𝒇	𝒇	NOUN
iajs-2485	61	9	𝒙	𝒙	PROPN
iajs-2485	61	10	𝑺	𝑺	PROPN
iajs-2485	61	11	𝒇	𝒇	PUNCT
iajs-2485	61	12	𝒙	𝒙	NUM
iajs-2485	61	13	𝑻	𝑻	NOUN
iajs-2485	61	14	𝒖	𝒖	ADJ
iajs-2485	61	15	1	1	NUM
iajs-2485	61	16	1	1	NUM
iajs-2485	61	17	𝒙𝜶	𝒙𝜶	NOUN
iajs-2485	61	18	𝚪	𝚪	NOUN
iajs-2485	61	19	𝟏	𝟏	NOUN
iajs-2485	61	20	𝜶	𝜶	NOUN
iajs-2485	61	21	𝒖𝜶	𝒖𝜶	ADP
iajs-2485	61	22	𝒆𝒙	𝒆𝒙	PROPN
iajs-2485	61	23	𝟏	𝟏	NUM
iajs-2485	61	24	𝟏	𝟏	NUM
iajs-2485	61	25	𝒂𝒖	𝒂𝒖	NOUN
iajs-2485	61	26	𝐬𝐢𝐧	𝐬𝐢𝐧	ADP
iajs-2485	61	27	𝒂𝒙	𝒂𝒙	ADP
iajs-2485	61	28	𝒂𝒖	𝒂𝒖	NOUN
iajs-2485	61	29	𝟏	𝟏	NUM
iajs-2485	61	30	𝒂𝟐𝒖𝟐	𝒂𝟐𝒖𝟐	PUNCT
iajs-2485	61	31	  	  	SPACE
iajs-2485	61	32	130	130	NUM
iajs-2485	61	33	  	  	SPACE
iajs-2485	61	34	ibn	ibn	PROPN
iajs-2485	61	35	al	al	PROPN
iajs-2485	61	36	-	-	PUNCT
iajs-2485	61	37	haitham	haitham	PROPN
iajs-2485	61	38	jour	jour	X
iajs-2485	61	39	.	.	PROPN
iajs-2485	62	1	for	for	ADP
iajs-2485	62	2	pure	pure	ADJ
iajs-2485	62	3	&	&	CCONJ
iajs-2485	62	4	appl	appl	PROPN
iajs-2485	62	5	.	.	PUNCT
iajs-2485	63	1	sci	sci	PROPN
iajs-2485	63	2	.	.	PROPN
iajs-2485	64	1	33	33	NUM
iajs-2485	64	2	(	(	PUNCT
iajs-2485	64	3	3	3	NUM
iajs-2485	64	4	)	)	PUNCT
iajs-2485	64	5	2020	2020	NUM
iajs-2485	64	6	𝐜𝐨𝐬	𝐜𝐨𝐬	VERB
iajs-2485	64	7	𝒂𝒙	𝒂𝒙	ADP
iajs-2485	64	8	𝟏	𝟏	NUM
iajs-2485	64	9	𝟏	𝟏	NUM
iajs-2485	64	10	𝒂𝟐𝒖𝟐	𝒂𝟐𝒖𝟐	PUNCT
iajs-2485	64	11	𝐬𝐢𝐧𝐡	𝐬𝐢𝐧𝐡	NOUN
iajs-2485	64	12	𝒂𝒙	𝒂𝒙	ADV
iajs-2485	64	13	𝒂𝒖	𝒂𝒖	NOUN
iajs-2485	64	14	𝟏	𝟏	NUM
iajs-2485	65	1	𝒂𝟐𝒖𝟐	𝒂𝟐𝒖𝟐	PUNCT
iajs-2485	65	2	𝒙𝜶𝒆𝒂𝒙	𝒙𝜶𝒆𝒂𝒙	ADJ
iajs-2485	65	3	𝚪	𝚪	NOUN
iajs-2485	65	4	𝟏	𝟏	NUM
iajs-2485	65	5	𝜶	𝜶	NOUN
iajs-2485	65	6	𝒖𝜶	𝒖𝜶	ADP
iajs-2485	65	7	𝟏	𝟏	NUM
iajs-2485	65	8	𝒂𝒖	𝒂𝒖	NOUN
iajs-2485	65	9	𝟏	𝟏	NUM
iajs-2485	65	10	𝜶	𝜶	NOUN
iajs-2485	65	11	𝐜𝐨𝐬𝐡	𝐜𝐨𝐬𝐡	NOUN
iajs-2485	65	12	𝒂𝒙	𝒂𝒙	ADP
iajs-2485	65	13	𝟏	𝟏	NUM
iajs-2485	65	14	𝟏	𝟏	NUM
iajs-2485	65	15	𝒂𝟐𝒖𝟐	𝒂𝟐𝒖𝟐	NOUN
iajs-2485	65	16	definition	definition	NOUN
iajs-2485	65	17	6	6	NUM
iajs-2485	65	18	:	:	PUNCT
iajs-2485	66	1	[	[	X
iajs-2485	66	2	3	3	NUM
iajs-2485	66	3	]	]	PUNCT
iajs-2485	66	4	.	.	PUNCT
iajs-2485	67	1	the	the	DET
iajs-2485	67	2	double	double	ADJ
iajs-2485	67	3	sumudu	sumudu	NOUN
iajs-2485	67	4	transform	transform	NOUN
iajs-2485	67	5	for	for	ADP
iajs-2485	67	6	the	the	DET
iajs-2485	67	7	function	function	NOUN
iajs-2485	67	8	𝑓	𝑓	PROPN
iajs-2485	67	9	𝑡	𝑡	NOUN
iajs-2485	67	10	,	,	PUNCT
iajs-2485	67	11	𝑥	𝑥	PROPN
iajs-2485	67	12	is	be	AUX
iajs-2485	67	13	given	give	VERB
iajs-2485	67	14	by	by	ADP
iajs-2485	67	15	:	:	PUNCT
iajs-2485	67	16	𝑆	𝑆	PROPN
iajs-2485	67	17	𝑓	𝑓	PROPN
iajs-2485	67	18	𝑥	𝑥	PROPN
iajs-2485	67	19	,	,	PUNCT
iajs-2485	67	20	𝑡	𝑡	VERB
iajs-2485	67	21	𝑇	𝑇	PROPN
iajs-2485	67	22	𝑢	𝑢	NOUN
iajs-2485	67	23	,	,	PUNCT
iajs-2485	67	24	𝑣	𝑣	DET
iajs-2485	67	25	𝑓	𝑓	PRON
iajs-2485	67	26	𝑥	𝑥	PROPN
iajs-2485	67	27	,	,	PUNCT
iajs-2485	67	28	𝑡	𝑡	NOUN
iajs-2485	67	29	𝑑𝑡	𝑑𝑡	ADP
iajs-2485	67	30	𝑑𝑥	𝑑𝑥	VERB
iajs-2485	67	31	we	we	PRON
iajs-2485	67	32	state	state	NOUN
iajs-2485	67	33	here	here	ADV
iajs-2485	67	34	some	some	PRON
iajs-2485	67	35	of	of	ADP
iajs-2485	67	36	the	the	DET
iajs-2485	67	37	important	important	ADJ
iajs-2485	67	38	properties	property	NOUN
iajs-2485	67	39	of	of	ADP
iajs-2485	67	40	double	double	ADJ
iajs-2485	67	41	sumudu	sumudu	NOUN
iajs-2485	67	42	transform	transform	NOUN
iajs-2485	67	43	which	which	PRON
iajs-2485	67	44	are	be	AUX
iajs-2485	67	45	needed	need	VERB
iajs-2485	67	46	1	1	NUM
iajs-2485	67	47	.	.	PUNCT
iajs-2485	68	1	𝑆	𝑆	PROPN
iajs-2485	68	2	𝑓	𝑓	PRON
iajs-2485	68	3	𝑎𝑥	𝑎𝑥	INTJ
iajs-2485	68	4	𝑔	𝑔	PROPN
iajs-2485	68	5	𝑏	𝑏	PROPN
iajs-2485	68	6	𝑡	𝑡	PROPN
iajs-2485	68	7	𝑇	𝑇	PROPN
iajs-2485	68	8	𝑎𝑢	𝑎𝑢	PROPN
iajs-2485	68	9	𝐺	𝐺	NOUN
iajs-2485	68	10	𝑏𝑣	𝑏𝑣	PRON
iajs-2485	68	11	2	2	NUM
iajs-2485	68	12	.	.	PUNCT
iajs-2485	69	1	𝑆	𝑆	PROPN
iajs-2485	69	2	𝐼	𝐼	PROPN
iajs-2485	69	3	𝑓	𝑓	PRON
iajs-2485	69	4	𝑥	𝑥	PROPN
iajs-2485	69	5	,	,	PUNCT
iajs-2485	69	6	𝑡	𝑡	VERB
iajs-2485	69	7	𝑢	𝑢	ADP
iajs-2485	69	8	𝑇	𝑇	PROPN
iajs-2485	69	9	𝑢	𝑢	NOUN
iajs-2485	69	10	,	,	PUNCT
iajs-2485	69	11	𝑣	𝑣	PRON
iajs-2485	69	12	theorem	theorem	NOUN
iajs-2485	69	13	1	1	NUM
iajs-2485	69	14	:	:	PUNCT
iajs-2485	69	15	[	[	X
iajs-2485	69	16	11	11	NUM
iajs-2485	69	17	]	]	PUNCT
iajs-2485	69	18	.	.	PUNCT
iajs-2485	70	1	if	if	SCONJ
iajs-2485	70	2	the	the	DET
iajs-2485	70	3	double	double	ADJ
iajs-2485	70	4	sumudu	sumudu	NOUN
iajs-2485	70	5	transform	transform	NOUN
iajs-2485	70	6	of	of	ADP
iajs-2485	70	7	the	the	DET
iajs-2485	70	8	function	function	NOUN
iajs-2485	70	9	f	f	PROPN
iajs-2485	70	10	(	(	PUNCT
iajs-2485	70	11	x	x	NOUN
iajs-2485	70	12	;	;	PUNCT
iajs-2485	70	13	t	t	PROPN
iajs-2485	70	14	)	)	PUNCT
iajs-2485	70	15	given	give	VERB
iajs-2485	70	16	by	by	ADP
iajs-2485	70	17	𝑆	𝑆	PROPN
iajs-2485	70	18	𝑓	𝑓	PROPN
iajs-2485	70	19	𝑥	𝑥	PROPN
iajs-2485	70	20	,	,	PUNCT
iajs-2485	70	21	𝑡	𝑡	VERB
iajs-2485	70	22	𝑇	𝑇	PROPN
iajs-2485	70	23	𝑢	𝑢	NOUN
iajs-2485	70	24	,	,	PUNCT
iajs-2485	70	25	𝑣	𝑣	X
iajs-2485	70	26	,	,	PUNCT
iajs-2485	70	27	then	then	ADV
iajs-2485	70	28	:	:	PUNCT
iajs-2485	70	29	1	1	X
iajs-2485	70	30	.	.	X
iajs-2485	70	31	𝑆	𝑆	PROPN
iajs-2485	70	32	𝑥	𝑥	PROPN
iajs-2485	70	33	𝑓	𝑓	PRON
iajs-2485	70	34	𝑥	𝑥	PROPN
iajs-2485	70	35	,	,	PUNCT
iajs-2485	70	36	𝑡	𝑡	VERB
iajs-2485	70	37	𝑢	𝑢	X
iajs-2485	70	38	∑	∑	PUNCT
iajs-2485	70	39	𝑎	𝑎	VERB
iajs-2485	70	40	𝑢	𝑢	PRON
iajs-2485	70	41	𝑇	𝑇	PROPN
iajs-2485	70	42	𝑢	𝑢	NOUN
iajs-2485	70	43	,	,	PUNCT
iajs-2485	70	44	𝑣	𝑣	PRON
iajs-2485	70	45	2	2	NUM
iajs-2485	70	46	.	.	PUNCT
iajs-2485	71	1	𝑆	𝑆	PROPN
iajs-2485	71	2	𝑥	𝑥	PROPN
iajs-2485	71	3	𝑡	𝑡	PROPN
iajs-2485	71	4	𝑓	𝑓	PRON
iajs-2485	71	5	𝑥	𝑥	PROPN
iajs-2485	71	6	,	,	PUNCT
iajs-2485	71	7	𝑡	𝑡	VERB
iajs-2485	71	8	𝑢	𝑢	PROPN
iajs-2485	71	9	𝑣	𝑣	X
iajs-2485	71	10	∑	∑	PUNCT
iajs-2485	71	11	𝑎	𝑎	PROPN
iajs-2485	71	12	𝑏	𝑏	NOUN
iajs-2485	71	13	𝑢	𝑢	NOUN
iajs-2485	71	14	𝑣	𝑣	ADP
iajs-2485	71	15	𝑇	𝑇	PROPN
iajs-2485	71	16	𝑢	𝑢	NOUN
iajs-2485	71	17	,	,	PUNCT
iajs-2485	71	18	𝑣	𝑣	ADP
iajs-2485	71	19	where	where	SCONJ
iajs-2485	71	20	𝑎	𝑎	DET
iajs-2485	71	21	1	1	NUM
iajs-2485	71	22	,	,	PUNCT
iajs-2485	71	23	𝑎	𝑎	NOUN
iajs-2485	71	24	1	1	NUM
iajs-2485	71	25	,	,	PUNCT
iajs-2485	71	26	𝑎	𝑎	NOUN
iajs-2485	71	27	𝑛	𝑛	NOUN
iajs-2485	71	28	!	!	NOUN
iajs-2485	71	29	𝑛	𝑛	NOUN
iajs-2485	71	30	,	,	PUNCT
iajs-2485	71	31	𝑎	𝑎	X
iajs-2485	71	32	𝑎	𝑎	NOUN
iajs-2485	71	33	𝑚	𝑚	NOUN
iajs-2485	71	34	𝑘	𝑘	DET
iajs-2485	71	35	𝑎	𝑎	NOUN
iajs-2485	71	36	,	,	PUNCT
iajs-2485	71	37	similarly	similarly	ADV
iajs-2485	71	38	for	for	ADP
iajs-2485	71	39	𝑏	𝑏	PROPN
iajs-2485	71	40	the	the	DET
iajs-2485	71	41	double	double	ADJ
iajs-2485	71	42	sumudu	sumudu	NOUN
iajs-2485	71	43	transform	transform	NOUN
iajs-2485	71	44	of	of	ADP
iajs-2485	71	45	the	the	DET
iajs-2485	71	46	partial	partial	ADJ
iajs-2485	71	47	caputo	caputo	PROPN
iajs-2485	71	48	fractional	fractional	ADJ
iajs-2485	71	49	derivatives	derivative	NOUN
iajs-2485	71	50	are	be	AUX
iajs-2485	71	51	given	give	VERB
iajs-2485	71	52	in	in	ADP
iajs-2485	71	53	the	the	DET
iajs-2485	71	54	following	follow	VERB
iajs-2485	71	55	theorem	theorem	NOUN
iajs-2485	71	56	:	:	PUNCT
iajs-2485	71	57	theorem	theorem	VERB
iajs-2485	71	58	2	2	NUM
iajs-2485	71	59	:	:	PUNCT
iajs-2485	71	60	[	[	X
iajs-2485	71	61	4	4	NUM
iajs-2485	71	62	]	]	PUNCT
iajs-2485	71	63	.	.	PUNCT
iajs-2485	72	1	let	let	VERB
iajs-2485	72	2	the	the	DET
iajs-2485	72	3	exponent	exponent	NOUN
iajs-2485	72	4	order	order	NOUN
iajs-2485	72	5	function	function	VERB
iajs-2485	72	6	𝑓	𝑓	DET
iajs-2485	72	7	𝑥	𝑥	PROPN
iajs-2485	72	8	,	,	PUNCT
iajs-2485	72	9	𝑡	𝑡	PROPN
iajs-2485	72	10	has	have	VERB
iajs-2485	72	11	a	a	DET
iajs-2485	72	12	continuous	continuous	ADJ
iajs-2485	72	13	partial	partial	ADJ
iajs-2485	72	14	derivative	derivative	NOUN
iajs-2485	72	15	on	on	ADP
iajs-2485	72	16	𝑅	𝑅	PROPN
iajs-2485	72	17	𝑅	𝑅	PROPN
iajs-2485	72	18	and	and	CCONJ
iajs-2485	72	19	𝑛	𝑛	DET
iajs-2485	72	20	1	1	NUM
iajs-2485	72	21	𝛼	𝛼	SYM
iajs-2485	72	22	𝑛	𝑛	NOUN
iajs-2485	72	23	,	,	PUNCT
iajs-2485	72	24	𝑚	𝑚	PROPN
iajs-2485	72	25	1	1	NUM
iajs-2485	72	26	𝛽	𝛽	NOUN
iajs-2485	72	27	𝑚	𝑚	NOUN
iajs-2485	72	28	,	,	PUNCT
iajs-2485	72	29	then	then	ADV
iajs-2485	72	30	:	:	PUNCT
iajs-2485	72	31	3	3	X
iajs-2485	72	32	.	.	X
iajs-2485	72	33	𝑆	𝑆	PROPN
iajs-2485	72	34	𝐷	𝐷	PROPN
iajs-2485	72	35	𝑓	𝑓	PROPN
iajs-2485	72	36	𝑥	𝑥	PROPN
iajs-2485	72	37	,	,	PUNCT
iajs-2485	72	38	𝑡	𝑡	VERB
iajs-2485	72	39	𝑢	𝑢	ADP
iajs-2485	72	40	𝑇	𝑇	PROPN
iajs-2485	72	41	𝑢	𝑢	NOUN
iajs-2485	72	42	,	,	PUNCT
iajs-2485	72	43	𝑣	𝑣	ADP
iajs-2485	72	44	∑	∑	PUNCT
iajs-2485	72	45	𝑢	𝑢	PROPN
iajs-2485	72	46	𝑇	𝑇	PROPN
iajs-2485	72	47	0	0	NUM
iajs-2485	72	48	,	,	PUNCT
iajs-2485	72	49	𝑣	𝑣	DET
iajs-2485	72	50	4	4	NUM
iajs-2485	72	51	.	.	PUNCT
iajs-2485	73	1	𝑆	𝑆	PROPN
iajs-2485	73	2	𝐷	𝐷	PROPN
iajs-2485	73	3	𝑓	𝑓	PROPN
iajs-2485	73	4	𝑥	𝑥	PROPN
iajs-2485	73	5	,	,	PUNCT
iajs-2485	73	6	𝑡	𝑡	VERB
iajs-2485	73	7	𝑣	𝑣	ADP
iajs-2485	73	8	𝑇	𝑇	PROPN
iajs-2485	73	9	𝑢	𝑢	NOUN
iajs-2485	73	10	,	,	PUNCT
iajs-2485	73	11	𝑣	𝑣	ADP
iajs-2485	73	12	∑	∑	PUNCT
iajs-2485	73	13	𝑣	𝑣	ADP
iajs-2485	73	14	𝑇	𝑇	PROPN
iajs-2485	73	15	𝑢	𝑢	NOUN
iajs-2485	73	16	,	,	PUNCT
iajs-2485	73	17	0	0	NUM
iajs-2485	73	18	5	5	NUM
iajs-2485	73	19	.	.	PUNCT
iajs-2485	73	20	s	s	PART
iajs-2485	74	1	d	d	X
iajs-2485	74	2	d	d	X
iajs-2485	74	3	f	f	PROPN
iajs-2485	74	4	x	x	PROPN
iajs-2485	74	5	,	,	PUNCT
iajs-2485	74	6	t	t	PROPN
iajs-2485	74	7	u	u	NOUN
iajs-2485	74	8	v	v	ADP
iajs-2485	74	9	t	t	PROPN
iajs-2485	74	10	u	u	PROPN
iajs-2485	74	11	,	,	PUNCT
iajs-2485	74	12	v	v	ADP
iajs-2485	74	13	∑	∑	PROPN
iajs-2485	74	14	u	u	NOUN
iajs-2485	74	15	t	t	PROPN
iajs-2485	74	16	0	0	NUM
iajs-2485	74	17	,	,	PUNCT
iajs-2485	74	18	v	v	ADP
iajs-2485	74	19	∑	∑	PROPN
iajs-2485	74	20	v	v	ADP
iajs-2485	74	21	t	t	PROPN
iajs-2485	74	22	u	u	PROPN
iajs-2485	74	23	,	,	PUNCT
iajs-2485	74	24	0	0	NUM
iajs-2485	74	25	∑	∑	PROPN
iajs-2485	74	26	∑	∑	PROPN
iajs-2485	74	27	u	u	PROPN
iajs-2485	74	28	v	v	NOUN
iajs-2485	74	29	f	f	NOUN
iajs-2485	74	30	0,0	0,0	NUM
iajs-2485	74	31	where	where	SCONJ
iajs-2485	74	32	𝑇	𝑇	PROPN
iajs-2485	74	33	0	0	NUM
iajs-2485	74	34	,	,	PUNCT
iajs-2485	74	35	𝑣	𝑣	DET
iajs-2485	74	36	𝑆	𝑆	PROPN
iajs-2485	74	37	𝑓	𝑓	PROPN
iajs-2485	74	38	0	0	NUM
iajs-2485	74	39	,	,	PUNCT
iajs-2485	74	40	𝑡	𝑡	NOUN
iajs-2485	74	41	and	and	CCONJ
iajs-2485	74	42	𝑇	𝑇	PROPN
iajs-2485	74	43	𝑢	𝑢	NOUN
iajs-2485	74	44	,	,	PUNCT
iajs-2485	74	45	0	0	X
iajs-2485	75	1	𝑆	𝑆	PROPN
iajs-2485	75	2	𝑓	𝑓	PROPN
iajs-2485	75	3	𝑥	𝑥	NOUN
iajs-2485	75	4	,	,	PUNCT
iajs-2485	75	5	0	0	NUM
iajs-2485	75	6	1	1	NUM
iajs-2485	75	7	.	.	PUNCT
iajs-2485	76	1	on	on	ADP
iajs-2485	76	2	invariant	invariant	ADJ
iajs-2485	76	3	subspace	subspace	NOUN
iajs-2485	76	4	method	method	NOUN
iajs-2485	76	5	in	in	ADP
iajs-2485	76	6	2018	2018	NUM
iajs-2485	76	7	,	,	PUNCT
iajs-2485	76	8	authors	author	NOUN
iajs-2485	76	9	,	,	PUNCT
iajs-2485	76	10	[	[	PUNCT
iajs-2485	76	11	7	7	NUM
iajs-2485	76	12	,	,	PUNCT
iajs-2485	76	13	9	9	NUM
iajs-2485	76	14	]	]	PUNCT
iajs-2485	76	15	.	.	PUNCT
iajs-2485	77	1	developed	develop	VERB
iajs-2485	77	2	the	the	DET
iajs-2485	77	3	invariant	invariant	ADJ
iajs-2485	77	4	subspace	subspace	NOUN
iajs-2485	77	5	method	method	NOUN
iajs-2485	77	6	for	for	ADP
iajs-2485	77	7	finding	find	VERB
iajs-2485	77	8	exact	exact	ADJ
iajs-2485	77	9	solutions	solution	NOUN
iajs-2485	77	10	to	to	ADP
iajs-2485	77	11	some	some	DET
iajs-2485	77	12	nonlinear	nonlinear	ADJ
iajs-2485	77	13	partial	partial	ADJ
iajs-2485	77	14	differential	differential	NOUN
iajs-2485	77	15	equations	equation	NOUN
iajs-2485	77	16	with	with	ADP
iajs-2485	77	17	fractional	fractional	ADJ
iajs-2485	77	18	-	-	PUNCT
iajs-2485	77	19	order	order	NOUN
iajs-2485	77	20	mixed	mixed	ADJ
iajs-2485	77	21	partial	partial	ADJ
iajs-2485	77	22	derivatives	derivative	NOUN
iajs-2485	77	23	(	(	PUNCT
iajs-2485	77	24	including	include	VERB
iajs-2485	77	25	both	both	CCONJ
iajs-2485	77	26	fractional	fractional	ADJ
iajs-2485	77	27	space	space	NOUN
iajs-2485	77	28	derivatives	derivative	NOUN
iajs-2485	77	29	and	and	CCONJ
iajs-2485	77	30	time	time	NOUN
iajs-2485	77	31	derivatives	derivative	NOUN
iajs-2485	77	32	)	)	PUNCT
iajs-2485	77	33	.	.	PUNCT
iajs-2485	78	1	these	these	DET
iajs-2485	78	2	equations	equation	NOUN
iajs-2485	78	3	are	be	AUX
iajs-2485	78	4	in	in	ADP
iajs-2485	78	5	the	the	DET
iajs-2485	78	6	form	form	NOUN
iajs-2485	78	7	:	:	PUNCT
iajs-2485	78	8	𝜆	𝜆	PRON
iajs-2485	78	9	𝜕	𝜕	PROPN
iajs-2485	78	10	𝜕𝑡	𝜕𝑡	PROPN
iajs-2485	78	11	𝑢	𝑢	PART
iajs-2485	78	12	𝑥	𝑥	PROPN
iajs-2485	78	13	,	,	PUNCT
iajs-2485	78	14	𝑡	𝑡	VERB
iajs-2485	78	15	𝑁	𝑁	PROPN
iajs-2485	78	16	𝑥	𝑥	PROPN
iajs-2485	78	17	,	,	PUNCT
iajs-2485	78	18	𝑢	𝑢	PROPN
iajs-2485	78	19	,	,	PUNCT
iajs-2485	78	20	𝜕	𝜕	NOUN
iajs-2485	78	21	𝜕𝑥	𝜕𝑥	X
iajs-2485	78	22	𝑢	𝑢	PROPN
iajs-2485	78	23	,	,	PUNCT
iajs-2485	78	24	𝜕	𝜕	NOUN
iajs-2485	78	25	𝜕𝑥	𝜕𝑥	X
iajs-2485	78	26	𝑢	𝑢	X
iajs-2485	78	27	,	,	PUNCT
iajs-2485	78	28	…	…	PUNCT
iajs-2485	78	29	,	,	PUNCT
iajs-2485	78	30	𝜕	𝜕	NOUN
iajs-2485	78	31	𝜕𝑥	𝜕𝑥	X
iajs-2485	78	32	𝑢	𝑢	X
iajs-2485	78	33	𝜇	𝜇	ADP
iajs-2485	78	34	𝜕	𝜕	PROPN
iajs-2485	78	35	𝜕𝑡	𝜕𝑡	PROPN
iajs-2485	78	36	𝜕	𝜕	PROPN
iajs-2485	78	37	𝜕𝑥	𝜕𝑥	X
iajs-2485	78	38	𝑢	𝑢	ADP
iajs-2485	78	39	1	1	NUM
iajs-2485	78	40	𝑎	𝑎	NOUN
iajs-2485	78	41	𝛼	𝛼	NOUN
iajs-2485	78	42	𝑎	𝑎	PROPN
iajs-2485	78	43	1	1	NUM
iajs-2485	78	44	,	,	PUNCT
iajs-2485	78	45	𝑏	𝑏	DET
iajs-2485	78	46	𝛽	𝛽	NOUN
iajs-2485	78	47	𝑏	𝑏	PROPN
iajs-2485	78	48	1	1	NUM
iajs-2485	78	49	,	,	PUNCT
iajs-2485	78	50	𝑎	𝑎	NOUN
iajs-2485	78	51	,	,	PUNCT
iajs-2485	78	52	𝑏	𝑏	NOUN
iajs-2485	78	53	,	,	PUNCT
iajs-2485	78	54	𝑚	𝑚	X
iajs-2485	78	55	,	,	PUNCT
iajs-2485	78	56	𝑛	𝑛	PRON
iajs-2485	78	57	∈	∈	PROPN
iajs-2485	78	58	𝑁	𝑁	PROPN
iajs-2485	78	59	,	,	PUNCT
iajs-2485	78	60	𝜆	𝜆	NOUN
iajs-2485	78	61	,	,	PUNCT
iajs-2485	78	62	𝜇	𝜇	ADP
iajs-2485	78	63	∈	∈	PROPN
iajs-2485	78	64	𝑅	𝑅	PROPN
iajs-2485	78	65	  	  	SPACE
iajs-2485	78	66	131	131	NUM
iajs-2485	78	67	  	  	SPACE
iajs-2485	78	68	ibn	ibn	PROPN
iajs-2485	78	69	al	al	PROPN
iajs-2485	78	70	-	-	PUNCT
iajs-2485	78	71	haitham	haitham	PROPN
iajs-2485	78	72	jour	jour	X
iajs-2485	78	73	.	.	PROPN
iajs-2485	79	1	for	for	ADP
iajs-2485	79	2	pure	pure	ADJ
iajs-2485	79	3	&	&	CCONJ
iajs-2485	79	4	appl	appl	PROPN
iajs-2485	79	5	.	.	PUNCT
iajs-2485	80	1	sci	sci	PROPN
iajs-2485	80	2	.	.	PROPN
iajs-2485	81	1	33	33	NUM
iajs-2485	81	2	(	(	PUNCT
iajs-2485	81	3	3	3	NUM
iajs-2485	81	4	)	)	PUNCT
iajs-2485	81	5	2020	2020	NUM
iajs-2485	81	6	theorem	theorem	VERB
iajs-2485	81	7	3	3	NUM
iajs-2485	81	8	:	:	PUNCT
iajs-2485	81	9	[	[	X
iajs-2485	81	10	9	9	NUM
iajs-2485	81	11	]	]	PUNCT
iajs-2485	81	12	.	.	PUNCT
iajs-2485	82	1	suppose	suppose	VERB
iajs-2485	82	2	𝐼	𝐼	ADP
iajs-2485	82	3	𝐿	𝐿	PROPN
iajs-2485	82	4	𝜙	𝜙	NOUN
iajs-2485	82	5	𝑥	𝑥	X
iajs-2485	82	6	,	,	PUNCT
iajs-2485	82	7	𝜙	𝜙	PROPN
iajs-2485	82	8	𝑥	𝑥	X
iajs-2485	82	9	,	,	PUNCT
iajs-2485	82	10	.	.	PUNCT
iajs-2485	82	11	.	.	PUNCT
iajs-2485	83	1	,	,	PUNCT
iajs-2485	83	2	𝜙	𝜙	PROPN
iajs-2485	84	1	𝑥	𝑥	NOUN
iajs-2485	84	2	is	be	AUX
iajs-2485	84	3	a	a	DET
iajs-2485	84	4	finitedimensional	finitedimensional	ADJ
iajs-2485	84	5	linear	linear	ADJ
iajs-2485	84	6	space	space	NOUN
iajs-2485	84	7	,	,	PUNCT
iajs-2485	84	8	and	and	CCONJ
iajs-2485	84	9	it	it	PRON
iajs-2485	84	10	is	be	AUX
iajs-2485	84	11	invariant	invariant	ADJ
iajs-2485	84	12	with	with	ADP
iajs-2485	84	13	respect	respect	NOUN
iajs-2485	84	14	to	to	ADP
iajs-2485	84	15	the	the	DET
iajs-2485	84	16	operators	operator	NOUN
iajs-2485	84	17	𝑁	𝑁	PROPN
iajs-2485	84	18	𝑢	𝑢	NOUN
iajs-2485	84	19	and	and	CCONJ
iajs-2485	84	20	𝑢	𝑢	PROPN
iajs-2485	84	21	,	,	PUNCT
iajs-2485	84	22	then	then	ADV
iajs-2485	84	23	fpde	fpde	NOUN
iajs-2485	84	24	(	(	PUNCT
iajs-2485	84	25	1	1	X
iajs-2485	84	26	)	)	PUNCT
iajs-2485	84	27	has	have	VERB
iajs-2485	84	28	an	an	DET
iajs-2485	84	29	exact	exact	ADJ
iajs-2485	84	30	solution	solution	NOUN
iajs-2485	84	31	as	as	SCONJ
iajs-2485	84	32	follows	follow	VERB
iajs-2485	84	33	:	:	PUNCT
iajs-2485	84	34	𝑢	𝑢	PRON
iajs-2485	84	35	𝑥	𝑥	PROPN
iajs-2485	84	36	,	,	PUNCT
iajs-2485	84	37	𝑡	𝑡	VERB
iajs-2485	84	38	𝑘	𝑘	ADP
iajs-2485	84	39	𝑡	𝑡	NOUN
iajs-2485	84	40	𝜙	𝜙	NOUN
iajs-2485	84	41	𝑥	𝑥	NOUN
iajs-2485	84	42	2	2	NUM
iajs-2485	84	43	where	where	SCONJ
iajs-2485	84	44	𝑘	𝑘	PRON
iajs-2485	84	45	𝑡	𝑡	PROPN
iajs-2485	84	46	satisfies	satisfy	VERB
iajs-2485	84	47	the	the	DET
iajs-2485	84	48	following	follow	VERB
iajs-2485	84	49	system	system	NOUN
iajs-2485	84	50	of	of	ADP
iajs-2485	84	51	fdes	fde	NOUN
iajs-2485	84	52	:	:	PUNCT
iajs-2485	84	53	𝜆	𝜆	DET
iajs-2485	84	54	𝜕	𝜕	PROPN
iajs-2485	84	55	𝜕𝑡	𝜕𝑡	PROPN
iajs-2485	84	56	𝑘	𝑘	PROPN
iajs-2485	84	57	𝑡	𝑡	X
iajs-2485	84	58	𝜓	𝜓	PROPN
iajs-2485	84	59	𝑘	𝑘	PROPN
iajs-2485	84	60	𝑡	𝑡	PROPN
iajs-2485	84	61	,	,	PUNCT
iajs-2485	84	62	𝑘	𝑘	PROPN
iajs-2485	84	63	𝑡	𝑡	PROPN
iajs-2485	84	64	,	,	PUNCT
iajs-2485	84	65	𝑘	𝑘	PROPN
iajs-2485	84	66	𝑡	𝑡	PROPN
iajs-2485	84	67	,	,	PUNCT
iajs-2485	84	68	…	…	PUNCT
iajs-2485	84	69	,	,	PUNCT
iajs-2485	84	70	𝑘	𝑘	X
iajs-2485	84	71	𝑡	𝑡	PROPN
iajs-2485	84	72	𝜇	𝜇	ADP
iajs-2485	84	73	𝑑	𝑑	PROPN
iajs-2485	84	74	𝜓	𝜓	NOUN
iajs-2485	84	75	𝑑𝑡	𝑑𝑡	ADP
iajs-2485	84	76	,	,	PUNCT
iajs-2485	84	77	𝑖	𝑖	NOUN
iajs-2485	84	78	0,1	0,1	NUM
iajs-2485	84	79	,	,	PUNCT
iajs-2485	84	80	…	…	PUNCT
iajs-2485	84	81	,	,	PUNCT
iajs-2485	84	82	𝑛	𝑛	PRON
iajs-2485	84	83	3	3	NUM
iajs-2485	84	84	where	where	SCONJ
iajs-2485	84	85	𝜓	𝜓	PROPN
iajs-2485	84	86	,	,	PUNCT
iajs-2485	84	87	𝜓	𝜓	PROPN
iajs-2485	84	88	,	,	PUNCT
iajs-2485	84	89	…	…	PUNCT
iajs-2485	84	90	,	,	PUNCT
iajs-2485	84	91	𝜓	𝜓	PROPN
iajs-2485	84	92	,	,	PUNCT
iajs-2485	84	93	𝜓	𝜓	PROPN
iajs-2485	84	94	,	,	PUNCT
iajs-2485	84	95	𝜓	𝜓	PROPN
iajs-2485	84	96	,	,	PUNCT
iajs-2485	84	97	…	…	PUNCT
iajs-2485	84	98	,	,	PUNCT
iajs-2485	84	99	𝜓	𝜓	PROPN
iajs-2485	84	100	are	be	AUX
iajs-2485	84	101	the	the	DET
iajs-2485	84	102	expansion	expansion	NOUN
iajs-2485	84	103	coefficients	coefficient	NOUN
iajs-2485	84	104	of	of	ADP
iajs-2485	84	105	𝑁	𝑁	PROPN
iajs-2485	84	106	𝑢	𝑢	NOUN
iajs-2485	84	107	and	and	CCONJ
iajs-2485	84	108	𝑢	𝑢	NOUN
iajs-2485	84	109	respectively	respectively	ADV
iajs-2485	84	110	with	with	ADP
iajs-2485	84	111	respect	respect	NOUN
iajs-2485	84	112	to	to	ADP
iajs-2485	84	113	𝜙	𝜙	PROPN
iajs-2485	84	114	𝑥	𝑥	INTJ
iajs-2485	84	115	,	,	PUNCT
iajs-2485	84	116	𝜙	𝜙	PROPN
iajs-2485	84	117	𝑥	𝑥	X
iajs-2485	84	118	,	,	PUNCT
iajs-2485	84	119	.	.	PUNCT
iajs-2485	84	120	.	.	PUNCT
iajs-2485	85	1	,	,	PUNCT
iajs-2485	86	1	𝜙	𝜙	PRON
iajs-2485	86	2	𝑥	𝑥	NOUN
iajs-2485	86	3	6	6	NUM
iajs-2485	86	4	.	.	PUNCT
iajs-2485	86	5	numerical	numerical	ADJ
iajs-2485	86	6	examples	example	NOUN
iajs-2485	86	7	in	in	ADP
iajs-2485	86	8	this	this	DET
iajs-2485	86	9	section	section	NOUN
iajs-2485	86	10	,	,	PUNCT
iajs-2485	86	11	we	we	PRON
iajs-2485	86	12	consider	consider	VERB
iajs-2485	86	13	that	that	SCONJ
iajs-2485	86	14	the	the	DET
iajs-2485	86	15	inverse	inverse	NOUN
iajs-2485	86	16	double	double	ADJ
iajs-2485	86	17	sumudu	sumudu	NOUN
iajs-2485	86	18	transform	transform	NOUN
iajs-2485	86	19	is	be	AUX
iajs-2485	86	20	exist	exist	NOUN
iajs-2485	86	21	.	.	PUNCT
iajs-2485	87	1	we	we	PRON
iajs-2485	87	2	apply	apply	VERB
iajs-2485	87	3	this	this	DET
iajs-2485	87	4	transform	transform	NOUN
iajs-2485	87	5	and	and	CCONJ
iajs-2485	87	6	technique	technique	NOUN
iajs-2485	87	7	of	of	ADP
iajs-2485	87	8	invariant	invariant	ADJ
iajs-2485	87	9	subspace	subspace	NOUN
iajs-2485	87	10	method	method	NOUN
iajs-2485	87	11	to	to	PART
iajs-2485	87	12	solve	solve	VERB
iajs-2485	87	13	some	some	PRON
iajs-2485	87	14	of	of	ADP
iajs-2485	87	15	the	the	DET
iajs-2485	87	16	fractional	fractional	ADJ
iajs-2485	87	17	diffusion	diffusion	NOUN
iajs-2485	87	18	heat	heat	NOUN
iajs-2485	87	19	and	and	CCONJ
iajs-2485	87	20	wave	wave	NOUN
iajs-2485	87	21	equations	equation	NOUN
iajs-2485	87	22	in	in	ADP
iajs-2485	87	23	one	one	NUM
iajs-2485	87	24	dimension	dimension	NOUN
iajs-2485	87	25	with	with	ADP
iajs-2485	87	26	initial	initial	ADJ
iajs-2485	87	27	and	and	CCONJ
iajs-2485	87	28	boundary	boundary	ADJ
iajs-2485	87	29	conditions	condition	NOUN
iajs-2485	87	30	and	and	CCONJ
iajs-2485	87	31	fractional	fractional	ADJ
iajs-2485	87	32	parabolic	parabolic	ADJ
iajs-2485	87	33	-	-	PUNCT
iajs-2485	87	34	hyperbolic	hyperbolic	ADJ
iajs-2485	87	35	differential	differential	NOUN
iajs-2485	87	36	equations	equation	NOUN
iajs-2485	87	37	.	.	PUNCT
iajs-2485	88	1	example	example	NOUN
iajs-2485	88	2	1	1	NUM
iajs-2485	88	3	:	:	PUNCT
iajs-2485	88	4	consider	consider	VERB
iajs-2485	88	5	the	the	DET
iajs-2485	88	6	homogeneous	homogeneous	ADJ
iajs-2485	88	7	fractional	fractional	ADJ
iajs-2485	88	8	wave	wave	NOUN
iajs-2485	88	9	equation	equation	NOUN
iajs-2485	88	10	:	:	PUNCT
iajs-2485	88	11	𝐷	𝐷	PROPN
iajs-2485	88	12	𝑓	𝑓	PRON
iajs-2485	88	13	𝑥	𝑥	PROPN
iajs-2485	88	14	,	,	PUNCT
iajs-2485	88	15	𝑡	𝑡	PROPN
iajs-2485	88	16	𝐷	𝐷	PROPN
iajs-2485	88	17	𝑓	𝑓	PRON
iajs-2485	88	18	𝑥	𝑥	PROPN
iajs-2485	88	19	,	,	PUNCT
iajs-2485	88	20	𝑡	𝑡	PROPN
iajs-2485	88	21	1	1	NUM
iajs-2485	88	22	𝛼	𝛼	NOUN
iajs-2485	88	23	,	,	PUNCT
iajs-2485	88	24	𝛽	𝛽	PROPN
iajs-2485	88	25	2	2	NUM
iajs-2485	88	26	4	4	NUM
iajs-2485	88	27	with	with	ADP
iajs-2485	88	28	the	the	DET
iajs-2485	88	29	initial	initial	ADJ
iajs-2485	88	30	and	and	CCONJ
iajs-2485	88	31	boundary	boundary	ADJ
iajs-2485	88	32	conditions	condition	NOUN
iajs-2485	88	33	𝑓	𝑓	DET
iajs-2485	88	34	𝑥	𝑥	NOUN
iajs-2485	88	35	,	,	PUNCT
iajs-2485	88	36	0	0	NUM
iajs-2485	88	37	𝑥𝐸	𝑥𝐸	ADJ
iajs-2485	88	38	,	,	PUNCT
iajs-2485	88	39	𝑥	𝑥	X
iajs-2485	88	40	,	,	PUNCT
iajs-2485	88	41	𝑓	𝑓	PRON
iajs-2485	88	42	𝑥	𝑥	NOUN
iajs-2485	88	43	,	,	PUNCT
iajs-2485	88	44	0	0	NUM
iajs-2485	88	45	2	2	NUM
iajs-2485	88	46	,	,	PUNCT
iajs-2485	88	47	𝑓	𝑓	PROPN
iajs-2485	88	48	0	0	NUM
iajs-2485	88	49	,	,	PUNCT
iajs-2485	88	50	𝑡	𝑡	PROPN
iajs-2485	88	51	2𝑡	2𝑡	NOUN
iajs-2485	88	52	,	,	PUNCT
iajs-2485	88	53	𝑓	𝑓	DET
iajs-2485	88	54	0	0	NUM
iajs-2485	88	55	,	,	PUNCT
iajs-2485	88	56	𝑡	𝑡	PROPN
iajs-2485	88	57	𝐸	𝐸	ADJ
iajs-2485	88	58	𝑡	𝑡	NOUN
iajs-2485	88	59	solution	solution	NOUN
iajs-2485	88	60	by	by	ADP
iajs-2485	88	61	double	double	ADJ
iajs-2485	88	62	sumudu	sumudu	NOUN
iajs-2485	88	63	transform	transform	NOUN
iajs-2485	88	64	method	method	NOUN
iajs-2485	88	65	.	.	PUNCT
iajs-2485	89	1	operating	operate	VERB
iajs-2485	89	2	double	double	ADJ
iajs-2485	89	3	sumudu	sumudu	NOUN
iajs-2485	89	4	transform	transform	NOUN
iajs-2485	89	5	of	of	ADP
iajs-2485	89	6	equation	equation	NOUN
iajs-2485	89	7	(	(	PUNCT
iajs-2485	89	8	4	4	NUM
iajs-2485	89	9	)	)	PUNCT
iajs-2485	89	10	,	,	PUNCT
iajs-2485	89	11	and	and	CCONJ
iajs-2485	89	12	using	use	VERB
iajs-2485	89	13	theorem	theorem	NOUN
iajs-2485	89	14	2	2	NUM
iajs-2485	89	15	,	,	PUNCT
iajs-2485	89	16	we	we	PRON
iajs-2485	89	17	get	get	VERB
iajs-2485	89	18	:	:	PUNCT
iajs-2485	89	19	v	v	ADP
iajs-2485	89	20	t	t	PROPN
iajs-2485	89	21	u	u	PROPN
iajs-2485	89	22	,	,	PUNCT
iajs-2485	89	23	v	v	ADP
iajs-2485	89	24	t	t	PROPN
iajs-2485	89	25	u	u	PROPN
iajs-2485	89	26	,	,	PUNCT
iajs-2485	89	27	0	0	NUM
iajs-2485	89	28	vt	vt	PROPN
iajs-2485	89	29	u	u	PROPN
iajs-2485	89	30	,	,	PUNCT
iajs-2485	89	31	0	0	NUM
iajs-2485	89	32	u	u	NOUN
iajs-2485	89	33	t	t	PROPN
iajs-2485	89	34	u	u	PROPN
iajs-2485	89	35	,	,	PUNCT
iajs-2485	89	36	v	v	ADP
iajs-2485	89	37	t	t	PROPN
iajs-2485	89	38	0	0	NUM
iajs-2485	89	39	,	,	PUNCT
iajs-2485	89	40	v	v	X
iajs-2485	89	41	ut	ut	PROPN
iajs-2485	89	42	0	0	NUM
iajs-2485	89	43	,	,	PUNCT
iajs-2485	89	44	v	v	NOUN
iajs-2485	89	45	(	(	PUNCT
iajs-2485	89	46	5	5	NUM
iajs-2485	89	47	)	)	PUNCT
iajs-2485	89	48	by	by	ADP
iajs-2485	89	49	applying	apply	VERB
iajs-2485	89	50	the	the	DET
iajs-2485	89	51	single	single	ADJ
iajs-2485	89	52	sumudu	sumudu	NOUN
iajs-2485	89	53	transform	transform	NOUN
iajs-2485	89	54	for	for	ADP
iajs-2485	89	55	conditions	condition	NOUN
iajs-2485	89	56	,	,	PUNCT
iajs-2485	89	57	and	and	CCONJ
iajs-2485	89	58	using	use	VERB
iajs-2485	89	59	properties	property	NOUN
iajs-2485	89	60	of	of	ADP
iajs-2485	89	61	mittagleffler	mittagleffler	NOUN
iajs-2485	89	62	function	function	NOUN
iajs-2485	89	63	,	,	PUNCT
iajs-2485	89	64	we	we	PRON
iajs-2485	89	65	get	get	VERB
iajs-2485	89	66	:	:	PUNCT
iajs-2485	89	67	t	t	PROPN
iajs-2485	89	68	u	u	PROPN
iajs-2485	89	69	,	,	PUNCT
iajs-2485	89	70	0	0	NUM
iajs-2485	89	71	u	u	NOUN
iajs-2485	89	72	1	1	NUM
iajs-2485	89	73	u	u	NOUN
iajs-2485	89	74	,	,	PUNCT
iajs-2485	89	75	t	t	PROPN
iajs-2485	89	76	u	u	PROPN
iajs-2485	89	77	,	,	PUNCT
iajs-2485	89	78	0	0	NUM
iajs-2485	89	79	2	2	NUM
iajs-2485	89	80	,	,	PUNCT
iajs-2485	89	81	t	t	PROPN
iajs-2485	89	82	0	0	NUM
iajs-2485	89	83	,	,	PUNCT
iajs-2485	89	84	v	v	ADJ
iajs-2485	89	85	2v	2v	NUM
iajs-2485	89	86	,	,	PUNCT
iajs-2485	89	87	t	t	PROPN
iajs-2485	89	88	0	0	NUM
iajs-2485	89	89	,	,	PUNCT
iajs-2485	89	90	v	v	NOUN
iajs-2485	89	91	v	v	NUM
iajs-2485	89	92	1	1	NUM
iajs-2485	89	93	v	v	NUM
iajs-2485	89	94	6	6	NUM
iajs-2485	89	95	by	by	ADP
iajs-2485	89	96	substitute	substitute	NOUN
iajs-2485	89	97	(	(	PUNCT
iajs-2485	89	98	6	6	NUM
iajs-2485	89	99	)	)	PUNCT
iajs-2485	89	100	in	in	ADP
iajs-2485	89	101	(	(	PUNCT
iajs-2485	89	102	5	5	NUM
iajs-2485	89	103	)	)	PUNCT
iajs-2485	89	104	,	,	PUNCT
iajs-2485	89	105	we	we	PRON
iajs-2485	89	106	obtain	obtain	VERB
iajs-2485	89	107	v	v	ADP
iajs-2485	89	108	t	t	PROPN
iajs-2485	89	109	u	u	PROPN
iajs-2485	89	110	,	,	PUNCT
iajs-2485	89	111	v	v	PROPN
iajs-2485	89	112	2v	2v	PROPN
iajs-2485	89	113	u	u	NOUN
iajs-2485	89	114	1	1	NUM
iajs-2485	89	115	u	u	NOUN
iajs-2485	89	116	u	u	PROPN
iajs-2485	89	117	t	t	PROPN
iajs-2485	89	118	u	u	PROPN
iajs-2485	89	119	,	,	PUNCT
iajs-2485	89	120	v	v	PROPN
iajs-2485	89	121	2v	2v	PROPN
iajs-2485	89	122	u	u	NOUN
iajs-2485	89	123	1	1	NUM
iajs-2485	89	124	v	v	NUM
iajs-2485	89	125	u	u	PROPN
iajs-2485	89	126	v	v	ADP
iajs-2485	89	127	t	t	PROPN
iajs-2485	89	128	u	u	PROPN
iajs-2485	89	129	,	,	PUNCT
iajs-2485	89	130	v	v	ADP
iajs-2485	89	131	u	u	PROPN
iajs-2485	89	132	2v	2v	PROPN
iajs-2485	89	133	u	u	NOUN
iajs-2485	89	134	1	1	NUM
iajs-2485	89	135	u	u	NOUN
iajs-2485	89	136	v	v	ADP
iajs-2485	89	137	2v	2v	PROPN
iajs-2485	89	138	u	u	NOUN
iajs-2485	89	139	1	1	NUM
iajs-2485	89	140	v	v	NUM
iajs-2485	89	141	2v	2v	PROPN
iajs-2485	89	142	u	u	NOUN
iajs-2485	89	143	v	v	ADP
iajs-2485	89	144	u	u	X
iajs-2485	89	145	u	u	NOUN
iajs-2485	89	146	v	v	NUM
iajs-2485	89	147	1	1	NUM
iajs-2485	89	148	u	u	NOUN
iajs-2485	89	149	1	1	NUM
iajs-2485	89	150	v	v	ADP
iajs-2485	89	151	  	  	SPACE
iajs-2485	89	152	132	132	NUM
iajs-2485	89	153	  	  	SPACE
iajs-2485	89	154	ibn	ibn	PROPN
iajs-2485	89	155	al	al	PROPN
iajs-2485	89	156	-	-	PUNCT
iajs-2485	89	157	haitham	haitham	PROPN
iajs-2485	89	158	jour	jour	X
iajs-2485	89	159	.	.	PROPN
iajs-2485	90	1	for	for	ADP
iajs-2485	90	2	pure	pure	ADJ
iajs-2485	90	3	&	&	CCONJ
iajs-2485	90	4	appl	appl	PROPN
iajs-2485	90	5	.	.	PUNCT
iajs-2485	91	1	sci	sci	PROPN
iajs-2485	91	2	.	.	PROPN
iajs-2485	92	1	33	33	NUM
iajs-2485	92	2	(	(	PUNCT
iajs-2485	92	3	3	3	NUM
iajs-2485	92	4	)	)	PUNCT
iajs-2485	92	5	2020	2020	NUM
iajs-2485	92	6	t	t	PROPN
iajs-2485	92	7	u	u	PROPN
iajs-2485	92	8	,	,	PUNCT
iajs-2485	92	9	v	v	PROPN
iajs-2485	92	10	2v	2v	PROPN
iajs-2485	92	11	(	(	PUNCT
iajs-2485	92	12	7	7	NUM
iajs-2485	92	13	)	)	PUNCT
iajs-2485	92	14	the	the	DET
iajs-2485	92	15	inverse	inverse	NOUN
iajs-2485	92	16	double	double	ADJ
iajs-2485	92	17	sumudu	sumudu	NOUN
iajs-2485	92	18	transformation	transformation	NOUN
iajs-2485	92	19	of	of	ADP
iajs-2485	92	20	(	(	PUNCT
iajs-2485	92	21	7	7	X
iajs-2485	92	22	)	)	PUNCT
iajs-2485	92	23	yields	yield	VERB
iajs-2485	92	24	the	the	DET
iajs-2485	92	25	exact	exact	ADJ
iajs-2485	92	26	solution	solution	NOUN
iajs-2485	92	27	of	of	ADP
iajs-2485	92	28	(	(	PUNCT
iajs-2485	92	29	4	4	NUM
iajs-2485	92	30	)	)	PUNCT
iajs-2485	92	31	as	as	ADP
iajs-2485	92	32	:	:	PUNCT
iajs-2485	92	33	f	f	PROPN
iajs-2485	92	34	x	x	PROPN
iajs-2485	92	35	,	,	PUNCT
iajs-2485	92	36	t	t	PROPN
iajs-2485	92	37	2	2	NUM
iajs-2485	92	38	t	t	NOUN
iajs-2485	92	39	xe	xe	PROPN
iajs-2485	92	40	,	,	PUNCT
iajs-2485	92	41	x	x	PUNCT
iajs-2485	92	42	e	e	NOUN
iajs-2485	92	43	t	t	NUM
iajs-2485	92	44	when	when	SCONJ
iajs-2485	92	45	𝛼	𝛼	X
iajs-2485	92	46	𝛽	𝛽	PROPN
iajs-2485	92	47	2	2	NUM
iajs-2485	92	48	,	,	PUNCT
iajs-2485	92	49	the	the	DET
iajs-2485	92	50	exact	exact	ADJ
iajs-2485	92	51	solution	solution	NOUN
iajs-2485	92	52	for	for	ADP
iajs-2485	92	53	standard	standard	ADJ
iajs-2485	92	54	wave	wave	NOUN
iajs-2485	92	55	equation	equation	NOUN
iajs-2485	92	56	𝑓	𝑓	DET
iajs-2485	92	57	𝑓	𝑓	PROPN
iajs-2485	92	58	is	be	AUX
iajs-2485	92	59	:	:	PUNCT
iajs-2485	92	60	f	f	PROPN
iajs-2485	92	61	x	x	PROPN
iajs-2485	92	62	,	,	PUNCT
iajs-2485	92	63	t	t	PROPN
iajs-2485	92	64	2	2	NUM
iajs-2485	92	65	t	t	NOUN
iajs-2485	92	66	sin	sin	NOUN
iajs-2485	92	67	x	x	PUNCT
iajs-2485	92	68	cos	cos	PROPN
iajs-2485	92	69	t	t	PROPN
iajs-2485	92	70	.	.	PUNCT
iajs-2485	93	1	solution	solution	NOUN
iajs-2485	93	2	by	by	ADP
iajs-2485	93	3	invariant	invariant	ADJ
iajs-2485	93	4	subspace	subspace	NOUN
iajs-2485	93	5	method	method	NOUN
iajs-2485	93	6	:	:	PUNCT
iajs-2485	93	7	let	let	VERB
iajs-2485	93	8	𝐼	𝐼	PROPN
iajs-2485	93	9	1	1	NUM
iajs-2485	93	10	,	,	PUNCT
iajs-2485	93	11	𝑥	𝑥	PROPN
iajs-2485	93	12	is	be	AUX
iajs-2485	93	13	invariant	invariant	ADJ
iajs-2485	93	14	subspace	subspace	NOUN
iajs-2485	93	15	under	under	ADP
iajs-2485	93	16	the	the	DET
iajs-2485	93	17	operator	operator	NOUN
iajs-2485	93	18	𝑁	𝑁	PROPN
iajs-2485	93	19	𝑓	𝑓	PRON
iajs-2485	93	20	𝑓	𝑓	PRON
iajs-2485	93	21	as	as	ADP
iajs-2485	93	22	:	:	PUNCT
iajs-2485	93	23	for	for	ADP
iajs-2485	93	24	𝑓	𝑓	DET
iajs-2485	93	25	∈	∈	PROPN
iajs-2485	93	26	𝐼	𝐼	NOUN
iajs-2485	93	27	,	,	PUNCT
iajs-2485	93	28	then	then	ADV
iajs-2485	93	29	𝑁	𝑁	PROPN
iajs-2485	93	30	𝑓	𝑓	PRON
iajs-2485	93	31	𝑘	𝑘	PRON
iajs-2485	93	32	𝑘	𝑘	PRON
iajs-2485	93	33	𝑥	𝑥	X
iajs-2485	93	34	𝑘	𝑘	ADP
iajs-2485	93	35	𝑘	𝑘	PRON
iajs-2485	93	36	𝑥	𝑥	X
iajs-2485	93	37	γ	γ	X
iajs-2485	93	38	1	1	NUM
iajs-2485	93	39	β	β	X
iajs-2485	93	40	𝑘	𝑘	X
iajs-2485	93	41	∈	∈	NOUN
iajs-2485	94	1	𝐼	𝐼	ADP
iajs-2485	94	2	then	then	ADV
iajs-2485	94	3	by	by	ADP
iajs-2485	94	4	[	[	X
iajs-2485	94	5	4	4	NUM
iajs-2485	94	6	]	]	PUNCT
iajs-2485	94	7	.	.	PUNCT
iajs-2485	95	1	we	we	PRON
iajs-2485	95	2	conclude	conclude	VERB
iajs-2485	95	3	the	the	DET
iajs-2485	95	4	following	follow	VERB
iajs-2485	95	5	fdes	fde	NOUN
iajs-2485	95	6	:	:	PUNCT
iajs-2485	95	7	𝑘	𝑘	NUM
iajs-2485	95	8	𝑡	𝑡	PROPN
iajs-2485	95	9	γ	γ	X
iajs-2485	95	10	1	1	NUM
iajs-2485	95	11	β	β	X
iajs-2485	95	12	𝑘	𝑘	X
iajs-2485	95	13	𝑡	𝑡	X
iajs-2485	95	14	(	(	PUNCT
iajs-2485	95	15	8)	8)	NUM
iajs-2485	95	16	𝑘	𝑘	PRON
iajs-2485	95	17	𝑡	𝑡	PROPN
iajs-2485	95	18	0	0	NUM
iajs-2485	95	19	⟹	⟹	NUM
iajs-2485	95	20	𝑘	𝑘	PRON
iajs-2485	95	21	𝑡	𝑡	PROPN
iajs-2485	95	22	𝑎	𝑎	NOUN
iajs-2485	95	23	𝑏𝑡	𝑏𝑡	NOUN
iajs-2485	95	24	(	(	PUNCT
iajs-2485	95	25	9	9	NUM
iajs-2485	95	26	)	)	PUNCT
iajs-2485	95	27	substitute	substitute	NOUN
iajs-2485	95	28	(	(	PUNCT
iajs-2485	95	29	9	9	NUM
iajs-2485	95	30	)	)	PUNCT
iajs-2485	95	31	in	in	ADP
iajs-2485	95	32	(	(	PUNCT
iajs-2485	95	33	8)	8)	NUM
iajs-2485	95	34	,	,	PUNCT
iajs-2485	95	35	we	we	PRON
iajs-2485	95	36	obtain	obtain	VERB
iajs-2485	95	37	𝑘	𝑘	PRON
iajs-2485	95	38	𝑡	𝑡	PROPN
iajs-2485	95	39	𝑡	𝑡	PROPN
iajs-2485	95	40	𝑡	𝑡	PROPN
iajs-2485	95	41	𝑐	𝑐	NOUN
iajs-2485	95	42	𝑑𝑡	𝑑𝑡	ADP
iajs-2485	95	43	for	for	ADP
iajs-2485	95	44	any	any	DET
iajs-2485	95	45	arbitrary	arbitrary	ADJ
iajs-2485	95	46	constants	constant	NOUN
iajs-2485	95	47	,	,	PUNCT
iajs-2485	95	48	𝑏	𝑏	NOUN
iajs-2485	95	49	,	,	PUNCT
iajs-2485	95	50	𝑐	𝑐	PROPN
iajs-2485	95	51	,	,	PUNCT
iajs-2485	95	52	𝑑	𝑑	VERB
iajs-2485	95	53	so	so	ADV
iajs-2485	95	54	,	,	PUNCT
iajs-2485	95	55	the	the	DET
iajs-2485	95	56	exact	exact	ADJ
iajs-2485	95	57	solution	solution	NOUN
iajs-2485	95	58	for	for	ADP
iajs-2485	95	59	equation	equation	NOUN
iajs-2485	95	60	(	(	PUNCT
iajs-2485	95	61	4	4	NUM
iajs-2485	95	62	)	)	PUNCT
iajs-2485	95	63	is	be	AUX
iajs-2485	95	64	:	:	PUNCT
iajs-2485	95	65	𝑓	𝑓	PRON
iajs-2485	95	66	𝑥	𝑥	NOUN
iajs-2485	95	67	,	,	PUNCT
iajs-2485	95	68	𝑡	𝑡	X
iajs-2485	95	69	𝑘	𝑘	ADP
iajs-2485	95	70	𝑡	𝑡	X
iajs-2485	95	71	𝑘	𝑘	ADP
iajs-2485	95	72	𝑡	𝑡	X
iajs-2485	95	73	𝑥	𝑥	NOUN
iajs-2485	95	74	𝑎γ	𝑎γ	ADP
iajs-2485	95	75	1	1	NUM
iajs-2485	95	76	β	β	X
iajs-2485	95	77	γ	γ	X
iajs-2485	95	78	1	1	NUM
iajs-2485	95	79	α	α	NUM
iajs-2485	95	80	𝑡	𝑡	NOUN
iajs-2485	95	81	𝑏γ	𝑏γ	ADP
iajs-2485	95	82	1	1	NUM
iajs-2485	95	83	β	β	X
iajs-2485	95	84	γ	γ	X
iajs-2485	95	85	2	2	NUM
iajs-2485	95	86	α	α	NUM
iajs-2485	95	87	𝑡	𝑡	PROPN
iajs-2485	95	88	𝑐	𝑐	NOUN
iajs-2485	95	89	𝑑𝑡	𝑑𝑡	ADP
iajs-2485	95	90	𝑎	𝑎	PROPN
iajs-2485	95	91	𝑏𝑡	𝑏𝑡	NOUN
iajs-2485	95	92	𝑥	𝑥	NOUN
iajs-2485	95	93	if	if	SCONJ
iajs-2485	95	94	we	we	PRON
iajs-2485	95	95	change	change	VERB
iajs-2485	95	96	the	the	DET
iajs-2485	95	97	invariant	invariant	ADJ
iajs-2485	95	98	subspace	subspace	NOUN
iajs-2485	95	99	,	,	PUNCT
iajs-2485	95	100	we	we	PRON
iajs-2485	95	101	get	get	VERB
iajs-2485	95	102	anew	anew	ADJ
iajs-2485	95	103	exact	exact	ADJ
iajs-2485	95	104	solution	solution	NOUN
iajs-2485	95	105	of	of	ADP
iajs-2485	95	106	the	the	DET
iajs-2485	95	107	same	same	ADJ
iajs-2485	95	108	equation	equation	NOUN
iajs-2485	95	109	(	(	PUNCT
iajs-2485	95	110	4	4	NUM
iajs-2485	95	111	)	)	PUNCT
iajs-2485	95	112	as	as	SCONJ
iajs-2485	95	113	if	if	SCONJ
iajs-2485	95	114	we	we	PRON
iajs-2485	95	115	consider	consider	VERB
iajs-2485	95	116	the	the	DET
iajs-2485	95	117	new	new	ADJ
iajs-2485	95	118	subspace	subspace	NOUN
iajs-2485	95	119	such	such	ADJ
iajs-2485	95	120	as	as	ADP
iajs-2485	95	121	𝐼	𝐼	PROPN
iajs-2485	95	122	1	1	NUM
iajs-2485	95	123	,	,	PUNCT
iajs-2485	95	124	𝑥𝐸	𝑥𝐸	ADJ
iajs-2485	95	125	,	,	PUNCT
iajs-2485	95	126	𝑥	𝑥	X
iajs-2485	95	127	,	,	PUNCT
iajs-2485	95	128	also	also	ADV
iajs-2485	95	129	,	,	PUNCT
iajs-2485	95	130	this	this	DET
iajs-2485	95	131	subspace	subspace	NOUN
iajs-2485	95	132	is	be	AUX
iajs-2485	95	133	an	an	DET
iajs-2485	95	134	invariant	invariant	NOUN
iajs-2485	95	135	under	under	ADP
iajs-2485	95	136	the	the	DET
iajs-2485	95	137	operator	operator	NOUN
iajs-2485	95	138	n	n	CCONJ
iajs-2485	95	139	,	,	PUNCT
iajs-2485	95	140	since	since	SCONJ
iajs-2485	95	141	𝑁	𝑁	PROPN
iajs-2485	95	142	𝑓	𝑓	PROPN
iajs-2485	95	143	𝐷	𝐷	NOUN
iajs-2485	95	144	𝑘	𝑘	NOUN
iajs-2485	95	145	𝑘	𝑘	PROPN
iajs-2485	95	146	𝑥𝐸	𝑥𝐸	ADJ
iajs-2485	95	147	,	,	PUNCT
iajs-2485	95	148	𝑥	𝑥	PROPN
iajs-2485	96	1	𝑘	𝑘	PRON
iajs-2485	96	2	𝑥	𝑥	VERB
iajs-2485	96	3	𝐸	𝐸	PROPN
iajs-2485	96	4	,	,	PUNCT
iajs-2485	96	5	𝑥	𝑥	PROPN
iajs-2485	96	6	𝑘	𝑘	PRON
iajs-2485	96	7	𝑥	𝑥	VERB
iajs-2485	96	8	𝐸	𝐸	PROPN
iajs-2485	96	9	,	,	PUNCT
iajs-2485	96	10	𝑥	𝑥	DET
iajs-2485	96	11	∈	∈	PROPN
iajs-2485	96	12	𝐼	𝐼	PROPN
iajs-2485	96	13	and	and	CCONJ
iajs-2485	96	14	we	we	PRON
iajs-2485	96	15	have	have	VERB
iajs-2485	96	16	the	the	DET
iajs-2485	96	17	following	follow	VERB
iajs-2485	96	18	new	new	ADJ
iajs-2485	96	19	fdes	fde	NOUN
iajs-2485	96	20	:	:	PUNCT
iajs-2485	96	21	𝑑	𝑑	NOUN
iajs-2485	96	22	𝑑𝑡	𝑑𝑡	ADP
iajs-2485	96	23	𝑘	𝑘	PRON
iajs-2485	96	24	𝑡	𝑡	PROPN
iajs-2485	96	25	𝑎	𝑎	PROPN
iajs-2485	96	26	𝑏𝑡	𝑏𝑡	NOUN
iajs-2485	96	27	𝑑	𝑑	NOUN
iajs-2485	96	28	𝑑𝑡	𝑑𝑡	ADP
iajs-2485	96	29	𝑘	𝑘	PRON
iajs-2485	96	30	𝑡	𝑡	NOUN
iajs-2485	96	31	𝑘	𝑘	PROPN
iajs-2485	96	32	𝑡	𝑡	NOUN
iajs-2485	96	33	⟹	⟹	ADP
iajs-2485	96	34	𝑘	𝑘	ADP
iajs-2485	96	35	𝑡	𝑡	PROPN
iajs-2485	96	36	𝐸	𝐸	VERB
iajs-2485	96	37	𝑡	𝑡	NOUN
iajs-2485	96	38	hence	hence	ADV
iajs-2485	96	39	,	,	PUNCT
iajs-2485	96	40	the	the	DET
iajs-2485	96	41	exact	exact	ADJ
iajs-2485	96	42	solution	solution	NOUN
iajs-2485	96	43	in	in	ADP
iajs-2485	96	44	this	this	DET
iajs-2485	96	45	case	case	NOUN
iajs-2485	96	46	is	be	AUX
iajs-2485	96	47	:	:	PUNCT
iajs-2485	96	48	𝑓	𝑓	PRON
iajs-2485	96	49	𝑥	𝑥	NOUN
iajs-2485	96	50	,	,	PUNCT
iajs-2485	96	51	𝑡	𝑡	VERB
iajs-2485	96	52	𝑘	𝑘	X
iajs-2485	96	53	𝑘	𝑘	PROPN
iajs-2485	96	54	𝑥𝐸	𝑥𝐸	ADJ
iajs-2485	96	55	,	,	PUNCT
iajs-2485	96	56	𝑥	𝑥	PROPN
iajs-2485	97	1	𝑎	𝑎	X
iajs-2485	97	2	𝑏𝑡	𝑏𝑡	NOUN
iajs-2485	97	3	𝐸	𝐸	PROPN
iajs-2485	97	4	𝑡	𝑡	PROPN
iajs-2485	97	5	𝑥𝐸	𝑥𝐸	PROPN
iajs-2485	97	6	,	,	PUNCT
iajs-2485	97	7	𝑥	𝑥	PROPN
iajs-2485	97	8	from	from	ADP
iajs-2485	97	9	our	our	PRON
iajs-2485	97	10	conditions	condition	NOUN
iajs-2485	97	11	,	,	PUNCT
iajs-2485	97	12	we	we	PRON
iajs-2485	97	13	get	get	VERB
iajs-2485	97	14	  	  	SPACE
iajs-2485	97	15	133	133	NUM
iajs-2485	97	16	  	  	SPACE
iajs-2485	97	17	ibn	ibn	PROPN
iajs-2485	97	18	al	al	PROPN
iajs-2485	97	19	-	-	PUNCT
iajs-2485	97	20	haitham	haitham	PROPN
iajs-2485	97	21	jour	jour	X
iajs-2485	97	22	.	.	PROPN
iajs-2485	98	1	for	for	ADP
iajs-2485	98	2	pure	pure	ADJ
iajs-2485	98	3	&	&	CCONJ
iajs-2485	98	4	appl	appl	PROPN
iajs-2485	98	5	.	.	PUNCT
iajs-2485	99	1	sci	sci	PROPN
iajs-2485	99	2	.	.	PROPN
iajs-2485	100	1	33	33	NUM
iajs-2485	100	2	(	(	PUNCT
iajs-2485	100	3	3	3	NUM
iajs-2485	100	4	)	)	PUNCT
iajs-2485	100	5	2020	2020	NUM
iajs-2485	101	1	𝑓	𝑓	DET
iajs-2485	101	2	𝑥	𝑥	NOUN
iajs-2485	101	3	,	,	PUNCT
iajs-2485	101	4	0	0	NUM
iajs-2485	101	5	0	0	NUM
iajs-2485	101	6	⟹	⟹	NUM
iajs-2485	102	1	𝑎	𝑎	PROPN
iajs-2485	102	2	0	0	NUM
iajs-2485	102	3	,	,	PUNCT
iajs-2485	102	4	𝑓	𝑓	DET
iajs-2485	102	5	0	0	NUM
iajs-2485	102	6	,	,	PUNCT
iajs-2485	102	7	𝑡	𝑡	PROPN
iajs-2485	102	8	2𝑡	2𝑡	NUM
iajs-2485	102	9	⟹	⟹	NUM
iajs-2485	102	10	𝑏	𝑏	ADV
iajs-2485	102	11	2	2	NUM
iajs-2485	102	12	so	so	ADV
iajs-2485	102	13	,	,	PUNCT
iajs-2485	102	14	the	the	DET
iajs-2485	102	15	exact	exact	ADJ
iajs-2485	102	16	solution	solution	NOUN
iajs-2485	102	17	is	be	AUX
iajs-2485	102	18	𝑓	𝑓	DET
iajs-2485	102	19	𝑥	𝑥	NOUN
iajs-2485	102	20	,	,	PUNCT
iajs-2485	102	21	𝑡	𝑡	PROPN
iajs-2485	102	22	2𝑡	2𝑡	NUM
iajs-2485	102	23	𝐸	𝐸	PROPN
iajs-2485	102	24	𝑡	𝑡	NOUN
iajs-2485	102	25	𝑥𝐸	𝑥𝐸	PROPN
iajs-2485	102	26	,	,	PUNCT
iajs-2485	102	27	𝑥	𝑥	PRON
iajs-2485	102	28	which	which	PRON
iajs-2485	102	29	agree	agree	VERB
iajs-2485	102	30	with	with	ADP
iajs-2485	102	31	that	that	PRON
iajs-2485	102	32	by	by	ADP
iajs-2485	102	33	double	double	ADJ
iajs-2485	102	34	sumudu	sumudu	NOUN
iajs-2485	102	35	transform	transform	NOUN
iajs-2485	102	36	.	.	PUNCT
iajs-2485	102	37	table	table	NOUN
iajs-2485	102	38	2	2	NUM
iajs-2485	102	39	.	.	PUNCT
iajs-2485	102	40	showing	show	VERB
iajs-2485	102	41	the	the	DET
iajs-2485	102	42	absolutely	absolutely	ADJ
iajs-2485	102	43	error	error	NOUN
iajs-2485	102	44	of	of	ADP
iajs-2485	102	45	some	some	PRON
iajs-2485	102	46	of	of	ADP
iajs-2485	102	47	10	10	NUM
iajs-2485	102	48	-	-	PUNCT
iajs-2485	102	49	order	order	NOUN
iajs-2485	102	50	approximate	approximate	ADJ
iajs-2485	102	51	solutions	solution	NOUN
iajs-2485	102	52	of	of	ADP
iajs-2485	102	53	equation	equation	NOUN
iajs-2485	102	54	(	(	PUNCT
iajs-2485	102	55	4	4	NUM
iajs-2485	102	56	)	)	PUNCT
iajs-2485	102	57	,	,	PUNCT
iajs-2485	102	58	for	for	ADP
iajs-2485	102	59	various	various	ADJ
iajs-2485	102	60	values	value	NOUN
iajs-2485	102	61	of	of	ADP
iajs-2485	102	62	𝛼	𝛼	NOUN
iajs-2485	102	63	,	,	PUNCT
iajs-2485	102	64	𝛽.	𝛽.	NOUN
iajs-2485	102	65	also	also	ADV
iajs-2485	102	66	,	,	PUNCT
iajs-2485	102	67	3	3	X
iajs-2485	102	68	-	-	SYM
iajs-2485	102	69	d	d	ADJ
iajs-2485	102	70	plotting	plotting	NOUN
iajs-2485	102	71	of	of	ADP
iajs-2485	102	72	these	these	DET
iajs-2485	102	73	solutions	solution	NOUN
iajs-2485	102	74	are	be	AUX
iajs-2485	102	75	illustrated	illustrate	VERB
iajs-2485	102	76	in	in	ADP
iajs-2485	102	77	figure	figure	NOUN
iajs-2485	102	78	1	1	NUM
iajs-2485	102	79	.	.	PUNCT
iajs-2485	102	80	table	table	NOUN
iajs-2485	102	81	2	2	NUM
iajs-2485	102	82	.	.	PUNCT
iajs-2485	103	1	absolutely	absolutely	ADV
iajs-2485	103	2	error	error	NOUN
iajs-2485	103	3	of	of	ADP
iajs-2485	103	4	10	10	NUM
iajs-2485	103	5	-	-	PUNCT
iajs-2485	103	6	order	order	NOUN
iajs-2485	103	7	approach	approach	NOUN
iajs-2485	103	8	solutions	solution	NOUN
iajs-2485	103	9	of	of	ADP
iajs-2485	103	10	equation	equation	NOUN
iajs-2485	103	11	(	(	PUNCT
iajs-2485	103	12	4	4	NUM
iajs-2485	103	13	)	)	PUNCT
iajs-2485	103	14	.	.	PUNCT
iajs-2485	104	1	figure	figure	VERB
iajs-2485	104	2	1	1	NUM
iajs-2485	104	3	.	.	PUNCT
iajs-2485	104	4	exact	exact	ADJ
iajs-2485	104	5	solution	solution	NOUN
iajs-2485	104	6	and	and	CCONJ
iajs-2485	104	7	10	10	NUM
iajs-2485	104	8	-	-	PUNCT
iajs-2485	104	9	order	order	NOUN
iajs-2485	104	10	approximate	approximate	ADJ
iajs-2485	104	11	solutions	solution	NOUN
iajs-2485	104	12	of	of	ADP
iajs-2485	104	13	equation	equation	NOUN
iajs-2485	104	14	(	(	PUNCT
iajs-2485	104	15	4	4	NUM
iajs-2485	104	16	)	)	PUNCT
iajs-2485	104	17	for	for	ADP
iajs-2485	104	18	various	various	ADJ
iajs-2485	104	19	values	value	NOUN
iajs-2485	104	20	of	of	ADP
iajs-2485	104	21	𝛼	𝛼	NOUN
iajs-2485	104	22	,	,	PUNCT
iajs-2485	104	23	𝛽.	𝛽.	NOUN
iajs-2485	104	24	  	  	SPACE
iajs-2485	104	25	134	134	NUM
iajs-2485	104	26	  	  	SPACE
iajs-2485	104	27	ibn	ibn	PROPN
iajs-2485	104	28	al	al	PROPN
iajs-2485	104	29	-	-	PUNCT
iajs-2485	104	30	haitham	haitham	PROPN
iajs-2485	104	31	jour	jour	X
iajs-2485	104	32	.	.	PROPN
iajs-2485	105	1	for	for	ADP
iajs-2485	105	2	pure	pure	ADJ
iajs-2485	105	3	&	&	CCONJ
iajs-2485	105	4	appl	appl	PROPN
iajs-2485	105	5	.	.	PUNCT
iajs-2485	106	1	sci	sci	PROPN
iajs-2485	106	2	.	.	PROPN
iajs-2485	107	1	33	33	NUM
iajs-2485	107	2	(	(	PUNCT
iajs-2485	107	3	3	3	NUM
iajs-2485	107	4	)	)	PUNCT
iajs-2485	107	5	2020	2020	NUM
iajs-2485	107	6	example	example	NOUN
iajs-2485	107	7	2	2	NUM
iajs-2485	107	8	:	:	PUNCT
iajs-2485	107	9	consider	consider	VERB
iajs-2485	107	10	the	the	DET
iajs-2485	107	11	following	follow	VERB
iajs-2485	107	12	inhomogeneous	inhomogeneous	ADJ
iajs-2485	107	13	fractional	fractional	ADJ
iajs-2485	107	14	wave	wave	NOUN
iajs-2485	107	15	equation	equation	NOUN
iajs-2485	107	16	:	:	PUNCT
iajs-2485	108	1	𝐷	𝐷	PROPN
iajs-2485	108	2	𝑓	𝑓	PRON
iajs-2485	108	3	𝑥	𝑥	PROPN
iajs-2485	108	4	,	,	PUNCT
iajs-2485	108	5	𝑡	𝑡	PROPN
iajs-2485	108	6	𝐷	𝐷	PROPN
iajs-2485	108	7	𝑓	𝑓	PRON
iajs-2485	108	8	𝑥	𝑥	PROPN
iajs-2485	108	9	,	,	PUNCT
iajs-2485	108	10	𝑡	𝑡	PROPN
iajs-2485	108	11	6𝑡	6𝑡	NOUN
iajs-2485	108	12	2𝑥	2𝑥	NOUN
iajs-2485	108	13	1	1	NUM
iajs-2485	108	14	𝛼	𝛼	NOUN
iajs-2485	108	15	,	,	PUNCT
iajs-2485	108	16	𝛽	𝛽	PROPN
iajs-2485	108	17	2	2	NUM
iajs-2485	108	18	10	10	NUM
iajs-2485	108	19	with	with	ADP
iajs-2485	108	20	conditions	condition	NOUN
iajs-2485	108	21	𝑓	𝑓	PRON
iajs-2485	108	22	𝑥	𝑥	NOUN
iajs-2485	108	23	,	,	PUNCT
iajs-2485	108	24	0	0	NUM
iajs-2485	108	25	0	0	NUM
iajs-2485	108	26	,	,	PUNCT
iajs-2485	108	27	𝑓	𝑓	PRON
iajs-2485	108	28	𝑥	𝑥	NOUN
iajs-2485	108	29	,	,	PUNCT
iajs-2485	108	30	0	0	NUM
iajs-2485	108	31	𝑥𝐸	𝑥𝐸	ADJ
iajs-2485	108	32	,	,	PUNCT
iajs-2485	108	33	𝑥	𝑥	X
iajs-2485	108	34	,	,	PUNCT
iajs-2485	108	35	𝑓	𝑓	PROPN
iajs-2485	108	36	0	0	NUM
iajs-2485	108	37	,	,	PUNCT
iajs-2485	108	38	𝑡	𝑡	PROPN
iajs-2485	108	39	𝑡	𝑡	PROPN
iajs-2485	108	40	,	,	PUNCT
iajs-2485	108	41	𝑓	𝑓	PROPN
iajs-2485	108	42	0	0	NUM
iajs-2485	108	43	,	,	PUNCT
iajs-2485	108	44	𝑡	𝑡	PROPN
iajs-2485	108	45	𝑡	𝑡	NOUN
iajs-2485	108	46	𝑡𝐸	𝑡𝐸	NOUN
iajs-2485	108	47	,	,	PUNCT
iajs-2485	108	48	𝑡	𝑡	PROPN
iajs-2485	108	49	solution	solution	NOUN
iajs-2485	108	50	by	by	ADP
iajs-2485	108	51	double	double	ADJ
iajs-2485	108	52	sumudu	sumudu	NOUN
iajs-2485	108	53	transform	transform	NOUN
iajs-2485	108	54	method	method	NOUN
iajs-2485	108	55	.	.	PUNCT
iajs-2485	109	1	by	by	ADP
iajs-2485	109	2	analogous	analogous	ADJ
iajs-2485	109	3	in	in	ADP
iajs-2485	109	4	previous	previous	ADJ
iajs-2485	109	5	examples	example	NOUN
iajs-2485	109	6	,	,	PUNCT
iajs-2485	109	7	we	we	PRON
iajs-2485	109	8	get	get	VERB
iajs-2485	109	9	𝑣	𝑣	DET
iajs-2485	109	10	𝑇	𝑇	PROPN
iajs-2485	109	11	𝑢	𝑢	NOUN
iajs-2485	109	12	,	,	PUNCT
iajs-2485	109	13	𝑣	𝑣	PRON
iajs-2485	109	14	𝑢𝑣	𝑢𝑣	NOUN
iajs-2485	109	15	1	1	NUM
iajs-2485	109	16	𝑢	𝑢	NOUN
iajs-2485	109	17	𝑢	𝑢	ADP
iajs-2485	109	18	𝑇	𝑇	PROPN
iajs-2485	109	19	𝑢	𝑢	NOUN
iajs-2485	109	20	,	,	PUNCT
iajs-2485	109	21	𝑣	𝑣	ADP
iajs-2485	109	22	6𝑣	6𝑣	NOUN
iajs-2485	109	23	𝑢	𝑢	ADP
iajs-2485	109	24	2𝑣	2𝑣	NUM
iajs-2485	109	25	𝑣	𝑣	ADP
iajs-2485	109	26	1	1	NUM
iajs-2485	109	27	𝑣	𝑣	ADP
iajs-2485	109	28	6𝑣	6𝑣	NOUN
iajs-2485	109	29	2𝑢	2𝑢	NUM
iajs-2485	109	30	𝑢	𝑢	NOUN
iajs-2485	109	31	𝑣	𝑣	ADP
iajs-2485	109	32	𝑇	𝑇	PROPN
iajs-2485	109	33	𝑢	𝑢	PROPN
iajs-2485	109	34	,	,	PUNCT
iajs-2485	109	35	𝑣	𝑣	ADP
iajs-2485	109	36	𝑢	𝑢	DET
iajs-2485	109	37	𝑣	𝑣	PROPN
iajs-2485	109	38	1	1	NUM
iajs-2485	109	39	𝑢	𝑢	NOUN
iajs-2485	109	40	𝑣	𝑣	ADP
iajs-2485	109	41	6𝑣	6𝑣	NUM
iajs-2485	109	42	2𝑢𝑣	2𝑢𝑣	NOUN
iajs-2485	109	43	𝑢𝑣	𝑢𝑣	NOUN
iajs-2485	109	44	1	1	NUM
iajs-2485	109	45	𝑣	𝑣	ADP
iajs-2485	109	46	2𝑢	2𝑢	NUM
iajs-2485	109	47	𝑣	𝑣	ADP
iajs-2485	109	48	𝑢	𝑢	PRON
iajs-2485	109	49	3𝑣	3𝑣	NUM
iajs-2485	109	50	𝑢𝑣	𝑢𝑣	NOUN
iajs-2485	109	51	𝑢	𝑢	PROPN
iajs-2485	109	52	𝑣	𝑣	PROPN
iajs-2485	109	53	1	1	NUM
iajs-2485	109	54	𝑢	𝑢	PROPN
iajs-2485	109	55	1	1	NUM
iajs-2485	109	56	𝑣	𝑣	ADP
iajs-2485	109	57	2𝑣	2𝑣	NUM
iajs-2485	109	58	𝑢	𝑢	PROPN
iajs-2485	109	59	3𝑣	3𝑣	NUM
iajs-2485	109	60	𝑢	𝑢	NOUN
iajs-2485	109	61	𝑣	𝑣	ADP
iajs-2485	109	62	𝑇	𝑇	PROPN
iajs-2485	109	63	𝑢	𝑢	PROPN
iajs-2485	109	64	,	,	PUNCT
iajs-2485	109	65	𝑣	𝑣	DET
iajs-2485	109	66	𝑢	𝑢	PROPN
iajs-2485	109	67	1	1	NUM
iajs-2485	109	68	𝑢	𝑢	NOUN
iajs-2485	109	69	𝑣	𝑣	ADP
iajs-2485	109	70	1	1	NUM
iajs-2485	109	71	𝑣	𝑣	ADP
iajs-2485	109	72	2𝑣	2𝑣	NUM
iajs-2485	109	73	𝑢	𝑢	PROPN
iajs-2485	109	74	3𝑣	3𝑣	NUM
iajs-2485	109	75	11	11	NUM
iajs-2485	109	76	the	the	DET
iajs-2485	109	77	inverse	inverse	NOUN
iajs-2485	109	78	double	double	ADJ
iajs-2485	109	79	sumudu	sumudu	NOUN
iajs-2485	109	80	transform	transform	NOUN
iajs-2485	109	81	of	of	ADP
iajs-2485	109	82	eq.(11	eq.(11	PROPN
iajs-2485	109	83	)	)	PUNCT
iajs-2485	109	84	reads	read	VERB
iajs-2485	109	85	𝑓	𝑓	PRON
iajs-2485	109	86	𝑥	𝑥	PROPN
iajs-2485	109	87	,	,	PUNCT
iajs-2485	109	88	𝑡	𝑡	PROPN
iajs-2485	109	89	𝑥𝐸	𝑥𝐸	ADV
iajs-2485	109	90	,	,	PUNCT
iajs-2485	109	91	𝑥	𝑥	PROPN
iajs-2485	109	92	𝑡𝐸	𝑡𝐸	NOUN
iajs-2485	109	93	,	,	PUNCT
iajs-2485	109	94	𝑡	𝑡	PROPN
iajs-2485	109	95	2𝑥𝑡	2𝑥𝑡	ADJ
iajs-2485	109	96	γ	γ	NOUN
iajs-2485	109	97	1	1	NUM
iajs-2485	109	98	𝛼	𝛼	NOUN
iajs-2485	109	99	6𝑡	6𝑡	NOUN
iajs-2485	110	1	γ	γ	X
iajs-2485	110	2	2	2	NUM
iajs-2485	110	3	𝛼	𝛼	NOUN
iajs-2485	110	4	note	note	NOUN
iajs-2485	110	5	that	that	SCONJ
iajs-2485	110	6	,	,	PUNCT
iajs-2485	110	7	when	when	SCONJ
iajs-2485	110	8	𝛽	𝛽	NOUN
iajs-2485	110	9	2	2	NUM
iajs-2485	110	10	,	,	PUNCT
iajs-2485	110	11	we	we	PRON
iajs-2485	110	12	have	have	VERB
iajs-2485	110	13	𝑓	𝑓	DET
iajs-2485	110	14	𝑥	𝑥	NOUN
iajs-2485	110	15	,	,	PUNCT
iajs-2485	110	16	𝑡	𝑡	PROPN
iajs-2485	110	17	𝑥𝑡	𝑥𝑡	ADP
iajs-2485	110	18	𝑡	𝑡	PROPN
iajs-2485	110	19	𝑠𝑖𝑛	𝑠𝑖𝑛	VERB
iajs-2485	110	20	𝑥	𝑥	DET
iajs-2485	110	21	𝑠𝑖𝑛𝑡	𝑠𝑖𝑛𝑡	NOUN
iajs-2485	110	22	which	which	PRON
iajs-2485	110	23	agree	agree	VERB
iajs-2485	110	24	with	with	ADP
iajs-2485	110	25	the	the	DET
iajs-2485	110	26	exact	exact	ADJ
iajs-2485	110	27	solution	solution	NOUN
iajs-2485	110	28	of	of	ADP
iajs-2485	110	29	standard	standard	ADJ
iajs-2485	110	30	non	non	ADJ
iajs-2485	110	31	-	-	ADJ
iajs-2485	110	32	homogeneous	homogeneous	ADJ
iajs-2485	110	33	wave	wave	NOUN
iajs-2485	110	34	equation	equation	NOUN
iajs-2485	110	35	𝑓	𝑓	PRON
iajs-2485	110	36	𝑓	𝑓	PRON
iajs-2485	110	37	2	2	NUM
iajs-2485	110	38	𝑥	𝑥	PROPN
iajs-2485	110	39	3𝑡	3𝑡	NUM
iajs-2485	110	40	.	.	PUNCT
iajs-2485	111	1	solution	solution	NOUN
iajs-2485	111	2	by	by	ADP
iajs-2485	111	3	invariant	invariant	ADJ
iajs-2485	111	4	subspace	subspace	NOUN
iajs-2485	111	5	method	method	NOUN
iajs-2485	111	6	    	    	SPACE
iajs-2485	111	7	the	the	DET
iajs-2485	111	8	inhomogeneous	inhomogeneous	ADJ
iajs-2485	111	9	fractional	fractional	ADJ
iajs-2485	111	10	partial	partial	ADJ
iajs-2485	111	11	differential	differential	NOUN
iajs-2485	111	12	equation	equation	NOUN
iajs-2485	111	13	(	(	PUNCT
iajs-2485	111	14	10	10	NUM
iajs-2485	111	15	)	)	PUNCT
iajs-2485	111	16	,	,	PUNCT
iajs-2485	111	17	can	can	AUX
iajs-2485	111	18	not	not	PART
iajs-2485	111	19	be	be	AUX
iajs-2485	111	20	solved	solve	VERB
iajs-2485	111	21	by	by	ADP
iajs-2485	111	22	invariant	invariant	ADJ
iajs-2485	111	23	subspace	subspace	NOUN
iajs-2485	111	24	method	method	NOUN
iajs-2485	111	25	directly	directly	ADV
iajs-2485	111	26	,	,	PUNCT
iajs-2485	111	27	in	in	ADP
iajs-2485	111	28	this	this	DET
iajs-2485	111	29	case	case	NOUN
iajs-2485	111	30	we	we	PRON
iajs-2485	111	31	find	find	VERB
iajs-2485	111	32	the	the	DET
iajs-2485	111	33	solution	solution	NOUN
iajs-2485	111	34	of	of	ADP
iajs-2485	111	35	homogeneous	homogeneous	ADJ
iajs-2485	111	36	equation	equation	NOUN
iajs-2485	111	37	directly	directly	ADV
iajs-2485	111	38	by	by	ADP
iajs-2485	111	39	invariant	invariant	ADJ
iajs-2485	111	40	subspace	subspace	NOUN
iajs-2485	111	41	method	method	NOUN
iajs-2485	111	42	and	and	CCONJ
iajs-2485	111	43	then	then	ADV
iajs-2485	111	44	we	we	PRON
iajs-2485	111	45	can	can	AUX
iajs-2485	111	46	be	be	AUX
iajs-2485	111	47	use	use	VERB
iajs-2485	111	48	any	any	DET
iajs-2485	111	49	suitable	suitable	ADJ
iajs-2485	111	50	numerical	numerical	ADJ
iajs-2485	111	51	method	method	NOUN
iajs-2485	111	52	”	"	PUNCT
iajs-2485	111	53	variation	variation	NOUN
iajs-2485	111	54	iteration	iteration	NOUN
iajs-2485	111	55	method	method	NOUN
iajs-2485	111	56	”	"	PUNCT
iajs-2485	111	57	,	,	PUNCT
iajs-2485	111	58	i.	i.	PROPN
iajs-2485	111	59	e	e	PROPN
iajs-2485	111	60	,	,	PUNCT
iajs-2485	111	61	coupled	couple	VERB
iajs-2485	111	62	invariant	invariant	ADJ
iajs-2485	111	63	subspace	subspace	NOUN
iajs-2485	111	64	method	method	NOUN
iajs-2485	111	65	with	with	ADP
iajs-2485	111	66	variation	variation	NOUN
iajs-2485	111	67	iteration	iteration	NOUN
iajs-2485	111	68	method(isvim	method(isvim	PROPN
iajs-2485	111	69	)	)	PUNCT
iajs-2485	111	70	to	to	PART
iajs-2485	111	71	find	find	VERB
iajs-2485	111	72	an	an	DET
iajs-2485	111	73	approximate	approximate	ADJ
iajs-2485	111	74	solution	solution	NOUN
iajs-2485	111	75	of	of	ADP
iajs-2485	111	76	the	the	DET
iajs-2485	111	77	original	original	ADJ
iajs-2485	111	78	equation	equation	NOUN
iajs-2485	111	79	.	.	PUNCT
iajs-2485	112	1	table	table	NOUN
iajs-2485	112	2	3	3	NUM
iajs-2485	112	3	.	.	PUNCT
iajs-2485	112	4	contains	contain	VERB
iajs-2485	112	5	the	the	DET
iajs-2485	112	6	absolutely	absolutely	ADJ
iajs-2485	112	7	error	error	NOUN
iajs-2485	112	8	of	of	ADP
iajs-2485	112	9	some	some	PRON
iajs-2485	112	10	of	of	ADP
iajs-2485	112	11	10	10	NUM
iajs-2485	112	12	-	-	PUNCT
iajs-2485	112	13	order	order	NOUN
iajs-2485	112	14	approximate	approximate	ADJ
iajs-2485	112	15	solutions	solution	NOUN
iajs-2485	112	16	of	of	ADP
iajs-2485	112	17	eq.(10	eq.(10	NOUN
iajs-2485	112	18	)	)	PUNCT
iajs-2485	112	19	for	for	ADP
iajs-2485	112	20	various	various	ADJ
iajs-2485	112	21	values	value	NOUN
iajs-2485	112	22	of	of	ADP
iajs-2485	112	23	α	α	NOUN
iajs-2485	112	24	,	,	PUNCT
iajs-2485	112	25	β	β	NOUN
iajs-2485	112	26	.	.	NOUN
iajs-2485	113	1	3	3	X
iajs-2485	113	2	-	-	SYM
iajs-2485	113	3	d	d	ADJ
iajs-2485	113	4	plotting	plotting	NOUN
iajs-2485	113	5	of	of	ADP
iajs-2485	113	6	these	these	DET
iajs-2485	113	7	solutions	solution	NOUN
iajs-2485	113	8	are	be	AUX
iajs-2485	113	9	illustrated	illustrate	VERB
iajs-2485	113	10	in	in	ADP
iajs-2485	113	11	figure	figure	NOUN
iajs-2485	113	12	2	2	NUM
iajs-2485	113	13	.	.	PUNCT
iajs-2485	113	14	  	  	SPACE
iajs-2485	113	15	135	135	NUM
iajs-2485	113	16	  	  	SPACE
iajs-2485	113	17	ibn	ibn	PROPN
iajs-2485	113	18	al	al	PROPN
iajs-2485	113	19	-	-	PUNCT
iajs-2485	113	20	haitham	haitham	PROPN
iajs-2485	113	21	jour	jour	X
iajs-2485	113	22	.	.	PROPN
iajs-2485	114	1	for	for	ADP
iajs-2485	114	2	pure	pure	ADJ
iajs-2485	114	3	&	&	CCONJ
iajs-2485	114	4	appl	appl	PROPN
iajs-2485	114	5	.	.	PUNCT
iajs-2485	115	1	sci	sci	PROPN
iajs-2485	115	2	.	.	PROPN
iajs-2485	116	1	33	33	NUM
iajs-2485	116	2	(	(	PUNCT
iajs-2485	116	3	3	3	NUM
iajs-2485	116	4	)	)	PUNCT
iajs-2485	116	5	2020	2020	NUM
iajs-2485	116	6	table	table	NOUN
iajs-2485	116	7	3	3	NUM
iajs-2485	116	8	.	.	PUNCT
iajs-2485	117	1	absolutely	absolutely	ADV
iajs-2485	117	2	error	error	NOUN
iajs-2485	117	3	of	of	ADP
iajs-2485	117	4	10	10	NUM
iajs-2485	117	5	-	-	PUNCT
iajs-2485	117	6	order	order	NOUN
iajs-2485	117	7	approximate	approximate	ADJ
iajs-2485	117	8	solutions	solution	NOUN
iajs-2485	117	9	of	of	ADP
iajs-2485	117	10	equation	equation	NOUN
iajs-2485	117	11	10	10	NUM
iajs-2485	117	12	.	.	PUNCT
iajs-2485	117	13	        	        	SPACE
iajs-2485	117	14	figure	figure	NOUN
iajs-2485	117	15	2	2	NUM
iajs-2485	117	16	.	.	NOUN
iajs-2485	117	17	exact	exact	ADJ
iajs-2485	117	18	solution	solution	NOUN
iajs-2485	117	19	and	and	CCONJ
iajs-2485	117	20	10	10	NUM
iajs-2485	117	21	-	-	PUNCT
iajs-2485	117	22	order	order	NOUN
iajs-2485	117	23	approximate	approximate	ADJ
iajs-2485	117	24	solutions	solution	NOUN
iajs-2485	117	25	of	of	ADP
iajs-2485	117	26	equation	equation	NOUN
iajs-2485	117	27	10	10	NUM
iajs-2485	117	28	,	,	PUNCT
iajs-2485	117	29	for	for	ADP
iajs-2485	117	30	various	various	ADJ
iajs-2485	117	31	values	value	NOUN
iajs-2485	117	32	of	of	ADP
iajs-2485	117	33	𝛼	𝛼	NOUN
iajs-2485	117	34	,	,	PUNCT
iajs-2485	117	35	𝛽.	𝛽.	ADJ
iajs-2485	117	36	example	example	NOUN
iajs-2485	117	37	3	3	NUM
iajs-2485	117	38	:	:	PUNCT
iajs-2485	117	39	consider	consider	VERB
iajs-2485	117	40	the	the	DET
iajs-2485	117	41	following	follow	VERB
iajs-2485	117	42	mixed	mixed	ADJ
iajs-2485	117	43	partial	partial	ADJ
iajs-2485	117	44	fractional	fractional	ADJ
iajs-2485	117	45	differential	differential	NOUN
iajs-2485	117	46	equation	equation	NOUN
iajs-2485	117	47	𝐷	𝐷	PROPN
iajs-2485	117	48	𝐷	𝐷	PROPN
iajs-2485	117	49	𝑓	𝑓	PRON
iajs-2485	117	50	𝑥	𝑥	PROPN
iajs-2485	117	51	,	,	PUNCT
iajs-2485	117	52	𝑡	𝑡	VERB
iajs-2485	117	53	𝑓	𝑓	PRON
iajs-2485	117	54	𝑥	𝑥	PROPN
iajs-2485	117	55	,	,	PUNCT
iajs-2485	117	56	𝑡	𝑡	PROPN
iajs-2485	117	57	0	0	NUM
iajs-2485	117	58	,	,	PUNCT
iajs-2485	117	59	0	0	NUM
iajs-2485	117	60	𝛼	𝛼	NOUN
iajs-2485	117	61	,	,	PUNCT
iajs-2485	117	62	𝛽	𝛽	PROPN
iajs-2485	117	63	1	1	NUM
iajs-2485	117	64	12	12	NUM
iajs-2485	117	65	with	with	ADP
iajs-2485	117	66	conditions	condition	NOUN
iajs-2485	117	67	𝑓	𝑓	ADP
iajs-2485	117	68	0	0	NUM
iajs-2485	117	69	,	,	PUNCT
iajs-2485	117	70	𝑡	𝑡	PROPN
iajs-2485	117	71	𝐸	𝐸	PROPN
iajs-2485	117	72	𝑡	𝑡	PROPN
iajs-2485	117	73	,	,	PUNCT
iajs-2485	117	74	𝑓	𝑓	DET
iajs-2485	117	75	𝑥	𝑥	NOUN
iajs-2485	117	76	,	,	PUNCT
iajs-2485	117	77	0	0	NUM
iajs-2485	117	78	𝐸	𝐸	NOUN
iajs-2485	117	79	𝑥	𝑥	NOUN
iajs-2485	117	80	solution	solution	NOUN
iajs-2485	117	81	by	by	ADP
iajs-2485	117	82	double	double	ADJ
iajs-2485	117	83	sumudu	sumudu	NOUN
iajs-2485	117	84	transform	transform	NOUN
iajs-2485	117	85	method	method	NOUN
iajs-2485	117	86	:	:	PUNCT
iajs-2485	117	87	by	by	ADP
iajs-2485	117	88	theorem	theorem	NOUN
iajs-2485	117	89	(	(	PUNCT
iajs-2485	117	90	2	2	NUM
iajs-2485	117	91	)	)	PUNCT
iajs-2485	117	92	one	one	NOUN
iajs-2485	117	93	can	can	AUX
iajs-2485	117	94	obtain	obtain	VERB
iajs-2485	117	95	u	u	PRON
iajs-2485	117	96	v	v	ADP
iajs-2485	117	97	t	t	PROPN
iajs-2485	117	98	u	u	PROPN
iajs-2485	117	99	,	,	PUNCT
iajs-2485	117	100	v	v	ADP
iajs-2485	117	101	t	t	PROPN
iajs-2485	117	102	u	u	PROPN
iajs-2485	117	103	,	,	PUNCT
iajs-2485	117	104	0	0	NUM
iajs-2485	117	105	vt	vt	PROPN
iajs-2485	117	106	u	u	PROPN
iajs-2485	117	107	,	,	PUNCT
iajs-2485	117	108	0	0	NUM
iajs-2485	117	109	t	t	PROPN
iajs-2485	117	110	u	u	PROPN
iajs-2485	117	111	,	,	PUNCT
iajs-2485	117	112	v	v	NOUN
iajs-2485	117	113	0	0	NUM
iajs-2485	117	114	1	1	NUM
iajs-2485	117	115	u	u	NOUN
iajs-2485	117	116	v	v	ADP
iajs-2485	117	117	𝑇	𝑇	PROPN
iajs-2485	117	118	𝑢	𝑢	PROPN
iajs-2485	117	119	,	,	PUNCT
iajs-2485	117	120	𝑣	𝑣	DET
iajs-2485	117	121	1	1	NUM
iajs-2485	117	122	1	1	NUM
iajs-2485	117	123	𝑣	𝑣	DET
iajs-2485	117	124	1	1	NUM
iajs-2485	117	125	1	1	NUM
iajs-2485	117	126	𝑢	𝑢	SYM
iajs-2485	117	127	1	1	NUM
iajs-2485	117	128	1	1	NUM
iajs-2485	117	129	𝑢	𝑢	NOUN
iajs-2485	117	130	𝑣	𝑣	ADP
iajs-2485	117	131	1	1	NUM
iajs-2485	117	132	𝑣	𝑣	PART
iajs-2485	117	133	1	1	NUM
iajs-2485	117	134	𝑢	𝑢	NOUN
iajs-2485	117	135	𝑇	𝑇	PROPN
iajs-2485	117	136	𝑢	𝑢	NOUN
iajs-2485	117	137	,	,	PUNCT
iajs-2485	117	138	𝑣	𝑣	DET
iajs-2485	117	139	1	1	NUM
iajs-2485	117	140	1	1	NUM
iajs-2485	117	141	𝑣	𝑣	DET
iajs-2485	117	142	1	1	NUM
iajs-2485	117	143	1	1	NUM
iajs-2485	117	144	𝑢	𝑢	NOUN
iajs-2485	117	145	𝑣	𝑣	ADP
iajs-2485	117	146	1	1	NUM
iajs-2485	117	147	𝑣	𝑣	PRON
iajs-2485	117	148	𝑢	𝑢	PROPN
iajs-2485	117	149	1	1	NUM
iajs-2485	117	150	𝑢	𝑢	DET
iajs-2485	117	151	13	13	NUM
iajs-2485	117	152	operating	operate	VERB
iajs-2485	117	153	inverse	inverse	NOUN
iajs-2485	117	154	double	double	ADJ
iajs-2485	117	155	sumudu	sumudu	NOUN
iajs-2485	117	156	transformation	transformation	NOUN
iajs-2485	117	157	of	of	ADP
iajs-2485	117	158	(	(	PUNCT
iajs-2485	117	159	13	13	NUM
iajs-2485	117	160	)	)	PUNCT
iajs-2485	117	161	reads	read	VERB
iajs-2485	117	162	the	the	DET
iajs-2485	117	163	exact	exact	ADJ
iajs-2485	117	164	solution	solution	NOUN
iajs-2485	117	165	of	of	ADP
iajs-2485	117	166	(	(	PUNCT
iajs-2485	117	167	12	12	NUM
iajs-2485	117	168	)	)	PUNCT
iajs-2485	117	169	as	as	ADP
iajs-2485	117	170	:	:	PUNCT
iajs-2485	117	171	2	2	NUM
iajs-2485	117	172	exact	exact	NOUN
iajs-2485	117	173	=	=	SYM
iajs-2485	118	1	=	=	SYM
iajs-2485	118	2	2	2	NUM
iajs-2485	118	3	1	1	NUM
iajs-2485	118	4	t	t	NOUN
iajs-2485	118	5	00	00	NUM
iajs-2485	118	6	1	1	NUM
iajs-2485	118	7	x	x	SYM
iajs-2485	118	8	10	10	NUM
iajs-2485	118	9	0	0	NUM
iajs-2485	118	10	2	2	NUM
iajs-2485	118	11	2	2	NUM
iajs-2485	118	12	1	1	NUM
iajs-2485	118	13	t	t	NOUN
iajs-2485	118	14	=	=	PUNCT
iajs-2485	119	1	=	=	NUM
iajs-2485	119	2	2	2	NUM
iajs-2485	119	3	00	00	NUM
iajs-2485	119	4	1	1	NUM
iajs-2485	119	5	x	x	SYM
iajs-2485	119	6	10	10	NUM
iajs-2485	119	7	0	0	NUM
iajs-2485	119	8	2	2	NUM
iajs-2485	119	9	2	2	NUM
iajs-2485	119	10	=	=	SYM
iajs-2485	119	11	1.6	1.6	NUM
iajs-2485	119	12	and	and	CCONJ
iajs-2485	119	13	=	=	NOUN
iajs-2485	119	14	1.3	1.3	NUM
iajs-2485	119	15	1	1	NUM
iajs-2485	119	16	t	t	NOUN
iajs-2485	119	17	00	00	NUM
iajs-2485	119	18	1	1	NUM
iajs-2485	119	19	x	x	SYM
iajs-2485	119	20	10	10	NUM
iajs-2485	119	21	0	0	NUM
iajs-2485	119	22	2	2	NUM
iajs-2485	119	23	2	2	NUM
iajs-2485	119	24	=	=	SYM
iajs-2485	119	25	1.8	1.8	NUM
iajs-2485	119	26	and	and	CCONJ
iajs-2485	119	27	=	=	NOUN
iajs-2485	119	28	1.3	1.3	NUM
iajs-2485	119	29	1	1	NUM
iajs-2485	119	30	t	t	NOUN
iajs-2485	119	31	00	00	NUM
iajs-2485	119	32	1	1	NUM
iajs-2485	119	33	x	x	SYM
iajs-2485	119	34	10	10	NUM
iajs-2485	119	35	0	0	NUM
iajs-2485	119	36	2	2	NUM
iajs-2485	119	37	2	2	NUM
iajs-2485	119	38	=	=	SYM
iajs-2485	119	39	1.1	1.1	NUM
iajs-2485	119	40	and	and	CCONJ
iajs-2485	119	41	=	=	NOUN
iajs-2485	119	42	1.4	1.4	NUM
iajs-2485	119	43	1	1	NUM
iajs-2485	119	44	t	t	NOUN
iajs-2485	119	45	00	00	NUM
iajs-2485	119	46	1	1	NUM
iajs-2485	119	47	x	x	SYM
iajs-2485	119	48	0	0	NUM
iajs-2485	119	49	10	10	NUM
iajs-2485	119	50	20	20	NUM
iajs-2485	119	51	2	2	NUM
iajs-2485	119	52	2	2	NUM
iajs-2485	119	53	=	=	SYM
iajs-2485	119	54	1.3	1.3	NUM
iajs-2485	119	55	and	and	CCONJ
iajs-2485	119	56	=	=	NOUN
iajs-2485	119	57	1.1	1.1	NUM
iajs-2485	119	58	1	1	NUM
iajs-2485	119	59	t	t	NOUN
iajs-2485	119	60	00	00	NUM
iajs-2485	119	61	1	1	NUM
iajs-2485	119	62	x	x	SYM
iajs-2485	119	63	0	0	NUM
iajs-2485	119	64	10	10	NUM
iajs-2485	119	65	20	20	NUM
iajs-2485	119	66	2	2	NUM
iajs-2485	119	67	  	  	SPACE
iajs-2485	119	68	136	136	NUM
iajs-2485	119	69	  	  	SPACE
iajs-2485	119	70	ibn	ibn	PROPN
iajs-2485	119	71	al	al	PROPN
iajs-2485	119	72	-	-	PUNCT
iajs-2485	119	73	haitham	haitham	PROPN
iajs-2485	119	74	jour	jour	X
iajs-2485	119	75	.	.	PROPN
iajs-2485	120	1	for	for	ADP
iajs-2485	120	2	pure	pure	ADJ
iajs-2485	120	3	&	&	CCONJ
iajs-2485	120	4	appl	appl	PROPN
iajs-2485	120	5	.	.	PUNCT
iajs-2485	121	1	sci	sci	PROPN
iajs-2485	121	2	.	.	PROPN
iajs-2485	122	1	33	33	NUM
iajs-2485	122	2	(	(	PUNCT
iajs-2485	122	3	3	3	NUM
iajs-2485	122	4	)	)	PUNCT
iajs-2485	122	5	2020	2020	NUM
iajs-2485	123	1	𝑓	𝑓	DET
iajs-2485	123	2	𝑥	𝑥	NOUN
iajs-2485	123	3	,	,	PUNCT
iajs-2485	123	4	𝑡	𝑡	PROPN
iajs-2485	123	5	𝐸	𝐸	PROPN
iajs-2485	123	6	𝑡	𝑡	PROPN
iajs-2485	123	7	𝐸	𝐸	NOUN
iajs-2485	123	8	𝑥	𝑥	X
iajs-2485	123	9	𝑡	𝑡	PROPN
iajs-2485	123	10	𝐸	𝐸	PROPN
iajs-2485	123	11	,	,	PUNCT
iajs-2485	123	12	𝑡	𝑡	X
iajs-2485	123	13	𝑥	𝑥	VERB
iajs-2485	123	14	𝐸	𝐸	PROPN
iajs-2485	123	15	,	,	PUNCT
iajs-2485	123	16	𝑡	𝑡	VERB
iajs-2485	123	17	for	for	ADP
iajs-2485	123	18	𝛼	𝛼	PART
iajs-2485	123	19	𝛽	𝛽	PROPN
iajs-2485	123	20	1	1	NUM
iajs-2485	123	21	,	,	PUNCT
iajs-2485	123	22	we	we	PRON
iajs-2485	123	23	obtain	obtain	VERB
iajs-2485	123	24	the	the	DET
iajs-2485	123	25	standard	standard	ADJ
iajs-2485	123	26	differential	differential	ADJ
iajs-2485	123	27	equation	equation	NOUN
iajs-2485	123	28	𝑓	𝑓	DET
iajs-2485	123	29	𝑓	𝑓	PROPN
iajs-2485	123	30	0	0	NUM
iajs-2485	123	31	,	,	PUNCT
iajs-2485	123	32	which	which	PRON
iajs-2485	123	33	has	have	VERB
iajs-2485	123	34	the	the	DET
iajs-2485	123	35	exact	exact	ADJ
iajs-2485	123	36	solution	solution	NOUN
iajs-2485	123	37	as	as	ADP
iajs-2485	123	38	𝑓	𝑓	DET
iajs-2485	123	39	𝑥	𝑥	PROPN
iajs-2485	123	40	,	,	PUNCT
iajs-2485	123	41	𝑡	𝑡	PROPN
iajs-2485	123	42	cosh	cosh	NOUN
iajs-2485	123	43	𝑥	𝑥	PROPN
iajs-2485	123	44	𝑡	𝑡	PROPN
iajs-2485	123	45	.	.	PUNCT
iajs-2485	124	1	solution	solution	NOUN
iajs-2485	124	2	by	by	ADP
iajs-2485	124	3	invariant	invariant	ADJ
iajs-2485	124	4	subspace	subspace	NOUN
iajs-2485	124	5	method	method	NOUN
iajs-2485	124	6	:	:	PUNCT
iajs-2485	124	7	using	use	VERB
iajs-2485	124	8	theorem	theorem	NOUN
iajs-2485	124	9	(	(	PUNCT
iajs-2485	124	10	3	3	NUM
iajs-2485	124	11	)	)	PUNCT
iajs-2485	124	12	,	,	PUNCT
iajs-2485	124	13	eq	eq	NOUN
iajs-2485	124	14	.	.	PUNCT
iajs-2485	125	1	(	(	PUNCT
iajs-2485	125	2	12	12	NUM
iajs-2485	125	3	)	)	PUNCT
iajs-2485	125	4	in	in	ADP
iajs-2485	125	5	the	the	DET
iajs-2485	125	6	operators	operator	NOUN
iajs-2485	125	7	form	form	NOUN
iajs-2485	125	8	is	be	AUX
iajs-2485	125	9	:	:	PUNCT
iajs-2485	125	10	n	n	PROPN
iajs-2485	125	11	f	f	PROPN
iajs-2485	125	12	𝑓	𝑓	ADV
iajs-2485	125	13	0	0	NUM
iajs-2485	125	14	where	where	SCONJ
iajs-2485	125	15	n	n	ADV
iajs-2485	125	16	f	f	PROPN
iajs-2485	125	17	𝑓	𝑓	ADV
iajs-2485	125	18	by	by	ADP
iajs-2485	125	19	consider	consider	VERB
iajs-2485	125	20	𝐼	𝐼	PROPN
iajs-2485	125	21	1	1	NUM
iajs-2485	125	22	,	,	PUNCT
iajs-2485	125	23	𝐸	𝐸	PROPN
iajs-2485	125	24	𝑥	𝑥	NOUN
iajs-2485	125	25	,	,	PUNCT
iajs-2485	125	26	𝐸	𝐸	PROPN
iajs-2485	125	27	𝑥	𝑥	PROPN
iajs-2485	125	28	is	be	AUX
iajs-2485	125	29	invariant	invariant	ADJ
iajs-2485	125	30	subspace	subspace	NOUN
iajs-2485	125	31	under	under	ADP
iajs-2485	125	32	the	the	DET
iajs-2485	125	33	operators	operator	NOUN
iajs-2485	125	34	𝑁	𝑁	PROPN
iajs-2485	125	35	𝑓	𝑓	PROPN
iajs-2485	125	36	and	and	CCONJ
iajs-2485	125	37	𝑓	𝑓	NOUN
iajs-2485	125	38	since	since	SCONJ
iajs-2485	125	39	∀𝑓	∀𝑓	PROPN
iajs-2485	125	40	𝑎	𝑎	PROPN
iajs-2485	125	41	𝑏𝐸	𝑏𝐸	NOUN
iajs-2485	125	42	𝑥	𝑥	X
iajs-2485	125	43	𝑐𝐸	𝑐𝐸	NOUN
iajs-2485	125	44	𝑥	𝑥	NOUN
iajs-2485	125	45	∈	∈	PROPN
iajs-2485	125	46	𝐼	𝐼	ADP
iajs-2485	125	47	𝑎	𝑎	PROPN
iajs-2485	125	48	,	,	PUNCT
iajs-2485	125	49	𝑏	𝑏	NOUN
iajs-2485	125	50	,	,	PUNCT
iajs-2485	125	51	𝑐	𝑐	PROPN
iajs-2485	125	52	are	be	AUX
iajs-2485	125	53	arbitrary	arbitrary	ADJ
iajs-2485	125	54	constants	constant	NOUN
iajs-2485	125	55	𝑁	𝑁	PROPN
iajs-2485	125	56	𝑓	𝑓	PRON
iajs-2485	125	57	𝑓	𝑓	DET
iajs-2485	125	58	∈	∈	NOUN
iajs-2485	125	59	𝐼	𝐼	PROPN
iajs-2485	125	60	,	,	PUNCT
iajs-2485	125	61	𝜕	𝜕	NOUN
iajs-2485	125	62	𝜕𝑥	𝜕𝑥	X
iajs-2485	126	1	𝑓	𝑓	X
iajs-2485	126	2	𝑏𝐸	𝑏𝐸	NOUN
iajs-2485	126	3	𝑥	𝑥	PRON
iajs-2485	126	4	𝑐𝐸	𝑐𝐸	NOUN
iajs-2485	126	5	𝑥	𝑥	NOUN
iajs-2485	126	6	,	,	PUNCT
iajs-2485	126	7	∈	∈	PROPN
iajs-2485	126	8	𝐼	𝐼	ADP
iajs-2485	126	9	according	accord	VERB
iajs-2485	126	10	to	to	ADP
iajs-2485	126	11	the	the	DET
iajs-2485	126	12	invariant	invariant	ADJ
iajs-2485	126	13	subspace	subspace	NOUN
iajs-2485	126	14	method	method	NOUN
iajs-2485	126	15	and	and	CCONJ
iajs-2485	126	16	by	by	ADP
iajs-2485	126	17	considering	consider	VERB
iajs-2485	126	18	𝑓	𝑓	PRON
iajs-2485	126	19	∑	∑	PUNCT
iajs-2485	126	20	𝐶	𝐶	PROPN
iajs-2485	126	21	𝑡	𝑡	NOUN
iajs-2485	126	22	𝜙	𝜙	NOUN
iajs-2485	126	23	𝑥	𝑥	X
iajs-2485	126	24	we	we	PRON
iajs-2485	126	25	have	have	VERB
iajs-2485	126	26	the	the	DET
iajs-2485	126	27	following	follow	VERB
iajs-2485	126	28	fdes	fde	NOUN
iajs-2485	126	29	𝐶	𝐶	PROPN
iajs-2485	126	30	𝑡	𝑡	PROPN
iajs-2485	126	31	0	0	PROPN
iajs-2485	126	32	𝑑	𝑑	VERB
iajs-2485	126	33	𝑑𝑡	𝑑𝑡	ADP
iajs-2485	126	34	𝐶	𝐶	PROPN
iajs-2485	126	35	𝑡	𝑡	PROPN
iajs-2485	126	36	𝐶	𝐶	PROPN
iajs-2485	126	37	𝑡	𝑡	PROPN
iajs-2485	126	38	0	0	NUM
iajs-2485	126	39	⟹	⟹	NUM
iajs-2485	126	40	𝐶	𝐶	PROPN
iajs-2485	126	41	𝑡	𝑡	PROPN
iajs-2485	126	42	𝐴𝐸	𝐴𝐸	PROPN
iajs-2485	126	43	𝑡	𝑡	PROPN
iajs-2485	126	44	𝑑	𝑑	PROPN
iajs-2485	126	45	𝑑𝑡	𝑑𝑡	ADP
iajs-2485	126	46	𝐶	𝐶	PROPN
iajs-2485	126	47	𝑡	𝑡	PROPN
iajs-2485	126	48	𝐶	𝐶	PROPN
iajs-2485	126	49	𝑡	𝑡	PROPN
iajs-2485	126	50	0	0	NUM
iajs-2485	126	51	⟹	⟹	NUM
iajs-2485	126	52	𝐶	𝐶	PROPN
iajs-2485	126	53	𝑡	𝑡	X
iajs-2485	126	54	𝐵𝐸	𝐵𝐸	PROPN
iajs-2485	126	55	𝑡	𝑡	NOUN
iajs-2485	126	56	so	so	ADV
iajs-2485	126	57	,	,	PUNCT
iajs-2485	126	58	the	the	DET
iajs-2485	126	59	solution	solution	NOUN
iajs-2485	126	60	of	of	ADP
iajs-2485	126	61	eq.(12	eq.(12	NOUN
iajs-2485	126	62	)	)	PUNCT
iajs-2485	126	63	is	be	AUX
iajs-2485	126	64	:	:	PUNCT
iajs-2485	126	65	𝒇	𝒇	NUM
iajs-2485	126	66	𝒙	𝒙	PROPN
iajs-2485	126	67	,	,	PUNCT
iajs-2485	126	68	𝒕	𝒕	X
iajs-2485	126	69	𝐶	𝐶	PROPN
iajs-2485	126	70	𝑡	𝑡	PROPN
iajs-2485	126	71	𝐶	𝐶	PROPN
iajs-2485	126	72	𝑡	𝑡	PROPN
iajs-2485	126	73	𝐸	𝐸	PROPN
iajs-2485	126	74	𝑥	𝑥	PROPN
iajs-2485	126	75	𝐶	𝐶	PROPN
iajs-2485	126	76	𝑡	𝑡	PROPN
iajs-2485	126	77	𝐸	𝐸	VERB
iajs-2485	126	78	𝑥	𝑥	PRON
iajs-2485	126	79	𝐴𝐸	𝐴𝐸	PROPN
iajs-2485	126	80	𝑡	𝑡	PROPN
iajs-2485	126	81	𝐸	𝐸	NOUN
iajs-2485	126	82	𝑥	𝑥	DET
iajs-2485	126	83	𝐵𝐸	𝐵𝐸	PROPN
iajs-2485	126	84	𝑡	𝑡	PROPN
iajs-2485	126	85	𝐸	𝐸	NOUN
iajs-2485	126	86	𝑥	𝑥	NOUN
iajs-2485	126	87	from	from	ADP
iajs-2485	126	88	our	our	PRON
iajs-2485	126	89	conditions	condition	NOUN
iajs-2485	126	90	,	,	PUNCT
iajs-2485	126	91	we	we	PRON
iajs-2485	126	92	have	have	VERB
iajs-2485	126	93	𝑓	𝑓	PRON
iajs-2485	126	94	𝑥	𝑥	NOUN
iajs-2485	126	95	,	,	PUNCT
iajs-2485	126	96	0	0	NUM
iajs-2485	126	97	𝐸	𝐸	NOUN
iajs-2485	127	1	𝑥	𝑥	PRON
iajs-2485	127	2	1	1	NUM
iajs-2485	127	3	2	2	NUM
iajs-2485	127	4	𝐸	𝐸	PROPN
iajs-2485	127	5	𝑥	𝑥	PRON
iajs-2485	127	6	𝐸	𝐸	NOUN
iajs-2485	127	7	𝑥	𝑥	X
iajs-2485	127	8	𝐴𝐸	𝐴𝐸	VERB
iajs-2485	127	9	𝑥	𝑥	PROPN
iajs-2485	127	10	𝐵𝐸	𝐵𝐸	PROPN
iajs-2485	127	11	𝑥	𝑥	PROPN
iajs-2485	127	12	thus	thus	ADV
iajs-2485	127	13	,	,	PUNCT
iajs-2485	127	14	𝐴	𝐴	PROPN
iajs-2485	127	15	𝐵	𝐵	PROPN
iajs-2485	127	16	and	and	CCONJ
iajs-2485	127	17	𝑓	𝑓	DET
iajs-2485	127	18	𝑥	𝑥	PROPN
iajs-2485	127	19	,	,	PUNCT
iajs-2485	127	20	𝑡	𝑡	PROPN
iajs-2485	127	21	𝐸	𝐸	ADJ
iajs-2485	127	22	𝑡	𝑡	PROPN
iajs-2485	127	23	𝐸	𝐸	NOUN
iajs-2485	127	24	𝑥	𝑥	PRON
iajs-2485	127	25	𝐸	𝐸	NOUN
iajs-2485	127	26	𝑡	𝑡	PROPN
iajs-2485	127	27	𝐸	𝐸	NOUN
iajs-2485	127	28	𝑥	𝑥	NOUN
iajs-2485	127	29	for	for	ADP
iajs-2485	127	30	𝛼	𝛼	NOUN
iajs-2485	127	31	𝛽	𝛽	NOUN
iajs-2485	127	32	1	1	NUM
iajs-2485	127	33	𝑓	𝑓	PRON
iajs-2485	127	34	𝑥	𝑥	PROPN
iajs-2485	127	35	,	,	PUNCT
iajs-2485	127	36	𝑡	𝑡	PROPN
iajs-2485	127	37	1	1	NUM
iajs-2485	127	38	2	2	NUM
iajs-2485	127	39	𝑒	𝑒	PROPN
iajs-2485	127	40	𝑒	𝑒	PROPN
iajs-2485	127	41	cosh	cosh	NOUN
iajs-2485	127	42	𝑥	𝑥	PROPN
iajs-2485	127	43	𝑡	𝑡	NOUN
iajs-2485	127	44	which	which	PRON
iajs-2485	127	45	agree	agree	VERB
iajs-2485	127	46	with	with	ADP
iajs-2485	127	47	that	that	PRON
iajs-2485	127	48	in	in	ADP
iajs-2485	127	49	double	double	ADJ
iajs-2485	127	50	sumudu	sumudu	NOUN
iajs-2485	127	51	transform	transform	NOUN
iajs-2485	127	52	method	method	NOUN
iajs-2485	127	53	.	.	PUNCT
iajs-2485	128	1	exact	exact	ADJ
iajs-2485	128	2	solution	solution	NOUN
iajs-2485	128	3	and	and	CCONJ
iajs-2485	128	4	10	10	NUM
iajs-2485	128	5	-	-	PUNCT
iajs-2485	128	6	order	order	NOUN
iajs-2485	128	7	approximate	approximate	ADJ
iajs-2485	128	8	solutions	solution	NOUN
iajs-2485	128	9	of	of	ADP
iajs-2485	128	10	equation	equation	NOUN
iajs-2485	128	11	14	14	NUM
iajs-2485	128	12	,	,	PUNCT
iajs-2485	128	13	are	be	AUX
iajs-2485	128	14	shown	show	VERB
iajs-2485	128	15	in	in	ADP
iajs-2485	128	16	figure	figure	NOUN
iajs-2485	128	17	3	3	NUM
iajs-2485	128	18	.	.	PUNCT
iajs-2485	129	1	for	for	ADP
iajs-2485	129	2	various	various	ADJ
iajs-2485	129	3	values	value	NOUN
iajs-2485	129	4	of	of	ADP
iajs-2485	129	5	𝛼	𝛼	NOUN
iajs-2485	129	6	,	,	PUNCT
iajs-2485	129	7	𝛽.	𝛽.	NOUN
iajs-2485	129	8	  	  	SPACE
iajs-2485	129	9	137	137	NUM
iajs-2485	129	10	  	  	SPACE
iajs-2485	129	11	ibn	ibn	PROPN
iajs-2485	129	12	al	al	PROPN
iajs-2485	129	13	-	-	PUNCT
iajs-2485	129	14	haitham	haitham	PROPN
iajs-2485	129	15	jour	jour	X
iajs-2485	129	16	.	.	PROPN
iajs-2485	130	1	for	for	ADP
iajs-2485	130	2	pure	pure	ADJ
iajs-2485	130	3	&	&	CCONJ
iajs-2485	130	4	appl	appl	PROPN
iajs-2485	130	5	.	.	PUNCT
iajs-2485	131	1	sci	sci	PROPN
iajs-2485	131	2	.	.	PROPN
iajs-2485	132	1	33	33	NUM
iajs-2485	132	2	(	(	PUNCT
iajs-2485	132	3	3	3	NUM
iajs-2485	132	4	)	)	PUNCT
iajs-2485	132	5	2020	2020	NUM
iajs-2485	132	6	figure	figure	VERB
iajs-2485	132	7	3	3	NUM
iajs-2485	132	8	.	.	NOUN
iajs-2485	132	9	exact	exact	ADJ
iajs-2485	132	10	solution	solution	NOUN
iajs-2485	132	11	and	and	CCONJ
iajs-2485	132	12	10	10	NUM
iajs-2485	132	13	-	-	PUNCT
iajs-2485	132	14	order	order	NOUN
iajs-2485	132	15	approximate	approximate	ADJ
iajs-2485	132	16	solutions	solution	NOUN
iajs-2485	132	17	of	of	ADP
iajs-2485	132	18	equation	equation	NOUN
iajs-2485	132	19	14	14	NUM
iajs-2485	132	20	,	,	PUNCT
iajs-2485	132	21	for	for	ADP
iajs-2485	132	22	various	various	ADJ
iajs-2485	132	23	values	value	NOUN
iajs-2485	132	24	of	of	ADP
iajs-2485	132	25	𝛼	𝛼	NOUN
iajs-2485	132	26	,	,	PUNCT
iajs-2485	132	27	𝛽.	𝛽.	ADJ
iajs-2485	132	28	example	example	NOUN
iajs-2485	132	29	4	4	NUM
iajs-2485	132	30	:	:	PUNCT
iajs-2485	132	31	consider	consider	VERB
iajs-2485	132	32	the	the	DET
iajs-2485	132	33	following	follow	VERB
iajs-2485	132	34	fractional	fractional	ADJ
iajs-2485	132	35	mixed	mixed	ADJ
iajs-2485	132	36	derivatives	derivative	NOUN
iajs-2485	132	37	diffusion	diffusion	NOUN
iajs-2485	132	38	equation	equation	NOUN
iajs-2485	132	39	𝐷	𝐷	PROPN
iajs-2485	132	40	𝑓	𝑓	PRON
iajs-2485	132	41	𝐷	𝐷	PROPN
iajs-2485	132	42	𝑓	𝑓	PRON
iajs-2485	132	43	𝐷	𝐷	PROPN
iajs-2485	132	44	𝐷	𝐷	PROPN
iajs-2485	132	45	𝑓	𝑓	ADV
iajs-2485	132	46	0	0	NUM
iajs-2485	132	47	𝛼	𝛼	SYM
iajs-2485	132	48	1	1	NUM
iajs-2485	132	49	,	,	PUNCT
iajs-2485	132	50	1	1	NUM
iajs-2485	132	51	𝛽	𝛽	NOUN
iajs-2485	132	52	2	2	NUM
iajs-2485	132	53	14	14	NUM
iajs-2485	132	54	with	with	ADP
iajs-2485	132	55	conditions	condition	NOUN
iajs-2485	132	56	𝑓	𝑓	ADP
iajs-2485	132	57	0	0	NUM
iajs-2485	132	58	,	,	PUNCT
iajs-2485	132	59	𝑡	𝑡	PROPN
iajs-2485	132	60	1	1	NUM
iajs-2485	132	61	γ	γ	SYM
iajs-2485	132	62	1	1	NUM
iajs-2485	132	63	𝛽	𝛽	NOUN
iajs-2485	132	64	γ	γ	NOUN
iajs-2485	132	65	1	1	NUM
iajs-2485	132	66	𝛼	𝛼	NOUN
iajs-2485	132	67	𝑡	𝑡	PROPN
iajs-2485	132	68	,	,	PUNCT
iajs-2485	132	69	𝑓	𝑓	PROPN
iajs-2485	132	70	0	0	NUM
iajs-2485	132	71	,	,	PUNCT
iajs-2485	132	72	𝑡	𝑡	PROPN
iajs-2485	132	73	0	0	NUM
iajs-2485	132	74	,	,	PUNCT
iajs-2485	132	75	𝑓	𝑓	PRON
iajs-2485	132	76	𝑥	𝑥	NOUN
iajs-2485	132	77	,	,	PUNCT
iajs-2485	132	78	0	0	NUM
iajs-2485	132	79	1	1	NUM
iajs-2485	132	80	𝑥	𝑥	NOUN
iajs-2485	132	81	solution	solution	NOUN
iajs-2485	132	82	by	by	ADP
iajs-2485	132	83	double	double	ADJ
iajs-2485	132	84	sumudu	sumudu	NOUN
iajs-2485	132	85	transform	transform	NOUN
iajs-2485	132	86	method	method	NOUN
iajs-2485	132	87	:	:	PUNCT
iajs-2485	132	88	operating	operate	VERB
iajs-2485	132	89	single	single	ADJ
iajs-2485	132	90	sumudu	sumudu	NOUN
iajs-2485	132	91	transform	transform	NOUN
iajs-2485	132	92	of	of	ADP
iajs-2485	132	93	conditions	condition	NOUN
iajs-2485	132	94	,	,	PUNCT
iajs-2485	132	95	we	we	PRON
iajs-2485	132	96	get	get	VERB
iajs-2485	132	97	𝑻𝟎	𝑻𝟎	PROPN
iajs-2485	132	98	𝟎	𝟎	PROPN
iajs-2485	132	99	,	,	PUNCT
iajs-2485	132	100	𝒗	𝒗	PROPN
iajs-2485	132	101	𝟏	𝟏	NUM
iajs-2485	132	102	γ	γ	PROPN
iajs-2485	132	103	1	1	NUM
iajs-2485	132	104	𝛽	𝛽	NOUN
iajs-2485	132	105	𝑣	𝑣	PROPN
iajs-2485	132	106	,	,	PUNCT
iajs-2485	132	107	𝑻𝟏	𝑻𝟏	NOUN
iajs-2485	132	108	𝟎	𝟎	PROPN
iajs-2485	132	109	,	,	PUNCT
iajs-2485	132	110	𝒗	𝒗	PROPN
iajs-2485	132	111	𝟎	𝟎	PROPN
iajs-2485	132	112	,	,	PUNCT
iajs-2485	132	113	𝑻𝟎	𝑻𝟎	NOUN
iajs-2485	132	114	𝒖	𝒖	NOUN
iajs-2485	132	115	,	,	PUNCT
iajs-2485	132	116	𝟎	𝟎	NUM
iajs-2485	132	117	𝟏	𝟏	NUM
iajs-2485	132	118	γ	γ	PROPN
iajs-2485	132	119	1	1	NUM
iajs-2485	132	120	𝛽	𝛽	NOUN
iajs-2485	132	121	𝒖𝜷	𝒖𝜷	NOUN
iajs-2485	132	122	using	use	VERB
iajs-2485	132	123	theorem	theorem	NOUN
iajs-2485	132	124	(	(	PUNCT
iajs-2485	132	125	2	2	NUM
iajs-2485	132	126	)	)	PUNCT
iajs-2485	132	127	,	,	PUNCT
iajs-2485	132	128	we	we	PRON
iajs-2485	132	129	get	get	VERB
iajs-2485	132	130	𝑣	𝑣	DET
iajs-2485	132	131	𝑇	𝑇	PROPN
iajs-2485	132	132	𝑢	𝑢	NOUN
iajs-2485	132	133	,	,	PUNCT
iajs-2485	132	134	𝑣	𝑣	PROPN
iajs-2485	132	135	𝑇	𝑇	PROPN
iajs-2485	132	136	𝑢	𝑢	NOUN
iajs-2485	132	137	,	,	PUNCT
iajs-2485	132	138	0	0	NUM
iajs-2485	132	139	𝑢	𝑢	PROPN
iajs-2485	132	140	𝑇	𝑇	PROPN
iajs-2485	132	141	𝑢	𝑢	PROPN
iajs-2485	132	142	,	,	PUNCT
iajs-2485	132	143	𝑣	𝑣	PROPN
iajs-2485	132	144	𝑇	𝑇	PROPN
iajs-2485	132	145	0	0	NUM
iajs-2485	132	146	,	,	PUNCT
iajs-2485	132	147	𝑣	𝑣	ADP
iajs-2485	132	148	𝑢𝑇	𝑢𝑇	NOUN
iajs-2485	132	149	0	0	NUM
iajs-2485	132	150	,	,	PUNCT
iajs-2485	132	151	𝑣	𝑣	ADP
iajs-2485	132	152	𝑣	𝑣	X
iajs-2485	132	153	𝑢	𝑢	ADP
iajs-2485	132	154	𝑇	𝑇	PROPN
iajs-2485	132	155	𝑢	𝑢	NOUN
iajs-2485	132	156	,	,	PUNCT
iajs-2485	132	157	𝑣	𝑣	PROPN
iajs-2485	132	158	𝑇	𝑇	PROPN
iajs-2485	132	159	0	0	NUM
iajs-2485	132	160	,	,	PUNCT
iajs-2485	132	161	𝑣	𝑣	ADP
iajs-2485	132	162	𝑢𝑇	𝑢𝑇	NOUN
iajs-2485	132	163	0	0	NUM
iajs-2485	132	164	,	,	PUNCT
iajs-2485	133	1	𝑣	𝑣	ADP
iajs-2485	133	2	𝑇	𝑇	PROPN
iajs-2485	133	3	𝑢	𝑢	NOUN
iajs-2485	133	4	,	,	PUNCT
iajs-2485	133	5	0	0	NUM
iajs-2485	133	6	1	1	NUM
iajs-2485	133	7	1	1	NUM
iajs-2485	133	8	𝑣	𝑣	PRON
iajs-2485	133	9	𝑢	𝑢	ADP
iajs-2485	133	10	𝑇	𝑇	PROPN
iajs-2485	133	11	𝑢	𝑢	NOUN
iajs-2485	133	12	,	,	PUNCT
iajs-2485	133	13	𝑣	𝑣	PRON
iajs-2485	133	14	𝑣	𝑣	ADP
iajs-2485	133	15	1	1	NUM
iajs-2485	133	16	𝑣	𝑣	ADP
iajs-2485	133	17	γ	γ	PROPN
iajs-2485	133	18	1	1	NUM
iajs-2485	133	19	𝛽	𝛽	PROPN
iajs-2485	133	20	𝑣	𝑣	PROPN
iajs-2485	133	21	𝑢	𝑢	PROPN
iajs-2485	133	22	γ	γ	X
iajs-2485	133	23	1	1	NUM
iajs-2485	133	24	𝛽	𝛽	NOUN
iajs-2485	133	25	1	1	NUM
iajs-2485	133	26	𝑢	𝑢	PROPN
iajs-2485	133	27	1	1	NUM
iajs-2485	133	28	𝑢	𝑢	PROPN
iajs-2485	133	29	γ	γ	PROPN
iajs-2485	133	30	1	1	NUM
iajs-2485	133	31	𝛽	𝛽	NOUN
iajs-2485	133	32	1	1	NUM
iajs-2485	133	33	𝑣	𝑣	PRON
iajs-2485	133	34	𝑢	𝑢	PROPN
iajs-2485	133	35	1	1	NUM
iajs-2485	133	36	𝑣	𝑣	PRON
iajs-2485	133	37	𝑢	𝑢	X
iajs-2485	133	38	γ	γ	PROPN
iajs-2485	133	39	1	1	NUM
iajs-2485	133	40	𝛽	𝛽	PROPN
iajs-2485	133	41	𝑇	𝑇	PROPN
iajs-2485	133	42	𝑢	𝑢	NOUN
iajs-2485	133	43	,	,	PUNCT
iajs-2485	133	44	𝑣	𝑣	ADP
iajs-2485	133	45	1	1	NUM
iajs-2485	133	46	𝑣	𝑣	ADP
iajs-2485	133	47	𝑢	𝑢	X
iajs-2485	133	48	γ	γ	PROPN
iajs-2485	133	49	1	1	NUM
iajs-2485	133	50	𝛽	𝛽	NOUN
iajs-2485	133	51	taking	take	VERB
iajs-2485	133	52	inverse	inverse	NOUN
iajs-2485	133	53	double	double	ADJ
iajs-2485	133	54	sumudu	sumudu	NOUN
iajs-2485	133	55	transform	transform	NOUN
iajs-2485	133	56	of	of	ADP
iajs-2485	133	57	the	the	DET
iajs-2485	133	58	last	last	ADJ
iajs-2485	133	59	equation	equation	NOUN
iajs-2485	133	60	,	,	PUNCT
iajs-2485	133	61	we	we	PRON
iajs-2485	133	62	can	can	AUX
iajs-2485	133	63	obtain	obtain	VERB
iajs-2485	133	64	the	the	DET
iajs-2485	133	65	exact	exact	ADJ
iajs-2485	133	66	solution	solution	NOUN
iajs-2485	133	67	of	of	ADP
iajs-2485	133	68	(	(	PUNCT
iajs-2485	133	69	14	14	NUM
iajs-2485	133	70	)	)	PUNCT
iajs-2485	133	71	as	as	ADP
iajs-2485	133	72	𝒇	𝒇	X
iajs-2485	133	73	𝒙	𝒙	NOUN
iajs-2485	133	74	,	,	PUNCT
iajs-2485	133	75	𝒕	𝒕	PROPN
iajs-2485	133	76	1	1	NUM
iajs-2485	133	77	𝑥	𝑥	NOUN
iajs-2485	133	78	γ	γ	PROPN
iajs-2485	133	79	1	1	NUM
iajs-2485	133	80	𝛽	𝛽	NOUN
iajs-2485	133	81	γ	γ	NOUN
iajs-2485	133	82	1	1	NUM
iajs-2485	133	83	𝛼	𝛼	NOUN
iajs-2485	133	84	𝑡	𝑡	NOUN
iajs-2485	133	85	which	which	PRON
iajs-2485	133	86	agree	agree	VERB
iajs-2485	133	87	with	with	ADP
iajs-2485	133	88	that	that	PRON
iajs-2485	133	89	for	for	ADP
iajs-2485	133	90	[	[	X
iajs-2485	133	91	9	9	NUM
iajs-2485	133	92	]	]	SYM
iajs-2485	133	93	.	.	PUNCT
iajs-2485	134	1	3	3	X
iajs-2485	134	2	-	-	SYM
iajs-2485	134	3	d	d	ADJ
iajs-2485	134	4	plotting	plotting	NOUN
iajs-2485	134	5	of	of	ADP
iajs-2485	134	6	the	the	DET
iajs-2485	134	7	exact	exact	ADJ
iajs-2485	134	8	solution	solution	NOUN
iajs-2485	134	9	and	and	CCONJ
iajs-2485	134	10	10	10	NUM
iajs-2485	134	11	-	-	PUNCT
iajs-2485	134	12	order	order	NOUN
iajs-2485	134	13	approximate	approximate	ADJ
iajs-2485	134	14	solutions	solution	NOUN
iajs-2485	134	15	for	for	ADP
iajs-2485	134	16	equation	equation	NOUN
iajs-2485	134	17	(	(	PUNCT
iajs-2485	134	18	14	14	NUM
iajs-2485	134	19	)	)	PUNCT
iajs-2485	134	20	for	for	ADP
iajs-2485	134	21	various	various	ADJ
iajs-2485	134	22	values	value	NOUN
iajs-2485	134	23	of	of	ADP
iajs-2485	134	24	𝛼	𝛼	PROPN
iajs-2485	134	25	,	,	PUNCT
iajs-2485	134	26	𝛽	𝛽	NOUN
iajs-2485	134	27	,	,	PUNCT
iajs-2485	134	28	are	be	AUX
iajs-2485	134	29	contained	contain	VERB
iajs-2485	134	30	in	in	ADP
iajs-2485	134	31	figure	figure	NOUN
iajs-2485	134	32	4	4	NUM
iajs-2485	134	33	.	.	SYM
iajs-2485	134	34	2	2	NUM
iajs-2485	134	35	exact	exact	NOUN
iajs-2485	134	36	=	=	SYM
iajs-2485	134	37	=	=	SYM
iajs-2485	134	38	1	1	NUM
iajs-2485	134	39	1	1	NUM
iajs-2485	134	40	t	t	NOUN
iajs-2485	134	41	00	00	NUM
iajs-2485	134	42	1	1	NUM
iajs-2485	134	43	x	x	SYM
iajs-2485	134	44	1	1	NUM
iajs-2485	134	45	2	2	NUM
iajs-2485	134	46	3	3	NUM
iajs-2485	134	47	2	2	NUM
iajs-2485	134	48	2	2	NUM
iajs-2485	134	49	=	=	SYM
iajs-2485	134	50	.9	.9	NUM
iajs-2485	134	51	and	and	CCONJ
iajs-2485	135	1	=	=	NOUN
iajs-2485	135	2	.95	.95	NUM
iajs-2485	135	3	1	1	NUM
iajs-2485	135	4	t	t	NOUN
iajs-2485	135	5	00	00	NUM
iajs-2485	135	6	1	1	NUM
iajs-2485	135	7	x	x	SYM
iajs-2485	135	8	4	4	NUM
iajs-2485	135	9	2	2	NUM
iajs-2485	135	10	2	2	NUM
iajs-2485	135	11	2	2	NUM
iajs-2485	135	12	=	=	SYM
iajs-2485	135	13	0.1	0.1	NUM
iajs-2485	135	14	and	and	CCONJ
iajs-2485	135	15	=	=	NOUN
iajs-2485	135	16	0.3	0.3	NUM
iajs-2485	135	17	1	1	NUM
iajs-2485	135	18	t	t	NOUN
iajs-2485	135	19	00	00	NUM
iajs-2485	135	20	1	1	NUM
iajs-2485	135	21	x	x	SYM
iajs-2485	135	22	5	5	NUM
iajs-2485	135	23	10	10	NUM
iajs-2485	135	24	15	15	NUM
iajs-2485	135	25	2	2	NUM
iajs-2485	135	26	2	2	NUM
iajs-2485	135	27	1	1	NUM
iajs-2485	135	28	t	t	NOUN
iajs-2485	135	29	=	=	PUNCT
iajs-2485	136	1	=	=	NUM
iajs-2485	136	2	1	1	NUM
iajs-2485	136	3	00	00	NUM
iajs-2485	136	4	1	1	NUM
iajs-2485	136	5	x	x	SYM
iajs-2485	136	6	1	1	NUM
iajs-2485	136	7	2	2	NUM
iajs-2485	136	8	3	3	NUM
iajs-2485	136	9	2	2	NUM
iajs-2485	136	10	2	2	NUM
iajs-2485	136	11	=	=	SYM
iajs-2485	136	12	0.3	0.3	NUM
iajs-2485	136	13	and	and	CCONJ
iajs-2485	136	14	=	=	NOUN
iajs-2485	136	15	0.4	0.4	NUM
iajs-2485	136	16	1	1	NUM
iajs-2485	136	17	t	t	NOUN
iajs-2485	136	18	00	00	NUM
iajs-2485	136	19	1	1	NUM
iajs-2485	136	20	x	x	SYM
iajs-2485	136	21	6	6	NUM
iajs-2485	136	22	10	10	NUM
iajs-2485	136	23	2	2	NUM
iajs-2485	136	24	2	2	NUM
iajs-2485	136	25	2	2	NUM
iajs-2485	136	26	=	=	SYM
iajs-2485	136	27	0.2	0.2	NUM
iajs-2485	136	28	and	and	CCONJ
iajs-2485	136	29	=	=	SYM
iajs-2485	136	30	0.5	0.5	NUM
iajs-2485	136	31	1	1	NUM
iajs-2485	136	32	t	t	NOUN
iajs-2485	136	33	00	00	NUM
iajs-2485	136	34	1	1	NUM
iajs-2485	136	35	x	x	SYM
iajs-2485	136	36	5	5	NUM
iajs-2485	136	37	10	10	NUM
iajs-2485	136	38	15	15	NUM
iajs-2485	136	39	2	2	NUM
iajs-2485	136	40	  	  	SPACE
iajs-2485	136	41	138	138	NUM
iajs-2485	136	42	  	  	SPACE
iajs-2485	136	43	ibn	ibn	PROPN
iajs-2485	136	44	al	al	PROPN
iajs-2485	136	45	-	-	PUNCT
iajs-2485	136	46	haitham	haitham	PROPN
iajs-2485	136	47	jour	jour	X
iajs-2485	136	48	.	.	PROPN
iajs-2485	136	49	for	for	ADP
iajs-2485	136	50	pure	pure	ADJ
iajs-2485	136	51	&	&	CCONJ
iajs-2485	136	52	appl	appl	PROPN
iajs-2485	136	53	.	.	PUNCT
iajs-2485	137	1	sci	sci	PROPN
iajs-2485	137	2	.	.	PROPN
iajs-2485	138	1	33	33	NUM
iajs-2485	138	2	(	(	PUNCT
iajs-2485	138	3	3	3	NUM
iajs-2485	138	4	)	)	PUNCT
iajs-2485	138	5	2020	2020	NUM
iajs-2485	138	6	figure	figure	VERB
iajs-2485	138	7	4	4	NUM
iajs-2485	138	8	.	.	NOUN
iajs-2485	138	9	exact	exact	ADJ
iajs-2485	138	10	solution	solution	NOUN
iajs-2485	138	11	and	and	CCONJ
iajs-2485	138	12	some	some	PRON
iajs-2485	138	13	of	of	ADP
iajs-2485	138	14	approximate	approximate	ADJ
iajs-2485	138	15	solution	solution	NOUN
iajs-2485	138	16	of	of	ADP
iajs-2485	138	17	equation	equation	NOUN
iajs-2485	138	18	16	16	NUM
iajs-2485	138	19	,	,	PUNCT
iajs-2485	138	20	for	for	ADP
iajs-2485	138	21	various	various	ADJ
iajs-2485	138	22	values	value	NOUN
iajs-2485	138	23	of	of	ADP
iajs-2485	138	24	𝛼	𝛼	NOUN
iajs-2485	138	25	,	,	PUNCT
iajs-2485	138	26	𝛽.	𝛽.	NOUN
iajs-2485	138	27	7	7	NUM
iajs-2485	138	28	.	.	PUNCT
iajs-2485	138	29	conclusion	conclusion	NOUN
iajs-2485	138	30	in	in	ADP
iajs-2485	138	31	this	this	DET
iajs-2485	138	32	paper	paper	NOUN
iajs-2485	138	33	,	,	PUNCT
iajs-2485	138	34	the	the	DET
iajs-2485	138	35	comparison	comparison	NOUN
iajs-2485	138	36	between	between	ADP
iajs-2485	138	37	the	the	DET
iajs-2485	138	38	analytical	analytical	ADJ
iajs-2485	138	39	subspace	subspace	NOUN
iajs-2485	138	40	method	method	NOUN
iajs-2485	138	41	and	and	CCONJ
iajs-2485	138	42	double	double	ADJ
iajs-2485	138	43	sumudu	sumudu	NOUN
iajs-2485	138	44	transform	transform	NOUN
iajs-2485	138	45	method	method	NOUN
iajs-2485	138	46	has	have	AUX
iajs-2485	138	47	been	be	AUX
iajs-2485	138	48	achieved	achieve	VERB
iajs-2485	138	49	.	.	PUNCT
iajs-2485	139	1	from	from	ADP
iajs-2485	139	2	this	this	DET
iajs-2485	139	3	study	study	NOUN
iajs-2485	139	4	,	,	PUNCT
iajs-2485	139	5	we	we	PRON
iajs-2485	139	6	insure	insure	VERB
iajs-2485	139	7	that	that	SCONJ
iajs-2485	139	8	the	the	DET
iajs-2485	139	9	double	double	ADJ
iajs-2485	139	10	sumudu	sumudu	NOUN
iajs-2485	139	11	transform	transform	NOUN
iajs-2485	139	12	method	method	NOUN
iajs-2485	139	13	is	be	AUX
iajs-2485	139	14	an	an	DET
iajs-2485	139	15	efficient	efficient	ADJ
iajs-2485	139	16	tool	tool	NOUN
iajs-2485	139	17	to	to	PART
iajs-2485	139	18	obtain	obtain	VERB
iajs-2485	139	19	an	an	DET
iajs-2485	139	20	exact	exact	ADJ
iajs-2485	139	21	solutions	solution	NOUN
iajs-2485	139	22	of	of	ADP
iajs-2485	139	23	many	many	ADJ
iajs-2485	139	24	types	type	NOUN
iajs-2485	139	25	of	of	ADP
iajs-2485	139	26	linear	linear	ADJ
iajs-2485	139	27	fractional	fractional	ADJ
iajs-2485	139	28	partial	partial	ADJ
iajs-2485	139	29	differential	differential	NOUN
iajs-2485	139	30	equations	equation	NOUN
iajs-2485	139	31	that	that	PRON
iajs-2485	139	32	have	have	AUX
iajs-2485	139	33	complicated	complicate	VERB
iajs-2485	139	34	using	use	VERB
iajs-2485	139	35	other	other	ADJ
iajs-2485	139	36	numerical	numerical	ADJ
iajs-2485	139	37	methods	method	NOUN
iajs-2485	139	38	,	,	PUNCT
iajs-2485	139	39	however	however	ADV
iajs-2485	139	40	,	,	PUNCT
iajs-2485	139	41	more	more	ADJ
iajs-2485	139	42	of	of	ADP
iajs-2485	139	43	homogeneous	homogeneous	ADJ
iajs-2485	139	44	type	type	NOUN
iajs-2485	139	45	of	of	ADP
iajs-2485	139	46	constant	constant	ADJ
iajs-2485	139	47	coefficients	coefficient	NOUN
iajs-2485	139	48	fractional	fractional	ADJ
iajs-2485	139	49	partial	partial	ADJ
iajs-2485	139	50	differential	differential	NOUN
iajs-2485	139	51	equations	equation	NOUN
iajs-2485	139	52	can	can	AUX
iajs-2485	139	53	be	be	AUX
iajs-2485	139	54	solved	solve	VERB
iajs-2485	139	55	analytically	analytically	ADV
iajs-2485	139	56	with	with	ADP
iajs-2485	139	57	the	the	DET
iajs-2485	139	58	invariant	invariant	ADJ
iajs-2485	139	59	subspace	subspace	NOUN
iajs-2485	139	60	method	method	NOUN
iajs-2485	139	61	than	than	ADP
iajs-2485	139	62	the	the	DET
iajs-2485	139	63	sumudu	sumudu	NOUN
iajs-2485	139	64	transform	transform	NOUN
iajs-2485	139	65	.	.	PUNCT
iajs-2485	140	1	in	in	ADP
iajs-2485	140	2	both	both	DET
iajs-2485	140	3	methods	method	NOUN
iajs-2485	140	4	,	,	PUNCT
iajs-2485	140	5	our	our	PRON
iajs-2485	140	6	example	example	NOUN
iajs-2485	140	7	illustrated	illustrate	VERB
iajs-2485	140	8	that	that	SCONJ
iajs-2485	140	9	the	the	DET
iajs-2485	140	10	solutions	solution	NOUN
iajs-2485	140	11	which	which	PRON
iajs-2485	140	12	have	have	AUX
iajs-2485	140	13	been	be	AUX
iajs-2485	140	14	achieved	achieve	VERB
iajs-2485	140	15	in	in	ADP
iajs-2485	140	16	terms	term	NOUN
iajs-2485	140	17	of	of	ADP
iajs-2485	140	18	the	the	DET
iajs-2485	140	19	infinite	infinite	ADJ
iajs-2485	140	20	series	series	NOUN
iajs-2485	140	21	mittag	mittag	ADJ
iajs-2485	140	22	-	-	PUNCT
iajs-2485	140	23	leffler	leffler	NOUN
iajs-2485	140	24	function	function	NOUN
iajs-2485	140	25	and	and	CCONJ
iajs-2485	140	26	we	we	PRON
iajs-2485	140	27	have	have	AUX
iajs-2485	140	28	done	do	VERB
iajs-2485	140	29	this	this	PRON
iajs-2485	140	30	by	by	ADP
iajs-2485	140	31	truncated	truncated	ADJ
iajs-2485	140	32	10order	10order	NUM
iajs-2485	140	33	approximate	approximate	NOUN
iajs-2485	140	34	of	of	ADP
iajs-2485	140	35	this	this	DET
iajs-2485	140	36	function	function	NOUN
iajs-2485	140	37	.	.	PUNCT
iajs-2485	141	1	this	this	PRON
iajs-2485	141	2	is	be	AUX
iajs-2485	141	3	the	the	DET
iajs-2485	141	4	reason	reason	NOUN
iajs-2485	141	5	for	for	ADP
iajs-2485	141	6	explaining	explain	VERB
iajs-2485	141	7	the	the	DET
iajs-2485	141	8	variance	variance	NOUN
iajs-2485	141	9	of	of	ADP
iajs-2485	141	10	the	the	DET
iajs-2485	141	11	absolute	absolute	ADJ
iajs-2485	141	12	error	error	NOUN
iajs-2485	141	13	for	for	ADP
iajs-2485	141	14	numerical	numerical	ADJ
iajs-2485	141	15	solutions	solution	NOUN
iajs-2485	141	16	.	.	PUNCT
iajs-2485	142	1	of	of	ADP
iajs-2485	142	2	course	course	ADV
iajs-2485	142	3	,	,	PUNCT
iajs-2485	142	4	for	for	ADP
iajs-2485	142	5	nonlinear	nonlinear	ADJ
iajs-2485	142	6	case	case	NOUN
iajs-2485	142	7	,	,	PUNCT
iajs-2485	142	8	we	we	PRON
iajs-2485	142	9	must	must	AUX
iajs-2485	142	10	couple	couple	VERB
iajs-2485	142	11	the	the	DET
iajs-2485	142	12	sumudu	sumudu	NOUN
iajs-2485	142	13	transform	transform	VERB
iajs-2485	142	14	with	with	ADP
iajs-2485	142	15	any	any	DET
iajs-2485	142	16	known	know	VERB
iajs-2485	142	17	numerical	numerical	ADJ
iajs-2485	142	18	method	method	NOUN
iajs-2485	142	19	,	,	PUNCT
iajs-2485	142	20	which	which	PRON
iajs-2485	142	21	need	need	VERB
iajs-2485	142	22	not	not	PART
iajs-2485	142	23	it	it	PRON
iajs-2485	142	24	with	with	ADP
iajs-2485	142	25	invariant	invariant	ADJ
iajs-2485	142	26	subspace	subspace	NOUN
iajs-2485	142	27	method	method	NOUN
iajs-2485	142	28	.	.	PUNCT
iajs-2485	143	1	furthermore	furthermore	ADV
iajs-2485	143	2	,	,	PUNCT
iajs-2485	143	3	the	the	DET
iajs-2485	143	4	invariant	invariant	ADJ
iajs-2485	143	5	subspace	subspace	NOUN
iajs-2485	143	6	method	method	NOUN
iajs-2485	143	7	is	be	AUX
iajs-2485	143	8	more	more	ADV
iajs-2485	143	9	suitable	suitable	ADJ
iajs-2485	143	10	for	for	ADP
iajs-2485	143	11	solving	solve	VERB
iajs-2485	143	12	some	some	PRON
iajs-2485	143	13	of	of	ADP
iajs-2485	143	14	fractional	fractional	ADJ
iajs-2485	143	15	differential	differential	ADJ
iajs-2485	143	16	equations	equation	NOUN
iajs-2485	143	17	with	with	ADP
iajs-2485	143	18	variable	variable	ADJ
iajs-2485	143	19	coefficients	coefficient	NOUN
iajs-2485	143	20	than	than	ADP
iajs-2485	143	21	the	the	DET
iajs-2485	143	22	double	double	ADJ
iajs-2485	143	23	sumudu	sumudu	NOUN
iajs-2485	143	24	transform	transform	NOUN
iajs-2485	143	25	method	method	NOUN
iajs-2485	143	26	.	.	PUNCT
iajs-2485	144	1	figures	figure	NOUN
iajs-2485	144	2	and	and	CCONJ
iajs-2485	144	3	tabulated	tabulate	VERB
iajs-2485	144	4	results	result	NOUN
iajs-2485	144	5	,	,	PUNCT
iajs-2485	144	6	show	show	VERB
iajs-2485	144	7	how	how	SCONJ
iajs-2485	144	8	the	the	DET
iajs-2485	144	9	two	two	NUM
iajs-2485	144	10	methods	method	NOUN
iajs-2485	144	11	are	be	AUX
iajs-2485	144	12	have	have	VERB
iajs-2485	144	13	high	high	ADJ
iajs-2485	144	14	accuracy	accuracy	NOUN
iajs-2485	144	15	.	.	PUNCT
iajs-2485	145	1	all	all	DET
iajs-2485	145	2	data	datum	NOUN
iajs-2485	145	3	type	type	NOUN
iajs-2485	145	4	achieved	achieve	VERB
iajs-2485	145	5	by	by	ADP
iajs-2485	145	6	help	help	NOUN
iajs-2485	145	7	of	of	ADP
iajs-2485	145	8	mathcad	mathcad	PROPN
iajs-2485	145	9	15	15	NUM
iajs-2485	145	10	and	and	CCONJ
iajs-2485	145	11	matlab	matlab	PROPN
iajs-2485	145	12	programs	program	NOUN
iajs-2485	145	13	.	.	PUNCT
iajs-2485	146	1	2	2	NUM
iajs-2485	146	2	=	=	SYM
iajs-2485	146	3	2	2	NUM
iajs-2485	146	4	and	and	CCONJ
iajs-2485	146	5	=	=	SYM
iajs-2485	146	6	1	1	NUM
iajs-2485	146	7	1	1	NUM
iajs-2485	146	8	t	t	NOUN
iajs-2485	146	9	00	00	NUM
iajs-2485	146	10	1	1	NUM
iajs-2485	146	11	x	x	SYM
iajs-2485	146	12	8	8	NUM
iajs-2485	146	13	2	2	NUM
iajs-2485	146	14	4	4	NUM
iajs-2485	146	15	6	6	NUM
iajs-2485	146	16	2	2	NUM
iajs-2485	146	17	2	2	NUM
iajs-2485	146	18	=	=	SYM
iajs-2485	146	19	1.99	1.99	NUM
iajs-2485	146	20	and	and	CCONJ
iajs-2485	146	21	=	=	NOUN
iajs-2485	147	1	.9	.9	NUM
iajs-2485	147	2	1	1	NUM
iajs-2485	147	3	t	t	NOUN
iajs-2485	147	4	00	00	NUM
iajs-2485	147	5	1	1	NUM
iajs-2485	147	6	x	x	SYM
iajs-2485	147	7	8	8	NUM
iajs-2485	147	8	2	2	NUM
iajs-2485	147	9	4	4	NUM
iajs-2485	147	10	6	6	NUM
iajs-2485	147	11	2	2	NUM
iajs-2485	147	12	2	2	NUM
iajs-2485	147	13	=	=	SYM
iajs-2485	147	14	1.6	1.6	NUM
iajs-2485	147	15	and	and	CCONJ
iajs-2485	147	16	=	=	SYM
iajs-2485	147	17	.8	.8	PROPN
iajs-2485	147	18	1	1	NUM
iajs-2485	147	19	t	t	NOUN
iajs-2485	147	20	00	00	NUM
iajs-2485	147	21	1	1	NUM
iajs-2485	147	22	x	x	SYM
iajs-2485	147	23	2	2	NUM
iajs-2485	147	24	4	4	NUM
iajs-2485	147	25	6	6	NUM
iajs-2485	147	26	2	2	NUM
iajs-2485	147	27	2	2	NUM
iajs-2485	147	28	=	=	SYM
iajs-2485	147	29	1.7	1.7	NUM
iajs-2485	147	30	and	and	CCONJ
iajs-2485	147	31	=	=	NOUN
iajs-2485	147	32	.5	.5	NUM
iajs-2485	147	33	1	1	NUM
iajs-2485	147	34	t	t	NOUN
iajs-2485	147	35	00	00	NUM
iajs-2485	147	36	1	1	NUM
iajs-2485	147	37	x	x	SYM
iajs-2485	147	38	2	2	NUM
iajs-2485	147	39	4	4	NUM
iajs-2485	147	40	6	6	NUM
iajs-2485	147	41	2	2	NUM
iajs-2485	147	42	2	2	NUM
iajs-2485	147	43	=	=	SYM
iajs-2485	147	44	1.3	1.3	NUM
iajs-2485	147	45	and	and	CCONJ
iajs-2485	147	46	=	=	NOUN
iajs-2485	147	47	.1	.1	NUM
iajs-2485	147	48	1	1	NUM
iajs-2485	147	49	t	t	NOUN
iajs-2485	147	50	00	00	NUM
iajs-2485	147	51	1	1	NUM
iajs-2485	147	52	x	x	SYM
iajs-2485	147	53	4	4	NUM
iajs-2485	147	54	2	2	NUM
iajs-2485	147	55	2	2	NUM
iajs-2485	147	56	2	2	NUM
iajs-2485	147	57	=	=	SYM
iajs-2485	147	58	1.2	1.2	NUM
iajs-2485	147	59	and	and	CCONJ
iajs-2485	147	60	=	=	NOUN
iajs-2485	147	61	.9	.9	NUM
iajs-2485	147	62	1	1	NUM
iajs-2485	147	63	t	t	NOUN
iajs-2485	147	64	00	00	NUM
iajs-2485	147	65	1	1	NUM
iajs-2485	147	66	x	x	SYM
iajs-2485	147	67	2	2	NUM
iajs-2485	147	68	4	4	NUM
iajs-2485	147	69	6	6	NUM
iajs-2485	147	70	2	2	NUM
iajs-2485	147	71	  	  	SPACE
iajs-2485	147	72	139	139	NUM
iajs-2485	147	73	  	  	SPACE
iajs-2485	147	74	ibn	ibn	PROPN
iajs-2485	147	75	al	al	PROPN
iajs-2485	147	76	-	-	PUNCT
iajs-2485	147	77	haitham	haitham	PROPN
iajs-2485	147	78	jour	jour	X
iajs-2485	147	79	.	.	PROPN
iajs-2485	147	80	for	for	ADP
iajs-2485	147	81	pure	pure	ADJ
iajs-2485	147	82	&	&	CCONJ
iajs-2485	147	83	appl	appl	PROPN
iajs-2485	147	84	.	.	PUNCT
iajs-2485	148	1	sci	sci	PROPN
iajs-2485	148	2	.	.	PROPN
iajs-2485	149	1	33	33	NUM
iajs-2485	149	2	(	(	PUNCT
iajs-2485	149	3	3	3	NUM
iajs-2485	149	4	)	)	PUNCT
iajs-2485	149	5	2020	2020	NUM
iajs-2485	149	6	references	reference	NOUN
iajs-2485	149	7	1	1	NUM
iajs-2485	149	8	.	.	PUNCT
iajs-2485	149	9	watugala	watugala	PROPN
iajs-2485	149	10	g.	g.	PROPN
iajs-2485	149	11	sumudu	sumudu	PROPN
iajs-2485	149	12	transform	transform	VERB
iajs-2485	149	13	a	a	DET
iajs-2485	149	14	new	new	ADJ
iajs-2485	149	15	integral	integral	ADJ
iajs-2485	149	16	transform	transform	NOUN
iajs-2485	149	17	to	to	PART
iajs-2485	149	18	solve	solve	VERB
iajs-2485	149	19	differential	differential	ADJ
iajs-2485	149	20	equations	equation	NOUN
iajs-2485	149	21	and	and	CCONJ
iajs-2485	149	22	control	control	NOUN
iajs-2485	149	23	engineering	engineering	NOUN
iajs-2485	149	24	problems	problem	NOUN
iajs-2485	149	25	.	.	PUNCT
iajs-2485	150	1	international	international	ADJ
iajs-2485	150	2	.journal	.journal	NOUN
iajs-2485	150	3	of	of	ADP
iajs-2485	150	4	mathematical	mathematical	ADJ
iajs-2485	150	5	education	education	NOUN
iajs-2485	150	6	in	in	ADP
iajs-2485	150	7	science	science	NOUN
iajs-2485	150	8	and	and	CCONJ
iajs-2485	150	9	technology	technology	NOUN
iajs-2485	150	10	.	.	PUNCT
iajs-2485	151	1	2006	2006	NUM
iajs-2485	151	2	,	,	PUNCT
iajs-2485	151	3	24	24	NUM
iajs-2485	151	4	,	,	PUNCT
iajs-2485	151	5	3543	3543	NUM
iajs-2485	151	6	,	,	PUNCT
iajs-2485	151	7	doi	doi	NOUN
iajs-2485	151	8	:	:	PUNCT
iajs-2485	151	9	org/10.1080/0020739930240105	org/10.1080/0020739930240105	ADJ
iajs-2485	151	10	.	.	NOUN
iajs-2485	152	1	2	2	X
iajs-2485	152	2	.	.	X
iajs-2485	152	3	watugala	watugala	ADJ
iajs-2485	152	4	,	,	PUNCT
iajs-2485	152	5	g.	g.	PROPN
iajs-2485	152	6	further	further	ADJ
iajs-2485	152	7	properties	property	NOUN
iajs-2485	152	8	of	of	ADP
iajs-2485	152	9	the	the	DET
iajs-2485	152	10	sumudu	sumudu	NOUN
iajs-2485	152	11	transform	transform	NOUN
iajs-2485	152	12	and	and	CCONJ
iajs-2485	152	13	its	its	PRON
iajs-2485	152	14	applications	application	NOUN
iajs-2485	152	15	,	,	PUNCT
iajs-2485	152	16	international	international	ADJ
iajs-2485	152	17	.journal	.journal	NOUN
iajs-2485	152	18	of	of	ADP
iajs-2485	152	19	mathematical	mathematical	ADJ
iajs-2485	152	20	education	education	NOUN
iajs-2485	152	21	in	in	ADP
iajs-2485	152	22	science	science	NOUN
iajs-2485	152	23	and	and	CCONJ
iajs-2485	152	24	technology.2010	technology.2010	PROPN
iajs-2485	152	25	,	,	PUNCT
iajs-2485	152	26	8	8	NUM
iajs-2485	152	27	,	,	PUNCT
iajs-2485	152	28	441	441	NUM
iajs-2485	152	29	-	-	SYM
iajs-2485	152	30	449	449	NUM
iajs-2485	152	31	.	.	PUNCT
iajs-2485	152	32	 	 	SPACE
iajs-2485	153	1	doi.org/10.1080/002073902760047940	doi.org/10.1080/002073902760047940	PROPN
iajs-2485	153	2	3	3	NUM
iajs-2485	153	3	.	.	PUNCT
iajs-2485	154	1	stoer	stoer	PROPN
iajs-2485	154	2	,	,	PUNCT
iajs-2485	154	3	j.	j.	PROPN
iajs-2485	154	4	;	;	PUNCT
iajs-2485	154	5	bulirsch	bulirsch	PROPN
iajs-2485	154	6	,	,	PUNCT
iajs-2485	154	7	r.	r.	PROPN
iajs-2485	154	8	introduction	introduction	NOUN
iajs-2485	154	9	to	to	ADP
iajs-2485	154	10	numerical	numerical	ADJ
iajs-2485	154	11	analysis	analysis	NOUN
iajs-2485	154	12	;	;	PUNCT
iajs-2485	154	13	2	2	NUM
iajs-2485	154	14	nd	nd	NOUN
iajs-2485	154	15	ed	ed	NOUN
iajs-2485	154	16	.	.	PUNCT
iajs-2485	154	17	;	;	PUNCT
iajs-2485	154	18	springer	springer	NOUN
iajs-2485	154	19	science	science	NOUN
iajs-2485	154	20	and	and	CCONJ
iajs-2485	154	21	business	business	NOUN
iajs-2485	154	22	media	medium	NOUN
iajs-2485	154	23	,	,	PUNCT
iajs-2485	154	24	2013	2013	NUM
iajs-2485	154	25	.	.	PUNCT
iajs-2485	155	1	4	4	NUM
iajs-2485	155	2	.	.	X
iajs-2485	155	3	jarad	jarad	PROPN
iajs-2485	155	4	,	,	PUNCT
iajs-2485	155	5	f.	f.	PROPN
iajs-2485	155	6	application	application	NOUN
iajs-2485	155	7	of	of	ADP
iajs-2485	155	8	sumudu	sumudu	NOUN
iajs-2485	155	9	and	and	CCONJ
iajs-2485	155	10	double	double	ADJ
iajs-2485	155	11	sumudu	sumudu	NOUN
iajs-2485	155	12	transforms	transform	VERB
iajs-2485	155	13	to	to	ADP
iajs-2485	155	14	caputo	caputo	PROPN
iajs-2485	155	15	-	-	PUNCT
iajs-2485	155	16	fractional	fractional	ADJ
iajs-2485	155	17	differential	differential	ADJ
iajs-2485	155	18	equations	equation	NOUN
iajs-2485	155	19	,	,	PUNCT
iajs-2485	155	20	journal	journal	NOUN
iajs-2485	155	21	of	of	ADP
iajs-2485	155	22	computational	computational	ADJ
iajs-2485	155	23	analysis	analysis	NOUN
iajs-2485	155	24	and	and	CCONJ
iajs-2485	155	25	applications.2012	applications.2012	PROPN
iajs-2485	155	26	,	,	PUNCT
iajs-2485	155	27	14	14	NUM
iajs-2485	155	28	,	,	PUNCT
iajs-2485	155	29	475	475	NUM
iajs-2485	155	30	-	-	SYM
iajs-2485	155	31	483	483	NUM
iajs-2485	155	32	.	.	PUNCT
iajs-2485	156	1	5	5	NUM
iajs-2485	156	2	.	.	X
iajs-2485	156	3	manoj	manoj	PROPN
iajs-2485	156	4	,	,	PUNCT
iajs-2485	156	5	k.	k.	PROPN
iajs-2485	156	6	;	;	PUNCT
iajs-2485	156	7	varsha	varsha	PROPN
iajs-2485	156	8	,	,	PUNCT
iajs-2485	156	9	g.	g.	PROPN
iajs-2485	156	10	exact	exact	ADJ
iajs-2485	156	11	solutions	solution	NOUN
iajs-2485	156	12	of	of	ADP
iajs-2485	156	13	fractional	fractional	ADJ
iajs-2485	156	14	partial	partial	ADJ
iajs-2485	156	15	differential	differential	NOUN
iajs-2485	156	16	equations	equation	NOUN
iajs-2485	156	17	by	by	ADP
iajs-2485	156	18	sumudu	sumudu	NOUN
iajs-2485	156	19	transform	transform	VERB
iajs-2485	156	20	iterative	iterative	NOUN
iajs-2485	156	21	method	method	NOUN
iajs-2485	156	22	,	,	PUNCT
iajs-2485	156	23	researchgate	researchgate	NOUN
iajs-2485	156	24	,	,	PUNCT
iajs-2485	156	25	arxiv:1806.03057v1	arxiv:1806.03057v1	PROPN
iajs-2485	156	26	,	,	PUNCT
iajs-2485	156	27	math	math	NOUN
iajs-2485	156	28	.	.	PUNCT
iajs-2485	157	1	ap	ap	PROPN
iajs-2485	157	2	.	.	PUNCT
iajs-2485	158	1	jun	jun	PROPN
iajs-2485	158	2	,	,	PUNCT
iajs-2485	158	3	2018	2018	NUM
iajs-2485	158	4	.	.	PUNCT
iajs-2485	159	1	6	6	NUM
iajs-2485	159	2	.	.	X
iajs-2485	159	3	berian	berian	PROPN
iajs-2485	159	4	,	,	PUNCT
iajs-2485	159	5	j.	j.	PROPN
iajs-2485	159	6	integral	integral	PROPN
iajs-2485	159	7	transforms	transform	VERB
iajs-2485	159	8	for	for	ADP
iajs-2485	159	9	you	you	PRON
iajs-2485	159	10	and	and	CCONJ
iajs-2485	159	11	me	i	PRON
iajs-2485	159	12	,	,	PUNCT
iajs-2485	159	13	royal	royal	ADJ
iajs-2485	159	14	observatory	observatory	PROPN
iajs-2485	159	15	edinburgh	edinburgh	PROPN
iajs-2485	159	16	institute	institute	PROPN
iajs-2485	159	17	for	for	ADP
iajs-2485	159	18	astronomy	astronomy	NOUN
iajs-2485	159	19	,	,	PUNCT
iajs-2485	159	20	march	march	PROPN
iajs-2485	159	21	,	,	PUNCT
iajs-2485	159	22	2008	2008	NUM
iajs-2485	159	23	.	.	PUNCT
iajs-2485	160	1	7	7	X
iajs-2485	160	2	.	.	NUM
iajs-2485	160	3	svirshchevskii	svirshchevskii	PROPN
iajs-2485	160	4	,	,	PUNCT
iajs-2485	160	5	s.r	s.r	PROPN
iajs-2485	160	6	.	.	PROPN
iajs-2485	160	7	invariant	invariant	ADJ
iajs-2485	160	8	linear	linear	PROPN
iajs-2485	160	9	spaces	space	NOUN
iajs-2485	160	10	and	and	CCONJ
iajs-2485	160	11	exact	exact	ADJ
iajs-2485	160	12	solutions	solution	NOUN
iajs-2485	160	13	of	of	ADP
iajs-2485	160	14	nonlinear	nonlinear	ADJ
iajs-2485	160	15	evolution	evolution	NOUN
iajs-2485	160	16	equations	equation	NOUN
iajs-2485	160	17	.	.	PUNCT
iajs-2485	161	1	j.	j.	PROPN
iajs-2485	161	2	nonlinear	nonlinear	PROPN
iajs-2485	161	3	math	math	PROPN
iajs-2485	161	4	.	.	PUNCT
iajs-2485	162	1	phys	phy	NOUN
iajs-2485	162	2	.	.	PUNCT
iajs-2485	163	1	1996	1996	NUM
iajs-2485	163	2	,	,	PUNCT
iajs-2485	163	3	18	18	NUM
iajs-2485	163	4	,	,	PUNCT
iajs-2485	163	5	1	1	NUM
iajs-2485	163	6	,	,	PUNCT
iajs-2485	163	7	146	146	NUM
iajs-2485	163	8	-	-	SYM
iajs-2485	163	9	162	162	NUM
iajs-2485	163	10	,	,	PUNCT
iajs-2485	163	11	doi:10.1515	doi:10.1515	NOUN
iajs-2485	163	12	/	/	SYM
iajs-2485	163	13	fca-2015	fca-2015	NOUN
iajs-2485	163	14	-	-	PUNCT
iajs-2485	163	15	0010	0010	NUM
iajs-2485	163	16	.	.	PUNCT
iajs-2485	164	1	8	8	NUM
iajs-2485	164	2	.	.	X
iajs-2485	165	1	zhukovsky	zhukovsky	ADJ
iajs-2485	165	2	,	,	PUNCT
iajs-2485	165	3	k.v	k.v	PROPN
iajs-2485	165	4	.	.	PROPN
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iajs-2485	165	6	solution	solution	NOUN
iajs-2485	165	7	for	for	ADP
iajs-2485	165	8	some	some	DET
iajs-2485	165	9	types	type	NOUN
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iajs-2485	165	12	order	order	NOUN
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iajs-2485	165	14	equations	equation	NOUN
iajs-2485	165	15	and	and	CCONJ
iajs-2485	165	16	for	for	ADP
iajs-2485	165	17	relevant	relevant	ADJ
iajs-2485	165	18	physical	physical	ADJ
iajs-2485	165	19	problems	problem	NOUN
iajs-2485	165	20	.	.	PUNCT
iajs-2485	166	1	journal	journal	PROPN
iajs-2485	166	2	of	of	ADP
iajs-2485	166	3	mathematical	mathematical	ADJ
iajs-2485	166	4	analysis	analysis	NOUN
iajs-2485	166	5	and	and	CCONJ
iajs-2485	166	6	applications.2016	applications.2016	PROPN
iajs-2485	166	7	,	,	PUNCT
iajs-2485	166	8	doi	doi	NOUN
iajs-2485	166	9	:	:	PUNCT
iajs-2485	166	10	10.1016	10.1016	NUM
iajs-2485	166	11	/	/	SYM
iajs-2485	166	12	j.jmaa.2016.08.054	j.jmaa.2016.08.054	PROPN
iajs-2485	166	13	.	.	PROPN
iajs-2485	167	1	9	9	NUM
iajs-2485	167	2	.	.	X
iajs-2485	167	3	jun	jun	PROPN
iajs-2485	167	4	,	,	PUNCT
iajs-2485	167	5	j.	j.	PROPN
iajs-2485	167	6	;	;	PUNCT
iajs-2485	167	7	yuqiang	yuqiang	PROPN
iajs-2485	167	8	,	,	PUNCT
iajs-2485	167	9	f.	f.	PROPN
iajs-2485	167	10	;	;	PUNCT
iajs-2485	167	11	shougui	shougui	PROPN
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iajs-2485	167	16	to	to	ADP
iajs-2485	167	17	the	the	DET
iajs-2485	167	18	fractional	fractional	ADJ
iajs-2485	167	19	differential	differential	ADJ
iajs-2485	167	20	equations	equation	NOUN
iajs-2485	167	21	with	with	ADP
iajs-2485	167	22	mixed	mixed	ADJ
iajs-2485	167	23	partial	partial	ADJ
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iajs-2485	167	25	.	.	PUNCT
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iajs-2485	172	2	,	,	PUNCT
iajs-2485	172	3	n.	n.	PROPN
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iajs-2485	172	6	,	,	PUNCT
iajs-2485	172	7	i.	i.	PROPN
iajs-2485	172	8	;	;	PUNCT
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iajs-2485	172	10	,	,	PUNCT
iajs-2485	172	11	d.	d.	PROPN
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iajs-2485	172	14	,	,	PUNCT
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iajs-2485	172	18	the	the	DET
iajs-2485	172	19	fourth	fourth	ADV
iajs-2485	172	20	iasted	iasted	ADJ
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iajs-2485	172	23	on	on	ADP
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iajs-2485	172	25	systems	system	NOUN
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iajs-2485	172	28	,	,	PUNCT
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iajs-2485	174	16	.	.	PUNCT
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iajs-2485	175	3	the	the	DET
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iajs-2485	176	8	,	,	PUNCT
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iajs-2485	176	10	/	/	SYM
iajs-2485	176	11	j.jfranklin.2010.03.008	j.jfranklin.2010.03.008	PROPN
iajs-2485	176	12	.	.	PUNCT