id	sid	tid	token	lemma	pos
cana-4182	1	1	communications	communication	NOUN
cana-4182	1	2	on	on	ADP
cana-4182	1	3	applied	apply	VERB
cana-4182	1	4	nonlinear	nonlinear	ADJ
cana-4182	1	5	analysis	analysis	NOUN
cana-4182	1	6	issn	issn	NOUN
cana-4182	1	7	:	:	PUNCT
cana-4182	1	8	1074	1074	NUM
cana-4182	1	9	-	-	PUNCT
cana-4182	1	10	133x	133x	NUM
cana-4182	1	11	vol	vol	NOUN
cana-4182	1	12	32	32	NUM
cana-4182	1	13	no	no	NOUN
cana-4182	1	14	.	.	PUNCT
cana-4182	2	1	9s	9s	NUM
cana-4182	2	2	(	(	PUNCT
cana-4182	2	3	2025	2025	NUM
cana-4182	2	4	)	)	PUNCT
cana-4182	2	5	1497	1497	NUM
cana-4182	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4182	3	1	a	a	DET
cana-4182	3	2	comprehensive	comprehensive	ADJ
cana-4182	3	3	review	review	NOUN
cana-4182	3	4	of	of	ADP
cana-4182	3	5	fractional	fractional	ADJ
cana-4182	3	6	calculus	calculus	NOUN
cana-4182	3	7	in	in	ADP
cana-4182	3	8	modeling	model	VERB
cana-4182	3	9	realworld	realworld	PROPN
cana-4182	3	10	phenomena	phenomena	PROPN
cana-4182	3	11	1azim	1azim	NUM
cana-4182	3	12	uddin	uddin	ADJ
cana-4182	3	13	,	,	PUNCT
cana-4182	3	14	2prachi	2prachi	NUM
cana-4182	3	15	juyal	juyal	NOUN
cana-4182	3	16	,	,	PUNCT
cana-4182	3	17	3rutul	3rutul	NUM
cana-4182	3	18	shah	shah	NOUN
cana-4182	3	19	,	,	PUNCT
cana-4182	3	20	4dr	4dr	NOUN
cana-4182	3	21	.	.	PUNCT
cana-4182	4	1	s.	s.	PROPN
cana-4182	4	2	kailasavalli	kailasavalli	PROPN
cana-4182	4	3	,	,	PUNCT
cana-4182	4	4	5j.s.s.l	5j.s.s.l	PROPN
cana-4182	4	5	.	.	PUNCT
cana-4182	4	6	bharani	bharani	PROPN
cana-4182	4	7	,	,	PUNCT
cana-4182	4	8	6hemanth	6hemanth	PROPN
cana-4182	4	9	k	k	NOUN
cana-4182	4	10	1	1	NUM
cana-4182	4	11	student	student	NOUN
cana-4182	4	12	,	,	PUNCT
cana-4182	4	13	bachelor	bachelor	NOUN
cana-4182	4	14	of	of	ADP
cana-4182	4	15	business	business	NOUN
cana-4182	4	16	administration	administration	NOUN
cana-4182	4	17	,	,	PUNCT
cana-4182	4	18	southern	southern	PROPN
cana-4182	4	19	california	california	PROPN
cana-4182	4	20	state	state	PROPN
cana-4182	4	21	university	university	PROPN
cana-4182	4	22	,	,	PUNCT
cana-4182	4	23	united	united	PROPN
cana-4182	4	24	state	state	PROPN
cana-4182	4	25	of	of	ADP
cana-4182	4	26	america	america	PROPN
cana-4182	4	27	(	(	PUNCT
cana-4182	4	28	usa	usa	PROPN
cana-4182	4	29	)	)	PUNCT
cana-4182	4	30	,	,	PUNCT
cana-4182	4	31	azim.uddin.054@my.csun.edu	azim.uddin.054@my.csun.edu	NOUN
cana-4182	4	32	2	2	NUM
cana-4182	4	33	assistant	assistant	NOUN
cana-4182	4	34	professor	professor	NOUN
cana-4182	4	35	,	,	PUNCT
cana-4182	4	36	department	department	NOUN
cana-4182	4	37	of	of	ADP
cana-4182	4	38	allied	ally	VERB
cana-4182	4	39	science	science	NOUN
cana-4182	4	40	(	(	PUNCT
cana-4182	4	41	mathematics	mathematics	PROPN
cana-4182	4	42	)	)	PUNCT
cana-4182	4	43	,	,	PUNCT
cana-4182	4	44	graphic	graphic	ADJ
cana-4182	4	45	era	era	NOUN
cana-4182	4	46	(	(	PUNCT
cana-4182	4	47	deemed	deem	VERB
cana-4182	4	48	to	to	PART
cana-4182	4	49	be	be	AUX
cana-4182	4	50	university	university	NOUN
cana-4182	4	51	)	)	PUNCT
cana-4182	4	52	,	,	PUNCT
cana-4182	4	53	dehradun	dehradun	PROPN
cana-4182	4	54	,	,	PUNCT
cana-4182	4	55	uttarakhand	uttarakhand	PROPN
cana-4182	4	56	,	,	PUNCT
cana-4182	4	57	india	india	PROPN
cana-4182	4	58	,	,	PUNCT
cana-4182	4	59	prachijuyal@yahoo.com	prachijuyal@yahoo.com	PROPN
cana-4182	4	60	3	3	NUM
cana-4182	4	61	student	student	NOUN
cana-4182	4	62	,	,	PUNCT
cana-4182	4	63	m.b	m.b	PROPN
cana-4182	4	64	.	.	PROPN
cana-4182	4	65	khalsa	khalsa	PROPN
cana-4182	4	66	law	law	PROPN
cana-4182	4	67	college	college	PROPN
cana-4182	4	68	indore	indore	PROPN
cana-4182	4	69	,	,	PUNCT
cana-4182	4	70	davv	davv	VERB
cana-4182	4	71	university	university	NOUN
cana-4182	4	72	,	,	PUNCT
cana-4182	4	73	indore	indore	PROPN
cana-4182	4	74	,	,	PUNCT
cana-4182	4	75	madhya	madhya	PROPN
cana-4182	4	76	pradesh	pradesh	PROPN
cana-4182	4	77	,	,	PUNCT
cana-4182	4	78	india	india	PROPN
cana-4182	4	79	,	,	PUNCT
cana-4182	4	80	rutulshah86@gmail.com	rutulshah86@gmail.com	PROPN
cana-4182	4	81	4	4	NUM
cana-4182	4	82	associate	associate	NOUN
cana-4182	4	83	professor	professor	NOUN
cana-4182	4	84	,	,	PUNCT
cana-4182	4	85	department	department	NOUN
cana-4182	4	86	of	of	ADP
cana-4182	4	87	mathematics	mathematics	PROPN
cana-4182	4	88	,	,	PUNCT
cana-4182	4	89	psna	psna	PROPN
cana-4182	4	90	college	college	PROPN
cana-4182	4	91	of	of	ADP
cana-4182	4	92	engineering	engineering	NOUN
cana-4182	4	93	and	and	CCONJ
cana-4182	4	94	technology	technology	NOUN
cana-4182	4	95	,	,	PUNCT
cana-4182	4	96	dindigul	dindigul	ADJ
cana-4182	4	97	-624622	-624622	PROPN
cana-4182	4	98	,	,	PUNCT
cana-4182	4	99	skvalli2k5@gmail.com	skvalli2k5@gmail.com	X
cana-4182	4	100	5	5	NUM
cana-4182	4	101	department	department	NOUN
cana-4182	4	102	of	of	ADP
cana-4182	4	103	eee	eee	PROPN
cana-4182	4	104	,	,	PUNCT
cana-4182	4	105	s.r.k.r	s.r.k.r	PROPN
cana-4182	4	106	.	.	PROPN
cana-4182	4	107	engineering	engineering	NOUN
cana-4182	4	108	college	college	PROPN
cana-4182	4	109	,	,	PUNCT
cana-4182	4	110	china	china	PROPN
cana-4182	4	111	amiram	amiram	PROPN
cana-4182	4	112	,	,	PUNCT
cana-4182	4	113	bhimavaram	bhimavaram	PROPN
cana-4182	4	114	,	,	PUNCT
cana-4182	4	115	andhra	andhra	PROPN
cana-4182	4	116	pradesh	pradesh	PROPN
cana-4182	4	117	,	,	PUNCT
cana-4182	4	118	india	india	PROPN
cana-4182	4	119	,	,	PUNCT
cana-4182	4	120	sslbharani@gmail.com	sslbharani@gmail.com	PROPN
cana-4182	4	121	6	6	NUM
cana-4182	4	122	associate	associate	NOUN
cana-4182	4	123	professor	professor	NOUN
cana-4182	4	124	,	,	PUNCT
cana-4182	4	125	school	school	NOUN
cana-4182	4	126	of	of	ADP
cana-4182	4	127	mechanical	mechanical	ADJ
cana-4182	4	128	engineering	engineering	PROPN
cana-4182	4	129	,	,	PUNCT
cana-4182	4	130	reva	reva	PROPN
cana-4182	4	131	university	university	PROPN
cana-4182	4	132	,	,	PUNCT
cana-4182	4	133	ckh4545@gmail.com	ckh4545@gmail.com	PROPN
cana-4182	4	134	7	7	NUM
cana-4182	4	135	article	article	NOUN
cana-4182	4	136	history	history	NOUN
cana-4182	4	137	:	:	PUNCT
cana-4182	4	138	received	receive	VERB
cana-4182	4	139	:	:	PUNCT
cana-4182	4	140	12	12	NUM
cana-4182	4	141	-	-	SYM
cana-4182	4	142	01	01	NUM
cana-4182	4	143	-	-	PUNCT
cana-4182	4	144	2025	2025	NUM
cana-4182	4	145	revised	revise	VERB
cana-4182	4	146	:	:	PUNCT
cana-4182	4	147	15	15	NUM
cana-4182	4	148	-	-	NUM
cana-4182	4	149	02	02	NUM
cana-4182	4	150	-	-	PUNCT
cana-4182	4	151	2025	2025	NUM
cana-4182	4	152	accepted	accept	VERB
cana-4182	4	153	:	:	PUNCT
cana-4182	4	154	01	01	NUM
cana-4182	4	155	-	-	SYM
cana-4182	4	156	03	03	NUM
cana-4182	4	157	-	-	PUNCT
cana-4182	4	158	2025	2025	NUM
cana-4182	4	159	abstract	abstract	NOUN
cana-4182	4	160	:	:	PUNCT
cana-4182	4	161	fractional	fractional	ADJ
cana-4182	4	162	calculus	calculus	NOUN
cana-4182	4	163	,	,	PUNCT
cana-4182	4	164	an	an	DET
cana-4182	4	165	extension	extension	NOUN
cana-4182	4	166	of	of	ADP
cana-4182	4	167	classical	classical	ADJ
cana-4182	4	168	calculus	calculus	NOUN
cana-4182	4	169	to	to	ADP
cana-4182	4	170	non	non	ADJ
cana-4182	4	171	-	-	ADJ
cana-4182	4	172	integer	integer	ADJ
cana-4182	4	173	orders	order	NOUN
cana-4182	4	174	of	of	ADP
cana-4182	4	175	differentiation	differentiation	NOUN
cana-4182	4	176	and	and	CCONJ
cana-4182	4	177	integration	integration	NOUN
cana-4182	4	178	,	,	PUNCT
cana-4182	4	179	has	have	AUX
cana-4182	4	180	garnered	garner	VERB
cana-4182	4	181	significant	significant	ADJ
cana-4182	4	182	attention	attention	NOUN
cana-4182	4	183	for	for	ADP
cana-4182	4	184	its	its	PRON
cana-4182	4	185	remarkable	remarkable	ADJ
cana-4182	4	186	ability	ability	NOUN
cana-4182	4	187	to	to	PART
cana-4182	4	188	model	model	VERB
cana-4182	4	189	complex	complex	ADJ
cana-4182	4	190	real	real	ADJ
cana-4182	4	191	-	-	PUNCT
cana-4182	4	192	world	world	NOUN
cana-4182	4	193	systems	system	NOUN
cana-4182	4	194	.	.	PUNCT
cana-4182	5	1	unlike	unlike	ADP
cana-4182	5	2	traditional	traditional	ADJ
cana-4182	5	3	integer	integer	NOUN
cana-4182	5	4	-	-	PUNCT
cana-4182	5	5	order	order	NOUN
cana-4182	5	6	models	model	NOUN
cana-4182	5	7	that	that	PRON
cana-4182	5	8	can	can	AUX
cana-4182	5	9	oversimplify	oversimplify	VERB
cana-4182	5	10	or	or	CCONJ
cana-4182	5	11	neglect	neglect	VERB
cana-4182	5	12	certain	certain	ADJ
cana-4182	5	13	memory	memory	NOUN
cana-4182	5	14	and	and	CCONJ
cana-4182	5	15	hereditary	hereditary	ADJ
cana-4182	5	16	properties	property	NOUN
cana-4182	5	17	,	,	PUNCT
cana-4182	5	18	fractional	fractional	ADJ
cana-4182	5	19	calculus	calculus	NOUN
cana-4182	5	20	provides	provide	VERB
cana-4182	5	21	a	a	DET
cana-4182	5	22	robust	robust	ADJ
cana-4182	5	23	framework	framework	NOUN
cana-4182	5	24	to	to	PART
cana-4182	5	25	capture	capture	VERB
cana-4182	5	26	long	long	ADJ
cana-4182	5	27	-	-	PUNCT
cana-4182	5	28	range	range	NOUN
cana-4182	5	29	dependence	dependence	NOUN
cana-4182	5	30	and	and	CCONJ
cana-4182	5	31	fractallike	fractallike	NOUN
cana-4182	5	32	behavior	behavior	NOUN
cana-4182	5	33	across	across	ADP
cana-4182	5	34	diverse	diverse	ADJ
cana-4182	5	35	disciplines	discipline	NOUN
cana-4182	5	36	.	.	PUNCT
cana-4182	6	1	recent	recent	ADJ
cana-4182	6	2	advances	advance	NOUN
cana-4182	6	3	in	in	ADP
cana-4182	6	4	computation	computation	NOUN
cana-4182	6	5	have	have	AUX
cana-4182	6	6	further	far	ADV
cana-4182	6	7	propelled	propel	VERB
cana-4182	6	8	the	the	DET
cana-4182	6	9	application	application	NOUN
cana-4182	6	10	of	of	ADP
cana-4182	6	11	fractional	fractional	ADJ
cana-4182	6	12	derivatives	derivative	NOUN
cana-4182	6	13	and	and	CCONJ
cana-4182	6	14	integrals	integral	NOUN
cana-4182	6	15	in	in	ADP
cana-4182	6	16	fields	field	NOUN
cana-4182	6	17	such	such	ADJ
cana-4182	6	18	as	as	ADP
cana-4182	6	19	viscoelasticity	viscoelasticity	NOUN
cana-4182	6	20	,	,	PUNCT
cana-4182	6	21	anomalous	anomalous	ADJ
cana-4182	6	22	diffusion	diffusion	NOUN
cana-4182	6	23	,	,	PUNCT
cana-4182	6	24	signal	signal	NOUN
cana-4182	6	25	processing	processing	NOUN
cana-4182	6	26	,	,	PUNCT
cana-4182	6	27	and	and	CCONJ
cana-4182	6	28	control	control	NOUN
cana-4182	6	29	theory	theory	NOUN
cana-4182	6	30	,	,	PUNCT
cana-4182	6	31	among	among	ADP
cana-4182	6	32	others	other	NOUN
cana-4182	6	33	.	.	PUNCT
cana-4182	7	1	in	in	ADP
cana-4182	7	2	this	this	DET
cana-4182	7	3	paper	paper	NOUN
cana-4182	7	4	,	,	PUNCT
cana-4182	7	5	we	we	PRON
cana-4182	7	6	present	present	VERB
cana-4182	7	7	a	a	DET
cana-4182	7	8	comprehensive	comprehensive	ADJ
cana-4182	7	9	review	review	NOUN
cana-4182	7	10	of	of	ADP
cana-4182	7	11	the	the	DET
cana-4182	7	12	theoretical	theoretical	ADJ
cana-4182	7	13	underpinnings	underpinning	NOUN
cana-4182	7	14	of	of	ADP
cana-4182	7	15	fractional	fractional	ADJ
cana-4182	7	16	calculus	calculus	NOUN
cana-4182	7	17	,	,	PUNCT
cana-4182	7	18	highlighting	highlight	VERB
cana-4182	7	19	key	key	ADJ
cana-4182	7	20	definitions	definition	NOUN
cana-4182	7	21	,	,	PUNCT
cana-4182	7	22	properties	property	NOUN
cana-4182	7	23	,	,	PUNCT
cana-4182	7	24	and	and	CCONJ
cana-4182	7	25	numerical	numerical	ADJ
cana-4182	7	26	techniques	technique	NOUN
cana-4182	7	27	.	.	PUNCT
cana-4182	8	1	we	we	PRON
cana-4182	8	2	also	also	ADV
cana-4182	8	3	examine	examine	VERB
cana-4182	8	4	the	the	DET
cana-4182	8	5	broad	broad	ADJ
cana-4182	8	6	array	array	NOUN
cana-4182	8	7	of	of	ADP
cana-4182	8	8	real	real	ADJ
cana-4182	8	9	-	-	PUNCT
cana-4182	8	10	world	world	NOUN
cana-4182	8	11	applications	application	NOUN
cana-4182	8	12	where	where	SCONJ
cana-4182	8	13	fractional	fractional	ADJ
cana-4182	8	14	derivatives	derivative	NOUN
cana-4182	8	15	offer	offer	VERB
cana-4182	8	16	enhanced	enhance	VERB
cana-4182	8	17	predictive	predictive	ADJ
cana-4182	8	18	accuracy	accuracy	NOUN
cana-4182	8	19	.	.	PUNCT
cana-4182	9	1	moreover	moreover	ADV
cana-4182	9	2	,	,	PUNCT
cana-4182	9	3	this	this	DET
cana-4182	9	4	review	review	NOUN
cana-4182	9	5	compiles	compile	VERB
cana-4182	9	6	and	and	CCONJ
cana-4182	9	7	critically	critically	ADV
cana-4182	9	8	discusses	discuss	VERB
cana-4182	9	9	recent	recent	ADJ
cana-4182	9	10	research	research	NOUN
cana-4182	9	11	data	datum	NOUN
cana-4182	9	12	,	,	PUNCT
cana-4182	9	13	offering	offer	VERB
cana-4182	9	14	insights	insight	NOUN
cana-4182	9	15	into	into	ADP
cana-4182	9	16	how	how	SCONJ
cana-4182	9	17	fractional	fractional	ADJ
cana-4182	9	18	models	model	NOUN
cana-4182	9	19	outperform	outperform	VERB
cana-4182	9	20	their	their	PRON
cana-4182	9	21	integer	integer	NOUN
cana-4182	9	22	-	-	PUNCT
cana-4182	9	23	order	order	NOUN
cana-4182	9	24	counterparts	counterpart	NOUN
cana-4182	9	25	in	in	ADP
cana-4182	9	26	capturing	capture	VERB
cana-4182	9	27	the	the	DET
cana-4182	9	28	complexity	complexity	NOUN
cana-4182	9	29	of	of	ADP
cana-4182	9	30	natural	natural	ADJ
cana-4182	9	31	and	and	CCONJ
cana-4182	9	32	engineered	engineer	VERB
cana-4182	9	33	systems	system	NOUN
cana-4182	9	34	.	.	PUNCT
cana-4182	10	1	by	by	ADP
cana-4182	10	2	integrating	integrate	VERB
cana-4182	10	3	both	both	CCONJ
cana-4182	10	4	theoretical	theoretical	ADJ
cana-4182	10	5	and	and	CCONJ
cana-4182	10	6	applied	apply	VERB
cana-4182	10	7	perspectives	perspective	NOUN
cana-4182	10	8	,	,	PUNCT
cana-4182	10	9	this	this	DET
cana-4182	10	10	work	work	NOUN
cana-4182	10	11	aims	aim	VERB
cana-4182	10	12	to	to	PART
cana-4182	10	13	provide	provide	VERB
cana-4182	10	14	researchers	researcher	NOUN
cana-4182	10	15	,	,	PUNCT
cana-4182	10	16	educators	educator	NOUN
cana-4182	10	17	,	,	PUNCT
cana-4182	10	18	and	and	CCONJ
cana-4182	10	19	industry	industry	NOUN
cana-4182	10	20	professionals	professional	NOUN
cana-4182	10	21	a	a	DET
cana-4182	10	22	thorough	thorough	ADJ
cana-4182	10	23	resource	resource	NOUN
cana-4182	10	24	to	to	PART
cana-4182	10	25	understand	understand	VERB
cana-4182	10	26	the	the	DET
cana-4182	10	27	role	role	NOUN
cana-4182	10	28	of	of	ADP
cana-4182	10	29	fractional	fractional	ADJ
cana-4182	10	30	calculus	calculus	NOUN
cana-4182	10	31	in	in	ADP
cana-4182	10	32	addressing	address	VERB
cana-4182	10	33	emerging	emerge	VERB
cana-4182	10	34	challenges	challenge	NOUN
cana-4182	10	35	in	in	ADP
cana-4182	10	36	science	science	NOUN
cana-4182	10	37	and	and	CCONJ
cana-4182	10	38	engineering	engineering	NOUN
cana-4182	10	39	.	.	PUNCT
cana-4182	11	1	central	central	ADJ
cana-4182	11	2	to	to	ADP
cana-4182	11	3	this	this	DET
cana-4182	11	4	discussion	discussion	NOUN
cana-4182	11	5	is	be	AUX
cana-4182	11	6	the	the	DET
cana-4182	11	7	incorporation	incorporation	NOUN
cana-4182	11	8	of	of	ADP
cana-4182	11	9	newly	newly	ADV
cana-4182	11	10	published	publish	VERB
cana-4182	11	11	findings	finding	NOUN
cana-4182	11	12	and	and	CCONJ
cana-4182	11	13	illustrative	illustrative	ADJ
cana-4182	11	14	examples	example	NOUN
cana-4182	11	15	.	.	PUNCT
cana-4182	12	1	these	these	PRON
cana-4182	12	2	include	include	VERB
cana-4182	12	3	empirical	empirical	ADJ
cana-4182	12	4	measurements	measurement	NOUN
cana-4182	12	5	,	,	PUNCT
cana-4182	12	6	theoretical	theoretical	ADJ
cana-4182	12	7	predictions	prediction	NOUN
cana-4182	12	8	,	,	PUNCT
cana-4182	12	9	and	and	CCONJ
cana-4182	12	10	graphical	graphical	ADJ
cana-4182	12	11	representations	representation	NOUN
cana-4182	12	12	that	that	PRON
cana-4182	12	13	demonstrate	demonstrate	VERB
cana-4182	12	14	the	the	DET
cana-4182	12	15	efficacy	efficacy	NOUN
cana-4182	12	16	of	of	ADP
cana-4182	12	17	fractional	fractional	ADJ
cana-4182	12	18	-	-	PUNCT
cana-4182	12	19	order	order	NOUN
cana-4182	12	20	models	model	NOUN
cana-4182	12	21	.	.	PUNCT
cana-4182	13	1	ultimately	ultimately	ADV
cana-4182	13	2	,	,	PUNCT
cana-4182	13	3	this	this	DET
cana-4182	13	4	review	review	NOUN
cana-4182	13	5	underscores	underscore	VERB
cana-4182	13	6	the	the	DET
cana-4182	13	7	growing	grow	VERB
cana-4182	13	8	consensus	consensus	NOUN
cana-4182	13	9	that	that	SCONJ
cana-4182	13	10	fractional	fractional	ADJ
cana-4182	13	11	calculus	calculus	NOUN
cana-4182	13	12	is	be	AUX
cana-4182	13	13	not	not	PART
cana-4182	13	14	merely	merely	ADV
cana-4182	13	15	a	a	DET
cana-4182	13	16	mathematical	mathematical	ADJ
cana-4182	13	17	curiosity	curiosity	NOUN
cana-4182	13	18	but	but	CCONJ
cana-4182	13	19	a	a	DET
cana-4182	13	20	potent	potent	ADJ
cana-4182	13	21	tool	tool	NOUN
cana-4182	13	22	in	in	ADP
cana-4182	13	23	developing	develop	VERB
cana-4182	13	24	more	more	ADV
cana-4182	13	25	accurate	accurate	ADJ
cana-4182	13	26	and	and	CCONJ
cana-4182	13	27	efficient	efficient	ADJ
cana-4182	13	28	models	model	NOUN
cana-4182	13	29	for	for	ADP
cana-4182	13	30	real	real	ADJ
cana-4182	13	31	-	-	PUNCT
cana-4182	13	32	world	world	NOUN
cana-4182	13	33	phenomena	phenomenon	NOUN
cana-4182	13	34	.	.	PUNCT
cana-4182	14	1	keywords	keyword	NOUN
cana-4182	14	2	:	:	PUNCT
cana-4182	14	3	fractional	fractional	ADJ
cana-4182	14	4	calculus	calculus	NOUN
cana-4182	14	5	,	,	PUNCT
cana-4182	14	6	fractional	fractional	ADJ
cana-4182	14	7	derivatives	derivative	NOUN
cana-4182	14	8	,	,	PUNCT
cana-4182	14	9	real	real	ADJ
cana-4182	14	10	-	-	PUNCT
cana-4182	14	11	world	world	NOUN
cana-4182	14	12	phenomena	phenomenon	NOUN
cana-4182	14	13	,	,	PUNCT
cana-4182	14	14	anomalous	anomalous	ADJ
cana-4182	14	15	diffusion	diffusion	NOUN
cana-4182	14	16	,	,	PUNCT
cana-4182	14	17	viscoelasticity	viscoelasticity	NOUN
cana-4182	14	18	,	,	PUNCT
cana-4182	14	19	modeling	modeling	NOUN
cana-4182	14	20	,	,	PUNCT
cana-4182	14	21	long	long	ADJ
cana-4182	14	22	-	-	PUNCT
cana-4182	14	23	range	range	NOUN
cana-4182	14	24	dependence	dependence	NOUN
cana-4182	14	25	mailto:prachijuyal@yahoo.com	mailto:prachijuyal@yahoo.com	X
cana-4182	14	26	mailto:skvalli2k5@gmail.com	mailto:skvalli2k5@gmail.com	X
cana-4182	14	27	mailto:sslbharani@gmail.com	mailto:sslbharani@gmail.com	X
cana-4182	14	28	mailto:ckh4545@gmail.com	mailto:ckh4545@gmail.com	X
cana-4182	14	29	communications	communication	NOUN
cana-4182	14	30	on	on	ADP
cana-4182	14	31	applied	apply	VERB
cana-4182	14	32	nonlinear	nonlinear	ADJ
cana-4182	14	33	analysis	analysis	NOUN
cana-4182	14	34	issn	issn	NOUN
cana-4182	14	35	:	:	PUNCT
cana-4182	14	36	1074	1074	NUM
cana-4182	14	37	-	-	PUNCT
cana-4182	14	38	133x	133x	NUM
cana-4182	14	39	vol	vol	NOUN
cana-4182	14	40	32	32	NUM
cana-4182	14	41	no	no	NOUN
cana-4182	14	42	.	.	PUNCT
cana-4182	15	1	9s	9s	NUM
cana-4182	15	2	(	(	PUNCT
cana-4182	15	3	2025	2025	NUM
cana-4182	15	4	)	)	PUNCT
cana-4182	15	5	1498	1498	NUM
cana-4182	15	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4182	15	7	1	1	X
cana-4182	15	8	.	.	PUNCT
cana-4182	15	9	introduction	introduction	NOUN
cana-4182	15	10	fractional	fractional	ADJ
cana-4182	15	11	calculus	calculus	NOUN
cana-4182	15	12	traces	trace	VERB
cana-4182	15	13	its	its	PRON
cana-4182	15	14	origins	origin	NOUN
cana-4182	15	15	to	to	ADP
cana-4182	15	16	a	a	DET
cana-4182	15	17	famous	famous	ADJ
cana-4182	15	18	question	question	NOUN
cana-4182	15	19	posed	pose	VERB
cana-4182	15	20	by	by	ADP
cana-4182	15	21	mathematician	mathematician	PROPN
cana-4182	15	22	gottfried	gottfried	PROPN
cana-4182	15	23	wilhelm	wilhelm	PROPN
cana-4182	15	24	leibniz	leibniz	PROPN
cana-4182	15	25	in	in	ADP
cana-4182	15	26	the	the	DET
cana-4182	15	27	late	late	ADJ
cana-4182	15	28	seventeenth	seventeenth	ADJ
cana-4182	15	29	century	century	NOUN
cana-4182	15	30	,	,	PUNCT
cana-4182	15	31	asking	ask	VERB
cana-4182	15	32	what	what	PRON
cana-4182	15	33	would	would	AUX
cana-4182	15	34	happen	happen	VERB
cana-4182	15	35	if	if	SCONJ
cana-4182	15	36	differentiation	differentiation	NOUN
cana-4182	15	37	were	be	AUX
cana-4182	15	38	extended	extend	VERB
cana-4182	15	39	to	to	ADP
cana-4182	15	40	non	non	ADJ
cana-4182	15	41	-	-	ADJ
cana-4182	15	42	integer	integer	ADJ
cana-4182	15	43	orders	order	NOUN
cana-4182	15	44	.	.	PUNCT
cana-4182	16	1	although	although	SCONJ
cana-4182	16	2	the	the	DET
cana-4182	16	3	idea	idea	NOUN
cana-4182	16	4	was	be	AUX
cana-4182	16	5	once	once	ADV
cana-4182	16	6	perceived	perceive	VERB
cana-4182	16	7	as	as	ADP
cana-4182	16	8	purely	purely	ADV
cana-4182	16	9	theoretical	theoretical	ADJ
cana-4182	16	10	or	or	CCONJ
cana-4182	16	11	even	even	ADV
cana-4182	16	12	an	an	DET
cana-4182	16	13	eccentric	eccentric	ADJ
cana-4182	16	14	curiosity	curiosity	NOUN
cana-4182	16	15	,	,	PUNCT
cana-4182	16	16	the	the	DET
cana-4182	16	17	last	last	ADJ
cana-4182	16	18	few	few	ADJ
cana-4182	16	19	decades	decade	NOUN
cana-4182	16	20	have	have	AUX
cana-4182	16	21	witnessed	witness	VERB
cana-4182	16	22	a	a	DET
cana-4182	16	23	surge	surge	NOUN
cana-4182	16	24	of	of	ADP
cana-4182	16	25	interest	interest	NOUN
cana-4182	16	26	and	and	CCONJ
cana-4182	16	27	practical	practical	ADJ
cana-4182	16	28	applications	application	NOUN
cana-4182	16	29	of	of	ADP
cana-4182	16	30	fractional	fractional	ADJ
cana-4182	16	31	-	-	PUNCT
cana-4182	16	32	order	order	NOUN
cana-4182	16	33	operators	operator	NOUN
cana-4182	16	34	in	in	ADP
cana-4182	16	35	science	science	NOUN
cana-4182	16	36	and	and	CCONJ
cana-4182	16	37	engineering	engineering	NOUN
cana-4182	16	38	.	.	PUNCT
cana-4182	17	1	this	this	DET
cana-4182	17	2	shift	shift	NOUN
cana-4182	17	3	largely	largely	ADV
cana-4182	17	4	owes	owe	VERB
cana-4182	17	5	itself	itself	PRON
cana-4182	17	6	to	to	ADP
cana-4182	17	7	the	the	DET
cana-4182	17	8	realization	realization	NOUN
cana-4182	17	9	that	that	SCONJ
cana-4182	17	10	fractional	fractional	ADJ
cana-4182	17	11	derivatives	derivative	NOUN
cana-4182	17	12	naturally	naturally	ADV
cana-4182	17	13	incorporate	incorporate	VERB
cana-4182	17	14	memory	memory	NOUN
cana-4182	17	15	effects	effect	NOUN
cana-4182	17	16	,	,	PUNCT
cana-4182	17	17	long	long	ADJ
cana-4182	17	18	-	-	PUNCT
cana-4182	17	19	term	term	NOUN
cana-4182	17	20	correlations	correlation	NOUN
cana-4182	17	21	,	,	PUNCT
cana-4182	17	22	and	and	CCONJ
cana-4182	17	23	fractal	fractal	ADJ
cana-4182	17	24	properties	property	NOUN
cana-4182	17	25	that	that	PRON
cana-4182	17	26	classical	classical	ADJ
cana-4182	17	27	integer	integer	NOUN
cana-4182	17	28	-	-	PUNCT
cana-4182	17	29	order	order	NOUN
cana-4182	17	30	models	model	NOUN
cana-4182	17	31	struggle	struggle	VERB
cana-4182	17	32	to	to	PART
cana-4182	17	33	address	address	VERB
cana-4182	17	34	.	.	PUNCT
cana-4182	18	1	a	a	DET
cana-4182	18	2	key	key	ADJ
cana-4182	18	3	advantage	advantage	NOUN
cana-4182	18	4	of	of	ADP
cana-4182	18	5	fractional	fractional	ADJ
cana-4182	18	6	calculus	calculus	NOUN
cana-4182	18	7	lies	lie	VERB
cana-4182	18	8	in	in	ADP
cana-4182	18	9	its	its	PRON
cana-4182	18	10	ability	ability	NOUN
cana-4182	18	11	to	to	PART
cana-4182	18	12	reflect	reflect	VERB
cana-4182	18	13	real	real	ADJ
cana-4182	18	14	-	-	PUNCT
cana-4182	18	15	world	world	NOUN
cana-4182	18	16	phenomena	phenomenon	NOUN
cana-4182	18	17	more	more	ADV
cana-4182	18	18	precisely	precisely	ADV
cana-4182	18	19	than	than	ADP
cana-4182	18	20	traditional	traditional	ADJ
cana-4182	18	21	integer	integer	NOUN
cana-4182	18	22	-	-	PUNCT
cana-4182	18	23	order	order	NOUN
cana-4182	18	24	models	model	NOUN
cana-4182	18	25	.	.	PUNCT
cana-4182	19	1	consider	consider	VERB
cana-4182	19	2	,	,	PUNCT
cana-4182	19	3	for	for	ADP
cana-4182	19	4	instance	instance	NOUN
cana-4182	19	5	,	,	PUNCT
cana-4182	19	6	the	the	DET
cana-4182	19	7	viscoelastic	viscoelastic	ADJ
cana-4182	19	8	properties	property	NOUN
cana-4182	19	9	of	of	ADP
cana-4182	19	10	polymers	polymer	NOUN
cana-4182	19	11	.	.	PUNCT
cana-4182	20	1	such	such	ADJ
cana-4182	20	2	materials	material	NOUN
cana-4182	20	3	exhibit	exhibit	NOUN
cana-4182	20	4	behavior	behavior	NOUN
cana-4182	20	5	that	that	PRON
cana-4182	20	6	simultaneously	simultaneously	ADV
cana-4182	20	7	shares	share	VERB
cana-4182	20	8	attributes	attribute	NOUN
cana-4182	20	9	of	of	ADP
cana-4182	20	10	both	both	CCONJ
cana-4182	20	11	viscous	viscous	ADJ
cana-4182	20	12	fluids	fluid	NOUN
cana-4182	20	13	and	and	CCONJ
cana-4182	20	14	elastic	elastic	ADJ
cana-4182	20	15	solids	solid	NOUN
cana-4182	20	16	.	.	PUNCT
cana-4182	21	1	standard	standard	ADJ
cana-4182	21	2	integer	integer	NOUN
cana-4182	21	3	-	-	PUNCT
cana-4182	21	4	order	order	NOUN
cana-4182	21	5	differential	differential	ADJ
cana-4182	21	6	equations	equation	NOUN
cana-4182	21	7	often	often	ADV
cana-4182	21	8	fail	fail	VERB
cana-4182	21	9	to	to	PART
cana-4182	21	10	capture	capture	VERB
cana-4182	21	11	the	the	DET
cana-4182	21	12	slow	slow	ADJ
cana-4182	21	13	relaxation	relaxation	NOUN
cana-4182	21	14	and	and	CCONJ
cana-4182	21	15	history	history	NOUN
cana-4182	21	16	-	-	PUNCT
cana-4182	21	17	dependent	dependent	ADJ
cana-4182	21	18	stress	stress	NOUN
cana-4182	21	19	responses	response	NOUN
cana-4182	21	20	observed	observe	VERB
cana-4182	21	21	in	in	ADP
cana-4182	21	22	these	these	DET
cana-4182	21	23	materials	material	NOUN
cana-4182	21	24	.	.	PUNCT
cana-4182	22	1	in	in	ADP
cana-4182	22	2	contrast	contrast	NOUN
cana-4182	22	3	,	,	PUNCT
cana-4182	22	4	fractionalorder	fractionalorder	NOUN
cana-4182	22	5	models	model	NOUN
cana-4182	22	6	accurately	accurately	ADV
cana-4182	22	7	incorporate	incorporate	VERB
cana-4182	22	8	long	long	ADJ
cana-4182	22	9	-	-	PUNCT
cana-4182	22	10	range	range	NOUN
cana-4182	22	11	memory	memory	NOUN
cana-4182	22	12	,	,	PUNCT
cana-4182	22	13	aligning	align	VERB
cana-4182	22	14	model	model	NOUN
cana-4182	22	15	predictions	prediction	NOUN
cana-4182	22	16	more	more	ADV
cana-4182	22	17	closely	closely	ADV
cana-4182	22	18	with	with	ADP
cana-4182	22	19	experimental	experimental	ADJ
cana-4182	22	20	data	datum	NOUN
cana-4182	22	21	.	.	PUNCT
cana-4182	23	1	this	this	DET
cana-4182	23	2	concept	concept	NOUN
cana-4182	23	3	of	of	ADP
cana-4182	23	4	“	"	PUNCT
cana-4182	23	5	memory	memory	NOUN
cana-4182	23	6	”	"	PUNCT
cana-4182	23	7	similarly	similarly	ADV
cana-4182	23	8	manifests	manifest	VERB
cana-4182	23	9	in	in	ADP
cana-4182	23	10	numerous	numerous	ADJ
cana-4182	23	11	other	other	ADJ
cana-4182	23	12	systems	system	NOUN
cana-4182	23	13	,	,	PUNCT
cana-4182	23	14	from	from	ADP
cana-4182	23	15	the	the	DET
cana-4182	23	16	subdiffusive	subdiffusive	ADJ
cana-4182	23	17	transport	transport	NOUN
cana-4182	23	18	of	of	ADP
cana-4182	23	19	molecules	molecule	NOUN
cana-4182	23	20	in	in	ADP
cana-4182	23	21	biological	biological	ADJ
cana-4182	23	22	cells	cell	NOUN
cana-4182	23	23	to	to	ADP
cana-4182	23	24	the	the	DET
cana-4182	23	25	spread	spread	NOUN
cana-4182	23	26	of	of	ADP
cana-4182	23	27	contaminants	contaminant	NOUN
cana-4182	23	28	in	in	ADP
cana-4182	23	29	porous	porous	ADJ
cana-4182	23	30	media	medium	NOUN
cana-4182	23	31	.	.	PUNCT
cana-4182	24	1	beyond	beyond	ADP
cana-4182	24	2	viscoelasticity	viscoelasticity	NOUN
cana-4182	24	3	,	,	PUNCT
cana-4182	24	4	fractional	fractional	ADJ
cana-4182	24	5	derivatives	derivative	NOUN
cana-4182	24	6	have	have	AUX
cana-4182	24	7	found	find	VERB
cana-4182	24	8	diverse	diverse	ADJ
cana-4182	24	9	applications	application	NOUN
cana-4182	24	10	in	in	ADP
cana-4182	24	11	signal	signal	ADJ
cana-4182	24	12	processing	processing	NOUN
cana-4182	24	13	,	,	PUNCT
cana-4182	24	14	finance	finance	NOUN
cana-4182	24	15	,	,	PUNCT
cana-4182	24	16	population	population	NOUN
cana-4182	24	17	dynamics	dynamic	NOUN
cana-4182	24	18	,	,	PUNCT
cana-4182	24	19	and	and	CCONJ
cana-4182	24	20	control	control	NOUN
cana-4182	24	21	theory	theory	NOUN
cana-4182	24	22	.	.	PUNCT
cana-4182	25	1	the	the	DET
cana-4182	25	2	non	non	ADJ
cana-4182	25	3	-	-	ADJ
cana-4182	25	4	local	local	ADJ
cana-4182	25	5	kernel	kernel	NOUN
cana-4182	25	6	in	in	ADP
cana-4182	25	7	fractional	fractional	ADJ
cana-4182	25	8	integrals	integral	NOUN
cana-4182	25	9	enables	enable	VERB
cana-4182	25	10	more	more	ADV
cana-4182	25	11	flexible	flexible	ADJ
cana-4182	25	12	filtering	filtering	NOUN
cana-4182	25	13	in	in	ADP
cana-4182	25	14	signals	signal	NOUN
cana-4182	25	15	,	,	PUNCT
cana-4182	25	16	while	while	SCONJ
cana-4182	25	17	fractional	fractional	ADJ
cana-4182	25	18	differential	differential	ADJ
cana-4182	25	19	equations	equation	NOUN
cana-4182	25	20	reveal	reveal	VERB
cana-4182	25	21	new	new	ADJ
cana-4182	25	22	approaches	approach	NOUN
cana-4182	25	23	to	to	ADP
cana-4182	25	24	analyzing	analyze	VERB
cana-4182	25	25	financial	financial	ADJ
cana-4182	25	26	time	time	NOUN
cana-4182	25	27	series	series	NOUN
cana-4182	25	28	with	with	ADP
cana-4182	25	29	heavy	heavy	ADJ
cana-4182	25	30	-	-	PUNCT
cana-4182	25	31	tailed	tail	VERB
cana-4182	25	32	distributions	distribution	NOUN
cana-4182	25	33	and	and	CCONJ
cana-4182	25	34	volatility	volatility	NOUN
cana-4182	25	35	clustering	clustering	NOUN
cana-4182	25	36	.	.	PUNCT
cana-4182	26	1	meanwhile	meanwhile	ADV
cana-4182	26	2	,	,	PUNCT
cana-4182	26	3	in	in	ADP
cana-4182	26	4	ecological	ecological	ADJ
cana-4182	26	5	and	and	CCONJ
cana-4182	26	6	epidemiological	epidemiological	ADJ
cana-4182	26	7	models	model	NOUN
cana-4182	26	8	,	,	PUNCT
cana-4182	26	9	fractional	fractional	ADJ
cana-4182	26	10	-	-	PUNCT
cana-4182	26	11	order	order	NOUN
cana-4182	26	12	frameworks	framework	NOUN
cana-4182	26	13	capture	capture	VERB
cana-4182	26	14	spatial	spatial	ADJ
cana-4182	26	15	dispersion	dispersion	NOUN
cana-4182	26	16	patterns	pattern	NOUN
cana-4182	26	17	that	that	PRON
cana-4182	26	18	reflect	reflect	VERB
cana-4182	26	19	the	the	DET
cana-4182	26	20	complexities	complexity	NOUN
cana-4182	26	21	of	of	ADP
cana-4182	26	22	the	the	DET
cana-4182	26	23	environment	environment	NOUN
cana-4182	26	24	.	.	PUNCT
cana-4182	27	1	control	control	NOUN
cana-4182	27	2	systems	system	NOUN
cana-4182	27	3	engineers	engineer	NOUN
cana-4182	27	4	have	have	AUX
cana-4182	27	5	adopted	adopt	VERB
cana-4182	27	6	fractional	fractional	ADJ
cana-4182	27	7	controllers	controller	NOUN
cana-4182	27	8	to	to	PART
cana-4182	27	9	leverage	leverage	VERB
cana-4182	27	10	the	the	DET
cana-4182	27	11	expanded	expand	VERB
cana-4182	27	12	tuning	tuning	NOUN
cana-4182	27	13	parameters	parameter	NOUN
cana-4182	27	14	offered	offer	VERB
cana-4182	27	15	by	by	ADP
cana-4182	27	16	fractional	fractional	ADJ
cana-4182	27	17	gains	gain	NOUN
cana-4182	27	18	and	and	CCONJ
cana-4182	27	19	orders	order	NOUN
cana-4182	27	20	,	,	PUNCT
cana-4182	27	21	yielding	yield	VERB
cana-4182	27	22	improved	improved	ADJ
cana-4182	27	23	robustness	robustness	NOUN
cana-4182	27	24	and	and	CCONJ
cana-4182	27	25	performance	performance	NOUN
cana-4182	27	26	in	in	ADP
cana-4182	27	27	specific	specific	ADJ
cana-4182	27	28	scenarios	scenario	NOUN
cana-4182	27	29	.	.	PUNCT
cana-4182	28	1	as	as	SCONJ
cana-4182	28	2	the	the	DET
cana-4182	28	3	body	body	NOUN
cana-4182	28	4	of	of	ADP
cana-4182	28	5	research	research	NOUN
cana-4182	28	6	expands	expand	VERB
cana-4182	28	7	,	,	PUNCT
cana-4182	28	8	so	so	ADV
cana-4182	28	9	does	do	VERB
cana-4182	28	10	the	the	DET
cana-4182	28	11	repertoire	repertoire	NOUN
cana-4182	28	12	of	of	ADP
cana-4182	28	13	numerical	numerical	ADJ
cana-4182	28	14	tools	tool	NOUN
cana-4182	28	15	.	.	PUNCT
cana-4182	29	1	efficient	efficient	ADJ
cana-4182	29	2	discretization	discretization	NOUN
cana-4182	29	3	methods	method	NOUN
cana-4182	29	4	,	,	PUNCT
cana-4182	29	5	such	such	ADJ
cana-4182	29	6	as	as	ADP
cana-4182	29	7	the	the	DET
cana-4182	29	8	grünwald	grünwald	NOUN
cana-4182	29	9	–	–	PUNCT
cana-4182	29	10	letnikov	letnikov	NOUN
cana-4182	29	11	approach	approach	NOUN
cana-4182	29	12	and	and	CCONJ
cana-4182	29	13	finite	finite	ADJ
cana-4182	29	14	difference	difference	NOUN
cana-4182	29	15	approximations	approximation	NOUN
cana-4182	29	16	of	of	ADP
cana-4182	29	17	fractional	fractional	ADJ
cana-4182	29	18	operators	operator	NOUN
cana-4182	29	19	,	,	PUNCT
cana-4182	29	20	have	have	AUX
cana-4182	29	21	emerged	emerge	VERB
cana-4182	29	22	to	to	PART
cana-4182	29	23	handle	handle	VERB
cana-4182	29	24	the	the	DET
cana-4182	29	25	computational	computational	ADJ
cana-4182	29	26	challenges	challenge	NOUN
cana-4182	29	27	posed	pose	VERB
cana-4182	29	28	by	by	ADP
cana-4182	29	29	fractional	fractional	ADJ
cana-4182	29	30	calculus	calculus	NOUN
cana-4182	29	31	.	.	PUNCT
cana-4182	30	1	these	these	DET
cana-4182	30	2	numerical	numerical	ADJ
cana-4182	30	3	techniques	technique	NOUN
cana-4182	30	4	,	,	PUNCT
cana-4182	30	5	coupled	couple	VERB
cana-4182	30	6	with	with	ADP
cana-4182	30	7	advances	advance	NOUN
cana-4182	30	8	in	in	ADP
cana-4182	30	9	high	high	ADJ
cana-4182	30	10	-	-	PUNCT
cana-4182	30	11	performance	performance	NOUN
cana-4182	30	12	computing	computing	NOUN
cana-4182	30	13	,	,	PUNCT
cana-4182	30	14	have	have	AUX
cana-4182	30	15	significantly	significantly	ADV
cana-4182	30	16	lowered	lower	VERB
cana-4182	30	17	the	the	DET
cana-4182	30	18	barrier	barrier	NOUN
cana-4182	30	19	to	to	ADP
cana-4182	30	20	simulating	simulate	VERB
cana-4182	30	21	complex	complex	ADJ
cana-4182	30	22	fractional	fractional	ADJ
cana-4182	30	23	systems	system	NOUN
cana-4182	30	24	.	.	PUNCT
cana-4182	31	1	in	in	ADP
cana-4182	31	2	this	this	DET
cana-4182	31	3	review	review	NOUN
cana-4182	31	4	,	,	PUNCT
cana-4182	31	5	we	we	PRON
cana-4182	31	6	synthesize	synthesize	VERB
cana-4182	31	7	the	the	DET
cana-4182	31	8	theoretical	theoretical	ADJ
cana-4182	31	9	foundations	foundation	NOUN
cana-4182	31	10	of	of	ADP
cana-4182	31	11	fractional	fractional	ADJ
cana-4182	31	12	calculus	calculus	NOUN
cana-4182	31	13	and	and	CCONJ
cana-4182	31	14	examine	examine	VERB
cana-4182	31	15	cuttingedge	cuttingedge	NOUN
cana-4182	31	16	research	research	NOUN
cana-4182	31	17	that	that	PRON
cana-4182	31	18	demonstrates	demonstrate	VERB
cana-4182	31	19	its	its	PRON
cana-4182	31	20	effectiveness	effectiveness	NOUN
cana-4182	31	21	across	across	ADP
cana-4182	31	22	a	a	DET
cana-4182	31	23	variety	variety	NOUN
cana-4182	31	24	of	of	ADP
cana-4182	31	25	real	real	ADJ
cana-4182	31	26	-	-	PUNCT
cana-4182	31	27	world	world	NOUN
cana-4182	31	28	applications	application	NOUN
cana-4182	31	29	.	.	PUNCT
cana-4182	32	1	we	we	PRON
cana-4182	32	2	provide	provide	VERB
cana-4182	32	3	an	an	DET
cana-4182	32	4	overview	overview	NOUN
cana-4182	32	5	of	of	ADP
cana-4182	32	6	seminal	seminal	ADJ
cana-4182	32	7	works	work	NOUN
cana-4182	32	8	and	and	CCONJ
cana-4182	32	9	new	new	ADJ
cana-4182	32	10	developments	development	NOUN
cana-4182	32	11	,	,	PUNCT
cana-4182	32	12	bolstered	bolster	VERB
cana-4182	32	13	by	by	ADP
cana-4182	32	14	diagrams	diagram	NOUN
cana-4182	32	15	,	,	PUNCT
cana-4182	32	16	tables	table	NOUN
cana-4182	32	17	,	,	PUNCT
cana-4182	32	18	and	and	CCONJ
cana-4182	32	19	equations	equation	NOUN
cana-4182	32	20	illustrating	illustrate	VERB
cana-4182	32	21	key	key	ADJ
cana-4182	32	22	concepts	concept	NOUN
cana-4182	32	23	.	.	PUNCT
cana-4182	33	1	by	by	ADP
cana-4182	33	2	offering	offer	VERB
cana-4182	33	3	a	a	DET
cana-4182	33	4	cohesive	cohesive	ADJ
cana-4182	33	5	and	and	CCONJ
cana-4182	33	6	up	up	ADP
cana-4182	33	7	-	-	PUNCT
cana-4182	33	8	to	to	ADP
cana-4182	33	9	-	-	PUNCT
cana-4182	33	10	date	date	NOUN
cana-4182	33	11	appraisal	appraisal	NOUN
cana-4182	33	12	of	of	ADP
cana-4182	33	13	the	the	DET
cana-4182	33	14	subject	subject	NOUN
cana-4182	33	15	,	,	PUNCT
cana-4182	33	16	this	this	DET
cana-4182	33	17	paper	paper	NOUN
cana-4182	33	18	aims	aim	VERB
cana-4182	33	19	to	to	PART
cana-4182	33	20	serve	serve	VERB
cana-4182	33	21	as	as	ADP
cana-4182	33	22	both	both	CCONJ
cana-4182	33	23	an	an	DET
cana-4182	33	24	introduction	introduction	NOUN
cana-4182	33	25	for	for	ADP
cana-4182	33	26	newcomers	newcomer	NOUN
cana-4182	33	27	and	and	CCONJ
cana-4182	33	28	a	a	DET
cana-4182	33	29	reference	reference	NOUN
cana-4182	33	30	resource	resource	NOUN
cana-4182	33	31	for	for	ADP
cana-4182	33	32	seasoned	seasoned	ADJ
cana-4182	33	33	researchers	researcher	NOUN
cana-4182	33	34	seeking	seek	VERB
cana-4182	33	35	deeper	deep	ADJ
cana-4182	33	36	insights	insight	NOUN
cana-4182	33	37	into	into	ADP
cana-4182	33	38	fractional	fractional	ADJ
cana-4182	33	39	calculus	calculus	NOUN
cana-4182	33	40	and	and	CCONJ
cana-4182	33	41	its	its	PRON
cana-4182	33	42	transformative	transformative	ADJ
cana-4182	33	43	role	role	NOUN
cana-4182	33	44	in	in	ADP
cana-4182	33	45	modeling	model	VERB
cana-4182	33	46	the	the	DET
cana-4182	33	47	complexities	complexity	NOUN
cana-4182	33	48	of	of	ADP
cana-4182	33	49	our	our	PRON
cana-4182	33	50	world	world	NOUN
cana-4182	33	51	.	.	PUNCT
cana-4182	34	1	communications	communication	NOUN
cana-4182	34	2	on	on	ADP
cana-4182	34	3	applied	apply	VERB
cana-4182	34	4	nonlinear	nonlinear	ADJ
cana-4182	34	5	analysis	analysis	NOUN
cana-4182	34	6	issn	issn	NOUN
cana-4182	34	7	:	:	PUNCT
cana-4182	34	8	1074	1074	NUM
cana-4182	34	9	-	-	PUNCT
cana-4182	34	10	133x	133x	NUM
cana-4182	34	11	vol	vol	NOUN
cana-4182	34	12	32	32	NUM
cana-4182	34	13	no	no	NOUN
cana-4182	34	14	.	.	PUNCT
cana-4182	35	1	9s	9s	NUM
cana-4182	35	2	(	(	PUNCT
cana-4182	35	3	2025	2025	NUM
cana-4182	35	4	)	)	PUNCT
cana-4182	35	5	1499	1499	NUM
cana-4182	35	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4182	35	7	2	2	X
cana-4182	35	8	.	.	PUNCT
cana-4182	35	9	real	real	ADJ
cana-4182	35	10	-	-	PUNCT
cana-4182	35	11	time	time	NOUN
cana-4182	35	12	research	research	NOUN
cana-4182	35	13	data	datum	NOUN
cana-4182	35	14	,	,	PUNCT
cana-4182	35	15	equations	equation	NOUN
cana-4182	35	16	,	,	PUNCT
cana-4182	35	17	and	and	CCONJ
cana-4182	35	18	tables	table	VERB
cana-4182	35	19	2.1	2.1	NUM
cana-4182	35	20	fundamental	fundamental	ADJ
cana-4182	35	21	equations	equation	NOUN
cana-4182	35	22	of	of	ADP
cana-4182	35	23	fractional	fractional	PROPN
cana-4182	35	24	calculus	calculus	NOUN
cana-4182	35	25	riemann	riemann	PROPN
cana-4182	35	26	–	–	PUNCT
cana-4182	35	27	liouville	liouville	VERB
cana-4182	35	28	fractional	fractional	ADJ
cana-4182	35	29	integral	integral	ADJ
cana-4182	35	30	this	this	DET
cana-4182	35	31	integral	integral	ADJ
cana-4182	35	32	operator	operator	NOUN
cana-4182	35	33	generalizes	generalize	VERB
cana-4182	35	34	the	the	DET
cana-4182	35	35	concept	concept	NOUN
cana-4182	35	36	of	of	ADP
cana-4182	35	37	repeated	repeat	VERB
cana-4182	35	38	integration	integration	NOUN
cana-4182	35	39	to	to	ADP
cana-4182	35	40	non	non	ADJ
cana-4182	35	41	-	-	ADJ
cana-4182	35	42	integer	integer	ADJ
cana-4182	35	43	orders	order	NOUN
cana-4182	35	44	α\alphaα	α\alphaα	PROPN
cana-4182	35	45	.	.	PUNCT
cana-4182	36	1	caputo	caputo	PROPN
cana-4182	36	2	fractional	fractional	PROPN
cana-4182	36	3	derivative	derivative	PROPN
cana-4182	36	4	widely	widely	ADV
cana-4182	36	5	used	use	VERB
cana-4182	36	6	in	in	ADP
cana-4182	36	7	engineering	engineering	NOUN
cana-4182	36	8	,	,	PUNCT
cana-4182	36	9	the	the	DET
cana-4182	36	10	caputo	caputo	PROPN
cana-4182	36	11	derivative	derivative	NOUN
cana-4182	36	12	allows	allow	VERB
cana-4182	36	13	for	for	ADP
cana-4182	36	14	more	more	ADV
cana-4182	36	15	convenient	convenient	ADJ
cana-4182	36	16	handling	handling	NOUN
cana-4182	36	17	of	of	ADP
cana-4182	36	18	initial	initial	ADJ
cana-4182	36	19	conditions	condition	NOUN
cana-4182	36	20	compared	compare	VERB
cana-4182	36	21	to	to	ADP
cana-4182	36	22	the	the	DET
cana-4182	36	23	riemann	riemann	PROPN
cana-4182	36	24	–	–	PUNCT
cana-4182	36	25	liouville	liouville	VERB
cana-4182	36	26	derivative	derivative	NOUN
cana-4182	36	27	.	.	PUNCT
cana-4182	37	1	2.2	2.2	NUM
cana-4182	37	2	example	example	NOUN
cana-4182	37	3	data	datum	NOUN
cana-4182	37	4	:	:	PUNCT
cana-4182	37	5	viscoelastic	viscoelastic	NOUN
cana-4182	37	6	material	material	NOUN
cana-4182	37	7	testing	testing	NOUN
cana-4182	37	8	below	below	ADV
cana-4182	37	9	is	be	AUX
cana-4182	37	10	a	a	DET
cana-4182	37	11	hypothetical	hypothetical	ADJ
cana-4182	37	12	dataset	dataset	NOUN
cana-4182	37	13	illustrating	illustrate	VERB
cana-4182	37	14	how	how	SCONJ
cana-4182	37	15	fractional	fractional	ADJ
cana-4182	37	16	calculus	calculus	NOUN
cana-4182	37	17	can	can	AUX
cana-4182	37	18	model	model	VERB
cana-4182	37	19	stress	stress	NOUN
cana-4182	37	20	-	-	PUNCT
cana-4182	37	21	strain	strain	NOUN
cana-4182	37	22	behavior	behavior	NOUN
cana-4182	37	23	in	in	ADP
cana-4182	37	24	a	a	DET
cana-4182	37	25	polymer	polymer	NOUN
cana-4182	37	26	under	under	ADP
cana-4182	37	27	cyclic	cyclic	ADJ
cana-4182	37	28	loading	loading	NOUN
cana-4182	37	29	.	.	PUNCT
cana-4182	38	1	the	the	DET
cana-4182	38	2	integer	integer	NOUN
cana-4182	38	3	-	-	PUNCT
cana-4182	38	4	order	order	NOUN
cana-4182	38	5	model	model	NOUN
cana-4182	38	6	is	be	AUX
cana-4182	38	7	compared	compare	VERB
cana-4182	38	8	with	with	ADP
cana-4182	38	9	a	a	DET
cana-4182	38	10	fractional	fractional	ADJ
cana-4182	38	11	-	-	PUNCT
cana-4182	38	12	order	order	NOUN
cana-4182	38	13	model	model	NOUN
cana-4182	38	14	:	:	PUNCT
cana-4182	38	15	cycle	cycle	NOUN
cana-4182	38	16	measured	measure	VERB
cana-4182	38	17	peak	peak	NOUN
cana-4182	38	18	stress	stress	NOUN
cana-4182	38	19	(	(	PUNCT
cana-4182	38	20	pa	pa	NOUN
cana-4182	38	21	)	)	PUNCT
cana-4182	38	22	integer	integer	NOUN
cana-4182	38	23	-	-	PUNCT
cana-4182	38	24	order	order	NOUN
cana-4182	38	25	model	model	NOUN
cana-4182	38	26	(	(	PUNCT
cana-4182	38	27	pa	pa	NOUN
cana-4182	38	28	)	)	PUNCT
cana-4182	38	29	fractional	fractional	ADJ
cana-4182	38	30	-	-	PUNCT
cana-4182	38	31	order	order	NOUN
cana-4182	38	32	model	model	NOUN
cana-4182	38	33	(	(	PUNCT
cana-4182	38	34	pa	pa	PROPN
cana-4182	38	35	)	)	PUNCT
cana-4182	38	36	1	1	NUM
cana-4182	38	37	10,500	10,500	NUM
cana-4182	38	38	10,400	10,400	NUM
cana-4182	38	39	10,450	10,450	NUM
cana-4182	38	40	2	2	NUM
cana-4182	38	41	10,200	10,200	NUM
cana-4182	38	42	9,800	9,800	NUM
cana-4182	38	43	10,130	10,130	NUM
cana-4182	38	44	3	3	NUM
cana-4182	38	45	9,900	9,900	NUM
cana-4182	38	46	9,300	9,300	NUM
cana-4182	38	47	9,870	9,870	NUM
cana-4182	38	48	4	4	NUM
cana-4182	38	49	9,650	9,650	NUM
cana-4182	38	50	8,900	8,900	NUM
cana-4182	38	51	9,620	9,620	NUM
cana-4182	38	52	the	the	DET
cana-4182	38	53	fractional	fractional	ADJ
cana-4182	38	54	model	model	NOUN
cana-4182	38	55	remains	remain	VERB
cana-4182	38	56	closer	close	ADJ
cana-4182	38	57	to	to	ADP
cana-4182	38	58	the	the	DET
cana-4182	38	59	measured	measure	VERB
cana-4182	38	60	data	datum	NOUN
cana-4182	38	61	across	across	ADP
cana-4182	38	62	the	the	DET
cana-4182	38	63	loading	loading	NOUN
cana-4182	38	64	cycles	cycle	NOUN
cana-4182	38	65	,	,	PUNCT
cana-4182	38	66	showcasing	showcase	VERB
cana-4182	38	67	the	the	DET
cana-4182	38	68	capacity	capacity	NOUN
cana-4182	38	69	of	of	ADP
cana-4182	38	70	fractional	fractional	ADJ
cana-4182	38	71	operators	operator	NOUN
cana-4182	38	72	to	to	PART
cana-4182	38	73	capture	capture	VERB
cana-4182	38	74	memory	memory	NOUN
cana-4182	38	75	effects	effect	NOUN
cana-4182	38	76	(	(	PUNCT
cana-4182	38	77	creep	creep	NOUN
cana-4182	38	78	,	,	PUNCT
cana-4182	38	79	relaxation	relaxation	NOUN
cana-4182	38	80	)	)	PUNCT
cana-4182	38	81	.	.	PUNCT
cana-4182	39	1	3	3	X
cana-4182	39	2	.	.	X
cana-4182	39	3	fractional	fractional	ADJ
cana-4182	39	4	-	-	PUNCT
cana-4182	39	5	order	order	NOUN
cana-4182	39	6	modeling	modeling	NOUN
cana-4182	39	7	in	in	ADP
cana-4182	39	8	biological	biological	ADJ
cana-4182	39	9	systems	system	NOUN
cana-4182	39	10	fractional	fractional	ADJ
cana-4182	39	11	calculus	calculus	NOUN
cana-4182	39	12	has	have	AUX
cana-4182	39	13	emerged	emerge	VERB
cana-4182	39	14	as	as	ADP
cana-4182	39	15	a	a	DET
cana-4182	39	16	powerful	powerful	ADJ
cana-4182	39	17	tool	tool	NOUN
cana-4182	39	18	in	in	ADP
cana-4182	39	19	modeling	model	VERB
cana-4182	39	20	various	various	ADJ
cana-4182	39	21	biological	biological	ADJ
cana-4182	39	22	processes	process	NOUN
cana-4182	39	23	where	where	SCONJ
cana-4182	39	24	memory	memory	NOUN
cana-4182	39	25	and	and	CCONJ
cana-4182	39	26	hereditary	hereditary	ADJ
cana-4182	39	27	effects	effect	NOUN
cana-4182	39	28	play	play	VERB
cana-4182	39	29	a	a	DET
cana-4182	39	30	crucial	crucial	ADJ
cana-4182	39	31	role	role	NOUN
cana-4182	39	32	.	.	PUNCT
cana-4182	40	1	living	living	NOUN
cana-4182	40	2	systems	system	NOUN
cana-4182	40	3	often	often	ADV
cana-4182	40	4	exhibit	exhibit	VERB
cana-4182	40	5	behavior	behavior	NOUN
cana-4182	40	6	that	that	PRON
cana-4182	40	7	can	can	AUX
cana-4182	40	8	not	not	PART
cana-4182	40	9	be	be	AUX
cana-4182	40	10	fully	fully	ADV
cana-4182	40	11	captured	capture	VERB
cana-4182	40	12	by	by	ADP
cana-4182	40	13	traditional	traditional	ADJ
cana-4182	40	14	integer	integer	NOUN
cana-4182	40	15	-	-	PUNCT
cana-4182	40	16	order	order	NOUN
cana-4182	40	17	differential	differential	ADJ
cana-4182	40	18	equations	equation	NOUN
cana-4182	40	19	.	.	PUNCT
cana-4182	41	1	biochemical	biochemical	ADJ
cana-4182	41	2	reactions	reaction	NOUN
cana-4182	41	3	,	,	PUNCT
cana-4182	41	4	intracellular	intracellular	ADJ
cana-4182	41	5	transport	transport	NOUN
cana-4182	41	6	,	,	PUNCT
cana-4182	41	7	population	population	NOUN
cana-4182	41	8	dynamics	dynamic	NOUN
cana-4182	41	9	,	,	PUNCT
cana-4182	41	10	and	and	CCONJ
cana-4182	41	11	neural	neural	ADJ
cana-4182	41	12	signal	signal	NOUN
cana-4182	41	13	propagation	propagation	NOUN
cana-4182	41	14	frequently	frequently	ADV
cana-4182	41	15	display	display	VERB
cana-4182	41	16	complex	complex	NOUN
cana-4182	41	17	,	,	PUNCT
cana-4182	41	18	history	history	NOUN
cana-4182	41	19	-	-	PUNCT
cana-4182	41	20	dependent	dependent	ADJ
cana-4182	41	21	behavior	behavior	NOUN
cana-4182	41	22	.	.	PUNCT
cana-4182	42	1	this	this	DET
cana-4182	42	2	complexity	complexity	NOUN
cana-4182	42	3	arises	arise	VERB
cana-4182	42	4	partly	partly	ADV
cana-4182	42	5	from	from	ADP
cana-4182	42	6	feedback	feedback	NOUN
cana-4182	42	7	mechanisms	mechanism	NOUN
cana-4182	42	8	,	,	PUNCT
cana-4182	42	9	structural	structural	ADJ
cana-4182	42	10	heterogeneity	heterogeneity	NOUN
cana-4182	42	11	,	,	PUNCT
cana-4182	42	12	and	and	CCONJ
cana-4182	42	13	multi	multi	ADJ
cana-4182	42	14	-	-	ADJ
cana-4182	42	15	scale	scale	ADJ
cana-4182	42	16	interactions	interaction	NOUN
cana-4182	42	17	—	—	PUNCT
cana-4182	42	18	characteristics	characteristic	NOUN
cana-4182	42	19	well	well	ADV
cana-4182	42	20	-	-	PUNCT
cana-4182	42	21	suited	suit	VERB
cana-4182	42	22	to	to	ADP
cana-4182	42	23	fractional	fractional	ADJ
cana-4182	42	24	-	-	PUNCT
cana-4182	42	25	order	order	NOUN
cana-4182	42	26	frameworks	framework	NOUN
cana-4182	42	27	.	.	PUNCT
cana-4182	43	1	one	one	NUM
cana-4182	43	2	of	of	ADP
cana-4182	43	3	the	the	DET
cana-4182	43	4	noteworthy	noteworthy	ADJ
cana-4182	43	5	applications	application	NOUN
cana-4182	43	6	of	of	ADP
cana-4182	43	7	fractional	fractional	ADJ
cana-4182	43	8	calculus	calculus	NOUN
cana-4182	43	9	in	in	ADP
cana-4182	43	10	biology	biology	NOUN
cana-4182	43	11	is	be	AUX
cana-4182	43	12	the	the	DET
cana-4182	43	13	modeling	modeling	NOUN
cana-4182	43	14	of	of	ADP
cana-4182	43	15	subdiffusion	subdiffusion	NOUN
cana-4182	43	16	in	in	ADP
cana-4182	43	17	crowded	crowded	ADJ
cana-4182	43	18	cellular	cellular	ADJ
cana-4182	43	19	environments	environment	NOUN
cana-4182	43	20	.	.	PUNCT
cana-4182	44	1	in	in	ADP
cana-4182	44	2	classical	classical	ADJ
cana-4182	44	3	diffusion	diffusion	NOUN
cana-4182	44	4	processes	process	NOUN
cana-4182	44	5	,	,	PUNCT
cana-4182	44	6	the	the	DET
cana-4182	44	7	mean	mean	ADJ
cana-4182	44	8	squared	square	VERB
cana-4182	44	9	displacement	displacement	NOUN
cana-4182	44	10	of	of	ADP
cana-4182	44	11	communications	communication	NOUN
cana-4182	44	12	on	on	ADP
cana-4182	44	13	applied	apply	VERB
cana-4182	44	14	nonlinear	nonlinear	ADJ
cana-4182	44	15	analysis	analysis	NOUN
cana-4182	44	16	issn	issn	NOUN
cana-4182	44	17	:	:	PUNCT
cana-4182	44	18	1074	1074	NUM
cana-4182	44	19	-	-	PUNCT
cana-4182	44	20	133x	133x	NUM
cana-4182	44	21	vol	vol	NOUN
cana-4182	44	22	32	32	NUM
cana-4182	44	23	no	no	NOUN
cana-4182	44	24	.	.	PUNCT
cana-4182	45	1	9s	9s	NUM
cana-4182	45	2	(	(	PUNCT
cana-4182	45	3	2025	2025	NUM
cana-4182	45	4	)	)	PUNCT
cana-4182	45	5	1500	1500	NUM
cana-4182	45	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4182	45	7	particles	particle	NOUN
cana-4182	45	8	typically	typically	ADV
cana-4182	45	9	grows	grow	VERB
cana-4182	45	10	linearly	linearly	ADV
cana-4182	45	11	with	with	ADP
cana-4182	45	12	time	time	NOUN
cana-4182	45	13	,	,	PUNCT
cana-4182	45	14	consistent	consistent	ADJ
cana-4182	45	15	with	with	ADP
cana-4182	45	16	brownian	brownian	ADJ
cana-4182	45	17	motion	motion	NOUN
cana-4182	45	18	.	.	PUNCT
cana-4182	46	1	however	however	ADV
cana-4182	46	2	,	,	PUNCT
cana-4182	46	3	in	in	ADP
cana-4182	46	4	biological	biological	ADJ
cana-4182	46	5	cells	cell	NOUN
cana-4182	46	6	,	,	PUNCT
cana-4182	46	7	macromolecular	macromolecular	NOUN
cana-4182	46	8	crowding	crowd	VERB
cana-4182	46	9	and	and	CCONJ
cana-4182	46	10	binding	bind	VERB
cana-4182	46	11	interactions	interaction	NOUN
cana-4182	46	12	can	can	AUX
cana-4182	46	13	restrict	restrict	VERB
cana-4182	46	14	particle	particle	NOUN
cana-4182	46	15	mobility	mobility	NOUN
cana-4182	46	16	,	,	PUNCT
cana-4182	46	17	resulting	result	VERB
cana-4182	46	18	in	in	ADP
cana-4182	46	19	anomalous	anomalous	ADJ
cana-4182	46	20	diffusion	diffusion	NOUN
cana-4182	46	21	.	.	PUNCT
cana-4182	47	1	by	by	ADP
cana-4182	47	2	introducing	introduce	VERB
cana-4182	47	3	a	a	DET
cana-4182	47	4	fractional	fractional	ADJ
cana-4182	47	5	order	order	NOUN
cana-4182	47	6	between	between	ADP
cana-4182	47	7	0	0	NUM
cana-4182	47	8	and	and	CCONJ
cana-4182	47	9	1	1	NUM
cana-4182	47	10	in	in	ADP
cana-4182	47	11	the	the	DET
cana-4182	47	12	differential	differential	ADJ
cana-4182	47	13	operator	operator	NOUN
cana-4182	47	14	,	,	PUNCT
cana-4182	47	15	researchers	researcher	NOUN
cana-4182	47	16	can	can	AUX
cana-4182	47	17	capture	capture	VERB
cana-4182	47	18	the	the	DET
cana-4182	47	19	slower	slow	ADJ
cana-4182	47	20	-	-	PUNCT
cana-4182	47	21	than	than	ADP
cana-4182	47	22	-	-	PUNCT
cana-4182	47	23	expected	expect	VERB
cana-4182	47	24	spread	spread	NOUN
cana-4182	47	25	of	of	ADP
cana-4182	47	26	particles	particle	NOUN
cana-4182	47	27	,	,	PUNCT
cana-4182	47	28	accurately	accurately	ADV
cana-4182	47	29	mirroring	mirror	VERB
cana-4182	47	30	experimental	experimental	ADJ
cana-4182	47	31	observations	observation	NOUN
cana-4182	47	32	.	.	PUNCT
cana-4182	48	1	this	this	DET
cana-4182	48	2	fractional	fractional	ADJ
cana-4182	48	3	approach	approach	NOUN
cana-4182	48	4	highlights	highlight	NOUN
cana-4182	48	5	how	how	SCONJ
cana-4182	48	6	the	the	DET
cana-4182	48	7	medium	medium	NOUN
cana-4182	48	8	’s	’s	NOUN
cana-4182	48	9	structure	structure	NOUN
cana-4182	48	10	and	and	CCONJ
cana-4182	48	11	past	past	ADJ
cana-4182	48	12	states	state	NOUN
cana-4182	48	13	influence	influence	VERB
cana-4182	48	14	current	current	ADJ
cana-4182	48	15	dynamics	dynamic	NOUN
cana-4182	48	16	.	.	PUNCT
cana-4182	49	1	another	another	DET
cana-4182	49	2	fascinating	fascinating	ADJ
cana-4182	49	3	area	area	NOUN
cana-4182	49	4	is	be	AUX
cana-4182	49	5	the	the	DET
cana-4182	49	6	study	study	NOUN
cana-4182	49	7	of	of	ADP
cana-4182	49	8	population	population	NOUN
cana-4182	49	9	dynamics	dynamic	NOUN
cana-4182	49	10	in	in	ADP
cana-4182	49	11	ecology	ecology	NOUN
cana-4182	49	12	,	,	PUNCT
cana-4182	49	13	where	where	SCONJ
cana-4182	49	14	species	specie	NOUN
cana-4182	49	15	spread	spread	VERB
cana-4182	49	16	,	,	PUNCT
cana-4182	49	17	interaction	interaction	NOUN
cana-4182	49	18	,	,	PUNCT
cana-4182	49	19	and	and	CCONJ
cana-4182	49	20	reproduction	reproduction	NOUN
cana-4182	49	21	can	can	AUX
cana-4182	49	22	be	be	AUX
cana-4182	49	23	influenced	influence	VERB
cana-4182	49	24	by	by	ADP
cana-4182	49	25	long	long	ADJ
cana-4182	49	26	-	-	PUNCT
cana-4182	49	27	range	range	NOUN
cana-4182	49	28	correlations	correlation	NOUN
cana-4182	49	29	and	and	CCONJ
cana-4182	49	30	memory	memory	NOUN
cana-4182	49	31	.	.	PUNCT
cana-4182	50	1	fractionalorder	fractionalorder	PROPN
cana-4182	50	2	differential	differential	PROPN
cana-4182	50	3	equations	equation	NOUN
cana-4182	50	4	allow	allow	VERB
cana-4182	50	5	for	for	ADP
cana-4182	50	6	more	more	ADV
cana-4182	50	7	nuanced	nuanced	ADJ
cana-4182	50	8	representations	representation	NOUN
cana-4182	50	9	of	of	ADP
cana-4182	50	10	birth	birth	NOUN
cana-4182	50	11	and	and	CCONJ
cana-4182	50	12	death	death	NOUN
cana-4182	50	13	processes	process	NOUN
cana-4182	50	14	,	,	PUNCT
cana-4182	50	15	accounting	account	VERB
cana-4182	50	16	for	for	ADP
cana-4182	50	17	historical	historical	ADJ
cana-4182	50	18	environmental	environmental	ADJ
cana-4182	50	19	conditions	condition	NOUN
cana-4182	50	20	or	or	CCONJ
cana-4182	50	21	events	event	NOUN
cana-4182	50	22	that	that	PRON
cana-4182	50	23	continue	continue	VERB
cana-4182	50	24	to	to	PART
cana-4182	50	25	affect	affect	VERB
cana-4182	50	26	the	the	DET
cana-4182	50	27	present	present	ADJ
cana-4182	50	28	state	state	NOUN
cana-4182	50	29	.	.	PUNCT
cana-4182	51	1	such	such	ADJ
cana-4182	51	2	considerations	consideration	NOUN
cana-4182	51	3	are	be	AUX
cana-4182	51	4	essential	essential	ADJ
cana-4182	51	5	when	when	SCONJ
cana-4182	51	6	modeling	model	VERB
cana-4182	51	7	invasive	invasive	ADJ
cana-4182	51	8	species	specie	NOUN
cana-4182	51	9	or	or	CCONJ
cana-4182	51	10	disease	disease	NOUN
cana-4182	51	11	vectors	vector	NOUN
cana-4182	51	12	,	,	PUNCT
cana-4182	51	13	as	as	SCONJ
cana-4182	51	14	the	the	DET
cana-4182	51	15	memory	memory	NOUN
cana-4182	51	16	effect	effect	NOUN
cana-4182	51	17	can	can	AUX
cana-4182	51	18	influence	influence	VERB
cana-4182	51	19	expansion	expansion	NOUN
cana-4182	51	20	rates	rate	NOUN
cana-4182	51	21	and	and	CCONJ
cana-4182	51	22	interaction	interaction	NOUN
cana-4182	51	23	strengths	strength	NOUN
cana-4182	51	24	long	long	ADV
cana-4182	51	25	after	after	ADP
cana-4182	51	26	initial	initial	ADJ
cana-4182	51	27	introduction	introduction	NOUN
cana-4182	51	28	.	.	PUNCT
cana-4182	52	1	fractional	fractional	ADJ
cana-4182	52	2	frameworks	framework	NOUN
cana-4182	52	3	have	have	AUX
cana-4182	52	4	,	,	PUNCT
cana-4182	52	5	therefore	therefore	ADV
cana-4182	52	6	,	,	PUNCT
cana-4182	52	7	shown	show	VERB
cana-4182	52	8	potential	potential	NOUN
cana-4182	52	9	in	in	ADP
cana-4182	52	10	refining	refining	NOUN
cana-4182	52	11	predictions	prediction	NOUN
cana-4182	52	12	of	of	ADP
cana-4182	52	13	population	population	NOUN
cana-4182	52	14	growth	growth	NOUN
cana-4182	52	15	,	,	PUNCT
cana-4182	52	16	migration	migration	NOUN
cana-4182	52	17	patterns	pattern	NOUN
cana-4182	52	18	,	,	PUNCT
cana-4182	52	19	and	and	CCONJ
cana-4182	52	20	ecosystem	ecosystem	NOUN
cana-4182	52	21	stability	stability	NOUN
cana-4182	52	22	.	.	PUNCT
cana-4182	53	1	neural	neural	ADJ
cana-4182	53	2	signaling	signal	VERB
cana-4182	53	3	presents	present	NOUN
cana-4182	53	4	another	another	DET
cana-4182	53	5	frontier	frontier	NOUN
cana-4182	53	6	for	for	ADP
cana-4182	53	7	fractional	fractional	ADJ
cana-4182	53	8	modeling	modeling	NOUN
cana-4182	53	9	.	.	PUNCT
cana-4182	54	1	the	the	DET
cana-4182	54	2	brain	brain	NOUN
cana-4182	54	3	’s	’s	PART
cana-4182	54	4	electrical	electrical	ADJ
cana-4182	54	5	activity	activity	NOUN
cana-4182	54	6	,	,	PUNCT
cana-4182	54	7	governed	govern	VERB
cana-4182	54	8	by	by	ADP
cana-4182	54	9	ionic	ionic	ADJ
cana-4182	54	10	currents	current	NOUN
cana-4182	54	11	and	and	CCONJ
cana-4182	54	12	membrane	membrane	NOUN
cana-4182	54	13	potentials	potential	NOUN
cana-4182	54	14	,	,	PUNCT
cana-4182	54	15	is	be	AUX
cana-4182	54	16	characterized	characterize	VERB
cana-4182	54	17	by	by	ADP
cana-4182	54	18	a	a	DET
cana-4182	54	19	combination	combination	NOUN
cana-4182	54	20	of	of	ADP
cana-4182	54	21	discrete	discrete	ADJ
cana-4182	54	22	action	action	NOUN
cana-4182	54	23	potentials	potential	NOUN
cana-4182	54	24	and	and	CCONJ
cana-4182	54	25	continuous	continuous	ADJ
cana-4182	54	26	background	background	NOUN
cana-4182	54	27	processes	process	NOUN
cana-4182	54	28	.	.	PUNCT
cana-4182	55	1	traditional	traditional	ADJ
cana-4182	55	2	models	model	NOUN
cana-4182	55	3	,	,	PUNCT
cana-4182	55	4	such	such	ADJ
cana-4182	55	5	as	as	ADP
cana-4182	55	6	the	the	DET
cana-4182	55	7	hodgkin	hodgkin	PROPN
cana-4182	55	8	–	–	PUNCT
cana-4182	55	9	huxley	huxley	PROPN
cana-4182	55	10	equations	equation	NOUN
cana-4182	55	11	,	,	PUNCT
cana-4182	55	12	have	have	AUX
cana-4182	55	13	been	be	AUX
cana-4182	55	14	supplemented	supplement	VERB
cana-4182	55	15	by	by	ADP
cana-4182	55	16	fractional	fractional	ADJ
cana-4182	55	17	extensions	extension	NOUN
cana-4182	55	18	to	to	PART
cana-4182	55	19	incorporate	incorporate	VERB
cana-4182	55	20	memory	memory	NOUN
cana-4182	55	21	-	-	PUNCT
cana-4182	55	22	like	like	ADJ
cana-4182	55	23	behavior	behavior	NOUN
cana-4182	55	24	in	in	ADP
cana-4182	55	25	neuronal	neuronal	ADJ
cana-4182	55	26	membranes	membrane	NOUN
cana-4182	55	27	or	or	CCONJ
cana-4182	55	28	ion	ion	NOUN
cana-4182	55	29	channel	channel	NOUN
cana-4182	55	30	dynamics	dynamic	NOUN
cana-4182	55	31	.	.	PUNCT
cana-4182	56	1	as	as	ADP
cana-4182	56	2	a	a	DET
cana-4182	56	3	result	result	NOUN
cana-4182	56	4	,	,	PUNCT
cana-4182	56	5	these	these	DET
cana-4182	56	6	fractional	fractional	ADJ
cana-4182	56	7	models	model	NOUN
cana-4182	56	8	can	can	AUX
cana-4182	56	9	exhibit	exhibit	VERB
cana-4182	56	10	more	more	ADV
cana-4182	56	11	realistic	realistic	ADJ
cana-4182	56	12	responses	response	NOUN
cana-4182	56	13	to	to	PART
cana-4182	56	14	stimuli	stimulus	NOUN
cana-4182	56	15	,	,	PUNCT
cana-4182	56	16	reflecting	reflect	VERB
cana-4182	56	17	the	the	DET
cana-4182	56	18	subtlety	subtlety	NOUN
cana-4182	56	19	of	of	ADP
cana-4182	56	20	short	short	ADJ
cana-4182	56	21	-	-	PUNCT
cana-4182	56	22	term	term	NOUN
cana-4182	56	23	memory	memory	NOUN
cana-4182	56	24	and	and	CCONJ
cana-4182	56	25	adaptation	adaptation	NOUN
cana-4182	56	26	phenomena	phenomenon	NOUN
cana-4182	56	27	in	in	ADP
cana-4182	56	28	neural	neural	ADJ
cana-4182	56	29	networks	network	NOUN
cana-4182	56	30	.	.	PUNCT
cana-4182	57	1	moreover	moreover	ADV
cana-4182	57	2	,	,	PUNCT
cana-4182	57	3	fractional	fractional	ADJ
cana-4182	57	4	calculus	calculus	NOUN
cana-4182	57	5	has	have	AUX
cana-4182	57	6	been	be	AUX
cana-4182	57	7	used	use	VERB
cana-4182	57	8	in	in	ADP
cana-4182	57	9	modeling	model	VERB
cana-4182	57	10	cardiovascular	cardiovascular	ADJ
cana-4182	57	11	dynamics	dynamic	NOUN
cana-4182	57	12	.	.	PUNCT
cana-4182	58	1	blood	blood	NOUN
cana-4182	58	2	flow	flow	NOUN
cana-4182	58	3	in	in	ADP
cana-4182	58	4	certain	certain	ADJ
cana-4182	58	5	physiological	physiological	ADJ
cana-4182	58	6	conditions	condition	NOUN
cana-4182	58	7	,	,	PUNCT
cana-4182	58	8	especially	especially	ADV
cana-4182	58	9	in	in	ADP
cana-4182	58	10	microcirculation	microcirculation	NOUN
cana-4182	58	11	or	or	CCONJ
cana-4182	58	12	in	in	ADP
cana-4182	58	13	diseased	diseased	ADJ
cana-4182	58	14	arteries	artery	NOUN
cana-4182	58	15	,	,	PUNCT
cana-4182	58	16	can	can	AUX
cana-4182	58	17	exhibit	exhibit	VERB
cana-4182	58	18	non	non	ADJ
cana-4182	58	19	-	-	ADJ
cana-4182	58	20	newtonian	newtonian	ADJ
cana-4182	58	21	and	and	CCONJ
cana-4182	58	22	viscoelastic	viscoelastic	NOUN
cana-4182	58	23	properties	property	NOUN
cana-4182	58	24	that	that	PRON
cana-4182	58	25	defy	defy	VERB
cana-4182	58	26	standard	standard	ADJ
cana-4182	58	27	integer	integer	NOUN
cana-4182	58	28	-	-	PUNCT
cana-4182	58	29	order	order	NOUN
cana-4182	58	30	models	model	NOUN
cana-4182	58	31	.	.	PUNCT
cana-4182	59	1	fractional	fractional	ADJ
cana-4182	59	2	-	-	PUNCT
cana-4182	59	3	order	order	NOUN
cana-4182	59	4	approaches	approach	NOUN
cana-4182	59	5	allow	allow	VERB
cana-4182	59	6	for	for	ADP
cana-4182	59	7	the	the	DET
cana-4182	59	8	modeling	modeling	NOUN
cana-4182	59	9	of	of	ADP
cana-4182	59	10	shear	shear	NOUN
cana-4182	59	11	-	-	PUNCT
cana-4182	59	12	thinning	thin	VERB
cana-4182	59	13	and	and	CCONJ
cana-4182	59	14	shear	shear	NOUN
cana-4182	59	15	-	-	PUNCT
cana-4182	59	16	thickening	thicken	VERB
cana-4182	59	17	behaviors	behavior	NOUN
cana-4182	59	18	along	along	ADP
cana-4182	59	19	with	with	ADP
cana-4182	59	20	memory	memory	NOUN
cana-4182	59	21	effects	effect	NOUN
cana-4182	59	22	in	in	ADP
cana-4182	59	23	vessel	vessel	NOUN
cana-4182	59	24	walls	wall	NOUN
cana-4182	59	25	,	,	PUNCT
cana-4182	59	26	yielding	yield	VERB
cana-4182	59	27	a	a	DET
cana-4182	59	28	more	more	ADV
cana-4182	59	29	faithful	faithful	ADJ
cana-4182	59	30	description	description	NOUN
cana-4182	59	31	of	of	ADP
cana-4182	59	32	hemodynamic	hemodynamic	ADJ
cana-4182	59	33	processes	process	NOUN
cana-4182	59	34	.	.	PUNCT
cana-4182	60	1	despite	despite	SCONJ
cana-4182	60	2	these	these	DET
cana-4182	60	3	successful	successful	ADJ
cana-4182	60	4	applications	application	NOUN
cana-4182	60	5	,	,	PUNCT
cana-4182	60	6	challenges	challenge	NOUN
cana-4182	60	7	remain	remain	VERB
cana-4182	60	8	.	.	PUNCT
cana-4182	61	1	parameter	parameter	PROPN
cana-4182	61	2	estimation	estimation	PROPN
cana-4182	61	3	,	,	PUNCT
cana-4182	61	4	for	for	ADP
cana-4182	61	5	instance	instance	NOUN
cana-4182	61	6	,	,	PUNCT
cana-4182	61	7	can	can	AUX
cana-4182	61	8	be	be	AUX
cana-4182	61	9	more	more	ADV
cana-4182	61	10	complicated	complicated	ADJ
cana-4182	61	11	for	for	ADP
cana-4182	61	12	fractional	fractional	ADJ
cana-4182	61	13	models	model	NOUN
cana-4182	61	14	,	,	PUNCT
cana-4182	61	15	as	as	SCONJ
cana-4182	61	16	additional	additional	ADJ
cana-4182	61	17	fractional	fractional	ADJ
cana-4182	61	18	orders	order	NOUN
cana-4182	61	19	introduce	introduce	VERB
cana-4182	61	20	nonlinearity	nonlinearity	NOUN
cana-4182	61	21	and	and	CCONJ
cana-4182	61	22	increase	increase	VERB
cana-4182	61	23	the	the	DET
cana-4182	61	24	dimensionality	dimensionality	NOUN
cana-4182	61	25	of	of	ADP
cana-4182	61	26	the	the	DET
cana-4182	61	27	parameter	parameter	NOUN
cana-4182	61	28	space	space	NOUN
cana-4182	61	29	.	.	PUNCT
cana-4182	62	1	data	datum	NOUN
cana-4182	62	2	availability	availability	NOUN
cana-4182	62	3	can	can	AUX
cana-4182	62	4	further	far	ADV
cana-4182	62	5	limit	limit	VERB
cana-4182	62	6	model	model	NOUN
cana-4182	62	7	accuracy	accuracy	NOUN
cana-4182	62	8	,	,	PUNCT
cana-4182	62	9	particularly	particularly	ADV
cana-4182	62	10	when	when	SCONJ
cana-4182	62	11	trying	try	VERB
cana-4182	62	12	to	to	PART
cana-4182	62	13	capture	capture	VERB
cana-4182	62	14	subtle	subtle	ADJ
cana-4182	62	15	memory	memory	NOUN
cana-4182	62	16	-	-	PUNCT
cana-4182	62	17	dependent	dependent	ADJ
cana-4182	62	18	phenomena	phenomenon	NOUN
cana-4182	62	19	in	in	ADP
cana-4182	62	20	complex	complex	ADJ
cana-4182	62	21	organisms	organism	NOUN
cana-4182	62	22	or	or	CCONJ
cana-4182	62	23	tissues	tissue	NOUN
cana-4182	62	24	.	.	PUNCT
cana-4182	63	1	nevertheless	nevertheless	ADV
cana-4182	63	2	,	,	PUNCT
cana-4182	63	3	continued	continued	ADJ
cana-4182	63	4	development	development	NOUN
cana-4182	63	5	of	of	ADP
cana-4182	63	6	computational	computational	ADJ
cana-4182	63	7	techniques	technique	NOUN
cana-4182	63	8	and	and	CCONJ
cana-4182	63	9	highfidelity	highfidelity	NOUN
cana-4182	63	10	experimental	experimental	ADJ
cana-4182	63	11	methods	method	NOUN
cana-4182	63	12	promises	promise	VERB
cana-4182	63	13	to	to	PART
cana-4182	63	14	expand	expand	VERB
cana-4182	63	15	the	the	DET
cana-4182	63	16	use	use	NOUN
cana-4182	63	17	of	of	ADP
cana-4182	63	18	fractional	fractional	ADJ
cana-4182	63	19	calculus	calculus	NOUN
cana-4182	63	20	in	in	ADP
cana-4182	63	21	biology	biology	NOUN
cana-4182	63	22	.	.	PUNCT
cana-4182	64	1	as	as	SCONJ
cana-4182	64	2	researchers	researcher	NOUN
cana-4182	64	3	refine	refine	VERB
cana-4182	64	4	these	these	DET
cana-4182	64	5	models	model	NOUN
cana-4182	64	6	,	,	PUNCT
cana-4182	64	7	the	the	DET
cana-4182	64	8	synergy	synergy	NOUN
cana-4182	64	9	between	between	ADP
cana-4182	64	10	theoretical	theoretical	ADJ
cana-4182	64	11	biology	biology	NOUN
cana-4182	64	12	,	,	PUNCT
cana-4182	64	13	computational	computational	ADJ
cana-4182	64	14	science	science	NOUN
cana-4182	64	15	,	,	PUNCT
cana-4182	64	16	and	and	CCONJ
cana-4182	64	17	experimental	experimental	ADJ
cana-4182	64	18	validation	validation	NOUN
cana-4182	64	19	will	will	AUX
cana-4182	64	20	likely	likely	ADV
cana-4182	64	21	yield	yield	VERB
cana-4182	64	22	deeper	deep	ADJ
cana-4182	64	23	insights	insight	NOUN
cana-4182	64	24	into	into	ADP
cana-4182	64	25	the	the	DET
cana-4182	64	26	fundamental	fundamental	ADJ
cana-4182	64	27	laws	law	NOUN
cana-4182	64	28	governing	govern	VERB
cana-4182	64	29	living	living	NOUN
cana-4182	64	30	systems	system	NOUN
cana-4182	64	31	.	.	PUNCT
cana-4182	65	1	4	4	X
cana-4182	65	2	.	.	X
cana-4182	65	3	numerical	numerical	ADJ
cana-4182	65	4	approaches	approach	NOUN
cana-4182	65	5	and	and	CCONJ
cana-4182	65	6	implementation	implementation	NOUN
cana-4182	65	7	implementing	implement	VERB
cana-4182	65	8	fractional	fractional	ADJ
cana-4182	65	9	calculus	calculus	NOUN
cana-4182	65	10	in	in	ADP
cana-4182	65	11	practical	practical	ADJ
cana-4182	65	12	applications	application	NOUN
cana-4182	65	13	demands	demand	VERB
cana-4182	65	14	specialized	specialized	ADJ
cana-4182	65	15	numerical	numerical	ADJ
cana-4182	65	16	methods	method	NOUN
cana-4182	65	17	due	due	ADP
cana-4182	65	18	to	to	ADP
cana-4182	65	19	the	the	DET
cana-4182	65	20	non	non	ADJ
cana-4182	65	21	-	-	ADJ
cana-4182	65	22	local	local	ADJ
cana-4182	65	23	nature	nature	NOUN
cana-4182	65	24	of	of	ADP
cana-4182	65	25	fractional	fractional	ADJ
cana-4182	65	26	derivatives	derivative	NOUN
cana-4182	65	27	.	.	PUNCT
cana-4182	66	1	unlike	unlike	ADP
cana-4182	66	2	integer	integer	NOUN
cana-4182	66	3	-	-	PUNCT
cana-4182	66	4	order	order	NOUN
cana-4182	66	5	derivatives	derivative	NOUN
cana-4182	66	6	,	,	PUNCT
cana-4182	66	7	where	where	SCONJ
cana-4182	66	8	the	the	DET
cana-4182	66	9	value	value	NOUN
cana-4182	66	10	of	of	ADP
cana-4182	66	11	a	a	DET
cana-4182	66	12	derivative	derivative	NOUN
cana-4182	66	13	at	at	ADP
cana-4182	66	14	a	a	DET
cana-4182	66	15	specific	specific	ADJ
cana-4182	66	16	point	point	NOUN
cana-4182	66	17	depends	depend	VERB
cana-4182	66	18	solely	solely	ADV
cana-4182	66	19	on	on	ADP
cana-4182	66	20	local	local	ADJ
cana-4182	66	21	information	information	NOUN
cana-4182	66	22	,	,	PUNCT
cana-4182	66	23	fractional	fractional	ADJ
cana-4182	66	24	derivatives	derivative	NOUN
cana-4182	66	25	communications	communication	NOUN
cana-4182	66	26	on	on	ADP
cana-4182	66	27	applied	apply	VERB
cana-4182	66	28	nonlinear	nonlinear	ADJ
cana-4182	66	29	analysis	analysis	NOUN
cana-4182	66	30	issn	issn	NOUN
cana-4182	66	31	:	:	PUNCT
cana-4182	66	32	1074	1074	NUM
cana-4182	66	33	-	-	PUNCT
cana-4182	66	34	133x	133x	NUM
cana-4182	66	35	vol	vol	NOUN
cana-4182	66	36	32	32	NUM
cana-4182	66	37	no	no	NOUN
cana-4182	66	38	.	.	PUNCT
cana-4182	67	1	9s	9s	NUM
cana-4182	67	2	(	(	PUNCT
cana-4182	67	3	2025	2025	NUM
cana-4182	67	4	)	)	PUNCT
cana-4182	67	5	1501	1501	NUM
cana-4182	67	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4182	67	7	often	often	ADV
cana-4182	67	8	require	require	VERB
cana-4182	67	9	knowledge	knowledge	NOUN
cana-4182	67	10	of	of	ADP
cana-4182	67	11	the	the	DET
cana-4182	67	12	entire	entire	ADJ
cana-4182	67	13	function	function	NOUN
cana-4182	67	14	history	history	NOUN
cana-4182	67	15	(	(	PUNCT
cana-4182	67	16	or	or	CCONJ
cana-4182	67	17	,	,	PUNCT
cana-4182	67	18	in	in	ADP
cana-4182	67	19	discrete	discrete	ADJ
cana-4182	67	20	terms	term	NOUN
cana-4182	67	21	,	,	PUNCT
cana-4182	67	22	all	all	DET
cana-4182	67	23	previous	previous	ADJ
cana-4182	67	24	points	point	NOUN
cana-4182	67	25	)	)	PUNCT
cana-4182	67	26	.	.	PUNCT
cana-4182	68	1	this	this	DET
cana-4182	68	2	memory	memory	NOUN
cana-4182	68	3	effect	effect	NOUN
cana-4182	68	4	can	can	AUX
cana-4182	68	5	significantly	significantly	ADV
cana-4182	68	6	increase	increase	VERB
cana-4182	68	7	computational	computational	ADJ
cana-4182	68	8	complexity	complexity	NOUN
cana-4182	68	9	if	if	SCONJ
cana-4182	68	10	not	not	PART
cana-4182	68	11	handled	handle	VERB
cana-4182	68	12	carefully	carefully	ADV
cana-4182	68	13	.	.	PUNCT
cana-4182	69	1	several	several	ADJ
cana-4182	69	2	numerical	numerical	ADJ
cana-4182	69	3	methods	method	NOUN
cana-4182	69	4	have	have	AUX
cana-4182	69	5	been	be	AUX
cana-4182	69	6	developed	develop	VERB
cana-4182	69	7	to	to	PART
cana-4182	69	8	tackle	tackle	VERB
cana-4182	69	9	fractional	fractional	ADJ
cana-4182	69	10	operators	operator	NOUN
cana-4182	69	11	.	.	PUNCT
cana-4182	70	1	the	the	DET
cana-4182	70	2	grünwald	grünwald	NOUN
cana-4182	70	3	–	–	PUNCT
cana-4182	70	4	letnikov	letnikov	NOUN
cana-4182	70	5	approach	approach	NOUN
cana-4182	70	6	discretizes	discretize	VERB
cana-4182	70	7	fractional	fractional	ADJ
cana-4182	70	8	derivatives	derivative	NOUN
cana-4182	70	9	by	by	ADP
cana-4182	70	10	approximating	approximate	VERB
cana-4182	70	11	the	the	DET
cana-4182	70	12	integral	integral	ADJ
cana-4182	70	13	or	or	CCONJ
cana-4182	70	14	derivative	derivative	NOUN
cana-4182	70	15	via	via	ADP
cana-4182	70	16	a	a	DET
cana-4182	70	17	summation	summation	NOUN
cana-4182	70	18	series	series	NOUN
cana-4182	70	19	with	with	ADP
cana-4182	70	20	specific	specific	ADJ
cana-4182	70	21	binomial	binomial	ADJ
cana-4182	70	22	-	-	PUNCT
cana-4182	70	23	like	like	ADJ
cana-4182	70	24	coefficients	coefficient	NOUN
cana-4182	70	25	.	.	PUNCT
cana-4182	71	1	in	in	ADP
cana-4182	71	2	practice	practice	NOUN
cana-4182	71	3	,	,	PUNCT
cana-4182	71	4	implementing	implement	VERB
cana-4182	71	5	the	the	DET
cana-4182	71	6	grünwald	grünwald	NOUN
cana-4182	71	7	–	–	PUNCT
cana-4182	71	8	letnikov	letnikov	NOUN
cana-4182	71	9	method	method	NOUN
cana-4182	71	10	requires	require	VERB
cana-4182	71	11	careful	careful	ADJ
cana-4182	71	12	consideration	consideration	NOUN
cana-4182	71	13	of	of	ADP
cana-4182	71	14	step	step	NOUN
cana-4182	71	15	size	size	NOUN
cana-4182	71	16	,	,	PUNCT
cana-4182	71	17	as	as	SCONJ
cana-4182	71	18	smaller	small	ADJ
cana-4182	71	19	steps	step	NOUN
cana-4182	71	20	increase	increase	NOUN
cana-4182	71	21	accuracy	accuracy	NOUN
cana-4182	71	22	but	but	CCONJ
cana-4182	71	23	can	can	AUX
cana-4182	71	24	result	result	VERB
cana-4182	71	25	in	in	ADP
cana-4182	71	26	prohibitive	prohibitive	ADJ
cana-4182	71	27	computational	computational	ADJ
cana-4182	71	28	costs	cost	NOUN
cana-4182	71	29	for	for	ADP
cana-4182	71	30	long	long	ADJ
cana-4182	71	31	-	-	PUNCT
cana-4182	71	32	time	time	NOUN
cana-4182	71	33	simulations	simulation	NOUN
cana-4182	71	34	.	.	PUNCT
cana-4182	72	1	another	another	DET
cana-4182	72	2	popular	popular	ADJ
cana-4182	72	3	approach	approach	NOUN
cana-4182	72	4	involves	involve	VERB
cana-4182	72	5	the	the	DET
cana-4182	72	6	finite	finite	ADJ
cana-4182	72	7	difference	difference	NOUN
cana-4182	72	8	schemes	scheme	NOUN
cana-4182	72	9	customized	customize	VERB
cana-4182	72	10	for	for	ADP
cana-4182	72	11	fractional	fractional	ADJ
cana-4182	72	12	derivatives	derivative	NOUN
cana-4182	72	13	.	.	PUNCT
cana-4182	73	1	for	for	ADP
cana-4182	73	2	instance	instance	NOUN
cana-4182	73	3	,	,	PUNCT
cana-4182	73	4	the	the	DET
cana-4182	73	5	l1	l1	PROPN
cana-4182	73	6	method	method	NOUN
cana-4182	73	7	is	be	AUX
cana-4182	73	8	often	often	ADV
cana-4182	73	9	applied	apply	VERB
cana-4182	73	10	to	to	ADP
cana-4182	73	11	the	the	DET
cana-4182	73	12	caputo	caputo	PROPN
cana-4182	73	13	fractional	fractional	PROPN
cana-4182	73	14	derivative	derivative	NOUN
cana-4182	73	15	,	,	PUNCT
cana-4182	73	16	approximating	approximate	VERB
cana-4182	73	17	the	the	DET
cana-4182	73	18	integral	integral	ADJ
cana-4182	73	19	term	term	NOUN
cana-4182	73	20	in	in	ADP
cana-4182	73	21	the	the	DET
cana-4182	73	22	derivative	derivative	ADJ
cana-4182	73	23	definition	definition	NOUN
cana-4182	73	24	through	through	ADP
cana-4182	73	25	trapezoidal	trapezoidal	ADJ
cana-4182	73	26	or	or	CCONJ
cana-4182	73	27	piecewise	piecewise	NOUN
cana-4182	73	28	linear	linear	ADJ
cana-4182	73	29	interpolation	interpolation	NOUN
cana-4182	73	30	.	.	PUNCT
cana-4182	74	1	the	the	DET
cana-4182	74	2	success	success	NOUN
cana-4182	74	3	of	of	ADP
cana-4182	74	4	these	these	DET
cana-4182	74	5	methods	method	NOUN
cana-4182	74	6	depends	depend	VERB
cana-4182	74	7	on	on	ADP
cana-4182	74	8	balancing	balance	VERB
cana-4182	74	9	accuracy	accuracy	NOUN
cana-4182	74	10	with	with	ADP
cana-4182	74	11	efficiency	efficiency	NOUN
cana-4182	74	12	,	,	PUNCT
cana-4182	74	13	as	as	SCONJ
cana-4182	74	14	finer	fine	ADJ
cana-4182	74	15	grids	grid	NOUN
cana-4182	74	16	yield	yield	VERB
cana-4182	74	17	better	well	ADJ
cana-4182	74	18	results	result	NOUN
cana-4182	74	19	but	but	CCONJ
cana-4182	74	20	also	also	ADV
cana-4182	74	21	require	require	VERB
cana-4182	74	22	more	more	ADV
cana-4182	74	23	computational	computational	ADJ
cana-4182	74	24	resources	resource	NOUN
cana-4182	74	25	.	.	PUNCT
cana-4182	75	1	spectral	spectral	ADJ
cana-4182	75	2	methods	method	NOUN
cana-4182	75	3	have	have	AUX
cana-4182	75	4	also	also	ADV
cana-4182	75	5	gained	gain	VERB
cana-4182	75	6	popularity	popularity	NOUN
cana-4182	75	7	for	for	ADP
cana-4182	75	8	problems	problem	NOUN
cana-4182	75	9	where	where	SCONJ
cana-4182	75	10	global	global	ADJ
cana-4182	75	11	accuracy	accuracy	NOUN
cana-4182	75	12	is	be	AUX
cana-4182	75	13	desired	desire	VERB
cana-4182	75	14	.	.	PUNCT
cana-4182	76	1	by	by	ADP
cana-4182	76	2	expanding	expand	VERB
cana-4182	76	3	the	the	DET
cana-4182	76	4	solution	solution	NOUN
cana-4182	76	5	in	in	ADP
cana-4182	76	6	terms	term	NOUN
cana-4182	76	7	of	of	ADP
cana-4182	76	8	orthogonal	orthogonal	ADJ
cana-4182	76	9	basis	basis	NOUN
cana-4182	76	10	functions	function	NOUN
cana-4182	76	11	(	(	PUNCT
cana-4182	76	12	such	such	ADJ
cana-4182	76	13	as	as	ADP
cana-4182	76	14	chebyshev	chebyshev	NOUN
cana-4182	76	15	or	or	CCONJ
cana-4182	76	16	fourier	fourier	NOUN
cana-4182	76	17	polynomials	polynomial	NOUN
cana-4182	76	18	)	)	PUNCT
cana-4182	76	19	,	,	PUNCT
cana-4182	76	20	these	these	DET
cana-4182	76	21	methods	method	NOUN
cana-4182	76	22	can	can	AUX
cana-4182	76	23	achieve	achieve	VERB
cana-4182	76	24	high	high	ADJ
cana-4182	76	25	accuracy	accuracy	NOUN
cana-4182	76	26	with	with	ADP
cana-4182	76	27	relatively	relatively	ADV
cana-4182	76	28	fewer	few	ADJ
cana-4182	76	29	degrees	degree	NOUN
cana-4182	76	30	of	of	ADP
cana-4182	76	31	freedom	freedom	NOUN
cana-4182	76	32	.	.	PUNCT
cana-4182	77	1	however	however	ADV
cana-4182	77	2	,	,	PUNCT
cana-4182	77	3	spectral	spectral	ADJ
cana-4182	77	4	methods	method	NOUN
cana-4182	77	5	must	must	AUX
cana-4182	77	6	be	be	AUX
cana-4182	77	7	tailored	tailor	VERB
cana-4182	77	8	to	to	ADP
cana-4182	77	9	fractional	fractional	VERB
cana-4182	77	10	operators	operator	NOUN
cana-4182	77	11	to	to	PART
cana-4182	77	12	accommodate	accommodate	VERB
cana-4182	77	13	the	the	DET
cana-4182	77	14	non	non	ADJ
cana-4182	77	15	-	-	ADJ
cana-4182	77	16	local	local	ADJ
cana-4182	77	17	interaction	interaction	NOUN
cana-4182	77	18	between	between	ADP
cana-4182	77	19	nodes	node	NOUN
cana-4182	77	20	in	in	ADP
cana-4182	77	21	the	the	DET
cana-4182	77	22	computational	computational	ADJ
cana-4182	77	23	domain	domain	NOUN
cana-4182	77	24	.	.	PUNCT
cana-4182	78	1	in	in	ADP
cana-4182	78	2	addition	addition	NOUN
cana-4182	78	3	to	to	ADP
cana-4182	78	4	direct	direct	ADJ
cana-4182	78	5	discretization	discretization	NOUN
cana-4182	78	6	approaches	approach	NOUN
cana-4182	78	7	,	,	PUNCT
cana-4182	78	8	researchers	researcher	NOUN
cana-4182	78	9	have	have	AUX
cana-4182	78	10	explored	explore	VERB
cana-4182	78	11	transform	transform	NOUN
cana-4182	78	12	-	-	PUNCT
cana-4182	78	13	based	base	VERB
cana-4182	78	14	methods	method	NOUN
cana-4182	78	15	,	,	PUNCT
cana-4182	78	16	such	such	ADJ
cana-4182	78	17	as	as	ADP
cana-4182	78	18	the	the	DET
cana-4182	78	19	laplace	laplace	NOUN
cana-4182	78	20	or	or	CCONJ
cana-4182	78	21	fourier	fourier	NOUN
cana-4182	78	22	transform	transform	NOUN
cana-4182	78	23	,	,	PUNCT
cana-4182	78	24	to	to	PART
cana-4182	78	25	handle	handle	VERB
cana-4182	78	26	fractional	fractional	ADJ
cana-4182	78	27	derivatives	derivative	NOUN
cana-4182	78	28	analytically	analytically	ADV
cana-4182	78	29	before	before	ADP
cana-4182	78	30	reverting	revert	VERB
cana-4182	78	31	to	to	ADP
cana-4182	78	32	the	the	DET
cana-4182	78	33	time	time	NOUN
cana-4182	78	34	or	or	CCONJ
cana-4182	78	35	spatial	spatial	ADJ
cana-4182	78	36	domain	domain	NOUN
cana-4182	78	37	.	.	PUNCT
cana-4182	79	1	these	these	DET
cana-4182	79	2	methods	method	NOUN
cana-4182	79	3	can	can	AUX
cana-4182	79	4	reduce	reduce	VERB
cana-4182	79	5	fractional	fractional	ADJ
cana-4182	79	6	differential	differential	ADJ
cana-4182	79	7	equations	equation	NOUN
cana-4182	79	8	to	to	ADP
cana-4182	79	9	algebraic	algebraic	ADJ
cana-4182	79	10	forms	form	NOUN
cana-4182	79	11	in	in	ADP
cana-4182	79	12	the	the	DET
cana-4182	79	13	transform	transform	NOUN
cana-4182	79	14	domain	domain	NOUN
cana-4182	79	15	,	,	PUNCT
cana-4182	79	16	simplifying	simplify	VERB
cana-4182	79	17	the	the	DET
cana-4182	79	18	solution	solution	NOUN
cana-4182	79	19	process	process	NOUN
cana-4182	79	20	.	.	PUNCT
cana-4182	80	1	nonetheless	nonetheless	ADV
cana-4182	80	2	,	,	PUNCT
cana-4182	80	3	transformbased	transformbase	VERB
cana-4182	80	4	solutions	solution	NOUN
cana-4182	80	5	often	often	ADV
cana-4182	80	6	require	require	VERB
cana-4182	80	7	inverse	inverse	NOUN
cana-4182	80	8	transforms	transform	NOUN
cana-4182	80	9	that	that	PRON
cana-4182	80	10	may	may	AUX
cana-4182	80	11	introduce	introduce	VERB
cana-4182	80	12	numerical	numerical	ADJ
cana-4182	80	13	challenges	challenge	NOUN
cana-4182	80	14	,	,	PUNCT
cana-4182	80	15	especially	especially	ADV
cana-4182	80	16	when	when	SCONJ
cana-4182	80	17	discontinuities	discontinuity	NOUN
cana-4182	80	18	or	or	CCONJ
cana-4182	80	19	complex	complex	ADJ
cana-4182	80	20	boundary	boundary	ADJ
cana-4182	80	21	conditions	condition	NOUN
cana-4182	80	22	are	be	AUX
cana-4182	80	23	present	present	ADJ
cana-4182	80	24	.	.	PUNCT
cana-4182	81	1	modern	modern	ADJ
cana-4182	81	2	computational	computational	ADJ
cana-4182	81	3	frameworks	framework	NOUN
cana-4182	81	4	increasingly	increasingly	ADV
cana-4182	81	5	incorporate	incorporate	VERB
cana-4182	81	6	fast	fast	ADJ
cana-4182	81	7	algorithms	algorithm	NOUN
cana-4182	81	8	to	to	PART
cana-4182	81	9	handle	handle	VERB
cana-4182	81	10	the	the	DET
cana-4182	81	11	convolution	convolution	NOUN
cana-4182	81	12	integrals	integral	NOUN
cana-4182	81	13	associated	associate	VERB
cana-4182	81	14	with	with	ADP
cana-4182	81	15	fractional	fractional	ADJ
cana-4182	81	16	operators	operator	NOUN
cana-4182	81	17	.	.	PUNCT
cana-4182	82	1	by	by	ADP
cana-4182	82	2	applying	apply	VERB
cana-4182	82	3	techniques	technique	NOUN
cana-4182	82	4	like	like	ADP
cana-4182	82	5	the	the	DET
cana-4182	82	6	fast	fast	ADJ
cana-4182	82	7	fourier	fourier	NOUN
cana-4182	82	8	transform	transform	NOUN
cana-4182	82	9	(	(	PUNCT
cana-4182	82	10	fft	fft	PROPN
cana-4182	82	11	)	)	PUNCT
cana-4182	82	12	,	,	PUNCT
cana-4182	82	13	it	it	PRON
cana-4182	82	14	becomes	become	VERB
cana-4182	82	15	feasible	feasible	ADJ
cana-4182	82	16	to	to	PART
cana-4182	82	17	compute	compute	VERB
cana-4182	82	18	convolution	convolution	NOUN
cana-4182	82	19	sums	sum	NOUN
cana-4182	82	20	in	in	ADP
cana-4182	82	21	o(n	o(n	PROPN
cana-4182	82	22	log	log	NOUN
cana-4182	82	23	n	n	CCONJ
cana-4182	82	24	)	)	PUNCT
cana-4182	82	25	time	time	NOUN
cana-4182	82	26	,	,	PUNCT
cana-4182	82	27	significantly	significantly	ADV
cana-4182	82	28	reducing	reduce	VERB
cana-4182	82	29	the	the	DET
cana-4182	82	30	computational	computational	ADJ
cana-4182	82	31	overhead	overhead	NOUN
cana-4182	82	32	compared	compare	VERB
cana-4182	82	33	to	to	ADP
cana-4182	82	34	naive	naive	ADJ
cana-4182	82	35	o(n2	o(n2	ADV
cana-4182	82	36	)	)	PUNCT
cana-4182	82	37	implementations	implementation	NOUN
cana-4182	82	38	.	.	PUNCT
cana-4182	83	1	parallel	parallel	ADJ
cana-4182	83	2	computing	computing	NOUN
cana-4182	83	3	architectures	architecture	NOUN
cana-4182	83	4	,	,	PUNCT
cana-4182	83	5	including	include	VERB
cana-4182	83	6	general	general	ADJ
cana-4182	83	7	-	-	PUNCT
cana-4182	83	8	purpose	purpose	NOUN
cana-4182	83	9	graphics	graphic	NOUN
cana-4182	83	10	processing	processing	NOUN
cana-4182	83	11	units	unit	NOUN
cana-4182	83	12	(	(	PUNCT
cana-4182	83	13	gpgpus	gpgpus	PROPN
cana-4182	83	14	)	)	PUNCT
cana-4182	83	15	,	,	PUNCT
cana-4182	83	16	further	far	ADV
cana-4182	83	17	accelerate	accelerate	VERB
cana-4182	83	18	these	these	DET
cana-4182	83	19	calculations	calculation	NOUN
cana-4182	83	20	,	,	PUNCT
cana-4182	83	21	making	make	VERB
cana-4182	83	22	real	real	ADJ
cana-4182	83	23	-	-	PUNCT
cana-4182	83	24	time	time	NOUN
cana-4182	83	25	or	or	CCONJ
cana-4182	83	26	large	large	ADJ
cana-4182	83	27	-	-	PUNCT
cana-4182	83	28	scale	scale	NOUN
cana-4182	83	29	simulations	simulation	NOUN
cana-4182	83	30	more	more	ADV
cana-4182	83	31	practical	practical	ADJ
cana-4182	83	32	.	.	PUNCT
cana-4182	84	1	from	from	ADP
cana-4182	84	2	an	an	DET
cana-4182	84	3	implementation	implementation	NOUN
cana-4182	84	4	standpoint	standpoint	NOUN
cana-4182	84	5	,	,	PUNCT
cana-4182	84	6	software	software	NOUN
cana-4182	84	7	libraries	library	NOUN
cana-4182	84	8	dedicated	dedicate	VERB
cana-4182	84	9	to	to	ADP
cana-4182	84	10	fractional	fractional	ADJ
cana-4182	84	11	calculus	calculus	NOUN
cana-4182	84	12	have	have	AUX
cana-4182	84	13	started	start	VERB
cana-4182	84	14	to	to	PART
cana-4182	84	15	appear	appear	VERB
cana-4182	84	16	,	,	PUNCT
cana-4182	84	17	allowing	allow	VERB
cana-4182	84	18	researchers	researcher	NOUN
cana-4182	84	19	to	to	PART
cana-4182	84	20	quickly	quickly	ADV
cana-4182	84	21	prototype	prototype	VERB
cana-4182	84	22	and	and	CCONJ
cana-4182	84	23	compare	compare	VERB
cana-4182	84	24	different	different	ADJ
cana-4182	84	25	numerical	numerical	ADJ
cana-4182	84	26	methods	method	NOUN
cana-4182	84	27	.	.	PUNCT
cana-4182	85	1	open	open	ADJ
cana-4182	85	2	-	-	PUNCT
cana-4182	85	3	source	source	NOUN
cana-4182	85	4	tools	tool	NOUN
cana-4182	85	5	,	,	PUNCT
cana-4182	85	6	often	often	ADV
cana-4182	85	7	written	write	VERB
cana-4182	85	8	in	in	ADP
cana-4182	85	9	languages	language	NOUN
cana-4182	85	10	such	such	ADJ
cana-4182	85	11	as	as	ADP
cana-4182	85	12	python	python	NOUN
cana-4182	85	13	,	,	PUNCT
cana-4182	85	14	matlab	matlab	PROPN
cana-4182	85	15	,	,	PUNCT
cana-4182	85	16	or	or	CCONJ
cana-4182	85	17	c++	c++	NOUN
cana-4182	85	18	,	,	PUNCT
cana-4182	85	19	offer	offer	VERB
cana-4182	85	20	modules	module	NOUN
cana-4182	85	21	for	for	ADP
cana-4182	85	22	fractional	fractional	ADJ
cana-4182	85	23	differential	differential	ADJ
cana-4182	85	24	operators	operator	NOUN
cana-4182	85	25	,	,	PUNCT
cana-4182	85	26	parameter	parameter	NOUN
cana-4182	85	27	estimation	estimation	NOUN
cana-4182	85	28	routines	routine	NOUN
cana-4182	85	29	,	,	PUNCT
cana-4182	85	30	and	and	CCONJ
cana-4182	85	31	solver	solver	VERB
cana-4182	85	32	interfaces	interface	NOUN
cana-4182	85	33	.	.	PUNCT
cana-4182	86	1	these	these	DET
cana-4182	86	2	libraries	library	NOUN
cana-4182	86	3	not	not	PART
cana-4182	86	4	only	only	ADV
cana-4182	86	5	lower	low	ADJ
cana-4182	86	6	the	the	DET
cana-4182	86	7	barrier	barrier	NOUN
cana-4182	86	8	of	of	ADP
cana-4182	86	9	entry	entry	NOUN
cana-4182	86	10	for	for	ADP
cana-4182	86	11	new	new	ADJ
cana-4182	86	12	researchers	researcher	NOUN
cana-4182	86	13	but	but	CCONJ
cana-4182	86	14	also	also	ADV
cana-4182	86	15	foster	foster	VERB
cana-4182	86	16	a	a	DET
cana-4182	86	17	community	community	NOUN
cana-4182	86	18	-	-	PUNCT
cana-4182	86	19	driven	drive	VERB
cana-4182	86	20	approach	approach	NOUN
cana-4182	86	21	to	to	ADP
cana-4182	86	22	improving	improve	VERB
cana-4182	86	23	and	and	CCONJ
cana-4182	86	24	testing	test	VERB
cana-4182	86	25	numerical	numerical	ADJ
cana-4182	86	26	methods	method	NOUN
cana-4182	86	27	.	.	PUNCT
cana-4182	87	1	looking	look	VERB
cana-4182	87	2	ahead	ahead	ADV
cana-4182	87	3	,	,	PUNCT
cana-4182	87	4	continued	continue	VERB
cana-4182	87	5	development	development	NOUN
cana-4182	87	6	of	of	ADP
cana-4182	87	7	robust	robust	ADJ
cana-4182	87	8	and	and	CCONJ
cana-4182	87	9	efficient	efficient	ADJ
cana-4182	87	10	algorithms	algorithm	NOUN
cana-4182	87	11	remains	remain	VERB
cana-4182	87	12	a	a	DET
cana-4182	87	13	key	key	ADJ
cana-4182	87	14	priority	priority	NOUN
cana-4182	87	15	.	.	PUNCT
cana-4182	88	1	as	as	SCONJ
cana-4182	88	2	fractional	fractional	ADJ
cana-4182	88	3	calculus	calculus	NOUN
cana-4182	88	4	gains	gain	NOUN
cana-4182	88	5	traction	traction	NOUN
cana-4182	88	6	in	in	ADP
cana-4182	88	7	areas	area	NOUN
cana-4182	88	8	like	like	ADP
cana-4182	88	9	biomedical	biomedical	ADJ
cana-4182	88	10	engineering	engineering	NOUN
cana-4182	88	11	,	,	PUNCT
cana-4182	88	12	robotics	robotic	NOUN
cana-4182	88	13	,	,	PUNCT
cana-4182	88	14	and	and	CCONJ
cana-4182	88	15	finance	finance	NOUN
cana-4182	88	16	,	,	PUNCT
cana-4182	88	17	the	the	DET
cana-4182	88	18	need	need	NOUN
cana-4182	88	19	for	for	ADP
cana-4182	88	20	scalable	scalable	ADJ
cana-4182	88	21	and	and	CCONJ
cana-4182	88	22	accurate	accurate	ADJ
cana-4182	88	23	solvers	solver	NOUN
cana-4182	88	24	will	will	AUX
cana-4182	88	25	only	only	ADV
cana-4182	88	26	increase	increase	VERB
cana-4182	88	27	.	.	PUNCT
cana-4182	89	1	by	by	ADP
cana-4182	89	2	uniting	unite	VERB
cana-4182	89	3	improved	improve	VERB
cana-4182	89	4	numerical	numerical	ADJ
cana-4182	89	5	techniques	technique	NOUN
cana-4182	89	6	with	with	ADP
cana-4182	89	7	communications	communication	NOUN
cana-4182	89	8	on	on	ADP
cana-4182	89	9	applied	apply	VERB
cana-4182	89	10	nonlinear	nonlinear	ADJ
cana-4182	89	11	analysis	analysis	NOUN
cana-4182	89	12	issn	issn	NOUN
cana-4182	89	13	:	:	PUNCT
cana-4182	89	14	1074	1074	NUM
cana-4182	89	15	-	-	PUNCT
cana-4182	89	16	133x	133x	NUM
cana-4182	89	17	vol	vol	NOUN
cana-4182	89	18	32	32	NUM
cana-4182	89	19	no	no	NOUN
cana-4182	89	20	.	.	PUNCT
cana-4182	90	1	9s	9s	NUM
cana-4182	90	2	(	(	PUNCT
cana-4182	90	3	2025	2025	NUM
cana-4182	90	4	)	)	PUNCT
cana-4182	90	5	1502	1502	NUM
cana-4182	90	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4182	91	1	better	well	ADJ
cana-4182	91	2	theoretical	theoretical	ADJ
cana-4182	91	3	understanding	understanding	NOUN
cana-4182	91	4	and	and	CCONJ
cana-4182	91	5	more	more	ADV
cana-4182	91	6	extensive	extensive	ADJ
cana-4182	91	7	experimental	experimental	ADJ
cana-4182	91	8	validation	validation	NOUN
cana-4182	91	9	,	,	PUNCT
cana-4182	91	10	the	the	DET
cana-4182	91	11	field	field	NOUN
cana-4182	91	12	stands	stand	VERB
cana-4182	91	13	poised	poise	VERB
cana-4182	91	14	to	to	PART
cana-4182	91	15	unlock	unlock	VERB
cana-4182	91	16	deeper	deep	ADJ
cana-4182	91	17	insights	insight	NOUN
cana-4182	91	18	into	into	ADP
cana-4182	91	19	the	the	DET
cana-4182	91	20	many	many	ADJ
cana-4182	91	21	complex	complex	ADJ
cana-4182	91	22	phenomena	phenomenon	NOUN
cana-4182	91	23	that	that	SCONJ
cana-4182	91	24	fractional	fractional	ADJ
cana-4182	91	25	models	model	NOUN
cana-4182	91	26	can	can	AUX
cana-4182	91	27	capture	capture	VERB
cana-4182	91	28	.	.	PUNCT
cana-4182	92	1	5	5	X
cana-4182	92	2	.	.	X
cana-4182	92	3	schematic	schematic	ADJ
cana-4182	92	4	diagram	diagram	NOUN
cana-4182	92	5	of	of	ADP
cana-4182	92	6	fractional	fractional	ADJ
cana-4182	92	7	derivative	derivative	ADJ
cana-4182	92	8	behavior	behavior	NOUN
cana-4182	92	9	below	below	ADV
cana-4182	92	10	is	be	AUX
cana-4182	92	11	a	a	DET
cana-4182	92	12	textual	textual	ADJ
cana-4182	92	13	(	(	PUNCT
cana-4182	92	14	ascii	ascii	NOUN
cana-4182	92	15	)	)	PUNCT
cana-4182	92	16	schematic	schematic	ADJ
cana-4182	92	17	diagram	diagram	NOUN
cana-4182	92	18	illustrating	illustrate	VERB
cana-4182	92	19	how	how	SCONJ
cana-4182	92	20	fractional	fractional	ADJ
cana-4182	92	21	derivatives	derivative	NOUN
cana-4182	92	22	incorporate	incorporate	VERB
cana-4182	92	23	past	past	ADP
cana-4182	92	24	states	state	NOUN
cana-4182	92	25	more	more	ADV
cana-4182	92	26	significantly	significantly	ADV
cana-4182	92	27	than	than	ADP
cana-4182	92	28	integer	integer	NOUN
cana-4182	92	29	-	-	PUNCT
cana-4182	92	30	order	order	NOUN
cana-4182	92	31	derivatives	derivative	NOUN
cana-4182	92	32	:	:	PUNCT
cana-4182	92	33	interpretation	interpretation	NOUN
cana-4182	92	34	:	:	PUNCT
cana-4182	92	35	unlike	unlike	ADP
cana-4182	92	36	traditional	traditional	ADJ
cana-4182	92	37	derivatives	derivative	NOUN
cana-4182	92	38	(	(	PUNCT
cana-4182	92	39	which	which	PRON
cana-4182	92	40	focus	focus	VERB
cana-4182	92	41	on	on	ADP
cana-4182	92	42	the	the	DET
cana-4182	92	43	instantaneous	instantaneous	ADJ
cana-4182	92	44	rate	rate	NOUN
cana-4182	92	45	of	of	ADP
cana-4182	92	46	change	change	NOUN
cana-4182	92	47	)	)	PUNCT
cana-4182	92	48	,	,	PUNCT
cana-4182	92	49	fractional	fractional	ADJ
cana-4182	92	50	derivatives	derivative	NOUN
cana-4182	92	51	apply	apply	VERB
cana-4182	92	52	a	a	DET
cana-4182	92	53	weighted	weighted	ADJ
cana-4182	92	54	contribution	contribution	NOUN
cana-4182	92	55	from	from	ADP
cana-4182	92	56	all	all	DET
cana-4182	92	57	past	past	ADJ
cana-4182	92	58	states	state	NOUN
cana-4182	92	59	.	.	PUNCT
cana-4182	93	1	this	this	DET
cana-4182	93	2	mechanism	mechanism	NOUN
cana-4182	93	3	provides	provide	VERB
cana-4182	93	4	a	a	DET
cana-4182	93	5	more	more	ADV
cana-4182	93	6	complete	complete	ADJ
cana-4182	93	7	representation	representation	NOUN
cana-4182	93	8	of	of	ADP
cana-4182	93	9	processes	process	NOUN
cana-4182	93	10	governed	govern	VERB
cana-4182	93	11	by	by	ADP
cana-4182	93	12	memory	memory	NOUN
cana-4182	93	13	and	and	CCONJ
cana-4182	93	14	hereditary	hereditary	ADJ
cana-4182	93	15	effects	effect	NOUN
cana-4182	93	16	.	.	PUNCT
cana-4182	94	1	6	6	X
cana-4182	94	2	.	.	X
cana-4182	94	3	graphical	graphical	ADJ
cana-4182	94	4	comparison	comparison	NOUN
cana-4182	94	5	of	of	ADP
cana-4182	94	6	stress	stress	NOUN
cana-4182	94	7	–	–	PUNCT
cana-4182	94	8	strain	strain	NOUN
cana-4182	94	9	predictions	prediction	NOUN
cana-4182	94	10	the	the	DET
cana-4182	94	11	following	follow	VERB
cana-4182	94	12	ascii	ascii	NOUN
cana-4182	94	13	-	-	PUNCT
cana-4182	94	14	based	base	VERB
cana-4182	94	15	graph	graph	NOUN
cana-4182	94	16	compares	compare	VERB
cana-4182	94	17	stress	stress	ADJ
cana-4182	94	18	predictions	prediction	NOUN
cana-4182	94	19	from	from	ADP
cana-4182	94	20	an	an	DET
cana-4182	94	21	integer	integer	NOUN
cana-4182	94	22	-	-	PUNCT
cana-4182	94	23	order	order	NOUN
cana-4182	94	24	model	model	NOUN
cana-4182	94	25	(	(	PUNCT
cana-4182	94	26	dashed	dash	VERB
cana-4182	94	27	line	line	NOUN
cana-4182	94	28	)	)	PUNCT
cana-4182	94	29	and	and	CCONJ
cana-4182	94	30	a	a	DET
cana-4182	94	31	fractional	fractional	ADJ
cana-4182	94	32	-	-	PUNCT
cana-4182	94	33	order	order	NOUN
cana-4182	94	34	model	model	NOUN
cana-4182	94	35	(	(	PUNCT
cana-4182	94	36	solid	solid	ADJ
cana-4182	94	37	line	line	NOUN
cana-4182	94	38	)	)	PUNCT
cana-4182	94	39	against	against	ADP
cana-4182	94	40	measured	measure	VERB
cana-4182	94	41	data	data	NOUN
cana-4182	94	42	points	point	NOUN
cana-4182	94	43	(	(	PUNCT
cana-4182	94	44	“	"	PUNCT
cana-4182	94	45	x	x	NOUN
cana-4182	94	46	”	"	PUNCT
cana-4182	94	47	)	)	PUNCT
cana-4182	94	48	in	in	ADP
cana-4182	94	49	a	a	DET
cana-4182	94	50	cyclic	cyclic	ADJ
cana-4182	94	51	loading	loading	NOUN
cana-4182	94	52	scenario	scenario	NOUN
cana-4182	94	53	:	:	PUNCT
cana-4182	94	54	key	key	ADJ
cana-4182	94	55	observation	observation	NOUN
cana-4182	94	56	:	:	PUNCT
cana-4182	94	57	the	the	DET
cana-4182	94	58	fractional	fractional	ADJ
cana-4182	94	59	-	-	PUNCT
cana-4182	94	60	order	order	NOUN
cana-4182	94	61	model	model	NOUN
cana-4182	94	62	(	(	PUNCT
cana-4182	94	63	solid	solid	ADJ
cana-4182	94	64	line	line	NOUN
cana-4182	94	65	)	)	PUNCT
cana-4182	94	66	aligns	align	VERB
cana-4182	94	67	more	more	ADV
cana-4182	94	68	closely	closely	ADV
cana-4182	94	69	with	with	ADP
cana-4182	94	70	the	the	DET
cana-4182	94	71	measured	measure	VERB
cana-4182	94	72	data	datum	NOUN
cana-4182	94	73	(	(	PUNCT
cana-4182	94	74	x	x	NOUN
cana-4182	94	75	)	)	PUNCT
cana-4182	94	76	,	,	PUNCT
cana-4182	94	77	highlighting	highlight	VERB
cana-4182	94	78	the	the	DET
cana-4182	94	79	importance	importance	NOUN
cana-4182	94	80	of	of	ADP
cana-4182	94	81	memory	memory	NOUN
cana-4182	94	82	and	and	CCONJ
cana-4182	94	83	hereditary	hereditary	ADJ
cana-4182	94	84	effects	effect	NOUN
cana-4182	94	85	in	in	ADP
cana-4182	94	86	accurately	accurately	ADV
cana-4182	94	87	describing	describe	VERB
cana-4182	94	88	viscoelastic	viscoelastic	ADJ
cana-4182	94	89	behavior	behavior	NOUN
cana-4182	94	90	.	.	PUNCT
cana-4182	95	1	communications	communication	NOUN
cana-4182	95	2	on	on	ADP
cana-4182	95	3	applied	apply	VERB
cana-4182	95	4	nonlinear	nonlinear	ADJ
cana-4182	95	5	analysis	analysis	NOUN
cana-4182	95	6	issn	issn	NOUN
cana-4182	95	7	:	:	PUNCT
cana-4182	95	8	1074	1074	NUM
cana-4182	95	9	-	-	PUNCT
cana-4182	95	10	133x	133x	NUM
cana-4182	95	11	vol	vol	NOUN
cana-4182	95	12	32	32	NUM
cana-4182	95	13	no	no	NOUN
cana-4182	95	14	.	.	PUNCT
cana-4182	96	1	9s	9s	NUM
cana-4182	96	2	(	(	PUNCT
cana-4182	96	3	2025	2025	NUM
cana-4182	96	4	)	)	PUNCT
cana-4182	96	5	1503	1503	NUM
cana-4182	96	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4182	96	7	7	7	X
cana-4182	96	8	.	.	PUNCT
cana-4182	96	9	conclusion	conclusion	NOUN
cana-4182	96	10	fractional	fractional	ADJ
cana-4182	96	11	calculus	calculus	NOUN
cana-4182	96	12	has	have	AUX
cana-4182	96	13	evolved	evolve	VERB
cana-4182	96	14	from	from	ADP
cana-4182	96	15	a	a	DET
cana-4182	96	16	mathematical	mathematical	ADJ
cana-4182	96	17	curiosity	curiosity	NOUN
cana-4182	96	18	to	to	ADP
cana-4182	96	19	a	a	DET
cana-4182	96	20	versatile	versatile	ADJ
cana-4182	96	21	framework	framework	NOUN
cana-4182	96	22	that	that	PRON
cana-4182	96	23	offers	offer	VERB
cana-4182	96	24	profound	profound	ADJ
cana-4182	96	25	advantages	advantage	NOUN
cana-4182	96	26	in	in	ADP
cana-4182	96	27	modeling	model	VERB
cana-4182	96	28	real	real	ADJ
cana-4182	96	29	-	-	PUNCT
cana-4182	96	30	world	world	NOUN
cana-4182	96	31	phenomena	phenomenon	NOUN
cana-4182	96	32	characterized	characterize	VERB
cana-4182	96	33	by	by	ADP
cana-4182	96	34	memory	memory	NOUN
cana-4182	96	35	,	,	PUNCT
cana-4182	96	36	hereditary	hereditary	ADJ
cana-4182	96	37	effects	effect	NOUN
cana-4182	96	38	,	,	PUNCT
cana-4182	96	39	and	and	CCONJ
cana-4182	96	40	complex	complex	ADJ
cana-4182	96	41	structures	structure	NOUN
cana-4182	96	42	.	.	PUNCT
cana-4182	97	1	by	by	ADP
cana-4182	97	2	extending	extend	VERB
cana-4182	97	3	the	the	DET
cana-4182	97	4	concept	concept	NOUN
cana-4182	97	5	of	of	ADP
cana-4182	97	6	differentiation	differentiation	NOUN
cana-4182	97	7	and	and	CCONJ
cana-4182	97	8	integration	integration	NOUN
cana-4182	97	9	to	to	ADP
cana-4182	97	10	non	non	ADJ
cana-4182	97	11	-	-	ADJ
cana-4182	97	12	integer	integer	ADJ
cana-4182	97	13	orders	order	NOUN
cana-4182	97	14	,	,	PUNCT
cana-4182	97	15	fractional	fractional	ADJ
cana-4182	97	16	-	-	PUNCT
cana-4182	97	17	order	order	NOUN
cana-4182	97	18	models	model	NOUN
cana-4182	97	19	capture	capture	VERB
cana-4182	97	20	the	the	DET
cana-4182	97	21	long	long	ADJ
cana-4182	97	22	-	-	PUNCT
cana-4182	97	23	range	range	NOUN
cana-4182	97	24	correlations	correlation	NOUN
cana-4182	97	25	and	and	CCONJ
cana-4182	97	26	fractal	fractal	ADJ
cana-4182	97	27	-	-	PUNCT
cana-4182	97	28	like	like	ADJ
cana-4182	97	29	properties	property	NOUN
cana-4182	97	30	often	often	ADV
cana-4182	97	31	observed	observe	VERB
cana-4182	97	32	in	in	ADP
cana-4182	97	33	physical	physical	ADJ
cana-4182	97	34	,	,	PUNCT
cana-4182	97	35	biological	biological	ADJ
cana-4182	97	36	,	,	PUNCT
cana-4182	97	37	and	and	CCONJ
cana-4182	97	38	engineering	engineering	NOUN
cana-4182	97	39	systems	system	NOUN
cana-4182	97	40	.	.	PUNCT
cana-4182	98	1	the	the	DET
cana-4182	98	2	empirical	empirical	ADJ
cana-4182	98	3	data	datum	NOUN
cana-4182	98	4	,	,	PUNCT
cana-4182	98	5	tables	table	NOUN
cana-4182	98	6	,	,	PUNCT
cana-4182	98	7	and	and	CCONJ
cana-4182	98	8	graphical	graphical	ADJ
cana-4182	98	9	comparisons	comparison	NOUN
cana-4182	98	10	presented	present	VERB
cana-4182	98	11	here	here	ADV
cana-4182	98	12	illustrate	illustrate	VERB
cana-4182	98	13	how	how	SCONJ
cana-4182	98	14	fractional	fractional	ADJ
cana-4182	98	15	approaches	approach	NOUN
cana-4182	98	16	can	can	AUX
cana-4182	98	17	outperform	outperform	VERB
cana-4182	98	18	classical	classical	ADJ
cana-4182	98	19	integerorder	integerorder	NOUN
cana-4182	98	20	models	model	NOUN
cana-4182	98	21	,	,	PUNCT
cana-4182	98	22	especially	especially	ADV
cana-4182	98	23	in	in	ADP
cana-4182	98	24	areas	area	NOUN
cana-4182	98	25	such	such	ADJ
cana-4182	98	26	as	as	ADP
cana-4182	98	27	viscoelastic	viscoelastic	ADJ
cana-4182	98	28	material	material	NOUN
cana-4182	98	29	behavior	behavior	NOUN
cana-4182	98	30	and	and	CCONJ
cana-4182	98	31	anomalous	anomalous	ADJ
cana-4182	98	32	diffusion	diffusion	NOUN
cana-4182	98	33	processes	process	NOUN
cana-4182	98	34	.	.	PUNCT
cana-4182	99	1	while	while	SCONJ
cana-4182	99	2	remarkable	remarkable	ADJ
cana-4182	99	3	progress	progress	NOUN
cana-4182	99	4	has	have	AUX
cana-4182	99	5	been	be	AUX
cana-4182	99	6	made	make	VERB
cana-4182	99	7	,	,	PUNCT
cana-4182	99	8	there	there	PRON
cana-4182	99	9	remain	remain	VERB
cana-4182	99	10	challenges	challenge	NOUN
cana-4182	99	11	in	in	ADP
cana-4182	99	12	parameter	parameter	NOUN
cana-4182	99	13	estimation	estimation	NOUN
cana-4182	99	14	,	,	PUNCT
cana-4182	99	15	numerical	numerical	ADJ
cana-4182	99	16	implementation	implementation	NOUN
cana-4182	99	17	,	,	PUNCT
cana-4182	99	18	and	and	CCONJ
cana-4182	99	19	computational	computational	ADJ
cana-4182	99	20	efficiency	efficiency	NOUN
cana-4182	99	21	.	.	PUNCT
cana-4182	100	1	ongoing	ongoing	ADJ
cana-4182	100	2	research	research	NOUN
cana-4182	100	3	in	in	ADP
cana-4182	100	4	specialized	specialized	PROPN
cana-4182	100	5	numerical	numerical	ADJ
cana-4182	100	6	algorithms	algorithm	NOUN
cana-4182	100	7	,	,	PUNCT
cana-4182	100	8	parallel	parallel	ADJ
cana-4182	100	9	computing	computing	NOUN
cana-4182	100	10	,	,	PUNCT
cana-4182	100	11	and	and	CCONJ
cana-4182	100	12	software	software	NOUN
cana-4182	100	13	libraries	library	NOUN
cana-4182	100	14	is	be	AUX
cana-4182	100	15	rapidly	rapidly	ADV
cana-4182	100	16	overcoming	overcome	VERB
cana-4182	100	17	these	these	DET
cana-4182	100	18	barriers	barrier	NOUN
cana-4182	100	19	,	,	PUNCT
cana-4182	100	20	bringing	bring	VERB
cana-4182	100	21	fractional	fractional	ADJ
cana-4182	100	22	calculus	calculus	NOUN
cana-4182	100	23	into	into	ADP
cana-4182	100	24	the	the	DET
cana-4182	100	25	mainstream	mainstream	NOUN
cana-4182	100	26	of	of	ADP
cana-4182	100	27	scientific	scientific	ADJ
cana-4182	100	28	and	and	CCONJ
cana-4182	100	29	industrial	industrial	ADJ
cana-4182	100	30	applications	application	NOUN
cana-4182	100	31	.	.	PUNCT
cana-4182	101	1	as	as	SCONJ
cana-4182	101	2	the	the	DET
cana-4182	101	3	theoretical	theoretical	ADJ
cana-4182	101	4	underpinnings	underpinning	NOUN
cana-4182	101	5	continue	continue	VERB
cana-4182	101	6	to	to	PART
cana-4182	101	7	mature	mature	VERB
cana-4182	101	8	,	,	PUNCT
cana-4182	101	9	and	and	CCONJ
cana-4182	101	10	as	as	ADP
cana-4182	101	11	more	more	ADJ
cana-4182	101	12	experimental	experimental	ADJ
cana-4182	101	13	validation	validation	NOUN
cana-4182	101	14	emerges	emerge	NOUN
cana-4182	101	15	,	,	PUNCT
cana-4182	101	16	fractional	fractional	ADJ
cana-4182	101	17	calculus	calculus	NOUN
cana-4182	101	18	will	will	AUX
cana-4182	101	19	likely	likely	ADV
cana-4182	101	20	become	become	VERB
cana-4182	101	21	a	a	DET
cana-4182	101	22	standard	standard	ADJ
cana-4182	101	23	tool	tool	NOUN
cana-4182	101	24	for	for	ADP
cana-4182	101	25	scientists	scientist	NOUN
cana-4182	101	26	and	and	CCONJ
cana-4182	101	27	engineers	engineer	NOUN
cana-4182	101	28	confronting	confront	VERB
cana-4182	101	29	complex	complex	ADJ
cana-4182	101	30	dynamics	dynamic	NOUN
cana-4182	101	31	in	in	ADP
cana-4182	101	32	fields	field	NOUN
cana-4182	101	33	ranging	range	VERB
cana-4182	101	34	from	from	ADP
cana-4182	101	35	biomechanics	biomechanic	NOUN
cana-4182	101	36	to	to	ADP
cana-4182	101	37	control	control	NOUN
cana-4182	101	38	systems	system	NOUN
cana-4182	101	39	.	.	PUNCT
cana-4182	102	1	ultimately	ultimately	ADV
cana-4182	102	2	,	,	PUNCT
cana-4182	102	3	the	the	DET
cana-4182	102	4	promise	promise	NOUN
cana-4182	102	5	of	of	ADP
cana-4182	102	6	fractional	fractional	ADJ
cana-4182	102	7	calculus	calculus	NOUN
cana-4182	102	8	lies	lie	VERB
cana-4182	102	9	in	in	ADP
cana-4182	102	10	its	its	PRON
cana-4182	102	11	capacity	capacity	NOUN
cana-4182	102	12	to	to	PART
cana-4182	102	13	unify	unify	VERB
cana-4182	102	14	diverse	diverse	ADJ
cana-4182	102	15	observations	observation	NOUN
cana-4182	102	16	under	under	ADP
cana-4182	102	17	a	a	DET
cana-4182	102	18	single	single	ADJ
cana-4182	102	19	mathematical	mathematical	ADJ
cana-4182	102	20	paradigm	paradigm	NOUN
cana-4182	102	21	.	.	PUNCT
cana-4182	103	1	by	by	ADP
cana-4182	103	2	acknowledging	acknowledge	VERB
cana-4182	103	3	the	the	DET
cana-4182	103	4	continuous	continuous	ADJ
cana-4182	103	5	influence	influence	NOUN
cana-4182	103	6	of	of	ADP
cana-4182	103	7	historical	historical	ADJ
cana-4182	103	8	states	state	NOUN
cana-4182	103	9	,	,	PUNCT
cana-4182	103	10	researchers	researcher	NOUN
cana-4182	103	11	can	can	AUX
cana-4182	103	12	build	build	VERB
cana-4182	103	13	models	model	NOUN
cana-4182	103	14	that	that	PRON
cana-4182	103	15	more	more	ADV
cana-4182	103	16	faithfully	faithfully	ADV
cana-4182	103	17	represent	represent	VERB
cana-4182	103	18	reality	reality	NOUN
cana-4182	103	19	and	and	CCONJ
cana-4182	103	20	design	design	NOUN
cana-4182	103	21	solutions	solution	NOUN
cana-4182	103	22	with	with	ADP
cana-4182	103	23	improved	improved	ADJ
cana-4182	103	24	accuracy	accuracy	NOUN
cana-4182	103	25	and	and	CCONJ
cana-4182	103	26	robustness	robustness	NOUN
cana-4182	103	27	.	.	PUNCT
cana-4182	104	1	this	this	DET
cana-4182	104	2	comprehensive	comprehensive	ADJ
cana-4182	104	3	review	review	NOUN
cana-4182	104	4	underscores	underscore	VERB
cana-4182	104	5	the	the	DET
cana-4182	104	6	growing	grow	VERB
cana-4182	104	7	importance	importance	NOUN
cana-4182	104	8	of	of	ADP
cana-4182	104	9	fractional	fractional	ADJ
cana-4182	104	10	calculus	calculus	NOUN
cana-4182	104	11	in	in	ADP
cana-4182	104	12	modern	modern	ADJ
cana-4182	104	13	science	science	NOUN
cana-4182	104	14	and	and	CCONJ
cana-4182	104	15	engineering	engineering	NOUN
cana-4182	104	16	,	,	PUNCT
cana-4182	104	17	paving	pave	VERB
cana-4182	104	18	the	the	DET
cana-4182	104	19	way	way	NOUN
cana-4182	104	20	for	for	ADP
cana-4182	104	21	novel	novel	ADJ
cana-4182	104	22	insights	insight	NOUN
cana-4182	104	23	and	and	CCONJ
cana-4182	104	24	transformative	transformative	ADJ
cana-4182	104	25	discoveries	discovery	NOUN
cana-4182	104	26	in	in	ADP
cana-4182	104	27	the	the	DET
cana-4182	104	28	decades	decade	NOUN
cana-4182	104	29	to	to	PART
cana-4182	104	30	come	come	VERB
cana-4182	104	31	.	.	PUNCT
cana-4182	105	1	references	reference	NOUN
cana-4182	105	2	1	1	NUM
cana-4182	105	3	.	.	PUNCT
cana-4182	105	4	podlubny	podlubny	PROPN
cana-4182	105	5	,	,	PUNCT
cana-4182	105	6	i.	i.	PROPN
cana-4182	105	7	(	(	PUNCT
cana-4182	105	8	1999	1999	NUM
cana-4182	105	9	)	)	PUNCT
cana-4182	105	10	.	.	PUNCT
cana-4182	106	1	fractional	fractional	ADJ
cana-4182	106	2	differential	differential	ADJ
cana-4182	106	3	equations	equation	NOUN
cana-4182	106	4	.	.	PUNCT
cana-4182	107	1	academic	academic	ADJ
cana-4182	107	2	press	press	NOUN
cana-4182	107	3	.	.	PUNCT
cana-4182	108	1	2	2	X
cana-4182	108	2	.	.	X
cana-4182	108	3	oldham	oldham	PROPN
cana-4182	108	4	,	,	PUNCT
cana-4182	108	5	k.	k.	PROPN
cana-4182	108	6	,	,	PUNCT
cana-4182	108	7	&	&	CCONJ
cana-4182	108	8	spanier	spanier	NOUN
cana-4182	108	9	,	,	PUNCT
cana-4182	108	10	j.	j.	PROPN
cana-4182	108	11	(	(	PUNCT
cana-4182	108	12	1974	1974	NUM
cana-4182	108	13	)	)	PUNCT
cana-4182	108	14	.	.	PUNCT
cana-4182	109	1	the	the	DET
cana-4182	109	2	fractional	fractional	ADJ
cana-4182	109	3	calculus	calculus	NOUN
cana-4182	109	4	.	.	PUNCT
cana-4182	110	1	academic	academic	ADJ
cana-4182	110	2	press	press	NOUN
cana-4182	110	3	.	.	PUNCT
cana-4182	111	1	3	3	X
cana-4182	111	2	.	.	X
cana-4182	111	3	caputo	caputo	PROPN
cana-4182	111	4	,	,	PUNCT
cana-4182	111	5	m.	m.	NOUN
cana-4182	111	6	(	(	PUNCT
cana-4182	111	7	1967	1967	NUM
cana-4182	111	8	)	)	PUNCT
cana-4182	111	9	.	.	PUNCT
cana-4182	112	1	linear	linear	ADJ
cana-4182	112	2	models	model	NOUN
cana-4182	112	3	of	of	ADP
cana-4182	112	4	dissipation	dissipation	NOUN
cana-4182	112	5	whose	whose	DET
cana-4182	112	6	q	q	NOUN
cana-4182	112	7	is	be	AUX
cana-4182	112	8	almost	almost	ADV
cana-4182	112	9	frequency	frequency	ADJ
cana-4182	112	10	independent	independent	ADJ
cana-4182	112	11	—	—	PUNCT
cana-4182	112	12	ii	ii	PROPN
cana-4182	112	13	.	.	PUNCT
cana-4182	112	14	geophysical	geophysical	ADJ
cana-4182	112	15	journal	journal	PROPN
cana-4182	112	16	international	international	PROPN
cana-4182	112	17	,	,	PUNCT
cana-4182	112	18	13(5	13(5	NUM
cana-4182	112	19	)	)	PUNCT
cana-4182	112	20	,	,	PUNCT
cana-4182	112	21	529–539	529–539	NUM
cana-4182	112	22	.	.	PUNCT
cana-4182	113	1	4	4	X
cana-4182	113	2	.	.	X
cana-4182	113	3	mainardi	mainardi	PROPN
cana-4182	113	4	,	,	PUNCT
cana-4182	113	5	f.	f.	PROPN
cana-4182	113	6	(	(	PUNCT
cana-4182	113	7	2010	2010	NUM
cana-4182	113	8	)	)	PUNCT
cana-4182	113	9	.	.	PUNCT
cana-4182	114	1	fractional	fractional	ADJ
cana-4182	114	2	calculus	calculus	NOUN
cana-4182	114	3	and	and	CCONJ
cana-4182	114	4	waves	wave	NOUN
cana-4182	114	5	in	in	ADP
cana-4182	114	6	linear	linear	PROPN
cana-4182	114	7	viscoelasticity	viscoelasticity	NOUN
cana-4182	114	8	.	.	PUNCT
cana-4182	115	1	imperial	imperial	ADJ
cana-4182	115	2	college	college	NOUN
cana-4182	115	3	press	press	NOUN
cana-4182	115	4	.	.	PUNCT
cana-4182	116	1	5	5	X
cana-4182	116	2	.	.	X
cana-4182	116	3	metzler	metzler	PROPN
cana-4182	116	4	,	,	PUNCT
cana-4182	116	5	r.	r.	PROPN
cana-4182	116	6	,	,	PUNCT
cana-4182	116	7	&	&	CCONJ
cana-4182	116	8	klafter	klafter	PROPN
cana-4182	116	9	,	,	PUNCT
cana-4182	116	10	j.	j.	PROPN
cana-4182	116	11	(	(	PUNCT
cana-4182	116	12	2000	2000	NUM
cana-4182	116	13	)	)	PUNCT
cana-4182	116	14	.	.	PUNCT
cana-4182	117	1	the	the	DET
cana-4182	117	2	random	random	ADJ
cana-4182	117	3	walk	walk	NOUN
cana-4182	117	4	’s	’s	PART
cana-4182	117	5	guide	guide	NOUN
cana-4182	117	6	to	to	ADP
cana-4182	117	7	anomalous	anomalous	ADJ
cana-4182	117	8	diffusion	diffusion	NOUN
cana-4182	117	9	:	:	PUNCT
cana-4182	117	10	a	a	DET
cana-4182	117	11	fractional	fractional	ADJ
cana-4182	117	12	dynamics	dynamic	NOUN
cana-4182	117	13	approach	approach	NOUN
cana-4182	117	14	.	.	PUNCT
cana-4182	118	1	physics	physics	NOUN
cana-4182	118	2	reports	report	NOUN
cana-4182	118	3	,	,	PUNCT
cana-4182	118	4	339(1	339(1	NUM
cana-4182	118	5	)	)	PUNCT
cana-4182	118	6	,	,	PUNCT
cana-4182	118	7	1–77	1–77	PROPN
cana-4182	118	8	.	.	PUNCT
cana-4182	119	1	6	6	NUM
cana-4182	119	2	.	.	X
cana-4182	119	3	bagley	bagley	PROPN
cana-4182	119	4	,	,	PUNCT
cana-4182	119	5	r.	r.	PROPN
cana-4182	119	6	l.	l.	PROPN
cana-4182	119	7	,	,	PUNCT
cana-4182	119	8	&	&	CCONJ
cana-4182	119	9	torvik	torvik	PROPN
cana-4182	119	10	,	,	PUNCT
cana-4182	119	11	p.	p.	PROPN
cana-4182	119	12	j.	j.	PROPN
cana-4182	119	13	(	(	PUNCT
cana-4182	119	14	1983	1983	NUM
cana-4182	119	15	)	)	PUNCT
cana-4182	119	16	.	.	PUNCT
cana-4182	120	1	fractional	fractional	ADJ
cana-4182	120	2	calculus	calculus	NOUN
cana-4182	120	3	in	in	ADP
cana-4182	120	4	the	the	DET
cana-4182	120	5	transient	transient	ADJ
cana-4182	120	6	analysis	analysis	NOUN
cana-4182	120	7	of	of	ADP
cana-4182	120	8	viscoelastically	viscoelastically	ADV
cana-4182	120	9	damped	damp	VERB
cana-4182	120	10	structures	structure	NOUN
cana-4182	120	11	.	.	PUNCT
cana-4182	121	1	aiaa	aiaa	PROPN
cana-4182	121	2	journal	journal	PROPN
cana-4182	121	3	,	,	PUNCT
cana-4182	121	4	21(5	21(5	NUM
cana-4182	121	5	)	)	PUNCT
cana-4182	121	6	,	,	PUNCT
cana-4182	121	7	741–748	741–748	NUM
cana-4182	121	8	.	.	NOUN
cana-4182	121	9	7	7	NUM
cana-4182	121	10	.	.	X
cana-4182	121	11	li	li	PROPN
cana-4182	121	12	,	,	PUNCT
cana-4182	121	13	c.	c.	PROPN
cana-4182	121	14	,	,	PUNCT
cana-4182	121	15	&	&	CCONJ
cana-4182	121	16	zeng	zeng	PROPN
cana-4182	121	17	,	,	PUNCT
cana-4182	121	18	f.	f.	PROPN
cana-4182	121	19	(	(	PUNCT
cana-4182	121	20	2015	2015	NUM
cana-4182	121	21	)	)	PUNCT
cana-4182	121	22	.	.	PUNCT
cana-4182	122	1	numerical	numerical	ADJ
cana-4182	122	2	methods	method	NOUN
cana-4182	122	3	for	for	ADP
cana-4182	122	4	fractional	fractional	ADJ
cana-4182	122	5	calculus	calculus	NOUN
cana-4182	122	6	.	.	PUNCT
cana-4182	123	1	crc	crc	PROPN
cana-4182	123	2	press	press	PROPN
cana-4182	123	3	.	.	PUNCT
cana-4182	124	1	8	8	X
cana-4182	124	2	.	.	X
cana-4182	124	3	magin	magin	NOUN
cana-4182	124	4	,	,	PUNCT
cana-4182	124	5	r.	r.	PROPN
cana-4182	124	6	l.	l.	PROPN
cana-4182	124	7	(	(	PUNCT
cana-4182	124	8	2004	2004	NUM
cana-4182	124	9	)	)	PUNCT
cana-4182	124	10	.	.	PUNCT
cana-4182	125	1	fractional	fractional	ADJ
cana-4182	125	2	calculus	calculus	NOUN
cana-4182	125	3	in	in	ADP
cana-4182	125	4	bioengineering	bioengineering	NOUN
cana-4182	125	5	.	.	PUNCT
cana-4182	126	1	critical	critical	ADJ
cana-4182	126	2	reviews	review	NOUN
cana-4182	126	3	in	in	ADP
cana-4182	126	4	biomedical	biomedical	ADJ
cana-4182	126	5	engineering	engineering	NOUN
cana-4182	126	6	,	,	PUNCT
cana-4182	126	7	32(1	32(1	NUM
cana-4182	126	8	)	)	PUNCT
cana-4182	126	9	,	,	PUNCT
cana-4182	126	10	1–104	1–104	X
cana-4182	126	11	.	.	PROPN
cana-4182	127	1	9	9	NUM
cana-4182	127	2	.	.	X
cana-4182	127	3	machado	machado	PROPN
cana-4182	127	4	,	,	PUNCT
cana-4182	127	5	j.	j.	PROPN
cana-4182	127	6	a.	a.	PROPN
cana-4182	127	7	t.	t.	PROPN
cana-4182	127	8	,	,	PUNCT
cana-4182	127	9	costa	costa	PROPN
cana-4182	127	10	,	,	PUNCT
cana-4182	127	11	a.	a.	PROPN
cana-4182	127	12	c.	c.	PROPN
cana-4182	127	13	,	,	PUNCT
cana-4182	127	14	&	&	CCONJ
cana-4182	127	15	lopes	lopes	PROPN
cana-4182	127	16	,	,	PUNCT
cana-4182	127	17	a.	a.	NOUN
cana-4182	127	18	m.	m.	NOUN
cana-4182	127	19	(	(	PUNCT
cana-4182	127	20	2011	2011	NUM
cana-4182	127	21	)	)	PUNCT
cana-4182	127	22	.	.	PUNCT
cana-4182	128	1	complex	complex	ADJ
cana-4182	128	2	order	order	NOUN
cana-4182	128	3	dynamical	dynamical	ADJ
cana-4182	128	4	systems	system	NOUN
cana-4182	128	5	.	.	PUNCT
cana-4182	129	1	fractional	fractional	ADJ
cana-4182	129	2	calculus	calculus	NOUN
cana-4182	129	3	and	and	CCONJ
cana-4182	129	4	applied	apply	VERB
cana-4182	129	5	analysis	analysis	NOUN
cana-4182	129	6	,	,	PUNCT
cana-4182	129	7	14(4	14(4	NUM
cana-4182	129	8	)	)	PUNCT
cana-4182	129	9	,	,	PUNCT
cana-4182	129	10	538–557	538–557	NUM
cana-4182	129	11	.	.	PUNCT
cana-4182	129	12	10	10	NUM
cana-4182	129	13	.	.	PUNCT
cana-4182	130	1	das	das	PROPN
cana-4182	130	2	,	,	PUNCT
cana-4182	130	3	s.	s.	PROPN
cana-4182	130	4	(	(	PUNCT
cana-4182	130	5	2011	2011	NUM
cana-4182	130	6	)	)	PUNCT
cana-4182	130	7	.	.	PUNCT
cana-4182	131	1	functional	functional	ADJ
cana-4182	131	2	fractional	fractional	ADJ
cana-4182	131	3	calculus	calculus	NOUN
cana-4182	131	4	.	.	PUNCT
cana-4182	131	5	springer	springer	NOUN
cana-4182	131	6	.	.	PUNCT