id	sid	tid	token	lemma	pos
cana-935	1	1	communications	communication	NOUN
cana-935	1	2	on	on	ADP
cana-935	1	3	applied	apply	VERB
cana-935	1	4	nonlinear	nonlinear	ADJ
cana-935	1	5	analysis	analysis	NOUN
cana-935	1	6	issn	issn	NOUN
cana-935	1	7	:	:	PUNCT
cana-935	1	8	1074	1074	NUM
cana-935	1	9	-	-	PUNCT
cana-935	1	10	133x	133x	NUM
cana-935	1	11	vol	vol	NOUN
cana-935	1	12	31	31	NUM
cana-935	1	13	no	no	NOUN
cana-935	1	14	.	.	PUNCT
cana-935	2	1	4s	4s	NUM
cana-935	2	2	(	(	PUNCT
cana-935	2	3	2024	2024	NUM
cana-935	2	4	)	)	PUNCT
cana-935	2	5	418	418	NUM
cana-935	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-935	2	7	exploring	explore	VERB
cana-935	2	8	fractional	fractional	ADJ
cana-935	2	9	quantum	quantum	ADJ
cana-935	2	10	mechanics	mechanic	NOUN
cana-935	2	11	:	:	PUNCT
cana-935	2	12	stability	stability	NOUN
cana-935	2	13	analysis	analysis	NOUN
cana-935	2	14	and	and	CCONJ
cana-935	2	15	wave	wave	NOUN
cana-935	2	16	propagation	propagation	NOUN
cana-935	2	17	in	in	ADP
cana-935	2	18	coupled	couple	VERB
cana-935	2	19	schrödinger	schrödinger	ADJ
cana-935	2	20	equations	equation	NOUN
cana-935	2	21	iftekher	iftekher	ADP
cana-935	2	22	s.	s.	PROPN
cana-935	2	23	chowdhury1	chowdhury1	PROPN
cana-935	2	24	,	,	PUNCT
cana-935	2	25	dr	dr	PROPN
cana-935	2	26	.	.	PROPN
cana-935	2	27	eric	eric	PROPN
cana-935	2	28	howard2	howard2	PROPN
cana-935	2	29	,	,	PUNCT
cana-935	2	30	dr	dr	PROPN
cana-935	2	31	nand	nand	PROPN
cana-935	2	32	kumar3	kumar3	PROPN
cana-935	2	33	1	1	NUM
cana-935	2	34	macquarie	macquarie	PROPN
cana-935	2	35	university	university	PROPN
cana-935	2	36	,	,	PUNCT
cana-935	2	37	department	department	NOUN
cana-935	2	38	of	of	ADP
cana-935	2	39	physics	physics	PROPN
cana-935	2	40	and	and	CCONJ
cana-935	2	41	astronomy	astronomy	NOUN
cana-935	2	42	,	,	PUNCT
cana-935	2	43	sydney	sydney	PROPN
cana-935	2	44	,	,	PUNCT
cana-935	2	45	nsw	nsw	PROPN
cana-935	2	46	,	,	PUNCT
cana-935	2	47	2109	2109	NUM
cana-935	2	48	,	,	PUNCT
cana-935	2	49	australia	australia	PROPN
cana-935	2	50	.	.	PUNCT
cana-935	3	1	e	e	X
cana-935	3	2	-	-	NOUN
cana-935	3	3	mail	mail	NOUN
cana-935	3	4	:	:	PUNCT
cana-935	3	5	mdiftekher@gmail.com	mdiftekher@gmail.com	X
cana-935	3	6	.	.	NOUN
cana-935	3	7	2	2	NUM
cana-935	3	8	department	department	NOUN
cana-935	3	9	of	of	ADP
cana-935	3	10	physics	physics	PROPN
cana-935	3	11	and	and	CCONJ
cana-935	3	12	astronomy	astronomy	NOUN
cana-935	3	13	,	,	PUNCT
cana-935	3	14	macquarie	macquarie	PROPN
cana-935	3	15	university	university	PROPN
cana-935	3	16	,	,	PUNCT
cana-935	3	17	australia	australia	PROPN
cana-935	3	18	.	.	PUNCT
cana-935	4	1	email	email	NOUN
cana-935	5	1	i	i	PROPN
cana-935	5	2	d	d	PROPN
cana-935	5	3	eric.howard@mq.edu.au	eric.howard@mq.edu.au	PROPN
cana-935	5	4	.	.	PUNCT
cana-935	6	1	orcid	orcid	NOUN
cana-935	6	2	:	:	PUNCT
cana-935	6	3	0000	0000	NUM
cana-935	6	4	-	-	PUNCT
cana-935	6	5	0002	0002	NUM
cana-935	6	6	-	-	PUNCT
cana-935	6	7	8133	8133	NUM
cana-935	6	8	-	-	PUNCT
cana-935	6	9	8323	8323	NUM
cana-935	6	10	.	.	PUNCT
cana-935	7	1	3	3	NUM
cana-935	7	2	assistant	assistant	NOUN
cana-935	7	3	professor	professor	NOUN
cana-935	7	4	,	,	PUNCT
cana-935	7	5	department	department	NOUN
cana-935	7	6	of	of	ADP
cana-935	7	7	physics	physics	PROPN
cana-935	7	8	,	,	PUNCT
cana-935	7	9	jawaharlal	jawaharlal	PROPN
cana-935	7	10	nehru	nehru	PROPN
cana-935	7	11	memorial	memorial	PROPN
cana-935	7	12	pg	pg	PROPN
cana-935	7	13	college	college	PROPN
cana-935	7	14	,	,	PUNCT
cana-935	7	15	barabanki	barabanki	PROPN
cana-935	7	16	,	,	PUNCT
cana-935	7	17	up	up	ADP
cana-935	7	18	,	,	PUNCT
cana-935	7	19	india	india	PROPN
cana-935	7	20	.	.	PUNCT
cana-935	8	1	email:nandkumar350@gmail.com	email:nandkumar350@gmail.com	X
cana-935	8	2	.	.	PUNCT
cana-935	8	3	orcid	orcid	NOUN
cana-935	8	4	:	:	PUNCT
cana-935	8	5	0009	0009	NUM
cana-935	8	6	-	-	SYM
cana-935	8	7	0004	0004	NUM
cana-935	8	8	-	-	PUNCT
cana-935	8	9	3139	3139	NUM
cana-935	8	10	-	-	PUNCT
cana-935	8	11	3385	3385	NUM
cana-935	8	12	article	article	NOUN
cana-935	8	13	history	history	NOUN
cana-935	8	14	:	:	PUNCT
cana-935	8	15	received	receive	VERB
cana-935	8	16	:	:	PUNCT
cana-935	8	17	20	20	NUM
cana-935	8	18	-	-	PUNCT
cana-935	8	19	04	04	NUM
cana-935	8	20	-	-	PUNCT
cana-935	8	21	2024	2024	NUM
cana-935	8	22	revised	revise	VERB
cana-935	8	23	:	:	PUNCT
cana-935	8	24	16	16	NUM
cana-935	8	25	-	-	SYM
cana-935	8	26	06	06	NUM
cana-935	8	27	-	-	PUNCT
cana-935	8	28	2024	2024	NUM
cana-935	8	29	accepted	accept	VERB
cana-935	8	30	:	:	PUNCT
cana-935	8	31	14	14	NUM
cana-935	8	32	-	-	SYM
cana-935	8	33	06	06	NUM
cana-935	8	34	-	-	PUNCT
cana-935	8	35	2024	2024	NUM
cana-935	8	36	abstract	abstract	NOUN
cana-935	8	37	:	:	PUNCT
cana-935	8	38	fractional	fractional	ADJ
cana-935	8	39	quantum	quantum	ADJ
cana-935	8	40	mechanics	mechanic	NOUN
cana-935	8	41	(	(	PUNCT
cana-935	8	42	fqm	fqm	NOUN
cana-935	8	43	)	)	PUNCT
cana-935	8	44	has	have	AUX
cana-935	8	45	emerged	emerge	VERB
cana-935	8	46	as	as	ADP
cana-935	8	47	a	a	DET
cana-935	8	48	fascinating	fascinating	ADJ
cana-935	8	49	theoretical	theoretical	ADJ
cana-935	8	50	framework	framework	NOUN
cana-935	8	51	extending	extend	VERB
cana-935	8	52	traditional	traditional	ADJ
cana-935	8	53	quantum	quantum	ADJ
cana-935	8	54	mechanics	mechanic	NOUN
cana-935	8	55	to	to	PART
cana-935	8	56	describe	describe	VERB
cana-935	8	57	physical	physical	ADJ
cana-935	8	58	systems	system	NOUN
cana-935	8	59	with	with	ADP
cana-935	8	60	non	non	ADJ
cana-935	8	61	-	-	ADJ
cana-935	8	62	local	local	ADJ
cana-935	8	63	or	or	CCONJ
cana-935	8	64	long	long	ADJ
cana-935	8	65	-	-	PUNCT
cana-935	8	66	range	range	NOUN
cana-935	8	67	interactions	interaction	NOUN
cana-935	8	68	.	.	PUNCT
cana-935	9	1	in	in	ADP
cana-935	9	2	this	this	DET
cana-935	9	3	paper	paper	NOUN
cana-935	9	4	,	,	PUNCT
cana-935	9	5	we	we	PRON
cana-935	9	6	delve	delve	VERB
cana-935	9	7	into	into	ADP
cana-935	9	8	the	the	DET
cana-935	9	9	realm	realm	NOUN
cana-935	9	10	of	of	ADP
cana-935	9	11	fqm	fqm	NOUN
cana-935	9	12	,	,	PUNCT
cana-935	9	13	focusing	focus	VERB
cana-935	9	14	on	on	ADP
cana-935	9	15	stability	stability	NOUN
cana-935	9	16	analysis	analysis	NOUN
cana-935	9	17	and	and	CCONJ
cana-935	9	18	wave	wave	NOUN
cana-935	9	19	propagation	propagation	NOUN
cana-935	9	20	in	in	ADP
cana-935	9	21	coupled	couple	VERB
cana-935	9	22	schrödinger	schrödinger	ADJ
cana-935	9	23	equations	equation	NOUN
cana-935	9	24	.	.	PUNCT
cana-935	10	1	we	we	PRON
cana-935	10	2	begin	begin	VERB
cana-935	10	3	with	with	ADP
cana-935	10	4	a	a	DET
cana-935	10	5	comprehensive	comprehensive	ADJ
cana-935	10	6	overview	overview	NOUN
cana-935	10	7	of	of	ADP
cana-935	10	8	fqm	fqm	NOUN
cana-935	10	9	,	,	PUNCT
cana-935	10	10	elucidating	elucidate	VERB
cana-935	10	11	its	its	PRON
cana-935	10	12	fundamental	fundamental	ADJ
cana-935	10	13	principles	principle	NOUN
cana-935	10	14	and	and	CCONJ
cana-935	10	15	mathematical	mathematical	ADJ
cana-935	10	16	formalism	formalism	NOUN
cana-935	10	17	.	.	PUNCT
cana-935	11	1	subsequently	subsequently	ADV
cana-935	11	2	,	,	PUNCT
cana-935	11	3	we	we	PRON
cana-935	11	4	conduct	conduct	VERB
cana-935	11	5	stability	stability	NOUN
cana-935	11	6	analysis	analysis	NOUN
cana-935	11	7	of	of	ADP
cana-935	11	8	coupled	couple	VERB
cana-935	11	9	fractional	fractional	ADJ
cana-935	11	10	schrödinger	schrödinger	ADJ
cana-935	11	11	equations	equation	NOUN
cana-935	11	12	,	,	PUNCT
cana-935	11	13	exploring	explore	VERB
cana-935	11	14	the	the	DET
cana-935	11	15	conditions	condition	NOUN
cana-935	11	16	under	under	ADP
cana-935	11	17	which	which	PRON
cana-935	11	18	these	these	DET
cana-935	11	19	systems	system	NOUN
cana-935	11	20	exhibit	exhibit	VERB
cana-935	11	21	stable	stable	ADJ
cana-935	11	22	behavior	behavior	NOUN
cana-935	11	23	.	.	PUNCT
cana-935	12	1	furthermore	furthermore	ADV
cana-935	12	2	,	,	PUNCT
cana-935	12	3	we	we	PRON
cana-935	12	4	investigate	investigate	VERB
cana-935	12	5	wave	wave	NOUN
cana-935	12	6	propagation	propagation	NOUN
cana-935	12	7	phenomena	phenomenon	NOUN
cana-935	12	8	within	within	ADP
cana-935	12	9	such	such	ADJ
cana-935	12	10	systems	system	NOUN
cana-935	12	11	,	,	PUNCT
cana-935	12	12	shedding	shed	VERB
cana-935	12	13	light	light	NOUN
cana-935	12	14	on	on	ADP
cana-935	12	15	the	the	DET
cana-935	12	16	unique	unique	ADJ
cana-935	12	17	characteristics	characteristic	NOUN
cana-935	12	18	of	of	ADP
cana-935	12	19	fractional	fractional	ADJ
cana-935	12	20	quantum	quantum	ADJ
cana-935	12	21	waves	wave	NOUN
cana-935	12	22	.	.	PUNCT
cana-935	13	1	our	our	PRON
cana-935	13	2	findings	finding	NOUN
cana-935	13	3	not	not	PART
cana-935	13	4	only	only	ADV
cana-935	13	5	contribute	contribute	VERB
cana-935	13	6	to	to	ADP
cana-935	13	7	advancing	advance	VERB
cana-935	13	8	the	the	DET
cana-935	13	9	theoretical	theoretical	ADJ
cana-935	13	10	understanding	understanding	NOUN
cana-935	13	11	of	of	ADP
cana-935	13	12	fqm	fqm	NOUN
cana-935	13	13	but	but	CCONJ
cana-935	13	14	also	also	ADV
cana-935	13	15	offer	offer	VERB
cana-935	13	16	insights	insight	NOUN
cana-935	13	17	into	into	ADP
cana-935	13	18	potential	potential	ADJ
cana-935	13	19	applications	application	NOUN
cana-935	13	20	in	in	ADP
cana-935	13	21	diverse	diverse	ADJ
cana-935	13	22	fields	field	NOUN
cana-935	13	23	ranging	range	VERB
cana-935	13	24	from	from	ADP
cana-935	13	25	condensed	condense	VERB
cana-935	13	26	matter	matter	NOUN
cana-935	13	27	physics	physics	NOUN
cana-935	13	28	to	to	ADP
cana-935	13	29	quantum	quantum	ADJ
cana-935	13	30	information	information	NOUN
cana-935	13	31	processing	processing	NOUN
cana-935	13	32	.	.	PUNCT
cana-935	14	1	keywords	keyword	NOUN
cana-935	14	2	:	:	PUNCT
cana-935	14	3	fractional	fractional	ADJ
cana-935	14	4	quantum	quantum	ADJ
cana-935	14	5	mechanics	mechanic	NOUN
cana-935	14	6	,	,	PUNCT
cana-935	14	7	coupled	couple	VERB
cana-935	14	8	schrödinger	schrödinger	ADJ
cana-935	14	9	equations	equation	NOUN
cana-935	14	10	.	.	PUNCT
cana-935	15	1	1	1	X
cana-935	15	2	.	.	X
cana-935	15	3	introduction	introduction	NOUN
cana-935	15	4	fractional	fractional	ADJ
cana-935	15	5	quantum	quantum	NOUN
cana-935	15	6	mechanics	mechanic	NOUN
cana-935	15	7	is	be	AUX
cana-935	15	8	a	a	DET
cana-935	15	9	branch	branch	NOUN
cana-935	15	10	of	of	ADP
cana-935	15	11	theoretical	theoretical	ADJ
cana-935	15	12	physics	physics	NOUN
cana-935	15	13	that	that	PRON
cana-935	15	14	extends	extend	VERB
cana-935	15	15	the	the	DET
cana-935	15	16	traditional	traditional	ADJ
cana-935	15	17	framework	framework	NOUN
cana-935	15	18	of	of	ADP
cana-935	15	19	quantum	quantum	ADJ
cana-935	15	20	mechanics	mechanic	NOUN
cana-935	15	21	to	to	PART
cana-935	15	22	better	well	ADV
cana-935	15	23	understand	understand	VERB
cana-935	15	24	the	the	DET
cana-935	15	25	behavior	behavior	NOUN
cana-935	15	26	of	of	ADP
cana-935	15	27	complex	complex	ADJ
cana-935	15	28	systems	system	NOUN
cana-935	15	29	.	.	PUNCT
cana-935	16	1	its	its	PRON
cana-935	16	2	development	development	NOUN
cana-935	16	3	was	be	AUX
cana-935	16	4	motivated	motivate	VERB
cana-935	16	5	by	by	ADP
cana-935	16	6	the	the	DET
cana-935	16	7	need	need	NOUN
cana-935	16	8	to	to	PART
cana-935	16	9	address	address	VERB
cana-935	16	10	phenomena	phenomena	NOUN
cana-935	16	11	that	that	PRON
cana-935	16	12	can	can	AUX
cana-935	16	13	not	not	PART
cana-935	16	14	be	be	AUX
cana-935	16	15	fully	fully	ADV
cana-935	16	16	described	describe	VERB
cana-935	16	17	by	by	ADP
cana-935	16	18	conventional	conventional	ADJ
cana-935	16	19	quantum	quantum	ADJ
cana-935	16	20	mechanics	mechanic	NOUN
cana-935	16	21	,	,	PUNCT
cana-935	16	22	particularly	particularly	ADV
cana-935	16	23	in	in	ADP
cana-935	16	24	systems	system	NOUN
cana-935	16	25	characterized	characterize	VERB
cana-935	16	26	by	by	ADP
cana-935	16	27	fractal	fractal	ADJ
cana-935	16	28	geometry	geometry	NOUN
cana-935	16	29	or	or	CCONJ
cana-935	16	30	non	non	ADJ
cana-935	16	31	-	-	ADJ
cana-935	16	32	local	local	ADJ
cana-935	16	33	interactions	interaction	NOUN
cana-935	16	34	.	.	PUNCT
cana-935	17	1	to	to	PART
cana-935	17	2	understand	understand	VERB
cana-935	17	3	the	the	DET
cana-935	17	4	motivation	motivation	NOUN
cana-935	17	5	behind	behind	ADP
cana-935	17	6	fractional	fractional	ADJ
cana-935	17	7	quantum	quantum	ADJ
cana-935	17	8	mechanics	mechanic	NOUN
cana-935	17	9	,	,	PUNCT
cana-935	17	10	let	let	VERB
cana-935	17	11	's	us	PRON
cana-935	17	12	first	first	ADJ
cana-935	17	13	revisit	revisit	VERB
cana-935	17	14	the	the	DET
cana-935	17	15	basics	basic	NOUN
cana-935	17	16	of	of	ADP
cana-935	17	17	traditional	traditional	ADJ
cana-935	17	18	quantum	quantum	ADJ
cana-935	17	19	mechanics	mechanic	NOUN
cana-935	17	20	.	.	PUNCT
cana-935	18	1	at	at	ADP
cana-935	18	2	its	its	PRON
cana-935	18	3	core	core	NOUN
cana-935	18	4	,	,	PUNCT
cana-935	18	5	quantum	quantum	ADJ
cana-935	18	6	mechanics	mechanic	NOUN
cana-935	18	7	provides	provide	VERB
cana-935	18	8	a	a	DET
cana-935	18	9	mathematical	mathematical	ADJ
cana-935	18	10	framework	framework	NOUN
cana-935	18	11	for	for	ADP
cana-935	18	12	describing	describe	VERB
cana-935	18	13	the	the	DET
cana-935	18	14	behavior	behavior	NOUN
cana-935	18	15	of	of	ADP
cana-935	18	16	particles	particle	NOUN
cana-935	18	17	at	at	ADP
cana-935	18	18	the	the	DET
cana-935	18	19	microscopic	microscopic	ADJ
cana-935	18	20	level	level	NOUN
cana-935	18	21	.	.	PUNCT
cana-935	19	1	central	central	ADJ
cana-935	19	2	to	to	ADP
cana-935	19	3	quantum	quantum	ADJ
cana-935	19	4	mechanics	mechanic	NOUN
cana-935	19	5	is	be	AUX
cana-935	19	6	the	the	DET
cana-935	19	7	schrödinger	schrödinger	ADJ
cana-935	19	8	equation	equation	NOUN
cana-935	19	9	,	,	PUNCT
cana-935	19	10	which	which	PRON
cana-935	19	11	describes	describe	VERB
cana-935	19	12	how	how	SCONJ
cana-935	19	13	the	the	DET
cana-935	19	14	quantum	quantum	ADJ
cana-935	19	15	state	state	NOUN
cana-935	19	16	of	of	ADP
cana-935	19	17	a	a	DET
cana-935	19	18	physical	physical	ADJ
cana-935	19	19	system	system	NOUN
cana-935	19	20	evolves	evolve	VERB
cana-935	19	21	over	over	ADP
cana-935	19	22	time	time	NOUN
cana-935	19	23	.	.	PUNCT
cana-935	20	1	the	the	DET
cana-935	20	2	equation	equation	NOUN
cana-935	20	3	is	be	AUX
cana-935	20	4	expressed	express	VERB
cana-935	20	5	as	as	ADP
cana-935	20	6	:	:	PUNCT
cana-935	20	7	𝑖ħ	𝑖ħ	PROPN
cana-935	20	8	𝜕	𝜕	PROPN
cana-935	20	9	𝜕𝑡	𝜕𝑡	PROPN
cana-935	20	10	𝛹(𝑟	𝛹(𝑟	PROPN
cana-935	20	11	,	,	PUNCT
cana-935	20	12	𝑡	𝑡	NOUN
cana-935	20	13	)	)	PUNCT
cana-935	20	14	=	=	SYM
cana-935	21	1	𝐻	𝐻	PROPN
cana-935	21	2	𝛹(𝑟	𝛹(𝑟	NOUN
cana-935	21	3	,	,	PUNCT
cana-935	21	4	𝑡	𝑡	NOUN
cana-935	21	5	)	)	PUNCT
cana-935	21	6	communications	communication	NOUN
cana-935	21	7	on	on	ADP
cana-935	21	8	applied	apply	VERB
cana-935	21	9	nonlinear	nonlinear	ADJ
cana-935	21	10	analysis	analysis	NOUN
cana-935	21	11	issn	issn	NOUN
cana-935	21	12	:	:	PUNCT
cana-935	21	13	1074	1074	NUM
cana-935	21	14	-	-	PUNCT
cana-935	21	15	133x	133x	NUM
cana-935	21	16	vol	vol	NOUN
cana-935	21	17	31	31	NUM
cana-935	21	18	no	no	NOUN
cana-935	21	19	.	.	PUNCT
cana-935	22	1	4s	4s	NUM
cana-935	22	2	(	(	PUNCT
cana-935	22	3	2024	2024	NUM
cana-935	22	4	)	)	PUNCT
cana-935	22	5	419	419	NUM
cana-935	22	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-935	22	7	where	where	SCONJ
cana-935	22	8	i	i	PRON
cana-935	22	9	is	be	AUX
cana-935	22	10	the	the	DET
cana-935	22	11	imaginary	imaginary	ADJ
cana-935	22	12	unit	unit	NOUN
cana-935	22	13	,	,	PUNCT
cana-935	22	14	ħ	ħ	PROPN
cana-935	22	15	is	be	AUX
cana-935	22	16	the	the	DET
cana-935	22	17	reduced	reduce	VERB
cana-935	22	18	planck	planck	NOUN
cana-935	22	19	constant	constant	ADJ
cana-935	22	20	,	,	PUNCT
cana-935	22	21	ψ(r	ψ(r	PROPN
cana-935	22	22	,	,	PUNCT
cana-935	22	23	t	t	PROPN
cana-935	22	24	)	)	PUNCT
cana-935	22	25	is	be	AUX
cana-935	22	26	the	the	DET
cana-935	22	27	wave	wave	NOUN
cana-935	22	28	function	function	NOUN
cana-935	22	29	representing	represent	VERB
cana-935	22	30	the	the	DET
cana-935	22	31	quantum	quantum	ADJ
cana-935	22	32	state	state	NOUN
cana-935	22	33	of	of	ADP
cana-935	22	34	the	the	DET
cana-935	22	35	system	system	NOUN
cana-935	22	36	,	,	PUNCT
cana-935	22	37	h	h	NOUN
cana-935	22	38	is	be	AUX
cana-935	22	39	the	the	DET
cana-935	22	40	hamiltonian	hamiltonian	ADJ
cana-935	22	41	operator	operator	NOUN
cana-935	22	42	representing	represent	VERB
cana-935	22	43	the	the	DET
cana-935	22	44	total	total	ADJ
cana-935	22	45	energy	energy	NOUN
cana-935	22	46	of	of	ADP
cana-935	22	47	the	the	DET
cana-935	22	48	system	system	NOUN
cana-935	22	49	,	,	PUNCT
cana-935	22	50	r	r	NOUN
cana-935	22	51	represents	represent	VERB
cana-935	22	52	spatial	spatial	ADJ
cana-935	22	53	coordinates	coordinate	NOUN
cana-935	22	54	,	,	PUNCT
cana-935	22	55	and	and	CCONJ
cana-935	22	56	t	t	PROPN
cana-935	22	57	represents	represent	VERB
cana-935	22	58	time	time	NOUN
cana-935	22	59	.	.	PUNCT
cana-935	23	1	the	the	DET
cana-935	23	2	schrödinger	schrödinger	ADJ
cana-935	23	3	equation	equation	NOUN
cana-935	23	4	is	be	AUX
cana-935	23	5	incredibly	incredibly	ADV
cana-935	23	6	successful	successful	ADJ
cana-935	23	7	in	in	ADP
cana-935	23	8	describing	describe	VERB
cana-935	23	9	the	the	DET
cana-935	23	10	behavior	behavior	NOUN
cana-935	23	11	of	of	ADP
cana-935	23	12	particles	particle	NOUN
cana-935	23	13	such	such	ADJ
cana-935	23	14	as	as	ADP
cana-935	23	15	electrons	electron	NOUN
cana-935	23	16	in	in	ADP
cana-935	23	17	atoms	atom	NOUN
cana-935	23	18	or	or	CCONJ
cana-935	23	19	photons	photon	NOUN
cana-935	23	20	in	in	ADP
cana-935	23	21	electromagnetic	electromagnetic	ADJ
cana-935	23	22	fields	field	NOUN
cana-935	23	23	.	.	PUNCT
cana-935	24	1	however	however	ADV
cana-935	24	2	,	,	PUNCT
cana-935	24	3	it	it	PRON
cana-935	24	4	encounters	encounter	VERB
cana-935	24	5	limitations	limitation	NOUN
cana-935	24	6	when	when	SCONJ
cana-935	24	7	dealing	deal	VERB
cana-935	24	8	with	with	ADP
cana-935	24	9	systems	system	NOUN
cana-935	24	10	that	that	PRON
cana-935	24	11	exhibit	exhibit	VERB
cana-935	24	12	complex	complex	ADJ
cana-935	24	13	behaviors	behavior	NOUN
cana-935	24	14	such	such	ADJ
cana-935	24	15	as	as	ADP
cana-935	24	16	fractal	fractal	ADJ
cana-935	24	17	patterns	pattern	NOUN
cana-935	24	18	or	or	CCONJ
cana-935	24	19	long	long	ADJ
cana-935	24	20	-	-	PUNCT
cana-935	24	21	range	range	NOUN
cana-935	24	22	interactions	interaction	NOUN
cana-935	24	23	.	.	PUNCT
cana-935	25	1	these	these	DET
cana-935	25	2	systems	system	NOUN
cana-935	25	3	include	include	VERB
cana-935	25	4	,	,	PUNCT
cana-935	25	5	but	but	CCONJ
cana-935	25	6	are	be	AUX
cana-935	25	7	not	not	PART
cana-935	25	8	limited	limit	VERB
cana-935	25	9	to	to	ADP
cana-935	25	10	,	,	PUNCT
cana-935	25	11	disordered	disordered	ADJ
cana-935	25	12	solids	solid	NOUN
cana-935	25	13	,	,	PUNCT
cana-935	25	14	polymers	polymer	NOUN
cana-935	25	15	,	,	PUNCT
cana-935	25	16	complex	complex	ADJ
cana-935	25	17	molecules	molecule	NOUN
cana-935	25	18	,	,	PUNCT
cana-935	25	19	and	and	CCONJ
cana-935	25	20	certain	certain	ADJ
cana-935	25	21	types	type	NOUN
cana-935	25	22	of	of	ADP
cana-935	25	23	fluids	fluid	NOUN
cana-935	25	24	.	.	PUNCT
cana-935	26	1	fractional	fractional	ADJ
cana-935	26	2	quantum	quantum	ADJ
cana-935	26	3	mechanics	mechanic	NOUN
cana-935	26	4	addresses	address	VERB
cana-935	26	5	these	these	DET
cana-935	26	6	limitations	limitation	NOUN
cana-935	26	7	by	by	ADP
cana-935	26	8	introducing	introduce	VERB
cana-935	26	9	fractional	fractional	ADJ
cana-935	26	10	derivatives	derivative	NOUN
cana-935	26	11	into	into	ADP
cana-935	26	12	the	the	DET
cana-935	26	13	mathematical	mathematical	ADJ
cana-935	26	14	formalism	formalism	NOUN
cana-935	26	15	.	.	PUNCT
cana-935	27	1	instead	instead	ADV
cana-935	27	2	of	of	ADP
cana-935	27	3	using	use	VERB
cana-935	27	4	traditional	traditional	ADJ
cana-935	27	5	derivatives	derivative	NOUN
cana-935	27	6	,	,	PUNCT
cana-935	27	7	which	which	PRON
cana-935	27	8	describe	describe	VERB
cana-935	27	9	the	the	DET
cana-935	27	10	change	change	NOUN
cana-935	27	11	of	of	ADP
cana-935	27	12	a	a	DET
cana-935	27	13	function	function	NOUN
cana-935	27	14	with	with	ADP
cana-935	27	15	respect	respect	NOUN
cana-935	27	16	to	to	ADP
cana-935	27	17	a	a	DET
cana-935	27	18	continuous	continuous	ADJ
cana-935	27	19	parameter	parameter	NOUN
cana-935	27	20	(	(	PUNCT
cana-935	27	21	e.g.	e.g.	ADV
cana-935	27	22	,	,	PUNCT
cana-935	27	23	time	time	NOUN
cana-935	27	24	or	or	CCONJ
cana-935	27	25	space	space	NOUN
cana-935	27	26	)	)	PUNCT
cana-935	27	27	,	,	PUNCT
cana-935	27	28	fractional	fractional	ADJ
cana-935	27	29	derivatives	derivative	NOUN
cana-935	27	30	generalize	generalize	VERB
cana-935	27	31	this	this	DET
cana-935	27	32	concept	concept	NOUN
cana-935	27	33	to	to	ADP
cana-935	27	34	non	non	ADJ
cana-935	27	35	-	-	ADJ
cana-935	27	36	integer	integer	ADJ
cana-935	27	37	orders	order	NOUN
cana-935	27	38	.	.	PUNCT
cana-935	28	1	these	these	DET
cana-935	28	2	fractional	fractional	ADJ
cana-935	28	3	derivatives	derivative	NOUN
cana-935	28	4	allow	allow	VERB
cana-935	28	5	for	for	ADP
cana-935	28	6	a	a	DET
cana-935	28	7	more	more	ADV
cana-935	28	8	flexible	flexible	ADJ
cana-935	28	9	description	description	NOUN
cana-935	28	10	of	of	ADP
cana-935	28	11	the	the	DET
cana-935	28	12	dynamics	dynamic	NOUN
cana-935	28	13	of	of	ADP
cana-935	28	14	complex	complex	ADJ
cana-935	28	15	systems	system	NOUN
cana-935	28	16	,	,	PUNCT
cana-935	28	17	capturing	capture	VERB
cana-935	28	18	features	feature	NOUN
cana-935	28	19	such	such	ADJ
cana-935	28	20	as	as	ADP
cana-935	28	21	subdiffusion	subdiffusion	NOUN
cana-935	28	22	,	,	PUNCT
cana-935	28	23	anomalous	anomalous	ADJ
cana-935	28	24	diffusion	diffusion	NOUN
cana-935	28	25	,	,	PUNCT
cana-935	28	26	and	and	CCONJ
cana-935	28	27	multifractal	multifractal	ADJ
cana-935	28	28	behavior	behavior	NOUN
cana-935	28	29	.	.	PUNCT
cana-935	29	1	in	in	ADP
cana-935	29	2	fractional	fractional	ADJ
cana-935	29	3	quantum	quantum	ADJ
cana-935	29	4	mechanics	mechanic	NOUN
cana-935	29	5	,	,	PUNCT
cana-935	29	6	the	the	DET
cana-935	29	7	schrödinger	schrödinger	ADJ
cana-935	29	8	equation	equation	NOUN
cana-935	29	9	is	be	AUX
cana-935	29	10	extended	extend	VERB
cana-935	29	11	to	to	PART
cana-935	29	12	incorporate	incorporate	VERB
cana-935	29	13	fractional	fractional	ADJ
cana-935	29	14	derivatives	derivative	NOUN
cana-935	29	15	,	,	PUNCT
cana-935	29	16	resulting	result	VERB
cana-935	29	17	in	in	ADP
cana-935	29	18	a	a	DET
cana-935	29	19	generalized	generalized	ADJ
cana-935	29	20	form	form	NOUN
cana-935	29	21	:	:	PUNCT
cana-935	30	1	𝑖ħ	𝑖ħ	ADP
cana-935	30	2	𝜕𝛼	𝜕𝛼	NOUN
cana-935	30	3	𝜕𝑡𝛼	𝜕𝑡𝛼	PUNCT
cana-935	31	1	𝛹(𝑟	𝛹(𝑟	ADP
cana-935	31	2	,	,	PUNCT
cana-935	31	3	𝑡	𝑡	NOUN
cana-935	31	4	)	)	PUNCT
cana-935	31	5	=	=	SYM
cana-935	32	1	𝐻	𝐻	PROPN
cana-935	32	2	𝛹(𝑟	𝛹(𝑟	NOUN
cana-935	32	3	,	,	PUNCT
cana-935	32	4	𝑡	𝑡	NOUN
cana-935	32	5	)	)	PUNCT
cana-935	32	6	where	where	SCONJ
cana-935	32	7	α	α	PRON
cana-935	32	8	represents	represent	VERB
cana-935	32	9	the	the	DET
cana-935	32	10	order	order	NOUN
cana-935	32	11	of	of	ADP
cana-935	32	12	the	the	DET
cana-935	32	13	fractional	fractional	ADJ
cana-935	32	14	derivative	derivative	NOUN
cana-935	32	15	.	.	PUNCT
cana-935	33	1	the	the	DET
cana-935	33	2	introduction	introduction	NOUN
cana-935	33	3	of	of	ADP
cana-935	33	4	fractional	fractional	ADJ
cana-935	33	5	derivatives	derivative	NOUN
cana-935	33	6	enables	enable	VERB
cana-935	33	7	a	a	DET
cana-935	33	8	more	more	ADV
cana-935	33	9	accurate	accurate	ADJ
cana-935	33	10	description	description	NOUN
cana-935	33	11	of	of	ADP
cana-935	33	12	the	the	DET
cana-935	33	13	dynamics	dynamic	NOUN
cana-935	33	14	of	of	ADP
cana-935	33	15	complex	complex	ADJ
cana-935	33	16	systems	system	NOUN
cana-935	33	17	,	,	PUNCT
cana-935	33	18	leading	lead	VERB
cana-935	33	19	to	to	ADP
cana-935	33	20	a	a	DET
cana-935	33	21	deeper	deep	ADJ
cana-935	33	22	understanding	understanding	NOUN
cana-935	33	23	of	of	ADP
cana-935	33	24	their	their	PRON
cana-935	33	25	behavior	behavior	NOUN
cana-935	33	26	.	.	PUNCT
cana-935	34	1	let	let	VERB
cana-935	34	2	's	us	PRON
cana-935	34	3	consider	consider	VERB
cana-935	34	4	a	a	DET
cana-935	34	5	fractional	fractional	ADJ
cana-935	34	6	schrödinger	schrödinger	ADJ
cana-935	34	7	equation	equation	NOUN
cana-935	34	8	with	with	ADP
cana-935	34	9	a	a	DET
cana-935	34	10	nonlinear	nonlinear	ADJ
cana-935	34	11	potential	potential	NOUN
cana-935	34	12	and	and	CCONJ
cana-935	34	13	discuss	discuss	VERB
cana-935	34	14	stability	stability	NOUN
cana-935	34	15	analysis	analysis	NOUN
cana-935	34	16	techniques	technique	NOUN
cana-935	34	17	using	use	VERB
cana-935	34	18	equations	equation	NOUN
cana-935	34	19	and	and	CCONJ
cana-935	34	20	examples	example	NOUN
cana-935	34	21	.	.	PUNCT
cana-935	35	1	the	the	DET
cana-935	35	2	fractional	fractional	ADJ
cana-935	35	3	schrödinger	schrödinger	ADJ
cana-935	35	4	equation	equation	NOUN
cana-935	35	5	we	we	PRON
cana-935	35	6	'll	will	AUX
cana-935	35	7	consider	consider	VERB
cana-935	35	8	is	be	AUX
cana-935	35	9	given	give	VERB
cana-935	35	10	by	by	ADP
cana-935	35	11	:	:	PUNCT
cana-935	35	12	𝑖ℏ	𝑖ℏ	PROPN
cana-935	35	13	𝜕	𝜕	PROPN
cana-935	35	14	𝜕𝑡	𝜕𝑡	PROPN
cana-935	35	15	𝜓(𝑥	𝜓(𝑥	PROPN
cana-935	35	16	,	,	PUNCT
cana-935	35	17	𝑡	𝑡	X
cana-935	35	18	)	)	PUNCT
cana-935	35	19	=	=	SYM
cana-935	35	20	−	−	NOUN
cana-935	35	21	ℏ2	ℏ2	NOUN
cana-935	35	22	2𝑚	2𝑚	NOUN
cana-935	35	23	(	(	PUNCT
cana-935	35	24	−𝛥	−𝛥	NUM
cana-935	35	25	)	)	PUNCT
cana-935	35	26	𝛼	𝛼	NOUN
cana-935	35	27	2𝜓(𝑥	2𝜓(𝑥	NOUN
cana-935	35	28	,	,	PUNCT
cana-935	35	29	𝑡	𝑡	X
cana-935	35	30	)	)	PUNCT
cana-935	35	31	+	+	X
cana-935	35	32	𝑉(𝑥)𝜓(𝑥	𝑉(𝑥)𝜓(𝑥	ADJ
cana-935	35	33	,	,	PUNCT
cana-935	35	34	𝑡	𝑡	NOUN
cana-935	35	35	)	)	PUNCT
cana-935	35	36	+	+	CCONJ
cana-935	35	37	𝑔	𝑔	PROPN
cana-935	35	38	∣	∣	ADJ
cana-935	35	39	𝜓(𝑥	𝜓(𝑥	PROPN
cana-935	35	40	,	,	PUNCT
cana-935	35	41	𝑡	𝑡	NOUN
cana-935	35	42	)	)	PUNCT
cana-935	35	43	∣2	∣2	X
cana-935	35	44	𝜓(𝑥	𝜓(𝑥	ADV
cana-935	35	45	,	,	PUNCT
cana-935	35	46	𝑡	𝑡	NOUN
cana-935	35	47	)	)	PUNCT
cana-935	35	48	where	where	SCONJ
cana-935	35	49	:	:	PUNCT
cana-935	35	50	•	•	NUM
cana-935	35	51	ψ(x	ψ(x	PROPN
cana-935	35	52	,	,	PUNCT
cana-935	35	53	t	t	PROPN
cana-935	35	54	)	)	PUNCT
cana-935	35	55	is	be	AUX
cana-935	35	56	the	the	DET
cana-935	35	57	wave	wave	NOUN
cana-935	35	58	function	function	NOUN
cana-935	35	59	.	.	PUNCT
cana-935	36	1	•	•	NUM
cana-935	36	2	ℏ	ℏ	PROPN
cana-935	36	3	is	be	AUX
cana-935	36	4	the	the	DET
cana-935	36	5	reduced	reduce	VERB
cana-935	36	6	planck	planck	NOUN
cana-935	36	7	constant	constant	ADJ
cana-935	36	8	.	.	PUNCT
cana-935	37	1	•	•	NUM
cana-935	37	2	m	m	NOUN
cana-935	37	3	is	be	AUX
cana-935	37	4	the	the	DET
cana-935	37	5	mass	mass	NOUN
cana-935	37	6	of	of	ADP
cana-935	37	7	the	the	DET
cana-935	37	8	particle	particle	NOUN
cana-935	37	9	.	.	PROPN
cana-935	38	1	•	•	NUM
cana-935	38	2	v(x	v(x	PROPN
cana-935	38	3	)	)	PUNCT
cana-935	38	4	is	be	AUX
cana-935	38	5	the	the	DET
cana-935	38	6	potential	potential	ADJ
cana-935	38	7	energy	energy	NOUN
cana-935	38	8	.	.	PUNCT
cana-935	39	1	•	•	NUM
cana-935	39	2	g	g	PROPN
cana-935	39	3	is	be	AUX
cana-935	39	4	the	the	DET
cana-935	39	5	strength	strength	NOUN
cana-935	39	6	of	of	ADP
cana-935	39	7	the	the	DET
cana-935	39	8	nonlinear	nonlinear	ADJ
cana-935	39	9	interaction	interaction	NOUN
cana-935	39	10	.	.	PUNCT
cana-935	40	1	•	•	NUM
cana-935	40	2	α	α	PRON
cana-935	40	3	is	be	AUX
cana-935	40	4	the	the	DET
cana-935	40	5	fractional	fractional	ADJ
cana-935	40	6	order	order	NOUN
cana-935	40	7	of	of	ADP
cana-935	40	8	the	the	DET
cana-935	40	9	laplacian	laplacian	ADJ
cana-935	40	10	operator	operator	NOUN
cana-935	40	11	(	(	PUNCT
cana-935	40	12	−𝛥	−𝛥	NOUN
cana-935	40	13	)	)	PUNCT
cana-935	40	14	𝛼	𝛼	PROPN
cana-935	40	15	2	2	NUM
cana-935	40	16	.	.	PUNCT
cana-935	41	1	now	now	ADV
cana-935	41	2	,	,	PUNCT
cana-935	41	3	let	let	VERB
cana-935	41	4	's	us	PRON
cana-935	41	5	discuss	discuss	VERB
cana-935	41	6	stability	stability	NOUN
cana-935	41	7	analysis	analysis	NOUN
cana-935	41	8	techniques	technique	NOUN
cana-935	41	9	:	:	PUNCT
cana-935	41	10	communications	communication	NOUN
cana-935	41	11	on	on	ADP
cana-935	41	12	applied	apply	VERB
cana-935	41	13	nonlinear	nonlinear	ADJ
cana-935	41	14	analysis	analysis	NOUN
cana-935	41	15	issn	issn	NOUN
cana-935	41	16	:	:	PUNCT
cana-935	41	17	1074	1074	NUM
cana-935	41	18	-	-	PUNCT
cana-935	41	19	133x	133x	NUM
cana-935	41	20	vol	vol	NOUN
cana-935	41	21	31	31	NUM
cana-935	41	22	no	no	NOUN
cana-935	41	23	.	.	PUNCT
cana-935	42	1	4s	4s	NUM
cana-935	42	2	(	(	PUNCT
cana-935	42	3	2024	2024	NUM
cana-935	42	4	)	)	PUNCT
cana-935	42	5	420	420	NUM
cana-935	43	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-935	43	2	2	2	X
cana-935	43	3	.	.	PUNCT
cana-935	44	1	lyapunov	lyapunov	ADJ
cana-935	44	2	stability	stability	NOUN
cana-935	44	3	analysis	analysis	NOUN
cana-935	44	4	:	:	PUNCT
cana-935	44	5	to	to	PART
cana-935	44	6	apply	apply	VERB
cana-935	44	7	lyapunov	lyapunov	ADJ
cana-935	44	8	stability	stability	NOUN
cana-935	44	9	analysis	analysis	NOUN
cana-935	44	10	,	,	PUNCT
cana-935	44	11	we	we	PRON
cana-935	44	12	need	need	VERB
cana-935	44	13	to	to	PART
cana-935	44	14	find	find	VERB
cana-935	44	15	a	a	DET
cana-935	44	16	lyapunov	lyapunov	ADJ
cana-935	44	17	function	function	NOUN
cana-935	44	18	l(ψ	l(ψ	PROPN
cana-935	44	19	)	)	PUNCT
cana-935	44	20	that	that	PRON
cana-935	44	21	characterizes	characterize	VERB
cana-935	44	22	the	the	DET
cana-935	44	23	system	system	NOUN
cana-935	44	24	's	's	PART
cana-935	44	25	energy	energy	NOUN
cana-935	44	26	.	.	PUNCT
cana-935	45	1	for	for	ADP
cana-935	45	2	example	example	NOUN
cana-935	45	3	,	,	PUNCT
cana-935	45	4	we	we	PRON
cana-935	45	5	might	might	AUX
cana-935	45	6	define	define	VERB
cana-935	45	7	the	the	DET
cana-935	45	8	lyapunov	lyapunov	ADJ
cana-935	45	9	function	function	NOUN
cana-935	45	10	as	as	ADP
cana-935	45	11	the	the	DET
cana-935	45	12	norm	norm	NOUN
cana-935	45	13	of	of	ADP
cana-935	45	14	the	the	DET
cana-935	45	15	wave	wave	NOUN
cana-935	45	16	function	function	NOUN
cana-935	45	17	:	:	PUNCT
cana-935	45	18	𝐿(𝜓	𝐿(𝜓	NUM
cana-935	45	19	)	)	PUNCT
cana-935	45	20	=	=	SYM
cana-935	45	21	∫	∫	PROPN
cana-935	45	22	∣	∣	PROPN
cana-935	45	23	𝜓(𝑥	𝜓(𝑥	PROPN
cana-935	45	24	,	,	PUNCT
cana-935	45	25	𝑡	𝑡	NOUN
cana-935	45	26	)	)	PUNCT
cana-935	45	27	∣2	∣2	PRON
cana-935	45	28	𝑑𝑥	𝑑𝑥	VERB
cana-935	45	29	then	then	ADV
cana-935	45	30	,	,	PUNCT
cana-935	45	31	we	we	PRON
cana-935	45	32	analyze	analyze	VERB
cana-935	45	33	the	the	DET
cana-935	45	34	time	time	NOUN
cana-935	45	35	derivative	derivative	NOUN
cana-935	45	36	of	of	ADP
cana-935	45	37	l(ψ	l(ψ	PROPN
cana-935	45	38	)	)	PUNCT
cana-935	45	39	along	along	ADP
cana-935	45	40	the	the	DET
cana-935	45	41	trajectories	trajectory	NOUN
cana-935	45	42	of	of	ADP
cana-935	45	43	the	the	DET
cana-935	45	44	system	system	NOUN
cana-935	45	45	.	.	PUNCT
cana-935	46	1	if	if	SCONJ
cana-935	46	2	𝑑𝐿	𝑑𝐿	ADJ
cana-935	46	3	𝑑𝑡	𝑑𝑡	ADP
cana-935	46	4	≤	≤	NUM
cana-935	46	5	0	0	NUM
cana-935	46	6	,	,	PUNCT
cana-935	46	7	the	the	DET
cana-935	46	8	equilibrium	equilibrium	NOUN
cana-935	46	9	is	be	AUX
cana-935	46	10	stable	stable	ADJ
cana-935	46	11	.	.	PUNCT
cana-935	47	1	3	3	X
cana-935	47	2	.	.	X
cana-935	47	3	energy	energy	NOUN
cana-935	47	4	methods	method	NOUN
cana-935	47	5	:	:	PUNCT
cana-935	47	6	we	we	PRON
cana-935	47	7	define	define	VERB
cana-935	47	8	the	the	DET
cana-935	47	9	energy	energy	NOUN
cana-935	47	10	functional	functional	ADJ
cana-935	47	11	for	for	ADP
cana-935	47	12	the	the	DET
cana-935	47	13	system	system	NOUN
cana-935	47	14	,	,	PUNCT
cana-935	47	15	typically	typically	ADV
cana-935	47	16	as	as	ADP
cana-935	47	17	a	a	DET
cana-935	47	18	sum	sum	NOUN
cana-935	47	19	of	of	ADP
cana-935	47	20	kinetic	kinetic	ADJ
cana-935	47	21	and	and	CCONJ
cana-935	47	22	potential	potential	ADJ
cana-935	47	23	energies	energy	NOUN
cana-935	47	24	.	.	PUNCT
cana-935	48	1	for	for	ADP
cana-935	48	2	example	example	NOUN
cana-935	48	3	:	:	PUNCT
cana-935	48	4	𝐸(𝜓	𝐸(𝜓	X
cana-935	48	5	)	)	PUNCT
cana-935	48	6	=	=	SYM
cana-935	49	1	∫	∫	PROPN
cana-935	49	2	[	[	PUNCT
cana-935	49	3	ℏ2	ℏ2	NOUN
cana-935	49	4	2𝑚	2𝑚	NUM
cana-935	49	5	∣	∣	ADJ
cana-935	49	6	∣	∣	ADJ
cana-935	49	7	∣	∣	ADJ
cana-935	49	8	𝛻𝜓(𝑥	𝛻𝜓(𝑥	NUM
cana-935	49	9	,	,	PUNCT
cana-935	49	10	𝑡	𝑡	NOUN
cana-935	49	11	)	)	PUNCT
cana-935	49	12	∣2	∣2	NOUN
cana-935	50	1	+	+	CCONJ
cana-935	50	2	𝑉(𝑥	𝑉(𝑥	X
cana-935	50	3	)	)	PUNCT
cana-935	50	4	∣	∣	ADJ
cana-935	50	5	∣	∣	ADJ
cana-935	50	6	∣	∣	ADJ
cana-935	50	7	𝜓(𝑥	𝜓(𝑥	ADV
cana-935	50	8	,	,	PUNCT
cana-935	50	9	𝑡	𝑡	NOUN
cana-935	50	10	)	)	PUNCT
cana-935	50	11	∣2	∣2	NOUN
cana-935	51	1	+	+	CCONJ
cana-935	51	2	𝑔	𝑔	PROPN
cana-935	51	3	2	2	NUM
cana-935	51	4	∣	∣	ADJ
cana-935	51	5	∣	∣	ADJ
cana-935	51	6	∣	∣	ADJ
cana-935	51	7	𝜓(𝑥	𝜓(𝑥	ADV
cana-935	51	8	,	,	PUNCT
cana-935	51	9	𝑡	𝑡	NOUN
cana-935	51	10	)	)	PUNCT
cana-935	51	11	∣4	∣4	NOUN
cana-935	51	12	]	]	PUNCT
cana-935	51	13	𝑑𝑥	𝑑𝑥	VERB
cana-935	51	14	then	then	ADV
cana-935	51	15	,	,	PUNCT
cana-935	51	16	we	we	PRON
cana-935	51	17	analyze	analyze	VERB
cana-935	51	18	the	the	DET
cana-935	51	19	time	time	NOUN
cana-935	51	20	derivative	derivative	ADJ
cana-935	51	21	of	of	ADP
cana-935	51	22	e(ψ	e(ψ	NOUN
cana-935	51	23	)	)	PUNCT
cana-935	51	24	under	under	ADP
cana-935	51	25	perturbations	perturbation	NOUN
cana-935	51	26	to	to	PART
cana-935	51	27	assess	assess	VERB
cana-935	51	28	stability	stability	NOUN
cana-935	51	29	.	.	PUNCT
cana-935	52	1	4	4	X
cana-935	52	2	.	.	X
cana-935	52	3	spectral	spectral	ADJ
cana-935	52	4	analysis	analysis	NOUN
cana-935	52	5	:	:	PUNCT
cana-935	52	6	we	we	PRON
cana-935	52	7	linearize	linearize	VERB
cana-935	52	8	the	the	DET
cana-935	52	9	equation	equation	NOUN
cana-935	52	10	around	around	ADP
cana-935	52	11	equilibrium	equilibrium	NOUN
cana-935	52	12	solutions	solution	NOUN
cana-935	52	13	and	and	CCONJ
cana-935	52	14	study	study	VERB
cana-935	52	15	the	the	DET
cana-935	52	16	eigenvalues	eigenvalue	NOUN
cana-935	52	17	of	of	ADP
cana-935	52	18	the	the	DET
cana-935	52	19	linearized	linearize	VERB
cana-935	52	20	operator	operator	NOUN
cana-935	52	21	.	.	PUNCT
cana-935	53	1	for	for	ADP
cana-935	53	2	example	example	NOUN
cana-935	53	3	,	,	PUNCT
cana-935	53	4	linearizing	linearize	VERB
cana-935	53	5	around	around	ADP
cana-935	53	6	the	the	DET
cana-935	53	7	stationary	stationary	ADJ
cana-935	53	8	solution	solution	NOUN
cana-935	53	9	ψ0(x	ψ0(x	NUM
cana-935	53	10	)	)	PUNCT
cana-935	53	11	,	,	PUNCT
cana-935	53	12	we	we	PRON
cana-935	53	13	obtain	obtain	VERB
cana-935	53	14	:	:	PUNCT
cana-935	53	15	𝑖ℏ	𝑖ℏ	ADP
cana-935	54	1	𝜕	𝜕	PROPN
cana-935	54	2	𝜕𝑡	𝜕𝑡	PROPN
cana-935	54	3	𝛿𝜓(𝑥	𝛿𝜓(𝑥	NOUN
cana-935	54	4	,	,	PUNCT
cana-935	54	5	𝑡	𝑡	X
cana-935	54	6	)	)	PUNCT
cana-935	54	7	=	=	SYM
cana-935	55	1	−	−	NOUN
cana-935	55	2	ℏ2	ℏ2	NOUN
cana-935	55	3	2𝑚	2𝑚	NOUN
cana-935	55	4	(	(	PUNCT
cana-935	55	5	−𝛥	−𝛥	NUM
cana-935	55	6	)	)	PUNCT
cana-935	55	7	𝛼	𝛼	NOUN
cana-935	55	8	2𝛿𝜓(𝑥	2𝛿𝜓(𝑥	PROPN
cana-935	55	9	,	,	PUNCT
cana-935	55	10	𝑡	𝑡	X
cana-935	55	11	)	)	PUNCT
cana-935	55	12	+	+	CCONJ
cana-935	55	13	[	[	PUNCT
cana-935	55	14	𝑉(𝑥	𝑉(𝑥	PROPN
cana-935	55	15	)	)	PUNCT
cana-935	55	16	+	+	CCONJ
cana-935	55	17	2𝑔	2𝑔	NUM
cana-935	55	18	∣∣	∣∣	NUM
cana-935	55	19	𝜓0(𝑥	𝜓0(𝑥	NUM
cana-935	55	20	)	)	PUNCT
cana-935	55	21	∣2	∣2	PRON
cana-935	55	22	]	]	X
cana-935	55	23	𝛿𝜓(𝑥	𝛿𝜓(𝑥	X
cana-935	55	24	,	,	PUNCT
cana-935	55	25	𝑡	𝑡	NOUN
cana-935	55	26	)	)	PUNCT
cana-935	55	27	then	then	ADV
cana-935	55	28	,	,	PUNCT
cana-935	55	29	we	we	PRON
cana-935	55	30	analyze	analyze	VERB
cana-935	55	31	the	the	DET
cana-935	55	32	spectrum	spectrum	NOUN
cana-935	55	33	of	of	ADP
cana-935	55	34	the	the	DET
cana-935	55	35	linear	linear	ADJ
cana-935	55	36	operator	operator	NOUN
cana-935	55	37	to	to	PART
cana-935	55	38	determine	determine	VERB
cana-935	55	39	stability	stability	NOUN
cana-935	55	40	.	.	PUNCT
cana-935	56	1	these	these	DET
cana-935	56	2	techniques	technique	NOUN
cana-935	56	3	provide	provide	VERB
cana-935	56	4	insights	insight	NOUN
cana-935	56	5	into	into	ADP
cana-935	56	6	the	the	DET
cana-935	56	7	stability	stability	NOUN
cana-935	56	8	properties	property	NOUN
cana-935	56	9	of	of	ADP
cana-935	56	10	solutions	solution	NOUN
cana-935	56	11	to	to	PART
cana-935	56	12	fractional	fractional	ADJ
cana-935	56	13	schrödinger	schrödinger	ADJ
cana-935	56	14	equations	equation	NOUN
cana-935	56	15	,	,	PUNCT
cana-935	56	16	helping	help	VERB
cana-935	56	17	us	we	PRON
cana-935	56	18	understand	understand	VERB
cana-935	56	19	the	the	DET
cana-935	56	20	long	long	ADJ
cana-935	56	21	-	-	PUNCT
cana-935	56	22	term	term	NOUN
cana-935	56	23	behavior	behavior	NOUN
cana-935	56	24	of	of	ADP
cana-935	56	25	quantum	quantum	NOUN
cana-935	56	26	systems	system	NOUN
cana-935	56	27	subjected	subject	VERB
cana-935	56	28	to	to	ADP
cana-935	56	29	nonlinear	nonlinear	ADJ
cana-935	56	30	potentials	potential	NOUN
cana-935	56	31	and	and	CCONJ
cana-935	56	32	fractional	fractional	ADJ
cana-935	56	33	derivatives	derivative	NOUN
cana-935	56	34	now	now	ADV
cana-935	56	35	we	we	PRON
cana-935	56	36	see	see	VERB
cana-935	56	37	how	how	SCONJ
cana-935	56	38	stability	stability	NOUN
cana-935	56	39	analysis	analysis	NOUN
cana-935	56	40	techniques	technique	NOUN
cana-935	56	41	can	can	AUX
cana-935	56	42	be	be	AUX
cana-935	56	43	applied	apply	VERB
cana-935	56	44	to	to	PART
cana-935	56	45	analyze	analyze	VERB
cana-935	56	46	the	the	DET
cana-935	56	47	stability	stability	NOUN
cana-935	56	48	of	of	ADP
cana-935	56	49	solutions	solution	NOUN
cana-935	56	50	to	to	PART
cana-935	56	51	fractional	fractional	VERB
cana-935	56	52	schrödinger	schrödinger	ADJ
cana-935	56	53	equations	equation	NOUN
cana-935	56	54	.	.	PUNCT
cana-935	57	1	example	example	NOUN
cana-935	57	2	:	:	PUNCT
cana-935	57	3	consider	consider	VERB
cana-935	57	4	a	a	DET
cana-935	57	5	one	one	NUM
cana-935	57	6	-	-	PUNCT
cana-935	57	7	dimensional	dimensional	ADJ
cana-935	57	8	quantum	quantum	ADJ
cana-935	57	9	harmonic	harmonic	NOUN
cana-935	57	10	oscillator	oscillator	NOUN
cana-935	57	11	with	with	ADP
cana-935	57	12	a	a	DET
cana-935	57	13	cubic	cubic	ADJ
cana-935	57	14	nonlinearity	nonlinearity	NOUN
cana-935	57	15	,	,	PUNCT
cana-935	57	16	described	describe	VERB
cana-935	57	17	by	by	ADP
cana-935	57	18	the	the	DET
cana-935	57	19	fractional	fractional	ADJ
cana-935	57	20	schrödinger	schrödinger	ADJ
cana-935	57	21	equation	equation	NOUN
cana-935	57	22	:	:	PUNCT
cana-935	57	23	𝑖ℏ	𝑖ℏ	PROPN
cana-935	57	24	𝜕	𝜕	PROPN
cana-935	57	25	𝜕𝑡	𝜕𝑡	PROPN
cana-935	57	26	𝜓(𝑥	𝜓(𝑥	PROPN
cana-935	57	27	,	,	PUNCT
cana-935	57	28	𝑡	𝑡	X
cana-935	57	29	)	)	PUNCT
cana-935	57	30	=	=	SYM
cana-935	58	1	−	−	NOUN
cana-935	58	2	ℏ2	ℏ2	NOUN
cana-935	58	3	2𝑚	2𝑚	NOUN
cana-935	58	4	(	(	PUNCT
cana-935	58	5	−	−	PROPN
cana-935	58	6	𝜕2	𝜕2	NOUN
cana-935	58	7	𝜕𝑥2	𝜕𝑥2	NOUN
cana-935	58	8	)	)	PUNCT
cana-935	59	1	𝛼	𝛼	PROPN
cana-935	59	2	2𝜓(𝑥	2𝜓(𝑥	NOUN
cana-935	59	3	,	,	PUNCT
cana-935	59	4	𝑡	𝑡	X
cana-935	59	5	)	)	PUNCT
cana-935	59	6	+	+	CCONJ
cana-935	59	7	1	1	NUM
cana-935	59	8	2	2	NUM
cana-935	59	9	𝑚𝜔2𝑥2𝜓(𝑥	𝑚𝜔2𝑥2𝜓(𝑥	NUM
cana-935	59	10	,	,	PUNCT
cana-935	59	11	𝑡	𝑡	NOUN
cana-935	59	12	)	)	PUNCT
cana-935	59	13	+	+	CCONJ
cana-935	59	14	𝑔	𝑔	PROPN
cana-935	59	15	∣	∣	ADJ
cana-935	59	16	𝜓(𝑥	𝜓(𝑥	PROPN
cana-935	59	17	,	,	PUNCT
cana-935	59	18	𝑡	𝑡	NOUN
cana-935	59	19	)	)	PUNCT
cana-935	59	20	∣2	∣2	X
cana-935	59	21	𝜓(𝑥	𝜓(𝑥	ADV
cana-935	59	22	,	,	PUNCT
cana-935	59	23	𝑡	𝑡	NOUN
cana-935	59	24	)	)	PUNCT
cana-935	59	25	where	where	SCONJ
cana-935	59	26	α	α	NOUN
cana-935	59	27	is	be	AUX
cana-935	59	28	the	the	DET
cana-935	59	29	fractional	fractional	ADJ
cana-935	59	30	order	order	NOUN
cana-935	59	31	of	of	ADP
cana-935	59	32	the	the	DET
cana-935	59	33	derivative	derivative	NOUN
cana-935	59	34	,	,	PUNCT
cana-935	59	35	ℏ	ℏ	PROPN
cana-935	59	36	is	be	AUX
cana-935	59	37	the	the	DET
cana-935	59	38	reduced	reduce	VERB
cana-935	59	39	planck	planck	NOUN
cana-935	59	40	constant	constant	ADJ
cana-935	59	41	,	,	PUNCT
cana-935	59	42	m	m	VERB
cana-935	59	43	is	be	AUX
cana-935	59	44	the	the	DET
cana-935	59	45	mass	mass	NOUN
cana-935	59	46	of	of	ADP
cana-935	59	47	the	the	DET
cana-935	59	48	particle	particle	NOUN
cana-935	59	49	,	,	PUNCT
cana-935	59	50	ω	ω	PROPN
cana-935	59	51	is	be	AUX
cana-935	59	52	the	the	DET
cana-935	59	53	frequency	frequency	NOUN
cana-935	59	54	of	of	ADP
cana-935	59	55	the	the	DET
cana-935	59	56	harmonic	harmonic	ADJ
cana-935	59	57	oscillator	oscillator	NOUN
cana-935	59	58	potential	potential	NOUN
cana-935	59	59	,	,	PUNCT
cana-935	59	60	and	and	CCONJ
cana-935	59	61	g	g	NOUN
cana-935	59	62	is	be	AUX
cana-935	59	63	the	the	DET
cana-935	59	64	strength	strength	NOUN
cana-935	59	65	of	of	ADP
cana-935	59	66	the	the	DET
cana-935	59	67	cubic	cubic	ADJ
cana-935	59	68	nonlinearity	nonlinearity	NOUN
cana-935	59	69	.	.	PUNCT
cana-935	60	1	lyapunov	lyapunov	ADJ
cana-935	60	2	stability	stability	NOUN
cana-935	60	3	analysis	analysis	NOUN
cana-935	60	4	:	:	PUNCT
cana-935	60	5	technique	technique	NOUN
cana-935	60	6	:	:	PUNCT
cana-935	60	7	focuses	focus	VERB
cana-935	60	8	on	on	ADP
cana-935	60	9	finding	find	VERB
cana-935	60	10	a	a	DET
cana-935	60	11	lyapunov	lyapunov	NOUN
cana-935	60	12	function	function	NOUN
cana-935	60	13	v(ψ	v(ψ	ADV
cana-935	60	14	)	)	PUNCT
cana-935	60	15	that	that	PRON
cana-935	60	16	ensures	ensure	VERB
cana-935	60	17	the	the	DET
cana-935	60	18	stability	stability	NOUN
cana-935	60	19	of	of	ADP
cana-935	60	20	the	the	DET
cana-935	60	21	system	system	NOUN
cana-935	60	22	.	.	PUNCT
cana-935	61	1	approach	approach	NOUN
cana-935	61	2	:	:	PUNCT
cana-935	61	3	seek	seek	VERB
cana-935	61	4	a	a	DET
cana-935	61	5	function	function	NOUN
cana-935	61	6	whose	whose	DET
cana-935	61	7	derivative	derivative	NOUN
cana-935	61	8	with	with	ADP
cana-935	61	9	respect	respect	NOUN
cana-935	61	10	to	to	ADP
cana-935	61	11	time	time	NOUN
cana-935	61	12	is	be	AUX
cana-935	61	13	negative	negative	ADJ
cana-935	61	14	or	or	CCONJ
cana-935	61	15	non	non	ADJ
cana-935	61	16	-	-	ADJ
cana-935	61	17	positive	positive	ADJ
cana-935	61	18	,	,	PUNCT
cana-935	61	19	indicating	indicate	VERB
cana-935	61	20	stability	stability	NOUN
cana-935	61	21	.	.	PUNCT
cana-935	62	1	for	for	ADP
cana-935	62	2	the	the	DET
cana-935	62	3	fractional	fractional	ADJ
cana-935	62	4	schrödinger	schrödinger	ADJ
cana-935	62	5	equation	equation	NOUN
cana-935	62	6	:	:	PUNCT
cana-935	62	7	𝑖	𝑖	SYM
cana-935	62	8	𝜕	𝜕	PROPN
cana-935	62	9	𝜕𝑡	𝜕𝑡	PROPN
cana-935	62	10	𝜓(𝑥	𝜓(𝑥	PROPN
cana-935	62	11	,	,	PUNCT
cana-935	62	12	𝑡	𝑡	NOUN
cana-935	62	13	)	)	PUNCT
cana-935	62	14	=	=	SYM
cana-935	62	15	−(−𝛥	−(−𝛥	X
cana-935	62	16	)	)	PUNCT
cana-935	62	17	𝛼	𝛼	PRON
cana-935	62	18	2𝜓(𝑥	2𝜓(𝑥	NUM
cana-935	62	19	,	,	PUNCT
cana-935	62	20	𝑡	𝑡	X
cana-935	62	21	)	)	PUNCT
cana-935	62	22	+	+	X
cana-935	62	23	𝑉(𝑥)𝜓(𝑥	𝑉(𝑥)𝜓(𝑥	ADJ
cana-935	62	24	,	,	PUNCT
cana-935	62	25	𝑡	𝑡	NOUN
cana-935	62	26	)	)	PUNCT
cana-935	62	27	communications	communication	NOUN
cana-935	62	28	on	on	ADP
cana-935	62	29	applied	apply	VERB
cana-935	62	30	nonlinear	nonlinear	ADJ
cana-935	62	31	analysis	analysis	NOUN
cana-935	62	32	issn	issn	NOUN
cana-935	62	33	:	:	PUNCT
cana-935	62	34	1074	1074	NUM
cana-935	62	35	-	-	PUNCT
cana-935	62	36	133x	133x	NUM
cana-935	62	37	vol	vol	NOUN
cana-935	62	38	31	31	NUM
cana-935	62	39	no	no	NOUN
cana-935	62	40	.	.	PUNCT
cana-935	63	1	4s	4s	NUM
cana-935	63	2	(	(	PUNCT
cana-935	63	3	2024	2024	NUM
cana-935	63	4	)	)	PUNCT
cana-935	63	5	421	421	NUM
cana-935	63	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-935	63	7	we	we	PRON
cana-935	63	8	aim	aim	VERB
cana-935	63	9	to	to	PART
cana-935	63	10	find	find	VERB
cana-935	63	11	a	a	DET
cana-935	63	12	lyapunov	lyapunov	NOUN
cana-935	63	13	function	function	NOUN
cana-935	63	14	v(ψ	v(ψ	ADV
cana-935	63	15	)	)	PUNCT
cana-935	63	16	such	such	ADJ
cana-935	63	17	that	that	SCONJ
cana-935	63	18	v˙(ψ	v˙(ψ	ADJ
cana-935	63	19	)	)	PUNCT
cana-935	63	20	≤	≤	NOUN
cana-935	63	21	0	0	NUM
cana-935	63	22	,	,	PUNCT
cana-935	63	23	where	where	SCONJ
cana-935	63	24	v˙(ψ	v˙(ψ	ADJ
cana-935	63	25	)	)	PUNCT
cana-935	63	26	=	=	SYM
cana-935	64	1	𝑑𝑉(𝜓	𝑑𝑉(𝜓	NUM
cana-935	64	2	)	)	PUNCT
cana-935	64	3	𝑑𝑡	𝑑𝑡	ADP
cana-935	64	4	.	.	PUNCT
cana-935	64	5	example	example	NOUN
cana-935	64	6	lyapunov	lyapunov	PROPN
cana-935	64	7	function	function	NOUN
cana-935	64	8	:	:	PUNCT
cana-935	64	9	let	let	VERB
cana-935	64	10	's	us	PRON
cana-935	64	11	consider	consider	VERB
cana-935	64	12	𝑉(𝜓	𝑉(𝜓	PRON
cana-935	64	13	)	)	PUNCT
cana-935	64	14	=	=	SYM
cana-935	65	1	∫	∫	PROPN
cana-935	66	1	|𝜓(𝑥)|2𝑑𝑥.	|𝜓(𝑥)|2𝑑𝑥.	PROPN
cana-935	66	2	taking	take	VERB
cana-935	66	3	the	the	DET
cana-935	66	4	time	time	NOUN
cana-935	66	5	derivative	derivative	ADJ
cana-935	66	6	:	:	PUNCT
cana-935	66	7	𝛻𝑉(𝜓	𝛻𝑉(𝜓	PROPN
cana-935	66	8	)	)	PUNCT
cana-935	66	9	=	=	SYM
cana-935	66	10	𝑑	𝑑	PROPN
cana-935	66	11	𝑑𝑡	𝑑𝑡	ADP
cana-935	66	12	∫	∫	PROPN
cana-935	66	13	|𝜓(𝑥)|2𝑑𝑥	|𝜓(𝑥)|2𝑑𝑥	PROPN
cana-935	66	14	using	use	VERB
cana-935	66	15	the	the	DET
cana-935	66	16	fractional	fractional	ADJ
cana-935	66	17	schrödinger	schrödinger	ADJ
cana-935	66	18	equation	equation	NOUN
cana-935	66	19	𝑖	𝑖	SYM
cana-935	66	20	𝜕	𝜕	PROPN
cana-935	66	21	𝜕𝑡	𝜕𝑡	PROPN
cana-935	66	22	𝜓(𝑥	𝜓(𝑥	PROPN
cana-935	66	23	,	,	PUNCT
cana-935	66	24	𝑡	𝑡	NOUN
cana-935	66	25	)	)	PUNCT
cana-935	66	26	=	=	SYM
cana-935	66	27	−(−𝛥	−(−𝛥	X
cana-935	66	28	)	)	PUNCT
cana-935	66	29	𝛼	𝛼	PRON
cana-935	66	30	2𝜓(𝑥	2𝜓(𝑥	NUM
cana-935	66	31	,	,	PUNCT
cana-935	66	32	𝑡	𝑡	X
cana-935	66	33	)	)	PUNCT
cana-935	66	34	+	+	X
cana-935	66	35	𝑉(𝑥)𝜓(𝑥	𝑉(𝑥)𝜓(𝑥	ADJ
cana-935	66	36	,	,	PUNCT
cana-935	66	37	𝑡	𝑡	PROPN
cana-935	66	38	)	)	PUNCT
cana-935	66	39	and	and	CCONJ
cana-935	66	40	its	its	PRON
cana-935	66	41	complex	complex	ADJ
cana-935	66	42	conjugate	conjugate	NOUN
cana-935	66	43	,	,	PUNCT
cana-935	66	44	then	then	ADV
cana-935	66	45	multiplying	multiply	VERB
cana-935	66	46	both	both	CCONJ
cana-935	66	47	by	by	ADP
cana-935	66	48	ψ	ψ	X
cana-935	66	49	*	*	PUNCT
cana-935	66	50	,	,	PUNCT
cana-935	66	51	integrating	integrate	VERB
cana-935	66	52	over	over	ADP
cana-935	66	53	x	x	NOUN
cana-935	66	54	,	,	PUNCT
cana-935	66	55	and	and	CCONJ
cana-935	66	56	adding	add	VERB
cana-935	66	57	them	they	PRON
cana-935	66	58	:	:	PUNCT
cana-935	66	59	𝑉˙(𝜓	𝑉˙(𝜓	PROPN
cana-935	66	60	)	)	PUNCT
cana-935	66	61	=	=	SYM
cana-935	66	62	∫	∫	PROPN
cana-935	66	63	(	(	PUNCT
cana-935	66	64	𝜓∗𝑖	𝜓∗𝑖	PROPN
cana-935	66	65	𝜕	𝜕	PROPN
cana-935	66	66	𝑡𝜕	𝑡𝜕	PROPN
cana-935	66	67	𝜓	𝜓	PROPN
cana-935	66	68	+	+	CCONJ
cana-935	66	69	𝜓	𝜓	X
cana-935	66	70	(	(	PUNCT
cana-935	66	71	−𝑖	−𝑖	PROPN
cana-935	66	72	𝜕	𝜕	PROPN
cana-935	66	73	𝑡𝜕	𝑡𝜕	PROPN
cana-935	66	74	𝜓	𝜓	NOUN
cana-935	66	75	∗	∗	NOUN
cana-935	66	76	)	)	PUNCT
cana-935	66	77	)	)	PUNCT
cana-935	66	78	𝑑𝑥	𝑑𝑥	VERB
cana-935	66	79	=	=	SYM
cana-935	66	80	𝑖	𝑖	SYM
cana-935	66	81	∫	∫	PROPN
cana-935	66	82	(	(	PUNCT
cana-935	66	83	𝜓∗	𝜓∗	PROPN
cana-935	66	84	𝜕𝜓	𝜕𝜓	NOUN
cana-935	66	85	𝑡𝜕	𝑡𝜕	NOUN
cana-935	66	86	−	−	PROPN
cana-935	66	87	𝜓	𝜓	PROPN
cana-935	66	88	𝜕𝜓	𝜕𝜓	NOUN
cana-935	66	89	∗	∗	NOUN
cana-935	66	90	𝑡𝜕	𝑡𝜕	NOUN
cana-935	66	91	)	)	PUNCT
cana-935	66	92	𝑑𝑥	𝑑𝑥	VERB
cana-935	66	93	=	=	PUNCT
cana-935	66	94	𝑖	𝑖	PROPN
cana-935	66	95	𝑑	𝑑	NOUN
cana-935	66	96	𝑡𝑑	𝑡𝑑	NOUN
cana-935	66	97	∫(|(𝑥)|2	∫(|(𝑥)|2	NOUN
cana-935	66	98	)	)	PUNCT
cana-935	66	99	𝑑𝑥	𝑑𝑥	SCONJ
cana-935	66	100	this	this	PRON
cana-935	66	101	indicates	indicate	VERB
cana-935	66	102	that	that	SCONJ
cana-935	66	103	𝑉(𝜓	𝑉(𝜓	ADP
cana-935	66	104	)	)	PUNCT
cana-935	66	105	=	=	SYM
cana-935	66	106	∫	∫	PROPN
cana-935	66	107	|𝜓(𝑥)|	|𝜓(𝑥)|	PROPN
cana-935	66	108	2𝑑𝑥	2𝑑𝑥	NOUN
cana-935	66	109	might	might	AUX
cana-935	66	110	not	not	PART
cana-935	66	111	be	be	AUX
cana-935	66	112	suitable	suitable	ADJ
cana-935	66	113	as	as	ADP
cana-935	66	114	a	a	DET
cana-935	66	115	lyapunov	lyapunov	ADJ
cana-935	66	116	function	function	NOUN
cana-935	66	117	for	for	ADP
cana-935	66	118	this	this	DET
cana-935	66	119	system	system	NOUN
cana-935	66	120	.	.	PUNCT
cana-935	67	1	energy	energy	NOUN
cana-935	67	2	methods	method	NOUN
cana-935	67	3	:	:	PUNCT
cana-935	67	4	technique	technique	NOUN
cana-935	67	5	:	:	PUNCT
cana-935	67	6	defines	define	VERB
cana-935	67	7	an	an	DET
cana-935	67	8	energy	energy	NOUN
cana-935	67	9	functional	functional	ADJ
cana-935	67	10	e[ψ	e[ψ	NOUN
cana-935	67	11	]	]	PUNCT
cana-935	67	12	and	and	CCONJ
cana-935	67	13	examines	examine	VERB
cana-935	67	14	its	its	PRON
cana-935	67	15	evolution	evolution	NOUN
cana-935	67	16	over	over	ADP
cana-935	67	17	time	time	NOUN
cana-935	67	18	.	.	PUNCT
cana-935	68	1	approach	approach	NOUN
cana-935	68	2	:	:	PUNCT
cana-935	68	3	the	the	DET
cana-935	68	4	energy	energy	NOUN
cana-935	68	5	should	should	AUX
cana-935	68	6	remain	remain	VERB
cana-935	68	7	bounded	bounded	ADJ
cana-935	68	8	or	or	CCONJ
cana-935	68	9	decrease	decrease	VERB
cana-935	68	10	over	over	ADP
cana-935	68	11	time	time	NOUN
cana-935	68	12	for	for	ADP
cana-935	68	13	stability	stability	NOUN
cana-935	68	14	.	.	PUNCT
cana-935	69	1	for	for	ADP
cana-935	69	2	the	the	DET
cana-935	69	3	fractional	fractional	ADJ
cana-935	69	4	schrödinger	schrödinger	ADJ
cana-935	69	5	equation	equation	NOUN
cana-935	69	6	:	:	PUNCT
cana-935	69	7	𝑖	𝑖	SYM
cana-935	69	8	𝜕	𝜕	PROPN
cana-935	69	9	𝜕𝑡	𝜕𝑡	PROPN
cana-935	69	10	𝜓(𝑥	𝜓(𝑥	PROPN
cana-935	69	11	,	,	PUNCT
cana-935	69	12	𝑡	𝑡	NOUN
cana-935	69	13	)	)	PUNCT
cana-935	69	14	=	=	SYM
cana-935	69	15	−(−𝛥	−(−𝛥	X
cana-935	69	16	)	)	PUNCT
cana-935	70	1	𝛼	𝛼	PRON
cana-935	70	2	2𝜓(𝑥	2𝜓(𝑥	NUM
cana-935	70	3	,	,	PUNCT
cana-935	70	4	𝑡	𝑡	X
cana-935	70	5	)	)	PUNCT
cana-935	70	6	+	+	X
cana-935	70	7	𝑉(𝑥)𝜓(𝑥	𝑉(𝑥)𝜓(𝑥	ADJ
cana-935	70	8	,	,	PUNCT
cana-935	70	9	𝑡	𝑡	NOUN
cana-935	70	10	)	)	PUNCT
cana-935	70	11	we	we	PRON
cana-935	70	12	define	define	VERB
cana-935	70	13	the	the	DET
cana-935	70	14	energy	energy	NOUN
cana-935	70	15	functional	functional	ADJ
cana-935	70	16	as	as	ADP
cana-935	70	17	:	:	PUNCT
cana-935	70	18	𝐸[𝜓	𝐸[𝜓	NOUN
cana-935	70	19	]	]	X
cana-935	70	20	=	=	SYM
cana-935	70	21	∫	∫	PROPN
cana-935	70	22	|𝛻𝜓|2	|𝛻𝜓|2	NOUN
cana-935	71	1	+	+	SYM
cana-935	71	2	𝑉(𝑥)|𝜓|2	𝑉(𝑥)|𝜓|2	NOUN
cana-935	71	3	r𝑛	r𝑛	NOUN
cana-935	71	4	𝑑𝑥	𝑑𝑥	VERB
cana-935	71	5	evolution	evolution	NOUN
cana-935	71	6	of	of	ADP
cana-935	71	7	energy	energy	NOUN
cana-935	71	8	:	:	PUNCT
cana-935	71	9	we	we	PRON
cana-935	71	10	compute	compute	VERB
cana-935	71	11	the	the	DET
cana-935	71	12	time	time	NOUN
cana-935	71	13	derivative	derivative	NOUN
cana-935	71	14	of	of	ADP
cana-935	71	15	the	the	DET
cana-935	71	16	energy	energy	NOUN
cana-935	71	17	:	:	PUNCT
cana-935	71	18	𝑑𝐸	𝑑𝐸	ADV
cana-935	71	19	𝑑𝑡	𝑑𝑡	SCONJ
cana-935	71	20	=	=	PROPN
cana-935	71	21	𝑑	𝑑	PROPN
cana-935	71	22	𝑑𝑡	𝑑𝑡	ADP
cana-935	71	23	∫	∫	PROPN
cana-935	71	24	|𝛻𝜓|2	|𝛻𝜓|2	PROPN
cana-935	71	25	+	+	SYM
cana-935	71	26	𝑉(𝑥)|𝜓|2	𝑉(𝑥)|𝜓|2	NOUN
cana-935	71	27	r𝑛	r𝑛	NOUN
cana-935	71	28	𝑑𝑥	𝑑𝑥	VERB
cana-935	71	29	using	use	VERB
cana-935	71	30	the	the	DET
cana-935	71	31	fractional	fractional	ADJ
cana-935	71	32	schrödinger	schrödinger	ADJ
cana-935	71	33	equation	equation	NOUN
cana-935	71	34	and	and	CCONJ
cana-935	71	35	its	its	PRON
cana-935	71	36	complex	complex	ADJ
cana-935	71	37	conjugate	conjugate	NOUN
cana-935	71	38	,	,	PUNCT
cana-935	71	39	we	we	PRON
cana-935	71	40	can	can	AUX
cana-935	71	41	express	express	VERB
cana-935	71	42	the	the	DET
cana-935	71	43	time	time	NOUN
cana-935	71	44	derivative	derivative	ADJ
cana-935	71	45	as	as	ADP
cana-935	71	46	:	:	PUNCT
cana-935	71	47	𝑑𝐸	𝑑𝐸	PROPN
cana-935	71	48	𝑑𝑡	𝑑𝑡	ADP
cana-935	71	49	=	=	SYM
cana-935	71	50	0	0	PROPN
cana-935	71	51	this	this	PRON
cana-935	71	52	indicates	indicate	VERB
cana-935	71	53	that	that	SCONJ
cana-935	71	54	the	the	DET
cana-935	71	55	energy	energy	NOUN
cana-935	71	56	remains	remain	VERB
cana-935	71	57	conserved	conserve	VERB
cana-935	71	58	over	over	ADP
cana-935	71	59	time	time	NOUN
cana-935	71	60	,	,	PUNCT
cana-935	71	61	suggesting	suggest	VERB
cana-935	71	62	stability	stability	NOUN
cana-935	71	63	.	.	PUNCT
cana-935	72	1	spectral	spectral	ADJ
cana-935	72	2	analysis	analysis	NOUN
cana-935	72	3	:	:	PUNCT
cana-935	72	4	technique	technique	NOUN
cana-935	72	5	:	:	PUNCT
cana-935	72	6	analyzes	analyze	VERB
cana-935	72	7	the	the	DET
cana-935	72	8	eigenvalues	eigenvalue	NOUN
cana-935	72	9	of	of	ADP
cana-935	72	10	the	the	DET
cana-935	72	11	linearized	linearize	VERB
cana-935	72	12	system	system	NOUN
cana-935	72	13	around	around	ADP
cana-935	72	14	equilibrium	equilibrium	NOUN
cana-935	72	15	.	.	PUNCT
cana-935	73	1	approach	approach	NOUN
cana-935	73	2	:	:	PUNCT
cana-935	73	3	stability	stability	NOUN
cana-935	73	4	determined	determine	VERB
cana-935	73	5	by	by	ADP
cana-935	73	6	the	the	DET
cana-935	73	7	real	real	ADJ
cana-935	73	8	parts	part	NOUN
cana-935	73	9	of	of	ADP
cana-935	73	10	eigenvalues	eigenvalue	NOUN
cana-935	73	11	;	;	PUNCT
cana-935	73	12	negative	negative	ADJ
cana-935	73	13	real	real	ADJ
cana-935	73	14	parts	part	NOUN
cana-935	73	15	indicate	indicate	VERB
cana-935	73	16	stability	stability	NOUN
cana-935	73	17	.	.	PUNCT
cana-935	74	1	for	for	ADP
cana-935	74	2	the	the	DET
cana-935	74	3	fractional	fractional	ADJ
cana-935	74	4	schrödinger	schrödinger	ADJ
cana-935	74	5	equation	equation	NOUN
cana-935	74	6	:	:	PUNCT
cana-935	74	7	communications	communication	NOUN
cana-935	74	8	on	on	ADP
cana-935	74	9	applied	apply	VERB
cana-935	74	10	nonlinear	nonlinear	ADJ
cana-935	74	11	analysis	analysis	NOUN
cana-935	74	12	issn	issn	NOUN
cana-935	74	13	:	:	PUNCT
cana-935	74	14	1074	1074	NUM
cana-935	74	15	-	-	PUNCT
cana-935	74	16	133x	133x	NUM
cana-935	74	17	vol	vol	NOUN
cana-935	74	18	31	31	NUM
cana-935	74	19	no	no	NOUN
cana-935	74	20	.	.	PUNCT
cana-935	75	1	4s	4s	NUM
cana-935	75	2	(	(	PUNCT
cana-935	75	3	2024	2024	NUM
cana-935	75	4	)	)	PUNCT
cana-935	75	5	422	422	NUM
cana-935	75	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-935	75	7	𝑖	𝑖	SYM
cana-935	75	8	𝜕	𝜕	PROPN
cana-935	75	9	𝜕𝑡	𝜕𝑡	PROPN
cana-935	75	10	𝜓(𝑥	𝜓(𝑥	PROPN
cana-935	75	11	,	,	PUNCT
cana-935	75	12	𝑡	𝑡	NOUN
cana-935	75	13	)	)	PUNCT
cana-935	75	14	=	=	SYM
cana-935	75	15	−(−𝛥	−(−𝛥	X
cana-935	75	16	)	)	PUNCT
cana-935	75	17	𝛼	𝛼	PRON
cana-935	75	18	2𝜓(𝑥	2𝜓(𝑥	NUM
cana-935	75	19	,	,	PUNCT
cana-935	75	20	𝑡	𝑡	X
cana-935	75	21	)	)	PUNCT
cana-935	75	22	+	+	X
cana-935	75	23	𝑉(𝑥)𝜓(𝑥	𝑉(𝑥)𝜓(𝑥	ADJ
cana-935	75	24	,	,	PUNCT
cana-935	75	25	𝑡	𝑡	NOUN
cana-935	75	26	)	)	PUNCT
cana-935	75	27	we	we	PRON
cana-935	75	28	linearize	linearize	VERB
cana-935	75	29	the	the	DET
cana-935	75	30	equation	equation	NOUN
cana-935	75	31	around	around	ADP
cana-935	75	32	equilibrium	equilibrium	NOUN
cana-935	75	33	:	:	PUNCT
cana-935	75	34	𝜕	𝜕	NOUN
cana-935	75	35	𝜕𝑡	𝜕𝑡	NOUN
cana-935	75	36	𝛿𝜓	𝛿𝜓	NOUN
cana-935	75	37	=	=	SYM
cana-935	75	38	−(−𝛥	−(−𝛥	X
cana-935	75	39	)	)	PUNCT
cana-935	75	40	𝛼	𝛼	X
cana-935	75	41	2𝛿𝜓	2𝛿𝜓	ADJ
cana-935	75	42	+	+	CCONJ
cana-935	75	43	𝑉(𝑥)𝛿𝜓	𝑉(𝑥)𝛿𝜓	NOUN
cana-935	75	44	where	where	SCONJ
cana-935	75	45	δψ	δψ	NOUN
cana-935	75	46	represents	represent	VERB
cana-935	75	47	small	small	ADJ
cana-935	75	48	perturbations	perturbation	NOUN
cana-935	75	49	around	around	ADP
cana-935	75	50	the	the	DET
cana-935	75	51	equilibrium	equilibrium	NOUN
cana-935	75	52	solution	solution	NOUN
cana-935	75	53	.	.	PUNCT
cana-935	76	1	eigenvalue	eigenvalue	ADJ
cana-935	76	2	analysis	analysis	NOUN
cana-935	76	3	:	:	PUNCT
cana-935	76	4	we	we	PRON
cana-935	76	5	solve	solve	VERB
cana-935	76	6	for	for	ADP
cana-935	76	7	the	the	DET
cana-935	76	8	eigenvalues	eigenvalues	PROPN
cana-935	76	9	λ	λ	PROPN
cana-935	76	10	of	of	ADP
cana-935	76	11	the	the	DET
cana-935	76	12	linear	linear	ADJ
cana-935	76	13	operator	operator	NOUN
cana-935	76	14	l	l	NOUN
cana-935	76	15	defined	define	VERB
cana-935	76	16	by	by	ADP
cana-935	76	17	:	:	PUNCT
cana-935	76	18	𝐿𝛿𝜓	𝐿𝛿𝜓	PROPN
cana-935	76	19	=	=	PUNCT
cana-935	76	20	𝜆	𝜆	DET
cana-935	76	21	𝛿𝜓	𝛿𝜓	ADV
cana-935	76	22	the	the	DET
cana-935	76	23	stability	stability	NOUN
cana-935	76	24	is	be	AUX
cana-935	76	25	determined	determine	VERB
cana-935	76	26	by	by	ADP
cana-935	76	27	the	the	DET
cana-935	76	28	sign	sign	NOUN
cana-935	76	29	of	of	ADP
cana-935	76	30	the	the	DET
cana-935	76	31	real	real	ADJ
cana-935	76	32	parts	part	NOUN
cana-935	76	33	of	of	ADP
cana-935	76	34	the	the	DET
cana-935	76	35	eigenvalues	eigenvalue	NOUN
cana-935	76	36	.	.	PUNCT
cana-935	77	1	if	if	SCONJ
cana-935	77	2	all	all	DET
cana-935	77	3	eigenvalues	eigenvalue	NOUN
cana-935	77	4	have	have	VERB
cana-935	77	5	negative	negative	ADJ
cana-935	77	6	real	real	ADJ
cana-935	77	7	parts	part	NOUN
cana-935	77	8	,	,	PUNCT
cana-935	77	9	the	the	DET
cana-935	77	10	equilibrium	equilibrium	NOUN
cana-935	77	11	is	be	AUX
cana-935	77	12	stable	stable	ADJ
cana-935	77	13	.	.	PUNCT
cana-935	78	1	in	in	ADP
cana-935	78	2	summary	summary	NOUN
cana-935	78	3	,	,	PUNCT
cana-935	78	4	each	each	DET
cana-935	78	5	stability	stability	NOUN
cana-935	78	6	analysis	analysis	NOUN
cana-935	78	7	technique	technique	NOUN
cana-935	78	8	provides	provide	VERB
cana-935	78	9	unique	unique	ADJ
cana-935	78	10	insights	insight	NOUN
cana-935	78	11	into	into	ADP
cana-935	78	12	the	the	DET
cana-935	78	13	stability	stability	NOUN
cana-935	78	14	of	of	ADP
cana-935	78	15	solutions	solution	NOUN
cana-935	78	16	of	of	ADP
cana-935	78	17	the	the	DET
cana-935	78	18	fractional	fractional	ADJ
cana-935	78	19	schrödinger	schrödinger	ADJ
cana-935	78	20	equation	equation	NOUN
cana-935	78	21	.	.	PUNCT
cana-935	79	1	lyapunov	lyapunov	ADJ
cana-935	79	2	stability	stability	NOUN
cana-935	79	3	analysis	analysis	NOUN
cana-935	79	4	,	,	PUNCT
cana-935	79	5	energy	energy	NOUN
cana-935	79	6	methods	method	NOUN
cana-935	79	7	,	,	PUNCT
cana-935	79	8	and	and	CCONJ
cana-935	79	9	spectral	spectral	ADJ
cana-935	79	10	analysis	analysis	NOUN
cana-935	79	11	offer	offer	VERB
cana-935	79	12	different	different	ADJ
cana-935	79	13	approaches	approach	NOUN
cana-935	79	14	to	to	PART
cana-935	79	15	understand	understand	VERB
cana-935	79	16	stability	stability	NOUN
cana-935	79	17	,	,	PUNCT
cana-935	79	18	with	with	ADP
cana-935	79	19	varying	vary	VERB
cana-935	79	20	degrees	degree	NOUN
cana-935	79	21	of	of	ADP
cana-935	79	22	complexity	complexity	NOUN
cana-935	79	23	and	and	CCONJ
cana-935	79	24	applicability	applicability	NOUN
cana-935	79	25	.	.	PUNCT
cana-935	80	1	5	5	X
cana-935	80	2	.	.	X
cana-935	80	3	results	result	NOUN
cana-935	80	4	and	and	CCONJ
cana-935	80	5	discussion	discussion	NOUN
cana-935	80	6	lyapunov	lyapunov	NOUN
cana-935	80	7	stability	stability	NOUN
cana-935	80	8	analysis	analysis	NOUN
cana-935	80	9	for	for	ADP
cana-935	80	10	the	the	DET
cana-935	80	11	fractional	fractional	ADJ
cana-935	80	12	schrödinger	schrödinger	ADJ
cana-935	80	13	equation	equation	NOUN
cana-935	80	14	,	,	PUNCT
cana-935	80	15	we	we	PRON
cana-935	80	16	explored	explore	VERB
cana-935	80	17	lyapunov	lyapunov	ADJ
cana-935	80	18	stability	stability	NOUN
cana-935	80	19	analysis	analysis	NOUN
cana-935	80	20	aiming	aim	VERB
cana-935	80	21	to	to	PART
cana-935	80	22	find	find	VERB
cana-935	80	23	a	a	DET
cana-935	80	24	lyapunov	lyapunov	NOUN
cana-935	80	25	function	function	NOUN
cana-935	80	26	v(ψ	v(ψ	ADV
cana-935	80	27	)	)	PUNCT
cana-935	80	28	such	such	ADJ
cana-935	80	29	that	that	DET
cana-935	80	30	v'(ψ	v'(ψ	NOUN
cana-935	80	31	)	)	PUNCT
cana-935	80	32	≤	≤	NOUN
cana-935	80	33	0	0	NUM
cana-935	80	34	.	.	PUNCT
cana-935	81	1	we	we	PRON
cana-935	81	2	considered	consider	VERB
cana-935	81	3	the	the	DET
cana-935	81	4	lyapunov	lyapunov	NOUN
cana-935	81	5	function	function	VERB
cana-935	81	6	𝑉(𝜓	𝑉(𝜓	NOUN
cana-935	81	7	)	)	PUNCT
cana-935	81	8	=	=	SYM
cana-935	81	9	∫	∫	PROPN
cana-935	81	10	|𝜓(𝑥)|2𝑑𝑥.	|𝜓(𝑥)|2𝑑𝑥.	PROPN
cana-935	81	11	however	however	ADV
cana-935	81	12	,	,	PUNCT
cana-935	81	13	upon	upon	SCONJ
cana-935	81	14	evaluating	evaluate	VERB
cana-935	81	15	its	its	PRON
cana-935	81	16	time	time	NOUN
cana-935	81	17	derivative	derivative	ADJ
cana-935	81	18	,	,	PUNCT
cana-935	81	19	v'(ψ	v'(ψ	NOUN
cana-935	81	20	)	)	PUNCT
cana-935	81	21	,	,	PUNCT
cana-935	81	22	we	we	PRON
cana-935	81	23	found	find	VERB
cana-935	81	24	that	that	SCONJ
cana-935	81	25	it	it	PRON
cana-935	81	26	did	do	AUX
cana-935	81	27	not	not	PART
cana-935	81	28	yield	yield	VERB
cana-935	81	29	a	a	DET
cana-935	81	30	negative	negative	ADJ
cana-935	81	31	or	or	CCONJ
cana-935	81	32	non	non	ADJ
cana-935	81	33	-	-	ADJ
cana-935	81	34	positive	positive	ADJ
cana-935	81	35	result	result	NOUN
cana-935	81	36	,	,	PUNCT
cana-935	81	37	indicating	indicate	VERB
cana-935	81	38	its	its	PRON
cana-935	81	39	inadequacy	inadequacy	NOUN
cana-935	81	40	as	as	ADP
cana-935	81	41	a	a	DET
cana-935	81	42	lyapunov	lyapunov	ADJ
cana-935	81	43	function	function	NOUN
cana-935	81	44	for	for	ADP
cana-935	81	45	this	this	DET
cana-935	81	46	system	system	NOUN
cana-935	81	47	.	.	PUNCT
cana-935	82	1	energy	energy	NOUN
cana-935	82	2	methods	method	NOUN
cana-935	82	3	we	we	PRON
cana-935	82	4	defined	define	VERB
cana-935	82	5	the	the	DET
cana-935	82	6	energy	energy	NOUN
cana-935	82	7	functional	functional	ADJ
cana-935	82	8	as	as	ADP
cana-935	82	9	𝐸[𝜓	𝐸[𝜓	NOUN
cana-935	82	10	]	]	X
cana-935	82	11	=	=	SYM
cana-935	82	12	∫	∫	PROPN
cana-935	82	13	|𝛻𝜓|2	|𝛻𝜓|2	X
cana-935	82	14	𝑅𝑛	𝑅𝑛	PROPN
cana-935	82	15	+	+	CCONJ
cana-935	82	16	𝑉(𝑥)|𝜓|2𝑑𝑥.	𝑉(𝑥)|𝜓|2𝑑𝑥.	X
cana-935	82	17	evaluating	evaluate	VERB
cana-935	82	18	the	the	DET
cana-935	82	19	time	time	NOUN
cana-935	82	20	derivative	derivative	NOUN
cana-935	82	21	of	of	ADP
cana-935	82	22	the	the	DET
cana-935	82	23	energy	energy	NOUN
cana-935	82	24	,	,	PUNCT
cana-935	82	25	de	de	PROPN
cana-935	82	26	/	/	SYM
cana-935	82	27	dt	dt	PROPN
cana-935	82	28	,	,	PUNCT
cana-935	82	29	using	use	VERB
cana-935	82	30	the	the	DET
cana-935	82	31	fractional	fractional	ADJ
cana-935	82	32	schrödinger	schrödinger	ADJ
cana-935	82	33	equation	equation	NOUN
cana-935	82	34	,	,	PUNCT
cana-935	82	35	we	we	PRON
cana-935	82	36	found	find	VERB
cana-935	82	37	that	that	SCONJ
cana-935	82	38	it	it	PRON
cana-935	82	39	equaled	equal	VERB
cana-935	82	40	zero	zero	NUM
cana-935	82	41	.	.	PUNCT
cana-935	83	1	this	this	PRON
cana-935	83	2	suggests	suggest	VERB
cana-935	83	3	that	that	SCONJ
cana-935	83	4	the	the	DET
cana-935	83	5	energy	energy	NOUN
cana-935	83	6	remains	remain	VERB
cana-935	83	7	conserved	conserve	VERB
cana-935	83	8	over	over	ADP
cana-935	83	9	time	time	NOUN
cana-935	83	10	,	,	PUNCT
cana-935	83	11	implying	imply	VERB
cana-935	83	12	stability	stability	NOUN
cana-935	83	13	of	of	ADP
cana-935	83	14	the	the	DET
cana-935	83	15	system	system	NOUN
cana-935	83	16	.	.	PUNCT
cana-935	84	1	spectral	spectral	ADJ
cana-935	84	2	analysis	analysis	NOUN
cana-935	84	3	linearizing	linearize	VERB
cana-935	84	4	the	the	DET
cana-935	84	5	fractional	fractional	ADJ
cana-935	84	6	schrödinger	schrödinger	ADJ
cana-935	84	7	equation	equation	NOUN
cana-935	84	8	around	around	ADP
cana-935	84	9	equilibrium	equilibrium	NOUN
cana-935	84	10	,	,	PUNCT
cana-935	84	11	we	we	PRON
cana-935	84	12	obtained	obtain	VERB
cana-935	84	13	an	an	DET
cana-935	84	14	equation	equation	NOUN
cana-935	84	15	for	for	ADP
cana-935	84	16	small	small	ADJ
cana-935	84	17	perturbations	perturbation	NOUN
cana-935	84	18	δψ	δψ	VERB
cana-935	84	19	.	.	PUNCT
cana-935	85	1	by	by	ADP
cana-935	85	2	solving	solve	VERB
cana-935	85	3	for	for	ADP
cana-935	85	4	the	the	DET
cana-935	85	5	eigenvalues	eigenvalue	NOUN
cana-935	85	6	of	of	ADP
cana-935	85	7	the	the	DET
cana-935	85	8	linear	linear	ADJ
cana-935	85	9	operator	operator	NOUN
cana-935	85	10	l	l	NOUN
cana-935	85	11	defined	define	VERB
cana-935	85	12	by	by	ADP
cana-935	85	13	lδψ	lδψ	NOUN
cana-935	85	14	=	=	SYM
cana-935	85	15	λ	λ	SYM
cana-935	85	16	δψ	δψ	NOUN
cana-935	85	17	,	,	PUNCT
cana-935	85	18	we	we	PRON
cana-935	85	19	analyzed	analyze	VERB
cana-935	85	20	the	the	DET
cana-935	85	21	stability	stability	NOUN
cana-935	85	22	based	base	VERB
cana-935	85	23	on	on	ADP
cana-935	85	24	the	the	DET
cana-935	85	25	real	real	ADJ
cana-935	85	26	parts	part	NOUN
cana-935	85	27	of	of	ADP
cana-935	85	28	the	the	DET
cana-935	85	29	eigenvalues	eigenvalue	NOUN
cana-935	85	30	.	.	PUNCT
cana-935	86	1	negative	negative	ADJ
cana-935	86	2	real	real	ADJ
cana-935	86	3	parts	part	NOUN
cana-935	86	4	of	of	ADP
cana-935	86	5	the	the	DET
cana-935	86	6	eigenvalues	eigenvalue	NOUN
cana-935	86	7	indicate	indicate	VERB
cana-935	86	8	stability	stability	NOUN
cana-935	86	9	.	.	PUNCT
cana-935	87	1	therefore	therefore	ADV
cana-935	87	2	,	,	PUNCT
cana-935	87	3	stability	stability	NOUN
cana-935	87	4	hinges	hinge	VERB
cana-935	87	5	upon	upon	SCONJ
cana-935	87	6	all	all	DET
cana-935	87	7	eigenvalues	eigenvalue	NOUN
cana-935	87	8	possessing	possess	VERB
cana-935	87	9	negative	negative	ADJ
cana-935	87	10	real	real	ADJ
cana-935	87	11	parts	part	NOUN
cana-935	87	12	.	.	PUNCT
cana-935	88	1	overall	overall	ADJ
cana-935	88	2	implications	implication	NOUN
cana-935	88	3	effect	effect	NOUN
cana-935	88	4	of	of	ADP
cana-935	88	5	nonlinearity	nonlinearity	NOUN
cana-935	88	6	:	:	PUNCT
cana-935	88	7	the	the	DET
cana-935	88	8	presence	presence	NOUN
cana-935	88	9	of	of	ADP
cana-935	88	10	cubic	cubic	ADJ
cana-935	88	11	nonlinearity	nonlinearity	NOUN
cana-935	88	12	complicates	complicate	VERB
cana-935	88	13	stability	stability	NOUN
cana-935	88	14	analysis	analysis	NOUN
cana-935	88	15	.	.	PUNCT
cana-935	89	1	while	while	SCONJ
cana-935	89	2	lyapunov	lyapunov	NOUN
cana-935	89	3	stability	stability	NOUN
cana-935	89	4	analysis	analysis	NOUN
cana-935	89	5	presents	present	NOUN
cana-935	89	6	challenges	challenge	NOUN
cana-935	89	7	,	,	PUNCT
cana-935	89	8	energy	energy	NOUN
cana-935	89	9	methods	method	NOUN
cana-935	89	10	and	and	CCONJ
cana-935	89	11	spectral	spectral	ADJ
cana-935	89	12	analysis	analysis	NOUN
cana-935	89	13	offer	offer	NOUN
cana-935	89	14	promising	promise	VERB
cana-935	89	15	avenues	avenue	NOUN
cana-935	89	16	for	for	ADP
cana-935	89	17	understanding	understand	VERB
cana-935	89	18	stability	stability	NOUN
cana-935	89	19	.	.	PUNCT
cana-935	90	1	conservation	conservation	NOUN
cana-935	90	2	of	of	ADP
cana-935	90	3	energy	energy	NOUN
cana-935	90	4	:	:	PUNCT
cana-935	90	5	the	the	DET
cana-935	90	6	conservation	conservation	NOUN
cana-935	90	7	of	of	ADP
cana-935	90	8	energy	energy	NOUN
cana-935	90	9	suggests	suggest	VERB
cana-935	90	10	that	that	SCONJ
cana-935	90	11	the	the	DET
cana-935	90	12	system	system	NOUN
cana-935	90	13	remains	remain	VERB
cana-935	90	14	stable	stable	ADJ
cana-935	90	15	over	over	ADP
cana-935	90	16	time	time	NOUN
cana-935	90	17	,	,	PUNCT
cana-935	90	18	despite	despite	SCONJ
cana-935	90	19	the	the	DET
cana-935	90	20	presence	presence	NOUN
cana-935	90	21	of	of	ADP
cana-935	90	22	cubic	cubic	ADJ
cana-935	90	23	nonlinearity	nonlinearity	NOUN
cana-935	90	24	.	.	PUNCT
cana-935	91	1	this	this	PRON
cana-935	91	2	implies	imply	VERB
cana-935	91	3	that	that	SCONJ
cana-935	91	4	the	the	DET
cana-935	91	5	system	system	NOUN
cana-935	91	6	's	's	PART
cana-935	91	7	energy	energy	NOUN
cana-935	91	8	does	do	AUX
cana-935	91	9	not	not	PART
cana-935	91	10	exhibit	exhibit	VERB
cana-935	91	11	unbounded	unbounded	ADJ
cana-935	91	12	growth	growth	NOUN
cana-935	91	13	or	or	CCONJ
cana-935	91	14	decay	decay	NOUN
cana-935	91	15	.	.	PUNCT
cana-935	92	1	linear	linear	ADJ
cana-935	92	2	stability	stability	NOUN
cana-935	92	3	analysis	analysis	NOUN
cana-935	92	4	:	:	PUNCT
cana-935	92	5	spectral	spectral	ADJ
cana-935	92	6	analysis	analysis	NOUN
cana-935	92	7	provides	provide	VERB
cana-935	92	8	a	a	DET
cana-935	92	9	robust	robust	ADJ
cana-935	92	10	method	method	NOUN
cana-935	92	11	for	for	ADP
cana-935	92	12	assessing	assess	VERB
cana-935	92	13	stability	stability	NOUN
cana-935	92	14	.	.	PUNCT
cana-935	93	1	by	by	ADP
cana-935	93	2	examining	examine	VERB
cana-935	93	3	the	the	DET
cana-935	93	4	eigenvalues	eigenvalue	NOUN
cana-935	93	5	of	of	ADP
cana-935	93	6	the	the	DET
cana-935	93	7	linearized	linearize	VERB
cana-935	93	8	system	system	NOUN
cana-935	93	9	,	,	PUNCT
cana-935	93	10	we	we	PRON
cana-935	93	11	can	can	AUX
cana-935	93	12	determine	determine	VERB
cana-935	93	13	the	the	DET
cana-935	93	14	stability	stability	NOUN
cana-935	93	15	of	of	ADP
cana-935	93	16	the	the	DET
cana-935	93	17	equilibrium	equilibrium	NOUN
cana-935	93	18	solution	solution	NOUN
cana-935	93	19	based	base	VERB
cana-935	93	20	on	on	ADP
cana-935	93	21	the	the	DET
cana-935	93	22	sign	sign	NOUN
cana-935	93	23	of	of	ADP
cana-935	93	24	their	their	PRON
cana-935	93	25	real	real	ADJ
cana-935	93	26	parts	part	NOUN
cana-935	93	27	.	.	PUNCT
cana-935	94	1	communications	communication	NOUN
cana-935	94	2	on	on	ADP
cana-935	94	3	applied	apply	VERB
cana-935	94	4	nonlinear	nonlinear	ADJ
cana-935	94	5	analysis	analysis	NOUN
cana-935	94	6	issn	issn	NOUN
cana-935	94	7	:	:	PUNCT
cana-935	94	8	1074	1074	NUM
cana-935	94	9	-	-	PUNCT
cana-935	94	10	133x	133x	NUM
cana-935	94	11	vol	vol	NOUN
cana-935	94	12	31	31	NUM
cana-935	94	13	no	no	NOUN
cana-935	94	14	.	.	PUNCT
cana-935	95	1	4s	4s	NUM
cana-935	95	2	(	(	PUNCT
cana-935	95	3	2024	2024	NUM
cana-935	95	4	)	)	PUNCT
cana-935	95	5	423	423	NUM
cana-935	95	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-935	95	7	6	6	NUM
cana-935	95	8	.	.	PUNCT
cana-935	95	9	novel	novel	NOUN
cana-935	95	10	findings	finding	VERB
cana-935	95	11	the	the	DET
cana-935	95	12	conservation	conservation	NOUN
cana-935	95	13	of	of	ADP
cana-935	95	14	energy	energy	NOUN
cana-935	95	15	in	in	ADP
cana-935	95	16	the	the	DET
cana-935	95	17	presence	presence	NOUN
cana-935	95	18	of	of	ADP
cana-935	95	19	cubic	cubic	ADJ
cana-935	95	20	nonlinearity	nonlinearity	NOUN
cana-935	95	21	is	be	AUX
cana-935	95	22	a	a	DET
cana-935	95	23	significant	significant	ADJ
cana-935	95	24	result	result	NOUN
cana-935	95	25	.	.	PUNCT
cana-935	96	1	despite	despite	SCONJ
cana-935	96	2	the	the	DET
cana-935	96	3	nonlinear	nonlinear	ADJ
cana-935	96	4	terms	term	NOUN
cana-935	96	5	,	,	PUNCT
cana-935	96	6	the	the	DET
cana-935	96	7	system	system	NOUN
cana-935	96	8	's	's	PART
cana-935	96	9	energy	energy	NOUN
cana-935	96	10	remains	remain	VERB
cana-935	96	11	bounded	bound	VERB
cana-935	96	12	,	,	PUNCT
cana-935	96	13	indicating	indicate	VERB
cana-935	96	14	a	a	DET
cana-935	96	15	stable	stable	ADJ
cana-935	96	16	dynamical	dynamical	ADJ
cana-935	96	17	evolution	evolution	NOUN
cana-935	96	18	.	.	PUNCT
cana-935	97	1	exploring	explore	VERB
cana-935	97	2	alternative	alternative	ADJ
cana-935	97	3	lyapunov	lyapunov	ADJ
cana-935	97	4	functions	function	NOUN
cana-935	97	5	or	or	CCONJ
cana-935	97	6	modifications	modification	NOUN
cana-935	97	7	to	to	ADP
cana-935	97	8	the	the	DET
cana-935	97	9	chosen	choose	VERB
cana-935	97	10	function	function	NOUN
cana-935	97	11	could	could	AUX
cana-935	97	12	provide	provide	VERB
cana-935	97	13	further	further	ADJ
cana-935	97	14	insights	insight	NOUN
cana-935	97	15	into	into	ADP
cana-935	97	16	stability	stability	NOUN
cana-935	97	17	properties	property	NOUN
cana-935	97	18	not	not	PART
cana-935	97	19	captured	capture	VERB
cana-935	97	20	by	by	ADP
cana-935	97	21	other	other	ADJ
cana-935	97	22	methods	method	NOUN
cana-935	97	23	.	.	PUNCT
cana-935	98	1	7	7	X
cana-935	98	2	.	.	X
cana-935	98	3	conclusion	conclusion	NOUN
cana-935	98	4	in	in	ADP
cana-935	98	5	conclusion	conclusion	NOUN
cana-935	98	6	,	,	PUNCT
cana-935	98	7	stability	stability	NOUN
cana-935	98	8	analysis	analysis	NOUN
cana-935	98	9	of	of	ADP
cana-935	98	10	the	the	DET
cana-935	98	11	fractional	fractional	ADJ
cana-935	98	12	schrödinger	schrödinger	ADJ
cana-935	98	13	equation	equation	NOUN
cana-935	98	14	with	with	ADP
cana-935	98	15	cubic	cubic	ADJ
cana-935	98	16	nonlinearity	nonlinearity	NOUN
cana-935	98	17	reveals	reveal	VERB
cana-935	98	18	complex	complex	ADJ
cana-935	98	19	dynamics	dynamic	NOUN
cana-935	98	20	.	.	PUNCT
cana-935	99	1	while	while	SCONJ
cana-935	99	2	lyapunov	lyapunov	NOUN
cana-935	99	3	stability	stability	NOUN
cana-935	99	4	analysis	analysis	NOUN
cana-935	99	5	faces	face	VERB
cana-935	99	6	challenges	challenge	NOUN
cana-935	99	7	,	,	PUNCT
cana-935	99	8	energy	energy	NOUN
cana-935	99	9	methods	method	NOUN
cana-935	99	10	and	and	CCONJ
cana-935	99	11	spectral	spectral	ADJ
cana-935	99	12	analysis	analysis	NOUN
cana-935	99	13	offer	offer	VERB
cana-935	99	14	valuable	valuable	ADJ
cana-935	99	15	tools	tool	NOUN
cana-935	99	16	for	for	ADP
cana-935	99	17	understanding	understand	VERB
cana-935	99	18	stability	stability	NOUN
cana-935	99	19	characteristics	characteristic	NOUN
cana-935	99	20	.	.	PUNCT
cana-935	100	1	the	the	DET
cana-935	100	2	conservation	conservation	NOUN
cana-935	100	3	of	of	ADP
cana-935	100	4	energy	energy	NOUN
cana-935	100	5	suggests	suggest	VERB
cana-935	100	6	stability	stability	NOUN
cana-935	100	7	in	in	ADP
cana-935	100	8	the	the	DET
cana-935	100	9	system	system	NOUN
cana-935	100	10	,	,	PUNCT
cana-935	100	11	despite	despite	SCONJ
cana-935	100	12	nonlinear	nonlinear	ADJ
cana-935	100	13	terms	term	NOUN
cana-935	100	14	.	.	PUNCT
cana-935	101	1	further	further	ADJ
cana-935	101	2	exploration	exploration	NOUN
cana-935	101	3	and	and	CCONJ
cana-935	101	4	refinement	refinement	NOUN
cana-935	101	5	of	of	ADP
cana-935	101	6	stability	stability	NOUN
cana-935	101	7	analysis	analysis	NOUN
cana-935	101	8	techniques	technique	NOUN
cana-935	101	9	could	could	AUX
cana-935	101	10	deepen	deepen	VERB
cana-935	101	11	our	our	PRON
cana-935	101	12	understanding	understanding	NOUN
cana-935	101	13	of	of	ADP
cana-935	101	14	the	the	DET
cana-935	101	15	quantum	quantum	ADJ
cana-935	101	16	harmonic	harmonic	NOUN
cana-935	101	17	oscillator	oscillator	NOUN
cana-935	101	18	with	with	ADP
cana-935	101	19	cubic	cubic	ADJ
cana-935	101	20	nonlinearity	nonlinearity	NOUN
cana-935	101	21	.	.	PUNCT
cana-935	102	1	references	reference	NOUN
cana-935	102	2	[	[	X
cana-935	102	3	1	1	NUM
cana-935	102	4	]	]	X
cana-935	102	5	herrmann	herrmann	PROPN
cana-935	102	6	,	,	PUNCT
cana-935	102	7	r.	r.	PROPN
cana-935	102	8	(	(	PUNCT
cana-935	102	9	2011	2011	NUM
cana-935	102	10	)	)	PUNCT
cana-935	102	11	.	.	PUNCT
cana-935	103	1	fractional	fractional	ADJ
cana-935	103	2	calculus	calculus	NOUN
cana-935	103	3	:	:	PUNCT
cana-935	103	4	an	an	DET
cana-935	103	5	introduction	introduction	NOUN
cana-935	103	6	for	for	ADP
cana-935	103	7	physicists	physicist	NOUN
cana-935	103	8	.	.	PUNCT
cana-935	104	1	world	world	NOUN
cana-935	104	2	scientific	scientific	ADJ
cana-935	104	3	publishing	publishing	NOUN
cana-935	104	4	company	company	NOUN
cana-935	104	5	.	.	PUNCT
cana-935	105	1	[	[	X
cana-935	105	2	2	2	NUM
cana-935	105	3	]	]	X
cana-935	105	4	mainardi	mainardi	PROPN
cana-935	105	5	,	,	PUNCT
cana-935	105	6	f.	f.	PROPN
cana-935	105	7	(	(	PUNCT
cana-935	105	8	2010	2010	NUM
cana-935	105	9	)	)	PUNCT
cana-935	105	10	.	.	PUNCT
cana-935	106	1	fractional	fractional	ADJ
cana-935	106	2	calculus	calculus	NOUN
cana-935	106	3	and	and	CCONJ
cana-935	106	4	waves	wave	NOUN
cana-935	106	5	in	in	ADP
cana-935	106	6	linear	linear	PROPN
cana-935	106	7	viscoelasticity	viscoelasticity	NOUN
cana-935	106	8	:	:	PUNCT
cana-935	106	9	an	an	DET
cana-935	106	10	introduction	introduction	NOUN
cana-935	106	11	to	to	ADP
cana-935	106	12	mathematical	mathematical	ADJ
cana-935	106	13	models	model	NOUN
cana-935	106	14	.	.	PUNCT
cana-935	107	1	imperial	imperial	ADJ
cana-935	107	2	college	college	NOUN
cana-935	107	3	press	press	NOUN
cana-935	107	4	.	.	PUNCT
cana-935	108	1	[	[	X
cana-935	108	2	3	3	NUM
cana-935	108	3	]	]	PUNCT
cana-935	108	4	tarasov	tarasov	NOUN
cana-935	108	5	,	,	PUNCT
cana-935	108	6	v.	v.	PROPN
cana-935	108	7	e.	e.	PROPN
cana-935	108	8	(	(	PUNCT
cana-935	108	9	2017	2017	NUM
cana-935	108	10	)	)	PUNCT
cana-935	108	11	.	.	PUNCT
cana-935	109	1	fractional	fractional	ADJ
cana-935	109	2	dynamics	dynamic	NOUN
cana-935	109	3	:	:	PUNCT
cana-935	109	4	applications	application	NOUN
cana-935	109	5	of	of	ADP
cana-935	109	6	fractional	fractional	ADJ
cana-935	109	7	calculus	calculus	NOUN
cana-935	109	8	to	to	ADP
cana-935	109	9	dynamics	dynamic	NOUN
cana-935	109	10	of	of	ADP
cana-935	109	11	particles	particle	NOUN
cana-935	109	12	,	,	PUNCT
cana-935	109	13	fields	field	NOUN
cana-935	109	14	,	,	PUNCT
cana-935	109	15	and	and	CCONJ
cana-935	109	16	media	medium	NOUN
cana-935	109	17	.	.	PUNCT
cana-935	110	1	springer	springer	NOUN
cana-935	110	2	.	.	PUNCT
cana-935	111	1	[	[	X
cana-935	111	2	4	4	NUM
cana-935	111	3	]	]	X
cana-935	111	4	gorenflo	gorenflo	NOUN
cana-935	111	5	,	,	PUNCT
cana-935	111	6	r.	r.	PROPN
cana-935	111	7	,	,	PUNCT
cana-935	111	8	mainardi	mainardi	PROPN
cana-935	111	9	,	,	PUNCT
cana-935	111	10	f.	f.	PROPN
cana-935	111	11	,	,	PUNCT
cana-935	111	12	moretti	moretti	PROPN
cana-935	111	13	,	,	PUNCT
cana-935	111	14	d.	d.	PROPN
cana-935	111	15	,	,	PUNCT
cana-935	111	16	&	&	CCONJ
cana-935	111	17	pagnini	pagnini	PROPN
cana-935	111	18	,	,	PUNCT
cana-935	111	19	g.	g.	PROPN
cana-935	111	20	(	(	PUNCT
cana-935	111	21	2002	2002	NUM
cana-935	111	22	)	)	PUNCT
cana-935	111	23	.	.	PUNCT
cana-935	112	1	fractional	fractional	ADJ
cana-935	112	2	calculus	calculus	NOUN
cana-935	112	3	and	and	CCONJ
cana-935	112	4	stable	stable	ADJ
cana-935	112	5	probability	probability	NOUN
cana-935	112	6	distributions	distribution	NOUN
cana-935	112	7	.	.	PUNCT
cana-935	113	1	archive	archive	NOUN
cana-935	113	2	for	for	ADP
cana-935	113	3	rational	rational	ADJ
cana-935	113	4	mechanics	mechanic	NOUN
cana-935	113	5	and	and	CCONJ
cana-935	113	6	analysis	analysis	NOUN
cana-935	113	7	,	,	PUNCT
cana-935	113	8	167(1	167(1	NUM
cana-935	113	9	)	)	PUNCT
cana-935	113	10	,	,	PUNCT
cana-935	113	11	125	125	NUM
cana-935	113	12	-	-	SYM
cana-935	113	13	145	145	NUM
cana-935	113	14	.	.	PUNCT
cana-935	114	1	[	[	X
cana-935	114	2	5	5	NUM
cana-935	114	3	]	]	PUNCT
cana-935	114	4	laskin	laskin	NOUN
cana-935	114	5	,	,	PUNCT
cana-935	114	6	n.	n.	PROPN
cana-935	114	7	(	(	PUNCT
cana-935	114	8	2003	2003	NUM
cana-935	114	9	)	)	PUNCT
cana-935	114	10	.	.	PUNCT
cana-935	115	1	fractional	fractional	ADJ
cana-935	115	2	quantum	quantum	ADJ
cana-935	115	3	mechanics	mechanic	NOUN
cana-935	115	4	.	.	PUNCT
cana-935	116	1	physical	physical	ADJ
cana-935	116	2	review	review	PROPN
cana-935	116	3	e	e	PROPN
cana-935	116	4	,	,	PUNCT
cana-935	116	5	66(5	66(5	PROPN
cana-935	116	6	)	)	PUNCT
cana-935	116	7	,	,	PUNCT
cana-935	116	8	056108	056108	NUM
cana-935	116	9	.	.	PUNCT
cana-935	117	1	[	[	X
cana-935	117	2	6	6	NUM
cana-935	117	3	]	]	SYM
cana-935	117	4	khalil	khalil	PROPN
cana-935	117	5	,	,	PUNCT
cana-935	117	6	r.	r.	PROPN
cana-935	117	7	,	,	PUNCT
cana-935	117	8	horani	horani	PROPN
cana-935	117	9	,	,	PUNCT
cana-935	117	10	m.	m.	NOUN
cana-935	117	11	,	,	PUNCT
cana-935	117	12	yousef	yousef	PROPN
cana-935	117	13	,	,	PUNCT
cana-935	117	14	a.	a.	PROPN
cana-935	117	15	,	,	PUNCT
cana-935	117	16	&	&	CCONJ
cana-935	117	17	sababheh	sababheh	PROPN
cana-935	117	18	,	,	PUNCT
cana-935	117	19	m.	m.	NOUN
cana-935	117	20	(	(	PUNCT
cana-935	117	21	2014	2014	NUM
cana-935	117	22	)	)	PUNCT
cana-935	117	23	.	.	PUNCT
cana-935	118	1	a	a	DET
cana-935	118	2	new	new	ADJ
cana-935	118	3	definition	definition	NOUN
cana-935	118	4	of	of	ADP
cana-935	118	5	fractional	fractional	ADJ
cana-935	118	6	derivative	derivative	NOUN
cana-935	118	7	.	.	PUNCT
cana-935	119	1	journal	journal	PROPN
cana-935	119	2	of	of	ADP
cana-935	119	3	computational	computational	ADJ
cana-935	119	4	and	and	CCONJ
cana-935	119	5	applied	applied	ADJ
cana-935	119	6	mathematics	mathematic	NOUN
cana-935	119	7	,	,	PUNCT
cana-935	119	8	264	264	NUM
cana-935	119	9	,	,	PUNCT
cana-935	119	10	65	65	NUM
cana-935	119	11	-	-	SYM
cana-935	119	12	70	70	NUM
cana-935	119	13	.	.	PUNCT
cana-935	120	1	[	[	X
cana-935	120	2	7	7	NUM
cana-935	120	3	]	]	X
cana-935	120	4	sabzikar	sabzikar	NOUN
cana-935	120	5	,	,	PUNCT
cana-935	120	6	f.	f.	PROPN
cana-935	120	7	,	,	PUNCT
cana-935	120	8	baleanu	baleanu	PROPN
cana-935	120	9	,	,	PUNCT
cana-935	120	10	d.	d.	PROPN
cana-935	120	11	,	,	PUNCT
cana-935	120	12	&	&	CCONJ
cana-935	120	13	golmankhaneh	golmankhaneh	PROPN
cana-935	120	14	,	,	PUNCT
cana-935	120	15	a.	a.	PROPN
cana-935	120	16	k.	k.	PROPN
cana-935	120	17	(	(	PUNCT
cana-935	120	18	2018	2018	NUM
cana-935	120	19	)	)	PUNCT
cana-935	120	20	.	.	PUNCT
cana-935	121	1	numerical	numerical	ADJ
cana-935	121	2	approximation	approximation	NOUN
cana-935	121	3	of	of	ADP
cana-935	121	4	fractional	fractional	ADJ
cana-935	121	5	order	order	NOUN
cana-935	121	6	systems	system	NOUN
cana-935	121	7	:	:	PUNCT
cana-935	121	8	a	a	DET
cana-935	121	9	survey	survey	NOUN
cana-935	121	10	and	and	CCONJ
cana-935	121	11	a	a	DET
cana-935	121	12	software	software	NOUN
cana-935	121	13	tutorial	tutorial	NOUN
cana-935	121	14	.	.	PUNCT
cana-935	122	1	computers	computer	NOUN
cana-935	122	2	&	&	CCONJ
cana-935	122	3	mathematics	mathematics	PROPN
cana-935	122	4	with	with	ADP
cana-935	122	5	applications	application	NOUN
cana-935	122	6	,	,	PUNCT
cana-935	122	7	75(3	75(3	NUM
cana-935	122	8	)	)	PUNCT
cana-935	122	9	,	,	PUNCT
cana-935	122	10	854	854	NUM
cana-935	122	11	-	-	SYM
cana-935	122	12	876	876	NUM
cana-935	122	13	.	.	PUNCT
cana-935	123	1	[	[	X
cana-935	123	2	8	8	NUM
cana-935	123	3	]	]	X
cana-935	123	4	magin	magin	NOUN
cana-935	123	5	,	,	PUNCT
cana-935	123	6	r.	r.	PROPN
cana-935	123	7	l.	l.	PROPN
cana-935	123	8	(	(	PUNCT
cana-935	123	9	2006	2006	NUM
cana-935	123	10	)	)	PUNCT
cana-935	123	11	.	.	PUNCT
cana-935	124	1	fractional	fractional	ADJ
cana-935	124	2	calculus	calculus	NOUN
cana-935	124	3	in	in	ADP
cana-935	124	4	bioengineering	bioengineering	NOUN
cana-935	124	5	,	,	PUNCT
cana-935	124	6	part	part	NOUN
cana-935	124	7	1	1	NUM
cana-935	124	8	.	.	PUNCT
cana-935	125	1	critical	critical	ADJ
cana-935	125	2	reviews	review	NOUN
cana-935	125	3	™	™	VERB
cana-935	125	4	in	in	ADP
cana-935	125	5	biomedical	biomedical	ADJ
cana-935	125	6	engineering	engineering	NOUN
cana-935	125	7	,	,	PUNCT
cana-935	125	8	32(1	32(1	NUM
cana-935	125	9	)	)	PUNCT
cana-935	125	10	,	,	PUNCT
cana-935	125	11	1	1	NUM
cana-935	125	12	-	-	SYM
cana-935	125	13	104	104	NUM
cana-935	125	14	.	.	PUNCT
cana-935	126	1	[	[	X
cana-935	126	2	9	9	NUM
cana-935	126	3	]	]	X
cana-935	126	4	daftardar	daftardar	NOUN
cana-935	126	5	-	-	PUNCT
cana-935	126	6	gejji	gejji	NOUN
cana-935	126	7	,	,	PUNCT
cana-935	126	8	v.	v.	PROPN
cana-935	126	9	,	,	PUNCT
cana-935	126	10	&	&	CCONJ
cana-935	126	11	babakhani	babakhani	PROPN
cana-935	126	12	,	,	PUNCT
cana-935	126	13	a.	a.	NOUN
cana-935	126	14	(	(	PUNCT
cana-935	126	15	2007	2007	NUM
cana-935	126	16	)	)	PUNCT
cana-935	126	17	.	.	PUNCT
cana-935	127	1	analysis	analysis	NOUN
cana-935	127	2	of	of	ADP
cana-935	127	3	a	a	DET
cana-935	127	4	system	system	NOUN
cana-935	127	5	of	of	ADP
cana-935	127	6	fractional	fractional	ADJ
cana-935	127	7	differential	differential	ADJ
cana-935	127	8	equations	equation	NOUN
cana-935	127	9	.	.	PUNCT
cana-935	128	1	journal	journal	PROPN
cana-935	128	2	of	of	ADP
cana-935	128	3	mathematical	mathematical	ADJ
cana-935	128	4	analysis	analysis	NOUN
cana-935	128	5	and	and	CCONJ
cana-935	128	6	applications	application	NOUN
cana-935	128	7	,	,	PUNCT
cana-935	128	8	328(2	328(2	NUM
cana-935	128	9	)	)	PUNCT
cana-935	128	10	,	,	PUNCT
cana-935	128	11	1026	1026	NUM
cana-935	128	12	-	-	SYM
cana-935	128	13	1036	1036	NUM
cana-935	128	14	.	.	PUNCT
cana-935	129	1	[	[	X
cana-935	129	2	10	10	NUM
cana-935	129	3	]	]	PUNCT
cana-935	129	4	băleanu	băleanu	NOUN
cana-935	129	5	,	,	PUNCT
cana-935	129	6	d.	d.	PROPN
cana-935	129	7	,	,	PUNCT
cana-935	129	8	&	&	CCONJ
cana-935	129	9	mustafa	mustafa	PROPN
cana-935	129	10	,	,	PUNCT
cana-935	129	11	o.	o.	PROPN
cana-935	129	12	g.	g.	PROPN
cana-935	129	13	(	(	PUNCT
cana-935	129	14	2012	2012	NUM
cana-935	129	15	)	)	PUNCT
cana-935	129	16	.	.	PUNCT
cana-935	130	1	on	on	ADP
cana-935	130	2	the	the	DET
cana-935	130	3	global	global	ADJ
cana-935	130	4	existence	existence	NOUN
cana-935	130	5	of	of	ADP
cana-935	130	6	solutions	solution	NOUN
cana-935	130	7	to	to	ADP
cana-935	130	8	a	a	DET
cana-935	130	9	class	class	NOUN
cana-935	130	10	of	of	ADP
cana-935	130	11	fractional	fractional	ADJ
cana-935	130	12	differential	differential	ADJ
cana-935	130	13	equations	equation	NOUN
cana-935	130	14	.	.	PUNCT
cana-935	131	1	computers	computer	NOUN
cana-935	131	2	&	&	CCONJ
cana-935	131	3	mathematics	mathematics	PROPN
cana-935	131	4	with	with	ADP
cana-935	131	5	applications	application	NOUN
cana-935	131	6	,	,	PUNCT
cana-935	131	7	59(5	59(5	NUM
cana-935	131	8	)	)	PUNCT
cana-935	131	9	,	,	PUNCT
cana-935	131	10	1835	1835	NUM
cana-935	131	11	-	-	SYM
cana-935	131	12	1841	1841	NUM
cana-935	131	13	.	.	PUNCT
cana-935	132	1	[	[	X
cana-935	132	2	11	11	NUM
cana-935	132	3	]	]	PUNCT
cana-935	132	4	ortigueira	ortigueira	PROPN
cana-935	132	5	,	,	PUNCT
cana-935	132	6	m.	m.	PROPN
cana-935	132	7	d.	d.	PROPN
cana-935	132	8	(	(	PUNCT
cana-935	132	9	2011	2011	NUM
cana-935	132	10	)	)	PUNCT
cana-935	132	11	.	.	PUNCT
cana-935	133	1	fractional	fractional	ADJ
cana-935	133	2	calculus	calculus	NOUN
cana-935	133	3	for	for	ADP
cana-935	133	4	scientists	scientist	NOUN
cana-935	133	5	and	and	CCONJ
cana-935	133	6	engineers	engineer	NOUN
cana-935	133	7	.	.	PUNCT
cana-935	134	1	springer	springer	NOUN
cana-935	134	2	.	.	PUNCT
cana-935	135	1	[	[	X
cana-935	135	2	12	12	NUM
cana-935	135	3	]	]	X
cana-935	135	4	west	west	PROPN
cana-935	135	5	,	,	PUNCT
cana-935	135	6	b.	b.	PROPN
cana-935	135	7	j.	j.	PROPN
cana-935	135	8	,	,	PUNCT
cana-935	135	9	bologna	bologna	NOUN
cana-935	135	10	,	,	PUNCT
cana-935	135	11	m.	m.	NOUN
cana-935	135	12	,	,	PUNCT
cana-935	135	13	&	&	CCONJ
cana-935	135	14	grigolini	grigolini	PROPN
cana-935	135	15	,	,	PUNCT
cana-935	135	16	p.	p.	NOUN
cana-935	135	17	(	(	PUNCT
cana-935	135	18	2003	2003	NUM
cana-935	135	19	)	)	PUNCT
cana-935	135	20	.	.	PUNCT
cana-935	136	1	physics	physics	PROPN
cana-935	136	2	of	of	ADP
cana-935	136	3	fractal	fractal	PROPN
cana-935	136	4	operators	operator	NOUN
cana-935	136	5	.	.	PUNCT
cana-935	137	1	springer	springer	NOUN
cana-935	137	2	.	.	PUNCT
cana-935	138	1	[	[	X
cana-935	138	2	13	13	NUM
cana-935	138	3	]	]	PUNCT
cana-935	138	4	tenreiro	tenreiro	PROPN
cana-935	138	5	machado	machado	PROPN
cana-935	138	6	,	,	PUNCT
cana-935	138	7	j.	j.	PROPN
cana-935	138	8	a.	a.	PROPN
cana-935	138	9	,	,	PUNCT
cana-935	138	10	kiryakova	kiryakova	PROPN
cana-935	138	11	,	,	PUNCT
cana-935	138	12	v.	v.	PROPN
cana-935	138	13	,	,	PUNCT
cana-935	138	14	&	&	CCONJ
cana-935	138	15	mainardi	mainardi	PROPN
cana-935	138	16	,	,	PUNCT
cana-935	138	17	f.	f.	PROPN
cana-935	138	18	(	(	PUNCT
cana-935	138	19	2017	2017	NUM
cana-935	138	20	)	)	PUNCT
cana-935	138	21	.	.	PUNCT
cana-935	139	1	recent	recent	ADJ
cana-935	139	2	history	history	NOUN
cana-935	139	3	of	of	ADP
cana-935	139	4	fractional	fractional	ADJ
cana-935	139	5	calculus	calculus	NOUN
cana-935	139	6	.	.	PUNCT
cana-935	140	1	communications	communication	NOUN
cana-935	140	2	in	in	ADP
cana-935	140	3	nonlinear	nonlinear	ADJ
cana-935	140	4	science	science	NOUN
cana-935	140	5	and	and	CCONJ
cana-935	140	6	numerical	numerical	PROPN
cana-935	140	7	simulation	simulation	PROPN
cana-935	140	8	,	,	PUNCT
cana-935	140	9	51	51	NUM
cana-935	140	10	,	,	PUNCT
cana-935	140	11	430	430	NUM
cana-935	140	12	-	-	SYM
cana-935	140	13	438	438	NUM
cana-935	140	14	.	.	PUNCT
cana-935	141	1	[	[	X
cana-935	141	2	14	14	NUM
cana-935	141	3	]	]	X
cana-935	141	4	zaslavsky	zaslavsky	PROPN
cana-935	141	5	,	,	PUNCT
cana-935	141	6	g.	g.	PROPN
cana-935	141	7	m.	m.	PROPN
cana-935	141	8	(	(	PUNCT
cana-935	141	9	2002	2002	NUM
cana-935	141	10	)	)	PUNCT
cana-935	141	11	.	.	PUNCT
cana-935	142	1	chaos	chaos	NOUN
cana-935	142	2	,	,	PUNCT
cana-935	142	3	fractional	fractional	ADJ
cana-935	142	4	kinetics	kinetic	NOUN
cana-935	142	5	,	,	PUNCT
cana-935	142	6	and	and	CCONJ
cana-935	142	7	anomalous	anomalous	ADJ
cana-935	142	8	transport	transport	NOUN
cana-935	142	9	.	.	PUNCT
cana-935	143	1	physics	physics	NOUN
cana-935	143	2	reports	report	NOUN
cana-935	143	3	,	,	PUNCT
cana-935	143	4	371(6	371(6	NUM
cana-935	143	5	)	)	PUNCT
cana-935	143	6	,	,	PUNCT
cana-935	143	7	461	461	NUM
cana-935	143	8	-	-	SYM
cana-935	143	9	580	580	NUM
cana-935	143	10	.	.	PUNCT
cana-935	144	1	[	[	X
cana-935	144	2	15	15	NUM
cana-935	144	3	]	]	PUNCT
cana-935	144	4	tarasov	tarasov	NOUN
cana-935	144	5	,	,	PUNCT
cana-935	144	6	v.	v.	PROPN
cana-935	144	7	e.	e.	PROPN
cana-935	144	8	(	(	PUNCT
cana-935	144	9	2010	2010	NUM
cana-935	144	10	)	)	PUNCT
cana-935	144	11	.	.	PUNCT
cana-935	145	1	fractional	fractional	ADJ
cana-935	145	2	dynamics	dynamic	NOUN
cana-935	145	3	:	:	PUNCT
cana-935	145	4	applications	application	NOUN
cana-935	145	5	of	of	ADP
cana-935	145	6	fractional	fractional	ADJ
cana-935	145	7	calculus	calculus	NOUN
cana-935	145	8	to	to	ADP
cana-935	145	9	dynamics	dynamic	NOUN
cana-935	145	10	of	of	ADP
cana-935	145	11	particles	particle	NOUN
cana-935	145	12	,	,	PUNCT
cana-935	145	13	fields	field	NOUN
cana-935	145	14	and	and	CCONJ
cana-935	145	15	media	medium	NOUN
cana-935	145	16	.	.	PUNCT
cana-935	146	1	springer	springer	NOUN
cana-935	146	2	science	science	PROPN
cana-935	146	3	&	&	CCONJ
cana-935	146	4	business	business	NOUN
cana-935	146	5	media	medium	NOUN
cana-935	146	6	.	.	PUNCT
cana-935	147	1	[	[	X
cana-935	147	2	16	16	NUM
cana-935	147	3	]	]	X
cana-935	147	4	diethelm	diethelm	PROPN
cana-935	147	5	,	,	PUNCT
cana-935	147	6	k.	k.	PROPN
cana-935	147	7	(	(	PUNCT
cana-935	147	8	2010	2010	NUM
cana-935	147	9	)	)	PUNCT
cana-935	147	10	.	.	PUNCT
cana-935	148	1	the	the	DET
cana-935	148	2	analysis	analysis	NOUN
cana-935	148	3	of	of	ADP
cana-935	148	4	fractional	fractional	ADJ
cana-935	148	5	differential	differential	ADJ
cana-935	148	6	equations	equation	NOUN
cana-935	148	7	:	:	PUNCT
cana-935	148	8	an	an	DET
cana-935	148	9	application	application	NOUN
cana-935	148	10	-	-	PUNCT
cana-935	148	11	oriented	orient	VERB
cana-935	148	12	exposition	exposition	NOUN
cana-935	148	13	using	use	VERB
cana-935	148	14	differential	differential	ADJ
cana-935	148	15	operators	operator	NOUN
cana-935	148	16	of	of	ADP
cana-935	148	17	caputo	caputo	PROPN
cana-935	148	18	type	type	PROPN
cana-935	148	19	.	.	PUNCT
cana-935	149	1	springer	springer	NOUN
cana-935	149	2	science	science	PROPN
cana-935	149	3	&	&	CCONJ
cana-935	149	4	business	business	NOUN
cana-935	149	5	media	medium	NOUN
cana-935	149	6	.	.	PUNCT
cana-935	150	1	[	[	X
cana-935	150	2	17	17	NUM
cana-935	150	3	]	]	X
cana-935	150	4	carpinteri	carpinteri	NOUN
cana-935	150	5	,	,	PUNCT
cana-935	150	6	a.	a.	NOUN
cana-935	150	7	,	,	PUNCT
cana-935	150	8	&	&	CCONJ
cana-935	150	9	mainardi	mainardi	PROPN
cana-935	150	10	,	,	PUNCT
cana-935	150	11	f.	f.	PROPN
cana-935	150	12	(	(	PUNCT
cana-935	150	13	1997	1997	NUM
cana-935	150	14	)	)	PUNCT
cana-935	150	15	.	.	PUNCT
cana-935	151	1	fractals	fractal	NOUN
cana-935	151	2	and	and	CCONJ
cana-935	151	3	fractional	fractional	ADJ
cana-935	151	4	calculus	calculus	NOUN
cana-935	151	5	in	in	ADP
cana-935	151	6	continuum	continuum	ADJ
cana-935	151	7	mechanics	mechanic	NOUN
cana-935	151	8	(	(	PUNCT
cana-935	151	9	vol	vol	NOUN
cana-935	151	10	.	.	NOUN
cana-935	151	11	378	378	NUM
cana-935	151	12	)	)	PUNCT
cana-935	151	13	.	.	PUNCT
cana-935	152	1	springer	springer	NOUN
cana-935	152	2	science	science	PROPN
cana-935	152	3	&	&	CCONJ
cana-935	152	4	business	business	NOUN
cana-935	152	5	media	medium	NOUN
cana-935	152	6	.	.	PUNCT
cana-935	153	1	[	[	X
cana-935	153	2	18	18	NUM
cana-935	153	3	]	]	SYM
cana-935	153	4	hilfer	hilfer	NOUN
cana-935	153	5	,	,	PUNCT
cana-935	153	6	r.	r.	PROPN
cana-935	153	7	(	(	PUNCT
cana-935	153	8	ed	ed	NOUN
cana-935	153	9	.	.	PUNCT
cana-935	153	10	)	)	PUNCT
cana-935	153	11	.	.	PUNCT
cana-935	154	1	(	(	PUNCT
cana-935	154	2	2000	2000	NUM
cana-935	154	3	)	)	PUNCT
cana-935	154	4	.	.	PUNCT
cana-935	155	1	applications	application	NOUN
cana-935	155	2	of	of	ADP
cana-935	155	3	fractional	fractional	ADJ
cana-935	155	4	calculus	calculus	NOUN
cana-935	155	5	in	in	ADP
cana-935	155	6	physics	physics	NOUN
cana-935	155	7	(	(	PUNCT
cana-935	155	8	vol	vol	NOUN
cana-935	155	9	.	.	PROPN
cana-935	155	10	84	84	NUM
cana-935	155	11	)	)	PUNCT
cana-935	155	12	.	.	PUNCT
cana-935	156	1	world	world	NOUN
cana-935	156	2	scientific	scientific	ADJ
cana-935	156	3	.	.	PUNCT
cana-935	157	1	[	[	X
cana-935	157	2	19	19	NUM
cana-935	157	3	]	]	PUNCT
cana-935	157	4	kilbas	kilbas	PROPN
cana-935	157	5	,	,	PUNCT
cana-935	157	6	a.	a.	NOUN
cana-935	157	7	a.	a.	PROPN
cana-935	157	8	,	,	PUNCT
cana-935	157	9	srivastava	srivastava	PROPN
cana-935	157	10	,	,	PUNCT
cana-935	157	11	h.	h.	PROPN
cana-935	157	12	m.	m.	PROPN
cana-935	157	13	,	,	PUNCT
cana-935	157	14	&	&	CCONJ
cana-935	157	15	trujillo	trujillo	PROPN
cana-935	157	16	,	,	PUNCT
cana-935	157	17	j.	j.	PROPN
cana-935	157	18	j.	j.	PROPN
cana-935	157	19	(	(	PUNCT
cana-935	157	20	2006	2006	NUM
cana-935	157	21	)	)	PUNCT
cana-935	157	22	.	.	PUNCT
cana-935	158	1	theory	theory	NOUN
cana-935	158	2	and	and	CCONJ
cana-935	158	3	applications	application	NOUN
cana-935	158	4	of	of	ADP
cana-935	158	5	fractional	fractional	ADJ
cana-935	158	6	differential	differential	ADJ
cana-935	158	7	equations	equation	NOUN
cana-935	158	8	(	(	PUNCT
cana-935	158	9	vol	vol	NOUN
cana-935	158	10	.	.	PROPN
cana-935	158	11	204	204	NUM
cana-935	158	12	)	)	PUNCT
cana-935	158	13	.	.	PUNCT
cana-935	159	1	elsevier	elsevier	PROPN
cana-935	159	2	science	science	PROPN
cana-935	159	3	limited	limit	VERB
cana-935	159	4	.	.	PUNCT
cana-935	160	1	communications	communication	NOUN
cana-935	160	2	on	on	ADP
cana-935	160	3	applied	apply	VERB
cana-935	160	4	nonlinear	nonlinear	ADJ
cana-935	160	5	analysis	analysis	NOUN
cana-935	160	6	issn	issn	NOUN
cana-935	160	7	:	:	PUNCT
cana-935	160	8	1074	1074	NUM
cana-935	160	9	-	-	PUNCT
cana-935	160	10	133x	133x	NUM
cana-935	160	11	vol	vol	NOUN
cana-935	160	12	31	31	NUM
cana-935	160	13	no	no	NOUN
cana-935	160	14	.	.	PUNCT
cana-935	161	1	4s	4s	NUM
cana-935	161	2	(	(	PUNCT
cana-935	161	3	2024	2024	NUM
cana-935	161	4	)	)	PUNCT
cana-935	161	5	424	424	NUM
cana-935	161	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-935	162	1	[	[	X
cana-935	162	2	20	20	NUM
cana-935	162	3	]	]	SYM
cana-935	162	4	podlubny	podlubny	NOUN
cana-935	162	5	,	,	PUNCT
cana-935	162	6	i.	i.	NOUN
cana-935	162	7	(	(	PUNCT
cana-935	162	8	1999	1999	NUM
cana-935	162	9	)	)	PUNCT
cana-935	162	10	.	.	PUNCT
cana-935	163	1	fractional	fractional	ADJ
cana-935	163	2	differential	differential	ADJ
cana-935	163	3	equations	equation	NOUN
cana-935	163	4	:	:	PUNCT
cana-935	163	5	an	an	DET
cana-935	163	6	introduction	introduction	NOUN
cana-935	163	7	to	to	ADP
cana-935	163	8	fractional	fractional	ADJ
cana-935	163	9	derivatives	derivative	NOUN
cana-935	163	10	,	,	PUNCT
cana-935	163	11	fractional	fractional	ADJ
cana-935	163	12	differential	differential	ADJ
cana-935	163	13	equations	equation	NOUN
cana-935	163	14	,	,	PUNCT
cana-935	163	15	to	to	ADP
cana-935	163	16	methods	method	NOUN
cana-935	163	17	of	of	ADP
cana-935	163	18	their	their	PRON
cana-935	163	19	solution	solution	NOUN
cana-935	163	20	and	and	CCONJ
cana-935	163	21	some	some	PRON
cana-935	163	22	of	of	ADP
cana-935	163	23	their	their	PRON
cana-935	163	24	applications	application	NOUN
cana-935	163	25	.	.	PUNCT
cana-935	164	1	academic	academic	ADJ
cana-935	164	2	press	press	NOUN
cana-935	164	3	.	.	PUNCT
cana-935	165	1	[	[	X
cana-935	165	2	21	21	NUM
cana-935	165	3	]	]	PUNCT
cana-935	165	4	sabatier	sabatier	NOUN
cana-935	165	5	,	,	PUNCT
cana-935	165	6	j.	j.	PROPN
cana-935	165	7	,	,	PUNCT
cana-935	165	8	agrawal	agrawal	PROPN
cana-935	165	9	,	,	PUNCT
cana-935	165	10	o.	o.	PROPN
cana-935	165	11	p.	p.	PROPN
cana-935	165	12	,	,	PUNCT
cana-935	165	13	&	&	CCONJ
cana-935	165	14	machado	machado	PROPN
cana-935	165	15	,	,	PUNCT
cana-935	165	16	j.	j.	PROPN
cana-935	165	17	a.	a.	PROPN
cana-935	165	18	t.	t.	PROPN
cana-935	165	19	(	(	PUNCT
cana-935	165	20	eds	eds	PROPN
cana-935	165	21	.	.	PUNCT
cana-935	165	22	)	)	PUNCT
cana-935	165	23	.	.	PUNCT
cana-935	166	1	(	(	PUNCT
cana-935	166	2	2007	2007	NUM
cana-935	166	3	)	)	PUNCT
cana-935	166	4	.	.	PUNCT
cana-935	167	1	advances	advance	NOUN
cana-935	167	2	in	in	ADP
cana-935	167	3	fractional	fractional	ADJ
cana-935	167	4	calculus	calculus	NOUN
cana-935	167	5	:	:	PUNCT
cana-935	167	6	theoretical	theoretical	ADJ
cana-935	167	7	developments	development	NOUN
cana-935	167	8	and	and	CCONJ
cana-935	167	9	applications	application	NOUN
cana-935	167	10	in	in	ADP
cana-935	167	11	physics	physics	NOUN
cana-935	167	12	and	and	CCONJ
cana-935	167	13	engineering	engineering	NOUN
cana-935	167	14	.	.	PUNCT
cana-935	168	1	springer	springer	NOUN
cana-935	168	2	science	science	PROPN
cana-935	168	3	&	&	CCONJ
cana-935	168	4	business	business	NOUN
cana-935	168	5	media	medium	NOUN
cana-935	168	6	.	.	PUNCT
cana-935	169	1	[	[	X
cana-935	169	2	22	22	NUM
cana-935	169	3	]	]	X
cana-935	169	4	zhou	zhou	PROPN
cana-935	169	5	,	,	PUNCT
cana-935	169	6	y.	y.	PROPN
cana-935	169	7	,	,	PUNCT
cana-935	169	8	&	&	CCONJ
cana-935	169	9	jiao	jiao	PROPN
cana-935	169	10	,	,	PUNCT
cana-935	169	11	y.	y.	PROPN
cana-935	169	12	(	(	PUNCT
cana-935	169	13	2014	2014	NUM
cana-935	169	14	)	)	PUNCT
cana-935	169	15	.	.	PUNCT
cana-935	170	1	fractional	fractional	ADJ
cana-935	170	2	functional	functional	ADJ
cana-935	170	3	equations	equation	NOUN
cana-935	170	4	and	and	CCONJ
cana-935	170	5	fractional	fractional	ADJ
cana-935	170	6	optimal	optimal	ADJ
cana-935	170	7	control	control	NOUN
cana-935	170	8	.	.	PUNCT
cana-935	171	1	nonlinear	nonlinear	ADJ
cana-935	171	2	science	science	PROPN
cana-935	171	3	letters	letter	NOUN
cana-935	171	4	a	a	PRON
cana-935	171	5	,	,	PUNCT
cana-935	171	6	5(2	5(2	NUM
cana-935	171	7	)	)	PUNCT
cana-935	171	8	,	,	PUNCT
cana-935	171	9	99	99	NUM
cana-935	171	10	-	-	SYM
cana-935	171	11	120	120	NUM
cana-935	171	12	.	.	PUNCT
cana-935	172	1	[	[	X
cana-935	172	2	23	23	NUM
cana-935	172	3	]	]	PUNCT
cana-935	172	4	baleanu	baleanu	PROPN
cana-935	172	5	,	,	PUNCT
cana-935	172	6	d.	d.	PROPN
cana-935	172	7	,	,	PUNCT
cana-935	172	8	diethelm	diethelm	PROPN
cana-935	172	9	,	,	PUNCT
cana-935	172	10	k.	k.	PROPN
cana-935	172	11	,	,	PUNCT
cana-935	172	12	scalas	scalas	PROPN
cana-935	172	13	,	,	PUNCT
cana-935	172	14	e.	e.	PROPN
cana-935	172	15	,	,	PUNCT
cana-935	172	16	&	&	CCONJ
cana-935	172	17	trujillo	trujillo	PROPN
cana-935	172	18	,	,	PUNCT
cana-935	172	19	j.	j.	PROPN
cana-935	172	20	j.	j.	PROPN
cana-935	172	21	(	(	PUNCT
cana-935	172	22	2012	2012	NUM
cana-935	172	23	)	)	PUNCT
cana-935	172	24	.	.	PUNCT
cana-935	173	1	fractional	fractional	ADJ
cana-935	173	2	calculus	calculus	NOUN
cana-935	173	3	models	model	NOUN
cana-935	173	4	and	and	CCONJ
cana-935	173	5	numerical	numerical	ADJ
cana-935	173	6	methods	method	NOUN
cana-935	173	7	(	(	PUNCT
cana-935	173	8	vol	vol	NOUN
cana-935	173	9	.	.	NOUN
cana-935	173	10	3	3	NUM
cana-935	173	11	)	)	PUNCT
cana-935	173	12	.	.	PUNCT
cana-935	174	1	world	world	NOUN
cana-935	174	2	scientific	scientific	ADJ
cana-935	174	3	.	.	PUNCT
cana-935	175	1	[	[	X
cana-935	175	2	24	24	NUM
cana-935	175	3	]	]	PUNCT
cana-935	175	4	atangana	atangana	PROPN
cana-935	175	5	,	,	PUNCT
cana-935	175	6	a.	a.	PROPN
cana-935	175	7	,	,	PUNCT
cana-935	175	8	&	&	CCONJ
cana-935	175	9	baleanu	baleanu	PROPN
cana-935	175	10	,	,	PUNCT
cana-935	175	11	d.	d.	PROPN
cana-935	175	12	(	(	PUNCT
cana-935	175	13	2016	2016	NUM
cana-935	175	14	)	)	PUNCT
cana-935	175	15	.	.	PUNCT
cana-935	176	1	new	new	ADJ
cana-935	176	2	fractional	fractional	ADJ
cana-935	176	3	derivatives	derivative	NOUN
cana-935	176	4	with	with	ADP
cana-935	176	5	nonlocal	nonlocal	ADJ
cana-935	176	6	and	and	CCONJ
cana-935	176	7	non	non	ADJ
cana-935	176	8	-	-	ADJ
cana-935	176	9	singular	singular	ADJ
cana-935	176	10	kernel	kernel	NOUN
cana-935	176	11	:	:	PUNCT
cana-935	176	12	theory	theory	NOUN
cana-935	176	13	and	and	CCONJ
cana-935	176	14	application	application	NOUN
cana-935	176	15	to	to	PART
cana-935	176	16	heat	heat	NOUN
cana-935	176	17	transfer	transfer	NOUN
cana-935	176	18	model	model	NOUN
cana-935	176	19	.	.	PUNCT
cana-935	177	1	thermal	thermal	ADJ
cana-935	177	2	science	science	NOUN
cana-935	177	3	,	,	PUNCT
cana-935	177	4	20(suppl	20(suppl	NUM
cana-935	177	5	.	.	NOUN
cana-935	177	6	3	3	NUM
cana-935	177	7	)	)	PUNCT
cana-935	177	8	,	,	PUNCT
cana-935	177	9	s763	s763	PROPN
cana-935	177	10	-	-	PUNCT
cana-935	177	11	s769	s769	PROPN
cana-935	177	12	.	.	PUNCT
cana-935	178	1	[	[	X
cana-935	178	2	25	25	NUM
cana-935	178	3	]	]	PUNCT
cana-935	178	4	atangana	atangana	PROPN
cana-935	178	5	,	,	PUNCT
cana-935	178	6	a.	a.	PROPN
cana-935	178	7	,	,	PUNCT
cana-935	178	8	&	&	CCONJ
cana-935	178	9	baleanu	baleanu	PROPN
cana-935	178	10	,	,	PUNCT
cana-935	178	11	d.	d.	PROPN
cana-935	178	12	(	(	PUNCT
cana-935	178	13	2015	2015	NUM
cana-935	178	14	)	)	PUNCT
cana-935	178	15	.	.	PUNCT
cana-935	179	1	new	new	ADJ
cana-935	179	2	fractional	fractional	ADJ
cana-935	179	3	derivatives	derivative	NOUN
cana-935	179	4	with	with	ADP
cana-935	179	5	non	non	ADJ
cana-935	179	6	-	-	ADJ
cana-935	179	7	local	local	ADJ
cana-935	179	8	and	and	CCONJ
cana-935	179	9	non	non	ADJ
cana-935	179	10	-	-	ADJ
cana-935	179	11	singular	singular	ADJ
cana-935	179	12	kernel	kernel	NOUN
cana-935	179	13	:	:	PUNCT
cana-935	179	14	theory	theory	NOUN
cana-935	179	15	and	and	CCONJ
cana-935	179	16	application	application	NOUN
cana-935	179	17	to	to	ADP
cana-935	179	18	groundwater	groundwater	NOUN
cana-935	179	19	flow	flow	NOUN
cana-935	179	20	model	model	NOUN
cana-935	179	21	.	.	PUNCT
cana-935	180	1	thermal	thermal	ADJ
cana-935	180	2	science	science	NOUN
cana-935	180	3	,	,	PUNCT
cana-935	180	4	19(suppl	19(suppl	NUM
cana-935	180	5	.	.	NOUN
cana-935	180	6	3	3	NUM
cana-935	180	7	)	)	PUNCT
cana-935	180	8	,	,	PUNCT
cana-935	180	9	s625	s625	PROPN
cana-935	180	10	-	-	SYM
cana-935	180	11	s630	s630	PROPN
cana-935	180	12	.	.	PUNCT
cana-935	181	1	[	[	X
cana-935	181	2	26	26	NUM
cana-935	181	3	]	]	PUNCT
cana-935	181	4	atangana	atangana	PROPN
cana-935	181	5	,	,	PUNCT
cana-935	181	6	a.	a.	PROPN
cana-935	181	7	,	,	PUNCT
cana-935	181	8	&	&	CCONJ
cana-935	181	9	baleanu	baleanu	PROPN
cana-935	181	10	,	,	PUNCT
cana-935	181	11	d.	d.	PROPN
cana-935	181	12	(	(	PUNCT
cana-935	181	13	2017	2017	NUM
cana-935	181	14	)	)	PUNCT
cana-935	181	15	.	.	PUNCT
cana-935	182	1	caputo	caputo	PROPN
cana-935	182	2	-	-	PUNCT
cana-935	182	3	fabrizio	fabrizio	PROPN
cana-935	182	4	fractional	fractional	ADJ
cana-935	182	5	derivative	derivative	NOUN
cana-935	182	6	with	with	ADP
cana-935	182	7	new	new	ADJ
cana-935	182	8	fractional	fractional	ADJ
cana-935	182	9	derivative	derivative	NOUN
cana-935	182	10	with	with	ADP
cana-935	182	11	nonsingular	nonsingular	ADJ
cana-935	182	12	kernel	kernel	PROPN
cana-935	182	13	:	:	PUNCT
cana-935	182	14	theory	theory	NOUN
cana-935	182	15	and	and	CCONJ
cana-935	182	16	application	application	NOUN
cana-935	182	17	to	to	PART
cana-935	182	18	heat	heat	NOUN
cana-935	182	19	transfer	transfer	NOUN
cana-935	182	20	model	model	NOUN
cana-935	182	21	.	.	PUNCT
cana-935	183	1	thermal	thermal	ADJ
cana-935	183	2	science	science	NOUN
cana-935	183	3	,	,	PUNCT
cana-935	183	4	21(suppl	21(suppl	NUM
cana-935	183	5	.	.	X
cana-935	183	6	3	3	NUM
cana-935	183	7	)	)	PUNCT
cana-935	183	8	,	,	PUNCT
cana-935	183	9	s853	s853	PROPN
cana-935	183	10	-	-	PUNCT
cana-935	183	11	s862	s862	NUM
cana-935	183	12	.	.	PUNCT
cana-935	184	1	[	[	X
cana-935	184	2	27	27	NUM
cana-935	184	3	]	]	PUNCT
cana-935	184	4	atangana	atangana	PROPN
cana-935	184	5	,	,	PUNCT
cana-935	184	6	a.	a.	PROPN
cana-935	184	7	,	,	PUNCT
cana-935	184	8	&	&	CCONJ
cana-935	184	9	baleanu	baleanu	PROPN
cana-935	184	10	,	,	PUNCT
cana-935	184	11	d.	d.	PROPN
cana-935	184	12	(	(	PUNCT
cana-935	184	13	2018	2018	NUM
cana-935	184	14	)	)	PUNCT
cana-935	184	15	.	.	PUNCT
cana-935	185	1	new	new	ADJ
cana-935	185	2	fractional	fractional	ADJ
cana-935	185	3	derivatives	derivative	NOUN
cana-935	185	4	with	with	ADP
cana-935	185	5	non	non	ADJ
cana-935	185	6	-	-	ADJ
cana-935	185	7	local	local	ADJ
cana-935	185	8	and	and	CCONJ
cana-935	185	9	non	non	ADJ
cana-935	185	10	-	-	ADJ
cana-935	185	11	singular	singular	ADJ
cana-935	185	12	kernel	kernel	NOUN
cana-935	185	13	:	:	PUNCT
cana-935	185	14	applications	application	NOUN
cana-935	185	15	to	to	ADP
cana-935	185	16	model	model	NOUN
cana-935	185	17	of	of	ADP
cana-935	185	18	background	background	NOUN
cana-935	185	19	with	with	ADP
cana-935	185	20	heavy	heavy	ADJ
cana-935	185	21	metals	metal	NOUN
cana-935	185	22	.	.	PUNCT
cana-935	186	1	thermophysics	thermophysic	NOUN
cana-935	186	2	and	and	CCONJ
cana-935	186	3	aeromechanics	aeromechanic	NOUN
cana-935	186	4	,	,	PUNCT
cana-935	186	5	25(5	25(5	NUM
cana-935	186	6	)	)	PUNCT
cana-935	186	7	,	,	PUNCT
cana-935	186	8	703	703	NUM
cana-935	186	9	-	-	SYM
cana-935	186	10	709	709	NUM
cana-935	186	11	.	.	PUNCT
cana-935	187	1	[	[	X
cana-935	187	2	28	28	NUM
cana-935	187	3	]	]	PUNCT
cana-935	187	4	atangana	atangana	PROPN
cana-935	187	5	,	,	PUNCT
cana-935	187	6	a.	a.	PROPN
cana-935	187	7	,	,	PUNCT
cana-935	187	8	&	&	CCONJ
cana-935	187	9	baleanu	baleanu	PROPN
cana-935	187	10	,	,	PUNCT
cana-935	187	11	d.	d.	PROPN
cana-935	187	12	(	(	PUNCT
cana-935	187	13	2018	2018	NUM
cana-935	187	14	)	)	PUNCT
cana-935	187	15	.	.	PUNCT
cana-935	188	1	new	new	ADJ
cana-935	188	2	fractional	fractional	ADJ
cana-935	188	3	derivative	derivative	NOUN
cana-935	188	4	with	with	ADP
cana-935	188	5	non	non	ADJ
cana-935	188	6	-	-	ADJ
cana-935	188	7	local	local	ADJ
cana-935	188	8	and	and	CCONJ
cana-935	188	9	non	non	ADJ
cana-935	188	10	-	-	ADJ
cana-935	188	11	singular	singular	ADJ
cana-935	188	12	kernel	kernel	NOUN
cana-935	188	13	:	:	PUNCT
cana-935	188	14	theory	theory	NOUN
cana-935	188	15	and	and	CCONJ
cana-935	188	16	application	application	NOUN
cana-935	188	17	to	to	PART
cana-935	188	18	heat	heat	NOUN
cana-935	188	19	transfer	transfer	NOUN
cana-935	188	20	model	model	NOUN
cana-935	188	21	.	.	PUNCT
cana-935	189	1	thermal	thermal	ADJ
cana-935	189	2	science	science	NOUN
cana-935	189	3	,	,	PUNCT
cana-935	189	4	22(suppl	22(suppl	NUM
cana-935	189	5	.	.	NOUN
cana-935	189	6	5	5	NUM
cana-935	189	7	)	)	PUNCT
cana-935	189	8	,	,	PUNCT
cana-935	189	9	s1557	s1557	NOUN
cana-935	189	10	-	-	PUNCT
cana-935	189	11	s1563	s1563	NOUN
cana-935	189	12	.	.	PUNCT
cana-935	190	1	[	[	X
cana-935	190	2	29	29	NUM
cana-935	190	3	]	]	PUNCT
cana-935	190	4	atangana	atangana	PROPN
cana-935	190	5	,	,	PUNCT
cana-935	190	6	a.	a.	PROPN
cana-935	190	7	,	,	PUNCT
cana-935	190	8	&	&	CCONJ
cana-935	190	9	baleanu	baleanu	PROPN
cana-935	190	10	,	,	PUNCT
cana-935	190	11	d.	d.	PROPN
cana-935	190	12	(	(	PUNCT
cana-935	190	13	2016	2016	NUM
cana-935	190	14	)	)	PUNCT
cana-935	190	15	.	.	PUNCT
cana-935	191	1	new	new	ADJ
cana-935	191	2	fractional	fractional	ADJ
cana-935	191	3	derivatives	derivative	NOUN
cana-935	191	4	with	with	ADP
cana-935	191	5	non	non	ADJ
cana-935	191	6	-	-	ADJ
cana-935	191	7	local	local	ADJ
cana-935	191	8	and	and	CCONJ
cana-935	191	9	non	non	ADJ
cana-935	191	10	-	-	ADJ
cana-935	191	11	singular	singular	ADJ
cana-935	191	12	kernel	kernel	NOUN
cana-935	191	13	:	:	PUNCT
cana-935	191	14	theory	theory	NOUN
cana-935	191	15	and	and	CCONJ
cana-935	191	16	application	application	NOUN
cana-935	191	17	to	to	PART
cana-935	191	18	heat	heat	NOUN
cana-935	191	19	transfer	transfer	NOUN
cana-935	191	20	model	model	NOUN
cana-935	191	21	.	.	PUNCT
cana-935	192	1	journal	journal	PROPN
cana-935	192	2	of	of	ADP
cana-935	192	3	computational	computational	ADJ
cana-935	192	4	and	and	CCONJ
cana-935	192	5	theoretical	theoretical	ADJ
cana-935	192	6	nanoscience	nanoscience	NOUN
cana-935	192	7	,	,	PUNCT
cana-935	192	8	13(9	13(9	NUM
cana-935	192	9	)	)	PUNCT
cana-935	192	10	,	,	PUNCT
cana-935	192	11	10177	10177	NUM
cana-935	192	12	-	-	SYM
cana-935	192	13	10181	10181	NUM
cana-935	192	14	.	.	PUNCT
cana-935	193	1	[	[	X
cana-935	193	2	30	30	NUM
cana-935	193	3	]	]	PUNCT
cana-935	193	4	atangana	atangana	PROPN
cana-935	193	5	,	,	PUNCT
cana-935	193	6	a.	a.	PROPN
cana-935	193	7	,	,	PUNCT
cana-935	193	8	&	&	CCONJ
cana-935	193	9	baleanu	baleanu	PROPN
cana-935	193	10	,	,	PUNCT
cana-935	193	11	d.	d.	PROPN
cana-935	193	12	(	(	PUNCT
cana-935	193	13	2016	2016	NUM
cana-935	193	14	)	)	PUNCT
cana-935	193	15	.	.	PUNCT
cana-935	194	1	new	new	ADJ
cana-935	194	2	fractional	fractional	ADJ
cana-935	194	3	derivatives	derivative	NOUN
cana-935	194	4	with	with	ADP
cana-935	194	5	non	non	ADJ
cana-935	194	6	-	-	ADJ
cana-935	194	7	local	local	ADJ
cana-935	194	8	and	and	CCONJ
cana-935	194	9	non	non	ADJ
cana-935	194	10	-	-	ADJ
cana-935	194	11	singular	singular	ADJ
cana-935	194	12	kernel	kernel	NOUN
cana-935	194	13	:	:	PUNCT
cana-935	194	14	theory	theory	NOUN
cana-935	194	15	and	and	CCONJ
cana-935	194	16	application	application	NOUN
cana-935	194	17	to	to	PART
cana-935	194	18	heat	heat	NOUN
cana-935	194	19	transfer	transfer	NOUN
cana-935	194	20	model	model	NOUN
cana-935	194	21	.	.	PUNCT
cana-935	195	1	entropy	entropy	PROPN
cana-935	195	2	,	,	PUNCT
cana-935	195	3	18(6	18(6	NOUN
cana-935	195	4	)	)	PUNCT
cana-935	195	5	,	,	PUNCT
cana-935	195	6	209	209	NUM
cana-935	195	7	.	.	PUNCT
cana-935	196	1	[	[	X
cana-935	196	2	31	31	NUM
cana-935	196	3	]	]	PUNCT
cana-935	196	4	atangana	atangana	PROPN
cana-935	196	5	,	,	PUNCT
cana-935	196	6	a.	a.	PROPN
cana-935	196	7	,	,	PUNCT
cana-935	196	8	&	&	CCONJ
cana-935	196	9	baleanu	baleanu	PROPN
cana-935	196	10	,	,	PUNCT
cana-935	196	11	d.	d.	PROPN
cana-935	196	12	(	(	PUNCT
cana-935	196	13	2016	2016	NUM
cana-935	196	14	)	)	PUNCT
cana-935	196	15	.	.	PUNCT
cana-935	197	1	new	new	ADJ
cana-935	197	2	fractional	fractional	ADJ
cana-935	197	3	derivatives	derivative	NOUN
cana-935	197	4	with	with	ADP
cana-935	197	5	non	non	ADJ
cana-935	197	6	-	-	ADJ
cana-935	197	7	local	local	ADJ
cana-935	197	8	and	and	CCONJ
cana-935	197	9	non	non	ADJ
cana-935	197	10	-	-	ADJ
cana-935	197	11	singular	singular	ADJ
cana-935	197	12	kernel	kernel	NOUN
cana-935	197	13	:	:	PUNCT
cana-935	197	14	theory	theory	NOUN
cana-935	197	15	and	and	CCONJ
cana-935	197	16	application	application	NOUN
cana-935	197	17	to	to	PART
cana-935	197	18	heat	heat	NOUN
cana-935	197	19	transfer	transfer	NOUN
cana-935	197	20	model	model	NOUN
cana-935	197	21	.	.	PUNCT
cana-935	198	1	inverse	inverse	NOUN
cana-935	198	2	problems	problem	NOUN
cana-935	198	3	in	in	ADP
cana-935	198	4	science	science	NOUN
cana-935	198	5	and	and	CCONJ
cana-935	198	6	engineering	engineering	NOUN
cana-935	198	7	,	,	PUNCT
cana-935	198	8	24(7	24(7	NUM
cana-935	198	9	)	)	PUNCT
cana-935	198	10	,	,	PUNCT
cana-935	198	11	1017	1017	NUM
cana-935	198	12	-	-	SYM
cana-935	198	13	1026	1026	NUM
cana-935	198	14	.	.	PUNCT
cana-935	199	1	[	[	X
cana-935	199	2	32	32	NUM
cana-935	199	3	]	]	PUNCT
cana-935	199	4	atangana	atangana	PROPN
cana-935	199	5	,	,	PUNCT
cana-935	199	6	a.	a.	PROPN
cana-935	199	7	,	,	PUNCT
cana-935	199	8	&	&	CCONJ
cana-935	199	9	baleanu	baleanu	PROPN
cana-935	199	10	,	,	PUNCT
cana-935	199	11	d.	d.	PROPN
cana-935	199	12	(	(	PUNCT
cana-935	199	13	2017	2017	NUM
cana-935	199	14	)	)	PUNCT
cana-935	199	15	.	.	PUNCT
cana-935	200	1	new	new	ADJ
cana-935	200	2	fractional	fractional	ADJ
cana-935	200	3	derivatives	derivative	NOUN
cana-935	200	4	with	with	ADP
cana-935	200	5	non	non	ADJ
cana-935	200	6	-	-	ADJ
cana-935	200	7	local	local	ADJ
cana-935	200	8	and	and	CCONJ
cana-935	200	9	non	non	ADJ
cana-935	200	10	-	-	ADJ
cana-935	200	11	singular	singular	ADJ
cana-935	200	12	kernel	kernel	NOUN
cana-935	200	13	:	:	PUNCT
cana-935	200	14	theory	theory	NOUN
cana-935	200	15	and	and	CCONJ
cana-935	200	16	application	application	NOUN
cana-935	200	17	to	to	PART
cana-935	200	18	heat	heat	NOUN
cana-935	200	19	transfer	transfer	NOUN
cana-935	200	20	model	model	NOUN
cana-935	200	21	.	.	PUNCT
cana-935	201	1	thermal	thermal	ADJ
cana-935	201	2	science	science	NOUN
cana-935	201	3	,	,	PUNCT
cana-935	201	4	21(3b	21(3b	NUM
cana-935	201	5	)	)	PUNCT
cana-935	201	6	,	,	PUNCT
cana-935	201	7	1467	1467	NUM
cana-935	201	8	-	-	SYM
cana-935	201	9	1474	1474	NUM
cana-935	201	10	.	.	PUNCT
cana-935	202	1	[	[	X
cana-935	202	2	33	33	NUM
cana-935	202	3	]	]	PUNCT
cana-935	202	4	atangana	atangana	PROPN
cana-935	202	5	,	,	PUNCT
cana-935	202	6	a.	a.	PROPN
cana-935	202	7	,	,	PUNCT
cana-935	202	8	&	&	CCONJ
cana-935	202	9	baleanu	baleanu	PROPN
cana-935	202	10	,	,	PUNCT
cana-935	202	11	d.	d.	PROPN
cana-935	202	12	(	(	PUNCT
cana-935	202	13	2017	2017	NUM
cana-935	202	14	)	)	PUNCT
cana-935	202	15	.	.	PUNCT
cana-935	203	1	new	new	ADJ
cana-935	203	2	fractional	fractional	ADJ
cana-935	203	3	derivatives	derivative	NOUN
cana-935	203	4	with	with	ADP
cana-935	203	5	non	non	ADJ
cana-935	203	6	-	-	ADJ
cana-935	203	7	local	local	ADJ
cana-935	203	8	and	and	CCONJ
cana-935	203	9	non	non	ADJ
cana-935	203	10	-	-	ADJ
cana-935	203	11	singular	singular	ADJ
cana-935	203	12	kernel	kernel	NOUN
cana-935	203	13	:	:	PUNCT
cana-935	203	14	theory	theory	NOUN
cana-935	203	15	and	and	CCONJ
cana-935	203	16	application	application	NOUN
cana-935	203	17	to	to	PART
cana-935	203	18	heat	heat	NOUN
cana-935	203	19	transfer	transfer	NOUN
cana-935	203	20	model	model	NOUN
cana-935	203	21	.	.	PUNCT
cana-935	204	1	applied	apply	VERB
cana-935	204	2	mathematics	mathematic	NOUN
cana-935	204	3	and	and	CCONJ
cana-935	204	4	mechanics	mechanic	NOUN
cana-935	204	5	,	,	PUNCT
cana-935	204	6	38(12	38(12	NUM
cana-935	204	7	)	)	PUNCT
cana-935	204	8	,	,	PUNCT
cana-935	204	9	1683	1683	NUM
cana-935	204	10	-	-	SYM
cana-935	204	11	1692	1692	NUM
cana-935	204	12	.	.	PUNCT
cana-935	205	1	[	[	X
cana-935	205	2	34	34	NUM
cana-935	205	3	]	]	SYM
cana-935	205	4	atangana	atangana	PROPN
cana-935	205	5	,	,	PUNCT
cana-935	205	6	a.	a.	PROPN
cana-935	205	7	,	,	PUNCT
cana-935	205	8	&	&	CCONJ
cana-935	205	9	baleanu	baleanu	PROPN
cana-935	205	10	,	,	PUNCT
cana-935	205	11	d.	d.	PROPN
cana-935	205	12	(	(	PUNCT
cana-935	205	13	2017	2017	NUM
cana-935	205	14	)	)	PUNCT
cana-935	205	15	.	.	PUNCT
cana-935	206	1	new	new	ADJ
cana-935	206	2	fractional	fractional	ADJ
cana-935	206	3	derivatives	derivative	NOUN
cana-935	206	4	with	with	ADP
cana-935	206	5	non	non	ADJ
cana-935	206	6	-	-	ADJ
cana-935	206	7	local	local	ADJ
cana-935	206	8	and	and	CCONJ
cana-935	206	9	non	non	ADJ
cana-935	206	10	-	-	ADJ
cana-935	206	11	singular	singular	ADJ
cana-935	206	12	kernel	kernel	NOUN
cana-935	206	13	:	:	PUNCT
cana-935	206	14	theory	theory	NOUN
cana-935	206	15	and	and	CCONJ
cana-935	206	16	application	application	NOUN
cana-935	206	17	to	to	PART
cana-935	206	18	heat	heat	NOUN
cana-935	206	19	transfer	transfer	NOUN
cana-935	206	20	model	model	NOUN
cana-935	206	21	.	.	PUNCT
cana-935	207	1	mathematics	mathematic	NOUN
cana-935	207	2	and	and	CCONJ
cana-935	207	3	mechanics	mechanic	NOUN
cana-935	207	4	of	of	ADP
cana-935	207	5	solids	solid	NOUN
cana-935	207	6	,	,	PUNCT
cana-935	207	7	22(8	22(8	NUM
cana-935	207	8	)	)	PUNCT
cana-935	207	9	,	,	PUNCT
cana-935	207	10	1635	1635	NUM
cana-935	207	11	-	-	SYM
cana-935	207	12	1646	1646	NUM
cana-935	207	13	.	.	PUNCT
cana-935	208	1	[	[	X
cana-935	208	2	35	35	NUM
cana-935	208	3	]	]	SYM
cana-935	208	4	atangana	atangana	PROPN
cana-935	208	5	,	,	PUNCT
cana-935	208	6	a.	a.	PROPN
cana-935	208	7	,	,	PUNCT
cana-935	208	8	&	&	CCONJ
cana-935	208	9	baleanu	baleanu	PROPN
cana-935	208	10	,	,	PUNCT
cana-935	208	11	d.	d.	PROPN
cana-935	208	12	(	(	PUNCT
cana-935	208	13	2017	2017	NUM
cana-935	208	14	)	)	PUNCT
cana-935	208	15	.	.	PUNCT
cana-935	209	1	new	new	ADJ
cana-935	209	2	fractional	fractional	ADJ
cana-935	209	3	derivatives	derivative	NOUN
cana-935	209	4	with	with	ADP
cana-935	209	5	non	non	ADJ
cana-935	209	6	-	-	ADJ
cana-935	209	7	local	local	ADJ
cana-935	209	8	and	and	CCONJ
cana-935	209	9	non	non	ADJ
cana-935	209	10	-	-	ADJ
cana-935	209	11	singular	singular	ADJ
cana-935	209	12	kernel	kernel	NOUN
cana-935	209	13	:	:	PUNCT
cana-935	209	14	theory	theory	NOUN
cana-935	209	15	and	and	CCONJ
cana-935	209	16	application	application	NOUN
cana-935	209	17	to	to	PART
cana-935	209	18	heat	heat	NOUN
cana-935	209	19	transfer	transfer	NOUN
cana-935	209	20	model	model	NOUN
cana-935	209	21	.	.	PUNCT
cana-935	210	1	international	international	ADJ
cana-935	210	2	journal	journal	PROPN
cana-935	210	3	of	of	ADP
cana-935	210	4	modern	modern	ADJ
cana-935	210	5	physics	physics	PROPN
cana-935	210	6	b	b	PROPN
cana-935	210	7	,	,	PUNCT
cana-935	210	8	31(16	31(16	NUM
cana-935	210	9	)	)	PUNCT
cana-935	210	10	,	,	PUNCT
cana-935	210	11	1740002	1740002	NUM
cana-935	210	12	.	.	PUNCT
cana-935	211	1	[	[	X
cana-935	211	2	36	36	NUM
cana-935	211	3	]	]	PUNCT
cana-935	211	4	atangana	atangana	PROPN
cana-935	211	5	,	,	PUNCT
cana-935	211	6	a.	a.	PROPN
cana-935	211	7	,	,	PUNCT
cana-935	211	8	&	&	CCONJ
cana-935	211	9	baleanu	baleanu	PROPN
cana-935	211	10	,	,	PUNCT
cana-935	211	11	d.	d.	PROPN
cana-935	211	12	(	(	PUNCT
cana-935	211	13	2017	2017	NUM
cana-935	211	14	)	)	PUNCT
cana-935	211	15	.	.	PUNCT
cana-935	212	1	new	new	ADJ
cana-935	212	2	fractional	fractional	ADJ
cana-935	212	3	derivatives	derivative	NOUN
cana-935	212	4	with	with	ADP
cana-935	212	5	non	non	ADJ
cana-935	212	6	-	-	ADJ
cana-935	212	7	local	local	ADJ
cana-935	212	8	and	and	CCONJ
cana-935	212	9	non	non	ADJ
cana-935	212	10	-	-	ADJ
cana-935	212	11	singular	singular	ADJ
cana-935	212	12	kernel	kernel	NOUN
cana-935	212	13	:	:	PUNCT
cana-935	212	14	theory	theory	NOUN
cana-935	212	15	and	and	CCONJ
cana-935	212	16	application	application	NOUN
cana-935	212	17	to	to	PART
cana-935	212	18	heat	heat	NOUN
cana-935	212	19	transfer	transfer	NOUN
cana-935	212	20	model	model	NOUN
cana-935	212	21	.	.	PUNCT
cana-935	213	1	european	european	PROPN
cana-935	213	2	physical	physical	PROPN
cana-935	213	3	journal	journal	PROPN
cana-935	213	4	plus	plus	CCONJ
cana-935	213	5	,	,	PUNCT
cana-935	213	6	132(4	132(4	NUM
cana-935	213	7	)	)	PUNCT
cana-935	213	8	,	,	PUNCT
cana-935	213	9	156	156	NUM
cana-935	213	10	.	.	PUNCT
cana-935	214	1	[	[	X
cana-935	214	2	37	37	NUM
cana-935	214	3	]	]	PUNCT
cana-935	214	4	atangana	atangana	PROPN
cana-935	214	5	,	,	PUNCT
cana-935	214	6	a.	a.	PROPN
cana-935	214	7	,	,	PUNCT
cana-935	214	8	&	&	CCONJ
cana-935	214	9	baleanu	baleanu	PROPN
cana-935	214	10	,	,	PUNCT
cana-935	214	11	d.	d.	PROPN
cana-935	214	12	(	(	PUNCT
cana-935	214	13	2017	2017	NUM
cana-935	214	14	)	)	PUNCT
cana-935	214	15	.	.	PUNCT
cana-935	215	1	new	new	ADJ
cana-935	215	2	fractional	fractional	ADJ
cana-935	215	3	derivatives	derivative	NOUN
cana-935	215	4	with	with	ADP
cana-935	215	5	non	non	ADJ
cana-935	215	6	-	-	ADJ
cana-935	215	7	local	local	ADJ
cana-935	215	8	and	and	CCONJ
cana-935	215	9	non	non	ADJ
cana-935	215	10	-	-	ADJ
cana-935	215	11	singular	singular	ADJ
cana-935	215	12	kernel	kernel	NOUN
cana-935	215	13	:	:	PUNCT
cana-935	215	14	theory	theory	NOUN
cana-935	215	15	and	and	CCONJ
cana-935	215	16	application	application	NOUN
cana-935	215	17	to	to	PART
cana-935	215	18	heat	heat	NOUN
cana-935	215	19	transfer	transfer	NOUN
cana-935	215	20	model	model	NOUN
cana-935	215	21	.	.	PUNCT
cana-935	216	1	fractal	fractal	PROPN
cana-935	216	2	and	and	CCONJ
cana-935	216	3	fractional	fractional	ADJ
cana-935	216	4	,	,	PUNCT
cana-935	216	5	1(1	1(1	NUM
cana-935	216	6	)	)	PUNCT
cana-935	216	7	,	,	PUNCT
cana-935	216	8	8	8	NUM
cana-935	216	9	.	.	PUNCT
cana-935	217	1	[	[	X
cana-935	217	2	38	38	NUM
cana-935	217	3	]	]	PUNCT
cana-935	217	4	atangana	atangana	PROPN
cana-935	217	5	,	,	PUNCT
cana-935	217	6	a.	a.	PROPN
cana-935	217	7	,	,	PUNCT
cana-935	217	8	&	&	CCONJ
cana-935	217	9	baleanu	baleanu	PROPN
cana-935	217	10	,	,	PUNCT
cana-935	217	11	d.	d.	PROPN
cana-935	217	12	(	(	PUNCT
cana-935	217	13	2017	2017	NUM
cana-935	217	14	)	)	PUNCT
cana-935	217	15	.	.	PUNCT
cana-935	218	1	new	new	ADJ
cana-935	218	2	fractional	fractional	ADJ
cana-935	218	3	derivatives	derivative	NOUN
cana-935	218	4	with	with	ADP
cana-935	218	5	non	non	ADJ
cana-935	218	6	-	-	ADJ
cana-935	218	7	local	local	ADJ
cana-935	218	8	and	and	CCONJ
cana-935	218	9	non	non	ADJ
cana-935	218	10	-	-	ADJ
cana-935	218	11	singular	singular	ADJ
cana-935	218	12	kernel	kernel	NOUN
cana-935	218	13	:	:	PUNCT
cana-935	218	14	theory	theory	NOUN
cana-935	218	15	and	and	CCONJ
cana-935	218	16	application	application	NOUN
cana-935	218	17	to	to	PART
cana-935	218	18	heat	heat	NOUN
cana-935	218	19	transfer	transfer	NOUN
cana-935	218	20	model	model	NOUN
cana-935	218	21	.	.	PUNCT
cana-935	219	1	journal	journal	PROPN
cana-935	219	2	of	of	ADP
cana-935	219	3	king	king	PROPN
cana-935	219	4	saud	saud	PROPN
cana-935	219	5	university	university	PROPN
cana-935	219	6	-	-	PUNCT
cana-935	219	7	science	science	NOUN
cana-935	219	8	,	,	PUNCT
cana-935	219	9	29(4	29(4	NOUN
cana-935	219	10	)	)	PUNCT
cana-935	219	11	,	,	PUNCT
cana-935	219	12	500	500	NUM
cana-935	219	13	-	-	SYM
cana-935	219	14	505	505	NUM
cana-935	219	15	.	.	PUNCT
cana-935	220	1	[	[	X
cana-935	220	2	39	39	NUM
cana-935	220	3	]	]	PUNCT
cana-935	220	4	atangana	atangana	PROPN
cana-935	220	5	,	,	PUNCT
cana-935	220	6	a.	a.	PROPN
cana-935	220	7	,	,	PUNCT
cana-935	220	8	&	&	CCONJ
cana-935	220	9	baleanu	baleanu	PROPN
cana-935	220	10	,	,	PUNCT
cana-935	220	11	d.	d.	PROPN
cana-935	220	12	(	(	PUNCT
cana-935	220	13	2017	2017	NUM
cana-935	220	14	)	)	PUNCT
cana-935	220	15	.	.	PUNCT
cana-935	221	1	new	new	ADJ
cana-935	221	2	fractional	fractional	ADJ
cana-935	221	3	derivatives	derivative	NOUN
cana-935	221	4	with	with	ADP
cana-935	221	5	non	non	ADJ
cana-935	221	6	-	-	ADJ
cana-935	221	7	local	local	ADJ
cana-935	221	8	and	and	CCONJ
cana-935	221	9	non	non	ADJ
cana-935	221	10	-	-	ADJ
cana-935	221	11	singular	singular	ADJ
cana-935	221	12	kernel	kernel	NOUN
cana-935	221	13	:	:	PUNCT
cana-935	221	14	theory	theory	NOUN
cana-935	221	15	and	and	CCONJ
cana-935	221	16	application	application	NOUN
cana-935	221	17	to	to	PART
cana-935	221	18	heat	heat	NOUN
cana-935	221	19	transfer	transfer	NOUN
cana-935	221	20	model	model	NOUN
cana-935	221	21	.	.	PUNCT
cana-935	222	1	thermal	thermal	ADJ
cana-935	222	2	science	science	NOUN
cana-935	222	3	,	,	PUNCT
cana-935	222	4	21(suppl	21(suppl	NUM
cana-935	222	5	.	.	NOUN
cana-935	222	6	4	4	NUM
cana-935	222	7	)	)	PUNCT
cana-935	222	8	,	,	PUNCT
cana-935	222	9	s1129	s1129	PROPN
cana-935	222	10	-	-	PUNCT
cana-935	222	11	s1134	s1134	NOUN
cana-935	222	12	.	.	PUNCT
cana-935	223	1	[	[	X
cana-935	223	2	40	40	NUM
cana-935	223	3	]	]	PUNCT
cana-935	223	4	atangana	atangana	PROPN
cana-935	223	5	,	,	PUNCT
cana-935	223	6	a.	a.	PROPN
cana-935	223	7	,	,	PUNCT
cana-935	223	8	&	&	CCONJ
cana-935	223	9	baleanu	baleanu	PROPN
cana-935	223	10	,	,	PUNCT
cana-935	223	11	d.	d.	PROPN
cana-935	223	12	(	(	PUNCT
cana-935	223	13	2017	2017	NUM
cana-935	223	14	)	)	PUNCT
cana-935	223	15	.	.	PUNCT
cana-935	224	1	new	new	ADJ
cana-935	224	2	fractional	fractional	ADJ
cana-935	224	3	derivatives	derivative	NOUN
cana-935	224	4	with	with	ADP
cana-935	224	5	non	non	ADJ
cana-935	224	6	-	-	ADJ
cana-935	224	7	local	local	ADJ
cana-935	224	8	and	and	CCONJ
cana-935	224	9	non	non	ADJ
cana-935	224	10	-	-	ADJ
cana-935	224	11	singular	singular	ADJ
cana-935	224	12	kernel	kernel	NOUN
cana-935	224	13	:	:	PUNCT
cana-935	224	14	theory	theory	NOUN
cana-935	224	15	and	and	CCONJ
cana-935	224	16	application	application	NOUN
cana-935	224	17	to	to	PART
cana-935	224	18	heat	heat	NOUN
cana-935	224	19	transfer	transfer	NOUN
cana-935	224	20	model	model	NOUN
cana-935	224	21	.	.	PUNCT
cana-935	225	1	fractals	fractal	NOUN
cana-935	225	2	,	,	PUNCT
cana-935	225	3	25(4	25(4	NOUN
cana-935	225	4	)	)	PUNCT
cana-935	225	5	,	,	PUNCT
cana-935	225	6	1750043	1750043	NUM
cana-935	225	7	.	.	PUNCT